LMFDB - Embedded newform 148.2.e.a.137.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [148,2,Mod(121,148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("148.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 148 = 2^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	148.e (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:	$1.18178594991$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			137.1
Root			$1.42789 - 2.47317i$ of defining polynomial
Character	$\chi$	$=$	148.137
Dual form			148.2.e.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42789 + 2.47317i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.07772 + 3.59871i) q^{7} +(-2.57772 - 4.46474i) q^{9} +O(q^{10})$	\(q+(-1.42789 + 2.47317i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.07772 + 3.59871i) q^{7} +(-2.57772 - 4.46474i) q^{9} -1.29966 q^{11} +(-1.77805 + 3.07968i) q^{13} +(1.42789 + 2.47317i) q^{15} +(1.79966 + 3.11711i) q^{17} +(2.42789 - 4.20522i) q^{19} +(-5.93349 - 10.2771i) q^{21} +5.01121 q^{23} +(2.00000 + 3.46410i) q^{25} +6.15544 q^{27} +8.86698 q^{29} +1.29966 q^{31} +(1.85577 - 3.21429i) q^{33} +(2.07772 + 3.59871i) q^{35} +(1.27805 - 5.94698i) q^{37} +(-5.07772 - 8.79487i) q^{39} +(-5.35577 + 9.27647i) q^{41} -10.3109 q^{43} -5.15544 q^{45} +8.72275 q^{47} +(-5.13383 - 8.89205i) q^{49} -10.2789 q^{51} +(-5.07772 - 8.79487i) q^{53} +(-0.649832 + 1.12554i) q^{55} +(6.93349 + 12.0092i) q^{57} +(4.63383 + 8.02602i) q^{59} +(-1.35577 + 2.34827i) q^{61} +21.4231 q^{63} +(1.77805 + 3.07968i) q^{65} +(-3.98399 + 6.90048i) q^{67} +(-7.15544 + 12.3936i) q^{69} +(5.63383 - 9.75807i) q^{71} +2.28845 q^{73} -11.4231 q^{75} +(2.70034 - 4.67712i) q^{77} +(-1.28366 + 2.22336i) q^{79} +(-1.05611 + 1.82923i) q^{81} +(-4.98399 - 8.63253i) q^{83} +3.59933 q^{85} +(-12.6610 + 21.9296i) q^{87} +(2.21155 + 3.83051i) q^{89} +(-7.38859 - 12.7974i) q^{91} +(-1.85577 + 3.21429i) q^{93} +(-2.42789 - 4.20522i) q^{95} +9.97920 q^{97} +(3.35017 + 5.80266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 3 q^{5} - q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q - q^3 + 3 * q^5 - q^7 - 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/148\mathbb{Z}\right)^\times$.

$n$	$75$	$113$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.42789	+	2.47317i	−0.824391	+	1.42789i	0.0779937	+	0.996954i	$0.475149\pi$
$3$	−1.42789	+	2.47317i	−0.824391	+	1.42789i	−0.902384	+	0.430932i	$0.858185\pi$
$4$		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	$0.454160\pi$
$7$	−2.07772	+	3.59871i	−0.785304	+	1.36019i	−0.928817	+	0.370538i	$0.879173\pi$
$8$		0			0
$9$	−2.57772	−	4.46474i	−0.859239	−	1.48825i
$10$		0			0
$11$	−1.29966			−0.391863			−0.195932	−	0.980618i	$-0.562773\pi$
$11$	−1.29966			−0.391863			−0.195932	+	0.980618i	$0.562773\pi$
$12$		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	$-0.645287\pi$
$19$	2.42789	−	4.20522i	0.556995	−	0.964744i	0.997745	−	0.0671143i	$-0.0213792\pi$
$20$		0			0
$21$	−5.93349	−	10.2771i	−1.29479	−	2.24265i
$22$		0			0
$23$	5.01121			1.04491			0.522455	−	0.852667i	$-0.325016\pi$
$23$	5.01121			1.04491			0.522455	+	0.852667i	$0.325016\pi$
$24$		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	$-0.462764\pi$
$31$	1.29966			0.233427			0.116713	+	0.993166i	$0.462764\pi$
$32$		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	$-0.787953\pi$
$43$	−10.3109			−1.57239			−0.786197	+	0.617976i	$0.787953\pi$
$44$		0			0
$45$	−5.15544			−0.768527
$46$		0			0
$47$	8.72275			1.27234			0.636172	−	0.771547i	$-0.280517\pi$
$47$	8.72275			1.27234			0.636172	+	0.771547i	$0.280517\pi$
$48$		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	$0.0394703\pi$
$59$	4.63383	+	8.02602i	0.603273	+	1.04490i	−0.389049	+	0.921217i	$0.627196\pi$
$60$		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	−0.999883	−	0.0152644i	$-0.995141\pi$
$67$	−3.98399	+	6.90048i	−0.486722	+	0.843028i	0.513161	+	0.858292i	$0.328474\pi$
$68$		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	$-0.600222\pi$
$71$	5.63383	−	9.75807i	0.668612	−	1.15807i	0.978292	−	0.207230i	$-0.0664447\pi$
$72$		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	−0.929157	−	0.369684i	$-0.879466\pi$
$79$	−1.28366	+	2.22336i	−0.144423	+	0.250148i	0.784735	+	0.619832i	$0.212799\pi$
$80$		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	$-0.982412\pi$
$83$	−4.98399	−	8.63253i	−0.547064	−	0.947543i	0.451409	−	0.892317i	$-0.350921\pi$
$84$		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	$-0.610203\pi$
$103$	−6.88778			−0.678673			−0.339337	+	0.940665i	$0.610203\pi$
$104$		0			0
$105$	−11.8670			−1.15810
$106$		0			0
$107$	1.63383	−	2.82987i	0.157948	−	0.273574i	−0.776181	−	0.630511i	$-0.782845\pi$
$107$	1.63383	−	2.82987i	0.157948	−	0.273574i	0.934129	+	0.356937i	$0.116179\pi$
$108$		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	0.941841	−	0.336058i	$-0.109094\pi$
$127$	2.02721	+	3.51124i	0.179886	+	0.311572i	−0.761955	+	0.647630i	$0.775760\pi$
$128$		0			0
$129$	14.7228	−	25.5006i	1.29627	−	2.24520i
$130$		0			0
$131$	−5.58332	−	9.67060i	−0.487817	−	0.844924i	0.512085	−	0.858935i	$-0.328873\pi$
$131$	−5.58332	−	9.67060i	−0.487817	−	0.844924i	−0.999902	+	0.0140108i	$0.995540\pi$
$132$		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	$0.0986315\pi$
$139$	8.72755	+	15.1166i	0.740261	+	1.28217i	−0.212115	+	0.977245i	$0.568035\pi$
$140$		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	−0.707641	−	0.706572i	$-0.750241\pi$
$151$	3.17144	−	5.49310i	0.258088	−	0.447022i	0.965730	+	0.259550i	$0.0835741\pi$
$152$		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	0.794919	−	0.606715i	$-0.207513\pi$
$163$	−1.63383	−	2.82987i	−0.127971	−	0.221653i	−0.922890	+	0.385063i	$0.874180\pi$
$164$		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	$-0.518860\pi$
$167$	10.7893	−	18.6876i	0.834898	−	1.44609i	0.894113	−	0.447841i	$-0.147807\pi$
$168$		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	$-0.514264\pi$
$179$	−1.19866			−0.0895918			−0.0447959	+	0.998996i	$0.514264\pi$
$180$		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	$-0.435200\pi$
$191$	5.58812			0.404342			0.202171	+	0.979350i	$0.435200\pi$
$192$		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	$-0.480932\pi$
$199$	1.68913			0.119739			0.0598695	+	0.998206i	$0.480932\pi$
$200$		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	$-0.377721\pi$
$211$	10.8878			0.749546			0.374773	+	0.927117i	$0.377721\pi$
$212$		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	$-0.501998\pi$
$223$	−0.187447			−0.0125524			−0.00627620	+	0.999980i	$0.501998\pi$
$224$		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	$-0.609924\pi$
$227$	9.72755	−	16.8486i	0.645640	−	1.11828i	0.984153	−	0.177320i	$-0.0567427\pi$
$228$		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	0.997037	−	0.0769219i	$-0.0245092\pi$
$239$	6.67705	+	11.5650i	0.431902	+	0.748077i	−0.565135	+	0.824999i	$0.691176\pi$
$240$		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	$-0.381671\pi$
$251$	11.5095			0.726475			0.363238	+	0.931697i	$0.381671\pi$
$252$		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	−0.999147	−	0.0413047i	$-0.986849\pi$
$263$	−7.52161	+	13.0278i	−0.463802	+	0.803329i	0.535344	+	0.844634i	$0.320182\pi$
$264$		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	$0.0313865\pi$
$271$	9.59453	+	16.6182i	0.582826	+	1.00948i	−0.412316	+	0.911041i	$0.635280\pi$
$272$		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	−0.961396	−	0.275168i	$-0.911266\pi$
$283$	−4.07772	+	7.06282i	−0.242395	+	0.419841i	0.719001	+	0.695009i	$0.244600\pi$
$284$		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	$-0.662391\pi$
$307$	−17.1122			−0.976646			−0.488323	+	0.872663i	$0.662391\pi$
$308$		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	$-0.840959\pi$
$311$	−15.0569	−	26.0793i	−0.853799	−	1.47882i	0.0239549	−	0.999713i	$-0.492374\pi$
$312$		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	0.897924	−	0.440151i	$-0.145075\pi$
$331$	1.23315	+	2.13589i	0.0677803	+	0.117399i	−0.830144	+	0.557550i	$0.811742\pi$
$332$		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	$-0.163742\pi$
$347$	32.4343			1.74116			0.870582	+	0.492023i	$0.163742\pi$
$348$		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	$-0.523930\pi$
$359$	−2.84618			−0.150216			−0.0751078	+	0.997175i	$0.523930\pi$
$360$		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	−0.896414	−	0.443217i	$-0.853837\pi$
$367$	−1.23315	+	2.13589i	−0.0643702	+	0.111492i	0.832044	+	0.554709i	$0.187171\pi$
$368$		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	$-0.861182\pi$
$379$	−15.9447	−	27.6170i	−0.819024	−	1.41859i	0.0873777	−	0.996175i	$-0.472151\pi$
$380$		0			0
$381$	−11.5785			−0.593186
$382$		0			0
$383$	3.94470	−	6.83242i	0.201565	−	0.349120i	−0.747468	−	0.664298i	$-0.768731\pi$
$383$	3.94470	−	6.83242i	0.201565	−	0.349120i	0.949033	+	0.315177i	$0.102064\pi$
$384$		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	0.673493	−	0.739194i	$-0.264793\pi$
$419$	−6.21074	−	10.7573i	−0.303414	−	0.525529i	−0.976907	+	0.213665i	$0.931460\pi$
$420$		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	−0.719175	−	0.694829i	$-0.755480\pi$
$431$	5.02721	−	8.70739i	0.242152	−	0.419420i	0.961327	+	0.275409i	$0.0888133\pi$
$432$		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	$0.378649\pi$
$439$	−12.9447	+	22.4209i	−0.617817	+	1.07009i	−0.989883	+	0.141884i	$0.954684\pi$
$440$		0			0
$441$	−26.4671	+	45.8424i	−1.26034	+	2.18297i
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		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	$-0.561252\pi$
$463$	16.2332	−	28.1166i	0.754419	−	1.30669i	0.945663	−	0.325149i	$-0.105414\pi$
$464$		0			0
$465$	1.85577	+	3.21429i	0.0860594	+	0.149059i
$466$		0			0
$467$	−27.4231			−1.26899			−0.634495	−	0.772927i	$-0.718792\pi$
$467$	−27.4231			−1.26899			−0.634495	+	0.772927i	$0.718792\pi$
$468$		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	0.914203	−	0.405257i	$-0.132818\pi$
$479$	2.32295	+	4.02347i	0.106138	+	0.183837i	−0.808064	+	0.589094i	$0.799485\pi$
$480$		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	$-0.401915\pi$
$487$	13.3861			0.606582			0.303291	+	0.952898i	$0.401915\pi$
$488$		0			0
$489$	9.33167			0.421993
$490$		0			0
$491$	17.3445			0.782746			0.391373	−	0.920232i	$-0.372000\pi$
$491$	17.3445			0.782746			0.391373	+	0.920232i	$0.372000\pi$
$492$		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	$-0.603975\pi$
$499$	14.7388	−	25.5283i	0.659797	−	1.14280i	0.980668	−	0.195680i	$-0.0626913\pi$
$500$		0			0
$501$	30.8117	+	53.3674i	1.37656	+	2.38428i
$502$		0			0
$503$	0.459897	+	0.796565i	0.0205058	+	0.0355171i	0.876096	−	0.482136i	$-0.160139\pi$
$503$	0.459897	+	0.796565i	0.0205058	+	0.0355171i	−0.855590	+	0.517653i	$0.826806\pi$
$504$		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	$0.487129\pi$
$523$	−19.3269	+	33.4751i	−0.845105	+	1.46377i	−0.885530	+	0.464583i	$0.846204\pi$
$524$		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	$-0.733542\pi$
$547$	−31.3221			−1.33924			−0.669618	+	0.742706i	$0.733542\pi$
$548$		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	$-0.610803\pi$
$563$	−16.1874			−0.682220			−0.341110	+	0.940023i	$0.610803\pi$
$564$		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	0.989482	−	0.144658i	$-0.0462081\pi$
$571$	8.82856	+	15.2915i	0.369464	+	0.639930i	−0.620018	+	0.784588i	$0.712875\pi$
$572$		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	−0.992333	−	0.123594i	$-0.960558\pi$
$587$	−9.42789	+	16.3296i	−0.389131	+	0.673994i	0.603202	+	0.797588i	$0.293891\pi$
$588$		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	$-0.596929\pi$
$599$	16.5513	−	28.6677i	0.676268	−	1.17133i	0.976096	−	0.217338i	$-0.0697373\pi$
$600$		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	$-0.988983\pi$
$607$	−13.0496	−	22.6026i	−0.529668	−	0.917412i	0.469733	−	0.882809i	$-0.344350\pi$
$608$		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	$-0.481517\pi$
$619$	2.88778			0.116070			0.0580349	+	0.998315i	$0.481517\pi$
$620$		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	0.992139	−	0.125141i	$-0.0399384\pi$
$631$	9.73876	+	16.8680i	0.387694	+	0.671506i	−0.604445	+	0.796647i	$0.706605\pi$
$632$		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	$-0.568966\pi$
$643$	−10.9024			−0.429947			−0.214973	+	0.976620i	$0.568966\pi$
$644$		0			0
$645$	−14.7228	−	25.5006i	−0.579708	−	1.00408i
$646$		0			0
$647$	6.54403	−	11.3346i	0.257272	−	0.445609i	−0.708238	−	0.705974i	$-0.750510\pi$
$647$	6.54403	−	11.3346i	0.257272	−	0.445609i	0.965510	+	0.260365i	$0.0838429\pi$
$648$		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	−0.913113	−	0.407706i	$-0.866329\pi$
$659$	−2.65624	+	4.60075i	−0.103473	+	0.179220i	0.809641	+	0.586926i	$0.199662\pi$
$660$		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	$0.0398243\pi$
$683$	15.7893	+	27.3478i	0.604159	+	1.04643i	−0.388024	+	0.921649i	$0.626842\pi$
$684$		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	0.952598	−	0.304232i	$-0.0983999\pi$
$691$	5.59453	+	9.69001i	0.212826	+	0.368625i	−0.739772	+	0.672858i	$0.765067\pi$
$692$		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	0.989678	−	0.143311i	$-0.0457748\pi$
$719$	9.94077	+	17.2179i	0.370728	+	0.642120i	−0.618949	+	0.785431i	$0.712441\pi$
$720$		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	−0.887987	−	0.459869i	$-0.847896\pi$
$727$	−1.23315	+	2.13589i	−0.0457352	+	0.0792157i	0.842252	+	0.539085i	$0.181230\pi$
$728$		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	$-0.668183\pi$
$739$	−27.4085			−1.00824			−0.504119	+	0.863634i	$0.668183\pi$
$740$		0			0
$741$	−49.3125			−1.81154
$742$		0			0
$743$	−5.69554	+	9.86496i	−0.208949	+	0.361910i	−0.951384	−	0.308008i	$-0.900338\pi$
$743$	−5.69554	+	9.86496i	−0.208949	+	0.361910i	0.742435	+	0.669918i	$0.233671\pi$
$744$		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	$-0.711040\pi$
$751$	−33.7340			−1.23097			−0.615485	+	0.788149i	$0.711040\pi$
$752$		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	$-0.471449\pi$
$787$	5.02578			0.179150			0.0895748	+	0.995980i	$0.471449\pi$
$788$		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	$-0.515840\pi$
$811$	23.9239	−	41.4374i	0.840082	−	1.45506i	0.889825	−	0.456302i	$-0.150826\pi$
$812$		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	0.917854	−	0.396918i	$-0.129920\pi$
$823$	3.30446	+	5.72349i	0.115186	+	0.199508i	−0.802668	+	0.596426i	$0.796587\pi$
$824$		0			0
$825$	14.8462			0.516878
$826$		0			0
$827$	1.34376	−	2.32745i	0.0467269	−	0.0809334i	−0.841716	−	0.539921i	$-0.818454\pi$
$827$	1.34376	−	2.32745i	0.0467269	−	0.0809334i	0.888443	+	0.458987i	$0.151788\pi$
$828$		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	0.987443	−	0.157976i	$-0.0504968\pi$
$839$	10.3381	+	17.9061i	0.356910	+	0.618187i	−0.630533	+	0.776163i	$0.717163\pi$
$840$		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	$-0.783779\pi$
$859$	−45.6059			−1.55605			−0.778027	+	0.628231i	$0.783779\pi$
$860$		0			0
$861$	127.114			4.33202
$862$		0			0
$863$	−25.9015	−	44.8627i	−0.881697	−	1.52714i	−0.849454	−	0.527663i	$-0.823068\pi$
$863$	−25.9015	−	44.8627i	−0.881697	−	1.52714i	−0.0322430	−	0.999480i	$-0.510265\pi$
$864$		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	$-0.479986\pi$
$883$	26.6170	−	46.1019i	0.895732	−	1.55145i	0.832896	−	0.553429i	$-0.186681\pi$
$884$		0			0
$885$	−13.2332	+	22.9205i	−0.444828	+	0.770464i
$886$		0			0
$887$	−20.6363			−0.692900			−0.346450	−	0.938069i	$-0.612613\pi$
$887$	−20.6363			−0.692900			−0.346450	+	0.938069i	$0.612613\pi$
$888$		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	$0.333797\pi$
$907$	−15.0962	+	26.1474i	−0.501261	+	0.868210i	−0.999999	+	0.00145724i	$0.999536\pi$
$908$		0			0
$909$	−7.33248	−	12.7002i	−0.243203	−	0.421240i
$910$		0			0
$911$	−5.76100			−0.190870			−0.0954352	−	0.995436i	$-0.530424\pi$
$911$	−5.76100			−0.190870			−0.0954352	+	0.995436i	$0.530424\pi$
$912$		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	$-0.604841\pi$
$919$	−19.6105			−0.646892			−0.323446	+	0.946247i	$0.604841\pi$
$920$		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	0.927951	−	0.372703i	$-0.121569\pi$
$947$	4.34537	+	7.52640i	0.141206	+	0.244575i	−0.786745	+	0.617278i	$0.788235\pi$
$948$		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	−0.583112	−	0.812392i	$-0.698165\pi$
$967$	12.8117	−	22.1905i	0.411996	−	0.713598i	0.995108	+	0.0987939i	$0.0314985\pi$
$968$		0			0
$969$	−24.9559	+	43.2249i	−0.801699	+	1.38858i
$970$		0			0
$971$	−5.48232	−	9.49565i	−0.175936	−	0.304730i	0.764549	−	0.644566i	$-0.222962\pi$
$971$	−5.48232	−	9.49565i	−0.175936	−	0.304730i	−0.940485	+	0.339836i	$0.889628\pi$
$972$		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	$-0.982157\pi$
$983$	−17.1731	−	29.7446i	−0.547736	−	0.948706i	0.450694	−	0.892679i	$-0.351177\pi$
$984$		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	$-0.107156\pi$
$991$	59.4263			1.88774			0.943870	+	0.330318i	$0.107156\pi$
$992$		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	148.2.e.a.137.1	yes	6
3.2	odd	2		1332.2.j.e.433.1		6
4.3	odd	2		592.2.i.f.433.3		6
37.10	even	3	inner	148.2.e.a.121.1	✓	6
37.11	even	6		5476.2.a.g.1.3		3
37.26	even	3		5476.2.a.f.1.3		3
111.47	odd	6		1332.2.j.e.1009.1		6
148.47	odd	6		592.2.i.f.417.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
148.2.e.a.121.1	✓	6	37.10	even	3	inner
148.2.e.a.137.1	yes	6	1.1	even	1	trivial
592.2.i.f.417.3		6	148.47	odd	6
592.2.i.f.433.3		6	4.3	odd	2
1332.2.j.e.433.1		6	3.2	odd	2
1332.2.j.e.1009.1		6	111.47	odd	6
5476.2.a.f.1.3		3	37.26	even	3
5476.2.a.g.1.3		3	37.11	even	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:	\( N \)	\(=\)	\( 148 = 2^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	148.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42789 + 2.47317i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.07772 + 3.59871i) q^{7} +(-2.57772 - 4.46474i) q^{9} +O(q^{10})\)	\(q+(-1.42789 + 2.47317i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.07772 + 3.59871i) q^{7} +(-2.57772 - 4.46474i) q^{9} -1.29966 q^{11} +(-1.77805 + 3.07968i) q^{13} +(1.42789 + 2.47317i) q^{15} +(1.79966 + 3.11711i) q^{17} +(2.42789 - 4.20522i) q^{19} +(-5.93349 - 10.2771i) q^{21} +5.01121 q^{23} +(2.00000 + 3.46410i) q^{25} +6.15544 q^{27} +8.86698 q^{29} +1.29966 q^{31} +(1.85577 - 3.21429i) q^{33} +(2.07772 + 3.59871i) q^{35} +(1.27805 - 5.94698i) q^{37} +(-5.07772 - 8.79487i) q^{39} +(-5.35577 + 9.27647i) q^{41} -10.3109 q^{43} -5.15544 q^{45} +8.72275 q^{47} +(-5.13383 - 8.89205i) q^{49} -10.2789 q^{51} +(-5.07772 - 8.79487i) q^{53} +(-0.649832 + 1.12554i) q^{55} +(6.93349 + 12.0092i) q^{57} +(4.63383 + 8.02602i) q^{59} +(-1.35577 + 2.34827i) q^{61} +21.4231 q^{63} +(1.77805 + 3.07968i) q^{65} +(-3.98399 + 6.90048i) q^{67} +(-7.15544 + 12.3936i) q^{69} +(5.63383 - 9.75807i) q^{71} +2.28845 q^{73} -11.4231 q^{75} +(2.70034 - 4.67712i) q^{77} +(-1.28366 + 2.22336i) q^{79} +(-1.05611 + 1.82923i) q^{81} +(-4.98399 - 8.63253i) q^{83} +3.59933 q^{85} +(-12.6610 + 21.9296i) q^{87} +(2.21155 + 3.83051i) q^{89} +(-7.38859 - 12.7974i) q^{91} +(-1.85577 + 3.21429i) q^{93} +(-2.42789 - 4.20522i) q^{95} +9.97920 q^{97} +(3.35017 + 5.80266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 3 q^{5} - q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q - q^3 + 3 * q^5 - q^7 - 4 * q^9	\( 6 q - q^{3} + 3 q^{5} - q^{7} - 4 q^{9} - 7 q^{13} + q^{15} + 3 q^{17} + 7 q^{19} - 9 q^{21} - 8 q^{23} + 12 q^{25} + 14 q^{27} - 4 q^{33} + q^{35} + 4 q^{37} - 19 q^{39} - 17 q^{41} - 16 q^{43} - 8 q^{45} - 16 q^{47} - 12 q^{49} + 14 q^{51} - 19 q^{53} + 15 q^{57} + 9 q^{59} + 7 q^{61} + 68 q^{63} + 7 q^{65} - 9 q^{67} - 20 q^{69} + 15 q^{71} + 44 q^{73} - 8 q^{75} + 24 q^{77} + 15 q^{79} + q^{81} - 15 q^{83} + 6 q^{85} - 34 q^{87} - 17 q^{89} + 13 q^{91} + 4 q^{93} - 7 q^{95} - 8 q^{97} + 24 q^{99}+O(q^{100}) \) 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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Database

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