LMFDB - Embedded newform 1512.2.j.d.323.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.9
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06881 - 0.926094i) q^{2} +(0.284699 + 1.97963i) q^{4} -2.85878 q^{5} -1.00000i q^{7} +(1.52904 - 2.37950i) q^{8} +O(q^{10})$	\(q+(-1.06881 - 0.926094i) q^{2} +(0.284699 + 1.97963i) q^{4} -2.85878 q^{5} -1.00000i q^{7} +(1.52904 - 2.37950i) q^{8} +(3.05549 + 2.64750i) q^{10} +4.98479i q^{11} -2.35304i q^{13} +(-0.926094 + 1.06881i) q^{14} +(-3.83789 + 1.12720i) q^{16} -8.19706i q^{17} +5.90589 q^{19} +(-0.813893 - 5.65934i) q^{20} +(4.61639 - 5.32778i) q^{22} -4.43848 q^{23} +3.17265 q^{25} +(-2.17914 + 2.51495i) q^{26} +(1.97963 - 0.284699i) q^{28} -6.41440 q^{29} +3.31678i q^{31} +(5.14586 + 2.34949i) q^{32} +(-7.59125 + 8.76108i) q^{34} +2.85878i q^{35} +5.51080i q^{37} +(-6.31226 - 5.46942i) q^{38} +(-4.37119 + 6.80249i) q^{40} +3.41549i q^{41} +1.37638 q^{43} +(-9.86806 + 1.41917i) q^{44} +(4.74388 + 4.11045i) q^{46} -2.60102 q^{47} -1.00000 q^{49} +(-3.39095 - 2.93817i) q^{50} +(4.65815 - 0.669908i) q^{52} +13.3184 q^{53} -14.2505i q^{55} +(-2.37950 - 1.52904i) q^{56} +(6.85576 + 5.94034i) q^{58} +10.6485i q^{59} +1.41211i q^{61} +(3.07165 - 3.54499i) q^{62} +(-3.32408 - 7.27671i) q^{64} +6.72683i q^{65} +0.221252 q^{67} +(16.2272 - 2.33369i) q^{68} +(2.64750 - 3.05549i) q^{70} +0.398786 q^{71} -10.7893 q^{73} +(5.10352 - 5.88998i) q^{74} +(1.68140 + 11.6915i) q^{76} +4.98479 q^{77} +9.76133i q^{79} +(10.9717 - 3.22242i) q^{80} +(3.16307 - 3.65050i) q^{82} -2.06831i q^{83} +23.4336i q^{85} +(-1.47108 - 1.27465i) q^{86} +(11.8613 + 7.62194i) q^{88} +17.6684i q^{89} -2.35304 q^{91} +(-1.26363 - 8.78656i) q^{92} +(2.77999 + 2.40879i) q^{94} -16.8837 q^{95} -3.62651 q^{97} +(1.06881 + 0.926094i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.06881	−	0.926094i	−0.755761	−	0.654847i
$2$	−1.06881	−	0.926094i	−0.755761	−	0.654847i
$3$		0			0
$3$		0			0
$4$	0.284699	+	1.97963i	0.142350	+	0.989816i
$5$	−2.85878			−1.27849			−0.639244	−	0.769004i	$-0.720753\pi$
$5$	−2.85878			−1.27849			−0.639244	+	0.769004i	$0.720753\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.52904	−	2.37950i	0.540597	−	0.841282i
$9$		0			0
$10$	3.05549	+	2.64750i	0.966231	+	0.837214i
$11$			4.98479i			1.50297i	0.659749	+	0.751486i	$0.270663\pi$
$11$			4.98479i			1.50297i	−0.659749	+	0.751486i	$0.729337\pi$
$12$		0			0
$13$		−	2.35304i		−	0.652615i	−0.945264	−	0.326308i	$-0.894195\pi$
$13$		−	2.35304i		−	0.652615i	0.945264	−	0.326308i	$-0.105805\pi$
$14$	−0.926094	+	1.06881i	−0.247509	+	0.285651i
$15$		0			0
$16$	−3.83789	+	1.12720i	−0.959473	+	0.281800i
$17$		−	8.19706i		−	1.98808i	−0.109021	−	0.994039i	$-0.534772\pi$
$17$		−	8.19706i		−	1.98808i	0.109021	−	0.994039i	$-0.465228\pi$
$18$		0			0
$19$	5.90589			1.35491			0.677453	−	0.735566i	$-0.263084\pi$
$19$	5.90589			1.35491			0.677453	+	0.735566i	$0.263084\pi$
$20$	−0.813893	−	5.65934i	−0.181992	−	1.26547i
$21$		0			0
$22$	4.61639	−	5.32778i	0.984217	−	1.13589i
$23$	−4.43848			−0.925487			−0.462744	−	0.886492i	$-0.653135\pi$
$23$	−4.43848			−0.925487			−0.462744	+	0.886492i	$0.653135\pi$
$24$		0			0
$25$	3.17265			0.634530
$26$	−2.17914	+	2.51495i	−0.427364	+	0.493221i
$27$		0			0
$28$	1.97963	−	0.284699i	0.374115	−	0.0538031i
$29$	−6.41440			−1.19112			−0.595562	−	0.803309i	$-0.703071\pi$
$29$	−6.41440			−1.19112			−0.595562	+	0.803309i	$0.703071\pi$
$30$		0			0
$31$			3.31678i			0.595710i	0.954611	+	0.297855i	$0.0962713\pi$
$31$			3.31678i			0.595710i	−0.954611	+	0.297855i	$0.903729\pi$
$32$	5.14586	+	2.34949i	0.909668	+	0.415335i
$33$		0			0
$34$	−7.59125	+	8.76108i	−1.30189	+	1.50251i
$35$			2.85878i			0.483223i
$36$		0			0
$37$			5.51080i			0.905970i	0.891518	+	0.452985i	$0.149641\pi$
$37$			5.51080i			0.905970i	−0.891518	+	0.452985i	$0.850359\pi$
$38$	−6.31226	−	5.46942i	−1.02398	−	0.887256i
$39$		0			0
$40$	−4.37119	+	6.80249i	−0.691146	+	1.07557i
$41$			3.41549i			0.533410i	0.963778	+	0.266705i	$0.0859349\pi$
$41$			3.41549i			0.533410i	−0.963778	+	0.266705i	$0.914065\pi$
$42$		0			0
$43$	1.37638			0.209895			0.104948	−	0.994478i	$-0.466532\pi$
$43$	1.37638			0.209895			0.104948	+	0.994478i	$0.466532\pi$
$44$	−9.86806	+	1.41917i	−1.48767	+	0.213947i
$45$		0			0
$46$	4.74388	+	4.11045i	0.699447	+	0.606053i
$47$	−2.60102			−0.379398			−0.189699	−	0.981842i	$-0.560751\pi$
$47$	−2.60102			−0.379398			−0.189699	+	0.981842i	$0.560751\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−3.39095	−	2.93817i	−0.479553	−	0.415521i
$51$		0			0
$52$	4.65815	−	0.669908i	0.645969	−	0.0928995i
$53$	13.3184			1.82942			0.914710	−	0.404110i	$-0.132419\pi$
$53$	13.3184			1.82942			0.914710	+	0.404110i	$0.132419\pi$
$54$		0			0
$55$		−	14.2505i		−	1.92153i
$56$	−2.37950	−	1.52904i	−0.317975	−	0.204326i
$57$		0			0
$58$	6.85576	+	5.94034i	0.900205	+	0.780005i
$59$			10.6485i			1.38631i	0.720788	+	0.693156i	$0.243780\pi$
$59$			10.6485i			1.38631i	−0.720788	+	0.693156i	$0.756220\pi$
$60$		0			0
$61$			1.41211i			0.180802i	0.995905	+	0.0904011i	$0.0288149\pi$
$61$			1.41211i			0.180802i	−0.995905	+	0.0904011i	$0.971185\pi$
$62$	3.07165	−	3.54499i	0.390100	−	0.450215i
$63$		0			0
$64$	−3.32408	−	7.27671i	−0.415511	−	0.909588i
$65$			6.72683i			0.834361i
$66$		0			0
$67$	0.221252			0.0270303			0.0135151	−	0.999909i	$-0.495698\pi$
$67$	0.221252			0.0270303			0.0135151	+	0.999909i	$0.495698\pi$
$68$	16.2272	−	2.33369i	1.96783	−	0.283002i
$69$		0			0
$70$	2.64750	−	3.05549i	0.316437	−	0.365201i
$71$	0.398786			0.0473271			0.0236636	−	0.999720i	$-0.492467\pi$
$71$	0.398786			0.0473271			0.0236636	+	0.999720i	$0.492467\pi$
$72$		0			0
$73$	−10.7893			−1.26279			−0.631397	−	0.775460i	$-0.717518\pi$
$73$	−10.7893			−1.26279			−0.631397	+	0.775460i	$0.717518\pi$
$74$	5.10352	−	5.88998i	0.593272	−	0.684697i
$75$		0			0
$76$	1.68140	+	11.6915i	0.192870	+	1.34111i
$77$	4.98479			0.568070
$78$		0			0
$79$			9.76133i			1.09824i	0.835745	+	0.549118i	$0.185036\pi$
$79$			9.76133i			1.09824i	−0.835745	+	0.549118i	$0.814964\pi$
$80$	10.9717	−	3.22242i	1.22667	−	0.360278i
$81$		0			0
$82$	3.16307	−	3.65050i	0.349302	−	0.403130i
$83$		−	2.06831i		−	0.227027i	−0.993536	−	0.113513i	$-0.963789\pi$
$83$		−	2.06831i		−	0.227027i	0.993536	−	0.113513i	$-0.0362105\pi$
$84$		0			0
$85$			23.4336i			2.54173i
$86$	−1.47108	−	1.27465i	−0.158631	−	0.137449i
$87$		0			0
$88$	11.8613	+	7.62194i	1.26442	+	0.812501i
$89$			17.6684i			1.87284i	0.350875	+	0.936422i	$0.385884\pi$
$89$			17.6684i			1.87284i	−0.350875	+	0.936422i	$0.614116\pi$
$90$		0			0
$91$	−2.35304			−0.246665
$92$	−1.26363	−	8.78656i	−0.131743	−	0.916062i
$93$		0			0
$94$	2.77999	+	2.40879i	0.286735	+	0.248448i
$95$	−16.8837			−1.73223
$96$		0			0
$97$	−3.62651			−0.368217			−0.184108	−	0.982906i	$-0.558940\pi$
$97$	−3.62651			−0.368217			−0.184108	+	0.982906i	$0.558940\pi$
$98$	1.06881	+	0.926094i	0.107966	+	0.0935496i
$99$		0			0
$100$	0.903251	+	6.28069i	0.0903251	+	0.628069i
$101$	10.4729			1.04209			0.521047	−	0.853528i	$-0.325541\pi$
$101$	10.4729			1.04209			0.521047	+	0.853528i	$0.325541\pi$
$102$		0			0
$103$			4.50892i			0.444277i	0.975015	+	0.222139i	$0.0713037\pi$
$103$			4.50892i			0.444277i	−0.975015	+	0.222139i	$0.928696\pi$
$104$	−5.59907	−	3.59789i	−0.549034	−	0.352802i
$105$		0			0
$106$	−14.2348	−	12.3341i	−1.38260	−	1.19799i
$107$			6.82640i			0.659933i	0.943993	+	0.329966i	$0.107037\pi$
$107$			6.82640i			0.659933i	−0.943993	+	0.329966i	$0.892963\pi$
$108$		0			0
$109$			13.1273i			1.25737i	0.777660	+	0.628685i	$0.216407\pi$
$109$			13.1273i			1.25737i	−0.777660	+	0.628685i	$0.783593\pi$
$110$	−13.1973	+	15.2310i	−1.25831	+	1.45222i
$111$		0			0
$112$	1.12720	+	3.83789i	0.106510	+	0.362647i
$113$			5.30759i			0.499297i	0.968337	+	0.249648i	$0.0803150\pi$
$113$			5.30759i			0.499297i	−0.968337	+	0.249648i	$0.919685\pi$
$114$		0			0
$115$	12.6887			1.18322
$116$	−1.82617	−	12.6982i	−0.169556	−	1.17899i
$117$		0			0
$118$	9.86148	−	11.3812i	0.907823	−	1.04772i
$119$	−8.19706			−0.751423
$120$		0			0
$121$	−13.8482			−1.25892
$122$	1.30775	−	1.50927i	0.118398	−	0.136643i
$123$		0			0
$124$	−6.56600	+	0.944283i	−0.589644	+	0.0847991i
$125$	5.22400			0.467248
$126$		0			0
$127$			1.80347i			0.160032i	0.996794	+	0.0800160i	$0.0254972\pi$
$127$			1.80347i			0.160032i	−0.996794	+	0.0800160i	$0.974503\pi$
$128$	−3.18611	+	10.8558i	−0.281615	+	0.959528i
$129$		0			0
$130$	6.22968	−	7.18969i	0.546379	−	0.630577i
$131$			9.93535i			0.868056i	0.900899	+	0.434028i	$0.142908\pi$
$131$			9.93535i			0.868056i	−0.900899	+	0.434028i	$0.857092\pi$
$132$		0			0
$133$		−	5.90589i		−	0.512106i
$134$	−0.236476	−	0.204901i	−0.0204284	−	0.0177007i
$135$		0			0
$136$	−19.5049	−	12.5336i	−1.67253	−	1.07475i
$137$			1.16258i			0.0993261i	0.998766	+	0.0496630i	$0.0158147\pi$
$137$			1.16258i			0.0993261i	−0.998766	+	0.0496630i	$0.984185\pi$
$138$		0			0
$139$	17.0996			1.45037			0.725186	−	0.688553i	$-0.241754\pi$
$139$	17.0996			1.45037			0.725186	+	0.688553i	$0.241754\pi$
$140$	−5.65934	+	0.813893i	−0.478302	+	0.0687865i
$141$		0			0
$142$	−0.426225	−	0.369313i	−0.0357680	−	0.0309921i
$143$	11.7294			0.980863
$144$		0			0
$145$	18.3374			1.52284
$146$	11.5317	+	9.99192i	0.954370	+	0.826937i
$147$		0			0
$148$	−10.9094	+	1.56892i	−0.896744	+	0.128964i
$149$	−23.1689			−1.89807			−0.949034	−	0.315173i	$-0.897937\pi$
$149$	−23.1689			−1.89807			−0.949034	+	0.315173i	$0.897937\pi$
$150$		0			0
$151$		−	1.67795i		−	0.136549i	−0.997667	−	0.0682747i	$-0.978251\pi$
$151$		−	1.67795i		−	0.136549i	0.997667	−	0.0682747i	$-0.0217494\pi$
$152$	9.03034	−	14.0531i	0.732457	−	1.13986i
$153$		0			0
$154$	−5.32778	−	4.61639i	−0.429325	−	0.371999i
$155$		−	9.48195i		−	0.761608i
$156$		0			0
$157$		−	2.22459i		−	0.177542i	−0.996052	−	0.0887710i	$-0.971706\pi$
$157$		−	2.22459i		−	0.177542i	0.996052	−	0.0887710i	$-0.0282939\pi$
$158$	9.03991	−	10.4330i	0.719177	−	0.830004i
$159$		0			0
$160$	−14.7109	−	6.71669i	−1.16300	−	0.531001i
$161$			4.43848i			0.349801i
$162$		0			0
$163$	−17.3358			−1.35785			−0.678924	−	0.734209i	$-0.737553\pi$
$163$	−17.3358			−1.35785			−0.678924	+	0.734209i	$0.737553\pi$
$164$	−6.76142	+	0.972387i	−0.527978	+	0.0759307i
$165$		0			0
$166$	−1.91545	+	2.21063i	−0.148668	+	0.171578i
$167$	21.4429			1.65930			0.829650	−	0.558284i	$-0.188540\pi$
$167$	21.4429			1.65930			0.829650	+	0.558284i	$0.188540\pi$
$168$		0			0
$169$	7.46321			0.574093
$170$	21.7017	−	25.0460i	1.66445	−	1.92094i
$171$		0			0
$172$	0.391853	+	2.72472i	0.0298785	+	0.207758i
$173$	−9.70545			−0.737892			−0.368946	−	0.929451i	$-0.620281\pi$
$173$	−9.70545			−0.737892			−0.368946	+	0.929451i	$0.620281\pi$
$174$		0			0
$175$		−	3.17265i		−	0.239830i
$176$	−5.61885	−	19.1311i	−0.423537	−	1.44206i
$177$		0			0
$178$	16.3626	−	18.8841i	1.22643	−	1.41542i
$179$		−	14.7350i		−	1.10134i	−0.834722	−	0.550671i	$-0.814372\pi$
$179$		−	14.7350i		−	1.10134i	0.834722	−	0.550671i	$-0.185628\pi$
$180$		0			0
$181$			17.7055i			1.31604i	0.753001	+	0.658019i	$0.228605\pi$
$181$			17.7055i			1.31604i	−0.753001	+	0.658019i	$0.771395\pi$
$182$	2.51495	+	2.17914i	0.186420	+	0.161528i
$183$		0			0
$184$	−6.78661	+	10.5614i	−0.500315	+	0.778596i
$185$		−	15.7542i		−	1.15827i
$186$		0			0
$187$	40.8606			2.98803
$188$	−0.740509	−	5.14907i	−0.0540072	−	0.375535i
$189$		0			0
$190$	18.0454	+	15.6359i	1.30915	+	1.13435i
$191$	17.9941			1.30201			0.651003	−	0.759075i	$-0.274348\pi$
$191$	17.9941			1.30201			0.651003	+	0.759075i	$0.274348\pi$
$192$		0			0
$193$	−24.8594			−1.78942			−0.894709	−	0.446649i	$-0.852617\pi$
$193$	−24.8594			−1.78942			−0.894709	+	0.446649i	$0.852617\pi$
$194$	3.87605	+	3.35849i	0.278284	+	0.241126i
$195$		0			0
$196$	−0.284699	−	1.97963i	−0.0203356	−	0.141402i
$197$	17.4145			1.24073			0.620367	−	0.784312i	$-0.286984\pi$
$197$	17.4145			1.24073			0.620367	+	0.784312i	$0.286984\pi$
$198$		0			0
$199$		−	20.0065i		−	1.41823i	−0.705095	−	0.709113i	$-0.749096\pi$
$199$		−	20.0065i		−	1.41823i	0.705095	−	0.709113i	$-0.250904\pi$
$200$	4.85110	−	7.54934i	0.343025	−	0.533819i
$201$		0			0
$202$	−11.1935	−	9.69891i	−0.787575	−	0.682413i
$203$			6.41440i			0.450203i
$204$		0			0
$205$		−	9.76415i		−	0.681958i
$206$	4.17569	−	4.81917i	0.290934	−	0.335767i
$207$		0			0
$208$	2.65234	+	9.03071i	0.183907	+	0.626167i
$209$			29.4397i			2.03638i
$210$		0			0
$211$	−15.0542			−1.03637			−0.518186	−	0.855268i	$-0.673392\pi$
$211$	−15.0542			−1.03637			−0.518186	+	0.855268i	$0.673392\pi$
$212$	3.79173	+	26.3655i	0.260417	+	1.81079i
$213$		0			0
$214$	6.32189	−	7.29610i	0.432155	−	0.498751i
$215$	−3.93476			−0.268349
$216$		0			0
$217$	3.31678			0.225157
$218$	12.1571	−	14.0306i	0.823386	−	0.950272i
$219$		0			0
$220$	28.2107	−	4.05709i	1.90196	−	0.273529i
$221$	−19.2880			−1.29745
$222$		0			0
$223$			12.7615i			0.854570i	0.904117	+	0.427285i	$0.140530\pi$
$223$			12.7615i			0.854570i	−0.904117	+	0.427285i	$0.859470\pi$
$224$	2.34949	−	5.14586i	0.156982	−	0.343822i
$225$		0			0
$226$	4.91533	−	5.67280i	0.326963	−	0.377349i
$227$			25.7167i			1.70688i	0.521194	+	0.853438i	$0.325487\pi$
$227$			25.7167i			1.70688i	−0.521194	+	0.853438i	$0.674513\pi$
$228$		0			0
$229$		−	10.7033i		−	0.707293i	−0.935379	−	0.353647i	$-0.884942\pi$
$229$		−	10.7033i		−	0.707293i	0.935379	−	0.353647i	$-0.115058\pi$
$230$	−13.5617	−	11.7509i	−0.894234	−	0.774831i
$231$		0			0
$232$	−9.80786	+	15.2631i	−0.643918	+	1.00207i
$233$			5.55917i			0.364194i	0.983281	+	0.182097i	$0.0582884\pi$
$233$			5.55917i			0.364194i	−0.983281	+	0.182097i	$0.941712\pi$
$234$		0			0
$235$	7.43577			0.485056
$236$	−21.0800	+	3.03161i	−1.37219	+	0.197341i
$237$		0			0
$238$	8.76108	+	7.59125i	0.567896	+	0.492068i
$239$	20.7187			1.34018			0.670092	−	0.742278i	$-0.266255\pi$
$239$	20.7187			1.34018			0.670092	+	0.742278i	$0.266255\pi$
$240$		0			0
$241$	6.03091			0.388485			0.194242	−	0.980954i	$-0.437775\pi$
$241$	6.03091			0.388485			0.194242	+	0.980954i	$0.437775\pi$
$242$	14.8010	+	12.8247i	0.951446	+	0.824403i
$243$		0			0
$244$	−2.79546	+	0.402027i	−0.178961	+	0.0257371i
$245$	2.85878			0.182641
$246$		0			0
$247$		−	13.8968i		−	0.884232i
$248$	7.89228	+	5.07148i	0.501160	+	0.322039i
$249$		0			0
$250$	−5.58345	−	4.83791i	−0.353128	−	0.305976i
$251$			8.01117i			0.505660i	0.967511	+	0.252830i	$0.0813614\pi$
$251$			8.01117i			0.505660i	−0.967511	+	0.252830i	$0.918639\pi$
$252$		0			0
$253$		−	22.1249i		−	1.39098i
$254$	1.67018	−	1.92756i	0.104797	−	0.120946i
$255$		0			0
$256$	13.4588	−	8.65214i	0.841178	−	0.540759i
$257$		−	14.1009i		−	0.879590i	−0.898098	−	0.439795i	$-0.855051\pi$
$257$		−	14.1009i		−	0.879590i	0.898098	−	0.439795i	$-0.144949\pi$
$258$		0			0
$259$	5.51080			0.342424
$260$	−13.3167	+	1.91512i	−0.825864	+	0.118771i
$261$		0			0
$262$	9.20107	−	10.6190i	0.568444	−	0.656043i
$263$	−24.6348			−1.51905			−0.759524	−	0.650479i	$-0.774568\pi$
$263$	−24.6348			−1.51905			−0.759524	+	0.650479i	$0.774568\pi$
$264$		0			0
$265$	−38.0744			−2.33889
$266$	−5.46942	+	6.31226i	−0.335351	+	0.387030i
$267$		0			0
$268$	0.0629903	+	0.437998i	0.00384775	+	0.0267550i
$269$	−9.64498			−0.588065			−0.294032	−	0.955795i	$-0.594997\pi$
$269$	−9.64498			−0.588065			−0.294032	+	0.955795i	$0.594997\pi$
$270$		0			0
$271$		−	13.3466i		−	0.810751i	−0.914150	−	0.405375i	$-0.867141\pi$
$271$		−	13.3466i		−	0.810751i	0.914150	−	0.405375i	$-0.132859\pi$
$272$	9.23972	+	31.4594i	0.560240	+	1.90751i
$273$		0			0
$274$	1.07666	−	1.24258i	0.0650434	−	0.0750668i
$275$			15.8150i			0.953681i
$276$		0			0
$277$			18.5217i			1.11286i	0.830895	+	0.556429i	$0.187829\pi$
$277$			18.5217i			1.11286i	−0.830895	+	0.556429i	$0.812171\pi$
$278$	−18.2762	−	15.8359i	−1.09614	−	0.949773i
$279$		0			0
$280$	6.80249	+	4.37119i	0.406527	+	0.261229i
$281$			18.7455i			1.11826i	0.829079	+	0.559131i	$0.188865\pi$
$281$			18.7455i			1.11826i	−0.829079	+	0.559131i	$0.811135\pi$
$282$		0			0
$283$	−2.32063			−0.137947			−0.0689736	−	0.997618i	$-0.521972\pi$
$283$	−2.32063			−0.137947			−0.0689736	+	0.997618i	$0.521972\pi$
$284$	0.113534	+	0.789449i	0.00673700	+	0.0468452i
$285$		0			0
$286$	−12.5365	−	10.8625i	−0.741298	−	0.642315i
$287$	3.41549			0.201610
$288$		0			0
$289$	−50.1918			−2.95246
$290$	−19.5991	−	16.9821i	−1.15090	−	0.997226i
$291$		0			0
$292$	−3.07171	−	21.3589i	−0.179758	−	1.24993i
$293$	−3.61125			−0.210972			−0.105486	−	0.994421i	$-0.533640\pi$
$293$	−3.61125			−0.210972			−0.105486	+	0.994421i	$0.533640\pi$
$294$		0			0
$295$		−	30.4417i		−	1.77238i
$296$	13.1130	+	8.42622i	0.762176	+	0.489764i
$297$		0			0
$298$	24.7631	+	21.4566i	1.43449	+	1.24295i
$299$			10.4439i			0.603987i
$300$		0			0
$301$		−	1.37638i		−	0.0793330i
$302$	−1.55394	+	1.79340i	−0.0894190	+	0.103199i
$303$		0			0
$304$	−22.6662	+	6.65712i	−1.30000	+	0.381812i
$305$		−	4.03692i		−	0.231153i
$306$		0			0
$307$	−19.9273			−1.13731			−0.568656	−	0.822576i	$-0.692536\pi$
$307$	−19.9273			−1.13731			−0.568656	+	0.822576i	$0.692536\pi$
$308$	1.41917	+	9.86806i	0.0808645	+	0.562285i
$309$		0			0
$310$	−8.78118	+	10.1344i	−0.498737	+	0.575594i
$311$	4.68722			0.265788			0.132894	−	0.991130i	$-0.457573\pi$
$311$	4.68722			0.265788			0.132894	+	0.991130i	$0.457573\pi$
$312$		0			0
$313$	−13.2179			−0.747118			−0.373559	−	0.927606i	$-0.621863\pi$
$313$	−13.2179			−0.747118			−0.373559	+	0.927606i	$0.621863\pi$
$314$	−2.06018	+	2.37766i	−0.116263	+	0.134179i
$315$		0			0
$316$	−19.3239	+	2.77904i	−1.08705	+	0.156333i
$317$	−13.8162			−0.775995			−0.387997	−	0.921660i	$-0.626833\pi$
$317$	−13.8162			−0.775995			−0.387997	+	0.921660i	$0.626833\pi$
$318$		0			0
$319$		−	31.9745i		−	1.79023i
$320$	9.50284	+	20.8025i	0.531225	+	1.16290i
$321$		0			0
$322$	4.11045	−	4.74388i	0.229067	−	0.264366i
$323$		−	48.4110i		−	2.69366i
$324$		0			0
$325$		−	7.46537i		−	0.414104i
$326$	18.5287	+	16.0546i	1.02621	+	0.889183i
$327$		0			0
$328$	8.12718	+	5.22242i	0.448748	+	0.288360i
$329$			2.60102i			0.143399i
$330$		0			0
$331$	9.70429			0.533396			0.266698	−	0.963780i	$-0.414067\pi$
$331$	9.70429			0.533396			0.266698	+	0.963780i	$0.414067\pi$
$332$	4.09450	−	0.588847i	0.224715	−	0.0323172i
$333$		0			0
$334$	−22.9183	−	19.8581i	−1.25403	−	1.08659i
$335$	−0.632513			−0.0345579
$336$		0			0
$337$	5.04484			0.274810			0.137405	−	0.990515i	$-0.456124\pi$
$337$	5.04484			0.274810			0.137405	+	0.990515i	$0.456124\pi$
$338$	−7.97674	−	6.91164i	−0.433877	−	0.375943i
$339$		0			0
$340$	−46.3900	+	6.67153i	−2.51585	+	0.361815i
$341$	−16.5334			−0.895336
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	2.10453	−	3.27509i	0.113469	−	0.176581i
$345$		0			0
$346$	10.3733	+	8.98816i	0.557670	+	0.483206i
$347$		−	2.01718i		−	0.108288i	−0.998533	−	0.0541440i	$-0.982757\pi$
$347$		−	2.01718i		−	0.108288i	0.998533	−	0.0541440i	$-0.0172430\pi$
$348$		0			0
$349$		−	0.528557i		−	0.0282930i	−0.999900	−	0.0141465i	$-0.995497\pi$
$349$		−	0.528557i		−	0.0282930i	0.999900	−	0.0141465i	$-0.00450312\pi$
$350$	−2.93817	+	3.39095i	−0.157052	+	0.181254i
$351$		0			0
$352$	−11.7117	+	25.6511i	−0.624237	+	1.36721i
$353$		−	10.3448i		−	0.550600i	−0.961358	−	0.275300i	$-0.911223\pi$
$353$		−	10.3448i		−	0.550600i	0.961358	−	0.275300i	$-0.0887772\pi$
$354$		0			0
$355$	−1.14004			−0.0605072
$356$	−34.9769	+	5.03017i	−1.85377	+	0.266599i
$357$		0			0
$358$	−13.6460	+	15.7488i	−0.721211	+	0.832352i
$359$	1.62306			0.0856618			0.0428309	−	0.999082i	$-0.486362\pi$
$359$	1.62306			0.0856618			0.0428309	+	0.999082i	$0.486362\pi$
$360$		0			0
$361$	15.8796			0.835768
$362$	16.3970	−	18.9238i	0.861805	−	0.994611i
$363$		0			0
$364$	−0.669908	−	4.65815i	−0.0351127	−	0.244154i
$365$	30.8443			1.61447
$366$		0			0
$367$		−	33.5635i		−	1.75200i	−0.482312	−	0.875999i	$-0.660203\pi$
$367$		−	33.5635i		−	1.75200i	0.482312	−	0.875999i	$-0.339797\pi$
$368$	17.0344	−	5.00305i	0.887980	−	0.260802i
$369$		0			0
$370$	−14.5899	+	16.8382i	−0.758491	+	0.875376i
$371$		−	13.3184i		−	0.691456i
$372$		0			0
$373$			20.4199i			1.05730i	0.848840	+	0.528650i	$0.177302\pi$
$373$			20.4199i			1.05730i	−0.848840	+	0.528650i	$0.822698\pi$
$374$	−43.6722	−	37.8408i	−2.25823	−	1.95670i
$375$		0			0
$376$	−3.97707	+	6.18915i	−0.205101	+	0.319181i
$377$			15.0933i			0.777346i
$378$		0			0
$379$	29.6529			1.52317			0.761583	−	0.648068i	$-0.224423\pi$
$379$	29.6529			1.52317			0.761583	+	0.648068i	$0.224423\pi$
$380$	−4.80677	−	33.4235i	−0.246582	−	1.71459i
$381$		0			0
$382$	−19.2322	−	16.6642i	−0.984006	−	0.852615i
$383$	4.82347			0.246468			0.123234	−	0.992378i	$-0.460673\pi$
$383$	4.82347			0.246468			0.123234	+	0.992378i	$0.460673\pi$
$384$		0			0
$385$	−14.2505			−0.726270
$386$	26.5699	+	23.0221i	1.35237	+	1.17180i
$387$		0			0
$388$	−1.03247	−	7.17917i	−0.0524155	−	0.364467i
$389$	−18.5242			−0.939214			−0.469607	−	0.882876i	$-0.655604\pi$
$389$	−18.5242			−0.939214			−0.469607	+	0.882876i	$0.655604\pi$
$390$		0			0
$391$			36.3825i			1.83994i
$392$	−1.52904	+	2.37950i	−0.0772281	+	0.120183i
$393$		0			0
$394$	−18.6128	−	16.1275i	−0.937699	−	0.812492i
$395$		−	27.9056i		−	1.40408i
$396$		0			0
$397$			2.91585i			0.146342i	0.997319	+	0.0731712i	$0.0233119\pi$
$397$			2.91585i			0.146342i	−0.997319	+	0.0731712i	$0.976688\pi$
$398$	−18.5279	+	21.3831i	−0.928722	+	1.07184i
$399$		0			0
$400$	−12.1763	+	3.57621i	−0.608815	+	0.178810i
$401$			2.62856i			0.131264i	0.997844	+	0.0656319i	$0.0209063\pi$
$401$			2.62856i			0.131264i	−0.997844	+	0.0656319i	$0.979094\pi$
$402$		0			0
$403$	7.80450			0.388770
$404$	2.98163	+	20.7325i	0.148342	+	1.03148i
$405$		0			0
$406$	5.94034	−	6.85576i	0.294814	−	0.340246i
$407$	−27.4702			−1.36165
$408$		0			0
$409$	26.0556			1.28836			0.644182	−	0.764872i	$-0.277198\pi$
$409$	26.0556			1.28836			0.644182	+	0.764872i	$0.277198\pi$
$410$	−9.04253	+	10.4360i	−0.446578	+	0.515397i
$411$		0			0
$412$	−8.92601	+	1.28369i	−0.439753	+	0.0632426i
$413$	10.6485			0.523977
$414$		0			0
$415$			5.91286i			0.290251i
$416$	5.52844	−	12.1084i	0.271054	−	0.593664i
$417$		0			0
$418$	27.2639	−	31.4653i	1.33352	−	1.53902i
$419$		−	9.43185i		−	0.460776i	−0.973099	−	0.230388i	$-0.926000\pi$
$419$		−	9.43185i		−	0.460776i	0.973099	−	0.230388i	$-0.0739995\pi$
$420$		0			0
$421$			22.3767i			1.09057i	0.838249	+	0.545287i	$0.183579\pi$
$421$			22.3767i			1.09057i	−0.838249	+	0.545287i	$0.816421\pi$
$422$	16.0900	+	13.9416i	0.783249	+	0.678665i
$423$		0			0
$424$	20.3643	−	31.6912i	0.988979	−	1.53906i
$425$		−	26.0064i		−	1.26150i
$426$		0			0
$427$	1.41211			0.0683368
$428$	−13.5138	+	1.94347i	−0.653212	+	0.0939411i
$429$		0			0
$430$	4.20550	+	3.64396i	0.202807	+	0.175727i
$431$	−14.1600			−0.682061			−0.341030	−	0.940052i	$-0.610776\pi$
$431$	−14.1600			−0.682061			−0.341030	+	0.940052i	$0.610776\pi$
$432$		0			0
$433$	9.47617			0.455396			0.227698	−	0.973732i	$-0.426880\pi$
$433$	9.47617			0.455396			0.227698	+	0.973732i	$0.426880\pi$
$434$	−3.54499	−	3.07165i	−0.170165	−	0.147444i
$435$		0			0
$436$	−25.9873	+	3.73734i	−1.24457	+	0.178986i
$437$	−26.2132			−1.25395
$438$		0			0
$439$		−	5.40493i		−	0.257963i	−0.991647	−	0.128982i	$-0.958829\pi$
$439$		−	5.40493i		−	0.257963i	0.991647	−	0.128982i	$-0.0411709\pi$
$440$	−33.9090	−	21.7895i	−1.61655	−	1.03877i
$441$		0			0
$442$	20.6152	+	17.8625i	0.980563	+	0.849632i
$443$		−	28.2417i		−	1.34180i	−0.741546	−	0.670902i	$-0.765907\pi$
$443$		−	28.2417i		−	1.34180i	0.741546	−	0.670902i	$-0.234093\pi$
$444$		0			0
$445$		−	50.5101i		−	2.39441i
$446$	11.8183	−	13.6395i	0.559613	−	0.645851i
$447$		0			0
$448$	−7.27671	+	3.32408i	−0.343792	+	0.157048i
$449$		−	31.0885i		−	1.46716i	−0.679605	−	0.733578i	$-0.737849\pi$
$449$		−	31.0885i		−	1.46716i	0.679605	−	0.733578i	$-0.262151\pi$
$450$		0			0
$451$	−17.0255			−0.801700
$452$	−10.5071	+	1.51107i	−0.494212	+	0.0710746i
$453$		0			0
$454$	23.8161	−	27.4862i	1.11774	−	1.28999i
$455$	6.72683			0.315359
$456$		0			0
$457$	15.4214			0.721383			0.360691	−	0.932685i	$-0.382541\pi$
$457$	15.4214			0.721383			0.360691	+	0.932685i	$0.382541\pi$
$458$	−9.91225	+	11.4398i	−0.463169	+	0.534545i
$459$		0			0
$460$	3.61245	+	25.1189i	0.168431	+	1.17117i
$461$	21.7699			1.01392			0.506962	−	0.861968i	$-0.330768\pi$
$461$	21.7699			1.01392			0.506962	+	0.861968i	$0.330768\pi$
$462$		0			0
$463$		−	33.1540i		−	1.54080i	−0.637563	−	0.770398i	$-0.720057\pi$
$463$		−	33.1540i		−	1.54080i	0.637563	−	0.770398i	$-0.279943\pi$
$464$	24.6178	−	7.23031i	1.14285	−	0.335659i
$465$		0			0
$466$	5.14832	−	5.94169i	0.238491	−	0.275243i
$467$			23.3233i			1.07927i	0.841898	+	0.539637i	$0.181439\pi$
$467$			23.3233i			1.07927i	−0.841898	+	0.539637i	$0.818561\pi$
$468$		0			0
$469$		−	0.221252i		−	0.0102165i
$470$	−7.94741	−	6.88622i	−0.366586	−	0.317638i
$471$		0			0
$472$	25.3381	+	16.2819i	1.16628	+	0.749435i
$473$			6.86095i			0.315467i
$474$		0			0
$475$	18.7373			0.859728
$476$	−2.33369	−	16.2272i	−0.106965	−	0.743771i
$477$		0			0
$478$	−22.1443	−	19.1875i	−1.01286	−	0.877616i
$479$	29.7837			1.36085			0.680426	−	0.732817i	$-0.261795\pi$
$479$	29.7837			1.36085			0.680426	+	0.732817i	$0.261795\pi$
$480$		0			0
$481$	12.9671			0.591250
$482$	−6.44588	−	5.58519i	−0.293602	−	0.254398i
$483$		0			0
$484$	−3.94256	−	27.4143i	−0.179207	−	1.24610i
$485$	10.3674			0.470761
$486$		0			0
$487$			7.61251i			0.344956i	0.985013	+	0.172478i	$0.0551773\pi$
$487$			7.61251i			0.344956i	−0.985013	+	0.172478i	$0.944823\pi$
$488$	3.36012	+	2.15917i	0.152106	+	0.0977411i
$489$		0			0
$490$	−3.05549	−	2.64750i	−0.138033	−	0.119602i
$491$			10.4249i			0.470471i	0.971938	+	0.235236i	$0.0755862\pi$
$491$			10.4249i			0.470471i	−0.971938	+	0.235236i	$0.924414\pi$
$492$		0			0
$493$			52.5792i			2.36805i
$494$	−12.8697	+	14.8530i	−0.579037	+	0.668268i
$495$		0			0
$496$	−3.73867	−	12.7294i	−0.167871	−	0.571568i
$497$		−	0.398786i		−	0.0178880i
$498$		0			0
$499$	−24.3685			−1.09088			−0.545441	−	0.838149i	$-0.683638\pi$
$499$	−24.3685			−1.09088			−0.545441	+	0.838149i	$0.683638\pi$
$500$	1.48727	+	10.3416i	0.0665126	+	0.462490i
$501$		0			0
$502$	7.41910	−	8.56240i	0.331130	−	0.382158i
$503$	−38.3668			−1.71069			−0.855345	−	0.518058i	$-0.826655\pi$
$503$	−38.3668			−1.71069			−0.855345	+	0.518058i	$0.826655\pi$
$504$		0			0
$505$	−29.9398			−1.33231
$506$	−20.4897	+	23.6473i	−0.910880	+	1.05125i
$507$		0			0
$508$	−3.57021	+	0.513446i	−0.158402	+	0.0227805i
$509$	11.6708			0.517298			0.258649	−	0.965971i	$-0.416723\pi$
$509$	11.6708			0.517298			0.258649	+	0.965971i	$0.416723\pi$
$510$		0			0
$511$			10.7893i			0.477291i
$512$	−22.3976	−	3.21669i	−0.989844	−	0.142159i
$513$		0			0
$514$	−13.0588	+	15.0711i	−0.575997	+	0.664760i
$515$		−	12.8900i		−	0.568003i
$516$		0			0
$517$		−	12.9656i		−	0.570225i
$518$	−5.88998	−	5.10352i	−0.258791	−	0.224236i
$519$		0			0
$520$	16.0065	+	10.2856i	0.701933	+	0.451053i
$521$			8.09319i			0.354569i	0.984160	+	0.177284i	$0.0567313\pi$
$521$			8.09319i			0.354569i	−0.984160	+	0.177284i	$0.943269\pi$
$522$		0			0
$523$	−12.5864			−0.550363			−0.275181	−	0.961392i	$-0.588738\pi$
$523$	−12.5864			−0.550363			−0.275181	+	0.961392i	$0.588738\pi$
$524$	−19.6684	+	2.82859i	−0.859216	+	0.123567i
$525$		0			0
$526$	26.3299	+	22.8142i	1.14804	+	0.994745i
$527$	27.1878			1.18432
$528$		0			0
$529$	−3.29989			−0.143473
$530$	40.6942	+	35.2605i	1.76764	+	1.53162i
$531$		0			0
$532$	11.6915	−	1.68140i	0.506891	−	0.0728980i
$533$	8.03678			0.348112
$534$		0			0
$535$		−	19.5152i		−	0.843716i
$536$	0.338303	−	0.526471i	0.0146125	−	0.0227401i
$537$		0			0
$538$	10.3086	+	8.93216i	0.444436	+	0.385093i
$539$		−	4.98479i		−	0.214710i
$540$		0			0
$541$			33.6824i			1.44812i	0.689738	+	0.724059i	$0.257726\pi$
$541$			33.6824i			1.44812i	−0.689738	+	0.724059i	$0.742274\pi$
$542$	−12.3602	+	14.2650i	−0.530918	+	0.612734i
$543$		0			0
$544$	19.2589	−	42.1809i	0.825719	−	1.80849i
$545$		−	37.5282i		−	1.60753i
$546$		0			0
$547$	−31.7087			−1.35576			−0.677882	−	0.735170i	$-0.737102\pi$
$547$	−31.7087			−1.35576			−0.677882	+	0.735170i	$0.737102\pi$
$548$	−2.30149	+	0.330986i	−0.0983146	+	0.0141390i
$549$		0			0
$550$	14.6462	−	16.9032i	0.624516	−	0.720755i
$551$	−37.8828			−1.61386
$552$		0			0
$553$	9.76133			0.415094
$554$	17.1528	−	19.7961i	0.728753	−	0.841055i
$555$		0			0
$556$	4.86825	+	33.8510i	0.206460	+	1.43560i
$557$	−29.0418			−1.23054			−0.615270	−	0.788316i	$-0.710953\pi$
$557$	−29.0418			−1.23054			−0.615270	+	0.788316i	$0.710953\pi$
$558$		0			0
$559$		−	3.23867i		−	0.136981i
$560$	−3.22242	−	10.9717i	−0.136172	−	0.463639i
$561$		0			0
$562$	17.3601	−	20.0353i	0.732291	−	0.845139i
$563$			34.5955i			1.45803i	0.684499	+	0.729013i	$0.260021\pi$
$563$			34.5955i			1.45803i	−0.684499	+	0.729013i	$0.739979\pi$
$564$		0			0
$565$		−	15.1733i		−	0.638344i
$566$	2.48031	+	2.14912i	0.104255	+	0.0903343i
$567$		0			0
$568$	0.609758	−	0.948912i	0.0255849	−	0.0398155i
$569$		−	44.7913i		−	1.87775i	−0.344258	−	0.938875i	$-0.611869\pi$
$569$		−	44.7913i		−	1.87775i	0.344258	−	0.938875i	$-0.388131\pi$
$570$		0			0
$571$	−13.8182			−0.578276			−0.289138	−	0.957287i	$-0.593369\pi$
$571$	−13.8182			−0.578276			−0.289138	+	0.957287i	$0.593369\pi$
$572$	3.33935	+	23.2199i	0.139625	+	0.970874i
$573$		0			0
$574$	−3.65050	−	3.16307i	−0.152369	−	0.132024i
$575$	−14.0818			−0.587250
$576$		0			0
$577$	−2.53927			−0.105711			−0.0528557	−	0.998602i	$-0.516832\pi$
$577$	−2.53927			−0.105711			−0.0528557	+	0.998602i	$0.516832\pi$
$578$	53.6453	+	46.4823i	2.23135	+	1.93341i
$579$		0			0
$580$	5.22064	+	36.3013i	0.216775	+	1.50733i
$581$	−2.06831			−0.0858081
$582$		0			0
$583$			66.3894i			2.74957i
$584$	−16.4973	+	25.6732i	−0.682662	+	1.06237i
$585$		0			0
$586$	3.85973	+	3.34436i	0.159444	+	0.138154i
$587$			1.23636i			0.0510300i	0.999674	+	0.0255150i	$0.00812256\pi$
$587$			1.23636i			0.0510300i	−0.999674	+	0.0255150i	$0.991877\pi$
$588$		0			0
$589$			19.5885i			0.807131i
$590$	−28.1918	+	32.5363i	−1.16064	+	1.33950i
$591$		0			0
$592$	−6.21177	−	21.1499i	−0.255302	−	0.869254i
$593$			2.47202i			0.101514i	0.998711	+	0.0507568i	$0.0161633\pi$
$593$			2.47202i			0.101514i	−0.998711	+	0.0507568i	$0.983837\pi$
$594$		0			0
$595$	23.4336			0.960685
$596$	−6.59616	−	45.8659i	−0.270189	−	1.87874i
$597$		0			0
$598$	9.67205	−	11.1625i	0.395520	−	0.456470i
$599$	−6.80798			−0.278166			−0.139083	−	0.990281i	$-0.544416\pi$
$599$	−6.80798			−0.278166			−0.139083	+	0.990281i	$0.544416\pi$
$600$		0			0
$601$	−0.857050			−0.0349598			−0.0174799	−	0.999847i	$-0.505564\pi$
$601$	−0.857050			−0.0349598			−0.0174799	+	0.999847i	$0.505564\pi$
$602$	−1.27465	+	1.47108i	−0.0519510	+	0.0599568i
$603$		0			0
$604$	3.32172	−	0.477710i	0.135159	−	0.0194377i
$605$	39.5889			1.60952
$606$		0			0
$607$			22.9929i			0.933252i	0.884455	+	0.466626i	$0.154531\pi$
$607$			22.9929i			0.933252i	−0.884455	+	0.466626i	$0.845469\pi$
$608$	30.3909	+	13.8758i	1.23251	+	0.562740i
$609$		0			0
$610$	−3.73857	+	4.31469i	−0.151370	+	0.174697i
$611$			6.12031i			0.247601i
$612$		0			0
$613$		−	10.9605i		−	0.442691i	−0.975195	−	0.221346i	$-0.928955\pi$
$613$		−	10.9605i		−	0.442691i	0.975195	−	0.221346i	$-0.0710449\pi$
$614$	21.2985	+	18.4546i	0.859536	+	0.744766i
$615$		0			0
$616$	7.62194	−	11.8613i	0.307097	−	0.477907i
$617$		−	15.9140i		−	0.640675i	−0.947304	−	0.320337i	$-0.896204\pi$
$617$		−	15.9140i		−	0.640675i	0.947304	−	0.320337i	$-0.103796\pi$
$618$		0			0
$619$	24.1115			0.969124			0.484562	−	0.874757i	$-0.338979\pi$
$619$	24.1115			0.969124			0.484562	+	0.874757i	$0.338979\pi$
$620$	18.7708	−	2.69950i	0.753853	−	0.108415i
$621$		0			0
$622$	−5.00974	−	4.34081i	−0.200872	−	0.174051i
$623$	17.6684			0.707869
$624$		0			0
$625$	−30.7975			−1.23190
$626$	14.1274	+	12.2410i	0.564643	+	0.489249i
$627$		0			0
$628$	4.40388	−	0.633340i	0.175734	−	0.0252730i
$629$	45.1723			1.80114
$630$		0			0
$631$			19.0647i			0.758955i	0.925201	+	0.379477i	$0.123896\pi$
$631$			19.0647i			0.758955i	−0.925201	+	0.379477i	$0.876104\pi$
$632$	23.2271	+	14.9255i	0.923926	+	0.593703i
$633$		0			0
$634$	14.7669	+	12.7951i	0.586467	+	0.508158i
$635$		−	5.15573i		−	0.204599i
$636$		0			0
$637$			2.35304i			0.0932308i
$638$	−29.6114	+	34.1745i	−1.17232	+	1.35298i
$639$		0			0
$640$	9.10840	−	31.0344i	0.360041	−	1.22674i
$641$			16.6996i			0.659595i	0.944052	+	0.329797i	$0.106980\pi$
$641$			16.6996i			0.659595i	−0.944052	+	0.329797i	$0.893020\pi$
$642$		0			0
$643$	15.2897			0.602966			0.301483	−	0.953472i	$-0.402518\pi$
$643$	15.2897			0.602966			0.301483	+	0.953472i	$0.402518\pi$
$644$	−8.78656	+	1.26363i	−0.346239	+	0.0497940i
$645$		0			0
$646$	−44.8331	+	51.7420i	−1.76394	+	2.03576i
$647$	42.6300			1.67596			0.837979	−	0.545702i	$-0.183737\pi$
$647$	42.6300			1.67596			0.837979	+	0.545702i	$0.183737\pi$
$648$		0			0
$649$	−53.0804			−2.08359
$650$	−6.91364	+	7.97904i	−0.271175	+	0.312964i
$651$		0			0
$652$	−4.93550	−	34.3186i	−0.193289	−	1.34402i
$653$	5.14973			0.201524			0.100762	−	0.994911i	$-0.467872\pi$
$653$	5.14973			0.201524			0.100762	+	0.994911i	$0.467872\pi$
$654$		0			0
$655$		−	28.4030i		−	1.10980i
$656$	−3.84994	−	13.1083i	−0.150315	−	0.511793i
$657$		0			0
$658$	2.40879	−	2.77999i	0.0939045	−	0.108375i
$659$		−	0.965465i		−	0.0376092i	−0.999823	−	0.0188046i	$-0.994014\pi$
$659$		−	0.965465i		−	0.0376092i	0.999823	−	0.0188046i	$-0.00598604\pi$
$660$		0			0
$661$		−	8.54386i		−	0.332318i	−0.986099	−	0.166159i	$-0.946864\pi$
$661$		−	8.54386i		−	0.332318i	0.986099	−	0.166159i	$-0.0531365\pi$
$662$	−10.3720	−	8.98709i	−0.403120	−	0.349293i
$663$		0			0
$664$	−4.92156	−	3.16253i	−0.190994	−	0.122730i
$665$			16.8837i			0.654721i
$666$		0			0
$667$	28.4702			1.10237
$668$	6.10477	+	42.4490i	0.236201	+	1.64240i
$669$		0			0
$670$	0.676035	+	0.585767i	0.0261175	+	0.0226301i
$671$	−7.03908			−0.271741
$672$		0			0
$673$	35.8364			1.38139			0.690695	−	0.723146i	$-0.257305\pi$
$673$	35.8364			1.38139			0.690695	+	0.723146i	$0.257305\pi$
$674$	−5.39197	−	4.67200i	−0.207691	−	0.179959i
$675$		0			0
$676$	2.12477	+	14.7744i	0.0817219	+	0.568247i
$677$	15.3770			0.590985			0.295493	−	0.955345i	$-0.404516\pi$
$677$	15.3770			0.590985			0.295493	+	0.955345i	$0.404516\pi$
$678$		0			0
$679$			3.62651i			0.139173i
$680$	55.7604	+	35.8309i	2.13831	+	1.37405i
$681$		0			0
$682$	17.6711	+	15.3115i	0.676660	+	0.586309i
$683$		−	31.3038i		−	1.19781i	−0.800822	−	0.598903i	$-0.795604\pi$
$683$		−	31.3038i		−	1.19781i	0.800822	−	0.598903i	$-0.204396\pi$
$684$		0			0
$685$		−	3.32357i		−	0.126987i
$686$	0.926094	−	1.06881i	0.0353584	−	0.0408073i
$687$		0			0
$688$	−5.28238	+	1.55145i	−0.201389	+	0.0591485i
$689$		−	31.3387i		−	1.19391i
$690$		0			0
$691$	38.1921			1.45289			0.726447	−	0.687222i	$-0.241170\pi$
$691$	38.1921			1.45289			0.726447	+	0.687222i	$0.241170\pi$
$692$	−2.76313	−	19.2132i	−0.105039	−	0.730377i
$693$		0			0
$694$	−1.86810	+	2.15598i	−0.0709121	+	0.0818398i
$695$	−48.8842			−1.85428
$696$		0			0
$697$	27.9970			1.06046
$698$	−0.489493	+	0.564925i	−0.0185276	+	0.0213827i
$699$		0			0
$700$	6.28069	−	0.903251i	0.237388	−	0.0341397i
$701$	45.5040			1.71866			0.859331	−	0.511419i	$-0.170880\pi$
$701$	45.5040			1.71866			0.859331	+	0.511419i	$0.170880\pi$
$702$		0			0
$703$			32.5462i			1.22750i
$704$	36.2729	−	16.5699i	1.36709	−	0.624501i
$705$		0			0
$706$	−9.58029	+	11.0566i	−0.360559	+	0.416122i
$707$		−	10.4729i		−	0.393875i
$708$		0			0
$709$		−	17.7256i		−	0.665698i	−0.942980	−	0.332849i	$-0.891990\pi$
$709$		−	17.7256i		−	0.665698i	0.942980	−	0.332849i	$-0.108010\pi$
$710$	1.21849	+	1.05579i	0.0457290	+	0.0396230i
$711$		0			0
$712$	42.0420	+	27.0156i	1.57559	+	1.01245i
$713$		−	14.7214i		−	0.551322i
$714$		0			0
$715$	−33.5319			−1.25402
$716$	29.1698	−	4.19503i	1.09013	−	0.156776i
$717$		0			0
$718$	−1.73474	−	1.50311i	−0.0647398	−	0.0560954i
$719$	−31.0561			−1.15820			−0.579098	−	0.815258i	$-0.696595\pi$
$719$	−31.0561			−1.15820			−0.579098	+	0.815258i	$0.696595\pi$
$720$		0			0
$721$	4.50892			0.167921
$722$	−16.9722	−	14.7060i	−0.631641	−	0.547301i
$723$		0			0
$724$	−35.0504	+	5.04074i	−1.30264	+	0.187337i
$725$	−20.3507			−0.755804
$726$		0			0
$727$		−	7.88096i		−	0.292289i	−0.989263	−	0.146144i	$-0.953314\pi$
$727$		−	7.88096i		−	0.292289i	0.989263	−	0.146144i	$-0.0466864\pi$
$728$	−3.59789	+	5.59907i	−0.133347	+	0.207515i
$729$		0			0
$730$	−32.9666	−	28.5647i	−1.22015	−	1.05723i
$731$		−	11.2822i		−	0.417288i
$732$		0			0
$733$			31.2981i			1.15602i	0.816029	+	0.578011i	$0.196171\pi$
$733$			31.2981i			1.15602i	−0.816029	+	0.578011i	$0.803829\pi$
$734$	−31.0829	+	35.8729i	−1.14729	+	1.32409i
$735$		0			0
$736$	−22.8398	−	10.4282i	−0.841886	−	0.384388i
$737$			1.10290i			0.0406257i
$738$		0			0
$739$	9.91989			0.364909			0.182455	−	0.983214i	$-0.441596\pi$
$739$	9.91989			0.364909			0.182455	+	0.983214i	$0.441596\pi$
$740$	31.1875	−	4.48520i	1.14648	−	0.164879i
$741$		0			0
$742$	−12.3341	+	14.2348i	−0.452798	+	0.522576i
$743$	21.2085			0.778065			0.389032	−	0.921224i	$-0.372809\pi$
$743$	21.2085			0.778065			0.389032	+	0.921224i	$0.372809\pi$
$744$		0			0
$745$	66.2348			2.42666
$746$	18.9107	−	21.8249i	0.692370	−	0.799066i
$747$		0			0
$748$	11.6330	+	80.8891i	0.425344	+	2.95760i
$749$	6.82640			0.249431
$750$		0			0
$751$		−	31.2986i		−	1.14210i	−0.820915	−	0.571051i	$-0.806536\pi$
$751$		−	31.2986i		−	1.14210i	0.820915	−	0.571051i	$-0.193464\pi$
$752$	9.98245	−	2.93187i	0.364023	−	0.106914i
$753$		0			0
$754$	13.9778	−	16.1319i	0.509043	−	0.587488i
$755$			4.79689i			0.174577i
$756$		0			0
$757$			50.1185i			1.82159i	0.412863	+	0.910793i	$0.364529\pi$
$757$			50.1185i			1.82159i	−0.412863	+	0.910793i	$0.635471\pi$
$758$	−31.6932	−	27.4613i	−1.15115	−	0.997441i
$759$		0			0
$760$	−25.8158	+	40.1748i	−0.936437	+	1.45729i
$761$		−	33.4522i		−	1.21264i	−0.795220	−	0.606321i	$-0.792645\pi$
$761$		−	33.4522i		−	1.21264i	0.795220	−	0.606321i	$-0.207355\pi$
$762$		0			0
$763$	13.1273			0.475241
$764$	5.12290	+	35.6217i	0.185340	+	1.28875i
$765$		0			0
$766$	−5.15536	−	4.46699i	−0.186271	−	0.161399i
$767$	25.0562			0.904728
$768$		0			0
$769$	−34.8586			−1.25703			−0.628516	−	0.777797i	$-0.716337\pi$
$769$	−34.8586			−1.25703			−0.628516	+	0.777797i	$0.716337\pi$
$770$	15.2310	+	13.1973i	0.548887	+	0.475596i
$771$		0			0
$772$	−7.07745	−	49.2125i	−0.254723	−	1.77120i
$773$	−0.819156			−0.0294630			−0.0147315	−	0.999891i	$-0.504689\pi$
$773$	−0.819156			−0.0294630			−0.0147315	+	0.999891i	$0.504689\pi$
$774$		0			0
$775$			10.5230i			0.377996i
$776$	−5.54508	+	8.62931i	−0.199057	+	0.309774i
$777$		0			0
$778$	19.7988	+	17.1552i	0.709822	+	0.615042i
$779$			20.1715i			0.722720i
$780$		0			0
$781$			1.98786i			0.0711314i
$782$	33.6936	−	38.8859i	1.20488	−	1.39056i
$783$		0			0
$784$	3.83789	−	1.12720i	0.137068	−	0.0402571i
$785$			6.35964i			0.226985i
$786$		0			0
$787$	21.1948			0.755514			0.377757	−	0.925905i	$-0.376695\pi$
$787$	21.1948			0.755514			0.377757	+	0.925905i	$0.376695\pi$
$788$	4.95790	+	34.4744i	0.176618	+	1.22810i
$789$		0			0
$790$	−25.8432	+	29.8257i	−0.919459	+	1.06115i
$791$	5.30759			0.188716
$792$		0			0
$793$	3.32275			0.117994
$794$	2.70035	−	3.11648i	0.0958319	−	0.110600i
$795$		0			0
$796$	39.6056	−	5.69584i	1.40378	−	0.201884i
$797$	−10.4236			−0.369221			−0.184611	−	0.982812i	$-0.559102\pi$
$797$	−10.4236			−0.369221			−0.184611	+	0.982812i	$0.559102\pi$
$798$		0			0
$799$			21.3207i			0.754274i
$800$	16.3260	+	7.45412i	0.577212	+	0.263543i
$801$		0			0
$802$	2.43429	−	2.80942i	0.0859578	−	0.0992041i
$803$		−	53.7825i		−	1.89794i
$804$		0			0
$805$		−	12.6887i		−	0.447217i
$806$	−8.34151	−	7.22770i	−0.293817	−	0.254585i
$807$		0			0
$808$	16.0135	−	24.9204i	0.563353	−	0.876696i
$809$			6.79289i			0.238825i	0.992845	+	0.119413i	$0.0381012\pi$
$809$			6.79289i			0.238825i	−0.992845	+	0.119413i	$0.961899\pi$
$810$		0			0
$811$	15.6600			0.549897			0.274949	−	0.961459i	$-0.411339\pi$
$811$	15.6600			0.549897			0.274949	+	0.961459i	$0.411339\pi$
$812$	−12.6982	+	1.82617i	−0.445618	+	0.0640861i
$813$		0			0
$814$	29.3603	+	25.4400i	1.02908	+	0.891671i
$815$	49.5594			1.73599
$816$		0			0
$817$	8.12873			0.284388
$818$	−27.8484	−	24.1299i	−0.973695	−	0.843682i
$819$		0			0
$820$	19.3294	−	2.77984i	0.675013	−	0.0970764i
$821$	−9.83489			−0.343240			−0.171620	−	0.985163i	$-0.554900\pi$
$821$	−9.83489			−0.343240			−0.171620	+	0.985163i	$0.554900\pi$
$822$		0			0
$823$			16.9492i			0.590811i	0.955372	+	0.295406i	$0.0954548\pi$
$823$			16.9492i			0.590811i	−0.955372	+	0.295406i	$0.904545\pi$
$824$	10.7290	+	6.89431i	0.373762	+	0.240175i
$825$		0			0
$826$	−11.3812	−	9.86148i	−0.396001	−	0.343125i
$827$			54.3499i			1.88993i	0.327169	+	0.944966i	$0.393905\pi$
$827$			54.3499i			1.88993i	−0.327169	+	0.944966i	$0.606095\pi$
$828$		0			0
$829$		−	0.679562i		−	0.0236022i	−0.999930	−	0.0118011i	$-0.996244\pi$
$829$		−	0.679562i		−	0.0236022i	0.999930	−	0.0118011i	$-0.00375649\pi$
$830$	5.47587	−	6.31971i	0.190070	−	0.219360i
$831$		0			0
$832$	−17.1224	+	7.82170i	−0.593611	+	0.271169i
$833$			8.19706i			0.284011i
$834$		0			0
$835$	−61.3006			−2.12139
$836$	−58.2797	+	8.38144i	−2.01565	+	0.289878i
$837$		0			0
$838$	−8.73478	+	10.0808i	−0.301738	+	0.348236i
$839$	46.0696			1.59050			0.795249	−	0.606283i	$-0.207340\pi$
$839$	46.0696			1.59050			0.795249	+	0.606283i	$0.207340\pi$
$840$		0			0
$841$	12.1445			0.418777
$842$	20.7229	−	23.9164i	0.714160	−	0.824213i
$843$		0			0
$844$	−4.28590	−	29.8017i	−0.147527	−	1.02582i
$845$	−21.3357			−0.733971
$846$		0			0
$847$			13.8482i			0.475828i
$848$	−51.1145	+	15.0125i	−1.75528	+	0.515530i
$849$		0			0
$850$	−24.0844	+	27.7958i	−0.826088	+	0.953390i
$851$		−	24.4596i		−	0.838463i
$852$		0			0
$853$		−	35.6910i		−	1.22204i	−0.791617	−	0.611018i	$-0.790760\pi$
$853$		−	35.6910i		−	1.22204i	0.791617	−	0.611018i	$-0.209240\pi$
$854$	−1.50927	−	1.30775i	−0.0516463	−	0.0447502i
$855$		0			0
$856$	16.2434	+	10.4378i	0.555189	+	0.356757i
$857$			27.4542i			0.937818i	0.883247	+	0.468909i	$0.155353\pi$
$857$			27.4542i			0.937818i	−0.883247	+	0.468909i	$0.844647\pi$
$858$		0			0
$859$	−20.8392			−0.711025			−0.355512	−	0.934672i	$-0.615694\pi$
$859$	−20.8392			−0.711025			−0.355512	+	0.934672i	$0.615694\pi$
$860$	−1.12022	−	7.78938i	−0.0381993	−	0.265616i
$861$		0			0
$862$	15.1343	+	13.1135i	0.515475	+	0.446646i
$863$	−25.8505			−0.879960			−0.439980	−	0.898008i	$-0.645014\pi$
$863$	−25.8505			−0.879960			−0.439980	+	0.898008i	$0.645014\pi$
$864$		0			0
$865$	27.7458			0.943385
$866$	−10.1282	−	8.77583i	−0.344170	−	0.298215i
$867$		0			0
$868$	0.944283	+	6.56600i	0.0320510	+	0.222864i
$869$	−48.6582			−1.65062
$870$		0			0
$871$		−	0.520615i		−	0.0176404i
$872$	31.2366	+	20.0722i	1.05780	+	0.679730i
$873$		0			0
$874$	28.0169	+	24.2759i	0.947685	+	0.821144i
$875$		−	5.22400i		−	0.176603i
$876$		0			0
$877$			12.7819i			0.431613i	0.976436	+	0.215806i	$0.0692380\pi$
$877$			12.7819i			0.431613i	−0.976436	+	0.215806i	$0.930762\pi$
$878$	−5.00548	+	5.77684i	−0.168927	+	0.194959i
$879$		0			0
$880$	16.0631	+	54.6917i	0.541487	+	1.84366i
$881$			9.54473i			0.321570i	0.986989	+	0.160785i	$0.0514026\pi$
$881$			9.54473i			0.321570i	−0.986989	+	0.160785i	$0.948597\pi$
$882$		0			0
$883$	−18.8835			−0.635479			−0.317740	−	0.948178i	$-0.602924\pi$
$883$	−18.8835			−0.635479			−0.317740	+	0.948178i	$0.602924\pi$
$884$	−5.49127	−	38.1831i	−0.184692	−	1.28424i
$885$		0			0
$886$	−26.1545	+	30.1850i	−0.878678	+	1.01408i
$887$	19.9738			0.670654			0.335327	−	0.942102i	$-0.391153\pi$
$887$	19.9738			0.670654			0.335327	+	0.942102i	$0.391153\pi$
$888$		0			0
$889$	1.80347			0.0604864
$890$	−46.7771	+	53.9856i	−1.56797	+	1.80960i
$891$		0			0
$892$	−25.2630	+	3.63317i	−0.845868	+	0.121648i
$893$	−15.3614			−0.514049
$894$		0			0
$895$			42.1241i			1.40805i
$896$	10.8558	+	3.18611i	0.362667	+	0.106440i
$897$		0			0
$898$	−28.7909	+	33.2276i	−0.960764	+	1.10882i
$899$		−	21.2751i		−	0.709565i
$900$		0			0
$901$		−	109.172i		−	3.63703i
$902$	18.1970	+	15.7672i	0.605894	+	0.524991i
$903$		0			0
$904$	12.6294	+	8.11551i	0.420049	+	0.269918i
$905$		−	50.6162i		−	1.68254i
$906$		0			0
$907$	7.50951			0.249349			0.124675	−	0.992198i	$-0.460211\pi$
$907$	7.50951			0.249349			0.124675	+	0.992198i	$0.460211\pi$
$908$	−50.9096	+	7.32151i	−1.68949	+	0.242973i
$909$		0			0
$910$	−7.18969	−	6.22968i	−0.238336	−	0.206512i
$911$	33.1774			1.09922			0.549609	−	0.835422i	$-0.314777\pi$
$911$	33.1774			1.09922			0.549609	+	0.835422i	$0.314777\pi$
$912$		0			0
$913$	10.3101			0.341215
$914$	−16.4825	−	14.2817i	−0.545193	−	0.472396i
$915$		0			0
$916$	21.1886	−	3.04722i	0.700091	−	0.100683i
$917$	9.93535			0.328094
$918$		0			0
$919$			13.2043i			0.435568i	0.975997	+	0.217784i	$0.0698829\pi$
$919$			13.2043i			0.435568i	−0.975997	+	0.217784i	$0.930117\pi$
$920$	19.4014	−	30.1927i	0.639647	−	0.995425i
$921$		0			0
$922$	−23.2678	−	20.1609i	−0.766284	−	0.663966i
$923$		−	0.938358i		−	0.0308864i
$924$		0			0
$925$			17.4838i			0.574865i
$926$	−30.7037	+	35.4352i	−1.00899	+	1.16447i
$927$		0			0
$928$	−33.0076	−	15.0706i	−1.08353	−	0.494716i
$929$		−	0.175426i		−	0.00575553i	−0.999996	−	0.00287776i	$-0.999084\pi$
$929$		−	0.175426i		−	0.00575553i	0.999996	−	0.00287776i	$-0.000916022\pi$
$930$		0			0
$931$	−5.90589			−0.193558
$932$	−11.0051	+	1.58269i	−0.360485	+	0.0518428i
$933$		0			0
$934$	21.5996	−	24.9281i	0.706760	−	0.815674i
$935$	−116.812			−3.82015
$936$		0			0
$937$	−10.2203			−0.333884			−0.166942	−	0.985967i	$-0.553389\pi$
$937$	−10.2203			−0.333884			−0.166942	+	0.985967i	$0.553389\pi$
$938$	−0.204901	+	0.236476i	−0.00669024	+	0.00772122i
$939$		0			0
$940$	2.11696	+	14.7201i	0.0690475	+	0.480116i
$941$	−18.9676			−0.618327			−0.309163	−	0.951009i	$-0.600049\pi$
$941$	−18.9676			−0.618327			−0.309163	+	0.951009i	$0.600049\pi$
$942$		0			0
$943$		−	15.1596i		−	0.493664i
$944$	−12.0029	−	40.8677i	−0.390662	−	1.33013i
$945$		0			0
$946$	6.35388	−	7.33303i	0.206583	−	0.238417i
$947$			6.01612i			0.195497i	0.995211	+	0.0977487i	$0.0311642\pi$
$947$			6.01612i			0.195497i	−0.995211	+	0.0977487i	$0.968836\pi$
$948$		0			0
$949$			25.3877i			0.824119i
$950$	−20.0266	−	17.3525i	−0.649749	−	0.562991i
$951$		0			0
$952$	−12.5336	+	19.5049i	−0.406217	+	0.632159i
$953$			18.9690i			0.614468i	0.951634	+	0.307234i	$0.0994034\pi$
$953$			18.9690i			0.614468i	−0.951634	+	0.307234i	$0.900597\pi$
$954$		0			0
$955$	−51.4412			−1.66460
$956$	5.89861	+	41.0155i	0.190775	+	1.32654i
$957$		0			0
$958$	−31.8330	−	27.5825i	−1.02848	−	0.891151i
$959$	1.16258			0.0375417
$960$		0			0
$961$	19.9990			0.645129
$962$	−13.8594	−	12.0088i	−0.446844	−	0.387178i
$963$		0			0
$964$	1.71699	+	11.9390i	0.0553006	+	0.384529i
$965$	71.0677			2.28775
$966$		0			0
$967$		−	28.6527i		−	0.921408i	−0.887554	−	0.460704i	$-0.847597\pi$
$967$		−	28.6527i		−	0.921408i	0.887554	−	0.460704i	$-0.152403\pi$
$968$	−21.1744	+	32.9518i	−0.680570	+	1.05911i
$969$		0			0
$970$	−11.0808	−	9.60121i	−0.355782	−	0.308276i
$971$		−	47.4986i		−	1.52430i	−0.647399	−	0.762151i	$-0.724143\pi$
$971$		−	47.4986i		−	1.52430i	0.647399	−	0.762151i	$-0.275857\pi$
$972$		0			0
$973$		−	17.0996i		−	0.548189i
$974$	7.04990	−	8.13631i	0.225893	−	0.260704i
$975$		0			0
$976$	−1.59173	−	5.41953i	−0.0509500	−	0.173475i
$977$		−	40.0015i		−	1.27976i	−0.768474	−	0.639881i	$-0.778984\pi$
$977$		−	40.0015i		−	1.27976i	0.768474	−	0.639881i	$-0.221016\pi$
$978$		0			0
$979$	−88.0732			−2.81483
$980$	0.813893	+	5.65934i	0.0259989	+	0.180781i
$981$		0			0
$982$	9.65448	−	11.1423i	0.308087	−	0.355564i
$983$	−22.0829			−0.704334			−0.352167	−	0.935937i	$-0.614555\pi$
$983$	−22.0829			−0.704334			−0.352167	+	0.935937i	$0.614555\pi$
$984$		0			0
$985$	−49.7844			−1.58626
$986$	48.6933	−	56.1971i	1.55071	−	1.78968i
$987$		0			0
$988$	27.5106	−	3.95640i	0.875227	−	0.125870i
$989$	−6.10902			−0.194255
$990$		0			0
$991$			17.2351i			0.547490i	0.961802	+	0.273745i	$0.0882625\pi$
$991$			17.2351i			0.547490i	−0.961802	+	0.273745i	$0.911738\pi$
$992$	−7.79274	+	17.0677i	−0.247420	+	0.541899i
$993$		0			0
$994$	−0.369313	+	0.426225i	−0.0117139	+	0.0135190i
$995$			57.1944i			1.81318i
$996$		0			0
$997$		−	21.9872i		−	0.696342i	−0.937431	−	0.348171i	$-0.886803\pi$
$997$		−	21.9872i		−	0.696342i	0.937431	−	0.348171i	$-0.113197\pi$
$998$	26.0452	+	22.5675i	0.824447	+	0.714362i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.9	✓	48
3.2	odd	2	inner	1512.2.j.d.323.40	yes	48
4.3	odd	2		6048.2.j.d.5615.10		48
8.3	odd	2	inner	1512.2.j.d.323.39	yes	48
8.5	even	2		6048.2.j.d.5615.40		48
12.11	even	2		6048.2.j.d.5615.39		48
24.5	odd	2		6048.2.j.d.5615.9		48
24.11	even	2	inner	1512.2.j.d.323.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.9	✓	48	1.1	even	1	trivial
1512.2.j.d.323.10	yes	48	24.11	even	2	inner
1512.2.j.d.323.39	yes	48	8.3	odd	2	inner
1512.2.j.d.323.40	yes	48	3.2	odd	2	inner
6048.2.j.d.5615.9		48	24.5	odd	2
6048.2.j.d.5615.10		48	4.3	odd	2
6048.2.j.d.5615.39		48	12.11	even	2
6048.2.j.d.5615.40		48	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06881 - 0.926094i) q^{2} +(0.284699 + 1.97963i) q^{4} -2.85878 q^{5} -1.00000i q^{7} +(1.52904 - 2.37950i) q^{8} +O(q^{10})\)	\(q+(-1.06881 - 0.926094i) q^{2} +(0.284699 + 1.97963i) q^{4} -2.85878 q^{5} -1.00000i q^{7} +(1.52904 - 2.37950i) q^{8} +(3.05549 + 2.64750i) q^{10} +4.98479i q^{11} -2.35304i q^{13} +(-0.926094 + 1.06881i) q^{14} +(-3.83789 + 1.12720i) q^{16} -8.19706i q^{17} +5.90589 q^{19} +(-0.813893 - 5.65934i) q^{20} +(4.61639 - 5.32778i) q^{22} -4.43848 q^{23} +3.17265 q^{25} +(-2.17914 + 2.51495i) q^{26} +(1.97963 - 0.284699i) q^{28} -6.41440 q^{29} +3.31678i q^{31} +(5.14586 + 2.34949i) q^{32} +(-7.59125 + 8.76108i) q^{34} +2.85878i q^{35} +5.51080i q^{37} +(-6.31226 - 5.46942i) q^{38} +(-4.37119 + 6.80249i) q^{40} +3.41549i q^{41} +1.37638 q^{43} +(-9.86806 + 1.41917i) q^{44} +(4.74388 + 4.11045i) q^{46} -2.60102 q^{47} -1.00000 q^{49} +(-3.39095 - 2.93817i) q^{50} +(4.65815 - 0.669908i) q^{52} +13.3184 q^{53} -14.2505i q^{55} +(-2.37950 - 1.52904i) q^{56} +(6.85576 + 5.94034i) q^{58} +10.6485i q^{59} +1.41211i q^{61} +(3.07165 - 3.54499i) q^{62} +(-3.32408 - 7.27671i) q^{64} +6.72683i q^{65} +0.221252 q^{67} +(16.2272 - 2.33369i) q^{68} +(2.64750 - 3.05549i) q^{70} +0.398786 q^{71} -10.7893 q^{73} +(5.10352 - 5.88998i) q^{74} +(1.68140 + 11.6915i) q^{76} +4.98479 q^{77} +9.76133i q^{79} +(10.9717 - 3.22242i) q^{80} +(3.16307 - 3.65050i) q^{82} -2.06831i q^{83} +23.4336i q^{85} +(-1.47108 - 1.27465i) q^{86} +(11.8613 + 7.62194i) q^{88} +17.6684i q^{89} -2.35304 q^{91} +(-1.26363 - 8.78656i) q^{92} +(2.77999 + 2.40879i) q^{94} -16.8837 q^{95} -3.62651 q^{97} +(1.06881 + 0.926094i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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