LMFDB - Embedded newform 360.2.bm.b.11.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 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("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913976 - 1.07919i) q^{2} +(-1.45808 + 0.934888i) q^{3} +(-0.329296 - 1.97270i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.323726 + 2.42800i) q^{6} +(1.98473 + 1.14588i) q^{7} +(-2.42989 - 1.44763i) q^{8} +(1.25197 - 2.72627i) q^{9} +O(q^{10})$	\(q+(0.913976 - 1.07919i) q^{2} +(-1.45808 + 0.934888i) q^{3} +(-0.329296 - 1.97270i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.323726 + 2.42800i) q^{6} +(1.98473 + 1.14588i) q^{7} +(-2.42989 - 1.44763i) q^{8} +(1.25197 - 2.72627i) q^{9} +(1.39159 + 0.251932i) q^{10} +(4.17386 + 2.40978i) q^{11} +(2.32440 + 2.56850i) q^{12} +(1.25308 - 0.723468i) q^{13} +(3.05062 - 1.09459i) q^{14} +(-1.53867 - 0.795287i) q^{15} +(-3.78313 + 1.29921i) q^{16} -5.75799i q^{17} +(-1.79789 - 3.84286i) q^{18} +5.54092 q^{19} +(1.54376 - 1.27153i) q^{20} +(-3.96515 + 0.184714i) q^{21} +(6.41541 - 2.30190i) q^{22} +(-0.878693 - 1.52194i) q^{23} +(4.89634 - 0.160918i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.364530 - 2.01355i) q^{26} +(0.723295 + 5.14557i) q^{27} +(1.60693 - 4.29262i) q^{28} +(-3.85587 + 6.67857i) q^{29} +(-2.26458 + 0.933647i) q^{30} +(2.38149 - 1.37495i) q^{31} +(-2.05560 + 5.27015i) q^{32} +(-8.33868 + 0.388451i) q^{33} +(-6.21396 - 5.26266i) q^{34} +2.29177i q^{35} +(-5.79040 - 1.57201i) q^{36} -1.48435i q^{37} +(5.06427 - 5.97970i) q^{38} +(-1.15073 + 2.22636i) q^{39} +(0.0387410 - 2.82816i) q^{40} +(5.84684 - 3.37568i) q^{41} +(-3.42471 + 4.44797i) q^{42} +(0.513317 - 0.889090i) q^{43} +(3.37935 - 9.02732i) q^{44} +(2.98701 - 0.278900i) q^{45} +(-2.44557 - 0.442742i) q^{46} +(-5.87002 + 10.1672i) q^{47} +(4.30147 - 5.43115i) q^{48} +(-0.873905 - 1.51365i) q^{49} +(0.477617 + 1.33112i) q^{50} +(5.38307 + 8.39558i) q^{51} +(-1.83983 - 2.23373i) q^{52} -14.2585 q^{53} +(6.21411 + 3.92235i) q^{54} +4.81956i q^{55} +(-3.16385 - 5.65752i) q^{56} +(-8.07909 + 5.18014i) q^{57} +(3.68326 + 10.2653i) q^{58} +(-7.06983 + 4.08177i) q^{59} +(-1.06219 + 3.29724i) q^{60} +(2.27929 + 1.31595i) q^{61} +(0.692789 - 3.82675i) q^{62} +(5.60881 - 3.97630i) q^{63} +(3.80873 + 7.03517i) q^{64} +(1.25308 + 0.723468i) q^{65} +(-7.20214 + 9.35404i) q^{66} +(-0.258738 - 0.448148i) q^{67} +(-11.3588 + 1.89608i) q^{68} +(2.70404 + 1.39763i) q^{69} +(2.47325 + 2.09462i) q^{70} -8.60697 q^{71} +(-6.98879 + 4.81216i) q^{72} +1.59208 q^{73} +(-1.60189 - 1.35666i) q^{74} +(-0.0805988 - 1.73017i) q^{75} +(-1.82461 - 10.9306i) q^{76} +(5.52265 + 9.56551i) q^{77} +(1.35093 + 3.27670i) q^{78} +(7.04303 + 4.06630i) q^{79} +(-3.01671 - 2.62668i) q^{80} +(-5.86515 - 6.82642i) q^{81} +(1.70088 - 9.39513i) q^{82} +(-7.73374 - 4.46508i) q^{83} +(1.67010 + 7.76125i) q^{84} +(4.98656 - 2.87899i) q^{85} +(-0.490337 - 1.36657i) q^{86} +(-0.621558 - 13.3427i) q^{87} +(-6.65355 - 11.8977i) q^{88} -7.90275i q^{89} +(2.42907 - 3.47845i) q^{90} +3.31604 q^{91} +(-2.71299 + 2.23457i) q^{92} +(-2.18696 + 4.23121i) q^{93} +(5.60724 + 15.6274i) q^{94} +(2.77046 + 4.79858i) q^{95} +(-1.92979 - 9.60604i) q^{96} +(1.55398 - 2.69157i) q^{97} +(-2.43224 - 0.440329i) q^{98} +(11.7953 - 8.36212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.913976	−	1.07919i	0.646279	−	0.763102i
$2$	0.913976	−	1.07919i	0.646279	−	0.763102i
$3$	−1.45808	+	0.934888i	−0.841820	+	0.539758i
$3$	−1.45808	+	0.934888i	−0.841820	+	0.539758i
$4$	−0.329296	−	1.97270i	−0.164648	−	0.986352i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.323726	+	2.42800i	−0.132160	+	0.991228i
$7$	1.98473	+	1.14588i	0.750156	+	0.433103i	0.825750	−	0.564036i	$-0.190752\pi$
$7$	1.98473	+	1.14588i	0.750156	+	0.433103i	−0.0755940	+	0.997139i	$0.524085\pi$
$8$	−2.42989	−	1.44763i	−0.859096	−	0.511815i
$9$	1.25197	−	2.72627i	0.417323	−	0.908758i
$10$	1.39159	+	0.251932i	0.440060	+	0.0796679i
$11$	4.17386	+	2.40978i	1.25847	+	0.726576i	0.972776	−	0.231746i	$-0.0744440\pi$
$11$	4.17386	+	2.40978i	1.25847	+	0.726576i	0.285690	+	0.958322i	$0.407777\pi$
$12$	2.32440	+	2.56850i	0.670996	+	0.741461i
$13$	1.25308	−	0.723468i	0.347543	−	0.200654i	−0.316060	−	0.948739i	$-0.602360\pi$
$13$	1.25308	−	0.723468i	0.347543	−	0.200654i	0.663603	+	0.748085i	$0.269027\pi$
$14$	3.05062	−	1.09459i	0.815312	−	0.292540i
$15$	−1.53867	−	0.795287i	−0.397284	−	0.205342i
$16$	−3.78313	+	1.29921i	−0.945782	+	0.324802i
$17$		−	5.75799i		−	1.39652i	−0.715846	−	0.698259i	$-0.753959\pi$
$17$		−	5.75799i		−	1.39652i	0.715846	−	0.698259i	$-0.246041\pi$
$18$	−1.79789	−	3.84286i	−0.423768	−	0.905771i
$19$	5.54092			1.27118			0.635588	−	0.772029i	$-0.280758\pi$
$19$	5.54092			1.27118			0.635588	+	0.772029i	$0.280758\pi$
$20$	1.54376	−	1.27153i	0.345196	−	0.284323i
$21$	−3.96515	+	0.184714i	−0.865268	+	0.0403078i
$22$	6.41541	−	2.30190i	1.36777	−	0.490767i
$23$	−0.878693	−	1.52194i	−0.183220	−	0.317347i	0.759755	−	0.650209i	$-0.225319\pi$
$23$	−0.878693	−	1.52194i	−0.183220	−	0.317347i	−0.942975	+	0.332863i	$0.891985\pi$
$24$	4.89634	−	0.160918i	0.999460	−	0.0328472i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.364530	−	2.01355i	0.0714901	−	0.394889i
$27$	0.723295	+	5.14557i	0.139198	+	0.990265i
$28$	1.60693	−	4.29262i	0.303680	−	0.811228i
$29$	−3.85587	+	6.67857i	−0.716018	+	1.24018i	0.246548	+	0.969131i	$0.420704\pi$
$29$	−3.85587	+	6.67857i	−0.716018	+	1.24018i	−0.962566	+	0.271048i	$0.912630\pi$
$30$	−2.26458	+	0.933647i	−0.413453	+	0.170460i
$31$	2.38149	−	1.37495i	0.427728	−	0.246949i	−0.270650	−	0.962678i	$-0.587239\pi$
$31$	2.38149	−	1.37495i	0.427728	−	0.246949i	0.698378	+	0.715729i	$0.253905\pi$
$32$	−2.05560	+	5.27015i	−0.363381	+	0.931640i
$33$	−8.33868	+	0.388451i	−1.45158	+	0.0676206i
$34$	−6.21396	−	5.26266i	−1.06568	−	0.902539i
$35$			2.29177i			0.387379i
$36$	−5.79040	−	1.57201i	−0.965067	−	0.262002i
$37$		−	1.48435i		−	0.244025i	−0.992529	−	0.122013i	$-0.961065\pi$
$37$		−	1.48435i		−	0.244025i	0.992529	−	0.122013i	$-0.0389349\pi$
$38$	5.06427	−	5.97970i	0.821533	−	0.970036i
$39$	−1.15073	+	2.22636i	−0.184264	+	0.356504i
$40$	0.0387410	−	2.82816i	0.00612548	−	0.447172i
$41$	5.84684	−	3.37568i	0.913124	−	0.527192i	0.0316887	−	0.999498i	$-0.489911\pi$
$41$	5.84684	−	3.37568i	0.913124	−	0.527192i	0.881435	+	0.472306i	$0.156578\pi$
$42$	−3.42471	+	4.44797i	−0.528445	+	0.686337i
$43$	0.513317	−	0.889090i	0.0782800	−	0.135585i	−0.824228	−	0.566258i	$-0.808391\pi$
$43$	0.513317	−	0.889090i	0.0782800	−	0.135585i	0.902508	+	0.430673i	$0.141724\pi$
$44$	3.37935	−	9.02732i	0.509456	−	1.36092i
$45$	2.98701	−	0.278900i	0.445277	−	0.0415760i
$46$	−2.44557	−	0.442742i	−0.360579	−	0.0652787i
$47$	−5.87002	+	10.1672i	−0.856230	+	1.48303i	0.0192693	+	0.999814i	$0.493866\pi$
$47$	−5.87002	+	10.1672i	−0.856230	+	1.48303i	−0.875499	+	0.483219i	$0.839467\pi$
$48$	4.30147	−	5.43115i	0.620864	−	0.783918i
$49$	−0.873905	−	1.51365i	−0.124844	−	0.216235i
$50$	0.477617	+	1.33112i	0.0675452	+	0.188249i
$51$	5.38307	+	8.39558i	0.753781	+	1.17562i
$52$	−1.83983	−	2.23373i	−0.255138	−	0.309763i
$53$	−14.2585			−1.95856			−0.979281	−	0.202506i	$-0.935091\pi$
$53$	−14.2585			−1.95856			−0.979281	+	0.202506i	$0.935091\pi$
$54$	6.21411	+	3.92235i	0.845633	+	0.533764i
$55$			4.81956i			0.649869i
$56$	−3.16385	−	5.65752i	−0.422787	−	0.756018i
$57$	−8.07909	+	5.18014i	−1.07010	+	0.686127i
$58$	3.68326	+	10.2653i	0.483636	+	1.34790i
$59$	−7.06983	+	4.08177i	−0.920413	+	0.531401i	−0.883767	−	0.467928i	$-0.845001\pi$
$59$	−7.06983	+	4.08177i	−0.920413	+	0.531401i	−0.0366461	+	0.999328i	$0.511667\pi$
$60$	−1.06219	+	3.29724i	−0.137128	+	0.425671i
$61$	2.27929	+	1.31595i	0.291833	+	0.168490i	0.638768	−	0.769399i	$-0.279444\pi$
$61$	2.27929	+	1.31595i	0.291833	+	0.168490i	−0.346935	+	0.937889i	$0.612778\pi$
$62$	0.692789	−	3.82675i	0.0879843	−	0.485997i
$63$	5.60881	−	3.97630i	0.706643	−	0.500967i
$64$	3.80873	+	7.03517i	0.476091	+	0.879396i
$65$	1.25308	+	0.723468i	0.155426	+	0.0897352i
$66$	−7.20214	+	9.35404i	−0.886522	+	1.15140i
$67$	−0.258738	−	0.448148i	−0.0316099	−	0.0547500i	0.849788	−	0.527125i	$-0.176730\pi$
$67$	−0.258738	−	0.448148i	−0.0316099	−	0.0547500i	−0.881398	+	0.472375i	$0.843397\pi$
$68$	−11.3588	+	1.89608i	−1.37746	+	0.229934i
$69$	2.70404	+	1.39763i	0.325529	+	0.168254i
$70$	2.47325	+	2.09462i	0.295610	+	0.250355i
$71$	−8.60697			−1.02146			−0.510730	−	0.859741i	$-0.670625\pi$
$71$	−8.60697			−1.02146			−0.510730	+	0.859741i	$0.670625\pi$
$72$	−6.98879	+	4.81216i	−0.823637	+	0.567118i
$73$	1.59208			0.186339			0.0931693	−	0.995650i	$-0.470300\pi$
$73$	1.59208			0.186339			0.0931693	+	0.995650i	$0.470300\pi$
$74$	−1.60189	−	1.35666i	−0.186216	−	0.157708i
$75$	−0.0805988	−	1.73017i	−0.00930675	−	0.199783i
$76$	−1.82461	−	10.9306i	−0.209297	−	1.25383i
$77$	5.52265	+	9.56551i	0.629364	+	1.09009i
$78$	1.35093	+	3.27670i	0.152963	+	0.371013i
$79$	7.04303	+	4.06630i	0.792403	+	0.457494i	0.840808	−	0.541334i	$-0.182080\pi$
$79$	7.04303	+	4.06630i	0.792403	+	0.457494i	−0.0484046	+	0.998828i	$0.515414\pi$
$80$	−3.01671	−	2.62668i	−0.337279	−	0.293672i
$81$	−5.86515	−	6.82642i	−0.651683	−	0.758492i
$82$	1.70088	−	9.39513i	0.187831	−	1.03752i
$83$	−7.73374	−	4.46508i	−0.848889	−	0.490106i	0.0113871	−	0.999935i	$-0.496375\pi$
$83$	−7.73374	−	4.46508i	−0.848889	−	0.490106i	−0.860276	+	0.509829i	$0.829709\pi$
$84$	1.67010	+	7.76125i	0.182222	+	0.846822i
$85$	4.98656	−	2.87899i	0.540869	−	0.312271i
$86$	−0.490337	−	1.36657i	−0.0528744	−	0.147361i
$87$	−0.621558	−	13.3427i	−0.0666380	−	1.43048i
$88$	−6.65355	−	11.8977i	−0.709270	−	1.26830i
$89$		−	7.90275i		−	0.837690i	−0.908058	−	0.418845i	$-0.862435\pi$
$89$		−	7.90275i		−	0.837690i	0.908058	−	0.418845i	$-0.137565\pi$
$90$	2.42907	−	3.47845i	0.256046	−	0.366661i
$91$	3.31604			0.347615
$92$	−2.71299	+	2.23457i	−0.282849	+	0.232970i
$93$	−2.18696	+	4.23121i	−0.226777	+	0.438756i
$94$	5.60724	+	15.6274i	0.578342	+	1.61184i
$95$	2.77046	+	4.79858i	0.284243	+	0.492324i
$96$	−1.92979	−	9.60604i	−0.196958	−	0.980412i
$97$	1.55398	−	2.69157i	0.157783	−	0.273287i	−0.776286	−	0.630381i	$-0.782899\pi$
$97$	1.55398	−	2.69157i	0.157783	−	0.273287i	0.934069	+	0.357093i	$0.116232\pi$
$98$	−2.43224	−	0.440329i	−0.245693	−	0.0444800i
$99$	11.7953	−	8.36212i	1.18547	−	0.840424i
$100$	1.87306	+	0.701173i	0.187306	+	0.0701173i
$101$	9.37499	−	16.2380i	0.932847	−	1.61574i	0.154417	−	0.988006i	$-0.450650\pi$
$101$	9.37499	−	16.2380i	0.932847	−	1.61574i	0.778429	−	0.627732i	$-0.216017\pi$
$102$	13.9804	+	1.86401i	1.38427	+	0.184564i
$103$	−6.86735	+	3.96487i	−0.676660	+	0.390670i	−0.798595	−	0.601868i	$-0.794423\pi$
$103$	−6.86735	+	3.96487i	−0.676660	+	0.390670i	0.121935	+	0.992538i	$0.461090\pi$
$104$	−4.09217	−	0.0560557i	−0.401270	−	0.00549672i
$105$	−2.14254	−	3.34157i	−0.209091	−	0.326104i
$106$	−13.0320	+	15.3877i	−1.26578	+	1.49458i
$107$			4.49063i			0.434125i	0.976158	+	0.217063i	$0.0696476\pi$
$107$			4.49063i			0.434125i	−0.976158	+	0.217063i	$0.930352\pi$
$108$	9.91250	−	3.12126i	0.953831	−	0.300344i
$109$			12.2276i			1.17119i	0.810604	+	0.585594i	$0.199139\pi$
$109$			12.2276i			1.17119i	−0.810604	+	0.585594i	$0.800861\pi$
$110$	5.20121	+	4.40496i	0.495916	+	0.419996i
$111$	1.38770	+	2.16429i	0.131715	+	0.205426i
$112$	−8.99722	−	1.75645i	−0.850157	−	0.165969i
$113$	−9.26205	+	5.34744i	−0.871300	+	0.503045i	−0.867780	−	0.496949i	$-0.834454\pi$
$113$	−9.26205	+	5.34744i	−0.871300	+	0.503045i	−0.00351996	+	0.999994i	$0.501120\pi$
$114$	−1.79374	+	13.4534i	−0.167999	+	1.26003i
$115$	0.878693	−	1.52194i	0.0819385	−	0.141922i
$116$	14.4446	+	5.40727i	1.34114	+	0.502052i
$117$	−0.403551	−	4.32201i	−0.0373083	−	0.399570i
$118$	−2.05665	+	11.3603i	−0.189330	+	1.04580i
$119$	6.59798	−	11.4280i	0.604836	−	1.04761i
$120$	2.58753	+	4.15989i	0.236208	+	0.379744i
$121$	6.11407	+	10.5899i	0.555824	+	0.962716i
$122$	3.50337	−	1.25704i	0.317180	−	0.113807i
$123$	−5.36926	+	10.3881i	−0.484130	+	0.936667i
$124$	−3.49659	−	4.24520i	−0.314003	−	0.381231i
$125$	−1.00000			−0.0894427
$126$	0.835136	−	9.68721i	0.0743999	−	0.863005i
$127$		−	18.2455i		−	1.61903i	−0.587101	−	0.809514i	$-0.699731\pi$
$127$		−	18.2455i		−	1.61903i	0.587101	−	0.809514i	$-0.300269\pi$
$128$	11.0734	+	2.31964i	0.978756	+	0.205029i
$129$	0.0827454	+	1.77625i	0.00728533	+	0.156390i
$130$	1.92605	−	0.691081i	0.168926	−	0.0606119i
$131$	3.74535	−	2.16238i	0.327233	−	0.188928i	−0.327379	−	0.944893i	$-0.606165\pi$
$131$	3.74535	−	2.16238i	0.327233	−	0.188928i	0.654612	+	0.755965i	$0.272832\pi$
$132$	3.51219	+	16.3218i	0.305697	+	1.42063i
$133$	10.9972	+	6.34925i	0.953580	+	0.550550i
$134$	−0.720117	−	0.130369i	−0.0622086	−	0.0112622i
$135$	−4.09454	+	3.19917i	−0.352402	+	0.275341i
$136$	−8.33545	+	13.9913i	−0.714759	+	1.19974i
$137$	8.45892	+	4.88376i	0.722694	+	0.417248i	0.815744	−	0.578414i	$-0.196328\pi$
$137$	8.45892	+	4.88376i	0.722694	+	0.417248i	−0.0930493	+	0.995662i	$0.529661\pi$
$138$	3.97973	−	1.64078i	0.338777	−	0.139672i
$139$	−8.38301	−	14.5198i	−0.711038	−	1.23155i	−0.964468	−	0.264200i	$-0.914892\pi$
$139$	−8.38301	−	14.5198i	−0.711038	−	1.23155i	0.253430	−	0.967354i	$-0.418441\pi$
$140$	4.52098	−	0.754670i	0.382092	−	0.0637813i
$141$	−0.946233	−	20.3123i	−0.0796872	−	1.71060i
$142$	−7.86656	+	9.28854i	−0.660147	+	0.779477i
$143$	6.97360			0.583161
$144$	−1.19436	+	11.9404i	−0.0995300	+	0.995035i
$145$	−7.71175			−0.640426
$146$	1.45512	−	1.71815i	0.120427	−	0.142195i
$147$	2.68931	+	1.39001i	0.221811	+	0.114646i
$148$	−2.92818	+	0.488790i	−0.240695	+	0.0401783i
$149$	−6.90081	−	11.9526i	−0.565337	−	0.979192i	−0.997018	−	0.0771658i	$-0.975413\pi$
$149$	−6.90081	−	11.9526i	−0.565337	−	0.979192i	0.431682	−	0.902026i	$-0.357920\pi$
$150$	−1.94085	−	1.49436i	−0.158470	−	0.122014i
$151$	5.39274	+	3.11350i	0.438855	+	0.253373i	0.703112	−	0.711079i	$-0.251793\pi$
$151$	5.39274	+	3.11350i	0.438855	+	0.253373i	−0.264257	+	0.964452i	$0.585127\pi$
$152$	−13.4638	−	8.02122i	−1.09206	−	0.650607i
$153$	−15.6979	−	7.20883i	−1.26910	−	0.582799i
$154$	15.3706	+	2.78266i	1.23859	+	0.224233i
$155$	2.38149	+	1.37495i	0.191286	+	0.110439i
$156$	4.77089	+	1.53692i	0.381977	+	0.123052i
$157$	2.84493	−	1.64252i	0.227050	−	0.131088i	−0.382160	−	0.924096i	$-0.624820\pi$
$157$	2.84493	−	1.64252i	0.227050	−	0.131088i	0.609211	+	0.793008i	$0.291486\pi$
$158$	10.8255	−	3.88427i	0.861228	−	0.309016i
$159$	20.7900	−	13.3301i	1.64876	−	1.05715i
$160$	−5.59189	+	0.854879i	−0.442077	+	0.0675841i
$161$		−	4.02752i		−	0.317413i
$162$	−12.7276	+	0.0904123i	−0.999975	+	0.00710346i
$163$	−9.36177			−0.733271			−0.366635	−	0.930365i	$-0.619490\pi$
$163$	−9.36177			−0.733271			−0.366635	+	0.930365i	$0.619490\pi$
$164$	−8.58456	−	10.4225i	−0.670341	−	0.813860i
$165$	−4.50575	−	7.02728i	−0.350772	−	0.547073i
$166$	−11.8871	+	4.26519i	−0.922619	+	0.331043i
$167$	−2.67257	−	4.62903i	−0.206810	−	0.358205i	0.743898	−	0.668293i	$-0.232975\pi$
$167$	−2.67257	−	4.62903i	−0.206810	−	0.358205i	−0.950708	+	0.310088i	$0.899641\pi$
$168$	9.90228	+	5.29125i	0.763978	+	0.408229i
$169$	−5.45319	+	9.44520i	−0.419476	+	0.726554i
$170$	1.45062	−	8.01278i	0.111258	−	0.614552i
$171$	6.93707	−	15.1061i	0.530491	−	1.15519i
$172$	−1.92295	−	0.719848i	−0.146623	−	0.0548879i
$173$	−3.20113	+	5.54452i	−0.243377	+	0.421542i	−0.961674	−	0.274195i	$-0.911589\pi$
$173$	−3.20113	+	5.54452i	−0.243377	+	0.421542i	0.718297	+	0.695737i	$0.244922\pi$
$174$	−14.9673	−	11.5241i	−1.13467	−	0.873640i
$175$	−1.98473	+	1.14588i	−0.150031	+	0.0866206i
$176$	−18.9211	−	3.69379i	−1.42623	−	0.278430i
$177$	6.49235	−	12.5610i	0.487995	−	0.944144i
$178$	−8.52856	−	7.22292i	−0.639242	−	0.541381i
$179$			24.4547i			1.82783i	0.405908	+	0.913914i	$0.366955\pi$
$179$			24.4547i			1.82783i	−0.405908	+	0.913914i	$0.633045\pi$
$180$	−1.53380	−	5.80064i	−0.114323	−	0.432354i
$181$		−	15.7625i		−	1.17161i	−0.810451	−	0.585807i	$-0.800778\pi$
$181$		−	15.7625i		−	1.17161i	0.810451	−	0.585807i	$-0.199222\pi$
$182$	3.03078	−	3.57863i	0.224656	−	0.265266i
$183$	−4.55364	+	0.212128i	−0.336615	+	0.0156809i
$184$	−0.0680828	+	4.97017i	−0.00501913	+	0.366406i
$185$	1.28548	−	0.742174i	0.0945106	−	0.0545657i
$186$	2.56744	+	6.22737i	0.188254	+	0.456613i
$187$	13.8755	−	24.0330i	1.01468	−	1.75747i
$188$	21.9898	+	8.23180i	1.60377	+	0.600366i
$189$	−4.46067	+	11.0414i	−0.324466	+	0.803140i
$190$	7.71071	+	1.39594i	0.559394	+	0.101272i
$191$	−9.45471	+	16.3760i	−0.684119	+	1.18493i	0.289594	+	0.957150i	$0.406480\pi$
$191$	−9.45471	+	16.3760i	−0.684119	+	1.18493i	−0.973713	+	0.227779i	$0.926854\pi$
$192$	−12.1305	−	6.69708i	−0.875444	−	0.483320i
$193$	9.04742	+	15.6706i	0.651247	+	1.12799i	0.982821	+	0.184564i	$0.0590873\pi$
$193$	9.04742	+	15.6706i	0.651247	+	1.12799i	−0.331573	+	0.943429i	$0.607579\pi$
$194$	−1.48441	−	4.13706i	−0.106575	−	0.297024i
$195$	−2.50345	+	0.116621i	−0.179276	+	0.00835143i
$196$	−2.69821	+	2.22240i	−0.192729	+	0.158743i
$197$	−5.73319			−0.408473			−0.204236	−	0.978922i	$-0.565471\pi$
$197$	−5.73319			−0.408473			−0.204236	+	0.978922i	$0.565471\pi$
$198$	1.75628	−	20.3721i	0.124814	−	1.44778i
$199$		−	10.6185i		−	0.752726i	−0.926472	−	0.376363i	$-0.877175\pi$
$199$		−	10.6185i		−	0.752726i	0.926472	−	0.376363i	$-0.122825\pi$
$200$	2.46863	−	1.38053i	0.174559	−	0.0976182i
$201$	0.796228	+	0.411542i	0.0561616	+	0.0290280i
$202$	−8.95531	−	24.9585i	−0.630093	−	1.75607i
$203$	−15.3057	+	8.83676i	−1.07425	+	0.620219i
$204$	14.7894	−	13.3839i	1.03546	−	0.937057i
$205$	5.84684	+	3.37568i	0.408361	+	0.235767i
$206$	−1.99775	+	11.0350i	−0.139190	+	0.768842i
$207$	−5.24932	+	0.490135i	−0.364853	+	0.0340667i
$208$	−3.80064	+	4.36499i	−0.263527	+	0.302658i
$209$	23.1270	+	13.3524i	1.59973	+	0.923605i
$210$	−5.56442	−	0.741903i	−0.383981	−	0.0511962i
$211$	−3.08700	−	5.34684i	−0.212518	−	0.368092i	0.739984	−	0.672625i	$-0.234833\pi$
$211$	−3.08700	−	5.34684i	−0.212518	−	0.368092i	−0.952502	+	0.304533i	$0.901500\pi$
$212$	4.69529	+	28.1279i	0.322474	+	1.93183i
$213$	12.5496	−	8.04655i	0.859885	−	0.551341i
$214$	4.84623	+	4.10432i	0.331282	+	0.280566i
$215$	1.02663			0.0700158
$216$	5.69136	−	13.5502i	0.387248	−	0.921976i
$217$	6.30214			0.427817
$218$	13.1959	+	11.1757i	0.893736	+	0.756914i
$219$	−2.32137	+	1.48841i	−0.156864	+	0.100578i
$220$	9.50756	−	1.58706i	0.641000	−	0.107000i
$221$	−4.16572	−	7.21524i	−0.280217	−	0.485350i
$222$	3.60400	+	0.480521i	0.241885	+	0.0322505i
$223$	−2.29703	−	1.32619i	−0.153820	−	0.0888083i	0.421114	−	0.907008i	$-0.361639\pi$
$223$	−2.29703	−	1.32619i	−0.153820	−	0.0888083i	−0.574935	+	0.818199i	$0.694973\pi$
$224$	−10.1188	+	8.10435i	−0.676089	+	0.541494i
$225$	1.73504	+	2.44737i	0.115669	+	0.163158i
$226$	−2.69438	+	14.8829i	−0.179228	+	0.989998i
$227$	−6.99203	−	4.03685i	−0.464077	−	0.267935i	0.249680	−	0.968328i	$-0.419675\pi$
$227$	−6.99203	−	4.03685i	−0.464077	−	0.267935i	−0.713757	+	0.700393i	$0.753008\pi$
$228$	12.8793	+	14.2319i	0.852953	+	0.942527i
$229$	−17.8582	+	10.3104i	−1.18010	+	0.681332i	−0.956038	−	0.293242i	$-0.905266\pi$
$229$	−17.8582	+	10.3104i	−1.18010	+	0.681332i	−0.224064	+	0.974575i	$0.571932\pi$
$230$	−0.839357	−	2.33929i	−0.0553456	−	0.154248i
$231$	−16.9951	−	8.78418i	−1.11820	−	0.577956i
$232$	19.0375	−	10.6463i	1.24987	−	0.698964i
$233$		−	25.6348i		−	1.67939i	−0.543059	−	0.839695i	$-0.682734\pi$
$233$		−	25.6348i		−	1.67939i	0.543059	−	0.839695i	$-0.317266\pi$
$234$	−5.03310	−	3.51471i	−0.329024	−	0.229764i
$235$	−11.7400			−0.765835
$236$	10.3802	+	12.6026i	0.675693	+	0.820357i
$237$	−14.0708	+	0.655478i	−0.913997	+	0.0425778i
$238$	−6.30261	−	17.5654i	−0.408538	−	1.13860i
$239$	5.42944	+	9.40407i	0.351202	+	0.608299i	0.986460	−	0.164000i	$-0.0524399\pi$
$239$	5.42944	+	9.40407i	0.351202	+	0.608299i	−0.635259	+	0.772299i	$0.719107\pi$
$240$	6.85425	+	1.00961i	0.442440	+	0.0651701i
$241$	−2.83295	+	4.90682i	−0.182487	+	0.316076i	−0.942727	−	0.333566i	$-0.891748\pi$
$241$	−2.83295	+	4.90682i	−0.182487	+	0.316076i	0.760240	+	0.649642i	$0.225081\pi$
$242$	17.0166	+	3.08066i	1.09387	+	0.198032i
$243$	14.9338	+	4.47019i	0.958002	+	0.286763i
$244$	1.84542	−	4.92970i	0.118141	−	0.315592i
$245$	0.873905	−	1.51365i	0.0558317	−	0.0967034i
$246$	6.30338	+	15.2890i	0.401889	+	0.974788i
$247$	6.94324	−	4.00868i	0.441788	−	0.255066i
$248$	−7.77717	−	0.106534i	−0.493851	−	0.00676491i
$249$	15.4507	−	0.719760i	0.979150	−	0.0456129i
$250$	−0.913976	+	1.07919i	−0.0578049	+	0.0682539i
$251$			9.57232i			0.604199i	0.953276	+	0.302100i	$0.0976876\pi$
$251$			9.57232i			0.604199i	−0.953276	+	0.302100i	$0.902312\pi$
$252$	−9.69103	−	9.75514i	−0.610477	−	0.614516i
$253$		−	8.46982i		−	0.532493i
$254$	−19.6904	−	16.6760i	−1.23548	−	1.04634i
$255$	−4.57925	+	8.85967i	−0.286764	+	0.554814i
$256$	12.6241	−	9.83015i	0.789007	−	0.614384i
$257$	16.8660	−	9.73761i	1.05207	−	0.607415i	0.128845	−	0.991665i	$-0.458873\pi$
$257$	16.8660	−	9.73761i	1.05207	−	0.607415i	0.923229	+	0.384250i	$0.125540\pi$
$258$	1.99254	+	1.53416i	0.124050	+	0.0955124i
$259$	1.70089	−	2.94603i	0.105688	−	0.183057i
$260$	1.01455	−	2.71020i	0.0629199	−	0.168079i
$261$	13.3802	+	18.8735i	0.828212	+	1.16824i
$262$	1.08955	−	6.01830i	0.0673123	−	0.371812i
$263$	8.27579	−	14.3341i	0.510307	−	0.883878i	−0.489621	−	0.871935i	$-0.662865\pi$
$263$	8.27579	−	14.3341i	0.510307	−	0.883878i	0.999929	−	0.0119430i	$-0.00380167\pi$
$264$	20.8244	+	11.1274i	1.28165	+	0.684847i
$265$	−7.12927	−	12.3483i	−0.437948	−	0.758548i
$266$	16.9032	−	6.06502i	1.03640	−	0.371870i
$267$	7.38818	+	11.5228i	0.452150	+	0.705184i
$268$	−0.798862	+	0.657988i	−0.0487983	+	0.0401930i
$269$	17.0665			1.04056			0.520280	−	0.853996i	$-0.325828\pi$
$269$	17.0665			1.04056			0.520280	+	0.853996i	$0.325828\pi$
$270$	−0.289800	+	7.34275i	−0.0176367	+	0.446866i
$271$			30.8888i			1.87636i	0.346144	+	0.938182i	$0.387491\pi$
$271$			30.8888i			1.87636i	−0.346144	+	0.938182i	$0.612509\pi$
$272$	7.48083	+	21.7832i	0.453592	+	1.32080i
$273$	−4.83504	+	3.10013i	−0.292630	+	0.187628i
$274$	13.0017	−	4.66513i	0.785464	−	0.281831i
$275$	−4.17386	+	2.40978i	−0.251693	+	0.145315i
$276$	1.86667	−	5.79451i	0.112360	−	0.348789i
$277$	10.7961	+	6.23311i	0.648673	+	0.374511i	0.787948	−	0.615742i	$-0.211144\pi$
$277$	10.7961	+	6.23311i	0.648673	+	0.374511i	−0.139275	+	0.990254i	$0.544477\pi$
$278$	−23.3315	−	4.22390i	−1.39933	−	0.253332i
$279$	−0.766948	−	8.21398i	−0.0459160	−	0.491758i
$280$	3.31763	−	5.56874i	0.198266	−	0.332796i
$281$	8.24335	+	4.75930i	0.491757	+	0.283916i	0.725303	−	0.688430i	$-0.241700\pi$
$281$	8.24335	+	4.75930i	0.491757	+	0.283916i	−0.233546	+	0.972346i	$0.575033\pi$
$282$	−22.7856	−	17.5438i	−1.35687	−	1.04472i
$283$	3.51759	+	6.09265i	0.209099	+	0.362171i	0.951431	−	0.307862i	$-0.0996135\pi$
$283$	3.51759	+	6.09265i	0.209099	+	0.362171i	−0.742332	+	0.670032i	$0.766280\pi$
$284$	2.83424	+	16.9790i	0.168181	+	1.00752i
$285$	−8.52568	−	4.40662i	−0.505018	−	0.261026i
$286$	6.37370	−	7.52583i	0.376885	−	0.445011i
$287$	15.4725			0.913314
$288$	11.7943	+	12.2022i	0.694988	+	0.719021i
$289$	−16.1544			−0.950261
$290$	−7.04835	+	8.32243i	−0.413893	+	0.488710i
$291$	0.250498	+	5.37730i	0.0146844	+	0.315223i
$292$	−0.524265	−	3.14070i	−0.0306803	−	0.183796i
$293$	10.0694	+	17.4407i	0.588261	+	1.01890i	0.994460	+	0.105113i	$0.0335204\pi$
$293$	10.0694	+	17.4407i	0.588261	+	1.01890i	−0.406200	+	0.913784i	$0.633146\pi$
$294$	3.95805	−	1.63184i	0.230838	−	0.0951707i
$295$	−7.06983	−	4.08177i	−0.411621	−	0.237650i
$296$	−2.14879	+	3.60680i	−0.124896	+	0.209641i
$297$	−9.38074	+	23.2198i	−0.544326	+	1.34735i
$298$	−19.2062	−	3.47707i	−1.11259	−	0.201421i
$299$	−2.20215	−	1.27141i	−0.127354	−	0.0735277i
$300$	−3.38658	+	0.728738i	−0.195524	+	0.0420737i
$301$	2.03759	−	1.17640i	0.117445	−	0.0678066i
$302$	8.28888	−	2.97412i	0.476972	−	0.171141i
$303$	1.51123	+	32.4407i	0.0868177	+	1.86367i
$304$	−20.9620	+	7.19882i	−1.20225	+	0.412881i
$305$			2.63190i			0.150702i
$306$	−22.1271	+	10.3523i	−1.26492	+	0.591799i
$307$	−26.8989			−1.53520			−0.767600	−	0.640929i	$-0.778549\pi$
$307$	−26.8989			−1.53520			−0.767600	+	0.640929i	$0.778549\pi$
$308$	17.0513	−	14.0444i	0.971590	−	0.800256i
$309$	6.30641	−	12.2013i	0.358759	−	0.694106i
$310$	3.66045	−	1.31340i	0.207900	−	0.0745961i
$311$	1.79373	+	3.10683i	0.101713	+	0.176172i	0.912391	−	0.409321i	$-0.134234\pi$
$311$	1.79373	+	3.10683i	0.101713	+	0.176172i	−0.810677	+	0.585493i	$0.800901\pi$
$312$	6.01910	−	3.74399i	0.340764	−	0.211962i
$313$	−0.999176	+	1.73062i	−0.0564768	+	0.0978206i	−0.892882	−	0.450292i	$-0.851320\pi$
$313$	−0.999176	+	1.73062i	−0.0564768	+	0.0978206i	0.836405	+	0.548112i	$0.184653\pi$
$314$	0.827608	−	4.57145i	0.0467046	−	0.257982i
$315$	6.24798	+	2.86922i	0.352034	+	0.161662i
$316$	5.70236	−	15.2328i	0.320783	−	0.856914i
$317$	−10.9863	+	19.0288i	−0.617050	+	1.06876i	0.372971	+	0.927843i	$0.378339\pi$
$317$	−10.9863	+	19.0288i	−0.617050	+	1.06876i	−0.990021	+	0.140919i	$0.954994\pi$
$318$	4.61586	−	34.6198i	0.258844	−	1.94138i
$319$	−32.1877	+	18.5836i	−1.80217	+	1.04048i
$320$	−4.18827	+	6.81604i	−0.234132	+	0.381028i
$321$	−4.19823	−	6.54767i	−0.234322	−	0.365455i
$322$	−4.34645	−	3.68105i	−0.242218	−	0.205137i
$323$		−	31.9046i		−	1.77522i
$324$	−11.5351	+	13.8181i	−0.640842	+	0.767673i
$325$			1.44694i			0.0802616i
$326$	−8.55643	+	10.1031i	−0.473897	+	0.559560i
$327$	−11.4314	−	17.8287i	−0.632158	−	0.985931i
$328$	−19.0939	−	0.261554i	−1.05429	−	0.0144419i
$329$	−23.3008	+	13.4527i	−1.28461	+	0.741672i
$330$	−11.7019	−	1.56021i	−0.644169	−	0.0858869i
$331$	5.84025	−	10.1156i	0.321009	−	0.556005i	−0.659687	−	0.751540i	$-0.729311\pi$
$331$	5.84025	−	10.1156i	0.321009	−	0.556005i	0.980697	+	0.195536i	$0.0626446\pi$
$332$	−6.26159	+	16.7267i	−0.343649	+	0.917998i
$333$	−4.04674	−	1.85836i	−0.221760	−	0.101837i
$334$	−7.43826	−	1.34661i	−0.407004	−	0.0736833i
$335$	0.258738	−	0.448148i	0.0141364	−	0.0244849i
$336$	14.7607	−	5.85036i	0.805262	−	0.319163i
$337$	8.74196	+	15.1415i	0.476205	+	0.824811i	0.999628	−	0.0272615i	$-0.00867866\pi$
$337$	8.74196	+	15.1415i	0.476205	+	0.824811i	−0.523423	+	0.852073i	$0.675345\pi$
$338$	5.20907	+	14.5177i	0.283336	+	0.789659i
$339$	8.50550	−	16.4560i	0.461955	−	0.893765i
$340$	−7.32146	−	8.88898i	−0.397062	−	0.482072i
$341$	13.2533			0.717708
$342$	−9.96200	−	21.2930i	−0.538683	−	1.15139i
$343$		−	20.0479i		−	1.08249i
$344$	−2.53438	+	1.41730i	−0.136644	+	0.0764156i
$345$	0.141643	+	3.04058i	0.00762581	+	0.163700i
$346$	3.05782	+	8.52217i	0.164390	+	0.458155i
$347$	15.1453	−	8.74414i	0.813042	−	0.469410i	−0.0349694	−	0.999388i	$-0.511133\pi$
$347$	15.1453	−	8.74414i	0.813042	−	0.469410i	0.848011	+	0.529979i	$0.177800\pi$
$348$	−26.1165	+	5.61984i	−1.39999	+	0.301255i
$349$	−8.45212	−	4.87983i	−0.452432	−	0.261212i	0.256425	−	0.966564i	$-0.417455\pi$
$349$	−8.45212	−	4.87983i	−0.452432	−	0.261212i	−0.708857	+	0.705353i	$0.750789\pi$
$350$	−0.577369	+	3.18920i	−0.0308617	+	0.170470i
$351$	4.62900	+	5.92454i	0.247078	+	0.316229i
$352$	−21.2797	+	17.0434i	−1.13421	+	0.908414i
$353$	16.2839	+	9.40153i	0.866706	+	0.500393i	0.866252	−	0.499607i	$-0.166522\pi$
$353$	16.2839	+	9.40153i	0.866706	+	0.500393i	0.000454058		1.00000i	$0.499855\pi$
$354$	−7.62186	−	18.4869i	−0.405097	−	0.982569i
$355$	−4.30348	−	7.45385i	−0.228405	−	0.395610i
$356$	−15.5898	+	2.60235i	−0.826257	+	0.137924i
$357$	1.06358	+	22.8313i	0.0562906	+	1.20836i
$358$	26.3912	+	22.3510i	1.39482	+	1.18129i
$359$	−14.3616			−0.757979			−0.378989	−	0.925401i	$-0.623728\pi$
$359$	−14.3616			−0.757979			−0.378989	+	0.925401i	$0.623728\pi$
$360$	−7.66184	−	3.64639i	−0.403815	−	0.192182i
$361$	11.7018			0.615887
$362$	−17.0107	−	14.4065i	−0.894060	−	0.757189i
$363$	−18.8151	−	9.72487i	−0.987538	−	0.510424i
$364$	−1.09196	−	6.54157i	−0.0572342	−	0.342871i
$365$	0.796039	+	1.37878i	0.0416666	+	0.0721686i
$366$	−3.93299	+	5.10812i	−0.205581	+	0.267006i
$367$	24.9275	+	14.3919i	1.30120	+	0.751250i	0.980610	−	0.195968i	$-0.0627847\pi$
$367$	24.9275	+	14.3919i	1.30120	+	0.751250i	0.320592	+	0.947217i	$0.396118\pi$
$368$	5.30153	+	4.61609i	0.276361	+	0.240630i
$369$	−1.88295	−	20.1663i	−0.0980226	−	1.04982i
$370$	0.373955	−	2.06561i	0.0194410	−	0.107386i
$371$	−28.2993	−	16.3386i	−1.46923	−	0.848259i
$372$	9.06708	+	2.92091i	0.470106	+	0.151442i
$373$	−16.4328	+	9.48746i	−0.850856	+	0.491242i	−0.860940	−	0.508707i	$-0.830124\pi$
$373$	−16.4328	+	9.48746i	−0.850856	+	0.491242i	0.0100833	+	0.999949i	$0.496790\pi$
$374$	−13.2543	−	36.9399i	−0.685365	−	1.91012i
$375$	1.45808	−	0.934888i	0.0752947	−	0.0482774i
$376$	28.9818	−	16.2075i	1.49462	−	0.835837i
$377$			11.1584i			0.574687i
$378$	7.83876	+	14.9054i	0.403182	+	0.766653i
$379$	−26.8299			−1.37816			−0.689079	−	0.724686i	$-0.741985\pi$
$379$	−26.8299			−1.37816			−0.689079	+	0.724686i	$0.741985\pi$
$380$	8.55388	−	7.04546i	0.438805	−	0.361424i
$381$	17.0575	+	26.6033i	0.873883	+	1.36293i
$382$	9.03146	+	25.1707i	0.462090	+	1.28785i
$383$	0.241421	+	0.418153i	0.0123360	+	0.0213666i	0.872128	−	0.489279i	$-0.162740\pi$
$383$	0.241421	+	0.418153i	0.0123360	+	0.0213666i	−0.859791	+	0.510645i	$0.829407\pi$
$384$	−18.3144	+	6.97014i	−0.934603	+	0.355693i
$385$	−5.52265	+	9.56551i	−0.281460	+	0.487503i
$386$	25.1806	+	4.55867i	1.28166	+	0.232030i
$387$	−1.78125	−	2.51256i	−0.0905459	−	0.127720i
$388$	−5.82139	−	2.17922i	−0.295536	−	0.110633i
$389$	11.4935	−	19.9073i	0.582742	−	1.00934i	−0.412410	−	0.910998i	$-0.635313\pi$
$389$	11.4935	−	19.9073i	0.582742	−	1.00934i	0.995153	−	0.0983412i	$-0.0313536\pi$
$390$	−2.16224	+	2.80829i	−0.109489	+	0.142203i
$391$	−8.76332	+	5.05950i	−0.443180	+	0.255870i
$392$	−0.0677118	+	4.94309i	−0.00341996	+	0.249664i
$393$	−3.43942	+	6.65440i	−0.173496	+	0.335670i
$394$	−5.24000	+	6.18719i	−0.263987	+	0.311706i
$395$			8.13260i			0.409195i
$396$	−20.3801	−	20.5150i	−1.02414	−	1.03092i
$397$		−	18.7393i		−	0.940500i	−0.882533	−	0.470250i	$-0.844164\pi$
$397$		−	18.7393i		−	0.940500i	0.882533	−	0.470250i	$-0.155836\pi$
$398$	−11.4594	−	9.70505i	−0.574406	−	0.486470i
$399$	−21.9706	+	1.02348i	−1.09991	+	0.0512383i
$400$	0.766416	−	3.92589i	0.0383208	−	0.196294i
$401$	−4.65969	+	2.69028i	−0.232694	+	0.134346i	−0.611814	−	0.791001i	$-0.709560\pi$
$401$	−4.65969	+	2.69028i	−0.232694	+	0.134346i	0.379120	+	0.925347i	$0.376227\pi$
$402$	1.17187	−	0.483141i	0.0584473	−	0.0240969i
$403$	1.98947	−	3.44586i	0.0991025	−	0.171651i
$404$	−35.1199	−	13.1470i	−1.74728	−	0.654087i
$405$	2.97928	−	8.49258i	0.148042	−	0.422000i
$406$	−4.45252	+	24.5943i	−0.220975	+	1.22060i
$407$	3.57695	−	6.19546i	0.177303	−	0.307098i
$408$	−0.926563	−	28.1930i	−0.0458717	−	1.39576i
$409$	8.16680	+	14.1453i	0.403822	+	0.699440i	0.994184	−	0.107699i	$-0.0343481\pi$
$409$	8.16680	+	14.1453i	0.403822	+	0.699440i	−0.590361	+	0.807139i	$0.701015\pi$
$410$	8.98687	−	3.22456i	0.443830	−	0.159250i
$411$	−16.8995	+	0.787251i	−0.833591	+	0.0388322i
$412$	10.0829	+	12.2416i	0.496749	+	0.603102i
$413$	−18.7089			−0.920605
$414$	−4.26881	+	6.11298i	−0.209800	+	0.300437i
$415$		−	8.93016i		−	0.438364i
$416$	1.23696	+	8.09110i	0.0606467	+	0.396699i
$417$	25.7974	+	13.3338i	1.26331	+	0.652959i
$418$	35.5473	−	12.7547i	1.73868	−	0.623851i
$419$	−12.7622	+	7.36828i	−0.623476	+	0.359964i	−0.778221	−	0.627990i	$-0.783878\pi$
$419$	−12.7622	+	7.36828i	−0.623476	+	0.359964i	0.154745	+	0.987954i	$0.450544\pi$
$420$	−5.88639	+	5.32697i	−0.287227	+	0.259930i
$421$	−28.7733	−	16.6123i	−1.40232	−	0.809632i	−0.407692	−	0.913119i	$-0.633666\pi$
$421$	−28.7733	−	16.6123i	−1.40232	−	0.809632i	−0.994631	+	0.103488i	$0.967000\pi$
$422$	−8.59170	−	1.55543i	−0.418237	−	0.0757171i
$423$	20.3694	+	28.7323i	0.990395	+	1.39701i
$424$	34.6467	+	20.6411i	1.68259	+	1.00242i
$425$	4.98656	+	2.87899i	0.241884	+	0.139652i
$426$	2.78630	−	20.8978i	0.134996	−	1.01250i
$427$	3.01585	+	5.22360i	0.145947	+	0.252788i
$428$	8.85868	−	1.47875i	0.428200	−	0.0714779i
$429$	−10.1680	+	6.51953i	−0.490917	+	0.314766i
$430$	0.938318	−	1.10793i	0.0452497	−	0.0534292i
$431$	−1.90474			−0.0917480			−0.0458740	−	0.998947i	$-0.514607\pi$
$431$	−1.90474			−0.0917480			−0.0458740	+	0.998947i	$0.514607\pi$
$432$	−9.42148	−	18.5266i	−0.453291	−	0.891362i
$433$	12.6894			0.609814			0.304907	−	0.952382i	$-0.401375\pi$
$433$	12.6894			0.609814			0.304907	+	0.952382i	$0.401375\pi$
$434$	5.76000	−	6.80119i	0.276489	−	0.326468i
$435$	11.2443	−	7.20962i	0.539123	−	0.345675i
$436$	24.1214	−	4.02649i	1.15520	−	0.192834i
$437$	−4.86877	−	8.43296i	−0.232905	−	0.403403i
$438$	−0.515396	+	3.86557i	−0.0246266	+	0.184704i
$439$	−5.92929	−	3.42328i	−0.282990	−	0.163384i	0.351786	−	0.936080i	$-0.385574\pi$
$439$	−5.92929	−	3.42328i	−0.282990	−	0.163384i	−0.634776	+	0.772696i	$0.718908\pi$
$440$	6.97694	−	11.7110i	0.332613	−	0.558300i
$441$	−5.22072	+	0.487464i	−0.248606	+	0.0232126i
$442$	−11.5940	−	2.09896i	−0.551469	−	0.0998372i
$443$	−8.00990	−	4.62452i	−0.380562	−	0.219717i	0.297501	−	0.954722i	$-0.403847\pi$
$443$	−8.00990	−	4.62452i	−0.380562	−	0.219717i	−0.678063	+	0.735004i	$0.737180\pi$
$444$	3.81254	−	3.45021i	0.180935	−	0.163740i
$445$	6.84398	−	3.95137i	0.324436	−	0.187313i
$446$	−3.53064	+	1.26682i	−0.167181	+	0.0599858i
$447$	21.2362	+	10.9762i	1.00444	+	0.519159i
$448$	−0.502198	+	18.3272i	−0.0237266	+	0.865881i
$449$			12.5301i			0.591333i	0.955291	+	0.295666i	$0.0955417\pi$
$449$			12.5301i			0.591333i	−0.955291	+	0.295666i	$0.904458\pi$
$450$	4.22696	+	0.364407i	0.199261	+	0.0171783i
$451$	32.5385			1.53218
$452$	13.5989	+	16.5104i	0.639638	+	0.776583i
$453$	−10.7738	+	0.501888i	−0.506197	+	0.0235808i
$454$	−10.7471	+	3.85613i	−0.504385	+	0.180977i
$455$	1.65802	+	2.87177i	0.0777292	+	0.134631i
$456$	27.1302	−	0.891634i	1.27049	−	0.0417546i
$457$	−6.70697	+	11.6168i	−0.313739	+	0.543411i	−0.979169	−	0.203049i	$-0.934915\pi$
$457$	−6.70697	+	11.6168i	−0.313739	+	0.543411i	0.665430	+	0.746460i	$0.268248\pi$
$458$	−5.19505	+	28.6958i	−0.242749	+	1.34087i
$459$	29.6281	−	4.16472i	1.38292	−	0.194393i
$460$	−3.29169	−	1.23223i	−0.153476	−	0.0574531i
$461$	10.0482	−	17.4040i	0.467991	−	0.810585i	−0.531340	−	0.847159i	$-0.678311\pi$
$461$	10.0482	−	17.4040i	0.467991	−	0.810585i	0.999331	+	0.0365742i	$0.0116445\pi$
$462$	−25.0129	+	10.3124i	−1.16371	+	0.479777i
$463$	−11.4573	+	6.61488i	−0.532466	+	0.307419i	−0.742020	−	0.670378i	$-0.766132\pi$
$463$	−11.4573	+	6.61488i	−0.532466	+	0.307419i	0.209554	+	0.977797i	$0.432799\pi$
$464$	5.91041	−	30.2755i	0.274384	−	1.40550i
$465$	−4.75781	+	0.221639i	−0.220638	+	0.0102783i
$466$	−27.6647	−	23.4296i	−1.28154	−	1.08535i
$467$			22.9628i			1.06259i	0.847187	+	0.531295i	$0.178294\pi$
$467$			22.9628i			1.06259i	−0.847187	+	0.531295i	$0.821706\pi$
$468$	−8.39316	+	2.21931i	−0.387974	+	0.102588i
$469$		−	1.18594i		−	0.0547614i
$470$	−10.7301	+	12.6697i	−0.494943	+	0.584410i
$471$	−2.61255	+	5.05462i	−0.120380	+	0.232905i
$472$	23.0878	+	0.316263i	1.06270	+	0.0145572i
$473$	4.28502	−	2.47396i	0.197026	−	0.113753i
$474$	−12.1530	+	15.7841i	−0.558206	+	0.724990i
$475$	−2.77046	+	4.79858i	−0.127118	+	0.220174i
$476$	−24.7168	−	9.25266i	−1.13289	−	0.424095i
$477$	−17.8513	+	38.8727i	−0.817353	+	1.77986i
$478$	15.1112	+	2.73570i	0.691168	+	0.125128i
$479$	13.6957	−	23.7216i	0.625771	−	1.08387i	−0.362621	−	0.931937i	$-0.618118\pi$
$479$	13.6957	−	23.7216i	0.625771	−	1.08387i	0.988391	−	0.151930i	$-0.0485487\pi$
$480$	7.35418	−	6.47426i	0.335671	−	0.295508i
$481$	−1.07388	−	1.86001i	−0.0489647	−	0.0848093i
$482$	2.70613	+	7.54200i	0.123261	+	0.343529i
$483$	3.76528	+	5.87242i	0.171326	+	0.267205i
$484$	18.8774	−	15.5485i	0.858062	−	0.706748i
$485$	3.10796			0.141125
$486$	18.4733	−	12.0307i	0.837965	−	0.545724i
$487$		−	13.4969i		−	0.611602i	−0.952096	−	0.305801i	$-0.901076\pi$
$487$		−	13.4969i		−	0.611602i	0.952096	−	0.305801i	$-0.0989241\pi$
$488$	−3.63341	−	6.49718i	−0.164477	−	0.294114i
$489$	13.6502	−	8.75221i	0.617282	−	0.395789i
$490$	−0.834784	−	2.32655i	−0.0377117	−	0.105103i
$491$	20.8309	−	12.0267i	0.940086	−	0.542759i	0.0500985	−	0.998744i	$-0.484046\pi$
$491$	20.8309	−	12.0267i	0.940086	−	0.542759i	0.889987	+	0.455986i	$0.150713\pi$
$492$	22.2608	+	7.17119i	1.00359	+	0.323302i
$493$	38.4551	+	22.2021i	1.73193	+	0.999931i
$494$	2.01983	−	11.1569i	0.0908765	−	0.501973i
$495$	13.1394	+	6.03394i	0.590574	+	0.271205i
$496$	−7.22312	+	8.29567i	−0.324328	+	0.372486i
$497$	−17.0825	−	9.86258i	−0.766254	−	0.442397i
$498$	13.3448	−	17.3321i	0.597996	−	0.776670i
$499$	3.24887	+	5.62721i	0.145440	+	0.251909i	0.929537	−	0.368729i	$-0.120207\pi$
$499$	3.24887	+	5.62721i	0.145440	+	0.251909i	−0.784097	+	0.620638i	$0.786874\pi$
$500$	0.329296	+	1.97270i	0.0147266	+	0.0882220i
$501$	8.22443	+	4.25092i	0.367441	+	0.189917i
$502$	10.3303	+	8.74887i	0.461066	+	0.390481i
$503$	−1.59845			−0.0712715			−0.0356358	−	0.999365i	$-0.511346\pi$
$503$	−1.59845			−0.0712715			−0.0356358	+	0.999365i	$0.511346\pi$
$504$	−19.3850	+	1.54248i	−0.863477	+	0.0687077i
$505$	18.7500			0.834363
$506$	−9.14054	−	7.74121i	−0.406346	−	0.344139i
$507$	−0.879041	−	18.8699i	−0.0390396	−	0.838043i
$508$	−35.9930	+	6.00818i	−1.59693	+	0.266570i
$509$	4.54557	+	7.87316i	0.201479	+	0.348972i	0.949005	−	0.315261i	$-0.102092\pi$
$509$	4.54557	+	7.87316i	0.201479	+	0.348972i	−0.747526	+	0.664232i	$0.768759\pi$
$510$	5.37593	+	13.0394i	0.238050	+	0.577394i
$511$	3.15984	+	1.82433i	0.139783	+	0.0807038i
$512$	0.929551	−	22.6083i	0.0410807	−	0.999156i
$513$	4.00772	+	28.5112i	0.176945	+	1.25880i
$514$	4.90643	−	27.1016i	0.216413	−	1.19540i
$515$	−6.86735	−	3.96487i	−0.302612	−	0.174713i
$516$	3.47678	−	0.748146i	0.153057	−	0.0329353i
$517$	−49.0013	+	28.2909i	−2.15507	+	1.24423i
$518$	−1.62475	−	4.52818i	−0.0713873	−	0.198957i
$519$	−0.516014	−	11.0770i	−0.0226505	−	0.486227i
$520$	−1.99754	−	3.57195i	−0.0875979	−	0.156640i
$521$		−	40.4109i		−	1.77044i	−0.465177	−	0.885218i	$-0.654009\pi$
$521$		−	40.4109i		−	1.77044i	0.465177	−	0.885218i	$-0.345991\pi$
$522$	32.5973	+	2.81022i	1.42674	+	0.123000i
$523$	42.9790			1.87934			0.939670	−	0.342084i	$-0.111133\pi$
$523$	42.9790			1.87934			0.939670	+	0.342084i	$0.111133\pi$
$524$	−5.49907	−	6.67641i	−0.240228	−	0.291660i
$525$	1.82261	−	3.52628i	0.0795452	−	0.153900i
$526$	−7.90532	−	22.0322i	−0.344688	−	0.960648i
$527$	−7.91696	−	13.7126i	−0.344868	−	0.597329i
$528$	31.0416	−	12.3032i	1.35091	−	0.535430i
$529$	9.95580	−	17.2439i	0.432861	−	0.749737i
$530$	−19.8421	−	3.59218i	−0.861885	−	0.156034i
$531$	2.27681	+	24.3845i	0.0988051	+	1.05820i
$532$	8.90385	−	23.7851i	0.386031	−	1.03121i
$533$	4.88439	−	8.46001i	0.211566	−	0.366444i
$534$	19.1879	+	2.55832i	0.830342	+	0.110709i
$535$	−3.88900	+	2.24531i	−0.168136	+	0.0970733i
$536$	−0.0200475	+	1.46351i	−0.000865922	+	0.0632139i
$537$	−22.8624	−	35.6568i	−0.986584	−	1.53870i
$538$	15.5983	−	18.4179i	0.672492	−	0.794053i
$539$		−	8.42367i		−	0.362833i
$540$	7.65934	+	7.02385i	0.329606	+	0.302258i
$541$		−	37.6705i		−	1.61958i	−0.586720	−	0.809790i	$-0.699581\pi$
$541$		−	37.6705i		−	1.61958i	0.586720	−	0.809790i	$-0.300419\pi$
$542$	33.3349	+	28.2316i	1.43186	+	1.21265i
$543$	14.7361	+	22.9828i	0.632388	+	0.986288i
$544$	30.3455	+	11.8361i	1.30105	+	0.507469i
$545$	−10.5894	+	6.11379i	−0.453600	+	0.261886i
$546$	−1.07349	+	8.05136i	−0.0459410	+	0.344566i
$547$	−6.28445	+	10.8850i	−0.268704	+	0.465408i	−0.968527	−	0.248907i	$-0.919929\pi$
$547$	−6.28445	+	10.8850i	−0.268704	+	0.465408i	0.699824	+	0.714316i	$0.253262\pi$
$548$	6.84872	−	18.2952i	0.292563	−	0.781530i
$549$	6.44124	−	4.56644i	0.274905	−	0.194891i
$550$	−1.21420	+	6.70686i	−0.0517737	+	0.285982i
$551$	−21.3651	+	37.0054i	−0.910184	+	1.57648i
$552$	−4.54728	−	7.31054i	−0.193545	−	0.311157i
$553$	9.31900	+	16.1410i	0.396284	+	0.686385i
$554$	16.5940	−	5.95408i	0.705014	−	0.252965i
$555$	−1.18048	+	2.28393i	−0.0501087	+	0.0969474i
$556$	−25.8828	+	21.3185i	−1.09767	+	0.904107i
$557$	28.9978			1.22868			0.614338	−	0.789043i	$-0.289423\pi$
$557$	28.9978			1.22868			0.614338	+	0.789043i	$0.289423\pi$
$558$	−9.56541	−	6.67970i	−0.404936	−	0.282774i
$559$		−	1.48547i		−	0.0628288i
$560$	−2.97748	−	8.67004i	−0.125822	−	0.366376i
$561$	2.23669	+	48.0140i	0.0944333	+	2.02715i
$562$	12.6704	−	4.54624i	0.534468	−	0.191772i
$563$	33.1963	−	19.1659i	1.39906	−	0.807746i	0.404763	−	0.914421i	$-0.367354\pi$
$563$	33.1963	−	19.1659i	1.39906	−	0.807746i	0.994294	+	0.106675i	$0.0340205\pi$
$564$	−39.7586	+	8.55541i	−1.67414	+	0.360248i
$565$	−9.26205	−	5.34744i	−0.389657	−	0.224969i
$566$	9.79012	+	1.77239i	0.411509	+	0.0744991i
$567$	−3.81843	−	20.2694i	−0.160359	−	0.851233i
$568$	20.9140	+	12.4597i	0.877531	+	0.522798i
$569$	−0.687580	−	0.396975i	−0.0288249	−	0.0166420i	0.485518	−	0.874226i	$-0.338631\pi$
$569$	−0.687580	−	0.396975i	−0.0288249	−	0.0166420i	−0.514343	+	0.857584i	$0.671964\pi$
$570$	−12.5478	+	5.17327i	−0.525571	+	0.216684i
$571$	5.57685	+	9.65939i	0.233384	+	0.404233i	0.958802	−	0.284076i	$-0.0916867\pi$
$571$	5.57685	+	9.65939i	0.233384	+	0.404233i	−0.725418	+	0.688309i	$0.758353\pi$
$572$	−2.29638	−	13.7568i	−0.0960165	−	0.575203i
$573$	−1.52408	−	32.7166i	−0.0636693	−	1.36676i
$574$	14.1415	−	16.6978i	0.590255	−	0.696951i
$575$	1.75739			0.0732880
$576$	23.9482	−	1.57582i	0.997842	−	0.0656590i
$577$	−18.2610			−0.760216			−0.380108	−	0.924942i	$-0.624113\pi$
$577$	−18.2610			−0.760216			−0.380108	+	0.924942i	$0.624113\pi$
$578$	−14.7648	+	17.4337i	−0.614133	+	0.725146i
$579$	−27.8421	−	14.3906i	−1.15708	−	0.598052i
$580$	2.53945	+	15.2130i	0.105445	+	0.631685i
$581$	−10.2329	−	17.7239i	−0.424533	−	0.735312i
$582$	6.03207	+	4.64439i	0.250038	+	0.192516i
$583$	−59.5132	−	34.3599i	−2.46478	−	1.42304i
$584$	−3.86857	−	2.30474i	−0.160083	−	0.0953709i
$585$	3.54120	−	2.51049i	0.146410	−	0.103796i
$586$	28.0250	+	5.07361i	1.15770	+	0.209589i
$587$	−29.5206	−	17.0437i	−1.21845	−	0.703470i	−0.253860	−	0.967241i	$-0.581700\pi$
$587$	−29.5206	−	17.0437i	−1.21845	−	0.703470i	−0.964585	+	0.263771i	$0.915034\pi$
$588$	1.85650	−	5.76294i	0.0765607	−	0.237660i
$589$	13.1956	−	7.61851i	0.543717	−	0.313915i
$590$	−10.8666	+	3.89904i	−0.447373	+	0.160521i
$591$	8.35943	−	5.35989i	0.343861	−	0.220476i
$592$	1.92848	+	5.61548i	0.0792600	+	0.230795i
$593$		−	40.7565i		−	1.67367i	−0.547455	−	0.836835i	$-0.684403\pi$
$593$		−	40.7565i		−	1.67367i	0.547455	−	0.836835i	$-0.315597\pi$
$594$	16.4848	+	31.3460i	0.676381	+	1.28614i
$595$	13.1960			0.540982
$596$	−21.3065	+	17.5492i	−0.872747	+	0.718843i
$597$	9.92711	+	15.4826i	0.406290	+	0.633660i
$598$	−3.38481	+	1.21450i	−0.138415	+	0.0496645i
$599$	−11.3357	−	19.6340i	−0.463163	−	0.802221i	0.535954	−	0.844247i	$-0.319952\pi$
$599$	−11.3357	−	19.6340i	−0.463163	−	0.802221i	−0.999117	+	0.0420259i	$0.986619\pi$
$600$	−2.30881	+	4.32081i	−0.0942567	+	0.176396i
$601$	2.06681	−	3.57983i	0.0843071	−	0.146024i	−0.820789	−	0.571232i	$-0.806466\pi$
$601$	2.06681	−	3.57983i	0.0843071	−	0.146024i	0.905096	+	0.425208i	$0.139799\pi$
$602$	0.592746	−	3.27414i	0.0241585	−	0.133444i
$603$	−1.54571	+	0.144324i	−0.0629460	+	0.00587734i
$604$	4.36620	−	11.6635i	0.177658	−	0.474583i
$605$	−6.11407	+	10.5899i	−0.248572	+	0.430540i
$606$	36.3909	+	28.0192i	1.47828	+	1.13820i
$607$	20.7120	−	11.9581i	0.840673	−	0.485363i	−0.0168199	−	0.999859i	$-0.505354\pi$
$607$	20.7120	−	11.9581i	0.840673	−	0.485363i	0.857493	+	0.514496i	$0.172021\pi$
$608$	−11.3899	+	29.2015i	−0.461922	+	1.18428i
$609$	14.0555	−	27.1938i	0.569558	−	1.10195i
$610$	2.84031	+	2.40549i	0.115001	+	0.0973955i
$611$			16.9871i			0.687224i
$612$	−9.05164	+	33.3411i	−0.365891	+	1.34773i
$613$			13.8172i			0.558071i	0.960281	+	0.279036i	$0.0900148\pi$
$613$			13.8172i			0.558071i	−0.960281	+	0.279036i	$0.909985\pi$
$614$	−24.5849	+	29.0290i	−0.992167	+	1.17151i
$615$	−11.6810	+	0.544151i	−0.471024	+	0.0219423i
$616$	0.427905	−	31.2379i	0.0172408	−	1.25861i
$617$	−2.89338	+	1.67049i	−0.116483	+	0.0672516i	−0.557110	−	0.830439i	$-0.688090\pi$
$617$	−2.89338	+	1.67049i	−0.116483	+	0.0672516i	0.440626	+	0.897691i	$0.354756\pi$
$618$	−7.40357	−	17.9575i	−0.297815	−	0.722356i
$619$	−13.2069	+	22.8750i	−0.530830	+	0.919424i	0.468523	+	0.883451i	$0.344786\pi$
$619$	−13.2069	+	22.8750i	−0.530830	+	0.919424i	−0.999353	+	0.0359725i	$0.988547\pi$
$620$	1.92816	−	5.15074i	0.0774367	−	0.206859i
$621$	7.19569	−	5.62218i	0.288753	−	0.225610i
$622$	4.99228	+	0.903795i	0.200172	+	0.0362389i
$623$	9.05562	−	15.6848i	0.362806	−	0.628398i
$624$	1.46084	−	9.91766i	0.0584806	−	0.397024i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.954447	+	2.66005i	0.0381474	+	0.106317i
$627$	−46.2040	+	2.15238i	−1.84521	+	0.0859576i
$628$	−4.17704	−	5.07134i	−0.166682	−	0.202368i
$629$	−8.54686			−0.340786
$630$	8.80693	−	4.12035i	0.350877	−	0.164159i
$631$		−	3.75024i		−	0.149295i	−0.997210	−	0.0746473i	$-0.976217\pi$
$631$		−	3.75024i		−	0.149295i	0.997210	−	0.0746473i	$-0.0237831\pi$
$632$	−11.2273	−	20.0764i	−0.446598	−	0.798595i
$633$	9.49978	+	4.91010i	0.377582	+	0.195159i
$634$	10.4945	+	29.2481i	0.416788	+	1.16159i
$635$	15.8011	−	9.12276i	0.627047	−	0.362026i
$636$	−33.1425	−	36.6230i	−1.31419	−	1.45220i
$637$	−2.19015	−	1.26449i	−0.0867770	−	0.0501007i
$638$	−9.36361	+	51.7216i	−0.370709	+	2.04768i
$639$	−10.7757	+	23.4650i	−0.426279	+	0.928260i
$640$	3.52781	+	10.7496i	0.139449	+	0.424916i
$641$	−39.2789	−	22.6777i	−1.55142	−	0.895714i	−0.998026	−	0.0627956i	$-0.979998\pi$
$641$	−39.2789	−	22.6777i	−1.55142	−	0.895714i	−0.553396	−	0.832918i	$-0.686668\pi$
$642$	−10.9033	−	1.45373i	−0.430317	−	0.0573742i
$643$	7.73762	+	13.4020i	0.305142	+	0.528522i	0.977293	−	0.211893i	$-0.0679627\pi$
$643$	7.73762	+	13.4020i	0.305142	+	0.528522i	−0.672151	+	0.740414i	$0.734629\pi$
$644$	−7.94510	+	1.32625i	−0.313081	+	0.0522614i
$645$	−1.49691	+	0.959787i	−0.0589407	+	0.0377916i
$646$	−34.4311	−	29.1600i	−1.35467	−	1.14729i
$647$	15.4442			0.607174			0.303587	−	0.952804i	$-0.401816\pi$
$647$	15.4442			0.607174			0.303587	+	0.952804i	$0.401816\pi$
$648$	4.36951	+	25.0780i	0.171651	+	0.985158i
$649$	−39.3446			−1.54441
$650$	1.56152	+	1.32247i	0.0612478	+	0.0518714i
$651$	−9.18899	+	5.89179i	−0.360145	+	0.230917i
$652$	3.08280	+	18.4680i	0.120732	+	0.723263i
$653$	−3.02021	−	5.23116i	−0.118190	−	0.204711i	0.800860	−	0.598851i	$-0.204376\pi$
$653$	−3.02021	−	5.23116i	−0.118190	−	0.204711i	−0.919050	+	0.394140i	$0.871043\pi$
$654$	−29.6886	−	3.95838i	−1.16092	−	0.154785i
$655$	3.74535	+	2.16238i	0.146343	+	0.0844912i
$656$	−17.7336	+	20.3669i	−0.692383	+	0.795193i
$657$	1.99323	−	4.34044i	0.0777634	−	0.169337i
$658$	−6.77833	+	37.4414i	−0.264247	+	1.45962i
$659$	17.7747	+	10.2623i	0.692406	+	0.399761i	0.804513	−	0.593936i	$-0.202427\pi$
$659$	17.7747	+	10.2623i	0.692406	+	0.399761i	−0.112107	+	0.993696i	$0.535760\pi$
$660$	−12.3790	+	11.2026i	−0.481853	+	0.436059i
$661$	8.31943	−	4.80322i	0.323588	−	0.186824i	−0.329403	−	0.944190i	$-0.606847\pi$
$661$	8.31943	−	4.80322i	0.323588	−	0.186824i	0.652991	+	0.757366i	$0.273514\pi$
$662$	−5.57881	−	15.5482i	−0.216827	−	0.604297i
$663$	12.8194	+	6.62589i	0.497864	+	0.257328i
$664$	12.3284	+	22.0453i	0.478433	+	0.855522i
$665$			12.6985i			0.492427i
$666$	−5.70414	+	2.66870i	−0.221031	+	0.103410i
$667$	13.5525			0.524755
$668$	−8.25164	+	6.79652i	−0.319266	+	0.262965i
$669$	4.58908	−	0.213779i	0.177424	−	0.00826516i
$670$	−0.247156	−	0.688824i	−0.00954845	−	0.0266116i
$671$	6.34229	+	10.9852i	0.244841	+	0.424078i
$672$	7.17729	−	21.2767i	0.276870	−	0.820765i
$673$	21.4029	−	37.0709i	0.825022	−	1.42898i	−0.0768807	−	0.997040i	$-0.524496\pi$
$673$	21.4029	−	37.0709i	0.825022	−	1.42898i	0.901903	−	0.431940i	$-0.142171\pi$
$674$	24.3305	+	4.40476i	0.937176	+	0.169665i
$675$	−4.81784	−	1.94639i	−0.185439	−	0.0749166i
$676$	20.4283	+	7.64726i	0.785704	+	0.294125i
$677$	4.77157	−	8.26459i	0.183386	−	0.317634i	−0.759645	−	0.650338i	$-0.774627\pi$
$677$	4.77157	−	8.26459i	0.183386	−	0.317634i	0.943032	+	0.332703i	$0.107961\pi$
$678$	−9.98525	−	24.2194i	−0.383481	−	0.930140i
$679$	6.16844	−	3.56135i	0.236723	−	0.136672i
$680$	−16.2845	−	0.223070i	−0.624483	−	0.00855435i
$681$	13.9689	−	0.650730i	0.535290	−	0.0249360i
$682$	12.1132	−	14.3028i	0.463839	−	0.547684i
$683$			23.4655i			0.897882i	0.893561	+	0.448941i	$0.148199\pi$
$683$			23.4655i			0.897882i	−0.893561	+	0.448941i	$0.851801\pi$
$684$	−32.0842	−	8.71041i	−1.22677	−	0.333051i
$685$			9.76752i			0.373198i
$686$	−21.6355	−	18.3233i	−0.826047	−	0.699588i
$687$	16.3995	−	31.7288i	0.625679	−	1.21053i
$688$	−0.786828	+	4.03045i	−0.0299975	+	0.153659i
$689$	−17.8672	+	10.3156i	−0.680684	+	0.392993i
$690$	3.41082	+	2.62616i	0.129848	+	0.0999762i
$691$	−18.1002	+	31.3506i	−0.688566	+	1.19263i	0.283736	+	0.958902i	$0.408426\pi$
$691$	−18.1002	+	31.3506i	−0.688566	+	1.19263i	−0.972302	+	0.233729i	$0.924907\pi$
$692$	11.9918	+	4.48909i	0.455860	+	0.170650i
$693$	32.9924	−	3.08053i	1.25328	−	0.117020i
$694$	4.40585	−	24.3365i	0.167244	−	0.923803i
$695$	8.38301	−	14.5198i	0.317986	−	0.550767i
$696$	−17.8049	+	33.3210i	−0.674895	+	1.26303i
$697$	−19.4371	−	33.6661i	−0.736233	−	1.27519i
$698$	−12.9913	+	4.66138i	−0.491728	+	0.176436i
$699$	23.9656	+	37.3774i	0.906463	+	1.41374i
$700$	2.91405	+	3.53795i	0.110141	+	0.133722i
$701$	24.8086			0.937006			0.468503	−	0.883462i	$-0.344793\pi$
$701$	24.8086			0.937006			0.468503	+	0.883462i	$0.344793\pi$
$702$	10.6245	+	0.419323i	0.400996	+	0.0158263i
$703$		−	8.22466i		−	0.310199i
$704$	−1.05612	+	38.5420i	−0.0398039	+	1.45261i
$705$	17.1179	−	10.9756i	0.644696	−	0.413366i
$706$	25.0292	−	8.98066i	0.941985	−	0.337992i
$707$	37.2136	−	21.4853i	1.39956	−	0.808037i
$708$	−26.9171	−	8.67119i	−1.01161	−	0.325883i
$709$	−2.45567	−	1.41778i	−0.0922247	−	0.0532460i	0.453178	−	0.891420i	$-0.350290\pi$
$709$	−2.45567	−	1.41778i	−0.0922247	−	0.0532460i	−0.545403	+	0.838174i	$0.683623\pi$
$710$	−11.9774	−	2.16837i	−0.449504	−	0.0813775i
$711$	19.9035	−	14.1104i	0.746440	−	0.529180i
$712$	−11.4403	+	19.2028i	−0.428742	+	0.719656i
$713$	−4.18519	−	2.41632i	−0.156737	−	0.0904919i
$714$	25.6114	+	19.7195i	0.958482	+	0.737983i
$715$	3.48680	+	6.03931i	0.130399	+	0.225857i
$716$	48.2418	−	8.05283i	1.80288	−	0.300949i
$717$	−16.7083	−	8.63593i	−0.623983	−	0.322515i
$718$	−13.1262	+	15.4989i	−0.489865	+	0.578415i
$719$	35.5060			1.32415			0.662076	−	0.749437i	$-0.269676\pi$
$719$	35.5060			1.32415			0.662076	+	0.749437i	$0.269676\pi$
$720$	−10.9379	+	4.93586i	−0.407631	+	0.183949i
$721$	−18.1731			−0.676801
$722$	10.6952	−	12.6285i	0.398034	−	0.469984i
$723$	−0.456665	−	9.80301i	−0.0169836	−	0.364578i
$724$	−31.0947	+	5.19052i	−1.15562	+	0.192904i
$725$	−3.85587	−	6.67857i	−0.143204	−	0.248036i
$726$	−27.6915	+	11.4168i	−1.02773	+	0.423716i
$727$	−1.95609	−	1.12935i	−0.0725472	−	0.0418852i	0.463288	−	0.886208i	$-0.346670\pi$
$727$	−1.95609	−	1.12935i	−0.0725472	−	0.0418852i	−0.535835	+	0.844323i	$0.680003\pi$
$728$	−8.05761	−	4.80040i	−0.298635	−	0.177915i
$729$	−25.9537	+	7.44352i	−0.961248	+	0.275686i
$730$	2.21552	+	0.401095i	0.0820002	+	0.0148452i
$731$	−5.11937	−	2.95567i	−0.189347	−	0.109319i
$732$	1.91796	+	8.91314i	0.0708900	+	0.329439i
$733$	43.5068	−	25.1187i	1.60696	−	0.927780i	0.616917	−	0.787028i	$-0.288381\pi$
$733$	43.5068	−	25.1187i	1.60696	−	0.927780i	0.990045	−	0.140752i	$-0.0449519\pi$
$734$	38.3146	−	13.7476i	1.41422	−	0.507433i
$735$	0.140871	+	3.02402i	0.00519612	+	0.111543i
$736$	9.82710	−	1.50235i	0.362232	−	0.0553774i
$737$		−	2.49401i		−	0.0918680i
$738$	−23.4843	−	16.3995i	−0.864468	−	0.603674i
$739$	−33.1684			−1.22012			−0.610060	−	0.792355i	$-0.708855\pi$
$739$	−33.1684			−1.22012			−0.610060	+	0.792355i	$0.708855\pi$
$740$	−1.88740	−	2.29148i	−0.0693820	−	0.0842366i
$741$	−6.37611	+	12.3361i	−0.234232	+	0.453179i
$742$	−43.4974	+	15.6072i	−1.59684	+	0.572958i
$743$	−15.9461	−	27.6194i	−0.585005	−	1.01326i	−0.994875	−	0.101115i	$-0.967759\pi$
$743$	−15.9461	−	27.6194i	−0.585005	−	1.01326i	0.409870	−	0.912144i	$-0.365574\pi$
$744$	11.4393	−	7.11545i	0.419385	−	0.260865i
$745$	6.90081	−	11.9526i	0.252826	−	0.437908i
$746$	−4.78039	+	26.4054i	−0.175023	+	0.966769i
$747$	−21.8554	+	15.4942i	−0.799649	+	0.566902i
$748$	−51.9792	−	19.4582i	−1.90055	−	0.711463i
$749$	−5.14573	+	8.91267i	−0.188021	+	0.325662i
$750$	0.323726	−	2.42800i	0.0118208	−	0.0886582i
$751$	39.2920	−	22.6852i	1.43378	−	0.827796i	0.436378	−	0.899763i	$-0.356261\pi$
$751$	39.2920	−	22.6852i	1.43378	−	0.827796i	0.997407	+	0.0719673i	$0.0229277\pi$
$752$	8.99775	−	46.0901i	0.328114	−	1.68073i
$753$	−8.94905	−	13.9572i	−0.326121	−	0.508627i
$754$	12.0420	+	10.1985i	0.438545	+	0.371408i
$755$			6.22700i			0.226624i
$756$	23.2502	+	5.16371i	0.845602	+	0.187802i
$757$		−	2.47825i		−	0.0900735i	−0.998985	−	0.0450367i	$-0.985660\pi$
$757$		−	2.47825i		−	0.0900735i	0.998985	−	0.0450367i	$-0.0143405\pi$
$758$	−24.5218	+	28.9545i	−0.890674	+	1.05167i
$759$	7.91833	+	12.3496i	0.287417	+	0.448264i
$760$	0.214661	−	15.6706i	0.00778656	−	0.568434i
$761$	−21.4218	+	12.3679i	−0.776539	+	0.448335i	−0.835202	−	0.549943i	$-0.814649\pi$
$761$	−21.4218	+	12.3679i	−0.776539	+	0.448335i	0.0586635	+	0.998278i	$0.481316\pi$
$762$	44.3002	+	5.90654i	1.60483	+	0.213971i
$763$	−14.0114	+	24.2684i	−0.507245	+	0.878575i
$764$	35.4185	+	13.2588i	1.28140	+	0.479686i
$765$	−1.60590	−	17.1992i	−0.0580616	−	0.621837i
$766$	0.671919	+	0.121643i	0.0242774	+	0.00439515i
$767$	−5.90606	+	10.2296i	−0.213255	+	0.369369i
$768$	−9.21683	+	26.1352i	−0.332584	+	0.943074i
$769$	−14.6214	−	25.3250i	−0.527262	−	0.913244i	−0.999495	−	0.0317706i	$-0.989885\pi$
$769$	−14.6214	−	25.3250i	−0.527262	−	0.913244i	0.472233	−	0.881474i	$-0.343448\pi$
$770$	5.27542	+	14.7026i	0.190113	+	0.529846i
$771$	−15.4884	+	29.9660i	−0.557800	+	1.07920i
$772$	27.9342	−	23.0081i	1.00537	−	0.828081i
$773$	−37.9604			−1.36534			−0.682671	−	0.730726i	$-0.739182\pi$
$773$	−37.9604			−1.36534			−0.682671	+	0.730726i	$0.739182\pi$
$774$	−4.33954	−	0.374113i	−0.155982	−	0.0134472i
$775$			2.74990i			0.0987795i
$776$	−7.67239	+	4.29063i	−0.275423	+	0.154024i
$777$	0.274179	+	5.88567i	0.00983613	+	0.211147i
$778$	−10.9790	−	30.5984i	−0.393615	−	1.09701i
$779$	32.3969	−	18.7044i	1.16074	−	0.670154i
$780$	1.05444	+	4.90017i	0.0377549	+	0.175454i
$781$	−35.9243	−	20.7409i	−1.28547	−	0.742168i
$782$	−2.54930	+	14.0815i	−0.0911628	+	0.503555i
$783$	−37.1539	−	15.0101i	−1.32777	−	0.536416i
$784$	5.27264	+	4.59094i	0.188309	+	0.163962i
$785$	2.84493	+	1.64252i	0.101540	+	0.0586242i
$786$	4.03780	+	9.79375i	0.144024	+	0.349331i
$787$	10.4918	+	18.1724i	0.373993	+	0.647776i	0.990176	−	0.139828i	$-0.0446549\pi$
$787$	10.4918	+	18.1724i	0.373993	+	0.647776i	−0.616182	+	0.787604i	$0.711322\pi$
$788$	1.88792	+	11.3099i	0.0672543	+	0.402898i
$789$	1.33404	+	28.6371i	0.0474930	+	1.01951i
$790$	8.77661	+	7.43300i	0.312258	+	0.264454i
$791$	−24.5102			−0.871482
$792$	−40.7665	+	3.24383i	−1.44857	+	0.115264i
$793$	3.80819			0.135233
$794$	−20.2233	−	17.1273i	−0.717697	−	0.607825i
$795$	21.9393	+	11.3396i	0.778105	+	0.402175i
$796$	−20.9472	+	3.49663i	−0.742453	+	0.123935i
$797$	−8.54378	−	14.7983i	−0.302636	−	0.524181i	0.674096	−	0.738644i	$-0.264533\pi$
$797$	−8.54378	−	14.7983i	−0.302636	−	0.524181i	−0.976732	+	0.214462i	$0.931200\pi$
$798$	−18.9761	+	24.6459i	−0.671746	+	0.872455i
$799$	58.5424	+	33.7995i	2.07108	+	1.19574i
$800$	−3.53629	−	4.41528i	−0.125027	−	0.156104i
$801$	−21.5451	−	9.89400i	−0.761257	−	0.349587i
$802$	−1.35553	+	7.48753i	−0.0478655	+	0.264394i
$803$	6.64511	+	3.83656i	0.234501	+	0.135389i
$804$	0.549656	−	1.70624i	0.0193849	−	0.0601745i
$805$	3.48793	−	2.01376i	0.122933	−	0.0709756i
$806$	−1.90041	−	5.29645i	−0.0669390	−	0.186559i
$807$	−24.8842	+	15.9552i	−0.875965	+	0.561651i
$808$	−46.2868	+	25.8849i	−1.62836	+	0.910628i
$809$			10.3555i			0.364081i	0.983291	+	0.182041i	$0.0582702\pi$
$809$			10.3555i			0.364081i	−0.983291	+	0.182041i	$0.941730\pi$
$810$	−6.44210	−	10.9772i	−0.226352	−	0.385700i
$811$	−7.56927			−0.265793			−0.132897	−	0.991130i	$-0.542428\pi$
$811$	−7.56927			−0.265793			−0.132897	+	0.991130i	$0.542428\pi$
$812$	22.4724	+	27.2837i	0.788628	+	0.957472i
$813$	−28.8776	−	45.0383i	−1.01278	−	1.57956i
$814$	−3.41682	−	9.52271i	−0.119760	−	0.333771i
$815$	−4.68089	−	8.10753i	−0.163964	−	0.283994i
$816$	−31.2725	−	24.7678i	−1.09476	−	0.867047i
$817$	2.84425	−	4.92638i	0.0995077	−	0.172352i
$818$	22.7297	+	4.11495i	0.794726	+	0.143876i
$819$	4.15158	−	9.04044i	0.145068	−	0.315898i
$820$	4.73387	−	12.6457i	0.165314	−	0.441607i
$821$	3.33349	−	5.77377i	0.116340	−	0.201506i	−0.801975	−	0.597358i	$-0.796217\pi$
$821$	3.33349	−	5.77377i	0.116340	−	0.201506i	0.918314	+	0.395852i	$0.129551\pi$
$822$	−14.5962	+	18.9573i	−0.509099	+	0.661211i
$823$	31.9184	−	18.4281i	1.11261	−	0.642364i	0.173104	−	0.984904i	$-0.444620\pi$
$823$	31.9184	−	18.4281i	1.11261	−	0.642364i	0.939503	+	0.342540i	$0.111287\pi$
$824$	22.4266	+	0.307205i	0.781266	+	0.0107020i
$825$	3.83293	−	7.41573i	0.133445	−	0.258183i
$826$	−17.0995	+	20.1904i	−0.594967	+	0.702515i
$827$			19.7107i			0.685407i	0.939444	+	0.342703i	$0.111343\pi$
$827$			19.7107i			0.685407i	−0.939444	+	0.342703i	$0.888657\pi$
$828$	2.69547	+	10.1940i	0.0936742	+	0.354265i
$829$			5.91969i			0.205599i	0.994702	+	0.102800i	$0.0327801\pi$
$829$			5.91969i			0.205599i	−0.994702	+	0.102800i	$0.967220\pi$
$830$	−9.63732	−	8.16195i	−0.334516	−	0.283305i
$831$	−21.5687	+	1.00476i	−0.748211	+	0.0348548i
$832$	9.86238	+	6.06017i	0.341916	+	0.210098i
$833$	−8.71557	+	5.03194i	−0.301977	+	0.174346i
$834$	37.9679	−	15.6535i	1.31472	−	0.542038i
$835$	2.67257	−	4.62903i	0.0924881	−	0.160194i
$836$	18.7247	−	50.0197i	0.647607	−	1.72997i
$837$	8.79742	+	11.2596i	0.304083	+	0.389189i
$838$	−3.71261	+	20.5073i	−0.128250	+	0.708413i
$839$	−22.1403	+	38.3482i	−0.764369	+	1.32393i	0.176210	+	0.984353i	$0.443616\pi$
$839$	−22.1403	+	38.3482i	−0.764369	+	1.32393i	−0.940579	+	0.339574i	$0.889717\pi$
$840$	0.368786	+	11.2213i	0.0127243	+	0.387170i
$841$	−15.2355	−	26.3887i	−0.525363	−	0.909955i
$842$	−44.2258	+	15.8686i	−1.52412	+	0.546868i
$843$	−16.4688	+	0.767188i	−0.567217	+	0.0264233i
$844$	−9.53121	+	7.85044i	−0.328078	+	0.270223i
$845$	−10.9064			−0.375191
$846$	49.6247	+	4.27816i	1.70613	+	0.147086i
$847$			28.0240i			0.962917i
$848$	53.9419	−	18.5248i	1.85237	−	0.636145i
$849$	−10.8249	−	5.59499i	−0.371508	−	0.192020i
$850$	7.66458	−	2.75011i	0.262893	−	0.0943281i
$851$	−2.25909	+	1.30429i	−0.0774406	+	0.0447104i
$852$	−20.0060	−	22.1070i	−0.685395	−	0.757373i
$853$	15.4640	+	8.92817i	0.529479	+	0.305695i	0.740804	−	0.671721i	$-0.234445\pi$
$853$	15.4640	+	8.92817i	0.529479	+	0.305695i	−0.211325	+	0.977416i	$0.567778\pi$
$854$	8.39366	+	1.51958i	0.287225	+	0.0519988i
$855$	16.5508	−	1.54536i	0.566025	−	0.0528503i
$856$	6.50077	−	10.9117i	0.222192	−	0.372955i
$857$	−13.8049	−	7.97024i	−0.471565	−	0.272258i	0.245330	−	0.969440i	$-0.421104\pi$
$857$	−13.8049	−	7.97024i	−0.471565	−	0.272258i	−0.716895	+	0.697182i	$0.754437\pi$
$858$	−2.25753	+	16.9319i	−0.0770708	+	0.578046i
$859$	−6.15291	−	10.6571i	−0.209934	−	0.363617i	0.741759	−	0.670666i	$-0.233992\pi$
$859$	−6.15291	−	10.6571i	−0.209934	−	0.363617i	−0.951694	+	0.307049i	$0.900658\pi$
$860$	−0.338067	−	2.02524i	−0.0115280	−	0.0690602i
$861$	−22.5601	+	14.4651i	−0.768846	+	0.492968i
$862$	−1.74089	+	2.05557i	−0.0592948	+	0.0700131i
$863$	51.7946			1.76311			0.881554	−	0.472084i	$-0.156498\pi$
$863$	51.7946			1.76311			0.881554	+	0.472084i	$0.156498\pi$
$864$	−28.6047	−	6.76533i	−0.973153	−	0.230161i
$865$	−6.40225			−0.217683
$866$	11.5978	−	13.6943i	0.394110	−	0.465350i
$867$	23.5544	−	15.1026i	0.799949	−	0.512911i
$868$	−2.07527	−	12.4323i	−0.0704393	−	0.421978i
$869$	19.5978	+	33.9443i	0.664808	+	1.15148i
$870$	2.49649	−	18.7241i	0.0846389	−	0.634808i
$871$	−0.648442	−	0.374378i	−0.0219716	−	0.0126853i
$872$	17.7010	−	29.7116i	0.599432	−	1.00616i
$873$	−5.39242	−	7.60633i	−0.182506	−	0.257435i
$874$	−13.5507	−	2.45320i	−0.458359	−	0.0829807i
$875$	−1.98473	−	1.14588i	−0.0670960	−	0.0387379i
$876$	3.70062	+	4.08925i	0.125032	+	0.138163i
$877$	−17.5941	+	10.1579i	−0.594110	+	0.343009i	−0.766721	−	0.641981i	$-0.778113\pi$
$877$	−17.5941	+	10.1579i	−0.594110	+	0.343009i	0.172611	+	0.984990i	$0.444780\pi$
$878$	−9.11360	+	3.27003i	−0.307569	+	0.110358i
$879$	−30.9871	−	16.0161i	−1.04517	−	0.540210i
$880$	−6.26161	−	18.2330i	−0.211079	−	0.614634i
$881$			25.8553i			0.871087i	0.900168	+	0.435544i	$0.143444\pi$
$881$			25.8553i			0.871087i	−0.900168	+	0.435544i	$0.856556\pi$
$882$	−4.24555	+	6.07967i	−0.142955	+	0.204713i
$883$	37.0631			1.24727			0.623637	−	0.781714i	$-0.285655\pi$
$883$	37.0631			1.24727			0.623637	+	0.781714i	$0.285655\pi$
$884$	−12.8618	+	10.5937i	−0.432589	+	0.356304i
$885$	14.1243	−	0.657971i	0.474784	−	0.0221175i
$886$	−12.3116	+	4.41749i	−0.413616	+	0.148409i
$887$	6.17784	+	10.7003i	0.207431	+	0.359282i	0.950905	−	0.309484i	$-0.100156\pi$
$887$	6.17784	+	10.7003i	0.207431	+	0.359282i	−0.743473	+	0.668766i	$0.766823\pi$
$888$	−0.238858	−	7.26787i	−0.00801556	−	0.243894i
$889$	20.9072	−	36.2124i	0.701206	−	1.21452i
$890$	1.99096	−	10.9974i	0.0667370	−	0.368634i
$891$	−8.03012	−	42.6262i	−0.269019	−	1.42803i
$892$	−1.85978	+	4.96807i	−0.0622700	+	0.166343i
$893$	−32.5253	+	56.3355i	−1.08842	+	1.88520i
$894$	31.2548	−	12.8859i	1.04532	−	0.430967i
$895$	−21.1784	+	12.2273i	−0.707915	+	0.408715i
$896$	19.3196	+	17.2926i	0.645421	+	0.577706i
$897$	4.39953	−	0.204949i	0.146896	−	0.00684304i
$898$	13.5224	+	11.4522i	0.451247	+	0.382166i
$899$			21.2066i			0.707278i
$900$	4.25661	−	4.22863i	0.141887	−	0.140954i
$901$			82.1005i			2.73517i
$902$	29.7394	−	35.1152i	0.990215	−	1.16921i
$903$	−1.87115	+	3.62020i	−0.0622680	+	0.120473i
$904$	30.2469	+	0.414330i	1.00600	+	0.0137804i
$905$	13.6507	−	7.88123i	0.453764	−	0.261981i
$906$	−9.30535	+	12.0857i	−0.309150	+	0.401519i
$907$	−17.2066	+	29.8026i	−0.571335	+	0.989581i	0.425095	+	0.905149i	$0.360241\pi$
$907$	−17.2066	+	29.8026i	−0.571335	+	0.989581i	−0.996429	+	0.0844316i	$0.973093\pi$
$908$	−5.66106	+	15.1225i	−0.187869	+	0.501859i
$909$	−32.5319	−	45.8882i	−1.07902	−	1.52202i
$910$	4.61458	+	0.835416i	0.152972	+	0.0276938i
$911$	−13.0418	+	22.5891i	−0.432095	+	0.748411i	−0.997054	−	0.0767083i	$-0.975559\pi$
$911$	−13.0418	+	22.5891i	−0.432095	+	0.748411i	0.564958	+	0.825120i	$0.308892\pi$
$912$	23.8341	−	30.0936i	0.789227	−	0.996498i
$913$	−21.5197	−	37.2732i	−0.712198	−	1.23356i
$914$	6.40672	+	17.8556i	0.211916	+	0.590610i
$915$	−2.46053	−	3.83751i	−0.0813426	−	0.126864i
$916$	26.2201	+	31.8337i	0.866335	+	1.05182i
$917$	9.91134			0.327301
$918$	22.5849	−	35.7808i	0.745411	−	1.18094i
$919$		−	2.46876i		−	0.0814370i	−0.999171	−	0.0407185i	$-0.987035\pi$
$919$		−	2.46876i		−	0.0814370i	0.999171	−	0.0407185i	$-0.0129647\pi$
$920$	−4.33834	+	2.42612i	−0.143031	+	0.0799869i
$921$	39.2206	−	25.1474i	1.29236	−	0.828636i
$922$	−9.59838	−	26.7507i	−0.316106	−	0.880988i
$923$	−10.7853	+	6.22687i	−0.355001	+	0.204960i
$924$	−11.7322	+	36.4189i	−0.385960	+	1.19810i
$925$	1.28548	+	0.742174i	0.0422664	+	0.0244025i
$926$	−3.33300	+	18.4104i	−0.109529	+	0.605004i
$927$	2.21160	+	23.6862i	0.0726386	+	0.777956i
$928$	−27.2710	−	34.0495i	−0.895213	−	1.11773i
$929$	39.4136	+	22.7554i	1.29312	+	0.746582i	0.979206	−	0.202870i	$-0.0650269\pi$
$929$	39.4136	+	22.7554i	1.29312	+	0.746582i	0.313912	+	0.949452i	$0.398360\pi$
$930$	−4.10934	+	5.33715i	−0.134750	+	0.175012i
$931$	−4.84224	−	8.38701i	−0.158698	−	0.274873i
$932$	−50.5698	+	8.44143i	−1.65647	+	0.276508i
$933$	−5.51993	−	2.85306i	−0.180714	−	0.0934049i
$934$	24.7812	+	20.9874i	0.810864	+	0.686729i
$935$	27.7510			0.907553
$936$	−5.27610	+	11.0862i	−0.172455	+	0.362364i
$937$	15.9322			0.520483			0.260241	−	0.965544i	$-0.416198\pi$
$937$	15.9322			0.520483			0.260241	+	0.965544i	$0.416198\pi$
$938$	−1.27985	−	1.08392i	−0.0417885	−	0.0353911i
$939$	−0.161065	−	3.45750i	−0.00525615	−	0.112831i
$940$	3.86595	+	23.1596i	0.126093	+	0.755384i
$941$	28.5435	+	49.4387i	0.930490	+	1.61166i	0.782485	+	0.622670i	$0.213952\pi$
$941$	28.5435	+	49.4387i	0.930490	+	1.61166i	0.148006	+	0.988987i	$0.452715\pi$
$942$	3.06708	+	7.43924i	0.0999307	+	0.242383i
$943$	−10.2752	−	5.93237i	−0.334605	−	0.193184i
$944$	21.4430	−	24.6270i	0.697910	−	0.801541i
$945$	−11.7924	+	1.65762i	−0.383608	+	0.0539225i
$946$	1.24654	−	6.88549i	0.0405285	−	0.223866i
$947$	−10.5114	−	6.06877i	−0.341575	−	0.197209i	0.319393	−	0.947622i	$-0.396521\pi$
$947$	−10.5114	−	6.06877i	−0.341575	−	0.197209i	−0.660968	+	0.750414i	$0.729854\pi$
$948$	5.92653	+	27.5417i	0.192485	+	0.894513i
$949$	1.99501	−	1.15182i	0.0647607	−	0.0373896i
$950$	2.64644	+	7.37564i	0.0858618	+	0.239297i
$951$	−1.77096	−	38.0163i	−0.0574273	−	1.23276i
$952$	−32.5760	+	18.2174i	−1.05579	+	0.590430i
$953$			54.1971i			1.75562i	0.479011	+	0.877809i	$0.340995\pi$
$953$			54.1971i			1.75562i	−0.479011	+	0.877809i	$0.659005\pi$
$954$	25.6354	+	54.7936i	0.829976	+	1.77401i
$955$	−18.9094			−0.611895
$956$	16.7636	−	13.8074i	0.542172	−	0.446564i
$957$	29.5586	−	57.1882i	0.955493	−	1.84863i
$958$	−13.0826	−	36.4611i	−0.422678	−	1.17801i
$959$	11.1924	+	19.3859i	0.361422	+	0.626002i
$960$	−0.265413	−	13.8539i	−0.00856617	−	0.447132i
$961$	−11.7190	+	20.2979i	−0.378033	+	0.654772i
$962$	−2.98880	−	0.541089i	−0.0963629	−	0.0174454i
$963$	12.2427	+	5.62213i	0.394515	+	0.181170i
$964$	10.6126	+	3.97278i	0.341808	+	0.127955i
$965$	−9.04742	+	15.6706i	−0.291247	+	0.504454i
$966$	9.77882	+	1.30381i	0.314628	+	0.0419494i
$967$	−35.4052	+	20.4412i	−1.13856	+	0.657345i	−0.946072	−	0.323955i	$-0.894987\pi$
$967$	−35.4052	+	20.4412i	−1.13856	+	0.657345i	−0.192483	+	0.981300i	$0.561654\pi$
$968$	0.473730	−	34.5832i	0.0152263	−	1.11154i
$969$	29.8272	+	46.5193i	0.958188	+	1.49442i
$970$	2.84060	−	3.35407i	0.0912060	−	0.107693i
$971$		−	26.5356i		−	0.851566i	−0.904825	−	0.425783i	$-0.859999\pi$
$971$		−	26.5356i		−	0.851566i	0.904825	−	0.425783i	$-0.140001\pi$
$972$	3.90073	−	30.9319i	0.125116	−	0.992142i
$973$		−	38.4238i		−	1.23181i
$974$	−14.5657	−	12.3358i	−0.466714	−	0.395265i
$975$	−1.35272	−	2.10974i	−0.0433218	−	0.0675659i
$976$	−10.3325	−	2.01713i	−0.330736	−	0.0645667i
$977$	−11.4431	+	6.60665i	−0.366096	+	0.211365i	−0.671751	−	0.740777i	$-0.734458\pi$
$977$	−11.4431	+	6.60665i	−0.366096	+	0.211365i	0.305656	+	0.952142i	$0.401124\pi$
$978$	3.03064	−	22.7304i	0.0969093	−	0.726839i
$979$	19.0439	−	32.9850i	0.608645	−	1.05420i
$980$	−3.27375	−	1.22552i	−0.104576	−	0.0391477i
$981$	33.3357	+	15.3085i	1.06433	+	0.488764i
$982$	6.05983	−	33.4726i	0.193377	−	1.06815i
$983$	11.6857	−	20.2403i	0.372717	−	0.645565i	−0.617265	−	0.786755i	$-0.711760\pi$
$983$	11.6857	−	20.2403i	0.372717	−	0.645565i	0.989983	+	0.141190i	$0.0450929\pi$
$984$	28.0849	−	17.4693i	0.895314	−	0.556901i
$985$	−2.86660	−	4.96509i	−0.0913373	−	0.158201i
$986$	59.1073	−	21.2082i	1.88236	−	0.675406i
$987$	21.3975	−	41.3987i	0.681090	−	1.31773i
$988$	−10.1943	−	12.3769i	−0.324325	−	0.393762i
$989$	−1.80419			−0.0573699
$990$	18.5209	−	8.66506i	0.588632	−	0.275394i
$991$			27.6218i			0.877434i	0.898625	+	0.438717i	$0.144567\pi$
$991$			27.6218i			0.877434i	−0.898625	+	0.438717i	$0.855433\pi$
$992$	2.35083	+	15.3771i	0.0746391	+	0.488225i
$993$	0.941435	+	20.2093i	0.0298755	+	0.641323i
$994$	−26.2566	+	9.42107i	−0.832808	+	0.298818i
$995$	9.19589	−	5.30925i	0.291529	−	0.168315i
$996$	−6.50774	−	30.2427i	−0.206206	−	0.958277i
$997$	−7.57095	−	4.37109i	−0.239774	−	0.138434i	0.375299	−	0.926904i	$-0.377540\pi$
$997$	−7.57095	−	4.37109i	−0.239774	−	0.138434i	−0.615073	+	0.788470i	$0.710873\pi$
$998$	9.04222	+	1.63699i	0.286226	+	0.0518180i
$999$	7.63781	−	1.07362i	0.241650	−	0.0339679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.17	yes	48
3.2	odd	2		1080.2.bm.a.251.8		48
4.3	odd	2		1440.2.cc.b.911.21		48
8.3	odd	2		360.2.bm.a.11.10	✓	48
8.5	even	2		1440.2.cc.a.911.21		48
9.4	even	3		1080.2.bm.b.611.15		48
9.5	odd	6		360.2.bm.a.131.10	yes	48
12.11	even	2		4320.2.cc.a.1871.6		48
24.5	odd	2		4320.2.cc.b.1871.19		48
24.11	even	2		1080.2.bm.b.251.15		48
36.23	even	6		1440.2.cc.a.1391.21		48
36.31	odd	6		4320.2.cc.b.3311.19		48
72.5	odd	6		1440.2.cc.b.1391.21		48
72.13	even	6		4320.2.cc.a.3311.6		48
72.59	even	6	inner	360.2.bm.b.131.17	yes	48
72.67	odd	6		1080.2.bm.a.611.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.10	✓	48	8.3	odd	2
360.2.bm.a.131.10	yes	48	9.5	odd	6
360.2.bm.b.11.17	yes	48	1.1	even	1	trivial
360.2.bm.b.131.17	yes	48	72.59	even	6	inner
1080.2.bm.a.251.8		48	3.2	odd	2
1080.2.bm.a.611.8		48	72.67	odd	6
1080.2.bm.b.251.15		48	24.11	even	2
1080.2.bm.b.611.15		48	9.4	even	3
1440.2.cc.a.911.21		48	8.5	even	2
1440.2.cc.a.1391.21		48	36.23	even	6
1440.2.cc.b.911.21		48	4.3	odd	2
1440.2.cc.b.1391.21		48	72.5	odd	6
4320.2.cc.a.1871.6		48	12.11	even	2
4320.2.cc.a.3311.6		48	72.13	even	6
4320.2.cc.b.1871.19		48	24.5	odd	2
4320.2.cc.b.3311.19		48	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913976 - 1.07919i) q^{2} +(-1.45808 + 0.934888i) q^{3} +(-0.329296 - 1.97270i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.323726 + 2.42800i) q^{6} +(1.98473 + 1.14588i) q^{7} +(-2.42989 - 1.44763i) q^{8} +(1.25197 - 2.72627i) q^{9} +O(q^{10})\)	\(q+(0.913976 - 1.07919i) q^{2} +(-1.45808 + 0.934888i) q^{3} +(-0.329296 - 1.97270i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.323726 + 2.42800i) q^{6} +(1.98473 + 1.14588i) q^{7} +(-2.42989 - 1.44763i) q^{8} +(1.25197 - 2.72627i) q^{9} +(1.39159 + 0.251932i) q^{10} +(4.17386 + 2.40978i) q^{11} +(2.32440 + 2.56850i) q^{12} +(1.25308 - 0.723468i) q^{13} +(3.05062 - 1.09459i) q^{14} +(-1.53867 - 0.795287i) q^{15} +(-3.78313 + 1.29921i) q^{16} -5.75799i q^{17} +(-1.79789 - 3.84286i) q^{18} +5.54092 q^{19} +(1.54376 - 1.27153i) q^{20} +(-3.96515 + 0.184714i) q^{21} +(6.41541 - 2.30190i) q^{22} +(-0.878693 - 1.52194i) q^{23} +(4.89634 - 0.160918i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.364530 - 2.01355i) q^{26} +(0.723295 + 5.14557i) q^{27} +(1.60693 - 4.29262i) q^{28} +(-3.85587 + 6.67857i) q^{29} +(-2.26458 + 0.933647i) q^{30} +(2.38149 - 1.37495i) q^{31} +(-2.05560 + 5.27015i) q^{32} +(-8.33868 + 0.388451i) q^{33} +(-6.21396 - 5.26266i) q^{34} +2.29177i q^{35} +(-5.79040 - 1.57201i) q^{36} -1.48435i q^{37} +(5.06427 - 5.97970i) q^{38} +(-1.15073 + 2.22636i) q^{39} +(0.0387410 - 2.82816i) q^{40} +(5.84684 - 3.37568i) q^{41} +(-3.42471 + 4.44797i) q^{42} +(0.513317 - 0.889090i) q^{43} +(3.37935 - 9.02732i) q^{44} +(2.98701 - 0.278900i) q^{45} +(-2.44557 - 0.442742i) q^{46} +(-5.87002 + 10.1672i) q^{47} +(4.30147 - 5.43115i) q^{48} +(-0.873905 - 1.51365i) q^{49} +(0.477617 + 1.33112i) q^{50} +(5.38307 + 8.39558i) q^{51} +(-1.83983 - 2.23373i) q^{52} -14.2585 q^{53} +(6.21411 + 3.92235i) q^{54} +4.81956i q^{55} +(-3.16385 - 5.65752i) q^{56} +(-8.07909 + 5.18014i) q^{57} +(3.68326 + 10.2653i) q^{58} +(-7.06983 + 4.08177i) q^{59} +(-1.06219 + 3.29724i) q^{60} +(2.27929 + 1.31595i) q^{61} +(0.692789 - 3.82675i) q^{62} +(5.60881 - 3.97630i) q^{63} +(3.80873 + 7.03517i) q^{64} +(1.25308 + 0.723468i) q^{65} +(-7.20214 + 9.35404i) q^{66} +(-0.258738 - 0.448148i) q^{67} +(-11.3588 + 1.89608i) q^{68} +(2.70404 + 1.39763i) q^{69} +(2.47325 + 2.09462i) q^{70} -8.60697 q^{71} +(-6.98879 + 4.81216i) q^{72} +1.59208 q^{73} +(-1.60189 - 1.35666i) q^{74} +(-0.0805988 - 1.73017i) q^{75} +(-1.82461 - 10.9306i) q^{76} +(5.52265 + 9.56551i) q^{77} +(1.35093 + 3.27670i) q^{78} +(7.04303 + 4.06630i) q^{79} +(-3.01671 - 2.62668i) q^{80} +(-5.86515 - 6.82642i) q^{81} +(1.70088 - 9.39513i) q^{82} +(-7.73374 - 4.46508i) q^{83} +(1.67010 + 7.76125i) q^{84} +(4.98656 - 2.87899i) q^{85} +(-0.490337 - 1.36657i) q^{86} +(-0.621558 - 13.3427i) q^{87} +(-6.65355 - 11.8977i) q^{88} -7.90275i q^{89} +(2.42907 - 3.47845i) q^{90} +3.31604 q^{91} +(-2.71299 + 2.23457i) q^{92} +(-2.18696 + 4.23121i) q^{93} +(5.60724 + 15.6274i) q^{94} +(2.77046 + 4.79858i) q^{95} +(-1.92979 - 9.60604i) q^{96} +(1.55398 - 2.69157i) q^{97} +(-2.43224 - 0.440329i) q^{98} +(11.7953 - 8.36212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Introduction

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