LMFDB - Embedded newform 555.2.g.a.184.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(184,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("555.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.g (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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			184.3
Character	$\chi$	$=$	555.184
Dual form			555.2.g.a.184.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49663 q^{2} -1.00000i q^{3} +4.23317 q^{4} +(2.05572 + 0.879776i) q^{5} +2.49663i q^{6} -3.27811i q^{7} -5.57542 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.49663 q^{2} -1.00000i q^{3} +4.23317 q^{4} +(2.05572 + 0.879776i) q^{5} +2.49663i q^{6} -3.27811i q^{7} -5.57542 q^{8} -1.00000 q^{9} +(-5.13238 - 2.19648i) q^{10} -2.24880 q^{11} -4.23317i q^{12} -3.94527 q^{13} +8.18423i q^{14} +(0.879776 - 2.05572i) q^{15} +5.45341 q^{16} -5.46297 q^{17} +2.49663 q^{18} -4.91284i q^{19} +(8.70223 + 3.72424i) q^{20} -3.27811 q^{21} +5.61443 q^{22} +0.293562 q^{23} +5.57542i q^{24} +(3.45199 + 3.61715i) q^{25} +9.84989 q^{26} +1.00000i q^{27} -13.8768i q^{28} +4.42445i q^{29} +(-2.19648 + 5.13238i) q^{30} -9.50346i q^{31} -2.46434 q^{32} +2.24880i q^{33} +13.6390 q^{34} +(2.88400 - 6.73888i) q^{35} -4.23317 q^{36} +(4.05995 + 4.52955i) q^{37} +12.2656i q^{38} +3.94527i q^{39} +(-11.4615 - 4.90511i) q^{40} -7.53868 q^{41} +8.18423 q^{42} -9.74531 q^{43} -9.51957 q^{44} +(-2.05572 - 0.879776i) q^{45} -0.732917 q^{46} +5.70765i q^{47} -5.45341i q^{48} -3.74599 q^{49} +(-8.61835 - 9.03069i) q^{50} +5.46297i q^{51} -16.7010 q^{52} -14.1262i q^{53} -2.49663i q^{54} +(-4.62291 - 1.97844i) q^{55} +18.2768i q^{56} -4.91284 q^{57} -11.0462i q^{58} -4.15907i q^{59} +(3.72424 - 8.70223i) q^{60} +1.76873i q^{61} +23.7266i q^{62} +3.27811i q^{63} -4.75427 q^{64} +(-8.11038 - 3.47095i) q^{65} -5.61443i q^{66} +2.23951i q^{67} -23.1257 q^{68} -0.293562i q^{69} +(-7.20029 + 16.8245i) q^{70} -1.23508 q^{71} +5.57542 q^{72} -2.78092i q^{73} +(-10.1362 - 11.3086i) q^{74} +(3.61715 - 3.45199i) q^{75} -20.7969i q^{76} +7.37181i q^{77} -9.84989i q^{78} +7.60105i q^{79} +(11.2107 + 4.79778i) q^{80} +1.00000 q^{81} +18.8213 q^{82} -7.35263i q^{83} -13.8768 q^{84} +(-11.2303 - 4.80619i) q^{85} +24.3305 q^{86} +4.42445 q^{87} +12.5380 q^{88} -11.7227i q^{89} +(5.13238 + 2.19648i) q^{90} +12.9330i q^{91} +1.24270 q^{92} -9.50346 q^{93} -14.2499i q^{94} +(4.32220 - 10.0994i) q^{95} +2.46434i q^{96} +8.37426 q^{97} +9.35235 q^{98} +2.24880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) $ 40 * q + 44 * q^4 - 40 * q^9	$ 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−2.49663			−1.76539			−0.882693	−	0.469950i	$-0.844272\pi$
$2$	−2.49663			−1.76539			−0.882693	+	0.469950i	$0.844272\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	4.23317			2.11659
$5$	2.05572	+	0.879776i	0.919347	+	0.393448i
$5$	2.05572	+	0.879776i	0.919347	+	0.393448i
$6$			2.49663i			1.01925i
$7$		−	3.27811i		−	1.23901i	−0.784993	−	0.619504i	$-0.787334\pi$
$7$		−	3.27811i		−	1.23901i	0.784993	−	0.619504i	$-0.212666\pi$
$8$	−5.57542			−1.97121
$9$	−1.00000			−0.333333
$10$	−5.13238	−	2.19648i	−1.62300	−	0.694587i
$11$	−2.24880			−0.678039			−0.339020	−	0.940779i	$-0.610095\pi$
$11$	−2.24880			−0.678039			−0.339020	+	0.940779i	$0.610095\pi$
$12$		−	4.23317i		−	1.22201i
$13$	−3.94527			−1.09422			−0.547110	−	0.837060i	$-0.684272\pi$
$13$	−3.94527			−1.09422			−0.547110	+	0.837060i	$0.684272\pi$
$14$			8.18423i			2.18733i
$15$	0.879776	−	2.05572i	0.227157	−	0.530785i
$16$	5.45341			1.36335
$17$	−5.46297			−1.32496			−0.662482	−	0.749078i	$-0.730497\pi$
$17$	−5.46297			−1.32496			−0.662482	+	0.749078i	$0.730497\pi$
$18$	2.49663			0.588462
$19$		−	4.91284i		−	1.12708i	−0.826088	−	0.563541i	$-0.809439\pi$
$19$		−	4.91284i		−	1.12708i	0.826088	−	0.563541i	$-0.190561\pi$
$20$	8.70223	+	3.72424i	1.94588	+	0.832766i
$21$	−3.27811			−0.715342
$22$	5.61443			1.19700
$23$	0.293562			0.0612119			0.0306060	−	0.999532i	$-0.490256\pi$
$23$	0.293562			0.0612119			0.0306060	+	0.999532i	$0.490256\pi$
$24$			5.57542i			1.13808i
$25$	3.45199	+	3.61715i	0.690398	+	0.723430i
$26$	9.84989			1.93172
$27$			1.00000i			0.192450i
$28$		−	13.8768i		−	2.62247i
$29$			4.42445i			0.821599i	0.911726	+	0.410799i	$0.134750\pi$
$29$			4.42445i			0.821599i	−0.911726	+	0.410799i	$0.865250\pi$
$30$	−2.19648	+	5.13238i	−0.401020	+	0.937041i
$31$		−	9.50346i		−	1.70687i	−0.521198	−	0.853436i	$-0.674515\pi$
$31$		−	9.50346i		−	1.70687i	0.521198	−	0.853436i	$-0.325485\pi$
$32$	−2.46434			−0.435638
$33$			2.24880i			0.391466i
$34$	13.6390			2.33907
$35$	2.88400	−	6.73888i	0.487485	−	1.13908i
$36$	−4.23317			−0.705529
$37$	4.05995	+	4.52955i	0.667451	+	0.744654i
$37$	4.05995	+	4.52955i	0.667451	+	0.744654i
$38$			12.2656i			1.98974i
$39$			3.94527i			0.631749i
$40$	−11.4615	−	4.90511i	−1.81222	−	0.775567i
$41$	−7.53868			−1.17734			−0.588672	−	0.808372i	$-0.700349\pi$
$41$	−7.53868			−1.17734			−0.588672	+	0.808372i	$0.700349\pi$
$42$	8.18423			1.26285
$43$	−9.74531			−1.48615			−0.743073	−	0.669210i	$-0.766633\pi$
$43$	−9.74531			−1.48615			−0.743073	+	0.669210i	$0.766633\pi$
$44$	−9.51957			−1.43513
$45$	−2.05572	−	0.879776i	−0.306449	−	0.131149i
$46$	−0.732917			−0.108063
$47$			5.70765i			0.832546i	0.909240	+	0.416273i	$0.136664\pi$
$47$			5.70765i			0.832546i	−0.909240	+	0.416273i	$0.863336\pi$
$48$		−	5.45341i		−	0.787133i
$49$	−3.74599			−0.535141
$50$	−8.61835	−	9.03069i	−1.21882	−	1.27713i
$51$			5.46297i			0.764968i
$52$	−16.7010			−2.31601
$53$		−	14.1262i		−	1.94038i	−0.242338	−	0.970192i	$-0.577914\pi$
$53$		−	14.1262i		−	1.94038i	0.242338	−	0.970192i	$-0.422086\pi$
$54$		−	2.49663i		−	0.339749i
$55$	−4.62291	−	1.97844i	−0.623353	−	0.266773i
$56$			18.2768i			2.44234i
$57$	−4.91284			−0.650721
$58$		−	11.0462i		−	1.45044i
$59$		−	4.15907i		−	0.541465i	−0.962655	−	0.270732i	$-0.912734\pi$
$59$		−	4.15907i		−	0.541465i	0.962655	−	0.270732i	$-0.0872658\pi$
$60$	3.72424	−	8.70223i	0.480798	−	1.12345i
$61$			1.76873i			0.226463i	0.993569	+	0.113232i	$0.0361202\pi$
$61$			1.76873i			0.226463i	−0.993569	+	0.113232i	$0.963880\pi$
$62$			23.7266i			3.01329i
$63$			3.27811i			0.413003i
$64$	−4.75427			−0.594284
$65$	−8.11038	−	3.47095i	−1.00597	−	0.430519i
$66$		−	5.61443i		−	0.691089i
$67$			2.23951i			0.273600i	0.990599	+	0.136800i	$0.0436817\pi$
$67$			2.23951i			0.273600i	−0.990599	+	0.136800i	$0.956318\pi$
$68$	−23.1257			−2.80440
$69$		−	0.293562i		−	0.0353407i
$70$	−7.20029	+	16.8245i	−0.860599	+	2.01091i
$71$	−1.23508			−0.146578			−0.0732888	−	0.997311i	$-0.523349\pi$
$71$	−1.23508			−0.146578			−0.0732888	+	0.997311i	$0.523349\pi$
$72$	5.57542			0.657069
$73$		−	2.78092i		−	0.325482i	−0.986669	−	0.162741i	$-0.947966\pi$
$73$		−	2.78092i		−	0.325482i	0.986669	−	0.162741i	$-0.0520336\pi$
$74$	−10.1362	−	11.3086i	−1.17831	−	1.31460i
$75$	3.61715	−	3.45199i	0.417672	−	0.398601i
$76$		−	20.7969i		−	2.38557i
$77$			7.37181i			0.840096i
$78$		−	9.84989i		−	1.11528i
$79$			7.60105i			0.855185i	0.903972	+	0.427592i	$0.140638\pi$
$79$			7.60105i			0.855185i	−0.903972	+	0.427592i	$0.859362\pi$
$80$	11.2107	+	4.79778i	1.25340	+	0.536408i
$81$	1.00000			0.111111
$82$	18.8213			2.07847
$83$		−	7.35263i		−	0.807056i	−0.914967	−	0.403528i	$-0.867784\pi$
$83$		−	7.35263i		−	0.807056i	0.914967	−	0.403528i	$-0.132216\pi$
$84$	−13.8768			−1.51408
$85$	−11.2303	−	4.80619i	−1.21810	−	0.521304i
$86$	24.3305			2.62362
$87$	4.42445			0.474350
$88$	12.5380			1.33656
$89$		−	11.7227i		−	1.24261i	−0.783569	−	0.621304i	$-0.786603\pi$
$89$		−	11.7227i		−	1.24261i	0.783569	−	0.621304i	$-0.213397\pi$
$90$	5.13238	+	2.19648i	0.541001	+	0.231529i
$91$			12.9330i			1.35575i
$92$	1.24270			0.129560
$93$	−9.50346			−0.985463
$94$		−	14.2499i		−	1.46976i
$95$	4.32220	−	10.0994i	0.443448	−	1.03618i
$96$			2.46434i			0.251516i
$97$	8.37426			0.850277			0.425138	−	0.905128i	$-0.360225\pi$
$97$	8.37426			0.850277			0.425138	+	0.905128i	$0.360225\pi$
$98$	9.35235			0.944730
$99$	2.24880			0.226013
$100$	14.6129	+	15.3120i	1.46129	+	1.53120i
$101$	−4.79078			−0.476701			−0.238350	−	0.971179i	$-0.576607\pi$
$101$	−4.79078			−0.476701			−0.238350	+	0.971179i	$0.576607\pi$
$102$		−	13.6390i		−	1.35046i
$103$	2.72811			0.268808			0.134404	−	0.990927i	$-0.457088\pi$
$103$	2.72811			0.268808			0.134404	+	0.990927i	$0.457088\pi$
$104$	21.9965			2.15694
$105$	−6.73888	−	2.88400i	−0.657647	−	0.281449i
$106$			35.2680i			3.42553i
$107$		−	2.86508i		−	0.276977i	−0.990364	−	0.138489i	$-0.955776\pi$
$107$		−	2.86508i		−	0.276977i	0.990364	−	0.138489i	$-0.0442245\pi$
$108$			4.23317i			0.407337i
$109$			2.88647i			0.276473i	0.990399	+	0.138237i	$0.0441435\pi$
$109$			2.88647i			0.276473i	−0.990399	+	0.138237i	$0.955857\pi$
$110$	11.5417	+	4.93944i	1.10046	+	0.470957i
$111$	4.52955	−	4.05995i	0.429926	−	0.385353i
$112$		−	17.8769i		−	1.68921i
$113$	−6.02335			−0.566629			−0.283314	−	0.959027i	$-0.591434\pi$
$113$	−6.02335			−0.566629			−0.283314	+	0.959027i	$0.591434\pi$
$114$	12.2656			1.14877
$115$	0.603482	+	0.258269i	0.0562750	+	0.0240837i
$116$			18.7294i			1.73899i
$117$	3.94527			0.364740
$118$			10.3837i			0.955894i
$119$			17.9082i			1.64164i
$120$	−4.90511	+	11.4615i	−0.447774	+	1.04629i
$121$	−5.94289			−0.540263
$122$		−	4.41588i		−	0.399795i
$123$			7.53868i			0.679740i
$124$		−	40.2298i		−	3.61274i
$125$	3.91405	+	10.4728i	0.350083	+	0.936719i
$126$		−	8.18423i		−	0.729109i
$127$			9.03468i			0.801698i	0.916144	+	0.400849i	$0.131285\pi$
$127$			9.03468i			0.801698i	−0.916144	+	0.400849i	$0.868715\pi$
$128$	16.7984			1.48478
$129$			9.74531i			0.858027i
$130$	20.2486	+	8.66569i	1.77592	+	0.760031i
$131$		−	19.2768i		−	1.68422i	−0.539303	−	0.842112i	$-0.681312\pi$
$131$		−	19.2768i		−	1.68422i	0.539303	−	0.842112i	$-0.318688\pi$
$132$			9.51957i			0.828572i
$133$	−16.1048			−1.39646
$134$		−	5.59124i		−	0.483009i
$135$	−0.879776	+	2.05572i	−0.0757190	+	0.176928i
$136$	30.4583			2.61178
$137$			10.1881i			0.870431i	0.900326	+	0.435215i	$0.143328\pi$
$137$			10.1881i			0.870431i	−0.900326	+	0.435215i	$0.856672\pi$
$138$			0.732917i			0.0623900i
$139$	21.3595			1.81169			0.905845	−	0.423609i	$-0.139237\pi$
$139$	21.3595			1.81169			0.905845	+	0.423609i	$0.139237\pi$
$140$	12.2085	−	28.5268i	1.03180	−	2.41096i
$141$	5.70765			0.480670
$142$	3.08355			0.258766
$143$	8.87213			0.741924
$144$	−5.45341			−0.454451
$145$	−3.89252	+	9.09543i	−0.323256	+	0.755334i
$146$			6.94294i			0.574602i
$147$			3.74599i			0.308964i
$148$	17.1865	+	19.1744i	1.41272	+	1.57612i
$149$	−19.5471			−1.60136			−0.800679	−	0.599093i	$-0.795528\pi$
$149$	−19.5471			−1.60136			−0.800679	+	0.599093i	$0.795528\pi$
$150$	−9.03069	+	8.61835i	−0.737353	+	0.703685i
$151$	13.5198			1.10023			0.550114	−	0.835090i	$-0.314584\pi$
$151$	13.5198			1.10023			0.550114	+	0.835090i	$0.314584\pi$
$152$			27.3911i			2.22171i
$153$	5.46297			0.441655
$154$		−	18.4047i		−	1.48309i
$155$	8.36091	−	19.5365i	0.671565	−	1.56921i
$156$			16.7010i			1.33715i
$157$		−	18.8036i		−	1.50069i	−0.661048	−	0.750344i	$-0.729888\pi$
$157$		−	18.8036i		−	1.50069i	0.661048	−	0.750344i	$-0.270112\pi$
$158$		−	18.9770i		−	1.50973i
$159$	−14.1262			−1.12028
$160$	−5.06600	−	2.16807i	−0.400503	−	0.171401i
$161$		−	0.962328i		−	0.0758421i
$162$	−2.49663			−0.196154
$163$	−19.9706			−1.56422			−0.782108	−	0.623142i	$-0.785856\pi$
$163$	−19.9706			−1.56422			−0.782108	+	0.623142i	$0.785856\pi$
$164$	−31.9125			−2.49195
$165$	−1.97844	+	4.62291i	−0.154021	+	0.359893i
$166$			18.3568i			1.42476i
$167$	12.8751			0.996304			0.498152	−	0.867090i	$-0.334012\pi$
$167$	12.8751			0.996304			0.498152	+	0.867090i	$0.334012\pi$
$168$	18.2768			1.41009
$169$	2.56515			0.197319
$170$	28.0380	+	11.9993i	2.15042	+	0.920303i
$171$			4.91284i			0.375694i
$172$	−41.2536			−3.14556
$173$			4.41795i			0.335890i	0.985796	+	0.167945i	$0.0537132\pi$
$173$			4.41795i			0.335890i	−0.985796	+	0.167945i	$0.946287\pi$
$174$	−11.0462			−0.837411
$175$	11.8574	−	11.3160i	0.896335	−	0.855409i
$176$	−12.2636			−0.924407
$177$	−4.15907			−0.312615
$178$			29.2674i			2.19368i
$179$			3.48796i			0.260702i	0.991468	+	0.130351i	$0.0416105\pi$
$179$			3.48796i			0.260702i	−0.991468	+	0.130351i	$0.958390\pi$
$180$	−8.70223	−	3.72424i	−0.648626	−	0.277589i
$181$	7.11036			0.528509			0.264254	−	0.964453i	$-0.414874\pi$
$181$	7.11036			0.528509			0.264254	+	0.964453i	$0.414874\pi$
$182$		−	32.2890i		−	2.39342i
$183$	1.76873			0.130749
$184$	−1.63673			−0.120661
$185$	4.36113	+	12.8833i	0.320637	+	0.947202i
$186$	23.7266			1.73972
$187$	12.2851			0.898377
$188$			24.1615i			1.76216i
$189$	3.27811			0.238447
$190$	−10.7909	+	25.2146i	−0.782857	+	1.82926i
$191$		−	13.5632i		−	0.981400i	−0.871329	−	0.490700i	$-0.836741\pi$
$191$		−	13.5632i		−	0.981400i	0.871329	−	0.490700i	$-0.163259\pi$
$192$			4.75427i			0.343110i
$193$	20.1029			1.44704			0.723521	−	0.690303i	$-0.242523\pi$
$193$	20.1029			1.44704			0.723521	+	0.690303i	$0.242523\pi$
$194$	−20.9074			−1.50107
$195$	−3.47095	+	8.11038i	−0.248560	+	0.580796i
$196$	−15.8574			−1.13267
$197$		−	24.6393i		−	1.75548i	−0.479138	−	0.877739i	$-0.659051\pi$
$197$		−	24.6393i		−	1.75548i	0.479138	−	0.877739i	$-0.340949\pi$
$198$	−5.61443			−0.399000
$199$		−	8.20604i		−	0.581711i	−0.956767	−	0.290855i	$-0.906060\pi$
$199$		−	8.20604i		−	0.581711i	0.956767	−	0.290855i	$-0.0939398\pi$
$200$	−19.2463	−	20.1671i	−1.36092	−	1.42603i
$201$	2.23951			0.157963
$202$	11.9608			0.841561
$203$	14.5038			1.01797
$204$			23.1257i			1.61912i
$205$	−15.4974	−	6.63234i	−1.08239	−	0.463223i
$206$	−6.81108			−0.474550
$207$	−0.293562			−0.0204040
$208$	−21.5152			−1.49181
$209$			11.0480i			0.764206i
$210$	16.8245	+	7.20029i	1.16100	+	0.496867i
$211$	−18.1205			−1.24747			−0.623734	−	0.781636i	$-0.714385\pi$
$211$	−18.1205			−1.24747			−0.623734	+	0.781636i	$0.714385\pi$
$212$		−	59.7987i		−	4.10699i
$213$			1.23508i			0.0846266i
$214$			7.15304i			0.488972i
$215$	−20.0337	−	8.57369i	−1.36628	−	0.584721i
$216$		−	5.57542i		−	0.379359i
$217$	−31.1534			−2.11483
$218$		−	7.20645i		−	0.488082i
$219$	−2.78092			−0.187917
$220$	−19.5696	−	8.37508i	−1.31938	−	0.564648i
$221$	21.5529			1.44980
$222$	−11.3086	+	10.1362i	−0.758985	+	0.680297i
$223$		−	4.24608i		−	0.284339i	−0.989842	−	0.142169i	$-0.954592\pi$
$223$		−	4.24608i		−	0.284339i	0.989842	−	0.142169i	$-0.0454078\pi$
$224$			8.07838i			0.539759i
$225$	−3.45199	−	3.61715i	−0.230133	−	0.241143i
$226$	15.0381			1.00032
$227$	20.9957			1.39353			0.696767	−	0.717297i	$-0.254621\pi$
$227$	20.9957			1.39353			0.696767	+	0.717297i	$0.254621\pi$
$228$	−20.7969			−1.37731
$229$	3.10365			0.205095			0.102547	−	0.994728i	$-0.467301\pi$
$229$	3.10365			0.205095			0.102547	+	0.994728i	$0.467301\pi$
$230$	−1.50667	−	0.644802i	−0.0993471	−	0.0425170i
$231$	7.37181			0.485030
$232$		−	24.6681i		−	1.61954i
$233$		−	21.6542i		−	1.41862i	−0.704898	−	0.709308i	$-0.749007\pi$
$233$		−	21.6542i		−	1.41862i	0.704898	−	0.709308i	$-0.250993\pi$
$234$	−9.84989			−0.643907
$235$	−5.02145	+	11.7333i	−0.327563	+	0.765398i
$236$		−	17.6061i		−	1.14606i
$237$	7.60105			0.493741
$238$		−	44.7102i		−	2.89813i
$239$			15.0302i			0.972220i	0.873898	+	0.486110i	$0.161585\pi$
$239$			15.0302i			0.972220i	−0.873898	+	0.486110i	$0.838415\pi$
$240$	4.79778	−	11.2107i	0.309695	−	0.723648i
$241$			4.79389i			0.308802i	0.988008	+	0.154401i	$0.0493447\pi$
$241$			4.79389i			0.308802i	−0.988008	+	0.154401i	$0.950655\pi$
$242$	14.8372			0.953773
$243$		−	1.00000i		−	0.0641500i
$244$			7.48736i			0.479329i
$245$	−7.70071	−	3.29563i	−0.491980	−	0.210550i
$246$		−	18.8213i		−	1.20000i
$247$			19.3825i			1.23328i
$248$			52.9857i			3.36460i
$249$	−7.35263			−0.465954
$250$	−9.77195	−	26.1468i	−0.618032	−	1.65367i
$251$			1.66688i			0.105212i	0.998615	+	0.0526061i	$0.0167528\pi$
$251$			1.66688i			0.105212i	−0.998615	+	0.0526061i	$0.983247\pi$
$252$			13.8768i			0.874156i
$253$	−0.660163			−0.0415041
$254$		−	22.5563i		−	1.41531i
$255$	−4.80619	+	11.2303i	−0.300975	+	0.703271i
$256$	−32.4308			−2.02692
$257$	−0.660038			−0.0411721			−0.0205860	−	0.999788i	$-0.506553\pi$
$257$	−0.660038			−0.0411721			−0.0205860	+	0.999788i	$0.506553\pi$
$258$		−	24.3305i		−	1.51475i
$259$	14.8484	−	13.3089i	0.922632	−	0.826977i
$260$	−34.3326	−	14.6931i	−2.12922	−	0.911230i
$261$		−	4.42445i		−	0.273866i
$262$			48.1271i			2.97330i
$263$			31.0600i			1.91524i	0.288033	+	0.957620i	$0.406999\pi$
$263$			31.0600i			1.91524i	−0.288033	+	0.957620i	$0.593001\pi$
$264$		−	12.5380i		−	0.771661i
$265$	12.4279	−	29.0396i	0.763439	−	1.78389i
$266$	40.2078			2.46530
$267$	−11.7227			−0.717421
$268$			9.48024i			0.579098i
$269$	15.9502			0.972498			0.486249	−	0.873820i	$-0.338365\pi$
$269$	15.9502			0.972498			0.486249	+	0.873820i	$0.338365\pi$
$270$	2.19648	−	5.13238i	0.133673	−	0.312347i
$271$	−15.1585			−0.920812			−0.460406	−	0.887708i	$-0.652296\pi$
$271$	−15.1585			−0.920812			−0.460406	+	0.887708i	$0.652296\pi$
$272$	−29.7918			−1.80639
$273$	12.9330			0.782742
$274$		−	25.4360i		−	1.53665i
$275$	−7.76284	−	8.13425i	−0.468117	−	0.490514i
$276$		−	1.24270i		−	0.0748017i
$277$	21.8593			1.31340			0.656699	−	0.754153i	$-0.271952\pi$
$277$	21.8593			1.31340			0.656699	+	0.754153i	$0.271952\pi$
$278$	−53.3269			−3.19833
$279$			9.50346i			0.568957i
$280$	−16.0795	+	37.5720i	−0.960933	+	2.24536i
$281$			17.3597i			1.03559i	0.855503	+	0.517797i	$0.173248\pi$
$281$			17.3597i			1.03559i	−0.855503	+	0.517797i	$0.826752\pi$
$282$	−14.2499			−0.848569
$283$	−2.82213			−0.167758			−0.0838792	−	0.996476i	$-0.526731\pi$
$283$	−2.82213			−0.167758			−0.0838792	+	0.996476i	$0.526731\pi$
$284$	−5.22833			−0.310244
$285$	−10.0994	−	4.32220i	−0.598239	−	0.256025i
$286$	−22.1504			−1.30978
$287$			24.7126i			1.45874i
$288$	2.46434			0.145213
$289$	12.8440			0.755530
$290$	9.71819	−	22.7079i	0.570672	−	1.33346i
$291$		−	8.37426i		−	0.490908i
$292$		−	11.7721i		−	0.688912i
$293$		−	1.78579i		−	0.104327i	−0.998639	−	0.0521635i	$-0.983388\pi$
$293$		−	1.78579i		−	0.104327i	0.998639	−	0.0521635i	$-0.0166117\pi$
$294$		−	9.35235i		−	0.545440i
$295$	3.65905	−	8.54989i	0.213038	−	0.497794i
$296$	−22.6359	−	25.2541i	−1.31568	−	1.46787i
$297$		−	2.24880i		−	0.130489i
$298$	48.8019			2.82702
$299$	−1.15818			−0.0669794
$300$	15.3120	−	14.6129i	0.884040	−	0.843675i
$301$			31.9462i			1.84135i
$302$	−33.7540			−1.94233
$303$			4.79078i			0.275223i
$304$		−	26.7917i		−	1.53661i
$305$	−1.55609	+	3.63603i	−0.0891014	+	0.208198i
$306$	−13.6390			−0.779691
$307$			10.3292i			0.589519i	0.955571	+	0.294759i	$0.0952395\pi$
$307$			10.3292i			0.589519i	−0.955571	+	0.294759i	$0.904760\pi$
$308$			31.2062i			1.77814i
$309$		−	2.72811i		−	0.155197i
$310$	−20.8741	+	48.7754i	−1.18557	+	2.77026i
$311$		−	4.44594i		−	0.252106i	−0.992024	−	0.126053i	$-0.959769\pi$
$311$		−	4.44594i		−	0.252106i	0.992024	−	0.126053i	$-0.0402309\pi$
$312$		−	21.9965i		−	1.24531i
$313$	−0.217282			−0.0122815			−0.00614075	−	0.999981i	$-0.501955\pi$
$313$	−0.217282			−0.0122815			−0.00614075	+	0.999981i	$0.501955\pi$
$314$			46.9456i			2.64929i
$315$	−2.88400	+	6.73888i	−0.162495	+	0.379693i
$316$			32.1766i			1.81007i
$317$			12.4745i			0.700638i	0.936631	+	0.350319i	$0.113927\pi$
$317$			12.4745i			0.700638i	−0.936631	+	0.350319i	$0.886073\pi$
$318$	35.2680			1.97773
$319$		−	9.94970i		−	0.557076i
$320$	−9.77346	−	4.18269i	−0.546353	−	0.233820i
$321$	−2.86508			−0.159913
$322$			2.40258i			0.133890i
$323$			26.8387i			1.49334i
$324$	4.23317			0.235176
$325$	−13.6190	−	14.2706i	−0.755448	−	0.791592i
$326$	49.8592			2.76145
$327$	2.88647			0.159622
$328$	42.0313			2.32079
$329$	18.7103			1.03153
$330$	4.93944	−	11.5417i	0.271907	−	0.635350i
$331$		−	8.00778i		−	0.440147i	−0.975483	−	0.220074i	$-0.929370\pi$
$331$		−	8.00778i		−	0.440147i	0.975483	−	0.220074i	$-0.0706298\pi$
$332$		−	31.1249i		−	1.70820i
$333$	−4.05995	−	4.52955i	−0.222484	−	0.248218i
$334$	−32.1443			−1.75886
$335$	−1.97027	+	4.60381i	−0.107647	+	0.251533i
$336$	−17.8769			−0.975264
$337$		−	9.43123i		−	0.513752i	−0.966444	−	0.256876i	$-0.917307\pi$
$337$		−	9.43123i		−	0.513752i	0.966444	−	0.256876i	$-0.0826932\pi$
$338$	−6.40423			−0.348344
$339$			6.02335i			0.327143i
$340$	−47.5400	−	20.3454i	−2.57822	−	1.10339i
$341$			21.3714i			1.15733i
$342$		−	12.2656i		−	0.663245i
$343$		−	10.6670i		−	0.575964i
$344$	54.3342			2.92950
$345$	0.258269	−	0.603482i	0.0139047	−	0.0324904i
$346$		−	11.0300i		−	0.592976i
$347$	26.9744			1.44806			0.724031	−	0.689767i	$-0.242287\pi$
$347$	26.9744			1.44806			0.724031	+	0.689767i	$0.242287\pi$
$348$	18.7294			1.00400
$349$	10.5736			0.565992			0.282996	−	0.959121i	$-0.408672\pi$
$349$	10.5736			0.565992			0.282996	+	0.959121i	$0.408672\pi$
$350$	−29.6036	+	28.2519i	−1.58238	+	1.51013i
$351$		−	3.94527i		−	0.210583i
$352$	5.54182			0.295380
$353$	−17.2335			−0.917246			−0.458623	−	0.888631i	$-0.651657\pi$
$353$	−17.2335			−0.917246			−0.458623	+	0.888631i	$0.651657\pi$
$354$	10.3837			0.551886
$355$	−2.53899	−	1.08660i	−0.134756	−	0.0576706i
$356$		−	49.6244i		−	2.63009i
$357$	17.9082			0.947802
$358$		−	8.70816i		−	0.460240i
$359$	36.9184			1.94848			0.974240	−	0.225513i	$-0.0724058\pi$
$359$	36.9184			1.94848			0.974240	+	0.225513i	$0.0724058\pi$
$360$	11.4615	+	4.90511i	0.604074	+	0.258522i
$361$	−5.13599			−0.270315
$362$	−17.7520			−0.933022
$363$			5.94289i			0.311921i
$364$			54.7477i			2.86956i
$365$	2.44659	−	5.71680i	0.128060	−	0.299231i
$366$	−4.41588			−0.230822
$367$		−	31.9868i		−	1.66970i	−0.550478	−	0.834850i	$-0.685554\pi$
$367$		−	31.9868i		−	1.66970i	0.550478	−	0.834850i	$-0.314446\pi$
$368$	1.60092			0.0834535
$369$	7.53868			0.392448
$370$	−10.8881	−	32.1650i	−0.566048	−	1.67218i
$371$	−46.3072			−2.40415
$372$	−40.2298			−2.08582
$373$		−	28.0603i		−	1.45291i	−0.687215	−	0.726454i	$-0.741167\pi$
$373$		−	28.0603i		−	1.45291i	0.687215	−	0.726454i	$-0.258833\pi$
$374$	−30.6714			−1.58598
$375$	10.4728	−	3.91405i	0.540815	−	0.202121i
$376$		−	31.8225i		−	1.64112i
$377$		−	17.4556i		−	0.899011i
$378$	−8.18423			−0.420951
$379$	30.3046			1.55664			0.778322	−	0.627865i	$-0.216071\pi$
$379$	30.3046			1.55664			0.778322	+	0.627865i	$0.216071\pi$
$380$	18.2966	−	42.7527i	0.938596	−	2.19317i
$381$	9.03468			0.462860
$382$			33.8624i			1.73255i
$383$	0.0693300			0.00354260			0.00177130	−	0.999998i	$-0.499436\pi$
$383$	0.0693300			0.00354260			0.00177130	+	0.999998i	$0.499436\pi$
$384$		−	16.7984i		−	0.857237i
$385$	−6.48554	+	15.1544i	−0.330534	+	0.772340i
$386$	−50.1897			−2.55459
$387$	9.74531			0.495382
$388$	35.4497			1.79969
$389$			21.3766i			1.08383i	0.840432	+	0.541917i	$0.182301\pi$
$389$			21.3766i			1.08383i	−0.840432	+	0.541917i	$0.817699\pi$
$390$	8.66569	−	20.2486i	0.438804	−	1.02533i
$391$	−1.60372			−0.0811036
$392$	20.8854			1.05487
$393$	−19.2768			−0.972387
$394$			61.5153i			3.09910i
$395$	−6.68722	+	15.6256i	−0.336470	+	0.786212i
$396$	9.51957			0.478376
$397$			33.6739i			1.69004i	0.534733	+	0.845021i	$0.320412\pi$
$397$			33.6739i			1.69004i	−0.534733	+	0.845021i	$0.679588\pi$
$398$			20.4875i			1.02694i
$399$			16.1048i			0.806249i
$400$	18.8251	+	19.7258i	0.941256	+	0.986291i
$401$			0.266817i			0.0133242i	0.999978	+	0.00666211i	$0.00212063\pi$
$401$			0.266817i			0.0133242i	−0.999978	+	0.00666211i	$0.997879\pi$
$402$	−5.59124			−0.278866
$403$			37.4937i			1.86769i
$404$	−20.2802			−1.00898
$405$	2.05572	+	0.879776i	0.102150	+	0.0437164i
$406$	−36.2107			−1.79711
$407$	−9.13001	−	10.1861i	−0.452558	−	0.504904i
$408$		−	30.4583i		−	1.50791i
$409$			13.6125i			0.673093i	0.941667	+	0.336546i	$0.109259\pi$
$409$			13.6125i			0.673093i	−0.941667	+	0.336546i	$0.890741\pi$
$410$	38.6914	+	16.5585i	1.91083	+	0.817767i
$411$	10.1881			0.502544
$412$	11.5485			0.568956
$413$	−13.6339			−0.670879
$414$	0.732917			0.0360209
$415$	6.46866	−	15.1150i	0.317534	−	0.741964i
$416$	9.72249			0.476684
$417$		−	21.3595i		−	1.04598i
$418$		−	27.5828i		−	1.34912i
$419$	−13.0502			−0.637546			−0.318773	−	0.947831i	$-0.603271\pi$
$419$	−13.0502			−0.637546			−0.318773	+	0.947831i	$0.603271\pi$
$420$	−28.5268	−	12.2085i	−1.39197	−	0.595712i
$421$			9.41547i			0.458882i	0.973323	+	0.229441i	$0.0736898\pi$
$421$			9.41547i			0.458882i	−0.973323	+	0.229441i	$0.926310\pi$
$422$	45.2403			2.20226
$423$		−	5.70765i		−	0.277515i
$424$			78.7595i			3.82490i
$425$	−18.8581	−	19.7604i	−0.914752	−	0.958519i
$426$		−	3.08355i		−	0.149399i
$427$	5.79810			0.280590
$428$		−	12.1284i		−	0.586247i
$429$		−	8.87213i		−	0.428350i
$430$	50.0167	+	21.4054i	2.41202	+	1.03226i
$431$		−	25.4274i		−	1.22480i	−0.790550	−	0.612398i	$-0.790205\pi$
$431$		−	25.4274i		−	1.22480i	0.790550	−	0.612398i	$-0.209795\pi$
$432$			5.45341i			0.262378i
$433$			33.2421i			1.59751i	0.601654	+	0.798757i	$0.294509\pi$
$433$			33.2421i			1.59751i	−0.601654	+	0.798757i	$0.705491\pi$
$434$	77.7785			3.73349
$435$	9.09543	+	3.89252i	0.436093	+	0.186632i
$436$			12.2189i			0.585180i
$437$		−	1.44222i		−	0.0689909i
$438$	6.94294			0.331747
$439$		−	36.4241i		−	1.73843i	−0.494435	−	0.869214i	$-0.664625\pi$
$439$		−	36.4241i		−	1.73843i	0.494435	−	0.869214i	$-0.335375\pi$
$440$	25.7747	+	11.0306i	1.22876	+	0.525865i
$441$	3.74599			0.178380
$442$	−53.8096			−2.55946
$443$		−	32.9382i		−	1.56494i	−0.622688	−	0.782470i	$-0.713959\pi$
$443$		−	32.9382i		−	1.56494i	0.622688	−	0.782470i	$-0.286041\pi$
$444$	19.1744	−	17.1865i	0.909976	−	0.815633i
$445$	10.3134	−	24.0987i	0.488902	−	1.14239i
$446$			10.6009i			0.501968i
$447$			19.5471i			0.924545i
$448$			15.5850i			0.736323i
$449$		−	20.2960i		−	0.957827i	−0.877862	−	0.478914i	$-0.841031\pi$
$449$		−	20.2960i		−	0.957827i	0.877862	−	0.478914i	$-0.158969\pi$
$450$	8.61835	+	9.03069i	0.406273	+	0.425711i
$451$	16.9530			0.798285
$452$	−25.4979			−1.19932
$453$		−	13.5198i		−	0.635217i
$454$	−52.4186			−2.46013
$455$	−11.3782	+	26.5867i	−0.533416	+	1.24640i
$456$	27.3911			1.28271
$457$	2.82194			0.132005			0.0660025	−	0.997819i	$-0.478975\pi$
$457$	2.82194			0.132005			0.0660025	+	0.997819i	$0.478975\pi$
$458$	−7.74866			−0.362071
$459$		−	5.46297i		−	0.254989i
$460$	2.55464	+	1.09330i	0.119111	+	0.0509752i
$461$		−	13.3804i		−	0.623186i	−0.950216	−	0.311593i	$-0.899137\pi$
$461$		−	13.3804i		−	0.623186i	0.950216	−	0.311593i	$-0.100863\pi$
$462$	−18.4047			−0.856264
$463$	23.0376			1.07065			0.535323	−	0.844647i	$-0.320190\pi$
$463$	23.0376			1.07065			0.535323	+	0.844647i	$0.320190\pi$
$464$			24.1283i			1.12013i
$465$	−19.5365	−	8.36091i	−0.905982	−	0.387728i
$466$			54.0627i			2.50441i
$467$	−3.28736			−0.152121			−0.0760604	−	0.997103i	$-0.524234\pi$
$467$	−3.28736			−0.152121			−0.0760604	+	0.997103i	$0.524234\pi$
$468$	16.7010			0.772004
$469$	7.34136			0.338992
$470$	12.5367	−	29.2938i	0.578275	−	1.35122i
$471$	−18.8036			−0.866422
$472$			23.1885i			1.06734i
$473$	21.9153			1.00767
$474$	−18.9770			−0.871644
$475$	17.7705	−	16.9591i	0.815365	−	0.778135i
$476$			75.8085i			3.47468i
$477$			14.1262i			0.646795i
$478$		−	37.5248i		−	1.71634i
$479$			29.4663i			1.34635i	0.739483	+	0.673176i	$0.235070\pi$
$479$			29.4663i			1.34635i	−0.739483	+	0.673176i	$0.764930\pi$
$480$	−2.16807	+	5.06600i	−0.0989583	+	0.231230i
$481$	−16.0176	−	17.8703i	−0.730339	−	0.814816i
$482$		−	11.9686i		−	0.545154i
$483$	−0.962328			−0.0437874
$484$	−25.1573			−1.14351
$485$	17.2151	+	7.36747i	0.781700	+	0.334539i
$486$			2.49663i			0.113250i
$487$	19.7608			0.895446			0.447723	−	0.894172i	$-0.352235\pi$
$487$	19.7608			0.895446			0.447723	+	0.894172i	$0.352235\pi$
$488$		−	9.86143i		−	0.446406i
$489$			19.9706i			0.903101i
$490$	19.2258	+	8.22797i	0.868535	+	0.371702i
$491$	−0.408100			−0.0184173			−0.00920865	−	0.999958i	$-0.502931\pi$
$491$	−0.408100			−0.0184173			−0.00920865	+	0.999958i	$0.502931\pi$
$492$			31.9125i			1.43873i
$493$		−	24.1706i		−	1.08859i
$494$		−	48.3909i		−	2.17721i
$495$	4.62291	+	1.97844i	0.207784	+	0.0889243i
$496$		−	51.8263i		−	2.32707i
$497$			4.04874i			0.181611i
$498$	18.3568			0.822588
$499$		−	3.64052i		−	0.162972i	−0.996674	−	0.0814859i	$-0.974033\pi$
$499$		−	3.64052i		−	0.162972i	0.996674	−	0.0814859i	$-0.0259666\pi$
$500$	16.5689	+	44.3333i	0.740982	+	1.98265i
$501$		−	12.8751i		−	0.575216i
$502$		−	4.16157i		−	0.185740i
$503$	−7.53880			−0.336138			−0.168069	−	0.985775i	$-0.553753\pi$
$503$	−7.53880			−0.336138			−0.168069	+	0.985775i	$0.553753\pi$
$504$		−	18.2768i		−	0.814114i
$505$	−9.84852	−	4.21481i	−0.438253	−	0.187557i
$506$	1.64818			0.0732707
$507$		−	2.56515i		−	0.113922i
$508$			38.2454i			1.69686i
$509$	−8.09964			−0.359010			−0.179505	−	0.983757i	$-0.557450\pi$
$509$	−8.09964			−0.359010			−0.179505	+	0.983757i	$0.557450\pi$
$510$	11.9993	−	28.0380i	0.531337	−	1.24155i
$511$	−9.11616			−0.403275
$512$	47.3710			2.09352
$513$	4.91284			0.216907
$514$	1.64787			0.0726846
$515$	5.60823	+	2.40012i	0.247128	+	0.105762i
$516$			41.2536i			1.81609i
$517$		−	12.8354i		−	0.564499i
$518$	−37.0709	+	33.2275i	−1.62880	+	1.45993i
$519$	4.41795			0.193926
$520$	45.2187	+	19.3520i	1.98297	+	0.848641i
$521$	25.6587			1.12413			0.562064	−	0.827094i	$-0.310007\pi$
$521$	25.6587			1.12413			0.562064	+	0.827094i	$0.310007\pi$
$522$			11.0462i			0.483480i
$523$	−11.2037			−0.489904			−0.244952	−	0.969535i	$-0.578772\pi$
$523$	−11.2037			−0.489904			−0.244952	+	0.969535i	$0.578772\pi$
$524$		−	81.6021i		−	3.56481i
$525$	−11.3160	−	11.8574i	−0.493870	−	0.517499i
$526$		−	77.5454i		−	3.38114i
$527$			51.9171i			2.26154i
$528$			12.2636i			0.533707i
$529$	−22.9138			−0.996253
$530$	−31.0279	+	72.5011i	−1.34777	+	3.14925i
$531$			4.15907i			0.180488i
$532$	−68.1745			−2.95574
$533$	29.7421			1.28827
$534$	29.2674			1.26652
$535$	2.52063	−	5.88980i	0.108976	−	0.254638i
$536$		−	12.4862i		−	0.539322i
$537$	3.48796			0.150517
$538$	−39.8217			−1.71683
$539$	8.42398			0.362846
$540$	−3.72424	+	8.70223i	−0.160266	+	0.374484i
$541$		−	5.62489i		−	0.241833i	−0.992663	−	0.120916i	$-0.961417\pi$
$541$		−	5.62489i		−	0.241833i	0.992663	−	0.120916i	$-0.0385833\pi$
$542$	37.8452			1.62559
$543$		−	7.11036i		−	0.305135i
$544$	13.4626			0.577205
$545$	−2.53944	+	5.93378i	−0.108778	+	0.254175i
$546$	−32.2890			−1.38184
$547$	16.8708			0.721343			0.360672	−	0.932693i	$-0.382548\pi$
$547$	16.8708			0.721343			0.360672	+	0.932693i	$0.382548\pi$
$548$			43.1281i			1.84234i
$549$		−	1.76873i		−	0.0754877i
$550$	19.3810	+	20.3082i	0.826407	+	0.865946i
$551$	21.7366			0.926010
$552$			1.63673i			0.0696639i
$553$	24.9171			1.05958
$554$	−54.5746			−2.31865
$555$	12.8833	−	4.36113i	0.546867	−	0.185120i
$556$	90.4186			3.83460
$557$	−31.0898			−1.31732			−0.658658	−	0.752443i	$-0.728875\pi$
$557$	−31.0898			−1.31732			−0.658658	+	0.752443i	$0.728875\pi$
$558$		−	23.7266i		−	1.00443i
$559$	38.4479			1.62617
$560$	15.7276	−	36.7499i	0.664614	−	1.55297i
$561$		−	12.2851i		−	0.518678i
$562$		−	43.3409i		−	1.82822i
$563$	15.6530			0.659697			0.329849	−	0.944034i	$-0.393002\pi$
$563$	15.6530			0.659697			0.329849	+	0.944034i	$0.393002\pi$
$564$	24.1615			1.01738
$565$	−12.3823	−	5.29920i	−0.520929	−	0.222939i
$566$	7.04583			0.296158
$567$		−	3.27811i		−	0.137668i
$568$	6.88611			0.288935
$569$		−	37.4530i		−	1.57011i	−0.619425	−	0.785056i	$-0.712634\pi$
$569$		−	37.4530i		−	1.57011i	0.619425	−	0.785056i	$-0.287366\pi$
$570$	25.2146	+	10.7909i	1.05612	+	0.451983i
$571$	0.722968			0.0302553			0.0151276	−	0.999886i	$-0.495185\pi$
$571$	0.722968			0.0302553			0.0151276	+	0.999886i	$0.495185\pi$
$572$	37.5573			1.57035
$573$	−13.5632			−0.566611
$574$		−	61.6983i		−	2.57524i
$575$	1.01337	+	1.06186i	0.0422606	+	0.0442825i
$576$	4.75427			0.198095
$577$	17.8039			0.741185			0.370593	−	0.928796i	$-0.379155\pi$
$577$	17.8039			0.741185			0.370593	+	0.928796i	$0.379155\pi$
$578$	−32.0668			−1.33380
$579$		−	20.1029i		−	0.835450i
$580$	−16.4777	+	38.5025i	−0.684200	+	1.59873i
$581$	−24.1027			−0.999948
$582$			20.9074i			0.866641i
$583$			31.7670i			1.31566i
$584$			15.5048i			0.641593i
$585$	8.11038	+	3.47095i	0.335323	+	0.143506i
$586$			4.45846i			0.184177i
$587$	−16.3848			−0.676271			−0.338136	−	0.941097i	$-0.609796\pi$
$587$	−16.3848			−0.676271			−0.338136	+	0.941097i	$0.609796\pi$
$588$			15.8574i			0.653949i
$589$	−46.6890			−1.92379
$590$	−9.13530	+	21.3459i	−0.376094	+	0.878798i
$591$	−24.6393			−1.01353
$592$	22.1406	+	24.7015i	0.909972	+	1.01523i
$593$			19.9232i			0.818148i	0.912501	+	0.409074i	$0.134148\pi$
$593$			19.9232i			0.818148i	−0.912501	+	0.409074i	$0.865852\pi$
$594$			5.61443i			0.230363i
$595$	−15.7552	+	36.8143i	−0.645900	+	1.50924i
$596$	−82.7462			−3.38941
$597$	−8.20604			−0.335851
$598$	2.89155			0.118244
$599$	−4.28569			−0.175109			−0.0875543	−	0.996160i	$-0.527905\pi$
$599$	−4.28569			−0.175109			−0.0875543	+	0.996160i	$0.527905\pi$
$600$	−20.1671	+	19.2463i	−0.823319	+	0.785726i
$601$	−14.8906			−0.607399			−0.303699	−	0.952768i	$-0.598222\pi$
$601$	−14.8906			−0.607399			−0.303699	+	0.952768i	$0.598222\pi$
$602$		−	79.7579i		−	3.25069i
$603$		−	2.23951i		−	0.0911999i
$604$	57.2318			2.32873
$605$	−12.2169	−	5.22841i	−0.496689	−	0.212565i
$606$		−	11.9608i		−	0.485875i
$607$	−35.6294			−1.44615			−0.723077	−	0.690767i	$-0.757273\pi$
$607$	−35.6294			−1.44615			−0.723077	+	0.690767i	$0.757273\pi$
$608$			12.1069i			0.491000i
$609$		−	14.5038i		−	0.587724i
$610$	3.88498	−	9.07782i	0.157298	−	0.367550i
$611$		−	22.5182i		−	0.910989i
$612$	23.1257			0.934801
$613$		−	32.0180i		−	1.29320i	−0.762831	−	0.646598i	$-0.776191\pi$
$613$		−	32.0180i		−	1.29320i	0.762831	−	0.646598i	$-0.223809\pi$
$614$		−	25.7882i		−	1.04073i
$615$	−6.63234	+	15.4974i	−0.267442	+	0.624917i
$616$		−	41.1009i		−	1.65600i
$617$			38.5318i			1.55123i	0.631204	+	0.775617i	$0.282561\pi$
$617$			38.5318i			1.55123i	−0.631204	+	0.775617i	$0.717439\pi$
$618$			6.81108i			0.273982i
$619$	−14.2983			−0.574695			−0.287348	−	0.957826i	$-0.592773\pi$
$619$	−14.2983			−0.574695			−0.287348	+	0.957826i	$0.592773\pi$
$620$	35.3932	−	82.7013i	1.42143	−	3.32136i
$621$			0.293562i			0.0117802i
$622$			11.0999i			0.445064i
$623$	−38.4284			−1.53960
$624$			21.5152i			0.861297i
$625$	−1.16754	+	24.9727i	−0.0467015	+	0.998909i
$626$	0.542473			0.0216816
$627$	11.0480			0.441215
$628$		−	79.5987i		−	3.17634i
$629$	−22.1793	−	24.7448i	−0.884348	−	0.986639i
$630$	7.20029	−	16.8245i	0.286866	−	0.670304i
$631$		−	8.75965i		−	0.348716i	−0.984682	−	0.174358i	$-0.944215\pi$
$631$		−	8.75965i		−	0.348716i	0.984682	−	0.174358i	$-0.0557850\pi$
$632$		−	42.3790i		−	1.68575i
$633$			18.1205i			0.720226i
$634$		−	31.1442i		−	1.23690i
$635$	−7.94849	+	18.5728i	−0.315426	+	0.737039i
$636$	−59.7987			−2.37117
$637$	14.7789			0.585562
$638$			24.8407i			0.983454i
$639$	1.23508			0.0488592
$640$	34.5328	+	14.7788i	1.36503	+	0.584183i
$641$	2.09453			0.0827288			0.0413644	−	0.999144i	$-0.486830\pi$
$641$	2.09453			0.0827288			0.0413644	+	0.999144i	$0.486830\pi$
$642$	7.15304			0.282308
$643$	−1.74331			−0.0687496			−0.0343748	−	0.999409i	$-0.510944\pi$
$643$	−1.74331			−0.0687496			−0.0343748	+	0.999409i	$0.510944\pi$
$644$		−	4.07370i		−	0.160526i
$645$	−8.57369	+	20.0337i	−0.337589	+	0.788825i
$646$		−	67.0063i		−	2.63633i
$647$	−13.2429			−0.520633			−0.260317	−	0.965523i	$-0.583827\pi$
$647$	−13.2429			−0.520633			−0.260317	+	0.965523i	$0.583827\pi$
$648$	−5.57542			−0.219023
$649$			9.35292i			0.367134i
$650$	34.0017	+	35.6285i	1.33366	+	1.39747i
$651$			31.1534i			1.22100i
$652$	−84.5390			−3.31080
$653$	−35.4013			−1.38536			−0.692680	−	0.721245i	$-0.743570\pi$
$653$	−35.4013			−1.38536			−0.692680	+	0.721245i	$0.743570\pi$
$654$	−7.20645			−0.281794
$655$	16.9593	−	39.6278i	0.662654	−	1.54839i
$656$	−41.1115			−1.60514
$657$			2.78092i			0.108494i
$658$	−46.7127			−1.82105
$659$	−40.1067			−1.56234			−0.781168	−	0.624320i	$-0.785376\pi$
$659$	−40.1067			−1.56234			−0.781168	+	0.624320i	$0.785376\pi$
$660$	−8.37508	+	19.5696i	−0.326000	+	0.761745i
$661$			10.9642i			0.426458i	0.977002	+	0.213229i	$0.0683981\pi$
$661$			10.9642i			0.426458i	−0.977002	+	0.213229i	$0.931602\pi$
$662$			19.9925i			0.777030i
$663$		−	21.5529i		−	0.837044i
$664$			40.9939i			1.59087i
$665$	−33.1070	−	14.1686i	−1.28384	−	0.549436i
$666$	10.1362	+	11.3086i	0.392769	+	0.438200i
$667$			1.29885i			0.0502916i
$668$	54.5025			2.10876
$669$	−4.24608			−0.164163
$670$	4.91903	−	11.4940i	0.190039	−	0.444053i
$671$		−	3.97753i		−	0.153551i
$672$	8.07838			0.311630
$673$			51.0171i			1.96656i	0.182092	+	0.983282i	$0.441713\pi$
$673$			51.0171i			1.96656i	−0.182092	+	0.983282i	$0.558287\pi$
$674$			23.5463i			0.906970i
$675$	−3.61715	+	3.45199i	−0.139224	+	0.132867i
$676$	10.8587			0.417643
$677$		−	30.8147i		−	1.18431i	−0.805825	−	0.592153i	$-0.798278\pi$
$677$		−	30.8147i		−	1.18431i	0.805825	−	0.592153i	$-0.201722\pi$
$678$		−	15.0381i		−	0.577534i
$679$		−	27.4517i		−	1.05350i
$680$	62.6138	+	26.7965i	2.40113	+	1.02760i
$681$		−	20.9957i		−	0.804557i
$682$		−	53.3565i		−	2.04313i
$683$	−6.15884			−0.235662			−0.117831	−	0.993034i	$-0.537594\pi$
$683$	−6.15884			−0.235662			−0.117831	+	0.993034i	$0.537594\pi$
$684$			20.7969i			0.795189i
$685$	−8.96327	+	20.9440i	−0.342469	+	0.800228i
$686$			26.6316i			1.01680i
$687$		−	3.10365i		−	0.118411i
$688$	−53.1452			−2.02614
$689$			55.7317i			2.12321i
$690$	−0.644802	+	1.50667i	−0.0245472	+	0.0573581i
$691$	−17.5439			−0.667400			−0.333700	−	0.942679i	$-0.608297\pi$
$691$	−17.5439			−0.667400			−0.333700	+	0.942679i	$0.608297\pi$
$692$			18.7019i			0.710941i
$693$		−	7.37181i		−	0.280032i
$694$	−67.3452			−2.55639
$695$	43.9092	+	18.7916i	1.66557	+	0.712805i
$696$	−24.6681			−0.935043
$697$	41.1835			1.55994
$698$	−26.3984			−0.999195
$699$	−21.6542			−0.819039
$700$	50.1944	−	47.9026i	1.89717	−	1.81055i
$701$		−	2.97672i		−	0.112429i	−0.998419	−	0.0562145i	$-0.982097\pi$
$701$		−	2.97672i		−	0.112429i	0.998419	−	0.0562145i	$-0.0179031\pi$
$702$			9.84989i			0.371760i
$703$	22.2530	−	19.9459i	0.839286	−	0.752272i
$704$	10.6914			0.402948
$705$	11.7333	+	5.02145i	0.441903	+	0.189119i
$706$	43.0257			1.61929
$707$			15.7047i			0.590636i
$708$	−17.6061			−0.661676
$709$			33.3854i			1.25382i	0.779094	+	0.626908i	$0.215680\pi$
$709$			33.3854i			1.25382i	−0.779094	+	0.626908i	$0.784320\pi$
$710$	6.33893	+	2.71283i	0.237896	+	0.101811i
$711$		−	7.60105i		−	0.285062i
$712$			65.3592i			2.44944i
$713$		−	2.78986i		−	0.104481i
$714$	−44.7102			−1.67324
$715$	18.2386	+	7.80548i	0.682086	+	0.291908i
$716$			14.7651i			0.551799i
$717$	15.0302			0.561311
$718$	−92.1718			−3.43982
$719$	−4.12414			−0.153805			−0.0769023	−	0.997039i	$-0.524503\pi$
$719$	−4.12414			−0.153805			−0.0769023	+	0.997039i	$0.524503\pi$
$720$	−11.2107	−	4.79778i	−0.417798	−	0.178803i
$721$		−	8.94302i		−	0.333056i
$722$	12.8227			0.477210
$723$	4.79389			0.178287
$724$	30.0994			1.11863
$725$	−16.0039	+	15.2731i	−0.594369	+	0.567230i
$726$		−	14.8372i		−	0.550661i
$727$	−50.8187			−1.88476			−0.942380	−	0.334545i	$-0.891417\pi$
$727$	−50.8187			−1.88476			−0.942380	+	0.334545i	$0.891417\pi$
$728$		−	72.1069i		−	2.67246i
$729$	−1.00000			−0.0370370
$730$	−6.10823	+	14.2728i	−0.226076	+	0.528259i
$731$	53.2383			1.96909
$732$	7.48736			0.276741
$733$			0.710903i			0.0262578i	0.999914	+	0.0131289i	$0.00417918\pi$
$733$			0.710903i			0.0262578i	−0.999914	+	0.0131289i	$0.995821\pi$
$734$			79.8594i			2.94766i
$735$	−3.29563	+	7.70071i	−0.121561	+	0.284045i
$736$	−0.723437			−0.0266663
$737$		−	5.03622i		−	0.185511i
$738$	−18.8213			−0.692822
$739$	1.59993			0.0588545			0.0294273	−	0.999567i	$-0.490632\pi$
$739$	1.59993			0.0588545			0.0294273	+	0.999567i	$0.490632\pi$
$740$	18.4614	+	54.5374i	0.678656	+	2.00484i
$741$	19.3825			0.712033
$742$	115.612			4.24425
$743$		−	24.0842i		−	0.883565i	−0.897122	−	0.441782i	$-0.854346\pi$
$743$		−	24.0842i		−	0.883565i	0.897122	−	0.441782i	$-0.145654\pi$
$744$	52.9857			1.94255
$745$	−40.1834	−	17.1970i	−1.47220	−	0.630051i
$746$			70.0563i			2.56494i
$747$			7.35263i			0.269019i
$748$	52.0051			1.90149
$749$	−9.39203			−0.343177
$750$	−26.1468	+	9.77195i	−0.954747	+	0.356821i
$751$	−16.8436			−0.614632			−0.307316	−	0.951608i	$-0.599431\pi$
$751$	−16.8436			−0.614632			−0.307316	+	0.951608i	$0.599431\pi$
$752$			31.1262i			1.13505i
$753$	1.66688			0.0607443
$754$			43.5803i			1.58710i
$755$	27.7930	+	11.8944i	1.01149	+	0.432882i
$756$	13.8768			0.504694
$757$	−54.8409			−1.99323			−0.996613	−	0.0822337i	$-0.973795\pi$
$757$	−54.8409			−1.99323			−0.996613	+	0.0822337i	$0.973795\pi$
$758$	−75.6596			−2.74808
$759$			0.660163i			0.0239624i
$760$	−24.0980	+	56.3085i	−0.874128	+	2.04253i
$761$	27.4677			0.995705			0.497853	−	0.867262i	$-0.334122\pi$
$761$	27.4677			0.995705			0.497853	+	0.867262i	$0.334122\pi$
$762$	−22.5563			−0.817127
$763$	9.46215			0.342553
$764$		−	57.4155i		−	2.07722i
$765$	11.2303	+	4.80619i	0.406034	+	0.173768i
$766$	−0.173091			−0.00625405
$767$			16.4086i			0.592482i
$768$			32.4308i			1.17024i
$769$			4.90565i			0.176902i	0.996081	+	0.0884512i	$0.0281917\pi$
$769$			4.90565i			0.176902i	−0.996081	+	0.0884512i	$0.971808\pi$
$770$	16.1920	−	37.8350i	0.583520	−	1.36348i
$771$			0.660038i			0.0237707i
$772$	85.0993			3.06279
$773$		−	3.39995i		−	0.122288i	−0.998129	−	0.0611439i	$-0.980525\pi$
$773$		−	3.39995i		−	0.122288i	0.998129	−	0.0611439i	$-0.0194749\pi$
$774$	−24.3305			−0.874541
$775$	34.3754	−	32.8058i	1.23480	−	1.17842i
$776$	−46.6900			−1.67607
$777$	−13.3089	−	14.8484i	−0.477455	−	0.532682i
$778$		−	53.3694i		−	1.91339i
$779$			37.0363i			1.32696i
$780$	−14.6931	+	34.3326i	−0.526099	+	1.22931i
$781$	2.77746			0.0993853
$782$	4.00390			0.143179
$783$	−4.42445			−0.158117
$784$	−20.4284			−0.729586
$785$	16.5429	−	38.6549i	0.590442	−	1.37965i
$786$	48.1271			1.71664
$787$		−	19.2002i		−	0.684414i	−0.939624	−	0.342207i	$-0.888826\pi$
$787$		−	19.2002i		−	0.684414i	0.939624	−	0.342207i	$-0.111174\pi$
$788$		−	104.303i		−	3.71562i
$789$	31.0600			1.10576
$790$	16.6955	−	39.0115i	0.594000	−	1.38797i
$791$			19.7452i			0.702058i
$792$	−12.5380			−0.445518
$793$		−	6.97813i		−	0.247801i
$794$		−	84.0713i		−	2.98358i
$795$	−29.0396	−	12.4279i	−1.02993	−	0.440772i
$796$		−	34.7376i		−	1.23124i
$797$	23.6541			0.837870			0.418935	−	0.908016i	$-0.362404\pi$
$797$	23.6541			0.837870			0.418935	+	0.908016i	$0.362404\pi$
$798$		−	40.2078i		−	1.42334i
$799$		−	31.1807i		−	1.10309i
$800$	−8.50688	−	8.91389i	−0.300764	−	0.315154i
$801$			11.7227i			0.414203i
$802$		−	0.666145i		−	0.0235224i
$803$			6.25374i			0.220690i
$804$	9.48024			0.334342
$805$	0.846633	−	1.97828i	0.0298399	−	0.0697252i
$806$		−	93.6080i		−	3.29720i
$807$		−	15.9502i		−	0.561472i
$808$	26.7106			0.939676
$809$		−	22.2243i		−	0.781366i	−0.920525	−	0.390683i	$-0.872239\pi$
$809$		−	22.2243i		−	0.781366i	0.920525	−	0.390683i	$-0.127761\pi$
$810$	−5.13238	−	2.19648i	−0.180334	−	0.0771763i
$811$	−21.8095			−0.765836			−0.382918	−	0.923782i	$-0.625081\pi$
$811$	−21.8095			−0.765836			−0.382918	+	0.923782i	$0.625081\pi$
$812$	61.3971			2.15462
$813$			15.1585i			0.531631i
$814$	22.7943	+	25.4309i	0.798939	+	0.891351i
$815$	−41.0540	−	17.5696i	−1.43806	−	0.615437i
$816$			29.7918i			1.04292i
$817$			47.8772i			1.67501i
$818$		−	33.9853i		−	1.18827i
$819$		−	12.9330i		−	0.451916i
$820$	−65.6033	−	28.0759i	−2.29097	−	0.980452i
$821$	−19.3381			−0.674904			−0.337452	−	0.941343i	$-0.609565\pi$
$821$	−19.3381			−0.674904			−0.337452	+	0.941343i	$0.609565\pi$
$822$	−25.4360			−0.887183
$823$		−	22.2966i		−	0.777211i	−0.921404	−	0.388606i	$-0.872957\pi$
$823$		−	22.2966i		−	0.777211i	0.921404	−	0.388606i	$-0.127043\pi$
$824$	−15.2103			−0.529877
$825$	−8.13425	+	7.76284i	−0.283198	+	0.270267i
$826$	34.0388			1.18436
$827$	18.7640			0.652487			0.326243	−	0.945286i	$-0.394217\pi$
$827$	18.7640			0.652487			0.326243	+	0.945286i	$0.394217\pi$
$828$	−1.24270			−0.0431868
$829$			21.4124i			0.743685i	0.928296	+	0.371842i	$0.121274\pi$
$829$			21.4124i			0.743685i	−0.928296	+	0.371842i	$0.878726\pi$
$830$	−16.1499	+	37.7365i	−0.560570	+	1.30985i
$831$		−	21.8593i		−	0.758291i
$832$	18.7569			0.650278
$833$	20.4642			0.709042
$834$			53.3269i			1.84656i
$835$	26.4676	+	11.3272i	0.915949	+	0.391993i
$836$			46.7681i			1.61751i
$837$	9.50346			0.328488
$838$	32.5817			1.12551
$839$	19.2864			0.665842			0.332921	−	0.942955i	$-0.391966\pi$
$839$	19.2864			0.665842			0.332921	+	0.942955i	$0.391966\pi$
$840$	37.5720	+	16.0795i	1.29636	+	0.554795i
$841$	9.42429			0.324975
$842$		−	23.5070i		−	0.810104i
$843$	17.3597			0.597901
$844$	−76.7074			−2.64038
$845$	5.27323	+	2.25676i	0.181405	+	0.0776347i
$846$			14.2499i			0.489921i
$847$			19.4814i			0.669390i
$848$		−	77.0361i		−	2.64543i
$849$			2.82213i			0.0968554i
$850$	47.0818	+	49.3344i	1.61489	+	1.69215i
$851$	1.19185	+	1.32970i	0.0408560	+	0.0455817i
$852$			5.22833i			0.179119i
$853$	−45.5229			−1.55868			−0.779338	−	0.626604i	$-0.784444\pi$
$853$	−45.5229			−1.55868			−0.779338	+	0.626604i	$0.784444\pi$
$854$	−14.4757			−0.495349
$855$	−4.32220	+	10.0994i	−0.147816	+	0.345393i
$856$			15.9740i			0.545980i
$857$	21.0092			0.717662			0.358831	−	0.933403i	$-0.383175\pi$
$857$	21.0092			0.717662			0.358831	+	0.933403i	$0.383175\pi$
$858$			22.1504i			0.756204i
$859$			35.0580i			1.19616i	0.801436	+	0.598081i	$0.204070\pi$
$859$			35.0580i			1.19616i	−0.801436	+	0.598081i	$0.795930\pi$
$860$	−84.8060	−	36.2939i	−2.89186	−	1.23761i
$861$	24.7126			0.842203
$862$			63.4829i			2.16224i
$863$		−	5.18866i		−	0.176624i	−0.996093	−	0.0883120i	$-0.971853\pi$
$863$		−	5.18866i		−	0.176624i	0.996093	−	0.0883120i	$-0.0281473\pi$
$864$		−	2.46434i		−	0.0838386i
$865$	−3.88680	+	9.08208i	−0.132155	+	0.308800i
$866$		−	82.9933i		−	2.82023i
$867$		−	12.8440i		−	0.436205i
$868$	−131.878			−4.47622
$869$		−	17.0932i		−	0.579849i
$870$	−22.7079	−	9.71819i	−0.769872	−	0.329478i
$871$		−	8.83547i		−	0.299379i
$872$		−	16.0933i		−	0.544986i
$873$	−8.37426			−0.283426
$874$			3.60070i			0.121796i
$875$	34.3311	−	12.8307i	1.16060	−	0.433756i
$876$	−11.7721			−0.397743
$877$		−	35.6915i		−	1.20522i	−0.798037	−	0.602608i	$-0.794128\pi$
$877$		−	35.6915i		−	1.20522i	0.798037	−	0.602608i	$-0.205872\pi$
$878$			90.9377i			3.06900i
$879$	−1.78579			−0.0602332
$880$	−25.2107	−	10.7893i	−0.849851	−	0.363706i
$881$	34.2013			1.15227			0.576135	−	0.817354i	$-0.304560\pi$
$881$	34.2013			1.15227			0.576135	+	0.817354i	$0.304560\pi$
$882$	−9.35235			−0.314910
$883$	23.9790			0.806958			0.403479	−	0.914989i	$-0.367801\pi$
$883$	23.9790			0.806958			0.403479	+	0.914989i	$0.367801\pi$
$884$	91.2371			3.06863
$885$	−8.54989	−	3.65905i	−0.287401	−	0.122998i
$886$			82.2345i			2.76272i
$887$			3.62960i			0.121870i	0.998142	+	0.0609350i	$0.0194082\pi$
$887$			3.62960i			0.121870i	−0.998142	+	0.0609350i	$0.980592\pi$
$888$	−25.2541	+	22.6359i	−0.847473	+	0.759610i
$889$	29.6166			0.993310
$890$	−25.7487	+	60.1656i	−0.863100	+	2.01676i
$891$	−2.24880			−0.0753377
$892$		−	17.9744i		−	0.601828i
$893$	28.0407			0.938348
$894$		−	48.8019i		−	1.63218i
$895$	−3.06862	+	7.17028i	−0.102573	+	0.239676i
$896$		−	55.0668i		−	1.83965i
$897$			1.15818i			0.0386705i
$898$			50.6716i			1.69093i
$899$	42.0475			1.40236
$900$	−14.6129	−	15.3120i	−0.487096	−	0.510401i
$901$			77.1710i			2.57094i
$902$	−42.3254			−1.40928
$903$	31.9462			1.06310
$904$	33.5827			1.11694
$905$	14.6169	+	6.25552i	0.485883	+	0.207941i
$906$			33.7540i			1.12140i
$907$	−6.09610			−0.202418			−0.101209	−	0.994865i	$-0.532271\pi$
$907$	−6.09610			−0.202418			−0.101209	+	0.994865i	$0.532271\pi$
$908$	88.8785			2.94954
$909$	4.79078			0.158900
$910$	28.4071	−	66.3772i	0.941685	−	2.20038i
$911$		−	21.4086i		−	0.709299i	−0.934999	−	0.354649i	$-0.884600\pi$
$911$		−	21.4086i		−	0.709299i	0.934999	−	0.354649i	$-0.115400\pi$
$912$	−26.7917			−0.887163
$913$			16.5346i			0.547215i
$914$	−7.04536			−0.233040
$915$	3.63603	+	1.55609i	0.120203	+	0.0514427i
$916$	13.1383			0.434101
$917$	−63.1915			−2.08677
$918$			13.6390i			0.450155i
$919$			45.5521i			1.50262i	0.659947	+	0.751312i	$0.270579\pi$
$919$			45.5521i			1.50262i	−0.659947	+	0.751312i	$0.729421\pi$
$920$	−3.36466	−	1.43996i	−0.110930	−	0.0474739i
$921$	10.3292			0.340359
$922$			33.4059i			1.10016i
$923$	4.87274			0.160388
$924$	31.2062			1.02661
$925$	−2.36918	+	30.3214i	−0.0778980	+	0.996961i
$926$	−57.5163			−1.89010
$927$	−2.72811			−0.0896028
$928$		−	10.9033i		−	0.357920i
$929$	20.1308			0.660469			0.330234	−	0.943899i	$-0.392872\pi$
$929$	20.1308			0.660469			0.330234	+	0.943899i	$0.392872\pi$
$930$	48.7754	+	20.8741i	1.59941	+	0.684490i
$931$			18.4034i			0.603148i
$932$		−	91.6662i		−	3.00263i
$933$	−4.44594			−0.145553
$934$	8.20733			0.268552
$935$	25.2548	+	10.8082i	0.825921	+	0.353464i
$936$	−21.9965			−0.718979
$937$		−	31.6527i		−	1.03405i	−0.855970	−	0.517025i	$-0.827039\pi$
$937$		−	31.6527i		−	1.03405i	0.855970	−	0.517025i	$-0.172961\pi$
$938$	−18.3287			−0.598452
$939$			0.217282i			0.00709073i
$940$	−21.2567	+	49.6692i	−0.693316	+	1.62003i
$941$	20.8621			0.680085			0.340042	−	0.940410i	$-0.389559\pi$
$941$	20.8621			0.680085			0.340042	+	0.940410i	$0.389559\pi$
$942$	46.9456			1.52957
$943$	−2.21307			−0.0720675
$944$		−	22.6811i		−	0.738208i
$945$	6.73888	+	2.88400i	0.219216	+	0.0938165i
$946$	−54.7144			−1.77892
$947$	−57.2571			−1.86061			−0.930304	−	0.366791i	$-0.880457\pi$
$947$	−57.2571			−1.86061			−0.930304	+	0.366791i	$0.880457\pi$
$948$	32.1766			1.04505
$949$			10.9715i			0.356150i
$950$	−44.3663	+	42.3406i	−1.43943	+	1.37371i
$951$	12.4745			0.404513
$952$		−	99.8456i		−	3.23601i
$953$		−	9.35637i		−	0.303082i	−0.988451	−	0.151541i	$-0.951576\pi$
$953$		−	9.35637i		−	0.303082i	0.988451	−	0.151541i	$-0.0484236\pi$
$954$		−	35.2680i		−	1.14184i
$955$	11.9326	−	27.8822i	0.386129	−	0.902247i
$956$			63.6253i			2.05779i
$957$	−9.94970			−0.321628
$958$		−	73.5666i		−	2.37683i
$959$	33.3978			1.07847
$960$	−4.18269	+	9.77346i	−0.134996	+	0.315437i
$961$	−59.3157			−1.91341
$962$	39.9900	+	44.6156i	1.28933	+	1.43846i
$963$			2.86508i			0.0923258i
$964$			20.2934i			0.653605i
$965$	41.3261	+	17.6861i	1.33033	+	0.569335i
$966$	2.40258			0.0773017
$967$	50.4867			1.62354			0.811772	−	0.583975i	$-0.198503\pi$
$967$	50.4867			1.62354			0.811772	+	0.583975i	$0.198503\pi$
$968$	33.1341			1.06497
$969$	26.8387			0.862182
$970$	−42.9799	−	18.3939i	−1.38000	−	0.590591i
$971$	−58.4363			−1.87531			−0.937655	−	0.347568i	$-0.887007\pi$
$971$	−58.4363			−1.87531			−0.937655	+	0.347568i	$0.887007\pi$
$972$		−	4.23317i		−	0.135779i
$973$		−	70.0188i		−	2.24470i
$974$	−49.3354			−1.58081
$975$	−14.2706	+	13.6190i	−0.457026	+	0.436158i
$976$			9.64564i			0.308749i
$977$	−48.0338			−1.53674			−0.768369	−	0.640008i	$-0.778931\pi$
$977$	−48.0338			−1.53674			−0.768369	+	0.640008i	$0.778931\pi$
$978$		−	49.8592i		−	1.59432i
$979$			26.3621i			0.842537i
$980$	−32.5984	−	13.9510i	−1.04132	−	0.445647i
$981$		−	2.88647i		−	0.0921578i
$982$	1.01888			0.0325137
$983$		−	27.3040i		−	0.870862i	−0.900222	−	0.435431i	$-0.856596\pi$
$983$		−	27.3040i		−	0.870862i	0.900222	−	0.435431i	$-0.143404\pi$
$984$		−	42.0313i		−	1.33991i
$985$	21.6771	−	50.6516i	0.690689	−	1.61389i
$986$			60.3451i			1.92178i
$987$		−	18.7103i		−	0.595555i
$988$			82.0494i			2.61034i
$989$	−2.86085			−0.0909699
$990$	−11.5417	−	4.93944i	−0.366820	−	0.156986i
$991$			7.39750i			0.234989i	0.993074	+	0.117495i	$0.0374863\pi$
$991$			7.39750i			0.234989i	−0.993074	+	0.117495i	$0.962514\pi$
$992$			23.4198i			0.743579i
$993$	−8.00778			−0.254119
$994$		−	10.1082i		−	0.320613i
$995$	7.21947	−	16.8693i	0.228873	−	0.534794i
$996$	−31.1249			−0.986232
$997$	−32.0225			−1.01416			−0.507081	−	0.861898i	$-0.669276\pi$
$997$	−32.0225			−1.01416			−0.507081	+	0.861898i	$0.669276\pi$
$998$			9.08903i			0.287708i
$999$	−4.52955	+	4.05995i	−0.143309	+	0.128451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.g.a.184.3	✓	40
3.2	odd	2		1665.2.g.e.739.38		40
5.4	even	2	inner	555.2.g.a.184.38	yes	40
15.14	odd	2		1665.2.g.e.739.3		40
37.36	even	2	inner	555.2.g.a.184.37	yes	40
111.110	odd	2		1665.2.g.e.739.4		40
185.184	even	2	inner	555.2.g.a.184.4	yes	40
555.554	odd	2		1665.2.g.e.739.37		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.3	✓	40	1.1	even	1	trivial
555.2.g.a.184.4	yes	40	185.184	even	2	inner
555.2.g.a.184.37	yes	40	37.36	even	2	inner
555.2.g.a.184.38	yes	40	5.4	even	2	inner
1665.2.g.e.739.3		40	15.14	odd	2
1665.2.g.e.739.4		40	111.110	odd	2
1665.2.g.e.739.37		40	555.554	odd	2
1665.2.g.e.739.38		40	3.2	odd	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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.49663 q^{2} -1.00000i q^{3} +4.23317 q^{4} +(2.05572 + 0.879776i) q^{5} +2.49663i q^{6} -3.27811i q^{7} -5.57542 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.49663 q^{2} -1.00000i q^{3} +4.23317 q^{4} +(2.05572 + 0.879776i) q^{5} +2.49663i q^{6} -3.27811i q^{7} -5.57542 q^{8} -1.00000 q^{9} +(-5.13238 - 2.19648i) q^{10} -2.24880 q^{11} -4.23317i q^{12} -3.94527 q^{13} +8.18423i q^{14} +(0.879776 - 2.05572i) q^{15} +5.45341 q^{16} -5.46297 q^{17} +2.49663 q^{18} -4.91284i q^{19} +(8.70223 + 3.72424i) q^{20} -3.27811 q^{21} +5.61443 q^{22} +0.293562 q^{23} +5.57542i q^{24} +(3.45199 + 3.61715i) q^{25} +9.84989 q^{26} +1.00000i q^{27} -13.8768i q^{28} +4.42445i q^{29} +(-2.19648 + 5.13238i) q^{30} -9.50346i q^{31} -2.46434 q^{32} +2.24880i q^{33} +13.6390 q^{34} +(2.88400 - 6.73888i) q^{35} -4.23317 q^{36} +(4.05995 + 4.52955i) q^{37} +12.2656i q^{38} +3.94527i q^{39} +(-11.4615 - 4.90511i) q^{40} -7.53868 q^{41} +8.18423 q^{42} -9.74531 q^{43} -9.51957 q^{44} +(-2.05572 - 0.879776i) q^{45} -0.732917 q^{46} +5.70765i q^{47} -5.45341i q^{48} -3.74599 q^{49} +(-8.61835 - 9.03069i) q^{50} +5.46297i q^{51} -16.7010 q^{52} -14.1262i q^{53} -2.49663i q^{54} +(-4.62291 - 1.97844i) q^{55} +18.2768i q^{56} -4.91284 q^{57} -11.0462i q^{58} -4.15907i q^{59} +(3.72424 - 8.70223i) q^{60} +1.76873i q^{61} +23.7266i q^{62} +3.27811i q^{63} -4.75427 q^{64} +(-8.11038 - 3.47095i) q^{65} -5.61443i q^{66} +2.23951i q^{67} -23.1257 q^{68} -0.293562i q^{69} +(-7.20029 + 16.8245i) q^{70} -1.23508 q^{71} +5.57542 q^{72} -2.78092i q^{73} +(-10.1362 - 11.3086i) q^{74} +(3.61715 - 3.45199i) q^{75} -20.7969i q^{76} +7.37181i q^{77} -9.84989i q^{78} +7.60105i q^{79} +(11.2107 + 4.79778i) q^{80} +1.00000 q^{81} +18.8213 q^{82} -7.35263i q^{83} -13.8768 q^{84} +(-11.2303 - 4.80619i) q^{85} +24.3305 q^{86} +4.42445 q^{87} +12.5380 q^{88} -11.7227i q^{89} +(5.13238 + 2.19648i) q^{90} +12.9330i q^{91} +1.24270 q^{92} -9.50346 q^{93} -14.2499i q^{94} +(4.32220 - 10.0994i) q^{95} +2.46434i q^{96} +8.37426 q^{97} +9.35235 q^{98} +2.24880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) \) 40 * q + 44 * q^4 - 40 * q^9	\( 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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