LMFDB - Embedded newform 1045.2.f.b.626.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.2
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.b.626.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69018 q^{2} +1.09158i q^{3} +5.23709 q^{4} +1.00000 q^{5} -2.93656i q^{6} +4.34570i q^{7} -8.70838 q^{8} +1.80845 q^{9} +O(q^{10})$	\(q-2.69018 q^{2} +1.09158i q^{3} +5.23709 q^{4} +1.00000 q^{5} -2.93656i q^{6} +4.34570i q^{7} -8.70838 q^{8} +1.80845 q^{9} -2.69018 q^{10} +(-1.85327 - 2.75052i) q^{11} +5.71672i q^{12} +5.00670 q^{13} -11.6907i q^{14} +1.09158i q^{15} +12.9530 q^{16} -1.42667i q^{17} -4.86506 q^{18} +(3.00243 + 3.15998i) q^{19} +5.23709 q^{20} -4.74369 q^{21} +(4.98564 + 7.39942i) q^{22} +2.49932 q^{23} -9.50591i q^{24} +1.00000 q^{25} -13.4689 q^{26} +5.24882i q^{27} +22.7588i q^{28} +5.84038 q^{29} -2.93656i q^{30} -2.48109i q^{31} -17.4291 q^{32} +(3.00243 - 2.02300i) q^{33} +3.83800i q^{34} +4.34570i q^{35} +9.47101 q^{36} +6.42482i q^{37} +(-8.07708 - 8.50092i) q^{38} +5.46523i q^{39} -8.70838 q^{40} +5.23599 q^{41} +12.7614 q^{42} -12.1518i q^{43} +(-9.70575 - 14.4048i) q^{44} +1.80845 q^{45} -6.72364 q^{46} +3.25447 q^{47} +14.1392i q^{48} -11.8851 q^{49} -2.69018 q^{50} +1.55733 q^{51} +26.2205 q^{52} -4.67695i q^{53} -14.1203i q^{54} +(-1.85327 - 2.75052i) q^{55} -37.8440i q^{56} +(-3.44937 + 3.27740i) q^{57} -15.7117 q^{58} -1.28138i q^{59} +5.71672i q^{60} -12.8133i q^{61} +6.67460i q^{62} +7.85897i q^{63} +20.9815 q^{64} +5.00670 q^{65} +(-8.07708 + 5.44224i) q^{66} -5.61402i q^{67} -7.47159i q^{68} +2.72822i q^{69} -11.6907i q^{70} +10.8281i q^{71} -15.7486 q^{72} +8.64312i q^{73} -17.2840i q^{74} +1.09158i q^{75} +(15.7240 + 16.5491i) q^{76} +(11.9530 - 8.05376i) q^{77} -14.7025i q^{78} -13.8381 q^{79} +12.9530 q^{80} -0.304176 q^{81} -14.0858 q^{82} +12.0589i q^{83} -24.8431 q^{84} -1.42667i q^{85} +32.6905i q^{86} +6.37526i q^{87} +(16.1390 + 23.9526i) q^{88} -5.26323i q^{89} -4.86506 q^{90} +21.7576i q^{91} +13.0892 q^{92} +2.70832 q^{93} -8.75512 q^{94} +(3.00243 + 3.15998i) q^{95} -19.0253i q^{96} -1.44957i q^{97} +31.9731 q^{98} +(-3.35154 - 4.97418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−2.69018			−1.90225			−0.951124	−	0.308810i	$-0.900069\pi$
$2$	−2.69018			−1.90225			−0.951124	+	0.308810i	$0.900069\pi$
$3$			1.09158i			0.630226i	0.949054	+	0.315113i	$0.102042\pi$
$3$			1.09158i			0.630226i	−0.949054	+	0.315113i	$0.897958\pi$
$4$	5.23709			2.61855
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		−	2.93656i		−	1.19885i
$7$			4.34570i			1.64252i	0.570554	+	0.821260i	$0.306728\pi$
$7$			4.34570i			1.64252i	−0.570554	+	0.821260i	$0.693272\pi$
$8$	−8.70838			−3.07888
$9$	1.80845			0.602816
$10$	−2.69018			−0.850711
$11$	−1.85327	−	2.75052i	−0.558782	−	0.829314i
$11$	−1.85327	−	2.75052i	−0.558782	−	0.829314i
$12$			5.71672i			1.65027i
$13$	5.00670			1.38861			0.694304	−	0.719682i	$-0.255712\pi$
$13$	5.00670			1.38861			0.694304	+	0.719682i	$0.255712\pi$
$14$		−	11.6907i		−	3.12448i
$15$			1.09158i			0.281845i
$16$	12.9530			3.23824
$17$		−	1.42667i		−	0.346018i	−0.984920	−	0.173009i	$-0.944651\pi$
$17$		−	1.42667i		−	0.346018i	0.984920	−	0.173009i	$-0.0553489\pi$
$18$	−4.86506			−1.14670
$19$	3.00243	+	3.15998i	0.688804	+	0.724948i
$19$	3.00243	+	3.15998i	0.688804	+	0.724948i
$20$	5.23709			1.17105
$21$	−4.74369			−1.03516
$22$	4.98564	+	7.39942i	1.06294	+	1.57756i
$23$	2.49932			0.521145			0.260572	−	0.965454i	$-0.416089\pi$
$23$	2.49932			0.521145			0.260572	+	0.965454i	$0.416089\pi$
$24$		−	9.50591i		−	1.94039i
$25$	1.00000			0.200000
$26$	−13.4689			−2.64148
$27$			5.24882i			1.01014i
$28$			22.7588i			4.30101i
$29$	5.84038			1.08453			0.542266	−	0.840207i	$-0.317567\pi$
$29$	5.84038			1.08453			0.542266	+	0.840207i	$0.317567\pi$
$30$		−	2.93656i		−	0.536140i
$31$		−	2.48109i		−	0.445618i	−0.974862	−	0.222809i	$-0.928477\pi$
$31$		−	2.48109i		−	0.445618i	0.974862	−	0.222809i	$-0.0715226\pi$
$32$	−17.4291			−3.08105
$33$	3.00243	−	2.02300i	0.522655	−	0.352159i
$34$			3.83800i			0.658211i
$35$			4.34570i			0.734557i
$36$	9.47101			1.57850
$37$			6.42482i			1.05623i	0.849171	+	0.528117i	$0.177102\pi$
$37$			6.42482i			1.05623i	−0.849171	+	0.528117i	$0.822898\pi$
$38$	−8.07708	−	8.50092i	−1.31027	−	1.37903i
$39$			5.46523i			0.875137i
$40$	−8.70838			−1.37692
$41$	5.23599			0.817725			0.408862	−	0.912596i	$-0.365926\pi$
$41$	5.23599			0.817725			0.408862	+	0.912596i	$0.365926\pi$
$42$	12.7614			1.96913
$43$		−	12.1518i		−	1.85313i	−0.376138	−	0.926564i	$-0.622748\pi$
$43$		−	12.1518i		−	1.85313i	0.376138	−	0.926564i	$-0.377252\pi$
$44$	−9.70575	−	14.4048i	−1.46320	−	2.17160i
$45$	1.80845			0.269587
$46$	−6.72364			−0.991346
$47$	3.25447			0.474713			0.237357	−	0.971423i	$-0.423719\pi$
$47$	3.25447			0.474713			0.237357	+	0.971423i	$0.423719\pi$
$48$			14.1392i			2.04082i
$49$	−11.8851			−1.69787
$50$	−2.69018			−0.380450
$51$	1.55733			0.218069
$52$	26.2205			3.63614
$53$		−	4.67695i		−	0.642429i	−0.947007	−	0.321214i	$-0.895909\pi$
$53$		−	4.67695i		−	0.642429i	0.947007	−	0.321214i	$-0.104091\pi$
$54$		−	14.1203i		−	1.92153i
$55$	−1.85327	−	2.75052i	−0.249895	−	0.370881i
$56$		−	37.8440i		−	5.05711i
$57$	−3.44937	+	3.27740i	−0.456881	+	0.434102i
$58$	−15.7117			−2.06305
$59$		−	1.28138i		−	0.166822i	−0.996515	−	0.0834111i	$-0.973419\pi$
$59$		−	1.28138i		−	0.166822i	0.996515	−	0.0834111i	$-0.0265814\pi$
$60$			5.71672i			0.738025i
$61$		−	12.8133i		−	1.64057i	−0.571952	−	0.820287i	$-0.693814\pi$
$61$		−	12.8133i		−	1.64057i	0.571952	−	0.820287i	$-0.306186\pi$
$62$			6.67460i			0.847675i
$63$			7.85897i			0.990137i
$64$	20.9815			2.62269
$65$	5.00670			0.621005
$66$	−8.07708	+	5.44224i	−0.994219	+	0.669893i
$67$		−	5.61402i		−	0.685862i	−0.939361	−	0.342931i	$-0.888580\pi$
$67$		−	5.61402i		−	0.685862i	0.939361	−	0.342931i	$-0.111420\pi$
$68$		−	7.47159i		−	0.906063i
$69$			2.72822i			0.328439i
$70$		−	11.6907i		−	1.39731i
$71$			10.8281i			1.28506i	0.766262	+	0.642528i	$0.222114\pi$
$71$			10.8281i			1.28506i	−0.766262	+	0.642528i	$0.777886\pi$
$72$	−15.7486			−1.85599
$73$			8.64312i			1.01160i	0.862651	+	0.505800i	$0.168803\pi$
$73$			8.64312i			1.01160i	−0.862651	+	0.505800i	$0.831197\pi$
$74$		−	17.2840i		−	2.00922i
$75$			1.09158i			0.126045i
$76$	15.7240	+	16.5491i	1.80366	+	1.89831i
$77$	11.9530	−	8.05376i	1.36217	−	0.917811i
$78$		−	14.7025i		−	1.66473i
$79$	−13.8381			−1.55690			−0.778452	−	0.627705i	$-0.783995\pi$
$79$	−13.8381			−1.55690			−0.778452	+	0.627705i	$0.783995\pi$
$80$	12.9530			1.44818
$81$	−0.304176			−0.0337974
$82$	−14.0858			−1.55551
$83$			12.0589i			1.32364i	0.749664	+	0.661819i	$0.230215\pi$
$83$			12.0589i			1.32364i	−0.749664	+	0.661819i	$0.769785\pi$
$84$	−24.8431			−2.71061
$85$		−	1.42667i		−	0.154744i
$86$			32.6905i			3.52511i
$87$			6.37526i			0.683500i
$88$	16.1390	+	23.9526i	1.72042	+	2.55336i
$89$		−	5.26323i		−	0.557901i	−0.960306	−	0.278950i	$-0.910013\pi$
$89$		−	5.26323i		−	0.557901i	0.960306	−	0.278950i	$-0.0899865\pi$
$90$	−4.86506			−0.512822
$91$			21.7576i			2.28082i
$92$	13.0892			1.36464
$93$	2.70832			0.280840
$94$	−8.75512			−0.903022
$95$	3.00243	+	3.15998i	0.308042	+	0.324207i
$96$		−	19.0253i		−	1.94176i
$97$		−	1.44957i		−	0.147182i	−0.997289	−	0.0735909i	$-0.976554\pi$
$97$		−	1.44957i		−	0.147182i	0.997289	−	0.0735909i	$-0.0234459\pi$
$98$	31.9731			3.22977
$99$	−3.35154	−	4.97418i	−0.336843	−	0.499924i
$100$	5.23709			0.523709
$101$			6.85556i			0.682154i	0.940035	+	0.341077i	$0.110792\pi$
$101$			6.85556i			0.682154i	−0.940035	+	0.341077i	$0.889208\pi$
$102$	−4.18949			−0.414821
$103$			10.9393i			1.07788i	0.842343	+	0.538941i	$0.181175\pi$
$103$			10.9393i			1.07788i	−0.842343	+	0.538941i	$0.818825\pi$
$104$	−43.6002			−4.27535
$105$	−4.74369			−0.462937
$106$			12.5819i			1.22206i
$107$	−18.7350			−1.81118			−0.905590	−	0.424155i	$-0.860571\pi$
$107$	−18.7350			−1.81118			−0.905590	+	0.424155i	$0.860571\pi$
$108$			27.4885i			2.64509i
$109$	8.81541			0.844363			0.422182	−	0.906511i	$-0.361264\pi$
$109$	8.81541			0.844363			0.422182	+	0.906511i	$0.361264\pi$
$110$	4.98564	+	7.39942i	0.475362	+	0.705507i
$111$	−7.01323			−0.665666
$112$			56.2896i			5.31887i
$113$		−	17.5453i		−	1.65052i	−0.564754	−	0.825259i	$-0.691029\pi$
$113$		−	17.5453i		−	1.65052i	0.564754	−	0.825259i	$-0.308971\pi$
$114$	9.27945	−	8.81680i	0.869100	−	0.825769i
$115$	2.49932			0.233063
$116$	30.5866			2.83990
$117$	9.05435			0.837075
$118$			3.44716i			0.317337i
$119$	6.19986			0.568341
$120$		−	9.50591i		−	0.867767i
$121$	−4.13077	+	10.1949i	−0.375525	+	0.926812i
$122$			34.4701i			3.12078i
$123$			5.71552i			0.515351i
$124$		−	12.9937i		−	1.16687i
$125$	1.00000			0.0894427
$126$		−	21.1421i		−	1.88349i
$127$	−1.37793			−0.122272			−0.0611359	−	0.998129i	$-0.519472\pi$
$127$	−1.37793			−0.122272			−0.0611359	+	0.998129i	$0.519472\pi$
$128$	−21.5860			−1.90795
$129$	13.2647			1.16789
$130$	−13.4689			−1.18130
$131$			15.6980i			1.37154i	0.727820	+	0.685768i	$0.240534\pi$
$131$			15.6980i			1.37154i	−0.727820	+	0.685768i	$0.759466\pi$
$132$	15.7240	−	10.5946i	1.36860	−	0.922144i
$133$	−13.7323	+	13.0476i	−1.19074	+	1.13137i
$134$			15.1027i			1.30468i
$135$			5.24882i			0.451746i
$136$			12.4240i			1.06535i
$137$	−17.4456			−1.49047			−0.745237	−	0.666800i	$-0.767664\pi$
$137$	−17.4456			−1.49047			−0.745237	+	0.666800i	$0.767664\pi$
$138$		−	7.33940i		−	0.624772i
$139$			9.68872i			0.821786i	0.911683	+	0.410893i	$0.134783\pi$
$139$			9.68872i			0.821786i	−0.911683	+	0.410893i	$0.865217\pi$
$140$			22.7588i			1.92347i
$141$			3.55252i			0.299176i
$142$		−	29.1295i		−	2.44449i
$143$	−9.27877	−	13.7711i	−0.775930	−	1.15159i
$144$	23.4247			1.95206
$145$	5.84038			0.485017
$146$		−	23.2516i		−	1.92431i
$147$		−	12.9736i		−	1.07004i
$148$			33.6474i			2.76580i
$149$			3.10806i			0.254622i	0.991863	+	0.127311i	$0.0406347\pi$
$149$			3.10806i			0.254622i	−0.991863	+	0.127311i	$0.959365\pi$
$150$		−	2.93656i		−	0.239769i
$151$	22.8611			1.86041			0.930206	−	0.367037i	$-0.119628\pi$
$151$	22.8611			1.86041			0.930206	+	0.367037i	$0.119628\pi$
$152$	−26.1462	−	27.5182i	−2.12074	−	2.23202i
$153$		−	2.58005i		−	0.208585i
$154$	−32.1556	+	21.6661i	−2.59118	+	1.74590i
$155$		−	2.48109i		−	0.199286i
$156$			28.6219i			2.29159i
$157$	4.87082			0.388734			0.194367	−	0.980929i	$-0.437735\pi$
$157$	4.87082			0.388734			0.194367	+	0.980929i	$0.437735\pi$
$158$	37.2269			2.96162
$159$	5.10528			0.404875
$160$	−17.4291			−1.37789
$161$			10.8613i			0.855990i
$162$	0.818291			0.0642910
$163$	21.3582			1.67290			0.836450	−	0.548043i	$-0.184627\pi$
$163$	21.3582			1.67290			0.836450	+	0.548043i	$0.184627\pi$
$164$	27.4214			2.14125
$165$	3.00243	−	2.02300i	0.233738	−	0.157490i
$166$		−	32.4407i		−	2.51789i
$167$	−4.20905			−0.325706			−0.162853	−	0.986650i	$-0.552070\pi$
$167$	−4.20905			−0.325706			−0.162853	+	0.986650i	$0.552070\pi$
$168$	41.3098			3.18712
$169$	12.0670			0.928234
$170$			3.83800i			0.294361i
$171$	5.42973	+	5.71465i	0.415222	+	0.437010i
$172$		−	63.6399i		−	4.85250i
$173$	−4.61496			−0.350869			−0.175435	−	0.984491i	$-0.556133\pi$
$173$	−4.61496			−0.350869			−0.175435	+	0.984491i	$0.556133\pi$
$174$		−	17.1506i		−	1.30019i
$175$			4.34570i			0.328504i
$176$	−24.0053	−	35.6274i	−1.80947	−	2.68552i
$177$	1.39874			0.105136
$178$			14.1590i			1.06127i
$179$		−	3.86569i		−	0.288935i	−0.989510	−	0.144467i	$-0.953853\pi$
$179$		−	3.86569i		−	0.288935i	0.989510	−	0.144467i	$-0.0461469\pi$
$180$	9.47101			0.705927
$181$			4.67190i			0.347260i	0.984811	+	0.173630i	$0.0555496\pi$
$181$			4.67190i			0.347260i	−0.984811	+	0.173630i	$0.944450\pi$
$182$		−	58.5320i		−	4.33868i
$183$	13.9868			1.03393
$184$	−21.7650			−1.60454
$185$			6.42482i			0.472362i
$186$	−7.28588			−0.534226
$187$	−3.92408	+	2.64400i	−0.286957	+	0.193348i
$188$	17.0440			1.24306
$189$	−22.8098			−1.65917
$190$	−8.07708	−	8.50092i	−0.585973	−	0.616721i
$191$	−14.8352			−1.07344			−0.536719	−	0.843761i	$-0.680337\pi$
$191$	−14.8352			−1.07344			−0.536719	+	0.843761i	$0.680337\pi$
$192$			22.9031i			1.65289i
$193$	−20.7964			−1.49696			−0.748480	−	0.663157i	$-0.769216\pi$
$193$	−20.7964			−1.49696			−0.748480	+	0.663157i	$0.769216\pi$
$194$			3.89962i			0.279976i
$195$			5.46523i			0.391373i
$196$	−62.2433			−4.44595
$197$			11.1083i			0.791433i	0.918373	+	0.395716i	$0.129504\pi$
$197$			11.1083i			0.791433i	−0.918373	+	0.395716i	$0.870496\pi$
$198$	9.01627	+	13.3815i	0.640758	+	0.950979i
$199$	−12.7372			−0.902918			−0.451459	−	0.892292i	$-0.649096\pi$
$199$	−12.7372			−0.902918			−0.451459	+	0.892292i	$0.649096\pi$
$200$	−8.70838			−0.615775
$201$	6.12817			0.432248
$202$		−	18.4427i		−	1.29762i
$203$			25.3805i			1.78136i
$204$	8.15586			0.571024
$205$	5.23599			0.365698
$206$		−	29.4288i		−	2.05040i
$207$	4.51989			0.314154
$208$	64.8515			4.49664
$209$	3.12728	−	14.1145i	0.216319	−	0.976323i
$210$	12.7614			0.880620
$211$	−7.78037			−0.535623			−0.267812	−	0.963471i	$-0.586300\pi$
$211$	−7.78037			−0.535623			−0.267812	+	0.963471i	$0.586300\pi$
$212$		−	24.4936i		−	1.68223i
$213$	−11.8197			−0.809875
$214$	50.4006			3.44531
$215$		−	12.1518i		−	0.828744i
$216$		−	45.7087i		−	3.11008i
$217$	10.7821			0.731936
$218$	−23.7151			−1.60619
$219$	−9.43468			−0.637536
$220$	−9.70575	−	14.4048i	−0.654362	−	0.971168i
$221$		−	7.14289i		−	0.480483i
$222$	18.8669			1.26626
$223$		−	7.49108i		−	0.501640i	−0.968034	−	0.250820i	$-0.919300\pi$
$223$		−	7.49108i		−	0.501640i	0.968034	−	0.250820i	$-0.0807003\pi$
$224$		−	75.7415i		−	5.06069i
$225$	1.80845			0.120563
$226$			47.2000i			3.13969i
$227$	−15.7217			−1.04348			−0.521742	−	0.853103i	$-0.674718\pi$
$227$	−15.7217			−1.04348			−0.521742	+	0.853103i	$0.674718\pi$
$228$	−18.0647	+	17.1640i	−1.19636	+	1.13672i
$229$	10.9216			0.721720			0.360860	−	0.932620i	$-0.382483\pi$
$229$	10.9216			0.721720			0.360860	+	0.932620i	$0.382483\pi$
$230$	−6.72364			−0.443343
$231$	8.79134	+	13.0476i	0.578428	+	0.858471i
$232$	−50.8602			−3.33914
$233$			5.15533i			0.337737i	0.985639	+	0.168868i	$0.0540113\pi$
$233$			5.15533i			0.337737i	−0.985639	+	0.168868i	$0.945989\pi$
$234$	−24.3579			−1.59232
$235$	3.25447			0.212298
$236$		−	6.71073i		−	0.436831i
$237$		−	15.1054i		−	0.981200i
$238$	−16.6788			−1.08112
$239$			0.283179i			0.0183174i	0.999958	+	0.00915868i	$0.00291534\pi$
$239$			0.283179i			0.0183174i	−0.999958	+	0.00915868i	$0.997085\pi$
$240$			14.1392i			0.912682i
$241$	2.92480			0.188403			0.0942016	−	0.995553i	$-0.469970\pi$
$241$	2.92480			0.188403			0.0942016	+	0.995553i	$0.469970\pi$
$242$	11.1125	−	27.4263i	0.714341	−	1.76303i
$243$			15.4144i			0.988835i
$244$		−	67.1044i		−	4.29592i
$245$	−11.8851			−0.759311
$246$		−	15.3758i		−	0.980325i
$247$	15.0322	+	15.8210i	0.956478	+	1.00667i
$248$			21.6063i			1.37200i
$249$	−13.1633			−0.834191
$250$	−2.69018			−0.170142
$251$	−4.42497			−0.279302			−0.139651	−	0.990201i	$-0.544598\pi$
$251$	−4.42497			−0.279302			−0.139651	+	0.990201i	$0.544598\pi$
$252$			41.1581i			2.59272i
$253$	−4.63192	−	6.87445i	−0.291206	−	0.432193i
$254$	3.70689			0.232591
$255$	1.55733			0.0975235
$256$	16.1073			1.00671
$257$		−	2.05583i		−	0.128239i	−0.997942	−	0.0641196i	$-0.979576\pi$
$257$		−	2.05583i		−	0.128239i	0.997942	−	0.0641196i	$-0.0204239\pi$
$258$	−35.6844			−2.22161
$259$	−27.9203			−1.73489
$260$	26.2205			1.62613
$261$	10.5620			0.653773
$262$		−	42.2304i		−	2.60900i
$263$		−	19.8088i		−	1.22146i	−0.791838	−	0.610732i	$-0.790875\pi$
$263$		−	19.8088i		−	1.22146i	0.791838	−	0.610732i	$-0.209125\pi$
$264$	−26.1462	+	17.6170i	−1.60919	+	1.08425i
$265$		−	4.67695i		−	0.287303i
$266$	36.9424	−	35.1005i	2.26508	−	2.15215i
$267$	5.74525			0.351603
$268$		−	29.4011i		−	1.79596i
$269$			1.52788i			0.0931566i	0.998915	+	0.0465783i	$0.0148317\pi$
$269$			1.52788i			0.0931566i	−0.998915	+	0.0465783i	$0.985168\pi$
$270$		−	14.1203i		−	0.859333i
$271$			2.17413i			0.132069i	0.997817	+	0.0660344i	$0.0210347\pi$
$271$			2.17413i			0.132069i	−0.997817	+	0.0660344i	$0.978965\pi$
$272$		−	18.4795i		−	1.12049i
$273$	−23.7502			−1.43743
$274$	46.9318			2.83525
$275$	−1.85327	−	2.75052i	−0.111756	−	0.165863i
$276$			14.2879i			0.860032i
$277$		−	12.0561i		−	0.724383i	−0.932104	−	0.362192i	$-0.882029\pi$
$277$		−	12.0561i		−	0.724383i	0.932104	−	0.362192i	$-0.117971\pi$
$278$		−	26.0644i		−	1.56324i
$279$		−	4.48693i		−	0.268625i
$280$		−	37.8440i		−	2.26161i
$281$	8.09776			0.483072			0.241536	−	0.970392i	$-0.422349\pi$
$281$	8.09776			0.483072			0.241536	+	0.970392i	$0.422349\pi$
$282$		−	9.55694i		−	0.569107i
$283$		−	11.4337i		−	0.679663i	−0.940486	−	0.339831i	$-0.889630\pi$
$283$		−	11.4337i		−	0.679663i	0.940486	−	0.339831i	$-0.110370\pi$
$284$			56.7076i			3.36498i
$285$	−3.44937	+	3.27740i	−0.204323	+	0.194136i
$286$	24.9616	+	37.0467i	1.47601	+	2.19062i
$287$			22.7540i			1.34313i
$288$	−31.5196			−1.85731
$289$	14.9646			0.880272
$290$	−15.7117			−0.922623
$291$	1.58233			0.0927577
$292$			45.2648i			2.64892i
$293$	6.07675			0.355007			0.177504	−	0.984120i	$-0.443198\pi$
$293$	6.07675			0.355007			0.177504	+	0.984120i	$0.443198\pi$
$294$			34.9013i			2.03548i
$295$		−	1.28138i		−	0.0746051i
$296$		−	55.9498i		−	3.25201i
$297$	14.4370	−	9.72748i	0.837720	−	0.564446i
$298$		−	8.36126i		−	0.484355i
$299$	12.5134			0.723666
$300$			5.71672i			0.330055i
$301$	52.8079			3.04380
$302$	−61.5007			−3.53897
$303$	−7.48341			−0.429911
$304$	38.8903	+	40.9310i	2.23051	+	2.34755i
$305$		−	12.8133i		−	0.733687i
$306$			6.94082i			0.396780i
$307$	−27.0934			−1.54630			−0.773150	−	0.634224i	$-0.781320\pi$
$307$	−27.0934			−1.54630			−0.773150	+	0.634224i	$0.781320\pi$
$308$	62.5987	−	42.1783i	3.56689	−	2.40333i
$309$	−11.9412			−0.679309
$310$			6.67460i			0.379092i
$311$	6.34212			0.359628			0.179814	−	0.983701i	$-0.442450\pi$
$311$	6.34212			0.359628			0.179814	+	0.983701i	$0.442450\pi$
$312$		−	47.5932i		−	2.69444i
$313$	−16.2928			−0.920921			−0.460460	−	0.887680i	$-0.652316\pi$
$313$	−16.2928			−0.920921			−0.460460	+	0.887680i	$0.652316\pi$
$314$	−13.1034			−0.739468
$315$			7.85897i			0.442803i
$316$	−72.4712			−4.07682
$317$			9.98541i			0.560837i	0.959878	+	0.280418i	$0.0904732\pi$
$317$			9.98541i			0.560837i	−0.959878	+	0.280418i	$0.909527\pi$
$318$	−13.7341			−0.770173
$319$	−10.8238	−	16.0641i	−0.606017	−	0.899418i
$320$	20.9815			1.17290
$321$		−	20.4508i		−	1.14145i
$322$		−	29.2189i		−	1.62831i
$323$	4.50823	−	4.28346i	0.250845	−	0.238338i
$324$	−1.59300			−0.0885000
$325$	5.00670			0.277722
$326$	−57.4574			−3.18227
$327$			9.62275i			0.532139i
$328$	−45.5970			−2.51767
$329$			14.1429i			0.779725i
$330$	−8.07708	+	5.44224i	−0.444628	+	0.299585i
$331$			2.91106i			0.160006i	0.996795	+	0.0800031i	$0.0254930\pi$
$331$			2.91106i			0.160006i	−0.996795	+	0.0800031i	$0.974507\pi$
$332$			63.1537i			3.46601i
$333$			11.6190i			0.636715i
$334$	11.3231			0.619574
$335$		−	5.61402i		−	0.306727i
$336$	−61.4448			−3.35209
$337$	−15.6328			−0.851572			−0.425786	−	0.904824i	$-0.640002\pi$
$337$	−15.6328			−0.851572			−0.425786	+	0.904824i	$0.640002\pi$
$338$	−32.4626			−1.76573
$339$	19.1521			1.04020
$340$		−	7.47159i		−	0.405204i
$341$	−6.82431	+	4.59814i	−0.369557	+	0.249003i
$342$	−14.6070	−	15.3735i	−0.789854	−	0.831301i
$343$		−	21.2291i		−	1.14627i
$344$			105.822i			5.70555i
$345$			2.72822i			0.146882i
$346$	12.4151			0.667440
$347$		−	28.4304i		−	1.52623i	−0.646265	−	0.763113i	$-0.723670\pi$
$347$		−	28.4304i		−	1.52623i	0.646265	−	0.763113i	$-0.276330\pi$
$348$			33.3878i			1.78978i
$349$		−	34.6917i		−	1.85700i	−0.371329	−	0.928501i	$-0.621098\pi$
$349$		−	34.6917i		−	1.85700i	0.371329	−	0.928501i	$-0.378902\pi$
$350$		−	11.6907i		−	0.624896i
$351$			26.2793i			1.40268i
$352$	32.3008	+	47.9391i	1.72164	+	2.55516i
$353$	−4.47262			−0.238054			−0.119027	−	0.992891i	$-0.537977\pi$
$353$	−4.47262			−0.238054			−0.119027	+	0.992891i	$0.537977\pi$
$354$	−3.76286			−0.199994
$355$			10.8281i			0.574694i
$356$		−	27.5640i		−	1.46089i
$357$			6.76766i			0.358183i
$358$			10.3994i			0.549626i
$359$		−	7.91846i		−	0.417921i	−0.977924	−	0.208960i	$-0.932992\pi$
$359$		−	7.91846i		−	0.417921i	0.977924	−	0.208960i	$-0.0670079\pi$
$360$	−15.7486			−0.830026
$361$	−0.970887	+	18.9752i	−0.0510993	+	0.998694i
$362$		−	12.5683i		−	0.660574i
$363$	−11.1286	−	4.50908i	−0.584101	−	0.236665i
$364$			113.947i			5.97242i
$365$			8.64312i			0.452401i
$366$	−37.6270			−1.96679
$367$	4.54615			0.237307			0.118654	−	0.992936i	$-0.462142\pi$
$367$	4.54615			0.237307			0.118654	+	0.992936i	$0.462142\pi$
$368$	32.3736			1.68759
$369$	9.46902			0.492937
$370$		−	17.2840i		−	0.898550i
$371$	20.3246			1.05520
$372$	14.1837			0.735391
$373$	9.43119			0.488329			0.244164	−	0.969734i	$-0.421486\pi$
$373$	9.43119			0.488329			0.244164	+	0.969734i	$0.421486\pi$
$374$	10.5565	−	7.11285i	0.545864	−	0.367797i
$375$			1.09158i			0.0563691i
$376$	−28.3411			−1.46158
$377$	29.2410			1.50599
$378$	61.3625			3.15615
$379$			2.32011i			0.119176i	0.998223	+	0.0595880i	$0.0189787\pi$
$379$			2.32011i			0.119176i	−0.998223	+	0.0595880i	$0.981021\pi$
$380$	15.7240	+	16.5491i	0.806623	+	0.848950i
$381$		−	1.50413i		−	0.0770588i
$382$	39.9095			2.04195
$383$			24.1040i			1.23166i	0.787880	+	0.615829i	$0.211179\pi$
$383$			24.1040i			1.23166i	−0.787880	+	0.615829i	$0.788821\pi$
$384$		−	23.5629i		−	1.20244i
$385$	11.9530	−	8.05376i	0.609179	−	0.410457i
$386$	55.9463			2.84759
$387$		−	21.9758i		−	1.11709i
$388$		−	7.59154i		−	0.385402i
$389$	4.71404			0.239011			0.119506	−	0.992834i	$-0.461869\pi$
$389$	4.71404			0.239011			0.119506	+	0.992834i	$0.461869\pi$
$390$		−	14.7025i		−	0.744488i
$391$		−	3.56570i		−	0.180325i
$392$	103.500			5.22753
$393$	−17.1356			−0.864377
$394$		−	29.8833i		−	1.50550i
$395$	−13.8381			−0.696268
$396$	−17.5523	−	26.0502i	−0.882038	−	1.30907i
$397$	−8.49072			−0.426137			−0.213068	−	0.977037i	$-0.568346\pi$
$397$	−8.49072			−0.426137			−0.213068	+	0.977037i	$0.568346\pi$
$398$	34.2655			1.71757
$399$	−14.2426	−	14.9899i	−0.713020	−	0.750436i
$400$	12.9530			0.647648
$401$		−	13.5757i		−	0.677936i	−0.940798	−	0.338968i	$-0.889922\pi$
$401$		−	13.5757i		−	0.677936i	0.940798	−	0.338968i	$-0.110078\pi$
$402$	−16.4859			−0.822242
$403$		−	12.4221i		−	0.618788i
$404$			35.9032i			1.78625i
$405$	−0.304176			−0.0151146
$406$		−	68.2783i		−	3.38860i
$407$	17.6716	−	11.9069i	0.875950	−	0.590205i
$408$	−13.5618			−0.671408
$409$	32.5953			1.61173			0.805866	−	0.592098i	$-0.201700\pi$
$409$	32.5953			1.61173			0.805866	+	0.592098i	$0.201700\pi$
$410$	−14.0858			−0.695647
$411$		−	19.0433i		−	0.939335i
$412$			57.2902i			2.82248i
$413$	5.56851			0.274009
$414$	−12.1593			−0.597599
$415$			12.0589i			0.591949i
$416$	−87.2621			−4.27838
$417$	−10.5760			−0.517911
$418$	−8.41297	+	37.9707i	−0.411492	+	1.85721i
$419$	−20.3387			−0.993609			−0.496804	−	0.867863i	$-0.665493\pi$
$419$	−20.3387			−0.993609			−0.496804	+	0.867863i	$0.665493\pi$
$420$	−24.8431			−1.21222
$421$		−	13.7445i		−	0.669864i	−0.942242	−	0.334932i	$-0.891287\pi$
$421$		−	13.7445i		−	0.669864i	0.942242	−	0.334932i	$-0.108713\pi$
$422$	20.9306			1.01889
$423$	5.88553			0.286164
$424$			40.7287i			1.97796i
$425$		−	1.42667i		−	0.0692035i
$426$	31.7973			1.54058
$427$	55.6827			2.69467
$428$	−98.1168			−4.74266
$429$	15.0322	−	10.1285i	0.725763	−	0.489011i
$430$			32.6905i			1.57648i
$431$	−18.7034			−0.900913			−0.450456	−	0.892798i	$-0.648739\pi$
$431$	−18.7034			−0.900913			−0.450456	+	0.892798i	$0.648739\pi$
$432$			67.9877i			3.27106i
$433$		−	23.8507i		−	1.14619i	−0.819489	−	0.573095i	$-0.805743\pi$
$433$		−	23.8507i		−	1.14619i	0.819489	−	0.573095i	$-0.194257\pi$
$434$	−29.0058			−1.39232
$435$			6.37526i			0.305670i
$436$	46.1671			2.21100
$437$	7.50403	+	7.89779i	0.358966	+	0.377803i
$438$	25.3810			1.21275
$439$	−6.14379			−0.293227			−0.146614	−	0.989194i	$-0.546837\pi$
$439$	−6.14379			−0.293227			−0.146614	+	0.989194i	$0.546837\pi$
$440$	16.1390	+	23.9526i	0.769396	+	1.14190i
$441$	−21.4936			−1.02350
$442$			19.2157i			0.913998i
$443$	14.8038			0.703349			0.351675	−	0.936122i	$-0.385612\pi$
$443$	14.8038			0.703349			0.351675	+	0.936122i	$0.385612\pi$
$444$	−36.7289			−1.74308
$445$		−	5.26323i		−	0.249501i
$446$			20.1524i			0.954244i
$447$	−3.39271			−0.160469
$448$			91.1794i			4.30782i
$449$		−	32.8151i		−	1.54864i	−0.632794	−	0.774320i	$-0.718092\pi$
$449$		−	32.8151i		−	1.54864i	0.632794	−	0.774320i	$-0.281908\pi$
$450$	−4.86506			−0.229341
$451$	−9.70371	−	14.4017i	−0.456930	−	0.678151i
$452$		−	91.8861i		−	4.32196i
$453$			24.9548i			1.17248i
$454$	42.2942			1.98497
$455$			21.7576i			1.02001i
$456$	30.0384	−	28.5408i	1.40668	−	1.33654i
$457$			22.4030i			1.04797i	0.851728	+	0.523984i	$0.175555\pi$
$457$			22.4030i			1.04797i	−0.851728	+	0.523984i	$0.824445\pi$
$458$	−29.3811			−1.37289
$459$	7.48832			0.349525
$460$	13.0892			0.610286
$461$			29.2926i			1.36429i	0.731217	+	0.682145i	$0.238953\pi$
$461$			29.2926i			1.36429i	−0.731217	+	0.682145i	$0.761047\pi$
$462$	−23.6503	−	35.1005i	−1.10031	−	1.63302i
$463$	−2.54003			−0.118045			−0.0590225	−	0.998257i	$-0.518798\pi$
$463$	−2.54003			−0.118045			−0.0590225	+	0.998257i	$0.518798\pi$
$464$	75.6502			3.51197
$465$	2.70832			0.125595
$466$		−	13.8688i		−	0.642459i
$467$	22.2163			1.02805			0.514024	−	0.857776i	$-0.328154\pi$
$467$	22.2163			1.02805			0.514024	+	0.857776i	$0.328154\pi$
$468$	47.4185			2.19192
$469$	24.3968			1.12654
$470$	−8.75512			−0.403844
$471$			5.31690i			0.244990i
$472$			11.1588i			0.513624i
$473$	−33.4237	+	22.5205i	−1.53683	+	1.03549i
$474$			40.6363i			1.86649i
$475$	3.00243	+	3.15998i	0.137761	+	0.144990i
$476$	32.4693			1.48823
$477$		−	8.45802i		−	0.387266i
$478$		−	0.761805i		−	0.0348441i
$479$		−	10.2092i		−	0.466471i	−0.972420	−	0.233236i	$-0.925069\pi$
$479$		−	10.2092i		−	0.466471i	0.972420	−	0.233236i	$-0.0749314\pi$
$480$		−	19.0253i		−	0.868381i
$481$			32.1672i			1.46670i
$482$	−7.86826			−0.358390
$483$	−11.8560			−0.539467
$484$	−21.6332	+	53.3918i	−0.983329	+	2.42690i
$485$		−	1.44957i		−	0.0658217i
$486$		−	41.4676i		−	1.88101i
$487$		−	21.8258i		−	0.989023i	−0.869171	−	0.494511i	$-0.835347\pi$
$487$		−	21.8258i		−	0.989023i	0.869171	−	0.494511i	$-0.164653\pi$
$488$			111.583i			5.05112i
$489$			23.3142i			1.05430i
$490$	31.9731			1.44440
$491$		−	9.36258i		−	0.422527i	−0.977429	−	0.211264i	$-0.932242\pi$
$491$		−	9.36258i		−	0.422527i	0.977429	−	0.211264i	$-0.0677578\pi$
$492$			29.9327i			1.34947i
$493$		−	8.33228i		−	0.375267i
$494$	−40.4395	−	42.5615i	−1.81946	−	1.91493i
$495$	−3.35154	−	4.97418i	−0.150641	−	0.223573i
$496$		−	32.1375i		−	1.44302i
$497$	−47.0555			−2.11073
$498$	35.4117			1.58684
$499$	−25.5330			−1.14301			−0.571506	−	0.820598i	$-0.693641\pi$
$499$	−25.5330			−1.14301			−0.571506	+	0.820598i	$0.693641\pi$
$500$	5.23709			0.234210
$501$		−	4.59453i		−	0.205268i
$502$	11.9040			0.531301
$503$		−	32.4699i		−	1.44776i	−0.689925	−	0.723881i	$-0.742356\pi$
$503$		−	32.4699i		−	1.44776i	0.689925	−	0.723881i	$-0.257644\pi$
$504$		−	68.4388i		−	3.04851i
$505$			6.85556i			0.305068i
$506$	12.4607	+	18.4935i	0.553947	+	0.822138i
$507$			13.1722i			0.584997i
$508$	−7.21636			−0.320174
$509$			12.5763i			0.557433i	0.960373	+	0.278717i	$0.0899090\pi$
$509$			12.5763i			0.557433i	−0.960373	+	0.278717i	$0.910091\pi$
$510$	−4.18949			−0.185514
$511$	−37.5604			−1.66157
$512$	−0.159654			−0.00705577
$513$	−16.5861	+	15.7592i	−0.732296	+	0.695785i
$514$			5.53056i			0.243943i
$515$			10.9393i			0.482044i
$516$	69.4683			3.05817
$517$	−6.03141	−	8.95150i	−0.265261	−	0.393686i
$518$	75.1109			3.30018
$519$		−	5.03762i		−	0.221127i
$520$	−43.6002			−1.91200
$521$			24.1792i			1.05931i	0.848214	+	0.529654i	$0.177678\pi$
$521$			24.1792i			1.05931i	−0.848214	+	0.529654i	$0.822322\pi$
$522$	−28.4138			−1.24364
$523$	39.1038			1.70989			0.854944	−	0.518720i	$-0.173591\pi$
$523$	39.1038			1.70989			0.854944	+	0.518720i	$0.173591\pi$
$524$			82.2116i			3.59143i
$525$	−4.74369			−0.207032
$526$			53.2894i			2.32353i
$527$	−3.53970			−0.154192
$528$	38.8903	−	26.2038i	1.69248	−	1.14037i
$529$	−16.7534			−0.728408
$530$			12.5819i			0.546521i
$531$		−	2.31732i		−	0.100563i
$532$	−71.9173	+	68.3317i	−3.11801	+	2.96255i
$533$	26.2150			1.13550
$534$	−15.4558			−0.668837
$535$	−18.7350			−0.809984
$536$			48.8890i			2.11168i
$537$	4.21972			0.182094
$538$		−	4.11028i		−	0.177207i
$539$	22.0263	+	32.6902i	0.948740	+	1.40807i
$540$			27.4885i			1.18292i
$541$		−	19.2596i		−	0.828036i	−0.910269	−	0.414018i	$-0.864125\pi$
$541$		−	19.2596i		−	0.828036i	0.910269	−	0.414018i	$-0.135875\pi$
$542$		−	5.84880i		−	0.251228i
$543$	−5.09977			−0.218852
$544$			24.8655i			1.06610i
$545$	8.81541			0.377611
$546$	63.8925			2.73435
$547$	−24.2493			−1.03683			−0.518413	−	0.855130i	$-0.673477\pi$
$547$	−24.2493			−1.03683			−0.518413	+	0.855130i	$0.673477\pi$
$548$	−91.3640			−3.90288
$549$		−	23.1722i		−	0.988964i
$550$	4.98564	+	7.39942i	0.212588	+	0.315512i
$551$	17.5353	+	18.4555i	0.747029	+	0.786229i
$552$		−	23.7583i		−	1.01122i
$553$		−	60.1360i		−	2.55724i
$554$			32.4332i			1.37796i
$555$	−7.01323			−0.297695
$556$			50.7407i			2.15189i
$557$		−	19.1829i		−	0.812804i	−0.913694	−	0.406402i	$-0.866783\pi$
$557$		−	19.1829i		−	0.812804i	0.913694	−	0.406402i	$-0.133217\pi$
$558$			12.0707i			0.510992i
$559$		−	60.8403i		−	2.57327i
$560$			56.2896i			2.37867i
$561$	−2.88615	−	4.28346i	−0.121853	−	0.180848i
$562$	−21.7845			−0.918922
$563$	14.1536			0.596505			0.298252	−	0.954487i	$-0.403596\pi$
$563$	14.1536			0.596505			0.298252	+	0.954487i	$0.403596\pi$
$564$			18.6049i			0.783407i
$565$		−	17.5453i		−	0.738134i
$566$			30.7588i			1.29289i
$567$		−	1.32186i		−	0.0555129i
$568$		−	94.2949i		−	3.95653i
$569$	−31.6087			−1.32511			−0.662553	−	0.749015i	$-0.730527\pi$
$569$	−31.6087			−1.32511			−0.662553	+	0.749015i	$0.730527\pi$
$570$	9.27945	−	8.81680i	0.388674	−	0.369295i
$571$		−	14.3917i		−	0.602272i	−0.953581	−	0.301136i	$-0.902634\pi$
$571$		−	14.3917i		−	0.602272i	0.953581	−	0.301136i	$-0.0973658\pi$
$572$	−48.5938	−	72.1203i	−2.03181	−	3.01550i
$573$		−	16.1939i		−	0.676508i
$574$		−	61.2126i		−	2.55496i
$575$	2.49932			0.104229
$576$	37.9440			1.58100
$577$	12.7503			0.530803			0.265401	−	0.964138i	$-0.414495\pi$
$577$	12.7503			0.530803			0.265401	+	0.964138i	$0.414495\pi$
$578$	−40.2576			−1.67450
$579$		−	22.7010i		−	0.943423i
$580$	30.5866			1.27004
$581$	−52.4044			−2.17410
$582$	−4.25675			−0.176448
$583$	−12.8641	+	8.66766i	−0.532775	+	0.358978i
$584$		−	75.2675i		−	3.11459i
$585$	9.05435			0.374351
$586$	−16.3476			−0.675312
$587$	9.50861			0.392462			0.196231	−	0.980558i	$-0.437130\pi$
$587$	9.50861			0.392462			0.196231	+	0.980558i	$0.437130\pi$
$588$		−	67.9437i		−	2.80195i
$589$	7.84020	−	7.44930i	0.323050	−	0.306943i
$590$			3.44716i			0.141917i
$591$	−12.1256			−0.498781
$592$			83.2204i			3.42034i
$593$		−	20.3446i		−	0.835454i	−0.908573	−	0.417727i	$-0.862827\pi$
$593$		−	20.3446i		−	0.835454i	0.908573	−	0.417727i	$-0.137173\pi$
$594$	−38.8382	+	26.1687i	−1.59355	+	1.07372i
$595$	6.19986			0.254170
$596$			16.2772i			0.666740i
$597$		−	13.9037i		−	0.569042i
$598$	−33.6632			−1.37659
$599$			9.76891i			0.399147i	0.979883	+	0.199574i	$0.0639557\pi$
$599$			9.76891i			0.399147i	−0.979883	+	0.199574i	$0.936044\pi$
$600$		−	9.50591i		−	0.388077i
$601$	−4.21513			−0.171939			−0.0859694	−	0.996298i	$-0.527399\pi$
$601$	−4.21513			−0.171939			−0.0859694	+	0.996298i	$0.527399\pi$
$602$	−142.063			−5.79006
$603$		−	10.1527i		−	0.413448i
$604$	119.726			4.87158
$605$	−4.13077	+	10.1949i	−0.167940	+	0.414483i
$606$	20.1317			0.817796
$607$	0.391712			0.0158991			0.00794956	−	0.999968i	$-0.497470\pi$
$607$	0.391712			0.0158991			0.00794956	+	0.999968i	$0.497470\pi$
$608$	−52.3295	−	55.0754i	−2.12224	−	2.23360i
$609$	−27.7050			−1.12266
$610$			34.4701i			1.39565i
$611$	16.2941			0.659191
$612$		−	13.5120i		−	0.546189i
$613$		−	44.1261i		−	1.78224i	−0.453772	−	0.891118i	$-0.649922\pi$
$613$		−	44.1261i		−	1.78224i	0.453772	−	0.891118i	$-0.350078\pi$
$614$	72.8861			2.94144
$615$			5.71552i			0.230472i
$616$	−104.091	+	70.1351i	−4.19394	+	2.82583i
$617$	−38.4312			−1.54718			−0.773592	−	0.633685i	$-0.781542\pi$
$617$	−38.4312			−1.54718			−0.773592	+	0.633685i	$0.781542\pi$
$618$	32.1239			1.29221
$619$	−17.5171			−0.704070			−0.352035	−	0.935987i	$-0.614510\pi$
$619$	−17.5171			−0.704070			−0.352035	+	0.935987i	$0.614510\pi$
$620$		−	12.9937i		−	0.521840i
$621$			13.1185i			0.526427i
$622$	−17.0615			−0.684102
$623$	22.8724			0.916363
$624$			70.7908i			2.83390i
$625$	1.00000			0.0400000
$626$	43.8305			1.75182
$627$	15.4072	+	3.41369i	0.615304	+	0.136330i
$628$	25.5089			1.01792
$629$	9.16608			0.365476
$630$		−	21.1421i		−	0.842320i
$631$	−12.3919			−0.493314			−0.246657	−	0.969103i	$-0.579332\pi$
$631$	−12.3919			−0.493314			−0.246657	+	0.969103i	$0.579332\pi$
$632$	120.507			4.79351
$633$		−	8.49292i		−	0.337563i
$634$		−	26.8626i		−	1.06685i
$635$	−1.37793			−0.0546816
$636$	26.7368			1.06018
$637$	−59.5051			−2.35768
$638$	29.1181	+	43.2154i	1.15279	+	1.71092i
$639$			19.5820i			0.774652i
$640$	−21.5860			−0.853263
$641$		−	24.3374i		−	0.961271i	−0.876920	−	0.480636i	$-0.840406\pi$
$641$		−	24.3374i		−	0.961271i	0.876920	−	0.480636i	$-0.159594\pi$
$642$			55.0164i			2.17132i
$643$	−28.2480			−1.11399			−0.556996	−	0.830515i	$-0.688046\pi$
$643$	−28.2480			−1.11399			−0.556996	+	0.830515i	$0.688046\pi$
$644$			56.8816i			2.24145i
$645$	13.2647			0.522296
$646$	−12.1280	+	11.5233i	−0.477169	+	0.453378i
$647$	7.40780			0.291231			0.145615	−	0.989341i	$-0.453484\pi$
$647$	7.40780			0.291231			0.145615	+	0.989341i	$0.453484\pi$
$648$	2.64888			0.104058
$649$	−3.52448	+	2.37475i	−0.138348	+	0.0932172i
$650$	−13.4689			−0.528295
$651$			11.7695i			0.461285i
$652$	111.855			4.38057
$653$	−7.73767			−0.302798			−0.151399	−	0.988473i	$-0.548378\pi$
$653$	−7.73767			−0.302798			−0.151399	+	0.988473i	$0.548378\pi$
$654$		−	25.8870i		−	1.01226i
$655$			15.6980i			0.613370i
$656$	67.8215			2.64799
$657$			15.6306i			0.609809i
$658$		−	38.0471i		−	1.48323i
$659$	28.4946			1.10999			0.554997	−	0.831853i	$-0.312720\pi$
$659$	28.4946			1.10999			0.554997	+	0.831853i	$0.312720\pi$
$660$	15.7240	−	10.5946i	0.612055	−	0.412395i
$661$		−	13.4989i		−	0.525046i	−0.964926	−	0.262523i	$-0.915445\pi$
$661$		−	13.4989i		−	0.525046i	0.964926	−	0.262523i	$-0.0845545\pi$
$662$		−	7.83129i		−	0.304372i
$663$	7.79706			0.302813
$664$		−	105.014i		−	4.07532i
$665$	−13.7323	+	13.0476i	−0.532516	+	0.505966i
$666$		−	31.2571i		−	1.21119i
$667$	14.5970			0.565198
$668$	−22.0432			−0.852877
$669$	8.17714			0.316146
$670$			15.1027i			0.583470i
$671$	−35.2433	+	23.7465i	−1.36055	+	0.916723i
$672$	82.6781			3.18938
$673$	4.29280			0.165475			0.0827376	−	0.996571i	$-0.473634\pi$
$673$	4.29280			0.165475			0.0827376	+	0.996571i	$0.473634\pi$
$674$	42.0551			1.61990
$675$			5.24882i			0.202027i
$676$	63.1962			2.43062
$677$	8.95628			0.344218			0.172109	−	0.985078i	$-0.444942\pi$
$677$	8.95628			0.344218			0.172109	+	0.985078i	$0.444942\pi$
$678$	−51.5227			−1.97872
$679$	6.29940			0.241749
$680$			12.4240i			0.476437i
$681$		−	17.1615i		−	0.657630i
$682$	18.3587	−	12.3698i	0.702989	−	0.473666i
$683$		−	2.61967i		−	0.100239i	−0.998743	−	0.0501194i	$-0.984040\pi$
$683$		−	2.61967i		−	0.100239i	0.998743	−	0.0501194i	$-0.0159602\pi$
$684$	28.4360	+	29.9281i	1.08728	+	1.14433i
$685$	−17.4456			−0.666560
$686$			57.1103i			2.18048i
$687$			11.9218i			0.454846i
$688$		−	157.401i		−	6.00087i
$689$		−	23.4161i		−	0.892082i
$690$		−	7.33940i		−	0.279406i
$691$	28.0928			1.06870			0.534350	−	0.845264i	$-0.320557\pi$
$691$	28.0928			1.06870			0.534350	+	0.845264i	$0.320557\pi$
$692$	−24.1690			−0.918767
$693$	21.6163	−	14.5648i	0.821135	−	0.553271i
$694$			76.4831i			2.90326i
$695$			9.68872i			0.367514i
$696$		−	55.5182i		−	2.10441i
$697$		−	7.47002i		−	0.282947i
$698$			93.3270i			3.53248i
$699$	−5.62747			−0.212850
$700$			22.7588i			0.860203i
$701$			22.5962i			0.853447i	0.904382	+	0.426724i	$0.140332\pi$
$701$			22.5962i			0.853447i	−0.904382	+	0.426724i	$0.859668\pi$
$702$		−	70.6960i		−	2.66825i
$703$	−20.3023	+	19.2901i	−0.765715	+	0.727538i
$704$	−38.8845	−	57.7102i	−1.46551	−	2.17504i
$705$			3.55252i			0.133796i
$706$	12.0322			0.452837
$707$	−29.7922			−1.12045
$708$	7.32532			0.275302
$709$	−0.0344602			−0.00129418			−0.000647090	−	1.00000i	$-0.500206\pi$
$709$	−0.0344602			−0.00129418			−0.000647090		1.00000i	$0.500206\pi$
$710$		−	29.1295i		−	1.09321i
$711$	−25.0254			−0.938526
$712$			45.8341i			1.71771i
$713$		−	6.20105i		−	0.232231i
$714$		−	18.2063i		−	0.681352i
$715$	−9.27877	−	13.7711i	−0.347006	−	0.515008i
$716$		−	20.2450i		−	0.756589i
$717$	−0.309114			−0.0115441
$718$			21.3021i			0.794988i
$719$	40.5802			1.51339			0.756693	−	0.653770i	$-0.226814\pi$
$719$	40.5802			1.51339			0.756693	+	0.653770i	$0.226814\pi$
$720$	23.4247			0.872988
$721$	−47.5389			−1.77044
$722$	2.61187	−	51.0467i	0.0972036	−	1.89976i
$723$			3.19267i			0.118736i
$724$			24.4672i			0.909316i
$725$	5.84038			0.216906
$726$	29.9380	+	12.1303i	1.11110	+	0.450196i
$727$	42.0855			1.56087			0.780433	−	0.625239i	$-0.214999\pi$
$727$	42.0855			1.56087			0.780433	+	0.625239i	$0.214999\pi$
$728$		−	189.473i		−	7.02235i
$729$	−17.7386			−0.656987
$730$		−	23.2516i		−	0.860580i
$731$	−17.3365			−0.641215
$732$	73.2500			2.70740
$733$		−	13.2580i		−	0.489695i	−0.969562	−	0.244848i	$-0.921262\pi$
$733$		−	13.2580i		−	0.489695i	0.969562	−	0.244848i	$-0.0787380\pi$
$734$	−12.2300			−0.451417
$735$		−	12.9736i		−	0.478537i
$736$	−43.5609			−1.60567
$737$	−15.4415	+	10.4043i	−0.568795	+	0.383247i
$738$	−25.4734			−0.937689
$739$			52.8772i			1.94512i	0.232652	+	0.972560i	$0.425260\pi$
$739$			52.8772i			1.94512i	−0.232652	+	0.972560i	$0.574740\pi$
$740$			33.6474i			1.23690i
$741$	−17.2700	+	16.4089i	−0.634429	+	0.602797i
$742$	−54.6770			−2.00726
$743$	5.89765			0.216364			0.108182	−	0.994131i	$-0.465497\pi$
$743$	5.89765			0.216364			0.108182	+	0.994131i	$0.465497\pi$
$744$	−23.5851			−0.864670
$745$			3.10806i			0.113871i
$746$	−25.3716			−0.928922
$747$			21.8079i			0.797910i
$748$	−20.5508	+	13.8469i	−0.751411	+	0.506292i
$749$		−	81.4166i		−	2.97490i
$750$		−	2.93656i		−	0.107228i
$751$			49.2991i			1.79895i	0.436972	+	0.899475i	$0.356051\pi$
$751$			49.2991i			1.79895i	−0.436972	+	0.899475i	$0.643949\pi$
$752$	42.1550			1.53723
$753$		−	4.83022i		−	0.176023i
$754$	−78.6638			−2.86477
$755$	22.8611			0.832002
$756$	−119.457			−4.34461
$757$	8.28484			0.301118			0.150559	−	0.988601i	$-0.451893\pi$
$757$	8.28484			0.301118			0.150559	+	0.988601i	$0.451893\pi$
$758$		−	6.24152i		−	0.226702i
$759$	7.50403	−	5.05612i	0.272379	−	0.183526i
$760$	−26.1462	−	27.5182i	−0.948424	−	0.998192i
$761$			38.3151i			1.38892i	0.719531	+	0.694460i	$0.244357\pi$
$761$			38.3151i			1.38892i	−0.719531	+	0.694460i	$0.755643\pi$
$762$			4.04638i			0.146585i
$763$			38.3091i			1.38688i
$764$	−77.6934			−2.81085
$765$		−	2.58005i		−	0.0932820i
$766$		−	64.8443i		−	2.34292i
$767$		−	6.41551i		−	0.231651i
$768$			17.5825i			0.634453i
$769$		−	28.5107i		−	1.02812i	−0.857753	−	0.514061i	$-0.828140\pi$
$769$		−	28.5107i		−	1.02812i	0.857753	−	0.514061i	$-0.171860\pi$
$770$	−32.1556	+	21.6661i	−1.15881	+	0.780792i
$771$	2.24411			0.0808196
$772$	−108.913			−3.91986
$773$			8.02168i			0.288520i	0.989540	+	0.144260i	$0.0460801\pi$
$773$			8.02168i			0.288520i	−0.989540	+	0.144260i	$0.953920\pi$
$774$			59.1190i			2.12499i
$775$		−	2.48109i		−	0.0891235i
$776$			12.6234i			0.453154i
$777$		−	30.4774i		−	1.09337i
$778$	−12.6816			−0.454658
$779$	15.7207	+	16.5456i	0.563252	+	0.592808i
$780$			28.6219i			1.02483i
$781$	29.7829	−	20.0674i	1.06572	−	0.718066i
$782$			9.59239i			0.343023i
$783$			30.6551i			1.09552i
$784$	−153.947			−5.49811
$785$	4.87082			0.173847
$786$	46.0980			1.64426
$787$	36.7149			1.30874			0.654372	−	0.756173i	$-0.272933\pi$
$787$	36.7149			1.30874			0.654372	+	0.756173i	$0.272933\pi$
$788$			58.1751i			2.07240i
$789$	21.6230			0.769798
$790$	37.2269			1.32447
$791$	76.2464			2.71101
$792$	29.1865	+	43.3170i	1.03710	+	1.53920i
$793$		−	64.1523i		−	2.27811i
$794$	22.8416			0.810618
$795$	5.10528			0.181066
$796$	−66.7061			−2.36433
$797$			41.9609i			1.48633i	0.669107	+	0.743166i	$0.266677\pi$
$797$			41.9609i			1.48633i	−0.669107	+	0.743166i	$0.733323\pi$
$798$	38.3151	+	40.3257i	1.35634	+	1.42751i
$799$		−	4.64304i		−	0.164259i
$800$	−17.4291			−0.616211
$801$		−	9.51827i		−	0.336311i
$802$			36.5210i			1.28960i
$803$	23.7731	−	16.0180i	0.838935	−	0.565264i
$804$	32.0938			1.13186
$805$			10.8613i			0.382810i
$806$			33.4177i			1.17709i
$807$	−1.66781			−0.0587097
$808$		−	59.7008i		−	2.10027i
$809$			0.0400469i			0.00140797i	1.00000		0.000703987i	$0.000224086\pi$
$809$			0.0400469i			0.00140797i	−1.00000		0.000703987i	$0.999776\pi$
$810$	0.818291			0.0287518
$811$	−9.32687			−0.327511			−0.163755	−	0.986501i	$-0.552361\pi$
$811$	−9.32687			−0.327511			−0.163755	+	0.986501i	$0.552361\pi$
$812$			132.920i			4.66459i
$813$	−2.37324			−0.0832331
$814$	−47.5400	+	32.0319i	−1.66627	+	1.12272i
$815$	21.3582			0.748144
$816$	20.1720			0.706160
$817$	38.3993	−	36.4848i	1.34342	−	1.27644i
$818$	−87.6872			−3.06591
$819$			39.3475i			1.37491i
$820$	27.4214			0.957596
$821$			16.6052i			0.579524i	0.957099	+	0.289762i	$0.0935762\pi$
$821$			16.6052i			0.579524i	−0.957099	+	0.289762i	$0.906424\pi$
$822$			51.2299i			1.78685i
$823$	44.4511			1.54947			0.774733	−	0.632288i	$-0.217884\pi$
$823$	44.4511			1.54947			0.774733	+	0.632288i	$0.217884\pi$
$824$		−	95.2636i		−	3.31866i
$825$	3.00243	−	2.02300i	0.104531	−	0.0704318i
$826$	−14.9803			−0.521232
$827$	−40.2143			−1.39839			−0.699195	−	0.714931i	$-0.746458\pi$
$827$	−40.2143			−1.39839			−0.699195	+	0.714931i	$0.746458\pi$
$828$	23.6711			0.822627
$829$			23.3026i			0.809334i	0.914464	+	0.404667i	$0.132613\pi$
$829$			23.3026i			0.809334i	−0.914464	+	0.404667i	$0.867387\pi$
$830$		−	32.4407i		−	1.12603i
$831$	13.1603			0.456525
$832$	105.048			3.64189
$833$			16.9561i			0.587493i
$834$	28.4515			0.985195
$835$	−4.20905			−0.145660
$836$	16.3779	−	73.9191i	0.566440	−	2.55655i
$837$	13.0228			0.450134
$838$	54.7147			1.89009
$839$		−	32.0243i		−	1.10560i	−0.833314	−	0.552800i	$-0.813559\pi$
$839$		−	32.0243i		−	1.10560i	0.833314	−	0.552800i	$-0.186441\pi$
$840$	41.3098			1.42532
$841$	5.11008			0.176210
$842$			36.9751i			1.27425i
$843$			8.83937i			0.304444i
$844$	−40.7465			−1.40255
$845$	12.0670			0.415119
$846$	−15.8332			−0.544356
$847$	−44.3041	−	17.9511i	−1.52231	−	0.616807i
$848$		−	60.5803i		−	2.08034i
$849$	12.4808			0.428341
$850$			3.83800i			0.131642i
$851$			16.0577i			0.550451i
$852$	−61.9010			−2.12069
$853$		−	53.2475i		−	1.82316i	−0.411123	−	0.911580i	$-0.634863\pi$
$853$		−	53.2475i		−	1.82316i	0.411123	−	0.911580i	$-0.365137\pi$
$854$	−149.797			−5.12594
$855$	5.42973	+	5.71465i	0.185693	+	0.195437i
$856$	163.151			5.57640
$857$	31.2012			1.06581			0.532907	−	0.846174i	$-0.321100\pi$
$857$	31.2012			1.06581			0.532907	+	0.846174i	$0.321100\pi$
$858$	−40.4395	+	27.2477i	−1.38058	+	0.930220i
$859$	−17.5957			−0.600357			−0.300179	−	0.953883i	$-0.597046\pi$
$859$	−17.5957			−0.600357			−0.300179	+	0.953883i	$0.597046\pi$
$860$		−	63.6399i		−	2.17010i
$861$	−24.8379			−0.846474
$862$	50.3157			1.71376
$863$		−	38.7116i		−	1.31776i	−0.752249	−	0.658879i	$-0.771031\pi$
$863$		−	38.7116i		−	1.31776i	0.752249	−	0.658879i	$-0.228969\pi$
$864$		−	91.4820i		−	3.11228i
$865$	−4.61496			−0.156914
$866$			64.1627i			2.18034i
$867$			16.3351i			0.554770i
$868$	56.4668			1.91661
$869$	25.6457	+	38.0619i	0.869970	+	1.29116i
$870$		−	17.1506i		−	0.581461i
$871$		−	28.1077i		−	0.952393i
$872$	−76.7679			−2.59969
$873$		−	2.62147i		−	0.0887235i
$874$	−20.1872	−	21.2465i	−0.682843	−	0.718674i
$875$			4.34570i			0.146911i
$876$	−49.4103			−1.66942
$877$	10.1163			0.341604			0.170802	−	0.985305i	$-0.445364\pi$
$877$	10.1163			0.341604			0.170802	+	0.985305i	$0.445364\pi$
$878$	16.5279			0.557791
$879$			6.63327i			0.223735i
$880$	−24.0053	−	35.6274i	−0.809219	−	1.20100i
$881$	−11.1062			−0.374177			−0.187089	−	0.982343i	$-0.559905\pi$
$881$	−11.1062			−0.374177			−0.187089	+	0.982343i	$0.559905\pi$
$882$	57.8217			1.94696
$883$	43.2348			1.45497			0.727484	−	0.686124i	$-0.240689\pi$
$883$	43.2348			1.45497			0.727484	+	0.686124i	$0.240689\pi$
$884$		−	37.4080i		−	1.25817i
$885$	1.39874			0.0470180
$886$	−39.8249			−1.33794
$887$	−6.35680			−0.213440			−0.106720	−	0.994289i	$-0.534035\pi$
$887$	−6.35680			−0.213440			−0.106720	+	0.994289i	$0.534035\pi$
$888$	61.0738			2.04950
$889$		−	5.98808i		−	0.200834i
$890$			14.1590i			0.474612i
$891$	0.563721	+	0.836645i	0.0188854	+	0.0280287i
$892$		−	39.2315i		−	1.31357i
$893$	9.77130	+	10.2840i	0.326984	+	0.344142i
$894$	9.12700			0.305253
$895$		−	3.86569i		−	0.129216i
$896$		−	93.8064i		−	3.13385i
$897$			13.6594i			0.456073i
$898$			88.2787i			2.94590i
$899$		−	14.4905i		−	0.483287i
$900$	9.47101			0.315700
$901$	−6.67245			−0.222292
$902$	26.1048	+	38.7433i	0.869194	+	1.29001i
$903$			57.6442i			1.91828i
$904$			152.791i			5.08174i
$905$			4.67190i			0.155299i
$906$		−	67.1331i		−	2.23035i
$907$		−	52.8991i		−	1.75649i	−0.478215	−	0.878243i	$-0.658716\pi$
$907$		−	52.8991i		−	1.75649i	0.478215	−	0.878243i	$-0.341284\pi$
$908$	−82.3359			−2.73241
$909$			12.3979i			0.411213i
$910$		−	58.5320i		−	1.94032i
$911$		−	55.4449i		−	1.83697i	−0.395456	−	0.918485i	$-0.629413\pi$
$911$		−	55.4449i		−	1.83697i	0.395456	−	0.918485i	$-0.370587\pi$
$912$	−44.6796	+	42.4519i	−1.47949	+	1.40572i
$913$	33.1684	−	22.3484i	1.09771	−	0.739626i
$914$		−	60.2682i		−	1.99349i
$915$	13.9868			0.462388
$916$	57.1974			1.88986
$917$	−68.2186			−2.25278
$918$	−20.1449			−0.664882
$919$			0.315110i			0.0103945i	0.999986	+	0.00519726i	$0.00165435\pi$
$919$			0.315110i			0.0103945i	−0.999986	+	0.00519726i	$0.998346\pi$
$920$	−21.7650			−0.717572
$921$		−	29.5746i		−	0.974517i
$922$		−	78.8024i		−	2.59522i
$923$			54.2129i			1.78444i
$924$	46.0411	+	68.3317i	1.51464	+	2.24795i
$925$			6.42482i			0.211247i
$926$	6.83314			0.224551
$927$			19.7832i			0.649764i
$928$	−101.792			−3.34150
$929$	−5.01658			−0.164589			−0.0822944	−	0.996608i	$-0.526225\pi$
$929$	−5.01658			−0.164589			−0.0822944	+	0.996608i	$0.526225\pi$
$930$	−7.28588			−0.238913
$931$	−35.6841	−	37.5566i	−1.16950	−	1.23087i
$932$			26.9989i			0.884380i
$933$			6.92294i			0.226647i
$934$	−59.7660			−1.95560
$935$	−3.92408	+	2.64400i	−0.128331	+	0.0864681i
$936$	−78.8487			−2.57725
$937$			29.2439i			0.955356i	0.878535	+	0.477678i	$0.158521\pi$
$937$			29.2439i			0.955356i	−0.878535	+	0.477678i	$0.841479\pi$
$938$	−65.6320			−2.14296
$939$		−	17.7849i		−	0.580388i
$940$	17.0440			0.555912
$941$	−7.88362			−0.256999			−0.128499	−	0.991710i	$-0.541016\pi$
$941$	−7.88362			−0.256999			−0.128499	+	0.991710i	$0.541016\pi$
$942$		−	14.3034i		−	0.466031i
$943$	13.0864			0.426153
$944$		−	16.5977i		−	0.540210i
$945$	−22.8098			−0.742002
$946$	89.9160	−	60.5844i	2.92342	−	1.96977i
$947$	26.3717			0.856965			0.428482	−	0.903550i	$-0.359048\pi$
$947$	26.3717			0.856965			0.428482	+	0.903550i	$0.359048\pi$
$948$		−	79.1083i		−	2.56932i
$949$			43.2735i			1.40472i
$950$	−8.07708	−	8.50092i	−0.262055	−	0.275806i
$951$	−10.8999			−0.353454
$952$	−53.9907			−1.74985
$953$	42.6928			1.38296			0.691478	−	0.722397i	$-0.256960\pi$
$953$	42.6928			1.38296			0.691478	+	0.722397i	$0.256960\pi$
$954$			22.7536i			0.736676i
$955$	−14.8352			−0.480056
$956$			1.48304i			0.0479648i
$957$	17.5353	−	11.8151i	0.566836	−	0.381928i
$958$			27.4647i			0.887344i
$959$		−	75.8131i		−	2.44813i
$960$			22.9031i			0.739193i
$961$	24.8442			0.801425
$962$		−	86.5356i		−	2.79002i
$963$	−33.8812			−1.09181
$964$	15.3175			0.493342
$965$	−20.7964			−0.669461
$966$	31.8948			1.02620
$967$			47.9133i			1.54079i	0.637568	+	0.770394i	$0.279940\pi$
$967$			47.9133i			1.54079i	−0.637568	+	0.770394i	$0.720060\pi$
$968$	35.9723	−	88.7813i	1.15619	−	2.85354i
$969$	4.67575	+	4.92111i	0.150207	+	0.158089i
$970$			3.89962i			0.125209i
$971$			39.7099i			1.27435i	0.770719	+	0.637175i	$0.219897\pi$
$971$			39.7099i			1.27435i	−0.770719	+	0.637175i	$0.780103\pi$
$972$			80.7267i			2.58931i
$973$	−42.1043			−1.34980
$974$			58.7155i			1.88137i
$975$			5.46523i			0.175027i
$976$		−	165.970i		−	5.31257i
$977$		−	29.0894i		−	0.930651i	−0.885140	−	0.465325i	$-0.845937\pi$
$977$		−	29.0894i		−	0.930651i	0.885140	−	0.465325i	$-0.154063\pi$
$978$		−	62.7195i		−	2.00555i
$979$	−14.4766	+	9.75418i	−0.462675	+	0.311745i
$980$	−62.2433			−1.98829
$981$	15.9422			0.508996
$982$			25.1871i			0.803751i
$983$		−	2.26195i		−	0.0721451i	−0.999349	−	0.0360725i	$-0.988515\pi$
$983$		−	2.26195i		−	0.0721451i	0.999349	−	0.0360725i	$-0.0114847\pi$
$984$		−	49.7729i		−	1.58670i
$985$			11.1083i			0.353939i
$986$			22.4154i			0.713851i
$987$	−15.4382			−0.491403
$988$	78.7252	+	82.8563i	2.50458	+	2.63601i
$989$		−	30.3712i		−	0.965747i
$990$	9.01627	+	13.3815i	0.286556	+	0.425291i
$991$		−	17.1395i		−	0.544455i	−0.962233	−	0.272227i	$-0.912240\pi$
$991$		−	17.1395i		−	0.544455i	0.962233	−	0.272227i	$-0.0877603\pi$
$992$			43.2432i			1.37297i
$993$	−3.17766			−0.100840
$994$	126.588			4.01513
$995$	−12.7372			−0.403797
$996$	−68.9375			−2.18437
$997$		−	21.3541i		−	0.676290i	−0.941094	−	0.338145i	$-0.890201\pi$
$997$		−	21.3541i		−	0.676290i	0.941094	−	0.338145i	$-0.109799\pi$
$998$	68.6883			2.17429
$999$	−33.7227			−1.06694

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.b.626.2	yes	40
11.10	odd	2	inner	1045.2.f.b.626.40	yes	40
19.18	odd	2	inner	1045.2.f.b.626.39	yes	40
209.208	even	2	inner	1045.2.f.b.626.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.b.626.1	✓	40	209.208	even	2	inner
1045.2.f.b.626.2	yes	40	1.1	even	1	trivial
1045.2.f.b.626.39	yes	40	19.18	odd	2	inner
1045.2.f.b.626.40	yes	40	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.69018 q^{2} +1.09158i q^{3} +5.23709 q^{4} +1.00000 q^{5} -2.93656i q^{6} +4.34570i q^{7} -8.70838 q^{8} +1.80845 q^{9} +O(q^{10})\)	\(q-2.69018 q^{2} +1.09158i q^{3} +5.23709 q^{4} +1.00000 q^{5} -2.93656i q^{6} +4.34570i q^{7} -8.70838 q^{8} +1.80845 q^{9} -2.69018 q^{10} +(-1.85327 - 2.75052i) q^{11} +5.71672i q^{12} +5.00670 q^{13} -11.6907i q^{14} +1.09158i q^{15} +12.9530 q^{16} -1.42667i q^{17} -4.86506 q^{18} +(3.00243 + 3.15998i) q^{19} +5.23709 q^{20} -4.74369 q^{21} +(4.98564 + 7.39942i) q^{22} +2.49932 q^{23} -9.50591i q^{24} +1.00000 q^{25} -13.4689 q^{26} +5.24882i q^{27} +22.7588i q^{28} +5.84038 q^{29} -2.93656i q^{30} -2.48109i q^{31} -17.4291 q^{32} +(3.00243 - 2.02300i) q^{33} +3.83800i q^{34} +4.34570i q^{35} +9.47101 q^{36} +6.42482i q^{37} +(-8.07708 - 8.50092i) q^{38} +5.46523i q^{39} -8.70838 q^{40} +5.23599 q^{41} +12.7614 q^{42} -12.1518i q^{43} +(-9.70575 - 14.4048i) q^{44} +1.80845 q^{45} -6.72364 q^{46} +3.25447 q^{47} +14.1392i q^{48} -11.8851 q^{49} -2.69018 q^{50} +1.55733 q^{51} +26.2205 q^{52} -4.67695i q^{53} -14.1203i q^{54} +(-1.85327 - 2.75052i) q^{55} -37.8440i q^{56} +(-3.44937 + 3.27740i) q^{57} -15.7117 q^{58} -1.28138i q^{59} +5.71672i q^{60} -12.8133i q^{61} +6.67460i q^{62} +7.85897i q^{63} +20.9815 q^{64} +5.00670 q^{65} +(-8.07708 + 5.44224i) q^{66} -5.61402i q^{67} -7.47159i q^{68} +2.72822i q^{69} -11.6907i q^{70} +10.8281i q^{71} -15.7486 q^{72} +8.64312i q^{73} -17.2840i q^{74} +1.09158i q^{75} +(15.7240 + 16.5491i) q^{76} +(11.9530 - 8.05376i) q^{77} -14.7025i q^{78} -13.8381 q^{79} +12.9530 q^{80} -0.304176 q^{81} -14.0858 q^{82} +12.0589i q^{83} -24.8431 q^{84} -1.42667i q^{85} +32.6905i q^{86} +6.37526i q^{87} +(16.1390 + 23.9526i) q^{88} -5.26323i q^{89} -4.86506 q^{90} +21.7576i q^{91} +13.0892 q^{92} +2.70832 q^{93} -8.75512 q^{94} +(3.00243 + 3.15998i) q^{95} -19.0253i q^{96} -1.44957i q^{97} +31.9731 q^{98} +(-3.35154 - 4.97418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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