LMFDB - Embedded newform 1445.2.b.f.579.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1445,2,Mod(579,1445)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1445.579"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 9x^{8} + 228x^{6} - 225x^{4} - 1250x^{2} + 15625 $ x^12 - 2x^10 - 9x^8 + 228x^6 - 225x^4 - 1250*x^2 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			579.5
Root			$2.08313 - 0.812746i$ of defining polynomial
Character	$\chi$	$=$	1445.579
Dual form			1445.2.b.f.579.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.232389i q^{2} -2.39435i q^{3} +1.94600 q^{4} +(-2.08313 + 0.812746i) q^{5} -0.556420 q^{6} +2.06570i q^{7} -0.917007i q^{8} -2.73289 q^{9} +(0.188874 + 0.484098i) q^{10} -0.480046 q^{11} -4.65939i q^{12} -4.07073i q^{13} +0.480046 q^{14} +(1.94600 + 4.98774i) q^{15} +3.67889 q^{16} +0.635095i q^{18} -4.00000 q^{19} +(-4.05377 + 1.58160i) q^{20} +4.94600 q^{21} +0.111558i q^{22} -8.15123i q^{23} -2.19563 q^{24} +(3.67889 - 3.38612i) q^{25} -0.945995 q^{26} -0.639548i q^{27} +4.01984i q^{28} -1.03647 q^{29} +(1.15910 - 0.452229i) q^{30} -6.06053 q^{31} -2.68895i q^{32} +1.14940i q^{33} +(-1.67889 - 4.30312i) q^{35} -5.31820 q^{36} -1.29684i q^{37} +0.929557i q^{38} -9.74675 q^{39} +(0.745294 + 1.91025i) q^{40} -10.7832 q^{41} -1.14940i q^{42} -7.45685i q^{43} -0.934167 q^{44} +(5.69298 - 2.22115i) q^{45} -1.89426 q^{46} +3.60596i q^{47} -8.80853i q^{48} +2.73289 q^{49} +(-0.786897 - 0.854934i) q^{50} -7.92163i q^{52} -6.14969i q^{53} -0.148624 q^{54} +(1.00000 - 0.390156i) q^{55} +1.89426 q^{56} +9.57738i q^{57} +0.240864i q^{58} -6.00000 q^{59} +(3.78690 + 9.70612i) q^{60} +5.65685 q^{61} +1.40840i q^{62} -5.64533i q^{63} +6.73289 q^{64} +(3.30847 + 8.47988i) q^{65} +0.267107 q^{66} +3.14118i q^{67} -19.5169 q^{69} +(-1.00000 + 0.390156i) q^{70} +1.81789 q^{71} +2.50608i q^{72} -12.1711i q^{73} -0.301373 q^{74} +(-8.10753 - 8.80853i) q^{75} -7.78398 q^{76} -0.991630i q^{77} +2.26504i q^{78} +10.2268 q^{79} +(-7.66361 + 2.99000i) q^{80} -9.72998 q^{81} +2.50590i q^{82} -2.23672i q^{83} +9.62488 q^{84} -1.73289 q^{86} +2.48166i q^{87} +0.440206i q^{88} +9.37220 q^{89} +(-0.516171 - 1.32299i) q^{90} +8.40891 q^{91} -15.8623i q^{92} +14.5110i q^{93} +0.837986 q^{94} +(8.33253 - 3.25098i) q^{95} -6.43827 q^{96} +16.7189i q^{97} -0.635095i q^{98} +1.31191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 28 q^{9} - 12 q^{15} + 4 q^{16} - 48 q^{19} + 24 q^{21} + 4 q^{25} + 24 q^{26} - 52 q^{30} + 20 q^{35} + 68 q^{36} + 28 q^{49} - 40 q^{50} + 12 q^{55} - 72 q^{59} + 76 q^{60} + 76 q^{64}+ \cdots - 96 q^{94}+O(q^{100}) $ 12 * q - 12 * q^4 - 28 * q^9 - 12 * q^15 + 4 * q^16 - 48 * q^19 + 24 * q^21 + 4 * q^25 + 24 * q^26 - 52 * q^30 + 20 * q^35 + 68 * q^36 + 28 * q^49 - 40 * q^50 + 12 * q^55 - 72 * q^59 + 76 * q^60 + 76 * q^64 + 8 * q^66 - 88 * q^69 - 12 * q^70 + 48 * q^76 + 60 * q^81 + 40 * q^84 - 16 * q^86 + 16 * q^89 - 96 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	0.232389i		−	0.164324i	−0.996619	−	0.0821620i	$-0.973817\pi$
$2$		−	0.232389i		−	0.164324i	0.996619	−	0.0821620i	$-0.0261825\pi$
$3$		−	2.39435i		−	1.38238i	−0.722675	−	0.691188i	$-0.757088\pi$
$3$		−	2.39435i		−	1.38238i	0.722675	−	0.691188i	$-0.242912\pi$
$4$	1.94600			0.972998
$5$	−2.08313	+	0.812746i	−0.931605	+	0.363471i
$5$	−2.08313	+	0.812746i	−0.931605	+	0.363471i
$6$	−0.556420			−0.227158
$7$			2.06570i			0.780760i	0.920654	+	0.390380i	$0.127656\pi$
$7$			2.06570i			0.780760i	−0.920654	+	0.390380i	$0.872344\pi$
$8$		−	0.917007i		−	0.324211i
$9$	−2.73289			−0.910964
$10$	0.188874	+	0.484098i	0.0597270	+	0.153085i
$11$	−0.480046			−0.144739			−0.0723697	−	0.997378i	$-0.523056\pi$
$11$	−0.480046			−0.144739			−0.0723697	+	0.997378i	$0.523056\pi$
$12$		−	4.65939i		−	1.34505i
$13$		−	4.07073i		−	1.12902i	−0.825427	−	0.564509i	$-0.809065\pi$
$13$		−	4.07073i		−	1.12902i	0.825427	−	0.564509i	$-0.190935\pi$
$14$	0.480046			0.128298
$15$	1.94600	+	4.98774i	0.502454	+	1.28783i
$16$	3.67889			0.919722
$17$		0			0
$17$		0			0
$18$			0.635095i			0.149693i
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	−4.05377	+	1.58160i	−0.906450	+	0.353656i
$21$	4.94600			1.07930
$22$			0.111558i			0.0237842i
$23$		−	8.15123i		−	1.69965i	−0.527065	−	0.849825i	$-0.676708\pi$
$23$		−	8.15123i		−	1.69965i	0.527065	−	0.849825i	$-0.323292\pi$
$24$	−2.19563			−0.448182
$25$	3.67889	−	3.38612i	0.735778	−	0.677223i
$26$	−0.945995			−0.185525
$27$		−	0.639548i		−	0.123081i
$28$			4.01984i			0.759678i
$29$	−1.03647			−0.192467			−0.0962335	−	0.995359i	$-0.530680\pi$
$29$	−1.03647			−0.192467			−0.0962335	+	0.995359i	$0.530680\pi$
$30$	1.15910	−	0.452229i	0.211621	−	0.0825653i
$31$	−6.06053			−1.08850			−0.544251	−	0.838922i	$-0.683186\pi$
$31$	−6.06053			−1.08850			−0.544251	+	0.838922i	$0.683186\pi$
$32$		−	2.68895i		−	0.475343i
$33$			1.14940i			0.200084i
$34$		0			0
$35$	−1.67889	−	4.30312i	−0.283784	−	0.727361i
$36$	−5.31820			−0.886366
$37$		−	1.29684i		−	0.213200i	−0.994302	−	0.106600i	$-0.966004\pi$
$37$		−	1.29684i		−	0.213200i	0.994302	−	0.106600i	$-0.0339964\pi$
$38$			0.929557i			0.150794i
$39$	−9.74675			−1.56073
$40$	0.745294	+	1.91025i	0.117841	+	0.302037i
$41$	−10.7832			−1.68405			−0.842027	−	0.539435i	$-0.818638\pi$
$41$	−10.7832			−1.68405			−0.842027	+	0.539435i	$0.818638\pi$
$42$		−	1.14940i		−	0.177356i
$43$		−	7.45685i		−	1.13716i	−0.822628	−	0.568580i	$-0.807493\pi$
$43$		−	7.45685i		−	1.13716i	0.822628	−	0.568580i	$-0.192507\pi$
$44$	−0.934167			−0.140831
$45$	5.69298	−	2.22115i	0.848659	−	0.331109i
$46$	−1.89426			−0.279293
$47$			3.60596i			0.525983i	0.964798	+	0.262991i	$0.0847091\pi$
$47$			3.60596i			0.525983i	−0.964798	+	0.262991i	$0.915291\pi$
$48$		−	8.80853i		−	1.27140i
$49$	2.73289			0.390413
$50$	−0.786897	−	0.854934i	−0.111284	−	0.120906i
$51$		0			0
$52$		−	7.92163i		−	1.09853i
$53$		−	6.14969i		−	0.844725i	−0.906427	−	0.422362i	$-0.861201\pi$
$53$		−	6.14969i		−	0.844725i	0.906427	−	0.422362i	$-0.138799\pi$
$54$	−0.148624			−0.0202252
$55$	1.00000	−	0.390156i	0.134840	−	0.0526086i
$56$	1.89426			0.253131
$57$			9.57738i			1.26856i
$58$			0.240864i			0.0316270i
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$	3.78690	+	9.70612i	0.488886	+	1.25305i
$61$	5.65685			0.724286			0.362143	−	0.932123i	$-0.382045\pi$
$61$	5.65685			0.724286			0.362143	+	0.932123i	$0.382045\pi$
$62$			1.40840i			0.178867i
$63$		−	5.64533i		−	0.711245i
$64$	6.73289			0.841612
$65$	3.30847	+	8.47988i	0.410366	+	1.05180i
$66$	0.267107			0.0328787
$67$			3.14118i			0.383756i	0.981419	+	0.191878i	$0.0614578\pi$
$67$			3.14118i			0.383756i	−0.981419	+	0.191878i	$0.938542\pi$
$68$		0			0
$69$	−19.5169			−2.34956
$70$	−1.00000	+	0.390156i	−0.119523	+	0.0466325i
$71$	1.81789			0.215743			0.107872	−	0.994165i	$-0.465596\pi$
$71$	1.81789			0.215743			0.107872	+	0.994165i	$0.465596\pi$
$72$			2.50608i			0.295345i
$73$		−	12.1711i		−	1.42452i	−0.701918	−	0.712258i	$-0.747673\pi$
$73$		−	12.1711i		−	1.42452i	0.701918	−	0.712258i	$-0.252327\pi$
$74$	−0.301373			−0.0350339
$75$	−8.10753	−	8.80853i	−0.936177	−	1.01712i
$76$	−7.78398			−0.892884
$77$		−	0.991630i		−	0.113007i
$78$			2.26504i			0.256465i
$79$	10.2268			1.15060			0.575302	−	0.817941i	$-0.304885\pi$
$79$	10.2268			1.15060			0.575302	+	0.817941i	$0.304885\pi$
$80$	−7.66361	+	2.99000i	−0.856818	+	0.334292i
$81$	−9.72998			−1.08111
$82$			2.50590i			0.276731i
$83$		−	2.23672i		−	0.245512i	−0.992437	−	0.122756i	$-0.960827\pi$
$83$		−	2.23672i		−	0.245512i	0.992437	−	0.122756i	$-0.0391732\pi$
$84$	9.62488			1.05016
$85$		0			0
$86$	−1.73289			−0.186863
$87$			2.48166i			0.266062i
$88$			0.440206i			0.0469261i
$89$	9.37220			0.993451			0.496726	−	0.867908i	$-0.334536\pi$
$89$	9.37220			0.993451			0.496726	+	0.867908i	$0.334536\pi$
$90$	−0.516171	−	1.32299i	−0.0544092	−	0.139455i
$91$	8.40891			0.881493
$92$		−	15.8623i		−	1.65376i
$93$			14.5110i			1.50472i
$94$	0.837986			0.0864316
$95$	8.33253	−	3.25098i	0.854900	−	0.333544i
$96$	−6.43827			−0.657103
$97$			16.7189i			1.69755i	0.528757	+	0.848774i	$0.322658\pi$
$97$			16.7189i			1.69755i	−0.528757	+	0.848774i	$0.677342\pi$
$98$		−	0.635095i		−	0.0641543i
$99$	1.31191			0.131852
$100$	7.15910	−	6.58937i	0.715910	−	0.658937i
$101$	−4.41178			−0.438989			−0.219494	−	0.975614i	$-0.570441\pi$
$101$	−4.41178			−0.438989			−0.219494	+	0.975614i	$0.570441\pi$
$102$		0			0
$103$			17.4323i			1.71766i	0.512262	+	0.858829i	$0.328808\pi$
$103$			17.4323i			1.71766i	−0.512262	+	0.858829i	$0.671192\pi$
$104$	−3.73289			−0.366040
$105$	−10.3032	+	4.01984i	−1.00549	+	0.392296i
$106$	−1.42912			−0.138809
$107$			5.21115i			0.503781i	0.967756	+	0.251890i	$0.0810522\pi$
$107$			5.21115i			0.503781i	−0.967756	+	0.251890i	$0.918948\pi$
$108$		−	1.24456i		−	0.119758i
$109$	8.10753			0.776561			0.388280	−	0.921541i	$-0.373069\pi$
$109$	8.10753			0.776561			0.388280	+	0.921541i	$0.373069\pi$
$110$	−0.0906680	−	0.232389i	−0.00864485	−	0.0221575i
$111$	−3.10509			−0.294722
$112$			7.59947i			0.718082i
$113$		−	3.47410i		−	0.326816i	−0.986559	−	0.163408i	$-0.947751\pi$
$113$		−	3.47410i		−	0.326816i	0.986559	−	0.163408i	$-0.0522487\pi$
$114$	2.22568			0.208454
$115$	6.62488	+	16.9801i	0.617774	+	1.58340i
$116$	−2.01696			−0.187270
$117$			11.1249i			1.02850i
$118$			1.39434i			0.128359i
$119$		0			0
$120$	4.57379	−	1.78449i	0.417528	−	0.162901i
$121$	−10.7696			−0.979051
$122$		−	1.31459i		−	0.119018i
$123$			25.8187i			2.32800i
$124$	−11.7938			−1.05911
$125$	−4.91156	+	10.0437i	−0.439303	+	0.898339i
$126$	−1.31191			−0.116875
$127$			2.98341i			0.264735i	0.991201	+	0.132367i	$0.0422579\pi$
$127$			2.98341i			0.264735i	−0.991201	+	0.132367i	$0.957742\pi$
$128$		−	6.94255i		−	0.613640i
$129$	−17.8543			−1.57198
$130$	1.97063	−	0.768854i	0.172836	−	0.0674329i
$131$	−7.19377			−0.628522			−0.314261	−	0.949337i	$-0.601757\pi$
$131$	−7.19377			−0.628522			−0.314261	+	0.949337i	$0.601757\pi$
$132$			2.23672i			0.194681i
$133$		−	8.26279i		−	0.716475i
$134$	0.729976			0.0630603
$135$	0.519790	+	1.33226i	0.0447364	+	0.114663i
$136$		0			0
$137$		−	0.526852i		−	0.0450120i	−0.999747	−	0.0225060i	$-0.992836\pi$
$137$		−	0.526852i		−	0.0450120i	0.999747	−	0.0225060i	$-0.00716448\pi$
$138$			4.53551i			0.386089i
$139$	17.6756			1.49923			0.749613	−	0.661877i	$-0.230240\pi$
$139$	17.6756			1.49923			0.749613	+	0.661877i	$0.230240\pi$
$140$	−3.26711	−	8.37386i	−0.276121	−	0.707720i
$141$	8.63391			0.727106
$142$		−	0.422457i		−	0.0354518i
$143$			1.95414i			0.163413i
$144$	−10.0540			−0.837834
$145$	2.15910	−	0.842384i	0.179303	−	0.0699562i
$146$	−2.82843			−0.234082
$147$		−	6.54349i		−	0.539698i
$148$		−	2.52365i		−	0.207443i
$149$	−7.32111			−0.599769			−0.299884	−	0.953976i	$-0.596948\pi$
$149$	−7.32111			−0.599769			−0.299884	+	0.953976i	$0.596948\pi$
$150$	−2.04701	+	1.88410i	−0.167138	+	0.153836i
$151$	7.46579			0.607557			0.303778	−	0.952743i	$-0.401752\pi$
$151$	7.46579			0.607557			0.303778	+	0.952743i	$0.401752\pi$
$152$			3.66803i			0.297516i
$153$		0			0
$154$	−0.230444			−0.0185697
$155$	12.6249	−	4.92567i	1.01405	−	0.395639i
$156$	−18.9671			−1.51859
$157$		−	12.4571i		−	0.994188i	−0.867697	−	0.497094i	$-0.834400\pi$
$157$		−	12.4571i		−	0.994188i	0.867697	−	0.497094i	$-0.165600\pi$
$158$		−	2.37660i		−	0.189072i
$159$	−14.7245			−1.16773
$160$	2.18543	+	5.60144i	0.172774	+	0.442833i
$161$	16.8380			1.32702
$162$			2.26114i			0.177652i
$163$		−	8.56767i		−	0.671071i	−0.942027	−	0.335536i	$-0.891083\pi$
$163$		−	8.56767i		−	0.671071i	0.942027	−	0.335536i	$-0.108917\pi$
$164$	−20.9841			−1.63858
$165$	−0.934167	−	2.39435i	−0.0727248	−	0.186400i
$166$	−0.519790			−0.0403435
$167$			9.44808i			0.731114i	0.930789	+	0.365557i	$0.119122\pi$
$167$			9.44808i			0.731114i	−0.930789	+	0.365557i	$0.880878\pi$
$168$		−	4.53551i		−	0.349922i
$169$	−3.57088			−0.274683
$170$		0			0
$171$	10.9316			0.835958
$172$		−	14.5110i		−	1.10645i
$173$		−	16.5433i		−	1.25777i	−0.777500	−	0.628883i	$-0.783512\pi$
$173$		−	16.5433i		−	1.25777i	0.777500	−	0.628883i	$-0.216488\pi$
$174$	0.576711			0.0437204
$175$	6.99469	+	7.59947i	0.528749	+	0.574466i
$176$	−1.76604			−0.133120
$177$			14.3661i			1.07982i
$178$		−	2.17800i		−	0.163248i
$179$	−19.5313			−1.45984			−0.729919	−	0.683534i	$-0.760442\pi$
$179$	−19.5313			−1.45984			−0.729919	+	0.683534i	$0.760442\pi$
$180$	11.0785	−	4.32234i	0.825743	−	0.322168i
$181$	10.4818			0.779109			0.389555	−	0.921003i	$-0.372629\pi$
$181$	10.4818			0.779109			0.389555	+	0.921003i	$0.372629\pi$
$182$		−	1.95414i		−	0.144851i
$183$		−	13.5445i		−	1.00124i
$184$	−7.47474			−0.551045
$185$	1.05400	+	2.70150i	0.0774920	+	0.198618i
$186$	3.37220			0.247262
$187$		0			0
$188$			7.01717i			0.511780i
$189$	1.32111			0.0960968
$190$	−0.755494	−	1.93639i	−0.0548093	−	0.140481i
$191$	5.32111			0.385022			0.192511	−	0.981295i	$-0.438337\pi$
$191$	5.32111			0.385022			0.192511	+	0.981295i	$0.438337\pi$
$192$		−	16.1209i		−	1.16342i
$193$		−	12.4820i		−	0.898472i	−0.893413	−	0.449236i	$-0.851696\pi$
$193$		−	12.4820i		−	0.898472i	0.893413	−	0.449236i	$-0.148304\pi$
$194$	3.88529			0.278948
$195$	20.3038	−	7.92163i	1.45398	−	0.567280i
$196$	5.31820			0.379871
$197$		−	0.551763i		−	0.0393115i	−0.999807	−	0.0196558i	$-0.993743\pi$
$197$		−	0.551763i		−	0.0393115i	0.999807	−	0.0196558i	$-0.00625702\pi$
$198$		−	0.304875i		−	0.0216665i
$199$	17.5992			1.24758			0.623788	−	0.781593i	$-0.285593\pi$
$199$	17.5992			1.24758			0.623788	+	0.781593i	$0.285593\pi$
$200$	−3.10509	−	3.37357i	−0.219563	−	0.238547i
$201$	7.52106			0.530495
$202$			1.02525i			0.0721364i
$203$		−	2.14103i		−	0.150271i
$204$		0			0
$205$	22.4629	−	8.76401i	1.56887	−	0.612105i
$206$	4.05109			0.282253
$207$			22.2764i			1.54832i
$208$		−	14.9758i		−	1.03838i
$209$	1.92018			0.132822
$210$	0.934167	+	2.39435i	0.0644637	+	0.165226i
$211$	12.8302			0.883269			0.441634	−	0.897195i	$-0.354399\pi$
$211$	12.8302			0.883269			0.441634	+	0.897195i	$0.354399\pi$
$212$		−	11.9673i		−	0.821915i
$213$		−	4.35265i		−	0.298238i
$214$	1.21102			0.0827833
$215$	6.06053	+	15.5336i	0.413324	+	1.05938i
$216$	−0.586470			−0.0399042
$217$		−	12.5192i		−	0.849860i
$218$		−	1.88410i		−	0.127608i
$219$	−29.1418			−1.96922
$220$	1.94600	−	0.759241i	0.131199	−	0.0511880i
$221$		0			0
$222$			0.721590i			0.0484300i
$223$		−	4.07073i		−	0.272597i	−0.990668	−	0.136298i	$-0.956479\pi$
$223$		−	4.07073i		−	0.272597i	0.990668	−	0.136298i	$-0.0435206\pi$
$224$	5.55456			0.371129
$225$	−10.0540	+	9.25389i	−0.670267	+	0.616926i
$226$	−0.807344			−0.0537037
$227$		−	15.7745i		−	1.04699i	−0.852029	−	0.523494i	$-0.824628\pi$
$227$		−	15.7745i		−	1.04699i	0.852029	−	0.523494i	$-0.175372\pi$
$228$			18.6375i			1.23430i
$229$	−14.9460			−0.987659			−0.493830	−	0.869559i	$-0.664403\pi$
$229$	−14.9460			−0.987659			−0.493830	+	0.869559i	$0.664403\pi$
$230$	3.94600	−	1.53955i	0.260191	−	0.101515i
$231$	−2.37431			−0.156218
$232$			0.950447i			0.0623999i
$233$			0.727332i			0.0476491i	0.999716	+	0.0238246i	$0.00758431\pi$
$233$			0.727332i			0.0476491i	−0.999716	+	0.0238246i	$0.992416\pi$
$234$	2.58530			0.169007
$235$	−2.93073	−	7.51169i	−0.191179	−	0.490008i
$236$	−11.6760			−0.760041
$237$		−	24.4865i		−	1.59057i
$238$		0			0
$239$	−9.57379			−0.619277			−0.309639	−	0.950854i	$-0.600208\pi$
$239$	−9.57379			−0.619277			−0.309639	+	0.950854i	$0.600208\pi$
$240$	7.15910	+	18.3493i	0.462118	+	1.18444i
$241$	8.48528			0.546585			0.273293	−	0.961931i	$-0.411887\pi$
$241$	8.48528			0.546585			0.273293	+	0.961931i	$0.411887\pi$
$242$			2.50273i			0.160882i
$243$			21.3783i			1.37142i
$244$	11.0082			0.704729
$245$	−5.69298	+	2.22115i	−0.363711	+	0.141904i
$246$	6.00000			0.382546
$247$			16.2829i			1.03606i
$248$			5.55755i			0.352905i
$249$	−5.35548			−0.339390
$250$	2.33406	+	1.14139i	0.147619	+	0.0721881i
$251$	6.03666			0.381031			0.190515	−	0.981684i	$-0.438984\pi$
$251$	6.03666			0.381031			0.190515	+	0.981684i	$0.438984\pi$
$252$		−	10.9858i		−	0.692039i
$253$			3.91297i			0.246006i
$254$	0.693313			0.0435023
$255$		0			0
$256$	11.8524			0.740776
$257$			27.2752i			1.70138i	0.525670	+	0.850689i	$0.323815\pi$
$257$			27.2752i			1.70138i	−0.525670	+	0.850689i	$0.676185\pi$
$258$			4.14914i			0.258314i
$259$	2.67889			0.166458
$260$	6.43827	+	16.5018i	0.399285	+	1.02340i
$261$	2.83255			0.175331
$262$			1.67175i			0.103281i
$263$		−	12.3700i		−	0.762765i	−0.924417	−	0.381382i	$-0.875448\pi$
$263$		−	12.3700i		−	0.762765i	0.924417	−	0.381382i	$-0.124552\pi$
$264$	1.05400			0.0648695
$265$	4.99813	+	12.8106i	0.307033	+	0.786950i
$266$	−1.92018			−0.117734
$267$		−	22.4403i		−	1.37332i
$268$			6.11272i			0.373394i
$269$	20.0758			1.22405			0.612023	−	0.790840i	$-0.290356\pi$
$269$	20.0758			1.22405			0.612023	+	0.790840i	$0.290356\pi$
$270$	0.309604	−	0.120794i	0.0188419	−	0.00735127i
$271$	−24.2102			−1.47066			−0.735332	−	0.677707i	$-0.762974\pi$
$271$	−24.2102			−1.47066			−0.735332	+	0.677707i	$0.762974\pi$
$272$		0			0
$273$		−	20.1338i		−	1.21855i
$274$	−0.122435			−0.00739655
$275$	−1.76604	+	1.62549i	−0.106496	+	0.0980209i
$276$	−37.9797			−2.28611
$277$			6.76058i			0.406204i	0.979158	+	0.203102i	$0.0651023\pi$
$277$			6.76058i			0.406204i	−0.979158	+	0.203102i	$0.934898\pi$
$278$		−	4.10762i		−	0.246359i
$279$	16.5628			0.991587
$280$	−3.94600	+	1.53955i	−0.235818	+	0.0920058i
$281$	18.0367			1.07598			0.537989	−	0.842952i	$-0.319184\pi$
$281$	18.0367			1.07598			0.537989	+	0.842952i	$0.319184\pi$
$282$		−	2.00643i		−	0.119481i
$283$			25.2165i			1.49897i	0.662023	+	0.749484i	$0.269698\pi$
$283$			25.2165i			1.49897i	−0.662023	+	0.749484i	$0.730302\pi$
$284$	3.53760			0.209918
$285$	−7.78398	−	19.9510i	−0.461083	−	1.18179i
$286$	0.454121			0.0268528
$287$		−	22.2749i		−	1.31484i
$288$			7.34861i			0.433021i
$289$		0			0
$290$	−0.195761	−	0.501751i	−0.0114955	−	0.0294639i
$291$	40.0308			2.34665
$292$		−	23.6848i		−	1.38605i
$293$		−	26.2584i		−	1.53403i	−0.641627	−	0.767017i	$-0.721740\pi$
$293$		−	26.2584i		−	1.53403i	0.641627	−	0.767017i	$-0.278260\pi$
$294$	−1.52064			−0.0886854
$295$	12.4988	−	4.87648i	0.727708	−	0.283919i
$296$	−1.18922			−0.0691217
$297$			0.307012i			0.0178147i
$298$			1.70135i			0.0985565i
$299$	−33.1815			−1.91894
$300$	−15.7772	−	17.1414i	−0.910898	−	0.989657i
$301$	15.4036			0.887849
$302$		−	1.73497i		−	0.0998362i
$303$			10.5633i			0.606847i
$304$	−14.7156			−0.843995
$305$	−11.7840	+	4.59759i	−0.674749	+	0.263257i
$306$		0			0
$307$			13.9136i			0.794088i	0.917800	+	0.397044i	$0.129964\pi$
$307$			13.9136i			0.794088i	−0.917800	+	0.397044i	$0.870036\pi$
$308$		−	1.92971i		−	0.109955i
$309$	41.7390			2.37445
$310$	−1.14467	−	2.93389i	−0.0650130	−	0.166634i
$311$	8.74033			0.495619			0.247809	−	0.968809i	$-0.420289\pi$
$311$	8.74033			0.495619			0.247809	+	0.968809i	$0.420289\pi$
$312$			8.93784i			0.506005i
$313$		−	6.94820i		−	0.392735i	−0.980530	−	0.196368i	$-0.937085\pi$
$313$		−	6.94820i		−	0.392735i	0.980530	−	0.196368i	$-0.0629146\pi$
$314$	−2.89491			−0.163369
$315$	4.58822	+	11.7600i	0.258517	+	0.662600i
$316$	19.9013			1.11953
$317$		−	4.21918i		−	0.236973i	−0.992956	−	0.118486i	$-0.962196\pi$
$317$		−	4.21918i		−	0.236973i	0.992956	−	0.118486i	$-0.0378042\pi$
$318$			3.42181i			0.191886i
$319$	0.497552			0.0278575
$320$	−14.0255	+	5.47213i	−0.784050	+	0.305901i
$321$	12.4773			0.696415
$322$		−	3.91297i		−	0.218061i
$323$		0			0
$324$	−18.9345			−1.05192
$325$	−13.7840	−	14.9758i	−0.764598	−	0.830707i
$326$	−1.99103			−0.110273
$327$		−	19.4122i		−	1.07350i
$328$			9.88828i			0.545989i
$329$	−7.44881			−0.410666
$330$	−0.556420	+	0.217091i	−0.0306299	+	0.0119504i
$331$	13.6760			0.751699			0.375850	−	0.926681i	$-0.377351\pi$
$331$	13.6760			0.751699			0.375850	+	0.926681i	$0.377351\pi$
$332$		−	4.35265i		−	0.238883i
$333$			3.54414i			0.194217i
$334$	2.19563			0.120140
$335$	−2.55298	−	6.54349i	−0.139484	−	0.357509i
$336$	18.1958			0.992660
$337$		−	6.48422i		−	0.353218i	−0.984281	−	0.176609i	$-0.943487\pi$
$337$		−	6.48422i		−	0.353218i	0.984281	−	0.176609i	$-0.0565128\pi$
$338$			0.829834i			0.0451370i
$339$	−8.31820			−0.451782
$340$		0			0
$341$	2.90933			0.157549
$342$		−	2.54038i		−	0.137368i
$343$			20.1052i			1.08558i
$344$	−6.83799			−0.368679
$345$	40.6562	−	15.8623i	2.18886	−	0.853995i
$346$	−3.84449			−0.206681
$347$			5.00578i			0.268724i	0.990932	+	0.134362i	$0.0428986\pi$
$347$			5.00578i			0.268724i	−0.990932	+	0.134362i	$0.957101\pi$
$348$			4.82930i			0.258878i
$349$	9.21310			0.493166			0.246583	−	0.969122i	$-0.420692\pi$
$349$	9.21310			0.493166			0.246583	+	0.969122i	$0.420692\pi$
$350$	1.76604	−	1.62549i	0.0943986	−	0.0868862i
$351$	−2.60343			−0.138961
$352$			1.29082i			0.0688009i
$353$			13.8600i			0.737693i	0.929490	+	0.368847i	$0.120247\pi$
$353$			13.8600i			0.737693i	−0.929490	+	0.368847i	$0.879753\pi$
$354$	3.33852			0.177440
$355$	−3.78690	+	1.47748i	−0.200988	+	0.0784165i
$356$	18.2383			0.966626
$357$		0			0
$358$			4.53887i			0.239886i
$359$	11.5024			0.607076			0.303538	−	0.952819i	$-0.401832\pi$
$359$	11.5024			0.607076			0.303538	+	0.952819i	$0.401832\pi$
$360$	−2.03681	−	5.22050i	−0.107349	−	0.275145i
$361$	−3.00000			−0.157895
$362$		−	2.43587i		−	0.128026i
$363$			25.7860i			1.35342i
$364$	16.3637			0.857691
$365$	9.89199	+	25.3540i	0.517770	+	1.32709i
$366$	−3.14759			−0.164527
$367$		−	19.4241i		−	1.01393i	−0.861966	−	0.506966i	$-0.830767\pi$
$367$		−	19.4241i		−	1.01393i	0.861966	−	0.506966i	$-0.169233\pi$
$368$		−	29.9875i		−	1.56321i
$369$	29.4694			1.53411
$370$	0.627799	−	0.244939i	0.0326377	−	0.0127338i
$371$	12.7034			0.659528
$372$			28.2383i			1.46409i
$373$		−	5.58922i		−	0.289399i	−0.989476	−	0.144699i	$-0.953779\pi$
$373$		−	5.58922i		−	0.289399i	0.989476	−	0.144699i	$-0.0462215\pi$
$374$		0			0
$375$	24.0482	+	11.7600i	1.24184	+	0.607282i
$376$	3.30669			0.170529
$377$			4.21918i			0.217299i
$378$		−	0.307012i		−	0.0157910i
$379$	0.556420			0.0285814			0.0142907	−	0.999898i	$-0.495451\pi$
$379$	0.556420			0.0285814			0.0142907	+	0.999898i	$0.495451\pi$
$380$	16.2151	−	6.32640i	0.831815	−	0.324537i
$381$	7.14332			0.365963
$382$		−	1.23657i		−	0.0632684i
$383$			24.8020i			1.26732i	0.773610	+	0.633662i	$0.218449\pi$
$383$			24.8020i			1.26732i	−0.773610	+	0.633662i	$0.781551\pi$
$384$	−16.6229			−0.848282
$385$	0.805944	+	2.06570i	0.0410747	+	0.105278i
$386$	−2.90068			−0.147641
$387$			20.3788i			1.03591i
$388$			32.5349i			1.65171i
$389$	8.76664			0.444486			0.222243	−	0.974991i	$-0.428662\pi$
$389$	8.76664			0.444486			0.222243	+	0.974991i	$0.428662\pi$
$390$	−1.84090	−	4.71838i	−0.0932177	−	0.238924i
$391$		0			0
$392$		−	2.50608i		−	0.126576i
$393$			17.2244i			0.868854i
$394$	−0.128224			−0.00645983
$395$	−21.3038	+	8.31179i	−1.07191	+	0.418211i
$396$	2.55298			0.128292
$397$			7.03598i			0.353126i	0.984289	+	0.176563i	$0.0564979\pi$
$397$			7.03598i			0.353126i	−0.984289	+	0.176563i	$0.943502\pi$
$398$		−	4.08987i		−	0.205007i
$399$	−19.7840			−0.990438
$400$	13.5342	−	12.4571i	0.676711	−	0.622857i
$401$	10.6346			0.531066			0.265533	−	0.964102i	$-0.414452\pi$
$401$	10.6346			0.531066			0.265533	+	0.964102i	$0.414452\pi$
$402$		−	1.74782i		−	0.0871731i
$403$			24.6708i			1.22894i
$404$	−8.58530			−0.427135
$405$	20.2688	−	7.90800i	1.00717	−	0.392952i
$406$	−0.497552			−0.0246931
$407$			0.622545i			0.0308584i
$408$		0			0
$409$	−2.53421			−0.125309			−0.0626544	−	0.998035i	$-0.519957\pi$
$409$	−2.53421			−0.125309			−0.0626544	+	0.998035i	$0.519957\pi$
$410$	−2.03666	−	5.22013i	−0.100584	−	0.257804i
$411$	−1.26146			−0.0622235
$412$			33.9232i			1.67128i
$413$		−	12.3942i		−	0.609878i
$414$	5.17681			0.254426
$415$	1.81789	+	4.65939i	0.0892365	+	0.228720i
$416$	−10.9460			−0.536672
$417$		−	42.3215i		−	2.07249i
$418$		−	0.446230i		−	0.0218258i
$419$	−26.3614			−1.28784			−0.643918	−	0.765094i	$-0.722692\pi$
$419$	−26.3614			−1.28784			−0.643918	+	0.765094i	$0.722692\pi$
$420$	−20.0499	+	7.82259i	−0.978336	+	0.381703i
$421$	7.94308			0.387122			0.193561	−	0.981088i	$-0.437996\pi$
$421$	7.94308			0.387122			0.193561	+	0.981088i	$0.437996\pi$
$422$		−	2.98161i		−	0.145142i
$423$		−	9.85469i		−	0.479151i
$424$	−5.63931			−0.273869
$425$		0			0
$426$	−1.01151			−0.0490078
$427$			11.6854i			0.565494i
$428$			10.1409i			0.490178i
$429$	4.67889			0.225899
$430$	3.60985	−	1.40840i	0.174082	−	0.0679192i
$431$	−11.3396			−0.546211			−0.273105	−	0.961984i	$-0.588051\pi$
$431$	−11.3396			−0.546211			−0.273105	+	0.961984i	$0.588051\pi$
$432$		−	2.35282i		−	0.113200i
$433$		−	6.24538i		−	0.300134i	−0.988676	−	0.150067i	$-0.952051\pi$
$433$		−	6.24538i		−	0.300134i	0.988676	−	0.150067i	$-0.0479489\pi$
$434$	−2.90933			−0.139652
$435$	−2.01696	−	5.16963i	−0.0967058	−	0.247865i
$436$	15.7772			0.755592
$437$			32.6049i			1.55971i
$438$			6.77223i			0.323590i
$439$	−10.5282			−0.502482			−0.251241	−	0.967925i	$-0.580839\pi$
$439$	−10.5282			−0.502482			−0.251241	+	0.967925i	$0.580839\pi$
$440$	−0.357775	−	0.917007i	−0.0170563	−	0.0437166i
$441$	−7.46870			−0.355652
$442$		0			0
$443$		−	29.2669i		−	1.39051i	−0.718761	−	0.695257i	$-0.755291\pi$
$443$		−	29.2669i		−	1.39051i	0.718761	−	0.695257i	$-0.244709\pi$
$444$	−6.04250			−0.286764
$445$	−19.5235	+	7.61722i	−0.925505	+	0.361091i
$446$	−0.945995			−0.0447942
$447$			17.5293i			0.829106i
$448$			13.9081i			0.657097i
$449$	32.7274			1.54450			0.772250	−	0.635318i	$-0.219131\pi$
$449$	32.7274			1.54450			0.772250	+	0.635318i	$0.219131\pi$
$450$	2.15051	+	2.33644i	0.101376	+	0.110141i
$451$	5.17644			0.243749
$452$		−	6.76058i		−	0.317991i
$453$		−	17.8757i		−	0.839872i
$454$	−3.66582			−0.172045
$455$	−17.5169	+	6.83431i	−0.821204	+	0.320397i
$456$	8.78253			0.411280
$457$		−	31.4752i		−	1.47235i	−0.676792	−	0.736174i	$-0.736631\pi$
$457$		−	31.4752i		−	1.47235i	0.676792	−	0.736174i	$-0.263369\pi$
$458$			3.47329i			0.162296i
$459$		0			0
$460$	12.8920	+	33.0432i	0.601092	+	1.54065i
$461$	26.6442			1.24094			0.620472	−	0.784228i	$-0.286941\pi$
$461$	26.6442			1.24094			0.620472	+	0.784228i	$0.286941\pi$
$462$			0.551763i			0.0256704i
$463$			14.2040i			0.660115i	0.943961	+	0.330058i	$0.107068\pi$
$463$			14.2040i			0.660115i	−0.943961	+	0.330058i	$0.892932\pi$
$464$	−3.81304			−0.177016
$465$	−11.7938	−	30.2283i	−0.546922	−	1.40181i
$466$	0.169024			0.00782990
$467$			29.1177i			1.34741i	0.739002	+	0.673703i	$0.235297\pi$
$467$			29.1177i			1.34741i	−0.739002	+	0.673703i	$0.764703\pi$
$468$			21.6490i			1.00072i
$469$	−6.48872			−0.299621
$470$	−1.74564	+	0.681069i	−0.0805202	+	0.0314154i
$471$	−29.8267			−1.37434
$472$			5.50204i			0.253252i
$473$			3.57963i			0.164592i
$474$	−5.69040			−0.261369
$475$	−14.7156	+	13.5445i	−0.675196	+	0.621463i
$476$		0			0
$477$			16.8064i			0.769514i
$478$			2.22485i			0.101762i
$479$	−1.96651			−0.0898521			−0.0449261	−	0.998990i	$-0.514305\pi$
$479$	−1.96651			−0.0898521			−0.0449261	+	0.998990i	$0.514305\pi$
$480$	13.4118	−	5.23268i	0.612161	−	0.238838i
$481$	−5.27911			−0.240707
$482$		−	1.97189i		−	0.0898171i
$483$		−	40.3160i		−	1.83444i
$484$	−20.9575			−0.952614
$485$	−13.5882	−	34.8277i	−0.617009	−	1.58144i
$486$	4.96809			0.225357
$487$			4.83495i			0.219093i	0.993982	+	0.109546i	$0.0349398\pi$
$487$			4.83495i			0.219093i	−0.993982	+	0.109546i	$0.965060\pi$
$488$		−	5.18738i		−	0.234821i
$489$	−20.5140			−0.927673
$490$	0.516171	+	1.32299i	0.0233182	+	0.0597665i
$491$	16.8949			0.762456			0.381228	−	0.924481i	$-0.375501\pi$
$491$	16.8949			0.762456			0.381228	+	0.924481i	$0.375501\pi$
$492$			50.2431i			2.26514i
$493$		0			0
$494$	3.78398			0.170249
$495$	−2.73289	+	1.06625i	−0.122834	+	0.0479245i
$496$	−22.2960			−1.00112
$497$			3.75520i			0.168444i
$498$			1.24456i			0.0557699i
$499$	4.34494			0.194506			0.0972531	−	0.995260i	$-0.468994\pi$
$499$	4.34494			0.194506			0.0972531	+	0.995260i	$0.468994\pi$
$500$	−9.55787	+	19.5451i	−0.427441	+	0.874081i
$501$	22.6220			1.01067
$502$		−	1.40286i		−	0.0626125i
$503$		−	11.5078i		−	0.513105i	−0.966530	−	0.256553i	$-0.917413\pi$
$503$		−	11.5078i		−	0.513105i	0.966530	−	0.256553i	$-0.0825867\pi$
$504$	−5.17681			−0.230593
$505$	9.19033	−	3.58566i	0.408964	−	0.159560i
$506$	0.909332			0.0404247
$507$			8.54992i			0.379715i
$508$			5.80570i			0.257586i
$509$	34.8177			1.54327			0.771634	−	0.636066i	$-0.219440\pi$
$509$	34.8177			1.54327			0.771634	+	0.636066i	$0.219440\pi$
$510$		0			0
$511$	25.1418			1.11221
$512$		−	16.6395i		−	0.735368i
$513$			2.55819i			0.112947i
$514$	6.33845			0.279577
$515$	−14.1681	−	36.3139i	−0.624319	−	1.60018i
$516$	−34.7443			−1.52953
$517$		−	1.73103i		−	0.0761304i
$518$		−	0.622545i		−	0.0273531i
$519$	−39.6105			−1.73871
$520$	7.77611	−	3.03389i	0.341005	−	0.133045i
$521$	22.4501			0.983559			0.491779	−	0.870720i	$-0.336347\pi$
$521$	22.4501			0.983559			0.491779	+	0.870720i	$0.336347\pi$
$522$		−	0.658255i		−	0.0288110i
$523$			16.4943i			0.721243i	0.932712	+	0.360622i	$0.117435\pi$
$523$			16.4943i			0.721243i	−0.932712	+	0.360622i	$0.882565\pi$
$524$	−13.9990			−0.611551
$525$	18.1958	−	16.7477i	0.794128	−	0.730930i
$526$	−2.87465			−0.125341
$527$		0			0
$528$			4.22850i			0.184022i
$529$	−43.4426			−1.88881
$530$	2.97705	−	1.16151i	0.129315	−	0.0504529i
$531$	16.3974			0.711585
$532$		−	16.0794i		−	0.697128i
$533$			43.8956i			1.90133i
$534$	−5.21488			−0.225670
$535$	−4.23534	−	10.8555i	−0.183110	−	0.469325i
$536$	2.88048			0.124418
$537$			46.7647i			2.01805i
$538$		−	4.66541i		−	0.201140i
$539$	−1.31191			−0.0565082
$540$	1.01151	+	2.59258i	0.0435284	+	0.111567i
$541$	−12.7279			−0.547216			−0.273608	−	0.961841i	$-0.588217\pi$
$541$	−12.7279			−0.547216			−0.273608	+	0.961841i	$0.588217\pi$
$542$			5.62619i			0.241666i
$543$		−	25.0972i		−	1.07702i
$544$		0			0
$545$	−16.8891	+	6.58937i	−0.723448	+	0.282257i
$546$	−4.67889			−0.200238
$547$		−	12.5057i		−	0.534707i	−0.963599	−	0.267354i	$-0.913851\pi$
$547$		−	12.5057i		−	0.534707i	0.963599	−	0.267354i	$-0.0861491\pi$
$548$		−	1.02525i		−	0.0437965i
$549$	−15.4596			−0.659799
$550$	0.377747	+	0.410408i	0.0161072	+	0.0174998i
$551$	4.14587			0.176620
$552$			17.8971i			0.761752i
$553$			21.1255i			0.898346i
$554$	1.57109			0.0667491
$555$	6.46832	−	2.52365i	0.274565	−	0.107123i
$556$	34.3966			1.45874
$557$		−	38.9354i		−	1.64975i	−0.565318	−	0.824873i	$-0.691247\pi$
$557$		−	38.9354i		−	1.64975i	0.565318	−	0.824873i	$-0.308753\pi$
$558$		−	3.84901i		−	0.162942i
$559$	−30.3549			−1.28387
$560$	−6.17644	−	15.8307i	−0.261002	−	0.668970i
$561$		0			0
$562$		−	4.19153i		−	0.176809i
$563$			8.17844i			0.344680i	0.985038	+	0.172340i	$0.0551328\pi$
$563$			8.17844i			0.344680i	−0.985038	+	0.172340i	$0.944867\pi$
$564$	16.8015			0.707472
$565$	2.82356	+	7.23701i	0.118788	+	0.304463i
$566$	5.86005			0.246316
$567$		−	20.0992i		−	0.844087i
$568$		−	1.66701i		−	0.0699463i
$569$	11.8920			0.498538			0.249269	−	0.968434i	$-0.419810\pi$
$569$	11.8920			0.498538			0.249269	+	0.968434i	$0.419810\pi$
$570$	−4.63639	+	1.80891i	−0.194197	+	0.0757671i
$571$	3.96719			0.166022			0.0830109	−	0.996549i	$-0.473546\pi$
$571$	3.96719			0.166022			0.0830109	+	0.996549i	$0.473546\pi$
$572$			3.80275i			0.159001i
$573$		−	12.7406i		−	0.532246i
$574$	−5.17644			−0.216060
$575$	−27.6010	−	29.9875i	−1.15104	−	1.25056i
$576$	−18.4003			−0.766678
$577$		−	6.58601i		−	0.274179i	−0.990559	−	0.137090i	$-0.956225\pi$
$577$		−	6.58601i		−	0.274179i	0.990559	−	0.137090i	$-0.0437749\pi$
$578$		0			0
$579$	−29.8862			−1.24203
$580$	4.20159	−	1.63928i	0.174462	−	0.0680672i
$581$	4.62039			0.191686
$582$		−	9.30274i		−	0.385611i
$583$			2.95213i			0.122265i
$584$	−11.1610			−0.461844
$585$	−9.04170	−	23.1746i	−0.373828	−	0.958152i
$586$	−6.10218			−0.252079
$587$			22.3369i			0.921944i	0.887415	+	0.460972i	$0.152499\pi$
$587$			22.3369i			0.921944i	−0.887415	+	0.460972i	$0.847501\pi$
$588$		−	12.7336i		−	0.525125i
$589$	24.2421			0.998879
$590$	−1.13324	−	2.90459i	−0.0466548	−	0.119580i
$591$	−1.32111			−0.0543433
$592$		−	4.77094i		−	0.196085i
$593$			30.1344i			1.23747i	0.785599	+	0.618736i	$0.212355\pi$
$593$			30.1344i			1.23747i	−0.785599	+	0.618736i	$0.787645\pi$
$594$	0.0713464			0.00292738
$595$		0			0
$596$	−14.2468			−0.583574
$597$		−	42.1387i		−	1.72462i
$598$			7.71103i			0.315327i
$599$	8.88907			0.363198			0.181599	−	0.983373i	$-0.441873\pi$
$599$	8.88907			0.363198			0.181599	+	0.983373i	$0.441873\pi$
$600$	−8.07748	+	7.43467i	−0.329762	+	0.303519i
$601$	24.2421			0.988856			0.494428	−	0.869219i	$-0.335378\pi$
$601$	24.2421			0.988856			0.494428	+	0.869219i	$0.335378\pi$
$602$		−	3.57963i		−	0.145895i
$603$		−	8.58450i		−	0.349588i
$604$	14.5284			0.591151
$605$	22.4344	−	8.75291i	0.912089	−	0.355857i
$606$	2.45480			0.0997196
$607$		−	14.9118i		−	0.605252i	−0.953109	−	0.302626i	$-0.902137\pi$
$607$		−	14.9118i		−	0.605252i	0.953109	−	0.302626i	$-0.0978633\pi$
$608$			10.7558i			0.436205i
$609$	−5.12636			−0.207731
$610$	1.06843	+	2.73847i	0.0432595	+	0.110877i
$611$	14.6789			0.593844
$612$		0			0
$613$		−	31.3459i		−	1.26605i	−0.774132	−	0.633024i	$-0.781813\pi$
$613$		−	31.3459i		−	1.26605i	0.774132	−	0.633024i	$-0.218187\pi$
$614$	3.23336			0.130488
$615$	−20.9841	−	53.7839i	−0.846160	−	2.16878i
$616$	−0.909332			−0.0366380
$617$			15.4221i			0.620869i	0.950595	+	0.310434i	$0.100474\pi$
$617$			15.4221i			0.620869i	−0.950595	+	0.310434i	$0.899526\pi$
$618$		−	9.69971i		−	0.390179i
$619$	−45.1035			−1.81286			−0.906431	−	0.422354i	$-0.861204\pi$
$619$	−45.1035			−1.81286			−0.906431	+	0.422354i	$0.861204\pi$
$620$	24.5680	−	9.58533i	0.986673	−	0.384956i
$621$	−5.21310			−0.209195
$622$		−	2.03116i		−	0.0814421i
$623$			19.3601i			0.775647i
$624$	−35.8572			−1.43544
$625$	2.06843	−	24.9143i	0.0827372	−	0.996571i
$626$	−1.61469			−0.0645359
$627$		−	4.59759i		−	0.183610i
$628$		−	24.2415i		−	0.967343i
$629$		0			0
$630$	2.73289	−	1.06625i	0.108881	−	0.0424805i
$631$	−29.7493			−1.18430			−0.592150	−	0.805827i	$-0.701721\pi$
$631$	−29.7493			−1.18430			−0.592150	+	0.805827i	$0.701721\pi$
$632$		−	9.37804i		−	0.373038i
$633$		−	30.7200i		−	1.22101i
$634$	−0.980492			−0.0389403
$635$	−2.42476	−	6.21484i	−0.0962235	−	0.246628i
$636$	−28.6538			−1.13620
$637$		−	11.1249i		−	0.440784i
$638$		−	0.115626i		−	0.00457767i
$639$	−4.96809			−0.196534
$640$	5.64253	+	14.4623i	0.223041	+	0.571671i
$641$	−44.1420			−1.74350			−0.871752	−	0.489947i	$-0.837016\pi$
$641$	−44.1420			−1.74350			−0.871752	+	0.489947i	$0.837016\pi$
$642$		−	2.89959i		−	0.114438i
$643$		−	7.58172i		−	0.298994i	−0.988762	−	0.149497i	$-0.952235\pi$
$643$		−	7.58172i		−	0.298994i	0.988762	−	0.149497i	$-0.0477654\pi$
$644$	32.7666			1.29119
$645$	37.1928	−	14.5110i	1.46447	−	0.571370i
$646$		0			0
$647$		−	10.2540i		−	0.403128i	−0.979475	−	0.201564i	$-0.935398\pi$
$647$		−	10.2540i		−	0.403128i	0.979475	−	0.201564i	$-0.0646024\pi$
$648$			8.92246i			0.350507i
$649$	2.88028			0.113061
$650$	−3.48021	+	3.20325i	−0.136505	+	0.125642i
$651$	−29.9753			−1.17483
$652$		−	16.6726i		−	0.652951i
$653$			14.3128i			0.560104i	0.959985	+	0.280052i	$0.0903518\pi$
$653$			14.3128i			0.560104i	−0.959985	+	0.280052i	$0.909648\pi$
$654$	−4.51120			−0.176402
$655$	14.9856	−	5.84671i	0.585535	−	0.228450i
$656$	−39.6702			−1.54886
$657$			33.2622i			1.29768i
$658$			1.73103i			0.0674824i
$659$	43.9653			1.71265			0.856323	−	0.516441i	$-0.172743\pi$
$659$	43.9653			1.71265			0.856323	+	0.516441i	$0.172743\pi$
$660$	−1.81789	−	4.65939i	−0.0707611	−	0.181366i
$661$	20.7077			0.805438			0.402719	−	0.915324i	$-0.368065\pi$
$661$	20.7077			0.805438			0.402719	+	0.915324i	$0.368065\pi$
$662$		−	3.17815i		−	0.123522i
$663$		0			0
$664$	−2.05109			−0.0795977
$665$	6.71555	+	17.2125i	0.260418	+	0.667472i
$666$	0.823619			0.0319146
$667$			8.44848i			0.327126i
$668$			18.3859i			0.711372i
$669$	−9.74675			−0.376831
$670$	−1.52064	+	0.593285i	−0.0587473	+	0.0229206i
$671$	−2.71555			−0.104833
$672$		−	13.2995i		−	0.513040i
$673$			46.2662i			1.78343i	0.452598	+	0.891715i	$0.350497\pi$
$673$			46.2662i			1.78343i	−0.452598	+	0.891715i	$0.649503\pi$
$674$	−1.50686			−0.0580422
$675$	−2.16558	−	2.35282i	−0.0833533	−	0.0905602i
$676$	−6.94891			−0.267266
$677$		−	1.76082i		−	0.0676739i	−0.999427	−	0.0338370i	$-0.989227\pi$
$677$		−	1.76082i		−	0.0676739i	0.999427	−	0.0338370i	$-0.0107727\pi$
$678$			1.93306i			0.0742387i
$679$	−34.5362			−1.32538
$680$		0			0
$681$	−37.7696			−1.44733
$682$		−	0.676098i		−	0.0258891i
$683$			22.9635i			0.878675i	0.898322	+	0.439338i	$0.144787\pi$
$683$			22.9635i			0.878675i	−0.898322	+	0.439338i	$0.855213\pi$
$684$	21.2728			0.813385
$685$	0.428197	+	1.09750i	0.0163605	+	0.0419334i
$686$	4.67224			0.178387
$687$			35.7859i			1.36532i
$688$		−	27.4329i		−	1.04587i
$689$	−25.0337			−0.953710
$690$	−3.68622	−	9.44808i	−0.140332	−	0.359682i
$691$	−25.7831			−0.980837			−0.490418	−	0.871487i	$-0.663156\pi$
$691$	−25.7831			−0.980837			−0.490418	+	0.871487i	$0.663156\pi$
$692$		−	32.1932i		−	1.22380i
$693$			2.71002i			0.102945i
$694$	1.16329			0.0441579
$695$	−36.8206	+	14.3658i	−1.39669	+	0.544925i
$696$	2.27570			0.0862602
$697$		0			0
$698$		−	2.14103i		−	0.0810391i
$699$	1.74148			0.0658690
$700$	13.6116	+	14.7885i	0.514472	+	0.558954i
$701$	25.1195			0.948751			0.474376	−	0.880323i	$-0.342674\pi$
$701$	25.1195			0.948751			0.474376	+	0.880323i	$0.342674\pi$
$702$			0.605009i			0.0228346i
$703$			5.18738i			0.195646i
$704$	−3.23210			−0.121814
$705$	−17.9856	+	7.01717i	−0.677376	+	0.264282i
$706$	3.22092			0.121221
$707$		−	9.11340i		−	0.342745i
$708$			27.9563i			1.05066i
$709$	33.5389			1.25958			0.629789	−	0.776766i	$-0.283141\pi$
$709$	33.5389			1.25958			0.629789	+	0.776766i	$0.283141\pi$
$710$	0.343350	+	0.880035i	0.0128857	+	0.0330271i
$711$	−27.9487			−1.04816
$712$		−	8.59437i		−	0.322088i
$713$			49.4008i			1.85007i
$714$		0			0
$715$	−1.58822	−	4.07073i	−0.0593961	−	0.152237i
$716$	−38.0078			−1.42042
$717$			22.9230i			0.856074i
$718$		−	2.67305i		−	0.0997572i
$719$	−41.6927			−1.55488			−0.777438	−	0.628960i	$-0.783481\pi$
$719$	−41.6927			−1.55488			−0.777438	+	0.628960i	$0.783481\pi$
$720$	20.9438	−	8.17135i	0.780530	−	0.304528i
$721$	−36.0099			−1.34108
$722$			0.697168i			0.0259459i
$723$		−	20.3167i		−	0.755586i
$724$	20.3976			0.758071
$725$	−3.81304	+	3.50960i	−0.141613	+	0.130343i
$726$	5.99240			0.222399
$727$		−	12.2458i		−	0.454172i	−0.973875	−	0.227086i	$-0.927080\pi$
$727$		−	12.2458i		−	0.454172i	0.973875	−	0.227086i	$-0.0729199\pi$
$728$		−	7.71103i		−	0.285790i
$729$	21.9971			0.814707
$730$	5.89199	−	2.29879i	0.218072	−	0.0850821i
$731$		0			0
$732$		−	26.3575i		−	0.974200i
$733$		−	32.8393i		−	1.21295i	−0.795104	−	0.606473i	$-0.792584\pi$
$733$		−	32.8393i		−	1.21295i	0.795104	−	0.606473i	$-0.207416\pi$
$734$	−4.51396			−0.166613
$735$	5.31820	+	13.6310i	0.196165	+	0.502786i
$736$	−21.9182			−0.807917
$737$		−	1.50791i		−	0.0555446i
$738$		−	6.84837i		−	0.252092i
$739$	−6.00000			−0.220714			−0.110357	−	0.993892i	$-0.535199\pi$
$739$	−6.00000			−0.220714			−0.110357	+	0.993892i	$0.535199\pi$
$740$	2.05109	+	5.25710i	0.0753995	+	0.193255i
$741$	38.9870			1.43222
$742$		−	2.95213i		−	0.108376i
$743$		−	22.8684i		−	0.838962i	−0.907764	−	0.419481i	$-0.862212\pi$
$743$		−	22.8684i		−	0.838962i	0.907764	−	0.419481i	$-0.137788\pi$
$744$	13.3067			0.487847
$745$	15.2509	−	5.95021i	0.558748	−	0.217999i
$746$	−1.29887			−0.0475552
$747$			6.11272i			0.223653i
$748$		0			0
$749$	−10.7647			−0.393332
$750$	2.73289	−	5.58854i	0.0997911	−	0.204065i
$751$	−32.0742			−1.17040			−0.585202	−	0.810888i	$-0.698985\pi$
$751$	−32.0742			−1.17040			−0.585202	+	0.810888i	$0.698985\pi$
$752$			13.2659i			0.483758i
$753$		−	14.4539i		−	0.526728i
$754$	0.980492			0.0357074
$755$	−15.5522	+	6.06779i	−0.566003	+	0.220829i
$756$	2.57088			0.0935019
$757$			36.2220i			1.31651i	0.752794	+	0.658256i	$0.228706\pi$
$757$			36.2220i			1.31651i	−0.752794	+	0.658256i	$0.771294\pi$
$758$		−	0.129306i		−	0.00469661i
$759$	9.36900			0.340073
$760$	−2.98118	−	7.64099i	−0.108139	−	0.277168i
$761$	−24.4851			−0.887584			−0.443792	−	0.896130i	$-0.646367\pi$
$761$	−24.4851			−0.887584			−0.443792	+	0.896130i	$0.646367\pi$
$762$		−	1.66003i		−	0.0601366i
$763$			16.7477i			0.606308i
$764$	10.3549			0.374626
$765$		0			0
$766$	5.76372			0.208252
$767$			24.4244i			0.881914i
$768$		−	28.3788i		−	1.02403i
$769$	5.55937			0.200476			0.100238	−	0.994963i	$-0.468040\pi$
$769$	5.55937			0.200476			0.100238	+	0.994963i	$0.468040\pi$
$770$	0.480046	−	0.187293i	0.0172997	−	0.00674956i
$771$	65.3061			2.35194
$772$		−	24.2899i		−	0.874211i
$773$		−	36.5376i		−	1.31416i	−0.753819	−	0.657082i	$-0.771790\pi$
$773$		−	36.5376i		−	1.31416i	0.753819	−	0.657082i	$-0.228210\pi$
$774$	4.73581			0.170225
$775$	−22.2960	+	20.5216i	−0.800896	+	0.737159i
$776$	15.3314			0.550363
$777$		−	6.41418i		−	0.230108i
$778$		−	2.03727i		−	0.0730398i
$779$	43.1329			1.54539
$780$	39.5110	−	15.4155i	1.41472	−	0.551962i
$781$	−0.872669			−0.0312265
$782$		0			0
$783$			0.662870i			0.0236890i
$784$	10.0540			0.359072
$785$	10.1245	+	25.9499i	0.361359	+	0.926191i
$786$	4.00276			0.142774
$787$		−	16.0499i		−	0.572116i	−0.958212	−	0.286058i	$-0.907655\pi$
$787$		−	16.0499i		−	0.572116i	0.958212	−	0.286058i	$-0.0923451\pi$
$788$		−	1.07373i		−	0.0382500i
$789$	−29.6180			−1.05443
$790$	1.93157	+	4.95077i	0.0687222	+	0.176140i
$791$	7.17644			0.255165
$792$		−	1.20303i		−	0.0427480i
$793$		−	23.0276i		−	0.817732i
$794$	1.63509			0.0580271
$795$	30.6731	−	11.9673i	1.08786	−	0.424435i
$796$	34.2480			1.21389
$797$			34.7907i			1.23235i	0.787609	+	0.616175i	$0.211319\pi$
$797$			34.7907i			1.23235i	−0.787609	+	0.616175i	$0.788681\pi$
$798$			4.59759i			0.162753i
$799$		0			0
$800$	−9.10509	−	9.89234i	−0.321914	−	0.349747i
$801$	−25.6132			−0.904999
$802$		−	2.47136i		−	0.0872669i
$803$			5.84268i			0.206184i
$804$	14.6360			0.516170
$805$	−35.0758	+	13.6850i	−1.23626	+	0.482333i
$806$	5.73323			0.201944
$807$		−	48.0685i		−	1.69209i
$808$			4.04563i			0.142325i
$809$	18.8866			0.664018			0.332009	−	0.943276i	$-0.392274\pi$
$809$	18.8866			0.664018			0.332009	+	0.943276i	$0.392274\pi$
$810$	−1.83773	−	4.71026i	−0.0645714	−	0.165502i
$811$	13.1316			0.461113			0.230556	−	0.973059i	$-0.425945\pi$
$811$	13.1316			0.461113			0.230556	+	0.973059i	$0.425945\pi$
$812$		−	4.16643i		−	0.146213i
$813$			57.9676i			2.03301i
$814$	0.144673			0.00507078
$815$	6.96334	+	17.8476i	0.243915	+	0.625174i
$816$		0			0
$817$			29.8274i			1.04353i
$818$			0.588924i			0.0205913i
$819$	−22.9806			−0.803009
$820$	43.7126	−	17.0547i	1.52651	−	0.595577i
$821$	39.3443			1.37313			0.686563	−	0.727070i	$-0.259118\pi$
$821$	39.3443			1.37313			0.686563	+	0.727070i	$0.259118\pi$
$822$			0.293151i			0.0102248i
$823$			40.2222i			1.40206i	0.713134	+	0.701028i	$0.247275\pi$
$823$			40.2222i			1.40206i	−0.713134	+	0.701028i	$0.752725\pi$
$824$	15.9856			0.556884
$825$	3.89199	+	4.22850i	0.135502	+	0.147217i
$826$	−2.88028			−0.100218
$827$		−	33.9078i		−	1.17909i	−0.807736	−	0.589545i	$-0.799307\pi$
$827$		−	33.9078i		−	1.17909i	0.807736	−	0.589545i	$-0.200693\pi$
$828$			43.3499i			1.50651i
$829$	8.18134			0.284150			0.142075	−	0.989856i	$-0.454623\pi$
$829$	8.18134			0.284150			0.142075	+	0.989856i	$0.454623\pi$
$830$	1.08279	−	0.422457i	0.0375842	−	0.0146637i
$831$	16.1872			0.561527
$832$		−	27.4078i		−	0.950195i
$833$		0			0
$834$	−9.83507			−0.340561
$835$	−7.67889	−	19.6816i	−0.265739	−	0.681110i
$836$	3.73667			0.129235
$837$			3.87600i			0.133974i
$838$			6.12610i			0.211623i
$839$	21.9742			0.758634			0.379317	−	0.925267i	$-0.376159\pi$
$839$	21.9742			0.758634			0.379317	+	0.925267i	$0.376159\pi$
$840$	3.68622	+	9.44808i	0.127187	+	0.325990i
$841$	−27.9257			−0.962956
$842$		−	1.84589i		−	0.0636135i
$843$		−	43.1860i		−	1.48741i
$844$	24.9675			0.859418
$845$	7.43861	−	2.90222i	0.255896	−	0.0998393i
$846$	−2.29012			−0.0787361
$847$		−	22.2466i		−	0.764404i
$848$		−	22.6240i		−	0.776912i
$849$	60.3771			2.07214
$850$		0			0
$851$	−10.5709			−0.362365
$852$		−	8.47023i		−	0.290185i
$853$		−	36.9651i		−	1.26566i	−0.774290	−	0.632831i	$-0.781893\pi$
$853$		−	36.9651i		−	1.26566i	0.774290	−	0.632831i	$-0.218107\pi$
$854$	2.71555			0.0929242
$855$	−22.7719	+	8.88459i	−0.778783	+	0.303847i
$856$	4.77866			0.163331
$857$		−	15.0234i		−	0.513189i	−0.966519	−	0.256594i	$-0.917400\pi$
$857$		−	15.0234i		−	0.513189i	0.966519	−	0.256594i	$-0.0826004\pi$
$858$		−	1.08732i		−	0.0371206i
$859$	40.2180			1.37222			0.686110	−	0.727498i	$-0.259317\pi$
$859$	40.2180			1.37222			0.686110	+	0.727498i	$0.259317\pi$
$860$	11.7938	+	30.2283i	0.402164	+	1.03078i
$861$	−53.3337			−1.81761
$862$			2.63521i			0.0897556i
$863$		−	12.3865i		−	0.421643i	−0.977525	−	0.210822i	$-0.932386\pi$
$863$		−	12.3865i		−	0.421643i	0.977525	−	0.210822i	$-0.0676139\pi$
$864$	−1.71971			−0.0585058
$865$	13.4455	+	34.4620i	0.457162	+	1.17174i
$866$	−1.45136			−0.0493192
$867$		0			0
$868$		−	24.3623i		−	0.826911i
$869$	−4.90933			−0.166538
$870$	−1.20137	+	0.468720i	−0.0407301	+	0.0158911i
$871$	12.7869			0.433267
$872$		−	7.43467i		−	0.251770i
$873$		−	45.6910i		−	1.54640i
$874$	7.57704			0.256297
$875$	−20.7473	−	10.1458i	−0.701387	−	0.342991i
$876$	−56.7097			−1.91604
$877$		−	45.1747i		−	1.52544i	−0.646728	−	0.762720i	$-0.723863\pi$
$877$		−	45.1747i		−	1.52544i	0.646728	−	0.762720i	$-0.276137\pi$
$878$			2.44663i			0.0825699i
$879$	−62.8717			−2.12061
$880$	3.67889	−	1.43534i	0.124015	−	0.0483853i
$881$	−17.0224			−0.573500			−0.286750	−	0.958006i	$-0.592575\pi$
$881$	−17.0224			−0.573500			−0.286750	+	0.958006i	$0.592575\pi$
$882$			1.73565i			0.0584423i
$883$		−	13.3497i		−	0.449254i	−0.974445	−	0.224627i	$-0.927884\pi$
$883$		−	13.3497i		−	0.449254i	0.974445	−	0.224627i	$-0.0721164\pi$
$884$		0			0
$885$	−11.6760	−	29.9264i	−0.392483	−	1.00597i
$886$	−6.80132			−0.228495
$887$		−	44.5291i		−	1.49514i	−0.664182	−	0.747571i	$-0.731220\pi$
$887$		−	44.5291i		−	1.49514i	0.664182	−	0.747571i	$-0.268780\pi$
$888$			2.84739i			0.0955522i
$889$	−6.16283			−0.206695
$890$	1.77016	+	4.53706i	0.0593359	+	0.152083i
$891$	4.67084			0.156479
$892$		−	7.92163i		−	0.265236i
$893$		−	14.4238i		−	0.482675i
$894$	4.07362			0.136242
$895$	40.6863	−	15.8740i	1.35999	−	0.530609i
$896$	14.3412			0.479106
$897$			79.4480i			2.65269i
$898$		−	7.60550i		−	0.253799i
$899$	6.28153			0.209501
$900$	−19.5650	+	18.0080i	−0.652168	+	0.600268i
$901$		0			0
$902$		−	1.20295i		−	0.0400538i
$903$		−	36.8815i		−	1.22734i
$904$	−3.18577			−0.105957
$905$	−21.8351	+	8.51907i	−0.725822	+	0.283184i
$906$	−4.15412			−0.138011
$907$			32.9453i			1.09393i	0.837155	+	0.546965i	$0.184217\pi$
$907$			32.9453i			1.09393i	−0.837155	+	0.546965i	$0.815783\pi$
$908$		−	30.6971i		−	1.01872i
$909$	12.0569			0.399903
$910$	1.58822	+	4.07073i	0.0526490	+	0.134944i
$911$	−35.5859			−1.17901			−0.589506	−	0.807764i	$-0.700678\pi$
$911$	−35.5859			−1.17901			−0.589506	+	0.807764i	$0.700678\pi$
$912$			35.2341i			1.16672i
$913$			1.07373i			0.0355352i
$914$	−7.31450			−0.241942
$915$	11.0082	+	28.2149i	0.363920	+	0.932757i
$916$	−29.0848			−0.960990
$917$		−	14.8601i		−	0.490725i
$918$		0			0
$919$	28.5997			0.943418			0.471709	−	0.881754i	$-0.343637\pi$
$919$	28.5997			0.943418			0.471709	+	0.881754i	$0.343637\pi$
$920$	15.5709	−	6.07507i	0.513357	−	0.200289i
$921$	33.3139			1.09773
$922$		−	6.19183i		−	0.203917i
$923$		−	7.40013i		−	0.243578i
$924$	−4.62039			−0.152000
$925$	−4.39126	−	4.77094i	−0.144384	−	0.156868i
$926$	3.30085			0.108473
$927$		−	47.6407i		−	1.56473i
$928$			2.78701i			0.0914879i
$929$	−12.7034			−0.416785			−0.208392	−	0.978045i	$-0.566823\pi$
$929$	−12.7034			−0.416785			−0.208392	+	0.978045i	$0.566823\pi$
$930$	−7.02474	+	2.74074i	−0.230350	+	0.0898725i
$931$	−10.9316			−0.358268
$932$			1.41538i			0.0463625i
$933$		−	20.9274i		−	0.685131i
$934$	6.76664			0.221411
$935$		0			0
$936$	10.2016			0.333450
$937$			30.7655i			1.00506i	0.864558	+	0.502532i	$0.167598\pi$
$937$			30.7655i			1.00506i	−0.864558	+	0.502532i	$0.832402\pi$
$938$			1.50791i			0.0492350i
$939$	−16.6364			−0.542908
$940$	−5.70318	−	14.6177i	−0.186017	−	0.476777i
$941$	−39.2476			−1.27943			−0.639717	−	0.768611i	$-0.720948\pi$
$941$	−39.2476			−1.27943			−0.639717	+	0.768611i	$0.720948\pi$
$942$			6.93141i			0.225837i
$943$			87.8965i			2.86230i
$944$	−22.0733			−0.718426
$945$	−2.75205	+	1.07373i	−0.0895243	+	0.0349284i
$946$	0.831868			0.0270464
$947$			3.56791i			0.115941i	0.998318	+	0.0579707i	$0.0184630\pi$
$947$			3.56791i			0.115941i	−0.998318	+	0.0579707i	$0.981537\pi$
$948$		−	47.6506i		−	1.54762i
$949$	−49.5452			−1.60831
$950$	3.14759	+	3.41974i	0.102121	+	0.110951i
$951$	−10.1022			−0.327586
$952$		0			0
$953$			53.8491i			1.74434i	0.489200	+	0.872172i	$0.337289\pi$
$953$			53.8491i			1.74434i	−0.489200	+	0.872172i	$0.662711\pi$
$954$	3.90564			0.126450
$955$	−11.0846	+	4.32471i	−0.358689	+	0.139944i
$956$	−18.6306			−0.602555
$957$		−	1.19131i		−	0.0385096i
$958$			0.456996i			0.0147649i
$959$	1.08832			0.0351436
$960$	13.1022	+	33.5819i	0.422871	+	1.08385i
$961$	5.72998			0.184838
$962$			1.22681i			0.0395539i
$963$		−	14.2415i		−	0.458926i
$964$	16.5123			0.531826
$965$	10.1447	+	26.0016i	0.326569	+	0.837021i
$966$	−9.36900			−0.301443
$967$			14.6688i			0.471716i	0.971788	+	0.235858i	$0.0757900\pi$
$967$			14.6688i			0.471716i	−0.971788	+	0.235858i	$0.924210\pi$
$968$			9.87576i			0.317419i
$969$		0			0
$970$	−8.09358	+	3.15776i	−0.259869	+	0.101389i
$971$	−14.2468			−0.457203			−0.228602	−	0.973520i	$-0.573415\pi$
$971$	−14.2468			−0.457203			−0.228602	+	0.973520i	$0.573415\pi$
$972$			41.6020i			1.33439i
$973$			36.5125i			1.17054i
$974$	1.12359			0.0360022
$975$	−35.8572	+	33.0036i	−1.14835	+	1.05696i
$976$	20.8109			0.666142
$977$			20.9141i			0.669103i	0.942378	+	0.334551i	$0.108585\pi$
$977$			20.9141i			0.669103i	−0.942378	+	0.334551i	$0.891415\pi$
$978$			4.76722i			0.152439i
$979$	−4.49909			−0.143791
$980$	−11.0785	+	4.32234i	−0.353890	+	0.138072i
$981$	−22.1570			−0.707419
$982$		−	3.92620i		−	0.125290i
$983$		−	17.4000i		−	0.554973i	−0.960730	−	0.277486i	$-0.910499\pi$
$983$		−	17.4000i		−	0.554973i	0.960730	−	0.277486i	$-0.0895014\pi$
$984$	23.6760			0.754762
$985$	0.448443	+	1.14940i	0.0142886	+	0.0366228i
$986$		0			0
$987$			17.8350i			0.567696i
$988$			31.6865i			1.00808i
$989$	−60.7825			−1.93277
$990$	0.247786	+	0.635095i	0.00787515	+	0.0201846i
$991$	−5.27771			−0.167652			−0.0838259	−	0.996480i	$-0.526714\pi$
$991$	−5.27771			−0.167652			−0.0838259	+	0.996480i	$0.526714\pi$
$992$			16.2964i			0.517413i
$993$		−	32.7450i		−	1.03913i
$994$	0.872669			0.0276794
$995$	−36.6615	+	14.3037i	−1.16225	+	0.453458i
$996$	−10.4217			−0.330226
$997$		−	25.6390i		−	0.811995i	−0.913874	−	0.405997i	$-0.866924\pi$
$997$		−	25.6390i		−	0.811995i	0.913874	−	0.405997i	$-0.133076\pi$
$998$		−	1.00972i		−	0.0319621i
$999$	−0.829394			−0.0262409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.b.f.579.5		12
5.2	odd	4		7225.2.a.bp.1.7		12
5.3	odd	4		7225.2.a.bp.1.6		12
5.4	even	2	inner	1445.2.b.f.579.8		12
17.2	even	8		85.2.j.c.4.4	yes	12
17.9	even	8		85.2.j.c.64.3	yes	12
17.16	even	2	inner	1445.2.b.f.579.6		12
51.2	odd	8		765.2.t.e.514.3		12
51.26	odd	8		765.2.t.e.64.4		12
85.2	odd	8		425.2.e.d.276.4		12
85.9	even	8		85.2.j.c.64.4	yes	12
85.19	even	8		85.2.j.c.4.3	✓	12
85.33	odd	4		7225.2.a.bp.1.5		12
85.43	odd	8		425.2.e.d.251.4		12
85.53	odd	8		425.2.e.d.276.3		12
85.67	odd	4		7225.2.a.bp.1.8		12
85.77	odd	8		425.2.e.d.251.3		12
85.84	even	2	inner	1445.2.b.f.579.7		12
255.104	odd	8		765.2.t.e.514.4		12
255.179	odd	8		765.2.t.e.64.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.3	✓	12	85.19	even	8
85.2.j.c.4.4	yes	12	17.2	even	8
85.2.j.c.64.3	yes	12	17.9	even	8
85.2.j.c.64.4	yes	12	85.9	even	8
425.2.e.d.251.3		12	85.77	odd	8
425.2.e.d.251.4		12	85.43	odd	8
425.2.e.d.276.3		12	85.53	odd	8
425.2.e.d.276.4		12	85.2	odd	8
765.2.t.e.64.3		12	255.179	odd	8
765.2.t.e.64.4		12	51.26	odd	8
765.2.t.e.514.3		12	51.2	odd	8
765.2.t.e.514.4		12	255.104	odd	8
1445.2.b.f.579.5		12	1.1	even	1	trivial
1445.2.b.f.579.6		12	17.16	even	2	inner
1445.2.b.f.579.7		12	85.84	even	2	inner
1445.2.b.f.579.8		12	5.4	even	2	inner
7225.2.a.bp.1.5		12	85.33	odd	4
7225.2.a.bp.1.6		12	5.3	odd	4
7225.2.a.bp.1.7		12	5.2	odd	4
7225.2.a.bp.1.8		12	85.67	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.232389i q^{2} -2.39435i q^{3} +1.94600 q^{4} +(-2.08313 + 0.812746i) q^{5} -0.556420 q^{6} +2.06570i q^{7} -0.917007i q^{8} -2.73289 q^{9} +(0.188874 + 0.484098i) q^{10} -0.480046 q^{11} -4.65939i q^{12} -4.07073i q^{13} +0.480046 q^{14} +(1.94600 + 4.98774i) q^{15} +3.67889 q^{16} +0.635095i q^{18} -4.00000 q^{19} +(-4.05377 + 1.58160i) q^{20} +4.94600 q^{21} +0.111558i q^{22} -8.15123i q^{23} -2.19563 q^{24} +(3.67889 - 3.38612i) q^{25} -0.945995 q^{26} -0.639548i q^{27} +4.01984i q^{28} -1.03647 q^{29} +(1.15910 - 0.452229i) q^{30} -6.06053 q^{31} -2.68895i q^{32} +1.14940i q^{33} +(-1.67889 - 4.30312i) q^{35} -5.31820 q^{36} -1.29684i q^{37} +0.929557i q^{38} -9.74675 q^{39} +(0.745294 + 1.91025i) q^{40} -10.7832 q^{41} -1.14940i q^{42} -7.45685i q^{43} -0.934167 q^{44} +(5.69298 - 2.22115i) q^{45} -1.89426 q^{46} +3.60596i q^{47} -8.80853i q^{48} +2.73289 q^{49} +(-0.786897 - 0.854934i) q^{50} -7.92163i q^{52} -6.14969i q^{53} -0.148624 q^{54} +(1.00000 - 0.390156i) q^{55} +1.89426 q^{56} +9.57738i q^{57} +0.240864i q^{58} -6.00000 q^{59} +(3.78690 + 9.70612i) q^{60} +5.65685 q^{61} +1.40840i q^{62} -5.64533i q^{63} +6.73289 q^{64} +(3.30847 + 8.47988i) q^{65} +0.267107 q^{66} +3.14118i q^{67} -19.5169 q^{69} +(-1.00000 + 0.390156i) q^{70} +1.81789 q^{71} +2.50608i q^{72} -12.1711i q^{73} -0.301373 q^{74} +(-8.10753 - 8.80853i) q^{75} -7.78398 q^{76} -0.991630i q^{77} +2.26504i q^{78} +10.2268 q^{79} +(-7.66361 + 2.99000i) q^{80} -9.72998 q^{81} +2.50590i q^{82} -2.23672i q^{83} +9.62488 q^{84} -1.73289 q^{86} +2.48166i q^{87} +0.440206i q^{88} +9.37220 q^{89} +(-0.516171 - 1.32299i) q^{90} +8.40891 q^{91} -15.8623i q^{92} +14.5110i q^{93} +0.837986 q^{94} +(8.33253 - 3.25098i) q^{95} -6.43827 q^{96} +16.7189i q^{97} -0.635095i q^{98} +1.31191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 28 q^{9} - 12 q^{15} + 4 q^{16} - 48 q^{19} + 24 q^{21} + 4 q^{25} + 24 q^{26} - 52 q^{30} + 20 q^{35} + 68 q^{36} + 28 q^{49} - 40 q^{50} + 12 q^{55} - 72 q^{59} + 76 q^{60} + 76 q^{64}+ \cdots - 96 q^{94}+O(q^{100}) \) 12 * q - 12 * q^4 - 28 * q^9 - 12 * q^15 + 4 * q^16 - 48 * q^19 + 24 * q^21 + 4 * q^25 + 24 * q^26 - 52 * q^30 + 20 * q^35 + 68 * q^36 + 28 * q^49 - 40 * q^50 + 12 * q^55 - 72 * q^59 + 76 * q^60 + 76 * q^64 + 8 * q^66 - 88 * q^69 - 12 * q^70 + 48 * q^76 + 60 * q^81 + 40 * q^84 - 16 * q^86 + 16 * q^89 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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