LMFDB - Embedded newform 1445.2.b.f.579.11

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			579.11
Root			$1.90494 + 1.17098i$ of defining polynomial
Character	$\chi$	$=$	1445.579
Dual form			1445.2.b.f.579.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.38621i q^{2} -3.15462i q^{3} -3.69399 q^{4} +(-1.90494 - 1.17098i) q^{5} +7.52757 q^{6} -0.219993i q^{7} -4.04223i q^{8} -6.95160 q^{9} +(2.79421 - 4.54559i) q^{10} -0.524950 q^{11} +11.6531i q^{12} -1.96713i q^{13} +0.524950 q^{14} +(-3.69399 + 6.00936i) q^{15} +2.25761 q^{16} -16.5880i q^{18} -4.00000 q^{19} +(7.03685 + 4.32560i) q^{20} -0.693995 q^{21} -1.25264i q^{22} -0.372668i q^{23} -12.7517 q^{24} +(2.25761 + 4.46130i) q^{25} +4.69399 q^{26} +12.4658i q^{27} +0.812655i q^{28} +7.00262 q^{29} +(-14.3396 - 8.81464i) q^{30} -2.92062 q^{31} -2.69733i q^{32} +1.65602i q^{33} +(-0.257608 + 0.419075i) q^{35} +25.6792 q^{36} +5.71657i q^{37} -9.54484i q^{38} -6.20555 q^{39} +(-4.73337 + 7.70021i) q^{40} +0.797070 q^{41} -1.65602i q^{42} +2.49417i q^{43} +1.93916 q^{44} +(13.2424 + 8.14019i) q^{45} +0.889263 q^{46} +6.73955i q^{47} -7.12189i q^{48} +6.95160 q^{49} +(-10.6456 + 5.38713i) q^{50} +7.26658i q^{52} +5.92169i q^{53} -29.7460 q^{54} +(1.00000 + 0.614707i) q^{55} -0.889263 q^{56} +12.6185i q^{57} +16.7097i q^{58} -6.00000 q^{59} +(13.6456 - 22.1985i) q^{60} -5.65685 q^{61} -6.96921i q^{62} +1.52931i q^{63} +10.9516 q^{64} +(-2.30348 + 3.74728i) q^{65} -3.95160 q^{66} +11.5120i q^{67} -1.17562 q^{69} +(-1.00000 - 0.614707i) q^{70} +7.16326 q^{71} +28.1000i q^{72} -1.18532i q^{73} -13.6409 q^{74} +(14.0737 - 7.12189i) q^{75} +14.7760 q^{76} +0.115486i q^{77} -14.8078i q^{78} +6.73050 q^{79} +(-4.30061 - 2.64362i) q^{80} +18.4700 q^{81} +1.90197i q^{82} +6.11732i q^{83} +2.56361 q^{84} -5.95160 q^{86} -22.0906i q^{87} +2.12197i q^{88} -15.9852 q^{89} +(-19.4242 + 31.5991i) q^{90} -0.432757 q^{91} +1.37663i q^{92} +9.21344i q^{93} -16.0820 q^{94} +(7.61977 + 4.68392i) q^{95} -8.50903 q^{96} -9.21517i q^{97} +16.5880i q^{98} +3.64925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.38621i			1.68730i	0.536890	+	0.843652i	$0.319599\pi$
$2$			2.38621i			1.68730i	−0.536890	+	0.843652i	$0.680401\pi$
$3$		−	3.15462i		−	1.82132i	−0.413158	−	0.910659i	$-0.635574\pi$
$3$		−	3.15462i		−	1.82132i	0.413158	−	0.910659i	$-0.364426\pi$
$4$	−3.69399			−1.84700
$5$	−1.90494	−	1.17098i	−0.851916	−	0.523679i
$5$	−1.90494	−	1.17098i	−0.851916	−	0.523679i
$6$	7.52757			3.07312
$7$		−	0.219993i		−	0.0831497i	−0.999135	−	0.0415749i	$-0.986762\pi$
$7$		−	0.219993i		−	0.0831497i	0.999135	−	0.0415749i	$-0.0132375\pi$
$8$		−	4.04223i		−	1.42914i
$9$	−6.95160			−2.31720
$10$	2.79421	−	4.54559i	0.883605	−	1.43744i
$11$	−0.524950			−0.158278			−0.0791392	−	0.996864i	$-0.525217\pi$
$11$	−0.524950			−0.158278			−0.0791392	+	0.996864i	$0.525217\pi$
$12$			11.6531i			3.36397i
$13$		−	1.96713i		−	0.545585i	−0.962073	−	0.272792i	$-0.912053\pi$
$13$		−	1.96713i		−	0.545585i	0.962073	−	0.272792i	$-0.0879472\pi$
$14$	0.524950			0.140299
$15$	−3.69399	+	6.00936i	−0.953785	+	1.55161i
$16$	2.25761			0.564402
$17$		0			0
$17$		0			0
$18$		−	16.5880i		−	3.90982i
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	7.03685	+	4.32560i	1.57349	+	0.967233i
$21$	−0.693995			−0.151442
$22$		−	1.25264i		−	0.267064i
$23$		−	0.372668i		−	0.0777066i	−0.999245	−	0.0388533i	$-0.987629\pi$
$23$		−	0.372668i		−	0.0777066i	0.999245	−	0.0388533i	$-0.0123705\pi$
$24$	−12.7517			−2.60292
$25$	2.25761	+	4.46130i	0.451522	+	0.892260i
$26$	4.69399			0.920568
$27$			12.4658i			2.39904i
$28$			0.812655i			0.153577i
$29$	7.00262			1.30035			0.650177	−	0.759783i	$-0.274695\pi$
$29$	7.00262			1.30035			0.650177	+	0.759783i	$0.274695\pi$
$30$	−14.3396	−	8.81464i	−2.61804	−	1.60933i
$31$	−2.92062			−0.524559			−0.262279	−	0.964992i	$-0.584474\pi$
$31$	−2.92062			−0.524559			−0.262279	+	0.964992i	$0.584474\pi$
$32$		−	2.69733i		−	0.476825i
$33$			1.65602i			0.288276i
$34$		0			0
$35$	−0.257608	+	0.419075i	−0.0435437	+	0.0708366i
$36$	25.6792			4.27986
$37$			5.71657i			0.939798i	0.882720	+	0.469899i	$0.155710\pi$
$37$			5.71657i			0.939798i	−0.882720	+	0.469899i	$0.844290\pi$
$38$		−	9.54484i		−	1.54838i
$39$	−6.20555			−0.993684
$40$	−4.73337	+	7.70021i	−0.748411	+	1.21751i
$41$	0.797070			0.124481			0.0622407	−	0.998061i	$-0.480175\pi$
$41$	0.797070			0.124481			0.0622407	+	0.998061i	$0.480175\pi$
$42$		−	1.65602i		−	0.255529i
$43$			2.49417i			0.380357i	0.981750	+	0.190178i	$0.0609066\pi$
$43$			2.49417i			0.380357i	−0.981750	+	0.190178i	$0.939093\pi$
$44$	1.93916			0.292340
$45$	13.2424	+	8.14019i	1.97406	+	1.21347i
$46$	0.889263			0.131115
$47$			6.73955i			0.983065i	0.870859	+	0.491532i	$0.163563\pi$
$47$			6.73955i			0.983065i	−0.870859	+	0.491532i	$0.836437\pi$
$48$		−	7.12189i		−	1.02796i
$49$	6.95160			0.993086
$50$	−10.6456	+	5.38713i	−1.50551	+	0.761855i
$51$		0			0
$52$			7.26658i			1.00769i
$53$			5.92169i			0.813406i	0.913560	+	0.406703i	$0.133322\pi$
$53$			5.92169i			0.813406i	−0.913560	+	0.406703i	$0.866678\pi$
$54$	−29.7460			−4.04792
$55$	1.00000	+	0.614707i	0.134840	+	0.0828870i
$56$	−0.889263			−0.118833
$57$			12.6185i			1.67136i
$58$			16.7097i			2.19409i
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$	13.6456	−	22.1985i	1.76164	−	2.86582i
$61$	−5.65685			−0.724286			−0.362143	−	0.932123i	$-0.617955\pi$
$61$	−5.65685			−0.724286			−0.362143	+	0.932123i	$0.617955\pi$
$62$		−	6.96921i		−	0.885091i
$63$			1.52931i			0.192675i
$64$	10.9516			1.36895
$65$	−2.30348	+	3.74728i	−0.285711	+	0.464793i
$66$	−3.95160			−0.486409
$67$			11.5120i			1.40641i	0.710987	+	0.703206i	$0.248249\pi$
$67$			11.5120i			1.40641i	−0.710987	+	0.703206i	$0.751751\pi$
$68$		0			0
$69$	−1.17562			−0.141528
$70$	−1.00000	−	0.614707i	−0.119523	−	0.0734715i
$71$	7.16326			0.850123			0.425061	−	0.905165i	$-0.360253\pi$
$71$	7.16326			0.850123			0.425061	+	0.905165i	$0.360253\pi$
$72$			28.1000i			3.31161i
$73$		−	1.18532i		−	0.138731i	−0.997591	−	0.0693657i	$-0.977902\pi$
$73$		−	1.18532i		−	0.138731i	0.997591	−	0.0693657i	$-0.0220975\pi$
$74$	−13.6409			−1.58573
$75$	14.0737	−	7.12189i	1.62509	−	0.822365i
$76$	14.7760			1.69492
$77$			0.115486i			0.0131608i
$78$		−	14.8078i		−	1.67665i
$79$	6.73050			0.757241			0.378620	−	0.925552i	$-0.376399\pi$
$79$	6.73050			0.757241			0.378620	+	0.925552i	$0.376399\pi$
$80$	−4.30061	−	2.64362i	−0.480823	−	0.295565i
$81$	18.4700			2.05222
$82$			1.90197i			0.210038i
$83$			6.11732i			0.671463i	0.941958	+	0.335731i	$0.108983\pi$
$83$			6.11732i			0.671463i	−0.941958	+	0.335731i	$0.891017\pi$
$84$	2.56361			0.279713
$85$		0			0
$86$	−5.95160			−0.641778
$87$		−	22.0906i		−	2.36836i
$88$			2.12197i			0.226203i
$89$	−15.9852			−1.69443			−0.847213	−	0.531253i	$-0.821721\pi$
$89$	−15.9852			−1.69443			−0.847213	+	0.531253i	$0.821721\pi$
$90$	−19.4242	+	31.5991i	−2.04749	+	3.33084i
$91$	−0.432757			−0.0453652
$92$			1.37663i			0.143524i
$93$			9.21344i			0.955389i
$94$	−16.0820			−1.65873
$95$	7.61977	+	4.68392i	0.781772	+	0.480560i
$96$	−8.50903			−0.868449
$97$		−	9.21517i		−	0.935659i	−0.883819	−	0.467829i	$-0.845036\pi$
$97$		−	9.21517i		−	0.935659i	0.883819	−	0.467829i	$-0.154964\pi$
$98$			16.5880i			1.67564i
$99$	3.64925			0.366763
$100$	−8.33959	−	16.4800i	−0.833959	−	1.64800i
$101$	−7.20921			−0.717343			−0.358672	−	0.933464i	$-0.616770\pi$
$101$	−7.20921			−0.717343			−0.358672	+	0.933464i	$0.616770\pi$
$102$		0			0
$103$			9.52456i			0.938482i	0.883070	+	0.469241i	$0.155472\pi$
$103$			9.52456i			0.938482i	−0.883070	+	0.469241i	$0.844528\pi$
$104$	−7.95160			−0.779719
$105$	1.32202	+	0.812655i	0.129016	+	0.0793070i
$106$	−14.1304			−1.37246
$107$		−	10.7838i		−	1.04251i	−0.853401	−	0.521255i	$-0.825464\pi$
$107$		−	10.7838i		−	1.04251i	0.853401	−	0.521255i	$-0.174536\pi$
$108$		−	46.0486i		−	4.43103i
$109$	−14.0737			−1.34802			−0.674008	−	0.738724i	$-0.735429\pi$
$109$	−14.0737			−1.34802			−0.674008	+	0.738724i	$0.735429\pi$
$110$	−1.46682	+	2.38621i	−0.139856	+	0.227516i
$111$	18.0336			1.71167
$112$		−	0.496659i		−	0.0469299i
$113$			7.18921i			0.676304i	0.941092	+	0.338152i	$0.109802\pi$
$113$			7.18921i			0.676304i	−0.941092	+	0.338152i	$0.890198\pi$
$114$	−30.1103			−2.82009
$115$	−0.436387	+	0.709910i	−0.0406933	+	0.0661995i
$116$	−25.8677			−2.40175
$117$			13.6747i			1.26423i
$118$		−	14.3173i		−	1.31801i
$119$		0			0
$120$	24.2912	+	14.9320i	2.21747	+	1.36310i
$121$	−10.7244			−0.974948
$122$		−	13.4984i		−	1.22209i
$123$		−	2.51445i		−	0.226720i
$124$	10.7888			0.968859
$125$	0.923485	−	11.1421i	0.0825990	−	0.996583i
$126$	−3.64925			−0.325101
$127$			9.74047i			0.864327i	0.901795	+	0.432163i	$0.142250\pi$
$127$			9.74047i			0.864327i	−0.901795	+	0.432163i	$0.857750\pi$
$128$			20.7382i			1.83301i
$129$	7.86814			0.692751
$130$	−8.94179	−	5.49658i	−0.784247	−	0.482082i
$131$	−19.6859			−1.71996			−0.859980	−	0.510327i	$-0.829524\pi$
$131$	−19.6859			−1.71996			−0.859980	+	0.510327i	$0.829524\pi$
$132$		−	6.11732i		−	0.532444i
$133$			0.879974i			0.0763034i
$134$	−27.4700			−2.37304
$135$	14.5972	−	23.7466i	1.25633	−	2.04378i
$136$		0			0
$137$		−	4.65693i		−	0.397869i	−0.980013	−	0.198934i	$-0.936252\pi$
$137$		−	4.65693i		−	0.397869i	0.980013	−	0.198934i	$-0.0637480\pi$
$138$		−	2.80528i		−	0.238802i
$139$	5.24785			0.445117			0.222558	−	0.974919i	$-0.428559\pi$
$139$	5.24785			0.445117			0.222558	+	0.974919i	$0.428559\pi$
$140$	0.951603	−	1.54806i	0.0804251	−	0.130835i
$141$	21.2607			1.79047
$142$			17.0930i			1.43442i
$143$			1.03265i			0.0863544i
$144$	−15.6940			−1.30783
$145$	−13.3396	−	8.19994i	−1.10779	−	0.680968i
$146$	2.82843			0.234082
$147$		−	21.9296i		−	1.80873i
$148$		−	21.1170i		−	1.73581i
$149$	−8.74239			−0.716205			−0.358102	−	0.933682i	$-0.616576\pi$
$149$	−8.74239			−0.716205			−0.358102	+	0.933682i	$0.616576\pi$
$150$	16.9943	+	33.5828i	1.38758	+	2.74202i
$151$	15.9032			1.29418			0.647092	−	0.762412i	$-0.275985\pi$
$151$	15.9032			1.29418			0.647092	+	0.762412i	$0.275985\pi$
$152$			16.1689i			1.31147i
$153$		0			0
$154$	−0.275573			−0.0222063
$155$	5.56361	+	3.41999i	0.446880	+	0.274700i
$156$	22.9233			1.83533
$157$			10.0719i			0.803823i	0.915679	+	0.401911i	$0.131654\pi$
$157$			10.0719i			0.803823i	−0.915679	+	0.401911i	$0.868346\pi$
$158$			16.0604i			1.27770i
$159$	18.6806			1.48147
$160$	−3.15852	+	5.13825i	−0.249703	+	0.406214i
$161$	−0.0819845			−0.00646128
$162$			44.0732i			3.46272i
$163$			9.58784i			0.750978i	0.926827	+	0.375489i	$0.122525\pi$
$163$			9.58784i			0.750978i	−0.926827	+	0.375489i	$0.877475\pi$
$164$	−2.94437			−0.229917
$165$	1.93916	−	3.15462i	0.150964	−	0.245587i
$166$	−14.5972			−1.13296
$167$		−	5.34390i		−	0.413524i	−0.978391	−	0.206762i	$-0.933707\pi$
$167$		−	5.34390i		−	0.413524i	0.978391	−	0.206762i	$-0.0662925\pi$
$168$			2.80528i			0.216432i
$169$	9.13038			0.702337
$170$		0			0
$171$	27.8064			2.12641
$172$		−	9.21344i		−	0.702518i
$173$		−	17.4551i		−	1.32708i	−0.748139	−	0.663542i	$-0.769052\pi$
$173$		−	17.4551i		−	1.32708i	0.748139	−	0.663542i	$-0.230948\pi$
$174$	52.7128			3.99614
$175$	0.981457	−	0.496659i	0.0741912	−	0.0375439i
$176$	−1.18513			−0.0893327
$177$			18.9277i			1.42269i
$178$		−	38.1440i		−	2.85901i
$179$	21.3248			1.59389			0.796945	−	0.604052i	$-0.206448\pi$
$179$	21.3248			1.59389			0.796945	+	0.604052i	$0.206448\pi$
$180$	−48.9174	−	30.0698i	−3.64608	−	2.24127i
$181$	−14.4380			−1.07317			−0.536584	−	0.843847i	$-0.680286\pi$
$181$	−14.4380			−1.07317			−0.536584	+	0.843847i	$0.680286\pi$
$182$		−	1.03265i		−	0.0765450i
$183$			17.8452i			1.31916i
$184$	−1.50641			−0.111054
$185$	6.69399	−	10.8897i	0.492152	−	0.800629i
$186$	−21.9852			−1.61203
$187$		0			0
$188$		−	24.8959i		−	1.81572i
$189$	2.74239			0.199480
$190$	−11.1768	+	18.1824i	−0.810852	+	1.31909i
$191$	6.74239			0.487862			0.243931	−	0.969793i	$-0.421563\pi$
$191$	6.74239			0.487862			0.243931	+	0.969793i	$0.421563\pi$
$192$		−	34.5481i		−	2.49329i
$193$			14.6551i			1.05490i	0.849587	+	0.527448i	$0.176851\pi$
$193$			14.6551i			1.05490i	−0.849587	+	0.527448i	$0.823149\pi$
$194$	21.9893			1.57874
$195$	11.8212	+	7.26658i	0.846535	+	0.520371i
$196$	−25.6792			−1.83423
$197$		−	0.869327i		−	0.0619370i	−0.999520	−	0.0309685i	$-0.990141\pi$
$197$		−	0.869327i		−	0.0619370i	0.999520	−	0.0309685i	$-0.00985915\pi$
$198$			8.70787i			0.618841i
$199$	13.3004			0.942838			0.471419	−	0.881909i	$-0.343742\pi$
$199$	13.3004			0.942838			0.471419	+	0.881909i	$0.343742\pi$
$200$	18.0336	−	9.12576i	1.27517	−	0.645289i
$201$	36.3159			2.56152
$202$		−	17.2027i		−	1.21038i
$203$		−	1.54053i		−	0.108124i
$204$		0			0
$205$	−1.51837	−	0.933353i	−0.106048	−	0.0651882i
$206$	−22.7276			−1.58351
$207$			2.59064i			0.180062i
$208$		−	4.44102i		−	0.307929i
$209$	2.09980			0.145246
$210$	−1.93916	+	3.15462i	−0.133815	+	0.217689i
$211$	−17.7914			−1.22481			−0.612405	−	0.790544i	$-0.709798\pi$
$211$	−17.7914			−1.22481			−0.612405	+	0.790544i	$0.709798\pi$
$212$		−	21.8747i		−	1.50236i
$213$		−	22.5973i		−	1.54834i
$214$	25.7324			1.75903
$215$	2.92062	−	4.75124i	0.199185	−	0.324032i
$216$	50.3895			3.42857
$217$			0.642517i			0.0436169i
$218$		−	33.5828i		−	2.27451i
$219$	−3.73924			−0.252674
$220$	−3.69399	−	2.27072i	−0.249049	−	0.153092i
$221$		0			0
$222$			43.0319i			2.88811i
$223$		−	1.96713i		−	0.131729i	−0.997829	−	0.0658645i	$-0.979019\pi$
$223$		−	1.96713i		−	0.131729i	0.997829	−	0.0658645i	$-0.0209805\pi$
$224$	−0.593394			−0.0396478
$225$	−15.6940	−	31.0132i	−1.04627	−	2.06755i
$226$	−17.1550			−1.14113
$227$		−	11.9585i		−	0.793712i	−0.917881	−	0.396856i	$-0.870101\pi$
$227$		−	11.9585i		−	0.793712i	0.917881	−	0.396856i	$-0.129899\pi$
$228$		−	46.6125i		−	3.08699i
$229$	−9.30601			−0.614958			−0.307479	−	0.951555i	$-0.599485\pi$
$229$	−9.30601			−0.614958			−0.307479	+	0.951555i	$0.599485\pi$
$230$	−1.69399	−	1.04131i	−0.111699	−	0.0686620i
$231$	0.364313			0.0239700
$232$		−	28.3062i		−	1.85839i
$233$		−	25.8009i		−	1.69027i	−0.534550	−	0.845137i	$-0.679519\pi$
$233$		−	25.8009i		−	1.69027i	0.534550	−	0.845137i	$-0.320481\pi$
$234$	−32.6308			−2.13314
$235$	7.89189	−	12.8385i	0.514810	−	0.837489i
$236$	22.1640			1.44275
$237$		−	21.2322i		−	1.37918i
$238$		0			0
$239$	−29.2912			−1.89469			−0.947345	−	0.320215i	$-0.896245\pi$
$239$	−29.2912			−1.89469			−0.947345	+	0.320215i	$0.896245\pi$
$240$	−8.33959	+	13.5668i	−0.538318	+	0.875732i
$241$	−8.48528			−0.546585			−0.273293	−	0.961931i	$-0.588113\pi$
$241$	−8.48528			−0.546585			−0.273293	+	0.961931i	$0.588113\pi$
$242$		−	25.5907i		−	1.64503i
$243$		−	20.8683i		−	1.33870i
$244$	20.8964			1.33775
$245$	−13.2424	−	8.14019i	−0.846026	−	0.520058i
$246$	6.00000			0.382546
$247$			7.86854i			0.500663i
$248$			11.8058i			0.749670i
$249$	19.2978			1.22295
$250$	26.5875	+	2.20363i	1.68154	+	0.139370i
$251$	1.77282			0.111900			0.0559498	−	0.998434i	$-0.482181\pi$
$251$	1.77282			0.111900			0.0559498	+	0.998434i	$0.482181\pi$
$252$		−	5.64925i		−	0.355869i
$253$			0.195632i			0.0122993i
$254$	−23.2428			−1.45838
$255$		0			0
$256$	−27.5824			−1.72390
$257$		−	7.40235i		−	0.461746i	−0.972984	−	0.230873i	$-0.925842\pi$
$257$		−	7.40235i		−	0.461746i	0.972984	−	0.230873i	$-0.0741582\pi$
$258$			18.7750i			1.16888i
$259$	1.25761			0.0781440
$260$	8.50903	−	13.8424i	0.527708	−	0.858471i
$261$	−48.6795			−3.01318
$262$		−	46.9746i		−	2.90210i
$263$		−	7.67291i		−	0.473132i	−0.971615	−	0.236566i	$-0.923978\pi$
$263$		−	7.67291i		−	0.473132i	0.971615	−	0.236566i	$-0.0760219\pi$
$264$	6.69399			0.411987
$265$	6.93418	−	11.2805i	0.425963	−	0.692954i
$266$	−2.09980			−0.128747
$267$			50.4271i			3.08609i
$268$		−	42.5252i		−	2.59764i
$269$	7.87260			0.480001			0.240000	−	0.970773i	$-0.422852\pi$
$269$	7.87260			0.480001			0.240000	+	0.970773i	$0.422852\pi$
$270$	56.6644	+	34.8320i	3.44848	+	2.11981i
$271$	18.0672			1.09750			0.548751	−	0.835986i	$-0.315103\pi$
$271$	18.0672			1.09750			0.548751	+	0.835986i	$0.315103\pi$
$272$		0			0
$273$			1.36518i			0.0826245i
$274$	11.1124			0.671326
$275$	−1.18513	−	2.34196i	−0.0714662	−	0.141226i
$276$	4.34275			0.261403
$277$			26.5569i			1.59565i	0.602890	+	0.797824i	$0.294016\pi$
$277$			26.5569i			1.59565i	−0.602890	+	0.797824i	$0.705984\pi$
$278$			12.5225i			0.751047i
$279$	20.3030			1.21551
$280$	1.69399	+	1.04131i	0.101236	+	0.0622302i
$281$	13.7728			0.821618			0.410809	−	0.911721i	$-0.365246\pi$
$281$	13.7728			0.821618			0.410809	+	0.911721i	$0.365246\pi$
$282$			50.7325i			3.02108i
$283$			13.7471i			0.817181i	0.912718	+	0.408591i	$0.133980\pi$
$283$			13.7471i			0.817181i	−0.912718	+	0.408591i	$0.866020\pi$
$284$	−26.4611			−1.57017
$285$	14.7760	−	24.0374i	0.875253	−	1.42386i
$286$	−2.46411			−0.145706
$287$		−	0.175350i		−	0.0103506i
$288$			18.7507i			1.10490i
$289$		0			0
$290$	19.5668	−	31.8311i	1.14900	−	1.86918i
$291$	−29.0703			−1.70413
$292$			4.37857i			0.256237i
$293$		−	19.8873i		−	1.16183i	−0.813966	−	0.580913i	$-0.802696\pi$
$293$		−	19.8873i		−	1.16183i	0.813966	−	0.580913i	$-0.197304\pi$
$294$	52.3287			3.05187
$295$	11.4297	+	7.02588i	0.665460	+	0.409063i
$296$	23.1077			1.34311
$297$		−	6.54392i		−	0.379717i
$298$		−	20.8612i		−	1.20846i
$299$	−0.733088			−0.0423955
$300$	−51.9881	+	26.3082i	−3.00154	+	1.51891i
$301$	0.548700			0.0316266
$302$			37.9484i			2.18368i
$303$			22.7423i			1.30651i
$304$	−9.03043			−0.517931
$305$	10.7760	+	6.62407i	0.617031	+	0.379293i
$306$		0			0
$307$		−	14.9598i		−	0.853799i	−0.904299	−	0.426900i	$-0.859606\pi$
$307$		−	14.9598i		−	0.853799i	0.904299	−	0.426900i	$-0.140394\pi$
$308$		−	0.426603i		−	0.0243080i
$309$	30.0463			1.70928
$310$	−8.16081	+	13.2759i	−0.463503	+	0.754023i
$311$	−29.6538			−1.68151			−0.840756	−	0.541414i	$-0.817889\pi$
$311$	−29.6538			−1.68151			−0.840756	+	0.541414i	$0.817889\pi$
$312$			25.0843i			1.42012i
$313$			14.3784i			0.812716i	0.913714	+	0.406358i	$0.133201\pi$
$313$			14.3784i			0.812716i	−0.913714	+	0.406358i	$0.866799\pi$
$314$	−24.0336			−1.35629
$315$	1.79079	−	2.91324i	0.100900	−	0.164143i
$316$	−24.8624			−1.39862
$317$			13.7751i			0.773687i	0.922145	+	0.386843i	$0.126435\pi$
$317$			13.7751i			0.773687i	−0.922145	+	0.386843i	$0.873565\pi$
$318$			44.5759i			2.49969i
$319$	−3.67603			−0.205818
$320$	−20.8622	−	12.8241i	−1.16623	−	0.716890i
$321$	−34.0188			−1.89874
$322$		−	0.195632i		−	0.0109021i
$323$		0			0
$324$	−68.2280			−3.79044
$325$	8.77598	−	4.44102i	0.486804	−	0.246343i
$326$	−22.8786			−1.26713
$327$			44.3971i			2.45516i
$328$		−	3.22194i		−	0.177902i
$329$	1.48266			0.0817415
$330$	7.52757	+	4.62725i	0.414379	+	0.254722i
$331$	−20.1640			−1.10831			−0.554156	−	0.832413i	$-0.686959\pi$
$331$	−20.1640			−1.10831			−0.554156	+	0.832413i	$0.686959\pi$
$332$		−	22.5973i		−	1.24019i
$333$		−	39.7393i		−	2.17770i
$334$	12.7517			0.697740
$335$	13.4803	−	21.9296i	0.736507	−	1.19814i
$336$	−1.56677			−0.0854742
$337$			28.5829i			1.55701i	0.627640	+	0.778504i	$0.284021\pi$
$337$			28.5829i			1.55701i	−0.627640	+	0.778504i	$0.715979\pi$
$338$			21.7870i			1.18506i
$339$	22.6792			1.23176
$340$		0			0
$341$	1.53318			0.0830264
$342$			66.3519i			3.58790i
$343$		−	3.06926i		−	0.165725i
$344$	10.0820			0.543584
$345$	2.23949	+	1.37663i	0.120570	+	0.0741154i
$346$	41.6514			2.23919
$347$			10.9365i			0.587101i	0.955944	+	0.293551i	$0.0948369\pi$
$347$			10.9365i			0.587101i	−0.955944	+	0.293551i	$0.905163\pi$
$348$			81.6025i			4.37435i
$349$	−0.645598			−0.0345581			−0.0172790	−	0.999851i	$-0.505500\pi$
$349$	−0.645598			−0.0345581			−0.0172790	+	0.999851i	$0.505500\pi$
$350$	1.18513	+	2.34196i	0.0633480	+	0.125183i
$351$	24.5219			1.30888
$352$			1.41596i			0.0754711i
$353$		−	14.3022i		−	0.761229i	−0.924734	−	0.380615i	$-0.875712\pi$
$353$		−	14.3022i		−	0.761229i	0.924734	−	0.380615i	$-0.124288\pi$
$354$	−45.1654			−2.40052
$355$	−13.6456	−	8.38804i	−0.724233	−	0.445191i
$356$	59.0492			3.12960
$357$		0			0
$358$			50.8854i			2.68938i
$359$	15.6760			0.827349			0.413675	−	0.910425i	$-0.364245\pi$
$359$	15.6760			0.827349			0.413675	+	0.910425i	$0.364245\pi$
$360$	32.9045	−	53.5288i	1.73422	−	2.82121i
$361$	−3.00000			−0.157895
$362$		−	34.4521i		−	1.81076i
$363$			33.8315i			1.77569i
$364$	1.59860			0.0837895
$365$	−1.38799	+	2.25797i	−0.0726507	+	0.118188i
$366$	−42.5824			−2.22582
$367$			21.9010i			1.14322i	0.820525	+	0.571610i	$0.193681\pi$
$367$			21.9010i			1.14322i	−0.820525	+	0.571610i	$0.806319\pi$
$368$		−	0.841338i		−	0.0438578i
$369$	−5.54091			−0.288448
$370$	25.9852	+	15.9733i	1.35091	+	0.830411i
$371$	1.30273			0.0676345
$372$		−	34.0344i		−	1.76460i
$373$		−	6.50858i		−	0.337002i	−0.985702	−	0.168501i	$-0.946107\pi$
$373$		−	6.50858i		−	0.337002i	0.985702	−	0.168501i	$-0.0538926\pi$
$374$		0			0
$375$	−35.1492	−	2.91324i	−1.81509	−	0.150439i
$376$	27.2428			1.40494
$377$		−	13.7751i		−	0.709454i
$378$			6.54392i			0.336583i
$379$	−7.52757			−0.386666			−0.193333	−	0.981133i	$-0.561930\pi$
$379$	−7.52757			−0.386666			−0.193333	+	0.981133i	$0.561930\pi$
$380$	−28.1474	−	17.3024i	−1.44393	−	0.887594i
$381$	30.7274			1.57421
$382$			16.0888i			0.823172i
$383$			24.7752i			1.26595i	0.774172	+	0.632976i	$0.218167\pi$
$383$			24.7752i			1.26595i	−0.774172	+	0.632976i	$0.781833\pi$
$384$	65.4209			3.33850
$385$	0.135231	−	0.219993i	0.00689203	−	0.0112119i
$386$	−34.9701			−1.77993
$387$		−	17.3385i		−	0.881363i
$388$			34.0408i			1.72816i
$389$	−23.6971			−1.20149			−0.600747	−	0.799440i	$-0.705130\pi$
$389$	−23.6971			−1.20149			−0.600747	+	0.799440i	$0.705130\pi$
$390$	−17.3396	+	28.2079i	−0.878024	+	1.42836i
$391$		0			0
$392$		−	28.1000i		−	1.41926i
$393$			62.1013i			3.13260i
$394$	2.07440			0.104507
$395$	−12.8212	−	7.88129i	−0.645106	−	0.396551i
$396$	−13.4803			−0.677410
$397$		−	27.7135i		−	1.39090i	−0.718573	−	0.695451i	$-0.755205\pi$
$397$		−	27.7135i		−	1.39090i	0.718573	−	0.695451i	$-0.244795\pi$
$398$			31.7375i			1.59086i
$399$	2.77598			0.138973
$400$	5.09679	+	10.0719i	0.254840	+	0.503593i
$401$	−30.5431			−1.52525			−0.762624	−	0.646842i	$-0.776089\pi$
$401$	−30.5431			−1.52525			−0.762624	+	0.646842i	$0.776089\pi$
$402$			86.6572i			4.32207i
$403$			5.74525i			0.286191i
$404$	26.6308			1.32493
$405$	−35.1842	−	21.6280i	−1.74832	−	1.07470i
$406$	3.67603			0.182438
$407$		−	3.00092i		−	0.148750i
$408$		0			0
$409$	5.90321			0.291895			0.145947	−	0.989292i	$-0.453377\pi$
$409$	5.90321			0.291895			0.145947	+	0.989292i	$0.453377\pi$
$410$	2.22718	−	3.62315i	0.109992	−	0.178935i
$411$	−14.6908			−0.724645
$412$		−	35.1837i		−	1.73337i
$413$			1.31996i			0.0649510i
$414$	−6.18180			−0.303819
$415$	7.16326	−	11.6531i	0.351631	−	0.572030i
$416$	−5.30601			−0.260148
$417$		−	16.5549i		−	0.810699i
$418$			5.01057i			0.245075i
$419$	−32.4867			−1.58708			−0.793539	−	0.608519i	$-0.791764\pi$
$419$	−32.4867			−1.58708			−0.793539	+	0.608519i	$0.791764\pi$
$420$	−4.88353	−	3.00194i	−0.238292	−	0.146480i
$421$	−30.1156			−1.46774			−0.733872	−	0.679288i	$-0.762289\pi$
$421$	−30.1156			−1.46774			−0.733872	+	0.679288i	$0.762289\pi$
$422$		−	42.4540i		−	2.06663i
$423$		−	46.8507i		−	2.27796i
$424$	23.9368			1.16247
$425$		0			0
$426$	53.9220			2.61253
$427$			1.24447i			0.0602242i
$428$			39.8353i			1.92551i
$429$	3.25761			0.157279
$430$	11.3375	+	6.96921i	0.546741	+	0.336085i
$431$	8.32464			0.400984			0.200492	−	0.979695i	$-0.435746\pi$
$431$	8.32464			0.400984			0.200492	+	0.979695i	$0.435746\pi$
$432$			28.1429i			1.35402i
$433$			13.5795i			0.652591i	0.945268	+	0.326295i	$0.105800\pi$
$433$			13.5795i			0.652591i	−0.945268	+	0.326295i	$0.894200\pi$
$434$	−1.53318			−0.0735950
$435$	−25.8677	+	42.0813i	−1.24026	+	2.01764i
$436$	51.9881			2.48978
$437$			1.49067i			0.0713085i
$438$		−	8.92260i		−	0.426338i
$439$	−20.3714			−0.972276			−0.486138	−	0.873882i	$-0.661595\pi$
$439$	−20.3714			−0.972276			−0.486138	+	0.873882i	$0.661595\pi$
$440$	2.48478	−	4.04223i	0.118457	−	0.192706i
$441$	−48.3248			−2.30118
$442$		0			0
$443$		−	2.45360i		−	0.116574i	−0.998300	−	0.0582871i	$-0.981436\pi$
$443$		−	2.45360i		−	0.116574i	0.998300	−	0.0582871i	$-0.0185639\pi$
$444$	−66.6160			−3.16145
$445$	30.4509	+	18.7184i	1.44351	+	0.887335i
$446$	4.69399			0.222267
$447$			27.5789i			1.30444i
$448$		−	2.40928i		−	0.113828i
$449$	3.19720			0.150885			0.0754426	−	0.997150i	$-0.475963\pi$
$449$	3.19720			0.150885			0.0754426	+	0.997150i	$0.475963\pi$
$450$	74.0040	−	37.4492i	3.48858	−	1.76537i
$451$	−0.418422			−0.0197027
$452$		−	26.5569i		−	1.24913i
$453$		−	50.1685i		−	2.35712i
$454$	28.5354			1.33923
$455$	0.824376	+	0.506750i	0.0386474	+	0.0237568i
$456$	51.0067			2.38861
$457$			30.1803i			1.41177i	0.708325	+	0.705887i	$0.249451\pi$
$457$			30.1803i			1.41177i	−0.708325	+	0.705887i	$0.750549\pi$
$458$		−	22.2061i		−	1.03762i
$459$		0			0
$460$	1.61201	−	2.62241i	0.0751604	−	0.122270i
$461$	5.41527			0.252214			0.126107	−	0.992017i	$-0.459752\pi$
$461$	5.41527			0.252214			0.126107	+	0.992017i	$0.459752\pi$
$462$			0.869327i			0.0404447i
$463$			15.7574i			0.732307i	0.930555	+	0.366153i	$0.119325\pi$
$463$			15.7574i			0.732307i	−0.930555	+	0.366153i	$0.880675\pi$
$464$	15.8092			0.733923
$465$	10.7888	−	17.5511i	0.500317	−	0.813911i
$466$	61.5664			2.85201
$467$			10.7690i			0.498331i	0.968461	+	0.249166i	$0.0801563\pi$
$467$			10.7690i			0.498331i	−0.968461	+	0.249166i	$0.919844\pi$
$468$		−	50.5144i		−	2.33503i
$469$	2.53256			0.116943
$470$	30.6352	+	18.8317i	1.41310	+	0.868641i
$471$	31.7729			1.46402
$472$			24.2534i			1.11635i
$473$		−	1.30931i		−	0.0602023i
$474$	50.6644			2.32709
$475$	−9.03043	−	17.8452i	−0.414345	−	0.818794i
$476$		0			0
$477$		−	41.1652i		−	1.88483i
$478$		−	69.8949i		−	3.19692i
$479$	−36.9092			−1.68643			−0.843213	−	0.537579i	$-0.819339\pi$
$479$	−36.9092			−1.68643			−0.843213	+	0.537579i	$0.819339\pi$
$480$	16.2092	+	9.96391i	0.739846	+	0.454788i
$481$	11.2453			0.512740
$482$		−	20.2477i		−	0.922256i
$483$			0.258629i			0.0117680i
$484$	39.6160			1.80073
$485$	−10.7908	+	17.5544i	−0.489984	+	0.797103i
$486$	49.7961			2.25880
$487$		−	38.3234i		−	1.73660i	−0.496041	−	0.868299i	$-0.665214\pi$
$487$		−	38.3234i		−	1.73660i	0.496041	−	0.868299i	$-0.334786\pi$
$488$			22.8663i			1.03511i
$489$	30.2460			1.36777
$490$	19.4242	−	31.5991i	0.877496	−	1.42750i
$491$	38.0336			1.71643			0.858216	−	0.513289i	$-0.171573\pi$
$491$	38.0336			1.71643			0.858216	+	0.513289i	$0.171573\pi$
$492$			9.28836i			0.418752i
$493$		0			0
$494$	−18.7760			−0.844771
$495$	−6.95160	−	4.27320i	−0.312451	−	0.192066i
$496$	−6.59362			−0.296062
$497$		−	1.57587i		−	0.0706875i
$498$			46.0486i			2.06349i
$499$	−9.30610			−0.416598			−0.208299	−	0.978065i	$-0.566793\pi$
$499$	−9.30610			−0.416598			−0.208299	+	0.978065i	$0.566793\pi$
$500$	−3.41135	+	41.1590i	−0.152560	+	1.84069i
$501$	−16.8580			−0.753158
$502$			4.23033i			0.188809i
$503$		−	1.56864i		−	0.0699421i	−0.999388	−	0.0349710i	$-0.988866\pi$
$503$		−	1.56864i		−	0.0699421i	0.999388	−	0.0349710i	$-0.0111339\pi$
$504$	6.18180			0.275359
$505$	13.7331	+	8.44185i	0.611116	+	0.375657i
$506$	−0.466819			−0.0207526
$507$		−	28.8028i		−	1.27918i
$508$		−	35.9812i		−	1.59641i
$509$	−24.4247			−1.08261			−0.541304	−	0.840827i	$-0.682069\pi$
$509$	−24.4247			−1.08261			−0.541304	+	0.840827i	$0.682069\pi$
$510$		0			0
$511$	−0.260763			−0.0115355
$512$		−	24.3410i		−	1.07573i
$513$		−	49.8632i		−	2.20151i
$514$	17.6636			0.779106
$515$	11.1531	−	18.1437i	0.491463	−	0.799508i
$516$	−29.0649			−1.27951
$517$		−	3.53793i		−	0.155598i
$518$			3.00092i			0.131853i
$519$	−55.0640			−2.41704
$520$	15.1473	+	9.31117i	0.664255	+	0.408322i
$521$	7.50829			0.328944			0.164472	−	0.986382i	$-0.447408\pi$
$521$	7.50829			0.328944			0.164472	+	0.986382i	$0.447408\pi$
$522$		−	116.159i		−	5.08416i
$523$			8.98247i			0.392776i	0.980526	+	0.196388i	$0.0629212\pi$
$523$			8.98247i			0.392776i	−0.980526	+	0.196388i	$0.937079\pi$
$524$	72.7194			3.17676
$525$	−1.56677	−	3.09612i	−0.0683794	−	0.135126i
$526$	18.3092			0.798317
$527$		0			0
$528$			3.73864i			0.162703i
$529$	22.8611			0.993962
$530$	26.9176	+	16.5464i	1.16922	+	0.718730i
$531$	41.7096			1.81004
$532$		−	3.25062i		−	0.140932i
$533$		−	1.56794i		−	0.0679152i
$534$	−120.330			−5.20718
$535$	−12.6276	+	20.5425i	−0.545940	+	0.888131i
$536$	46.5340			2.00996
$537$		−	67.2715i		−	2.90298i
$538$			18.7857i			0.809908i
$539$	−3.64925			−0.157184
$540$	−53.9220	+	87.7198i	−2.32043	+	3.77486i
$541$	12.7279			0.547216			0.273608	−	0.961841i	$-0.411783\pi$
$541$	12.7279			0.547216			0.273608	+	0.961841i	$0.411783\pi$
$542$			43.1121i			1.85182i
$543$			45.5464i			1.95458i
$544$		0			0
$545$	26.8096	+	16.4800i	1.14840	+	0.705927i
$546$	−3.25761			−0.139413
$547$			2.57260i			0.109997i	0.998486	+	0.0549983i	$0.0175153\pi$
$547$			2.57260i			0.109997i	−0.998486	+	0.0549983i	$0.982485\pi$
$548$			17.2027i			0.734862i
$549$	39.3242			1.67832
$550$	5.58841	−	2.82797i	0.238291	−	0.120585i
$551$	−28.0105			−1.19329
$552$			4.75214i			0.202264i
$553$		−	1.48067i		−	0.0629644i
$554$	−63.3703			−2.69235
$555$	−34.3529	−	21.1170i	−1.45820	−	0.896366i
$556$	−19.3855			−0.822129
$557$		−	21.0162i		−	0.890487i	−0.895410	−	0.445243i	$-0.853117\pi$
$557$		−	21.0162i		−	0.890487i	0.895410	−	0.445243i	$-0.146883\pi$
$558$			48.4472i			2.05093i
$559$	4.90636			0.207517
$560$	−0.581578	+	0.946106i	−0.0245762	+	0.0399803i
$561$		0			0
$562$			32.8648i			1.38632i
$563$			40.5377i			1.70846i	0.519893	+	0.854231i	$0.325972\pi$
$563$			40.5377i			1.70846i	−0.519893	+	0.854231i	$0.674028\pi$
$564$	−78.5369			−3.30700
$565$	8.41842	−	13.6950i	0.354166	−	0.576154i
$566$	−32.8035			−1.37883
$567$		−	4.06327i		−	0.170641i
$568$		−	28.9555i		−	1.21495i
$569$	0.612010			0.0256568			0.0128284	−	0.999918i	$-0.495916\pi$
$569$	0.612010			0.0256568			0.0128284	+	0.999918i	$0.495916\pi$
$570$	57.3584	+	35.2586i	2.40248	+	1.47682i
$571$	−14.8945			−0.623316			−0.311658	−	0.950194i	$-0.600884\pi$
$571$	−14.8945			−0.623316			−0.311658	+	0.950194i	$0.600884\pi$
$572$		−	3.81460i		−	0.159496i
$573$		−	21.2697i		−	0.888553i
$574$	0.418422			0.0174646
$575$	1.66258	−	0.841338i	0.0693345	−	0.0350862i
$576$	−76.1312			−3.17213
$577$			37.2107i			1.54910i	0.632513	+	0.774550i	$0.282024\pi$
$577$			37.2107i			1.54910i	−0.632513	+	0.774550i	$0.717976\pi$
$578$		0			0
$579$	46.2311			1.92130
$580$	49.2764	+	30.2905i	2.04609	+	1.25775i
$581$	1.34577			0.0558319
$582$		−	69.3679i		−	2.87539i
$583$		−	3.10859i		−	0.128745i
$584$	−4.79134			−0.198267
$585$	16.0129	−	26.0496i	0.662050	−	1.07702i
$586$	47.4552			1.96035
$587$			9.60470i			0.396428i	0.980159	+	0.198214i	$0.0635142\pi$
$587$			9.60470i			0.396428i	−0.980159	+	0.198214i	$0.936486\pi$
$588$			81.0080i			3.34071i
$589$	11.6825			0.481368
$590$	−16.7652	+	27.2735i	−0.690214	+	1.12283i
$591$	−2.74239			−0.112807
$592$			12.9058i			0.530424i
$593$		−	16.5206i		−	0.678419i	−0.940711	−	0.339210i	$-0.889840\pi$
$593$		−	16.5206i		−	0.678419i	0.940711	−	0.339210i	$-0.110160\pi$
$594$	15.6152			0.640698
$595$		0			0
$596$	32.2944			1.32283
$597$		−	41.9576i		−	1.71721i
$598$		−	1.74930i		−	0.0715342i
$599$	−34.8096			−1.42228			−0.711140	−	0.703050i	$-0.751821\pi$
$599$	−34.8096			−1.42228			−0.711140	+	0.703050i	$0.751821\pi$
$600$	−28.7883	−	56.8890i	−1.17528	−	2.32249i
$601$	11.6825			0.476538			0.238269	−	0.971199i	$-0.423420\pi$
$601$	11.6825			0.476538			0.238269	+	0.971199i	$0.423420\pi$
$602$			1.30931i			0.0533636i
$603$		−	80.0267i		−	3.25894i
$604$	−58.7464			−2.39036
$605$	20.4294	+	12.5581i	0.830574	+	0.510559i
$606$	−54.2679			−2.20448
$607$		−	26.9296i		−	1.09304i	−0.837447	−	0.546519i	$-0.815953\pi$
$607$		−	26.9296i		−	1.09304i	0.837447	−	0.546519i	$-0.184047\pi$
$608$			10.7893i			0.437564i
$609$	−4.85978			−0.196928
$610$	−15.8064	+	25.7137i	−0.639983	+	1.04112i
$611$	13.2576			0.536345
$612$		0			0
$613$			5.43522i			0.219526i	0.993958	+	0.109763i	$0.0350092\pi$
$613$			5.43522i			0.219526i	−0.993958	+	0.109763i	$0.964991\pi$
$614$	35.6971			1.44062
$615$	−2.94437	+	4.78988i	−0.118728	+	0.193147i
$616$	0.466819			0.0188087
$617$		−	3.49860i		−	0.140848i	−0.997517	−	0.0704242i	$-0.977565\pi$
$617$		−	3.49860i		−	0.140848i	0.997517	−	0.0704242i	$-0.0224353\pi$
$618$			71.6968i			2.88407i
$619$	12.1301			0.487549			0.243774	−	0.969832i	$-0.421614\pi$
$619$	12.1301			0.487549			0.243774	+	0.969832i	$0.421614\pi$
$620$	−20.5520	−	12.6334i	−0.825387	−	0.507371i
$621$	4.64560			0.186421
$622$		−	70.7602i		−	2.83722i
$623$			3.51664i			0.140891i
$624$	−14.0097			−0.560837
$625$	−14.8064	+	20.1437i	−0.592256	+	0.805750i
$626$	−34.3099			−1.37130
$627$		−	6.62407i		−	0.264540i
$628$		−	37.2054i		−	1.48466i
$629$		0			0
$630$	6.95160	+	4.27320i	0.276958	+	0.170248i
$631$	12.6183			0.502327			0.251164	−	0.967945i	$-0.419187\pi$
$631$	12.6183			0.502327			0.251164	+	0.967945i	$0.419187\pi$
$632$		−	27.2062i		−	1.08221i
$633$			56.1250i			2.23077i
$634$	−32.8703			−1.30545
$635$	11.4059	−	18.5550i	0.452629	−	0.736334i
$636$	−69.0062			−2.73627
$637$		−	13.6747i		−	0.541813i
$638$		−	8.77178i		−	0.347278i
$639$	−49.7961			−1.96991
$640$	24.2840	−	39.5050i	0.959909	−	1.56157i
$641$	30.1997			1.19282			0.596408	−	0.802681i	$-0.296594\pi$
$641$	30.1997			1.19282			0.596408	+	0.802681i	$0.296594\pi$
$642$		−	81.1759i		−	3.20376i
$643$			19.7117i			0.777352i	0.921374	+	0.388676i	$0.127068\pi$
$643$			19.7117i			0.777352i	−0.921374	+	0.388676i	$0.872932\pi$
$644$	0.302850			0.0119340
$645$	−14.9883	−	9.21344i	−0.590166	−	0.362779i
$646$		0			0
$647$			21.0418i			0.827237i	0.910450	+	0.413618i	$0.135735\pi$
$647$			21.0418i			0.827237i	−0.910450	+	0.413618i	$0.864265\pi$
$648$		−	74.6598i		−	2.93291i
$649$	3.14970			0.123637
$650$	10.5972	+	20.9413i	0.415656	+	0.821386i
$651$	2.02690			0.0794403
$652$		−	35.4174i		−	1.38705i
$653$		−	38.7173i		−	1.51513i	−0.652762	−	0.757563i	$-0.726390\pi$
$653$		−	38.7173i		−	1.51513i	0.652762	−	0.757563i	$-0.273610\pi$
$654$	−105.941			−4.14261
$655$	37.5004	+	23.0518i	1.46526	+	0.900707i
$656$	1.79947			0.0702575
$657$			8.23989i			0.321469i
$658$			3.53793i			0.137923i
$659$	24.1577			0.941049			0.470524	−	0.882387i	$-0.344065\pi$
$659$	24.1577			0.941049			0.470524	+	0.882387i	$0.344065\pi$
$660$	−7.16326	+	11.6531i	−0.278830	+	0.453598i
$661$	−25.7432			−1.00129			−0.500647	−	0.865651i	$-0.666905\pi$
$661$	−25.7432			−1.00129			−0.500647	+	0.865651i	$0.666905\pi$
$662$		−	48.1155i		−	1.87006i
$663$		0			0
$664$	24.7276			0.959616
$665$	1.03043	−	1.67630i	0.0399585	−	0.0650041i
$666$	94.8264			3.67445
$667$		−	2.60965i		−	0.101046i
$668$			19.7404i			0.763777i
$669$	−6.20555			−0.239921
$670$	52.3287	+	32.1668i	2.02163	+	1.24271i
$671$	2.96957			0.114639
$672$			1.87193i			0.0722113i
$673$		−	10.4958i		−	0.404583i	−0.979325	−	0.202292i	$-0.935161\pi$
$673$		−	10.4958i		−	0.404583i	0.979325	−	0.202292i	$-0.0648389\pi$
$674$	−68.2047			−2.62715
$675$	−55.6136	+	28.1429i	−2.14057	+	1.08322i
$676$	−33.7276			−1.29721
$677$		−	8.48787i		−	0.326215i	−0.986608	−	0.163108i	$-0.947848\pi$
$677$		−	8.48787i		−	0.326215i	0.986608	−	0.163108i	$-0.0521518\pi$
$678$			54.1173i			2.07836i
$679$	−2.02728			−0.0777998
$680$		0			0
$681$	−37.7244			−1.44560
$682$			3.65849i			0.140091i
$683$			14.2898i			0.546784i	0.961903	+	0.273392i	$0.0881456\pi$
$683$			14.2898i			0.546784i	−0.961903	+	0.273392i	$0.911854\pi$
$684$	−102.717			−3.92747
$685$	−5.45318	+	8.87119i	−0.208355	+	0.338951i
$686$	7.32390			0.279628
$687$			29.3569i			1.12003i
$688$			5.63085i			0.214674i
$689$	11.6488			0.443782
$690$	−3.28493	+	5.34390i	−0.125055	+	0.203439i
$691$	8.82584			0.335751			0.167875	−	0.985808i	$-0.446309\pi$
$691$	8.82584			0.335751			0.167875	+	0.985808i	$0.446309\pi$
$692$			64.4789i			2.45112i
$693$		−	0.802810i		−	0.0304962i
$694$	−26.0967			−0.990619
$695$	−9.99684	−	6.14513i	−0.379202	−	0.233098i
$696$	−89.2952			−3.38472
$697$		0			0
$698$		−	1.54053i		−	0.0583100i
$699$	−81.3920			−3.07853
$700$	−3.62550	+	1.83466i	−0.137031	+	0.0693435i
$701$	−18.5340			−0.700019			−0.350010	−	0.936746i	$-0.613822\pi$
$701$	−18.5340			−0.700019			−0.350010	+	0.936746i	$0.613822\pi$
$702$			58.5144i			2.20848i
$703$		−	22.8663i		−	0.862418i
$704$	−5.74905			−0.216675
$705$	−40.5004	−	24.8959i	−1.52533	−	0.937633i
$706$	34.1280			1.28443
$707$			1.58598i			0.0596469i
$708$		−	69.9188i		−	2.62771i
$709$	−25.4989			−0.957631			−0.478815	−	0.877916i	$-0.658934\pi$
$709$	−25.4989			−0.957631			−0.478815	+	0.877916i	$0.658934\pi$
$710$	20.0156	−	32.5613i	0.751173	−	1.22200i
$711$	−46.7878			−1.75468
$712$			64.6158i			2.42158i
$713$			1.08842i			0.0407617i
$714$		0			0
$715$	1.20921	−	1.96713i	0.0452219	−	0.0735667i
$716$	−78.7736			−2.94391
$717$			92.4025i			3.45083i
$718$			37.4063i			1.39599i
$719$	4.76313			0.177635			0.0888174	−	0.996048i	$-0.471691\pi$
$719$	4.76313			0.177635			0.0888174	+	0.996048i	$0.471691\pi$
$720$	29.8961	+	18.3774i	1.11416	+	0.684884i
$721$	2.09534			0.0780345
$722$		−	7.15863i		−	0.266417i
$723$			26.7678i			0.995505i
$724$	53.3339			1.98214
$725$	15.8092	+	31.2408i	0.587138	+	1.16025i
$726$	−80.7289			−2.99613
$727$			11.1858i			0.414858i	0.978250	+	0.207429i	$0.0665096\pi$
$727$			11.1858i			0.414858i	−0.978250	+	0.207429i	$0.933490\pi$
$728$			1.74930i			0.0648334i
$729$	−10.4216			−0.385984
$730$	−5.38799	−	3.31203i	−0.199418	−	0.122584i
$731$		0			0
$732$		−	65.9201i		−	2.43648i
$733$		−	26.2804i		−	0.970687i	−0.874324	−	0.485344i	$-0.838695\pi$
$733$		−	26.2804i		−	0.970687i	0.874324	−	0.485344i	$-0.161305\pi$
$734$	−52.2603			−1.92896
$735$	−25.6792	+	41.7747i	−0.947191	+	1.54088i
$736$	−1.00521			−0.0370524
$737$		−	6.04321i		−	0.222605i
$738$		−	13.2218i		−	0.486700i
$739$	−6.00000			−0.220714			−0.110357	−	0.993892i	$-0.535199\pi$
$739$	−6.00000			−0.220714			−0.110357	+	0.993892i	$0.535199\pi$
$740$	−24.7276	+	40.2266i	−0.909004	+	1.47876i
$741$	24.8222			0.911867
$742$			3.10859i			0.114120i
$743$			34.0401i			1.24881i	0.781101	+	0.624405i	$0.214659\pi$
$743$			34.0401i			1.24881i	−0.781101	+	0.624405i	$0.785341\pi$
$744$	37.2428			1.36539
$745$	16.6537	+	10.2372i	0.610146	+	0.375061i
$746$	15.5308			0.568624
$747$		−	42.5252i		−	1.55591i
$748$		0			0
$749$	−2.37237			−0.0866844
$750$	6.95160	−	83.8733i	0.253837	−	3.06262i
$751$	13.0431			0.475949			0.237974	−	0.971271i	$-0.423517\pi$
$751$	13.0431			0.475949			0.237974	+	0.971271i	$0.423517\pi$
$752$			15.2153i			0.554844i
$753$		−	5.59258i		−	0.203805i
$754$	32.8703			1.19707
$755$	−30.2947	−	18.6223i	−1.10254	−	0.677737i
$756$	−10.1304			−0.368438
$757$		−	31.8716i		−	1.15839i	−0.815188	−	0.579197i	$-0.803366\pi$
$757$		−	31.8716i		−	1.15839i	0.815188	−	0.579197i	$-0.196634\pi$
$758$		−	17.9624i		−	0.652423i
$759$	0.617144			0.0224009
$760$	18.9335	−	30.8008i	0.686789	−	1.11726i
$761$	−18.7549			−0.679863			−0.339932	−	0.940450i	$-0.610404\pi$
$761$	−18.7549			−0.679863			−0.339932	+	0.940450i	$0.610404\pi$
$762$			73.3221i			2.65618i
$763$			3.09612i			0.112087i
$764$	−24.9064			−0.901081
$765$		0			0
$766$	−59.1187			−2.13605
$767$			11.8028i			0.426175i
$768$			87.0119i			3.13977i
$769$	47.7916			1.72341			0.861705	−	0.507410i	$-0.169397\pi$
$769$	47.7916			1.72341			0.861705	+	0.507410i	$0.169397\pi$
$770$	0.524950	+	0.322691i	0.0189179	+	0.0116290i
$771$	−23.3516			−0.840987
$772$		−	54.1358i		−	1.94839i
$773$			28.3286i			1.01891i	0.860497	+	0.509455i	$0.170153\pi$
$773$			28.3286i			1.01891i	−0.860497	+	0.509455i	$0.829847\pi$
$774$	41.3732			1.48713
$775$	−6.59362	−	13.0298i	−0.236850	−	0.468043i
$776$	−37.2498			−1.33719
$777$		−	3.96727i		−	0.142325i
$778$		−	56.5464i		−	2.02729i
$779$	−3.18828			−0.114232
$780$	−43.6675	−	26.8427i	−1.56355	−	0.961124i
$781$	−3.76036			−0.134556
$782$		0			0
$783$			87.2932i			3.11961i
$784$	15.6940			0.560500
$785$	11.7940	−	19.1863i	0.420945	−	0.684789i
$786$	−148.187			−5.28565
$787$			42.3119i			1.50826i	0.656727	+	0.754129i	$0.271941\pi$
$787$			42.3119i			1.50826i	−0.656727	+	0.754129i	$0.728059\pi$
$788$			3.21129i			0.114397i
$789$	−24.2051			−0.861723
$790$	18.8064	−	30.5941i	0.669102	−	1.08849i
$791$	1.58158			0.0562344
$792$		−	14.7511i		−	0.524157i
$793$			11.1278i			0.395160i
$794$	66.1303			2.34688
$795$	−35.5855	−	21.8747i	−1.26209	−	0.775815i
$796$	−49.1315			−1.74142
$797$		−	54.1578i		−	1.91837i	−0.282780	−	0.959185i	$-0.591257\pi$
$797$		−	54.1578i		−	1.91837i	0.282780	−	0.959185i	$-0.408743\pi$
$798$			6.62407i			0.234489i
$799$		0			0
$800$	12.0336	−	6.08951i	0.425452	−	0.215297i
$801$	111.123			3.92633
$802$		−	72.8821i		−	2.57356i
$803$			0.622235i			0.0219582i
$804$	−134.151			−4.73113
$805$	0.156176	+	0.0960022i	0.00550447	+	0.00338363i
$806$	−13.7094			−0.482892
$807$		−	24.8350i		−	0.874234i
$808$			29.1413i			1.02519i
$809$	30.9803			1.08921			0.544604	−	0.838693i	$-0.316680\pi$
$809$	30.9803			1.08921			0.544604	+	0.838693i	$0.316680\pi$
$810$	51.6089	−	83.9569i	1.81335	−	2.94995i
$811$	−4.15045			−0.145742			−0.0728710	−	0.997341i	$-0.523216\pi$
$811$	−4.15045			−0.145742			−0.0728710	+	0.997341i	$0.523216\pi$
$812$			5.69071i			0.199705i
$813$		−	56.9950i		−	1.99890i
$814$	7.16081			0.250986
$815$	11.2272	−	18.2643i	0.393271	−	0.639770i
$816$		0			0
$817$		−	9.97667i		−	0.349039i
$818$			14.0863i			0.492515i
$819$	3.00835			0.105120
$820$	5.60886	+	3.44780i	0.195870	+	0.120402i
$821$	−1.40975			−0.0492007			−0.0246003	−	0.999697i	$-0.507831\pi$
$821$	−1.40975			−0.0492007			−0.0246003	+	0.999697i	$0.507831\pi$
$822$		−	35.0554i		−	1.22270i
$823$			20.2090i			0.704442i	0.935917	+	0.352221i	$0.114573\pi$
$823$			20.2090i			0.704442i	−0.935917	+	0.352221i	$0.885427\pi$
$824$	38.5004			1.34123
$825$	−7.38799	+	3.73864i	−0.257217	+	0.130163i
$826$	−3.14970			−0.109592
$827$			11.3584i			0.394971i	0.980306	+	0.197486i	$0.0632776\pi$
$827$			11.3584i			0.394971i	−0.980306	+	0.197486i	$0.936722\pi$
$828$		−	9.56980i		−	0.332574i
$829$	10.9336			0.379741			0.189870	−	0.981809i	$-0.439193\pi$
$829$	10.9336			0.379741			0.189870	+	0.981809i	$0.439193\pi$
$830$	27.8068	+	17.0930i	0.965189	+	0.593308i
$831$	83.7768			2.90618
$832$		−	21.5433i		−	0.746879i
$833$		0			0
$834$	39.5036			1.36790
$835$	−6.25761	+	10.1798i	−0.216553	+	0.352287i
$836$	−7.75666			−0.268270
$837$		−	36.4078i		−	1.25844i
$838$		−	77.5200i		−	2.67788i
$839$	−38.8677			−1.34186			−0.670931	−	0.741520i	$-0.734105\pi$
$839$	−38.8677			−1.34186			−0.670931	+	0.741520i	$0.734105\pi$
$840$	3.28493	−	5.34390i	0.113341	−	0.184382i
$841$	20.0367			0.690922
$842$		−	71.8621i		−	2.47653i
$843$		−	43.4480i		−	1.49643i
$844$	65.7213			2.26222
$845$	−17.3928	−	10.6915i	−0.598332	−	0.367799i
$846$	111.796			3.84361
$847$			2.35930i			0.0810666i
$848$			13.3688i			0.459088i
$849$	43.3669			1.48835
$850$		0			0
$851$	2.13038			0.0730285
$852$			83.4745i			2.85979i
$853$		−	32.0255i		−	1.09653i	−0.836304	−	0.548266i	$-0.815288\pi$
$853$		−	32.0255i		−	1.09653i	0.836304	−	0.548266i	$-0.184712\pi$
$854$	−2.96957			−0.101617
$855$	−52.9696	−	32.5608i	−1.81152	−	1.11355i
$856$	−43.5906			−1.48990
$857$		−	25.6769i		−	0.877107i	−0.898705	−	0.438553i	$-0.855491\pi$
$857$		−	25.6769i		−	0.877107i	0.898705	−	0.438553i	$-0.144509\pi$
$858$			7.77333i			0.265377i
$859$	38.7065			1.32065			0.660324	−	0.750981i	$-0.270419\pi$
$859$	38.7065			1.32065			0.660324	+	0.750981i	$0.270419\pi$
$860$	−10.7888	+	17.5511i	−0.367894	+	0.598486i
$861$	−0.553162			−0.0188517
$862$			19.8643i			0.676582i
$863$			29.5881i			1.00719i	0.863939	+	0.503596i	$0.167990\pi$
$863$			29.5881i			1.00719i	−0.863939	+	0.503596i	$0.832010\pi$
$864$	33.6243			1.14392
$865$	−20.4395	+	33.2509i	−0.694965	+	1.13056i
$866$	−32.4036			−1.10112
$867$		0			0
$868$		−	2.37346i		−	0.0805603i
$869$	−3.53318			−0.119855
$870$	−100.415	−	61.7256i	−3.40438	−	2.09270i
$871$	22.6456			0.767317
$872$			56.8890i			1.92651i
$873$			64.0602i			2.16811i
$874$	−3.55705			−0.120319
$875$	−2.45120	−	0.203161i	−0.0828656	−	0.00686808i
$876$	13.8127			0.466689
$877$			26.4995i			0.894825i	0.894328	+	0.447413i	$0.147654\pi$
$877$			26.4995i			0.894825i	−0.894328	+	0.447413i	$0.852346\pi$
$878$		−	48.6105i		−	1.64053i
$879$	−62.7367			−2.11606
$880$	2.25761	+	1.38777i	0.0761040	+	0.0467816i
$881$	10.9924			0.370344			0.185172	−	0.982706i	$-0.440716\pi$
$881$	10.9924			0.370344			0.185172	+	0.982706i	$0.440716\pi$
$882$		−	115.313i		−	3.88279i
$883$			56.2202i			1.89196i	0.324225	+	0.945980i	$0.394896\pi$
$883$			56.2202i			1.89196i	−0.324225	+	0.945980i	$0.605104\pi$
$884$		0			0
$885$	22.1640	−	36.0562i	0.745034	−	1.21201i
$886$	5.85481			0.196696
$887$			6.90120i			0.231720i	0.993266	+	0.115860i	$0.0369623\pi$
$887$			6.90120i			0.231720i	−0.993266	+	0.115860i	$0.963038\pi$
$888$		−	72.8958i		−	2.44622i
$889$	2.14284			0.0718685
$890$	−44.6659	+	72.6621i	−1.49720	+	2.43564i
$891$	−9.69582			−0.324822
$892$			7.26658i			0.243303i
$893$		−	26.9582i		−	0.902122i
$894$	−65.8090			−2.20098
$895$	−40.6225	−	24.9709i	−1.35786	−	0.834685i
$896$	4.56226			0.152414
$897$			2.31261i			0.0772158i
$898$			7.62919i			0.254589i
$899$	−20.4520			−0.682113
$900$	57.9735	+	114.563i	1.93245	+	3.81875i
$901$		0			0
$902$		−	0.998442i		−	0.0332445i
$903$		−	1.73094i		−	0.0576020i
$904$	29.0604			0.966534
$905$	27.5036	+	16.9066i	0.914249	+	0.561995i
$906$	119.713			3.97718
$907$			31.2128i			1.03640i	0.855258	+	0.518202i	$0.173399\pi$
$907$			31.2128i			1.03640i	−0.855258	+	0.518202i	$0.826601\pi$
$908$			44.1746i			1.46598i
$909$	50.1156			1.66223
$910$	−1.20921	+	1.96713i	−0.0400850	+	0.0652099i
$911$	42.4932			1.40786			0.703931	−	0.710268i	$-0.251426\pi$
$911$	42.4932			1.40786			0.703931	+	0.710268i	$0.251426\pi$
$912$			28.4875i			0.943317i
$913$		−	3.21129i		−	0.106278i
$914$	−72.0164			−2.38209
$915$	20.8964	−	33.9941i	0.690813	−	1.12381i
$916$	34.3763			1.13583
$917$			4.33076i			0.143014i
$918$		0			0
$919$	−29.1312			−0.960949			−0.480475	−	0.877009i	$-0.659536\pi$
$919$	−29.1312			−0.960949			−0.480475	+	0.877009i	$0.659536\pi$
$920$	2.86962	+	1.76397i	0.0946085	+	0.0581565i
$921$	−47.1923			−1.55504
$922$			12.9220i			0.425562i
$923$		−	14.0911i		−	0.463814i
$924$	−1.34577			−0.0442726
$925$	−25.5033	+	12.9058i	−0.838545	+	0.424339i
$926$	−37.6004			−1.23562
$927$		−	66.2109i		−	2.17465i
$928$		−	18.8884i		−	0.620041i
$929$	−1.30273			−0.0427412			−0.0213706	−	0.999772i	$-0.506803\pi$
$929$	−1.30273			−0.0427412			−0.0213706	+	0.999772i	$0.506803\pi$
$930$	41.8805	+	25.7442i	1.37332	+	0.844187i
$931$	−27.8064			−0.911318
$932$			95.3084i			3.12193i
$933$			93.5463i			3.06257i
$934$	−25.6971			−0.840836
$935$		0			0
$936$	55.2764			1.80677
$937$		−	9.43458i		−	0.308214i	−0.988054	−	0.154107i	$-0.950750\pi$
$937$		−	9.43458i		−	0.308214i	0.988054	−	0.154107i	$-0.0492501\pi$
$938$			6.04321i			0.197318i
$939$	45.3584			1.48021
$940$	−29.1526	+	47.4252i	−0.950853	+	1.54684i
$941$	25.1776			0.820767			0.410383	−	0.911913i	$-0.365395\pi$
$941$	25.1776			0.820767			0.410383	+	0.911913i	$0.365395\pi$
$942$			75.8167i			2.47024i
$943$		−	0.297042i		−	0.00967302i
$944$	−13.5456			−0.440873
$945$	−5.22410	−	3.21129i	−0.169940	−	0.104463i
$946$	3.12430			0.101580
$947$		−	27.6569i		−	0.898727i	−0.893349	−	0.449364i	$-0.851651\pi$
$947$		−	27.6569i		−	0.898727i	0.893349	−	0.449364i	$-0.148349\pi$
$948$			78.4315i			2.54734i
$949$	−2.33169			−0.0756898
$950$	42.5824	−	21.5485i	1.38156	−	0.699126i
$951$	43.4552			1.40913
$952$		0			0
$953$			16.0279i			0.519195i	0.965717	+	0.259598i	$0.0835899\pi$
$953$			16.0279i			0.519195i	−0.965717	+	0.259598i	$0.916410\pi$
$954$	98.2288			3.18027
$955$	−12.8439	−	7.89521i	−0.415618	−	0.255483i
$956$	108.202			3.49949
$957$			11.5965i			0.374860i
$958$		−	88.0732i		−	2.84552i
$959$	−1.02449			−0.0330827
$960$	−40.4552	+	65.8121i	−1.30568	+	2.12408i
$961$	−22.4700			−0.724838
$962$			26.8336i			0.865149i
$963$			74.9648i			2.41571i
$964$	31.3446			1.00954
$965$	17.1608	−	27.9171i	0.552426	−	0.898682i
$966$	−0.617144			−0.0198563
$967$			10.9849i			0.353252i	0.984278	+	0.176626i	$0.0565183\pi$
$967$			10.9849i			0.353252i	−0.984278	+	0.176626i	$0.943482\pi$
$968$			43.3506i			1.39334i
$969$		0			0
$970$	−41.8884	−	25.7491i	−1.34496	−	0.826753i
$971$	32.2944			1.03638			0.518188	−	0.855267i	$-0.326607\pi$
$971$	32.2944			1.03638			0.518188	+	0.855267i	$0.326607\pi$
$972$			77.0874i			2.47258i
$973$		−	1.15449i		−	0.0370113i
$974$	91.4476			2.93017
$975$	−14.0097	−	27.6848i	−0.448670	−	0.886625i
$976$	−12.7710			−0.408788
$977$		−	2.59459i		−	0.0830084i	−0.999138	−	0.0415042i	$-0.986785\pi$
$977$		−	2.59459i		−	0.0830084i	0.999138	−	0.0415042i	$-0.0132150\pi$
$978$			72.1732i			2.30784i
$979$	8.39143			0.268191
$980$	48.9174	+	30.0698i	1.56261	+	0.960546i
$981$	97.8347			3.12362
$982$			90.7561i			2.89614i
$983$		−	9.61652i		−	0.306719i	−0.988170	−	0.153360i	$-0.950991\pi$
$983$		−	9.61652i		−	0.306719i	0.988170	−	0.153360i	$-0.0490093\pi$
$984$	−10.1640			−0.324015
$985$	−1.01796	+	1.65602i	−0.0324351	+	0.0527651i
$986$		0			0
$987$		−	4.67721i		−	0.148877i
$988$		−	29.0663i		−	0.924723i
$989$	0.929495			0.0295562
$990$	10.1967	−	16.5880i	0.324074	−	0.527201i
$991$	28.2650			0.897867			0.448933	−	0.893565i	$-0.351804\pi$
$991$	28.2650			0.897867			0.448933	+	0.893565i	$0.351804\pi$
$992$			7.87787i			0.250123i
$993$			63.6096i			2.01859i
$994$	3.76036			0.119271
$995$	−25.3364	−	15.5745i	−0.803219	−	0.493744i
$996$	−71.2859			−2.25878
$997$			3.34593i			0.105967i	0.998595	+	0.0529833i	$0.0168730\pi$
$997$			3.34593i			0.105967i	−0.998595	+	0.0529833i	$0.983127\pi$
$998$		−	22.2063i		−	0.702928i
$999$	−71.2616			−2.25462

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.b.f.579.11		12
5.2	odd	4		7225.2.a.bp.1.1		12
5.3	odd	4		7225.2.a.bp.1.12		12
5.4	even	2	inner	1445.2.b.f.579.2		12
17.8	even	8		85.2.j.c.64.6	yes	12
17.15	even	8		85.2.j.c.4.1	✓	12
17.16	even	2	inner	1445.2.b.f.579.12		12
51.8	odd	8		765.2.t.e.64.1		12
51.32	odd	8		765.2.t.e.514.6		12
85.8	odd	8		425.2.e.d.251.1		12
85.32	odd	8		425.2.e.d.276.1		12
85.33	odd	4		7225.2.a.bp.1.11		12
85.42	odd	8		425.2.e.d.251.6		12
85.49	even	8		85.2.j.c.4.6	yes	12
85.59	even	8		85.2.j.c.64.1	yes	12
85.67	odd	4		7225.2.a.bp.1.2		12
85.83	odd	8		425.2.e.d.276.6		12
85.84	even	2	inner	1445.2.b.f.579.1		12
255.59	odd	8		765.2.t.e.64.6		12
255.134	odd	8		765.2.t.e.514.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.1	✓	12	17.15	even	8
85.2.j.c.4.6	yes	12	85.49	even	8
85.2.j.c.64.1	yes	12	85.59	even	8
85.2.j.c.64.6	yes	12	17.8	even	8
425.2.e.d.251.1		12	85.8	odd	8
425.2.e.d.251.6		12	85.42	odd	8
425.2.e.d.276.1		12	85.32	odd	8
425.2.e.d.276.6		12	85.83	odd	8
765.2.t.e.64.1		12	51.8	odd	8
765.2.t.e.64.6		12	255.59	odd	8
765.2.t.e.514.1		12	255.134	odd	8
765.2.t.e.514.6		12	51.32	odd	8
1445.2.b.f.579.1		12	85.84	even	2	inner
1445.2.b.f.579.2		12	5.4	even	2	inner
1445.2.b.f.579.11		12	1.1	even	1	trivial
1445.2.b.f.579.12		12	17.16	even	2	inner
7225.2.a.bp.1.1		12	5.2	odd	4
7225.2.a.bp.1.2		12	85.67	odd	4
7225.2.a.bp.1.11		12	85.33	odd	4
7225.2.a.bp.1.12		12	5.3	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)

\(f(q)\)	\(=\)	\(q+2.38621i q^{2} -3.15462i q^{3} -3.69399 q^{4} +(-1.90494 - 1.17098i) q^{5} +7.52757 q^{6} -0.219993i q^{7} -4.04223i q^{8} -6.95160 q^{9} +(2.79421 - 4.54559i) q^{10} -0.524950 q^{11} +11.6531i q^{12} -1.96713i q^{13} +0.524950 q^{14} +(-3.69399 + 6.00936i) q^{15} +2.25761 q^{16} -16.5880i q^{18} -4.00000 q^{19} +(7.03685 + 4.32560i) q^{20} -0.693995 q^{21} -1.25264i q^{22} -0.372668i q^{23} -12.7517 q^{24} +(2.25761 + 4.46130i) q^{25} +4.69399 q^{26} +12.4658i q^{27} +0.812655i q^{28} +7.00262 q^{29} +(-14.3396 - 8.81464i) q^{30} -2.92062 q^{31} -2.69733i q^{32} +1.65602i q^{33} +(-0.257608 + 0.419075i) q^{35} +25.6792 q^{36} +5.71657i q^{37} -9.54484i q^{38} -6.20555 q^{39} +(-4.73337 + 7.70021i) q^{40} +0.797070 q^{41} -1.65602i q^{42} +2.49417i q^{43} +1.93916 q^{44} +(13.2424 + 8.14019i) q^{45} +0.889263 q^{46} +6.73955i q^{47} -7.12189i q^{48} +6.95160 q^{49} +(-10.6456 + 5.38713i) q^{50} +7.26658i q^{52} +5.92169i q^{53} -29.7460 q^{54} +(1.00000 + 0.614707i) q^{55} -0.889263 q^{56} +12.6185i q^{57} +16.7097i q^{58} -6.00000 q^{59} +(13.6456 - 22.1985i) q^{60} -5.65685 q^{61} -6.96921i q^{62} +1.52931i q^{63} +10.9516 q^{64} +(-2.30348 + 3.74728i) q^{65} -3.95160 q^{66} +11.5120i q^{67} -1.17562 q^{69} +(-1.00000 - 0.614707i) q^{70} +7.16326 q^{71} +28.1000i q^{72} -1.18532i q^{73} -13.6409 q^{74} +(14.0737 - 7.12189i) q^{75} +14.7760 q^{76} +0.115486i q^{77} -14.8078i q^{78} +6.73050 q^{79} +(-4.30061 - 2.64362i) q^{80} +18.4700 q^{81} +1.90197i q^{82} +6.11732i q^{83} +2.56361 q^{84} -5.95160 q^{86} -22.0906i q^{87} +2.12197i q^{88} -15.9852 q^{89} +(-19.4242 + 31.5991i) q^{90} -0.432757 q^{91} +1.37663i q^{92} +9.21344i q^{93} -16.0820 q^{94} +(7.61977 + 4.68392i) q^{95} -8.50903 q^{96} -9.21517i q^{97} +16.5880i q^{98} +3.64925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 28 q^{9} - 12 q^{15} + 4 q^{16} - 48 q^{19} + 24 q^{21} + 4 q^{25} + 24 q^{26} - 52 q^{30} + 20 q^{35} + 68 q^{36} + 28 q^{49} - 40 q^{50} + 12 q^{55} - 72 q^{59} + 76 q^{60} + 76 q^{64}+ \cdots - 96 q^{94}+O(q^{100}) \) 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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