LMFDB - Embedded newform 1110.2.d.h.889.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1110,2,Mod(889,1110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1110, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("1110.889"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4,4,4] 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			889.3
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1110.889
Dual form			1110.2.d.h.889.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-0.224745 + 2.22474i) q^{5} +1.00000 q^{6} +3.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-2.22474 - 0.224745i) q^{10} +1.44949 q^{11} +1.00000i q^{12} -0.550510i q^{13} -3.44949 q^{14} +(2.22474 + 0.224745i) q^{15} +1.00000 q^{16} +3.44949i q^{17} -1.00000i q^{18} -3.00000 q^{19} +(0.224745 - 2.22474i) q^{20} +3.44949 q^{21} +1.44949i q^{22} -1.00000i q^{23} -1.00000 q^{24} +(-4.89898 - 1.00000i) q^{25} +0.550510 q^{26} +1.00000i q^{27} -3.44949i q^{28} -3.55051 q^{29} +(-0.224745 + 2.22474i) q^{30} -2.00000 q^{31} +1.00000i q^{32} -1.44949i q^{33} -3.44949 q^{34} +(-7.67423 - 0.775255i) q^{35} +1.00000 q^{36} -1.00000i q^{37} -3.00000i q^{38} -0.550510 q^{39} +(2.22474 + 0.224745i) q^{40} -0.449490 q^{41} +3.44949i q^{42} +6.89898i q^{43} -1.44949 q^{44} +(0.224745 - 2.22474i) q^{45} +1.00000 q^{46} -6.44949i q^{47} -1.00000i q^{48} -4.89898 q^{49} +(1.00000 - 4.89898i) q^{50} +3.44949 q^{51} +0.550510i q^{52} +3.00000i q^{53} -1.00000 q^{54} +(-0.325765 + 3.22474i) q^{55} +3.44949 q^{56} +3.00000i q^{57} -3.55051i q^{58} +3.34847 q^{59} +(-2.22474 - 0.224745i) q^{60} -14.8990 q^{61} -2.00000i q^{62} -3.44949i q^{63} -1.00000 q^{64} +(1.22474 + 0.123724i) q^{65} +1.44949 q^{66} +6.89898i q^{67} -3.44949i q^{68} -1.00000 q^{69} +(0.775255 - 7.67423i) q^{70} -1.34847 q^{71} +1.00000i q^{72} +8.79796i q^{73} +1.00000 q^{74} +(-1.00000 + 4.89898i) q^{75} +3.00000 q^{76} +5.00000i q^{77} -0.550510i q^{78} -13.3485 q^{79} +(-0.224745 + 2.22474i) q^{80} +1.00000 q^{81} -0.449490i q^{82} +1.44949i q^{83} -3.44949 q^{84} +(-7.67423 - 0.775255i) q^{85} -6.89898 q^{86} +3.55051i q^{87} -1.44949i q^{88} -0.348469 q^{89} +(2.22474 + 0.224745i) q^{90} +1.89898 q^{91} +1.00000i q^{92} +2.00000i q^{93} +6.44949 q^{94} +(0.674235 - 6.67423i) q^{95} +1.00000 q^{96} +3.34847i q^{97} -4.89898i q^{98} -1.44949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{14} + 4 q^{15} + 4 q^{16} - 12 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{24} + 12 q^{26} - 24 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{34} - 16 q^{35}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^14 + 4 * q^15 + 4 * q^16 - 12 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^24 + 12 * q^26 - 24 * q^29 + 4 * q^30 - 8 * q^31 - 4 * q^34 - 16 * q^35 + 4 * q^36 - 12 * q^39 + 4 * q^40 + 8 * q^41 + 4 * q^44 - 4 * q^45 + 4 * q^46 + 4 * q^50 + 4 * q^51 - 4 * q^54 - 16 * q^55 + 4 * q^56 - 16 * q^59 - 4 * q^60 - 40 * q^61 - 4 * q^64 - 4 * q^66 - 4 * q^69 + 8 * q^70 + 24 * q^71 + 4 * q^74 - 4 * q^75 + 12 * q^76 - 24 * q^79 + 4 * q^80 + 4 * q^81 - 4 * q^84 - 16 * q^85 - 8 * q^86 + 28 * q^89 + 4 * q^90 - 12 * q^91 + 16 * q^94 - 12 * q^95 + 4 * q^96 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	−0.224745	+	2.22474i	−0.100509	+	0.994936i
$5$	−0.224745	+	2.22474i	−0.100509	+	0.994936i
$6$	1.00000			0.408248
$7$			3.44949i			1.30378i	0.758312	+	0.651892i	$0.226025\pi$
$7$			3.44949i			1.30378i	−0.758312	+	0.651892i	$0.773975\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−2.22474	−	0.224745i	−0.703526	−	0.0710706i
$11$	1.44949			0.437038			0.218519	−	0.975833i	$-0.429878\pi$
$11$	1.44949			0.437038			0.218519	+	0.975833i	$0.429878\pi$
$12$			1.00000i			0.288675i
$13$		−	0.550510i		−	0.152684i	−0.997082	−	0.0763420i	$-0.975676\pi$
$13$		−	0.550510i		−	0.152684i	0.997082	−	0.0763420i	$-0.0243241\pi$
$14$	−3.44949			−0.921915
$15$	2.22474	+	0.224745i	0.574427	+	0.0580289i
$16$	1.00000			0.250000
$17$			3.44949i			0.836624i	0.908303	+	0.418312i	$0.137378\pi$
$17$			3.44949i			0.836624i	−0.908303	+	0.418312i	$0.862622\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−3.00000			−0.688247			−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000			−0.688247			−0.344124	+	0.938924i	$0.611824\pi$
$20$	0.224745	−	2.22474i	0.0502545	−	0.497468i
$21$	3.44949			0.752740
$22$			1.44949i			0.309032i
$23$		−	1.00000i		−	0.208514i	−0.994550	−	0.104257i	$-0.966753\pi$
$23$		−	1.00000i		−	0.208514i	0.994550	−	0.104257i	$-0.0332465\pi$
$24$	−1.00000			−0.204124
$25$	−4.89898	−	1.00000i	−0.979796	−	0.200000i
$26$	0.550510			0.107964
$27$			1.00000i			0.192450i
$28$		−	3.44949i		−	0.651892i
$29$	−3.55051			−0.659313			−0.329657	−	0.944101i	$-0.606933\pi$
$29$	−3.55051			−0.659313			−0.329657	+	0.944101i	$0.606933\pi$
$30$	−0.224745	+	2.22474i	−0.0410326	+	0.406181i
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$			1.00000i			0.176777i
$33$		−	1.44949i		−	0.252324i
$34$	−3.44949			−0.591583
$35$	−7.67423	−	0.775255i	−1.29718	−	0.131042i
$36$	1.00000			0.166667
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		−	3.00000i		−	0.486664i
$39$	−0.550510			−0.0881522
$40$	2.22474	+	0.224745i	0.351763	+	0.0355353i
$41$	−0.449490			−0.0701985			−0.0350993	−	0.999384i	$-0.511175\pi$
$41$	−0.449490			−0.0701985			−0.0350993	+	0.999384i	$0.511175\pi$
$42$			3.44949i			0.532268i
$43$			6.89898i			1.05208i	0.850458	+	0.526042i	$0.176325\pi$
$43$			6.89898i			1.05208i	−0.850458	+	0.526042i	$0.823675\pi$
$44$	−1.44949			−0.218519
$45$	0.224745	−	2.22474i	0.0335030	−	0.331645i
$46$	1.00000			0.147442
$47$		−	6.44949i		−	0.940755i	−0.882465	−	0.470377i	$-0.844118\pi$
$47$		−	6.44949i		−	0.940755i	0.882465	−	0.470377i	$-0.155882\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−4.89898			−0.699854
$50$	1.00000	−	4.89898i	0.141421	−	0.692820i
$51$	3.44949			0.483025
$52$			0.550510i			0.0763420i
$53$			3.00000i			0.412082i	0.978543	+	0.206041i	$0.0660580\pi$
$53$			3.00000i			0.412082i	−0.978543	+	0.206041i	$0.933942\pi$
$54$	−1.00000			−0.136083
$55$	−0.325765	+	3.22474i	−0.0439262	+	0.434825i
$56$	3.44949			0.460957
$57$			3.00000i			0.397360i
$58$		−	3.55051i		−	0.466205i
$59$	3.34847			0.435934			0.217967	−	0.975956i	$-0.430058\pi$
$59$	3.34847			0.435934			0.217967	+	0.975956i	$0.430058\pi$
$60$	−2.22474	−	0.224745i	−0.287213	−	0.0290144i
$61$	−14.8990			−1.90762			−0.953809	−	0.300412i	$-0.902876\pi$
$61$	−14.8990			−1.90762			−0.953809	+	0.300412i	$0.902876\pi$
$62$		−	2.00000i		−	0.254000i
$63$		−	3.44949i		−	0.434595i
$64$	−1.00000			−0.125000
$65$	1.22474	+	0.123724i	0.151911	+	0.0153461i
$66$	1.44949			0.178420
$67$			6.89898i			0.842844i	0.906865	+	0.421422i	$0.138469\pi$
$67$			6.89898i			0.842844i	−0.906865	+	0.421422i	$0.861531\pi$
$68$		−	3.44949i		−	0.418312i
$69$	−1.00000			−0.120386
$70$	0.775255	−	7.67423i	0.0926607	−	0.917246i
$71$	−1.34847			−0.160034			−0.0800169	−	0.996794i	$-0.525497\pi$
$71$	−1.34847			−0.160034			−0.0800169	+	0.996794i	$0.525497\pi$
$72$			1.00000i			0.117851i
$73$			8.79796i			1.02972i	0.857273	+	0.514862i	$0.172157\pi$
$73$			8.79796i			1.02972i	−0.857273	+	0.514862i	$0.827843\pi$
$74$	1.00000			0.116248
$75$	−1.00000	+	4.89898i	−0.115470	+	0.565685i
$76$	3.00000			0.344124
$77$			5.00000i			0.569803i
$78$		−	0.550510i		−	0.0623330i
$79$	−13.3485			−1.50182			−0.750910	−	0.660404i	$-0.770385\pi$
$79$	−13.3485			−1.50182			−0.750910	+	0.660404i	$0.770385\pi$
$80$	−0.224745	+	2.22474i	−0.0251272	+	0.248734i
$81$	1.00000			0.111111
$82$		−	0.449490i		−	0.0496378i
$83$			1.44949i			0.159102i	0.996831	+	0.0795511i	$0.0253487\pi$
$83$			1.44949i			0.159102i	−0.996831	+	0.0795511i	$0.974651\pi$
$84$	−3.44949			−0.376370
$85$	−7.67423	−	0.775255i	−0.832388	−	0.0840882i
$86$	−6.89898			−0.743936
$87$			3.55051i			0.380655i
$88$		−	1.44949i		−	0.154516i
$89$	−0.348469			−0.0369377			−0.0184688	−	0.999829i	$-0.505879\pi$
$89$	−0.348469			−0.0369377			−0.0184688	+	0.999829i	$0.505879\pi$
$90$	2.22474	+	0.224745i	0.234509	+	0.0236902i
$91$	1.89898			0.199067
$92$			1.00000i			0.104257i
$93$			2.00000i			0.207390i
$94$	6.44949			0.665214
$95$	0.674235	−	6.67423i	0.0691750	−	0.684762i
$96$	1.00000			0.102062
$97$			3.34847i			0.339986i	0.985445	+	0.169993i	$0.0543744\pi$
$97$			3.34847i			0.339986i	−0.985445	+	0.169993i	$0.945626\pi$
$98$		−	4.89898i		−	0.494872i
$99$	−1.44949			−0.145679
$100$	4.89898	+	1.00000i	0.489898	+	0.100000i
$101$	10.0000			0.995037			0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000			0.995037			0.497519	+	0.867453i	$0.334245\pi$
$102$			3.44949i			0.341550i
$103$			10.2474i			1.00971i	0.863204	+	0.504856i	$0.168454\pi$
$103$			10.2474i			1.00971i	−0.863204	+	0.504856i	$0.831546\pi$
$104$	−0.550510			−0.0539820
$105$	−0.775255	+	7.67423i	−0.0756572	+	0.748929i
$106$	−3.00000			−0.291386
$107$			1.65153i			0.159660i	0.996809	+	0.0798298i	$0.0254377\pi$
$107$			1.65153i			0.159660i	−0.996809	+	0.0798298i	$0.974562\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−2.34847			−0.224943			−0.112471	−	0.993655i	$-0.535877\pi$
$109$	−2.34847			−0.224943			−0.112471	+	0.993655i	$0.535877\pi$
$110$	−3.22474	−	0.325765i	−0.307467	−	0.0310605i
$111$	−1.00000			−0.0949158
$112$			3.44949i			0.325946i
$113$		−	7.10102i		−	0.668008i	−0.942572	−	0.334004i	$-0.891600\pi$
$113$		−	7.10102i		−	0.668008i	0.942572	−	0.334004i	$-0.108400\pi$
$114$	−3.00000			−0.280976
$115$	2.22474	+	0.224745i	0.207459	+	0.0209576i
$116$	3.55051			0.329657
$117$			0.550510i			0.0508947i
$118$			3.34847i			0.308252i
$119$	−11.8990			−1.09078
$120$	0.224745	−	2.22474i	0.0205163	−	0.203090i
$121$	−8.89898			−0.808998
$122$		−	14.8990i		−	1.34889i
$123$			0.449490i			0.0405291i
$124$	2.00000			0.179605
$125$	3.32577	−	10.6742i	0.297465	−	0.954733i
$126$	3.44949			0.307305
$127$			15.4495i			1.37092i	0.728110	+	0.685460i	$0.240399\pi$
$127$			15.4495i			1.37092i	−0.728110	+	0.685460i	$0.759601\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	6.89898			0.607421
$130$	−0.123724	+	1.22474i	−0.0108513	+	0.107417i
$131$	20.4495			1.78668			0.893340	−	0.449381i	$-0.148355\pi$
$131$	20.4495			1.78668			0.893340	+	0.449381i	$0.148355\pi$
$132$			1.44949i			0.126162i
$133$		−	10.3485i		−	0.897326i
$134$	−6.89898			−0.595981
$135$	−2.22474	−	0.224745i	−0.191476	−	0.0193430i
$136$	3.44949			0.295791
$137$		−	7.34847i		−	0.627822i	−0.949452	−	0.313911i	$-0.898361\pi$
$137$		−	7.34847i		−	0.627822i	0.949452	−	0.313911i	$-0.101639\pi$
$138$		−	1.00000i		−	0.0851257i
$139$	16.6969			1.41622			0.708108	−	0.706104i	$-0.249549\pi$
$139$	16.6969			1.41622			0.708108	+	0.706104i	$0.249549\pi$
$140$	7.67423	+	0.775255i	0.648591	+	0.0655210i
$141$	−6.44949			−0.543145
$142$		−	1.34847i		−	0.113161i
$143$		−	0.797959i		−	0.0667287i
$144$	−1.00000			−0.0833333
$145$	0.797959	−	7.89898i	0.0662669	−	0.655975i
$146$	−8.79796			−0.728124
$147$			4.89898i			0.404061i
$148$			1.00000i			0.0821995i
$149$	3.10102			0.254045			0.127023	−	0.991900i	$-0.459458\pi$
$149$	3.10102			0.254045			0.127023	+	0.991900i	$0.459458\pi$
$150$	−4.89898	−	1.00000i	−0.400000	−	0.0816497i
$151$	7.24745			0.589789			0.294895	−	0.955530i	$-0.404715\pi$
$151$	7.24745			0.589789			0.294895	+	0.955530i	$0.404715\pi$
$152$			3.00000i			0.243332i
$153$		−	3.44949i		−	0.278875i
$154$	−5.00000			−0.402911
$155$	0.449490	−	4.44949i	0.0361039	−	0.357392i
$156$	0.550510			0.0440761
$157$		−	4.00000i		−	0.319235i	−0.987179	−	0.159617i	$-0.948974\pi$
$157$		−	4.00000i		−	0.319235i	0.987179	−	0.159617i	$-0.0510260\pi$
$158$		−	13.3485i		−	1.06195i
$159$	3.00000			0.237915
$160$	−2.22474	−	0.224745i	−0.175882	−	0.0177676i
$161$	3.44949			0.271858
$162$			1.00000i			0.0785674i
$163$			2.10102i			0.164565i	0.996609	+	0.0822823i	$0.0262209\pi$
$163$			2.10102i			0.164565i	−0.996609	+	0.0822823i	$0.973779\pi$
$164$	0.449490			0.0350993
$165$	3.22474	+	0.325765i	0.251046	+	0.0253608i
$166$	−1.44949			−0.112502
$167$		−	0.797959i		−	0.0617479i	−0.999523	−	0.0308740i	$-0.990171\pi$
$167$		−	0.797959i		−	0.0617479i	0.999523	−	0.0308740i	$-0.00982905\pi$
$168$		−	3.44949i		−	0.266134i
$169$	12.6969			0.976688
$170$	0.775255	−	7.67423i	0.0594594	−	0.588587i
$171$	3.00000			0.229416
$172$		−	6.89898i		−	0.526042i
$173$		−	19.6969i		−	1.49753i	−0.662835	−	0.748765i	$-0.730647\pi$
$173$		−	19.6969i		−	1.49753i	0.662835	−	0.748765i	$-0.269353\pi$
$174$	−3.55051			−0.269163
$175$	3.44949	−	16.8990i	0.260757	−	1.27744i
$176$	1.44949			0.109259
$177$		−	3.34847i		−	0.251686i
$178$		−	0.348469i		−	0.0261189i
$179$	22.6969			1.69645			0.848224	−	0.529637i	$-0.177672\pi$
$179$	22.6969			1.69645			0.848224	+	0.529637i	$0.177672\pi$
$180$	−0.224745	+	2.22474i	−0.0167515	+	0.165823i
$181$	3.34847			0.248890			0.124445	−	0.992227i	$-0.460285\pi$
$181$	3.34847			0.248890			0.124445	+	0.992227i	$0.460285\pi$
$182$			1.89898i			0.140762i
$183$			14.8990i			1.10136i
$184$	−1.00000			−0.0737210
$185$	2.22474	+	0.224745i	0.163566	+	0.0165236i
$186$	−2.00000			−0.146647
$187$			5.00000i			0.365636i
$188$			6.44949i			0.470377i
$189$	−3.44949			−0.250913
$190$	6.67423	+	0.674235i	0.484200	+	0.0489141i
$191$	−5.69694			−0.412216			−0.206108	−	0.978529i	$-0.566080\pi$
$191$	−5.69694			−0.412216			−0.206108	+	0.978529i	$0.566080\pi$
$192$			1.00000i			0.0721688i
$193$		−	17.5959i		−	1.26658i	−0.773914	−	0.633291i	$-0.781704\pi$
$193$		−	17.5959i		−	1.26658i	0.773914	−	0.633291i	$-0.218296\pi$
$194$	−3.34847			−0.240406
$195$	0.123724	−	1.22474i	0.00886009	−	0.0877058i
$196$	4.89898			0.349927
$197$			20.7980i			1.48179i	0.671619	+	0.740897i	$0.265599\pi$
$197$			20.7980i			1.48179i	−0.671619	+	0.740897i	$0.734401\pi$
$198$		−	1.44949i		−	0.103011i
$199$	21.7980			1.54522			0.772608	−	0.634883i	$-0.218952\pi$
$199$	21.7980			1.54522			0.772608	+	0.634883i	$0.218952\pi$
$200$	−1.00000	+	4.89898i	−0.0707107	+	0.346410i
$201$	6.89898			0.486616
$202$			10.0000i			0.703598i
$203$		−	12.2474i		−	0.859602i
$204$	−3.44949			−0.241513
$205$	0.101021	−	1.00000i	0.00705558	−	0.0698430i
$206$	−10.2474			−0.713974
$207$			1.00000i			0.0695048i
$208$		−	0.550510i		−	0.0381710i
$209$	−4.34847			−0.300790
$210$	−7.67423	−	0.775255i	−0.529573	−	0.0534977i
$211$	8.44949			0.581687			0.290843	−	0.956771i	$-0.406064\pi$
$211$	8.44949			0.581687			0.290843	+	0.956771i	$0.406064\pi$
$212$		−	3.00000i		−	0.206041i
$213$			1.34847i			0.0923956i
$214$	−1.65153			−0.112896
$215$	−15.3485	−	1.55051i	−1.04676	−	0.105744i
$216$	1.00000			0.0680414
$217$		−	6.89898i		−	0.468333i
$218$		−	2.34847i		−	0.159058i
$219$	8.79796			0.594511
$220$	0.325765	−	3.22474i	0.0219631	−	0.217412i
$221$	1.89898			0.127739
$222$		−	1.00000i		−	0.0671156i
$223$			15.5959i			1.04438i	0.852829	+	0.522190i	$0.174885\pi$
$223$			15.5959i			1.04438i	−0.852829	+	0.522190i	$0.825115\pi$
$224$	−3.44949			−0.230479
$225$	4.89898	+	1.00000i	0.326599	+	0.0666667i
$226$	7.10102			0.472353
$227$		−	8.00000i		−	0.530979i	−0.964114	−	0.265489i	$-0.914466\pi$
$227$		−	8.00000i		−	0.530979i	0.964114	−	0.265489i	$-0.0855335\pi$
$228$		−	3.00000i		−	0.198680i
$229$	1.55051			0.102461			0.0512303	−	0.998687i	$-0.483686\pi$
$229$	1.55051			0.102461			0.0512303	+	0.998687i	$0.483686\pi$
$230$	−0.224745	+	2.22474i	−0.0148192	+	0.146695i
$231$	5.00000			0.328976
$232$			3.55051i			0.233102i
$233$			2.89898i			0.189918i	0.995481	+	0.0949592i	$0.0302721\pi$
$233$			2.89898i			0.189918i	−0.995481	+	0.0949592i	$0.969728\pi$
$234$	−0.550510			−0.0359880
$235$	14.3485	+	1.44949i	0.935991	+	0.0945543i
$236$	−3.34847			−0.217967
$237$			13.3485i			0.867076i
$238$		−	11.8990i		−	0.771296i
$239$	−2.00000			−0.129369			−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000			−0.129369			−0.0646846	+	0.997906i	$0.520604\pi$
$240$	2.22474	+	0.224745i	0.143607	+	0.0145072i
$241$	−14.2474			−0.917759			−0.458879	−	0.888499i	$-0.651749\pi$
$241$	−14.2474			−0.917759			−0.458879	+	0.888499i	$0.651749\pi$
$242$		−	8.89898i		−	0.572048i
$243$		−	1.00000i		−	0.0641500i
$244$	14.8990			0.953809
$245$	1.10102	−	10.8990i	0.0703416	−	0.696310i
$246$	−0.449490			−0.0286584
$247$			1.65153i			0.105084i
$248$			2.00000i			0.127000i
$249$	1.44949			0.0918577
$250$	10.6742	+	3.32577i	0.675098	+	0.210340i
$251$	8.69694			0.548946			0.274473	−	0.961595i	$-0.411497\pi$
$251$	8.69694			0.548946			0.274473	+	0.961595i	$0.411497\pi$
$252$			3.44949i			0.217297i
$253$		−	1.44949i		−	0.0911286i
$254$	−15.4495			−0.969387
$255$	−0.775255	+	7.67423i	−0.0485484	+	0.480579i
$256$	1.00000			0.0625000
$257$		−	5.44949i		−	0.339930i	−0.985450	−	0.169965i	$-0.945635\pi$
$257$		−	5.44949i		−	0.339930i	0.985450	−	0.169965i	$-0.0543654\pi$
$258$			6.89898i			0.429512i
$259$	3.44949			0.214341
$260$	−1.22474	−	0.123724i	−0.0759555	−	0.00767306i
$261$	3.55051			0.219771
$262$			20.4495i			1.26337i
$263$			22.4495i			1.38429i	0.721756	+	0.692147i	$0.243335\pi$
$263$			22.4495i			1.38429i	−0.721756	+	0.692147i	$0.756665\pi$
$264$	−1.44949			−0.0892099
$265$	−6.67423	−	0.674235i	−0.409995	−	0.0414179i
$266$	10.3485			0.634505
$267$			0.348469i			0.0213260i
$268$		−	6.89898i		−	0.421422i
$269$	−22.5959			−1.37770			−0.688849	−	0.724905i	$-0.741884\pi$
$269$	−22.5959			−1.37770			−0.688849	+	0.724905i	$0.741884\pi$
$270$	0.224745	−	2.22474i	0.0136775	−	0.135394i
$271$	−12.8990			−0.783557			−0.391779	−	0.920060i	$-0.628140\pi$
$271$	−12.8990			−0.783557			−0.391779	+	0.920060i	$0.628140\pi$
$272$			3.44949i			0.209156i
$273$		−	1.89898i		−	0.114931i
$274$	7.34847			0.443937
$275$	−7.10102	−	1.44949i	−0.428208	−	0.0874075i
$276$	1.00000			0.0601929
$277$			15.4495i			0.928270i	0.885765	+	0.464135i	$0.153635\pi$
$277$			15.4495i			0.928270i	−0.885765	+	0.464135i	$0.846365\pi$
$278$			16.6969i			1.00142i
$279$	2.00000			0.119737
$280$	−0.775255	+	7.67423i	−0.0463304	+	0.458623i
$281$	4.34847			0.259408			0.129704	−	0.991553i	$-0.458597\pi$
$281$	4.34847			0.259408			0.129704	+	0.991553i	$0.458597\pi$
$282$		−	6.44949i		−	0.384062i
$283$			21.6969i			1.28975i	0.764288	+	0.644875i	$0.223090\pi$
$283$			21.6969i			1.28975i	−0.764288	+	0.644875i	$0.776910\pi$
$284$	1.34847			0.0800169
$285$	−6.67423	−	0.674235i	−0.395348	−	0.0399382i
$286$	0.797959			0.0471843
$287$		−	1.55051i		−	0.0915237i
$288$		−	1.00000i		−	0.0589256i
$289$	5.10102			0.300060
$290$	7.89898	+	0.797959i	0.463844	+	0.0468578i
$291$	3.34847			0.196291
$292$		−	8.79796i		−	0.514862i
$293$			16.1010i			0.940632i	0.882498	+	0.470316i	$0.155860\pi$
$293$			16.1010i			0.940632i	−0.882498	+	0.470316i	$0.844140\pi$
$294$	−4.89898			−0.285714
$295$	−0.752551	+	7.44949i	−0.0438152	+	0.433726i
$296$	−1.00000			−0.0581238
$297$			1.44949i			0.0841079i
$298$			3.10102i			0.179637i
$299$	−0.550510			−0.0318368
$300$	1.00000	−	4.89898i	0.0577350	−	0.282843i
$301$	−23.7980			−1.37169
$302$			7.24745i			0.417044i
$303$		−	10.0000i		−	0.574485i
$304$	−3.00000			−0.172062
$305$	3.34847	−	33.1464i	0.191733	−	1.89796i
$306$	3.44949			0.197194
$307$			20.4495i			1.16711i	0.812072	+	0.583557i	$0.198340\pi$
$307$			20.4495i			1.16711i	−0.812072	+	0.583557i	$0.801660\pi$
$308$		−	5.00000i		−	0.284901i
$309$	10.2474			0.582957
$310$	4.44949	+	0.449490i	0.252714	+	0.0255293i
$311$	30.4949			1.72921			0.864603	−	0.502455i	$-0.167570\pi$
$311$	30.4949			1.72921			0.864603	+	0.502455i	$0.167570\pi$
$312$			0.550510i			0.0311665i
$313$		−	13.5505i		−	0.765920i	−0.923765	−	0.382960i	$-0.874905\pi$
$313$		−	13.5505i		−	0.765920i	0.923765	−	0.382960i	$-0.125095\pi$
$314$	4.00000			0.225733
$315$	7.67423	+	0.775255i	0.432394	+	0.0436807i
$316$	13.3485			0.750910
$317$			8.89898i			0.499816i	0.968270	+	0.249908i	$0.0804005\pi$
$317$			8.89898i			0.499816i	−0.968270	+	0.249908i	$0.919600\pi$
$318$			3.00000i			0.168232i
$319$	−5.14643			−0.288145
$320$	0.224745	−	2.22474i	0.0125636	−	0.124367i
$321$	1.65153			0.0921795
$322$			3.44949i			0.192233i
$323$		−	10.3485i		−	0.575804i
$324$	−1.00000			−0.0555556
$325$	−0.550510	+	2.69694i	−0.0305368	+	0.149599i
$326$	−2.10102			−0.116365
$327$			2.34847i			0.129871i
$328$			0.449490i			0.0248189i
$329$	22.2474			1.22654
$330$	−0.325765	+	3.22474i	−0.0179328	+	0.177516i
$331$	−28.6969			−1.57733			−0.788663	−	0.614825i	$-0.789226\pi$
$331$	−28.6969			−1.57733			−0.788663	+	0.614825i	$0.789226\pi$
$332$		−	1.44949i		−	0.0795511i
$333$			1.00000i			0.0547997i
$334$	0.797959			0.0436624
$335$	−15.3485	−	1.55051i	−0.838576	−	0.0847134i
$336$	3.44949			0.188185
$337$		−	0.101021i		−	0.00550294i	−0.999996	−	0.00275147i	$-0.999124\pi$
$337$		−	0.101021i		−	0.00550294i	0.999996	−	0.00275147i	$-0.000875821\pi$
$338$			12.6969i			0.690622i
$339$	−7.10102			−0.385674
$340$	7.67423	+	0.775255i	0.416194	+	0.0420441i
$341$	−2.89898			−0.156989
$342$			3.00000i			0.162221i
$343$			7.24745i			0.391325i
$344$	6.89898			0.371968
$345$	0.224745	−	2.22474i	0.0120999	−	0.119776i
$346$	19.6969			1.05891
$347$			15.5505i			0.834795i	0.908724	+	0.417398i	$0.137058\pi$
$347$			15.5505i			0.834795i	−0.908724	+	0.417398i	$0.862942\pi$
$348$		−	3.55051i		−	0.190327i
$349$	31.1464			1.66723			0.833615	−	0.552346i	$-0.186267\pi$
$349$	31.1464			1.66723			0.833615	+	0.552346i	$0.186267\pi$
$350$	16.8990	+	3.44949i	0.903288	+	0.184383i
$351$	0.550510			0.0293841
$352$			1.44949i			0.0772581i
$353$		−	16.6969i		−	0.888688i	−0.895856	−	0.444344i	$-0.853437\pi$
$353$		−	16.6969i		−	0.888688i	0.895856	−	0.444344i	$-0.146563\pi$
$354$	3.34847			0.177969
$355$	0.303062	−	3.00000i	0.0160848	−	0.159223i
$356$	0.348469			0.0184688
$357$			11.8990i			0.629761i
$358$			22.6969i			1.19957i
$359$	2.44949			0.129279			0.0646396	−	0.997909i	$-0.479410\pi$
$359$	2.44949			0.129279			0.0646396	+	0.997909i	$0.479410\pi$
$360$	−2.22474	−	0.224745i	−0.117254	−	0.0118451i
$361$	−10.0000			−0.526316
$362$			3.34847i			0.175992i
$363$			8.89898i			0.467075i
$364$	−1.89898			−0.0995336
$365$	−19.5732	−	1.97730i	−1.02451	−	0.103496i
$366$	−14.8990			−0.778782
$367$			25.2474i			1.31791i	0.752184	+	0.658953i	$0.229000\pi$
$367$			25.2474i			1.31791i	−0.752184	+	0.658953i	$0.771000\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	0.449490			0.0233995
$370$	−0.224745	+	2.22474i	−0.0116839	+	0.115659i
$371$	−10.3485			−0.537266
$372$		−	2.00000i		−	0.103695i
$373$		−	31.8434i		−	1.64879i	−0.566017	−	0.824394i	$-0.691516\pi$
$373$		−	31.8434i		−	1.64879i	0.566017	−	0.824394i	$-0.308484\pi$
$374$	−5.00000			−0.258544
$375$	−10.6742	−	3.32577i	−0.551215	−	0.171742i
$376$	−6.44949			−0.332607
$377$			1.95459i			0.100667i
$378$		−	3.44949i		−	0.177423i
$379$	14.6515			0.752599			0.376299	−	0.926498i	$-0.377196\pi$
$379$	14.6515			0.752599			0.376299	+	0.926498i	$0.377196\pi$
$380$	−0.674235	+	6.67423i	−0.0345875	+	0.342381i
$381$	15.4495			0.791501
$382$		−	5.69694i		−	0.291481i
$383$			4.79796i			0.245164i	0.992458	+	0.122582i	$0.0391175\pi$
$383$			4.79796i			0.245164i	−0.992458	+	0.122582i	$0.960883\pi$
$384$	−1.00000			−0.0510310
$385$	−11.1237	−	1.12372i	−0.566917	−	0.0572703i
$386$	17.5959			0.895609
$387$		−	6.89898i		−	0.350695i
$388$		−	3.34847i		−	0.169993i
$389$	0.202041			0.0102439			0.00512194	−	0.999987i	$-0.498370\pi$
$389$	0.202041			0.0102439			0.00512194	+	0.999987i	$0.498370\pi$
$390$	1.22474	+	0.123724i	0.0620174	+	0.00626503i
$391$	3.44949			0.174448
$392$			4.89898i			0.247436i
$393$		−	20.4495i		−	1.03154i
$394$	−20.7980			−1.04779
$395$	3.00000	−	29.6969i	0.150946	−	1.49422i
$396$	1.44949			0.0728396
$397$		−	3.10102i		−	0.155636i	−0.996968	−	0.0778179i	$-0.975205\pi$
$397$		−	3.10102i		−	0.155636i	0.996968	−	0.0778179i	$-0.0247953\pi$
$398$			21.7980i			1.09263i
$399$	−10.3485			−0.518071
$400$	−4.89898	−	1.00000i	−0.244949	−	0.0500000i
$401$	27.9444			1.39548			0.697738	−	0.716353i	$-0.254190\pi$
$401$	27.9444			1.39548			0.697738	+	0.716353i	$0.254190\pi$
$402$			6.89898i			0.344090i
$403$			1.10102i			0.0548457i
$404$	−10.0000			−0.497519
$405$	−0.224745	+	2.22474i	−0.0111677	+	0.110548i
$406$	12.2474			0.607831
$407$		−	1.44949i		−	0.0718485i
$408$		−	3.44949i		−	0.170775i
$409$	3.75255			0.185552			0.0927759	−	0.995687i	$-0.470426\pi$
$409$	3.75255			0.185552			0.0927759	+	0.995687i	$0.470426\pi$
$410$	1.00000	+	0.101021i	0.0493865	+	0.00498905i
$411$	−7.34847			−0.362473
$412$		−	10.2474i		−	0.504856i
$413$			11.5505i			0.568363i
$414$	−1.00000			−0.0491473
$415$	−3.22474	−	0.325765i	−0.158296	−	0.0159912i
$416$	0.550510			0.0269910
$417$		−	16.6969i		−	0.817653i
$418$		−	4.34847i		−	0.212691i
$419$	28.5505			1.39478			0.697392	−	0.716690i	$-0.254344\pi$
$419$	28.5505			1.39478			0.697392	+	0.716690i	$0.254344\pi$
$420$	0.775255	−	7.67423i	0.0378286	−	0.374464i
$421$	−12.8990			−0.628658			−0.314329	−	0.949314i	$-0.601779\pi$
$421$	−12.8990			−0.628658			−0.314329	+	0.949314i	$0.601779\pi$
$422$			8.44949i			0.411315i
$423$			6.44949i			0.313585i
$424$	3.00000			0.145693
$425$	3.44949	−	16.8990i	0.167325	−	0.819721i
$426$	−1.34847			−0.0653335
$427$		−	51.3939i		−	2.48712i
$428$		−	1.65153i		−	0.0798298i
$429$	−0.797959			−0.0385258
$430$	1.55051	−	15.3485i	0.0747722	−	0.740169i
$431$	−19.0000			−0.915198			−0.457599	−	0.889159i	$-0.651290\pi$
$431$	−19.0000			−0.915198			−0.457599	+	0.889159i	$0.651290\pi$
$432$			1.00000i			0.0481125i
$433$			0.595918i			0.0286380i	0.999897	+	0.0143190i	$0.00455803\pi$
$433$			0.595918i			0.0286380i	−0.999897	+	0.0143190i	$0.995442\pi$
$434$	6.89898			0.331162
$435$	−7.89898	−	0.797959i	−0.378727	−	0.0382592i
$436$	2.34847			0.112471
$437$			3.00000i			0.143509i
$438$			8.79796i			0.420383i
$439$	−8.44949			−0.403272			−0.201636	−	0.979461i	$-0.564626\pi$
$439$	−8.44949			−0.403272			−0.201636	+	0.979461i	$0.564626\pi$
$440$	3.22474	+	0.325765i	0.153734	+	0.0155303i
$441$	4.89898			0.233285
$442$			1.89898i			0.0903252i
$443$			13.5959i			0.645962i	0.946406	+	0.322981i	$0.104685\pi$
$443$			13.5959i			0.645962i	−0.946406	+	0.322981i	$0.895315\pi$
$444$	1.00000			0.0474579
$445$	0.0783167	−	0.775255i	0.00371257	−	0.0367506i
$446$	−15.5959			−0.738488
$447$		−	3.10102i		−	0.146673i
$448$		−	3.44949i		−	0.162973i
$449$	3.30306			0.155881			0.0779406	−	0.996958i	$-0.475166\pi$
$449$	3.30306			0.155881			0.0779406	+	0.996958i	$0.475166\pi$
$450$	−1.00000	+	4.89898i	−0.0471405	+	0.230940i
$451$	−0.651531			−0.0306794
$452$			7.10102i			0.334004i
$453$		−	7.24745i		−	0.340515i
$454$	8.00000			0.375459
$455$	−0.426786	+	4.22474i	−0.0200080	+	0.198059i
$456$	3.00000			0.140488
$457$			35.5959i			1.66511i	0.553945	+	0.832553i	$0.313122\pi$
$457$			35.5959i			1.66511i	−0.553945	+	0.832553i	$0.686878\pi$
$458$			1.55051i			0.0724506i
$459$	−3.44949			−0.161008
$460$	−2.22474	−	0.224745i	−0.103729	−	0.0104788i
$461$	8.69694			0.405057			0.202528	−	0.979276i	$-0.435084\pi$
$461$	8.69694			0.405057			0.202528	+	0.979276i	$0.435084\pi$
$462$			5.00000i			0.232621i
$463$		−	25.3485i		−	1.17804i	−0.808117	−	0.589022i	$-0.799513\pi$
$463$		−	25.3485i		−	1.17804i	0.808117	−	0.589022i	$-0.200487\pi$
$464$	−3.55051			−0.164828
$465$	−4.44949	−	0.449490i	−0.206340	−	0.0208446i
$466$	−2.89898			−0.134293
$467$			25.8434i			1.19589i	0.801538	+	0.597944i	$0.204016\pi$
$467$			25.8434i			1.19589i	−0.801538	+	0.597944i	$0.795984\pi$
$468$		−	0.550510i		−	0.0254473i
$469$	−23.7980			−1.09889
$470$	−1.44949	+	14.3485i	−0.0668600	+	0.661846i
$471$	−4.00000			−0.184310
$472$		−	3.34847i		−	0.154126i
$473$			10.0000i			0.459800i
$474$	−13.3485			−0.613115
$475$	14.6969	+	3.00000i	0.674342	+	0.137649i
$476$	11.8990			0.545389
$477$		−	3.00000i		−	0.137361i
$478$		−	2.00000i		−	0.0914779i
$479$	−42.5959			−1.94626			−0.973129	−	0.230262i	$-0.926042\pi$
$479$	−42.5959			−1.94626			−0.973129	+	0.230262i	$0.926042\pi$
$480$	−0.224745	+	2.22474i	−0.0102582	+	0.101545i
$481$	−0.550510			−0.0251011
$482$		−	14.2474i		−	0.648954i
$483$		−	3.44949i		−	0.156957i
$484$	8.89898			0.404499
$485$	−7.44949	−	0.752551i	−0.338264	−	0.0341716i
$486$	1.00000			0.0453609
$487$		−	15.7980i		−	0.715874i	−0.933746	−	0.357937i	$-0.883480\pi$
$487$		−	15.7980i		−	0.715874i	0.933746	−	0.357937i	$-0.116520\pi$
$488$			14.8990i			0.674445i
$489$	2.10102			0.0950114
$490$	10.8990	+	1.10102i	0.492366	+	0.0497390i
$491$	−17.9444			−0.809819			−0.404909	−	0.914357i	$-0.632697\pi$
$491$	−17.9444			−0.809819			−0.404909	+	0.914357i	$0.632697\pi$
$492$		−	0.449490i		−	0.0202646i
$493$		−	12.2474i		−	0.551597i
$494$	−1.65153			−0.0743059
$495$	0.325765	−	3.22474i	0.0146421	−	0.144942i
$496$	−2.00000			−0.0898027
$497$		−	4.65153i		−	0.208650i
$498$			1.44949i			0.0649532i
$499$	−10.5959			−0.474338			−0.237169	−	0.971468i	$-0.576220\pi$
$499$	−10.5959			−0.474338			−0.237169	+	0.971468i	$0.576220\pi$
$500$	−3.32577	+	10.6742i	−0.148733	+	0.477366i
$501$	−0.797959			−0.0356502
$502$			8.69694i			0.388163i
$503$		−	6.00000i		−	0.267527i	−0.991013	−	0.133763i	$-0.957294\pi$
$503$		−	6.00000i		−	0.267527i	0.991013	−	0.133763i	$-0.0427062\pi$
$504$	−3.44949			−0.153652
$505$	−2.24745	+	22.2474i	−0.100010	+	0.989998i
$506$	1.44949			0.0644377
$507$		−	12.6969i		−	0.563891i
$508$		−	15.4495i		−	0.685460i
$509$	16.5959			0.735601			0.367801	−	0.929905i	$-0.380111\pi$
$509$	16.5959			0.735601			0.367801	+	0.929905i	$0.380111\pi$
$510$	−7.67423	−	0.775255i	−0.339821	−	0.0343289i
$511$	−30.3485			−1.34254
$512$			1.00000i			0.0441942i
$513$		−	3.00000i		−	0.132453i
$514$	5.44949			0.240367
$515$	−22.7980	−	2.30306i	−1.00460	−	0.101485i
$516$	−6.89898			−0.303711
$517$		−	9.34847i		−	0.411145i
$518$			3.44949i			0.151562i
$519$	−19.6969			−0.864600
$520$	0.123724	−	1.22474i	0.00542567	−	0.0537086i
$521$	−7.14643			−0.313091			−0.156545	−	0.987671i	$-0.550036\pi$
$521$	−7.14643			−0.313091			−0.156545	+	0.987671i	$0.550036\pi$
$522$			3.55051i			0.155402i
$523$		−	31.3939i		−	1.37276i	−0.727244	−	0.686379i	$-0.759199\pi$
$523$		−	31.3939i		−	1.37276i	0.727244	−	0.686379i	$-0.240801\pi$
$524$	−20.4495			−0.893340
$525$	−16.8990	−	3.44949i	−0.737532	−	0.150548i
$526$	−22.4495			−0.978844
$527$		−	6.89898i		−	0.300524i
$528$		−	1.44949i		−	0.0630809i
$529$	22.0000			0.956522
$530$	0.674235	−	6.67423i	0.0292869	−	0.289910i
$531$	−3.34847			−0.145311
$532$			10.3485i			0.448663i
$533$			0.247449i			0.0107182i
$534$	−0.348469			−0.0150797
$535$	−3.67423	−	0.371173i	−0.158851	−	0.0160472i
$536$	6.89898			0.297991
$537$		−	22.6969i		−	0.979445i
$538$		−	22.5959i		−	0.974179i
$539$	−7.10102			−0.305863
$540$	2.22474	+	0.224745i	0.0957378	+	0.00967148i
$541$	−42.3485			−1.82070			−0.910351	−	0.413836i	$-0.864189\pi$
$541$	−42.3485			−1.82070			−0.910351	+	0.413836i	$0.864189\pi$
$542$		−	12.8990i		−	0.554059i
$543$		−	3.34847i		−	0.143697i
$544$	−3.44949			−0.147896
$545$	0.527806	−	5.22474i	0.0226087	−	0.223803i
$546$	1.89898			0.0812688
$547$			22.7980i			0.974770i	0.873187	+	0.487385i	$0.162049\pi$
$547$			22.7980i			0.974770i	−0.873187	+	0.487385i	$0.837951\pi$
$548$			7.34847i			0.313911i
$549$	14.8990			0.635873
$550$	1.44949	−	7.10102i	0.0618065	−	0.302789i
$551$	10.6515			0.453770
$552$			1.00000i			0.0425628i
$553$		−	46.0454i		−	1.95805i
$554$	−15.4495			−0.656386
$555$	0.224745	−	2.22474i	0.00953989	−	0.0944352i
$556$	−16.6969			−0.708108
$557$			21.5505i			0.913124i	0.889691	+	0.456562i	$0.150919\pi$
$557$			21.5505i			0.913124i	−0.889691	+	0.456562i	$0.849081\pi$
$558$			2.00000i			0.0846668i
$559$	3.79796			0.160637
$560$	−7.67423	−	0.775255i	−0.324296	−	0.0327605i
$561$	5.00000			0.211100
$562$			4.34847i			0.183429i
$563$			28.7423i			1.21135i	0.795714	+	0.605673i	$0.207096\pi$
$563$			28.7423i			1.21135i	−0.795714	+	0.605673i	$0.792904\pi$
$564$	6.44949			0.271573
$565$	15.7980	+	1.59592i	0.664625	+	0.0671408i
$566$	−21.6969			−0.911990
$567$			3.44949i			0.144865i
$568$			1.34847i			0.0565805i
$569$	14.3485			0.601519			0.300760	−	0.953700i	$-0.402760\pi$
$569$	14.3485			0.601519			0.300760	+	0.953700i	$0.402760\pi$
$570$	0.674235	−	6.67423i	0.0282406	−	0.279553i
$571$	−4.44949			−0.186205			−0.0931027	−	0.995657i	$-0.529678\pi$
$571$	−4.44949			−0.186205			−0.0931027	+	0.995657i	$0.529678\pi$
$572$			0.797959i			0.0333643i
$573$			5.69694i			0.237993i
$574$	1.55051			0.0647170
$575$	−1.00000	+	4.89898i	−0.0417029	+	0.204302i
$576$	1.00000			0.0416667
$577$		−	28.6969i		−	1.19467i	−0.801992	−	0.597335i	$-0.796226\pi$
$577$		−	28.6969i		−	1.19467i	0.801992	−	0.597335i	$-0.203774\pi$
$578$			5.10102i			0.212174i
$579$	−17.5959			−0.731261
$580$	−0.797959	+	7.89898i	−0.0331334	+	0.327987i
$581$	−5.00000			−0.207435
$582$			3.34847i			0.138799i
$583$			4.34847i			0.180095i
$584$	8.79796			0.364062
$585$	−1.22474	−	0.123724i	−0.0506370	−	0.00511537i
$586$	−16.1010			−0.665127
$587$			46.2929i			1.91071i	0.295459	+	0.955355i	$0.404527\pi$
$587$			46.2929i			1.91071i	−0.295459	+	0.955355i	$0.595473\pi$
$588$		−	4.89898i		−	0.202031i
$589$	6.00000			0.247226
$590$	−7.44949	−	0.752551i	−0.306691	−	0.0309820i
$591$	20.7980			0.855514
$592$		−	1.00000i		−	0.0410997i
$593$		−	24.0000i		−	0.985562i	−0.870153	−	0.492781i	$-0.835980\pi$
$593$		−	24.0000i		−	0.985562i	0.870153	−	0.492781i	$-0.164020\pi$
$594$	−1.44949			−0.0594733
$595$	2.67423	−	26.4722i	0.109633	−	1.08525i
$596$	−3.10102			−0.127023
$597$		−	21.7980i		−	0.892131i
$598$		−	0.550510i		−	0.0225120i
$599$	29.1464			1.19089			0.595445	−	0.803396i	$-0.296976\pi$
$599$	29.1464			1.19089			0.595445	+	0.803396i	$0.296976\pi$
$600$	4.89898	+	1.00000i	0.200000	+	0.0408248i
$601$	−7.00000			−0.285536			−0.142768	−	0.989756i	$-0.545600\pi$
$601$	−7.00000			−0.285536			−0.142768	+	0.989756i	$0.545600\pi$
$602$		−	23.7980i		−	0.969932i
$603$		−	6.89898i		−	0.280948i
$604$	−7.24745			−0.294895
$605$	2.00000	−	19.7980i	0.0813116	−	0.804901i
$606$	10.0000			0.406222
$607$		−	38.8990i		−	1.57886i	−0.613840	−	0.789430i	$-0.710376\pi$
$607$		−	38.8990i		−	1.57886i	0.613840	−	0.789430i	$-0.289624\pi$
$608$		−	3.00000i		−	0.121666i
$609$	−12.2474			−0.496292
$610$	33.1464	+	3.34847i	1.34206	+	0.135576i
$611$	−3.55051			−0.143638
$612$			3.44949i			0.139437i
$613$		−	22.0000i		−	0.888572i	−0.895885	−	0.444286i	$-0.853457\pi$
$613$		−	22.0000i		−	0.888572i	0.895885	−	0.444286i	$-0.146543\pi$
$614$	−20.4495			−0.825274
$615$	−1.00000	−	0.101021i	−0.0403239	−	0.00407354i
$616$	5.00000			0.201456
$617$		−	32.7423i		−	1.31816i	−0.752074	−	0.659079i	$-0.770946\pi$
$617$		−	32.7423i		−	1.31816i	0.752074	−	0.659079i	$-0.229054\pi$
$618$			10.2474i			0.412213i
$619$	13.5505			0.544641			0.272320	−	0.962207i	$-0.412209\pi$
$619$	13.5505			0.544641			0.272320	+	0.962207i	$0.412209\pi$
$620$	−0.449490	+	4.44949i	−0.0180519	+	0.178696i
$621$	1.00000			0.0401286
$622$			30.4949i			1.22273i
$623$		−	1.20204i		−	0.0481588i
$624$	−0.550510			−0.0220380
$625$	23.0000	+	9.79796i	0.920000	+	0.391918i
$626$	13.5505			0.541587
$627$			4.34847i			0.173661i
$628$			4.00000i			0.159617i
$629$	3.44949			0.137540
$630$	−0.775255	+	7.67423i	−0.0308869	+	0.305749i
$631$	−30.6969			−1.22203			−0.611013	−	0.791621i	$-0.709238\pi$
$631$	−30.6969			−1.22203			−0.611013	+	0.791621i	$0.709238\pi$
$632$			13.3485i			0.530974i
$633$		−	8.44949i		−	0.335837i
$634$	−8.89898			−0.353424
$635$	−34.3712	−	3.47219i	−1.36398	−	0.137790i
$636$	−3.00000			−0.118958
$637$			2.69694i			0.106857i
$638$		−	5.14643i		−	0.203749i
$639$	1.34847			0.0533446
$640$	2.22474	+	0.224745i	0.0879408	+	0.00888382i
$641$	−11.1010			−0.438464			−0.219232	−	0.975673i	$-0.570355\pi$
$641$	−11.1010			−0.438464			−0.219232	+	0.975673i	$0.570355\pi$
$642$			1.65153i			0.0651807i
$643$			18.3031i			0.721802i	0.932604	+	0.360901i	$0.117531\pi$
$643$			18.3031i			0.721802i	−0.932604	+	0.360901i	$0.882469\pi$
$644$	−3.44949			−0.135929
$645$	−1.55051	+	15.3485i	−0.0610513	+	0.604345i
$646$	10.3485			0.407155
$647$		−	29.2020i		−	1.14805i	−0.818838	−	0.574025i	$-0.805381\pi$
$647$		−	29.2020i		−	1.14805i	0.818838	−	0.574025i	$-0.194619\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	4.85357			0.190519
$650$	−2.69694	−	0.550510i	−0.105783	−	0.0215928i
$651$	−6.89898			−0.270392
$652$		−	2.10102i		−	0.0822823i
$653$			34.6969i			1.35780i	0.734233	+	0.678898i	$0.237542\pi$
$653$			34.6969i			1.35780i	−0.734233	+	0.678898i	$0.762458\pi$
$654$	−2.34847			−0.0918324
$655$	−4.59592	+	45.4949i	−0.179577	+	1.77763i
$656$	−0.449490			−0.0175496
$657$		−	8.79796i		−	0.343241i
$658$			22.2474i			0.867296i
$659$	−1.30306			−0.0507601			−0.0253800	−	0.999678i	$-0.508080\pi$
$659$	−1.30306			−0.0507601			−0.0253800	+	0.999678i	$0.508080\pi$
$660$	−3.22474	−	0.325765i	−0.125523	−	0.0126804i
$661$	−39.9444			−1.55366			−0.776828	−	0.629712i	$-0.783173\pi$
$661$	−39.9444			−1.55366			−0.776828	+	0.629712i	$0.783173\pi$
$662$		−	28.6969i		−	1.11534i
$663$		−	1.89898i		−	0.0737503i
$664$	1.44949			0.0562511
$665$	23.0227	+	2.32577i	0.892782	+	0.0901893i
$666$	−1.00000			−0.0387492
$667$			3.55051i			0.137476i
$668$			0.797959i			0.0308740i
$669$	15.5959			0.602973
$670$	1.55051	−	15.3485i	0.0599014	−	0.592963i
$671$	−21.5959			−0.833701
$672$			3.44949i			0.133067i
$673$			5.69694i			0.219601i	0.993954	+	0.109800i	$0.0350212\pi$
$673$			5.69694i			0.219601i	−0.993954	+	0.109800i	$0.964979\pi$
$674$	0.101021			0.00389116
$675$	1.00000	−	4.89898i	0.0384900	−	0.188562i
$676$	−12.6969			−0.488344
$677$			7.00000i			0.269032i	0.990911	+	0.134516i	$0.0429479\pi$
$677$			7.00000i			0.269032i	−0.990911	+	0.134516i	$0.957052\pi$
$678$		−	7.10102i		−	0.272713i
$679$	−11.5505			−0.443268
$680$	−0.775255	+	7.67423i	−0.0297297	+	0.294293i
$681$	−8.00000			−0.306561
$682$		−	2.89898i		−	0.111008i
$683$		−	12.9444i		−	0.495303i	−0.968849	−	0.247652i	$-0.920341\pi$
$683$		−	12.9444i		−	0.495303i	0.968849	−	0.247652i	$-0.0796588\pi$
$684$	−3.00000			−0.114708
$685$	16.3485	+	1.65153i	0.624643	+	0.0631017i
$686$	−7.24745			−0.276709
$687$		−	1.55051i		−	0.0591557i
$688$			6.89898i			0.263021i
$689$	1.65153			0.0629183
$690$	2.22474	+	0.224745i	0.0846946	+	0.00855589i
$691$	39.1464			1.48920			0.744600	−	0.667511i	$-0.232640\pi$
$691$	39.1464			1.48920			0.744600	+	0.667511i	$0.232640\pi$
$692$			19.6969i			0.748765i
$693$		−	5.00000i		−	0.189934i
$694$	−15.5505			−0.590289
$695$	−3.75255	+	37.1464i	−0.142342	+	1.40904i
$696$	3.55051			0.134582
$697$		−	1.55051i		−	0.0587298i
$698$			31.1464i			1.17891i
$699$	2.89898			0.109649
$700$	−3.44949	+	16.8990i	−0.130378	+	0.638721i
$701$	−35.5959			−1.34444			−0.672220	−	0.740352i	$-0.734659\pi$
$701$	−35.5959			−1.34444			−0.672220	+	0.740352i	$0.734659\pi$
$702$			0.550510i			0.0207777i
$703$			3.00000i			0.113147i
$704$	−1.44949			−0.0546297
$705$	1.44949	−	14.3485i	0.0545909	−	0.540395i
$706$	16.6969			0.628398
$707$			34.4949i			1.29731i
$708$			3.34847i			0.125843i
$709$	40.8434			1.53390			0.766952	−	0.641704i	$-0.221772\pi$
$709$	40.8434			1.53390			0.766952	+	0.641704i	$0.221772\pi$
$710$	3.00000	+	0.303062i	0.112588	+	0.0113737i
$711$	13.3485			0.500607
$712$			0.348469i			0.0130594i
$713$			2.00000i			0.0749006i
$714$	−11.8990			−0.445308
$715$	1.77526	+	0.179337i	0.0663908	+	0.00670683i
$716$	−22.6969			−0.848224
$717$			2.00000i			0.0746914i
$718$			2.44949i			0.0914141i
$719$	−1.75255			−0.0653591			−0.0326796	−	0.999466i	$-0.510404\pi$
$719$	−1.75255			−0.0653591			−0.0326796	+	0.999466i	$0.510404\pi$
$720$	0.224745	−	2.22474i	0.00837575	−	0.0829113i
$721$	−35.3485			−1.31645
$722$		−	10.0000i		−	0.372161i
$723$			14.2474i			0.529868i
$724$	−3.34847			−0.124445
$725$	17.3939	+	3.55051i	0.645992	+	0.131863i
$726$	−8.89898			−0.330272
$727$			31.8434i			1.18101i	0.807036	+	0.590503i	$0.201070\pi$
$727$			31.8434i			1.18101i	−0.807036	+	0.590503i	$0.798930\pi$
$728$		−	1.89898i		−	0.0703809i
$729$	−1.00000			−0.0370370
$730$	1.97730	−	19.5732i	0.0731830	−	0.724437i
$731$	−23.7980			−0.880199
$732$		−	14.8990i		−	0.550682i
$733$		−	6.40408i		−	0.236540i	−0.992981	−	0.118270i	$-0.962265\pi$
$733$		−	6.40408i		−	0.236540i	0.992981	−	0.118270i	$-0.0377349\pi$
$734$	−25.2474			−0.931900
$735$	−10.8990	−	1.10102i	−0.402015	−	0.0406118i
$736$	1.00000			0.0368605
$737$			10.0000i			0.368355i
$738$			0.449490i			0.0165459i
$739$	−12.2020			−0.448859			−0.224430	−	0.974490i	$-0.572052\pi$
$739$	−12.2020			−0.448859			−0.224430	+	0.974490i	$0.572052\pi$
$740$	−2.22474	−	0.224745i	−0.0817832	−	0.00826179i
$741$	1.65153			0.0606705
$742$		−	10.3485i		−	0.379904i
$743$			40.0454i			1.46912i	0.678542	+	0.734562i	$0.262612\pi$
$743$			40.0454i			1.46912i	−0.678542	+	0.734562i	$0.737388\pi$
$744$	2.00000			0.0733236
$745$	−0.696938	+	6.89898i	−0.0255338	+	0.252759i
$746$	31.8434			1.16587
$747$		−	1.44949i		−	0.0530341i
$748$		−	5.00000i		−	0.182818i
$749$	−5.69694			−0.208162
$750$	3.32577	−	10.6742i	0.121440	−	0.389768i
$751$	12.8990			0.470690			0.235345	−	0.971912i	$-0.424378\pi$
$751$	12.8990			0.470690			0.235345	+	0.971912i	$0.424378\pi$
$752$		−	6.44949i		−	0.235189i
$753$		−	8.69694i		−	0.316934i
$754$	−1.95459			−0.0711821
$755$	−1.62883	+	16.1237i	−0.0592791	+	0.586802i
$756$	3.44949			0.125457
$757$			41.0454i			1.49182i	0.666046	+	0.745910i	$0.267985\pi$
$757$			41.0454i			1.49182i	−0.666046	+	0.745910i	$0.732015\pi$
$758$			14.6515i			0.532168i
$759$	−1.44949			−0.0526131
$760$	−6.67423	−	0.674235i	−0.242100	−	0.0244571i
$761$	−45.1918			−1.63820			−0.819101	−	0.573649i	$-0.805527\pi$
$761$	−45.1918			−1.63820			−0.819101	+	0.573649i	$0.805527\pi$
$762$			15.4495i			0.559676i
$763$		−	8.10102i		−	0.293277i
$764$	5.69694			0.206108
$765$	7.67423	+	0.775255i	0.277463	+	0.0280294i
$766$	−4.79796			−0.173357
$767$		−	1.84337i		−	0.0665601i
$768$		−	1.00000i		−	0.0360844i
$769$	−8.44949			−0.304696			−0.152348	−	0.988327i	$-0.548684\pi$
$769$	−8.44949			−0.304696			−0.152348	+	0.988327i	$0.548684\pi$
$770$	1.12372	−	11.1237i	0.0404962	−	0.400871i
$771$	−5.44949			−0.196259
$772$			17.5959i			0.633291i
$773$		−	5.69694i		−	0.204905i	−0.994738	−	0.102452i	$-0.967331\pi$
$773$		−	5.69694i		−	0.204905i	0.994738	−	0.102452i	$-0.0326689\pi$
$774$	6.89898			0.247979
$775$	9.79796	+	2.00000i	0.351953	+	0.0718421i
$776$	3.34847			0.120203
$777$		−	3.44949i		−	0.123750i
$778$			0.202041i			0.00724352i
$779$	1.34847			0.0483139
$780$	−0.123724	+	1.22474i	−0.00443004	+	0.0438529i
$781$	−1.95459			−0.0699408
$782$			3.44949i			0.123354i
$783$		−	3.55051i		−	0.126885i
$784$	−4.89898			−0.174964
$785$	8.89898	+	0.898979i	0.317618	+	0.0320860i
$786$	20.4495			0.729409
$787$		−	33.1010i		−	1.17992i	−0.807431	−	0.589962i	$-0.799143\pi$
$787$		−	33.1010i		−	1.17992i	0.807431	−	0.589962i	$-0.200857\pi$
$788$		−	20.7980i		−	0.740897i
$789$	22.4495			0.799223
$790$	29.6969	+	3.00000i	1.05657	+	0.106735i
$791$	24.4949			0.870938
$792$			1.44949i			0.0515054i
$793$			8.20204i			0.291263i
$794$	3.10102			0.110051
$795$	−0.674235	+	6.67423i	−0.0239126	+	0.236711i
$796$	−21.7980			−0.772608
$797$		−	14.2474i		−	0.504671i	−0.967640	−	0.252335i	$-0.918801\pi$
$797$		−	14.2474i		−	0.504671i	0.967640	−	0.252335i	$-0.0811986\pi$
$798$		−	10.3485i		−	0.366332i
$799$	22.2474			0.787058
$800$	1.00000	−	4.89898i	0.0353553	−	0.173205i
$801$	0.348469			0.0123126
$802$			27.9444i			0.986751i
$803$			12.7526i			0.450028i
$804$	−6.89898			−0.243308
$805$	−0.775255	+	7.67423i	−0.0273242	+	0.270481i
$806$	−1.10102			−0.0387818
$807$			22.5959i			0.795414i
$808$		−	10.0000i		−	0.351799i
$809$	44.1464			1.55211			0.776053	−	0.630668i	$-0.217219\pi$
$809$	44.1464			1.55211			0.776053	+	0.630668i	$0.217219\pi$
$810$	−2.22474	−	0.224745i	−0.0781696	−	0.00789673i
$811$	43.1918			1.51667			0.758335	−	0.651865i	$-0.226013\pi$
$811$	43.1918			1.51667			0.758335	+	0.651865i	$0.226013\pi$
$812$			12.2474i			0.429801i
$813$			12.8990i			0.452387i
$814$	1.44949			0.0508046
$815$	−4.67423	−	0.472194i	−0.163731	−	0.0165402i
$816$	3.44949			0.120756
$817$		−	20.6969i		−	0.724094i
$818$			3.75255i			0.131205i
$819$	−1.89898			−0.0663557
$820$	−0.101021	+	1.00000i	−0.00352779	+	0.0349215i
$821$	22.1918			0.774500			0.387250	−	0.921975i	$-0.373425\pi$
$821$	22.1918			0.774500			0.387250	+	0.921975i	$0.373425\pi$
$822$		−	7.34847i		−	0.256307i
$823$		−	16.3485i		−	0.569872i	−0.958547	−	0.284936i	$-0.908028\pi$
$823$		−	16.3485i		−	0.569872i	0.958547	−	0.284936i	$-0.0919723\pi$
$824$	10.2474			0.356987
$825$	−1.44949	+	7.10102i	−0.0504648	+	0.247226i
$826$	−11.5505			−0.401894
$827$			32.0454i			1.11433i	0.830402	+	0.557164i	$0.188111\pi$
$827$			32.0454i			1.11433i	−0.830402	+	0.557164i	$0.811889\pi$
$828$		−	1.00000i		−	0.0347524i
$829$	−29.9444			−1.04001			−0.520006	−	0.854163i	$-0.674070\pi$
$829$	−29.9444			−1.04001			−0.520006	+	0.854163i	$0.674070\pi$
$830$	0.325765	−	3.22474i	0.0113075	−	0.111933i
$831$	15.4495			0.535937
$832$			0.550510i			0.0190855i
$833$		−	16.8990i		−	0.585515i
$834$	16.6969			0.578168
$835$	1.77526	+	0.179337i	0.0614352	+	0.00620622i
$836$	4.34847			0.150395
$837$		−	2.00000i		−	0.0691301i
$838$			28.5505i			0.986261i
$839$	21.3485			0.737031			0.368516	−	0.929622i	$-0.379866\pi$
$839$	21.3485			0.737031			0.368516	+	0.929622i	$0.379866\pi$
$840$	7.67423	+	0.775255i	0.264786	+	0.0267488i
$841$	−16.3939			−0.565306
$842$		−	12.8990i		−	0.444528i
$843$		−	4.34847i		−	0.149769i
$844$	−8.44949			−0.290843
$845$	−2.85357	+	28.2474i	−0.0981659	+	0.971742i
$846$	−6.44949			−0.221738
$847$		−	30.6969i		−	1.05476i
$848$			3.00000i			0.103020i
$849$	21.6969			0.744637
$850$	16.8990	+	3.44949i	0.579630	+	0.118317i
$851$	−1.00000			−0.0342796
$852$		−	1.34847i		−	0.0461978i
$853$			14.8434i			0.508227i	0.967174	+	0.254114i	$0.0817837\pi$
$853$			14.8434i			0.508227i	−0.967174	+	0.254114i	$0.918216\pi$
$854$	51.3939			1.75866
$855$	−0.674235	+	6.67423i	−0.0230583	+	0.228254i
$856$	1.65153			0.0564482
$857$			3.24745i			0.110931i	0.998461	+	0.0554654i	$0.0176642\pi$
$857$			3.24745i			0.110931i	−0.998461	+	0.0554654i	$0.982336\pi$
$858$		−	0.797959i		−	0.0272419i
$859$	16.7980			0.573139			0.286569	−	0.958059i	$-0.407485\pi$
$859$	16.7980			0.573139			0.286569	+	0.958059i	$0.407485\pi$
$860$	15.3485	+	1.55051i	0.523378	+	0.0528720i
$861$	−1.55051			−0.0528412
$862$		−	19.0000i		−	0.647143i
$863$		−	2.44949i		−	0.0833816i	−0.999131	−	0.0416908i	$-0.986726\pi$
$863$		−	2.44949i		−	0.0833816i	0.999131	−	0.0416908i	$-0.0132744\pi$
$864$	−1.00000			−0.0340207
$865$	43.8207	+	4.42679i	1.48995	+	0.150515i
$866$	−0.595918			−0.0202501
$867$		−	5.10102i		−	0.173240i
$868$			6.89898i			0.234167i
$869$	−19.3485			−0.656352
$870$	0.797959	−	7.89898i	0.0270533	−	0.267800i
$871$	3.79796			0.128689
$872$			2.34847i			0.0795292i
$873$		−	3.34847i		−	0.113329i
$874$	−3.00000			−0.101477
$875$	36.8207	+	11.4722i	1.24477	+	0.387831i
$876$	−8.79796			−0.297255
$877$		−	41.3485i		−	1.39624i	−0.715981	−	0.698119i	$-0.754021\pi$
$877$		−	41.3485i		−	1.39624i	0.715981	−	0.698119i	$-0.245979\pi$
$878$		−	8.44949i		−	0.285156i
$879$	16.1010			0.543074
$880$	−0.325765	+	3.22474i	−0.0109815	+	0.108706i
$881$	17.3939			0.586015			0.293007	−	0.956110i	$-0.405344\pi$
$881$	17.3939			0.586015			0.293007	+	0.956110i	$0.405344\pi$
$882$			4.89898i			0.164957i
$883$			21.0000i			0.706706i	0.935490	+	0.353353i	$0.114959\pi$
$883$			21.0000i			0.706706i	−0.935490	+	0.353353i	$0.885041\pi$
$884$	−1.89898			−0.0638696
$885$	7.44949	+	0.752551i	0.250412	+	0.0252967i
$886$	−13.5959			−0.456764
$887$		−	40.2929i		−	1.35290i	−0.736488	−	0.676451i	$-0.763517\pi$
$887$		−	40.2929i		−	1.35290i	0.736488	−	0.676451i	$-0.236483\pi$
$888$			1.00000i			0.0335578i
$889$	−53.2929			−1.78739
$890$	0.775255	+	0.0783167i	0.0259866	+	0.00262518i
$891$	1.44949			0.0485597
$892$		−	15.5959i		−	0.522190i
$893$			19.3485i			0.647472i
$894$	3.10102			0.103714
$895$	−5.10102	+	50.4949i	−0.170508	+	1.68786i
$896$	3.44949			0.115239
$897$			0.550510i			0.0183810i
$898$			3.30306i			0.110225i
$899$	7.10102			0.236832
$900$	−4.89898	−	1.00000i	−0.163299	−	0.0333333i
$901$	−10.3485			−0.344757
$902$		−	0.651531i		−	0.0216936i
$903$			23.7980i			0.791946i
$904$	−7.10102			−0.236176
$905$	−0.752551	+	7.44949i	−0.0250157	+	0.247629i
$906$	7.24745			0.240780
$907$		−	49.2929i		−	1.63674i	−0.574690	−	0.818371i	$-0.694877\pi$
$907$		−	49.2929i		−	1.63674i	0.574690	−	0.818371i	$-0.305123\pi$
$908$			8.00000i			0.265489i
$909$	−10.0000			−0.331679
$910$	−4.22474	−	0.426786i	−0.140049	−	0.0141478i
$911$	14.2020			0.470535			0.235267	−	0.971931i	$-0.424403\pi$
$911$	14.2020			0.470535			0.235267	+	0.971931i	$0.424403\pi$
$912$			3.00000i			0.0993399i
$913$			2.10102i			0.0695336i
$914$	−35.5959			−1.17741
$915$	−33.1464	−	3.34847i	−1.09579	−	0.110697i
$916$	−1.55051			−0.0512303
$917$			70.5403i			2.32945i
$918$		−	3.44949i		−	0.113850i
$919$	−35.1464			−1.15937			−0.579687	−	0.814839i	$-0.696825\pi$
$919$	−35.1464			−1.15937			−0.579687	+	0.814839i	$0.696825\pi$
$920$	0.224745	−	2.22474i	0.00740962	−	0.0733477i
$921$	20.4495			0.673834
$922$			8.69694i			0.286418i
$923$			0.742346i			0.0244346i
$924$	−5.00000			−0.164488
$925$	−1.00000	+	4.89898i	−0.0328798	+	0.161077i
$926$	25.3485			0.833002
$927$		−	10.2474i		−	0.336570i
$928$		−	3.55051i		−	0.116551i
$929$	−1.10102			−0.0361233			−0.0180617	−	0.999837i	$-0.505750\pi$
$929$	−1.10102			−0.0361233			−0.0180617	+	0.999837i	$0.505750\pi$
$930$	0.449490	−	4.44949i	0.0147393	−	0.145905i
$931$	14.6969			0.481673
$932$		−	2.89898i		−	0.0949592i
$933$		−	30.4949i		−	0.998358i
$934$	−25.8434			−0.845621
$935$	−11.1237	−	1.12372i	−0.363785	−	0.0367497i
$936$	0.550510			0.0179940
$937$		−	40.9898i		−	1.33908i	−0.742777	−	0.669539i	$-0.766492\pi$
$937$		−	40.9898i		−	1.33908i	0.742777	−	0.669539i	$-0.233508\pi$
$938$		−	23.7980i		−	0.777031i
$939$	−13.5505			−0.442204
$940$	−14.3485	−	1.44949i	−0.467995	−	0.0472771i
$941$	27.5959			0.899601			0.449801	−	0.893129i	$-0.351495\pi$
$941$	27.5959			0.899601			0.449801	+	0.893129i	$0.351495\pi$
$942$		−	4.00000i		−	0.130327i
$943$			0.449490i			0.0146374i
$944$	3.34847			0.108983
$945$	0.775255	−	7.67423i	0.0252191	−	0.249643i
$946$	−10.0000			−0.325128
$947$		−	27.5505i		−	0.895271i	−0.894216	−	0.447636i	$-0.852266\pi$
$947$		−	27.5505i		−	0.895271i	0.894216	−	0.447636i	$-0.147734\pi$
$948$		−	13.3485i		−	0.433538i
$949$	4.84337			0.157222
$950$	−3.00000	+	14.6969i	−0.0973329	+	0.476832i
$951$	8.89898			0.288569
$952$			11.8990i			0.385648i
$953$		−	17.5505i		−	0.568517i	−0.958748	−	0.284258i	$-0.908253\pi$
$953$		−	17.5505i		−	0.568517i	0.958748	−	0.284258i	$-0.0917474\pi$
$954$	3.00000			0.0971286
$955$	1.28036	−	12.6742i	0.0414314	−	0.410129i
$956$	2.00000			0.0646846
$957$			5.14643i			0.166360i
$958$		−	42.5959i		−	1.37621i
$959$	25.3485			0.818545
$960$	−2.22474	−	0.224745i	−0.0718033	−	0.00725361i
$961$	−27.0000			−0.870968
$962$		−	0.550510i		−	0.0177492i
$963$		−	1.65153i		−	0.0532198i
$964$	14.2474			0.458879
$965$	39.1464	+	3.95459i	1.26017	+	0.127303i
$966$	3.44949			0.110986
$967$		−	59.8434i		−	1.92443i	−0.272286	−	0.962216i	$-0.587780\pi$
$967$		−	59.8434i		−	1.92443i	0.272286	−	0.962216i	$-0.412220\pi$
$968$			8.89898i			0.286024i
$969$	−10.3485			−0.332441
$970$	0.752551	−	7.44949i	0.0241630	−	0.239189i
$971$	−13.5959			−0.436314			−0.218157	−	0.975914i	$-0.570004\pi$
$971$	−13.5959			−0.436314			−0.218157	+	0.975914i	$0.570004\pi$
$972$			1.00000i			0.0320750i
$973$			57.5959i			1.84644i
$974$	15.7980			0.506199
$975$	2.69694	+	0.550510i	0.0863712	+	0.0176304i
$976$	−14.8990			−0.476905
$977$			50.1464i			1.60433i	0.597105	+	0.802163i	$0.296318\pi$
$977$			50.1464i			1.60433i	−0.597105	+	0.802163i	$0.703682\pi$
$978$			2.10102i			0.0671832i
$979$	−0.505103			−0.0161431
$980$	−1.10102	+	10.8990i	−0.0351708	+	0.348155i
$981$	2.34847			0.0749809
$982$		−	17.9444i		−	0.572628i
$983$		−	11.3031i		−	0.360512i	−0.983620	−	0.180256i	$-0.942307\pi$
$983$		−	11.3031i		−	0.360512i	0.983620	−	0.180256i	$-0.0576926\pi$
$984$	0.449490			0.0143292
$985$	−46.2702	−	4.67423i	−1.47429	−	0.148933i
$986$	12.2474			0.390038
$987$		−	22.2474i		−	0.708144i
$988$		−	1.65153i		−	0.0525422i
$989$	6.89898			0.219375
$990$	3.22474	+	0.325765i	0.102489	+	0.0103535i
$991$	−10.2020			−0.324079			−0.162039	−	0.986784i	$-0.551807\pi$
$991$	−10.2020			−0.324079			−0.162039	+	0.986784i	$0.551807\pi$
$992$		−	2.00000i		−	0.0635001i
$993$			28.6969i			0.910670i
$994$	4.65153			0.147538
$995$	−4.89898	+	48.4949i	−0.155308	+	1.53739i
$996$	−1.44949			−0.0459288
$997$		−	3.24745i		−	0.102848i	−0.998677	−	0.0514239i	$-0.983624\pi$
$997$		−	3.24745i		−	0.102848i	0.998677	−	0.0514239i	$-0.0163759\pi$
$998$		−	10.5959i		−	0.335408i
$999$	1.00000			0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.d.h.889.3	yes	4
3.2	odd	2		3330.2.d.h.1999.2		4
5.2	odd	4		5550.2.a.bt.1.1		2
5.3	odd	4		5550.2.a.cc.1.2		2
5.4	even	2	inner	1110.2.d.h.889.1	✓	4
15.14	odd	2		3330.2.d.h.1999.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.d.h.889.1	✓	4	5.4	even	2	inner
1110.2.d.h.889.3	yes	4	1.1	even	1	trivial
3330.2.d.h.1999.2		4	3.2	odd	2
3330.2.d.h.1999.4		4	15.14	odd	2
5550.2.a.bt.1.1		2	5.2	odd	4
5550.2.a.cc.1.2		2	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-0.224745 + 2.22474i) q^{5} +1.00000 q^{6} +3.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-2.22474 - 0.224745i) q^{10} +1.44949 q^{11} +1.00000i q^{12} -0.550510i q^{13} -3.44949 q^{14} +(2.22474 + 0.224745i) q^{15} +1.00000 q^{16} +3.44949i q^{17} -1.00000i q^{18} -3.00000 q^{19} +(0.224745 - 2.22474i) q^{20} +3.44949 q^{21} +1.44949i q^{22} -1.00000i q^{23} -1.00000 q^{24} +(-4.89898 - 1.00000i) q^{25} +0.550510 q^{26} +1.00000i q^{27} -3.44949i q^{28} -3.55051 q^{29} +(-0.224745 + 2.22474i) q^{30} -2.00000 q^{31} +1.00000i q^{32} -1.44949i q^{33} -3.44949 q^{34} +(-7.67423 - 0.775255i) q^{35} +1.00000 q^{36} -1.00000i q^{37} -3.00000i q^{38} -0.550510 q^{39} +(2.22474 + 0.224745i) q^{40} -0.449490 q^{41} +3.44949i q^{42} +6.89898i q^{43} -1.44949 q^{44} +(0.224745 - 2.22474i) q^{45} +1.00000 q^{46} -6.44949i q^{47} -1.00000i q^{48} -4.89898 q^{49} +(1.00000 - 4.89898i) q^{50} +3.44949 q^{51} +0.550510i q^{52} +3.00000i q^{53} -1.00000 q^{54} +(-0.325765 + 3.22474i) q^{55} +3.44949 q^{56} +3.00000i q^{57} -3.55051i q^{58} +3.34847 q^{59} +(-2.22474 - 0.224745i) q^{60} -14.8990 q^{61} -2.00000i q^{62} -3.44949i q^{63} -1.00000 q^{64} +(1.22474 + 0.123724i) q^{65} +1.44949 q^{66} +6.89898i q^{67} -3.44949i q^{68} -1.00000 q^{69} +(0.775255 - 7.67423i) q^{70} -1.34847 q^{71} +1.00000i q^{72} +8.79796i q^{73} +1.00000 q^{74} +(-1.00000 + 4.89898i) q^{75} +3.00000 q^{76} +5.00000i q^{77} -0.550510i q^{78} -13.3485 q^{79} +(-0.224745 + 2.22474i) q^{80} +1.00000 q^{81} -0.449490i q^{82} +1.44949i q^{83} -3.44949 q^{84} +(-7.67423 - 0.775255i) q^{85} -6.89898 q^{86} +3.55051i q^{87} -1.44949i q^{88} -0.348469 q^{89} +(2.22474 + 0.224745i) q^{90} +1.89898 q^{91} +1.00000i q^{92} +2.00000i q^{93} +6.44949 q^{94} +(0.674235 - 6.67423i) q^{95} +1.00000 q^{96} +3.34847i q^{97} -4.89898i q^{98} -1.44949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{14} + 4 q^{15} + 4 q^{16} - 12 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{24} + 12 q^{26} - 24 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{34} - 16 q^{35}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^14 + 4 * q^15 + 4 * q^16 - 12 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^24 + 12 * q^26 - 24 * q^29 + 4 * q^30 - 8 * q^31 - 4 * q^34 - 16 * q^35 + 4 * q^36 - 12 * q^39 + 4 * q^40 + 8 * q^41 + 4 * q^44 - 4 * q^45 + 4 * q^46 + 4 * q^50 + 4 * q^51 - 4 * q^54 - 16 * q^55 + 4 * q^56 - 16 * q^59 - 4 * q^60 - 40 * q^61 - 4 * q^64 - 4 * q^66 - 4 * q^69 + 8 * q^70 + 24 * q^71 + 4 * q^74 - 4 * q^75 + 12 * q^76 - 24 * q^79 + 4 * q^80 + 4 * q^81 - 4 * q^84 - 16 * q^85 - 8 * q^86 + 28 * q^89 + 4 * q^90 - 12 * q^91 + 16 * q^94 - 12 * q^95 + 4 * q^96 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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