LMFDB - Embedded newform 1100.2.q.b.221.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(221,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.4
Character	$\chi$	$=$	1100.221
Dual form			1100.2.q.b.881.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67142 - 1.21436i) q^{3} +(-1.73889 + 1.40580i) q^{5} +1.74835 q^{7} +(0.391935 + 1.20625i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(0.100424 + 0.309072i) q^{13} +(4.61356 - 0.238044i) q^{15} +(-1.79902 + 1.30707i) q^{17} +(2.27220 - 1.65085i) q^{19} +(-2.92223 - 2.12312i) q^{21} +(0.734063 - 2.25921i) q^{23} +(1.04747 - 4.88905i) q^{25} +(-1.10555 + 3.40252i) q^{27} +(0.659243 + 0.478968i) q^{29} +(5.39273 - 3.91805i) q^{31} +(1.67142 - 1.21436i) q^{33} +(-3.04018 + 2.45782i) q^{35} +(0.177894 + 0.547502i) q^{37} +(0.207474 - 0.638540i) q^{39} +(-3.01067 - 9.26590i) q^{41} -6.16418 q^{43} +(-2.37728 - 1.54656i) q^{45} +(-4.31299 - 3.13357i) q^{47} -3.94328 q^{49} +4.59418 q^{51} +(-10.3030 - 7.48559i) q^{53} +(-0.799646 - 2.08820i) q^{55} -5.80254 q^{57} +(1.20707 + 3.71498i) q^{59} +(3.77774 - 11.6267i) q^{61} +(0.685239 + 2.10895i) q^{63} +(-0.609118 - 0.396267i) q^{65} +(-0.675894 + 0.491066i) q^{67} +(-3.97043 + 2.88469i) q^{69} +(-4.87541 - 3.54219i) q^{71} +(3.35224 - 10.3171i) q^{73} +(-7.68784 + 6.89967i) q^{75} +(-0.540269 + 1.66278i) q^{77} +(3.79577 + 2.75779i) q^{79} +(9.05802 - 6.58104i) q^{81} +(-4.51203 + 3.27818i) q^{83} +(1.29083 - 4.80190i) q^{85} +(-0.520234 - 1.60112i) q^{87} +(0.0518342 - 0.159529i) q^{89} +(0.175575 + 0.540365i) q^{91} -13.7715 q^{93} +(-1.63034 + 6.06490i) q^{95} +(-11.5887 - 8.41970i) q^{97} -1.26833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) $ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.67142	−	1.21436i	−0.964997	−	0.701111i	−0.0106911	−	0.999943i	$-0.503403\pi$
$3$	−1.67142	−	1.21436i	−0.964997	−	0.701111i	−0.954306	+	0.298832i	$0.903403\pi$
$4$		0			0
$5$	−1.73889	+	1.40580i	−0.777655	+	0.628691i
$5$	−1.73889	+	1.40580i	−0.777655	+	0.628691i
$6$		0			0
$7$	1.74835			0.660813			0.330407	−	0.943839i	$-0.392814\pi$
$7$	1.74835			0.660813			0.330407	+	0.943839i	$0.392814\pi$
$8$		0			0
$9$	0.391935	+	1.20625i	0.130645	+	0.402084i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$		0			0
$13$	0.100424	+	0.309072i	0.0278525	+	0.0857211i	0.964016	−	0.265842i	$-0.0856501\pi$
$13$	0.100424	+	0.309072i	0.0278525	+	0.0857211i	−0.936164	+	0.351564i	$0.885650\pi$
$14$		0			0
$15$	4.61356	−	0.238044i	1.19122	−	0.0614627i
$16$		0			0
$17$	−1.79902	+	1.30707i	−0.436327	+	0.317010i	−0.784174	−	0.620541i	$-0.786913\pi$
$17$	−1.79902	+	1.30707i	−0.436327	+	0.317010i	0.347847	+	0.937551i	$0.386913\pi$
$18$		0			0
$19$	2.27220	−	1.65085i	0.521279	−	0.378731i	−0.295807	−	0.955248i	$-0.595588\pi$
$19$	2.27220	−	1.65085i	0.521279	−	0.378731i	0.817085	+	0.576517i	$0.195588\pi$
$20$		0			0
$21$	−2.92223	−	2.12312i	−0.637683	−	0.463304i
$22$		0			0
$23$	0.734063	−	2.25921i	0.153063	−	0.471079i	−0.844897	−	0.534930i	$-0.820338\pi$
$23$	0.734063	−	2.25921i	0.153063	−	0.471079i	0.997959	+	0.0638508i	$0.0203382\pi$
$24$		0			0
$25$	1.04747	−	4.88905i	0.209494	−	0.977810i
$26$		0			0
$27$	−1.10555	+	3.40252i	−0.212762	+	0.654815i
$28$		0			0
$29$	0.659243	+	0.478968i	0.122418	+	0.0889421i	0.647310	−	0.762227i	$-0.275894\pi$
$29$	0.659243	+	0.478968i	0.122418	+	0.0889421i	−0.524891	+	0.851169i	$0.675894\pi$
$30$		0			0
$31$	5.39273	−	3.91805i	0.968563	−	0.703702i	0.0134391	−	0.999910i	$-0.495722\pi$
$31$	5.39273	−	3.91805i	0.968563	−	0.703702i	0.955124	+	0.296208i	$0.0957221\pi$
$32$		0			0
$33$	1.67142	−	1.21436i	0.290958	−	0.211393i
$34$		0			0
$35$	−3.04018	+	2.45782i	−0.513885	+	0.415448i
$36$		0			0
$37$	0.177894	+	0.547502i	0.0292456	+	0.0900087i	0.964614	−	0.263666i	$-0.0849318\pi$
$37$	0.177894	+	0.547502i	0.0292456	+	0.0900087i	−0.935368	+	0.353675i	$0.884932\pi$
$38$		0			0
$39$	0.207474	−	0.638540i	0.0332225	−	0.102248i
$40$		0			0
$41$	−3.01067	−	9.26590i	−0.470188	−	1.44709i	−0.852338	−	0.522991i	$-0.824816\pi$
$41$	−3.01067	−	9.26590i	−0.470188	−	1.44709i	0.382150	−	0.924100i	$-0.375184\pi$
$42$		0			0
$43$	−6.16418			−0.940028			−0.470014	−	0.882659i	$-0.655751\pi$
$43$	−6.16418			−0.940028			−0.470014	+	0.882659i	$0.655751\pi$
$44$		0			0
$45$	−2.37728	−	1.54656i	−0.354384	−	0.230547i
$46$		0			0
$47$	−4.31299	−	3.13357i	−0.629114	−	0.457078i	0.226979	−	0.973900i	$-0.427115\pi$
$47$	−4.31299	−	3.13357i	−0.629114	−	0.457078i	−0.856093	+	0.516822i	$0.827115\pi$
$48$		0			0
$49$	−3.94328			−0.563326
$50$		0			0
$51$	4.59418			0.643314
$52$		0			0
$53$	−10.3030	−	7.48559i	−1.41523	−	1.02822i	−0.992536	−	0.121953i	$-0.961084\pi$
$53$	−10.3030	−	7.48559i	−1.41523	−	1.02822i	−0.422694	−	0.906272i	$-0.638916\pi$
$54$		0			0
$55$	−0.799646	−	2.08820i	−0.107824	−	0.281572i
$56$		0			0
$57$	−5.80254			−0.768565
$58$		0			0
$59$	1.20707	+	3.71498i	0.157147	+	0.483649i	0.998372	−	0.0570360i	$-0.0181650\pi$
$59$	1.20707	+	3.71498i	0.157147	+	0.483649i	−0.841225	+	0.540685i	$0.818165\pi$
$60$		0			0
$61$	3.77774	−	11.6267i	0.483690	−	1.48864i	−0.350180	−	0.936683i	$-0.613879\pi$
$61$	3.77774	−	11.6267i	0.483690	−	1.48864i	0.833869	−	0.551962i	$-0.186121\pi$
$62$		0			0
$63$	0.685239	+	2.10895i	0.0863320	+	0.265703i
$64$		0			0
$65$	−0.609118	−	0.396267i	−0.0755517	−	0.0491508i
$66$		0			0
$67$	−0.675894	+	0.491066i	−0.0825736	+	0.0599932i	−0.628306	−	0.777966i	$-0.716251\pi$
$67$	−0.675894	+	0.491066i	−0.0825736	+	0.0599932i	0.545733	+	0.837959i	$0.316251\pi$
$68$		0			0
$69$	−3.97043	+	2.88469i	−0.477984	+	0.347276i
$70$		0			0
$71$	−4.87541	−	3.54219i	−0.578604	−	0.420381i	0.259616	−	0.965712i	$-0.416404\pi$
$71$	−4.87541	−	3.54219i	−0.578604	−	0.420381i	−0.838221	+	0.545331i	$0.816404\pi$
$72$		0			0
$73$	3.35224	−	10.3171i	0.392350	−	1.20753i	−0.538657	−	0.842525i	$-0.681068\pi$
$73$	3.35224	−	10.3171i	0.392350	−	1.20753i	0.931006	−	0.365003i	$-0.118932\pi$
$74$		0			0
$75$	−7.68784	+	6.89967i	−0.887715	+	0.796705i
$76$		0			0
$77$	−0.540269	+	1.66278i	−0.0615694	+	0.189491i
$78$		0			0
$79$	3.79577	+	2.75779i	0.427058	+	0.310276i	0.780471	−	0.625192i	$-0.214979\pi$
$79$	3.79577	+	2.75779i	0.427058	+	0.310276i	−0.353414	+	0.935467i	$0.614979\pi$
$80$		0			0
$81$	9.05802	−	6.58104i	1.00645	−	0.731226i
$82$		0			0
$83$	−4.51203	+	3.27818i	−0.495260	+	0.359828i	−0.807204	−	0.590273i	$-0.799020\pi$
$83$	−4.51203	+	3.27818i	−0.495260	+	0.359828i	0.311943	+	0.950101i	$0.399020\pi$
$84$		0			0
$85$	1.29083	−	4.80190i	0.140010	−	0.520839i
$86$		0			0
$87$	−0.520234	−	1.60112i	−0.0557750	−	0.171658i
$88$		0			0
$89$	0.0518342	−	0.159529i	0.00549441	−	0.0169101i	−0.948272	−	0.317460i	$-0.897170\pi$
$89$	0.0518342	−	0.159529i	0.00549441	−	0.0169101i	0.953766	+	0.300550i	$0.0971701\pi$
$90$		0			0
$91$	0.175575	+	0.540365i	0.0184053	+	0.0566457i
$92$		0			0
$93$	−13.7715			−1.42803
$94$		0			0
$95$	−1.63034	+	6.06490i	−0.167270	+	0.622245i
$96$		0			0
$97$	−11.5887	−	8.41970i	−1.17666	−	0.854891i	−0.184866	−	0.982764i	$-0.559185\pi$
$97$	−11.5887	−	8.41970i	−1.17666	−	0.854891i	−0.991791	+	0.127872i	$0.959185\pi$
$98$		0			0
$99$	−1.26833			−0.127472
$100$		0			0
$101$	−8.24164			−0.820074			−0.410037	−	0.912069i	$-0.634484\pi$
$101$	−8.24164			−0.820074			−0.410037	+	0.912069i	$0.634484\pi$
$102$		0			0
$103$	−7.48983	−	5.44168i	−0.737995	−	0.536185i	0.154087	−	0.988057i	$-0.450756\pi$
$103$	−7.48983	−	5.44168i	−0.737995	−	0.536185i	−0.892083	+	0.451872i	$0.850756\pi$
$104$		0			0
$105$	8.06612	−	0.416184i	0.787172	−	0.0406154i
$106$		0			0
$107$	10.0605			0.972582			0.486291	−	0.873797i	$-0.338349\pi$
$107$	10.0605			0.972582			0.486291	+	0.873797i	$0.338349\pi$
$108$		0			0
$109$	2.59773	+	7.99499i	0.248817	+	0.765781i	0.994985	+	0.100023i	$0.0318917\pi$
$109$	2.59773	+	7.99499i	0.248817	+	0.765781i	−0.746168	+	0.665758i	$0.768108\pi$
$110$		0			0
$111$	0.367528	−	1.13113i	0.0348842	−	0.107363i
$112$		0			0
$113$	−1.80571	−	5.55740i	−0.169867	−	0.522796i	0.829495	−	0.558514i	$-0.188628\pi$
$113$	−1.80571	−	5.55740i	−0.169867	−	0.522796i	−0.999362	+	0.0357176i	$0.988628\pi$
$114$		0			0
$115$	1.89954	+	4.96047i	0.177133	+	0.462566i
$116$		0			0
$117$	−0.333459	+	0.242272i	−0.0308283	+	0.0223981i
$118$		0			0
$119$	−3.14532	+	2.28521i	−0.288331	+	0.209485i
$120$		0			0
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$		0			0
$123$	−6.22003	+	19.1433i	−0.560842	+	1.72609i
$124$		0			0
$125$	5.05157	+	9.97405i	0.451827	+	0.892106i
$126$		0			0
$127$	1.83212	−	5.63870i	0.162575	−	0.500353i	−0.836275	−	0.548311i	$-0.815271\pi$
$127$	1.83212	−	5.63870i	0.162575	−	0.500353i	0.998849	+	0.0479573i	$0.0152712\pi$
$128$		0			0
$129$	10.3030	+	7.48554i	0.907125	+	0.659065i
$130$		0			0
$131$	4.66788	−	3.39141i	0.407834	−	0.296309i	−0.364890	−	0.931051i	$-0.618893\pi$
$131$	4.66788	−	3.39141i	0.407834	−	0.296309i	0.772725	+	0.634742i	$0.218893\pi$
$132$		0			0
$133$	3.97260	−	2.88626i	0.344468	−	0.250271i
$134$		0			0
$135$	−2.86083	−	7.47078i	−0.246221	−	0.642982i
$136$		0			0
$137$	0.517849	+	1.59378i	0.0442428	+	0.136165i	0.970738	−	0.240141i	$-0.0771938\pi$
$137$	0.517849	+	1.59378i	0.0442428	+	0.136165i	−0.926495	+	0.376307i	$0.877194\pi$
$138$		0			0
$139$	1.91282	−	5.88704i	0.162243	−	0.499333i	−0.836580	−	0.547845i	$-0.815448\pi$
$139$	1.91282	−	5.88704i	0.162243	−	0.499333i	0.998823	+	0.0485128i	$0.0154482\pi$
$140$		0			0
$141$	3.40355	+	10.4750i	0.286630	+	0.882157i
$142$		0			0
$143$	−0.324977			−0.0271760
$144$		0			0
$145$	−1.81968	+	0.0938893i	−0.151116	+	0.00779708i
$146$		0			0
$147$	6.59089	+	4.78856i	0.543608	+	0.394954i
$148$		0			0
$149$	10.3812			0.850462			0.425231	−	0.905085i	$-0.360193\pi$
$149$	10.3812			0.850462			0.425231	+	0.905085i	$0.360193\pi$
$150$		0			0
$151$	17.2713			1.40552			0.702761	−	0.711426i	$-0.251950\pi$
$151$	17.2713			1.40552			0.702761	+	0.711426i	$0.251950\pi$
$152$		0			0
$153$	−2.28175	−	1.65779i	−0.184469	−	0.134024i
$154$		0			0
$155$	−3.86938	+	14.3941i	−0.310796	+	1.15616i
$156$		0			0
$157$	−7.03604			−0.561537			−0.280769	−	0.959775i	$-0.590589\pi$
$157$	−7.03604			−0.561537			−0.280769	+	0.959775i	$0.590589\pi$
$158$		0			0
$159$	8.13053	+	25.0232i	0.644793	+	1.98447i
$160$		0			0
$161$	1.28340	−	3.94989i	0.101146	−	0.311295i
$162$		0			0
$163$	5.03718	+	15.5028i	0.394542	+	1.21428i	0.929317	+	0.369282i	$0.120396\pi$
$163$	5.03718	+	15.5028i	0.394542	+	1.21428i	−0.534775	+	0.844994i	$0.679604\pi$
$164$		0			0
$165$	−1.19928	+	4.46132i	−0.0933636	+	0.347313i
$166$		0			0
$167$	−6.19137	+	4.49830i	−0.479103	+	0.348089i	−0.800978	−	0.598693i	$-0.795687\pi$
$167$	−6.19137	+	4.49830i	−0.479103	+	0.348089i	0.321875	+	0.946782i	$0.395687\pi$
$168$		0			0
$169$	10.4318	−	7.57913i	0.802445	−	0.583010i
$170$		0			0
$171$	2.88190	+	2.09382i	0.220384	+	0.160119i
$172$		0			0
$173$	5.46807	−	16.8290i	0.415730	−	1.27949i	−0.495866	−	0.868399i	$-0.665149\pi$
$173$	5.46807	−	16.8290i	0.415730	−	1.27949i	0.911596	−	0.411086i	$-0.134851\pi$
$174$		0			0
$175$	1.83134	−	8.54776i	0.138437	−	0.646150i
$176$		0			0
$177$	2.49380	−	7.67513i	0.187445	−	0.576898i
$178$		0			0
$179$	5.72170	+	4.15706i	0.427660	+	0.310713i	0.780712	−	0.624891i	$-0.214856\pi$
$179$	5.72170	+	4.15706i	0.427660	+	0.310713i	−0.353053	+	0.935603i	$0.614856\pi$
$180$		0			0
$181$	8.75637	−	6.36187i	0.650856	−	0.472874i	−0.212707	−	0.977116i	$-0.568228\pi$
$181$	8.75637	−	6.36187i	0.650856	−	0.472874i	0.863563	+	0.504242i	$0.168228\pi$
$182$		0			0
$183$	−20.4332	+	14.8456i	−1.51046	+	1.09742i
$184$		0			0
$185$	−1.07901	−	0.701962i	−0.0793307	−	0.0516093i
$186$		0			0
$187$	−0.687165	−	2.11488i	−0.0502505	−	0.154655i
$188$		0			0
$189$	−1.93288	+	5.94879i	−0.140596	+	0.432711i
$190$		0			0
$191$	1.25397	+	3.85933i	0.0907344	+	0.279252i	0.986119	−	0.166043i	$-0.0530990\pi$
$191$	1.25397	+	3.85933i	0.0907344	+	0.279252i	−0.895384	+	0.445294i	$0.853099\pi$
$192$		0			0
$193$	16.1255			1.16074			0.580369	−	0.814353i	$-0.302908\pi$
$193$	16.1255			1.16074			0.580369	+	0.814353i	$0.302908\pi$
$194$		0			0
$195$	0.536883	+	1.40202i	0.0384470	+	0.100401i
$196$		0			0
$197$	−13.3863	−	9.72574i	−0.953737	−	0.692930i	−0.00204917	−	0.999998i	$-0.500652\pi$
$197$	−13.3863	−	9.72574i	−0.953737	−	0.692930i	−0.951688	+	0.307067i	$0.900652\pi$
$198$		0			0
$199$	5.47040			0.387787			0.193893	−	0.981023i	$-0.437888\pi$
$199$	5.47040			0.387787			0.193893	+	0.981023i	$0.437888\pi$
$200$		0			0
$201$	1.72604			0.121745
$202$		0			0
$203$	1.15259	+	0.837403i	0.0808957	+	0.0587741i
$204$		0			0
$205$	18.2612	+	11.8800i	1.27542	+	0.829734i
$206$		0			0
$207$	3.01289			0.209410
$208$		0			0
$209$	0.867903	+	2.67113i	0.0600341	+	0.184766i
$210$		0			0
$211$	−0.223135	+	0.686740i	−0.0153613	+	0.0472772i	−0.958443	−	0.285283i	$-0.907912\pi$
$211$	−0.223135	+	0.686740i	−0.0153613	+	0.0472772i	0.943082	+	0.332560i	$0.107912\pi$
$212$		0			0
$213$	3.84737	+	11.8410i	0.263618	+	0.811332i
$214$		0			0
$215$	10.7188	−	8.66558i	0.731018	−	0.590988i
$216$		0			0
$217$	9.42837	−	6.85011i	0.640039	−	0.465016i
$218$		0			0
$219$	−18.1317	+	13.1735i	−1.22523	+	0.890180i
$220$		0			0
$221$	−0.584642	−	0.424767i	−0.0393272	−	0.0285729i
$222$		0			0
$223$	3.31271	−	10.1955i	0.221836	−	0.682740i	−0.776762	−	0.629795i	$-0.783139\pi$
$223$	3.31271	−	10.1955i	0.221836	−	0.682740i	0.998597	−	0.0529453i	$-0.0168609\pi$
$224$		0			0
$225$	6.30797	−	0.652676i	0.420531	−	0.0435118i
$226$		0			0
$227$	1.33032	−	4.09429i	0.0882961	−	0.271748i	−0.897153	−	0.441721i	$-0.854368\pi$
$227$	1.33032	−	4.09429i	0.0882961	−	0.271748i	0.985449	+	0.169973i	$0.0543682\pi$
$228$		0			0
$229$	−12.4608	−	9.05333i	−0.823435	−	0.598261i	0.0942592	−	0.995548i	$-0.469952\pi$
$229$	−12.4608	−	9.05333i	−0.823435	−	0.598261i	−0.917694	+	0.397287i	$0.869952\pi$
$230$		0			0
$231$	2.92223	−	2.12312i	0.192269	−	0.139691i
$232$		0			0
$233$	−10.4415	+	7.58622i	−0.684048	+	0.496990i	−0.874698	−	0.484668i	$-0.838940\pi$
$233$	−10.4415	+	7.58622i	−0.684048	+	0.496990i	0.190650	+	0.981658i	$0.438940\pi$
$234$		0			0
$235$	11.9050	−	0.614255i	0.776594	−	0.0400696i
$236$		0			0
$237$	−2.99539	−	9.21887i	−0.194572	−	0.598830i
$238$		0			0
$239$	0.351486	−	1.08176i	0.0227357	−	0.0699734i	−0.939045	−	0.343795i	$-0.888288\pi$
$239$	0.351486	−	1.08176i	0.0227357	−	0.0699734i	0.961781	+	0.273821i	$0.0882876\pi$
$240$		0			0
$241$	0.684088	+	2.10541i	0.0440660	+	0.135621i	0.970669	−	0.240420i	$-0.0772852\pi$
$241$	0.684088	+	2.10541i	0.0440660	+	0.135621i	−0.926603	+	0.376041i	$0.877285\pi$
$242$		0			0
$243$	−12.3987			−0.795376
$244$		0			0
$245$	6.85693	−	5.54345i	0.438073	−	0.354158i
$246$		0			0
$247$	0.738414	+	0.536489i	0.0469841	+	0.0341360i
$248$		0			0
$249$	11.5224			0.730204
$250$		0			0
$251$	9.53442			0.601807			0.300904	−	0.953655i	$-0.402712\pi$
$251$	9.53442			0.601807			0.300904	+	0.953655i	$0.402712\pi$
$252$		0			0
$253$	1.92180	+	1.39627i	0.120823	+	0.0877828i
$254$		0			0
$255$	−7.98877	+	6.45848i	−0.500276	+	0.404446i
$256$		0			0
$257$	8.59764			0.536306			0.268153	−	0.963376i	$-0.413587\pi$
$257$	8.59764			0.536306			0.268153	+	0.963376i	$0.413587\pi$
$258$		0			0
$259$	0.311021	+	0.957223i	0.0193259	+	0.0594790i
$260$		0			0
$261$	−0.319376	+	0.982938i	−0.0197689	+	0.0608423i
$262$		0			0
$263$	8.66561	+	26.6700i	0.534344	+	1.64454i	0.745061	+	0.666996i	$0.232420\pi$
$263$	8.66561	+	26.6700i	0.534344	+	1.64454i	−0.210717	+	0.977547i	$0.567580\pi$
$264$		0			0
$265$	28.4390	−	1.46736i	1.74700	−	0.0901390i
$266$		0			0
$267$	−0.280363	+	0.203696i	−0.0171579	+	0.0124660i
$268$		0			0
$269$	−18.7231	+	13.6031i	−1.14157	+	0.829398i	−0.987337	−	0.158637i	$-0.949290\pi$
$269$	−18.7231	+	13.6031i	−1.14157	+	0.829398i	−0.154231	+	0.988035i	$0.549290\pi$
$270$		0			0
$271$	−18.8131	−	13.6685i	−1.14282	−	0.830304i	−0.155306	−	0.987866i	$-0.549636\pi$
$271$	−18.8131	−	13.6685i	−1.14282	−	0.830304i	−0.987509	+	0.157563i	$0.949636\pi$
$272$		0			0
$273$	0.362737	−	1.11639i	0.0219539	−	0.0675671i
$274$		0			0
$275$	4.32608	+	2.50700i	0.260872	+	0.151178i
$276$		0			0
$277$	−3.07970	+	9.47835i	−0.185041	+	0.569499i	−0.999949	−	0.0100920i	$-0.996788\pi$
$277$	−3.07970	+	9.47835i	−0.185041	+	0.569499i	0.814908	+	0.579591i	$0.196788\pi$
$278$		0			0
$279$	6.83975	+	4.96937i	0.409485	+	0.297508i
$280$		0			0
$281$	24.1156	−	17.5210i	1.43862	−	1.04522i	0.450289	−	0.892883i	$-0.351321\pi$
$281$	24.1156	−	17.5210i	1.43862	−	1.04522i	0.988329	−	0.152335i	$-0.0486792\pi$
$282$		0			0
$283$	−15.2435	+	11.0750i	−0.906130	+	0.658342i	−0.940033	−	0.341083i	$-0.889206\pi$
$283$	−15.2435	+	11.0750i	−0.906130	+	0.658342i	0.0339030	+	0.999425i	$0.489206\pi$
$284$		0			0
$285$	10.0900	−	8.15719i	0.597678	−	0.483190i
$286$		0			0
$287$	−5.26371	−	16.2000i	−0.310707	−	0.956257i
$288$		0			0
$289$	−3.72523	+	11.4651i	−0.219131	+	0.674416i
$290$		0			0
$291$	9.14512	+	28.1458i	0.536096	+	1.64993i
$292$		0			0
$293$	−19.1918			−1.12119			−0.560597	−	0.828089i	$-0.689428\pi$
$293$	−19.1918			−1.12119			−0.560597	+	0.828089i	$0.689428\pi$
$294$		0			0
$295$	−7.32147	−	4.76304i	−0.426272	−	0.277315i
$296$		0			0
$297$	−2.89436	−	2.10287i	−0.167948	−	0.122021i
$298$		0			0
$299$	0.771977			0.0446446
$300$		0			0
$301$	−10.7771			−0.621183
$302$		0			0
$303$	13.7753	+	10.0083i	0.791369	+	0.574963i
$304$		0			0
$305$	9.77569	+	25.5282i	0.559754	+	1.46174i
$306$		0			0
$307$	−22.6263			−1.29135			−0.645675	−	0.763613i	$-0.723424\pi$
$307$	−22.6263			−1.29135			−0.645675	+	0.763613i	$0.723424\pi$
$308$		0			0
$309$	5.91052	+	18.1907i	0.336238	+	1.03483i
$310$		0			0
$311$	−2.28436	+	7.03055i	−0.129534	+	0.398666i	−0.994700	−	0.102820i	$-0.967213\pi$
$311$	−2.28436	+	7.03055i	−0.129534	+	0.398666i	0.865165	+	0.501486i	$0.167213\pi$
$312$		0			0
$313$	0.746122	+	2.29633i	0.0421733	+	0.129796i	0.969926	−	0.243399i	$-0.0782623\pi$
$313$	0.746122	+	2.29633i	0.0421733	+	0.129796i	−0.927753	+	0.373195i	$0.878262\pi$
$314$		0			0
$315$	−4.15631	−	2.70392i	−0.234181	−	0.152349i
$316$		0			0
$317$	−18.9730	+	13.7847i	−1.06563	+	0.774224i	−0.975121	−	0.221672i	$-0.928848\pi$
$317$	−18.9730	+	13.7847i	−1.06563	+	0.774224i	−0.0905061	+	0.995896i	$0.528848\pi$
$318$		0			0
$319$	−0.659243	+	0.478968i	−0.0369105	+	0.0268171i
$320$		0			0
$321$	−16.8153	−	12.2170i	−0.938539	−	0.681888i
$322$		0			0
$323$	−1.92997	+	5.93983i	−0.107386	+	0.330501i
$324$		0			0
$325$	1.61626	−	0.167232i	0.0896539	−	0.00927636i
$326$		0			0
$327$	5.36689	−	16.5176i	0.296790	−	0.913426i
$328$		0			0
$329$	−7.54060	−	5.47857i	−0.415727	−	0.302043i
$330$		0			0
$331$	14.6509	−	10.6445i	0.805286	−	0.585075i	−0.107174	−	0.994240i	$-0.534180\pi$
$331$	14.6509	−	10.6445i	0.805286	−	0.585075i	0.912460	+	0.409166i	$0.134180\pi$
$332$		0			0
$333$	−0.590702	+	0.429170i	−0.0323703	+	0.0235184i
$334$		0			0
$335$	0.484966	−	1.80408i	0.0264965	−	0.0985673i
$336$		0			0
$337$	3.88665	+	11.9619i	0.211719	+	0.651605i	0.999370	+	0.0354833i	$0.0112971\pi$
$337$	3.88665	+	11.9619i	0.211719	+	0.651605i	−0.787651	+	0.616122i	$0.788703\pi$
$338$		0			0
$339$	−3.73058	+	11.4816i	−0.202617	+	0.623593i
$340$		0			0
$341$	2.05984	+	6.33953i	0.111547	+	0.343305i
$342$		0			0
$343$	−19.1327			−1.03307
$344$		0			0
$345$	2.84886	−	10.5978i	0.153377	−	0.570565i
$346$		0			0
$347$	2.41079	+	1.75154i	0.129418	+	0.0940277i	0.650611	−	0.759411i	$-0.274513\pi$
$347$	2.41079	+	1.75154i	0.129418	+	0.0940277i	−0.521193	+	0.853439i	$0.674513\pi$
$348$		0			0
$349$	−30.4670			−1.63086			−0.815431	−	0.578855i	$-0.803500\pi$
$349$	−30.4670			−1.63086			−0.815431	+	0.578855i	$0.803500\pi$
$350$		0			0
$351$	−1.16265			−0.0620575
$352$		0			0
$353$	12.3262	+	8.95553i	0.656059	+	0.476655i	0.865330	−	0.501203i	$-0.167109\pi$
$353$	12.3262	+	8.95553i	0.656059	+	0.476655i	−0.209271	+	0.977858i	$0.567109\pi$
$354$		0			0
$355$	13.4574	−	0.694355i	0.714244	−	0.0368525i
$356$		0			0
$357$	8.03222			0.425110
$358$		0			0
$359$	−2.35516	−	7.24845i	−0.124301	−	0.382559i	0.869472	−	0.493982i	$-0.164459\pi$
$359$	−2.35516	−	7.24845i	−0.124301	−	0.382559i	−0.993773	+	0.111423i	$0.964459\pi$
$360$		0			0
$361$	−3.43373	+	10.5679i	−0.180723	+	0.556208i
$362$		0			0
$363$	0.638427	+	1.96488i	0.0335087	+	0.103129i
$364$		0			0
$365$	8.67461	+	22.6529i	0.454050	+	1.18571i
$366$		0			0
$367$	10.9829	−	7.97952i	0.573301	−	0.416528i	−0.263002	−	0.964795i	$-0.584713\pi$
$367$	10.9829	−	7.97952i	0.573301	−	0.416528i	0.836303	+	0.548268i	$0.184713\pi$
$368$		0			0
$369$	9.99703	−	7.26327i	0.520425	−	0.378111i
$370$		0			0
$371$	−18.0133	−	13.0874i	−0.935203	−	0.679465i
$372$		0			0
$373$	5.87765	−	18.0895i	0.304333	−	0.936641i	−0.675592	−	0.737276i	$-0.736112\pi$
$373$	5.87765	−	18.0895i	0.304333	−	0.936641i	0.979925	−	0.199365i	$-0.0638880\pi$
$374$		0			0
$375$	3.66876	−	22.8053i	0.189454	−	1.17766i
$376$		0			0
$377$	−0.0818320	+	0.251853i	−0.00421456	+	0.0129711i
$378$		0			0
$379$	−23.6837	−	17.2072i	−1.21655	−	0.883877i	−0.220743	−	0.975332i	$-0.570848\pi$
$379$	−23.6837	−	17.2072i	−1.21655	−	0.883877i	−0.995809	+	0.0914554i	$0.970848\pi$
$380$		0			0
$381$	−9.90966	+	7.19979i	−0.507687	+	0.368856i
$382$		0			0
$383$	11.2104	−	8.14480i	0.572822	−	0.416180i	−0.263307	−	0.964712i	$-0.584813\pi$
$383$	11.2104	−	8.14480i	0.572822	−	0.416180i	0.836129	+	0.548532i	$0.184813\pi$
$384$		0			0
$385$	−1.39806	−	3.65089i	−0.0712517	−	0.186067i
$386$		0			0
$387$	−2.41596	−	7.43556i	−0.122810	−	0.377971i
$388$		0			0
$389$	2.24516	−	6.90990i	0.113834	−	0.350346i	−0.877868	−	0.478903i	$-0.841035\pi$
$389$	2.24516	−	6.90990i	0.113834	−	0.350346i	0.991702	+	0.128557i	$0.0410346\pi$
$390$		0			0
$391$	1.63235	+	5.02385i	0.0825513	+	0.254067i
$392$		0			0
$393$	−11.9204			−0.601305
$394$		0			0
$395$	−10.4773	+	0.540594i	−0.527171	+	0.0272002i
$396$		0			0
$397$	−3.27789	−	2.38152i	−0.164512	−	0.119525i	0.502483	−	0.864587i	$-0.332420\pi$
$397$	−3.27789	−	2.38152i	−0.164512	−	0.119525i	−0.666995	+	0.745062i	$0.732420\pi$
$398$		0			0
$399$	−10.1449			−0.507878
$400$		0			0
$401$	−28.9000			−1.44320			−0.721599	−	0.692311i	$-0.756593\pi$
$401$	−28.9000			−1.44320			−0.721599	+	0.692311i	$0.756593\pi$
$402$		0			0
$403$	1.75251	+	1.27328i	0.0872990	+	0.0634264i
$404$		0			0
$405$	−6.49929	+	24.1774i	−0.322952	+	1.20139i
$406$		0			0
$407$	−0.575677			−0.0285353
$408$		0			0
$409$	−3.18855	−	9.81335i	−0.157664	−	0.485239i	0.840757	−	0.541412i	$-0.182110\pi$
$409$	−3.18855	−	9.81335i	−0.157664	−	0.485239i	−0.998421	+	0.0561731i	$0.982110\pi$
$410$		0			0
$411$	1.06987	−	3.29273i	0.0527729	−	0.162418i
$412$		0			0
$413$	2.11038	+	6.49508i	0.103845	+	0.319602i
$414$		0			0
$415$	3.23747	−	12.0434i	0.158921	−	0.591187i
$416$		0			0
$417$	−10.3461	+	7.51690i	−0.506652	+	0.368104i
$418$		0			0
$419$	11.1189	−	8.07835i	0.543194	−	0.394653i	−0.282076	−	0.959392i	$-0.591023\pi$
$419$	11.1189	−	8.07835i	0.543194	−	0.394653i	0.825270	+	0.564739i	$0.191023\pi$
$420$		0			0
$421$	15.5572	+	11.3030i	0.758212	+	0.550873i	0.898361	−	0.439257i	$-0.144758\pi$
$421$	15.5572	+	11.3030i	0.758212	+	0.550873i	−0.140150	+	0.990130i	$0.544758\pi$
$422$		0			0
$423$	2.08946	−	6.43071i	0.101593	−	0.312672i
$424$		0			0
$425$	4.50589	+	10.1646i	0.218568	+	0.493057i
$426$		0			0
$427$	6.60480	−	20.3275i	0.319629	−	0.983716i
$428$		0			0
$429$	0.543175	+	0.394640i	0.0262247	+	0.0190534i
$430$		0			0
$431$	1.52715	−	1.10954i	0.0735604	−	0.0534448i	−0.550397	−	0.834903i	$-0.685524\pi$
$431$	1.52715	−	1.10954i	0.0735604	−	0.0534448i	0.623958	+	0.781458i	$0.285524\pi$
$432$		0			0
$433$	13.8284	−	10.0469i	0.664550	−	0.482824i	−0.203646	−	0.979044i	$-0.565279\pi$
$433$	13.8284	−	10.0469i	0.664550	−	0.482824i	0.868196	+	0.496221i	$0.165279\pi$
$434$		0			0
$435$	3.15547	+	2.05282i	0.151293	+	0.0984252i
$436$		0			0
$437$	−2.06169	−	6.34522i	−0.0986238	−	0.303533i
$438$		0			0
$439$	−8.54433	+	26.2967i	−0.407799	+	1.25508i	0.510737	+	0.859737i	$0.329373\pi$
$439$	−8.54433	+	26.2967i	−0.407799	+	1.25508i	−0.918536	+	0.395338i	$0.870627\pi$
$440$		0			0
$441$	−1.54551	−	4.75659i	−0.0735957	−	0.226504i
$442$		0			0
$443$	26.8259			1.27454			0.637269	−	0.770641i	$-0.280064\pi$
$443$	26.8259			1.27454			0.637269	+	0.770641i	$0.280064\pi$
$444$		0			0
$445$	0.134132	+	0.350272i	0.00635846	+	0.0166045i
$446$		0			0
$447$	−17.3514	−	12.6065i	−0.820694	−	0.596269i
$448$		0			0
$449$	−32.1660			−1.51801			−0.759003	−	0.651087i	$-0.774313\pi$
$449$	−32.1660			−1.51801			−0.759003	+	0.651087i	$0.774313\pi$
$450$		0			0
$451$	9.74275			0.458768
$452$		0			0
$453$	−28.8677	−	20.9736i	−1.35632	−	0.985427i
$454$		0			0
$455$	−1.06495	−	0.692812i	−0.0499256	−	0.0324795i
$456$		0			0
$457$	−3.99000			−0.186644			−0.0933221	−	0.995636i	$-0.529749\pi$
$457$	−3.99000			−0.186644			−0.0933221	+	0.995636i	$0.529749\pi$
$458$		0			0
$459$	−2.45842	−	7.56623i	−0.114749	−	0.353161i
$460$		0			0
$461$	−6.24025	+	19.2055i	−0.290637	+	0.894490i	0.694015	+	0.719961i	$0.255840\pi$
$461$	−6.24025	+	19.2055i	−0.290637	+	0.894490i	−0.984652	+	0.174529i	$0.944160\pi$
$462$		0			0
$463$	5.25488	+	16.1728i	0.244215	+	0.751616i	0.995765	+	0.0919396i	$0.0293067\pi$
$463$	5.25488	+	16.1728i	0.244215	+	0.751616i	−0.751550	+	0.659676i	$0.770693\pi$
$464$		0			0
$465$	23.9470	−	19.3599i	1.11052	−	0.897792i
$466$		0			0
$467$	22.2193	−	16.1433i	1.02819	−	0.747021i	0.0602409	−	0.998184i	$-0.480813\pi$
$467$	22.2193	−	16.1433i	1.02819	−	0.747021i	0.967945	+	0.251163i	$0.0808131\pi$
$468$		0			0
$469$	−1.18170	+	0.858554i	−0.0545657	+	0.0396443i
$470$		0			0
$471$	11.7602	+	8.54429i	0.541882	+	0.393700i
$472$		0			0
$473$	1.90484	−	5.86248i	0.0875845	−	0.269557i
$474$		0			0
$475$	−5.69103	−	12.8381i	−0.261122	−	0.589053i
$476$		0			0
$477$	4.99139	−	15.3619i	0.228540	−	0.703374i
$478$		0			0
$479$	−7.01815	−	5.09899i	−0.320668	−	0.232979i	0.415793	−	0.909459i	$-0.363504\pi$
$479$	−7.01815	−	5.09899i	−0.320668	−	0.232979i	−0.736460	+	0.676481i	$0.763504\pi$
$480$		0			0
$481$	−0.151353	+	0.109964i	−0.00690109	+	0.00501393i
$482$		0			0
$483$	−6.94170	+	5.04344i	−0.315858	+	0.229484i
$484$		0			0
$485$	31.9879	−	1.65047i	1.45250	−	0.0749438i
$486$		0			0
$487$	−7.27809	−	22.3997i	−0.329802	−	1.01503i	−0.969226	−	0.246172i	$-0.920827\pi$
$487$	−7.27809	−	22.3997i	−0.329802	−	1.01503i	0.639424	−	0.768854i	$-0.279173\pi$
$488$		0			0
$489$	10.4068	−	32.0288i	0.470611	−	1.44839i
$490$		0			0
$491$	−8.60911	−	26.4961i	−0.388524	−	1.19575i	−0.933892	−	0.357556i	$-0.883610\pi$
$491$	−8.60911	−	26.4961i	−0.388524	−	1.19575i	0.545368	−	0.838197i	$-0.316390\pi$
$492$		0			0
$493$	−1.81203			−0.0816099
$494$		0			0
$495$	2.20548	−	1.78301i	0.0991291	−	0.0801405i
$496$		0			0
$497$	−8.52391	−	6.19298i	−0.382349	−	0.277793i
$498$		0			0
$499$	27.2291			1.21894			0.609471	−	0.792809i	$-0.291382\pi$
$499$	27.2291			1.21894			0.609471	+	0.792809i	$0.291382\pi$
$500$		0			0
$501$	15.8110			0.706382
$502$		0			0
$503$	−23.6886	−	17.2108i	−1.05622	−	0.767390i	−0.0828364	−	0.996563i	$-0.526398\pi$
$503$	−23.6886	−	17.2108i	−1.05622	−	0.767390i	−0.973386	+	0.229173i	$0.926398\pi$
$504$		0			0
$505$	14.3313	−	11.5861i	0.637735	−	0.515574i
$506$		0			0
$507$	−26.6397			−1.18311
$508$		0			0
$509$	9.44632	+	29.0728i	0.418701	+	1.28863i	0.908899	+	0.417017i	$0.136925\pi$
$509$	9.44632	+	29.0728i	0.418701	+	1.28863i	−0.490198	+	0.871611i	$0.663075\pi$
$510$		0			0
$511$	5.86088	−	18.0379i	0.259270	−	0.797951i
$512$		0			0
$513$	3.10503	+	9.55630i	0.137090	+	0.421921i
$514$		0			0
$515$	20.6739	−	1.06670i	0.911000	−	0.0470045i
$516$		0			0
$517$	4.31299	−	3.13357i	0.189685	−	0.137814i
$518$		0			0
$519$	−29.5759	+	21.4882i	−1.29824	+	0.943226i
$520$		0			0
$521$	−22.6794	−	16.4776i	−0.993603	−	0.721895i	−0.0328956	−	0.999459i	$-0.510473\pi$
$521$	−22.6794	−	16.4776i	−0.993603	−	0.721895i	−0.960707	+	0.277564i	$0.910473\pi$
$522$		0			0
$523$	−1.66506	+	5.12454i	−0.0728082	+	0.224080i	−0.980838	−	0.194825i	$-0.937586\pi$
$523$	−1.66506	+	5.12454i	−0.0728082	+	0.224080i	0.908030	+	0.418905i	$0.137586\pi$
$524$		0			0
$525$	−13.4410	+	12.0630i	−0.586614	+	0.526473i
$526$		0			0
$527$	−4.58049	+	14.0973i	−0.199529	+	0.614088i
$528$		0			0
$529$	14.0422	+	10.2022i	0.610530	+	0.443576i
$530$		0			0
$531$	−4.00811	+	2.91206i	−0.173937	+	0.126373i
$532$		0			0
$533$	2.56149	−	1.86103i	0.110950	−	0.0806101i
$534$		0			0
$535$	−17.4940	+	14.1430i	−0.756333	+	0.611454i
$536$		0			0
$537$	−4.51521	−	13.8964i	−0.194846	−	0.599674i
$538$		0			0
$539$	1.21854	−	3.75028i	0.0524862	−	0.161536i
$540$		0			0
$541$	−8.30266	−	25.5530i	−0.356959	−	1.09861i	−0.954865	−	0.297041i	$-0.904000\pi$
$541$	−8.30266	−	25.5530i	−0.356959	−	1.09861i	0.597905	−	0.801567i	$-0.296000\pi$
$542$		0			0
$543$	−22.3612			−0.959611
$544$		0			0
$545$	−15.7565	−	10.2505i	−0.674934	−	0.439084i
$546$		0			0
$547$	36.7569	+	26.7055i	1.57161	+	1.14184i	0.925592	+	0.378522i	$0.123567\pi$
$547$	36.7569	+	26.7055i	1.57161	+	1.14184i	0.646019	+	0.763321i	$0.276433\pi$
$548$		0			0
$549$	15.5053			0.661752
$550$		0			0
$551$	2.28864			0.0974992
$552$		0			0
$553$	6.63633	+	4.82158i	0.282205	+	0.205034i
$554$		0			0
$555$	0.951055	+	2.48359i	0.0403701	+	0.105422i
$556$		0			0
$557$	−5.65711			−0.239699			−0.119850	−	0.992792i	$-0.538241\pi$
$557$	−5.65711			−0.239699			−0.119850	+	0.992792i	$0.538241\pi$
$558$		0			0
$559$	−0.619029	−	1.90517i	−0.0261821	−	0.0805803i
$560$		0			0
$561$	−1.41968	+	4.36932i	−0.0599389	+	0.184473i
$562$		0			0
$563$	11.5907	+	35.6726i	0.488491	+	1.50342i	0.826861	+	0.562407i	$0.190125\pi$
$563$	11.5907	+	35.6726i	0.488491	+	1.50342i	−0.338370	+	0.941013i	$0.609875\pi$
$564$		0			0
$565$	10.9525	+	7.12525i	0.460775	+	0.299761i
$566$		0			0
$567$	15.8366	−	11.5059i	0.665073	−	0.483204i
$568$		0			0
$569$	3.88533	−	2.82286i	0.162882	−	0.118340i	−0.503359	−	0.864078i	$-0.667903\pi$
$569$	3.88533	−	2.82286i	0.162882	−	0.118340i	0.666240	+	0.745737i	$0.267903\pi$
$570$		0			0
$571$	−7.68528	−	5.58368i	−0.321619	−	0.233670i	0.415247	−	0.909709i	$-0.363695\pi$
$571$	−7.68528	−	5.58368i	−0.321619	−	0.233670i	−0.736866	+	0.676039i	$0.763695\pi$
$572$		0			0
$573$	2.59070	−	7.97336i	0.108228	−	0.333092i
$574$		0			0
$575$	−10.2765	−	5.95533i	−0.428560	−	0.248355i
$576$		0			0
$577$	3.06216	−	9.42437i	0.127479	−	0.392342i	−0.866865	−	0.498543i	$-0.833869\pi$
$577$	3.06216	−	9.42437i	0.127479	−	0.392342i	0.994345	+	0.106201i	$0.0338687\pi$
$578$		0			0
$579$	−26.9525	−	19.5822i	−1.12011	−	0.813807i
$580$		0			0
$581$	−7.88861	+	5.73141i	−0.327275	+	0.237779i
$582$		0			0
$583$	10.3030	−	7.48559i	0.426708	−	0.310021i
$584$		0			0
$585$	0.239263	−	0.890060i	0.00989231	−	0.0367995i
$586$		0			0
$587$	−1.65132	−	5.08225i	−0.0681574	−	0.209767i	0.911177	−	0.412016i	$-0.135175\pi$
$587$	−1.65132	−	5.08225i	−0.0681574	−	0.209767i	−0.979334	+	0.202249i	$0.935175\pi$
$588$		0			0
$589$	5.78525	−	17.8052i	0.238377	−	0.733649i
$590$		0			0
$591$	10.5637	+	32.5117i	0.434532	+	1.33735i
$592$		0			0
$593$	17.6964			0.726704			0.363352	−	0.931652i	$-0.381632\pi$
$593$	17.6964			0.726704			0.363352	+	0.931652i	$0.381632\pi$
$594$		0			0
$595$	2.25682	−	8.39540i	0.0925206	−	0.344178i
$596$		0			0
$597$	−9.14336	−	6.64304i	−0.374213	−	0.271882i
$598$		0			0
$599$	46.2007			1.88771			0.943854	−	0.330363i	$-0.107171\pi$
$599$	46.2007			1.88771			0.943854	+	0.330363i	$0.107171\pi$
$600$		0			0
$601$	−6.21990			−0.253715			−0.126857	−	0.991921i	$-0.540489\pi$
$601$	−6.21990			−0.253715			−0.126857	+	0.991921i	$0.540489\pi$
$602$		0			0
$603$	−0.857256	−	0.622833i	−0.0349102	−	0.0253637i
$604$		0			0
$605$	2.23310	−	0.115220i	0.0907883	−	0.00468436i
$606$		0			0
$607$	−11.3786			−0.461842			−0.230921	−	0.972973i	$-0.574174\pi$
$607$	−11.3786			−0.461842			−0.230921	+	0.972973i	$0.574174\pi$
$608$		0			0
$609$	−0.909551	−	2.79931i	−0.0368569	−	0.113434i
$610$		0			0
$611$	0.535372	−	1.64771i	0.0216588	−	0.0666591i
$612$		0			0
$613$	0.894918	+	2.75427i	0.0361454	+	0.111244i	0.967501	−	0.252866i	$-0.0813732\pi$
$613$	0.894918	+	2.75427i	0.0361454	+	0.111244i	−0.931356	+	0.364110i	$0.881373\pi$
$614$		0			0
$615$	−16.0956	−	42.0322i	−0.649039	−	1.69490i
$616$		0			0
$617$	−10.5958	+	7.69833i	−0.426573	+	0.309923i	−0.780277	−	0.625434i	$-0.784922\pi$
$617$	−10.5958	+	7.69833i	−0.426573	+	0.309923i	0.353704	+	0.935357i	$0.384922\pi$
$618$		0			0
$619$	−38.0148	+	27.6194i	−1.52795	+	1.11012i	−0.570578	+	0.821243i	$0.693281\pi$
$619$	−38.0148	+	27.6194i	−1.52795	+	1.11012i	−0.957367	+	0.288874i	$0.906719\pi$
$620$		0			0
$621$	6.87548	+	4.99533i	0.275904	+	0.200456i
$622$		0			0
$623$	0.0906242	−	0.278913i	0.00363078	−	0.0111744i
$624$		0			0
$625$	−22.8056	−	10.2423i	−0.912224	−	0.409691i
$626$		0			0
$627$	1.79308	−	5.51854i	0.0716088	−	0.220389i
$628$		0			0
$629$	−1.03566	−	0.752448i	−0.0412943	−	0.0300021i
$630$		0			0
$631$	40.0914	−	29.1281i	1.59601	−	1.15957i	0.701365	−	0.712802i	$-0.252574\pi$
$631$	40.0914	−	29.1281i	1.59601	−	1.15957i	0.894649	−	0.446770i	$-0.147426\pi$
$632$		0			0
$633$	1.20690	−	0.876867i	0.0479701	−	0.0348524i
$634$		0			0
$635$	4.74100	+	12.3807i	0.188141	+	0.491311i
$636$		0			0
$637$	−0.395998	−	1.21876i	−0.0156900	−	0.0482889i
$638$		0			0
$639$	2.36193	−	7.26928i	0.0934366	−	0.287568i
$640$		0			0
$641$	11.8534	+	36.4810i	0.468181	+	1.44091i	0.854938	+	0.518730i	$0.173595\pi$
$641$	11.8534	+	36.4810i	0.468181	+	1.44091i	−0.386757	+	0.922182i	$0.626405\pi$
$642$		0			0
$643$	8.65335			0.341255			0.170627	−	0.985336i	$-0.445421\pi$
$643$	8.65335			0.341255			0.170627	+	0.985336i	$0.445421\pi$
$644$		0			0
$645$	−28.4388	+	1.46735i	−1.11978	+	0.0577767i
$646$		0			0
$647$	5.79057	+	4.20710i	0.227651	+	0.165398i	0.695764	−	0.718271i	$-0.255066\pi$
$647$	5.79057	+	4.20710i	0.227651	+	0.165398i	−0.468113	+	0.883669i	$0.655066\pi$
$648$		0			0
$649$	−3.90616			−0.153330
$650$		0			0
$651$	−24.0773			−0.943664
$652$		0			0
$653$	−6.96189	−	5.05811i	−0.272440	−	0.197939i	0.443173	−	0.896436i	$-0.353853\pi$
$653$	−6.96189	−	5.05811i	−0.272440	−	0.197939i	−0.715613	+	0.698497i	$0.753853\pi$
$654$		0			0
$655$	−3.34929	+	12.4594i	−0.130867	+	0.486828i
$656$		0			0
$657$	13.7589			0.536786
$658$		0			0
$659$	5.72658	+	17.6246i	0.223076	+	0.686557i	0.998481	+	0.0550931i	$0.0175456\pi$
$659$	5.72658	+	17.6246i	0.223076	+	0.686557i	−0.775405	+	0.631464i	$0.782454\pi$
$660$		0			0
$661$	−3.32378	+	10.2296i	−0.129280	+	0.397884i	−0.994657	−	0.103239i	$-0.967079\pi$
$661$	−3.32378	+	10.2296i	−0.129280	+	0.397884i	0.865376	+	0.501122i	$0.167079\pi$
$662$		0			0
$663$	0.461364	+	1.41993i	0.0179179	+	0.0551456i
$664$		0			0
$665$	−2.85041	+	10.6036i	−0.110534	+	0.411188i
$666$		0			0
$667$	1.56602	−	1.13778i	0.0606364	−	0.0440549i
$668$		0			0
$669$	−17.9179	+	13.0181i	−0.692747	+	0.503310i
$670$		0			0
$671$	9.89025	+	7.18569i	0.381809	+	0.277400i
$672$		0			0
$673$	6.89629	−	21.2246i	0.265832	−	0.818148i	−0.725668	−	0.688045i	$-0.758469\pi$
$673$	6.89629	−	21.2246i	0.265832	−	0.818148i	0.991500	−	0.130103i	$-0.0415308\pi$
$674$		0			0
$675$	15.4771	+	8.96911i	0.595712	+	0.345221i
$676$		0			0
$677$	−2.37248	+	7.30175i	−0.0911819	+	0.280629i	−0.986240	−	0.165321i	$-0.947134\pi$
$677$	−2.37248	+	7.30175i	−0.0911819	+	0.280629i	0.895058	+	0.445950i	$0.147134\pi$
$678$		0			0
$679$	−20.2611	−	14.7206i	−0.777551	−	0.564924i
$680$		0			0
$681$	−7.19547	+	5.22781i	−0.275731	+	0.200330i
$682$		0			0
$683$	0.644187	−	0.468029i	0.0246491	−	0.0179086i	−0.575392	−	0.817877i	$-0.695151\pi$
$683$	0.644187	−	0.468029i	0.0246491	−	0.0179086i	0.600042	+	0.799969i	$0.295151\pi$
$684$		0			0
$685$	−3.14101	−	2.04341i	−0.120012	−	0.0780746i
$686$		0			0
$687$	9.83334	+	30.2639i	0.375165	+	1.15464i
$688$		0			0
$689$	1.27892	−	3.93611i	0.0487229	−	0.149954i
$690$		0			0
$691$	−1.02912	−	3.16731i	−0.0391497	−	0.120490i	0.929572	−	0.368642i	$-0.120177\pi$
$691$	−1.02912	−	3.16731i	−0.0391497	−	0.120490i	−0.968721	+	0.248151i	$0.920177\pi$
$692$		0			0
$693$	−2.21748			−0.0842351
$694$		0			0
$695$	4.94981	+	12.9260i	0.187757	+	0.490309i
$696$		0			0
$697$	17.5274	+	12.7344i	0.663898	+	0.482350i
$698$		0			0
$699$	26.6646			1.00855
$700$		0			0
$701$	−46.3709			−1.75141			−0.875703	−	0.482850i	$-0.839601\pi$
$701$	−46.3709			−1.75141			−0.875703	+	0.482850i	$0.839601\pi$
$702$		0			0
$703$	1.30805	+	0.950357i	0.0493342	+	0.0358434i
$704$		0			0
$705$	−20.6442	−	13.4302i	−0.777504	−	0.505812i
$706$		0			0
$707$	−14.4093			−0.541916
$708$		0			0
$709$	−1.51337	−	4.65768i	−0.0568358	−	0.174923i	0.918608	−	0.395169i	$-0.129314\pi$
$709$	−1.51337	−	4.65768i	−0.0568358	−	0.174923i	−0.975444	+	0.220246i	$0.929314\pi$
$710$		0			0
$711$	−1.83889	+	5.65953i	−0.0689639	+	0.212249i
$712$		0			0
$713$	−4.89310	−	15.0594i	−0.183248	−	0.563980i
$714$		0			0
$715$	0.565100	−	0.456852i	0.0211335	−	0.0170853i
$716$		0			0
$717$	−1.90113	+	1.38125i	−0.0709990	+	0.0515838i
$718$		0			0
$719$	11.2325	−	8.16088i	0.418901	−	0.304349i	−0.358295	−	0.933609i	$-0.616642\pi$
$719$	11.2325	−	8.16088i	0.418901	−	0.304349i	0.777195	+	0.629259i	$0.216642\pi$
$720$		0			0
$721$	−13.0948	−	9.51395i	−0.487677	−	0.354318i
$722$		0			0
$723$	1.41332	−	4.34975i	0.0525620	−	0.161769i
$724$		0			0
$725$	3.03224	−	2.72137i	0.112614	−	0.101069i
$726$		0			0
$727$	−9.84164	+	30.2894i	−0.365006	+	1.12337i	0.584971	+	0.811054i	$0.301106\pi$
$727$	−9.84164	+	30.2894i	−0.365006	+	1.12337i	−0.949977	+	0.312319i	$0.898894\pi$
$728$		0			0
$729$	−6.45062	−	4.68665i	−0.238912	−	0.173579i
$730$		0			0
$731$	11.0895	−	8.05699i	0.410160	−	0.297999i
$732$		0			0
$733$	−19.0662	+	13.8524i	−0.704226	+	0.511650i	−0.881306	−	0.472546i	$-0.843335\pi$
$733$	−19.0662	+	13.8524i	−0.704226	+	0.511650i	0.177080	+	0.984197i	$0.443335\pi$
$734$		0			0
$735$	−18.1926	+	0.938674i	−0.671043	+	0.0346235i
$736$		0			0
$737$	−0.258169	−	0.794561i	−0.00950976	−	0.0292680i
$738$		0			0
$739$	14.1078	−	43.4194i	0.518964	−	1.59721i	−0.256986	−	0.966415i	$-0.582730\pi$
$739$	14.1078	−	43.4194i	0.518964	−	1.59721i	0.775951	−	0.630793i	$-0.217270\pi$
$740$		0			0
$741$	−0.582711	−	1.79340i	−0.0214064	−	0.0658822i
$742$		0			0
$743$	−14.1967			−0.520828			−0.260414	−	0.965497i	$-0.583859\pi$
$743$	−14.1967			−0.520828			−0.260414	+	0.965497i	$0.583859\pi$
$744$		0			0
$745$	−18.0518	+	14.5939i	−0.661366	+	0.534678i
$746$		0			0
$747$	−5.72274	−	4.15782i	−0.209384	−	0.152127i
$748$		0			0
$749$	17.5892			0.642695
$750$		0			0
$751$	18.3126			0.668236			0.334118	−	0.942531i	$-0.391562\pi$
$751$	18.3126			0.668236			0.334118	+	0.942531i	$0.391562\pi$
$752$		0			0
$753$	−15.9361	−	11.5782i	−0.580742	−	0.421934i
$754$		0			0
$755$	−30.0330	+	24.2800i	−1.09301	+	0.883640i
$756$		0			0
$757$	13.3919			0.486738			0.243369	−	0.969934i	$-0.421747\pi$
$757$	13.3919			0.486738			0.243369	+	0.969934i	$0.421747\pi$
$758$		0			0
$759$	−1.51657	−	4.66752i	−0.0550480	−	0.169420i
$760$		0			0
$761$	−1.85646	+	5.71359i	−0.0672966	+	0.207117i	−0.979050	−	0.203621i	$-0.934729\pi$
$761$	−1.85646	+	5.71359i	−0.0672966	+	0.207117i	0.911753	+	0.410738i	$0.134729\pi$
$762$		0			0
$763$	4.54174	+	13.9780i	0.164422	+	0.506039i
$764$		0			0
$765$	6.29823	−	0.324967i	0.227713	−	0.0117492i
$766$		0			0
$767$	−1.02698	+	0.746143i	−0.0370820	+	0.0269417i
$768$		0			0
$769$	15.3583	−	11.1585i	0.553834	−	0.402384i	−0.275363	−	0.961340i	$-0.588798\pi$
$769$	15.3583	−	11.1585i	0.553834	−	0.402384i	0.829197	+	0.558956i	$0.188798\pi$
$770$		0			0
$771$	−14.3703	−	10.4406i	−0.517534	−	0.376010i
$772$		0			0
$773$	15.5611	−	47.8922i	0.559694	−	1.72256i	−0.123518	−	0.992342i	$-0.539418\pi$
$773$	15.5611	−	47.8922i	0.559694	−	1.72256i	0.683212	−	0.730220i	$-0.260582\pi$
$774$		0			0
$775$	−13.5068	−	30.4694i	−0.485179	−	1.09449i
$776$		0			0
$777$	0.642567	−	1.97762i	0.0230520	−	0.0709466i
$778$		0			0
$779$	−22.1375	−	16.0838i	−0.793157	−	0.576263i
$780$		0			0
$781$	4.87541	−	3.54219i	0.174456	−	0.126750i
$782$		0			0
$783$	−2.35852	+	1.71357i	−0.0842867	+	0.0612378i
$784$		0			0
$785$	12.2349	−	9.89124i	0.436682	−	0.353034i
$786$		0			0
$787$	2.74797	+	8.45739i	0.0979546	+	0.301473i	0.988012	−	0.154374i	$-0.0493362\pi$
$787$	2.74797	+	8.45739i	0.0979546	+	0.301473i	−0.890058	+	0.455848i	$0.849336\pi$
$788$		0			0
$789$	17.9031	−	55.1001i	0.637367	−	1.96161i
$790$		0			0
$791$	−3.15701	−	9.71627i	−0.112250	−	0.345471i
$792$		0			0
$793$	3.97285			0.141080
$794$		0			0
$795$	−49.3156	−	32.0827i	−1.74904	−	1.13786i
$796$		0			0
$797$	−34.2772	−	24.9039i	−1.21416	−	0.882140i	−0.218559	−	0.975824i	$-0.570136\pi$
$797$	−34.2772	−	24.9039i	−1.21416	−	0.882140i	−0.995602	+	0.0936838i	$0.970136\pi$
$798$		0			0
$799$	11.8549			0.419398
$800$		0			0
$801$	0.212748			0.00751709
$802$		0			0
$803$	8.77627	+	6.37633i	0.309708	+	0.225016i
$804$		0			0
$805$	3.32106	+	8.67262i	0.117052	+	0.305670i
$806$		0			0
$807$	47.8134			1.68311
$808$		0			0
$809$	3.60366	+	11.0909i	0.126698	+	0.389936i	0.994207	−	0.107486i	$-0.0342801\pi$
$809$	3.60366	+	11.0909i	0.126698	+	0.389936i	−0.867509	+	0.497422i	$0.834280\pi$
$810$		0			0
$811$	4.78381	−	14.7230i	0.167982	−	0.516996i	−0.831261	−	0.555882i	$-0.812381\pi$
$811$	4.78381	−	14.7230i	0.167982	−	0.516996i	0.999244	+	0.0388855i	$0.0123808\pi$
$812$		0			0
$813$	14.8462	+	45.6918i	0.520678	+	1.60248i
$814$		0			0
$815$	−30.5529	−	19.8765i	−1.07022	−	0.696242i
$816$		0			0
$817$	−14.0063	+	10.1761i	−0.490017	+	0.356018i
$818$		0			0
$819$	−0.583003	+	0.423576i	−0.0203718	+	0.0148010i
$820$		0			0
$821$	−15.3854	−	11.1781i	−0.536953	−	0.390119i	0.285999	−	0.958230i	$-0.407675\pi$
$821$	−15.3854	−	11.1781i	−0.536953	−	0.390119i	−0.822952	+	0.568111i	$0.807675\pi$
$822$		0			0
$823$	13.2354	−	40.7342i	0.461355	−	1.41991i	−0.402153	−	0.915572i	$-0.631738\pi$
$823$	13.2354	−	40.7342i	0.461355	−	1.41991i	0.863509	−	0.504334i	$-0.168262\pi$
$824$		0			0
$825$	−4.18630	−	9.44368i	−0.145748	−	0.328787i
$826$		0			0
$827$	−6.99228	+	21.5200i	−0.243145	+	0.748324i	0.752791	+	0.658260i	$0.228707\pi$
$827$	−6.99228	+	21.5200i	−0.243145	+	0.748324i	−0.995936	+	0.0900644i	$0.971293\pi$
$828$		0			0
$829$	−6.98575	−	5.07544i	−0.242625	−	0.176277i	0.459827	−	0.888009i	$-0.347911\pi$
$829$	−6.98575	−	5.07544i	−0.242625	−	0.176277i	−0.702452	+	0.711731i	$0.747911\pi$
$830$		0			0
$831$	16.6576	−	12.1025i	0.577846	−	0.419830i
$832$		0			0
$833$	7.09405	−	5.15413i	0.245794	−	0.178580i
$834$		0			0
$835$	4.44242	−	16.5259i	0.153736	−	0.571901i
$836$		0			0
$837$	7.36932	+	22.6804i	0.254721	+	0.783951i
$838$		0			0
$839$	−14.4850	+	44.5802i	−0.500077	+	1.53908i	0.308816	+	0.951122i	$0.400067\pi$
$839$	−14.4850	+	44.5802i	−0.500077	+	1.53908i	−0.808893	+	0.587956i	$0.799933\pi$
$840$		0			0
$841$	−8.75630	−	26.9491i	−0.301941	−	0.929280i
$842$		0			0
$843$	−61.5843			−2.12108
$844$		0			0
$845$	−7.48499	+	27.8442i	−0.257491	+	0.957871i
$846$		0			0
$847$	−1.41444	−	1.02765i	−0.0486008	−	0.0353106i
$848$		0			0
$849$	38.9274			1.33598
$850$		0			0
$851$	1.36751			0.0468776
$852$		0			0
$853$	24.1270	+	17.5293i	0.826094	+	0.600192i	0.918451	−	0.395534i	$-0.129440\pi$
$853$	24.1270	+	17.5293i	0.826094	+	0.600192i	−0.0923578	+	0.995726i	$0.529440\pi$
$854$		0			0
$855$	−7.95479	+	0.410440i	−0.272048	+	0.0140367i
$856$		0			0
$857$	−50.9378			−1.74000			−0.870001	−	0.493050i	$-0.835882\pi$
$857$	−50.9378			−1.74000			−0.870001	+	0.493050i	$0.835882\pi$
$858$		0			0
$859$	−4.69756	−	14.4576i	−0.160279	−	0.493287i	0.838379	−	0.545088i	$-0.183504\pi$
$859$	−4.69756	−	14.4576i	−0.160279	−	0.493287i	−0.998657	+	0.0518011i	$0.983504\pi$
$860$		0			0
$861$	−10.8748	+	33.4691i	−0.370612	+	1.14063i
$862$		0			0
$863$	−3.21891	−	9.90680i	−0.109573	−	0.337231i	0.881203	−	0.472737i	$-0.156734\pi$
$863$	−3.21891	−	9.90680i	−0.109573	−	0.337231i	−0.990777	+	0.135506i	$0.956734\pi$
$864$		0			0
$865$	14.1498	+	36.9508i	0.481107	+	1.25636i
$866$		0			0
$867$	20.1492	−	14.6392i	0.684302	−	0.497174i
$868$		0			0
$869$	−3.79577	+	2.75779i	−0.128763	+	0.0935516i
$870$		0			0
$871$	−0.219650	−	0.159585i	−0.00744257	−	0.00540734i
$872$		0			0
$873$	5.61426	−	17.2789i	0.190014	−	0.584802i
$874$		0			0
$875$	8.83191	+	17.4381i	0.298573	+	0.589515i
$876$		0			0
$877$	−10.2502	+	31.5470i	−0.346126	+	1.06527i	0.614853	+	0.788642i	$0.289215\pi$
$877$	−10.2502	+	31.5470i	−0.346126	+	1.06527i	−0.960978	+	0.276623i	$0.910785\pi$
$878$		0			0
$879$	32.0776	+	23.3057i	1.08195	+	0.786082i
$880$		0			0
$881$	−12.2728	+	8.91669i	−0.413480	+	0.300411i	−0.775009	−	0.631950i	$-0.782255\pi$
$881$	−12.2728	+	8.91669i	−0.413480	+	0.300411i	0.361529	+	0.932361i	$0.382255\pi$
$882$		0			0
$883$	7.09604	−	5.15558i	0.238801	−	0.173499i	−0.461948	−	0.886907i	$-0.652849\pi$
$883$	7.09604	−	5.15558i	0.238801	−	0.173499i	0.700749	+	0.713408i	$0.252849\pi$
$884$		0			0
$885$	6.45323	+	16.8520i	0.216923	+	0.566473i
$886$		0			0
$887$	6.84212	+	21.0579i	0.229736	+	0.707054i	0.997776	+	0.0666530i	$0.0212320\pi$
$887$	6.84212	+	21.0579i	0.229736	+	0.707054i	−0.768040	+	0.640402i	$0.778768\pi$
$888$		0			0
$889$	3.20319	−	9.85840i	0.107432	−	0.330640i
$890$		0			0
$891$	3.45986	+	10.6483i	0.115910	+	0.356733i
$892$		0			0
$893$	−14.9730			−0.501053
$894$		0			0
$895$	−15.7934	+	0.814883i	−0.527914	+	0.0272385i
$896$		0			0
$897$	−1.29030	−	0.937458i	−0.0430819	−	0.0313008i
$898$		0			0
$899$	5.43174			0.181159
$900$		0			0
$901$	28.3195			0.943461
$902$		0			0
$903$	18.0132	+	13.0873i	0.599440	+	0.435519i
$904$		0			0
$905$	−6.28285	+	23.3723i	−0.208849	+	0.776920i
$906$		0			0
$907$	50.9928			1.69319			0.846593	−	0.532240i	$-0.178650\pi$
$907$	50.9928			1.69319			0.846593	+	0.532240i	$0.178650\pi$
$908$		0			0
$909$	−3.23019	−	9.94150i	−0.107139	−	0.329739i
$910$		0			0
$911$	−11.6991	+	36.0060i	−0.387608	+	1.19293i	0.546963	+	0.837157i	$0.315784\pi$
$911$	−11.6991	+	36.0060i	−0.387608	+	1.19293i	−0.934571	+	0.355777i	$0.884216\pi$
$912$		0			0
$913$	−1.72344	−	5.30421i	−0.0570377	−	0.175544i
$914$		0			0
$915$	14.6612	−	54.5397i	0.484684	−	1.80303i
$916$		0			0
$917$	8.16108	−	5.92937i	0.269502	−	0.195805i
$918$		0			0
$919$	−25.0216	+	18.1793i	−0.825387	+	0.599678i	−0.918250	−	0.396000i	$-0.870398\pi$
$919$	−25.0216	+	18.1793i	−0.825387	+	0.599678i	0.0928638	+	0.995679i	$0.470398\pi$
$920$		0			0
$921$	37.8181	+	27.4764i	1.24615	+	0.905380i
$922$		0			0
$923$	0.605186	−	1.86257i	0.0199199	−	0.0613072i
$924$		0			0
$925$	2.86310	−	0.296241i	0.0941382	−	0.00974034i
$926$		0			0
$927$	3.62851	−	11.1674i	0.119176	−	0.366786i
$928$		0			0
$929$	−12.6078	−	9.16008i	−0.413647	−	0.300532i	0.361429	−	0.932399i	$-0.382289\pi$
$929$	−12.6078	−	9.16008i	−0.413647	−	0.300532i	−0.775077	+	0.631867i	$0.782289\pi$
$930$		0			0
$931$	−8.95992	+	6.50976i	−0.293650	+	0.213349i
$932$		0			0
$933$	12.3558	−	8.97699i	0.404510	−	0.293893i
$934$		0			0
$935$	4.16799	+	2.71152i	0.136308	+	0.0886763i
$936$		0			0
$937$	0.209052	+	0.643396i	0.00682943	+	0.0210188i	0.954413	−	0.298489i	$-0.0964825\pi$
$937$	0.209052	+	0.643396i	0.00682943	+	0.0210188i	−0.947584	+	0.319508i	$0.896483\pi$
$938$		0			0
$939$	1.54148	−	4.74420i	0.0503044	−	0.154821i
$940$		0			0
$941$	11.7788	+	36.2513i	0.383977	+	1.18176i	0.937220	+	0.348739i	$0.113390\pi$
$941$	11.7788	+	36.2513i	0.383977	+	1.18176i	−0.553243	+	0.833020i	$0.686610\pi$
$942$		0			0
$943$	−23.1437			−0.753662
$944$		0			0
$945$	−5.00173	−	13.0615i	−0.162706	−	0.424891i
$946$		0			0
$947$	28.9890	+	21.0618i	0.942016	+	0.684415i	0.948905	−	0.315561i	$-0.102193\pi$
$947$	28.9890	+	21.0618i	0.942016	+	0.684415i	−0.00688882	+	0.999976i	$0.502193\pi$
$948$		0			0
$949$	3.52538			0.114439
$950$		0			0
$951$	48.4514			1.57114
$952$		0			0
$953$	−5.08940	−	3.69767i	−0.164862	−	0.119779i	0.502295	−	0.864696i	$-0.332489\pi$
$953$	−5.08940	−	3.69767i	−0.164862	−	0.119779i	−0.667157	+	0.744917i	$0.732489\pi$
$954$		0			0
$955$	−7.60596	−	4.94812i	−0.246123	−	0.160117i
$956$		0			0
$957$	1.68351			0.0544203
$958$		0			0
$959$	0.905381	+	2.78648i	0.0292363	+	0.0899800i
$960$		0			0
$961$	4.15090	−	12.7752i	0.133900	−	0.412102i
$962$		0			0
$963$	3.94305	+	12.1355i	0.127063	+	0.391060i
$964$		0			0
$965$	−28.0404	+	22.6692i	−0.902654	+	0.729746i
$966$		0			0
$967$	−42.1954	+	30.6568i	−1.35691	+	0.985855i	−0.358278	+	0.933615i	$0.616636\pi$
$967$	−42.1954	+	30.6568i	−1.35691	+	0.985855i	−0.998635	+	0.0522402i	$0.983364\pi$
$968$		0			0
$969$	10.4389	−	7.58430i	0.335346	−	0.243643i
$970$		0			0
$971$	0.596921	+	0.433689i	0.0191561	+	0.0139177i	0.597322	−	0.802001i	$-0.296231\pi$
$971$	0.596921	+	0.433689i	0.0191561	+	0.0139177i	−0.578166	+	0.815919i	$0.696231\pi$
$972$		0			0
$973$	3.34427	−	10.2926i	0.107212	−	0.329966i
$974$		0			0
$975$	−2.90453	−	1.68320i	−0.0930195	−	0.0539057i
$976$		0			0
$977$	−1.72465	+	5.30792i	−0.0551763	+	0.169815i	−0.974847	−	0.222875i	$-0.928456\pi$
$977$	−1.72465	+	5.30792i	−0.0551763	+	0.169815i	0.919671	+	0.392691i	$0.128456\pi$
$978$		0			0
$979$	0.135704	+	0.0985945i	0.00433711	+	0.00315109i
$980$		0			0
$981$	−8.62584	+	6.26704i	−0.275402	+	0.200091i
$982$		0			0
$983$	47.4311	−	34.4607i	1.51282	−	1.09913i	0.547910	−	0.836537i	$-0.315424\pi$
$983$	47.4311	−	34.4607i	1.51282	−	1.09913i	0.964908	−	0.262589i	$-0.0845764\pi$
$984$		0			0
$985$	36.9498	−	1.90648i	1.17732	−	0.0607455i
$986$		0			0
$987$	5.95058	+	18.3140i	0.189409	+	0.582941i
$988$		0			0
$989$	−4.52490	+	13.9262i	−0.143883	+	0.442827i
$990$		0			0
$991$	3.80445	+	11.7089i	0.120852	+	0.371946i	0.993123	−	0.117079i	$-0.0373529\pi$
$991$	3.80445	+	11.7089i	0.120852	+	0.371946i	−0.872270	+	0.489024i	$0.837353\pi$
$992$		0			0
$993$	−37.4141			−1.18730
$994$		0			0
$995$	−9.51243	+	7.69028i	−0.301564	+	0.243798i
$996$		0			0
$997$	47.7602	+	34.6998i	1.51258	+	1.09895i	0.965016	+	0.262190i	$0.0844448\pi$
$997$	47.7602	+	34.6998i	1.51258	+	1.09895i	0.547564	+	0.836764i	$0.315555\pi$
$998$		0			0
$999$	−2.05956			−0.0651615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.221.4	✓	52
25.6	even	5	inner	1100.2.q.b.881.4	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.4	✓	52	1.1	even	1	trivial
1100.2.q.b.881.4	yes	52	25.6	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67142 - 1.21436i) q^{3} +(-1.73889 + 1.40580i) q^{5} +1.74835 q^{7} +(0.391935 + 1.20625i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(0.100424 + 0.309072i) q^{13} +(4.61356 - 0.238044i) q^{15} +(-1.79902 + 1.30707i) q^{17} +(2.27220 - 1.65085i) q^{19} +(-2.92223 - 2.12312i) q^{21} +(0.734063 - 2.25921i) q^{23} +(1.04747 - 4.88905i) q^{25} +(-1.10555 + 3.40252i) q^{27} +(0.659243 + 0.478968i) q^{29} +(5.39273 - 3.91805i) q^{31} +(1.67142 - 1.21436i) q^{33} +(-3.04018 + 2.45782i) q^{35} +(0.177894 + 0.547502i) q^{37} +(0.207474 - 0.638540i) q^{39} +(-3.01067 - 9.26590i) q^{41} -6.16418 q^{43} +(-2.37728 - 1.54656i) q^{45} +(-4.31299 - 3.13357i) q^{47} -3.94328 q^{49} +4.59418 q^{51} +(-10.3030 - 7.48559i) q^{53} +(-0.799646 - 2.08820i) q^{55} -5.80254 q^{57} +(1.20707 + 3.71498i) q^{59} +(3.77774 - 11.6267i) q^{61} +(0.685239 + 2.10895i) q^{63} +(-0.609118 - 0.396267i) q^{65} +(-0.675894 + 0.491066i) q^{67} +(-3.97043 + 2.88469i) q^{69} +(-4.87541 - 3.54219i) q^{71} +(3.35224 - 10.3171i) q^{73} +(-7.68784 + 6.89967i) q^{75} +(-0.540269 + 1.66278i) q^{77} +(3.79577 + 2.75779i) q^{79} +(9.05802 - 6.58104i) q^{81} +(-4.51203 + 3.27818i) q^{83} +(1.29083 - 4.80190i) q^{85} +(-0.520234 - 1.60112i) q^{87} +(0.0518342 - 0.159529i) q^{89} +(0.175575 + 0.540365i) q^{91} -13.7715 q^{93} +(-1.63034 + 6.06490i) q^{95} +(-11.5887 - 8.41970i) q^{97} -1.26833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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