LMFDB - Embedded newform 1100.2.q.b.441.7

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			441.7
Character	$\chi$	$=$	1100.441
Dual form			1100.2.q.b.661.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0181419 - 0.0558349i) q^{3} +(-0.144597 - 2.23139i) q^{5} -1.97462 q^{7} +(2.42426 - 1.76133i) q^{9} +(0.809017 + 0.587785i) q^{11} +(-4.83503 + 3.51285i) q^{13} +(-0.121966 + 0.0485551i) q^{15} +(0.510441 - 1.57098i) q^{17} +(2.25718 - 6.94688i) q^{19} +(0.0358233 + 0.110253i) q^{21} +(-1.96235 - 1.42573i) q^{23} +(-4.95818 + 0.645304i) q^{25} +(-0.284812 - 0.206928i) q^{27} +(-0.340135 - 1.04683i) q^{29} +(2.45740 - 7.56311i) q^{31} +(0.0181419 - 0.0558349i) q^{33} +(0.285524 + 4.40615i) q^{35} +(-7.22608 + 5.25005i) q^{37} +(0.283856 + 0.206234i) q^{39} +(-8.26865 + 6.00753i) q^{41} -1.32037 q^{43} +(-4.28075 - 5.15479i) q^{45} +(1.29876 + 3.99718i) q^{47} -3.10087 q^{49} -0.0969756 q^{51} +(-1.27728 - 3.93107i) q^{53} +(1.19460 - 1.89022i) q^{55} -0.428828 q^{57} +(-3.41125 + 2.47842i) q^{59} +(-8.24554 - 5.99074i) q^{61} +(-4.78700 + 3.47796i) q^{63} +(8.53767 + 10.2809i) q^{65} +(3.91755 - 12.0570i) q^{67} +(-0.0440049 + 0.135433i) q^{69} +(-4.34884 - 13.3843i) q^{71} +(1.45820 + 1.05944i) q^{73} +(0.125981 + 0.265133i) q^{75} +(-1.59750 - 1.16065i) q^{77} +(2.44522 + 7.52562i) q^{79} +(2.77157 - 8.53002i) q^{81} +(2.94224e-5 - 9.05529e-5i) q^{83} +(-3.57926 - 0.911833i) q^{85} +(-0.0522788 + 0.0379828i) q^{87} +(4.66291 + 3.38780i) q^{89} +(9.54735 - 6.93655i) q^{91} -0.466868 q^{93} +(-15.8276 - 4.03214i) q^{95} +(3.11800 + 9.59623i) q^{97} +2.99655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

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

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
$3$	−0.0181419	−	0.0558349i	−0.0104742	−	0.0322363i	0.945683	−	0.325091i	$-0.105395\pi$
$3$	−0.0181419	−	0.0558349i	−0.0104742	−	0.0322363i	−0.956157	+	0.292854i	$0.905395\pi$
$4$		0			0
$5$	−0.144597	−	2.23139i	−0.0646658	−	0.997907i
$5$	−0.144597	−	2.23139i	−0.0646658	−	0.997907i
$6$		0			0
$7$	−1.97462			−0.746337			−0.373168	−	0.927764i	$-0.621729\pi$
$7$	−1.97462			−0.746337			−0.373168	+	0.927764i	$0.621729\pi$
$8$		0			0
$9$	2.42426	−	1.76133i	0.808088	−	0.587110i
$10$		0			0
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$12$		0			0
$13$	−4.83503	+	3.51285i	−1.34099	+	0.974290i	−0.341588	+	0.939850i	$0.610965\pi$
$13$	−4.83503	+	3.51285i	−1.34099	+	0.974290i	−0.999407	+	0.0344401i	$0.989035\pi$
$14$		0			0
$15$	−0.121966	+	0.0485551i	−0.0314915	+	0.0125369i
$16$		0			0
$17$	0.510441	−	1.57098i	0.123800	−	0.381018i	−0.869880	−	0.493263i	$-0.835804\pi$
$17$	0.510441	−	1.57098i	0.123800	−	0.381018i	0.993681	+	0.112245i	$0.0358042\pi$
$18$		0			0
$19$	2.25718	−	6.94688i	0.517832	−	1.59372i	−0.260237	−	0.965545i	$-0.583801\pi$
$19$	2.25718	−	6.94688i	0.517832	−	1.59372i	0.778069	−	0.628179i	$-0.216199\pi$
$20$		0			0
$21$	0.0358233	+	0.110253i	0.00781728	+	0.0240591i
$22$		0			0
$23$	−1.96235	−	1.42573i	−0.409179	−	0.297286i	0.364090	−	0.931364i	$-0.381380\pi$
$23$	−1.96235	−	1.42573i	−0.409179	−	0.297286i	−0.773269	+	0.634078i	$0.781380\pi$
$24$		0			0
$25$	−4.95818	+	0.645304i	−0.991637	+	0.129061i
$26$		0			0
$27$	−0.284812	−	0.206928i	−0.0548122	−	0.0398234i
$28$		0			0
$29$	−0.340135	−	1.04683i	−0.0631615	−	0.194391i	0.914496	−	0.404595i	$-0.132587\pi$
$29$	−0.340135	−	1.04683i	−0.0631615	−	0.194391i	−0.977658	+	0.210204i	$0.932587\pi$
$30$		0			0
$31$	2.45740	−	7.56311i	0.441363	−	1.35838i	−0.445061	−	0.895500i	$-0.646818\pi$
$31$	2.45740	−	7.56311i	0.441363	−	1.35838i	0.886424	−	0.462875i	$-0.153182\pi$
$32$		0			0
$33$	0.0181419	−	0.0558349i	0.00315809	−	0.00971961i
$34$		0			0
$35$	0.285524	+	4.40615i	0.0482624	+	0.744775i
$36$		0			0
$37$	−7.22608	+	5.25005i	−1.18796	+	0.863104i	−0.993047	−	0.117717i	$-0.962442\pi$
$37$	−7.22608	+	5.25005i	−1.18796	+	0.863104i	−0.194913	+	0.980821i	$0.562442\pi$
$38$		0			0
$39$	0.283856	+	0.206234i	0.0454534	+	0.0330238i
$40$		0			0
$41$	−8.26865	+	6.00753i	−1.29135	+	0.938218i	−0.999832	−	0.0183482i	$-0.994159\pi$
$41$	−8.26865	+	6.00753i	−1.29135	+	0.938218i	−0.291515	+	0.956566i	$0.594159\pi$
$42$		0			0
$43$	−1.32037			−0.201355			−0.100677	−	0.994919i	$-0.532101\pi$
$43$	−1.32037			−0.201355			−0.100677	+	0.994919i	$0.532101\pi$
$44$		0			0
$45$	−4.28075	−	5.15479i	−0.638137	−	0.768430i
$46$		0			0
$47$	1.29876	+	3.99718i	0.189444	+	0.583049i	0.999997	−	0.00261712i	$-0.000833055\pi$
$47$	1.29876	+	3.99718i	0.189444	+	0.583049i	−0.810553	+	0.585666i	$0.800833\pi$
$48$		0			0
$49$	−3.10087			−0.442982
$50$		0			0
$51$	−0.0969756			−0.0135793
$52$		0			0
$53$	−1.27728	−	3.93107i	−0.175448	−	0.539974i	0.824206	−	0.566291i	$-0.191622\pi$
$53$	−1.27728	−	3.93107i	−0.175448	−	0.539974i	−0.999654	+	0.0263171i	$0.991622\pi$
$54$		0			0
$55$	1.19460	−	1.89022i	0.161079	−	0.254878i
$56$		0			0
$57$	−0.428828			−0.0567996
$58$		0			0
$59$	−3.41125	+	2.47842i	−0.444107	+	0.322663i	−0.787265	−	0.616615i	$-0.788503\pi$
$59$	−3.41125	+	2.47842i	−0.444107	+	0.322663i	0.343158	+	0.939278i	$0.388503\pi$
$60$		0			0
$61$	−8.24554	−	5.99074i	−1.05573	−	0.767035i	−0.0824391	−	0.996596i	$-0.526271\pi$
$61$	−8.24554	−	5.99074i	−1.05573	−	0.767035i	−0.973294	+	0.229561i	$0.926271\pi$
$62$		0			0
$63$	−4.78700	+	3.47796i	−0.603105	+	0.438182i
$64$		0			0
$65$	8.53767	+	10.2809i	1.05897	+	1.27519i
$66$		0			0
$67$	3.91755	−	12.0570i	0.478605	−	1.47300i	−0.362428	−	0.932012i	$-0.618052\pi$
$67$	3.91755	−	12.0570i	0.478605	−	1.47300i	0.841033	−	0.540984i	$-0.181948\pi$
$68$		0			0
$69$	−0.0440049	+	0.135433i	−0.00529757	+	0.0163042i
$70$		0			0
$71$	−4.34884	−	13.3843i	−0.516112	−	1.58843i	−0.781249	−	0.624219i	$-0.785417\pi$
$71$	−4.34884	−	13.3843i	−0.516112	−	1.58843i	0.265137	−	0.964211i	$-0.414583\pi$
$72$		0			0
$73$	1.45820	+	1.05944i	0.170669	+	0.123998i	0.669841	−	0.742505i	$-0.266362\pi$
$73$	1.45820	+	1.05944i	0.170669	+	0.123998i	−0.499172	+	0.866503i	$0.666362\pi$
$74$		0			0
$75$	0.125981	+	0.265133i	0.0145471	+	0.0306149i
$76$		0			0
$77$	−1.59750	−	1.16065i	−0.182052	−	0.132269i
$78$		0			0
$79$	2.44522	+	7.52562i	0.275109	+	0.846698i	0.989191	+	0.146636i	$0.0468446\pi$
$79$	2.44522	+	7.52562i	0.275109	+	0.846698i	−0.714082	+	0.700063i	$0.753155\pi$
$80$		0			0
$81$	2.77157	−	8.53002i	0.307952	−	0.947780i
$82$		0			0
$83$	2.94224e−5	0	9.05529e-5i	3.22953e−6	0	9.93947e-6i	−0.951055	−	0.309022i	$-0.899998\pi$
$83$	2.94224e−5	0	9.05529e-5i	3.22953e−6	0	9.93947e-6i	0.951058	+	0.309012i	$0.0999983\pi$
$84$		0			0
$85$	−3.57926	−	0.911833i	−0.388226	−	0.0989022i
$86$		0			0
$87$	−0.0522788	+	0.0379828i	−0.00560488	+	0.00407218i
$88$		0			0
$89$	4.66291	+	3.38780i	0.494268	+	0.359106i	0.806823	−	0.590793i	$-0.201185\pi$
$89$	4.66291	+	3.38780i	0.494268	+	0.359106i	−0.312556	+	0.949899i	$0.601185\pi$
$90$		0			0
$91$	9.54735	−	6.93655i	1.00083	−	0.727148i
$92$		0			0
$93$	−0.466868			−0.0484119
$94$		0			0
$95$	−15.8276	−	4.03214i	−1.62387	−	0.413689i
$96$		0			0
$97$	3.11800	+	9.59623i	0.316585	+	0.974350i	0.975097	+	0.221779i	$0.0711864\pi$
$97$	3.11800	+	9.59623i	0.316585	+	0.974350i	−0.658512	+	0.752571i	$0.728814\pi$
$98$		0			0
$99$	2.99655			0.301165
$100$		0			0
$101$	−5.14273			−0.511720			−0.255860	−	0.966714i	$-0.582359\pi$
$101$	−5.14273			−0.511720			−0.255860	+	0.966714i	$0.582359\pi$
$102$		0			0
$103$	−5.64496	−	17.3734i	−0.556215	−	1.71185i	−0.692714	−	0.721212i	$-0.743585\pi$
$103$	−5.64496	−	17.3734i	−0.556215	−	1.71185i	0.136500	−	0.990640i	$-0.456415\pi$
$104$		0			0
$105$	0.240837	−	0.0958779i	0.0235033	−	0.00935673i
$106$		0			0
$107$	10.9806			1.06154			0.530770	−	0.847516i	$-0.321903\pi$
$107$	10.9806			1.06154			0.530770	+	0.847516i	$0.321903\pi$
$108$		0			0
$109$	9.48992	−	6.89483i	0.908970	−	0.660405i	−0.0317845	−	0.999495i	$-0.510119\pi$
$109$	9.48992	−	6.89483i	0.908970	−	0.660405i	0.940754	+	0.339090i	$0.110119\pi$
$110$		0			0
$111$	0.424231	+	0.308222i	0.0402662	+	0.0292551i
$112$		0			0
$113$	11.2076	−	8.14281i	1.05432	−	0.766011i	0.0812943	−	0.996690i	$-0.474095\pi$
$113$	11.2076	−	8.14281i	1.05432	−	0.766011i	0.973030	+	0.230679i	$0.0740946\pi$
$114$		0			0
$115$	−2.89761	+	4.58493i	−0.270204	+	0.427547i
$116$		0			0
$117$	−5.53408	+	17.0322i	−0.511626	+	1.57462i
$118$		0			0
$119$	−1.00793	+	3.10208i	−0.0923966	+	0.284367i
$120$		0			0
$121$	0.309017	+	0.951057i	0.0280925	+	0.0864597i
$122$		0			0
$123$	0.485438	+	0.352692i	0.0437705	+	0.0318011i
$124$		0			0
$125$	2.15686	+	10.9703i	0.192916	+	0.981215i
$126$		0			0
$127$	5.89681	+	4.28429i	0.523258	+	0.380169i	0.817830	−	0.575460i	$-0.195177\pi$
$127$	5.89681	+	4.28429i	0.523258	+	0.380169i	−0.294572	+	0.955629i	$0.595177\pi$
$128$		0			0
$129$	0.0239540	+	0.0737228i	0.00210903	+	0.00649093i
$130$		0			0
$131$	−4.99141	+	15.3620i	−0.436101	+	1.34218i	0.455853	+	0.890055i	$0.349334\pi$
$131$	−4.99141	+	15.3620i	−0.436101	+	1.34218i	−0.891954	+	0.452126i	$0.850666\pi$
$132$		0			0
$133$	−4.45707	+	13.7175i	−0.386477	+	1.18945i
$134$		0			0
$135$	−0.420554	+	0.665448i	−0.0361955	+	0.0572726i
$136$		0			0
$137$	13.9130	−	10.1084i	1.18867	−	0.863619i	0.195546	−	0.980694i	$-0.437352\pi$
$137$	13.9130	−	10.1084i	1.18867	−	0.863619i	0.993123	+	0.117076i	$0.0373520\pi$
$138$		0			0
$139$	7.25332	+	5.26984i	0.615218	+	0.446982i	0.851248	−	0.524764i	$-0.175846\pi$
$139$	7.25332	+	5.26984i	0.615218	+	0.446982i	−0.236030	+	0.971746i	$0.575846\pi$
$140$		0			0
$141$	0.199620	−	0.145033i	0.0168111	−	0.0122139i
$142$		0			0
$143$	−5.97642			−0.499773
$144$		0			0
$145$	−2.28670	+	0.910341i	−0.189900	+	0.0755997i
$146$		0			0
$147$	0.0562556	+	0.173137i	0.00463988	+	0.0142801i
$148$		0			0
$149$	−12.5807			−1.03065			−0.515324	−	0.856996i	$-0.672328\pi$
$149$	−12.5807			−1.03065			−0.515324	+	0.856996i	$0.672328\pi$
$150$		0			0
$151$	12.7753			1.03964			0.519819	−	0.854277i	$-0.326000\pi$
$151$	12.7753			1.03964			0.519819	+	0.854277i	$0.326000\pi$
$152$		0			0
$153$	−1.52956	−	4.70751i	−0.123658	−	0.380580i
$154$		0			0
$155$	−17.2316	−	4.38982i	−1.38407	−	0.352599i
$156$		0			0
$157$	14.9139			1.19026			0.595129	−	0.803630i	$-0.297101\pi$
$157$	14.9139			1.19026			0.595129	+	0.803630i	$0.297101\pi$
$158$		0			0
$159$	−0.196318	+	0.142634i	−0.0155691	+	0.0113116i
$160$		0			0
$161$	3.87491	+	2.81528i	0.305385	+	0.221875i
$162$		0			0
$163$	−7.91720	+	5.75219i	−0.620123	+	0.450546i	−0.852965	−	0.521969i	$-0.825198\pi$
$163$	−7.91720	+	5.75219i	−0.620123	+	0.450546i	0.232841	+	0.972515i	$0.425198\pi$
$164$		0			0
$165$	−0.127213	−	0.0324080i	−0.00990349	−	0.00252296i
$166$		0			0
$167$	2.14283	−	6.59495i	0.165817	−	0.510332i	−0.833279	−	0.552853i	$-0.813539\pi$
$167$	2.14283	−	6.59495i	0.165817	−	0.510332i	0.999096	+	0.0425211i	$0.0135390\pi$
$168$		0			0
$169$	7.02013	−	21.6057i	0.540010	−	1.66198i
$170$		0			0
$171$	−6.76375	−	20.8167i	−0.517237	−	1.59189i
$172$		0			0
$173$	−19.0882	−	13.8684i	−1.45125	−	1.05439i	−0.985538	−	0.169454i	$-0.945799\pi$
$173$	−19.0882	−	13.8684i	−1.45125	−	1.05439i	−0.465709	−	0.884938i	$-0.654201\pi$
$174$		0			0
$175$	9.79053	−	1.27423i	0.740095	−	0.0963228i
$176$		0			0
$177$	0.200269	+	0.145504i	0.0150531	+	0.0109367i
$178$		0			0
$179$	−3.44626	−	10.6065i	−0.257586	−	0.792767i	−0.993309	−	0.115485i	$-0.963158\pi$
$179$	−3.44626	−	10.6065i	−0.257586	−	0.792767i	0.735723	−	0.677282i	$-0.236842\pi$
$180$		0			0
$181$	1.42040	−	4.37153i	0.105577	−	0.324933i	−0.884288	−	0.466941i	$-0.845356\pi$
$181$	1.42040	−	4.37153i	0.105577	−	0.324933i	0.989865	+	0.142008i	$0.0453559\pi$
$182$		0			0
$183$	−0.184903	+	0.569072i	−0.0136684	+	0.0420670i
$184$		0			0
$185$	12.7598	+	15.3650i	0.938117	+	1.12966i
$186$		0			0
$187$	1.33635	−	0.970916i	0.0977237	−	0.0710004i
$188$		0			0
$189$	0.562396	+	0.408605i	0.0409083	+	0.0297216i
$190$		0			0
$191$	−9.11843	+	6.62493i	−0.659786	+	0.479363i	−0.866591	−	0.499020i	$-0.833694\pi$
$191$	−9.11843	+	6.62493i	−0.659786	+	0.479363i	0.206804	+	0.978382i	$0.433694\pi$
$192$		0			0
$193$	−0.396852			−0.0285660			−0.0142830	−	0.999898i	$-0.504547\pi$
$193$	−0.396852			−0.0285660			−0.0142830	+	0.999898i	$0.504547\pi$
$194$		0			0
$195$	0.419142	−	0.663214i	0.0300154	−	0.0474937i
$196$		0			0
$197$	6.60750	+	20.3358i	0.470765	+	1.44887i	0.851585	+	0.524216i	$0.175642\pi$
$197$	6.60750	+	20.3358i	0.470765	+	1.44887i	−0.380820	+	0.924649i	$0.624358\pi$
$198$		0			0
$199$	11.7761			0.834786			0.417393	−	0.908726i	$-0.362944\pi$
$199$	11.7761			0.834786			0.417393	+	0.908726i	$0.362944\pi$
$200$		0			0
$201$	−0.744273			−0.0524969
$202$		0			0
$203$	0.671638	+	2.06709i	0.0471397	+	0.145081i
$204$		0			0
$205$	14.6007	+	17.5819i	1.01976	+	1.22797i
$206$		0			0
$207$	−7.26845			−0.505192
$208$		0			0
$209$	5.90937	−	4.29341i	0.408760	−	0.296981i
$210$		0			0
$211$	11.0386	+	8.02003i	0.759930	+	0.552122i	0.898889	−	0.438177i	$-0.144376\pi$
$211$	11.0386	+	8.02003i	0.759930	+	0.552122i	−0.138959	+	0.990298i	$0.544376\pi$
$212$		0			0
$213$	−0.668418	+	0.485634i	−0.0457992	+	0.0332751i
$214$		0			0
$215$	0.190922	+	2.94626i	0.0130208	+	0.200933i
$216$		0			0
$217$	−4.85244	+	14.9343i	−0.329405	+	1.01381i
$218$		0			0
$219$	0.0326995	−	0.100639i	0.00220962	−	0.00680053i
$220$		0			0
$221$	3.05061	+	9.38881i	0.205206	+	0.631560i
$222$		0			0
$223$	2.04854	+	1.48835i	0.137181	+	0.0996675i	0.654259	−	0.756270i	$-0.272981\pi$
$223$	2.04854	+	1.48835i	0.137181	+	0.0996675i	−0.517079	+	0.855938i	$0.672981\pi$
$224$		0			0
$225$	−10.8833	+	10.2974i	−0.725556	+	0.686492i
$226$		0			0
$227$	−6.14577	−	4.46516i	−0.407909	−	0.296363i	0.364846	−	0.931068i	$-0.381122\pi$
$227$	−6.14577	−	4.46516i	−0.407909	−	0.296363i	−0.772755	+	0.634705i	$0.781122\pi$
$228$		0			0
$229$	5.78666	+	17.8095i	0.382393	+	1.17689i	0.938354	+	0.345677i	$0.112351\pi$
$229$	5.78666	+	17.8095i	0.382393	+	1.17689i	−0.555960	+	0.831209i	$0.687649\pi$
$230$		0			0
$231$	−0.0358233	+	0.110253i	−0.00235700	+	0.00725410i
$232$		0			0
$233$	−3.56506	+	10.9721i	−0.233555	+	0.718808i	0.763755	+	0.645506i	$0.223354\pi$
$233$	−3.56506	+	10.9721i	−0.233555	+	0.718808i	−0.997310	+	0.0733018i	$0.976646\pi$
$234$		0			0
$235$	8.73146	−	3.47602i	0.569578	−	0.226751i
$236$		0			0
$237$	0.375831	−	0.273057i	0.0244129	−	0.0177370i
$238$		0			0
$239$	12.4707	+	9.06046i	0.806660	+	0.586073i	0.912860	−	0.408272i	$-0.133869\pi$
$239$	12.4707	+	9.06046i	0.806660	+	0.586073i	−0.106200	+	0.994345i	$0.533869\pi$
$240$		0			0
$241$	−0.0783056	+	0.0568923i	−0.00504411	+	0.00366476i	−0.590304	−	0.807181i	$-0.700992\pi$
$241$	−0.0783056	+	0.0568923i	−0.00504411	+	0.00366476i	0.585260	+	0.810845i	$0.300992\pi$
$242$		0			0
$243$	−1.58270			−0.101530
$244$		0			0
$245$	0.448377	+	6.91925i	0.0286457	+	0.442054i
$246$		0			0
$247$	13.4898	+	41.5175i	0.858338	+	2.64169i
$248$		0			0
$249$	−5.58979e−6	0		−3.54238e−7	0
$250$		0			0
$251$	23.0654			1.45588			0.727938	−	0.685643i	$-0.240479\pi$
$251$	23.0654			1.45588			0.727938	+	0.685643i	$0.240479\pi$
$252$		0			0
$253$	−0.749552	−	2.30689i	−0.0471240	−	0.145033i
$254$		0			0
$255$	0.0140224	+	0.216390i	0.000878116	+	0.0135509i
$256$		0			0
$257$	−5.92827			−0.369795			−0.184898	−	0.982758i	$-0.559195\pi$
$257$	−5.92827			−0.369795			−0.184898	+	0.982758i	$0.559195\pi$
$258$		0			0
$259$	14.2688	−	10.3669i	0.886618	−	0.644166i
$260$		0			0
$261$	−2.66839	−	1.93870i	−0.165169	−	0.120002i
$262$		0			0
$263$	5.63791	−	4.09618i	0.347649	−	0.252581i	−0.400233	−	0.916413i	$-0.631071\pi$
$263$	5.63791	−	4.09618i	0.347649	−	0.252581i	0.747882	+	0.663832i	$0.231071\pi$
$264$		0			0
$265$	−8.58704	+	3.41853i	−0.527498	+	0.209999i
$266$		0			0
$267$	0.104564	−	0.321814i	0.00639920	−	0.0196947i
$268$		0			0
$269$	−2.29436	+	7.06132i	−0.139890	+	0.430536i	−0.996319	−	0.0857288i	$-0.972678\pi$
$269$	−2.29436	+	7.06132i	−0.139890	+	0.430536i	0.856429	+	0.516265i	$0.172678\pi$
$270$		0			0
$271$	−0.757408	−	2.33106i	−0.0460093	−	0.141602i	0.925413	−	0.378961i	$-0.123718\pi$
$271$	−0.757408	−	2.33106i	−0.0460093	−	0.141602i	−0.971422	+	0.237359i	$0.923718\pi$
$272$		0			0
$273$	−0.560508	−	0.407233i	−0.0339235	−	0.0246469i
$274$		0			0
$275$	−4.39055	−	2.39228i	−0.264760	−	0.144260i
$276$		0			0
$277$	16.2996	+	11.8423i	0.979347	+	0.711537i	0.957563	−	0.288225i	$-0.0930652\pi$
$277$	16.2996	+	11.8423i	0.979347	+	0.711537i	0.0217846	+	0.999763i	$0.493065\pi$
$278$		0			0
$279$	−7.36374	−	22.6633i	−0.440856	−	1.35681i
$280$		0			0
$281$	8.36121	−	25.7332i	0.498788	−	1.53511i	−0.312181	−	0.950023i	$-0.601060\pi$
$281$	8.36121	−	25.7332i	0.498788	−	1.53511i	0.810969	−	0.585089i	$-0.198940\pi$
$282$		0			0
$283$	4.24546	−	13.0662i	0.252366	−	0.776703i	−0.741971	−	0.670432i	$-0.766109\pi$
$283$	4.24546	−	13.0662i	0.252366	−	0.776703i	0.994337	−	0.106271i	$-0.0338912\pi$
$284$		0			0
$285$	0.0620072	+	0.956881i	0.00367299	+	0.0566807i
$286$		0			0
$287$	16.3275	−	11.8626i	0.963779	−	0.700227i
$288$		0			0
$289$	11.5459	+	8.38857i	0.679169	+	0.493445i
$290$		0			0
$291$	0.479238	−	0.348187i	0.0280934	−	0.0204111i
$292$		0			0
$293$	−25.8502			−1.51018			−0.755092	−	0.655619i	$-0.772408\pi$
$293$	−25.8502			−1.51018			−0.755092	+	0.655619i	$0.772408\pi$
$294$		0			0
$295$	6.02357	+	7.25345i	0.350706	+	0.422312i
$296$		0			0
$297$	−0.108789	−	0.334817i	−0.00631256	−	0.0194280i
$298$		0			0
$299$	14.4964			0.838350
$300$		0			0
$301$	2.60723			0.150278
$302$		0			0
$303$	0.0932986	+	0.287144i	0.00535987	+	0.0164960i
$304$		0			0
$305$	−12.1754	+	19.2652i	−0.697160	+	1.10312i
$306$		0			0
$307$	−17.8918			−1.02114			−0.510570	−	0.859836i	$-0.670566\pi$
$307$	−17.8918			−1.02114			−0.510570	+	0.859836i	$0.670566\pi$
$308$		0			0
$309$	−0.867632	+	0.630372i	−0.0493579	+	0.0358606i
$310$		0			0
$311$	−13.8617	−	10.0711i	−0.786024	−	0.571080i	0.120757	−	0.992682i	$-0.461468\pi$
$311$	−13.8617	−	10.0711i	−0.786024	−	0.571080i	−0.906781	+	0.421602i	$0.861468\pi$
$312$		0			0
$313$	6.50652	−	4.72726i	0.367770	−	0.267201i	−0.388516	−	0.921442i	$-0.627012\pi$
$313$	6.50652	−	4.72726i	0.367770	−	0.267201i	0.756286	+	0.654242i	$0.227012\pi$
$314$		0			0
$315$	8.45286	+	10.1788i	0.476265	+	0.573508i
$316$		0			0
$317$	−7.19006	+	22.1287i	−0.403834	+	1.24287i	0.518031	+	0.855362i	$0.326665\pi$
$317$	−7.19006	+	22.1287i	−0.403834	+	1.24287i	−0.921865	+	0.387511i	$0.873335\pi$
$318$		0			0
$319$	0.340135	−	1.04683i	0.0190439	−	0.0586111i
$320$		0			0
$321$	−0.199209	−	0.613103i	−0.0111188	−	0.0342201i
$322$		0			0
$323$	−9.76122	−	7.09194i	−0.543129	−	0.394606i
$324$		0			0
$325$	21.7061	−	20.5374i	1.20404	−	1.13921i
$326$		0			0
$327$	−0.557137	−	0.404784i	−0.0308097	−	0.0223846i
$328$		0			0
$329$	−2.56457	−	7.89292i	−0.141389	−	0.435151i
$330$		0			0
$331$	7.18930	−	22.1264i	0.395160	−	1.21618i	−0.533677	−	0.845688i	$-0.679190\pi$
$331$	7.18930	−	22.1264i	0.395160	−	1.21618i	0.928837	−	0.370488i	$-0.120810\pi$
$332$		0			0
$333$	−8.27084	+	25.4550i	−0.453239	+	1.39493i
$334$		0			0
$335$	−27.4703	−	6.99818i	−1.50086	−	0.382351i
$336$		0			0
$337$	24.8461	−	18.0518i	1.35346	−	0.983343i	0.354624	−	0.935009i	$-0.384609\pi$
$337$	24.8461	−	18.0518i	1.35346	−	0.983343i	0.998831	−	0.0483339i	$-0.0153912\pi$
$338$		0			0
$339$	−0.657980	−	0.478051i	−0.0357366	−	0.0259641i
$340$		0			0
$341$	6.43357	−	4.67426i	0.348397	−	0.253125i
$342$		0			0
$343$	19.9454			1.07695
$344$		0			0
$345$	0.308567	+	0.0786088i	0.0166127	+	0.00423216i
$346$		0			0
$347$	−6.49444	−	19.9878i	−0.348640	−	1.07300i	−0.959606	−	0.281347i	$-0.909219\pi$
$347$	−6.49444	−	19.9878i	−0.348640	−	1.07300i	0.610966	−	0.791657i	$-0.290781\pi$
$348$		0			0
$349$	5.40578			0.289365			0.144682	−	0.989478i	$-0.453784\pi$
$349$	5.40578			0.289365			0.144682	+	0.989478i	$0.453784\pi$
$350$		0			0
$351$	2.10398			0.112302
$352$		0			0
$353$	−0.458410	−	1.41084i	−0.0243987	−	0.0750915i	0.938116	−	0.346322i	$-0.112569\pi$
$353$	−0.458410	−	1.41084i	−0.0243987	−	0.0750915i	−0.962514	+	0.271230i	$0.912569\pi$
$354$		0			0
$355$	−29.2368	+	11.6393i	−1.55173	+	0.617749i
$356$		0			0
$357$	0.191490			0.0101347
$358$		0			0
$359$	29.6055	−	21.5096i	1.56252	−	1.13523i	0.628607	−	0.777723i	$-0.283625\pi$
$359$	29.6055	−	21.5096i	1.56252	−	1.13523i	0.933909	−	0.357512i	$-0.116375\pi$
$360$		0			0
$361$	−27.7930	−	20.1928i	−1.46279	−	1.06278i
$362$		0			0
$363$	0.0474960	−	0.0345079i	0.00249289	−	0.00181119i
$364$		0			0
$365$	2.15318	−	3.40700i	0.112702	−	0.178330i
$366$		0			0
$367$	7.10197	−	21.8576i	0.370720	−	1.14096i	−0.575601	−	0.817730i	$-0.695232\pi$
$367$	7.10197	−	21.8576i	0.370720	−	1.14096i	0.946321	−	0.323228i	$-0.104768\pi$
$368$		0			0
$369$	−9.46415	+	29.1276i	−0.492684	+	1.51632i
$370$		0			0
$371$	2.52215	+	7.76237i	0.130943	+	0.403002i
$372$		0			0
$373$	−6.60151	−	4.79628i	−0.341813	−	0.248342i	0.403613	−	0.914930i	$-0.367754\pi$
$373$	−6.60151	−	4.79628i	−0.341813	−	0.248342i	−0.745426	+	0.666588i	$0.767754\pi$
$374$		0			0
$375$	0.573397	−	0.319450i	0.0296101	−	0.0164963i
$376$		0			0
$377$	5.32191	+	3.86660i	0.274092	+	0.199140i
$378$		0			0
$379$	−1.02439	−	3.15275i	−0.0526193	−	0.161946i	0.921294	−	0.388868i	$-0.127134\pi$
$379$	−1.02439	−	3.15275i	−0.0526193	−	0.161946i	−0.973913	+	0.226922i	$0.927134\pi$
$380$		0			0
$381$	0.132234	−	0.406973i	0.00677453	−	0.0208499i
$382$		0			0
$383$	−5.45429	+	16.7866i	−0.278701	+	0.857754i	0.709515	+	0.704690i	$0.248914\pi$
$383$	−5.45429	+	16.7866i	−0.278701	+	0.857754i	−0.988216	+	0.153064i	$0.951086\pi$
$384$		0			0
$385$	−2.35887	+	3.73247i	−0.120219	+	0.190224i
$386$		0			0
$387$	−3.20093	+	2.32561i	−0.162712	+	0.118217i
$388$		0			0
$389$	−10.6158	−	7.71286i	−0.538245	−	0.391058i	0.285188	−	0.958472i	$-0.407944\pi$
$389$	−10.6158	−	7.71286i	−0.538245	−	0.391058i	−0.823433	+	0.567414i	$0.807944\pi$
$390$		0			0
$391$	−3.24146	+	2.35506i	−0.163928	+	0.119100i
$392$		0			0
$393$	0.948287			0.0478348
$394$		0			0
$395$	16.4390	−	6.54442i	0.827136	−	0.329286i
$396$		0			0
$397$	−6.75862	−	20.8009i	−0.339205	−	1.04397i	−0.964613	−	0.263669i	$-0.915067\pi$
$397$	−6.75862	−	20.8009i	−0.339205	−	1.04397i	0.625408	−	0.780298i	$-0.284933\pi$
$398$		0			0
$399$	0.846772			0.0423916
$400$		0			0
$401$	−0.453451			−0.0226442			−0.0113221	−	0.999936i	$-0.503604\pi$
$401$	−0.453451			−0.0226442			−0.0113221	+	0.999936i	$0.503604\pi$
$402$		0			0
$403$	14.6865	+	45.2003i	0.731586	+	2.25159i
$404$		0			0
$405$	−19.4345	−	4.95103i	−0.965710	−	0.246019i
$406$		0			0
$407$	−8.93193			−0.442739
$408$		0			0
$409$	−10.4348	+	7.58136i	−0.515970	+	0.374874i	−0.815084	−	0.579343i	$-0.803309\pi$
$409$	−10.4348	+	7.58136i	−0.515970	+	0.374874i	0.299114	+	0.954217i	$0.403309\pi$
$410$		0			0
$411$	−0.816809	−	0.593447i	−0.0402902	−	0.0292726i
$412$		0			0
$413$	6.73593	−	4.89394i	0.331453	−	0.240815i
$414$		0			0
$415$	−0.000206313	0	5.25591e-5i	−1.01275e−5	0	2.58003e-6i
$416$		0			0
$417$	0.162653	−	0.500593i	0.00796513	−	0.0245141i
$418$		0			0
$419$	4.99591	−	15.3758i	0.244066	−	0.751158i	−0.751723	−	0.659480i	$-0.770777\pi$
$419$	4.99591	−	15.3758i	0.244066	−	0.751158i	0.995789	−	0.0916787i	$-0.0292233\pi$
$420$		0			0
$421$	6.95891	+	21.4173i	0.339156	+	1.04382i	0.964638	+	0.263577i	$0.0849024\pi$
$421$	6.95891	+	21.4173i	0.339156	+	1.04382i	−0.625482	+	0.780239i	$0.715098\pi$
$422$		0			0
$423$	10.1889	+	7.40267i	0.495401	+	0.359930i
$424$		0			0
$425$	−1.51710	+	8.11857i	−0.0735903	+	0.393809i
$426$		0			0
$427$	16.2818	+	11.8294i	0.787933	+	0.572467i
$428$		0			0
$429$	0.108423	+	0.333693i	0.00523473	+	0.0161108i
$430$		0			0
$431$	−3.43714	+	10.5784i	−0.165561	+	0.509545i	−0.999077	−	0.0429502i	$-0.986324\pi$
$431$	−3.43714	+	10.5784i	−0.165561	+	0.509545i	0.833516	+	0.552495i	$0.186324\pi$
$432$		0			0
$433$	5.23507	−	16.1119i	0.251581	−	0.774287i	−0.742903	−	0.669399i	$-0.766552\pi$
$433$	5.23507	−	16.1119i	0.251581	−	0.774287i	0.994484	−	0.104888i	$-0.0334484\pi$
$434$		0			0
$435$	0.0923137	+	0.111162i	0.00442610	+	0.00532982i
$436$		0			0
$437$	−14.3338	+	10.4141i	−0.685678	+	0.498174i
$438$		0			0
$439$	0.921388	+	0.669428i	0.0439754	+	0.0319500i	0.609556	−	0.792743i	$-0.291348\pi$
$439$	0.921388	+	0.669428i	0.0439754	+	0.0319500i	−0.565580	+	0.824693i	$0.691348\pi$
$440$		0			0
$441$	−7.51732	+	5.46166i	−0.357968	+	0.260079i
$442$		0			0
$443$	−22.3986			−1.06419			−0.532096	−	0.846684i	$-0.678595\pi$
$443$	−22.3986			−1.06419			−0.532096	+	0.846684i	$0.678595\pi$
$444$		0			0
$445$	6.88526	−	10.8946i	0.326393	−	0.516455i
$446$		0			0
$447$	0.228236	+	0.702440i	0.0107952	+	0.0332243i
$448$		0			0
$449$	41.6951			1.96771			0.983856	−	0.178963i	$-0.0572743\pi$
$449$	41.6951			1.96771			0.983856	+	0.178963i	$0.0572743\pi$
$450$		0			0
$451$	−10.2206			−0.481270
$452$		0			0
$453$	−0.231767	−	0.713306i	−0.0108894	−	0.0335141i
$454$		0			0
$455$	−16.8587	−	20.3008i	−0.790346	−	0.951717i
$456$		0			0
$457$	−23.6694			−1.10721			−0.553604	−	0.832780i	$-0.686748\pi$
$457$	−23.6694			−1.10721			−0.553604	+	0.832780i	$0.686748\pi$
$458$		0			0
$459$	−0.470459	+	0.341808i	−0.0219591	+	0.0159543i
$460$		0			0
$461$	−11.5115	−	8.36363i	−0.536146	−	0.389533i	0.286506	−	0.958079i	$-0.407506\pi$
$461$	−11.5115	−	8.36363i	−0.536146	−	0.389533i	−0.822652	+	0.568546i	$0.807506\pi$
$462$		0			0
$463$	−18.2288	+	13.2440i	−0.847163	+	0.615500i	−0.924362	−	0.381515i	$-0.875402\pi$
$463$	−18.2288	+	13.2440i	−0.847163	+	0.615500i	0.0771991	+	0.997016i	$0.475402\pi$
$464$		0			0
$465$	0.0675077	+	1.04176i	0.00313059	+	0.0483106i
$466$		0			0
$467$	2.47762	−	7.62534i	0.114651	−	0.352858i	−0.877223	−	0.480083i	$-0.840607\pi$
$467$	2.47762	−	7.62534i	0.114651	−	0.352858i	0.991874	+	0.127224i	$0.0406067\pi$
$468$		0			0
$469$	−7.73569	+	23.8080i	−0.357201	+	1.09935i
$470$		0			0
$471$	−0.270566	−	0.832716i	−0.0124670	−	0.0383695i
$472$		0			0
$473$	−1.06820	−	0.776095i	−0.0491160	−	0.0356849i
$474$		0			0
$475$	−6.70865	+	35.9005i	−0.307814	+	1.64723i
$476$		0			0
$477$	−10.0204	−	7.28022i	−0.458801	−	0.333339i
$478$		0			0
$479$	4.79590	+	14.7603i	0.219130	+	0.674414i	0.998835	+	0.0482657i	$0.0153694\pi$
$479$	4.79590	+	14.7603i	0.219130	+	0.674414i	−0.779704	+	0.626148i	$0.784631\pi$
$480$		0			0
$481$	16.4956	−	50.7683i	0.752135	−	2.31483i
$482$		0			0
$483$	0.0868931	−	0.267429i	0.00395377	−	0.0121685i
$484$		0			0
$485$	20.9621	−	8.34506i	0.951838	−	0.378930i
$486$		0			0
$487$	3.51862	−	2.55643i	0.159444	−	0.115843i	−0.505202	−	0.863001i	$-0.668582\pi$
$487$	3.51862	−	2.55643i	0.159444	−	0.115843i	0.664646	+	0.747158i	$0.268582\pi$
$488$		0			0
$489$	0.464805	+	0.337701i	0.0210192	+	0.0152714i
$490$		0			0
$491$	−10.5361	+	7.65495i	−0.475489	+	0.345463i	−0.799577	−	0.600564i	$-0.794943\pi$
$491$	−10.5361	+	7.65495i	−0.475489	+	0.345463i	0.324088	+	0.946027i	$0.394943\pi$
$492$		0			0
$493$	−1.81816			−0.0818858
$494$		0			0
$495$	−0.433293	−	6.68647i	−0.0194751	−	0.300535i
$496$		0			0
$497$	8.58731	+	26.4290i	0.385193	+	1.18550i
$498$		0			0
$499$	18.2846			0.818533			0.409266	−	0.912415i	$-0.365785\pi$
$499$	18.2846			0.818533			0.409266	+	0.912415i	$0.365785\pi$
$500$		0			0
$501$	−0.407103			−0.0181880
$502$		0			0
$503$	−4.81001	−	14.8037i	−0.214468	−	0.660064i	−0.999191	−	0.0402176i	$-0.987195\pi$
$503$	−4.81001	−	14.8037i	−0.214468	−	0.660064i	0.784723	−	0.619846i	$-0.212805\pi$
$504$		0			0
$505$	0.743623	+	11.4754i	0.0330908	+	0.510649i
$506$		0			0
$507$	−1.33371			−0.0592322
$508$		0			0
$509$	−21.6480	+	15.7282i	−0.959532	+	0.697141i	−0.953042	−	0.302838i	$-0.902066\pi$
$509$	−21.6480	+	15.7282i	−0.959532	+	0.697141i	−0.00648986	+	0.999979i	$0.502066\pi$
$510$		0			0
$511$	−2.87939	−	2.09200i	−0.127377	−	0.0925446i
$512$		0			0
$513$	−2.08038	+	1.51148i	−0.0918509	+	0.0667336i
$514$		0			0
$515$	−37.9506	+	15.1082i	−1.67230	+	0.665749i
$516$		0			0
$517$	−1.29876	+	3.99718i	−0.0571195	+	0.175796i
$518$		0			0
$519$	−0.428044	+	1.31738i	−0.0187890	+	0.0578267i
$520$		0			0
$521$	−7.28943	−	22.4346i	−0.319356	−	0.982875i	−0.973924	−	0.226873i	$-0.927150\pi$
$521$	−7.28943	−	22.4346i	−0.319356	−	0.982875i	0.654569	−	0.756002i	$-0.272850\pi$
$522$		0			0
$523$	−11.5862	−	8.41787i	−0.506629	−	0.368088i	0.304914	−	0.952380i	$-0.401372\pi$
$523$	−11.5862	−	8.41787i	−0.506629	−	0.368088i	−0.811543	+	0.584292i	$0.801372\pi$
$524$		0			0
$525$	−0.248765	−	0.523537i	−0.0108570	−	0.0228490i
$526$		0			0
$527$	−10.6271	−	7.72104i	−0.462924	−	0.336334i
$528$		0			0
$529$	−5.28927	−	16.2787i	−0.229968	−	0.707770i
$530$		0			0
$531$	−3.90445	+	12.0167i	−0.169439	+	0.521479i
$532$		0			0
$533$	18.8756	−	58.0931i	0.817593	−	2.51629i
$534$		0			0
$535$	−1.58777	−	24.5021i	−0.0686453	−	1.05932i
$536$		0			0
$537$	−0.529692	+	0.384843i	−0.0228579	+	0.0166072i
$538$		0			0
$539$	−2.50866	−	1.82265i	−0.108056	−	0.0785069i
$540$		0			0
$541$	−7.01058	+	5.09348i	−0.301408	+	0.218986i	−0.728201	−	0.685364i	$-0.759643\pi$
$541$	−7.01058	+	5.09348i	−0.301408	+	0.218986i	0.426793	+	0.904349i	$0.359643\pi$
$542$		0			0
$543$	−0.269853			−0.0115805
$544$		0			0
$545$	−16.7573	−	20.1787i	−0.717802	−	0.864361i
$546$		0			0
$547$	10.2067	+	31.4130i	0.436407	+	1.34312i	0.891638	+	0.452749i	$0.149557\pi$
$547$	10.2067	+	31.4130i	0.436407	+	1.34312i	−0.455231	+	0.890374i	$0.650443\pi$
$548$		0			0
$549$	−30.5410			−1.30346
$550$		0			0
$551$	−8.03993			−0.342513
$552$		0			0
$553$	−4.82839	−	14.8602i	−0.205324	−	0.631922i
$554$		0			0
$555$	0.626420	−	0.991191i	0.0265900	−	0.0420737i
$556$		0			0
$557$	−1.01783			−0.0431269			−0.0215634	−	0.999767i	$-0.506864\pi$
$557$	−1.01783			−0.0431269			−0.0215634	+	0.999767i	$0.506864\pi$
$558$		0			0
$559$	6.38403	−	4.63827i	0.270016	−	0.196178i
$560$		0			0
$561$	−0.0784549	−	0.0570008i	−0.00331237	−	0.00240658i
$562$		0			0
$563$	−25.8418	+	18.7751i	−1.08910	+	0.791277i	−0.979247	−	0.202670i	$-0.935038\pi$
$563$	−25.8418	+	18.7751i	−1.08910	+	0.791277i	−0.109853	+	0.993948i	$0.535038\pi$
$564$		0			0
$565$	−19.7904	−	23.8311i	−0.832587	−	1.00258i
$566$		0			0
$567$	−5.47280	+	16.8436i	−0.229836	+	0.707363i
$568$		0			0
$569$	−0.430057	+	1.32358i	−0.0180289	+	0.0554873i	−0.959666	−	0.281142i	$-0.909287\pi$
$569$	−0.430057	+	1.32358i	−0.0180289	+	0.0554873i	0.941637	+	0.336629i	$0.109287\pi$
$570$		0			0
$571$	9.55540	+	29.4085i	0.399881	+	1.23071i	0.925095	+	0.379737i	$0.123985\pi$
$571$	9.55540	+	29.4085i	0.399881	+	1.23071i	−0.525214	+	0.850970i	$0.676015\pi$
$572$		0			0
$573$	0.535327	+	0.388938i	0.0223636	+	0.0162481i
$574$		0			0
$575$	10.6497	+	5.80273i	0.444125	+	0.241991i
$576$		0			0
$577$	−15.4264	−	11.2080i	−0.642211	−	0.466594i	0.218398	−	0.975860i	$-0.429917\pi$
$577$	−15.4264	−	11.2080i	−0.642211	−	0.466594i	−0.860609	+	0.509266i	$0.829917\pi$
$578$		0			0
$579$	0.00719962	+	0.0221582i	0.000299206	+	0.000920862i
$580$		0			0
$581$	−5.80981e−5	0	0.000178808i	−2.41032e−6	0	7.41819e-6i
$582$		0			0
$583$	1.27728	−	3.93107i	0.0528996	−	0.162808i
$584$		0			0
$585$	38.8055	+	9.88588i	1.60441	+	0.408731i
$586$		0			0
$587$	31.7433	−	23.0629i	1.31019	−	0.951907i	0.310188	−	0.950675i	$-0.399608\pi$
$587$	31.7433	−	23.0629i	1.31019	−	0.951907i	0.999999	−	0.00123168i	$-0.000392058\pi$
$588$		0			0
$589$	−46.9932	−	34.1426i	−1.93632	−	1.40682i
$590$		0			0
$591$	1.01557	−	0.737858i	0.0417752	−	0.0303514i
$592$		0			0
$593$	−4.39022			−0.180285			−0.0901423	−	0.995929i	$-0.528732\pi$
$593$	−4.39022			−0.180285			−0.0901423	+	0.995929i	$0.528732\pi$
$594$		0			0
$595$	7.06769	+	1.80053i	0.289747	+	0.0738143i
$596$		0			0
$597$	−0.213640	−	0.657518i	−0.00874372	−	0.0269104i
$598$		0			0
$599$	11.4296			0.467002			0.233501	−	0.972357i	$-0.424982\pi$
$599$	11.4296			0.467002			0.233501	+	0.972357i	$0.424982\pi$
$600$		0			0
$601$	23.7698			0.969589			0.484795	−	0.874628i	$-0.338894\pi$
$601$	23.7698			0.969589			0.484795	+	0.874628i	$0.338894\pi$
$602$		0			0
$603$	−11.7392	−	36.1294i	−0.478055	−	1.47130i
$604$		0			0
$605$	2.07749	−	0.827057i	0.0844621	−	0.0336246i
$606$		0			0
$607$	−17.8329			−0.723816			−0.361908	−	0.932214i	$-0.617875\pi$
$607$	−17.8329			−0.723816			−0.361908	+	0.932214i	$0.617875\pi$
$608$		0			0
$609$	0.103231	−	0.0750017i	0.00418313	−	0.00303922i
$610$		0			0
$611$	−20.3211	−	14.7641i	−0.822102	−	0.597292i
$612$		0			0
$613$	36.8819	−	26.7962i	1.48964	−	1.08229i	0.515359	−	0.856974i	$-0.327659\pi$
$613$	36.8819	−	26.7962i	1.48964	−	1.08229i	0.974286	−	0.225316i	$-0.0723414\pi$
$614$		0			0
$615$	0.716799	−	1.13420i	0.0289041	−	0.0457353i
$616$		0			0
$617$	−7.55158	+	23.2414i	−0.304015	+	0.935662i	0.676028	+	0.736876i	$0.263700\pi$
$617$	−7.55158	+	23.2414i	−0.304015	+	0.935662i	−0.980043	+	0.198786i	$0.936300\pi$
$618$		0			0
$619$	8.25604	−	25.4095i	0.331838	−	1.02129i	−0.636420	−	0.771342i	$-0.719586\pi$
$619$	8.25604	−	25.4095i	0.331838	−	1.02129i	0.968259	−	0.249951i	$-0.0804144\pi$
$620$		0			0
$621$	0.263878	+	0.812133i	0.0105891	+	0.0325898i
$622$		0			0
$623$	−9.20748	−	6.68963i	−0.368890	−	0.268014i
$624$		0			0
$625$	24.1672	−	6.39907i	0.966687	−	0.255963i
$626$		0			0
$627$	−0.346929	−	0.252059i	−0.0138550	−	0.0100663i
$628$		0			0
$629$	4.55922	+	14.0318i	0.181788	+	0.559486i
$630$		0			0
$631$	−4.48962	+	13.8176i	−0.178729	+	0.550071i	−0.999784	−	0.0207776i	$-0.993386\pi$
$631$	−4.48962	+	13.8176i	−0.178729	+	0.550071i	0.821055	+	0.570849i	$0.193386\pi$
$632$		0			0
$633$	0.247536	−	0.761839i	0.00983869	−	0.0302804i
$634$		0			0
$635$	8.70724	−	13.7776i	0.345536	−	0.546746i
$636$		0			0
$637$	14.9928	−	10.8929i	0.594036	−	0.431592i
$638$		0			0
$639$	−34.1170	−	24.7874i	−1.34965	−	0.980576i
$640$		0			0
$641$	−15.5402	+	11.2906i	−0.613802	+	0.445953i	−0.850751	−	0.525569i	$-0.823853\pi$
$641$	−15.5402	+	11.2906i	−0.613802	+	0.445953i	0.236949	+	0.971522i	$0.423853\pi$
$642$		0			0
$643$	−33.6648			−1.32761			−0.663806	−	0.747905i	$-0.731060\pi$
$643$	−33.6648			−1.32761			−0.663806	+	0.747905i	$0.731060\pi$
$644$		0			0
$645$	0.161040	−	0.0641107i	0.00634096	−	0.00252436i
$646$		0			0
$647$	0.419339	+	1.29059i	0.0164859	+	0.0507384i	0.958961	−	0.283538i	$-0.0915082\pi$
$647$	0.419339	+	1.29059i	0.0164859	+	0.0507384i	−0.942475	+	0.334276i	$0.891508\pi$
$648$		0			0
$649$	−4.21654			−0.165514
$650$		0			0
$651$	0.921887			0.0361316
$652$		0			0
$653$	−7.18156	−	22.1026i	−0.281036	−	0.864941i	−0.987559	−	0.157250i	$-0.949737\pi$
$653$	−7.18156	−	22.1026i	−0.281036	−	0.864941i	0.706522	−	0.707691i	$-0.250263\pi$
$654$		0			0
$655$	35.0003	+	8.91647i	1.36757	+	0.348395i
$656$		0			0
$657$	5.40108			0.210716
$658$		0			0
$659$	−35.7726	+	25.9903i	−1.39350	+	1.01244i	−0.398033	+	0.917371i	$0.630307\pi$
$659$	−35.7726	+	25.9903i	−1.39350	+	1.01244i	−0.995471	+	0.0950688i	$0.969693\pi$
$660$		0			0
$661$	−11.3030	−	8.21207i	−0.439634	−	0.319413i	0.345856	−	0.938288i	$-0.387589\pi$
$661$	−11.3030	−	8.21207i	−0.439634	−	0.319413i	−0.785489	+	0.618875i	$0.787589\pi$
$662$		0			0
$663$	0.468880	−	0.340661i	0.0182098	−	0.0132302i
$664$		0			0
$665$	31.2534	+	7.96195i	1.21196	+	0.308751i
$666$		0			0
$667$	−0.825032	+	2.53919i	−0.0319454	+	0.0983178i
$668$		0			0
$669$	0.0459377	−	0.141382i	0.00177605	−	0.00546613i
$670$		0			0
$671$	−3.14952	−	9.69322i	−0.121586	−	0.374202i
$672$		0			0
$673$	38.7748	+	28.1715i	1.49466	+	1.08593i	0.972449	+	0.233116i	$0.0748923\pi$
$673$	38.7748	+	28.1715i	1.49466	+	1.08593i	0.522210	+	0.852817i	$0.325108\pi$
$674$		0			0
$675$	1.54568	+	0.842198i	0.0594934	+	0.0324162i
$676$		0			0
$677$	−27.1246	−	19.7072i	−1.04248	−	0.757408i	−0.0717136	−	0.997425i	$-0.522847\pi$
$677$	−27.1246	−	19.7072i	−1.04248	−	0.757408i	−0.970769	+	0.240018i	$0.922847\pi$
$678$		0			0
$679$	−6.15688	−	18.9489i	−0.236279	−	0.727193i
$680$		0			0
$681$	−0.137816	+	0.424155i	−0.00528113	+	0.0162537i
$682$		0			0
$683$	1.97972	−	6.09295i	0.0757519	−	0.233140i	−0.906010	−	0.423257i	$-0.860887\pi$
$683$	1.97972	−	6.09295i	0.0757519	−	0.233140i	0.981761	+	0.190117i	$0.0608867\pi$
$684$		0			0
$685$	−24.5675	−	29.5837i	−0.938677	−	1.13033i
$686$		0			0
$687$	0.889411	−	0.646195i	0.0339332	−	0.0246539i
$688$		0			0
$689$	19.9849	+	14.5199i	0.761366	+	0.553165i
$690$		0			0
$691$	14.5279	−	10.5551i	0.552666	−	0.401535i	−0.276102	−	0.961128i	$-0.589043\pi$
$691$	14.5279	−	10.5551i	0.552666	−	0.401535i	0.828767	+	0.559593i	$0.189043\pi$
$692$		0			0
$693$	−5.91706			−0.224770
$694$		0			0
$695$	10.7103	−	16.9470i	0.406263	−	0.642835i
$696$		0			0
$697$	5.21702	+	16.0563i	0.197609	+	0.608177i
$698$		0			0
$699$	0.677305			0.0256180
$700$		0			0
$701$	−27.2840			−1.03050			−0.515251	−	0.857040i	$-0.672301\pi$
$701$	−27.2840			−1.03050			−0.515251	+	0.857040i	$0.672301\pi$
$702$		0			0
$703$	20.1609	+	62.0490i	0.760384	+	2.34022i
$704$		0			0
$705$	−0.352488	−	0.424459i	−0.0132755	−	0.0159860i
$706$		0			0
$707$	10.1549			0.381916
$708$		0			0
$709$	−12.1023	+	8.79285i	−0.454512	+	0.330222i	−0.791375	−	0.611331i	$-0.790634\pi$
$709$	−12.1023	+	8.79285i	−0.454512	+	0.330222i	0.336863	+	0.941554i	$0.390634\pi$
$710$		0			0
$711$	19.1830	+	13.9372i	0.719417	+	0.522687i
$712$		0			0
$713$	−15.6053	+	11.3379i	−0.584422	+	0.424608i
$714$		0			0
$715$	0.864173	+	13.3357i	0.0323182	+	0.498727i
$716$		0			0
$717$	0.279649	−	0.860672i	0.0104437	−	0.0321424i
$718$		0			0
$719$	2.46471	−	7.58560i	0.0919182	−	0.282895i	−0.894520	−	0.447028i	$-0.852483\pi$
$719$	2.46471	−	7.58560i	0.0919182	−	0.282895i	0.986438	+	0.164133i	$0.0524825\pi$
$720$		0			0
$721$	11.1467	+	34.3059i	0.415123	+	1.27762i
$722$		0			0
$723$	0.00459719	+	0.00334005i	0.000170971	+	0.000124218i
$724$		0			0
$725$	2.36197	+	4.97087i	0.0877215	+	0.184614i
$726$		0			0
$727$	−19.6564	−	14.2812i	−0.729015	−	0.529660i	0.160237	−	0.987079i	$-0.448774\pi$
$727$	−19.6564	−	14.2812i	−0.729015	−	0.529660i	−0.889252	+	0.457418i	$0.848774\pi$
$728$		0			0
$729$	−8.28600	−	25.5017i	−0.306889	−	0.944507i
$730$		0			0
$731$	−0.673971	+	2.07427i	−0.0249277	+	0.0767197i
$732$		0			0
$733$	5.68576	−	17.4990i	0.210008	−	0.646339i	−0.789462	−	0.613799i	$-0.789640\pi$
$733$	5.68576	−	17.4990i	0.210008	−	0.646339i	0.999470	−	0.0325396i	$-0.0103595\pi$
$734$		0			0
$735$	0.378201	−	0.150563i	0.0139502	−	0.00555360i
$736$		0			0
$737$	10.2563	−	7.45163i	0.377795	−	0.274484i
$738$		0			0
$739$	−30.6568	−	22.2735i	−1.12773	−	0.819343i	−0.142366	−	0.989814i	$-0.545471\pi$
$739$	−30.6568	−	22.2735i	−1.12773	−	0.819343i	−0.985363	+	0.170471i	$0.945471\pi$
$740$		0			0
$741$	2.07339	−	1.50641i	0.0761680	−	0.0553393i
$742$		0			0
$743$	−18.2287			−0.668747			−0.334373	−	0.942441i	$-0.608525\pi$
$743$	−18.2287			−0.668747			−0.334373	+	0.942441i	$0.608525\pi$
$744$		0			0
$745$	1.81913	+	28.0723i	0.0666476	+	1.02849i
$746$		0			0
$747$	−8.81658e−5	0	0.000271346i	−3.22582e−6	0	9.92805e-6i
$748$		0			0
$749$	−21.6826			−0.792266
$750$		0			0
$751$	35.0202			1.27791			0.638953	−	0.769245i	$-0.279368\pi$
$751$	35.0202			1.27791			0.638953	+	0.769245i	$0.279368\pi$
$752$		0			0
$753$	−0.418449	−	1.28785i	−0.0152491	−	0.0469320i
$754$		0			0
$755$	−1.84727	−	28.5066i	−0.0672289	−	1.03746i
$756$		0			0
$757$	−29.1242			−1.05854			−0.529268	−	0.848455i	$-0.677533\pi$
$757$	−29.1242			−1.05854			−0.529268	+	0.848455i	$0.677533\pi$
$758$		0			0
$759$	−0.115206	+	0.0837024i	−0.00418173	+	0.00303820i
$760$		0			0
$761$	−8.82632	−	6.41270i	−0.319954	−	0.232460i	0.416202	−	0.909272i	$-0.363361\pi$
$761$	−8.82632	−	6.41270i	−0.319954	−	0.232460i	−0.736156	+	0.676812i	$0.763361\pi$
$762$		0			0
$763$	−18.7390	+	13.6147i	−0.678397	+	0.492885i
$764$		0			0
$765$	−10.2831	+	4.09374i	−0.371787	+	0.148010i
$766$		0			0
$767$	7.78717	−	23.9664i	0.281178	−	0.865378i
$768$		0			0
$769$	−5.89371	+	18.1390i	−0.212533	+	0.654109i	0.786787	+	0.617225i	$0.211743\pi$
$769$	−5.89371	+	18.1390i	−0.212533	+	0.654109i	−0.999320	+	0.0368838i	$0.988257\pi$
$770$		0			0
$771$	0.107550	+	0.331004i	0.00387331	+	0.0119208i
$772$		0			0
$773$	−1.50650	−	1.09454i	−0.0541851	−	0.0393678i	0.560363	−	0.828247i	$-0.310662\pi$
$773$	−1.50650	−	1.09454i	−0.0541851	−	0.0393678i	−0.614548	+	0.788879i	$0.710662\pi$
$774$		0			0
$775$	−7.30375	+	39.0851i	−0.262359	+	1.40398i
$776$		0			0
$777$	−0.837695	−	0.608621i	−0.0300521	−	0.0218342i
$778$		0			0
$779$	23.0697	+	71.0014i	0.826559	+	2.54389i
$780$		0			0
$781$	4.34884	−	13.3843i	0.155614	−	0.478930i
$782$		0			0
$783$	−0.119744	+	0.368533i	−0.00427929	+	0.0131703i
$784$		0			0
$785$	−2.15651	−	33.2787i	−0.0769690	−	1.18777i
$786$		0			0
$787$	43.6822	−	31.7370i	1.55710	−	1.13130i	0.618768	−	0.785574i	$-0.287632\pi$
$787$	43.6822	−	31.7370i	1.55710	−	1.13130i	0.938335	−	0.345727i	$-0.112368\pi$
$788$		0			0
$789$	−0.330992	−	0.240480i	−0.0117836	−	0.00856131i
$790$		0			0
$791$	−22.1308	+	16.0790i	−0.786881	+	0.571702i
$792$		0			0
$793$	60.9120			2.16305
$794$		0			0
$795$	0.346658	+	0.417438i	0.0122947	+	0.0148050i
$796$		0			0
$797$	5.43628	+	16.7312i	0.192563	+	0.592648i	0.999996	+	0.00268925i	$0.000856016\pi$
$797$	5.43628	+	16.7312i	0.192563	+	0.592648i	−0.807433	+	0.589959i	$0.799144\pi$
$798$		0			0
$799$	6.94242			0.245605
$800$		0			0
$801$	17.2712			0.610246
$802$		0			0
$803$	0.556982	+	1.71421i	0.0196555	+	0.0604933i
$804$		0			0
$805$	5.72169	−	9.05350i	0.201663	−	0.319094i
$806$		0			0
$807$	0.435892			0.0153441
$808$		0			0
$809$	34.6265	−	25.1576i	1.21740	−	0.884494i	0.221520	−	0.975156i	$-0.428898\pi$
$809$	34.6265	−	25.1576i	1.21740	−	0.884494i	0.995882	+	0.0906613i	$0.0288981\pi$
$810$		0			0
$811$	0.300317	+	0.218193i	0.0105456	+	0.00766180i	0.593046	−	0.805169i	$-0.297925\pi$
$811$	0.300317	+	0.218193i	0.0105456	+	0.00766180i	−0.582500	+	0.812831i	$0.697925\pi$
$812$		0			0
$813$	−0.116414	+	0.0845797i	−0.00408281	+	0.00296634i
$814$		0			0
$815$	13.9802	+	16.8346i	0.489704	+	0.589690i
$816$		0			0
$817$	−2.98031	+	9.17246i	−0.104268	+	0.320904i
$818$		0			0
$819$	10.9277	−	33.6320i	0.381845	−	1.17520i
$820$		0			0
$821$	0.567544	+	1.74672i	0.0198074	+	0.0609610i	0.960472	−	0.278378i	$-0.0897967\pi$
$821$	0.567544	+	1.74672i	0.0198074	+	0.0609610i	−0.940664	+	0.339339i	$0.889797\pi$
$822$		0			0
$823$	−3.86780	−	2.81012i	−0.134823	−	0.0979546i	0.518330	−	0.855181i	$-0.326554\pi$
$823$	−3.86780	−	2.81012i	−0.134823	−	0.0979546i	−0.653153	+	0.757226i	$0.726554\pi$
$824$		0			0
$825$	−0.0539202	+	0.288547i	−0.00187726	+	0.0100459i
$826$		0			0
$827$	−33.2891	−	24.1859i	−1.15757	−	0.841027i	−0.168104	−	0.985769i	$-0.553765\pi$
$827$	−33.2891	−	24.1859i	−1.15757	−	0.841027i	−0.989469	+	0.144743i	$0.953765\pi$
$828$		0			0
$829$	10.3245	+	31.7756i	0.358586	+	1.10361i	0.953901	+	0.300121i	$0.0970272\pi$
$829$	10.3245	+	31.7756i	0.358586	+	1.10361i	−0.595315	+	0.803492i	$0.702973\pi$
$830$		0			0
$831$	0.365511	−	1.12493i	0.0126794	−	0.0390233i
$832$		0			0
$833$	−1.58281	+	4.87139i	−0.0548412	+	0.168784i
$834$		0			0
$835$	−15.0257	−	3.82787i	−0.519987	−	0.132469i
$836$		0			0
$837$	−2.26492	+	1.64556i	−0.0782871	+	0.0568789i
$838$		0			0
$839$	45.1521	+	32.8049i	1.55882	+	1.13255i	0.936965	+	0.349423i	$0.113623\pi$
$839$	45.1521	+	32.8049i	1.55882	+	1.13255i	0.621859	+	0.783129i	$0.286377\pi$
$840$		0			0
$841$	22.4813	−	16.3336i	0.775218	−	0.563229i
$842$		0			0
$843$	−1.58850			−0.0547107
$844$		0			0
$845$	−49.2258	−	12.5405i	−1.69342	−	0.431406i
$846$		0			0
$847$	−0.610192	−	1.87798i	−0.0209664	−	0.0645280i
$848$		0			0
$849$	−0.806569			−0.0276814
$850$		0			0
$851$	21.6653			0.742677
$852$		0			0
$853$	3.09742	+	9.53289i	0.106054	+	0.326400i	0.989976	−	0.141233i	$-0.0451068\pi$
$853$	3.09742	+	9.53289i	0.106054	+	0.326400i	−0.883923	+	0.467633i	$0.845107\pi$
$854$		0			0
$855$	−45.4721	+	18.1026i	−1.55511	+	0.619096i
$856$		0			0
$857$	32.3026			1.10343			0.551717	−	0.834031i	$-0.313973\pi$
$857$	32.3026			1.10343			0.551717	+	0.834031i	$0.313973\pi$
$858$		0			0
$859$	−21.2302	+	15.4246i	−0.724364	+	0.526281i	−0.887775	−	0.460277i	$-0.847750\pi$
$859$	−21.2302	+	15.4246i	−0.724364	+	0.526281i	0.163412	+	0.986558i	$0.447750\pi$
$860$		0			0
$861$	−0.958557	−	0.696432i	−0.0326675	−	0.0237344i
$862$		0			0
$863$	−40.7811	+	29.6292i	−1.38820	+	1.00859i	−0.392144	+	0.919904i	$0.628266\pi$
$863$	−40.7811	+	29.6292i	−1.38820	+	1.00859i	−0.996060	+	0.0886850i	$0.971734\pi$
$864$		0			0
$865$	−28.1856	+	44.5984i	−0.958340	+	1.51639i
$866$		0			0
$867$	0.258911	−	0.796847i	0.00879309	−	0.0270623i
$868$		0			0
$869$	−2.44522	+	7.52562i	−0.0829485	+	0.255289i
$870$		0			0
$871$	23.4129	+	72.0576i	0.793318	+	2.44158i
$872$		0			0
$873$	24.4610	+	17.7719i	0.827879	+	0.601489i
$874$		0			0
$875$	−4.25899	−	21.6622i	−0.143980	−	0.732317i
$876$		0			0
$877$	9.95187	+	7.23046i	0.336051	+	0.244155i	0.742994	−	0.669298i	$-0.233405\pi$
$877$	9.95187	+	7.23046i	0.336051	+	0.244155i	−0.406943	+	0.913454i	$0.633405\pi$
$878$		0			0
$879$	0.468970	+	1.44334i	0.0158180	+	0.0486827i
$880$		0			0
$881$	−13.6256	+	41.9353i	−0.459058	+	1.41284i	0.407246	+	0.913319i	$0.366489\pi$
$881$	−13.6256	+	41.9353i	−0.459058	+	1.41284i	−0.866304	+	0.499517i	$0.833511\pi$
$882$		0			0
$883$	16.0728	−	49.4671i	0.540894	−	1.66470i	−0.189664	−	0.981849i	$-0.560740\pi$
$883$	16.0728	−	49.4671i	0.540894	−	1.66470i	0.730558	−	0.682851i	$-0.239260\pi$
$884$		0			0
$885$	0.295717	−	0.467916i	0.00994041	−	0.0157288i
$886$		0			0
$887$	−9.99889	+	7.26462i	−0.335730	+	0.243922i	−0.742858	−	0.669449i	$-0.766530\pi$
$887$	−9.99889	+	7.26462i	−0.335730	+	0.243922i	0.407128	+	0.913371i	$0.366530\pi$
$888$		0			0
$889$	−11.6440	−	8.45984i	−0.390526	−	0.283734i
$890$		0			0
$891$	7.25607	−	5.27184i	0.243087	−	0.176613i
$892$		0			0
$893$	30.6995			1.02732
$894$		0			0
$895$	−23.1689	+	9.22362i	−0.774451	+	0.308312i
$896$		0			0
$897$	−0.262992	−	0.809406i	−0.00878105	−	0.0270253i
$898$		0			0
$899$	−8.75313			−0.291933
$900$		0			0
$901$	−6.82759			−0.227460
$902$		0			0
$903$	−0.0473001	−	0.145575i	−0.00157405	−	0.00484442i
$904$		0			0
$905$	−9.95997	−	2.53734i	−0.331080	−	0.0843442i
$906$		0			0
$907$	−49.4104			−1.64065			−0.820323	−	0.571901i	$-0.806206\pi$
$907$	−49.4104			−1.64065			−0.820323	+	0.571901i	$0.806206\pi$
$908$		0			0
$909$	−12.4673	+	9.05804i	−0.413515	+	0.300436i
$910$		0			0
$911$	30.0012	+	21.7972i	0.993984	+	0.722172i	0.960790	−	0.277277i	$-0.0894320\pi$
$911$	30.0012	+	21.7972i	0.993984	+	0.722172i	0.0331943	+	0.999449i	$0.489432\pi$
$912$		0			0
$913$	7.70289e−5	0	5.59647e-5i	2.54928e−6	0	1.85216e-6i
$914$		0			0
$915$	1.29656	+	0.330304i	0.0428628	+	0.0109195i
$916$		0			0
$917$	9.85614	−	30.3341i	0.325478	−	1.00172i
$918$		0			0
$919$	12.1124	−	37.2782i	0.399552	−	1.22969i	−0.525807	−	0.850604i	$-0.676237\pi$
$919$	12.1124	−	37.2782i	0.399552	−	1.22969i	0.925359	−	0.379091i	$-0.123763\pi$
$920$		0			0
$921$	0.324591	+	0.998988i	0.0106956	+	0.0329178i
$922$		0			0
$923$	68.0440	+	49.4368i	2.23969	+	1.62723i
$924$		0			0
$925$	32.4403	−	30.6937i	1.06663	−	1.00920i
$926$		0			0
$927$	−44.2852	−	32.1751i	−1.45452	−	1.05677i
$928$		0			0
$929$	−5.42086	−	16.6837i	−0.177853	−	0.547374i	0.821900	−	0.569632i	$-0.192914\pi$
$929$	−5.42086	−	16.6837i	−0.177853	−	0.547374i	−0.999752	+	0.0222584i	$0.992914\pi$
$930$		0			0
$931$	−6.99922	+	21.5414i	−0.229390	+	0.705990i
$932$		0			0
$933$	−0.310842	+	0.956675i	−0.0101765	+	0.0313201i
$934$		0			0
$935$	−2.35972	−	2.84153i	−0.0771712	−	0.0929279i
$936$		0			0
$937$	39.1321	−	28.4311i	1.27839	−	0.928804i	0.278887	−	0.960324i	$-0.410035\pi$
$937$	39.1321	−	28.4311i	1.27839	−	0.928804i	0.999503	+	0.0315196i	$0.0100347\pi$
$938$		0			0
$939$	−0.381986	−	0.277529i	−0.0124657	−	0.00905683i
$940$		0			0
$941$	−26.7880	+	19.4626i	−0.873263	+	0.634463i	−0.931461	−	0.363842i	$-0.881465\pi$
$941$	−26.7880	+	19.4626i	−0.873263	+	0.634463i	0.0581973	+	0.998305i	$0.481465\pi$
$942$		0			0
$943$	24.7912			0.807311
$944$		0			0
$945$	0.830435	−	1.31401i	0.0270141	−	0.0427447i
$946$		0			0
$947$	−0.0897871	−	0.276336i	−0.00291769	−	0.00897972i	0.949587	−	0.313503i	$-0.101503\pi$
$947$	−0.0897871	−	0.276336i	−0.00291769	−	0.00897972i	−0.952505	+	0.304524i	$0.901503\pi$
$948$		0			0
$949$	−10.7721			−0.349677
$950$		0			0
$951$	1.36600			0.0442955
$952$		0			0
$953$	3.87993	+	11.9412i	0.125683	+	0.386813i	0.994025	−	0.109153i	$-0.0348139\pi$
$953$	3.87993	+	11.9412i	0.125683	+	0.386813i	−0.868342	+	0.495966i	$0.834814\pi$
$954$		0			0
$955$	16.1013	+	19.3888i	0.521025	+	0.627407i
$956$		0			0
$957$	−0.0646202			−0.00208887
$958$		0			0
$959$	−27.4729	+	19.9603i	−0.887148	+	0.644550i
$960$		0			0
$961$	−26.0823	−	18.9499i	−0.841365	−	0.611287i
$962$		0			0
$963$	26.6200	−	19.3405i	0.857817	−	0.623240i
$964$		0			0
$965$	0.0573836	+	0.885530i	0.00184724	+	0.0285062i
$966$		0			0
$967$	9.46568	−	29.1324i	0.304396	−	0.936834i	−0.675506	−	0.737354i	$-0.736075\pi$
$967$	9.46568	−	29.1324i	0.304396	−	0.936834i	0.979902	−	0.199480i	$-0.0639252\pi$
$968$		0			0
$969$	−0.218891	+	0.673678i	−0.00703180	+	0.0216416i
$970$		0			0
$971$	8.50231	+	26.1674i	0.272852	+	0.839752i	0.989780	+	0.142605i	$0.0455477\pi$
$971$	8.50231	+	26.1674i	0.272852	+	0.839752i	−0.716928	+	0.697147i	$0.754452\pi$
$972$		0			0
$973$	−14.3226	−	10.4059i	−0.459160	−	0.333599i
$974$		0			0
$975$	−1.54049	−	0.839370i	−0.0493353	−	0.0268814i
$976$		0			0
$977$	37.6674	+	27.3670i	1.20509	+	0.875548i	0.994776	−	0.102086i	$-0.0325518\pi$
$977$	37.6674	+	27.3670i	1.20509	+	0.875548i	0.210313	+	0.977634i	$0.432552\pi$
$978$		0			0
$979$	1.78107	+	5.48158i	0.0569233	+	0.175192i
$980$		0			0
$981$	10.8620	−	33.4298i	0.346797	−	1.06733i
$982$		0			0
$983$	−10.7311	+	33.0270i	−0.342270	+	1.05340i	0.620759	+	0.784001i	$0.286824\pi$
$983$	−10.7311	+	33.0270i	−0.342270	+	1.05340i	−0.963029	+	0.269397i	$0.913176\pi$
$984$		0			0
$985$	44.4216	−	17.6844i	1.41539	−	0.563472i
$986$		0			0
$987$	−0.394174	+	0.286384i	−0.0125467	+	0.00911572i
$988$		0			0
$989$	2.59104	+	1.88250i	0.0823901	+	0.0598599i
$990$		0			0
$991$	−12.3785	+	8.99348i	−0.393215	+	0.285687i	−0.766772	−	0.641920i	$-0.778138\pi$
$991$	−12.3785	+	8.99348i	−0.393215	+	0.285687i	0.373557	+	0.927607i	$0.378138\pi$
$992$		0			0
$993$	−1.36585			−0.0433440
$994$		0			0
$995$	−1.70279	−	26.2771i	−0.0539821	−	0.833039i
$996$		0			0
$997$	1.47803	+	4.54891i	0.0468097	+	0.144065i	0.971730	−	0.236097i	$-0.0758682\pi$
$997$	1.47803	+	4.54891i	0.0468097	+	0.144065i	−0.924920	+	0.380162i	$0.875868\pi$
$998$		0			0
$999$	3.14446			0.0994863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.441.7	✓	52
25.11	even	5	inner	1100.2.q.b.661.7	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.441.7	✓	52	1.1	even	1	trivial
1100.2.q.b.661.7	yes	52	25.11	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)

\(f(q)\)	\(=\)	\(q+(-0.0181419 - 0.0558349i) q^{3} +(-0.144597 - 2.23139i) q^{5} -1.97462 q^{7} +(2.42426 - 1.76133i) q^{9} +(0.809017 + 0.587785i) q^{11} +(-4.83503 + 3.51285i) q^{13} +(-0.121966 + 0.0485551i) q^{15} +(0.510441 - 1.57098i) q^{17} +(2.25718 - 6.94688i) q^{19} +(0.0358233 + 0.110253i) q^{21} +(-1.96235 - 1.42573i) q^{23} +(-4.95818 + 0.645304i) q^{25} +(-0.284812 - 0.206928i) q^{27} +(-0.340135 - 1.04683i) q^{29} +(2.45740 - 7.56311i) q^{31} +(0.0181419 - 0.0558349i) q^{33} +(0.285524 + 4.40615i) q^{35} +(-7.22608 + 5.25005i) q^{37} +(0.283856 + 0.206234i) q^{39} +(-8.26865 + 6.00753i) q^{41} -1.32037 q^{43} +(-4.28075 - 5.15479i) q^{45} +(1.29876 + 3.99718i) q^{47} -3.10087 q^{49} -0.0969756 q^{51} +(-1.27728 - 3.93107i) q^{53} +(1.19460 - 1.89022i) q^{55} -0.428828 q^{57} +(-3.41125 + 2.47842i) q^{59} +(-8.24554 - 5.99074i) q^{61} +(-4.78700 + 3.47796i) q^{63} +(8.53767 + 10.2809i) q^{65} +(3.91755 - 12.0570i) q^{67} +(-0.0440049 + 0.135433i) q^{69} +(-4.34884 - 13.3843i) q^{71} +(1.45820 + 1.05944i) q^{73} +(0.125981 + 0.265133i) q^{75} +(-1.59750 - 1.16065i) q^{77} +(2.44522 + 7.52562i) q^{79} +(2.77157 - 8.53002i) q^{81} +(2.94224e-5 - 9.05529e-5i) q^{83} +(-3.57926 - 0.911833i) q^{85} +(-0.0522788 + 0.0379828i) q^{87} +(4.66291 + 3.38780i) q^{89} +(9.54735 - 6.93655i) q^{91} -0.466868 q^{93} +(-15.8276 - 4.03214i) q^{95} +(3.11800 + 9.59623i) q^{97} +2.99655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 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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