LMFDB - Embedded newform 675.2.ba.c.518.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] 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("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [288] 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$24$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			518.7
Character	$\chi$	$=$	675.518
Dual form			675.2.ba.c.632.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60897 - 0.140766i) q^{2} +(0.575232 - 1.63374i) q^{3} +(0.599344 + 0.105680i) q^{4} +(-1.15550 + 2.54766i) q^{6} +(1.11982 + 0.784107i) q^{7} +(2.17071 + 0.581640i) q^{8} +(-2.33822 - 1.87956i) q^{9} +(-1.36918 + 3.76179i) q^{11} +(0.517416 - 0.918381i) q^{12} +(-0.563766 - 6.44387i) q^{13} +(-1.69138 - 1.41923i) q^{14} +(-4.55450 - 1.65770i) q^{16} +(6.11402 - 1.63825i) q^{17} +(3.49753 + 3.35329i) q^{18} +(0.488800 - 0.282209i) q^{19} +(1.92518 - 1.37845i) q^{21} +(2.73250 - 5.85987i) q^{22} +(-0.971342 - 1.38722i) q^{23} +(2.19891 - 3.21180i) q^{24} +10.4473i q^{26} +(-4.41573 + 2.73886i) q^{27} +(0.588292 + 0.588292i) q^{28} +(5.06125 - 4.24689i) q^{29} +(0.238769 - 1.35412i) q^{31} +(3.02123 + 1.40882i) q^{32} +(5.35820 + 4.40079i) q^{33} +(-10.0679 + 1.77524i) q^{34} +(-1.20276 - 1.37361i) q^{36} +(-1.73942 - 6.49160i) q^{37} +(-0.826189 + 0.385258i) q^{38} +(-10.8519 - 2.78567i) q^{39} +(-1.33886 + 1.59560i) q^{41} +(-3.29160 + 1.94688i) q^{42} +(-1.45769 - 3.12602i) q^{43} +(-1.21816 + 2.10991i) q^{44} +(1.36758 + 2.36872i) q^{46} +(0.771171 - 1.10135i) q^{47} +(-5.32815 + 6.48731i) q^{48} +(-1.75497 - 4.82173i) q^{49} +(0.840508 - 10.9311i) q^{51} +(0.343102 - 3.92167i) q^{52} +(-7.66637 + 7.66637i) q^{53} +(7.49030 - 3.78515i) q^{54} +(1.97474 + 2.35340i) q^{56} +(-0.179883 - 0.960908i) q^{57} +(-8.74120 + 6.12066i) q^{58} +(-6.76439 + 2.46204i) q^{59} +(-1.59070 - 9.02132i) q^{61} +(-0.574786 + 2.14513i) q^{62} +(-1.14461 - 3.93818i) q^{63} +(3.73216 + 2.15476i) q^{64} +(-8.00168 - 7.83498i) q^{66} +(-5.57647 + 0.487878i) q^{67} +(3.83753 - 0.335740i) q^{68} +(-2.82510 + 0.788948i) q^{69} +(0.594251 + 0.343091i) q^{71} +(-3.98237 - 5.43998i) q^{72} +(1.88104 - 7.02013i) q^{73} +(1.88487 + 10.6896i) q^{74} +(0.322783 - 0.117483i) q^{76} +(-4.48288 + 3.13895i) q^{77} +(17.0682 + 6.00964i) q^{78} +(8.21845 + 9.79437i) q^{79} +(1.93452 + 8.78963i) q^{81} +(2.37879 - 2.37879i) q^{82} +(1.45031 - 16.5771i) q^{83} +(1.29952 - 0.622713i) q^{84} +(1.90533 + 5.23485i) q^{86} +(-4.02693 - 10.7117i) q^{87} +(-5.16010 + 7.36939i) q^{88} +(-0.301153 - 0.521612i) q^{89} +(4.42137 - 7.65803i) q^{91} +(-0.435565 - 0.934073i) q^{92} +(-2.07494 - 1.16902i) q^{93} +(-1.39582 + 1.66348i) q^{94} +(4.03955 - 4.12550i) q^{96} +(14.8333 - 6.91688i) q^{97} +(2.14495 + 8.00504i) q^{98} +(10.2720 - 6.22243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) $ 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.60897	−	0.140766i	−1.13771	−	0.0995368i	−0.497307	−	0.867575i	$-0.665678\pi$
$2$	−1.60897	−	0.140766i	−1.13771	−	0.0995368i	−0.640404	+	0.768038i	$0.721233\pi$
$3$	0.575232	−	1.63374i	0.332110	−	0.943241i
$3$	0.575232	−	1.63374i	0.332110	−	0.943241i
$4$	0.599344	+	0.105680i	0.299672	+	0.0528402i
$5$		0			0
$5$		0			0
$6$	−1.15550	+	2.54766i	−0.471733	+	1.04008i
$7$	1.11982	+	0.784107i	0.423252	+	0.296365i	0.765731	−	0.643161i	$-0.222377\pi$
$7$	1.11982	+	0.784107i	0.423252	+	0.296365i	−0.342478	+	0.939526i	$0.611266\pi$
$8$	2.17071	+	0.581640i	0.767462	+	0.205641i
$9$	−2.33822	−	1.87956i	−0.779406	−	0.626520i
$10$		0			0
$11$	−1.36918	+	3.76179i	−0.412823	+	1.13422i	0.542859	+	0.839824i	$0.317342\pi$
$11$	−1.36918	+	3.76179i	−0.412823	+	1.13422i	−0.955682	+	0.294399i	$0.904880\pi$
$12$	0.517416	−	0.918381i	0.149365	−	0.265114i
$13$	−0.563766	−	6.44387i	−0.156360	−	1.78721i	−0.518493	−	0.855082i	$-0.673507\pi$
$13$	−0.563766	−	6.44387i	−0.156360	−	1.78721i	0.362133	−	0.932127i	$-0.382049\pi$
$14$	−1.69138	−	1.41923i	−0.452040	−	0.379306i
$15$		0			0
$16$	−4.55450	−	1.65770i	−1.13863	−	0.414426i
$17$	6.11402	−	1.63825i	1.48287	−	0.397333i	0.575546	−	0.817770i	$-0.304790\pi$
$17$	6.11402	−	1.63825i	1.48287	−	0.397333i	0.907322	+	0.420436i	$0.138123\pi$
$18$	3.49753	+	3.35329i	0.824377	+	0.790378i
$19$	0.488800	−	0.282209i	0.112138	−	0.0647432i	−0.442882	−	0.896580i	$-0.646044\pi$
$19$	0.488800	−	0.282209i	0.112138	−	0.0647432i	0.555020	+	0.831837i	$0.312711\pi$
$20$		0			0
$21$	1.92518	−	1.37845i	0.420109	−	0.300803i
$22$	2.73250	−	5.85987i	0.582571	−	1.24933i
$23$	−0.971342	−	1.38722i	−0.202539	−	0.289255i	0.705014	−	0.709193i	$-0.250941\pi$
$23$	−0.971342	−	1.38722i	−0.202539	−	0.289255i	−0.907553	+	0.419938i	$0.862052\pi$
$24$	2.19891	−	3.21180i	0.448851	−	0.655606i
$25$		0			0
$26$			10.4473i			2.04889i
$27$	−4.41573	+	2.73886i	−0.849807	+	0.527094i
$28$	0.588292	+	0.588292i	0.111177	+	0.111177i
$29$	5.06125	−	4.24689i	0.939851	−	0.788628i	−0.0377087	−	0.999289i	$-0.512006\pi$
$29$	5.06125	−	4.24689i	0.939851	−	0.788628i	0.977559	+	0.210660i	$0.0675614\pi$
$30$		0			0
$31$	0.238769	−	1.35412i	0.0428841	−	0.243208i	−0.955829	−	0.293923i	$-0.905039\pi$
$31$	0.238769	−	1.35412i	0.0428841	−	0.243208i	0.998713	+	0.0507153i	$0.0161501\pi$
$32$	3.02123	+	1.40882i	0.534082	+	0.249047i
$33$	5.35820	+	4.40079i	0.932742	+	0.766079i
$34$	−10.0679	+	1.77524i	−1.72662	+	0.304451i
$35$		0			0
$36$	−1.20276	−	1.37361i	−0.200460	−	0.228934i
$37$	−1.73942	−	6.49160i	−0.285959	−	1.06721i	−0.948136	−	0.317866i	$-0.897034\pi$
$37$	−1.73942	−	6.49160i	−0.285959	−	1.06721i	0.662177	−	0.749348i	$-0.269633\pi$
$38$	−0.826189	+	0.385258i	−0.134026	+	0.0624971i
$39$	−10.8519	−	2.78567i	−1.73770	−	0.446065i
$40$		0			0
$41$	−1.33886	+	1.59560i	−0.209095	+	0.249190i	−0.860392	−	0.509633i	$-0.829781\pi$
$41$	−1.33886	+	1.59560i	−0.209095	+	0.249190i	0.651296	+	0.758824i	$0.274226\pi$
$42$	−3.29160	+	1.94688i	−0.507904	+	0.300411i
$43$	−1.45769	−	3.12602i	−0.222295	−	0.476713i	0.763255	−	0.646097i	$-0.223600\pi$
$43$	−1.45769	−	3.12602i	−0.222295	−	0.476713i	−0.985550	+	0.169384i	$0.945822\pi$
$44$	−1.21816	+	2.10991i	−0.183644	+	0.318081i
$45$		0			0
$46$	1.36758	+	2.36872i	0.201639	+	0.349249i
$47$	0.771171	−	1.10135i	0.112487	−	0.160648i	−0.758961	−	0.651136i	$-0.774293\pi$
$47$	0.771171	−	1.10135i	0.112487	−	0.160648i	0.871448	+	0.490488i	$0.163182\pi$
$48$	−5.32815	+	6.48731i	−0.769052	+	0.936362i
$49$	−1.75497	−	4.82173i	−0.250709	−	0.688819i
$50$		0			0
$51$	0.840508	−	10.9311i	0.117695	−	1.53066i
$52$	0.343102	−	3.92167i	0.0475797	−	0.543838i
$53$	−7.66637	+	7.66637i	−1.05306	+	1.05306i	−0.0545457	+	0.998511i	$0.517371\pi$
$53$	−7.66637	+	7.66637i	−1.05306	+	1.05306i	−0.998511	+	0.0545457i	$0.982629\pi$
$54$	7.49030	−	3.78515i	1.01930	−	0.515093i
$55$		0			0
$56$	1.97474	+	2.35340i	0.263886	+	0.314487i
$57$	−0.179883	−	0.960908i	−0.0238261	−	0.127275i
$58$	−8.74120	+	6.12066i	−1.14778	+	0.803682i
$59$	−6.76439	+	2.46204i	−0.880648	+	0.320530i	−0.742471	−	0.669878i	$-0.766346\pi$
$59$	−6.76439	+	2.46204i	−0.880648	+	0.320530i	−0.138177	+	0.990408i	$0.544124\pi$
$60$		0			0
$61$	−1.59070	−	9.02132i	−0.203669	−	1.15506i	−0.899521	−	0.436877i	$-0.856084\pi$
$61$	−1.59070	−	9.02132i	−0.203669	−	1.15506i	0.695852	−	0.718185i	$-0.255027\pi$
$62$	−0.574786	+	2.14513i	−0.0729979	+	0.272432i
$63$	−1.14461	−	3.93818i	−0.144207	−	0.496164i
$64$	3.73216	+	2.15476i	0.466520	+	0.269346i
$65$		0			0
$66$	−8.00168	−	7.83498i	−0.984939	−	0.964419i
$67$	−5.57647	+	0.487878i	−0.681274	+	0.0596038i	−0.422539	−	0.906345i	$-0.638861\pi$
$67$	−5.57647	+	0.487878i	−0.681274	+	0.0596038i	−0.258735	+	0.965948i	$0.583306\pi$
$68$	3.83753	−	0.335740i	0.465369	−	0.0407145i
$69$	−2.82510	+	0.788948i	−0.340102	+	0.0949781i
$70$		0			0
$71$	0.594251	+	0.343091i	0.0705246	+	0.0407174i	0.534848	−	0.844949i	$-0.320369\pi$
$71$	0.594251	+	0.343091i	0.0705246	+	0.0407174i	−0.464323	+	0.885666i	$0.653702\pi$
$72$	−3.98237	−	5.43998i	−0.469326	−	0.641108i
$73$	1.88104	−	7.02013i	0.220159	−	0.821644i	−0.764128	−	0.645065i	$-0.776830\pi$
$73$	1.88104	−	7.02013i	0.220159	−	0.821644i	0.984287	−	0.176579i	$-0.0565030\pi$
$74$	1.88487	+	10.6896i	0.219112	+	1.24264i
$75$		0			0
$76$	0.322783	−	0.117483i	0.0370258	−	0.0134763i
$77$	−4.48288	+	3.13895i	−0.510872	+	0.357716i
$78$	17.0682	+	6.00964i	1.93260	+	0.680457i
$79$	8.21845	+	9.79437i	0.924648	+	1.10195i	0.994536	+	0.104398i	$0.0332915\pi$
$79$	8.21845	+	9.79437i	0.924648	+	1.10195i	−0.0698876	+	0.997555i	$0.522264\pi$
$80$		0			0
$81$	1.93452	+	8.78963i	0.214946	+	0.976626i
$82$	2.37879	−	2.37879i	0.262694	−	0.262694i
$83$	1.45031	−	16.5771i	0.159192	−	1.81958i	−0.326223	−	0.945293i	$-0.605776\pi$
$83$	1.45031	−	16.5771i	0.159192	−	1.81958i	0.485416	−	0.874283i	$-0.338668\pi$
$84$	1.29952	−	0.622713i	0.141789	−	0.0679435i
$85$		0			0
$86$	1.90533	+	5.23485i	0.205457	+	0.564488i
$87$	−4.02693	−	10.7117i	−0.431732	−	1.14842i
$88$	−5.16010	+	7.36939i	−0.550069	+	0.785580i
$89$	−0.301153	−	0.521612i	−0.0319221	−	0.0552908i	0.849623	−	0.527391i	$-0.176830\pi$
$89$	−0.301153	−	0.521612i	−0.0319221	−	0.0552908i	−0.881545	+	0.472100i	$0.843496\pi$
$90$		0			0
$91$	4.42137	−	7.65803i	0.463485	−	0.802780i
$92$	−0.435565	−	0.934073i	−0.0454108	−	0.0973838i
$93$	−2.07494	−	1.16902i	−0.215161	−	0.121222i
$94$	−1.39582	+	1.66348i	−0.143968	+	0.171574i
$95$		0			0
$96$	4.03955	−	4.12550i	0.412285	−	0.421057i
$97$	14.8333	−	6.91688i	1.50609	−	0.702302i	0.517888	−	0.855448i	$-0.326718\pi$
$97$	14.8333	−	6.91688i	1.50609	−	0.702302i	0.988204	+	0.153146i	$0.0489404\pi$
$98$	2.14495	+	8.00504i	0.216672	+	0.808632i
$99$	10.2720	−	6.22243i	1.03237	−	0.625378i
$100$		0			0
$101$	−9.25810	+	1.63245i	−0.921215	+	0.162435i	−0.614092	−	0.789235i	$-0.710478\pi$
$101$	−9.25810	+	1.63245i	−0.921215	+	0.162435i	−0.307124	+	0.951670i	$0.599366\pi$
$102$	−2.89108	+	17.4695i	−0.286260	+	1.72973i
$103$	−16.4213	−	7.65736i	−1.61803	−	0.754502i	−0.618523	−	0.785767i	$-0.712269\pi$
$103$	−16.4213	−	7.65736i	−1.61803	−	0.754502i	−0.999511	+	0.0312651i	$0.990046\pi$
$104$	2.52424	−	14.3157i	0.247522	−	1.40377i
$105$		0			0
$106$	13.4141	−	11.2558i	1.30289	−	1.09326i
$107$	1.55188	+	1.55188i	0.150026	+	0.150026i	0.778130	−	0.628104i	$-0.216169\pi$
$107$	1.55188	+	1.55188i	0.150026	+	0.150026i	−0.628104	+	0.778130i	$0.716169\pi$
$108$	−2.93598	+	1.17486i	−0.282515	+	0.113051i
$109$			2.31464i			0.221703i	0.993837	+	0.110851i	$0.0353577\pi$
$109$			2.31464i			0.221703i	−0.993837	+	0.110851i	$0.964642\pi$
$110$		0			0
$111$	−11.6062	−	0.892415i	−1.10161	−	0.0847043i
$112$	−3.80041	−	5.42754i	−0.359105	−	0.512855i
$113$	−0.285981	+	0.613289i	−0.0269029	+	0.0576934i	−0.919300	−	0.393557i	$-0.871244\pi$
$113$	−0.285981	+	0.613289i	−0.0269029	+	0.0576934i	0.892397	+	0.451251i	$0.149022\pi$
$114$	0.154162	+	1.57139i	0.0144386	+	0.147174i
$115$		0			0
$116$	3.48224	−	2.01047i	0.323318	−	0.186668i
$117$	−10.7934	+	16.1268i	−0.997853	+	1.49092i
$118$	11.2302	−	3.00913i	1.03383	−	0.277013i
$119$	8.13117	+	2.95950i	0.745383	+	0.271297i
$120$		0			0
$121$	−3.84994	−	3.23048i	−0.349995	−	0.293680i
$122$	1.28949	+	14.7389i	0.116745	+	1.33440i
$123$	1.83663	+	3.10519i	0.165604	+	0.279986i
$124$	0.286209	−	0.786352i	0.0257023	−	0.0706165i
$125$		0			0
$126$	1.28727	+	6.49752i	0.114679	+	0.578845i
$127$	−4.12205	−	1.10450i	−0.365773	−	0.0980085i	0.0712511	−	0.997458i	$-0.477301\pi$
$127$	−4.12205	−	1.10450i	−0.365773	−	0.0980085i	−0.437024	+	0.899450i	$0.643967\pi$
$128$	−11.1630	−	7.81640i	−0.986677	−	0.690879i
$129$	−5.94561	+	0.583296i	−0.523481	+	0.0513564i
$130$		0			0
$131$	10.6271	+	1.87385i	0.928496	+	0.163719i	0.617391	−	0.786656i	$-0.288190\pi$
$131$	10.6271	+	1.87385i	0.928496	+	0.163719i	0.311105	+	0.950375i	$0.399301\pi$
$132$	2.74632	+	3.20384i	0.239037	+	0.278859i
$133$	0.768651	+	0.0672482i	0.0666505	+	0.00583116i
$134$	9.04103			0.781026
$135$		0			0
$136$	14.2246			1.21975
$137$	16.2532	+	1.42197i	1.38860	+	0.121487i	0.756803	−	0.653643i	$-0.226760\pi$
$137$	16.2532	+	1.42197i	1.38860	+	0.121487i	0.631801	+	0.775131i	$0.282316\pi$
$138$	4.65655	−	0.871711i	0.396392	−	0.0742050i
$139$	17.7679	+	3.13296i	1.50705	+	0.265734i	0.865330	−	0.501202i	$-0.167109\pi$
$139$	17.7679	+	3.13296i	1.50705	+	0.265734i	0.641723	+	0.766937i	$0.278220\pi$
$140$		0			0
$141$	−1.35571	−	1.89342i	−0.114172	−	0.159455i
$142$	−0.907834	−	0.635672i	−0.0761837	−	0.0533444i
$143$	25.0124	+	6.70205i	2.09164	+	0.560454i
$144$	7.53366	+	12.4365i	0.627805	+	1.03638i
$145$		0			0
$146$	−4.01472	+	11.0304i	−0.332261	+	0.912879i
$147$	−8.88697	+	0.0935477i	−0.732985	+	0.00771568i
$148$	−0.356475	−	4.07452i	−0.0293020	−	0.334924i
$149$	−7.44284	−	6.24528i	−0.609741	−	0.511633i	0.284819	−	0.958581i	$-0.408066\pi$
$149$	−7.44284	−	6.24528i	−0.609741	−	0.511633i	−0.894560	+	0.446948i	$0.852511\pi$
$150$		0			0
$151$	2.08611	+	0.759282i	0.169765	+	0.0617895i	0.425505	−	0.904956i	$-0.360097\pi$
$151$	2.08611	+	0.759282i	0.169765	+	0.0617895i	−0.255739	+	0.966746i	$0.582319\pi$
$152$	1.22519	−	0.328288i	0.0993759	−	0.0266277i
$153$	−17.3751	−	7.66108i	−1.40469	−	0.619362i
$154$	7.65467	−	4.41943i	0.616831	−	0.356127i
$155$		0			0
$156$	−6.20963	−	2.81641i	−0.497168	−	0.225493i
$157$	−7.66606	+	16.4399i	−0.611818	+	1.31205i	0.319412	+	0.947616i	$0.396515\pi$
$157$	−7.66606	+	16.4399i	−0.611818	+	1.31205i	−0.931230	+	0.364432i	$0.881263\pi$
$158$	−11.8445	−	16.9157i	−0.942298	−	1.34574i
$159$	8.11492	+	16.9348i	0.643555	+	1.34302i
$160$		0			0
$161$		−	2.31507i		−	0.182453i
$162$	−1.87529	−	14.4145i	−0.147337	−	1.13251i
$163$	14.0631	+	14.0631i	1.10151	+	1.10151i	0.994229	+	0.107281i	$0.0342144\pi$
$163$	14.0631	+	14.0631i	1.10151	+	1.10151i	0.107281	+	0.994229i	$0.465786\pi$
$164$	−0.971063	+	0.814818i	−0.0758273	+	0.0636266i
$165$		0			0
$166$	−4.66700	+	26.4679i	−0.362230	+	2.05431i
$167$	17.5324	+	8.17550i	1.35670	+	0.632639i	0.958614	−	0.284709i	$-0.0918969\pi$
$167$	17.5324	+	8.17550i	1.35670	+	0.632639i	0.398086	+	0.917348i	$0.369675\pi$
$168$	4.98078	−	1.87246i	0.384276	−	0.144463i
$169$	−28.4031	+	5.00824i	−2.18486	+	0.385249i
$170$		0			0
$171$	−1.67335	−	0.258863i	−0.127964	−	0.0197958i
$172$	−0.543295	−	2.02761i	−0.0414259	−	0.154604i
$173$	14.7368	−	6.87190i	1.12042	−	0.522461i	0.227999	−	0.973661i	$-0.426782\pi$
$173$	14.7368	−	6.87190i	1.12042	−	0.522461i	0.892423	+	0.451200i	$0.149004\pi$
$174$	4.97135	+	17.8017i	0.376877	+	1.34954i
$175$		0			0
$176$	12.4719	−	14.8634i	0.940102	−	1.12037i
$177$	0.131238	+	12.4675i	0.00986443	+	0.937114i
$178$	0.411119	+	0.881649i	0.0308147	+	0.0660824i
$179$	−5.29497	+	9.17116i	−0.395765	+	0.685485i	−0.993199	−	0.116433i	$-0.962854\pi$
$179$	−5.29497	+	9.17116i	−0.395765	+	0.685485i	0.597434	+	0.801918i	$0.296187\pi$
$180$		0			0
$181$	5.21970	+	9.04078i	0.387977	+	0.671996i	0.992177	−	0.124836i	$-0.0398406\pi$
$181$	5.21970	+	9.04078i	0.387977	+	0.671996i	−0.604200	+	0.796833i	$0.706507\pi$
$182$	−8.19183	+	11.6991i	−0.607219	+	0.867198i
$183$	−15.6535	−	2.59056i	−1.15714	−	0.191499i
$184$	−1.30164	−	3.57622i	−0.0959581	−	0.263643i
$185$		0			0
$186$	3.17395	+	2.17300i	0.232725	+	0.159332i
$187$	−2.20845	+	25.2427i	−0.161498	+	1.84593i
$188$	0.578587	−	0.578587i	0.0421978	−	0.0421978i
$189$	−7.09238	−	0.395373i	−0.515895	−	0.0287591i
$190$		0			0
$191$	−4.58915	−	5.46914i	−0.332060	−	0.395733i	0.574019	−	0.818842i	$-0.305383\pi$
$191$	−4.58915	−	5.46914i	−0.332060	−	0.395733i	−0.906079	+	0.423108i	$0.860939\pi$
$192$	5.66718	−	4.85789i	0.408994	−	0.350588i
$193$	−8.91592	+	6.24300i	−0.641782	+	0.449381i	−0.848626	−	0.528993i	$-0.822570\pi$
$193$	−8.91592	+	6.24300i	−0.641782	+	0.449381i	0.206844	+	0.978374i	$0.433681\pi$
$194$	−24.8399	+	9.04099i	−1.78340	+	0.649106i
$195$		0			0
$196$	−0.542265	−	3.07534i	−0.0387332	−	0.219667i
$197$	0.249308	−	0.930429i	0.0177624	−	0.0662904i	−0.956476	−	0.291812i	$-0.905742\pi$
$197$	0.249308	−	0.930429i	0.0177624	−	0.0662904i	0.974238	+	0.225521i	$0.0724086\pi$
$198$	−17.4031	+	8.56574i	−1.23679	+	0.608741i
$199$	13.5074	+	7.79853i	0.957517	+	0.552823i	0.895408	−	0.445247i	$-0.146884\pi$
$199$	13.5074	+	7.79853i	0.957517	+	0.552823i	0.0621092	+	0.998069i	$0.480217\pi$
$200$		0			0
$201$	−2.41070	+	9.39115i	−0.170037	+	0.662401i
$202$	15.1258	−	1.32333i	1.06425	−	0.0931094i
$203$	8.99771	−	0.787198i	0.631515	−	0.0552504i
$204$	1.65896	−	6.46266i	0.116150	−	0.452476i
$205$		0			0
$206$	25.3434	+	14.6320i	1.76575	+	1.01946i
$207$	−0.336153	+	5.06931i	−0.0233643	+	0.352342i
$208$	−8.11435	+	30.2832i	−0.562629	+	2.09976i
$209$	0.392356	+	2.22516i	0.0271398	+	0.153918i
$210$		0			0
$211$	4.84666	−	1.76404i	0.333658	−	0.121442i	−0.169758	−	0.985486i	$-0.554299\pi$
$211$	4.84666	−	1.76404i	0.333658	−	0.121442i	0.503416	+	0.864044i	$0.332076\pi$
$212$	−5.40497	+	3.78460i	−0.371215	+	0.259928i
$213$	0.902353	−	0.773495i	0.0618282	−	0.0529990i
$214$	−2.27847	−	2.71538i	−0.155753	−	0.185619i
$215$		0			0
$216$	−11.1783	+	3.37690i	−0.760587	+	0.229769i
$217$	1.32916	−	1.32916i	0.0902290	−	0.0902290i
$218$	0.325824	−	3.72418i	0.0220676	−	0.252233i
$219$	−10.3870	−	7.11133i	−0.701891	−	0.480539i
$220$		0			0
$221$	−14.0035	−	38.4744i	−0.941979	−	2.58807i
$222$	18.5483	+	3.06962i	1.24488	+	0.206020i
$223$	13.3598	−	19.0798i	0.894638	−	1.27768i	−0.0654150	−	0.997858i	$-0.520837\pi$
$223$	13.3598	−	19.0798i	0.894638	−	1.27768i	0.960053	−	0.279818i	$-0.0902740\pi$
$224$	2.27857	+	3.94659i	0.152243	+	0.263693i
$225$		0			0
$226$	0.546465	−	0.946505i	0.0363503	−	0.0629606i
$227$	−2.74583	−	5.88846i	−0.182247	−	0.390831i	0.793866	−	0.608093i	$-0.208065\pi$
$227$	−2.74583	−	5.88846i	−0.182247	−	0.390831i	−0.976113	+	0.217262i	$0.930287\pi$
$228$	−0.00626240	−	0.594924i	−0.000414738	−	0.0393998i
$229$	12.2060	−	14.5465i	0.806595	−	0.961263i	−0.193207	−	0.981158i	$-0.561889\pi$
$229$	12.2060	−	14.5465i	0.806595	−	0.961263i	0.999802	+	0.0198953i	$0.00633329\pi$
$230$		0			0
$231$	2.54953	+	9.12949i	0.167747	+	0.600677i
$232$	13.4567	−	6.27495i	0.883474	−	0.411971i
$233$	6.06355	+	22.6295i	0.397236	+	1.48251i	0.817937	+	0.575307i	$0.195118\pi$
$233$	6.06355	+	22.6295i	0.397236	+	1.48251i	−0.420701	+	0.907199i	$0.638216\pi$
$234$	19.6364	−	24.4281i	1.28367	−	1.59692i
$235$		0			0
$236$	−4.31438	+	0.760742i	−0.280842	+	0.0495201i
$237$	20.7290	−	7.79279i	1.34649	−	0.506196i
$238$	−12.6662	−	5.90634i	−0.821026	−	0.382851i
$239$	0.177210	−	1.00501i	0.0114627	−	0.0650084i	−0.978540	−	0.206058i	$-0.933937\pi$
$239$	0.177210	−	1.00501i	0.0114627	−	0.0650084i	0.990003	+	0.141049i	$0.0450476\pi$
$240$		0			0
$241$	3.23680	−	2.71599i	0.208500	−	0.174953i	−0.532557	−	0.846394i	$-0.678769\pi$
$241$	3.23680	−	2.71599i	0.208500	−	0.174953i	0.741058	+	0.671441i	$0.234324\pi$
$242$	5.73968	+	5.73968i	0.368961	+	0.368961i
$243$	15.4728	+	1.89558i	0.992579	+	0.121601i
$244$		−	5.57498i		−	0.356901i
$245$		0			0
$246$	−2.51797	−	5.25469i	−0.160540	−	0.335027i
$247$	−2.09409	−	2.99067i	−0.133244	−	0.190292i
$248$	1.30591	−	2.80053i	0.0829254	−	0.177834i
$249$	−26.2485	−	11.9051i	−1.66343	−	0.754456i
$250$		0			0
$251$	−20.9072	+	12.0708i	−1.31965	+	0.761900i	−0.983672	−	0.179970i	$-0.942400\pi$
$251$	−20.9072	+	12.0708i	−1.31965	+	0.761900i	−0.335977	+	0.941870i	$0.609066\pi$
$252$	−0.269825	−	2.48129i	−0.0169974	−	0.156306i
$253$	6.54837	−	1.75463i	0.411693	−	0.110313i
$254$	6.47677	+	2.35735i	0.406388	+	0.147913i
$255$		0			0
$256$	10.2580	+	8.60748i	0.641125	+	0.537968i
$257$	−1.78815	−	20.4386i	−0.111542	−	1.27493i	−0.821306	−	0.570487i	$-0.806754\pi$
$257$	−1.78815	−	20.4386i	−0.111542	−	1.27493i	0.709765	−	0.704439i	$-0.248801\pi$
$258$	9.64839	−	0.101563i	0.600683	−	0.00632302i
$259$	3.14227	−	8.63332i	0.195251	−	0.536449i
$260$		0			0
$261$	−19.8166	+	0.417240i	−1.22662	+	0.0258265i
$262$	−16.8349	−	4.51090i	−1.04006	−	0.278685i
$263$	−3.67390	−	2.57249i	−0.226542	−	0.158627i	0.454795	−	0.890596i	$-0.349712\pi$
$263$	−3.67390	−	2.57249i	−0.226542	−	0.158627i	−0.681337	+	0.731969i	$0.738601\pi$
$264$	9.07142	+	12.6694i	0.558307	+	0.779747i
$265$		0			0
$266$	−1.22727	−	0.216400i	−0.0752486	−	0.0132684i
$267$	−1.02541	+	0.191958i	−0.0627542	+	0.0117476i
$268$	−3.39378	−	0.296917i	−0.207308	−	0.0181371i
$269$	−7.32723			−0.446749			−0.223374	−	0.974733i	$-0.571707\pi$
$269$	−7.32723			−0.446749			−0.223374	+	0.974733i	$0.571707\pi$
$270$		0			0
$271$	19.5478			1.18745			0.593723	−	0.804669i	$-0.297657\pi$
$271$	19.5478			1.18745			0.593723	+	0.804669i	$0.297657\pi$
$272$	−30.5620	−	2.67383i	−1.85310	−	0.162125i
$273$	−9.96793	−	11.6285i	−0.603286	−	0.703789i
$274$	−25.9507	−	4.57580i	−1.56774	−	0.276434i
$275$		0			0
$276$	−1.77658	+	0.174292i	−0.106938	+	0.0104912i
$277$	−17.0942	−	11.9695i	−1.02709	−	0.719177i	−0.0666833	−	0.997774i	$-0.521242\pi$
$277$	−17.0942	−	11.9695i	−1.02709	−	0.719177i	−0.960408	+	0.278597i	$0.910131\pi$
$278$	−28.1469	−	7.54195i	−1.68814	−	0.452336i
$279$	−3.10345	+	2.71746i	−0.185799	+	0.162690i
$280$		0			0
$281$	−1.84144	+	5.05932i	−0.109851	+	0.301814i	−0.982422	−	0.186674i	$-0.940229\pi$
$281$	−1.84144	+	5.05932i	−0.109851	+	0.301814i	0.872571	+	0.488488i	$0.162451\pi$
$282$	1.91477	+	3.23730i	0.114023	+	0.192778i
$283$	0.707935	+	8.09174i	0.0420824	+	0.481004i	0.987769	+	0.155924i	$0.0498355\pi$
$283$	0.707935	+	8.09174i	0.0420824	+	0.481004i	−0.945687	+	0.325080i	$0.894609\pi$
$284$	0.319902	+	0.268430i	0.0189827	+	0.0159284i
$285$		0			0
$286$	−39.3007	−	14.3043i	−2.32390	−	0.845830i
$287$	−2.75040	+	0.736969i	−0.162351	+	0.0435019i
$288$	−4.41632	−	8.97270i	−0.260234	−	0.528722i
$289$	19.9750	−	11.5325i	1.17500	−	0.678385i
$290$		0			0
$291$	−2.76780	−	28.2125i	−0.162252	−	1.65385i
$292$	1.86928	−	4.00868i	0.109391	−	0.234590i
$293$	−3.30800	−	4.72431i	−0.193255	−	0.275997i	0.710817	−	0.703377i	$-0.248326\pi$
$293$	−3.30800	−	4.72431i	−0.193255	−	0.275997i	−0.904072	+	0.427380i	$0.859437\pi$
$294$	14.3120	+	1.10047i	0.834693	+	0.0641808i
$295$		0			0
$296$		−	15.1031i		−	0.877851i
$297$	−4.25709	−	20.3610i	−0.247021	−	1.18147i
$298$	11.0961	+	11.0961i	0.642783	+	0.642783i
$299$	−8.39145	+	7.04127i	−0.485290	+	0.407207i
$300$		0			0
$301$	0.818784	−	4.64356i	0.0471940	−	0.267650i
$302$	−3.24960	−	1.51531i	−0.186994	−	0.0871966i
$303$	−2.65855	+	16.0644i	−0.152730	+	0.922874i
$304$	−2.69406	+	0.475035i	−0.154515	+	0.0272451i
$305$		0			0
$306$	26.8775	+	14.7723i	1.53649	+	0.844474i
$307$	−2.60928	−	9.73795i	−0.148919	−	0.555774i	−0.999550	−	0.0300101i	$-0.990446\pi$
$307$	−2.60928	−	9.73795i	−0.148919	−	0.555774i	0.850630	−	0.525764i	$-0.176221\pi$
$308$	−3.01851	+	1.40756i	−0.171996	+	0.0802029i
$309$	−21.9562	+	22.4233i	−1.24904	+	1.27562i
$310$		0			0
$311$	13.2713	−	15.8161i	0.752548	−	0.896851i	−0.244805	−	0.969572i	$-0.578724\pi$
$311$	13.2713	−	15.8161i	0.752548	−	0.896851i	0.997352	+	0.0727212i	$0.0231683\pi$
$312$	−21.9361	−	12.3588i	−1.24189	−	0.699679i
$313$	6.13505	+	13.1567i	0.346773	+	0.743658i	0.999908	−	0.0135841i	$-0.00432408\pi$
$313$	6.13505	+	13.1567i	0.346773	+	0.743658i	−0.653134	+	0.757242i	$0.726546\pi$
$314$	14.6486	−	25.3722i	0.826670	−	1.43183i
$315$		0			0
$316$	3.89060	+	6.73872i	0.218863	+	0.379083i
$317$	17.2229	−	24.5968i	0.967334	−	1.38150i	0.0433528	−	0.999060i	$-0.486196\pi$
$317$	17.2229	−	24.5968i	0.967334	−	1.38150i	0.923982	−	0.382437i	$-0.124915\pi$
$318$	−10.6728	−	28.3898i	−0.598500	−	1.59202i
$319$	9.04617	+	24.8541i	0.506488	+	1.39156i
$320$		0			0
$321$	3.42806	−	1.64268i	0.191336	−	0.0916854i
$322$	−0.325884	+	3.72487i	−0.0181608	+	0.207579i
$323$	2.52621	−	2.52621i	0.140562	−	0.140562i
$324$	0.230548	+	5.47245i	0.0128082	+	0.304025i
$325$		0			0
$326$	−20.6475	−	24.6067i	−1.14356	−	1.36284i
$327$	3.78153	+	1.33146i	0.209119	+	0.0736297i
$328$	−3.83435	+	2.68484i	−0.211717	+	0.148245i
$329$	1.72715	−	0.628630i	0.0952207	−	0.0346575i
$330$		0			0
$331$	5.01737	+	28.4549i	0.275779	+	1.56402i	0.736475	+	0.676465i	$0.236489\pi$
$331$	5.01737	+	28.4549i	0.275779	+	1.56402i	−0.460695	+	0.887558i	$0.652400\pi$
$332$	2.62111	−	9.78212i	0.143852	−	0.536864i
$333$	−8.13421	+	18.4481i	−0.445752	+	1.01095i
$334$	−27.0582	−	15.6221i	−1.48056	−	0.854803i
$335$		0			0
$336$	−11.0533	+	3.08678i	−0.603008	+	0.168398i
$337$	−17.2575	+	1.50984i	−0.940078	+	0.0822462i	−0.546883	−	0.837209i	$-0.684186\pi$
$337$	−17.2575	+	1.50984i	−0.940078	+	0.0822462i	−0.393195	+	0.919455i	$0.628630\pi$
$338$	46.4047	−	4.05989i	2.52408	−	0.220829i
$339$	0.837450	+	0.820003i	0.0454840	+	0.0445364i
$340$		0			0
$341$	4.76702	+	2.75224i	0.258148	+	0.149042i
$342$	2.65592	+	0.652053i	0.143616	+	0.0352590i
$343$	4.29223	−	16.0188i	0.231759	−	0.864935i
$344$	−1.34600	−	7.63352i	−0.0725713	−	0.411572i
$345$		0			0
$346$	−24.6784	+	8.98221i	−1.32672	+	0.482887i
$347$	−10.1052	+	7.07573i	−0.542475	+	0.379845i	−0.812458	−	0.583020i	$-0.801871\pi$
$347$	−10.1052	+	7.07573i	−0.542475	+	0.379845i	0.269983	+	0.962865i	$0.412982\pi$
$348$	−1.28150	−	6.84557i	−0.0686954	−	0.366961i
$349$	8.50408	+	10.1348i	0.455213	+	0.542502i	0.944019	−	0.329891i	$-0.107012\pi$
$349$	8.50408	+	10.1348i	0.455213	+	0.542502i	−0.488806	+	0.872392i	$0.662567\pi$
$350$		0			0
$351$	20.1383	+	26.9103i	1.07490	+	1.43637i
$352$	−9.43630	+	9.43630i	−0.502956	+	0.502956i
$353$	−1.90514	+	21.7758i	−0.101400	+	1.15901i	0.759595	+	0.650396i	$0.225397\pi$
$353$	−1.90514	+	21.7758i	−0.101400	+	1.15901i	−0.860995	+	0.508613i	$0.830159\pi$
$354$	1.54385	−	20.0783i	0.0820545	−	1.06715i
$355$		0			0
$356$	−0.125370	−	0.344451i	−0.00664459	−	0.0182559i
$357$	9.51236	−	11.5818i	0.503448	−	0.612975i
$358$	9.81043	−	14.0107i	0.518497	−	0.740491i
$359$	2.83192	+	4.90502i	0.149463	+	0.258877i	0.931029	−	0.364945i	$-0.118912\pi$
$359$	2.83192	+	4.90502i	0.149463	+	0.258877i	−0.781566	+	0.623822i	$0.785579\pi$
$360$		0			0
$361$	−9.34072	+	16.1786i	−0.491617	+	0.851505i
$362$	−7.12568	−	15.2811i	−0.374518	−	0.803156i
$363$	−7.49238	+	4.43153i	−0.393248	+	0.232595i
$364$	3.45922	−	4.12254i	0.181312	−	0.216080i
$365$		0			0
$366$	24.8213	+	6.37161i	1.29743	+	0.333049i
$367$	−1.39490	+	0.650455i	−0.0728134	+	0.0339535i	−0.458684	−	0.888600i	$-0.651679\pi$
$367$	−1.39490	+	0.650455i	−0.0728134	+	0.0339535i	0.385870	+	0.922553i	$0.373901\pi$
$368$	2.12438	+	7.92829i	0.110741	+	0.413290i
$369$	6.12957	−	1.21438i	0.319093	−	0.0632179i
$370$		0			0
$371$	−14.5962	+	2.57371i	−0.757798	+	0.133620i
$372$	−1.12006	−	0.919926i	−0.0580724	−	0.0476959i
$373$	15.4081	+	7.18493i	0.797802	+	0.372021i	0.778383	−	0.627790i	$-0.216040\pi$
$373$	15.4081	+	7.18493i	0.797802	+	0.372021i	0.0194197	+	0.999811i	$0.493818\pi$
$374$	7.10666	−	40.3038i	0.367476	−	2.08406i
$375$		0			0
$376$	2.31458	−	1.94216i	0.119365	−	0.100159i
$377$	−30.2198	−	30.2198i	−1.55640	−	1.55640i
$378$	11.3557	+	1.63451i	0.584077	+	0.0840701i
$379$		−	37.4048i		−	1.92136i	−0.277663	−	0.960679i	$-0.589560\pi$
$379$		−	37.4048i		−	1.92136i	0.277663	−	0.960679i	$-0.410440\pi$
$380$		0			0
$381$	−4.17560	+	6.09902i	−0.213922	+	0.312462i
$382$	6.61393	+	9.44567i	0.338398	+	0.483282i
$383$	−10.1678	+	21.8049i	−0.519550	+	1.11418i	0.455099	+	0.890441i	$0.349604\pi$
$383$	−10.1678	+	21.8049i	−0.519550	+	1.11418i	−0.974649	+	0.223738i	$0.928174\pi$
$384$	−19.1913	+	13.7412i	−0.979351	+	0.701226i
$385$		0			0
$386$	15.2242	−	8.78971i	0.774893	−	0.447385i
$387$	−2.46715	+	10.0491i	−0.125412	+	0.510825i
$388$	9.62121	−	2.57800i	0.488443	−	0.130878i
$389$	−5.94474	−	2.16371i	−0.301410	−	0.109704i	0.186888	−	0.982381i	$-0.440160\pi$
$389$	−5.94474	−	2.16371i	−0.301410	−	0.109704i	−0.488298	+	0.872677i	$0.662382\pi$
$390$		0			0
$391$	−8.21141	−	6.89019i	−0.415269	−	0.348452i
$392$	−1.00501	−	11.4873i	−0.0507608	−	0.580198i
$393$	9.17444	−	16.2841i	0.462789	−	0.821423i
$394$	−0.532101	+	1.46194i	−0.0268069	+	0.0736513i
$395$		0			0
$396$	6.81402	−	2.64383i	0.342417	−	0.132857i
$397$	29.5283	+	7.91207i	1.48198	+	0.397095i	0.907021	−	0.421086i	$-0.138351\pi$
$397$	29.5283	+	7.91207i	1.48198	+	0.397095i	0.574960	+	0.818182i	$0.305018\pi$
$398$	−20.6353	−	14.4490i	−1.03435	−	0.724261i
$399$	0.552018	−	1.21709i	0.0276355	−	0.0609308i
$400$		0			0
$401$	−2.27324	−	0.400833i	−0.113520	−	0.0200167i	0.116599	−	0.993179i	$-0.462801\pi$
$401$	−2.27324	−	0.400833i	−0.113520	−	0.0200167i	−0.230120	+	0.973162i	$0.573912\pi$
$402$	5.20069	−	14.7707i	0.259387	−	0.736696i
$403$	−8.86041	−	0.775186i	−0.441369	−	0.0386147i
$404$	−5.72130			−0.284645
$405$		0			0
$406$	−14.5878			−0.723982
$407$	26.8017	+	2.34484i	1.32851	+	0.116229i
$408$	8.18246	−	23.2394i	0.405092	−	1.15052i
$409$	13.8912	+	2.44939i	0.686874	+	0.121114i	0.506184	−	0.862426i	$-0.331056\pi$
$409$	13.8912	+	2.44939i	0.686874	+	0.121114i	0.180690	+	0.983540i	$0.442167\pi$
$410$		0			0
$411$	11.6725	−	25.7355i	0.575761	−	1.26944i
$412$	−9.03274	−	6.32479i	−0.445011	−	0.311600i
$413$	−9.50540	−	2.54696i	−0.467730	−	0.125328i
$414$	1.25445	−	8.10904i	0.0616528	−	0.398537i
$415$		0			0
$416$	7.37500	−	20.2626i	0.361589	−	0.993458i
$417$	15.3391	−	27.2260i	0.751159	−	1.33326i
$418$	−0.318060	−	3.63544i	−0.0155568	−	0.177815i
$419$	22.4508	+	18.8385i	1.09679	+	0.920320i	0.997205	−	0.0747090i	$-0.0238028\pi$
$419$	22.4508	+	18.8385i	1.09679	+	0.920320i	0.0995889	+	0.995029i	$0.468247\pi$
$420$		0			0
$421$	−19.6404	−	7.14853i	−0.957216	−	0.348398i	−0.184274	−	0.982875i	$-0.558993\pi$
$421$	−19.6404	−	7.14853i	−0.957216	−	0.348398i	−0.772942	+	0.634477i	$0.781216\pi$
$422$	−8.04644	+	2.15604i	−0.391694	+	0.104954i
$423$	−3.87321	+	1.12573i	−0.188322	+	0.0547347i
$424$	−21.1005	+	12.1824i	−1.02473	+	0.591630i
$425$		0			0
$426$	−1.56074	+	1.11751i	−0.0756180	+	0.0541434i
$427$	5.29238	−	11.3495i	0.256116	−	0.549243i
$428$	0.766106	+	1.09411i	0.0370311	+	0.0528859i
$429$	25.3373	−	37.0085i	1.22330	−	1.78679i
$430$		0			0
$431$			22.4642i			1.08206i	0.841003	+	0.541030i	$0.181966\pi$
$431$			22.4642i			1.08206i	−0.841003	+	0.541030i	$0.818034\pi$
$432$	24.6516	−	5.15417i	1.18605	−	0.247980i
$433$	−7.75200	−	7.75200i	−0.372537	−	0.372537i	0.495863	−	0.868401i	$-0.334852\pi$
$433$	−7.75200	−	7.75200i	−0.372537	−	0.372537i	−0.868401	+	0.495863i	$0.834852\pi$
$434$	−2.32567	+	1.95147i	−0.111636	+	0.0936734i
$435$		0			0
$436$	−0.244612	+	1.38727i	−0.0117148	+	0.0664380i
$437$	−0.866278	−	0.403952i	−0.0414397	−	0.0193236i
$438$	15.7114	+	12.9040i	0.750718	+	0.616579i
$439$	−26.6574	+	4.70041i	−1.27229	+	0.224338i	−0.768702	−	0.639608i	$-0.779097\pi$
$439$	−26.6574	+	4.70041i	−1.27229	+	0.224338i	−0.503585	+	0.863946i	$0.667986\pi$
$440$		0			0
$441$	−4.95923	+	14.5728i	−0.236154	+	0.693944i
$442$	17.1153	+	63.8752i	0.814092	+	3.03823i
$443$	−37.4589	+	17.4674i	−1.77973	+	0.829901i	−0.809724	+	0.586810i	$0.800383\pi$
$443$	−37.4589	+	17.4674i	−1.77973	+	0.829901i	−0.970004	+	0.243090i	$0.921839\pi$
$444$	−6.86177	−	1.76141i	−0.325645	−	0.0835927i
$445$		0			0
$446$	−24.1813	+	28.8181i	−1.14502	+	1.36458i
$447$	−14.4845	+	8.56718i	−0.685094	+	0.405214i
$448$	2.48979	+	5.33936i	0.117631	+	0.252261i
$449$	5.23440	−	9.06624i	0.247027	−	0.427862i	−0.715673	−	0.698436i	$-0.753880\pi$
$449$	5.23440	−	9.06624i	0.247027	−	0.427862i	0.962699	+	0.270573i	$0.0872132\pi$
$450$		0			0
$451$	−4.16915	−	7.22119i	−0.196318	−	0.340032i
$452$	−0.236214	+	0.337348i	−0.0111106	+	0.0158675i
$453$	2.44047	−	2.97140i	0.114663	−	0.139609i
$454$	3.58906	+	9.86086i	0.168443	+	0.462793i
$455$		0			0
$456$	0.168429	−	2.19048i	0.00788743	−	0.102579i
$457$	−3.03365	+	34.6748i	−0.141908	+	1.62202i	0.507550	+	0.861622i	$0.330551\pi$
$457$	−3.03365	+	34.6748i	−0.141908	+	1.62202i	−0.649458	+	0.760397i	$0.725004\pi$
$458$	−21.6867	+	21.6867i	−1.01335	+	1.01335i
$459$	−22.5109	+	23.9795i	−1.05072	+	1.11927i
$460$		0			0
$461$	20.9800	+	25.0030i	0.977135	+	1.16450i	0.986369	+	0.164546i	$0.0526161\pi$
$461$	20.9800	+	25.0030i	0.977135	+	1.16450i	−0.00923458	+	0.999957i	$0.502939\pi$
$462$	−2.81699	−	15.0479i	−0.131058	−	0.700093i
$463$	4.82297	−	3.37708i	0.224143	−	0.156946i	−0.456112	−	0.889923i	$-0.650758\pi$
$463$	4.82297	−	3.37708i	0.224143	−	0.156946i	0.680254	+	0.732976i	$0.261869\pi$
$464$	−30.0916	+	10.9524i	−1.39697	+	0.508454i
$465$		0			0
$466$	−6.57058	−	37.2636i	−0.304376	−	1.72620i
$467$	−5.29691	+	19.7683i	−0.245112	+	0.914769i	0.728216	+	0.685348i	$0.240350\pi$
$467$	−5.29691	+	19.7683i	−0.245112	+	0.914769i	−0.973327	+	0.229421i	$0.926317\pi$
$468$	−8.17326	+	8.52484i	−0.377809	+	0.394061i
$469$	−6.62720	−	3.82621i	−0.306015	−	0.176678i
$470$		0			0
$471$	22.4488	+	21.9811i	1.03439	+	1.01284i
$472$	−16.1155	+	1.40993i	−0.741778	+	0.0648972i
$473$	13.7553	−	1.20343i	0.632467	−	0.0553337i
$474$	−34.4492	+	9.62039i	−1.58230	+	0.441879i
$475$		0			0
$476$	4.56060	+	2.63306i	0.209035	+	0.120686i
$477$	32.3350	−	3.51624i	1.48052	−	0.160998i
$478$	−0.426596	+	1.59208i	−0.0195120	+	0.0728199i
$479$	1.10017	+	6.23936i	0.0502679	+	0.285083i	0.999571	−	0.0292779i	$-0.00932077\pi$
$479$	1.10017	+	6.23936i	0.0502679	+	0.285083i	−0.949303	+	0.314361i	$0.898210\pi$
$480$		0			0
$481$	−40.8504	+	14.8683i	−1.86262	+	0.677938i
$482$	−5.59022	+	3.91431i	−0.254627	+	0.178292i
$483$	−3.78223	−	1.33170i	−0.172097	−	0.0605946i
$484$	−1.96604	−	2.34303i	−0.0893654	−	0.106501i
$485$		0			0
$486$	−24.6283	−	5.22796i	−1.11716	−	0.237145i
$487$	4.69365	−	4.69365i	0.212690	−	0.212690i	−0.592719	−	0.805409i	$-0.701946\pi$
$487$	4.69365	−	4.69365i	0.212690	−	0.212690i	0.805409	+	0.592719i	$0.201946\pi$
$488$	1.79421	−	20.5079i	0.0812200	−	0.928349i
$489$	31.0651	−	14.8860i	1.40481	−	0.673166i
$490$		0			0
$491$	2.14176	+	5.88443i	0.0966562	+	0.265561i	0.978592	−	0.205808i	$-0.0659823\pi$
$491$	2.14176	+	5.88443i	0.0966562	+	0.265561i	−0.881936	+	0.471369i	$0.843760\pi$
$492$	0.772616	+	2.05517i	0.0348322	+	0.0926544i
$493$	23.9871	−	34.2572i	1.08033	−	1.54287i
$494$	2.94833	+	5.10666i	0.132652	+	0.229759i
$495$		0			0
$496$	−3.33221	+	5.77155i	−0.149620	+	0.259150i
$497$	0.396434	+	0.850156i	0.0177825	+	0.0381347i
$498$	40.5571	+	22.8498i	1.81741	+	1.02393i
$499$	−15.3830	+	18.3328i	−0.688638	+	0.820687i	−0.991190	−	0.132446i	$-0.957717\pi$
$499$	−15.3830	+	18.3328i	−0.688638	+	0.820687i	0.302552	+	0.953133i	$0.402161\pi$
$500$		0			0
$501$	23.4419	−	23.9406i	1.04730	−	1.06959i
$502$	35.3381	−	16.4784i	1.57722	−	0.735468i
$503$	1.93816	+	7.23333i	0.0864185	+	0.322518i	0.995579	−	0.0939277i	$-0.0299423\pi$
$503$	1.93816	+	7.23333i	0.0864185	+	0.322518i	−0.909161	+	0.416446i	$0.863276\pi$
$504$	−0.194010	−	9.21440i	−0.00864190	−	0.410442i
$505$		0			0
$506$	−10.7831	+	1.90135i	−0.479368	+	0.0845255i
$507$	−8.15622	+	49.2843i	−0.362231	+	2.18879i
$508$	−2.35380	−	1.09759i	−0.104433	−	0.0486979i
$509$	−1.85342	+	10.5113i	−0.0821515	+	0.465904i	0.915783	+	0.401672i	$0.131571\pi$
$509$	−1.85342	+	10.5113i	−0.0821515	+	0.465904i	−0.997935	+	0.0642321i	$0.979540\pi$
$510$		0			0
$511$	7.61095	−	6.38635i	0.336689	−	0.282515i
$512$	3.97904	+	3.97904i	0.175850	+	0.175850i
$513$	−1.38548	+	2.58491i	−0.0611704	+	0.114127i
$514$			33.1368i			1.46160i
$515$		0			0
$516$	−3.62510	−	0.278739i	−0.159586	−	0.0122708i
$517$	3.08717	+	4.40893i	0.135773	+	0.193905i
$518$	−6.27109	+	13.4484i	−0.275536	+	0.590889i
$519$	−2.74981	−	28.0291i	−0.120703	−	1.23034i
$520$		0			0
$521$	12.8647	−	7.42744i	0.563613	−	0.325402i	−0.190982	−	0.981594i	$-0.561167\pi$
$521$	12.8647	−	7.42744i	0.563613	−	0.325402i	0.754594	+	0.656192i	$0.227834\pi$
$522$	31.9430	+	2.11818i	1.39811	+	0.0927103i
$523$	−21.0978	+	5.65314i	−0.922542	+	0.247194i	−0.688672	−	0.725073i	$-0.741806\pi$
$523$	−21.0978	+	5.65314i	−0.922542	+	0.247194i	−0.233870	+	0.972268i	$0.575139\pi$
$524$	6.17127	+	2.24616i	0.269593	+	0.0981239i
$525$		0			0
$526$	5.54906	+	4.65621i	0.241951	+	0.203021i
$527$	−0.758553	−	8.67030i	−0.0330431	−	0.377684i
$528$	−17.1087	−	28.9257i	−0.744561	−	1.25883i
$529$	6.88559	−	18.9180i	0.299373	−	0.822522i
$530$		0			0
$531$	20.4441	+	6.95729i	0.887200	+	0.301921i
$532$	0.453579	+	0.121536i	0.0196651	+	0.00526926i
$533$	11.0366	+	7.72792i	0.478049	+	0.334734i
$534$	1.67687	−	0.164510i	0.0725654	−	0.00711906i
$535$		0			0
$536$	−12.3887	−	2.18446i	−0.535109	−	0.0943542i
$537$	11.9375	+	13.9262i	0.515140	+	0.600958i
$538$	11.7893	+	1.03143i	0.508271	+	0.0444680i
$539$	20.5412			0.884773
$540$		0			0
$541$	−4.75367			−0.204376			−0.102188	−	0.994765i	$-0.532584\pi$
$541$	−4.75367			−0.204376			−0.102188	+	0.994765i	$0.532584\pi$
$542$	−31.4518	−	2.75168i	−1.35097	−	0.118195i
$543$	17.7728	−	3.32709i	0.762705	−	0.142779i
$544$	20.7798	+	3.66405i	0.890928	+	0.157095i
$545$		0			0
$546$	14.4012	+	20.1130i	0.616313	+	0.860758i
$547$	−14.9586	−	10.4741i	−0.639582	−	0.447840i	0.208271	−	0.978071i	$-0.433216\pi$
$547$	−14.9586	−	10.4741i	−0.639582	−	0.447840i	−0.847853	+	0.530231i	$0.822105\pi$
$548$	9.59097	+	2.56989i	0.409706	+	0.109780i
$549$	−13.2367	+	24.0836i	−0.564929	+	1.02786i
$550$		0			0
$551$	1.27543	−	3.50421i	0.0543351	−	0.149284i
$552$	−6.59137	+	0.0693833i	−0.280547	+	0.00295315i
$553$	1.52336	+	17.4121i	0.0647798	+	0.740437i
$554$	25.8191	+	21.6648i	1.09695	+	0.920449i
$555$		0			0
$556$	10.3180	+	3.75544i	0.437580	+	0.159266i
$557$	−16.8064	+	4.50326i	−0.712110	+	0.190809i	−0.596649	−	0.802503i	$-0.703501\pi$
$557$	−16.8064	+	4.50326i	−0.712110	+	0.190809i	−0.115461	+	0.993312i	$0.536835\pi$
$558$	5.37587	−	3.93544i	0.227579	−	0.166600i
$559$	−19.3219	+	11.1555i	−0.817227	+	0.471826i
$560$		0			0
$561$	39.9697	+	18.1285i	1.68752	+	0.765384i
$562$	3.67500	−	7.88106i	0.155020	−	0.332442i
$563$	−4.88633	−	6.97840i	−0.205934	−	0.294104i	0.702878	−	0.711311i	$-0.251898\pi$
$563$	−4.88633	−	6.97840i	−0.205934	−	0.294104i	−0.908812	+	0.417206i	$0.863009\pi$
$564$	−0.612440	−	1.27808i	−0.0257884	−	0.0538170i
$565$		0			0
$566$		−	13.1190i		−	0.551432i
$567$	−4.72570	+	11.3597i	−0.198461	+	0.477062i
$568$	1.09039	+	1.09039i	0.0457518	+	0.0457518i
$569$	1.30840	−	1.09788i	0.0548512	−	0.0460256i	−0.614950	−	0.788566i	$-0.710824\pi$
$569$	1.30840	−	1.09788i	0.0548512	−	0.0460256i	0.669801	+	0.742541i	$0.266379\pi$
$570$		0			0
$571$	−2.38472	+	13.5244i	−0.0997975	+	0.565980i	0.893374	+	0.449314i	$0.148332\pi$
$571$	−2.38472	+	13.5244i	−0.0997975	+	0.565980i	−0.993171	+	0.116665i	$0.962779\pi$
$572$	14.2827	+	6.66015i	0.597192	+	0.278475i
$573$	−11.5750	+	4.35147i	−0.483552	+	0.181785i
$574$	4.52905	−	0.798594i	0.189039	−	0.0333327i
$575$		0			0
$576$	−4.67660	−	12.0531i	−0.194858	−	0.502213i
$577$	−7.71384	−	28.7885i	−0.321131	−	1.19848i	−0.918144	−	0.396247i	$-0.870312\pi$
$577$	−7.71384	−	28.7885i	−0.321131	−	1.19848i	0.597013	−	0.802232i	$-0.296354\pi$
$578$	−33.7624	+	15.7437i	−1.40433	+	0.654851i
$579$	5.07072	+	18.1575i	0.210732	+	0.754599i
$580$		0			0
$581$	14.6223	−	17.4262i	0.606636	−	0.722961i
$582$	0.481926	+	45.7827i	0.0199765	+	1.89775i
$583$	−18.3427	−	39.3359i	−0.759675	−	1.62913i
$584$	8.16638	−	14.1446i	0.337927	−	0.585307i
$585$		0			0
$586$	4.65744	+	8.06692i	0.192397	+	0.333241i
$587$	−9.86144	+	14.0836i	−0.407025	+	0.581292i	−0.969368	−	0.245612i	$-0.921011\pi$
$587$	−9.86144	+	14.0836i	−0.407025	+	0.581292i	0.562343	+	0.826904i	$0.309900\pi$
$588$	−5.33623	−	0.883112i	−0.220063	−	0.0364189i
$589$	−0.265436	−	0.729279i	−0.0109371	−	0.0300494i
$590$		0			0
$591$	−1.37667	−	0.942517i	−0.0566287	−	0.0387700i
$592$	−2.83896	+	32.4495i	−0.116681	+	1.33366i
$593$	−3.89096	+	3.89096i	−0.159783	+	0.159783i	−0.782470	−	0.622688i	$-0.786041\pi$
$593$	−3.89096	+	3.89096i	−0.159783	+	0.159783i	0.622688	+	0.782470i	$0.286041\pi$
$594$	3.98336	+	33.3595i	0.163439	+	1.36876i
$595$		0			0
$596$	−3.80081	−	4.52963i	−0.155687	−	0.185541i
$597$	20.5107	−	17.5817i	0.839446	−	0.719571i
$598$	14.4927	−	10.1479i	0.592652	−	0.414980i
$599$	8.34437	−	3.03710i	0.340942	−	0.124093i	−0.165874	−	0.986147i	$-0.553045\pi$
$599$	8.34437	−	3.03710i	0.340942	−	0.124093i	0.506816	+	0.862054i	$0.330822\pi$
$600$		0			0
$601$	6.49256	+	36.8211i	0.264837	+	1.50197i	0.769499	+	0.638649i	$0.220506\pi$
$601$	6.49256	+	36.8211i	0.264837	+	1.50197i	−0.504661	+	0.863317i	$0.668383\pi$
$602$	−1.97105	+	7.35607i	−0.0803341	+	0.299811i
$603$	13.9560	+	9.34054i	0.568332	+	0.380376i
$604$	1.17006	+	0.675532i	0.0476089	+	0.0274870i
$605$		0			0
$606$	6.53884	−	25.4728i	0.265622	−	1.03476i
$607$	24.9336	−	2.18141i	1.01202	−	0.0885406i	0.430937	−	0.902382i	$-0.358183\pi$
$607$	24.9336	−	2.18141i	1.01202	−	0.0885406i	0.581087	+	0.813841i	$0.302628\pi$
$608$	1.87436	−	0.163985i	0.0760153	−	0.00665047i
$609$	3.88969	−	15.1527i	0.157618	−	0.614020i
$610$		0			0
$611$	−7.53170	−	4.34843i	−0.304700	−	0.175919i
$612$	−9.60402	−	6.42783i	−0.388219	−	0.259830i
$613$	−1.60494	+	5.98971i	−0.0648229	+	0.241922i	−0.990733	−	0.135820i	$-0.956633\pi$
$613$	−1.60494	+	5.98971i	−0.0648229	+	0.241922i	0.925911	+	0.377743i	$0.123300\pi$
$614$	2.82746	+	16.0353i	0.114107	+	0.647134i
$615$		0			0
$616$	−11.5568	+	4.20633i	−0.465636	+	0.169478i
$617$	−7.00927	+	4.90794i	−0.282182	+	0.197586i	−0.706096	−	0.708117i	$-0.749545\pi$
$617$	−7.00927	+	4.90794i	−0.282182	+	0.197586i	0.423913	+	0.905703i	$0.360656\pi$
$618$	38.4832	−	32.9877i	1.54802	−	1.32696i
$619$	7.05535	+	8.40824i	0.283579	+	0.337956i	0.888964	−	0.457976i	$-0.151426\pi$
$619$	7.05535	+	8.40824i	0.283579	+	0.337956i	−0.605386	+	0.795932i	$0.706981\pi$
$620$		0			0
$621$	8.08858	+	3.46522i	0.324583	+	0.139054i
$622$	−23.5795	+	23.5795i	−0.945452	+	0.945452i
$623$	0.0717624	−	0.820248i	0.00287510	−	0.0328625i
$624$	44.8072	+	30.6766i	1.79372	+	1.22805i
$625$		0			0
$626$	−8.01907	−	22.0322i	−0.320507	−	0.880585i
$627$	3.86103	+	0.638975i	0.154195	+	0.0255182i
$628$	−6.33198	+	9.04301i	−0.252674	+	0.360855i
$629$	−21.2697	−	36.8402i	−0.848079	−	1.46892i
$630$		0			0
$631$	17.7048	−	30.6656i	0.704816	−	1.22078i	−0.261942	−	0.965084i	$-0.584363\pi$
$631$	17.7048	−	30.6656i	0.704816	−	1.22078i	0.966758	−	0.255694i	$-0.0823038\pi$
$632$	12.1431	+	26.0409i	0.483026	+	1.03585i
$633$	−0.0940314	−	8.93292i	−0.00373741	−	0.355052i
$634$	−31.1735	+	37.1511i	−1.23806	+	1.47546i
$635$		0			0
$636$	3.07395	+	11.0074i	0.121890	+	0.436470i
$637$	−30.0812	+	14.0271i	−1.19186	+	0.555774i
$638$	−11.0564	−	41.2629i	−0.437725	−	1.63361i
$639$	−0.744628	−	1.91915i	−0.0294570	−	0.0759204i
$640$		0			0
$641$	−14.4883	+	2.55468i	−0.572254	+	0.100904i	−0.452285	−	0.891874i	$-0.649391\pi$
$641$	−14.4883	+	2.55468i	−0.572254	+	0.100904i	−0.119970	+	0.992778i	$0.538280\pi$
$642$	−5.74687	+	2.16046i	−0.226811	+	0.0852666i
$643$	−9.20060	−	4.29031i	−0.362836	−	0.169193i	0.232647	−	0.972561i	$-0.425261\pi$
$643$	−9.20060	−	4.29031i	−0.362836	−	0.169193i	−0.595483	+	0.803368i	$0.703039\pi$
$644$	0.244658	−	1.38752i	0.00964087	−	0.0546761i
$645$		0			0
$646$	−4.42019	+	3.70898i	−0.173910	+	0.145928i
$647$	2.41506	+	2.41506i	0.0949459	+	0.0949459i	0.752984	−	0.658038i	$-0.228614\pi$
$647$	2.41506	+	2.41506i	0.0949459	+	0.0949459i	−0.658038	+	0.752984i	$0.728614\pi$
$648$	−0.913126	+	20.2049i	−0.0358710	+	0.793725i
$649$		−	28.8172i		−	1.13117i
$650$		0			0
$651$	−1.40692	−	2.93607i	−0.0551417	−	0.115074i
$652$	6.94245	+	9.91484i	0.271887	+	0.388295i
$653$	−13.5667	+	29.0939i	−0.530907	+	1.13853i	0.439763	+	0.898114i	$0.355063\pi$
$653$	−13.5667	+	29.0939i	−0.530907	+	1.13853i	−0.970669	+	0.240419i	$0.922715\pi$
$654$	−5.89692	−	2.67458i	−0.230588	−	0.104584i
$655$		0			0
$656$	8.74288	−	5.04770i	0.341352	−	0.197080i
$657$	−17.5930	+	12.8791i	−0.686369	+	0.502460i
$658$	−2.86741	+	0.768321i	−0.111783	+	0.0299523i
$659$	1.04455	+	0.380185i	0.0406898	+	0.0148099i	0.362285	−	0.932067i	$-0.381997\pi$
$659$	1.04455	+	0.380185i	0.0406898	+	0.0148099i	−0.321595	+	0.946877i	$0.604219\pi$
$660$		0			0
$661$	−2.09875	−	1.76106i	−0.0816318	−	0.0684972i	0.601059	−	0.799205i	$-0.294746\pi$
$661$	−2.09875	−	1.76106i	−0.0816318	−	0.0684972i	−0.682690	+	0.730708i	$0.739190\pi$
$662$	−4.06728	−	46.4893i	−0.158080	−	1.80686i
$663$	−70.9124	+	0.746452i	−2.75401	+	0.0289898i
$664$	12.7901	−	35.1406i	0.496353	−	1.36372i
$665$		0			0
$666$	15.6846	−	28.5374i	0.607764	−	1.10580i
$667$	−10.8076	−	2.89588i	−0.418471	−	0.112129i
$668$	9.64395	+	6.75277i	0.373136	+	0.261272i
$669$	−23.4864	−	32.8017i	−0.908037	−	1.26819i
$670$		0			0
$671$	36.1143	+	6.36793i	1.39418	+	0.245831i
$672$	7.75841	−	1.45238i	0.299287	−	0.0560268i
$673$	20.5328	+	1.79638i	0.791479	+	0.0692455i	0.475723	−	0.879595i	$-0.342186\pi$
$673$	20.5328	+	1.79638i	0.791479	+	0.0692455i	0.315756	+	0.948840i	$0.397742\pi$
$674$	27.9793			1.07772
$675$		0			0
$676$	−17.5525			−0.675097
$677$	5.16710	+	0.452063i	0.198588	+	0.0173742i	0.186016	−	0.982547i	$-0.440443\pi$
$677$	5.16710	+	0.452063i	0.198588	+	0.0173742i	0.0125721	+	0.999921i	$0.495998\pi$
$678$	−1.23200	−	1.43724i	−0.0473147	−	0.0551970i
$679$	22.0342	+	3.88522i	0.845595	+	0.149101i
$680$		0			0
$681$	−11.1997	+	1.09875i	−0.429174	+	0.0421043i
$682$	−7.28255	−	5.09930i	−0.278863	−	0.195262i
$683$	4.07571	+	1.09208i	0.155953	+	0.0417874i	0.335951	−	0.941880i	$-0.390942\pi$
$683$	4.07571	+	1.09208i	0.155953	+	0.0417874i	−0.179998	+	0.983667i	$0.557609\pi$
$684$	−0.975554	−	0.331988i	−0.0373013	−	0.0126939i
$685$		0			0
$686$	−9.16097	+	25.1696i	−0.349767	+	0.960978i
$687$	−16.7440	−	28.3091i	−0.638824	−	1.08006i
$688$	1.45702	+	16.6538i	0.0555485	+	0.634922i
$689$	53.7231	+	45.0791i	2.04669	+	1.71738i
$690$		0			0
$691$	−5.69285	−	2.07203i	−0.216566	−	0.0788236i	0.231459	−	0.972845i	$-0.425650\pi$
$691$	−5.69285	−	2.07203i	−0.216566	−	0.0788236i	−0.448025	+	0.894021i	$0.647872\pi$
$692$	9.55866	−	2.56124i	0.363366	−	0.0973636i
$693$	16.3818	+	1.08630i	0.622293	+	0.0412651i
$694$	17.2549	−	9.96215i	0.654989	−	0.378158i
$695$		0			0
$696$	−2.51094	−	25.5943i	−0.0951768	−	0.970148i
$697$	−5.57186	+	11.9489i	−0.211049	+	0.452597i
$698$	−12.2562	−	17.5036i	−0.463902	−	0.662521i
$699$	40.4587	+	3.11092i	1.53029	+	0.117666i
$700$		0			0
$701$			31.6966i			1.19716i	0.801062	+	0.598581i	$0.204269\pi$
$701$			31.6966i			1.19716i	−0.801062	+	0.598581i	$0.795731\pi$
$702$	−28.6138	−	46.1326i	−1.07996	−	1.74116i
$703$	−2.68222	−	2.68222i	−0.101162	−	0.101162i
$704$	−13.2158	+	11.0894i	−0.498088	+	0.417946i
$705$		0			0
$706$	6.13060	−	34.7684i	0.230728	−	1.30852i
$707$	−11.6474	−	5.43129i	−0.438047	−	0.204265i
$708$	−1.23891	+	7.48618i	−0.0465612	+	0.281348i
$709$	20.0118	−	3.52862i	0.751559	−	0.132520i	0.215270	−	0.976555i	$-0.430937\pi$
$709$	20.0118	−	3.52862i	0.751559	−	0.132520i	0.536289	+	0.844035i	$0.319826\pi$
$710$		0			0
$711$	−0.807430	−	38.3484i	−0.0302810	−	1.43818i
$712$	−0.350325	−	1.30743i	−0.0131290	−	0.0489981i
$713$	−2.11039	+	0.984093i	−0.0790348	+	0.0368546i
$714$	−16.9354	+	17.2957i	−0.633792	+	0.647277i
$715$		0			0
$716$	−4.14272	+	4.93710i	−0.154821	+	0.184508i
$717$	−1.53998	−	0.867626i	−0.0575117	−	0.0324021i
$718$	−3.86600	−	8.29065i	−0.144278	−	0.309404i
$719$	−5.78147	+	10.0138i	−0.215612	+	0.373452i	−0.953462	−	0.301514i	$-0.902508\pi$
$719$	−5.78147	+	10.0138i	−0.215612	+	0.373452i	0.737849	+	0.674965i	$0.235841\pi$
$720$		0			0
$721$	−12.3847	−	21.4509i	−0.461229	−	0.798872i
$722$	17.3063	−	24.7160i	0.644074	−	0.919833i
$723$	−2.57532	−	6.85041i	−0.0957773	−	0.254770i
$724$	2.17296	+	5.97016i	0.0807574	+	0.221879i
$725$		0			0
$726$	12.6788	−	6.07551i	0.470554	−	0.225483i
$727$	1.70574	−	19.4967i	0.0632625	−	0.723094i	−0.896640	−	0.442760i	$-0.853999\pi$
$727$	1.70574	−	19.4967i	0.0632625	−	0.723094i	0.959903	−	0.280334i	$-0.0904451\pi$
$728$	14.0517	−	14.0517i	0.520792	−	0.520792i
$729$	11.9973	−	24.1881i	0.444345	−	0.895856i
$730$		0			0
$731$	−14.0335	−	16.7245i	−0.519048	−	0.618577i
$732$	−9.10807	−	3.20690i	−0.336644	−	0.118531i
$733$	20.0010	−	14.0049i	0.738755	−	0.517282i	−0.142575	−	0.989784i	$-0.545538\pi$
$733$	20.0010	−	14.0049i	0.738755	−	0.517282i	0.881329	+	0.472502i	$0.156649\pi$
$734$	2.33592	−	0.850204i	0.0862203	−	0.0313816i
$735$		0			0
$736$	−0.980299	−	5.55955i	−0.0361343	−	0.204928i
$737$	5.79990	−	21.6455i	0.213642	−	0.797323i
$738$	−10.0332	+	1.09105i	−0.369328	+	0.0401622i
$739$	−3.92364	−	2.26531i	−0.144333	−	0.0833310i	0.426094	−	0.904679i	$-0.359889\pi$
$739$	−3.92364	−	2.26531i	−0.144333	−	0.0833310i	−0.570428	+	0.821348i	$0.693223\pi$
$740$		0			0
$741$	−6.09056	+	1.70087i	−0.223742	+	0.0624830i
$742$	23.8471	−	2.08635i	0.875455	−	0.0765924i
$743$	44.0909	−	3.85745i	1.61754	−	0.141516i	0.757882	−	0.652391i	$-0.226234\pi$
$743$	44.0909	−	3.85745i	1.61754	−	0.141516i	0.859655	+	0.510875i	$0.170679\pi$
$744$	−3.82415	−	3.74448i	−0.140200	−	0.137279i
$745$		0			0
$746$	−23.7798	−	13.7293i	−0.870639	−	0.502664i
$747$	−34.5488	+	36.0350i	−1.26408	+	1.31845i
$748$	−3.99128	+	14.8957i	−0.145936	+	0.544640i
$749$	0.520987	+	2.95467i	0.0190365	+	0.107961i
$750$		0			0
$751$	21.6380	−	7.87559i	0.789582	−	0.287384i	0.0844197	−	0.996430i	$-0.473096\pi$
$751$	21.6380	−	7.87559i	0.789582	−	0.287384i	0.705162	+	0.709046i	$0.250874\pi$
$752$	−5.33801	+	3.73771i	−0.194657	+	0.136300i
$753$	7.69403	+	41.1004i	0.280386	+	1.49778i
$754$	44.3687	+	52.8766i	1.61581	+	1.92565i
$755$		0			0
$756$	−4.20899	−	0.986490i	−0.153079	−	0.0358783i
$757$	−7.64204	+	7.64204i	−0.277755	+	0.277755i	−0.832212	−	0.554457i	$-0.812926\pi$
$757$	−7.64204	+	7.64204i	−0.277755	+	0.277755i	0.554457	+	0.832212i	$0.312926\pi$
$758$	−5.26534	+	60.1831i	−0.191246	+	2.18595i
$759$	0.900219	−	11.7077i	0.0326759	−	0.424961i
$760$		0			0
$761$	7.73791	+	21.2597i	0.280499	+	0.770664i	0.997303	+	0.0733901i	$0.0233818\pi$
$761$	7.73791	+	21.2597i	0.280499	+	0.770664i	−0.716804	+	0.697274i	$0.754396\pi$
$762$	7.57694	−	9.22533i	0.274484	−	0.334199i
$763$	−1.81493	+	2.59198i	−0.0657048	+	0.0938361i
$764$	−2.17250	−	3.76288i	−0.0785983	−	0.136136i
$765$		0			0
$766$	19.4291	−	33.6521i	0.702000	−	1.21590i
$767$	19.6786	+	42.2008i	0.710552	+	1.52378i
$768$	19.9631	−	11.8076i	0.720357	−	0.426071i
$769$	19.5257	−	23.2698i	0.704115	−	0.839132i	−0.288870	−	0.957368i	$-0.593280\pi$
$769$	19.5257	−	23.2698i	0.704115	−	0.839132i	0.992985	+	0.118236i	$0.0377240\pi$
$770$		0			0
$771$	−34.4200	−	8.83557i	−1.23961	−	0.318205i
$772$	−6.00346	+	2.79946i	−0.216069	+	0.100755i
$773$	−11.9583	−	44.6289i	−0.430109	−	1.60519i	−0.752506	−	0.658585i	$-0.771155\pi$
$773$	−11.9583	−	44.6289i	−0.430109	−	1.60519i	0.322397	−	0.946604i	$-0.395511\pi$
$774$	5.38413	−	15.8214i	0.193529	−	0.568688i
$775$		0			0
$776$	36.2219	−	6.38690i	1.30029	−	0.229276i
$777$	−12.2971	−	10.0998i	−0.441155	−	0.362329i
$778$	9.26032	+	4.31816i	0.331999	+	0.154813i
$779$	−0.204146	+	1.15777i	−0.00731427	+	0.0414813i
$780$		0			0
$781$	−2.10427	+	1.76569i	−0.0752968	+	0.0631815i
$782$	12.2420	+	12.2420i	0.437772	+	0.437772i
$783$	−10.7175	+	32.6152i	−0.383011	+	1.16557i
$784$			24.8698i			0.888207i
$785$		0			0
$786$	−17.0536	+	24.9091i	−0.608283	+	0.888477i
$787$	1.74764	+	2.49588i	0.0622965	+	0.0889687i	0.849092	−	0.528246i	$-0.177150\pi$
$787$	1.74764	+	2.49588i	0.0622965	+	0.0889687i	−0.786795	+	0.617214i	$0.788261\pi$
$788$	0.247749	−	0.531300i	0.00882570	−	0.0189268i
$789$	−6.31613	+	4.52242i	−0.224860	+	0.161002i
$790$		0			0
$791$	−0.801132	+	0.462534i	−0.0284850	+	0.0164458i
$792$	25.9167	−	7.53252i	0.920908	−	0.267656i
$793$	−57.2355	+	15.3362i	−2.03249	+	0.544604i
$794$	−46.3962	−	16.8868i	−1.64654	−	0.599292i
$795$		0			0
$796$	7.27145	+	6.10147i	0.257730	+	0.216261i
$797$	−2.52513	−	28.8623i	−0.0894446	−	1.02236i	−0.899767	−	0.436372i	$-0.856263\pi$
$797$	−2.52513	−	28.8623i	−0.0894446	−	1.02236i	0.810322	−	0.585985i	$-0.199292\pi$
$798$	−1.05950	+	1.88056i	−0.0375061	+	0.0665709i
$799$	2.91068	−	7.99703i	0.102972	−	0.282914i
$800$		0			0
$801$	−0.276240	+	1.78568i	−0.00976045	+	0.0630938i
$802$	3.60114	+	0.964923i	0.127161	+	0.0340726i
$803$	23.8328	+	16.6879i	0.841041	+	0.588903i
$804$	−2.43730	+	5.37376i	−0.0859568	+	0.189518i
$805$		0			0
$806$	14.1470	+	2.49450i	0.498306	+	0.0878649i
$807$	−4.21485	+	11.9708i	−0.148370	+	0.421392i
$808$	−21.0462	−	1.84130i	−0.740401	−	0.0647767i
$809$	−7.83479			−0.275456			−0.137728	−	0.990470i	$-0.543980\pi$
$809$	−7.83479			−0.275456			−0.137728	+	0.990470i	$0.543980\pi$
$810$		0			0
$811$	33.4667			1.17517			0.587587	−	0.809161i	$-0.300078\pi$
$811$	33.4667			1.17517			0.587587	+	0.809161i	$0.300078\pi$
$812$	5.47591	+	0.479080i	0.192167	+	0.0168124i
$813$	11.2445	−	31.9361i	0.394363	−	1.12005i
$814$	−42.7929	−	7.54554i	−1.49989	−	0.264471i
$815$		0			0
$816$	−21.9486	+	48.3924i	−0.768355	+	1.69407i
$817$	−1.59471	−	1.11663i	−0.0557917	−	0.0390658i
$818$	−22.0056	−	5.89639i	−0.769409	−	0.206163i
$819$	−24.7318	+	9.59592i	−0.864200	+	0.335309i
$820$		0			0
$821$	15.4155	−	42.3537i	0.538004	−	1.47815i	−0.311332	−	0.950301i	$-0.600775\pi$
$821$	15.4155	−	42.3537i	0.538004	−	1.47815i	0.849336	−	0.527853i	$-0.177003\pi$
$822$	−22.4033	+	39.7645i	−0.781406	+	1.38695i
$823$	2.39852	+	27.4152i	0.0836071	+	0.955633i	0.915929	+	0.401341i	$0.131456\pi$
$823$	2.39852	+	27.4152i	0.0836071	+	0.955633i	−0.832322	+	0.554293i	$0.812989\pi$
$824$	−31.1920	−	26.1732i	−1.08662	−	0.911785i
$825$		0			0
$826$	14.9353	+	5.43602i	0.519667	+	0.189143i
$827$	−54.7376	+	14.6669i	−1.90341	+	0.510018i	−0.907458	+	0.420142i	$0.861980\pi$
$827$	−54.7376	+	14.6669i	−1.90341	+	0.510018i	−0.995953	+	0.0898754i	$0.971353\pi$
$828$	−0.737199	+	3.00274i	−0.0256194	+	0.104352i
$829$	−12.0181	+	6.93865i	−0.417405	+	0.240989i	−0.693967	−	0.720007i	$-0.744138\pi$
$829$	−12.0181	+	6.93865i	−0.417405	+	0.240989i	0.276561	+	0.960996i	$0.410805\pi$
$830$		0			0
$831$	−29.3882	+	21.0423i	−1.01946	+	0.729948i
$832$	11.7810	−	25.2643i	0.408431	−	0.875884i
$833$	−18.6291	−	26.6051i	−0.645460	−	0.921812i
$834$	−28.5126	+	41.6464i	−0.987310	+	1.44210i
$835$		0			0
$836$			1.37510i			0.0475588i
$837$	2.65442	+	6.63340i	0.0917501	+	0.229284i
$838$	−33.4708	−	33.4708i	−1.15623	−	1.15623i
$839$	−16.4142	+	13.7731i	−0.566679	+	0.475501i	−0.880542	−	0.473968i	$-0.842821\pi$
$839$	−16.4142	+	13.7731i	−0.566679	+	0.475501i	0.313863	+	0.949468i	$0.398377\pi$
$840$		0			0
$841$	2.54436	−	14.4298i	0.0877364	−	0.497578i
$842$	30.5945	+	14.2665i	1.05436	+	0.491655i
$843$	7.20636	+	5.91872i	0.248200	+	0.203851i
$844$	3.09124	−	0.545069i	0.106405	−	0.0187620i
$845$		0			0
$846$	6.39034	−	1.26604i	0.219704	−	0.0435273i
$847$	−1.77820	−	6.63633i	−0.0610996	−	0.228027i
$848$	47.6250	−	22.2079i	1.63545	−	0.762623i
$849$	13.6270	+	3.49804i	0.467678	+	0.120052i
$850$		0			0
$851$	−7.31571	+	8.71852i	−0.250779	+	0.298867i
$852$	0.622563	−	0.368228i	0.0213287	−	0.0126153i
$853$	0.844662	+	1.81138i	0.0289207	+	0.0620206i	0.920237	−	0.391361i	$-0.127995\pi$
$853$	0.844662	+	1.81138i	0.0289207	+	0.0620206i	−0.891317	+	0.453381i	$0.850218\pi$
$854$	−10.1129	+	17.5161i	−0.346056	+	0.599387i
$855$		0			0
$856$	2.46605	+	4.27132i	0.0842877	+	0.145991i
$857$	−13.2564	+	18.9321i	−0.452830	+	0.646709i	−0.979045	−	0.203643i	$-0.934722\pi$
$857$	−13.2564	+	18.9321i	−0.452830	+	0.646709i	0.526215	+	0.850352i	$0.323611\pi$
$858$	−45.9765	+	55.9789i	−1.56961	+	1.91109i
$859$	−7.86080	−	21.5974i	−0.268207	−	0.736893i	−0.998551	−	0.0538131i	$-0.982862\pi$
$859$	−7.86080	−	21.5974i	−0.268207	−	0.736893i	0.730344	−	0.683079i	$-0.239360\pi$
$860$		0			0
$861$	−0.378104	+	4.91738i	−0.0128858	+	0.167584i
$862$	3.16220	−	36.1441i	0.107705	−	1.23107i
$863$	−2.45592	+	2.45592i	−0.0836006	+	0.0836006i	−0.747671	−	0.664070i	$-0.768828\pi$
$863$	−2.45592	+	2.45592i	−0.0836006	+	0.0836006i	0.664070	+	0.747671i	$0.268828\pi$
$864$	−17.1995	+	2.05374i	−0.585138	+	0.0698697i
$865$		0			0
$866$	11.3815	+	13.5639i	0.386759	+	0.460921i
$867$	−7.35096	−	39.2678i	−0.249652	−	1.33360i
$868$	0.937087	−	0.656155i	0.0318068	−	0.0222714i
$869$	−48.0969	+	17.5059i	−1.63158	+	0.593845i
$870$		0			0
$871$	6.28765	+	35.6590i	0.213049	+	1.20826i
$872$	−1.34629	+	5.02442i	−0.0455911	+	0.170148i
$873$	−47.6841	−	11.7069i	−1.61386	−	0.396218i
$874$	1.33695	+	0.771888i	0.0452230	+	0.0261095i
$875$		0			0
$876$	−5.47387	−	5.35983i	−0.184945	−	0.181092i
$877$	−12.2844	+	1.07474i	−0.414814	+	0.0362915i	−0.292653	−	0.956219i	$-0.594538\pi$
$877$	−12.2844	+	1.07474i	−0.414814	+	0.0362915i	−0.122161	+	0.992510i	$0.538983\pi$
$878$	43.5525	−	3.81035i	1.46982	−	0.128593i
$879$	−9.62117	+	2.68684i	−0.324514	+	0.0906248i
$880$		0			0
$881$	−26.2526	−	15.1569i	−0.884473	−	0.510651i	−0.0123422	−	0.999924i	$-0.503929\pi$
$881$	−26.2526	−	15.1569i	−0.884473	−	0.510651i	−0.872131	+	0.489273i	$0.837262\pi$
$882$	10.0306	−	22.7491i	0.337748	−	0.766001i
$883$	−1.48572	+	5.54478i	−0.0499984	+	0.186597i	−0.986409	−	0.164311i	$-0.947460\pi$
$883$	−1.48572	+	5.54478i	−0.0499984	+	0.186597i	0.936410	+	0.350907i	$0.114127\pi$
$884$	−4.32693	−	24.5393i	−0.145531	−	0.825345i
$885$		0			0
$886$	62.7290	−	22.8315i	2.10742	−	0.767039i
$887$	1.17106	−	0.819982i	0.0393202	−	0.0275323i	−0.553751	−	0.832682i	$-0.686804\pi$
$887$	1.17106	−	0.819982i	0.0393202	−	0.0275323i	0.593071	+	0.805150i	$0.297915\pi$
$888$	−24.6746	−	8.68779i	−0.828024	−	0.291543i
$889$	−3.74991	−	4.46897i	−0.125768	−	0.149884i
$890$		0			0
$891$	−35.7135	−	4.75734i	−1.19645	−	0.159377i
$892$	10.0235	−	10.0235i	0.335610	−	0.335610i
$893$	0.0661388	−	0.755970i	0.00221325	−	0.0252976i
$894$	24.5111	−	11.7454i	0.819773	−	0.392824i
$895$		0			0
$896$	−6.37164	−	17.5059i	−0.212862	−	0.584832i
$897$	6.67657	+	17.7598i	0.222924	+	0.592983i
$898$	−9.69819	+	13.8505i	−0.323633	+	0.462196i
$899$	−4.54235	−	7.86759i	−0.151496	−	0.262399i
$900$		0			0
$901$	−34.3129	+	59.4318i	−1.14313	+	1.97996i
$902$	5.69153	+	12.2055i	0.189507	+	0.406400i
$903$	−7.11538	−	4.00880i	−0.236785	−	0.133405i
$904$	−0.977497	+	1.16494i	−0.0325111	+	0.0387452i
$905$		0			0
$906$	−4.34491	+	4.43735i	−0.144350	+	0.147421i
$907$	16.8099	−	7.83856i	0.558162	−	0.260275i	−0.123002	−	0.992406i	$-0.539252\pi$
$907$	16.8099	−	7.83856i	0.558162	−	0.260275i	0.681164	+	0.732131i	$0.261474\pi$
$908$	−1.02340	−	3.81939i	−0.0339628	−	0.126751i
$909$	24.7157	+	13.5841i	0.819769	+	0.450557i
$910$		0			0
$911$	19.9191	−	3.51228i	0.659950	−	0.116367i	0.166364	−	0.986064i	$-0.446797\pi$
$911$	19.9191	−	3.51228i	0.659950	−	0.116367i	0.493585	+	0.869697i	$0.335686\pi$
$912$	−0.773624	+	4.67465i	−0.0256172	+	0.154793i
$913$	60.3740	+	28.1528i	1.99809	+	0.931723i
$914$	9.76209	−	55.3636i	0.322901	−	1.83126i
$915$		0			0
$916$	8.85287	−	7.42844i	0.292507	−	0.245443i
$917$	10.4312	+	10.4312i	0.344468	+	0.344468i
$918$	39.5948	−	35.4134i	1.30682	−	1.16882i
$919$		−	5.56015i		−	0.183412i	−0.995786	−	0.0917062i	$-0.970768\pi$
$919$		−	5.56015i		−	0.183412i	0.995786	−	0.0917062i	$-0.0292320\pi$
$920$		0			0
$921$	−17.4102	−	1.33870i	−0.573687	−	0.0441116i
$922$	−30.2365	−	43.1822i	−0.995786	−	1.42213i
$923$	1.87581	−	4.02270i	0.0617432	−	0.132409i
$924$	0.563237	+	5.74114i	0.0185291	+	0.188870i
$925$		0			0
$926$	−8.23538	+	4.75470i	−0.270631	+	0.156249i
$927$	24.0040	+	48.7693i	0.788395	+	1.60179i
$928$	21.2743	−	5.70043i	0.698363	−	0.187126i
$929$	10.4908	+	3.81834i	0.344192	+	0.125276i	0.508331	−	0.861162i	$-0.330263\pi$
$929$	10.4908	+	3.81834i	0.344192	+	0.125276i	−0.164140	+	0.986437i	$0.552485\pi$
$930$		0			0
$931$	−2.21856	−	1.86160i	−0.0727105	−	0.0610113i
$932$	1.24266	+	14.2036i	0.0407046	+	0.465255i
$933$	−18.2054	−	30.7798i	−0.596018	−	1.00769i
$934$	11.3053	−	31.0610i	0.369920	−	1.01635i
$935$		0			0
$936$	−32.8094	+	28.7287i	−1.07241	+	0.939028i
$937$	−3.17051	−	0.849536i	−0.103576	−	0.0277531i	0.206659	−	0.978413i	$-0.433741\pi$
$937$	−3.17051	−	0.849536i	−0.103576	−	0.0277531i	−0.310235	+	0.950660i	$0.600408\pi$
$938$	10.1243	+	7.08914i	0.330571	+	0.231469i
$939$	25.0236	−	2.45495i	0.816615	−	0.0801144i
$940$		0			0
$941$	−35.8375	−	6.31912i	−1.16827	−	0.205997i	−0.444331	−	0.895863i	$-0.646559\pi$
$941$	−35.8375	−	6.31912i	−1.16827	−	0.205997i	−0.723938	+	0.689865i	$0.757670\pi$
$942$	−33.0252	−	38.5269i	−1.07602	−	1.25527i
$943$	3.51394	+	0.307430i	0.114429	+	0.0100113i
$944$	34.8897			1.13556
$945$		0			0
$946$	−22.3012			−0.725073
$947$	51.2682	+	4.48539i	1.66599	+	0.145756i	0.880798	−	0.473492i	$-0.157007\pi$
$947$	51.2682	+	4.48539i	1.66599	+	0.145756i	0.785196	+	0.619248i	$0.212562\pi$
$948$	13.2473	−	2.47991i	0.430253	−	0.0805437i
$949$	−46.2973	−	8.16346i	−1.50287	−	0.264997i
$950$		0			0
$951$	−30.2777	−	42.2866i	−0.981822	−	1.37124i
$952$	15.9290	+	11.1536i	0.516263	+	0.361491i
$953$	19.0607	+	5.10731i	0.617438	+	0.165442i	0.553963	−	0.832541i	$-0.313115\pi$
$953$	19.0607	+	5.10731i	0.617438	+	0.165442i	0.0634751	+	0.997983i	$0.479782\pi$
$954$	−52.5210	+	1.10583i	−1.70043	+	0.0358027i
$955$		0			0
$956$	0.212419	−	0.583616i	0.00687012	−	0.0188755i
$957$	45.8089	−	0.482202i	1.48079	−	0.0155874i
$958$	−0.891840	−	10.1938i	−0.0288141	−	0.329346i
$959$	17.0857	+	14.3366i	0.551725	+	0.462953i
$960$		0			0
$961$	27.3538	+	9.95598i	0.882382	+	0.321161i
$962$	67.8200	−	18.1723i	2.18660	−	0.585899i
$963$	−0.711782	−	6.54548i	−0.0229369	−	0.210925i
$964$	2.22698	−	1.28575i	0.0717262	−	0.0414111i
$965$		0			0
$966$	5.89802	+	2.67508i	0.189766	+	0.0860692i
$967$	−3.44802	+	7.39431i	−0.110881	+	0.237785i	−0.953916	−	0.300074i	$-0.902989\pi$
$967$	−3.44802	+	7.39431i	−0.110881	+	0.237785i	0.843035	+	0.537859i	$0.180767\pi$
$968$	−6.47813	−	9.25173i	−0.208215	−	0.297362i
$969$	−2.67401	−	5.58032i	−0.0859017	−	0.179266i
$970$		0			0
$971$			0.500263i			0.0160542i	0.999968	+	0.00802710i	$0.00255513\pi$
$971$			0.500263i			0.0160542i	−0.999968	+	0.00802710i	$0.997445\pi$
$972$	9.07318	+	2.77127i	0.291022	+	0.0888885i
$973$	17.4403	+	17.4403i	0.559110	+	0.559110i
$974$	−8.21264	+	6.89122i	−0.263150	+	0.220809i
$975$		0			0
$976$	−7.70982	+	43.7245i	−0.246785	+	1.39959i
$977$	12.1170	+	5.65025i	0.387657	+	0.180767i	0.606669	−	0.794955i	$-0.292506\pi$
$977$	12.1170	+	5.65025i	0.387657	+	0.180767i	−0.219012	+	0.975722i	$0.570283\pi$
$978$	−52.0781	+	19.5781i	−1.66527	+	0.626038i
$979$	2.37453	−	0.418693i	0.0758903	−	0.0133815i
$980$		0			0
$981$	4.35051	−	5.41214i	0.138901	−	0.172796i
$982$	−2.61769	−	9.76934i	−0.0835337	−	0.311752i
$983$	19.5355	−	9.10955i	0.623085	−	0.290549i	−0.0853218	−	0.996353i	$-0.527192\pi$
$983$	19.5355	−	9.10955i	0.623085	−	0.290549i	0.708407	+	0.705804i	$0.249414\pi$
$984$	2.18069	+	7.80874i	0.0695180	+	0.248933i
$985$		0			0
$986$	−43.4168	+	51.7421i	−1.38267	+	1.64780i
$987$	−0.0335089	−	3.18332i	−0.00106660	−	0.101326i
$988$	−0.939023	−	2.01374i	−0.0298743	−	0.0640656i
$989$	−2.92056	+	5.05856i	−0.0928684	+	0.160853i
$990$		0			0
$991$	12.2325	+	21.1872i	0.388577	+	0.673035i	0.992258	−	0.124191i	$-0.0396334\pi$
$991$	12.2325	+	21.1872i	0.388577	+	0.673035i	−0.603681	+	0.797226i	$0.706300\pi$
$992$	2.62909	−	3.75473i	0.0834738	−	0.119213i
$993$	49.3741	+	8.17109i	1.56684	+	0.259302i
$994$	−0.518176	−	1.42368i	−0.0164356	−	0.0451563i
$995$		0			0
$996$	−14.4737	−	9.90921i	−0.458617	−	0.313985i
$997$	3.94689	−	45.1132i	0.124999	−	1.42875i	−0.631816	−	0.775119i	$-0.717690\pi$
$997$	3.94689	−	45.1132i	0.124999	−	1.42875i	0.756815	−	0.653629i	$-0.226754\pi$
$998$	27.3314	−	27.3314i	0.865160	−	0.865160i
$999$	25.4604	+	23.9011i	0.805531	+	0.756198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.c.518.7	yes	288
5.2	odd	4	inner	675.2.ba.c.32.18	yes	288
5.3	odd	4	inner	675.2.ba.c.32.7	✓	288
5.4	even	2	inner	675.2.ba.c.518.18	yes	288
27.11	odd	18	inner	675.2.ba.c.443.18	yes	288
135.38	even	36	inner	675.2.ba.c.632.18	yes	288
135.92	even	36	inner	675.2.ba.c.632.7	yes	288
135.119	odd	18	inner	675.2.ba.c.443.7	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.ba.c.32.7	✓	288	5.3	odd	4	inner
675.2.ba.c.32.18	yes	288	5.2	odd	4	inner
675.2.ba.c.443.7	yes	288	135.119	odd	18	inner
675.2.ba.c.443.18	yes	288	27.11	odd	18	inner
675.2.ba.c.518.7	yes	288	1.1	even	1	trivial
675.2.ba.c.518.18	yes	288	5.4	even	2	inner
675.2.ba.c.632.7	yes	288	135.92	even	36	inner
675.2.ba.c.632.18	yes	288	135.38	even	36	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60897 - 0.140766i) q^{2} +(0.575232 - 1.63374i) q^{3} +(0.599344 + 0.105680i) q^{4} +(-1.15550 + 2.54766i) q^{6} +(1.11982 + 0.784107i) q^{7} +(2.17071 + 0.581640i) q^{8} +(-2.33822 - 1.87956i) q^{9} +(-1.36918 + 3.76179i) q^{11} +(0.517416 - 0.918381i) q^{12} +(-0.563766 - 6.44387i) q^{13} +(-1.69138 - 1.41923i) q^{14} +(-4.55450 - 1.65770i) q^{16} +(6.11402 - 1.63825i) q^{17} +(3.49753 + 3.35329i) q^{18} +(0.488800 - 0.282209i) q^{19} +(1.92518 - 1.37845i) q^{21} +(2.73250 - 5.85987i) q^{22} +(-0.971342 - 1.38722i) q^{23} +(2.19891 - 3.21180i) q^{24} +10.4473i q^{26} +(-4.41573 + 2.73886i) q^{27} +(0.588292 + 0.588292i) q^{28} +(5.06125 - 4.24689i) q^{29} +(0.238769 - 1.35412i) q^{31} +(3.02123 + 1.40882i) q^{32} +(5.35820 + 4.40079i) q^{33} +(-10.0679 + 1.77524i) q^{34} +(-1.20276 - 1.37361i) q^{36} +(-1.73942 - 6.49160i) q^{37} +(-0.826189 + 0.385258i) q^{38} +(-10.8519 - 2.78567i) q^{39} +(-1.33886 + 1.59560i) q^{41} +(-3.29160 + 1.94688i) q^{42} +(-1.45769 - 3.12602i) q^{43} +(-1.21816 + 2.10991i) q^{44} +(1.36758 + 2.36872i) q^{46} +(0.771171 - 1.10135i) q^{47} +(-5.32815 + 6.48731i) q^{48} +(-1.75497 - 4.82173i) q^{49} +(0.840508 - 10.9311i) q^{51} +(0.343102 - 3.92167i) q^{52} +(-7.66637 + 7.66637i) q^{53} +(7.49030 - 3.78515i) q^{54} +(1.97474 + 2.35340i) q^{56} +(-0.179883 - 0.960908i) q^{57} +(-8.74120 + 6.12066i) q^{58} +(-6.76439 + 2.46204i) q^{59} +(-1.59070 - 9.02132i) q^{61} +(-0.574786 + 2.14513i) q^{62} +(-1.14461 - 3.93818i) q^{63} +(3.73216 + 2.15476i) q^{64} +(-8.00168 - 7.83498i) q^{66} +(-5.57647 + 0.487878i) q^{67} +(3.83753 - 0.335740i) q^{68} +(-2.82510 + 0.788948i) q^{69} +(0.594251 + 0.343091i) q^{71} +(-3.98237 - 5.43998i) q^{72} +(1.88104 - 7.02013i) q^{73} +(1.88487 + 10.6896i) q^{74} +(0.322783 - 0.117483i) q^{76} +(-4.48288 + 3.13895i) q^{77} +(17.0682 + 6.00964i) q^{78} +(8.21845 + 9.79437i) q^{79} +(1.93452 + 8.78963i) q^{81} +(2.37879 - 2.37879i) q^{82} +(1.45031 - 16.5771i) q^{83} +(1.29952 - 0.622713i) q^{84} +(1.90533 + 5.23485i) q^{86} +(-4.02693 - 10.7117i) q^{87} +(-5.16010 + 7.36939i) q^{88} +(-0.301153 - 0.521612i) q^{89} +(4.42137 - 7.65803i) q^{91} +(-0.435565 - 0.934073i) q^{92} +(-2.07494 - 1.16902i) q^{93} +(-1.39582 + 1.66348i) q^{94} +(4.03955 - 4.12550i) q^{96} +(14.8333 - 6.91688i) q^{97} +(2.14495 + 8.00504i) q^{98} +(10.2720 - 6.22243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) \) 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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