LMFDB - Embedded newform 275.2.bm.b.107.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(7,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.bm (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	275.107
Dual form			275.2.bm.b.18.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0763931 - 0.482327i) q^{2} +(1.01518 + 0.517260i) q^{3} +(1.67531 + 0.544341i) q^{4} +(0.327041 - 0.450133i) q^{6} +(1.32402 + 2.59854i) q^{7} +(0.833936 - 1.63669i) q^{8} +(-1.00032 - 1.37683i) q^{9} +(-3.15977 + 1.00788i) q^{11} +(1.41917 + 1.41917i) q^{12} +(2.89049 + 0.457808i) q^{13} +(1.35449 - 0.440102i) q^{14} +(2.12449 + 1.54353i) q^{16} +(-5.20325 + 0.824113i) q^{17} +(-0.740500 + 0.377304i) q^{18} +(-1.26677 - 3.89873i) q^{19} +3.32285i q^{21} +(0.244743 + 1.60104i) q^{22} +(2.12046 - 2.12046i) q^{23} +(1.69319 - 1.23017i) q^{24} +(0.441627 - 1.35919i) q^{26} +(-0.838037 - 5.29116i) q^{27} +(0.803656 + 5.07408i) q^{28} +(-0.817241 + 2.51521i) q^{29} +(5.45328 - 3.96204i) q^{31} +(3.50456 - 3.50456i) q^{32} +(-3.72907 - 0.611244i) q^{33} +2.57262i q^{34} +(-0.926389 - 2.85113i) q^{36} +(-1.03649 + 0.528116i) q^{37} +(-1.97724 + 0.313163i) q^{38} +(2.69755 + 1.95989i) q^{39} +(-3.38136 + 1.09867i) q^{41} +(1.60270 + 0.253843i) q^{42} +(-5.07292 - 5.07292i) q^{43} +(-5.84223 - 0.0314826i) q^{44} +(-0.860769 - 1.18475i) q^{46} +(-1.67145 + 3.28041i) q^{47} +(1.35833 + 2.66588i) q^{48} +(-0.884888 + 1.21794i) q^{49} +(-5.70851 - 1.85481i) q^{51} +(4.59325 + 2.34038i) q^{52} +(0.231169 - 1.45955i) q^{53} -2.61609 q^{54} +5.35716 q^{56} +(0.730652 - 4.61316i) q^{57} +(1.15072 + 0.586323i) q^{58} +(1.52672 + 0.496061i) q^{59} +(-4.07810 + 5.61302i) q^{61} +(-1.49441 - 2.93294i) q^{62} +(2.25330 - 4.42234i) q^{63} +(1.66445 + 2.29092i) q^{64} +(-0.579695 + 1.75194i) q^{66} +(-1.31471 - 1.31471i) q^{67} +(-9.16564 - 1.45170i) q^{68} +(3.24948 - 1.05582i) q^{69} +(-2.32441 - 1.68878i) q^{71} +(-3.08765 + 0.489036i) q^{72} +(-13.1886 + 6.71992i) q^{73} +(0.175544 + 0.540270i) q^{74} -7.22113i q^{76} +(-6.80264 - 6.87635i) q^{77} +(1.15138 - 1.15138i) q^{78} +(-12.3342 + 8.96129i) q^{79} +(0.308439 - 0.949277i) q^{81} +(0.271606 + 1.71486i) q^{82} +(1.04540 + 6.60041i) q^{83} +(-1.80876 + 5.56680i) q^{84} +(-2.83434 + 2.05927i) q^{86} +(-2.13066 + 2.13066i) q^{87} +(-0.985459 + 6.01208i) q^{88} -11.1726i q^{89} +(2.63744 + 8.11720i) q^{91} +(4.70669 - 2.39818i) q^{92} +(7.58545 - 1.20142i) q^{93} +(1.45454 + 1.05679i) q^{94} +(5.37052 - 1.74499i) q^{96} +(9.94447 + 1.57505i) q^{97} +(0.519848 + 0.519848i) q^{98} +(4.54848 + 3.34226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0763931	−	0.482327i	0.0540181	−	0.341057i	−0.945847	−	0.324614i	$-0.894766\pi$
$2$	0.0763931	−	0.482327i	0.0540181	−	0.341057i	0.999865	−	0.0164432i	$-0.00523428\pi$
$3$	1.01518	+	0.517260i	0.586114	+	0.298640i	0.721789	−	0.692114i	$-0.243320\pi$
$3$	1.01518	+	0.517260i	0.586114	+	0.298640i	−0.135675	+	0.990753i	$0.543320\pi$
$4$	1.67531	+	0.544341i	0.837655	+	0.272170i
$5$		0			0
$5$		0			0
$6$	0.327041	−	0.450133i	0.133514	−	0.183766i
$7$	1.32402	+	2.59854i	0.500434	+	0.982157i	0.993678	+	0.112266i	$0.0358109\pi$
$7$	1.32402	+	2.59854i	0.500434	+	0.982157i	−0.493244	+	0.869891i	$0.664189\pi$
$8$	0.833936	−	1.63669i	0.294841	−	0.578658i
$9$	−1.00032	−	1.37683i	−0.333442	−	0.458943i
$10$		0			0
$11$	−3.15977	+	1.00788i	−0.952708	+	0.303888i
$11$	−3.15977	+	1.00788i	−0.952708	+	0.303888i
$12$	1.41917	+	1.41917i	0.409680	+	0.409680i
$13$	2.89049	+	0.457808i	0.801677	+	0.126973i	0.543811	−	0.839208i	$-0.316981\pi$
$13$	2.89049	+	0.457808i	0.801677	+	0.126973i	0.257866	+	0.966181i	$0.416981\pi$
$14$	1.35449	−	0.440102i	0.362004	−	0.117622i
$15$		0			0
$16$	2.12449	+	1.54353i	0.531123	+	0.385884i
$17$	−5.20325	+	0.824113i	−1.26197	+	0.199877i	−0.751336	−	0.659920i	$-0.770590\pi$
$17$	−5.20325	+	0.824113i	−1.26197	+	0.199877i	−0.510636	+	0.859797i	$0.670590\pi$
$18$	−0.740500	+	0.377304i	−0.174538	+	0.0889313i
$19$	−1.26677	−	3.89873i	−0.290618	−	0.894429i	−0.984658	−	0.174494i	$-0.944171\pi$
$19$	−1.26677	−	3.89873i	−0.290618	−	0.894429i	0.694041	−	0.719936i	$-0.255829\pi$
$20$		0			0
$21$			3.32285i			0.725105i
$22$	0.244743	+	1.60104i	0.0521795	+	0.341343i
$23$	2.12046	−	2.12046i	0.442147	−	0.442147i	−0.450586	−	0.892733i	$-0.648785\pi$
$23$	2.12046	−	2.12046i	0.442147	−	0.442147i	0.892733	+	0.450586i	$0.148785\pi$
$24$	1.69319	−	1.23017i	0.345621	−	0.251108i
$25$		0			0
$26$	0.441627	−	1.35919i	0.0866101	−	0.266558i
$27$	−0.838037	−	5.29116i	−0.161280	−	1.01828i
$28$	0.803656	+	5.07408i	0.151877	+	0.958912i
$29$	−0.817241	+	2.51521i	−0.151758	+	0.467063i	−0.997818	−	0.0660248i	$-0.978968\pi$
$29$	−0.817241	+	2.51521i	−0.151758	+	0.467063i	0.846060	+	0.533088i	$0.178968\pi$
$30$		0			0
$31$	5.45328	−	3.96204i	0.979438	−	0.711603i	0.0218548	−	0.999761i	$-0.493043\pi$
$31$	5.45328	−	3.96204i	0.979438	−	0.711603i	0.957583	+	0.288158i	$0.0930429\pi$
$32$	3.50456	−	3.50456i	0.619524	−	0.619524i
$33$	−3.72907	−	0.611244i	−0.649148	−	0.106404i
$34$			2.57262i			0.441201i
$35$		0			0
$36$	−0.926389	−	2.85113i	−0.154398	−	0.475189i
$37$	−1.03649	+	0.528116i	−0.170397	+	0.0868218i	−0.537109	−	0.843513i	$-0.680484\pi$
$37$	−1.03649	+	0.528116i	−0.170397	+	0.0868218i	0.366712	+	0.930335i	$0.380484\pi$
$38$	−1.97724	+	0.313163i	−0.320750	+	0.0508018i
$39$	2.69755	+	1.95989i	0.431954	+	0.313833i
$40$		0			0
$41$	−3.38136	+	1.09867i	−0.528080	+	0.171584i	−0.560909	−	0.827877i	$-0.689548\pi$
$41$	−3.38136	+	1.09867i	−0.528080	+	0.171584i	0.0328289	+	0.999461i	$0.489548\pi$
$42$	1.60270	+	0.253843i	0.247302	+	0.0391688i
$43$	−5.07292	−	5.07292i	−0.773613	−	0.773613i	0.205123	−	0.978736i	$-0.434241\pi$
$43$	−5.07292	−	5.07292i	−0.773613	−	0.773613i	−0.978736	+	0.205123i	$0.934241\pi$
$44$	−5.84223	−	0.0314826i	−0.880749	−	0.00474618i
$45$		0			0
$46$	−0.860769	−	1.18475i	−0.126913	−	0.174681i
$47$	−1.67145	+	3.28041i	−0.243806	+	0.478497i	−0.980188	−	0.198070i	$-0.936533\pi$
$47$	−1.67145	+	3.28041i	−0.243806	+	0.478497i	0.736382	+	0.676566i	$0.236533\pi$
$48$	1.35833	+	2.66588i	0.196058	+	0.384786i
$49$	−0.884888	+	1.21794i	−0.126413	+	0.173992i
$50$		0			0
$51$	−5.70851	−	1.85481i	−0.799351	−	0.259725i
$52$	4.59325	+	2.34038i	0.636970	+	0.324552i
$53$	0.231169	−	1.45955i	0.0317536	−	0.200484i	−0.966712	−	0.255869i	$-0.917639\pi$
$53$	0.231169	−	1.45955i	0.0317536	−	0.200484i	0.998465	+	0.0553847i	$0.0176385\pi$
$54$	−2.61609			−0.356005
$55$		0			0
$56$	5.35716			0.715881
$57$	0.730652	−	4.61316i	0.0967773	−	0.611028i
$58$	1.15072	+	0.586323i	0.151097	+	0.0769879i
$59$	1.52672	+	0.496061i	0.198762	+	0.0645817i	0.406706	−	0.913559i	$-0.366677\pi$
$59$	1.52672	+	0.496061i	0.198762	+	0.0645817i	−0.207944	+	0.978141i	$0.566677\pi$
$60$		0			0
$61$	−4.07810	+	5.61302i	−0.522147	+	0.718674i	−0.985908	−	0.167286i	$-0.946500\pi$
$61$	−4.07810	+	5.61302i	−0.522147	+	0.718674i	0.463761	+	0.885960i	$0.346500\pi$
$62$	−1.49441	−	2.93294i	−0.189790	−	0.372483i
$63$	2.25330	−	4.42234i	0.283889	−	0.557163i
$64$	1.66445	+	2.29092i	0.208056	+	0.286365i
$65$		0			0
$66$	−0.579695	+	1.75194i	−0.0713556	+	0.215649i
$67$	−1.31471	−	1.31471i	−0.160617	−	0.160617i	0.622223	−	0.782840i	$-0.286230\pi$
$67$	−1.31471	−	1.31471i	−0.160617	−	0.160617i	−0.782840	+	0.622223i	$0.786230\pi$
$68$	−9.16564	−	1.45170i	−1.11150	−	0.176044i
$69$	3.24948	−	1.05582i	0.391192	−	0.127106i
$70$		0			0
$71$	−2.32441	−	1.68878i	−0.275857	−	0.200422i	0.441251	−	0.897384i	$-0.354535\pi$
$71$	−2.32441	−	1.68878i	−0.275857	−	0.200422i	−0.717108	+	0.696962i	$0.754535\pi$
$72$	−3.08765	+	0.489036i	−0.363883	+	0.0576334i
$73$	−13.1886	+	6.71992i	−1.54361	+	0.786507i	−0.998649	−	0.0519568i	$-0.983454\pi$
$73$	−13.1886	+	6.71992i	−1.54361	+	0.786507i	−0.544957	+	0.838464i	$0.683454\pi$
$74$	0.175544	+	0.540270i	0.0204066	+	0.0628051i
$75$		0			0
$76$		−	7.22113i		−	0.828321i
$77$	−6.80264	−	6.87635i	−0.775232	−	0.783633i
$78$	1.15138	−	1.15138i	0.130368	−	0.130368i
$79$	−12.3342	+	8.96129i	−1.38770	+	1.00822i	−0.391589	+	0.920140i	$0.628074\pi$
$79$	−12.3342	+	8.96129i	−1.38770	+	1.00822i	−0.996113	+	0.0880839i	$0.971926\pi$
$80$		0			0
$81$	0.308439	−	0.949277i	0.0342710	−	0.105475i
$82$	0.271606	+	1.71486i	0.0299939	+	0.189374i
$83$	1.04540	+	6.60041i	0.114748	+	0.724489i	0.976236	+	0.216711i	$0.0695329\pi$
$83$	1.04540	+	6.60041i	0.114748	+	0.724489i	−0.861488	+	0.507778i	$0.830467\pi$
$84$	−1.80876	+	5.56680i	−0.197352	+	0.607388i
$85$		0			0
$86$	−2.83434	+	2.05927i	−0.305635	+	0.222057i
$87$	−2.13066	+	2.13066i	−0.228431	+	0.228431i
$88$	−0.985459	+	6.01208i	−0.105050	+	0.640890i
$89$		−	11.1726i		−	1.18429i	−0.805830	−	0.592147i	$-0.798281\pi$
$89$		−	11.1726i		−	1.18429i	0.805830	−	0.592147i	$-0.201719\pi$
$90$		0			0
$91$	2.63744	+	8.11720i	0.276479	+	0.850914i
$92$	4.70669	−	2.39818i	0.490706	−	0.250027i
$93$	7.58545	−	1.20142i	0.786575	−	0.124581i
$94$	1.45454	+	1.05679i	0.150025	+	0.108999i
$95$		0			0
$96$	5.37052	−	1.74499i	0.548126	−	0.178097i
$97$	9.94447	+	1.57505i	1.00971	+	0.159922i	0.639308	−	0.768951i	$-0.279221\pi$
$97$	9.94447	+	1.57505i	1.00971	+	0.159922i	0.370400	+	0.928873i	$0.379221\pi$
$98$	0.519848	+	0.519848i	0.0525126	+	0.0525126i
$99$	4.54848	+	3.34226i	0.457140	+	0.335910i
$100$		0			0
$101$	−1.12216	−	1.54452i	−0.111659	−	0.153686i	0.749530	−	0.661971i	$-0.230280\pi$
$101$	−1.12216	−	1.54452i	−0.111659	−	0.153686i	−0.861189	+	0.508285i	$0.830280\pi$
$102$	−1.33071	+	2.61167i	−0.131760	+	0.258594i
$103$	−2.80172	−	5.49869i	−0.276062	−	0.541802i	0.710795	−	0.703399i	$-0.248335\pi$
$103$	−2.80172	−	5.49869i	−0.276062	−	0.541802i	−0.986857	+	0.161597i	$0.948335\pi$
$104$	3.15977	−	4.34905i	0.309841	−	0.426459i
$105$		0			0
$106$	−0.686319	−	0.222999i	−0.0666612	−	0.0216595i
$107$	−0.388059	−	0.197726i	−0.0375151	−	0.0191149i	0.435132	−	0.900367i	$-0.356702\pi$
$107$	−0.388059	−	0.197726i	−0.0375151	−	0.0191149i	−0.472647	+	0.881252i	$0.656702\pi$
$108$	1.47622	−	9.32051i	0.142050	−	0.896866i
$109$	9.46672			0.906748			0.453374	−	0.891320i	$-0.350220\pi$
$109$	9.46672			0.906748			0.453374	+	0.891320i	$0.350220\pi$
$110$		0			0
$111$	−1.32539			−0.125801
$112$	−1.19806	+	7.56426i	−0.113206	+	0.714755i
$113$	18.0576	+	9.20080i	1.69871	+	0.865538i	0.986537	+	0.163539i	$0.0522910\pi$
$113$	18.0576	+	9.20080i	1.69871	+	0.865538i	0.712178	+	0.701999i	$0.247709\pi$
$114$	−2.16923	−	0.704827i	−0.203167	−	0.0660131i
$115$		0			0
$116$	−2.73826	+	3.76890i	−0.254241	+	0.349933i
$117$	−2.26110	−	4.43766i	−0.209039	−	0.410262i
$118$	0.355895	−	0.698483i	0.0327628	−	0.0643005i
$119$	−9.03071	−	12.4297i	−0.827844	−	1.13943i
$120$		0			0
$121$	8.96835	−	6.36935i	0.815305	−	0.579032i
$122$	2.39578	+	2.39578i	0.216903	+	0.216903i
$123$	−4.00099	−	0.633694i	−0.360757	−	0.0571383i
$124$	11.2926	−	3.66920i	1.01411	−	0.329504i
$125$		0			0
$126$	−1.96088	−	1.42466i	−0.174689	−	0.126919i
$127$	9.31359	−	1.47513i	0.826447	−	0.130896i	0.271138	−	0.962540i	$-0.412600\pi$
$127$	9.31359	−	1.47513i	0.826447	−	0.130896i	0.555309	+	0.831644i	$0.312600\pi$
$128$	10.0641	−	5.12793i	0.889551	−	0.453249i
$129$	−2.52591	−	7.77394i	−0.222394	−	0.684457i
$130$		0			0
$131$		−	7.51676i		−	0.656743i	−0.944549	−	0.328371i	$-0.893500\pi$
$131$		−	7.51676i		−	0.656743i	0.944549	−	0.328371i	$-0.106500\pi$
$132$	−5.91462	−	3.05391i	−0.514802	−	0.265809i
$133$	8.45377	−	8.45377i	0.733035	−	0.733035i
$134$	−0.734554	+	0.533685i	−0.0634558	+	0.0461034i
$135$		0			0
$136$	−2.99035	+	9.20336i	−0.256421	+	0.789182i
$137$	2.40429	+	15.1801i	0.205413	+	1.29692i	0.847706	+	0.530466i	$0.177983\pi$
$137$	2.40429	+	15.1801i	0.205413	+	1.29692i	−0.642294	+	0.766458i	$0.722017\pi$
$138$	−0.261013	−	1.64797i	−0.0222189	−	0.140285i
$139$	−1.28625	+	3.95867i	−0.109098	+	0.335770i	−0.990670	−	0.136279i	$-0.956486\pi$
$139$	−1.28625	+	3.95867i	−0.109098	+	0.335770i	0.881572	+	0.472049i	$0.156486\pi$
$140$		0			0
$141$	−3.39364	+	2.46563i	−0.285796	+	0.207643i
$142$	−0.992116	+	0.992116i	−0.0832565	+	0.0832565i
$143$	−9.59470	+	1.46670i	−0.802349	+	0.122651i
$144$		−	4.46910i		−	0.372425i
$145$		0			0
$146$	2.23368	+	6.87457i	0.184861	+	0.568943i
$147$	−1.52831	+	0.778714i	−0.126053	+	0.0642273i
$148$	−2.02391	+	0.320556i	−0.166364	+	0.0263495i
$149$	14.5440	+	10.5669i	1.19149	+	0.865672i	0.993421	−	0.114516i	$-0.0365316\pi$
$149$	14.5440	+	10.5669i	1.19149	+	0.865672i	0.198073	+	0.980187i	$0.436532\pi$
$150$		0			0
$151$	16.9214	−	5.49808i	1.37704	−	0.447427i	0.475345	−	0.879800i	$-0.342323\pi$
$151$	16.9214	−	5.49808i	1.37704	−	0.447427i	0.901695	+	0.432372i	$0.142323\pi$
$152$	−7.43742	−	1.17797i	−0.603254	−	0.0955461i
$153$	6.33960	+	6.33960i	0.512526	+	0.512526i
$154$	−3.83633	+	2.75579i	−0.309140	+	0.222068i
$155$		0			0
$156$	3.45239	+	4.75181i	0.276413	+	0.380449i
$157$	−9.74483	+	19.1253i	−0.777722	+	1.52636i	0.0709708	+	0.997478i	$0.477390\pi$
$157$	−9.74483	+	19.1253i	−0.777722	+	1.52636i	−0.848693	+	0.528887i	$0.822610\pi$
$158$	3.38003	+	6.63368i	0.268901	+	0.527748i
$159$	0.989642	−	1.36213i	0.0784837	−	0.108024i
$160$		0			0
$161$	8.31766	+	2.70257i	0.655524	+	0.212993i
$162$	−0.434300	−	0.221287i	−0.0341218	−	0.0173859i
$163$	1.63083	−	10.2967i	0.127737	−	0.806497i	−0.837752	−	0.546051i	$-0.816130\pi$
$163$	1.63083	−	10.2967i	0.127737	−	0.806497i	0.965488	−	0.260446i	$-0.0838696\pi$
$164$	−6.26288			−0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	1.76660	−	11.1538i	0.136703	−	0.863110i	−0.820067	−	0.572267i	$-0.806064\pi$
$167$	1.76660	−	11.1538i	0.136703	−	0.863110i	0.956771	−	0.290843i	$-0.0939359\pi$
$168$	5.43848	+	2.77104i	0.419588	+	0.213791i
$169$	−4.21842	−	1.37065i	−0.324493	−	0.105434i
$170$		0			0
$171$	−4.10070	+	5.64412i	−0.313588	+	0.431617i
$172$	−5.73731	−	11.2601i	−0.437466	−	0.858575i
$173$	5.99367	−	11.7632i	0.455691	−	0.894343i	−0.542823	−	0.839847i	$-0.682645\pi$
$173$	5.99367	−	11.7632i	0.455691	−	0.894343i	0.998514	−	0.0544963i	$-0.0173553\pi$
$174$	0.864909	+	1.19044i	0.0655686	+	0.0902474i
$175$		0			0
$176$	−8.26862	−	2.73598i	−0.623270	−	0.206233i
$177$	1.29330	+	1.29330i	0.0972104	+	0.0972104i
$178$	−5.38885	−	0.853510i	−0.403912	−	0.0639733i
$179$	−2.11776	+	0.688100i	−0.158288	+	0.0514310i	−0.387089	−	0.922042i	$-0.626520\pi$
$179$	−2.11776	+	0.688100i	−0.158288	+	0.0514310i	0.228801	+	0.973473i	$0.426520\pi$
$180$		0			0
$181$	−3.50687	−	2.54789i	−0.260664	−	0.189383i	0.449776	−	0.893141i	$-0.351504\pi$
$181$	−3.50687	−	2.54789i	−0.260664	−	0.189383i	−0.710440	+	0.703758i	$0.751504\pi$
$182$	4.11663	−	0.652010i	0.305145	−	0.0483302i
$183$	−7.04339	+	3.58879i	−0.520663	+	0.265291i
$184$	−1.70221	−	5.23888i	−0.125489	−	0.386215i
$185$		0			0
$186$		−	3.75045i		−	0.274996i
$187$	15.6105	−	7.84826i	1.14155	−	0.573922i
$188$	−4.58586	+	4.58586i	−0.334458	+	0.334458i
$189$	12.6397	−	9.18329i	0.919404	−	0.667986i
$190$		0			0
$191$	−1.26010	+	3.87820i	−0.0911779	+	0.280617i	−0.986239	−	0.165327i	$-0.947132\pi$
$191$	−1.26010	+	3.87820i	−0.0911779	+	0.280617i	0.895061	+	0.445944i	$0.147132\pi$
$192$	0.504715	+	3.18664i	0.0364247	+	0.229976i
$193$	3.26960	+	20.6434i	0.235351	+	1.48595i	0.768459	+	0.639899i	$0.221024\pi$
$193$	3.26960	+	20.6434i	0.235351	+	1.48595i	−0.533108	+	0.846047i	$0.678976\pi$
$194$	1.51938	−	4.67617i	0.109085	−	0.335729i
$195$		0			0
$196$	−2.14544	+	1.55875i	−0.153246	+	0.111339i
$197$	−0.213782	+	0.213782i	−0.0152313	+	0.0152313i	−0.714681	−	0.699450i	$-0.753428\pi$
$197$	−0.213782	+	0.213782i	−0.0152313	+	0.0152313i	0.699450	+	0.714681i	$0.253428\pi$
$198$	1.95954	−	1.93853i	0.139258	−	0.137765i
$199$			11.0815i			0.785549i	0.919635	+	0.392775i	$0.128485\pi$
$199$			11.0815i			0.785549i	−0.919635	+	0.392775i	$0.871515\pi$
$200$		0			0
$201$	−0.654619	−	2.01471i	−0.0461733	−	0.142107i
$202$	−0.830691	+	0.423258i	−0.0584472	+	0.0297803i
$203$	−7.61793	+	1.20656i	−0.534674	+	0.0846840i
$204$	−8.55387	−	6.21475i	−0.598890	−	0.435119i
$205$		0			0
$206$	−2.86620	+	0.931285i	−0.199698	+	0.0648857i
$207$	−5.04067	−	0.798364i	−0.350351	−	0.0554901i
$208$	5.43417	+	5.43417i	0.376792	+	0.376792i
$209$	7.93217	+	11.0423i	0.548680	+	0.763815i
$210$		0			0
$211$	−5.20512	−	7.16423i	−0.358335	−	0.493206i	0.591349	−	0.806416i	$-0.298596\pi$
$211$	−5.20512	−	7.16423i	−0.358335	−	0.493206i	−0.949684	+	0.313210i	$0.898596\pi$
$212$	1.18177	−	2.31936i	0.0811644	−	0.159294i
$213$	−1.48615	−	2.91674i	−0.101830	−	0.199852i
$214$	−0.125014	+	0.172067i	−0.00854576	+	0.0117622i
$215$		0			0
$216$	−9.35886	−	3.04088i	−0.636790	−	0.206906i
$217$	17.5158	+	8.92474i	1.18905	+	0.605851i
$218$	0.723193	−	4.56606i	0.0489808	−	0.309253i
$219$	−16.8647			−1.13961
$220$		0			0
$221$	−15.4172			−1.03707
$222$	−0.101251	+	0.639273i	−0.00679551	+	0.0429052i
$223$	−5.50839	−	2.80667i	−0.368869	−	0.187948i	0.259723	−	0.965683i	$-0.416369\pi$
$223$	−5.50839	−	2.80667i	−0.368869	−	0.187948i	−0.628593	+	0.777735i	$0.716369\pi$
$224$	13.7469	+	4.46662i	0.918500	+	0.298439i
$225$		0			0
$226$	5.81727	−	8.00679i	0.386959	−	0.532604i
$227$	1.50576	+	2.95522i	0.0999406	+	0.196145i	0.935563	−	0.353160i	$-0.114893\pi$
$227$	1.50576	+	2.95522i	0.0999406	+	0.196145i	−0.835622	+	0.549304i	$0.814893\pi$
$228$	3.73520	−	7.33074i	0.247370	−	0.485490i
$229$	−3.13876	−	4.32013i	−0.207415	−	0.285482i	0.692618	−	0.721305i	$-0.256457\pi$
$229$	−3.13876	−	4.32013i	−0.207415	−	0.285482i	−0.900032	+	0.435823i	$0.856457\pi$
$230$		0			0
$231$	−3.34904	−	10.4995i	−0.220350	−	0.690813i
$232$	3.43509	+	3.43509i	0.225525	+	0.225525i
$233$	−4.36386	−	0.691167i	−0.285886	−	0.0452799i	0.0118446	−	0.999930i	$-0.496230\pi$
$233$	−4.36386	−	0.691167i	−0.285886	−	0.0452799i	−0.297730	+	0.954650i	$0.596230\pi$
$234$	−2.31314	+	0.751584i	−0.151215	+	0.0491326i
$235$		0			0
$236$	2.28770	+	1.66211i	0.148917	+	0.108194i
$237$	−17.1567	+	2.71735i	−1.11445	+	0.176511i
$238$	−6.68507	+	3.40621i	−0.433329	+	0.220792i
$239$	3.23012	+	9.94128i	0.208939	+	0.643048i	0.999529	+	0.0307017i	$0.00977418\pi$
$239$	3.23012	+	9.94128i	0.208939	+	0.643048i	−0.790590	+	0.612346i	$0.790226\pi$
$240$		0			0
$241$			27.8579i			1.79449i	0.441536	+	0.897243i	$0.354434\pi$
$241$			27.8579i			1.79449i	−0.441536	+	0.897243i	$0.645566\pi$
$242$	−2.38699	−	4.81226i	−0.153442	−	0.309344i
$243$	−10.5600	+	10.5600i	−0.677425	+	0.677425i
$244$	−9.88748	+	7.18367i	−0.632981	+	0.459888i
$245$		0			0
$246$	−0.611296	+	1.88138i	−0.0389748	+	0.119952i
$247$	−1.87672	−	11.8492i	−0.119413	−	0.753944i
$248$	−1.93695	−	12.2294i	−0.122996	−	0.776569i
$249$	−2.35285	+	7.24134i	−0.149106	+	0.458901i
$250$		0			0
$251$	8.04670	−	5.84627i	0.507903	−	0.369013i	−0.304124	−	0.952632i	$-0.598364\pi$
$251$	8.04670	−	5.84627i	0.507903	−	0.369013i	0.812028	+	0.583619i	$0.198364\pi$
$252$	6.18223	−	6.18223i	0.389444	−	0.389444i
$253$	−4.56302	+	8.83737i	−0.286874	+	0.555601i
$254$		−	4.60489i		−	0.288936i
$255$		0			0
$256$	0.0455968	+	0.140332i	0.00284980	+	0.00877078i
$257$	−3.77828	+	1.92513i	−0.235683	+	0.120086i	−0.567844	−	0.823136i	$-0.692222\pi$
$257$	−3.77828	+	1.92513i	−0.235683	+	0.120086i	0.332161	+	0.943223i	$0.392222\pi$
$258$	−3.94254	+	0.624438i	−0.245452	+	0.0388758i
$259$	−2.74467	−	1.99412i	−0.170545	−	0.123908i
$260$		0			0
$261$	4.28052	−	1.39083i	0.264958	−	0.0860899i
$262$	−3.62554	−	0.574229i	−0.223987	−	0.0354760i
$263$	−16.1830	−	16.1830i	−0.997884	−	0.997884i	0.00211364	−	0.999998i	$-0.499327\pi$
$263$	−16.1830	−	16.1830i	−0.997884	−	0.997884i	−0.999998	+	0.00211364i	$0.999327\pi$
$264$	−4.11022	+	5.59360i	−0.252967	+	0.344262i
$265$		0			0
$266$	−3.43167	−	4.72330i	−0.210409	−	0.289604i
$267$	5.77914	−	11.3422i	0.353677	−	0.694131i
$268$	−1.48689	−	2.91819i	−0.0908265	−	0.178257i
$269$	−13.4435	+	18.5034i	−0.819666	+	1.12817i	0.170094	+	0.985428i	$0.445593\pi$
$269$	−13.4435	+	18.5034i	−0.819666	+	1.12817i	−0.989759	+	0.142745i	$0.954407\pi$
$270$		0			0
$271$	−1.32229	−	0.429640i	−0.0803237	−	0.0260987i	0.268580	−	0.963258i	$-0.413446\pi$
$271$	−1.32229	−	0.429640i	−0.0803237	−	0.0260987i	−0.348903	+	0.937159i	$0.613446\pi$
$272$	−12.3263	−	6.28057i	−0.747392	−	0.380815i
$273$	−1.52123	+	9.60465i	−0.0920688	+	0.581300i
$274$	7.50545			0.453421
$275$		0			0
$276$	6.01861			0.362278
$277$	2.23010	−	14.0803i	0.133994	−	0.846002i	−0.825527	−	0.564363i	$-0.809122\pi$
$277$	2.23010	−	14.0803i	0.133994	−	0.846002i	0.959520	−	0.281639i	$-0.0908781\pi$
$278$	1.81111	+	0.922808i	0.108623	+	0.0553464i
$279$	−10.9101	−	3.54491i	−0.653171	−	0.212228i
$280$		0			0
$281$	14.9161	−	20.5302i	0.889818	−	1.22473i	−0.0837853	−	0.996484i	$-0.526701\pi$
$281$	14.9161	−	20.5302i	0.889818	−	1.22473i	0.973604	−	0.228246i	$-0.0732990\pi$
$282$	0.929988	+	1.82520i	0.0553800	+	0.108689i
$283$	−3.36440	+	6.60300i	−0.199993	+	0.392508i	−0.969121	−	0.246587i	$-0.920691\pi$
$283$	−3.36440	+	6.60300i	−0.199993	+	0.392508i	0.769128	+	0.639095i	$0.220691\pi$
$284$	−2.97484	−	4.09451i	−0.176524	−	0.242964i
$285$		0			0
$286$	−0.0255420	+	4.73983i	−0.00151033	+	0.280272i
$287$	−7.33195	−	7.33195i	−0.432791	−	0.432791i
$288$	−8.33087	−	1.31948i	−0.490901	−	0.0777511i
$289$	10.2266	−	3.32284i	0.601567	−	0.195461i
$290$		0			0
$291$	9.28071	+	6.74283i	0.544045	+	0.395272i
$292$	−25.7529	+	4.07886i	−1.50707	+	0.238697i
$293$	13.0777	−	6.66340i	0.764005	−	0.389280i	−0.0281472	−	0.999604i	$-0.508961\pi$
$293$	13.0777	−	6.66340i	0.764005	−	0.389280i	0.792152	+	0.610324i	$0.208961\pi$
$294$	0.258843	+	0.796636i	0.0150960	+	0.0464607i
$295$		0			0
$296$			2.13682i			0.124200i
$297$	7.98087	+	15.8742i	0.463097	+	0.921116i
$298$	6.20775	−	6.20775i	0.359606	−	0.359606i
$299$	7.09994	−	5.15841i	0.410600	−	0.298318i
$300$		0			0
$301$	6.46553	−	19.8989i	0.372667	−	1.14695i
$302$	−1.35920	−	8.58165i	−0.0782131	−	0.493818i
$303$	−0.340276	−	2.14842i	−0.0195483	−	0.123423i
$304$	3.32657	−	10.2381i	0.190792	−	0.587197i
$305$		0			0
$306$	3.54206	−	2.57346i	0.202486	−	0.147115i
$307$	0.874954	−	0.874954i	0.0499363	−	0.0499363i	−0.681698	−	0.731634i	$-0.738758\pi$
$307$	0.874954	−	0.874954i	0.0499363	−	0.0499363i	0.731634	+	0.681698i	$0.238758\pi$
$308$	−7.65344	−	15.2230i	−0.436095	−	0.867409i
$309$		−	7.03137i		−	0.400001i
$310$		0			0
$311$	4.37162	+	13.4545i	0.247892	+	0.762933i	0.995147	+	0.0983958i	$0.0313711\pi$
$311$	4.37162	+	13.4545i	0.247892	+	0.762933i	−0.747256	+	0.664537i	$0.768629\pi$
$312$	5.45732	−	2.78064i	0.308960	−	0.157423i
$313$	−0.730542	+	0.115706i	−0.0412927	+	0.00654011i	−0.177047	−	0.984202i	$-0.556654\pi$
$313$	−0.730542	+	0.115706i	−0.0412927	+	0.00654011i	0.135754	+	0.990743i	$0.456654\pi$
$314$	8.48022	+	6.16124i	0.478566	+	0.347699i
$315$		0			0
$316$	−25.5415	+	8.29895i	−1.43682	+	0.466852i
$317$	16.8560	+	2.66972i	0.946726	+	0.149947i	0.610661	−	0.791892i	$-0.290904\pi$
$317$	16.8560	+	2.66972i	0.946726	+	0.149947i	0.336065	+	0.941839i	$0.390904\pi$
$318$	−0.581389	−	0.581389i	−0.0326027	−	0.0326027i
$319$	0.0472661	−	8.77118i	0.00264640	−	0.491092i
$320$		0			0
$321$	−0.291674	−	0.401454i	−0.0162796	−	0.0224070i
$322$	1.93894	−	3.80538i	0.108053	−	0.212065i
$323$	9.80433	+	19.2421i	0.545527	+	1.07066i
$324$	1.03346	−	1.42244i	0.0574145	−	0.0790243i
$325$		0			0
$326$	−4.84178	−	1.57319i	−0.268161	−	0.0871309i
$327$	9.61042	+	4.89675i	0.531457	+	0.270791i
$328$	−1.02165	+	6.45047i	−0.0564114	+	0.356168i
$329$	−10.7373			−0.591967
$330$		0			0
$331$	−14.9189			−0.820016			−0.410008	−	0.912082i	$-0.634474\pi$
$331$	−14.9189			−0.820016			−0.410008	+	0.912082i	$0.634474\pi$
$332$	−1.84150	+	11.6268i	−0.101065	+	0.638102i
$333$	1.76395	+	0.898777i	0.0966638	+	0.0492527i
$334$	−5.24485	−	1.70415i	−0.286985	−	0.0932472i
$335$		0			0
$336$	−5.12893	+	7.05937i	−0.279806	+	0.385120i
$337$	4.28455	+	8.40891i	0.233394	+	0.458062i	0.977765	−	0.209705i	$-0.0672503\pi$
$337$	4.28455	+	8.40891i	0.233394	+	0.458062i	−0.744370	+	0.667767i	$0.767250\pi$
$338$	−0.983358	+	1.92995i	−0.0534876	+	0.104975i
$339$	13.5725	+	18.6809i	0.737156	+	1.01461i
$340$		0			0
$341$	−13.2379	+	18.0154i	−0.716871	+	0.975589i
$342$	2.40905	+	2.40905i	0.130267	+	0.130267i
$343$	15.8271	+	2.50676i	0.854581	+	0.135352i
$344$	−12.5333	+	4.07231i	−0.675750	+	0.219564i
$345$		0			0
$346$	−5.21586	−	3.78954i	−0.280406	−	0.203727i
$347$	19.0026	−	3.00971i	1.02011	−	0.161570i	0.376094	−	0.926581i	$-0.377267\pi$
$347$	19.0026	−	3.00971i	1.02011	−	0.161570i	0.644016	+	0.765012i	$0.277267\pi$
$348$	−4.72933	+	2.40971i	−0.253518	+	0.129174i
$349$	−4.59599	−	14.1450i	−0.246018	−	0.757164i	−0.995467	−	0.0951031i	$-0.969682\pi$
$349$	−4.59599	−	14.1450i	−0.246018	−	0.757164i	0.749450	−	0.662061i	$-0.230318\pi$
$350$		0			0
$351$		−	15.6777i		−	0.836813i
$352$	−7.54143	+	14.6058i	−0.401960	+	0.778491i
$353$	−1.78406	+	1.78406i	−0.0949560	+	0.0949560i	−0.752989	−	0.658033i	$-0.771389\pi$
$353$	−1.78406	+	1.78406i	−0.0949560	+	0.0949560i	0.658033	+	0.752989i	$0.271389\pi$
$354$	0.722594	−	0.524995i	0.0384054	−	0.0279032i
$355$		0			0
$356$	6.08171	−	18.7176i	0.322330	−	0.992029i
$357$	−2.73840	−	17.2896i	−0.144932	−	0.915063i
$358$	0.170108	+	1.07402i	0.00899047	+	0.0567636i
$359$	2.62416	−	8.07635i	0.138498	−	0.426253i	−0.857620	−	0.514285i	$-0.828058\pi$
$359$	2.62416	−	8.07635i	0.138498	−	0.426253i	0.996118	+	0.0880312i	$0.0280575\pi$
$360$		0			0
$361$	1.77596	−	1.29031i	0.0934717	−	0.0679111i
$362$	−1.49682	+	1.49682i	−0.0786711	+	0.0786711i
$363$	12.3991	−	1.82707i	0.650783	−	0.0958962i
$364$			15.0345i			0.788021i
$365$		0			0
$366$	1.19290	+	3.67138i	0.0623541	+	0.191906i
$367$	−18.9156	+	9.63799i	−0.987387	+	0.503099i	−0.871622	−	0.490178i	$-0.836932\pi$
$367$	−18.9156	+	9.63799i	−0.987387	+	0.503099i	−0.115765	+	0.993277i	$0.536932\pi$
$368$	7.77792	−	1.23190i	0.405452	−	0.0642173i
$369$	4.89515	+	3.55653i	0.254831	+	0.185146i
$370$		0			0
$371$	4.09877	−	1.33177i	0.212797	−	0.0691420i
$372$	13.3620	+	2.11633i	0.692786	+	0.109726i
$373$	−2.57445	−	2.57445i	−0.133300	−	0.133300i	0.637309	−	0.770609i	$-0.280048\pi$
$373$	−2.57445	−	2.57445i	−0.133300	−	0.133300i	−0.770609	+	0.637309i	$0.780048\pi$
$374$	−2.59290	−	8.12891i	−0.134076	−	0.420336i
$375$		0			0
$376$	3.97513	+	5.47130i	0.205002	+	0.282161i
$377$	−3.51371	+	6.89604i	−0.180965	+	0.355164i
$378$	−3.46377	−	6.79802i	−0.178157	−	0.349653i
$379$	9.74713	−	13.4158i	0.500677	−	0.689122i	−0.481636	−	0.876371i	$-0.659957\pi$
$379$	9.74713	−	13.4158i	0.500677	−	0.689122i	0.982312	+	0.187249i	$0.0599572\pi$
$380$		0			0
$381$	10.2180	+	3.32002i	0.523483	+	0.170090i
$382$	1.77430	+	0.904051i	0.0907810	+	0.0462553i
$383$	−1.77402	+	11.2007i	−0.0906481	+	0.572330i	0.900000	+	0.435890i	$0.143566\pi$
$383$	−1.77402	+	11.2007i	−0.0906481	+	0.572330i	−0.990648	+	0.136440i	$0.956434\pi$
$384$	12.8694			0.656736
$385$		0			0
$386$	10.2067			0.519505
$387$	−1.90998	+	12.0591i	−0.0970895	+	0.612999i
$388$	15.8027	+	8.05188i	0.802260	+	0.408772i
$389$	−0.777554	−	0.252643i	−0.0394236	−	0.0128095i	0.289239	−	0.957257i	$-0.406598\pi$
$389$	−0.777554	−	0.252643i	−0.0394236	−	0.0128095i	−0.328662	+	0.944447i	$0.606598\pi$
$390$		0			0
$391$	−9.28580	+	12.7808i	−0.469603	+	0.646353i
$392$	1.25546	+	2.46398i	0.0634102	+	0.124450i
$393$	3.88812	−	7.63086i	0.196130	−	0.384926i
$394$	0.0867814	+	0.119444i	0.00437198	+	0.00601752i
$395$		0			0
$396$	5.80078	+	8.07525i	0.291500	+	0.405796i
$397$	−11.8504	−	11.8504i	−0.594752	−	0.594752i	0.344159	−	0.938911i	$-0.388164\pi$
$397$	−11.8504	−	11.8504i	−0.594752	−	0.594752i	−0.938911	+	0.344159i	$0.888164\pi$
$398$	5.34493	+	0.846553i	0.267917	+	0.0424339i
$399$	12.9549	−	4.20930i	0.648555	−	0.210728i
$400$		0			0
$401$	23.0228	+	16.7270i	1.14970	+	0.835308i	0.988441	−	0.151603i	$-0.0484436\pi$
$401$	23.0228	+	16.7270i	1.14970	+	0.835308i	0.161262	+	0.986912i	$0.448444\pi$
$402$	−1.02176	+	0.161831i	−0.0509607	+	0.00807137i
$403$	17.5765	−	8.95566i	0.875547	−	0.446113i
$404$	−1.03922	−	3.19839i	−0.0517032	−	0.159126i
$405$		0			0
$406$			3.76651i			0.186929i
$407$	2.74279	−	2.71338i	0.135955	−	0.134497i
$408$	−7.79627	+	7.79627i	−0.385973	+	0.385973i
$409$	−1.95998	+	1.42401i	−0.0969146	+	0.0704126i	−0.635187	−	0.772358i	$-0.719077\pi$
$409$	−1.95998	+	1.42401i	−0.0969146	+	0.0704126i	0.538273	+	0.842771i	$0.319077\pi$
$410$		0			0
$411$	−5.41127	+	16.6542i	−0.266918	+	0.821490i
$412$	−1.70059	−	10.7371i	−0.0837820	−	0.528979i
$413$	0.732376	+	4.62404i	0.0360379	+	0.227534i
$414$	−0.770145	+	2.37026i	−0.0378506	+	0.116492i
$415$		0			0
$416$	11.7343	−	8.52546i	0.575321	−	0.417995i
$417$	−3.35343	+	3.35343i	−0.164218	+	0.164218i
$418$	5.93199	−	2.98234i	0.290143	−	0.145871i
$419$		−	16.4371i		−	0.803006i	−0.915858	−	0.401503i	$-0.868488\pi$
$419$		−	16.4371i		−	0.803006i	0.915858	−	0.401503i	$-0.131512\pi$
$420$		0			0
$421$	−3.85294	−	11.8581i	−0.187781	−	0.577930i	0.812204	−	0.583373i	$-0.198267\pi$
$421$	−3.85294	−	11.8581i	−0.187781	−	0.577930i	−0.999985	+	0.00544310i	$0.998267\pi$
$422$	−3.85314	+	1.96327i	−0.187568	+	0.0955707i
$423$	6.18855	−	0.980171i	0.300898	−	0.0476575i
$424$	−2.19605	−	1.59552i	−0.106649	−	0.0774853i
$425$		0			0
$426$	−1.52036	+	0.493994i	−0.0736615	+	0.0239341i
$427$	−19.9852	−	3.16534i	−0.967151	−	0.153182i
$428$	−0.542488	−	0.542488i	−0.0262222	−	0.0262222i
$429$	−10.4990	−	3.47399i	−0.506896	−	0.167726i
$430$		0			0
$431$	−11.6588	−	16.0470i	−0.561586	−	0.772957i	0.429941	−	0.902857i	$-0.358534\pi$
$431$	−11.6588	−	16.0470i	−0.561586	−	0.772957i	−0.991527	+	0.129900i	$0.958534\pi$
$432$	6.38668	−	12.5346i	0.307279	−	0.603070i
$433$	−12.9956	−	25.5054i	−0.624531	−	1.22571i	−0.959027	−	0.283314i	$-0.908566\pi$
$433$	−12.9956	−	25.5054i	−0.624531	−	1.22571i	0.334496	−	0.942397i	$-0.391434\pi$
$434$	5.64273	−	7.76656i	0.270860	−	0.372807i
$435$		0			0
$436$	15.8597	+	5.15313i	0.759541	+	0.246790i
$437$	−10.9533	−	5.58097i	−0.523966	−	0.266974i
$438$	−1.28835	+	8.13431i	−0.0615597	+	0.388672i
$439$	−3.12279			−0.149043			−0.0745214	−	0.997219i	$-0.523743\pi$
$439$	−3.12279			−0.149043			−0.0745214	+	0.997219i	$0.523743\pi$
$440$		0			0
$441$	2.56208			0.122004
$442$	−1.17777	+	7.43613i	−0.0560207	+	0.353701i
$443$	−28.2787	−	14.4087i	−1.34356	−	0.684579i	−0.373545	−	0.927612i	$-0.621858\pi$
$443$	−28.2787	−	14.4087i	−1.34356	−	0.684579i	−0.970018	+	0.243033i	$0.921858\pi$
$444$	−2.22044	−	0.721465i	−0.105378	−	0.0342392i
$445$		0			0
$446$	−1.77454	+	2.44244i	−0.0840267	+	0.115653i
$447$	9.29900	+	18.2503i	0.439827	+	0.863210i
$448$	−3.74928	+	7.35837i	−0.177137	+	0.347650i
$449$	20.5693	+	28.3112i	0.970726	+	1.33609i	0.941679	+	0.336511i	$0.109247\pi$
$449$	20.5693	+	28.3112i	0.970726	+	1.33609i	0.0290462	+	0.999578i	$0.490753\pi$
$450$		0			0
$451$	9.57702	−	6.87957i	0.450964	−	0.323946i
$452$	25.2437	+	25.2437i	1.18736	+	1.18736i
$453$	20.0221	+	3.17119i	0.940722	+	0.148996i
$454$	1.54041	−	0.500510i	0.0722951	−	0.0234901i
$455$		0			0
$456$	−6.94099	−	5.04293i	−0.325042	−	0.236157i
$457$	5.03728	−	0.797826i	0.235634	−	0.0373207i	−0.0375006	−	0.999297i	$-0.511940\pi$
$457$	5.03728	−	0.797826i	0.235634	−	0.0373207i	0.273134	+	0.961976i	$0.411940\pi$
$458$	−2.32350	+	1.18388i	−0.108570	+	0.0553191i
$459$	8.72103	+	26.8406i	0.407063	+	1.25281i
$460$		0			0
$461$			12.4703i			0.580801i	0.956905	+	0.290400i	$0.0937885\pi$
$461$			12.4703i			0.580801i	−0.956905	+	0.290400i	$0.906211\pi$
$462$	−5.32002	+	0.813245i	−0.247510	+	0.0378356i
$463$	19.2728	−	19.2728i	0.895684	−	0.895684i	−0.0993669	−	0.995051i	$-0.531682\pi$
$463$	19.2728	−	19.2728i	0.895684	−	0.895684i	0.995051	+	0.0993669i	$0.0316818\pi$
$464$	−5.61854	+	4.08211i	−0.260834	+	0.189507i
$465$		0			0
$466$	−0.666738	+	2.05201i	−0.0308860	+	0.0950574i
$467$	6.20937	+	39.2044i	0.287335	+	1.81416i	0.534476	+	0.845184i	$0.320509\pi$
$467$	6.20937	+	39.2044i	0.287335	+	1.81416i	−0.247141	+	0.968980i	$0.579491\pi$
$468$	−1.37244	−	8.66527i	−0.0634412	−	0.400552i
$469$	1.67562	−	5.15703i	0.0773730	−	0.238130i
$470$		0			0
$471$	−19.7855	+	14.3750i	−0.911667	+	0.662365i
$472$	2.08508	−	2.08508i	0.0959738	−	0.0959738i
$473$	21.1422	+	10.9164i	0.972119	+	0.501936i
$474$			8.48273i			0.389625i
$475$		0			0
$476$	−8.36324	−	25.7394i	−0.383328	−	1.17976i
$477$	−2.24079	+	1.14174i	−0.102599	+	0.0522767i
$478$	5.04171	−	0.798528i	0.230602	−	0.0365238i
$479$	−30.9491	−	22.4858i	−1.41410	−	1.02740i	−0.992711	−	0.120523i	$-0.961543\pi$
$479$	−30.9491	−	22.4858i	−1.41410	−	1.02740i	−0.421388	−	0.906880i	$-0.638457\pi$
$480$		0			0
$481$	−3.23773	+	1.05200i	−0.147628	+	0.0479671i
$482$	13.4366	+	2.12815i	0.612022	+	0.0969348i
$483$	7.04599	+	7.04599i	0.320603	+	0.320603i
$484$	18.4919	−	5.78879i	0.840539	−	0.263127i
$485$		0			0
$486$	4.28667	+	5.90009i	0.194447	+	0.267634i
$487$	12.3391	−	24.2169i	0.559139	−	1.09737i	−0.422454	−	0.906384i	$-0.638831\pi$
$487$	12.3391	−	24.2169i	0.559139	−	1.09737i	0.981593	−	0.190987i	$-0.0611688\pi$
$488$	5.78591	+	11.3555i	0.261916	+	0.514039i
$489$	6.98164	−	9.60940i	0.315720	−	0.434552i
$490$		0			0
$491$	3.77748	+	1.22738i	0.170475	+	0.0553907i	0.393011	−	0.919534i	$-0.371433\pi$
$491$	3.77748	+	1.22738i	0.170475	+	0.0553907i	−0.222536	+	0.974925i	$0.571433\pi$
$492$	−6.35795	−	3.23954i	−0.286638	−	0.146050i
$493$	2.17949	−	13.7608i	0.0981593	−	0.619753i
$494$	−5.85854			−0.263588
$495$		0			0
$496$	17.7010			0.794798
$497$	1.31080	−	8.27608i	0.0587975	−	0.371233i
$498$	3.31295	+	1.68803i	0.148457	+	0.0756426i
$499$	6.11060	+	1.98546i	0.273548	+	0.0888812i	0.442579	−	0.896730i	$-0.354064\pi$
$499$	6.11060	+	1.98546i	0.273548	+	0.0888812i	−0.169031	+	0.985611i	$0.554064\pi$
$500$		0			0
$501$	7.56284	−	10.4094i	0.337883	−	0.465056i
$502$	−2.20510	−	4.32776i	−0.0984186	−	0.193157i
$503$	−18.4896	+	36.2878i	−0.824409	+	1.61799i	−0.0388190	+	0.999246i	$0.512360\pi$
$503$	−18.4896	+	36.2878i	−0.824409	+	1.61799i	−0.785590	+	0.618747i	$0.787640\pi$
$504$	−5.35890	−	7.37590i	−0.238704	−	0.328549i
$505$		0			0
$506$	3.91392	+	2.87598i	0.173995	+	0.127853i
$507$	−3.57347	−	3.57347i	−0.158703	−	0.158703i
$508$	16.4061	+	2.59847i	0.727904	+	0.115289i
$509$	−8.83124	+	2.86944i	−0.391438	+	0.127186i	−0.498122	−	0.867107i	$-0.665977\pi$
$509$	−8.83124	+	2.86944i	−0.391438	+	0.127186i	0.106684	+	0.994293i	$0.465977\pi$
$510$		0			0
$511$	−34.9240	−	25.3738i	−1.54495	−	1.12247i
$512$	22.3835	−	3.54520i	0.989220	−	0.156677i
$513$	−19.5672	+	9.96998i	−0.863912	+	0.440185i
$514$	0.639909	+	1.96944i	0.0282252	+	0.0868681i
$515$		0			0
$516$		−	14.3987i		−	0.633868i
$517$	1.97515	−	12.0500i	0.0868669	−	0.529957i
$518$	−1.17149	+	1.17149i	−0.0514723	+	0.0514723i
$519$	12.1693	−	8.84152i	0.534173	−	0.388099i
$520$		0			0
$521$	−4.57564	+	14.0824i	−0.200462	+	0.616960i	0.799407	+	0.600790i	$0.205147\pi$
$521$	−4.57564	+	14.0824i	−0.200462	+	0.616960i	−0.999869	+	0.0161698i	$0.994853\pi$
$522$	−0.343831	−	2.17086i	−0.0150491	−	0.0950160i
$523$	−6.07643	−	38.3651i	−0.265704	−	1.67759i	−0.654344	−	0.756197i	$-0.727055\pi$
$523$	−6.07643	−	38.3651i	−0.265704	−	1.67759i	0.388640	−	0.921390i	$-0.372945\pi$
$524$	4.09168	−	12.5929i	0.178746	−	0.550124i
$525$		0			0
$526$	−9.04175	+	6.56922i	−0.394239	+	0.286431i
$527$	−25.1096	+	25.1096i	−1.09379	+	1.09379i
$528$	−6.97891	−	7.05453i	−0.303718	−	0.307009i
$529$			14.0073i			0.609011i
$530$		0			0
$531$	−0.844224	−	2.59825i	−0.0366362	−	0.112755i
$532$	18.7644	−	9.56095i	0.813541	−	0.414520i
$533$	−10.2768	+	1.62768i	−0.445136	+	0.0705027i
$534$	−5.02916	−	3.65390i	−0.217633	−	0.158120i
$535$		0			0
$536$	−3.24815	+	1.05539i	−0.140299	+	0.0455859i
$537$	−2.50583	−	0.396884i	−0.108134	−	0.0171268i
$538$	7.89771	+	7.89771i	0.340495	+	0.340495i
$539$	1.56850	−	4.74029i	0.0675603	−	0.204179i
$540$		0			0
$541$	10.2392	+	14.0930i	0.440217	+	0.605907i	0.970260	−	0.242064i	$-0.0778243\pi$
$541$	10.2392	+	14.0930i	0.440217	+	0.605907i	−0.530043	+	0.847971i	$0.677824\pi$
$542$	−0.308241	+	0.604957i	−0.0132401	+	0.0259851i
$543$	−2.24218	−	4.40053i	−0.0962213	−	0.188845i
$544$	−15.3469	+	21.1232i	−0.657994	+	0.905650i
$545$		0			0
$546$	4.51637	+	1.46746i	0.193283	+	0.0628014i
$547$	−34.9333	−	17.7994i	−1.49364	−	0.761048i	−0.499215	−	0.866478i	$-0.666378\pi$
$547$	−34.9333	−	17.7994i	−1.49364	−	0.761048i	−0.994427	+	0.105430i	$0.966378\pi$
$548$	−4.23522	+	26.7401i	−0.180920	+	1.14228i
$549$	11.8076			0.503936
$550$		0			0
$551$	10.8414			0.461858
$552$	0.981807	−	6.19888i	0.0417885	−	0.263842i
$553$	−39.6170	−	20.1859i	−1.68469	−	0.858391i
$554$	−6.62094	−	2.15127i	−0.281297	−	0.0913989i
$555$		0			0
$556$	−4.30973	+	5.93184i	−0.182773	+	0.251566i
$557$	−16.6620	−	32.7010i	−0.705991	−	1.38558i	−0.913291	−	0.407307i	$-0.866468\pi$
$557$	−16.6620	−	32.7010i	−0.705991	−	1.38558i	0.207301	−	0.978277i	$-0.433532\pi$
$558$	−2.54326	+	4.99143i	−0.107665	+	0.211304i
$559$	−12.3408	−	16.9856i	−0.521959	−	0.718416i
$560$		0			0
$561$	19.9070	+	0.107275i	0.840475	+	0.00452915i
$562$	−8.76280	−	8.76280i	−0.369636	−	0.369636i
$563$	−16.6732	−	2.64077i	−0.702690	−	0.111295i	−0.205143	−	0.978732i	$-0.565766\pi$
$563$	−16.6732	−	2.64077i	−0.702690	−	0.111295i	−0.497547	+	0.867437i	$0.665766\pi$
$564$	−7.02754	+	2.28339i	−0.295913	+	0.0961480i
$565$		0			0
$566$	2.92779	+	2.12716i	0.123064	+	0.0894114i
$567$	2.87512	−	0.455374i	0.120744	−	0.0191239i
$568$	−4.70243	+	2.39601i	−0.197310	+	0.100534i
$569$	−0.818531	−	2.51918i	−0.0343146	−	0.105609i	0.932432	−	0.361345i	$-0.117682\pi$
$569$	−0.818531	−	2.51918i	−0.0343146	−	0.105609i	−0.966747	+	0.255736i	$0.917682\pi$
$570$		0			0
$571$		−	29.8675i		−	1.24992i	−0.780658	−	0.624959i	$-0.785116\pi$
$571$		−	29.8675i		−	1.24992i	0.780658	−	0.624959i	$-0.214884\pi$
$572$	−16.8725	−	2.76562i	−0.705473	−	0.115636i
$573$	−3.28527	+	3.28527i	−0.137244	+	0.137244i
$574$	−4.09651	+	2.97629i	−0.170985	+	0.124228i
$575$		0			0
$576$	1.48921	−	4.58332i	0.0620505	−	0.190972i
$577$	0.0561437	+	0.354477i	0.00233729	+	0.0147571i	0.988829	−	0.149052i	$-0.0476220\pi$
$577$	0.0561437	+	0.354477i	0.00233729	+	0.0147571i	−0.986492	+	0.163809i	$0.947622\pi$
$578$	−0.821450	−	5.18643i	−0.0341678	−	0.215727i
$579$	−7.35878	+	22.6480i	−0.305821	+	0.941219i
$580$		0			0
$581$	−15.7673	+	11.4556i	−0.654138	+	0.475259i
$582$	3.96123	−	3.96123i	0.164198	−	0.164198i
$583$	0.740605	+	4.84483i	0.0306727	+	0.200652i
$584$			27.1896i			1.12511i
$585$		0			0
$586$	−2.21490	−	6.81675i	−0.0914965	−	0.281597i
$587$	23.0298	−	11.7343i	0.950543	−	0.484326i	0.0912603	−	0.995827i	$-0.470910\pi$
$587$	23.0298	−	11.7343i	0.950543	−	0.484326i	0.859282	+	0.511501i	$0.170910\pi$
$588$	−2.98428	+	0.472664i	−0.123070	+	0.0194923i
$589$	−22.3550	−	16.2418i	−0.921121	−	0.669233i
$590$		0			0
$591$	−0.327608	+	0.106446i	−0.0134760	+	0.00437861i
$592$	−3.01717	−	0.477873i	−0.124005	−	0.0196405i
$593$	9.56872	+	9.56872i	0.392940	+	0.392940i	0.875734	−	0.482794i	$-0.160378\pi$
$593$	9.56872	+	9.56872i	0.392940	+	0.392940i	−0.482794	+	0.875734i	$0.660378\pi$
$594$	8.26626	−	2.63671i	0.339169	−	0.108185i
$595$		0			0
$596$	18.6138	+	25.6197i	0.762451	+	1.04942i
$597$	−5.73203	+	11.2497i	−0.234596	+	0.460421i
$598$	−1.94565	−	3.81856i	−0.0795637	−	0.156153i
$599$	−6.65542	+	9.16040i	−0.271933	+	0.374284i	−0.923041	−	0.384701i	$-0.874304\pi$
$599$	−6.65542	+	9.16040i	−0.271933	+	0.374284i	0.651108	+	0.758985i	$0.274304\pi$
$600$		0			0
$601$	−15.6822	−	5.09545i	−0.639689	−	0.207848i	−0.0288267	−	0.999584i	$-0.509177\pi$
$601$	−15.6822	−	5.09545i	−0.639689	−	0.207848i	−0.610862	+	0.791737i	$0.709177\pi$
$602$	−9.10384	−	4.63864i	−0.371045	−	0.189057i
$603$	−0.494993	+	3.12526i	−0.0201577	+	0.127271i
$604$	31.3413			1.27526
$605$		0			0
$606$	−1.06223			−0.0431503
$607$	0.779724	−	4.92298i	0.0316480	−	0.199818i	−0.966798	−	0.255541i	$-0.917746\pi$
$607$	0.779724	−	4.92298i	0.0316480	−	0.199818i	0.998446	+	0.0557232i	$0.0177465\pi$
$608$	−18.1028	−	9.22383i	−0.734165	−	0.374076i
$609$	−8.35766	−	2.71557i	−0.338670	−	0.110040i
$610$		0			0
$611$	−6.33310	+	8.71677i	−0.256210	+	0.352643i
$612$	7.16989	+	14.0717i	0.289825	+	0.568814i
$613$	−8.29879	+	16.2873i	−0.335185	+	0.657837i	−0.995666	−	0.0930058i	$-0.970352\pi$
$613$	−8.29879	+	16.2873i	−0.335185	+	0.657837i	0.660481	+	0.750843i	$0.270352\pi$
$614$	−0.355174	−	0.488855i	−0.0143337	−	0.0197286i
$615$		0			0
$616$	−16.9274	+	5.39938i	−0.682025	+	0.217547i
$617$	−15.4942	−	15.4942i	−0.623773	−	0.623773i	0.322721	−	0.946494i	$-0.395402\pi$
$617$	−15.4942	−	15.4942i	−0.623773	−	0.623773i	−0.946494	+	0.322721i	$0.895402\pi$
$618$	−3.39142	−	0.537149i	−0.136423	−	0.0216073i
$619$	−46.8070	+	15.2085i	−1.88133	+	0.611282i	−0.895114	+	0.445837i	$0.852906\pi$
$619$	−46.8070	+	15.2085i	−1.88133	+	0.611282i	−0.986219	+	0.165445i	$0.947094\pi$
$620$		0			0
$621$	−12.9967	−	9.44269i	−0.521541	−	0.378922i
$622$	6.82342	−	1.08072i	0.273594	−	0.0433330i
$623$	29.0325	−	14.7928i	1.16316	−	0.592661i
$624$	2.70578	+	8.32754i	0.108318	+	0.333368i
$625$		0			0
$626$			0.361199i			0.0144364i
$627$	2.34082	+	15.3129i	0.0934832	+	0.611540i
$628$	−26.7363	+	26.7363i	−1.06689	+	1.06689i
$629$	4.95787	−	3.60210i	0.197683	−	0.143625i
$630$		0			0
$631$	−2.79731	+	8.60924i	−0.111359	+	0.342729i	−0.991170	−	0.132595i	$-0.957669\pi$
$631$	−2.79731	+	8.60924i	−0.111359	+	0.342729i	0.879811	+	0.475324i	$0.157669\pi$
$632$	4.38097	+	27.6604i	0.174266	+	1.10027i
$633$	−1.57836	−	9.96538i	−0.0627342	−	0.396088i
$634$	2.57536	−	7.92615i	0.102281	−	0.314788i
$635$		0			0
$636$	2.39942	−	1.74328i	0.0951431	−	0.0691255i
$637$	−3.11534	+	3.11534i	−0.123434	+	0.123434i
$638$	−4.22697	−	0.692856i	−0.167347	−	0.0274304i
$639$			4.88965i			0.193432i
$640$		0			0
$641$	−8.63030	−	26.5613i	−0.340876	−	1.04911i	−0.963755	−	0.266791i	$-0.914037\pi$
$641$	−8.63030	−	26.5613i	−0.340876	−	1.04911i	0.622878	−	0.782319i	$-0.285963\pi$
$642$	−0.215914	+	0.110014i	−0.00852146	+	0.00434190i
$643$	9.51085	−	1.50637i	0.375071	−	0.0594055i	0.0339470	−	0.999424i	$-0.489192\pi$
$643$	9.51085	−	1.50637i	0.375071	−	0.0594055i	0.341124	+	0.940018i	$0.389192\pi$
$644$	12.4635	+	9.05529i	0.491132	+	0.356828i
$645$		0			0
$646$	10.0300	−	3.25893i	0.394624	−	0.128221i
$647$	−30.5702	−	4.84185i	−1.20184	−	0.190353i	−0.476770	−	0.879028i	$-0.658193\pi$
$647$	−30.5702	−	4.84185i	−1.20184	−	0.190353i	−0.725070	+	0.688675i	$0.758193\pi$
$648$	−1.29645	−	1.29645i	−0.0509296	−	0.0509296i
$649$	−5.32406	−	0.0286903i	−0.208988	−	0.00112619i
$650$		0			0
$651$	13.1653	+	18.1204i	0.515987	+	0.710195i
$652$	8.33705	−	16.3624i	0.326504	−	0.640800i
$653$	−2.77406	−	5.44440i	−0.108557	−	0.213056i	0.830337	−	0.557262i	$-0.188148\pi$
$653$	−2.77406	−	5.44440i	−0.108557	−	0.213056i	−0.938894	+	0.344206i	$0.888148\pi$
$654$	3.09601	−	4.26129i	0.121063	−	0.166630i
$655$		0			0
$656$	−8.87952	−	2.88513i	−0.346687	−	0.112645i
$657$	22.4450	+	11.4363i	0.875665	+	0.446173i
$658$	−0.820257	+	5.17890i	−0.0319770	+	0.201895i
$659$	12.0647			0.469975			0.234988	−	0.971998i	$-0.424495\pi$
$659$	12.0647			0.469975			0.234988	+	0.971998i	$0.424495\pi$
$660$		0			0
$661$	−29.6228			−1.15219			−0.576097	−	0.817382i	$-0.695425\pi$
$661$	−29.6228			−1.15219			−0.576097	+	0.817382i	$0.695425\pi$
$662$	−1.13970	+	7.19579i	−0.0442957	+	0.279672i
$663$	−15.6512	−	7.97469i	−0.607843	−	0.309711i
$664$	11.6746	+	3.79331i	0.453063	+	0.147209i
$665$		0			0
$666$	0.568258	−	0.782140i	0.0220196	−	0.0303073i
$667$	3.60048	+	7.06635i	0.139411	+	0.273610i
$668$	9.03109	−	17.7245i	0.349423	−	0.685782i
$669$	−4.14023	−	5.69854i	−0.160071	−	0.220318i
$670$		0			0
$671$	7.22862	−	21.8461i	0.279058	−	0.843361i
$672$	11.6451	+	11.6451i	0.449220	+	0.449220i
$673$	4.97380	+	0.787773i	0.191726	+	0.0303664i	0.251559	−	0.967842i	$-0.419057\pi$
$673$	4.97380	+	0.787773i	0.191726	+	0.0303664i	−0.0598329	+	0.998208i	$0.519057\pi$
$674$	4.38316	−	1.42417i	0.168833	−	0.0548571i
$675$		0			0
$676$	−6.32105	−	4.59251i	−0.243117	−	0.176635i
$677$	35.9579	−	5.69516i	1.38197	−	0.218883i	0.579208	−	0.815180i	$-0.303362\pi$
$677$	35.9579	−	5.69516i	1.38197	−	0.218883i	0.802764	+	0.596297i	$0.203362\pi$
$678$	10.0472	−	5.11928i	0.385859	−	0.196605i
$679$	9.07388	+	27.9265i	0.348223	+	1.07172i
$680$		0			0
$681$			3.77894i			0.144809i
$682$	7.67804	+	7.76124i	0.294007	+	0.297193i
$683$	8.07353	−	8.07353i	0.308925	−	0.308925i	−0.535567	−	0.844492i	$-0.679902\pi$
$683$	8.07353	−	8.07353i	0.308925	−	0.308925i	0.844492	+	0.535567i	$0.179902\pi$
$684$	−9.94226	+	7.22348i	−0.380152	+	0.276197i
$685$		0			0
$686$	2.41816	−	7.44232i	0.0923257	−	0.284149i
$687$	−0.951773	−	6.00926i	−0.0363124	−	0.229267i
$688$	−2.94716	−	18.6076i	−0.112359	−	0.709408i
$689$	1.33638	−	4.11297i	0.0509122	−	0.156692i
$690$		0			0
$691$	9.61076	−	6.98263i	0.365611	−	0.265632i	−0.389778	−	0.920909i	$-0.627448\pi$
$691$	9.61076	−	6.98263i	0.365611	−	0.265632i	0.755388	+	0.655277i	$0.227448\pi$
$692$	16.4445	−	16.4445i	0.625125	−	0.625125i
$693$	−2.66271	+	16.2447i	−0.101148	+	0.617083i
$694$		−	9.39538i		−	0.356644i
$695$		0			0
$696$	1.71040	+	5.26407i	0.0648326	+	0.199534i
$697$	16.6886	−	8.50329i	0.632127	−	0.322085i
$698$	−7.17362	+	1.13619i	−0.271526	+	0.0430054i
$699$	−4.07258	−	2.95891i	−0.154039	−	0.111916i
$700$		0			0
$701$	−25.2475	+	8.20342i	−0.953586	+	0.309839i	−0.744172	−	0.667988i	$-0.767156\pi$
$701$	−25.2475	+	8.20342i	−0.953586	+	0.309839i	−0.209414	+	0.977827i	$0.567156\pi$
$702$	−7.56177	−	1.19767i	−0.285401	−	0.0452030i
$703$	3.37197	+	3.37197i	0.127176	+	0.127176i
$704$	−7.56826	−	5.56122i	−0.285239	−	0.209596i
$705$		0			0
$706$	0.724212	+	0.996792i	0.0272561	+	0.0375148i
$707$	2.52774	−	4.96097i	0.0950654	−	0.186576i
$708$	1.46268	+	2.87068i	0.0549710	+	0.107887i
$709$	10.4984	−	14.4498i	0.394275	−	0.542673i	−0.565021	−	0.825077i	$-0.691132\pi$
$709$	10.4984	−	14.4498i	0.394275	−	0.542673i	0.959296	+	0.282404i	$0.0911318\pi$
$710$		0			0
$711$	24.6763	+	8.01783i	0.925435	+	0.300692i
$712$	−18.2861	−	9.31723i	−0.685301	−	0.349178i
$713$	3.16212	−	19.9648i	0.118422	−	0.747689i
$714$	−8.54844			−0.319917
$715$		0			0
$716$	−3.92246			−0.146589
$717$	−1.86307	+	11.7630i	−0.0695778	+	0.439297i
$718$	−3.69497	−	1.88268i	−0.137895	−	0.0702611i
$719$	31.1609	+	10.1248i	1.16211	+	0.377592i	0.825691	−	0.564122i	$-0.190785\pi$
$719$	31.1609	+	10.1248i	1.16211	+	0.377592i	0.336416	+	0.941714i	$0.390785\pi$
$720$		0			0
$721$	10.5790	−	14.5608i	0.393984	−	0.542272i
$722$	−0.486681	−	0.955166i	−0.0181124	−	0.0355476i
$723$	−14.4098	+	28.2808i	−0.535905	+	1.05177i
$724$	−4.48818	−	6.17744i	−0.166802	−	0.229583i
$725$		0			0
$726$	0.0659608	−	6.12000i	0.00244803	−	0.227134i
$727$	−0.964903	−	0.964903i	−0.0357863	−	0.0357863i	0.688987	−	0.724773i	$-0.258056\pi$
$727$	−0.964903	−	0.964903i	−0.0357863	−	0.0357863i	−0.724773	+	0.688987i	$0.758056\pi$
$728$	15.4848	+	2.45255i	0.573905	+	0.0908976i
$729$	−19.0304	+	6.18335i	−0.704830	+	0.229013i
$730$		0			0
$731$	30.5763	+	22.2150i	1.13091	+	0.821651i
$732$	−13.7534	+	2.17832i	−0.508340	+	0.0805131i
$733$	10.5079	−	5.35405i	0.388119	−	0.197756i	−0.249033	−	0.968495i	$-0.580113\pi$
$733$	10.5079	−	5.35405i	0.388119	−	0.197756i	0.637151	+	0.770739i	$0.280113\pi$
$734$	3.20364	+	9.85979i	0.118249	+	0.363932i
$735$		0			0
$736$		−	14.8626i		−	0.547842i
$737$	5.47925	+	2.82911i	0.201831	+	0.104212i
$738$	2.08937	−	2.08937i	0.0769107	−	0.0769107i
$739$	34.8645	−	25.3305i	1.28251	−	0.931798i	0.282884	−	0.959154i	$-0.408709\pi$
$739$	34.8645	−	25.3305i	1.28251	−	0.931798i	0.999626	+	0.0273561i	$0.00870880\pi$
$740$		0			0
$741$	4.22388	−	12.9998i	0.155168	−	0.477558i
$742$	−0.329231	−	2.07868i	−0.0120865	−	0.0763109i
$743$	5.93105	+	37.4472i	0.217589	+	1.37380i	0.818509	+	0.574494i	$0.194801\pi$
$743$	5.93105	+	37.4472i	0.217589	+	1.37380i	−0.600920	+	0.799309i	$0.705199\pi$
$744$	4.35943	−	13.4170i	0.159825	−	0.491889i
$745$		0			0
$746$	−1.43840	+	1.04506i	−0.0526636	+	0.0382623i
$747$	8.04189	−	8.04189i	0.294237	−	0.294237i
$748$	30.4245	−	4.65085i	1.11243	−	0.170052i
$749$		−	1.27018i		−	0.0464114i
$750$		0			0
$751$	10.7881	+	33.2025i	0.393665	+	1.21158i	0.929996	+	0.367569i	$0.119810\pi$
$751$	10.7881	+	33.2025i	0.393665	+	1.21158i	−0.536331	+	0.844008i	$0.680190\pi$
$752$	−8.61441	+	4.38926i	−0.314135	+	0.160060i
$753$	11.1929	−	1.77278i	0.407891	−	0.0646036i
$754$	3.05772	+	2.22157i	0.111356	+	0.0809047i
$755$		0			0
$756$	26.1743	−	8.50454i	0.951950	−	0.309307i
$757$	−34.0513	−	5.39320i	−1.23762	−	0.196019i	−0.496883	−	0.867818i	$-0.665522\pi$
$757$	−34.0513	−	5.39320i	−1.23762	−	0.196019i	−0.740734	+	0.671798i	$0.765522\pi$
$758$	−5.72618	−	5.72618i	−0.207984	−	0.207984i
$759$	−9.20349	+	6.61125i	−0.334065	+	0.239973i
$760$		0			0
$761$	−8.17878	−	11.2571i	−0.296481	−	0.408071i	0.634625	−	0.772820i	$-0.281155\pi$
$761$	−8.17878	−	11.2571i	−0.296481	−	0.408071i	−0.931106	+	0.364750i	$0.881155\pi$
$762$	2.38192	−	4.67478i	0.0862879	−	0.169350i
$763$	12.5342	+	24.5997i	0.453767	+	0.890568i
$764$	−4.22213	+	5.81126i	−0.152751	+	0.210244i
$765$		0			0
$766$	5.26689	+	1.71132i	0.190300	+	0.0618323i
$767$	4.18586	+	2.13280i	0.151143	+	0.0770110i
$768$	−0.0262994	+	0.166048i	−0.000948998	+	0.00599174i
$769$	−13.3273			−0.480596			−0.240298	−	0.970699i	$-0.577245\pi$
$769$	−13.3273			−0.480596			−0.240298	+	0.970699i	$0.577245\pi$
$770$		0			0
$771$	−4.83143			−0.174000
$772$	−5.75948	+	36.3639i	−0.207288	+	1.30877i
$773$	−11.1372	−	5.67471i	−0.400579	−	0.204105i	0.242082	−	0.970256i	$-0.422170\pi$
$773$	−11.1372	−	5.67471i	−0.400579	−	0.204105i	−0.642661	+	0.766151i	$0.722170\pi$
$774$	5.67053	+	1.84247i	0.203823	+	0.0662261i
$775$		0			0
$776$	10.8709	−	14.9625i	0.390243	−	0.537124i
$777$	−1.75485	−	3.44409i	−0.0629549	−	0.123556i
$778$	−0.181256	+	0.355735i	−0.00649835	+	0.0127537i
$779$	8.56685	+	11.7913i	0.306939	+	0.422465i
$780$		0			0
$781$	9.04671	+	2.99345i	0.323717	+	0.107114i
$782$	5.45516	+	5.45516i	0.195076	+	0.195076i
$783$	13.9933	+	2.21631i	0.500078	+	0.0792046i
$784$	−3.75988	+	1.22166i	−0.134281	+	0.0436306i
$785$		0			0
$786$	−3.38355	−	2.45829i	−0.120687	−	0.0876843i
$787$	6.21530	−	0.984406i	0.221551	−	0.0350903i	−0.0446718	−	0.999002i	$-0.514224\pi$
$787$	6.21530	−	0.984406i	0.221551	−	0.0350903i	0.266223	+	0.963911i	$0.414224\pi$
$788$	−0.474521	+	0.241781i	−0.0169041	+	0.00861308i
$789$	−8.05781	−	24.7994i	−0.286866	−	0.882882i
$790$		0			0
$791$			59.1055i			2.10155i
$792$	9.26339	−	4.65723i	0.329160	−	0.165487i
$793$	−14.3574	+	14.3574i	−0.509846	+	0.509846i
$794$	−6.62104	+	4.81046i	−0.234972	+	0.170717i
$795$		0			0
$796$	−6.03213	+	18.5650i	−0.213803	+	0.658019i
$797$	0.276667	+	1.74680i	0.00980003	+	0.0618750i	0.992104	−	0.125420i	$-0.0400279\pi$
$797$	0.276667	+	1.74680i	0.00980003	+	0.0618750i	−0.982304	+	0.187295i	$0.940028\pi$
$798$	−1.04059	−	6.57006i	−0.0368367	−	0.232577i
$799$	5.99354	−	18.4462i	0.212036	−	0.652581i
$800$		0			0
$801$	−15.3828	+	11.1762i	−0.543523	+	0.394893i
$802$	9.82669	−	9.82669i	0.346992	−	0.346992i
$803$	34.9001	−	34.5259i	1.23160	−	1.21839i
$804$		−	3.73160i		−	0.131603i
$805$		0			0
$806$	−2.97684	−	9.16176i	−0.104855	−	0.322709i
$807$	−23.2186	+	11.8305i	−0.817335	+	0.416453i
$808$	−3.46372	+	0.548599i	−0.121853	+	0.0192996i
$809$	14.9294	+	10.8468i	0.524889	+	0.381354i	0.818443	−	0.574588i	$-0.194838\pi$
$809$	14.9294	+	10.8468i	0.524889	+	0.381354i	−0.293553	+	0.955943i	$0.594838\pi$
$810$		0			0
$811$	−12.4057	+	4.03086i	−0.435624	+	0.141543i	−0.518616	−	0.855007i	$-0.673552\pi$
$811$	−12.4057	+	4.03086i	−0.435624	+	0.141543i	0.0829918	+	0.996550i	$0.473552\pi$
$812$	−13.4192	−	2.12539i	−0.470920	−	0.0745865i
$813$	−1.12013	−	1.12013i	−0.0392847	−	0.0392847i
$814$	−1.09921	−	1.53020i	−0.0385273	−	0.0536336i
$815$		0			0
$816$	−9.26472	−	12.7518i	−0.324330	−	0.446402i
$817$	−13.3517	+	26.2042i	−0.467117	+	0.916768i
$818$	0.537108	+	1.05413i	0.0187796	+	0.0368569i
$819$	8.53770	−	11.7511i	0.298331	−	0.410618i
$820$		0			0
$821$	−24.7703	−	8.04835i	−0.864489	−	0.280889i	−0.156987	−	0.987601i	$-0.550178\pi$
$821$	−24.7703	−	8.04835i	−0.864489	−	0.280889i	−0.707502	+	0.706711i	$0.750178\pi$
$822$	7.61938	+	3.88227i	0.265756	+	0.135410i
$823$	−0.785962	+	4.96237i	−0.0273969	+	0.172977i	−0.997593	−	0.0693449i	$-0.977909\pi$
$823$	−0.785962	+	4.96237i	−0.0273969	+	0.172977i	0.970196	+	0.242322i	$0.0779091\pi$
$824$	−11.3361			−0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	−1.90393	+	12.0210i	−0.0662062	+	0.418010i	0.932218	+	0.361897i	$0.117871\pi$
$827$	−1.90393	+	12.0210i	−0.0662062	+	0.418010i	−0.998424	+	0.0561130i	$0.982129\pi$
$828$	−8.01010	−	4.08135i	−0.278370	−	0.141837i
$829$	−10.4727	−	3.40277i	−0.363730	−	0.118183i	0.121449	−	0.992598i	$-0.461246\pi$
$829$	−10.4727	−	3.40277i	−0.363730	−	0.118183i	−0.485180	+	0.874415i	$0.661246\pi$
$830$		0			0
$831$	9.54711	−	13.1405i	0.331185	−	0.455838i
$832$	3.76227	+	7.38386i	0.130433	+	0.255989i
$833$	3.60057	−	7.06651i	0.124752	−	0.244840i
$834$	1.36127	+	1.87363i	0.0471370	+	0.0648785i
$835$		0			0
$836$	7.27804	+	22.8171i	0.251716	+	0.789148i
$837$	−25.5338	−	25.5338i	−0.882578	−	0.882578i
$838$	−7.92807	−	1.25568i	−0.273871	−	0.0433769i
$839$	8.83685	−	2.87127i	0.305082	−	0.0991272i	−0.152475	−	0.988307i	$-0.548724\pi$
$839$	8.83685	−	2.87127i	0.305082	−	0.0991272i	0.457557	+	0.889180i	$0.348724\pi$
$840$		0			0
$841$	17.8031	+	12.9347i	0.613900	+	0.446024i
$842$	−6.01384	+	0.952498i	−0.207251	+	0.0328253i
$843$	25.7619	−	13.1264i	0.887288	−	0.452096i
$844$	−4.82040	−	14.8357i	−0.165925	−	0.510665i
$845$		0			0
$846$		−	3.05979i		−	0.105198i
$847$	28.4253	+	14.8715i	0.976706	+	0.510990i
$848$	2.74398	−	2.74398i	0.0942286	−	0.0942286i
$849$	−6.83093	+	4.96296i	−0.234437	+	0.170328i
$850$		0			0
$851$	−1.07798	+	3.31768i	−0.0369527	+	0.113729i
$852$	−0.902066	−	5.69542i	−0.0309043	−	0.195122i
$853$	−4.23097	−	26.7133i	−0.144866	−	0.914645i	−0.947867	−	0.318667i	$-0.896765\pi$
$853$	−4.23097	−	26.7133i	−0.144866	−	0.914645i	0.803001	−	0.595978i	$-0.203235\pi$
$854$	−3.05346	+	9.39759i	−0.104487	+	0.321579i
$855$		0			0
$856$	−0.647232	+	0.470242i	−0.0221220	+	0.0160725i
$857$	−33.1497	+	33.1497i	−1.13237	+	1.13237i	−0.142591	+	0.989782i	$0.545543\pi$
$857$	−33.1497	+	33.1497i	−1.13237	+	1.13237i	−0.989782	+	0.142591i	$0.954457\pi$
$858$	−2.47765	+	4.79856i	−0.0845857	+	0.163820i
$859$		−	47.2517i		−	1.61221i	−0.591775	−	0.806103i	$-0.701573\pi$
$859$		−	47.2517i		−	1.61221i	0.591775	−	0.806103i	$-0.298427\pi$
$860$		0			0
$861$	−3.65072	−	11.2358i	−0.124416	−	0.382914i
$862$	−8.63057	+	4.39749i	−0.293958	+	0.149779i
$863$	−15.3690	+	2.43422i	−0.523168	+	0.0828617i	−0.412432	−	0.910988i	$-0.635321\pi$
$863$	−15.3690	+	2.43422i	−0.523168	+	0.0828617i	−0.110736	+	0.993850i	$0.535321\pi$
$864$	−21.4801	−	15.6062i	−0.730768	−	0.530934i
$865$		0			0
$866$	−13.2947	+	4.31972i	−0.451773	+	0.146790i
$867$	12.1006	+	1.91655i	0.410959	+	0.0650896i
$868$	24.4863	+	24.4863i	0.831118	+	0.831118i
$869$	29.9413	−	40.7470i	1.01569	−	1.38225i
$870$		0			0
$871$	−3.19826	−	4.40203i	−0.108369	−	0.149157i
$872$	7.89464	−	15.4941i	0.267346	−	0.524696i
$873$	−7.77913	−	15.2674i	−0.263284	−	0.516723i
$874$	−3.52861	+	4.85671i	−0.119357	+	0.164281i
$875$		0			0
$876$	−28.2536	−	9.18015i	−0.954601	−	0.310169i
$877$	25.9562	+	13.2254i	0.876480	+	0.446589i	0.833521	−	0.552488i	$-0.186321\pi$
$877$	25.9562	+	13.2254i	0.876480	+	0.446589i	0.0429592	+	0.999077i	$0.486321\pi$
$878$	−0.238560	+	1.50621i	−0.00805101	+	0.0508321i
$879$	16.7229			0.564048
$880$		0			0
$881$	4.18815			0.141102			0.0705512	−	0.997508i	$-0.477524\pi$
$881$	4.18815			0.141102			0.0705512	+	0.997508i	$0.477524\pi$
$882$	0.195725	−	1.23576i	0.00659041	−	0.0416102i
$883$	40.7349	+	20.7555i	1.37084	+	0.698477i	0.975488	−	0.220053i	$-0.0706229\pi$
$883$	40.7349	+	20.7555i	1.37084	+	0.698477i	0.395351	+	0.918530i	$0.370623\pi$
$884$	−25.8286	−	8.39221i	−0.868709	−	0.282261i
$885$		0			0
$886$	−9.11003	+	12.5389i	−0.306057	+	0.421252i
$887$	15.6438	+	30.7027i	0.525267	+	1.03090i	0.989412	+	0.145136i	$0.0463619\pi$
$887$	15.6438	+	30.7027i	0.525267	+	1.03090i	−0.464144	+	0.885760i	$0.653638\pi$
$888$	−1.10529	+	2.16926i	−0.0370912	+	0.0727955i
$889$	16.1646	+	22.2487i	0.542143	+	0.746196i
$890$		0			0
$891$	−0.0178389	+	3.31037i	−0.000597626	+	0.110902i
$892$	−7.70048	−	7.70048i	−0.257831	−	0.257831i
$893$	14.9068	+	2.36100i	0.498836	+	0.0790078i
$894$	9.51300	−	3.09096i	0.318162	−	0.103377i
$895$		0			0
$896$	26.6503	+	19.3626i	0.890323	+	0.646857i
$897$	9.87594	−	1.56420i	0.329748	−	0.0522270i
$898$	15.2266	−	7.75836i	0.508119	−	0.258900i
$899$	5.50871	+	16.9541i	0.183726	+	0.565450i
$900$		0			0
$901$			7.78489i			0.259352i
$902$	−2.58659	−	5.14481i	−0.0861239	−	0.171303i
$903$	16.8566	−	16.8566i	0.560951	−	0.560951i
$904$	30.1177	−	21.8818i	1.00170	−	0.727778i
$905$		0			0
$906$	3.05911	−	9.41497i	0.101632	−	0.312791i
$907$	−6.02474	−	38.0387i	−0.200048	−	1.26306i	−0.859433	−	0.511249i	$-0.829183\pi$
$907$	−6.02474	−	38.0387i	−0.200048	−	1.26306i	0.659384	−	0.751806i	$-0.270817\pi$
$908$	0.913965	+	5.77055i	0.0303310	+	0.191502i
$909$	−1.00402	+	3.09005i	−0.0333012	+	0.102490i
$910$		0			0
$911$	29.8280	−	21.6713i	0.988244	−	0.718002i	0.0287085	−	0.999588i	$-0.490861\pi$
$911$	29.8280	−	21.6713i	0.988244	−	0.718002i	0.959536	+	0.281586i	$0.0908605\pi$
$912$	8.67283	−	8.67283i	0.287186	−	0.287186i
$913$	−9.95566	−	19.8022i	−0.329484	−	0.655356i
$914$		−	2.49056i		−	0.0823805i
$915$		0			0
$916$	−2.90677	−	8.94611i	−0.0960423	−	0.295588i
$917$	19.5326	−	9.95237i	0.645024	−	0.328656i
$918$	13.6122	−	2.15595i	0.449268	−	0.0711571i
$919$	24.5973	+	17.8710i	0.811392	+	0.589510i	0.914234	−	0.405187i	$-0.132794\pi$
$919$	24.5973	+	17.8710i	0.811392	+	0.589510i	−0.102842	+	0.994698i	$0.532794\pi$
$920$		0			0
$921$	1.34081	−	0.435657i	0.0441813	−	0.0143554i
$922$	6.01478	+	0.952647i	0.198086	+	0.0313738i
$923$	−5.94554	−	5.94554i	−0.195700	−	0.195700i
$924$	0.104612	−	19.4129i	0.00344148	−	0.638636i
$925$		0			0
$926$	−7.82350	−	10.7681i	−0.257096	−	0.353862i
$927$	−4.76812	+	9.35797i	−0.156606	+	0.307356i
$928$	5.95063	+	11.6788i	0.195339	+	0.383374i
$929$	−13.6936	+	18.8477i	−0.449273	+	0.618372i	−0.972241	−	0.233981i	$-0.924825\pi$
$929$	−13.6936	+	18.8477i	−0.449273	+	0.618372i	0.522968	+	0.852352i	$0.324825\pi$
$930$		0			0
$931$	5.86938	+	1.90708i	0.192361	+	0.0625020i
$932$	−6.93458	−	3.53335i	−0.227150	−	0.115739i
$933$	−2.52147	+	15.9199i	−0.0825493	+	0.521196i
$934$	19.3837			0.634254
$935$		0			0
$936$	−9.14869			−0.299034
$937$	−1.25828	+	7.94449i	−0.0411063	+	0.259535i	−0.999680	−	0.0253108i	$-0.991942\pi$
$937$	−1.25828	+	7.94449i	−0.0411063	+	0.259535i	0.958573	+	0.284846i	$0.0919425\pi$
$938$	−2.35937	−	1.20216i	−0.0770362	−	0.0392519i
$939$	−0.801481	−	0.260417i	−0.0261553	−	0.00849838i
$940$		0			0
$941$	28.1490	−	38.7438i	0.917631	−	1.26301i	−0.0468615	−	0.998901i	$-0.514922\pi$
$941$	28.1490	−	38.7438i	0.917631	−	1.26301i	0.964493	−	0.264110i	$-0.0850781\pi$
$942$	5.42198	+	10.6412i	0.176658	+	0.346710i
$943$	−4.84037	+	9.49976i	−0.157624	+	0.309355i
$944$	2.47782	+	3.41042i	0.0806460	+	0.111000i
$945$		0			0
$946$	6.88039	−	9.36352i	0.223701	−	0.304434i
$947$	−9.38618	−	9.38618i	−0.305010	−	0.305010i	0.537960	−	0.842970i	$-0.319195\pi$
$947$	−9.38618	−	9.38618i	−0.305010	−	0.305010i	−0.842970	+	0.537960i	$0.819195\pi$
$948$	−30.2219	−	4.78668i	−0.981563	−	0.155464i
$949$	−41.1978	+	13.3860i	−1.33734	+	0.434528i
$950$		0			0
$951$	15.7309	+	11.4292i	0.510109	+	0.370616i
$952$	−27.8746	+	4.41491i	−0.903422	+	0.143088i
$953$	−47.4428	+	24.1733i	−1.53682	+	0.783051i	−0.998228	−	0.0595128i	$-0.981045\pi$
$953$	−47.4428	+	24.1733i	−1.53682	+	0.783051i	−0.538597	+	0.842564i	$0.681045\pi$
$954$	0.379511	+	1.16802i	0.0122871	+	0.0378159i
$955$		0			0
$956$			18.4130i			0.595519i
$957$	4.58496	−	8.87987i	0.148211	−	0.287045i
$958$	−13.2098	+	13.2098i	−0.426790	+	0.426790i
$959$	−36.2628	+	26.3465i	−1.17099	+	0.850772i
$960$		0			0
$961$	4.46097	−	13.7294i	0.143902	−	0.442885i
$962$	0.260069	+	1.64201i	0.00838495	+	0.0529405i
$963$	0.115950	+	0.732081i	0.00373644	+	0.0235910i
$964$	−15.1642	+	46.6706i	−0.488406	+	1.50316i
$965$		0			0
$966$	3.93674	−	2.86021i	0.126662	−	0.0920256i
$967$	38.6475	−	38.6475i	1.24282	−	1.24282i	0.283994	−	0.958826i	$-0.408340\pi$
$967$	38.6475	−	38.6475i	1.24282	−	1.24282i	0.958826	−	0.283994i	$-0.0916596\pi$
$968$	−2.94563	−	19.9901i	−0.0946763	−	0.642505i
$969$			24.6055i			0.790443i
$970$		0			0
$971$	2.55556	+	7.86521i	0.0820119	+	0.252407i	0.983652	−	0.180081i	$-0.0576360\pi$
$971$	2.55556	+	7.86521i	0.0820119	+	0.252407i	−0.901640	+	0.432487i	$0.857636\pi$
$972$	−23.4395	+	11.9430i	−0.751823	+	0.383073i
$973$	−11.9898	+	1.89900i	−0.384375	+	0.0608790i
$974$	−10.7378	−	7.80149i	−0.344062	−	0.249976i
$975$		0			0
$976$	−17.3278	+	5.63014i	−0.554649	+	0.180216i
$977$	54.0805	+	8.56551i	1.73019	+	0.274035i	0.940579	−	0.339575i	$-0.110283\pi$
$977$	54.0805	+	8.56551i	1.73019	+	0.274035i	0.789610	+	0.613610i	$0.210283\pi$
$978$	−4.10153	−	4.10153i	−0.131152	−	0.131152i
$979$	11.2607	+	35.3029i	0.359892	+	1.12829i
$980$		0			0
$981$	−9.46980	−	13.0341i	−0.302347	−	0.416145i
$982$	0.880571	−	1.72822i	0.0281001	−	0.0551496i
$983$	6.19202	+	12.1525i	0.197495	+	0.387606i	0.968422	−	0.249318i	$-0.0802065\pi$
$983$	6.19202	+	12.1525i	0.197495	+	0.387606i	−0.770927	+	0.636924i	$0.780207\pi$
$984$	−4.37373	+	6.01992i	−0.139429	+	0.191908i
$985$		0			0
$986$	−6.47069	−	2.10245i	−0.206069	−	0.0669558i
$987$	−10.9003	−	5.55398i	−0.346960	−	0.176785i
$988$	3.30589	−	20.8726i	0.105174	−	0.664045i
$989$	−21.5139			−0.684102
$990$		0			0
$991$	6.43457			0.204401			0.102200	−	0.994764i	$-0.467412\pi$
$991$	6.43457			0.204401			0.102200	+	0.994764i	$0.467412\pi$
$992$	5.22613	−	32.9965i	0.165930	−	1.04764i
$993$	−15.1453	−	7.71694i	−0.480623	−	0.244890i
$994$	−3.89164	−	1.26447i	−0.123435	−	0.0401066i
$995$		0			0
$996$	−7.88351	+	10.8507i	−0.249799	+	0.343818i
$997$	9.65934	+	18.9575i	0.305914	+	0.600391i	0.991870	−	0.127252i	$-0.0406158\pi$
$997$	9.65934	+	18.9575i	0.305914	+	0.600391i	−0.685956	+	0.727643i	$0.740616\pi$
$998$	1.42445	−	2.79564i	0.0450901	−	0.0884943i
$999$	3.66296	+	5.04163i	0.115891	+	0.159510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.bm.b.107.3		32
5.2	odd	4		55.2.l.a.8.3	yes	32
5.3	odd	4	inner	275.2.bm.b.118.2		32
5.4	even	2		55.2.l.a.52.2	yes	32
11.7	odd	10	inner	275.2.bm.b.7.2		32
15.2	even	4		495.2.bj.a.118.2		32
15.14	odd	2		495.2.bj.a.217.3		32
20.7	even	4		880.2.cm.a.833.2		32
20.19	odd	2		880.2.cm.a.657.3		32
55.2	even	20		605.2.e.b.483.9		32
55.4	even	10		605.2.m.e.282.2		32
55.7	even	20		55.2.l.a.18.2	yes	32
55.9	even	10		605.2.e.b.362.9		32
55.14	even	10		605.2.m.c.457.3		32
55.17	even	20		605.2.m.c.233.3		32
55.18	even	20	inner	275.2.bm.b.18.3		32
55.19	odd	10		605.2.m.d.457.2		32
55.24	odd	10		605.2.e.b.362.8		32
55.27	odd	20		605.2.m.d.233.2		32
55.29	odd	10		55.2.l.a.7.3	✓	32
55.32	even	4		605.2.m.e.118.2		32
55.37	odd	20		605.2.m.e.403.3		32
55.39	odd	10		605.2.m.c.112.3		32
55.42	odd	20		605.2.e.b.483.8		32
55.47	odd	20		605.2.m.c.578.3		32
55.49	even	10		605.2.m.d.112.2		32
55.52	even	20		605.2.m.d.578.2		32
55.54	odd	2		605.2.m.e.602.3		32
165.29	even	10		495.2.bj.a.172.2		32
165.62	odd	20		495.2.bj.a.73.3		32
220.7	odd	20		880.2.cm.a.513.3		32
220.139	even	10		880.2.cm.a.337.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	55.29	odd	10
55.2.l.a.8.3	yes	32	5.2	odd	4
55.2.l.a.18.2	yes	32	55.7	even	20
55.2.l.a.52.2	yes	32	5.4	even	2
275.2.bm.b.7.2		32	11.7	odd	10	inner
275.2.bm.b.18.3		32	55.18	even	20	inner
275.2.bm.b.107.3		32	1.1	even	1	trivial
275.2.bm.b.118.2		32	5.3	odd	4	inner
495.2.bj.a.73.3		32	165.62	odd	20
495.2.bj.a.118.2		32	15.2	even	4
495.2.bj.a.172.2		32	165.29	even	10
495.2.bj.a.217.3		32	15.14	odd	2
605.2.e.b.362.8		32	55.24	odd	10
605.2.e.b.362.9		32	55.9	even	10
605.2.e.b.483.8		32	55.42	odd	20
605.2.e.b.483.9		32	55.2	even	20
605.2.m.c.112.3		32	55.39	odd	10
605.2.m.c.233.3		32	55.17	even	20
605.2.m.c.457.3		32	55.14	even	10
605.2.m.c.578.3		32	55.47	odd	20
605.2.m.d.112.2		32	55.49	even	10
605.2.m.d.233.2		32	55.27	odd	20
605.2.m.d.457.2		32	55.19	odd	10
605.2.m.d.578.2		32	55.52	even	20
605.2.m.e.118.2		32	55.32	even	4
605.2.m.e.282.2		32	55.4	even	10
605.2.m.e.403.3		32	55.37	odd	20
605.2.m.e.602.3		32	55.54	odd	2
880.2.cm.a.337.2		32	220.139	even	10
880.2.cm.a.513.3		32	220.7	odd	20
880.2.cm.a.657.3		32	20.19	odd	2
880.2.cm.a.833.2		32	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.bm (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0763931 - 0.482327i) q^{2} +(1.01518 + 0.517260i) q^{3} +(1.67531 + 0.544341i) q^{4} +(0.327041 - 0.450133i) q^{6} +(1.32402 + 2.59854i) q^{7} +(0.833936 - 1.63669i) q^{8} +(-1.00032 - 1.37683i) q^{9} +(-3.15977 + 1.00788i) q^{11} +(1.41917 + 1.41917i) q^{12} +(2.89049 + 0.457808i) q^{13} +(1.35449 - 0.440102i) q^{14} +(2.12449 + 1.54353i) q^{16} +(-5.20325 + 0.824113i) q^{17} +(-0.740500 + 0.377304i) q^{18} +(-1.26677 - 3.89873i) q^{19} +3.32285i q^{21} +(0.244743 + 1.60104i) q^{22} +(2.12046 - 2.12046i) q^{23} +(1.69319 - 1.23017i) q^{24} +(0.441627 - 1.35919i) q^{26} +(-0.838037 - 5.29116i) q^{27} +(0.803656 + 5.07408i) q^{28} +(-0.817241 + 2.51521i) q^{29} +(5.45328 - 3.96204i) q^{31} +(3.50456 - 3.50456i) q^{32} +(-3.72907 - 0.611244i) q^{33} +2.57262i q^{34} +(-0.926389 - 2.85113i) q^{36} +(-1.03649 + 0.528116i) q^{37} +(-1.97724 + 0.313163i) q^{38} +(2.69755 + 1.95989i) q^{39} +(-3.38136 + 1.09867i) q^{41} +(1.60270 + 0.253843i) q^{42} +(-5.07292 - 5.07292i) q^{43} +(-5.84223 - 0.0314826i) q^{44} +(-0.860769 - 1.18475i) q^{46} +(-1.67145 + 3.28041i) q^{47} +(1.35833 + 2.66588i) q^{48} +(-0.884888 + 1.21794i) q^{49} +(-5.70851 - 1.85481i) q^{51} +(4.59325 + 2.34038i) q^{52} +(0.231169 - 1.45955i) q^{53} -2.61609 q^{54} +5.35716 q^{56} +(0.730652 - 4.61316i) q^{57} +(1.15072 + 0.586323i) q^{58} +(1.52672 + 0.496061i) q^{59} +(-4.07810 + 5.61302i) q^{61} +(-1.49441 - 2.93294i) q^{62} +(2.25330 - 4.42234i) q^{63} +(1.66445 + 2.29092i) q^{64} +(-0.579695 + 1.75194i) q^{66} +(-1.31471 - 1.31471i) q^{67} +(-9.16564 - 1.45170i) q^{68} +(3.24948 - 1.05582i) q^{69} +(-2.32441 - 1.68878i) q^{71} +(-3.08765 + 0.489036i) q^{72} +(-13.1886 + 6.71992i) q^{73} +(0.175544 + 0.540270i) q^{74} -7.22113i q^{76} +(-6.80264 - 6.87635i) q^{77} +(1.15138 - 1.15138i) q^{78} +(-12.3342 + 8.96129i) q^{79} +(0.308439 - 0.949277i) q^{81} +(0.271606 + 1.71486i) q^{82} +(1.04540 + 6.60041i) q^{83} +(-1.80876 + 5.56680i) q^{84} +(-2.83434 + 2.05927i) q^{86} +(-2.13066 + 2.13066i) q^{87} +(-0.985459 + 6.01208i) q^{88} -11.1726i q^{89} +(2.63744 + 8.11720i) q^{91} +(4.70669 - 2.39818i) q^{92} +(7.58545 - 1.20142i) q^{93} +(1.45454 + 1.05679i) q^{94} +(5.37052 - 1.74499i) q^{96} +(9.94447 + 1.57505i) q^{97} +(0.519848 + 0.519848i) q^{98} +(4.54848 + 3.34226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 4 q^{3} - 20 q^{6} + 10 q^{8} - 24 q^{11} - 12 q^{12} + 10 q^{13} - 8 q^{16} + 10 q^{18} - 10 q^{22} + 24 q^{23} + 20 q^{26} + 16 q^{27} - 50 q^{28} - 28 q^{31} - 66 q^{33} + 24 q^{36}+ \cdots + 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 4 * q^3 - 20 * q^6 + 10 * q^8 - 24 * q^11 - 12 * q^12 + 10 * q^13 - 8 * q^16 + 10 * q^18 - 10 * q^22 + 24 * q^23 + 20 * q^26 + 16 * q^27 - 50 * q^28 - 28 * q^31 - 66 * q^33 + 24 * q^36 + 8 * q^37 - 10 * q^38 + 40 * q^41 + 10 * q^42 + 60 * q^46 + 28 * q^47 + 54 * q^48 + 20 * q^51 + 50 * q^52 + 24 * q^53 - 80 * q^56 - 30 * q^57 + 50 * q^58 - 60 * q^61 - 100 * q^62 + 30 * q^63 - 100 * q^66 + 8 * q^67 + 30 * q^68 + 24 * q^71 - 80 * q^72 - 50 * q^73 - 70 * q^77 - 60 * q^78 - 12 * q^81 + 10 * q^82 - 90 * q^83 + 100 * q^86 - 170 * q^88 + 20 * q^91 + 68 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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