LMFDB - Embedded newform 550.2.bh.b.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(7,550)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("550.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.bh (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	550.107
Dual form			550.2.bh.b.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.156434 + 0.987688i) q^{2} +(-2.86091 - 1.45771i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.88730 - 2.59765i) q^{6} +(0.692077 + 1.35828i) q^{7} +(0.453990 - 0.891007i) q^{8} +(4.29653 + 5.91367i) q^{9} +(-2.70495 + 1.91918i) q^{11} +(2.27043 + 2.27043i) q^{12} +(-1.04553 - 0.165595i) q^{13} +(-1.44982 + 0.471075i) q^{14} +(0.809017 + 0.587785i) q^{16} +(2.19616 - 0.347837i) q^{17} +(-6.51299 + 3.31853i) q^{18} +(-1.91500 - 5.89375i) q^{19} -4.89475i q^{21} +(-1.47241 - 2.97187i) q^{22} +(3.05791 - 3.05791i) q^{23} +(-2.59765 + 1.88730i) q^{24} +(0.327113 - 1.00675i) q^{26} +(-2.16472 - 13.6675i) q^{27} +(-0.238474 - 1.50566i) q^{28} +(1.39938 - 4.30686i) q^{29} +(2.32781 - 1.69125i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(10.5362 - 1.54760i) q^{33} +2.22353i q^{34} +(-2.25882 - 6.95193i) q^{36} +(-1.24018 + 0.631904i) q^{37} +(6.12076 - 0.969434i) q^{38} +(2.74977 + 1.99782i) q^{39} +(2.38365 - 0.774496i) q^{41} +(4.83449 + 0.765708i) q^{42} +(-6.40957 - 6.40957i) q^{43} +(3.16562 - 0.989379i) q^{44} +(2.54190 + 3.49862i) q^{46} +(2.03678 - 3.99740i) q^{47} +(-1.45771 - 2.86091i) q^{48} +(2.74855 - 3.78305i) q^{49} +(-6.79005 - 2.20622i) q^{51} +(0.943185 + 0.480577i) q^{52} +(-0.594995 + 3.75665i) q^{53} +13.8379 q^{54} +1.52443 q^{56} +(-3.11273 + 19.6530i) q^{57} +(4.03492 + 2.05589i) q^{58} +(4.27154 + 1.38791i) q^{59} +(3.48115 - 4.79140i) q^{61} +(1.30628 + 2.56372i) q^{62} +(-5.05887 + 9.92860i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.119682 + 10.6486i) q^{66} +(-5.40776 - 5.40776i) q^{67} +(-2.19616 - 0.347837i) q^{68} +(-13.2059 + 4.29086i) q^{69} +(-7.19862 - 5.23010i) q^{71} +(7.21970 - 1.14349i) q^{72} +(10.1633 - 5.17847i) q^{73} +(-0.430117 - 1.32376i) q^{74} +6.19706i q^{76} +(-4.47882 - 2.34584i) q^{77} +(-2.40339 + 2.40339i) q^{78} +(-4.69179 + 3.40879i) q^{79} +(-6.95367 + 21.4012i) q^{81} +(0.392075 + 2.47546i) q^{82} +(0.200087 + 1.26330i) q^{83} +(-1.51256 + 4.65519i) q^{84} +(7.33334 - 5.32798i) q^{86} +(-10.2816 + 10.2816i) q^{87} +(0.481987 + 3.28142i) q^{88} -10.5518i q^{89} +(-0.498662 - 1.53472i) q^{91} +(-3.85319 + 1.96330i) q^{92} +(-9.12499 + 1.44526i) q^{93} +(3.62956 + 2.63703i) q^{94} +(3.05372 - 0.992214i) q^{96} +(-6.92020 - 1.09605i) q^{97} +(3.30651 + 3.30651i) q^{98} +(-22.9713 - 7.75031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{3} + 20 q^{7} + 12 q^{11} + 16 q^{12} + 12 q^{16} + 20 q^{17} + 4 q^{22} + 8 q^{23} + 8 q^{26} - 8 q^{27} + 20 q^{28} + 16 q^{31} + 104 q^{33} - 4 q^{36} - 20 q^{37} + 36 q^{38} - 20 q^{41}+ \cdots - 72 q^{97}+O(q^{100}) $ 48 * q + 4 * q^3 + 20 * q^7 + 12 * q^11 + 16 * q^12 + 12 * q^16 + 20 * q^17 + 4 * q^22 + 8 * q^23 + 8 * q^26 - 8 * q^27 + 20 * q^28 + 16 * q^31 + 104 * q^33 - 4 * q^36 - 20 * q^37 + 36 * q^38 - 20 * q^41 + 20 * q^42 + 40 * q^46 - 40 * q^47 - 4 * q^48 + 40 * q^51 - 40 * q^52 - 8 * q^56 - 48 * q^58 + 80 * q^61 - 40 * q^62 - 100 * q^63 + 24 * q^66 - 20 * q^68 - 56 * q^71 + 20 * q^73 + 96 * q^77 - 16 * q^78 - 68 * q^81 - 56 * q^86 + 4 * q^88 - 68 * q^91 + 12 * q^92 - 76 * q^93 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$	−2.86091	−	1.45771i	−1.65175	−	0.841606i	−0.996261	−	0.0863983i	$-0.972464\pi$
$3$	−2.86091	−	1.45771i	−1.65175	−	0.841606i	−0.655485	−	0.755208i	$-0.727536\pi$
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$		0			0
$5$		0			0
$6$	1.88730	−	2.59765i	0.770488	−	1.06049i
$7$	0.692077	+	1.35828i	0.261581	+	0.513381i	0.984021	−	0.178052i	$-0.0569796\pi$
$7$	0.692077	+	1.35828i	0.261581	+	0.513381i	−0.722440	+	0.691433i	$0.756980\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$	4.29653	+	5.91367i	1.43218	+	1.97122i
$10$		0			0
$11$	−2.70495	+	1.91918i	−0.815572	+	0.578656i
$11$	−2.70495	+	1.91918i	−0.815572	+	0.578656i
$12$	2.27043	+	2.27043i	0.655416	+	0.655416i
$13$	−1.04553	−	0.165595i	−0.289977	−	0.0459279i	0.00975110	−	0.999952i	$-0.496896\pi$
$13$	−1.04553	−	0.165595i	−0.289977	−	0.0459279i	−0.299728	+	0.954025i	$0.596896\pi$
$14$	−1.44982	+	0.471075i	−0.387481	+	0.125900i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	2.19616	−	0.347837i	0.532646	−	0.0843629i	0.115683	−	0.993286i	$-0.463094\pi$
$17$	2.19616	−	0.347837i	0.532646	−	0.0843629i	0.416963	+	0.908923i	$0.363094\pi$
$18$	−6.51299	+	3.31853i	−1.53513	+	0.782186i
$19$	−1.91500	−	5.89375i	−0.439330	−	1.35212i	−0.888583	−	0.458715i	$-0.848310\pi$
$19$	−1.91500	−	5.89375i	−0.439330	−	1.35212i	0.449253	−	0.893405i	$-0.351690\pi$
$20$		0			0
$21$		−	4.89475i		−	1.06812i
$22$	−1.47241	−	2.97187i	−0.313919	−	0.633605i
$23$	3.05791	−	3.05791i	0.637617	−	0.637617i	−0.312350	−	0.949967i	$-0.601116\pi$
$23$	3.05791	−	3.05791i	0.637617	−	0.637617i	0.949967	+	0.312350i	$0.101116\pi$
$24$	−2.59765	+	1.88730i	−0.530243	+	0.385244i
$25$		0			0
$26$	0.327113	−	1.00675i	0.0641522	−	0.197440i
$27$	−2.16472	−	13.6675i	−0.416601	−	2.63031i
$28$	−0.238474	−	1.50566i	−0.0450673	−	0.284544i
$29$	1.39938	−	4.30686i	0.259859	−	0.799763i	−0.732975	−	0.680256i	$-0.761869\pi$
$29$	1.39938	−	4.30686i	0.259859	−	0.799763i	0.992833	−	0.119507i	$-0.0381314\pi$
$30$		0			0
$31$	2.32781	−	1.69125i	0.418087	−	0.303758i	−0.358781	−	0.933422i	$-0.616807\pi$
$31$	2.32781	−	1.69125i	0.418087	−	0.303758i	0.776868	+	0.629664i	$0.216807\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	10.5362	−	1.54760i	1.83412	−	0.269402i
$34$			2.22353i			0.381333i
$35$		0			0
$36$	−2.25882	−	6.95193i	−0.376470	−	1.15866i
$37$	−1.24018	+	0.631904i	−0.203885	+	0.103884i	−0.552952	−	0.833213i	$-0.686499\pi$
$37$	−1.24018	+	0.631904i	−0.203885	+	0.103884i	0.349067	+	0.937098i	$0.386499\pi$
$38$	6.12076	−	0.969434i	0.992919	−	0.157263i
$39$	2.74977	+	1.99782i	0.440316	+	0.319908i
$40$		0			0
$41$	2.38365	−	0.774496i	0.372264	−	0.120956i	−0.116909	−	0.993143i	$-0.537299\pi$
$41$	2.38365	−	0.774496i	0.372264	−	0.120956i	0.489173	+	0.872187i	$0.337299\pi$
$42$	4.83449	+	0.765708i	0.745978	+	0.118151i
$43$	−6.40957	−	6.40957i	−0.977450	−	0.977450i	0.0223009	−	0.999751i	$-0.492901\pi$
$43$	−6.40957	−	6.40957i	−0.977450	−	0.977450i	−0.999751	+	0.0223009i	$0.992901\pi$
$44$	3.16562	−	0.989379i	0.477235	−	0.149155i
$45$		0			0
$46$	2.54190	+	3.49862i	0.374782	+	0.515843i
$47$	2.03678	−	3.99740i	0.297095	−	0.583081i	−0.693413	−	0.720541i	$-0.743894\pi$
$47$	2.03678	−	3.99740i	0.297095	−	0.583081i	0.990507	+	0.137460i	$0.0438937\pi$
$48$	−1.45771	−	2.86091i	−0.210402	−	0.412936i
$49$	2.74855	−	3.78305i	0.392650	−	0.540436i
$50$		0			0
$51$	−6.79005	−	2.20622i	−0.950797	−	0.308933i
$52$	0.943185	+	0.480577i	0.130796	+	0.0666440i
$53$	−0.594995	+	3.75665i	−0.0817288	+	0.516016i	0.912530	+	0.409011i	$0.134126\pi$
$53$	−0.594995	+	3.75665i	−0.0817288	+	0.516016i	−0.994258	+	0.107005i	$0.965874\pi$
$54$	13.8379			1.88310
$55$		0			0
$56$	1.52443			0.203711
$57$	−3.11273	+	19.6530i	−0.412291	+	2.60310i
$58$	4.03492	+	2.05589i	0.529811	+	0.269952i
$59$	4.27154	+	1.38791i	0.556107	+	0.180690i	0.573569	−	0.819158i	$-0.305559\pi$
$59$	4.27154	+	1.38791i	0.556107	+	0.180690i	−0.0174620	+	0.999848i	$0.505559\pi$
$60$		0			0
$61$	3.48115	−	4.79140i	0.445716	−	0.613475i	−0.525754	−	0.850636i	$-0.676217\pi$
$61$	3.48115	−	4.79140i	0.445716	−	0.613475i	0.971470	+	0.237161i	$0.0762169\pi$
$62$	1.30628	+	2.56372i	0.165898	+	0.325593i
$63$	−5.05887	+	9.92860i	−0.637358	+	1.25089i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$		0			0
$66$	−0.119682	+	10.6486i	−0.0147318	+	1.31075i
$67$	−5.40776	−	5.40776i	−0.660663	−	0.660663i	0.294873	−	0.955536i	$-0.404723\pi$
$67$	−5.40776	−	5.40776i	−0.660663	−	0.660663i	−0.955536	+	0.294873i	$0.904723\pi$
$68$	−2.19616	−	0.347837i	−0.266323	−	0.0421814i
$69$	−13.2059	+	4.29086i	−1.58980	+	0.516559i
$70$		0			0
$71$	−7.19862	−	5.23010i	−0.854319	−	0.620699i	0.0720143	−	0.997404i	$-0.477057\pi$
$71$	−7.19862	−	5.23010i	−0.854319	−	0.620699i	−0.926334	+	0.376704i	$0.877057\pi$
$72$	7.21970	−	1.14349i	0.850850	−	0.134761i
$73$	10.1633	−	5.17847i	1.18953	−	0.606094i	0.256725	−	0.966485i	$-0.417357\pi$
$73$	10.1633	−	5.17847i	1.18953	−	0.606094i	0.932801	+	0.360391i	$0.117357\pi$
$74$	−0.430117	−	1.32376i	−0.0500001	−	0.153884i
$75$		0			0
$76$			6.19706i			0.710852i
$77$	−4.47882	−	2.34584i	−0.510409	−	0.267334i
$78$	−2.40339	+	2.40339i	−0.272130	+	0.272130i
$79$	−4.69179	+	3.40879i	−0.527868	+	0.383518i	−0.819560	−	0.572994i	$-0.805782\pi$
$79$	−4.69179	+	3.40879i	−0.527868	+	0.383518i	0.291692	+	0.956512i	$0.405782\pi$
$80$		0			0
$81$	−6.95367	+	21.4012i	−0.772631	+	2.37791i
$82$	0.392075	+	2.47546i	0.0432974	+	0.273369i
$83$	0.200087	+	1.26330i	0.0219624	+	0.138665i	0.996233	−	0.0867161i	$-0.0276373\pi$
$83$	0.200087	+	1.26330i	0.0219624	+	0.138665i	−0.974271	+	0.225381i	$0.927637\pi$
$84$	−1.51256	+	4.65519i	−0.165034	+	0.507922i
$85$		0			0
$86$	7.33334	−	5.32798i	0.790774	−	0.574531i
$87$	−10.2816	+	10.2816i	−1.10231	+	1.10231i
$88$	0.481987	+	3.28142i	0.0513800	+	0.349800i
$89$		−	10.5518i		−	1.11849i	−0.829004	−	0.559243i	$-0.811092\pi$
$89$		−	10.5518i		−	1.11849i	0.829004	−	0.559243i	$-0.188908\pi$
$90$		0			0
$91$	−0.498662	−	1.53472i	−0.0522740	−	0.160883i
$92$	−3.85319	+	1.96330i	−0.401722	+	0.204688i
$93$	−9.12499	+	1.44526i	−0.946218	+	0.149866i
$94$	3.62956	+	2.63703i	0.374361	+	0.271989i
$95$		0			0
$96$	3.05372	−	0.992214i	0.311669	−	0.101267i
$97$	−6.92020	−	1.09605i	−0.702639	−	0.111287i	−0.205116	−	0.978738i	$-0.565757\pi$
$97$	−6.92020	−	1.09605i	−0.702639	−	0.111287i	−0.497523	+	0.867451i	$0.665757\pi$
$98$	3.30651	+	3.30651i	0.334008	+	0.334008i
$99$	−22.9713	−	7.75031i	−2.30870	−	0.778936i
$100$		0			0
$101$	10.3519	+	14.2481i	1.03005	+	1.41774i	0.904912	+	0.425599i	$0.139937\pi$
$101$	10.3519	+	14.2481i	1.03005	+	1.41774i	0.125136	+	0.992140i	$0.460063\pi$
$102$	3.24125	−	6.36132i	0.320932	−	0.629865i
$103$	−1.45835	−	2.86217i	−0.143695	−	0.282018i	0.807930	−	0.589278i	$-0.200588\pi$
$103$	−1.45835	−	2.86217i	−0.143695	−	0.282018i	−0.951625	+	0.307260i	$0.900588\pi$
$104$	−0.622206	+	0.856394i	−0.0610124	+	0.0839763i
$105$		0			0
$106$	−3.61732	−	1.17534i	−0.351345	−	0.114159i
$107$	14.7175	+	7.49892i	1.42279	+	0.724948i	0.984745	−	0.174006i	$-0.0556711\pi$
$107$	14.7175	+	7.49892i	1.42279	+	0.724948i	0.438045	+	0.898953i	$0.355671\pi$
$108$	−2.16472	+	13.6675i	−0.208300	+	1.31516i
$109$	1.88801			0.180839			0.0904195	−	0.995904i	$-0.471179\pi$
$109$	1.88801			0.180839			0.0904195	+	0.995904i	$0.471179\pi$
$110$		0			0
$111$	4.46917			0.424195
$112$	−0.238474	+	1.50566i	−0.0225336	+	0.142272i
$113$	3.55455	+	1.81113i	0.334384	+	0.170377i	0.613118	−	0.789991i	$-0.289915\pi$
$113$	3.55455	+	1.81113i	0.334384	+	0.170377i	−0.278734	+	0.960368i	$0.589915\pi$
$114$	−18.9241	−	6.14881i	−1.77240	−	0.575889i
$115$		0			0
$116$	−2.66178	+	3.66363i	−0.247140	+	0.340160i
$117$	−3.51287	−	6.89439i	−0.324765	−	0.637387i
$118$	−2.03903	+	4.00183i	−0.187708	+	0.368398i
$119$	1.99237	+	2.74226i	0.182640	+	0.251383i
$120$		0			0
$121$	3.63346	−	10.3826i	0.330314	−	0.943871i
$122$	4.18783	+	4.18783i	0.379149	+	0.379149i
$123$	−7.94840	−	1.25890i	−0.716683	−	0.113511i
$124$	−2.73650	+	0.889144i	−0.245745	+	0.0798475i
$125$		0			0
$126$	−9.01498	−	6.54977i	−0.803118	−	0.583500i
$127$	16.7564	−	2.65395i	1.48689	−	0.235500i	0.640456	−	0.767995i	$-0.278746\pi$
$127$	16.7564	−	2.65395i	1.48689	−	0.235500i	0.846433	+	0.532495i	$0.178746\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$	8.99392	+	27.6805i	0.791871	+	2.43713i
$130$		0			0
$131$			9.77651i			0.854177i	0.904210	+	0.427089i	$0.140461\pi$
$131$			9.77651i			0.854177i	−0.904210	+	0.427089i	$0.859539\pi$
$132$	−10.4988	−	1.78401i	−0.913800	−	0.155278i
$133$	6.68003	−	6.68003i	0.579232	−	0.579232i
$134$	6.18714	−	4.49522i	0.534488	−	0.388328i
$135$		0			0
$136$	0.687109	−	2.11471i	0.0589191	−	0.181334i
$137$	0.386515	+	2.44036i	0.0330222	+	0.208494i	0.998683	−	0.0513136i	$-0.0163408\pi$
$137$	0.386515	+	2.44036i	0.0330222	+	0.208494i	−0.965660	+	0.259808i	$0.916341\pi$
$138$	−2.17217	−	13.7146i	−0.184908	−	1.16746i
$139$	2.32161	−	7.14518i	0.196916	−	0.606046i	−0.803032	−	0.595935i	$-0.796781\pi$
$139$	2.32161	−	7.14518i	0.196916	−	0.606046i	0.999949	−	0.0101112i	$-0.00321854\pi$
$140$		0			0
$141$	−11.6541	+	8.46717i	−0.981449	+	0.713065i
$142$	6.29183	−	6.29183i	0.527998	−	0.527998i
$143$	3.14590	−	1.55864i	0.263074	−	0.130340i
$144$			7.30970i			0.609141i
$145$		0			0
$146$	3.52482	+	10.8483i	0.291716	+	0.897810i
$147$	−13.3779	+	6.81639i	−1.10339	+	0.562206i
$148$	1.37475	−	0.217739i	0.113004	−	0.0178981i
$149$	−0.0269615	−	0.0195887i	−0.00220877	−	0.00160477i	0.586680	−	0.809819i	$-0.300435\pi$
$149$	−0.0269615	−	0.0195887i	−0.00220877	−	0.00160477i	−0.588889	+	0.808214i	$0.700435\pi$
$150$		0			0
$151$	−20.1481	+	6.54653i	−1.63963	+	0.532749i	−0.976457	−	0.215714i	$-0.930792\pi$
$151$	−20.1481	+	6.54653i	−1.63963	+	0.532749i	−0.663176	+	0.748463i	$0.730792\pi$
$152$	−6.12076	−	0.969434i	−0.496459	−	0.0786315i
$153$	11.4929	+	11.4929i	0.929142	+	0.929142i
$154$	3.01760	−	4.05671i	0.243165	−	0.326899i
$155$		0			0
$156$	−1.99782	−	2.74977i	−0.159954	−	0.220158i
$157$	0.891858	−	1.75037i	0.0711780	−	0.139695i	−0.852676	−	0.522441i	$-0.825022\pi$
$157$	0.891858	−	1.75037i	0.0711780	−	0.139695i	0.923854	+	0.382746i	$0.125022\pi$
$158$	−2.63286	−	5.16728i	−0.209459	−	0.411087i
$159$	7.17831	−	9.88010i	0.569277	−	0.783543i
$160$		0			0
$161$	6.26979	+	2.03718i	0.494129	+	0.160552i
$162$	−20.0499	−	10.2160i	−1.57527	−	0.802641i
$163$	0.340601	−	2.15047i	0.0266779	−	0.168438i	−0.970752	−	0.240084i	$-0.922825\pi$
$163$	0.340601	−	2.15047i	0.0266779	−	0.168438i	0.997430	+	0.0716458i	$0.0228251\pi$
$164$	−2.50632			−0.195711
$165$		0			0
$166$	−1.27905			−0.0992732
$167$	3.35583	−	21.1879i	0.259682	−	1.63957i	−0.421053	−	0.907036i	$-0.638339\pi$
$167$	3.35583	−	21.1879i	0.259682	−	1.63957i	0.680735	−	0.732530i	$-0.261661\pi$
$168$	−4.36126	−	2.22217i	−0.336478	−	0.171444i
$169$	−11.2980	−	3.67095i	−0.869079	−	0.282381i
$170$		0			0
$171$	26.6259	−	36.6474i	2.03613	−	2.80249i
$172$	4.11520	+	8.07653i	0.313781	+	0.615830i
$173$	−5.98965	+	11.7553i	−0.455384	+	0.893742i	0.543151	+	0.839635i	$0.317231\pi$
$173$	−5.98965	+	11.7553i	−0.455384	+	0.893742i	−0.998535	+	0.0541069i	$0.982769\pi$
$174$	−8.54665	−	11.7634i	−0.647920	−	0.891785i
$175$		0			0
$176$	−3.31642	−	0.0372739i	−0.249984	−	0.00280962i
$177$	−10.1973	−	10.1973i	−0.766477	−	0.766477i
$178$	10.4219	+	1.65066i	0.781152	+	0.123722i
$179$	12.8887	−	4.18779i	0.963346	−	0.313010i	0.215219	−	0.976566i	$-0.430953\pi$
$179$	12.8887	−	4.18779i	0.963346	−	0.313010i	0.748127	+	0.663555i	$0.230953\pi$
$180$		0			0
$181$	−13.9517	−	10.1365i	−1.03702	−	0.753441i	−0.0673204	−	0.997731i	$-0.521445\pi$
$181$	−13.9517	−	10.1365i	−1.03702	−	0.753441i	−0.969702	+	0.244290i	$0.921445\pi$
$182$	1.59384	−	0.252439i	0.118143	−	0.0187120i
$183$	−16.9437	+	8.63324i	−1.25251	+	0.638188i
$184$	−1.33635	−	4.11287i	−0.0985173	−	0.303205i
$185$		0			0
$186$		−	9.23874i		−	0.677417i
$187$	−5.27292	+	5.15571i	−0.385594	+	0.377023i
$188$	−3.17236	+	3.17236i	−0.231368	+	0.231368i
$189$	17.0661	−	12.3993i	1.24138	−	0.901914i
$190$		0			0
$191$	−3.89136	+	11.9764i	−0.281569	+	0.866580i	0.705837	+	0.708374i	$0.250571\pi$
$191$	−3.89136	+	11.9764i	−0.281569	+	0.866580i	−0.987406	+	0.158206i	$0.949429\pi$
$192$	0.502291	+	3.17134i	0.0362497	+	0.228872i
$193$	−0.599973	−	3.78808i	−0.0431870	−	0.272672i	0.956640	−	0.291273i	$-0.0940788\pi$
$193$	−0.599973	−	3.78808i	−0.0431870	−	0.272672i	−0.999827	+	0.0186009i	$0.994079\pi$
$194$	2.16511	−	6.66354i	0.155446	−	0.478414i
$195$		0			0
$196$	−3.78305	+	2.74855i	−0.270218	+	0.196325i
$197$	7.40013	−	7.40013i	0.527238	−	0.527238i	−0.392510	−	0.919748i	$-0.628393\pi$
$197$	7.40013	−	7.40013i	0.527238	−	0.527238i	0.919748	+	0.392510i	$0.128393\pi$
$198$	11.2484	−	21.4761i	0.799389	−	1.52624i
$199$			9.10742i			0.645608i	0.946466	+	0.322804i	$0.104625\pi$
$199$			9.10742i			0.645608i	−0.946466	+	0.322804i	$0.895375\pi$
$200$		0			0
$201$	7.58818	+	23.3540i	0.535229	+	1.64727i
$202$	−15.6921	+	7.99551i	−1.10409	+	0.562562i
$203$	6.81839	−	1.07993i	0.478557	−	0.0757960i
$204$	5.77596	+	4.19648i	0.404398	+	0.293812i
$205$		0			0
$206$	3.05507	−	0.992651i	0.212857	−	0.0691613i
$207$	31.2218	+	4.94505i	2.17007	+	0.343705i
$208$	−0.748516	−	0.748516i	−0.0519002	−	0.0519002i
$209$	16.4912	+	12.2671i	1.14072	+	0.848530i
$210$		0			0
$211$	−14.7378	−	20.2849i	−1.01459	−	1.39647i	−0.915926	−	0.401347i	$-0.868542\pi$
$211$	−14.7378	−	20.2849i	−1.01459	−	1.39647i	−0.0986665	−	0.995121i	$-0.531458\pi$
$212$	1.72674	−	3.38892i	0.118593	−	0.232752i
$213$	12.9706	+	25.4563i	0.888734	+	1.74424i
$214$	−9.70891	+	13.3632i	−0.663687	+	0.913487i
$215$		0			0
$216$	−13.1606	−	4.27614i	−0.895466	−	0.290954i
$217$	3.90821	+	1.99133i	0.265307	+	0.135181i
$218$	−0.295350	+	1.86477i	−0.0200037	+	0.126298i
$219$	−36.6250			−2.47489
$220$		0			0
$221$	−2.35374			−0.158330
$222$	−0.699133	+	4.41415i	−0.0469227	+	0.296258i
$223$	−4.44282	−	2.26373i	−0.297513	−	0.151590i	0.298862	−	0.954296i	$-0.403393\pi$
$223$	−4.44282	−	2.26373i	−0.297513	−	0.151590i	−0.596375	+	0.802706i	$0.703393\pi$
$224$	−1.44982	−	0.471075i	−0.0968702	−	0.0314750i
$225$		0			0
$226$	−2.34489	+	3.22746i	−0.155980	+	0.214688i
$227$	−0.926486	−	1.81833i	−0.0614931	−	0.120687i	0.858214	−	0.513292i	$-0.171574\pi$
$227$	−0.926486	−	1.81833i	−0.0614931	−	0.120687i	−0.919707	+	0.392605i	$0.871574\pi$
$228$	9.03349	−	17.7292i	0.598257	−	1.17415i
$229$	−0.895888	−	1.23308i	−0.0592020	−	0.0814845i	0.778389	−	0.627782i	$-0.216037\pi$
$229$	−0.895888	−	1.23308i	−0.0592020	−	0.0814845i	−0.837591	+	0.546297i	$0.816037\pi$
$230$		0			0
$231$	9.39394	+	13.2400i	0.618076	+	0.871131i
$232$	−3.20213	−	3.20213i	−0.210230	−	0.210230i
$233$	−21.9164	−	3.47122i	−1.43579	−	0.227407i	−0.610457	−	0.792050i	$-0.709014\pi$
$233$	−21.9164	−	3.47122i	−1.43579	−	0.227407i	−0.825336	+	0.564642i	$0.809014\pi$
$234$	7.35904	−	2.39110i	0.481076	−	0.156311i
$235$		0			0
$236$	−3.63358	−	2.63995i	−0.236526	−	0.171846i
$237$	18.3918	−	2.91297i	1.19468	−	0.189218i
$238$	−3.02018	+	1.53886i	−0.195769	+	0.0997492i
$239$	7.65870	+	23.5711i	0.495400	+	1.52468i	0.816332	+	0.577583i	$0.196004\pi$
$239$	7.65870	+	23.5711i	0.495400	+	1.52468i	−0.320932	+	0.947102i	$0.603996\pi$
$240$		0			0
$241$		−	0.0562577i		−	0.00362387i	−0.999998	−	0.00181194i	$-0.999423\pi$
$241$		−	0.0562577i		−	0.00362387i	0.999998	−	0.00181194i	$-0.000576758\pi$
$242$	9.68636	+	5.21292i	0.622662	+	0.335099i
$243$	21.7359	−	21.7359i	1.39436	−	1.39436i
$244$	−4.79140	+	3.48115i	−0.306738	+	0.222858i
$245$		0			0
$246$	2.48681	−	7.65360i	0.158553	−	0.487976i
$247$	1.02620	+	6.47920i	0.0652958	+	0.412262i
$248$	−0.450114	−	2.84191i	−0.0285822	−	0.180461i
$249$	1.26909	−	3.90585i	0.0804251	−	0.247523i
$250$		0			0
$251$	6.81505	−	4.95143i	0.430162	−	0.312531i	−0.351551	−	0.936169i	$-0.614346\pi$
$251$	6.81505	−	4.95143i	0.430162	−	0.312531i	0.781714	+	0.623637i	$0.214346\pi$
$252$	7.87938	−	7.87938i	0.496354	−	0.496354i
$253$	−2.40278	+	14.1402i	−0.151062	+	0.888984i
$254$			16.9653i			1.06449i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.35527	−	4.76675i	0.583566	−	0.297342i	−0.137175	−	0.990547i	$-0.543802\pi$
$257$	9.35527	−	4.76675i	0.583566	−	0.297342i	0.720740	+	0.693205i	$0.243802\pi$
$258$	−28.7466	+	4.55302i	−1.78969	+	0.283458i
$259$	−1.71660	−	1.24718i	−0.106664	−	0.0774963i
$260$		0			0
$261$	31.4818	−	10.2291i	1.94868	−	0.633163i
$262$	−9.65614	−	1.52938i	−0.596558	−	0.0944856i
$263$	3.20922	+	3.20922i	0.197889	+	0.197889i	0.799095	−	0.601205i	$-0.205313\pi$
$263$	3.20922	+	3.20922i	0.197889	+	0.197889i	−0.601205	+	0.799095i	$0.705313\pi$
$264$	3.40442	−	10.0904i	0.209527	−	0.621022i
$265$		0			0
$266$	5.55280	+	7.64278i	0.340464	+	0.468609i
$267$	−15.3814	+	30.1877i	−0.941325	+	1.84746i
$268$	3.47200	+	6.81417i	0.212086	+	0.416242i
$269$	15.2248	−	20.9551i	0.928272	−	1.27766i	−0.0322573	−	0.999480i	$-0.510270\pi$
$269$	15.2248	−	20.9551i	0.928272	−	1.27766i	0.960530	−	0.278178i	$-0.0897304\pi$
$270$		0			0
$271$	20.4415	+	6.64186i	1.24173	+	0.403464i	0.854952	−	0.518707i	$-0.173586\pi$
$271$	20.4415	+	6.64186i	1.24173	+	0.403464i	0.386783	+	0.922171i	$0.373586\pi$
$272$	1.98118	+	1.00946i	0.120127	+	0.0612077i
$273$	−0.810549	+	5.11760i	−0.0490566	+	0.309731i
$274$	−2.47078			−0.149265
$275$		0			0
$276$	13.8855			0.835810
$277$	−2.14809	+	13.5625i	−0.129066	+	0.814893i	0.835198	+	0.549950i	$0.185353\pi$
$277$	−2.14809	+	13.5625i	−0.129066	+	0.814893i	−0.964264	+	0.264943i	$0.914647\pi$
$278$	6.69403	+	3.41078i	0.401481	+	0.204565i
$279$	20.0030	+	6.49937i	1.19755	+	0.389107i
$280$		0			0
$281$	5.82266	−	8.01420i	0.347351	−	0.478087i	−0.599220	−	0.800585i	$-0.704522\pi$
$281$	5.82266	−	8.01420i	0.347351	−	0.478087i	0.946570	+	0.322498i	$0.104522\pi$
$282$	−6.53983	−	12.8351i	−0.389441	−	0.764322i
$283$	0.935154	−	1.83534i	0.0555891	−	0.109100i	−0.861541	−	0.507689i	$-0.830500\pi$
$283$	0.935154	−	1.83534i	0.0555891	−	0.109100i	0.917130	+	0.398589i	$0.130500\pi$
$284$	5.23010	+	7.19862i	0.310350	+	0.427160i
$285$		0			0
$286$	1.04732	+	3.35100i	0.0619292	+	0.198149i
$287$	2.70165	+	2.70165i	0.159473	+	0.159473i
$288$	−7.21970	−	1.14349i	−0.425425	−	0.0673807i
$289$	−11.4658	+	3.72548i	−0.674461	+	0.219146i
$290$		0			0
$291$	18.2003	+	13.2233i	1.06692	+	0.775164i
$292$	−11.2661	+	1.78438i	−0.659300	+	0.104423i
$293$	17.5019	−	8.91767i	1.02247	−	0.520976i	0.139412	−	0.990234i	$-0.455479\pi$
$293$	17.5019	−	8.91767i	1.02247	−	0.520976i	0.883061	+	0.469259i	$0.155479\pi$
$294$	−4.63970	−	14.2795i	−0.270593	−	0.832799i
$295$		0			0
$296$			1.39189i			0.0809018i
$297$	32.0859	+	32.8154i	1.86181	+	1.90414i
$298$	0.0235652	−	0.0235652i	0.00136510	−	0.00136510i
$299$	−3.70350	+	2.69075i	−0.214179	+	0.155610i
$300$		0			0
$301$	4.27006	−	13.1419i	0.246122	−	0.757486i
$302$	−3.31407	−	20.9242i	−0.190703	−	1.20405i
$303$	−8.84616	−	55.8524i	−0.508199	−	3.20864i
$304$	1.91500	−	5.89375i	0.109833	−	0.338030i
$305$		0			0
$306$	−13.1492	+	9.55348i	−0.751692	+	0.546136i
$307$	−8.35315	+	8.35315i	−0.476740	+	0.476740i	−0.904087	−	0.427348i	$-0.859448\pi$
$307$	−8.35315	+	8.35315i	−0.476740	+	0.476740i	0.427348	+	0.904087i	$0.359448\pi$
$308$	3.53470	+	3.61506i	0.201408	+	0.205987i
$309$			10.3142i			0.586757i
$310$		0			0
$311$	−4.29712	−	13.2252i	−0.243667	−	0.749931i	−0.995853	−	0.0909796i	$-0.971000\pi$
$311$	−4.29712	−	13.2252i	−0.243667	−	0.749931i	0.752185	−	0.658952i	$-0.229000\pi$
$312$	3.02844	−	1.54307i	0.171452	−	0.0873591i
$313$	−29.8201	+	4.72303i	−1.68553	+	0.266962i	−0.924341	−	0.381569i	$-0.875384\pi$
$313$	−29.8201	+	4.72303i	−1.68553	+	0.266962i	−0.761189	+	0.648530i	$0.775384\pi$
$314$	1.58930	+	1.15470i	0.0896895	+	0.0651633i
$315$		0			0
$316$	5.51553	−	1.79211i	0.310273	−	0.100814i
$317$	−30.2851	−	4.79669i	−1.70098	−	0.269409i	−0.770951	−	0.636894i	$-0.780219\pi$
$317$	−30.2851	−	4.79669i	−1.70098	−	0.269409i	−0.930029	+	0.367485i	$0.880219\pi$
$318$	8.63552	+	8.63552i	0.484256	+	0.484256i
$319$	4.48040	+	14.3355i	0.250854	+	0.802633i
$320$		0			0
$321$	−31.1741	−	42.9074i	−1.73997	−	2.39486i
$322$	−2.99291	+	5.87392i	−0.166788	+	0.327341i
$323$	−6.25570	−	12.2775i	−0.348076	−	0.683139i
$324$	13.2267	−	18.2050i	0.734815	−	1.01139i
$325$		0			0
$326$	2.07071	+	0.672816i	0.114686	+	0.0372638i
$327$	−5.40143	−	2.75217i	−0.298700	−	0.152195i
$328$	0.392075	−	2.47546i	0.0216487	−	0.136685i
$329$	6.83919			0.377057
$330$		0			0
$331$	14.2522			0.783372			0.391686	−	0.920099i	$-0.371892\pi$
$331$	14.2522			0.783372			0.391686	+	0.920099i	$0.371892\pi$
$332$	0.200087	−	1.26330i	0.0109812	−	0.0693325i
$333$	−9.06535	−	4.61903i	−0.496778	−	0.253121i
$334$	20.4020	+	6.62902i	1.11635	+	0.362724i
$335$		0			0
$336$	2.87706	−	3.95994i	0.156957	−	0.216032i
$337$	−6.23713	−	12.2410i	−0.339758	−	0.666812i	0.656398	−	0.754415i	$-0.272079\pi$
$337$	−6.23713	−	12.2410i	−0.339758	−	0.666812i	−0.996155	+	0.0876027i	$0.972079\pi$
$338$	5.39316	−	10.5847i	0.293349	−	0.575730i
$339$	−7.52914	−	10.3630i	−0.408927	−	0.562839i
$340$		0			0
$341$	−3.05077	+	9.04224i	−0.165208	+	0.489665i
$342$	32.0310	+	32.0310i	1.73204	+	1.73204i
$343$	17.5803	+	2.78444i	0.949246	+	0.150346i
$344$	−8.62085	+	2.80109i	−0.464805	+	0.151024i
$345$		0			0
$346$	−10.6736	−	7.75484i	−0.573818	−	0.416903i
$347$	−17.5163	+	2.77431i	−0.940326	+	0.148933i	−0.607737	−	0.794139i	$-0.707922\pi$
$347$	−17.5163	+	2.77431i	−0.940326	+	0.148933i	−0.332589	+	0.943072i	$0.607922\pi$
$348$	12.9556	−	6.60121i	0.694494	−	0.353862i
$349$	−5.50175	−	16.9327i	−0.294502	−	0.906384i	−0.983388	−	0.181515i	$-0.941900\pi$
$349$	−5.50175	−	16.9327i	−0.294502	−	0.906384i	0.688886	−	0.724870i	$-0.258100\pi$
$350$		0			0
$351$			14.6482i			0.781865i
$352$	0.555617	−	3.26975i	0.0296145	−	0.174278i
$353$	−12.3974	+	12.3974i	−0.659845	+	0.659845i	−0.955343	−	0.295499i	$-0.904514\pi$
$353$	−12.3974	+	12.3974i	−0.659845	+	0.659845i	0.295499	+	0.955343i	$0.404514\pi$
$354$	11.6670	−	8.47655i	0.620093	−	0.450524i
$355$		0			0
$356$	−3.26068	+	10.0353i	−0.172816	+	0.531872i
$357$	−1.70258	−	10.7496i	−0.0901099	−	0.568932i
$358$	2.12000	+	13.3851i	0.112045	+	0.707426i
$359$	2.37480	−	7.30888i	0.125337	−	0.385748i	−0.868625	−	0.495470i	$-0.834996\pi$
$359$	2.37480	−	7.30888i	0.125337	−	0.385748i	0.993962	+	0.109722i	$0.0349959\pi$
$360$		0			0
$361$	−15.6978	+	11.4051i	−0.826200	+	0.600270i
$362$	12.1942	−	12.1942i	0.640915	−	0.640915i
$363$	−25.5297	+	24.4071i	−1.33996	+	1.28104i
$364$			1.61370i			0.0845810i
$365$		0			0
$366$	−5.87638	−	18.0856i	−0.307163	−	0.945351i
$367$	32.2443	−	16.4293i	1.68314	−	0.857603i	0.692452	−	0.721464i	$-0.256531\pi$
$367$	32.2443	−	16.4293i	1.68314	−	0.857603i	0.990690	−	0.136139i	$-0.0434694\pi$
$368$	4.27129	−	0.676506i	0.222656	−	0.0352653i
$369$	14.8215	+	10.7685i	0.771579	+	0.560585i
$370$		0			0
$371$	−5.51436	+	1.79172i	−0.286291	+	0.0930217i
$372$	9.12499	+	1.44526i	0.473109	+	0.0749331i
$373$	−11.5350	−	11.5350i	−0.597259	−	0.597259i	0.342323	−	0.939582i	$-0.388786\pi$
$373$	−11.5350	−	11.5350i	−0.597259	−	0.597259i	−0.939582	+	0.342323i	$0.888786\pi$
$374$	−4.26737	−	6.01453i	−0.220660	−	0.311004i
$375$		0			0
$376$	−2.63703	−	3.62956i	−0.135995	−	0.187181i
$377$	−2.17629	+	4.27121i	−0.112085	+	0.219978i
$378$	9.57688	+	18.7957i	0.492582	+	0.966746i
$379$	−3.86753	+	5.32320i	−0.198662	+	0.273434i	−0.896712	−	0.442614i	$-0.854051\pi$
$379$	−3.86753	+	5.32320i	−0.198662	+	0.273434i	0.698050	+	0.716049i	$0.254051\pi$
$380$		0			0
$381$	−51.8071	−	16.8332i	−2.65416	−	0.862389i
$382$	−11.2202	−	5.71697i	−0.574074	−	0.292505i
$383$	−4.57876	+	28.9091i	−0.233963	+	1.47719i	0.538768	+	0.842454i	$0.318890\pi$
$383$	−4.57876	+	28.9091i	−0.233963	+	1.47719i	−0.772731	+	0.634733i	$0.781110\pi$
$384$	−3.21087			−0.163854
$385$		0			0
$386$	3.83530			0.195212
$387$	10.3652	−	65.4430i	0.526890	−	3.32665i
$388$	6.24280	+	3.18087i	0.316930	+	0.161484i
$389$	4.21993	+	1.37114i	0.213959	+	0.0695195i	0.414035	−	0.910261i	$-0.364119\pi$
$389$	4.21993	+	1.37114i	0.213959	+	0.0695195i	−0.200076	+	0.979780i	$0.564119\pi$
$390$		0			0
$391$	5.65199	−	7.77930i	0.285833	−	0.393416i
$392$	−2.12291	−	4.16644i	−0.107223	−	0.210437i
$393$	14.2513	−	27.9697i	0.718881	−	1.41088i
$394$	6.15139	+	8.46666i	0.309903	+	0.426544i
$395$		0			0
$396$	19.4520	+	14.4695i	0.977501	+	0.727120i
$397$	−6.59354	−	6.59354i	−0.330920	−	0.330920i	0.522016	−	0.852936i	$-0.325180\pi$
$397$	−6.59354	−	6.59354i	−0.330920	−	0.330920i	−0.852936	+	0.522016i	$0.825180\pi$
$398$	−8.99529	−	1.42471i	−0.450893	−	0.0714145i
$399$	−28.8485	+	9.37344i	−1.44423	+	0.469259i
$400$		0			0
$401$	−7.12541	−	5.17691i	−0.355826	−	0.258523i	0.395483	−	0.918473i	$-0.370577\pi$
$401$	−7.12541	−	5.17691i	−0.355826	−	0.258523i	−0.751309	+	0.659951i	$0.770577\pi$
$402$	−24.2535	+	3.84138i	−1.20966	+	0.191591i
$403$	−2.71385	+	1.38278i	−0.135187	+	0.0688811i
$404$	−5.44229	−	16.7496i	−0.270764	−	0.833326i
$405$		0			0
$406$			6.90338i			0.342609i
$407$	2.14188	−	4.08940i	0.106169	−	0.202704i
$408$	−5.04837	+	5.04837i	−0.249932	+	0.249932i
$409$	−14.0728	+	10.2245i	−0.695853	+	0.505567i	−0.878579	−	0.477597i	$-0.841508\pi$
$409$	−14.0728	+	10.2245i	−0.695853	+	0.505567i	0.182726	+	0.983164i	$0.441508\pi$
$410$		0			0
$411$	2.45154	−	7.54507i	0.120926	−	0.372171i
$412$	0.502512	+	3.17274i	0.0247570	+	0.156310i
$413$	1.07107	+	6.76247i	0.0527039	+	0.332759i
$414$	−9.76834	+	30.0639i	−0.480088	+	1.47756i
$415$		0			0
$416$	0.856394	−	0.622206i	0.0419882	−	0.0305062i
$417$	−17.0575	+	17.0575i	−0.835309	+	0.835309i
$418$	−14.6958	+	14.3691i	−0.718796	+	0.702818i
$419$			16.4015i			0.801265i	0.916239	+	0.400632i	$0.131210\pi$
$419$			16.4015i			0.801265i	−0.916239	+	0.400632i	$0.868790\pi$
$420$		0			0
$421$	8.15001	+	25.0832i	0.397207	+	1.22248i	0.927229	+	0.374494i	$0.122184\pi$
$421$	8.15001	+	25.0832i	0.397207	+	1.22248i	−0.530022	+	0.847984i	$0.677816\pi$
$422$	22.3406	−	11.3831i	1.08752	−	0.554121i
$423$	32.3904	−	5.13013i	1.57487	−	0.249436i
$424$	3.07708	+	2.23563i	0.149436	+	0.108572i
$425$		0			0
$426$	−27.1720	+	8.82870i	−1.31649	+	0.427752i
$427$	8.91727	+	1.41236i	0.431537	+	0.0683488i
$428$	−11.6798	−	11.6798i	−0.564566	−	0.564566i
$429$	−11.2722	−	0.126690i	−0.544226	−	0.00611667i
$430$		0			0
$431$	−5.58501	−	7.68711i	−0.269020	−	0.370275i	0.653038	−	0.757325i	$-0.273494\pi$
$431$	−5.58501	−	7.68711i	−0.269020	−	0.370275i	−0.922059	+	0.387050i	$0.873494\pi$
$432$	6.28227	−	12.3296i	0.302256	−	0.593210i
$433$	−11.3232	−	22.2230i	−0.544158	−	1.06797i	−0.985348	−	0.170557i	$-0.945443\pi$
$433$	−11.3232	−	22.2230i	−0.544158	−	1.06797i	0.441190	−	0.897414i	$-0.354557\pi$
$434$	−2.57820	+	3.54858i	−0.123757	+	0.170338i
$435$		0			0
$436$	−1.79561	−	0.583428i	−0.0859940	−	0.0279411i
$437$	−23.8784	−	12.1667i	−1.14226	−	0.582011i
$438$	5.72941	−	36.1741i	0.273762	−	1.72846i
$439$	−1.69115			−0.0807143			−0.0403571	−	0.999185i	$-0.512850\pi$
$439$	−1.69115			−0.0807143			−0.0403571	+	0.999185i	$0.512850\pi$
$440$		0			0
$441$	34.1809			1.62766
$442$	0.368207	−	2.32477i	0.0175138	−	0.110578i
$443$	18.0946	+	9.21964i	0.859698	+	0.438038i	0.827515	−	0.561444i	$-0.189754\pi$
$443$	18.0946	+	9.21964i	0.859698	+	0.438038i	0.0321835	+	0.999482i	$0.489754\pi$
$444$	−4.25044	−	1.38105i	−0.201717	−	0.0655418i
$445$		0			0
$446$	2.93087	−	4.03399i	0.138781	−	0.191015i
$447$	0.0485798	+	0.0953432i	0.00229775	+	0.00450958i
$448$	0.692077	−	1.35828i	0.0326976	−	0.0641726i
$449$	−24.7166	−	34.0195i	−1.16645	−	1.60548i	−0.683806	−	0.729664i	$-0.739677\pi$
$449$	−24.7166	−	34.0195i	−1.16645	−	1.60548i	−0.482643	−	0.875817i	$-0.660323\pi$
$450$		0			0
$451$	−4.96125	+	6.66964i	−0.233616	+	0.314061i
$452$	−2.82091	−	2.82091i	−0.132684	−	0.132684i
$453$	67.1849	+	10.6410i	3.15662	+	0.499960i
$454$	1.94088	−	0.630630i	0.0910900	−	0.0295969i
$455$		0			0
$456$	16.0978	+	11.6957i	0.753848	+	0.547703i
$457$	9.99618	−	1.58324i	0.467602	−	0.0740608i	0.0818123	−	0.996648i	$-0.473929\pi$
$457$	9.99618	−	1.58324i	0.467602	−	0.0740608i	0.385789	+	0.922587i	$0.373929\pi$
$458$	1.35805	−	0.691961i	0.0634575	−	0.0323332i
$459$	−9.50814	−	29.2630i	−0.443802	−	1.36588i
$460$		0			0
$461$		−	27.4513i		−	1.27854i	−0.768984	−	0.639268i	$-0.779237\pi$
$461$		−	27.4513i		−	1.27854i	0.768984	−	0.639268i	$-0.220763\pi$
$462$	−14.5466	+	7.20708i	−0.676768	+	0.335304i
$463$	−12.8080	+	12.8080i	−0.595237	+	0.595237i	−0.939041	−	0.343804i	$-0.888284\pi$
$463$	−12.8080	+	12.8080i	−0.595237	+	0.595237i	0.343804	+	0.939041i	$0.388284\pi$
$464$	3.66363	−	2.66178i	0.170080	−	0.123570i
$465$		0			0
$466$	6.85697	−	21.1036i	0.317643	−	0.977604i
$467$	3.41594	+	21.5674i	0.158071	+	0.998021i	0.931395	+	0.364010i	$0.118593\pi$
$467$	3.41594	+	21.5674i	0.158071	+	0.998021i	−0.773324	+	0.634011i	$0.781407\pi$
$468$	1.21045	+	7.64249i	0.0559532	+	0.353274i
$469$	3.60265	−	11.0878i	0.166355	−	0.511988i
$470$		0			0
$471$	−5.10305	+	3.70758i	−0.235136	+	0.170836i
$472$	3.17587	−	3.17587i	0.146181	−	0.146181i
$473$	29.6387	+	5.03639i	1.36279	+	0.231573i
$474$			18.6210i			0.855293i
$475$		0			0
$476$	−1.04745	−	3.22372i	−0.0480098	−	0.147759i
$477$	−24.7720	+	12.6220i	−1.13423	+	0.577920i
$478$	−24.4789	+	3.87708i	−1.11964	+	0.177334i
$479$	5.27636	+	3.83350i	0.241083	+	0.175157i	0.701766	−	0.712408i	$-0.252395\pi$
$479$	5.27636	+	3.83350i	0.241083	+	0.175157i	−0.460683	+	0.887565i	$0.652395\pi$
$480$		0			0
$481$	1.40128	−	0.455305i	0.0638931	−	0.0207601i
$482$	0.0555650	+	0.00880064i	0.00253092	+	0.000400858i
$483$	−14.9677	−	14.9677i	−0.681054	−	0.681054i
$484$	−6.66402	+	8.75162i	−0.302910	+	0.397801i
$485$		0			0
$486$	18.0681	+	24.8685i	0.819583	+	1.12806i
$487$	−1.33144	+	2.61310i	−0.0603334	+	0.118411i	−0.919204	−	0.393782i	$-0.871167\pi$
$487$	−1.33144	+	2.61310i	−0.0603334	+	0.118411i	0.858871	+	0.512193i	$0.171167\pi$
$488$	−2.68875	−	5.27698i	−0.121714	−	0.238878i
$489$	−4.10918	+	5.65580i	−0.185824	+	0.255764i
$490$		0			0
$491$	12.6664	+	4.11555i	0.571625	+	0.185732i	0.580545	−	0.814228i	$-0.302839\pi$
$491$	12.6664	+	4.11555i	0.571625	+	0.185732i	−0.00892018	+	0.999960i	$0.502839\pi$
$492$	7.17035	+	3.65348i	0.323264	+	0.164711i
$493$	1.57518	−	9.94529i	0.0709425	−	0.447913i
$494$	−6.55996			−0.295147
$495$		0			0
$496$	2.87733			0.129196
$497$	2.12193	−	13.3974i	0.0951818	−	0.600954i
$498$	3.65923	+	1.86447i	0.163974	+	0.0835490i
$499$	−22.2265	−	7.22182i	−0.994994	−	0.323293i	−0.234130	−	0.972205i	$-0.575224\pi$
$499$	−22.2265	−	7.22182i	−0.994994	−	0.323293i	−0.760863	+	0.648912i	$0.775224\pi$
$500$		0			0
$501$	−40.4864	+	55.7247i	−1.80880	+	2.48960i
$502$	3.82436	+	7.50572i	0.170689	+	0.334997i
$503$	−10.5487	+	20.7030i	−0.470344	+	0.923103i	0.526972	+	0.849883i	$0.323327\pi$
$503$	−10.5487	+	20.7030i	−0.470344	+	0.923103i	−0.997316	+	0.0732197i	$0.976673\pi$
$504$	6.54977	+	9.01498i	0.291750	+	0.401559i
$505$		0			0
$506$	−13.5902	−	4.58521i	−0.604158	−	0.203837i
$507$	26.9714	+	26.9714i	1.19784	+	1.19784i
$508$	−16.7564	−	2.65395i	−0.743444	−	0.117750i
$509$	21.9064	−	7.11784i	0.970986	−	0.315493i	0.219772	−	0.975551i	$-0.429469\pi$
$509$	21.9064	−	7.11784i	0.970986	−	0.315493i	0.751214	+	0.660059i	$0.229469\pi$
$510$		0			0
$511$	14.0676	+	10.2207i	0.622314	+	0.452138i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	−76.4075	+	38.9316i	−3.37347	+	1.71887i
$514$	3.24457	+	9.98577i	0.143112	+	0.440454i
$515$		0			0
$516$		−	29.1050i		−	1.28127i
$517$	2.16238	+	14.7217i	0.0951014	+	0.647460i
$518$	1.50037	−	1.50037i	0.0659223	−	0.0659223i
$519$	34.2716	−	24.8998i	1.50436	−	1.09298i
$520$		0			0
$521$	−9.62530	+	29.6236i	−0.421692	+	1.29783i	0.484435	+	0.874827i	$0.339025\pi$
$521$	−9.62530	+	29.6236i	−0.421692	+	1.29783i	−0.906127	+	0.423007i	$0.860975\pi$
$522$	5.17828	+	32.6944i	0.226647	+	1.43099i
$523$	0.813774	+	5.13797i	0.0355838	+	0.224668i	0.999071	−	0.0430856i	$-0.0137188\pi$
$523$	0.813774	+	5.13797i	0.0355838	+	0.224668i	−0.963488	+	0.267753i	$0.913719\pi$
$524$	3.02111	−	9.29801i	0.131978	−	0.406185i
$525$		0			0
$526$	−3.67174	+	2.66768i	−0.160096	+	0.116316i
$527$	4.52395	−	4.52395i	0.197067	−	0.197067i
$528$	9.43362	+	4.94099i	0.410546	+	0.215029i
$529$			4.29842i			0.186888i
$530$		0			0
$531$	10.1452	+	31.2236i	0.440263	+	1.35499i
$532$	−8.41733	+	4.28884i	−0.364938	+	0.185945i
$533$	−2.62043	+	0.415035i	−0.113503	+	0.0179772i
$534$	−27.4098	−	19.9144i	−1.18614	−	0.861781i
$535$		0			0
$536$	−7.27342	+	2.36328i	−0.314164	+	0.102078i
$537$	−42.9779	−	6.80704i	−1.85463	−	0.293745i
$538$	18.3155	+	18.3155i	0.789636	+	0.789636i
$539$	−0.174297	+	15.5079i	−0.00750749	+	0.667973i
$540$		0			0
$541$	7.63567	+	10.5096i	0.328283	+	0.451843i	0.940974	−	0.338480i	$-0.109913\pi$
$541$	7.63567	+	10.5096i	0.328283	+	0.451843i	−0.612690	+	0.790323i	$0.709913\pi$
$542$	−9.75785	+	19.1509i	−0.419135	+	0.822600i
$543$	25.1385	+	49.3371i	1.07880	+	2.11726i
$544$	−1.30696	+	1.79888i	−0.0560354	+	0.0771262i
$545$		0			0
$546$	−4.92780	−	1.60114i	−0.210890	−	0.0685224i
$547$	−4.19261	−	2.13624i	−0.179263	−	0.0913391i	0.362056	−	0.932156i	$-0.382075\pi$
$547$	−4.19261	−	2.13624i	−0.179263	−	0.0913391i	−0.541319	+	0.840817i	$0.682075\pi$
$548$	0.386515	−	2.44036i	0.0165111	−	0.104247i
$549$	43.2916			1.84764
$550$		0			0
$551$	−28.0634			−1.19554
$552$	−2.17217	+	13.7146i	−0.0924538	+	0.583731i
$553$	−7.87716	−	4.01362i	−0.334971	−	0.170676i
$554$	−13.0595	−	4.24329i	−0.554845	−	0.180280i
$555$		0			0
$556$	−4.41597	+	6.07806i	−0.187279	+	0.257767i
$557$	14.8729	+	29.1897i	0.630185	+	1.23681i	0.956551	+	0.291564i	$0.0941757\pi$
$557$	14.8729	+	29.1897i	0.630185	+	1.23681i	−0.326366	+	0.945243i	$0.605824\pi$
$558$	−9.54851	+	18.7400i	−0.404221	+	0.793328i
$559$	5.63999	+	7.76278i	0.238546	+	0.328331i
$560$		0			0
$561$	22.6008	−	7.06365i	0.954209	−	0.298228i
$562$	7.00467	+	7.00467i	0.295474	+	0.295474i
$563$	−3.28421	−	0.520168i	−0.138413	−	0.0219225i	0.0868434	−	0.996222i	$-0.472322\pi$
$563$	−3.28421	−	0.520168i	−0.138413	−	0.0219225i	−0.225257	+	0.974299i	$0.572322\pi$
$564$	13.7002	−	4.45146i	0.576882	−	0.187440i
$565$		0			0
$566$	1.66646	+	1.21075i	0.0700464	+	0.0508917i
$567$	−33.8813	+	5.36627i	−1.42288	+	0.225362i
$568$	−7.92816	+	4.03960i	−0.332658	+	0.169498i
$569$	2.18501	+	6.72478i	0.0916005	+	0.281917i	0.986353	−	0.164645i	$-0.0526480\pi$
$569$	2.18501	+	6.72478i	0.0916005	+	0.281917i	−0.894752	+	0.446563i	$0.852648\pi$
$570$		0			0
$571$			24.2620i			1.01533i	0.861553	+	0.507667i	$0.169492\pi$
$571$			24.2620i			1.01533i	−0.861553	+	0.507667i	$0.830508\pi$
$572$	−3.47358	+	0.510212i	−0.145238	+	0.0213330i
$573$	28.5908	−	28.5908i	1.19440	−	1.19440i
$574$	−3.09102	+	2.24576i	−0.129017	+	0.0937362i
$575$		0			0
$576$	2.25882	−	6.95193i	0.0941175	−	0.289664i
$577$	−1.00746	−	6.36086i	−0.0419412	−	0.264806i	0.957803	−	0.287426i	$-0.0927994\pi$
$577$	−1.00746	−	6.36086i	−0.0419412	−	0.264806i	−0.999744	+	0.0226195i	$0.992799\pi$
$578$	−1.88596	−	11.9075i	−0.0784455	−	0.495286i
$579$	−3.80544	+	11.7119i	−0.158149	+	0.486731i
$580$		0			0
$581$	−1.57744	+	1.14607i	−0.0654430	+	0.0475471i
$582$	−15.9077	+	15.9077i	−0.659394	+	0.659394i
$583$	−5.60028	−	11.3034i	−0.231940	−	0.468141i
$584$		−	11.4066i		−	0.472007i
$585$		0			0
$586$	6.06998	+	18.6815i	0.250748	+	0.771724i
$587$	4.91253	−	2.50306i	0.202762	−	0.103312i	−0.349661	−	0.936876i	$-0.613703\pi$
$587$	4.91253	−	2.50306i	0.202762	−	0.103312i	0.552423	+	0.833564i	$0.313703\pi$
$588$	14.8295	−	2.34877i	0.611560	−	0.0968615i
$589$	−14.4256	−	10.4808i	−0.594395	−	0.431853i
$590$		0			0
$591$	−31.9583	+	10.3839i	−1.31459	+	0.427136i
$592$	−1.37475	−	0.217739i	−0.0565019	−	0.00894903i
$593$	−11.4901	−	11.4901i	−0.471841	−	0.471841i	0.430669	−	0.902510i	$-0.358278\pi$
$593$	−11.4901	−	11.4901i	−0.471841	−	0.471841i	−0.902510	+	0.430669i	$0.858278\pi$
$594$	−37.4307	+	26.5574i	−1.53580	+	1.08967i
$595$		0			0
$596$	0.0195887	+	0.0269615i	0.000802383	+	0.00110439i
$597$	13.2759	−	26.0555i	0.543348	−	1.06638i
$598$	−2.07827	−	4.07883i	−0.0849867	−	0.166796i
$599$	−24.2507	+	33.3782i	−0.990856	+	1.36380i	−0.0600854	+	0.998193i	$0.519137\pi$
$599$	−24.2507	+	33.3782i	−0.990856	+	1.36380i	−0.930771	+	0.365603i	$0.880863\pi$
$600$		0			0
$601$	42.1453	+	13.6938i	1.71914	+	0.558583i	0.991812	−	0.127705i	$-0.0407609\pi$
$601$	42.1453	+	13.6938i	1.71914	+	0.558583i	0.727330	+	0.686288i	$0.240761\pi$
$602$	12.3121	+	6.27334i	0.501804	+	0.255682i
$603$	8.74509	−	55.2143i	0.356127	−	2.24850i
$604$	21.1850			0.862006
$605$		0			0
$606$	56.5487			2.29713
$607$	−2.64036	+	16.6706i	−0.107169	+	0.676638i	0.874353	+	0.485290i	$0.161286\pi$
$607$	−2.64036	+	16.6706i	−0.107169	+	0.676638i	−0.981522	+	0.191348i	$0.938714\pi$
$608$	5.52162	+	2.81341i	0.223931	+	0.114099i
$609$	−21.0810	−	6.84963i	−0.854245	−	0.277561i
$610$		0			0
$611$	−2.79146	+	3.84212i	−0.112930	+	0.155435i
$612$	−7.37886	−	14.4818i	−0.298273	−	0.585394i
$613$	11.0412	−	21.6696i	0.445949	−	0.875225i	−0.553162	−	0.833074i	$-0.686579\pi$
$613$	11.0412	−	21.6696i	0.445949	−	0.875225i	0.999111	−	0.0421512i	$-0.0134211\pi$
$614$	−6.94359	−	9.55703i	−0.280221	−	0.385691i
$615$		0			0
$616$	−4.12350	+	2.92567i	−0.166141	+	0.117878i
$617$	2.46606	+	2.46606i	0.0992799	+	0.0992799i	0.755002	−	0.655722i	$-0.227636\pi$
$617$	2.46606	+	2.46606i	0.0992799	+	0.0992799i	−0.655722	+	0.755002i	$0.727636\pi$
$618$	−10.1873	−	1.61350i	−0.409791	−	0.0649046i
$619$	28.7652	−	9.34637i	1.15617	−	0.375662i	0.332706	−	0.943031i	$-0.392038\pi$
$619$	28.7652	−	9.34637i	1.15617	−	0.375662i	0.823464	+	0.567369i	$0.192038\pi$
$620$		0			0
$621$	−48.4135	−	35.1745i	−1.94277	−	1.41150i
$622$	13.7346	−	2.17534i	0.550706	−	0.0872233i
$623$	14.3323	−	7.30265i	0.574210	−	0.292574i
$624$	1.05032	+	3.23255i	0.0420464	+	0.129406i
$625$		0			0
$626$		−	30.1918i		−	1.20671i
$627$	−29.2980	−	59.1342i	−1.17005	−	2.36159i
$628$	−1.38910	+	1.38910i	−0.0554312	+	0.0554312i
$629$	−2.50383	+	1.81914i	−0.0998344	+	0.0725339i
$630$		0			0
$631$	9.75833	−	30.0330i	0.388473	−	1.19560i	−0.545456	−	0.838139i	$-0.683644\pi$
$631$	9.75833	−	30.0330i	0.388473	−	1.19560i	0.933929	−	0.357458i	$-0.116356\pi$
$632$	0.907222	+	5.72797i	0.0360874	+	0.227847i
$633$	12.5942	+	79.5165i	0.500573	+	3.16050i
$634$	9.47527	−	29.1619i	0.376311	−	1.15817i
$635$		0			0
$636$	−9.88010	+	7.17831i	−0.391771	+	0.284639i
$637$	−3.50014	+	3.50014i	−0.138681	+	0.138681i
$638$	−14.8599	+	2.18268i	−0.588308	+	0.0864129i
$639$		−	65.0416i		−	2.57300i
$640$		0			0
$641$	−1.51513	−	4.66309i	−0.0598440	−	0.184181i	0.916665	−	0.399655i	$-0.130870\pi$
$641$	−1.51513	−	4.66309i	−0.0598440	−	0.184181i	−0.976509	+	0.215474i	$0.930870\pi$
$642$	47.2558	−	24.0781i	1.86504	−	0.950285i
$643$	−16.1752	+	2.56190i	−0.637888	+	0.101031i	−0.466998	−	0.884259i	$-0.654664\pi$
$643$	−16.1752	+	2.56190i	−0.637888	+	0.101031i	−0.170890	+	0.985290i	$0.554664\pi$
$644$	−5.33341	−	3.87495i	−0.210166	−	0.152694i
$645$		0			0
$646$	13.1050	−	4.25806i	0.515608	−	0.167531i
$647$	−42.4816	−	6.72843i	−1.67012	−	0.264522i	−0.751523	−	0.659707i	$-0.770681\pi$
$647$	−42.4816	−	6.72843i	−1.67012	−	0.264522i	−0.918602	+	0.395185i	$0.870681\pi$
$648$	15.9117	+	15.9117i	0.625071	+	0.625071i
$649$	−14.2179	+	4.44366i	−0.558102	+	0.174429i
$650$		0			0
$651$	−8.27826	−	11.3940i	−0.324451	−	0.446568i
$652$	−0.988463	+	1.93997i	−0.0387112	+	0.0759750i
$653$	−1.54616	−	3.03452i	−0.0605061	−	0.118750i	0.858773	−	0.512356i	$-0.171227\pi$
$653$	−1.54616	−	3.03452i	−0.0605061	−	0.118750i	−0.919279	+	0.393606i	$0.871227\pi$
$654$	3.56325	−	4.90440i	0.139334	−	0.191777i
$655$		0			0
$656$	2.38365	+	0.774496i	0.0930660	+	0.0302390i
$657$	74.2907	+	37.8530i	2.89836	+	1.47679i
$658$	−1.06989	+	6.75499i	−0.0417085	+	0.263337i
$659$	1.70430			0.0663902			0.0331951	−	0.999449i	$-0.489432\pi$
$659$	1.70430			0.0663902			0.0331951	+	0.999449i	$0.489432\pi$
$660$		0			0
$661$	−3.81557			−0.148409			−0.0742043	−	0.997243i	$-0.523642\pi$
$661$	−3.81557			−0.148409			−0.0742043	+	0.997243i	$0.523642\pi$
$662$	−2.22953	+	14.0767i	−0.0866533	+	0.547108i
$663$	6.73385	+	3.43107i	0.261521	+	0.133252i
$664$	1.21644	+	0.395247i	0.0472072	+	0.0153386i
$665$		0			0
$666$	5.98029	−	8.23116i	0.231732	−	0.318951i
$667$	−8.89078	−	17.4491i	−0.344252	−	0.675634i
$668$	−9.73899	+	19.1138i	−0.376813	+	0.739537i
$669$	9.41064	+	12.9526i	0.363836	+	0.500778i
$670$		0			0
$671$	−0.220754	+	19.6414i	−0.00852212	+	0.758249i
$672$	3.46111	+	3.46111i	0.133515	+	0.133515i
$673$	26.0401	+	4.12434i	1.00377	+	0.158982i	0.636619	−	0.771179i	$-0.280333\pi$
$673$	26.0401	+	4.12434i	1.00377	+	0.158982i	0.367153	+	0.930161i	$0.380333\pi$
$674$	13.0660	−	4.24541i	0.503285	−	0.163527i
$675$		0			0
$676$	9.61068	+	6.98256i	0.369641	+	0.268560i
$677$	−11.6875	+	1.85111i	−0.449185	+	0.0711440i	−0.376929	−	0.926242i	$-0.623020\pi$
$677$	−11.6875	+	1.85111i	−0.449185	+	0.0711440i	−0.0722563	+	0.997386i	$0.523020\pi$
$678$	11.4132	−	5.81532i	0.438321	−	0.223336i
$679$	−3.30057	−	10.1581i	−0.126664	−	0.389832i
$680$		0			0
$681$			6.55262i			0.251097i
$682$	−8.45367	−	4.42773i	−0.323708	−	0.169546i
$683$	19.2371	−	19.2371i	0.736087	−	0.736087i	−0.235731	−	0.971818i	$-0.575748\pi$
$683$	19.2371	−	19.2371i	0.736087	−	0.736087i	0.971818	+	0.235731i	$0.0757484\pi$
$684$	−36.6474	+	26.6259i	−1.40125	+	1.01807i
$685$		0			0
$686$	−5.50033	+	16.9283i	−0.210003	+	0.646324i
$687$	0.765580	+	4.83368i	0.0292087	+	0.184416i
$688$	−1.41800	−	8.95290i	−0.0540608	−	0.341326i
$689$	1.24417	−	3.82916i	0.0473990	−	0.145879i
$690$		0			0
$691$	−2.86279	+	2.07994i	−0.108906	+	0.0791246i	−0.640905	−	0.767620i	$-0.721441\pi$
$691$	−2.86279	+	2.07994i	−0.108906	+	0.0791246i	0.531999	+	0.846745i	$0.321441\pi$
$692$	9.32909	−	9.32909i	0.354639	−	0.354639i
$693$	−5.37084	−	36.5652i	−0.204021	−	1.38900i
$694$		−	17.7347i		−	0.673199i
$695$		0			0
$696$	4.49324	+	13.8288i	0.170316	+	0.524178i
$697$	4.96548	−	2.53004i	0.188081	−	0.0958320i
$698$	17.5849	−	2.78517i	0.665596	−	0.105420i
$699$	57.6408	+	41.8785i	2.18018	+	1.58399i
$700$		0			0
$701$	37.5991	−	12.2167i	1.42010	−	0.461418i	0.504466	−	0.863432i	$-0.331689\pi$
$701$	37.5991	−	12.2167i	1.42010	−	0.461418i	0.915634	+	0.402013i	$0.131689\pi$
$702$	−14.4679	−	2.29149i	−0.546055	−	0.0864867i
$703$	6.09923	+	6.09923i	0.230037	+	0.230037i
$704$	3.14258	+	1.06028i	0.118440	+	0.0399607i
$705$		0			0
$706$	−10.3053	−	14.1841i	−0.387847	−	0.533826i
$707$	−12.1886	+	23.9215i	−0.458400	+	0.899660i
$708$	6.54708	+	12.8494i	0.246054	+	0.482908i
$709$	−23.7291	+	32.6603i	−0.891166	+	1.22658i	0.0820353	+	0.996629i	$0.473858\pi$
$709$	−23.7291	+	32.6603i	−0.891166	+	1.22658i	−0.973201	+	0.229955i	$0.926142\pi$
$710$		0			0
$711$	−40.3169	−	13.0997i	−1.51200	−	0.491279i
$712$	−9.40171	−	4.79041i	−0.352344	−	0.179528i
$713$	1.94653	−	12.2899i	0.0728982	−	0.460261i
$714$	10.8836			0.407310
$715$		0			0
$716$	−13.5520			−0.506461
$717$	12.4488	−	78.5987i	0.464910	−	2.93532i
$718$	6.84740	+	3.48892i	0.255543	+	0.130205i
$719$	−6.32991	−	2.05671i	−0.236066	−	0.0767024i	0.188595	−	0.982055i	$-0.439607\pi$
$719$	−6.32991	−	2.05671i	−0.236066	−	0.0767024i	−0.424661	+	0.905353i	$0.639607\pi$
$720$		0			0
$721$	2.87833	−	3.96168i	0.107195	−	0.147541i
$722$	−8.80903	−	17.2887i	−0.327838	−	0.643418i
$723$	−0.0820071	+	0.160948i	−0.00304988	+	0.00598572i
$724$	10.1365	+	13.9517i	0.376720	+	0.518511i
$725$		0			0
$726$	−20.1129	−	29.0335i	−0.746459	−	1.07754i
$727$	−13.3487	−	13.3487i	−0.495074	−	0.495074i	0.414826	−	0.909901i	$-0.363842\pi$
$727$	−13.3487	−	13.3487i	−0.495074	−	0.495074i	−0.909901	+	0.414826i	$0.863842\pi$
$728$	−1.59384	−	0.252439i	−0.0590715	−	0.00935600i
$729$	−29.6653	+	9.63884i	−1.09871	+	0.356994i
$730$		0			0
$731$	−16.3059	−	11.8469i	−0.603096	−	0.438175i
$732$	18.7822	−	2.97481i	0.694211	−	0.109952i
$733$	24.8515	−	12.6624i	0.917909	−	0.467698i	0.0698250	−	0.997559i	$-0.477756\pi$
$733$	24.8515	−	12.6624i	0.917909	−	0.467698i	0.848084	+	0.529861i	$0.177756\pi$
$734$	11.1829	+	34.4175i	0.412769	+	1.27037i
$735$		0			0
$736$			4.32453i			0.159404i
$737$	25.0062	+	4.24920i	0.921115	+	0.156521i
$738$	−12.9545	+	12.9545i	−0.476862	+	0.476862i
$739$	−8.88327	+	6.45407i	−0.326776	+	0.237417i	−0.739061	−	0.673638i	$-0.764731\pi$
$739$	−8.88327	+	6.45407i	−0.326776	+	0.237417i	0.412285	+	0.911055i	$0.364731\pi$
$740$		0			0
$741$	6.50889	−	20.0323i	0.239110	−	0.735905i
$742$	−0.907029	−	5.72675i	−0.0332981	−	0.210236i
$743$	−3.77987	−	23.8652i	−0.138670	−	0.875527i	−0.954711	−	0.297534i	$-0.903836\pi$
$743$	−3.77987	−	23.8652i	−0.138670	−	0.875527i	0.816041	−	0.577994i	$-0.196164\pi$
$744$	−2.85493	+	8.78656i	−0.104667	+	0.322131i
$745$		0			0
$746$	13.1974	−	9.58850i	0.483193	−	0.351060i
$747$	−6.61105	+	6.61105i	−0.241886	+	0.241886i
$748$	6.60805	−	3.27395i	0.241614	−	0.119708i
$749$			25.1802i			0.920065i
$750$		0			0
$751$	−15.1449	−	46.6112i	−0.552645	−	1.70087i	−0.702082	−	0.712096i	$-0.747746\pi$
$751$	−15.1449	−	46.6112i	−0.552645	−	1.70087i	0.149437	−	0.988771i	$-0.452254\pi$
$752$	3.99740	−	2.03678i	0.145770	−	0.0742737i
$753$	−26.7150	+	4.23123i	−0.973547	+	0.154195i
$754$	−3.87818	−	2.81766i	−0.141235	−	0.102613i
$755$		0			0
$756$	−20.0624	+	6.51868i	−0.729664	+	0.237082i
$757$	49.9645	+	7.91360i	1.81599	+	0.287625i	0.969556	−	0.244869i	$-0.0787448\pi$
$757$	49.9645	+	7.91360i	1.81599	+	0.287625i	0.846434	+	0.532493i	$0.178745\pi$
$758$	−4.65265	−	4.65265i	−0.168992	−	0.168992i
$759$	27.4863	−	36.9511i	0.997690	−	1.34124i
$760$		0			0
$761$	18.7749	+	25.8415i	0.680591	+	0.936753i	0.999941	−	0.0108837i	$-0.00346445\pi$
$761$	18.7749	+	25.8415i	0.680591	+	0.936753i	−0.319350	+	0.947637i	$0.603464\pi$
$762$	24.7303	−	48.5360i	0.895886	−	1.75827i
$763$	1.30665	+	2.56445i	0.0473040	+	0.0928392i
$764$	7.40180	−	10.1877i	0.267788	−	0.368578i
$765$		0			0
$766$	−27.8369	−	9.04477i	−1.00579	−	0.326801i
$767$	−4.23618	−	2.15844i	−0.152960	−	0.0779368i
$768$	0.502291	−	3.17134i	0.0181249	−	0.114436i
$769$	41.4875			1.49608			0.748039	−	0.663655i	$-0.230996\pi$
$769$	41.4875			1.49608			0.748039	+	0.663655i	$0.230996\pi$
$770$		0			0
$771$	−33.7131			−1.21415
$772$	−0.599973	+	3.78808i	−0.0215935	+	0.136336i
$773$	19.4460	+	9.90821i	0.699422	+	0.356373i	0.767272	−	0.641322i	$-0.221614\pi$
$773$	19.4460	+	9.90821i	0.699422	+	0.356373i	−0.0678495	+	0.997696i	$0.521614\pi$
$774$	63.0158	+	20.4751i	2.26506	+	0.735962i
$775$		0			0
$776$	−4.11829	+	5.66834i	−0.147838	+	0.203482i
$777$	3.09301	+	6.07038i	0.110961	+	0.217774i
$778$	−2.01440	+	3.95348i	−0.0722197	+	0.141739i
$779$	−9.12937	−	12.5655i	−0.327094	−	0.450206i
$780$		0			0
$781$	29.5094	+	0.331662i	1.05593	+	0.0118678i
$782$	6.79935	+	6.79935i	0.243144	+	0.243144i
$783$	−61.8933	−	9.80293i	−2.21189	−	0.350328i
$784$	4.44724	−	1.44500i	0.158830	−	0.0516070i
$785$		0			0
$786$	25.3959	+	18.4512i	0.905843	+	0.658134i
$787$	29.9410	−	4.74219i	1.06728	−	0.169041i	0.402005	−	0.915637i	$-0.368313\pi$
$787$	29.9410	−	4.74219i	1.06728	−	0.169041i	0.665277	+	0.746596i	$0.268313\pi$
$788$	−9.32471	+	4.75118i	−0.332179	+	0.169254i
$789$	−4.50319	−	13.8594i	−0.160318	−	0.493407i
$790$		0			0
$791$			6.08151i			0.216234i
$792$	−17.3343	+	16.9490i	−0.615949	+	0.602257i
$793$	−4.43308	+	4.43308i	−0.157423	+	0.157423i
$794$	7.54381	−	5.48090i	0.267720	−	0.194510i
$795$		0			0
$796$	2.81435	−	8.66167i	0.0997519	−	0.307005i
$797$	−8.39878	−	53.0278i	−0.297500	−	1.87834i	−0.454505	−	0.890744i	$-0.650184\pi$
$797$	−8.39878	−	53.0278i	−0.297500	−	1.87834i	0.157004	−	0.987598i	$-0.449816\pi$
$798$	−4.74514	−	29.9596i	−0.167976	−	1.06056i
$799$	3.08264	−	9.48739i	0.109056	−	0.335640i
$800$		0			0
$801$	62.3997	−	45.3361i	2.20479	−	1.60187i
$802$	6.22783	−	6.22783i	0.219912	−	0.219912i
$803$	−17.5528	+	33.5128i	−0.619424	+	1.18264i
$804$		−	24.5559i		−	0.866019i
$805$		0			0
$806$	−0.941213	−	2.89676i	−0.0331528	−	0.102034i
$807$	−74.1031	+	37.7574i	−2.60855	+	1.32912i
$808$	17.3948	−	2.75506i	0.611947	−	0.0969228i
$809$	−25.4737	−	18.5077i	−0.895608	−	0.650697i	0.0417260	−	0.999129i	$-0.486714\pi$
$809$	−25.4737	−	18.5077i	−0.895608	−	0.650697i	−0.937334	+	0.348432i	$0.886714\pi$
$810$		0			0
$811$	−6.48163	+	2.10601i	−0.227601	+	0.0739520i	−0.420597	−	0.907247i	$-0.638179\pi$
$811$	−6.48163	+	2.10601i	−0.227601	+	0.0739520i	0.192996	+	0.981199i	$0.438179\pi$
$812$	−6.81839	−	1.07993i	−0.239279	−	0.0378980i
$813$	−48.7995	−	48.7995i	−1.71147	−	1.71147i
$814$	3.70399	+	2.75524i	0.129825	+	0.0965710i
$815$		0			0
$816$	−4.19648	−	5.77596i	−0.146906	−	0.202199i
$817$	−25.5021	+	50.0507i	−0.892206	+	1.75105i
$818$	−7.89712	−	15.4990i	−0.276116	−	0.541908i
$819$	6.93333	−	9.54290i	0.242270	−	0.333456i
$820$		0			0
$821$	−0.216685	−	0.0704052i	−0.00756235	−	0.00245716i	0.305233	−	0.952278i	$-0.401266\pi$
$821$	−0.216685	−	0.0704052i	−0.00756235	−	0.00245716i	−0.312796	+	0.949820i	$0.601266\pi$
$822$	7.06867	+	3.60167i	0.246548	+	0.125623i
$823$	−3.59018	+	22.6675i	−0.125146	+	0.790139i	0.842661	+	0.538445i	$0.180988\pi$
$823$	−3.59018	+	22.6675i	−0.125146	+	0.790139i	−0.967807	+	0.251695i	$0.919012\pi$
$824$	−3.21229			−0.111905
$825$		0			0
$826$	−6.84677			−0.238229
$827$	−6.32782	+	39.9523i	−0.220040	+	1.38928i	0.592124	+	0.805847i	$0.298290\pi$
$827$	−6.32782	+	39.9523i	−0.220040	+	1.38928i	−0.812164	+	0.583430i	$0.801710\pi$
$828$	−28.1656	−	14.3511i	−0.978823	−	0.498735i
$829$	−25.8477	−	8.39841i	−0.897726	−	0.291689i	−0.176428	−	0.984314i	$-0.556454\pi$
$829$	−25.8477	−	8.39841i	−0.897726	−	0.291689i	−0.721298	+	0.692625i	$0.756454\pi$
$830$		0			0
$831$	25.9156	−	35.6698i	0.899004	−	1.23737i
$832$	0.480577	+	0.943185i	0.0166610	+	0.0326990i
$833$	4.72036	−	9.26422i	0.163551	−	0.320986i
$834$	−14.1791	−	19.5159i	−0.490982	−	0.675779i
$835$		0			0
$836$	−11.8933	−	16.7627i	−0.411338	−	0.579750i
$837$	−28.1543	−	28.1543i	−0.973154	−	0.973154i
$838$	−16.1996	−	2.56576i	−0.559604	−	0.0886326i
$839$	−20.9575	+	6.80951i	−0.723533	+	0.235090i	−0.647554	−	0.762019i	$-0.724208\pi$
$839$	−20.9575	+	6.80951i	−0.723533	+	0.235090i	−0.0759789	+	0.997109i	$0.524208\pi$
$840$		0			0
$841$	6.87075	+	4.99189i	0.236922	+	0.172134i
$842$	−26.0493	+	4.12580i	−0.897718	+	0.142185i
$843$	−28.3404	+	14.4402i	−0.976096	+	0.497346i
$844$	7.74813	+	23.8463i	0.266701	+	0.820823i
$845$		0			0
$846$			32.7941i			1.12749i
$847$	16.6171	−	2.25030i	0.570969	−	0.0773212i
$848$	−2.68946	+	2.68946i	−0.0923566	+	0.0923566i
$849$	−5.35078	+	3.88757i	−0.183638	+	0.133421i
$850$		0			0
$851$	−1.86005	+	5.72466i	−0.0637619	+	0.196239i
$852$	−4.46938	−	28.2185i	−0.153118	−	0.966751i
$853$	−5.72190	−	36.1266i	−0.195914	−	1.23695i	−0.868032	−	0.496508i	$-0.834615\pi$
$853$	−5.72190	−	36.1266i	−0.195914	−	1.23695i	0.672118	−	0.740444i	$-0.265385\pi$
$854$	−2.78994	+	8.58655i	−0.0954697	+	0.293826i
$855$		0			0
$856$	13.3632	−	9.70891i	0.456744	−	0.331844i
$857$	8.98140	−	8.98140i	0.306799	−	0.306799i	−0.536868	−	0.843666i	$-0.680393\pi$
$857$	8.98140	−	8.98140i	0.306799	−	0.306799i	0.843666	+	0.536868i	$0.180393\pi$
$858$	1.88849	−	11.1136i	0.0644719	−	0.379411i
$859$		−	54.6972i		−	1.86624i	−0.359559	−	0.933122i	$-0.617073\pi$
$859$		−	54.6972i		−	1.86624i	0.359559	−	0.933122i	$-0.382927\pi$
$860$		0			0
$861$	−3.79096	−	11.6674i	−0.129196	−	0.397624i
$862$	8.46615	−	4.31372i	0.288358	−	0.146926i
$863$	14.0924	−	2.23202i	0.479711	−	0.0759788i	0.0881040	−	0.996111i	$-0.471919\pi$
$863$	14.0924	−	2.23202i	0.479711	−	0.0759788i	0.391607	+	0.920132i	$0.371919\pi$
$864$	11.1951	+	8.13370i	0.380864	+	0.276714i
$865$		0			0
$866$	23.7208	−	7.70734i	0.806064	−	0.261906i
$867$	38.2334	+	6.05557i	1.29847	+	0.205658i
$868$	−3.10158	−	3.10158i	−0.105274	−	0.105274i
$869$	6.14895	−	18.2250i	0.208589	−	0.618241i
$870$		0			0
$871$	4.75846	+	6.54946i	0.161234	+	0.221920i
$872$	0.857140	−	1.68223i	0.0290264	−	0.0569676i
$873$	−23.2512	−	45.6330i	−0.786932	−	1.54444i
$874$	15.7523	−	21.6812i	0.532829	−	0.733376i
$875$		0			0
$876$	34.8324	+	11.3177i	1.17688	+	0.382391i
$877$	−13.7086	−	6.98490i	−0.462908	−	0.235863i	0.206952	−	0.978351i	$-0.433646\pi$
$877$	−13.7086	−	6.98490i	−0.462908	−	0.235863i	−0.669860	+	0.742488i	$0.733646\pi$
$878$	0.264554	−	1.67033i	0.00892828	−	0.0563710i
$879$	−63.0707			−2.12732
$880$		0			0
$881$	−27.4651			−0.925323			−0.462662	−	0.886535i	$-0.653106\pi$
$881$	−27.4651			−0.925323			−0.462662	+	0.886535i	$0.653106\pi$
$882$	−5.34708	+	33.7601i	−0.180045	+	1.13676i
$883$	48.3824	+	24.6520i	1.62820	+	0.829607i	0.998612	+	0.0526752i	$0.0167748\pi$
$883$	48.3824	+	24.6520i	1.62820	+	0.829607i	0.629584	+	0.776932i	$0.283225\pi$
$884$	2.23854	+	0.727347i	0.0752904	+	0.0244633i
$885$		0			0
$886$	−11.9367	+	16.4295i	−0.401023	+	0.551960i
$887$	26.8712	+	52.7376i	0.902246	+	1.77076i	0.551111	+	0.834432i	$0.314204\pi$
$887$	26.8712	+	52.7376i	0.902246	+	1.77076i	0.351134	+	0.936325i	$0.385796\pi$
$888$	2.02896	−	3.98206i	0.0680875	−	0.133629i
$889$	15.2015	+	20.9231i	0.509843	+	0.701738i
$890$		0			0
$891$	−22.2636	−	71.2345i	−0.745858	−	2.38645i
$892$	3.52584	+	3.52584i	0.118054	+	0.118054i
$893$	−27.4601	−	4.34926i	−0.918918	−	0.145542i
$894$	−0.101769	+	0.0330667i	−0.00340366	+	0.00110592i
$895$		0			0
$896$	1.23329	+	0.896038i	0.0412014	+	0.0299345i
$897$	14.5177	−	2.29938i	0.484732	−	0.0767740i
$898$	37.4672	−	19.0905i	1.25030	−	0.637058i
$899$	−4.02649	−	12.3922i	−0.134291	−	0.413305i
$900$		0			0
$901$			8.45716i			0.281749i
$902$	−5.81141	−	5.94353i	−0.193499	−	0.197898i
$903$	−31.3733	+	31.3733i	−1.04404	+	1.04404i
$904$	3.22746	−	2.34489i	0.107344	−	0.0779899i
$905$		0			0
$906$	−21.0201	+	64.6931i	−0.698345	+	2.14928i
$907$	2.36980	+	14.9623i	0.0786880	+	0.496817i	0.995284	+	0.0970022i	$0.0309254\pi$
$907$	2.36980	+	14.9623i	0.0786880	+	0.496817i	−0.916596	+	0.399814i	$0.869075\pi$
$908$	0.319245	+	2.01564i	0.0105945	+	0.0668912i
$909$	−39.7815	+	122.435i	−1.31947	+	4.06091i
$910$		0			0
$911$	5.44856	−	3.95861i	0.180519	−	0.131155i	−0.493856	−	0.869544i	$-0.664413\pi$
$911$	5.44856	−	3.95861i	0.180519	−	0.131155i	0.674375	+	0.738389i	$0.264413\pi$
$912$	−14.0700	+	14.0700i	−0.465904	+	0.465904i
$913$	−2.96573	−	3.03315i	−0.0981512	−	0.100383i
$914$			10.1208i			0.334766i
$915$		0			0
$916$	0.470996	+	1.44958i	0.0155622	+	0.0478954i
$917$	−13.2792	+	6.76610i	−0.438518	+	0.223436i
$918$	30.3902	−	4.81333i	1.00302	−	0.158863i
$919$	47.2044	+	34.2960i	1.55713	+	1.13132i	0.938315	+	0.345782i	$0.112386\pi$
$919$	47.2044	+	34.2960i	1.55713	+	1.13132i	0.618813	+	0.785538i	$0.287614\pi$
$920$		0			0
$921$	36.0740	−	11.7212i	1.18868	−	0.386226i
$922$	27.1134	+	4.29433i	0.892931	+	0.141426i
$923$	6.66028	+	6.66028i	0.219226	+	0.219226i
$924$	−4.84277	−	15.4949i	−0.159315	−	0.509745i
$925$		0			0
$926$	−10.6467	−	14.6539i	−0.349872	−	0.481557i
$927$	10.6601	−	20.9216i	0.350123	−	0.687155i
$928$	2.05589	+	4.03492i	0.0674881	+	0.132453i
$929$	5.89306	−	8.11110i	0.193345	−	0.266117i	−0.701327	−	0.712839i	$-0.747409\pi$
$929$	5.89306	−	8.11110i	0.193345	−	0.266117i	0.894672	+	0.446723i	$0.147409\pi$
$930$		0			0
$931$	−27.5598	−	8.95473i	−0.903237	−	0.293480i
$932$	19.7711	+	10.0739i	0.647624	+	0.329981i
$933$	−6.98475	+	44.1000i	−0.228670	+	1.44377i
$934$	−21.8363			−0.714505
$935$		0			0
$936$	−7.73776			−0.252917
$937$	−6.52746	+	41.2128i	−0.213243	+	1.34636i	0.616120	+	0.787652i	$0.288703\pi$
$937$	−6.52746	+	41.2128i	−0.213243	+	1.34636i	−0.829363	+	0.558710i	$0.811297\pi$
$938$	10.3877	+	5.29282i	0.339172	+	0.172817i
$939$	92.1972	+	29.9567i	3.00874	+	0.977600i
$940$		0			0
$941$	14.4754	−	19.9237i	0.471885	−	0.649494i	−0.505035	−	0.863099i	$-0.668520\pi$
$941$	14.4754	−	19.9237i	0.471885	−	0.649494i	0.976920	+	0.213605i	$0.0685205\pi$
$942$	−2.86364	−	5.62021i	−0.0933025	−	0.183116i
$943$	4.92065	−	9.65732i	0.160238	−	0.314486i
$944$	2.63995	+	3.63358i	0.0859232	+	0.118263i
$945$		0			0
$946$	−9.61089	+	28.4859i	−0.312477	+	0.926157i
$947$	6.72877	+	6.72877i	0.218656	+	0.218656i	0.807932	−	0.589276i	$-0.200587\pi$
$947$	6.72877	+	6.72877i	0.218656	+	0.218656i	−0.589276	+	0.807932i	$0.700587\pi$
$948$	−18.3918	−	2.91297i	−0.597338	−	0.0946090i
$949$	−11.4836	+	3.73124i	−0.372772	+	0.121121i
$950$		0			0
$951$	79.6507	+	57.8696i	2.58285	+	1.87655i
$952$	3.34789	−	0.530254i	0.108506	−	0.0171856i
$953$	31.2897	−	15.9429i	1.01357	−	0.516441i	0.133384	−	0.991064i	$-0.457416\pi$
$953$	31.2897	−	15.9429i	1.01357	−	0.516441i	0.880189	+	0.474623i	$0.157416\pi$
$954$	−8.59137	−	26.4415i	−0.278156	−	0.856076i
$955$		0			0
$956$		−	24.7841i		−	0.801574i
$957$	8.07890	−	47.5436i	0.261154	−	1.53687i
$958$	−4.61171	+	4.61171i	−0.148998	+	0.148998i
$959$	−3.04719	+	2.21391i	−0.0983989	+	0.0714910i
$960$		0			0
$961$	−7.02117	+	21.6089i	−0.226489	+	0.697062i
$962$	0.230490	+	1.45526i	0.00743130	+	0.0469194i
$963$	18.8879	+	119.253i	0.608654	+	3.84289i
$964$	−0.0173846	+	0.0535042i	−0.000559919	+	0.00172325i
$965$		0			0
$966$	17.1249	−	12.4420i	0.550984	−	0.400313i
$967$	43.6347	−	43.6347i	1.40320	−	1.40320i	0.613512	−	0.789685i	$-0.289756\pi$
$967$	43.6347	−	43.6347i	1.40320	−	1.40320i	0.789685	−	0.613512i	$-0.210244\pi$
$968$	−7.60139	−	7.95103i	−0.244318	−	0.255556i
$969$			44.2438i			1.42131i
$970$		0			0
$971$	8.80597	+	27.1020i	0.282597	+	0.869744i	0.987109	+	0.160052i	$0.0511661\pi$
$971$	8.80597	+	27.1020i	0.282597	+	0.869744i	−0.704512	+	0.709693i	$0.748834\pi$
$972$	−27.3888	+	13.9553i	−0.878497	+	0.447617i
$973$	11.3119	−	1.79163i	0.362642	−	0.0574369i
$974$	−2.37265	−	1.72383i	−0.0760245	−	0.0552350i
$975$		0			0
$976$	5.63262	−	1.83015i	0.180296	−	0.0585817i
$977$	51.0116	+	8.07944i	1.63201	+	0.258484i	0.904140	−	0.427236i	$-0.140513\pi$
$977$	51.0116	+	8.07944i	1.63201	+	0.258484i	0.727865	+	0.685720i	$0.240513\pi$
$978$	−4.94335	−	4.94335i	−0.158071	−	0.158071i
$979$	20.2508	+	28.5420i	0.647219	+	0.912206i
$980$		0			0
$981$	8.11191	+	11.1651i	0.258993	+	0.356474i
$982$	−6.04634	+	11.8666i	−0.192946	+	0.378679i
$983$	−24.7809	−	48.6352i	−0.790387	−	1.55122i	−0.833737	−	0.552161i	$-0.813803\pi$
$983$	−24.7809	−	48.6352i	−0.790387	−	1.55122i	0.0433506	−	0.999060i	$-0.486197\pi$
$984$	−4.73019	+	6.51054i	−0.150793	+	0.207549i
$985$		0			0
$986$	9.57644	+	3.11157i	0.304976	+	0.0990927i
$987$	−19.5663	−	9.96952i	−0.622802	−	0.317333i
$988$	1.02620	−	6.47920i	0.0326479	−	0.206131i
$989$	−39.1997			−1.24648
$990$		0			0
$991$	1.67436			0.0531879			0.0265939	−	0.999646i	$-0.491534\pi$
$991$	1.67436			0.0531879			0.0265939	+	0.999646i	$0.491534\pi$
$992$	−0.450114	+	2.84191i	−0.0142911	+	0.0902306i
$993$	−40.7742	−	20.7755i	−1.29393	−	0.659291i
$994$	12.9005	+	4.19162i	0.409178	+	0.132950i
$995$		0			0
$996$	−2.41395	+	3.32251i	−0.0764888	+	0.105278i
$997$	13.5579	+	26.6089i	0.429384	+	0.842713i	0.999772	+	0.0213379i	$0.00679257\pi$
$997$	13.5579	+	26.6089i	0.429384	+	0.842713i	−0.570389	+	0.821375i	$0.693207\pi$
$998$	10.6099	−	20.8231i	0.335850	−	0.659143i
$999$	11.3212	+	15.5823i	0.358187	+	0.493002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.bh.b.107.1		48
5.2	odd	4		110.2.k.a.63.1	yes	48
5.3	odd	4	inner	550.2.bh.b.393.6		48
5.4	even	2		110.2.k.a.107.6	yes	48
11.7	odd	10	inner	550.2.bh.b.7.6		48
15.2	even	4		990.2.bh.c.613.6		48
15.14	odd	2		990.2.bh.c.217.2		48
20.7	even	4		880.2.cm.c.833.6		48
20.19	odd	2		880.2.cm.c.657.1		48
55.7	even	20		110.2.k.a.73.6	yes	48
55.18	even	20	inner	550.2.bh.b.293.1		48
55.29	odd	10		110.2.k.a.7.1	✓	48
165.29	even	10		990.2.bh.c.667.6		48
165.62	odd	20		990.2.bh.c.73.2		48
220.7	odd	20		880.2.cm.c.513.1		48
220.139	even	10		880.2.cm.c.337.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.1	✓	48	55.29	odd	10
110.2.k.a.63.1	yes	48	5.2	odd	4
110.2.k.a.73.6	yes	48	55.7	even	20
110.2.k.a.107.6	yes	48	5.4	even	2
550.2.bh.b.7.6		48	11.7	odd	10	inner
550.2.bh.b.107.1		48	1.1	even	1	trivial
550.2.bh.b.293.1		48	55.18	even	20	inner
550.2.bh.b.393.6		48	5.3	odd	4	inner
880.2.cm.c.337.6		48	220.139	even	10
880.2.cm.c.513.1		48	220.7	odd	20
880.2.cm.c.657.1		48	20.19	odd	2
880.2.cm.c.833.6		48	20.7	even	4
990.2.bh.c.73.2		48	165.62	odd	20
990.2.bh.c.217.2		48	15.14	odd	2
990.2.bh.c.613.6		48	15.2	even	4
990.2.bh.c.667.6		48	165.29	even	10

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-2.86091 - 1.45771i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.88730 - 2.59765i) q^{6} +(0.692077 + 1.35828i) q^{7} +(0.453990 - 0.891007i) q^{8} +(4.29653 + 5.91367i) q^{9} +(-2.70495 + 1.91918i) q^{11} +(2.27043 + 2.27043i) q^{12} +(-1.04553 - 0.165595i) q^{13} +(-1.44982 + 0.471075i) q^{14} +(0.809017 + 0.587785i) q^{16} +(2.19616 - 0.347837i) q^{17} +(-6.51299 + 3.31853i) q^{18} +(-1.91500 - 5.89375i) q^{19} -4.89475i q^{21} +(-1.47241 - 2.97187i) q^{22} +(3.05791 - 3.05791i) q^{23} +(-2.59765 + 1.88730i) q^{24} +(0.327113 - 1.00675i) q^{26} +(-2.16472 - 13.6675i) q^{27} +(-0.238474 - 1.50566i) q^{28} +(1.39938 - 4.30686i) q^{29} +(2.32781 - 1.69125i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(10.5362 - 1.54760i) q^{33} +2.22353i q^{34} +(-2.25882 - 6.95193i) q^{36} +(-1.24018 + 0.631904i) q^{37} +(6.12076 - 0.969434i) q^{38} +(2.74977 + 1.99782i) q^{39} +(2.38365 - 0.774496i) q^{41} +(4.83449 + 0.765708i) q^{42} +(-6.40957 - 6.40957i) q^{43} +(3.16562 - 0.989379i) q^{44} +(2.54190 + 3.49862i) q^{46} +(2.03678 - 3.99740i) q^{47} +(-1.45771 - 2.86091i) q^{48} +(2.74855 - 3.78305i) q^{49} +(-6.79005 - 2.20622i) q^{51} +(0.943185 + 0.480577i) q^{52} +(-0.594995 + 3.75665i) q^{53} +13.8379 q^{54} +1.52443 q^{56} +(-3.11273 + 19.6530i) q^{57} +(4.03492 + 2.05589i) q^{58} +(4.27154 + 1.38791i) q^{59} +(3.48115 - 4.79140i) q^{61} +(1.30628 + 2.56372i) q^{62} +(-5.05887 + 9.92860i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.119682 + 10.6486i) q^{66} +(-5.40776 - 5.40776i) q^{67} +(-2.19616 - 0.347837i) q^{68} +(-13.2059 + 4.29086i) q^{69} +(-7.19862 - 5.23010i) q^{71} +(7.21970 - 1.14349i) q^{72} +(10.1633 - 5.17847i) q^{73} +(-0.430117 - 1.32376i) q^{74} +6.19706i q^{76} +(-4.47882 - 2.34584i) q^{77} +(-2.40339 + 2.40339i) q^{78} +(-4.69179 + 3.40879i) q^{79} +(-6.95367 + 21.4012i) q^{81} +(0.392075 + 2.47546i) q^{82} +(0.200087 + 1.26330i) q^{83} +(-1.51256 + 4.65519i) q^{84} +(7.33334 - 5.32798i) q^{86} +(-10.2816 + 10.2816i) q^{87} +(0.481987 + 3.28142i) q^{88} -10.5518i q^{89} +(-0.498662 - 1.53472i) q^{91} +(-3.85319 + 1.96330i) q^{92} +(-9.12499 + 1.44526i) q^{93} +(3.62956 + 2.63703i) q^{94} +(3.05372 - 0.992214i) q^{96} +(-6.92020 - 1.09605i) q^{97} +(3.30651 + 3.30651i) q^{98} +(-22.9713 - 7.75031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{3} + 20 q^{7} + 12 q^{11} + 16 q^{12} + 12 q^{16} + 20 q^{17} + 4 q^{22} + 8 q^{23} + 8 q^{26} - 8 q^{27} + 20 q^{28} + 16 q^{31} + 104 q^{33} - 4 q^{36} - 20 q^{37} + 36 q^{38} - 20 q^{41}+ \cdots - 72 q^{97}+O(q^{100}) \) 48 * q + 4 * q^3 + 20 * q^7 + 12 * q^11 + 16 * q^12 + 12 * q^16 + 20 * q^17 + 4 * q^22 + 8 * q^23 + 8 * q^26 - 8 * q^27 + 20 * q^28 + 16 * q^31 + 104 * q^33 - 4 * q^36 - 20 * q^37 + 36 * q^38 - 20 * q^41 + 20 * q^42 + 40 * q^46 - 40 * q^47 - 4 * q^48 + 40 * q^51 - 40 * q^52 - 8 * q^56 - 48 * q^58 + 80 * q^61 - 40 * q^62 - 100 * q^63 + 24 * q^66 - 20 * q^68 - 56 * q^71 + 20 * q^73 + 96 * q^77 - 16 * q^78 - 68 * q^81 - 56 * q^86 + 4 * q^88 - 68 * q^91 + 12 * q^92 - 76 * q^93 - 72 * q^97

Introduction

L-functions

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