LMFDB - Embedded newform 980.2.x.m.863.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			863.8
Character	$\chi$	$=$	980.863
Dual form			980.2.x.m.67.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.667698 - 1.24667i) q^{2} +(-2.02821 - 0.543458i) q^{3} +(-1.10836 + 1.66480i) q^{4} +(0.518800 - 2.17505i) q^{5} +(0.676724 + 2.89137i) q^{6} +(2.81549 + 0.270171i) q^{8} +(1.22023 + 0.704499i) q^{9} +(-3.05797 + 0.805507i) q^{10} +(-0.366133 + 0.211387i) q^{11} +(3.15273 - 2.77421i) q^{12} +(1.56422 + 1.56422i) q^{13} +(-2.23429 + 4.12952i) q^{15} +(-1.54309 - 3.69038i) q^{16} +(4.41198 + 1.18219i) q^{17} +(0.0635313 - 1.99161i) q^{18} +(-3.66683 + 6.35114i) q^{19} +(3.04600 + 3.27443i) q^{20} +(0.507996 + 0.315303i) q^{22} +(1.72616 + 6.44210i) q^{23} +(-5.56360 - 2.07807i) q^{24} +(-4.46169 - 2.25683i) q^{25} +(0.905634 - 2.99449i) q^{26} +(2.36225 + 2.36225i) q^{27} -4.72835i q^{29} +(6.63997 + 0.0281364i) q^{30} +(1.70170 - 0.982474i) q^{31} +(-3.57035 + 4.38778i) q^{32} +(0.857477 - 0.229760i) q^{33} +(-1.47208 - 6.28961i) q^{34} +(-2.52529 + 1.25059i) q^{36} +(1.92971 + 7.20177i) q^{37} +(10.3661 + 0.330672i) q^{38} +(-2.32248 - 4.02266i) q^{39} +(2.04832 - 5.98368i) q^{40} +4.01882 q^{41} +(1.88664 - 1.88664i) q^{43} +(0.0538902 - 0.843830i) q^{44} +(2.16537 - 2.28856i) q^{45} +(6.87860 - 6.45332i) q^{46} +(6.35786 - 1.70358i) q^{47} +(1.12414 + 8.32348i) q^{48} +(0.165546 + 7.06913i) q^{50} +(-8.30597 - 4.79545i) q^{51} +(-4.33782 + 0.870391i) q^{52} +(-0.209015 + 0.780053i) q^{53} +(1.36767 - 4.52221i) q^{54} +(0.269828 + 0.906026i) q^{55} +(10.8887 - 10.8887i) q^{57} +(-5.89468 + 3.15711i) q^{58} +(-1.35717 - 2.35069i) q^{59} +(-4.39842 - 8.29662i) q^{60} +(-0.925760 + 1.60346i) q^{61} +(-2.36104 - 1.46545i) q^{62} +(7.85401 + 1.52133i) q^{64} +(4.21378 - 2.59074i) q^{65} +(-0.858970 - 0.915577i) q^{66} +(2.33152 - 8.70137i) q^{67} +(-6.85815 + 6.03476i) q^{68} -14.0041i q^{69} -3.16317i q^{71} +(3.24521 + 2.31318i) q^{72} +(1.78752 - 6.67113i) q^{73} +(7.68975 - 7.21432i) q^{74} +(7.82277 + 7.00208i) q^{75} +(-6.50918 - 13.1438i) q^{76} +(-3.46420 + 5.58129i) q^{78} +(1.77995 - 3.08296i) q^{79} +(-8.82731 + 1.44173i) q^{80} +(-5.62086 - 9.73561i) q^{81} +(-2.68336 - 5.01013i) q^{82} +(-4.71846 + 4.71846i) q^{83} +(4.86025 - 8.98296i) q^{85} +(-3.61172 - 1.09231i) q^{86} +(-2.56966 + 9.59011i) q^{87} +(-1.08796 + 0.496241i) q^{88} +(10.0333 + 5.79271i) q^{89} +(-4.29889 - 1.17143i) q^{90} +(-12.6380 - 4.26646i) q^{92} +(-3.98534 + 1.06787i) q^{93} +(-6.36893 - 6.78865i) q^{94} +(11.9117 + 11.2705i) q^{95} +(9.62601 - 6.95901i) q^{96} +(4.64008 - 4.64008i) q^{97} -0.595688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) $ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.667698	−	1.24667i	−0.472134	−	0.881527i
$2$	−0.667698	−	1.24667i	−0.472134	−	0.881527i
$3$	−2.02821	−	0.543458i	−1.17099	−	0.313766i	−0.379643	−	0.925133i	$-0.623953\pi$
$3$	−2.02821	−	0.543458i	−1.17099	−	0.313766i	−0.791347	+	0.611367i	$0.790620\pi$
$4$	−1.10836	+	1.66480i	−0.554179	+	0.832398i
$5$	0.518800	−	2.17505i	0.232014	−	0.972712i
$5$	0.518800	−	2.17505i	0.232014	−	0.972712i
$6$	0.676724	+	2.89137i	0.276271	+	1.18040i
$7$		0			0
$7$		0			0
$8$	2.81549	+	0.270171i	0.995428	+	0.0955200i
$9$	1.22023	+	0.704499i	0.406742	+	0.234833i
$10$	−3.05797	+	0.805507i	−0.967014	+	0.254724i
$11$	−0.366133	+	0.211387i	−0.110393	+	0.0637356i	−0.554180	−	0.832397i	$-0.686968\pi$
$11$	−0.366133	+	0.211387i	−0.110393	+	0.0637356i	0.443787	+	0.896132i	$0.353635\pi$
$12$	3.15273	−	2.77421i	0.910115	−	0.800847i
$13$	1.56422	+	1.56422i	0.433837	+	0.433837i	0.889931	−	0.456095i	$-0.150752\pi$
$13$	1.56422	+	1.56422i	0.433837	+	0.433837i	−0.456095	+	0.889931i	$0.650752\pi$
$14$		0			0
$15$	−2.23429	+	4.12952i	−0.576890	+	1.06624i
$16$	−1.54309	−	3.69038i	−0.385772	−	0.922594i
$17$	4.41198	+	1.18219i	1.07006	+	0.286722i	0.750519	−	0.660849i	$-0.229804\pi$
$17$	4.41198	+	1.18219i	1.07006	+	0.286722i	0.319544	+	0.947572i	$0.396470\pi$
$18$	0.0635313	−	1.99161i	0.0149745	−	0.469427i
$19$	−3.66683	+	6.35114i	−0.841228	+	1.45705i	0.0476283	+	0.998865i	$0.484834\pi$
$19$	−3.66683	+	6.35114i	−0.841228	+	1.45705i	−0.888857	+	0.458185i	$0.848500\pi$
$20$	3.04600	+	3.27443i	0.681106	+	0.732185i
$21$		0			0
$22$	0.507996	+	0.315303i	0.108305	+	0.0672229i
$23$	1.72616	+	6.44210i	0.359928	+	1.34327i	0.874168	+	0.485624i	$0.161408\pi$
$23$	1.72616	+	6.44210i	0.359928	+	1.34327i	−0.514239	+	0.857647i	$0.671926\pi$
$24$	−5.56360	−	2.07807i	−1.13566	−	0.424184i
$25$	−4.46169	−	2.25683i	−0.892339	−	0.451367i
$26$	0.905634	−	2.99449i	0.177610	−	0.587268i
$27$	2.36225	+	2.36225i	0.454615	+	0.454615i
$28$		0			0
$29$		−	4.72835i		−	0.878033i	−0.898479	−	0.439016i	$-0.855327\pi$
$29$		−	4.72835i		−	0.878033i	0.898479	−	0.439016i	$-0.144673\pi$
$30$	6.63997	+	0.0281364i	1.21229	+	0.00513698i
$31$	1.70170	−	0.982474i	0.305634	−	0.176458i	−0.339337	−	0.940665i	$-0.610203\pi$
$31$	1.70170	−	0.982474i	0.305634	−	0.176458i	0.644971	+	0.764207i	$0.276869\pi$
$32$	−3.57035	+	4.38778i	−0.631155	+	0.775656i
$33$	0.857477	−	0.229760i	0.149268	−	0.0399961i
$34$	−1.47208	−	6.28961i	−0.252459	−	1.07866i
$35$		0			0
$36$	−2.52529	+	1.25059i	−0.420882	+	0.208432i
$37$	1.92971	+	7.20177i	0.317242	+	1.18396i	0.921884	+	0.387467i	$0.126650\pi$
$37$	1.92971	+	7.20177i	0.317242	+	1.18396i	−0.604641	+	0.796498i	$0.706684\pi$
$38$	10.3661	+	0.330672i	1.68160	+	0.0536422i
$39$	−2.32248	−	4.02266i	−0.371895	−	0.644141i
$40$	2.04832	−	5.98368i	0.323867	−	0.946103i
$41$	4.01882			0.627634			0.313817	−	0.949483i	$-0.398392\pi$
$41$	4.01882			0.627634			0.313817	+	0.949483i	$0.398392\pi$
$42$		0			0
$43$	1.88664	−	1.88664i	0.287710	−	0.287710i	−0.548464	−	0.836174i	$-0.684787\pi$
$43$	1.88664	−	1.88664i	0.287710	−	0.287710i	0.836174	+	0.548464i	$0.184787\pi$
$44$	0.0538902	−	0.843830i	0.00812426	−	0.127212i
$45$	2.16537	−	2.28856i	0.322795	−	0.341159i
$46$	6.87860	−	6.45332i	1.01419	−	0.951491i
$47$	6.35786	−	1.70358i	0.927389	−	0.248493i	0.236648	−	0.971595i	$-0.423951\pi$
$47$	6.35786	−	1.70358i	0.927389	−	0.248493i	0.690741	+	0.723102i	$0.257284\pi$
$48$	1.12414	+	8.32348i	0.162256	+	1.20139i
$49$		0			0
$50$	0.165546	+	7.06913i	0.0234117	+	0.999726i
$51$	−8.30597	−	4.79545i	−1.16307	−	0.671498i
$52$	−4.33782	+	0.870391i	−0.601548	+	0.120702i
$53$	−0.209015	+	0.780053i	−0.0287104	+	0.107149i	−0.978794	−	0.204846i	$-0.934331\pi$
$53$	−0.209015	+	0.780053i	−0.0287104	+	0.107149i	0.950084	+	0.311995i	$0.100997\pi$
$54$	1.36767	−	4.52221i	0.186116	−	0.615395i
$55$	0.269828	+	0.906026i	0.0363836	+	0.122169i
$56$		0			0
$57$	10.8887	−	10.8887i	1.44224	−	1.44224i
$58$	−5.89468	+	3.15711i	−0.774009	+	0.414549i
$59$	−1.35717	−	2.35069i	−0.176689	−	0.306034i	0.764056	−	0.645151i	$-0.223205\pi$
$59$	−1.35717	−	2.35069i	−0.176689	−	0.306034i	−0.940744	+	0.339116i	$0.889872\pi$
$60$	−4.39842	−	8.29662i	−0.567834	−	1.07109i
$61$	−0.925760	+	1.60346i	−0.118531	+	0.205302i	−0.919186	−	0.393824i	$-0.871152\pi$
$61$	−0.925760	+	1.60346i	−0.118531	+	0.205302i	0.800654	+	0.599126i	$0.204485\pi$
$62$	−2.36104	−	1.46545i	−0.299852	−	0.186112i
$63$		0			0
$64$	7.85401	+	1.52133i	0.981752	+	0.190167i
$65$	4.21378	−	2.59074i	0.522655	−	0.321342i
$66$	−0.858970	−	0.915577i	−0.105732	−	0.112700i
$67$	2.33152	−	8.70137i	0.284841	−	1.06304i	−0.664114	−	0.747631i	$-0.731191\pi$
$67$	2.33152	−	8.70137i	0.284841	−	1.06304i	0.948955	−	0.315410i	$-0.102142\pi$
$68$	−6.85815	+	6.03476i	−0.831673	+	0.731822i
$69$		−	14.0041i		−	1.68589i
$70$		0			0
$71$		−	3.16317i		−	0.375400i	−0.982226	−	0.187700i	$-0.939897\pi$
$71$		−	3.16317i		−	0.375400i	0.982226	−	0.187700i	$-0.0601032\pi$
$72$	3.24521	+	2.31318i	0.382451	+	0.272611i
$73$	1.78752	−	6.67113i	0.209214	−	0.780797i	−0.778910	−	0.627136i	$-0.784227\pi$
$73$	1.78752	−	6.67113i	0.209214	−	0.780797i	0.988124	−	0.153661i	$-0.0491063\pi$
$74$	7.68975	−	7.21432i	0.893915	−	0.838648i
$75$	7.82277	+	7.00208i	0.903296	+	0.808531i
$76$	−6.50918	−	13.1438i	−0.746654	−	1.50770i
$77$		0			0
$78$	−3.46420	+	5.58129i	−0.392243	+	0.631957i
$79$	1.77995	−	3.08296i	0.200260	−	0.346860i	−0.748352	−	0.663301i	$-0.769155\pi$
$79$	1.77995	−	3.08296i	0.200260	−	0.346860i	0.948612	+	0.316441i	$0.102488\pi$
$80$	−8.82731	+	1.44173i	−0.986923	+	0.161190i
$81$	−5.62086	−	9.73561i	−0.624540	−	1.08173i
$82$	−2.68336	−	5.01013i	−0.296328	−	0.553276i
$83$	−4.71846	+	4.71846i	−0.517919	+	0.517919i	−0.916941	−	0.399022i	$-0.869350\pi$
$83$	−4.71846	+	4.71846i	−0.517919	+	0.517919i	0.399022	+	0.916941i	$0.369350\pi$
$84$		0			0
$85$	4.86025	−	8.98296i	0.527168	−	0.974339i
$86$	−3.61172	−	1.09231i	−0.389462	−	0.117786i
$87$	−2.56966	+	9.59011i	−0.275497	+	1.02817i
$88$	−1.08796	+	0.496241i	−0.115977	+	0.0528994i
$89$	10.0333	+	5.79271i	1.06352	+	0.614026i	0.926405	−	0.376529i	$-0.122882\pi$
$89$	10.0333	+	5.79271i	1.06352	+	0.614026i	0.137119	+	0.990555i	$0.456216\pi$
$90$	−4.29889	−	1.17143i	−0.453143	−	0.123480i
$91$		0			0
$92$	−12.6380	−	4.26646i	−1.31760	−	0.444809i
$93$	−3.98534	+	1.06787i	−0.413260	+	0.110733i
$94$	−6.36893	−	6.78865i	−0.656905	−	0.700196i
$95$	11.9117	+	11.2705i	1.22211	+	1.15633i
$96$	9.62601	−	6.95901i	0.982451	−	0.710251i
$97$	4.64008	−	4.64008i	0.471128	−	0.471128i	−0.431151	−	0.902280i	$-0.641892\pi$
$97$	4.64008	−	4.64008i	0.471128	−	0.471128i	0.902280	+	0.431151i	$0.141892\pi$
$98$		0			0
$99$	−0.595688			−0.0598689
$100$	8.70232	−	4.92643i	0.870232	−	0.492643i
$101$	2.12019	+	3.67228i	0.210967	+	0.365406i	0.952017	−	0.306044i	$-0.0990054\pi$
$101$	2.12019	+	3.67228i	0.210967	+	0.365406i	−0.741050	+	0.671449i	$0.765672\pi$
$102$	−0.432451	+	13.5567i	−0.0428190	+	1.34231i
$103$	−4.06958	−	15.1879i	−0.400987	−	1.49651i	−0.811338	−	0.584577i	$-0.801260\pi$
$103$	−4.06958	−	15.1879i	−0.400987	−	1.49651i	0.410351	−	0.911928i	$-0.365406\pi$
$104$	3.98145	+	4.82666i	0.390413	+	0.473293i
$105$		0			0
$106$	1.11203	−	0.260269i	0.108009	−	0.0252795i
$107$	−0.542724	+	0.145422i	−0.0524671	+	0.0140585i	−0.284957	−	0.958540i	$-0.591979\pi$
$107$	−0.542724	+	0.145422i	−0.0524671	+	0.0140585i	0.232490	+	0.972599i	$0.425313\pi$
$108$	−6.55088	+	1.31445i	−0.630359	+	0.126483i
$109$	−4.52802	+	2.61425i	−0.433706	+	0.250400i	−0.700924	−	0.713236i	$-0.747229\pi$
$109$	−4.52802	+	2.61425i	−0.433706	+	0.250400i	0.267218	+	0.963636i	$0.413895\pi$
$110$	0.949350	−	0.941338i	0.0905169	−	0.0897530i
$111$		−	15.6555i		−	1.48595i
$112$		0			0
$113$	9.46096	+	9.46096i	0.890012	+	0.890012i	0.994524	−	0.104511i	$-0.0333278\pi$
$113$	9.46096	+	9.46096i	0.890012	+	0.890012i	−0.104511	+	0.994524i	$0.533328\pi$
$114$	−20.8449	−	6.30421i	−1.95231	−	0.590443i
$115$	14.9074	−	0.412314i	1.39012	−	0.0384485i
$116$	7.87174	+	5.24070i	0.730872	+	0.486587i
$117$	0.806713	+	3.01070i	0.0745807	+	0.278339i
$118$	−2.02435	+	3.26150i	−0.186357	+	0.300245i
$119$		0			0
$120$	−7.40630	+	11.0230i	−0.676100	+	1.00626i
$121$	−5.41063	+	9.37149i	−0.491876	+	0.851953i
$122$	2.61711	+	0.0834845i	0.236942	+	0.00755833i
$123$	−8.15103	−	2.18406i	−0.734953	−	0.196930i
$124$	−0.250468	+	3.92191i	−0.0224927	+	0.352198i
$125$	−7.22345	+	8.53356i	−0.646085	+	0.763265i
$126$		0			0
$127$	15.7173	+	15.7173i	1.39469	+	1.39469i	0.814439	+	0.580249i	$0.197045\pi$
$127$	15.7173	+	15.7173i	1.39469	+	1.39469i	0.580249	+	0.814439i	$0.302955\pi$
$128$	−3.34752	−	10.8071i	−0.295882	−	0.955225i
$129$	−4.85182	+	2.80120i	−0.427179	+	0.246632i
$130$	−6.04332	−	3.52334i	−0.530035	−	0.309018i
$131$	−15.5632	−	8.98542i	−1.35976	−	0.785060i	−0.370171	−	0.928963i	$-0.620701\pi$
$131$	−15.5632	−	8.98542i	−1.35976	−	0.785060i	−0.989592	+	0.143904i	$0.954034\pi$
$132$	−0.567887	+	1.68218i	−0.0494282	+	0.146415i
$133$		0			0
$134$	−12.4045	+	2.90326i	−1.07158	+	0.250803i
$135$	6.36355	−	3.91248i	0.547687	−	0.336733i
$136$	12.1025	+	4.52043i	1.03778	+	0.387624i
$137$	12.9822	+	3.47858i	1.10915	+	0.297195i	0.766485	−	0.642263i	$-0.222004\pi$
$137$	12.9822	+	3.47858i	1.10915	+	0.297195i	0.342664	+	0.939458i	$0.388671\pi$
$138$	−17.4584	+	9.35048i	−1.48616	+	0.795966i
$139$	6.16658			0.523043			0.261521	−	0.965198i	$-0.415776\pi$
$139$	6.16658			0.523043			0.261521	+	0.965198i	$0.415776\pi$
$140$		0			0
$141$	−13.8209			−1.16393
$142$	−3.94343	+	2.11205i	−0.330925	+	0.177239i
$143$	−0.903369	−	0.242057i	−0.0755435	−	0.0202418i
$144$	0.716948	−	5.59020i	0.0597457	−	0.465850i
$145$	−10.2844	−	2.45307i	−0.854073	−	0.203716i
$146$	−9.51021	+	2.22586i	−0.787070	+	0.184213i
$147$		0			0
$148$	−14.1283	−	4.76957i	−1.16134	−	0.392056i
$149$	4.22837	+	2.44125i	0.346401	+	0.199995i	0.663099	−	0.748532i	$-0.269241\pi$
$149$	4.22837	+	2.44125i	0.346401	+	0.199995i	−0.316698	+	0.948526i	$0.602574\pi$
$150$	3.50601	−	14.4277i	0.286265	−	1.17801i
$151$	−3.04218	+	1.75640i	−0.247569	+	0.142934i	−0.618651	−	0.785666i	$-0.712320\pi$
$151$	−3.04218	+	1.75640i	−0.247569	+	0.142934i	0.371082	+	0.928600i	$0.378987\pi$
$152$	−12.0398	+	16.8909i	−0.976559	+	1.37003i
$153$	4.55077	+	4.55077i	0.367908	+	0.367908i
$154$		0			0
$155$	−1.25409	−	4.21098i	−0.100731	−	0.338234i
$156$	9.27105	+	0.592085i	0.742278	+	0.0474048i
$157$	13.0349	+	3.49270i	1.04030	+	0.278748i	0.738238	−	0.674541i	$-0.235658\pi$
$157$	13.0349	+	3.49270i	1.04030	+	0.278748i	0.302062	+	0.953288i	$0.402325\pi$
$158$	−5.03189	−	0.160515i	−0.400316	−	0.0127699i
$159$	0.847853	−	1.46852i	0.0672391	−	0.116462i
$160$	7.69133	+	10.0421i	0.608053	+	0.793896i
$161$		0			0
$162$	−8.38403	+	13.5078i	−0.658712	+	1.06127i
$163$	−1.49311	−	5.57237i	−0.116950	−	0.436462i	0.882476	−	0.470358i	$-0.155875\pi$
$163$	−1.49311	−	5.57237i	−0.116950	−	0.436462i	−0.999425	+	0.0338961i	$0.989208\pi$
$164$	−4.45429	+	6.69051i	−0.347822	+	0.522441i
$165$	−0.0548811	−	1.98426i	−0.00427249	−	0.154474i
$166$	9.03287	+	2.73184i	0.701086	+	0.212032i
$167$	6.11518	+	6.11518i	0.473207	+	0.473207i	0.902951	−	0.429744i	$-0.141396\pi$
$167$	6.11518	+	6.11518i	0.473207	+	0.473207i	−0.429744	+	0.902951i	$0.641396\pi$
$168$		0			0
$169$		−	8.10643i		−	0.623572i
$170$	−14.4439	−	0.0612051i	−1.10780	−	0.00469422i
$171$	−8.94873	+	5.16655i	−0.684327	+	0.395096i
$172$	1.04980	+	5.23194i	0.0800463	+	0.398932i
$173$	4.22300	−	1.13155i	0.321069	−	0.0860302i	−0.0946850	−	0.995507i	$-0.530184\pi$
$173$	4.22300	−	1.13155i	0.321069	−	0.0860302i	0.415754	+	0.909477i	$0.363518\pi$
$174$	13.6714	−	3.19979i	1.03643	−	0.242575i
$175$		0			0
$176$	1.34507	+	1.02498i	0.101389	+	0.0772609i
$177$	1.47513	+	5.50528i	0.110878	+	0.413802i
$178$	0.522383	−	16.3759i	0.0391542	−	1.22743i
$179$	9.00305	+	15.5937i	0.672920	+	1.16553i	0.977072	+	0.212908i	$0.0682934\pi$
$179$	9.00305	+	15.5937i	0.672920	+	1.16553i	−0.304152	+	0.952623i	$0.598373\pi$
$180$	1.40998	+	6.14145i	0.105094	+	0.457757i
$181$	−14.5671			−1.08276			−0.541382	−	0.840777i	$-0.682099\pi$
$181$	−14.5671			−1.08276			−0.541382	+	0.840777i	$0.682099\pi$
$182$		0			0
$183$	2.74905	−	2.74905i	0.203216	−	0.203216i
$184$	3.11951	+	18.6041i	0.229973	+	1.37151i
$185$	16.6654	−	0.460935i	1.22526	−	0.0338886i
$186$	3.99228	+	4.25537i	0.292728	+	0.312019i
$187$	−1.86527	+	0.499798i	−0.136402	+	0.0365489i
$188$	−4.21066	+	12.4727i	−0.307094	+	0.909666i
$189$		0			0
$190$	6.09716	−	22.3752i	0.442334	−	1.62327i
$191$	8.77337	+	5.06530i	0.634818	+	0.366513i	0.782616	−	0.622505i	$-0.213885\pi$
$191$	8.77337	+	5.06530i	0.634818	+	0.366513i	−0.147797	+	0.989018i	$0.547218\pi$
$192$	−15.1028	−	7.35392i	−1.08995	−	0.530723i
$193$	−5.49463	+	20.5062i	−0.395512	+	1.47607i	0.425395	+	0.905008i	$0.360135\pi$
$193$	−5.49463	+	20.5062i	−0.395512	+	1.47607i	−0.820907	+	0.571063i	$0.806531\pi$
$194$	−8.88280	−	2.68646i	−0.637748	−	0.192876i
$195$	−9.95440	+	2.96456i	−0.712849	+	0.212297i
$196$		0			0
$197$	−14.1612	+	14.1612i	−1.00895	+	1.00895i	−0.00898613	+	0.999960i	$0.502860\pi$
$197$	−14.1612	+	14.1612i	−1.00895	+	1.00895i	−0.999960	+	0.00898613i	$0.997140\pi$
$198$	0.397740	+	0.742625i	0.0282661	+	0.0527760i
$199$	3.64221	+	6.30849i	0.258189	+	0.447197i	0.965757	−	0.259449i	$-0.0835408\pi$
$199$	3.64221	+	6.30849i	0.258189	+	0.447197i	−0.707568	+	0.706646i	$0.750207\pi$
$200$	−11.9521	−	7.55952i	−0.845144	−	0.534539i
$201$	−9.45766	+	16.3811i	−0.667092	+	1.15544i
$202$	3.16246	−	5.09515i	0.222510	−	0.358494i
$203$		0			0
$204$	17.1894	−	8.51266i	1.20350	−	0.596005i
$205$	2.08496	−	8.74114i	0.145620	−	0.610508i
$206$	−16.2170	+	15.2143i	−1.12989	+	1.06003i
$207$	−2.43215	+	9.07690i	−0.169046	+	0.630888i
$208$	3.35883	−	8.18629i	0.232893	−	0.567617i
$209$		−	3.10048i		−	0.214465i
$210$		0			0
$211$		−	17.4066i		−	1.19832i	−0.800630	−	0.599159i	$-0.795502\pi$
$211$		−	17.4066i		−	1.19832i	0.800630	−	0.599159i	$-0.204498\pi$
$212$	−1.06697	−	1.21254i	−0.0732795	−	0.0832779i
$213$	−1.71905	+	6.41559i	−0.117788	+	0.439589i
$214$	0.543669	+	0.579497i	0.0371644	+	0.0396136i
$215$	−3.12475	−	5.08233i	−0.213106	−	0.346612i
$216$	6.01269	+	7.28911i	0.409112	+	0.495961i
$217$		0			0
$218$	6.28245	+	3.89940i	0.425502	+	0.264101i
$219$	−7.25096	+	12.5590i	−0.489975	+	0.848661i
$220$	−1.80741	−	0.554993i	−0.121856	−	0.0374176i
$221$	5.05211	+	8.75051i	0.339842	+	0.588623i
$222$	−19.5171	+	10.4531i	−1.30990	+	0.701568i
$223$	−1.68218	+	1.68218i	−0.112647	+	0.112647i	−0.761183	−	0.648537i	$-0.775381\pi$
$223$	−1.68218	+	1.68218i	−0.112647	+	0.112647i	0.648537	+	0.761183i	$0.275381\pi$
$224$		0			0
$225$	−3.85434	−	5.89711i	−0.256956	−	0.393140i
$226$	5.47760	−	18.1117i	0.364364	−	1.20477i
$227$	4.05161	−	15.1208i	0.268915	−	1.00360i	−0.690895	−	0.722955i	$-0.742783\pi$
$227$	4.05161	−	15.1208i	0.268915	−	1.00360i	0.959810	−	0.280650i	$-0.0905499\pi$
$228$	6.05888	+	30.1960i	0.401259	+	1.99978i
$229$	14.7843	+	8.53574i	0.976976	+	0.564057i	0.901356	−	0.433079i	$-0.142573\pi$
$229$	14.7843	+	8.53574i	0.976976	+	0.564057i	0.0756201	+	0.997137i	$0.475906\pi$
$230$	−10.4677	−	18.3093i	−0.690219	−	1.20728i
$231$		0			0
$232$	1.27747	−	13.3126i	0.0838697	−	0.874018i
$233$	13.4441	−	3.60234i	0.880753	−	0.235997i	0.210021	−	0.977697i	$-0.432647\pi$
$233$	13.4441	−	3.60234i	0.880753	−	0.235997i	0.670732	+	0.741700i	$0.265980\pi$
$234$	3.21469	−	3.01594i	0.210151	−	0.197158i
$235$	−0.406922	−	14.7125i	−0.0265447	−	0.959737i
$236$	5.41766	+	0.345993i	0.352659	+	0.0225222i
$237$	−5.28558	+	5.28558i	−0.343335	+	0.343335i
$238$		0			0
$239$	7.51141			0.485873			0.242936	−	0.970042i	$-0.421889\pi$
$239$	7.51141			0.485873			0.242936	+	0.970042i	$0.421889\pi$
$240$	18.6872	+	1.87315i	1.20625	+	0.120911i
$241$	−3.62580	−	6.28008i	−0.233559	−	0.404535i	0.725294	−	0.688439i	$-0.241704\pi$
$241$	−3.62580	−	6.28008i	−0.233559	−	0.404535i	−0.958853	+	0.283904i	$0.908370\pi$
$242$	15.2958	+	0.487927i	0.983251	+	0.0313652i
$243$	3.51547	+	13.1199i	0.225518	+	0.841644i
$244$	−1.64336	−	3.31841i	−0.105206	−	0.212439i
$245$		0			0
$246$	2.71963	+	11.6199i	0.173397	+	0.740858i
$247$	−15.6703	+	4.19885i	−0.997078	+	0.267166i
$248$	5.05655	−	2.30640i	0.321091	−	0.146457i
$249$	12.1343	−	7.00577i	0.768983	−	0.443972i
$250$	15.4616	+	3.30740i	0.977878	+	0.209178i
$251$			3.63825i			0.229644i	0.993386	+	0.114822i	$0.0366298\pi$
$251$			3.63825i			0.229644i	−0.993386	+	0.114822i	$0.963370\pi$
$252$		0			0
$253$	−1.99378	−	1.99378i	−0.125348	−	0.125348i
$254$	9.09984	−	30.0887i	0.570975	−	1.88793i
$255$	−14.7395	+	15.5780i	−0.923023	+	0.975534i
$256$	−11.2378	+	11.3891i	−0.702360	+	0.711822i
$257$	1.80480	+	6.73562i	0.112581	+	0.420156i	0.999095	−	0.0425454i	$-0.0135467\pi$
$257$	1.80480	+	6.73562i	0.112581	+	0.420156i	−0.886514	+	0.462702i	$0.846880\pi$
$258$	6.73171	+	4.17825i	0.419098	+	0.260126i
$259$		0			0
$260$	−0.357317	+	9.88654i	−0.0221599	+	0.613137i
$261$	3.33112	−	5.76966i	0.206191	−	0.357133i
$262$	−0.810300	+	25.4017i	−0.0500605	+	1.56932i
$263$	−24.5021	−	6.56533i	−1.51087	−	0.404836i	−0.594144	−	0.804359i	$-0.702509\pi$
$263$	−24.5021	−	6.56533i	−1.51087	−	0.404836i	−0.916723	+	0.399523i	$0.869176\pi$
$264$	2.47630	−	0.415223i	0.152405	−	0.0255552i
$265$	1.58822	+	0.859309i	0.0975635	+	0.0527869i
$266$		0			0
$267$	−17.2015	−	17.2015i	−1.05271	−	1.05271i
$268$	11.9018	+	13.5257i	0.727020	+	0.826216i
$269$	−16.4868	+	9.51864i	−1.00522	+	0.580361i	−0.909787	−	0.415075i	$-0.863755\pi$
$269$	−16.4868	+	9.51864i	−1.00522	+	0.580361i	−0.0954283	+	0.995436i	$0.530422\pi$
$270$	−9.12649	−	5.32087i	−0.555420	−	0.323818i
$271$	18.2717	+	10.5492i	1.10993	+	0.640817i	0.938811	−	0.344434i	$-0.111929\pi$
$271$	18.2717	+	10.5492i	1.10993	+	0.640817i	0.171117	+	0.985251i	$0.445262\pi$
$272$	−2.44536	−	18.1061i	−0.148271	−	1.09784i
$273$		0			0
$274$	−4.33159	−	18.5072i	−0.261681	−	1.11806i
$275$	2.11064	−	0.116843i	0.127276	−	0.00704588i
$276$	23.3139	+	15.5215i	1.40333	+	0.934284i
$277$	15.5701	+	4.17199i	0.935515	+	0.250670i	0.694205	−	0.719778i	$-0.255756\pi$
$277$	15.5701	+	4.17199i	0.935515	+	0.250670i	0.241310	+	0.970448i	$0.422423\pi$
$278$	−4.11742	−	7.68767i	−0.246946	−	0.461076i
$279$	2.76861			0.165752
$280$		0			0
$281$	−6.00749			−0.358377			−0.179189	−	0.983815i	$-0.557347\pi$
$281$	−6.00749			−0.358377			−0.179189	+	0.983815i	$0.557347\pi$
$282$	9.22821	+	17.2301i	0.549532	+	1.02604i
$283$	1.60792	+	0.430842i	0.0955812	+	0.0256109i	0.306293	−	0.951937i	$-0.400911\pi$
$283$	1.60792	+	0.430842i	0.0955812	+	0.0256109i	−0.210711	+	0.977548i	$0.567578\pi$
$284$	5.26604	+	3.50593i	0.312482	+	0.208039i
$285$	−18.0344	−	29.3325i	−1.06827	−	1.73751i
$286$	0.301414	+	1.28782i	0.0178230	+	0.0761505i
$287$		0			0
$288$	−7.44783	+	2.83877i	−0.438867	+	0.167276i
$289$	3.34556	+	1.93156i	0.196798	+	0.113621i
$290$	3.80872	+	14.4591i	0.223656	+	0.849070i
$291$	−11.9328	+	6.88938i	−0.699510	+	0.403863i
$292$	9.12485	+	10.3699i	0.533992	+	0.606850i
$293$	14.2453	+	14.2453i	0.832220	+	0.832220i	0.987820	−	0.155600i	$-0.0497311\pi$
$293$	14.2453	+	14.2453i	0.832220	+	0.832220i	−0.155600	+	0.987820i	$0.549731\pi$
$294$		0			0
$295$	−5.81698	+	1.73238i	−0.338678	+	0.100863i
$296$	3.48737	+	20.7979i	0.202699	+	1.20885i
$297$	−1.36425	−	0.365549i	−0.0791617	−	0.0212113i
$298$	0.220150	−	6.90138i	0.0127530	−	0.399786i
$299$	−7.37678	+	12.7770i	−0.426610	+	0.738910i
$300$	−20.3275	+	5.26250i	−1.17361	+	0.303831i
$301$		0			0
$302$	4.22091	+	2.61984i	0.242886	+	0.150755i
$303$	−2.30447	−	8.60041i	−0.132388	−	0.494081i
$304$	29.0963	+	3.73163i	1.66879	+	0.214024i
$305$	3.00733	+	2.84545i	0.172199	+	0.162930i
$306$	2.63475	−	8.71184i	0.150619	−	0.498023i
$307$	−3.60252	−	3.60252i	−0.205607	−	0.205607i	0.596790	−	0.802397i	$-0.296442\pi$
$307$	−3.60252	−	3.60252i	−0.205607	−	0.205607i	−0.802397	+	0.596790i	$0.796442\pi$
$308$		0			0
$309$			33.0159i			1.87821i
$310$	−4.41234	+	4.37510i	−0.250604	+	0.248489i
$311$	0.374701	−	0.216334i	0.0212473	−	0.0122672i	−0.489339	−	0.872094i	$-0.662762\pi$
$311$	0.374701	−	0.216334i	0.0212473	−	0.0122672i	0.510586	+	0.859827i	$0.329428\pi$
$312$	−5.45213	−	11.9532i	−0.308666	−	0.676719i
$313$	0.994998	−	0.266609i	0.0562406	−	0.0150696i	−0.230589	−	0.973051i	$-0.574065\pi$
$313$	0.994998	−	0.266609i	0.0562406	−	0.0150696i	0.286830	+	0.957982i	$0.407399\pi$
$314$	−4.34917	−	18.5823i	−0.245438	−	1.04866i
$315$		0			0
$316$	3.15968	+	6.38027i	0.177746	+	0.358918i
$317$	−7.29750	−	27.2346i	−0.409868	−	1.52965i	−0.794897	−	0.606744i	$-0.792475\pi$
$317$	−7.29750	−	27.2346i	−0.409868	−	1.52965i	0.385029	−	0.922905i	$-0.374192\pi$
$318$	−2.39687	−	0.0764588i	−0.134410	−	0.00428760i
$319$	0.999513	+	1.73121i	0.0559620	+	0.0969290i
$320$	7.38364	−	16.2936i	0.412758	−	0.910841i
$321$	1.17979			0.0658495
$322$		0			0
$323$	−23.6862	+	23.6862i	−1.31794	+	1.31794i
$324$	22.4377	+	1.43296i	1.24654	+	0.0796089i
$325$	−3.44889	−	10.5093i	−0.191310	−	0.582949i
$326$	−5.94994	+	5.58208i	−0.329537	+	0.309163i
$327$	10.6045	−	2.84147i	0.586432	−	0.157134i
$328$	11.3150	+	1.08577i	0.624765	+	0.0599517i
$329$		0			0
$330$	−2.43706	+	1.39330i	−0.134156	+	0.0766988i
$331$	22.3187	+	12.8857i	1.22675	+	0.708262i	0.966348	−	0.257239i	$-0.0828127\pi$
$331$	22.3187	+	12.8857i	1.22675	+	0.708262i	0.260398	+	0.965501i	$0.416146\pi$
$332$	−2.62553	−	13.0850i	−0.144095	−	0.718134i
$333$	−2.71896	+	10.1473i	−0.148998	+	0.556068i
$334$	3.54050	−	11.7067i	0.193727	−	0.640562i
$335$	−17.7163	−	9.58546i	−0.967946	−	0.523709i
$336$		0			0
$337$	10.4788	−	10.4788i	0.570816	−	0.570816i	−0.361540	−	0.932356i	$-0.617749\pi$
$337$	10.4788	−	10.4788i	0.570816	−	0.570816i	0.932356	+	0.361540i	$0.117749\pi$
$338$	−10.1060	+	5.41265i	−0.549695	+	0.294409i
$339$	−14.0472	−	24.3305i	−0.762940	−	1.32145i
$340$	9.56790	+	18.0477i	0.518892	+	0.978772i
$341$	−0.415365	+	0.719433i	−0.0224933	+	0.0389595i
$342$	12.4160	+	7.70639i	0.671382	+	0.416714i
$343$		0			0
$344$	5.82154	−	4.80211i	0.313876	−	0.258912i
$345$	−30.4595	−	7.26530i	−1.63989	−	0.391151i
$346$	−4.23036	−	4.50914i	−0.227425	−	0.242413i
$347$	4.86030	−	18.1389i	0.260914	−	0.973746i	−0.703789	−	0.710409i	$-0.748510\pi$
$347$	4.86030	−	18.1389i	0.260914	−	0.973746i	0.964704	−	0.263337i	$-0.0848232\pi$
$348$	−13.1175	−	14.9072i	−0.703170	−	0.799111i
$349$		−	7.53504i		−	0.403341i	−0.979453	−	0.201671i	$-0.935363\pi$
$349$		−	7.53504i		−	0.403341i	0.979453	−	0.201671i	$-0.0646371\pi$
$350$		0			0
$351$			7.39016i			0.394457i
$352$	0.379706	−	2.36124i	0.0202384	−	0.125854i
$353$	−9.54063	+	35.6061i	−0.507796	+	1.89512i	−0.0664384	+	0.997791i	$0.521164\pi$
$353$	−9.54063	+	35.6061i	−0.507796	+	1.89512i	−0.441358	+	0.897331i	$0.645503\pi$
$354$	5.87830	−	5.51487i	0.312428	−	0.293112i
$355$	−6.88006	−	1.64106i	−0.365156	−	0.0870982i
$356$	−20.7641	+	10.2829i	−1.10050	+	0.544995i
$357$		0			0
$358$	13.4289	−	21.6357i	0.709739	−	1.14348i
$359$	9.04771	−	15.6711i	0.477520	−	0.827089i	−0.522148	−	0.852855i	$-0.674869\pi$
$359$	9.04771	−	15.6711i	0.477520	−	0.827089i	0.999668	+	0.0257661i	$0.00820252\pi$
$360$	6.71490	−	5.85841i	0.353907	−	0.308765i
$361$	−17.3913	−	30.1226i	−0.915331	−	1.58540i
$362$	9.72643	+	18.1603i	0.511210	+	0.954485i
$363$	16.0669	−	16.0669i	0.843295	−	0.843295i
$364$		0			0
$365$	−13.5827	−	7.34894i	−0.710950	−	0.384661i
$366$	−5.26269	−	1.59162i	−0.275085	−	0.0831951i
$367$	6.06169	−	22.6225i	0.316417	−	1.18089i	−0.606245	−	0.795278i	$-0.707325\pi$
$367$	6.06169	−	22.6225i	0.316417	−	1.18089i	0.922663	−	0.385608i	$-0.126008\pi$
$368$	21.1102	−	16.3109i	1.10044	−	0.850264i
$369$	4.90388	+	2.83125i	0.255286	+	0.147389i
$370$	−11.7021	−	20.4684i	−0.608362	−	1.06410i
$371$		0			0
$372$	2.63940	−	7.81835i	0.136846	−	0.405362i
$373$	−5.60369	+	1.50150i	−0.290148	+	0.0777450i	−0.400957	−	0.916097i	$-0.631322\pi$
$373$	−5.60369	+	1.50150i	−0.290148	+	0.0777450i	0.110809	+	0.993842i	$0.464656\pi$
$374$	1.86852	+	1.99166i	0.0966189	+	0.102986i
$375$	19.2883	−	13.3822i	0.996046	−	0.691056i
$376$	18.3608	−	3.07872i	0.946885	−	0.158773i
$377$	7.39618	−	7.39618i	0.380923	−	0.380923i
$378$		0			0
$379$	−20.3909			−1.04741			−0.523706	−	0.851899i	$-0.675451\pi$
$379$	−20.3909			−1.04741			−0.523706	+	0.851899i	$0.675451\pi$
$380$	−31.9655	+	7.33877i	−1.63980	+	0.376471i
$381$	−23.3364	−	40.4198i	−1.19556	−	2.07077i
$382$	0.456786	−	14.3196i	0.0233712	−	0.732652i
$383$	2.73132	+	10.1934i	0.139564	+	0.520860i	0.999937	+	0.0111957i	$0.00356377\pi$
$383$	2.73132	+	10.1934i	0.139564	+	0.520860i	−0.860373	+	0.509664i	$0.829770\pi$
$384$	0.916257	+	23.7384i	0.0467576	+	1.21140i
$385$		0			0
$386$	29.2332	−	6.84201i	1.48793	−	0.348249i
$387$	3.63127	−	0.972995i	0.184588	−	0.0494601i
$388$	2.58191	+	12.8676i	0.131077	+	0.653256i
$389$	−1.96021	+	1.13173i	−0.0993866	+	0.0573809i	−0.548869	−	0.835908i	$-0.684942\pi$
$389$	−1.96021	+	1.13173i	−0.0993866	+	0.0573809i	0.449483	+	0.893289i	$0.351608\pi$
$390$	10.3424	+	10.4304i	0.523706	+	0.528163i
$391$			30.4631i			1.54058i
$392$		0			0
$393$	26.6823	+	26.6823i	1.34594	+	1.34594i
$394$	27.1098	+	8.19891i	1.36577	+	0.413055i
$395$	−5.78216	−	5.47092i	−0.290932	−	0.275272i
$396$	0.660235	−	0.991699i	0.0331781	−	0.0498347i
$397$	−4.47408	−	16.6975i	−0.224548	−	0.838024i	−0.982585	−	0.185813i	$-0.940508\pi$
$397$	−4.47408	−	16.6975i	−0.224548	−	0.838024i	0.758037	−	0.652211i	$-0.226158\pi$
$398$	5.43269	−	8.75279i	0.272316	−	0.438738i
$399$		0			0
$400$	−1.44378	+	19.9478i	−0.0721892	+	0.997391i
$401$	−2.49166	+	4.31568i	−0.124428	+	0.215515i	−0.921509	−	0.388357i	$-0.873043\pi$
$401$	−2.49166	+	4.31568i	−0.124428	+	0.215515i	0.797081	+	0.603872i	$0.206376\pi$
$402$	26.7367	+	0.852886i	1.33351	+	0.0425381i
$403$	4.19863	+	1.12502i	0.209149	+	0.0560413i
$404$	−8.46353	−	0.540514i	−0.421076	−	0.0268916i
$405$	−24.0916	+	7.17482i	−1.19712	+	0.356520i
$406$		0			0
$407$	−2.22889	−	2.22889i	−0.110482	−	0.110482i
$408$	−22.0898	−	15.7456i	−1.09361	−	0.779524i
$409$	1.80679	−	1.04315i	0.0893400	−	0.0515805i	−0.454664	−	0.890663i	$-0.650241\pi$
$409$	1.80679	−	1.04315i	0.0893400	−	0.0515805i	0.544004	+	0.839082i	$0.316907\pi$
$410$	−12.2894	+	3.23719i	−0.606931	+	0.159873i
$411$	−24.4403	−	14.1106i	−1.20555	−	0.696025i
$412$	29.7952	+	10.0586i	1.46791	+	0.495550i
$413$		0			0
$414$	12.9398	−	3.02855i	0.635957	−	0.148845i
$415$	7.81496	+	12.7108i	0.383621	+	0.623951i
$416$	−12.4483	+	1.27863i	−0.610326	+	0.0626898i
$417$	−12.5071	−	3.35128i	−0.612477	−	0.164113i
$418$	−3.86527	+	2.07019i	−0.189057	+	0.101256i
$419$	−3.19769			−0.156217			−0.0781086	−	0.996945i	$-0.524888\pi$
$419$	−3.19769			−0.156217			−0.0781086	+	0.996945i	$0.524888\pi$
$420$		0			0
$421$	−39.6161			−1.93077			−0.965386	−	0.260824i	$-0.916006\pi$
$421$	−39.6161			−1.93077			−0.965386	+	0.260824i	$0.916006\pi$
$422$	−21.7002	+	11.6223i	−1.05635	+	0.565767i
$423$	8.95821	+	2.40034i	0.435563	+	0.116709i
$424$	−0.799228	+	2.13977i	−0.0388139	+	0.103916i
$425$	−17.0169	−	15.2317i	−0.825441	−	0.738844i
$426$	9.14592	−	2.14059i	0.443121	−	0.103712i
$427$		0			0
$428$	0.359433	−	1.06470i	0.0173739	−	0.0514644i
$429$	1.70068	+	0.981887i	0.0821095	+	0.0474059i
$430$	−4.24958	+	7.28898i	−0.204933	+	0.351506i
$431$	12.7288	−	7.34896i	0.613123	−	0.353987i	−0.161064	−	0.986944i	$-0.551492\pi$
$431$	12.7288	−	7.34896i	0.613123	−	0.353987i	0.774187	+	0.632957i	$0.218159\pi$
$432$	5.07243	−	12.3628i	0.244048	−	0.594803i
$433$	−6.03281	−	6.03281i	−0.289919	−	0.289919i	0.547129	−	0.837048i	$-0.315721\pi$
$433$	−6.03281	−	6.03281i	−0.289919	−	0.289919i	−0.837048	+	0.547129i	$0.815721\pi$
$434$		0			0
$435$	19.5258	+	10.5645i	0.936192	+	0.506529i
$436$	0.666468	−	10.4358i	0.0319180	−	0.499782i
$437$	−47.2442	−	12.6590i	−2.26000	−	0.605564i
$438$	20.4984	+	0.653887i	0.979451	+	0.0312439i
$439$	3.31217	−	5.73685i	0.158081	−	0.273805i	−0.776095	−	0.630616i	$-0.782802\pi$
$439$	3.31217	−	5.73685i	0.158081	−	0.273805i	0.934177	+	0.356810i	$0.116136\pi$
$440$	0.514916	+	2.62381i	0.0245477	+	0.125085i
$441$		0			0
$442$	7.53568	−	12.1410i	0.358436	−	0.577488i
$443$	−2.52589	−	9.42675i	−0.120009	−	0.447879i	0.879604	−	0.475707i	$-0.157808\pi$
$443$	−2.52589	−	9.42675i	−0.120009	−	0.447879i	−0.999613	+	0.0278280i	$0.991141\pi$
$444$	26.0631	+	17.3518i	1.23690	+	0.823482i
$445$	17.8047	−	18.8176i	0.844023	−	0.892040i
$446$	3.22030	+	0.973927i	0.152486	+	0.0461168i
$447$	−7.24931	−	7.24931i	−0.342881	−	0.342881i
$448$		0			0
$449$			18.0135i			0.850109i	0.905168	+	0.425055i	$0.139745\pi$
$449$			18.0135i			0.850109i	−0.905168	+	0.425055i	$0.860255\pi$
$450$	−4.77819	+	8.74257i	−0.225246	+	0.412129i
$451$	−1.47142	+	0.849527i	−0.0692867	+	0.0400027i
$452$	−26.2367	+	5.26444i	−1.23407	+	0.247618i
$453$	7.12472	−	1.90906i	0.334749	−	0.0896956i
$454$	−21.5559	+	5.04514i	−1.01167	+	0.236780i
$455$		0			0
$456$	33.5989	−	27.7152i	1.57341	−	1.29788i
$457$	0.328686	+	1.22667i	0.0153753	+	0.0573813i	0.973187	−	0.230014i	$-0.0738773\pi$
$457$	0.328686	+	1.22667i	0.0153753	+	0.0573813i	−0.957812	+	0.287396i	$0.907211\pi$
$458$	0.769747	−	24.1304i	0.0359679	−	1.12754i
$459$	7.62958	+	13.2148i	0.356118	+	0.616815i
$460$	−15.8363	+	25.2748i	−0.738373	+	1.17844i
$461$	17.6021			0.819811			0.409906	−	0.912128i	$-0.365562\pi$
$461$	17.6021			0.819811			0.409906	+	0.912128i	$0.365562\pi$
$462$		0			0
$463$	13.7264	−	13.7264i	0.637919	−	0.637919i	−0.312123	−	0.950042i	$-0.601040\pi$
$463$	13.7264	−	13.7264i	0.637919	−	0.637919i	0.950042	+	0.312123i	$0.101040\pi$
$464$	−17.4494	+	7.29626i	−0.810068	+	0.338720i
$465$	0.255073	+	9.22232i	0.0118287	+	0.427675i
$466$	−13.4675	−	14.3551i	−0.623871	−	0.664985i
$467$	−12.3923	+	3.32051i	−0.573447	+	0.153655i	−0.533877	−	0.845562i	$-0.679266\pi$
$467$	−12.3923	+	3.32051i	−0.573447	+	0.153655i	−0.0395701	+	0.999217i	$0.512599\pi$
$468$	−5.90632	−	1.99391i	−0.273020	−	0.0921687i
$469$		0			0
$470$	−18.0699	+	10.3308i	−0.833501	+	0.476524i
$471$	−24.5395	−	14.1679i	−1.13072	−	0.652821i
$472$	−3.18602	−	6.98503i	−0.146649	−	0.321512i
$473$	−0.291950	+	1.08957i	−0.0134239	+	0.0500986i
$474$	10.1185	+	3.06018i	0.464759	+	0.140559i
$475$	30.6937	−	20.0614i	1.40832	−	0.920480i
$476$		0			0
$477$	−0.804592	+	0.804592i	−0.0368397	+	0.0368397i
$478$	−5.01536	−	9.36423i	−0.229397	−	0.428310i
$479$	7.41948	+	12.8509i	0.339005	+	0.587173i	0.984246	−	0.176806i	$-0.0565764\pi$
$479$	7.41948	+	12.8509i	0.339005	+	0.587173i	−0.645241	+	0.763979i	$0.723243\pi$
$480$	−10.1422	−	24.5474i	−0.462927	−	1.12043i
$481$	−8.24667	+	14.2837i	−0.376016	+	0.651279i
$482$	−5.40822	+	8.71337i	−0.246338	+	0.396883i
$483$		0			0
$484$	−9.60470	−	19.3946i	−0.436577	−	0.881571i
$485$	−7.68513	−	12.4997i	−0.348964	−	0.567581i
$486$	14.0089	−	13.1428i	0.635457	−	0.596169i
$487$	−9.04342	+	33.7505i	−0.409796	+	1.52938i	0.385239	+	0.922817i	$0.374119\pi$
$487$	−9.04342	+	33.7505i	−0.409796	+	1.52938i	−0.795035	+	0.606564i	$0.792548\pi$
$488$	−3.03968	+	4.26443i	−0.137600	+	0.193042i
$489$			12.1134i			0.547787i
$490$		0			0
$491$			5.19048i			0.234243i	0.993118	+	0.117122i	$0.0373667\pi$
$491$			5.19048i			0.234243i	−0.993118	+	0.117122i	$0.962633\pi$
$492$	12.6703	−	11.1491i	0.571220	−	0.502639i
$493$	5.58979	−	20.8614i	0.251752	−	0.939550i
$494$	15.6976	+	16.7321i	0.706268	+	0.752812i
$495$	−0.309043	+	1.29565i	−0.0138904	+	0.0582352i
$496$	−6.25157	−	4.76385i	−0.280704	−	0.213903i
$497$		0			0
$498$	−16.8359	−	10.4497i	−0.754436	−	0.468264i
$499$	−5.42096	+	9.38938i	−0.242675	+	0.420326i	−0.961475	−	0.274891i	$-0.911358\pi$
$499$	−5.42096	+	9.38938i	−0.242675	+	0.420326i	0.718800	+	0.695217i	$0.244692\pi$
$500$	−6.20047	−	21.4838i	−0.277293	−	0.960785i
$501$	−9.07955	−	15.7262i	−0.405644	−	0.702597i
$502$	4.53569	−	2.42925i	0.202438	−	0.108423i
$503$	−2.03813	+	2.03813i	−0.0908758	+	0.0908758i	−0.751083	−	0.660207i	$-0.770468\pi$
$503$	−2.03813	+	2.03813i	−0.0908758	+	0.0908758i	0.660207	+	0.751083i	$0.270468\pi$
$504$		0			0
$505$	9.08736	−	2.70635i	0.404382	−	0.120431i
$506$	−1.15434	+	3.81683i	−0.0513165	+	0.169679i
$507$	−4.40551	+	16.4416i	−0.195655	+	0.730196i
$508$	−43.5866	+	8.74572i	−1.93384	+	0.388029i
$509$	−10.5939	−	6.11641i	−0.469568	−	0.271105i	0.246491	−	0.969145i	$-0.420722\pi$
$509$	−10.5939	−	6.11641i	−0.469568	−	0.271105i	−0.716059	+	0.698040i	$0.754056\pi$
$510$	29.2621	+	7.97382i	1.29575	+	0.353087i
$511$		0			0
$512$	21.7019	+	6.40523i	0.959098	+	0.283074i
$513$	−23.6649	+	6.34100i	−1.04483	+	0.279962i
$514$	7.19201	−	6.74735i	0.317226	−	0.297613i
$515$	−35.1457	+	0.972069i	−1.54870	+	0.0428345i
$516$	0.714127	−	11.1820i	0.0314377	−	0.492261i
$517$	−1.96771	+	1.96771i	−0.0865397	+	0.0865397i
$518$		0			0
$519$	−9.18010			−0.402962
$520$	12.5638	−	6.15577i	0.550959	−	0.269949i
$521$	1.56024	+	2.70242i	0.0683554	+	0.118395i	0.898178	−	0.439633i	$-0.144891\pi$
$521$	1.56024	+	2.70242i	0.0683554	+	0.118395i	−0.829822	+	0.558028i	$0.811558\pi$
$522$	−9.41703	−	0.300398i	−0.412172	−	0.0131481i
$523$	1.80211	+	6.72558i	0.0788010	+	0.294089i	0.994068	−	0.108758i	$-0.0346873\pi$
$523$	1.80211	+	6.72558i	0.0788010	+	0.294089i	−0.915267	+	0.402847i	$0.868021\pi$
$524$	32.2085	−	15.9505i	1.40703	−	0.696800i
$525$		0			0
$526$	8.17527	+	34.9297i	0.356459	+	1.52301i
$527$	8.66931	−	2.32294i	0.377641	−	0.101189i
$528$	−2.17106	−	2.80987i	−0.0944834	−	0.122284i
$529$	−18.6025	+	10.7401i	−0.808803	+	0.466963i
$530$	0.0108213	−	2.55374i	0.000470046	−	0.110927i
$531$		−	3.82451i		−	0.165970i
$532$		0			0
$533$	6.28632	+	6.28632i	0.272291	+	0.272291i
$534$	−9.95913	+	32.9300i	−0.430974	+	1.42502i
$535$	0.0347359	+	1.25590i	0.00150177	+	0.0542971i
$536$	8.91526	−	23.8687i	0.385080	−	1.03097i
$537$	−9.78557	−	36.5202i	−0.422278	−	1.57596i
$538$	22.8748	+	14.1979i	0.986201	+	0.612116i
$539$		0			0
$540$	−0.539612	+	14.9304i	−0.0232212	+	0.642503i
$541$	1.93050	−	3.34372i	0.0829986	−	0.143758i	−0.821538	−	0.570154i	$-0.806884\pi$
$541$	1.93050	−	3.34372i	0.0829986	−	0.143758i	0.904537	+	0.426396i	$0.140217\pi$
$542$	0.951319	−	29.8224i	0.0408626	−	1.28098i
$543$	29.5452	+	7.91661i	1.26791	+	0.339734i
$544$	−20.9395	+	15.1379i	−0.897774	+	0.649034i
$545$	3.33700	+	11.2049i	0.142941	+	0.479967i
$546$		0			0
$547$	25.7583	+	25.7583i	1.10135	+	1.10135i	0.994249	+	0.107098i	$0.0341557\pi$
$547$	25.7583	+	25.7583i	1.10135	+	1.10135i	0.107098	+	0.994249i	$0.465844\pi$
$548$	−20.1801	+	17.7573i	−0.862051	+	0.758553i
$549$	−2.25928	+	1.30439i	−0.0964235	+	0.0556701i
$550$	−1.55494	−	2.55325i	−0.0663027	−	0.108871i
$551$	30.0304	+	17.3381i	1.27934	+	0.738626i
$552$	3.78350	−	39.4283i	0.161036	−	1.67818i
$553$		0			0
$554$	−5.19503	−	22.1963i	−0.220716	−	0.943032i
$555$	−34.0514	−	8.12205i	−1.44540	−	0.344762i
$556$	−6.83478	+	10.2661i	−0.289859	+	0.435379i
$557$	−16.2233	−	4.34701i	−0.687402	−	0.184189i	−0.101821	−	0.994803i	$-0.532467\pi$
$557$	−16.2233	−	4.34701i	−0.687402	−	0.184189i	−0.585581	+	0.810614i	$0.699134\pi$
$558$	−1.84859	−	3.45153i	−0.0782573	−	0.146115i
$559$	5.90224			0.249638
$560$		0			0
$561$	4.05479			0.171193
$562$	4.01119	+	7.48934i	0.169202	+	0.315919i
$563$	10.8007	+	2.89404i	0.455195	+	0.121969i	0.479129	−	0.877744i	$-0.340953\pi$
$563$	10.8007	+	2.89404i	0.455195	+	0.121969i	−0.0239343	+	0.999714i	$0.507619\pi$
$564$	15.3185	−	23.0090i	0.645026	−	0.968854i
$565$	25.4864	−	15.6697i	1.07222	−	0.659230i
$566$	−0.536492	−	2.29222i	−0.0225504	−	0.0963491i
$567$		0			0
$568$	0.854600	−	8.90590i	0.0358582	−	0.373683i
$569$	14.1920	+	8.19376i	0.594960	+	0.343500i	0.767056	−	0.641580i	$-0.221721\pi$
$569$	14.1920	+	8.19376i	0.594960	+	0.343500i	−0.172096	+	0.985080i	$0.555054\pi$
$570$	−24.5263	+	42.0682i	−1.02729	+	1.76204i
$571$	39.2390	−	22.6547i	1.64210	−	0.948068i	0.662018	−	0.749488i	$-0.269700\pi$
$571$	39.2390	−	22.6547i	1.64210	−	0.948068i	0.980085	−	0.198580i	$-0.0636329\pi$
$572$	1.40423	−	1.23564i	0.0587139	−	0.0516647i
$573$	−15.0415	−	15.0415i	−0.628367	−	0.628367i
$574$		0			0
$575$	6.83717	−	32.6383i	0.285130	−	1.36111i
$576$	8.51191	+	7.38951i	0.354663	+	0.307896i
$577$	30.7727	+	8.24552i	1.28108	+	0.343265i	0.834267	−	0.551360i	$-0.185891\pi$
$577$	30.7727	+	8.24552i	1.28108	+	0.343265i	0.446817	+	0.894626i	$0.352558\pi$
$578$	0.174187	−	5.46051i	0.00724523	−	0.227127i
$579$	22.2886	−	38.6049i	0.926281	−	1.60437i
$580$	15.4827	−	14.4026i	0.642882	−	0.598033i
$581$		0			0
$582$	16.5562	+	10.2761i	0.686278	+	0.425960i
$583$	−0.0883660	−	0.329786i	−0.00365975	−	0.0136584i
$584$	6.83511	−	18.2996i	0.282839	−	0.757242i
$585$	6.96694	−	0.192694i	0.288047	−	0.00796690i
$586$	8.24759	−	27.2707i	0.340705	−	1.12654i
$587$	14.5087	+	14.5087i	0.598837	+	0.598837i	0.940003	−	0.341166i	$-0.110822\pi$
$587$	14.5087	+	14.5087i	0.598837	+	0.598837i	−0.341166	+	0.940003i	$0.610822\pi$
$588$		0			0
$589$			14.4103i			0.593765i
$590$	6.04369	+	6.09513i	0.248815	+	0.250933i
$591$	36.4180	−	21.0260i	1.49804	−	0.864892i
$592$	23.5996	−	18.2343i	0.969936	−	0.749426i
$593$	42.6687	−	11.4330i	1.75219	−	0.469498i	0.767100	−	0.641527i	$-0.221699\pi$
$593$	42.6687	−	11.4330i	1.75219	−	0.469498i	0.985092	+	0.172029i	$0.0550322\pi$
$594$	0.455188	+	1.94484i	0.0186766	+	0.0797977i
$595$		0			0
$596$	−8.75072	+	4.33359i	−0.358443	+	0.177511i
$597$	−3.95878	−	14.7744i	−0.162022	−	0.604674i
$598$	20.8541	+	0.665233i	0.852786	+	0.0272034i
$599$	−20.0977	−	34.8103i	−0.821170	−	1.42231i	−0.904811	−	0.425813i	$-0.859988\pi$
$599$	−20.0977	−	34.8103i	−0.821170	−	1.42231i	0.0836409	−	0.996496i	$-0.473345\pi$
$600$	20.1332	+	21.8278i	0.821935	+	0.891117i
$601$	−17.3374			−0.707207			−0.353604	−	0.935395i	$-0.615044\pi$
$601$	−17.3374			−0.707207			−0.353604	+	0.935395i	$0.615044\pi$
$602$		0			0
$603$	8.97509	−	8.97509i	0.365494	−	0.365494i
$604$	0.447771	−	7.01133i	0.0182195	−	0.285287i
$605$	17.5764	+	16.6303i	0.714583	+	0.676119i
$606$	−9.18315	+	8.61539i	−0.373040	+	0.349976i
$607$	−1.27852	+	0.342579i	−0.0518936	+	0.0139048i	−0.284672	−	0.958625i	$-0.591885\pi$
$607$	−1.27852	+	0.342579i	−0.0518936	+	0.0139048i	0.232779	+	0.972530i	$0.425218\pi$
$608$	−14.7755	−	38.7650i	−0.599225	−	1.57213i
$609$		0			0
$610$	1.53934	−	5.64904i	0.0623261	−	0.228723i
$611$	12.6099	+	7.28031i	0.510141	+	0.294530i
$612$	−12.6200	+	2.53222i	−0.510132	+	0.102359i
$613$	3.75107	−	13.9992i	0.151504	−	0.565422i	−0.847875	−	0.530196i	$-0.822118\pi$
$613$	3.75107	−	13.9992i	0.151504	−	0.565422i	0.999379	−	0.0352258i	$-0.0112150\pi$
$614$	−2.08575	+	6.89654i	−0.0841738	+	0.278322i
$615$	−8.97920	+	16.5958i	−0.362076	+	0.669208i
$616$		0			0
$617$	11.3496	−	11.3496i	0.456918	−	0.456918i	−0.440725	−	0.897642i	$-0.645278\pi$
$617$	11.3496	−	11.3496i	0.456918	−	0.456918i	0.897642	+	0.440725i	$0.145278\pi$
$618$	41.1598	−	22.0447i	1.65569	−	0.886766i
$619$	10.7582	+	18.6337i	0.432407	+	0.748951i	0.997080	−	0.0763640i	$-0.0243311\pi$
$619$	10.7582	+	18.6337i	0.432407	+	0.748951i	−0.564673	+	0.825315i	$0.690998\pi$
$620$	8.40041	+	2.57947i	0.337368	+	0.103594i
$621$	−11.1402	+	19.2955i	−0.447043	+	0.774300i
$622$	−0.519883	−	0.322681i	−0.0208454	−	0.0129383i
$623$		0			0
$624$	−11.2613	+	14.7782i	−0.450814	+	0.591600i
$625$	14.8134	+	20.1386i	0.592536	+	0.805544i
$626$	−0.996731	−	1.06242i	−0.0398374	−	0.0424627i
$627$	−1.68498	+	6.28844i	−0.0672917	+	0.251136i
$628$	−20.2620	+	17.8293i	−0.808541	+	0.711467i
$629$			34.0554i			1.35788i
$630$		0			0
$631$			7.18172i			0.285900i	0.989730	+	0.142950i	$0.0456588\pi$
$631$			7.18172i			0.285900i	−0.989730	+	0.142950i	$0.954341\pi$
$632$	5.84436	−	8.19917i	0.232476	−	0.326145i
$633$	−9.45974	+	35.3042i	−0.375991	+	1.40322i
$634$	−29.0800	+	27.2821i	−1.15491	+	1.08351i
$635$	42.3402	−	26.0319i	1.68022	−	1.03304i
$636$	1.50507	+	3.03915i	0.0596798	+	0.120510i
$637$		0			0
$638$	1.49087	−	2.40198i	0.0590239	−	0.0950955i
$639$	2.22845	−	3.85979i	0.0881562	−	0.152691i
$640$	−25.2428	+	1.67428i	−0.997808	+	0.0661818i
$641$	13.1001	+	22.6901i	0.517425	+	0.896206i	0.999795	+	0.0202384i	$0.00644252\pi$
$641$	13.1001	+	22.6901i	0.517425	+	0.896206i	−0.482371	+	0.875967i	$0.660224\pi$
$642$	−0.787744	−	1.47081i	−0.0310898	−	0.0580481i
$643$	−30.8400	+	30.8400i	−1.21621	+	1.21621i	−0.247263	+	0.968948i	$0.579531\pi$
$643$	−30.8400	+	30.8400i	−1.21621	+	1.21621i	−0.968948	+	0.247263i	$0.920469\pi$
$644$		0			0
$645$	3.57563	+	12.0062i	0.140790	+	0.472744i
$646$	45.3440	+	13.7136i	1.78404	+	0.539553i
$647$	−3.74467	+	13.9753i	−0.147218	+	0.549425i	0.852429	+	0.522844i	$0.175129\pi$
$647$	−3.74467	+	13.9753i	−0.147218	+	0.549425i	−0.999647	+	0.0265817i	$0.991538\pi$
$648$	−13.1952	−	28.9292i	−0.518357	−	1.13644i
$649$	0.993813	+	0.573778i	0.0390106	+	0.0225228i
$650$	−10.7987	+	11.3166i	−0.423561	+	0.443875i
$651$		0			0
$652$	10.9318	+	3.69045i	0.428121	+	0.144529i
$653$	36.4766	−	9.77388i	1.42744	−	0.382481i	0.539323	−	0.842099i	$-0.318680\pi$
$653$	36.4766	−	9.77388i	1.42744	−	0.382481i	0.888117	+	0.459618i	$0.152014\pi$
$654$	−10.6230	−	11.3231i	−0.415392	−	0.442767i
$655$	−27.6179	+	29.1891i	−1.07912	+	1.14051i
$656$	−6.20139	−	14.8310i	−0.242124	−	0.579052i
$657$	6.88099	−	6.88099i	0.268453	−	0.268453i
$658$		0			0
$659$	5.66966			0.220859			0.110429	−	0.993884i	$-0.464777\pi$
$659$	5.66966			0.220859			0.110429	+	0.993884i	$0.464777\pi$
$660$	3.36421	+	2.10790i	0.130952	+	0.0820498i
$661$	−14.4408	−	25.0122i	−0.561682	−	0.972861i	−0.997350	−	0.0727540i	$-0.976821\pi$
$661$	−14.4408	−	25.0122i	−0.561682	−	0.972861i	0.435668	−	0.900107i	$-0.356512\pi$
$662$	1.16202	−	36.4277i	0.0451634	−	1.41580i
$663$	−5.49122	−	20.4935i	−0.213261	−	0.795902i
$664$	−14.5596	+	12.0100i	−0.565022	+	0.466079i
$665$		0			0
$666$	14.4657	−	3.38569i	0.560535	−	0.131193i
$667$	30.4605	−	8.16187i	1.17944	−	0.316029i
$668$	−16.9583	+	3.40272i	−0.656138	+	0.131655i
$669$	4.32600	−	2.49762i	0.167253	−	0.0965636i
$670$	−0.120710	+	28.4866i	−0.00466342	+	1.10053i
$671$		−	0.782775i		−	0.0302187i
$672$		0			0
$673$	−6.90378	−	6.90378i	−0.266121	−	0.266121i	0.561414	−	0.827535i	$-0.310258\pi$
$673$	−6.90378	−	6.90378i	−0.266121	−	0.266121i	−0.827535	+	0.561414i	$0.810258\pi$
$674$	−20.0602	−	6.06689i	−0.772691	−	0.233688i
$675$	−5.20843	−	15.8708i	−0.200473	−	0.610869i
$676$	13.4955	+	8.98482i	0.519060	+	0.345570i
$677$	−3.63810	−	13.5776i	−0.139824	−	0.521829i	−0.999931	−	0.0117165i	$-0.996270\pi$
$677$	−3.63810	−	13.5776i	−0.139824	−	0.521829i	0.860108	−	0.510112i	$-0.170396\pi$
$678$	−20.9527	+	33.7576i	−0.804684	+	1.29645i
$679$		0			0
$680$	16.1109	−	23.9784i	0.617827	−	0.919529i
$681$	−16.4351	+	28.4664i	−0.629794	+	1.09083i
$682$	1.17423	+	0.0374574i	0.0449637	+	0.00143432i
$683$	31.3572	+	8.40215i	1.19985	+	0.321499i	0.802773	−	0.596285i	$-0.203357\pi$
$683$	31.3572	+	8.40215i	1.19985	+	0.321499i	0.397079	+	0.917784i	$0.370024\pi$
$684$	1.31714	−	20.6242i	0.0503622	−	0.788586i
$685$	14.3013	−	26.4324i	0.546424	−	1.00993i
$686$		0			0
$687$	−25.3470	−	25.3470i	−0.967047	−	0.967047i
$688$	−9.87366	−	4.05116i	−0.376430	−	0.154449i
$689$	−1.54712	+	0.893230i	−0.0589406	+	0.0340294i
$690$	11.2804	+	42.8239i	0.429436	+	1.63028i
$691$	−3.27810	−	1.89261i	−0.124705	−	0.0719984i	0.436350	−	0.899777i	$-0.356271\pi$
$691$	−3.27810	−	1.89261i	−0.124705	−	0.0719984i	−0.561055	+	0.827779i	$0.689604\pi$
$692$	−2.79680	+	8.28460i	−0.106318	+	0.314933i
$693$		0			0
$694$	−25.8583	+	6.05213i	−0.981570	+	0.229736i
$695$	3.19922	−	13.4126i	0.121353	−	0.508770i
$696$	−9.82584	+	26.3066i	−0.372447	+	0.997151i
$697$	17.7310	+	4.75099i	0.671608	+	0.179957i
$698$	−9.39368	+	5.03113i	−0.355556	+	0.190431i
$699$	−29.2253			−1.10540
$700$		0			0
$701$	−5.66595			−0.214000			−0.107000	−	0.994259i	$-0.534124\pi$
$701$	−5.66595			−0.214000			−0.107000	+	0.994259i	$0.534124\pi$
$702$	9.21307	−	4.93440i	0.347725	−	0.186237i
$703$	−52.8154	−	14.1518i	−1.99197	−	0.533747i
$704$	−3.19721	+	1.10323i	−0.120499	+	0.0415795i
$705$	−7.17030	+	30.0612i	−0.270049	+	1.13217i
$706$	50.7592	−	11.8802i	1.91035	−	0.447116i
$707$		0			0
$708$	−10.8001	−	3.64602i	−0.405894	−	0.137026i
$709$	−10.3830	−	5.99462i	−0.389941	−	0.225133i	0.292193	−	0.956359i	$-0.405615\pi$
$709$	−10.3830	−	5.99462i	−0.389941	−	0.225133i	−0.682135	+	0.731227i	$0.738948\pi$
$710$	2.54796	+	9.67288i	0.0956232	+	0.363017i
$711$	4.34388	−	2.50794i	0.162908	−	0.0940552i
$712$	26.6836	+	19.0200i	1.00001	+	0.712806i
$713$	9.26659	+	9.26659i	0.347037	+	0.347037i
$714$		0			0
$715$	−0.995155	+	1.83929i	−0.0372167	+	0.0687857i
$716$	−35.9390	−	2.29520i	−1.34310	−	0.0857758i
$717$	−15.2348	−	4.08214i	−0.568952	−	0.152450i
$718$	−25.5778	−	0.815917i	−0.954554	−	0.0304498i
$719$	−12.5797	+	21.7886i	−0.469142	+	0.812578i	−0.999378	−	0.0352721i	$-0.988770\pi$
$719$	−12.5797	+	21.7886i	−0.469142	+	0.812578i	0.530235	+	0.847850i	$0.322104\pi$
$720$	−11.7870	−	4.45960i	−0.439276	−	0.166199i
$721$		0			0
$722$	−25.9407	+	41.7939i	−0.965413	+	1.55541i
$723$	3.94095	+	14.7078i	0.146565	+	0.546989i
$724$	16.1456	−	24.2512i	0.600045	−	0.901290i
$725$	−10.6711	+	21.0964i	−0.396315	+	0.783502i
$726$	−30.7580	−	9.30225i	−1.14154	−	0.345239i
$727$	−20.9986	−	20.9986i	−0.778795	−	0.778795i	0.200831	−	0.979626i	$-0.435636\pi$
$727$	−20.9986	−	20.9986i	−0.778795	−	0.778795i	−0.979626	+	0.200831i	$0.935636\pi$
$728$		0			0
$729$			5.20463i			0.192764i
$730$	−0.0925452	+	21.8400i	−0.00342525	+	0.808333i
$731$	10.5542	−	6.09346i	0.390360	−	0.225375i
$732$	1.52968	+	7.62355i	0.0565385	+	0.281774i
$733$	−18.0645	+	4.84038i	−0.667229	+	0.178783i	−0.576506	−	0.817093i	$-0.695584\pi$
$733$	−18.0645	+	4.84038i	−0.667229	+	0.178783i	−0.0907227	+	0.995876i	$0.528918\pi$
$734$	−32.2501	+	7.54812i	−1.19037	+	0.278606i
$735$		0			0
$736$	−34.4295	−	15.4266i	−1.26909	−	0.568632i
$737$	0.985709	+	3.67872i	0.0363091	+	0.135507i
$738$	0.255321	−	8.00392i	0.00939849	−	0.294629i
$739$	−8.20856	−	14.2176i	−0.301957	−	0.523004i	0.674622	−	0.738163i	$-0.264306\pi$
$739$	−8.20856	−	14.2176i	−0.301957	−	0.523004i	−0.976579	+	0.215159i	$0.930973\pi$
$740$	−17.7038	+	28.2553i	−0.650805	+	1.03869i
$741$	34.0646			1.25140
$742$		0			0
$743$	−11.1710	+	11.1710i	−0.409825	+	0.409825i	−0.881678	−	0.471852i	$-0.843586\pi$
$743$	−11.1710	+	11.1710i	−0.409825	+	0.409825i	0.471852	+	0.881678i	$0.343586\pi$
$744$	−11.5092	+	1.92985i	−0.421948	+	0.0707518i
$745$	7.50352	−	7.93039i	0.274908	−	0.290547i
$746$	5.61345	+	5.98339i	0.205523	+	0.219067i
$747$	−9.08175	+	2.43345i	−0.332284	+	0.0890352i
$748$	1.23533	−	3.65925i	0.0451680	−	0.133795i
$749$		0			0
$750$	−29.5620	−	15.1108i	−1.07945	−	0.551770i
$751$	−24.0345	−	13.8763i	−0.877032	−	0.506355i	−0.00735334	−	0.999973i	$-0.502341\pi$
$751$	−24.0345	−	13.8763i	−0.877032	−	0.506355i	−0.869679	+	0.493618i	$0.835674\pi$
$752$	−16.0976	−	20.8341i	−0.587019	−	0.759742i
$753$	1.97724	−	7.37915i	0.0720545	−	0.268911i
$754$	−14.1590	−	4.28216i	−0.515640	−	0.155947i
$755$	2.24198	+	7.52812i	0.0815941	+	0.273976i
$756$		0			0
$757$	−4.34481	+	4.34481i	−0.157915	+	0.157915i	−0.781642	−	0.623727i	$-0.785618\pi$
$757$	−4.34481	+	4.34481i	−0.157915	+	0.157915i	0.623727	+	0.781642i	$0.285618\pi$
$758$	13.6150	+	25.4207i	0.494519	+	0.923322i
$759$	2.96028	+	5.12735i	0.107451	+	0.186111i
$760$	30.4923	+	34.9503i	1.10607	+	1.26778i
$761$	−11.7897	+	20.4203i	−0.427376	+	0.740236i	−0.996639	−	0.0819190i	$-0.973895\pi$
$761$	−11.7897	+	20.4203i	−0.427376	+	0.740236i	0.569263	+	0.822155i	$0.307228\pi$
$762$	−34.8084	+	56.0810i	−1.26098	+	2.03160i
$763$		0			0
$764$	−18.1567	+	8.99169i	−0.656887	+	0.325308i
$765$	12.2591	−	7.53722i	0.443229	−	0.272509i
$766$	10.8841	−	10.2112i	0.393259	−	0.368945i
$767$	1.55408	−	5.79992i	0.0561147	−	0.209423i
$768$	28.9821	−	16.9924i	1.04580	−	0.613159i
$769$		−	11.6924i		−	0.421638i	−0.977525	−	0.210819i	$-0.932387\pi$
$769$		−	11.6924i		−	0.421638i	0.977525	−	0.210819i	$-0.0676131\pi$
$770$		0			0
$771$		−	14.6421i		−	0.527323i
$772$	−28.0487	−	31.8757i	−1.00949	−	1.14723i
$773$	4.86514	−	18.1569i	0.174987	−	0.653060i	−0.821567	−	0.570112i	$-0.806900\pi$
$773$	4.86514	−	18.1569i	0.174987	−	0.653060i	0.996554	−	0.0829479i	$-0.0264335\pi$
$774$	−3.63759	−	3.87731i	−0.130750	−	0.139367i
$775$	−9.80972	+	0.543056i	−0.352376	+	0.0195071i
$776$	14.3177	−	11.8105i	0.513976	−	0.423972i
$777$		0			0
$778$	2.71972	+	1.68808i	0.0975066	+	0.0605205i
$779$	−14.7363	+	25.5241i	−0.527984	+	0.914495i
$780$	6.09764	−	19.8578i	0.218330	−	0.711024i
$781$	0.668654	+	1.15814i	0.0239263	+	0.0414416i
$782$	37.9773	−	20.3401i	1.35807	−	0.727362i
$783$	11.1695	−	11.1695i	0.399167	−	0.399167i
$784$		0			0
$785$	14.3593	−	26.5396i	0.512506	−	0.947239i
$786$	15.4482	−	51.0797i	0.551019	−	1.82195i
$787$	−13.2968	+	49.6245i	−0.473982	+	1.76892i	0.151262	+	0.988494i	$0.451666\pi$
$787$	−13.2968	+	49.6245i	−0.473982	+	1.76892i	−0.625244	+	0.780429i	$0.715001\pi$
$788$	−7.87984	−	39.2713i	−0.280708	−	1.39898i
$789$	46.1276	+	26.6318i	1.64219	+	0.948117i
$790$	−2.95967	+	10.8614i	−0.105301	+	0.386430i
$791$		0			0
$792$	−1.67716	−	0.160938i	−0.0595951	−	0.00571868i
$793$	−3.95626	+	1.06008i	−0.140491	+	0.0376444i
$794$	−17.8289	+	16.7266i	−0.632724	+	0.593605i
$795$	−2.75425	−	2.60599i	−0.0976831	−	0.0924250i
$796$	−14.5392	−	0.928531i	−0.515329	−	0.0329109i
$797$	−1.34897	+	1.34897i	−0.0477829	+	0.0477829i	−0.730594	−	0.682812i	$-0.760757\pi$
$797$	−1.34897	+	1.34897i	−0.0477829	+	0.0477829i	0.682812	+	0.730594i	$0.260757\pi$
$798$		0			0
$799$	30.0647			1.06361
$800$	25.8323	−	11.5192i	0.913310	−	0.407266i
$801$	8.16191	+	14.1368i	0.288387	+	0.499501i
$802$	7.04390	+	0.224696i	0.248729	+	0.00793431i
$803$	0.755719	+	2.82038i	0.0266688	+	0.0995292i
$804$	−16.7888	−	33.9012i	−0.592095	−	1.19560i
$805$		0			0
$806$	−1.40089	−	5.98547i	−0.0493444	−	0.210829i
$807$	38.6117	−	10.3460i	1.35919	−	0.364195i
$808$	4.97724	+	10.9121i	0.175099	+	0.383886i
$809$	−3.46174	+	1.99864i	−0.121708	+	0.0702684i	−0.559618	−	0.828750i	$-0.689052\pi$
$809$	−3.46174	+	1.99864i	−0.121708	+	0.0702684i	0.437910	+	0.899019i	$0.355719\pi$
$810$	25.0305	+	25.2435i	0.879482	+	0.886967i
$811$		−	41.2999i		−	1.45024i	−0.688625	−	0.725118i	$-0.741785\pi$
$811$		−	41.2999i		−	1.45024i	0.688625	−	0.725118i	$-0.258215\pi$
$812$		0			0
$813$	−31.3259	−	31.3259i	−1.09865	−	1.09865i
$814$	−1.29046	+	4.26692i	−0.0452306	+	0.149555i
$815$	−12.8948	+	0.356648i	−0.451686	+	0.0124928i
$816$	−4.88020	+	38.0520i	−0.170841	+	1.33208i
$817$	5.06432	+	18.9003i	0.177178	+	0.661238i
$818$	−2.50685	−	1.55596i	−0.0876501	−	0.0544027i
$819$		0			0
$820$	12.2413	+	13.1593i	0.427486	+	0.459544i
$821$	26.7751	−	46.3758i	0.934457	−	1.61853i	0.158857	−	0.987302i	$-0.449219\pi$
$821$	26.7751	−	46.3758i	0.934457	−	1.61853i	0.775600	−	0.631225i	$-0.217448\pi$
$822$	−1.27249	+	39.8906i	−0.0443831	+	1.39134i
$823$	−0.366523	−	0.0982095i	−0.0127762	−	0.00342337i	0.252425	−	0.967616i	$-0.418772\pi$
$823$	−0.366523	−	0.0982095i	−0.0127762	−	0.00342337i	−0.265201	+	0.964193i	$0.585438\pi$
$824$	−7.35454	−	43.8608i	−0.256208	−	1.52796i
$825$	−4.34433	−	0.910063i	−0.151250	−	0.0316843i
$826$		0			0
$827$	2.07441	+	2.07441i	0.0721345	+	0.0721345i	0.742254	−	0.670119i	$-0.233757\pi$
$827$	2.07441	+	2.07441i	0.0721345	+	0.0721345i	−0.670119	+	0.742254i	$0.733757\pi$
$828$	−12.4155	−	14.1095i	−0.431468	−	0.490339i
$829$	−23.1175	+	13.3469i	−0.802903	+	0.463556i	−0.844485	−	0.535579i	$-0.820094\pi$
$829$	−23.1175	+	13.3469i	−0.802903	+	0.463556i	0.0415820	+	0.999135i	$0.486760\pi$
$830$	10.6281	−	18.2297i	0.368908	−	0.632761i
$831$	−29.3121	−	16.9234i	−1.01683	−	0.587065i
$832$	9.90571	+	14.6651i	0.343419	+	0.508421i
$833$		0			0
$834$	4.17307	+	17.8299i	0.144502	+	0.617398i
$835$	16.4734	−	10.1283i	0.570085	−	0.350503i
$836$	5.16167	+	3.43644i	0.178520	+	0.118852i
$837$	6.34068	+	1.69898i	0.219166	+	0.0587253i
$838$	2.13509	+	3.98645i	0.0737555	+	0.137710i
$839$	23.5830			0.814175			0.407087	−	0.913389i	$-0.366544\pi$
$839$	23.5830			0.814175			0.407087	+	0.913389i	$0.366544\pi$
$840$		0			0
$841$	6.64270			0.229059
$842$	26.4516	+	49.3881i	0.911584	+	1.70203i
$843$	12.1845	+	3.26482i	0.419656	+	0.112446i
$844$	28.9784	+	19.2927i	0.997477	+	0.664082i
$845$	−17.6319	−	4.20562i	−0.606556	−	0.144678i
$846$	−2.98895	−	12.7706i	−0.102762	−	0.439063i
$847$		0			0
$848$	3.20122	−	0.432347i	0.109930	−	0.0148469i
$849$	−3.02707	−	1.74768i	−0.103889	−	0.0599802i
$850$	−7.62664	+	31.3846i	−0.261592	+	1.07648i
$851$	−43.0636	+	24.8628i	−1.47620	+	0.852285i
$852$	−8.77532	−	9.97264i	−0.300638	−	0.341657i
$853$	−35.4043	−	35.4043i	−1.21222	−	1.21222i	−0.970295	−	0.241926i	$-0.922221\pi$
$853$	−35.4043	−	35.4043i	−1.21222	−	1.21222i	−0.241926	−	0.970295i	$-0.577779\pi$
$854$		0			0
$855$	6.59491	+	22.1444i	0.225541	+	0.757321i
$856$	−1.56732	+	0.262807i	−0.0535700	+	0.00898257i
$857$	38.0169	+	10.1866i	1.29863	+	0.347967i	0.840932	−	0.541140i	$-0.182007\pi$
$857$	38.0169	+	10.1866i	1.29863	+	0.347967i	0.457699	+	0.889107i	$0.348674\pi$
$858$	0.0885460	−	2.77578i	0.00302291	−	0.0947637i
$859$	−15.9154	+	27.5663i	−0.543026	+	0.940549i	0.455702	+	0.890132i	$0.349388\pi$
$859$	−15.9154	+	27.5663i	−0.543026	+	0.940549i	−0.998728	+	0.0504166i	$0.983945\pi$
$860$	11.9244	+	0.430968i	0.406618	+	0.0146959i
$861$		0			0
$862$	−17.6607	−	10.9616i	−0.601525	−	0.373355i
$863$	10.0303	+	37.4334i	0.341434	+	1.27425i	0.896723	+	0.442592i	$0.145941\pi$
$863$	10.0303	+	37.4334i	0.341434	+	1.27425i	−0.555289	+	0.831657i	$0.687392\pi$
$864$	−18.7991	+	1.93095i	−0.639558	+	0.0656923i
$865$	−0.270285	−	9.77229i	−0.00918996	−	0.332268i
$866$	−3.49281	+	11.5490i	−0.118690	+	0.392451i
$867$	−5.73580	−	5.73580i	−0.194798	−	0.194798i
$868$		0			0
$869$			1.50503i			0.0510547i
$870$	0.133039	−	31.3961i	0.00451043	−	1.06443i
$871$	17.2579	−	9.96384i	0.584761	−	0.337612i
$872$	−13.4549	+	6.13707i	−0.455641	+	0.207828i
$873$	8.93088	−	2.39302i	0.302264	−	0.0809915i
$874$	15.7633	+	67.3502i	0.533200	+	2.27815i
$875$		0			0
$876$	−12.8716	−	25.9913i	−0.434890	−	0.878164i
$877$	0.720839	+	2.69021i	0.0243410	+	0.0908419i	0.977028	−	0.213112i	$-0.0683599\pi$
$877$	0.720839	+	2.69021i	0.0243410	+	0.0908419i	−0.952687	+	0.303954i	$0.901693\pi$
$878$	−9.36348	−	0.298690i	−0.316002	−	0.0100803i
$879$	−21.1508	−	36.6343i	−0.713399	−	1.23564i
$880$	2.92721	−	2.39384i	0.0986763	−	0.0806965i
$881$	40.5035			1.36460			0.682299	−	0.731074i	$-0.260980\pi$
$881$	40.5035			1.36460			0.682299	+	0.731074i	$0.260980\pi$
$882$		0			0
$883$	−17.0113	+	17.0113i	−0.572477	+	0.572477i	−0.932820	−	0.360343i	$-0.882660\pi$
$883$	−17.0113	+	17.0113i	−0.572477	+	0.572477i	0.360343	+	0.932820i	$0.382660\pi$
$884$	−20.1673	−	1.28796i	−0.678301	−	0.0433189i
$885$	12.7396	−	0.352354i	0.428236	−	0.0118443i
$886$	−10.0655	+	9.44317i	−0.338157	+	0.317250i
$887$	−37.6278	+	10.0823i	−1.26342	+	0.338532i	−0.827505	−	0.561458i	$-0.810241\pi$
$887$	−37.6278	+	10.0823i	−1.26342	+	0.338532i	−0.435912	+	0.899989i	$0.643574\pi$
$888$	4.22966	−	44.0778i	0.141938	−	1.47916i
$889$		0			0
$890$	−35.3474	−	9.63204i	−1.18485	−	0.322867i
$891$	4.11597	+	2.37636i	0.137890	+	0.0796109i
$892$	−0.936026	−	4.66493i	−0.0313405	−	0.156193i
$893$	−12.4935	+	46.6264i	−0.418079	+	1.56029i
$894$	−4.19712	+	13.8778i	−0.140373	+	0.464144i
$895$	38.5880	−	11.4921i	1.28985	−	0.384137i
$896$		0			0
$897$	21.9054	−	21.9054i	0.731401	−	0.731401i
$898$	22.4568	−	12.0276i	0.749394	−	0.401366i
$899$	−4.64548	−	8.04621i	−0.154936	−	0.268356i
$900$	14.0895	+	0.119408i	0.469649	+	0.00398028i
$901$	−1.84434	+	3.19448i	−0.0614438	+	0.106424i
$902$	2.04155	+	1.26715i	0.0679760	+	0.0421914i
$903$		0			0
$904$	24.0812	+	29.1934i	0.800929	+	0.970957i
$905$	−7.55741	+	31.6842i	−0.251217	+	1.05322i
$906$	−7.13713	−	7.60748i	−0.237115	−	0.252741i
$907$	−5.92604	+	22.1163i	−0.196771	+	0.734359i	0.795030	+	0.606569i	$0.207455\pi$
$907$	−5.92604	+	22.1163i	−0.196771	+	0.734359i	−0.991801	+	0.127789i	$0.959212\pi$
$908$	20.6824	+	23.5044i	0.686371	+	0.780021i
$909$			5.97469i			0.198168i
$910$		0			0
$911$			43.8022i			1.45123i	0.688100	+	0.725616i	$0.258445\pi$
$911$			43.8022i			1.45123i	−0.688100	+	0.725616i	$0.741555\pi$
$912$	−56.9856	−	23.3812i	−1.88698	−	0.774228i
$913$	0.730164	−	2.72501i	0.0241649	−	0.0901847i
$914$	1.30979	−	1.22881i	0.0433240	−	0.0406454i
$915$	−4.55312	−	7.40554i	−0.150522	−	0.244820i
$916$	−30.5966	+	15.1522i	−1.01094	+	0.500644i
$917$		0			0
$918$	11.3802	−	18.3351i	0.375603	−	0.605147i
$919$	−16.0826	+	27.8558i	−0.530515	+	0.918879i	0.468851	+	0.883277i	$0.344668\pi$
$919$	−16.0826	+	27.8558i	−0.530515	+	0.918879i	−0.999366	+	0.0356018i	$0.988665\pi$
$920$	42.0832	+	2.86670i	1.38744	+	0.0945121i
$921$	5.34886	+	9.26450i	0.176251	+	0.305276i
$922$	−11.7529	−	21.9440i	−0.387061	−	0.722686i
$923$	4.94790	−	4.94790i	0.162862	−	0.162862i
$924$		0			0
$925$	7.64343	−	36.4871i	0.251315	−	1.19969i
$926$	−26.2773	−	7.94714i	−0.863526	−	0.261159i
$927$	5.73402	−	21.3997i	0.188330	−	0.702857i
$928$	20.7469	+	16.8819i	0.681052	+	0.554175i
$929$	−35.6942	−	20.6080i	−1.17109	−	0.676128i	−0.217152	−	0.976138i	$-0.569677\pi$
$929$	−35.6942	−	20.6080i	−1.17109	−	0.676128i	−0.953936	+	0.300010i	$0.903010\pi$
$930$	11.3268	−	6.47572i	0.371422	−	0.212347i
$931$		0			0
$932$	−8.90373	+	26.3744i	−0.291651	+	0.863921i
$933$	−0.877541	+	0.235137i	−0.0287294	+	0.00769802i
$934$	12.4139	+	13.2320i	0.406195	+	0.432963i
$935$	0.119383	+	4.31636i	0.00390424	+	0.141160i
$936$	1.45789	+	8.69455i	0.0476527	+	0.284190i
$937$	−25.3650	+	25.3650i	−0.828637	+	0.828637i	−0.987328	−	0.158691i	$-0.949273\pi$
$937$	−25.3650	+	25.3650i	−0.828637	+	0.828637i	0.158691	+	0.987328i	$0.449273\pi$
$938$		0			0
$939$	−2.16296			−0.0705855
$940$	24.9443	+	15.6293i	0.813593	+	0.509770i
$941$	11.4729	+	19.8717i	0.374007	+	0.647799i	0.990178	−	0.139814i	$-0.0446504\pi$
$941$	11.4729	+	19.8717i	0.374007	+	0.647799i	−0.616171	+	0.787612i	$0.711317\pi$
$942$	−1.27765	+	40.0524i	−0.0416281	+	1.30498i
$943$	6.93711	+	25.8897i	0.225903	+	0.843083i
$944$	−6.58071	+	8.63581i	−0.214184	+	0.281072i
$945$		0			0
$946$	1.55327	−	0.363542i	0.0505012	−	0.0118198i
$947$	−29.3070	+	7.85278i	−0.952348	+	0.255181i	−0.701359	−	0.712809i	$-0.747423\pi$
$947$	−29.3070	+	7.85278i	−0.952348	+	0.255181i	−0.250990	+	0.967990i	$0.580756\pi$
$948$	−2.94109	−	14.6577i	−0.0955223	−	0.476060i
$949$	13.2312	−	7.63904i	0.429503	−	0.247974i
$950$	−45.5040	−	24.8699i	−1.47635	−	0.806886i
$951$			59.2035i			1.91981i
$952$		0			0
$953$	−1.41682	−	1.41682i	−0.0458953	−	0.0458953i	0.683787	−	0.729682i	$-0.260332\pi$
$953$	−1.41682	−	1.41682i	−0.0458953	−	0.0458953i	−0.729682	+	0.683787i	$0.760332\pi$
$954$	1.54028	+	0.465833i	0.0498685	+	0.0150819i
$955$	15.5689	−	16.4546i	0.503798	−	0.532459i
$956$	−8.32533	+	12.5050i	−0.269260	+	0.404440i
$957$	−1.08639	−	4.05445i	−0.0351179	−	0.131062i
$958$	11.0668	−	17.8302i	0.357553	−	0.576066i
$959$		0			0
$960$	−23.8305	+	29.0342i	−0.769126	+	0.937076i
$961$	−13.5695	+	23.5030i	−0.437725	+	0.758163i
$962$	23.3132	+	0.743680i	0.751649	+	0.0239772i
$963$	−0.764696	−	0.204900i	−0.0246420	−	0.00660280i
$964$	14.4737	+	0.924348i	0.466167	+	0.0297713i
$965$	41.7515	+	22.5897i	1.34403	+	0.727189i
$966$		0			0
$967$	−30.6644	−	30.6644i	−0.986102	−	0.986102i	0.0138026	−	0.999905i	$-0.495606\pi$
$967$	−30.6644	−	30.6644i	−0.986102	−	0.986102i	−0.999905	+	0.0138026i	$0.995606\pi$
$968$	−17.7655	+	24.9236i	−0.571005	+	0.801074i
$969$	60.9131	−	35.1682i	1.95681	−	1.12977i
$970$	−10.4516	+	17.9268i	−0.335580	+	0.575595i
$971$	24.2994	+	14.0293i	0.779806	+	0.450221i	0.836362	−	0.548178i	$-0.184678\pi$
$971$	24.2994	+	14.0293i	0.779806	+	0.450221i	−0.0565554	+	0.998399i	$0.518012\pi$
$972$	−25.7384	−	8.68902i	−0.825559	−	0.278701i
$973$		0			0
$974$	48.1139	−	11.2610i	1.54167	−	0.360826i
$975$	1.28374	+	23.1893i	0.0411125	+	0.742653i
$976$	7.34591	+	0.942119i	0.235137	+	0.0301565i
$977$	−26.6150	−	7.13146i	−0.851488	−	0.228156i	−0.193422	−	0.981116i	$-0.561959\pi$
$977$	−26.6150	−	7.13146i	−0.851488	−	0.228156i	−0.658066	+	0.752960i	$0.728625\pi$
$978$	15.1014	−	8.08810i	0.482889	−	0.258629i
$979$	−4.89802			−0.156541
$980$		0			0
$981$	−7.36695			−0.235209
$982$	6.47080	−	3.46567i	0.206491	−	0.110594i
$983$	−32.6601	−	8.75124i	−1.04169	−	0.279121i	−0.302879	−	0.953029i	$-0.597948\pi$
$983$	−32.6601	−	8.75124i	−1.04169	−	0.279121i	−0.738815	+	0.673908i	$0.764614\pi$
$984$	−22.3591	−	8.35139i	−0.712782	−	0.266232i
$985$	23.4545	+	38.1482i	0.747324	+	1.21550i
$986$	−29.7395	+	6.96051i	−0.947099	+	0.221668i
$987$		0			0
$988$	10.3781	−	30.7417i	0.330171	−	0.978023i
$989$	15.4106	+	8.89729i	0.490027	+	0.282917i
$990$	1.82159	−	0.479831i	0.0578940	−	0.0152500i
$991$	38.7625	−	22.3796i	1.23133	−	0.710910i	0.264025	−	0.964516i	$-0.414950\pi$
$991$	38.7625	−	22.3796i	1.23133	−	0.710910i	0.967308	+	0.253605i	$0.0816165\pi$
$992$	−1.76478	+	10.9744i	−0.0560318	+	0.348439i
$993$	−38.2642	−	38.2642i	−1.21428	−	1.21428i
$994$		0			0
$995$	15.6109	−	4.64914i	0.494898	−	0.147388i
$996$	−1.78602	+	27.9661i	−0.0565923	+	0.886139i
$997$	8.01061	+	2.14644i	0.253699	+	0.0679784i	0.383427	−	0.923571i	$-0.374744\pi$
$997$	8.01061	+	2.14644i	0.253699	+	0.0679784i	−0.129728	+	0.991550i	$0.541410\pi$
$998$	15.3250	+	0.488859i	0.485104	+	0.0154746i
$999$	−12.4539	+	21.5708i	−0.394025	+	0.682471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.863.8		72
4.3	odd	2	inner	980.2.x.m.863.10		72
5.2	odd	4	inner	980.2.x.m.667.16		72
7.2	even	3		980.2.k.j.883.6		36
7.3	odd	6		140.2.w.b.123.18	yes	72
7.4	even	3	inner	980.2.x.m.263.18		72
7.5	odd	6		980.2.k.k.883.6		36
7.6	odd	2		140.2.w.b.23.8	✓	72
20.7	even	4	inner	980.2.x.m.667.18		72
28.3	even	6		140.2.w.b.123.16	yes	72
28.11	odd	6	inner	980.2.x.m.263.16		72
28.19	even	6		980.2.k.k.883.5		36
28.23	odd	6		980.2.k.j.883.5		36
28.27	even	2		140.2.w.b.23.10	yes	72
35.2	odd	12		980.2.k.j.687.5		36
35.3	even	12		700.2.be.e.207.9		72
35.12	even	12		980.2.k.k.687.5		36
35.13	even	4		700.2.be.e.107.3		72
35.17	even	12		140.2.w.b.67.10	yes	72
35.24	odd	6		700.2.be.e.543.1		72
35.27	even	4		140.2.w.b.107.16	yes	72
35.32	odd	12	inner	980.2.x.m.67.10		72
35.34	odd	2		700.2.be.e.443.11		72
140.3	odd	12		700.2.be.e.207.11		72
140.27	odd	4		140.2.w.b.107.18	yes	72
140.47	odd	12		980.2.k.k.687.6		36
140.59	even	6		700.2.be.e.543.3		72
140.67	even	12	inner	980.2.x.m.67.8		72
140.83	odd	4		700.2.be.e.107.1		72
140.87	odd	12		140.2.w.b.67.8	yes	72
140.107	even	12		980.2.k.j.687.6		36
140.139	even	2		700.2.be.e.443.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.8	✓	72	7.6	odd	2
140.2.w.b.23.10	yes	72	28.27	even	2
140.2.w.b.67.8	yes	72	140.87	odd	12
140.2.w.b.67.10	yes	72	35.17	even	12
140.2.w.b.107.16	yes	72	35.27	even	4
140.2.w.b.107.18	yes	72	140.27	odd	4
140.2.w.b.123.16	yes	72	28.3	even	6
140.2.w.b.123.18	yes	72	7.3	odd	6
700.2.be.e.107.1		72	140.83	odd	4
700.2.be.e.107.3		72	35.13	even	4
700.2.be.e.207.9		72	35.3	even	12
700.2.be.e.207.11		72	140.3	odd	12
700.2.be.e.443.9		72	140.139	even	2
700.2.be.e.443.11		72	35.34	odd	2
700.2.be.e.543.1		72	35.24	odd	6
700.2.be.e.543.3		72	140.59	even	6
980.2.k.j.687.5		36	35.2	odd	12
980.2.k.j.687.6		36	140.107	even	12
980.2.k.j.883.5		36	28.23	odd	6
980.2.k.j.883.6		36	7.2	even	3
980.2.k.k.687.5		36	35.12	even	12
980.2.k.k.687.6		36	140.47	odd	12
980.2.k.k.883.5		36	28.19	even	6
980.2.k.k.883.6		36	7.5	odd	6
980.2.x.m.67.8		72	140.67	even	12	inner
980.2.x.m.67.10		72	35.32	odd	12	inner
980.2.x.m.263.16		72	28.11	odd	6	inner
980.2.x.m.263.18		72	7.4	even	3	inner
980.2.x.m.667.16		72	5.2	odd	4	inner
980.2.x.m.667.18		72	20.7	even	4	inner
980.2.x.m.863.8		72	1.1	even	1	trivial
980.2.x.m.863.10		72	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.667698 - 1.24667i) q^{2} +(-2.02821 - 0.543458i) q^{3} +(-1.10836 + 1.66480i) q^{4} +(0.518800 - 2.17505i) q^{5} +(0.676724 + 2.89137i) q^{6} +(2.81549 + 0.270171i) q^{8} +(1.22023 + 0.704499i) q^{9} +(-3.05797 + 0.805507i) q^{10} +(-0.366133 + 0.211387i) q^{11} +(3.15273 - 2.77421i) q^{12} +(1.56422 + 1.56422i) q^{13} +(-2.23429 + 4.12952i) q^{15} +(-1.54309 - 3.69038i) q^{16} +(4.41198 + 1.18219i) q^{17} +(0.0635313 - 1.99161i) q^{18} +(-3.66683 + 6.35114i) q^{19} +(3.04600 + 3.27443i) q^{20} +(0.507996 + 0.315303i) q^{22} +(1.72616 + 6.44210i) q^{23} +(-5.56360 - 2.07807i) q^{24} +(-4.46169 - 2.25683i) q^{25} +(0.905634 - 2.99449i) q^{26} +(2.36225 + 2.36225i) q^{27} -4.72835i q^{29} +(6.63997 + 0.0281364i) q^{30} +(1.70170 - 0.982474i) q^{31} +(-3.57035 + 4.38778i) q^{32} +(0.857477 - 0.229760i) q^{33} +(-1.47208 - 6.28961i) q^{34} +(-2.52529 + 1.25059i) q^{36} +(1.92971 + 7.20177i) q^{37} +(10.3661 + 0.330672i) q^{38} +(-2.32248 - 4.02266i) q^{39} +(2.04832 - 5.98368i) q^{40} +4.01882 q^{41} +(1.88664 - 1.88664i) q^{43} +(0.0538902 - 0.843830i) q^{44} +(2.16537 - 2.28856i) q^{45} +(6.87860 - 6.45332i) q^{46} +(6.35786 - 1.70358i) q^{47} +(1.12414 + 8.32348i) q^{48} +(0.165546 + 7.06913i) q^{50} +(-8.30597 - 4.79545i) q^{51} +(-4.33782 + 0.870391i) q^{52} +(-0.209015 + 0.780053i) q^{53} +(1.36767 - 4.52221i) q^{54} +(0.269828 + 0.906026i) q^{55} +(10.8887 - 10.8887i) q^{57} +(-5.89468 + 3.15711i) q^{58} +(-1.35717 - 2.35069i) q^{59} +(-4.39842 - 8.29662i) q^{60} +(-0.925760 + 1.60346i) q^{61} +(-2.36104 - 1.46545i) q^{62} +(7.85401 + 1.52133i) q^{64} +(4.21378 - 2.59074i) q^{65} +(-0.858970 - 0.915577i) q^{66} +(2.33152 - 8.70137i) q^{67} +(-6.85815 + 6.03476i) q^{68} -14.0041i q^{69} -3.16317i q^{71} +(3.24521 + 2.31318i) q^{72} +(1.78752 - 6.67113i) q^{73} +(7.68975 - 7.21432i) q^{74} +(7.82277 + 7.00208i) q^{75} +(-6.50918 - 13.1438i) q^{76} +(-3.46420 + 5.58129i) q^{78} +(1.77995 - 3.08296i) q^{79} +(-8.82731 + 1.44173i) q^{80} +(-5.62086 - 9.73561i) q^{81} +(-2.68336 - 5.01013i) q^{82} +(-4.71846 + 4.71846i) q^{83} +(4.86025 - 8.98296i) q^{85} +(-3.61172 - 1.09231i) q^{86} +(-2.56966 + 9.59011i) q^{87} +(-1.08796 + 0.496241i) q^{88} +(10.0333 + 5.79271i) q^{89} +(-4.29889 - 1.17143i) q^{90} +(-12.6380 - 4.26646i) q^{92} +(-3.98534 + 1.06787i) q^{93} +(-6.36893 - 6.78865i) q^{94} +(11.9117 + 11.2705i) q^{95} +(9.62601 - 6.95901i) q^{96} +(4.64008 - 4.64008i) q^{97} -0.595688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) \) 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

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