LMFDB - Embedded newform 980.2.x.m.667.16

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			667.16
Character	$\chi$	$=$	980.667
Dual form			980.2.x.m.263.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24667 - 0.667698i) q^{2} +(-0.543458 + 2.02821i) q^{3} +(1.10836 - 1.66480i) q^{4} +(1.62425 - 1.53682i) q^{5} +(0.676724 + 2.89137i) q^{6} +(0.270171 - 2.81549i) q^{8} +(-1.22023 - 0.704499i) q^{9} +(0.998766 - 3.00041i) q^{10} +(-0.366133 + 0.211387i) q^{11} +(2.77421 + 3.15273i) q^{12} +(1.56422 - 1.56422i) q^{13} +(2.23429 + 4.12952i) q^{15} +(-1.54309 - 3.69038i) q^{16} +(-1.18219 + 4.41198i) q^{17} +(-1.99161 - 0.0635313i) q^{18} +(3.66683 - 6.35114i) q^{19} +(-0.758241 - 4.40739i) q^{20} +(-0.315303 + 0.507996i) q^{22} +(6.44210 - 1.72616i) q^{23} +(5.56360 + 2.07807i) q^{24} +(0.276371 - 4.99236i) q^{25} +(0.905634 - 2.99449i) q^{26} +(-2.36225 + 2.36225i) q^{27} +4.72835i q^{29} +(5.54269 + 3.65631i) q^{30} +(1.70170 - 0.982474i) q^{31} +(-4.38778 - 3.57035i) q^{32} +(-0.229760 - 0.857477i) q^{33} +(1.47208 + 6.28961i) q^{34} +(-2.52529 + 1.25059i) q^{36} +(-7.20177 + 1.92971i) q^{37} +(0.330672 - 10.3661i) q^{38} +(2.32248 + 4.02266i) q^{39} +(-3.88808 - 4.98827i) q^{40} +4.01882 q^{41} +(-1.88664 - 1.88664i) q^{43} +(-0.0538902 + 0.843830i) q^{44} +(-3.06464 + 0.730988i) q^{45} +(6.87860 - 6.45332i) q^{46} +(1.70358 + 6.35786i) q^{47} +(8.32348 - 1.12414i) q^{48} +(-2.98885 - 6.40834i) q^{50} +(-8.30597 - 4.79545i) q^{51} +(-0.870391 - 4.33782i) q^{52} +(0.780053 + 0.209015i) q^{53} +(-1.36767 + 4.52221i) q^{54} +(-0.269828 + 0.906026i) q^{55} +(10.8887 + 10.8887i) q^{57} +(3.15711 + 5.89468i) q^{58} +(1.35717 + 2.35069i) q^{59} +(9.35120 + 0.857356i) q^{60} +(-0.925760 + 1.60346i) q^{61} +(1.46545 - 2.36104i) q^{62} +(-7.85401 - 1.52133i) q^{64} +(0.136759 - 4.94461i) q^{65} +(-0.858970 - 0.915577i) q^{66} +(8.70137 + 2.33152i) q^{67} +(6.03476 + 6.85815i) q^{68} +14.0041i q^{69} -3.16317i q^{71} +(-2.31318 + 3.24521i) q^{72} +(-6.67113 - 1.78752i) q^{73} +(-7.68975 + 7.21432i) q^{74} +(9.97537 + 3.27368i) q^{75} +(-6.50918 - 13.1438i) q^{76} +(5.58129 + 3.46420i) q^{78} +(-1.77995 + 3.08296i) q^{79} +(-8.17780 - 3.62265i) q^{80} +(-5.62086 - 9.73561i) q^{81} +(5.01013 - 2.68336i) q^{82} +(4.71846 + 4.71846i) q^{83} +(4.86025 + 8.98296i) q^{85} +(-3.61172 - 1.09231i) q^{86} +(-9.59011 - 2.56966i) q^{87} +(0.496241 + 1.08796i) q^{88} +(-10.0333 - 5.79271i) q^{89} +(-3.33251 + 2.95755i) q^{90} +(4.26646 - 12.6380i) q^{92} +(1.06787 + 3.98534i) q^{93} +(6.36893 + 6.78865i) q^{94} +(-3.80470 - 15.9511i) 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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.24667	−	0.667698i	0.881527	−	0.472134i
$2$	1.24667	−	0.667698i	0.881527	−	0.472134i
$3$	−0.543458	+	2.02821i	−0.313766	+	1.17099i	0.611367	+	0.791347i	$0.290620\pi$
$3$	−0.543458	+	2.02821i	−0.313766	+	1.17099i	−0.925133	+	0.379643i	$0.876047\pi$
$4$	1.10836	−	1.66480i	0.554179	−	0.832398i
$5$	1.62425	−	1.53682i	0.726386	−	0.687287i
$5$	1.62425	−	1.53682i	0.726386	−	0.687287i
$6$	0.676724	+	2.89137i	0.276271	+	1.18040i
$7$		0			0
$7$		0			0
$8$	0.270171	−	2.81549i	0.0955200	−	0.995428i
$9$	−1.22023	−	0.704499i	−0.406742	−	0.234833i
$10$	0.998766	−	3.00041i	0.315838	−	0.948813i
$11$	−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	$0.353635\pi$
$12$	2.77421	+	3.15273i	0.800847	+	0.910115i
$13$	1.56422	−	1.56422i	0.433837	−	0.433837i	−0.456095	−	0.889931i	$-0.650752\pi$
$13$	1.56422	−	1.56422i	0.433837	−	0.433837i	0.889931	+	0.456095i	$0.150752\pi$
$14$		0			0
$15$	2.23429	+	4.12952i	0.576890	+	1.06624i
$16$	−1.54309	−	3.69038i	−0.385772	−	0.922594i
$17$	−1.18219	+	4.41198i	−0.286722	+	1.07006i	0.660849	+	0.750519i	$0.270196\pi$
$17$	−1.18219	+	4.41198i	−0.286722	+	1.07006i	−0.947572	+	0.319544i	$0.896470\pi$
$18$	−1.99161	−	0.0635313i	−0.469427	−	0.0149745i
$19$	3.66683	−	6.35114i	0.841228	−	1.45705i	−0.0476283	−	0.998865i	$-0.515166\pi$
$19$	3.66683	−	6.35114i	0.841228	−	1.45705i	0.888857	−	0.458185i	$-0.151500\pi$
$20$	−0.758241	−	4.40739i	−0.169548	−	0.985522i
$21$		0			0
$22$	−0.315303	+	0.507996i	−0.0672229	+	0.108305i
$23$	6.44210	−	1.72616i	1.34327	−	0.359928i	0.485624	−	0.874168i	$-0.338592\pi$
$23$	6.44210	−	1.72616i	1.34327	−	0.359928i	0.857647	+	0.514239i	$0.171926\pi$
$24$	5.56360	+	2.07807i	1.13566	+	0.424184i
$25$	0.276371	−	4.99236i	0.0552743	−	0.998471i
$26$	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	$0.144673\pi$
$29$			4.72835i			0.878033i	−0.898479	+	0.439016i	$0.855327\pi$
$30$	5.54269	+	3.65631i	1.01195	+	0.667548i
$31$	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	$0.276869\pi$
$32$	−4.38778	−	3.57035i	−0.775656	−	0.631155i
$33$	−0.229760	−	0.857477i	−0.0399961	−	0.149268i
$34$	1.47208	+	6.28961i	0.252459	+	1.07866i
$35$		0			0
$36$	−2.52529	+	1.25059i	−0.420882	+	0.208432i
$37$	−7.20177	+	1.92971i	−1.18396	+	0.317242i	−0.796498	−	0.604641i	$-0.793316\pi$
$37$	−7.20177	+	1.92971i	−1.18396	+	0.317242i	−0.387467	+	0.921884i	$0.626650\pi$
$38$	0.330672	−	10.3661i	0.0536422	−	1.68160i
$39$	2.32248	+	4.02266i	0.371895	+	0.644141i
$40$	−3.88808	−	4.98827i	−0.614760	−	0.788715i
$41$	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	$-0.315213\pi$
$43$	−1.88664	−	1.88664i	−0.287710	−	0.287710i	−0.836174	+	0.548464i	$0.815213\pi$
$44$	−0.0538902	+	0.843830i	−0.00812426	+	0.127212i
$45$	−3.06464	+	0.730988i	−0.456850	+	0.108969i
$46$	6.87860	−	6.45332i	1.01419	−	0.951491i
$47$	1.70358	+	6.35786i	0.248493	+	0.927389i	0.971595	+	0.236648i	$0.0760488\pi$
$47$	1.70358	+	6.35786i	0.248493	+	0.927389i	−0.723102	+	0.690741i	$0.757284\pi$
$48$	8.32348	−	1.12414i	1.20139	−	0.162256i
$49$		0			0
$50$	−2.98885	−	6.40834i	−0.422687	−	0.906276i
$51$	−8.30597	−	4.79545i	−1.16307	−	0.671498i
$52$	−0.870391	−	4.33782i	−0.120702	−	0.601548i
$53$	0.780053	+	0.209015i	0.107149	+	0.0287104i	0.311995	−	0.950084i	$-0.399003\pi$
$53$	0.780053	+	0.209015i	0.107149	+	0.0287104i	−0.204846	+	0.978794i	$0.565669\pi$
$54$	−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
$58$	3.15711	+	5.89468i	0.414549	+	0.774009i
$59$	1.35717	+	2.35069i	0.176689	+	0.306034i	0.940744	−	0.339116i	$-0.110128\pi$
$59$	1.35717	+	2.35069i	0.176689	+	0.306034i	−0.764056	+	0.645151i	$0.776795\pi$
$60$	9.35120	+	0.857356i	1.20723	+	0.110684i
$61$	−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	$0.204485\pi$
$62$	1.46545	−	2.36104i	0.186112	−	0.299852i
$63$		0			0
$64$	−7.85401	−	1.52133i	−0.981752	−	0.190167i
$65$	0.136759	−	4.94461i	0.0169629	−	0.613303i
$66$	−0.858970	−	0.915577i	−0.105732	−	0.112700i
$67$	8.70137	+	2.33152i	1.06304	+	0.284841i	0.747631	−	0.664114i	$-0.231191\pi$
$67$	8.70137	+	2.33152i	1.06304	+	0.284841i	0.315410	+	0.948955i	$0.397858\pi$
$68$	6.03476	+	6.85815i	0.731822	+	0.831673i
$69$			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	$-0.0601032\pi$
$72$	−2.31318	+	3.24521i	−0.272611	+	0.382451i
$73$	−6.67113	−	1.78752i	−0.780797	−	0.209214i	−0.153661	−	0.988124i	$-0.549106\pi$
$73$	−6.67113	−	1.78752i	−0.780797	−	0.209214i	−0.627136	+	0.778910i	$0.715773\pi$
$74$	−7.68975	+	7.21432i	−0.893915	+	0.838648i
$75$	9.97537	+	3.27368i	1.15186	+	0.378012i
$76$	−6.50918	−	13.1438i	−0.746654	−	1.50770i
$77$		0			0
$78$	5.58129	+	3.46420i	0.631957	+	0.392243i
$79$	−1.77995	+	3.08296i	−0.200260	+	0.346860i	−0.948612	−	0.316441i	$-0.897512\pi$
$79$	−1.77995	+	3.08296i	−0.200260	+	0.346860i	0.748352	+	0.663301i	$0.230845\pi$
$80$	−8.17780	−	3.62265i	−0.914306	−	0.405024i
$81$	−5.62086	−	9.73561i	−0.624540	−	1.08173i
$82$	5.01013	−	2.68336i	0.553276	−	0.296328i
$83$	4.71846	+	4.71846i	0.517919	+	0.517919i	0.916941	−	0.399022i	$-0.130650\pi$
$83$	4.71846	+	4.71846i	0.517919	+	0.517919i	−0.399022	+	0.916941i	$0.630650\pi$
$84$		0			0
$85$	4.86025	+	8.98296i	0.527168	+	0.974339i
$86$	−3.61172	−	1.09231i	−0.389462	−	0.117786i
$87$	−9.59011	−	2.56966i	−1.02817	−	0.275497i
$88$	0.496241	+	1.08796i	0.0528994	+	0.115977i
$89$	−10.0333	−	5.79271i	−1.06352	−	0.614026i	−0.137119	−	0.990555i	$-0.543784\pi$
$89$	−10.0333	−	5.79271i	−1.06352	−	0.614026i	−0.926405	+	0.376529i	$0.877118\pi$
$90$	−3.33251	+	2.95755i	−0.351277	+	0.311754i
$91$		0			0
$92$	4.26646	−	12.6380i	0.444809	−	1.31760i
$93$	1.06787	+	3.98534i	0.110733	+	0.413260i
$94$	6.36893	+	6.78865i	0.656905	+	0.700196i
$95$	−3.80470	−	15.9511i	−0.390354	−	1.63655i
$96$	9.62601	−	6.95901i	0.982451	−	0.710251i
$97$	4.64008	+	4.64008i	0.471128	+	0.471128i	0.902280	−	0.431151i	$-0.141892\pi$
$97$	4.64008	+	4.64008i	0.471128	+	0.471128i	−0.431151	+	0.902280i	$0.641892\pi$
$98$		0			0
$99$	0.595688			0.0598689
$100$	−8.00493	−	5.99342i	−0.800493	−	0.599342i
$101$	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	$0.765672\pi$
$102$	−13.5567	−	0.432451i	−1.34231	−	0.0428190i
$103$	−15.1879	+	4.06958i	−1.49651	+	0.400987i	−0.911928	−	0.410351i	$-0.865406\pi$
$103$	−15.1879	+	4.06958i	−1.49651	+	0.400987i	−0.584577	+	0.811338i	$0.698740\pi$
$104$	−3.98145	−	4.82666i	−0.390413	−	0.473293i
$105$		0			0
$106$	1.11203	−	0.260269i	0.108009	−	0.0252795i
$107$	−0.145422	−	0.542724i	−0.0140585	−	0.0524671i	0.958540	−	0.284957i	$-0.0919794\pi$
$107$	−0.145422	−	0.542724i	−0.0140585	−	0.0524671i	−0.972599	+	0.232490i	$0.925313\pi$
$108$	1.31445	+	6.55088i	0.126483	+	0.630359i
$109$	4.52802	−	2.61425i	0.433706	−	0.250400i	−0.267218	−	0.963636i	$-0.586105\pi$
$109$	4.52802	−	2.61425i	0.433706	−	0.250400i	0.700924	+	0.713236i	$0.252771\pi$
$110$	0.268567	+	1.30968i	0.0256068	+	0.124873i
$111$		−	15.6555i		−	1.48595i
$112$		0			0
$113$	9.46096	−	9.46096i	0.890012	−	0.890012i	−0.104511	−	0.994524i	$-0.533328\pi$
$113$	9.46096	−	9.46096i	0.890012	−	0.890012i	0.994524	+	0.104511i	$0.0333278\pi$
$114$	20.8449	+	6.30421i	1.95231	+	0.590443i
$115$	7.81079	−	12.7041i	0.728360	−	1.18466i
$116$	7.87174	+	5.24070i	0.730872	+	0.486587i
$117$	−3.01070	+	0.806713i	−0.278339	+	0.0745807i
$118$	3.26150	+	2.02435i	0.300245	+	0.186357i
$119$		0			0
$120$	12.2303	−	5.17494i	1.11647	−	0.472405i
$121$	−5.41063	+	9.37149i	−0.491876	+	0.851953i
$122$	−0.0834845	+	2.61711i	−0.00755833	+	0.236942i
$123$	−2.18406	+	8.15103i	−0.196930	+	0.734953i
$124$	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	−0.580249	+	0.814439i	$0.697045\pi$
$127$	−15.7173	+	15.7173i	−1.39469	+	1.39469i	−0.814439	+	0.580249i	$0.802955\pi$
$128$	−10.8071	+	3.34752i	−0.955225	+	0.295882i
$129$	4.85182	−	2.80120i	0.427179	−	0.246632i
$130$	−3.13101	−	6.25559i	−0.274608	−	0.548652i
$131$	−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	$0.954034\pi$
$132$	−1.68218	−	0.567887i	−0.146415	−	0.0494282i
$133$		0			0
$134$	12.4045	−	2.90326i	1.07158	−	0.250803i
$135$	−0.206531	+	7.46723i	−0.0177753	+	0.642677i
$136$	12.1025	+	4.52043i	1.03778	+	0.387624i
$137$	−3.47858	+	12.9822i	−0.297195	+	1.10915i	0.642263	+	0.766485i	$0.277996\pi$
$137$	−3.47858	+	12.9822i	−0.297195	+	1.10915i	−0.939458	+	0.342664i	$0.888671\pi$
$138$	9.35048	+	17.4584i	0.795966	+	1.48616i
$139$	−6.16658			−0.523043			−0.261521	−	0.965198i	$-0.584224\pi$
$139$	−6.16658			−0.523043			−0.261521	+	0.965198i	$0.584224\pi$
$140$		0			0
$141$	−13.8209			−1.16393
$142$	−2.11205	−	3.94343i	−0.177239	−	0.330925i
$143$	−0.242057	+	0.903369i	−0.0202418	+	0.0755435i
$144$	−0.716948	+	5.59020i	−0.0597457	+	0.465850i
$145$	7.26662	+	7.68002i	0.603460	+	0.637791i
$146$	−9.51021	+	2.22586i	−0.787070	+	0.184213i
$147$		0			0
$148$	−4.76957	+	14.1283i	−0.392056	+	1.16134i
$149$	−4.22837	−	2.44125i	−0.346401	−	0.199995i	0.316698	−	0.948526i	$-0.397426\pi$
$149$	−4.22837	−	2.44125i	−0.346401	−	0.199995i	−0.663099	+	0.748532i	$0.730759\pi$
$150$	14.6218	−	2.57935i	1.19386	−	0.210603i
$151$	−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	$0.378987\pi$
$152$	−16.8909	−	12.0398i	−1.37003	−	0.976559i
$153$	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
$157$	−3.49270	+	13.0349i	−0.278748	+	1.04030i	0.674541	+	0.738238i	$0.264342\pi$
$157$	−3.49270	+	13.0349i	−0.278748	+	1.04030i	−0.953288	+	0.302062i	$0.902325\pi$
$158$	−0.160515	+	5.03189i	−0.0127699	+	0.400316i
$159$	−0.847853	+	1.46852i	−0.0672391	+	0.116462i
$160$	−12.6138	+	0.944073i	−0.997211	+	0.0746355i
$161$		0			0
$162$	−13.5078	−	8.38403i	−1.06127	−	0.658712i
$163$	−5.57237	+	1.49311i	−0.436462	+	0.116950i	−0.470358	−	0.882476i	$-0.655875\pi$
$163$	−5.57237	+	1.49311i	−0.436462	+	0.116950i	0.0338961	+	0.999425i	$0.489208\pi$
$164$	4.45429	−	6.69051i	0.347822	−	0.522441i
$165$	−1.69097	−	1.03966i	−0.131642	−	0.0809371i
$166$	9.03287	+	2.73184i	0.701086	+	0.212032i
$167$	−6.11518	+	6.11518i	−0.473207	+	0.473207i	−0.902951	−	0.429744i	$-0.858604\pi$
$167$	−6.11518	+	6.11518i	−0.473207	+	0.473207i	0.429744	+	0.902951i	$0.358604\pi$
$168$		0			0
$169$			8.10643i			0.623572i
$170$	12.0570	+	7.95358i	0.924732	+	0.610012i
$171$	−8.94873	+	5.16655i	−0.684327	+	0.395096i
$172$	−5.23194	+	1.04980i	−0.398932	+	0.0800463i
$173$	−1.13155	−	4.22300i	−0.0860302	−	0.321069i	0.909477	−	0.415754i	$-0.136482\pi$
$173$	−1.13155	−	4.22300i	−0.0860302	−	0.321069i	−0.995507	+	0.0946850i	$0.969816\pi$
$174$	−13.6714	+	3.19979i	−1.03643	+	0.242575i
$175$		0			0
$176$	1.34507	+	1.02498i	0.101389	+	0.0772609i
$177$	−5.50528	+	1.47513i	−0.413802	+	0.110878i
$178$	−16.3759	−	0.522383i	−1.22743	−	0.0391542i
$179$	−9.00305	−	15.5937i	−0.672920	−	1.16553i	−0.977072	−	0.212908i	$-0.931707\pi$
$179$	−9.00305	−	15.5937i	−0.672920	−	1.16553i	0.304152	−	0.952623i	$-0.401627\pi$
$180$	−2.17977	+	5.91220i	−0.162471	+	0.440669i
$181$	−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
$185$	−8.73186	+	14.2022i	−0.641979	+	1.04416i
$186$	3.99228	+	4.25537i	0.292728	+	0.312019i
$187$	−0.499798	−	1.86527i	−0.0365489	−	0.136402i
$188$	12.4727	+	4.21066i	0.909666	+	0.307094i
$189$		0			0
$190$	−15.3937	−	17.3453i	−1.11678	−	1.25836i
$191$	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	$0.547218\pi$
$192$	7.35392	−	15.1028i	0.530723	−	1.08995i
$193$	20.5062	+	5.49463i	1.47607	+	0.395512i	0.905008	−	0.425395i	$-0.139865\pi$
$193$	20.5062	+	5.49463i	1.47607	+	0.395512i	0.571063	+	0.820907i	$0.306531\pi$
$194$	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	−0.999960	−	0.00898613i	$-0.997140\pi$
$197$	−14.1612	−	14.1612i	−1.00895	−	1.00895i	−0.00898613	−	0.999960i	$-0.502860\pi$
$198$	0.742625	−	0.397740i	0.0527760	−	0.0282661i
$199$	−3.64221	−	6.30849i	−0.258189	−	0.447197i	0.707568	−	0.706646i	$-0.249793\pi$
$199$	−3.64221	−	6.30849i	−0.258189	−	0.447197i	−0.965757	+	0.259449i	$0.916459\pi$
$200$	−13.9813	−	2.12691i	−0.988626	−	0.150396i
$201$	−9.45766	+	16.3811i	−0.667092	+	1.15544i
$202$	5.09515	+	3.16246i	0.358494	+	0.222510i
$203$		0			0
$204$	−17.1894	+	8.51266i	−1.20350	+	0.596005i
$205$	6.52757	−	6.17620i	0.455905	−	0.431365i
$206$	−16.2170	+	15.2143i	−1.12989	+	1.06003i
$207$	−9.07690	−	2.43215i	−0.630888	−	0.169046i
$208$	−8.18629	−	3.35883i	−0.567617	−	0.232893i
$209$			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	$-0.204498\pi$
$212$	1.21254	−	1.06697i	0.0832779	−	0.0732795i
$213$	6.41559	+	1.71905i	0.439589	+	0.117788i
$214$	−0.543669	−	0.579497i	−0.0371644	−	0.0396136i
$215$	−5.96380	−	0.164948i	−0.406728	−	0.0112494i
$216$	6.01269	+	7.28911i	0.409112	+	0.495961i
$217$		0			0
$218$	3.89940	−	6.28245i	0.264101	−	0.425502i
$219$	7.25096	−	12.5590i	0.489975	−	0.848661i
$220$	1.20928	+	1.45341i	0.0815298	+	0.0979888i
$221$	5.05211	+	8.75051i	0.339842	+	0.588623i
$222$	−10.4531	−	19.5171i	−0.701568	−	1.30990i
$223$	1.68218	+	1.68218i	0.112647	+	0.112647i	0.761183	−	0.648537i	$-0.224619\pi$
$223$	1.68218	+	1.68218i	0.112647	+	0.112647i	−0.648537	+	0.761183i	$0.724619\pi$
$224$		0			0
$225$	−3.85434	+	5.89711i	−0.256956	+	0.393140i
$226$	5.47760	−	18.1117i	0.364364	−	1.20477i
$227$	15.1208	+	4.05161i	1.00360	+	0.268915i	0.722955	−	0.690895i	$-0.242783\pi$
$227$	15.1208	+	4.05161i	1.00360	+	0.268915i	0.280650	+	0.959810i	$0.409450\pi$
$228$	30.1960	−	6.05888i	1.99978	−	0.401259i
$229$	−14.7843	−	8.53574i	−0.976976	−	0.564057i	−0.0756201	−	0.997137i	$-0.524094\pi$
$229$	−14.7843	−	8.53574i	−0.976976	−	0.564057i	−0.901356	+	0.433079i	$0.857427\pi$
$230$	1.25497	−	21.0530i	0.0827506	−	1.38819i
$231$		0			0
$232$	13.3126	+	1.27747i	0.874018	+	0.0838697i
$233$	−3.60234	−	13.4441i	−0.235997	−	0.880753i	−0.977697	−	0.210021i	$-0.932647\pi$
$233$	−3.60234	−	13.4441i	−0.235997	−	0.880753i	0.741700	−	0.670732i	$-0.234020\pi$
$234$	−3.21469	+	3.01594i	−0.210151	+	0.197158i
$235$	12.5379	+	7.70865i	0.817884	+	0.502857i
$236$	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	$-0.578111\pi$
$239$	−7.51141			−0.485873			−0.242936	+	0.970042i	$0.578111\pi$
$240$	11.7918	−	14.6176i	0.761157	−	0.943560i
$241$	−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	$0.908370\pi$
$242$	−0.487927	+	15.2958i	−0.0313652	+	0.983251i
$243$	13.1199	−	3.51547i	0.841644	−	0.225518i
$244$	1.64336	+	3.31841i	0.105206	+	0.212439i
$245$		0			0
$246$	2.71963	+	11.6199i	0.173397	+	0.740858i
$247$	−4.19885	−	15.6703i	−0.267166	−	0.997078i
$248$	−2.30640	−	5.05655i	−0.146457	−	0.321091i
$249$	−12.1343	+	7.00577i	−0.768983	+	0.443972i
$250$	−14.7031	−	5.81542i	−0.929905	−	0.367800i
$251$			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
$255$	−20.8607	+	4.97576i	−1.30635	+	0.311594i
$256$	−11.2378	+	11.3891i	−0.702360	+	0.711822i
$257$	−6.73562	+	1.80480i	−0.420156	+	0.112581i	−0.462702	−	0.886514i	$-0.653120\pi$
$257$	−6.73562	+	1.80480i	−0.420156	+	0.112581i	0.0425454	+	0.999095i	$0.486453\pi$
$258$	4.17825	−	6.73171i	0.260126	−	0.419098i
$259$		0			0
$260$	−8.08018	−	5.70807i	−0.501112	−	0.353999i
$261$	3.33112	−	5.76966i	0.206191	−	0.357133i
$262$	−25.4017	−	0.810300i	−1.56932	−	0.0500605i
$263$	−6.56533	+	24.5021i	−0.404836	+	1.51087i	0.399523	+	0.916723i	$0.369176\pi$
$263$	−6.56533	+	24.5021i	−0.404836	+	1.51087i	−0.804359	+	0.594144i	$0.797491\pi$
$264$	−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
$268$	13.5257	−	11.9018i	0.826216	−	0.727020i
$269$	16.4868	−	9.51864i	1.00522	−	0.580361i	0.0954283	−	0.995436i	$-0.469578\pi$
$269$	16.4868	−	9.51864i	1.00522	−	0.580361i	0.909787	+	0.415075i	$0.136245\pi$
$270$	4.72839	+	9.44706i	0.287760	+	0.574929i
$271$	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	$0.445262\pi$
$272$	18.1061	−	2.44536i	1.09784	−	0.148271i
$273$		0			0
$274$	4.33159	+	18.5072i	0.261681	+	1.11806i
$275$	0.954131	+	1.88629i	0.0575363	+	0.113748i
$276$	23.3139	+	15.5215i	1.40333	+	0.934284i
$277$	−4.17199	+	15.5701i	−0.250670	+	0.935515i	0.719778	+	0.694205i	$0.244244\pi$
$277$	−4.17199	+	15.5701i	−0.250670	+	0.935515i	−0.970448	+	0.241310i	$0.922423\pi$
$278$	−7.68767	+	4.11742i	−0.461076	+	0.246946i
$279$	−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	$0.557347\pi$
$282$	−17.2301	+	9.22821i	−1.02604	+	0.549532i
$283$	0.430842	−	1.60792i	0.0256109	−	0.0955812i	−0.951937	−	0.306293i	$-0.900911\pi$
$283$	0.430842	−	1.60792i	0.0256109	−	0.0955812i	0.977548	+	0.210711i	$0.0675781\pi$
$284$	−5.26604	−	3.50593i	−0.312482	−	0.208039i
$285$	34.4199	+	0.951995i	2.03886	+	0.0563913i
$286$	0.301414	+	1.28782i	0.0178230	+	0.0761505i
$287$		0			0
$288$	2.83877	+	7.44783i	0.167276	+	0.438867i
$289$	−3.34556	−	1.93156i	−0.196798	−	0.113621i
$290$	14.1870	+	4.72252i	0.833089	+	0.277316i
$291$	−11.9328	+	6.88938i	−0.699510	+	0.403863i
$292$	−10.3699	+	9.12485i	−0.606850	+	0.533992i
$293$	14.2453	−	14.2453i	0.832220	−	0.832220i	−0.155600	−	0.987820i	$-0.549731\pi$
$293$	14.2453	−	14.2453i	0.832220	−	0.832220i	0.987820	+	0.155600i	$0.0497311\pi$
$294$		0			0
$295$	5.81698	+	1.73238i	0.338678	+	0.100863i
$296$	3.48737	+	20.7979i	0.202699	+	1.20885i
$297$	0.365549	−	1.36425i	0.0212113	−	0.0791617i
$298$	−6.90138	−	0.220150i	−0.399786	−	0.0127530i
$299$	7.37678	−	12.7770i	0.426610	−	0.738910i
$300$	16.5063	−	12.9785i	0.952990	−	0.749316i
$301$		0			0
$302$	−2.61984	+	4.22091i	−0.150755	+	0.242886i
$303$	−8.60041	+	2.30447i	−0.494081	+	0.132388i
$304$	−29.0963	−	3.73163i	−1.66879	−	0.214024i
$305$	0.960569	+	4.02715i	0.0550020	+	0.230594i
$306$	2.63475	−	8.71184i	0.150619	−	0.498023i
$307$	3.60252	−	3.60252i	0.205607	−	0.205607i	−0.596790	−	0.802397i	$-0.703558\pi$
$307$	3.60252	−	3.60252i	0.205607	−	0.205607i	0.802397	+	0.596790i	$0.203558\pi$
$308$		0			0
$309$		−	33.0159i		−	1.87821i
$310$	−1.24823	−	6.08705i	−0.0708948	−	0.345721i
$311$	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	$0.329428\pi$
$312$	11.9532	−	5.45213i	0.676719	−	0.308666i
$313$	−0.266609	−	0.994998i	−0.0150696	−	0.0562406i	0.957982	−	0.286830i	$-0.0926014\pi$
$313$	−0.266609	−	0.994998i	−0.0150696	−	0.0562406i	−0.973051	+	0.230589i	$0.925935\pi$
$314$	4.34917	+	18.5823i	0.245438	+	1.04866i
$315$		0			0
$316$	3.15968	+	6.38027i	0.177746	+	0.358918i
$317$	27.2346	−	7.29750i	1.52965	−	0.409868i	0.606744	−	0.794897i	$-0.292475\pi$
$317$	27.2346	−	7.29750i	1.52965	−	0.409868i	0.922905	+	0.385029i	$0.125808\pi$
$318$	−0.0764588	+	2.39687i	−0.00428760	+	0.134410i
$319$	−0.999513	−	1.73121i	−0.0559620	−	0.0969290i
$320$	−15.0949	+	9.59918i	−0.843830	+	0.536610i
$321$	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
$325$	−7.37684	−	8.24145i	−0.409193	−	0.457153i
$326$	−5.94994	+	5.58208i	−0.329537	+	0.309163i
$327$	2.84147	+	10.6045i	0.157134	+	0.586432i
$328$	1.08577	−	11.3150i	0.0599517	−	0.624765i
$329$		0			0
$330$	−2.80226	−	0.167044i	−0.154259	−	0.00919545i
$331$	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	$0.416146\pi$
$332$	13.0850	−	2.62553i	0.718134	−	0.144095i
$333$	10.1473	+	2.71896i	0.556068	+	0.148998i
$334$	−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	0.932356	−	0.361540i	$-0.117749\pi$
$337$	10.4788	+	10.4788i	0.570816	+	0.570816i	−0.361540	+	0.932356i	$0.617749\pi$
$338$	5.41265	+	10.1060i	0.294409	+	0.549695i
$339$	14.0472	+	24.3305i	0.762940	+	1.32145i
$340$	20.3417	+	1.86501i	1.10318	+	0.101144i
$341$	−0.415365	+	0.719433i	−0.0224933	+	0.0389595i
$342$	−7.70639	+	12.4160i	−0.416714	+	0.671382i
$343$		0			0
$344$	−5.82154	+	4.80211i	−0.313876	+	0.258912i
$345$	21.5217	+	22.7461i	1.15869	+	1.22461i
$346$	−4.23036	−	4.50914i	−0.227425	−	0.242413i
$347$	18.1389	+	4.86030i	0.973746	+	0.260914i	0.710409	−	0.703789i	$-0.248510\pi$
$347$	18.1389	+	4.86030i	0.973746	+	0.260914i	0.263337	+	0.964704i	$0.415177\pi$
$348$	−14.9072	+	13.1175i	−0.799111	+	0.703170i
$349$			7.53504i			0.403341i	0.979453	+	0.201671i	$0.0646371\pi$
$349$			7.53504i			0.403341i	−0.979453	+	0.201671i	$0.935363\pi$
$350$		0			0
$351$			7.39016i			0.394457i
$352$	2.36124	+	0.379706i	0.125854	+	0.0202384i
$353$	35.6061	+	9.54063i	1.89512	+	0.507796i	0.997791	+	0.0664384i	$0.0211636\pi$
$353$	35.6061	+	9.54063i	1.89512	+	0.507796i	0.897331	+	0.441358i	$0.145503\pi$
$354$	−5.87830	+	5.51487i	−0.312428	+	0.293112i
$355$	−4.86123	−	5.13778i	−0.258007	−	0.272685i
$356$	−20.7641	+	10.2829i	−1.10050	+	0.544995i
$357$		0			0
$358$	−21.6357	−	13.4289i	−1.14348	−	0.709739i
$359$	−9.04771	+	15.6711i	−0.477520	+	0.827089i	−0.999668	−	0.0257661i	$-0.991797\pi$
$359$	−9.04771	+	15.6711i	−0.477520	+	0.827089i	0.522148	+	0.852855i	$0.325131\pi$
$360$	1.23011	+	8.82597i	0.0648327	+	0.465169i
$361$	−17.3913	−	30.1226i	−0.915331	−	1.58540i
$362$	−18.1603	+	9.72643i	−0.954485	+	0.511210i
$363$	−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
$367$	22.6225	+	6.06169i	1.18089	+	0.316417i	0.795278	−	0.606245i	$-0.207325\pi$
$367$	22.6225	+	6.06169i	1.18089	+	0.316417i	0.385608	+	0.922663i	$0.373992\pi$
$368$	−16.3109	−	21.1102i	−0.850264	−	1.10044i
$369$	−4.90388	−	2.83125i	−0.255286	−	0.147389i
$370$	−1.40297	+	23.5356i	−0.0729367	+	1.22356i
$371$		0			0
$372$	7.81835	+	2.63940i	0.405362	+	0.136846i
$373$	1.50150	+	5.60369i	0.0777450	+	0.290148i	0.993842	−	0.110809i	$-0.0353442\pi$
$373$	1.50150	+	5.60369i	0.0777450	+	0.290148i	−0.916097	+	0.400957i	$0.868678\pi$
$374$	−1.86852	−	1.99166i	−0.0966189	−	0.102986i
$375$	21.2335	−	10.0131i	1.09650	−	0.517073i
$376$	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	$-0.324549\pi$
$379$	20.3909			1.04741			0.523706	+	0.851899i	$0.324549\pi$
$380$	−30.7723	−	11.3454i	−1.57858	−	0.582009i
$381$	−23.3364	−	40.4198i	−1.19556	−	2.07077i
$382$	14.3196	+	0.456786i	0.732652	+	0.0233712i
$383$	10.1934	−	2.73132i	0.520860	−	0.139564i	0.0111957	−	0.999937i	$-0.496436\pi$
$383$	10.1934	−	2.73132i	0.520860	−	0.139564i	0.509664	+	0.860373i	$0.329770\pi$
$384$	−0.916257	−	23.7384i	−0.0467576	−	1.21140i
$385$		0			0
$386$	29.2332	−	6.84201i	1.48793	−	0.348249i
$387$	0.972995	+	3.63127i	0.0494601	+	0.184588i
$388$	12.8676	−	2.58191i	0.653256	−	0.131077i
$389$	1.96021	−	1.13173i	0.0993866	−	0.0573809i	−0.449483	−	0.893289i	$-0.648392\pi$
$389$	1.96021	−	1.13173i	0.0993866	−	0.0573809i	0.548869	+	0.835908i	$0.315058\pi$
$390$	14.3893	−	2.95071i	0.728628	−	0.149415i
$391$			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
$395$	1.84687	+	7.74296i	0.0929263	+	0.389590i
$396$	0.660235	−	0.991699i	0.0331781	−	0.0498347i
$397$	16.6975	−	4.47408i	0.838024	−	0.224548i	0.185813	−	0.982585i	$-0.440508\pi$
$397$	16.6975	−	4.47408i	0.838024	−	0.224548i	0.652211	+	0.758037i	$0.273842\pi$
$398$	−8.75279	−	5.43269i	−0.438738	−	0.272316i
$399$		0			0
$400$	−18.8501	+	6.68373i	−0.942507	+	0.334186i
$401$	−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	$0.206376\pi$
$402$	−0.852886	+	26.7367i	−0.0425381	+	1.33351i
$403$	1.12502	−	4.19863i	0.0560413	−	0.209149i
$404$	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
$408$	−15.7456	+	22.0898i	−0.779524	+	1.09361i
$409$	−1.80679	+	1.04315i	−0.0893400	+	0.0515805i	−0.544004	−	0.839082i	$-0.683093\pi$
$409$	−1.80679	+	1.04315i	−0.0893400	+	0.0515805i	0.454664	+	0.890663i	$0.349759\pi$
$410$	4.01386	−	12.0581i	0.198230	−	0.595508i
$411$	−24.4403	−	14.1106i	−1.20555	−	0.696025i
$412$	−10.0586	+	29.7952i	−0.495550	+	1.46791i
$413$		0			0
$414$	−12.9398	+	3.02855i	−0.635957	+	0.148845i
$415$	14.9154	+	0.412534i	0.732168	+	0.0202505i
$416$	−12.4483	+	1.27863i	−0.610326	+	0.0626898i
$417$	3.35128	−	12.5071i	0.164113	−	0.612477i
$418$	2.07019	+	3.86527i	0.101256	+	0.189057i
$419$	3.19769			0.156217			0.0781086	−	0.996945i	$-0.475112\pi$
$419$	3.19769			0.156217			0.0781086	+	0.996945i	$0.475112\pi$
$420$		0			0
$421$	−39.6161			−1.93077			−0.965386	−	0.260824i	$-0.916006\pi$
$421$	−39.6161			−1.93077			−0.965386	+	0.260824i	$0.916006\pi$
$422$	−11.6223	−	21.7002i	−0.565767	−	1.05635i
$423$	2.40034	−	8.95821i	0.116709	−	0.435563i
$424$	0.799228	−	2.13977i	0.0388139	−	0.103916i
$425$	21.6994	+	7.12124i	1.05258	+	0.345431i
$426$	9.14592	−	2.14059i	0.443121	−	0.103712i
$427$		0			0
$428$	−1.06470	−	0.359433i	−0.0514644	−	0.0173739i
$429$	−1.70068	−	0.981887i	−0.0821095	−	0.0474059i
$430$	−7.54501	+	3.77638i	−0.363853	+	0.182113i
$431$	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	$0.218159\pi$
$432$	12.3628	+	5.07243i	0.594803	+	0.244048i
$433$	−6.03281	+	6.03281i	−0.289919	+	0.289919i	−0.837048	−	0.547129i	$-0.815721\pi$
$433$	−6.03281	+	6.03281i	−0.289919	+	0.289919i	0.547129	+	0.837048i	$0.315721\pi$
$434$		0			0
$435$	−19.5258	+	10.5645i	−0.936192	+	0.506529i
$436$	0.666468	−	10.4358i	0.0319180	−	0.499782i
$437$	12.6590	−	47.2442i	0.605564	−	2.26000i
$438$	0.653887	−	20.4984i	0.0312439	−	0.979451i
$439$	−3.31217	+	5.73685i	−0.158081	+	0.273805i	−0.934177	−	0.356810i	$-0.883864\pi$
$439$	−3.31217	+	5.73685i	−0.158081	+	0.273805i	0.776095	+	0.630616i	$0.217198\pi$
$440$	2.47801	+	1.00448i	0.118135	+	0.0478868i
$441$		0			0
$442$	12.1410	+	7.53568i	0.577488	+	0.358436i
$443$	−9.42675	+	2.52589i	−0.447879	+	0.120009i	−0.475707	−	0.879604i	$-0.657808\pi$
$443$	−9.42675	+	2.52589i	−0.447879	+	0.120009i	0.0278280	+	0.999613i	$0.491141\pi$
$444$	−26.0631	−	17.3518i	−1.23690	−	0.823482i
$445$	−25.1989	+	6.01051i	−1.19454	+	0.284926i
$446$	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	$-0.860255\pi$
$449$		−	18.0135i		−	0.850109i	0.905168	−	0.425055i	$-0.139745\pi$
$450$	−0.867595	+	9.92527i	−0.0408988	+	0.467882i
$451$	−1.47142	+	0.849527i	−0.0692867	+	0.0400027i
$452$	−5.26444	−	26.2367i	−0.247618	−	1.23407i
$453$	−1.90906	−	7.12472i	−0.0896956	−	0.334749i
$454$	21.5559	−	5.04514i	1.01167	−	0.236780i
$455$		0			0
$456$	33.5989	−	27.7152i	1.57341	−	1.29788i
$457$	−1.22667	+	0.328686i	−0.0573813	+	0.0153753i	−0.287396	−	0.957812i	$-0.592789\pi$
$457$	−1.22667	+	0.328686i	−0.0573813	+	0.0153753i	0.230014	+	0.973187i	$0.426123\pi$
$458$	−24.1304	−	0.769747i	−1.12754	−	0.0359679i
$459$	−7.62958	−	13.2148i	−0.356118	−	0.616815i
$460$	−12.4925	−	27.0840i	−0.582466	−	1.26280i
$461$	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	$-0.398960\pi$
$463$	−13.7264	−	13.7264i	−0.637919	−	0.637919i	−0.950042	+	0.312123i	$0.898960\pi$
$464$	17.4494	−	7.29626i	0.810068	−	0.338720i
$465$	7.85922	+	4.83206i	0.364463	+	0.224081i
$466$	−13.4675	−	14.3551i	−0.623871	−	0.664985i
$467$	−3.32051	−	12.3923i	−0.153655	−	0.573447i	−0.999217	−	0.0395701i	$-0.987401\pi$
$467$	−3.32051	−	12.3923i	−0.153655	−	0.573447i	0.845562	−	0.533877i	$-0.179266\pi$
$468$	−1.99391	+	5.90632i	−0.0921687	+	0.273020i
$469$		0			0
$470$	20.7777	+	1.23856i	0.958403	+	0.0571307i
$471$	−24.5395	−	14.1679i	−1.13072	−	0.652821i
$472$	6.98503	−	3.18602i	0.321512	−	0.146649i
$473$	1.08957	+	0.291950i	0.0500986	+	0.0134239i
$474$	−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
$478$	−9.36423	+	5.01536i	−0.428310	+	0.229397i
$479$	−7.41948	−	12.8509i	−0.339005	−	0.587173i	0.645241	−	0.763979i	$-0.276757\pi$
$479$	−7.41948	−	12.8509i	−0.339005	−	0.587173i	−0.984246	+	0.176806i	$0.943424\pi$
$480$	4.94031	−	26.0966i	0.225493	−	1.19114i
$481$	−8.24667	+	14.2837i	−0.376016	+	0.651279i
$482$	−8.71337	−	5.40822i	−0.396883	−	0.246338i
$483$		0			0
$484$	9.60470	+	19.3946i	0.436577	+	0.881571i
$485$	14.6676	+	0.405681i	0.666022	+	0.0184210i
$486$	14.0089	−	13.1428i	0.635457	−	0.596169i
$487$	−33.7505	−	9.04342i	−1.52938	−	0.409796i	−0.606564	−	0.795035i	$-0.707452\pi$
$487$	−33.7505	−	9.04342i	−1.52938	−	0.409796i	−0.922817	+	0.385239i	$0.874119\pi$
$488$	4.26443	+	3.03968i	0.193042	+	0.137600i
$489$		−	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	$0.962633\pi$
$492$	11.1491	+	12.6703i	0.502639	+	0.571220i
$493$	−20.8614	−	5.58979i	−0.939550	−	0.251752i
$494$	−15.6976	−	16.7321i	−0.706268	−	0.752812i
$495$	0.967546	−	0.915465i	0.0434879	−	0.0411471i
$496$	−6.25157	−	4.76385i	−0.280704	−	0.213903i
$497$		0			0
$498$	−10.4497	+	16.8359i	−0.468264	+	0.754436i
$499$	5.42096	−	9.38938i	0.242675	−	0.420326i	−0.718800	−	0.695217i	$-0.755308\pi$
$499$	5.42096	−	9.38938i	0.242675	−	0.420326i	0.961475	+	0.274891i	$0.0886417\pi$
$500$	−22.2128	+	2.56733i	−0.993387	+	0.114815i
$501$	−9.07955	−	15.7262i	−0.405644	−	0.702597i
$502$	2.42925	+	4.53569i	0.108423	+	0.202438i
$503$	2.03813	+	2.03813i	0.0908758	+	0.0908758i	0.751083	−	0.660207i	$-0.229532\pi$
$503$	2.03813	+	2.03813i	0.0908758	+	0.0908758i	−0.660207	+	0.751083i	$0.729532\pi$
$504$		0			0
$505$	9.08736	+	2.70635i	0.404382	+	0.120431i
$506$	−1.15434	+	3.81683i	−0.0513165	+	0.169679i
$507$	−16.4416	−	4.40551i	−0.730196	−	0.195655i
$508$	8.74572	+	43.5866i	0.388029	+	1.93384i
$509$	10.5939	+	6.11641i	0.469568	+	0.271105i	0.716059	−	0.698040i	$-0.245944\pi$
$509$	10.5939	+	6.11641i	0.469568	+	0.271105i	−0.246491	+	0.969145i	$0.579278\pi$
$510$	−22.6840	+	20.1318i	−1.00447	+	0.891450i
$511$		0			0
$512$	−6.40523	+	21.7019i	−0.283074	+	0.959098i
$513$	6.34100	+	23.6649i	0.279962	+	1.04483i
$514$	−7.19201	+	6.74735i	−0.317226	+	0.297613i
$515$	−18.4147	+	29.9510i	−0.811448	+	1.31980i
$516$	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
$520$	−13.8846	−	1.72094i	−0.608878	−	0.0754681i
$521$	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	$0.811558\pi$
$522$	0.300398	−	9.41703i	0.0131481	−	0.412172i
$523$	6.72558	−	1.80211i	0.294089	−	0.0788010i	−0.108758	−	0.994068i	$-0.534687\pi$
$523$	6.72558	−	1.80211i	0.294089	−	0.0788010i	0.402847	+	0.915267i	$0.368021\pi$
$524$	−32.2085	+	15.9505i	−1.40703	+	0.696800i
$525$		0			0
$526$	8.17527	+	34.9297i	0.356459	+	1.52301i
$527$	2.32294	+	8.66931i	0.101189	+	0.377641i
$528$	−2.80987	+	2.17106i	−0.122284	+	0.0944834i
$529$	18.6025	−	10.7401i	0.808803	−	0.466963i
$530$	1.40622	−	2.13172i	0.0610823	−	0.0925962i
$531$		−	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
$535$	−1.07027	−	0.658030i	−0.0462718	−	0.0284491i
$536$	8.91526	−	23.8687i	0.385080	−	1.03097i
$537$	36.5202	−	9.78557i	1.57596	−	0.422278i
$538$	14.1979	−	22.8748i	0.612116	−	0.986201i
$539$		0			0
$540$	12.2025	+	8.62020i	0.525112	+	0.370954i
$541$	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	$0.140217\pi$
$542$	29.8224	+	0.951319i	1.28098	+	0.0408626i
$543$	7.91661	−	29.5452i	0.339734	−	1.26791i
$544$	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	−0.107098	+	0.994249i	$0.534156\pi$
$547$	−25.7583	+	25.7583i	−1.10135	+	1.10135i	−0.994249	+	0.107098i	$0.965844\pi$
$548$	17.7573	+	20.1801i	0.758553	+	0.862051i
$549$	2.25928	−	1.30439i	0.0964235	−	0.0556701i
$550$	2.44896	+	1.71450i	0.104424	+	0.0731066i
$551$	30.0304	+	17.3381i	1.27934	+	0.738626i
$552$	39.4283	+	3.78350i	1.67818	+	0.161036i
$553$		0			0
$554$	5.19503	+	22.1963i	0.220716	+	0.943032i
$555$	−24.0596	−	25.4284i	−1.02127	−	1.07937i
$556$	−6.83478	+	10.2661i	−0.289859	+	0.435379i
$557$	4.34701	−	16.2233i	0.184189	−	0.687402i	−0.810614	−	0.585581i	$-0.800866\pi$
$557$	4.34701	−	16.2233i	0.184189	−	0.687402i	0.994803	−	0.101821i	$-0.0324668\pi$
$558$	−3.45153	+	1.84859i	−0.146115	+	0.0782573i
$559$	−5.90224			−0.249638
$560$		0			0
$561$	4.05479			0.171193
$562$	−7.48934	+	4.01119i	−0.315919	+	0.169202i
$563$	2.89404	−	10.8007i	0.121969	−	0.455195i	−0.877744	−	0.479129i	$-0.840953\pi$
$563$	2.89404	−	10.8007i	0.121969	−	0.455195i	0.999714	+	0.0239343i	$0.00761925\pi$
$564$	−15.3185	+	23.0090i	−0.645026	+	0.968854i
$565$	0.827169	−	29.9067i	0.0347993	−	1.25819i
$566$	−0.536492	−	2.29222i	−0.0225504	−	0.0963491i
$567$		0			0
$568$	−8.90590	−	0.854600i	−0.373683	−	0.0358582i
$569$	−14.1920	−	8.19376i	−0.594960	−	0.343500i	0.172096	−	0.985080i	$-0.444946\pi$
$569$	−14.1920	−	8.19376i	−0.594960	−	0.343500i	−0.767056	+	0.641580i	$0.778279\pi$
$570$	43.5458	−	21.7953i	1.82393	−	0.912904i
$571$	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	$-0.0636329\pi$
$572$	1.23564	+	1.40423i	0.0516647	+	0.0587139i
$573$	−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
$577$	−8.24552	+	30.7727i	−0.343265	+	1.28108i	0.551360	+	0.834267i	$0.314109\pi$
$577$	−8.24552	+	30.7727i	−0.343265	+	1.28108i	−0.894626	+	0.446817i	$0.852558\pi$
$578$	−5.46051	−	0.174187i	−0.227127	−	0.00724523i
$579$	−22.2886	+	38.6049i	−0.926281	+	1.60437i
$580$	20.8397	−	3.58523i	0.865321	−	0.148869i
$581$		0			0
$582$	−10.2761	+	16.5562i	−0.425960	+	0.686278i
$583$	−0.329786	+	0.0883660i	−0.0136584	+	0.00365975i
$584$	−6.83511	+	18.2996i	−0.282839	+	0.757242i
$585$	−3.65035	+	5.93720i	−0.150923	+	0.245473i
$586$	8.24759	−	27.2707i	0.340705	−	1.12654i
$587$	−14.5087	+	14.5087i	−0.598837	+	0.598837i	−0.940003	−	0.341166i	$-0.889178\pi$
$587$	−14.5087	+	14.5087i	−0.598837	+	0.598837i	0.341166	+	0.940003i	$0.389178\pi$
$588$		0			0
$589$		−	14.4103i		−	0.593765i
$590$	8.40855	−	1.72429i	0.346174	−	0.0709877i
$591$	36.4180	−	21.0260i	1.49804	−	0.864892i
$592$	18.2343	+	23.5996i	0.749426	+	0.969936i
$593$	−11.4330	−	42.6687i	−0.469498	−	1.75219i	−0.641527	−	0.767100i	$-0.721699\pi$
$593$	−11.4330	−	42.6687i	−0.469498	−	1.75219i	0.172029	−	0.985092i	$-0.444968\pi$
$594$	−0.455188	−	1.94484i	−0.0186766	−	0.0797977i
$595$		0			0
$596$	−8.75072	+	4.33359i	−0.358443	+	0.177511i
$597$	14.7744	−	3.95878i	0.604674	−	0.162022i
$598$	0.665233	−	20.8541i	0.0272034	−	0.852786i
$599$	20.0977	+	34.8103i	0.821170	+	1.42231i	0.904811	+	0.425813i	$0.140012\pi$
$599$	20.0977	+	34.8103i	0.821170	+	1.42231i	−0.0836409	+	0.996496i	$0.526655\pi$
$600$	11.9121	−	27.2011i	0.486309	−	1.11048i
$601$	−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
$605$	5.61407	+	23.5368i	0.228244	+	0.956907i
$606$	−9.18315	+	8.61539i	−0.373040	+	0.349976i
$607$	−0.342579	−	1.27852i	−0.0139048	−	0.0518936i	0.958625	−	0.284672i	$-0.0918848\pi$
$607$	−0.342579	−	1.27852i	−0.0139048	−	0.0518936i	−0.972530	+	0.232779i	$0.925218\pi$
$608$	−38.7650	+	14.7755i	−1.57213	+	0.599225i
$609$		0			0
$610$	3.88643	+	4.37914i	0.157357	+	0.177306i
$611$	12.6099	+	7.28031i	0.510141	+	0.294530i
$612$	−2.53222	−	12.6200i	−0.102359	−	0.510132i
$613$	−13.9992	−	3.75107i	−0.565422	−	0.151504i	−0.0352258	−	0.999379i	$-0.511215\pi$
$613$	−13.9992	−	3.75107i	−0.565422	−	0.151504i	−0.530196	+	0.847875i	$0.677882\pi$
$614$	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	0.897642	−	0.440725i	$-0.145278\pi$
$617$	11.3496	+	11.3496i	0.456918	+	0.456918i	−0.440725	+	0.897642i	$0.645278\pi$
$618$	−22.0447	−	41.1598i	−0.886766	−	1.65569i
$619$	−10.7582	−	18.6337i	−0.432407	−	0.748951i	0.564673	−	0.825315i	$-0.309002\pi$
$619$	−10.7582	−	18.6337i	−0.432407	−	0.748951i	−0.997080	+	0.0763640i	$0.975669\pi$
$620$	−5.62044	−	6.75508i	−0.225722	−	0.271291i
$621$	−11.1402	+	19.2955i	−0.447043	+	0.774300i
$622$	0.322681	−	0.519883i	0.0129383	−	0.0208454i
$623$		0			0
$624$	11.2613	−	14.7782i	0.450814	−	0.591600i
$625$	−24.8472	−	2.75949i	−0.993890	−	0.110380i
$626$	−0.996731	−	1.06242i	−0.0398374	−	0.0424627i
$627$	−6.28844	−	1.68498i	−0.251136	−	0.0672917i
$628$	17.8293	+	20.2620i	0.711467	+	0.808541i
$629$		−	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	$0.954341\pi$
$632$	8.19917	+	5.84436i	0.326145	+	0.232476i
$633$	35.3042	+	9.45974i	1.40322	+	0.375991i
$634$	29.0800	−	27.2821i	1.15491	−	1.08351i
$635$	−1.37416	+	49.6836i	−0.0545320	+	1.97163i
$636$	1.50507	+	3.03915i	0.0596798	+	0.120510i
$637$		0			0
$638$	−2.40198	−	1.49087i	−0.0950955	−	0.0590239i
$639$	−2.22845	+	3.85979i	−0.0881562	+	0.152691i
$640$	−12.4089	+	22.0458i	−0.490507	+	0.871437i
$641$	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	$0.660224\pi$
$642$	1.47081	−	0.787744i	0.0580481	−	0.0310898i
$643$	30.8400	+	30.8400i	1.21621	+	1.21621i	0.968948	+	0.247263i	$0.0795312\pi$
$643$	30.8400	+	30.8400i	1.21621	+	1.21621i	0.247263	+	0.968948i	$0.420469\pi$
$644$		0			0
$645$	3.57563	−	12.0062i	0.140790	−	0.472744i
$646$	45.3440	+	13.7136i	1.78404	+	0.539553i
$647$	−13.9753	−	3.74467i	−0.549425	−	0.147218i	−0.0265817	−	0.999647i	$-0.508462\pi$
$647$	−13.9753	−	3.74467i	−0.549425	−	0.147218i	−0.522844	+	0.852429i	$0.675129\pi$
$648$	−28.9292	+	13.1952i	−1.13644	+	0.518357i
$649$	−0.993813	−	0.573778i	−0.0390106	−	0.0225228i
$650$	−14.6993	−	5.34884i	−0.576553	−	0.209799i
$651$		0			0
$652$	−3.69045	+	10.9318i	−0.144529	+	0.428121i
$653$	−9.77388	−	36.4766i	−0.382481	−	1.42744i	−0.842099	−	0.539323i	$-0.818680\pi$
$653$	−9.77388	−	36.4766i	−0.382481	−	1.42744i	0.459618	−	0.888117i	$-0.347986\pi$
$654$	10.6230	+	11.3231i	0.415392	+	0.442767i
$655$	−39.0875	+	9.32327i	−1.52727	+	0.364290i
$656$	−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	$-0.535223\pi$
$659$	−5.66966			−0.220859			−0.110429	+	0.993884i	$0.535223\pi$
$660$	−3.60502	+	1.66282i	−0.140325	+	0.0647250i
$661$	−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	$-0.356512\pi$
$662$	36.4277	+	1.16202i	1.41580	+	0.0451634i
$663$	−20.4935	+	5.49122i	−0.795902	+	0.213261i
$664$	14.5596	−	12.0100i	0.565022	−	0.466079i
$665$		0			0
$666$	14.4657	−	3.38569i	0.560535	−	0.131193i
$667$	8.16187	+	30.4605i	0.316029	+	1.17944i
$668$	3.40272	+	16.9583i	0.131655	+	0.656138i
$669$	−4.32600	+	2.49762i	−0.167253	+	0.0965636i
$670$	15.6862	−	23.7790i	0.606009	−	0.918664i
$671$		−	0.782775i		−	0.0302187i
$672$		0			0
$673$	−6.90378	+	6.90378i	−0.266121	+	0.266121i	−0.827535	−	0.561414i	$-0.810258\pi$
$673$	−6.90378	+	6.90378i	−0.266121	+	0.266121i	0.561414	+	0.827535i	$0.310258\pi$
$674$	20.0602	+	6.06689i	0.772691	+	0.233688i
$675$	11.1403	+	12.4461i	0.428792	+	0.479049i
$676$	13.4955	+	8.98482i	0.519060	+	0.345570i
$677$	13.5776	−	3.63810i	0.521829	−	0.139824i	0.0117165	−	0.999931i	$-0.496270\pi$
$677$	13.5776	−	3.63810i	0.521829	−	0.139824i	0.510112	+	0.860108i	$0.329604\pi$
$678$	33.7576	+	20.9527i	1.29645	+	0.804684i
$679$		0			0
$680$	26.6046	−	11.2571i	1.02024	−	0.431689i
$681$	−16.4351	+	28.4664i	−0.629794	+	1.09083i
$682$	−0.0374574	+	1.17423i	−0.00143432	+	0.0449637i
$683$	8.40215	−	31.3572i	0.321499	−	1.19985i	−0.596285	−	0.802773i	$-0.703357\pi$
$683$	8.40215	−	31.3572i	0.321499	−	1.19985i	0.917784	−	0.397079i	$-0.129976\pi$
$684$	−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
$688$	−4.05116	+	9.87366i	−0.154449	+	0.376430i
$689$	1.54712	−	0.893230i	0.0589406	−	0.0340294i
$690$	42.0179	+	13.9868i	1.59959	+	0.532467i
$691$	−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	$0.689604\pi$
$692$	−8.28460	−	2.79680i	−0.314933	−	0.106318i
$693$		0			0
$694$	25.8583	−	6.05213i	0.981570	−	0.229736i
$695$	−10.0161	+	9.47692i	−0.379931	+	0.359480i
$696$	−9.82584	+	26.3066i	−0.372447	+	0.997151i
$697$	−4.75099	+	17.7310i	−0.179957	+	0.671608i
$698$	5.03113	+	9.39368i	0.190431	+	0.355556i
$699$	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	$0.534124\pi$
$702$	4.93440	+	9.21307i	0.186237	+	0.347725i
$703$	−14.1518	+	52.8154i	−0.533747	+	1.99197i
$704$	3.19721	−	1.10323i	0.120499	−	0.0415795i
$705$	−22.4486	+	21.2403i	−0.845464	+	0.799955i
$706$	50.7592	−	11.8802i	1.91035	−	0.447116i
$707$		0			0
$708$	−3.64602	+	10.8001i	−0.137026	+	0.405894i
$709$	10.3830	+	5.99462i	0.389941	+	0.225133i	0.682135	−	0.731227i	$-0.261052\pi$
$709$	10.3830	+	5.99462i	0.389941	+	0.225133i	−0.292193	+	0.956359i	$0.594385\pi$
$710$	−9.49082	−	3.15927i	−0.356184	−	0.118565i
$711$	4.34388	−	2.50794i	0.162908	−	0.0940552i
$712$	−19.0200	+	26.6836i	−0.712806	+	1.00001i
$713$	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
$717$	4.08214	−	15.2348i	0.152450	−	0.568952i
$718$	−0.815917	+	25.5778i	−0.0304498	+	0.954554i
$719$	12.5797	−	21.7886i	0.469142	−	0.812578i	−0.530235	−	0.847850i	$-0.677896\pi$
$719$	12.5797	−	21.7886i	0.469142	−	0.812578i	0.999378	+	0.0352721i	$0.0112298\pi$
$720$	7.42663	+	10.1817i	0.276774	+	0.379450i
$721$		0			0
$722$	−41.7939	−	25.9407i	−1.55541	−	0.965413i
$723$	14.7078	−	3.94095i	0.546989	−	0.146565i
$724$	−16.1456	+	24.2512i	−0.600045	+	0.901290i
$725$	23.6056	+	1.30678i	0.876690	+	0.0485326i
$726$	−30.7580	−	9.30225i	−1.14154	−	0.345239i
$727$	20.9986	−	20.9986i	0.778795	−	0.778795i	−0.200831	−	0.979626i	$-0.564364\pi$
$727$	20.9986	−	20.9986i	0.778795	−	0.778795i	0.979626	+	0.200831i	$0.0643643\pi$
$728$		0			0
$729$		−	5.20463i		−	0.192764i
$730$	−12.0262	+	18.2308i	−0.445110	+	0.674753i
$731$	10.5542	−	6.09346i	0.390360	−	0.225375i
$732$	−7.62355	+	1.52968i	−0.281774	+	0.0565385i
$733$	4.84038	+	18.0645i	0.178783	+	0.667229i	0.995876	+	0.0907227i	$0.0289177\pi$
$733$	4.84038	+	18.0645i	0.178783	+	0.667229i	−0.817093	+	0.576506i	$0.804416\pi$
$734$	32.2501	−	7.54812i	1.19037	−	0.278606i
$735$		0			0
$736$	−34.4295	−	15.4266i	−1.26909	−	0.568632i
$737$	−3.67872	+	0.985709i	−0.135507	+	0.0363091i
$738$	−8.00392	−	0.255321i	−0.294629	−	0.00939849i
$739$	8.20856	+	14.2176i	0.301957	+	0.523004i	0.976579	−	0.215159i	$-0.0690269\pi$
$739$	8.20856	+	14.2176i	0.301957	+	0.523004i	−0.674622	+	0.738163i	$0.735694\pi$
$740$	13.9657	+	30.2778i	0.513388	+	1.11304i
$741$	34.0646			1.25140
$742$		0			0
$743$	11.1710	+	11.1710i	0.409825	+	0.409825i	0.881678	−	0.471852i	$-0.156414\pi$
$743$	11.1710	+	11.1710i	0.409825	+	0.409825i	−0.471852	+	0.881678i	$0.656414\pi$
$744$	11.5092	−	1.92985i	0.421948	−	0.0707518i
$745$	−10.6197	+	2.53304i	−0.389075	+	0.0928034i
$746$	5.61345	+	5.98339i	0.205523	+	0.219067i
$747$	−2.43345	−	9.08175i	−0.0890352	−	0.332284i
$748$	−3.65925	−	1.23533i	−0.133795	−	0.0451680i
$749$		0			0
$750$	19.7854	−	26.6606i	0.722462	−	0.973506i
$751$	−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	$0.835674\pi$
$752$	20.8341	−	16.0976i	0.759742	−	0.587019i
$753$	−7.37915	−	1.97724i	−0.268911	−	0.0720545i
$754$	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	0.623727	−	0.781642i	$-0.285618\pi$
$757$	−4.34481	−	4.34481i	−0.157915	−	0.157915i	−0.781642	+	0.623727i	$0.785618\pi$
$758$	25.4207	−	13.6150i	0.923322	−	0.494519i
$759$	−2.96028	−	5.12735i	−0.107451	−	0.186111i
$760$	−45.9381	+	6.40259i	−1.66635	+	0.232246i
$761$	−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	$0.307228\pi$
$762$	−56.0810	−	34.8084i	−2.03160	−	1.26098i
$763$		0			0
$764$	18.1567	−	8.99169i	0.656887	−	0.325308i
$765$	0.397873	−	14.3853i	0.0143851	−	0.520101i
$766$	10.8841	−	10.2112i	0.393259	−	0.368945i
$767$	5.79992	+	1.55408i	0.209423	+	0.0561147i
$768$	−16.9924	−	28.9821i	−0.613159	−	1.04580i
$769$			11.6924i			0.421638i	0.977525	+	0.210819i	$0.0676131\pi$
$769$			11.6924i			0.421638i	−0.977525	+	0.210819i	$0.932387\pi$
$770$		0			0
$771$		−	14.6421i		−	0.527323i
$772$	31.8757	−	28.0487i	1.14723	−	1.00949i
$773$	−18.1569	−	4.86514i	−0.653060	−	0.174987i	−0.0829479	−	0.996554i	$-0.526434\pi$
$773$	−18.1569	−	4.86514i	−0.653060	−	0.174987i	−0.570112	+	0.821567i	$0.693100\pi$
$774$	3.63759	+	3.87731i	0.130750	+	0.139367i
$775$	−4.43456	−	8.76700i	−0.159294	−	0.314920i
$776$	14.3177	−	11.8105i	0.513976	−	0.423972i
$777$		0			0
$778$	1.68808	−	2.71972i	0.0605205	−	0.0975066i
$779$	14.7363	−	25.5241i	0.527984	−	0.914495i
$780$	15.9684	−	13.2862i	0.571761	−	0.475724i
$781$	0.668654	+	1.15814i	0.0239263	+	0.0414416i
$782$	20.3401	+	37.9773i	0.727362	+	1.35807i
$783$	−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
$787$	−49.6245	−	13.2968i	−1.76892	−	0.473982i	−0.780429	−	0.625244i	$-0.784999\pi$
$787$	−49.6245	−	13.2968i	−1.76892	−	0.473982i	−0.988494	+	0.151262i	$0.951666\pi$
$788$	−39.2713	+	7.87984i	−1.39898	+	0.280708i
$789$	−46.1276	−	26.6318i	−1.64219	−	0.948117i
$790$	7.47240	+	8.41973i	0.265856	+	0.299561i
$791$		0			0
$792$	0.160938	−	1.67716i	0.00571868	−	0.0595951i
$793$	1.06008	+	3.95626i	0.0376444	+	0.140491i
$794$	17.8289	−	16.7266i	0.632724	−	0.593605i
$795$	0.879732	+	3.68825i	0.0312009	+	0.130809i
$796$	−14.5392	−	0.928531i	−0.515329	−	0.0329109i
$797$	−1.34897	−	1.34897i	−0.0477829	−	0.0477829i	0.682812	−	0.730594i	$-0.260757\pi$
$797$	−1.34897	−	1.34897i	−0.0477829	−	0.0477829i	−0.730594	+	0.682812i	$0.760757\pi$
$798$		0			0
$799$	−30.0647			−1.06361
$800$	−19.0371	+	20.9186i	−0.673064	+	0.739584i
$801$	8.16191	+	14.1368i	0.288387	+	0.499501i
$802$	−0.224696	+	7.04390i	−0.00793431	+	0.248729i
$803$	2.82038	−	0.755719i	0.0995292	−	0.0266688i
$804$	16.7888	+	33.9012i	0.592095	+	1.19560i
$805$		0			0
$806$	−1.40089	−	5.98547i	−0.0493444	−	0.210829i
$807$	10.3460	+	38.6117i	0.364195	+	1.35919i
$808$	10.9121	−	4.97724i	0.383886	−	0.175099i
$809$	3.46174	−	1.99864i	0.121708	−	0.0702684i	−0.437910	−	0.899019i	$-0.644281\pi$
$809$	3.46174	−	1.99864i	0.121708	−	0.0702684i	0.559618	+	0.828750i	$0.310948\pi$
$810$	−34.8248	+	7.14129i	−1.22362	+	0.250919i
$811$		−	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
$815$	−6.75627	+	10.9889i	−0.236662	+	0.384925i
$816$	−4.88020	+	38.0520i	−0.170841	+	1.33208i
$817$	−18.9003	+	5.06432i	−0.661238	+	0.177178i
$818$	−1.55596	+	2.50685i	−0.0544027	+	0.0876501i
$819$		0			0
$820$	−3.04724	−	17.7125i	−0.106414	−	0.618547i
$821$	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	$-0.217448\pi$
$822$	−39.8906	−	1.27249i	−1.39134	−	0.0443831i
$823$	−0.0982095	+	0.366523i	−0.00342337	+	0.0127762i	−0.967616	−	0.252425i	$-0.918772\pi$
$823$	−0.0982095	+	0.366523i	−0.00342337	+	0.0127762i	0.964193	+	0.265201i	$0.0854385\pi$
$824$	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	$-0.766243\pi$
$827$	−2.07441	+	2.07441i	−0.0721345	+	0.0721345i	0.670119	+	0.742254i	$0.266243\pi$
$828$	−14.1095	+	12.4155i	−0.490339	+	0.431468i
$829$	23.1175	−	13.3469i	0.802903	−	0.463556i	−0.0415820	−	0.999135i	$-0.513240\pi$
$829$	23.1175	−	13.3469i	0.802903	−	0.463556i	0.844485	+	0.535579i	$0.179906\pi$
$830$	18.8700	−	9.44469i	0.654986	−	0.327830i
$831$	−29.3121	−	16.9234i	−1.01683	−	0.587065i
$832$	−14.6651	+	9.90571i	−0.508421	+	0.343419i
$833$		0			0
$834$	−4.17307	−	17.8299i	−0.144502	−	0.617398i
$835$	−0.534649	+	19.3305i	−0.0185023	+	0.668960i
$836$	5.16167	+	3.43644i	0.178520	+	0.118852i
$837$	−1.69898	+	6.34068i	−0.0587253	+	0.219166i
$838$	3.98645	−	2.13509i	0.137710	−	0.0737555i
$839$	−23.5830			−0.814175			−0.407087	−	0.913389i	$-0.633456\pi$
$839$	−23.5830			−0.814175			−0.407087	+	0.913389i	$0.633456\pi$
$840$		0			0
$841$	6.64270			0.229059
$842$	−49.3881	+	26.4516i	−1.70203	+	0.911584i
$843$	3.26482	−	12.1845i	0.112446	−	0.419656i
$844$	−28.9784	−	19.2927i	−0.997477	−	0.664082i
$845$	12.4581	+	13.1669i	0.428572	+	0.452954i
$846$	−2.98895	−	12.7706i	−0.102762	−	0.439063i
$847$		0			0
$848$	−0.432347	−	3.20122i	−0.0148469	−	0.109930i
$849$	3.02707	+	1.74768i	0.103889	+	0.0599802i
$850$	31.8068	−	5.61087i	1.09097	−	0.192451i
$851$	−43.0636	+	24.8628i	−1.47620	+	0.852285i
$852$	9.97264	−	8.77532i	0.341657	−	0.300638i
$853$	−35.4043	+	35.4043i	−1.21222	+	1.21222i	−0.241926	+	0.970295i	$0.577779\pi$
$853$	−35.4043	+	35.4043i	−1.21222	+	1.21222i	−0.970295	+	0.241926i	$0.922221\pi$
$854$		0			0
$855$	−6.59491	+	22.1444i	−0.225541	+	0.757321i
$856$	−1.56732	+	0.262807i	−0.0535700	+	0.00898257i
$857$	−10.1866	+	38.0169i	−0.347967	+	1.29863i	0.541140	+	0.840932i	$0.317993\pi$
$857$	−10.1866	+	38.0169i	−0.347967	+	1.29863i	−0.889107	+	0.457699i	$0.848674\pi$
$858$	−2.77578	−	0.0885460i	−0.0947637	−	0.00302291i
$859$	15.9154	−	27.5663i	0.543026	−	0.940549i	−0.455702	−	0.890132i	$-0.650612\pi$
$859$	15.9154	−	27.5663i	0.543026	−	0.940549i	0.998728	−	0.0504166i	$-0.0160549\pi$
$860$	−6.88463	+	9.74568i	−0.234764	+	0.332325i
$861$		0			0
$862$	10.9616	−	17.6607i	0.373355	−	0.601525i
$863$	37.4334	−	10.0303i	1.27425	−	0.341434i	0.442592	−	0.896723i	$-0.354059\pi$
$863$	37.4334	−	10.0303i	1.27425	−	0.341434i	0.831657	+	0.555289i	$0.187392\pi$
$864$	18.7991	−	1.93095i	0.639558	−	0.0656923i
$865$	−8.32791	−	5.12022i	−0.283158	−	0.174093i
$866$	−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
$870$	−17.2883	+	26.2078i	−0.586129	+	0.888527i
$871$	17.2579	−	9.96384i	0.584761	−	0.337612i
$872$	−6.13707	−	13.4549i	−0.207828	−	0.455641i
$873$	−2.39302	−	8.93088i	−0.0809915	−	0.302264i
$874$	−15.7633	−	67.3502i	−0.533200	−	2.27815i
$875$		0			0
$876$	−12.8716	−	25.9913i	−0.434890	−	0.878164i
$877$	−2.69021	+	0.720839i	−0.0908419	+	0.0243410i	−0.303954	−	0.952687i	$-0.598307\pi$
$877$	−2.69021	+	0.720839i	−0.0908419	+	0.0243410i	0.213112	+	0.977028i	$0.431640\pi$
$878$	−0.298690	+	9.36348i	−0.0100803	+	0.316002i
$879$	21.1508	+	36.6343i	0.713399	+	1.23564i
$880$	3.75995	−	0.402311i	0.126748	−	0.0135619i
$881$	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	$-0.117340\pi$
$883$	17.0113	+	17.0113i	0.572477	+	0.572477i	−0.360343	+	0.932820i	$0.617340\pi$
$884$	20.1673	+	1.28796i	0.678301	+	0.0433189i
$885$	−6.67493	+	10.8566i	−0.224375	+	0.364941i
$886$	−10.0655	+	9.44317i	−0.338157	+	0.317250i
$887$	−10.0823	−	37.6278i	−0.338532	−	1.26342i	−0.899989	−	0.435912i	$-0.856426\pi$
$887$	−10.0823	−	37.6278i	−0.338532	−	1.26342i	0.561458	−	0.827505i	$-0.310241\pi$
$888$	−44.0778	−	4.22966i	−1.47916	−	0.141938i
$889$		0			0
$890$	−27.4014	+	24.3184i	−0.918496	+	0.815153i
$891$	4.11597	+	2.37636i	0.137890	+	0.0796109i
$892$	4.66493	−	0.936026i	0.156193	−	0.0313405i
$893$	46.6264	+	12.4935i	1.56029	+	0.418079i
$894$	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
$898$	−12.0276	−	22.4568i	−0.401366	−	0.749394i
$899$	4.64548	+	8.04621i	0.154936	+	0.268356i
$900$	5.54548	+	12.9528i	0.184849	+	0.431760i
$901$	−1.84434	+	3.19448i	−0.0614438	+	0.106424i
$902$	−1.26715	+	2.04155i	−0.0421914	+	0.0679760i
$903$		0			0
$904$	−24.0812	−	29.1934i	−0.800929	−	0.970957i
$905$	−23.6606	+	22.3870i	−0.786505	+	0.744169i
$906$	−7.13713	−	7.60748i	−0.237115	−	0.252741i
$907$	−22.1163	−	5.92604i	−0.734359	−	0.196771i	−0.127789	−	0.991801i	$-0.540788\pi$
$907$	−22.1163	−	5.92604i	−0.734359	−	0.196771i	−0.606569	+	0.795030i	$0.707455\pi$
$908$	23.5044	−	20.6824i	0.780021	−	0.686371i
$909$		−	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	$0.741555\pi$
$912$	23.3812	−	56.9856i	0.774228	−	1.88698i
$913$	−2.72501	−	0.730164i	−0.0901847	−	0.0241649i
$914$	−1.30979	+	1.22881i	−0.0433240	+	0.0406454i
$915$	−8.68995	−	0.240349i	−0.287281	−	0.00794569i
$916$	−30.5966	+	15.1522i	−1.01094	+	0.500644i
$917$		0			0
$918$	−18.3351	−	11.3802i	−0.605147	−	0.375603i
$919$	16.0826	−	27.8558i	0.530515	−	0.918879i	−0.468851	−	0.883277i	$-0.655332\pi$
$919$	16.0826	−	27.8558i	0.530515	−	0.918879i	0.999366	−	0.0356018i	$-0.0113348\pi$
$920$	−33.6579	−	25.4235i	−1.10967	−	0.838188i
$921$	5.34886	+	9.26450i	0.176251	+	0.305276i
$922$	21.9440	−	11.7529i	0.722686	−	0.387061i
$923$	−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
$927$	21.3997	+	5.73402i	0.702857	+	0.188330i
$928$	16.8819	−	20.7469i	0.554175	−	0.681052i
$929$	35.6942	+	20.6080i	1.17109	+	0.676128i	0.953936	−	0.300010i	$-0.0969900\pi$
$929$	35.6942	+	20.6080i	1.17109	+	0.676128i	0.217152	+	0.976138i	$0.430323\pi$
$930$	13.0242	+	0.776376i	0.427080	+	0.0254584i
$931$		0			0
$932$	−26.3744	−	8.90373i	−0.863921	−	0.291651i
$933$	0.235137	+	0.877541i	0.00769802	+	0.0287294i
$934$	−12.4139	−	13.2320i	−0.406195	−	0.432963i
$935$	−3.67838	−	2.26157i	−0.120296	−	0.0739611i
$936$	1.45789	+	8.69455i	0.0476527	+	0.284190i
$937$	−25.3650	−	25.3650i	−0.828637	−	0.828637i	0.158691	−	0.987328i	$-0.449273\pi$
$937$	−25.3650	−	25.3650i	−0.828637	−	0.828637i	−0.987328	+	0.158691i	$0.949273\pi$
$938$		0			0
$939$	2.16296			0.0705855
$940$	26.7298	−	12.3291i	0.871831	−	0.402132i
$941$	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	$0.711317\pi$
$942$	−40.0524	−	1.27765i	−1.30498	−	0.0416281i
$943$	25.8897	−	6.93711i	0.843083	−	0.225903i
$944$	6.58071	−	8.63581i	0.214184	−	0.281072i
$945$		0			0
$946$	1.55327	−	0.363542i	0.0505012	−	0.0118198i
$947$	−7.85278	−	29.3070i	−0.255181	−	0.952348i	−0.967990	−	0.250990i	$-0.919244\pi$
$947$	−7.85278	−	29.3070i	−0.255181	−	0.952348i	0.712809	−	0.701359i	$-0.247423\pi$
$948$	−14.6577	+	2.94109i	−0.476060	+	0.0955223i
$949$	−13.2312	+	7.63904i	−0.429503	+	0.247974i
$950$	−51.6598	−	4.51573i	−1.67607	−	0.146509i
$951$			59.2035i			1.91981i
$952$		0			0
$953$	−1.41682	+	1.41682i	−0.0458953	+	0.0458953i	−0.729682	−	0.683787i	$-0.760332\pi$
$953$	−1.41682	+	1.41682i	−0.0458953	+	0.0458953i	0.683787	+	0.729682i	$0.260332\pi$
$954$	−1.54028	−	0.465833i	−0.0498685	−	0.0150819i
$955$	22.0346	−	5.25576i	0.713023	−	0.170072i
$956$	−8.32533	+	12.5050i	−0.269260	+	0.404440i
$957$	4.05445	−	1.08639i	0.131062	−	0.0351179i
$958$	−17.8302	−	11.0668i	−0.576066	−	0.357553i
$959$		0			0
$960$	−11.2657	−	35.8324i	−0.363600	−	1.15649i
$961$	−13.5695	+	23.5030i	−0.437725	+	0.758163i
$962$	−0.743680	+	23.3132i	−0.0239772	+	0.751649i
$963$	−0.204900	+	0.764696i	−0.00660280	+	0.0246420i
$964$	−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	$-0.504394\pi$
$967$	30.6644	−	30.6644i	0.986102	−	0.986102i	0.999905	+	0.0138026i	$0.00439363\pi$
$968$	24.9236	+	17.7655i	0.801074	+	0.571005i
$969$	−60.9131	+	35.1682i	−1.95681	+	1.12977i
$970$	18.5565	−	9.28779i	0.595813	−	0.298213i
$971$	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	$0.518012\pi$
$972$	8.68902	−	25.7384i	0.278701	−	0.825559i
$973$		0			0
$974$	−48.1139	+	11.2610i	−1.54167	+	0.360826i
$975$	20.7244	−	10.4829i	0.663713	−	0.335722i
$976$	7.34591	+	0.942119i	0.235137	+	0.0301565i
$977$	7.13146	−	26.6150i	0.228156	−	0.851488i	−0.752960	−	0.658066i	$-0.771375\pi$
$977$	7.13146	−	26.6150i	0.228156	−	0.851488i	0.981116	−	0.193422i	$-0.0619587\pi$
$978$	−8.08810	−	15.1014i	−0.258629	−	0.482889i
$979$	4.89802			0.156541
$980$		0			0
$981$	−7.36695			−0.235209
$982$	3.46567	+	6.47080i	0.110594	+	0.206491i
$983$	−8.75124	+	32.6601i	−0.279121	+	1.04169i	0.673908	+	0.738815i	$0.264614\pi$
$983$	−8.75124	+	32.6601i	−0.279121	+	1.04169i	−0.953029	+	0.302879i	$0.902052\pi$
$984$	22.3591	+	8.35139i	0.712782	+	0.266232i
$985$	−44.7646	−	1.23811i	−1.42632	−	0.0394495i
$986$	−29.7395	+	6.96051i	−0.947099	+	0.221668i
$987$		0			0
$988$	−30.7417	−	10.3781i	−0.978023	−	0.330171i
$989$	−15.4106	−	8.89729i	−0.490027	−	0.282917i
$990$	0.594953	−	1.78731i	0.0189088	−	0.0568044i
$991$	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	$0.0816165\pi$
$992$	−10.9744	−	1.76478i	−0.348439	−	0.0560318i
$993$	−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
$997$	−2.14644	+	8.01061i	−0.0679784	+	0.253699i	−0.991550	−	0.129728i	$-0.958590\pi$
$997$	−2.14644	+	8.01061i	−0.0679784	+	0.253699i	0.923571	+	0.383427i	$0.125256\pi$
$998$	0.488859	−	15.3250i	0.0154746	−	0.485104i
$999$	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.667.16		72
4.3	odd	2	inner	980.2.x.m.667.18		72
5.3	odd	4	inner	980.2.x.m.863.8		72
7.2	even	3		980.2.k.j.687.5		36
7.3	odd	6		140.2.w.b.67.10	yes	72
7.4	even	3	inner	980.2.x.m.67.10		72
7.5	odd	6		980.2.k.k.687.5		36
7.6	odd	2		140.2.w.b.107.16	yes	72
20.3	even	4	inner	980.2.x.m.863.10		72
28.3	even	6		140.2.w.b.67.8	yes	72
28.11	odd	6	inner	980.2.x.m.67.8		72
28.19	even	6		980.2.k.k.687.6		36
28.23	odd	6		980.2.k.j.687.6		36
28.27	even	2		140.2.w.b.107.18	yes	72
35.3	even	12		140.2.w.b.123.18	yes	72
35.13	even	4		140.2.w.b.23.8	✓	72
35.17	even	12		700.2.be.e.543.1		72
35.18	odd	12	inner	980.2.x.m.263.18		72
35.23	odd	12		980.2.k.j.883.6		36
35.24	odd	6		700.2.be.e.207.9		72
35.27	even	4		700.2.be.e.443.11		72
35.33	even	12		980.2.k.k.883.6		36
35.34	odd	2		700.2.be.e.107.3		72
140.3	odd	12		140.2.w.b.123.16	yes	72
140.23	even	12		980.2.k.j.883.5		36
140.27	odd	4		700.2.be.e.443.9		72
140.59	even	6		700.2.be.e.207.11		72
140.83	odd	4		140.2.w.b.23.10	yes	72
140.87	odd	12		700.2.be.e.543.3		72
140.103	odd	12		980.2.k.k.883.5		36
140.123	even	12	inner	980.2.x.m.263.16		72
140.139	even	2		700.2.be.e.107.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.8	✓	72	35.13	even	4
140.2.w.b.23.10	yes	72	140.83	odd	4
140.2.w.b.67.8	yes	72	28.3	even	6
140.2.w.b.67.10	yes	72	7.3	odd	6
140.2.w.b.107.16	yes	72	7.6	odd	2
140.2.w.b.107.18	yes	72	28.27	even	2
140.2.w.b.123.16	yes	72	140.3	odd	12
140.2.w.b.123.18	yes	72	35.3	even	12
700.2.be.e.107.1		72	140.139	even	2
700.2.be.e.107.3		72	35.34	odd	2
700.2.be.e.207.9		72	35.24	odd	6
700.2.be.e.207.11		72	140.59	even	6
700.2.be.e.443.9		72	140.27	odd	4
700.2.be.e.443.11		72	35.27	even	4
700.2.be.e.543.1		72	35.17	even	12
700.2.be.e.543.3		72	140.87	odd	12
980.2.k.j.687.5		36	7.2	even	3
980.2.k.j.687.6		36	28.23	odd	6
980.2.k.j.883.5		36	140.23	even	12
980.2.k.j.883.6		36	35.23	odd	12
980.2.k.k.687.5		36	7.5	odd	6
980.2.k.k.687.6		36	28.19	even	6
980.2.k.k.883.5		36	140.103	odd	12
980.2.k.k.883.6		36	35.33	even	12
980.2.x.m.67.8		72	28.11	odd	6	inner
980.2.x.m.67.10		72	7.4	even	3	inner
980.2.x.m.263.16		72	140.123	even	12	inner
980.2.x.m.263.18		72	35.18	odd	12	inner
980.2.x.m.667.16		72	1.1	even	1	trivial
980.2.x.m.667.18		72	4.3	odd	2	inner
980.2.x.m.863.8		72	5.3	odd	4	inner
980.2.x.m.863.10		72	20.3	even	4	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+(1.24667 - 0.667698i) q^{2} +(-0.543458 + 2.02821i) q^{3} +(1.10836 - 1.66480i) q^{4} +(1.62425 - 1.53682i) q^{5} +(0.676724 + 2.89137i) q^{6} +(0.270171 - 2.81549i) q^{8} +(-1.22023 - 0.704499i) q^{9} +(0.998766 - 3.00041i) q^{10} +(-0.366133 + 0.211387i) q^{11} +(2.77421 + 3.15273i) q^{12} +(1.56422 - 1.56422i) q^{13} +(2.23429 + 4.12952i) q^{15} +(-1.54309 - 3.69038i) q^{16} +(-1.18219 + 4.41198i) q^{17} +(-1.99161 - 0.0635313i) q^{18} +(3.66683 - 6.35114i) q^{19} +(-0.758241 - 4.40739i) q^{20} +(-0.315303 + 0.507996i) q^{22} +(6.44210 - 1.72616i) q^{23} +(5.56360 + 2.07807i) q^{24} +(0.276371 - 4.99236i) q^{25} +(0.905634 - 2.99449i) q^{26} +(-2.36225 + 2.36225i) q^{27} +4.72835i q^{29} +(5.54269 + 3.65631i) q^{30} +(1.70170 - 0.982474i) q^{31} +(-4.38778 - 3.57035i) q^{32} +(-0.229760 - 0.857477i) q^{33} +(1.47208 + 6.28961i) q^{34} +(-2.52529 + 1.25059i) q^{36} +(-7.20177 + 1.92971i) q^{37} +(0.330672 - 10.3661i) q^{38} +(2.32248 + 4.02266i) q^{39} +(-3.88808 - 4.98827i) q^{40} +4.01882 q^{41} +(-1.88664 - 1.88664i) q^{43} +(-0.0538902 + 0.843830i) q^{44} +(-3.06464 + 0.730988i) q^{45} +(6.87860 - 6.45332i) q^{46} +(1.70358 + 6.35786i) q^{47} +(8.32348 - 1.12414i) q^{48} +(-2.98885 - 6.40834i) q^{50} +(-8.30597 - 4.79545i) q^{51} +(-0.870391 - 4.33782i) q^{52} +(0.780053 + 0.209015i) q^{53} +(-1.36767 + 4.52221i) q^{54} +(-0.269828 + 0.906026i) q^{55} +(10.8887 + 10.8887i) q^{57} +(3.15711 + 5.89468i) q^{58} +(1.35717 + 2.35069i) q^{59} +(9.35120 + 0.857356i) q^{60} +(-0.925760 + 1.60346i) q^{61} +(1.46545 - 2.36104i) q^{62} +(-7.85401 - 1.52133i) q^{64} +(0.136759 - 4.94461i) q^{65} +(-0.858970 - 0.915577i) q^{66} +(8.70137 + 2.33152i) q^{67} +(6.03476 + 6.85815i) q^{68} +14.0041i q^{69} -3.16317i q^{71} +(-2.31318 + 3.24521i) q^{72} +(-6.67113 - 1.78752i) q^{73} +(-7.68975 + 7.21432i) q^{74} +(9.97537 + 3.27368i) q^{75} +(-6.50918 - 13.1438i) q^{76} +(5.58129 + 3.46420i) q^{78} +(-1.77995 + 3.08296i) q^{79} +(-8.17780 - 3.62265i) q^{80} +(-5.62086 - 9.73561i) q^{81} +(5.01013 - 2.68336i) q^{82} +(4.71846 + 4.71846i) q^{83} +(4.86025 + 8.98296i) q^{85} +(-3.61172 - 1.09231i) q^{86} +(-9.59011 - 2.56966i) q^{87} +(0.496241 + 1.08796i) q^{88} +(-10.0333 - 5.79271i) q^{89} +(-3.33251 + 2.95755i) q^{90} +(4.26646 - 12.6380i) q^{92} +(1.06787 + 3.98534i) q^{93} +(6.36893 + 6.78865i) q^{94} +(-3.80470 - 15.9511i) 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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