LMFDB - Embedded newform 875.2.bb.a.257.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			257.5
Character	$\chi$	$=$	875.257
Dual form			875.2.bb.a.143.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0848016 + 1.61811i) q^{2} +(-2.12290 + 1.71909i) q^{3} +(-0.622046 - 0.0653797i) q^{4} +(-2.60166 - 3.58087i) q^{6} +(2.64114 + 0.156130i) q^{7} +(-0.348409 + 2.19977i) q^{8} +(0.927701 - 4.36449i) q^{9} +(-3.84181 + 0.816603i) q^{11} +(1.43294 - 0.930561i) q^{12} +(0.0441012 - 0.0865535i) q^{13} +(-0.476608 + 4.26042i) q^{14} +(-4.75353 - 1.01039i) q^{16} +(-3.12891 + 1.20108i) q^{17} +(6.98356 + 1.87124i) q^{18} +(-0.637130 - 6.06189i) q^{19} +(-5.87529 + 4.20892i) q^{21} +(-0.995562 - 6.28573i) q^{22} +(-5.23739 - 0.274480i) q^{23} +(-3.04197 - 5.26884i) q^{24} +(0.136313 + 0.0787005i) q^{26} +(1.81310 + 3.55840i) q^{27} +(-1.63270 - 0.269797i) q^{28} +(-2.51245 + 3.45809i) q^{29} +(-0.287036 + 0.644694i) q^{31} +(0.885159 - 3.30346i) q^{32} +(6.75198 - 8.33800i) q^{33} +(-1.67814 - 5.16477i) q^{34} +(-0.862422 + 2.65426i) q^{36} +(-4.20336 - 6.47261i) q^{37} +(9.86284 - 0.516889i) q^{38} +(0.0551709 + 0.259559i) q^{39} +(0.124652 - 0.0405019i) q^{41} +(-6.31226 - 9.86378i) q^{42} +(-8.25770 + 8.25770i) q^{43} +(2.44318 - 0.256788i) q^{44} +(0.888279 - 8.45141i) q^{46} +(0.970816 - 2.52906i) q^{47} +(11.8282 - 6.02679i) q^{48} +(6.95125 + 0.824720i) q^{49} +(4.57761 - 7.92865i) q^{51} +(-0.0330918 + 0.0509570i) q^{52} +(7.40118 + 9.13970i) q^{53} +(-5.91164 + 2.63203i) q^{54} +(-1.26365 + 5.75550i) q^{56} +(11.7735 + 11.7735i) q^{57} +(-5.38252 - 4.35867i) q^{58} +(3.45304 - 3.83499i) q^{59} +(5.30099 - 4.77304i) q^{61} +(-1.01885 - 0.519128i) q^{62} +(3.13162 - 11.3824i) q^{63} +(-3.97346 - 1.29105i) q^{64} +(12.9192 + 11.6325i) q^{66} +(0.200027 + 0.521089i) q^{67} +(2.02485 - 0.542557i) q^{68} +(11.5903 - 8.42087i) q^{69} +(0.818370 + 0.594581i) q^{71} +(9.27765 + 3.56136i) q^{72} +(-1.78952 - 1.16213i) q^{73} +(10.8299 - 6.25262i) q^{74} +3.81243i q^{76} +(-10.2743 + 1.55694i) q^{77} +(-0.424673 + 0.0672616i) q^{78} +(6.28497 + 14.1163i) q^{79} +(2.26247 + 1.00731i) q^{81} +(0.0549659 + 0.205136i) q^{82} +(-10.6837 - 1.69214i) q^{83} +(3.92988 - 2.23402i) q^{84} +(-12.6616 - 14.0621i) q^{86} +(-0.611092 - 11.6603i) q^{87} +(-0.457814 - 8.73562i) q^{88} +(0.671570 + 0.745854i) q^{89} +(0.129991 - 0.221714i) q^{91} +(3.23996 + 0.513159i) q^{92} +(-0.498939 - 1.86207i) q^{93} +(4.00998 + 1.78536i) q^{94} +(3.79985 + 8.53459i) q^{96} +(11.1837 - 1.77133i) q^{97} +(-1.92397 + 11.1779i) q^{98} +17.5251i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.0848016	+	1.61811i	−0.0599638	+	1.14418i	0.788539	+	0.614985i	$0.210838\pi$
$2$	−0.0848016	+	1.61811i	−0.0599638	+	1.14418i	−0.848502	+	0.529192i	$0.822495\pi$
$3$	−2.12290	+	1.71909i	−1.22566	+	0.992519i	−0.225827	+	0.974167i	$0.572508\pi$
$3$	−2.12290	+	1.71909i	−1.22566	+	0.992519i	−0.999832	+	0.0183512i	$0.994158\pi$
$4$	−0.622046	−	0.0653797i	−0.311023	−	0.0326899i
$5$		0			0
$5$		0			0
$6$	−2.60166	−	3.58087i	−1.06212	−	1.46189i
$7$	2.64114	+	0.156130i	0.998257	+	0.0590114i
$7$	2.64114	+	0.156130i	0.998257	+	0.0590114i
$8$	−0.348409	+	2.19977i	−0.123181	+	0.777736i
$9$	0.927701	−	4.36449i	0.309234	−	1.45483i
$10$		0			0
$11$	−3.84181	+	0.816603i	−1.15835	+	0.246215i	−0.746722	−	0.665137i	$-0.768373\pi$
$11$	−3.84181	+	0.816603i	−1.15835	+	0.246215i	−0.411629	+	0.911352i	$0.635040\pi$
$12$	1.43294	−	0.930561i	0.413653	−	0.268630i
$13$	0.0441012	−	0.0865535i	0.0122315	−	0.0240056i	−0.884810	−	0.465952i	$-0.845712\pi$
$13$	0.0441012	−	0.0865535i	0.0122315	−	0.0240056i	0.897041	+	0.441946i	$0.145712\pi$
$14$	−0.476608	+	4.26042i	−0.127379	+	1.13864i
$15$		0			0
$16$	−4.75353	−	1.01039i	−1.18838	−	0.252599i
$17$	−3.12891	+	1.20108i	−0.758872	+	0.291304i	−0.706870	−	0.707343i	$-0.749893\pi$
$17$	−3.12891	+	1.20108i	−0.758872	+	0.291304i	−0.0520016	+	0.998647i	$0.516560\pi$
$18$	6.98356	+	1.87124i	1.64604	+	0.441055i
$19$	−0.637130	−	6.06189i	−0.146168	−	1.39069i	−0.784116	−	0.620614i	$-0.786883\pi$
$19$	−0.637130	−	6.06189i	−0.146168	−	1.39069i	0.637948	−	0.770079i	$-0.279783\pi$
$20$		0			0
$21$	−5.87529	+	4.20892i	−1.28209	+	0.918461i
$22$	−0.995562	−	6.28573i	−0.212254	−	1.34012i
$23$	−5.23739	−	0.274480i	−1.09207	−	0.0572331i	−0.502217	−	0.864742i	$-0.667482\pi$
$23$	−5.23739	−	0.274480i	−1.09207	−	0.0572331i	−0.589856	+	0.807509i	$0.700815\pi$
$24$	−3.04197	−	5.26884i	−0.620939	−	1.07550i
$25$		0			0
$26$	0.136313	+	0.0787005i	0.0267332	+	0.0154344i
$27$	1.81310	+	3.55840i	0.348930	+	0.684814i
$28$	−1.63270	−	0.269797i	−0.308552	−	0.0509868i
$29$	−2.51245	+	3.45809i	−0.466550	+	0.642152i	−0.975851	−	0.218437i	$-0.929904\pi$
$29$	−2.51245	+	3.45809i	−0.466550	+	0.642152i	0.509301	+	0.860589i	$0.329904\pi$
$30$		0			0
$31$	−0.287036	+	0.644694i	−0.0515533	+	0.115791i	−0.937486	−	0.348024i	$-0.886853\pi$
$31$	−0.287036	+	0.644694i	−0.0515533	+	0.115791i	0.885932	+	0.463814i	$0.153520\pi$
$32$	0.885159	−	3.30346i	0.156475	−	0.583975i
$33$	6.75198	−	8.33800i	1.17537	−	1.45146i
$34$	−1.67814	−	5.16477i	−0.287798	−	0.885751i
$35$		0			0
$36$	−0.862422	+	2.65426i	−0.143737	+	0.442377i
$37$	−4.20336	−	6.47261i	−0.691029	−	1.06409i	−0.993817	−	0.111033i	$-0.964584\pi$
$37$	−4.20336	−	6.47261i	−0.691029	−	1.06409i	0.302788	−	0.953058i	$-0.402083\pi$
$38$	9.86284	−	0.516889i	1.59996	−	0.0838505i
$39$	0.0551709	+	0.259559i	0.00883442	+	0.0415627i
$40$		0			0
$41$	0.124652	−	0.0405019i	0.0194674	−	0.00632534i	−0.299267	−	0.954169i	$-0.596742\pi$
$41$	0.124652	−	0.0405019i	0.0194674	−	0.00632534i	0.318735	+	0.947844i	$0.396742\pi$
$42$	−6.31226	−	9.86378i	−0.974003	−	1.52202i
$43$	−8.25770	+	8.25770i	−1.25929	+	1.25929i	−0.307854	+	0.951434i	$0.599611\pi$
$43$	−8.25770	+	8.25770i	−1.25929	+	1.25929i	−0.951434	+	0.307854i	$0.900389\pi$
$44$	2.44318	−	0.256788i	0.368323	−	0.0387123i
$45$		0			0
$46$	0.888279	−	8.45141i	0.130970	−	1.24609i
$47$	0.970816	−	2.52906i	0.141608	−	0.368902i	−0.844374	−	0.535755i	$-0.820027\pi$
$47$	0.970816	−	2.52906i	0.141608	−	0.368902i	0.985982	+	0.166853i	$0.0533605\pi$
$48$	11.8282	−	6.02679i	1.70726	−	0.869893i
$49$	6.95125	+	0.824720i	0.993035	+	0.117817i
$50$		0			0
$51$	4.57761	−	7.92865i	0.640993	−	1.11023i
$52$	−0.0330918	+	0.0509570i	−0.00458901	+	0.00706646i
$53$	7.40118	+	9.13970i	1.01663	+	1.25543i	0.966493	+	0.256691i	$0.0826324\pi$
$53$	7.40118	+	9.13970i	1.01663	+	1.25543i	0.0501369	+	0.998742i	$0.484034\pi$
$54$	−5.91164	+	2.63203i	−0.804472	+	0.358174i
$55$		0			0
$56$	−1.26365	+	5.75550i	−0.168862	+	0.769111i
$57$	11.7735	+	11.7735i	1.55944	+	1.55944i
$58$	−5.38252	−	4.35867i	−0.706759	−	0.572322i
$59$	3.45304	−	3.83499i	0.449548	−	0.499273i	−0.475188	−	0.879885i	$-0.657620\pi$
$59$	3.45304	−	3.83499i	0.449548	−	0.499273i	0.924735	+	0.380611i	$0.124286\pi$
$60$		0			0
$61$	5.30099	−	4.77304i	0.678723	−	0.611125i	−0.255926	−	0.966696i	$-0.582380\pi$
$61$	5.30099	−	4.77304i	0.678723	−	0.611125i	0.934649	+	0.355572i	$0.115714\pi$
$62$	−1.01885	−	0.519128i	−0.129394	−	0.0659293i
$63$	3.13162	−	11.3824i	0.394546	−	1.43405i
$64$	−3.97346	−	1.29105i	−0.496682	−	0.161382i
$65$		0			0
$66$	12.9192	+	11.6325i	1.59025	+	1.43187i
$67$	0.200027	+	0.521089i	0.0244372	+	0.0636611i	0.945256	−	0.326329i	$-0.105812\pi$
$67$	0.200027	+	0.521089i	0.0244372	+	0.0636611i	−0.920819	+	0.389990i	$0.872478\pi$
$68$	2.02485	−	0.542557i	0.245549	−	0.0657947i
$69$	11.5903	−	8.42087i	1.39531	−	1.01375i
$70$		0			0
$71$	0.818370	+	0.594581i	0.0971227	+	0.0705637i	0.635287	−	0.772276i	$-0.280882\pi$
$71$	0.818370	+	0.594581i	0.0971227	+	0.0705637i	−0.538164	+	0.842840i	$0.680882\pi$
$72$	9.27765	+	3.56136i	1.09338	+	0.419710i
$73$	−1.78952	−	1.16213i	−0.209448	−	0.136017i	0.435652	−	0.900115i	$-0.356518\pi$
$73$	−1.78952	−	1.16213i	−0.209448	−	0.136017i	−0.645100	+	0.764098i	$0.723184\pi$
$74$	10.8299	−	6.25262i	1.25894	−	0.726852i
$75$		0			0
$76$			3.81243i			0.437316i
$77$	−10.2743	+	1.55694i	−1.17086	+	0.177430i
$78$	−0.424673	+	0.0672616i	−0.0480848	+	0.00761588i
$79$	6.28497	+	14.1163i	0.707114	+	1.58820i	0.805184	+	0.593025i	$0.202067\pi$
$79$	6.28497	+	14.1163i	0.707114	+	1.58820i	−0.0980696	+	0.995180i	$0.531267\pi$
$80$		0			0
$81$	2.26247	+	1.00731i	0.251385	+	0.111924i
$82$	0.0549659	+	0.205136i	0.00606997	+	0.0226534i
$83$	−10.6837	−	1.69214i	−1.17269	−	0.185736i	−0.460461	−	0.887680i	$-0.652316\pi$
$83$	−10.6837	−	1.69214i	−1.17269	−	0.185736i	−0.712232	+	0.701944i	$0.752316\pi$
$84$	3.92988	−	2.23402i	0.428785	−	0.243751i
$85$		0			0
$86$	−12.6616	−	14.0621i	−1.36534	−	1.51636i
$87$	−0.611092	−	11.6603i	−0.0655159	−	1.25012i
$88$	−0.457814	−	8.73562i	−0.0488032	−	0.931220i
$89$	0.671570	+	0.745854i	0.0711863	+	0.0790604i	0.777686	−	0.628653i	$-0.216393\pi$
$89$	0.671570	+	0.745854i	0.0711863	+	0.0790604i	−0.706500	+	0.707713i	$0.749727\pi$
$90$		0			0
$91$	0.129991	−	0.221714i	0.0136268	−	0.0232420i
$92$	3.23996	+	0.513159i	0.337789	+	0.0535005i
$93$	−0.498939	−	1.86207i	−0.0517376	−	0.193087i
$94$	4.00998	+	1.78536i	0.413597	+	0.184145i
$95$		0			0
$96$	3.79985	+	8.53459i	0.387820	+	0.871058i
$97$	11.1837	−	1.77133i	1.13554	−	0.179851i	0.439764	−	0.898113i	$-0.355062\pi$
$97$	11.1837	−	1.77133i	1.13554	−	0.179851i	0.695773	+	0.718262i	$0.255062\pi$
$98$	−1.92397	+	11.1779i	−0.194350	+	1.12914i
$99$			17.5251i			1.76134i
$100$		0			0
$101$	−10.1623	+	5.86718i	−1.01118	+	0.583807i	−0.911538	−	0.411216i	$-0.865104\pi$
$101$	−10.1623	+	5.86718i	−1.01118	+	0.583807i	−0.0996449	+	0.995023i	$0.531771\pi$
$102$	12.4412	+	8.07944i	1.23187	+	0.799983i
$103$	−9.40258	−	3.60931i	−0.926464	−	0.355636i	−0.152092	−	0.988366i	$-0.548601\pi$
$103$	−9.40258	−	3.60931i	−0.926464	−	0.355636i	−0.774372	+	0.632730i	$0.781934\pi$
$104$	0.175032	+	0.127168i	0.0171633	+	0.0124699i
$105$		0			0
$106$	−15.4167	+	11.2009i	−1.49740	+	1.08792i
$107$	−1.09349	+	0.292999i	−0.105711	+	0.0283253i	−0.311287	−	0.950316i	$-0.600760\pi$
$107$	−1.09349	+	0.292999i	−0.105711	+	0.0283253i	0.205576	+	0.978641i	$0.434093\pi$
$108$	−0.895182	−	2.33203i	−0.0861389	−	0.224400i
$109$	2.17553	+	1.95886i	0.208378	+	0.187624i	0.766711	−	0.641993i	$-0.221892\pi$
$109$	2.17553	+	1.95886i	0.208378	+	0.187624i	−0.558333	+	0.829617i	$0.688559\pi$
$110$		0			0
$111$	20.0504	+	6.51476i	1.90310	+	0.618353i
$112$	−12.3970	−	3.41076i	−1.17141	−	0.322287i
$113$	−4.16270	−	2.12100i	−0.391594	−	0.199527i	0.247097	−	0.968991i	$-0.420523\pi$
$113$	−4.16270	−	2.12100i	−0.391594	−	0.199527i	−0.638690	+	0.769464i	$0.720523\pi$
$114$	−20.0493	+	18.0524i	−1.87779	+	1.69077i
$115$		0			0
$116$	1.78895	−	1.98683i	0.166100	−	0.184473i
$117$	−0.336849	−	0.272775i	−0.0311417	−	0.0252181i
$118$	5.91261	+	5.91261i	0.544300	+	0.544300i
$119$	−8.45141	+	2.68369i	−0.774739	+	0.246014i
$120$		0			0
$121$	4.04370	−	1.80037i	0.367609	−	0.163670i
$122$	7.27377	+	8.98236i	0.658536	+	0.813224i
$123$	−0.194998	+	0.300270i	−0.0175824	+	0.0270745i
$124$	0.220700	−	0.382263i	0.0198194	−	0.0343283i
$125$		0			0
$126$	18.1524	+	6.03254i	1.61714	+	0.537422i
$127$	−14.7555	+	7.51832i	−1.30934	+	0.667143i	−0.962628	−	0.270829i	$-0.912702\pi$
$127$	−14.7555	+	7.51832i	−1.30934	+	0.667143i	−0.346713	+	0.937971i	$0.612702\pi$
$128$	4.87725	−	12.7057i	0.431092	−	1.12303i
$129$	3.33454	−	31.7260i	0.293590	−	2.79332i
$130$		0			0
$131$	−0.400325	+	0.0420758i	−0.0349765	+	0.00367618i	−0.122001	−	0.992530i	$-0.538931\pi$
$131$	−0.400325	+	0.0420758i	−0.0349765	+	0.00367618i	0.0870240	+	0.996206i	$0.472264\pi$
$132$	−4.74518	+	4.74518i	−0.413015	+	0.413015i
$133$	−0.736311	−	16.1098i	−0.0638462	−	1.39690i
$134$	−0.860142	+	0.279477i	−0.0743049	+	0.0241431i
$135$		0			0
$136$	−1.55195	−	7.30134i	−0.133078	−	0.626085i
$137$	12.6497	−	0.662940i	1.08073	−	0.0566388i	0.496354	−	0.868120i	$-0.334672\pi$
$137$	12.6497	−	0.662940i	1.08073	−	0.0566388i	0.584378	+	0.811481i	$0.301338\pi$
$138$	12.6430	+	19.4685i	1.07625	+	1.65727i
$139$	−4.44619	+	13.6840i	−0.377121	+	1.16066i	0.564915	+	0.825149i	$0.308909\pi$
$139$	−4.44619	+	13.6840i	−0.377121	+	1.16066i	−0.942036	+	0.335511i	$0.891091\pi$
$140$		0			0
$141$	2.28674	+	7.03788i	0.192579	+	0.592696i
$142$	−1.03150	+	1.27379i	−0.0865612	+	0.106894i
$143$	−0.0987488	+	0.368536i	−0.00825779	+	0.0308185i
$144$	−8.81972	+	19.8094i	−0.734976	+	1.65078i
$145$		0			0
$146$	2.03221	−	2.79710i	0.168187	−	0.231489i
$147$	−16.1746	+	10.1990i	−1.33406	+	0.841202i
$148$	2.19151	+	4.30108i	0.180141	+	0.353547i
$149$	−9.24670	−	5.33859i	−0.757519	−	0.437354i	0.0708851	−	0.997484i	$-0.477418\pi$
$149$	−9.24670	−	5.33859i	−0.757519	−	0.437354i	−0.828404	+	0.560131i	$0.810751\pi$
$150$		0			0
$151$	−10.4396	−	18.0820i	−0.849565	−	1.47149i	−0.881597	−	0.472003i	$-0.843531\pi$
$151$	−10.4396	−	18.0820i	−0.849565	−	1.47149i	0.0320315	−	0.999487i	$-0.489802\pi$
$152$	13.5567	+	0.710479i	1.09960	+	0.0576274i
$153$	2.33939	+	14.7703i	0.189128	+	1.19411i
$154$	−1.64803	−	16.7569i	−0.132802	−	1.35031i
$155$		0			0
$156$	−0.0173490	−	0.165065i	−0.00138903	−	0.0132157i
$157$	−11.5468	−	3.09395i	−0.921533	−	0.246924i	−0.233293	−	0.972407i	$-0.574950\pi$
$157$	−11.5468	−	3.09395i	−0.921533	−	0.246924i	−0.688241	+	0.725483i	$0.741617\pi$
$158$	−23.3747	+	8.97269i	−1.85959	+	0.713829i
$159$	−31.4240	−	6.67937i	−2.49208	−	0.529709i
$160$		0			0
$161$	−13.7898	−	1.54265i	−1.08679	−	0.121578i
$162$	−1.82181	+	3.57550i	−0.143135	+	0.280918i
$163$	−12.1623	+	7.89827i	−0.952622	+	0.618640i	−0.924589	−	0.380967i	$-0.875591\pi$
$163$	−12.1623	+	7.89827i	−0.952622	+	0.618640i	−0.0280333	+	0.999607i	$0.508924\pi$
$164$	−0.0801874	+	0.0170444i	−0.00626159	+	0.00133094i
$165$		0			0
$166$	3.64407	−	17.1440i	0.282834	−	1.33063i
$167$	0.261681	−	1.65219i	0.0202495	−	0.127850i	−0.975493	−	0.220032i	$-0.929384\pi$
$167$	0.261681	−	1.65219i	0.0202495	−	0.127850i	0.995742	+	0.0921813i	$0.0293839\pi$
$168$	−7.21164	−	14.3907i	−0.556390	−	1.11027i
$169$	7.63566	+	10.5096i	0.587359	+	0.808430i
$170$		0			0
$171$	−27.0481	−	2.84287i	−2.06842	−	0.217400i
$172$	5.67656	−	4.59679i	0.432834	−	0.350502i
$173$	0.0147195	−	0.280864i	0.00111910	−	0.0213537i	−0.998013	−	0.0630098i	$-0.979930\pi$
$173$	0.0147195	−	0.280864i	0.00111910	−	0.0213537i	0.999132	+	0.0416561i	$0.0132634\pi$
$174$	18.9195			1.43429
$175$		0			0
$176$	19.0873			1.43876
$177$	−0.737766	+	14.0774i	−0.0554539	+	1.05812i
$178$	−1.26383	+	1.02343i	−0.0947277	+	0.0767090i
$179$	−13.0417	−	1.37074i	−0.974782	−	0.102454i	−0.396275	−	0.918132i	$-0.629697\pi$
$179$	−13.0417	−	1.37074i	−0.974782	−	0.102454i	−0.578506	+	0.815678i	$0.696364\pi$
$180$		0			0
$181$	13.5383	+	18.6338i	1.00629	+	1.38504i	0.921384	+	0.388653i	$0.127060\pi$
$181$	13.5383	+	18.6338i	1.00629	+	1.38504i	0.0849076	+	0.996389i	$0.472940\pi$
$182$	0.347735	+	0.229142i	0.0257758	+	0.0169851i
$183$	−3.04820	+	19.2456i	−0.225330	+	1.42268i
$184$	2.42855	−	11.4254i	0.179035	−	0.842294i
$185$		0			0
$186$	3.05534	−	0.649432i	0.224028	−	0.0476187i
$187$	11.0399	−	7.16938i	0.807316	−	0.524277i
$188$	−0.769242	+	1.50972i	−0.0561027	+	0.110108i
$189$	4.23307	+	9.68131i	0.307910	+	0.704212i
$190$		0			0
$191$	−3.95786	−	0.841270i	−0.286381	−	0.0608722i	0.0624813	−	0.998046i	$-0.480099\pi$
$191$	−3.95786	−	0.841270i	−0.286381	−	0.0608722i	−0.348862	+	0.937174i	$0.613432\pi$
$192$	10.6547	−	4.08996i	0.768937	−	0.295167i
$193$	2.96976	+	0.795745i	0.213768	+	0.0572790i	0.364114	−	0.931355i	$-0.381372\pi$
$193$	2.96976	+	0.795745i	0.213768	+	0.0572790i	−0.150346	+	0.988634i	$0.548039\pi$
$194$	1.91781	+	18.2467i	0.137691	+	1.31004i
$195$		0			0
$196$	−4.27008	−	0.967485i	−0.305006	−	0.0691061i
$197$	−1.97286	−	12.4561i	−0.140560	−	0.887464i	−0.952681	−	0.303973i	$-0.901687\pi$
$197$	−1.97286	−	12.4561i	−0.140560	−	0.887464i	0.812120	−	0.583490i	$-0.198313\pi$
$198$	−28.3576	−	1.48616i	−2.01529	−	0.105617i
$199$	2.17496	+	3.76715i	0.154179	+	0.267046i	0.932760	−	0.360498i	$-0.117393\pi$
$199$	2.17496	+	3.76715i	0.154179	+	0.267046i	−0.778581	+	0.627545i	$0.784060\pi$
$200$		0			0
$201$	−1.32044	−	0.762355i	−0.0931365	−	0.0537724i
$202$	−8.63198	−	16.9412i	−0.607344	−	1.19198i
$203$	−7.17565	+	8.74104i	−0.503632	+	0.613501i
$204$	−3.36586	+	4.63270i	−0.235657	+	0.324354i
$205$		0			0
$206$	6.63762	−	14.9083i	0.462465	−	1.03871i
$207$	−6.05670	+	22.6039i	−0.420970	+	1.57108i
$208$	−0.297090	+	0.366875i	−0.0205995	+	0.0254382i
$209$	7.39789	+	22.7684i	0.511723	+	1.57492i
$210$		0			0
$211$	2.05986	−	6.33961i	0.141807	−	0.436437i	−0.854780	−	0.518991i	$-0.826308\pi$
$211$	2.05986	−	6.33961i	0.141807	−	0.436437i	0.996587	+	0.0825543i	$0.0263078\pi$
$212$	−4.00633	−	6.16920i	−0.275156	−	0.423703i
$213$	−2.75946	+	0.144617i	−0.189075	+	0.00990900i
$214$	−0.381375	−	1.79423i	−0.0260703	−	0.122651i
$215$		0			0
$216$	−8.45936	+	2.74861i	−0.575586	+	0.187019i
$217$	−0.858760	+	1.65791i	−0.0582964	+	0.112547i
$218$	−3.35413	+	3.35413i	−0.227171	+	0.227171i
$219$	5.79680	−	0.609268i	0.391711	−	0.0411705i
$220$		0			0
$221$	−0.0340314	+	0.323787i	−0.00228920	+	0.0217803i
$222$	−12.2419	+	31.8912i	−0.821622	+	2.14040i
$223$	13.7309	−	6.99626i	0.919491	−	0.468504i	0.0708583	−	0.997486i	$-0.477426\pi$
$223$	13.7309	−	6.99626i	0.919491	−	0.468504i	0.848633	+	0.528982i	$0.177426\pi$
$224$	2.85360	−	8.58670i	0.190664	−	0.573723i
$225$		0			0
$226$	3.78502	−	6.55584i	0.251776	−	0.436088i
$227$	−7.21647	+	11.1124i	−0.478974	+	0.737556i	−0.992728	−	0.120382i	$-0.961588\pi$
$227$	−7.21647	+	11.1124i	−0.478974	+	0.737556i	0.513753	+	0.857938i	$0.328255\pi$
$228$	−6.55393	−	8.09342i	−0.434044	−	0.536000i
$229$	3.78909	−	1.68701i	0.250390	−	0.111481i	−0.277704	−	0.960667i	$-0.589574\pi$
$229$	3.78909	−	1.68701i	0.250390	−	0.111481i	0.528094	+	0.849186i	$0.322907\pi$
$230$		0			0
$231$	19.1347	−	20.9677i	1.25897	−	1.37957i
$232$	−6.73164	−	6.73164i	−0.441954	−	0.441954i
$233$	20.0258	+	16.2166i	1.31194	+	1.06238i	0.993427	+	0.114464i	$0.0365152\pi$
$233$	20.0258	+	16.2166i	1.31194	+	1.06238i	0.318508	+	0.947920i	$0.396818\pi$
$234$	0.469946	−	0.521927i	0.0307213	−	0.0341195i
$235$		0			0
$236$	−2.39868	+	2.15978i	−0.156141	+	0.140590i
$237$	−37.6096	−	19.1630i	−2.44300	−	1.24477i
$238$	−3.62582	−	13.9029i	−0.235027	−	0.901191i
$239$	0.618920	+	0.201099i	0.0400346	+	0.0130080i	0.328966	−	0.944342i	$-0.393300\pi$
$239$	0.618920	+	0.201099i	0.0400346	+	0.0130080i	−0.288931	+	0.957350i	$0.593300\pi$
$240$		0			0
$241$	−0.853202	−	0.768226i	−0.0549596	−	0.0494858i	0.641193	−	0.767379i	$-0.278440\pi$
$241$	−0.853202	−	0.768226i	−0.0549596	−	0.0494858i	−0.696153	+	0.717894i	$0.745106\pi$
$242$	2.57029	+	6.69582i	0.165224	+	0.430424i
$243$	−18.1075	+	4.85188i	−1.16159	+	0.311248i
$244$	−3.60952	+	2.62247i	−0.231076	+	0.167887i
$245$		0			0
$246$	−0.469334	−	0.340991i	−0.0299237	−	0.0217408i
$247$	−0.552776	−	0.212191i	−0.0351723	−	0.0135014i
$248$	−1.31817	−	0.856031i	−0.0837040	−	0.0543580i
$249$	25.5895	−	14.7741i	1.62167	−	0.936270i
$250$		0			0
$251$			13.8492i			0.874153i	0.899424	+	0.437076i	$0.143986\pi$
$251$			13.8492i			0.874153i	−0.899424	+	0.437076i	$0.856014\pi$
$252$	−2.69219	+	6.87563i	−0.169592	+	0.433124i
$253$	20.3452	−	3.22237i	1.27909	−	0.202589i
$254$	−10.9142	−	24.5136i	−0.684816	−	1.53812i
$255$		0			0
$256$	12.5121	+	5.57076i	0.782008	+	0.348172i
$257$	0.0943752	+	0.352213i	0.00588696	+	0.0219704i	0.968807	−	0.247817i	$-0.0797132\pi$
$257$	0.0943752	+	0.352213i	0.00588696	+	0.0219704i	−0.962920	+	0.269788i	$0.913047\pi$
$258$	51.0535	+	8.08608i	3.17845	+	0.503417i
$259$	−10.0911	−	17.7513i	−0.627031	−	1.10302i
$260$		0			0
$261$	12.7620	+	14.1736i	0.789948	+	0.877327i
$262$	−0.0341352	−	0.651338i	−0.00210888	−	0.0402398i
$263$	1.55688	+	29.7070i	0.0960011	+	1.83181i	0.445968	+	0.895049i	$0.352859\pi$
$263$	1.55688	+	29.7070i	0.0960011	+	1.83181i	−0.349967	+	0.936762i	$0.613807\pi$
$264$	15.9892	+	17.7578i	0.984069	+	1.09292i
$265$		0			0
$266$	26.1298	+	0.174703i	1.60212	+	0.0107117i
$267$	−2.70787	−	0.428885i	−0.165719	−	0.0262473i
$268$	−0.0903576	−	0.337219i	−0.00551947	−	0.0205989i
$269$	−18.9335	−	8.42973i	−1.15439	−	0.513970i	−0.261930	−	0.965087i	$-0.584359\pi$
$269$	−18.9335	−	8.42973i	−1.15439	−	0.513970i	−0.892465	+	0.451117i	$0.851026\pi$
$270$		0			0
$271$	−2.28034	−	5.12174i	−0.138521	−	0.311123i	0.830943	−	0.556358i	$-0.187802\pi$
$271$	−2.28034	−	5.12174i	−0.138521	−	0.311123i	−0.969464	+	0.245235i	$0.921135\pi$
$272$	16.0869	−	2.54792i	0.975413	−	0.154490i
$273$	0.105189	+	0.694145i	0.00636635	+	0.0420116i
$274$			20.5248i			1.23995i
$275$		0			0
$276$	−7.76028	+	4.48040i	−0.467114	+	0.269688i
$277$	4.95771	+	3.21957i	0.297880	+	0.193445i	0.684922	−	0.728617i	$-0.259836\pi$
$277$	4.95771	+	3.21957i	0.297880	+	0.193445i	−0.387042	+	0.922062i	$0.626503\pi$
$278$	−21.7651	−	8.35486i	−1.30539	−	0.501091i
$279$	2.54748	+	1.85085i	0.152514	+	0.110808i
$280$		0			0
$281$	−6.92124	+	5.02858i	−0.412887	+	0.299980i	−0.774769	−	0.632244i	$-0.782134\pi$
$281$	−6.92124	+	5.02858i	−0.412887	+	0.299980i	0.361883	+	0.932224i	$0.382134\pi$
$282$	−11.5820	+	3.10338i	−0.689697	+	0.184804i
$283$	5.40796	+	14.0882i	0.321470	+	0.837458i	0.995144	+	0.0984291i	$0.0313818\pi$
$283$	5.40796	+	14.0882i	0.321470	+	0.837458i	−0.673674	+	0.739028i	$0.735285\pi$
$284$	−0.470191	−	0.423361i	−0.0279007	−	0.0251219i
$285$		0			0
$286$	−0.587957	−	0.191039i	−0.0347666	−	0.0112964i
$287$	0.335547	−	0.0875094i	0.0198067	−	0.00516552i
$288$	−13.5968	−	6.92789i	−0.801196	−	0.408230i
$289$	−4.28598	+	3.85911i	−0.252116	+	0.227007i
$290$		0			0
$291$	−20.6969	+	22.9863i	−1.21327	+	1.34748i
$292$	1.03719	+	0.839898i	0.0606968	+	0.0491513i
$293$	−7.80680	−	7.80680i	−0.456078	−	0.456078i	0.441288	−	0.897366i	$-0.354522\pi$
$293$	−7.80680	−	7.80680i	−0.456078	−	0.456078i	−0.897366	+	0.441288i	$0.854522\pi$
$294$	−15.1315	−	27.0372i	−0.882489	−	1.57684i
$295$		0			0
$296$	15.7027	−	6.99131i	0.912703	−	0.406362i
$297$	−9.87137	−	12.1901i	−0.572795	−	0.707343i
$298$	9.42256	−	14.5095i	0.545834	−	0.840511i
$299$	−0.254733	+	0.441210i	−0.0147316	+	0.0255158i
$300$		0			0
$301$	−23.0990	+	20.5205i	−1.33141	+	1.18278i
$302$	30.1439	−	15.3591i	1.73459	−	0.883817i
$303$	11.4873	−	29.9253i	0.659926	−	1.71917i
$304$	−3.09628	+	29.4592i	−0.177584	+	1.68960i
$305$		0			0
$306$	−24.0984	+	2.53284i	−1.37761	+	0.144793i
$307$	−8.14095	+	8.14095i	−0.464628	+	0.464628i	−0.900169	−	0.435541i	$-0.856557\pi$
$307$	−8.14095	+	8.14095i	−0.464628	+	0.464628i	0.435541	+	0.900169i	$0.356557\pi$
$308$	6.49286	−	0.296762i	0.369965	−	0.0169096i
$309$	26.1655	−	8.50169i	1.48850	−	0.483644i
$310$		0			0
$311$	5.97488	+	28.1096i	0.338804	+	1.59395i	0.736504	+	0.676433i	$0.236475\pi$
$311$	5.97488	+	28.1096i	0.338804	+	1.59395i	−0.397700	+	0.917516i	$0.630192\pi$
$312$	−0.590191	+	0.0309306i	−0.0334130	+	0.00175110i
$313$	−5.18386	−	7.98245i	−0.293009	−	0.451195i	0.661254	−	0.750162i	$-0.270025\pi$
$313$	−5.18386	−	7.98245i	−0.293009	−	0.451195i	−0.954263	+	0.298967i	$0.903358\pi$
$314$	5.98554	−	18.4216i	0.337783	−	1.03959i
$315$		0			0
$316$	−2.98662	−	9.19189i	−0.168011	−	0.517084i
$317$	−4.91231	+	6.06620i	−0.275903	+	0.340712i	−0.896196	−	0.443658i	$-0.853680\pi$
$317$	−4.91231	+	6.06620i	−0.275903	+	0.340712i	0.620293	+	0.784370i	$0.287014\pi$
$318$	13.4728	−	50.2810i	0.755515	−	2.81962i
$319$	6.82848	−	15.3370i	0.382322	−	0.858708i
$320$		0			0
$321$	1.81768	−	2.50182i	0.101453	−	0.139638i
$322$	3.66558	−	22.1827i	0.204275	−	1.23619i
$323$	9.27431	+	18.2019i	0.516036	+	1.01278i
$324$	−1.34150	−	0.774516i	−0.0745278	−	0.0430287i
$325$		0			0
$326$	−11.7489	−	20.3497i	−0.650711	−	1.12706i
$327$	−7.98590	−	0.418523i	−0.441621	−	0.0231444i
$328$	0.0456650	+	0.288317i	0.00252143	+	0.0159197i
$329$	2.95892	−	6.52804i	0.163131	−	0.359902i
$330$		0			0
$331$	−0.108165	−	1.02912i	−0.00594527	−	0.0565654i	0.991147	−	0.132769i	$-0.0423868\pi$
$331$	−0.108165	−	1.02912i	−0.00594527	−	0.0565654i	−0.997092	+	0.0762035i	$0.975720\pi$
$332$	6.53515	+	1.75109i	0.358663	+	0.0961035i
$333$	−32.1491	+	12.3409i	−1.76176	+	0.676277i
$334$	2.65124	+	0.563538i	0.145069	+	0.0308354i
$335$		0			0
$336$	32.1810	−	14.0709i	1.75562	−	0.767629i
$337$	−0.849753	+	1.66773i	−0.0462890	+	0.0908472i	−0.912992	−	0.407977i	$-0.866235\pi$
$337$	−0.849753	+	1.66773i	−0.0462890	+	0.0908472i	0.866703	+	0.498824i	$0.166235\pi$
$338$	−17.6532	+	11.4641i	−0.960207	+	0.623566i
$339$	12.4832	−	2.65339i	0.677994	−	0.144112i
$340$		0			0
$341$	0.576281	−	2.71119i	0.0312074	−	0.146819i
$342$	6.89381	−	43.5258i	0.372774	−	2.35361i
$343$	18.2305	+	3.26350i	0.984352	+	0.176212i
$344$	−15.2880	−	21.0421i	−0.824272	−	1.13451i
$345$		0			0
$346$	0.453221	+	0.0476355i	0.0243653	+	0.00256090i
$347$	1.54512	−	1.25122i	0.0829465	−	0.0671688i	−0.586950	−	0.809623i	$-0.699672\pi$
$347$	1.54512	−	1.25122i	0.0829465	−	0.0671688i	0.669897	+	0.742454i	$0.266338\pi$
$348$	−0.382221	+	7.29322i	−0.0204892	+	0.390958i
$349$	4.37015			0.233929			0.116964	−	0.993136i	$-0.462684\pi$
$349$	4.37015			0.233929			0.116964	+	0.993136i	$0.462684\pi$
$350$		0			0
$351$	0.387952			0.0207073
$352$	−0.703003	+	13.4141i	−0.0374702	+	0.714974i
$353$	14.5133	−	11.7526i	0.772464	−	0.625529i	−0.159865	−	0.987139i	$-0.551106\pi$
$353$	14.5133	−	11.7526i	0.772464	−	0.625529i	0.932330	+	0.361610i	$0.117773\pi$
$354$	−22.7162	−	2.38757i	−1.20735	−	0.126898i
$355$		0			0
$356$	−0.368984	−	0.507863i	−0.0195561	−	0.0269167i
$357$	13.3280	−	20.2260i	0.705393	−	1.07047i
$358$	3.32396	−	20.9867i	0.175677	−	1.10918i
$359$	3.47497	−	16.3485i	0.183402	−	0.862838i	−0.786166	−	0.618016i	$-0.787937\pi$
$359$	3.47497	−	16.3485i	0.183402	−	0.862838i	0.969568	−	0.244823i	$-0.0787298\pi$
$360$		0			0
$361$	−17.7558	+	3.77411i	−0.934515	+	0.198637i
$362$	−31.2997	+	20.3262i	−1.64507	+	1.06832i
$363$	−5.48937	+	10.7735i	−0.288117	+	0.565462i
$364$	−0.0953561	+	0.129418i	−0.00499802	+	0.00678334i
$365$		0			0
$366$	−30.8830	−	6.56439i	−1.61428	−	0.343126i
$367$	9.01861	−	3.46192i	0.470768	−	0.180711i	−0.111406	−	0.993775i	$-0.535536\pi$
$367$	9.01861	−	3.46192i	0.470768	−	0.180711i	0.582174	+	0.813064i	$0.302202\pi$
$368$	24.6188	+	6.59659i	1.28334	+	0.343871i
$369$	−0.0611304	−	0.581617i	−0.00318232	−	0.0302778i
$370$		0			0
$371$	18.1206	+	25.2948i	0.940774	+	1.31324i
$372$	0.188622	+	1.19091i	0.00977959	+	0.0617459i
$373$	−4.91126	−	0.257388i	−0.254295	−	0.0133271i	−0.0752376	−	0.997166i	$-0.523972\pi$
$373$	−4.91126	−	0.257388i	−0.254295	−	0.0133271i	−0.179058	+	0.983839i	$0.557305\pi$
$374$	10.6647	+	18.4717i	0.551456	+	0.955150i
$375$		0			0
$376$	5.22511	+	3.01672i	0.269465	+	0.155575i
$377$	0.188508	+	0.369967i	0.00970865	+	0.0190543i
$378$	−16.0244	+	6.02858i	−0.824206	+	0.310077i
$379$	−7.39900	+	10.1839i	−0.380061	+	0.523109i	−0.955601	−	0.294665i	$-0.904792\pi$
$379$	−7.39900	+	10.1839i	−0.380061	+	0.523109i	0.575540	+	0.817774i	$0.304792\pi$
$380$		0			0
$381$	18.3999	−	41.3268i	0.942654	−	2.11723i
$382$	1.69690	−	6.33292i	0.0868210	−	0.324020i
$383$	11.2845	−	13.9353i	0.576613	−	0.712058i	−0.402489	−	0.915425i	$-0.631855\pi$
$383$	11.2845	−	13.9353i	0.576613	−	0.712058i	0.979103	+	0.203366i	$0.0651883\pi$
$384$	11.4883	+	35.3574i	0.586260	+	1.80432i
$385$		0			0
$386$	−1.53944	+	4.73792i	−0.0783556	+	0.241154i
$387$	28.3800	+	43.7013i	1.44264	+	2.22146i
$388$	−7.07262	+	0.370660i	−0.359058	+	0.0188174i
$389$	2.47971	+	11.6661i	0.125726	+	0.591495i	0.995229	+	0.0975672i	$0.0311061\pi$
$389$	2.47971	+	11.6661i	0.125726	+	0.591495i	−0.869503	+	0.493928i	$0.835561\pi$
$390$		0			0
$391$	16.7170	−	5.43168i	0.845415	−	0.274692i
$392$	−4.23607	+	15.0038i	−0.213954	+	0.757806i
$393$	0.777518	−	0.777518i	0.0392206	−	0.0392206i
$394$	20.3227	−	2.13600i	1.02384	−	0.107610i
$395$		0			0
$396$	1.14579	−	10.9014i	0.0575780	−	0.547818i
$397$	13.4462	−	35.0286i	0.674846	−	1.75803i	0.0229366	−	0.999737i	$-0.492698\pi$
$397$	13.4462	−	35.0286i	0.674846	−	1.75803i	0.651909	−	0.758297i	$-0.273968\pi$
$398$	−6.28010	+	3.19987i	−0.314793	+	0.160395i
$399$	29.2573	+	32.9337i	1.46470	+	1.64875i
$400$		0			0
$401$	0.106730	−	0.184861i	0.00532982	−	0.00923152i	−0.863348	−	0.504609i	$-0.831637\pi$
$401$	0.106730	−	0.184861i	0.00532982	−	0.00923152i	0.868678	+	0.495377i	$0.164970\pi$
$402$	1.34555	−	2.07197i	0.0671099	−	0.103340i
$403$	0.0431419	+	0.0532758i	0.00214905	+	0.00265386i
$404$	6.70499	−	2.98525i	0.333586	−	0.148522i
$405$		0			0
$406$	−13.5355	−	12.3522i	−0.671754	−	0.613032i
$407$	21.4341	+	21.4341i	1.06245	+	1.06245i
$408$	15.8463	+	12.8321i	0.784509	+	0.635283i
$409$	−21.3736	+	23.7377i	−1.05685	+	1.17376i	−0.0725340	+	0.997366i	$0.523109\pi$
$409$	−21.3736	+	23.7377i	−1.05685	+	1.17376i	−0.984320	+	0.176390i	$0.943558\pi$
$410$		0			0
$411$	−25.7143	+	23.1533i	−1.26839	+	1.14207i
$412$	5.61287	+	2.85990i	0.276526	+	0.140897i
$413$	9.71872	−	9.58962i	0.478227	−	0.471875i
$414$	−36.0620	−	11.7173i	−1.77235	−	0.575872i
$415$		0			0
$416$	−0.246889	−	0.222300i	−0.0121047	−	0.0108992i
$417$	−14.0852	−	36.6932i	−0.689755	−	1.79687i
$418$	−37.4691	+	10.0398i	−1.83267	+	0.491063i
$419$	−8.57555	+	6.23050i	−0.418943	+	0.304380i	−0.777212	−	0.629238i	$-0.783367\pi$
$419$	−8.57555	+	6.23050i	−0.418943	+	0.304380i	0.358269	+	0.933618i	$0.383367\pi$
$420$		0			0
$421$	7.12732	+	5.17830i	0.347364	+	0.252375i	0.747762	−	0.663966i	$-0.231128\pi$
$421$	7.12732	+	5.17830i	0.347364	+	0.252375i	−0.400398	+	0.916341i	$0.631128\pi$
$422$	10.0835	+	3.87070i	0.490858	+	0.188423i
$423$	−10.1374	−	6.58333i	−0.492899	−	0.320093i
$424$	−22.6839	+	13.0965i	−1.10163	+	0.636024i
$425$		0			0
$426$		−	4.47737i		−	0.216929i
$427$	14.7459	−	11.7786i	0.713603	−	0.570007i
$428$	0.699356	−	0.110767i	0.0338047	−	0.00535413i
$429$	−0.423913	−	0.952124i	−0.0204667	−	0.0459690i
$430$		0			0
$431$	5.59847	+	2.49260i	0.269669	+	0.120064i	0.537116	−	0.843508i	$-0.319514\pi$
$431$	5.59847	+	2.49260i	0.269669	+	0.120064i	−0.267448	+	0.963572i	$0.586180\pi$
$432$	−5.02322	−	18.7469i	−0.241680	−	0.901961i
$433$	−35.2854	−	5.58866i	−1.69571	−	0.268574i	−0.767613	−	0.640913i	$-0.778556\pi$
$433$	−35.2854	−	5.58866i	−1.69571	−	0.268574i	−0.928097	+	0.372339i	$0.878556\pi$
$434$	−2.60986	−	1.53016i	−0.125277	−	0.0734501i
$435$		0			0
$436$	−1.22521	−	1.36074i	−0.0586770	−	0.0651674i
$437$	1.67303	+	31.9234i	0.0800321	+	1.52710i
$438$	0.494285	+	9.43153i	0.0236179	+	0.450656i
$439$	17.4485	+	19.3785i	0.832769	+	0.924884i	0.998116	−	0.0613516i	$-0.0195411\pi$
$439$	17.4485	+	19.3785i	0.832769	+	0.924884i	−0.165347	+	0.986235i	$0.552874\pi$
$440$		0			0
$441$	10.0482	−	29.5736i	0.478484	−	1.40826i
$442$	−0.521037	−	0.0825241i	−0.0247832	−	0.00392527i
$443$	8.76626	+	32.7161i	0.416498	+	1.55439i	0.781817	+	0.623508i	$0.214293\pi$
$443$	8.76626	+	32.7161i	0.416498	+	1.55439i	−0.365319	+	0.930882i	$0.619040\pi$
$444$	−12.0463	−	5.36337i	−0.571693	−	0.254534i
$445$		0			0
$446$	10.1563	+	22.8115i	0.480915	+	1.08015i
$447$	28.8074	−	4.56264i	1.36254	−	0.215805i
$448$	−10.2929	−	4.03023i	−0.486293	−	0.190410i
$449$			17.8247i			0.841199i	0.907246	+	0.420600i	$0.138180\pi$
$449$			17.8247i			0.841199i	−0.907246	+	0.420600i	$0.861820\pi$
$450$		0			0
$451$	−0.445816	+	0.257392i	−0.0209927	+	0.0121201i
$452$	2.45072	+	1.59152i	0.115272	+	0.0748586i
$453$	53.2469	+	20.4396i	2.50176	+	0.960335i
$454$	−17.3691	−	12.6194i	−0.815173	−	0.592258i
$455$		0			0
$456$	−30.0010	+	21.7970i	−1.40493	+	1.02074i
$457$	−8.24133	+	2.20826i	−0.385513	+	0.103298i	−0.446370	−	0.894849i	$-0.647283\pi$
$457$	−8.24133	+	2.20826i	−0.385513	+	0.103298i	0.0608568	+	0.998147i	$0.480617\pi$
$458$	2.40845	+	6.27422i	0.112539	+	0.293175i
$459$	−9.94691	−	8.95624i	−0.464282	−	0.418042i
$460$		0			0
$461$	−25.2246	−	8.19596i	−1.17483	−	0.381724i	−0.344384	−	0.938829i	$-0.611912\pi$
$461$	−25.2246	−	8.19596i	−1.17483	−	0.381724i	−0.830442	+	0.557105i	$0.811912\pi$
$462$	32.3053	+	32.7402i	1.50298	+	1.52321i
$463$	−20.3912	−	10.3899i	−0.947661	−	0.482857i	−0.0893575	−	0.996000i	$-0.528481\pi$
$463$	−20.3912	−	10.3899i	−0.947661	−	0.482857i	−0.858304	+	0.513142i	$0.828481\pi$
$464$	15.4371	−	13.8996i	0.716647	−	0.645272i
$465$		0			0
$466$	−27.9385	+	31.0288i	−1.29422	+	1.43738i
$467$	6.92961	+	5.61149i	0.320664	+	0.259669i	0.776114	−	0.630593i	$-0.217188\pi$
$467$	6.92961	+	5.61149i	0.320664	+	0.259669i	−0.455450	+	0.890262i	$0.650521\pi$
$468$	0.191702	+	0.191702i	0.00886142	+	0.00886142i
$469$	0.446943	+	1.40750i	0.0206379	+	0.0649922i
$470$		0			0
$471$	29.8315	−	13.2818i	1.37456	−	0.611994i
$472$	7.23302	+	8.93204i	0.332927	+	0.411130i
$473$	24.9813	−	38.4678i	1.14864	−	1.76875i
$474$	34.1972	−	59.2314i	1.57073	−	2.72059i
$475$		0			0
$476$	5.43263	−	1.11683i	0.249004	−	0.0511899i
$477$	46.7562	−	23.8235i	2.14082	−	1.09080i
$478$	−0.377886	+	0.984427i	−0.0172841	+	0.0450266i
$479$	0.250187	−	2.38037i	0.0114314	−	0.108762i	−0.987318	−	0.158753i	$-0.949253\pi$
$479$	0.250187	−	2.38037i	0.0114314	−	0.108762i	0.998750	+	0.0499911i	$0.0159193\pi$
$480$		0			0
$481$	−0.745601	+	0.0783658i	−0.0339965	+	0.00357317i
$482$	1.31543	−	1.31543i	0.0599161	−	0.0599161i
$483$	31.9265	−	20.4311i	1.45270	−	0.929648i
$484$	−2.63308	+	0.855538i	−0.119685	+	0.0388881i
$485$		0			0
$486$	−6.31534	−	29.7113i	−0.286470	−	1.34773i
$487$	−4.83930	+	0.253617i	−0.219290	+	0.0114925i	−0.161664	−	0.986846i	$-0.551686\pi$
$487$	−4.83930	+	0.253617i	−0.219290	+	0.0114925i	−0.0576252	+	0.998338i	$0.518353\pi$
$488$	8.65266	+	13.3239i	0.391688	+	0.603146i
$489$	12.2414	−	37.6753i	0.553577	−	1.70374i
$490$		0			0
$491$	−9.20020	−	28.3153i	−0.415199	−	1.27785i	−0.912073	−	0.410029i	$-0.865519\pi$
$491$	−9.20020	−	28.3153i	−0.415199	−	1.27785i	0.496874	−	0.867823i	$-0.334481\pi$
$492$	0.140929	−	0.174033i	0.00635358	−	0.00784602i
$493$	3.70780	−	13.8377i	0.166991	−	0.623218i
$494$	0.390225	−	0.876459i	0.0175570	−	0.0394337i
$495$		0			0
$496$	2.01583	−	2.77456i	0.0905136	−	0.124581i
$497$	2.06860	+	1.69814i	0.0927893	+	0.0761721i
$498$	21.7361	+	42.6595i	0.974018	+	1.91162i
$499$	−33.6862	−	19.4488i	−1.50800	−	0.870646i	−0.999957	−	0.00931623i	$-0.997035\pi$
$499$	−33.6862	−	19.4488i	−1.50800	−	0.870646i	−0.508046	−	0.861330i	$-0.669632\pi$
$500$		0			0
$501$	2.28474	+	3.95729i	0.102075	+	0.176799i
$502$	−22.4095	−	1.17443i	−1.00019	−	0.0524175i
$503$	−5.93752	−	37.4880i	−0.264741	−	1.67151i	−0.658719	−	0.752389i	$-0.728902\pi$
$503$	−5.93752	−	37.4880i	−0.264741	−	1.67151i	0.393979	−	0.919120i	$-0.371098\pi$
$504$	23.9475	+	10.8546i	1.06671	+	0.483501i
$505$		0			0
$506$	3.48884	+	33.1941i	0.155098	+	1.47566i
$507$	−34.2767	−	9.18442i	−1.52228	−	0.407894i
$508$	9.67017	−	3.71203i	0.429044	−	0.164695i
$509$	10.1538	+	2.15825i	0.450057	+	0.0956626i	0.427364	−	0.904080i	$-0.359442\pi$
$509$	10.1538	+	2.15825i	0.450057	+	0.0956626i	0.0226937	+	0.999742i	$0.492776\pi$
$510$		0			0
$511$	−4.54494	−	3.34875i	−0.201056	−	0.148140i
$512$	2.28214	−	4.47894i	0.100857	−	0.197943i
$513$	20.4155	−	13.2579i	0.901364	−	0.585353i
$514$	−0.577923	+	0.122841i	−0.0254911	+	0.00541830i
$515$		0			0
$516$	−4.14848	+	19.5171i	−0.182627	+	0.859191i
$517$	−1.66446	+	10.5090i	−0.0732027	+	0.462184i
$518$	29.5794	−	14.8232i	1.29964	−	0.651293i
$519$	0.451584	+	0.621552i	0.0198223	+	0.0272831i
$520$		0			0
$521$	−11.9577	−	1.25680i	−0.523874	−	0.0550614i	−0.161099	−	0.986938i	$-0.551504\pi$
$521$	−11.9577	−	1.25680i	−0.523874	−	0.0550614i	−0.362775	+	0.931877i	$0.618171\pi$
$522$	−24.0168	+	19.4484i	−1.05119	+	0.851233i
$523$	1.25486	−	23.9442i	0.0548713	−	1.04701i	−0.822979	−	0.568071i	$-0.807690\pi$
$523$	1.25486	−	23.9442i	0.0548713	−	1.04701i	0.877850	−	0.478935i	$-0.158977\pi$
$524$	0.251771			0.0109987
$525$		0			0
$526$	−48.2012			−2.10167
$527$	0.123784	−	2.36194i	0.00539212	−	0.102888i
$528$	−40.5204	+	32.8128i	−1.76343	+	1.42799i
$529$	4.48096	+	0.470968i	0.194824	+	0.0204769i
$530$		0			0
$531$	−13.5344	−	18.6285i	−0.587342	−	0.808407i
$532$	−0.595233	+	10.0692i	−0.0258066	+	0.436554i
$533$	0.00199173	−	0.0125753i	8.62712e−5	−	0.000544695i
$534$	0.923615	−	4.34527i	0.0399687	−	0.188038i
$535$		0			0
$536$	−1.21597	+	0.258462i	−0.0525217	+	0.0111638i
$537$	30.0427	−	19.5099i	1.29644	−	0.841916i
$538$	15.2458	−	29.9216i	0.657294	−	1.29001i
$539$	−27.3789	+	2.50799i	−1.17929	+	0.108027i
$540$		0			0
$541$	18.7246	+	3.98003i	0.805031	+	0.171115i	0.592008	−	0.805932i	$-0.298336\pi$
$541$	18.7246	+	3.98003i	0.805031	+	0.171115i	0.213024	+	0.977047i	$0.431669\pi$
$542$	8.48091	−	3.25552i	0.364286	−	0.139836i
$543$	−60.7737	−	16.2843i	−2.60805	−	0.698825i
$544$	1.19812	+	11.3994i	0.0513690	+	0.488744i
$545$		0			0
$546$	−1.13212	+	0.111343i	−0.0484504	+	0.00476506i
$547$	1.95187	+	12.3236i	0.0834558	+	0.526919i	0.993630	+	0.112693i	$0.0359477\pi$
$547$	1.95187	+	12.3236i	0.0834558	+	0.526919i	−0.910174	+	0.414226i	$0.864052\pi$
$548$	−7.91201	−	0.414651i	−0.337984	−	0.0177130i
$549$	−15.9141	−	27.5641i	−0.679199	−	1.17641i
$550$		0			0
$551$	22.5633	+	13.0269i	0.961230	+	0.554967i
$552$	14.4858	+	28.4300i	0.616556	+	1.21006i
$553$	14.3955	+	38.2643i	0.612160	+	1.62716i
$554$	−5.63005	+	7.74910i	−0.239198	+	0.329228i
$555$		0			0
$556$	3.66039	−	8.22138i	0.155235	−	0.348664i
$557$	5.89390	−	21.9963i	0.249732	−	0.932014i	−0.721213	−	0.692713i	$-0.756415\pi$
$557$	5.89390	−	21.9963i	0.249732	−	0.932014i	0.970946	−	0.239301i	$-0.0769182\pi$
$558$	−3.21091	+	3.96515i	−0.135929	+	0.167858i
$559$	0.350558	+	1.07891i	0.0148270	+	0.0456329i
$560$		0			0
$561$	−11.1118	+	34.1985i	−0.469139	+	1.44386i
$562$	−7.54986	−	11.6258i	−0.318472	−	0.490403i
$563$	−29.1436	+	1.52735i	−1.22826	+	0.0643701i	−0.655397	−	0.755284i	$-0.727499\pi$
$563$	−29.1436	+	1.52735i	−1.22826	+	0.0643701i	−0.572858	+	0.819654i	$0.694165\pi$
$564$	−0.962327	−	4.52739i	−0.0405213	−	0.190638i
$565$		0			0
$566$	−23.2549	+	7.55597i	−0.977476	+	0.317601i
$567$	5.81822	+	3.01370i	0.244342	+	0.126563i
$568$	−1.59307	+	1.59307i	−0.0668436	+	0.0668436i
$569$	1.57943	−	0.166005i	0.0662130	−	0.00695927i	−0.0713640	−	0.997450i	$-0.522735\pi$
$569$	1.57943	−	0.166005i	0.0662130	−	0.00695927i	0.137577	+	0.990491i	$0.456069\pi$
$570$		0			0
$571$	−0.375690	+	3.57445i	−0.0157221	+	0.149586i	−0.999567	−	0.0294394i	$-0.990628\pi$
$571$	−0.375690	+	3.57445i	−0.0157221	+	0.149586i	0.983844	+	0.179025i	$0.0572945\pi$
$572$	0.0855211	−	0.222790i	0.00357582	−	0.00931532i
$573$	9.84838	−	5.01800i	0.411422	−	0.209630i
$574$	0.113145	+	0.550374i	0.00472258	+	0.0229722i
$575$		0			0
$576$	−9.32098	+	16.1444i	−0.388374	+	0.672683i
$577$	12.1657	−	18.7335i	0.506465	−	0.779887i	−0.489272	−	0.872131i	$-0.662737\pi$
$577$	12.1657	−	18.7335i	0.506465	−	0.779887i	0.995736	+	0.0922444i	$0.0294041\pi$
$578$	−5.88101	−	7.26245i	−0.244618	−	0.302078i
$579$	−7.67247	+	3.41601i	−0.318857	+	0.141964i
$580$		0			0
$581$	−27.9531	−	6.13722i	−1.15969	−	0.254615i
$582$	−35.4392	−	35.4392i	−1.46900	−	1.46900i
$583$	−35.8975	−	29.0692i	−1.48672	−	1.20392i
$584$	3.17991	−	3.53164i	0.131585	−	0.146140i
$585$		0			0
$586$	13.2943	−	11.9702i	0.549182	−	0.494486i
$587$	−38.6684	−	19.7026i	−1.59602	−	0.813211i	−0.999947	−	0.0102788i	$-0.996728\pi$
$587$	−38.6684	−	19.7026i	−1.59602	−	0.813211i	−0.596070	−	0.802933i	$-0.703272\pi$
$588$	10.7282	−	5.28678i	0.442422	−	0.218023i
$589$	4.09095	+	1.32923i	0.168565	+	0.0547699i
$590$		0			0
$591$	25.6015	+	23.0517i	1.05310	+	0.948218i
$592$	13.4409	+	35.0148i	0.552419	+	1.43910i
$593$	12.4912	−	3.34701i	0.512953	−	0.137445i	0.00694789	−	0.999976i	$-0.497788\pi$
$593$	12.4912	−	3.34701i	0.512953	−	0.137445i	0.506005	+	0.862531i	$0.331122\pi$
$594$	20.5621	−	14.9392i	0.843673	−	0.612964i
$595$		0			0
$596$	5.40284	+	3.92539i	0.221309	+	0.160790i
$597$	−11.0933	−	4.25833i	−0.454019	−	0.174282i
$598$	−0.692325	−	0.449601i	−0.0283113	−	0.0183855i
$599$	19.9444	−	11.5149i	0.814905	−	0.470485i	−0.0337516	−	0.999430i	$-0.510745\pi$
$599$	19.9444	−	11.5149i	0.814905	−	0.470485i	0.848656	+	0.528945i	$0.177412\pi$
$600$		0			0
$601$		−	14.0409i		−	0.572740i	−0.958119	−	0.286370i	$-0.907551\pi$
$601$		−	14.0409i		−	0.572740i	0.958119	−	0.286370i	$-0.0924486\pi$
$602$	−31.2456	−	39.1169i	−1.27347	−	1.59429i
$603$	2.45985	−	0.389602i	0.100173	−	0.0158658i
$604$	5.31174	+	11.9304i	0.216132	+	0.485440i
$605$		0			0
$606$	47.4483	+	21.1254i	1.92746	+	0.858159i
$607$	−10.2468	−	38.2415i	−0.415904	−	1.55218i	−0.783017	−	0.622000i	$-0.786320\pi$
$607$	−10.2468	−	38.2415i	−0.415904	−	1.55218i	0.367113	−	0.930176i	$-0.380346\pi$
$608$	−20.5892	−	3.26100i	−0.835001	−	0.132251i
$609$	0.206542	−	30.8920i	0.00836952	−	1.25181i
$610$		0			0
$611$	−0.176085	−	0.195562i	−0.00712364	−	0.00791160i
$612$	−0.489529	−	9.34078i	−0.0197881	−	0.377579i
$613$	−0.203103	−	3.87544i	−0.00820325	−	0.156527i	−0.999660	−	0.0260887i	$-0.991695\pi$
$613$	−0.203103	−	3.87544i	−0.00820325	−	0.156527i	0.991456	−	0.130439i	$-0.0416386\pi$
$614$	−12.4826	−	13.8633i	−0.503756	−	0.559478i
$615$		0			0
$616$	0.154736	−	23.1435i	0.00623450	−	0.932477i
$617$	27.5463	+	4.36290i	1.10897	+	0.175644i	0.683943	−	0.729536i	$-0.260264\pi$
$617$	27.5463	+	4.36290i	1.10897	+	0.175644i	0.425029	+	0.905180i	$0.360264\pi$
$618$	11.5378	+	43.0597i	0.464118	+	1.73211i
$619$	24.6623	+	10.9803i	0.991260	+	0.441337i	0.837302	−	0.546740i	$-0.184131\pi$
$619$	24.6623	+	10.9803i	0.991260	+	0.441337i	0.153958	+	0.988077i	$0.450798\pi$
$620$		0			0
$621$	−8.51918	−	19.1344i	−0.341863	−	0.767837i
$622$	−45.9911	+	7.28427i	−1.84408	+	0.292073i
$623$	1.65726	+	2.07476i	0.0663968	+	0.0831234i
$624$		−	1.28957i		−	0.0516239i
$625$		0			0
$626$	13.3561	−	7.71114i	0.533816	−	0.308199i
$627$	−54.8460	−	35.6174i	−2.19034	−	1.42242i
$628$	6.98035	+	2.67950i	0.278546	+	0.106924i
$629$	20.9260	+	15.2037i	0.834376	+	0.606209i
$630$		0			0
$631$	8.70119	−	6.32178i	0.346389	−	0.251666i	−0.400964	−	0.916094i	$-0.631325\pi$
$631$	8.70119	−	6.32178i	0.346389	−	0.251666i	0.747353	+	0.664428i	$0.231325\pi$
$632$	−33.2423	+	8.90724i	−1.32231	+	0.354311i
$633$	6.52549	+	16.9995i	0.259365	+	0.675668i
$634$	−9.39921	−	8.46309i	−0.373290	−	0.336112i
$635$		0			0
$636$	19.1105	+	6.20937i	0.757780	+	0.246217i
$637$	0.377941	−	0.565284i	0.0149746	−	0.0223974i
$638$	24.2379	+	12.3498i	0.959589	+	0.488935i
$639$	3.35424	−	3.02018i	0.132692	−	0.119476i
$640$		0			0
$641$	20.1580	−	22.3877i	0.796191	−	0.884260i	−0.199219	−	0.979955i	$-0.563841\pi$
$641$	20.1580	−	22.3877i	0.796191	−	0.884260i	0.995411	+	0.0956947i	$0.0305073\pi$
$642$	3.89407	+	3.15336i	0.153687	+	0.124453i
$643$	20.4056	+	20.4056i	0.804720	+	0.804720i	0.983829	−	0.179110i	$-0.0573217\pi$
$643$	20.4056	+	20.4056i	0.804720	+	0.804720i	−0.179110	+	0.983829i	$0.557322\pi$
$644$	8.47706	+	1.86118i	0.334043	+	0.0733407i
$645$		0			0
$646$	−30.2391	+	13.4633i	−1.18974	+	0.529707i
$647$	12.0473	+	14.8771i	0.473627	+	0.584880i	0.956837	−	0.290624i	$-0.0938628\pi$
$647$	12.0473	+	14.8771i	0.473627	+	0.584880i	−0.483211	+	0.875504i	$0.660529\pi$
$648$	−3.00412	+	4.62594i	−0.118013	+	0.181724i
$649$	−10.1343	+	17.5531i	−0.397805	+	0.689019i
$650$		0			0
$651$	−1.02704	−	4.99588i	−0.0402531	−	0.195804i
$652$	8.08188	−	4.11792i	0.316511	−	0.161270i
$653$	4.32563	−	11.2686i	0.169275	−	0.440976i	−0.822533	−	0.568718i	$-0.807440\pi$
$653$	4.32563	−	11.2686i	0.169275	−	0.440976i	0.991807	+	0.127742i	$0.0407729\pi$
$654$	1.35443	−	12.8866i	0.0529625	−	0.503905i
$655$		0			0
$656$	−0.633461	+	0.0665794i	−0.0247325	+	0.00259949i
$657$	−6.73225	+	6.73225i	−0.262650	+	0.262650i
$658$	10.3122	+	5.34145i	0.402010	+	0.208232i
$659$	−15.5052	+	5.03793i	−0.603995	+	0.196250i	−0.595022	−	0.803710i	$-0.702856\pi$
$659$	−15.5052	+	5.03793i	−0.603995	+	0.196250i	−0.00897383	+	0.999960i	$0.502856\pi$
$660$		0			0
$661$	−2.91594	−	13.7184i	−0.113417	−	0.533585i	−0.997769	−	0.0667642i	$-0.978732\pi$
$661$	−2.91594	−	13.7184i	−0.113417	−	0.533585i	0.884352	−	0.466821i	$-0.154601\pi$
$662$	1.67440	−	0.0877515i	0.0650774	−	0.00341056i
$663$	−0.484374	−	0.745871i	−0.0188115	−	0.0289672i
$664$	7.44463	−	22.9122i	0.288908	−	0.889166i
$665$		0			0
$666$	−17.2426	−	53.0674i	−0.668138	−	2.05632i
$667$	14.1079	−	17.4218i	0.546259	−	0.674574i
$668$	−0.270798	+	1.01063i	−0.0104775	+	0.0391025i
$669$	−17.1222	+	38.4571i	−0.661983	+	1.48684i
$670$		0			0
$671$	−16.4678	+	22.6659i	−0.635731	+	0.875008i
$672$	8.70342	+	23.1343i	0.335742	+	0.892426i
$673$	−0.128682	−	0.252552i	−0.00496031	−	0.00973515i	0.888513	−	0.458851i	$-0.151739\pi$
$673$	−0.128682	−	0.252552i	−0.00496031	−	0.00973515i	−0.893473	+	0.449116i	$0.851739\pi$
$674$	−2.62652	−	1.51642i	−0.101170	−	0.0584103i
$675$		0			0
$676$	−4.06262	−	7.03667i	−0.156255	−	0.270641i
$677$	−33.4491	−	1.75299i	−1.28555	−	0.0673729i	−0.602723	−	0.797951i	$-0.705917\pi$
$677$	−33.4491	−	1.75299i	−1.28555	−	0.0673729i	−0.682829	+	0.730578i	$0.739251\pi$
$678$	3.23488	+	20.4242i	0.124235	+	0.784387i
$679$	29.8144	−	2.93222i	1.14417	−	0.112528i
$680$		0			0
$681$	−3.78337	−	35.9963i	−0.144979	−	1.37938i
$682$	4.33814	+	1.16240i	0.166116	+	0.0445106i
$683$	21.1225	−	8.10815i	0.808228	−	0.310250i	0.0810601	−	0.996709i	$-0.474169\pi$
$683$	21.1225	−	8.10815i	0.808228	−	0.310250i	0.727168	+	0.686460i	$0.240836\pi$
$684$	16.6393	+	3.53680i	0.636221	+	0.135233i
$685$		0			0
$686$	−6.82667	+	29.2221i	−0.260644	+	1.11571i
$687$	−5.14374	+	10.0951i	−0.196246	+	0.385154i
$688$	47.5968	−	30.9097i	1.81461	−	1.17842i
$689$	1.11747	−	0.237526i	0.0425724	−	0.00904903i
$690$		0			0
$691$	−5.91700	+	27.8373i	−0.225093	+	1.05898i	0.709897	+	0.704306i	$0.248742\pi$
$691$	−5.91700	+	27.8373i	−0.225093	+	1.05898i	−0.934990	+	0.354674i	$0.884592\pi$
$692$	−0.0275190	+	0.173748i	−0.00104612	+	0.00660492i
$693$	−2.73619	+	46.2863i	−0.103939	+	1.75827i
$694$	1.89358	+	2.60628i	0.0718792	+	0.0989332i
$695$		0			0
$696$	25.8629	+	2.71830i	0.980332	+	0.103037i
$697$	−0.341379	+	0.276443i	−0.0129307	+	0.0104710i
$698$	−0.370596	+	7.07139i	−0.0140273	+	0.267656i
$699$	−70.3907			−2.66242
$700$		0			0
$701$	29.7376			1.12317			0.561587	−	0.827418i	$-0.310191\pi$
$701$	29.7376			1.12317			0.561587	+	0.827418i	$0.310191\pi$
$702$	−0.0328989	+	0.627749i	−0.00124169	+	0.0236928i
$703$	−36.5582	+	29.6042i	−1.37882	+	1.11654i
$704$	16.3196	+	1.71525i	0.615067	+	0.0646461i
$705$		0			0
$706$	17.7863	+	24.4807i	0.669396	+	0.921345i
$707$	−27.7560	+	13.9094i	−1.04387	+	0.523118i
$708$	1.37930	−	8.70856i	0.0518373	−	0.327288i
$709$	1.79995	−	8.46811i	0.0675986	−	0.318026i	−0.931337	−	0.364159i	$-0.881356\pi$
$709$	1.79995	−	8.46811i	0.0675986	−	0.318026i	0.998935	+	0.0461328i	$0.0146897\pi$
$710$		0			0
$711$	67.4409	−	14.3350i	2.52923	−	0.537605i
$712$	−1.87469	+	1.21744i	−0.0702569	+	0.0456254i
$713$	1.68028	−	3.29773i	0.0629269	−	0.123501i
$714$	31.5976	+	23.2814i	1.18251	+	0.871283i
$715$		0			0
$716$	8.02292	+	1.70532i	0.299830	+	0.0637309i
$717$	−1.65961	+	0.637066i	−0.0619794	+	0.0237917i
$718$	26.1589	+	7.00926i	0.976242	+	0.261583i
$719$	2.82649	+	26.8922i	0.105410	+	1.00291i	0.911551	+	0.411187i	$0.134886\pi$
$719$	2.82649	+	26.8922i	0.105410	+	1.00291i	−0.806141	+	0.591724i	$0.798448\pi$
$720$		0			0
$721$	−24.2700	−	11.0007i	−0.903863	−	0.409689i
$722$	−4.60121	−	29.0509i	−0.171239	−	1.08116i
$723$	3.13192	+	0.164137i	0.116477	+	0.00610431i
$724$	−7.20316	−	12.4762i	−0.267703	−	0.463676i
$725$		0			0
$726$	−16.9672	−	9.79602i	−0.629712	−	0.363565i
$727$	7.90873	+	15.5218i	0.293318	+	0.575670i	0.989893	−	0.141814i	$-0.0452936\pi$
$727$	7.90873	+	15.5218i	0.293318	+	0.575670i	−0.696575	+	0.717484i	$0.745294\pi$
$728$	0.442430	+	0.363198i	0.0163976	+	0.0134610i
$729$	25.7325	−	35.4177i	0.953055	−	1.31177i
$730$		0			0
$731$	15.9195	−	35.7557i	0.588803	−	1.32247i
$732$	3.15439	−	11.7724i	0.116590	−	0.435119i
$733$	−28.8928	+	35.6797i	−1.06718	+	1.31786i	−0.121562	+	0.992584i	$0.538790\pi$
$733$	−28.8928	+	35.6797i	−1.06718	+	1.31786i	−0.945619	+	0.325275i	$0.894543\pi$
$734$	4.83698	+	14.8867i	0.178536	+	0.549477i
$735$		0			0
$736$	−5.54266	+	17.0586i	−0.204305	+	0.628787i
$737$	−1.19399	−	1.83858i	−0.0439812	−	0.0677251i
$738$	0.946304	−	0.0495937i	0.0348339	−	0.00182557i
$739$	5.11747	+	24.0758i	0.188249	+	0.885642i	0.966296	+	0.257435i	$0.0828774\pi$
$739$	5.11747	+	24.0758i	0.188249	+	0.885642i	−0.778046	+	0.628207i	$0.783789\pi$
$740$		0			0
$741$	1.53827	−	0.499813i	0.0565096	−	0.0183611i
$742$	−42.4664	+	27.1761i	−1.55899	+	0.997665i
$743$	10.2323	−	10.2323i	0.375388	−	0.375388i	−0.494047	−	0.869435i	$-0.664483\pi$
$743$	10.2323	−	10.2323i	0.375388	−	0.375388i	0.869435	+	0.494047i	$0.164483\pi$
$744$	4.26995	−	0.448790i	0.156544	−	0.0164534i
$745$		0			0
$746$	0.832965	−	7.92513i	0.0304970	−	0.290160i
$747$	−17.2966	+	45.0593i	−0.632851	+	1.64863i
$748$	−7.33605	+	3.73790i	−0.268233	+	0.136671i
$749$	−2.93380	+	0.603126i	−0.107199	+	0.0220377i
$750$		0			0
$751$	5.60583	−	9.70959i	0.204560	−	0.354308i	−0.745433	−	0.666581i	$-0.767757\pi$
$751$	5.60583	−	9.70959i	0.204560	−	0.354308i	0.949992	+	0.312273i	$0.101090\pi$
$752$	−7.17016	+	11.0411i	−0.261469	+	0.402627i
$753$	−23.8080	−	29.4005i	−0.867613	−	1.07141i
$754$	−0.614634	+	0.273653i	−0.0223836	+	0.00996584i
$755$		0			0
$756$	−2.00020	−	6.29898i	−0.0727467	−	0.229092i
$757$	34.2009	+	34.2009i	1.24305	+	1.24305i	0.958728	+	0.284326i	$0.0917697\pi$
$757$	34.2009	+	34.2009i	1.24305	+	1.24305i	0.284326	+	0.958728i	$0.408230\pi$
$758$	−15.8511	−	12.8360i	−0.575740	−	0.466225i
$759$	−37.6514	+	41.8161i	−1.36666	+	1.51783i
$760$		0			0
$761$	12.7666	−	11.4951i	0.462789	−	0.416697i	−0.404472	−	0.914550i	$-0.632545\pi$
$761$	12.7666	−	11.4951i	0.462789	−	0.416697i	0.867261	+	0.497853i	$0.165878\pi$
$762$	65.3109	+	33.2776i	2.36597	+	1.20552i
$763$	5.44005	+	5.51328i	0.196943	+	0.199594i
$764$	2.40697	+	0.782073i	0.0870812	+	0.0282944i
$765$		0			0
$766$	21.5918	+	19.4414i	0.780145	+	0.702445i
$767$	−0.179649	−	0.468000i	−0.00648673	−	0.0168985i
$768$	−36.1387	+	9.68333i	−1.30404	+	0.349417i
$769$	15.2142	−	11.0538i	0.548638	−	0.398609i	−0.278645	−	0.960394i	$-0.589885\pi$
$769$	15.2142	−	11.0538i	0.548638	−	0.398609i	0.827283	+	0.561785i	$0.189885\pi$
$770$		0			0
$771$	−0.805836	−	0.585474i	−0.0290215	−	0.0210853i
$772$	−1.79530	−	0.689152i	−0.0646144	−	0.0248031i
$773$	27.1011	+	17.5997i	0.974759	+	0.633016i	0.930611	−	0.366009i	$-0.119276\pi$
$773$	27.1011	+	17.5997i	0.974759	+	0.633016i	0.0441474	+	0.999025i	$0.485943\pi$
$774$	−73.1203	+	42.2160i	−2.62825	+	1.51742i
$775$		0			0
$776$			25.2188i			0.905302i
$777$	51.9387	+	20.3368i	1.86329	+	0.729580i
$778$	−19.0873	+	3.02314i	−0.684314	+	0.108385i
$779$	−0.324938	−	0.729823i	−0.0116421	−	0.0261486i
$780$		0			0
$781$	−3.62956	−	1.61599i	−0.129876	−	0.0578245i
$782$	7.37143	+	27.5106i	0.263602	+	0.983776i
$783$	−16.8606	−	2.67045i	−0.602548	−	0.0954343i
$784$	−32.2097	−	10.9438i	−1.15035	−	0.390851i
$785$		0			0
$786$	1.19218	+	1.32405i	0.0425235	+	0.0472271i
$787$	0.695360	+	13.2683i	0.0247869	+	0.472962i	0.982619	+	0.185634i	$0.0594338\pi$
$787$	0.695360	+	13.2683i	0.0247869	+	0.472962i	−0.957832	+	0.287328i	$0.907233\pi$
$788$	0.412831	+	7.87728i	0.0147065	+	0.280617i
$789$	−54.3742	−	60.3886i	−1.93577	−	2.14989i
$790$		0			0
$791$	−10.6631	−	6.25178i	−0.379137	−	0.222288i
$792$	−38.5512	−	6.10592i	−1.36986	−	0.216964i
$793$	−0.179343	−	0.669316i	−0.00636865	−	0.0237681i
$794$	55.5398	+	24.7279i	1.97104	+	0.877561i
$795$		0			0
$796$	−1.10663	−	2.48554i	−0.0392236	−	0.0880976i
$797$	−37.9724	+	6.01424i	−1.34505	+	0.213035i	−0.787094	−	0.616833i	$-0.788415\pi$
$797$	−37.9724	+	6.01424i	−1.34505	+	0.213035i	−0.557959	+	0.829869i	$0.688415\pi$
$798$	−55.7715	+	44.5488i	−1.97429	+	1.57701i
$799$			9.07923i			0.321200i
$800$		0			0
$801$	3.87829	−	2.23913i	0.137033	−	0.0791159i
$802$	0.290075	+	0.188377i	0.0102429	+	0.00665182i
$803$	7.82402	+	3.00336i	0.276104	+	0.105986i
$804$	0.771531	+	0.560550i	0.0272098	+	0.0197691i
$805$		0			0
$806$	−0.0898647	+	0.0652905i	−0.00316535	+	0.00229976i
$807$	54.6854	−	14.6529i	1.92502	−	0.515807i
$808$	−9.36582	−	24.3988i	−0.329488	−	0.858347i
$809$	0.858767	+	0.773238i	0.0301927	+	0.0271856i	0.684089	−	0.729399i	$-0.260200\pi$
$809$	0.858767	+	0.773238i	0.0301927	+	0.0271856i	−0.653896	+	0.756584i	$0.726867\pi$
$810$		0			0
$811$	−11.7589	−	3.82070i	−0.412911	−	0.134163i	0.0951926	−	0.995459i	$-0.469653\pi$
$811$	−11.7589	−	3.82070i	−0.412911	−	0.134163i	−0.508104	+	0.861296i	$0.669653\pi$
$812$	5.03507	−	4.96819i	0.176696	−	0.174349i
$813$	13.6457	+	6.95282i	0.478575	+	0.243846i
$814$	−36.5004	+	32.8651i	−1.27934	+	1.15192i
$815$		0			0
$816$	−29.7709	+	33.0639i	−1.04219	+	1.15747i
$817$	55.3185	+	44.7960i	1.93535	+	1.56722i
$818$	−36.5978	−	36.5978i	−1.27961	−	1.27961i
$819$	−0.847078	−	0.773030i	−0.0295993	−	0.0270118i
$820$		0			0
$821$	−33.8881	+	15.0880i	−1.18270	+	0.526574i	−0.901376	−	0.433038i	$-0.857442\pi$
$821$	−33.8881	+	15.0880i	−1.18270	+	0.526574i	−0.281328	+	0.959612i	$0.590775\pi$
$822$	−35.2840	−	43.5721i	−1.23067	−	1.51975i
$823$	−27.3912	+	42.1788i	−0.954799	+	1.47026i	−0.0737269	+	0.997278i	$0.523489\pi$
$823$	−27.3912	+	42.1788i	−0.954799	+	1.47026i	−0.881072	+	0.472983i	$0.843177\pi$
$824$	11.2156	−	19.4260i	0.390714	−	0.676737i
$825$		0			0
$826$	14.6929	+	16.5392i	0.511232	+	0.575472i
$827$	−17.5564	+	8.94542i	−0.610495	+	0.311063i	−0.731765	−	0.681557i	$-0.761303\pi$
$827$	−17.5564	+	8.94542i	−0.610495	+	0.311063i	0.121270	+	0.992620i	$0.461303\pi$
$828$	5.24539	−	13.6647i	0.182290	−	0.474881i
$829$	−2.37030	+	22.5519i	−0.0823239	+	0.783260i	0.873004	+	0.487713i	$0.162169\pi$
$829$	−2.37030	+	22.5519i	−0.0823239	+	0.783260i	−0.955328	+	0.295547i	$0.904498\pi$
$830$		0			0
$831$	−16.0595	+	1.68792i	−0.557097	+	0.0585533i
$832$	−0.286979	+	0.286979i	−0.00994922	+	0.00994922i
$833$	−22.7404	+	5.76850i	−0.787907	+	0.199867i
$834$	60.5681	−	19.6798i	2.09730	−	0.681454i
$835$		0			0
$836$	−3.11324	−	14.6467i	−0.107674	−	0.506565i
$837$	−2.81450	+	0.147502i	−0.0972835	+	0.00509841i
$838$	−9.35442	−	14.4045i	−0.323143	−	0.497597i
$839$	−5.77620	+	17.7773i	−0.199417	+	0.613742i	0.800480	+	0.599360i	$0.204578\pi$
$839$	−5.77620	+	17.7773i	−0.199417	+	0.613742i	−0.999897	+	0.0143819i	$0.995422\pi$
$840$		0			0
$841$	3.31550	+	10.2041i	0.114328	+	0.351864i
$842$	−8.98347	+	11.0937i	−0.309591	+	0.382313i
$843$	6.04853	−	22.5734i	0.208323	−	0.777470i
$844$	−1.69581	+	3.80886i	−0.0583723	+	0.131106i
$845$		0			0
$846$	11.5122	−	15.8452i	0.395799	−	0.544770i
$847$	10.9611	−	4.12369i	0.376627	−	0.141692i
$848$	−25.9471	−	50.9240i	−0.891025	−	1.74874i
$849$	−35.6995	−	20.6111i	−1.22520	−	0.707372i
$850$		0			0
$851$	20.2381	+	35.0534i	0.693752	+	1.20161i
$852$	1.72597	+	0.0904541i	0.0591306	+	0.00309891i
$853$	5.30806	+	33.5138i	0.181744	+	1.14749i	0.894828	+	0.446410i	$0.147298\pi$
$853$	5.30806	+	33.5138i	0.181744	+	1.14749i	−0.713084	+	0.701079i	$0.752702\pi$
$854$	17.8086	+	24.8593i	0.609399	+	0.850668i
$855$		0			0
$856$	−0.263549	−	2.50750i	−0.00900793	−	0.0857047i
$857$	8.64649	+	2.31682i	0.295358	+	0.0791410i	0.403455	−	0.914999i	$-0.367809\pi$
$857$	8.64649	+	2.31682i	0.295358	+	0.0791410i	−0.108097	+	0.994140i	$0.534476\pi$
$858$	1.57659	−	0.605196i	0.0538239	−	0.0206611i
$859$	22.5915	+	4.80196i	0.770810	+	0.163841i	0.576498	−	0.817099i	$-0.304419\pi$
$859$	22.5915	+	4.80196i	0.770810	+	0.163841i	0.194313	+	0.980940i	$0.437752\pi$
$860$		0			0
$861$	−0.561898	+	0.762611i	−0.0191494	+	0.0259897i
$862$	−4.50806	+	8.84757i	−0.153545	+	0.301349i
$863$	3.09204	−	2.00799i	0.105254	−	0.0683529i	−0.490939	−	0.871194i	$-0.663346\pi$
$863$	3.09204	−	2.00799i	0.105254	−	0.0683529i	0.596193	+	0.802841i	$0.296679\pi$
$864$	13.3599	−	2.83974i	0.454513	−	0.0966098i
$865$		0			0
$866$	12.0353	−	56.6218i	0.408977	−	1.92409i
$867$	2.46454	−	15.5605i	0.0837003	−	0.528463i
$868$	0.642582	−	0.975154i	0.0218107	−	0.0330989i
$869$	−35.6731	−	49.0998i	−1.21013	−	1.66560i
$870$		0			0
$871$	0.0539235	+	0.00566759i	0.00182713	+	0.000192039i
$872$	−5.06701	+	4.10318i	−0.171590	+	0.138951i
$873$	2.64421	−	50.4546i	0.0894931	−	1.70763i
$874$	−51.7975			−1.75208
$875$		0			0
$876$	−3.64571			−0.123177
$877$	1.57330	−	30.0203i	0.0531265	−	1.01371i	−0.833877	−	0.551951i	$-0.813884\pi$
$877$	1.57330	−	30.0203i	0.0531265	−	1.01371i	0.887003	−	0.461763i	$-0.152783\pi$
$878$	−32.8362	+	26.5902i	−1.10817	+	0.897376i
$879$	29.9937	+	3.15246i	1.01166	+	0.106330i
$880$		0			0
$881$	26.3597	+	36.2810i	0.888079	+	1.22234i	0.974117	+	0.226045i	$0.0725795\pi$
$881$	26.3597	+	36.2810i	0.888079	+	1.22234i	−0.0860376	+	0.996292i	$0.527421\pi$
$882$	47.0012	+	18.7669i	1.58261	+	0.631915i
$883$	4.53057	−	28.6049i	0.152466	−	0.962631i	−0.786242	−	0.617918i	$-0.787976\pi$
$883$	4.53057	−	28.6049i	0.152466	−	0.962631i	0.938708	−	0.344713i	$-0.112024\pi$
$884$	0.0423382	−	0.199185i	0.00142399	−	0.00669933i
$885$		0			0
$886$	−53.6817	+	11.4104i	−1.80347	+	0.383340i
$887$	20.2001	−	13.1181i	0.678253	−	0.440463i	−0.159000	−	0.987279i	$-0.550827\pi$
$887$	20.2001	−	13.1181i	0.678253	−	0.440463i	0.837253	+	0.546816i	$0.184160\pi$
$888$	−21.3167	+	41.8363i	−0.715341	+	1.40394i
$889$	−40.1452	+	17.5532i	−1.34643	+	0.588714i
$890$		0			0
$891$	−9.51455	−	2.02238i	−0.318749	−	0.0677523i
$892$	−8.99869	+	3.45427i	−0.301298	+	0.115658i
$893$	−15.9494	−	4.27364i	−0.533728	−	0.143012i
$894$	4.93994	+	47.0004i	0.165216	+	1.57193i
$895$		0			0
$896$	14.8652	−	32.7960i	0.496613	−	1.09564i
$897$	−0.217708	−	1.37455i	−0.00726906	−	0.0458950i
$898$	−28.8423	−	1.51156i	−0.962481	−	0.0504415i
$899$	−1.50825	−	2.61236i	−0.0503029	−	0.0871271i
$900$		0			0
$901$	−34.1351	−	19.7079i	−1.13720	−	0.656565i
$902$	−0.378683	−	0.743207i	−0.0126088	−	0.0247461i
$903$	13.7604	−	83.2723i	0.457916	−	2.77113i
$904$	6.11603	−	8.41800i	0.203416	−	0.279978i
$905$		0			0
$906$	−37.5889	+	84.4261i	−1.24881	+	2.80487i
$907$	−0.937438	+	3.49857i	−0.0311271	+	0.116168i	−0.979741	−	0.200267i	$-0.935819\pi$
$907$	−0.937438	+	3.49857i	−0.0311271	+	0.116168i	0.948614	+	0.316435i	$0.102486\pi$
$908$	5.21551	−	6.44061i	0.173083	−	0.213739i
$909$	16.1797	+	49.7961i	0.536648	+	1.65163i
$910$		0			0
$911$	2.97054	−	9.14238i	0.0984183	−	0.302900i	−0.889711	−	0.456524i	$-0.849094\pi$
$911$	2.97054	−	9.14238i	0.0984183	−	0.302900i	0.988129	+	0.153623i	$0.0490943\pi$
$912$	−44.0699	−	67.8617i	−1.45930	−	2.24713i
$913$	42.4268	−	2.22349i	1.40412	−	0.0735869i
$914$	−2.87433	−	13.5226i	−0.0950743	−	0.447289i
$915$		0			0
$916$	−2.46728	+	0.801669i	−0.0815213	+	0.0264879i
$917$	−1.06388	+	0.0486256i	−0.0351325	+	0.00160576i
$918$	15.3357	−	15.3357i	0.506154	−	0.506154i
$919$	7.32146	−	0.769517i	0.241513	−	0.0253840i	0.0170013	−	0.999855i	$-0.494588\pi$
$919$	7.32146	−	0.769517i	0.241513	−	0.0253840i	0.224511	+	0.974471i	$0.427921\pi$
$920$		0			0
$921$	3.28740	−	31.2775i	0.108323	−	1.03063i
$922$	15.4011	−	40.1211i	0.507207	−	1.32132i
$923$	0.0875541	−	0.0446111i	0.00288188	−	0.00146839i
$924$	−13.2736	+	11.7918i	−0.436668	+	0.387923i
$925$		0			0
$926$	18.5411	−	32.1142i	0.609300	−	1.05534i
$927$	−24.4756	+	37.6891i	−0.803884	+	1.23787i
$928$	9.19975	+	11.3607i	0.301996	+	0.372935i
$929$	−53.5074	+	23.8230i	−1.75552	+	0.781608i	−0.765034	+	0.643989i	$0.777278\pi$
$929$	−53.5074	+	23.8230i	−1.75552	+	0.781608i	−0.990485	+	0.137618i	$0.956055\pi$
$930$		0			0
$931$	0.570514	−	42.6632i	0.0186978	−	1.39823i
$932$	−11.3968	−	11.3968i	−0.373313	−	0.373313i
$933$	−61.0071	−	49.4026i	−1.99728	−	1.61737i
$934$	−9.66765	+	10.7370i	−0.316335	+	0.351326i
$935$		0			0
$936$	0.717404	−	0.645953i	0.0234491	−	0.0211136i
$937$	4.14402	+	2.11148i	0.135379	+	0.0689791i	0.520368	−	0.853942i	$-0.325795\pi$
$937$	4.14402	+	2.11148i	0.135379	+	0.0689791i	−0.384989	+	0.922921i	$0.625795\pi$
$938$	−2.31539	+	0.603844i	−0.0756002	+	0.0197162i
$939$	24.7274	+	8.03442i	0.806948	+	0.262193i
$940$		0			0
$941$	21.7072	+	19.5452i	0.707634	+	0.637157i	0.942242	−	0.334933i	$-0.108714\pi$
$941$	21.7072	+	19.5452i	0.707634	+	0.637157i	−0.234608	+	0.972090i	$0.575381\pi$
$942$	18.9617	+	49.3969i	0.617806	+	1.60944i
$943$	−0.663969	+	0.177910i	−0.0216218	+	0.00579355i
$944$	−20.2890	+	14.7408i	−0.660350	+	0.479773i
$945$		0			0
$946$	60.1267	+	43.6846i	1.95489	+	1.42031i
$947$	−5.68779	−	2.18334i	−0.184828	−	0.0709490i	0.264194	−	0.964470i	$-0.414894\pi$
$947$	−5.68779	−	2.18334i	−0.184828	−	0.0709490i	−0.449022	+	0.893521i	$0.648228\pi$
$948$	22.1420	+	14.3792i	0.719139	+	0.467015i
$949$	−0.179507	+	0.103638i	−0.00582703	+	0.00336424i
$950$		0			0
$951$		−	21.3227i		−	0.691435i
$952$	−2.95896	−	19.5262i	−0.0959003	−	0.632847i
$953$	5.50713	−	0.872243i	0.178393	−	0.0282547i	−0.0665986	−	0.997780i	$-0.521215\pi$
$953$	5.50713	−	0.872243i	0.178393	−	0.0282547i	0.244992	+	0.969525i	$0.421215\pi$
$954$	34.5840	+	77.6770i	1.11970	+	2.51488i
$955$		0			0
$956$	−0.371849	−	0.165558i	−0.0120265	−	0.00535452i
$957$	11.8696	+	44.2978i	0.383688	+	1.43194i
$958$	3.83049	+	0.606690i	0.123758	+	0.0196013i
$959$	33.5130	+	0.224067i	1.08219	+	0.00723549i
$960$		0			0
$961$	20.4098	+	22.6674i	0.658381	+	0.731206i
$962$	−0.0635764	−	1.21311i	−0.00204979	−	0.0391122i
$963$	0.264362	+	5.04433i	0.00851895	+	0.162551i
$964$	0.480505	+	0.533655i	0.0154760	+	0.0171879i
$965$		0			0
$966$	30.3524	+	53.3931i	0.976572	+	1.71790i
$967$	−58.4215	−	9.25305i	−1.87871	−	0.297558i	−0.891016	−	0.453972i	$-0.850007\pi$
$967$	−58.4215	−	9.25305i	−1.87871	−	0.297558i	−0.987692	+	0.156414i	$0.950007\pi$
$968$	2.55154	+	9.52247i	0.0820095	+	0.306064i
$969$	−50.9791	−	22.6974i	−1.63769	−	0.729145i
$970$		0			0
$971$	−21.4670	−	48.2157i	−0.688909	−	1.54731i	−0.830273	−	0.557357i	$-0.811815\pi$
$971$	−21.4670	−	48.2157i	−0.688909	−	1.54731i	0.141364	−	0.989958i	$-0.454851\pi$
$972$	11.5809	−	1.83423i	0.371458	−	0.0588331i
$973$	−13.8795	+	35.4471i	−0.444956	+	1.13638i
$974$		−	7.85203i		−	0.251595i
$975$		0			0
$976$	−30.0211	+	17.3327i	−0.960952	+	0.554806i
$977$	11.0553	+	7.17937i	0.353689	+	0.229688i	0.709238	−	0.704969i	$-0.249039\pi$
$977$	11.0553	+	7.17937i	0.353689	+	0.229688i	−0.355549	+	0.934658i	$0.615706\pi$
$978$	59.9247	+	23.0029i	1.91618	+	0.735553i
$979$	−3.18912	−	2.31703i	−0.101925	−	0.0740525i
$980$		0			0
$981$	10.5677	−	7.67785i	0.337399	−	0.245135i
$982$	46.5975	−	12.4858i	1.48699	−	0.398436i
$983$	19.2414	+	50.1256i	0.613706	+	1.59876i	0.789103	+	0.614260i	$0.210546\pi$
$983$	19.2414	+	50.1256i	0.613706	+	1.59876i	−0.175398	+	0.984498i	$0.556121\pi$
$984$	−0.592586	−	0.533567i	−0.0188910	−	0.0170095i
$985$		0			0
$986$	22.0765	+	7.17309i	0.703059	+	0.228438i
$987$	4.94079	+	18.9451i	0.157267	+	0.603028i
$988$	0.329979	+	0.168133i	0.0104980	+	0.00534902i
$989$	45.5154	−	40.9823i	1.44731	−	1.30316i
$990$		0			0
$991$	7.06342	−	7.84472i	0.224377	−	0.249196i	−0.620437	−	0.784257i	$-0.713045\pi$
$991$	7.06342	−	7.84472i	0.224377	−	0.249196i	0.844814	+	0.535061i	$0.179711\pi$
$992$	1.87565	+	1.51887i	0.0595519	+	0.0482242i
$993$	1.99877	+	1.99877i	0.0634291	+	0.0634291i
$994$	−2.92320	+	3.20322i	−0.0927184	+	0.101600i
$995$		0			0
$996$	−16.8838	+	7.51714i	−0.534983	+	0.238190i
$997$	37.6753	+	46.5252i	1.19319	+	1.47347i	0.843940	+	0.536437i	$0.180230\pi$
$997$	37.6753	+	46.5252i	1.19319	+	1.47347i	0.349249	+	0.937030i	$0.386437\pi$
$998$	34.3269	−	52.8588i	1.08660	−	1.67321i
$999$	15.4110	−	26.6927i	0.487584	−	0.844520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.257.5		288
5.2	odd	4		175.2.x.a.103.5	yes	288
5.3	odd	4		875.2.bb.c.243.14		288
5.4	even	2		875.2.bb.b.257.14		288
7.3	odd	6	inner	875.2.bb.a.507.5		288
25.6	even	5		875.2.bb.c.607.5		288
25.8	odd	20	inner	875.2.bb.a.768.5		288
25.17	odd	20		875.2.bb.b.768.14		288
25.19	even	10		175.2.x.a.117.14	yes	288
35.3	even	12		875.2.bb.c.493.5		288
35.17	even	12		175.2.x.a.3.14	✓	288
35.24	odd	6		875.2.bb.b.507.14		288
175.17	even	60		875.2.bb.b.143.14		288
175.31	odd	30		875.2.bb.c.857.14		288
175.94	odd	30		175.2.x.a.17.5	yes	288
175.108	even	60	inner	875.2.bb.a.143.5		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.14	✓	288	35.17	even	12
175.2.x.a.17.5	yes	288	175.94	odd	30
175.2.x.a.103.5	yes	288	5.2	odd	4
175.2.x.a.117.14	yes	288	25.19	even	10
875.2.bb.a.143.5		288	175.108	even	60	inner
875.2.bb.a.257.5		288	1.1	even	1	trivial
875.2.bb.a.507.5		288	7.3	odd	6	inner
875.2.bb.a.768.5		288	25.8	odd	20	inner
875.2.bb.b.143.14		288	175.17	even	60
875.2.bb.b.257.14		288	5.4	even	2
875.2.bb.b.507.14		288	35.24	odd	6
875.2.bb.b.768.14		288	25.17	odd	20
875.2.bb.c.243.14		288	5.3	odd	4
875.2.bb.c.493.5		288	35.3	even	12
875.2.bb.c.607.5		288	25.6	even	5
875.2.bb.c.857.14		288	175.31	odd	30

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0848016 + 1.61811i) q^{2} +(-2.12290 + 1.71909i) q^{3} +(-0.622046 - 0.0653797i) q^{4} +(-2.60166 - 3.58087i) q^{6} +(2.64114 + 0.156130i) q^{7} +(-0.348409 + 2.19977i) q^{8} +(0.927701 - 4.36449i) q^{9} +(-3.84181 + 0.816603i) q^{11} +(1.43294 - 0.930561i) q^{12} +(0.0441012 - 0.0865535i) q^{13} +(-0.476608 + 4.26042i) q^{14} +(-4.75353 - 1.01039i) q^{16} +(-3.12891 + 1.20108i) q^{17} +(6.98356 + 1.87124i) q^{18} +(-0.637130 - 6.06189i) q^{19} +(-5.87529 + 4.20892i) q^{21} +(-0.995562 - 6.28573i) q^{22} +(-5.23739 - 0.274480i) q^{23} +(-3.04197 - 5.26884i) q^{24} +(0.136313 + 0.0787005i) q^{26} +(1.81310 + 3.55840i) q^{27} +(-1.63270 - 0.269797i) q^{28} +(-2.51245 + 3.45809i) q^{29} +(-0.287036 + 0.644694i) q^{31} +(0.885159 - 3.30346i) q^{32} +(6.75198 - 8.33800i) q^{33} +(-1.67814 - 5.16477i) q^{34} +(-0.862422 + 2.65426i) q^{36} +(-4.20336 - 6.47261i) q^{37} +(9.86284 - 0.516889i) q^{38} +(0.0551709 + 0.259559i) q^{39} +(0.124652 - 0.0405019i) q^{41} +(-6.31226 - 9.86378i) q^{42} +(-8.25770 + 8.25770i) q^{43} +(2.44318 - 0.256788i) q^{44} +(0.888279 - 8.45141i) q^{46} +(0.970816 - 2.52906i) q^{47} +(11.8282 - 6.02679i) q^{48} +(6.95125 + 0.824720i) q^{49} +(4.57761 - 7.92865i) q^{51} +(-0.0330918 + 0.0509570i) q^{52} +(7.40118 + 9.13970i) q^{53} +(-5.91164 + 2.63203i) q^{54} +(-1.26365 + 5.75550i) q^{56} +(11.7735 + 11.7735i) q^{57} +(-5.38252 - 4.35867i) q^{58} +(3.45304 - 3.83499i) q^{59} +(5.30099 - 4.77304i) q^{61} +(-1.01885 - 0.519128i) q^{62} +(3.13162 - 11.3824i) q^{63} +(-3.97346 - 1.29105i) q^{64} +(12.9192 + 11.6325i) q^{66} +(0.200027 + 0.521089i) q^{67} +(2.02485 - 0.542557i) q^{68} +(11.5903 - 8.42087i) q^{69} +(0.818370 + 0.594581i) q^{71} +(9.27765 + 3.56136i) q^{72} +(-1.78952 - 1.16213i) q^{73} +(10.8299 - 6.25262i) q^{74} +3.81243i q^{76} +(-10.2743 + 1.55694i) q^{77} +(-0.424673 + 0.0672616i) q^{78} +(6.28497 + 14.1163i) q^{79} +(2.26247 + 1.00731i) q^{81} +(0.0549659 + 0.205136i) q^{82} +(-10.6837 - 1.69214i) q^{83} +(3.92988 - 2.23402i) q^{84} +(-12.6616 - 14.0621i) q^{86} +(-0.611092 - 11.6603i) q^{87} +(-0.457814 - 8.73562i) q^{88} +(0.671570 + 0.745854i) q^{89} +(0.129991 - 0.221714i) q^{91} +(3.23996 + 0.513159i) q^{92} +(-0.498939 - 1.86207i) q^{93} +(4.00998 + 1.78536i) q^{94} +(3.79985 + 8.53459i) q^{96} +(11.1837 - 1.77133i) q^{97} +(-1.92397 + 11.1779i) q^{98} +17.5251i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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