LMFDB - Embedded newform 875.2.bb.a.82.18

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			82.18
Character	$\chi$	$=$	875.82
Dual form			875.2.bb.a.843.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.43619 + 0.935166i) q^{2} +(0.773359 - 0.0405301i) q^{3} +(3.57420 + 3.21822i) q^{4} +(1.92195 + 0.624480i) q^{6} +(0.425622 + 2.61129i) q^{7} +(3.32847 + 6.53248i) q^{8} +(-2.38712 + 0.250897i) q^{9} +(0.495569 - 4.71502i) q^{11} +(2.89457 + 2.34398i) q^{12} +(0.279137 + 0.0442109i) q^{13} +(-1.40509 + 6.75963i) q^{14} +(0.994352 + 9.46062i) q^{16} +(-1.58570 + 2.44177i) q^{17} +(-6.05012 - 1.62112i) q^{18} +(1.61629 + 1.79507i) q^{19} +(0.434995 + 2.00222i) q^{21} +(5.61663 - 11.0233i) q^{22} +(1.14403 - 2.98029i) q^{23} +(2.83886 + 4.91706i) q^{24} +(0.638685 + 0.368745i) q^{26} +(-4.13059 + 0.654222i) q^{27} +(-6.88246 + 10.7030i) q^{28} +(4.79292 - 1.55732i) q^{29} +(-0.511871 - 2.40816i) q^{31} +(-2.62972 + 9.81424i) q^{32} +(0.192153 - 3.66649i) q^{33} +(-6.14653 + 4.46572i) q^{34} +(-9.33949 - 6.78554i) q^{36} +(6.78294 - 8.37624i) q^{37} +(2.25890 + 5.88464i) q^{38} +(0.217665 + 0.0228775i) q^{39} +(-6.53043 - 8.98836i) q^{41} +(-0.812674 + 5.28457i) q^{42} +(-0.337796 + 0.337796i) q^{43} +(16.9453 - 15.2576i) q^{44} +(5.57414 - 6.19070i) q^{46} +(-3.82251 + 2.48237i) q^{47} +(1.15243 + 7.27616i) q^{48} +(-6.63769 + 2.22285i) q^{49} +(-1.12735 + 1.95263i) q^{51} +(0.855409 + 1.05634i) q^{52} +(0.328143 + 6.26134i) q^{53} +(-10.6747 - 2.26898i) q^{54} +(-15.6416 + 11.4720i) q^{56} +(1.32273 + 1.32273i) q^{57} +(13.1328 + 0.688262i) q^{58} +(-11.2057 - 4.98909i) q^{59} +(4.93535 + 11.0850i) q^{61} +(1.00502 - 6.34542i) q^{62} +(-1.67118 - 6.12669i) q^{63} +(-4.40154 + 6.05820i) q^{64} +(3.89690 - 8.75258i) q^{66} +(0.112905 + 0.0733217i) q^{67} +(-13.5258 + 3.62422i) q^{68} +(0.763953 - 2.35120i) q^{69} +(0.706194 + 2.17344i) q^{71} +(-9.58444 - 14.7587i) q^{72} +(4.84717 - 3.92516i) q^{73} +(24.3577 - 14.0629i) q^{74} +11.6175i q^{76} +(12.5232 - 0.712744i) q^{77} +(0.508878 + 0.259287i) q^{78} +(-0.0833737 + 0.392243i) q^{79} +(3.87554 - 0.823772i) q^{81} +(-7.50376 - 28.0044i) q^{82} +(9.66389 - 4.92400i) q^{83} +(-4.88882 + 8.55623i) q^{84} +(-1.13883 + 0.507041i) q^{86} +(3.64354 - 1.39862i) q^{87} +(32.4503 - 12.4565i) q^{88} +(-15.0511 + 6.70116i) q^{89} +(0.00335924 + 0.747724i) q^{91} +(13.6802 - 6.97042i) q^{92} +(-0.493463 - 1.84163i) q^{93} +(-11.6338 + 2.47284i) q^{94} +(-1.63594 + 7.69652i) q^{96} +(8.67698 + 4.42114i) q^{97} +(-18.2494 - 0.792060i) q^{98} +11.3797i 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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.43619	+	0.935166i	1.72265	+	0.661262i	0.999565	−	0.0295002i	$-0.00939157\pi$
$2$	2.43619	+	0.935166i	1.72265	+	0.661262i	0.723082	+	0.690762i	$0.242725\pi$
$3$	0.773359	−	0.0405301i	0.446499	−	0.0234000i	0.172238	−	0.985055i	$-0.444900\pi$
$3$	0.773359	−	0.0405301i	0.446499	−	0.0234000i	0.274261	+	0.961655i	$0.411567\pi$
$4$	3.57420	+	3.21822i	1.78710	+	1.60911i
$5$		0			0
$5$		0			0
$6$	1.92195	+	0.624480i	0.784634	+	0.254943i
$7$	0.425622	+	2.61129i	0.160870	+	0.986976i
$7$	0.425622	+	2.61129i	0.160870	+	0.986976i
$8$	3.32847	+	6.53248i	1.17679	+	2.30958i
$9$	−2.38712	+	0.250897i	−0.795708	+	0.0836323i
$10$		0			0
$11$	0.495569	−	4.71502i	0.149420	−	1.42163i	−0.620857	−	0.783924i	$-0.713215\pi$
$11$	0.495569	−	4.71502i	0.149420	−	1.42163i	0.770277	−	0.637709i	$-0.220118\pi$
$12$	2.89457	+	2.34398i	0.835592	+	0.676649i
$13$	0.279137	+	0.0442109i	0.0774185	+	0.0122619i	0.195024	−	0.980799i	$-0.437522\pi$
$13$	0.279137	+	0.0442109i	0.0774185	+	0.0122619i	−0.117605	+	0.993060i	$0.537522\pi$
$14$	−1.40509	+	6.75963i	−0.375527	+	1.80659i
$15$		0			0
$16$	0.994352	+	9.46062i	0.248588	+	2.36516i
$17$	−1.58570	+	2.44177i	−0.384590	+	0.592216i	−0.976953	−	0.213455i	$-0.931528\pi$
$17$	−1.58570	+	2.44177i	−0.384590	+	0.592216i	0.592363	+	0.805671i	$0.298195\pi$
$18$	−6.05012	−	1.62112i	−1.42603	−	0.382103i
$19$	1.61629	+	1.79507i	0.370803	+	0.411818i	0.899450	−	0.437023i	$-0.143967\pi$
$19$	1.61629	+	1.79507i	0.370803	+	0.411818i	−0.528647	+	0.848841i	$0.677301\pi$
$20$		0			0
$21$	0.434995	+	2.00222i	0.0949237	+	0.436920i
$22$	5.61663	−	11.0233i	1.19747	−	2.35017i
$23$	1.14403	−	2.98029i	0.238546	−	0.621434i	−0.761083	−	0.648654i	$-0.775332\pi$
$23$	1.14403	−	2.98029i	0.238546	−	0.621434i	0.999629	+	0.0272202i	$0.00866553\pi$
$24$	2.83886	+	4.91706i	0.579481	+	1.00369i
$25$		0			0
$26$	0.638685	+	0.368745i	0.125256	+	0.0723169i
$27$	−4.13059	+	0.654222i	−0.794933	+	0.125905i
$28$	−6.88246	+	10.7030i	−1.30066	+	2.02268i
$29$	4.79292	−	1.55732i	0.890024	−	0.289186i	0.171911	−	0.985113i	$-0.445006\pi$
$29$	4.79292	−	1.55732i	0.890024	−	0.289186i	0.718113	+	0.695926i	$0.245006\pi$
$30$		0			0
$31$	−0.511871	−	2.40816i	−0.0919347	−	0.432519i	−0.999909	−	0.0134928i	$-0.995705\pi$
$31$	−0.511871	−	2.40816i	−0.0919347	−	0.432519i	0.907974	−	0.419026i	$-0.137628\pi$
$32$	−2.62972	+	9.81424i	−0.464873	+	1.73493i
$33$	0.192153	−	3.66649i	0.0334495	−	0.638254i
$34$	−6.14653	+	4.46572i	−1.05412	+	0.765864i
$35$		0			0
$36$	−9.33949	−	6.78554i	−1.55658	−	1.13092i
$37$	6.78294	−	8.37624i	1.11511	−	1.37704i	0.197148	−	0.980374i	$-0.436832\pi$
$37$	6.78294	−	8.37624i	1.11511	−	1.37704i	0.917961	−	0.396671i	$-0.129835\pi$
$38$	2.25890	+	5.88464i	0.366442	+	0.954615i
$39$	0.217665	+	0.0228775i	0.0348543	+	0.00366333i
$40$		0			0
$41$	−6.53043	−	8.98836i	−1.01988	−	1.40375i	−0.912287	−	0.409552i	$-0.865685\pi$
$41$	−6.53043	−	8.98836i	−1.01988	−	1.40375i	−0.107595	−	0.994195i	$-0.534315\pi$
$42$	−0.812674	+	5.28457i	−0.125398	+	0.815427i
$43$	−0.337796	+	0.337796i	−0.0515135	+	0.0515135i	−0.732394	−	0.680881i	$-0.761597\pi$
$43$	−0.337796	+	0.337796i	−0.0515135	+	0.0515135i	0.680881	+	0.732394i	$0.261597\pi$
$44$	16.9453	−	15.2576i	2.55459	−	2.30017i
$45$		0			0
$46$	5.57414	−	6.19070i	0.821861	−	0.912770i
$47$	−3.82251	+	2.48237i	−0.557570	+	0.362090i	−0.792453	−	0.609934i	$-0.791196\pi$
$47$	−3.82251	+	2.48237i	−0.557570	+	0.362090i	0.234883	+	0.972024i	$0.424529\pi$
$48$	1.15243	+	7.27616i	0.166339	+	1.05022i
$49$	−6.63769	+	2.22285i	−0.948242	+	0.317550i
$50$		0			0
$51$	−1.12735	+	1.95263i	−0.157861	+	0.273423i
$52$	0.855409	+	1.05634i	0.118624	+	0.146488i
$53$	0.328143	+	6.26134i	0.0450739	+	0.860061i	0.923833	+	0.382796i	$0.125039\pi$
$53$	0.328143	+	6.26134i	0.0450739	+	0.860061i	−0.878759	+	0.477265i	$0.841628\pi$
$54$	−10.6747	−	2.26898i	−1.45265	−	0.308769i
$55$		0			0
$56$	−15.6416	+	11.4720i	−2.09019	+	1.53301i
$57$	1.32273	+	1.32273i	0.175200	+	0.175200i
$58$	13.1328	+	0.688262i	1.72442	+	0.0903733i
$59$	−11.2057	−	4.98909i	−1.45886	−	0.649525i	−0.484552	−	0.874762i	$-0.661018\pi$
$59$	−11.2057	−	4.98909i	−1.45886	−	0.649525i	−0.974304	+	0.225238i	$0.927684\pi$
$60$		0			0
$61$	4.93535	+	11.0850i	0.631907	+	1.41929i	0.891255	+	0.453503i	$0.149826\pi$
$61$	4.93535	+	11.0850i	0.631907	+	1.41929i	−0.259348	+	0.965784i	$0.583508\pi$
$62$	1.00502	−	6.34542i	0.127637	−	0.805870i
$63$	−1.67118	−	6.12669i	−0.210549	−	0.771890i
$64$	−4.40154	+	6.05820i	−0.550193	+	0.757275i
$65$		0			0
$66$	3.89690	−	8.75258i	0.479675	−	1.07737i
$67$	0.112905	+	0.0733217i	0.0137936	+	0.00895767i	0.551517	−	0.834163i	$-0.314049\pi$
$67$	0.112905	+	0.0733217i	0.0137936	+	0.00895767i	−0.537724	+	0.843121i	$0.680716\pi$
$68$	−13.5258	+	3.62422i	−1.64024	+	0.439501i
$69$	0.763953	−	2.35120i	0.0919691	−	0.283052i
$70$		0			0
$71$	0.706194	+	2.17344i	0.0838098	+	0.257940i	0.984176	−	0.177192i	$-0.0567015\pi$
$71$	0.706194	+	2.17344i	0.0838098	+	0.257940i	−0.900366	+	0.435133i	$0.856702\pi$
$72$	−9.58444	−	14.7587i	−1.12954	−	1.73933i
$73$	4.84717	−	3.92516i	0.567318	−	0.459405i	−0.302243	−	0.953231i	$-0.597735\pi$
$73$	4.84717	−	3.92516i	0.567318	−	0.459405i	0.869561	+	0.493826i	$0.164402\pi$
$74$	24.3577	−	14.0629i	2.83153	−	1.63478i
$75$		0			0
$76$			11.6175i			1.33262i
$77$	12.5232	−	0.712744i	1.42715	−	0.0812248i
$78$	0.508878	+	0.259287i	0.0576191	+	0.0293584i
$79$	−0.0833737	+	0.392243i	−0.00938028	+	0.0441307i	−0.982589	−	0.185793i	$-0.940514\pi$
$79$	−0.0833737	+	0.392243i	−0.00938028	+	0.0441307i	0.973209	+	0.229924i	$0.0738478\pi$
$80$		0			0
$81$	3.87554	−	0.823772i	0.430616	−	0.0915302i
$82$	−7.50376	−	28.0044i	−0.828651	−	3.09257i
$83$	9.66389	−	4.92400i	1.06075	−	0.540479i	0.165576	−	0.986197i	$-0.447052\pi$
$83$	9.66389	−	4.92400i	1.06075	−	0.540479i	0.895174	+	0.445718i	$0.147052\pi$
$84$	−4.88882	+	8.55623i	−0.533414	+	0.933561i
$85$		0			0
$86$	−1.13883	+	0.507041i	−0.122803	+	0.0546756i
$87$	3.64354	−	1.39862i	0.390628	−	0.149948i
$88$	32.4503	−	12.4565i	3.45921	−	1.32787i
$89$	−15.0511	+	6.70116i	−1.59541	+	0.710322i	−0.995935	−	0.0900724i	$-0.971290\pi$
$89$	−15.0511	+	6.70116i	−1.59541	+	0.710322i	−0.599474	+	0.800394i	$0.704623\pi$
$90$		0			0
$91$	0.00335924	+	0.747724i	0.000352144	+	0.0783828i
$92$	13.6802	−	6.97042i	1.42626	−	0.726717i
$93$	−0.493463	−	1.84163i	−0.0511697	−	0.190968i
$94$	−11.6338	+	2.47284i	−1.19993	+	0.255054i
$95$		0			0
$96$	−1.63594	+	7.69652i	−0.166968	+	0.785522i
$97$	8.67698	+	4.42114i	0.881014	+	0.448899i	0.835133	−	0.550048i	$-0.185391\pi$
$97$	8.67698	+	4.42114i	0.881014	+	0.448899i	0.0458808	+	0.998947i	$0.485391\pi$
$98$	−18.2494	−	0.792060i	−1.84347	−	0.0800101i
$99$			11.3797i			1.14370i
$100$		0			0
$101$	−1.40381	+	0.810489i	−0.139684	+	0.0806467i	−0.568213	−	0.822881i	$-0.692365\pi$
$101$	−1.40381	+	0.810489i	−0.139684	+	0.0806467i	0.428529	+	0.903528i	$0.359032\pi$
$102$	−4.57248	+	3.70273i	−0.452743	+	0.366624i
$103$	−0.371713	−	0.572388i	−0.0366260	−	0.0563991i	0.819883	−	0.572531i	$-0.194038\pi$
$103$	−0.371713	−	0.572388i	−0.0366260	−	0.0563991i	−0.856509	+	0.516132i	$0.827372\pi$
$104$	0.640290	+	1.97061i	0.0627856	+	0.193234i
$105$		0			0
$106$	−5.05597	+	15.5607i	−0.491079	+	1.51139i
$107$	−9.13222	+	2.44697i	−0.882845	+	0.236558i	−0.671634	−	0.740883i	$-0.734407\pi$
$107$	−9.13222	+	2.44697i	−0.882845	+	0.236558i	−0.211211	+	0.977441i	$0.567741\pi$
$108$	−16.8690	−	10.9549i	−1.62322	−	1.05413i
$109$	−1.44661	+	3.24914i	−0.138560	+	0.311211i	−0.969476	−	0.245187i	$-0.921151\pi$
$109$	−1.44661	+	3.24914i	−0.138560	+	0.311211i	0.830916	+	0.556398i	$0.187817\pi$
$110$		0			0
$111$	4.90616	−	6.75276i	0.465672	−	0.640943i
$112$	−24.2812	+	6.62319i	−2.29436	+	0.625833i
$113$	0.382820	−	2.41703i	0.0360127	−	0.227375i	−0.963117	−	0.269082i	$-0.913280\pi$
$113$	0.382820	−	2.41703i	0.0360127	−	0.227375i	0.999130	+	0.0417071i	$0.0132796\pi$
$114$	1.98545	+	4.45939i	0.185954	+	0.417660i
$115$		0			0
$116$	22.1427	+	9.85854i	2.05589	+	0.915343i
$117$	−0.677426	−	0.0355024i	−0.0626280	−	0.00328220i
$118$	−22.6336	−	22.6336i	−2.08359	−	2.08359i
$119$	−7.05108	−	3.10146i	−0.646372	−	0.284311i
$120$		0			0
$121$	−11.2262	−	2.38621i	−1.02057	−	0.216928i
$122$	1.65716	+	31.6205i	0.150032	+	2.86279i
$123$	−5.41467	−	6.68656i	−0.488224	−	0.602907i
$124$	5.92047	−	10.2546i	0.531674	−	0.920887i
$125$		0			0
$126$	1.65816	−	16.4886i	0.147721	−	1.46892i
$127$	0.524783	+	3.31335i	0.0465669	+	0.294012i	0.999970	−	0.00768604i	$-0.00244657\pi$
$127$	0.524783	+	3.31335i	0.0465669	+	0.294012i	−0.953404	+	0.301698i	$0.902447\pi$
$128$	0.654120	−	0.424791i	0.0578166	−	0.0375466i
$129$	−0.247547	+	0.274929i	−0.0217953	+	0.0242061i
$130$		0			0
$131$	−9.68473	+	8.72017i	−0.846159	+	0.761885i	−0.973187	−	0.230014i	$-0.926123\pi$
$131$	−9.68473	+	8.72017i	−0.846159	+	0.761885i	0.127028	+	0.991899i	$0.459456\pi$
$132$	12.4864	−	12.4864i	1.08680	−	1.08680i
$133$	−3.99953	+	4.98463i	−0.346803	+	0.432222i
$134$	0.206491	+	0.284211i	0.0178381	+	0.0245521i
$135$		0			0
$136$	−21.2288	−	2.23123i	−1.82035	−	0.191327i
$137$	−1.88769	−	4.91759i	−0.161276	−	0.420138i	0.829001	−	0.559247i	$-0.188910\pi$
$137$	−1.88769	−	4.91759i	−0.161276	−	0.420138i	−0.990277	+	0.139109i	$0.955576\pi$
$138$	4.05990	−	5.01356i	0.345602	−	0.426783i
$139$	6.71583	+	4.87933i	0.569629	+	0.413860i	0.834970	−	0.550295i	$-0.185485\pi$
$139$	6.71583	+	4.87933i	0.569629	+	0.413860i	−0.265341	+	0.964155i	$0.585485\pi$
$140$		0			0
$141$	−2.85556	+	2.07469i	−0.240482	+	0.174720i
$142$	−0.312105	+	5.95533i	−0.0261913	+	0.499760i
$143$	0.346787	−	1.29423i	0.0289998	−	0.108229i
$144$	−4.74728	−	22.3342i	−0.395607	−	1.86118i
$145$		0			0
$146$	15.4793	−	5.02953i	1.28108	−	0.416247i
$147$	−5.04323	+	1.98809i	−0.415959	+	0.163975i
$148$	51.2002	−	8.10931i	4.20863	−	0.666581i
$149$	−19.7979	−	11.4303i	−1.62190	−	0.936407i	−0.986410	−	0.164302i	$-0.947463\pi$
$149$	−19.7979	−	11.4303i	−1.62190	−	0.936407i	−0.635495	−	0.772105i	$-0.719204\pi$
$150$		0			0
$151$	−5.50839	−	9.54081i	−0.448266	−	0.776420i	0.550007	−	0.835160i	$-0.314625\pi$
$151$	−5.50839	−	9.54081i	−0.448266	−	0.776420i	−0.998273	+	0.0587398i	$0.981292\pi$
$152$	−6.34652	+	16.5332i	−0.514771	+	1.34102i
$153$	3.17264	−	6.22665i	0.256493	−	0.503395i
$154$	31.1755	+	9.97491i	2.51219	+	0.803801i
$155$		0			0
$156$	0.704352	+	0.782262i	0.0563933	+	0.0626311i
$157$	−3.44756	−	0.923771i	−0.275145	−	0.0737249i	0.118608	−	0.992941i	$-0.462157\pi$
$157$	−3.44756	−	0.923771i	−0.275145	−	0.0737249i	−0.393753	+	0.919216i	$0.628823\pi$
$158$	−0.569926	+	0.877609i	−0.0453409	+	0.0698189i
$159$	0.507545	+	4.82897i	0.0402509	+	0.382962i
$160$		0			0
$161$	8.26934	+	1.71891i	0.651715	+	0.135469i
$162$	10.2119	+	1.61741i	0.802325	+	0.127076i
$163$	15.0269	+	12.1685i	1.17700	+	0.953112i	0.999519	−	0.0310128i	$-0.00987325\pi$
$163$	15.0269	+	12.1685i	1.17700	+	0.953112i	0.177477	+	0.984125i	$0.443207\pi$
$164$	5.58551	−	53.1426i	0.436155	−	4.14974i
$165$		0			0
$166$	28.1478	−	2.95846i	2.18470	−	0.229621i
$167$	−4.79701	−	9.41466i	−0.371204	−	0.728528i	0.627543	−	0.778582i	$-0.284061\pi$
$167$	−4.79701	−	9.41466i	−0.371204	−	0.728528i	−0.998747	+	0.0500536i	$0.984061\pi$
$168$	−11.6316	+	9.50591i	−0.897396	+	0.733397i
$169$	−12.2878	−	3.99254i	−0.945213	−	0.307118i
$170$		0			0
$171$	−4.30867	−	3.87954i	−0.329492	−	0.296676i
$172$	−2.29446	+	0.120247i	−0.174951	+	0.00916877i
$173$	6.03804	+	2.31779i	0.459064	+	0.176218i	0.576900	−	0.816815i	$-0.304262\pi$
$173$	6.03804	+	2.31779i	0.459064	+	0.176218i	−0.117836	+	0.993033i	$0.537596\pi$
$174$	10.1843			0.772069
$175$		0			0
$176$	45.0998			3.39953
$177$	−8.86823	−	3.40420i	−0.666577	−	0.255875i
$178$	−42.9339	+	2.25007i	−3.21804	+	0.168650i
$179$	4.69545	+	4.22780i	0.350954	+	0.316001i	0.825686	−	0.564130i	$-0.190788\pi$
$179$	4.69545	+	4.22780i	0.350954	+	0.316001i	−0.474732	+	0.880131i	$0.657455\pi$
$180$		0			0
$181$	−2.32364	−	0.754995i	−0.172715	−	0.0561183i	0.221383	−	0.975187i	$-0.428943\pi$
$181$	−2.32364	−	0.754995i	−0.172715	−	0.0561183i	−0.394098	+	0.919069i	$0.628943\pi$
$182$	−0.691062	+	1.82474i	−0.0512249	+	0.135259i
$183$	4.26608	+	8.37265i	0.315357	+	0.618924i
$184$	23.2766	−	2.44647i	1.71597	−	0.180356i
$185$		0			0
$186$	0.520059	−	4.94803i	0.0381325	−	0.362807i
$187$	10.7272	+	8.68669i	0.784448	+	0.635234i
$188$	−21.6512	−	3.42921i	−1.57908	−	0.250101i
$189$	−3.46644	−	10.5077i	−0.252146	−	0.764325i
$190$		0			0
$191$	−0.378911	−	3.60510i	−0.0274170	−	0.260856i	−0.999641	−	0.0268022i	$-0.991468\pi$
$191$	−0.378911	−	3.60510i	−0.0274170	−	0.260856i	0.972224	−	0.234053i	$-0.0751991\pi$
$192$	−3.15843	+	4.86356i	−0.227940	+	0.350997i
$193$	4.08034	+	1.09332i	0.293709	+	0.0786992i	0.402665	−	0.915347i	$-0.368084\pi$
$193$	4.08034	+	1.09332i	0.293709	+	0.0786992i	−0.108956	+	0.994047i	$0.534751\pi$
$194$	17.0043	+	18.8852i	1.22084	+	1.35588i
$195$		0			0
$196$	−30.8780	−	13.4167i	−2.20557	−	0.958333i
$197$	−3.46067	+	6.79194i	−0.246562	+	0.483906i	−0.980807	−	0.194979i	$-0.937536\pi$
$197$	−3.46067	+	6.79194i	−0.246562	+	0.483906i	0.734245	+	0.678884i	$0.237536\pi$
$198$	−10.6419	+	27.7231i	−0.756286	+	1.97019i
$199$	7.76221	+	13.4445i	0.550248	+	0.953058i	0.998256	+	0.0590284i	$0.0188002\pi$
$199$	7.76221	+	13.4445i	0.550248	+	0.953058i	−0.448008	+	0.894030i	$0.647866\pi$
$200$		0			0
$201$	0.0902882	+	0.0521279i	0.00636844	+	0.00367682i
$202$	−4.17789	+	0.661712i	−0.293955	+	0.0465579i
$203$	6.10658	+	11.8529i	0.428598	+	0.831910i
$204$	−10.3134	+	3.35103i	−0.722082	+	0.234619i
$205$		0			0
$206$	−0.370286	−	1.74206i	−0.0257991	−	0.121375i
$207$	−1.98319	+	7.40136i	−0.137841	+	0.514430i
$208$	−0.140703	+	2.68477i	−0.00975597	+	0.186155i
$209$	9.26480	−	6.73127i	0.640859	−	0.465612i
$210$		0			0
$211$	4.18676	+	3.04186i	0.288228	+	0.209410i	0.722498	−	0.691373i	$-0.242994\pi$
$211$	4.18676	+	3.04186i	0.288228	+	0.209410i	−0.434270	+	0.900783i	$0.642994\pi$
$212$	−18.9775	+	23.4353i	−1.30338	+	1.60954i
$213$	0.634232	+	1.65223i	0.0434568	+	0.113209i
$214$	−24.5361	−	2.57885i	−1.67726	−	0.176287i
$215$		0			0
$216$	−18.0222	−	24.8055i	−1.22626	−	1.68780i
$217$	6.07055	−	2.36161i	0.412096	−	0.160317i
$218$	−6.56270	+	6.56270i	−0.444482	+	0.444482i
$219$	3.58952	−	3.23201i	0.242557	−	0.218399i
$220$		0			0
$221$	−0.550580	+	0.611482i	−0.0370361	+	0.0411327i
$222$	18.2673	−	11.8629i	1.22602	−	0.796187i
$223$	1.89329	+	11.9537i	0.126784	+	0.800482i	0.966351	+	0.257226i	$0.0828086\pi$
$223$	1.89329	+	11.9537i	0.126784	+	0.800482i	−0.839567	+	0.543256i	$0.817191\pi$
$224$	−26.7471	−	2.68980i	−1.78712	−	0.179720i
$225$		0			0
$226$	3.19295	−	5.53035i	0.212392	−	0.367873i
$227$	−16.2024	−	20.0083i	−1.07539	−	1.32800i	−0.941503	−	0.337004i	$-0.890586\pi$
$227$	−16.2024	−	20.0083i	−1.07539	−	1.32800i	−0.133890	−	0.990996i	$-0.542747\pi$
$228$	0.470859	+	8.98453i	0.0311834	+	0.595015i
$229$	−5.43513	−	1.15527i	−0.359164	−	0.0763426i	0.0247959	−	0.999693i	$-0.492106\pi$
$229$	−5.43513	−	1.15527i	−0.359164	−	0.0763426i	−0.383959	+	0.923350i	$0.625440\pi$
$230$		0			0
$231$	9.65607	−	1.05877i	0.635323	−	0.0696623i
$232$	26.1262	+	26.1262i	1.71527	+	1.71527i
$233$	−9.72157	−	0.509486i	−0.636881	−	0.0333775i	−0.268837	−	0.963186i	$-0.586639\pi$
$233$	−9.72157	−	0.509486i	−0.636881	−	0.0333775i	−0.368044	+	0.929808i	$0.619973\pi$
$234$	−1.61714	−	0.719996i	−0.105716	−	0.0470676i
$235$		0			0
$236$	−23.9953	−	53.8944i	−1.56196	−	3.50823i
$237$	−0.0485803	+	0.306724i	−0.00315563	+	0.0199238i
$238$	−14.2774	−	14.1497i	−0.925466	−	0.917188i
$239$	5.98429	−	8.23666i	0.387091	−	0.532785i	−0.570355	−	0.821399i	$-0.693194\pi$
$239$	5.98429	−	8.23666i	0.387091	−	0.532785i	0.957446	+	0.288613i	$0.0931942\pi$
$240$		0			0
$241$	2.42608	−	5.44906i	0.156278	−	0.351005i	−0.818390	−	0.574663i	$-0.805133\pi$
$241$	2.42608	−	5.44906i	0.156278	−	0.351005i	0.974668	+	0.223658i	$0.0717998\pi$
$242$	−25.1177	−	16.3116i	−1.61463	−	1.04855i
$243$	15.0825	−	4.04136i	0.967546	−	0.259253i
$244$	−18.0340	+	55.5030i	−1.15451	+	3.55321i
$245$		0			0
$246$	−6.93812	−	21.3533i	−0.442358	−	1.36144i
$247$	0.371804	+	0.572528i	0.0236573	+	0.0364291i
$248$	14.0275	−	11.3593i	0.890749	−	0.721315i
$249$	7.27409	−	4.19970i	0.460977	−	0.266145i
$250$		0			0
$251$			23.8276i			1.50398i	0.659173	+	0.751991i	$0.270906\pi$
$251$			23.8276i			1.50398i	−0.659173	+	0.751991i	$0.729094\pi$
$252$	13.7439	−	27.2762i	0.865786	−	1.71824i
$253$	−13.4852	−	6.87105i	−0.847807	−	0.431979i
$254$	−1.82006	+	8.56270i	−0.114201	+	0.537272i
$255$		0			0
$256$	16.6402	−	3.53699i	1.04001	−	0.221062i
$257$	5.68725	+	21.2251i	0.354761	+	1.32399i	0.880785	+	0.473517i	$0.157016\pi$
$257$	5.68725	+	21.2251i	0.354761	+	1.32399i	−0.526024	+	0.850470i	$0.676318\pi$
$258$	−0.860176	+	0.438282i	−0.0535522	+	0.0272862i
$259$	24.7598	+	14.1471i	1.53850	+	0.879060i
$260$		0			0
$261$	−11.0506	+	4.92003i	−0.684014	+	0.304542i
$262$	−31.7487	+	12.1872i	−1.96144	+	0.752926i
$263$	8.93735	−	3.43073i	0.551100	−	0.211548i	−0.0668524	−	0.997763i	$-0.521296\pi$
$263$	8.93735	−	3.43073i	0.551100	−	0.211548i	0.617953	+	0.786215i	$0.287962\pi$
$264$	24.5909	−	10.9486i	1.51346	−	0.673838i
$265$		0			0
$266$	−14.4051	+	8.40329i	−0.883232	+	0.515239i
$267$	−11.3683	+	5.79243i	−0.695727	+	0.354491i
$268$	0.167581	+	0.625421i	0.0102366	+	0.0382037i
$269$	1.89482	−	0.402756i	0.115529	−	0.0245565i	−0.149784	−	0.988719i	$-0.547858\pi$
$269$	1.89482	−	0.402756i	0.115529	−	0.0245565i	0.265313	+	0.964162i	$0.414525\pi$
$270$		0			0
$271$	−3.03375	+	14.2726i	−0.184287	+	0.867002i	0.784697	+	0.619879i	$0.212818\pi$
$271$	−3.03375	+	14.2726i	−0.184287	+	0.867002i	−0.968984	+	0.247123i	$0.920515\pi$
$272$	−24.6774	−	12.5738i	−1.49629	−	0.762396i
$273$	0.0329032	+	0.578123i	0.00199139	+	0.0349896i
$274$		−	13.7455i		−	0.830395i
$275$		0			0
$276$	10.2972	−	5.94510i	0.619820	−	0.357853i
$277$	−2.16467	+	1.75291i	−0.130062	+	0.105322i	−0.692144	−	0.721759i	$-0.743334\pi$
$277$	−2.16467	+	1.75291i	−0.130062	+	0.105322i	0.562082	+	0.827082i	$0.310001\pi$
$278$	11.7980	+	18.1674i	0.707600	+	1.08961i
$279$	1.82610	+	5.62015i	0.109326	+	0.336470i
$280$		0			0
$281$	−1.84423	+	5.67596i	−0.110018	+	0.338600i	−0.990875	−	0.134782i	$-0.956967\pi$
$281$	−1.84423	+	5.67596i	−0.110018	+	0.338600i	0.880858	+	0.473381i	$0.156967\pi$
$282$	−8.89687	+	2.38391i	−0.529801	+	0.141960i
$283$	−11.6799	−	7.58503i	−0.694299	−	0.450883i	0.148641	−	0.988891i	$-0.452510\pi$
$283$	−11.6799	−	7.58503i	−0.694299	−	0.450883i	−0.842940	+	0.538008i	$0.819177\pi$
$284$	−4.47054	+	10.0410i	−0.265278	+	0.595824i
$285$		0			0
$286$	2.05515	−	2.82868i	0.121524	−	0.167263i
$287$	20.6917	−	20.8785i	1.22140	−	1.23242i
$288$	3.81510	−	24.0876i	0.224807	−	1.41937i
$289$	3.46674	+	7.78643i	0.203926	+	0.458025i
$290$		0			0
$291$	6.88961	+	3.06745i	0.403876	+	0.179817i
$292$	29.9568	+	1.56997i	1.75309	+	0.0918754i
$293$	9.79347	+	9.79347i	0.572141	+	0.572141i	0.932726	−	0.360585i	$-0.117423\pi$
$293$	9.79347	+	9.79347i	0.572141	+	0.572141i	−0.360585	+	0.932726i	$0.617423\pi$
$294$	−14.1455	+	0.127103i	−0.824980	+	0.00741278i
$295$		0			0
$296$	77.2944	+	16.4294i	4.49265	+	0.954942i
$297$	1.03768	+	19.8001i	0.0602121	+	1.14892i
$298$	−37.5422	−	46.3607i	−2.17476	−	2.68560i
$299$	0.451101	−	0.781330i	0.0260879	−	0.0451855i
$300$		0			0
$301$	−1.02586	−	0.738311i	−0.0591295	−	0.0425556i
$302$	−4.49725	−	28.3945i	−0.258787	−	1.63392i
$303$	−1.05280	+	0.683696i	−0.0604818	+	0.0392773i
$304$	−15.3754	+	17.0761i	−0.881837	+	0.979379i
$305$		0			0
$306$	13.5521	−	12.2024i	0.774722	−	0.697563i
$307$	−2.89048	+	2.89048i	−0.164968	+	0.164968i	−0.784764	−	0.619795i	$-0.787216\pi$
$307$	−2.89048	+	2.89048i	−0.164968	+	0.164968i	0.619795	+	0.784764i	$0.287216\pi$
$308$	47.0543	+	37.7550i	2.68117	+	2.15129i
$309$	−0.310667	−	0.427596i	−0.0176732	−	0.0243251i
$310$		0			0
$311$	13.4403	+	1.41263i	0.762128	+	0.0801029i	0.477615	−	0.878569i	$-0.341501\pi$
$311$	13.4403	+	1.41263i	0.762128	+	0.0801029i	0.284513	+	0.958672i	$0.408168\pi$
$312$	0.575043	+	1.49804i	0.0325554	+	0.0848097i
$313$	−9.05310	+	11.1796i	−0.511712	+	0.631911i	−0.965875	−	0.259007i	$-0.916605\pi$
$313$	−9.05310	+	11.1796i	−0.511712	+	0.631911i	0.454164	+	0.890918i	$0.349938\pi$
$314$	−7.53503	−	5.47452i	−0.425226	−	0.308945i
$315$		0			0
$316$	−1.56032	+	1.13364i	−0.0877748	+	0.0637721i
$317$	−1.71306	+	32.6872i	−0.0962152	+	1.83590i	0.345126	+	0.938557i	$0.387836\pi$
$317$	−1.71306	+	32.6872i	−0.0962152	+	1.83590i	−0.441341	+	0.897340i	$0.645497\pi$
$318$	−3.27941	+	12.2389i	−0.183900	+	0.686324i
$319$	−4.96755	−	23.3705i	−0.278130	−	1.30850i
$320$		0			0
$321$	−6.96331	+	2.26252i	−0.388654	+	0.126281i
$322$	18.5382	+	11.9208i	1.03309	+	0.664320i
$323$	−6.94611	+	1.10016i	−0.386492	+	0.0612143i
$324$	16.5030	+	9.52804i	0.916836	+	0.529335i
$325$		0			0
$326$	25.2287	+	43.6975i	1.39729	+	2.42018i
$327$	−0.987062	+	2.57138i	−0.0545846	+	0.142198i
$328$	36.9800	−	72.5774i	2.04188	−	4.00742i
$329$	−8.10912	−	8.92513i	−0.447070	−	0.492058i
$330$		0			0
$331$	14.4255	+	16.0212i	0.792898	+	0.880603i	0.995113	−	0.0987384i	$-0.0314807\pi$
$331$	14.4255	+	16.0212i	0.792898	+	0.880603i	−0.202215	+	0.979341i	$0.564814\pi$
$332$	50.3872	+	13.5012i	2.76536	+	0.740975i
$333$	−14.0902	+	21.6969i	−0.772136	+	1.18898i
$334$	−2.88216	−	27.4219i	−0.157705	−	1.50046i
$335$		0			0
$336$	−18.5097	+	6.10623i	−1.00979	+	0.333122i
$337$	3.80587	+	0.602791i	0.207319	+	0.0328361i	0.259230	−	0.965816i	$-0.416531\pi$
$337$	3.80587	+	0.602791i	0.207319	+	0.0328361i	−0.0519110	+	0.998652i	$0.516531\pi$
$338$	−26.2017	−	21.2177i	−1.42518	−	1.15409i
$339$	0.198095	−	1.88475i	0.0107591	−	0.102366i
$340$		0			0
$341$	−11.6082	+	1.22007i	−0.628620	+	0.0660706i
$342$	−6.86872	−	13.4806i	−0.371418	−	0.728948i
$343$	−8.62966	−	16.3869i	−0.465958	−	0.884807i
$344$	−3.33099	−	1.08231i	−0.179595	−	0.0583540i
$345$		0			0
$346$	12.5423	+	11.2931i	0.674278	+	0.607123i
$347$	17.3953	−	0.911650i	0.933830	−	0.0489399i	0.420652	−	0.907222i	$-0.361801\pi$
$347$	17.3953	−	0.911650i	0.933830	−	0.0489399i	0.513178	+	0.858282i	$0.328468\pi$
$348$	17.5238	+	6.72676i	0.939374	+	0.360592i
$349$	−13.3482			−0.714513			−0.357256	−	0.934006i	$-0.616288\pi$
$349$	−13.3482			−0.714513			−0.357256	+	0.934006i	$0.616288\pi$
$350$		0			0
$351$	−1.18192			−0.0630864
$352$	44.9711	+	17.2628i	2.39697	+	0.920111i
$353$	9.60439	−	0.503345i	0.511190	−	0.0267904i	0.205002	−	0.978761i	$-0.434280\pi$
$353$	9.60439	−	0.503345i	0.511190	−	0.0267904i	0.306188	+	0.951971i	$0.400946\pi$
$354$	−18.4212	−	16.5865i	−0.979077	−	0.881564i
$355$		0			0
$356$	−75.3613	−	24.4864i	−3.99414	−	1.29778i
$357$	−5.57872	−	2.11276i	−0.295257	−	0.111819i
$358$	7.48531	+	14.6908i	0.395611	+	0.776430i
$359$	16.6034	−	1.74509i	0.876294	−	0.0921022i	0.344310	−	0.938856i	$-0.388113\pi$
$359$	16.6034	−	1.74509i	0.876294	−	0.0921022i	0.531985	+	0.846754i	$0.321446\pi$
$360$		0			0
$361$	1.37615	−	13.0932i	0.0724289	−	0.689115i
$362$	−4.95477	−	4.01230i	−0.260417	−	0.210882i
$363$	−8.77862	−	1.39040i	−0.460758	−	0.0729769i
$364$	−2.39434	+	2.68332i	−0.125497	+	0.140644i
$365$		0			0
$366$	2.56316	+	24.3868i	0.133979	+	1.27472i
$367$	6.17133	−	9.50302i	0.322141	−	0.496054i	−0.640086	−	0.768304i	$-0.721101\pi$
$367$	6.17133	−	9.50302i	0.322141	−	0.496054i	0.962227	+	0.272250i	$0.0877678\pi$
$368$	29.3330	+	7.85975i	1.52909	+	0.409718i
$369$	17.8441	+	19.8179i	0.928926	+	1.03168i
$370$		0			0
$371$	−16.2105	+	3.52184i	−0.841608	+	0.182845i
$372$	4.16304	−	8.17042i	0.215843	−	0.423616i
$373$	−8.79662	+	22.9160i	−0.455472	+	1.18654i	0.493097	+	0.869974i	$0.335865\pi$
$373$	−8.79662	+	22.9160i	−0.455472	+	1.18654i	−0.948569	+	0.316571i	$0.897469\pi$
$374$	18.0099	+	31.1941i	0.931272	+	1.61301i
$375$		0			0
$376$	−28.9391	−	16.7080i	−1.49242	−	0.861649i
$377$	1.40673	−	0.222804i	0.0724503	−	0.0114750i
$378$	1.38157	−	28.8405i	0.0710605	−	1.48340i
$379$	−7.11319	+	2.31121i	−0.365380	+	0.118719i	−0.485952	−	0.873985i	$-0.661527\pi$
$379$	−7.11319	+	2.31121i	−0.365380	+	0.118719i	0.120572	+	0.992705i	$0.461527\pi$
$380$		0			0
$381$	0.540136	+	2.54114i	0.0276720	+	0.130186i
$382$	2.44826	−	9.13705i	0.125264	−	0.467492i
$383$	1.90055	−	36.2646i	0.0971135	−	1.85304i	−0.324036	−	0.946045i	$-0.605040\pi$
$383$	1.90055	−	36.2646i	0.0971135	−	1.85304i	0.421150	−	0.906991i	$-0.361627\pi$
$384$	0.488653	−	0.355028i	0.0249365	−	0.0181174i
$385$		0			0
$386$	8.91805	+	6.47934i	0.453917	+	0.329790i
$387$	0.721610	−	0.891114i	0.0366815	−	0.0452979i
$388$	16.7850	+	43.7265i	0.852131	+	2.21988i
$389$	24.0859	+	2.53153i	1.22120	+	0.128353i	0.693109	−	0.720833i	$-0.256241\pi$
$389$	24.0859	+	2.53153i	1.22120	+	0.128353i	0.528093	+	0.849187i	$0.322907\pi$
$390$		0			0
$391$	5.46310	+	7.51931i	0.276281	+	0.380268i
$392$	−36.6141	−	35.9619i	−1.84929	−	1.81635i
$393$	−7.13635	+	7.13635i	−0.359981	+	0.359981i
$394$	−14.7824	+	13.3102i	−0.744728	+	0.670556i
$395$		0			0
$396$	−36.6223	+	40.6732i	−1.84034	+	2.04391i
$397$	−11.6310	+	7.55329i	−0.583746	+	0.379089i	−0.802465	−	0.596699i	$-0.796479\pi$
$397$	−11.6310	+	7.55329i	−0.583746	+	0.379089i	0.218720	+	0.975788i	$0.429812\pi$
$398$	6.33734	+	40.0124i	0.317662	+	2.00564i
$399$	−2.89105	+	4.01701i	−0.144733	+	0.201102i
$400$		0			0
$401$	−1.39267	+	2.41218i	−0.0695467	+	0.120458i	−0.898702	−	0.438560i	$-0.855489\pi$
$401$	−1.39267	+	2.41218i	−0.0695467	+	0.120458i	0.829155	+	0.559019i	$0.188822\pi$
$402$	0.171211	+	0.211428i	0.00853923	+	0.0105451i
$403$	−0.0364148	−	0.694836i	−0.00181395	−	0.0346123i
$404$	−7.62583	−	1.62092i	−0.379399	−	0.0806438i
$405$		0			0
$406$	3.79237	+	34.5866i	0.188212	+	1.71650i
$407$	−36.1327	−	36.1327i	−1.79103	−	1.79103i
$408$	−16.5079	−	0.865143i	−0.817263	−	0.0428310i
$409$	−16.6880	−	7.42995i	−0.825166	−	0.367388i	−0.0496901	−	0.998765i	$-0.515823\pi$
$409$	−16.6880	−	7.42995i	−0.825166	−	0.367388i	−0.775476	+	0.631377i	$0.782490\pi$
$410$		0			0
$411$	−1.65917	−	3.72656i	−0.0818408	−	0.183817i
$412$	0.513496	−	3.24208i	0.0252981	−	0.159726i
$413$	8.25859	−	31.3848i	0.406379	−	1.54434i
$414$	−11.7529	+	16.1765i	−0.577625	+	0.795032i
$415$		0			0
$416$	−1.16795	+	2.62325i	−0.0572633	+	0.128615i
$417$	5.39151	+	3.50129i	0.264023	+	0.171459i
$418$	28.8657	−	7.73453i	1.41187	−	0.378308i
$419$	9.21580	−	28.3633i	0.450221	−	1.38564i	−0.426434	−	0.904519i	$-0.640230\pi$
$419$	9.21580	−	28.3633i	0.450221	−	1.38564i	0.876655	−	0.481119i	$-0.159770\pi$
$420$		0			0
$421$	−11.0026	−	33.8625i	−0.536234	−	1.65036i	−0.740968	−	0.671540i	$-0.765633\pi$
$421$	−11.0026	−	33.8625i	−0.536234	−	1.65036i	0.204735	−	0.978818i	$-0.434367\pi$
$422$	7.35509	+	11.3259i	0.358040	+	0.551334i
$423$	8.50198	−	6.88477i	0.413380	−	0.334749i
$424$	−39.8099	+	22.9842i	−1.93334	+	1.11621i
$425$		0			0
$426$			4.61826i			0.223755i
$427$	−26.8455	+	17.6057i	−1.29915	+	0.851998i
$428$	−40.5153	−	20.6436i	−1.95838	−	0.997844i
$429$	0.215736	−	1.01496i	0.0104158	−	0.0490026i
$430$		0			0
$431$	−16.7627	+	3.56303i	−0.807432	+	0.171625i	−0.593092	−	0.805134i	$-0.702093\pi$
$431$	−16.7627	+	3.56303i	−0.807432	+	0.171625i	−0.214339	+	0.976759i	$0.568760\pi$
$432$	−10.2966	−	38.4275i	−0.495396	−	1.84884i
$433$	−15.9018	+	8.10236i	−0.764191	+	0.389375i	−0.792222	−	0.610232i	$-0.791076\pi$
$433$	−15.9018	+	8.10236i	−0.764191	+	0.389375i	0.0280318	+	0.999607i	$0.491076\pi$
$434$	16.9975	−	0.0763633i	0.815907	−	0.00366555i
$435$		0			0
$436$	−15.6269	+	6.95756i	−0.748394	+	0.333206i
$437$	7.19893	−	2.76341i	0.344371	−	0.132192i
$438$	11.7672	−	4.51701i	0.562259	−	0.215831i
$439$	2.27922	−	1.01477i	0.108781	−	0.0484325i	−0.351625	−	0.936141i	$-0.614371\pi$
$439$	2.27922	−	1.01477i	0.108781	−	0.0484325i	0.460406	+	0.887709i	$0.347704\pi$
$440$		0			0
$441$	15.2873	−	6.97159i	0.727966	−	0.331980i
$442$	−1.91316	+	0.974801i	−0.0909995	+	0.0463666i
$443$	7.83980	+	29.2585i	0.372480	+	1.39011i	0.856992	+	0.515330i	$0.172331\pi$
$443$	7.83980	+	29.2585i	0.372480	+	1.39011i	−0.484512	+	0.874785i	$0.661003\pi$
$444$	39.2675	−	8.34656i	1.86355	−	0.396110i
$445$		0			0
$446$	−6.56633	+	30.8921i	−0.310925	+	1.46279i
$447$	−15.7741	−	8.03733i	−0.746091	−	0.380153i
$448$	−17.6931	−	8.91520i	−0.835922	−	0.421204i
$449$			6.87805i			0.324595i	0.986742	+	0.162298i	$0.0518905\pi$
$449$			6.87805i			0.324595i	−0.986742	+	0.162298i	$0.948110\pi$
$450$		0			0
$451$	−45.6166	+	26.3368i	−2.14800	+	1.24015i
$452$	9.14682	−	7.40695i	0.430230	−	0.348393i
$453$	−4.64666	−	7.15522i	−0.218319	−	0.336182i
$454$	−20.7611	−	63.8961i	−0.974367	−	2.99879i
$455$		0			0
$456$	−4.23805	+	13.0434i	−0.198465	+	0.610811i
$457$	−22.9176	+	6.14074i	−1.07204	+	0.287252i	−0.751330	−	0.659926i	$-0.770587\pi$
$457$	−22.9176	+	6.14074i	−1.07204	+	0.287252i	−0.320708	+	0.947178i	$0.603921\pi$
$458$	−12.1606	−	7.89721i	−0.568229	−	0.369013i
$459$	4.95244	−	11.1234i	0.231160	−	0.519194i
$460$		0			0
$461$	−4.63007	+	6.37275i	−0.215644	+	0.296809i	−0.903111	−	0.429407i	$-0.858723\pi$
$461$	−4.63007	+	6.37275i	−0.215644	+	0.296809i	0.687467	+	0.726216i	$0.258723\pi$
$462$	24.5141	+	6.45065i	1.14050	+	0.300111i
$463$	−1.89995	+	11.9958i	−0.0882982	+	0.557493i	0.903389	+	0.428822i	$0.141071\pi$
$463$	−1.89995	+	11.9958i	−0.0882982	+	0.557493i	−0.991687	+	0.128671i	$0.958929\pi$
$464$	19.4990	+	43.7955i	0.905220	+	2.03316i
$465$		0			0
$466$	−23.2071	−	10.3325i	−1.07505	−	0.478643i
$467$	27.5033	+	1.44139i	1.27270	+	0.0666994i	0.676684	−	0.736273i	$-0.263416\pi$
$467$	27.5033	+	1.44139i	1.27270	+	0.0666994i	0.596016	+	0.802973i	$0.296750\pi$
$468$	−2.30700	−	2.30700i	−0.106641	−	0.106641i
$469$	−0.143409	+	0.326036i	−0.00662202	+	0.0150550i
$470$		0			0
$471$	−2.70364	−	0.574677i	−0.124577	−	0.0264797i
$472$	−4.70659	−	89.8070i	−0.216638	−	4.13370i
$473$	1.42532	+	1.76012i	0.0655361	+	0.0809304i
$474$	−0.405188	+	0.701807i	−0.0186109	+	0.0322350i
$475$		0			0
$476$	−15.2208	−	33.7772i	−0.697643	−	1.54818i
$477$	−2.35427	−	14.8643i	−0.107794	−	0.680588i
$478$	22.2815	−	14.4698i	1.01913	−	0.661832i
$479$	2.77126	−	3.07780i	0.126622	−	0.140628i	−0.676500	−	0.736443i	$-0.736504\pi$
$479$	2.77126	−	3.07780i	0.126622	−	0.140628i	0.803122	+	0.595815i	$0.203171\pi$
$480$		0			0
$481$	2.26369	−	2.03823i	0.103215	−	0.0929355i
$482$	11.0062	−	11.0062i	0.501317	−	0.501317i
$483$	6.46484	+	0.994178i	0.294160	+	0.0452367i
$484$	−32.4454	−	44.6573i	−1.47479	−	2.02988i
$485$		0			0
$486$	40.5233	+	4.25917i	1.83817	+	0.193200i
$487$	−7.16670	−	18.6699i	−0.324754	−	0.846013i	−0.994626	−	0.103536i	$-0.966984\pi$
$487$	−7.16670	−	18.6699i	−0.324754	−	0.846013i	0.669872	−	0.742477i	$-0.266349\pi$
$488$	−55.9853	+	69.1361i	−2.53434	+	3.12964i
$489$	12.1144	+	8.80160i	0.547831	+	0.398022i
$490$		0			0
$491$	14.5355	−	10.5607i	0.655977	−	0.476595i	−0.209325	−	0.977846i	$-0.567127\pi$
$491$	14.5355	−	10.5607i	0.655977	−	0.476595i	0.865302	+	0.501251i	$0.167127\pi$
$492$	2.16574	−	41.3247i	0.0976389	−	1.86306i
$493$	−3.79755	+	14.1727i	−0.171033	+	0.638304i
$494$	0.370377	+	1.74249i	0.0166640	+	0.0783982i
$495$		0			0
$496$	22.2737	−	7.23717i	1.00012	−	0.324959i
$497$	−5.37492	+	2.76914i	−0.241098	+	0.124213i
$498$	21.6485	−	3.42878i	0.970092	−	0.153647i
$499$	−13.8459	−	7.99395i	−0.619829	−	0.357858i	0.156974	−	0.987603i	$-0.449826\pi$
$499$	−13.8459	−	7.99395i	−0.619829	−	0.357858i	−0.776802	+	0.629745i	$0.783160\pi$
$500$		0			0
$501$	−4.09139	−	7.08650i	−0.182790	−	0.316601i
$502$	−22.2827	+	58.0485i	−0.994526	+	2.59083i
$503$	−1.85207	+	3.63489i	−0.0825797	+	0.162072i	−0.928604	−	0.371073i	$-0.878990\pi$
$503$	−1.85207	+	3.63489i	−0.0825797	+	0.162072i	0.846024	+	0.533145i	$0.178990\pi$
$504$	34.4600	−	31.3094i	1.53497	−	1.39463i
$505$		0			0
$506$	−26.4269	−	29.3501i	−1.17482	−	1.30477i
$507$	−9.66468	−	2.58964i	−0.429224	−	0.115010i
$508$	−8.78741	+	13.5314i	−0.389878	+	0.600360i
$509$	−0.293596	−	2.79338i	−0.0130134	−	0.123814i	0.986087	−	0.166233i	$-0.0531604\pi$
$509$	−0.293596	−	2.79338i	−0.0130134	−	0.123814i	−0.999100	+	0.0424186i	$0.986494\pi$
$510$		0			0
$511$	12.3128	+	10.9867i	0.544686	+	0.486024i
$512$	42.3058	+	6.70057i	1.86967	+	0.296126i
$513$	−7.85062	−	6.35731i	−0.346613	−	0.280682i
$514$	−5.99377	+	57.0270i	−0.264374	+	2.51535i
$515$		0			0
$516$	−1.76956	+	0.185989i	−0.0779008	+	0.00818770i
$517$	9.81009	+	19.2534i	0.431447	+	0.846763i
$518$	47.0896	+	57.6196i	2.06900	+	2.53166i
$519$	4.76351	+	1.54776i	0.209095	+	0.0679391i
$520$		0			0
$521$	5.04315	+	4.54087i	0.220944	+	0.198939i	0.772168	−	0.635418i	$-0.219172\pi$
$521$	5.04315	+	4.54087i	0.220944	+	0.198939i	−0.551224	+	0.834357i	$0.685839\pi$
$522$	−31.5224	+	1.65202i	−1.37970	+	0.0723068i
$523$	1.53648	+	0.589801i	0.0671858	+	0.0257902i	0.391729	−	0.920081i	$-0.371877\pi$
$523$	1.53648	+	0.589801i	0.0671858	+	0.0257902i	−0.324543	+	0.945871i	$0.605210\pi$
$524$	−62.6786			−2.73813
$525$		0			0
$526$	24.9814			1.08924
$527$	6.69185	+	2.56876i	0.291502	+	0.111897i
$528$	34.8784	−	1.82790i	1.51789	−	0.0795491i
$529$	9.51899	+	8.57093i	0.413869	+	0.372649i
$530$		0			0
$531$	28.0011	+	9.09811i	1.21514	+	0.394824i
$532$	−30.3368	+	4.94468i	−1.31527	+	0.214379i
$533$	−1.42550	−	2.79770i	−0.0617452	−	0.121182i
$534$	−33.1122	+	3.48023i	−1.43290	+	0.150604i
$535$		0			0
$536$	−0.103171	+	0.981602i	−0.00445629	+	0.0423987i
$537$	3.80262	+	3.07930i	0.164095	+	0.132882i
$538$	4.99278	+	0.790778i	0.215254	+	0.0340929i
$539$	7.19135	+	32.3984i	0.309753	+	1.39550i
$540$		0			0
$541$	−2.08730	−	19.8594i	−0.0897401	−	0.853820i	−0.943103	−	0.332502i	$-0.892107\pi$
$541$	−2.08730	−	19.8594i	−0.0897401	−	0.853820i	0.853362	−	0.521318i	$-0.174560\pi$
$542$	−20.7381	+	31.9338i	−0.890777	+	1.37168i
$543$	−1.82761	−	0.489706i	−0.0784301	−	0.0210153i
$544$	−19.7942	−	21.9836i	−0.848667	−	0.942540i
$545$		0			0
$546$	−0.460483	+	1.43919i	−0.0197068	+	0.0615916i
$547$	−15.3869	+	30.1986i	−0.657898	+	1.29120i	0.285131	+	0.958488i	$0.407963\pi$
$547$	−15.3869	+	30.1986i	−0.657898	+	1.29120i	−0.943029	+	0.332709i	$0.892037\pi$
$548$	9.07893	−	23.6514i	0.387833	−	1.01034i
$549$	−14.5625	−	25.2230i	−0.621512	−	1.07649i
$550$		0			0
$551$	10.5423	+	6.08658i	0.449115	+	0.259297i
$552$	17.9020	−	2.83540i	0.761960	−	0.120683i
$553$	−1.05975	−	0.0507659i	−0.0450650	−	0.00215879i
$554$	−6.91281	+	2.24611i	−0.293697	+	0.0954280i
$555$		0			0
$556$	8.30091	+	39.0527i	0.352037	+	1.65620i
$557$	5.81837	−	21.7145i	0.246532	−	0.920071i	−0.726075	−	0.687616i	$-0.758657\pi$
$557$	5.81837	−	21.7145i	0.246532	−	0.920071i	0.972607	−	0.232455i	$-0.0746759\pi$
$558$	−0.807052	+	15.3995i	−0.0341652	+	0.651911i
$559$	−0.109226	+	0.0793570i	−0.00461975	+	0.00335644i
$560$		0			0
$561$	8.64803	+	6.28316i	0.365120	+	0.265275i
$562$	−9.80087	+	12.1031i	−0.413425	+	0.510537i
$563$	8.02417	+	20.9037i	0.338178	+	0.880985i	0.992217	+	0.124523i	$0.0397402\pi$
$563$	8.02417	+	20.9037i	0.338178	+	0.880985i	−0.654038	+	0.756462i	$0.726926\pi$
$564$	−16.8831	−	1.77449i	−0.710909	−	0.0747195i
$565$		0			0
$566$	−21.3612	−	29.4012i	−0.897880	−	1.23583i
$567$	3.80063	+	9.76956i	0.159611	+	0.410283i
$568$	−11.8474	+	11.8474i	−0.497107	+	0.497107i
$569$	−16.3183	+	14.6931i	−0.684101	+	0.615967i	−0.936089	−	0.351763i	$-0.885582\pi$
$569$	−16.3183	+	14.6931i	−0.684101	+	0.615967i	0.251988	+	0.967730i	$0.418916\pi$
$570$		0			0
$571$	25.3696	−	28.1758i	1.06168	−	1.17912i	0.0784213	−	0.996920i	$-0.475012\pi$
$571$	25.3696	−	28.1758i	1.06168	−	1.17912i	0.983262	−	0.182198i	$-0.0583213\pi$
$572$	5.40459	−	3.50978i	0.225977	−	0.146751i
$573$	−0.439149	−	2.77268i	−0.0183457	−	0.115830i
$574$	69.9339	−	31.5138i	2.91898	−	1.31536i
$575$		0			0
$576$	8.98704	−	15.5660i	0.374460	−	0.648584i
$577$	−8.93692	−	11.0362i	−0.372049	−	0.459442i	0.556393	−	0.830919i	$-0.312185\pi$
$577$	−8.93692	−	11.0362i	−0.372049	−	0.459442i	−0.928442	+	0.371477i	$0.878851\pi$
$578$	1.16404	+	22.2112i	0.0484177	+	0.923864i
$579$	3.19988	+	0.680156i	0.132983	+	0.0282663i
$580$		0			0
$581$	16.9712	+	23.1395i	0.704083	+	0.959987i
$582$	13.9158	+	13.9158i	0.576830	+	0.576830i
$583$	29.6850	+	1.55572i	1.22943	+	0.0644315i
$584$	41.7747	+	18.5993i	1.72865	+	0.769644i
$585$		0			0
$586$	14.7002	+	33.0173i	0.607261	+	1.36393i
$587$	4.70283	−	29.6925i	0.194107	−	1.22554i	−0.677570	−	0.735459i	$-0.736967\pi$
$587$	4.70283	−	29.6925i	0.194107	−	1.22554i	0.871676	−	0.490082i	$-0.163033\pi$
$588$	−24.4236	−	9.12442i	−1.00721	−	0.376285i
$589$	3.49550	−	4.81114i	0.144029	−	0.198239i
$590$		0			0
$591$	−2.40106	+	5.39287i	−0.0987665	+	0.221833i
$592$	85.9891	+	55.8419i	3.53413	+	2.29509i
$593$	26.3077	−	7.04913i	1.08033	−	0.289473i	0.325598	−	0.945508i	$-0.394434\pi$
$593$	26.3077	−	7.04913i	1.08033	−	0.289473i	0.754730	+	0.656035i	$0.227768\pi$
$594$	−15.9884	+	49.2071i	−0.656010	+	2.01899i
$595$		0			0
$596$	−33.9762	−	104.568i	−1.39172	−	4.28328i
$597$	6.54788	+	10.0829i	0.267987	+	0.412664i
$598$	1.82964	−	1.48161i	0.0748196	−	0.0605877i
$599$	21.6329	−	12.4898i	0.883897	−	0.510318i	0.0119557	−	0.999929i	$-0.496194\pi$
$599$	21.6329	−	12.4898i	0.883897	−	0.510318i	0.871941	+	0.489610i	$0.162861\pi$
$600$		0			0
$601$		−	13.5128i		−	0.551198i	−0.961273	−	0.275599i	$-0.911124\pi$
$601$		−	13.5128i		−	0.551198i	0.961273	−	0.275599i	$-0.0888762\pi$
$602$	−1.80874	−	2.75801i	−0.0737189	−	0.112408i
$603$	−0.287915	−	0.146700i	−0.0117248	−	0.00597410i
$604$	11.0164	−	51.8280i	0.448250	−	2.10885i
$605$		0			0
$606$	−3.20419	+	0.681072i	−0.130161	+	0.0276666i
$607$	6.91704	+	25.8147i	0.280754	+	1.04779i	0.951887	+	0.306450i	$0.0991413\pi$
$607$	6.91704	+	25.8147i	0.280754	+	1.04779i	−0.671133	+	0.741337i	$0.734192\pi$
$608$	−21.8677	+	11.1421i	−0.886851	+	0.451873i
$609$	5.20298	+	8.91905i	0.210835	+	0.361418i
$610$		0			0
$611$	−1.17675	+	0.523922i	−0.0476062	+	0.0211956i
$612$	31.3784	−	12.0450i	1.26840	−	0.486892i
$613$	−32.7881	+	12.5862i	−1.32430	+	0.508351i	−0.914781	−	0.403951i	$-0.867637\pi$
$613$	−32.7881	+	12.5862i	−1.32430	+	0.508351i	−0.409519	+	0.912302i	$0.634303\pi$
$614$	−9.74484	+	4.33868i	−0.393270	+	0.175095i
$615$		0			0
$616$	46.3391	+	79.4354i	1.86706	+	3.20055i
$617$	−0.609749	+	0.310683i	−0.0245476	+	0.0125076i	−0.466221	−	0.884668i	$-0.654385\pi$
$617$	−0.609749	+	0.310683i	−0.0245476	+	0.0125076i	0.441674	+	0.897176i	$0.354385\pi$
$618$	−0.356970	−	1.33223i	−0.0143594	−	0.0535902i
$619$	40.9705	−	8.70855i	1.64674	−	0.350026i	0.711132	−	0.703059i	$-0.248183\pi$
$619$	40.9705	−	8.70855i	1.64674	−	0.350026i	0.935611	+	0.353033i	$0.114850\pi$
$620$		0			0
$621$	−2.77574	+	13.0588i	−0.111387	+	0.524033i
$622$	31.4220	+	16.0103i	1.25991	+	0.641956i
$623$	−23.9048	−	36.4505i	−0.957724	−	1.46036i
$624$			2.08199i			0.0833464i
$625$		0			0
$626$	−32.5099	+	18.7696i	−1.29936	+	0.750184i
$627$	6.89220	−	5.58119i	0.275248	−	0.222891i
$628$	−9.34936	−	14.3967i	−0.373080	−	0.574493i
$629$	9.69710	+	29.8446i	0.386649	+	1.18998i
$630$		0			0
$631$	2.57606	−	7.92831i	0.102551	−	0.315621i	−0.886597	−	0.462544i	$-0.846937\pi$
$631$	2.57606	−	7.92831i	0.102551	−	0.315621i	0.989148	+	0.146923i	$0.0469368\pi$
$632$	−2.83983	+	0.760929i	−0.112962	+	0.0302681i
$633$	3.36115	+	2.18276i	0.133594	+	0.0867569i
$634$	−34.7413	+	78.0302i	−1.37975	+	3.09898i
$635$		0			0
$636$	−13.7266	+	18.8931i	−0.544296	+	0.749159i
$637$	−1.95110	+	0.327020i	−0.0773052	+	0.0129570i
$638$	9.75339	−	61.5805i	0.386140	−	2.43800i
$639$	−2.23108	−	5.01109i	−0.0882603	−	0.198236i
$640$		0			0
$641$	−22.9775	−	10.2302i	−0.907556	−	0.404070i	−0.100767	−	0.994910i	$-0.532130\pi$
$641$	−22.9775	−	10.2302i	−0.907556	−	0.404070i	−0.806789	+	0.590840i	$0.798796\pi$
$642$	−19.0798	−	0.999929i	−0.753019	−	0.0394641i
$643$	−29.1194	−	29.1194i	−1.14836	−	1.14836i	−0.986876	−	0.161480i	$-0.948373\pi$
$643$	−29.1194	−	29.1194i	−1.14836	−	1.14836i	−0.161480	−	0.986876i	$-0.551627\pi$
$644$	24.0244	+	32.7563i	0.946695	+	1.29078i
$645$		0			0
$646$	−17.9509	−	3.81558i	−0.706268	−	0.150122i
$647$	−0.626754	−	11.9592i	−0.0246402	−	0.470164i	−0.982886	−	0.184217i	$-0.941025\pi$
$647$	−0.626754	−	11.9592i	−0.0246402	−	0.470164i	0.958245	−	0.285947i	$-0.0923081\pi$
$648$	18.2809	+	22.5750i	0.718142	+	0.886831i
$649$	−29.0769	+	50.3626i	−1.14137	+	1.97691i
$650$		0			0
$651$	4.59900	−	2.07241i	0.180249	−	0.0812243i
$652$	14.5480	+	91.8525i	0.569744	+	3.59722i
$653$	−5.30253	+	3.44351i	−0.207504	+	0.134755i	−0.644207	−	0.764851i	$-0.722813\pi$
$653$	−5.30253	+	3.44351i	−0.207504	+	0.134755i	0.436703	+	0.899606i	$0.356146\pi$
$654$	−4.80934	+	5.34131i	−0.188060	+	0.208862i
$655$		0			0
$656$	78.5420	−	70.7195i	3.06655	−	2.76113i
$657$	−10.5860	+	10.5860i	−0.412998	+	0.412998i
$658$	−11.4089	−	29.3267i	−0.444765	−	1.14327i
$659$	−11.1996	−	15.4150i	−0.436276	−	0.600482i	0.533104	−	0.846050i	$-0.321026\pi$
$659$	−11.1996	−	15.4150i	−0.436276	−	0.600482i	−0.969379	+	0.245568i	$0.921026\pi$
$660$		0			0
$661$	−43.8748	−	4.61143i	−1.70653	−	0.179364i	−0.799569	−	0.600574i	$-0.794939\pi$
$661$	−43.8748	−	4.61143i	−1.70653	−	0.179364i	−0.906963	+	0.421210i	$0.861606\pi$
$662$	20.1609	+	52.5209i	0.783574	+	2.04128i
$663$	−0.401013	+	0.495210i	−0.0155741	+	0.0192324i
$664$	64.3319	+	46.7399i	2.49656	+	1.81386i
$665$		0			0
$666$	−54.6165	+	39.6812i	−2.11635	+	1.53762i
$667$	0.841980	−	16.0659i	0.0326016	−	0.622075i
$668$	13.1530	−	49.0877i	0.508905	−	1.89926i
$669$	1.94868	+	9.16781i	0.0753402	+	0.354448i
$670$		0			0
$671$	54.7118	−	17.7769i	2.11212	−	0.686271i
$672$	−20.7941	−	0.996120i	−0.802152	−	0.0384262i
$673$	6.12934	−	0.970793i	0.236269	−	0.0374213i	−0.0371770	−	0.999309i	$-0.511837\pi$
$673$	6.12934	−	0.970793i	0.236269	−	0.0374213i	0.273446	+	0.961887i	$0.411837\pi$
$674$	8.70812	+	5.02763i	0.335424	+	0.193657i
$675$		0			0
$676$	−31.0701	−	53.8149i	−1.19500	−	2.06980i
$677$	12.7098	−	33.1102i	0.488478	−	1.27253i	−0.438945	−	0.898514i	$-0.644648\pi$
$677$	12.7098	−	33.1102i	0.488478	−	1.27253i	0.927423	−	0.374015i	$-0.122019\pi$
$678$	2.24515	−	4.40636i	0.0862245	−	0.169225i
$679$	−7.85178	+	24.5399i	−0.301324	+	0.941754i
$680$		0			0
$681$	−13.3412	−	14.8170i	−0.511238	−	0.567787i
$682$	−29.4208	−	7.88327i	−1.12658	−	0.301866i
$683$	−11.6609	+	17.9562i	−0.446192	+	0.687076i	−0.988178	−	0.153312i	$-0.951006\pi$
$683$	−11.6609	+	17.9562i	−0.446192	+	0.687076i	0.541986	+	0.840388i	$0.317673\pi$
$684$	−2.91480	−	27.7325i	−0.111450	−	1.06038i
$685$		0			0
$686$	−5.69906	−	47.9917i	−0.217591	−	1.83233i
$687$	−4.25013	−	0.673155i	−0.162153	−	0.0256825i
$688$	−3.53165	−	2.85988i	−0.134643	−	0.109032i
$689$	−0.185223	+	1.76228i	−0.00705642	+	0.0671374i
$690$		0			0
$691$	36.5287	−	3.83932i	1.38962	−	0.146055i	0.620020	−	0.784586i	$-0.287124\pi$
$691$	36.5287	−	3.83932i	1.38962	−	0.146055i	0.769596	+	0.638531i	$0.220458\pi$
$692$	14.1220	+	27.7160i	0.536838	+	1.05360i
$693$	−29.7157	+	4.84345i	−1.12880	+	0.183987i
$694$	43.2308	+	14.0466i	1.64102	+	0.533200i
$695$		0			0
$696$	21.2639	+	19.1461i	0.806005	+	0.725730i
$697$	32.3028	−	1.69292i	1.22356	−	0.0641239i
$698$	−32.5188	−	12.4828i	−1.23085	−	0.472480i
$699$	−7.53892			−0.285148
$700$		0			0
$701$	24.9570			0.942612			0.471306	−	0.881970i	$-0.343783\pi$
$701$	24.9570			0.942612			0.471306	+	0.881970i	$0.343783\pi$
$702$	−2.87939	−	1.10529i	−0.108676	−	0.0417167i
$703$	25.9992	−	1.36256i	0.980577	−	0.0513899i
$704$	26.3833	+	23.7556i	0.994358	+	0.895324i
$705$		0			0
$706$	23.8688	+	7.75546i	0.898316	+	0.291881i
$707$	−2.71392	−	3.32079i	−0.102067	−	0.124891i
$708$	−20.7414	−	40.7072i	−0.779508	−	1.52987i
$709$	−17.5535	+	1.84494i	−0.659234	+	0.0692883i	−0.428237	−	0.903666i	$-0.640865\pi$
$709$	−17.5535	+	1.84494i	−0.659234	+	0.0692883i	−0.230997	+	0.972955i	$0.574199\pi$
$710$		0			0
$711$	0.100611	−	0.957250i	0.00377321	−	0.0358997i
$712$	−93.8722	−	76.0162i	−3.51801	−	2.84883i
$713$	−7.76262	−	1.22948i	−0.290712	−	0.0460443i
$714$	−11.6150	−	10.3641i	−0.434682	−	0.387868i
$715$		0			0
$716$	3.17646	+	30.2220i	0.118710	+	1.12945i
$717$	4.29417	−	6.61244i	0.160369	−	0.246946i
$718$	42.0810	+	11.2756i	1.57045	+	0.420801i
$719$	−30.6434	−	34.0330i	−1.14281	−	1.26922i	−0.958104	−	0.286421i	$-0.907534\pi$
$719$	−30.6434	−	34.0330i	−1.14281	−	1.26922i	−0.184703	−	0.982794i	$-0.559132\pi$
$720$		0			0
$721$	1.33646	−	1.21427i	0.0497725	−	0.0452219i
$722$	15.5969	−	30.6106i	0.580455	−	1.13921i
$723$	1.65538	−	4.31241i	0.0615643	−	0.160380i
$724$	−5.87539	−	10.1765i	−0.218357	−	0.378206i
$725$		0			0
$726$	−20.0861	−	11.5967i	−0.745467	−	0.430395i
$727$	46.3709	−	7.34443i	1.71980	−	0.272390i	0.782942	−	0.622095i	$-0.213718\pi$
$727$	46.3709	−	7.34443i	1.71980	−	0.272390i	0.936860	+	0.349705i	$0.113718\pi$
$728$	−4.87332	+	2.51072i	−0.180617	+	0.0930534i
$729$	0.195818	−	0.0636252i	0.00725253	−	0.00235649i
$730$		0			0
$731$	−0.289176	−	1.36047i	−0.0106956	−	0.0503186i
$732$	−11.6972	+	43.6547i	−0.432342	+	1.61352i
$733$	−0.0919661	+	1.75482i	−0.00339684	+	0.0648156i	−0.999802	−	0.0199006i	$-0.993665\pi$
$733$	−0.0919661	+	1.75482i	−0.00339684	+	0.0648156i	0.996405	+	0.0847162i	$0.0269984\pi$
$734$	23.9214	−	17.3799i	0.882956	−	0.641505i
$735$		0			0
$736$	26.2408	+	19.0651i	0.967250	+	0.702748i
$737$	0.401666	−	0.496016i	0.0147955	−	0.0182710i
$738$	24.9386	+	64.9673i	0.918003	+	2.39148i
$739$	29.4507	+	3.09540i	1.08336	+	0.113866i	0.629344	−	0.777126i	$-0.283323\pi$
$739$	29.4507	+	3.09540i	1.08336	+	0.113866i	0.454018	+	0.890992i	$0.349990\pi$
$740$		0			0
$741$	0.310743	+	0.427701i	0.0114154	+	0.0157120i
$742$	−42.7854	−	6.57964i	−1.57070	−	0.241546i
$743$	7.74707	−	7.74707i	0.284213	−	0.284213i	−0.550574	−	0.834786i	$-0.685591\pi$
$743$	7.74707	−	7.74707i	0.284213	−	0.284213i	0.834786	+	0.550574i	$0.185591\pi$
$744$	10.3879	−	9.35334i	0.380840	−	0.342910i
$745$		0			0
$746$	−42.8605	+	47.6014i	−1.56923	+	1.74281i
$747$	−21.8335	+	14.1788i	−0.798846	+	0.518776i
$748$	10.3853	+	65.5704i	0.379725	+	2.39749i
$749$	−10.2766	−	22.8054i	−0.375500	−	0.833291i
$750$		0			0
$751$	−9.59566	+	16.6202i	−0.350151	+	0.606479i	−0.986276	−	0.165107i	$-0.947203\pi$
$751$	−9.59566	+	16.6202i	−0.350151	+	0.606479i	0.636125	+	0.771586i	$0.280536\pi$
$752$	−27.2856	−	33.6950i	−0.995005	−	1.22873i
$753$	0.965732	+	18.4273i	0.0351932	+	0.671527i
$754$	3.63542	+	0.772733i	0.132394	+	0.0281413i
$755$		0			0
$756$	21.4265	−	48.7125i	0.779274	−	1.77166i
$757$	25.0019	+	25.0019i	0.908708	+	0.908708i	0.996168	−	0.0874597i	$-0.0278749\pi$
$757$	25.0019	+	25.0019i	0.908708	+	0.908708i	−0.0874597	+	0.996168i	$0.527875\pi$
$758$	−19.4904	−	1.02145i	−0.707925	−	0.0371008i
$759$	−10.7074	−	4.76724i	−0.388654	−	0.173040i
$760$		0			0
$761$	11.2517	+	25.2717i	0.407873	+	0.916098i	0.994352	+	0.106134i	$0.0338471\pi$
$761$	11.2517	+	25.2717i	0.407873	+	0.916098i	−0.586479	+	0.809965i	$0.699486\pi$
$762$	−1.06051	+	6.69581i	−0.0384183	+	0.242564i
$763$	−9.10016	−	2.39461i	−0.329448	−	0.0866909i
$764$	10.2477	−	14.1048i	0.370749	−	0.510292i
$765$		0			0
$766$	38.5435	−	86.5702i	1.39263	−	3.12791i
$767$	−2.90734	−	1.88805i	−0.104978	−	0.0681736i
$768$	12.7255	−	3.40979i	0.459193	−	0.123040i
$769$	5.46599	−	16.8226i	0.197109	−	0.606638i	−0.802837	−	0.596199i	$-0.796677\pi$
$769$	5.46599	−	16.8226i	0.197109	−	0.606638i	0.999946	−	0.0104392i	$-0.00332297\pi$
$770$		0			0
$771$	5.25855	+	16.1841i	0.189382	+	0.582858i
$772$	11.0654	+	17.0392i	0.398252	+	0.613255i
$773$	15.9118	−	12.8851i	0.572307	−	0.463445i	−0.298952	−	0.954268i	$-0.596637\pi$
$773$	15.9118	−	12.8851i	0.572307	−	0.463445i	0.871259	+	0.490823i	$0.163304\pi$
$774$	2.59132	−	1.49610i	0.0931430	−	0.0537761i
$775$		0			0
$776$			71.3979i			2.56303i
$777$	19.7216	+	9.93730i	0.707508	+	0.356499i
$778$	56.3103	+	28.6916i	2.01882	+	1.02864i
$779$	5.57970	−	26.2504i	0.199913	−	0.940519i
$780$		0			0
$781$	10.5978	−	2.25263i	0.379219	−	0.0806055i
$782$	6.27735	+	23.4274i	0.224477	+	0.837761i
$783$	−18.7788	+	9.56828i	−0.671100	+	0.341942i
$784$	−27.6297	−	60.5864i	−0.986776	−	2.16380i
$785$		0			0
$786$	−24.0592	+	10.7118i	−0.858162	+	0.382078i
$787$	28.0035	−	10.7496i	0.998218	−	0.383180i	0.196255	−	0.980553i	$-0.437122\pi$
$787$	28.0035	−	10.7496i	0.998218	−	0.383180i	0.801964	+	0.597373i	$0.203789\pi$
$788$	−34.2271	+	13.1385i	−1.21929	+	0.468041i
$789$	6.77273	−	3.01542i	0.241116	−	0.107352i
$790$		0			0
$791$	6.47451	−	0.0290875i	0.230207	−	0.00103423i
$792$	−74.3376	+	37.8769i	−2.64147	+	1.34590i
$793$	0.887560	+	3.31242i	0.0315182	+	0.117627i
$794$	−35.3990	+	7.52429i	−1.25626	+	0.267027i
$795$		0			0
$796$	−15.5238	+	73.0339i	−0.550228	+	2.58862i
$797$	1.23383	+	0.628667i	0.0437044	+	0.0222685i	0.475706	−	0.879604i	$-0.342193\pi$
$797$	1.23383	+	0.628667i	0.0437044	+	0.0222685i	−0.432002	+	0.901873i	$0.642193\pi$
$798$	−10.7997	+	7.08260i	−0.382306	+	0.250721i
$799$		−	13.2700i		−	0.469458i
$800$		0			0
$801$	34.2474	−	19.7728i	1.21007	−	0.698636i
$802$	−5.64860	+	4.57415i	−0.199459	+	0.161519i
$803$	−16.1051	−	24.7997i	−0.568337	−	0.875162i
$804$	0.154949	+	0.476883i	0.00546462	+	0.0168184i
$805$		0			0
$806$	0.561074	−	1.72681i	0.0197630	−	0.0608242i
$807$	1.44905	−	0.388272i	0.0510090	−	0.0136678i
$808$	−9.96704	−	6.47267i	−0.350639	−	0.227708i
$809$	−1.21662	+	2.73257i	−0.0427740	+	0.0960720i	−0.933669	−	0.358138i	$-0.883412\pi$
$809$	−1.21662	+	2.73257i	−0.0427740	+	0.0960720i	0.890895	+	0.454210i	$0.150078\pi$
$810$		0			0
$811$	23.5629	−	32.4316i	0.827407	−	1.13883i	−0.160993	−	0.986955i	$-0.551470\pi$
$811$	23.5629	−	32.4316i	0.827407	−	1.13883i	0.988400	−	0.151872i	$-0.0485302\pi$
$812$	−16.3191	+	62.0169i	−0.572689	+	2.17637i
$813$	−1.76770	+	11.1608i	−0.0619961	+	0.391428i
$814$	−54.2361	−	121.816i	−1.90097	−	4.26966i
$815$		0			0
$816$	−19.5941	−	8.72386i	−0.685931	−	0.305396i
$817$	−1.15235	−	0.0603919i	−0.0403155	−	0.00211285i
$818$	−33.7068	−	33.7068i	−1.17853	−	1.17853i
$819$	−0.195620	−	1.78407i	−0.00683553	−	0.0623403i
$820$		0			0
$821$	−51.2768	−	10.8992i	−1.78957	−	0.380386i	−0.810799	−	0.585324i	$-0.800967\pi$
$821$	−51.2768	−	10.8992i	−1.78957	−	0.380386i	−0.978775	+	0.204938i	$0.934301\pi$
$822$	−0.557105	−	10.6302i	−0.0194313	−	0.370771i
$823$	7.63102	+	9.42352i	0.266001	+	0.328483i	0.892593	−	0.450864i	$-0.148884\pi$
$823$	7.63102	+	9.42352i	0.266001	+	0.328483i	−0.626592	+	0.779347i	$0.715551\pi$
$824$	2.50188	−	4.33339i	0.0871572	−	0.150961i
$825$		0			0
$826$	49.4695	−	68.7362i	1.72126	−	2.39164i
$827$	−4.79027	−	30.2446i	−0.166574	−	1.05171i	−0.919353	−	0.393434i	$-0.871287\pi$
$827$	−4.79027	−	30.2446i	−0.166574	−	1.05171i	0.752779	−	0.658274i	$-0.228713\pi$
$828$	−30.9075	+	20.0716i	−1.07411	+	0.697536i
$829$	12.4506	−	13.8278i	0.432429	−	0.480261i	−0.487065	−	0.873366i	$-0.661932\pi$
$829$	12.4506	−	13.8278i	0.432429	−	0.480261i	0.919494	+	0.393105i	$0.128599\pi$
$830$		0			0
$831$	−1.60302	+	1.44337i	−0.0556082	+	0.0500699i
$832$	−1.49647	+	1.49647i	−0.0518807	+	0.0518807i
$833$	5.09773	−	19.7325i	0.176626	−	0.683690i
$834$	9.86046	+	13.5718i	0.341440	+	0.469951i
$835$		0			0
$836$	54.7769	+	5.75729i	1.89450	+	0.199120i
$837$	3.68980	+	9.61226i	0.127538	+	0.332248i
$838$	48.9758	−	60.4801i	1.69184	−	2.08925i
$839$	−23.8488	−	17.3272i	−0.823352	−	0.598200i	0.0943190	−	0.995542i	$-0.469933\pi$
$839$	−23.8488	−	17.3272i	−0.823352	−	0.598200i	−0.917671	+	0.397342i	$0.869933\pi$
$840$		0			0
$841$	−2.91460	+	2.11758i	−0.100503	+	0.0730199i
$842$	4.86264	−	92.7848i	0.167578	−	3.19757i
$843$	−1.19621	+	4.46431i	−0.0411996	+	0.153759i
$844$	5.17493	+	24.3461i	0.178128	+	0.838028i
$845$		0			0
$846$	27.1508	−	8.82184i	0.933465	−	0.303301i
$847$	1.45295	−	30.3306i	0.0499240	−	1.04217i
$848$	−58.9099	+	9.33041i	−2.02297	+	0.320408i
$849$	−9.34019	−	5.39256i	−0.320555	−	0.185072i
$850$		0			0
$851$	−17.2038	−	29.7978i	−0.589738	−	1.02146i
$852$	−3.05037	+	7.94650i	−0.104504	+	0.272242i
$853$	5.29169	−	10.3855i	0.181184	−	0.355594i	−0.782495	−	0.622657i	$-0.786053\pi$
$853$	5.29169	−	10.3855i	0.181184	−	0.355594i	0.963679	+	0.267063i	$0.0860532\pi$
$854$	−81.8650	+	17.7857i	−2.80136	+	0.608615i
$855$		0			0
$856$	−46.3811	−	51.5114i	−1.58527	−	1.76062i
$857$	23.0922	+	6.18754i	0.788815	+	0.211362i	0.630667	−	0.776053i	$-0.282781\pi$
$857$	23.0922	+	6.18754i	0.788815	+	0.211362i	0.158147	+	0.987416i	$0.449448\pi$
$858$	1.47473	−	2.27088i	0.0503463	−	0.0775265i
$859$	1.45583	+	13.8513i	0.0496722	+	0.472599i	0.990878	+	0.134765i	$0.0430278\pi$
$859$	1.45583	+	13.8513i	0.0496722	+	0.472599i	−0.941205	+	0.337835i	$0.890306\pi$
$860$		0			0
$861$	15.1560	−	16.9852i	0.516513	−	0.578855i
$862$	−44.1692	−	6.99571i	−1.50441	−	0.238275i
$863$	18.8914	+	15.2979i	0.643069	+	0.520747i	0.894465	−	0.447137i	$-0.147556\pi$
$863$	18.8914	+	15.2979i	0.643069	+	0.520747i	−0.251396	+	0.967884i	$0.580890\pi$
$864$	4.44161	−	42.2591i	0.151107	−	1.43768i
$865$		0			0
$866$	−46.3168	+	4.86809i	−1.57391	+	0.165425i
$867$	2.99662	+	5.88120i	0.101771	+	0.199736i
$868$	29.2975	+	11.0955i	0.994423	+	0.376606i
$869$	1.80812	+	0.587492i	0.0613361	+	0.0199293i
$870$		0			0
$871$	0.0282744	+	0.0254584i	0.000958042	+	0.000862625i
$872$	−26.0399	+	1.36470i	−0.881824	+	0.0462144i
$873$	−21.8223	−	8.37679i	−0.738572	−	0.283511i
$874$	20.1222			0.680643
$875$		0			0
$876$	23.2310			0.784902
$877$	−7.53375	−	2.89194i	−0.254397	−	0.0976538i	0.227828	−	0.973701i	$-0.426838\pi$
$877$	−7.53375	−	2.89194i	−0.254397	−	0.0976538i	−0.482224	+	0.876048i	$0.660171\pi$
$878$	6.50159	−	0.340734i	0.219418	−	0.0114992i
$879$	7.97080	+	7.17694i	0.268849	+	0.242072i
$880$		0			0
$881$	−44.5498	−	14.4751i	−1.50092	−	0.487678i	−0.560633	−	0.828064i	$-0.689442\pi$
$881$	−44.5498	−	14.4751i	−1.50092	−	0.487678i	−0.940286	+	0.340386i	$0.889442\pi$
$882$	43.7623	−	2.68797i	1.47355	−	0.0905088i
$883$	18.8301	+	36.9562i	0.633684	+	1.24367i	0.954973	+	0.296694i	$0.0958840\pi$
$883$	18.8301	+	36.9562i	0.633684	+	1.24367i	−0.321289	+	0.946981i	$0.604116\pi$
$884$	−3.93577	+	0.413666i	−0.132374	+	0.0139131i
$885$		0			0
$886$	−8.26233	+	78.6108i	−0.277578	+	2.64098i
$887$	−14.8757	−	12.0461i	−0.499477	−	0.404469i	0.346202	−	0.938160i	$-0.387471\pi$
$887$	−14.8757	−	12.0461i	−0.499477	−	0.404469i	−0.845679	+	0.533691i	$0.820804\pi$
$888$	60.4423	+	9.57312i	2.02831	+	0.321253i
$889$	−8.42876	+	2.78060i	−0.282691	+	0.0932582i
$890$		0			0
$891$	−1.96351	−	18.6815i	−0.0657799	−	0.625854i
$892$	−31.7028	+	48.8181i	−1.06149	+	1.63455i
$893$	−10.6343	−	2.84946i	−0.355864	−	0.0953534i
$894$	−30.9126	−	34.3319i	−1.03387	−	1.14823i
$895$		0			0
$896$	1.38766	+	1.52730i	0.0463585	+	0.0510235i
$897$	0.317196	−	0.622532i	0.0105909	−	0.0207857i
$898$	−6.43212	+	16.7562i	−0.214643	+	0.559163i
$899$	−6.20363	−	10.7450i	−0.206902	−	0.358366i
$900$		0			0
$901$	−15.8091	−	9.12738i	−0.526677	−	0.304077i
$902$	−135.760	+	21.5023i	−4.52031	+	0.715947i
$903$	−0.823281	−	0.529402i	−0.0273971	−	0.0176174i
$904$	17.0634	−	5.54424i	0.567521	−	0.184399i
$905$		0			0
$906$	−4.62882	−	21.7769i	−0.153782	−	0.723488i
$907$	8.32893	−	31.0840i	0.276558	−	1.03213i	−0.678233	−	0.734847i	$-0.737254\pi$
$907$	8.32893	−	31.0840i	0.276558	−	1.03213i	0.954790	−	0.297280i	$-0.0960795\pi$
$908$	6.48058	−	123.657i	0.215066	−	4.10370i
$909$	3.14772	−	2.28695i	0.104403	−	0.0758533i
$910$		0			0
$911$	−17.7729	−	12.9128i	−0.588842	−	0.427819i	0.253059	−	0.967451i	$-0.418563\pi$
$911$	−17.7729	−	12.9128i	−0.588842	−	0.427819i	−0.841901	+	0.539632i	$0.818563\pi$
$912$	−11.1986	+	13.8291i	−0.370822	+	0.457927i
$913$	−18.4276	−	48.0057i	−0.609866	−	1.58876i
$914$	−61.5742	−	6.47170i	−2.03669	−	0.214065i
$915$		0			0
$916$	−15.7083	−	21.6206i	−0.519017	−	0.714366i
$917$	−26.8930	−	21.5782i	−0.888083	−	0.712574i
$918$	22.4673	−	22.4673i	0.741530	−	0.741530i
$919$	−14.9159	+	13.4304i	−0.492031	+	0.443027i	−0.877417	−	0.479729i	$-0.840735\pi$
$919$	−14.9159	+	13.4304i	−0.492031	+	0.443027i	0.385386	+	0.922756i	$0.374068\pi$
$920$		0			0
$921$	−2.11823	+	2.35253i	−0.0697980	+	0.0775185i
$922$	−17.2393	+	11.1953i	−0.567747	+	0.368699i
$923$	0.101035	+	0.637909i	0.00332560	+	0.0209970i
$924$	37.9201	+	27.2911i	1.24748	+	0.897811i
$925$		0			0
$926$	−15.8467	+	27.4473i	−0.520756	+	0.901975i
$927$	1.03094	+	1.27310i	0.0338604	+	0.0418141i
$928$	2.67983	+	51.1342i	0.0879697	+	1.67856i
$929$	31.5791	+	6.71234i	1.03608	+	0.220225i	0.694397	−	0.719592i	$-0.255671\pi$
$929$	31.5791	+	6.71234i	1.03608	+	0.220225i	0.341679	+	0.939817i	$0.389005\pi$
$930$		0			0
$931$	−14.7186	−	8.32237i	−0.482383	−	0.272755i
$932$	−33.1072	−	33.1072i	−1.08446	−	1.08446i
$933$	10.4514	+	0.547736i	0.342164	+	0.0179321i
$934$	65.6553	+	29.2316i	2.14831	+	0.956488i
$935$		0			0
$936$	−2.02287	−	4.54344i	−0.0661196	−	0.148507i
$937$	6.54594	−	41.3294i	0.213846	−	1.35017i	−0.614039	−	0.789276i	$-0.710456\pi$
$937$	6.54594	−	41.3294i	0.213846	−	1.35017i	0.827885	−	0.560898i	$-0.189544\pi$
$938$	−0.654270	+	0.660175i	−0.0213627	+	0.0215555i
$939$	−6.54819	+	9.01281i	−0.213692	+	0.294122i
$940$		0			0
$941$	−10.1969	+	22.9027i	−0.332411	+	0.746607i	0.667587	+	0.744532i	$0.267327\pi$
$941$	−10.1969	+	22.9027i	−0.332411	+	0.746607i	−0.999998	+	0.00207509i	$0.999339\pi$
$942$	−6.04917	−	3.92838i	−0.197093	−	0.127993i
$943$	−34.2589	+	9.17966i	−1.11562	+	0.298931i
$944$	36.0575	−	110.974i	1.17357	−	3.61189i
$945$		0			0
$946$	1.82634	+	5.62089i	0.0593794	+	0.182751i
$947$	13.1901	+	20.3109i	0.428620	+	0.660016i	0.985324	−	0.170694i	$-0.0546011\pi$
$947$	13.1901	+	20.3109i	0.428620	+	0.660016i	−0.556704	+	0.830711i	$0.687934\pi$
$948$	−1.16074	+	0.939949i	−0.0376991	+	0.0305281i
$949$	1.52656	−	0.881357i	0.0495541	−	0.0286101i
$950$		0			0
$951$			25.3484i			0.821978i
$952$	−3.20904	−	56.3842i	−0.104006	−	1.82742i
$953$	−52.1740	−	26.5840i	−1.69008	−	0.861140i	−0.988975	−	0.148086i	$-0.952689\pi$
$953$	−52.1740	−	26.5840i	−1.69008	−	0.861140i	−0.701108	−	0.713055i	$-0.747311\pi$
$954$	8.16510	−	38.4138i	0.264355	−	1.24369i
$955$		0			0
$956$	47.8964	−	10.1807i	1.54908	−	0.329267i
$957$	−4.78891	−	17.8725i	−0.154804	−	0.577735i
$958$	9.62957	−	4.90651i	0.311117	−	0.158522i
$959$	12.0378	−	7.02233i	0.388721	−	0.226763i
$960$		0			0
$961$	22.7827	−	10.1435i	0.734925	−	0.327210i
$962$	7.42086	−	2.84860i	0.239258	−	0.0918426i
$963$	21.1858	−	8.13247i	0.682703	−	0.262065i
$964$	26.2076	−	11.6684i	0.844090	−	0.375813i
$965$		0			0
$966$	14.8199	+	8.46770i	0.476821	+	0.272444i
$967$	−10.1572	+	5.17536i	−0.326634	+	0.166428i	−0.609616	−	0.792697i	$-0.708676\pi$
$967$	−10.1572	+	5.17536i	−0.326634	+	0.166428i	0.282982	+	0.959125i	$0.408676\pi$
$968$	−21.7783	−	81.2776i	−0.699980	−	2.61236i
$969$	−5.32725	+	1.13234i	−0.171136	+	0.0363761i
$970$		0			0
$971$	2.52232	−	11.8666i	0.0809453	−	0.380817i	−0.918963	−	0.394343i	$-0.870972\pi$
$971$	2.52232	−	11.8666i	0.0809453	−	0.380817i	0.999909	+	0.0135257i	$0.00430548\pi$
$972$	66.9140	+	34.0944i	2.14627	+	1.09358i
$973$	−9.88296	+	19.6137i	−0.316833	+	0.628788i
$974$		−	52.1854i		−	1.67213i
$975$		0			0
$976$	−99.9634	+	57.7139i	−3.19975	+	1.84738i
$977$	22.1160	−	17.9092i	0.707553	−	0.572965i	−0.206555	−	0.978435i	$-0.566225\pi$
$977$	22.1160	−	17.9092i	0.707553	−	0.572965i	0.914108	+	0.405470i	$0.132892\pi$
$978$	21.2819	+	32.7713i	0.680522	+	1.04791i
$979$	24.1373	+	74.2870i	0.771432	+	2.37422i
$980$		0			0
$981$	2.63804	−	8.11905i	0.0842261	−	0.259221i
$982$	45.2872	−	12.1347i	1.44517	−	0.387233i
$983$	24.2999	+	15.7805i	0.775047	+	0.503321i	0.870533	−	0.492110i	$-0.163774\pi$
$983$	24.2999	+	15.7805i	0.775047	+	0.503321i	−0.0954866	+	0.995431i	$0.530441\pi$
$984$	25.6573	−	57.6272i	0.817925	−	1.83709i
$985$		0			0
$986$	−22.5053	+	30.9759i	−0.716716	+	0.986475i
$987$	−6.63300	−	6.57367i	−0.211131	−	0.209242i
$988$	−0.513621	+	3.24288i	−0.0163405	+	0.103170i
$989$	0.620284	+	1.39318i	0.0197239	+	0.0443006i
$990$		0			0
$991$	−7.20214	−	3.20660i	−0.228784	−	0.101861i	0.289144	−	0.957286i	$-0.406630\pi$
$991$	−7.20214	−	3.20660i	−0.228784	−	0.101861i	−0.517927	+	0.855425i	$0.673296\pi$
$992$	24.9803	+	1.30916i	0.793127	+	0.0415660i
$993$	11.8055	+	11.8055i	0.374635	+	0.374635i
$994$	−15.6839	+	1.71972i	−0.497464	+	0.0545463i
$995$		0			0
$996$	39.5146	+	8.39909i	1.25207	+	0.266135i
$997$	−0.0483602	−	0.922768i	−0.00153158	−	0.0292244i	0.997757	−	0.0669425i	$-0.0213244\pi$
$997$	−0.0483602	−	0.922768i	−0.00153158	−	0.0292244i	−0.999288	+	0.0377182i	$0.987991\pi$
$998$	−26.2556	−	32.4230i	−0.831108	−	1.02633i
$999$	−22.5377	+	39.0364i	−0.713060	+	1.23506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.82.18		288
5.2	odd	4		175.2.x.a.138.1	yes	288
5.3	odd	4		875.2.bb.c.418.18		288
5.4	even	2		875.2.bb.b.82.1		288
7.3	odd	6	inner	875.2.bb.a.332.1		288
25.2	odd	20		875.2.bb.b.593.18		288
25.11	even	5		875.2.bb.c.782.18		288
25.14	even	10		175.2.x.a.152.1	yes	288
25.23	odd	20	inner	875.2.bb.a.593.1		288
35.3	even	12		875.2.bb.c.668.18		288
35.17	even	12		175.2.x.a.38.1	✓	288
35.24	odd	6		875.2.bb.b.332.18		288
175.52	even	60		875.2.bb.b.843.1		288
175.73	even	60	inner	875.2.bb.a.843.18		288
175.136	odd	30		875.2.bb.c.157.18		288
175.164	odd	30		175.2.x.a.52.1	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.38.1	✓	288	35.17	even	12
175.2.x.a.52.1	yes	288	175.164	odd	30
175.2.x.a.138.1	yes	288	5.2	odd	4
175.2.x.a.152.1	yes	288	25.14	even	10
875.2.bb.a.82.18		288	1.1	even	1	trivial
875.2.bb.a.332.1		288	7.3	odd	6	inner
875.2.bb.a.593.1		288	25.23	odd	20	inner
875.2.bb.a.843.18		288	175.73	even	60	inner
875.2.bb.b.82.1		288	5.4	even	2
875.2.bb.b.332.18		288	35.24	odd	6
875.2.bb.b.593.18		288	25.2	odd	20
875.2.bb.b.843.1		288	175.52	even	60
875.2.bb.c.157.18		288	175.136	odd	30
875.2.bb.c.418.18		288	5.3	odd	4
875.2.bb.c.668.18		288	35.3	even	12
875.2.bb.c.782.18		288	25.11	even	5

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+(2.43619 + 0.935166i) q^{2} +(0.773359 - 0.0405301i) q^{3} +(3.57420 + 3.21822i) q^{4} +(1.92195 + 0.624480i) q^{6} +(0.425622 + 2.61129i) q^{7} +(3.32847 + 6.53248i) q^{8} +(-2.38712 + 0.250897i) q^{9} +(0.495569 - 4.71502i) q^{11} +(2.89457 + 2.34398i) q^{12} +(0.279137 + 0.0442109i) q^{13} +(-1.40509 + 6.75963i) q^{14} +(0.994352 + 9.46062i) q^{16} +(-1.58570 + 2.44177i) q^{17} +(-6.05012 - 1.62112i) q^{18} +(1.61629 + 1.79507i) q^{19} +(0.434995 + 2.00222i) q^{21} +(5.61663 - 11.0233i) q^{22} +(1.14403 - 2.98029i) q^{23} +(2.83886 + 4.91706i) q^{24} +(0.638685 + 0.368745i) q^{26} +(-4.13059 + 0.654222i) q^{27} +(-6.88246 + 10.7030i) q^{28} +(4.79292 - 1.55732i) q^{29} +(-0.511871 - 2.40816i) q^{31} +(-2.62972 + 9.81424i) q^{32} +(0.192153 - 3.66649i) q^{33} +(-6.14653 + 4.46572i) q^{34} +(-9.33949 - 6.78554i) q^{36} +(6.78294 - 8.37624i) q^{37} +(2.25890 + 5.88464i) q^{38} +(0.217665 + 0.0228775i) q^{39} +(-6.53043 - 8.98836i) q^{41} +(-0.812674 + 5.28457i) q^{42} +(-0.337796 + 0.337796i) q^{43} +(16.9453 - 15.2576i) q^{44} +(5.57414 - 6.19070i) q^{46} +(-3.82251 + 2.48237i) q^{47} +(1.15243 + 7.27616i) q^{48} +(-6.63769 + 2.22285i) q^{49} +(-1.12735 + 1.95263i) q^{51} +(0.855409 + 1.05634i) q^{52} +(0.328143 + 6.26134i) q^{53} +(-10.6747 - 2.26898i) q^{54} +(-15.6416 + 11.4720i) q^{56} +(1.32273 + 1.32273i) q^{57} +(13.1328 + 0.688262i) q^{58} +(-11.2057 - 4.98909i) q^{59} +(4.93535 + 11.0850i) q^{61} +(1.00502 - 6.34542i) q^{62} +(-1.67118 - 6.12669i) q^{63} +(-4.40154 + 6.05820i) q^{64} +(3.89690 - 8.75258i) q^{66} +(0.112905 + 0.0733217i) q^{67} +(-13.5258 + 3.62422i) q^{68} +(0.763953 - 2.35120i) q^{69} +(0.706194 + 2.17344i) q^{71} +(-9.58444 - 14.7587i) q^{72} +(4.84717 - 3.92516i) q^{73} +(24.3577 - 14.0629i) q^{74} +11.6175i q^{76} +(12.5232 - 0.712744i) q^{77} +(0.508878 + 0.259287i) q^{78} +(-0.0833737 + 0.392243i) q^{79} +(3.87554 - 0.823772i) q^{81} +(-7.50376 - 28.0044i) q^{82} +(9.66389 - 4.92400i) q^{83} +(-4.88882 + 8.55623i) q^{84} +(-1.13883 + 0.507041i) q^{86} +(3.64354 - 1.39862i) q^{87} +(32.4503 - 12.4565i) q^{88} +(-15.0511 + 6.70116i) q^{89} +(0.00335924 + 0.747724i) q^{91} +(13.6802 - 6.97042i) q^{92} +(-0.493463 - 1.84163i) q^{93} +(-11.6338 + 2.47284i) q^{94} +(-1.63594 + 7.69652i) q^{96} +(8.67698 + 4.42114i) q^{97} +(-18.2494 - 0.792060i) q^{98} +11.3797i 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

Related objects

Downloads

Learn more