LMFDB - Embedded newform 840.2.dj.a.67.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(67,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dj (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.3
Character	$\chi$	$=$	840.67
Dual form			840.2.dj.a.163.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41188 - 0.0812078i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.98681 + 0.229311i) q^{4} +(1.69040 + 1.46374i) q^{5} +(0.286981 + 1.38479i) q^{6} +(2.19039 - 1.48397i) q^{7} +(-2.78652 - 0.485105i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-2.26778 - 2.20390i) q^{10} +(-2.78550 + 4.82463i) q^{11} +(-0.292727 - 1.97846i) q^{12} +(4.22999 + 4.22999i) q^{13} +(-3.21308 + 1.91732i) q^{14} +(0.976356 - 2.01165i) q^{15} +(3.89483 + 0.911196i) q^{16} +(0.357434 - 0.0957741i) q^{17} +(1.26333 - 0.635612i) q^{18} +(-3.88557 + 2.24334i) q^{19} +(3.02286 + 3.29580i) q^{20} +(-2.00032 - 1.73168i) q^{21} +(4.32459 - 6.58559i) q^{22} +(-1.37208 + 5.12067i) q^{23} +(0.252628 + 2.81712i) q^{24} +(0.714927 + 4.94862i) q^{25} +(-5.62873 - 6.31574i) q^{26} +(0.707107 + 0.707107i) q^{27} +(4.69219 - 2.44609i) q^{28} +2.15497 q^{29} +(-1.54186 + 2.76092i) q^{30} +(-7.57009 - 4.37059i) q^{31} +(-5.42504 - 1.60279i) q^{32} +(5.38117 + 1.44188i) q^{33} +(-0.512431 + 0.106195i) q^{34} +(5.87480 + 0.697653i) q^{35} +(-1.83528 + 0.794816i) q^{36} +(-1.48811 - 0.398738i) q^{37} +(5.66814 - 2.85178i) q^{38} +(2.99105 - 5.18066i) q^{39} +(-4.00027 - 4.89876i) q^{40} -6.48184 q^{41} +(2.68359 + 2.60736i) q^{42} +(-4.80750 + 4.80750i) q^{43} +(-6.64060 + 8.94687i) q^{44} +(-2.19580 - 0.422435i) q^{45} +(2.35305 - 7.11835i) q^{46} +(1.25370 + 0.335928i) q^{47} +(-0.127909 - 3.99795i) q^{48} +(2.59564 - 6.50097i) q^{49} +(-0.607525 - 7.04492i) q^{50} +(-0.185021 - 0.320466i) q^{51} +(7.43420 + 9.37417i) q^{52} +(1.73077 - 0.463759i) q^{53} +(-0.940927 - 1.05577i) q^{54} +(-11.7706 + 4.07832i) q^{55} +(-6.82345 + 3.07255i) q^{56} +(3.17256 + 3.17256i) q^{57} +(-3.04256 - 0.175001i) q^{58} +(-2.91223 - 1.68137i) q^{59} +(2.40113 - 3.77287i) q^{60} +(9.74986 - 5.62909i) q^{61} +(10.3331 + 6.78550i) q^{62} +(-1.15495 + 2.38036i) q^{63} +(7.52935 + 2.70350i) q^{64} +(0.958781 + 13.3420i) q^{65} +(-7.48048 - 2.47276i) q^{66} +(13.9525 - 3.73855i) q^{67} +(0.732115 - 0.108321i) q^{68} +5.30131 q^{69} +(-8.23786 - 1.46208i) q^{70} +10.8638i q^{71} +(2.65575 - 0.973145i) q^{72} +(1.90004 + 7.09104i) q^{73} +(2.06866 + 0.683817i) q^{74} +(4.59497 - 1.97136i) q^{75} +(-8.23432 + 3.56608i) q^{76} +(1.05828 + 14.7014i) q^{77} +(-4.64372 + 7.07157i) q^{78} +(-0.655100 - 1.13467i) q^{79} +(5.25008 + 7.24131i) q^{80} +(0.500000 - 0.866025i) q^{81} +(9.15159 + 0.526376i) q^{82} +(6.80401 - 6.80401i) q^{83} +(-3.57717 - 3.89921i) q^{84} +(0.744396 + 0.361294i) q^{85} +(7.17802 - 6.39721i) q^{86} +(-0.557748 - 2.08154i) q^{87} +(10.1023 - 12.0926i) q^{88} +(3.23303 - 1.86659i) q^{89} +(3.06590 + 0.774744i) q^{90} +(15.5425 + 2.98815i) q^{91} +(-3.90029 + 9.85917i) q^{92} +(-2.26238 + 8.44333i) q^{93} +(-1.74279 - 0.576100i) q^{94} +(-9.85185 - 1.89533i) q^{95} +(-0.144073 + 5.65502i) q^{96} +(5.31523 + 5.31523i) q^{97} +(-4.19267 + 8.96781i) q^{98} -5.57100i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) $ 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.41188	−	0.0812078i	−0.998350	−	0.0574226i
$2$	−1.41188	−	0.0812078i	−0.998350	−	0.0574226i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	1.98681	+	0.229311i	0.993405	+	0.114656i
$5$	1.69040	+	1.46374i	0.755971	+	0.654605i
$5$	1.69040	+	1.46374i	0.755971	+	0.654605i
$6$	0.286981	+	1.38479i	0.117159	+	0.565338i
$7$	2.19039	−	1.48397i	0.827891	−	0.560889i
$7$	2.19039	−	1.48397i	0.827891	−	0.560889i
$8$	−2.78652	−	0.485105i	−0.985182	−	0.171510i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−2.26778	−	2.20390i	−0.717135	−	0.696934i
$11$	−2.78550	+	4.82463i	−0.839860	+	1.45468i	0.0501521	+	0.998742i	$0.484029\pi$
$11$	−2.78550	+	4.82463i	−0.839860	+	1.45468i	−0.890012	+	0.455938i	$0.849304\pi$
$12$	−0.292727	−	1.97846i	−0.0845029	−	0.571133i
$13$	4.22999	+	4.22999i	1.17319	+	1.17319i	0.981445	+	0.191742i	$0.0614138\pi$
$13$	4.22999	+	4.22999i	1.17319	+	1.17319i	0.191742	+	0.981445i	$0.438586\pi$
$14$	−3.21308	+	1.91732i	−0.858732	+	0.512424i
$15$	0.976356	−	2.01165i	0.252094	−	0.519405i
$16$	3.89483	+	0.911196i	0.973708	+	0.227799i
$17$	0.357434	−	0.0957741i	0.0866904	−	0.0232286i	−0.215213	−	0.976567i	$-0.569045\pi$
$17$	0.357434	−	0.0957741i	0.0866904	−	0.0232286i	0.301904	+	0.953338i	$0.402378\pi$
$18$	1.26333	−	0.635612i	0.297769	−	0.149815i
$19$	−3.88557	+	2.24334i	−0.891412	+	0.514657i	−0.874404	−	0.485198i	$-0.838747\pi$
$19$	−3.88557	+	2.24334i	−0.891412	+	0.514657i	−0.0170079	+	0.999855i	$0.505414\pi$
$20$	3.02286	+	3.29580i	0.675932	+	0.736964i
$21$	−2.00032	−	1.73168i	−0.436506	−	0.377883i
$22$	4.32459	−	6.58559i	0.922005	−	1.40405i
$23$	−1.37208	+	5.12067i	−0.286098	+	1.06773i	0.661934	+	0.749562i	$0.269736\pi$
$23$	−1.37208	+	5.12067i	−0.286098	+	1.06773i	−0.948033	+	0.318172i	$0.896931\pi$
$24$	0.252628	+	2.81712i	0.0515676	+	0.575043i
$25$	0.714927	+	4.94862i	0.142985	+	0.989725i
$26$	−5.62873	−	6.31574i	−1.10388	−	1.23862i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	4.69219	−	2.44609i	0.886740	−	0.462268i
$29$	2.15497			0.400168			0.200084	−	0.979779i	$-0.435878\pi$
$29$	2.15497			0.400168			0.200084	+	0.979779i	$0.435878\pi$
$30$	−1.54186	+	2.76092i	−0.281504	+	0.504072i
$31$	−7.57009	−	4.37059i	−1.35963	−	0.784981i	−0.370054	−	0.929010i	$-0.620661\pi$
$31$	−7.57009	−	4.37059i	−1.35963	−	0.784981i	−0.989574	+	0.144029i	$0.953994\pi$
$32$	−5.42504	−	1.60279i	−0.959021	−	0.283336i
$33$	5.38117	+	1.44188i	0.936742	+	0.250999i
$34$	−0.512431	+	0.106195i	−0.0878813	+	0.0182123i
$35$	5.87480	+	0.697653i	0.993023	+	0.117925i
$36$	−1.83528	+	0.794816i	−0.305881	+	0.132469i
$37$	−1.48811	−	0.398738i	−0.244644	−	0.0655522i	0.134413	−	0.990925i	$-0.457085\pi$
$37$	−1.48811	−	0.398738i	−0.244644	−	0.0655522i	−0.379057	+	0.925373i	$0.623752\pi$
$38$	5.66814	−	2.85178i	0.919494	−	0.462621i
$39$	2.99105	−	5.18066i	0.478952	−	0.829569i
$40$	−4.00027	−	4.89876i	−0.632498	−	0.774562i
$41$	−6.48184			−1.01229			−0.506147	−	0.862447i	$-0.668931\pi$
$41$	−6.48184			−1.01229			−0.506147	+	0.862447i	$0.668931\pi$
$42$	2.68359	+	2.60736i	0.414087	+	0.402325i
$43$	−4.80750	+	4.80750i	−0.733137	+	0.733137i	−0.971240	−	0.238103i	$-0.923474\pi$
$43$	−4.80750	+	4.80750i	−0.733137	+	0.733137i	0.238103	+	0.971240i	$0.423474\pi$
$44$	−6.64060	+	8.94687i	−1.00111	+	1.34879i
$45$	−2.19580	−	0.422435i	−0.327331	−	0.0629729i
$46$	2.35305	−	7.11835i	0.346938	−	1.04954i
$47$	1.25370	+	0.335928i	0.182871	+	0.0490001i	0.349092	−	0.937088i	$-0.386490\pi$
$47$	1.25370	+	0.335928i	0.182871	+	0.0490001i	−0.166221	+	0.986088i	$0.553157\pi$
$48$	−0.127909	−	3.99795i	−0.0184620	−	0.577055i
$49$	2.59564	−	6.50097i	0.370806	−	0.928710i
$50$	−0.607525	−	7.04492i	−0.0859170	−	0.996302i
$51$	−0.185021	−	0.320466i	−0.0259082	−	0.0448743i
$52$	7.43420	+	9.37417i	1.03094	+	1.29996i
$53$	1.73077	−	0.463759i	0.237740	−	0.0637022i	−0.137982	−	0.990435i	$-0.544062\pi$
$53$	1.73077	−	0.463759i	0.237740	−	0.0637022i	0.375722	+	0.926733i	$0.377395\pi$
$54$	−0.940927	−	1.05577i	−0.128044	−	0.143672i
$55$	−11.7706	+	4.07832i	−1.58715	+	0.549920i
$56$	−6.82345	+	3.07255i	−0.911822	+	0.410586i
$57$	3.17256	+	3.17256i	0.420216	+	0.420216i
$58$	−3.04256	−	0.175001i	−0.399508	−	0.0229787i
$59$	−2.91223	−	1.68137i	−0.379140	−	0.218896i	0.298304	−	0.954471i	$-0.403579\pi$
$59$	−2.91223	−	1.68137i	−0.379140	−	0.218896i	−0.677444	+	0.735574i	$0.736912\pi$
$60$	2.40113	−	3.77287i	0.309984	−	0.487076i
$61$	9.74986	−	5.62909i	1.24834	−	0.720731i	0.277563	−	0.960707i	$-0.410473\pi$
$61$	9.74986	−	5.62909i	1.24834	−	0.720731i	0.970779	+	0.239977i	$0.0771398\pi$
$62$	10.3331	+	6.78550i	1.31231	+	0.861760i
$63$	−1.15495	+	2.38036i	−0.145510	+	0.299897i
$64$	7.52935	+	2.70350i	0.941168	+	0.337938i
$65$	0.958781	+	13.3420i	0.118922	+	1.65487i
$66$	−7.48048	−	2.47276i	−0.920783	−	0.304375i
$67$	13.9525	−	3.73855i	1.70456	−	0.456736i	0.730481	−	0.682933i	$-0.239296\pi$
$67$	13.9525	−	3.73855i	1.70456	−	0.456736i	0.974082	+	0.226196i	$0.0726291\pi$
$68$	0.732115	−	0.108321i	0.0887820	−	0.0131359i
$69$	5.30131			0.638203
$70$	−8.23786	−	1.46208i	−0.984612	−	0.174752i
$71$			10.8638i			1.28929i	0.764481	+	0.644646i	$0.222995\pi$
$71$			10.8638i			1.28929i	−0.764481	+	0.644646i	$0.777005\pi$
$72$	2.65575	−	0.973145i	0.312983	−	0.114686i
$73$	1.90004	+	7.09104i	0.222383	+	0.829944i	0.983436	+	0.181255i	$0.0580158\pi$
$73$	1.90004	+	7.09104i	0.222383	+	0.829944i	−0.761053	+	0.648689i	$0.775318\pi$
$74$	2.06866	+	0.683817i	0.240476	+	0.0794921i
$75$	4.59497	−	1.97136i	0.530581	−	0.227634i
$76$	−8.23432	+	3.56608i	−0.944542	+	0.409057i
$77$	1.05828	+	14.7014i	0.120602	+	1.67538i
$78$	−4.64372	+	7.07157i	−0.525798	+	0.800698i
$79$	−0.655100	−	1.13467i	−0.0737045	−	0.127660i	0.826818	−	0.562470i	$-0.190149\pi$
$79$	−0.655100	−	1.13467i	−0.0737045	−	0.127660i	−0.900522	+	0.434810i	$0.856816\pi$
$80$	5.25008	+	7.24131i	0.586977	+	0.809603i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	9.15159	+	0.526376i	1.01062	+	0.0581285i
$83$	6.80401	−	6.80401i	0.746837	−	0.746837i	−0.227047	−	0.973884i	$-0.572907\pi$
$83$	6.80401	−	6.80401i	0.746837	−	0.746837i	0.973884	+	0.227047i	$0.0729070\pi$
$84$	−3.57717	−	3.89921i	−0.390301	−	0.425439i
$85$	0.744396	+	0.361294i	0.0807411	+	0.0391878i
$86$	7.17802	−	6.39721i	0.774026	−	0.689829i
$87$	−0.557748	−	2.08154i	−0.0597968	−	0.223165i
$88$	10.1023	−	12.0926i	1.07691	−	1.28908i
$89$	3.23303	−	1.86659i	0.342700	−	0.197858i	−0.318765	−	0.947834i	$-0.603268\pi$
$89$	3.23303	−	1.86659i	0.342700	−	0.197858i	0.661465	+	0.749976i	$0.269935\pi$
$90$	3.06590	+	0.774744i	0.323175	+	0.0816651i
$91$	15.5425	+	2.98815i	1.62930	+	0.313243i
$92$	−3.90029	+	9.85917i	−0.406633	+	1.02789i
$93$	−2.26238	+	8.44333i	−0.234598	+	0.875533i
$94$	−1.74279	−	0.576100i	−0.179755	−	0.0594201i
$95$	−9.85185	−	1.89533i	−1.01078	−	0.194457i
$96$	−0.144073	+	5.65502i	−0.0147044	+	0.577163i
$97$	5.31523	+	5.31523i	0.539679	+	0.539679i	0.923435	−	0.383755i	$-0.125369\pi$
$97$	5.31523	+	5.31523i	0.539679	+	0.539679i	−0.383755	+	0.923435i	$0.625369\pi$
$98$	−4.19267	+	8.96781i	−0.423523	+	0.905885i
$99$		−	5.57100i		−	0.559906i
$100$	0.285650	+	9.99592i	0.0285650	+	0.999592i
$101$	12.1989	+	7.04305i	1.21384	+	0.700810i	0.963593	−	0.267373i	$-0.0861556\pi$
$101$	12.1989	+	7.04305i	1.21384	+	0.700810i	0.250245	+	0.968183i	$0.419489\pi$
$102$	0.235204	+	0.467485i	0.0232886	+	0.0462879i
$103$	2.38479	−	8.90017i	0.234981	−	0.876960i	−0.743177	−	0.669095i	$-0.766682\pi$
$103$	2.38479	−	8.90017i	0.234981	−	0.876960i	0.978158	−	0.207865i	$-0.0666514\pi$
$104$	−9.73495	−	13.8389i	−0.954590	−	1.35702i
$105$	−0.846629	−	5.85519i	−0.0826226	−	0.571408i
$106$	−2.48130	+	0.514220i	−0.241005	+	0.0499454i
$107$	2.00387	−	7.47856i	0.193722	−	0.722979i	−0.798872	−	0.601501i	$-0.794570\pi$
$107$	2.00387	−	7.47856i	0.193722	−	0.722979i	0.992594	−	0.121479i	$-0.0387636\pi$
$108$	1.24274	+	1.56703i	0.119583	+	0.150788i
$109$	−2.51427	+	4.35484i	−0.240823	+	0.417118i	−0.960949	−	0.276725i	$-0.910751\pi$
$109$	−2.51427	+	4.35484i	−0.240823	+	0.417118i	0.720126	+	0.693844i	$0.244084\pi$
$110$	16.9499	−	4.80223i	1.61611	−	0.457874i
$111$			1.54061i			0.146228i
$112$	9.88341	−	3.78395i	0.933894	−	0.357550i
$113$	1.95011	−	1.95011i	0.183451	−	0.183451i	−0.609407	−	0.792858i	$-0.708592\pi$
$113$	1.95011	−	1.95011i	0.183451	−	0.183451i	0.792858	+	0.609407i	$0.208592\pi$
$114$	−4.22164	−	4.73691i	−0.395392	−	0.443652i
$115$	−9.81470	+	6.64763i	−0.915226	+	0.619895i
$116$	4.28152	+	0.494159i	0.397529	+	0.0458816i
$117$	−5.77827	−	1.54828i	−0.534201	−	0.143139i
$118$	3.97517	+	2.61040i	0.365944	+	0.240306i
$119$	0.640794	−	0.740205i	0.0587415	−	0.0678545i
$120$	−3.69649	+	5.13186i	−0.337442	+	0.468472i
$121$	−10.0180	−	17.3517i	−0.910728	−	1.57743i
$122$	−14.2228	+	7.15583i	−1.28767	+	0.647858i
$123$	1.67762	+	6.26098i	0.151266	+	0.564534i
$124$	−14.0381	−	10.4194i	−1.26066	−	0.935694i
$125$	−6.03499	+	9.41164i	−0.539786	+	0.841803i
$126$	1.82395	−	3.26699i	0.162491	−	0.291046i
$127$	14.2525	−	14.2525i	1.26471	−	1.26471i	0.315919	−	0.948786i	$-0.397687\pi$
$127$	14.2525	−	14.2525i	1.26471	−	1.26471i	0.948786	−	0.315919i	$-0.102313\pi$
$128$	−10.4110	−	4.42846i	−0.920210	−	0.391425i
$129$	5.88796	+	3.39942i	0.518406	+	0.299302i
$130$	−0.270211	−	18.9152i	−0.0236990	−	1.65897i
$131$	1.17297	+	2.03165i	0.102483	+	0.177506i	0.912707	−	0.408614i	$-0.133988\pi$
$131$	1.17297	+	2.03165i	0.102483	+	0.177506i	−0.810224	+	0.586120i	$0.800655\pi$
$132$	10.3607	+	4.09871i	0.901786	+	0.356747i
$133$	−5.18188	+	10.6799i	−0.449326	+	0.926063i
$134$	−20.0028	+	4.14533i	−1.72798	+	0.358102i
$135$	0.160275	+	2.23032i	0.0137943	+	0.191955i
$136$	−1.04246	+	0.0934833i	−0.0893898	+	0.00801613i
$137$	−4.18186	+	1.12053i	−0.357281	+	0.0957331i	−0.432995	−	0.901396i	$-0.642543\pi$
$137$	−4.18186	+	1.12053i	−0.357281	+	0.0957331i	0.0757139	+	0.997130i	$0.475876\pi$
$138$	−7.48481	−	0.430508i	−0.637150	−	0.0366472i
$139$			19.6140i			1.66364i	0.555046	+	0.831819i	$0.312700\pi$
$139$			19.6140i			1.66364i	−0.555046	+	0.831819i	$0.687300\pi$
$140$	11.5121	+	2.73326i	0.972953	+	0.231003i
$141$		−	1.29792i		−	0.109305i
$142$	0.882223	−	15.3383i	0.0740345	−	1.28716i
$143$	−32.1907	+	8.62548i	−2.69192	+	0.721299i
$144$	−3.82862	+	1.15830i	−0.319052	+	0.0965248i
$145$	3.64277	+	3.15432i	0.302516	+	0.261952i
$146$	−2.10678	−	10.1660i	−0.174358	−	0.841344i
$147$	−6.95126	−	0.824624i	−0.573330	−	0.0680139i
$148$	−2.86516	−	1.13346i	−0.235515	−	0.0931697i
$149$	−9.37590	−	16.2395i	−0.768103	−	1.33039i	−0.938590	−	0.345034i	$-0.887867\pi$
$149$	−9.37590	−	16.2395i	−0.768103	−	1.33039i	0.170487	−	0.985360i	$-0.445466\pi$
$150$	−6.64763	+	2.41018i	−0.542777	+	0.196791i
$151$	−11.9413	−	6.89433i	−0.971771	−	0.561052i	−0.0719956	−	0.997405i	$-0.522937\pi$
$151$	−11.9413	−	6.89433i	−0.971771	−	0.561052i	−0.899776	+	0.436352i	$0.856270\pi$
$152$	11.9155	−	4.36619i	0.966472	−	0.354145i
$153$	−0.261660	+	0.261660i	−0.0211539	+	0.0211539i
$154$	−0.300293	−	20.8426i	−0.0241983	−	1.67954i
$155$	−6.39909	−	18.4687i	−0.513987	−	1.48344i
$156$	7.13064	−	9.60710i	0.570908	−	0.769184i
$157$	1.25403	+	4.68010i	0.100082	+	0.373512i	0.997741	−	0.0671792i	$-0.0213999\pi$
$157$	1.25403	+	4.68010i	0.100082	+	0.373512i	−0.897659	+	0.440692i	$0.854733\pi$
$158$	0.832779	+	1.65521i	0.0662524	+	0.131682i
$159$	−0.895913	−	1.55177i	−0.0710506	−	0.123063i
$160$	−6.82444	−	10.6502i	−0.539519	−	0.841973i
$161$	4.59355	+	13.2524i	0.362022	+	1.04444i
$162$	−0.776268	+	1.18212i	−0.0609894	+	0.0928761i
$163$	−2.58344	−	0.692231i	−0.202351	−	0.0542197i	0.156220	−	0.987722i	$-0.450069\pi$
$163$	−2.58344	−	0.692231i	−0.202351	−	0.0542197i	−0.358571	+	0.933503i	$0.616736\pi$
$164$	−12.8782	−	1.48636i	−1.00562	−	0.116065i
$165$	6.98581	+	10.3140i	0.543845	+	0.802944i
$166$	−10.1590	+	9.05391i	−0.788490	+	0.702720i
$167$	13.5322	−	13.5322i	1.04715	−	1.04715i	0.0483210	−	0.998832i	$-0.484613\pi$
$167$	13.5322	−	13.5322i	1.04715	−	1.04715i	0.998832	−	0.0483210i	$-0.0153870\pi$
$168$	4.73389	+	5.79571i	0.365228	+	0.447149i
$169$			22.7856i			1.75274i
$170$	−1.02166	−	0.570554i	−0.0783576	−	0.0437595i
$171$	2.24334	−	3.88557i	0.171552	−	0.297137i
$172$	−10.6540	+	8.44918i	−0.812361	+	0.644244i
$173$	1.74590	−	6.51581i	0.132739	−	0.495388i	−0.867258	−	0.497859i	$-0.834120\pi$
$173$	1.74590	−	6.51581i	0.132739	−	0.495388i	0.999997	+	0.00247098i	$0.000786537\pi$
$174$	0.618435	+	2.98418i	0.0468835	+	0.226230i
$175$	8.90960	+	9.77850i	0.673502	+	0.739185i
$176$	−15.2452	+	16.2530i	−1.14915	+	1.22511i
$177$	−0.870344	+	3.24817i	−0.0654190	+	0.244147i
$178$	−4.71623	+	2.37285i	−0.353496	+	0.177853i
$179$	1.10843	+	0.639953i	0.0828481	+	0.0478324i	0.540852	−	0.841118i	$-0.318102\pi$
$179$	1.10843	+	0.639953i	0.0828481	+	0.0478324i	−0.458004	+	0.888950i	$0.651435\pi$
$180$	−4.26577	−	1.34282i	−0.317952	−	0.100088i
$181$			19.3108i			1.43536i	0.696374	+	0.717679i	$0.254795\pi$
$181$			19.3108i			1.43536i	−0.696374	+	0.717679i	$0.745205\pi$
$182$	−21.7015	−	5.48108i	−1.60862	−	0.406285i
$183$	−7.96073	−	7.96073i	−0.588474	−	0.588474i
$184$	6.30739	−	13.6032i	0.464987	−	1.00284i
$185$	−1.93186	−	2.85224i	−0.142033	−	0.209701i
$186$	3.87988	−	11.7373i	0.284487	−	0.860617i
$187$	−0.533557	+	1.99126i	−0.0390176	+	0.145616i
$188$	2.41383	+	0.954912i	0.176047	+	0.0696441i
$189$	2.59817	+	0.499514i	0.188989	+	0.0363343i
$190$	13.7557	+	3.47602i	0.997945	+	0.252177i
$191$	11.9792	−	6.91618i	0.866783	−	0.500437i	0.000505095	−	1.00000i	$-0.499839\pi$
$191$	11.9792	−	6.91618i	0.866783	−	0.500437i	0.866278	+	0.499563i	$0.166506\pi$
$192$	0.662646	−	7.97251i	0.0478223	−	0.575366i
$193$	−4.98883	−	18.6186i	−0.359104	−	1.34019i	−0.875241	−	0.483688i	$-0.839297\pi$
$193$	−4.98883	−	18.6186i	−0.359104	−	1.34019i	0.516137	−	0.856506i	$-0.327370\pi$
$194$	−7.07282	−	7.93610i	−0.507799	−	0.569779i
$195$	12.6392	−	4.37927i	0.905114	−	0.313606i
$196$	6.64780	−	12.3210i	0.474843	−	0.880071i
$197$	8.87857	−	8.87857i	0.632572	−	0.632572i	−0.316140	−	0.948712i	$-0.602387\pi$
$197$	8.87857	−	8.87857i	0.632572	−	0.632572i	0.948712	+	0.316140i	$0.102387\pi$
$198$	−0.452408	+	7.86558i	−0.0321513	+	0.558982i
$199$	6.58171	−	11.3999i	0.466565	−	0.808115i	−0.532705	−	0.846301i	$-0.678825\pi$
$199$	6.58171	−	11.3999i	0.466565	−	0.808115i	0.999271	+	0.0381859i	$0.0121579\pi$
$200$	0.408443	−	14.1362i	0.0288813	−	0.999583i
$201$	−7.22232	−	12.5094i	−0.509423	−	0.882347i
$202$	−16.6515	−	10.9346i	−1.17159	−	0.769355i
$203$	4.72024	−	3.19792i	0.331296	−	0.224450i
$204$	−0.294116	−	0.679134i	−0.0205922	−	0.0475489i
$205$	−10.9569	−	9.48774i	−0.765265	−	0.662652i
$206$	−4.08981	+	12.3723i	−0.284950	+	0.862020i
$207$	−1.37208	−	5.12067i	−0.0953662	−	0.355911i
$208$	12.6207	+	20.3294i	0.875091	+	1.40959i
$209$		−	24.9953i		−	1.72896i
$210$	0.719852	+	8.33558i	0.0496745	+	0.575209i
$211$	−0.281828			−0.0194019			−0.00970093	−	0.999953i	$-0.503088\pi$
$211$	−0.281828			−0.0194019			−0.00970093	+	0.999953i	$0.503088\pi$
$212$	3.54506	−	0.524516i	0.243476	−	0.0360239i
$213$	10.4936	−	2.81175i	0.719009	−	0.192658i
$214$	−3.43655	+	10.3961i	−0.234917	+	0.710662i
$215$	−15.1636	+	1.08968i	−1.03415	+	0.0743157i
$216$	−1.62734	−	2.31339i	−0.110727	−	0.157406i
$217$	−23.0673	+	1.66050i	−1.56591	+	0.112722i
$218$	3.90349	−	5.94434i	0.264378	−	0.402601i
$219$	6.35766	−	3.67059i	0.429611	−	0.248036i
$220$	−24.3212	+	5.40371i	−1.63973	+	0.364318i
$221$	1.91706	+	1.10682i	0.128956	+	0.0744526i
$222$	0.125109	−	2.17515i	0.00839679	−	0.145987i
$223$	0.661316	+	0.661316i	0.0442850	+	0.0442850i	0.728902	−	0.684618i	$-0.240031\pi$
$223$	0.661316	+	0.661316i	0.0442850	+	0.0442850i	−0.684618	+	0.728902i	$0.740031\pi$
$224$	−14.2615	+	4.53988i	−0.952885	+	0.303333i
$225$	−3.09346	−	3.92817i	−0.206230	−	0.261878i
$226$	−2.91169	+	2.59496i	−0.193682	+	0.172614i
$227$	21.4090	−	5.73653i	1.42097	−	0.380747i	0.535140	−	0.844763i	$-0.320259\pi$
$227$	21.4090	−	5.73653i	1.42097	−	0.380747i	0.885827	+	0.464016i	$0.153592\pi$
$228$	5.57577	+	7.03078i	0.369264	+	0.465625i
$229$	−2.38356	−	4.12844i	−0.157510	−	0.272815i	0.776460	−	0.630166i	$-0.217013\pi$
$229$	−2.38356	−	4.12844i	−0.157510	−	0.272815i	−0.933970	+	0.357351i	$0.883680\pi$
$230$	14.3970	−	8.58863i	0.949312	−	0.566317i
$231$	13.9266	−	4.82723i	0.916302	−	0.317608i
$232$	−6.00486	−	1.04539i	−0.394239	−	0.0686330i
$233$	0.0109131	+	0.00292416i	0.000714941	+	0.000191568i	0.259176	−	0.965830i	$-0.416549\pi$
$233$	0.0109131	+	0.00292416i	0.000714941	+	0.000191568i	−0.258462	+	0.966022i	$0.583216\pi$
$234$	8.03249	+	2.65523i	0.525101	+	0.173578i
$235$	1.62755	+	2.40294i	0.106169	+	0.156751i
$236$	−5.40048	−	4.00838i	−0.351542	−	0.260923i
$237$	−0.926452	+	0.926452i	−0.0601795	+	0.0601795i
$238$	−0.964835	+	0.993044i	−0.0625410	+	0.0643695i
$239$	10.3228			0.667723			0.333862	−	0.942622i	$-0.391648\pi$
$239$	10.3228			0.667723			0.333862	+	0.942622i	$0.391648\pi$
$240$	5.63575	−	6.94538i	0.363786	−	0.448322i
$241$	−5.14413	+	8.90990i	−0.331363	+	0.573937i	−0.982779	−	0.184783i	$-0.940842\pi$
$241$	−5.14413	+	8.90990i	−0.331363	+	0.573937i	0.651417	+	0.758720i	$0.274175\pi$
$242$	12.7351	+	25.3121i	0.818645	+	1.62712i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	20.6619	−	8.94817i	1.32275	−	0.572848i
$245$	13.9034	−	7.18992i	0.888257	−	0.459347i
$246$	−1.86016	−	8.97599i	−0.118600	−	0.572288i
$247$	−25.9252	−	6.94664i	−1.64958	−	0.442004i
$248$	18.9740	+	15.8510i	1.20485	+	1.00654i
$249$	−8.33318	−	4.81116i	−0.528094	−	0.304895i
$250$	9.28497	−	12.7980i	0.587233	−	0.809418i
$251$	−1.10630			−0.0698290			−0.0349145	−	0.999390i	$-0.511116\pi$
$251$	−1.10630			−0.0698290			−0.0349145	+	0.999390i	$0.511116\pi$
$252$	−2.84051	+	4.46447i	−0.178935	+	0.281235i
$253$	−20.8834	−	20.8834i	−1.31293	−	1.31293i
$254$	−21.2802	+	18.9654i	−1.33524	+	1.19000i
$255$	0.156319	−	0.812541i	0.00978907	−	0.0508833i
$256$	14.3394	+	7.09791i	0.896215	+	0.443620i
$257$	5.27272	−	19.6781i	0.328903	−	1.22748i	−0.581426	−	0.813599i	$-0.697505\pi$
$257$	5.27272	−	19.6781i	0.328903	−	1.22748i	0.910329	−	0.413884i	$-0.135828\pi$
$258$	−8.03704	−	5.27772i	−0.500364	−	0.328576i
$259$	−3.85127	+	1.33493i	−0.239306	+	0.0829482i
$260$	−1.15455	+	26.7279i	−0.0716023	+	1.65759i
$261$	−1.86626	+	1.07749i	−0.115519	+	0.0666947i
$262$	−1.49111	−	2.96370i	−0.0921211	−	0.183098i
$263$	−15.7050	+	4.20813i	−0.968410	+	0.259485i	−0.708156	−	0.706056i	$-0.750473\pi$
$263$	−15.7050	+	4.20813i	−0.968410	+	0.259485i	−0.260254	+	0.965540i	$0.583806\pi$
$264$	−14.2953	−	6.62825i	−0.879812	−	0.407941i
$265$	3.60453	+	1.74946i	0.221424	+	0.107469i
$266$	8.18349	−	14.6579i	0.501762	−	0.898734i
$267$	−2.63976	−	2.63976i	−0.161550	−	0.161550i
$268$	28.5782	−	4.22833i	1.74569	−	0.258286i
$269$	2.46307	−	4.26616i	0.150176	−	0.260112i	−0.781116	−	0.624386i	$-0.785349\pi$
$269$	2.46307	−	4.26616i	0.150176	−	0.260112i	0.931292	+	0.364274i	$0.118683\pi$
$270$	−0.0451698	−	3.16196i	−0.00274895	−	0.192430i
$271$	9.47009	−	5.46756i	0.575267	−	0.332130i	−0.183983	−	0.982929i	$-0.558899\pi$
$271$	9.47009	−	5.46756i	0.575267	−	0.332130i	0.759250	+	0.650799i	$0.225566\pi$
$272$	1.47941	−	0.0473317i	0.0897027	−	0.00286991i
$273$	−1.13638	−	15.7863i	−0.0687766	−	0.955432i
$274$	5.99529	−	1.24245i	0.362188	−	0.0750591i
$275$	−25.8667	−	10.3351i	−1.55982	−	0.623232i
$276$	10.5327	+	1.21565i	0.633994	+	0.0731736i
$277$	−2.91014	−	10.8608i	−0.174854	−	0.652562i	−0.996577	−	0.0826752i	$-0.973654\pi$
$277$	−2.91014	−	10.8608i	−0.174854	−	0.652562i	0.821723	−	0.569887i	$-0.193013\pi$
$278$	1.59281	−	27.6926i	0.0955304	−	1.66089i
$279$	8.74118			0.523321
$280$	−16.0318	−	4.79391i	−0.958083	−	0.286491i
$281$	−12.9485			−0.772444			−0.386222	−	0.922406i	$-0.626220\pi$
$281$	−12.9485			−0.772444			−0.386222	+	0.922406i	$0.626220\pi$
$282$	−0.105402	+	1.83251i	−0.00627657	+	0.109125i
$283$	5.96390	+	22.2576i	0.354517	+	1.32308i	0.881091	+	0.472947i	$0.156810\pi$
$283$	5.96390	+	22.2576i	0.354517	+	1.32308i	−0.526574	+	0.850129i	$0.676524\pi$
$284$	−2.49118	+	21.5842i	−0.147825	+	1.28079i
$285$	0.719101	+	10.0067i	0.0425959	+	0.592746i
$286$	46.1499	−	9.56401i	2.72890	−	0.565532i
$287$	−14.1978	+	9.61888i	−0.838069	+	0.567785i
$288$	5.49962	−	1.32446i	0.324068	−	0.0780447i
$289$	−14.6038	+	8.43153i	−0.859050	+	0.495973i
$290$	−4.88700	−	4.74934i	−0.286975	−	0.278891i
$291$	3.75843	−	6.50980i	0.220323	−	0.381611i
$292$	2.14896	+	14.5243i	0.125758	+	0.849968i
$293$	7.48370	+	7.48370i	0.437203	+	0.437203i	0.891070	−	0.453867i	$-0.149956\pi$
$293$	7.48370	+	7.48370i	0.437203	+	0.437203i	−0.453867	+	0.891070i	$0.649956\pi$
$294$	9.74738	+	1.72877i	0.568479	+	0.100824i
$295$	−2.46174	−	7.10495i	−0.143328	−	0.413666i
$296$	3.95322	+	1.83298i	0.229776	+	0.106540i
$297$	−5.38117	+	1.44188i	−0.312247	+	0.0836664i
$298$	11.9189	+	23.6897i	0.690441	+	1.37231i
$299$	−27.4643	+	15.8565i	−1.58830	+	0.917005i
$300$	9.58139	−	2.86305i	0.553182	−	0.165298i
$301$	−3.39611	+	17.6645i	−0.195749	+	1.01817i
$302$	16.2998	+	10.7037i	0.937951	+	0.615928i
$303$	3.64575	−	13.6061i	0.209443	−	0.781652i
$304$	−17.1778	+	5.19690i	−0.985213	+	0.298063i
$305$	24.7207	+	4.75584i	1.41550	+	0.272319i
$306$	0.390681	−	0.348183i	0.0223337	−	0.0199043i
$307$	−20.7138	−	20.7138i	−1.18220	−	1.18220i	−0.979173	−	0.203028i	$-0.934922\pi$
$307$	−20.7138	−	20.7138i	−1.18220	−	1.18220i	−0.203028	−	0.979173i	$-0.565078\pi$
$308$	−1.26860	+	29.4516i	−0.0722854	+	1.67816i
$309$	−9.21414			−0.524174
$310$	7.53494	+	26.5953i	0.427956	+	1.51051i
$311$	−9.94499	−	5.74174i	−0.563928	−	0.325584i	0.190792	−	0.981630i	$-0.438894\pi$
$311$	−9.94499	−	5.74174i	−0.563928	−	0.325584i	−0.754721	+	0.656046i	$0.772228\pi$
$312$	−10.8478	+	12.9850i	−0.614135	+	0.735131i
$313$	11.0195	+	2.95266i	0.622857	+	0.166894i	0.556426	−	0.830897i	$-0.312172\pi$
$313$	11.0195	+	2.95266i	0.622857	+	0.166894i	0.0664309	+	0.997791i	$0.478839\pi$
$314$	−1.39048	−	6.70957i	−0.0784692	−	0.378643i
$315$	−5.43655	+	2.33322i	−0.306315	+	0.131462i
$316$	−1.04137	−	2.40459i	−0.0585815	−	0.135269i
$317$	4.76290	+	1.27621i	0.267511	+	0.0716794i	0.390081	−	0.920780i	$-0.372447\pi$
$317$	4.76290	+	1.27621i	0.267511	+	0.0716794i	−0.122570	+	0.992460i	$0.539114\pi$
$318$	1.13891	+	2.26366i	0.0638667	+	0.126940i
$319$	−6.00267	+	10.3969i	−0.336085	+	0.582116i
$320$	8.77041	+	15.5910i	0.490281	+	0.871565i
$321$	−7.74237			−0.432137
$322$	−5.40934	−	19.0839i	−0.301451	−	1.06350i
$323$	−1.17398	+	1.17398i	−0.0653221	+	0.0653221i
$324$	1.19199	−	1.60597i	0.0662219	−	0.0892207i
$325$	−17.9085	+	23.9568i	−0.993384	+	1.32888i
$326$	3.59129	+	1.18714i	0.198903	+	0.0657497i
$327$	4.85720	+	1.30148i	0.268604	+	0.0719721i
$328$	18.0618	+	3.14437i	0.997294	+	0.173619i
$329$	3.24460	−	1.12464i	0.178881	−	0.0620035i
$330$	−9.02555	−	15.1294i	−0.496840	−	0.832848i
$331$	2.95564	+	5.11931i	0.162456	+	0.281383i	0.935749	−	0.352666i	$-0.114725\pi$
$331$	2.95564	+	5.11931i	0.162456	+	0.281383i	−0.773293	+	0.634049i	$0.781392\pi$
$332$	15.0785	−	11.9580i	0.827541	−	0.656283i
$333$	1.48811	−	0.398738i	0.0815480	−	0.0218507i
$334$	−20.2048	+	18.0069i	−1.10556	+	0.985295i
$335$	29.0575	+	14.1031i	1.58758	+	0.770535i
$336$	−6.21303	−	8.56728i	−0.338949	−	0.467383i
$337$	22.1222	+	22.1222i	1.20507	+	1.20507i	0.972604	+	0.232469i	$0.0746804\pi$
$337$	22.1222	+	22.1222i	1.20507	+	1.20507i	0.232469	+	0.972604i	$0.425320\pi$
$338$	1.85037	−	32.1705i	0.100647	−	1.74985i
$339$	−2.38839	−	1.37894i	−0.129719	−	0.0748935i
$340$	1.39612	+	0.888520i	0.0757155	+	0.0481868i
$341$	42.1729	−	24.3486i	2.28379	−	1.31855i
$342$	−3.48286	+	5.30379i	−0.188332	+	0.286796i
$343$	−3.96179	−	18.0916i	−0.213917	−	0.976852i
$344$	15.7283	−	11.0640i	0.848014	−	0.596533i
$345$	8.96135	+	7.75974i	0.482463	+	0.417770i
$346$	−2.99414	+	9.05776i	−0.160966	+	0.486948i
$347$	−16.2451	+	4.35285i	−0.872081	+	0.233673i	−0.666988	−	0.745069i	$-0.732417\pi$
$347$	−16.2451	+	4.35285i	−0.872081	+	0.233673i	−0.205094	+	0.978742i	$0.565750\pi$
$348$	−0.630818	−	4.26353i	−0.0338154	−	0.228549i
$349$	0.714880			0.0382667			0.0191333	−	0.999817i	$-0.493909\pi$
$349$	0.714880			0.0382667			0.0191333	+	0.999817i	$0.493909\pi$
$350$	−11.7852	−	14.5296i	−0.629945	−	0.776640i
$351$			5.98211i			0.319301i
$352$	22.8443	−	21.7092i	1.21761	−	1.15711i
$353$	0.394510	+	1.47233i	0.0209977	+	0.0783643i	0.975630	−	0.219424i	$-0.0704178\pi$
$353$	0.394510	+	1.47233i	0.0209977	+	0.0783643i	−0.954632	+	0.297788i	$0.903751\pi$
$354$	1.49260	−	4.51534i	0.0793307	−	0.239988i
$355$	−15.9017	+	18.3641i	−0.843976	+	0.974668i
$356$	6.85144	−	2.96719i	0.363126	−	0.157261i
$357$	−0.880833	−	0.427381i	−0.0466186	−	0.0226194i
$358$	−1.51300	−	0.993551i	−0.0799647	−	0.0525108i
$359$	−8.03539	−	13.9177i	−0.424092	−	0.734548i	0.572243	−	0.820084i	$-0.306073\pi$
$359$	−8.03539	−	13.9177i	−0.424092	−	0.734548i	−0.996335	+	0.0855354i	$0.972740\pi$
$360$	5.91371	+	2.24232i	0.311680	+	0.118180i
$361$	0.565127	−	0.978828i	0.0297435	−	0.0515173i
$362$	1.56818	−	27.2645i	0.0824220	−	1.43299i
$363$	−14.1676	+	14.1676i	−0.743606	+	0.743606i
$364$	30.1948	+	9.50096i	1.58264	+	0.497986i
$365$	−7.16761	+	14.7679i	−0.375170	+	0.772987i
$366$	10.5931	+	11.8861i	0.553711	+	0.621295i
$367$	4.71685	+	17.6035i	0.246218	+	0.918897i	0.972767	+	0.231783i	$0.0744560\pi$
$367$	4.71685	+	17.6035i	0.246218	+	0.918897i	−0.726550	+	0.687114i	$0.758877\pi$
$368$	−10.0100	+	18.6939i	−0.521805	+	0.974488i
$369$	5.61344	−	3.24092i	0.292224	−	0.168716i
$370$	2.49593	+	4.18390i	0.129757	+	0.217511i
$371$	3.10286	−	3.58423i	0.161093	−	0.186084i
$372$	−6.43108	+	16.2565i	−0.333436	+	0.842861i
$373$	−3.83202	+	14.3013i	−0.198414	+	0.740493i	0.792942	+	0.609297i	$0.208548\pi$
$373$	−3.83202	+	14.3013i	−0.198414	+	0.740493i	−0.991356	+	0.131196i	$0.958118\pi$
$374$	0.915025	−	2.76810i	0.0473148	−	0.143135i
$375$	10.6529	+	3.39344i	0.550114	+	0.175236i
$376$	−3.33049	−	1.54424i	−0.171757	−	0.0796382i
$377$	9.11551	+	9.11551i	0.469472	+	0.469472i
$378$	−3.62774	−	0.916245i	−0.186591	−	0.0471266i
$379$			21.4047i			1.09949i	0.835334	+	0.549743i	$0.185274\pi$
$379$			21.4047i			1.09949i	−0.835334	+	0.549743i	$0.814726\pi$
$380$	−19.1391	−	6.02480i	−0.981817	−	0.309066i
$381$	−17.4557	−	10.0780i	−0.894282	−	0.516314i
$382$	−17.4748	+	8.79202i	−0.894089	+	0.449839i
$383$	−4.78061	+	17.8415i	−0.244278	+	0.911658i	0.729467	+	0.684016i	$0.239768\pi$
$383$	−4.78061	+	17.8415i	−0.244278	+	0.911658i	−0.973745	+	0.227642i	$0.926899\pi$
$384$	−1.58301	+	11.2024i	−0.0807824	+	0.571671i
$385$	−19.7302	+	26.4004i	−1.00554	+	1.34549i
$386$	5.53166	+	26.6923i	0.281554	+	1.35860i
$387$	1.75967	−	6.56717i	0.0894489	−	0.333828i
$388$	9.34151	+	11.7792i	0.474243	+	0.597998i
$389$	12.1014	−	20.9602i	0.613563	−	1.06272i	−0.377072	−	0.926184i	$-0.623069\pi$
$389$	12.1014	−	20.9602i	0.613563	−	1.06272i	0.990635	−	0.136538i	$-0.0435977\pi$
$390$	−18.2007	+	5.15661i	−0.921628	+	0.261115i
$391$			1.96171i			0.0992080i
$392$	−10.3865	+	16.8559i	−0.524595	+	0.851352i
$393$	1.65883	−	1.65883i	0.0836771	−	0.0836771i
$394$	−13.2565	+	11.8145i	−0.667852	+	0.595205i
$395$	0.553474	−	2.87694i	0.0278483	−	0.144755i
$396$	1.27749	−	11.0685i	0.0641964	−	0.556214i
$397$	4.18281	+	1.12078i	0.209929	+	0.0562504i	0.362251	−	0.932081i	$-0.382008\pi$
$397$	4.18281	+	1.12078i	0.209929	+	0.0562504i	−0.152322	+	0.988331i	$0.548675\pi$
$398$	−10.2183	+	15.5608i	−0.512200	+	0.779990i
$399$	11.6571	+	2.24116i	0.583587	+	0.112198i
$400$	−1.72465	+	19.9255i	−0.0862323	+	0.996275i
$401$	−13.4159	−	23.2370i	−0.669958	−	1.16040i	−0.977915	−	0.209001i	$-0.932979\pi$
$401$	−13.4159	−	23.2370i	−0.669958	−	1.16040i	0.307958	−	0.951400i	$-0.400355\pi$
$402$	9.18119	+	18.2483i	0.457916	+	0.910143i
$403$	−13.5338	−	50.5089i	−0.674168	−	2.51603i
$404$	22.6219	+	16.7906i	1.12548	+	0.835361i
$405$	2.11284	−	0.732062i	0.104988	−	0.0363765i
$406$	−6.92410	+	4.13176i	−0.343637	+	0.205056i
$407$	6.06890	−	6.06890i	0.300824	−	0.300824i
$408$	0.360105	+	0.982740i	0.0178279	+	0.0486529i
$409$	−12.0607	−	6.96325i	−0.596364	−	0.344311i	0.171246	−	0.985228i	$-0.445221\pi$
$409$	−12.0607	−	6.96325i	−0.596364	−	0.344311i	−0.767610	+	0.640918i	$0.778554\pi$
$410$	14.6994	+	14.2853i	0.725951	+	0.705502i
$411$	2.16469	+	3.74936i	0.106776	+	0.184942i
$412$	6.77904	−	17.1361i	0.333980	−	0.844235i
$413$	−8.87404	+	0.638796i	−0.436663	+	0.0314331i
$414$	1.52137	+	7.34120i	0.0747715	+	0.360800i
$415$	21.4608	−	1.54222i	1.05347	−	0.0757044i
$416$	−16.1681	−	29.7276i	−0.792705	−	1.45752i
$417$	18.9457	−	5.07648i	0.927774	−	0.248596i
$418$	−2.02981	+	35.2903i	−0.0992812	+	1.72611i
$419$			1.69659i			0.0828841i	0.999141	+	0.0414420i	$0.0131952\pi$
$419$			1.69659i			0.0828841i	−0.999141	+	0.0414420i	$0.986805\pi$
$420$	−0.339431	−	11.8273i	−0.0165625	−	0.577113i
$421$			10.8090i			0.526800i	0.964687	+	0.263400i	$0.0848439\pi$
$421$			10.8090i			0.526800i	−0.964687	+	0.263400i	$0.915156\pi$
$422$	0.397908	+	0.0228867i	0.0193699	+	0.00111411i
$423$	−1.25370	+	0.335928i	−0.0609569	+	0.0163334i
$424$	−5.04780	+	0.452666i	−0.245143	+	0.0219834i
$425$	0.729489	+	1.70033i	0.0353854	+	0.0824783i
$426$	−15.0440	+	3.11769i	−0.728886	+	0.151053i
$427$	13.0026	−	26.7985i	0.629241	−	1.29687i
$428$	5.69623	−	14.3990i	0.275338	−	0.696000i
$429$	16.6632	+	28.8614i	0.804505	+	1.39344i
$430$	21.4976	−	0.307102i	1.03671	−	0.0148098i
$431$	2.61429	+	1.50936i	0.125926	+	0.0727034i	0.561640	−	0.827382i	$-0.310171\pi$
$431$	2.61429	+	1.50936i	0.125926	+	0.0727034i	−0.435714	+	0.900085i	$0.643504\pi$
$432$	2.10975	+	3.39838i	0.101505	+	0.163504i
$433$	−8.45880	+	8.45880i	−0.406504	+	0.406504i	−0.880518	−	0.474014i	$-0.842805\pi$
$433$	−8.45880	+	8.45880i	−0.406504	+	0.406504i	0.474014	+	0.880518i	$0.342805\pi$
$434$	32.7031	−	0.471176i	1.56980	−	0.0226172i
$435$	2.10402	−	4.33505i	0.100880	−	0.207850i
$436$	−5.99399	+	8.07570i	−0.287060	+	0.386756i
$437$	−6.15608	−	22.9748i	−0.294485	−	1.09903i
$438$	−9.27433	+	4.66615i	−0.443145	+	0.222957i
$439$	−5.28278	−	9.15005i	−0.252133	−	0.436708i	0.711980	−	0.702200i	$-0.247799\pi$
$439$	−5.28278	−	9.15005i	−0.252133	−	0.436708i	−0.964113	+	0.265492i	$0.914466\pi$
$440$	34.7774	−	5.65431i	1.65795	−	0.269559i
$441$	1.00259	+	6.92783i	0.0477425	+	0.329897i
$442$	−2.61678	−	1.71837i	−0.124468	−	0.0817347i
$443$	−28.9120	−	7.74694i	−1.37365	−	0.368068i	−0.504839	−	0.863213i	$-0.668448\pi$
$443$	−28.9120	−	7.74694i	−1.37365	−	0.368068i	−0.868810	+	0.495145i	$0.835115\pi$
$444$	−0.353279	+	3.06089i	−0.0167659	+	0.145264i
$445$	8.19732	+	1.57702i	0.388590	+	0.0747581i
$446$	−0.879995	−	0.987403i	−0.0416689	−	0.0467549i
$447$	−13.2595	+	13.2595i	−0.627154	+	0.627154i
$448$	20.5042	−	5.25162i	0.968730	−	0.248116i
$449$		−	4.41290i		−	0.208257i	−0.994564	−	0.104129i	$-0.966795\pi$
$449$		−	4.41290i		−	0.208257i	0.994564	−	0.104129i	$-0.0332054\pi$
$450$	4.04859	+	5.79732i	0.190852	+	0.273288i
$451$	18.0552	−	31.2725i	0.850185	−	1.47256i
$452$	4.32168	−	3.42732i	0.203275	−	0.161207i
$453$	−3.56877	+	13.3188i	−0.167675	+	0.625773i
$454$	−30.6928	+	6.36071i	−1.44049	+	0.298523i
$455$	21.8993	+	27.8014i	1.02665	+	1.30335i
$456$	−7.30136	−	10.3794i	−0.341918	−	0.486060i
$457$	9.61767	−	35.8936i	0.449896	−	1.67903i	−0.252780	−	0.967524i	$-0.581345\pi$
$457$	9.61767	−	35.8936i	0.449896	−	1.67903i	0.702676	−	0.711510i	$-0.251988\pi$
$458$	3.03003	+	6.02242i	0.141584	+	0.281409i
$459$	0.320466	+	0.185021i	0.0149581	+	0.00863606i
$460$	−21.0243	+	10.9570i	−0.980265	+	0.510871i
$461$			15.8272i			0.737148i	0.929598	+	0.368574i	$0.120154\pi$
$461$			15.8272i			0.737148i	−0.929598	+	0.368574i	$0.879846\pi$
$462$	−20.0547	+	5.68452i	−0.933028	+	0.264468i
$463$	8.81202	+	8.81202i	0.409529	+	0.409529i	0.881574	−	0.472045i	$-0.156484\pi$
$463$	8.81202	+	8.81202i	0.409529	+	0.409529i	−0.472045	+	0.881574i	$0.656484\pi$
$464$	8.39325	+	1.96360i	0.389647	+	0.0911580i
$465$	−16.1832	+	10.9611i	−0.750478	+	0.508309i
$466$	−0.0151705	−	0.00501479i	−0.000702761	−	0.000232305i
$467$	−8.77747	+	32.7580i	−0.406173	+	1.51586i	0.395709	+	0.918376i	$0.370499\pi$
$467$	−8.77747	+	32.7580i	−0.406173	+	1.51586i	−0.801882	+	0.597482i	$0.796168\pi$
$468$	−11.1253	−	4.40117i	−0.514267	−	0.203444i
$469$	25.0134	−	28.8940i	1.15501	−	1.33420i
$470$	−2.10276	−	3.52484i	−0.0969932	−	0.162589i
$471$	4.19606	−	2.42260i	0.193344	−	0.111627i
$472$	7.29932	+	6.09791i	0.335979	+	0.280679i
$473$	−9.80311	−	36.5857i	−0.450747	−	1.68221i
$474$	1.38327	−	1.23280i	0.0635359	−	0.0566245i
$475$	−13.8793	−	17.6244i	−0.636828	−	0.808664i
$476$	1.44287	−	1.32371i	0.0661340	−	0.0606720i
$477$	−1.26701	+	1.26701i	−0.0580125	+	0.0580125i
$478$	−14.5745	−	0.838288i	−0.666621	−	0.0383424i
$479$	9.32972	−	16.1595i	0.426286	−	0.738348i	−0.570254	−	0.821468i	$-0.693155\pi$
$479$	9.32972	−	16.1595i	0.426286	−	0.738348i	0.996540	+	0.0831201i	$0.0264885\pi$
$480$	−8.52102	+	9.34838i	−0.388930	+	0.426693i
$481$	−4.60804	−	7.98136i	−0.210108	−	0.363918i
$482$	7.98645	−	12.1620i	0.363773	−	0.553962i
$483$	11.6120	−	7.86700i	0.528362	−	0.357961i
$484$	−15.9249	−	36.7718i	−0.723861	−	1.67144i
$485$	1.20476	+	16.7650i	0.0547055	+	0.761259i
$486$	1.34275	+	0.443862i	0.0609085	+	0.0201340i
$487$	−4.66866	−	17.4237i	−0.211557	−	0.789542i	−0.987350	−	0.158554i	$-0.949317\pi$
$487$	−4.66866	−	17.4237i	−0.211557	−	0.789542i	0.775793	−	0.630987i	$-0.217350\pi$
$488$	−29.8988	+	10.9558i	−1.35346	+	0.495947i
$489$			2.67457i			0.120948i
$490$	−20.2138	+	9.02223i	−0.913168	+	0.407583i
$491$	20.1191			0.907962			0.453981	−	0.891011i	$-0.350003\pi$
$491$	20.1191			0.907962			0.453981	+	0.891011i	$0.350003\pi$
$492$	1.89741	+	12.8241i	0.0855418	+	0.578154i
$493$	0.770260	−	0.206391i	0.0346908	−	0.00929536i
$494$	36.0392	+	11.9132i	1.62148	+	0.535998i
$495$	8.15450	−	9.41723i	0.366517	−	0.423273i
$496$	−25.5018	−	23.9206i	−1.14506	−	1.07406i
$497$	16.1215	+	23.7959i	0.723150	+	1.06739i
$498$	11.3747	+	7.46950i	0.509714	+	0.334716i
$499$	8.51618	−	4.91682i	0.381237	−	0.220107i	−0.297119	−	0.954840i	$-0.596026\pi$
$499$	8.51618	−	4.91682i	0.381237	−	0.220107i	0.678356	+	0.734733i	$0.262693\pi$
$500$	−14.1486	+	17.3153i	−0.632743	+	0.774362i
$501$	−16.5735	−	9.56871i	−0.740449	−	0.427498i
$502$	1.56196	+	0.0898401i	0.0697138	+	0.00400976i
$503$	11.2005	+	11.2005i	0.499406	+	0.499406i	0.911253	−	0.411847i	$-0.135116\pi$
$503$	11.2005	+	11.2005i	0.499406	+	0.499406i	−0.411847	+	0.911253i	$0.635116\pi$
$504$	4.37301	−	6.07263i	0.194789	−	0.270496i
$505$	10.3119	+	29.7616i	0.458873	+	1.32438i
$506$	27.7890	+	31.1808i	1.23537	+	1.38615i
$507$	22.0092	−	5.89735i	0.977463	−	0.261910i
$508$	31.5853	−	25.0488i	1.40137	−	1.11136i
$509$	2.28874	+	3.96422i	0.101447	+	0.175711i	0.912281	−	0.409565i	$-0.134320\pi$
$509$	2.28874	+	3.96422i	0.101447	+	0.175711i	−0.810834	+	0.585276i	$0.800986\pi$
$510$	−0.286688	+	1.13452i	−0.0126948	+	0.0502372i
$511$	14.6848	+	12.7126i	0.649615	+	0.562371i
$512$	−19.6692	−	11.1859i	−0.869263	−	0.494351i
$513$	−4.33380	−	1.16124i	−0.191342	−	0.0512699i
$514$	−9.04246	+	27.3549i	−0.398846	+	1.20657i
$515$	17.0588	−	11.5542i	0.751701	−	0.509137i
$516$	10.9187	+	8.10418i	0.480671	+	0.356766i
$517$	−5.11290	+	5.11290i	−0.224865	+	0.224865i
$518$	5.54593	−	1.57200i	0.243674	−	0.0690698i
$519$	−6.74566			−0.296102
$520$	3.80060	−	37.6428i	0.166667	−	1.65075i
$521$	−10.5312	+	18.2406i	−0.461382	+	0.799137i	−0.999030	−	0.0440323i	$-0.985980\pi$
$521$	−10.5312	+	18.2406i	−0.461382	+	0.799137i	0.537648	+	0.843169i	$0.319313\pi$
$522$	2.72244	−	1.36973i	0.119158	−	0.0599513i
$523$	−0.539666	−	0.144603i	−0.0235980	−	0.00632305i	0.247001	−	0.969015i	$-0.420555\pi$
$523$	−0.539666	−	0.144603i	−0.0235980	−	0.00632305i	−0.270599	+	0.962692i	$0.587222\pi$
$524$	1.86459	+	4.30548i	0.0814552	+	0.188086i
$525$	7.13933	−	11.1369i	0.311586	−	0.486053i
$526$	22.5153	−	4.66601i	0.981712	−	0.203448i
$527$	−3.12439	−	0.837179i	−0.136101	−	0.0364681i
$528$	19.6449	+	10.5192i	0.854936	+	0.457789i
$529$	−4.42010	−	2.55195i	−0.192178	−	0.110954i
$530$	−4.94709	−	2.76274i	−0.214888	−	0.120006i
$531$	3.36275			0.145931
$532$	−12.7444	+	20.0306i	−0.552541	+	0.868438i
$533$	−27.4181	−	27.4181i	−1.18761	−	1.18761i
$534$	3.51265	+	3.94139i	0.152007	+	0.170561i
$535$	14.3340	−	9.70863i	0.619714	−	0.419741i
$536$	−40.6923	+	3.64913i	−1.75764	+	0.157618i
$537$	0.331264	−	1.23630i	0.0142951	−	0.0533501i
$538$	−3.82400	+	5.82328i	−0.164864	+	0.251060i
$539$	24.1346	+	30.6315i	1.03955	+	1.31939i
$540$	−0.193001	+	4.46797i	−0.00830544	+	0.192271i
$541$	11.9490	−	6.89877i	0.513728	−	0.296601i	−0.220637	−	0.975356i	$-0.570813\pi$
$541$	11.9490	−	6.89877i	0.513728	−	0.296601i	0.734365	+	0.678755i	$0.237480\pi$
$542$	−13.8146	+	6.95049i	−0.593389	+	0.298549i
$543$	18.6528	−	4.99799i	0.800467	−	0.214484i
$544$	−2.09260	−	0.0533133i	−0.0897194	−	0.00228579i
$545$	−10.6245	+	3.68120i	−0.455103	+	0.157685i
$546$	0.322453	+	22.3807i	0.0137997	+	0.957804i
$547$	−2.63775	−	2.63775i	−0.112782	−	0.112782i	0.648464	−	0.761246i	$-0.275412\pi$
$547$	−2.63775	−	2.63775i	−0.112782	−	0.112782i	−0.761246	+	0.648464i	$0.775412\pi$
$548$	−8.56552	+	1.26733i	−0.365901	+	0.0541375i
$549$	−5.62909	+	9.74986i	−0.240244	+	0.416114i
$550$	35.6814	+	16.6925i	1.52146	+	0.711772i
$551$	−8.37330	+	4.83433i	−0.356715	+	0.205949i
$552$	−14.7722	−	2.57169i	−0.628746	−	0.109458i
$553$	−3.11874	−	1.51322i	−0.132622	−	0.0643485i
$554$	3.22679	+	15.5705i	0.137093	+	0.661526i
$555$	−2.25505	+	2.60425i	−0.0957215	+	0.110544i
$556$	−4.49772	+	38.9693i	−0.190746	+	1.65267i
$557$	−4.70498	−	17.5592i	−0.199356	−	0.744008i	−0.991096	−	0.133149i	$-0.957491\pi$
$557$	−4.70498	−	17.5592i	−0.199356	−	0.744008i	0.791740	−	0.610859i	$-0.209176\pi$
$558$	−12.3415	−	0.709852i	−0.522457	−	0.0300504i
$559$	−40.6714			−1.72022
$560$	22.2457	+	8.07034i	0.940051	+	0.341034i
$561$	2.06151			0.0870369
$562$	18.2818	+	1.05152i	0.771170	+	0.0443557i
$563$	6.51198	+	24.3030i	0.274447	+	1.02425i	0.956211	+	0.292678i	$0.0945465\pi$
$563$	6.51198	+	24.3030i	0.274447	+	1.02425i	−0.681764	+	0.731572i	$0.738787\pi$
$564$	0.297629	−	2.57873i	0.0125324	−	0.108584i
$565$	6.15093	−	0.442018i	0.258772	−	0.0185958i
$566$	−6.61283	−	31.9094i	−0.277958	−	1.34125i
$567$	−0.189962	−	2.63892i	−0.00797767	−	0.110824i
$568$	5.27006	−	30.2721i	0.221127	−	1.27019i
$569$	13.9329	−	8.04416i	0.584097	−	0.337229i	−0.178663	−	0.983910i	$-0.557177\pi$
$569$	13.9329	−	8.04416i	0.584097	−	0.337229i	0.762760	+	0.646682i	$0.223844\pi$
$570$	−0.202662	−	14.1867i	−0.00848859	−	0.594214i
$571$	−20.7948	+	36.0177i	−0.870236	+	1.50729i	−0.00848298	+	0.999964i	$0.502700\pi$
$571$	−20.7948	+	36.0177i	−0.870236	+	1.50729i	−0.861753	+	0.507328i	$0.830633\pi$
$572$	−65.9348	+	9.75550i	−2.75687	+	0.407898i
$573$	−9.78096	−	9.78096i	−0.408605	−	0.408605i
$574$	20.8267	−	12.4277i	0.869290	−	0.518724i
$575$	−26.3212	−	3.12900i	−1.09767	−	0.130488i
$576$	−7.87236	+	1.42337i	−0.328015	+	0.0593071i
$577$	−31.9623	+	8.56429i	−1.33061	+	0.356536i	−0.852943	−	0.522005i	$-0.825184\pi$
$577$	−31.9623	+	8.56429i	−1.33061	+	0.356536i	−0.477667	+	0.878541i	$0.658518\pi$
$578$	21.3036	−	10.7184i	0.886112	−	0.445825i
$579$	−16.6929	+	9.63768i	−0.693735	+	0.400528i
$580$	6.51418	+	7.10236i	0.270486	+	0.294910i
$581$	4.80649	−	25.0004i	0.199407	−	1.03719i
$582$	−5.83510	+	8.88584i	−0.241873	+	0.368330i
$583$	−2.58360	+	9.64213i	−0.107002	+	0.399336i
$584$	−1.85459	−	20.6810i	−0.0767436	−	0.855787i
$585$	−7.50133	−	11.0751i	−0.310142	−	0.457900i
$586$	−9.95836	−	11.1738i	−0.411376	−	0.461587i
$587$	−22.3262	−	22.3262i	−0.921501	−	0.921501i	0.0756346	−	0.997136i	$-0.475902\pi$
$587$	−22.3262	−	22.3262i	−0.921501	−	0.921501i	−0.997136	+	0.0756346i	$0.975902\pi$
$588$	−13.6217	−	3.23237i	−0.561751	−	0.133301i
$589$	39.2188			1.61598
$590$	2.89871	+	10.2312i	0.119338	+	0.421214i
$591$	−10.8740	−	6.27810i	−0.447296	−	0.258247i
$592$	−5.43262	−	2.90898i	−0.223279	−	0.119558i
$593$	15.6366	+	4.18981i	0.642117	+	0.172055i	0.565162	−	0.824980i	$-0.308814\pi$
$593$	15.6366	+	4.18981i	0.642117	+	0.172055i	0.0769548	+	0.997035i	$0.475480\pi$
$594$	7.71466	−	1.59877i	0.316536	−	0.0655983i
$595$	2.16667	−	0.313289i	0.0888248	−	0.0128436i
$596$	−14.9042	−	34.4149i	−0.610501	−	1.40969i
$597$	−12.7149	−	3.40695i	−0.520386	−	0.139437i
$598$	40.0639	−	20.1572i	1.63834	−	0.824288i
$599$	1.79982	−	3.11738i	0.0735386	−	0.127373i	−0.826911	−	0.562332i	$-0.809904\pi$
$599$	1.79982	−	3.11738i	0.0735386	−	0.127373i	0.900450	+	0.434960i	$0.143237\pi$
$600$	−13.7603	+	3.26420i	−0.561761	+	0.133260i
$601$	17.5729			0.716814			0.358407	−	0.933565i	$-0.383320\pi$
$601$	17.5729			0.716814			0.358407	+	0.933565i	$0.383320\pi$
$602$	6.22940	−	24.6644i	0.253891	−	1.00525i
$603$	−10.2139	+	10.2139i	−0.415942	+	0.415942i
$604$	−22.1442	−	16.4360i	−0.901035	−	0.668772i
$605$	8.46391	−	43.9951i	0.344107	−	1.78866i
$606$	−6.25229	+	18.9142i	−0.253982	+	0.768335i
$607$	43.1013	+	11.5490i	1.74943	+	0.468758i	0.984504	−	0.175362i	$-0.0561096\pi$
$607$	43.1013	+	11.5490i	1.74943	+	0.468758i	0.764924	+	0.644120i	$0.222776\pi$
$608$	24.6750	−	5.94243i	1.00070	−	0.240998i
$609$	−4.31064	−	3.73171i	−0.174676	−	0.151217i
$610$	−34.5165	−	8.72220i	−1.39753	−	0.353151i
$611$	3.88216	+	6.72410i	0.157055	+	0.272028i
$612$	−0.579870	+	0.459867i	−0.0234399	+	0.0185890i
$613$	−39.1507	+	10.4904i	−1.58128	+	0.423703i	−0.939323	−	0.343035i	$-0.888545\pi$
$613$	−39.1507	+	10.4904i	−1.58128	+	0.423703i	−0.641960	+	0.766738i	$0.721879\pi$
$614$	27.5633	+	30.9276i	1.11236	+	1.24813i
$615$	−6.32859	+	13.0392i	−0.255193	+	0.525791i
$616$	4.18282	−	41.4792i	0.168531	−	1.67124i
$617$	6.80159	+	6.80159i	0.273822	+	0.273822i	0.830637	−	0.556815i	$-0.187977\pi$
$617$	6.80159	+	6.80159i	0.273822	+	0.273822i	−0.556815	+	0.830637i	$0.687977\pi$
$618$	13.0093	+	0.748260i	0.523309	+	0.0300994i
$619$	17.8113	+	10.2834i	0.715898	+	0.413324i	0.813241	−	0.581927i	$-0.197701\pi$
$619$	17.8113	+	10.2834i	0.715898	+	0.413324i	−0.0973433	+	0.995251i	$0.531034\pi$
$620$	−8.47869	−	38.1612i	−0.340513	−	1.53259i
$621$	−4.59107	+	2.65066i	−0.184233	+	0.106367i
$622$	13.5749	+	8.91426i	0.544302	+	0.357429i
$623$	4.31163	−	8.88629i	0.172742	−	0.356022i
$624$	16.3702	−	17.4524i	0.655334	−	0.698653i
$625$	−23.9778	+	7.07581i	−0.959110	+	0.283033i
$626$	−15.3184	−	5.06367i	−0.612246	−	0.202385i
$627$	−24.1436	+	6.46925i	−0.964201	+	0.258357i
$628$	1.41832	+	9.58603i	0.0565970	+	0.382524i
$629$	−0.570090			−0.0227310
$630$	7.86524	−	2.85273i	0.313358	−	0.113655i
$631$			39.2014i			1.56058i	0.625416	+	0.780291i	$0.284929\pi$
$631$			39.2014i			1.56058i	−0.625416	+	0.780291i	$0.715071\pi$
$632$	1.27502	+	3.47956i	0.0507174	+	0.138409i
$633$	0.0729425	+	0.272225i	0.00289921	+	0.0108200i
$634$	−6.62100	−	2.18865i	−0.262954	−	0.0869223i
$635$	44.9544	−	3.23051i	1.78396	−	0.128199i
$636$	−1.42417	−	3.28851i	−0.0564721	−	0.130398i
$637$	38.4786	−	16.5195i	1.52458	−	0.654526i
$638$	9.31936	−	14.1918i	0.368957	−	0.561857i
$639$	−5.43188	−	9.40830i	−0.214882	−	0.372187i
$640$	−11.1166	−	22.7249i	−0.439424	−	0.898280i
$641$	−1.84164	+	3.18982i	−0.0727406	+	0.125990i	−0.900101	−	0.435680i	$-0.856508\pi$
$641$	−1.84164	+	3.18982i	−0.0727406	+	0.125990i	0.827361	+	0.561671i	$0.189841\pi$
$642$	10.9313	+	0.628741i	0.431424	+	0.0248144i
$643$	−1.34191	+	1.34191i	−0.0529196	+	0.0529196i	−0.733071	−	0.680152i	$-0.761914\pi$
$643$	−1.34191	+	1.34191i	−0.0529196	+	0.0529196i	0.680152	+	0.733071i	$0.261914\pi$
$644$	6.08758	+	27.3834i	0.239884	+	1.07906i
$645$	4.97717	+	14.3648i	0.195976	+	0.565615i
$646$	1.75286	−	1.56219i	0.0689653	−	0.0614634i
$647$	7.67253	+	28.6343i	0.301638	+	1.12573i	0.935801	+	0.352530i	$0.114678\pi$
$647$	7.67253	+	28.6343i	0.301638	+	1.12573i	−0.634162	+	0.773200i	$0.718655\pi$
$648$	−1.81337	+	2.17064i	−0.0712359	+	0.0852709i
$649$	16.2240	−	9.36694i	0.636848	−	0.367684i
$650$	27.2301	−	32.3698i	1.06805	−	1.26965i
$651$	7.57417	+	21.8515i	0.296855	+	0.856429i
$652$	−4.97407	−	1.96774i	−0.194800	−	0.0770628i
$653$	8.32776	−	31.0796i	0.325890	−	1.21624i	−0.587523	−	0.809207i	$-0.699897\pi$
$653$	8.32776	−	31.0796i	0.325890	−	1.21624i	0.913414	−	0.407032i	$-0.133436\pi$
$654$	−6.75209	−	2.23198i	−0.264027	−	0.0872772i
$655$	−0.991009	+	5.15123i	−0.0387219	+	0.201275i
$656$	−25.2457	−	5.90623i	−0.985679	−	0.230600i
$657$	−5.19100	−	5.19100i	−0.202520	−	0.202520i
$658$	−4.67232	+	1.32437i	−0.182146	+	0.0516295i
$659$		−	45.5239i		−	1.77336i	−0.462382	−	0.886681i	$-0.653005\pi$
$659$		−	45.5239i		−	1.77336i	0.462382	−	0.886681i	$-0.346995\pi$
$660$	11.5144	+	22.0939i	0.448196	+	0.860003i
$661$	−27.4916	−	15.8723i	−1.06930	−	0.617360i	−0.141309	−	0.989966i	$-0.545131\pi$
$661$	−27.4916	−	15.8723i	−1.06930	−	0.617360i	−0.927990	+	0.372606i	$0.878464\pi$
$662$	−3.75728	−	7.46788i	−0.146031	−	0.290247i
$663$	0.572931	−	2.13821i	0.0222508	−	0.0830411i
$664$	−22.2601	+	15.6588i	−0.863861	+	0.607680i
$665$	−24.3920	+	10.4684i	−0.945883	+	0.405946i
$666$	−2.13342	+	0.442125i	−0.0826682	+	0.0171320i
$667$	−2.95679	+	11.0349i	−0.114488	+	0.427273i
$668$	29.9890	−	23.7828i	1.16031	−	0.920185i
$669$	0.467621	−	0.809943i	0.0180793	−	0.0313142i
$670$	−39.8805	−	22.2716i	−1.54072	−	0.860427i
$671$			62.7193i			2.42125i
$672$	8.07632	+	12.6005i	0.311551	+	0.486075i
$673$	26.2642	−	26.2642i	1.01241	−	1.01241i	0.0124869	−	0.999922i	$-0.496025\pi$
$673$	26.2642	−	26.2642i	1.01241	−	1.01241i	0.999922	−	0.0124869i	$-0.00397481\pi$
$674$	−29.4374	−	33.0304i	−1.13389	−	1.27228i
$675$	−2.99368	+	4.00474i	−0.115227	+	0.154142i
$676$	−5.22500	+	45.2707i	−0.200961	+	1.74118i
$677$	7.10904	+	1.90486i	0.273223	+	0.0732098i	0.392829	−	0.919612i	$-0.371496\pi$
$677$	7.10904	+	1.90486i	0.273223	+	0.0732098i	−0.119606	+	0.992821i	$0.538163\pi$
$678$	3.26014	+	2.14085i	0.125205	+	0.0822188i
$679$	19.5301	+	3.75478i	0.749496	+	0.144095i
$680$	−1.89901	−	1.36786i	−0.0728236	−	0.0524550i
$681$	−11.0821	−	19.1948i	−0.424668	−	0.735546i
$682$	−61.5204	+	30.9525i	−2.35574	+	1.18523i
$683$	3.89621	+	14.5409i	0.149084	+	0.556391i	0.999540	+	0.0303430i	$0.00965997\pi$
$683$	3.89621	+	14.5409i	0.149084	+	0.556391i	−0.850455	+	0.526048i	$0.823673\pi$
$684$	5.34809	−	7.20548i	0.204489	−	0.275508i
$685$	−8.70920	−	4.22702i	−0.332761	−	0.161506i
$686$	4.12440	+	25.8648i	0.157470	+	0.987524i
$687$	−3.37086	+	3.37086i	−0.128606	+	0.128606i
$688$	−23.1050	+	14.3438i	−0.880870	+	0.546854i
$689$	9.28284	+	5.35945i	0.353648	+	0.204179i
$690$	−12.0222	−	11.6836i	−0.457677	−	0.444785i
$691$	20.5402	+	35.5766i	0.781385	+	1.35340i	0.931135	+	0.364674i	$0.118820\pi$
$691$	20.5402	+	35.5766i	0.781385	+	1.35340i	−0.149750	+	0.988724i	$0.547847\pi$
$692$	4.96293	−	12.5453i	0.188662	−	0.476901i
$693$	−8.26721	−	12.2027i	−0.314046	−	0.463541i
$694$	23.2896	−	4.82648i	0.884061	−	0.183211i
$695$	−28.7098	+	33.1556i	−1.08903	+	1.25766i
$696$	0.544407	+	6.07082i	0.0206357	+	0.230114i
$697$	−2.31683	+	0.620793i	−0.0877562	+	0.0235142i
$698$	−1.00933	−	0.0580538i	−0.0382035	−	0.00219737i
$699$		−	0.0112981i		−	0.000427332i
$700$	15.4594	+	21.4711i	0.584309	+	0.811531i
$701$		−	34.1172i		−	1.28859i	−0.764777	−	0.644295i	$-0.777151\pi$
$701$		−	34.1172i		−	1.28859i	0.764777	−	0.644295i	$-0.222849\pi$
$702$	0.485794	−	8.44602i	0.0183351	−	0.318774i
$703$	6.67668	−	1.78901i	0.251816	−	0.0674738i
$704$	−34.0164	+	28.7957i	−1.28204	+	1.08528i
$705$	1.89982	−	2.19402i	0.0715515	−	0.0826314i
$706$	−0.437436	−	2.11079i	−0.0164631	−	0.0794408i
$707$	37.1721	−	2.67583i	1.39800	−	0.100635i
$708$	−2.47405	+	6.25391i	−0.0929805	+	0.235036i
$709$	−0.746144	−	1.29236i	−0.0280220	−	0.0485356i	0.851674	−	0.524071i	$-0.175588\pi$
$709$	−0.746144	−	1.29236i	−0.0280220	−	0.0485356i	−0.879696	+	0.475536i	$0.842254\pi$
$710$	23.9427	−	24.6366i	0.898552	−	0.924596i
$711$	1.13467	+	0.655100i	0.0425533	+	0.0245682i
$712$	−9.91437	+	3.63293i	−0.371557	+	0.136150i
$713$	32.7671	−	32.7671i	1.22714	−	1.22714i
$714$	1.20892	+	0.674941i	0.0452429	+	0.0252590i
$715$	−67.0408	−	32.5383i	−2.50718	−	1.21687i
$716$	2.05550	+	1.52564i	0.0768175	+	0.0570159i
$717$	−2.67172	−	9.97101i	−0.0997774	−	0.372374i
$718$	10.2148	+	20.3027i	0.381212	+	0.757689i
$719$	4.78565	+	8.28900i	0.178475	+	0.309127i	0.941358	−	0.337409i	$-0.109550\pi$
$719$	4.78565	+	8.28900i	0.178475	+	0.309127i	−0.762884	+	0.646536i	$0.776217\pi$
$720$	−8.16736	−	3.64612i	−0.304380	−	0.135883i
$721$	−7.98398	−	23.0338i	−0.297339	−	0.857825i
$722$	−0.877380	+	1.33610i	−0.0326527	+	0.0497243i
$723$	9.93770	+	2.66280i	0.369587	+	0.0990305i
$724$	−4.42818	+	38.3668i	−0.164572	+	1.42589i
$725$	1.54065	+	10.6641i	0.0572182	+	0.396056i
$726$	21.1535	−	18.8524i	0.785079	−	0.699680i
$727$	−5.91197	+	5.91197i	−0.219263	+	0.219263i	−0.808188	−	0.588925i	$-0.799551\pi$
$727$	−5.91197	+	5.91197i	−0.219263	+	0.219263i	0.588925	+	0.808188i	$0.299551\pi$
$728$	−41.8599	−	15.8663i	−1.55143	−	0.588043i
$729$			1.00000i			0.0370370i
$730$	11.3191	−	20.2684i	0.418938	−	0.750168i
$731$	−1.25793	+	2.17880i	−0.0465262	+	0.0805858i
$732$	−13.9910	−	17.6419i	−0.517121	−	0.652065i
$733$	3.12580	−	11.6657i	0.115454	−	0.430881i	−0.883866	−	0.467740i	$-0.845068\pi$
$733$	3.12580	−	11.6657i	0.115454	−	0.430881i	0.999320	+	0.0368587i	$0.0117352\pi$
$734$	−5.23009	−	25.2371i	−0.193046	−	0.931519i
$735$	−10.5434	−	11.5688i	−0.388899	−	0.426721i
$736$	15.6510	−	25.5807i	0.576902	−	0.942917i
$737$	−20.8274	+	77.7291i	−0.767189	+	2.86319i
$738$	−8.18869	+	4.11994i	−0.301430	+	0.151657i
$739$	−0.587739	−	0.339331i	−0.0216203	−	0.0124825i	0.489151	−	0.872199i	$-0.337307\pi$
$739$	−0.587739	−	0.339331i	−0.0216203	−	0.0124825i	−0.510771	+	0.859717i	$0.670640\pi$
$740$	−3.18419	−	6.10986i	−0.117053	−	0.224603i
$741$			26.8398i			0.985984i
$742$	−4.67194	+	4.80853i	−0.171512	+	0.176527i
$743$	−24.0328	−	24.0328i	−0.881679	−	0.881679i	0.112026	−	0.993705i	$-0.464266\pi$
$743$	−24.0328	−	24.0328i	−0.881679	−	0.881679i	−0.993705	+	0.112026i	$0.964266\pi$
$744$	10.4001	−	22.4300i	0.381285	−	0.822324i
$745$	7.92141	−	41.1752i	0.290218	−	1.50854i
$746$	6.57173	−	19.8805i	0.240608	−	0.727877i
$747$	−2.49044	+	9.29445i	−0.0911205	+	0.340066i
$748$	−1.51670	+	3.83391i	−0.0554559	+	0.140182i
$749$	−6.70871	−	19.3547i	−0.245131	−	0.707204i
$750$	−14.7651	−	5.65623i	−0.539144	−	0.206536i
$751$	−2.78825	+	1.60979i	−0.101745	+	0.0587422i	−0.550009	−	0.835159i	$-0.685376\pi$
$751$	−2.78825	+	1.60979i	−0.101745	+	0.0587422i	0.448264	+	0.893901i	$0.352042\pi$
$752$	4.57685	+	2.45075i	0.166901	+	0.0893696i
$753$	0.286331	+	1.06860i	0.0104345	+	0.0389420i
$754$	−12.1298	−	13.6103i	−0.441739	−	0.495656i
$755$	−10.0942	−	29.1332i	−0.367364	−	1.06027i
$756$	5.04753	+	1.58823i	0.183577	+	0.0577633i
$757$	−15.5635	+	15.5635i	−0.565666	+	0.565666i	−0.930911	−	0.365245i	$-0.880985\pi$
$757$	−15.5635	+	15.5635i	−0.565666	+	0.565666i	0.365245	+	0.930911i	$0.380985\pi$
$758$	1.73823	−	30.2209i	0.0631353	−	1.09767i
$759$	−14.7668	+	25.5768i	−0.536001	+	0.928380i
$760$	26.5329	+	10.0605i	0.962450	+	0.364934i
$761$	−20.2867	−	35.1375i	−0.735391	−	1.27373i	−0.954552	−	0.298046i	$-0.903665\pi$
$761$	−20.2867	−	35.1375i	−0.735391	−	1.27373i	0.219161	−	0.975689i	$-0.429668\pi$
$762$	23.8269	+	15.6465i	0.863158	+	0.566814i
$763$	0.955233	+	13.2699i	0.0345818	+	0.480404i
$764$	25.3863	−	10.9942i	0.918445	−	0.397756i
$765$	−0.825313	+	0.0593086i	−0.0298392	+	0.00214431i
$766$	8.19852	−	24.8018i	0.296225	−	0.896126i
$767$	−5.20649	−	19.4309i	−0.187995	−	0.701608i
$768$	3.14474	−	15.6879i	0.113476	−	0.566089i
$769$		−	7.68776i		−	0.277228i	−0.990347	−	0.138614i	$-0.955735\pi$
$769$		−	7.68776i		−	0.277228i	0.990347	−	0.138614i	$-0.0442647\pi$
$770$	30.0005	−	35.6720i	1.08114	−	1.28553i
$771$	−20.3722			−0.733688
$772$	−5.64241	−	38.1356i	−0.203075	−	1.37253i
$773$	−11.7703	+	3.15384i	−0.423348	+	0.113436i	−0.464202	−	0.885729i	$-0.653659\pi$
$773$	−11.7703	+	3.15384i	−0.423348	+	0.113436i	0.0408542	+	0.999165i	$0.486992\pi$
$774$	−3.01775	+	9.12916i	−0.108471	+	0.328141i
$775$	16.2164	−	40.5862i	0.582509	−	1.45790i
$776$	−12.2325	−	17.3894i	−0.439122	−	0.624243i
$777$	2.28622	+	3.37453i	0.0820177	+	0.121061i
$778$	−18.7878	+	28.6105i	−0.673575	+	1.02574i
$779$	25.1857	−	14.5410i	0.902371	−	0.520984i
$780$	26.1160	−	5.80247i	0.935101	−	0.207762i
$781$	−52.4136	−	30.2610i	−1.87551	−	1.08282i
$782$	0.159306	−	2.76970i	0.00569678	−	0.0990443i
$783$	1.52380	+	1.52380i	0.0544560	+	0.0544560i
$784$	16.0333	−	22.9551i	0.572616	−	0.819823i
$785$	−4.73063	+	9.74682i	−0.168844	+	0.347879i
$786$	−2.47678	+	2.20736i	−0.0883440	+	0.0787341i
$787$	3.73852	−	1.00173i	0.133264	−	0.0357079i	−0.191571	−	0.981479i	$-0.561358\pi$
$787$	3.73852	−	1.00173i	0.133264	−	0.0357079i	0.324834	+	0.945771i	$0.394691\pi$
$788$	19.6760	−	15.6041i	0.700929	−	0.555873i
$789$	8.12949	+	14.0807i	0.289418	+	0.501286i
$790$	−1.01507	+	4.01695i	−0.0361146	+	0.142917i
$791$	1.37760	−	7.16542i	0.0489817	−	0.254773i
$792$	−2.70252	+	15.5237i	−0.0960297	+	0.551610i
$793$	65.0528	+	17.4308i	2.31009	+	0.618987i
$794$	−5.81461	−	1.92209i	−0.206353	−	0.0682123i
$795$	0.756930	−	3.93450i	0.0268455	−	0.139542i
$796$	15.6907	−	21.1401i	0.556143	−	0.749291i
$797$	−13.1189	+	13.1189i	−0.464694	+	0.464694i	−0.900191	−	0.435496i	$-0.856573\pi$
$797$	−13.1189	+	13.1189i	−0.464694	+	0.464694i	0.435496	+	0.900191i	$0.356573\pi$
$798$	−16.2765	−	4.11090i	−0.576181	−	0.145524i
$799$	0.480288			0.0169914
$800$	4.05310	−	27.9924i	0.143299	−	0.989679i
$801$	−1.86659	+	3.23303i	−0.0659527	+	0.114233i
$802$	17.0546	+	33.8973i	0.602219	+	1.19696i
$803$	−39.5042	−	10.5851i	−1.39407	−	0.373541i
$804$	−11.4808	−	26.5100i	−0.404898	−	0.934936i
$805$	−11.6331	+	29.1257i	−0.410015	+	1.02655i
$806$	15.0064	+	72.4116i	0.528579	+	2.55059i
$807$	−4.75828	−	1.27498i	−0.167499	−	0.0448813i
$808$	−30.5759	−	25.5433i	−1.07566	−	0.898611i
$809$	37.5240	+	21.6645i	1.31927	+	0.761683i	0.983612	−	0.180300i	$-0.0577067\pi$
$809$	37.5240	+	21.6645i	1.31927	+	0.761683i	0.335662	+	0.941983i	$0.391040\pi$
$810$	−3.04252	+	0.862005i	−0.106903	+	0.0302878i
$811$	37.8178			1.32796			0.663981	−	0.747749i	$-0.268865\pi$
$811$	37.8178			1.32796			0.663981	+	0.747749i	$0.268865\pi$
$812$	10.1115	−	5.27126i	0.354845	−	0.184985i
$813$	−7.73229	−	7.73229i	−0.271183	−	0.271183i
$814$	−9.06140	+	8.07571i	−0.317602	+	0.283054i
$815$	−3.35381	−	4.95164i	−0.117479	−	0.173448i
$816$	−0.428619	−	1.41675i	−0.0150047	−	0.0495963i
$817$	7.89506	−	29.4648i	0.276213	−	1.03084i
$818$	16.4628	+	10.8107i	0.575608	+	0.377987i
$819$	−14.9543	+	5.18345i	−0.522545	+	0.181125i
$820$	−19.5937	−	21.3629i	−0.684242	−	0.746024i
$821$	−32.9300	+	19.0121i	−1.14926	+	0.663528i	−0.948708	−	0.316154i	$-0.897608\pi$
$821$	−32.9300	+	19.0121i	−1.14926	+	0.663528i	−0.200557	+	0.979682i	$0.564275\pi$
$822$	−2.75181	−	5.46943i	−0.0959804	−	0.190768i
$823$	−6.34518	+	1.70018i	−0.221179	+	0.0592647i	−0.367707	−	0.929942i	$-0.619857\pi$
$823$	−6.34518	+	1.70018i	−0.221179	+	0.0592647i	0.146528	+	0.989207i	$0.453190\pi$
$824$	−10.9628	+	23.6436i	−0.381907	+	0.823664i
$825$	−3.28818	+	27.6602i	−0.114480	+	0.963006i
$826$	12.5810	−	0.181262i	0.437747	−	0.00630692i
$827$	−7.93806	−	7.93806i	−0.276033	−	0.276033i	0.555490	−	0.831523i	$-0.312531\pi$
$827$	−7.93806	−	7.93806i	−0.276033	−	0.276033i	−0.831523	+	0.555490i	$0.812531\pi$
$828$	−1.55183	−	10.4884i	−0.0539300	−	0.364498i
$829$	−14.2927	+	24.7556i	−0.496405	+	0.859798i	−0.999991	−	0.00414644i	$-0.998680\pi$
$829$	−14.2927	+	24.7556i	−0.496405	+	0.859798i	0.503587	+	0.863945i	$0.332013\pi$
$830$	−30.4254	+	0.434638i	−1.05608	+	0.0150865i
$831$	−9.73753	+	5.62196i	−0.337791	+	0.195024i
$832$	20.4133	+	43.2848i	0.707702	+	1.50063i
$833$	0.305146	−	2.57226i	0.0105727	−	0.0891236i
$834$	−27.1613	+	5.62884i	−0.940518	+	0.194911i
$835$	42.6825	−	3.06725i	1.47709	−	0.106146i
$836$	5.73170	−	49.6608i	0.198235	−	1.71756i
$837$	−2.26238	−	8.44333i	−0.0781995	−	0.291844i
$838$	0.137777	−	2.39539i	0.00475942	−	0.0827473i
$839$	−38.6351			−1.33383			−0.666916	−	0.745133i	$-0.732386\pi$
$839$	−38.6351			−1.33383			−0.666916	+	0.745133i	$0.732386\pi$
$840$	−0.481232	+	16.7263i	−0.0166041	+	0.577111i
$841$	−24.3561			−0.839865
$842$	0.877778	−	15.2611i	0.0302502	−	0.525931i
$843$	3.35132	+	12.5073i	0.115426	+	0.430775i
$844$	−0.559940	−	0.0646264i	−0.0192739	−	0.00222453i
$845$	−33.3522	+	38.5169i	−1.14735	+	1.32502i
$846$	1.79735	−	0.372479i	0.0617942	−	0.0128061i
$847$	−47.6928	−	23.1406i	−1.63875	−	0.795120i
$848$	7.16364	−	0.229190i	0.246000	−	0.00787043i
$849$	19.9556	−	11.5214i	0.684875	−	0.395413i
$850$	−0.891871	−	2.45991i	−0.0305909	−	0.0843742i
$851$	4.08362	−	7.07303i	0.139985	−	0.242460i
$852$	21.4935	−	3.18011i	0.736357	−	0.108949i
$853$	−4.38108	−	4.38108i	−0.150005	−	0.150005i	0.628115	−	0.778120i	$-0.283827\pi$
$853$	−4.38108	−	4.38108i	−0.150005	−	0.150005i	−0.778120	+	0.628115i	$0.783827\pi$
$854$	−20.5344	+	36.7803i	−0.702672	+	1.25860i
$855$	9.47962	−	3.28452i	0.324196	−	0.112328i
$856$	−9.21171	+	19.8670i	−0.314850	+	0.679041i
$857$	25.6762	−	6.87991i	0.877082	−	0.235013i	0.207934	−	0.978143i	$-0.433326\pi$
$857$	25.6762	−	6.87991i	0.877082	−	0.235013i	0.669148	+	0.743129i	$0.266659\pi$
$858$	−21.1826	−	42.1021i	−0.723162	−	1.43734i
$859$	−24.4080	+	14.0920i	−0.832791	+	0.480812i	−0.854807	−	0.518945i	$-0.826325\pi$
$859$	−24.4080	+	14.0920i	−0.832791	+	0.480812i	0.0220160	+	0.999758i	$0.492992\pi$
$860$	−30.3770	−	1.31218i	−1.03585	−	0.0447450i
$861$	12.9658	+	11.2245i	0.441873	+	0.382528i
$862$	−3.56849	−	2.34334i	−0.121543	−	0.0798145i
$863$	−8.21769	+	30.6688i	−0.279733	+	1.04398i	0.672869	+	0.739761i	$0.265062\pi$
$863$	−8.21769	+	30.6688i	−0.279733	+	1.04398i	−0.952603	+	0.304218i	$0.901605\pi$
$864$	−2.70274	−	4.96943i	−0.0919490	−	0.169063i
$865$	12.4887	−	8.45879i	0.424630	−	0.287607i
$866$	12.6297	−	11.2559i	0.429176	−	0.382491i
$867$	11.9240	+	11.9240i	0.404960	+	0.404960i
$868$	−46.2111	−	1.99050i	−1.56851	−	0.0675621i
$869$	7.29913			0.247606
$870$	−3.32266	+	5.94970i	−0.112649	+	0.201714i
$871$	74.8327	+	43.2047i	2.53561	+	1.46394i
$872$	9.11861	−	10.9152i	0.308795	−	0.369634i
$873$	−7.26073	−	1.94551i	−0.245739	−	0.0658455i
$874$	6.82591	+	32.9376i	0.230890	+	1.11413i
$875$	0.747633	+	29.5709i	0.0252746	+	0.999681i
$876$	13.4732	−	5.83489i	0.455216	−	0.197143i
$877$	−39.1450	−	10.4889i	−1.32183	−	0.354184i	−0.472169	−	0.881508i	$-0.656529\pi$
$877$	−39.1450	−	10.4889i	−1.32183	−	0.354184i	−0.849664	+	0.527324i	$0.823195\pi$
$878$	6.71560	+	13.3478i	0.226640	+	0.450465i
$879$	5.29178	−	9.16563i	0.178487	−	0.309149i
$880$	−49.5607	+	5.15902i	−1.67069	+	0.173910i
$881$	−4.02287			−0.135534			−0.0677669	−	0.997701i	$-0.521587\pi$
$881$	−4.02287			−0.135534			−0.0677669	+	0.997701i	$0.521587\pi$
$882$	−0.852946	−	9.86268i	−0.0287202	−	0.332094i
$883$	40.5197	−	40.5197i	1.36360	−	1.36360i	0.494314	−	0.869283i	$-0.335419\pi$
$883$	40.5197	−	40.5197i	1.36360	−	1.36360i	0.869283	−	0.494314i	$-0.164581\pi$
$884$	3.55504	+	2.63864i	0.119569	+	0.0887471i
$885$	−6.22571	+	4.21675i	−0.209275	+	0.141745i
$886$	40.1911	+	13.2856i	1.35025	+	0.446339i
$887$	17.8287	+	4.77718i	0.598628	+	0.160402i	0.545394	−	0.838180i	$-0.316380\pi$
$887$	17.8287	+	4.77718i	0.598628	+	0.160402i	0.0532347	+	0.998582i	$0.483047\pi$
$888$	0.747356	−	4.29293i	0.0250796	−	0.144061i
$889$	10.0682	−	52.3689i	0.337678	−	1.75640i
$890$	−11.4456	−	2.89226i	−0.383656	−	0.0969486i
$891$	2.78550	+	4.82463i	0.0933177	+	0.161631i
$892$	1.16226	+	1.46556i	0.0389154	+	0.0490705i
$893$	−5.62494	+	1.50720i	−0.188231	+	0.0504365i
$894$	19.7976	−	17.6441i	0.662132	−	0.590106i
$895$	0.936971	+	2.70424i	0.0313195	+	0.0903926i
$896$	−29.3759	+	5.74956i	−0.981379	+	0.192079i
$897$	22.4245	+	22.4245i	0.748732	+	0.748732i
$898$	−0.358362	+	6.23048i	−0.0119587	+	0.207914i
$899$	−16.3133	−	9.41850i	−0.544080	−	0.314125i
$900$	−5.24534	−	8.51390i	−0.174845	−	0.283797i
$901$	0.574220	−	0.331526i	0.0191301	−	0.0110447i
$902$	−28.0313	+	42.6868i	−0.933340	+	1.42131i
$903$	17.9416	−	1.29152i	0.597059	−	0.0429792i
$904$	−6.38002	+	4.48801i	−0.212196	+	0.149269i
$905$	−28.2659	+	32.6430i	−0.939592	+	1.08509i
$906$	6.12026	−	18.5148i	0.203332	−	0.615112i
$907$	−2.53449	+	0.679115i	−0.0841564	+	0.0225496i	−0.300652	−	0.953734i	$-0.597204\pi$
$907$	−2.53449	+	0.679115i	−0.0841564	+	0.0225496i	0.216495	+	0.976284i	$0.430537\pi$
$908$	43.8511	−	6.48807i	1.45525	−	0.215314i
$909$	−14.0861			−0.467206
$910$	−28.6615	−	41.0306i	−0.950118	−	1.36015i
$911$		−	38.3707i		−	1.27128i	−0.771986	−	0.635639i	$-0.780737\pi$
$911$		−	38.3707i		−	1.27128i	0.771986	−	0.635639i	$-0.219263\pi$
$912$	9.46576	+	15.2474i	0.313443	+	0.504892i
$913$	13.8742	+	51.7794i	0.459170	+	1.71365i
$914$	−16.4938	+	49.8965i	−0.545568	+	1.65043i
$915$	−1.80440	−	25.1093i	−0.0596517	−	0.830087i
$916$	−3.78898	−	8.74900i	−0.125191	−	0.289075i
$917$	5.58418	+	2.70945i	0.184406	+	0.0894738i
$918$	−0.437435	−	0.287252i	−0.0144375	−	0.00948074i
$919$	27.3963	+	47.4518i	0.903722	+	1.56529i	0.822624	+	0.568586i	$0.192509\pi$
$919$	27.3963	+	47.4518i	0.903722	+	1.56529i	0.0810976	+	0.996706i	$0.474157\pi$
$920$	30.5736	−	13.7626i	1.00798	−	0.453739i
$921$	−14.6469	+	25.3692i	−0.482631	+	0.835942i
$922$	1.28530	−	22.3462i	0.0423289	−	0.735932i
$923$	−45.9536	+	45.9536i	−1.51258	+	1.51258i
$924$	28.7764	−	6.39727i	0.946675	−	0.210455i
$925$	0.909314	−	7.64918i	0.0298981	−	0.251503i
$926$	−11.7259	−	13.1571i	−0.385337	−	0.432370i
$927$	2.38479	+	8.90017i	0.0783269	+	0.292320i
$928$	−11.6908	−	3.45397i	−0.383770	−	0.113382i
$929$	33.4605	−	19.3184i	1.09780	−	0.633817i	0.162160	−	0.986764i	$-0.448154\pi$
$929$	33.4605	−	19.3184i	1.09780	−	0.633817i	0.935643	+	0.352948i	$0.114821\pi$
$930$	23.7389	−	14.1616i	0.778428	−	0.464376i
$931$	4.49830	+	31.0829i	0.147426	+	1.01870i
$932$	0.0210117	+	0.00831224i	0.000688262	+	0.000272276i
$933$	−2.97214	+	11.0922i	−0.0973036	+	0.363142i
$934$	15.0529	−	45.5375i	0.492547	−	1.49003i
$935$	−3.81662	+	2.58505i	−0.124817	+	0.0845401i
$936$	15.3502	+	7.11738i	0.501736	+	0.232639i
$937$	−30.8098	−	30.8098i	−1.00651	−	1.00651i	−0.999979	−	0.00653468i	$-0.997920\pi$
$937$	−30.8098	−	30.8098i	−1.00651	−	1.00651i	−0.00653468	−	0.999979i	$-0.502080\pi$
$938$	−37.6624	+	38.7635i	−1.22972	+	1.26567i
$939$		−	11.4082i		−	0.372292i
$940$	2.68260	+	5.14741i	0.0874969	+	0.167890i
$941$	44.6989	+	25.8069i	1.45714	+	0.841282i	0.998870	−	0.0475297i	$-0.0151349\pi$
$941$	44.6989	+	25.8069i	1.45714	+	0.841282i	0.458273	+	0.888812i	$0.348468\pi$
$942$	−6.12107	+	3.07966i	−0.199435	+	0.100341i
$943$	8.89361	−	33.1914i	0.289616	−	1.08086i
$944$	−9.81057	−	9.20228i	−0.319307	−	0.299509i
$945$	3.66080	+	4.64743i	0.119086	+	0.151181i
$946$	10.8698	+	52.4507i	0.353407	+	1.70532i
$947$	0.438657	−	1.63709i	0.0142544	−	0.0531983i	−0.958432	−	0.285320i	$-0.907900\pi$
$947$	0.438657	−	1.63709i	0.0142544	−	0.0531983i	0.972687	+	0.232122i	$0.0745668\pi$
$948$	−2.05313	+	1.62824i	−0.0666826	+	0.0528827i
$949$	−21.9579	+	38.0322i	−0.712783	+	1.23458i
$950$	18.1647	+	26.0107i	0.589341	+	0.843898i
$951$		−	4.93092i		−	0.159896i
$952$	−2.14466	+	1.75174i	−0.0695089	+	0.0567743i
$953$	−4.60430	+	4.60430i	−0.149148	+	0.149148i	−0.777737	−	0.628589i	$-0.783633\pi$
$953$	−4.60430	+	4.60430i	−0.149148	+	0.149148i	0.628589	+	0.777737i	$0.283633\pi$
$954$	1.89176	−	1.68598i	0.0612480	−	0.0545856i
$955$	30.3731	+	5.84327i	0.982852	+	0.189084i
$956$	20.5093	+	2.36712i	0.663320	+	0.0765582i
$957$	11.5963	+	3.10721i	0.374854	+	0.100442i
$958$	−14.4847	+	22.0577i	−0.467980	+	0.712652i
$959$	−7.49709	+	8.66017i	−0.242094	+	0.279652i
$960$	12.7898	−	12.5068i	0.412790	−	0.403656i
$961$	22.7041	+	39.3247i	0.732392	+	1.26854i
$962$	5.85785	+	11.6429i	0.188865	+	0.375383i
$963$	2.00387	+	7.47856i	0.0645739	+	0.240993i
$964$	−12.2636	+	16.5227i	−0.394982	+	0.532159i
$965$	18.8196	−	38.7752i	0.605825	−	1.24822i
$966$	−17.0335	+	10.1643i	−0.548045	+	0.327031i
$967$	11.1120	−	11.1120i	0.357336	−	0.357336i	−0.505494	−	0.862830i	$-0.668690\pi$
$967$	11.1120	−	11.1120i	0.357336	−	0.357336i	0.862830	+	0.505494i	$0.168690\pi$
$968$	19.4980	+	53.2106i	0.626688	+	1.71025i
$969$	1.43783	+	0.830131i	0.0461897	+	0.0266676i
$970$	−0.339535	−	23.7680i	−0.0109018	−	0.763144i
$971$	30.9372	+	53.5848i	0.992822	+	1.71962i	0.599986	+	0.800011i	$0.295173\pi$
$971$	30.9372	+	53.5848i	0.992822	+	1.71962i	0.392837	+	0.919608i	$0.371494\pi$
$972$	−1.85976	−	0.735722i	−0.0596519	−	0.0235983i
$973$	29.1067	+	42.9624i	0.933117	+	1.37731i
$974$	5.17665	+	24.9793i	0.165870	+	0.800387i
$975$	27.7755	+	11.0978i	0.889528	+	0.355414i
$976$	43.1033	−	13.0403i	1.37970	−	0.417410i
$977$	20.2303	−	5.42070i	0.647226	−	0.173424i	0.0797515	−	0.996815i	$-0.474587\pi$
$977$	20.2303	−	5.42070i	0.647226	−	0.173424i	0.567474	+	0.823391i	$0.307921\pi$
$978$	0.217196	−	3.77618i	0.00694517	−	0.120749i
$979$			20.7975i			0.664692i
$980$	29.2722	−	11.0968i	0.935066	−	0.354474i
$981$		−	5.02854i		−	0.160549i
$982$	−28.4057	−	1.63383i	−0.906464	−	0.0521375i
$983$	32.0901	−	8.59852i	1.02352	−	0.274250i	0.292249	−	0.956342i	$-0.405596\pi$
$983$	32.0901	−	8.59852i	1.02352	−	0.274250i	0.731266	+	0.682092i	$0.238930\pi$
$984$	−1.63750	−	18.2601i	−0.0522015	−	0.582112i
$985$	28.0043	−	2.01244i	0.892291	−	0.0641218i
$986$	−1.10428	+	0.228848i	−0.0351673	+	0.00728799i
$987$	−1.92609	−	2.84296i	−0.0613080	−	0.0904926i
$988$	−49.9156	−	19.7466i	−1.58803	−	0.628223i
$989$	−18.0214	−	31.2139i	−0.573046	−	0.992545i
$990$	−12.2779	+	12.6338i	−0.390218	+	0.401528i
$991$	−23.8565	−	13.7735i	−0.757826	−	0.437531i	0.0706886	−	0.997498i	$-0.477480\pi$
$991$	−23.8565	−	13.7735i	−0.757826	−	0.437531i	−0.828515	+	0.559967i	$0.810814\pi$
$992$	34.0629	+	35.8439i	1.08150	+	1.13804i
$993$	4.17990	−	4.17990i	0.132645	−	0.132645i
$994$	−20.8293	−	34.9062i	−0.660664	−	1.10716i
$995$	27.8122	−	9.63645i	0.881706	−	0.305496i
$996$	−15.4532	−	11.4698i	−0.489653	−	0.363433i
$997$	−11.8870	−	44.3628i	−0.376464	−	1.40498i	−0.851194	−	0.524852i	$-0.824121\pi$
$997$	−11.8870	−	44.3628i	−0.376464	−	1.40498i	0.474730	−	0.880132i	$-0.342546\pi$
$998$	−12.4231	+	6.25038i	−0.393247	+	0.197852i
$999$	−0.770303	−	1.33420i	−0.0243713	−	0.0422124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dj.a.67.3	✓	384
5.3	odd	4	inner	840.2.dj.a.403.48	yes	384
7.2	even	3	inner	840.2.dj.a.667.64	yes	384
8.3	odd	2	inner	840.2.dj.a.67.82	yes	384
35.23	odd	12	inner	840.2.dj.a.163.82	yes	384
40.3	even	4	inner	840.2.dj.a.403.64	yes	384
56.51	odd	6	inner	840.2.dj.a.667.48	yes	384
280.163	even	12	inner	840.2.dj.a.163.3	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dj.a.67.3	✓	384	1.1	even	1	trivial
840.2.dj.a.67.82	yes	384	8.3	odd	2	inner
840.2.dj.a.163.3	yes	384	280.163	even	12	inner
840.2.dj.a.163.82	yes	384	35.23	odd	12	inner
840.2.dj.a.403.48	yes	384	5.3	odd	4	inner
840.2.dj.a.403.64	yes	384	40.3	even	4	inner
840.2.dj.a.667.48	yes	384	56.51	odd	6	inner
840.2.dj.a.667.64	yes	384	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41188 - 0.0812078i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.98681 + 0.229311i) q^{4} +(1.69040 + 1.46374i) q^{5} +(0.286981 + 1.38479i) q^{6} +(2.19039 - 1.48397i) q^{7} +(-2.78652 - 0.485105i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-2.26778 - 2.20390i) q^{10} +(-2.78550 + 4.82463i) q^{11} +(-0.292727 - 1.97846i) q^{12} +(4.22999 + 4.22999i) q^{13} +(-3.21308 + 1.91732i) q^{14} +(0.976356 - 2.01165i) q^{15} +(3.89483 + 0.911196i) q^{16} +(0.357434 - 0.0957741i) q^{17} +(1.26333 - 0.635612i) q^{18} +(-3.88557 + 2.24334i) q^{19} +(3.02286 + 3.29580i) q^{20} +(-2.00032 - 1.73168i) q^{21} +(4.32459 - 6.58559i) q^{22} +(-1.37208 + 5.12067i) q^{23} +(0.252628 + 2.81712i) q^{24} +(0.714927 + 4.94862i) q^{25} +(-5.62873 - 6.31574i) q^{26} +(0.707107 + 0.707107i) q^{27} +(4.69219 - 2.44609i) q^{28} +2.15497 q^{29} +(-1.54186 + 2.76092i) q^{30} +(-7.57009 - 4.37059i) q^{31} +(-5.42504 - 1.60279i) q^{32} +(5.38117 + 1.44188i) q^{33} +(-0.512431 + 0.106195i) q^{34} +(5.87480 + 0.697653i) q^{35} +(-1.83528 + 0.794816i) q^{36} +(-1.48811 - 0.398738i) q^{37} +(5.66814 - 2.85178i) q^{38} +(2.99105 - 5.18066i) q^{39} +(-4.00027 - 4.89876i) q^{40} -6.48184 q^{41} +(2.68359 + 2.60736i) q^{42} +(-4.80750 + 4.80750i) q^{43} +(-6.64060 + 8.94687i) q^{44} +(-2.19580 - 0.422435i) q^{45} +(2.35305 - 7.11835i) q^{46} +(1.25370 + 0.335928i) q^{47} +(-0.127909 - 3.99795i) q^{48} +(2.59564 - 6.50097i) q^{49} +(-0.607525 - 7.04492i) q^{50} +(-0.185021 - 0.320466i) q^{51} +(7.43420 + 9.37417i) q^{52} +(1.73077 - 0.463759i) q^{53} +(-0.940927 - 1.05577i) q^{54} +(-11.7706 + 4.07832i) q^{55} +(-6.82345 + 3.07255i) q^{56} +(3.17256 + 3.17256i) q^{57} +(-3.04256 - 0.175001i) q^{58} +(-2.91223 - 1.68137i) q^{59} +(2.40113 - 3.77287i) q^{60} +(9.74986 - 5.62909i) q^{61} +(10.3331 + 6.78550i) q^{62} +(-1.15495 + 2.38036i) q^{63} +(7.52935 + 2.70350i) q^{64} +(0.958781 + 13.3420i) q^{65} +(-7.48048 - 2.47276i) q^{66} +(13.9525 - 3.73855i) q^{67} +(0.732115 - 0.108321i) q^{68} +5.30131 q^{69} +(-8.23786 - 1.46208i) q^{70} +10.8638i q^{71} +(2.65575 - 0.973145i) q^{72} +(1.90004 + 7.09104i) q^{73} +(2.06866 + 0.683817i) q^{74} +(4.59497 - 1.97136i) q^{75} +(-8.23432 + 3.56608i) q^{76} +(1.05828 + 14.7014i) q^{77} +(-4.64372 + 7.07157i) q^{78} +(-0.655100 - 1.13467i) q^{79} +(5.25008 + 7.24131i) q^{80} +(0.500000 - 0.866025i) q^{81} +(9.15159 + 0.526376i) q^{82} +(6.80401 - 6.80401i) q^{83} +(-3.57717 - 3.89921i) q^{84} +(0.744396 + 0.361294i) q^{85} +(7.17802 - 6.39721i) q^{86} +(-0.557748 - 2.08154i) q^{87} +(10.1023 - 12.0926i) q^{88} +(3.23303 - 1.86659i) q^{89} +(3.06590 + 0.774744i) q^{90} +(15.5425 + 2.98815i) q^{91} +(-3.90029 + 9.85917i) q^{92} +(-2.26238 + 8.44333i) q^{93} +(-1.74279 - 0.576100i) q^{94} +(-9.85185 - 1.89533i) q^{95} +(-0.144073 + 5.65502i) q^{96} +(5.31523 + 5.31523i) q^{97} +(-4.19267 + 8.96781i) q^{98} -5.57100i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) \) 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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