LMFDB - Embedded newform 841.2.d.q.190.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] 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("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,4,6,-6,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.7
Character	$\chi$	$=$	841.190
Dual form			841.2.d.q.571.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.15716 + 1.03884i) q^{2} +(-1.31018 + 1.64292i) q^{3} +(2.32720 + 2.91821i) q^{4} +(2.18748 + 1.05344i) q^{5} +(-4.53300 + 2.18298i) q^{6} +(-0.235910 + 0.295821i) q^{7} +(0.923050 + 4.04415i) q^{8} +(-0.315036 - 1.38026i) q^{9} +(3.62441 + 4.54487i) q^{10} +(0.854560 - 3.74407i) q^{11} -7.84343 q^{12} +(-1.24465 + 5.45318i) q^{13} +(-0.816205 + 0.393064i) q^{14} +(-4.59671 + 2.21366i) q^{15} +(-0.548899 + 2.40488i) q^{16} +1.82620 q^{17} +(0.754282 - 3.30472i) q^{18} +(0.348089 + 0.436490i) q^{19} +(2.01655 + 8.83509i) q^{20} +(-0.176925 - 0.775161i) q^{21} +(5.73290 - 7.18883i) q^{22} +(0.302036 - 0.145453i) q^{23} +(-7.85357 - 3.78208i) q^{24} +(0.557905 + 0.699590i) q^{25} +(-8.34987 + 10.4704i) q^{26} +(-2.99939 - 1.44443i) q^{27} -1.41228 q^{28} -12.2155 q^{30} +(-3.66522 - 1.76508i) q^{31} +(1.49032 - 1.86880i) q^{32} +(5.03157 + 6.30939i) q^{33} +(3.93942 + 1.89712i) q^{34} +(-0.827677 + 0.398588i) q^{35} +(3.29475 - 4.13148i) q^{36} +(-1.79355 - 7.85806i) q^{37} +(0.297444 + 1.30319i) q^{38} +(-7.32840 - 9.18952i) q^{39} +(-2.24109 + 9.81888i) q^{40} +7.79555 q^{41} +(0.423607 - 1.85594i) q^{42} +(0.0204474 - 0.00984695i) q^{43} +(12.9147 - 6.21940i) q^{44} +(0.764883 - 3.35117i) q^{45} +0.802642 q^{46} +(1.69759 - 7.43765i) q^{47} +(-3.23187 - 4.05264i) q^{48} +(1.52579 + 6.68492i) q^{49} +(0.476732 + 2.08870i) q^{50} +(-2.39266 + 3.00030i) q^{51} +(-18.8101 + 9.05845i) q^{52} +(-5.74151 - 2.76496i) q^{53} +(-4.96966 - 6.23175i) q^{54} +(5.81348 - 7.28987i) q^{55} +(-1.41410 - 0.680996i) q^{56} -1.17318 q^{57} +8.13681 q^{59} +(-17.1574 - 8.26256i) q^{60} +(-6.46666 + 8.10894i) q^{61} +(-6.07285 - 7.61512i) q^{62} +(0.482632 + 0.232423i) q^{63} +(9.60112 - 4.62366i) q^{64} +(-8.46723 + 10.6176i) q^{65} +(4.29951 + 18.8374i) q^{66} +(2.67816 + 11.7338i) q^{67} +(4.24993 + 5.32924i) q^{68} +(-0.156755 + 0.686790i) q^{69} -2.19950 q^{70} +(3.46221 - 15.1689i) q^{71} +(5.29119 - 2.54810i) q^{72} +(-6.24784 + 3.00880i) q^{73} +(4.29425 - 18.8143i) q^{74} -1.88033 q^{75} +(-0.463699 + 2.03160i) q^{76} +(0.905978 + 1.13606i) q^{77} +(-6.26216 - 27.4363i) q^{78} +(1.66029 + 7.27418i) q^{79} +(-3.73410 + 4.68241i) q^{80} +(10.1295 - 4.87811i) q^{81} +(16.8163 + 8.09829i) q^{82} +(0.418549 + 0.524844i) q^{83} +(1.85034 - 2.32026i) q^{84} +(3.99479 + 1.92379i) q^{85} +0.0543377 q^{86} +15.9304 q^{88} +(8.68459 + 4.18228i) q^{89} +(5.13129 - 6.43444i) q^{90} +(-1.31954 - 1.65465i) q^{91} +(1.12736 + 0.542907i) q^{92} +(7.70198 - 3.70908i) q^{93} +(11.3885 - 14.2807i) q^{94} +(0.301625 + 1.32151i) q^{95} +(1.11769 + 4.89693i) q^{96} +(-2.77777 - 3.48321i) q^{97} +(-3.65315 + 16.0055i) q^{98} -5.43702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 6 q^{3} - 6 q^{4} + q^{5} - 3 q^{6} + 15 q^{8} - 8 q^{9} - 3 q^{10} + 5 q^{11} - 72 q^{12} + 4 q^{13} + 15 q^{14} - 7 q^{15} + 2 q^{16} - 54 q^{17} - 11 q^{18} + 17 q^{19} + 7 q^{20} + 25 q^{21}+ \cdots - 90 q^{99}+O(q^{100}) $ 48 * q + 4 * q^2 + 6 * q^3 - 6 * q^4 + q^5 - 3 * q^6 + 15 * q^8 - 8 * q^9 - 3 * q^10 + 5 * q^11 - 72 * q^12 + 4 * q^13 + 15 * q^14 - 7 * q^15 + 2 * q^16 - 54 * q^17 - 11 * q^18 + 17 * q^19 + 7 * q^20 + 25 * q^21 - 25 * q^22 + 7 * q^23 - 25 * q^24 + 13 * q^25 + 3 * q^26 + 18 * q^27 + 150 * q^28 - 156 * q^30 + q^31 - 6 * q^32 - 12 * q^34 + 5 * q^35 + 19 * q^36 + 6 * q^37 + 14 * q^38 + 27 * q^39 - 25 * q^40 - 36 * q^41 - 15 * q^42 - 5 * q^43 + 20 * q^44 + q^45 - 84 * q^46 + 31 * q^47 + 11 * q^48 - 4 * q^49 + 11 * q^50 - 23 * q^51 - 2 * q^52 - 19 * q^53 + 46 * q^54 + 20 * q^55 + 20 * q^56 - 36 * q^57 - 6 * q^59 - 9 * q^60 + 21 * q^61 + 12 * q^62 + 10 * q^63 - q^64 + 17 * q^65 + 5 * q^66 - 2 * q^67 + 8 * q^68 - 14 * q^69 + 30 * q^70 + 12 * q^71 - 34 * q^73 + 27 * q^74 - 24 * q^75 - 16 * q^76 - 10 * q^77 - 6 * q^78 + 29 * q^79 + 41 * q^80 - 12 * q^81 + 22 * q^82 + 3 * q^83 - 10 * q^84 + 2 * q^85 - 30 * q^86 - 90 * q^88 + 36 * q^89 - 38 * q^90 + 4 * q^92 - 2 * q^93 - 13 * q^94 + 11 * q^95 + 2 * q^96 - 18 * q^97 + 27 * q^98 - 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	2.15716	+	1.03884i	1.52534	+	0.734567i	0.993665	−	0.112378i	$-0.0358469\pi$
$2$	2.15716	+	1.03884i	1.52534	+	0.734567i	0.531679	+	0.846946i	$0.321561\pi$
$3$	−1.31018	+	1.64292i	−0.756435	+	0.948539i	−0.999771	−	0.0214029i	$-0.993187\pi$
$3$	−1.31018	+	1.64292i	−0.756435	+	0.948539i	0.243336	+	0.969942i	$0.421758\pi$
$4$	2.32720	+	2.91821i	1.16360	+	1.45911i
$5$	2.18748	+	1.05344i	0.978272	+	0.471111i	0.853510	−	0.521076i	$-0.174469\pi$
$5$	2.18748	+	1.05344i	0.978272	+	0.471111i	0.124762	+	0.992187i	$0.460183\pi$
$6$	−4.53300	+	2.18298i	−1.85059	+	0.891197i
$7$	−0.235910	+	0.295821i	−0.0891655	+	0.111810i	−0.824413	−	0.565989i	$-0.808495\pi$
$7$	−0.235910	+	0.295821i	−0.0891655	+	0.111810i	0.735247	+	0.677799i	$0.237066\pi$
$8$	0.923050	+	4.04415i	0.326348	+	1.42982i
$9$	−0.315036	−	1.38026i	−0.105012	−	0.460088i
$10$	3.62441	+	4.54487i	1.14614	+	1.43721i
$11$	0.854560	−	3.74407i	0.257660	−	1.12888i	−0.666086	−	0.745875i	$-0.732032\pi$
$11$	0.854560	−	3.74407i	0.257660	−	1.12888i	0.923746	−	0.383006i	$-0.125111\pi$
$12$	−7.84343			−2.26420
$13$	−1.24465	+	5.45318i	−0.345204	+	1.51244i	0.442716	+	0.896662i	$0.354015\pi$
$13$	−1.24465	+	5.45318i	−0.345204	+	1.51244i	−0.787920	+	0.615777i	$0.788842\pi$
$14$	−0.816205	+	0.393064i	−0.218140	+	0.105051i
$15$	−4.59671	+	2.21366i	−1.18687	+	0.571565i
$16$	−0.548899	+	2.40488i	−0.137225	+	0.601221i
$17$	1.82620			0.442919			0.221460	−	0.975170i	$-0.428918\pi$
$17$	1.82620			0.442919			0.221460	+	0.975170i	$0.428918\pi$
$18$	0.754282	−	3.30472i	0.177786	−	0.778931i
$19$	0.348089	+	0.436490i	0.0798572	+	0.100138i	0.820155	−	0.572141i	$-0.193887\pi$
$19$	0.348089	+	0.436490i	0.0798572	+	0.100138i	−0.740298	+	0.672279i	$0.765316\pi$
$20$	2.01655	+	8.83509i	0.450915	+	1.97559i
$21$	−0.176925	−	0.775161i	−0.0386083	−	0.169154i
$22$	5.73290	−	7.18883i	1.22226	−	1.53266i
$23$	0.302036	−	0.145453i	0.0629788	−	0.0303290i	−0.402129	−	0.915583i	$-0.631730\pi$
$23$	0.302036	−	0.145453i	0.0629788	−	0.0303290i	0.465108	+	0.885254i	$0.346015\pi$
$24$	−7.85357	−	3.78208i	−1.60310	−	0.772014i
$25$	0.557905	+	0.699590i	0.111581	+	0.139918i
$26$	−8.34987	+	10.4704i	−1.63754	+	2.05342i
$27$	−2.99939	−	1.44443i	−0.577234	−	0.277981i
$28$	−1.41228			−0.266895
$29$		0			0
$29$		0			0
$30$	−12.2155			−2.23023
$31$	−3.66522	−	1.76508i	−0.658293	−	0.317017i	0.0747474	−	0.997203i	$-0.476185\pi$
$31$	−3.66522	−	1.76508i	−0.658293	−	0.317017i	−0.733040	+	0.680185i	$0.761899\pi$
$32$	1.49032	−	1.86880i	0.263453	−	0.330360i
$33$	5.03157	+	6.30939i	0.875885	+	1.09832i
$34$	3.93942	+	1.89712i	0.675604	+	0.325354i
$35$	−0.827677	+	0.398588i	−0.139903	+	0.0673737i
$36$	3.29475	−	4.13148i	0.549125	−	0.688581i
$37$	−1.79355	−	7.85806i	−0.294858	−	1.29186i	−0.877676	−	0.479255i	$-0.840907\pi$
$37$	−1.79355	−	7.85806i	−0.294858	−	1.29186i	0.582818	−	0.812603i	$-0.301950\pi$
$38$	0.297444	+	1.30319i	0.0482518	+	0.211405i
$39$	−7.32840	−	9.18952i	−1.17348	−	1.47150i
$40$	−2.24109	+	9.81888i	−0.354348	+	1.55250i
$41$	7.79555			1.21746			0.608730	−	0.793377i	$-0.291679\pi$
$41$	7.79555			1.21746			0.608730	+	0.793377i	$0.291679\pi$
$42$	0.423607	−	1.85594i	0.0653640	−	0.286378i
$43$	0.0204474	−	0.00984695i	0.00311820	−	0.00150165i	−0.432324	−	0.901718i	$-0.642306\pi$
$43$	0.0204474	−	0.00984695i	0.00311820	−	0.00150165i	0.435442	+	0.900217i	$0.356592\pi$
$44$	12.9147	−	6.21940i	1.94697	−	0.937610i
$45$	0.764883	−	3.35117i	0.114022	−	0.499563i
$46$	0.802642			0.118343
$47$	1.69759	−	7.43765i	0.247620	−	1.08489i	−0.686274	−	0.727343i	$-0.740755\pi$
$47$	1.69759	−	7.43765i	0.247620	−	1.08489i	0.933894	−	0.357550i	$-0.116388\pi$
$48$	−3.23187	−	4.05264i	−0.466480	−	0.584948i
$49$	1.52579	+	6.68492i	0.217970	+	0.954989i
$50$	0.476732	+	2.08870i	0.0674201	+	0.295387i
$51$	−2.39266	+	3.00030i	−0.335039	+	0.420126i
$52$	−18.8101	+	9.05845i	−2.60849	+	1.25618i
$53$	−5.74151	−	2.76496i	−0.788657	−	0.379797i	−0.00420840	−	0.999991i	$-0.501340\pi$
$53$	−5.74151	−	2.76496i	−0.788657	−	0.379797i	−0.784448	+	0.620194i	$0.787054\pi$
$54$	−4.96966	−	6.23175i	−0.676285	−	0.848034i
$55$	5.81348	−	7.28987i	0.783889	−	0.982966i
$56$	−1.41410	−	0.680996i	−0.188967	−	0.0910019i
$57$	−1.17318			−0.155391
$58$		0			0
$59$	8.13681			1.05932			0.529661	−	0.848209i	$-0.322319\pi$
$59$	8.13681			1.05932			0.529661	+	0.848209i	$0.322319\pi$
$60$	−17.1574	−	8.26256i	−2.21501	−	1.06669i
$61$	−6.46666	+	8.10894i	−0.827971	+	1.03824i	0.170628	+	0.985335i	$0.445420\pi$
$61$	−6.46666	+	8.10894i	−0.827971	+	1.03824i	−0.998599	+	0.0529074i	$0.983151\pi$
$62$	−6.07285	−	7.61512i	−0.771253	−	0.967121i
$63$	0.482632	+	0.232423i	0.0608059	+	0.0292826i
$64$	9.60112	−	4.62366i	1.20014	−	0.577957i
$65$	−8.46723	+	10.6176i	−1.05023	+	1.31695i
$66$	4.29951	+	18.8374i	0.529233	+	2.31872i
$67$	2.67816	+	11.7338i	0.327189	+	1.43351i	0.824463	+	0.565917i	$0.191478\pi$
$67$	2.67816	+	11.7338i	0.327189	+	1.43351i	−0.497273	+	0.867594i	$0.665665\pi$
$68$	4.24993	+	5.32924i	0.515380	+	0.646266i
$69$	−0.156755	+	0.686790i	−0.0188711	+	0.0826798i
$70$	−2.19950			−0.262891
$71$	3.46221	−	15.1689i	0.410889	−	1.80022i	−0.169102	−	0.985599i	$-0.554087\pi$
$71$	3.46221	−	15.1689i	0.410889	−	1.80022i	0.579991	−	0.814623i	$-0.303056\pi$
$72$	5.29119	−	2.54810i	0.623573	−	0.300297i
$73$	−6.24784	+	3.00880i	−0.731254	+	0.352153i	−0.762177	−	0.647368i	$-0.775870\pi$
$73$	−6.24784	+	3.00880i	−0.731254	+	0.352153i	0.0309231	+	0.999522i	$0.490155\pi$
$74$	4.29425	−	18.8143i	0.499196	−	2.18712i
$75$	−1.88033			−0.217121
$76$	−0.463699	+	2.03160i	−0.0531899	+	0.233040i
$77$	0.905978	+	1.13606i	0.103246	+	0.129466i
$78$	−6.26216	−	27.4363i	−0.709050	−	3.10655i
$79$	1.66029	+	7.27418i	0.186797	+	0.818410i	0.978291	+	0.207234i	$0.0664461\pi$
$79$	1.66029	+	7.27418i	0.186797	+	0.818410i	−0.791495	+	0.611176i	$0.790697\pi$
$80$	−3.73410	+	4.68241i	−0.417485	+	0.523510i
$81$	10.1295	−	4.87811i	1.12550	−	0.542013i
$82$	16.8163	+	8.09829i	1.85705	+	0.894307i
$83$	0.418549	+	0.524844i	0.0459417	+	0.0576091i	0.804272	−	0.594262i	$-0.202556\pi$
$83$	0.418549	+	0.524844i	0.0459417	+	0.0576091i	−0.758330	+	0.651871i	$0.773984\pi$
$84$	1.85034	−	2.32026i	0.201889	−	0.253161i
$85$	3.99479	+	1.92379i	0.433295	+	0.208664i
$86$	0.0543377			0.00585939
$87$		0			0
$88$	15.9304			1.69818
$89$	8.68459	+	4.18228i	0.920564	+	0.443320i	0.833273	−	0.552862i	$-0.186465\pi$
$89$	8.68459	+	4.18228i	0.920564	+	0.443320i	0.0872917	+	0.996183i	$0.472179\pi$
$90$	5.13129	−	6.43444i	0.540886	−	0.678249i
$91$	−1.31954	−	1.65465i	−0.138326	−	0.173455i
$92$	1.12736	+	0.542907i	0.117535	+	0.0566020i
$93$	7.70198	−	3.70908i	0.798658	−	0.384614i
$94$	11.3885	−	14.2807i	1.17463	−	1.47294i
$95$	0.301625	+	1.32151i	0.0309461	+	0.135584i
$96$	1.11769	+	4.89693i	0.114074	+	0.499791i
$97$	−2.77777	−	3.48321i	−0.282039	−	0.353666i	0.620551	−	0.784166i	$-0.286909\pi$
$97$	−2.77777	−	3.48321i	−0.282039	−	0.353666i	−0.902591	+	0.430500i	$0.858337\pi$
$98$	−3.65315	+	16.0055i	−0.369024	+	1.61680i
$99$	−5.43702			−0.546441
$100$	−0.743199	+	3.25617i	−0.0743199	+	0.325617i
$101$	5.44097	−	2.62023i	0.541397	−	0.260723i	−0.143139	−	0.989703i	$-0.545719\pi$
$101$	5.44097	−	2.62023i	0.541397	−	0.260723i	0.684535	+	0.728980i	$0.260005\pi$
$102$	−8.27817	+	3.98656i	−0.819661	+	0.394728i
$103$	−1.37929	+	6.04304i	−0.135905	+	0.595439i	0.860405	+	0.509611i	$0.170211\pi$
$103$	−1.37929	+	6.04304i	−0.135905	+	0.595439i	−0.996310	+	0.0858279i	$0.972646\pi$
$104$	−23.2023			−2.27518
$105$	0.429561	−	1.88203i	0.0419209	−	0.183667i
$106$	−9.51303	−	11.9290i	−0.923987	−	1.15864i
$107$	−1.17970	−	5.16861i	−0.114046	−	0.499668i	−0.999396	−	0.0347435i	$-0.988939\pi$
$107$	−1.17970	−	5.16861i	−0.114046	−	0.499668i	0.885350	−	0.464925i	$-0.153919\pi$
$108$	−2.76502	−	12.1143i	−0.266064	−	1.16570i
$109$	3.92755	−	4.92499i	0.376191	−	0.471729i	−0.557309	−	0.830305i	$-0.688166\pi$
$109$	3.92755	−	4.92499i	0.376191	−	0.471729i	0.933500	+	0.358576i	$0.116738\pi$
$110$	20.1136	−	9.68620i	1.91776	−	0.923543i
$111$	15.2600	+	7.34884i	1.44842	+	0.697521i
$112$	−0.581926	−	0.729712i	−0.0549868	−	0.0689513i
$113$	−8.36105	+	10.4844i	−0.786541	+	0.986291i	0.213415	+	0.976962i	$0.431541\pi$
$113$	−8.36105	+	10.4844i	−0.786541	+	0.986291i	−0.999956	+	0.00932976i	$0.997030\pi$
$114$	−2.53074	−	1.21874i	−0.237025	−	0.114145i
$115$	0.813923			0.0758987
$116$		0			0
$117$	7.91893			0.732105
$118$	17.5524	+	8.45281i	1.61583	+	0.778144i
$119$	−0.430819	+	0.540230i	−0.0394931	+	0.0495228i
$120$	−13.1954	−	16.5465i	−1.20457	−	1.51048i
$121$	−3.37715	−	1.62635i	−0.307014	−	0.147850i
$122$	−22.3735	+	10.7745i	−2.02560	+	0.975478i
$123$	−10.2136	+	12.8075i	−0.920930	+	1.15481i
$124$	−3.37882	−	14.8036i	−0.303427	−	1.32940i
$125$	−2.21789	−	9.71719i	−0.198374	−	0.869132i
$126$	0.799666	+	1.00275i	0.0712399	+	0.0893320i
$127$	−1.29737	+	5.68415i	−0.115123	+	0.504386i	0.884183	+	0.467140i	$0.154716\pi$
$127$	−1.29737	+	5.68415i	−0.115123	+	0.504386i	−0.999306	+	0.0372461i	$0.988141\pi$
$128$	20.7338			1.83263
$129$	−0.0106121	+	0.0464947i	−0.000934344	+	0.00409363i
$130$	−29.2951	+	14.1078i	−2.56935	+	1.23733i
$131$	−0.475897	+	0.229180i	−0.0415793	+	0.0200235i	−0.454558	−	0.890717i	$-0.650203\pi$
$131$	−0.475897	+	0.229180i	−0.0415793	+	0.0200235i	0.412979	+	0.910741i	$0.364488\pi$
$132$	−6.70269	+	29.3664i	−0.583394	+	2.55602i
$133$	−0.211241			−0.0183169
$134$	−6.41224	+	28.0939i	−0.553933	+	2.42694i
$135$	−5.03951	−	6.31934i	−0.433732	−	0.543882i
$136$	1.68568	+	7.38543i	0.144546	+	0.633295i
$137$	1.74946	+	7.66489i	0.149467	+	0.654856i	0.993034	+	0.117832i	$0.0375943\pi$
$137$	1.74946	+	7.66489i	0.149467	+	0.654856i	−0.843567	+	0.537024i	$0.819549\pi$
$138$	−1.05161	+	1.31867i	−0.0895188	+	0.112253i
$139$	8.33239	−	4.01267i	0.706744	−	0.340350i	−0.0457464	−	0.998953i	$-0.514567\pi$
$139$	8.33239	−	4.01267i	0.706744	−	0.340350i	0.752491	+	0.658603i	$0.228852\pi$
$140$	−3.08933	−	1.48774i	−0.261096	−	0.125737i
$141$	9.99528	+	12.5337i	0.841755	+	1.05553i
$142$	23.2266	−	29.1252i	1.94913	−	2.44413i
$143$	19.3535	+	9.32014i	1.61842	+	0.779389i
$144$	3.49230			0.291025
$145$		0			0
$146$	−16.6033			−1.37410
$147$	−12.9818	−	6.25172i	−1.07072	−	0.515634i
$148$	18.7575	−	23.5212i	1.54186	−	1.93343i
$149$	−0.320646	−	0.402077i	−0.0262683	−	0.0329394i	0.768524	−	0.639821i	$-0.220992\pi$
$149$	−0.320646	−	0.402077i	−0.0262683	−	0.0329394i	−0.794792	+	0.606882i	$0.792420\pi$
$150$	−4.05617	−	1.95335i	−0.331185	−	0.159490i
$151$	5.90345	−	2.84295i	0.480416	−	0.231356i	−0.177971	−	0.984036i	$-0.556953\pi$
$151$	5.90345	−	2.84295i	0.480416	−	0.231356i	0.658387	+	0.752680i	$0.271239\pi$
$152$	−1.44393	+	1.81063i	−0.117118	+	0.146861i
$153$	−0.575320	−	2.52064i	−0.0465118	−	0.203782i
$154$	0.774163	+	3.39183i	0.0623838	+	0.273321i
$155$	−6.15821	−	7.72215i	−0.494639	−	0.620258i
$156$	9.76235	−	42.7716i	0.781613	−	3.42447i
$157$	−11.4559			−0.914282			−0.457141	−	0.889394i	$-0.651126\pi$
$157$	−11.4559			−0.914282			−0.457141	+	0.889394i	$0.651126\pi$
$158$	−3.97517	+	17.4164i	−0.316248	+	1.38557i
$159$	12.0650	−	5.81022i	0.956820	−	0.460780i
$160$	5.22870	−	2.51801i	0.413365	−	0.199066i
$161$	−0.0282251	+	0.123662i	−0.00222445	+	0.00974596i
$162$	26.9186			2.11492
$163$	4.05723	−	17.7759i	0.317787	−	1.39231i	−0.523639	−	0.851940i	$-0.675426\pi$
$163$	4.05723	−	17.7759i	0.317787	−	1.39231i	0.841425	−	0.540373i	$-0.181717\pi$
$164$	18.1418	+	22.7491i	1.41663	+	1.77640i
$165$	4.35994	+	19.1021i	0.339421	+	1.48710i
$166$	0.357652	+	1.56698i	0.0277592	+	0.121621i
$167$	1.57982	−	1.98103i	0.122250	−	0.153297i	−0.716940	−	0.697135i	$-0.754458\pi$
$167$	1.57982	−	1.98103i	0.122250	−	0.153297i	0.839190	+	0.543838i	$0.183029\pi$
$168$	2.97155	−	1.43102i	0.229260	−	0.110406i
$169$	−16.4754	−	7.93413i	−1.26734	−	0.610318i
$170$	6.61891	+	8.29985i	0.507647	+	0.636569i
$171$	0.492811	−	0.617965i	0.0376862	−	0.0472570i
$172$	0.0763206	+	0.0367541i	0.00581939	+	0.00280247i
$173$	8.48473			0.645082			0.322541	−	0.946556i	$-0.395463\pi$
$173$	8.48473			0.645082			0.322541	+	0.946556i	$0.395463\pi$
$174$		0			0
$175$	−0.338569			−0.0255934
$176$	8.53500	+	4.11024i	0.643349	+	0.309821i
$177$	−10.6607	+	13.3681i	−0.801308	+	1.00481i
$178$	14.3894	+	18.0437i	1.07853	+	1.35243i
$179$	−11.6702	−	5.62006i	−0.872269	−	0.420063i	−0.0564745	−	0.998404i	$-0.517986\pi$
$179$	−11.6702	−	5.62006i	−0.872269	−	0.420063i	−0.815795	+	0.578341i	$0.803700\pi$
$180$	11.5595	−	5.56674i	0.861591	−	0.414921i
$181$	10.2358	−	12.8353i	0.760822	−	0.954041i	−0.239034	−	0.971011i	$-0.576831\pi$
$181$	10.2358	−	12.8353i	0.760822	−	0.954041i	0.999856	+	0.0169702i	$0.00540204\pi$
$182$	−1.12755	−	4.94014i	−0.0835799	−	0.366188i
$183$	−4.84981	−	21.2484i	−0.358508	−	1.57073i
$184$	0.867027	+	1.08722i	0.0639181	+	0.0801507i
$185$	4.35460	−	19.0788i	0.320157	−	1.40270i
$186$	20.4676			1.50075
$187$	1.56060	−	6.83743i	0.114122	−	0.500003i
$188$	25.6553	−	12.3549i	1.87110	−	0.901075i
$189$	1.13488	−	0.546530i	0.0825504	−	0.0397542i
$190$	−0.722172	+	3.16404i	−0.0523918	+	0.229544i
$191$	−7.42138			−0.536992			−0.268496	−	0.963281i	$-0.586527\pi$
$191$	−7.42138			−0.536992			−0.268496	+	0.963281i	$0.586527\pi$
$192$	−4.98294	+	21.8317i	−0.359613	+	1.57557i
$193$	13.6978	+	17.1765i	0.985992	+	1.23640i	0.971632	+	0.236498i	$0.0759997\pi$
$193$	13.6978	+	17.1765i	0.985992	+	1.23640i	0.0143602	+	0.999897i	$0.495429\pi$
$194$	−2.37362	−	10.3995i	−0.170416	−	0.746640i
$195$	−6.35017	−	27.8219i	−0.454745	−	1.99237i
$196$	−15.9572	+	20.0097i	−1.13980	+	1.42926i
$197$	−17.7529	+	8.54936i	−1.26484	+	0.609117i	−0.941452	−	0.337148i	$-0.890538\pi$
$197$	−17.7529	+	8.54936i	−1.26484	+	0.609117i	−0.323393	+	0.946265i	$0.604824\pi$
$198$	−11.7285	−	5.64817i	−0.833512	−	0.401398i
$199$	−10.1244	−	12.6956i	−0.717698	−	0.899965i	0.280507	−	0.959852i	$-0.409497\pi$
$199$	−10.1244	−	12.6956i	−0.717698	−	0.899965i	−0.998205	+	0.0598870i	$0.980926\pi$
$200$	−2.31427	+	2.90201i	−0.163644	+	0.205203i
$201$	−22.7865	−	10.9734i	−1.60724	−	0.774005i
$202$	14.4591			1.01734
$203$		0			0
$204$	−14.3237			−1.00286
$205$	17.0526	+	8.21212i	1.19101	+	0.573559i
$206$	−9.25307	+	11.6030i	−0.644692	+	0.808418i
$207$	−0.295915	−	0.371066i	−0.0205675	−	0.0257909i
$208$	−12.4311	−	5.98649i	−0.861940	−	0.415088i
$209$	1.93172	−	0.930265i	0.133620	−	0.0643478i
$210$	2.88175	−	3.61360i	0.198860	−	0.249362i
$211$	−5.23722	−	22.9458i	−0.360545	−	1.57965i	−0.751814	−	0.659376i	$-0.770821\pi$
$211$	−5.23722	−	22.9458i	−0.360545	−	1.57965i	0.391268	−	0.920277i	$-0.372036\pi$
$212$	−5.29286	−	23.1895i	−0.363515	−	1.59266i
$213$	20.3852	+	25.5622i	1.39677	+	1.75149i
$214$	2.82452	−	12.3750i	0.193080	−	0.845941i
$215$	0.0551015			0.00375789
$216$	3.07291	−	13.4633i	0.209085	−	0.916060i
$217$	1.38681	−	0.667852i	0.0941427	−	0.0453367i
$218$	13.5886	−	6.54394i	0.920338	−	0.443211i
$219$	3.24260	−	14.2068i	0.219115	−	0.960004i
$220$	34.8025			2.34638
$221$	−2.27299	+	9.95860i	−0.152898	+	0.669888i
$222$	25.2841	+	31.7053i	1.69696	+	2.12792i
$223$	0.156194	+	0.684332i	0.0104595	+	0.0458263i	0.979888	−	0.199546i	$-0.0639468\pi$
$223$	0.156194	+	0.684332i	0.0104595	+	0.0458263i	−0.969429	+	0.245373i	$0.921090\pi$
$224$	0.201250	+	0.881734i	0.0134466	+	0.0589134i
$225$	0.789859	−	0.990451i	0.0526572	−	0.0660301i
$226$	−28.9277	+	13.9309i	−1.92424	+	0.926667i
$227$	6.66942	+	3.21182i	0.442665	+	0.213176i	0.641920	−	0.766772i	$-0.278138\pi$
$227$	6.66942	+	3.21182i	0.442665	+	0.213176i	−0.199255	+	0.979948i	$0.563852\pi$
$228$	−2.73022	−	3.42358i	−0.180813	−	0.226732i
$229$	−6.69982	+	8.40131i	−0.442737	+	0.555174i	−0.952262	−	0.305281i	$-0.901250\pi$
$229$	−6.69982	+	8.40131i	−0.442737	+	0.555174i	0.509526	+	0.860456i	$0.329821\pi$
$230$	1.75577	+	0.845532i	0.115772	+	0.0557527i
$231$	−3.05345			−0.200902
$232$		0			0
$233$	−15.5888			−1.02126			−0.510630	−	0.859801i	$-0.670588\pi$
$233$	−15.5888			−1.02126			−0.510630	+	0.859801i	$0.670588\pi$
$234$	17.0824	+	8.22646i	1.11671	+	0.537781i
$235$	11.5485	−	14.4814i	0.753344	−	0.944664i
$236$	18.9360	+	23.7449i	1.23263	+	1.54566i
$237$	−14.1262	−	6.80280i	−0.917593	−	0.441890i
$238$	−1.49056	+	0.717814i	−0.0966184	+	0.0465290i
$239$	4.64126	−	5.81995i	0.300218	−	0.376461i	−0.608725	−	0.793381i	$-0.708319\pi$
$239$	4.64126	−	5.81995i	0.300218	−	0.376461i	0.908943	+	0.416920i	$0.136890\pi$
$240$	−2.80046	−	12.2696i	−0.180769	−	0.792002i
$241$	1.17199	+	5.13483i	0.0754946	+	0.330763i	0.998546	−	0.0539142i	$-0.0171698\pi$
$241$	1.17199	+	5.13483i	0.0754946	+	0.330763i	−0.923051	+	0.384678i	$0.874313\pi$
$242$	−5.59556	−	7.01661i	−0.359696	−	0.451045i
$243$	−3.03480	+	13.2963i	−0.194683	+	0.852960i
$244$	−38.7128			−2.47833
$245$	−3.70450	+	16.2305i	−0.236672	+	1.03693i
$246$	−35.3372	+	17.0175i	−2.25302	+	1.08500i
$247$	−2.81351	+	1.35491i	−0.179019	+	0.0862112i
$248$	3.75505	−	16.4519i	0.238446	−	1.04470i
$249$	−1.41065			−0.0893964
$250$	5.31022	−	23.2656i	0.335848	−	1.47144i
$251$	−17.4350	−	21.8628i	−1.10049	−	1.37997i	−0.917915	−	0.396776i	$-0.870129\pi$
$251$	−17.4350	−	21.8628i	−1.10049	−	1.37997i	−0.182573	−	0.983192i	$-0.558443\pi$
$252$	0.444918	+	1.94931i	0.0280272	+	0.122795i
$253$	−0.286478	−	1.25514i	−0.0180107	−	0.0789101i
$254$	−8.70353	+	10.9139i	−0.546108	+	0.684798i
$255$	−8.39453	+	4.04259i	−0.525686	+	0.253157i
$256$	25.5240	+	12.2917i	1.59525	+	0.768233i
$257$	−11.8891	−	14.9084i	−0.741620	−	0.929962i	0.257722	−	0.966219i	$-0.417028\pi$
$257$	−11.8891	−	14.9084i	−0.741620	−	0.929962i	−0.999343	+	0.0362568i	$0.988457\pi$
$258$	−0.0711924	+	0.0892724i	−0.00443224	+	0.00555786i
$259$	2.74770	+	1.32322i	0.170734	+	0.0822210i
$260$	−50.6892			−3.14361
$261$		0			0
$262$	−1.26467			−0.0781315
$263$	−6.41027	−	3.08702i	−0.395274	−	0.190354i	0.225679	−	0.974202i	$-0.427540\pi$
$263$	−6.41027	−	3.08702i	−0.395274	−	0.190354i	−0.620953	+	0.783848i	$0.713254\pi$
$264$	−20.8717	+	26.1723i	−1.28457	+	1.61079i
$265$	−9.64674	−	12.0966i	−0.592594	−	0.743090i
$266$	−0.455681	−	0.219444i	−0.0279396	−	0.0134550i
$267$	−18.2495	+	8.78851i	−1.11685	+	0.537848i
$268$	−28.0091	+	35.1223i	−1.71093	+	2.14543i
$269$	1.32535	+	5.80674i	0.0808081	+	0.354043i	0.999126	−	0.0418004i	$-0.0133094\pi$
$269$	1.32535	+	5.80674i	0.0808081	+	0.354043i	−0.918318	+	0.395844i	$0.870452\pi$
$270$	−4.30629	−	18.8671i	−0.262072	−	1.14821i
$271$	3.20069	+	4.01354i	0.194428	+	0.243805i	0.869484	−	0.493962i	$-0.164452\pi$
$271$	3.20069	+	4.01354i	0.194428	+	0.243805i	−0.675055	+	0.737767i	$0.735880\pi$
$272$	−1.00240	+	4.39180i	−0.0607795	+	0.266292i
$273$	4.44730			0.269163
$274$	−4.18868	+	18.3518i	−0.253048	+	1.10867i
$275$	3.09608	−	1.49099i	0.186701	−	0.0899103i
$276$	−2.36900	+	1.14085i	−0.142597	+	0.0686710i
$277$	−4.45167	+	19.5040i	−0.267475	+	1.17188i	0.645465	+	0.763790i	$0.276664\pi$
$277$	−4.45167	+	19.5040i	−0.267475	+	1.17188i	−0.912940	+	0.408094i	$0.866194\pi$
$278$	22.1428			1.32804
$279$	−1.28159	+	5.61503i	−0.0767270	+	0.336163i
$280$	−2.37594	−	2.97933i	−0.141989	−	0.178049i
$281$	2.61043	+	11.4370i	0.155725	+	0.682276i	0.991158	+	0.132684i	$0.0423597\pi$
$281$	2.61043	+	11.4370i	0.155725	+	0.682276i	−0.835433	+	0.549592i	$0.814783\pi$
$282$	8.54102	+	37.4207i	0.508611	+	2.22837i
$283$	−18.4693	+	23.1597i	−1.09788	+	1.37670i	−0.178223	+	0.983990i	$0.557035\pi$
$283$	−18.4693	+	23.1597i	−1.09788	+	1.37670i	−0.919661	+	0.392713i	$0.871537\pi$
$284$	52.3234	−	25.1976i	3.10482	−	1.49520i
$285$	−2.56631	−	1.23587i	−0.152015	−	0.0732066i
$286$	32.0665	+	40.2101i	1.89613	+	2.37767i
$287$	−1.83905	+	2.30609i	−0.108556	+	0.136124i
$288$	−3.04893	−	1.46829i	−0.179660	−	0.0865198i
$289$	−13.6650			−0.803823
$290$		0			0
$291$	9.36201			0.548811
$292$	−23.3203	−	11.2304i	−1.36471	−	0.657212i
$293$	4.90178	−	6.14664i	0.286365	−	0.359090i	−0.617754	−	0.786372i	$-0.711957\pi$
$293$	4.90178	−	6.14664i	0.286365	−	0.359090i	0.904119	+	0.427281i	$0.140529\pi$
$294$	−21.5094	−	26.9720i	−1.25446	−	1.57304i
$295$	17.7991	+	8.57161i	1.03631	+	0.499059i
$296$	30.1236	−	14.5068i	1.75090	−	0.843189i
$297$	−7.97122	+	9.99560i	−0.462537	+	0.580003i
$298$	−0.273993	−	1.20044i	−0.0158720	−	0.0695398i
$299$	0.417250	+	1.82809i	0.0241302	+	0.105721i
$300$	−4.37589	−	5.48719i	−0.252642	−	0.316803i
$301$	−0.00191080	+	0.00837177i	−0.000110137	+	0.000482541i
$302$	15.6881			0.902747
$303$	−2.82384	+	12.3721i	−0.162225	+	0.710756i
$304$	−1.24077	+	0.597526i	−0.0711633	+	0.0342704i
$305$	−22.6880	+	10.9259i	−1.29911	+	0.625618i
$306$	1.37747	−	6.03509i	0.0787448	−	0.345003i
$307$	−28.3811			−1.61979			−0.809897	−	0.586572i	$-0.800477\pi$
$307$	−28.3811			−1.61979			−0.809897	+	0.586572i	$0.800477\pi$
$308$	−1.20688	+	5.28767i	−0.0687681	+	0.301293i
$309$	−8.12111	−	10.1835i	−0.461994	−	0.579322i
$310$	−5.26222	−	23.0553i	−0.298874	−	1.30945i
$311$	1.90740	+	8.35687i	0.108159	+	0.473875i	0.999778	+	0.0210878i	$0.00671296\pi$
$311$	1.90740	+	8.35687i	0.108159	+	0.473875i	−0.891619	+	0.452787i	$0.850430\pi$
$312$	30.3993	−	38.1195i	1.72102	−	2.15809i
$313$	−0.791956	+	0.381386i	−0.0447640	+	0.0215572i	−0.456132	−	0.889912i	$-0.650765\pi$
$313$	−0.791956	+	0.381386i	−0.0447640	+	0.0215572i	0.411368	+	0.911469i	$0.365051\pi$
$314$	−24.7123	−	11.9008i	−1.39459	−	0.671601i
$315$	0.810905	+	1.01684i	0.0456893	+	0.0572926i
$316$	−17.3638	+	21.7735i	−0.976790	+	1.22486i
$317$	−23.9889	−	11.5524i	−1.34735	−	0.648849i	−0.385570	−	0.922679i	$-0.625995\pi$
$317$	−23.9889	−	11.5524i	−1.34735	−	0.648849i	−0.961778	+	0.273830i	$0.911709\pi$
$318$	32.0621			1.79795
$319$		0			0
$320$	25.8730			1.44635
$321$	10.0372	+	4.83367i	0.560223	+	0.269789i
$322$	−0.189351	+	0.237439i	−0.0105521	+	0.0132319i
$323$	0.635682	+	0.797119i	0.0353703	+	0.0443529i
$324$	37.8087	+	18.2077i	2.10048	+	1.01154i
$325$	−4.50939	+	2.17161i	−0.250136	+	0.120459i
$326$	27.2183	−	34.1307i	1.50748	−	1.89032i
$327$	2.94555	+	12.9053i	0.162889	+	0.713664i
$328$	7.19569	+	31.5264i	0.397315	+	1.74075i
$329$	1.79974	+	2.25680i	0.0992227	+	0.124421i
$330$	−10.4389	+	45.7357i	−0.574641	+	2.51767i
$331$	−18.6487			−1.02502			−0.512512	−	0.858680i	$-0.671285\pi$
$331$	−18.6487			−1.02502			−0.512512	+	0.858680i	$0.671285\pi$
$332$	−0.557560	+	2.44283i	−0.0306001	+	0.134068i
$333$	−10.2812	+	4.95115i	−0.563404	+	0.271321i
$334$	5.46590	−	2.63224i	0.299081	−	0.144030i
$335$	−6.50237	+	28.4887i	−0.355262	+	1.55651i
$336$	1.96129			0.106997
$337$	−1.34575	+	5.89610i	−0.0733074	+	0.321181i	−0.998264	−	0.0588910i	$-0.981244\pi$
$337$	−1.34575	+	5.89610i	−0.0733074	+	0.321181i	0.924957	+	0.380072i	$0.124101\pi$
$338$	−27.2979	−	34.2304i	−1.48481	−	1.86189i
$339$	−6.27054	−	27.4730i	−0.340569	−	1.49213i
$340$	3.68263	+	16.1347i	0.199719	+	0.875025i
$341$	−9.74073	+	12.2145i	−0.527490	+	0.661451i
$342$	1.70504	−	0.821103i	0.0921979	−	0.0444001i
$343$	−4.72379	−	2.27486i	−0.255061	−	0.122831i
$344$	0.0586965	+	0.0736031i	0.00316470	+	0.00396841i
$345$	−1.06639	+	1.33721i	−0.0574124	+	0.0719929i
$346$	18.3029	+	8.81423i	0.983972	+	0.473856i
$347$	−14.4469			−0.775548			−0.387774	−	0.921754i	$-0.626756\pi$
$347$	−14.4469			−0.775548			−0.387774	+	0.921754i	$0.626756\pi$
$348$		0			0
$349$	11.5232			0.616825			0.308413	−	0.951253i	$-0.400202\pi$
$349$	11.5232			0.616825			0.308413	+	0.951253i	$0.400202\pi$
$350$	−0.730348	−	0.351717i	−0.0390388	−	0.0188001i
$351$	11.6099	−	14.5584i	0.619693	−	0.777071i
$352$	−5.72335	−	7.17685i	−0.305055	−	0.382527i
$353$	7.63413	+	3.67640i	0.406324	+	0.195675i	0.625871	−	0.779927i	$-0.284744\pi$
$353$	7.63413	+	3.67640i	0.406324	+	0.195675i	−0.219547	+	0.975602i	$0.570458\pi$
$354$	−36.8842	+	17.7625i	−1.96037	+	0.944065i
$355$	23.5530	−	29.5346i	1.25007	−	1.56753i
$356$	8.00597	+	35.0764i	0.424315	+	1.85905i
$357$	−0.323101	−	1.41560i	−0.0171003	−	0.0749215i
$358$	−19.3361	−	24.2468i	−1.02195	−	1.28148i
$359$	−1.09820	+	4.81153i	−0.0579608	+	0.253943i	−0.995605	−	0.0936544i	$-0.970145\pi$
$359$	−1.09820	+	4.81153i	−0.0579608	+	0.253943i	0.937644	+	0.347597i	$0.113002\pi$
$360$	14.2587			0.751497
$361$	4.15854	−	18.2198i	0.218871	−	0.958934i
$362$	35.4141	−	17.0545i	1.86132	−	0.896366i
$363$	7.09665	−	3.41757i	0.372478	−	0.179376i
$364$	1.75779	−	7.70140i	0.0921334	−	0.403663i
$365$	−16.8366			−0.881269
$366$	11.6117	−	50.8744i	0.606956	−	2.65925i
$367$	−1.81250	−	2.27280i	−0.0946117	−	0.118639i	0.732272	−	0.681012i	$-0.238460\pi$
$367$	−1.81250	−	2.27280i	−0.0946117	−	0.118639i	−0.826884	+	0.562373i	$0.809889\pi$
$368$	0.184010	+	0.806200i	0.00959218	+	0.0420261i
$369$	−2.45588	−	10.7599i	−0.127848	−	0.560139i
$370$	29.2133	−	36.6323i	1.51873	−	1.90442i
$371$	2.17241	−	1.04618i	0.112786	−	0.0543149i
$372$	28.7479	+	13.8443i	1.49051	+	0.717791i
$373$	−19.4192	−	24.3509i	−1.00549	−	1.26084i	−0.965161	−	0.261658i	$-0.915731\pi$
$373$	−19.4192	−	24.3509i	−1.00549	−	1.26084i	−0.0403289	−	0.999186i	$-0.512841\pi$
$374$	10.4694	−	13.1283i	0.541362	−	0.678846i
$375$	18.8704	+	9.08750i	0.974462	+	0.469276i
$376$	31.6459			1.63201
$377$		0			0
$378$	3.01588			0.155120
$379$	−21.8717	−	10.5329i	−1.12348	−	0.541037i	−0.222511	−	0.974930i	$-0.571425\pi$
$379$	−21.8717	−	10.5329i	−1.12348	−	0.541037i	−0.900964	+	0.433893i	$0.857140\pi$
$380$	−3.15449	+	3.95561i	−0.161822	+	0.202918i
$381$	−7.63879	−	9.57874i	−0.391347	−	0.490734i
$382$	−16.0091	−	7.70959i	−0.819098	−	0.394457i
$383$	26.8199	−	12.9158i	1.37043	−	0.659966i	0.403496	−	0.914981i	$-0.367795\pi$
$383$	26.8199	−	12.9158i	1.37043	−	0.659966i	0.966937	+	0.255015i	$0.0820805\pi$
$384$	−27.1651	+	34.0640i	−1.38626	+	1.73832i
$385$	0.785044	+	3.43950i	0.0400096	+	0.175293i
$386$	11.7049	+	51.2824i	0.595763	+	2.61021i
$387$	−0.0200331	−	0.0251207i	−0.00101834	−	0.00127695i
$388$	3.70033	−	16.2122i	0.187856	−	0.823051i
$389$	10.7861			0.546879			0.273440	−	0.961889i	$-0.411839\pi$
$389$	10.7861			0.546879			0.273440	+	0.961889i	$0.411839\pi$
$390$	15.2040	−	66.6132i	0.769886	−	3.37309i
$391$	0.551578	−	0.265626i	0.0278945	−	0.0134333i
$392$	−25.6264	+	12.3410i	−1.29433	+	0.623316i
$393$	0.246989	−	1.08213i	0.0124589	−	0.0545861i
$394$	−47.1774			−2.37676
$395$	−4.03104	+	17.6612i	−0.202824	+	0.888629i
$396$	−12.6530	−	15.8664i	−0.635838	−	0.797316i
$397$	−0.254236	−	1.11388i	−0.0127598	−	0.0559041i	0.968147	−	0.250382i	$-0.0805561\pi$
$397$	−0.254236	−	1.11388i	−0.0127598	−	0.0559041i	−0.980907	+	0.194477i	$0.937699\pi$
$398$	−8.65133	−	37.9040i	−0.433652	−	1.89995i
$399$	0.276764	−	0.347051i	0.0138555	−	0.0173743i
$400$	−1.98867	+	0.957691i	−0.0994333	+	0.0478846i
$401$	3.47018	+	1.67115i	0.173293	+	0.0834534i	0.518519	−	0.855066i	$-0.326484\pi$
$401$	3.47018	+	1.67115i	0.173293	+	0.0834534i	−0.345226	+	0.938519i	$0.612198\pi$
$402$	−37.7547	−	47.3429i	−1.88303	−	2.36125i
$403$	14.1872	−	17.7902i	0.706715	−	0.886192i
$404$	20.3086	+	9.78010i	1.01039	+	0.486578i
$405$	27.2969			1.35639
$406$		0			0
$407$	−30.9539			−1.53433
$408$	−14.3422	−	6.90684i	−0.710045	−	0.341939i
$409$	−12.0024	+	15.0506i	−0.593483	+	0.744204i	−0.984346	−	0.176245i	$-0.943605\pi$
$409$	−12.0024	+	15.0506i	−0.593483	+	0.744204i	0.390864	+	0.920449i	$0.372176\pi$
$410$	28.2543	+	35.4298i	1.39538	+	1.74975i
$411$	−14.8849	−	7.16819i	−0.734218	−	0.353581i
$412$	−20.8447	+	10.0383i	−1.02695	+	0.494552i
$413$	−1.91955	+	2.40704i	−0.0944550	+	0.118443i
$414$	−0.252861	−	1.10786i	−0.0124274	−	0.0544482i
$415$	0.362679	+	1.58900i	0.0178032	+	0.0780011i
$416$	8.33595	+	10.4530i	0.408704	+	0.512498i
$417$	−4.32448	+	18.9468i	−0.211770	+	0.927827i
$418$	5.13342			0.251084
$419$	0.446090	−	1.95445i	0.0217929	−	0.0954810i	−0.962862	−	0.269994i	$-0.912978\pi$
$419$	0.446090	−	1.95445i	0.0217929	−	0.0954810i	0.984655	+	0.174513i	$0.0558353\pi$
$420$	6.49183	−	3.12630i	0.316769	−	0.152548i
$421$	35.9093	−	17.2930i	1.75011	−	0.842810i	0.771746	−	0.635931i	$-0.219384\pi$
$421$	35.9093	−	17.2930i	1.75011	−	0.842810i	0.978366	−	0.206879i	$-0.0663307\pi$
$422$	12.5393	−	54.9384i	0.610405	−	2.67436i
$423$	−10.8007			−0.525149
$424$	5.88222	−	25.7717i	0.285666	−	1.25158i
$425$	1.01885	+	1.27759i	0.0494213	+	0.0619724i
$426$	17.4193	+	76.3187i	0.843965	+	3.69765i
$427$	−0.873249	−	3.82595i	−0.0422595	−	0.185151i
$428$	12.3377	−	15.4710i	0.596365	−	0.747818i
$429$	−40.6688	+	19.5851i	−1.96351	+	0.945576i
$430$	0.118863	+	0.0572413i	0.00573208	+	0.00276042i
$431$	8.92514	+	11.1918i	0.429909	+	0.539088i	0.948852	−	0.315720i	$-0.102246\pi$
$431$	8.92514	+	11.1918i	0.429909	+	0.539088i	−0.518944	+	0.854808i	$0.673675\pi$
$432$	5.12006	−	6.42035i	0.246339	−	0.308899i
$433$	7.95919	+	3.83294i	0.382494	+	0.184200i	0.615243	−	0.788337i	$-0.289058\pi$
$433$	7.95919	+	3.83294i	0.382494	+	0.184200i	−0.232749	+	0.972537i	$0.574772\pi$
$434$	3.68536			0.176903
$435$		0			0
$436$	23.5123			1.12604
$437$	0.168624	+	0.0812051i	0.00806639	+	0.00388457i
$438$	21.7533	−	27.2778i	1.03941	−	1.30338i
$439$	−7.22162	−	9.05563i	−0.344669	−	0.432202i	0.579038	−	0.815301i	$-0.303428\pi$
$439$	−7.22162	−	9.05563i	−0.344669	−	0.432202i	−0.923707	+	0.383099i	$0.874857\pi$
$440$	34.8474	+	16.7816i	1.66129	+	0.800034i
$441$	8.74627	−	4.21198i	0.416489	−	0.200571i
$442$	−15.2485	+	19.1211i	−0.725300	+	0.909497i
$443$	7.89706	+	34.5993i	0.375201	+	1.64386i	0.711923	+	0.702258i	$0.247825\pi$
$443$	7.89706	+	34.5993i	0.375201	+	1.64386i	−0.336722	+	0.941604i	$0.609318\pi$
$444$	14.0676	+	61.6342i	0.667619	+	2.92503i
$445$	14.5916	+	18.2973i	0.691709	+	0.867376i
$446$	−0.373972	+	1.63848i	−0.0177081	+	0.0775841i
$447$	1.08068			0.0511146
$448$	−0.897221	+	3.93098i	−0.0423897	+	0.185721i
$449$	−18.6938	+	9.00245i	−0.882214	+	0.424852i	−0.819433	−	0.573176i	$-0.805711\pi$
$449$	−18.6938	+	9.00245i	−0.882214	+	0.424852i	−0.0627811	+	0.998027i	$0.519997\pi$
$450$	2.73277	−	1.31603i	0.128824	−	0.0620384i
$451$	6.66177	−	29.1871i	0.313691	−	1.37437i
$452$	−50.0535			−2.35432
$453$	−3.06387	+	13.4237i	−0.143953	+	0.630699i
$454$	11.0505	+	13.8568i	0.518624	+	0.650334i
$455$	−1.14340	−	5.00958i	−0.0536036	−	0.234853i
$456$	−1.08290	−	4.74451i	−0.0507116	−	0.222182i
$457$	23.7573	−	29.7907i	1.11132	−	1.39355i	0.201023	−	0.979586i	$-0.435573\pi$
$457$	23.7573	−	29.7907i	1.11132	−	1.39355i	0.910294	−	0.413962i	$-0.135855\pi$
$458$	−23.1802	+	11.1630i	−1.08314	+	0.521612i
$459$	−5.47750	−	2.63783i	−0.255668	−	0.123123i
$460$	1.89416	+	2.37520i	0.0883156	+	0.110744i
$461$	11.0510	−	13.8575i	0.514695	−	0.645407i	−0.454778	−	0.890605i	$-0.650281\pi$
$461$	11.0510	−	13.8575i	0.514695	−	0.645407i	0.969473	+	0.245198i	$0.0788529\pi$
$462$	−6.58679	−	3.17203i	−0.306445	−	0.147576i
$463$	9.21914			0.428450			0.214225	−	0.976784i	$-0.431277\pi$
$463$	9.21914			0.428450			0.214225	+	0.976784i	$0.431277\pi$
$464$		0			0
$465$	20.7552			0.962501
$466$	−33.6277	−	16.1942i	−1.55777	−	0.750184i
$467$	4.86457	−	6.09998i	0.225105	−	0.282273i	−0.656434	−	0.754383i	$-0.727936\pi$
$467$	4.86457	−	6.09998i	0.225105	−	0.282273i	0.881540	+	0.472110i	$0.156507\pi$
$468$	18.4289	+	23.1091i	0.851876	+	1.06822i
$469$	−4.10291	−	1.97586i	−0.189455	−	0.0912366i
$470$	39.9559	−	19.2418i	1.84303	−	0.887556i
$471$	15.0093	−	18.8211i	0.691594	−	0.867232i
$472$	7.51069	+	32.9065i	0.345707	+	1.51464i
$473$	−0.0193942	−	0.0849714i	−0.000891744	−	0.00390699i
$474$	−23.4055	−	29.3495i	−1.07505	−	1.34807i
$475$	−0.111164	+	0.487040i	−0.00510054	+	0.0223469i
$476$	−2.57910			−0.118213
$477$	−2.00760	+	8.79586i	−0.0919216	+	0.402735i
$478$	16.0579	−	7.73309i	0.734472	−	0.353703i
$479$	15.9676	−	7.68958i	0.729578	−	0.351346i	−0.0319405	−	0.999490i	$-0.510169\pi$
$479$	15.9676	−	7.68958i	0.729578	−	0.351346i	0.761518	+	0.648144i	$0.224454\pi$
$480$	−2.71367	+	11.8894i	−0.123862	+	0.542673i
$481$	45.0838			2.05564
$482$	−2.80606	+	12.2942i	−0.127813	+	0.559984i
$483$	−0.166187	−	0.208392i	−0.00756177	−	0.00948216i
$484$	−3.11326	−	13.6401i	−0.141512	−	0.620004i
$485$	−2.40698	−	10.5457i	−0.109295	−	0.478854i
$486$	−20.3593	+	25.5297i	−0.923515	+	1.15805i
$487$	19.0636	−	9.18054i	0.863854	−	0.416010i	0.0511526	−	0.998691i	$-0.483711\pi$
$487$	19.0636	−	9.18054i	0.863854	−	0.416010i	0.812701	+	0.582681i	$0.197996\pi$
$488$	−38.7628	−	18.6672i	−1.75471	−	0.845023i
$489$	23.8886	+	29.9553i	1.08028	+	1.35463i
$490$	−24.8520	+	31.1634i	−1.12270	+	1.40782i
$491$	−15.9529	−	7.68250i	−0.719943	−	0.346706i	0.0377770	−	0.999286i	$-0.487972\pi$
$491$	−15.9529	−	7.68250i	−0.719943	−	0.346706i	−0.757720	+	0.652580i	$0.773687\pi$
$492$	−61.1439			−2.75658
$493$		0			0
$494$	−7.47673			−0.336394
$495$	−11.8934	−	5.72756i	−0.534568	−	0.257435i
$496$	6.25664	−	7.84558i	0.280931	−	0.352277i
$497$	3.67053	+	4.60270i	0.164646	+	0.206459i
$498$	−3.04301	−	1.46543i	−0.136360	−	0.0656677i
$499$	−26.3129	+	12.6716i	−1.17793	+	0.567260i	−0.917307	−	0.398181i	$-0.869641\pi$
$499$	−26.3129	+	12.6716i	−1.17793	+	0.567260i	−0.260621	+	0.965441i	$0.583927\pi$
$500$	23.1954	−	29.0861i	1.03733	−	1.30077i
$501$	1.18482	+	5.19104i	0.0529339	+	0.231918i
$502$	−14.8983	−	65.2738i	−0.664944	−	2.91331i
$503$	−26.8626	−	33.6846i	−1.19774	−	1.50192i	−0.816397	−	0.577491i	$-0.804032\pi$
$503$	−26.8626	−	33.6846i	−1.19774	−	1.50192i	−0.381346	−	0.924432i	$-0.624539\pi$
$504$	−0.494460	+	2.16637i	−0.0220250	+	0.0964978i
$505$	14.6623			0.652463
$506$	0.685906	−	3.00515i	0.0304922	−	0.133595i
$507$	34.6209	−	16.6725i	1.53757	−	0.740454i
$508$	−19.6068	+	9.44212i	−0.869910	+	0.418926i
$509$	−7.23028	+	31.6779i	−0.320476	+	1.40410i	0.516231	+	0.856449i	$0.327334\pi$
$509$	−7.23028	+	31.6779i	−0.320476	+	1.40410i	−0.836708	+	0.547650i	$0.815523\pi$
$510$	−22.3079			−0.987813
$511$	0.583858	−	2.55805i	0.0258284	−	0.113161i
$512$	16.4358	+	20.6098i	0.726365	+	0.910833i
$513$	−0.413577	−	1.81200i	−0.0182599	−	0.0800017i
$514$	−10.1593	−	44.5107i	−0.448106	−	1.96328i
$515$	−9.38313	+	11.7661i	−0.413470	+	0.518475i
$516$	−0.160378	+	0.0772339i	−0.00706024	+	0.00340003i
$517$	−26.3964	−	12.7118i	−1.16091	−	0.559066i
$518$	4.55263	+	5.70881i	0.200031	+	0.250831i
$519$	−11.1165	+	13.9397i	−0.487962	+	0.611885i
$520$	−50.7547	−	24.4422i	−2.22574	−	1.07186i
$521$	28.2658			1.23835			0.619173	−	0.785254i	$-0.287468\pi$
$521$	28.2658			1.23835			0.619173	+	0.785254i	$0.287468\pi$
$522$		0			0
$523$	−8.63499			−0.377582			−0.188791	−	0.982017i	$-0.560457\pi$
$523$	−8.63499			−0.377582			−0.188791	+	0.982017i	$0.560457\pi$
$524$	−1.77630	−	0.855422i	−0.0775981	−	0.0373693i
$525$	0.443587	−	0.556241i	0.0193597	−	0.0242763i
$526$	−10.6211	−	13.3184i	−0.463102	−	0.580711i
$527$	−6.69343	−	3.22339i	−0.291570	−	0.140413i
$528$	−17.9352	+	8.63713i	−0.780529	+	0.375883i
$529$	−14.2702	+	17.8943i	−0.620443	+	0.778011i
$530$	−8.24319	−	36.1158i	−0.358061	−	1.56877i
$531$	−2.56339	−	11.2309i	−0.111242	−	0.487381i
$532$	−0.491599	−	0.616445i	−0.0213135	−	0.0267263i
$533$	−9.70275	+	42.5105i	−0.420273	+	1.84134i
$534$	−48.4970			−2.09867
$535$	2.86422	−	12.5490i	0.123831	−	0.542540i
$536$	−44.9811	+	21.6618i	−1.94289	+	0.935645i
$537$	24.5234	−	11.8098i	1.05826	−	0.509632i
$538$	−3.17325	+	13.9029i	−0.136808	+	0.599397i
$539$	26.3327			1.13423
$540$	6.71325	−	29.4127i	0.288892	−	1.26572i
$541$	−6.57451	−	8.24418i	−0.282660	−	0.354445i	0.620150	−	0.784483i	$-0.287072\pi$
$541$	−6.57451	−	8.24418i	−0.282660	−	0.354445i	−0.902811	+	0.430038i	$0.858500\pi$
$542$	2.73501	+	11.9829i	0.117479	+	0.514708i
$543$	7.67656	+	33.6332i	0.329433	+	1.44334i
$544$	2.72162	−	3.41280i	0.116688	−	0.146323i
$545$	13.7796	−	6.63591i	0.590254	−	0.284251i
$546$	9.59355	+	4.62001i	0.410566	+	0.197718i
$547$	24.1414	+	30.2723i	1.03221	+	1.29435i	0.954767	+	0.297353i	$0.0961039\pi$
$547$	24.1414	+	30.2723i	1.03221	+	1.29435i	0.0774423	+	0.996997i	$0.475325\pi$
$548$	−18.2964	+	22.9430i	−0.781584	+	0.980076i
$549$	13.2297	+	6.37109i	0.564630	+	0.271911i
$550$	8.22765			0.350828
$551$		0			0
$552$	−2.92217			−0.124376
$553$	−2.54354	−	1.22490i	−0.108162	−	0.0520882i
$554$	−29.8644	+	37.4488i	−1.26882	+	1.59105i
$555$	25.6395	+	32.1509i	1.08834	+	1.36473i
$556$	31.1009	+	14.9774i	1.31897	+	0.635184i
$557$	−7.55664	+	3.63909i	−0.320185	+	0.154193i	−0.587072	−	0.809535i	$-0.699719\pi$
$557$	−7.55664	+	3.63909i	−0.320185	+	0.154193i	0.266887	+	0.963728i	$0.414005\pi$
$558$	−8.59770	+	10.7812i	−0.363970	+	0.456403i
$559$	0.0282473	+	0.123759i	0.00119473	+	0.00523446i
$560$	−0.504248	−	2.20925i	−0.0213084	−	0.0933580i
$561$	9.18867	+	11.5222i	0.387946	+	0.486469i
$562$	−6.25007	+	27.3834i	−0.263643	+	1.15510i
$563$	−27.6892			−1.16696			−0.583480	−	0.812127i	$-0.698309\pi$
$563$	−27.6892			−1.16696			−0.583480	+	0.812127i	$0.698309\pi$
$564$	−13.3150	+	58.3367i	−0.560661	+	2.45642i
$565$	−29.3343	+	14.1267i	−1.23410	+	0.594313i
$566$	−63.9004	+	30.7728i	−2.68593	+	1.29348i
$567$	−0.946599	+	4.14732i	−0.0397534	+	0.174171i
$568$	64.5412			2.70809
$569$	2.18035	−	9.55276i	0.0914052	−	0.400472i	−0.908441	−	0.418013i	$-0.862727\pi$
$569$	2.18035	−	9.55276i	0.0914052	−	0.400472i	0.999846	+	0.0175408i	$0.00558370\pi$
$570$	−4.25208	−	5.33194i	−0.178100	−	0.223330i
$571$	3.20470	+	14.0407i	0.134113	+	0.587585i	0.996664	+	0.0816158i	$0.0260080\pi$
$571$	3.20470	+	14.0407i	0.134113	+	0.587585i	−0.862551	+	0.505970i	$0.831135\pi$
$572$	17.8412	+	78.1673i	0.745977	+	3.26834i
$573$	9.72336	−	12.1927i	0.406199	−	0.509358i
$574$	−6.36277	+	3.06415i	−0.265577	+	0.127895i
$575$	0.270264	+	0.130153i	0.0112708	+	0.00542774i
$576$	−9.40656	−	11.7955i	−0.391940	−	0.491477i
$577$	6.47830	−	8.12353i	0.269695	−	0.338187i	−0.628479	−	0.777826i	$-0.716322\pi$
$577$	6.47830	−	8.12353i	0.269695	−	0.338187i	0.898174	+	0.439639i	$0.144894\pi$
$578$	−29.4776	−	14.1957i	−1.22611	−	0.590462i
$579$	−46.1663			−1.91861
$580$		0			0
$581$	−0.254000			−0.0105377
$582$	20.1954	+	9.72558i	0.837126	+	0.403138i
$583$	−15.2587	+	19.1338i	−0.631951	+	0.792441i
$584$	−17.9351	−	22.4899i	−0.742160	−	0.930639i
$585$	17.3225	+	8.34209i	0.716198	+	0.344903i
$586$	16.9593	−	8.16716i	0.700581	−	0.337382i
$587$	1.01444	−	1.27206i	0.0418703	−	0.0525037i	−0.760455	−	0.649390i	$-0.775024\pi$
$587$	1.01444	−	1.27206i	0.0418703	−	0.0525037i	0.802326	+	0.596886i	$0.203596\pi$
$588$	−11.9674	−	52.4327i	−0.493528	−	2.16229i
$589$	−0.505385	−	2.21424i	−0.0208240	−	0.0912360i
$590$	29.4912	+	36.9807i	1.21413	+	1.52247i
$591$	9.21370	−	40.3679i	0.379001	−	1.66051i
$592$	19.8822			0.817154
$593$	−6.91114	+	30.2797i	−0.283806	+	1.24344i	0.609063	+	0.793122i	$0.291545\pi$
$593$	−6.91114	+	30.2797i	−0.283806	+	1.24344i	−0.892870	+	0.450315i	$0.851312\pi$
$594$	−27.5790	+	13.2814i	−1.13158	+	0.544940i
$595$	−1.51151	+	0.727903i	−0.0619657	+	0.0298411i
$596$	0.427140	−	1.87142i	0.0174963	−	0.0766565i
$597$	34.1226			1.39654
$598$	−0.999010	+	4.37695i	−0.0408526	+	0.178987i
$599$	10.1857	+	12.7725i	0.416177	+	0.521869i	0.945091	−	0.326806i	$-0.105972\pi$
$599$	10.1857	+	12.7725i	0.416177	+	0.521869i	−0.528915	+	0.848675i	$0.677401\pi$
$600$	−1.73564	−	7.60432i	−0.0708570	−	0.310445i
$601$	−2.21487	−	9.70398i	−0.0903464	−	0.395834i	0.909454	−	0.415804i	$-0.136500\pi$
$601$	−2.21487	−	9.70398i	−0.0903464	−	0.395834i	−0.999801	+	0.0199707i	$0.993643\pi$
$602$	−0.0128188	+	0.0160743i	−0.000522455	+	0.000655138i
$603$	15.3520	−	7.39313i	0.625182	−	0.301072i
$604$	22.0348	+	10.6114i	0.896584	+	0.431772i
$605$	−5.67421	−	7.11523i	−0.230689	−	0.289275i
$606$	−18.9440	+	23.7550i	−0.769548	+	0.964982i
$607$	23.6146	+	11.3722i	0.958487	+	0.461583i	0.846654	−	0.532144i	$-0.178613\pi$
$607$	23.6146	+	11.3722i	0.958487	+	0.461583i	0.111833	+	0.993727i	$0.464328\pi$
$608$	1.33447			0.0541201
$609$		0			0
$610$	−60.2919			−2.44115
$611$	38.4459	+	18.5146i	1.55535	+	0.749019i
$612$	6.01688	−	7.54492i	0.243218	−	0.304986i
$613$	−28.9569	−	36.3108i	−1.16956	−	1.46658i	−0.855974	−	0.517019i	$-0.827042\pi$
$613$	−28.9569	−	36.3108i	−1.16956	−	1.46658i	−0.313584	−	0.949560i	$-0.601530\pi$
$614$	−61.2226	−	29.4833i	−2.47074	−	1.18985i
$615$	−35.8339	+	17.2567i	−1.44496	+	0.695858i
$616$	−3.75813	+	4.71255i	−0.151419	+	0.189874i
$617$	−2.13080	−	9.33563i	−0.0857826	−	0.375838i	0.913754	−	0.406267i	$-0.133170\pi$
$617$	−2.13080	−	9.33563i	−0.0857826	−	0.375838i	−0.999537	+	0.0304289i	$0.990313\pi$
$618$	−6.93953	−	30.4041i	−0.279149	−	1.22303i
$619$	12.5154	+	15.6938i	0.503036	+	0.630788i	0.966911	−	0.255113i	$-0.0821127\pi$
$619$	12.5154	+	15.6938i	0.503036	+	0.630788i	−0.463875	+	0.885901i	$0.653541\pi$
$620$	8.20350	−	35.9419i	0.329461	−	1.44346i
$621$	−1.11602			−0.0447844
$622$	−4.56683	+	20.0086i	−0.183113	+	0.802272i
$623$	−3.28598	+	1.58245i	−0.131650	+	0.0633994i
$624$	26.1223	−	12.5798i	1.04573	−	0.503596i
$625$	6.38042	−	27.9545i	0.255217	−	1.11818i
$626$	−2.10457			−0.0841157
$627$	−1.00255	+	4.39247i	−0.0400381	+	0.175418i
$628$	−26.6602	−	33.4308i	−1.06386	−	1.33403i
$629$	−3.27539	−	14.3504i	−0.130598	−	0.572188i
$630$	0.692923	+	3.03589i	0.0276067	+	0.120953i
$631$	−17.8102	+	22.3333i	−0.709014	+	0.889075i	−0.997661	−	0.0683607i	$-0.978223\pi$
$631$	−17.8102	+	22.3333i	−0.709014	+	0.889075i	0.288647	+	0.957436i	$0.406795\pi$
$632$	−27.8853	+	13.4289i	−1.10922	+	0.534172i
$633$	44.5598	+	21.4588i	1.77109	+	0.852913i
$634$	−39.7468	−	49.8409i	−1.57855	−	1.97944i
$635$	−8.82586	+	11.0673i	−0.350243	+	0.439191i
$636$	45.0331	+	21.6868i	1.78568	+	0.859938i
$637$	−38.3531			−1.51961
$638$		0			0
$639$	−22.0278			−0.871408
$640$	45.3549	+	21.8418i	1.79281	+	0.863372i
$641$	4.65868	−	5.84180i	0.184007	−	0.230737i	−0.681269	−	0.732033i	$-0.738572\pi$
$641$	4.65868	−	5.84180i	0.184007	−	0.230737i	0.865276	+	0.501296i	$0.167143\pi$
$642$	16.6305	+	20.8540i	0.656355	+	0.823043i
$643$	18.8373	+	9.07156i	0.742870	+	0.357747i	0.766732	−	0.641968i	$-0.221882\pi$
$643$	18.8373	+	9.07156i	0.742870	+	0.357747i	−0.0238613	+	0.999715i	$0.507596\pi$
$644$	−0.426558	+	0.205420i	−0.0168088	+	0.00809467i
$645$	−0.0721930	+	0.0905272i	−0.00284260	+	0.00356450i
$646$	0.543193	+	2.37989i	0.0213717	+	0.0936353i
$647$	2.03349	+	8.90930i	0.0799447	+	0.350261i	0.999042	−	0.0437710i	$-0.0139372\pi$
$647$	2.03349	+	8.90930i	0.0799447	+	0.350261i	−0.919097	+	0.394032i	$0.871080\pi$
$648$	29.0779	+	36.4625i	1.14229	+	1.43238i
$649$	6.95340	−	30.4648i	0.272945	−	1.19585i
$650$	−11.9834			−0.470029
$651$	−0.719747	+	3.15342i	−0.0282091	+	0.123592i
$652$	61.3157	−	29.5281i	2.40131	−	1.15641i
$653$	13.1895	−	6.35171i	0.516144	−	0.248562i	−0.157632	−	0.987498i	$-0.550386\pi$
$653$	13.1895	−	6.35171i	0.516144	−	0.248562i	0.673775	+	0.738936i	$0.264672\pi$
$654$	−7.05244	+	30.8987i	−0.275772	+	1.20824i
$655$	−1.28244			−0.0501092
$656$	−4.27897	+	18.7474i	−0.167066	+	0.731963i
$657$	6.12123	+	7.67578i	0.238812	+	0.299461i
$658$	1.53788	+	6.73791i	0.0599530	+	0.262671i
$659$	8.53232	+	37.3826i	0.332372	+	1.45622i	0.814524	+	0.580130i	$0.196998\pi$
$659$	8.53232	+	37.3826i	0.332372	+	1.45622i	−0.482152	+	0.876088i	$0.660145\pi$
$660$	−45.5976	+	57.1776i	−1.77489	+	2.22564i
$661$	21.7034	−	10.4518i	0.844163	−	0.406528i	0.0387556	−	0.999249i	$-0.487661\pi$
$661$	21.7034	−	10.4518i	0.844163	−	0.406528i	0.805408	+	0.592721i	$0.201946\pi$
$662$	−40.2282	−	19.3729i	−1.56351	−	0.752949i
$663$	−13.3831	−	16.7819i	−0.519758	−	0.651756i
$664$	−1.73620	+	2.17713i	−0.0673778	+	0.0844891i
$665$	−0.462086	−	0.222529i	−0.0179189	−	0.00862930i
$666$	−27.3216			−1.05869
$667$		0			0
$668$	9.45763			0.365927
$669$	−1.32894	−	0.639986i	−0.0513800	−	0.0247433i
$670$	−43.6218	+	54.7000i	−1.68526	+	2.11324i
$671$	24.8343	+	31.1412i	0.958717	+	1.20219i
$672$	−1.71229	−	0.824596i	−0.0660531	−	0.0318095i
$673$	1.81125	−	0.872252i	0.0698186	−	0.0336229i	−0.398649	−	0.917104i	$-0.630521\pi$
$673$	1.81125	−	0.872252i	0.0698186	−	0.0336229i	0.468467	+	0.883481i	$0.344806\pi$
$674$	−9.02806	+	11.3208i	−0.347748	+	0.436062i
$675$	−0.662865	−	2.90420i	−0.0255137	−	0.111783i
$676$	−15.1880	−	66.5429i	−0.584153	−	2.55934i
$677$	10.2655	+	12.8726i	0.394537	+	0.494733i	0.938936	−	0.344093i	$-0.111814\pi$
$677$	10.2655	+	12.8726i	0.394537	+	0.494733i	−0.544399	+	0.838827i	$0.683242\pi$
$678$	15.0134	−	65.7779i	0.576585	−	2.52618i
$679$	1.68571			0.0646916
$680$	−4.09269	+	17.9313i	−0.156948	+	0.687632i
$681$	−14.0149	+	6.74923i	−0.537053	+	0.258631i
$682$	−33.7012	+	16.2296i	−1.29048	+	0.621465i
$683$	0.986397	−	4.32169i	0.0377434	−	0.165365i	−0.952544	−	0.304402i	$-0.901544\pi$
$683$	0.986397	−	4.32169i	0.0377434	−	0.165365i	0.990287	+	0.139037i	$0.0444007\pi$
$684$	2.95022			0.112804
$685$	−4.24756	+	18.6098i	−0.162291	+	0.711042i
$686$	−7.82678	−	9.81447i	−0.298828	−	0.374718i
$687$	−5.02467	−	22.0145i	−0.191703	−	0.839906i
$688$	0.0124572	+	0.0545786i	0.000474927	+	0.00208079i
$689$	22.2240	−	27.8680i	0.846668	−	1.06169i
$690$	−3.68951	+	1.77678i	−0.140457	+	0.0676407i
$691$	−18.1752	−	8.75273i	−0.691418	−	0.332970i	0.0549627	−	0.998488i	$-0.482496\pi$
$691$	−18.1752	−	8.75273i	−0.691418	−	0.332970i	−0.746381	+	0.665519i	$0.768210\pi$
$692$	19.7456	+	24.7602i	0.750616	+	0.941242i
$693$	1.28265	−	1.60839i	0.0487237	−	0.0610976i
$694$	−31.1642	−	15.0079i	−1.18298	−	0.569692i
$695$	22.4541			0.851731
$696$		0			0
$697$	14.2363			0.539237
$698$	24.8575	+	11.9708i	0.940871	+	0.453100i
$699$	20.4242	−	25.6112i	0.772516	−	0.968704i
$700$	−0.787916	−	0.988015i	−0.0297804	−	0.0373435i
$701$	28.7103	+	13.8261i	1.08437	+	0.522206i	0.888712	−	0.458466i	$-0.151601\pi$
$701$	28.7103	+	13.8261i	1.08437	+	0.522206i	0.195660	+	0.980672i	$0.437315\pi$
$702$	40.1684	−	19.3441i	1.51606	−	0.730094i
$703$	2.80565	−	3.51818i	0.105817	−	0.132691i
$704$	−9.10657	−	39.8985i	−0.343217	−	1.50373i
$705$	8.66107	+	37.9466i	0.326195	+	1.42915i
$706$	12.6489	+	15.8612i	0.476047	+	0.596944i
$707$	−0.508457	+	2.22769i	−0.0191225	+	0.0837811i
$708$	−63.8205			−2.39852
$709$	10.4064	−	45.5935i	0.390821	−	1.71230i	−0.270950	−	0.962593i	$-0.587338\pi$
$709$	10.4064	−	45.5935i	0.390821	−	1.71230i	0.661771	−	0.749706i	$-0.269805\pi$
$710$	81.4893	−	39.2432i	3.05824	−	1.47277i
$711$	9.51724	−	4.58326i	0.356924	−	0.171886i
$712$	−8.89743	+	38.9822i	−0.333445	+	1.46092i
$713$	−1.36376			−0.0510733
$714$	0.773592	−	3.38933i	0.0289510	−	0.126842i
$715$	32.5172	+	40.7753i	1.21607	+	1.52491i
$716$	−10.7583	−	47.1350i	−0.402055	−	1.76152i
$717$	3.48081	+	15.2504i	0.129993	+	0.569537i
$718$	−7.36738	+	9.23840i	−0.274948	+	0.344774i
$719$	−31.3248	+	15.0852i	−1.16822	+	0.562584i	−0.914457	−	0.404683i	$-0.867382\pi$
$719$	−31.3248	+	15.0852i	−1.16822	+	0.562584i	−0.253760	+	0.967267i	$0.581667\pi$
$720$	7.63934	+	3.67891i	0.284701	+	0.137105i
$721$	−1.46228	−	1.83364i	−0.0544580	−	0.0682881i
$722$	27.8980	−	34.9829i	1.03825	−	1.30193i
$723$	−9.97162	−	4.80208i	−0.370849	−	0.178591i
$724$	61.2769			2.27734
$725$		0			0
$726$	18.8589			0.699920
$727$	20.7766	+	10.0055i	0.770560	+	0.371082i	0.777491	−	0.628894i	$-0.216492\pi$
$727$	20.7766	+	10.0055i	0.770560	+	0.371082i	−0.00693131	+	0.999976i	$0.502206\pi$
$728$	5.47365	−	6.86375i	0.202867	−	0.254387i
$729$	3.16086	+	3.96360i	0.117069	+	0.146800i
$730$	−36.3193	−	17.4905i	−1.34424	−	0.647351i
$731$	0.0373411	−	0.0179825i	0.00138111	−	0.000665107i
$732$	50.7208	−	63.6019i	1.87470	−	2.35079i
$733$	8.55618	+	37.4871i	0.316030	+	1.38462i	0.844450	+	0.535634i	$0.179927\pi$
$733$	8.55618	+	37.4871i	0.316030	+	1.38462i	−0.528421	+	0.848983i	$0.677216\pi$
$734$	−1.54879	−	6.78569i	−0.0571669	−	0.250464i
$735$	−21.8118	−	27.3511i	−0.804539	−	1.00886i
$736$	0.178307	−	0.781214i	0.00657248	−	0.0287959i
$737$	46.2208			1.70257
$738$	5.88004	−	25.7622i	0.216447	−	0.948318i
$739$	−26.2001	+	12.6173i	−0.963788	+	0.464136i	−0.848499	−	0.529196i	$-0.822494\pi$
$739$	−26.2001	+	12.6173i	−0.963788	+	0.464136i	−0.115288	+	0.993332i	$0.536779\pi$
$740$	65.8099	−	31.6924i	2.41922	−	1.16503i
$741$	1.46020	−	6.39755i	0.0536418	−	0.235020i
$742$	5.77306			0.211936
$743$	7.26306	−	31.8215i	0.266456	−	1.16742i	−0.647648	−	0.761939i	$-0.724247\pi$
$743$	7.26306	−	31.8215i	0.266456	−	1.16742i	0.914104	−	0.405479i	$-0.132895\pi$
$744$	22.1094	+	27.7243i	0.810569	+	1.01642i
$745$	−0.277844	−	1.21732i	−0.0101794	−	0.0445990i
$746$	−16.5938	−	72.7023i	−0.607543	−	2.66182i
$747$	0.592565	−	0.743053i	0.0216808	−	0.0271869i
$748$	23.5849	−	11.3579i	0.862349	−	0.415285i
$749$	1.80729	+	0.870344i	0.0660369	+	0.0318017i
$750$	31.2661	+	39.2064i	1.14168	+	1.43162i
$751$	0.0867780	−	0.108816i	0.00316657	−	0.00397076i	−0.780246	−	0.625473i	$-0.784906\pi$
$751$	0.0867780	−	0.108816i	0.00316657	−	0.00397076i	0.783412	+	0.621502i	$0.213477\pi$
$752$	16.9549	+	8.16504i	0.618281	+	0.297748i
$753$	58.7619			2.14140
$754$		0			0
$755$	15.9086			0.578972
$756$	4.23598	+	2.03994i	0.154061	+	0.0741919i
$757$	−1.06821	+	1.33950i	−0.0388249	+	0.0486849i	−0.800865	−	0.598845i	$-0.795627\pi$
$757$	−1.06821	+	1.33950i	−0.0388249	+	0.0486849i	0.762040	+	0.647530i	$0.224198\pi$
$758$	−36.2390	−	45.4422i	−1.31626	−	1.65054i
$759$	2.43743	+	1.17381i	0.0884733	+	0.0426065i
$760$	−5.06595	+	2.43963i	−0.183761	+	0.0884947i
$761$	−24.1330	+	30.2618i	−0.874819	+	1.09699i	0.119739	+	0.992805i	$0.461794\pi$
$761$	−24.1330	+	30.2618i	−0.874819	+	1.09699i	−0.994558	+	0.104183i	$0.966777\pi$
$762$	−6.52739	−	28.5984i	−0.236462	−	1.03601i
$763$	0.530371	+	2.32371i	0.0192007	+	0.0841239i
$764$	−17.2710	−	21.6571i	−0.624843	−	0.783528i
$765$	1.39683	−	6.11992i	0.0505025	−	0.221266i
$766$	71.2723			2.57517
$767$	−10.1275	+	44.3715i	−0.365683	+	1.60216i
$768$	−53.6355	+	25.8295i	−1.93540	+	0.932041i
$769$	−40.9280	+	19.7099i	−1.47590	+	0.710756i	−0.986871	−	0.161510i	$-0.948363\pi$
$769$	−40.9280	+	19.7099i	−1.47590	+	0.710756i	−0.489030	+	0.872267i	$0.662649\pi$
$770$	−1.87961	+	8.23510i	−0.0677364	+	0.296772i
$771$	40.0702			1.44309
$772$	−18.2472	+	79.9464i	−0.656732	+	2.87733i
$773$	31.5866	+	39.6083i	1.13609	+	1.42461i	0.890350	+	0.455277i	$0.150460\pi$
$773$	31.5866	+	39.6083i	1.13609	+	1.42461i	0.245740	+	0.969336i	$0.420969\pi$
$774$	−0.0171183	−	0.0750004i	−0.000615306	−	0.00269583i
$775$	−0.810012	−	3.54890i	−0.0290965	−	0.127480i
$776$	11.5226	−	14.4489i	0.413637	−	0.518684i
$777$	−5.77393	+	2.78058i	−0.207139	+	0.0997528i
$778$	23.2675	+	11.2050i	0.834179	+	0.401720i
$779$	2.71355	+	3.40268i	0.0972230	+	0.121914i
$780$	66.4122	−	83.2782i	2.37794	−	2.98184i
$781$	−53.8349	−	25.9255i	−1.92637	−	0.927689i
$782$	1.46579			0.0524164
$783$		0			0
$784$	−16.9140			−0.604070
$785$	−25.0596	−	12.0681i	−0.894416	−	0.430728i
$786$	1.65695	−	2.07775i	0.0591013	−	0.0741107i
$787$	24.9822	+	31.3267i	0.890518	+	1.11667i	0.992543	+	0.121893i	$0.0388964\pi$
$787$	24.9822	+	31.3267i	0.890518	+	1.11667i	−0.102025	+	0.994782i	$0.532532\pi$
$788$	−66.2634	−	31.9108i	−2.36054	−	1.13677i
$789$	13.4704	−	6.48698i	0.479557	−	0.230943i
$790$	−27.0427	+	33.9104i	−0.962134	+	1.20648i
$791$	−1.12906	−	4.94675i	−0.0401449	−	0.175886i
$792$	−5.01865	−	21.9881i	−0.178330	−	0.781314i
$793$	−36.1707	−	45.3567i	−1.28446	−	1.61066i
$794$	0.608710	−	2.66693i	0.0216023	−	0.0946460i
$795$	32.5128			1.15311
$796$	13.4869	−	59.0901i	0.478032	−	2.09439i
$797$	−8.21474	+	3.95601i	−0.290981	+	0.140129i	−0.573680	−	0.819080i	$-0.694485\pi$
$797$	−8.21474	+	3.95601i	−0.290981	+	0.140129i	0.282699	+	0.959209i	$0.408770\pi$
$798$	0.957555	−	0.461134i	0.0338971	−	0.0163240i
$799$	3.10015	−	13.5826i	0.109675	−	0.480520i
$800$	2.13885			0.0756196
$801$	3.03668	−	13.3046i	0.107296	−	0.470094i
$802$	5.74970	+	7.20990i	0.203029	+	0.254590i
$803$	5.92601	+	25.9636i	0.209125	+	0.916234i
$804$	−21.0060	−	92.0332i	−0.740824	−	3.24576i
$805$	−0.192012	+	0.240776i	−0.00676755	+	0.00848624i
$806$	49.0852	−	23.6382i	1.72895	−	0.832619i
$807$	−11.2765	−	5.43045i	−0.396950	−	0.191161i
$808$	15.6189	+	19.5855i	0.549471	+	0.689015i
$809$	−2.69023	+	3.37344i	−0.0945833	+	0.118604i	−0.826871	−	0.562392i	$-0.809881\pi$
$809$	−2.69023	+	3.37344i	−0.0945833	+	0.118604i	0.732288	+	0.680996i	$0.238453\pi$
$810$	58.8839	+	28.3570i	2.06897	+	0.996363i
$811$	−46.7124			−1.64029			−0.820147	−	0.572153i	$-0.806108\pi$
$811$	−46.7124			−1.64029			−0.820147	+	0.572153i	$0.806108\pi$
$812$		0			0
$813$	−10.7874			−0.378331
$814$	−66.7725	−	32.1560i	−2.34038	−	1.12707i
$815$	27.6009	−	34.6104i	0.966816	−	1.21235i
$816$	−5.90205	−	7.40093i	−0.206613	−	0.259084i
$817$	0.0114156	+	0.00549747i	0.000399382	+	0.000192332i
$818$	−41.5263	+	19.9980i	−1.45193	+	0.699214i
$819$	−1.86815	+	2.34259i	−0.0652785	+	0.0818567i
$820$	15.7201	+	68.8744i	0.548971	+	2.40520i
$821$	0.507206	+	2.22222i	0.0177016	+	0.0775559i	0.983007	−	0.183567i	$-0.0587644\pi$
$821$	0.507206	+	2.22222i	0.0177016	+	0.0775559i	−0.965306	+	0.261123i	$0.915907\pi$
$822$	−24.6626	−	30.9259i	−0.860206	−	1.07866i
$823$	5.81036	−	25.4569i	0.202537	−	0.887371i	−0.766849	−	0.641827i	$-0.778177\pi$
$823$	5.81036	−	25.4569i	0.202537	−	0.887371i	0.969386	−	0.245543i	$-0.0789663\pi$
$824$	−25.7121			−0.895724
$825$	−1.60685	+	7.04008i	−0.0559434	+	0.245104i
$826$	−6.64131	+	3.19829i	−0.231081	+	0.111283i
$827$	−23.0681	+	11.1090i	−0.802157	+	0.386298i	−0.789599	−	0.613623i	$-0.789712\pi$
$827$	−23.0681	+	11.1090i	−0.802157	+	0.386298i	−0.0125576	+	0.999921i	$0.503997\pi$
$828$	0.394196	−	1.72709i	0.0136993	−	0.0600204i
$829$	−43.4804			−1.51014			−0.755069	−	0.655645i	$-0.772397\pi$
$829$	−43.4804			−1.51014			−0.755069	+	0.655645i	$0.772397\pi$
$830$	−0.868353	+	3.80450i	−0.0301410	+	0.132056i
$831$	−26.2110	−	32.8676i	−0.909250	−	1.14016i
$832$	13.2636	+	58.1115i	0.459831	+	2.01465i
$833$	2.78640	+	12.2080i	0.0965430	+	0.422983i
$834$	−29.0112	+	36.3789i	−1.00457	+	1.25970i
$835$	5.54273	−	2.66924i	0.191814	−	0.0923728i
$836$	7.21019	+	3.47224i	0.249370	+	0.120090i
$837$	8.44390	+	10.5883i	0.291864	+	0.365986i
$838$	2.99264	−	3.75265i	0.103379	−	0.129633i
$839$	42.3399	+	20.3898i	1.46174	+	0.703935i	0.984588	−	0.174889i	$-0.0559566\pi$
$839$	42.3399	+	20.3898i	1.46174	+	0.703935i	0.477147	+	0.878823i	$0.341671\pi$
$840$	8.00771			0.276292
$841$		0			0
$842$	95.4268			3.28863
$843$	−22.2103	−	10.6959i	−0.764962	−	0.368386i
$844$	54.7726	−	68.6826i	1.88535	−	2.36415i
$845$	−27.6815	−	34.7115i	−0.952274	−	1.19411i
$846$	−23.2989	−	11.2202i	−0.801033	−	0.385757i
$847$	1.27781	−	0.615362i	0.0439062	−	0.0211441i
$848$	9.80093	−	12.2900i	0.336565	−	0.422040i
$849$	−13.8514	−	60.6870i	−0.475379	−	2.08277i
$850$	0.870610	+	3.81439i	0.0298617	+	0.130833i
$851$	−1.68469	−	2.11254i	−0.0577506	−	0.0724169i
$852$	−27.1556	+	118.977i	−0.930336	+	4.07607i
$853$	25.7853			0.882872			0.441436	−	0.897293i	$-0.354469\pi$
$853$	25.7853			0.882872			0.441436	+	0.897293i	$0.354469\pi$
$854$	2.09079	−	9.16037i	0.0715455	−	0.313461i
$855$	1.72900	−	0.832644i	0.0591306	−	0.0284758i
$856$	19.8137	−	9.54177i	0.677218	−	0.326131i
$857$	11.4333	−	50.0927i	0.390555	−	1.71113i	−0.272152	−	0.962254i	$-0.587735\pi$
$857$	11.4333	−	50.0927i	0.390555	−	1.71113i	0.662707	−	0.748879i	$-0.269408\pi$
$858$	−108.075			−3.68962
$859$	−4.04340	+	17.7153i	−0.137959	+	0.604438i	0.857923	+	0.513778i	$0.171755\pi$
$859$	−4.04340	+	17.7153i	−0.137959	+	0.604438i	−0.995882	+	0.0906594i	$0.971103\pi$
$860$	0.128232	+	0.160798i	0.00437267	+	0.00548316i
$861$	−1.37923	−	6.04281i	−0.0470041	−	0.205938i
$862$	7.62658	+	33.4142i	0.259762	+	1.13809i
$863$	−9.12750	+	11.4455i	−0.310704	+	0.389610i	−0.912525	−	0.409020i	$-0.865870\pi$
$863$	−9.12750	+	11.4455i	−0.310704	+	0.389610i	0.601821	+	0.798631i	$0.294442\pi$
$864$	−7.16939	+	3.45260i	−0.243908	+	0.117460i
$865$	18.5602	+	8.93812i	0.631066	+	0.303905i
$866$	13.1875	+	16.5366i	0.448129	+	0.561936i
$867$	17.9036	−	22.4505i	0.608039	−	0.762457i
$868$	5.17631	+	2.49278i	0.175695	+	0.0846104i
$869$	28.6539			0.972017
$870$		0			0
$871$	−67.3198			−2.28105
$872$	23.5427	+	11.3376i	0.797257	+	0.383939i
$873$	−3.93265	+	4.93139i	−0.133100	+	0.166902i
$874$	0.279391	+	0.350345i	0.00945055	+	0.0118506i
$875$	3.39777	+	1.63628i	0.114866	+	0.0553164i
$876$	49.0045	−	23.5993i	1.65571	−	0.797347i
$877$	12.5827	−	15.7782i	0.424888	−	0.532792i	−0.522603	−	0.852576i	$-0.675039\pi$
$877$	12.5827	−	15.7782i	0.424888	−	0.532792i	0.947491	+	0.319784i	$0.103610\pi$
$878$	−6.17092	−	27.0365i	−0.208258	−	0.912439i
$879$	3.67619	+	16.1064i	0.123995	+	0.543257i
$880$	14.3403	+	17.9821i	0.483411	+	0.606178i
$881$	−3.90720	+	17.1186i	−0.131637	+	0.576740i	0.865486	+	0.500934i	$0.167010\pi$
$881$	−3.90720	+	17.1186i	−0.131637	+	0.576740i	−0.997123	+	0.0758058i	$0.975847\pi$
$882$	23.2427			0.782622
$883$	1.88963	−	8.27901i	0.0635911	−	0.278611i	−0.933129	−	0.359543i	$-0.882933\pi$
$883$	1.88963	−	8.27901i	0.0635911	−	0.278611i	0.996720	+	0.0809323i	$0.0257897\pi$
$884$	−34.3510	+	16.5426i	−1.15535	+	0.556387i
$885$	−37.4026	+	18.0121i	−1.25727	+	0.605471i
$886$	−18.9077	+	82.8401i	−0.635217	+	2.78307i
$887$	−9.27160			−0.311310			−0.155655	−	0.987812i	$-0.549749\pi$
$887$	−9.27160			−0.311310			−0.155655	+	0.987812i	$0.549749\pi$
$888$	−15.6340	+	68.4972i	−0.524644	+	2.29861i
$889$	−1.37543	−	1.72473i	−0.0461304	−	0.0578457i
$890$	12.4686	+	54.6286i	0.417949	+	1.83115i
$891$	−9.60774	−	42.0943i	−0.321871	−	1.41021i
$892$	−1.63353	+	2.04838i	−0.0546947	+	0.0685849i
$893$	3.83738	−	1.84798i	0.128413	−	0.0618404i
$894$	2.33121	+	1.12265i	0.0779674	+	0.0375471i
$895$	−19.6079	−	24.5876i	−0.655421	−	0.821871i
$896$	−4.89131	+	6.13351i	−0.163407	+	0.204906i
$897$	−3.55008	−	1.70963i	−0.118534	−	0.0570828i
$898$	−49.6776			−1.65776
$899$		0			0
$900$	4.72850			0.157617
$901$	−10.4852	−	5.04938i	−0.349311	−	0.168219i
$902$	44.6911	−	56.0409i	1.48805	−	1.86596i
$903$	−0.0112506	−	0.0141078i	−0.000374398	−	0.000469480i
$904$	−50.1182	−	24.1357i	−1.66691	−	0.802740i
$905$	35.9119	−	17.2942i	1.19375	−	0.574880i
$906$	−20.5542	+	25.7742i	−0.682869	+	0.856291i
$907$	−4.44721	−	19.4845i	−0.147667	−	0.646972i	−0.993530	−	0.113572i	$-0.963771\pi$
$907$	−4.44721	−	19.4845i	−0.147667	−	0.646972i	0.845863	−	0.533401i	$-0.179086\pi$
$908$	6.14826	+	26.9373i	0.204037	+	0.893946i
$909$	−5.33071	−	6.68450i	−0.176809	−	0.221711i
$910$	2.73762	−	11.9943i	0.0907511	−	0.397607i
$911$	−14.2969			−0.473676			−0.236838	−	0.971549i	$-0.576111\pi$
$911$	−14.2969			−0.473676			−0.236838	+	0.971549i	$0.576111\pi$
$912$	0.643957	−	2.82136i	0.0213235	−	0.0934245i
$913$	2.32273	−	1.11857i	0.0768711	−	0.0370192i
$914$	82.1959	−	39.5834i	2.71880	−	1.30930i
$915$	11.7750	−	51.5894i	0.389268	−	1.70549i
$916$	−40.1086			−1.32523
$917$	0.0444724	−	0.194846i	0.00146861	−	0.00643439i
$918$	−9.07560	−	11.3804i	−0.299539	−	0.375610i
$919$	−12.8832	−	56.4448i	−0.424976	−	1.86194i	−0.501929	−	0.864909i	$-0.667376\pi$
$919$	−12.8832	−	56.4448i	−0.424976	−	1.86194i	0.0769528	−	0.997035i	$-0.475481\pi$
$920$	0.751292	+	3.29163i	0.0247694	+	0.108522i
$921$	37.1844	−	46.6278i	1.22527	−	1.53644i
$922$	38.2344	−	18.4127i	1.25918	−	0.606390i
$923$	78.4097	+	37.7601i	2.58089	+	1.24289i
$924$	−7.10598	−	8.91061i	−0.233770	−	0.293138i
$925$	4.49679	−	5.63880i	0.147854	−	0.185403i
$926$	19.8872	+	9.57716i	0.653534	+	0.314725i
$927$	8.77552			0.288226
$928$		0			0
$929$	28.1340			0.923048			0.461524	−	0.887128i	$-0.347303\pi$
$929$	28.1340			0.923048			0.461524	+	0.887128i	$0.347303\pi$
$930$	44.7724	+	21.5613i	1.46815	+	0.707022i
$931$	−2.38679	+	2.99294i	−0.0782240	+	0.0980897i
$932$	−36.2783	−	45.4915i	−1.18833	−	1.49012i
$933$	−16.2287	−	7.81533i	−0.531304	−	0.255862i
$934$	16.8305	−	8.10516i	0.550712	−	0.265209i
$935$	10.6166	−	13.3128i	0.347199	−	0.435374i
$936$	7.30957	+	32.0253i	0.238921	+	1.04678i
$937$	10.5004	+	46.0051i	0.343032	+	1.50292i	0.792637	+	0.609694i	$0.208708\pi$
$937$	10.5004	+	46.0051i	0.343032	+	1.50292i	−0.449604	+	0.893228i	$0.648435\pi$
$938$	−6.79806	−	8.52450i	−0.221964	−	0.278335i
$939$	0.411022	−	1.80080i	0.0134132	−	0.0587670i
$940$	69.1356			2.25495
$941$	4.93623	−	21.6271i	0.160917	−	0.705022i	−0.828508	−	0.559977i	$-0.810810\pi$
$941$	4.93623	−	21.6271i	0.160917	−	0.705022i	0.989425	−	0.145045i	$-0.0463328\pi$
$942$	51.9297	−	25.0080i	1.69196	−	0.814805i
$943$	2.35454	−	1.13388i	0.0766743	−	0.0369244i
$944$	−4.46629	+	19.5681i	−0.145365	+	0.636887i
$945$	3.05827			0.0994854
$946$	0.0464349	−	0.203444i	0.00150973	−	0.00661455i
$947$	19.3703	+	24.2896i	0.629450	+	0.789305i	0.989640	−	0.143574i	$-0.0458595\pi$
$947$	19.3703	+	24.2896i	0.629450	+	0.789305i	−0.360190	+	0.932879i	$0.617288\pi$
$948$	−13.0223	−	57.0546i	−0.422946	−	1.85305i
$949$	−8.63114	−	37.8155i	−0.280179	−	1.22754i
$950$	−0.745752	+	0.935144i	−0.0241954	+	0.0303401i
$951$	50.4095	−	24.2759i	1.63464	−	0.787201i
$952$	−2.58244	−	1.24364i	−0.0836972	−	0.0403065i
$953$	12.6298	+	15.8372i	0.409119	+	0.513018i	0.943114	−	0.332469i	$-0.107882\pi$
$953$	12.6298	+	15.8372i	0.409119	+	0.513018i	−0.533996	+	0.845487i	$0.679310\pi$
$954$	−13.4682	+	16.8885i	−0.436048	+	0.546787i
$955$	−16.2341	−	7.81795i	−0.525324	−	0.252983i
$956$	27.7850			0.898630
$957$		0			0
$958$	42.4329			1.37094
$959$	−2.68015	−	1.29069i	−0.0865466	−	0.0416787i
$960$	−33.8984	+	42.5072i	−1.09407	+	1.37192i
$961$	−9.00985	−	11.2980i	−0.290640	−	0.364451i
$962$	97.2530	+	46.8346i	3.13556	+	1.51001i
$963$	−6.76239	+	3.25660i	−0.217915	+	0.104942i
$964$	−12.2571	+	15.3699i	−0.394773	+	0.495030i
$965$	11.8694	+	52.0032i	0.382089	+	1.67404i
$966$	−0.142008	−	0.622176i	−0.00456902	−	0.0200182i
$967$	16.2664	+	20.3974i	0.523091	+	0.655935i	0.971262	−	0.238013i	$-0.0764960\pi$
$967$	16.2664	+	20.3974i	0.523091	+	0.655935i	−0.448171	+	0.893948i	$0.647925\pi$
$968$	3.45992	−	15.1589i	0.111206	−	0.487226i
$969$	−2.14246			−0.0688258
$970$	5.76296	−	25.2492i	0.185037	−	0.810702i
$971$	13.8408	−	6.66536i	0.444171	−	0.213901i	−0.198410	−	0.980119i	$-0.563578\pi$
$971$	13.8408	−	6.66536i	0.444171	−	0.213901i	0.642581	+	0.766218i	$0.277864\pi$
$972$	−45.8641	+	22.0870i	−1.47109	+	0.708440i
$973$	−0.778659	+	3.41153i	−0.0249627	+	0.109369i
$974$	50.6603			1.62326
$975$	2.34035	−	10.2538i	0.0749513	−	0.328383i
$976$	−15.9515	−	20.0026i	−0.510595	−	0.640266i
$977$	−9.44463	−	41.3796i	−0.302161	−	1.32385i	−0.866859	−	0.498554i	$-0.833864\pi$
$977$	−9.44463	−	41.3796i	−0.302161	−	1.32385i	0.564698	−	0.825298i	$-0.308993\pi$
$978$	20.4129	+	89.4349i	0.652733	+	2.85981i
$979$	23.0802	−	28.9417i	0.737648	−	0.924981i
$980$	−55.9850	+	26.9610i	−1.78838	+	0.861237i
$981$	−8.03511	−	3.86950i	−0.256541	−	0.123544i
$982$	−26.4321	−	33.1448i	−0.843482	−	1.05769i
$983$	−18.6663	+	23.4068i	−0.595362	+	0.746560i	−0.984647	−	0.174557i	$-0.944151\pi$
$983$	−18.6663	+	23.4068i	−0.595362	+	0.746560i	0.389285	+	0.921117i	$0.372722\pi$
$984$	−61.2229	−	29.4834i	−1.95171	−	0.939896i
$985$	−47.8405			−1.52432
$986$		0			0
$987$	−6.06572			−0.193074
$988$	−10.5015	−	5.05726i	−0.334098	−	0.160893i
$989$	0.00474358	−	0.00594826i	0.000150837	−	0.000189144i
$990$	−19.7060	−	24.7106i	−0.626298	−	0.785353i
$991$	45.7358	+	22.0252i	1.45285	+	0.699654i	0.983087	−	0.183141i	$-0.0586264\pi$
$991$	45.7358	+	22.0252i	1.45285	+	0.699654i	0.469759	+	0.882795i	$0.344341\pi$
$992$	−8.76090	+	4.21903i	−0.278159	+	0.133954i
$993$	24.4332	−	30.6382i	0.775364	−	0.972275i
$994$	3.13649	+	13.7418i	0.0994833	+	0.435865i
$995$	−8.77293	−	38.4367i	−0.278121	−	1.21853i
$996$	−3.28286	−	4.11658i	−0.104021	−	0.130439i
$997$	−1.82756	+	8.00705i	−0.0578793	+	0.253586i	−0.995587	−	0.0938381i	$-0.970086\pi$
$997$	−1.82756	+	8.00705i	−0.0578793	+	0.253586i	0.937708	+	0.347424i	$0.112944\pi$
$998$	−69.9250			−2.21344
$999$	−5.97087	+	26.1601i	−0.188910	+	0.827669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.q.190.7		48
29.2	odd	28		841.2.e.m.267.15		96
29.3	odd	28		841.2.b.f.840.15		16
29.4	even	14		841.2.d.p.778.7		48
29.5	even	14		841.2.d.p.574.7		48
29.6	even	14		841.2.d.p.605.2		48
29.7	even	7		841.2.a.i.1.2	✓	8
29.8	odd	28		841.2.e.m.270.15		96
29.9	even	14		841.2.d.p.571.2		48
29.10	odd	28		841.2.e.m.63.15		96
29.11	odd	28		841.2.e.m.196.15		96
29.12	odd	4		841.2.e.m.651.2		96
29.13	even	14		841.2.d.p.645.2		48
29.14	odd	28		841.2.e.m.236.2		96
29.15	odd	28		841.2.e.m.236.15		96
29.16	even	7	inner	841.2.d.q.645.7		48
29.17	odd	4		841.2.e.m.651.15		96
29.18	odd	28		841.2.e.m.196.2		96
29.19	odd	28		841.2.e.m.63.2		96
29.20	even	7	inner	841.2.d.q.571.7		48
29.21	odd	28		841.2.e.m.270.2		96
29.22	even	14		841.2.a.j.1.7	yes	8
29.23	even	7	inner	841.2.d.q.605.7		48
29.24	even	7	inner	841.2.d.q.574.2		48
29.25	even	7	inner	841.2.d.q.778.2		48
29.26	odd	28		841.2.b.f.840.2		16
29.27	odd	28		841.2.e.m.267.2		96
29.28	even	2		841.2.d.p.190.2		48
87.65	odd	14		7569.2.a.bi.1.7		8
87.80	odd	14		7569.2.a.bd.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.i.1.2	✓	8	29.7	even	7
841.2.a.j.1.7	yes	8	29.22	even	14
841.2.b.f.840.2		16	29.26	odd	28
841.2.b.f.840.15		16	29.3	odd	28
841.2.d.p.190.2		48	29.28	even	2
841.2.d.p.571.2		48	29.9	even	14
841.2.d.p.574.7		48	29.5	even	14
841.2.d.p.605.2		48	29.6	even	14
841.2.d.p.645.2		48	29.13	even	14
841.2.d.p.778.7		48	29.4	even	14
841.2.d.q.190.7		48	1.1	even	1	trivial
841.2.d.q.571.7		48	29.20	even	7	inner
841.2.d.q.574.2		48	29.24	even	7	inner
841.2.d.q.605.7		48	29.23	even	7	inner
841.2.d.q.645.7		48	29.16	even	7	inner
841.2.d.q.778.2		48	29.25	even	7	inner
841.2.e.m.63.2		96	29.19	odd	28
841.2.e.m.63.15		96	29.10	odd	28
841.2.e.m.196.2		96	29.18	odd	28
841.2.e.m.196.15		96	29.11	odd	28
841.2.e.m.236.2		96	29.14	odd	28
841.2.e.m.236.15		96	29.15	odd	28
841.2.e.m.267.2		96	29.27	odd	28
841.2.e.m.267.15		96	29.2	odd	28
841.2.e.m.270.2		96	29.21	odd	28
841.2.e.m.270.15		96	29.8	odd	28
841.2.e.m.651.2		96	29.12	odd	4
841.2.e.m.651.15		96	29.17	odd	4
7569.2.a.bd.1.2		8	87.80	odd	14
7569.2.a.bi.1.7		8	87.65	odd	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.15716 + 1.03884i) q^{2} +(-1.31018 + 1.64292i) q^{3} +(2.32720 + 2.91821i) q^{4} +(2.18748 + 1.05344i) q^{5} +(-4.53300 + 2.18298i) q^{6} +(-0.235910 + 0.295821i) q^{7} +(0.923050 + 4.04415i) q^{8} +(-0.315036 - 1.38026i) q^{9} +(3.62441 + 4.54487i) q^{10} +(0.854560 - 3.74407i) q^{11} -7.84343 q^{12} +(-1.24465 + 5.45318i) q^{13} +(-0.816205 + 0.393064i) q^{14} +(-4.59671 + 2.21366i) q^{15} +(-0.548899 + 2.40488i) q^{16} +1.82620 q^{17} +(0.754282 - 3.30472i) q^{18} +(0.348089 + 0.436490i) q^{19} +(2.01655 + 8.83509i) q^{20} +(-0.176925 - 0.775161i) q^{21} +(5.73290 - 7.18883i) q^{22} +(0.302036 - 0.145453i) q^{23} +(-7.85357 - 3.78208i) q^{24} +(0.557905 + 0.699590i) q^{25} +(-8.34987 + 10.4704i) q^{26} +(-2.99939 - 1.44443i) q^{27} -1.41228 q^{28} -12.2155 q^{30} +(-3.66522 - 1.76508i) q^{31} +(1.49032 - 1.86880i) q^{32} +(5.03157 + 6.30939i) q^{33} +(3.93942 + 1.89712i) q^{34} +(-0.827677 + 0.398588i) q^{35} +(3.29475 - 4.13148i) q^{36} +(-1.79355 - 7.85806i) q^{37} +(0.297444 + 1.30319i) q^{38} +(-7.32840 - 9.18952i) q^{39} +(-2.24109 + 9.81888i) q^{40} +7.79555 q^{41} +(0.423607 - 1.85594i) q^{42} +(0.0204474 - 0.00984695i) q^{43} +(12.9147 - 6.21940i) q^{44} +(0.764883 - 3.35117i) q^{45} +0.802642 q^{46} +(1.69759 - 7.43765i) q^{47} +(-3.23187 - 4.05264i) q^{48} +(1.52579 + 6.68492i) q^{49} +(0.476732 + 2.08870i) q^{50} +(-2.39266 + 3.00030i) q^{51} +(-18.8101 + 9.05845i) q^{52} +(-5.74151 - 2.76496i) q^{53} +(-4.96966 - 6.23175i) q^{54} +(5.81348 - 7.28987i) q^{55} +(-1.41410 - 0.680996i) q^{56} -1.17318 q^{57} +8.13681 q^{59} +(-17.1574 - 8.26256i) q^{60} +(-6.46666 + 8.10894i) q^{61} +(-6.07285 - 7.61512i) q^{62} +(0.482632 + 0.232423i) q^{63} +(9.60112 - 4.62366i) q^{64} +(-8.46723 + 10.6176i) q^{65} +(4.29951 + 18.8374i) q^{66} +(2.67816 + 11.7338i) q^{67} +(4.24993 + 5.32924i) q^{68} +(-0.156755 + 0.686790i) q^{69} -2.19950 q^{70} +(3.46221 - 15.1689i) q^{71} +(5.29119 - 2.54810i) q^{72} +(-6.24784 + 3.00880i) q^{73} +(4.29425 - 18.8143i) q^{74} -1.88033 q^{75} +(-0.463699 + 2.03160i) q^{76} +(0.905978 + 1.13606i) q^{77} +(-6.26216 - 27.4363i) q^{78} +(1.66029 + 7.27418i) q^{79} +(-3.73410 + 4.68241i) q^{80} +(10.1295 - 4.87811i) q^{81} +(16.8163 + 8.09829i) q^{82} +(0.418549 + 0.524844i) q^{83} +(1.85034 - 2.32026i) q^{84} +(3.99479 + 1.92379i) q^{85} +0.0543377 q^{86} +15.9304 q^{88} +(8.68459 + 4.18228i) q^{89} +(5.13129 - 6.43444i) q^{90} +(-1.31954 - 1.65465i) q^{91} +(1.12736 + 0.542907i) q^{92} +(7.70198 - 3.70908i) q^{93} +(11.3885 - 14.2807i) q^{94} +(0.301625 + 1.32151i) q^{95} +(1.11769 + 4.89693i) q^{96} +(-2.77777 - 3.48321i) q^{97} +(-3.65315 + 16.0055i) q^{98} -5.43702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 6 q^{3} - 6 q^{4} + q^{5} - 3 q^{6} + 15 q^{8} - 8 q^{9} - 3 q^{10} + 5 q^{11} - 72 q^{12} + 4 q^{13} + 15 q^{14} - 7 q^{15} + 2 q^{16} - 54 q^{17} - 11 q^{18} + 17 q^{19} + 7 q^{20} + 25 q^{21}+ \cdots - 90 q^{99}+O(q^{100}) \) 48 * q + 4 * q^2 + 6 * q^3 - 6 * q^4 + q^5 - 3 * q^6 + 15 * q^8 - 8 * q^9 - 3 * q^10 + 5 * q^11 - 72 * q^12 + 4 * q^13 + 15 * q^14 - 7 * q^15 + 2 * q^16 - 54 * q^17 - 11 * q^18 + 17 * q^19 + 7 * q^20 + 25 * q^21 - 25 * q^22 + 7 * q^23 - 25 * q^24 + 13 * q^25 + 3 * q^26 + 18 * q^27 + 150 * q^28 - 156 * q^30 + q^31 - 6 * q^32 - 12 * q^34 + 5 * q^35 + 19 * q^36 + 6 * q^37 + 14 * q^38 + 27 * q^39 - 25 * q^40 - 36 * q^41 - 15 * q^42 - 5 * q^43 + 20 * q^44 + q^45 - 84 * q^46 + 31 * q^47 + 11 * q^48 - 4 * q^49 + 11 * q^50 - 23 * q^51 - 2 * q^52 - 19 * q^53 + 46 * q^54 + 20 * q^55 + 20 * q^56 - 36 * q^57 - 6 * q^59 - 9 * q^60 + 21 * q^61 + 12 * q^62 + 10 * q^63 - q^64 + 17 * q^65 + 5 * q^66 - 2 * q^67 + 8 * q^68 - 14 * q^69 + 30 * q^70 + 12 * q^71 - 34 * q^73 + 27 * q^74 - 24 * q^75 - 16 * q^76 - 10 * q^77 - 6 * q^78 + 29 * q^79 + 41 * q^80 - 12 * q^81 + 22 * q^82 + 3 * q^83 - 10 * q^84 + 2 * q^85 - 30 * q^86 - 90 * q^88 + 36 * q^89 - 38 * q^90 + 4 * q^92 - 2 * q^93 - 13 * q^94 + 11 * q^95 + 2 * q^96 - 18 * q^97 + 27 * q^98 - 90 * q^99

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