LMFDB - Embedded newform 127.2.c.a.107.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [127,2,Mod(19,127)] 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("127.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(127, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	127.c (of order $3$, degree $2$, 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:	$1.01410010567$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 12 x^{16} - 7 x^{15} + 92 x^{14} - 46 x^{13} + 388 x^{12} - 105 x^{11} + 1128 x^{10} + \cdots + 9 $ x^18 - x^17 + 12x^16 - 7x^15 + 92x^14 - 46x^13 + 388x^12 - 105x^11 + 1128x^10 - 250x^9 + 1865x^8 - 14x^7 + 1885x^6 - 360x^5 + 552x^4 - 129x^3 + 126x^2 - 27x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			107.6
Root			$-0.267368 + 0.463096i$ of defining polynomial
Character	$\chi$	$=$	127.107
Dual form			127.2.c.a.19.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.534737 q^{2} +(-1.38643 - 2.40137i) q^{3} -1.71406 q^{4} -0.988660 q^{5} +(-0.741376 - 1.28410i) q^{6} +(-0.163967 - 0.283999i) q^{7} -1.98604 q^{8} +(-2.34438 + 4.06058i) q^{9} -0.528673 q^{10} +(2.49207 - 4.31640i) q^{11} +(2.37642 + 4.11608i) q^{12} +(-1.76368 - 3.05478i) q^{13} +(-0.0876791 - 0.151865i) q^{14} +(1.37071 + 2.37414i) q^{15} +2.36610 q^{16} +(0.276879 - 0.479568i) q^{17} +(-1.25363 + 2.17134i) q^{18} +5.21195 q^{19} +1.69462 q^{20} +(-0.454657 + 0.787489i) q^{21} +(1.33260 - 2.30814i) q^{22} +(2.05171 + 3.55366i) q^{23} +(2.75351 + 4.76922i) q^{24} -4.02255 q^{25} +(-0.943104 - 1.63350i) q^{26} +4.68270 q^{27} +(0.281048 + 0.486790i) q^{28} +(2.93487 - 5.08335i) q^{29} +(0.732968 + 1.26954i) q^{30} +(-2.61179 - 4.52376i) q^{31} +5.23733 q^{32} -13.8203 q^{33} +(0.148057 - 0.256443i) q^{34} +(0.162107 + 0.280778i) q^{35} +(4.01840 - 6.96007i) q^{36} +(-4.37338 + 7.57492i) q^{37} +2.78702 q^{38} +(-4.89044 + 8.47049i) q^{39} +1.96352 q^{40} +(-0.970700 + 1.68130i) q^{41} +(-0.243122 + 0.421100i) q^{42} +(-2.43046 + 4.20967i) q^{43} +(-4.27155 + 7.39855i) q^{44} +(2.31779 - 4.01454i) q^{45} +(1.09712 + 1.90027i) q^{46} +2.39356 q^{47} +(-3.28044 - 5.68188i) q^{48} +(3.44623 - 5.96905i) q^{49} -2.15101 q^{50} -1.53549 q^{51} +(3.02305 + 5.23607i) q^{52} +(1.39912 - 2.42335i) q^{53} +2.50401 q^{54} +(-2.46381 + 4.26745i) q^{55} +(0.325645 + 0.564034i) q^{56} +(-7.22601 - 12.5158i) q^{57} +(1.56939 - 2.71825i) q^{58} +(6.81913 - 11.8111i) q^{59} +(-2.34947 - 4.06940i) q^{60} +2.72107 q^{61} +(-1.39662 - 2.41902i) q^{62} +1.53760 q^{63} -1.93161 q^{64} +(1.74368 + 3.02014i) q^{65} -7.39025 q^{66} +(4.67954 + 8.10521i) q^{67} +(-0.474586 + 0.822006i) q^{68} +(5.68909 - 9.85380i) q^{69} +(0.0866848 + 0.150142i) q^{70} +(5.95907 + 10.3214i) q^{71} +(4.65604 - 8.06450i) q^{72} -14.1420 q^{73} +(-2.33861 + 4.05059i) q^{74} +(5.57699 + 9.65963i) q^{75} -8.93358 q^{76} -1.63447 q^{77} +(-2.61510 + 4.52948i) q^{78} +(-7.78350 - 13.4814i) q^{79} -2.33927 q^{80} +(0.540907 + 0.936878i) q^{81} +(-0.519069 + 0.899054i) q^{82} +(8.60664 - 14.9071i) q^{83} +(0.779308 - 1.34980i) q^{84} +(-0.273739 + 0.474129i) q^{85} +(-1.29965 + 2.25107i) q^{86} -16.2760 q^{87} +(-4.94936 + 8.57255i) q^{88} +16.4473 q^{89} +(1.23941 - 2.14672i) q^{90} +(-0.578370 + 1.00177i) q^{91} +(-3.51674 - 6.09117i) q^{92} +(-7.24214 + 12.5438i) q^{93} +1.27992 q^{94} -5.15285 q^{95} +(-7.26119 - 12.5768i) q^{96} +(0.114046 + 0.197534i) q^{97} +(1.84283 - 3.19187i) q^{98} +(11.6847 + 20.2385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + 5 q^{7} - 6 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 8 q^{14} + 3 q^{15} - 6 q^{16} - 6 q^{17} + 16 q^{19} - 32 q^{20} + 3 q^{21} + 6 q^{22} + 13 q^{23} - 6 q^{24}+ \cdots + 17 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + 5 * q^7 - 6 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 8 * q^14 + 3 * q^15 - 6 * q^16 - 6 * q^17 + 16 * q^19 - 32 * q^20 + 3 * q^21 + 6 * q^22 + 13 * q^23 - 6 * q^24 + 6 * q^25 - 14 * q^26 + 10 * q^27 - 2 * q^28 - 5 * q^29 - 23 * q^30 - 11 * q^31 - 4 * q^32 - 16 * q^33 - 2 * q^34 - 16 * q^35 + 15 * q^36 - 4 * q^37 + 4 * q^38 - 7 * q^39 - 36 * q^40 - 11 * q^41 + 9 * q^43 - 15 * q^44 + 14 * q^45 + 15 * q^46 - 10 * q^47 + 20 * q^48 + 12 * q^49 + 32 * q^50 + 4 * q^51 + 26 * q^52 - 2 * q^53 + 2 * q^54 - q^55 + 12 * q^56 + 28 * q^57 + 10 * q^58 + 6 * q^60 + 28 * q^61 + 8 * q^62 - 12 * q^63 - 50 * q^64 + 15 * q^65 + 36 * q^66 - 12 * q^67 - 41 * q^68 + 33 * q^69 + 21 * q^70 - 4 * q^71 + 31 * q^72 + 52 * q^73 + 13 * q^74 - 11 * q^75 + 26 * q^76 - 40 * q^77 + q^78 - 35 * q^79 + 26 * q^80 + 27 * q^81 - 26 * q^82 + 13 * q^83 + 22 * q^84 + 15 * q^85 - 5 * q^86 - 64 * q^87 - q^88 + 8 * q^89 - 30 * q^90 - 16 * q^91 + 11 * q^92 - 6 * q^93 - 62 * q^94 - 38 * q^95 - 31 * q^96 + 28 * q^97 + 32 * q^98 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/127\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.534737			0.378116			0.189058	−	0.981966i	$-0.439457\pi$
$2$	0.534737			0.378116			0.189058	+	0.981966i	$0.439457\pi$
$3$	−1.38643	−	2.40137i	−0.800456	−	1.38643i	−0.919316	−	0.393520i	$-0.871257\pi$
$3$	−1.38643	−	2.40137i	−0.800456	−	1.38643i	0.118860	−	0.992911i	$-0.462076\pi$
$4$	−1.71406			−0.857028
$5$	−0.988660			−0.442142			−0.221071	−	0.975258i	$-0.570955\pi$
$5$	−0.988660			−0.442142			−0.221071	+	0.975258i	$0.570955\pi$
$6$	−0.741376	−	1.28410i	−0.302665	−	0.524232i
$7$	−0.163967	−	0.283999i	−0.0619736	−	0.107341i	0.833374	−	0.552710i	$-0.186406\pi$
$7$	−0.163967	−	0.283999i	−0.0619736	−	0.107341i	−0.895348	+	0.445368i	$0.853073\pi$
$8$	−1.98604			−0.702172
$9$	−2.34438	+	4.06058i	−0.781460	+	1.35353i
$10$	−0.528673			−0.167181
$11$	2.49207	−	4.31640i	0.751388	−	1.30144i	−0.195762	−	0.980651i	$-0.562718\pi$
$11$	2.49207	−	4.31640i	0.751388	−	1.30144i	0.947150	−	0.320791i	$-0.103949\pi$
$12$	2.37642	+	4.11608i	0.686013	+	1.18821i
$13$	−1.76368	−	3.05478i	−0.489157	−	0.847244i	0.510766	−	0.859720i	$-0.329362\pi$
$13$	−1.76368	−	3.05478i	−0.489157	−	0.847244i	−0.999922	+	0.0124760i	$0.996029\pi$
$14$	−0.0876791	−	0.151865i	−0.0234332	−	0.0405875i
$15$	1.37071	+	2.37414i	0.353915	+	0.612999i
$16$	2.36610			0.591525
$17$	0.276879	−	0.479568i	0.0671529	−	0.116312i	−0.830494	−	0.557027i	$-0.811942\pi$
$17$	0.276879	−	0.479568i	0.0671529	−	0.116312i	0.897647	+	0.440715i	$0.145275\pi$
$18$	−1.25363	+	2.17134i	−0.295483	+	0.511791i
$19$	5.21195			1.19570			0.597852	−	0.801607i	$-0.296021\pi$
$19$	5.21195			1.19570			0.597852	+	0.801607i	$0.296021\pi$
$20$	1.69462			0.378928
$21$	−0.454657	+	0.787489i	−0.0992143	+	0.171844i
$22$	1.33260	−	2.30814i	0.284112	−	0.492096i
$23$	2.05171	+	3.55366i	0.427810	+	0.740989i	0.996678	−	0.0814398i	$-0.0259518\pi$
$23$	2.05171	+	3.55366i	0.427810	+	0.740989i	−0.568868	+	0.822429i	$0.692619\pi$
$24$	2.75351	+	4.76922i	0.562058	+	0.973513i
$25$	−4.02255			−0.804510
$26$	−0.943104	−	1.63350i	−0.184958	−	0.320357i
$27$	4.68270			0.901185
$28$	0.281048	+	0.486790i	0.0531131	+	0.0919947i
$29$	2.93487	−	5.08335i	0.544992	−	0.943954i	−0.453615	−	0.891198i	$-0.649866\pi$
$29$	2.93487	−	5.08335i	0.544992	−	0.943954i	0.998607	−	0.0527566i	$-0.0168007\pi$
$30$	0.732968	+	1.26954i	0.133821	+	0.231785i
$31$	−2.61179	−	4.52376i	−0.469092	−	0.812491i	0.530284	−	0.847820i	$-0.322085\pi$
$31$	−2.61179	−	4.52376i	−0.469092	−	0.812491i	−0.999376	+	0.0353293i	$0.988752\pi$
$32$	5.23733			0.925838
$33$	−13.8203			−2.40581
$34$	0.148057	−	0.256443i	0.0253916	−	0.0439796i
$35$	0.162107	+	0.280778i	0.0274011	+	0.0474602i
$36$	4.01840	−	6.96007i	0.669733	−	1.16001i
$37$	−4.37338	+	7.57492i	−0.718980	+	1.24531i	0.242424	+	0.970170i	$0.422057\pi$
$37$	−4.37338	+	7.57492i	−0.718980	+	1.24531i	−0.961404	+	0.275140i	$0.911276\pi$
$38$	2.78702			0.452115
$39$	−4.89044	+	8.47049i	−0.783097	+	1.35636i
$40$	1.96352			0.310460
$41$	−0.970700	+	1.68130i	−0.151598	+	0.262575i	−0.931815	−	0.362934i	$-0.881775\pi$
$41$	−0.970700	+	1.68130i	−0.151598	+	0.262575i	0.780217	+	0.625509i	$0.215109\pi$
$42$	−0.243122	+	0.421100i	−0.0375145	+	0.0649771i
$43$	−2.43046	+	4.20967i	−0.370641	+	0.641969i	−0.989664	−	0.143404i	$-0.954195\pi$
$43$	−2.43046	+	4.20967i	−0.370641	+	0.641969i	0.619023	+	0.785373i	$0.287529\pi$
$44$	−4.27155	+	7.39855i	−0.643961	+	1.11537i
$45$	2.31779	−	4.01454i	0.345516	−	0.598452i
$46$	1.09712	+	1.90027i	0.161762	+	0.280180i
$47$	2.39356			0.349136			0.174568	−	0.984645i	$-0.444147\pi$
$47$	2.39356			0.349136			0.174568	+	0.984645i	$0.444147\pi$
$48$	−3.28044	−	5.68188i	−0.473490	−	0.820109i
$49$	3.44623	−	5.96905i	0.492319	−	0.852721i
$50$	−2.15101			−0.304198
$51$	−1.53549			−0.215012
$52$	3.02305	+	5.23607i	0.419221	+	0.726112i
$53$	1.39912	−	2.42335i	0.192184	−	0.332873i	−0.753790	−	0.657116i	$-0.771776\pi$
$53$	1.39912	−	2.42335i	0.192184	−	0.332873i	0.945974	+	0.324243i	$0.105110\pi$
$54$	2.50401			0.340753
$55$	−2.46381	+	4.26745i	−0.332220	+	0.575422i
$56$	0.325645	+	0.564034i	0.0435162	+	0.0753722i
$57$	−7.22601	−	12.5158i	−0.957108	−	1.65776i
$58$	1.56939	−	2.71825i	0.206070	−	0.356924i
$59$	6.81913	−	11.8111i	0.887775	−	1.53767i	0.0452750	−	0.998975i	$-0.485584\pi$
$59$	6.81913	−	11.8111i	0.887775	−	1.53767i	0.842500	−	0.538697i	$-0.181083\pi$
$60$	−2.34947	−	4.06940i	−0.303315	−	0.525358i
$61$	2.72107			0.348397			0.174199	−	0.984711i	$-0.444267\pi$
$61$	2.72107			0.348397			0.174199	+	0.984711i	$0.444267\pi$
$62$	−1.39662	−	2.41902i	−0.177371	−	0.307216i
$63$	1.53760			0.193720
$64$	−1.93161			−0.241451
$65$	1.74368	+	3.02014i	0.216277	+	0.374602i
$66$	−7.39025			−0.909677
$67$	4.67954	+	8.10521i	0.571697	+	0.990209i	0.996392	+	0.0848721i	$0.0270482\pi$
$67$	4.67954	+	8.10521i	0.571697	+	0.990209i	−0.424695	+	0.905337i	$0.639619\pi$
$68$	−0.474586	+	0.822006i	−0.0575520	+	0.0996829i
$69$	5.68909	−	9.85380i	0.684887	−	1.18626i
$70$	0.0866848	+	0.150142i	0.0103608	+	0.0179455i
$71$	5.95907	+	10.3214i	0.707211	+	1.22493i	0.965888	+	0.258961i	$0.0833802\pi$
$71$	5.95907	+	10.3214i	0.707211	+	1.22493i	−0.258677	+	0.965964i	$0.583286\pi$
$72$	4.65604	−	8.06450i	0.548720	−	0.950410i
$73$	−14.1420			−1.65520			−0.827599	−	0.561320i	$-0.810294\pi$
$73$	−14.1420			−1.65520			−0.827599	+	0.561320i	$0.810294\pi$
$74$	−2.33861	+	4.05059i	−0.271858	+	0.470872i
$75$	5.57699	+	9.65963i	0.643975	+	1.11540i
$76$	−8.93358			−1.02475
$77$	−1.63447			−0.186265
$78$	−2.61510	+	4.52948i	−0.296101	+	0.512863i
$79$	−7.78350	−	13.4814i	−0.875712	−	1.51678i	−0.856002	−	0.516973i	$-0.827059\pi$
$79$	−7.78350	−	13.4814i	−0.875712	−	1.51678i	−0.0197103	−	0.999806i	$-0.506274\pi$
$80$	−2.33927			−0.261538
$81$	0.540907	+	0.936878i	0.0601008	+	0.104098i
$82$	−0.519069	+	0.899054i	−0.0573216	+	0.0992839i
$83$	8.60664	−	14.9071i	0.944702	−	1.63627i	0.188355	−	0.982101i	$-0.439685\pi$
$83$	8.60664	−	14.9071i	0.944702	−	1.63627i	0.756347	−	0.654170i	$-0.226982\pi$
$84$	0.779308	−	1.34980i	0.0850295	−	0.147275i
$85$	−0.273739	+	0.474129i	−0.0296911	+	0.0514266i
$86$	−1.29965	+	2.25107i	−0.140145	+	0.242739i
$87$	−16.2760			−1.74497
$88$	−4.94936	+	8.57255i	−0.527604	+	0.913837i
$89$	16.4473			1.74341			0.871703	−	0.490035i	$-0.163016\pi$
$89$	16.4473			1.74341			0.871703	+	0.490035i	$0.163016\pi$
$90$	1.23941	−	2.14672i	0.130645	−	0.226284i
$91$	−0.578370	+	1.00177i	−0.0606296	+	0.105014i
$92$	−3.51674	−	6.09117i	−0.366645	−	0.635048i
$93$	−7.24214	+	12.5438i	−0.750975	+	1.30073i
$94$	1.27992			0.132014
$95$	−5.15285			−0.528671
$96$	−7.26119	−	12.5768i	−0.741092	−	1.28361i
$97$	0.114046	+	0.197534i	0.0115796	+	0.0200565i	0.871757	−	0.489938i	$-0.162981\pi$
$97$	0.114046	+	0.197534i	0.0115796	+	0.0200565i	−0.860178	+	0.509995i	$0.829647\pi$
$98$	1.84283	−	3.19187i	0.186154	−	0.322427i
$99$	11.6847	+	20.2385i	1.17436	+	2.03405i
$100$	6.89488			0.689488
$101$	2.75203	+	4.76665i	0.273837	+	0.474300i	0.969841	−	0.243738i	$-0.0783738\pi$
$101$	2.75203	+	4.76665i	0.273837	+	0.474300i	−0.696004	+	0.718038i	$0.745040\pi$
$102$	−0.821084			−0.0812995
$103$	−0.0417406	−	0.0722969i	−0.00411283	−	0.00712363i	0.863962	−	0.503558i	$-0.167976\pi$
$103$	−0.0417406	−	0.0722969i	−0.00411283	−	0.00712363i	−0.868074	+	0.496434i	$0.834642\pi$
$104$	3.50274	+	6.06693i	0.343472	+	0.594911i
$105$	0.449501	−	0.778559i	0.0438668	−	0.0759796i
$106$	0.748162	−	1.29585i	0.0726679	−	0.125864i
$107$	0.868944			0.0840040			0.0420020	−	0.999118i	$-0.486626\pi$
$107$	0.868944			0.0840040			0.0420020	+	0.999118i	$0.486626\pi$
$108$	−8.02640			−0.772341
$109$	−6.82826	+	11.8269i	−0.654029	+	1.13281i	0.328107	+	0.944640i	$0.393589\pi$
$109$	−6.82826	+	11.8269i	−0.654029	+	1.13281i	−0.982136	+	0.188171i	$0.939744\pi$
$110$	−1.31749	+	2.28196i	−0.125618	+	0.217577i
$111$	24.2536			2.30205
$112$	−0.387962	−	0.671970i	−0.0366590	−	0.0634952i
$113$	−1.28149	−	2.21960i	−0.120552	−	0.208802i	0.799433	−	0.600755i	$-0.205133\pi$
$113$	−1.28149	−	2.21960i	−0.120552	−	0.208802i	−0.919986	+	0.391952i	$0.871800\pi$
$114$	−3.86401	−	6.69267i	−0.361898	−	0.626826i
$115$	−2.02844	−	3.51336i	−0.189153	−	0.327622i
$116$	−5.03054	+	8.71315i	−0.467074	+	0.808995i
$117$	16.5389			1.52902
$118$	3.64644	−	6.31582i	0.335682	−	0.581418i
$119$	−0.181596			−0.0166468
$120$	−2.72229	−	4.71514i	−0.248510	−	0.430431i
$121$	−6.92085	−	11.9873i	−0.629168	−	1.08975i
$122$	1.45506			0.131735
$123$	5.38323			0.485390
$124$	4.47676	+	7.75397i	0.402025	+	0.696327i
$125$	8.92023			0.797850
$126$	0.822213			0.0732485
$127$	11.1078	+	1.90171i	0.985659	+	0.168750i
$127$	11.1078	+	1.90171i	0.985659	+	0.168750i
$128$	−11.5076			−1.01713
$129$	13.4786			1.18673
$130$	0.932409	+	1.61498i	0.0817777	+	0.141643i
$131$	−2.17852			−0.190339			−0.0951693	−	0.995461i	$-0.530339\pi$
$131$	−2.17852			−0.190339			−0.0951693	+	0.995461i	$0.530339\pi$
$132$	23.6888			2.06185
$133$	−0.854587	−	1.48019i	−0.0741021	−	0.128349i
$134$	2.50233	+	4.33415i	0.216168	+	0.374414i
$135$	−4.62959			−0.398452
$136$	−0.549893	+	0.952443i	−0.0471529	+	0.0816713i
$137$	5.25091			0.448615			0.224308	−	0.974518i	$-0.427988\pi$
$137$	5.25091			0.448615			0.224308	+	0.974518i	$0.427988\pi$
$138$	3.04217	−	5.26919i	0.258967	−	0.448543i
$139$	4.89732	+	8.48241i	0.415386	+	0.719469i	0.995469	−	0.0950882i	$-0.0303133\pi$
$139$	4.89732	+	8.48241i	0.415386	+	0.719469i	−0.580083	+	0.814557i	$0.696980\pi$
$140$	−0.277861	−	0.481270i	−0.0234836	−	0.0406747i
$141$	−3.31850	−	5.74781i	−0.279468	−	0.484053i
$142$	3.18653	+	5.51924i	0.267408	+	0.463164i
$143$	−17.5809			−1.47019
$144$	−5.54704	+	9.60776i	−0.462253	+	0.800646i
$145$	−2.90159	+	5.02570i	−0.240964	+	0.417362i
$146$	−7.56226			−0.625857
$147$	−19.1118			−1.57632
$148$	7.49623	−	12.9838i	0.616186	−	1.06727i
$149$	−7.82862	+	13.5596i	−0.641346	+	1.11084i	0.343787	+	0.939048i	$0.388290\pi$
$149$	−7.82862	+	13.5596i	−0.641346	+	1.11084i	−0.985133	+	0.171795i	$0.945043\pi$
$150$	2.98222	+	5.16536i	0.243497	+	0.421750i
$151$	7.92915	+	13.7337i	0.645265	+	1.11763i	0.984240	+	0.176836i	$0.0565863\pi$
$151$	7.92915	+	13.7337i	0.645265	+	1.11763i	−0.338975	+	0.940795i	$0.610080\pi$
$152$	−10.3512			−0.839590
$153$	1.29822	+	2.24858i	0.104955	+	0.181787i
$154$	−0.874011			−0.0704298
$155$	2.58217	+	4.47246i	0.207405	+	0.359236i
$156$	8.38248	−	14.5189i	0.671136	−	1.16244i
$157$	−4.35686	−	7.54630i	−0.347715	−	0.602260i	0.638128	−	0.769930i	$-0.279709\pi$
$157$	−4.35686	−	7.54630i	−0.347715	−	0.602260i	−0.985843	+	0.167670i	$0.946376\pi$
$158$	−4.16213	−	7.20901i	−0.331121	−	0.573518i
$159$	−7.75914			−0.615340
$160$	−5.17794			−0.409352
$161$	0.672823	−	1.16536i	0.0530259	−	0.0918436i
$162$	0.289243	+	0.500984i	0.0227251	+	0.0393610i
$163$	4.11435	−	7.12626i	0.322260	−	0.558171i	−0.658694	−	0.752411i	$-0.728891\pi$
$163$	4.11435	−	7.12626i	0.322260	−	0.558171i	0.980954	+	0.194240i	$0.0622240\pi$
$164$	1.66383	−	2.88185i	0.129924	−	0.225034i
$165$	13.6636			1.06371
$166$	4.60229	−	7.97140i	0.357207	−	0.618701i
$167$	3.71905			0.287789			0.143894	−	0.989593i	$-0.454037\pi$
$167$	3.71905			0.287789			0.143894	+	0.989593i	$0.454037\pi$
$168$	0.902969	−	1.56399i	0.0696656	−	0.120664i
$169$	0.278873	−	0.483023i	0.0214518	−	0.0371556i
$170$	−0.146378	+	0.253535i	−0.0112267	+	0.0194452i
$171$	−12.2188	+	21.1636i	−0.934394	+	1.61842i
$172$	4.16594	−	7.21562i	0.317650	−	0.550186i
$173$	−0.0741552	−	0.128441i	−0.00563791	−	0.00976515i	0.863193	−	0.504875i	$-0.168461\pi$
$173$	−0.0741552	−	0.128441i	−0.00563791	−	0.00976515i	−0.868831	+	0.495109i	$0.835128\pi$
$174$	−8.70337			−0.659801
$175$	0.659565	+	1.14240i	0.0498584	+	0.0863573i
$176$	5.89650	−	10.2130i	0.444465	−	0.769836i
$177$	−37.8170			−2.84250
$178$	8.79495			0.659210
$179$	−7.13397	−	12.3564i	−0.533218	−	0.923561i	−0.999247	−	0.0387914i	$-0.987649\pi$
$179$	−7.13397	−	12.3564i	−0.533218	−	0.923561i	0.466029	−	0.884769i	$-0.345684\pi$
$180$	−3.97283	+	6.88114i	−0.296117	+	0.512890i
$181$	−11.7328			−0.872091			−0.436045	−	0.899925i	$-0.643621\pi$
$181$	−11.7328			−0.872091			−0.436045	+	0.899925i	$0.643621\pi$
$182$	−0.309276	+	0.535681i	−0.0229250	+	0.0397073i
$183$	−3.77257	−	6.53429i	−0.278877	−	0.483029i
$184$	−4.07478	−	7.05772i	−0.300396	−	0.520302i
$185$	4.32379	−	7.48902i	0.317891	−	0.550604i
$186$	−3.87264	+	6.70761i	−0.283956	+	0.491826i
$187$	−1.38000	−	2.39024i	−0.100916	−	0.174791i
$188$	−4.10269			−0.299220
$189$	−0.767807	−	1.32988i	−0.0558497	−	0.0967345i
$190$	−2.75542			−0.199899
$191$	−25.5857			−1.85132			−0.925658	−	0.378360i	$-0.876488\pi$
$191$	−25.5857			−1.85132			−0.925658	+	0.378360i	$0.876488\pi$
$192$	2.67804	+	4.63851i	0.193271	+	0.334755i
$193$	7.38295			0.531436			0.265718	−	0.964051i	$-0.414391\pi$
$193$	7.38295			0.531436			0.265718	+	0.964051i	$0.414391\pi$
$194$	0.0609847	+	0.105629i	0.00437845	+	0.00758369i
$195$	4.83498	−	8.37443i	0.346240	−	0.599705i
$196$	−5.90703	+	10.2313i	−0.421931	+	0.730806i
$197$	4.17840	+	7.23721i	0.297699	+	0.515630i	0.975609	−	0.219515i	$-0.0704475\pi$
$197$	4.17840	+	7.23721i	0.297699	+	0.515630i	−0.677910	+	0.735145i	$0.737114\pi$
$198$	6.24826	+	10.8223i	0.444044	+	0.769107i
$199$	−2.30835	+	3.99818i	−0.163635	+	0.283423i	−0.936170	−	0.351549i	$-0.885655\pi$
$199$	−2.30835	+	3.99818i	−0.163635	+	0.283423i	0.772535	+	0.634972i	$0.218988\pi$
$200$	7.98896			0.564905
$201$	12.9757	−	22.4746i	0.915237	−	1.58524i
$202$	1.47161	+	2.54890i	0.103542	+	0.179340i
$203$	−1.92489			−0.135101
$204$	2.63192			0.184271
$205$	0.959692	−	1.66224i	0.0670278	−	0.116096i
$206$	−0.0223203	−	0.0386598i	−0.00155513	−	0.00269356i
$207$	−19.2399			−1.33727
$208$	−4.17304	−	7.22792i	−0.289349	−	0.501166i
$209$	12.9886	−	22.4968i	0.898438	−	1.55614i
$210$	0.240365	−	0.416324i	0.0165868	−	0.0287291i
$211$	12.0389	−	20.8521i	0.828795	−	1.43552i	−0.0701882	−	0.997534i	$-0.522360\pi$
$211$	12.0389	−	20.8521i	0.828795	−	1.43552i	0.898984	−	0.437982i	$-0.144307\pi$
$212$	−2.39817	+	4.15376i	−0.164707	+	0.285281i
$213$	16.5237	−	28.6198i	1.13218	−	1.96100i
$214$	0.464656			0.0317633
$215$	2.40289	−	4.16193i	0.163876	−	0.283842i
$216$	−9.30004			−0.632787
$217$	−0.856495	+	1.48349i	−0.0581426	+	0.100706i
$218$	−3.65132	+	6.32428i	−0.247299	+	0.428334i
$219$	19.6069	+	33.9602i	1.32491	+	2.29482i
$220$	4.22311	−	7.31464i	0.284722	−	0.493153i
$221$	−1.95330			−0.131393
$222$	12.9693			0.870441
$223$	1.07620	+	1.86403i	0.0720675	+	0.124825i	0.899807	−	0.436288i	$-0.143707\pi$
$223$	1.07620	+	1.86403i	0.0720675	+	0.124825i	−0.827740	+	0.561112i	$0.810374\pi$
$224$	−0.858748	−	1.48740i	−0.0573775	−	0.0993808i
$225$	9.43039	−	16.3339i	0.628693	−	1.08893i
$226$	−0.685258	−	1.18690i	−0.0455827	−	0.0789515i
$227$	−13.5371			−0.898490			−0.449245	−	0.893408i	$-0.648307\pi$
$227$	−13.5371			−0.898490			−0.449245	+	0.893408i	$0.648307\pi$
$228$	12.3858	+	21.4528i	0.820269	+	1.42075i
$229$	6.63882			0.438706			0.219353	−	0.975646i	$-0.429605\pi$
$229$	6.63882			0.438706			0.219353	+	0.975646i	$0.429605\pi$
$230$	−1.08468	−	1.87872i	−0.0715218	−	0.123879i
$231$	2.26608	+	3.92496i	0.149097	+	0.258244i
$232$	−5.82878	+	10.0958i	−0.382678	+	0.662819i
$233$	3.78356	−	6.55333i	0.247870	−	0.429323i	−0.715065	−	0.699058i	$-0.753603\pi$
$233$	3.78356	−	6.55333i	0.247870	−	0.429323i	0.962934	+	0.269735i	$0.0869362\pi$
$234$	8.84398			0.578149
$235$	−2.36641			−0.154368
$236$	−11.6884	+	20.2449i	−0.760848	+	1.31783i
$237$	−21.5826	+	37.3821i	−1.40194	+	2.42823i
$238$	−0.0971059			−0.00629444
$239$	2.10745	+	3.65021i	0.136320	+	0.236112i	0.926101	−	0.377276i	$-0.123139\pi$
$239$	2.10745	+	3.65021i	0.136320	+	0.236112i	−0.789781	+	0.613389i	$0.789806\pi$
$240$	3.24323	+	5.61745i	0.209350	+	0.362605i
$241$	−0.860812	−	1.49097i	−0.0554498	−	0.0960418i	0.836968	−	0.547252i	$-0.184326\pi$
$241$	−0.860812	−	1.49097i	−0.0554498	−	0.0960418i	−0.892418	+	0.451210i	$0.850993\pi$
$242$	−3.70084	−	6.41004i	−0.237899	−	0.412053i
$243$	8.52390	−	14.7638i	0.546809	−	0.947100i
$244$	−4.66407			−0.298586
$245$	−3.40715	+	5.90135i	−0.217675	+	0.377024i
$246$	2.87861			0.183534
$247$	−9.19221	−	15.9214i	−0.584886	−	1.01305i
$248$	5.18713	+	8.98438i	0.329383	+	0.570509i
$249$	−47.7301			−3.02477
$250$	4.76998			0.301680
$251$	9.86081	+	17.0794i	0.622409	+	1.07804i	0.989036	+	0.147676i	$0.0471793\pi$
$251$	9.86081	+	17.0794i	0.622409	+	1.07804i	−0.366627	+	0.930368i	$0.619487\pi$
$252$	−2.63554			−0.166023
$253$	20.4520			1.28581
$254$	5.93976	+	1.01692i	0.372694	+	0.0638070i
$255$	1.51808			0.0950658
$256$	−2.29030			−0.143144
$257$	−0.578769	−	1.00246i	−0.0361026	−	0.0625316i	0.847410	−	0.530940i	$-0.178161\pi$
$257$	−0.578769	−	1.00246i	−0.0361026	−	0.0625316i	−0.883512	+	0.468408i	$0.844828\pi$
$258$	7.20752			0.448721
$259$	2.86836			0.178231
$260$	−2.98876	−	5.17669i	−0.185355	−	0.321045i
$261$	13.7609	+	23.8346i	0.851779	+	1.47532i
$262$	−1.16494			−0.0719701
$263$	−4.26919	+	7.39445i	−0.263249	+	0.455961i	−0.967103	−	0.254383i	$-0.918128\pi$
$263$	−4.26919	+	7.39445i	−0.263249	+	0.455961i	0.703854	+	0.710345i	$0.251461\pi$
$264$	27.4478			1.68930
$265$	−1.38325	+	2.39587i	−0.0849727	+	0.147177i
$266$	−0.456979	−	0.791511i	−0.0280192	−	0.0485307i
$267$	−22.8030	−	39.4959i	−1.39552	−	2.41711i
$268$	−8.02100	−	13.8928i	−0.489961	−	0.848637i
$269$	9.20301	+	15.9401i	0.561118	+	0.971884i	0.997399	+	0.0720741i	$0.0229618\pi$
$269$	9.20301	+	15.9401i	0.561118	+	0.971884i	−0.436282	+	0.899810i	$0.643705\pi$
$270$	−2.47561			−0.150661
$271$	1.85465	−	3.21235i	0.112662	−	0.195137i	−0.804181	−	0.594385i	$-0.797396\pi$
$271$	1.85465	−	3.21235i	0.112662	−	0.195137i	0.916843	+	0.399248i	$0.130729\pi$
$272$	0.655123	−	1.13471i	0.0397227	−	0.0688017i
$273$	3.20748			0.194125
$274$	2.80786			0.169629
$275$	−10.0245	+	17.3629i	−0.604500	+	1.04702i
$276$	−9.75143	+	16.8900i	−0.586967	+	1.01666i
$277$	10.9593	+	18.9821i	0.658481	+	1.14052i	0.981009	+	0.193963i	$0.0621341\pi$
$277$	10.9593	+	18.9821i	0.658481	+	1.14052i	−0.322528	+	0.946560i	$0.604533\pi$
$278$	2.61878	+	4.53586i	0.157064	+	0.272043i
$279$	24.4921			1.46631
$280$	−0.321952	−	0.557638i	−0.0192403	−	0.0333252i
$281$	−30.2868			−1.80676			−0.903378	−	0.428845i	$-0.858921\pi$
$281$	−30.2868			−1.80676			−0.903378	+	0.428845i	$0.858921\pi$
$282$	−1.77453	−	3.07357i	−0.105671	−	0.183028i
$283$	9.66360	−	16.7379i	0.574442	−	0.994962i	−0.421660	−	0.906754i	$-0.638553\pi$
$283$	9.66360	−	16.7379i	0.574442	−	0.994962i	0.996102	−	0.0882082i	$-0.0281141\pi$
$284$	−10.2142	−	17.6915i	−0.606100	−	1.04980i
$285$	7.14406	+	12.3739i	0.423178	+	0.732965i
$286$	−9.40114			−0.555901
$287$	0.636650			0.0375803
$288$	−12.2783	+	21.2666i	−0.723505	+	1.25315i
$289$	8.34668	+	14.4569i	0.490981	+	0.850404i
$290$	−1.55159	+	2.68743i	−0.0911124	+	0.157811i
$291$	0.316234	−	0.547734i	0.0185380	−	0.0321087i
$292$	24.2402			1.41855
$293$	8.28926	−	14.3574i	0.484264	−	0.838770i	−0.515573	−	0.856846i	$-0.672421\pi$
$293$	8.28926	−	14.3574i	0.484264	−	0.838770i	0.999837	+	0.0180761i	$0.00575410\pi$
$294$	−10.2198			−0.596031
$295$	−6.74180	+	11.6771i	−0.392523	+	0.679869i
$296$	8.68573	−	15.0441i	0.504848	−	0.874422i
$297$	11.6696	−	20.2124i	0.677140	−	1.17284i
$298$	−4.18625	+	7.25080i	−0.242503	+	0.420028i
$299$	7.23710	−	12.5350i	0.418532	−	0.724919i
$300$	−9.55927	−	16.5571i	−0.551905	−	0.955927i
$301$	1.59406			0.0918799
$302$	4.24001	+	7.34391i	0.243985	+	0.422595i
$303$	7.63099	−	13.2173i	0.438389	−	0.759312i
$304$	12.3320			0.707289
$305$	−2.69021			−0.154041
$306$	0.694205	+	1.20240i	0.0396850	+	0.0687365i
$307$	6.77125	−	11.7281i	0.386456	−	0.669361i	−0.605514	−	0.795834i	$-0.707033\pi$
$307$	6.77125	−	11.7281i	0.386456	−	0.669361i	0.991970	+	0.126474i	$0.0403659\pi$
$308$	2.80157			0.159634
$309$	−0.115741	+	0.200469i	−0.00658428	+	0.0114043i
$310$	1.38078	+	2.39159i	0.0784233	+	0.135833i
$311$	3.90640	+	6.76608i	0.221511	+	0.383669i	0.955267	−	0.295744i	$-0.0955677\pi$
$311$	3.90640	+	6.76608i	0.221511	+	0.383669i	−0.733756	+	0.679413i	$0.762234\pi$
$312$	9.71262	−	16.8227i	0.549869	−	0.952401i
$313$	−16.8469	+	29.1796i	−0.952242	+	1.64933i	−0.211684	+	0.977338i	$0.567895\pi$
$313$	−16.8469	+	29.1796i	−0.952242	+	1.64933i	−0.740557	+	0.671993i	$0.765438\pi$
$314$	−2.32977	−	4.03529i	−0.131477	−	0.227724i
$315$	−1.52016			−0.0856516
$316$	13.3414	+	23.1079i	0.750510	+	1.29992i
$317$	−2.08467			−0.117087			−0.0585433	−	0.998285i	$-0.518646\pi$
$317$	−2.08467			−0.117087			−0.0585433	+	0.998285i	$0.518646\pi$
$318$	−4.14910			−0.232670
$319$	−14.6278	−	25.3362i	−0.819001	−	1.41855i
$320$	1.90971			0.106756
$321$	−1.20473	−	2.08665i	−0.0672415	−	0.116466i
$322$	0.359783	−	0.623163i	0.0200499	−	0.0347275i
$323$	1.44308	−	2.49948i	0.0802950	−	0.139075i
$324$	−0.927145	−	1.60586i	−0.0515081	−	0.0892146i
$325$	7.09449	+	12.2880i	0.393532	+	0.681617i
$326$	2.20009	−	3.81067i	0.121852	−	0.211054i
$327$	37.8676			2.09409
$328$	1.92785	−	3.33914i	0.106448	−	0.184373i
$329$	−0.392464	−	0.679768i	−0.0216372	−	0.0374768i
$330$	7.30644			0.402206
$331$	19.9624			1.09723			0.548617	−	0.836074i	$-0.315155\pi$
$331$	19.9624			1.09723			0.548617	+	0.836074i	$0.315155\pi$
$332$	−14.7523	+	25.5517i	−0.809636	+	1.40233i
$333$	−20.5057	−	35.5170i	−1.12371	−	1.94632i
$334$	1.98871			0.108818
$335$	−4.62648	−	8.01329i	−0.252771	−	0.437813i
$336$	−1.07577	+	1.86328i	−0.0586878	+	0.101650i
$337$	−11.6157	+	20.1190i	−0.632747	+	1.09595i	0.354241	+	0.935154i	$0.384739\pi$
$337$	−11.6157	+	20.1190i	−0.632747	+	1.09595i	−0.986988	+	0.160796i	$0.948594\pi$
$338$	0.149124	−	0.258290i	0.00811127	−	0.0140491i
$339$	−3.55338	+	6.15464i	−0.192993	+	0.334274i
$340$	0.469204	−	0.812685i	0.0254461	−	0.0440740i
$341$	−26.0351			−1.40988
$342$	−6.53384	+	11.3169i	−0.353310	+	0.611950i
$343$	−4.55580			−0.245990
$344$	4.82699	−	8.36059i	0.260254	−	0.450773i
$345$	−5.62458	+	9.74206i	−0.302817	+	0.524495i
$346$	−0.0396535	−	0.0686819i	−0.00213179	−	0.00369236i
$347$	9.62419	−	16.6696i	0.516653	−	0.894870i	−0.483160	−	0.875532i	$-0.660511\pi$
$347$	9.62419	−	16.6696i	0.516653	−	0.894870i	0.999813	−	0.0193378i	$-0.00615578\pi$
$348$	27.8980			1.49549
$349$	−25.8327			−1.38280			−0.691398	−	0.722475i	$-0.743005\pi$
$349$	−25.8327			−1.38280			−0.691398	+	0.722475i	$0.743005\pi$
$350$	0.352694	+	0.610884i	0.0188523	+	0.0326531i
$351$	−8.25877	−	14.3046i	−0.440821	−	0.763524i
$352$	13.0518	−	22.6064i	0.695663	−	1.20492i
$353$	10.8671	+	18.8224i	0.578399	+	1.00182i	0.995663	+	0.0930309i	$0.0296555\pi$
$353$	10.8671	+	18.8224i	0.578399	+	1.00182i	−0.417264	+	0.908785i	$0.637011\pi$
$354$	−20.2221			−1.07479
$355$	−5.89149	−	10.2044i	−0.312688	−	0.541591i
$356$	−28.1915			−1.49415
$357$	0.251770	+	0.436078i	0.0133251	+	0.0230797i
$358$	−3.81480	−	6.60742i	−0.201618	−	0.349213i
$359$	−5.77003	+	9.99399i	−0.304531	+	0.527463i	−0.977157	−	0.212520i	$-0.931833\pi$
$359$	−5.77003	+	9.99399i	−0.304531	+	0.527463i	0.672626	+	0.739983i	$0.265166\pi$
$360$	−4.60324	+	7.97304i	−0.242612	+	0.420216i
$361$	8.16443			0.429707
$362$	−6.27395			−0.329752
$363$	−19.1906	+	33.2390i	−1.00724	+	1.74460i
$364$	0.991358	−	1.71708i	0.0519613	−	0.0899996i
$365$	13.9816			0.731833
$366$	−2.01733	−	3.49413i	−0.105448	−	0.182641i
$367$	1.35333	+	2.34403i	0.0706431	+	0.122357i	0.899183	−	0.437572i	$-0.144162\pi$
$367$	1.35333	+	2.34403i	0.0706431	+	0.122357i	−0.828540	+	0.559930i	$0.810828\pi$
$368$	4.85454	+	8.40832i	0.253061	+	0.438314i
$369$	−4.55138	−	7.88322i	−0.236935	−	0.410384i
$370$	2.31209	−	4.00466i	0.120200	−	0.208192i
$371$	−0.917638			−0.0476414
$372$	12.4134	−	21.5007i	0.643606	−	1.11476i
$373$	9.01091			0.466567			0.233284	−	0.972409i	$-0.425053\pi$
$373$	9.01091			0.466567			0.233284	+	0.972409i	$0.425053\pi$
$374$	−0.737939	−	1.27815i	−0.0381579	−	0.0660914i
$375$	−12.3673	−	21.4208i	−0.638644	−	1.10616i
$376$	−4.75371			−0.245154
$377$	−20.7047			−1.06635
$378$	−0.410575	−	0.711136i	−0.0211177	−	0.0365769i
$379$	−17.0083			−0.873655			−0.436828	−	0.899545i	$-0.643898\pi$
$379$	−17.0083			−0.873655			−0.436828	+	0.899545i	$0.643898\pi$
$380$	8.83227			0.453086
$381$	−10.8335	−	29.3105i	−0.555017	−	1.50162i
$382$	−13.6816			−0.700013
$383$	−7.66327			−0.391575			−0.195787	−	0.980646i	$-0.562726\pi$
$383$	−7.66327			−0.391575			−0.195787	+	0.980646i	$0.562726\pi$
$384$	15.9544	+	27.6339i	0.814171	+	1.41019i
$385$	1.61593			0.0823556
$386$	3.94794			0.200945
$387$	−11.3958	−	19.7381i	−0.579282	−	1.00335i
$388$	−0.195482	−	0.338584i	−0.00992407	−	0.0171890i
$389$	26.6252			1.34995			0.674977	−	0.737839i	$-0.264154\pi$
$389$	26.6252			1.34995			0.674977	+	0.737839i	$0.264154\pi$
$390$	2.58544	−	4.47812i	0.130919	−	0.226758i
$391$	2.27229			0.114915
$392$	−6.84436	+	11.8548i	−0.345692	+	0.598757i
$393$	3.02037	+	5.23144i	0.152358	+	0.263891i
$394$	2.23435	+	3.87000i	0.112565	+	0.194968i
$395$	7.69523	+	13.3285i	0.387189	+	0.670631i
$396$	−20.0283	−	34.6900i	−1.00646	−	1.74324i
$397$	−34.4410			−1.72854			−0.864271	−	0.503026i	$-0.832220\pi$
$397$	−34.4410			−1.72854			−0.864271	+	0.503026i	$0.832220\pi$
$398$	−1.23436	+	2.13797i	−0.0618728	+	0.107167i
$399$	−2.36965	+	4.10436i	−0.118631	+	0.205475i
$400$	−9.51777			−0.475888
$401$	−22.0330			−1.10028			−0.550138	−	0.835074i	$-0.685425\pi$
$401$	−22.0330			−1.10028			−0.550138	+	0.835074i	$0.685425\pi$
$402$	6.93860	−	12.0180i	0.346066	−	0.599404i
$403$	−9.21273	+	15.9569i	−0.458919	+	0.794870i
$404$	−4.71713	−	8.17031i	−0.234686	−	0.406488i
$405$	−0.534773	−	0.926254i	−0.0265731	−	0.0460259i
$406$	−1.02931			−0.0510837
$407$	21.7976	+	37.7545i	1.08047	+	1.87142i
$408$	3.04955			0.150975
$409$	2.87684	+	4.98283i	0.142251	+	0.246385i	0.928344	−	0.371723i	$-0.121233\pi$
$409$	2.87684	+	4.98283i	0.142251	+	0.246385i	−0.786093	+	0.618108i	$0.787899\pi$
$410$	0.513183	−	0.888859i	0.0253443	−	0.0438976i
$411$	−7.28002	−	12.6094i	−0.359097	−	0.621974i
$412$	0.0715458	+	0.123921i	0.00352481	+	0.00610515i
$413$	−4.47244			−0.220075
$414$	−10.2883			−0.505642
$415$	−8.50904	+	14.7381i	−0.417692	+	0.723464i
$416$	−9.23697	−	15.9989i	−0.452880	−	0.784410i
$417$	13.5796	−	23.5206i	0.664996	−	1.15181i
$418$	6.94546	−	12.0299i	0.339714	−	0.588401i
$419$	−8.80865			−0.430331			−0.215165	−	0.976578i	$-0.569029\pi$
$419$	−8.80865			−0.430331			−0.215165	+	0.976578i	$0.569029\pi$
$420$	−0.770470	+	1.33449i	−0.0375951	+	0.0651166i
$421$	35.0969			1.71052			0.855259	−	0.518202i	$-0.173398\pi$
$421$	35.0969			1.71052			0.855259	+	0.518202i	$0.173398\pi$
$422$	6.43767	−	11.1504i	0.313381	−	0.542792i
$423$	−5.61141	+	9.71924i	−0.272836	+	0.472566i
$424$	−2.77872	+	4.81288i	−0.134946	+	0.233734i
$425$	−1.11376	+	1.92909i	−0.0540252	+	0.0935745i
$426$	8.83581	−	15.3041i	0.428097	−	0.741485i
$427$	−0.446165	−	0.772781i	−0.0215914	−	0.0373975i
$428$	−1.48942			−0.0719938
$429$	24.3746	+	42.2181i	1.17682	+	2.03831i
$430$	1.28492	−	2.22554i	0.0619642	−	0.107325i
$431$	24.2442			1.16780			0.583902	−	0.811824i	$-0.301525\pi$
$431$	24.2442			1.16780			0.583902	+	0.811824i	$0.301525\pi$
$432$	11.0797			0.533074
$433$	4.91126	+	8.50655i	0.236020	+	0.408799i	0.959569	−	0.281475i	$-0.0908236\pi$
$433$	4.91126	+	8.50655i	0.236020	+	0.408799i	−0.723549	+	0.690273i	$0.757490\pi$
$434$	−0.457999	+	0.793278i	−0.0219847	+	0.0380786i
$435$	16.0914			0.771524
$436$	11.7040	−	20.2720i	0.560521	−	0.970851i
$437$	10.6934	+	18.5215i	0.511534	+	0.886003i
$438$	10.4845	+	18.1598i	0.500971	+	0.867707i
$439$	12.9761	−	22.4752i	0.619315	−	1.07268i	−0.370296	−	0.928914i	$-0.620744\pi$
$439$	12.9761	−	22.4752i	0.619315	−	1.07268i	0.989611	−	0.143771i	$-0.0459228\pi$
$440$	4.89324	−	8.47533i	0.233276	−	0.404046i
$441$	16.1585	+	27.9874i	0.769454	+	1.33273i
$442$	−1.04450			−0.0496819
$443$	−16.2113	−	28.0789i	−0.770224	−	1.33407i	−0.937440	−	0.348147i	$-0.886811\pi$
$443$	−16.2113	−	28.0789i	−0.770224	−	1.33407i	0.167216	−	0.985920i	$-0.446522\pi$
$444$	−41.5720			−1.97292
$445$	−16.2607			−0.770833
$446$	0.575483	+	0.996765i	0.0272499	+	0.0471982i
$447$	43.4154			2.05348
$448$	0.316720	+	0.548575i	0.0149636	+	0.0259177i
$449$	6.33779	−	10.9774i	0.299099	−	0.518054i	−0.676831	−	0.736138i	$-0.736647\pi$
$449$	6.33779	−	10.9774i	0.299099	−	0.518054i	0.975930	+	0.218084i	$0.0699806\pi$
$450$	5.04278	−	8.73435i	0.237719	−	0.411741i
$451$	4.83811	+	8.37985i	0.227818	+	0.394592i
$452$	2.19654	+	3.80452i	0.103317	+	0.178949i
$453$	21.9864	−	38.0816i	1.03301	−	1.78923i
$454$	−7.23880			−0.339734
$455$	0.571811	−	0.990405i	0.0268069	−	0.0464309i
$456$	14.3512	+	24.8569i	0.672055	+	1.16403i
$457$	−20.3814			−0.953403			−0.476701	−	0.879065i	$-0.658168\pi$
$457$	−20.3814			−0.953403			−0.476701	+	0.879065i	$0.658168\pi$
$458$	3.55002			0.165882
$459$	1.29654	−	2.24567i	0.0605172	−	0.104819i
$460$	3.47686	+	6.02209i	0.162109	+	0.280782i
$461$	11.5167			0.536384			0.268192	−	0.963365i	$-0.413574\pi$
$461$	11.5167			0.536384			0.268192	+	0.963365i	$0.413574\pi$
$462$	1.21176	+	2.09882i	0.0563760	+	0.0976460i
$463$	−11.0325	+	19.1088i	−0.512723	+	0.888062i	0.487169	+	0.873308i	$0.338030\pi$
$463$	−11.0325	+	19.1088i	−0.512723	+	0.888062i	−0.999891	+	0.0147536i	$0.995304\pi$
$464$	6.94421	−	12.0277i	0.322377	−	0.558373i
$465$	7.16001	−	12.4015i	0.332037	−	0.575106i
$466$	2.02321	−	3.50431i	0.0937235	−	0.162334i
$467$	−5.23007	+	9.05875i	−0.242019	+	0.419189i	−0.961289	−	0.275541i	$-0.911143\pi$
$467$	−5.23007	+	9.05875i	−0.242019	+	0.419189i	0.719270	+	0.694730i	$0.244476\pi$
$468$	−28.3487			−1.31042
$469$	1.53458	−	2.65797i	0.0708603	−	0.122734i
$470$	−1.26541			−0.0583690
$471$	−12.0810	+	20.9248i	−0.556661	+	0.964166i
$472$	−13.5431	+	23.4573i	−0.623371	+	1.07971i
$473$	12.1137	+	20.9816i	0.556991	+	0.964736i
$474$	−11.5410	+	19.9896i	−0.530096	+	0.918153i
$475$	−20.9653			−0.961956
$476$	0.311265			0.0142668
$477$	6.56014	+	11.3625i	0.300368	+	0.520253i
$478$	1.12693	+	1.95190i	0.0515446	+	0.0892779i
$479$	5.93788	−	10.2847i	0.271308	−	0.469920i	−0.697889	−	0.716206i	$-0.745877\pi$
$479$	5.93788	−	10.2847i	0.271308	−	0.469920i	0.969197	+	0.246286i	$0.0792103\pi$
$480$	7.17885	+	12.4341i	0.327668	+	0.567538i
$481$	30.8530			1.40677
$482$	−0.460308	−	0.797277i	−0.0209664	−	0.0363149i
$483$	−3.73129			−0.169780
$484$	11.8627	+	20.5469i	0.539215	+	0.933948i
$485$	−0.112753	−	0.195294i	−0.00511984	−	0.00886783i
$486$	4.55805	−	7.89477i	0.206757	−	0.358114i
$487$	19.3917	−	33.5874i	0.878722	−	1.52199i	0.0259775	−	0.999663i	$-0.491730\pi$
$487$	19.3917	−	33.5874i	0.878722	−	1.52199i	0.852744	−	0.522328i	$-0.174937\pi$
$488$	−5.40416			−0.244635
$489$	−22.8170			−1.03182
$490$	−1.82193	+	3.15567i	−0.0823063	+	0.142559i
$491$	−10.0353	+	17.3816i	−0.452886	+	0.784421i	−0.998564	−	0.0535736i	$-0.982939\pi$
$491$	−10.0353	+	17.3816i	−0.452886	+	0.784421i	0.545678	+	0.837995i	$0.316272\pi$
$492$	−9.22717			−0.415993
$493$	−1.62521	−	2.81494i	−0.0731957	−	0.126779i
$494$	−4.91541	−	8.51375i	−0.221155	−	0.383052i
$495$	−11.5522	−	20.0090i	−0.519234	−	0.899339i
$496$	−6.17977	−	10.7037i	−0.277480	−	0.480609i
$497$	1.95418	−	3.38474i	0.0876569	−	0.151826i
$498$	−25.5230			−1.14371
$499$	3.86675	−	6.69740i	0.173099	−	0.299817i	−0.766402	−	0.642361i	$-0.777955\pi$
$499$	3.86675	−	6.69740i	0.173099	−	0.299817i	0.939502	+	0.342544i	$0.111288\pi$
$500$	−15.2898			−0.683780
$501$	−5.15620	−	8.93080i	−0.230362	−	0.398999i
$502$	5.27294	+	9.13300i	0.235343	+	0.407626i
$503$	−17.7725			−0.792435			−0.396217	−	0.918157i	$-0.629677\pi$
$503$	−17.7725			−0.792435			−0.396217	+	0.918157i	$0.629677\pi$
$504$	−3.05374			−0.136025
$505$	−2.72082	−	4.71260i	−0.121075	−	0.209708i
$506$	10.9364			0.486184
$507$	−1.54655			−0.0686849
$508$	−19.0394	−	3.25964i	−0.844737	−	0.144623i
$509$	29.0603			1.28808			0.644038	−	0.764993i	$-0.277258\pi$
$509$	29.0603			1.28808			0.644038	+	0.764993i	$0.277258\pi$
$510$	0.811773			0.0359459
$511$	2.31882	+	4.01632i	0.102579	+	0.177671i
$512$	21.7904			0.963009
$513$	24.4060			1.07755
$514$	−0.309489	−	0.536051i	−0.0136510	−	0.0236442i
$515$	0.0412673	+	0.0714771i	0.00181845	+	0.00314966i
$516$	−23.1031			−1.01706
$517$	5.96492	−	10.3315i	0.262337	−	0.454381i
$518$	1.53382			0.0673921
$519$	−0.205622	+	0.356148i	−0.00902580	+	0.0156332i
$520$	−3.46302	−	5.99813i	−0.151863	−	0.263035i
$521$	2.80308	+	4.85507i	0.122805	+	0.212704i	0.920873	−	0.389863i	$-0.127478\pi$
$521$	2.80308	+	4.85507i	0.122805	+	0.212704i	−0.798068	+	0.602568i	$0.794144\pi$
$522$	7.35847	+	12.7452i	0.322071	+	0.557844i
$523$	6.88476	+	11.9248i	0.301049	+	0.521433i	0.976374	−	0.216088i	$-0.0693297\pi$
$523$	6.88476	+	11.9248i	0.301049	+	0.521433i	−0.675324	+	0.737521i	$0.735996\pi$
$524$	3.73411			0.163125
$525$	1.82888	−	3.16772i	0.0798190	−	0.138251i
$526$	−2.28289	+	3.95409i	−0.0995388	+	0.172406i
$527$	−2.89260			−0.126004
$528$	−32.7003			−1.42310
$529$	3.08101	−	5.33646i	0.133957	−	0.232020i
$530$	−0.739677	+	1.28116i	−0.0321295	+	0.0556500i
$531$	31.9732	+	55.3793i	1.38752	+	2.40326i
$532$	1.46481	+	2.53713i	0.0635076	+	0.109998i
$533$	6.84801			0.296620
$534$	−12.1936	−	21.1199i	−0.527668	−	0.913949i
$535$	−0.859090			−0.0371417
$536$	−9.29378	−	16.0973i	−0.401430	−	0.695297i
$537$	−19.7815	+	34.2626i	−0.853635	+	1.47854i
$538$	4.92119	+	8.52375i	0.212168	+	0.367485i
$539$	−17.1765	−	29.7506i	−0.739845	−	1.28145i
$540$	7.93538			0.341484
$541$	5.36414			0.230622			0.115311	−	0.993329i	$-0.463214\pi$
$541$	5.36414			0.230622			0.115311	+	0.993329i	$0.463214\pi$
$542$	0.991752	−	1.71776i	0.0425994	−	0.0737843i
$543$	16.2667	+	28.1747i	0.698070	+	1.20909i
$544$	1.45010	−	2.51165i	0.0621727	−	0.107686i
$545$	6.75083	−	11.6928i	0.289174	−	0.500864i
$546$	1.71516			0.0734019
$547$	−15.1727	+	26.2799i	−0.648737	+	1.12365i	0.334687	+	0.942329i	$0.391369\pi$
$547$	−15.1727	+	26.2799i	−0.648737	+	1.12365i	−0.983425	+	0.181317i	$0.941964\pi$
$548$	−9.00036			−0.384476
$549$	−6.37922	+	11.0491i	−0.272258	+	0.471566i
$550$	−5.36047	+	9.28460i	−0.228571	+	0.395897i
$551$	15.2964	−	26.4942i	0.651649	−	1.12869i
$552$	−11.2988	+	19.5701i	−0.480908	+	0.832958i
$553$	−2.55247	+	4.42101i	−0.108542	+	0.188001i
$554$	5.86035	+	10.1504i	0.248982	+	0.431250i
$555$	−23.9785			−1.01783
$556$	−8.39429	−	14.5393i	−0.355997	−	0.616605i
$557$	2.36419	−	4.09489i	0.100174	−	0.173506i	−0.811582	−	0.584238i	$-0.801393\pi$
$557$	2.36419	−	4.09489i	0.100174	−	0.173506i	0.911756	+	0.410732i	$0.134727\pi$
$558$	13.0968			0.554434
$559$	17.1462			0.725206
$560$	0.383563	+	0.664350i	0.0162085	+	0.0280739i
$561$	−3.82656	+	6.62779i	−0.161557	+	0.279826i
$562$	−16.1954			−0.683164
$563$	2.71698	−	4.70595i	0.114507	−	0.198332i	−0.803076	−	0.595877i	$-0.796804\pi$
$563$	2.71698	−	4.70595i	0.114507	−	0.198332i	0.917583	+	0.397545i	$0.130138\pi$
$564$	5.68810	+	9.85208i	0.239512	+	0.414847i
$565$	1.26695	+	2.19443i	0.0533011	+	0.0923203i
$566$	5.16749	−	8.95035i	0.217206	−	0.376211i
$567$	0.177382	−	0.307234i	0.00744933	−	0.0129026i
$568$	−11.8350	−	20.4988i	−0.496584	−	0.860109i
$569$	25.7241			1.07841			0.539206	−	0.842174i	$-0.318724\pi$
$569$	25.7241			1.07841			0.539206	+	0.842174i	$0.318724\pi$
$570$	3.82019	+	6.61677i	0.160010	+	0.277146i
$571$	33.4578			1.40017			0.700083	−	0.714062i	$-0.253146\pi$
$571$	33.4578			1.40017			0.700083	+	0.714062i	$0.253146\pi$
$572$	30.1346			1.25999
$573$	35.4728	+	61.4407i	1.48190	+	2.56672i
$574$	0.340440			0.0142097
$575$	−8.25309	−	14.2948i	−0.344178	−	0.596133i
$576$	4.52843	−	7.84347i	0.188685	−	0.326811i
$577$	4.54329	−	7.86921i	0.189140	−	0.327600i	−0.755824	−	0.654775i	$-0.772763\pi$
$577$	4.54329	−	7.86921i	0.189140	−	0.327600i	0.944964	+	0.327175i	$0.106097\pi$
$578$	4.46328	+	7.73062i	0.185648	+	0.321551i
$579$	−10.2360	−	17.7292i	−0.425392	−	0.736800i
$580$	4.97349	−	8.61434i	0.206513	−	0.357691i
$581$	−5.64481			−0.234186
$582$	0.169102	−	0.292893i	0.00700951	−	0.0121408i
$583$	−6.97342	−	12.0783i	−0.288810	−	0.500233i
$584$	28.0867			1.16223
$585$	−16.3514			−0.676046
$586$	4.43258	−	7.67745i	0.183108	−	0.317152i
$587$	−9.47994	−	16.4197i	−0.391279	−	0.677715i	0.601340	−	0.798994i	$-0.294634\pi$
$587$	−9.47994	−	16.4197i	−0.391279	−	0.677715i	−0.992619	+	0.121279i	$0.961301\pi$
$588$	32.7588			1.35095
$589$	−13.6125	−	23.5776i	−0.560895	−	0.971498i
$590$	−3.60509	+	6.24420i	−0.148419	+	0.257069i
$591$	11.5861	−	20.0678i	0.476590	−	0.825478i
$592$	−10.3479	+	17.9230i	−0.425295	+	0.736632i
$593$	8.33509	−	14.4368i	0.342281	−	0.592849i	−0.642575	−	0.766223i	$-0.722134\pi$
$593$	8.33509	−	14.4368i	0.342281	−	0.592849i	0.984856	+	0.173375i	$0.0554671\pi$
$594$	6.24018	−	10.8083i	0.256038	−	0.443470i
$595$	0.179536			0.00736027
$596$	13.4187	−	23.2419i	0.549651	−	0.952024i
$597$	12.8015			0.523929
$598$	3.86994	−	6.70294i	0.158254	−	0.274104i
$599$	9.45101	−	16.3696i	0.386158	−	0.668845i	−0.605771	−	0.795639i	$-0.707135\pi$
$599$	9.45101	−	16.3696i	0.386158	−	0.668845i	0.991929	+	0.126794i	$0.0404686\pi$
$600$	−11.0761	−	19.1844i	−0.452182	−	0.783202i
$601$	−14.7291	+	25.5116i	−0.600814	+	1.04064i	0.391884	+	0.920015i	$0.371824\pi$
$601$	−14.7291	+	25.5116i	−0.600814	+	1.04064i	−0.992698	+	0.120626i	$0.961510\pi$
$602$	0.852401			0.0347413
$603$	−43.8825			−1.78703
$604$	−13.5910	−	23.5403i	−0.553010	−	0.957842i
$605$	6.84237	+	11.8513i	0.278182	+	0.481825i
$606$	4.08057	−	7.06776i	0.165762	−	0.287108i
$607$	−12.5229	−	21.6902i	−0.508287	−	0.880379i	−0.999954	−	0.00959597i	$-0.996945\pi$
$607$	−12.5229	−	21.6902i	−0.508287	−	0.880379i	0.491667	−	0.870784i	$-0.336388\pi$
$608$	27.2967			1.10703
$609$	2.66872	+	4.62236i	0.108142	+	0.187308i
$610$	−1.43856			−0.0582454
$611$	−4.22147	−	7.31180i	−0.170782	−	0.295804i
$612$	−2.22522	−	3.85419i	−0.0899491	−	0.155796i
$613$	−3.04000	+	5.26544i	−0.122785	+	0.212669i	−0.920865	−	0.389882i	$-0.872516\pi$
$613$	−3.04000	+	5.26544i	−0.122785	+	0.212669i	0.798080	+	0.602551i	$0.205849\pi$
$614$	3.62084	−	6.27147i	0.146125	−	0.253096i
$615$	−5.32219			−0.214611
$616$	3.24613			0.130790
$617$	14.2495	−	24.6809i	0.573664	−	0.993615i	−0.422522	−	0.906353i	$-0.638855\pi$
$617$	14.2495	−	24.6809i	0.573664	−	0.993615i	0.996185	−	0.0872619i	$-0.0278117\pi$
$618$	−0.0618910	+	0.107198i	−0.00248962	+	0.00431215i
$619$	−15.2453			−0.612762			−0.306381	−	0.951909i	$-0.599118\pi$
$619$	−15.2453			−0.612762			−0.306381	+	0.951909i	$0.599118\pi$
$620$	−4.42599	−	7.66604i	−0.177752	−	0.307876i
$621$	9.60751	+	16.6407i	0.385536	+	0.667768i
$622$	2.08889	+	3.61807i	0.0837570	+	0.145071i
$623$	−2.69680	−	4.67100i	−0.108045	−	0.187140i
$624$	−11.5713	+	20.0420i	−0.463222	+	0.802323i
$625$	11.2937			0.451747
$626$	−9.00865	+	15.6034i	−0.360058	+	0.623639i
$627$	−72.0310			−2.87664
$628$	7.46790	+	12.9348i	0.298002	+	0.516154i
$629$	2.42179	+	4.19467i	0.0965632	+	0.167252i
$630$	−0.812888			−0.0323862
$631$	−16.5440			−0.658606			−0.329303	−	0.944224i	$-0.606814\pi$
$631$	−16.5440			−0.658606			−0.329303	+	0.944224i	$0.606814\pi$
$632$	15.4584	+	26.7747i	0.614901	+	1.06504i
$633$	−66.7647			−2.65366
$634$	−1.11475			−0.0442724
$635$	−10.9818	−	1.88015i	−0.435801	−	0.0746114i
$636$	13.2996			0.527363
$637$	−24.3122			−0.963283
$638$	−7.82204	−	13.5482i	−0.309678	−	0.536377i
$639$	−55.8812			−2.21063
$640$	11.3771			0.449718
$641$	0.272398	+	0.471807i	0.0107591	+	0.0186353i	0.871355	−	0.490653i	$-0.163242\pi$
$641$	0.272398	+	0.471807i	0.0107591	+	0.0186353i	−0.860596	+	0.509289i	$0.829909\pi$
$642$	−0.644214	−	1.11581i	−0.0254251	−	0.0440375i
$643$	−28.4567			−1.12222			−0.561112	−	0.827740i	$-0.689626\pi$
$643$	−28.4567			−1.12222			−0.561112	+	0.827740i	$0.689626\pi$
$644$	−1.15326	+	1.99750i	−0.0454447	+	0.0787125i
$645$	−13.3258			−0.524702
$646$	0.771667	−	1.33657i	0.0303608	−	0.0525865i
$647$	16.6012	+	28.7542i	0.652662	+	1.13044i	0.982474	+	0.186397i	$0.0596811\pi$
$647$	16.6012	+	28.7542i	0.652662	+	1.13044i	−0.329813	+	0.944046i	$0.606986\pi$
$648$	−1.07426	−	1.86068i	−0.0422011	−	0.0730945i
$649$	−33.9875	−	58.8681i	−1.33413	−	2.31078i
$650$	3.79369	+	6.57086i	0.148801	+	0.257730i
$651$	4.74988			0.186163
$652$	−7.05222	+	12.2148i	−0.276186	+	0.478369i
$653$	−15.9537	+	27.6326i	−0.624316	+	1.08135i	0.364356	+	0.931260i	$0.381289\pi$
$653$	−15.9537	+	27.6326i	−0.624316	+	1.08135i	−0.988673	+	0.150088i	$0.952044\pi$
$654$	20.2492			0.791808
$655$	2.15382			0.0841567
$656$	−2.29678	+	3.97813i	−0.0896740	+	0.155320i
$657$	33.1543	−	57.4249i	1.29347	−	2.24036i
$658$	−0.209865	−	0.363497i	−0.00818139	−	0.0141706i
$659$	2.73228	+	4.73245i	0.106435	+	0.184350i	0.914323	−	0.404985i	$-0.132723\pi$
$659$	2.73228	+	4.73245i	0.106435	+	0.184350i	−0.807889	+	0.589335i	$0.799390\pi$
$660$	−23.4202			−0.911630
$661$	−3.53659	−	6.12556i	−0.137557	−	0.238257i	0.789014	−	0.614375i	$-0.210592\pi$
$661$	−3.53659	−	6.12556i	−0.137557	−	0.238257i	−0.926572	+	0.376119i	$0.877259\pi$
$662$	10.6746			0.414882
$663$	2.70812	+	4.69059i	0.105174	+	0.182168i
$664$	−17.0932	+	29.6062i	−0.663343	+	1.14894i
$665$	0.844896	+	1.46340i	0.0327636	+	0.0567483i
$666$	−10.9652	−	18.9923i	−0.424892	−	0.735935i
$667$	24.0860			0.932613
$668$	−6.37466			−0.246643
$669$	2.98415	−	5.16870i	0.115374	−	0.199833i
$670$	−2.47395	−	4.28500i	−0.0955770	−	0.165544i
$671$	6.78110	−	11.7452i	0.261782	−	0.453419i
$672$	−2.38119	+	4.12434i	−0.0918564	+	0.159100i
$673$	22.0975			0.851796			0.425898	−	0.904771i	$-0.359958\pi$
$673$	22.0975			0.851796			0.425898	+	0.904771i	$0.359958\pi$
$674$	−6.21134	+	10.7584i	−0.239252	+	0.414396i
$675$	−18.8364			−0.725013
$676$	−0.478005	+	0.827929i	−0.0183848	+	0.0318434i
$677$	23.6396	−	40.9450i	0.908543	−	1.57364i	0.0924542	−	0.995717i	$-0.470529\pi$
$677$	23.6396	−	40.9450i	0.908543	−	1.57364i	0.816089	−	0.577926i	$-0.196138\pi$
$678$	−1.90013	+	3.29111i	−0.0729739	+	0.126394i
$679$	0.0373996	−	0.0647780i	0.00143526	−	0.00248595i
$680$	0.543657	−	0.941642i	0.0208483	−	0.0361103i
$681$	18.7683	+	32.5076i	0.719202	+	1.24569i
$682$	−13.9219			−0.533098
$683$	5.10452	+	8.84128i	0.195319	+	0.338302i	0.947005	−	0.321219i	$-0.104092\pi$
$683$	5.10452	+	8.84128i	0.195319	+	0.338302i	−0.751686	+	0.659521i	$0.770759\pi$
$684$	20.9437	−	36.2755i	0.800802	−	1.38703i
$685$	−5.19136			−0.198352
$686$	−2.43616			−0.0930129
$687$	−9.20426	−	15.9422i	−0.351165	−	0.608235i
$688$	−5.75071	+	9.96052i	−0.219244	+	0.379741i
$689$	−9.87040			−0.376032
$690$	−3.00767	+	5.20944i	−0.114500	+	0.198320i
$691$	−4.19613	−	7.26791i	−0.159628	−	0.276484i	0.775106	−	0.631831i	$-0.217696\pi$
$691$	−4.19613	−	7.26791i	−0.159628	−	0.276484i	−0.934735	+	0.355346i	$0.884363\pi$
$692$	0.127106	+	0.220154i	0.00483185	+	0.00836901i
$693$	3.83182	−	6.63690i	0.145559	−	0.252115i
$694$	5.14641	−	8.91384i	0.195355	−	0.338365i
$695$	−4.84179	−	8.38622i	−0.183659	−	0.318108i
$696$	32.3248			1.22527
$697$	0.537532	+	0.931033i	0.0203605	+	0.0352654i
$698$	−13.8137			−0.522857
$699$	−20.9826			−0.793635
$700$	−1.13053	−	1.95814i	−0.0427301	−	0.0740107i
$701$	−26.5517			−1.00285			−0.501423	−	0.865202i	$-0.667190\pi$
$701$	−26.5517			−1.00285			−0.501423	+	0.865202i	$0.667190\pi$
$702$	−4.41627	−	7.64920i	−0.166681	−	0.288701i
$703$	−22.7939	+	39.4801i	−0.859687	+	1.48902i
$704$	−4.81371	+	8.33760i	−0.181424	+	0.314235i
$705$	3.28087	+	5.68263i	0.123565	+	0.214020i
$706$	5.81105	+	10.0650i	0.218702	+	0.378803i
$707$	0.902482	−	1.56315i	0.0339413	−	0.0587881i
$708$	64.8205			2.43610
$709$	−4.71778	+	8.17144i	−0.177180	+	0.306885i	−0.940914	−	0.338647i	$-0.890031\pi$
$709$	−4.71778	+	8.17144i	−0.177180	+	0.306885i	0.763734	+	0.645532i	$0.223364\pi$
$710$	−3.15040	−	5.45665i	−0.118232	−	0.204784i
$711$	72.9899			2.73734
$712$	−32.6650			−1.22417
$713$	10.7173	−	18.5628i	0.401364	−	0.695184i
$714$	0.134631	+	0.233187i	0.00503842	+	0.00872681i
$715$	17.3815			0.650031
$716$	12.2280	+	21.1796i	0.456983	+	0.791517i
$717$	5.84366	−	10.1215i	0.218236	−	0.377995i
$718$	−3.08545	+	5.34416i	−0.115148	+	0.199442i
$719$	−9.10441	+	15.7693i	−0.339537	+	0.588095i	−0.984346	−	0.176249i	$-0.943604\pi$
$719$	−9.10441	+	15.7693i	−0.339537	+	0.588095i	0.644809	+	0.764344i	$0.276937\pi$
$720$	5.48414	−	9.49880i	0.204382	−	0.353999i
$721$	−0.0136882	+	0.0237086i	−0.000509774	+	0.000882954i
$722$	4.36582			0.162479
$723$	−2.38691	+	4.13425i	−0.0887702	+	0.153754i
$724$	20.1107			0.747406
$725$	−11.8057	+	20.4480i	−0.438452	+	0.759421i
$726$	−10.2619	+	17.7741i	−0.380855	+	0.659660i
$727$	23.6286	+	40.9260i	0.876337	+	1.51786i	0.855332	+	0.518081i	$0.173353\pi$
$727$	23.6286	+	40.9260i	0.876337	+	1.51786i	0.0210056	+	0.999779i	$0.493313\pi$
$728$	1.14867	−	1.98955i	0.0425724	−	0.0737376i
$729$	−44.0258			−1.63058
$730$	7.47650			0.276718
$731$	1.34588	+	2.33114i	0.0497793	+	0.0862202i
$732$	6.46640	+	11.2001i	0.239005	+	0.413969i
$733$	−14.1480	+	24.5050i	−0.522568	+	0.905115i	0.477087	+	0.878856i	$0.341693\pi$
$733$	−14.1480	+	24.5050i	−0.522568	+	0.905115i	−0.999655	+	0.0262586i	$0.991641\pi$
$734$	0.723674	+	1.25344i	0.0267113	+	0.0462653i
$735$	18.8951			0.696956
$736$	10.7455	+	18.6117i	0.396083	+	0.686036i
$737$	46.6471			1.71827
$738$	−2.43379	−	4.21545i	−0.0895891	−	0.155173i
$739$	−17.7129	−	30.6796i	−0.651578	−	1.12857i	−0.982740	−	0.184992i	$-0.940774\pi$
$739$	−17.7129	−	30.6796i	−0.651578	−	1.12857i	0.331162	−	0.943574i	$-0.392559\pi$
$740$	−7.41122	+	12.8366i	−0.272442	+	0.471883i
$741$	−25.4887	+	44.1478i	−0.936351	+	1.62181i
$742$	−0.490695			−0.0180140
$743$	36.6546			1.34473			0.672363	−	0.740222i	$-0.265279\pi$
$743$	36.6546			1.34473			0.672363	+	0.740222i	$0.265279\pi$
$744$	14.3832	−	24.9124i	0.527314	−	0.913334i
$745$	7.73984	−	13.4058i	0.283566	−	0.491150i
$746$	4.81847			0.176417
$747$	40.3545	+	69.8960i	1.47649	+	2.55736i
$748$	2.36540	+	4.09700i	0.0864877	+	0.149801i
$749$	−0.142478	−	0.246779i	−0.00520603	−	0.00901711i
$750$	−6.61324	−	11.4545i	−0.241482	−	0.418258i
$751$	−9.44803	+	16.3645i	−0.344763	+	0.597148i	−0.985311	−	0.170771i	$-0.945374\pi$
$751$	−9.44803	+	16.3645i	−0.344763	+	0.597148i	0.640547	+	0.767919i	$0.278708\pi$
$752$	5.66340			0.206523
$753$	27.3427	−	47.3589i	0.996422	−	1.72585i
$754$	−11.0716			−0.403203
$755$	−7.83923	−	13.5779i	−0.285299	−	0.494152i
$756$	1.31606	+	2.27949i	0.0478648	+	0.0829042i
$757$	26.1262			0.949574			0.474787	−	0.880101i	$-0.342525\pi$
$757$	26.1262			0.949574			0.474787	+	0.880101i	$0.342525\pi$
$758$	−9.09494			−0.330343
$759$	−28.3553	−	49.1128i	−1.02923	−	1.78268i
$760$	10.2338			0.371218
$761$	12.5601			0.455305			0.227652	−	0.973742i	$-0.426895\pi$
$761$	12.5601			0.455305			0.227652	+	0.973742i	$0.426895\pi$
$762$	−5.79307	−	15.6734i	−0.209861	−	0.567788i
$763$	4.47843			0.162130
$764$	43.8553			1.58663
$765$	−1.28350	−	2.22308i	−0.0464049	−	0.0803756i
$766$	−4.09783			−0.148061
$767$	−48.1070			−1.73704
$768$	3.17534	+	5.49985i	0.114580	+	0.198459i
$769$	−3.80231	−	6.58579i	−0.137115	−	0.237490i	0.789289	−	0.614022i	$-0.210450\pi$
$769$	−3.80231	−	6.58579i	−0.137115	−	0.237490i	−0.926403	+	0.376533i	$0.877116\pi$
$770$	0.864099			0.0311400
$771$	−1.60485	+	2.77968i	−0.0577972	+	0.100108i
$772$	−12.6548			−0.455456
$773$	18.0992	−	31.3487i	0.650983	−	1.12754i	−0.331902	−	0.943314i	$-0.607690\pi$
$773$	18.0992	−	31.3487i	0.650983	−	1.12754i	0.982885	−	0.184221i	$-0.0589763\pi$
$774$	−6.09377	−	10.5547i	−0.219036	−	0.379381i
$775$	10.5061	+	18.1970i	0.377389	+	0.653657i
$776$	−0.226501	−	0.392311i	−0.00813090	−	0.0140831i
$777$	−3.97678	−	6.88799i	−0.142666	−	0.247105i
$778$	14.2375			0.510439
$779$	−5.05924	+	8.76286i	−0.181266	+	0.313962i
$780$	−8.28742	+	14.3542i	−0.296737	+	0.513964i
$781$	59.4017			2.12556
$782$	1.21508			0.0434512
$783$	13.7431	−	23.8038i	0.491139	−	0.850678i
$784$	8.15413	−	14.1234i	0.291219	−	0.504406i
$785$	4.30745	+	7.46072i	0.153739	+	0.266285i
$786$	1.61510	+	2.79744i	0.0576089	+	0.0997815i
$787$	22.5995			0.805585			0.402792	−	0.915291i	$-0.368040\pi$
$787$	22.5995			0.805585			0.402792	+	0.915291i	$0.368040\pi$
$788$	−7.16202	−	12.4050i	−0.255136	−	0.441909i
$789$	23.6757			0.842878
$790$	4.11493	+	7.12726i	0.146403	+	0.253577i
$791$	−0.420242	+	0.727881i	−0.0149421	+	0.0258805i
$792$	−23.2064	−	40.1946i	−0.824603	−	1.42825i
$793$	−4.79909	−	8.31227i	−0.170421	−	0.295177i
$794$	−18.4169			−0.653590
$795$	7.67115			0.272068
$796$	3.95664	−	6.85310i	0.140239	−	0.242902i
$797$	−14.4240	−	24.9831i	−0.510923	−	0.884945i	−0.999920	−	0.0126594i	$-0.995970\pi$
$797$	−14.4240	−	24.9831i	−0.510923	−	0.884945i	0.488997	−	0.872286i	$-0.337363\pi$
$798$	−1.26714	+	2.19475i	−0.0448563	+	0.0776933i
$799$	0.662725	−	1.14787i	0.0234455	−	0.0406088i
$800$	−21.0674			−0.744846
$801$	−38.5586	+	66.7855i	−1.36240	+	2.35975i
$802$	−11.7819			−0.416032
$803$	−35.2429	+	61.0425i	−1.24370	+	2.15414i
$804$	−22.2411	+	38.5228i	−0.784384	+	1.35859i
$805$	−0.665193	+	1.15215i	−0.0234450	+	0.0406079i
$806$	−4.92639	+	8.53275i	−0.173525	+	0.300553i
$807$	25.5187	−	44.1997i	0.898300	−	1.55590i
$808$	−5.46565	−	9.46678i	−0.192281	−	0.333040i
$809$	8.86451			0.311660			0.155830	−	0.987784i	$-0.450195\pi$
$809$	8.86451			0.311660			0.155830	+	0.987784i	$0.450195\pi$
$810$	−0.285963	−	0.495302i	−0.0100477	−	0.0174031i
$811$	−2.12530	+	3.68112i	−0.0746292	+	0.129262i	−0.900925	−	0.433975i	$-0.857111\pi$
$811$	−2.12530	+	3.68112i	−0.0746292	+	0.129262i	0.826296	+	0.563236i	$0.190444\pi$
$812$	3.29936			0.115785
$813$	−10.2854			−0.360725
$814$	11.6560	+	20.1887i	0.408542	+	0.707615i
$815$	−4.06769	+	7.04544i	−0.142485	+	0.246791i
$816$	−3.63313			−0.127185
$817$	−12.6674	+	21.9406i	−0.443177	+	0.767605i
$818$	1.53835	+	2.66451i	0.0537873	+	0.0931623i
$819$	−2.71184	−	4.69704i	−0.0947592	−	0.164128i
$820$	−1.64497	+	2.84917i	−0.0574447	+	0.0994972i
$821$	−6.65909	+	11.5339i	−0.232404	+	0.402535i	−0.958515	−	0.285042i	$-0.907992\pi$
$821$	−6.65909	+	11.5339i	−0.232404	+	0.402535i	0.726111	+	0.687577i	$0.241326\pi$
$822$	−3.89290	−	6.74270i	−0.135780	−	0.235179i
$823$	49.5810			1.72829			0.864143	−	0.503247i	$-0.167861\pi$
$823$	49.5810			1.72829			0.864143	+	0.503247i	$0.167861\pi$
$824$	0.0828987	+	0.143585i	0.00288791	+	0.00500201i
$825$	55.5931			1.93550
$826$	−2.39158			−0.0832137
$827$	2.96851	+	5.14161i	0.103225	+	0.178791i	0.913012	−	0.407933i	$-0.133750\pi$
$827$	2.96851	+	5.14161i	0.103225	+	0.178791i	−0.809786	+	0.586725i	$0.800417\pi$
$828$	32.9783			1.14607
$829$	7.64749	+	13.2458i	0.265608	+	0.460047i	0.967723	−	0.252017i	$-0.0810939\pi$
$829$	7.64749	+	13.2458i	0.265608	+	0.460047i	−0.702115	+	0.712064i	$0.747761\pi$
$830$	−4.55010	+	7.88100i	−0.157936	+	0.273554i
$831$	30.3886	−	52.6347i	1.05417	−	1.82588i
$832$	3.40674	+	5.90065i	0.118107	+	0.204568i
$833$	−1.90837	−	3.30540i	−0.0661213	−	0.114525i
$834$	7.26151	−	12.5773i	0.251446	−	0.435517i
$835$	−3.67687			−0.127243
$836$	−22.2631	+	38.5609i	−0.769986	+	1.33366i
$837$	−12.2302	−	21.1834i	−0.422739	−	0.732205i
$838$	−4.71031			−0.162715
$839$	−52.0160			−1.79579			−0.897896	−	0.440208i	$-0.854905\pi$
$839$	−52.0160			−1.79579			−0.897896	+	0.440208i	$0.854905\pi$
$840$	−0.892729	+	1.54625i	−0.0308021	+	0.0533508i
$841$	−2.72696	−	4.72323i	−0.0940331	−	0.162870i
$842$	18.7676			0.646774
$843$	41.9905	+	72.7296i	1.44623	+	2.50494i
$844$	−20.6354	+	35.7416i	−0.710301	+	1.23028i
$845$	−0.275711	+	0.477545i	−0.00948474	+	0.0164281i
$846$	−3.00063	+	5.19724i	−0.103164	+	0.178685i
$847$	−2.26958	+	3.93103i	−0.0779837	+	0.135072i
$848$	3.31046	−	5.73389i	0.113682	−	0.196903i
$849$	−53.5917			−1.83926
$850$	−0.595568	+	1.03155i	−0.0204278	+	0.0353820i
$851$	−35.8916			−1.23035
$852$	−28.3225	+	49.0560i	−0.970312	+	1.68063i
$853$	13.7980	−	23.8988i	0.472433	−	0.818278i	−0.527069	−	0.849822i	$-0.676709\pi$
$853$	13.7980	−	23.8988i	0.472433	−	0.818278i	0.999502	+	0.0315440i	$0.0100424\pi$
$854$	−0.238581	−	0.413234i	−0.00816407	−	0.0141406i
$855$	12.0802	−	20.9236i	0.413135	−	0.715571i
$856$	−1.72576			−0.0589853
$857$	−5.68465			−0.194184			−0.0970919	−	0.995275i	$-0.530954\pi$
$857$	−5.68465			−0.194184			−0.0970919	+	0.995275i	$0.530954\pi$
$858$	13.0340	+	22.5756i	0.444974	+	0.770718i
$859$	−17.9725	−	31.1293i	−0.613214	−	1.06212i	−0.990695	−	0.136101i	$-0.956543\pi$
$859$	−17.9725	−	31.1293i	−0.613214	−	1.06212i	0.377481	−	0.926017i	$-0.376790\pi$
$860$	−4.11870	+	7.13379i	−0.140446	+	0.243260i
$861$	−0.882672	−	1.52883i	−0.0300814	−	0.0521025i
$862$	12.9643			0.441565
$863$	12.2222	+	21.1694i	0.416048	+	0.720616i	0.995538	−	0.0943633i	$-0.0300815\pi$
$863$	12.2222	+	21.1694i	0.416048	+	0.720616i	−0.579490	+	0.814979i	$0.696748\pi$
$864$	24.5248			0.834351
$865$	0.0733142	+	0.126984i	0.00249276	+	0.00431758i
$866$	2.62623	+	4.54877i	0.0892430	+	0.154573i
$867$	23.1442	−	40.0869i	0.786017	−	1.36142i
$868$	1.46808	−	2.54279i	0.0498299	−	0.0863079i
$869$	−77.5882			−2.63200
$870$	8.60468			0.291726
$871$	16.5064	−	28.5900i	0.559299	−	0.968734i
$872$	13.5612	−	23.4887i	0.459241	−	0.795429i
$873$	−1.06947			−0.0361961
$874$	5.71815	+	9.90413i	0.193419	+	0.335012i
$875$	−1.46262	−	2.53334i	−0.0494457	−	0.0856424i
$876$	−33.6074	−	58.2097i	−1.13549	−	1.96672i
$877$	−24.1259	−	41.7873i	−0.814674	−	1.41106i	−0.909562	−	0.415568i	$-0.863583\pi$
$877$	−24.1259	−	41.7873i	−0.814674	−	1.41106i	0.0948884	−	0.995488i	$-0.469751\pi$
$878$	6.93879	−	12.0183i	0.234173	−	0.405599i
$879$	−45.9700			−1.55053
$880$	−5.82963	+	10.0972i	−0.196517	+	0.340377i
$881$	−41.2789			−1.39072			−0.695361	−	0.718661i	$-0.744755\pi$
$881$	−41.2789			−1.39072			−0.695361	+	0.718661i	$0.744755\pi$
$882$	8.64057	+	14.9659i	0.290943	+	0.503928i
$883$	13.7023	+	23.7331i	0.461120	+	0.798683i	0.999017	−	0.0443276i	$-0.0141145\pi$
$883$	13.7023	+	23.7331i	0.461120	+	0.798683i	−0.537897	+	0.843010i	$0.680781\pi$
$884$	3.34807			0.112608
$885$	37.3881			1.25679
$886$	−8.66881	−	15.0148i	−0.291234	−	0.504433i
$887$	35.4807			1.19133			0.595663	−	0.803235i	$-0.296889\pi$
$887$	35.4807			1.19133			0.595663	+	0.803235i	$0.296889\pi$
$888$	−48.1687			−1.61643
$889$	−1.28123	−	3.46642i	−0.0429710	−	0.116260i
$890$	−8.69522			−0.291464
$891$	5.39192			0.180636
$892$	−1.84466	−	3.19505i	−0.0617639	−	0.106978i
$893$	12.4751			0.417463
$894$	23.2158			0.776452
$895$	7.05307	+	12.2163i	0.235758	+	0.408345i
$896$	1.88686	+	3.26813i	0.0630355	+	0.109181i
$897$	−40.1349			−1.34007
$898$	3.38905	−	5.87001i	0.113094	−	0.195885i
$899$	−30.6611			−1.02261
$900$	−16.1642	+	27.9972i	−0.538807	+	0.933242i
$901$	−0.774774	−	1.34195i	−0.0258114	−	0.0447067i
$902$	2.58712	+	4.48102i	0.0861416	+	0.149202i
$903$	−2.21005	−	3.82792i	−0.0735458	−	0.127385i
$904$	2.54509	+	4.40822i	0.0846483	+	0.146615i
$905$	11.5997			0.385588
$906$	11.7570	−	20.3636i	0.390599	−	0.676537i
$907$	5.56383	−	9.63684i	0.184744	−	0.319986i	−0.758746	−	0.651386i	$-0.774188\pi$
$907$	5.56383	−	9.63684i	0.184744	−	0.319986i	0.943490	+	0.331400i	$0.107521\pi$
$908$	23.2034			0.770032
$909$	−25.8072			−0.855970
$910$	0.305768	−	0.529606i	0.0101361	−	0.0175563i
$911$	−17.2205	+	29.8268i	−0.570541	+	0.988206i	0.425969	+	0.904738i	$0.359933\pi$
$911$	−17.2205	+	29.8268i	−0.570541	+	0.988206i	−0.996510	+	0.0834684i	$0.973400\pi$
$912$	−17.0975	−	29.6137i	−0.566154	−	0.980607i
$913$	−42.8968	−	74.2994i	−1.41968	−	2.45895i
$914$	−10.8987			−0.360497
$915$	3.72979	+	6.46019i	0.123303	+	0.213567i
$916$	−11.3793			−0.375983
$917$	0.357206	+	0.618698i	0.0117960	+	0.0204312i
$918$	0.693307	−	1.20084i	0.0228825	−	0.0396337i
$919$	23.4270	+	40.5767i	0.772785	+	1.33850i	0.936031	+	0.351917i	$0.114470\pi$
$919$	23.4270	+	40.5767i	0.772785	+	1.33850i	−0.163247	+	0.986585i	$0.552197\pi$
$920$	4.02857	+	6.97768i	0.132818	+	0.230047i
$921$	−37.5515			−1.23736
$922$	6.15838			0.202815
$923$	21.0198	−	36.4073i	0.691874	−	1.19836i
$924$	−3.88418	−	6.72761i	−0.127780	−	0.221322i
$925$	17.5922	−	30.4705i	0.578427	−	1.00186i
$926$	−5.89947	+	10.2182i	−0.193869	+	0.335790i
$927$	0.391424			0.0128560
$928$	15.3709	−	26.6232i	0.504574	−	0.873948i
$929$	−5.13856			−0.168591			−0.0842954	−	0.996441i	$-0.526864\pi$
$929$	−5.13856			−0.168591			−0.0842954	+	0.996441i	$0.526864\pi$
$930$	3.82872	−	6.63154i	0.125549	−	0.217457i
$931$	17.9616	−	31.1104i	0.588667	−	1.01960i
$932$	−6.48524	+	11.2328i	−0.212431	+	0.367942i
$933$	10.8319	−	18.7614i	0.354620	−	0.614220i
$934$	−2.79671	+	4.84405i	−0.0915113	+	0.158502i
$935$	1.36435	+	2.36313i	0.0446191	+	0.0772826i
$936$	−32.8470			−1.07364
$937$	−12.1955	−	21.1233i	−0.398411	−	0.690067i	0.595119	−	0.803637i	$-0.297105\pi$
$937$	−12.1955	−	21.1233i	−0.398411	−	0.690067i	−0.993530	+	0.113570i	$0.963771\pi$
$938$	0.820597	−	1.42131i	0.0267934	−	0.0464076i
$939$	93.4281			3.04891
$940$	4.05617			0.132298
$941$	6.86197	+	11.8853i	0.223694	+	0.387449i	0.955927	−	0.293605i	$-0.0948551\pi$
$941$	6.86197	+	11.8853i	0.223694	+	0.387449i	−0.732233	+	0.681054i	$0.761522\pi$
$942$	−6.46014	+	11.1893i	−0.210483	+	0.364567i
$943$	−7.96636			−0.259420
$944$	16.1348	−	27.9462i	0.525141	−	0.909572i
$945$	0.759099	+	1.31480i	0.0246935	+	0.0427704i
$946$	6.47767	+	11.2197i	0.210607	+	0.364782i
$947$	−11.7015	+	20.2675i	−0.380247	+	0.658607i	−0.991097	−	0.133139i	$-0.957494\pi$
$947$	−11.7015	+	20.2675i	−0.380247	+	0.658607i	0.610851	+	0.791746i	$0.290828\pi$
$948$	36.9937	−	64.0750i	1.20150	−	2.08106i
$949$	24.9420	+	43.2008i	0.809651	+	1.40236i
$950$	−11.2109			−0.363731
$951$	2.89025	+	5.00606i	0.0937227	+	0.162333i
$952$	0.360657			0.0116890
$953$	29.9918			0.971529			0.485765	−	0.874090i	$-0.338541\pi$
$953$	29.9918			0.971529			0.485765	+	0.874090i	$0.338541\pi$
$954$	3.50795	+	6.07595i	0.113574	+	0.196716i
$955$	25.2956			0.818545
$956$	−3.61229	−	6.25666i	−0.116830	−	0.202355i
$957$	−40.5610	+	70.2536i	−1.31115	+	2.27098i
$958$	3.17520	−	5.49961i	0.102586	−	0.177684i
$959$	−0.860975	−	1.49125i	−0.0278023	−	0.0481550i
$960$	−2.64767	−	4.58591i	−0.0854533	−	0.148009i
$961$	1.85708	−	3.21656i	0.0599059	−	0.103760i
$962$	16.4982			0.531924
$963$	−2.03713	+	3.52842i	−0.0656457	+	0.113702i
$964$	1.47548	+	2.55561i	0.0475220	+	0.0823105i
$965$	−7.29923			−0.234970
$966$	−1.99526			−0.0641964
$967$	−19.7020	+	34.1249i	−0.633574	+	1.09738i	0.353241	+	0.935532i	$0.385080\pi$
$967$	−19.7020	+	34.1249i	−0.633574	+	1.09738i	−0.986815	+	0.161851i	$0.948254\pi$
$968$	13.7451	+	23.8072i	0.441785	+	0.765193i
$969$	−8.00291			−0.257091
$970$	−0.0602931	−	0.104431i	−0.00193590	−	0.00335307i
$971$	−14.2586	+	24.6966i	−0.457580	+	0.792552i	−0.998832	−	0.0483085i	$-0.984617\pi$
$971$	−14.2586	+	24.6966i	−0.457580	+	0.792552i	0.541253	+	0.840860i	$0.317950\pi$
$972$	−14.6104	+	25.3060i	−0.468630	+	0.811692i
$973$	1.60600	−	2.78167i	0.0514859	−	0.0891762i
$974$	10.3695	−	17.9604i	0.332259	−	0.575489i
$975$	19.6720	−	34.0730i	0.630009	−	1.09121i
$976$	6.43833			0.206086
$977$	−18.6142	+	32.2407i	−0.595520	+	1.03147i	0.397953	+	0.917406i	$0.369721\pi$
$977$	−18.6142	+	32.2407i	−0.595520	+	1.03147i	−0.993473	+	0.114065i	$0.963613\pi$
$978$	−12.2011			−0.390148
$979$	40.9878	−	70.9929i	1.30997	−	2.26894i
$980$	5.84004	−	10.1153i	0.186553	−	0.323120i
$981$	−32.0161	−	55.4535i	−1.02219	−	1.77049i
$982$	−5.36623	+	9.29459i	−0.171243	+	0.296602i
$983$	−46.3999			−1.47993			−0.739963	−	0.672647i	$-0.765157\pi$
$983$	−46.3999			−1.47993			−0.739963	+	0.672647i	$0.765157\pi$
$984$	−10.6913			−0.340827
$985$	−4.13102	−	7.15513i	−0.131625	−	0.227982i
$986$	−0.869059	−	1.50525i	−0.0276765	−	0.0479370i
$987$	−1.08825	+	1.88490i	−0.0346393	+	0.0599971i
$988$	15.7560	+	27.2901i	0.501264	+	0.868215i
$989$	−19.9463			−0.634256
$990$	−6.17740	−	10.6996i	−0.196331	−	0.340055i
$991$	−20.5966			−0.654272			−0.327136	−	0.944977i	$-0.606083\pi$
$991$	−20.5966			−0.654272			−0.327136	+	0.944977i	$0.606083\pi$
$992$	−13.6788	−	23.6924i	−0.434303	−	0.752235i
$993$	−27.6765	−	47.9371i	−0.878287	−	1.52124i
$994$	1.04497	−	1.80994i	0.0331445	−	0.0574079i
$995$	2.28217	−	3.95284i	0.0723497	−	0.125313i
$996$	81.8120			2.59231
$997$	−1.57451			−0.0498654			−0.0249327	−	0.999689i	$-0.507937\pi$
$997$	−1.57451			−0.0498654			−0.0249327	+	0.999689i	$0.507937\pi$
$998$	2.06769	−	3.58135i	0.0654517	−	0.113366i
$999$	−20.4792	+	35.4711i	−0.647934	+	1.12225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	127.2.c.a.107.6	yes	18
127.19	even	3	inner	127.2.c.a.19.6	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
127.2.c.a.19.6	✓	18	127.19	even	3	inner
127.2.c.a.107.6	yes	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	127.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.534737 q^{2} +(-1.38643 - 2.40137i) q^{3} -1.71406 q^{4} -0.988660 q^{5} +(-0.741376 - 1.28410i) q^{6} +(-0.163967 - 0.283999i) q^{7} -1.98604 q^{8} +(-2.34438 + 4.06058i) q^{9} -0.528673 q^{10} +(2.49207 - 4.31640i) q^{11} +(2.37642 + 4.11608i) q^{12} +(-1.76368 - 3.05478i) q^{13} +(-0.0876791 - 0.151865i) q^{14} +(1.37071 + 2.37414i) q^{15} +2.36610 q^{16} +(0.276879 - 0.479568i) q^{17} +(-1.25363 + 2.17134i) q^{18} +5.21195 q^{19} +1.69462 q^{20} +(-0.454657 + 0.787489i) q^{21} +(1.33260 - 2.30814i) q^{22} +(2.05171 + 3.55366i) q^{23} +(2.75351 + 4.76922i) q^{24} -4.02255 q^{25} +(-0.943104 - 1.63350i) q^{26} +4.68270 q^{27} +(0.281048 + 0.486790i) q^{28} +(2.93487 - 5.08335i) q^{29} +(0.732968 + 1.26954i) q^{30} +(-2.61179 - 4.52376i) q^{31} +5.23733 q^{32} -13.8203 q^{33} +(0.148057 - 0.256443i) q^{34} +(0.162107 + 0.280778i) q^{35} +(4.01840 - 6.96007i) q^{36} +(-4.37338 + 7.57492i) q^{37} +2.78702 q^{38} +(-4.89044 + 8.47049i) q^{39} +1.96352 q^{40} +(-0.970700 + 1.68130i) q^{41} +(-0.243122 + 0.421100i) q^{42} +(-2.43046 + 4.20967i) q^{43} +(-4.27155 + 7.39855i) q^{44} +(2.31779 - 4.01454i) q^{45} +(1.09712 + 1.90027i) q^{46} +2.39356 q^{47} +(-3.28044 - 5.68188i) q^{48} +(3.44623 - 5.96905i) q^{49} -2.15101 q^{50} -1.53549 q^{51} +(3.02305 + 5.23607i) q^{52} +(1.39912 - 2.42335i) q^{53} +2.50401 q^{54} +(-2.46381 + 4.26745i) q^{55} +(0.325645 + 0.564034i) q^{56} +(-7.22601 - 12.5158i) q^{57} +(1.56939 - 2.71825i) q^{58} +(6.81913 - 11.8111i) q^{59} +(-2.34947 - 4.06940i) q^{60} +2.72107 q^{61} +(-1.39662 - 2.41902i) q^{62} +1.53760 q^{63} -1.93161 q^{64} +(1.74368 + 3.02014i) q^{65} -7.39025 q^{66} +(4.67954 + 8.10521i) q^{67} +(-0.474586 + 0.822006i) q^{68} +(5.68909 - 9.85380i) q^{69} +(0.0866848 + 0.150142i) q^{70} +(5.95907 + 10.3214i) q^{71} +(4.65604 - 8.06450i) q^{72} -14.1420 q^{73} +(-2.33861 + 4.05059i) q^{74} +(5.57699 + 9.65963i) q^{75} -8.93358 q^{76} -1.63447 q^{77} +(-2.61510 + 4.52948i) q^{78} +(-7.78350 - 13.4814i) q^{79} -2.33927 q^{80} +(0.540907 + 0.936878i) q^{81} +(-0.519069 + 0.899054i) q^{82} +(8.60664 - 14.9071i) q^{83} +(0.779308 - 1.34980i) q^{84} +(-0.273739 + 0.474129i) q^{85} +(-1.29965 + 2.25107i) q^{86} -16.2760 q^{87} +(-4.94936 + 8.57255i) q^{88} +16.4473 q^{89} +(1.23941 - 2.14672i) q^{90} +(-0.578370 + 1.00177i) q^{91} +(-3.51674 - 6.09117i) q^{92} +(-7.24214 + 12.5438i) q^{93} +1.27992 q^{94} -5.15285 q^{95} +(-7.26119 - 12.5768i) q^{96} +(0.114046 + 0.197534i) q^{97} +(1.84283 - 3.19187i) q^{98} +(11.6847 + 20.2385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + 5 q^{7} - 6 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 8 q^{14} + 3 q^{15} - 6 q^{16} - 6 q^{17} + 16 q^{19} - 32 q^{20} + 3 q^{21} + 6 q^{22} + 13 q^{23} - 6 q^{24}+ \cdots + 17 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + 5 * q^7 - 6 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 8 * q^14 + 3 * q^15 - 6 * q^16 - 6 * q^17 + 16 * q^19 - 32 * q^20 + 3 * q^21 + 6 * q^22 + 13 * q^23 - 6 * q^24 + 6 * q^25 - 14 * q^26 + 10 * q^27 - 2 * q^28 - 5 * q^29 - 23 * q^30 - 11 * q^31 - 4 * q^32 - 16 * q^33 - 2 * q^34 - 16 * q^35 + 15 * q^36 - 4 * q^37 + 4 * q^38 - 7 * q^39 - 36 * q^40 - 11 * q^41 + 9 * q^43 - 15 * q^44 + 14 * q^45 + 15 * q^46 - 10 * q^47 + 20 * q^48 + 12 * q^49 + 32 * q^50 + 4 * q^51 + 26 * q^52 - 2 * q^53 + 2 * q^54 - q^55 + 12 * q^56 + 28 * q^57 + 10 * q^58 + 6 * q^60 + 28 * q^61 + 8 * q^62 - 12 * q^63 - 50 * q^64 + 15 * q^65 + 36 * q^66 - 12 * q^67 - 41 * q^68 + 33 * q^69 + 21 * q^70 - 4 * q^71 + 31 * q^72 + 52 * q^73 + 13 * q^74 - 11 * q^75 + 26 * q^76 - 40 * q^77 + q^78 - 35 * q^79 + 26 * q^80 + 27 * q^81 - 26 * q^82 + 13 * q^83 + 22 * q^84 + 15 * q^85 - 5 * q^86 - 64 * q^87 - q^88 + 8 * q^89 - 30 * q^90 - 16 * q^91 + 11 * q^92 - 6 * q^93 - 62 * q^94 - 38 * q^95 - 31 * q^96 + 28 * q^97 + 32 * q^98 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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