LMFDB - Embedded newform 138.4.f.a.5.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [138,4,Mod(5,138)] 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("138.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(138, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	138.f (of order $22$, degree $10$, 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:	$8.14226358079$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.16
Character	$\chi$	$=$	138.5
Dual form			138.4.f.a.83.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.563465 - 1.91899i) q^{2} +(-3.80483 + 3.53882i) q^{3} +(-3.36501 - 2.16256i) q^{4} +(-0.260866 + 1.81436i) q^{5} +(4.64705 + 9.29542i) q^{6} +(-4.44632 + 2.03056i) q^{7} +(-6.04600 + 5.23889i) q^{8} +(1.95351 - 26.9292i) q^{9} +(3.33474 + 1.52293i) q^{10} +(60.8494 - 17.8670i) q^{11} +(20.4562 - 3.67999i) q^{12} +(24.2320 - 53.0606i) q^{13} +(1.39128 + 9.67657i) q^{14} +(-5.42815 - 7.82650i) q^{15} +(6.64664 + 14.5541i) q^{16} +(-60.2044 + 38.6910i) q^{17} +(-50.5761 - 18.9224i) q^{18} +(56.2301 - 87.4958i) q^{19} +(4.80149 - 5.54121i) q^{20} +(9.73169 - 23.4607i) q^{21} -126.836i q^{22} +(71.2495 - 84.2051i) q^{23} +(4.46454 - 41.3288i) q^{24} +(116.713 + 34.2700i) q^{25} +(-88.1688 - 76.3987i) q^{26} +(87.8649 + 109.374i) q^{27} +(19.3531 + 2.78256i) q^{28} +(4.36531 + 6.79256i) q^{29} +(-18.0775 + 6.00658i) q^{30} +(-193.914 - 223.788i) q^{31} +(31.6743 - 4.55407i) q^{32} +(-168.294 + 283.316i) q^{33} +(40.3244 + 137.332i) q^{34} +(-2.52429 - 8.59693i) q^{35} +(-64.8098 + 86.3927i) q^{36} +(-51.7905 + 7.44635i) q^{37} +(-136.219 - 157.206i) q^{38} +(95.5734 + 287.640i) q^{39} +(-7.92804 - 12.3363i) q^{40} +(374.085 + 53.7852i) q^{41} +(-39.5372 - 31.8942i) q^{42} +(-263.588 - 228.400i) q^{43} +(-243.397 - 71.4679i) q^{44} +(48.3497 + 10.5693i) q^{45} +(-121.442 - 184.174i) q^{46} +282.518i q^{47} +(-76.7937 - 31.8547i) q^{48} +(-208.971 + 241.165i) q^{49} +(131.527 - 204.660i) q^{50} +(92.1472 - 360.265i) q^{51} +(-196.288 + 126.147i) q^{52} +(134.514 + 294.544i) q^{53} +(259.397 - 106.983i) q^{54} +(16.5436 + 115.064i) q^{55} +(16.2445 - 35.5705i) q^{56} +(95.6856 + 531.895i) q^{57} +(15.4945 - 4.54960i) q^{58} +(338.243 + 154.471i) q^{59} +(1.34049 + 38.0750i) q^{60} +(401.234 - 347.671i) q^{61} +(-538.710 + 246.021i) q^{62} +(45.9956 + 123.703i) q^{63} +(9.10815 - 63.3486i) q^{64} +(89.9499 + 57.8073i) q^{65} +(448.851 + 482.592i) q^{66} +(-78.3293 + 266.765i) q^{67} +286.260 q^{68} +(26.8942 + 572.526i) q^{69} -17.9197 q^{70} +(266.675 - 908.210i) q^{71} +(129.268 + 173.048i) q^{72} +(-140.068 - 90.0161i) q^{73} +(-14.8927 + 103.581i) q^{74} +(-565.348 + 282.634i) q^{75} +(-378.430 + 172.823i) q^{76} +(-234.275 + 203.001i) q^{77} +(605.828 - 21.3292i) q^{78} +(152.273 + 69.5408i) q^{79} +(-28.1403 + 8.26273i) q^{80} +(-721.368 - 105.213i) q^{81} +(313.997 - 687.557i) q^{82} +(-101.415 - 705.358i) q^{83} +(-83.4825 + 57.9001i) q^{84} +(-54.4942 - 119.326i) q^{85} +(-586.820 + 377.126i) q^{86} +(-40.6469 - 10.3965i) q^{87} +(-274.292 + 426.807i) q^{88} +(-226.170 + 261.014i) q^{89} +(47.5257 - 86.8271i) q^{90} +285.129i q^{91} +(-421.855 + 129.270i) q^{92} +(1529.75 + 165.252i) q^{93} +(542.148 + 159.189i) q^{94} +(144.080 + 124.846i) q^{95} +(-104.399 + 129.417i) q^{96} +(-1352.18 - 194.414i) q^{97} +(345.045 + 536.900i) q^{98} +(-362.274 - 1673.53i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} + 96 q^{4} - 8 q^{6} - 36 q^{9} + 32 q^{12} - 96 q^{13} - 748 q^{15} - 384 q^{16} - 40 q^{18} + 1320 q^{21} + 32 q^{24} - 144 q^{25} - 56 q^{27} - 1496 q^{30} - 72 q^{31} - 1936 q^{33} + 144 q^{36}+ \cdots + 2310 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 + 96 * q^4 - 8 * q^6 - 36 * q^9 + 32 * q^12 - 96 * q^13 - 748 * q^15 - 384 * q^16 - 40 * q^18 + 1320 * q^21 + 32 * q^24 - 144 * q^25 - 56 * q^27 - 1496 * q^30 - 72 * q^31 - 1936 * q^33 + 144 * q^36 - 1188 * q^37 + 660 * q^39 + 1716 * q^43 + 96 * q^46 - 128 * q^48 + 4860 * q^49 + 384 * q^52 + 3036 * q^54 + 3708 * q^55 + 4224 * q^57 + 1032 * q^58 + 88 * q^60 - 1056 * q^61 - 4180 * q^63 + 1536 * q^64 - 5456 * q^66 - 2904 * q^67 - 7832 * q^69 - 6432 * q^70 - 1952 * q^72 + 576 * q^73 - 6914 * q^75 + 1372 * q^78 + 3696 * q^79 + 9264 * q^81 + 3672 * q^82 + 3784 * q^84 + 4104 * q^85 + 938 * q^87 + 2924 * q^93 + 1296 * q^94 - 128 * q^96 - 25344 * q^97 + 2310 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{1}{22}\right)$

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 $

$2$	0.563465	−	1.91899i	0.199215	−	0.678464i
$2$	0.563465	−	1.91899i	0.199215	−	0.678464i
$3$	−3.80483	+	3.53882i	−0.732240	+	0.681046i
$3$	−3.80483	+	3.53882i	−0.732240	+	0.681046i
$4$	−3.36501	−	2.16256i	−0.420627	−	0.270320i
$5$	−0.260866	+	1.81436i	−0.0233325	+	0.162281i	−0.998156	−	0.0606952i	$-0.980668\pi$
$5$	−0.260866	+	1.81436i	−0.0233325	+	0.162281i	0.974824	+	0.222977i	$0.0715773\pi$
$6$	4.64705	+	9.29542i	0.316192	+	0.632473i
$7$	−4.44632	+	2.03056i	−0.240078	+	0.109640i	−0.531821	−	0.846857i	$-0.678492\pi$
$7$	−4.44632	+	2.03056i	−0.240078	+	0.109640i	0.291743	+	0.956497i	$0.405765\pi$
$8$	−6.04600	+	5.23889i	−0.267198	+	0.231528i
$9$	1.95351	−	26.9292i	0.0723523	−	0.997379i
$10$	3.33474	+	1.52293i	0.105454	+	0.0481592i
$11$	60.8494	−	17.8670i	1.66789	−	0.489736i	0.694614	−	0.719383i	$-0.255575\pi$
$11$	60.8494	−	17.8670i	1.66789	−	0.489736i	0.973274	+	0.229646i	$0.0737570\pi$
$12$	20.4562	−	3.67999i	0.492101	−	0.0885267i
$13$	24.2320	−	53.0606i	0.516980	−	1.13203i	−0.453590	−	0.891210i	$-0.649857\pi$
$13$	24.2320	−	53.0606i	0.516980	−	1.13203i	0.970570	−	0.240818i	$-0.0774158\pi$
$14$	1.39128	+	9.67657i	0.0265597	+	0.184727i
$15$	−5.42815	−	7.82650i	−0.0934361	−	0.134720i
$16$	6.64664	+	14.5541i	0.103854	+	0.227408i
$17$	−60.2044	+	38.6910i	−0.858924	+	0.551997i	−0.894346	−	0.447375i	$-0.852359\pi$
$17$	−60.2044	+	38.6910i	−0.858924	+	0.551997i	0.0354220	+	0.999372i	$0.488722\pi$
$18$	−50.5761	−	18.9224i	−0.662272	−	0.247781i
$19$	56.2301	−	87.4958i	0.678951	−	1.05647i	−0.315258	−	0.949006i	$-0.602091\pi$
$19$	56.2301	−	87.4958i	0.678951	−	1.05647i	0.994209	−	0.107463i	$-0.0342727\pi$
$20$	4.80149	−	5.54121i	0.0536823	−	0.0619526i
$21$	9.73169	−	23.4607i	0.101125	−	0.243788i
$22$		−	126.836i		−	1.22916i
$23$	71.2495	−	84.2051i	0.645937	−	0.763391i
$23$	71.2495	−	84.2051i	0.645937	−	0.763391i
$24$	4.46454	−	41.3288i	0.0379717	−	0.351508i
$25$	116.713	+	34.2700i	0.933702	+	0.274160i
$26$	−88.1688	−	76.3987i	−0.665051	−	0.576270i
$27$	87.8649	+	109.374i	0.626282	+	0.779597i
$28$	19.3531	+	2.78256i	0.130621	+	0.0187805i
$29$	4.36531	+	6.79256i	0.0279523	+	0.0434947i	0.854949	−	0.518713i	$-0.173589\pi$
$29$	4.36531	+	6.79256i	0.0279523	+	0.0434947i	−0.826996	+	0.562207i	$0.809952\pi$
$30$	−18.0775	+	6.00658i	−0.110016	+	0.0365549i
$31$	−193.914	−	223.788i	−1.12348	−	1.29657i	−0.950182	−	0.311696i	$-0.899103\pi$
$31$	−193.914	−	223.788i	−1.12348	−	1.29657i	−0.173299	−	0.984869i	$-0.555443\pi$
$32$	31.6743	−	4.55407i	0.174977	−	0.0251579i
$33$	−168.294	+	283.316i	−0.887762	+	1.49451i
$34$	40.3244	+	137.332i	0.203400	+	0.692715i
$35$	−2.52429	−	8.59693i	−0.0121909	−	0.0415184i
$36$	−64.8098	+	86.3927i	−0.300045	+	0.399966i
$37$	−51.7905	+	7.44635i	−0.230116	+	0.0330857i	−0.256408	−	0.966569i	$-0.582539\pi$
$37$	−51.7905	+	7.44635i	−0.230116	+	0.0330857i	0.0262919	+	0.999654i	$0.491630\pi$
$38$	−136.219	−	157.206i	−0.581519	−	0.671109i
$39$	95.5734	+	287.640i	0.392410	+	1.18100i
$40$	−7.92804	−	12.3363i	−0.0313383	−	0.0487634i
$41$	374.085	+	53.7852i	1.42493	+	0.204874i	0.811259	−	0.584687i	$-0.198782\pi$
$41$	374.085	+	53.7852i	1.42493	+	0.204874i	0.613672	+	0.789561i	$0.289692\pi$
$42$	−39.5372	−	31.8942i	−0.145255	−	0.117176i
$43$	−263.588	−	228.400i	−0.934810	−	0.810017i	0.0471925	−	0.998886i	$-0.484973\pi$
$43$	−263.588	−	228.400i	−0.934810	−	0.810017i	−0.982002	+	0.188868i	$0.939518\pi$
$44$	−243.397	−	71.4679i	−0.833944	−	0.244868i
$45$	48.3497	+	10.5693i	0.160168	+	0.0350128i
$46$	−121.442	−	184.174i	−0.389253	−	0.590324i
$47$			282.518i			0.876797i	0.898781	+	0.438399i	$0.144454\pi$
$47$			282.518i			0.876797i	−0.898781	+	0.438399i	$0.855546\pi$
$48$	−76.7937	−	31.8547i	−0.230921	−	0.0957881i
$49$	−208.971	+	241.165i	−0.609244	+	0.703105i
$50$	131.527	−	204.660i	0.372015	−	0.578867i
$51$	92.1472	−	360.265i	0.253004	−	0.989162i
$52$	−196.288	+	126.147i	−0.523466	+	0.336411i
$53$	134.514	+	294.544i	0.348620	+	0.763372i	0.999989	+	0.00461077i	$0.00146766\pi$
$53$	134.514	+	294.544i	0.348620	+	0.763372i	−0.651369	+	0.758761i	$0.725805\pi$
$54$	259.397	−	106.983i	0.653693	−	0.269602i
$55$	16.5436	+	115.064i	0.0405590	+	0.282094i
$56$	16.2445	−	35.5705i	0.0387637	−	0.0848806i
$57$	95.6856	+	531.895i	0.222348	+	1.23599i
$58$	15.4945	−	4.54960i	0.0350781	−	0.0102999i
$59$	338.243	+	154.471i	0.746365	+	0.340854i	0.752029	−	0.659130i	$-0.229075\pi$
$59$	338.243	+	154.471i	0.746365	+	0.340854i	−0.00566351	+	0.999984i	$0.501803\pi$
$60$	1.34049	+	38.0750i	0.00288428	+	0.0819243i
$61$	401.234	−	347.671i	0.842175	−	0.729749i	−0.122704	−	0.992443i	$-0.539157\pi$
$61$	401.234	−	347.671i	0.842175	−	0.729749i	0.964879	+	0.262694i	$0.0846111\pi$
$62$	−538.710	+	246.021i	−1.10349	+	0.503946i
$63$	45.9956	+	123.703i	0.0919826	+	0.247382i
$64$	9.10815	−	63.3486i	0.0177894	−	0.123728i
$65$	89.9499	+	57.8073i	0.171645	+	0.110309i
$66$	448.851	+	482.592i	0.837118	+	0.900044i
$67$	−78.3293	+	266.765i	−0.142828	+	0.486426i	−0.999570	−	0.0293182i	$-0.990666\pi$
$67$	−78.3293	+	266.765i	−0.142828	+	0.486426i	0.856743	+	0.515744i	$0.172485\pi$
$68$	286.260			0.510503
$69$	26.8942	+	572.526i	0.0469229	+	0.998899i
$70$	−17.9197			−0.0305974
$71$	266.675	−	908.210i	0.445753	−	1.51809i	−0.364043	−	0.931382i	$-0.618604\pi$
$71$	266.675	−	908.210i	0.445753	−	1.51809i	0.809796	−	0.586712i	$-0.199578\pi$
$72$	129.268	+	173.048i	0.211589	+	0.283249i
$73$	−140.068	−	90.0161i	−0.224571	−	0.144323i	0.423518	−	0.905888i	$-0.360795\pi$
$73$	−140.068	−	90.0161i	−0.224571	−	0.144323i	−0.648089	+	0.761565i	$0.724432\pi$
$74$	−14.8927	+	103.581i	−0.0233952	+	0.162717i
$75$	−565.348	+	282.634i	−0.870410	+	0.435143i
$76$	−378.430	+	172.823i	−0.571170	+	0.260845i
$77$	−234.275	+	203.001i	−0.346729	+	0.300443i
$78$	605.828	−	21.3292i	0.879443	−	0.0309622i
$79$	152.273	+	69.5408i	0.216862	+	0.0990374i	0.520884	−	0.853628i	$-0.325602\pi$
$79$	152.273	+	69.5408i	0.216862	+	0.0990374i	−0.304022	+	0.952665i	$0.598330\pi$
$80$	−28.1403	+	8.26273i	−0.0393273	+	0.0115475i
$81$	−721.368	−	105.213i	−0.989530	−	0.144325i
$82$	313.997	−	687.557i	0.422868	−	0.925951i
$83$	−101.415	−	705.358i	−0.134118	−	0.932808i	−0.940107	−	0.340879i	$-0.889275\pi$
$83$	−101.415	−	705.358i	−0.134118	−	0.932808i	0.805990	−	0.591930i	$-0.201634\pi$
$84$	−83.4825	+	57.9001i	−0.108437	+	0.0752074i
$85$	−54.4942	−	119.326i	−0.0695380	−	0.152267i
$86$	−586.820	+	377.126i	−0.735796	+	0.472867i
$87$	−40.6469	−	10.3965i	−0.0500897	−	0.0128117i
$88$	−274.292	+	426.807i	−0.332268	+	0.517020i
$89$	−226.170	+	261.014i	−0.269371	+	0.310870i	−0.874278	−	0.485426i	$-0.838665\pi$
$89$	−226.170	+	261.014i	−0.269371	+	0.310870i	0.604907	+	0.796296i	$0.293210\pi$
$90$	47.5257	−	86.8271i	0.0556628	−	0.101693i
$91$			285.129i			0.328458i
$92$	−421.855	+	129.270i	−0.478059	+	0.146493i
$93$	1529.75	+	165.252i	1.70568	+	0.184256i
$94$	542.148	+	159.189i	0.594876	+	0.174671i
$95$	144.080	+	124.846i	0.155604	+	0.134831i
$96$	−104.399	+	129.417i	−0.110992	+	0.137589i
$97$	−1352.18	−	194.414i	−1.41539	−	0.203503i	−0.608197	−	0.793786i	$-0.708107\pi$
$97$	−1352.18	−	194.414i	−1.41539	−	0.203503i	−0.807196	+	0.590284i	$0.799016\pi$
$98$	345.045	+	536.900i	0.355661	+	0.553419i
$99$	−362.274	−	1673.53i	−0.367777	−	1.69895i
$100$	−318.629	−	367.718i	−0.318629	−	0.367718i
$101$	−1524.79	+	219.232i	−1.50220	+	0.215984i	−0.843790	−	0.536673i	$-0.819681\pi$
$101$	−1524.79	+	219.232i	−1.50220	+	0.215984i	−0.658412	+	0.752657i	$0.728772\pi$
$102$	−639.423	−	379.826i	−0.620709	−	0.368710i
$103$	−339.953	−	1157.77i	−0.325209	−	1.10756i	−0.946157	−	0.323709i	$-0.895070\pi$
$103$	−339.953	−	1157.77i	−0.325209	−	1.10756i	0.620948	−	0.783852i	$-0.286748\pi$
$104$	131.472	+	447.753i	0.123961	+	0.422171i
$105$	40.0275	+	23.7769i	0.0372027	+	0.0220989i
$106$	641.019	−	92.1646i	0.587371	−	0.0844511i
$107$	−26.9839	−	31.1410i	−0.0243797	−	0.0281357i	0.743429	−	0.668815i	$-0.233198\pi$
$107$	−26.9839	−	31.1410i	−0.0243797	−	0.0281357i	−0.767808	+	0.640679i	$0.778653\pi$
$108$	−59.1377	−	558.060i	−0.0526901	−	0.497216i
$109$	−12.6469	−	19.6790i	−0.0111133	−	0.0172927i	0.835652	−	0.549259i	$-0.185090\pi$
$109$	−12.6469	−	19.6790i	−0.0111133	−	0.0172927i	−0.846766	+	0.531966i	$0.821453\pi$
$110$	230.127	+	33.0873i	0.199471	+	0.0286795i
$111$	170.703	−	211.609i	0.145968	−	0.180947i
$112$	−59.1061	−	51.2157i	−0.0498661	−	0.0432092i
$113$	553.688	+	162.577i	0.460943	+	0.135345i	0.503956	−	0.863729i	$-0.331877\pi$
$113$	553.688	+	162.577i	0.460943	+	0.135345i	−0.0430126	+	0.999075i	$0.513696\pi$
$114$	1074.61	+	116.085i	0.882868	+	0.0953717i
$115$	134.192	+	151.239i	0.108813	+	0.122635i
$116$		−	32.2973i		−	0.0258511i
$117$	−1381.55	−	756.203i	−1.09166	−	0.597530i
$118$	487.015	−	562.046i	0.379944	−	0.438479i
$119$	189.123	−	294.281i	0.145688	−	0.226695i
$120$	73.8207	+	18.8815i	0.0561573	+	0.0143637i
$121$	2263.71	−	1454.80i	1.70076	−	1.09301i
$122$	−441.094	−	965.862i	−0.327335	−	0.716763i
$123$	−1613.67	+	1119.17i	−1.18292	+	0.820427i
$124$	168.566	+	1172.40i	0.122078	+	0.849070i
$125$	−187.807	+	411.241i	−0.134384	+	0.294260i
$126$	263.301	−	18.5628i	0.186164	−	0.0131247i
$127$	937.678	−	275.327i	0.655162	−	0.192373i	0.0627763	−	0.998028i	$-0.480005\pi$
$127$	937.678	−	275.327i	0.655162	−	0.192373i	0.592385	+	0.805655i	$0.298186\pi$
$128$	−116.433	−	53.1731i	−0.0804009	−	0.0367178i
$129$	1811.18	−	63.7654i	1.23616	−	0.0435212i
$130$	161.615	−	140.040i	0.109035	−	0.0944795i
$131$	−1662.48	+	759.228i	−1.10879	+	0.506367i	−0.883739	−	0.467980i	$-0.844982\pi$
$131$	−1662.48	+	759.228i	−1.10879	+	0.506367i	−0.225050	+	0.974347i	$0.572255\pi$
$132$	1179.00	−	589.416i	0.777414	−	0.388652i
$133$	−72.3511	+	503.213i	−0.0471702	+	0.328076i
$134$	467.783	+	300.626i	0.301569	+	0.193807i
$135$	−221.366	+	130.887i	−0.141127	+	0.0834439i
$136$	161.298	−	549.330i	0.101700	−	0.346358i
$137$	3035.98			1.89329			0.946647	−	0.322273i	$-0.104447\pi$
$137$	3035.98			1.89329			0.946647	+	0.322273i	$0.104447\pi$
$138$	1113.82	+	270.989i	0.687064	+	0.167160i
$139$	721.481			0.440253			0.220127	−	0.975471i	$-0.429353\pi$
$139$	721.481			0.440253			0.220127	+	0.975471i	$0.429353\pi$
$140$	−10.0971	+	34.3877i	−0.00609546	+	0.0207592i
$141$	−999.780	−	1074.93i	−0.597140	−	0.642027i
$142$	−1592.58	−	1023.49i	−0.941172	−	0.604854i
$143$	526.467	−	3661.66i	0.307870	−	2.14128i
$144$	404.915	−	150.557i	0.234326	−	0.0871281i
$145$	−13.4629	+	6.14830i	−0.00771058	+	0.00352130i
$146$	−251.663	+	218.067i	−0.142656	+	0.123612i
$147$	−58.3409	−	1657.10i	−0.0327339	−	0.929765i
$148$	190.379	+	86.9432i	0.105737	+	0.0482884i
$149$	292.558	−	85.9028i	0.160854	−	0.0472311i	−0.200314	−	0.979732i	$-0.564196\pi$
$149$	292.558	−	85.9028i	0.160854	−	0.0472311i	0.361168	+	0.932501i	$0.382378\pi$
$150$	223.817	+	1244.15i	0.121830	+	0.677229i
$151$	−126.311	+	276.582i	−0.0680729	+	0.149059i	−0.940610	−	0.339489i	$-0.889746\pi$
$151$	−126.311	+	276.582i	−0.0680729	+	0.149059i	0.872537	+	0.488548i	$0.162473\pi$
$152$	118.413	+	823.583i	0.0631881	+	0.439483i
$153$	924.310	+	1696.84i	0.488405	+	0.896612i
$154$	257.550	+	563.955i	0.134766	+	0.295096i
$155$	456.618	−	293.450i	0.236622	−	0.152068i
$156$	300.433	−	1174.59i	0.154192	−	0.602839i
$157$	−1874.43	+	2916.67i	−0.952838	+	1.48265i	−0.0787410	+	0.996895i	$0.525090\pi$
$157$	−1874.43	+	2916.67i	−0.952838	+	1.48265i	−0.874098	+	0.485750i	$0.838546\pi$
$158$	219.248	−	253.026i	0.110395	−	0.127403i
$159$	−1554.14	−	644.670i	−0.775165	−	0.321545i
$160$			58.6566i			0.0289826i
$161$	−145.814	+	519.079i	−0.0713773	+	0.254094i
$162$	−608.368	+	1325.01i	−0.295049	+	0.642609i
$163$	1381.26	+	405.575i	0.663735	+	0.194890i	0.596211	−	0.802828i	$-0.296672\pi$
$163$	1381.26	+	405.575i	0.663735	+	0.194890i	0.0675234	+	0.997718i	$0.478490\pi$
$164$	−1142.49	−	989.970i	−0.543983	−	0.471364i
$165$	−470.135	−	379.253i	−0.221818	−	0.178938i
$166$	−1410.72	−	202.830i	−0.659595	−	0.0948355i
$167$	340.782	+	530.267i	0.157907	+	0.245708i	0.911188	−	0.411991i	$-0.135166\pi$
$167$	340.782	+	530.267i	0.157907	+	0.245708i	−0.753281	+	0.657699i	$0.771530\pi$
$168$	64.0700	+	192.826i	0.0294233	+	0.0885528i
$169$	−789.514	−	911.147i	−0.359360	−	0.414723i
$170$	−259.690	+	37.3378i	−0.117161	+	0.0168452i
$171$	−2246.35	−	1685.16i	−1.00458	−	0.753610i
$172$	393.048	+	1338.60i	0.174242	+	0.593413i
$173$	556.879	+	1896.56i	0.244732	+	0.833482i	0.986631	+	0.162970i	$0.0521074\pi$
$173$	556.879	+	1896.56i	0.244732	+	0.833482i	−0.741899	+	0.670512i	$0.766074\pi$
$174$	−42.8538	+	72.1428i	−0.0186709	+	0.0314318i
$175$	−588.529	+	84.6177i	−0.254221	+	0.0365514i
$176$	664.482	+	766.853i	0.284586	+	0.328430i
$177$	−1833.60	+	609.248i	−0.778656	+	0.258722i
$178$	373.444	+	581.090i	0.157252	+	0.244688i
$179$	428.772	+	61.6482i	0.179039	+	0.0257419i	0.231251	−	0.972894i	$-0.425718\pi$
$179$	428.772	+	61.6482i	0.179039	+	0.0257419i	−0.0522122	+	0.998636i	$0.516627\pi$
$180$	−139.841	−	140.125i	−0.0579062	−	0.0580240i
$181$	1709.44	+	1481.24i	0.701999	+	0.608285i	0.930947	−	0.365153i	$-0.118983\pi$
$181$	1709.44	+	1481.24i	0.701999	+	0.608285i	−0.228949	+	0.973438i	$0.573529\pi$
$182$	547.159	+	160.660i	0.222847	+	0.0654337i
$183$	−296.282	+	2742.72i	−0.119682	+	1.10791i
$184$	10.3666	+	882.372i	0.00415347	+	0.353529i
$185$		−	95.9092i		−	0.0381156i
$186$	1179.08	−	2842.46i	0.464808	−	1.12054i
$187$	−2972.11	+	3430.00i	−1.16226	+	1.34132i
$188$	610.963	−	950.677i	0.237016	−	0.368804i
$189$	−612.767	−	307.898i	−0.235832	−	0.118499i
$190$	320.763	−	206.142i	0.122477	−	0.0787110i
$191$	−556.362	−	1218.26i	−0.210769	−	0.461521i	0.774490	−	0.632586i	$-0.218006\pi$
$191$	−556.362	−	1218.26i	−0.210769	−	0.461521i	−0.985260	+	0.171065i	$0.945279\pi$
$192$	189.524	+	273.263i	0.0712382	+	0.102714i
$193$	−138.051	−	960.165i	−0.0514877	−	0.358105i	−0.999236	−	0.0390853i	$-0.987556\pi$
$193$	−138.051	−	960.165i	−0.0514877	−	0.358105i	0.947748	−	0.319019i	$-0.103354\pi$
$194$	−1134.98	+	2485.27i	−0.420037	+	0.919752i
$195$	−546.814	+	98.3693i	−0.200811	+	0.0361250i
$196$	1224.72	−	359.611i	0.446328	−	0.131054i
$197$	57.4699	+	26.2456i	0.0207846	+	0.00949200i	0.425780	−	0.904827i	$-0.360000\pi$
$197$	57.4699	+	26.2456i	0.0207846	+	0.00949200i	−0.404996	+	0.914319i	$0.632727\pi$
$198$	−3415.61	−	247.777i	−1.22594	−	0.0889329i
$199$	−1445.46	+	1252.50i	−0.514905	+	0.446167i	−0.873144	−	0.487462i	$-0.837923\pi$
$199$	−1445.46	+	1252.50i	−0.514905	+	0.446167i	0.358239	+	0.933630i	$0.383377\pi$
$200$	−885.181	+	404.249i	−0.312959	+	0.142924i
$201$	−646.004	−	1292.19i	−0.226694	−	0.453453i
$202$	−438.464	+	3049.58i	−0.152724	+	1.06222i
$203$	−33.2023	−	21.3378i	−0.0114795	−	0.00737744i
$204$	−1089.17	+	1013.02i	−0.373811	+	0.347676i
$205$	−195.172	+	664.694i	−0.0664945	+	0.226460i
$206$	−2413.30			−0.816227
$207$	−2128.39	−	2083.19i	−0.714655	−	0.699477i
$208$	933.312			0.311123
$209$	1858.28	−	6328.73i	0.615024	−	2.09458i
$210$	68.1816	−	63.4147i	0.0224046	−	0.0208382i
$211$	2954.31	+	1898.62i	0.963901	+	0.619462i	0.925075	−	0.379784i	$-0.124002\pi$
$211$	2954.31	+	1898.62i	0.963901	+	0.619462i	0.0388261	+	0.999246i	$0.487638\pi$
$212$	184.329	−	1282.04i	0.0597160	−	0.415334i
$213$	2199.34	+	4399.30i	0.707494	+	1.41519i
$214$	−74.9637	+	34.2348i	−0.0239459	+	0.0109357i
$215$	483.162	−	418.662i	0.153262	−	0.132802i
$216$	−1104.23	−	200.963i	−0.347840	−	0.0633046i
$217$	1316.62	+	601.279i	0.411879	+	0.188099i
$218$	−44.8897	+	13.1808i	−0.0139464	+	0.00409503i
$219$	851.486	−	153.178i	0.262731	−	0.0472641i
$220$	193.163	−	422.967i	0.0591956	−	0.129620i
$221$	594.098	+	4132.05i	0.180830	+	1.25770i
$222$	−309.890	−	446.811i	−0.0936868	−	0.135081i
$223$	1683.73	+	3686.86i	0.505610	+	1.10713i	0.974605	+	0.223930i	$0.0718888\pi$
$223$	1683.73	+	3686.86i	0.505610	+	1.10713i	−0.468995	+	0.883201i	$0.655384\pi$
$224$	−131.587	+	84.5655i	−0.0392500	+	0.0252244i
$225$	1150.86	−	3076.04i	0.340997	−	0.911419i
$226$	623.968	−	970.913i	0.183654	−	0.285771i
$227$	−3096.43	+	3573.48i	−0.905364	+	1.04485i	0.0934241	+	0.995626i	$0.470219\pi$
$227$	−3096.43	+	3573.48i	−0.905364	+	1.04485i	−0.998788	+	0.0492192i	$0.984327\pi$
$228$	828.274	−	1996.76i	0.240587	−	0.579994i
$229$			1911.89i			0.551710i	0.961199	+	0.275855i	$0.0889610\pi$
$229$			1911.89i			0.551710i	−0.961199	+	0.275855i	$0.911039\pi$
$230$	365.837	−	172.295i	0.104881	−	0.0493947i
$231$	172.996	−	1601.44i	0.0492739	−	0.456135i
$232$	−61.9781	−	18.1984i	−0.0175391	−	0.00514993i
$233$	−452.253	−	391.879i	−0.127159	−	0.110184i	0.588960	−	0.808162i	$-0.299538\pi$
$233$	−452.253	−	391.879i	−0.127159	−	0.110184i	−0.716119	+	0.697978i	$0.754083\pi$
$234$	−2229.60	+	2225.07i	−0.622877	+	0.621613i
$235$	−512.590	−	73.6992i	−0.142288	−	0.0204579i
$236$	−804.141	−	1251.27i	−0.221801	−	0.345130i
$237$	−825.466	+	274.276i	−0.226244	+	0.0751736i
$238$	−458.158	−	528.742i	−0.124781	−	0.144005i
$239$	5022.15	−	722.077i	1.35923	−	0.195428i	0.576148	−	0.817345i	$-0.304555\pi$
$239$	5022.15	−	722.077i	1.35923	−	0.195428i	0.783083	+	0.621918i	$0.213646\pi$
$240$	77.8288	−	131.022i	0.0209326	−	0.0352392i
$241$	950.198	+	3236.08i	0.253974	+	0.864955i	0.983486	+	0.180987i	$0.0579291\pi$
$241$	950.198	+	3236.08i	0.253974	+	0.864955i	−0.729512	+	0.683968i	$0.760253\pi$
$242$	−1516.21	−	5163.75i	−0.402752	−	1.37165i
$243$	3117.01	−	2152.47i	0.822866	−	0.568235i
$244$	−2102.02	+	302.224i	−0.551508	+	0.0792948i
$245$	−383.047	−	442.060i	−0.0998856	−	0.115274i
$246$	1238.43	+	3727.22i	0.320974	+	0.966011i
$247$	−3280.02	−	5103.80i	−0.844949	−	1.31477i
$248$	2344.80	+	337.132i	0.600383	+	0.0863221i
$249$	2882.00	+	2324.88i	0.733492	+	0.591700i
$250$	683.342	+	592.119i	0.172873	+	0.149796i
$251$	3810.82	+	1118.96i	0.958314	+	0.281386i	0.723244	−	0.690592i	$-0.242650\pi$
$251$	3810.82	+	1118.96i	0.958314	+	0.281386i	0.235069	+	0.971979i	$0.424468\pi$
$252$	112.739	−	515.730i	0.0281821	−	0.128920i
$253$	2831.00	−	6396.84i	0.703491	−	1.58959i
$254$		−	1954.53i		−	0.482827i
$255$	629.613	+	261.169i	0.154619	+	0.0641374i
$256$	−167.644	+	193.472i	−0.0409288	+	0.0472343i
$257$	241.388	−	375.607i	0.0585889	−	0.0911661i	−0.810723	−	0.585430i	$-0.800926\pi$
$257$	241.388	−	375.607i	0.0585889	−	0.0911661i	0.869312	+	0.494264i	$0.164562\pi$
$258$	898.170	−	3511.55i	0.216735	−	0.847363i
$259$	215.157	−	138.273i	0.0516185	−	0.0331732i
$260$	−177.671	−	389.045i	−0.0423795	−	0.0927981i
$261$	191.446	−	104.285i	0.0454031	−	0.0247321i
$262$	520.200	+	3618.07i	0.122664	+	0.853150i
$263$	−2368.07	+	5185.35i	−0.555215	+	1.21575i	0.399089	+	0.916912i	$0.369326\pi$
$263$	−2368.07	+	5185.35i	−0.555215	+	1.21575i	−0.954304	+	0.298838i	$0.903401\pi$
$264$	−466.756	−	2594.60i	−0.108814	−	0.604873i
$265$	−569.499	+	167.220i	−0.132015	+	0.0387632i
$266$	924.891	+	422.384i	0.213191	+	0.0973609i
$267$	−63.1427	−	1793.49i	−0.0144729	−	0.411086i
$268$	840.476	−	728.276i	0.191568	−	0.165995i
$269$	−7174.96	+	3276.69i	−1.62626	+	0.742690i	−0.999338	−	0.0363890i	$-0.988414\pi$
$269$	−7174.96	+	3276.69i	−1.62626	+	0.742690i	−0.626926	+	0.779079i	$0.715687\pi$
$270$	126.438	+	498.547i	0.0284991	+	0.112373i
$271$	1096.39	−	7625.58i	0.245761	−	1.70930i	−0.376437	−	0.926442i	$-0.622851\pi$
$271$	1096.39	−	7625.58i	0.245761	−	1.70930i	0.622198	−	0.782860i	$-0.286240\pi$
$272$	−963.271	−	619.056i	−0.214731	−	0.137999i
$273$	−1009.02	−	1084.87i	−0.223695	−	0.240510i
$274$	1710.67	−	5826.00i	0.377172	−	1.28453i
$275$	7714.20			1.69158
$276$	1147.62	−	1984.72i	0.250286	−	0.432848i
$277$	−1308.38			−0.283802			−0.141901	−	0.989881i	$-0.545321\pi$
$277$	−1308.38			−0.283802			−0.141901	+	0.989881i	$0.545321\pi$
$278$	406.529	−	1384.51i	0.0877050	−	0.298696i
$279$	−6405.26	+	4784.77i	−1.37445	+	1.02673i
$280$	60.3001	+	38.7525i	0.0128701	+	0.00827110i
$281$	−1058.43	+	7361.51i	−0.224699	+	1.56281i	0.495227	+	0.868764i	$0.335085\pi$
$281$	−1058.43	+	7361.51i	−0.224699	+	1.56281i	−0.719926	+	0.694051i	$0.755824\pi$
$282$	−2626.12	+	1312.88i	−0.554551	+	0.277236i
$283$	245.116	−	111.941i	0.0514863	−	0.0235130i	−0.389505	−	0.921024i	$-0.627354\pi$
$283$	245.116	−	111.941i	0.0514863	−	0.0235130i	0.440992	+	0.897511i	$0.354627\pi$
$284$	−2861.42	+	2479.44i	−0.597867	+	0.518055i
$285$	−990.011	+	34.8549i	−0.205766	+	0.00724430i
$286$	−6730.03	−	3073.50i	−1.39145	−	0.635454i
$287$	−1772.51	+	520.457i	−0.364558	+	0.107044i
$288$	−60.7617	−	861.861i	−0.0124320	−	0.176339i
$289$	86.6417	−	189.719i	0.0176352	−	0.0386157i
$290$	4.21263	+	29.2995i	0.000853014	+	0.00593284i
$291$	5832.82	−	4045.41i	1.17500	−	0.814935i
$292$	276.665	+	605.811i	0.0554472	+	0.121412i
$293$	197.579	−	126.976i	0.0393948	−	0.0253175i	−0.520795	−	0.853682i	$-0.674364\pi$
$293$	197.579	−	126.976i	0.0393948	−	0.0253175i	0.560190	+	0.828364i	$0.310728\pi$
$294$	−3212.83	−	821.764i	−0.637333	−	0.163014i
$295$	−368.502	+	573.400i	−0.0727288	+	0.113168i
$296$	274.115	−	316.345i	0.0538263	−	0.0621189i
$297$	7300.71	+	5085.48i	1.42637	+	0.993567i
$298$		−	609.818i		−	0.118543i
$299$	−2741.46	−	5821.00i	−0.530243	−	1.12588i
$300$	2513.62	+	271.533i	0.483746	+	0.0522566i
$301$	1635.78	+	480.308i	0.313238	+	0.0919750i
$302$	459.585	+	398.232i	0.0875700	+	0.0758798i
$303$	5025.76	−	6230.10i	0.952878	−	1.18122i
$304$	1647.17	+	236.827i	0.310761	+	0.0446807i
$305$	526.132	+	818.678i	0.0987746	+	0.153696i
$306$	3777.03	−	817.626i	0.705616	−	0.152747i
$307$	−1475.72	−	1703.07i	−0.274345	−	0.316611i	0.601811	−	0.798638i	$-0.294446\pi$
$307$	−1475.72	−	1703.07i	−0.274345	−	0.316611i	−0.876156	+	0.482027i	$0.839901\pi$
$308$	1227.34	−	176.465i	0.227059	−	0.0326462i
$309$	5390.61	+	3202.10i	0.992431	+	0.589518i
$310$	−305.839	−	1041.59i	−0.0560338	−	0.190834i
$311$	−2190.39	−	7459.79i	−0.399375	−	1.36015i	−0.876538	−	0.481333i	$-0.840153\pi$
$311$	−2190.39	−	7459.79i	−0.399375	−	1.36015i	0.477163	−	0.878815i	$-0.341665\pi$
$312$	−2084.75	−	1238.37i	−0.378287	−	0.224708i
$313$	1932.07	−	277.790i	0.348904	−	0.0501648i	0.0343650	−	0.999409i	$-0.489059\pi$
$313$	1932.07	−	277.790i	0.348904	−	0.0501648i	0.314539	+	0.949244i	$0.398150\pi$
$314$	4540.87	+	5240.44i	0.816102	+	0.941832i
$315$	−236.440	+	51.1829i	−0.0422917	+	0.00915501i
$316$	−362.015	−	563.306i	−0.0644460	−	0.100280i
$317$	−4035.50	−	580.217i	−0.715003	−	0.102802i	−0.224794	−	0.974406i	$-0.572171\pi$
$317$	−4035.50	−	580.217i	−0.715003	−	0.102802i	−0.490210	+	0.871604i	$0.663080\pi$
$318$	−2112.82	+	2619.12i	−0.372581	+	0.461865i
$319$	386.989	+	335.328i	0.0679223	+	0.0588550i
$320$	112.561	+	33.0509i	0.0196636	+	0.00577376i
$321$	212.872	+	22.9954i	0.0370135	+	0.00399838i
$322$	913.945	+	572.298i	0.158174	+	0.0990464i
$323$			7443.23i			1.28221i
$324$	2199.88	+	1914.05i	0.377209	+	0.328197i
$325$	4646.57	−	5362.43i	0.793062	−	0.915243i
$326$	1556.59	−	2422.09i	0.264452	−	0.411495i
$327$	117.760	+	30.1201i	0.0199147	+	0.00509371i
$328$	−2543.49	+	1634.60i	−0.428173	+	0.275170i
$329$	−573.671	−	1256.16i	−0.0961322	−	0.210500i
$330$	−992.685	+	688.487i	−0.165593	+	0.114848i
$331$	−1309.81	−	9109.93i	−0.217504	−	1.51277i	−0.747209	−	0.664589i	$-0.768607\pi$
$331$	−1309.81	−	9109.93i	−0.217504	−	1.51277i	0.529706	−	0.848181i	$-0.322302\pi$
$332$	−1184.12	+	2592.86i	−0.195744	+	0.428619i
$333$	99.3512	+	1409.23i	0.0163496	+	0.231907i
$334$	1209.59	−	355.169i	0.198162	−	0.0581855i
$335$	−463.575	−	211.708i	−0.0756054	−	0.0345278i
$336$	406.132	−	14.2985i	0.0659415	−	0.00232157i
$337$	−6668.74	+	5778.50i	−1.07795	+	0.934050i	−0.998029	−	0.0627513i	$-0.980013\pi$
$337$	−6668.74	+	5778.50i	−1.07795	+	0.934050i	−0.0799218	+	0.996801i	$0.525467\pi$
$338$	−2193.34	+	1001.67i	−0.352965	+	0.161194i
$339$	−2682.02	+	1340.82i	−0.429698	+	0.214818i
$340$	−74.6755	+	519.380i	−0.0119113	+	0.0828451i
$341$	−15797.9	−	10152.7i	−2.50882	−	1.61232i
$342$	−4499.53	+	3361.18i	−0.711424	+	0.531439i
$343$	911.801	−	3105.31i	0.143535	−	0.488836i
$344$	2790.22			0.437321
$345$	−1045.78	−	100.557i	−0.163197	−	0.0156921i
$346$	3953.24			0.614242
$347$	−724.983	+	2469.07i	−0.112159	+	0.381978i	−0.996372	−	0.0851058i	$-0.972877\pi$
$347$	−724.983	+	2469.07i	−0.112159	+	0.381978i	0.884213	+	0.467084i	$0.154695\pi$
$348$	114.294	+	122.886i	0.0176058	+	0.0189292i
$349$	−3634.82	−	2335.96i	−0.557500	−	0.358284i	0.231349	−	0.972871i	$-0.425686\pi$
$349$	−3634.82	−	2335.96i	−0.557500	−	0.358284i	−0.788849	+	0.614587i	$0.789323\pi$
$350$	−169.235	+	1177.06i	−0.0258458	+	0.179761i
$351$	7932.62	−	2011.81i	1.20630	−	0.305933i
$352$	1845.99	−	843.036i	0.279522	−	0.127653i
$353$	−1404.88	+	1217.34i	−0.211825	+	0.183548i	−0.754311	−	0.656517i	$-0.772029\pi$
$353$	−1404.88	+	1217.34i	−0.211825	+	0.183548i	0.542485	+	0.840065i	$0.317483\pi$
$354$	135.966	+	3861.95i	0.0204139	+	0.579831i
$355$	1578.25	+	720.765i	0.235958	+	0.107758i
$356$	1325.53	−	389.209i	0.197339	−	0.0579440i
$357$	321.827	+	1788.96i	0.0477111	+	0.265216i
$358$	359.900	−	788.072i	0.0531322	−	0.116343i
$359$	−1716.48	−	11938.4i	−0.252346	−	1.75510i	−0.584047	−	0.811720i	$-0.698532\pi$
$359$	−1716.48	−	11938.4i	−0.252346	−	1.75510i	0.331701	−	0.943385i	$-0.392378\pi$
$360$	−347.694	+	189.397i	−0.0509030	+	0.0277280i
$361$	−1644.35	−	3600.63i	−0.239737	−	0.524950i
$362$	3805.69	−	2445.77i	0.552548	−	0.355101i
$363$	−3464.77	+	13546.1i	−0.500973	+	1.95864i
$364$	616.609	−	959.463i	0.0887888	−	0.138158i
$365$	199.861	−	230.652i	0.0286608	−	0.0330763i
$366$	5096.30	+	2113.99i	0.727836	+	0.301913i
$367$			3558.36i			0.506117i	0.967451	+	0.253059i	$0.0814365\pi$
$367$			3558.36i			0.506117i	−0.967451	+	0.253059i	$0.918563\pi$
$368$	1699.10	+	477.292i	0.240684	+	0.0676103i
$369$	2179.17	−	9968.74i	0.307434	−	1.40637i
$370$	−184.048	−	54.0415i	−0.0258600	−	0.00759319i
$371$	−1196.18	−	1036.50i	−0.167392	−	0.145046i
$372$	−4790.28	−	3864.26i	−0.667646	−	0.538583i
$373$	−7217.46	−	1037.71i	−1.00189	−	0.144050i	−0.378203	−	0.925723i	$-0.623458\pi$
$373$	−7217.46	−	1037.71i	−1.00189	−	0.144050i	−0.623690	+	0.781672i	$0.714367\pi$
$374$	4907.43	+	7636.12i	0.678496	+	1.05576i
$375$	−740.731	−	2229.32i	−0.102003	−	0.306991i
$376$	−1480.08	−	1708.10i	−0.203003	−	0.234278i
$377$	466.198	−	67.0291i	0.0636880	−	0.00915696i
$378$	−936.124	+	1002.40i	−0.127378	+	0.136397i
$379$	2298.70	+	7828.66i	0.311547	+	1.06103i	0.955260	+	0.295766i	$0.0955748\pi$
$379$	2298.70	+	7828.66i	0.311547	+	1.06103i	−0.643713	+	0.765267i	$0.722607\pi$
$380$	−214.844	−	731.693i	−0.0290034	−	0.0987765i
$381$	−2593.38	+	4365.85i	−0.348721	+	0.587058i
$382$	−2651.32	+	381.202i	−0.355114	+	0.0510576i
$383$	7101.22	+	8195.24i	0.947403	+	1.09336i	0.995523	+	0.0945199i	$0.0301316\pi$
$383$	7101.22	+	8195.24i	0.947403	+	1.09336i	−0.0481199	+	0.998842i	$0.515323\pi$
$384$	631.178	−	209.720i	0.0838793	−	0.0278704i
$385$	−307.202	−	478.016i	−0.0406662	−	0.0632778i
$386$	−1920.33	−	276.102i	−0.253218	−	0.0364073i
$387$	−6665.57	+	6652.05i	−0.875530	+	0.873753i
$388$	4129.67	+	3578.38i	0.540341	+	0.468208i
$389$	11169.8	+	3279.76i	1.45587	+	0.427481i	0.911477	−	0.411351i	$-0.134943\pi$
$389$	11169.8	+	3279.76i	1.45587	+	0.427481i	0.544390	+	0.838832i	$0.316761\pi$
$390$	−119.341	+	1104.76i	−0.0154951	+	0.143440i
$391$	−1031.55	+	7826.24i	−0.133422	+	1.01225i
$392$		−	2552.86i		−	0.328925i
$393$	3638.68	−	8771.95i	0.467041	−	1.12592i
$394$	82.7473	−	95.4955i	0.0105806	−	0.0122106i
$395$	−165.895	+	258.138i	−0.0211319	+	0.0328818i
$396$	−2400.06	+	6414.89i	−0.304564	+	0.814042i
$397$	6867.57	−	4413.52i	0.868195	−	0.557955i	−0.0290051	−	0.999579i	$-0.509234\pi$
$397$	6867.57	−	4413.52i	0.868195	−	0.557955i	0.897200	+	0.441624i	$0.145598\pi$
$398$	1589.06	+	3479.56i	0.200132	+	0.438227i
$399$	−1505.50	−	2170.68i	−0.188895	−	0.272355i
$400$	276.979	+	1926.43i	0.0346224	+	0.240804i
$401$	−630.870	+	1381.41i	−0.0785640	+	0.172031i	−0.944838	−	0.327538i	$-0.893781\pi$
$401$	−630.870	+	1381.41i	−0.0785640	+	0.172031i	0.866274	+	0.499569i	$0.166508\pi$
$402$	−2843.70	+	511.568i	−0.352813	+	0.0634694i
$403$	−16573.3	+	4866.35i	−2.04857	+	0.601514i
$404$	5605.05	+	2559.74i	0.690251	+	0.315227i
$405$	379.075	−	1281.37i	0.0465096	−	0.157215i
$406$	−59.6553	+	51.6916i	−0.00729222	+	0.00631874i
$407$	−3018.37	+	1378.45i	−0.367605	+	0.167880i
$408$	1330.27	+	2660.91i	0.161417	+	0.322879i
$409$	118.086	−	821.304i	0.0142762	−	0.0992931i	−0.981438	−	0.191782i	$-0.938573\pi$
$409$	118.086	−	821.304i	0.0142762	−	0.0992931i	0.995714	+	0.0924892i	$0.0294824\pi$
$410$	1165.57	+	749.063i	0.140398	+	0.0902283i
$411$	−11551.4	+	10743.8i	−1.38635	+	1.28942i
$412$	−1359.81	+	4631.09i	−0.162605	+	0.553780i
$413$	−1817.60			−0.216557
$414$	−5196.89	+	2910.55i	−0.616940	+	0.345521i
$415$	1306.23			0.154507
$416$	525.889	−	1791.01i	0.0619803	−	0.211086i
$417$	−2745.11	+	2553.19i	−0.322371	+	0.299833i
$418$	−11097.7	−	7132.03i	−1.29857	−	0.834543i
$419$	−680.717	+	4734.49i	−0.0793680	+	0.552017i	0.910877	+	0.412678i	$0.135407\pi$
$419$	−680.717	+	4734.49i	−0.0793680	+	0.552017i	−0.990245	+	0.139338i	$0.955502\pi$
$420$	−83.2739	−	166.571i	−0.00967465	−	0.0193520i
$421$	−3802.12	+	1736.37i	−0.440152	+	0.201010i	−0.623149	−	0.782103i	$-0.714147\pi$
$421$	−3802.12	+	1736.37i	−0.440152	+	0.201010i	0.182998	+	0.983113i	$0.441420\pi$
$422$	5308.08	−	4599.47i	0.612306	−	0.530566i
$423$	7607.99	+	551.902i	0.874500	+	0.0634383i
$424$	−2356.35	−	1076.11i	−0.269893	−	0.123256i
$425$	−8352.56	+	2452.53i	−0.953315	+	0.279919i
$426$	9681.45	−	1741.65i	1.10110	−	0.198083i
$427$	−1078.04	+	2360.59i	−0.122178	+	0.267533i
$428$	23.4566	+	163.144i	0.00264911	+	0.0184250i
$429$	10954.8	+	15795.1i	1.23288	+	1.77761i
$430$	−531.162	−	1163.08i	−0.0595696	−	0.130439i
$431$	9495.36	−	6102.30i	1.06120	−	0.681989i	0.111056	−	0.993814i	$-0.464577\pi$
$431$	9495.36	−	6102.30i	1.06120	−	0.681989i	0.950140	+	0.311825i	$0.100940\pi$
$432$	−1007.84	+	2005.77i	−0.112245	+	0.223386i
$433$	−2356.63	+	3666.98i	−0.261553	+	0.406984i	−0.947047	−	0.321094i	$-0.895950\pi$
$433$	−2356.63	+	3666.98i	−0.261553	+	0.406984i	0.685495	+	0.728078i	$0.259586\pi$
$434$	1895.71	−	2187.77i	0.209671	−	0.241973i
$435$	29.4664	−	71.0361i	0.00324783	−	0.00782970i
$436$			93.5697i			0.0102779i
$437$	−3361.22	−	10968.9i	−0.367939	−	1.20072i
$438$	185.835	−	1720.30i	0.0202729	−	0.187669i
$439$	−8029.52	−	2357.68i	−0.872956	−	0.256323i	−0.185584	−	0.982628i	$-0.559418\pi$
$439$	−8029.52	−	2357.68i	−0.872956	−	0.256323i	−0.687372	+	0.726305i	$0.741236\pi$
$440$	−702.828	−	609.004i	−0.0761500	−	0.0659843i
$441$	6086.16	+	6098.54i	0.657182	+	0.658519i
$442$	8264.09	+	1188.20i	0.889327	+	0.127866i
$443$	3915.77	+	6093.05i	0.419963	+	0.653475i	0.985191	−	0.171459i	$-0.0548482\pi$
$443$	3915.77	+	6093.05i	0.419963	+	0.653475i	−0.565228	+	0.824935i	$0.691212\pi$
$444$	−1032.04	+	342.913i	−0.110311	+	0.0366530i
$445$	−414.574	−	478.444i	−0.0441634	−	0.0509672i
$446$	8023.75	−	1153.64i	0.851874	−	0.122481i
$447$	−809.140	+	1362.16i	−0.0856175	+	0.144134i
$448$	88.1356	+	300.162i	0.00929468	+	0.0316548i
$449$	−5154.56	−	17554.8i	−0.541779	−	1.84513i	−0.534518	−	0.845157i	$-0.679507\pi$
$449$	−5154.56	−	17554.8i	−0.541779	−	1.84513i	−0.00726163	−	0.999974i	$-0.502311\pi$
$450$	−5254.40	−	3941.73i	−0.550433	−	0.412922i
$451$	23723.8	−	3410.97i	2.47696	−	0.356133i
$452$	−1511.58	−	1744.46i	−0.157299	−	0.181532i
$453$	−498.182	−	1499.34i	−0.0516703	−	0.155508i
$454$	5112.72	+	7955.54i	0.528528	+	0.822406i
$455$	−517.327	−	74.3804i	−0.0533025	−	0.00766375i
$456$	−3365.05	−	2714.55i	−0.345577	−	0.278773i
$457$	−34.5530	−	29.9404i	−0.00353681	−	0.00306466i	0.653091	−	0.757280i	$-0.273472\pi$
$457$	−34.5530	−	29.9404i	−0.00353681	−	0.00306466i	−0.656627	+	0.754215i	$0.728018\pi$
$458$	3668.90	+	1077.29i	0.374315	+	0.109909i
$459$	−9521.66	−	3185.24i	−0.968264	−	0.323909i
$460$	−124.495	−	799.119i	−0.0126187	−	0.0809980i
$461$		−	10760.1i		−	1.08709i	−0.839380	−	0.543546i	$-0.817081\pi$
$461$		−	10760.1i		−	1.08709i	0.839380	−	0.543546i	$-0.182919\pi$
$462$	−2975.67	−	1234.33i	−0.299655	−	0.124300i
$463$	1594.50	−	1840.15i	0.160049	−	0.184706i	−0.670061	−	0.742306i	$-0.733732\pi$
$463$	1594.50	−	1840.15i	0.160049	−	0.184706i	0.830110	+	0.557600i	$0.188278\pi$
$464$	−69.8450	+	108.681i	−0.00698808	+	0.0108737i
$465$	−698.886	+	2732.42i	−0.0696991	+	0.272501i
$466$	−1006.84	+	647.057i	−0.100088	+	0.0643226i
$467$	7105.25	+	15558.3i	0.704051	+	1.54166i	0.834990	+	0.550265i	$0.185473\pi$
$467$	7105.25	+	15558.3i	0.704051	+	1.54166i	−0.130939	+	0.991390i	$0.541799\pi$
$468$	3013.58	+	5532.31i	0.297656	+	0.546434i
$469$	−193.407	−	1345.17i	−0.0190420	−	0.132440i
$470$	−430.254	+	942.125i	−0.0422258	+	0.0924617i
$471$	−3189.67	−	17730.7i	−0.312043	−	1.73458i
$472$	−2854.27	+	838.090i	−0.278344	+	0.0817293i
$473$	−20120.0	−	9188.50i	−1.95585	−	0.893208i
$474$	61.2103	+	1738.60i	0.00593140	+	0.168474i
$475$	9561.25	−	8284.87i	0.923580	−	0.800286i
$476$	−1272.80	+	581.270i	−0.122561	+	0.0559716i
$477$	8194.61	−	3046.96i	0.786594	−	0.292475i
$478$	1444.15	−	10044.3i	0.138188	−	0.961121i
$479$	9264.05	+	5953.64i	0.883685	+	0.567910i	0.901910	−	0.431924i	$-0.142165\pi$
$479$	9264.05	+	5953.64i	0.883685	+	0.567910i	−0.0182248	+	0.999834i	$0.505801\pi$
$480$	−207.575	−	223.179i	−0.0197385	−	0.0212222i
$481$	−859.879	+	2928.48i	−0.0815116	+	0.277603i
$482$	6745.39			0.637436
$483$	−1282.13	−	2491.02i	−0.120785	−	0.234669i
$484$	−10763.5			−1.01085
$485$	705.475	−	2402.63i	0.0660494	−	0.224944i
$486$	−2374.23	−	7194.35i	−0.221600	−	0.671486i
$487$	8758.78	+	5628.93i	0.814986	+	0.523760i	0.880474	−	0.474094i	$-0.157224\pi$
$487$	8758.78	+	5628.93i	0.814986	+	0.523760i	−0.0654884	+	0.997853i	$0.520861\pi$
$488$	−604.449	+	4204.03i	−0.0560699	+	0.389975i
$489$	−6690.73	+	3344.89i	−0.618743	+	0.309328i
$490$	−1064.14	+	485.977i	−0.0981081	+	0.0448045i
$491$	−12938.8	+	11211.5i	−1.18924	+	1.03049i	−0.190436	+	0.981700i	$0.560990\pi$
$491$	−12938.8	+	11211.5i	−1.18924	+	1.03049i	−0.998809	+	0.0487870i	$0.984464\pi$
$492$	7850.29	−	276.382i	0.719347	−	0.0253257i
$493$	−525.622	−	240.043i	−0.0480179	−	0.0219290i
$494$	−11642.3	+	3418.49i	−1.06035	+	0.311346i
$495$	3130.89	−	220.730i	0.284289	−	0.0200426i
$496$	1968.16	−	4309.68i	0.178172	−	0.390142i
$497$	658.460	+	4579.69i	0.0594285	+	0.413334i
$498$	6085.32	−	4220.53i	0.547570	−	0.379772i
$499$	−6542.63	−	14326.4i	−0.586951	−	1.28524i	−0.937267	−	0.348612i	$-0.886653\pi$
$499$	−6542.63	−	14326.4i	−0.586951	−	1.28524i	0.350316	−	0.936631i	$-0.386074\pi$
$500$	1521.31	−	977.686i	0.136070	−	0.0874469i
$501$	−3173.14	−	811.612i	−0.282965	−	0.0723755i
$502$	4294.53	−	6682.41i	0.381821	−	0.594125i
$503$	−5027.45	+	5801.98i	−0.445652	+	0.514309i	−0.933480	−	0.358630i	$-0.883244\pi$
$503$	−5027.45	+	5801.98i	−0.445652	+	0.514309i	0.487828	+	0.872940i	$0.337789\pi$
$504$	−926.153	−	506.940i	−0.0818535	−	0.0448034i
$505$		−	2823.71i		−	0.248819i
$506$	−10680.3	−	9037.04i	−0.938333	−	0.793963i
$507$	6228.35	+	672.817i	0.545584	+	0.0589366i
$508$	−3750.71	−	1101.31i	−0.327581	−	0.0961864i
$509$	−7208.25	−	6245.99i	−0.627702	−	0.543907i	0.281871	−	0.959452i	$-0.409045\pi$
$509$	−7208.25	−	6245.99i	−0.627702	−	0.543907i	−0.909572	+	0.415546i	$0.863591\pi$
$510$	855.945	−	1061.06i	0.0743174	−	0.0921265i
$511$	805.570	+	115.823i	0.0697384	+	0.0100269i
$512$	276.808	+	430.722i	0.0238932	+	0.0371785i
$513$	14510.5	−	1537.68i	1.24883	−	0.132339i
$514$	−584.770	−	674.861i	−0.0501811	−	0.0579121i
$515$	2189.30	−	314.774i	0.187324	−	0.0269332i
$516$	−6232.53	−	3702.21i	−0.531729	−	0.315854i
$517$	5047.74	+	17191.0i	0.429399	+	1.46240i
$518$	−144.110	−	490.794i	−0.0122236	−	0.0416299i
$519$	−8830.40	−	5245.38i	−0.746843	−	0.443635i
$520$	−846.682	+	121.735i	−0.0714028	+	0.0102662i
$521$	7363.77	+	8498.24i	0.619218	+	0.714616i	0.975558	−	0.219740i	$-0.0705210\pi$
$521$	7363.77	+	8498.24i	0.619218	+	0.714616i	−0.356340	+	0.934356i	$0.615976\pi$
$522$	−92.2486	−	426.143i	−0.00773489	−	0.0357314i
$523$	−3389.90	−	5274.78i	−0.283422	−	0.441013i	0.670129	−	0.742245i	$-0.266239\pi$
$523$	−3389.90	−	5274.78i	−0.283422	−	0.441013i	−0.953551	+	0.301231i	$0.902602\pi$
$524$	7236.14	+	1040.40i	0.603268	+	0.0867368i
$525$	1939.81	−	2404.65i	0.161257	−	0.199900i
$526$	8616.29	+	7466.06i	0.714236	+	0.618889i
$527$	20333.0	+	5970.32i	1.68069	+	0.493494i
$528$	−5242.00	−	566.266i	−0.432062	−	0.0466734i
$529$	−2014.01	−	11999.2i	−0.165530	−	0.986205i
$530$			1187.08i			0.0972898i
$531$	4820.54	−	8806.88i	0.393961	−	0.719747i
$532$	1331.69	−	1536.85i	0.108527	−	0.125246i
$533$	11918.7	−	18545.8i	0.968585	−	1.50715i
$534$	−3477.26	−	889.400i	−0.281790	−	0.0720751i
$535$	63.5403	−	40.8348i	0.00513474	−	0.00329990i
$536$	−923.973	−	2023.22i	−0.0744582	−	0.163041i
$537$	−1849.57	+	1282.79i	−0.148631	+	0.103084i
$538$	2245.09	+	15614.9i	0.179912	+	1.25132i
$539$	−8406.84	+	18408.4i	−0.671815	+	1.47107i
$540$	1027.95	+	38.2815i	0.0819183	+	0.00305069i
$541$	6844.15	−	2009.62i	0.543906	−	0.159705i	0.00177377	−	0.999998i	$-0.499435\pi$
$541$	6844.15	−	2009.62i	0.543906	−	0.159705i	0.542132	+	0.840293i	$0.317617\pi$
$542$	−14015.6	−	6400.71i	−1.11074	−	0.507258i
$543$	−11746.0	+	413.536i	−0.928302	+	0.0326824i
$544$	−1730.73	+	1499.69i	−0.136405	+	0.118196i
$545$	39.0039	−	17.8125i	0.00306558	−	0.00140000i
$546$	−2650.39	+	1325.01i	−0.207741	+	0.103856i
$547$	−1648.10	+	11462.8i	−0.128826	+	0.896004i	0.818220	+	0.574905i	$0.194961\pi$
$547$	−1648.10	+	11462.8i	−0.128826	+	0.896004i	−0.947046	+	0.321098i	$0.895948\pi$
$548$	−10216.1	−	6565.50i	−0.796370	−	0.511796i
$549$	−8578.70	−	11484.1i	−0.666903	−	0.892767i
$550$	4346.68	−	14803.4i	0.336987	−	1.14767i
$551$	839.782			0.0649291
$552$	−3162.00	−	3320.59i	−0.243811	−	0.256040i
$553$	−818.262			−0.0629223
$554$	−737.228	+	2510.77i	−0.0565376	+	0.192549i
$555$	339.405	+	364.918i	0.0259585	+	0.0279098i
$556$	−2427.79	−	1560.25i	−0.185182	−	0.119009i
$557$	2104.33	−	14635.9i	0.160077	−	1.11336i	−0.738406	−	0.674356i	$-0.764421\pi$
$557$	2104.33	−	14635.9i	0.160077	−	1.11336i	0.898484	−	0.439007i	$-0.144670\pi$
$558$	5572.77	+	14987.6i	0.422785	+	1.13706i
$559$	−18506.3	+	8451.56i	−1.40024	+	0.639469i
$560$	108.343	−	93.8794i	0.00817555	−	0.00708416i
$561$	−829.760	−	23568.3i	−0.0624465	−	1.77372i
$562$	13530.3	+	6179.06i	1.01555	+	0.463786i
$563$	−16089.5	+	4724.32i	−1.20443	+	0.353652i	−0.821545	−	0.570144i	$-0.806887\pi$
$563$	−16089.5	+	4724.32i	−1.20443	+	0.353652i	−0.382884	+	0.923796i	$0.625069\pi$
$564$	1039.66	+	5779.26i	0.0776200	+	0.431473i
$565$	−439.412	+	962.179i	−0.0327190	+	0.0716446i
$566$	−76.6983	−	533.449i	−0.00569589	−	0.0396158i
$567$	3421.07	−	996.972i	0.253389	−	0.0738429i
$568$	3145.70	+	6888.11i	0.232378	+	0.508836i
$569$	−1116.51	+	717.540i	−0.0822614	+	0.0528662i	−0.581125	−	0.813814i	$-0.697387\pi$
$569$	−1116.51	+	717.540i	−0.0822614	+	0.0528662i	0.498864	+	0.866681i	$0.333751\pi$
$570$	−490.951	+	1919.46i	−0.0360766	+	0.141048i
$571$	8478.68	−	13193.1i	0.621404	−	0.966923i	−0.377755	−	0.925906i	$-0.623304\pi$
$571$	8478.68	−	13193.1i	0.621404	−	0.966923i	0.999158	−	0.0410176i	$-0.0130600\pi$
$572$	−9690.14	+	11183.0i	−0.708330	+	0.817457i
$573$	6428.08	+	2666.42i	0.468651	+	0.194400i
$574$			3694.69i			0.268664i
$575$	11201.4	−	7386.10i	0.812404	−	0.535690i
$576$	−1688.14	−	369.028i	−0.122116	−	0.0266947i
$577$	3750.75	+	1101.32i	0.270616	+	0.0794601i	0.414225	−	0.910174i	$-0.364053\pi$
$577$	3750.75	+	1101.32i	0.270616	+	0.0794601i	−0.143609	+	0.989635i	$0.545871\pi$
$578$	−315.248	−	273.164i	−0.0226862	−	0.0196577i
$579$	3923.11	+	3164.73i	0.281587	+	0.227153i
$580$	58.5990	+	8.42526i	0.00419515	+	0.000603172i
$581$	1883.20	+	2930.31i	0.134472	+	0.209243i
$582$	−4476.49	−	13472.5i	−0.318826	−	0.959544i
$583$	13447.7	+	15519.4i	0.955310	+	1.10249i
$584$	1318.43	−	189.562i	0.0934198	−	0.0134317i
$585$	1732.42	−	2309.35i	0.122439	−	0.163214i
$586$	−132.337	−	450.698i	−0.00932899	−	0.0317716i
$587$	2928.77	+	9974.47i	0.205934	+	0.701347i	0.996082	+	0.0884310i	$0.0281853\pi$
$587$	2928.77	+	9974.47i	0.205934	+	0.701347i	−0.790148	+	0.612916i	$0.789997\pi$
$588$	−3387.27	+	5702.34i	−0.237566	+	0.399933i
$589$	−30484.3	+	4382.98i	−2.13257	+	0.306617i
$590$	892.708	+	1030.24i	0.0622919	+	0.0718886i
$591$	−311.542	+	103.515i	−0.0216838	+	0.00720483i
$592$	−452.608	−	704.272i	−0.0314224	−	0.0488942i
$593$	10811.2	+	1554.41i	0.748670	+	0.107643i	0.506080	−	0.862486i	$-0.331094\pi$
$593$	10811.2	+	1554.41i	0.748670	+	0.107643i	0.242590	+	0.970129i	$0.422003\pi$
$594$	13872.7	−	11144.5i	0.958253	−	0.769804i
$595$	484.597	+	419.906i	0.0333891	+	0.0289319i
$596$	−1170.23	−	343.611i	−0.0804271	−	0.0236155i
$597$	1067.37	−	9880.78i	0.0731734	−	0.677376i
$598$	−12715.1	+	1980.89i	−0.869500	+	0.135459i
$599$		−	2056.00i		−	0.140244i	−0.997538	−	0.0701218i	$-0.977661\pi$
$599$		−	2056.00i		−	0.140244i	0.997538	−	0.0701218i	$-0.0223388\pi$
$600$	1937.40	−	4670.60i	0.131824	−	0.317794i
$601$	3844.46	−	4436.75i	0.260930	−	0.301129i	−0.610135	−	0.792298i	$-0.708885\pi$
$601$	3844.46	−	4436.75i	0.260930	−	0.301129i	0.871065	+	0.491169i	$0.163430\pi$
$602$	1843.41	−	2868.40i	0.124803	−	0.194198i
$603$	7030.76	+	2630.48i	0.474817	+	0.177647i
$604$	1023.16	−	657.547i	0.0689270	−	0.0442967i
$605$	2049.00	+	4486.69i	0.137692	+	0.301504i
$606$	−9123.64	−	13154.8i	−0.611589	−	0.881811i
$607$	−144.200	−	1002.93i	−0.00964234	−	0.0670640i	0.984432	−	0.175765i	$-0.0562399\pi$
$607$	−144.200	−	1002.93i	−0.00964234	−	0.0670640i	−0.994074	+	0.108701i	$0.965331\pi$
$608$	1382.59	−	3027.44i	0.0922225	−	0.201939i
$609$	201.840	−	36.3101i	0.0134301	−	0.00241602i
$610$	1867.49	−	548.344i	0.123955	−	0.0363964i
$611$	14990.6	+	6845.97i	0.992560	+	0.453287i
$612$	559.213	−	7708.78i	0.0369360	−	0.509165i
$613$	16953.6	−	14690.4i	1.11705	−	0.967928i	0.117365	−	0.993089i	$-0.462555\pi$
$613$	16953.6	−	14690.4i	1.11705	−	0.967928i	0.999683	+	0.0251613i	$0.00800992\pi$
$614$	−4099.69	+	1872.27i	−0.269463	+	0.123060i
$615$	−1609.64	−	3219.73i	−0.105539	−	0.211109i
$616$	352.930	−	2454.68i	0.0230844	−	0.160555i
$617$	−7857.88	−	5049.95i	−0.512717	−	0.329503i	0.258568	−	0.965993i	$-0.416749\pi$
$617$	−7857.88	−	5049.95i	−0.512717	−	0.329503i	−0.771285	+	0.636490i	$0.780386\pi$
$618$	9182.21	−	8540.24i	0.597674	−	0.555888i
$619$	−6125.04	+	20860.0i	−0.397716	+	1.35450i	0.480820	+	0.876819i	$0.340339\pi$
$619$	−6125.04	+	20860.0i	−0.397716	+	1.35450i	−0.878536	+	0.477676i	$0.841479\pi$
$620$	−2171.13			−0.140637
$621$	15470.2	+	394.196i	0.999676	+	0.0254727i
$622$	−15549.4			−1.00237
$623$	475.618	−	1619.80i	0.0305862	−	0.104167i
$624$	−3551.10	+	3302.82i	−0.227817	+	0.211889i
$625$	12094.1	+	7772.42i	0.774024	+	0.497435i
$626$	555.579	−	3864.14i	0.0354719	−	0.246713i
$627$	15325.8	+	30655.9i	0.976160	+	1.95260i
$628$	12615.0	−	5761.06i	0.801579	−	0.366069i
$629$	2829.91	−	2452.13i	0.179389	−	0.155442i
$630$	−35.0064	+	482.565i	−0.00221379	+	0.0305172i
$631$	10382.7	+	4741.63i	0.655040	+	0.299147i	0.715073	−	0.699050i	$-0.246393\pi$
$631$	10382.7	+	4741.63i	0.655040	+	0.299147i	−0.0600334	+	0.998196i	$0.519121\pi$
$632$	−1284.96	+	377.298i	−0.0808749	+	0.0237470i
$633$	−17959.5	+	3230.84i	−1.12769	+	0.202866i
$634$	−3387.29	+	7417.13i	−0.212187	+	0.464624i
$635$	254.935	+	1773.11i	0.0159319	+	0.110809i
$636$	3835.56	+	5530.25i	0.239135	+	0.344794i
$637$	7732.60	+	16932.0i	0.480968	+	1.05317i
$638$	861.544	−	553.681i	0.0534621	−	0.0343580i
$639$	−23936.4	−	8955.54i	−1.48186	−	0.554422i
$640$	126.849	−	197.380i	0.00783458	−	0.0121908i
$641$	−13805.1	+	15931.9i	−0.850651	+	0.981703i	−0.999975	−	0.00708486i	$-0.997745\pi$
$641$	−13805.1	+	15931.9i	−0.850651	+	0.981703i	0.149324	+	0.988788i	$0.452290\pi$
$642$	164.074	−	395.541i	0.0100864	−	0.0243158i
$643$		−	5317.33i		−	0.326120i	−0.986616	−	0.163060i	$-0.947864\pi$
$643$		−	5317.33i		−	0.326120i	0.986616	−	0.163060i	$-0.0521364\pi$
$644$	1613.21	−	1431.38i	0.0987101	−	0.0875841i
$645$	−356.781	+	3302.76i	−0.0217802	+	0.201622i
$646$	14283.5	+	4194.00i	0.869931	+	0.255435i
$647$	4710.85	+	4081.98i	0.286248	+	0.248036i	0.786134	−	0.618056i	$-0.212079\pi$
$647$	4710.85	+	4081.98i	0.286248	+	0.248036i	−0.499886	+	0.866091i	$0.666625\pi$
$648$	4912.59	−	3143.04i	0.297816	−	0.190541i
$649$	23341.8	+	3356.05i	1.41178	+	0.202984i
$650$	−7672.24	−	11938.2i	−0.462969	−	0.720394i
$651$	−7137.33	+	2371.50i	−0.429699	+	0.142775i
$652$	−3770.88	−	4351.83i	−0.226502	−	0.261397i
$653$	3782.45	−	543.834i	0.226675	−	0.0325909i	−0.0280414	−	0.999607i	$-0.508927\pi$
$653$	3782.45	−	543.834i	0.226675	−	0.0325909i	0.254716	+	0.967016i	$0.418018\pi$
$654$	124.153	−	209.007i	0.00742321	−	0.0124967i
$655$	−943.831	−	3214.39i	−0.0563031	−	0.191751i
$656$	1703.61	+	5801.96i	0.101394	+	0.345318i
$657$	−2697.69	+	3596.07i	−0.160193	+	0.213541i
$658$	−2733.80	+	393.062i	−0.161968	+	0.0232875i
$659$	13644.1	+	15746.1i	0.806521	+	0.930775i	0.998720	−	0.0505810i	$-0.0161073\pi$
$659$	13644.1	+	15746.1i	0.806521	+	0.930775i	−0.192199	+	0.981356i	$0.561562\pi$
$660$	761.853	+	2292.89i	0.0449320	+	0.135228i
$661$	2782.04	+	4328.94i	0.163705	+	0.254729i	0.913409	−	0.407044i	$-0.133440\pi$
$661$	2782.04	+	4328.94i	0.163705	+	0.254729i	−0.749704	+	0.661773i	$0.769804\pi$
$662$	−18219.9	−	2619.62i	−1.06969	−	0.153798i
$663$	−16883.0	−	13619.3i	−0.988962	−	0.797785i
$664$	4308.45	+	3733.29i	0.251807	+	0.218192i
$665$	−894.136	−	262.542i	−0.0521400	−	0.0153097i
$666$	2760.26	+	603.396i	0.160598	+	0.0351068i
$667$	882.994	+	116.385i	0.0512589	+	0.00675628i
$668$		−	2521.32i		−	0.146037i
$669$	−19453.4	−	8069.46i	−1.12424	−	0.466343i
$670$	−667.472	+	770.304i	−0.0384876	+	0.0444171i
$671$	18203.0	−	28324.4i	1.04727	−	1.62958i
$672$	201.403	−	787.419i	0.0115614	−	0.0452014i
$673$	−6576.32	+	4226.34i	−0.376669	+	0.242071i	−0.715253	−	0.698866i	$-0.753689\pi$
$673$	−6576.32	+	4226.34i	−0.376669	+	0.242071i	0.338584	+	0.940936i	$0.390052\pi$
$674$	7331.25	+	16053.2i	0.418975	+	0.917428i
$675$	6506.70	+	15776.5i	0.371027	+	0.899612i
$676$	686.311	+	4773.40i	0.0390482	+	0.271586i
$677$	−5621.84	+	12310.1i	−0.319150	+	0.698842i	−0.999418	−	0.0341222i	$-0.989136\pi$
$677$	−5621.84	+	12310.1i	−0.319150	+	0.698842i	0.680267	+	0.732964i	$0.261864\pi$
$678$	1061.79	+	5902.27i	0.0601444	+	0.334329i
$679$	6406.99	−	1881.26i	0.362117	−	0.106327i
$680$	954.605	+	435.954i	0.0538345	+	0.0245854i
$681$	−864.470	−	24554.2i	−0.0486440	−	1.38167i
$682$	−28384.5	+	24595.3i	−1.59369	+	1.38094i
$683$	−22782.7	+	10404.5i	−1.27636	+	0.582895i	−0.934201	−	0.356747i	$-0.883886\pi$
$683$	−22782.7	+	10404.5i	−1.27636	+	0.582895i	−0.342160	+	0.939642i	$0.611159\pi$
$684$	3914.73	+	10528.5i	0.218836	+	0.588546i
$685$	−791.983	+	5508.36i	−0.0441753	+	0.307246i
$686$	−5445.27	−	3499.46i	−0.303063	−	0.194767i
$687$	−6765.85	−	7274.44i	−0.375740	−	0.403984i
$688$	1572.19	−	5354.39i	0.0871209	−	0.296707i
$689$	18888.2			1.04439
$690$	−782.229	+	1950.18i	−0.0431579	+	0.107597i
$691$	−33759.2			−1.85856			−0.929278	−	0.369382i	$-0.879569\pi$
$691$	−33759.2			−1.85856			−0.929278	+	0.369382i	$0.879569\pi$
$692$	2227.52	−	7586.22i	0.122366	−	0.416741i
$693$	5009.00	+	6705.42i	0.274569	+	0.367558i
$694$	4329.60	+	2782.46i	0.236815	+	0.152191i
$695$	−188.210	+	1309.03i	−0.0102722	+	0.0714449i
$696$	300.217	−	150.087i	0.0163501	−	0.00817392i
$697$	−24602.5	+	11235.6i	−1.33700	+	0.610587i
$698$	−6530.77	+	5658.94i	−0.354145	+	0.306868i
$699$	3107.54	−	109.406i	0.168151	−	0.00592004i
$700$	2163.40	+	987.992i	0.116813	+	0.0533465i
$701$	3914.60	−	1149.43i	0.210916	−	0.0619306i	−0.174568	−	0.984645i	$-0.555853\pi$
$701$	3914.60	−	1149.43i	0.210916	−	0.0619306i	0.385484	+	0.922715i	$0.374035\pi$
$702$	609.115	−	16356.2i	0.0327487	−	0.879378i
$703$	−2260.66	+	4950.16i	−0.121284	+	0.265574i
$704$	−577.623	−	4017.45i	−0.0309233	−	0.215076i
$705$	2211.13	−	1533.55i	0.118122	−	0.0819245i
$706$	1544.45	+	3381.88i	0.0823318	+	0.180281i
$707$	6334.54	−	4070.96i	0.336966	−	0.216555i
$708$	7487.64	+	1915.16i	0.397461	+	0.101661i
$709$	−19294.6	+	30022.9i	−1.02203	+	1.59032i	−0.236369	+	0.971663i	$0.575958\pi$
$709$	−19294.6	+	30022.9i	−1.02203	+	1.59032i	−0.785665	+	0.618653i	$0.787679\pi$
$710$	2272.43	−	2622.52i	0.120117	−	0.138622i
$711$	2170.15	−	3964.75i	0.114468	−	0.209128i
$712$		−	2762.97i		−	0.145431i
$713$	−32660.4	+	383.714i	−1.71548	+	0.0201545i
$714$	3614.34	+	390.438i	0.189444	+	0.0204647i
$715$	6506.23	+	1910.40i	0.340307	+	0.0999231i
$716$	−1309.51	−	1134.69i	−0.0683500	−	0.0592256i
$717$	−16553.2	+	20519.9i	−0.862188	+	1.06880i
$718$	−23876.7	−	3432.95i	−1.24105	−	0.178436i
$719$	−18790.7	−	29239.0i	−0.974654	−	1.51659i	−0.851601	−	0.524191i	$-0.824368\pi$
$719$	−18790.7	−	29239.0i	−0.974654	−	1.51659i	−0.123053	−	0.992400i	$-0.539269\pi$
$720$	167.537	+	773.938i	0.00867184	+	0.0400597i
$721$	3862.47	+	4457.53i	0.199509	+	0.230246i
$722$	−7836.10	+	1126.66i	−0.403919	+	0.0580748i
$723$	−15067.2	−	8950.15i	−0.775044	−	0.460387i
$724$	−2549.02	−	8681.17i	−0.130848	−	0.445626i
$725$	276.707	+	942.377i	0.0141747	+	0.0482745i
$726$	24042.5	+	14281.6i	1.22907	+	0.730082i
$727$	8896.38	−	1279.11i	0.453849	−	0.0652537i	0.0884003	−	0.996085i	$-0.471825\pi$
$727$	8896.38	−	1279.11i	0.453849	−	0.0652537i	0.365449	+	0.930831i	$0.380915\pi$
$728$	−1493.76	−	1723.89i	−0.0760472	−	0.0877631i
$729$	−4242.51	+	19220.3i	−0.215542	+	0.976495i
$730$	−330.002	−	513.494i	−0.0167314	−	0.0260346i
$731$	24706.2	+	3552.22i	1.25006	+	0.179731i
$732$	6928.31	−	8588.57i	0.349833	−	0.433665i
$733$	−10339.2	−	8958.99i	−0.520993	−	0.451443i	0.354233	−	0.935157i	$-0.384742\pi$
$733$	−10339.2	−	8958.99i	−0.520993	−	0.451443i	−0.875226	+	0.483714i	$0.839288\pi$
$734$	6828.45	+	2005.01i	0.343382	+	0.100826i
$735$	3021.80	+	326.430i	0.151647	+	0.0163817i
$736$	1873.30	−	2991.61i	0.0938190	−	0.149827i
$737$			17632.0i			0.881252i
$738$	−17902.0	−	9798.84i	−0.892929	−	0.488754i
$739$	14020.6	−	16180.6i	0.697910	−	0.805431i	−0.290558	−	0.956857i	$-0.593841\pi$
$739$	14020.6	−	16180.6i	0.697910	−	0.805431i	0.988469	+	0.151426i	$0.0483865\pi$
$740$	−207.410	+	322.736i	−0.0103034	+	0.0160324i
$741$	30541.4	+	7811.74i	1.51412	+	0.387276i
$742$	−2663.03	+	1711.42i	−0.131756	+	0.0846743i
$743$	−8204.19	−	17964.7i	−0.405091	−	0.887026i	−0.996729	−	0.0808215i	$-0.974246\pi$
$743$	−8204.19	−	17964.7i	−0.405091	−	0.887026i	0.591638	−	0.806204i	$-0.298482\pi$
$744$	−10114.6	+	7015.10i	−0.498414	+	0.345680i
$745$	79.5403	+	553.215i	0.00391158	+	0.0272057i
$746$	−6058.15	+	13265.5i	−0.297325	+	0.651051i
$747$	−19192.9	+	1353.11i	−0.940067	+	0.0662753i
$748$	17418.8	−	5114.61i	0.851461	−	0.250012i
$749$	183.213	+	83.6704i	0.00893785	+	0.00408178i
$750$	−4695.41	+	165.309i	−0.228603	+	0.00804832i
$751$	−16075.9	+	13929.9i	−0.781117	+	0.676842i	−0.951196	−	0.308589i	$-0.900143\pi$
$751$	−16075.9	+	13929.9i	−0.781117	+	0.676842i	0.170078	+	0.985431i	$0.445598\pi$
$752$	−4111.80	+	1877.80i	−0.199391	+	0.0910587i
$753$	−18459.3	+	9228.35i	−0.893353	+	0.446613i
$754$	134.058	−	932.395i	0.00647495	−	0.0450343i
$755$	−468.869	−	301.324i	−0.0226012	−	0.0145249i
$756$	1396.12	+	2361.23i	0.0671646	+	0.113594i
$757$	−991.059	+	3375.24i	−0.0475834	+	0.162054i	−0.979857	−	0.199699i	$-0.936004\pi$
$757$	−991.059	+	3375.24i	−0.0475834	+	0.162054i	0.932274	+	0.361753i	$0.117822\pi$
$758$	16318.3			0.781937
$759$	11865.8	+	34357.3i	0.567459	+	1.64307i
$760$	−1525.17			−0.0727942
$761$	−1066.49	+	3632.14i	−0.0508021	+	0.173016i	−0.980986	−	0.194077i	$-0.937829\pi$
$761$	−1066.49	+	3632.14i	−0.0508021	+	0.173016i	0.930184	+	0.367093i	$0.119647\pi$
$762$	6916.73	+	7436.66i	0.328827	+	0.353546i
$763$	96.1915	+	61.8185i	0.00456404	+	0.00293313i
$764$	−762.405	+	5302.64i	−0.0361032	+	0.251103i
$765$	−3319.80	+	1234.38i	−0.156899	+	0.0583389i
$766$	19727.8	−	9009.41i	0.930543	−	0.424965i
$767$	16392.6	−	14204.3i	0.771712	−	0.668692i
$768$	−46.8033	−	1329.39i	−0.00219905	−	0.0624613i
$769$	30274.5	+	13825.9i	1.41967	+	0.648341i	0.969609	−	0.244658i	$-0.0786758\pi$
$769$	30274.5	+	13825.9i	1.41967	+	0.648341i	0.450059	+	0.892999i	$0.351403\pi$
$770$	−1090.40	+	320.171i	−0.0510330	+	0.0149846i
$771$	410.764	+	2283.35i	0.0191872	+	0.106657i
$772$	−1611.87	+	3529.51i	−0.0751459	+	0.164547i
$773$	1087.09	+	7560.85i	0.0505818	+	0.351804i	0.999357	+	0.0358526i	$0.0114147\pi$
$773$	1087.09	+	7560.85i	0.0505818	+	0.351804i	−0.948775	+	0.315952i	$0.897676\pi$
$774$	9009.37	+	16539.3i	0.418391	+	0.768080i
$775$	−14963.0	−	32764.3i	−0.693530	−	1.51862i
$776$	9193.79	−	5908.49i	0.425306	−	0.273328i
$777$	−329.313	+	1287.51i	−0.0152047	+	0.0594453i
$778$	12587.6	−	19586.7i	0.580061	−	0.902593i
$779$	25740.8	−	29706.5i	1.18390	−	1.36630i
$780$	2052.77	+	851.505i	0.0942318	+	0.0390882i
$781$		−	60028.7i		−	2.75031i
$782$	14437.2	+	6389.35i	0.660196	+	0.292177i
$783$	−359.374	+	1074.28i	−0.0164023	+	0.0490315i
$784$	−4898.90	−	1438.45i	−0.223164	−	0.0655269i
$785$	−4802.91	−	4161.75i	−0.218374	−	0.189222i
$786$	−14783.0	−	11925.3i	−0.670854	−	0.541171i
$787$	−14275.4	−	2052.50i	−0.646587	−	0.0929652i	−0.188784	−	0.982019i	$-0.560455\pi$
$787$	−14275.4	−	2052.50i	−0.646587	−	0.0929652i	−0.457803	+	0.889053i	$0.651364\pi$
$788$	−136.629	−	212.599i	−0.00617667	−	0.00961109i
$789$	−9339.91	−	28109.6i	−0.421431	−	1.26835i
$790$	401.886	+	463.802i	0.0180993	+	0.0208877i
$791$	−2792.00	+	401.428i	−0.125502	+	0.0180444i
$792$	10957.7	+	8220.24i	0.491624	+	0.368805i
$793$	−8724.95	−	29714.5i	−0.390709	−	1.33063i
$794$	−4599.84	−	15665.6i	−0.205595	−	0.700192i
$795$	1575.09	−	2651.60i	0.0702674	−	0.118292i
$796$	7572.61	−	1088.78i	0.337191	−	0.0484807i
$797$	−12485.1	−	14408.6i	−0.554889	−	0.640376i	0.407126	−	0.913372i	$-0.366531\pi$
$797$	−12485.1	−	14408.6i	−0.554889	−	0.640376i	−0.962015	+	0.272996i	$0.911986\pi$
$798$	−5013.80	+	1665.92i	−0.222414	+	0.0739011i
$799$	−10930.9	−	17008.8i	−0.483990	−	0.753103i
$800$	3852.86	+	553.958i	0.170274	+	0.0244817i
$801$	6587.09	+	6600.48i	0.290566	+	0.291157i
$802$	2295.44	+	1989.01i	0.101066	+	0.0875740i
$803$	−10131.4	−	2974.83i	−0.445240	−	0.130734i
$804$	−620.631	+	5745.26i	−0.0272239	+	0.252015i
$805$	−903.759	−	399.969i	−0.0395694	−	0.0175119i
$806$			34545.9i			1.50971i
$807$	15703.9	−	37858.2i	0.685010	−	1.65139i
$808$	8070.35	−	9313.69i	0.351379	−	0.405513i
$809$	8256.13	−	12846.8i	0.358801	−	0.558305i	−0.614187	−	0.789160i	$-0.710516\pi$
$809$	8256.13	−	12846.8i	0.358801	−	0.558305i	0.972988	+	0.230855i	$0.0741523\pi$
$810$	−2245.34	−	1449.45i	−0.0973992	−	0.0628746i
$811$	28773.3	−	18491.5i	1.24583	−	0.800645i	0.259549	−	0.965730i	$-0.416426\pi$
$811$	28773.3	−	18491.5i	1.24583	−	0.800645i	0.986279	+	0.165085i	$0.0527899\pi$
$812$	65.5818	+	143.604i	0.00283432	+	0.00620630i
$813$	22814.0	+	32894.0i	0.984158	+	1.41899i
$814$	944.469	+	6568.93i	0.0406678	+	0.282851i
$815$	−1096.18	+	2400.31i	−0.0471136	+	0.103164i
$816$	5855.81	−	1053.43i	0.251219	−	0.0451931i
$817$	−34805.7	+	10219.9i	−1.49045	+	0.437635i
$818$	−1509.53	−	689.381i	−0.0645227	−	0.0294665i
$819$	7678.31	+	557.003i	0.327597	+	0.0237647i
$820$	2094.20	−	1814.63i	0.0891860	−	0.0772801i
$821$	−8869.21	+	4050.43i	−0.377025	+	0.172181i	−0.594909	−	0.803793i	$-0.702812\pi$
$821$	−8869.21	+	4050.43i	−0.377025	+	0.172181i	0.217884	+	0.975975i	$0.430085\pi$
$822$	14108.4	+	28220.7i	0.598644	+	1.19746i
$823$	1525.06	−	10607.0i	0.0645932	−	0.449255i	−0.931700	−	0.363229i	$-0.881674\pi$
$823$	1525.06	−	10607.0i	0.0645932	−	0.449255i	0.996293	−	0.0860259i	$-0.0274168\pi$
$824$	8120.79	+	5218.92i	0.343327	+	0.220643i
$825$	−29351.2	+	27299.2i	−1.23864	+	1.15204i
$826$	−1024.15	+	3487.95i	−0.0431415	+	0.146926i
$827$	21088.6			0.886728			0.443364	−	0.896342i	$-0.353785\pi$
$827$	21088.6			0.886728			0.443364	+	0.896342i	$0.353785\pi$
$828$	2657.04	+	11612.8i	0.111520	+	0.487405i
$829$	33390.9			1.39893			0.699466	−	0.714666i	$-0.253421\pi$
$829$	33390.9			1.39893			0.699466	+	0.714666i	$0.253421\pi$
$830$	736.015	−	2506.64i	0.0307801	−	0.104827i
$831$	4978.18	−	4630.13i	0.207811	−	0.193282i
$832$	−3140.61	−	2018.35i	−0.130867	−	0.0841028i
$833$	3250.04	−	22604.5i	0.135183	−	0.940215i
$834$	3352.76	+	6706.47i	0.139205	+	0.278448i
$835$	−1050.99	+	479.973i	−0.0435583	+	0.0198924i
$836$	−19939.4	+	17277.6i	−0.824903	+	0.714783i
$837$	7438.49	−	40872.3i	0.307183	−	1.68788i
$838$	8701.86	+	3974.01i	0.358712	+	0.163818i
$839$	1824.08	−	535.597i	0.0750585	−	0.0220392i	−0.243988	−	0.969778i	$-0.578456\pi$
$839$	1824.08	−	535.597i	0.0750585	−	0.0220392i	0.319046	+	0.947739i	$0.396637\pi$
$840$	−366.570	+	65.9443i	−0.0150570	+	0.00270869i
$841$	10104.5	−	22125.7i	0.414305	−	0.907200i
$842$	1189.71	+	8274.59i	0.0486936	+	0.338671i
$843$	−22023.9	−	31754.9i	−0.899815	−	1.29739i
$844$	−5835.41	−	12777.8i	−0.237990	−	0.521124i
$845$	1859.11	−	1194.78i	0.0756867	−	0.0486409i
$846$	5345.93	−	14288.7i	0.217254	−	0.580679i
$847$	−7111.10	+	11065.1i	−0.288477	+	0.448879i
$848$	−3392.76	+	3915.45i	−0.137391	+	0.158558i
$849$	−536.487	+	1293.34i	−0.0216869	+	0.0522817i
$850$			17410.4i			0.702554i
$851$	−3063.03	+	4891.58i	−0.123383	+	0.197040i
$852$	2112.96	−	19559.9i	0.0849633	−	0.786516i
$853$	7858.23	+	2307.39i	0.315429	+	0.0926182i	0.435615	−	0.900133i	$-0.356531\pi$
$853$	7858.23	+	2307.39i	0.315429	+	0.0926182i	−0.120186	+	0.992751i	$0.538349\pi$
$854$	3922.49	+	3398.86i	0.157172	+	0.136190i
$855$	3643.48	−	3636.09i	0.145736	−	0.145440i
$856$	326.289	+	46.9132i	0.0130284	+	0.00187320i
$857$	21985.0	+	34209.3i	0.876304	+	1.36356i	0.930987	+	0.365053i	$0.118949\pi$
$857$	21985.0	+	34209.3i	0.876304	+	1.36356i	−0.0546825	+	0.998504i	$0.517415\pi$
$858$	36483.2	−	12122.2i	1.45165	−	0.482337i
$859$	9663.12	+	11151.8i	0.383820	+	0.442952i	0.914479	−	0.404634i	$-0.132601\pi$
$859$	9663.12	+	11151.8i	0.383820	+	0.442952i	−0.530659	+	0.847585i	$0.678056\pi$
$860$	−2531.23	+	363.936i	−0.100365	+	0.0144304i
$861$	4902.31	−	8252.85i	0.194042	−	0.326663i
$862$	−6359.92	−	21659.9i	−0.251299	−	0.855846i
$863$	−5372.31	−	18296.4i	−0.211907	−	0.721688i	−0.995008	−	0.0997939i	$-0.968182\pi$
$863$	−5372.31	−	18296.4i	−0.211907	−	0.721688i	0.783101	−	0.621894i	$-0.213637\pi$
$864$	3281.16	+	3064.21i	0.129198	+	0.120656i
$865$	−3586.31	+	515.633i	−0.140969	+	0.0202683i
$866$	5709.01	+	6588.55i	0.224019	+	0.258531i
$867$	341.724	+	1028.46i	0.0133859	+	0.0402864i
$868$	−3130.13	−	4870.58i	−0.122400	−	0.190459i
$869$	10508.2	+	1510.85i	0.410203	+	0.0589783i
$870$	−119.714	−	96.5719i	−0.00466515	−	0.00376333i
$871$	12256.7	+	10620.5i	0.476809	+	0.413158i
$872$	179.559	+	52.7232i	0.00697320	+	0.00204752i
$873$	−7876.92	+	36033.4i	−0.305376	+	1.39696i
$874$	−22943.1	+	269.549i	−0.887943	+	0.0104321i
$875$		−	2209.86i		−	0.0853794i
$876$	−3196.52	−	1325.94i	−0.123288	−	0.0511410i
$877$	24560.7	−	28344.5i	0.945673	−	1.09137i	−0.0500285	−	0.998748i	$-0.515931\pi$
$877$	24560.7	−	28344.5i	0.945673	−	1.09137i	0.995702	−	0.0926173i	$-0.0295233\pi$
$878$	−9048.70	+	14080.1i	−0.347812	+	0.541206i
$879$	−302.409	+	1182.32i	−0.0116041	+	0.0453682i
$880$	−1564.69	+	1005.56i	−0.0599382	+	0.0385200i
$881$	1179.26	+	2582.21i	0.0450966	+	0.0987478i	0.930839	−	0.365429i	$-0.119078\pi$
$881$	1179.26	+	2582.21i	0.0450966	+	0.0987478i	−0.885743	+	0.464177i	$0.846350\pi$
$882$	15132.4	−	8242.95i	0.577702	−	0.314688i
$883$	4490.20	+	31230.0i	0.171129	+	1.19023i	0.876504	+	0.481395i	$0.159870\pi$
$883$	4490.20	+	31230.0i	0.171129	+	1.19023i	−0.705375	+	0.708835i	$0.749221\pi$
$884$	6936.66	−	15189.2i	0.263920	−	0.577904i
$885$	−627.071	−	3485.75i	−0.0238178	−	0.132398i
$886$	13898.9	−	4081.08i	0.527022	−	0.154748i
$887$	−23949.6	−	10937.4i	−0.906593	−	0.414027i	−0.0931366	−	0.995653i	$-0.529689\pi$
$887$	−23949.6	−	10937.4i	−0.906593	−	0.414027i	−0.813456	+	0.581626i	$0.802417\pi$
$888$	76.5280	+	2173.68i	0.00289202	+	0.0821442i
$889$	−3610.15	+	3128.21i	−0.136198	+	0.118017i
$890$	−1151.73	+	525.975i	−0.0433774	+	0.0198098i
$891$	−45774.6	+	6486.51i	−1.72111	+	0.243890i
$892$	2307.28	−	16047.5i	0.0866071	−	0.602366i
$893$	24719.1	+	15886.0i	0.926309	+	0.595303i
$894$	2158.04	+	2320.26i	0.0807332	+	0.0868020i
$895$	−223.704	+	761.866i	−0.00835486	+	0.0284540i
$896$	625.669			0.0233283
$897$	31030.3	+	12446.4i	1.15504	+	0.463293i
$898$	−36591.9			−1.35979
$899$	673.601	−	2294.07i	0.0249898	−	0.0851075i
$900$	−10524.8	+	7862.10i	−0.389807	+	0.291189i
$901$	−19494.5	−	12528.4i	−0.720817	−	0.463241i
$902$	6821.93	−	47447.6i	0.251824	−	1.75148i
$903$	−7923.59	+	3961.23i	−0.292005	+	0.145982i
$904$	−4199.32	+	1917.77i	−0.154499	+	0.0705575i
$905$	−3133.44	+	2715.14i	−0.115093	+	0.0997285i
$906$	−3157.92	+	111.179i	−0.115800	+	0.00407692i
$907$	−25308.0	−	11557.8i	−0.926502	−	0.423119i	−0.105743	−	0.994393i	$-0.533722\pi$
$907$	−25308.0	−	11557.8i	−0.926502	−	0.423119i	−0.820759	+	0.571274i	$0.806449\pi$
$908$	18147.4	−	5328.56i	0.663263	−	0.194752i
$909$	2925.05	+	41489.7i	0.106730	+	1.51389i
$910$	−434.231	+	950.832i	−0.0158182	+	0.0346371i
$911$	4606.88	+	32041.6i	0.167544	+	1.16530i	0.883939	+	0.467602i	$0.154882\pi$
$911$	4606.88	+	32041.6i	0.167544	+	1.16530i	−0.716395	+	0.697695i	$0.754209\pi$
$912$	−7105.27	+	4927.93i	−0.257982	+	0.178926i
$913$	−18773.7	−	41108.6i	−0.680523	−	1.49014i
$914$	−76.9246	+	49.4364i	−0.00278385	+	0.00178907i
$915$	−4899.00	−	1253.05i	−0.177001	−	0.0452726i
$916$	4134.59	−	6433.55i	0.149138	−	0.232064i
$917$	5850.24	−	6751.54i	0.210678	−	0.243136i
$918$	−11477.5	+	16477.2i	−0.412653	+	0.592405i
$919$		−	17014.9i		−	0.610738i	−0.952234	−	0.305369i	$-0.901220\pi$
$919$		−	17014.9i		−	0.610738i	0.952234	−	0.305369i	$-0.0987798\pi$
$920$	−1603.65	−	211.372i	−0.0574681	−	0.00757470i
$921$	11641.8	+	1257.60i	0.416513	+	0.0449938i
$922$	−20648.5	−	6062.96i	−0.737552	−	0.216565i
$923$	−41728.2	−	36157.6i	−1.48808	−	1.28943i
$924$	−4045.35	+	5014.76i	−0.144029	+	0.178543i
$925$	−6299.80	−	905.774i	−0.223931	−	0.0321964i
$926$	−2632.78	−	4096.68i	−0.0934325	−	0.145384i
$927$	−31842.0	+	6892.95i	−1.12819	+	0.244222i
$928$	169.202	+	195.269i	0.00598526	+	0.00690736i
$929$	2537.68	−	364.864i	0.0896219	−	0.0128857i	−0.0973580	−	0.995249i	$-0.531039\pi$
$929$	2537.68	−	364.864i	0.0896219	−	0.0128857i	0.186980	+	0.982364i	$0.440130\pi$
$930$	4849.67	+	2880.78i	0.170997	+	0.101575i
$931$	9350.48	+	31844.8i	0.329162	+	1.12102i
$932$	674.374	+	2296.71i	0.0237015	+	0.0807201i
$933$	34732.9	+	20631.9i	1.21876	+	0.723962i
$934$	33859.8	−	4868.30i	1.18622	−	0.170552i
$935$	−5447.93	−	6287.24i	−0.190552	−	0.219909i
$936$	12314.5	−	2665.75i	0.430034	−	0.0930907i
$937$	3369.84	+	5243.57i	0.117490	+	0.182817i	0.895017	−	0.446031i	$-0.147163\pi$
$937$	3369.84	+	5243.57i	0.117490	+	0.182817i	−0.777528	+	0.628849i	$0.783527\pi$
$938$	−2690.35	−	386.814i	−0.0936493	−	0.0134647i
$939$	−6368.15	+	7894.19i	−0.221317	+	0.274353i
$940$	1565.49	+	1356.51i	0.0543199	+	0.0470685i
$941$	−30734.3	−	9024.40i	−1.06473	−	0.312632i	−0.297975	−	0.954574i	$-0.596311\pi$
$941$	−30734.3	−	9024.40i	−1.06473	−	0.312632i	−0.766754	+	0.641941i	$0.778129\pi$
$942$	−35822.2	−	3869.69i	−1.23901	−	0.133844i
$943$	31182.3	−	27667.7i	1.07682	−	0.955444i
$944$			5949.54i			0.205128i
$945$	718.487	−	1031.46i	0.0247327	−	0.0355063i
$946$	−28969.5	+	33432.6i	−0.995645	+	1.14904i
$947$	−29484.5	+	45878.8i	−1.01174	+	1.57430i	−0.209048	+	0.977905i	$0.567037\pi$
$947$	−29484.5	+	45878.8i	−1.01174	+	1.57430i	−0.802692	+	0.596393i	$0.796600\pi$
$948$	3370.84	+	862.180i	0.115485	+	0.0295383i
$949$	−8170.44	+	5250.82i	−0.279477	+	0.179609i
$950$	−10511.1	−	23016.1i	−0.358975	−	0.786045i
$951$	17407.7	−	12073.3i	0.593567	−	0.411675i
$952$	398.269	+	2770.02i	0.0135588	+	0.0943034i
$953$	−6486.42	+	14203.3i	−0.220478	+	0.482780i	−0.987258	−	0.159131i	$-0.949131\pi$
$953$	−6486.42	+	14203.3i	−0.220478	+	0.482780i	0.766779	+	0.641911i	$0.221858\pi$
$954$	−1229.69	−	17442.2i	−0.0417322	−	0.591941i
$955$	2355.50	−	691.639i	0.0798140	−	0.0234355i
$956$	−18461.2	−	8430.93i	−0.624557	−	0.285226i
$957$	−2659.09	+	93.6176i	−0.0898184	+	0.00316220i
$958$	16644.9	−	14422.9i	0.561350	−	0.486412i
$959$	−13498.9	+	6164.75i	−0.454539	+	0.207581i
$960$	−545.238	+	272.580i	−0.0183307	+	0.00916405i
$961$	−8238.97	+	57303.3i	−0.276559	+	1.92351i
$962$	5135.20	+	3300.19i	0.172105	+	0.110605i
$963$	−891.318	+	665.821i	−0.0298259	+	0.0222801i
$964$	3800.79	−	12944.3i	0.126987	−	0.432477i
$965$	1778.10			0.0593151
$966$	−5502.67	+	1056.79i	−0.183277	+	0.0351983i
$967$	−180.219			−0.00599323			−0.00299662	−	0.999996i	$-0.500954\pi$
$967$	−180.219			−0.00599323			−0.00299662	+	0.999996i	$0.500954\pi$
$968$	−6064.85	+	20655.0i	−0.201376	+	0.685823i
$969$	−26340.3	−	28320.3i	−0.873242	−	0.938883i
$970$	−4213.10	−	2707.59i	−0.139458	−	0.0896243i
$971$	−573.718	+	3990.30i	−0.0189614	+	0.131879i	−0.997103	−	0.0760591i	$-0.975766\pi$
$971$	−573.718	+	3990.30i	−0.0189614	+	0.131879i	0.978142	+	0.207938i	$0.0666753\pi$
$972$	−15143.7	+	502.357i	−0.499725	+	0.0165773i
$973$	−3207.93	+	1465.01i	−0.105695	+	0.0482694i
$974$	15737.1	−	13636.3i	0.517710	−	0.448598i
$975$	1297.24	+	36846.5i	0.0426102	+	1.21029i
$976$	7726.90	+	3528.76i	0.253414	+	0.115730i
$977$	2678.59	−	786.505i	0.0877131	−	0.0257549i	−0.237582	−	0.971368i	$-0.576355\pi$
$977$	2678.59	−	786.505i	0.0877131	−	0.0257549i	0.325295	+	0.945613i	$0.394537\pi$
$978$	2648.81	+	14724.1i	0.0866048	+	0.481417i
$979$	−9098.77	+	19923.5i	−0.297036	+	0.650417i
$980$	332.976	+	2315.90i	0.0108536	+	0.0754885i
$981$	−554.645	+	302.128i	−0.0180514	+	0.00983304i
$982$	14224.2	+	31146.7i	0.462233	+	1.01215i
$983$	49329.9	−	31702.4i	1.60059	−	1.02864i	0.633654	−	0.773616i	$-0.281554\pi$
$983$	49329.9	−	31702.4i	1.60059	−	1.02864i	0.966936	−	0.255020i	$-0.0820822\pi$
$984$	3892.99	−	15220.3i	0.126122	−	0.493096i
$985$	−62.6110	+	97.4246i	−0.00202533	+	0.00315148i
$986$	−756.810	+	873.405i	−0.0244439	+	0.0282098i
$987$	6628.06	+	2749.38i	0.213752	+	0.0886663i
$988$			24267.6i			0.781433i
$989$	−38013.0	+	5922.05i	−1.22219	+	0.190405i
$990$	1340.57	−	6132.51i	0.0430365	−	0.196873i
$991$	−22936.1	−	6734.66i	−0.735208	−	0.215876i	−0.107368	−	0.994219i	$-0.534242\pi$
$991$	−22936.1	−	6734.66i	−0.735208	−	0.215876i	−0.627839	+	0.778343i	$0.716061\pi$
$992$	−7161.22	−	6205.23i	−0.229203	−	0.198605i
$993$	37222.0	+	30026.6i	1.18953	+	0.959582i
$994$	9159.38	+	1316.92i	0.292271	+	0.0420223i
$995$	−1895.41	−	2949.32i	−0.0603906	−	0.0939696i
$996$	−4670.28	−	14055.8i	−0.148578	−	0.447163i
$997$	614.132	+	708.746i	0.0195083	+	0.0225138i	0.765420	−	0.643531i	$-0.222531\pi$
$997$	614.132	+	708.746i	0.0195083	+	0.0225138i	−0.745912	+	0.666045i	$0.767986\pi$
$998$	−31178.6	+	4482.81i	−0.988920	+	0.142185i
$999$	−5365.01	−	5010.28i	−0.169911	−	0.158677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.4.f.a.5.16	yes	240
3.2	odd	2	inner	138.4.f.a.5.4	✓	240
23.14	odd	22	inner	138.4.f.a.83.4	yes	240
69.14	even	22	inner	138.4.f.a.83.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.4.f.a.5.4	✓	240	3.2	odd	2	inner
138.4.f.a.5.16	yes	240	1.1	even	1	trivial
138.4.f.a.83.4	yes	240	23.14	odd	22	inner
138.4.f.a.83.16	yes	240	69.14	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.563465 - 1.91899i) q^{2} +(-3.80483 + 3.53882i) q^{3} +(-3.36501 - 2.16256i) q^{4} +(-0.260866 + 1.81436i) q^{5} +(4.64705 + 9.29542i) q^{6} +(-4.44632 + 2.03056i) q^{7} +(-6.04600 + 5.23889i) q^{8} +(1.95351 - 26.9292i) q^{9} +(3.33474 + 1.52293i) q^{10} +(60.8494 - 17.8670i) q^{11} +(20.4562 - 3.67999i) q^{12} +(24.2320 - 53.0606i) q^{13} +(1.39128 + 9.67657i) q^{14} +(-5.42815 - 7.82650i) q^{15} +(6.64664 + 14.5541i) q^{16} +(-60.2044 + 38.6910i) q^{17} +(-50.5761 - 18.9224i) q^{18} +(56.2301 - 87.4958i) q^{19} +(4.80149 - 5.54121i) q^{20} +(9.73169 - 23.4607i) q^{21} -126.836i q^{22} +(71.2495 - 84.2051i) q^{23} +(4.46454 - 41.3288i) q^{24} +(116.713 + 34.2700i) q^{25} +(-88.1688 - 76.3987i) q^{26} +(87.8649 + 109.374i) q^{27} +(19.3531 + 2.78256i) q^{28} +(4.36531 + 6.79256i) q^{29} +(-18.0775 + 6.00658i) q^{30} +(-193.914 - 223.788i) q^{31} +(31.6743 - 4.55407i) q^{32} +(-168.294 + 283.316i) q^{33} +(40.3244 + 137.332i) q^{34} +(-2.52429 - 8.59693i) q^{35} +(-64.8098 + 86.3927i) q^{36} +(-51.7905 + 7.44635i) q^{37} +(-136.219 - 157.206i) q^{38} +(95.5734 + 287.640i) q^{39} +(-7.92804 - 12.3363i) q^{40} +(374.085 + 53.7852i) q^{41} +(-39.5372 - 31.8942i) q^{42} +(-263.588 - 228.400i) q^{43} +(-243.397 - 71.4679i) q^{44} +(48.3497 + 10.5693i) q^{45} +(-121.442 - 184.174i) q^{46} +282.518i q^{47} +(-76.7937 - 31.8547i) q^{48} +(-208.971 + 241.165i) q^{49} +(131.527 - 204.660i) q^{50} +(92.1472 - 360.265i) q^{51} +(-196.288 + 126.147i) q^{52} +(134.514 + 294.544i) q^{53} +(259.397 - 106.983i) q^{54} +(16.5436 + 115.064i) q^{55} +(16.2445 - 35.5705i) q^{56} +(95.6856 + 531.895i) q^{57} +(15.4945 - 4.54960i) q^{58} +(338.243 + 154.471i) q^{59} +(1.34049 + 38.0750i) q^{60} +(401.234 - 347.671i) q^{61} +(-538.710 + 246.021i) q^{62} +(45.9956 + 123.703i) q^{63} +(9.10815 - 63.3486i) q^{64} +(89.9499 + 57.8073i) q^{65} +(448.851 + 482.592i) q^{66} +(-78.3293 + 266.765i) q^{67} +286.260 q^{68} +(26.8942 + 572.526i) q^{69} -17.9197 q^{70} +(266.675 - 908.210i) q^{71} +(129.268 + 173.048i) q^{72} +(-140.068 - 90.0161i) q^{73} +(-14.8927 + 103.581i) q^{74} +(-565.348 + 282.634i) q^{75} +(-378.430 + 172.823i) q^{76} +(-234.275 + 203.001i) q^{77} +(605.828 - 21.3292i) q^{78} +(152.273 + 69.5408i) q^{79} +(-28.1403 + 8.26273i) q^{80} +(-721.368 - 105.213i) q^{81} +(313.997 - 687.557i) q^{82} +(-101.415 - 705.358i) q^{83} +(-83.4825 + 57.9001i) q^{84} +(-54.4942 - 119.326i) q^{85} +(-586.820 + 377.126i) q^{86} +(-40.6469 - 10.3965i) q^{87} +(-274.292 + 426.807i) q^{88} +(-226.170 + 261.014i) q^{89} +(47.5257 - 86.8271i) q^{90} +285.129i q^{91} +(-421.855 + 129.270i) q^{92} +(1529.75 + 165.252i) q^{93} +(542.148 + 159.189i) q^{94} +(144.080 + 124.846i) q^{95} +(-104.399 + 129.417i) q^{96} +(-1352.18 - 194.414i) q^{97} +(345.045 + 536.900i) q^{98} +(-362.274 - 1673.53i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} + 96 q^{4} - 8 q^{6} - 36 q^{9} + 32 q^{12} - 96 q^{13} - 748 q^{15} - 384 q^{16} - 40 q^{18} + 1320 q^{21} + 32 q^{24} - 144 q^{25} - 56 q^{27} - 1496 q^{30} - 72 q^{31} - 1936 q^{33} + 144 q^{36}+ \cdots + 2310 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 + 96 * q^4 - 8 * q^6 - 36 * q^9 + 32 * q^12 - 96 * q^13 - 748 * q^15 - 384 * q^16 - 40 * q^18 + 1320 * q^21 + 32 * q^24 - 144 * q^25 - 56 * q^27 - 1496 * q^30 - 72 * q^31 - 1936 * q^33 + 144 * q^36 - 1188 * q^37 + 660 * q^39 + 1716 * q^43 + 96 * q^46 - 128 * q^48 + 4860 * q^49 + 384 * q^52 + 3036 * q^54 + 3708 * q^55 + 4224 * q^57 + 1032 * q^58 + 88 * q^60 - 1056 * q^61 - 4180 * q^63 + 1536 * q^64 - 5456 * q^66 - 2904 * q^67 - 7832 * q^69 - 6432 * q^70 - 1952 * q^72 + 576 * q^73 - 6914 * q^75 + 1372 * q^78 + 3696 * q^79 + 9264 * q^81 + 3672 * q^82 + 3784 * q^84 + 4104 * q^85 + 938 * q^87 + 2924 * q^93 + 1296 * q^94 - 128 * q^96 - 25344 * q^97 + 2310 * q^99

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