LMFDB - Embedded newform 19.10.c.a.7.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,10,Mod(7,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.7"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	19.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:	$9.78568088711$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	19.7
Dual form			19.10.c.a.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-17.0666 - 29.5602i) q^{2} +(-104.220 - 180.515i) q^{3} +(-326.535 + 565.575i) q^{4} +(1253.36 + 2170.89i) q^{5} +(-3557.37 + 6161.54i) q^{6} +4067.64 q^{7} +4815.16 q^{8} +(-11882.3 + 20580.7i) q^{9} +(42781.2 - 74099.2i) q^{10} -30956.0 q^{11} +136126. q^{12} +(-70574.7 + 122239. i) q^{13} +(-69420.6 - 120240. i) q^{14} +(261252. - 452501. i) q^{15} +(85007.7 + 147238. i) q^{16} +(201124. + 348358. i) q^{17} +811158. q^{18} +(336217. - 457871. i) q^{19} -1.63707e6 q^{20} +(-423931. - 734270. i) q^{21} +(528313. + 915065. i) q^{22} +(-353001. + 611416. i) q^{23} +(-501838. - 869208. i) q^{24} +(-2.16527e6 + 3.75036e6i) q^{25} +4.81787e6 q^{26} +850757. q^{27} +(-1.32823e6 + 2.30056e6i) q^{28} +(1.86928e6 - 3.23768e6i) q^{29} -1.78347e7 q^{30} -2.57084e6 q^{31} +(4.13426e6 - 7.16075e6i) q^{32} +(3.22625e6 + 5.58803e6i) q^{33} +(6.86500e6 - 1.18905e7i) q^{34} +(5.09823e6 + 8.83039e6i) q^{35} +(-7.75995e6 - 1.34406e7i) q^{36} -1.01623e6 q^{37} +(-1.92728e7 - 2.12434e6i) q^{38} +2.94213e7 q^{39} +(6.03514e6 + 1.04532e7i) q^{40} +(1.77553e7 + 3.07531e7i) q^{41} +(-1.44701e7 + 2.50629e7i) q^{42} +(3.77610e6 + 6.54040e6i) q^{43} +(1.01082e7 - 1.75080e7i) q^{44} -5.95711e7 q^{45} +2.40981e7 q^{46} +(858969. - 1.48778e6i) q^{47} +(1.77191e7 - 3.06903e7i) q^{48} -2.38079e7 q^{49} +1.47815e8 q^{50} +(4.19225e7 - 7.26119e7i) q^{51} +(-4.60902e7 - 7.98307e7i) q^{52} +(-3.16597e7 + 5.48361e7i) q^{53} +(-1.45195e7 - 2.51485e7i) q^{54} +(-3.87991e7 - 6.72021e7i) q^{55} +1.95863e7 q^{56} +(-1.17693e8 - 1.29727e7i) q^{57} -1.27608e8 q^{58} +(6.46912e7 + 1.12048e8i) q^{59} +(1.70616e8 + 2.95515e8i) q^{60} +(4.08625e7 - 7.07759e7i) q^{61} +(4.38754e7 + 7.59945e7i) q^{62} +(-4.83328e7 + 8.37148e7i) q^{63} -1.95182e8 q^{64} -3.53823e8 q^{65} +(1.10122e8 - 1.90737e8i) q^{66} +(-5.92231e7 + 1.02577e8i) q^{67} -2.62697e8 q^{68} +1.47160e8 q^{69} +(1.74018e8 - 3.01409e8i) q^{70} +(8.10616e7 + 1.40403e8i) q^{71} +(-5.72150e7 + 9.90993e7i) q^{72} +(1.52206e7 + 2.63628e7i) q^{73} +(1.73435e7 + 3.00399e7i) q^{74} +9.02662e8 q^{75} +(1.49174e8 + 3.39667e8i) q^{76} -1.25918e8 q^{77} +(-5.02120e8 - 8.69698e8i) q^{78} +(-3.15499e8 - 5.46461e8i) q^{79} +(-2.13091e8 + 3.69084e8i) q^{80} +(1.45212e8 + 2.51515e8i) q^{81} +(6.06044e8 - 1.04970e9i) q^{82} +2.53183e8 q^{83} +5.53713e8 q^{84} +(-5.04163e8 + 8.73237e8i) q^{85} +(1.28890e8 - 2.23244e8i) q^{86} -7.79266e8 q^{87} -1.49058e8 q^{88} +(3.09600e8 - 5.36243e8i) q^{89} +(1.01667e9 + 1.76093e9i) q^{90} +(-2.87073e8 + 4.97224e8i) q^{91} +(-2.30534e8 - 3.99297e8i) q^{92} +(2.67934e8 + 4.64075e8i) q^{93} -5.86386e7 q^{94} +(1.41539e9 + 1.56011e8i) q^{95} -1.72350e9 q^{96} +(2.80838e8 + 4.86425e8i) q^{97} +(4.06319e8 + 7.03765e8i) q^{98} +(3.67828e8 - 6.37096e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + 41180 q^{10} - 114810 q^{11} + 235458 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} - 279203 q^{16}+ \cdots - 736622698 q^{99}+O(q^{100}) $ 28 * q + 15 * q^2 - 74 * q^3 - 2987 * q^4 - 285 * q^5 - 535 * q^6 - 2676 * q^7 - 24270 * q^8 - 57928 * q^9 + 41180 * q^10 - 114810 * q^11 + 235458 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 - 279203 * q^16 + 466251 * q^17 + 734964 * q^18 + 387157 * q^19 - 3343620 * q^20 + 689090 * q^21 - 1689395 * q^22 - 3087747 * q^23 - 234183 * q^24 - 3260823 * q^25 + 9033144 * q^26 + 4216540 * q^27 - 703814 * q^28 + 7831383 * q^29 - 11859224 * q^30 - 9265632 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 - 13222428 * q^35 + 7355018 * q^36 + 27205020 * q^37 - 67677738 * q^38 - 20775702 * q^39 - 16500258 * q^40 + 20419440 * q^41 - 10220798 * q^42 + 27415427 * q^43 + 41775405 * q^44 - 85982588 * q^45 - 137234708 * q^46 - 90906681 * q^47 + 33057375 * q^48 + 229824892 * q^49 + 44406714 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 - 130507669 * q^54 - 157712310 * q^55 + 382459116 * q^56 - 162912873 * q^57 - 344026048 * q^58 + 255540 * q^59 + 287916794 * q^60 + 304035459 * q^61 + 693626280 * q^62 - 122148024 * q^63 - 908491514 * q^64 - 1424960190 * q^65 - 611099417 * q^66 + 165758480 * q^67 + 357518508 * q^68 + 271237278 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 - 602867050 * q^73 - 82104492 * q^74 + 1900274774 * q^75 - 1298297525 * q^76 - 491994756 * q^77 - 911449840 * q^78 + 78162339 * q^79 + 227607150 * q^80 + 1230916118 * q^81 + 360208019 * q^82 + 413839926 * q^83 - 467304924 * q^84 - 1440537237 * q^85 + 936824310 * q^86 - 678876318 * q^87 - 1646777694 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 - 677003592 * q^92 - 492493440 * q^93 - 848375184 * q^94 - 2034458607 * q^95 - 6041588930 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 - 736622698 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−17.0666	−	29.5602i	−0.754243	−	1.30639i	−0.945750	−	0.324895i	$-0.894671\pi$
$2$	−17.0666	−	29.5602i	−0.754243	−	1.30639i	0.191507	−	0.981491i	$-0.438662\pi$
$3$	−104.220	−	180.515i	−0.742860	−	1.28667i	−0.951188	−	0.308612i	$-0.900136\pi$
$3$	−104.220	−	180.515i	−0.742860	−	1.28667i	0.208328	−	0.978059i	$-0.433198\pi$
$4$	−326.535	+	565.575i	−0.637764	+	1.10464i
$5$	1253.36	+	2170.89i	0.896833	+	1.55336i	0.831519	+	0.555496i	$0.187472\pi$
$5$	1253.36	+	2170.89i	0.896833	+	1.55336i	0.0653138	+	0.997865i	$0.479195\pi$
$6$	−3557.37	+	6161.54i	−1.12059	+	1.94092i
$7$	4067.64			0.640326			0.320163	−	0.947362i	$-0.396262\pi$
$7$	4067.64			0.640326			0.320163	+	0.947362i	$0.396262\pi$
$8$	4815.16			0.415629
$9$	−11882.3	+	20580.7i	−0.603682	+	1.04561i
$10$	42781.2	−	74099.2i	1.35286	−	2.34322i
$11$	−30956.0			−0.637497			−0.318748	−	0.947839i	$-0.603263\pi$
$11$	−30956.0			−0.637497			−0.318748	+	0.947839i	$0.603263\pi$
$12$	136126.			1.89508
$13$	−70574.7	+	122239.i	−0.685337	+	1.18704i	0.287994	+	0.957632i	$0.407012\pi$
$13$	−70574.7	+	122239.i	−0.685337	+	1.18704i	−0.973331	+	0.229406i	$0.926322\pi$
$14$	−69420.6	−	120240.i	−0.482961	−	0.836514i
$15$	261252.	−	452501.i	1.33244	−	2.30786i
$16$	85007.7	+	147238.i	0.324279	+	0.561667i
$17$	201124.	+	348358.i	0.584043	+	1.01159i	0.994994	+	0.0999342i	$0.0318632\pi$
$17$	201124.	+	348358.i	0.584043	+	1.01159i	−0.410951	+	0.911657i	$0.634803\pi$
$18$	811158.			1.82129
$19$	336217.	−	457871.i	0.591873	−	0.806031i
$19$	336217.	−	457871.i	0.591873	−	0.806031i
$20$	−1.63707e6			−2.28787
$21$	−423931.	−	734270.i	−0.475673	−	0.823889i
$22$	528313.	+	915065.i	0.480827	+	0.832817i
$23$	−353001.	+	611416.i	−0.263027	+	0.455576i	−0.967045	−	0.254606i	$-0.918054\pi$
$23$	−353001.	+	611416.i	−0.263027	+	0.455576i	0.704018	+	0.710182i	$0.251388\pi$
$24$	−501838.	−	869208.i	−0.308754	−	0.534778i
$25$	−2.16527e6	+	3.75036e6i	−1.10862	+	1.92019i
$26$	4.81787e6			2.06764
$27$	850757.			0.308084
$28$	−1.32823e6	+	2.30056e6i	−0.408377	+	0.707329i
$29$	1.86928e6	−	3.23768e6i	0.490775	−	0.850047i	−0.509169	−	0.860667i	$-0.670047\pi$
$29$	1.86928e6	−	3.23768e6i	0.490775	−	0.850047i	0.999944	+	0.0106197i	$0.00338042\pi$
$30$	−1.78347e7			−4.01994
$31$	−2.57084e6			−0.499974			−0.249987	−	0.968249i	$-0.580426\pi$
$31$	−2.57084e6			−0.499974			−0.249987	+	0.968249i	$0.580426\pi$
$32$	4.13426e6	−	7.16075e6i	0.696984	−	1.20721i
$33$	3.22625e6	+	5.58803e6i	0.473571	+	0.820249i
$34$	6.86500e6	−	1.18905e7i	0.881020	−	1.52597i
$35$	5.09823e6	+	8.83039e6i	0.574266	+	0.994658i
$36$	−7.75995e6	−	1.34406e7i	−0.770012	−	1.33370i
$37$	−1.01623e6			−0.0891424			−0.0445712	−	0.999006i	$-0.514192\pi$
$37$	−1.01623e6			−0.0891424			−0.0445712	+	0.999006i	$0.514192\pi$
$38$	−1.92728e7	−	2.12434e6i	−1.49940	−	0.165271i
$39$	2.94213e7			2.03644
$40$	6.03514e6	+	1.04532e7i	0.372750	+	0.645622i
$41$	1.77553e7	+	3.07531e7i	0.981298	+	1.69966i	0.657355	+	0.753581i	$0.271675\pi$
$41$	1.77553e7	+	3.07531e7i	0.981298	+	1.69966i	0.323943	+	0.946077i	$0.394991\pi$
$42$	−1.44701e7	+	2.50629e7i	−0.717545	+	1.24282i
$43$	3.77610e6	+	6.54040e6i	0.168436	+	0.291740i	0.937870	−	0.346986i	$-0.112795\pi$
$43$	3.77610e6	+	6.54040e6i	0.168436	+	0.291740i	−0.769434	+	0.638726i	$0.779462\pi$
$44$	1.01082e7	−	1.75080e7i	0.406572	−	0.704204i
$45$	−5.95711e7			−2.16561
$46$	2.40981e7			0.793545
$47$	858969.	−	1.48778e6i	0.0256766	−	0.0444732i	−0.852902	−	0.522072i	$-0.825159\pi$
$47$	858969.	−	1.48778e6i	0.0256766	−	0.0444732i	0.878578	+	0.477599i	$0.158493\pi$
$48$	1.77191e7	−	3.06903e7i	0.481787	−	0.834480i
$49$	−2.38079e7			−0.589982
$50$	1.47815e8			3.34467
$51$	4.19225e7	−	7.26119e7i	0.867724	−	1.50294i
$52$	−4.60902e7	−	7.98307e7i	−0.874166	−	1.51410i
$53$	−3.16597e7	+	5.48361e7i	−0.551144	+	0.954609i	0.447049	+	0.894510i	$0.352475\pi$
$53$	−3.16597e7	+	5.48361e7i	−0.551144	+	0.954609i	−0.998192	+	0.0600992i	$0.980858\pi$
$54$	−1.45195e7	−	2.51485e7i	−0.232370	−	0.402476i
$55$	−3.87991e7	−	6.72021e7i	−0.571728	−	0.990263i
$56$	1.95863e7			0.266138
$57$	−1.17693e8	−	1.29727e7i	−1.47678	−	0.162777i
$58$	−1.27608e8			−1.48065
$59$	6.46912e7	+	1.12048e8i	0.695042	+	1.20385i	0.970166	+	0.242440i	$0.0779477\pi$
$59$	6.46912e7	+	1.12048e8i	0.695042	+	1.20385i	−0.275124	+	0.961409i	$0.588719\pi$
$60$	1.70616e8	+	2.95515e8i	1.69957	+	2.94374i
$61$	4.08625e7	−	7.07759e7i	0.377868	−	0.654487i	−0.612884	−	0.790173i	$-0.709991\pi$
$61$	4.08625e7	−	7.07759e7i	0.377868	−	0.654487i	0.990752	+	0.135686i	$0.0433239\pi$
$62$	4.38754e7	+	7.59945e7i	0.377102	+	0.653160i
$63$	−4.83328e7	+	8.37148e7i	−0.386553	+	0.669530i
$64$	−1.95182e8			−1.45422
$65$	−3.53823e8			−2.45853
$66$	1.10122e8	−	1.90737e8i	0.714375	−	1.23733i
$67$	−5.92231e7	+	1.02577e8i	−0.359050	+	0.621892i	−0.987802	−	0.155713i	$-0.950232\pi$
$67$	−5.92231e7	+	1.02577e8i	−0.359050	+	0.621892i	0.628753	+	0.777605i	$0.283566\pi$
$68$	−2.62697e8			−1.48992
$69$	1.47160e8			0.781569
$70$	1.74018e8	−	3.01409e8i	0.866271	−	1.50043i
$71$	8.10616e7	+	1.40403e8i	0.378575	+	0.655712i	0.990855	−	0.134929i	$-0.0430808\pi$
$71$	8.10616e7	+	1.40403e8i	0.378575	+	0.655712i	−0.612280	+	0.790641i	$0.709747\pi$
$72$	−5.72150e7	+	9.90993e7i	−0.250908	+	0.434585i
$73$	1.52206e7	+	2.63628e7i	0.0627305	+	0.108652i	0.895685	−	0.444689i	$-0.146686\pi$
$73$	1.52206e7	+	2.63628e7i	0.0627305	+	0.108652i	−0.832955	+	0.553341i	$0.813352\pi$
$74$	1.73435e7	+	3.00399e7i	0.0672350	+	0.116454i
$75$	9.02662e8			3.29420
$76$	1.49174e8	+	3.39667e8i	0.512899	+	1.16786i
$77$	−1.25918e8			−0.408206
$78$	−5.02120e8	−	8.69698e8i	−1.53597	−	2.66037i
$79$	−3.15499e8	−	5.46461e8i	−0.911332	−	1.57847i	−0.812184	−	0.583401i	$-0.801722\pi$
$79$	−3.15499e8	−	5.46461e8i	−0.911332	−	1.57847i	−0.0991476	−	0.995073i	$-0.531612\pi$
$80$	−2.13091e8	+	3.69084e8i	−0.581648	+	1.00744i
$81$	1.45212e8	+	2.51515e8i	0.374819	+	0.649205i
$82$	6.06044e8	−	1.04970e9i	1.48027	−	2.56391i
$83$	2.53183e8			0.585576			0.292788	−	0.956177i	$-0.405417\pi$
$83$	2.53183e8			0.585576			0.292788	+	0.956177i	$0.405417\pi$
$84$	5.53713e8			1.21347
$85$	−5.04163e8	+	8.73237e8i	−1.04758	+	1.81446i
$86$	1.28890e8	−	2.23244e8i	0.254084	−	0.440086i
$87$	−7.79266e8			−1.45831
$88$	−1.49058e8			−0.264962
$89$	3.09600e8	−	5.36243e8i	0.523053	−	0.905954i	−0.476587	−	0.879127i	$-0.658126\pi$
$89$	3.09600e8	−	5.36243e8i	0.523053	−	0.905954i	0.999640	−	0.0268270i	$-0.00854034\pi$
$90$	1.01667e9	+	1.76093e9i	1.63339	+	2.82912i
$91$	−2.87073e8	+	4.97224e8i	−0.438839	+	0.760092i
$92$	−2.30534e8	−	3.99297e8i	−0.335498	−	0.581100i
$93$	2.67934e8	+	4.64075e8i	0.371411	+	0.643303i
$94$	−5.86386e7			−0.0774655
$95$	1.41539e9	+	1.56011e8i	1.78287	+	0.196516i
$96$	−1.72350e9			−2.07105
$97$	2.80838e8	+	4.86425e8i	0.322094	+	0.557883i	0.980920	−	0.194412i	$-0.0622799\pi$
$97$	2.80838e8	+	4.86425e8i	0.322094	+	0.557883i	−0.658826	+	0.752296i	$0.728947\pi$
$98$	4.06319e8	+	7.03765e8i	0.444990	+	0.770745i
$99$	3.67828e8	−	6.37096e8i	0.384845	−	0.666571i
$100$	−1.41407e9	−	2.44925e9i	−1.41407	−	2.44925i
$101$	2.16212e8	−	3.74490e8i	0.206744	−	0.358091i	−0.743943	−	0.668243i	$-0.767047\pi$
$101$	2.16212e8	−	3.74490e8i	0.206744	−	0.358091i	0.950687	+	0.310152i	$0.100380\pi$
$102$	−2.86189e9			−2.61790
$103$	−6.31374e8			−0.552738			−0.276369	−	0.961052i	$-0.589131\pi$
$103$	−6.31374e8			−0.552738			−0.276369	+	0.961052i	$0.589131\pi$
$104$	−3.39829e8	+	5.88600e8i	−0.284846	+	0.493368i
$105$	1.06268e9	−	1.84061e9i	0.853198	−	1.47778i
$106$	2.16129e9			1.66278
$107$	−1.19398e9			−0.880581			−0.440290	−	0.897855i	$-0.645125\pi$
$107$	−1.19398e9			−0.880581			−0.440290	+	0.897855i	$0.645125\pi$
$108$	−2.77802e8	+	4.81167e8i	−0.196485	+	0.340321i
$109$	−1.34702e8	−	2.33311e8i	−0.0914018	−	0.158313i	0.816699	−	0.577063i	$-0.195801\pi$
$109$	−1.34702e8	−	2.33311e8i	−0.0914018	−	0.158313i	−0.908101	+	0.418751i	$0.862468\pi$
$110$	−1.32434e9	+	2.29382e9i	−0.862444	+	1.49380i
$111$	1.05912e8	+	1.83445e8i	0.0662203	+	0.114697i
$112$	3.45781e8	+	5.98910e8i	0.207644	+	0.359650i
$113$	4.67502e8			0.269731			0.134866	−	0.990864i	$-0.456940\pi$
$113$	4.67502e8			0.269731			0.134866	+	0.990864i	$0.456940\pi$
$114$	1.62514e9	+	3.70043e9i	0.901197	+	2.05201i
$115$	−1.76975e9			−0.943566
$116$	1.22077e9	+	2.11443e9i	0.625997	+	1.08426i
$117$	−1.67718e9	−	2.90495e9i	−0.827451	−	1.43319i
$118$	2.20811e9	−	3.82456e9i	1.04846	−	1.81599i
$119$	8.18101e8	+	1.41699e9i	0.373978	+	0.647749i
$120$	1.25797e9	−	2.17887e9i	0.553802	−	0.959213i
$121$	−1.39967e9			−0.593598
$122$	−2.78953e9			−1.14002
$123$	3.70093e9	−	6.41020e9i	1.45793	−	2.52522i
$124$	8.39470e8	−	1.45400e9i	0.318866	−	0.552291i
$125$	−5.95954e9			−2.18332
$126$	3.29950e9			1.16622
$127$	−1.93263e9	+	3.34741e9i	−0.659222	+	1.14181i	0.321595	+	0.946877i	$0.395781\pi$
$127$	−1.93263e9	+	3.34741e9i	−0.659222	+	1.14181i	−0.980817	+	0.194929i	$0.937552\pi$
$128$	1.21435e9	+	2.10332e9i	0.399853	+	0.692565i
$129$	7.87093e8	−	1.36329e9i	0.250249	−	0.433444i
$130$	6.03854e9	+	1.04591e10i	1.85433	+	3.21179i
$131$	4.04562e8	+	7.00722e8i	0.120023	+	0.207886i	0.919776	−	0.392443i	$-0.128370\pi$
$131$	4.04562e8	+	7.00722e8i	0.120023	+	0.207886i	−0.799754	+	0.600328i	$0.795037\pi$
$132$	−4.21393e9			−1.20811
$133$	1.36761e9	−	1.86245e9i	0.378992	−	0.516123i
$134$	4.04294e9			1.08324
$135$	1.06631e9	+	1.84690e9i	0.276300	+	0.478565i
$136$	9.68446e8	+	1.67740e9i	0.242745	+	0.420447i
$137$	3.06967e8	−	5.31682e8i	0.0744473	−	0.128946i	−0.826399	−	0.563086i	$-0.809614\pi$
$137$	3.06967e8	−	5.31682e8i	0.0744473	−	0.128946i	0.900846	+	0.434139i	$0.142947\pi$
$138$	−2.51151e9	−	4.35006e9i	−0.589493	−	1.02103i
$139$	−1.49487e8	+	2.58919e8i	−0.0339654	+	0.0588298i	−0.882508	−	0.470297i	$-0.844147\pi$
$139$	−1.49487e8	+	2.58919e8i	−0.0339654	+	0.0588298i	0.848543	+	0.529126i	$0.177480\pi$
$140$	−6.65900e9			−1.46498
$141$	−3.58088e8			−0.0762964
$142$	2.76688e9	−	4.79238e9i	0.571075	−	0.989131i
$143$	2.18471e9	−	3.78404e9i	0.436900	−	0.756734i
$144$	−4.04034e9			−0.783044
$145$	9.37152e9			1.76057
$146$	5.19526e8	−	8.99846e8i	0.0946280	−	0.163901i
$147$	2.48127e9	+	4.29768e9i	0.438274	+	0.759113i
$148$	3.31835e8	−	5.74754e8i	0.0568518	−	0.0984701i
$149$	4.25959e9	+	7.37783e9i	0.707994	+	1.22628i	0.965600	+	0.260032i	$0.0837331\pi$
$149$	4.25959e9	+	7.37783e9i	0.707994	+	1.22628i	−0.257606	+	0.966250i	$0.582934\pi$
$150$	−1.54053e10	−	2.66828e10i	−2.48462	−	4.30349i
$151$	−2.60207e8			−0.0407308			−0.0203654	−	0.999793i	$-0.506483\pi$
$151$	−2.60207e8			−0.0407308			−0.0203654	+	0.999793i	$0.506483\pi$
$152$	1.61894e9	−	2.20472e9i	0.245999	−	0.335010i
$153$	−9.55925e9			−1.41030
$154$	2.14899e9	+	3.72215e9i	0.307886	+	0.533275i
$155$	−3.22220e9	−	5.58101e9i	−0.448394	−	0.776641i
$156$	−9.60708e9	+	1.66400e10i	−1.29877	+	2.24953i
$157$	2.07006e8	+	3.58545e8i	0.0271916	+	0.0470972i	0.879301	−	0.476267i	$-0.158010\pi$
$157$	2.07006e8	+	3.58545e8i	0.0271916	+	0.0470972i	−0.852109	+	0.523364i	$0.824677\pi$
$158$	−1.07690e10	+	1.86524e10i	−1.37473	+	2.38110i
$159$	1.31983e10			1.63769
$160$	2.07269e10			2.50031
$161$	−1.43588e9	+	2.48702e9i	−0.168423	+	0.291718i
$162$	4.95655e9	−	8.58500e9i	0.565408	−	0.979316i
$163$	−6.26572e9			−0.695227			−0.347614	−	0.937638i	$-0.613008\pi$
$163$	−6.26572e9			−0.695227			−0.347614	+	0.937638i	$0.613008\pi$
$164$	−2.31909e10			−2.50334
$165$	−8.08732e9	+	1.40076e10i	−0.849428	+	1.47125i
$166$	−4.32096e9	−	7.48412e9i	−0.441666	−	0.764988i
$167$	−6.21619e9	+	1.07668e10i	−0.618444	+	1.07118i	0.371326	+	0.928502i	$0.378903\pi$
$167$	−6.21619e9	+	1.07668e10i	−0.618444	+	1.07118i	−0.989770	+	0.142673i	$0.954430\pi$
$168$	−2.04129e9	−	3.53563e9i	−0.197703	−	0.342432i
$169$	−4.65934e9	−	8.07021e9i	−0.439374	−	0.761018i
$170$	3.44173e10			3.16051
$171$	5.42828e9	+	1.23601e10i	0.485490	+	1.10545i
$172$	−4.93212e9			−0.429690
$173$	−1.18024e9	−	2.04423e9i	−0.100176	−	0.173509i	0.811581	−	0.584240i	$-0.198607\pi$
$173$	−1.18024e9	−	2.04423e9i	−0.100176	−	0.173509i	−0.911757	+	0.410730i	$0.865274\pi$
$174$	1.32994e10	+	2.30352e10i	1.09992	+	1.90511i
$175$	−8.80755e9	+	1.52551e10i	−0.709878	+	1.22955i
$176$	−2.63150e9	−	4.55789e9i	−0.206727	−	0.358061i
$177$	1.34843e10	−	2.33555e10i	1.03264	−	1.78858i
$178$	−2.11352e10			−1.57804
$179$	1.13959e9			0.0829680			0.0414840	−	0.999139i	$-0.486791\pi$
$179$	1.13959e9			0.0829680			0.0414840	+	0.999139i	$0.486791\pi$
$180$	1.94521e10	−	3.36920e10i	1.38115	−	2.39221i
$181$	6.72301e9	−	1.16446e10i	0.465597	−	0.806438i	−0.533631	−	0.845717i	$-0.679173\pi$
$181$	6.72301e9	−	1.16446e10i	0.465597	−	0.806438i	0.999228	+	0.0392794i	$0.0125062\pi$
$182$	1.95974e10			1.32397
$183$	−1.70348e10			−1.12281
$184$	−1.69976e9	+	2.94406e9i	−0.109322	+	0.189351i
$185$	−1.27370e9	−	2.20612e9i	−0.0799458	−	0.138470i
$186$	9.14543e9	−	1.58403e10i	0.560268	−	0.970412i
$187$	−6.22601e9	−	1.07838e10i	−0.372325	−	0.644886i
$188$	5.60967e8	+	9.71624e8i	0.0327512	+	0.0567267i
$189$	3.46057e9			0.197274
$190$	−1.95441e10	−	4.45017e10i	−1.08799	−	2.47734i
$191$	−2.51377e9			−0.136671			−0.0683354	−	0.997662i	$-0.521769\pi$
$191$	−2.51377e9			−0.136671			−0.0683354	+	0.997662i	$0.521769\pi$
$192$	2.03420e10	+	3.52334e10i	1.08028	+	1.87111i
$193$	−1.58831e10	−	2.75104e10i	−0.824003	−	1.42721i	−0.902679	−	0.430315i	$-0.858403\pi$
$193$	−1.58831e10	−	2.75104e10i	−0.824003	−	1.42721i	0.0786762	−	0.996900i	$-0.474931\pi$
$194$	9.58587e9	−	1.66032e10i	0.485874	−	0.841559i
$195$	3.68756e10	+	6.38703e10i	1.82634	+	3.16332i
$196$	7.77412e9	−	1.34652e10i	0.376269	−	0.651717i
$197$	3.13458e10			1.48280			0.741399	−	0.671065i	$-0.234163\pi$
$197$	3.13458e10			1.48280			0.741399	+	0.671065i	$0.234163\pi$
$198$	−2.51102e10			−1.16107
$199$	8.01959e8	−	1.38903e9i	0.0362505	−	0.0627876i	−0.847331	−	0.531065i	$-0.821792\pi$
$199$	8.01959e8	−	1.38903e9i	0.0362505	−	0.0627876i	0.883581	+	0.468278i	$0.155125\pi$
$200$	−1.04261e10	+	1.80586e10i	−0.460774	+	0.798084i
$201$	2.46890e10			1.06689
$202$	−1.47600e10			−0.623741
$203$	7.60354e9	−	1.31697e10i	0.314256	−	0.544307i
$204$	2.73783e10	+	4.74207e10i	1.10681	+	1.91704i
$205$	−4.45077e10	+	7.70896e10i	−1.76012	+	3.04862i
$206$	1.07754e10	+	1.86635e10i	0.416898	+	0.722089i
$207$	−8.38890e9	−	1.45300e10i	−0.317569	−	0.550046i
$208$	−2.39976e10			−0.888961
$209$	−1.04079e10	+	1.41739e10i	−0.377317	+	0.513843i
$210$	−7.25450e10			−2.57407
$211$	−2.09826e10	−	3.63430e10i	−0.728767	−	1.26226i	−0.957405	−	0.288750i	$-0.906760\pi$
$211$	−2.09826e10	−	3.63430e10i	−0.728767	−	1.26226i	0.228638	−	0.973512i	$-0.426573\pi$
$212$	−2.06760e10	−	3.58118e10i	−0.702999	−	1.21763i
$213$	1.68965e10	−	2.92656e10i	0.562457	−	0.974204i
$214$	2.03771e10	+	3.52942e10i	0.664172	+	1.15038i
$215$	−9.46564e9	+	1.63950e10i	−0.302118	+	0.523284i
$216$	4.09653e9			0.128048
$217$	−1.04573e10			−0.320147
$218$	−4.59780e9	+	7.96362e9i	−0.137878	+	0.238812i
$219$	3.17259e9	−	5.49509e9i	0.0931999	−	0.161427i
$220$	5.06771e10			1.45851
$221$	−5.67772e10			−1.60106
$222$	3.61510e9	−	6.26154e9i	0.0998923	−	0.173019i
$223$	6.21835e9	+	1.07705e10i	0.168385	+	0.291651i	0.937852	−	0.347035i	$-0.112812\pi$
$223$	6.21835e9	+	1.07705e10i	0.168385	+	0.291651i	−0.769467	+	0.638686i	$0.779478\pi$
$224$	1.68167e10	−	2.91273e10i	0.446297	−	0.773009i
$225$	−5.14567e10	−	8.91256e10i	−1.33851	−	2.31836i
$226$	−7.97866e9	−	1.38194e10i	−0.203443	−	0.352373i
$227$	5.60406e10			1.40083			0.700416	−	0.713735i	$-0.252998\pi$
$227$	5.60406e10			1.40083			0.700416	+	0.713735i	$0.252998\pi$
$228$	4.57680e10	−	6.23283e10i	1.12164	−	1.52749i
$229$	5.10125e10			1.22579			0.612896	−	0.790164i	$-0.290004\pi$
$229$	5.10125e10			1.22579			0.612896	+	0.790164i	$0.290004\pi$
$230$	3.02036e10	+	5.23142e10i	0.711678	+	1.23266i
$231$	1.31232e10	+	2.27301e10i	0.303240	+	0.525227i
$232$	9.00086e9	−	1.55899e10i	0.203980	−	0.353304i
$233$	−4.01469e10	−	6.95364e10i	−0.892381	−	1.54565i	−0.837013	−	0.547182i	$-0.815700\pi$
$233$	−4.01469e10	−	6.95364e10i	−0.892381	−	1.54565i	−0.0553671	−	0.998466i	$-0.517633\pi$
$234$	−5.72472e10	+	9.91551e10i	−1.24820	+	2.16194i
$235$	4.30640e9			0.0921105
$236$	−8.44958e10			−1.77309
$237$	−6.57629e10	+	1.13905e11i	−1.35398	+	2.34517i
$238$	2.79244e10	−	4.83664e10i	0.564140	−	0.977119i
$239$	1.25824e10			0.249444			0.124722	−	0.992192i	$-0.460196\pi$
$239$	1.25824e10			0.249444			0.124722	+	0.992192i	$0.460196\pi$
$240$	8.88337e10			1.72833
$241$	2.23954e10	−	3.87900e10i	0.427644	−	0.740701i	−0.569019	−	0.822324i	$-0.692677\pi$
$241$	2.23954e10	−	3.87900e10i	0.427644	−	0.740701i	0.996663	+	0.0816229i	$0.0260103\pi$
$242$	2.38876e10	+	4.13745e10i	0.447717	+	0.775468i
$243$	3.86409e10	−	6.69280e10i	0.710917	−	1.23134i
$244$	2.66860e10	+	4.62216e10i	0.481981	+	0.834816i
$245$	−2.98399e10	−	5.16843e10i	−0.529116	−	0.916455i
$246$	−2.52649e11			−4.39854
$247$	3.22413e10	+	7.34130e10i	0.551158	+	1.25498i
$248$	−1.23790e10			−0.207804
$249$	−2.63868e10	−	4.57033e10i	−0.435001	−	0.753443i
$250$	1.01709e11	+	1.76165e11i	1.64675	+	2.85226i
$251$	3.70614e10	−	6.41922e10i	0.589372	−	1.02082i	−0.404943	−	0.914342i	$-0.632708\pi$
$251$	3.70614e10	−	6.41922e10i	0.589372	−	1.02082i	0.994315	−	0.106481i	$-0.0339582\pi$
$252$	−3.15647e10	−	5.46716e10i	−0.493059	−	0.854004i
$253$	1.09275e10	−	1.89270e10i	0.167679	−	0.290429i
$254$	1.31933e11			1.98885
$255$	2.10176e11			3.11281
$256$	−8.51707e9	+	1.47520e10i	−0.123940	+	0.214670i
$257$	−4.68270e10	+	8.11068e10i	−0.669573	+	1.15973i	0.308451	+	0.951240i	$0.400189\pi$
$257$	−4.68270e10	+	8.11068e10i	−0.669573	+	1.15973i	−0.978024	+	0.208493i	$0.933144\pi$
$258$	−5.37319e10			−0.754994
$259$	−4.13366e9			−0.0570802
$260$	1.15536e11	−	2.00113e11i	1.56796	−	2.71579i
$261$	4.44225e10	+	7.69419e10i	0.592544	+	1.02632i
$262$	1.38090e10	−	2.39178e10i	0.181053	−	0.313593i
$263$	3.90262e10	+	6.75954e10i	0.502986	+	0.871197i	0.999994	+	0.00345091i	$0.00109846\pi$
$263$	3.90262e10	+	6.75954e10i	0.502986	+	0.871197i	−0.497008	+	0.867746i	$0.665568\pi$
$264$	1.55349e10	+	2.69072e10i	0.196830	+	0.340919i
$265$	−1.58724e11			−1.97714
$266$	−7.83948e10	−	8.64104e9i	−0.960108	−	0.105828i
$267$	−1.29066e11			−1.55422
$268$	−3.86768e10	−	6.69902e10i	−0.457978	−	0.793240i
$269$	−3.53043e10	−	6.11488e10i	−0.411095	−	0.712037i	0.583915	−	0.811815i	$-0.301520\pi$
$269$	−3.53043e10	−	6.11488e10i	−0.411095	−	0.712037i	−0.995010	+	0.0997777i	$0.968187\pi$
$270$	3.63964e10	−	6.30404e10i	0.416794	−	0.721908i
$271$	1.74173e10	+	3.01676e10i	0.196163	+	0.339765i	0.947281	−	0.320403i	$-0.103818\pi$
$271$	1.74173e10	+	3.01676e10i	0.196163	+	0.339765i	−0.751118	+	0.660168i	$0.770485\pi$
$272$	−3.41942e10	+	5.92262e10i	−0.378785	+	0.656075i
$273$	1.19675e11			1.30398
$274$	−2.09555e10			−0.224605
$275$	6.70282e10	−	1.16096e11i	0.706742	−	1.22411i
$276$	−4.80527e10	+	8.32298e10i	−0.498457	+	0.863352i
$277$	−1.79253e10			−0.182940			−0.0914699	−	0.995808i	$-0.529157\pi$
$277$	−1.79253e10			−0.182940			−0.0914699	+	0.995808i	$0.529157\pi$
$278$	1.02049e10			0.102473
$279$	3.05474e10	−	5.29097e10i	0.301825	−	0.522777i
$280$	2.45488e10	+	4.25197e10i	0.238681	+	0.413408i
$281$	−3.05939e10	+	5.29902e10i	−0.292723	+	0.507010i	−0.974453	−	0.224593i	$-0.927895\pi$
$281$	−3.05939e10	+	5.29902e10i	−0.292723	+	0.507010i	0.681730	+	0.731604i	$0.261228\pi$
$282$	6.11134e9	+	1.05851e10i	0.0575460	+	0.0996726i
$283$	9.03020e10	+	1.56408e11i	0.836871	+	1.44950i	0.892498	+	0.451051i	$0.148951\pi$
$283$	9.03020e10	+	1.56408e11i	0.836871	+	1.44950i	−0.0556273	+	0.998452i	$0.517716\pi$
$284$	−1.05878e11			−0.965766
$285$	−1.19350e11	−	2.71758e11i	−1.07157	−	2.43995i
$286$	−1.49142e11			−1.31812
$287$	7.22222e10	+	1.25093e11i	0.628351	+	1.08834i
$288$	9.82487e10	+	1.70172e11i	0.841513	+	1.45754i
$289$	−2.16081e10	+	3.74263e10i	−0.182211	+	0.315600i
$290$	−1.59940e11	−	2.77024e11i	−1.32790	−	2.29999i
$291$	5.85380e10	−	1.01391e11i	0.478542	−	0.828858i
$292$	−1.98802e10			−0.160029
$293$	−1.52036e10			−0.120515			−0.0602577	−	0.998183i	$-0.519192\pi$
$293$	−1.52036e10			−0.120515			−0.0602577	+	0.998183i	$0.519192\pi$
$294$	8.46935e10	−	1.46693e11i	0.661130	−	1.14511i
$295$	−1.62163e11	+	2.80875e11i	−1.24667	+	2.15930i
$296$	−4.89331e9			−0.0370501
$297$	−2.63361e10			−0.196402
$298$	1.45393e11	−	2.51828e11i	1.06800	−	1.84983i
$299$	−4.98259e10	−	8.63010e10i	−0.360525	−	0.624447i
$300$	−2.94751e11	+	5.10523e11i	−2.10092	+	3.63890i
$301$	1.53598e10	+	2.66040e10i	0.107854	+	0.186809i
$302$	4.44084e9	+	7.69176e9i	0.0307209	+	0.0532101i
$303$	−9.01347e10			−0.614328
$304$	9.59969e10	+	1.05812e10i	0.644653	+	0.0710567i
$305$	2.04862e11			1.35554
$306$	1.63144e11	+	2.82573e11i	1.06371	+	1.84240i
$307$	−7.67910e10	−	1.33006e11i	−0.493387	−	0.854572i	0.506584	−	0.862191i	$-0.330908\pi$
$307$	−7.67910e10	−	1.33006e11i	−0.493387	−	0.854572i	−0.999971	+	0.00761900i	$0.997575\pi$
$308$	4.11166e10	−	7.12161e10i	0.260339	−	0.450920i
$309$	6.58020e10	+	1.13972e11i	0.410607	+	0.711192i
$310$	−1.09984e11	+	1.90497e11i	−0.676395	+	1.17155i
$311$	7.14306e9			0.0432974			0.0216487	−	0.999766i	$-0.493108\pi$
$311$	7.14306e9			0.0432974			0.0216487	+	0.999766i	$0.493108\pi$
$312$	1.41668e11			0.846402
$313$	5.13179e10	−	8.88852e10i	0.302217	−	0.523456i	−0.674421	−	0.738347i	$-0.735607\pi$
$313$	5.13179e10	−	8.88852e10i	0.302217	−	0.523456i	0.976638	+	0.214892i	$0.0689399\pi$
$314$	7.06576e9	−	1.22383e10i	0.0410181	−	0.0710454i
$315$	−2.42314e11			−1.38669
$316$	4.12086e11			2.32486
$317$	1.36072e10	−	2.35683e10i	0.0756835	−	0.131088i	−0.825700	−	0.564110i	$-0.809219\pi$
$317$	1.36072e10	−	2.35683e10i	0.0756835	−	0.131088i	0.901383	+	0.433022i	$0.142553\pi$
$318$	−2.25250e11	−	3.90144e11i	−1.23522	−	2.13946i
$319$	−5.78653e10	+	1.00226e11i	−0.312868	+	0.541902i
$320$	−2.44634e11	−	4.23719e11i	−1.30420	−	2.25893i
$321$	1.24437e11	+	2.15531e11i	0.654148	+	1.13302i
$322$	9.80222e10			0.508128
$323$	2.27124e11	+	2.50347e10i	1.16105	+	0.127977i
$324$	−1.89668e11			−0.956183
$325$	−3.05627e11	−	5.29362e11i	−1.51956	−	2.63195i
$326$	1.06934e11	+	1.85216e11i	0.524370	+	0.908235i
$327$	−2.80774e10	+	4.86314e10i	−0.135797	+	0.235208i
$328$	8.54946e10	+	1.48081e11i	0.407856	+	0.706427i
$329$	3.49398e9	−	6.05175e9i	0.0164414	−	0.0284773i
$330$	5.52091e11			2.56270
$331$	3.18775e10			0.145968			0.0729841	−	0.997333i	$-0.476748\pi$
$331$	3.18775e10			0.145968			0.0729841	+	0.997333i	$0.476748\pi$
$332$	−8.26731e10	+	1.43194e11i	−0.373459	+	0.646850i
$333$	1.20751e10	−	2.09147e10i	0.0538136	−	0.0932079i
$334$	4.24356e11			1.86583
$335$	−2.96912e11			−1.28803
$336$	7.20748e10	−	1.24837e11i	0.308501	−	0.534339i
$337$	2.18485e11	+	3.78427e11i	0.922755	+	1.59826i	0.795133	+	0.606436i	$0.207401\pi$
$337$	2.18485e11	+	3.78427e11i	0.922755	+	1.59826i	0.127622	+	0.991823i	$0.459265\pi$
$338$	−1.59038e11	+	2.75462e11i	−0.662789	+	1.14798i
$339$	−4.87233e10	−	8.43912e10i	−0.200372	−	0.347055i
$340$	−3.29254e11	−	5.70285e11i	−1.33621	−	2.31439i
$341$	7.95831e10			0.318732
$342$	2.72725e11	−	3.71406e11i	1.07797	−	1.46802i
$343$	−2.60986e11			−1.01811
$344$	1.81825e10	+	3.14931e10i	0.0700070	+	0.121256i
$345$	1.84444e11	+	3.19467e11i	0.700937	+	1.21406i
$346$	−4.02852e10	+	6.97761e10i	−0.151114	+	0.261736i
$347$	−4.18533e10	−	7.24921e10i	−0.154970	−	0.268416i	0.778078	−	0.628167i	$-0.216195\pi$
$347$	−4.18533e10	−	7.24921e10i	−0.154970	−	0.268416i	−0.933048	+	0.359752i	$0.882861\pi$
$348$	2.54458e11	−	4.40734e11i	0.930056	−	1.61090i
$349$	1.29123e11			0.465896			0.232948	−	0.972489i	$-0.425163\pi$
$349$	1.29123e11			0.465896			0.232948	+	0.972489i	$0.425163\pi$
$350$	6.01258e11			2.14168
$351$	−6.00420e10	+	1.03996e11i	−0.211141	+	0.365707i
$352$	−1.27980e11	+	2.21668e11i	−0.444325	+	0.769594i
$353$	6.74363e10			0.231157			0.115579	−	0.993298i	$-0.463128\pi$
$353$	6.74363e10			0.231157			0.115579	+	0.993298i	$0.463128\pi$
$354$	−9.20521e11			−3.11544
$355$	−2.03199e11	+	3.51951e11i	−0.679038	+	1.17613i
$356$	2.02190e11	+	3.50204e11i	0.667168	+	1.15557i
$357$	1.70526e11	−	2.95359e11i	0.555626	−	0.962373i
$358$	−1.94489e10	−	3.36865e10i	−0.0625780	−	0.108388i
$359$	−2.26160e11	−	3.91721e11i	−0.718606	−	1.24466i	−0.961552	−	0.274622i	$-0.911447\pi$
$359$	−2.26160e11	−	3.91721e11i	−0.718606	−	1.24466i	0.242946	−	0.970040i	$-0.421886\pi$
$360$	−2.86845e11			−0.900089
$361$	−9.66041e10	−	3.07888e11i	−0.299373	−	0.954136i
$362$	−4.58955e11			−1.40469
$363$	1.45874e11	+	2.52662e11i	0.440960	+	0.763765i
$364$	−1.87479e11	−	3.24722e11i	−0.559752	−	0.969518i
$365$	−3.81538e10	+	6.60844e10i	−0.112518	+	0.194886i
$366$	2.90725e11	+	5.03551e11i	0.846873	+	1.46683i
$367$	8.46755e10	−	1.46662e11i	0.243647	−	0.422009i	−0.718104	−	0.695936i	$-0.754990\pi$
$367$	8.46755e10	−	1.46662e11i	0.243647	−	0.422009i	0.961750	+	0.273928i	$0.0883229\pi$
$368$	−1.20031e11			−0.341176
$369$	−8.43893e11			−2.36957
$370$	−4.34755e10	+	7.53018e10i	−0.120597	+	0.208880i
$371$	−1.28780e11	+	2.23054e11i	−0.352912	+	0.611261i
$372$	−3.49959e11			−0.947490
$373$	2.28609e11			0.611510			0.305755	−	0.952110i	$-0.401091\pi$
$373$	2.28609e11			0.611510			0.305755	+	0.952110i	$0.401091\pi$
$374$	−2.12513e11	+	3.68084e11i	−0.561647	+	0.972802i
$375$	6.21105e11	+	1.07579e12i	1.62190	+	2.80922i
$376$	4.13607e9	−	7.16389e9i	0.0106719	−	0.0184843i
$377$	2.63847e11	+	4.56997e11i	0.672692	+	1.16514i
$378$	−5.90601e10	−	1.02295e11i	−0.148792	−	0.257716i
$379$	5.28445e11			1.31560			0.657799	−	0.753193i	$-0.271487\pi$
$379$	5.28445e11			1.31560			0.657799	+	0.753193i	$0.271487\pi$
$380$	−5.50410e11	+	7.49565e11i	−1.35413	+	1.84410i
$381$	8.05677e11			1.95884
$382$	4.29014e10	+	7.43075e10i	0.103083	+	0.178545i
$383$	−6.21991e10	−	1.07732e11i	−0.147703	−	0.255829i	0.782675	−	0.622430i	$-0.213855\pi$
$383$	−6.21991e10	−	1.07732e11i	−0.147703	−	0.255829i	−0.930378	+	0.366601i	$0.880521\pi$
$384$	2.53120e11	−	4.38418e11i	0.594069	−	1.02896i
$385$	−1.57821e11	−	2.73354e11i	−0.366093	−	0.634091i
$386$	−5.42141e11	+	9.39016e11i	−1.24300	+	2.15293i
$387$	−1.79474e11			−0.406727
$388$	−3.66814e11			−0.821680
$389$	1.73273e11	−	3.00118e11i	0.383671	−	0.664537i	−0.607913	−	0.794004i	$-0.707993\pi$
$389$	1.73273e11	−	3.00118e11i	0.383671	−	0.664537i	0.991584	+	0.129466i	$0.0413264\pi$
$390$	1.25868e12	−	2.18009e12i	2.75501	−	4.77182i
$391$	−2.83988e11			−0.614476
$392$	−1.14639e11			−0.245214
$393$	8.43272e10	−	1.46059e11i	0.178320	−	0.308860i
$394$	−5.34965e11	−	9.26587e11i	−1.11839	−	1.93711i
$395$	7.90870e11	−	1.36983e12i	1.63463	−	2.83125i
$396$	2.40217e11	+	4.16068e11i	0.490881	+	0.850230i
$397$	−2.70830e11	−	4.69091e11i	−0.547192	−	0.947764i	−0.998465	−	0.0553782i	$-0.982364\pi$
$397$	−2.70830e11	−	4.69091e11i	−0.547192	−	0.947764i	0.451274	−	0.892386i	$-0.350970\pi$
$398$	−5.47468e10			−0.109367
$399$	−4.78734e11	−	5.27683e10i	−0.945618	−	0.104230i
$400$	−7.36259e11			−1.43801
$401$	2.17120e11	+	3.76063e11i	0.419325	+	0.726292i	0.995872	−	0.0907723i	$-0.0289335\pi$
$401$	2.17120e11	+	3.76063e11i	0.419325	+	0.726292i	−0.576547	+	0.817064i	$0.695600\pi$
$402$	−4.21356e11	−	7.29811e11i	−0.804697	−	1.39378i
$403$	1.81437e11	−	3.14257e11i	0.342651	−	0.593489i
$404$	1.41201e11	+	2.44568e11i	0.263708	+	0.456755i
$405$	−3.64008e11	+	6.30480e11i	−0.672300	+	1.16446i
$406$	−5.19065e11			−0.948101
$407$	3.14584e10			0.0568280
$408$	2.01864e11	−	3.49638e11i	0.360651	−	0.624666i
$409$	−1.78905e11	+	3.09873e11i	−0.316131	+	0.547556i	−0.979677	−	0.200580i	$-0.935717\pi$
$409$	−1.78905e11	+	3.09873e11i	−0.316131	+	0.547556i	0.663546	+	0.748136i	$0.269051\pi$
$410$	3.03837e12			5.31023
$411$	−1.27969e11			−0.221216
$412$	2.06166e11	−	3.57089e11i	0.352516	−	0.610576i
$413$	2.63141e11	+	4.55773e11i	0.445054	+	0.770856i
$414$	−2.86339e11	+	4.95954e11i	−0.479049	+	0.829737i
$415$	3.17330e11	+	5.49632e11i	0.525164	+	0.909610i
$416$	5.83549e11	+	1.01074e12i	0.955338	+	1.65469i
$417$	6.23184e10			0.100926
$418$	5.96609e11	+	6.57611e10i	0.955866	+	0.105360i
$419$	−3.09461e11			−0.490504			−0.245252	−	0.969459i	$-0.578871\pi$
$419$	−3.09461e11			−0.490504			−0.245252	+	0.969459i	$0.578871\pi$
$420$	6.94003e11	+	1.20205e12i	1.08828	+	1.88495i
$421$	1.02624e11	+	1.77751e11i	0.159214	+	0.275767i	0.934586	−	0.355739i	$-0.115771\pi$
$421$	1.02624e11	+	1.77751e11i	0.159214	+	0.275767i	−0.775371	+	0.631506i	$0.782437\pi$
$422$	−7.16202e11	+	1.24050e12i	−1.09933	+	1.90410i
$423$	2.04130e10	+	3.53564e10i	0.0310010	+	0.0536953i
$424$	−1.52446e11	+	2.64045e11i	−0.229071	+	0.396763i
$425$	−1.74196e12			−2.58992
$426$	−1.15346e12			−1.69692
$427$	1.66214e11	−	2.87891e11i	0.241959	−	0.419085i
$428$	3.89876e11	−	6.75284e11i	0.561603	−	0.972724i
$429$	−9.10767e11			−1.29822
$430$	6.46184e11			0.911482
$431$	4.18473e11	−	7.24816e11i	0.584143	−	1.01177i	−0.410838	−	0.911708i	$-0.634764\pi$
$431$	4.18473e11	−	7.24816e11i	0.584143	−	1.01177i	0.994982	−	0.100058i	$-0.0319028\pi$
$432$	7.23209e10	+	1.25263e11i	0.0999050	+	0.173040i
$433$	7.70728e10	−	1.33494e11i	0.105367	−	0.182502i	−0.808521	−	0.588467i	$-0.799732\pi$
$433$	7.70728e10	−	1.33494e11i	0.105367	−	0.182502i	0.913888	+	0.405966i	$0.133065\pi$
$434$	1.78469e11	+	3.09118e11i	0.241468	+	0.418235i
$435$	−9.76703e11	−	1.69170e12i	−1.30786	−	2.26528i
$436$	1.75940e11			0.233171
$437$	1.61265e11	+	3.67197e11i	0.211530	+	0.481651i
$438$	−2.16581e11			−0.281181
$439$	1.47483e11	+	2.55449e11i	0.189519	+	0.328257i	0.945090	−	0.326810i	$-0.105974\pi$
$439$	1.47483e11	+	2.55449e11i	0.189519	+	0.328257i	−0.755571	+	0.655067i	$0.772640\pi$
$440$	−1.86824e11	−	3.23589e11i	−0.237627	−	0.411582i
$441$	2.82892e11	−	4.89983e11i	0.356161	−	0.616890i
$442$	9.68992e11	+	1.67834e12i	1.20759	+	2.09161i
$443$	6.12549e11	−	1.06097e12i	0.755655	−	1.30883i	−0.189393	−	0.981901i	$-0.560652\pi$
$443$	6.12549e11	−	1.06097e12i	0.755655	−	1.30883i	0.945048	−	0.326932i	$-0.106015\pi$
$444$	−1.38336e11			−0.168932
$445$	1.55216e12			1.87636
$446$	2.12252e11	−	3.67630e11i	0.254006	−	0.439951i
$447$	8.87872e11	−	1.53784e12i	1.05188	−	1.82191i
$448$	−7.93932e11			−0.931177
$449$	−1.38448e12			−1.60760			−0.803802	−	0.594897i	$-0.797193\pi$
$449$	−1.38448e12			−1.60760			−0.803802	+	0.594897i	$0.797193\pi$
$450$	−1.75638e12	+	3.04213e12i	−2.01912	+	3.49721i
$451$	−5.49634e11	−	9.51994e11i	−0.625574	−	1.08353i
$452$	−1.52656e11	+	2.64408e11i	−0.172025	+	0.297955i
$453$	2.71189e10	+	4.69713e10i	0.0302573	+	0.0524071i
$454$	−9.56420e11	−	1.65657e12i	−1.05657	−	1.83003i
$455$	−1.43922e12			−1.57426
$456$	−5.66712e11	−	6.24656e10i	−0.613791	−	0.0676549i
$457$	1.41558e12			1.51814			0.759070	−	0.651009i	$-0.225654\pi$
$457$	1.41558e12			1.51814			0.759070	+	0.651009i	$0.225654\pi$
$458$	−8.70608e11	−	1.50794e12i	−0.924544	−	1.60136i
$459$	1.71108e11	+	2.96368e11i	0.179934	+	0.311655i
$460$	5.77886e11	−	1.00093e12i	0.601772	−	1.04230i
$461$	−4.97280e10	−	8.61315e10i	−0.0512799	−	0.0888194i	0.839246	−	0.543752i	$-0.182997\pi$
$461$	−4.97280e10	−	8.61315e10i	−0.0512799	−	0.0888194i	−0.890526	+	0.454932i	$0.849663\pi$
$462$	4.47936e11	−	7.75849e11i	0.457433	−	0.792297i
$463$	9.82855e11			0.993974			0.496987	−	0.867758i	$-0.334440\pi$
$463$	9.82855e11			0.993974			0.496987	+	0.867758i	$0.334440\pi$
$464$	6.35611e11			0.636591
$465$	−6.71637e11	+	1.16331e12i	−0.666187	+	1.15387i
$466$	−1.37034e12	+	2.37350e12i	−1.34614	+	2.33159i
$467$	−1.82782e12			−1.77831			−0.889157	−	0.457603i	$-0.848708\pi$
$467$	−1.82782e12			−1.77831			−0.889157	+	0.457603i	$0.848708\pi$
$468$	2.19063e12			2.11087
$469$	−2.40898e11	+	4.17248e11i	−0.229909	+	0.398214i
$470$	−7.34954e10	−	1.27298e11i	−0.0694736	−	0.120332i
$471$	4.31485e10	−	7.47353e10i	0.0403991	−	0.0699732i
$472$	3.11498e11	+	5.39531e11i	0.288880	+	0.500354i
$473$	−1.16893e11	−	2.02465e11i	−0.107378	−	0.185983i
$474$	4.48939e12			4.08493
$475$	9.89181e11	+	2.25235e12i	0.891568	+	2.03009i
$476$	−1.06856e12			−0.954038
$477$	−7.52377e11	−	1.30316e12i	−0.665431	−	1.15256i
$478$	−2.14738e11	−	3.71937e11i	−0.188141	−	0.325870i
$479$	−9.99569e11	+	1.73130e12i	−0.867567	+	1.50267i	−0.00309103	+	0.999995i	$0.500984\pi$
$479$	−9.99569e11	+	1.73130e12i	−0.867567	+	1.50267i	−0.864476	+	0.502675i	$0.832349\pi$
$480$	−2.16017e12	−	3.74152e12i	−1.85738	−	3.21708i
$481$	7.17202e10	−	1.24223e11i	0.0610926	−	0.105815i
$482$	−1.52885e12			−1.29019
$483$	5.98592e11			0.500459
$484$	4.57042e11	−	7.91620e11i	0.378575	−	0.655711i
$485$	−7.03983e11	+	1.21933e12i	−0.577729	+	1.00066i
$486$	−2.63787e12			−2.14482
$487$	−1.44418e12			−1.16343			−0.581716	−	0.813392i	$-0.697618\pi$
$487$	−1.44418e12			−1.16343			−0.581716	+	0.813392i	$0.697618\pi$
$488$	1.96759e11	−	3.40797e11i	0.157053	−	0.272024i
$489$	6.53016e11	+	1.13106e12i	0.516456	+	0.894529i
$490$	−1.01853e12	+	1.76415e12i	−0.798163	+	1.38246i
$491$	7.65057e11	+	1.32512e12i	0.594056	+	1.02893i	0.993679	+	0.112255i	$0.0358075\pi$
$491$	7.65057e11	+	1.32512e12i	0.594056	+	1.02893i	−0.399624	+	0.916679i	$0.630859\pi$
$492$	2.41697e12	+	4.18631e12i	1.85963	+	3.22098i
$493$	1.50383e12			1.14653
$494$	1.61985e12	−	2.20596e12i	1.22378	−	1.66658i
$495$	1.84409e12			1.38057
$496$	−2.18541e11	−	3.78525e11i	−0.162131	−	0.280819i
$497$	3.29729e11	+	5.71108e11i	0.242412	+	0.419869i
$498$	−9.00664e11	+	1.56000e12i	−0.656192	+	1.13656i
$499$	1.62680e8	+	2.81770e8i	0.000117458	+	0.000203443i	0.866084	−	0.499898i	$-0.166629\pi$
$499$	1.62680e8	+	2.81770e8i	0.000117458	+	0.000203443i	−0.865967	+	0.500102i	$0.833296\pi$
$500$	1.94600e12	−	3.37057e12i	1.39244	−	2.41178i
$501$	2.59141e12			1.83767
$502$	−2.53004e12			−1.77812
$503$	−2.60490e11	+	4.51183e11i	−0.181441	+	0.314265i	−0.942372	−	0.334568i	$-0.891410\pi$
$503$	−2.60490e11	+	4.51183e11i	−0.181441	+	0.314265i	0.760930	+	0.648834i	$0.224743\pi$
$504$	−2.32730e11	+	4.03100e11i	−0.160663	+	0.278276i
$505$	1.08397e12			0.741660
$506$	−7.45980e11			−0.505883
$507$	−9.71196e11	+	1.68216e12i	−0.652786	+	1.13066i
$508$	−1.26214e12	−	2.18609e12i	−0.840856	−	1.45640i
$509$	3.35370e11	−	5.80877e11i	0.221459	−	0.383579i	−0.733792	−	0.679374i	$-0.762251\pi$
$509$	3.35370e11	−	5.80877e11i	0.221459	−	0.383579i	0.955251	+	0.295796i	$0.0955847\pi$
$510$	−3.58699e12	−	6.21284e12i	−2.34782	−	4.06654i
$511$	6.19119e10	+	1.07235e11i	0.0401680	+	0.0695730i
$512$	1.82493e12			1.17363
$513$	2.86039e11	−	3.89537e11i	0.182346	−	0.248325i
$514$	3.19671e12			2.02008
$515$	−7.91341e11	−	1.37064e12i	−0.495714	−	0.858601i
$516$	5.14027e11	+	8.90321e11i	0.319199	+	0.552870i
$517$	−2.65903e10	+	4.60557e10i	−0.0163687	+	0.0283515i
$518$	7.05473e10	+	1.22192e11i	0.0430523	+	0.0745688i
$519$	−2.46010e11	+	4.26102e11i	−0.148833	+	0.257786i
$520$	−1.70371e12			−1.02184
$521$	2.52718e12			1.50268			0.751339	−	0.659917i	$-0.229408\pi$
$521$	2.52718e12			1.50268			0.751339	+	0.659917i	$0.229408\pi$
$522$	1.51628e12	−	2.62627e12i	0.893843	−	1.54818i
$523$	5.33270e11	−	9.23651e11i	0.311666	−	0.539822i	−0.667057	−	0.745007i	$-0.732446\pi$
$523$	5.33270e11	−	9.23651e11i	0.311666	−	0.539822i	0.978723	+	0.205185i	$0.0657796\pi$
$524$	−5.28414e11			−0.306185
$525$	3.67170e12			2.10936
$526$	1.33209e12	−	2.30724e12i	0.758746	−	1.31419i
$527$	−5.17059e11	−	8.95572e11i	−0.292006	−	0.505770i
$528$	−5.48512e11	+	9.50051e11i	−0.307138	+	0.531978i
$529$	6.51357e11	+	1.12818e12i	0.361633	+	0.626367i
$530$	2.70887e12	+	4.69191e12i	1.49124	+	2.58290i
$531$	−3.07471e12			−1.67834
$532$	6.06786e11	+	1.38164e12i	0.328423	+	0.747814i
$533$	−5.01231e12			−2.69008
$534$	2.20272e12	+	3.81522e12i	1.17226	+	2.03041i
$535$	−1.49649e12	−	2.59199e12i	−0.789734	−	1.36786i
$536$	−2.85169e11	+	4.93927e11i	−0.149231	+	0.258476i
$537$	−1.18769e11	−	2.05713e11i	−0.0616336	−	0.106752i
$538$	−1.20505e12	+	2.08720e12i	−0.620130	+	1.07410i
$539$	7.36998e11			0.376112
$540$	−1.39275e12			−0.704855
$541$	−8.41570e11	+	1.45764e12i	−0.422379	+	0.731582i	−0.996172	−	0.0874186i	$-0.972138\pi$
$541$	−8.41570e11	+	1.45764e12i	−0.422379	+	0.731582i	0.573793	+	0.819001i	$0.305472\pi$
$542$	5.94505e11	−	1.02971e12i	0.295910	−	0.512530i
$543$	−2.80270e12			−1.38349
$544$	3.32600e12			1.62827
$545$	3.37661e11	−	5.84846e11i	0.163944	−	0.283960i
$546$	−2.04245e12	−	3.53762e12i	−0.983521	−	1.70351i
$547$	−1.30590e12	+	2.26189e12i	−0.623690	+	1.08026i	0.365103	+	0.930967i	$0.381034\pi$
$547$	−1.30590e12	+	2.26189e12i	−0.623690	+	1.08026i	−0.988793	+	0.149295i	$0.952300\pi$
$548$	2.00471e11	+	3.47226e11i	0.0949595	+	0.164475i
$549$	9.71077e11	+	1.68196e12i	0.456224	+	0.790203i
$550$	−4.57577e12			−2.13222
$551$	−8.53958e11	−	1.94445e12i	−0.394688	−	0.898700i
$552$	7.08597e11			0.324843
$553$	−1.28334e12	−	2.22281e12i	−0.583550	−	1.01074i
$554$	3.05924e11	+	5.29875e11i	0.137981	+	0.238990i
$555$	−2.65492e11	+	4.59845e11i	−0.118777	+	0.205728i
$556$	−9.76255e10	−	1.69092e11i	−0.0433238	−	0.0750390i
$557$	2.61712e11	−	4.53298e11i	0.115206	−	0.199542i	−0.802656	−	0.596442i	$-0.796581\pi$
$557$	2.61712e11	−	4.53298e11i	0.115206	−	0.199542i	0.917862	+	0.396900i	$0.129914\pi$
$558$	−2.08536e12			−0.910598
$559$	−1.06599e12			−0.461742
$560$	−8.66777e11	+	1.50130e12i	−0.372444	+	0.645093i
$561$	−1.29775e12	+	2.24778e12i	−0.553171	+	0.958121i
$562$	2.08853e12			0.883135
$563$	2.15892e12			0.905625			0.452813	−	0.891606i	$-0.350421\pi$
$563$	2.15892e12			0.905625			0.452813	+	0.891606i	$0.350421\pi$
$564$	1.16928e11	−	2.02526e11i	0.0486591	−	0.0842800i
$565$	5.85950e11	+	1.01490e12i	0.241904	+	0.418990i
$566$	3.08229e12	−	5.33868e12i	1.26241	−	2.18655i
$567$	5.90672e11	+	1.02307e12i	0.240006	+	0.415703i
$568$	3.90324e11	+	6.76061e11i	0.157347	+	0.272533i
$569$	3.81657e11			0.152640			0.0763199	−	0.997083i	$-0.475683\pi$
$569$	3.81657e11			0.152640			0.0763199	+	0.997083i	$0.475683\pi$
$570$	−5.99632e12	+	8.16598e12i	−2.37929	+	3.24020i
$571$	4.13241e12			1.62683			0.813413	−	0.581687i	$-0.197607\pi$
$571$	4.13241e12			1.62683			0.813413	+	0.581687i	$0.197607\pi$
$572$	1.42677e12	+	2.47124e12i	0.557278	+	0.965234i
$573$	2.61986e11	+	4.53773e11i	0.101527	+	0.175850i
$574$	2.46517e12	−	4.26980e12i	0.947858	−	1.64174i
$575$	−1.52869e12	−	2.64776e12i	−0.583194	−	1.01012i
$576$	2.31921e12	−	4.01699e12i	0.877887	−	1.52055i
$577$	−3.52348e12			−1.32337			−0.661684	−	0.749783i	$-0.730158\pi$
$577$	−3.52348e12			−1.32337			−0.661684	+	0.749783i	$0.730158\pi$
$578$	1.47510e12			0.549727
$579$	−3.31069e12	+	5.73429e12i	−1.22424	+	2.12044i
$580$	−3.06013e12	+	5.30030e12i	−1.12283	+	1.94480i
$581$	1.02986e12			0.374959
$582$	−3.99617e12			−1.44375
$583$	9.80057e11	−	1.69751e12i	0.351352	−	0.608560i
$584$	7.32896e10	+	1.26941e11i	0.0260726	+	0.0451591i
$585$	4.20422e12	−	7.28192e12i	1.48417	−	2.57066i
$586$	2.59473e11	+	4.49421e11i	0.0908978	+	0.157440i
$587$	5.13063e11	+	8.88651e11i	0.178361	+	0.308930i	0.941319	−	0.337518i	$-0.109587\pi$
$587$	5.13063e11	+	8.88651e11i	0.178361	+	0.308930i	−0.762959	+	0.646447i	$0.776254\pi$
$588$	−3.24088e12			−1.11806
$589$	−8.64361e11	+	1.17711e12i	−0.295921	+	0.402995i
$590$	1.10703e13			3.76118
$591$	−3.26687e12	−	5.65839e12i	−1.10151	−	1.90787i
$592$	−8.63874e10	−	1.49627e11i	−0.0289070	−	0.0500683i
$593$	1.00369e12	−	1.73844e12i	0.333313	−	0.577315i	−0.649846	−	0.760066i	$-0.725167\pi$
$593$	1.00369e12	−	1.73844e12i	0.333313	−	0.577315i	0.983159	+	0.182751i	$0.0585001\pi$
$594$	4.49466e11	+	7.78498e11i	0.148135	+	0.256577i
$595$	−2.05076e12	+	3.55201e12i	−0.670791	+	1.16184i
$596$	−5.56362e12			−1.80613
$597$	−3.34322e11			−0.107716
$598$	−1.70071e12	+	2.94572e12i	−0.543846	+	0.941969i
$599$	2.95597e11	−	5.11989e11i	0.0938165	−	0.162495i	−0.815298	−	0.579042i	$-0.803427\pi$
$599$	2.95597e11	−	5.11989e11i	0.0938165	−	0.162495i	0.909114	+	0.416547i	$0.136760\pi$
$600$	4.34646e12			1.36916
$601$	2.13322e11			0.0666961			0.0333481	−	0.999444i	$-0.489383\pi$
$601$	2.13322e11			0.0666961			0.0333481	+	0.999444i	$0.489383\pi$
$602$	5.24278e11	−	9.08077e11i	0.162696	−	0.281798i
$603$	−1.40741e12	−	2.43770e12i	−0.433503	−	0.750850i
$604$	8.49667e10	−	1.47167e11i	0.0259766	−	0.0449928i
$605$	−1.75430e12	−	3.03853e12i	−0.532358	−	0.922071i
$606$	1.53829e12	+	2.66440e12i	0.463352	+	0.802550i
$607$	2.87264e12			0.858880			0.429440	−	0.903095i	$-0.358711\pi$
$607$	2.87264e12			0.858880			0.429440	+	0.903095i	$0.358711\pi$
$608$	−1.88869e12	−	4.30052e12i	−0.560525	−	1.27631i
$609$	−3.16977e12			−0.933793
$610$	−3.49629e12	−	6.05575e12i	−1.02240	−	1.77086i
$611$	1.21243e11	+	2.09999e11i	0.0351942	+	0.0609582i
$612$	3.12143e12	−	5.40648e12i	0.899440	−	1.55788i
$613$	3.02952e12	+	5.24729e12i	0.866567	+	1.50094i	0.865483	+	0.500939i	$0.167012\pi$
$613$	3.02952e12	+	5.24729e12i	0.866567	+	1.50094i	0.00108464	+	0.999999i	$0.499655\pi$
$614$	−2.62112e12	+	4.53991e12i	−0.744267	+	1.28911i
$615$	1.85544e13			5.23009
$616$	−6.06315e11			−0.169662
$617$	−6.51234e11	+	1.12797e12i	−0.180906	+	0.313339i	−0.942189	−	0.335081i	$-0.891236\pi$
$617$	−6.51234e11	+	1.12797e12i	−0.180906	+	0.313339i	0.761283	+	0.648420i	$0.224570\pi$
$618$	2.24603e12	−	3.89024e12i	0.619394	−	1.07282i
$619$	−1.00261e11			−0.0274489			−0.0137245	−	0.999906i	$-0.504369\pi$
$619$	−1.00261e11			−0.0274489			−0.0137245	+	0.999906i	$0.504369\pi$
$620$	4.20864e12			1.14388
$621$	−3.00318e11	+	5.20166e11i	−0.0810344	+	0.140356i
$622$	−1.21907e11	−	2.11150e11i	−0.0326568	−	0.0565632i
$623$	1.25934e12	−	2.18124e12i	0.334925	−	0.580106i
$624$	2.50104e12	+	4.33192e12i	0.660373	+	1.14380i
$625$	−3.24041e12	−	5.61256e12i	−0.849455	−	1.47130i
$626$	−3.50328e12			−0.911780
$627$	3.64331e12	+	4.01583e11i	0.941440	+	0.103770i
$628$	−2.70379e11			−0.0693672
$629$	−2.04389e11	−	3.54011e11i	−0.0520629	−	0.0901756i
$630$	4.13547e12	+	7.16284e12i	1.04590	+	1.81156i
$631$	3.03375e11	−	5.25461e11i	0.0761812	−	0.131950i	−0.825418	−	0.564522i	$-0.809061\pi$
$631$	3.03375e11	−	5.25461e11i	0.0761812	−	0.131950i	0.901599	+	0.432572i	$0.142394\pi$
$632$	−1.51918e12	−	2.63130e12i	−0.378776	−	0.656059i
$633$	−4.37363e12	+	7.57535e12i	−1.08274	+	1.87537i
$634$	−9.28910e11			−0.228335
$635$	−9.68914e12			−2.36485
$636$	−4.30971e12	+	7.46464e12i	−1.04446	+	1.80906i
$637$	1.68024e12	−	2.91026e12i	0.404337	−	0.700332i
$638$	3.95025e12			0.943912
$639$	−3.85278e12			−0.914156
$640$	−3.04405e12	+	5.27244e12i	−0.717202	+	1.24223i
$641$	2.51949e12	+	4.36389e12i	0.589457	+	1.02097i	0.994304	+	0.106585i	$0.0339915\pi$
$641$	2.51949e12	+	4.36389e12i	0.589457	+	1.02097i	−0.404847	+	0.914385i	$0.632675\pi$
$642$	4.24742e12	−	7.35674e12i	0.986773	−	1.70914i
$643$	−1.83883e12	−	3.18495e12i	−0.424221	−	0.734772i	0.572126	−	0.820165i	$-0.306119\pi$
$643$	−1.83883e12	−	3.18495e12i	−0.424221	−	0.734772i	−0.996347	+	0.0853932i	$0.972785\pi$
$644$	−9.37731e11	−	1.62420e12i	−0.214828	−	0.372094i
$645$	3.94605e12			0.897726
$646$	−3.13620e12	−	7.14108e12i	−0.708529	−	1.61331i
$647$	1.29323e11			0.0290139			0.0145070	−	0.999895i	$-0.495382\pi$
$647$	1.29323e11			0.0290139			0.0145070	+	0.999895i	$0.495382\pi$
$648$	6.99221e11	+	1.21109e12i	0.155785	+	0.269828i
$649$	−2.00258e12	−	3.46857e12i	−0.443087	−	0.767450i
$650$	−1.04320e13	+	1.80688e13i	−2.29223	+	3.97025i
$651$	1.08986e12	+	1.88769e12i	0.237824	+	0.411924i
$652$	2.04598e12	−	3.54374e12i	0.443391	−	0.767975i
$653$	−5.47148e12			−1.17759			−0.588796	−	0.808281i	$-0.700398\pi$
$653$	−5.47148e12			−1.17759			−0.588796	+	0.808281i	$0.700398\pi$
$654$	1.91674e12			0.409697
$655$	−1.01413e12	+	1.75652e12i	−0.215281	+	0.372878i
$656$	−3.01868e12	+	5.22850e12i	−0.636428	+	1.10233i
$657$	−7.23420e11			−0.151477
$658$	−2.38521e11			−0.0496032
$659$	2.86012e12	−	4.95387e12i	0.590744	−	1.02320i	−0.403388	−	0.915029i	$-0.632168\pi$
$659$	2.86012e12	−	4.95387e12i	0.590744	−	1.02320i	0.994132	−	0.108170i	$-0.0344991\pi$
$660$	−5.28158e12	−	9.14797e12i	−1.08347	−	1.87662i
$661$	1.78065e12	−	3.08418e12i	0.362805	−	0.628397i	−0.625616	−	0.780131i	$-0.715152\pi$
$661$	1.78065e12	−	3.08418e12i	0.362805	−	0.628397i	0.988421	+	0.151734i	$0.0484858\pi$
$662$	−5.44039e11	−	9.42303e11i	−0.110095	−	0.190691i
$663$	5.91734e12	+	1.02491e13i	1.18937	+	2.06004i
$664$	1.21912e12			0.243382
$665$	5.75729e12	+	6.34595e11i	1.14162	+	0.125834i
$666$	−8.24322e11			−0.162354
$667$	1.31971e12	+	2.28581e12i	0.258174	+	0.447171i
$668$	−4.05961e12	−	7.03144e12i	−0.788842	−	1.36631i
$669$	1.29616e12	−	2.24501e12i	0.250173	−	0.433312i
$670$	5.06727e12	+	8.77676e12i	0.971487	+	1.68267i
$671$	−1.26494e12	+	2.19094e12i	−0.240890	+	0.417233i
$672$	−7.01056e12			−1.32615
$673$	1.33660e12			0.251151			0.125575	−	0.992084i	$-0.459922\pi$
$673$	1.33660e12			0.251151			0.125575	+	0.992084i	$0.459922\pi$
$674$	7.45756e12	−	1.29169e13i	1.39196	−	2.41095i
$675$	−1.84212e12	+	3.19065e12i	−0.341548	+	0.591578i
$676$	6.08575e12			1.12087
$677$	−1.01411e13			−1.85539			−0.927694	−	0.373343i	$-0.878212\pi$
$677$	−1.01411e13			−1.85539			−0.927694	+	0.373343i	$0.878212\pi$
$678$	−1.66308e12	+	2.88053e12i	−0.302259	+	0.523527i
$679$	1.14235e12	+	1.97860e12i	0.206245	+	0.357227i
$680$	−2.42763e12	+	4.20477e12i	−0.435403	+	0.754141i
$681$	−5.84057e12	−	1.01162e13i	−1.04062	−	1.80241i
$682$	−1.35821e12	−	2.35249e12i	−0.240401	−	0.416387i
$683$	8.19823e12			1.44154			0.720770	−	0.693174i	$-0.243788\pi$
$683$	8.19823e12			1.44154			0.720770	+	0.693174i	$0.243788\pi$
$684$	−8.76310e12	−	9.65910e11i	−1.53075	−	0.168727i
$685$	1.53896e12			0.267067
$686$	4.45413e12	+	7.71478e12i	0.767900	+	1.33004i
$687$	−5.31654e12	−	9.20852e12i	−0.910592	−	1.57719i
$688$	−6.41995e11	+	1.11197e12i	−0.109241	+	0.189210i
$689$	−4.46874e12	−	7.74009e12i	−0.755438	−	1.30846i
$690$	6.29566e12	−	1.09044e13i	1.05735	−	1.83139i
$691$	7.58904e12			1.26630			0.633148	−	0.774031i	$-0.281762\pi$
$691$	7.58904e12			1.26630			0.633148	+	0.774031i	$0.281762\pi$
$692$	1.54156e12			0.255554
$693$	1.49619e12	−	2.59148e12i	0.246427	−	0.426823i
$694$	−1.42858e12	+	2.47438e12i	−0.233770	+	0.404901i
$695$	−7.49446e11			−0.121845
$696$	−3.75229e12			−0.606115
$697$	−7.14205e12	+	1.23704e13i	−1.14624	+	1.98535i
$698$	−2.20369e12	−	3.81690e12i	−0.351399	−	0.608641i
$699$	−8.36824e12	+	1.44942e13i	−1.32583	+	2.29640i
$700$	−5.75195e12	−	9.96266e12i	−0.905469	−	1.56832i
$701$	2.58426e12	+	4.47607e12i	0.404208	+	0.700109i	0.994229	−	0.107279i	$-0.0342137\pi$
$701$	2.58426e12	+	4.47607e12i	0.404208	+	0.700109i	−0.590021	+	0.807388i	$0.700880\pi$
$702$	4.09884e12			0.637007
$703$	−3.41674e11	+	4.65302e11i	−0.0527609	+	0.0718515i
$704$	6.04207e12			0.927063
$705$	−4.48815e11	−	7.77370e11i	−0.0684252	−	0.118516i
$706$	−1.15090e12	−	1.99343e12i	−0.174349	−	0.301980i
$707$	8.79472e11	−	1.52329e12i	0.132384	−	0.229295i
$708$	8.80618e12	+	1.52527e13i	1.31716	+	2.28138i
$709$	6.09485e12	−	1.05566e13i	0.905848	−	1.56897i	0.0860720	−	0.996289i	$-0.472568\pi$
$709$	6.09485e12	−	1.05566e13i	0.905848	−	1.56897i	0.819775	−	0.572685i	$-0.194098\pi$
$710$	1.38716e13			2.04864
$711$	1.49954e13			2.20062
$712$	1.49077e12	−	2.58209e12i	0.217396	−	0.376541i
$713$	9.07510e11	−	1.57185e12i	0.131507	−	0.227777i
$714$	−1.16411e13			−1.67631
$715$	1.09530e13			1.56731
$716$	−3.72116e11	+	6.44525e11i	−0.0529140	+	0.0916497i
$717$	−1.31134e12	−	2.27131e12i	−0.185302	−	0.320952i
$718$	−7.71955e12	+	1.33707e13i	−1.08401	+	1.87755i
$719$	−3.59754e12	−	6.23112e12i	−0.502025	−	0.869533i	−0.999997	−	0.00234018i	$-0.999255\pi$
$719$	−3.59754e12	−	6.23112e12i	−0.502025	−	0.869533i	0.497972	−	0.867193i	$-0.334078\pi$
$720$	−5.06401e12	−	8.77112e12i	−0.702260	−	1.21635i
$721$	−2.56820e12			−0.353933
$722$	−7.45252e12	+	8.11022e12i	−1.02067	+	1.11075i
$723$	−9.33623e12			−1.27072
$724$	4.39060e12	+	7.60474e12i	0.593882	+	1.02863i
$725$	8.09498e12	+	1.40209e13i	1.08817	+	1.88476i
$726$	4.97915e12	−	8.62413e12i	0.665181	−	1.15213i
$727$	−1.34640e12	−	2.33204e12i	−0.178760	−	0.309621i	0.762696	−	0.646757i	$-0.223875\pi$
$727$	−1.34640e12	−	2.33204e12i	−0.178760	−	0.309621i	−0.941456	+	0.337136i	$0.890542\pi$
$728$	−1.38230e12	+	2.39421e12i	−0.182394	+	0.315916i
$729$	−1.03922e13			−1.36281
$730$	2.60462e12			0.339462
$731$	−1.51893e12	+	2.63087e12i	−0.196748	+	0.340777i
$732$	5.56246e12	−	9.63446e12i	0.716089	−	1.24030i
$733$	1.42163e12			0.181894			0.0909470	−	0.995856i	$-0.471011\pi$
$733$	1.42163e12			0.181894			0.0909470	+	0.995856i	$0.471011\pi$
$734$	−5.78048e12			−0.735075
$735$	−6.21986e12	+	1.07731e13i	−0.786118	+	1.36160i
$736$	2.91880e12	+	5.05550e12i	0.366652	+	0.635059i
$737$	1.83331e12	−	3.17539e12i	0.228893	−	0.396454i
$738$	1.44024e13	+	2.49456e13i	1.78723	+	3.09557i
$739$	−5.09723e12	−	8.82866e12i	−0.628687	−	1.08892i	−0.987816	−	0.155629i	$-0.950259\pi$
$739$	−5.09723e12	−	8.82866e12i	−0.628687	−	1.08892i	0.359129	−	0.933288i	$-0.383074\pi$
$740$	1.66364e12			0.203946
$741$	9.89194e12	−	1.34712e13i	1.20531	−	1.64143i
$742$	8.79133e12			1.06472
$743$	3.20811e12	+	5.55662e12i	0.386189	+	0.668899i	0.991933	−	0.126760i	$-0.0404578\pi$
$743$	3.20811e12	+	5.55662e12i	0.386189	+	0.668899i	−0.605744	+	0.795659i	$0.707125\pi$
$744$	1.29015e12	+	2.23460e12i	0.154369	+	0.267375i
$745$	−1.06776e13	+	1.84942e13i	−1.26991	+	2.19954i
$746$	−3.90157e12	−	6.75771e12i	−0.461227	−	0.798868i
$747$	−3.00839e12	+	5.21068e12i	−0.353501	+	0.612282i
$748$	8.13204e12			0.949822
$749$	−4.85667e12			−0.563859
$750$	2.12003e13	−	3.67199e13i	2.44661	−	4.23766i
$751$	3.92436e12	−	6.79720e12i	0.450183	−	0.779740i	−0.548214	−	0.836338i	$-0.684692\pi$
$751$	3.92436e12	−	6.79720e12i	0.450183	−	0.779740i	0.998397	+	0.0565979i	$0.0180253\pi$
$752$	2.92076e11			0.0333055
$753$	−1.54502e13			−1.75128
$754$	9.00593e12	−	1.55987e13i	1.01475	−	1.75759i
$755$	−3.26134e11	−	5.64880e11i	−0.0365287	−	0.0632696i
$756$	−1.13000e12	+	1.95721e12i	−0.125814	+	0.217917i
$757$	8.85821e12	+	1.53429e13i	0.980425	+	1.69815i	0.660726	+	0.750627i	$0.270249\pi$
$757$	8.85821e12	+	1.53429e13i	0.980425	+	1.69815i	0.319699	+	0.947519i	$0.396418\pi$
$758$	−9.01874e12	−	1.56209e13i	−0.992281	−	1.71868i
$759$	−4.55548e12			−0.498248
$760$	6.81532e12	+	7.51216e11i	0.741012	+	0.0816778i
$761$	−1.63568e11			−0.0176794			−0.00883972	−	0.999961i	$-0.502814\pi$
$761$	−1.63568e11			−0.0176794			−0.00883972	+	0.999961i	$0.502814\pi$
$762$	−1.37501e13	−	2.38159e13i	−1.47744	−	2.55900i
$763$	−5.47919e11	−	9.49024e11i	−0.0585270	−	0.101372i
$764$	8.20835e11	−	1.42173e12i	0.0871637	−	0.150972i
$765$	−1.19812e13	−	2.07521e13i	−1.26481	−	2.19071i
$766$	−2.12305e12	+	3.67723e12i	−0.222808	+	0.385915i
$767$	−1.82623e13			−1.90535
$768$	3.55061e12			0.368279
$769$	−5.63229e12	+	9.75541e12i	−0.580786	+	1.00595i	0.414600	+	0.910004i	$0.363921\pi$
$769$	−5.63229e12	+	9.75541e12i	−0.580786	+	1.00595i	−0.995386	+	0.0959473i	$0.969412\pi$
$770$	−5.38692e12	+	9.33042e12i	−0.552245	+	0.956517i
$771$	1.95213e13			1.98959
$772$	2.07456e13			2.10208
$773$	−9.18502e11	+	1.59089e12i	−0.0925278	+	0.160263i	−0.908574	−	0.417724i	$-0.862828\pi$
$773$	−9.18502e11	+	1.59089e12i	−0.0925278	+	0.160263i	0.816046	+	0.577986i	$0.196161\pi$
$774$	3.06301e12	+	5.30529e12i	0.306771	+	0.531343i
$775$	5.56657e12	−	9.64159e12i	0.554281	−	0.960043i
$776$	1.35228e12	+	2.34222e12i	0.133872	+	0.231872i
$777$	4.30811e11	+	7.46187e11i	0.0424026	+	0.0734434i
$778$	−1.18287e13			−1.15752
$779$	2.00506e13	+	2.21007e12i	1.95078	+	0.215024i
$780$	−4.81646e13			−4.65911
$781$	−2.50934e12	−	4.34631e12i	−0.241341	−	0.418014i
$782$	4.84670e12	+	8.39474e12i	0.463464	+	0.802744i
$783$	1.59030e12	−	2.75448e12i	0.151200	−	0.261886i
$784$	−2.02386e12	−	3.50542e12i	−0.191319	−	0.331374i
$785$	−5.18907e11	+	8.98773e11i	−0.0487726	+	0.0844766i
$786$	−5.75670e12			−0.537987
$787$	5.98053e11			0.0555716			0.0277858	−	0.999614i	$-0.491154\pi$
$787$	5.98053e11			0.0555716			0.0277858	+	0.999614i	$0.491154\pi$
$788$	−1.02355e13	+	1.77284e13i	−0.945674	+	1.63796i
$789$	8.13465e12	−	1.40896e13i	0.747296	−	1.29435i
$790$	−5.39897e13			−4.93162
$791$	1.90163e12			0.172716
$792$	1.77115e12	−	3.06772e12i	0.159953	−	0.277046i
$793$	5.76772e12	+	9.98998e12i	0.517934	+	0.897088i
$794$	−9.24427e12	+	1.60115e13i	−0.825430	+	1.42969i
$795$	1.65423e13	+	2.86521e13i	1.46873	+	2.54392i
$796$	5.23736e11	+	9.07137e11i	0.0462385	+	0.0800874i
$797$	9.81580e12			0.861715			0.430857	−	0.902420i	$-0.358211\pi$
$797$	9.81580e12			0.861715			0.430857	+	0.902420i	$0.358211\pi$
$798$	6.61050e12	+	1.50520e13i	0.577060	+	1.31396i
$799$	6.91039e11			0.0599849
$800$	1.79036e13	+	3.10099e13i	1.54538	+	2.67668i
$801$	7.35749e12	+	1.27436e13i	0.631515	+	1.09382i
$802$	7.41099e12	−	1.28362e13i	0.632545	−	1.09560i
$803$	−4.71169e11	−	8.16089e11i	−0.0399905	−	0.0692656i
$804$	−8.06182e12	+	1.39635e13i	−0.680426	+	1.17853i
$805$	−7.19872e12			−0.604190
$806$	−1.23860e13			−1.03377
$807$	−7.35885e12	+	1.27459e13i	−0.610772	+	1.05789i
$808$	1.04109e12	−	1.80323e12i	0.0859289	−	0.148833i
$809$	1.46061e12			0.119886			0.0599429	−	0.998202i	$-0.480908\pi$
$809$	1.46061e12			0.119886			0.0599429	+	0.998202i	$0.480908\pi$
$810$	2.48494e13			2.02831
$811$	3.60443e11	−	6.24305e11i	0.0292579	−	0.0506761i	−0.851026	−	0.525124i	$-0.824019\pi$
$811$	3.60443e11	−	6.24305e11i	0.0292579	−	0.0506761i	0.880284	+	0.474448i	$0.157352\pi$
$812$	4.96564e12	+	8.60075e12i	0.400842	+	0.694279i
$813$	3.63047e12	−	6.28815e12i	0.291444	−	0.504796i
$814$	−5.36887e11	−	9.29916e11i	−0.0428621	−	0.0742393i
$815$	−7.85322e12	−	1.36022e13i	−0.623503	−	1.07994i
$816$	1.42549e13			1.12554
$817$	4.26425e12	+	4.70025e11i	0.334844	+	0.0369081i
$818$	1.22132e13			0.953759
$819$	−6.82215e12	−	1.18163e13i	−0.529839	−	0.917707i
$820$	−2.90666e13	−	5.03449e13i	−2.24508	−	3.88860i
$821$	4.79042e12	−	8.29725e12i	0.367984	−	0.637367i	−0.621266	−	0.783600i	$-0.713381\pi$
$821$	4.79042e12	−	8.29725e12i	0.367984	−	0.637367i	0.989250	+	0.146232i	$0.0467147\pi$
$822$	2.18399e12	+	3.78278e12i	0.166850	+	0.288993i
$823$	−2.50837e12	+	4.34462e12i	−0.190586	+	0.330105i	−0.945445	−	0.325782i	$-0.894372\pi$
$823$	−2.50837e12	+	4.34462e12i	−0.190586	+	0.330105i	0.754858	+	0.655888i	$0.227706\pi$
$824$	−3.04017e12			−0.229734
$825$	−2.79428e13			−2.10004
$826$	8.98181e12	−	1.55569e13i	0.671357	−	1.16282i
$827$	−4.67498e11	+	8.09729e11i	−0.0347540	+	0.0601957i	−0.882879	−	0.469600i	$-0.844398\pi$
$827$	−4.67498e11	+	8.09729e11i	−0.0347540	+	0.0601957i	0.848125	+	0.529796i	$0.177731\pi$
$828$	1.09571e13			0.810137
$829$	−1.49880e13			−1.10217			−0.551085	−	0.834449i	$-0.685786\pi$
$829$	−1.49880e13			−1.10217			−0.551085	+	0.834449i	$0.685786\pi$
$830$	1.08315e13	−	1.87606e13i	0.792201	−	1.37213i
$831$	1.86818e12	+	3.23579e12i	0.135899	+	0.235383i
$832$	1.37750e13	−	2.38589e13i	0.996633	−	1.72622i
$833$	−4.78835e12	−	8.29367e12i	−0.344575	−	0.596821i
$834$	−1.06356e12	−	1.84214e12i	−0.0761228	−	0.131849i
$835$	−3.11646e13			−2.21856
$836$	−4.61783e12	−	1.05147e13i	−0.326971	−	0.744509i
$837$	−2.18716e12			−0.154034
$838$	5.28143e12	+	9.14770e12i	0.369959	+	0.640787i
$839$	7.93540e12	+	1.37445e13i	0.552892	+	0.957636i	0.998064	+	0.0621917i	$0.0198090\pi$
$839$	7.93540e12	+	1.37445e13i	0.552892	+	0.957636i	−0.445173	+	0.895445i	$0.646858\pi$
$840$	5.11696e12	−	8.86284e12i	0.354614	−	0.614209i
$841$	2.65191e11	+	4.59325e11i	0.0182800	+	0.0316620i
$842$	3.50289e12	−	6.06719e12i	0.240172	−	0.415990i
$843$	1.27540e13			0.869808
$844$	2.74062e13			1.85912
$845$	1.16797e13	−	2.02298e13i	0.788090	−	1.36501i
$846$	6.96760e11	−	1.20682e12i	0.0467645	−	0.0809985i
$847$	−5.69336e12			−0.380096
$848$	−1.07653e13			−0.714897
$849$	1.88226e13	−	3.26017e13i	1.24336	−	2.15355i
$850$	2.97292e13	+	5.14925e13i	1.95343	+	3.38344i
$851$	3.58730e11	−	6.21339e11i	0.0234469	−	0.0406112i
$852$	1.10346e13	+	1.91125e13i	0.717429	+	1.24262i
$853$	1.81756e12	+	3.14810e12i	0.117549	+	0.203600i	0.918796	−	0.394733i	$-0.129163\pi$
$853$	1.81756e12	+	3.14810e12i	0.117549	+	0.203600i	−0.801247	+	0.598334i	$0.795830\pi$
$854$	−1.13468e13			−0.729983
$855$	−2.00288e13	+	2.72759e13i	−1.28176	+	1.74555i
$856$	−5.74919e12			−0.365995
$857$	1.16909e13	+	2.02492e13i	0.740345	+	1.28231i	0.952338	+	0.305044i	$0.0986711\pi$
$857$	1.16909e13	+	2.02492e13i	0.740345	+	1.28231i	−0.211994	+	0.977271i	$0.567996\pi$
$858$	1.55437e13	+	2.69224e13i	0.979175	+	1.69598i
$859$	1.34459e13	−	2.32889e13i	0.842595	−	1.45942i	−0.0450978	−	0.998983i	$-0.514360\pi$
$859$	1.34459e13	−	2.32889e13i	0.842595	−	1.45942i	0.887693	−	0.460435i	$-0.152307\pi$
$860$	−6.18173e12	−	1.07071e13i	−0.385360	−	0.667463i
$861$	1.50540e13	−	2.60744e13i	0.933553	−	1.61696i
$862$	−2.85676e13			−1.76234
$863$	2.63772e13			1.61875			0.809375	−	0.587293i	$-0.199806\pi$
$863$	2.63772e13			1.61875			0.809375	+	0.587293i	$0.199806\pi$
$864$	3.51725e12	−	6.09206e12i	0.214729	−	0.371922i
$865$	2.95853e12	−	5.12433e12i	0.179682	−	0.311218i
$866$	−5.26147e12			−0.317890
$867$	9.00800e12			0.541430
$868$	3.41466e12	−	5.91437e12i	0.204178	−	0.353647i
$869$	9.76661e12	+	1.69163e13i	0.580971	+	1.00627i
$870$	−3.33379e13	+	5.77430e13i	−1.97289	+	3.41714i
$871$	−8.35931e12	−	1.44787e13i	−0.492140	−	0.852412i
$872$	−6.48611e11	−	1.12343e12i	−0.0379892	−	0.0657993i
$873$	−1.33480e13			−0.777769
$874$	8.10217e12	−	1.10338e13i	0.469678	−	0.639622i
$875$	−2.42413e13			−1.39804
$876$	2.07192e12	+	3.58868e12i	0.118879	+	0.205905i
$877$	3.04305e12	+	5.27071e12i	0.173704	+	0.300865i	0.939712	−	0.341967i	$-0.111093\pi$
$877$	3.04305e12	+	5.27071e12i	0.173704	+	0.300865i	−0.766008	+	0.642831i	$0.777760\pi$
$878$	5.03407e12	−	8.71927e12i	0.285887	−	0.495170i
$879$	1.58453e12	+	2.74448e12i	0.0895260	+	0.155064i
$880$	6.59645e12	−	1.14254e13i	0.370799	−	0.642242i
$881$	−2.57026e13			−1.43743			−0.718713	−	0.695307i	$-0.755269\pi$
$881$	−2.57026e13			−1.43743			−0.718713	+	0.695307i	$0.755269\pi$
$882$	−1.93120e13			−1.07453
$883$	6.04744e12	−	1.04745e13i	0.334771	−	0.579841i	−0.648669	−	0.761070i	$-0.724674\pi$
$883$	6.04744e12	−	1.04745e13i	0.334771	−	0.579841i	0.983441	+	0.181229i	$0.0580076\pi$
$884$	1.85397e13	−	3.21118e13i	1.02110	−	1.76860i
$885$	6.76028e13			3.70442
$886$	−4.18164e13			−2.27979
$887$	−1.11657e13	+	1.93396e13i	−0.605661	+	1.04904i	0.386286	+	0.922379i	$0.373758\pi$
$887$	−1.11657e13	+	1.93396e13i	−0.605661	+	1.04904i	−0.991947	+	0.126656i	$0.959575\pi$
$888$	5.09982e11	+	8.83315e11i	0.0275231	+	0.0476713i
$889$	−7.86124e12	+	1.36161e13i	−0.422117	+	0.731128i
$890$	−2.64901e13	−	4.58822e13i	−1.41523	−	2.45126i
$891$	−4.49520e12	−	7.78591e12i	−0.238946	−	0.413866i
$892$	−8.12203e12			−0.429559
$893$	−3.92411e11	−	8.93514e11i	−0.0206495	−	0.0470186i
$894$	−6.06117e13			−3.17349
$895$	1.42832e12	+	2.47392e12i	0.0744084	+	0.128879i
$896$	4.93955e12	+	8.55555e12i	0.256036	+	0.443468i
$897$	−1.03857e13	+	1.79886e13i	−0.535639	+	0.927753i
$898$	2.36284e13	+	4.09255e13i	1.21252	+	2.10015i
$899$	−4.80561e12	+	8.32356e12i	−0.245375	+	0.425002i
$900$	6.72096e13			3.41460
$901$	−2.54701e13			−1.28757
$902$	−1.87607e13	+	3.24945e13i	−0.943670	+	1.63448i
$903$	3.20161e12	−	5.54535e12i	0.160241	−	0.277546i
$904$	2.25110e12			0.112108
$905$	3.37055e13			1.67025
$906$	9.25652e11	−	1.60328e12i	0.0456426	−	0.0790554i
$907$	−1.58198e13	−	2.74007e13i	−0.776190	−	1.34440i	−0.934123	−	0.356950i	$-0.883817\pi$
$907$	−1.58198e13	−	2.74007e13i	−0.776190	−	1.34440i	0.157934	−	0.987450i	$-0.449517\pi$
$908$	−1.82992e13	+	3.16952e13i	−0.893400	+	1.54741i
$909$	5.13817e12	+	8.89958e12i	0.249615	+	0.432346i
$910$	2.45626e13	+	4.25437e13i	1.18738	+	2.05660i
$911$	2.77199e13			1.33340			0.666698	−	0.745328i	$-0.267707\pi$
$911$	2.77199e13			1.33340			0.666698	+	0.745328i	$0.267707\pi$
$912$	−8.09476e12	−	1.84317e13i	−0.387460	−	0.882242i
$913$	−7.83754e12			−0.373303
$914$	−2.41591e13	−	4.18448e13i	−1.14505	−	1.98328i
$915$	−2.13508e13	−	3.69806e13i	−1.00698	−	1.74413i
$916$	−1.66574e13	+	2.88514e13i	−0.781766	+	1.35406i
$917$	1.64561e12	+	2.85028e12i	0.0768538	+	0.133115i
$918$	5.84045e12	−	1.01160e13i	0.271428	−	0.470127i
$919$	1.66068e13			0.768008			0.384004	−	0.923331i	$-0.374545\pi$
$919$	1.66068e13			0.768008			0.384004	+	0.923331i	$0.374545\pi$
$920$	−8.52164e12			−0.392173
$921$	−1.60064e13	+	2.77239e13i	−0.733035	+	1.26965i
$922$	−1.69737e12	+	2.93994e12i	−0.0773549	+	0.133983i
$923$	−2.28836e13			−1.03781
$924$	−1.71408e13			−0.773582
$925$	2.20041e12	−	3.81123e12i	0.0988250	−	0.171170i
$926$	−1.67740e13	−	2.90533e13i	−0.749697	−	1.29851i
$927$	7.50215e12	−	1.29941e13i	0.333678	−	0.577947i
$928$	−1.54561e13	−	2.67708e13i	−0.684124	−	1.18494i
$929$	3.10249e12	+	5.37367e12i	0.136659	+	0.236701i	0.926230	−	0.376959i	$-0.123030\pi$
$929$	3.10249e12	+	5.37367e12i	0.136659	+	0.236701i	−0.789571	+	0.613660i	$0.789697\pi$
$930$	4.58501e13			2.00987
$931$	−8.00462e12	+	1.09010e13i	−0.349194	+	0.475544i
$932$	5.24374e13			2.27651
$933$	−7.44452e11	−	1.28943e12i	−0.0321639	−	0.0557096i
$934$	3.11947e13	+	5.40307e13i	1.34128	+	2.32316i
$935$	1.56069e13	−	2.70319e13i	0.667828	−	1.15671i
$936$	−8.07587e12	−	1.39878e13i	−0.343912	−	0.595674i
$937$	4.48304e12	−	7.76486e12i	0.189996	−	0.329083i	−0.755253	−	0.655434i	$-0.772486\pi$
$937$	4.48304e12	−	7.76486e12i	0.189996	−	0.329083i	0.945249	+	0.326351i	$0.105819\pi$
$938$	1.64452e13			0.693628
$939$	−2.13935e13			−0.898020
$940$	−1.40619e12	+	2.43559e12i	−0.0587447	+	0.101749i
$941$	−1.76891e13	+	3.06385e13i	−0.735450	+	1.27384i	0.219076	+	0.975708i	$0.429696\pi$
$941$	−1.76891e13	+	3.06385e13i	−0.735450	+	1.27384i	−0.954526	+	0.298128i	$0.903638\pi$
$942$	−2.94558e12			−0.121883
$943$	−2.50706e13			−1.03243
$944$	−1.09985e13	+	1.90500e13i	−0.450775	+	0.780765i
$945$	4.33735e12	+	7.51252e12i	0.176922	+	0.306438i
$946$	−3.98993e12	+	6.91075e12i	−0.161977	+	0.280553i
$947$	−2.09844e13	−	3.63460e13i	−0.847854	−	1.46853i	−0.883119	−	0.469148i	$-0.844561\pi$
$947$	−2.09844e13	−	3.63460e13i	−0.847854	−	1.46853i	0.0352652	−	0.999378i	$-0.488772\pi$
$948$	−4.29478e13	−	7.43878e13i	−1.72704	−	2.99133i
$949$	−4.29676e12			−0.171966
$950$	4.96979e13	−	6.76802e13i	1.97962	−	2.69591i
$951$	−5.67258e12			−0.224889
$952$	3.93929e12	+	6.82305e12i	0.155436	+	0.269223i
$953$	−1.32822e13	−	2.30054e13i	−0.521617	−	0.903467i	−0.999684	−	0.0251435i	$-0.991996\pi$
$953$	−1.32822e13	−	2.30054e13i	−0.521617	−	0.903467i	0.478067	−	0.878323i	$-0.341338\pi$
$954$	−2.56810e13	+	4.44808e13i	−1.00379	+	1.73862i
$955$	−3.15067e12	−	5.45712e12i	−0.122571	−	0.212299i
$956$	−4.10859e12	+	7.11629e12i	−0.159086	+	0.275545i
$957$	2.41230e13			0.929667
$958$	6.82368e13			2.61742
$959$	1.24863e12	−	2.16269e12i	0.0476705	−	0.0825678i
$960$	−5.09918e13	+	8.83203e13i	−1.93767	+	3.35614i
$961$	−1.98304e13			−0.750026
$962$	−4.89607e12			−0.184314
$963$	1.41872e13	−	2.45729e13i	0.531590	−	0.920742i
$964$	1.46258e13	+	2.53326e13i	0.545472	+	0.944785i
$965$	3.98147e13	−	6.89611e13i	1.47799	−	2.55995i
$966$	−1.02159e13	−	1.76945e13i	−0.377468	−	0.653793i
$967$	7.48673e12	+	1.29674e13i	0.275343	+	0.476907i	0.970221	−	0.242219i	$-0.0778754\pi$
$967$	7.48673e12	+	1.29674e13i	0.275343	+	0.476907i	−0.694879	+	0.719127i	$0.744542\pi$
$968$	−6.73964e12			−0.246716
$969$	−1.91518e13	−	4.36084e13i	−0.697836	−	1.58896i
$970$	4.80583e13			1.74299
$971$	2.01262e13	+	3.48595e13i	0.726565	+	1.25845i	0.958326	+	0.285675i	$0.0922178\pi$
$971$	2.01262e13	+	3.48595e13i	0.726565	+	1.25845i	−0.231761	+	0.972773i	$0.574449\pi$
$972$	2.52352e13	+	4.37087e13i	0.906794	+	1.57061i
$973$	−6.08059e11	+	1.05319e12i	−0.0217489	+	0.0376703i
$974$	2.46472e13	+	4.26902e13i	0.877510	+	1.51989i
$975$	−6.37051e13	+	1.10341e14i	−2.25763	+	3.91034i
$976$	1.38945e13			0.490138
$977$	−2.48678e12			−0.0873198			−0.0436599	−	0.999046i	$-0.513902\pi$
$977$	−2.48678e12			−0.0873198			−0.0436599	+	0.999046i	$0.513902\pi$
$978$	2.22895e13	−	3.86065e13i	0.779067	−	1.34938i
$979$	−9.58398e12	+	1.65999e13i	−0.333445	+	0.577543i
$980$	3.89751e13			1.34980
$981$	6.40226e12			0.220710
$982$	2.61138e13	−	4.52304e13i	0.896124	−	1.55213i
$983$	−8.68800e11	−	1.50481e12i	−0.0296776	−	0.0514031i	0.850805	−	0.525481i	$-0.176115\pi$
$983$	−8.68800e11	−	1.50481e12i	−0.0296776	−	0.0514031i	−0.880483	+	0.474078i	$0.842781\pi$
$984$	1.78206e13	−	3.08661e13i	0.605959	−	1.04955i
$985$	3.92877e13	+	6.80483e13i	1.32982	+	2.30332i
$986$	−2.56652e13	−	4.44534e13i	−0.864765	−	1.49782i
$987$	−1.45657e12			−0.0488546
$988$	−5.20485e13	−	5.73702e12i	−1.73781	−	0.191549i
$989$	−5.33187e12			−0.177213
$990$	−3.14722e13	−	5.45115e13i	−1.04128	−	1.80356i
$991$	−2.34011e13	−	4.05319e13i	−0.770735	−	1.33495i	−0.937160	−	0.348899i	$-0.886556\pi$
$991$	−2.34011e13	−	4.05319e13i	−0.770735	−	1.33495i	0.166425	−	0.986054i	$-0.446778\pi$
$992$	−1.06285e13	+	1.84092e13i	−0.348474	+	0.603575i
$993$	−3.32228e12	−	5.75436e12i	−0.108434	−	0.187813i
$994$	1.12547e13	−	1.94937e13i	0.365675	−	0.633367i
$995$	4.02058e12			0.130042
$996$	3.44649e13			1.10971
$997$	7.16612e12	−	1.24121e13i	0.229697	−	0.397847i	−0.728021	−	0.685555i	$-0.759560\pi$
$997$	7.16612e12	−	1.24121e13i	0.229697	−	0.397847i	0.957718	+	0.287707i	$0.0928931\pi$
$998$	5.55277e9	−	9.61768e9i	0.000177183	−	0.000306890i
$999$	−8.64565e11			−0.0274633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.10.c.a.7.2	✓	28
19.7	even	3		361.10.a.e.1.13		14
19.11	even	3	inner	19.10.c.a.11.2	yes	28
19.12	odd	6		361.10.a.f.1.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.c.a.7.2	✓	28	1.1	even	1	trivial
19.10.c.a.11.2	yes	28	19.11	even	3	inner
361.10.a.e.1.13		14	19.7	even	3
361.10.a.f.1.2		14	19.12	odd	6

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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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-17.0666 - 29.5602i) q^{2} +(-104.220 - 180.515i) q^{3} +(-326.535 + 565.575i) q^{4} +(1253.36 + 2170.89i) q^{5} +(-3557.37 + 6161.54i) q^{6} +4067.64 q^{7} +4815.16 q^{8} +(-11882.3 + 20580.7i) q^{9} +(42781.2 - 74099.2i) q^{10} -30956.0 q^{11} +136126. q^{12} +(-70574.7 + 122239. i) q^{13} +(-69420.6 - 120240. i) q^{14} +(261252. - 452501. i) q^{15} +(85007.7 + 147238. i) q^{16} +(201124. + 348358. i) q^{17} +811158. q^{18} +(336217. - 457871. i) q^{19} -1.63707e6 q^{20} +(-423931. - 734270. i) q^{21} +(528313. + 915065. i) q^{22} +(-353001. + 611416. i) q^{23} +(-501838. - 869208. i) q^{24} +(-2.16527e6 + 3.75036e6i) q^{25} +4.81787e6 q^{26} +850757. q^{27} +(-1.32823e6 + 2.30056e6i) q^{28} +(1.86928e6 - 3.23768e6i) q^{29} -1.78347e7 q^{30} -2.57084e6 q^{31} +(4.13426e6 - 7.16075e6i) q^{32} +(3.22625e6 + 5.58803e6i) q^{33} +(6.86500e6 - 1.18905e7i) q^{34} +(5.09823e6 + 8.83039e6i) q^{35} +(-7.75995e6 - 1.34406e7i) q^{36} -1.01623e6 q^{37} +(-1.92728e7 - 2.12434e6i) q^{38} +2.94213e7 q^{39} +(6.03514e6 + 1.04532e7i) q^{40} +(1.77553e7 + 3.07531e7i) q^{41} +(-1.44701e7 + 2.50629e7i) q^{42} +(3.77610e6 + 6.54040e6i) q^{43} +(1.01082e7 - 1.75080e7i) q^{44} -5.95711e7 q^{45} +2.40981e7 q^{46} +(858969. - 1.48778e6i) q^{47} +(1.77191e7 - 3.06903e7i) q^{48} -2.38079e7 q^{49} +1.47815e8 q^{50} +(4.19225e7 - 7.26119e7i) q^{51} +(-4.60902e7 - 7.98307e7i) q^{52} +(-3.16597e7 + 5.48361e7i) q^{53} +(-1.45195e7 - 2.51485e7i) q^{54} +(-3.87991e7 - 6.72021e7i) q^{55} +1.95863e7 q^{56} +(-1.17693e8 - 1.29727e7i) q^{57} -1.27608e8 q^{58} +(6.46912e7 + 1.12048e8i) q^{59} +(1.70616e8 + 2.95515e8i) q^{60} +(4.08625e7 - 7.07759e7i) q^{61} +(4.38754e7 + 7.59945e7i) q^{62} +(-4.83328e7 + 8.37148e7i) q^{63} -1.95182e8 q^{64} -3.53823e8 q^{65} +(1.10122e8 - 1.90737e8i) q^{66} +(-5.92231e7 + 1.02577e8i) q^{67} -2.62697e8 q^{68} +1.47160e8 q^{69} +(1.74018e8 - 3.01409e8i) q^{70} +(8.10616e7 + 1.40403e8i) q^{71} +(-5.72150e7 + 9.90993e7i) q^{72} +(1.52206e7 + 2.63628e7i) q^{73} +(1.73435e7 + 3.00399e7i) q^{74} +9.02662e8 q^{75} +(1.49174e8 + 3.39667e8i) q^{76} -1.25918e8 q^{77} +(-5.02120e8 - 8.69698e8i) q^{78} +(-3.15499e8 - 5.46461e8i) q^{79} +(-2.13091e8 + 3.69084e8i) q^{80} +(1.45212e8 + 2.51515e8i) q^{81} +(6.06044e8 - 1.04970e9i) q^{82} +2.53183e8 q^{83} +5.53713e8 q^{84} +(-5.04163e8 + 8.73237e8i) q^{85} +(1.28890e8 - 2.23244e8i) q^{86} -7.79266e8 q^{87} -1.49058e8 q^{88} +(3.09600e8 - 5.36243e8i) q^{89} +(1.01667e9 + 1.76093e9i) q^{90} +(-2.87073e8 + 4.97224e8i) q^{91} +(-2.30534e8 - 3.99297e8i) q^{92} +(2.67934e8 + 4.64075e8i) q^{93} -5.86386e7 q^{94} +(1.41539e9 + 1.56011e8i) q^{95} -1.72350e9 q^{96} +(2.80838e8 + 4.86425e8i) q^{97} +(4.06319e8 + 7.03765e8i) q^{98} +(3.67828e8 - 6.37096e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + 41180 q^{10} - 114810 q^{11} + 235458 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} - 279203 q^{16}+ \cdots - 736622698 q^{99}+O(q^{100}) \) 28 * q + 15 * q^2 - 74 * q^3 - 2987 * q^4 - 285 * q^5 - 535 * q^6 - 2676 * q^7 - 24270 * q^8 - 57928 * q^9 + 41180 * q^10 - 114810 * q^11 + 235458 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 - 279203 * q^16 + 466251 * q^17 + 734964 * q^18 + 387157 * q^19 - 3343620 * q^20 + 689090 * q^21 - 1689395 * q^22 - 3087747 * q^23 - 234183 * q^24 - 3260823 * q^25 + 9033144 * q^26 + 4216540 * q^27 - 703814 * q^28 + 7831383 * q^29 - 11859224 * q^30 - 9265632 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 - 13222428 * q^35 + 7355018 * q^36 + 27205020 * q^37 - 67677738 * q^38 - 20775702 * q^39 - 16500258 * q^40 + 20419440 * q^41 - 10220798 * q^42 + 27415427 * q^43 + 41775405 * q^44 - 85982588 * q^45 - 137234708 * q^46 - 90906681 * q^47 + 33057375 * q^48 + 229824892 * q^49 + 44406714 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 - 130507669 * q^54 - 157712310 * q^55 + 382459116 * q^56 - 162912873 * q^57 - 344026048 * q^58 + 255540 * q^59 + 287916794 * q^60 + 304035459 * q^61 + 693626280 * q^62 - 122148024 * q^63 - 908491514 * q^64 - 1424960190 * q^65 - 611099417 * q^66 + 165758480 * q^67 + 357518508 * q^68 + 271237278 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 - 602867050 * q^73 - 82104492 * q^74 + 1900274774 * q^75 - 1298297525 * q^76 - 491994756 * q^77 - 911449840 * q^78 + 78162339 * q^79 + 227607150 * q^80 + 1230916118 * q^81 + 360208019 * q^82 + 413839926 * q^83 - 467304924 * q^84 - 1440537237 * q^85 + 936824310 * q^86 - 678876318 * q^87 - 1646777694 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 - 677003592 * q^92 - 492493440 * q^93 - 848375184 * q^94 - 2034458607 * q^95 - 6041588930 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 - 736622698 * q^99

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