LMFDB - Embedded newform 13.14.c.a.9.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,14,Mod(3,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 14, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.3"); S:= CuspForms(chi, 14); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	13.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:	$13.9400207637$
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			9.6
Character	$\chi$	$=$	13.9
Dual form			13.14.c.a.3.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-16.9887 + 29.4253i) q^{2} +(797.844 - 1381.91i) q^{3} +(3518.77 + 6094.69i) q^{4} -28205.3 q^{5} +(27108.7 + 46953.6i) q^{6} +(177172. + 306871. i) q^{7} -517460. q^{8} +(-475948. - 824367. i) q^{9} +(479171. - 829948. i) q^{10} +(2.48521e6 - 4.30450e6i) q^{11} +1.12297e7 q^{12} +(1.11242e7 + 1.33839e7i) q^{13} -1.20397e7 q^{14} +(-2.25034e7 + 3.89770e7i) q^{15} +(-2.00348e7 + 3.47012e7i) q^{16} +(5.35538e7 + 9.27579e7i) q^{17} +3.23430e7 q^{18} +(1.61956e8 + 2.80516e8i) q^{19} +(-9.92478e7 - 1.71902e8i) q^{20} +5.65422e8 q^{21} +(8.44408e7 + 1.46256e8i) q^{22} +(2.62992e8 - 4.55516e8i) q^{23} +(-4.12852e8 + 7.15081e8i) q^{24} -4.25166e8 q^{25} +(-5.82809e8 + 9.99576e7i) q^{26} +1.02511e9 q^{27} +(-1.24685e9 + 2.15961e9i) q^{28} +(6.01457e8 - 1.04175e9i) q^{29} +(-7.64607e8 - 1.32434e9i) q^{30} +3.17736e9 q^{31} +(-2.80025e9 - 4.85017e9i) q^{32} +(-3.96561e9 - 6.86864e9i) q^{33} -3.63924e9 q^{34} +(-4.99718e9 - 8.65537e9i) q^{35} +(3.34950e9 - 5.80151e9i) q^{36} +(-9.24426e9 + 1.60115e10i) q^{37} -1.10057e10 q^{38} +(2.73706e10 - 4.69433e9i) q^{39} +1.45951e10 q^{40} +(-1.08755e10 + 1.88370e10i) q^{41} +(-9.60578e9 + 1.66377e10i) q^{42} +(-2.57930e10 - 4.46747e10i) q^{43} +3.49795e10 q^{44} +(1.34242e10 + 2.32515e10i) q^{45} +(8.93579e9 + 1.54772e10i) q^{46} +1.84645e10 q^{47} +(3.19692e10 + 5.53724e10i) q^{48} +(-1.43352e10 + 2.48294e10i) q^{49} +(7.22303e9 - 1.25106e10i) q^{50} +1.70910e11 q^{51} +(-4.24271e10 + 1.14893e11i) q^{52} -1.97464e11 q^{53} +(-1.74153e10 + 3.01642e10i) q^{54} +(-7.00959e10 + 1.21410e11i) q^{55} +(-9.16794e10 - 1.58793e11i) q^{56} +5.16862e11 q^{57} +(2.04360e10 + 3.53961e10i) q^{58} +(-7.27492e10 - 1.26005e11i) q^{59} -3.16737e11 q^{60} +(-3.18051e11 - 5.50881e11i) q^{61} +(-5.39791e10 + 9.34946e10i) q^{62} +(1.68649e11 - 2.92109e11i) q^{63} -1.37960e11 q^{64} +(-3.13760e11 - 3.77495e11i) q^{65} +2.69482e11 q^{66} +(3.30986e11 - 5.73285e11i) q^{67} +(-3.76887e11 + 6.52787e11i) q^{68} +(-4.19654e11 - 7.26861e11i) q^{69} +3.39582e11 q^{70} +(8.77967e11 + 1.52068e12i) q^{71} +(2.46284e11 + 4.26577e11i) q^{72} -1.33173e12 q^{73} +(-3.14096e11 - 5.44030e11i) q^{74} +(-3.39217e11 + 5.87540e11i) q^{75} +(-1.13977e12 + 1.97414e12i) q^{76} +1.76123e12 q^{77} +(-3.26859e11 + 8.85139e11i) q^{78} +1.34409e12 q^{79} +(5.65086e11 - 9.78758e11i) q^{80} +(1.57669e12 - 2.73092e12i) q^{81} +(-3.69523e11 - 6.40032e11i) q^{82} +2.49195e12 q^{83} +(1.98959e12 + 3.44607e12i) q^{84} +(-1.51050e12 - 2.61626e12i) q^{85} +1.75276e12 q^{86} +(-9.59738e11 - 1.66232e12i) q^{87} +(-1.28599e12 + 2.22741e12i) q^{88} +(-3.25403e12 + 5.63614e12i) q^{89} -9.12242e11 q^{90} +(-2.13623e12 + 5.78493e12i) q^{91} +3.70163e12 q^{92} +(2.53503e12 - 4.39081e12i) q^{93} +(-3.13687e11 + 5.43322e11i) q^{94} +(-4.56801e12 - 7.91203e12i) q^{95} -8.93664e12 q^{96} +(-3.39959e11 - 5.88827e11i) q^{97} +(-4.87074e11 - 8.43637e11i) q^{98} -4.73132e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 65 q^{2} + 728 q^{3} - 53249 q^{4} + 41860 q^{5} + 143910 q^{6} - 173992 q^{7} + 2616978 q^{8} - 5231838 q^{9} + 2769243 q^{10} + 10986144 q^{11} - 45205464 q^{12} + 25107706 q^{13} - 23731756 q^{14}+ \cdots + 33239809172544 q^{99}+O(q^{100}) $ 28 * q - 65 * q^2 + 728 * q^3 - 53249 * q^4 + 41860 * q^5 + 143910 * q^6 - 173992 * q^7 + 2616978 * q^8 - 5231838 * q^9 + 2769243 * q^10 + 10986144 * q^11 - 45205464 * q^12 + 25107706 * q^13 - 23731756 * q^14 - 75354448 * q^15 - 273433217 * q^16 + 255934950 * q^17 - 350685842 * q^18 - 266623552 * q^19 - 225433091 * q^20 - 2515875856 * q^21 + 77223114 * q^22 + 1914406544 * q^23 - 680727216 * q^24 + 5225878768 * q^25 - 9205789749 * q^26 + 3550452320 * q^27 - 3680076400 * q^28 + 6211296126 * q^29 + 5703660004 * q^30 + 6997674944 * q^31 + 2312486527 * q^32 + 5621901584 * q^33 - 23373723594 * q^34 + 23009265024 * q^35 + 23496114839 * q^36 + 19577630774 * q^37 + 51648723644 * q^38 + 31282255680 * q^39 - 111700587858 * q^40 - 6039692074 * q^41 + 143590583874 * q^42 + 16878499784 * q^43 - 489551846992 * q^44 - 148673926778 * q^45 + 177583142490 * q^46 + 369404914944 * q^47 + 92920518608 * q^48 - 195653684766 * q^49 - 753661423970 * q^50 + 617169279136 * q^51 - 727838751302 * q^52 - 287550769100 * q^53 + 365361720282 * q^54 + 855926433792 * q^55 + 192505368988 * q^56 - 1924513438848 * q^57 - 660641292207 * q^58 + 637655529992 * q^59 + 2555257062384 * q^60 + 1530666437030 * q^61 + 1907899186036 * q^62 - 832654573712 * q^63 + 632232280450 * q^64 - 2489693680994 * q^65 - 270853649100 * q^66 - 1120398677944 * q^67 + 4085795015901 * q^68 + 1473200404976 * q^69 - 9377684744688 * q^70 + 1506585643472 * q^71 + 3521118562923 * q^72 - 852513981436 * q^73 + 4665118313621 * q^74 + 2605103918408 * q^75 - 6106356745372 * q^76 + 2854115035024 * q^77 - 8622775525858 * q^78 - 7032676662784 * q^79 + 5983641421745 * q^80 + 2512348302642 * q^81 - 8600700659175 * q^82 + 2033940247872 * q^83 - 4374201207844 * q^84 + 2527554975426 * q^85 - 7547295057588 * q^86 - 1118899666832 * q^87 - 5943200108772 * q^88 + 5229645042596 * q^89 + 4220465391930 * q^90 + 18401936100704 * q^91 + 3830251788320 * q^92 - 1283055655752 * q^93 - 32271602536104 * q^94 + 8980600417472 * q^95 + 51692558969792 * q^96 + 3129146550452 * q^97 - 5503659823363 * q^98 + 33239809172544 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

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

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 $

$2$	−16.9887	+	29.4253i	−0.187700	+	0.325107i	−0.944483	−	0.328560i	$-0.893437\pi$
$2$	−16.9887	+	29.4253i	−0.187700	+	0.325107i	0.756783	+	0.653666i	$0.226770\pi$
$3$	797.844	−	1381.91i	0.631873	−	1.09444i	−0.355295	−	0.934754i	$-0.615620\pi$
$3$	797.844	−	1381.91i	0.631873	−	1.09444i	0.987168	−	0.159682i	$-0.0510469\pi$
$4$	3518.77	+	6094.69i	0.429537	+	0.743980i
$5$	−28205.3			−0.807282			−0.403641	−	0.914918i	$-0.632255\pi$
$5$	−28205.3			−0.807282			−0.403641	+	0.914918i	$0.632255\pi$
$6$	27108.7	+	46953.6i	0.237206	+	0.410852i
$7$	177172.	+	306871.i	0.569190	+	0.985867i	0.996646	+	0.0818304i	$0.0260766\pi$
$7$	177172.	+	306871.i	0.569190	+	0.985867i	−0.427456	+	0.904036i	$0.640590\pi$
$8$	−517460.			−0.697898
$9$	−475948.	−	824367.i	−0.298527	−	0.517064i
$10$	479171.	−	829948.i	0.151527	−	0.262453i
$11$	2.48521e6	−	4.30450e6i	0.422970	−	0.732606i	−0.573258	−	0.819375i	$-0.694321\pi$
$11$	2.48521e6	−	4.30450e6i	0.422970	−	0.732606i	0.996228	+	0.0867687i	$0.0276541\pi$
$12$	1.12297e7			1.08565
$13$	1.11242e7	+	1.33839e7i	0.639199	+	0.769041i
$13$	1.11242e7	+	1.33839e7i	0.639199	+	0.769041i
$14$	−1.20397e7			−0.427349
$15$	−2.25034e7	+	3.89770e7i	−0.510099	+	0.883518i
$16$	−2.00348e7	+	3.47012e7i	−0.298541	+	0.517089i
$17$	5.35538e7	+	9.27579e7i	0.538112	+	0.932037i	0.999006	+	0.0445817i	$0.0141955\pi$
$17$	5.35538e7	+	9.27579e7i	0.538112	+	0.932037i	−0.460894	+	0.887455i	$0.652471\pi$
$18$	3.23430e7			0.224135
$19$	1.61956e8	+	2.80516e8i	0.789766	+	1.36792i	0.926110	+	0.377254i	$0.123132\pi$
$19$	1.61956e8	+	2.80516e8i	0.789766	+	1.36792i	−0.136344	+	0.990662i	$0.543535\pi$
$20$	−9.92478e7	−	1.71902e8i	−0.346757	−	0.600601i
$21$	5.65422e8			1.43862
$22$	8.44408e7	+	1.46256e8i	0.158783	+	0.275021i
$23$	2.62992e8	−	4.55516e8i	0.370435	−	0.641612i	−0.619197	−	0.785235i	$-0.712542\pi$
$23$	2.62992e8	−	4.55516e8i	0.370435	−	0.641612i	0.989632	+	0.143623i	$0.0458753\pi$
$24$	−4.12852e8	+	7.15081e8i	−0.440983	+	0.763805i
$25$	−4.25166e8			−0.348296
$26$	−5.82809e8	+	9.99576e7i	−0.369998	+	0.0634584i
$27$	1.02511e9			0.509221
$28$	−1.24685e9	+	2.15961e9i	−0.488977	+	0.846933i
$29$	6.01457e8	−	1.04175e9i	0.187766	−	0.325221i	−0.756739	−	0.653717i	$-0.773209\pi$
$29$	6.01457e8	−	1.04175e9i	0.187766	−	0.325221i	0.944505	+	0.328496i	$0.106542\pi$
$30$	−7.64607e8	−	1.32434e9i	−0.191492	−	0.331673i
$31$	3.17736e9			0.643006			0.321503	−	0.946909i	$-0.395812\pi$
$31$	3.17736e9			0.643006			0.321503	+	0.946909i	$0.395812\pi$
$32$	−2.80025e9	−	4.85017e9i	−0.461022	−	0.798513i
$33$	−3.96561e9	−	6.86864e9i	−0.534527	−	0.925828i
$34$	−3.63924e9			−0.404015
$35$	−4.99718e9	−	8.65537e9i	−0.459497	−	0.795872i
$36$	3.34950e9	−	5.80151e9i	0.256457	−	0.444196i
$37$	−9.24426e9	+	1.60115e10i	−0.592326	+	1.02594i	0.401592	+	0.915819i	$0.368457\pi$
$37$	−9.24426e9	+	1.60115e10i	−0.592326	+	1.02594i	−0.993918	+	0.110120i	$0.964876\pi$
$38$	−1.10057e10			−0.592958
$39$	2.73706e10	−	4.69433e9i	1.24556	−	0.213626i
$40$	1.45951e10			0.563400
$41$	−1.08755e10	+	1.88370e10i	−0.357566	+	0.619322i	−0.987554	−	0.157283i	$-0.949726\pi$
$41$	−1.08755e10	+	1.88370e10i	−0.357566	+	0.619322i	0.629988	+	0.776605i	$0.283060\pi$
$42$	−9.60578e9	+	1.66377e10i	−0.270030	+	0.467706i
$43$	−2.57930e10	−	4.46747e10i	−0.622238	−	1.07775i	−0.989068	−	0.147459i	$-0.952890\pi$
$43$	−2.57930e10	−	4.46747e10i	−0.622238	−	1.07775i	0.366830	−	0.930288i	$-0.380443\pi$
$44$	3.49795e10			0.726726
$45$	1.34242e10	+	2.32515e10i	0.240995	+	0.417416i
$46$	8.93579e9	+	1.54772e10i	0.139062	+	0.240862i
$47$	1.84645e10			0.249862			0.124931	−	0.992165i	$-0.460129\pi$
$47$	1.84645e10			0.249862			0.124931	+	0.992165i	$0.460129\pi$
$48$	3.19692e10	+	5.53724e10i	0.377281	+	0.653469i
$49$	−1.43352e10	+	2.48294e10i	−0.147955	+	0.256266i
$50$	7.22303e9	−	1.25106e10i	0.0653754	−	0.113233i
$51$	1.70910e11			1.36007
$52$	−4.24271e10	+	1.14893e11i	−0.297592	+	0.805883i
$53$	−1.97464e11			−1.22376			−0.611878	−	0.790952i	$-0.709586\pi$
$53$	−1.97464e11			−1.22376			−0.611878	+	0.790952i	$0.709586\pi$
$54$	−1.74153e10	+	3.01642e10i	−0.0955811	+	0.165551i
$55$	−7.00959e10	+	1.21410e11i	−0.341456	+	0.591419i
$56$	−9.16794e10	−	1.58793e11i	−0.397237	−	0.688034i
$57$	5.16862e11			1.99613
$58$	2.04360e10	+	3.53961e10i	0.0704877	+	0.122088i
$59$	−7.27492e10	−	1.26005e11i	−0.224538	−	0.388912i	0.731643	−	0.681688i	$-0.238754\pi$
$59$	−7.27492e10	−	1.26005e11i	−0.224538	−	0.388912i	−0.956181	+	0.292777i	$0.905421\pi$
$60$	−3.16737e11			−0.876427
$61$	−3.18051e11	−	5.50881e11i	−0.790411	−	1.36903i	−0.925713	−	0.378227i	$-0.876534\pi$
$61$	−3.18051e11	−	5.50881e11i	−0.790411	−	1.36903i	0.135302	−	0.990804i	$-0.456800\pi$
$62$	−5.39791e10	+	9.34946e10i	−0.120692	+	0.209045i
$63$	1.68649e11	−	2.92109e11i	0.339837	−	0.588616i
$64$	−1.37960e11			−0.250947
$65$	−3.13760e11	−	3.77495e11i	−0.516013	−	0.620833i
$66$	2.69482e11			0.401324
$67$	3.30986e11	−	5.73285e11i	0.447017	−	0.774256i	−0.551173	−	0.834391i	$-0.685820\pi$
$67$	3.30986e11	−	5.73285e11i	0.447017	−	0.774256i	0.998190	+	0.0601349i	$0.0191531\pi$
$68$	−3.76887e11	+	6.52787e11i	−0.462278	+	0.800689i
$69$	−4.19654e11	−	7.26861e11i	−0.468136	−	0.810835i
$70$	3.39582e11			0.344991
$71$	8.77967e11	+	1.52068e12i	0.813390	+	1.40883i	0.910478	+	0.413557i	$0.135714\pi$
$71$	8.77967e11	+	1.52068e12i	0.813390	+	1.40883i	−0.0970885	+	0.995276i	$0.530953\pi$
$72$	2.46284e11	+	4.26577e11i	0.208341	+	0.360858i
$73$	−1.33173e12			−1.02995			−0.514975	−	0.857205i	$-0.672199\pi$
$73$	−1.33173e12			−1.02995			−0.514975	+	0.857205i	$0.672199\pi$
$74$	−3.14096e11	−	5.44030e11i	−0.222360	−	0.385138i
$75$	−3.39217e11	+	5.87540e11i	−0.220079	+	0.381188i
$76$	−1.13977e12	+	1.97414e12i	−0.678468	+	1.17514i
$77$	1.76123e12			0.963002
$78$	−3.26859e11	+	8.85139e11i	−0.164341	+	0.445037i
$79$	1.34409e12			0.622088			0.311044	−	0.950396i	$-0.399321\pi$
$79$	1.34409e12			0.622088			0.311044	+	0.950396i	$0.399321\pi$
$80$	5.65086e11	−	9.78758e11i	0.241007	−	0.417436i
$81$	1.57669e12	−	2.73092e12i	0.620290	−	1.07437i
$82$	−3.69523e11	−	6.40032e11i	−0.134230	−	0.232494i
$83$	2.49195e12			0.836628			0.418314	−	0.908302i	$-0.362621\pi$
$83$	2.49195e12			0.836628			0.418314	+	0.908302i	$0.362621\pi$
$84$	1.98959e12	+	3.44607e12i	0.617942	+	1.07031i
$85$	−1.51050e12	−	2.61626e12i	−0.434408	−	0.752416i
$86$	1.75276e12			0.467177
$87$	−9.59738e11	−	1.66232e12i	−0.237289	−	0.410997i
$88$	−1.28599e12	+	2.22741e12i	−0.295190	+	0.511284i
$89$	−3.25403e12	+	5.63614e12i	−0.694042	+	1.20212i	0.276460	+	0.961025i	$0.410839\pi$
$89$	−3.25403e12	+	5.63614e12i	−0.694042	+	1.20212i	−0.970502	+	0.241091i	$0.922495\pi$
$90$	−9.12242e11			−0.180940
$91$	−2.13623e12	+	5.78493e12i	−0.394346	+	1.06790i
$92$	3.70163e12			0.636462
$93$	2.53503e12	−	4.39081e12i	0.406298	−	0.703729i
$94$	−3.13687e11	+	5.43322e11i	−0.0468992	+	0.0812318i
$95$	−4.56801e12	−	7.91203e12i	−0.637564	−	1.10429i
$96$	−8.93664e12			−1.16523
$97$	−3.39959e11	−	5.88827e11i	−0.0414391	−	0.0717747i	0.844562	−	0.535458i	$-0.179861\pi$
$97$	−3.39959e11	−	5.88827e11i	−0.0414391	−	0.0717747i	−0.886001	+	0.463683i	$0.846528\pi$
$98$	−4.87074e11	−	8.43637e11i	−0.0555425	−	0.0962024i
$99$	−4.73132e12			−0.505072
$100$	−1.49606e12	−	2.59126e12i	−0.149606	−	0.259126i
$101$	8.84795e12	−	1.53251e13i	0.829380	−	1.43653i	−0.0691449	−	0.997607i	$-0.522027\pi$
$101$	8.84795e12	−	1.53251e13i	0.829380	−	1.43653i	0.898525	−	0.438922i	$-0.144640\pi$
$102$	−2.90354e12	+	5.02909e12i	−0.255286	+	0.442169i
$103$	2.04628e13			1.68859			0.844293	−	0.535882i	$-0.180021\pi$
$103$	2.04628e13			1.68859			0.844293	+	0.535882i	$0.180021\pi$
$104$	−5.75632e12	−	6.92562e12i	−0.446096	−	0.536712i
$105$	−1.59479e13			−1.16137
$106$	3.35466e12	−	5.81043e12i	0.229699	−	0.397851i
$107$	3.68001e12	−	6.37396e12i	0.237058	−	0.410596i	−0.722811	−	0.691046i	$-0.757150\pi$
$107$	3.68001e12	−	6.37396e12i	0.237058	−	0.410596i	0.959869	+	0.280450i	$0.0904837\pi$
$108$	3.60713e12	+	6.24773e12i	0.218730	+	0.378851i
$109$	−3.07635e12			−0.175697			−0.0878483	−	0.996134i	$-0.527999\pi$
$109$	−3.07635e12			−0.175697			−0.0878483	+	0.996134i	$0.527999\pi$
$110$	−2.38168e12	−	4.12518e12i	−0.128183	−	0.222019i
$111$	1.47510e13	+	2.55494e13i	0.748550	+	1.29653i
$112$	−1.41984e13			−0.679708
$113$	1.54922e12	+	2.68334e12i	0.0700010	+	0.121245i	0.898901	−	0.438151i	$-0.144366\pi$
$113$	1.54922e12	+	2.68334e12i	0.0700010	+	0.121245i	−0.828900	+	0.559396i	$0.811033\pi$
$114$	−8.78082e12	+	1.52088e13i	−0.374674	+	0.648954i
$115$	−7.41776e12	+	1.28479e13i	−0.299045	+	0.517962i
$116$	8.46556e12			0.322611
$117$	5.73868e12	−	1.55404e13i	0.206825	−	0.560086i
$118$	4.94366e12			0.168584
$119$	−1.89765e13	+	3.28682e13i	−0.612576	+	1.06101i
$120$	1.16446e13	−	2.01691e13i	0.355997	−	0.616606i
$121$	4.90886e12	+	8.50240e12i	0.142192	+	0.246284i
$122$	2.16131e13			0.593442
$123$	1.73540e13	+	3.00580e13i	0.451872	+	0.782666i
$124$	1.11804e13	+	1.93650e13i	0.276195	+	0.478384i
$125$	4.64222e13			1.08845
$126$	5.73027e12	+	9.92511e12i	0.127575	+	0.220967i
$127$	2.26452e13	−	3.92227e13i	0.478909	−	0.829494i	−0.520799	−	0.853680i	$-0.674366\pi$
$127$	2.26452e13	−	3.92227e13i	0.478909	−	0.829494i	0.999707	+	0.0241852i	$0.00769912\pi$
$128$	2.52834e13	−	4.37921e13i	0.508125	−	0.880097i
$129$	−8.23150e13			−1.57270
$130$	1.64383e13	−	2.81933e12i	0.298693	−	0.0512288i
$131$	−9.41327e13			−1.62734			−0.813668	−	0.581330i	$-0.802532\pi$
$131$	−9.41327e13			−1.62734			−0.813668	+	0.581330i	$0.802532\pi$
$132$	2.79081e13	−	4.83383e13i	0.459198	−	0.795355i
$133$	−5.73881e13	+	9.93991e13i	−0.899055	+	1.55721i
$134$	1.12461e13	+	1.94787e13i	0.167810	+	0.290656i
$135$	−2.89135e13			−0.411085
$136$	−2.77120e13	−	4.79985e13i	−0.375547	−	0.650467i
$137$	−1.21325e13	−	2.10141e13i	−0.156771	−	0.271535i	0.776931	−	0.629585i	$-0.216775\pi$
$137$	−1.21325e13	−	2.10141e13i	−0.156771	−	0.271535i	−0.933702	+	0.358050i	$0.883442\pi$
$138$	2.85175e13			0.351477
$139$	−3.73304e12	−	6.46582e12i	−0.0439002	−	0.0760374i	0.843240	−	0.537537i	$-0.180645\pi$
$139$	−3.73304e12	−	6.46582e12i	−0.0439002	−	0.0760374i	−0.887141	+	0.461499i	$0.847312\pi$
$140$	3.51678e13	−	6.09125e13i	0.394742	−	0.683713i
$141$	1.47318e13	−	2.55162e13i	0.157881	−	0.273458i
$142$	−5.96620e13			−0.610694
$143$	8.52567e13	−	1.46224e13i	0.833767	−	0.142999i
$144$	3.81421e13			0.356491
$145$	−1.69643e13	+	2.93830e13i	−0.151580	+	0.262545i
$146$	2.26243e13	−	3.91864e13i	0.193322	−	0.334844i
$147$	2.28746e13	+	3.96199e13i	0.186978	+	0.323855i
$148$	−1.30114e14			−1.01770
$149$	−5.61490e13	−	9.72529e13i	−0.420369	−	0.728101i	0.575606	−	0.817727i	$-0.304766\pi$
$149$	−5.61490e13	−	9.72529e13i	−0.420369	−	0.728101i	−0.995976	+	0.0896259i	$0.971433\pi$
$150$	−1.15257e13	−	1.99631e13i	−0.0826179	−	0.143098i
$151$	3.36374e12			0.0230926			0.0115463	−	0.999933i	$-0.496325\pi$
$151$	3.36374e12			0.0230926			0.0115463	+	0.999933i	$0.496325\pi$
$152$	−8.38058e13	−	1.45156e14i	−0.551176	−	0.954665i
$153$	5.09777e13	−	8.82960e13i	0.321282	−	0.556476i
$154$	−2.99211e13	+	5.18248e13i	−0.180756	+	0.313078i
$155$	−8.96181e13			−0.519087
$156$	1.24921e14	+	1.50297e14i	0.693947	+	0.834911i
$157$	1.62804e14			0.867597			0.433799	−	0.901010i	$-0.357173\pi$
$157$	1.62804e14			0.867597			0.433799	+	0.901010i	$0.357173\pi$
$158$	−2.28343e13	+	3.95502e13i	−0.116766	+	0.202245i
$159$	−1.57545e14	+	2.72877e14i	−0.773258	+	1.33932i
$160$	7.89817e13	+	1.36800e14i	0.372174	+	0.644625i
$161$	1.86379e14			0.843392
$162$	5.35720e13	+	9.27894e13i	0.232857	+	0.403321i
$163$	7.09213e13	+	1.22839e14i	0.296181	+	0.513001i	0.975259	−	0.221066i	$-0.0709535\pi$
$163$	7.09213e13	+	1.22839e14i	0.296181	+	0.513001i	−0.679078	+	0.734066i	$0.737620\pi$
$164$	−1.53074e14			−0.614351
$165$	1.11851e14	+	1.93732e14i	0.431514	+	0.747404i
$166$	−4.23351e13	+	7.33265e13i	−0.157035	+	0.271993i
$167$	2.19874e14	−	3.80833e14i	0.784363	−	1.35856i	−0.145016	−	0.989429i	$-0.546323\pi$
$167$	2.19874e14	−	3.80833e14i	0.784363	−	1.35856i	0.929379	−	0.369127i	$-0.120343\pi$
$168$	−2.92583e14			−1.00401
$169$	−5.53806e13	+	2.97769e14i	−0.182850	+	0.983141i
$170$	1.02646e14			0.326154
$171$	1.54165e14	−	2.67022e14i	0.471533	−	0.816719i
$172$	1.81519e14	−	3.14400e14i	0.534548	−	0.925865i
$173$	1.04589e14	+	1.81153e14i	0.296609	+	0.513742i	0.975358	−	0.220628i	$-0.0708108\pi$
$173$	1.04589e14	+	1.81153e14i	0.296609	+	0.513742i	−0.678749	+	0.734371i	$0.737477\pi$
$174$	6.52188e13			0.178157
$175$	−7.53275e13	−	1.30471e14i	−0.198247	−	0.343374i
$176$	9.95811e13	+	1.72479e14i	0.252548	+	0.437427i
$177$	−2.32170e14			−0.567519
$178$	−1.10563e14	−	1.91501e14i	−0.260544	−	0.451275i
$179$	1.68918e14	−	2.92575e14i	0.383824	−	0.664802i	−0.607782	−	0.794104i	$-0.707940\pi$
$179$	1.68918e14	−	2.92575e14i	0.383824	−	0.664802i	0.991605	+	0.129302i	$0.0412738\pi$
$180$	−9.44736e13	+	1.63633e14i	−0.207033	+	0.358592i
$181$	6.90056e13			0.145873			0.0729363	−	0.997337i	$-0.476763\pi$
$181$	6.90056e13			0.145873			0.0729363	+	0.997337i	$0.476763\pi$
$182$	−1.33931e14	−	1.61137e14i	−0.273161	−	0.328649i
$183$	−1.01502e15			−1.99776
$184$	−1.36088e14	+	2.35711e14i	−0.258526	+	0.447780i
$185$	2.60737e14	−	4.51609e14i	0.478174	−	0.828222i
$186$	8.61339e13	+	1.49188e14i	0.152525	+	0.264180i
$187$	5.32369e14			0.910421
$188$	6.49721e13	+	1.12535e14i	0.107325	+	0.185892i
$189$	1.81621e14	+	3.14577e14i	0.289844	+	0.502024i
$190$	3.10418e14			0.478684
$191$	−5.58864e14	−	9.67981e14i	−0.832893	−	1.44261i	−0.895734	−	0.444590i	$-0.853349\pi$
$191$	−5.58864e14	−	9.67981e14i	−0.832893	−	1.44261i	0.0628412	−	0.998024i	$-0.479984\pi$
$192$	−1.10070e14	+	1.90647e14i	−0.158567	+	0.274646i
$193$	−6.40430e14	+	1.10926e15i	−0.891968	+	1.54493i	−0.0544552	+	0.998516i	$0.517342\pi$
$193$	−6.40430e14	+	1.10926e15i	−0.891968	+	1.54493i	−0.837513	+	0.546418i	$0.815991\pi$
$194$	2.31019e13			0.0311126
$195$	−7.71995e14	+	1.32405e14i	−1.00552	+	0.172456i
$196$	−2.01769e14			−0.254209
$197$	6.84483e14	−	1.18556e15i	0.834319	−	1.44508i	−0.0602639	−	0.998182i	$-0.519194\pi$
$197$	6.84483e14	−	1.18556e15i	0.834319	−	1.44508i	0.894583	−	0.446901i	$-0.147472\pi$
$198$	8.03790e13	−	1.39220e14i	0.0948023	−	0.164202i
$199$	−4.29568e14	−	7.44034e14i	−0.490328	−	0.849274i	0.509610	−	0.860406i	$-0.329790\pi$
$199$	−4.29568e14	−	7.44034e14i	−0.490328	−	0.849274i	−0.999938	+	0.0111322i	$0.996456\pi$
$200$	2.20007e14			0.243075
$201$	−5.28151e14	−	9.14784e14i	−0.564916	−	0.978463i
$202$	3.00630e14	+	5.20707e14i	0.311350	+	0.539274i
$203$	4.26245e14			0.427499
$204$	6.01394e14	+	1.04164e15i	0.584202	+	1.01187i
$205$	3.06747e14	−	5.31302e14i	0.288656	−	0.499967i
$206$	−3.47636e14	+	6.02124e14i	−0.316948	+	0.548970i
$207$	−5.00683e14			−0.442339
$208$	−6.87307e14	+	1.17880e14i	−0.588490	+	0.100932i
$209$	1.60998e15			1.33619
$210$	2.70934e14	−	4.69271e14i	0.217990	−	0.377571i
$211$	−3.14991e14	+	5.45581e14i	−0.245732	+	0.425621i	−0.962337	−	0.271858i	$-0.912362\pi$
$211$	−3.14991e14	+	5.45581e14i	−0.245732	+	0.425621i	0.716605	+	0.697479i	$0.245695\pi$
$212$	−6.94830e14	−	1.20348e15i	−0.525648	−	0.910450i
$213$	2.80192e15			2.05584
$214$	1.25037e14	+	2.16570e14i	0.0889916	+	0.154138i
$215$	7.27497e14	+	1.26006e15i	0.502321	+	0.870045i
$216$	−5.30454e14			−0.355385
$217$	5.62938e14	+	9.75037e14i	0.365993	+	0.633918i
$218$	5.22631e13	−	9.05224e13i	0.0329783	−	0.0571201i
$219$	−1.06251e15	+	1.84032e15i	−0.650798	+	1.12721i
$220$	−9.86605e14			−0.586672
$221$	−6.45718e14	+	1.74861e15i	−0.372815	+	1.00959i
$222$	−1.00240e15			−0.562012
$223$	−2.09221e14	+	3.62381e14i	−0.113926	+	0.197326i	−0.917350	−	0.398082i	$-0.869676\pi$
$223$	−2.09221e14	+	3.62381e14i	−0.113926	+	0.197326i	0.803424	+	0.595408i	$0.203009\pi$
$224$	9.92250e14	−	1.71863e15i	0.524818	−	0.909012i
$225$	2.02357e14	+	3.50493e14i	0.103976	+	0.180091i
$226$	−1.05277e14			−0.0525569
$227$	−1.91874e14	−	3.32335e14i	−0.0930782	−	0.161216i	0.815727	−	0.578437i	$-0.196337\pi$
$227$	−1.91874e14	−	3.32335e14i	−0.0930782	−	0.161216i	−0.908805	+	0.417221i	$0.863004\pi$
$228$	1.81872e15	+	3.15011e15i	0.857411	+	1.48508i
$229$	9.04228e13			0.0414331			0.0207165	−	0.999785i	$-0.493405\pi$
$229$	9.04228e13			0.0414331			0.0207165	+	0.999785i	$0.493405\pi$
$230$	−2.52036e14	−	4.36540e14i	−0.112262	−	0.194443i
$231$	1.40519e15	−	2.43386e15i	0.608495	−	1.05394i
$232$	−3.11230e14	+	5.39067e14i	−0.131042	+	0.226971i
$233$	−3.15966e15			−1.29368			−0.646839	−	0.762626i	$-0.723910\pi$
$233$	−3.15966e15			−1.29368			−0.646839	+	0.762626i	$0.723910\pi$
$234$	3.59789e14	+	4.32874e14i	0.143267	+	0.172369i
$235$	−5.20795e14			−0.201709
$236$	5.11975e14	−	8.86767e14i	0.192895	−	0.334104i
$237$	1.07237e15	−	1.85740e15i	0.393080	−	0.680835i
$238$	−6.44771e14	−	1.11678e15i	−0.229961	−	0.398305i
$239$	1.59971e15			0.555206			0.277603	−	0.960696i	$-0.410460\pi$
$239$	1.59971e15			0.555206			0.277603	+	0.960696i	$0.410460\pi$
$240$	−9.01701e14	−	1.56179e15i	−0.304572	−	0.527534i
$241$	−1.59347e15	−	2.75997e15i	−0.523882	−	0.907390i	−0.999614	−	0.0277994i	$-0.991150\pi$
$241$	−1.59347e15	−	2.75997e15i	−0.523882	−	0.907390i	0.475732	−	0.879590i	$-0.342183\pi$
$242$	−3.33581e14			−0.106758
$243$	−1.69873e15	−	2.94229e15i	−0.529279	−	0.916737i
$244$	2.23830e15	−	3.87684e15i	0.679022	−	1.17610i
$245$	4.04329e14	−	7.00318e14i	0.119442	−	0.206879i
$246$	−1.17929e15			−0.339266
$247$	−1.95276e15	+	5.28811e15i	−0.547166	+	1.48173i
$248$	−1.64415e15			−0.448752
$249$	1.98819e15	−	3.44365e15i	0.528643	−	0.915636i
$250$	−7.88652e14	+	1.36599e15i	−0.204303	+	0.353864i
$251$	3.38741e15	+	5.86717e15i	0.855045	+	1.48098i	0.876603	+	0.481214i	$0.159804\pi$
$251$	3.38741e15	+	5.86717e15i	0.855045	+	1.48098i	−0.0215575	+	0.999768i	$0.506862\pi$
$252$	2.37375e15			0.583891
$253$	−1.30718e15	−	2.26410e15i	−0.313366	−	0.542766i
$254$	7.69426e14	+	1.33269e15i	0.179783	+	0.311393i
$255$	−4.82057e15			−1.09796
$256$	2.93981e14	+	5.09189e14i	0.0652768	+	0.113063i
$257$	−2.75459e15	+	4.77110e15i	−0.596338	+	1.03289i	0.397019	+	0.917810i	$0.370045\pi$
$257$	−2.75459e15	+	4.77110e15i	−0.596338	+	1.03289i	−0.993357	+	0.115077i	$0.963289\pi$
$258$	1.39843e15	−	2.42214e15i	0.295197	−	0.511295i
$259$	−6.55129e15			−1.34859
$260$	1.19667e15	−	3.24059e15i	0.240241	−	0.650575i
$261$	−1.14505e15			−0.224213
$262$	1.59919e15	−	2.76988e15i	0.305451	−	0.529057i
$263$	−3.34308e15	+	5.79039e15i	−0.622924	+	1.07894i	0.366015	+	0.930609i	$0.380722\pi$
$263$	−3.34308e15	+	5.79039e15i	−0.622924	+	1.07894i	−0.988938	+	0.148327i	$0.952611\pi$
$264$	2.05205e15	+	3.55425e15i	0.373045	+	0.646133i
$265$	5.56952e15			0.987915
$266$	−1.94990e15	−	3.37732e15i	−0.337506	−	0.584577i
$267$	5.19241e15	+	8.99352e15i	0.877093	+	1.51917i
$268$	4.65866e15			0.768041
$269$	−4.99932e15	−	8.65907e15i	−0.804491	−	1.39342i	−0.916634	−	0.399727i	$-0.869105\pi$
$269$	−4.99932e15	−	8.65907e15i	−0.804491	−	1.39342i	0.112144	−	0.993692i	$-0.464228\pi$
$270$	4.91203e14	−	8.50789e14i	0.0771608	−	0.133646i
$271$	4.22034e15	−	7.30985e15i	0.647213	−	1.12101i	−0.336572	−	0.941658i	$-0.609268\pi$
$271$	4.22034e15	−	7.30985e15i	0.647213	−	1.12101i	0.983786	−	0.179349i	$-0.0573990\pi$
$272$	−4.29175e15			−0.642595
$273$	6.28985e15	+	7.56753e15i	0.919567	+	1.10636i
$274$	8.24460e14			0.117704
$275$	−1.05663e15	+	1.83013e15i	−0.147319	+	0.255164i
$276$	2.95333e15	−	5.11531e15i	0.402163	−	0.696567i
$277$	7.06739e15	+	1.22411e16i	0.940028	+	1.62818i	0.765414	+	0.643539i	$0.222534\pi$
$277$	7.06739e15	+	1.22411e16i	0.940028	+	1.62818i	0.174614	+	0.984637i	$0.444132\pi$
$278$	2.53678e14			0.0329604
$279$	−1.51226e15	−	2.61931e15i	−0.191955	−	0.332475i
$280$	2.58584e15	+	4.47881e15i	0.320682	+	0.555437i
$281$	6.65234e15			0.806089			0.403045	−	0.915180i	$-0.367952\pi$
$281$	6.65234e15			0.806089			0.403045	+	0.915180i	$0.367952\pi$
$282$	5.00547e14	+	8.66972e14i	0.0592687	+	0.102656i
$283$	5.22279e15	−	9.04614e15i	0.604353	−	1.04677i	−0.387800	−	0.921744i	$-0.626765\pi$
$283$	5.22279e15	−	9.04614e15i	0.604353	−	1.04677i	0.992153	−	0.125027i	$-0.0399018\pi$
$284$	−6.17872e15	+	1.07019e16i	−0.698762	+	1.21029i
$285$	−1.45782e16			−1.61144
$286$	−1.01813e15	+	2.75712e15i	−0.110008	+	0.297904i
$287$	−7.70736e15			−0.814092
$288$	−2.66555e15	+	4.61686e15i	−0.275255	+	0.476755i
$289$	−7.83734e14	+	1.35747e15i	−0.0791285	+	0.137055i
$290$	−5.76402e14	−	9.98357e14i	−0.0569034	−	0.0985596i
$291$	−1.08494e15			−0.104737
$292$	−4.68603e15	−	8.11645e15i	−0.442402	−	0.766263i
$293$	3.21187e15	+	5.56313e15i	0.296564	+	0.513665i	0.975348	−	0.220674i	$-0.0708257\pi$
$293$	3.21187e15	+	5.56313e15i	0.296564	+	0.513665i	−0.678783	+	0.734339i	$0.737492\pi$
$294$	−1.55444e15			−0.140383
$295$	2.05191e15	+	3.55401e15i	0.181266	+	0.313961i
$296$	4.78354e15	−	8.28533e15i	0.413383	−	0.716001i
$297$	2.54761e15	−	4.41260e15i	0.215386	−	0.373059i
$298$	3.81559e15			0.315614
$299$	9.02213e15	−	1.54739e15i	0.730208	−	0.125238i
$300$	−4.77450e15			−0.378129
$301$	9.13957e15	−	1.58302e16i	0.708343	−	1.22689i
$302$	−5.71456e13	+	9.89791e13i	−0.00433449	+	0.00750755i
$303$	−1.41186e16	−	2.44541e16i	−1.04813	−	1.81541i
$304$	−1.29790e16			−0.943112
$305$	8.97071e15	+	1.55377e16i	0.638084	+	1.10519i
$306$	1.73209e15	+	3.00007e15i	0.120609	+	0.208902i
$307$	−1.06113e16			−0.723384			−0.361692	−	0.932298i	$-0.617801\pi$
$307$	−1.06113e16			−0.723384			−0.361692	+	0.932298i	$0.617801\pi$
$308$	6.19737e15	+	1.07342e16i	0.413645	+	0.716455i
$309$	1.63261e16	−	2.82777e16i	1.06697	−	1.84805i
$310$	1.52250e15	−	2.63704e15i	0.0974328	−	0.168759i
$311$	−2.79778e16			−1.75336			−0.876680	−	0.481075i	$-0.840247\pi$
$311$	−2.79778e16			−1.75336			−0.876680	+	0.481075i	$0.840247\pi$
$312$	−1.41632e16	+	2.42913e15i	−0.869273	+	0.149089i
$313$	8.49575e14			0.0510697			0.0255349	−	0.999674i	$-0.491871\pi$
$313$	8.49575e14			0.0510697			0.0255349	+	0.999674i	$0.491871\pi$
$314$	−2.76583e15	+	4.79056e15i	−0.162848	+	0.282062i
$315$	−4.75680e15	+	8.23902e15i	−0.274344	+	0.475179i
$316$	4.72953e15	+	8.19179e15i	0.267210	+	0.462821i
$317$	2.39229e16			1.32412			0.662062	−	0.749449i	$-0.269681\pi$
$317$	2.39229e16			1.32412			0.662062	+	0.749449i	$0.269681\pi$
$318$	−5.35298e15	−	9.27164e15i	−0.290282	−	0.502783i
$319$	−2.98949e15	−	5.17795e15i	−0.158839	−	0.275118i
$320$	3.89119e15			0.202585
$321$	−5.87214e15	−	1.01708e16i	−0.299581	−	0.518889i
$322$	−3.16634e15	+	5.48427e15i	−0.158305	+	0.274192i
$323$	−1.73467e16	+	3.00454e16i	−0.849965	+	1.47218i
$324$	2.21921e16			1.06575
$325$	−4.72963e15	−	5.69037e15i	−0.222631	−	0.267854i
$326$	−4.81944e15			−0.222373
$327$	−2.45445e15	+	4.25122e15i	−0.111018	+	0.192289i
$328$	5.62766e15	−	9.74739e15i	0.249544	−	0.432223i
$329$	3.27138e15	+	5.66620e15i	0.142219	+	0.246331i
$330$	−7.60082e15			−0.323981
$331$	−9.89997e15	−	1.71473e16i	−0.413763	−	0.716659i	0.581534	−	0.813522i	$-0.302453\pi$
$331$	−9.89997e15	−	1.71473e16i	−0.413763	−	0.716659i	−0.995298	+	0.0968628i	$0.969119\pi$
$332$	8.76861e15	+	1.51877e16i	0.359363	+	0.622435i
$333$	1.75992e16			0.707301
$334$	7.47075e15	+	1.29397e16i	0.294451	+	0.510003i
$335$	−9.33556e15	+	1.61697e16i	−0.360868	+	0.625042i
$336$	−1.13281e16	+	1.96208e16i	−0.429489	+	0.743896i
$337$	3.87319e16			1.44037			0.720185	−	0.693782i	$-0.244057\pi$
$337$	3.87319e16			1.44037			0.720185	+	0.693782i	$0.244057\pi$
$338$	−7.82109e15	−	6.68830e15i	−0.285305	−	0.243982i
$339$	4.94416e15			0.176927
$340$	1.06302e16	−	1.84120e16i	0.373188	−	0.646381i
$341$	7.89638e15	−	1.36769e16i	0.271972	−	0.471070i
$342$	5.23814e15	+	9.07272e15i	0.177014	+	0.306597i
$343$	2.41728e16			0.801522
$344$	1.33468e16	+	2.31174e16i	0.434258	+	0.752158i
$345$	1.18364e16	+	2.05013e16i	0.377917	+	0.654572i
$346$	−7.10730e15			−0.222695
$347$	−1.74206e16	−	3.01733e16i	−0.535699	−	0.927858i	−0.999129	−	0.0417247i	$-0.986715\pi$
$347$	−1.74206e16	−	3.01733e16i	−0.535699	−	0.927858i	0.463430	−	0.886134i	$-0.346619\pi$
$348$	6.75419e15	−	1.16986e16i	0.203849	−	0.353077i
$349$	−2.49581e15	+	4.32287e15i	−0.0739343	+	0.128058i	−0.900622	−	0.434603i	$-0.856889\pi$
$349$	−2.49581e15	+	4.32287e15i	−0.0739343	+	0.128058i	0.826688	+	0.562661i	$0.190222\pi$
$350$	5.11887e15			0.148844
$351$	1.14035e16	+	1.37200e16i	0.325494	+	0.391612i
$352$	−2.78367e16			−0.779994
$353$	4.58083e15	−	7.93423e15i	0.126011	−	0.218258i	−0.796117	−	0.605143i	$-0.793116\pi$
$353$	4.58083e15	−	7.93423e15i	0.126011	−	0.218258i	0.922128	+	0.386886i	$0.126449\pi$
$354$	3.94427e15	−	6.83167e15i	0.106523	−	0.184504i
$355$	−2.47633e16	−	4.28913e16i	−0.656635	−	1.13732i
$356$	−4.58006e16			−1.19247
$357$	3.02805e16	+	5.24474e16i	0.774140	+	1.34085i
$358$	5.73940e15	+	9.94093e15i	0.144088	+	0.249567i
$359$	−5.08836e16			−1.25448			−0.627240	−	0.778826i	$-0.715816\pi$
$359$	−5.08836e16			−1.25448			−0.627240	+	0.778826i	$0.715816\pi$
$360$	−6.94651e15	−	1.20317e16i	−0.168190	−	0.291314i
$361$	−3.14330e16	+	5.44435e16i	−0.747462	+	1.29464i
$362$	−1.17232e15	+	2.03051e15i	−0.0273804	+	0.0474242i
$363$	1.56660e16			0.359390
$364$	−4.27742e16	+	7.33620e15i	−0.963880	+	0.165315i
$365$	3.75617e16			0.831460
$366$	1.72439e16	−	2.98673e16i	0.374980	−	0.649484i
$367$	2.25598e15	−	3.90747e15i	0.0481954	−	0.0834769i	−0.840921	−	0.541157i	$-0.817986\pi$
$367$	2.25598e15	−	3.90747e15i	0.0481954	−	0.0834769i	0.889117	+	0.457681i	$0.151320\pi$
$368$	1.05380e16	+	1.82523e16i	0.221180	+	0.383096i
$369$	2.07048e16			0.426972
$370$	8.85916e15	+	1.53445e16i	0.179507	+	0.310915i
$371$	−3.49851e16	−	6.05959e16i	−0.696550	−	1.20646i
$372$	3.56808e16			0.698080
$373$	−1.77656e16	−	3.07710e16i	−0.341565	−	0.591608i	0.643158	−	0.765733i	$-0.277624\pi$
$373$	−1.77656e16	−	3.07710e16i	−0.341565	−	0.591608i	−0.984724	+	0.174125i	$0.944290\pi$
$374$	−9.04426e15	+	1.56651e16i	−0.170886	+	0.295984i
$375$	3.70377e16	−	6.41511e16i	0.687765	−	1.19124i
$376$	−9.55462e15			−0.174378
$377$	2.06334e16	−	3.53884e15i	0.370129	−	0.0634807i
$378$	−1.23420e16			−0.217615
$379$	−3.87981e16	+	6.72004e16i	−0.672444	+	1.16471i	0.304765	+	0.952428i	$0.401422\pi$
$379$	−3.87981e16	+	6.72004e16i	−0.672444	+	1.16471i	−0.977209	+	0.212280i	$0.931911\pi$
$380$	3.21475e16	−	5.56812e16i	0.547715	−	0.948670i
$381$	−3.61347e16	−	6.25872e16i	−0.605219	−	1.04827i
$382$	3.79775e16			0.625337
$383$	−1.64420e16	−	2.84783e16i	−0.266172	−	0.461023i	0.701698	−	0.712474i	$-0.252425\pi$
$383$	−1.64420e16	−	2.84783e16i	−0.266172	−	0.461023i	−0.967870	+	0.251451i	$0.919092\pi$
$384$	−4.03444e16	−	6.98785e16i	−0.642140	−	1.11222i
$385$	−4.96761e16			−0.777414
$386$	−2.17602e16	−	3.76897e16i	−0.334845	−	0.579969i
$387$	−2.45522e16	+	4.25257e16i	−0.371509	+	0.643473i
$388$	2.39248e15	−	4.14389e15i	0.0355993	−	0.0616598i
$389$	4.57248e16			0.669082			0.334541	−	0.942381i	$-0.391419\pi$
$389$	4.57248e16			0.669082			0.334541	+	0.942381i	$0.391419\pi$
$390$	9.21914e15	−	2.49656e16i	0.132669	−	0.359270i
$391$	5.63370e16			0.797342
$392$	7.41791e15	−	1.28482e16i	0.103258	−	0.178847i
$393$	−7.51032e16	+	1.30083e17i	−1.02827	+	1.78101i
$394$	2.32570e16	+	4.02822e16i	0.313204	+	0.542486i
$395$	−3.79103e16			−0.502200
$396$	−1.66484e16	−	2.88359e16i	−0.216947	−	0.375764i
$397$	−4.84612e16	−	8.39373e16i	−0.621235	−	1.07601i	−0.989256	−	0.146193i	$-0.953298\pi$
$397$	−4.84612e16	−	8.39373e16i	−0.621235	−	1.07601i	0.368021	−	0.929818i	$-0.380036\pi$
$398$	2.91912e16			0.368139
$399$	9.15735e16	+	1.58610e17i	1.13618	+	1.96792i
$400$	8.51812e15	−	1.47538e16i	0.103981	−	0.180100i
$401$	−5.31265e15	+	9.20177e15i	−0.0638076	+	0.110518i	−0.896164	−	0.443722i	$-0.853658\pi$
$401$	−5.31265e15	+	9.20177e15i	−0.0638076	+	0.110518i	0.832357	+	0.554240i	$0.186991\pi$
$402$	3.58904e16			0.424140
$403$	3.53455e16	+	4.25253e16i	0.411009	+	0.494498i
$404$	1.24536e17			1.42500
$405$	−4.44711e16	+	7.70262e16i	−0.500749	+	0.867323i
$406$	−7.24135e15	+	1.25424e16i	−0.0802418	+	0.138983i
$407$	4.59478e16	+	7.95839e16i	0.501073	+	0.867884i
$408$	−8.84393e16			−0.949192
$409$	1.42658e16	+	2.47090e16i	0.150693	+	0.261008i	0.931482	−	0.363786i	$-0.118516\pi$
$409$	1.42658e16	+	2.47090e16i	0.150693	+	0.261008i	−0.780789	+	0.624794i	$0.785183\pi$
$410$	1.04225e16	+	1.80523e16i	0.108362	+	0.187688i
$411$	−3.87193e16			−0.396237
$412$	7.20039e16	+	1.24714e17i	0.725310	+	1.25627i
$413$	2.57782e16	−	4.46492e16i	0.255610	−	0.442729i
$414$	8.50595e15	−	1.47327e16i	0.0830273	−	0.143807i
$415$	−7.02862e16			−0.675395
$416$	3.37636e16	−	9.14322e16i	0.319405	−	0.864953i
$417$	−1.19135e16			−0.110957
$418$	−2.73514e16	+	4.73740e16i	−0.250804	+	0.434404i
$419$	−3.90895e16	+	6.77049e16i	−0.352914	+	0.611264i	−0.986759	−	0.162196i	$-0.948142\pi$
$419$	−3.90895e16	+	6.77049e16i	−0.352914	+	0.611264i	0.633845	+	0.773460i	$0.281476\pi$
$420$	−5.61169e16	−	9.71973e16i	−0.498854	−	0.864040i
$421$	6.34549e15			0.0555433			0.0277716	−	0.999614i	$-0.491159\pi$
$421$	6.34549e15			0.0555433			0.0277716	+	0.999614i	$0.491159\pi$
$422$	−1.07026e16	−	1.85374e16i	−0.0922481	−	0.159778i
$423$	−8.78813e15	−	1.52215e16i	−0.0745906	−	0.129195i
$424$	1.02180e17			0.854057
$425$	−2.27693e16	−	3.94376e16i	−0.187422	−	0.324625i
$426$	−4.76010e16	+	8.24474e16i	−0.385881	+	0.668366i
$427$	1.12699e17	−	1.95201e17i	0.899789	−	1.55848i
$428$	5.17963e16			0.407300
$429$	4.78148e16	−	1.29483e17i	0.370331	−	1.00286i
$430$	−4.94369e16			−0.377143
$431$	−6.73501e15	+	1.16654e16i	−0.0506100	+	0.0876590i	−0.890221	−	0.455530i	$-0.849450\pi$
$431$	−6.73501e15	+	1.16654e16i	−0.0506100	+	0.0876590i	0.839611	+	0.543189i	$0.182783\pi$
$432$	−2.05379e16	+	3.55727e16i	−0.152024	+	0.263313i
$433$	−4.78330e15	−	8.28492e15i	−0.0348784	−	0.0604111i	0.848059	−	0.529901i	$-0.177771\pi$
$433$	−4.78330e15	−	8.28492e15i	−0.0348784	−	0.0604111i	−0.882938	+	0.469490i	$0.844438\pi$
$434$	−3.82543e16			−0.274788
$435$	2.70697e16	+	4.68860e16i	0.191559	+	0.331790i
$436$	−1.08250e16	−	1.87494e16i	−0.0754682	−	0.130715i
$437$	1.70373e17			1.17023
$438$	−3.61013e16	−	6.25293e16i	−0.244310	−	0.423157i
$439$	−1.03351e17	+	1.79010e17i	−0.689122	+	1.19360i	0.283000	+	0.959120i	$0.408670\pi$
$439$	−1.03351e17	+	1.79010e17i	−0.689122	+	1.19360i	−0.972122	+	0.234475i	$0.924663\pi$
$440$	3.62718e16	−	6.28246e16i	0.238302	−	0.412750i
$441$	2.72913e16			0.176675
$442$	−4.04835e16	−	4.87071e16i	−0.258246	−	0.310704i
$443$	−1.91066e16			−0.120104			−0.0600522	−	0.998195i	$-0.519127\pi$
$443$	−1.91066e16			−0.120104			−0.0600522	+	0.998195i	$0.519127\pi$
$444$	−1.03810e17	+	1.79805e17i	−0.643060	+	1.11381i
$445$	9.17806e16	−	1.58969e17i	0.560288	−	0.970447i
$446$	−7.10878e15	−	1.23128e16i	−0.0427680	−	0.0740763i
$447$	−1.79193e17			−1.06248
$448$	−2.44426e16	−	4.23358e16i	−0.142837	−	0.247400i
$449$	−1.18166e17	−	2.04670e17i	−0.680600	−	1.17883i	−0.974798	−	0.223089i	$-0.928386\pi$
$449$	−1.18166e17	−	2.04670e17i	−0.680600	−	1.17883i	0.294198	−	0.955745i	$-0.404948\pi$
$450$	−1.37512e16			−0.0780652
$451$	5.40559e16	+	9.36276e16i	0.302479	+	0.523910i
$452$	−1.09027e16	+	1.88841e16i	−0.0601361	+	0.104159i
$453$	2.68374e15	−	4.64838e15i	0.0145916	−	0.0252734i
$454$	1.30388e16			0.0698832
$455$	6.02528e16	−	1.63165e17i	0.318349	−	0.862093i
$456$	−2.67456e17			−1.39309
$457$	−8.20892e16	+	1.42183e17i	−0.421532	+	0.730115i	−0.996090	−	0.0883493i	$-0.971841\pi$
$457$	−8.20892e16	+	1.42183e17i	−0.421532	+	0.730115i	0.574558	+	0.818464i	$0.305174\pi$
$458$	−1.53617e15	+	2.66072e15i	−0.00777701	+	0.0134702i
$459$	5.48986e16	+	9.50872e16i	0.274018	+	0.474613i
$460$	−1.04406e17			−0.513804
$461$	−1.19180e17	−	2.06425e17i	−0.578291	−	1.00163i	−0.995676	−	0.0928988i	$-0.970387\pi$
$461$	−1.19180e17	−	2.06425e17i	−0.578291	−	1.00163i	0.417385	−	0.908730i	$-0.362947\pi$
$462$	4.77447e16	+	8.26963e16i	0.228430	+	0.395652i
$463$	4.47197e16			0.210971			0.105485	−	0.994421i	$-0.466360\pi$
$463$	4.47197e16			0.210971			0.105485	+	0.994421i	$0.466360\pi$
$464$	2.41001e16	+	4.17427e16i	0.112112	+	0.194184i
$465$	−7.15013e16	+	1.23844e17i	−0.327997	+	0.568107i
$466$	5.36785e16	−	9.29738e16i	0.242824	−	0.420584i
$467$	2.83964e17			1.26678			0.633392	−	0.773831i	$-0.281662\pi$
$467$	2.83964e17			1.26678			0.633392	+	0.773831i	$0.281662\pi$
$468$	1.14907e17	−	1.97077e16i	0.505532	−	0.0867038i
$469$	2.34566e17			1.01775
$470$	8.84763e15	−	1.53245e16i	0.0378609	−	0.0655770i
$471$	1.29892e17	−	2.24980e17i	0.548211	−	0.949530i
$472$	3.76448e16	+	6.52027e16i	0.156705	+	0.271421i
$473$	−2.56403e17			−1.05275
$474$	3.64364e16	+	6.31097e16i	0.147563	+	0.255586i
$475$	−6.88583e16	−	1.19266e17i	−0.275073	−	0.476440i
$476$	−2.67095e17			−1.05250
$477$	9.39827e16	+	1.62783e17i	0.365324	+	0.632760i
$478$	−2.71769e16	+	4.70718e16i	−0.104212	+	0.180501i
$479$	−2.14934e16	+	3.72277e16i	−0.0813064	+	0.140827i	−0.903811	−	0.427931i	$-0.859243\pi$
$479$	−2.14934e16	+	3.72277e16i	−0.0813064	+	0.140827i	0.822505	+	0.568758i	$0.192576\pi$
$480$	2.52060e17			0.940668
$481$	−3.17131e17	+	5.43911e16i	−1.16760	+	0.200256i
$482$	1.08284e17			0.393331
$483$	1.48702e17	−	2.57559e17i	0.532917	−	0.923039i
$484$	−3.45463e16	+	5.98359e16i	−0.122154	+	0.211576i
$485$	9.58864e15	+	1.66080e16i	0.0334531	+	0.0579424i
$486$	1.15437e17			0.397383
$487$	1.86643e17	+	3.23275e17i	0.633977	+	1.09808i	0.986731	+	0.162364i	$0.0519119\pi$
$487$	1.86643e17	+	3.23275e17i	0.633977	+	1.09808i	−0.352754	+	0.935716i	$0.614755\pi$
$488$	1.64579e17	+	2.85059e17i	0.551626	+	0.955445i
$489$	2.26337e17			0.748595
$490$	1.37380e16	+	2.37950e16i	0.0448384	+	0.0776625i
$491$	1.53186e17	−	2.65325e17i	0.493388	−	0.854573i	−0.506583	−	0.862191i	$-0.669092\pi$
$491$	1.53186e17	−	2.65325e17i	0.493388	−	0.854573i	0.999971	+	0.00761829i	$0.00242500\pi$
$492$	−1.22129e17	+	2.11534e17i	−0.388192	+	0.672368i
$493$	1.28841e17			0.404157
$494$	−1.22429e17	−	1.47299e17i	−0.379018	−	0.456009i
$495$	1.33448e17			0.407736
$496$	−6.36576e16	+	1.10258e17i	−0.191964	+	0.332491i
$497$	−3.11102e17	+	5.38844e17i	−0.925947	+	1.60379i
$498$	6.75536e16	+	1.17006e17i	0.198453	+	0.343731i
$499$	−2.26621e17			−0.657122			−0.328561	−	0.944483i	$-0.606564\pi$
$499$	−2.26621e17			−0.657122			−0.328561	+	0.944483i	$0.606564\pi$
$500$	1.63349e17	+	2.82929e17i	0.467532	+	0.809789i
$501$	−3.50851e17	−	6.07691e17i	−0.991236	−	1.71687i
$502$	−2.30191e17			−0.641969
$503$	−1.21741e17	−	2.10862e17i	−0.335155	−	0.580506i	0.648359	−	0.761334i	$-0.275455\pi$
$503$	−1.21741e17	−	2.10862e17i	−0.335155	−	0.580506i	−0.983515	+	0.180829i	$0.942122\pi$
$504$	−8.72693e16	+	1.51155e17i	−0.237172	+	0.410794i
$505$	−2.49559e17	+	4.32248e17i	−0.669543	+	1.15968i
$506$	8.88291e16			0.235276
$507$	3.67304e17	+	3.14104e17i	0.960447	+	0.821337i
$508$	3.18733e17			0.822836
$509$	1.23052e17	−	2.13132e17i	0.313634	−	0.543229i	−0.665513	−	0.746387i	$-0.731787\pi$
$509$	1.23052e17	−	2.13132e17i	0.313634	−	0.543229i	0.979146	+	0.203157i	$0.0651203\pi$
$510$	8.18952e16	−	1.41847e17i	0.206088	−	0.356955i
$511$	−2.35944e17	−	4.08668e17i	−0.586238	−	1.01539i
$512$	3.94265e17			0.967239
$513$	1.66023e17	+	2.87560e17i	0.402166	+	0.696572i
$514$	−9.35939e16	−	1.62109e17i	−0.223866	−	0.387747i
$515$	−5.77159e17			−1.36316
$516$	−2.89648e17	−	5.01684e17i	−0.675533	−	1.17006i
$517$	4.58880e16	−	7.94803e16i	0.105684	−	0.183051i
$518$	1.11298e17	−	1.92774e17i	0.253130	−	0.438434i
$519$	3.33782e17			0.749678
$520$	1.62358e17	+	1.95339e17i	0.360125	+	0.433278i
$521$	−6.84199e16			−0.149878			−0.0749389	−	0.997188i	$-0.523876\pi$
$521$	−6.84199e16			−0.149878			−0.0749389	+	0.997188i	$0.523876\pi$
$522$	1.94529e16	−	3.36935e16i	0.0420849	−	0.0728933i
$523$	3.89968e17	−	6.75445e17i	0.833236	−	1.44321i	−0.0622219	−	0.998062i	$-0.519819\pi$
$523$	3.89968e17	−	6.75445e17i	0.833236	−	1.44321i	0.895458	−	0.445145i	$-0.146848\pi$
$524$	−3.31231e17	−	5.73709e17i	−0.699001	−	1.21071i
$525$	−2.40398e17			−0.501068
$526$	−1.13589e17	−	1.96742e17i	−0.233846	−	0.405033i
$527$	1.70160e17	+	2.94725e17i	0.346009	+	0.599305i
$528$	3.17801e17			0.638314
$529$	1.13688e17	+	1.96914e17i	0.225556	+	0.390674i
$530$	−9.46189e16	+	1.63885e17i	−0.185432	+	0.321178i
$531$	−6.92498e16	+	1.19944e17i	−0.134061	+	0.232201i
$532$	−8.07742e17			−1.54471
$533$	−3.73093e17	+	6.39892e16i	−0.704840	+	0.120887i
$534$	−3.52849e17			−0.658523
$535$	−1.03796e17	+	1.79779e17i	−0.191372	+	0.331466i
$536$	−1.71272e17	+	2.96652e17i	−0.311972	+	0.540352i
$537$	−2.69541e17	−	4.66858e17i	−0.485055	−	0.840141i
$538$	3.39728e17			0.604013
$539$	7.12520e16	+	1.23412e17i	0.125161	+	0.216786i
$540$	−1.01740e17	−	1.76219e17i	−0.176576	−	0.305839i
$541$	2.29126e17			0.392910			0.196455	−	0.980513i	$-0.437057\pi$
$541$	2.29126e17			0.392910			0.196455	+	0.980513i	$0.437057\pi$
$542$	1.43396e17	+	2.48370e17i	0.242964	+	0.420827i
$543$	5.50557e16	−	9.53593e16i	0.0921730	−	0.159648i
$544$	2.99928e17	−	5.19490e17i	0.496162	−	0.859378i
$545$	8.67692e16			0.141837
$546$	−3.29533e17	+	5.65182e16i	−0.532288	+	0.0912928i
$547$	2.50993e16			0.0400631			0.0200316	−	0.999799i	$-0.493623\pi$
$547$	2.50993e16			0.0400631			0.0200316	+	0.999799i	$0.493623\pi$
$548$	8.53827e16	−	1.47887e17i	0.134678	−	0.233269i
$549$	−3.02752e17	+	5.24382e17i	−0.471918	+	0.817386i
$550$	−3.59014e16	−	6.21831e16i	−0.0553037	−	0.0957888i
$551$	3.89639e17			0.593166
$552$	2.17154e17	+	3.76122e17i	0.326711	+	0.565880i
$553$	2.38135e17	+	4.12461e17i	0.354086	+	0.613295i
$554$	−4.80263e17			−0.705774
$555$	−4.16054e17	−	7.20627e17i	−0.604291	−	1.04666i
$556$	2.62714e16	−	4.55034e16i	0.0377136	−	0.0653218i
$557$	−4.67078e17	+	8.09003e17i	−0.662721	+	1.14787i	0.317176	+	0.948367i	$0.397265\pi$
$557$	−4.67078e17	+	8.09003e17i	−0.662721	+	1.14787i	−0.979898	+	0.199501i	$0.936068\pi$
$558$	1.02765e17			0.144120
$559$	3.10995e17	−	8.42179e17i	0.431099	−	1.16742i
$560$	4.00469e17			0.548715
$561$	4.24747e17	−	7.35684e17i	0.575271	−	0.996398i
$562$	−1.13015e17	+	1.95747e17i	−0.151303	+	0.262065i
$563$	6.38992e17	+	1.10677e18i	0.845650	+	1.46471i	0.885055	+	0.465486i	$0.154121\pi$
$563$	6.38992e17	+	1.10677e18i	0.845650	+	1.46471i	−0.0394047	+	0.999223i	$0.512546\pi$
$564$	2.07351e17			0.271263
$565$	−4.36963e16	−	7.56842e16i	−0.0565106	−	0.0978792i
$566$	1.77457e17	+	3.07364e17i	0.226875	+	0.392959i
$567$	1.11738e18			1.41225
$568$	−4.54313e17	−	7.86893e17i	−0.567663	−	0.983221i
$569$	1.33532e17	−	2.31284e17i	0.164951	−	0.285704i	−0.771687	−	0.636003i	$-0.780587\pi$
$569$	1.33532e17	−	2.31284e17i	0.164951	−	0.285704i	0.936638	+	0.350299i	$0.113920\pi$
$570$	2.47665e17	−	4.28969e17i	0.302467	−	0.523889i
$571$	−6.71054e17			−0.810257			−0.405129	−	0.914260i	$-0.632773\pi$
$571$	−6.71054e17			−0.810257			−0.405129	+	0.914260i	$0.632773\pi$
$572$	3.89118e17	+	4.68160e17i	0.464522	+	0.558882i
$573$	−1.78355e18			−2.10513
$574$	1.30938e17	−	2.26791e17i	0.152805	−	0.264667i
$575$	−1.11815e17	+	1.93670e17i	−0.129021	+	0.223471i
$576$	6.56617e16	+	1.13729e17i	0.0749145	+	0.129756i
$577$	1.55405e18			1.75316			0.876579	−	0.481258i	$-0.159820\pi$
$577$	1.55405e18			1.75316			0.876579	+	0.481258i	$0.159820\pi$
$578$	−2.66292e16	−	4.61232e16i	−0.0297049	−	0.0514504i
$579$	1.02193e18	+	1.77003e18i	1.12722	+	1.95240i
$580$	−2.38773e17			−0.260438
$581$	4.41504e17	+	7.64708e17i	0.476201	+	0.824804i
$582$	1.84317e16	−	3.19246e16i	0.0196592	−	0.0340507i
$583$	−4.90739e17	+	8.49984e17i	−0.517612	+	0.896531i
$584$	6.89115e17			0.718800
$585$	−1.61861e17	+	4.38322e17i	−0.166966	+	0.452147i
$586$	−2.18262e17			−0.222661
$587$	−7.01763e17	+	1.21549e18i	−0.708016	+	1.22632i	0.257577	+	0.966258i	$0.417076\pi$
$587$	−7.01763e17	+	1.21549e18i	−0.708016	+	1.22632i	−0.965592	+	0.260061i	$0.916257\pi$
$588$	−1.60981e17	+	2.78827e17i	−0.160628	+	0.278216i
$589$	5.14592e17	+	8.91299e17i	0.507824	+	0.879577i
$590$	−1.39437e17			−0.136094
$591$	−1.09222e18	−	1.89178e18i	−1.05437	−	1.82622i
$592$	−3.70413e17	−	6.41575e17i	−0.353668	−	0.612571i
$593$	−1.73606e18			−1.63949			−0.819744	−	0.572731i	$-0.805884\pi$
$593$	−1.73606e18			−1.63949			−0.819744	+	0.572731i	$0.805884\pi$
$594$	8.65613e16	+	1.49929e17i	0.0808559	+	0.140047i
$595$	5.35236e17	−	9.27056e17i	0.494521	−	0.856536i
$596$	3.95151e17	−	6.84421e17i	0.361129	−	0.625493i
$597$	−1.37091e18			−1.23930
$598$	−1.07742e17	+	2.91767e17i	−0.0963447	+	0.260903i
$599$	8.77681e16			0.0776358			0.0388179	−	0.999246i	$-0.487641\pi$
$599$	8.77681e16			0.0776358			0.0388179	+	0.999246i	$0.487641\pi$
$600$	1.75531e17	−	3.04029e17i	0.153593	−	0.266030i
$601$	7.27989e17	−	1.26091e18i	0.630145	−	1.09144i	−0.357376	−	0.933960i	$-0.616329\pi$
$601$	7.27989e17	−	1.26091e18i	0.630145	−	1.09144i	0.987522	−	0.157483i	$-0.0503380\pi$
$602$	3.10539e17	+	5.37869e17i	0.265913	+	0.460574i
$603$	−6.30130e17			−0.533786
$604$	1.18362e16	+	2.05010e16i	0.00991913	+	0.0171804i
$605$	−1.38456e17	−	2.39812e17i	−0.114789	−	0.198821i
$606$	9.59424e17			0.786935
$607$	7.02879e17	+	1.21742e18i	0.570367	+	0.987904i	0.996528	+	0.0832572i	$0.0265323\pi$
$607$	7.02879e17	+	1.21742e18i	0.570367	+	0.987904i	−0.426161	+	0.904647i	$0.640134\pi$
$608$	9.07033e17	−	1.57103e18i	0.728199	−	1.26128i
$609$	3.40077e17	−	5.89031e17i	0.270125	−	0.467871i
$610$	−6.09603e17			−0.479075
$611$	2.05402e17	+	2.47126e17i	0.159712	+	0.192154i
$612$	7.17515e17			0.552010
$613$	1.35703e17	−	2.35044e17i	0.103299	−	0.178919i	−0.809743	−	0.586785i	$-0.800394\pi$
$613$	1.35703e17	−	2.35044e17i	0.103299	−	0.178919i	0.913042	+	0.407866i	$0.133727\pi$
$614$	1.80272e17	−	3.12241e17i	0.135780	−	0.235177i
$615$	−4.89473e17	−	8.47792e17i	−0.364788	−	0.631832i
$616$	−9.11368e17			−0.672077
$617$	−1.17461e18	−	2.03449e18i	−0.857118	−	1.48457i	−0.874667	−	0.484725i	$-0.838920\pi$
$617$	−1.17461e18	−	2.03449e18i	−0.857118	−	1.48457i	0.0175489	−	0.999846i	$-0.494414\pi$
$618$	5.54719e17	+	9.60802e17i	0.400542	+	0.693759i
$619$	1.31985e18			0.943054			0.471527	−	0.881852i	$-0.343703\pi$
$619$	1.31985e18			0.943054			0.471527	+	0.881852i	$0.343703\pi$
$620$	−3.15345e17	−	5.46194e17i	−0.222967	−	0.386190i
$621$	2.69596e17	−	4.66955e17i	0.188633	−	0.326723i
$622$	4.75306e17	−	8.23255e17i	0.329106	−	0.570029i
$623$	−2.30609e18			−1.58017
$624$	−3.85465e17	+	1.04384e18i	−0.261388	+	0.707841i
$625$	−7.90348e17			−0.530393
$626$	−1.44332e16	+	2.49990e16i	−0.00958581	+	0.0166031i
$627$	1.28451e18	−	2.22484e18i	0.844303	−	1.46238i
$628$	5.72871e17	+	9.92241e17i	0.372665	+	0.645475i
$629$	−1.98026e18			−1.27495
$630$	−1.61624e17	−	2.79940e17i	−0.102989	−	0.178382i
$631$	2.49506e17	+	4.32156e17i	0.157358	+	0.272552i	0.933915	−	0.357495i	$-0.116369\pi$
$631$	2.49506e17	+	4.32156e17i	0.157358	+	0.272552i	−0.776557	+	0.630047i	$0.783036\pi$
$632$	−6.95512e17			−0.434154
$633$	5.02628e17	+	8.70576e17i	0.310543	+	0.537877i
$634$	−4.06419e17	+	7.03939e17i	−0.248539	+	0.430482i
$635$	−6.38715e17	+	1.10629e18i	−0.386614	+	0.669636i
$636$	−2.21746e18			−1.32857
$637$	−4.91780e17	+	8.43452e16i	−0.291652	+	0.0500212i
$638$	2.03150e17			0.119257
$639$	8.35734e17	−	1.44753e18i	0.485638	−	0.841149i
$640$	−7.13124e17	+	1.23517e18i	−0.410200	+	0.710486i
$641$	8.30605e17	+	1.43865e18i	0.472953	+	0.819178i	0.999521	−	0.0309550i	$-0.00985486\pi$
$641$	8.30605e17	+	1.43865e18i	0.472953	+	0.819178i	−0.526568	+	0.850133i	$0.676522\pi$
$642$	3.99040e17			0.224926
$643$	1.19813e17	+	2.07522e17i	0.0668548	+	0.115796i	0.897515	−	0.440983i	$-0.145370\pi$
$643$	1.19813e17	+	2.07522e17i	0.0668548	+	0.115796i	−0.830660	+	0.556779i	$0.812037\pi$
$644$	6.55826e17	+	1.13592e18i	0.362268	+	0.627467i
$645$	2.32172e18			1.26961
$646$	−5.89397e17	−	1.02086e18i	−0.319078	−	0.552658i
$647$	3.40869e17	−	5.90402e17i	0.182688	−	0.316424i	−0.760107	−	0.649798i	$-0.774854\pi$
$647$	3.40869e17	−	5.90402e17i	0.182688	−	0.316424i	0.942795	+	0.333373i	$0.108187\pi$
$648$	−8.15876e17	+	1.41314e18i	−0.432899	+	0.749804i
$649$	−7.23187e17			−0.379892
$650$	2.47791e17	−	4.24986e16i	0.128869	−	0.0221023i
$651$	1.79655e18			0.925044
$652$	−4.99111e17	+	8.64486e17i	−0.254442	+	0.440706i
$653$	−1.95396e17	+	3.38436e17i	−0.0986235	+	0.170821i	−0.911115	−	0.412152i	$-0.864777\pi$
$653$	−1.95396e17	+	3.38436e17i	−0.0986235	+	0.170821i	0.812492	+	0.582973i	$0.198111\pi$
$654$	−8.33957e16	−	1.44446e17i	−0.0416762	−	0.0721853i
$655$	2.65504e18			1.31372
$656$	−4.35778e17	−	7.54790e17i	−0.213496	−	0.369786i
$657$	6.33833e17	+	1.09783e18i	0.307468	+	0.532550i
$658$	−2.22306e17			−0.106778
$659$	4.29484e17	+	7.43889e17i	0.204264	+	0.353796i	0.949898	−	0.312560i	$-0.101187\pi$
$659$	4.29484e17	+	7.43889e17i	0.204264	+	0.353796i	−0.745634	+	0.666356i	$0.767853\pi$
$660$	−7.87156e17	+	1.36339e18i	−0.370702	+	0.642076i
$661$	1.23396e17	−	2.13729e17i	0.0575431	−	0.0996676i	−0.835819	−	0.549005i	$-0.815007\pi$
$661$	1.23396e17	−	2.13729e17i	0.0575431	−	0.0996676i	0.893362	+	0.449338i	$0.148340\pi$
$662$	6.72750e17			0.310654
$663$	1.90124e18	+	2.28744e18i	0.869357	+	1.04595i
$664$	−1.28949e18			−0.583881
$665$	1.61865e18	−	2.80358e18i	0.725790	−	1.25711i
$666$	−2.98987e17	+	5.17861e17i	−0.132761	+	0.229948i
$667$	−3.16357e17	−	5.47947e17i	−0.139110	−	0.240946i
$668$	3.09475e18			1.34765
$669$	3.33851e17	+	5.78247e17i	0.143974	+	0.249370i
$670$	−3.17198e17	−	5.49403e17i	−0.135470	−	0.234641i
$671$	−3.16169e18			−1.33728
$672$	−1.58332e18	−	2.74239e18i	−0.663237	−	1.14876i
$673$	1.53058e18	−	2.65104e18i	0.634976	−	1.09981i	−0.351544	−	0.936171i	$-0.614343\pi$
$673$	1.53058e18	−	2.65104e18i	0.634976	−	1.09981i	0.986520	−	0.163640i	$-0.0523235\pi$
$674$	−6.58004e17	+	1.13970e18i	−0.270358	+	0.468274i
$675$	−4.35843e17			−0.177360
$676$	−2.00968e18	+	7.10252e17i	−0.809978	+	0.286259i
$677$	1.84266e18			0.735561			0.367780	−	0.929913i	$-0.380118\pi$
$677$	1.84266e18			0.735561			0.367780	+	0.929913i	$0.380118\pi$
$678$	−8.39948e16	+	1.45483e17i	−0.0332093	+	0.0575202i
$679$	1.20462e17	−	2.08647e17i	0.0471735	−	0.0817069i
$680$	7.81623e17	+	1.35381e18i	0.303172	+	0.525110i
$681$	−6.12342e17			−0.235254
$682$	2.68299e17	+	4.64707e17i	0.102099	+	0.176840i
$683$	1.25389e17	+	2.17180e17i	0.0472633	+	0.0818624i	0.888689	−	0.458510i	$-0.151617\pi$
$683$	1.25389e17	+	2.17180e17i	0.0472633	+	0.0818624i	−0.841426	+	0.540372i	$0.818283\pi$
$684$	2.16989e18			0.810164
$685$	3.42200e17	+	5.92707e17i	0.126558	+	0.219206i
$686$	−4.10665e17	+	7.11292e17i	−0.150446	+	0.260580i
$687$	7.21433e16	−	1.24956e17i	0.0261805	−	0.0453459i
$688$	2.06702e18			0.743055
$689$	−2.19662e18	−	2.64283e18i	−0.782223	−	0.941119i
$690$	−8.04343e17			−0.283741
$691$	9.57527e14	−	1.65848e15i	0.000334614	−	0.000579568i	−0.865858	−	0.500290i	$-0.833227\pi$
$691$	9.57527e14	−	1.65848e15i	0.000334614	−	0.000579568i	0.866193	+	0.499710i	$0.166560\pi$
$692$	−7.36046e17	+	1.27487e18i	−0.254809	+	0.441343i
$693$	−8.38257e17	−	1.45190e18i	−0.287482	−	0.497934i
$694$	1.18381e18			0.402204
$695$	1.05291e17	+	1.82370e17i	0.0354398	+	0.0613836i
$696$	4.96626e17	+	8.60182e17i	0.165604	+	0.286834i
$697$	−2.32971e18			−0.769641
$698$	−8.48011e16	−	1.46880e17i	−0.0277550	−	0.0480731i
$699$	−2.52091e18	+	4.36635e18i	−0.817441	+	1.41585i
$700$	5.30120e17	−	9.18195e17i	0.170309	−	0.294984i
$701$	−4.81575e17			−0.153284			−0.0766421	−	0.997059i	$-0.524420\pi$
$701$	−4.81575e17			−0.153284			−0.0766421	+	0.997059i	$0.524420\pi$
$702$	−5.97445e17	+	1.02468e17i	−0.188411	+	0.0323144i
$703$	−5.98865e18			−1.87120
$704$	−3.42858e17	+	5.93848e17i	−0.106143	+	0.183845i
$705$	−4.15513e17	+	7.19690e17i	−0.127455	+	0.220758i
$706$	1.55645e17	+	2.69585e17i	0.0473047	+	0.0819341i
$707$	6.27043e18			1.88830
$708$	−8.16953e17	−	1.41500e18i	−0.243770	−	0.422222i
$709$	−4.36098e17	−	7.55344e17i	−0.128939	−	0.223329i	0.794327	−	0.607491i	$-0.207824\pi$
$709$	−4.36098e17	−	7.55344e17i	−0.128939	−	0.223329i	−0.923266	+	0.384162i	$0.874490\pi$
$710$	1.68278e18			0.493002
$711$	−6.39716e17	−	1.10802e18i	−0.185710	−	0.321659i
$712$	1.68383e18	−	2.91648e18i	0.484371	−	0.838955i
$713$	8.35620e17	−	1.44734e18i	0.238192	−	0.412560i
$714$	−2.05771e18			−0.581226
$715$	−2.40469e18	+	4.12428e17i	−0.673084	+	0.115441i
$716$	2.37754e18			0.659466
$717$	1.27632e18	−	2.21064e18i	0.350819	−	0.607637i
$718$	8.64447e17	−	1.49727e18i	0.235467	−	0.407840i
$719$	−3.01319e18	−	5.21900e18i	−0.813371	−	1.40880i	−0.910492	−	0.413528i	$-0.864297\pi$
$719$	−3.01319e18	−	5.21900e18i	−0.813371	−	1.40880i	0.0971204	−	0.995273i	$-0.469037\pi$
$720$	−1.07581e18			−0.287788
$721$	3.62543e18	+	6.27943e18i	0.961127	+	1.66472i
$722$	−1.06801e18	−	1.84985e18i	−0.280598	−	0.486009i
$723$	−5.08536e18			−1.32411
$724$	2.42815e17	+	4.20568e17i	0.0626577	+	0.108526i
$725$	−2.55720e17	+	4.42919e17i	−0.0653984	+	0.113273i
$726$	−2.66145e17	+	4.60977e17i	−0.0674576	+	0.116840i
$727$	1.62464e18			0.408116			0.204058	−	0.978959i	$-0.434587\pi$
$727$	1.62464e18			0.408116			0.204058	+	0.978959i	$0.434587\pi$
$728$	1.10541e18	−	2.99347e18i	0.275214	−	0.745282i
$729$	−3.93775e17			−0.0971670
$730$	−6.38124e17	+	1.10526e18i	−0.156065	+	0.270313i
$731$	2.76262e18	−	4.78500e18i	0.669667	−	1.15990i
$732$	−3.57162e18	−	6.18623e18i	−0.858111	−	1.48629i
$733$	−7.33094e16			−0.0174576			−0.00872878	−	0.999962i	$-0.502778\pi$
$733$	−7.33094e16			−0.0174576			−0.00872878	+	0.999962i	$0.502778\pi$
$734$	7.66523e16	+	1.32766e17i	0.0180926	+	0.0313373i
$735$	−6.45183e17	−	1.11749e18i	−0.150944	−	0.261442i
$736$	−2.94577e18			−0.683114
$737$	−1.64514e18	−	2.84946e18i	−0.378150	−	0.654974i
$738$	−3.51747e17	+	6.09244e17i	−0.0801428	+	0.138811i
$739$	−1.98549e18	+	3.43897e18i	−0.448414	+	0.776676i	−0.998283	−	0.0585750i	$-0.981344\pi$
$739$	−1.98549e18	+	3.43897e18i	−0.448414	+	0.776676i	0.549869	+	0.835251i	$0.314678\pi$
$740$	3.66989e18			0.821574
$741$	5.74967e18	+	6.91762e18i	1.27592	+	1.53511i
$742$	2.37740e18			0.522971
$743$	−2.64547e18	+	4.58208e18i	−0.576866	+	0.999162i	0.418970	+	0.908000i	$0.362391\pi$
$743$	−2.64547e18	+	4.58208e18i	−0.576866	+	0.999162i	−0.995836	+	0.0911615i	$0.970942\pi$
$744$	−1.31178e18	+	2.27207e18i	−0.283555	+	0.491131i
$745$	1.58370e18	+	2.74304e18i	0.339357	+	0.587783i
$746$	1.20726e18			0.256448
$747$	−1.18604e18	−	2.05428e18i	−0.249756	−	0.432590i
$748$	1.87328e18	+	3.24462e18i	0.391060	+	0.677335i
$749$	2.60797e18			0.539724
$750$	1.25844e18	+	2.17969e18i	0.258188	+	0.447194i
$751$	9.53194e16	−	1.65098e17i	0.0193875	−	0.0335801i	−0.856169	−	0.516696i	$-0.827162\pi$
$751$	9.53194e16	−	1.65098e17i	0.0193875	−	0.0335801i	0.875556	+	0.483116i	$0.160495\pi$
$752$	−3.69931e17	+	6.40740e17i	−0.0745942	+	0.129201i
$753$	1.08105e19			2.16112
$754$	−2.46404e17	+	6.67265e17i	−0.0488353	+	0.132247i
$755$	−9.48753e16			−0.0186422
$756$	−1.27816e18	+	2.21384e18i	−0.248997	+	0.431276i
$757$	−4.71418e18	+	8.16521e18i	−0.910507	+	1.57704i	−0.0971578	+	0.995269i	$0.530975\pi$
$757$	−4.71418e18	+	8.16521e18i	−0.910507	+	1.57704i	−0.813349	+	0.581776i	$0.802358\pi$
$758$	−1.31826e18	−	2.28329e18i	−0.252436	−	0.437232i
$759$	−4.17170e18			−0.792030
$760$	2.36376e18	+	4.09416e18i	0.444954	+	0.770684i
$761$	−1.15879e18	−	2.00708e18i	−0.216274	−	0.374597i	0.737392	−	0.675465i	$-0.236057\pi$
$761$	−1.15879e18	−	2.00708e18i	−0.216274	−	0.374597i	−0.953666	+	0.300868i	$0.902724\pi$
$762$	2.45553e18			0.454399
$763$	−5.45042e17	−	9.44041e17i	−0.100005	−	0.173213i
$764$	3.93303e18	−	6.81220e18i	0.715517	−	1.23931i
$765$	−1.43784e18	+	2.49041e18i	−0.259365	+	0.449233i
$766$	1.11731e18			0.199842
$767$	8.77164e17	−	2.37537e18i	0.155565	−	0.421271i
$768$	9.38203e17			0.164987
$769$	2.34947e18	−	4.06940e18i	0.409684	−	0.709594i	−0.585170	−	0.810911i	$-0.698972\pi$
$769$	2.34947e18	−	4.06940e18i	0.409684	−	0.709594i	0.994854	+	0.101317i	$0.0323056\pi$
$770$	8.43932e17	−	1.46173e18i	0.145921	−	0.252742i
$771$	4.39547e18	+	7.61318e18i	0.753619	+	1.30531i
$772$	−9.01410e18			−1.53253
$773$	−1.03214e16	−	1.78773e16i	−0.00174010	−	0.00301394i	0.865154	−	0.501506i	$-0.167221\pi$
$773$	−1.03214e16	−	1.78773e16i	−0.00174010	−	0.00301394i	−0.866894	+	0.498492i	$0.833887\pi$
$774$	−8.34221e17	−	1.44491e18i	−0.139465	−	0.241560i
$775$	−1.35091e18			−0.223957
$776$	1.75915e17	+	3.04694e17i	0.0289203	+	0.0500914i
$777$	−5.22691e18	+	9.05327e18i	−0.852135	+	1.47594i
$778$	−7.76805e17	+	1.34547e18i	−0.125587	+	0.217523i
$779$	−7.04544e18			−1.12957
$780$	−3.52344e18	−	4.23916e18i	−0.560211	−	0.674008i
$781$	8.72771e18			1.37616
$782$	−9.57092e17	+	1.65773e18i	−0.149661	+	0.259221i
$783$	6.16561e17	−	1.06792e18i	0.0956147	−	0.165609i
$784$	−5.74406e17	−	9.94901e17i	−0.0883415	−	0.153012i
$785$	−4.59194e18			−0.700395
$786$	−2.55181e18	−	4.41987e18i	−0.386013	−	0.668594i
$787$	−3.62694e18	−	6.28205e18i	−0.544133	−	0.942466i	−0.998661	−	0.0517332i	$-0.983525\pi$
$787$	−3.62694e18	−	6.28205e18i	−0.544133	−	0.942466i	0.454528	−	0.890732i	$-0.349808\pi$
$788$	9.63415e18			1.43348
$789$	5.33452e18	+	9.23966e18i	0.787217	+	1.36350i
$790$	6.44047e17	−	1.11552e18i	0.0942631	−	0.163268i
$791$	−5.48958e17	+	9.50823e17i	−0.0796878	+	0.138023i
$792$	2.44827e18			0.352489
$793$	3.83486e18	−	1.03848e19i	0.547613	−	1.48294i
$794$	3.29317e18			0.466424
$795$	4.44361e18	−	7.69656e18i	0.624237	−	1.08121i
$796$	3.02310e18	−	5.23616e18i	0.421228	−	0.729589i
$797$	3.56000e18	+	6.16610e18i	0.492007	+	0.852181i	0.999958	−	0.00920520i	$-0.00293015\pi$
$797$	3.56000e18	+	6.16610e18i	0.492007	+	0.852181i	−0.507951	+	0.861386i	$0.669597\pi$
$798$	−6.22286e18			−0.853043
$799$	9.88842e17	+	1.71273e18i	0.134454	+	0.232881i
$800$	1.19057e18	+	2.06213e18i	0.160572	+	0.278119i
$801$	6.19499e18			0.828761
$802$	−1.80510e17	−	3.12652e17i	−0.0239534	−	0.0414886i
$803$	−3.30961e18	+	5.73242e18i	−0.435638	+	0.754548i
$804$	3.71688e18	−	6.43783e18i	0.485305	−	0.840572i
$805$	−5.25688e18			−0.680855
$806$	−1.85179e18	+	3.17601e17i	−0.237911	+	0.0408041i
$807$	−1.59547e19			−2.03334
$808$	−4.57846e18	+	7.93013e18i	−0.578823	+	1.00255i
$809$	1.33062e18	−	2.30470e18i	0.166874	−	0.289034i	−0.770445	−	0.637506i	$-0.779966\pi$
$809$	1.33062e18	−	2.30470e18i	0.166874	−	0.289034i	0.937319	+	0.348472i	$0.113299\pi$
$810$	−1.51101e18	−	2.61715e18i	−0.187982	−	0.325594i
$811$	−1.00968e19			−1.24609			−0.623044	−	0.782187i	$-0.714104\pi$
$811$	−1.00968e19			−1.24609			−0.623044	+	0.782187i	$0.714104\pi$
$812$	1.49986e18	+	2.59783e18i	0.183627	+	0.318051i
$813$	−6.73435e18	−	1.16642e19i	−0.817913	−	1.41667i
$814$	−3.12237e18			−0.376206
$815$	−2.00035e18	−	3.46472e18i	−0.239102	−	0.414136i
$816$	−3.42415e18	+	5.93080e18i	−0.406038	+	0.703279i
$817$	8.35465e18	−	1.44707e19i	0.982845	−	1.70234i
$818$	−9.69426e17			−0.113141
$819$	5.78564e18	−	9.92294e17i	0.669893	−	0.114893i
$820$	4.31749e18			0.495954
$821$	−4.96368e18	+	8.59735e18i	−0.565684	+	0.979793i	0.431302	+	0.902208i	$0.358054\pi$
$821$	−4.96368e18	+	8.59735e18i	−0.565684	+	0.979793i	−0.996986	+	0.0775852i	$0.975279\pi$
$822$	6.57790e17	−	1.13933e18i	0.0743739	−	0.128819i
$823$	2.26374e18	+	3.92092e18i	0.253938	+	0.439834i	0.964607	−	0.263693i	$-0.0849406\pi$
$823$	2.26374e18	+	3.92092e18i	0.253938	+	0.439834i	−0.710668	+	0.703527i	$0.751607\pi$
$824$	−1.05887e19			−1.17846
$825$	1.68605e18	+	2.92032e18i	0.186174	+	0.322463i
$826$	8.75877e17	+	1.51706e18i	0.0959562	+	0.166201i
$827$	−1.50983e19			−1.64113			−0.820564	−	0.571555i	$-0.806340\pi$
$827$	−1.50983e19			−1.64113			−0.820564	+	0.571555i	$0.806340\pi$
$828$	−1.76179e18	−	3.05150e18i	−0.190001	−	0.329092i
$829$	6.63157e18	−	1.14862e19i	0.709597	−	1.22906i	−0.255410	−	0.966833i	$-0.582210\pi$
$829$	6.63157e18	−	1.14862e19i	0.709597	−	1.22906i	0.965007	−	0.262225i	$-0.0844563\pi$
$830$	1.19407e18	−	2.06819e18i	0.126772	−	0.219575i
$831$	2.25547e19			2.37591
$832$	−1.53469e18	−	1.84643e18i	−0.160405	−	0.192989i
$833$	−3.07083e18			−0.318466
$834$	2.02396e17	−	3.50559e17i	0.0208268	−	0.0360730i
$835$	−6.20161e18	+	1.07415e19i	−0.633202	+	1.09674i
$836$	5.66513e18	+	9.81230e18i	0.573944	+	0.994099i
$837$	3.25714e18			0.327432
$838$	−1.32816e18	−	2.30044e18i	−0.132484	−	0.229469i
$839$	−3.72075e18	−	6.44452e18i	−0.368279	−	0.637878i	0.621017	−	0.783797i	$-0.286720\pi$
$839$	−3.72075e18	−	6.44452e18i	−0.368279	−	0.637878i	−0.989297	+	0.145918i	$0.953386\pi$
$840$	8.25239e18			0.810521
$841$	4.40681e18	+	7.63282e18i	0.429488	+	0.743894i
$842$	−1.07802e17	+	1.86718e17i	−0.0104255	+	0.0180575i
$843$	5.30753e18	−	9.19290e18i	0.509346	−	0.882213i
$844$	−4.43352e18			−0.422205
$845$	1.56202e18	−	8.39865e18i	0.147611	−	0.793672i
$846$	5.97196e17			0.0560027
$847$	−1.73942e18	+	3.01277e18i	−0.161869	+	0.280365i
$848$	3.95615e18	−	6.85225e18i	0.365342	−	0.632790i
$849$	−8.33395e18	−	1.44348e19i	−0.763749	−	1.32285i
$850$	1.54728e18			0.140717
$851$	4.86234e18	+	8.42181e18i	0.438837	+	0.760087i
$852$	9.85931e18	+	1.70768e19i	0.883058	+	1.52950i
$853$	−2.21083e18			−0.196511			−0.0982554	−	0.995161i	$-0.531326\pi$
$853$	−2.21083e18			−0.196511			−0.0982554	+	0.995161i	$0.531326\pi$
$854$	3.82923e18	+	6.63243e18i	0.337781	+	0.585054i
$855$	−4.34827e18	+	7.53143e18i	−0.380660	+	0.659322i
$856$	−1.90426e18	+	3.29827e18i	−0.165442	+	0.286554i
$857$	−4.25774e18			−0.367117			−0.183558	−	0.983009i	$-0.558762\pi$
$857$	−4.25774e18			−0.367117			−0.183558	+	0.983009i	$0.558762\pi$
$858$	2.99777e18	+	3.60672e18i	0.256526	+	0.308635i
$859$	5.49014e18			0.466260			0.233130	−	0.972446i	$-0.425103\pi$
$859$	5.49014e18			0.466260			0.233130	+	0.972446i	$0.425103\pi$
$860$	−5.11979e18	+	8.86773e18i	−0.431531	+	0.747434i
$861$	−6.14927e18	+	1.06508e19i	−0.514403	+	0.890971i
$862$	−2.28838e17	−	3.96359e17i	−0.0189990	−	0.0329073i
$863$	1.00892e19			0.831352			0.415676	−	0.909513i	$-0.363545\pi$
$863$	1.00892e19			0.831352			0.415676	+	0.909513i	$0.363545\pi$
$864$	−2.87056e18	−	4.97196e18i	−0.234762	−	0.406620i
$865$	−2.94995e18	−	5.10946e18i	−0.239447	−	0.414735i
$866$	3.25048e17			0.0261868
$867$	1.25059e18	+	2.16609e18i	0.0999983	+	0.173202i
$868$	−3.96170e18	+	6.86186e18i	−0.314415	+	0.544583i
$869$	3.34033e18	−	5.78563e18i	0.263125	−	0.455745i
$870$	−1.83951e18			−0.143823
$871$	1.13547e19	−	1.94745e18i	0.881167	−	0.151129i
$872$	1.59189e18			0.122618
$873$	−3.23606e17	+	5.60502e17i	−0.0247414	+	0.0428534i
$874$	−2.89441e18	+	5.01327e18i	−0.219652	+	0.380449i
$875$	8.22470e18	+	1.42456e19i	0.619538	+	1.07307i
$876$	−1.49549e19			−1.11817
$877$	−6.61231e17	−	1.14528e18i	−0.0490745	−	0.0849995i	0.840445	−	0.541897i	$-0.182294\pi$
$877$	−6.61231e17	−	1.14528e18i	−0.0490745	−	0.0849995i	−0.889519	+	0.456898i	$0.848960\pi$
$878$	−3.51161e18	−	6.08228e18i	−0.258697	−	0.448077i
$879$	1.02503e19			0.749564
$880$	−2.80871e18	−	4.86483e18i	−0.203878	−	0.353126i
$881$	−1.09217e19	+	1.89169e19i	−0.786947	+	1.36303i	0.140883	+	0.990026i	$0.455006\pi$
$881$	−1.09217e19	+	1.89169e19i	−0.786947	+	1.36303i	−0.927829	+	0.373005i	$0.878327\pi$
$882$	−4.63644e17	+	8.03055e17i	−0.0331619	+	0.0574381i
$883$	1.53200e19			1.08772			0.543858	−	0.839177i	$-0.316963\pi$
$883$	1.53200e19			1.08772			0.543858	+	0.839177i	$0.316963\pi$
$884$	−1.29294e19	+	2.21752e18i	−0.911250	+	0.156288i
$885$	6.54842e18			0.458147
$886$	3.24596e17	−	5.62217e17i	0.0225437	−	0.0390468i
$887$	−3.30049e18	+	5.71662e18i	−0.227549	+	0.394127i	−0.957081	−	0.289820i	$-0.906405\pi$
$887$	−3.30049e18	+	5.71662e18i	−0.227549	+	0.394127i	0.729532	+	0.683947i	$0.239738\pi$
$888$	−7.63303e18	−	1.32208e19i	−0.522411	−	0.904843i
$889$	1.60484e19			1.09036
$890$	3.11847e18	+	5.40134e18i	0.210332	+	0.364306i
$891$	−7.83682e18	−	1.35738e19i	−0.524729	−	0.908857i
$892$	−2.94480e18			−0.195742
$893$	2.99043e18	+	5.17958e18i	0.197333	+	0.341790i
$894$	3.04425e18	−	5.27279e18i	0.199428	−	0.345419i
$895$	−4.76438e18	+	8.25215e18i	−0.309854	+	0.536682i
$896$	1.79180e19			1.15688
$897$	5.05991e18	−	1.37023e19i	0.324334	−	0.878300i
$898$	8.02996e18			0.510996
$899$	1.91104e18	−	3.31003e18i	0.120735	−	0.209119i
$900$	−1.42410e18	+	2.46661e18i	−0.0893230	+	0.154712i
$901$	−1.05749e19	−	1.83164e19i	−0.658517	−	1.14059i
$902$	−3.67336e18			−0.227102
$903$	−1.45839e19	−	2.52601e19i	−0.895166	−	1.55047i
$904$	−8.01662e17	−	1.38852e18i	−0.0488536	−	0.0846169i
$905$	−1.94632e18			−0.117760
$906$	9.11866e16	+	1.57940e17i	0.00547769	+	0.00948764i
$907$	8.49776e18	−	1.47186e19i	0.506824	−	0.877845i	−0.493145	−	0.869947i	$-0.664153\pi$
$907$	8.49776e18	−	1.47186e19i	0.506824	−	0.877845i	0.999969	−	0.00789756i	$-0.00251390\pi$
$908$	1.35032e18	−	2.33882e18i	0.0799611	−	0.138497i
$909$	−1.68447e19			−0.990370
$910$	3.77757e18	+	4.54492e18i	0.220518	+	0.265312i
$911$	−1.07698e19			−0.624223			−0.312112	−	0.950045i	$-0.601036\pi$
$911$	−1.07698e19			−0.624223			−0.312112	+	0.950045i	$0.601036\pi$
$912$	−1.03552e19	+	1.79358e19i	−0.595927	+	1.03218i
$913$	6.19302e18	−	1.07266e19i	0.353869	−	0.612919i
$914$	−2.78918e18	−	4.83100e18i	−0.158243	−	0.274086i
$915$	2.86289e19			1.61275
$916$	3.18177e17	+	5.51099e17i	0.0177971	+	0.0308254i
$917$	−1.66777e19	−	2.88866e19i	−0.926264	−	1.60434i
$918$	−3.73063e18			−0.205733
$919$	−1.19441e18	−	2.06877e18i	−0.0654035	−	0.113282i	0.831469	−	0.555571i	$-0.187500\pi$
$919$	−1.19441e18	−	2.06877e18i	−0.0654035	−	0.113282i	−0.896873	+	0.442288i	$0.854167\pi$
$920$	3.83840e18	−	6.64830e18i	0.208703	−	0.361484i
$921$	−8.46616e18	+	1.46638e19i	−0.457087	+	0.791698i
$922$	8.09883e18			0.434181
$923$	−1.05860e19	+	2.86669e19i	−0.563533	+	1.52605i
$924$	1.97782e19			1.04549
$925$	3.93035e18	−	6.80757e18i	0.206305	−	0.357331i
$926$	−7.59729e17	+	1.31589e18i	−0.0395993	+	0.0685879i
$927$	−9.73924e18	−	1.68689e19i	−0.504088	−	0.873107i
$928$	−6.73692e18			−0.346258
$929$	1.31033e19	+	2.26955e19i	0.668771	+	1.15835i	0.978248	+	0.207439i	$0.0665128\pi$
$929$	1.31033e19	+	2.26955e19i	0.668771	+	1.15835i	−0.309477	+	0.950907i	$0.600154\pi$
$930$	−2.42943e18	−	4.20789e18i	−0.123130	−	0.213268i
$931$	−9.28671e18			−0.467400
$932$	−1.11181e19	−	1.92571e19i	−0.555683	−	0.962471i
$933$	−2.23219e19	+	3.86627e19i	−1.10790	+	1.91894i
$934$	−4.82417e18	+	8.35571e18i	−0.237776	+	0.411840i
$935$	−1.50156e19			−0.734966
$936$	−2.96954e18	+	8.04155e18i	−0.144343	+	0.390883i
$937$	−1.48285e19			−0.715799			−0.357899	−	0.933760i	$-0.616507\pi$
$937$	−1.48285e19			−0.715799			−0.357899	+	0.933760i	$0.616507\pi$
$938$	−3.98497e18	+	6.90217e18i	−0.191032	+	0.330877i
$939$	6.77829e17	−	1.17403e18i	0.0322696	−	0.0558926i
$940$	−1.83256e18	−	3.17408e18i	−0.0866416	−	0.150068i
$941$	1.63127e19			0.765938			0.382969	−	0.923761i	$-0.374902\pi$
$941$	1.63127e19			0.765938			0.382969	+	0.923761i	$0.374902\pi$
$942$	4.41341e18	+	7.64425e18i	0.205799	+	0.356454i
$943$	5.72037e18	+	9.90796e18i	0.264910	+	0.458837i
$944$	5.83006e18			0.268136
$945$	−5.12267e18	−	8.87272e18i	−0.233986	−	0.405275i
$946$	4.35596e18	−	7.54474e18i	0.197602	−	0.342257i
$947$	−6.61395e18	+	1.14557e19i	−0.297979	+	0.516115i	−0.975674	−	0.219229i	$-0.929646\pi$
$947$	−6.61395e18	+	1.14557e19i	−0.297979	+	0.516115i	0.677694	+	0.735344i	$0.262979\pi$
$948$	1.50937e19			0.675370
$949$	−1.48144e19	−	1.78236e19i	−0.658343	−	0.792075i
$950$	4.67925e18			0.206525
$951$	1.90868e19	−	3.30592e19i	0.836679	−	1.44917i
$952$	9.81956e18	−	1.70080e19i	0.427515	−	0.740479i
$953$	6.18123e18	+	1.07062e19i	0.267283	+	0.462948i	0.968159	−	0.250335i	$-0.0805408\pi$
$953$	6.18123e18	+	1.07062e19i	0.267283	+	0.462948i	−0.700876	+	0.713283i	$0.747208\pi$
$954$	−6.38657e18			−0.274286
$955$	1.57629e19	+	2.73022e19i	0.672379	+	1.16460i
$956$	5.62899e18	+	9.74970e18i	0.238481	+	0.413062i
$957$	−9.54059e18			−0.401465
$958$	−7.30290e17	−	1.26490e18i	−0.0305225	−	0.0528665i
$959$	4.29907e18	−	7.44620e18i	0.178465	−	0.309111i
$960$	3.10456e18	−	5.37725e18i	0.128008	−	0.221716i
$961$	−1.43220e19			−0.586544
$962$	3.78717e18	−	1.02557e19i	0.154055	−	0.417184i
$963$	−7.00597e18			−0.283072
$964$	1.12141e19	−	1.94234e19i	0.450053	−	0.779515i
$965$	1.80635e19	−	3.12869e19i	0.720069	−	1.24720i
$966$	5.05249e18	+	8.75118e18i	0.200057	+	0.346509i
$967$	2.63801e18			0.103754			0.0518770	−	0.998653i	$-0.483480\pi$
$967$	2.63801e18			0.103754			0.0518770	+	0.998653i	$0.483480\pi$
$968$	−2.54014e18	−	4.39965e18i	−0.0992356	−	0.171881i
$969$	2.76800e19	+	4.79431e19i	1.07414	+	1.86046i
$970$	−6.51594e17			−0.0251166
$971$	1.63228e19	+	2.82720e19i	0.624986	+	1.08251i	0.988544	+	0.150936i	$0.0482288\pi$
$971$	1.63228e19	+	2.82720e19i	0.624986	+	1.08251i	−0.363557	+	0.931572i	$0.618438\pi$
$972$	1.19549e19	−	2.07065e19i	0.454690	−	0.787546i
$973$	1.32278e18	−	2.29112e18i	0.0499752	−	0.0865595i
$974$	−1.26833e19			−0.475991
$975$	−1.16371e19	+	1.99587e18i	−0.433824	+	0.0744051i
$976$	2.54883e19			0.943882
$977$	3.83774e18	−	6.64717e18i	0.141176	−	0.244524i	−0.786764	−	0.617254i	$-0.788245\pi$
$977$	3.83774e18	−	6.64717e18i	0.141176	−	0.244524i	0.927940	+	0.372730i	$0.121578\pi$
$978$	−3.84516e18	+	6.66002e18i	−0.140512	+	0.243373i
$979$	1.61738e19	+	2.80139e19i	0.587119	+	1.01692i
$980$	5.69096e18			0.205218
$981$	1.46418e18	+	2.53604e18i	0.0524502	+	0.0908463i
$982$	5.20485e18	+	9.01507e18i	0.185218	+	0.320807i
$983$	−5.57748e18			−0.197170			−0.0985848	−	0.995129i	$-0.531432\pi$
$983$	−5.57748e18			−0.197170			−0.0985848	+	0.995129i	$0.531432\pi$
$984$	−8.97999e18	−	1.55538e19i	−0.315361	−	0.546221i
$985$	−1.93060e19	+	3.34390e19i	−0.673531	+	1.16659i
$986$	−2.18885e18	+	3.79120e18i	−0.0758605	+	0.131394i
$987$	1.04402e19			0.359458
$988$	−3.91007e19	+	6.70615e18i	−1.33741	+	0.229379i
$989$	−2.71334e19			−0.921994
$990$	−2.26711e18	+	3.92675e18i	−0.0765321	+	0.132558i
$991$	5.66096e18	−	9.80507e18i	0.189850	−	0.328830i	−0.755350	−	0.655322i	$-0.772533\pi$
$991$	5.66096e18	−	9.80507e18i	0.189850	−	0.328830i	0.945200	+	0.326491i	$0.105866\pi$
$992$	−8.89738e18	−	1.54107e19i	−0.296440	−	0.513448i
$993$	−3.15945e19			−1.04578
$994$	−1.05704e19	−	1.83085e19i	−0.347601	−	0.602063i
$995$	1.21161e19	+	2.09857e19i	0.395833	+	0.685603i
$996$	2.79839e19			0.908287
$997$	2.13978e19	+	3.70620e19i	0.690001	+	1.19512i	0.971837	+	0.235654i	$0.0757232\pi$
$997$	2.13978e19	+	3.70620e19i	0.690001	+	1.19512i	−0.281836	+	0.959463i	$0.590943\pi$
$998$	3.84999e18	−	6.66838e18i	0.123342	−	0.213635i
$999$	−9.47640e18	+	1.64136e19i	−0.301625	+	0.522430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.14.c.a.9.6	yes	28
13.3	even	3	inner	13.14.c.a.3.6	✓	28
13.4	even	6		169.14.a.c.1.6		14
13.9	even	3		169.14.a.e.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.c.a.3.6	✓	28	13.3	even	3	inner
13.14.c.a.9.6	yes	28	1.1	even	1	trivial
169.14.a.c.1.6		14	13.4	even	6
169.14.a.e.1.9		14	13.9	even	3

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	13.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-16.9887 + 29.4253i) q^{2} +(797.844 - 1381.91i) q^{3} +(3518.77 + 6094.69i) q^{4} -28205.3 q^{5} +(27108.7 + 46953.6i) q^{6} +(177172. + 306871. i) q^{7} -517460. q^{8} +(-475948. - 824367. i) q^{9} +(479171. - 829948. i) q^{10} +(2.48521e6 - 4.30450e6i) q^{11} +1.12297e7 q^{12} +(1.11242e7 + 1.33839e7i) q^{13} -1.20397e7 q^{14} +(-2.25034e7 + 3.89770e7i) q^{15} +(-2.00348e7 + 3.47012e7i) q^{16} +(5.35538e7 + 9.27579e7i) q^{17} +3.23430e7 q^{18} +(1.61956e8 + 2.80516e8i) q^{19} +(-9.92478e7 - 1.71902e8i) q^{20} +5.65422e8 q^{21} +(8.44408e7 + 1.46256e8i) q^{22} +(2.62992e8 - 4.55516e8i) q^{23} +(-4.12852e8 + 7.15081e8i) q^{24} -4.25166e8 q^{25} +(-5.82809e8 + 9.99576e7i) q^{26} +1.02511e9 q^{27} +(-1.24685e9 + 2.15961e9i) q^{28} +(6.01457e8 - 1.04175e9i) q^{29} +(-7.64607e8 - 1.32434e9i) q^{30} +3.17736e9 q^{31} +(-2.80025e9 - 4.85017e9i) q^{32} +(-3.96561e9 - 6.86864e9i) q^{33} -3.63924e9 q^{34} +(-4.99718e9 - 8.65537e9i) q^{35} +(3.34950e9 - 5.80151e9i) q^{36} +(-9.24426e9 + 1.60115e10i) q^{37} -1.10057e10 q^{38} +(2.73706e10 - 4.69433e9i) q^{39} +1.45951e10 q^{40} +(-1.08755e10 + 1.88370e10i) q^{41} +(-9.60578e9 + 1.66377e10i) q^{42} +(-2.57930e10 - 4.46747e10i) q^{43} +3.49795e10 q^{44} +(1.34242e10 + 2.32515e10i) q^{45} +(8.93579e9 + 1.54772e10i) q^{46} +1.84645e10 q^{47} +(3.19692e10 + 5.53724e10i) q^{48} +(-1.43352e10 + 2.48294e10i) q^{49} +(7.22303e9 - 1.25106e10i) q^{50} +1.70910e11 q^{51} +(-4.24271e10 + 1.14893e11i) q^{52} -1.97464e11 q^{53} +(-1.74153e10 + 3.01642e10i) q^{54} +(-7.00959e10 + 1.21410e11i) q^{55} +(-9.16794e10 - 1.58793e11i) q^{56} +5.16862e11 q^{57} +(2.04360e10 + 3.53961e10i) q^{58} +(-7.27492e10 - 1.26005e11i) q^{59} -3.16737e11 q^{60} +(-3.18051e11 - 5.50881e11i) q^{61} +(-5.39791e10 + 9.34946e10i) q^{62} +(1.68649e11 - 2.92109e11i) q^{63} -1.37960e11 q^{64} +(-3.13760e11 - 3.77495e11i) q^{65} +2.69482e11 q^{66} +(3.30986e11 - 5.73285e11i) q^{67} +(-3.76887e11 + 6.52787e11i) q^{68} +(-4.19654e11 - 7.26861e11i) q^{69} +3.39582e11 q^{70} +(8.77967e11 + 1.52068e12i) q^{71} +(2.46284e11 + 4.26577e11i) q^{72} -1.33173e12 q^{73} +(-3.14096e11 - 5.44030e11i) q^{74} +(-3.39217e11 + 5.87540e11i) q^{75} +(-1.13977e12 + 1.97414e12i) q^{76} +1.76123e12 q^{77} +(-3.26859e11 + 8.85139e11i) q^{78} +1.34409e12 q^{79} +(5.65086e11 - 9.78758e11i) q^{80} +(1.57669e12 - 2.73092e12i) q^{81} +(-3.69523e11 - 6.40032e11i) q^{82} +2.49195e12 q^{83} +(1.98959e12 + 3.44607e12i) q^{84} +(-1.51050e12 - 2.61626e12i) q^{85} +1.75276e12 q^{86} +(-9.59738e11 - 1.66232e12i) q^{87} +(-1.28599e12 + 2.22741e12i) q^{88} +(-3.25403e12 + 5.63614e12i) q^{89} -9.12242e11 q^{90} +(-2.13623e12 + 5.78493e12i) q^{91} +3.70163e12 q^{92} +(2.53503e12 - 4.39081e12i) q^{93} +(-3.13687e11 + 5.43322e11i) q^{94} +(-4.56801e12 - 7.91203e12i) q^{95} -8.93664e12 q^{96} +(-3.39959e11 - 5.88827e11i) q^{97} +(-4.87074e11 - 8.43637e11i) q^{98} -4.73132e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 65 q^{2} + 728 q^{3} - 53249 q^{4} + 41860 q^{5} + 143910 q^{6} - 173992 q^{7} + 2616978 q^{8} - 5231838 q^{9} + 2769243 q^{10} + 10986144 q^{11} - 45205464 q^{12} + 25107706 q^{13} - 23731756 q^{14}+ \cdots + 33239809172544 q^{99}+O(q^{100}) \) 28 * q - 65 * q^2 + 728 * q^3 - 53249 * q^4 + 41860 * q^5 + 143910 * q^6 - 173992 * q^7 + 2616978 * q^8 - 5231838 * q^9 + 2769243 * q^10 + 10986144 * q^11 - 45205464 * q^12 + 25107706 * q^13 - 23731756 * q^14 - 75354448 * q^15 - 273433217 * q^16 + 255934950 * q^17 - 350685842 * q^18 - 266623552 * q^19 - 225433091 * q^20 - 2515875856 * q^21 + 77223114 * q^22 + 1914406544 * q^23 - 680727216 * q^24 + 5225878768 * q^25 - 9205789749 * q^26 + 3550452320 * q^27 - 3680076400 * q^28 + 6211296126 * q^29 + 5703660004 * q^30 + 6997674944 * q^31 + 2312486527 * q^32 + 5621901584 * q^33 - 23373723594 * q^34 + 23009265024 * q^35 + 23496114839 * q^36 + 19577630774 * q^37 + 51648723644 * q^38 + 31282255680 * q^39 - 111700587858 * q^40 - 6039692074 * q^41 + 143590583874 * q^42 + 16878499784 * q^43 - 489551846992 * q^44 - 148673926778 * q^45 + 177583142490 * q^46 + 369404914944 * q^47 + 92920518608 * q^48 - 195653684766 * q^49 - 753661423970 * q^50 + 617169279136 * q^51 - 727838751302 * q^52 - 287550769100 * q^53 + 365361720282 * q^54 + 855926433792 * q^55 + 192505368988 * q^56 - 1924513438848 * q^57 - 660641292207 * q^58 + 637655529992 * q^59 + 2555257062384 * q^60 + 1530666437030 * q^61 + 1907899186036 * q^62 - 832654573712 * q^63 + 632232280450 * q^64 - 2489693680994 * q^65 - 270853649100 * q^66 - 1120398677944 * q^67 + 4085795015901 * q^68 + 1473200404976 * q^69 - 9377684744688 * q^70 + 1506585643472 * q^71 + 3521118562923 * q^72 - 852513981436 * q^73 + 4665118313621 * q^74 + 2605103918408 * q^75 - 6106356745372 * q^76 + 2854115035024 * q^77 - 8622775525858 * q^78 - 7032676662784 * q^79 + 5983641421745 * q^80 + 2512348302642 * q^81 - 8600700659175 * q^82 + 2033940247872 * q^83 - 4374201207844 * q^84 + 2527554975426 * q^85 - 7547295057588 * q^86 - 1118899666832 * q^87 - 5943200108772 * q^88 + 5229645042596 * q^89 + 4220465391930 * q^90 + 18401936100704 * q^91 + 3830251788320 * q^92 - 1283055655752 * q^93 - 32271602536104 * q^94 + 8980600417472 * q^95 + 51692558969792 * q^96 + 3129146550452 * q^97 - 5503659823363 * q^98 + 33239809172544 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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