LMFDB - Embedded newform 13.14.e.a.10.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,14,Mod(4,13)] 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([1])) N = Newforms(chi, 14, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.4"); S:= CuspForms(chi, 14); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	13.e (of order $6$, 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:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	13.10
Dual form			13.14.e.a.4.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-148.000 + 85.4479i) q^{2} +(1092.19 + 1891.73i) q^{3} +(10506.7 - 18198.1i) q^{4} +22940.5i q^{5} +(-323289. - 186651. i) q^{6} +(137378. + 79315.3i) q^{7} +2.19112e6i q^{8} +(-1.58860e6 + 2.75154e6i) q^{9} +(-1.96022e6 - 3.39519e6i) q^{10} +(-7.86928e6 + 4.54333e6i) q^{11} +4.59012e7 q^{12} +(-4.51763e6 - 1.68067e7i) q^{13} -2.71093e7 q^{14} +(-4.33972e7 + 2.50554e7i) q^{15} +(-1.01156e8 - 1.75207e8i) q^{16} +(-2.61354e7 + 4.52679e7i) q^{17} -5.42971e8i q^{18} +(1.26376e8 + 7.29630e7i) q^{19} +(4.17473e8 + 2.41028e8i) q^{20} +3.46510e8i q^{21} +(7.76436e8 - 1.34483e9i) q^{22} +(-2.28630e8 - 3.95999e8i) q^{23} +(-4.14500e9 + 2.39312e9i) q^{24} +6.94437e8 q^{25} +(2.10471e9 + 2.10138e9i) q^{26} -3.45762e9 q^{27} +(2.88678e9 - 1.66668e9i) q^{28} +(-4.76768e8 - 8.25786e8i) q^{29} +(4.28186e9 - 7.41640e9i) q^{30} +2.35624e9i q^{31} +(1.43972e10 + 8.31224e9i) q^{32} +(-1.71895e10 - 9.92437e9i) q^{33} -8.93287e9i q^{34} +(-1.81953e9 + 3.15152e9i) q^{35} +(3.33819e10 + 5.78191e10i) q^{36} +(-1.48972e10 + 8.60090e9i) q^{37} -2.49381e10 q^{38} +(2.68597e10 - 2.69023e10i) q^{39} -5.02653e10 q^{40} +(1.53805e10 - 8.87991e9i) q^{41} +(-2.96085e10 - 5.12835e10i) q^{42} +(3.02273e10 - 5.23553e10i) q^{43} +1.90941e11i q^{44} +(-6.31217e10 - 3.64433e10i) q^{45} +(6.76746e10 + 3.90719e10i) q^{46} +6.05199e10i q^{47} +(2.20962e11 - 3.82718e11i) q^{48} +(-3.58627e10 - 6.21160e10i) q^{49} +(-1.02777e11 + 5.93382e10i) q^{50} -1.14180e11 q^{51} +(-3.53316e11 - 9.43707e10i) q^{52} +9.17588e10 q^{53} +(5.11728e11 - 2.95446e11i) q^{54} +(-1.04226e11 - 1.80525e11i) q^{55} +(-1.73789e11 + 3.01012e11i) q^{56} +3.18758e11i q^{57} +(1.41123e11 + 8.14776e10i) q^{58} +(5.43911e10 + 3.14027e10i) q^{59} +1.05300e12i q^{60} +(-2.18987e11 + 3.79296e11i) q^{61} +(-2.01336e11 - 3.48724e11i) q^{62} +(-4.36479e11 + 2.52001e11i) q^{63} -1.18372e12 q^{64} +(3.85555e11 - 1.03637e11i) q^{65} +3.39207e12 q^{66} +(9.63195e10 - 5.56101e10i) q^{67} +(5.49193e11 + 9.51231e11i) q^{68} +(4.99416e11 - 8.65014e11i) q^{69} -6.21901e11i q^{70} +(-4.78482e11 - 2.76251e11i) q^{71} +(-6.02895e12 - 3.48081e12i) q^{72} +2.17792e12i q^{73} +(1.46986e12 - 2.54587e12i) q^{74} +(7.58458e11 + 1.31369e12i) q^{75} +(2.65558e12 - 1.53320e12i) q^{76} -1.44142e12 q^{77} +(-1.67649e12 + 6.27665e12i) q^{78} -1.53437e12 q^{79} +(4.01932e12 - 2.32056e12i) q^{80} +(-1.24364e12 - 2.15405e12i) q^{81} +(-1.51754e12 + 2.62845e12i) q^{82} -3.98247e12i q^{83} +(6.30583e12 + 3.64067e12i) q^{84} +(-1.03847e12 - 5.99560e11i) q^{85} +1.03314e13i q^{86} +(1.04144e12 - 1.80383e12i) q^{87} +(-9.95497e12 - 1.72425e13i) q^{88} +(-1.19532e12 + 6.90120e11i) q^{89} +1.24560e13 q^{90} +(7.12408e11 - 2.66719e12i) q^{91} -9.60858e12 q^{92} +(-4.45738e12 + 2.57347e12i) q^{93} +(-5.17130e12 - 8.95695e12i) q^{94} +(-1.67381e12 + 2.89912e12i) q^{95} +3.63142e13i q^{96} +(2.97449e12 + 1.71732e12i) q^{97} +(1.06154e13 + 6.12878e12i) q^{98} -2.88702e13i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 730 q^{3} + 65535 q^{4} - 382584 q^{6} + 438984 q^{7} - 9117071 q^{9} + 3893475 q^{10} - 5364528 q^{11} + 27694876 q^{12} - 1794135 q^{13} + 61125588 q^{14} - 113380170 q^{15} - 350182521 q^{16}+ \cdots + 86959564160763 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 - 730 * q^3 + 65535 * q^4 - 382584 * q^6 + 438984 * q^7 - 9117071 * q^9 + 3893475 * q^10 - 5364528 * q^11 + 27694876 * q^12 - 1794135 * q^13 + 61125588 * q^14 - 113380170 * q^15 - 350182521 * q^16 - 23524899 * q^17 + 92116746 * q^19 + 959687745 * q^20 - 128185362 * q^22 + 417086886 * q^23 - 4232784354 * q^24 - 11926991364 * q^25 + 5442553119 * q^26 + 5605403288 * q^27 + 22569369732 * q^28 - 8810189577 * q^29 - 9936679242 * q^30 + 9137241117 * q^32 + 12085621392 * q^33 + 1059240720 * q^35 + 55900963715 * q^36 - 72651649419 * q^37 - 45168847944 * q^38 - 41492436530 * q^39 + 137282090274 * q^40 - 3909896103 * q^41 - 34124964786 * q^42 + 138326640480 * q^43 - 259122942393 * q^45 - 288578831832 * q^46 + 630595691198 * q^48 + 114277635303 * q^49 - 553717814136 * q^50 - 178343342508 * q^51 - 1243882821894 * q^52 + 938994404670 * q^53 + 1180281528282 * q^54 - 140610123120 * q^55 + 932974200720 * q^56 - 768032047215 * q^58 - 1420851272556 * q^59 + 284498233437 * q^61 + 2574083847030 * q^62 - 3219361289664 * q^63 - 4989806279958 * q^64 - 931161533727 * q^65 + 12037245084948 * q^66 + 2624227676622 * q^67 - 3124046642277 * q^68 + 1206986427996 * q^69 - 1317657850698 * q^71 - 2571404508735 * q^72 + 1723434230073 * q^74 + 1909848151684 * q^75 - 5741418039246 * q^76 - 8153714196816 * q^77 - 13064083856250 * q^78 + 10732970056200 * q^79 + 11699811454875 * q^80 + 26873856445 * q^81 - 924448017327 * q^82 + 5758359493380 * q^84 - 14711656818213 * q^85 - 6442966126134 * q^87 - 11094606812688 * q^88 + 18293004024660 * q^89 + 53932182551466 * q^90 + 2271787574784 * q^91 - 48706576133844 * q^92 - 50634402753492 * q^93 + 3529466920146 * q^94 + 11308314514950 * q^95 - 4972913690148 * q^97 + 86959564160763 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−148.000	+	85.4479i	−1.63519	+	0.944075i	−0.652727	+	0.757593i	$0.726375\pi$
$2$	−148.000	+	85.4479i	−1.63519	+	0.944075i	−0.982459	+	0.186481i	$0.940292\pi$
$3$	1092.19	+	1891.73i	0.864989	+	1.49821i	0.867058	+	0.498207i	$0.166008\pi$
$3$	1092.19	+	1891.73i	0.864989	+	1.49821i	−0.00206896	+	0.999998i	$0.500659\pi$
$4$	10506.7	−	18198.1i	1.28255	−	2.22145i
$5$			22940.5i			0.656595i	0.944574	+	0.328298i	$0.106475\pi$
$5$			22940.5i			0.656595i	−0.944574	+	0.328298i	$0.893525\pi$
$6$	−323289.	−	186651.i	−2.82883	−	1.63323i
$7$	137378.	+	79315.3i	0.441347	+	0.254812i	0.704169	−	0.710033i	$-0.251320\pi$
$7$	137378.	+	79315.3i	0.441347	+	0.254812i	−0.262822	+	0.964844i	$0.584653\pi$
$8$			2.19112e6i			2.95516i
$9$	−1.58860e6	+	2.75154e6i	−0.996412	+	1.72584i
$10$	−1.96022e6	−	3.39519e6i	−0.619875	−	1.07365i
$11$	−7.86928e6	+	4.54333e6i	−1.33931	+	0.773253i	−0.986706	−	0.162518i	$-0.948039\pi$
$11$	−7.86928e6	+	4.54333e6i	−1.33931	+	0.773253i	−0.352609	+	0.935771i	$0.614705\pi$
$12$	4.59012e7			4.43758
$13$	−4.51763e6	−	1.68067e7i	−0.259584	−	0.965720i
$13$	−4.51763e6	−	1.68067e7i	−0.259584	−	0.965720i
$14$	−2.71093e7			−0.962246
$15$	−4.33972e7	+	2.50554e7i	−0.983714	+	0.567948i
$16$	−1.01156e8	−	1.75207e8i	−1.50734	−	2.61078i
$17$	−2.61354e7	+	4.52679e7i	−0.262610	+	0.454854i	−0.966935	−	0.255024i	$-0.917917\pi$
$17$	−2.61354e7	+	4.52679e7i	−0.262610	+	0.454854i	0.704324	+	0.709878i	$0.251250\pi$
$18$		−	5.42971e8i		−	3.76275i
$19$	1.26376e8	+	7.29630e7i	0.616261	+	0.355798i	0.775412	−	0.631456i	$-0.217542\pi$
$19$	1.26376e8	+	7.29630e7i	0.616261	+	0.355798i	−0.159151	+	0.987254i	$0.550876\pi$
$20$	4.17473e8	+	2.41028e8i	1.45859	+	0.842119i
$21$			3.46510e8i			0.881638i
$22$	7.76436e8	−	1.34483e9i	1.46002	−	2.52883i
$23$	−2.28630e8	−	3.95999e8i	−0.322035	−	0.557780i	0.658873	−	0.752254i	$-0.271033\pi$
$23$	−2.28630e8	−	3.95999e8i	−0.322035	−	0.557780i	−0.980908	+	0.194474i	$0.937700\pi$
$24$	−4.14500e9	+	2.39312e9i	−4.42743	+	2.55618i
$25$	6.94437e8			0.568883
$26$	2.10471e9	+	2.10138e9i	1.33618	+	1.33406i
$27$	−3.45762e9			−1.71756
$28$	2.88678e9	−	1.66668e9i	1.13210	−	0.653620i
$29$	−4.76768e8	−	8.25786e8i	−0.148840	−	0.257799i	0.781959	−	0.623330i	$-0.214221\pi$
$29$	−4.76768e8	−	8.25786e8i	−0.148840	−	0.257799i	−0.930799	+	0.365531i	$0.880887\pi$
$30$	4.28186e9	−	7.41640e9i	1.07237	−	1.85740i
$31$			2.35624e9i			0.476836i	0.971163	+	0.238418i	$0.0766288\pi$
$31$			2.35624e9i			0.476836i	−0.971163	+	0.238418i	$0.923371\pi$
$32$	1.43972e10	+	8.31224e9i	2.37030	+	1.36850i
$33$	−1.71895e10	−	9.92437e9i	−2.31698	−	1.33771i
$34$		−	8.93287e9i		−	0.991695i
$35$	−1.81953e9	+	3.15152e9i	−0.167308	+	0.289786i
$36$	3.33819e10	+	5.78191e10i	2.55590	+	4.42696i
$37$	−1.48972e10	+	8.60090e9i	−0.954538	+	0.551103i	−0.894488	−	0.447092i	$-0.852460\pi$
$37$	−1.48972e10	+	8.60090e9i	−0.954538	+	0.551103i	−0.0600505	+	0.998195i	$0.519126\pi$
$38$	−2.49381e10			−1.34360
$39$	2.68597e10	−	2.69023e10i	1.22231	−	1.22425i
$40$	−5.02653e10			−1.94034
$41$	1.53805e10	−	8.87991e9i	0.505678	−	0.291953i	−0.225377	−	0.974272i	$-0.572361\pi$
$41$	1.53805e10	−	8.87991e9i	0.505678	−	0.291953i	0.731055	+	0.682318i	$0.239028\pi$
$42$	−2.96085e10	−	5.12835e10i	−0.832332	−	1.44164i
$43$	3.02273e10	−	5.23553e10i	0.729214	−	1.26304i	−0.228002	−	0.973661i	$-0.573219\pi$
$43$	3.02273e10	−	5.23553e10i	0.729214	−	1.26304i	0.957216	−	0.289375i	$-0.0934475\pi$
$44$			1.90941e11i			3.96696i
$45$	−6.31217e10	−	3.64433e10i	−1.13318	−	0.654239i
$46$	6.76746e10	+	3.90719e10i	1.05317	+	0.608050i
$47$			6.05199e10i			0.818959i	0.912319	+	0.409479i	$0.134290\pi$
$47$			6.05199e10i			0.818959i	−0.912319	+	0.409479i	$0.865710\pi$
$48$	2.20962e11	−	3.82718e11i	2.60766	−	4.51659i
$49$	−3.58627e10	−	6.21160e10i	−0.370142	−	0.641104i
$50$	−1.02777e11	+	5.93382e10i	−0.930229	+	0.537068i
$51$	−1.14180e11			−0.908620
$52$	−3.53316e11	−	9.43707e10i	−2.47823	−	0.661935i
$53$	9.17588e10			0.568663			0.284331	−	0.958726i	$-0.408228\pi$
$53$	9.17588e10			0.568663			0.284331	+	0.958726i	$0.408228\pi$
$54$	5.11728e11	−	2.95446e11i	2.80854	−	1.62151i
$55$	−1.04226e11	−	1.80525e11i	−0.507714	−	0.879387i
$56$	−1.73789e11	+	3.01012e11i	−0.753009	+	1.30425i
$57$			3.18758e11i			1.23105i
$58$	1.41123e11	+	8.14776e10i	0.486762	+	0.281032i
$59$	5.43911e10	+	3.14027e10i	0.167876	+	0.0969235i	0.581584	−	0.813486i	$-0.302433\pi$
$59$	5.43911e10	+	3.14027e10i	0.167876	+	0.0969235i	−0.413708	+	0.910410i	$0.635766\pi$
$60$			1.05300e12i			2.91369i
$61$	−2.18987e11	+	3.79296e11i	−0.544219	+	0.942615i	0.454437	+	0.890779i	$0.349841\pi$
$61$	−2.18987e11	+	3.79296e11i	−0.544219	+	0.942615i	−0.998656	+	0.0518358i	$0.983493\pi$
$62$	−2.01336e11	−	3.48724e11i	−0.450169	−	0.779715i
$63$	−4.36479e11	+	2.52001e11i	−0.879527	+	0.507795i
$64$	−1.18372e12			−2.15318
$65$	3.85555e11	−	1.03637e11i	0.634087	−	0.170442i
$66$	3.39207e12			5.05160
$67$	9.63195e10	−	5.56101e10i	0.130085	−	0.0751048i	−0.433545	−	0.901132i	$-0.642738\pi$
$67$	9.63195e10	−	5.56101e10i	0.130085	−	0.0751048i	0.563630	+	0.826027i	$0.309404\pi$
$68$	5.49193e11	+	9.51231e11i	0.673624	+	1.16675i
$69$	4.99416e11	−	8.65014e11i	0.557113	−	0.964948i
$70$		−	6.21901e11i		−	0.631806i
$71$	−4.78482e11	−	2.76251e11i	−0.443288	−	0.255932i	0.261703	−	0.965148i	$-0.415716\pi$
$71$	−4.78482e11	−	2.76251e11i	−0.443288	−	0.255932i	−0.704991	+	0.709216i	$0.749049\pi$
$72$	−6.02895e12	−	3.48081e12i	−5.10012	−	2.94455i
$73$			2.17792e12i			1.68439i	0.539173	+	0.842195i	$0.318737\pi$
$73$			2.17792e12i			1.68439i	−0.539173	+	0.842195i	$0.681263\pi$
$74$	1.46986e12	−	2.54587e12i	1.04056	−	1.80231i
$75$	7.58458e11	+	1.31369e12i	0.492078	+	0.852303i
$76$	2.65558e12	−	1.53320e12i	1.58078	−	0.912661i
$77$	−1.44142e12			−0.788137
$78$	−1.67649e12	+	6.27665e12i	−0.842921	+	3.15582i
$79$	−1.53437e12			−0.710155			−0.355077	−	0.934837i	$-0.615545\pi$
$79$	−1.53437e12			−0.710155			−0.355077	+	0.934837i	$0.615545\pi$
$80$	4.01932e12	−	2.32056e12i	1.71423	−	0.989709i
$81$	−1.24364e12	−	2.15405e12i	−0.489262	−	0.847427i
$82$	−1.51754e12	+	2.62845e12i	−0.551252	+	0.954796i
$83$		−	3.98247e12i		−	1.33704i	−0.743693	−	0.668521i	$-0.766928\pi$
$83$		−	3.98247e12i		−	1.33704i	0.743693	−	0.668521i	$-0.233072\pi$
$84$	6.30583e12	+	3.64067e12i	1.95851	+	1.13075i
$85$	−1.03847e12	−	5.99560e11i	−0.298655	−	0.172429i
$86$			1.03314e13i			2.75373i
$87$	1.04144e12	−	1.80383e12i	0.257490	−	0.445986i
$88$	−9.95497e12	−	1.72425e13i	−2.28509	−	3.95788i
$89$	−1.19532e12	+	6.90120e11i	−0.254947	+	0.147194i	−0.622027	−	0.782995i	$-0.713691\pi$
$89$	−1.19532e12	+	6.90120e11i	−0.254947	+	0.147194i	0.367080	+	0.930189i	$0.380357\pi$
$90$	1.24560e13			2.47060
$91$	7.12408e11	−	2.66719e12i	0.131510	−	0.492363i
$92$	−9.60858e12			−1.65211
$93$	−4.45738e12	+	2.57347e12i	−0.714398	+	0.412458i
$94$	−5.17130e12	−	8.95695e12i	−0.773158	−	1.33915i
$95$	−1.67381e12	+	2.89912e12i	−0.233616	+	0.404634i
$96$			3.63142e13i			4.73493i
$97$	2.97449e12	+	1.71732e12i	0.362574	+	0.209332i	0.670209	−	0.742172i	$-0.266204\pi$
$97$	2.97449e12	+	1.71732e12i	0.362574	+	0.209332i	−0.307636	+	0.951504i	$0.599538\pi$
$98$	1.06154e13	+	6.12878e12i	1.21050	+	0.698883i
$99$		−	2.88702e13i		−	3.08192i
$100$	7.29623e12	−	1.26374e13i	0.729623	−	1.26374i
$101$	7.52656e12	+	1.30364e13i	0.705517	+	1.22199i	0.966505	+	0.256649i	$0.0826186\pi$
$101$	7.52656e12	+	1.30364e13i	0.705517	+	1.22199i	−0.260987	+	0.965342i	$0.584048\pi$
$102$	1.68986e13	−	9.75641e12i	1.48576	−	0.857805i
$103$	−2.05112e13			−1.69258			−0.846288	−	0.532726i	$-0.821168\pi$
$103$	−2.05112e13			−1.69258			−0.846288	+	0.532726i	$0.821168\pi$
$104$	3.68255e13	−	9.89865e12i	2.85386	−	0.767113i
$105$	−7.94911e12			−0.578879
$106$	−1.35803e13	+	7.84060e12i	−0.929869	+	0.536860i
$107$	9.91823e11	+	1.71789e12i	0.0638910	+	0.110662i	0.896202	−	0.443647i	$-0.146316\pi$
$107$	9.91823e11	+	1.71789e12i	0.0638910	+	0.110662i	−0.832311	+	0.554310i	$0.812982\pi$
$108$	−3.63281e13	+	6.29222e13i	−2.20287	+	3.81548i
$109$			2.69863e13i			1.54124i	0.637293	+	0.770622i	$0.280054\pi$
$109$			2.69863e13i			1.54124i	−0.637293	+	0.770622i	$0.719946\pi$
$110$	3.08510e13	+	1.78118e13i	1.66041	+	0.958641i
$111$	−3.25412e13	−	1.87877e13i	−1.65133	−	0.953396i
$112$		−	3.20927e13i		−	1.53635i
$113$	−1.02215e13	+	1.77042e13i	−0.461855	+	0.799956i	−0.999053	−	0.0434996i	$-0.986149\pi$
$113$	−1.02215e13	+	1.77042e13i	−0.461855	+	0.799956i	0.537198	+	0.843456i	$0.319483\pi$
$114$	−2.72372e13	−	4.71762e13i	−1.16220	−	2.01299i
$115$	9.08441e12	−	5.24489e12i	0.366236	−	0.211446i
$116$	−2.00370e13			−0.763581
$117$	5.34211e13	+	1.42688e13i	1.92533	+	0.514255i
$118$	−1.07332e13			−0.366012
$119$	−7.18088e12	+	4.14588e12i	−0.231805	+	0.133832i
$120$	−5.48993e13	−	9.50884e13i	−1.67837	−	2.90703i
$121$	2.40223e13	−	4.16079e13i	0.695842	−	1.20523i
$122$		−	7.48478e13i		−	2.05513i
$123$	3.35968e13	+	1.93971e13i	0.874812	+	0.505073i
$124$	4.28792e13	+	2.47563e13i	1.05927	+	0.611568i
$125$			4.39343e13i			1.03012i
$126$	4.30659e13	−	7.45923e13i	0.958793	−	1.66068i
$127$	1.44687e13	+	2.50605e13i	0.305989	+	0.529988i	0.977481	−	0.211023i	$-0.0676796\pi$
$127$	1.44687e13	+	2.50605e13i	0.305989	+	0.529988i	−0.671492	+	0.741012i	$0.734346\pi$
$128$	5.72488e13	−	3.30526e13i	1.15054	−	0.664264i
$129$	1.32056e14			2.52305
$130$	−4.82066e13	+	4.82830e13i	−0.875940	+	0.877330i
$131$	3.96009e13			0.684608			0.342304	−	0.939589i	$-0.388793\pi$
$131$	3.96009e13			0.684608			0.342304	+	0.939589i	$0.388793\pi$
$132$	−3.61210e14	+	2.08544e14i	−5.94331	+	3.43137i
$133$	1.15742e13	+	2.00470e13i	0.181323	+	0.314061i
$134$	−9.50353e12	+	1.64606e13i	−0.141809	+	0.245620i
$135$		−	7.93195e13i		−	1.12774i
$136$	−9.91873e13	−	5.72658e13i	−1.34417	−	0.776055i
$137$	−7.56914e13	−	4.37004e13i	−0.978054	−	0.564680i	−0.0763718	−	0.997079i	$-0.524334\pi$
$137$	−7.56914e13	−	4.37004e13i	−0.978054	−	0.564680i	−0.901682	+	0.432400i	$0.857667\pi$
$138$			1.70696e14i			2.10382i
$139$	4.05310e12	−	7.02018e12i	0.0476641	−	0.0825567i	−0.841209	−	0.540710i	$-0.818156\pi$
$139$	4.05310e12	−	7.02018e12i	0.0476641	−	0.0825567i	0.888873	+	0.458153i	$0.151489\pi$
$140$	3.82345e13	+	6.62241e13i	0.429164	+	0.743333i
$141$	−1.14487e14	+	6.60993e13i	−1.22697	+	0.708390i
$142$	9.44204e13			0.966477
$143$	1.11909e14	+	1.11732e14i	1.09441	+	1.09268i
$144$	6.42784e14			6.00771
$145$	1.89439e13	−	1.09373e13i	0.169269	−	0.0977276i
$146$	−1.86098e14	−	3.22332e14i	−1.59019	−	2.75429i
$147$	7.83378e13	−	1.35685e14i	0.640337	−	1.10910i
$148$			3.61468e14i			2.82728i
$149$	−8.98817e13	−	5.18932e13i	−0.672916	−	0.388508i	0.124265	−	0.992249i	$-0.460343\pi$
$149$	−8.98817e13	−	5.18932e13i	−0.672916	−	0.388508i	−0.797181	+	0.603741i	$0.793676\pi$
$150$	−2.24504e14	−	1.29617e14i	−1.60928	−	0.929116i
$151$			2.04728e14i			1.40549i	0.711443	+	0.702744i	$0.248042\pi$
$151$			2.04728e14i			1.40549i	−0.711443	+	0.702744i	$0.751958\pi$
$152$	−1.59870e14	+	2.76904e14i	−1.05144	+	1.82115i
$153$	−8.30377e13	−	1.43825e14i	−0.523336	−	0.906445i
$154$	2.13331e14	−	1.23166e14i	1.28875	−	0.744060i
$155$	−5.40534e13			−0.313088
$156$	−2.07365e14	−	7.71450e14i	−1.15193	−	4.28546i
$157$	−8.13662e13			−0.433607			−0.216803	−	0.976215i	$-0.569563\pi$
$157$	−8.13662e13			−0.433607			−0.216803	+	0.976215i	$0.569563\pi$
$158$	2.27086e14	−	1.31108e14i	1.16123	−	0.670439i
$159$	1.00218e14	+	1.73583e14i	0.491887	+	0.851973i
$160$	−1.90687e14	+	3.30279e14i	−0.898547	+	1.55633i
$161$		−	7.25355e13i		−	0.328233i
$162$	3.68117e14	+	2.12533e14i	1.60007	+	0.923800i
$163$	−1.58206e14	−	9.13405e13i	−0.660701	−	0.381456i	0.131843	−	0.991271i	$-0.457910\pi$
$163$	−1.58206e14	−	9.13405e13i	−0.660701	−	0.381456i	−0.792544	+	0.609815i	$0.791244\pi$
$164$		−	3.73194e14i		−	1.49778i
$165$	2.27670e14	−	3.94336e14i	0.878335	−	1.52132i
$166$	3.40294e14	+	5.89406e14i	1.26227	+	2.18631i
$167$	−1.28131e14	+	7.39762e13i	−0.457084	+	0.263897i	−0.710817	−	0.703377i	$-0.751675\pi$
$167$	−1.28131e14	+	7.39762e13i	−0.457084	+	0.263897i	0.253734	+	0.967274i	$0.418341\pi$
$168$	−7.59244e14			−2.60538
$169$	−2.62057e14	+	1.51853e14i	−0.865232	+	0.501372i
$170$	2.04924e14			0.651142
$171$	−4.01521e14	+	2.31818e14i	−1.22810	+	0.709044i
$172$	−6.35178e14	−	1.10016e15i	−1.87051	−	3.23982i
$173$	2.10376e14	−	3.64382e14i	0.596618	−	1.03337i	−0.396698	−	0.917949i	$-0.629844\pi$
$173$	2.10376e14	−	3.64382e14i	0.596618	−	1.03337i	0.993316	−	0.115424i	$-0.0368227\pi$
$174$			3.55956e14i			0.972359i
$175$	9.54005e13	+	5.50795e13i	0.251075	+	0.144958i
$176$	1.59204e15	+	9.19166e14i	4.03759	+	2.33110i
$177$			1.37191e14i			0.335351i
$178$	1.17939e14	−	2.04276e14i	0.277924	−	0.481378i
$179$	2.12234e14	+	3.67600e14i	0.482248	+	0.835279i	0.999792	−	0.0203780i	$-0.00648696\pi$
$179$	2.12234e14	+	3.67600e14i	0.482248	+	0.835279i	−0.517544	+	0.855657i	$0.673154\pi$
$180$	−1.32640e15	+	7.65797e14i	−2.90672	+	1.67819i
$181$	5.39377e14			1.14020			0.570101	−	0.821574i	$-0.306904\pi$
$181$	5.39377e14			1.14020			0.570101	+	0.821574i	$0.306904\pi$
$182$	1.22470e14	+	4.55619e14i	0.249784	+	0.929260i
$183$	−9.56701e14			−1.88297
$184$	8.67680e14	−	5.00955e14i	1.64833	−	0.951663i
$185$	−1.97309e14	−	3.41749e14i	−0.361851	−	0.626745i
$186$	4.39795e14	−	7.61747e14i	0.778782	−	1.34889i
$187$		−	4.74968e14i		−	0.812257i
$188$	1.10135e15	+	6.35863e14i	1.81927	+	1.05036i
$189$	−4.75002e14	−	2.74242e14i	−0.758042	−	0.437656i
$190$		−	5.72093e14i		−	0.882202i
$191$	−2.04773e14	+	3.54676e14i	−0.305179	+	0.528586i	−0.977301	−	0.211855i	$-0.932050\pi$
$191$	−2.04773e14	+	3.54676e14i	−0.305179	+	0.528586i	0.672122	+	0.740440i	$0.265383\pi$
$192$	−1.29285e15	−	2.23928e15i	−1.86247	−	3.22590i
$193$	7.58388e14	−	4.37855e14i	1.05625	−	0.609829i	0.131861	−	0.991268i	$-0.457905\pi$
$193$	7.58388e14	−	4.37855e14i	1.05625	−	0.609829i	0.924394	+	0.381439i	$0.124571\pi$
$194$	−5.86966e14			−0.790500
$195$	6.17152e14	+	6.16175e14i	0.803835	+	0.802562i
$196$	−1.50719e15			−1.89891
$197$	−4.94682e14	+	2.85605e14i	−0.602970	+	0.348125i	−0.770209	−	0.637791i	$-0.779848\pi$
$197$	−4.94682e14	+	2.85605e14i	−0.602970	+	0.348125i	0.167239	+	0.985916i	$0.446515\pi$
$198$	2.46690e15	+	4.27279e15i	2.90956	+	5.03950i
$199$	4.15414e14	−	7.19518e14i	0.474172	−	0.821290i	−0.525391	−	0.850861i	$-0.676081\pi$
$199$	4.15414e14	−	7.19518e14i	0.474172	−	0.821290i	0.999563	+	0.0295713i	$0.00941420\pi$
$200$			1.52159e15i			1.68114i
$201$	2.10399e14	+	1.21474e14i	0.225045	+	0.129930i
$202$	−2.22786e15	−	1.28626e15i	−2.30730	−	1.33212i
$203$		−	1.51260e14i		−	0.151705i
$204$	−1.19965e15	+	2.07785e15i	−1.16535	+	2.01845i
$205$	2.03709e14	+	3.52835e14i	0.191695	+	0.332026i
$206$	3.03565e15	−	1.75264e15i	2.76768	−	1.59792i
$207$	1.45281e15			1.28352
$208$	−2.48767e15	+	2.49161e15i	−2.13000	+	2.13338i
$209$	−1.32598e15			−1.10049
$210$	1.17647e15	−	6.79234e14i	0.946575	−	0.546505i
$211$	7.21980e14	+	1.25051e15i	0.563234	+	0.975551i	0.997212	+	0.0746267i	$0.0237765\pi$
$211$	7.21980e14	+	1.25051e15i	0.563234	+	0.975551i	−0.433977	+	0.900924i	$0.642890\pi$
$212$	9.64081e14	−	1.66984e15i	0.729340	−	1.26325i
$213$		−	1.20688e15i		−	0.885515i
$214$	−2.93580e14	−	1.69498e14i	−0.208947	−	0.120636i
$215$	1.20106e15	+	6.93430e14i	0.829303	+	0.478798i
$216$		−	7.57605e15i		−	5.07567i
$217$	−1.86886e14	+	3.23696e14i	−0.121504	+	0.210450i
$218$	−2.30592e15	−	3.99397e15i	−1.45505	−	2.52022i
$219$	−4.12003e15	+	2.37870e15i	−2.52356	+	1.45698i
$220$	−4.38029e15			−2.60468
$221$	8.78876e14	+	2.34748e14i	0.507432	+	0.135535i
$222$	6.42146e15			3.60031
$223$	−1.24287e14	+	7.17572e13i	−0.0676775	+	0.0390736i	−0.533457	−	0.845827i	$-0.679107\pi$
$223$	−1.24287e14	+	7.17572e13i	−0.0676775	+	0.0390736i	0.465779	+	0.884901i	$0.345774\pi$
$224$	1.31858e15	+	2.28384e15i	0.697418	+	1.20796i
$225$	−1.10318e15	+	1.91077e15i	−0.566842	+	0.981799i
$226$		−	3.49363e15i		−	1.74410i
$227$	−2.05064e15	−	1.18394e15i	−0.994768	−	0.574330i	−0.0880719	−	0.996114i	$-0.528071\pi$
$227$	−2.05064e15	−	1.18394e15i	−0.994768	−	0.574330i	−0.906696	+	0.421785i	$0.861404\pi$
$228$	5.80079e15	+	3.34909e15i	2.73471	+	1.57888i
$229$		−	1.30188e15i		−	0.596539i	−0.954482	−	0.298270i	$-0.903591\pi$
$229$		−	1.30188e15i		−	0.596539i	0.954482	−	0.298270i	$-0.0964094\pi$
$230$	−8.96329e14	+	1.55249e15i	−0.399242	+	0.691508i
$231$	−1.57431e15	−	2.72678e15i	−0.681730	−	1.18079i
$232$	1.80939e15	−	1.04465e15i	0.761835	−	0.439846i
$233$	2.03251e15			0.832182			0.416091	−	0.909323i	$-0.363400\pi$
$233$	2.03251e15			0.832182			0.416091	+	0.909323i	$0.363400\pi$
$234$	−9.12557e15	+	2.45294e15i	−3.63376	+	0.976751i
$235$	−1.38836e15			−0.537724
$236$	1.14294e15	−	6.59876e14i	0.430621	−	0.248619i
$237$	−1.67582e15	−	2.90261e15i	−0.614276	−	1.06396i
$238$	7.08513e14	−	1.22718e15i	0.252696	−	0.437682i
$239$			9.78953e14i			0.339762i	0.985465	+	0.169881i	$0.0543384\pi$
$239$			9.78953e14i			0.339762i	−0.985465	+	0.169881i	$0.945662\pi$
$240$	8.77974e15	+	5.06899e15i	2.96557	+	1.71217i
$241$	2.81028e15	+	1.62252e15i	0.923929	+	0.533431i	0.884886	−	0.465807i	$-0.154236\pi$
$241$	2.81028e15	+	1.62252e15i	0.923929	+	0.533431i	0.0390426	+	0.999238i	$0.487569\pi$
$242$			8.21063e15i			2.62771i
$243$	−3.96991e13	+	6.87608e13i	−0.0123691	+	0.0214240i
$244$	4.60165e15	+	7.97028e15i	1.39598	+	2.41791i
$245$	1.42497e15	−	8.22707e14i	0.420946	−	0.243033i
$246$	−6.62977e15			−1.90731
$247$	6.55351e14	−	2.45358e15i	0.183630	−	0.687496i
$248$	−5.16280e15			−1.40913
$249$	7.53377e15	−	4.34962e15i	2.00316	−	1.15653i
$250$	−3.75409e15	−	6.50227e15i	−0.972511	−	1.68444i
$251$	−2.53509e13	+	4.39090e13i	−0.00639903	+	0.0110834i	−0.869207	−	0.494448i	$-0.835370\pi$
$251$	−2.53509e13	+	4.39090e13i	−0.00639903	+	0.0110834i	0.862808	+	0.505531i	$0.168704\pi$
$252$			1.05908e16i			2.60510i
$253$	3.59831e15	+	2.07748e15i	0.862611	+	0.498029i
$254$	−4.28274e15	−	2.47264e15i	−1.00070	−	0.577753i
$255$		−	2.61934e15i		−	0.596596i
$256$	−8.00026e14	+	1.38568e15i	−0.177641	+	0.307684i
$257$	−6.27050e14	−	1.08608e15i	−0.135749	−	0.235124i	0.790134	−	0.612934i	$-0.210011\pi$
$257$	−6.27050e14	−	1.08608e15i	−0.135749	−	0.235124i	−0.925883	+	0.377810i	$0.876677\pi$
$258$	−1.95443e16	+	1.12839e16i	−4.12565	+	2.38195i
$259$	−2.72873e15			−0.561710
$260$	2.16491e15	−	8.10524e15i	0.434623	−	1.62719i
$261$	3.02958e15			0.593224
$262$	−5.86094e15	+	3.38382e15i	−1.11946	+	0.646321i
$263$	2.29541e15	+	3.97576e15i	0.427708	+	0.740812i	0.996669	−	0.0815525i	$-0.0259878\pi$
$263$	2.29541e15	+	3.97576e15i	0.427708	+	0.740812i	−0.568961	+	0.822364i	$0.692654\pi$
$264$	2.17455e16	−	3.76642e16i	3.95315	−	6.84705i
$265$			2.10499e15i			0.373381i
$266$	−3.42595e15	−	1.97797e15i	−0.592995	−	0.342366i
$267$	−2.61104e15	−	1.50749e15i	−0.441053	−	0.254642i
$268$		−	2.33711e15i		−	0.385304i
$269$	−5.05512e15	+	8.75573e15i	−0.813471	+	1.40897i	0.0969500	+	0.995289i	$0.469091\pi$
$269$	−5.05512e15	+	8.75573e15i	−0.813471	+	1.40897i	−0.910421	+	0.413683i	$0.864242\pi$
$270$	6.77769e15	+	1.17393e16i	1.06467	+	1.84407i
$271$	8.70183e15	−	5.02400e15i	1.33447	−	0.770459i	0.348492	−	0.937312i	$-0.386694\pi$
$271$	8.70183e15	−	5.02400e15i	1.33447	−	0.770459i	0.985982	+	0.166852i	$0.0533604\pi$
$272$	1.05750e16			1.58337
$273$	5.82370e15	−	1.56540e15i	0.851416	−	0.228859i
$274$	1.49364e16			2.13240
$275$	−5.46472e15	+	3.15506e15i	−0.761913	+	0.439891i
$276$	−1.04944e16	−	1.81768e16i	−1.42905	−	2.47520i
$277$	−6.52760e15	+	1.13061e16i	−0.868230	+	1.50382i	−0.00442664	+	0.999990i	$0.501409\pi$
$277$	−6.52760e15	+	1.13061e16i	−0.868230	+	1.50382i	−0.863804	+	0.503829i	$0.831924\pi$
$278$			1.38532e15i			0.179994i
$279$	−6.48330e15	−	3.74314e15i	−0.822941	−	0.475125i
$280$	−6.90535e15	−	3.98681e15i	−0.856364	−	0.494422i
$281$		−	6.94161e15i		−	0.841141i	−0.907260	−	0.420571i	$-0.861830\pi$
$281$		−	6.94161e15i		−	0.841141i	0.907260	−	0.420571i	$-0.138170\pi$
$282$	1.12961e16	−	1.95654e16i	1.33755	−	2.31670i
$283$	7.46580e15	+	1.29311e16i	0.863902	+	1.49632i	0.868133	+	0.496332i	$0.165320\pi$
$283$	7.46580e15	+	1.29311e16i	0.863902	+	1.49632i	−0.00423067	+	0.999991i	$0.501347\pi$
$284$	−1.00545e16	+	5.80497e15i	−1.13708	+	0.656494i
$285$	−7.31247e15			−0.808299
$286$	−2.61098e16	−	6.97392e15i	−2.82114	−	0.753526i
$287$	2.81725e15			0.297573
$288$	−4.57429e16	+	2.64097e16i	−4.72360	+	2.72717i
$289$	3.58617e15	+	6.21142e15i	0.362072	+	0.627126i
$290$	−1.86914e15	+	3.23744e15i	−0.184524	+	0.319606i
$291$			7.50258e15i			0.724279i
$292$	3.96339e16	+	2.28827e16i	3.74178	+	2.16032i
$293$	4.34586e15	+	2.50908e15i	0.401269	+	0.231673i	0.687031	−	0.726628i	$-0.258913\pi$
$293$	4.34586e15	+	2.50908e15i	0.401269	+	0.231673i	−0.285762	+	0.958301i	$0.592247\pi$
$294$			2.67752e16i			2.41810i
$295$	−7.20393e14	+	1.24776e15i	−0.0636395	+	0.110227i
$296$	−1.88456e16	−	3.26415e16i	−1.62860	−	2.82081i
$297$	2.72090e16	−	1.57091e16i	2.30036	−	1.32811i
$298$	1.77367e16			1.46712
$299$	−5.62258e15	+	5.63150e15i	−0.455065	+	0.455787i
$300$	3.18755e16			2.52446
$301$	8.30515e15	−	4.79498e15i	0.643673	−	0.371625i
$302$	−1.74936e16	−	3.02998e16i	−1.32689	−	2.29823i
$303$	−1.64409e16	+	2.84765e16i	−1.22053	+	2.11402i
$304$		−	2.95224e16i		−	2.14523i
$305$	−8.70123e15	−	5.02366e15i	−0.618916	−	0.357331i
$306$	2.45792e16	+	1.41908e16i	1.71150	+	0.988137i
$307$		−	2.09374e16i		−	1.42733i	−0.700488	−	0.713664i	$-0.747034\pi$
$307$		−	2.09374e16i		−	1.42733i	0.700488	−	0.713664i	$-0.252966\pi$
$308$	−1.51446e16	+	2.62312e16i	−1.01083	+	1.75081i
$309$	−2.24021e16	−	3.88016e16i	−1.46406	−	2.53583i
$310$	7.99990e15	−	4.61875e15i	0.511957	−	0.295579i
$311$	2.77376e15			0.173831			0.0869155	−	0.996216i	$-0.472299\pi$
$311$	2.77376e15			0.173831			0.0869155	+	0.996216i	$0.472299\pi$
$312$	5.89461e16	+	5.88527e16i	3.61785	+	3.61212i
$313$	4.13260e15			0.248419			0.124210	−	0.992256i	$-0.460360\pi$
$313$	4.13260e15			0.248419			0.124210	+	0.992256i	$0.460360\pi$
$314$	1.20422e16	−	6.95257e15i	0.709027	−	0.409357i
$315$	−5.78103e15	−	1.00130e16i	−0.333416	−	0.577493i
$316$	−1.61211e16	+	2.79226e16i	−0.910812	+	1.57757i
$317$			3.43112e15i			0.189911i	0.995482	+	0.0949556i	$0.0302709\pi$
$317$			3.43112e15i			0.189911i	−0.995482	+	0.0949556i	$0.969729\pi$
$318$	−2.96646e16	−	1.71269e16i	−1.60865	−	0.928756i
$319$	7.50363e15	+	4.33223e15i	0.398687	+	0.230182i
$320$		−	2.71551e16i		−	1.41376i
$321$	−2.16652e15	+	3.75252e15i	−0.110530	+	0.191444i
$322$	6.19800e15	+	1.07353e16i	0.309877	+	0.536722i
$323$	−6.60576e15	+	3.81384e15i	−0.323673	+	0.186873i
$324$	−5.22661e16			−2.51002
$325$	−3.13721e15	−	1.16712e16i	−0.147673	−	0.549382i
$326$	3.12194e16			1.44049
$327$	−5.10508e16	+	2.94742e16i	−2.30910	+	1.33316i
$328$	1.94569e16	+	3.37004e16i	0.862768	+	1.49436i
$329$	−4.80015e15	+	8.31411e15i	−0.208680	+	0.361445i
$330$			7.78157e16i			3.31685i
$331$	−3.01721e15	−	1.74199e15i	−0.126103	−	0.0728053i	0.435622	−	0.900130i	$-0.356529\pi$
$331$	−3.01721e15	−	1.74199e15i	−0.126103	−	0.0728053i	−0.561724	+	0.827324i	$0.689862\pi$
$332$	−7.24735e16	−	4.18426e16i	−2.97017	−	1.71483i
$333$		−	5.46537e16i		−	2.19650i
$334$	1.26422e16	−	2.18970e16i	0.498278	−	0.863042i
$335$	1.27572e15	+	2.20962e15i	0.0493134	+	0.0854133i
$336$	6.07108e16	−	3.50514e16i	2.30176	−	1.32892i
$337$	4.27561e16			1.59002			0.795012	−	0.606594i	$-0.207465\pi$
$337$	4.27561e16			1.59002			0.795012	+	0.606594i	$0.207465\pi$
$338$	2.58090e16	−	4.48665e16i	0.941482	−	1.63668i
$339$	−4.46554e16			−1.59800
$340$	−2.18217e16	+	1.25988e16i	−0.766083	+	0.442298i
$341$	−1.07052e16	−	1.85419e16i	−0.368715	−	0.638633i
$342$	3.96168e16	−	6.86183e16i	1.33878	−	2.31884i
$343$		−	2.67474e16i		−	0.886890i
$344$	1.14717e17	+	6.62316e16i	3.73247	+	2.15494i
$345$	1.98438e16	+	1.14568e16i	0.633580	+	0.365798i
$346$			7.19047e16i			2.25301i
$347$	−1.59617e16	+	2.76464e16i	−0.490836	+	0.850153i	−0.999944	−	0.0105496i	$-0.996642\pi$
$347$	−1.59617e16	+	2.76464e16i	−0.490836	+	0.850153i	0.509108	+	0.860702i	$0.329975\pi$
$348$	−2.18842e16	−	3.79046e16i	−0.660490	−	1.14400i
$349$	−8.71102e15	+	5.02931e15i	−0.258050	+	0.148985i	−0.623445	−	0.781867i	$-0.714267\pi$
$349$	−8.71102e15	+	5.02931e15i	−0.258050	+	0.148985i	0.365395	+	0.930853i	$0.380934\pi$
$350$	−1.88257e16			−0.547405
$351$	1.56202e16	+	5.81113e16i	0.445853	+	1.65869i
$352$	−1.51061e17			−4.23277
$353$	4.05733e16	−	2.34250e16i	1.11611	−	0.644384i	0.175701	−	0.984443i	$-0.443781\pi$
$353$	4.05733e16	−	2.34250e16i	1.11611	−	0.644384i	0.940404	+	0.340060i	$0.110447\pi$
$354$	−1.17227e16	−	2.03043e16i	−0.316596	−	0.548361i
$355$	6.33734e15	−	1.09766e16i	0.168044	−	0.291061i
$356$			2.90035e16i			0.755136i
$357$	−1.56858e16	−	9.05619e15i	−0.401017	−	0.231527i
$358$	−6.28214e16	−	3.62699e16i	−1.57713	−	0.910557i
$359$			6.05858e14i			0.0149368i	0.999972	+	0.00746839i	$0.00237729\pi$
$359$			6.05858e14i			0.0149368i	−0.999972	+	0.00746839i	$0.997623\pi$
$360$	7.98516e16	−	1.38307e17i	1.93338	−	3.34871i
$361$	−1.03793e16	−	1.79775e16i	−0.246815	−	0.427496i
$362$	−7.98279e16	+	4.60887e16i	−1.86444	+	1.07644i
$363$	1.04948e17			2.40758
$364$	−4.10528e16	−	4.09878e16i	−0.925090	−	0.923626i
$365$	−4.99625e16			−1.10596
$366$	1.41592e17	−	8.17481e16i	3.07901	−	1.77767i
$367$	−1.79284e15	−	3.10528e15i	−0.0383011	−	0.0663394i	0.846239	−	0.532803i	$-0.178861\pi$
$367$	−1.79284e15	−	3.10528e15i	−0.0383011	−	0.0663394i	−0.884540	+	0.466463i	$0.845528\pi$
$368$	−4.62544e16	+	8.01150e16i	−0.970828	+	1.68152i
$369$			5.64266e16i			1.16362i
$370$	5.84034e16	+	3.37192e16i	1.18339	+	0.683230i
$371$	1.26057e16	+	7.27788e15i	0.250978	+	0.144902i
$372$			1.08154e17i			2.11600i
$373$	4.99860e16	−	8.65782e16i	0.961038	−	1.66457i	0.241136	−	0.970491i	$-0.422480\pi$
$373$	4.99860e16	−	8.65782e16i	0.961038	−	1.66457i	0.719902	−	0.694075i	$-0.244187\pi$
$374$	4.05850e16	+	7.02953e16i	0.766832	+	1.32819i
$375$	−8.31118e16	+	4.79846e16i	−1.54333	+	0.891043i
$376$	−1.32606e17			−2.42015
$377$	−1.17249e16	+	1.17435e16i	−0.210325	+	0.210658i
$378$	9.37337e16			1.65272
$379$	−3.10940e16	+	1.79521e16i	−0.538917	+	0.311144i	−0.744640	−	0.667466i	$-0.767379\pi$
$379$	−3.10940e16	+	1.79521e16i	−0.538917	+	0.311144i	0.205723	+	0.978610i	$0.434045\pi$
$380$	3.51723e16	+	6.09202e16i	0.599249	+	1.03793i
$381$	−3.16052e16	+	5.47418e16i	−0.529354	+	0.916868i
$382$		−	6.99895e16i		−	1.15245i
$383$	1.34762e16	+	7.78047e15i	0.218160	+	0.125955i	0.605098	−	0.796151i	$-0.293134\pi$
$383$	1.34762e16	+	7.78047e15i	0.218160	+	0.125955i	−0.386938	+	0.922106i	$0.626467\pi$
$384$	1.25053e17	+	7.21995e16i	1.99041	+	1.14916i
$385$		−	3.30669e16i		−	0.517487i
$386$	−7.48276e16	+	1.29605e17i	−1.15145	+	1.99437i
$387$	9.60385e16	+	1.66344e17i	1.45320	+	2.51701i
$388$	6.25040e16	−	3.60867e16i	0.930040	−	0.536959i
$389$	−5.86108e16			−0.857641			−0.428821	−	0.903390i	$-0.641071\pi$
$389$	−5.86108e16			−0.857641			−0.428821	+	0.903390i	$0.641071\pi$
$390$	−1.43989e17	−	3.84596e16i	−2.07210	−	0.553458i
$391$	2.39014e16			0.338279
$392$	1.36103e17	−	7.85793e16i	1.89456	−	1.09383i
$393$	4.32518e16	+	7.49143e16i	0.592179	+	1.02568i
$394$	4.88087e16	−	8.45391e16i	0.657312	−	1.13850i
$395$		−	3.51991e16i		−	0.466284i
$396$	−5.25383e17	−	3.03330e17i	−6.84632	−	3.95272i
$397$	−2.34134e16	−	1.35177e16i	−0.300141	−	0.173287i	0.342365	−	0.939567i	$-0.388772\pi$
$397$	−2.34134e16	−	1.35177e16i	−0.300141	−	0.173287i	−0.642506	+	0.766280i	$0.722105\pi$
$398$			1.41985e17i			1.79061i
$399$	−2.52824e16	+	4.37904e16i	−0.313685	+	0.543319i
$400$	−7.02462e16	−	1.21670e17i	−0.857497	−	1.48523i
$401$	1.37613e17	−	7.94510e16i	1.65281	−	0.954248i	0.676894	−	0.736081i	$-0.263326\pi$
$401$	1.37613e17	−	7.94510e16i	1.65281	−	0.954248i	0.975911	−	0.218167i	$-0.0700078\pi$
$402$	−4.15187e16			−0.490653
$403$	3.96007e16	−	1.06446e16i	0.460490	−	0.123779i
$404$	3.16317e17			3.61946
$405$	4.94149e16	−	2.85297e16i	0.556416	−	0.321247i
$406$	1.29248e16	+	2.23865e16i	0.143221	+	0.248066i
$407$	7.81535e16	−	1.35366e17i	0.852284	−	1.47620i
$408$		−	2.50181e17i		−	2.68512i
$409$	1.41122e17	+	8.14766e16i	1.49071	+	0.860660i	0.999943	−	0.0106329i	$-0.00338463\pi$
$409$	1.41122e17	+	8.14766e16i	1.49071	+	0.860660i	0.490763	+	0.871293i	$0.336718\pi$
$410$	−6.02980e16	−	3.48131e16i	−0.626914	−	0.361949i
$411$		−	1.90917e17i		−	1.95377i
$412$	−2.15504e17	+	3.73264e17i	−2.17082	+	3.75997i
$413$	4.98143e15	+	8.62809e15i	0.0493945	+	0.0855538i
$414$	−2.15016e17	+	1.24140e17i	−2.09879	+	1.21174i
$415$	9.13599e16			0.877895
$416$	7.46603e16	−	2.79522e17i	0.706290	−	2.64429i
$417$	1.77071e16			0.164916
$418$	1.96245e17	−	1.13302e17i	1.79950	−	1.03894i
$419$	−7.14085e16	−	1.23683e17i	−0.644701	−	1.11666i	−0.984370	−	0.176110i	$-0.943648\pi$
$419$	−7.14085e16	−	1.23683e17i	−0.644701	−	1.11666i	0.339669	−	0.940545i	$-0.389685\pi$
$420$	−8.35187e16	+	1.44659e17i	−0.742444	+	1.28595i
$421$		−	8.43088e16i		−	0.737971i	−0.929435	−	0.368985i	$-0.879705\pi$
$421$		−	8.43088e16i		−	0.737971i	0.929435	−	0.368985i	$-0.120295\pi$
$422$	−2.13706e17	−	1.23383e17i	−1.84199	−	1.06347i
$423$	−1.66523e17	−	9.61421e16i	−1.41339	−	0.816021i
$424$			2.01054e17i			1.68049i
$425$	−1.81494e16	+	3.14357e16i	−0.149395	+	0.258759i
$426$	1.03125e17	+	1.78618e17i	0.835992	+	1.44798i
$427$	−6.01679e16	+	3.47380e16i	−0.480379	+	0.277347i
$428$	4.16831e16			0.327775
$429$	−8.91404e16	+	3.33734e17i	−0.690402	+	2.58481i
$430$	−2.37008e17			−1.80809
$431$	−1.32995e17	+	7.67850e16i	−0.999389	+	0.576998i	−0.908067	−	0.418824i	$-0.862442\pi$
$431$	−1.32995e17	+	7.67850e16i	−0.999389	+	0.576998i	−0.0913216	+	0.995821i	$0.529109\pi$
$432$	3.49758e17	+	6.05798e17i	2.58895	+	4.48418i
$433$	−2.72187e16	+	4.71442e16i	−0.198471	+	0.343761i	−0.948033	−	0.318173i	$-0.896931\pi$
$433$	−2.72187e16	+	4.71442e16i	−0.198471	+	0.343761i	0.749562	+	0.661934i	$0.230264\pi$
$434$		−	6.38761e16i		−	0.458834i
$435$	4.13808e16	+	2.38912e16i	0.292832	+	0.169067i
$436$	4.91100e17	+	2.83536e17i	3.42379	+	1.97673i
$437$		−	6.67261e16i		−	0.458318i
$438$	4.06510e17	−	7.04096e17i	2.75099	−	4.76486i
$439$	−1.48415e16	−	2.57062e16i	−0.0989597	−	0.171403i	0.812295	−	0.583247i	$-0.198218\pi$
$439$	−1.48415e16	−	2.57062e16i	−0.0989597	−	0.171403i	−0.911254	+	0.411844i	$0.864885\pi$
$440$	3.95552e17	−	2.28372e17i	2.59873	−	1.50038i
$441$	2.27886e17			1.47526
$442$	−1.50132e17	+	4.03554e16i	−0.957700	+	0.257429i
$443$	−2.94235e17			−1.84957			−0.924785	−	0.380490i	$-0.875755\pi$
$443$	−2.94235e17			−1.84957			−0.924785	+	0.380490i	$0.875755\pi$
$444$	−6.83800e17	+	3.94792e17i	−4.23584	+	2.44556i
$445$	−1.58317e16	−	2.74213e16i	−0.0966467	−	0.167397i
$446$	1.22630e16	−	2.12401e16i	0.0737769	−	0.127785i
$447$		−	2.26709e17i		−	1.34422i
$448$	−1.62617e17	−	9.38872e16i	−0.950298	−	0.548655i
$449$	−1.67005e17	−	9.64201e16i	−0.961894	−	0.555350i	−0.0651384	−	0.997876i	$-0.520749\pi$
$449$	−1.67005e17	−	9.64201e16i	−0.961894	−	0.555350i	−0.896755	+	0.442527i	$0.854082\pi$
$450$		−	3.77059e17i		−	2.14056i
$451$	−8.06887e16	+	1.39757e17i	−0.451508	+	0.782035i
$452$	2.14789e17	+	3.72025e17i	1.18471	+	2.05197i
$453$	−3.87290e17	+	2.23602e17i	−2.10571	+	1.21573i
$454$	4.04660e17			2.16884
$455$	6.11867e16	+	1.63430e16i	0.323283	+	0.0863490i
$456$	−6.98436e17			−3.63794
$457$	2.48018e17	−	1.43193e17i	1.27359	−	0.735305i	0.297925	−	0.954589i	$-0.403706\pi$
$457$	2.48018e17	−	1.43193e17i	1.27359	−	0.735305i	0.975661	+	0.219284i	$0.0703722\pi$
$458$	1.11243e17	+	1.92678e17i	0.563177	+	0.975452i
$459$	9.03665e16	−	1.56519e17i	0.451050	−	0.781242i
$460$		−	2.20425e17i		−	1.08477i
$461$	−1.83509e17	−	1.05949e17i	−0.890433	−	0.514092i	−0.0163490	−	0.999866i	$-0.505204\pi$
$461$	−1.83509e17	−	1.05949e17i	−0.890433	−	0.514092i	−0.874084	+	0.485775i	$0.838538\pi$
$462$	4.65996e17	+	2.69043e17i	2.22951	+	1.28721i
$463$			9.04069e16i			0.426506i	0.976997	+	0.213253i	$0.0684058\pi$
$463$			9.04069e16i			0.426506i	−0.976997	+	0.213253i	$0.931594\pi$
$464$	−9.64554e16	+	1.67066e17i	−0.448704	+	0.777177i
$465$	−5.90366e16	−	1.02254e17i	−0.270818	−	0.469070i
$466$	−3.00811e17	+	1.73673e17i	−1.36077	+	0.785642i
$467$	1.84304e17			0.822196			0.411098	−	0.911591i	$-0.365145\pi$
$467$	1.84304e17			0.822196			0.411098	+	0.911591i	$0.365145\pi$
$468$	8.20944e17	−	8.22246e17i	3.61173	−	3.61746i
$469$	1.76429e16			0.0765503
$470$	2.05477e17	−	1.18632e17i	0.879279	−	0.507652i
$471$	−8.88674e16	−	1.53923e17i	−0.375065	−	0.649632i
$472$	−6.88070e16	+	1.19177e17i	−0.286424	+	0.496101i
$473$			5.49331e17i			2.25547i
$474$	4.96043e17	+	2.86391e17i	2.00891	+	1.15984i
$475$	8.77599e16	+	5.06682e16i	0.350580	+	0.202408i
$476$			1.74238e17i			0.686589i
$477$	−1.45768e17	+	2.52478e17i	−0.566622	+	0.981419i
$478$	−8.36494e16	−	1.44885e17i	−0.320761	−	0.555574i
$479$	4.28904e17	−	2.47628e17i	1.62248	−	0.936740i	0.636227	−	0.771502i	$-0.280494\pi$
$479$	4.28904e17	−	2.47628e17i	1.62248	−	0.936740i	0.986254	−	0.165238i	$-0.0528393\pi$
$480$	−8.33066e17			−3.10893
$481$	2.11853e17	+	2.11517e17i	0.779995	+	0.778759i
$482$	−5.54562e17			−2.01439
$483$	1.37218e17	−	7.92226e16i	0.491760	−	0.283918i
$484$	−5.04790e17	−	8.74322e17i	−1.78491	−	3.09155i
$485$	−3.93962e16	+	6.82362e16i	−0.137446	+	0.238064i
$486$		−	1.35688e16i		−	0.0467096i
$487$	−4.24636e17	−	2.45163e17i	−1.44237	−	0.832755i	−0.444367	−	0.895845i	$-0.646571\pi$
$487$	−4.24636e17	−	2.45163e17i	−1.44237	−	0.832755i	−0.998008	+	0.0630895i	$0.979905\pi$
$488$	−8.31082e17	−	4.79825e17i	−2.78558	−	1.60825i
$489$		−	3.99045e17i		−	1.31982i
$490$	−1.40597e17	+	2.43521e17i	−0.458883	+	0.794809i
$491$	2.22195e17	+	3.84853e17i	0.715657	+	1.23955i	0.962706	+	0.270551i	$0.0872058\pi$
$491$	2.22195e17	+	3.84853e17i	0.715657	+	1.23955i	−0.247049	+	0.969003i	$0.579461\pi$
$492$	7.05982e17	−	4.07599e17i	2.24399	−	1.29557i
$493$	4.98421e16			0.156348
$494$	1.12661e17	+	4.19128e17i	0.348778	+	1.29754i
$495$	6.62296e17			2.02357
$496$	4.12829e17	−	2.38347e17i	1.24491	−	0.718752i
$497$	−4.38219e16	−	7.59018e16i	−0.130429	−	0.225910i
$498$	−7.43332e17	+	1.28749e18i	−2.18370	+	3.78227i
$499$			5.17643e17i			1.50099i	0.660878	+	0.750493i	$0.270184\pi$
$499$			5.17643e17i			1.50099i	−0.660878	+	0.750493i	$0.729816\pi$
$500$	7.99520e17	+	4.61603e17i	2.28836	+	1.32119i
$501$	−2.79886e17	−	1.61592e17i	−0.790745	−	0.456537i
$502$		−	8.66472e15i		−	0.0241646i
$503$	−1.35797e17	+	2.35208e17i	−0.373851	+	0.647529i	−0.990154	−	0.139980i	$-0.955296\pi$
$503$	−1.35797e17	+	2.35208e17i	−0.373851	+	0.647529i	0.616303	+	0.787509i	$0.288630\pi$
$504$	−5.52164e17	−	9.56376e17i	−1.50062	−	2.59914i
$505$	−2.99061e17	+	1.72663e17i	−0.802354	+	0.463239i
$506$	−7.10067e17			−1.88071
$507$	−5.73482e17	−	3.29889e17i	−1.49957	−	0.862614i
$508$	6.08073e17			1.56979
$509$	2.00054e17	−	1.15501e17i	0.509896	−	0.294388i	−0.222895	−	0.974842i	$-0.571551\pi$
$509$	2.00054e17	−	1.15501e17i	0.509896	−	0.294388i	0.732791	+	0.680454i	$0.238217\pi$
$510$	2.23817e17	+	3.87662e17i	0.563231	+	0.975544i
$511$	−1.72742e17	+	2.99198e17i	−0.429203	+	0.743401i
$512$			2.68092e17i			0.657701i
$513$	−4.36959e17	−	2.52278e17i	−1.05847	−	0.611107i
$514$	1.85607e17	+	1.07160e17i	0.443950	+	0.256314i
$515$		−	4.70536e17i		−	1.11134i
$516$	1.38747e18	−	2.40317e18i	3.23595	−	5.60482i
$517$	−2.74962e17	−	4.76248e17i	−0.633263	−	1.09684i
$518$	4.03853e17	−	2.33164e17i	0.918500	−	0.530296i
$519$	9.19084e17			2.06427
$520$	2.27080e17	+	8.44795e17i	0.503682	+	1.87383i
$521$	7.69215e17			1.68501			0.842505	−	0.538689i	$-0.181080\pi$
$521$	7.69215e17			1.68501			0.842505	+	0.538689i	$0.181080\pi$
$522$	−4.48378e17	+	2.58871e17i	−0.970031	+	0.560048i
$523$	−1.87563e17	−	3.24869e17i	−0.400762	−	0.694140i	0.593056	−	0.805161i	$-0.297921\pi$
$523$	−1.87563e17	−	3.24869e17i	−0.400762	−	0.694140i	−0.993818	+	0.111021i	$0.964588\pi$
$524$	4.16075e17	−	7.20662e17i	0.878047	−	1.52082i
$525$			2.40629e17i			0.501549i
$526$	−6.79441e17	−	3.92275e17i	−1.39876	−	0.807577i
$527$	−1.06662e17	−	6.15815e16i	−0.216891	−	0.125222i
$528$			4.01562e18i			8.06552i
$529$	1.47475e17	−	2.55434e17i	0.292587	−	0.506776i
$530$	−1.79867e17	−	3.11539e17i	−0.352500	−	0.610547i
$531$	−1.72812e17	+	9.97728e16i	−0.334548	+	0.193151i
$532$	4.86424e17			0.930228
$533$	−2.18725e17	−	2.18379e17i	−0.413211	−	0.412557i
$534$	5.15246e17			0.961604
$535$	−3.94092e16	+	2.27529e16i	−0.0726604	+	0.0419505i
$536$	1.21848e17	+	2.11047e17i	0.221946	+	0.384422i
$537$	−4.63601e17	+	8.02980e17i	−0.834279	+	1.44501i
$538$		−	1.72780e18i		−	3.07191i
$539$	5.64427e17	+	3.25872e17i	0.991472	+	0.572427i
$540$	−1.44347e18	−	8.33385e17i	−2.50523	−	1.44639i
$541$			9.65064e17i			1.65491i	0.561534	+	0.827454i	$0.310211\pi$
$541$			9.65064e17i			1.65491i	−0.561534	+	0.827454i	$0.689789\pi$
$542$	−8.58581e17	+	1.48711e18i	−1.45474	+	2.51969i
$543$	5.89103e17	+	1.02036e18i	0.986263	+	1.70826i
$544$	−7.52556e17	+	4.34488e17i	−1.24493	+	0.718762i
$545$	−6.19079e17			−1.01197
$546$	−7.28148e17	+	7.29303e17i	−1.17616	+	1.17803i
$547$	4.51277e17			0.720321			0.360160	−	0.932890i	$-0.382722\pi$
$547$	4.51277e17			0.720321			0.360160	+	0.932890i	$0.382722\pi$
$548$	−1.59053e18	+	9.18293e17i	−2.50881	+	1.44846i
$549$	−6.95766e17	−	1.20510e18i	−1.08453	−	1.87847i
$550$	5.39186e17	−	9.33897e17i	0.830579	−	1.43861i
$551$		−	1.39146e17i		−	0.211828i
$552$	1.89535e18	+	1.09428e18i	2.85157	+	1.64636i
$553$	−2.10788e17	−	1.21699e17i	−0.313425	−	0.180956i
$554$		−	2.23108e18i		−	3.27870i
$555$	4.30998e17	−	7.46511e17i	0.625995	−	1.08426i
$556$	−8.51693e16	−	1.47518e17i	−0.122264	−	0.211767i
$557$	3.20625e17	−	1.85113e17i	0.454923	−	0.262650i	−0.254984	−	0.966945i	$-0.582070\pi$
$557$	3.20625e17	−	1.85113e17i	0.454923	−	0.262650i	0.709907	+	0.704295i	$0.248737\pi$
$558$	1.27937e18			1.79422
$559$	−1.01648e18	−	2.71501e17i	−1.40903	−	0.376353i
$560$	7.36223e17			1.00876
$561$	8.98511e17	−	5.18756e17i	1.21693	−	0.702594i
$562$	5.93146e17	+	1.02736e18i	0.794100	+	1.37542i
$563$	−1.05468e17	+	1.82676e17i	−0.139577	+	0.241755i	−0.927337	−	0.374228i	$-0.877908\pi$
$563$	−1.05468e17	+	1.82676e17i	−0.139577	+	0.241755i	0.787759	+	0.615983i	$0.211241\pi$
$564$			2.77794e18i			3.63420i
$565$	−4.06143e17	−	2.34487e17i	−0.525247	−	0.303252i
$566$	−2.20988e18	−	1.27587e18i	−2.82528	−	1.63118i
$567$		−	3.94558e17i		−	0.498679i
$568$	6.05299e17	−	1.04841e18i	0.756321	−	1.30999i
$569$	1.53388e17	+	2.65676e17i	0.189480	+	0.328188i	0.945077	−	0.326848i	$-0.105987\pi$
$569$	1.53388e17	+	2.65676e17i	0.189480	+	0.328188i	−0.755597	+	0.655036i	$0.772653\pi$
$570$	1.08225e18	−	6.24835e17i	1.32172	−	0.763095i
$571$	−6.18457e17			−0.746749			−0.373374	−	0.927681i	$-0.621799\pi$
$571$	−6.18457e17			−0.746749			−0.373374	+	0.927681i	$0.621799\pi$
$572$	3.20910e18	−	8.62602e17i	3.83097	−	1.02976i
$573$	−8.94603e17			−1.05591
$574$	−4.16953e17	+	2.40728e17i	−0.486587	+	0.280931i
$575$	−1.58769e17	−	2.74996e17i	−0.183200	−	0.317312i
$576$	1.88046e18	−	3.25706e18i	2.14545	−	3.71603i
$577$			1.06004e18i			1.19586i	0.801549	+	0.597929i	$0.204010\pi$
$577$			1.06004e18i			1.19586i	−0.801549	+	0.597929i	$0.795990\pi$
$578$	−1.06151e18	−	6.12861e17i	−1.18411	−	0.683645i
$579$	1.65661e18	+	9.56444e17i	1.82730	+	1.05499i
$580$		−	4.59658e17i		−	0.501364i
$581$	3.15871e17	−	5.47105e17i	0.340694	−	0.590100i
$582$	−6.41079e17	−	1.11038e18i	−0.683774	−	1.18433i
$583$	−7.22076e17	+	4.16891e17i	−0.761618	+	0.439720i
$584$	−4.77207e18			−4.97764
$585$	−3.27333e17	+	1.22551e18i	−0.337658	+	1.26416i
$586$	−8.57583e17			−0.874866
$587$	1.61028e18	−	9.29694e17i	1.62462	−	0.937977i	0.638964	−	0.769237i	$-0.279363\pi$
$587$	1.61028e18	−	9.29694e17i	1.62462	−	0.937977i	0.985661	−	0.168740i	$-0.0539699\pi$
$588$	−1.64614e18	−	2.85120e18i	−1.64253	−	2.84495i
$589$	−1.71919e17	+	2.97772e17i	−0.169658	+	0.293856i
$590$		−	2.46224e17i		−	0.240322i
$591$	−1.08058e18	−	6.23871e17i	−1.04313	−	0.602249i
$592$	3.01387e18	+	1.74006e18i	2.87762	+	1.66139i
$593$		−	2.75182e16i		−	0.0259875i	−0.999916	−	0.0129938i	$-0.995864\pi$
$593$		−	2.75182e16i		−	0.0259875i	0.999916	−	0.0129938i	$-0.00413616\pi$
$594$	−2.68462e18	+	4.64990e18i	−2.50767	+	4.34342i
$595$	−9.51085e16	−	1.64733e17i	−0.0878737	−	0.152202i
$596$	−1.88872e18	+	1.09045e18i	−1.72610	+	0.996565i
$597$	1.81485e18			1.64061
$598$	3.50943e17	−	1.31390e18i	0.313819	−	1.17491i
$599$	1.48977e18			1.31778			0.658892	−	0.752237i	$-0.271025\pi$
$599$	1.48977e18			1.31778			0.658892	+	0.752237i	$0.271025\pi$
$600$	−2.87844e18	+	1.66187e18i	−2.51869	+	1.45417i
$601$	2.32104e17	+	4.02016e17i	0.200909	+	0.347984i	0.948821	−	0.315813i	$-0.102277\pi$
$601$	2.32104e17	+	4.02016e17i	0.200909	+	0.347984i	−0.747913	+	0.663797i	$0.768944\pi$
$602$	−8.19442e17	+	1.41932e18i	−0.701683	+	1.21535i
$603$			3.53369e17i			0.299341i
$604$	3.72566e18	+	2.15101e18i	3.12222	+	1.80261i
$605$	9.54506e17	+	5.51084e17i	0.791350	+	0.456886i
$606$		−	5.61936e18i		−	4.60908i
$607$	5.62948e17	−	9.75054e17i	0.456816	−	0.791229i	−0.541974	−	0.840395i	$-0.682323\pi$
$607$	5.62948e17	−	9.75054e17i	0.456816	−	0.791229i	0.998791	+	0.0491660i	$0.0156563\pi$
$608$	1.21297e18	+	2.10093e18i	0.973817	+	1.68670i
$609$	2.86143e17	−	1.65205e17i	0.227285	−	0.131223i
$610$	1.71704e18			1.34939
$611$	1.01714e18	−	2.73406e17i	0.790885	−	0.212589i
$612$	−3.48980e18			−2.68483
$613$	−2.21569e17	+	1.27923e17i	−0.168661	+	0.0973766i	−0.581954	−	0.813221i	$-0.697712\pi$
$613$	−2.21569e17	+	1.27923e17i	−0.168661	+	0.0973766i	0.413293	+	0.910598i	$0.364378\pi$
$614$	1.78906e18	+	3.09874e18i	1.34750	+	2.33395i
$615$	−4.44979e17	+	7.70727e17i	−0.331628	+	0.574397i
$616$		−	3.15832e18i		−	2.32907i
$617$	−1.48021e17	−	8.54598e16i	−0.108011	−	0.0623603i	0.445021	−	0.895520i	$-0.353196\pi$
$617$	−1.48021e17	−	8.54598e16i	−0.108011	−	0.0623603i	−0.553032	+	0.833160i	$0.686529\pi$
$618$	6.63103e18	+	3.82843e18i	4.78802	+	2.76436i
$619$		−	2.87835e17i		−	0.205662i	−0.994699	−	0.102831i	$-0.967210\pi$
$619$		−	2.87835e17i		−	0.205662i	0.994699	−	0.102831i	$-0.0327901\pi$
$620$	−5.67922e17	+	9.83669e17i	−0.401553	+	0.695509i
$621$	7.90517e17	+	1.36922e18i	0.553115	+	0.958024i
$622$	−4.10517e17	+	2.37012e17i	−0.284246	+	0.164109i
$623$	−2.18948e17			−0.150027
$624$	−7.43047e18	−	1.98468e18i	−5.03867	−	1.34583i
$625$	−1.60172e17			−0.107489
$626$	−6.11625e17	+	3.53122e17i	−0.406211	+	0.234526i
$627$	−1.44822e18	−	2.50840e18i	−0.951911	−	1.64876i
$628$	−8.54888e17	+	1.48071e18i	−0.556124	+	0.963235i
$629$		−	8.99153e17i		−	0.578901i
$630$	1.71118e18	+	9.87953e17i	1.09039	+	0.629539i
$631$	−4.15325e17	−	2.39788e17i	−0.261937	−	0.151230i	0.363281	−	0.931680i	$-0.381657\pi$
$631$	−4.15325e17	−	2.39788e17i	−0.261937	−	0.151230i	−0.625218	+	0.780450i	$0.714990\pi$
$632$		−	3.36198e18i		−	2.09862i
$633$	−1.57708e18	+	2.73158e18i	−0.974383	+	1.68768i
$634$	−2.93182e17	−	5.07806e17i	−0.179290	−	0.310540i
$635$	−5.74901e17	+	3.31919e17i	−0.347988	+	0.200911i
$636$	4.21184e18			2.52349
$637$	−8.81952e17	+	8.83351e17i	−0.523045	+	0.523874i
$638$	−1.48072e18			−0.869236
$639$	1.52023e18	−	8.77708e17i	0.883395	−	0.510028i
$640$	7.58242e17	+	1.31331e18i	0.436152	+	0.755438i
$641$	1.19006e18	−	2.06125e18i	0.677629	−	1.17369i	−0.298064	−	0.954546i	$-0.596341\pi$
$641$	1.19006e18	−	2.06125e18i	0.677629	−	1.17369i	0.975693	−	0.219142i	$-0.0703259\pi$
$642$		−	7.40499e17i		−	0.417394i
$643$	−1.25716e18	−	7.25821e17i	−0.701486	−	0.405003i	0.106415	−	0.994322i	$-0.466063\pi$
$643$	−1.25716e18	−	7.25821e17i	−0.701486	−	0.405003i	−0.807901	+	0.589319i	$0.799396\pi$
$644$	−1.32001e18	−	7.62107e17i	−0.729153	−	0.420977i
$645$			3.02943e18i			1.65662i
$646$	6.51769e17	−	1.12890e18i	0.352844	−	0.611143i
$647$	−7.16522e17	−	1.24105e18i	−0.384018	−	0.665139i	0.607614	−	0.794232i	$-0.292127\pi$
$647$	−7.16522e17	−	1.24105e18i	−0.384018	−	0.665139i	−0.991632	+	0.129093i	$0.958793\pi$
$648$	4.71977e18	−	2.72496e18i	2.50428	−	1.44585i
$649$	−5.70691e17			−0.299786
$650$	1.46159e18	+	1.45927e18i	0.760130	+	0.758927i
$651$	−8.16462e17			−0.420397
$652$	−3.32445e18	+	1.91937e18i	−1.69477	+	0.978475i
$653$	1.38832e18	+	2.40464e18i	0.700734	+	1.21371i	0.968209	+	0.250143i	$0.0804775\pi$
$653$	1.38832e18	+	2.40464e18i	0.700734	+	1.21371i	−0.267475	+	0.963565i	$0.586189\pi$
$654$	5.03702e18	−	8.72437e18i	2.51720	−	4.35992i
$655$			9.08465e17i			0.449510i
$656$	−3.11164e18	−	1.79650e18i	−1.52445	−	0.880143i
$657$	−5.99262e18	−	3.45984e18i	−2.90698	−	1.67835i
$658$		−	1.64065e18i		−	0.788040i
$659$	−1.00534e18	+	1.74130e18i	−0.478143	+	0.828169i	−0.999686	−	0.0250565i	$-0.992023\pi$
$659$	−1.00534e18	+	1.74130e18i	−0.478143	+	0.828169i	0.521543	+	0.853225i	$0.325357\pi$
$660$	−4.78411e18	−	8.28632e18i	−2.25302	−	3.90235i
$661$	−1.20564e18	+	6.96074e17i	−0.562221	+	0.324598i	−0.754036	−	0.656833i	$-0.771896\pi$
$661$	−1.20564e18	+	6.96074e17i	−0.562221	+	0.324598i	0.191816	+	0.981431i	$0.438562\pi$
$662$	5.95397e17			0.274935
$663$	5.15821e17	+	1.91899e18i	0.235864	+	0.877473i
$664$	8.72606e18			3.95117
$665$	−4.59889e17	+	2.65517e17i	−0.206211	+	0.119056i
$666$	4.67004e18	+	8.08875e18i	2.07366	+	3.59169i
$667$	−2.18007e17	+	3.77599e17i	−0.0958633	+	0.166040i
$668$			3.10898e18i			1.35385i
$669$	−2.71491e17	−	1.56745e17i	−0.117081	−	0.0675966i
$670$	−3.77614e17	−	2.18016e17i	−0.161273	−	0.0931111i
$671$		−	3.97971e18i		−	1.68328i
$672$	−2.88027e18	+	4.98878e18i	−1.20652	+	2.08975i
$673$	1.87422e18	+	3.24624e18i	0.777540	+	1.34674i	0.933356	+	0.358952i	$0.116866\pi$
$673$	1.87422e18	+	3.24624e18i	0.777540	+	1.34674i	−0.155817	+	0.987786i	$0.549801\pi$
$674$	−6.32790e18	+	3.65342e18i	−2.59998	+	1.50110i
$675$	−2.40110e18			−0.977093
$676$	1.00867e16	+	6.36442e18i	0.00406531	+	2.56510i
$677$	1.65587e18			0.660997			0.330498	−	0.943807i	$-0.392783\pi$
$677$	1.65587e18			0.660997			0.330498	+	0.943807i	$0.392783\pi$
$678$	6.60901e18	−	3.81571e18i	2.61302	−	1.50863i
$679$	2.72420e17	+	4.71845e17i	0.106681	+	0.184776i
$680$	1.31371e18	−	2.27540e18i	0.509554	−	0.882573i
$681$		−	5.17235e18i		−	1.98716i
$682$	3.16874e18	+	1.82947e18i	1.20584	+	0.696189i
$683$	−4.15235e18	−	2.39736e18i	−1.56516	−	0.903646i	−0.996720	−	0.0809214i	$-0.974214\pi$
$683$	−4.15235e18	−	2.39736e18i	−1.56516	−	0.903646i	−0.568440	−	0.822725i	$-0.692453\pi$
$684$			9.74257e18i			3.63755i
$685$	1.00251e18	−	1.73640e18i	0.370766	−	0.642185i
$686$	2.28551e18	+	3.95862e18i	0.837290	+	1.45023i
$687$	2.46280e18	−	1.42190e18i	0.893738	−	0.516000i
$688$	−1.22307e19			−4.39668
$689$	−4.14532e17	−	1.54217e18i	−0.147616	−	0.549169i
$690$	−3.91585e18			−1.38136
$691$	−1.90156e18	+	1.09787e18i	−0.664514	+	0.383657i	−0.793995	−	0.607925i	$-0.792002\pi$
$691$	−1.90156e18	+	1.09787e18i	−0.664514	+	0.383657i	0.129481	+	0.991582i	$0.458669\pi$
$692$	−4.42071e18	−	7.65689e18i	−1.53039	−	2.65071i
$693$	2.28985e18	−	3.96613e18i	0.785309	−	1.36020i
$694$		−	5.45556e18i		−	1.85354i
$695$	1.61046e17	+	9.29802e16i	0.0542063	+	0.0312960i
$696$	3.95241e18	+	2.28192e18i	1.31796	+	0.760923i
$697$			9.28321e17i			0.306680i
$698$	8.59488e17	−	1.48868e18i	0.281306	−	0.487237i
$699$	2.21988e18	+	3.84495e18i	0.719828	+	1.24678i
$700$	2.00468e18	−	1.15741e18i	0.644034	−	0.371833i
$701$	5.21258e18			1.65915			0.829576	−	0.558394i	$-0.188582\pi$
$701$	5.21258e18			1.65915			0.829576	+	0.558394i	$0.188582\pi$
$702$	−7.27729e18	−	7.26576e18i	−2.29498	−	2.29134i
$703$	−2.51019e18			−0.784326
$704$	9.31503e18	−	5.37804e18i	2.88378	−	1.66495i
$705$	−1.51635e18	−	2.62640e18i	−0.465126	−	0.805621i
$706$	−4.00324e18	+	6.93381e18i	−1.21669	+	2.10737i
$707$			2.38789e18i			0.719097i
$708$	2.49662e18	+	1.44142e18i	0.744965	+	0.430106i
$709$	2.34267e18	+	1.35254e18i	0.692643	+	0.399898i	0.804602	−	0.593815i	$-0.202379\pi$
$709$	2.34267e18	+	1.35254e18i	0.692643	+	0.399898i	−0.111958	+	0.993713i	$0.535712\pi$
$710$			2.16605e18i			0.634584i
$711$	2.43750e18	−	4.22187e18i	0.707607	−	1.22561i
$712$	−1.51213e18	−	2.61909e18i	−0.434981	−	0.753409i
$713$	9.33070e17	−	5.38708e17i	0.265970	−	0.153558i
$714$	3.09533e18			0.874316
$715$	−2.56318e18	+	2.56725e18i	−0.717447	+	0.718585i
$716$	8.91951e18			2.47404
$717$	−1.85191e18	+	1.06920e18i	−0.509034	+	0.293891i
$718$	−5.17693e16	−	8.96671e16i	−0.0141014	−	0.0244244i
$719$	6.60991e17	−	1.14487e18i	0.178426	−	0.309043i	−0.762916	−	0.646498i	$-0.776233\pi$
$719$	6.60991e17	−	1.14487e18i	0.178426	−	0.309043i	0.941342	+	0.337455i	$0.109566\pi$
$720$			1.47458e19i			3.94463i
$721$	−2.81778e18	−	1.62685e18i	−0.747014	−	0.431289i
$722$	3.07228e18	+	1.77378e18i	0.807176	+	0.466023i
$723$			7.08839e18i			1.84565i
$724$	5.66707e18	−	9.81565e18i	1.46237	−	2.53290i
$725$	−3.31085e17	−	5.73456e17i	−0.0846726	−	0.146657i
$726$	−1.55323e19	+	8.96758e18i	−3.93684	+	2.27294i
$727$	−3.75028e18			−0.942086			−0.471043	−	0.882110i	$-0.656122\pi$
$727$	−3.75028e18			−0.942086			−0.471043	+	0.882110i	$0.656122\pi$
$728$	5.84413e18	+	1.56097e18i	1.45501	+	0.388633i
$729$	−4.13896e18			−1.02132
$730$	7.39445e18	−	4.26919e18i	1.80845	−	1.04411i
$731$	1.58001e18	+	2.73666e18i	0.382998	+	0.663372i
$732$	−1.00518e19	+	1.74102e19i	−2.41502	+	4.18293i
$733$		−	4.94079e18i		−	1.17658i	−0.808651	−	0.588289i	$-0.799802\pi$
$733$		−	4.94079e18i		−	1.17658i	0.808651	−	0.588289i	$-0.200198\pi$
$734$	5.30680e17	+	3.06388e17i	0.125259	+	0.0723182i
$735$	3.11268e18	+	1.79711e18i	0.728227	+	0.420442i
$736$		−	7.60172e18i		−	1.76281i
$737$	−5.05310e17	+	8.75223e17i	−0.116150	+	0.201178i
$738$	−4.82153e18	−	8.35114e18i	−1.09855	−	1.90274i
$739$	3.90385e18	−	2.25389e18i	0.881666	−	0.509030i	0.0104584	−	0.999945i	$-0.496671\pi$
$739$	3.90385e18	−	2.25389e18i	0.881666	−	0.509030i	0.871207	+	0.490915i	$0.163338\pi$
$740$	−8.29224e18			−1.85638
$741$	5.35728e18	−	1.44003e18i	1.18885	−	0.319561i
$742$	−2.48752e18			−0.547193
$743$	−9.20574e17	+	5.31494e17i	−0.200739	+	0.115897i	−0.597000	−	0.802241i	$-0.703641\pi$
$743$	−9.20574e17	+	5.31494e17i	−0.200739	+	0.115897i	0.396261	+	0.918138i	$0.370307\pi$
$744$	−5.63877e18	−	9.76664e18i	−1.21888	−	2.11116i
$745$	1.19046e18	−	2.06193e18i	0.255093	−	0.441833i
$746$			1.70848e19i			3.62917i
$747$	1.09579e19	+	6.32657e18i	2.30752	+	1.33225i
$748$	−8.64351e18	−	4.99033e18i	−1.80439	−	1.04176i
$749$			3.14667e17i			0.0651207i
$750$	8.20037e18	−	1.42035e19i	1.68242	−	2.91404i
$751$	1.42537e18	+	2.46882e18i	0.289914	+	0.502145i	0.973789	−	0.227454i	$-0.0730400\pi$
$751$	1.42537e18	+	2.46882e18i	0.289914	+	0.502145i	−0.683875	+	0.729599i	$0.739707\pi$
$752$	1.06035e19	−	6.12192e18i	2.13812	−	1.23445i
$753$	−1.10752e17			−0.0221404
$754$	7.31829e17	−	2.73991e18i	0.145043	−	0.543028i
$755$	−4.69656e18			−0.922837
$756$	−9.98138e18	+	5.76275e18i	−1.94446	+	1.12263i
$757$	−2.01010e17	−	3.48160e17i	−0.0388235	−	0.0672443i	0.845961	−	0.533245i	$-0.179028\pi$
$757$	−2.01010e17	−	3.48160e17i	−0.0388235	−	0.0672443i	−0.884784	+	0.466001i	$0.845694\pi$
$758$	3.06795e18	−	5.31384e18i	0.587486	−	1.01756i
$759$			9.07604e18i			1.72316i
$760$	−6.35230e18	−	3.66750e18i	−1.19576	−	0.690371i
$761$	3.52403e18	+	2.03460e18i	0.657717	+	0.379733i	0.791406	−	0.611290i	$-0.209349\pi$
$761$	3.52403e18	+	2.03460e18i	0.657717	+	0.379733i	−0.133690	+	0.991023i	$0.542683\pi$
$762$		−	1.08024e19i		−	1.99900i
$763$	−2.14043e18	+	3.70733e18i	−0.392727	+	0.680223i
$764$	4.30296e18	+	7.45295e18i	0.782817	+	1.35588i
$765$	3.29943e18	−	1.90492e18i	0.595167	−	0.343620i
$766$	−2.65930e18			−0.475642
$767$	2.82058e17	−	1.05600e18i	0.0500229	−	0.187281i
$768$	−3.49512e18			−0.614631
$769$	−2.55855e18	+	1.47718e18i	−0.446142	+	0.257580i	−0.706200	−	0.708013i	$-0.749592\pi$
$769$	−2.55855e18	+	1.47718e18i	−0.446142	+	0.257580i	0.260057	+	0.965593i	$0.416259\pi$
$770$	2.82550e18	+	4.89391e18i	0.488546	+	0.846187i
$771$	1.36972e18	−	2.37242e18i	0.234843	−	0.406760i
$772$		−	1.84016e19i		−	3.12855i
$773$	1.99250e18	+	1.15037e18i	0.335917	+	0.193942i	0.658465	−	0.752611i	$-0.271206\pi$
$773$	1.99250e18	+	1.15037e18i	0.335917	+	0.193942i	−0.322548	+	0.946553i	$0.604539\pi$
$774$	−2.84274e19	−	1.64126e19i	−4.75249	−	2.74385i
$775$			1.63626e18i			0.271264i
$776$	−3.76285e18	+	6.51745e18i	−0.618609	+	1.07146i
$777$	−2.98030e18	−	5.16203e18i	−0.485873	−	0.841557i
$778$	8.67441e18	−	5.00817e18i	1.40240	−	0.809677i
$779$	2.59162e18			0.415506
$780$	1.76974e19	−	4.75705e18i	2.81381	−	0.756349i
$781$	5.02041e18			0.791602
$782$	−3.53741e18	+	2.04232e18i	−0.553148	+	0.319360i
$783$	1.64848e18	+	2.85525e18i	0.255642	+	0.442786i
$784$	−7.25542e18	+	1.25667e19i	−1.11586	+	1.93272i
$785$		−	1.86658e18i		−	0.284704i
$786$	−1.28025e19	−	7.39155e18i	−1.93664	−	1.11812i
$787$	1.08342e18	+	6.25514e17i	0.162541	+	0.0938429i	0.579064	−	0.815282i	$-0.303418\pi$
$787$	1.08342e18	+	6.25514e17i	0.162541	+	0.0938429i	−0.416523	+	0.909125i	$0.636752\pi$
$788$			1.20030e19i			1.78596i
$789$	−5.01405e18	+	8.68459e18i	−0.739925	+	1.28159i
$790$	3.00769e18	+	5.20947e18i	0.440207	+	0.762461i
$791$	−2.80843e18	+	1.62145e18i	−0.407677	+	0.235372i
$792$	6.32580e19			9.10755
$793$	7.36402e18	+	1.96693e18i	1.05157	+	0.280875i
$794$	4.62024e18			0.654382
$795$	−3.98208e18	+	2.29905e18i	−0.559401	+	0.322971i
$796$	−8.72924e18	−	1.51195e19i	−1.21630	−	2.10670i
$797$	2.91437e18	−	5.04784e18i	0.402778	−	0.697632i	−0.591282	−	0.806465i	$-0.701378\pi$
$797$	2.91437e18	−	5.04784e18i	0.402778	−	0.697632i	0.994060	+	0.108833i	$0.0347114\pi$
$798$		−	8.64131e18i		−	1.18457i
$799$	−2.73961e18	−	1.58171e18i	−0.372507	−	0.215067i
$800$	9.99797e18	+	5.77233e18i	1.34843	+	0.778514i
$801$		−	4.38530e18i		−	0.586663i
$802$	−1.35778e19	+	2.35175e19i	−1.80176	+	3.12074i
$803$	−9.89499e18	−	1.71386e19i	−1.30246	−	2.25593i
$804$	4.42118e18	−	2.55257e18i	0.577264	−	0.333283i
$805$	1.66400e18			0.215516
$806$	−4.95135e18	+	4.95921e18i	−0.636130	+	0.637139i
$807$	−2.20847e19			−2.81457
$808$	−2.85642e19	+	1.64916e19i	−3.61118	+	2.08491i
$809$	−5.13815e18	−	8.89954e18i	−0.644380	−	1.11610i	−0.984444	−	0.175696i	$-0.943782\pi$
$809$	−5.13815e18	−	8.89954e18i	−0.644380	−	1.11610i	0.340065	−	0.940402i	$-0.389551\pi$
$810$	−4.87560e18	+	8.44479e18i	−0.606563	+	1.05060i
$811$			2.14398e18i			0.264597i	0.991210	+	0.132298i	$0.0422357\pi$
$811$			2.14398e18i			0.264597i	−0.991210	+	0.132298i	$0.957764\pi$
$812$	−2.75264e18	−	1.58924e18i	−0.337005	−	0.194570i
$813$	1.90081e19	+	1.09743e19i	2.30861	+	1.33288i
$814$			2.67122e19i			3.21848i
$815$	2.09540e18	−	3.62933e18i	0.250462	−	0.433813i
$816$	1.15499e19	+	2.00050e19i	1.36960	+	2.37221i
$817$	7.63999e18	−	4.41095e18i	0.898772	−	0.518906i
$818$	−2.78480e19			−3.25011
$819$	6.20716e18	+	6.19733e18i	0.718700	+	0.717562i
$820$	8.56124e18			0.983437
$821$	−1.14077e18	+	6.58623e17i	−0.130007	+	0.0750596i	−0.563593	−	0.826053i	$-0.690581\pi$
$821$	−1.14077e18	+	6.58623e17i	−0.130007	+	0.0750596i	0.433586	+	0.901112i	$0.357248\pi$
$822$	1.63135e19	+	2.82557e19i	1.84450	+	3.19477i
$823$	2.21579e18	−	3.83787e18i	0.248559	−	0.430517i	−0.714567	−	0.699567i	$-0.753376\pi$
$823$	2.21579e18	−	3.83787e18i	0.248559	−	0.430517i	0.963126	+	0.269050i	$0.0867096\pi$
$824$		−	4.49423e19i		−	5.00183i
$825$	−1.19370e19	−	6.89185e18i	−1.31809	−	0.761001i
$826$	−1.47450e18	−	8.51305e17i	−0.161538	−	0.0932642i
$827$		−	1.15817e18i		−	0.125889i	−0.998017	−	0.0629443i	$-0.979951\pi$
$827$		−	1.15817e18i		−	0.125889i	0.998017	−	0.0629443i	$-0.0200490\pi$
$828$	1.52642e19	−	2.64384e19i	1.64618	−	2.85127i
$829$	−4.19633e18	−	7.26826e18i	−0.449020	−	0.777725i	0.549303	−	0.835623i	$-0.314893\pi$
$829$	−4.19633e18	−	7.26826e18i	−0.449020	−	0.777725i	−0.998322	+	0.0578984i	$0.981560\pi$
$830$	−1.35213e19	+	7.80651e18i	−1.43552	+	0.828799i
$831$	−2.85175e19			−3.00404
$832$	5.34761e18	+	1.98945e19i	0.558931	+	2.07937i
$833$	3.74915e18			0.388812
$834$	−2.62065e18	+	1.51303e18i	−0.269668	+	0.155693i
$835$	−1.69705e18	−	2.93938e18i	−0.173274	−	0.300119i
$836$	−1.39316e19	+	2.41303e19i	−1.41144	+	2.44468i
$837$		−	8.14700e18i		−	0.818997i
$838$	2.11369e19	+	1.22034e19i	2.10841	+	1.21729i
$839$	7.80445e18	+	4.50590e18i	0.772484	+	0.445994i	0.833760	−	0.552127i	$-0.186184\pi$
$839$	7.80445e18	+	4.50590e18i	0.772484	+	0.445994i	−0.0612758	+	0.998121i	$0.519517\pi$
$840$		−	1.74174e19i		−	1.71068i
$841$	4.67570e18	−	8.09855e18i	0.455693	−	0.789284i
$842$	7.20401e18	+	1.24777e19i	0.696699	+	1.20672i
$843$	1.31317e19	−	7.58156e18i	1.26020	−	0.727578i
$844$	3.03425e19			2.88951
$845$	−3.48358e18	−	6.01172e18i	−0.329198	−	0.568107i
$846$	3.28605e19			3.08154
$847$	6.60029e18	−	3.81068e18i	0.614215	−	0.354617i
$848$	−9.28191e18	−	1.60767e19i	−0.857165	−	1.48465i
$849$	−1.63082e19	+	2.82466e19i	−1.49453	+	2.58861i
$850$		−	6.20332e18i		−	0.564158i
$851$	6.81190e18	+	3.93285e18i	0.614789	+	0.354948i
$852$	−2.19629e19	−	1.26803e19i	−1.96713	−	1.13572i
$853$		−	1.38437e18i		−	0.123051i	−0.998106	−	0.0615253i	$-0.980404\pi$
$853$		−	1.38437e18i		−	0.123051i	0.998106	−	0.0615253i	$-0.0195965\pi$
$854$	5.93657e18	−	1.02824e19i	0.523672	−	0.907027i
$855$	−5.31803e18	−	9.21109e18i	−0.465555	−	0.806364i
$856$	−3.76409e18	+	2.17320e18i	−0.327025	+	0.188808i
$857$	−5.89774e18			−0.508523			−0.254262	−	0.967136i	$-0.581832\pi$
$857$	−5.89774e18			−0.508523			−0.254262	+	0.967136i	$0.581832\pi$
$858$	−1.53241e19	−	5.70095e19i	−1.31132	−	4.87843i
$859$	1.13255e19			0.961841			0.480921	−	0.876764i	$-0.340302\pi$
$859$	1.13255e19			0.961841			0.480921	+	0.876764i	$0.340302\pi$
$860$	2.52382e19	−	1.45713e19i	2.12725	−	1.22817i
$861$	3.07698e18	+	5.32948e18i	0.257397	+	0.445825i
$862$	1.31222e19	−	2.27284e19i	1.08946	−	1.88700i
$863$			1.24806e18i			0.102841i	0.998677	+	0.0514204i	$0.0163748\pi$
$863$			1.24806e18i			0.102841i	−0.998677	+	0.0514204i	$0.983625\pi$
$864$	−4.97802e19	−	2.87406e19i	−4.07115	−	2.35048i
$865$	8.35910e18	+	4.82613e18i	0.678508	+	0.391737i
$866$		−	9.30312e18i		−	0.749484i
$867$	−7.83356e18	+	1.35681e19i	−0.626376	+	1.08492i
$868$	3.92711e18	+	6.80195e18i	0.311670	+	0.539828i
$869$	1.20744e19	−	6.97113e18i	0.951120	−	0.549129i
$870$	−8.16581e18			−0.638446
$871$	−1.36976e18	−	1.36759e18i	−0.106298	−	0.106130i
$872$	−5.91301e19			−4.55462
$873$	−9.45056e18	+	5.45629e18i	−0.722545	+	0.417162i
$874$	5.70161e18	+	9.87547e18i	0.432686	+	0.749434i
$875$	−3.48466e18	+	6.03561e18i	−0.262487	+	0.454641i
$876$			9.99690e19i			7.47461i
$877$	−1.58218e19	−	9.13472e18i	−1.17424	−	0.677951i	−0.219569	−	0.975597i	$-0.570465\pi$
$877$	−1.58218e19	−	9.13472e18i	−1.17424	−	0.677951i	−0.954676	+	0.297646i	$0.903798\pi$
$878$	4.39309e18	+	2.53635e18i	0.323635	+	0.186851i
$879$			1.09616e19i			0.801578i
$880$	−2.10861e19	+	3.65222e19i	−1.53059	+	2.65106i
$881$	8.20197e18	+	1.42062e19i	0.590982	+	1.02361i	0.994100	+	0.108464i	$0.0345931\pi$
$881$	8.20197e18	+	1.42062e19i	0.590982	+	1.02361i	−0.403118	+	0.915148i	$0.632074\pi$
$882$	−3.37272e19	+	1.94724e19i	−2.41232	+	1.39275i
$883$	−4.66137e18			−0.330955			−0.165478	−	0.986214i	$-0.552917\pi$
$883$	−4.66137e18			−0.330955			−0.165478	+	0.986214i	$0.552917\pi$
$884$	1.35060e19	−	1.35275e19i	0.951893	−	0.953402i
$885$	−3.14723e18			−0.220190
$886$	4.35469e19	−	2.51418e19i	3.02439	−	1.74613i
$887$	−1.18724e19	−	2.05637e19i	−0.818534	−	1.41774i	−0.906763	−	0.421642i	$-0.861454\pi$
$887$	−1.18724e19	−	2.05637e19i	−0.818534	−	1.41774i	0.0882290	−	0.996100i	$-0.471879\pi$
$888$	4.11660e19	−	7.13015e19i	2.81744	−	4.87994i
$889$			4.59036e18i			0.311878i
$890$	4.68618e18	+	2.70557e18i	0.316071	+	0.182483i
$891$	1.95731e19	+	1.13005e19i	1.31055	+	0.756647i
$892$			3.01572e18i			0.200456i
$893$	−4.41571e18	+	7.64824e18i	−0.291384	+	0.504692i
$894$	1.93718e19	+	3.35530e19i	1.26905	+	2.19805i
$895$	−8.43293e18	+	4.86876e18i	−0.548440	+	0.316642i
$896$	1.04863e19			0.677049
$897$	−1.67942e19	−	4.48574e18i	−1.07649	−	0.287530i
$898$	3.29556e19			2.09717
$899$	1.94575e18	−	1.12338e18i	0.122928	−	0.0709723i
$900$	2.31816e19	+	4.01518e19i	1.45401	+	2.51842i
$901$	−2.39816e18	+	4.15373e18i	−0.149337	+	0.258659i
$902$		−	2.75787e19i		−	1.70503i
$903$	1.81416e19	+	1.04741e19i	1.11354	+	0.642903i
$904$	−3.87920e19	−	2.23965e19i	−2.36400	−	1.36485i
$905$			1.23736e19i			0.748651i
$906$	3.82127e19	−	6.61863e19i	2.29548	−	3.97589i
$907$	−5.01400e18	−	8.68450e18i	−0.299045	−	0.517962i	0.676872	−	0.736100i	$-0.263335\pi$
$907$	−5.01400e18	−	8.68450e18i	−0.299045	−	0.517962i	−0.975918	+	0.218139i	$0.930002\pi$
$908$	−4.30909e19	+	2.48785e19i	−2.55169	+	1.47322i
$909$	−4.78269e19			−2.81194
$910$	−1.04521e19	+	2.80951e18i	−0.610148	+	0.164007i
$911$	−1.14733e19			−0.664995			−0.332498	−	0.943104i	$-0.607891\pi$
$911$	−1.14733e19			−0.664995			−0.332498	+	0.943104i	$0.607891\pi$
$912$	5.58485e19	−	3.22442e19i	3.21399	−	1.85560i
$913$	1.80937e19	+	3.13392e19i	1.03387	+	1.79072i
$914$	−2.44711e19	+	4.23853e19i	−1.38837	+	2.40472i
$915$		−	2.19472e19i		−	1.23635i
$916$	−2.36917e19	−	1.36784e19i	−1.32518	−	0.765094i
$917$	5.44030e18	+	3.14096e18i	0.302150	+	0.174446i
$918$			3.08865e19i			1.70330i
$919$	−6.41297e16	+	1.11076e17i	−0.00351162	+	0.00608231i	−0.867776	−	0.496956i	$-0.834451\pi$
$919$	−6.41297e16	+	1.11076e17i	−0.00351162	+	0.00608231i	0.864264	+	0.503038i	$0.167784\pi$
$920$	1.14922e19	+	1.99050e19i	0.624857	+	1.08228i
$921$	3.96080e19	−	2.28677e19i	2.13843	−	1.23462i
$922$	3.62125e19			1.94136
$923$	−2.48128e18	+	9.28971e18i	−0.132089	+	0.494528i
$924$	−6.61631e19			−3.49742
$925$	−1.03452e19	+	5.97278e18i	−0.543021	+	0.313513i
$926$	−7.72508e18	−	1.33802e19i	−0.402653	−	0.697416i
$927$	3.25841e19	−	5.64373e19i	1.68650	−	2.92111i
$928$		−	1.58520e19i		−	0.814748i
$929$	1.20472e19	+	6.95548e18i	0.614873	+	0.354997i	0.774870	−	0.632120i	$-0.217815\pi$
$929$	1.20472e19	+	6.95548e18i	0.614873	+	0.354997i	−0.159997	+	0.987117i	$0.551148\pi$
$930$	1.74749e19	+	1.00891e19i	0.885675	+	0.511345i
$931$		−	1.04666e19i		−	0.526783i
$932$	2.13549e19	−	3.69877e19i	1.06732	−	1.84865i
$933$	3.02948e18	+	5.24722e18i	0.150362	+	0.260434i
$934$	−2.72770e19	+	1.57484e19i	−1.34444	+	0.776215i
$935$	1.08960e19			0.533324
$936$	−3.12646e19	+	1.17052e20i	−1.51971	+	5.68965i
$937$	8.88142e18			0.428721			0.214361	−	0.976755i	$-0.431233\pi$
$937$	8.88142e18			0.428721			0.214361	+	0.976755i	$0.431233\pi$
$938$	−2.61115e18	+	1.50755e18i	−0.125174	+	0.0722692i
$939$	4.51359e18	+	7.81777e18i	0.214880	+	0.372183i
$940$	−1.45870e19	+	2.52654e19i	−0.689660	+	1.19453i
$941$			5.48430e18i			0.257507i	0.991677	+	0.128753i	$0.0410975\pi$
$941$			5.48430e18i			0.257507i	−0.991677	+	0.128753i	$0.958902\pi$
$942$	2.63048e19	+	1.51871e19i	1.22660	+	0.708179i
$943$	−7.03287e18	−	4.06043e18i	−0.325692	−	0.188038i
$944$		−	1.27062e19i		−	0.584385i
$945$	6.29125e18	−	1.08968e19i	0.287363	−	0.497727i
$946$	−4.69392e19	−	8.13011e19i	−2.12933	−	3.68811i
$947$	−1.03622e19	+	5.98261e18i	−0.466849	+	0.269536i	−0.714920	−	0.699206i	$-0.753537\pi$
$947$	−1.03622e19	+	5.98261e18i	−0.466849	+	0.269536i	0.248071	+	0.968742i	$0.420203\pi$
$948$	−7.04293e19			−3.15137
$949$	3.66036e19	−	9.83901e18i	1.62665	−	0.437241i
$950$	−1.73180e19			−0.764352
$951$	−6.49075e18	+	3.74744e18i	−0.284526	+	0.164271i
$952$	−9.08411e18	−	1.57341e19i	−0.395496	−	0.685019i
$953$	1.11200e19	−	1.92604e19i	0.480841	−	0.832841i	−0.518917	−	0.854824i	$-0.673665\pi$
$953$	1.11200e19	−	1.92604e19i	0.480841	−	0.832841i	0.999758	+	0.0219834i	$0.00699811\pi$
$954$		−	4.98224e19i		−	2.13974i
$955$	−8.13645e18	−	4.69758e18i	−0.347067	−	0.200379i
$956$	1.78151e19	+	1.02855e19i	0.754765	+	0.435764i
$957$			1.89265e19i			0.796420i
$958$	−4.23186e19	+	7.32979e19i	−1.76870	+	3.06349i
$959$	−6.93223e18	−	1.20070e19i	−0.287774	−	0.498439i
$960$	5.13702e19	−	2.96586e19i	2.11811	−	1.22289i
$961$	1.88657e19			0.772627
$962$	−4.94280e19	−	1.32022e19i	−2.01064	−	0.537043i
$963$	−6.30245e18			−0.254647
$964$	5.90534e19	−	3.40945e19i	2.36998	−	1.36831i
$965$	1.00446e19	+	1.73978e19i	0.400411	+	0.693532i
$966$	−1.35388e19	+	2.34499e19i	−0.536080	+	0.928517i
$967$			1.87148e19i			0.736061i	0.929814	+	0.368031i	$0.119968\pi$
$967$			1.87148e19i			0.736061i	−0.929814	+	0.368031i	$0.880032\pi$
$968$	9.11678e19	+	5.26357e19i	3.56165	+	2.05632i
$969$	−1.44295e19	−	8.33088e18i	−0.559947	−	0.323286i
$970$		−	1.34653e19i		−	0.519038i
$971$	−1.97359e19	+	3.41835e19i	−0.755668	+	1.30886i	0.189373	+	0.981905i	$0.439355\pi$
$971$	−1.97359e19	+	3.41835e19i	−0.755668	+	1.30886i	−0.945041	+	0.326951i	$0.893979\pi$
$972$	8.34211e17	+	1.44490e18i	0.0317282	+	0.0549548i
$973$	1.11362e18	−	6.42946e17i	0.0420728	−	0.0242908i
$974$	8.37948e19			3.14473
$975$	1.86524e19	−	1.86820e19i	0.695351	−	0.696454i
$976$	8.86069e19			3.28128
$977$	−3.50337e18	+	2.02267e18i	−0.128876	+	0.0744065i	−0.563052	−	0.826422i	$-0.690373\pi$
$977$	−3.50337e18	+	2.02267e18i	−0.128876	+	0.0744065i	0.434176	+	0.900828i	$0.357040\pi$
$978$	3.40976e19	+	5.90588e19i	1.24601	+	2.15815i
$979$	6.27088e18	−	1.08615e19i	0.227636	−	0.394277i
$980$		−	3.45757e19i		−	1.24681i
$981$	−7.42539e19	−	4.28705e19i	−2.65993	−	1.53571i
$982$	−6.57698e19	−	3.79722e19i	−2.34046	−	1.35127i
$983$		−	8.51220e18i		−	0.300915i	−0.988616	−	0.150458i	$-0.951925\pi$
$983$		−	8.51220e18i		−	0.300915i	0.988616	−	0.150458i	$-0.0480747\pi$
$984$	−4.25014e19	+	7.36145e19i	−1.49257	+	2.58521i
$985$	−6.55192e18	−	1.13483e19i	−0.228577	−	0.395907i
$986$	−7.37664e18	+	4.25890e18i	−0.255657	+	0.147604i
$987$	−2.09707e19			−0.722025
$988$	−3.77649e19	−	3.77051e19i	−1.29172	−	1.28967i
$989$	−2.76435e19			−0.939329
$990$	−9.80199e19	+	5.65918e19i	−3.30891	+	1.91040i
$991$	−4.46009e18	−	7.72511e18i	−0.149577	−	0.259075i	0.781494	−	0.623913i	$-0.214458\pi$
$991$	−4.46009e18	−	7.72511e18i	−0.149577	−	0.259075i	−0.931071	+	0.364837i	$0.881125\pi$
$992$	−1.95857e19	+	3.39234e19i	−0.652548	+	1.13025i
$993$		−	7.61034e18i		−	0.251903i
$994$	1.29713e19	+	7.48898e18i	0.426552	+	0.246270i
$995$	1.65061e19	+	9.52979e18i	0.539255	+	0.311339i
$996$		−	1.82800e20i		−	5.93323i
$997$	−1.64842e19	+	2.85515e19i	−0.531558	+	0.920685i	0.467764	+	0.883853i	$0.345060\pi$
$997$	−1.64842e19	+	2.85515e19i	−0.531558	+	0.920685i	−0.999321	+	0.0368313i	$0.988274\pi$
$998$	−4.42315e19	−	7.66112e19i	−1.41704	−	2.45439i
$999$	5.15089e19	−	2.97387e19i	1.63948	−	0.946555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.14.e.a.10.1	yes	30
13.2	odd	12		169.14.a.f.1.2		30
13.4	even	6	inner	13.14.e.a.4.1	✓	30
13.11	odd	12		169.14.a.f.1.29		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.e.a.4.1	✓	30	13.4	even	6	inner
13.14.e.a.10.1	yes	30	1.1	even	1	trivial
169.14.a.f.1.2		30	13.2	odd	12
169.14.a.f.1.29		30	13.11	odd	12

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.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-148.000 + 85.4479i) q^{2} +(1092.19 + 1891.73i) q^{3} +(10506.7 - 18198.1i) q^{4} +22940.5i q^{5} +(-323289. - 186651. i) q^{6} +(137378. + 79315.3i) q^{7} +2.19112e6i q^{8} +(-1.58860e6 + 2.75154e6i) q^{9} +(-1.96022e6 - 3.39519e6i) q^{10} +(-7.86928e6 + 4.54333e6i) q^{11} +4.59012e7 q^{12} +(-4.51763e6 - 1.68067e7i) q^{13} -2.71093e7 q^{14} +(-4.33972e7 + 2.50554e7i) q^{15} +(-1.01156e8 - 1.75207e8i) q^{16} +(-2.61354e7 + 4.52679e7i) q^{17} -5.42971e8i q^{18} +(1.26376e8 + 7.29630e7i) q^{19} +(4.17473e8 + 2.41028e8i) q^{20} +3.46510e8i q^{21} +(7.76436e8 - 1.34483e9i) q^{22} +(-2.28630e8 - 3.95999e8i) q^{23} +(-4.14500e9 + 2.39312e9i) q^{24} +6.94437e8 q^{25} +(2.10471e9 + 2.10138e9i) q^{26} -3.45762e9 q^{27} +(2.88678e9 - 1.66668e9i) q^{28} +(-4.76768e8 - 8.25786e8i) q^{29} +(4.28186e9 - 7.41640e9i) q^{30} +2.35624e9i q^{31} +(1.43972e10 + 8.31224e9i) q^{32} +(-1.71895e10 - 9.92437e9i) q^{33} -8.93287e9i q^{34} +(-1.81953e9 + 3.15152e9i) q^{35} +(3.33819e10 + 5.78191e10i) q^{36} +(-1.48972e10 + 8.60090e9i) q^{37} -2.49381e10 q^{38} +(2.68597e10 - 2.69023e10i) q^{39} -5.02653e10 q^{40} +(1.53805e10 - 8.87991e9i) q^{41} +(-2.96085e10 - 5.12835e10i) q^{42} +(3.02273e10 - 5.23553e10i) q^{43} +1.90941e11i q^{44} +(-6.31217e10 - 3.64433e10i) q^{45} +(6.76746e10 + 3.90719e10i) q^{46} +6.05199e10i q^{47} +(2.20962e11 - 3.82718e11i) q^{48} +(-3.58627e10 - 6.21160e10i) q^{49} +(-1.02777e11 + 5.93382e10i) q^{50} -1.14180e11 q^{51} +(-3.53316e11 - 9.43707e10i) q^{52} +9.17588e10 q^{53} +(5.11728e11 - 2.95446e11i) q^{54} +(-1.04226e11 - 1.80525e11i) q^{55} +(-1.73789e11 + 3.01012e11i) q^{56} +3.18758e11i q^{57} +(1.41123e11 + 8.14776e10i) q^{58} +(5.43911e10 + 3.14027e10i) q^{59} +1.05300e12i q^{60} +(-2.18987e11 + 3.79296e11i) q^{61} +(-2.01336e11 - 3.48724e11i) q^{62} +(-4.36479e11 + 2.52001e11i) q^{63} -1.18372e12 q^{64} +(3.85555e11 - 1.03637e11i) q^{65} +3.39207e12 q^{66} +(9.63195e10 - 5.56101e10i) q^{67} +(5.49193e11 + 9.51231e11i) q^{68} +(4.99416e11 - 8.65014e11i) q^{69} -6.21901e11i q^{70} +(-4.78482e11 - 2.76251e11i) q^{71} +(-6.02895e12 - 3.48081e12i) q^{72} +2.17792e12i q^{73} +(1.46986e12 - 2.54587e12i) q^{74} +(7.58458e11 + 1.31369e12i) q^{75} +(2.65558e12 - 1.53320e12i) q^{76} -1.44142e12 q^{77} +(-1.67649e12 + 6.27665e12i) q^{78} -1.53437e12 q^{79} +(4.01932e12 - 2.32056e12i) q^{80} +(-1.24364e12 - 2.15405e12i) q^{81} +(-1.51754e12 + 2.62845e12i) q^{82} -3.98247e12i q^{83} +(6.30583e12 + 3.64067e12i) q^{84} +(-1.03847e12 - 5.99560e11i) q^{85} +1.03314e13i q^{86} +(1.04144e12 - 1.80383e12i) q^{87} +(-9.95497e12 - 1.72425e13i) q^{88} +(-1.19532e12 + 6.90120e11i) q^{89} +1.24560e13 q^{90} +(7.12408e11 - 2.66719e12i) q^{91} -9.60858e12 q^{92} +(-4.45738e12 + 2.57347e12i) q^{93} +(-5.17130e12 - 8.95695e12i) q^{94} +(-1.67381e12 + 2.89912e12i) q^{95} +3.63142e13i q^{96} +(2.97449e12 + 1.71732e12i) q^{97} +(1.06154e13 + 6.12878e12i) q^{98} -2.88702e13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 730 q^{3} + 65535 q^{4} - 382584 q^{6} + 438984 q^{7} - 9117071 q^{9} + 3893475 q^{10} - 5364528 q^{11} + 27694876 q^{12} - 1794135 q^{13} + 61125588 q^{14} - 113380170 q^{15} - 350182521 q^{16}+ \cdots + 86959564160763 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 - 730 * q^3 + 65535 * q^4 - 382584 * q^6 + 438984 * q^7 - 9117071 * q^9 + 3893475 * q^10 - 5364528 * q^11 + 27694876 * q^12 - 1794135 * q^13 + 61125588 * q^14 - 113380170 * q^15 - 350182521 * q^16 - 23524899 * q^17 + 92116746 * q^19 + 959687745 * q^20 - 128185362 * q^22 + 417086886 * q^23 - 4232784354 * q^24 - 11926991364 * q^25 + 5442553119 * q^26 + 5605403288 * q^27 + 22569369732 * q^28 - 8810189577 * q^29 - 9936679242 * q^30 + 9137241117 * q^32 + 12085621392 * q^33 + 1059240720 * q^35 + 55900963715 * q^36 - 72651649419 * q^37 - 45168847944 * q^38 - 41492436530 * q^39 + 137282090274 * q^40 - 3909896103 * q^41 - 34124964786 * q^42 + 138326640480 * q^43 - 259122942393 * q^45 - 288578831832 * q^46 + 630595691198 * q^48 + 114277635303 * q^49 - 553717814136 * q^50 - 178343342508 * q^51 - 1243882821894 * q^52 + 938994404670 * q^53 + 1180281528282 * q^54 - 140610123120 * q^55 + 932974200720 * q^56 - 768032047215 * q^58 - 1420851272556 * q^59 + 284498233437 * q^61 + 2574083847030 * q^62 - 3219361289664 * q^63 - 4989806279958 * q^64 - 931161533727 * q^65 + 12037245084948 * q^66 + 2624227676622 * q^67 - 3124046642277 * q^68 + 1206986427996 * q^69 - 1317657850698 * q^71 - 2571404508735 * q^72 + 1723434230073 * q^74 + 1909848151684 * q^75 - 5741418039246 * q^76 - 8153714196816 * q^77 - 13064083856250 * q^78 + 10732970056200 * q^79 + 11699811454875 * q^80 + 26873856445 * q^81 - 924448017327 * q^82 + 5758359493380 * q^84 - 14711656818213 * q^85 - 6442966126134 * q^87 - 11094606812688 * q^88 + 18293004024660 * q^89 + 53932182551466 * q^90 + 2271787574784 * q^91 - 48706576133844 * q^92 - 50634402753492 * q^93 + 3529466920146 * q^94 + 11308314514950 * q^95 - 4972913690148 * q^97 + 86959564160763 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more