LMFDB - Embedded newform 13.8.c.a.3.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,8,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, 8, 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, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 8 $
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:	$4.06100533129$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 796 x^{14} - 475 x^{13} + 449889 x^{12} - 92038 x^{11} + 116806037 x^{10} + \cdots + 11\!\cdots\!00 $ x^16 - x^15 + 796x^14 - 475x^13 + 449889x^12 - 92038x^11 + 116806037x^10 + 198490961x^9 + 21546318357x^8 + 32373621530x^7 + 2116860322049x^6 + 2147931692741x^5 + 148294262896076x^4 + 71847528967407x^3 + 4924011367741489x^2 - 2411116235274240x + 113340278793830400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{12}\cdot 3\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.1
Root			$10.3972 + 18.0085i$ of defining polynomial
Character	$\chi$	$=$	13.3
Dual form			13.8.c.a.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-10.8972 - 18.8745i) q^{2} +(33.9160 + 58.7442i) q^{3} +(-173.499 + 300.509i) q^{4} +157.804 q^{5} +(739.180 - 1280.30i) q^{6} +(-421.054 + 729.287i) q^{7} +4772.94 q^{8} +(-1207.09 + 2090.74i) q^{9} +(-1719.62 - 2978.47i) q^{10} +(995.582 + 1724.40i) q^{11} -23537.6 q^{12} +(4212.97 + 6708.16i) q^{13} +18353.3 q^{14} +(5352.06 + 9270.04i) q^{15} +(-29804.0 - 51622.0i) q^{16} +(-4810.45 + 8331.95i) q^{17} +52615.6 q^{18} +(4219.62 - 7308.60i) q^{19} +(-27378.8 + 47421.4i) q^{20} -57121.8 q^{21} +(21698.2 - 37582.3i) q^{22} +(-17066.2 - 29559.5i) q^{23} +(161879. + 280383. i) q^{24} -53223.0 q^{25} +(80703.9 - 152618. i) q^{26} -15409.7 q^{27} +(-146105. - 253061. i) q^{28} +(4836.45 + 8376.97i) q^{29} +(116645. - 202035. i) q^{30} +205412. q^{31} +(-344092. + 595986. i) q^{32} +(-67532.3 + 116969. i) q^{33} +209682. q^{34} +(-66443.8 + 115084. i) q^{35} +(-418857. - 725481. i) q^{36} +(-216001. - 374125. i) q^{37} -183929. q^{38} +(-251179. + 475001. i) q^{39} +753187. q^{40} +(-56793.2 - 98368.8i) q^{41} +(622469. + 1.07815e6i) q^{42} +(200181. - 346724. i) q^{43} -690930. q^{44} +(-190483. + 329926. i) q^{45} +(-371948. + 644233. i) q^{46} +1.32924e6 q^{47} +(2.02166e6 - 3.50162e6i) q^{48} +(57198.6 + 99070.9i) q^{49} +(579983. + 1.00456e6i) q^{50} -652605. q^{51} +(-2.74681e6 + 102175. i) q^{52} +298608. q^{53} +(167923. + 290851. i) q^{54} +(157106. + 272116. i) q^{55} +(-2.00967e6 + 3.48084e6i) q^{56} +572451. q^{57} +(105408. - 182571. i) q^{58} +(817121. - 1.41529e6i) q^{59} -3.71431e6 q^{60} +(-831187. + 1.43966e6i) q^{61} +(-2.23842e6 - 3.87706e6i) q^{62} +(-1.01650e6 - 1.76063e6i) q^{63} +7.36880e6 q^{64} +(664821. + 1.05857e6i) q^{65} +2.94366e6 q^{66} +(-711527. - 1.23240e6i) q^{67} +(-1.66922e6 - 2.89117e6i) q^{68} +(1.15763e6 - 2.00508e6i) q^{69} +2.89621e6 q^{70} +(519805. - 900329. i) q^{71} +(-5.76136e6 + 9.97896e6i) q^{72} +4.43080e6 q^{73} +(-4.70763e6 + 8.15385e6i) q^{74} +(-1.80511e6 - 3.12655e6i) q^{75} +(1.46420e6 + 2.53607e6i) q^{76} -1.67678e6 q^{77} +(1.17026e7 - 435311. i) q^{78} -7.40813e6 q^{79} +(-4.70317e6 - 8.14613e6i) q^{80} +(2.11727e6 + 3.66721e6i) q^{81} +(-1.23778e6 + 2.14389e6i) q^{82} +753809. q^{83} +(9.91058e6 - 1.71656e7i) q^{84} +(-759106. + 1.31481e6i) q^{85} -8.72569e6 q^{86} +(-328066. + 568226. i) q^{87} +(4.75186e6 + 8.23046e6i) q^{88} +(1.24588e6 + 2.15793e6i) q^{89} +8.30293e6 q^{90} +(-6.66606e6 + 247963. i) q^{91} +1.18439e7 q^{92} +(6.96676e6 + 1.20668e7i) q^{93} +(-1.44851e7 - 2.50888e7i) q^{94} +(665872. - 1.15332e6i) q^{95} -4.66809e7 q^{96} +(-3.19399e6 + 5.53216e6i) q^{97} +(1.24661e6 - 2.15919e6i) q^{98} -4.80702e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 9 q^{2} - 28 q^{3} - 577 q^{4} + 384 q^{5} + 342 q^{6} + 196 q^{7} + 5922 q^{8} - 5988 q^{9} - 6813 q^{10} + 5052 q^{11} - 15816 q^{12} + 17064 q^{13} + 14484 q^{14} - 184 q^{15} - 61377 q^{16} - 22824 q^{17}+ \cdots + 27386736 q^{99}+O(q^{100}) $ 16 * q - 9 * q^2 - 28 * q^3 - 577 * q^4 + 384 * q^5 + 342 * q^6 + 196 * q^7 + 5922 * q^8 - 5988 * q^9 - 6813 * q^10 + 5052 * q^11 - 15816 * q^12 + 17064 * q^13 + 14484 * q^14 - 184 * q^15 - 61377 * q^16 - 22824 * q^17 + 226318 * q^18 + 63692 * q^19 - 121971 * q^20 - 271240 * q^21 - 73726 * q^22 - 72468 * q^23 + 224952 * q^24 + 58488 * q^25 + 154443 * q^26 + 358616 * q^27 - 172816 * q^28 - 221772 * q^29 - 258116 * q^30 + 58432 * q^31 + 77823 * q^32 - 352372 * q^33 + 643334 * q^34 + 31560 * q^35 - 1162993 * q^36 - 368884 * q^37 + 2364492 * q^38 - 672996 * q^39 + 766030 * q^40 - 385824 * q^41 + 1560954 * q^42 + 391492 * q^43 - 6149616 * q^44 + 232096 * q^45 - 2599078 * q^46 + 1089984 * q^47 + 4585712 * q^48 - 1108780 * q^49 + 1626894 * q^50 + 8040712 * q^51 - 1312478 * q^52 + 3329328 * q^53 - 5616702 * q^54 - 418216 * q^55 - 3609156 * q^56 - 12068664 * q^57 + 3685081 * q^58 - 6318924 * q^59 + 1448784 * q^60 + 1763548 * q^61 - 12998388 * q^62 + 6641128 * q^63 + 32227074 * q^64 + 9500508 * q^65 + 16245108 * q^66 - 8607964 * q^67 - 10118091 * q^68 - 4618492 * q^69 - 25381840 * q^70 + 9473220 * q^71 - 35174445 * q^72 + 5020888 * q^73 + 2206221 * q^74 - 21834988 * q^75 + 18702876 * q^76 + 35263992 * q^77 + 28395902 * q^78 + 12644416 * q^79 - 24671247 * q^80 - 9316272 * q^81 - 9347751 * q^82 - 22158432 * q^83 + 37532636 * q^84 - 36911824 * q^85 - 30103956 * q^86 + 5199988 * q^87 - 36676404 * q^88 + 18469860 * q^89 + 132263562 * q^90 - 9614540 * q^91 + 64127424 * q^92 - 26340696 * q^93 - 6026128 * q^94 - 16267080 * q^95 - 164216320 * q^96 + 19660916 * q^97 - 51546651 * q^98 + 27386736 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−10.8972	−	18.8745i	−0.963188	−	1.66829i	−0.714407	−	0.699730i	$-0.753304\pi$
$2$	−10.8972	−	18.8745i	−0.963188	−	1.66829i	−0.248781	−	0.968560i	$-0.580030\pi$
$3$	33.9160	+	58.7442i	0.725237	+	1.25615i	0.958876	+	0.283824i	$0.0916032\pi$
$3$	33.9160	+	58.7442i	0.725237	+	1.25615i	−0.233639	+	0.972323i	$0.575064\pi$
$4$	−173.499	+	300.509i	−1.35546	+	2.34773i
$5$	157.804			0.564575			0.282288	−	0.959330i	$-0.408907\pi$
$5$	157.804			0.564575			0.282288	+	0.959330i	$0.408907\pi$
$6$	739.180	−	1280.30i	1.39708	−	2.41981i
$7$	−421.054	+	729.287i	−0.463975	+	0.803628i	−0.999155	−	0.0411099i	$-0.986911\pi$
$7$	−421.054	+	729.287i	−0.463975	+	0.803628i	0.535180	+	0.844738i	$0.320244\pi$
$8$	4772.94			3.29588
$9$	−1207.09	+	2090.74i	−0.551937	+	0.955984i
$10$	−1719.62	−	2978.47i	−0.543792	−	0.941875i
$11$	995.582	+	1724.40i	0.225529	+	0.390628i	0.956478	−	0.291804i	$-0.0942556\pi$
$11$	995.582	+	1724.40i	0.225529	+	0.390628i	−0.730949	+	0.682432i	$0.760922\pi$
$12$	−23537.6			−3.93212
$13$	4212.97	+	6708.16i	0.531846	+	0.846841i
$13$	4212.97	+	6708.16i	0.531846	+	0.846841i
$14$	18353.3			1.78758
$15$	5352.06	+	9270.04i	0.409451	+	0.709190i
$16$	−29804.0	−	51622.0i	−1.81909	−	3.15075i
$17$	−4810.45	+	8331.95i	−0.237473	+	0.411316i	−0.959989	−	0.280039i	$-0.909653\pi$
$17$	−4810.45	+	8331.95i	−0.237473	+	0.411316i	0.722515	+	0.691355i	$0.242986\pi$
$18$	52615.6			2.12648
$19$	4219.62	−	7308.60i	0.141135	−	0.244454i	−0.786789	−	0.617222i	$-0.788258\pi$
$19$	4219.62	−	7308.60i	0.141135	−	0.244454i	0.927924	+	0.372768i	$0.121591\pi$
$20$	−27378.8	+	47421.4i	−0.765260	+	1.32547i
$21$	−57121.8			−1.34597
$22$	21698.2	−	37582.3i	0.434454	−	0.752496i
$23$	−17066.2	−	29559.5i	−0.292475	−	0.506581i	0.681919	−	0.731427i	$-0.261145\pi$
$23$	−17066.2	−	29559.5i	−0.292475	−	0.506581i	−0.974394	+	0.224846i	$0.927812\pi$
$24$	161879.	+	280383.i	2.39029	+	4.14011i
$25$	−53223.0			−0.681255
$26$	80703.9	−	152618.i	0.900508	−	1.70294i
$27$	−15409.7			−0.150668
$28$	−146105.	−	253061.i	−1.25780	−	2.17857i
$29$	4836.45	+	8376.97i	0.0368242	+	0.0637814i	0.883850	−	0.467770i	$-0.154943\pi$
$29$	4836.45	+	8376.97i	0.0368242	+	0.0637814i	−0.847026	+	0.531552i	$0.821609\pi$
$30$	116645.	−	202035.i	0.788756	−	1.36617i
$31$	205412.			1.23840			0.619199	−	0.785234i	$-0.287457\pi$
$31$	205412.			1.23840			0.619199	+	0.785234i	$0.287457\pi$
$32$	−344092.	+	595986.i	−1.85631	+	3.21522i
$33$	−67532.3	+	116969.i	−0.327124	+	0.566596i
$34$	209682.			0.914925
$35$	−66443.8	+	115084.i	−0.261949	+	0.453709i
$36$	−418857.	−	725481.i	−1.49626	−	2.59160i
$37$	−216001.	−	374125.i	−0.701052	−	1.21426i	−0.968098	−	0.250574i	$-0.919381\pi$
$37$	−216001.	−	374125.i	−0.701052	−	1.21426i	0.267046	−	0.963684i	$-0.413953\pi$
$38$	−183929.			−0.543760
$39$	−251179.	+	475001.i	−0.678042	+	1.28224i
$40$	753187.			1.86077
$41$	−56793.2	−	98368.8i	−0.128692	−	0.222902i	0.794478	−	0.607293i	$-0.207745\pi$
$41$	−56793.2	−	98368.8i	−0.128692	−	0.222902i	−0.923170	+	0.384391i	$0.874411\pi$
$42$	622469.	+	1.07815e6i	1.29642	+	2.24546i
$43$	200181.	−	346724.i	0.383958	−	0.665035i	−0.607666	−	0.794193i	$-0.707894\pi$
$43$	200181.	−	346724.i	0.383958	−	0.665035i	0.991624	+	0.129158i	$0.0412273\pi$
$44$	−690930.			−1.22278
$45$	−190483.	+	329926.i	−0.311610	+	0.539725i
$46$	−371948.	+	644233.i	−0.563417	+	0.975866i
$47$	1.32924e6			1.86750			0.933752	−	0.357920i	$-0.116514\pi$
$47$	1.32924e6			1.86750			0.933752	+	0.357920i	$0.116514\pi$
$48$	2.02166e6	−	3.50162e6i	2.63854	−	4.57009i
$49$	57198.6	+	99070.9i	0.0694543	+	0.120298i
$50$	579983.	+	1.00456e6i	0.656176	+	1.13653i
$51$	−652605.			−0.688898
$52$	−2.74681e6	+	102175.i	−2.70905	+	0.100771i
$53$	298608.			0.275509			0.137755	−	0.990466i	$-0.456011\pi$
$53$	298608.			0.275509			0.137755	+	0.990466i	$0.456011\pi$
$54$	167923.	+	290851.i	0.145121	+	0.251358i
$55$	157106.	+	272116.i	0.127328	+	0.220539i
$56$	−2.00967e6	+	3.48084e6i	−1.52921	+	2.64866i
$57$	572451.			0.409427
$58$	105408.	−	182571.i	0.0709372	−	0.122867i
$59$	817121.	−	1.41529e6i	0.517970	−	0.897150i	−0.481812	−	0.876274i	$-0.660021\pi$
$59$	817121.	−	1.41529e6i	0.517970	−	0.897150i	0.999782	−	0.0208753i	$-0.00664531\pi$
$60$	−3.71431e6			−2.21998
$61$	−831187.	+	1.43966e6i	−0.468861	+	0.812091i	−0.999366	−	0.0355904i	$-0.988669\pi$
$61$	−831187.	+	1.43966e6i	−0.468861	+	0.812091i	0.530505	+	0.847682i	$0.322002\pi$
$62$	−2.23842e6	−	3.87706e6i	−1.19281	−	2.06601i
$63$	−1.01650e6	−	1.76063e6i	−0.512170	−	0.887105i
$64$	7.36880e6			3.51372
$65$	664821.	+	1.05857e6i	0.300267	+	0.478105i
$66$	2.94366e6			1.26033
$67$	−711527.	−	1.23240e6i	−0.289021	−	0.500599i	0.684555	−	0.728961i	$-0.259996\pi$
$67$	−711527.	−	1.23240e6i	−0.289021	−	0.500599i	−0.973576	+	0.228362i	$0.926663\pi$
$68$	−1.66922e6	−	2.89117e6i	−0.643771	−	1.11504i
$69$	1.15763e6	−	2.00508e6i	0.424227	−	0.734783i
$70$	2.89621e6			1.00922
$71$	519805.	−	900329.i	0.172360	−	0.298536i	−0.766885	−	0.641785i	$-0.778194\pi$
$71$	519805.	−	900329.i	0.172360	−	0.298536i	0.939244	+	0.343249i	$0.111527\pi$
$72$	−5.76136e6	+	9.97896e6i	−1.81912	+	3.15081i
$73$	4.43080e6			1.33307			0.666533	−	0.745475i	$-0.267778\pi$
$73$	4.43080e6			1.33307			0.666533	+	0.745475i	$0.267778\pi$
$74$	−4.70763e6	+	8.15385e6i	−1.35049	+	2.33912i
$75$	−1.80511e6	−	3.12655e6i	−0.494071	−	0.855757i
$76$	1.46420e6	+	2.53607e6i	0.382607	+	0.662695i
$77$	−1.67678e6			−0.418560
$78$	1.17026e7	−	435311.i	2.79223	−	0.103865i
$79$	−7.40813e6			−1.69049			−0.845247	−	0.534376i	$-0.820547\pi$
$79$	−7.40813e6			−1.69049			−0.845247	+	0.534376i	$0.820547\pi$
$80$	−4.70317e6	−	8.14613e6i	−1.02701	−	1.77884i
$81$	2.11727e6	+	3.66721e6i	0.442668	+	0.766723i
$82$	−1.23778e6	+	2.14389e6i	−0.247910	+	0.429393i
$83$	753809.			0.144706			0.0723532	−	0.997379i	$-0.476949\pi$
$83$	753809.			0.144706			0.0723532	+	0.997379i	$0.476949\pi$
$84$	9.91058e6	−	1.71656e7i	1.82441	−	3.15997i
$85$	−759106.	+	1.31481e6i	−0.134071	+	0.232219i
$86$	−8.72569e6			−1.47930
$87$	−328066.	+	568226.i	−0.0534126	+	0.0925133i
$88$	4.75186e6	+	8.23046e6i	0.743317	+	1.28746i
$89$	1.24588e6	+	2.15793e6i	0.187332	+	0.324469i	0.944360	−	0.328914i	$-0.106683\pi$
$89$	1.24588e6	+	2.15793e6i	0.187332	+	0.324469i	−0.757028	+	0.653383i	$0.773349\pi$
$90$	8.30293e6			1.20056
$91$	−6.66606e6	+	247963.i	−0.927309	+	0.0344939i
$92$	1.18439e7			1.58575
$93$	6.96676e6	+	1.20668e7i	0.898132	+	1.55561i
$94$	−1.44851e7	−	2.50888e7i	−1.79876	−	3.11554i
$95$	665872.	−	1.15332e6i	0.0796816	−	0.138013i
$96$	−4.66809e7			−5.38505
$97$	−3.19399e6	+	5.53216e6i	−0.355331	+	0.615451i	−0.987175	−	0.159645i	$-0.948965\pi$
$97$	−3.19399e6	+	5.53216e6i	−0.355331	+	0.615451i	0.631844	+	0.775096i	$0.282298\pi$
$98$	1.24661e6	−	2.15919e6i	0.133795	−	0.231740i
$99$	−4.80702e6			−0.497912
$100$	9.23415e6	−	1.59940e7i	0.923415	−	1.59940i
$101$	6.89507e6	+	1.19426e7i	0.665908	+	1.15339i	0.979038	+	0.203676i	$0.0652889\pi$
$101$	6.89507e6	+	1.19426e7i	0.665908	+	1.15339i	−0.313131	+	0.949710i	$0.601378\pi$
$102$	7.11158e6	+	1.23176e7i	0.663538	+	1.14928i
$103$	1.00557e7			0.906740			0.453370	−	0.891322i	$-0.350222\pi$
$103$	1.00557e7			0.906740			0.453370	+	0.891322i	$0.350222\pi$
$104$	2.01082e7	+	3.20177e7i	1.75290	+	2.79108i
$105$	−9.01403e6			−0.759900
$106$	−3.25400e6	−	5.63610e6i	−0.265367	−	0.459630i
$107$	3.31209e6	+	5.73670e6i	0.261372	+	0.452709i	0.966607	−	0.256265i	$-0.0824918\pi$
$107$	3.31209e6	+	5.73670e6i	0.261372	+	0.452709i	−0.705235	+	0.708974i	$0.749159\pi$
$108$	2.67357e6	−	4.63075e6i	0.204224	−	0.353727i
$109$	−2.15505e7			−1.59391			−0.796957	−	0.604036i	$-0.793558\pi$
$109$	−2.15505e7			−1.59391			−0.796957	+	0.604036i	$0.793558\pi$
$110$	3.42405e6	−	5.93062e6i	0.245282	−	0.424840i
$111$	1.46518e7	−	2.53776e7i	1.01686	−	1.76125i
$112$	5.01963e7			3.37605
$113$	6.51663e6	−	1.12871e7i	0.424863	−	0.735884i	−0.571545	−	0.820571i	$-0.693656\pi$
$113$	6.51663e6	−	1.12871e7i	0.424863	−	0.735884i	0.996408	+	0.0846870i	$0.0269890\pi$
$114$	−6.23813e6	−	1.08048e7i	−0.394355	−	0.683043i
$115$	−2.69310e6	−	4.66459e6i	−0.165124	−	0.286003i
$116$	−3.35647e6			−0.199655
$117$	−1.91104e7	+	710867.i	−1.10311	+	0.0410334i
$118$	−3.56174e7			−1.99561
$119$	−4.05092e6	−	7.01640e6i	−0.220363	−	0.381680i
$120$	2.55451e7	+	4.42454e7i	1.34950	+	2.33740i
$121$	7.76122e6	−	1.34428e7i	0.398273	−	0.689829i
$122$	3.62305e7			1.80640
$123$	3.85240e6	−	6.67255e6i	0.186665	−	0.323313i
$124$	−3.56388e7	+	6.17283e7i	−1.67860	+	2.90742i
$125$	−2.07272e7			−0.949195
$126$	−2.21540e7	+	3.83719e7i	−0.986633	+	1.70890i
$127$	−3.71720e6	−	6.43838e6i	−0.161029	−	0.278910i	0.774209	−	0.632930i	$-0.218148\pi$
$127$	−3.71720e6	−	6.43838e6i	−0.161029	−	0.278910i	−0.935238	+	0.354020i	$0.884814\pi$
$128$	−3.62556e7	−	6.27966e7i	−1.52806	−	2.64668i
$129$	2.71574e7			1.11384
$130$	1.27354e7	−	2.40837e7i	0.508404	−	0.961438i
$131$	1.19177e7			0.463173			0.231586	−	0.972814i	$-0.425608\pi$
$131$	1.19177e7			0.463173			0.231586	+	0.972814i	$0.425608\pi$
$132$	−2.34336e7	−	4.05881e7i	−0.886808	−	1.53600i
$133$	3.55338e6	+	6.15463e6i	0.130967	+	0.226841i
$134$	−1.55073e7	+	2.68595e7i	−0.556763	+	0.964342i
$135$	−2.43170e6			−0.0850633
$136$	−2.29600e7	+	3.97679e7i	−0.782683	+	1.35565i
$137$	2.45601e7	−	4.25394e7i	0.816034	−	1.41341i	−0.0925486	−	0.995708i	$-0.529501\pi$
$137$	2.45601e7	−	4.25394e7i	0.816034	−	1.41341i	0.908583	−	0.417705i	$-0.137165\pi$
$138$	−5.04599e7			−1.63444
$139$	9.38121e6	−	1.62487e7i	0.296283	−	0.513177i	−0.678999	−	0.734139i	$-0.737586\pi$
$139$	9.38121e6	−	1.62487e7i	0.296283	−	0.513177i	0.975283	+	0.220961i	$0.0709195\pi$
$140$	−2.30559e7	−	3.99339e7i	−0.710123	−	1.22997i
$141$	4.50826e7	+	7.80853e7i	1.35438	+	2.34586i
$142$	−2.26577e7			−0.664060
$143$	−7.37319e6	+	1.39434e7i	−0.210853	+	0.398741i
$144$	1.43904e8			4.01609
$145$	763208.	+	1.32192e6i	0.0207900	+	0.0360094i
$146$	−4.82834e7	−	8.36293e7i	−1.28399	−	2.22394i
$147$	−3.87989e6	+	6.72017e6i	−0.100742	+	0.174490i
$148$	1.49904e8			3.80099
$149$	−2.27990e7	+	3.94891e7i	−0.564631	+	0.977969i	0.432453	+	0.901656i	$0.357648\pi$
$149$	−2.27990e7	+	3.94891e7i	−0.564631	+	0.977969i	−0.997084	+	0.0763125i	$0.975685\pi$
$150$	−3.93414e7	+	6.81413e7i	−0.951767	+	1.64851i
$151$	−3.04360e7			−0.719397			−0.359699	−	0.933069i	$-0.617120\pi$
$151$	−3.04360e7			−0.719397			−0.359699	+	0.933069i	$0.617120\pi$
$152$	2.01400e7	−	3.48835e7i	0.465165	−	0.805690i
$153$	−1.16133e7	−	2.01148e7i	−0.262141	−	0.454041i
$154$	1.82722e7	+	3.16484e7i	0.403151	+	0.698279i
$155$	3.24148e7			0.699169
$156$	−9.91629e7	−	1.57894e8i	−2.09129	−	3.32988i
$157$	−7.21167e7			−1.48726			−0.743631	−	0.668591i	$-0.766898\pi$
$157$	−7.21167e7			−1.48726			−0.743631	+	0.668591i	$0.766898\pi$
$158$	8.07281e7	+	1.39825e8i	1.62826	+	2.82023i
$159$	1.01276e7	+	1.75415e7i	0.199810	+	0.346080i
$160$	−5.42990e7	+	9.40486e7i	−1.04803	+	1.81523i
$161$	2.87431e7			0.542804
$162$	4.61446e7	−	7.99248e7i	0.852744	−	1.47700i
$163$	1.37296e7	−	2.37803e7i	0.248313	−	0.430091i	−0.714745	−	0.699385i	$-0.753457\pi$
$163$	1.37296e7	−	2.37803e7i	0.248313	−	0.430091i	0.963058	+	0.269294i	$0.0867905\pi$
$164$	3.94143e7			0.697751
$165$	−1.06568e7	+	1.84582e7i	−0.184686	+	0.319886i
$166$	−8.21443e6	−	1.42278e7i	−0.139380	−	0.241412i
$167$	−2.82767e6	−	4.89767e6i	−0.0469809	−	0.0813733i	0.841579	−	0.540135i	$-0.181627\pi$
$167$	−2.82767e6	−	4.89767e6i	−0.0469809	−	0.0813733i	−0.888560	+	0.458761i	$0.848293\pi$
$168$	−2.72639e8			−4.43615
$169$	−2.72503e7	+	5.65225e7i	−0.434279	+	0.900779i
$170$	3.30886e7			0.516544
$171$	1.01869e7	+	1.76442e7i	0.155796	+	0.269846i
$172$	6.94626e7	+	1.20313e8i	1.04088	+	1.80286i
$173$	3.13857e7	−	5.43616e7i	0.460861	−	0.798235i	−0.538143	−	0.842853i	$-0.680874\pi$
$173$	3.13857e7	−	5.43616e7i	0.460861	−	0.798235i	0.999004	+	0.0446188i	$0.0142073\pi$
$174$	1.43000e7			0.205785
$175$	2.24098e7	−	3.88149e7i	0.316085	−	0.547476i
$176$	5.93446e7	−	1.02788e8i	0.820515	−	1.42117i
$177$	1.10854e8			1.50260
$178$	2.71533e7	−	4.70310e7i	0.360872	−	0.625049i
$179$	−6.69698e7	−	1.15995e8i	−0.872757	−	1.51166i	−0.859133	−	0.511752i	$-0.828997\pi$
$179$	−6.69698e7	−	1.15995e8i	−0.872757	−	1.51166i	−0.0136231	−	0.999907i	$-0.504337\pi$
$180$	−6.60971e7	−	1.14484e8i	−0.844751	−	1.46315i
$181$	−7.06325e6			−0.0885379			−0.0442690	−	0.999020i	$-0.514096\pi$
$181$	−7.06325e6			−0.0885379			−0.0442690	+	0.999020i	$0.514096\pi$
$182$	7.73218e7	+	1.23117e8i	0.950718	+	1.51380i
$183$	−1.12762e8			−1.36014
$184$	−8.14559e7	−	1.41086e8i	−0.963962	−	1.66963i
$185$	−3.40858e7	−	5.90383e7i	−0.395796	−	0.685540i
$186$	1.51837e8	−	2.62989e8i	1.73014	−	2.99669i
$187$	−1.91568e7			−0.214229
$188$	−2.30622e8	+	3.99449e8i	−2.53133	+	4.38439i
$189$	6.48831e6	−	1.12381e7i	0.0699061	−	0.121081i
$190$	−2.90246e7			−0.306993
$191$	−8.20398e7	+	1.42097e8i	−0.851938	+	1.47560i	0.0275191	+	0.999621i	$0.491239\pi$
$191$	−8.20398e7	+	1.42097e8i	−0.851938	+	1.47560i	−0.879457	+	0.475978i	$0.842094\pi$
$192$	2.49920e8	+	4.32874e8i	2.54828	+	4.41375i
$193$	−3.96822e6	−	6.87316e6i	−0.0397324	−	0.0688186i	0.845475	−	0.534014i	$-0.179317\pi$
$193$	−3.96822e6	−	6.87316e6i	−0.0397324	−	0.0688186i	−0.885208	+	0.465196i	$0.845984\pi$
$194$	1.39223e8			1.36900
$195$	−3.96369e7	+	7.49569e7i	−0.382806	+	0.723920i
$196$	−3.96956e7			−0.376570
$197$	−2.51323e7	−	4.35303e7i	−0.234207	−	0.405658i	0.724835	−	0.688923i	$-0.241916\pi$
$197$	−2.51323e7	−	4.35303e7i	−0.234207	−	0.405658i	−0.959042	+	0.283264i	$0.908583\pi$
$198$	5.23831e7	+	9.07303e7i	0.479583	+	0.830661i
$199$	−3.41981e7	+	5.92328e7i	−0.307621	+	0.532815i	−0.977841	−	0.209347i	$-0.932866\pi$
$199$	−3.41981e7	+	5.92328e7i	−0.307621	+	0.532815i	0.670221	+	0.742162i	$0.266200\pi$
$200$	−2.54031e8			−2.24533
$201$	4.82643e7	−	8.35962e7i	0.419218	−	0.726106i
$202$	1.50274e8	−	2.60283e8i	1.28279	−	2.22185i
$203$	−8.14562e6			−0.0683420
$204$	1.13226e8	−	1.96114e8i	0.933774	−	1.61734i
$205$	−8.96217e6	−	1.55229e7i	−0.0726566	−	0.125845i
$206$	−1.09579e8	−	1.89797e8i	−0.873361	−	1.51271i
$207$	8.24014e7			0.645712
$208$	2.20725e8	−	4.17411e8i	1.70071	−	3.21620i
$209$	1.68039e7			0.127321
$210$	9.82279e7	+	1.70136e8i	0.731926	+	1.26773i
$211$	1.26058e8	+	2.18339e8i	0.923810	+	1.60009i	0.793464	+	0.608617i	$0.208275\pi$
$211$	1.26058e8	+	2.18339e8i	0.923810	+	1.60009i	0.130346	+	0.991469i	$0.458391\pi$
$212$	−5.18083e7	+	8.97345e7i	−0.373442	+	0.646821i
$213$	7.05188e7			0.500007
$214$	7.21851e7	−	1.25028e8i	0.503500	−	0.872088i
$215$	3.15893e7	−	5.47143e7i	0.216773	−	0.375462i
$216$	−7.35495e7			−0.496583
$217$	−8.64896e7	+	1.49804e8i	−0.574586	+	0.995212i
$218$	2.34841e8	+	4.06756e8i	1.53524	+	2.65911i
$219$	1.50275e8	+	2.60284e8i	0.966789	+	1.67453i
$220$	−1.09031e8			−0.690353
$221$	−7.61583e7	+	2.83293e6i	−0.474618	+	0.0176548i
$222$	−6.38655e8			−3.91770
$223$	−6.20215e7	−	1.07424e8i	−0.374520	−	0.648688i	0.615735	−	0.787954i	$-0.288859\pi$
$223$	−6.20215e7	−	1.07424e8i	−0.374520	−	0.648688i	−0.990255	+	0.139265i	$0.955526\pi$
$224$	−2.89763e8	−	5.01884e8i	−1.72256	−	2.98356i
$225$	6.42449e7	−	1.11275e8i	0.376010	−	0.651269i
$226$	−2.84053e8			−1.63689
$227$	6.54460e7	−	1.13356e8i	0.371358	−	0.643210i	−0.618417	−	0.785850i	$-0.712226\pi$
$227$	6.54460e7	−	1.13356e8i	0.371358	−	0.643210i	0.989775	+	0.142640i	$0.0455591\pi$
$228$	−9.93197e7	+	1.72027e8i	−0.554962	+	0.961222i
$229$	1.06750e8			0.587414			0.293707	−	0.955895i	$-0.405111\pi$
$229$	1.06750e8			0.587414			0.293707	+	0.955895i	$0.405111\pi$
$230$	−5.86947e7	+	1.01662e8i	−0.318091	+	0.550950i
$231$	−5.68695e7	−	9.85008e7i	−0.303555	−	0.525772i
$232$	2.30841e7	+	3.99828e7i	0.121368	+	0.210216i
$233$	−2.23039e8			−1.15514			−0.577571	−	0.816340i	$-0.695999\pi$
$233$	−2.23039e8			−1.15514			−0.577571	+	0.816340i	$0.695999\pi$
$234$	2.21668e8	+	3.52954e8i	1.13096	+	1.80079i
$235$	2.09759e8			1.05435
$236$	2.83539e8	+	4.91105e8i	1.40418	+	2.43210i
$237$	−2.51254e8	−	4.35185e8i	−1.22601	−	2.12351i
$238$	−8.82876e7	+	1.52919e8i	−0.424502	+	0.735260i
$239$	1.68042e8			0.796204			0.398102	−	0.917341i	$-0.369669\pi$
$239$	1.68042e8			0.796204			0.398102	+	0.917341i	$0.369669\pi$
$240$	3.19025e8	−	5.52568e8i	1.48965	−	2.58016i
$241$	3.11270e7	−	5.39135e7i	0.143244	−	0.248106i	−0.785472	−	0.618897i	$-0.787580\pi$
$241$	3.11270e7	−	5.39135e7i	0.143244	−	0.248106i	0.928716	+	0.370791i	$0.120913\pi$
$242$	−3.38303e8			−1.53445
$243$	−1.60469e8	+	2.77940e8i	−0.717412	+	1.24259i
$244$	−2.88420e8	−	4.99558e8i	−1.27105	−	2.20152i
$245$	9.02614e6	+	1.56337e7i	0.0392122	+	0.0679174i
$246$	−1.67922e8			−0.719174
$247$	6.68044e7	−	2.48498e6i	0.282076	−	0.0104926i
$248$	9.80421e8			4.08161
$249$	2.55662e7	+	4.42819e7i	0.104947	+	0.181773i
$250$	2.25869e8	+	3.91216e8i	0.914253	+	1.58353i
$251$	1.13889e8	−	1.97262e8i	0.454596	−	0.787383i	−0.544069	−	0.839040i	$-0.683117\pi$
$251$	1.13889e8	−	1.97262e8i	0.454596	−	0.787383i	0.998665	+	0.0516574i	$0.0164504\pi$
$252$	7.05445e8			2.77691
$253$	3.39815e7	−	5.88578e7i	0.131923	−	0.228498i
$254$	−8.10143e7	+	1.40321e8i	−0.310201	+	0.537285i
$255$	−1.02983e8			−0.388934
$256$	−3.18568e8	+	5.51777e8i	−1.18676	+	2.05553i
$257$	6.08787e6	+	1.05445e7i	0.0223717	+	0.0387490i	0.876995	−	0.480500i	$-0.159545\pi$
$257$	6.08787e6	+	1.05445e7i	0.0223717	+	0.0387490i	−0.854623	+	0.519249i	$0.826212\pi$
$258$	−2.95940e8	−	5.12583e8i	−1.07284	−	1.85821i
$259$	3.63793e8			1.30108
$260$	−4.33456e8	+	1.61236e7i	−1.52946	+	0.0568927i
$261$	−2.33520e7			−0.0812986
$262$	−1.29870e8	−	2.24941e8i	−0.446122	−	0.772707i
$263$	−1.73808e8	−	3.01045e8i	−0.589149	−	1.02044i	−0.994344	−	0.106206i	$-0.966130\pi$
$263$	−1.73808e8	−	3.01045e8i	−0.589149	−	1.02044i	0.405195	−	0.914230i	$-0.367204\pi$
$264$	−3.22328e8	+	5.58288e8i	−1.07816	+	1.86743i
$265$	4.71214e7			0.155546
$266$	7.74440e7	−	1.34137e8i	0.252291	−	0.436981i
$267$	−8.45107e7	+	1.46377e8i	−0.271720	+	0.470634i
$268$	4.93797e8			1.56703
$269$	2.49465e7	−	4.32086e7i	0.0781406	−	0.135343i	−0.824307	−	0.566143i	$-0.808435\pi$
$269$	2.49465e7	−	4.32086e7i	0.0781406	−	0.135343i	0.902448	+	0.430799i	$0.141768\pi$
$270$	2.64988e7	+	4.58973e7i	0.0819319	+	0.141910i
$271$	1.79648e8	+	3.11160e8i	0.548315	+	0.949710i	0.998390	+	0.0567189i	$0.0180639\pi$
$271$	1.79648e8	+	3.11160e8i	0.548315	+	0.949710i	−0.450075	+	0.892991i	$0.648603\pi$
$272$	5.73482e8			1.72794
$273$	−2.40652e8	−	3.83182e8i	−0.715848	−	1.13982i
$274$	−1.07055e9			−3.14398
$275$	−5.29879e7	−	9.17777e7i	−0.153643	−	0.266117i
$276$	4.01696e8	+	6.95758e8i	1.15005	+	1.99194i
$277$	6.27158e6	−	1.08627e7i	0.0177296	−	0.0307085i	−0.857025	−	0.515276i	$-0.827690\pi$
$277$	6.27158e6	−	1.08627e7i	0.0177296	−	0.0307085i	0.874754	+	0.484567i	$0.161023\pi$
$278$	−4.08917e8			−1.14151
$279$	−2.47950e8	+	4.29463e8i	−0.683518	+	1.18389i
$280$	−3.17132e8	+	5.49290e8i	−0.863351	+	1.49537i
$281$	−4.40328e8			−1.18387			−0.591935	−	0.805986i	$-0.701636\pi$
$281$	−4.40328e8			−1.18387			−0.591935	+	0.805986i	$0.701636\pi$
$282$	9.82550e8	−	1.70183e9i	2.60905	−	4.51901i
$283$	1.52612e8	+	2.64331e8i	0.400254	+	0.693260i	0.993756	−	0.111572i	$-0.0355887\pi$
$283$	1.52612e8	+	2.64331e8i	0.400254	+	0.693260i	−0.593503	+	0.804832i	$0.702255\pi$
$284$	1.80371e8	+	3.12412e8i	0.467254	+	0.809308i
$285$	9.03348e7			0.231152
$286$	3.43522e8	−	1.27783e7i	0.868307	−	0.0322992i
$287$	9.56521e7			0.238840
$288$	−8.30699e8	−	1.43881e9i	−2.04913	−	3.54920i
$289$	1.58888e8	+	2.75203e8i	0.387213	+	0.670672i
$290$	1.66337e7	−	2.88104e7i	0.0400494	−	0.0693676i
$291$	−4.33310e8			−1.03080
$292$	−7.68739e8	+	1.33149e9i	−1.80692	+	3.12968i
$293$	2.30752e8	−	3.99674e8i	0.535931	−	0.928260i	−0.463186	−	0.886261i	$-0.653294\pi$
$293$	2.30752e8	−	3.99674e8i	0.535931	−	0.928260i	0.999118	−	0.0419992i	$-0.0133727\pi$
$294$	1.69120e8			0.388132
$295$	1.28945e8	−	2.23339e8i	0.292433	−	0.506508i
$296$	−1.03096e9	−	1.78568e9i	−2.31058	−	4.00205i
$297$	−1.53416e7	−	2.65724e7i	−0.0339800	−	0.0588551i
$298$	9.93784e8			2.17538
$299$	1.26391e8	−	2.39016e8i	0.273442	−	0.517103i
$300$	1.25274e9			2.67878
$301$	1.68574e8	+	2.91979e8i	0.356294	+	0.617120i
$302$	3.31668e8	+	5.74466e8i	0.692915	+	1.20016i
$303$	−4.67706e8	+	8.10091e8i	−0.965882	+	1.67296i
$304$	−5.03046e8			−1.02695
$305$	−1.31164e8	+	2.27183e8i	−0.264707	+	0.458486i
$306$	−2.53105e8	+	4.38390e8i	−0.504981	+	0.874654i
$307$	−5.05856e7			−0.0997797			−0.0498899	−	0.998755i	$-0.515887\pi$
$307$	−5.05856e7			−0.0997797			−0.0498899	+	0.998755i	$0.515887\pi$
$308$	2.90919e8	−	5.03886e8i	0.567341	−	0.982664i
$309$	3.41050e8	+	5.90715e8i	0.657602	+	1.13900i
$310$	−3.53231e8	−	6.11814e8i	−0.673431	−	1.16642i
$311$	−3.43240e8			−0.647049			−0.323524	−	0.946220i	$-0.604868\pi$
$311$	−3.43240e8			−0.647049			−0.323524	+	0.946220i	$0.604868\pi$
$312$	−1.19886e9	+	2.26715e9i	−2.23474	+	4.22610i
$313$	4.91976e8			0.906856			0.453428	−	0.891293i	$-0.350201\pi$
$313$	4.91976e8			0.906856			0.453428	+	0.891293i	$0.350201\pi$
$314$	7.85872e8	+	1.36117e9i	1.43251	+	2.48118i
$315$	−1.60407e8	−	2.77833e8i	−0.289159	−	0.500837i
$316$	1.28530e9	−	2.22621e9i	2.29140	−	3.96882i
$317$	2.73731e8			0.482633			0.241316	−	0.970447i	$-0.422421\pi$
$317$	2.73731e8			0.482633			0.241316	+	0.970447i	$0.422421\pi$
$318$	2.20725e8	−	3.82307e8i	0.384908	−	0.666681i
$319$	−9.63016e6	+	1.66799e7i	−0.0166099	+	0.0287691i
$320$	1.16282e9			1.98376
$321$	−2.24665e8	+	3.89132e8i	−0.379113	+	0.656643i
$322$	−3.13220e8	−	5.42513e8i	−0.522822	−	0.905555i
$323$	4.05966e7	+	7.03154e7i	0.0670318	+	0.116102i
$324$	−1.46937e9			−2.40007
$325$	−2.24227e8	−	3.57029e8i	−0.362323	−	0.576914i
$326$	−5.98456e8			−0.956689
$327$	−7.30907e8	−	1.26597e9i	−1.15597	−	2.00219i
$328$	−2.71071e8	−	4.69509e8i	−0.424155	−	0.734658i
$329$	−5.59683e8	+	9.69399e8i	−0.866476	+	1.50078i
$330$	4.64520e8			0.711550
$331$	4.67784e7	−	8.10226e7i	0.0709002	−	0.122803i	−0.828396	−	0.560143i	$-0.810746\pi$
$331$	4.67784e7	−	8.10226e7i	0.0709002	−	0.122803i	0.899296	+	0.437340i	$0.144079\pi$
$332$	−1.30785e8	+	2.26527e8i	−0.196144	+	0.339731i
$333$	1.04293e9			1.54775
$334$	−6.16276e7	+	1.06742e8i	−0.0905029	+	0.156756i
$335$	−1.12281e8	−	1.94477e8i	−0.163174	−	0.282626i
$336$	1.70246e9	+	2.94874e9i	2.44843	+	4.24081i
$337$	−5.83618e8			−0.830661			−0.415331	−	0.909671i	$-0.636334\pi$
$337$	−5.83618e8			−0.830661			−0.415331	+	0.909671i	$0.636334\pi$
$338$	1.36379e9	−	1.01601e8i	1.92105	−	0.143116i
$339$	8.84072e8			1.23250
$340$	−2.63408e8	−	4.56237e8i	−0.363457	−	0.629527i
$341$	2.04505e8	+	3.54213e8i	0.279295	+	0.483753i
$342$	2.22018e8	−	3.84547e8i	0.300121	−	0.519826i
$343$	−7.89847e8			−1.05685
$344$	9.55454e8	−	1.65490e9i	1.26548	−	2.19188i
$345$	1.82678e8	−	3.16408e8i	0.239508	−	0.414840i
$346$	−1.36807e9			−1.77558
$347$	2.78938e8	−	4.83136e8i	0.358389	−	0.620749i	−0.629302	−	0.777160i	$-0.716659\pi$
$347$	2.78938e8	−	4.83136e8i	0.358389	−	0.620749i	0.987692	+	0.156412i	$0.0499927\pi$
$348$	−1.13838e8	−	1.97173e8i	−0.144797	−	0.250796i
$349$	−2.73819e8	−	4.74268e8i	−0.344806	−	0.597221i	0.640513	−	0.767948i	$-0.278722\pi$
$349$	−2.73819e8	−	4.74268e8i	−0.344806	−	0.597221i	−0.985318	+	0.170727i	$0.945389\pi$
$350$	−9.76817e8			−1.21780
$351$	−6.49205e7	−	1.03371e8i	−0.0801322	−	0.127592i
$352$	−1.37029e9			−1.67461
$353$	−1.18184e8	−	2.04700e8i	−0.143003	−	0.247689i	0.785623	−	0.618705i	$-0.212343\pi$
$353$	−1.18184e8	−	2.04700e8i	−0.143003	−	0.247689i	−0.928626	+	0.371017i	$0.879009\pi$
$354$	−1.20800e9	−	2.09232e9i	−1.44729	−	2.50678i
$355$	8.20271e7	−	1.42075e8i	0.0973101	−	0.168546i
$356$	−8.64638e8			−1.01569
$357$	2.74782e8	−	4.75936e8i	0.319631	−	0.553618i
$358$	−1.45957e9	+	2.52805e9i	−1.68126	+	2.91202i
$359$	9.18618e8			1.04786			0.523931	−	0.851761i	$-0.324465\pi$
$359$	9.18618e8			1.04786			0.523931	+	0.851761i	$0.324465\pi$
$360$	−9.09163e8	+	1.57472e9i	−1.02703	+	1.77887i
$361$	4.11325e8	+	7.12436e8i	0.460162	+	0.797023i
$362$	7.69698e7	+	1.33316e8i	0.0852787	+	0.147707i
$363$	1.05292e9			1.15537
$364$	1.08204e9	−	2.04623e9i	1.17595	−	2.22382i
$365$	6.99195e8			0.752616
$366$	1.22879e9	+	2.12833e9i	1.31007	+	2.26911i
$367$	−3.68304e8	−	6.37921e8i	−0.388933	−	0.673652i	0.603373	−	0.797459i	$-0.293823\pi$
$367$	−3.68304e8	−	6.37921e8i	−0.388933	−	0.673652i	−0.992306	+	0.123807i	$0.960490\pi$
$368$	−1.01728e9	+	1.76198e9i	−1.06408	+	1.84303i
$369$	2.74218e8			0.284121
$370$	−7.42880e8	+	1.28671e9i	−0.762453	+	1.32061i
$371$	−1.25730e8	+	2.17771e8i	−0.127829	+	0.221407i
$372$	−4.83490e9			−4.86953
$373$	−5.15417e8	+	8.92728e8i	−0.514254	+	0.890714i	0.485609	+	0.874176i	$0.338598\pi$
$373$	−5.15417e8	+	8.92728e8i	−0.514254	+	0.890714i	−0.999863	+	0.0165381i	$0.994736\pi$
$374$	2.08756e8	+	3.61576e8i	0.206342	+	0.357395i
$375$	−7.02983e8	−	1.21760e9i	−0.688391	−	1.19233i
$376$	6.34440e9			6.15507
$377$	−3.58183e7	+	6.77356e7i	−0.0344279	+	0.0651061i
$378$	−2.82818e8			−0.269331
$379$	−7.57556e8	−	1.31213e9i	−0.714788	−	1.23805i	−0.963041	−	0.269355i	$-0.913190\pi$
$379$	−7.57556e8	−	1.31213e9i	−0.714788	−	1.23805i	0.248253	−	0.968695i	$-0.420144\pi$
$380$	2.31056e8	+	4.00201e8i	0.216011	+	0.374141i
$381$	2.52145e8	−	4.36728e8i	0.233568	−	0.404551i
$382$	3.57603e9			3.28230
$383$	1.98290e8	−	3.43448e8i	0.180345	−	0.312367i	−0.761653	−	0.647985i	$-0.775612\pi$
$383$	1.98290e8	−	3.43448e8i	0.180345	−	0.312367i	0.941998	+	0.335618i	$0.108945\pi$
$384$	2.45929e9	−	4.25962e9i	2.21641	−	3.83894i
$385$	−2.64601e8			−0.236308
$386$	−8.64852e7	+	1.49797e8i	−0.0765396	+	0.132570i
$387$	4.83273e8	+	8.37053e8i	0.423842	+	0.734116i
$388$	−1.10831e9	−	1.91965e9i	−0.963275	−	1.66844i
$389$	−2.09780e9			−1.80693			−0.903464	−	0.428664i	$-0.858984\pi$
$389$	−2.09780e9			−1.80693			−0.903464	+	0.428664i	$0.858984\pi$
$390$	1.84671e9	−	6.86936e7i	1.57642	−	0.0586395i
$391$	3.28384e8			0.277820
$392$	2.73006e8	+	4.72860e8i	0.228913	+	0.396489i
$393$	4.04201e8	+	7.00096e8i	0.335910	+	0.581813i
$394$	−5.47744e8	+	9.48720e8i	−0.451170	+	0.781450i
$395$	−1.16903e9			−0.954411
$396$	8.34013e8	−	1.44455e9i	0.674900	−	1.16896i
$397$	3.09705e8	−	5.36425e8i	0.248417	−	0.430271i	−0.714670	−	0.699462i	$-0.753423\pi$
$397$	3.09705e8	−	5.36425e8i	0.248417	−	0.430271i	0.963087	+	0.269191i	$0.0867563\pi$
$398$	1.49066e9			1.18519
$399$	−2.41033e8	+	4.17481e8i	−0.189964	+	0.329027i
$400$	1.58626e9	+	2.74748e9i	1.23926	+	2.14647i
$401$	−3.62788e8	−	6.28367e8i	−0.280962	−	0.486640i	0.690660	−	0.723180i	$-0.257320\pi$
$401$	−3.62788e8	−	6.28367e8i	−0.280962	−	0.486640i	−0.971622	+	0.236539i	$0.923987\pi$
$402$	−2.10379e9			−1.61514
$403$	8.65395e8	+	1.37794e9i	0.658638	+	1.04873i
$404$	−4.78515e9			−3.61045
$405$	3.34112e8	+	5.78699e8i	0.249919	+	0.432873i
$406$	8.87646e7	+	1.53745e8i	0.0658262	+	0.114014i
$407$	4.30094e8	−	7.44944e8i	0.316215	−	0.547701i
$408$	−3.11484e9			−2.27052
$409$	−6.36206e8	+	1.10194e9i	−0.459797	+	0.796392i	−0.998950	−	0.0458159i	$-0.985411\pi$
$409$	−6.36206e8	+	1.10194e9i	−0.459797	+	0.796392i	0.539153	+	0.842208i	$0.318745\pi$
$410$	−1.95326e8	+	3.38314e8i	−0.139964	+	0.242424i
$411$	3.33192e9			2.36727
$412$	−1.74466e9	+	3.02184e9i	−1.22905	+	2.12878i
$413$	6.88104e8	+	1.19183e9i	0.480650	+	0.832510i
$414$	−8.97947e8	−	1.55529e9i	−0.621941	−	1.07723i
$415$	1.18954e8			0.0816977
$416$	−5.44762e9	+	2.02640e8i	−3.71005	+	0.138006i
$417$	1.27269e9			0.859502
$418$	−1.83116e8	−	3.17167e8i	−0.122634	−	0.212408i
$419$	1.31115e9	+	2.27098e9i	0.870768	+	1.50822i	0.861203	+	0.508261i	$0.169711\pi$
$419$	1.31115e9	+	2.27098e9i	0.870768	+	1.50822i	0.00956540	+	0.999954i	$0.496955\pi$
$420$	1.56392e9	−	2.70880e9i	1.03001	−	1.78404i
$421$	−1.20869e9			−0.789457			−0.394729	−	0.918798i	$-0.629161\pi$
$421$	−1.20869e9			−0.789457			−0.394729	+	0.918798i	$0.629161\pi$
$422$	2.74737e9	−	4.75858e9i	1.77960	−	3.08237i
$423$	−1.60451e9	+	2.77910e9i	−1.03075	+	1.78530i
$424$	1.42524e9			0.908045
$425$	2.56027e8	−	4.43452e8i	0.161780	−	0.280211i
$426$	−7.68459e8	−	1.33101e9i	−0.481601	−	0.834157i
$427$	−6.99949e8	−	1.21235e9i	−0.435080	−	0.753580i
$428$	−2.29858e9			−1.41712
$429$	−1.06916e9	+	3.97705e7i	−0.653796	+	0.0243198i
$430$	−1.37694e9			−0.835174
$431$	−4.81989e8	−	8.34830e8i	−0.289979	−	0.502259i	0.683825	−	0.729646i	$-0.260315\pi$
$431$	−4.81989e8	−	8.34830e8i	−0.289979	−	0.502259i	−0.973804	+	0.227387i	$0.926982\pi$
$432$	4.59269e8	+	7.95478e8i	0.274078	+	0.474717i
$433$	−9.27391e8	+	1.60629e9i	−0.548978	+	0.950858i	0.449367	+	0.893347i	$0.351650\pi$
$433$	−9.27391e8	+	1.60629e9i	−0.548978	+	0.950858i	−0.998345	+	0.0575106i	$0.981684\pi$
$434$	3.76999e9			2.21374
$435$	−5.17699e7	+	8.96681e7i	−0.0301554	+	0.0522307i
$436$	3.73899e9	−	6.47613e9i	2.16049	−	3.74208i
$437$	−2.88051e8			−0.165114
$438$	3.27516e9	−	5.67274e9i	1.86240	−	3.22577i
$439$	−1.60256e9	−	2.77571e9i	−0.904041	−	1.56585i	−0.822199	−	0.569200i	$-0.807253\pi$
$439$	−1.60256e9	−	2.77571e9i	−0.904041	−	1.56585i	−0.0818424	−	0.996645i	$-0.526080\pi$
$440$	7.49860e8	+	1.29879e9i	0.419658	+	0.726869i
$441$	−2.76175e8			−0.153338
$442$	8.83385e8	+	1.40658e9i	0.486600	+	0.774796i
$443$	1.69743e9			0.927639			0.463819	−	0.885930i	$-0.346479\pi$
$443$	1.69743e9			0.927639			0.463819	+	0.885930i	$0.346479\pi$
$444$	5.08414e9	+	8.80599e9i	2.75662	+	4.77461i
$445$	1.96605e8	+	3.40529e8i	0.105763	+	0.183187i
$446$	−1.35173e9	+	2.34126e9i	−0.721467	+	1.24962i
$447$	−3.09301e9			−1.63796
$448$	−3.10266e9	+	5.37397e9i	−1.63028	+	2.82372i
$449$	1.50695e9	−	2.61011e9i	0.785663	−	1.36081i	−0.142940	−	0.989731i	$-0.545656\pi$
$449$	1.50695e9	−	2.61011e9i	0.785663	−	1.36081i	0.928602	−	0.371076i	$-0.121011\pi$
$450$	−2.80036e9			−1.44867
$451$	1.13085e8	−	1.95868e8i	0.0580478	−	0.100542i
$452$	2.26126e9	+	3.91661e9i	1.15177	+	1.99492i
$453$	−1.03227e9	−	1.78794e9i	−0.521734	−	0.903669i
$454$	−2.85272e9			−1.43075
$455$	−1.05193e9	+	3.91295e7i	−0.523535	+	0.0194744i
$456$	2.73227e9			1.34942
$457$	−1.06847e9	−	1.85065e9i	−0.523668	−	0.907020i	−0.999620	−	0.0275490i	$-0.991230\pi$
$457$	−1.06847e9	−	1.85065e9i	−0.523668	−	0.907020i	0.475952	−	0.879471i	$-0.342104\pi$
$458$	−1.16328e9	−	2.01486e9i	−0.565790	−	0.979977i
$459$	7.41275e7	−	1.28393e8i	0.0357796	−	0.0619720i
$460$	1.86900e9			0.895277
$461$	−8.76980e8	+	1.51897e9i	−0.416904	+	0.722100i	−0.995626	−	0.0934253i	$-0.970218\pi$
$461$	−8.76980e8	+	1.51897e9i	−0.416904	+	0.722100i	0.578722	+	0.815525i	$0.303552\pi$
$462$	−1.23944e9	+	2.14677e9i	−0.584761	+	1.01284i
$463$	−2.44183e9			−1.14336			−0.571679	−	0.820477i	$-0.693708\pi$
$463$	−2.44183e9			−1.14336			−0.571679	+	0.820477i	$0.693708\pi$
$464$	2.88290e8	−	4.99334e8i	0.133973	−	0.232048i
$465$	1.09938e9	+	1.90418e9i	0.507063	+	0.878259i
$466$	2.43051e9	+	4.20976e9i	1.11262	+	1.92711i
$467$	3.10574e9			1.41110			0.705548	−	0.708662i	$-0.250701\pi$
$467$	3.10574e9			1.41110			0.705548	+	0.708662i	$0.250701\pi$
$468$	3.10202e9	−	5.86619e9i	1.39889	−	2.64543i
$469$	1.19837e9			0.536394
$470$	−2.28579e9	−	3.95911e9i	−1.01553	−	1.75896i
$471$	−2.44591e9	−	4.23644e9i	−1.07862	−	1.86822i
$472$	3.90007e9	−	6.75512e9i	1.70717	−	2.95690i
$473$	7.97188e8			0.346375
$474$	−5.47594e9	+	9.48461e9i	−2.36175	+	4.09068i
$475$	−2.24581e8	+	3.88986e8i	−0.0961493	+	0.166535i
$476$	2.81132e9			1.19478
$477$	−3.60446e8	+	6.24311e8i	−0.152064	+	0.263382i
$478$	−1.83119e9	−	3.17171e9i	−0.766893	−	1.32830i
$479$	1.94677e9	+	3.37190e9i	0.809357	+	1.40185i	0.913310	+	0.407265i	$0.133517\pi$
$479$	1.94677e9	+	3.37190e9i	0.809357	+	1.40185i	−0.103954	+	0.994582i	$0.533149\pi$
$480$	−7.36641e9			−3.04027
$481$	1.59969e9	−	3.02515e9i	0.655431	−	1.23948i
$482$	−1.35679e9			−0.551884
$483$	9.74851e8	+	1.68849e9i	0.393662	+	0.681842i
$484$	2.69313e9	+	4.66463e9i	1.07969	+	1.87007i
$485$	−5.04024e8	+	8.72994e8i	−0.200611	+	0.347468i
$486$	6.99466e9			2.76401
$487$	9.04079e8	−	1.56591e9i	0.354695	−	0.614350i	−0.632371	−	0.774666i	$-0.717918\pi$
$487$	9.04079e8	−	1.56591e9i	0.354695	−	0.614350i	0.987066	+	0.160316i	$0.0512514\pi$
$488$	−3.96721e9	+	6.87140e9i	−1.54531	+	2.67655i
$489$	1.86260e9			0.720344
$490$	1.96720e8	−	3.40729e8i	0.0755373	−	0.130835i
$491$	−3.73400e8	−	6.46747e8i	−0.142360	−	0.246575i	0.786025	−	0.618195i	$-0.212136\pi$
$491$	−3.73400e8	−	6.46747e8i	−0.142360	−	0.246575i	−0.928385	+	0.371620i	$0.878802\pi$
$492$	1.33677e9	+	2.31536e9i	0.506035	+	0.876478i
$493$	−9.30620e7			−0.0349791
$494$	−7.74886e8	−	1.23382e9i	−0.289197	−	0.460478i
$495$	−7.58564e8			−0.281109
$496$	−6.12210e9	−	1.06038e10i	−2.25276	−	3.90189i
$497$	4.37732e8	+	7.58174e8i	0.159941	+	0.277027i
$498$	5.57201e8	−	9.65100e8i	0.202166	−	0.350162i
$499$	8.17396e8			0.294497			0.147248	−	0.989100i	$-0.452958\pi$
$499$	8.17396e8			0.294497			0.147248	+	0.989100i	$0.452958\pi$
$500$	3.59615e9	−	6.22871e9i	1.28660	−	2.22845i
$501$	1.91807e8	−	3.32219e8i	0.0681446	−	0.118030i
$502$	−4.96432e9			−1.75144
$503$	−6.56684e8	+	1.13741e9i	−0.230075	+	0.398501i	−0.957830	−	0.287336i	$-0.907230\pi$
$503$	−6.56684e8	+	1.13741e9i	−0.230075	+	0.398501i	0.727755	+	0.685837i	$0.240564\pi$
$504$	−4.85169e9	−	8.40337e9i	−1.68805	−	2.92379i
$505$	1.08807e9	+	1.88459e9i	0.375955	+	0.651173i
$506$	−1.48122e9			−0.508267
$507$	−4.24459e9	+	3.16217e8i	−1.44647	+	0.107760i
$508$	2.57972e9			0.873072
$509$	1.17600e8	+	2.03688e8i	0.0395270	+	0.0684627i	0.885112	−	0.465378i	$-0.154082\pi$
$509$	1.17600e8	+	2.03688e8i	0.0395270	+	0.0684627i	−0.845585	+	0.533841i	$0.820748\pi$
$510$	1.12223e9	+	1.94376e9i	0.374617	+	0.648855i
$511$	−1.86560e9	+	3.23132e9i	−0.618509	+	1.07129i
$512$	4.60460e9			1.51617
$513$	−6.50231e7	+	1.12623e8i	−0.0212646	+	0.0368313i
$514$	1.32682e8	−	2.29812e8i	0.0430964	−	0.0746451i
$515$	1.58683e9			0.511923
$516$	−4.71178e9	+	8.16104e9i	−1.50977	+	2.61500i
$517$	1.32337e9	+	2.29214e9i	0.421177	+	0.729499i
$518$	−3.96433e9	−	6.86642e9i	−1.25319	−	2.17058i
$519$	4.25790e9			1.33693
$520$	3.17315e9	+	5.05250e9i	0.989645	+	1.57578i
$521$	−3.47965e9			−1.07796			−0.538982	−	0.842318i	$-0.681191\pi$
$521$	−3.47965e9			−1.07796			−0.538982	+	0.842318i	$0.681191\pi$
$522$	2.54473e8	+	4.40759e8i	0.0783058	+	0.135630i
$523$	−1.95749e8	−	3.39048e8i	−0.0598335	−	0.103635i	0.834557	−	0.550921i	$-0.185724\pi$
$523$	−1.95749e8	−	3.39048e8i	−0.0598335	−	0.103635i	−0.894391	+	0.447287i	$0.852390\pi$
$524$	−2.06771e9	+	3.58138e9i	−0.627813	+	1.08740i
$525$	3.04020e9			0.916947
$526$	−3.78805e9	+	6.56110e9i	−1.13492	+	1.96574i
$527$	−9.88126e8	+	1.71148e9i	−0.294086	+	0.509373i
$528$	8.05091e9			2.38027
$529$	1.11990e9	−	1.93973e9i	0.328917	−	0.569701i
$530$	−5.13493e8	−	8.89396e8i	−0.149820	−	0.259495i
$531$	1.97267e9	+	3.41677e9i	0.571774	+	0.990341i
$532$	−2.46603e9			−0.710081
$533$	4.20606e8	−	7.95403e8i	0.120318	−	0.227532i
$534$	3.68373e9			1.04687
$535$	5.22659e8	+	9.05272e8i	0.147564	+	0.255588i
$536$	−3.39608e9	−	5.88218e9i	−0.952579	−	1.64991i
$537$	4.54269e9	−	7.86817e9i	1.26591	−	2.19262i
$538$	−1.08739e9			−0.301056
$539$	−1.13892e8	+	1.97266e8i	−0.0313279	+	0.0542616i
$540$	4.21898e8	−	7.30749e8i	0.115300	−	0.199705i
$541$	−5.01138e9			−1.36071			−0.680357	−	0.732881i	$-0.738175\pi$
$541$	−5.01138e9			−1.36071			−0.680357	+	0.732881i	$0.738175\pi$
$542$	3.91533e9	−	6.78155e9i	1.05626	−	1.82950i
$543$	−2.39557e8	−	4.14925e8i	−0.0642110	−	0.111217i
$544$	−3.31048e9	−	5.73392e9i	−0.881647	−	1.52706i
$545$	−3.40075e9			−0.899884
$546$	−4.60995e9	+	8.71783e9i	−1.21205	+	2.29210i
$547$	1.06296e9			0.277692			0.138846	−	0.990314i	$-0.455661\pi$
$547$	1.06296e9			0.277692			0.138846	+	0.990314i	$0.455661\pi$
$548$	8.52231e9	+	1.47611e10i	2.21221	+	3.83165i
$549$	−2.00663e9	−	3.47558e9i	−0.517564	−	0.896447i
$550$	−1.15484e9	+	2.00025e9i	−0.295974	+	0.512642i
$551$	8.16320e7			0.0207888
$552$	5.52531e9	−	9.57012e9i	1.39820	−	2.42176i
$553$	3.11922e9	−	5.40265e9i	0.784347	−	1.35853i
$554$	−2.73371e8			−0.0683076
$555$	2.31210e9	−	4.00468e9i	0.574093	−	0.994357i
$556$	3.25526e9	+	5.63828e9i	0.803201	+	1.39118i
$557$	2.13504e9	+	3.69799e9i	0.523495	+	0.906719i	0.999626	+	0.0273451i	$0.00870531\pi$
$557$	2.13504e9	+	3.69799e9i	0.523495	+	0.906719i	−0.476131	+	0.879374i	$0.657961\pi$
$558$	1.08079e10			2.63343
$559$	3.16924e9	−	1.17889e8i	0.767386	−	0.0285451i
$560$	7.92115e9			1.90603
$561$	−6.49722e8	−	1.12535e9i	−0.155366	−	0.269103i
$562$	4.79835e9	+	8.31099e9i	1.14029	+	1.97504i
$563$	−2.46244e9	+	4.26507e9i	−0.581549	+	1.00727i	0.413747	+	0.910392i	$0.364220\pi$
$563$	−2.46244e9	+	4.26507e9i	−0.581549	+	1.00727i	−0.995296	+	0.0968809i	$0.969113\pi$
$564$	−3.12871e10			−7.34326
$565$	1.02835e9	−	1.78115e9i	0.239867	−	0.415462i
$566$	3.32609e9	−	5.76095e9i	0.771039	−	1.33548i
$567$	−3.56593e9			−0.821547
$568$	2.48100e9	−	4.29722e9i	0.568077	−	0.983939i
$569$	−2.45883e9	−	4.25881e9i	−0.559545	−	0.969160i	−0.997534	−	0.0701801i	$-0.977643\pi$
$569$	−2.45883e9	−	4.25881e9i	−0.559545	−	0.969160i	0.437989	−	0.898980i	$-0.355691\pi$
$570$	−9.84398e8	−	1.70503e9i	−0.222643	−	0.385629i
$571$	1.02161e9			0.229647			0.114823	−	0.993386i	$-0.463370\pi$
$571$	1.02161e9			0.229647			0.114823	+	0.993386i	$0.463370\pi$
$572$	−2.91087e9	−	4.63487e9i	−0.650333	−	1.03550i
$573$	−1.11298e10			−2.47143
$574$	−1.04234e9	−	1.80539e9i	−0.230048	−	0.398455i
$575$	9.08314e8	+	1.57325e9i	0.199250	+	0.345111i
$576$	−8.89478e9	+	1.54062e10i	−1.93935	+	3.35906i
$577$	4.24754e9			0.920496			0.460248	−	0.887790i	$-0.347761\pi$
$577$	4.24754e9			0.920496			0.460248	+	0.887790i	$0.347761\pi$
$578$	3.46289e9	−	5.99789e9i	0.745917	−	1.29197i
$579$	2.69172e8	−	4.66220e8i	0.0576309	−	0.0998196i
$580$	−5.29664e8			−0.112720
$581$	−3.17394e8	+	5.49743e8i	−0.0671402	+	0.116290i
$582$	4.72187e9	+	8.17852e9i	0.992851	+	1.71967i
$583$	2.97289e8	+	5.14920e8i	0.0621354	+	0.107622i
$584$	2.11479e10			4.39362
$585$	−3.01569e9	+	1.12177e8i	−0.622790	+	0.0231664i
$586$	−1.00582e10			−2.06481
$587$	2.55076e8	+	4.41805e8i	0.0520519	+	0.0901565i	0.890877	−	0.454244i	$-0.150091\pi$
$587$	2.55076e8	+	4.41805e8i	0.0520519	+	0.0901565i	−0.838825	+	0.544400i	$0.816757\pi$
$588$	−1.34632e9	−	2.33189e9i	−0.273103	−	0.473028i
$589$	8.66763e8	−	1.50128e9i	0.174782	−	0.302731i
$590$	−5.62055e9			−1.12667
$591$	1.70477e9	−	2.95275e9i	0.339711	−	0.588397i
$592$	−1.28754e10	+	2.23008e10i	−2.55055	+	4.41768i
$593$	−5.55218e9			−1.09338			−0.546691	−	0.837334i	$-0.684113\pi$
$593$	−5.55218e9			−1.09338			−0.546691	+	0.837334i	$0.684113\pi$
$594$	−3.34362e8	+	5.79132e8i	−0.0654582	+	0.113377i
$595$	−6.39249e8	−	1.10721e9i	−0.124412	−	0.215487i
$596$	−7.91122e9	−	1.37026e10i	−1.53067	−	2.65120i
$597$	−4.63944e9			−0.892392
$598$	−5.88862e9	+	2.19044e8i	−1.12605	+	0.0418868i
$599$	2.67091e9			0.507769			0.253884	−	0.967235i	$-0.418292\pi$
$599$	2.67091e9			0.507769			0.253884	+	0.967235i	$0.418292\pi$
$600$	−8.61569e9	−	1.49228e10i	−1.62840	−	2.82047i
$601$	1.16848e9	+	2.02386e9i	0.219563	+	0.380295i	0.954675	−	0.297652i	$-0.0962034\pi$
$601$	1.16848e9	+	2.02386e9i	0.219563	+	0.380295i	−0.735111	+	0.677947i	$0.762870\pi$
$602$	3.67399e9	−	6.36353e9i	0.686356	−	1.18880i
$603$	3.43550e9			0.638086
$604$	5.28062e9	−	9.14631e9i	0.975115	−	1.68895i
$605$	1.22475e9	−	2.12133e9i	0.224855	−	0.389461i
$606$	2.03868e10			3.72130
$607$	−4.28530e9	+	7.42235e9i	−0.777715	+	1.34704i	0.155541	+	0.987830i	$0.450288\pi$
$607$	−4.28530e9	+	7.42235e9i	−0.777715	+	1.34704i	−0.933256	+	0.359213i	$0.883045\pi$
$608$	2.90388e9	+	5.02967e9i	0.523982	+	0.907564i
$609$	−2.76267e8	−	4.78508e8i	−0.0495642	−	0.0858477i
$610$	5.71730e9			1.01985
$611$	5.60005e9	+	8.91677e9i	0.993226	+	1.58148i
$612$	8.05956e9			1.42129
$613$	2.91721e9	+	5.05276e9i	0.511513	+	0.885966i	0.999911	+	0.0133451i	$0.00424800\pi$
$613$	2.91721e9	+	5.05276e9i	0.511513	+	0.885966i	−0.488398	+	0.872621i	$0.662419\pi$
$614$	5.51242e8	+	9.54780e8i	0.0961066	+	0.166462i
$615$	6.07922e8	−	1.05295e9i	0.105386	−	0.182535i
$616$	−8.00315e9			−1.37952
$617$	−2.82691e9	+	4.89635e9i	−0.484523	+	0.839218i	−0.999842	−	0.0177804i	$-0.994340\pi$
$617$	−2.82691e9	+	4.89635e9i	−0.484523	+	0.839218i	0.515319	+	0.856998i	$0.327673\pi$
$618$	7.43299e9	−	1.28743e10i	1.26679	−	2.19414i
$619$	2.81131e9			0.476422			0.238211	−	0.971213i	$-0.423439\pi$
$619$	2.81131e9			0.476422			0.238211	+	0.971213i	$0.423439\pi$
$620$	−5.62393e9	+	9.74094e9i	−0.947696	+	1.64146i
$621$	2.62984e8	+	4.55502e8i	0.0440666	+	0.0763255i
$622$	3.74037e9	+	6.47851e9i	0.623229	+	1.07946i
$623$	−2.09834e9			−0.347670
$624$	3.20066e10	−	1.19058e9i	5.27344	−	0.196161i
$625$	8.87227e8			0.145363
$626$	−5.36117e9	−	9.28582e9i	−0.873473	−	1.51290i
$627$	5.69922e8	+	9.87133e8i	0.0923377	+	0.159934i
$628$	1.25122e10	−	2.16717e10i	2.01592	−	3.49168i
$629$	4.15625e9			0.665924
$630$	−3.49598e9	+	6.05522e9i	−0.557028	+	0.964801i
$631$	−7.02211e8	+	1.21626e9i	−0.111267	+	0.192719i	−0.916281	−	0.400536i	$-0.868824\pi$
$631$	−7.02211e8	+	1.21626e9i	−0.111267	+	0.192719i	0.805015	+	0.593255i	$0.202157\pi$
$632$	−3.53586e10			−5.57166
$633$	−8.55078e9	+	1.48104e10i	−1.33996	+	2.32088i
$634$	−2.98291e9	−	5.16655e9i	−0.464866	−	0.805171i
$635$	−5.86587e8	−	1.01600e9i	−0.0909127	−	0.157465i
$636$	−7.02851e9			−1.08334
$637$	−4.23608e8	+	8.01080e8i	−0.0649345	+	0.122797i
$638$	4.19768e8			0.0639937
$639$	1.25490e9	+	2.17355e9i	0.190264	+	0.329547i
$640$	−5.72127e9	−	9.90952e9i	−0.862705	−	1.49425i
$641$	4.64799e9	−	8.05056e9i	0.697047	−	1.20732i	−0.272438	−	0.962173i	$-0.587830\pi$
$641$	4.64799e9	−	8.05056e9i	0.697047	−	1.20732i	0.969486	−	0.245148i	$-0.0788366\pi$
$642$	9.79292e9			1.46063
$643$	1.00945e9	−	1.74842e9i	0.149743	−	0.259363i	−0.781389	−	0.624044i	$-0.785489\pi$
$643$	1.00945e9	−	1.74842e9i	0.149743	−	0.259363i	0.931133	+	0.364681i	$0.118822\pi$
$644$	−4.98690e9	+	8.63757e9i	−0.735750	+	1.27436i
$645$	4.28553e9			0.628848
$646$	8.84781e8	−	1.53249e9i	0.129128	−	0.223657i
$647$	−5.74640e9	−	9.95306e9i	−0.834125	−	1.44475i	−0.894741	−	0.446586i	$-0.852640\pi$
$647$	−5.74640e9	−	9.95306e9i	−0.834125	−	1.44475i	0.0606156	−	0.998161i	$-0.480694\pi$
$648$	1.01056e10	+	1.75034e10i	1.45898	+	2.52703i
$649$	3.25404e9			0.467269
$650$	−4.29531e9	+	8.12280e9i	−0.613476	+	1.16014i
$651$	−1.17335e10			−1.66684
$652$	4.76413e9	+	8.25171e9i	0.673158	+	1.16594i
$653$	−1.88159e9	−	3.25901e9i	−0.264441	−	0.458025i	0.702976	−	0.711214i	$-0.251854\pi$
$653$	−1.88159e9	−	3.25901e9i	−0.264441	−	0.458025i	−0.967417	+	0.253188i	$0.918521\pi$
$654$	−1.59297e10	+	2.75911e10i	−2.22682	+	3.85697i
$655$	1.88066e9			0.261496
$656$	−3.38533e9	+	5.86356e9i	−0.468206	+	0.810957i
$657$	−5.34836e9	+	9.26363e9i	−0.735769	+	1.27439i
$658$	2.43960e10			3.33831
$659$	−9.85714e8	+	1.70731e9i	−0.134169	+	0.232387i	−0.925280	−	0.379286i	$-0.876170\pi$
$659$	−9.85714e8	+	1.70731e9i	−0.134169	+	0.232387i	0.791111	+	0.611673i	$0.209503\pi$
$660$	−3.69790e9	−	6.40495e9i	−0.500670	−	0.867186i
$661$	−4.61696e8	−	7.99680e8i	−0.0621800	−	0.107699i	0.833260	−	0.552882i	$-0.186472\pi$
$661$	−4.61696e8	−	7.99680e8i	−0.0621800	−	0.107699i	−0.895440	+	0.445183i	$0.853139\pi$
$662$	−2.03902e9			−0.273161
$663$	−2.74940e9	−	4.37778e9i	−0.366388	−	0.583387i
$664$	3.59789e9			0.476935
$665$	5.60736e8	+	9.71223e8i	0.0739405	+	0.128069i
$666$	−1.13650e10	−	1.96848e10i	−1.49077	−	2.58209i
$667$	1.65079e8	−	2.85926e8i	0.0215403	−	0.0373089i
$668$	1.96239e9			0.254723
$669$	4.20704e9	−	7.28681e9i	0.543232	−	0.940906i
$670$	−2.44711e9	+	4.23852e9i	−0.314335	+	0.544444i
$671$	−3.31006e9			−0.422967
$672$	1.96552e10	−	3.40438e10i	2.49853	−	4.32758i
$673$	−3.44288e8	−	5.96323e8i	−0.0435380	−	0.0754100i	0.843435	−	0.537231i	$-0.180530\pi$
$673$	−3.44288e8	−	5.96323e8i	−0.0435380	−	0.0754100i	−0.886973	+	0.461821i	$0.847196\pi$
$674$	6.35982e9	+	1.10155e10i	0.800083	+	1.38578i
$675$	8.20150e8			0.102643
$676$	−1.22576e10	−	1.79956e10i	−1.52613	−	2.24054i
$677$	8.91263e9			1.10394			0.551970	−	0.833864i	$-0.313876\pi$
$677$	8.91263e9			1.10394			0.551970	+	0.833864i	$0.313876\pi$
$678$	−9.63393e9	−	1.66865e10i	−1.18713	−	2.05618i
$679$	−2.68969e9	−	4.65868e9i	−0.329729	−	0.571108i
$680$	−3.62317e9	+	6.27552e9i	−0.441883	+	0.765364i
$681$	8.87865e9			1.07729
$682$	4.45707e9	−	7.71987e9i	0.538027	−	0.931890i
$683$	5.09848e9	−	8.83082e9i	0.612305	−	1.06054i	−0.378546	−	0.925583i	$-0.623576\pi$
$683$	5.09848e9	−	8.83082e9i	0.612305	−	1.06054i	0.990851	−	0.134961i	$-0.0430910\pi$
$684$	−7.06968e9			−0.844701
$685$	3.87567e9	−	6.71286e9i	0.460713	−	0.797978i
$686$	8.60714e9	+	1.49080e10i	1.01795	+	1.76313i
$687$	3.62054e9	+	6.27095e9i	0.426015	+	0.737879i
$688$	−2.38648e10			−2.79382
$689$	1.25803e9	+	2.00311e9i	0.146529	+	0.233313i
$690$	−7.96275e9			−0.922765
$691$	1.91919e9	+	3.32414e9i	0.221282	+	0.383271i	0.955197	−	0.295970i	$-0.0956427\pi$
$691$	1.91919e9	+	3.32414e9i	0.221282	+	0.383271i	−0.733916	+	0.679240i	$0.762309\pi$
$692$	1.08908e10	+	1.88634e10i	1.24936	+	2.16395i
$693$	2.02401e9	−	3.50569e9i	0.231019	−	0.400136i
$694$	−1.21586e10			−1.38079
$695$	1.48039e9	−	2.56411e9i	0.167274	−	0.289727i
$696$	−1.56584e9	+	2.71211e9i	−0.176041	+	0.304912i
$697$	1.09280e9			0.122244
$698$	−5.96773e9	+	1.03364e10i	−0.664225	+	1.15047i
$699$	−7.56459e9	−	1.31023e10i	−0.837752	−	1.45103i
$700$	7.77615e9	+	1.34687e10i	0.856883	+	1.48416i
$701$	−1.78976e9			−0.196237			−0.0981185	−	0.995175i	$-0.531282\pi$
$701$	−1.78976e9			−0.196237			−0.0981185	+	0.995175i	$0.531282\pi$
$702$	−1.24362e9	+	2.35180e9i	−0.135678	+	0.256578i
$703$	−3.64578e9			−0.395773
$704$	7.33624e9	+	1.27067e10i	0.792446	+	1.37256i
$705$	7.11419e9	+	1.23221e10i	0.764651	+	1.32441i
$706$	−2.57574e9	+	4.46132e9i	−0.275478	+	0.477141i
$707$	−1.16128e10			−1.23586
$708$	−1.92330e10	+	3.33126e10i	−2.03672	+	3.52770i
$709$	2.64858e9	−	4.58747e9i	0.279094	−	0.483406i	−0.692066	−	0.721835i	$-0.743299\pi$
$709$	2.64858e9	−	4.58747e9i	0.279094	−	0.483406i	0.971160	+	0.238429i	$0.0766325\pi$
$710$	−3.57547e9			−0.374912
$711$	8.94226e9	−	1.54884e10i	0.933047	−	1.61609i
$712$	5.94653e9	+	1.02997e10i	0.617424	+	1.06941i
$713$	−3.50560e9	−	6.07188e9i	−0.362201	−	0.627350i
$714$	−1.19774e10			−1.23146
$715$	−1.16352e9	+	2.20031e9i	−0.119042	+	0.225119i
$716$	4.64768e10			4.73195
$717$	5.69929e9	+	9.87147e9i	0.577436	+	1.00015i
$718$	−1.00104e10	−	1.73385e10i	−1.00929	−	1.74814i
$719$	2.95986e9	−	5.12663e9i	0.296975	−	0.514376i	−0.678467	−	0.734631i	$-0.737355\pi$
$719$	2.95986e9	−	5.12663e9i	0.296975	−	0.514376i	0.975442	+	0.220255i	$0.0706888\pi$
$720$	2.27085e10			2.26739
$721$	−4.23400e9	+	7.33351e9i	−0.420705	+	0.728682i
$722$	8.96461e9	−	1.55272e10i	0.886444	−	1.53537i
$723$	4.22280e9			0.415544
$724$	1.22547e9	−	2.12257e9i	0.120010	−	0.207863i
$725$	−2.57410e8	−	4.45848e8i	−0.0250867	−	0.0434514i
$726$	−1.14739e10	−	1.98733e10i	−1.11284	−	1.92749i
$727$	−6.36378e9			−0.614249			−0.307125	−	0.951669i	$-0.599367\pi$
$727$	−6.36378e9			−0.614249			−0.307125	+	0.951669i	$0.599367\pi$
$728$	−3.18167e10	+	1.18351e9i	−3.05630	+	0.113688i
$729$	−1.25089e10			−1.19584
$730$	−7.61929e9	−	1.31970e10i	−0.724910	−	1.25558i
$731$	1.92593e9	+	3.33580e9i	0.182360	+	0.315856i
$732$	1.95641e10	−	3.38860e10i	1.84362	−	3.19324i
$733$	−2.70194e9			−0.253403			−0.126702	−	0.991941i	$-0.540439\pi$
$733$	−2.70194e9			−0.253403			−0.126702	+	0.991941i	$0.540439\pi$
$734$	−8.02698e9	+	1.39031e10i	−0.749231	+	1.29771i
$735$	−6.12261e8	+	1.06047e9i	−0.0568762	+	0.0985125i
$736$	2.34894e10			2.17170
$737$	1.41677e9	−	2.45391e9i	0.130365	−	0.225799i
$738$	−2.98821e9	−	5.17573e9i	−0.273662	−	0.473996i
$739$	−4.13913e9	−	7.16919e9i	−0.377271	−	0.653453i	0.613393	−	0.789778i	$-0.289804\pi$
$739$	−4.13913e9	−	7.16919e9i	−0.377271	−	0.653453i	−0.990664	+	0.136325i	$0.956471\pi$
$740$	2.36554e10			2.14595
$741$	2.41172e9	+	3.84009e9i	0.217752	+	0.346719i
$742$	5.48044e9			0.492495
$743$	1.65839e9	+	2.87241e9i	0.148329	+	0.256913i	0.930610	−	0.366013i	$-0.119277\pi$
$743$	1.65839e9	+	2.87241e9i	0.148329	+	0.256913i	−0.782281	+	0.622925i	$0.785944\pi$
$744$	3.32519e10	+	5.75940e10i	2.96014	+	5.12710i
$745$	−3.59777e9	+	6.23152e9i	−0.318776	+	0.552137i
$746$	2.24665e10			1.98129
$747$	−9.09913e8	+	1.57602e9i	−0.0798689	+	0.138337i
$748$	3.32369e9	−	5.75679e9i	0.290378	−	0.502950i
$749$	−5.57827e9			−0.485080
$750$	−1.53211e10	+	2.65370e10i	−1.32610	+	2.29687i
$751$	3.47042e9	+	6.01095e9i	0.298980	+	0.517849i	0.975903	−	0.218205i	$-0.0700201\pi$
$751$	3.47042e9	+	6.01095e9i	0.298980	+	0.517849i	−0.676923	+	0.736054i	$0.736687\pi$
$752$	−3.96167e10	−	6.86181e10i	−3.39716	−	5.88405i
$753$	1.54507e10			1.31876
$754$	1.66880e9	−	6.20757e7i	0.141776	−	0.00527378i
$755$	−4.80291e9			−0.406154
$756$	2.25143e9	+	3.89959e9i	0.189510	+	0.328241i
$757$	6.46303e9	+	1.11943e10i	0.541503	+	0.937911i	0.998818	+	0.0486060i	$0.0154779\pi$
$757$	6.46303e9	+	1.11943e10i	0.541503	+	0.937911i	−0.457315	+	0.889305i	$0.651189\pi$
$758$	−1.65105e10	+	2.85971e10i	−1.37695	+	2.38495i
$759$	4.61007e9			0.382702
$760$	3.17817e9	−	5.50475e9i	0.262621	−	0.454873i
$761$	−1.07631e10	+	1.86422e10i	−0.885301	+	1.53339i	−0.0399322	+	0.999202i	$0.512714\pi$
$761$	−1.07631e10	+	1.86422e10i	−0.885301	+	1.53339i	−0.845369	+	0.534184i	$0.820619\pi$
$762$	−1.09907e10			−0.899878
$763$	9.07393e9	−	1.57165e10i	0.739536	−	1.28091i
$764$	−2.84677e10	−	4.93074e10i	−2.30954	−	4.00024i
$765$	−1.83262e9	−	3.17418e9i	−0.147998	−	0.256340i
$766$	−8.64322e9			−0.694824
$767$	1.29365e10	−	4.81211e8i	1.03522	−	0.0385081i
$768$	−4.32182e10			−3.44273
$769$	−4.98505e9	−	8.63435e9i	−0.395300	−	0.684680i	0.597839	−	0.801616i	$-0.296026\pi$
$769$	−4.98505e9	−	8.63435e9i	−0.395300	−	0.684680i	−0.993139	+	0.116936i	$0.962693\pi$
$770$	2.88342e9	+	4.99422e9i	0.227609	+	0.394231i
$771$	−4.12952e8	+	7.15254e8i	−0.0324496	+	0.0562044i
$772$	2.75393e9			0.215423
$773$	6.21620e8	−	1.07668e9i	0.0484057	−	0.0838412i	−0.840807	−	0.541334i	$-0.817919\pi$
$773$	6.21620e8	−	1.07668e9i	0.0484057	−	0.0838412i	0.889213	+	0.457493i	$0.151253\pi$
$774$	1.05327e10	−	1.82431e10i	0.816479	−	1.41418i
$775$	−1.09327e10			−0.843665
$776$	−1.52447e10	+	2.64047e10i	−1.17113	+	2.02845i
$777$	1.23384e10	+	2.13707e10i	0.943593	+	1.63435i
$778$	2.28602e10	+	3.95951e10i	1.74041	+	3.01448i
$779$	−9.58585e8			−0.0726523
$780$	−1.56483e10	−	2.49162e10i	−1.18069	−	1.87997i
$781$	2.07003e9			0.155489
$782$	−3.57847e9	−	6.19810e9i	−0.267593	−	0.463484i
$783$	−7.45281e7	−	1.29086e8i	−0.00554822	−	0.00960980i
$784$	3.40949e9	−	5.90541e9i	0.252687	−	0.437667i
$785$	−1.13803e10			−0.839671
$786$	8.80933e9	−	1.52582e10i	0.647089	−	1.12079i
$787$	−2.71046e9	+	4.69465e9i	−0.198212	+	0.343314i	−0.947949	−	0.318422i	$-0.896847\pi$
$787$	−2.71046e9	+	4.69465e9i	−0.198212	+	0.343314i	0.749736	+	0.661737i	$0.230180\pi$
$788$	1.74417e10			1.26983
$789$	1.17898e10	−	2.04204e10i	0.854545	−	1.48012i
$790$	1.27392e10	+	2.20649e10i	0.919277	+	1.59223i
$791$	5.48771e9	+	9.50499e9i	0.394251	+	0.682863i
$792$	−2.29436e10			−1.64106
$793$	−1.31592e10	+	4.89495e8i	−0.937074	+	0.0348572i
$794$	−1.34997e10			−0.957090
$795$	1.59817e9	+	2.76811e9i	0.112808	+	0.195388i
$796$	−1.18667e10	−	2.05537e10i	−0.833936	−	1.44442i
$797$	−6.54352e8	+	1.13337e9i	−0.0457834	+	0.0792991i	−0.888009	−	0.459826i	$-0.847912\pi$
$797$	−6.54352e8	+	1.13337e9i	−0.0457834	+	0.0792991i	0.842226	+	0.539125i	$0.181245\pi$
$798$	1.05064e10			0.731883
$799$	−6.39426e9	+	1.10752e10i	−0.443482	+	0.768134i
$800$	1.83136e10	−	3.17202e10i	1.26462	−	2.19039i
$801$	−6.01556e9			−0.413583
$802$	−7.90676e9	+	1.36949e10i	−0.541238	+	0.937452i
$803$	4.41122e9	+	7.64046e9i	0.300645	+	0.520733i
$804$	1.67476e10	+	2.90077e10i	1.13647	+	1.96842i
$805$	4.53577e9			0.306454
$806$	1.65776e10	−	3.13496e10i	1.11519	−	2.10892i
$807$	3.38434e9			0.226682
$808$	3.29098e10	+	5.70014e10i	2.19475	+	3.80142i
$809$	−1.18673e10	−	2.05548e10i	−0.788011	−	1.36488i	−0.927183	−	0.374608i	$-0.877777\pi$
$809$	−1.18673e10	−	2.05548e10i	−0.788011	−	1.36488i	0.139172	−	0.990268i	$-0.455556\pi$
$810$	7.28179e9	−	1.26124e10i	0.481438	−	0.833875i
$811$	−2.50297e10			−1.64772			−0.823859	−	0.566795i	$-0.808183\pi$
$811$	−2.50297e10			−1.64772			−0.823859	+	0.566795i	$0.808183\pi$
$812$	1.41326e9	−	2.44783e9i	0.0926350	−	0.160449i
$813$	−1.21859e10	+	2.11066e10i	−0.795317	+	1.37753i
$814$	−1.87473e10			−1.21830
$815$	2.16657e9	−	3.75261e9i	0.140191	−	0.242819i
$816$	1.94502e10	+	3.36887e10i	1.25317	+	2.17055i
$817$	−1.68938e9	−	2.92609e9i	−0.108380	−	0.187720i
$818$	2.77315e10			1.77148
$819$	7.52809e9	−	1.42363e10i	0.478841	−	0.905531i
$820$	6.21971e9			0.393933
$821$	−3.08611e9	−	5.34531e9i	−0.194631	−	0.337110i	0.752149	−	0.658993i	$-0.229017\pi$
$821$	−3.08611e9	−	5.34531e9i	−0.194631	−	0.337110i	−0.946779	+	0.321883i	$0.895684\pi$
$822$	−3.63087e10	−	6.28885e10i	−2.28013	−	3.94930i
$823$	−5.44436e9	+	9.42991e9i	−0.340445	+	0.589669i	−0.984515	−	0.175298i	$-0.943911\pi$
$823$	−5.44436e9	+	9.42991e9i	−0.340445	+	0.589669i	0.644070	+	0.764967i	$0.277245\pi$
$824$	4.79954e10			2.98851
$825$	3.59427e9	−	6.22546e9i	0.222855	−	0.385996i
$826$	1.49968e10	−	2.59753e10i	0.925912	−	1.60373i
$827$	6.98237e9			0.429273			0.214637	−	0.976694i	$-0.431143\pi$
$827$	6.98237e9			0.429273			0.214637	+	0.976694i	$0.431143\pi$
$828$	−1.42966e10	+	2.47624e10i	−0.875237	+	1.51595i
$829$	5.39241e9	+	9.33993e9i	0.328732	+	0.569381i	0.982261	−	0.187521i	$-0.0600453\pi$
$829$	5.39241e9	+	9.33993e9i	0.328732	+	0.569381i	−0.653528	+	0.756902i	$0.726712\pi$
$830$	−1.29627e9	−	2.24520e9i	−0.0786902	−	0.136295i
$831$	8.50827e8			0.0514325
$832$	3.10445e10	+	4.94311e10i	1.86876	+	2.97556i
$833$	−1.10060e9			−0.0659741
$834$	−1.38688e10	−	2.40215e10i	−0.827862	−	1.43390i
$835$	−4.46217e8	−	7.72870e8i	−0.0265242	−	0.0459413i
$836$	−2.91547e9	+	5.04973e9i	−0.172578	+	0.298914i
$837$	−3.16534e9			−0.186587
$838$	2.85758e10	−	4.94947e10i	1.67743	−	2.90539i
$839$	7.05979e9	−	1.22279e10i	0.412691	−	0.714801i	−0.582492	−	0.812836i	$-0.697922\pi$
$839$	7.05979e9	−	1.22279e10i	0.412691	−	0.714801i	0.995183	+	0.0980350i	$0.0312557\pi$
$840$	−4.30234e10			−2.50454
$841$	8.57816e9	−	1.48578e10i	0.497288	−	0.861328i
$842$	1.31714e10	+	2.28135e10i	0.760396	+	1.31704i
$843$	−1.49342e10	−	2.58667e10i	−0.858587	−	1.48712i
$844$	−8.74839e10			−5.00875
$845$	−4.30020e9	+	8.91945e9i	−0.245183	+	0.508557i
$846$	6.99389e10			3.97121
$847$	6.53578e9	+	1.13203e10i	0.369578	+	0.640127i
$848$	−8.89971e9	−	1.54147e10i	−0.501176	−	0.868062i
$849$	−1.03519e10	+	1.79301e10i	−0.580557	+	1.00555i
$850$	−1.11599e10			−0.623297
$851$	−7.37263e9	+	1.27698e10i	−0.410080	+	0.710280i
$852$	−1.22349e10	+	2.11915e10i	−0.677740	+	1.17388i
$853$	−1.78844e10			−0.986628			−0.493314	−	0.869851i	$-0.664215\pi$
$853$	−1.78844e10			−0.986628			−0.493314	+	0.869851i	$0.664215\pi$
$854$	−1.52550e10	+	2.64224e10i	−0.838127	+	1.45168i
$855$	1.60753e9	+	2.78432e9i	0.0879585	+	0.152349i
$856$	1.58084e10	+	2.73810e10i	0.861449	+	1.49207i
$857$	1.24146e10			0.673754			0.336877	−	0.941549i	$-0.390629\pi$
$857$	1.24146e10			0.673754			0.336877	+	0.941549i	$0.390629\pi$
$858$	1.24015e10	+	1.97465e10i	0.670301	+	1.06730i
$859$	4.99039e9			0.268632			0.134316	−	0.990939i	$-0.457116\pi$
$859$	4.99039e9			0.268632			0.134316	+	0.990939i	$0.457116\pi$
$860$	1.09614e10	+	1.89858e10i	0.587656	+	1.01785i
$861$	3.24413e9	+	5.61901e9i	0.173216	+	0.300019i
$862$	−1.05047e10	+	1.81947e10i	−0.558609	+	0.967539i
$863$	2.82593e10			1.49666			0.748331	−	0.663326i	$-0.230856\pi$
$863$	2.82593e10			1.49666			0.748331	+	0.663326i	$0.230856\pi$
$864$	5.30236e9	−	9.18395e9i	0.279686	−	0.484430i
$865$	4.95277e9	−	8.57845e9i	0.260191	−	0.450663i
$866$	4.04239e10			2.11508
$867$	−1.07777e10	+	1.86675e10i	−0.561642	+	0.972793i
$868$	−3.00117e10	−	5.19819e10i	−1.55766	−	2.69794i
$869$	−7.37540e9	−	1.27746e10i	−0.381256	−	0.660354i
$870$	2.25659e9			0.116181
$871$	5.26951e9	−	9.96510e9i	0.270213	−	0.510997i
$872$	−1.02859e11			−5.25335
$873$	−7.71086e9	−	1.33556e10i	−0.392241	−	0.679381i
$874$	3.13896e9	+	5.43684e9i	0.159036	+	0.275459i
$875$	8.72726e9	−	1.51161e10i	0.440403	−	0.762800i
$876$	−1.04290e11			−5.24178
$877$	6.43281e9	−	1.11420e10i	0.322034	−	0.557780i	−0.658873	−	0.752254i	$-0.728967\pi$
$877$	6.43281e9	−	1.11420e10i	0.322034	−	0.557780i	0.980908	+	0.194474i	$0.0623000\pi$
$878$	−3.49269e10	+	6.04952e10i	−1.74152	+	3.01641i
$879$	3.13047e10			1.55471
$880$	9.36478e9	−	1.62203e10i	0.463242	−	0.802359i
$881$	−3.48665e9	−	6.03905e9i	−0.171788	−	0.297545i	0.767257	−	0.641340i	$-0.221621\pi$
$881$	−3.48665e9	−	6.03905e9i	−0.171788	−	0.297545i	−0.939045	+	0.343794i	$0.888288\pi$
$882$	3.00954e9	+	5.21267e9i	0.147693	+	0.255812i
$883$	−1.25092e10			−0.611458			−0.305729	−	0.952119i	$-0.598900\pi$
$883$	−1.25092e10			−0.611458			−0.305729	+	0.952119i	$0.598900\pi$
$884$	1.23621e10	−	2.33778e10i	0.601878	−	1.13820i
$885$	1.74931e10			0.848332
$886$	−1.84973e10	−	3.20382e10i	−0.893490	−	1.54757i
$887$	3.81254e9	+	6.60351e9i	0.183435	+	0.317718i	0.943048	−	0.332657i	$-0.107945\pi$
$887$	3.81254e9	+	6.60351e9i	0.183435	+	0.317718i	−0.759613	+	0.650375i	$0.774612\pi$
$888$	6.99321e10	−	1.21126e11i	3.35144	−	5.80486i
$889$	6.26057e9			0.298853
$890$	4.28489e9	−	7.42165e9i	0.203739	−	0.352887i
$891$	−4.21582e9	+	7.30202e9i	−0.199669	+	0.345837i
$892$	4.30427e10			2.03059
$893$	5.60890e9	−	9.71491e9i	0.263571	−	0.456519i
$894$	3.37052e10	+	5.83791e10i	1.57767	+	2.73260i
$895$	−1.05681e10	−	1.83044e10i	−0.492737	−	0.853445i
$896$	6.10623e10			2.83593
$897$	1.83274e10	−	6.81742e8i	0.847868	−	0.0315389i
$898$	−6.56862e10			−3.02696
$899$	9.93465e8	+	1.72073e9i	0.0456030	+	0.0789868i
$900$	2.22928e10	+	3.86123e10i	1.01933	+	1.76554i
$901$	−1.43644e9	+	2.48799e9i	−0.0654261	+	0.113321i
$902$	−4.92924e9			−0.223644
$903$	−1.14347e10	+	1.98055e10i	−0.516795	+	0.895116i
$904$	3.11035e10	−	5.38728e10i	1.40030	−	2.42538i
$905$	−1.11461e9			−0.0499863
$906$	−2.24977e10	+	3.89672e10i	−1.00505	+	1.74081i
$907$	−2.30227e9	−	3.98765e9i	−0.102454	−	0.177456i	0.810241	−	0.586097i	$-0.199336\pi$
$907$	−2.30227e9	−	3.98765e9i	−0.102454	−	0.177456i	−0.912695	+	0.408641i	$0.866003\pi$
$908$	2.27096e10	+	3.93342e10i	1.00672	+	1.74369i
$909$	−3.32918e10			−1.47016
$910$	1.22016e10	+	1.94283e10i	0.536752	+	0.854651i
$911$	3.96389e9			0.173703			0.0868515	−	0.996221i	$-0.472319\pi$
$911$	3.96389e9			0.173703			0.0868515	+	0.996221i	$0.472319\pi$
$912$	−1.70613e10	−	2.95510e10i	−0.744784	−	1.29000i
$913$	7.50479e8	+	1.29987e9i	0.0326355	+	0.0565264i
$914$	−2.32868e10	+	4.03338e10i	−1.00878	+	1.74726i
$915$	−1.77942e10			−0.767902
$916$	−1.85211e10	+	3.20794e10i	−0.796217	+	1.37909i
$917$	−5.01800e9	+	8.69143e9i	−0.214901	+	0.372219i
$918$	−3.23114e9			−0.137850
$919$	2.21570e9	−	3.83770e9i	0.0941685	−	0.163105i	−0.815093	−	0.579330i	$-0.803314\pi$
$919$	2.21570e9	−	3.83770e9i	0.0941685	−	0.163105i	0.909261	+	0.416226i	$0.136647\pi$
$920$	−1.28540e10	−	2.22638e10i	−0.544229	−	0.942632i
$921$	−1.71566e9	−	2.97161e9i	−0.0723640	−	0.125338i
$922$	3.82266e10			1.60623
$923$	8.22947e9	−	3.06119e8i	0.344482	−	0.0128140i
$924$	3.94672e10			1.64583
$925$	1.14962e10	+	1.99121e10i	0.477595	+	0.827219i
$926$	2.66092e10	+	4.60885e10i	1.10127	+	1.90745i
$927$	−1.21381e10	+	2.10239e10i	−0.500464	+	0.866829i
$928$	−6.65674e9			−0.273428
$929$	1.24931e10	−	2.16387e10i	0.511229	−	0.885474i	−0.488687	−	0.872459i	$-0.662524\pi$
$929$	1.24931e10	−	2.16387e10i	0.511229	−	0.885474i	0.999915	−	0.0130148i	$-0.00414284\pi$
$930$	2.39604e10	−	4.15006e10i	0.976794	−	1.69186i
$931$	9.65426e8			0.0392099
$932$	3.86971e10	−	6.70253e10i	1.56575	−	2.71196i
$933$	−1.16413e10	−	2.01634e10i	−0.469264	−	0.812788i
$934$	−3.38440e10	−	5.86195e10i	−1.35915	−	2.35412i
$935$	−3.02301e9			−0.120948
$936$	−9.12129e10	+	3.39293e9i	−3.63572	+	0.135241i
$937$	4.15588e10			1.65034			0.825171	−	0.564883i	$-0.191079\pi$
$937$	4.15588e10			1.65034			0.825171	+	0.564883i	$0.191079\pi$
$938$	−1.30589e10	−	2.26186e10i	−0.516649	−	0.894862i
$939$	1.66858e10	+	2.89007e10i	0.657686	+	1.13914i
$940$	−3.63930e10	+	6.30345e10i	−1.42913	+	2.47532i
$941$	−9.79910e9			−0.383374			−0.191687	−	0.981456i	$-0.561396\pi$
$941$	−9.79910e9			−0.383374			−0.191687	+	0.981456i	$0.561396\pi$
$942$	−5.33073e10	+	9.23309e10i	−2.07782	+	3.59889i
$943$	−1.93849e9	+	3.35756e9i	−0.0752787	+	0.130386i
$944$	−9.74137e10			−3.76893
$945$	1.02388e9	−	1.77341e9i	0.0394673	−	0.0683593i
$946$	−8.68714e9	−	1.50466e10i	−0.333624	−	0.577854i
$947$	−1.68223e10	−	2.91371e10i	−0.643666	−	1.11486i	−0.984608	−	0.174777i	$-0.944079\pi$
$947$	−1.68223e10	−	2.91371e10i	−0.643666	−	1.11486i	0.340942	−	0.940084i	$-0.389254\pi$
$948$	1.74369e11			6.64723
$949$	1.86668e10	+	2.97225e10i	0.708987	+	1.12889i
$950$	9.78925e9			0.370439
$951$	9.28386e9	+	1.60801e10i	0.350023	+	0.606258i
$952$	−1.93348e10	−	3.34889e10i	−0.726291	−	1.25797i
$953$	1.66261e10	−	2.87972e10i	0.622249	−	1.07777i	−0.366817	−	0.930293i	$-0.619552\pi$
$953$	1.66261e10	−	2.87972e10i	0.622249	−	1.07777i	0.989066	−	0.147474i	$-0.0471143\pi$
$954$	1.57115e10			0.585864
$955$	−1.29462e10	+	2.24234e10i	−0.480983	+	0.833087i
$956$	−2.91551e10	+	5.04980e10i	−1.07922	+	1.86927i
$957$	−1.30646e9			−0.0481843
$958$	4.24287e10	−	7.34887e10i	1.55912	−	2.70048i
$959$	2.06823e10	+	3.58227e10i	0.757239	+	1.31158i
$960$	3.94383e10	+	6.83091e10i	1.43869	+	2.49189i
$961$	1.46816e10			0.533631
$962$	−7.45304e10	+	2.77237e9i	−2.69911	+	0.100401i
$963$	−1.59919e10			−0.577043
$964$	1.08010e10	+	1.87079e10i	0.388324	+	0.672597i
$965$	−6.26199e8	−	1.08461e9i	−0.0224320	−	0.0388533i
$966$	2.12463e10	−	3.67997e10i	0.758340	−	1.31348i
$967$	4.41653e9			0.157068			0.0785341	−	0.996911i	$-0.474976\pi$
$967$	4.41653e9			0.157068			0.0785341	+	0.996911i	$0.474976\pi$
$968$	3.70438e10	−	6.41618e10i	1.31266	−	2.27359i
$969$	−2.75375e9	+	4.76963e9i	−0.0972279	+	0.168404i
$970$	2.19698e10			0.772904
$971$	−1.95794e10	+	3.39124e10i	−0.686327	+	1.18875i	0.286691	+	0.958023i	$0.407445\pi$
$971$	−1.95794e10	+	3.39124e10i	−0.686327	+	1.18875i	−0.973018	+	0.230730i	$0.925889\pi$
$972$	−5.56823e10	−	9.64446e10i	−1.94485	−	3.36857i
$973$	7.89999e9	+	1.36832e10i	0.274936	+	0.476203i
$974$	−3.94078e10			−1.36655
$975$	1.33685e10	−	2.52810e10i	0.461920	−	0.873531i
$976$	9.90906e10			3.41160
$977$	−2.13899e10	−	3.70485e10i	−0.733801	−	1.27098i	−0.955247	−	0.295808i	$-0.904411\pi$
$977$	−2.13899e10	−	3.70485e10i	−0.733801	−	1.27098i	0.221446	−	0.975173i	$-0.428922\pi$
$978$	−2.02972e10	−	3.51558e10i	−0.693826	−	1.20174i
$979$	−2.48076e9	+	4.29680e9i	−0.0844977	+	0.146354i
$980$	−6.26411e9			−0.212602
$981$	2.60133e10	−	4.50564e10i	0.879741	−	1.52376i
$982$	−8.13804e9	+	1.40955e10i	−0.274239	+	0.474996i
$983$	4.08692e10			1.37233			0.686166	−	0.727445i	$-0.259292\pi$
$983$	4.08692e10			1.37233			0.686166	+	0.727445i	$0.259292\pi$
$984$	1.83873e10	−	3.18477e10i	0.615226	−	1.06560i
$985$	−3.96596e9	−	6.86924e9i	−0.132227	−	0.229025i
$986$	1.01412e9	+	1.75650e9i	0.0336914	+	0.0583552i
$987$	−7.59288e10			−2.51360
$988$	−1.08437e10	+	2.05065e10i	−0.357709	+	0.676460i
$989$	−1.36653e10			−0.449193
$990$	8.26625e9	+	1.43176e10i	0.270760	+	0.468971i
$991$	−2.14343e10	−	3.71254e10i	−0.699604	−	1.21175i	−0.968604	−	0.248609i	$-0.920027\pi$
$991$	−2.14343e10	−	3.71254e10i	−0.699604	−	1.21175i	0.269000	−	0.963140i	$-0.413307\pi$
$992$	−7.06808e10	+	1.22423e11i	−2.29885	+	3.98172i
$993$	6.34614e9			0.205678
$994$	9.54013e9	−	1.65240e10i	0.308107	−	0.533657i
$995$	−5.39658e9	+	9.34714e9i	−0.173675	+	0.300814i
$996$	−1.77428e10			−0.569004
$997$	2.43412e9	−	4.21602e9i	0.0777874	−	0.134732i	−0.824508	−	0.565851i	$-0.808548\pi$
$997$	2.43412e9	−	4.21602e9i	0.0777874	−	0.134732i	0.902295	+	0.431119i	$0.141881\pi$
$998$	−8.90735e9	−	1.54280e10i	−0.283656	−	0.491306i
$999$	3.32851e9	+	5.76515e9i	0.105626	+	0.182950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.8.c.a.3.1	✓	16
3.2	odd	2		117.8.g.d.55.8		16
4.3	odd	2		208.8.i.d.81.2		16
13.2	odd	12		169.8.b.e.168.1		16
13.3	even	3		169.8.a.f.1.8		8
13.9	even	3	inner	13.8.c.a.9.1	yes	16
13.10	even	6		169.8.a.e.1.1		8
13.11	odd	12		169.8.b.e.168.16		16
39.35	odd	6		117.8.g.d.100.8		16
52.35	odd	6		208.8.i.d.113.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.c.a.3.1	✓	16	1.1	even	1	trivial
13.8.c.a.9.1	yes	16	13.9	even	3	inner
117.8.g.d.55.8		16	3.2	odd	2
117.8.g.d.100.8		16	39.35	odd	6
169.8.a.e.1.1		8	13.10	even	6
169.8.a.f.1.8		8	13.3	even	3
169.8.b.e.168.1		16	13.2	odd	12
169.8.b.e.168.16		16	13.11	odd	12
208.8.i.d.81.2		16	4.3	odd	2
208.8.i.d.113.2		16	52.35	odd	6

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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	13.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.8972 - 18.8745i) q^{2} +(33.9160 + 58.7442i) q^{3} +(-173.499 + 300.509i) q^{4} +157.804 q^{5} +(739.180 - 1280.30i) q^{6} +(-421.054 + 729.287i) q^{7} +4772.94 q^{8} +(-1207.09 + 2090.74i) q^{9} +(-1719.62 - 2978.47i) q^{10} +(995.582 + 1724.40i) q^{11} -23537.6 q^{12} +(4212.97 + 6708.16i) q^{13} +18353.3 q^{14} +(5352.06 + 9270.04i) q^{15} +(-29804.0 - 51622.0i) q^{16} +(-4810.45 + 8331.95i) q^{17} +52615.6 q^{18} +(4219.62 - 7308.60i) q^{19} +(-27378.8 + 47421.4i) q^{20} -57121.8 q^{21} +(21698.2 - 37582.3i) q^{22} +(-17066.2 - 29559.5i) q^{23} +(161879. + 280383. i) q^{24} -53223.0 q^{25} +(80703.9 - 152618. i) q^{26} -15409.7 q^{27} +(-146105. - 253061. i) q^{28} +(4836.45 + 8376.97i) q^{29} +(116645. - 202035. i) q^{30} +205412. q^{31} +(-344092. + 595986. i) q^{32} +(-67532.3 + 116969. i) q^{33} +209682. q^{34} +(-66443.8 + 115084. i) q^{35} +(-418857. - 725481. i) q^{36} +(-216001. - 374125. i) q^{37} -183929. q^{38} +(-251179. + 475001. i) q^{39} +753187. q^{40} +(-56793.2 - 98368.8i) q^{41} +(622469. + 1.07815e6i) q^{42} +(200181. - 346724. i) q^{43} -690930. q^{44} +(-190483. + 329926. i) q^{45} +(-371948. + 644233. i) q^{46} +1.32924e6 q^{47} +(2.02166e6 - 3.50162e6i) q^{48} +(57198.6 + 99070.9i) q^{49} +(579983. + 1.00456e6i) q^{50} -652605. q^{51} +(-2.74681e6 + 102175. i) q^{52} +298608. q^{53} +(167923. + 290851. i) q^{54} +(157106. + 272116. i) q^{55} +(-2.00967e6 + 3.48084e6i) q^{56} +572451. q^{57} +(105408. - 182571. i) q^{58} +(817121. - 1.41529e6i) q^{59} -3.71431e6 q^{60} +(-831187. + 1.43966e6i) q^{61} +(-2.23842e6 - 3.87706e6i) q^{62} +(-1.01650e6 - 1.76063e6i) q^{63} +7.36880e6 q^{64} +(664821. + 1.05857e6i) q^{65} +2.94366e6 q^{66} +(-711527. - 1.23240e6i) q^{67} +(-1.66922e6 - 2.89117e6i) q^{68} +(1.15763e6 - 2.00508e6i) q^{69} +2.89621e6 q^{70} +(519805. - 900329. i) q^{71} +(-5.76136e6 + 9.97896e6i) q^{72} +4.43080e6 q^{73} +(-4.70763e6 + 8.15385e6i) q^{74} +(-1.80511e6 - 3.12655e6i) q^{75} +(1.46420e6 + 2.53607e6i) q^{76} -1.67678e6 q^{77} +(1.17026e7 - 435311. i) q^{78} -7.40813e6 q^{79} +(-4.70317e6 - 8.14613e6i) q^{80} +(2.11727e6 + 3.66721e6i) q^{81} +(-1.23778e6 + 2.14389e6i) q^{82} +753809. q^{83} +(9.91058e6 - 1.71656e7i) q^{84} +(-759106. + 1.31481e6i) q^{85} -8.72569e6 q^{86} +(-328066. + 568226. i) q^{87} +(4.75186e6 + 8.23046e6i) q^{88} +(1.24588e6 + 2.15793e6i) q^{89} +8.30293e6 q^{90} +(-6.66606e6 + 247963. i) q^{91} +1.18439e7 q^{92} +(6.96676e6 + 1.20668e7i) q^{93} +(-1.44851e7 - 2.50888e7i) q^{94} +(665872. - 1.15332e6i) q^{95} -4.66809e7 q^{96} +(-3.19399e6 + 5.53216e6i) q^{97} +(1.24661e6 - 2.15919e6i) q^{98} -4.80702e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 9 q^{2} - 28 q^{3} - 577 q^{4} + 384 q^{5} + 342 q^{6} + 196 q^{7} + 5922 q^{8} - 5988 q^{9} - 6813 q^{10} + 5052 q^{11} - 15816 q^{12} + 17064 q^{13} + 14484 q^{14} - 184 q^{15} - 61377 q^{16} - 22824 q^{17}+ \cdots + 27386736 q^{99}+O(q^{100}) \) 16 * q - 9 * q^2 - 28 * q^3 - 577 * q^4 + 384 * q^5 + 342 * q^6 + 196 * q^7 + 5922 * q^8 - 5988 * q^9 - 6813 * q^10 + 5052 * q^11 - 15816 * q^12 + 17064 * q^13 + 14484 * q^14 - 184 * q^15 - 61377 * q^16 - 22824 * q^17 + 226318 * q^18 + 63692 * q^19 - 121971 * q^20 - 271240 * q^21 - 73726 * q^22 - 72468 * q^23 + 224952 * q^24 + 58488 * q^25 + 154443 * q^26 + 358616 * q^27 - 172816 * q^28 - 221772 * q^29 - 258116 * q^30 + 58432 * q^31 + 77823 * q^32 - 352372 * q^33 + 643334 * q^34 + 31560 * q^35 - 1162993 * q^36 - 368884 * q^37 + 2364492 * q^38 - 672996 * q^39 + 766030 * q^40 - 385824 * q^41 + 1560954 * q^42 + 391492 * q^43 - 6149616 * q^44 + 232096 * q^45 - 2599078 * q^46 + 1089984 * q^47 + 4585712 * q^48 - 1108780 * q^49 + 1626894 * q^50 + 8040712 * q^51 - 1312478 * q^52 + 3329328 * q^53 - 5616702 * q^54 - 418216 * q^55 - 3609156 * q^56 - 12068664 * q^57 + 3685081 * q^58 - 6318924 * q^59 + 1448784 * q^60 + 1763548 * q^61 - 12998388 * q^62 + 6641128 * q^63 + 32227074 * q^64 + 9500508 * q^65 + 16245108 * q^66 - 8607964 * q^67 - 10118091 * q^68 - 4618492 * q^69 - 25381840 * q^70 + 9473220 * q^71 - 35174445 * q^72 + 5020888 * q^73 + 2206221 * q^74 - 21834988 * q^75 + 18702876 * q^76 + 35263992 * q^77 + 28395902 * q^78 + 12644416 * q^79 - 24671247 * q^80 - 9316272 * q^81 - 9347751 * q^82 - 22158432 * q^83 + 37532636 * q^84 - 36911824 * q^85 - 30103956 * q^86 + 5199988 * q^87 - 36676404 * q^88 + 18469860 * q^89 + 132263562 * q^90 - 9614540 * q^91 + 64127424 * q^92 - 26340696 * q^93 - 6026128 * q^94 - 16267080 * q^95 - 164216320 * q^96 + 19660916 * q^97 - 51546651 * q^98 + 27386736 * q^99

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