LMFDB - Embedded newform 13.11.d.a.8.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,11,Mod(5,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 11, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.5"); S:= CuspForms(chi, 11); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, 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:	$8.25964428476$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 18 x^{18} + 32284 x^{17} + 16288321 x^{16} - 1399914 x^{15} + 236338034 x^{14} + \cdots + 84\!\cdots\!04 $ x^20 - 6x^19 + 18x^18 + 32284x^17 + 16288321x^16 - 1399914x^15 + 236338034x^14 + 223248859576x^13 + 68334664655952x^12 + 197812095245952x^11 + 941899764571520x^10 + 335247771330255360x^9 + 58398135128630811648x^8 + 300750323152050266112x^7 + 1118531393884122341376x^6 + 105977196796457311174656x^5 + 10666527336316281117671424x^4 + 85502397039865581748617216x^3 + 318723107626870315852234752x^2 - 2323063126834144103834320896*x + 8466004130416338670089928704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{6}\cdot 13^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.6
Root			$2.27503 - 2.27503i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.11.d.a.5.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.275033 + 0.275033i) q^{2} -117.626 q^{3} -1023.85i q^{4} +(1857.78 + 1857.78i) q^{5} +(-32.3511 - 32.3511i) q^{6} +(-14253.6 + 14253.6i) q^{7} +(563.227 - 563.227i) q^{8} -45213.1 q^{9} +1021.90i q^{10} +(-85226.6 + 85226.6i) q^{11} +120431. i q^{12} +(-158225. + 335892. i) q^{13} -7840.45 q^{14} +(-218523. - 218523. i) q^{15} -1.04811e6 q^{16} +60580.0i q^{17} +(-12435.1 - 12435.1i) q^{18} +(1.97108e6 + 1.97108e6i) q^{19} +(1.90208e6 - 1.90208e6i) q^{20} +(1.67660e6 - 1.67660e6i) q^{21} -46880.3 q^{22} -7.43471e6i q^{23} +(-66250.2 + 66250.2i) q^{24} -2.86297e6i q^{25} +(-135899. + 48864.4i) q^{26} +1.22639e7 q^{27} +(1.45936e7 + 1.45936e7i) q^{28} -3.35241e7 q^{29} -120202. i q^{30} +(89469.4 + 89469.4i) q^{31} +(-865010. - 865010. i) q^{32} +(1.00249e7 - 1.00249e7i) q^{33} +(-16661.5 + 16661.5i) q^{34} -5.29601e7 q^{35} +4.62914e7i q^{36} +(-6.68503e7 + 6.68503e7i) q^{37} +1.08422e6i q^{38} +(1.86114e7 - 3.95097e7i) q^{39} +2.09270e6 q^{40} +(8.26950e7 + 8.26950e7i) q^{41} +922242. q^{42} -2.46375e8i q^{43} +(8.72591e7 + 8.72591e7i) q^{44} +(-8.39958e7 - 8.39958e7i) q^{45} +(2.04479e6 - 2.04479e6i) q^{46} +(8.57798e7 - 8.57798e7i) q^{47} +1.23285e8 q^{48} -1.23857e8i q^{49} +(787411. - 787411. i) q^{50} -7.12579e6i q^{51} +(3.43902e8 + 1.61998e8i) q^{52} +3.14733e7 q^{53} +(3.37300e6 + 3.37300e6i) q^{54} -3.16664e8 q^{55} +1.60561e7i q^{56} +(-2.31850e8 - 2.31850e8i) q^{57} +(-9.22025e6 - 9.22025e6i) q^{58} +(-5.55793e8 + 5.55793e8i) q^{59} +(-2.23734e8 + 2.23734e8i) q^{60} +8.42632e7 q^{61} +49214.1i q^{62} +(6.44451e8 - 6.44451e8i) q^{63} +1.07279e9i q^{64} +(-9.17958e8 + 3.30065e8i) q^{65} +5.51435e6 q^{66} +(-4.13937e8 - 4.13937e8i) q^{67} +6.20248e7 q^{68} +8.74516e8i q^{69} +(-1.45658e7 - 1.45658e7i) q^{70} +(-3.93719e7 - 3.93719e7i) q^{71} +(-2.54652e7 + 2.54652e7i) q^{72} +(5.31914e8 - 5.31914e8i) q^{73} -3.67721e7 q^{74} +3.36760e8i q^{75} +(2.01809e9 - 2.01809e9i) q^{76} -2.42958e9i q^{77} +(1.59852e7 - 5.74773e6i) q^{78} +2.57494e9 q^{79} +(-1.94716e9 - 1.94716e9i) q^{80} +1.22723e9 q^{81} +4.54878e7i q^{82} +(3.60465e9 + 3.60465e9i) q^{83} +(-1.71659e9 - 1.71659e9i) q^{84} +(-1.12544e8 + 1.12544e8i) q^{85} +(6.77612e7 - 6.77612e7i) q^{86} +3.94331e9 q^{87} +9.60038e7i q^{88} +(-7.08957e9 + 7.08957e9i) q^{89} -4.62033e7i q^{90} +(-2.53240e9 - 7.04296e9i) q^{91} -7.61201e9 q^{92} +(-1.05239e7 - 1.05239e7i) q^{93} +4.71846e7 q^{94} +7.32364e9i q^{95} +(1.01748e8 + 1.01748e8i) q^{96} +(2.54605e9 + 2.54605e9i) q^{97} +(3.40648e7 - 3.40648e7i) q^{98} +(3.85336e9 - 3.85336e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 34 q^{2} - 4 q^{3} - 7792 q^{5} - 19264 q^{6} - 38312 q^{7} - 1200 q^{8} + 236192 q^{9} + 331856 q^{11} - 445380 q^{13} + 2007244 q^{14} + 379412 q^{15} - 1736492 q^{16} - 5990914 q^{18} - 2277428 q^{19}+ \cdots + 64175005436 q^{99}+O(q^{100}) $ 20 * q - 34 * q^2 - 4 * q^3 - 7792 * q^5 - 19264 * q^6 - 38312 * q^7 - 1200 * q^8 + 236192 * q^9 + 331856 * q^11 - 445380 * q^13 + 2007244 * q^14 + 379412 * q^15 - 1736492 * q^16 - 5990914 * q^18 - 2277428 * q^19 + 3611836 * q^20 - 9480856 * q^21 + 5001216 * q^22 + 41307672 * q^24 + 6769646 * q^26 - 4427116 * q^27 - 113669380 * q^28 + 37095424 * q^29 + 17376308 * q^31 - 1963204 * q^32 - 118752028 * q^33 - 32678040 * q^34 + 283757932 * q^35 + 138434576 * q^37 - 180959428 * q^39 - 8799876 * q^40 - 431088064 * q^41 + 1089534556 * q^42 + 102766076 * q^44 - 551620384 * q^45 - 682329276 * q^46 - 316356304 * q^47 - 332833468 * q^48 + 653613022 * q^50 - 1360524100 * q^52 + 882722032 * q^53 + 206912984 * q^54 - 1205505576 * q^55 + 2161977296 * q^57 + 450412980 * q^58 + 1130230868 * q^59 + 4118247964 * q^60 - 1735259352 * q^61 - 3186516460 * q^63 + 2833033736 * q^65 + 1165082704 * q^66 - 626922128 * q^67 - 11230951788 * q^68 - 3144181512 * q^70 - 196931776 * q^71 + 614552052 * q^72 + 5765831656 * q^73 + 10475267944 * q^74 - 5350301912 * q^76 + 8069244872 * q^78 + 1110987384 * q^79 + 870087872 * q^80 - 21624920380 * q^81 + 13391403584 * q^83 - 25726991224 * q^84 + 1992219096 * q^85 + 32878542048 * q^86 + 194656048 * q^87 + 5940615128 * q^89 + 670762144 * q^91 - 12619717320 * q^92 - 27707434216 * q^93 - 31866209148 * q^94 + 34182859808 * q^96 - 14392811236 * q^97 - 58567835410 * q^98 + 64175005436 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.275033	+	0.275033i	0.00859479	+	0.00859479i	0.711391	−	0.702796i	$-0.248065\pi$
$2$	0.275033	+	0.275033i	0.00859479	+	0.00859479i	−0.702796	+	0.711391i	$0.748065\pi$
$3$	−117.626			−0.484058			−0.242029	−	0.970269i	$-0.577813\pi$
$3$	−117.626			−0.484058			−0.242029	+	0.970269i	$0.577813\pi$
$4$		−	1023.85i		−	0.999852i
$5$	1857.78	+	1857.78i	0.594488	+	0.594488i	0.938840	−	0.344352i	$-0.111901\pi$
$5$	1857.78	+	1857.78i	0.594488	+	0.594488i	−0.344352	+	0.938840i	$0.611901\pi$
$6$	−32.3511	−	32.3511i	−0.00416038	−	0.00416038i
$7$	−14253.6	+	14253.6i	−0.848077	+	0.848077i	−0.989893	−	0.141816i	$-0.954706\pi$
$7$	−14253.6	+	14253.6i	−0.848077	+	0.848077i	0.141816	+	0.989893i	$0.454706\pi$
$8$	563.227	−	563.227i	0.0171883	−	0.0171883i
$9$	−45213.1			−0.765688
$10$			1021.90i			0.0102190i
$11$	−85226.6	+	85226.6i	−0.529190	+	0.529190i	−0.920331	−	0.391141i	$-0.872081\pi$
$11$	−85226.6	+	85226.6i	−0.529190	+	0.529190i	0.391141	+	0.920331i	$0.372081\pi$
$12$			120431.i			0.483987i
$13$	−158225.	+	335892.i	−0.426146	+	0.904655i
$13$	−158225.	+	335892.i	−0.426146	+	0.904655i
$14$	−7840.45			−0.0145781
$15$	−218523.	−	218523.i	−0.287767	−	0.287767i
$16$	−1.04811e6			−0.999557
$17$			60580.0i			0.0426663i	0.999772	+	0.0213331i	$0.00679106\pi$
$17$			60580.0i			0.0426663i	−0.999772	+	0.0213331i	$0.993209\pi$
$18$	−12435.1	−	12435.1i	−0.00658093	−	0.00658093i
$19$	1.97108e6	+	1.97108e6i	0.796042	+	0.796042i	0.982469	−	0.186427i	$-0.0596909\pi$
$19$	1.97108e6	+	1.97108e6i	0.796042	+	0.796042i	−0.186427	+	0.982469i	$0.559691\pi$
$20$	1.90208e6	−	1.90208e6i	0.594400	−	0.594400i
$21$	1.67660e6	−	1.67660e6i	0.410519	−	0.410519i
$22$	−46880.3			−0.00909656
$23$		−	7.43471e6i		−	1.15511i	−0.816351	−	0.577557i	$-0.804006\pi$
$23$		−	7.43471e6i		−	1.15511i	0.816351	−	0.577557i	$-0.195994\pi$
$24$	−66250.2	+	66250.2i	−0.00832015	+	0.00832015i
$25$		−	2.86297e6i		−	0.293168i
$26$	−135899.	+	48864.4i	−0.0114380	+	0.00411269i
$27$	1.22639e7			0.854696
$28$	1.45936e7	+	1.45936e7i	0.847952	+	0.847952i
$29$	−3.35241e7			−1.63443			−0.817216	−	0.576331i	$-0.804484\pi$
$29$	−3.35241e7			−1.63443			−0.817216	+	0.576331i	$0.804484\pi$
$30$		−	120202.i		−	0.00494659i
$31$	89469.4	+	89469.4i	0.00312511	+	0.00312511i	0.708668	−	0.705542i	$-0.249297\pi$
$31$	89469.4	+	89469.4i	0.00312511	+	0.00312511i	−0.705542	+	0.708668i	$0.749297\pi$
$32$	−865010.	−	865010.i	−0.0257793	−	0.0257793i
$33$	1.00249e7	−	1.00249e7i	0.256159	−	0.256159i
$34$	−16661.5	+	16661.5i	−0.000366708	+	0.000366708i
$35$	−5.29601e7			−1.00834
$36$			4.62914e7i			0.765574i
$37$	−6.68503e7	+	6.68503e7i	−0.964039	+	0.964039i	−0.999375	−	0.0353362i	$-0.988750\pi$
$37$	−6.68503e7	+	6.68503e7i	−0.964039	+	0.964039i	0.0353362	+	0.999375i	$0.488750\pi$
$38$			1.08422e6i			0.0136836i
$39$	1.86114e7	−	3.95097e7i	0.206279	−	0.437906i
$40$	2.09270e6			0.0204365
$41$	8.26950e7	+	8.26950e7i	0.713773	+	0.713773i	0.967322	−	0.253550i	$-0.0815982\pi$
$41$	8.26950e7	+	8.26950e7i	0.713773	+	0.713773i	−0.253550	+	0.967322i	$0.581598\pi$
$42$	922242.			0.00705665
$43$		−	2.46375e8i		−	1.67592i	−0.545731	−	0.837961i	$-0.683748\pi$
$43$		−	2.46375e8i		−	1.67592i	0.545731	−	0.837961i	$-0.316252\pi$
$44$	8.72591e7	+	8.72591e7i	0.529112	+	0.529112i
$45$	−8.39958e7	−	8.39958e7i	−0.455192	−	0.455192i
$46$	2.04479e6	−	2.04479e6i	0.00992796	−	0.00992796i
$47$	8.57798e7	−	8.57798e7i	0.374021	−	0.374021i	−0.494919	−	0.868939i	$-0.664802\pi$
$47$	8.57798e7	−	8.57798e7i	0.374021	−	0.374021i	0.868939	+	0.494919i	$0.164802\pi$
$48$	1.23285e8			0.483844
$49$		−	1.23857e8i		−	0.438470i
$50$	787411.	−	787411.i	0.00251972	−	0.00251972i
$51$		−	7.12579e6i		−	0.0206530i
$52$	3.43902e8	+	1.61998e8i	0.904521	+	0.426083i
$53$	3.14733e7			0.0752598			0.0376299	−	0.999292i	$-0.488019\pi$
$53$	3.14733e7			0.0752598			0.0376299	+	0.999292i	$0.488019\pi$
$54$	3.37300e6	+	3.37300e6i	0.00734593	+	0.00734593i
$55$	−3.16664e8			−0.629195
$56$			1.60561e7i			0.0291540i
$57$	−2.31850e8	−	2.31850e8i	−0.385331	−	0.385331i
$58$	−9.22025e6	−	9.22025e6i	−0.0140476	−	0.0140476i
$59$	−5.55793e8	+	5.55793e8i	−0.777415	+	0.777415i	−0.979391	−	0.201975i	$-0.935264\pi$
$59$	−5.55793e8	+	5.55793e8i	−0.777415	+	0.777415i	0.201975	+	0.979391i	$0.435264\pi$
$60$	−2.23734e8	+	2.23734e8i	−0.287724	+	0.287724i
$61$	8.42632e7			0.0997674			0.0498837	−	0.998755i	$-0.484115\pi$
$61$	8.42632e7			0.0997674			0.0498837	+	0.998755i	$0.484115\pi$
$62$			49214.1i			5.37194e-5i
$63$	6.44451e8	−	6.44451e8i	0.649362	−	0.649362i
$64$			1.07279e9i			0.999114i
$65$	−9.17958e8	+	3.30065e8i	−0.791145	+	0.284468i
$66$	5.51435e6			0.00440327
$67$	−4.13937e8	−	4.13937e8i	−0.306591	−	0.306591i	0.536994	−	0.843586i	$-0.319560\pi$
$67$	−4.13937e8	−	4.13937e8i	−0.306591	−	0.306591i	−0.843586	+	0.536994i	$0.819560\pi$
$68$	6.20248e7			0.0426600
$69$			8.74516e8i			0.559142i
$70$	−1.45658e7	−	1.45658e7i	−0.00866651	−	0.00866651i
$71$	−3.93719e7	−	3.93719e7i	−0.0218220	−	0.0218220i	0.696112	−	0.717934i	$-0.254912\pi$
$71$	−3.93719e7	−	3.93719e7i	−0.0218220	−	0.0218220i	−0.717934	+	0.696112i	$0.754912\pi$
$72$	−2.54652e7	+	2.54652e7i	−0.0131609	+	0.0131609i
$73$	5.31914e8	−	5.31914e8i	0.256582	−	0.256582i	−0.567080	−	0.823663i	$-0.691927\pi$
$73$	5.31914e8	−	5.31914e8i	0.256582	−	0.256582i	0.823663	+	0.567080i	$0.191927\pi$
$74$	−3.67721e7			−0.0165714
$75$			3.36760e8i			0.141910i
$76$	2.01809e9	−	2.01809e9i	0.795924	−	0.795924i
$77$		−	2.42958e9i		−	0.897588i
$78$	1.59852e7	−	5.74773e6i	0.00553664	−	0.00199078i
$79$	2.57494e9			0.836820			0.418410	−	0.908258i	$-0.362588\pi$
$79$	2.57494e9			0.836820			0.418410	+	0.908258i	$0.362588\pi$
$80$	−1.94716e9	−	1.94716e9i	−0.594225	−	0.594225i
$81$	1.22723e9			0.351965
$82$			4.54878e7i			0.0122695i
$83$	3.60465e9	+	3.60465e9i	0.915109	+	0.915109i	0.996669	−	0.0815592i	$-0.0259900\pi$
$83$	3.60465e9	+	3.60465e9i	0.915109	+	0.915109i	−0.0815592	+	0.996669i	$0.525990\pi$
$84$	−1.71659e9	−	1.71659e9i	−0.410458	−	0.410458i
$85$	−1.12544e8	+	1.12544e8i	−0.0253646	+	0.0253646i
$86$	6.77612e7	−	6.77612e7i	0.0144042	−	0.0144042i
$87$	3.94331e9			0.791161
$88$			9.60038e7i			0.0181918i
$89$	−7.08957e9	+	7.08957e9i	−1.26961	+	1.26961i	−0.323318	+	0.946291i	$0.604798\pi$
$89$	−7.08957e9	+	7.08957e9i	−1.26961	+	1.26961i	−0.946291	+	0.323318i	$0.895202\pi$
$90$		−	4.62033e7i		−	0.00782456i
$91$	−2.53240e9	−	7.04296e9i	−0.405813	−	1.12862i
$92$	−7.61201e9			−1.15494
$93$	−1.05239e7	−	1.05239e7i	−0.00151274	−	0.00151274i
$94$	4.71846e7			0.00642926
$95$			7.32364e9i			0.946474i
$96$	1.01748e8	+	1.01748e8i	0.0124787	+	0.0124787i
$97$	2.54605e9	+	2.54605e9i	0.296489	+	0.296489i	0.839637	−	0.543148i	$-0.182768\pi$
$97$	2.54605e9	+	2.54605e9i	0.296489	+	0.296489i	−0.543148	+	0.839637i	$0.682768\pi$
$98$	3.40648e7	−	3.40648e7i	0.00376856	−	0.00376856i
$99$	3.85336e9	−	3.85336e9i	0.405194	−	0.405194i
$100$	−2.93124e9			−0.293124
$101$			6.33493e9i			0.602747i	0.953506	+	0.301373i	$0.0974451\pi$
$101$			6.33493e9i			0.602747i	−0.953506	+	0.301373i	$0.902555\pi$
$102$	1.95983e6	−	1.95983e6i	0.000177508	−	0.000177508i
$103$			7.39693e9i			0.638066i	0.947744	+	0.319033i	$0.103358\pi$
$103$			7.39693e9i			0.638066i	−0.947744	+	0.319033i	$0.896642\pi$
$104$	1.00067e8	+	2.78300e8i	0.00822476	+	0.0228742i
$105$	6.22949e9			0.488097
$106$	8.65621e6	+	8.65621e6i	0.000646842	+	0.000646842i
$107$	−2.40264e10			−1.71305			−0.856524	−	0.516107i	$-0.827381\pi$
$107$	−2.40264e10			−1.71305			−0.856524	+	0.516107i	$0.827381\pi$
$108$		−	1.25564e10i		−	0.854569i
$109$	−6.53087e8	−	6.53087e8i	−0.0424462	−	0.0424462i	0.685565	−	0.728011i	$-0.259555\pi$
$109$	−6.53087e8	−	6.53087e8i	−0.0424462	−	0.0424462i	−0.728011	+	0.685565i	$0.759555\pi$
$110$	−8.70931e7	−	8.70931e7i	−0.00540780	−	0.00540780i
$111$	7.86335e9	−	7.86335e9i	0.466651	−	0.466651i
$112$	1.49394e10	−	1.49394e10i	0.847701	−	0.847701i
$113$	8.59196e9			0.466337			0.233169	−	0.972436i	$-0.425091\pi$
$113$	8.59196e9			0.466337			0.233169	+	0.972436i	$0.425091\pi$
$114$		−	1.27533e8i		−	0.00662367i
$115$	1.38120e10	−	1.38120e10i	0.686701	−	0.686701i
$116$			3.43236e10i			1.63419i
$117$	7.15384e9	−	1.51867e10i	0.326294	−	0.692683i
$118$	−3.05723e8			−0.0133635
$119$	−8.63485e8	−	8.63485e8i	−0.0361843	−	0.0361843i
$120$	−2.46156e8			−0.00989246
$121$			1.14103e10i			0.439916i
$122$	2.31752e7	+	2.31752e7i	0.000857480	+	0.000857480i
$123$	−9.72709e9	−	9.72709e9i	−0.345508	−	0.345508i
$124$	9.16031e7	−	9.16031e7i	0.00312465	−	0.00312465i
$125$	2.34611e10	−	2.34611e10i	0.768773	−	0.768773i
$126$	3.54491e8			0.0111623
$127$		−	6.23041e9i		−	0.188581i	−0.995545	−	0.0942905i	$-0.969942\pi$
$127$		−	6.23041e9i		−	0.188581i	0.995545	−	0.0942905i	$-0.0300583\pi$
$128$	−1.18082e9	+	1.18082e9i	−0.0343665	+	0.0343665i
$129$			2.89801e10i			0.811244i
$130$	−3.43248e8	−	1.61690e8i	−0.00924467	−	0.00435478i
$131$	−3.68003e10			−0.953882			−0.476941	−	0.878935i	$-0.658255\pi$
$131$	−3.68003e10			−0.953882			−0.476941	+	0.878935i	$0.658255\pi$
$132$	−1.02640e10	−	1.02640e10i	−0.256121	−	0.256121i
$133$	−5.61900e10			−1.35021
$134$		−	2.27693e8i		−	0.00527018i
$135$	2.27837e10	+	2.27837e10i	0.508106	+	0.508106i
$136$	3.41203e7	+	3.41203e7i	0.000733361	+	0.000733361i
$137$	−6.40008e10	+	6.40008e10i	−1.32612	+	1.32612i	−0.417392	+	0.908726i	$0.637056\pi$
$137$	−6.40008e10	+	6.40008e10i	−1.32612	+	1.32612i	−0.908726	+	0.417392i	$0.862944\pi$
$138$	−2.40521e8	+	2.40521e8i	−0.00480571	+	0.00480571i
$139$	8.37112e10			1.61328			0.806640	−	0.591043i	$-0.201284\pi$
$139$	8.37112e10			1.61328			0.806640	+	0.591043i	$0.201284\pi$
$140$			5.42231e10i			1.00819i
$141$	−1.00900e10	+	1.00900e10i	−0.181048	+	0.181048i
$142$		−	2.16572e7i		−	0.000375112i
$143$	−1.51420e10	−	4.21119e10i	−0.253222	−	0.704246i
$144$	4.73883e10			0.765348
$145$	−6.22802e10	−	6.22802e10i	−0.971651	−	0.971651i
$146$	2.92588e8			0.00441054
$147$			1.45688e10i			0.212245i
$148$	6.84446e10	+	6.84446e10i	0.963897	+	0.963897i
$149$	−9.15989e10	−	9.15989e10i	−1.24727	−	1.24727i	−0.956923	−	0.290342i	$-0.906231\pi$
$149$	−9.15989e10	−	9.15989e10i	−1.24727	−	1.24727i	−0.290342	−	0.956923i	$-0.593769\pi$
$150$	−9.26202e7	+	9.26202e7i	−0.00121969	+	0.00121969i
$151$	6.02180e10	−	6.02180e10i	0.767081	−	0.767081i	−0.210510	−	0.977592i	$-0.567513\pi$
$151$	6.02180e10	−	6.02180e10i	0.767081	−	0.767081i	0.977592	+	0.210510i	$0.0675125\pi$
$152$	2.22033e9			0.0273652
$153$		−	2.73901e9i		−	0.0326690i
$154$	6.68215e8	−	6.68215e8i	0.00771459	−	0.00771459i
$155$			3.32428e8i			0.00371569i
$156$	−4.04519e10	−	1.90552e10i	−0.437841	−	0.206249i
$157$	8.28385e10			0.868428			0.434214	−	0.900810i	$-0.357026\pi$
$157$	8.28385e10			0.868428			0.434214	+	0.900810i	$0.357026\pi$
$158$	7.08195e8	+	7.08195e8i	0.00719230	+	0.00719230i
$159$	−3.70208e9			−0.0364301
$160$		−	3.21399e9i		−	0.0306510i
$161$	1.05972e11	+	1.05972e11i	0.979625	+	0.979625i
$162$	3.37528e8	+	3.37528e8i	0.00302507	+	0.00302507i
$163$	−5.39603e10	+	5.39603e10i	−0.468961	+	0.468961i	−0.901578	−	0.432617i	$-0.857590\pi$
$163$	−5.39603e10	+	5.39603e10i	−0.468961	+	0.468961i	0.432617	+	0.901578i	$0.357590\pi$
$164$	8.46671e10	−	8.46671e10i	0.713667	−	0.713667i
$165$	3.72479e10			0.304567
$166$			1.98280e9i			0.0157304i
$167$	1.33019e11	−	1.33019e11i	1.02407	−	1.02407i	0.0243696	−	0.999703i	$-0.492242\pi$
$167$	1.33019e11	−	1.33019e11i	1.02407	−	1.02407i	0.999703	−	0.0243696i	$-0.00775785\pi$
$168$		−	1.88861e9i		−	0.0141123i
$169$	−8.77882e10	−	1.06293e11i	−0.636800	−	0.771029i
$170$	−6.19067e7			−0.000436007
$171$	−8.91185e10	−	8.91185e10i	−0.609519	−	0.609519i
$172$	−2.52250e11			−1.67567
$173$			2.08175e11i			1.34338i	0.740834	+	0.671688i	$0.234430\pi$
$173$			2.08175e11i			1.34338i	−0.740834	+	0.671688i	$0.765570\pi$
$174$	1.08454e9	+	1.08454e9i	0.00679986	+	0.00679986i
$175$	4.08077e10	+	4.08077e10i	0.248629	+	0.248629i
$176$	8.93270e10	−	8.93270e10i	0.528956	−	0.528956i
$177$	6.53758e10	−	6.53758e10i	0.376314	−	0.376314i
$178$	−3.89974e9			−0.0218240
$179$			8.56531e10i			0.466099i	0.972465	+	0.233049i	$0.0748704\pi$
$179$			8.56531e10i			0.466099i	−0.972465	+	0.233049i	$0.925130\pi$
$180$	−8.59989e10	+	8.59989e10i	−0.455125	+	0.455125i
$181$			3.55529e11i			1.83013i	0.403304	+	0.915066i	$0.367862\pi$
$181$			3.55529e11i			1.83013i	−0.403304	+	0.915066i	$0.632138\pi$
$182$	1.24055e9	−	2.63354e9i	0.00621239	−	0.0131881i
$183$	−9.91155e9			−0.0482932
$184$	−4.18743e9	−	4.18743e9i	−0.0198545	−	0.0198545i
$185$	−2.48386e11			−1.14622
$186$		−	5.78887e6i		−	2.60033e-5i
$187$	−5.16303e9	−	5.16303e9i	−0.0225786	−	0.0225786i
$188$	−8.78255e10	−	8.78255e10i	−0.373966	−	0.373966i
$189$	−1.74806e11	+	1.74806e11i	−0.724848	+	0.724848i
$190$	−2.01425e9	+	2.01425e9i	−0.00813475	+	0.00813475i
$191$	2.88285e11			1.13411			0.567055	−	0.823680i	$-0.308083\pi$
$191$	2.88285e11			1.13411			0.567055	+	0.823680i	$0.308083\pi$
$192$		−	1.26188e11i		−	0.483629i
$193$	−4.94978e10	+	4.94978e10i	−0.184842	+	0.184842i	−0.793462	−	0.608620i	$-0.791723\pi$
$193$	−4.94978e10	+	4.94978e10i	−0.184842	+	0.184842i	0.608620	+	0.793462i	$0.291723\pi$
$194$			1.40050e9i			0.00509652i
$195$	1.07976e11	−	3.88243e10i	0.382960	−	0.137699i
$196$	−1.26811e11			−0.438405
$197$	1.14555e10	+	1.14555e10i	0.0386087	+	0.0386087i	0.726148	−	0.687539i	$-0.241309\pi$
$197$	1.14555e10	+	1.14555e10i	0.0386087	+	0.0386087i	−0.687539	+	0.726148i	$0.741309\pi$
$198$	2.11960e9			0.00696512
$199$		−	2.97746e11i		−	0.954072i	−0.878884	−	0.477036i	$-0.841711\pi$
$199$		−	2.97746e11i		−	0.954072i	0.878884	−	0.477036i	$-0.158289\pi$
$200$	−1.61250e9	−	1.61250e9i	−0.00503906	−	0.00503906i
$201$	4.86898e10	+	4.86898e10i	0.148408	+	0.148408i
$202$	−1.74232e9	+	1.74232e9i	−0.00518048	+	0.00518048i
$203$	4.77840e11	−	4.77840e11i	1.38613	−	1.38613i
$204$	−7.29573e9			−0.0206499
$205$			3.07257e11i			0.848659i
$206$	−2.03440e9	+	2.03440e9i	−0.00548404	+	0.00548404i
$207$			3.36146e11i			0.884456i
$208$	1.65837e11	−	3.52052e11i	0.425957	−	0.904254i
$209$	−3.35977e11			−0.842515
$210$	1.71332e9	+	1.71332e9i	0.00419509	+	0.00419509i
$211$	2.92564e11			0.699533			0.349767	−	0.936837i	$-0.386261\pi$
$211$	2.92564e11			0.699533			0.349767	+	0.936837i	$0.386261\pi$
$212$		−	3.22239e10i		−	0.0752487i
$213$	4.63117e9	+	4.63117e9i	0.0105631	+	0.0105631i
$214$	−6.60806e9	−	6.60806e9i	−0.0147233	−	0.0147233i
$215$	4.57709e11	−	4.57709e11i	0.996315	−	0.996315i
$216$	6.90739e9	−	6.90739e9i	0.0146908	−	0.0146908i
$217$	−2.55053e9			−0.00530068
$218$		−	3.59241e8i		−	0.000729632i
$219$	−6.25670e10	+	6.25670e10i	−0.124201	+	0.124201i
$220$			3.24216e11i			0.629102i
$221$	−2.03483e10	−	9.58526e9i	−0.0385982	−	0.0181820i
$222$	4.32537e9			0.00802154
$223$	−2.59124e11	−	2.59124e11i	−0.469877	−	0.469877i	0.431998	−	0.901875i	$-0.357809\pi$
$223$	−2.59124e11	−	2.59124e11i	−0.469877	−	0.469877i	−0.901875	+	0.431998i	$0.857809\pi$
$224$	2.46591e10			0.0437257
$225$			1.29444e11i			0.224475i
$226$	2.36308e9	+	2.36308e9i	0.00400807	+	0.00400807i
$227$	−3.12801e11	−	3.12801e11i	−0.518966	−	0.518966i	0.398292	−	0.917259i	$-0.369603\pi$
$227$	−3.12801e11	−	3.12801e11i	−0.518966	−	0.518966i	−0.917259	+	0.398292i	$0.869603\pi$
$228$	−2.37380e11	+	2.37380e11i	−0.385274	+	0.385274i
$229$	−6.03874e11	+	6.03874e11i	−0.958891	+	0.958891i	−0.999188	−	0.0402971i	$-0.987170\pi$
$229$	−6.03874e11	+	6.03874e11i	−0.958891	+	0.958891i	0.0402971	+	0.999188i	$0.487170\pi$
$230$	7.59753e9			0.0118041
$231$			2.85782e11i			0.434485i
$232$	−1.88817e10	+	1.88817e10i	−0.0280932	+	0.0280932i
$233$		−	7.49574e11i		−	1.09153i	−0.837939	−	0.545764i	$-0.816240\pi$
$233$		−	7.49574e11i		−	1.09153i	0.837939	−	0.545764i	$-0.183760\pi$
$234$	6.14440e9	−	2.20931e9i	0.00875790	−	0.00314903i
$235$	3.18719e11			0.444702
$236$	5.69048e11	+	5.69048e11i	0.777301	+	0.777301i
$237$	−3.02881e11			−0.405070
$238$		−	4.74975e8i		−	0.000621993i
$239$	3.21550e11	+	3.21550e11i	0.412344	+	0.412344i	0.882554	−	0.470211i	$-0.155822\pi$
$239$	3.21550e11	+	3.21550e11i	0.412344	+	0.412344i	−0.470211	+	0.882554i	$0.655822\pi$
$240$	2.29036e11	+	2.29036e11i	0.287639	+	0.287639i
$241$	−3.58841e11	+	3.58841e11i	−0.441384	+	0.441384i	−0.892477	−	0.451093i	$-0.851034\pi$
$241$	−3.58841e11	+	3.58841e11i	−0.441384	+	0.441384i	0.451093	+	0.892477i	$0.351034\pi$
$242$	−3.13821e9	+	3.13821e9i	−0.00378098	+	0.00378098i
$243$	−8.68528e11			−1.02507
$244$		−	8.62727e10i		−	0.0997527i
$245$	2.30098e11	−	2.30098e11i	0.260665	−	0.260665i
$246$		−	5.35055e9i		−	0.00593913i
$247$	−9.73943e11	+	3.50195e11i	−1.05937	+	0.380913i
$248$	1.00783e8			0.000107431
$249$	−4.24002e11	−	4.24002e11i	−0.442966	−	0.442966i
$250$	1.29052e10			0.0132149
$251$			1.09333e12i			1.09744i	0.836005	+	0.548722i	$0.184885\pi$
$251$			1.09333e12i			1.09744i	−0.836005	+	0.548722i	$0.815115\pi$
$252$	−6.59820e11	−	6.59820e11i	−0.649266	−	0.649266i
$253$	6.33635e11	+	6.33635e11i	0.611275	+	0.611275i
$254$	1.71357e9	−	1.71357e9i	0.00162081	−	0.00162081i
$255$	1.32381e10	−	1.32381e10i	0.0122779	−	0.0122779i
$256$	1.09789e12			0.998523
$257$		−	1.81187e12i		−	1.61608i	−0.589131	−	0.808038i	$-0.700530\pi$
$257$		−	1.81187e12i		−	1.61608i	0.589131	−	0.808038i	$-0.299470\pi$
$258$	−7.97049e9	+	7.97049e9i	−0.00697247	+	0.00697247i
$259$		−	1.90572e12i		−	1.63516i
$260$	3.37937e11	+	9.39850e11i	0.284426	+	0.791028i
$261$	1.51573e12			1.25146
$262$	−1.01213e10	−	1.01213e10i	−0.00819842	−	0.00819842i
$263$	8.51476e11			0.676696			0.338348	−	0.941021i	$-0.390132\pi$
$263$	8.51476e11			0.676696			0.338348	+	0.941021i	$0.390132\pi$
$264$		−	1.12926e10i		−	0.00880588i
$265$	5.84703e10	+	5.84703e10i	0.0447410	+	0.0447410i
$266$	−1.54541e10	−	1.54541e10i	−0.0116048	−	0.0116048i
$267$	8.33919e11	−	8.33919e11i	0.614564	−	0.614564i
$268$	−4.23808e11	+	4.23808e11i	−0.306546	+	0.306546i
$269$	−1.09025e12			−0.774045			−0.387023	−	0.922070i	$-0.626496\pi$
$269$	−1.09025e12			−0.774045			−0.387023	+	0.922070i	$0.626496\pi$
$270$			1.25325e10i			0.00873414i
$271$	2.74116e11	−	2.74116e11i	0.187538	−	0.187538i	−0.607093	−	0.794631i	$-0.707664\pi$
$271$	2.74116e11	−	2.74116e11i	0.187538	−	0.187538i	0.794631	+	0.607093i	$0.207664\pi$
$272$		−	6.34946e10i		−	0.0426474i
$273$	2.97877e11	+	8.28437e11i	0.196437	+	0.546319i
$274$	−3.52047e10			−0.0227954
$275$	2.44001e11	+	2.44001e11i	0.155142	+	0.155142i
$276$	8.95372e11			0.559060
$277$		−	2.30211e12i		−	1.41165i	−0.708386	−	0.705826i	$-0.750576\pi$
$277$		−	2.30211e12i		−	1.41165i	0.708386	−	0.705826i	$-0.249424\pi$
$278$	2.30234e10	+	2.30234e10i	0.0138658	+	0.0138658i
$279$	−4.04519e9	−	4.04519e9i	−0.00239286	−	0.00239286i
$280$	−2.98285e10	+	2.98285e10i	−0.0173317	+	0.0173317i
$281$	−1.98437e12	+	1.98437e12i	−1.13264	+	1.13264i	−0.142901	+	0.989737i	$0.545643\pi$
$281$	−1.98437e12	+	1.98437e12i	−1.13264	+	1.13264i	−0.989737	+	0.142901i	$0.954357\pi$
$282$	−5.55015e9			−0.00311214
$283$			1.05542e12i			0.581423i	0.956811	+	0.290712i	$0.0938920\pi$
$283$			1.05542e12i			0.581423i	−0.956811	+	0.290712i	$0.906108\pi$
$284$	−4.03109e10	+	4.03109e10i	−0.0218188	+	0.0218188i
$285$		−	8.61452e11i		−	0.458149i
$286$	7.41764e9	−	1.57467e10i	0.00387646	−	0.00822924i
$287$	−2.35741e12			−1.21067
$288$	3.91098e10	+	3.91098e10i	0.0197389	+	0.0197389i
$289$	2.01232e12			0.998180
$290$		−	3.42583e10i		−	0.0167023i
$291$	−2.99482e11	−	2.99482e11i	−0.143518	−	0.143518i
$292$	−5.44599e11	−	5.44599e11i	−0.256544	−	0.256544i
$293$	−1.29627e12	+	1.29627e12i	−0.600286	+	0.600286i	−0.940388	−	0.340102i	$-0.889538\pi$
$293$	−1.29627e12	+	1.29627e12i	−0.600286	+	0.600286i	0.340102	+	0.940388i	$0.389538\pi$
$294$	−4.00691e9	+	4.00691e9i	−0.00182420	+	0.00182420i
$295$	−2.06508e12			−0.924328
$296$			7.53038e10i			0.0331404i
$297$	−1.04521e12	+	1.04521e12i	−0.452297	+	0.452297i
$298$		−	5.03855e10i		−	0.0214400i
$299$	2.49726e12	+	1.17636e12i	1.04498	+	0.492247i
$300$	3.44791e11			0.141889
$301$	3.51173e12	+	3.51173e12i	1.42131	+	1.42131i
$302$	3.31239e10			0.0131858
$303$		−	7.45154e11i		−	0.291765i
$304$	−2.06591e12	−	2.06591e12i	−0.795689	−	0.795689i
$305$	1.56542e11	+	1.56542e11i	0.0593105	+	0.0593105i
$306$	7.53319e8	−	7.53319e8i	0.000280784	−	0.000280784i
$307$	−1.61161e12	+	1.61161e12i	−0.590974	+	0.590974i	−0.937895	−	0.346920i	$-0.887227\pi$
$307$	−1.61161e12	+	1.61161e12i	−0.590974	+	0.590974i	0.346920	+	0.937895i	$0.387227\pi$
$308$	−2.48752e12			−0.897456
$309$		−	8.70072e11i		−	0.308861i
$310$	−9.14288e7	+	9.14288e7i	−3.19356e−5	+	3.19356e-5i
$311$			8.34996e11i			0.287000i	0.989650	+	0.143500i	$0.0458358\pi$
$311$			8.34996e11i			0.287000i	−0.989650	+	0.143500i	$0.954164\pi$
$312$	−1.17705e10	−	3.27353e10i	−0.00398126	−	0.0110725i
$313$	−2.24081e11			−0.0745903			−0.0372952	−	0.999304i	$-0.511874\pi$
$313$	−2.24081e11			−0.0745903			−0.0372952	+	0.999304i	$0.511874\pi$
$314$	2.27834e10	+	2.27834e10i	0.00746396	+	0.00746396i
$315$	2.39449e12			0.772076
$316$		−	2.63635e12i		−	0.836697i
$317$	−2.98243e12	−	2.98243e12i	−0.931695	−	0.931695i	0.0661172	−	0.997812i	$-0.478939\pi$
$317$	−2.98243e12	−	2.98243e12i	−0.931695	−	0.931695i	−0.997812	+	0.0661172i	$0.978939\pi$
$318$	−1.01820e9	−	1.01820e9i	−0.000313109	−	0.000313109i
$319$	2.85714e12	−	2.85714e12i	0.864926	−	0.864926i
$320$	−1.99300e12	+	1.99300e12i	−0.593961	+	0.593961i
$321$	2.82613e12			0.829215
$322$			5.82914e10i			0.0168394i
$323$	−1.19408e11	+	1.19408e11i	−0.0339641	+	0.0339641i
$324$		−	1.25649e12i		−	0.351913i
$325$	9.61647e11	+	4.52993e11i	0.265216	+	0.124932i
$326$	−2.96818e10			−0.00806124
$327$	7.68201e10	+	7.68201e10i	0.0205464	+	0.0205464i
$328$	9.31520e10			0.0245371
$329$			2.44535e12i			0.634397i
$330$	1.02444e10	+	1.02444e10i	0.00261769	+	0.00261769i
$331$	5.20249e12	+	5.20249e12i	1.30940	+	1.30940i	0.921850	+	0.387547i	$0.126678\pi$
$331$	5.20249e12	+	5.20249e12i	1.30940	+	1.30940i	0.387547	+	0.921850i	$0.373322\pi$
$332$	3.69062e12	−	3.69062e12i	0.914974	−	0.914974i
$333$	3.02251e12	−	3.02251e12i	0.738153	−	0.738153i
$334$	7.31692e10			0.0176034
$335$		−	1.53800e12i		−	0.364530i
$336$	−1.75726e12	+	1.75726e12i	−0.410337	+	0.410337i
$337$		−	3.49787e12i		−	0.804737i	−0.915478	−	0.402368i	$-0.868187\pi$
$337$		−	3.49787e12i		−	0.804737i	0.915478	−	0.402368i	$-0.131813\pi$
$338$	5.08941e9	−	5.33788e10i	0.00115368	−	0.0121000i
$339$	−1.01064e12			−0.225734
$340$	1.15228e11	+	1.15228e11i	0.0253608	+	0.0253608i
$341$	−1.52503e10			−0.00330756
$342$		−	4.90211e10i		−	0.0104774i
$343$	−2.26089e12	−	2.26089e12i	−0.476221	−	0.476221i
$344$	−1.38765e11	−	1.38765e11i	−0.0288063	−	0.0288063i
$345$	−1.62465e12	+	1.62465e12i	−0.332403	+	0.332403i
$346$	−5.72550e10	+	5.72550e10i	−0.0115460	+	0.0115460i
$347$	−6.54232e12			−1.30042			−0.650212	−	0.759753i	$-0.725320\pi$
$347$	−6.54232e12			−1.30042			−0.650212	+	0.759753i	$0.725320\pi$
$348$		−	4.03735e12i		−	0.791044i
$349$	1.54433e12	−	1.54433e12i	0.298272	−	0.298272i	−0.542065	−	0.840337i	$-0.682357\pi$
$349$	1.54433e12	−	1.54433e12i	0.298272	−	0.298272i	0.840337	+	0.542065i	$0.182357\pi$
$350$			2.24470e10i			0.00427383i
$351$	−1.94046e12	+	4.11936e12i	−0.364225	+	0.773204i
$352$	1.47444e11			0.0272843
$353$	−4.71579e10	−	4.71579e10i	−0.00860361	−	0.00860361i	0.702792	−	0.711396i	$-0.251937\pi$
$353$	−4.71579e10	−	4.71579e10i	−0.00860361	−	0.00860361i	−0.711396	+	0.702792i	$0.751937\pi$
$354$	3.59611e10			0.00646869
$355$		−	1.46288e11i		−	0.0259459i
$356$	7.25864e12	+	7.25864e12i	1.26942	+	1.26942i
$357$	1.01568e11	+	1.01568e11i	0.0175153	+	0.0175153i
$358$	−2.35575e10	+	2.35575e10i	−0.00400602	+	0.00400602i
$359$	−6.44230e12	+	6.44230e12i	−1.08036	+	1.08036i	−0.0838846	+	0.996475i	$0.526733\pi$
$359$	−6.44230e12	+	6.44230e12i	−1.08036	+	1.08036i	−0.996475	+	0.0838846i	$0.973267\pi$
$360$	−9.46173e10			−0.0156480
$361$			1.63923e12i			0.267364i
$362$	−9.77824e10	+	9.77824e10i	−0.0157296	+	0.0157296i
$363$		−	1.34215e12i		−	0.212945i
$364$	−7.21093e12	+	2.59280e12i	−1.12845	+	0.405753i
$365$	1.97635e12			0.305070
$366$	−2.72601e9	−	2.72601e9i	−0.000415070	−	0.000415070i
$367$	−2.20570e12			−0.331296			−0.165648	−	0.986185i	$-0.552971\pi$
$367$	−2.20570e12			−0.331296			−0.165648	+	0.986185i	$0.552971\pi$
$368$			7.79240e12i			1.15460i
$369$	−3.73889e12	−	3.73889e12i	−0.546527	−	0.546527i
$370$	−6.83144e10	−	6.83144e10i	−0.00985152	−	0.00985152i
$371$	−4.48609e11	+	4.48609e11i	−0.0638261	+	0.0638261i
$372$	−1.07749e10	+	1.07749e10i	−0.00151251	+	0.00151251i
$373$	4.33370e12			0.600225			0.300113	−	0.953904i	$-0.402976\pi$
$373$	4.33370e12			0.600225			0.300113	+	0.953904i	$0.402976\pi$
$374$		−	2.84001e9i		−	0.000388116i
$375$	−2.75964e12	+	2.75964e12i	−0.372131	+	0.372131i
$376$		−	9.66270e10i		−	0.0128576i
$377$	5.30435e12	−	1.12605e13i	0.696507	−	1.47860i
$378$	−9.61549e10			−0.0124598
$379$	−6.01821e12	−	6.01821e12i	−0.769611	−	0.769611i	0.208427	−	0.978038i	$-0.433166\pi$
$379$	−6.01821e12	−	6.01821e12i	−0.769611	−	0.769611i	−0.978038	+	0.208427i	$0.933166\pi$
$380$	7.49830e12			0.946335
$381$			7.32859e11i			0.0912842i
$382$	7.92880e10	+	7.92880e10i	0.00974744	+	0.00974744i
$383$	−4.32408e12	−	4.32408e12i	−0.524687	−	0.524687i	0.394297	−	0.918983i	$-0.370988\pi$
$383$	−4.32408e12	−	4.32408e12i	−0.524687	−	0.524687i	−0.918983	+	0.394297i	$0.870988\pi$
$384$	1.38896e11	−	1.38896e11i	0.0166354	−	0.0166354i
$385$	4.51361e12	−	4.51361e12i	0.533606	−	0.533606i
$386$	−2.72271e10			−0.00317735
$387$			1.11394e13i			1.28323i
$388$	2.60677e12	−	2.60677e12i	0.296445	−	0.296445i
$389$		−	4.15392e12i		−	0.466348i	−0.972435	−	0.233174i	$-0.925089\pi$
$389$		−	4.15392e12i		−	0.466348i	0.972435	−	0.233174i	$-0.0749112\pi$
$390$	4.03750e10	+	1.90190e10i	0.00447496	+	0.00210797i
$391$	4.50394e11			0.0492844
$392$	−6.97596e10	−	6.97596e10i	−0.00753657	−	0.00753657i
$393$	4.32868e12			0.461735
$394$			6.30132e9i			0.000663667i
$395$	4.78367e12	+	4.78367e12i	0.497480	+	0.497480i
$396$	−3.94526e12	−	3.94526e12i	−0.405134	−	0.405134i
$397$	−8.87461e12	+	8.87461e12i	−0.899905	+	0.899905i	−0.995427	−	0.0955223i	$-0.969548\pi$
$397$	−8.87461e12	+	8.87461e12i	−0.899905	+	0.899905i	0.0955223	+	0.995427i	$0.469548\pi$
$398$	8.18902e10	−	8.18902e10i	0.00820005	−	0.00820005i
$399$	6.60942e12			0.653580
$400$			3.00071e12i			0.293038i
$401$	7.10243e12	−	7.10243e12i	0.684991	−	0.684991i	−0.276129	−	0.961121i	$-0.589052\pi$
$401$	7.10243e12	−	7.10243e12i	0.684991	−	0.684991i	0.961121	+	0.276129i	$0.0890518\pi$
$402$			2.67826e10i			0.00255107i
$403$	−4.42083e10	+	1.58958e10i	−0.00415890	+	0.00149540i
$404$	6.48601e12			0.602658
$405$	2.27991e12	+	2.27991e12i	0.209239	+	0.209239i
$406$	2.62844e11			0.0238269
$407$		−	1.13948e13i		−	1.02032i
$408$	−4.01344e9	−	4.01344e9i	−0.000354990	−	0.000354990i
$409$	−3.21348e12	−	3.21348e12i	−0.280776	−	0.280776i	0.552643	−	0.833418i	$-0.313619\pi$
$409$	−3.21348e12	−	3.21348e12i	−0.280776	−	0.280776i	−0.833418	+	0.552643i	$0.813619\pi$
$410$	−8.45060e10	+	8.45060e10i	−0.00729405	+	0.00729405i
$411$	7.52817e12	−	7.52817e12i	0.641919	−	0.641919i
$412$	7.57334e12			0.637971
$413$		−	1.58441e13i		−	1.31862i
$414$	−9.24514e10	+	9.24514e10i	−0.00760172	+	0.00760172i
$415$			1.33933e13i			1.08804i
$416$	4.27416e11	−	1.53684e11i	0.0343071	−	0.0123356i
$417$	−9.84663e12			−0.780921
$418$	−9.24048e10	−	9.24048e10i	−0.00724124	−	0.00724124i
$419$	−2.23911e13			−1.73382			−0.866911	−	0.498464i	$-0.833898\pi$
$419$	−2.23911e13			−1.73382			−0.866911	+	0.498464i	$0.833898\pi$
$420$		−	6.37806e12i		−	0.488025i
$421$	5.43309e12	+	5.43309e12i	0.410806	+	0.410806i	0.882019	−	0.471213i	$-0.156184\pi$
$421$	5.43309e12	+	5.43309e12i	0.410806	+	0.410806i	−0.471213	+	0.882019i	$0.656184\pi$
$422$	8.04648e10	+	8.04648e10i	0.00601234	+	0.00601234i
$423$	−3.87837e12	+	3.87837e12i	−0.286383	+	0.286383i
$424$	1.77266e10	−	1.77266e10i	0.00129359	−	0.00129359i
$425$	1.73439e11			0.0125084
$426$			2.54745e9i			0.000181576i
$427$	−1.20106e12	+	1.20106e12i	−0.0846105	+	0.0846105i
$428$			2.45994e13i			1.71280i
$429$	1.78109e12	+	4.95346e12i	0.122574	+	0.340896i
$430$	2.51770e11			0.0171262
$431$	−6.63869e12	−	6.63869e12i	−0.446371	−	0.446371i	0.447775	−	0.894146i	$-0.352217\pi$
$431$	−6.63869e12	−	6.63869e12i	−0.446371	−	0.446371i	−0.894146	+	0.447775i	$0.852217\pi$
$432$	−1.28540e13			−0.854317
$433$			1.10875e13i			0.728439i	0.931313	+	0.364220i	$0.118664\pi$
$433$			1.10875e13i			0.728439i	−0.931313	+	0.364220i	$0.881336\pi$
$434$	−7.01480e8	−	7.01480e8i	−4.55582e−5	−	4.55582e-5i
$435$	7.32579e12	+	7.32579e12i	0.470336	+	0.470336i
$436$	−6.68662e11	+	6.68662e11i	−0.0424399	+	0.0424399i
$437$	1.46544e13	−	1.46544e13i	0.919518	−	0.919518i
$438$	−3.44160e10			−0.00213496
$439$			2.01501e13i			1.23582i	0.786250	+	0.617908i	$0.212020\pi$
$439$			2.01501e13i			1.23582i	−0.786250	+	0.617908i	$0.787980\pi$
$440$	−1.78354e11	+	1.78354e11i	−0.0108148	+	0.0108148i
$441$			5.59996e12i			0.335731i
$442$	−2.96020e9	−	8.23274e9i	−0.000175473	−	0.000488015i
$443$	8.83517e11			0.0517841			0.0258920	−	0.999665i	$-0.491757\pi$
$443$	8.83517e11			0.0517841			0.0258920	+	0.999665i	$0.491757\pi$
$444$	−8.05088e12	−	8.05088e12i	−0.466582	−	0.466582i
$445$	−2.63416e13			−1.50953
$446$		−	1.42536e11i		−	0.00807699i
$447$	1.07744e13	+	1.07744e13i	0.603749	+	0.603749i
$448$	−1.52912e13	−	1.52912e13i	−0.847326	−	0.847326i
$449$	3.65774e12	−	3.65774e12i	0.200438	−	0.200438i	−0.599750	−	0.800188i	$-0.704733\pi$
$449$	3.65774e12	−	3.65774e12i	0.200438	−	0.200438i	0.800188	+	0.599750i	$0.204733\pi$
$450$	−3.56013e10	+	3.56013e10i	−0.00192932	+	0.00192932i
$451$	−1.40956e13			−0.755443
$452$		−	8.79687e12i		−	0.466268i
$453$	−7.08321e12	+	7.08321e12i	−0.371312	+	0.371312i
$454$		−	1.72062e11i		−	0.00892082i
$455$	8.37961e12	−	1.77889e13i	0.429701	−	0.912203i
$456$	−2.61169e11			−0.0132464
$457$	1.74070e13	+	1.74070e13i	0.873259	+	0.873259i	0.992826	−	0.119567i	$-0.0381506\pi$
$457$	1.74070e13	+	1.74070e13i	0.873259	+	0.873259i	−0.119567	+	0.992826i	$0.538151\pi$
$458$	−3.32171e11			−0.0164829
$459$			7.42950e11i			0.0364667i
$460$	−1.41414e13	−	1.41414e13i	−0.686600	−	0.686600i
$461$	9.83525e12	+	9.83525e12i	0.472368	+	0.472368i	0.902680	−	0.430312i	$-0.141596\pi$
$461$	9.83525e12	+	9.83525e12i	0.472368	+	0.472368i	−0.430312	+	0.902680i	$0.641596\pi$
$462$	−7.85996e10	+	7.85996e10i	−0.00373431	+	0.00373431i
$463$	2.24886e13	−	2.24886e13i	1.05696	−	1.05696i	0.0586828	−	0.998277i	$-0.481310\pi$
$463$	2.24886e13	−	2.24886e13i	1.05696	−	1.05696i	0.998277	−	0.0586828i	$-0.0186901\pi$
$464$	3.51370e13			1.63371
$465$		−	3.91022e10i		−	0.00179861i
$466$	2.06158e11	−	2.06158e11i	0.00938146	−	0.00938146i
$467$			2.70794e12i			0.121915i	0.998140	+	0.0609573i	$0.0194153\pi$
$467$			2.70794e12i			0.121915i	−0.998140	+	0.0609573i	$0.980585\pi$
$468$	−1.55489e13	−	7.32445e12i	−0.692580	−	0.326246i
$469$	1.18002e13			0.520026
$470$	8.76584e10	+	8.76584e10i	0.00382212	+	0.00382212i
$471$	−9.74398e12			−0.420370
$472$			6.26075e11i			0.0267249i
$473$	2.09977e13	+	2.09977e13i	0.886881	+	0.886881i
$474$	−8.33023e10	−	8.33023e10i	−0.00348149	−	0.00348149i
$475$	5.64313e12	−	5.64313e12i	0.233374	−	0.233374i
$476$	−8.84078e11	+	8.84078e11i	−0.0361789	+	0.0361789i
$477$	−1.42300e12			−0.0576255
$478$			1.76874e11i			0.00708802i
$479$	1.07785e13	−	1.07785e13i	0.427445	−	0.427445i	−0.460312	−	0.887757i	$-0.652263\pi$
$479$	1.07785e13	−	1.07785e13i	0.427445	−	0.427445i	0.887757	+	0.460312i	$0.152263\pi$
$480$			3.78049e11i			0.0148369i
$481$	−1.18771e13	−	3.30319e13i	−0.461301	−	1.28294i
$482$	−1.97386e11			−0.00758721
$483$	−1.24650e13	−	1.24650e13i	−0.474196	−	0.474196i
$484$	1.16824e13			0.439851
$485$			9.45998e12i			0.352518i
$486$	−2.38874e11	−	2.38874e11i	−0.00881024	−	0.00881024i
$487$	−1.04641e13	−	1.04641e13i	−0.381994	−	0.381994i	0.489826	−	0.871820i	$-0.337060\pi$
$487$	−1.04641e13	−	1.04641e13i	−0.381994	−	0.381994i	−0.871820	+	0.489826i	$0.837060\pi$
$488$	4.74593e10	−	4.74593e10i	0.00171483	−	0.00171483i
$489$	6.34715e12	−	6.34715e12i	0.227004	−	0.227004i
$490$	1.26570e11			0.00448073
$491$			2.60553e13i			0.913038i	0.889714	+	0.456519i	$0.150904\pi$
$491$			2.60553e13i			0.913038i	−0.889714	+	0.456519i	$0.849096\pi$
$492$	−9.95907e12	+	9.95907e12i	−0.345456	+	0.345456i
$493$		−	2.03089e12i		−	0.0697352i
$494$	−3.64182e11	−	1.71551e11i	−0.0123790	−	0.00583122i
$495$	1.43173e13			0.481766
$496$	−9.37739e10	−	9.37739e10i	−0.00312373	−	0.00312373i
$497$	1.12239e12			0.0370135
$498$		−	2.33229e11i		−	0.00761441i
$499$	2.22414e13	+	2.22414e13i	0.718884	+	0.718884i	0.968377	−	0.249493i	$-0.0802638\pi$
$499$	2.22414e13	+	2.22414e13i	0.718884	+	0.718884i	−0.249493	+	0.968377i	$0.580264\pi$
$500$	−2.40206e13	−	2.40206e13i	−0.768659	−	0.768659i
$501$	−1.56465e13	+	1.56465e13i	−0.495711	+	0.495711i
$502$	−3.00702e11	+	3.00702e11i	−0.00943230	+	0.00943230i
$503$	−1.14338e13			−0.355100			−0.177550	−	0.984112i	$-0.556817\pi$
$503$	−1.14338e13			−0.355100			−0.177550	+	0.984112i	$0.556817\pi$
$504$		−	7.25944e11i		−	0.0223229i
$505$	−1.17689e13	+	1.17689e13i	−0.358326	+	0.358326i
$506$			3.48541e11i			0.0105076i
$507$	1.03262e13	+	1.25028e13i	0.308248	+	0.373223i
$508$	−6.37900e12			−0.188553
$509$	−3.37502e13	−	3.37502e13i	−0.987842	−	0.987842i	0.0120847	−	0.999927i	$-0.496153\pi$
$509$	−3.37502e13	−	3.37502e13i	−0.987842	−	0.987842i	−0.999927	+	0.0120847i	$0.996153\pi$
$510$	7.28185e9			0.000211053
$511$			1.51634e13i			0.435203i
$512$	1.51112e12	+	1.51112e12i	0.0429486	+	0.0429486i
$513$	2.41732e13	+	2.41732e13i	0.680373	+	0.680373i
$514$	4.98325e11	−	4.98325e11i	0.0138898	−	0.0138898i
$515$	−1.37418e13	+	1.37418e13i	−0.379322	+	0.379322i
$516$	2.96712e13			0.811124
$517$			1.46214e13i			0.395856i
$518$	5.24137e11	−	5.24137e11i	0.0140539	−	0.0140539i
$519$		−	2.44868e13i		−	0.650272i
$520$	−3.31117e11	+	7.02920e11i	−0.00870893	+	0.0184880i
$521$	−7.28642e13			−1.89813			−0.949064	−	0.315085i	$-0.897967\pi$
$521$	−7.28642e13			−1.89813			−0.949064	+	0.315085i	$0.897967\pi$
$522$	4.16876e11	+	4.16876e11i	0.0107561	+	0.0107561i
$523$	3.75707e13			0.960154			0.480077	−	0.877226i	$-0.340609\pi$
$523$	3.75707e13			0.960154			0.480077	+	0.877226i	$0.340609\pi$
$524$			3.76779e13i			0.953741i
$525$	−4.80005e12	−	4.80005e12i	−0.120351	−	0.120351i
$526$	2.34184e11	+	2.34184e11i	0.00581606	+	0.00581606i
$527$	−5.42005e9	+	5.42005e9i	−0.000133337	+	0.000133337i
$528$	−1.05072e13	+	1.05072e13i	−0.256045	+	0.256045i
$529$	−1.38483e13			−0.334287
$530$			3.21626e10i			0.000769080i
$531$	2.51291e13	−	2.51291e13i	0.595257	−	0.595257i
$532$			5.75301e13i			1.35001i
$533$	−4.08610e13	+	1.46922e13i	−0.949889	+	0.341546i
$534$	4.58711e11			0.0105641
$535$	−4.46356e13	−	4.46356e13i	−1.01839	−	1.01839i
$536$	−4.66280e11			−0.0105396
$537$		−	1.00751e13i		−	0.225619i
$538$	−2.99856e11	−	2.99856e11i	−0.00665276	−	0.00665276i
$539$	1.05559e13	+	1.05559e13i	0.232034	+	0.232034i
$540$	2.33270e13	−	2.33270e13i	0.508031	−	0.508031i
$541$	2.30054e13	−	2.30054e13i	0.496414	−	0.496414i	−0.413906	−	0.910320i	$-0.635836\pi$
$541$	2.30054e13	−	2.30054e13i	0.496414	−	0.496414i	0.910320	+	0.413906i	$0.135836\pi$
$542$	1.50782e11			0.00322370
$543$		−	4.18195e13i		−	0.885891i
$544$	5.24023e10	−	5.24023e10i	0.00109991	−	0.00109991i
$545$		−	2.42658e12i		−	0.0504675i
$546$	−1.45922e11	+	3.09774e11i	−0.00300716	+	0.00638383i
$547$	5.03266e13			1.02769			0.513844	−	0.857884i	$-0.328221\pi$
$547$	5.03266e13			1.02769			0.513844	+	0.857884i	$0.328221\pi$
$548$	6.55271e13	+	6.55271e13i	1.32592	+	1.32592i
$549$	−3.80980e12			−0.0763906
$550$			1.34217e11i			0.00266682i
$551$	−6.60786e13	−	6.60786e13i	−1.30108	−	1.30108i
$552$	4.92551e11	+	4.92551e11i	0.00961071	+	0.00961071i
$553$	−3.67023e13	+	3.67023e13i	−0.709688	+	0.709688i
$554$	6.33157e11	−	6.33157e11i	0.0121329	−	0.0121329i
$555$	2.92167e13			0.554837
$556$		−	8.57076e13i		−	1.61304i
$557$	4.41697e13	−	4.41697e13i	0.823850	−	0.823850i	−0.162808	−	0.986658i	$-0.552055\pi$
$557$	4.41697e13	−	4.41697e13i	0.823850	−	0.823850i	0.986658	+	0.162808i	$0.0520550\pi$
$558$		−	2.22512e9i		−	4.11323e-5i
$559$	8.27552e13	+	3.89826e13i	1.51613	+	0.714187i
$560$	5.55081e13			1.00790
$561$	6.07307e11	+	6.07307e11i	0.0109293	+	0.0109293i
$562$	−1.09154e12			−0.0194696
$563$		−	4.17155e13i		−	0.737488i	−0.929531	−	0.368744i	$-0.879788\pi$
$563$		−	4.17155e13i		−	0.737488i	0.929531	−	0.368744i	$-0.120212\pi$
$564$	1.03306e13	+	1.03306e13i	0.181021	+	0.181021i
$565$	1.59619e13	+	1.59619e13i	0.277232	+	0.277232i
$566$	−2.90275e11	+	2.90275e11i	−0.00499721	+	0.00499721i
$567$	−1.74924e13	+	1.74924e13i	−0.298493	+	0.298493i
$568$	−4.43507e10			−0.000750168
$569$			9.73258e13i			1.63180i	0.578194	+	0.815899i	$0.303758\pi$
$569$			9.73258e13i			1.63180i	−0.578194	+	0.815899i	$0.696242\pi$
$570$	2.36928e11	−	2.36928e11i	0.00393769	−	0.00393769i
$571$		−	9.12604e13i		−	1.50349i	−0.659451	−	0.751747i	$-0.729211\pi$
$571$		−	9.12604e13i		−	1.50349i	0.659451	−	0.751747i	$-0.270789\pi$
$572$	−4.31162e13	+	1.55031e13i	−0.704142	+	0.253185i
$573$	−3.39098e13			−0.548975
$574$	−6.48366e11	−	6.48366e11i	−0.0104054	−	0.0104054i
$575$	−2.12853e13			−0.338642
$576$		−	4.85041e13i		−	0.765009i
$577$	−2.43599e13	−	2.43599e13i	−0.380888	−	0.380888i	0.490534	−	0.871422i	$-0.336802\pi$
$577$	−2.43599e13	−	2.43599e13i	−0.380888	−	0.380888i	−0.871422	+	0.490534i	$0.836802\pi$
$578$	5.53456e11	+	5.53456e11i	0.00857915	+	0.00857915i
$579$	5.82224e12	−	5.82224e12i	0.0894741	−	0.0894741i
$580$	−6.37655e13	+	6.37655e13i	−0.971507	+	0.971507i
$581$	−1.02759e14			−1.55217
$582$		−	1.64735e11i		−	0.00246701i
$583$	−2.68236e12	+	2.68236e12i	−0.0398267	+	0.0398267i
$584$		−	5.99176e11i		−	0.00882044i
$585$	4.15037e13	−	1.49233e13i	0.605770	−	0.217813i
$586$	−7.13037e11			−0.0103187
$587$	8.86349e13	+	8.86349e13i	1.27179	+	1.27179i	0.945150	+	0.326636i	$0.105915\pi$
$587$	8.86349e13	+	8.86349e13i	1.27179	+	1.27179i	0.326636	+	0.945150i	$0.394085\pi$
$588$	1.49163e13			0.212214
$589$			3.52702e11i			0.00497544i
$590$	−5.67965e11	−	5.67965e11i	−0.00794441	−	0.00794441i
$591$	−1.34747e12	−	1.34747e12i	−0.0186888	−	0.0186888i
$592$	7.00666e13	−	7.00666e13i	0.963612	−	0.963612i
$593$	−8.80206e12	+	8.80206e12i	−0.120036	+	0.120036i	−0.764573	−	0.644537i	$-0.777050\pi$
$593$	−8.80206e12	+	8.80206e12i	−0.120036	+	0.120036i	0.644537	+	0.764573i	$0.277050\pi$
$594$	−5.74938e11			−0.00777479
$595$		−	3.20832e12i		−	0.0430223i
$596$	−9.37834e13	+	9.37834e13i	−1.24708	+	1.24708i
$597$			3.50228e13i			0.461826i
$598$	3.63292e11	+	1.01037e12i	0.00475062	+	0.0132121i
$599$	−4.13451e13			−0.536155			−0.268077	−	0.963397i	$-0.586388\pi$
$599$	−4.13451e13			−0.536155			−0.268077	+	0.963397i	$0.586388\pi$
$600$	1.89672e11	+	1.89672e11i	0.00243920	+	0.00243920i
$601$	6.94305e13			0.885479			0.442739	−	0.896650i	$-0.354007\pi$
$601$	6.94305e13			0.885479			0.442739	+	0.896650i	$0.354007\pi$
$602$			1.93169e12i			0.0244317i
$603$	1.87154e13	+	1.87154e13i	0.234753	+	0.234753i
$604$	−6.16541e13	−	6.16541e13i	−0.766968	−	0.766968i
$605$	−2.11977e13	+	2.11977e13i	−0.261525	+	0.261525i
$606$	2.04942e11	−	2.04942e11i	0.00250766	−	0.00250766i
$607$	−9.09194e13			−1.10335			−0.551675	−	0.834059i	$-0.686011\pi$
$607$	−9.09194e13			−1.10335			−0.551675	+	0.834059i	$0.686011\pi$
$608$		−	3.41000e12i		−	0.0410428i
$609$	−5.62065e13	+	5.62065e13i	−0.670966	+	0.670966i
$610$			8.61086e10i			0.00101952i
$611$	1.52402e13	+	4.23852e13i	0.178972	+	0.497747i
$612$	−2.80433e12			−0.0326642
$613$	3.93135e13	+	3.93135e13i	0.454191	+	0.454191i	0.896743	−	0.442552i	$-0.145927\pi$
$613$	3.93135e13	+	3.93135e13i	0.454191	+	0.454191i	−0.442552	+	0.896743i	$0.645927\pi$
$614$	−8.86494e11			−0.0101586
$615$		−	3.61415e13i		−	0.410800i
$616$	−1.36840e12	−	1.36840e12i	−0.0154280	−	0.0154280i
$617$	6.95333e13	+	6.95333e13i	0.777619	+	0.777619i	0.979425	−	0.201806i	$-0.0646812\pi$
$617$	6.95333e13	+	6.95333e13i	0.777619	+	0.777619i	−0.201806	+	0.979425i	$0.564681\pi$
$618$	2.39299e11	−	2.39299e11i	0.00265460	−	0.00265460i
$619$	−6.32818e13	+	6.32818e13i	−0.696346	+	0.696346i	−0.963621	−	0.267274i	$-0.913877\pi$
$619$	−6.32818e13	+	6.32818e13i	−0.696346	+	0.696346i	0.267274	+	0.963621i	$0.413877\pi$
$620$	3.40356e11			0.00371514
$621$		−	9.11789e13i		−	0.987270i
$622$	−2.29652e11	+	2.29652e11i	−0.00246671	+	0.00246671i
$623$		−	2.02104e14i		−	2.15345i
$624$	−1.95068e13	+	4.14105e13i	−0.206188	+	0.437711i
$625$	5.92122e13			0.620885
$626$	−6.16296e10	−	6.16296e10i	−0.000641089	−	0.000641089i
$627$	3.95196e13			0.407826
$628$		−	8.48141e13i		−	0.868300i
$629$	−4.04979e12	−	4.04979e12i	−0.0411320	−	0.0411320i
$630$	6.58565e11	+	6.58565e11i	0.00663584	+	0.00663584i
$631$	−2.73014e13	+	2.73014e13i	−0.272922	+	0.272922i	−0.830275	−	0.557354i	$-0.811817\pi$
$631$	−2.73014e13	+	2.73014e13i	−0.272922	+	0.272922i	0.557354	+	0.830275i	$0.311817\pi$
$632$	1.45028e12	−	1.45028e12i	0.0143835	−	0.0143835i
$633$	−3.44132e13			−0.338615
$634$		−	1.64053e12i		−	0.0160154i
$635$	1.15747e13	−	1.15747e13i	0.112109	−	0.112109i
$636$			3.79037e12i			0.0364247i
$637$	4.16026e13	+	1.95973e13i	0.396664	+	0.186852i
$638$	1.57162e12			0.0148677
$639$	1.78013e12	+	1.78013e12i	0.0167089	+	0.0167089i
$640$	−4.38741e12			−0.0408609
$641$		−	3.19734e13i		−	0.295460i	−0.989028	−	0.147730i	$-0.952803\pi$
$641$		−	3.19734e13i		−	0.295460i	0.989028	−	0.147730i	$-0.0471967\pi$
$642$	7.77281e11	+	7.77281e11i	0.00712693	+	0.00712693i
$643$	1.08680e14	+	1.08680e14i	0.988768	+	0.988768i	0.999938	−	0.0111696i	$-0.00355547\pi$
$643$	1.08680e14	+	1.08680e14i	0.988768	+	0.988768i	−0.0111696	+	0.999938i	$0.503555\pi$
$644$	1.08499e14	−	1.08499e14i	0.979481	−	0.979481i
$645$	−5.38385e13	+	5.38385e13i	−0.482275	+	0.482275i
$646$	−6.56823e10			−0.000583829
$647$			5.10919e13i			0.450641i	0.974285	+	0.225321i	$0.0723430\pi$
$647$			5.10919e13i			0.450641i	−0.974285	+	0.225321i	$0.927657\pi$
$648$	6.91206e11	−	6.91206e11i	0.00604969	−	0.00604969i
$649$		−	9.47367e13i		−	0.822801i
$650$	1.39897e11	+	3.89073e11i	0.00120571	+	0.00335324i
$651$	3.00009e11			0.00256584
$652$	5.52472e13	+	5.52472e13i	0.468891	+	0.468891i
$653$	1.53480e14			1.29266			0.646332	−	0.763056i	$-0.276302\pi$
$653$	1.53480e14			1.29266			0.646332	+	0.763056i	$0.276302\pi$
$654$			4.22562e10i			0.000353184i
$655$	−6.83667e13	−	6.83667e13i	−0.567072	−	0.567072i
$656$	−8.66735e13	−	8.66735e13i	−0.713456	−	0.713456i
$657$	−2.40495e13	+	2.40495e13i	−0.196462	+	0.196462i
$658$	−6.72552e11	+	6.72552e11i	−0.00545251	+	0.00545251i
$659$	1.62213e14			1.30514			0.652571	−	0.757727i	$-0.273690\pi$
$659$	1.62213e14			1.30514			0.652571	+	0.757727i	$0.273690\pi$
$660$		−	3.81363e13i		−	0.304522i
$661$	8.85074e13	−	8.85074e13i	0.701411	−	0.701411i	−0.263303	−	0.964713i	$-0.584812\pi$
$661$	8.85074e13	−	8.85074e13i	0.701411	−	0.701411i	0.964713	+	0.263303i	$0.0848118\pi$
$662$			2.86172e12i			0.0225080i
$663$	2.39350e12	+	1.12748e12i	0.0186838	+	0.00880117i
$664$	4.06047e12			0.0314584
$665$	−1.04388e14	−	1.04388e14i	−0.802684	−	0.802684i
$666$	1.66258e12			0.0126885
$667$			2.49242e14i			1.88796i
$668$	−1.36191e14	−	1.36191e14i	−1.02392	−	1.02392i
$669$	3.04798e13	+	3.04798e13i	0.227448	+	0.227448i
$670$	4.23002e11	−	4.23002e11i	0.00313306	−	0.00313306i
$671$	−7.18146e12	+	7.18146e12i	−0.0527959	+	0.0527959i
$672$	−2.90055e12			−0.0211658
$673$		−	9.09780e13i		−	0.658963i	−0.944162	−	0.329481i	$-0.893126\pi$
$673$		−	9.09780e13i		−	0.658963i	0.944162	−	0.329481i	$-0.106874\pi$
$674$	9.62030e11	−	9.62030e11i	0.00691655	−	0.00691655i
$675$		−	3.51113e13i		−	0.250569i
$676$	−1.08828e14	+	8.98819e13i	−0.770915	+	0.636706i
$677$	−2.22417e12			−0.0156396			−0.00781978	−	0.999969i	$-0.502489\pi$
$677$	−2.22417e12			−0.0156396			−0.00781978	+	0.999969i	$0.502489\pi$
$678$	−2.77960e11	−	2.77960e11i	−0.00194014	−	0.00194014i
$679$	−7.25810e13			−0.502891
$680$			1.26776e11i			0.000871949i
$681$	3.67936e13	+	3.67936e13i	0.251210	+	0.251210i
$682$	−4.19435e9	−	4.19435e9i	−2.84278e−5	−	2.84278e-5i
$683$	−5.37856e13	+	5.37856e13i	−0.361879	+	0.361879i	−0.864504	−	0.502626i	$-0.832367\pi$
$683$	−5.37856e13	+	5.37856e13i	−0.361879	+	0.361879i	0.502626	+	0.864504i	$0.332367\pi$
$684$	−9.12439e13	+	9.12439e13i	−0.609429	+	0.609429i
$685$	−2.37798e14			−1.57672
$686$		−	1.24364e12i		−	0.00818604i
$687$	7.10314e13	−	7.10314e13i	0.464159	−	0.464159i
$688$			2.58228e14i			1.67518i
$689$	−4.97986e12	+	1.05716e13i	−0.0320716	+	0.0680841i
$690$	−8.93668e11			−0.00571388
$691$	2.00301e13	+	2.00301e13i	0.127143	+	0.127143i	0.767815	−	0.640672i	$-0.221344\pi$
$691$	2.00301e13	+	2.00301e13i	0.127143	+	0.127143i	−0.640672	+	0.767815i	$0.721344\pi$
$692$	2.13139e14			1.34318
$693$			1.09849e14i			0.687272i
$694$	−1.79936e12	−	1.79936e12i	−0.0111769	−	0.0111769i
$695$	1.55517e14	+	1.55517e14i	0.959076	+	0.959076i
$696$	2.22098e12	−	2.22098e12i	0.0135987	−	0.0135987i
$697$	−5.00966e12	+	5.00966e12i	−0.0304540	+	0.0304540i
$698$	8.49483e11			0.00512717
$699$			8.81695e13i			0.528363i
$700$	4.17809e13	−	4.17809e13i	0.248592	−	0.248592i
$701$			5.99447e12i			0.0354129i	0.999843	+	0.0177064i	$0.00563643\pi$
$701$			5.99447e12i			0.0354129i	−0.999843	+	0.0177064i	$0.994364\pi$
$702$	−1.66665e12	+	5.99270e11i	−0.00977597	+	0.00351509i
$703$	−2.63534e14			−1.53483
$704$	−9.14303e13	−	9.14303e13i	−0.528721	−	0.528721i
$705$	−3.74897e13			−0.215262
$706$		−	2.59400e10i		−	0.000147893i
$707$	−9.02958e13	−	9.02958e13i	−0.511176	−	0.511176i
$708$	−6.69350e13	−	6.69350e13i	−0.376259	−	0.376259i
$709$	4.00780e13	−	4.00780e13i	0.223704	−	0.223704i	−0.586352	−	0.810056i	$-0.699436\pi$
$709$	4.00780e13	−	4.00780e13i	0.223704	−	0.223704i	0.810056	+	0.586352i	$0.199436\pi$
$710$	4.02342e10	−	4.02342e10i	0.000222999	−	0.000222999i
$711$	−1.16421e14			−0.640743
$712$			7.98607e12i			0.0436449i
$713$	6.65178e11	−	6.65178e11i	0.00360986	−	0.00360986i
$714$			5.58694e10i			0.000301081i
$715$	5.01041e13	−	1.06365e14i	0.268129	−	0.569204i
$716$	8.76959e13			0.466030
$717$	−3.78227e13	−	3.78227e13i	−0.199598	−	0.199598i
$718$	−3.54369e12			−0.0185709
$719$		−	1.17524e14i		−	0.611622i	−0.952092	−	0.305811i	$-0.901072\pi$
$719$		−	1.17524e14i		−	0.611622i	0.952092	−	0.305811i	$-0.0989276\pi$
$720$	8.80369e13	+	8.80369e13i	0.454990	+	0.454990i
$721$	−1.05433e14	−	1.05433e14i	−0.541129	−	0.541129i
$722$	−4.50843e11	+	4.50843e11i	−0.00229794	+	0.00229794i
$723$	4.22091e13	−	4.22091e13i	0.213656	−	0.213656i
$724$	3.64008e14			1.82986
$725$			9.59784e13i			0.479163i
$726$	3.69135e11	−	3.69135e11i	0.00183022	−	0.00183022i
$727$		−	2.42137e14i		−	1.19231i	−0.802870	−	0.596154i	$-0.796695\pi$
$727$		−	2.42137e14i		−	1.19231i	0.802870	−	0.596154i	$-0.203305\pi$
$728$	−5.39310e12	−	2.54047e12i	−0.0263743	−	0.0124239i
$729$	2.96952e13			0.144227
$730$	5.43563e11	+	5.43563e11i	0.00262202	+	0.00262202i
$731$	1.49254e13			0.0715053
$732$			1.01479e13i			0.0482861i
$733$	2.26924e14	+	2.26924e14i	1.07241	+	1.07241i	0.997165	+	0.0752420i	$0.0239729\pi$
$733$	2.26924e14	+	2.26924e14i	1.07241	+	1.07241i	0.0752420	+	0.997165i	$0.476027\pi$
$734$	−6.06641e11	−	6.06641e11i	−0.00284742	−	0.00284742i
$735$	−2.70656e13	+	2.70656e13i	−0.126177	+	0.126177i
$736$	−6.43109e12	+	6.43109e12i	−0.0297780	+	0.0297780i
$737$	7.05568e13			0.324490
$738$		−	2.05664e12i		−	0.00939457i
$739$	−1.99563e14	+	1.99563e14i	−0.905438	+	0.905438i	−0.995900	−	0.0904620i	$-0.971166\pi$
$739$	−1.99563e14	+	1.99563e14i	−0.905438	+	0.905438i	0.0904620	+	0.995900i	$0.471166\pi$
$740$			2.54309e14i			1.14605i
$741$	1.14561e14	−	4.11922e13i	0.512798	−	0.184384i
$742$	−2.46765e11			−0.00109714
$743$	−5.30426e12	−	5.30426e12i	−0.0234251	−	0.0234251i	0.695297	−	0.718722i	$-0.255273\pi$
$743$	−5.30426e12	−	5.30426e12i	−0.0234251	−	0.0234251i	−0.718722	+	0.695297i	$0.755273\pi$
$744$	−1.18547e10			−5.20028e−5
$745$		−	3.40340e14i		−	1.48297i
$746$	1.19191e12	+	1.19191e12i	0.00515881	+	0.00515881i
$747$	−1.62977e14	−	1.62977e14i	−0.700688	−	0.700688i
$748$	−5.28616e12	+	5.28616e12i	−0.0225752	+	0.0225752i
$749$	3.42463e14	−	3.42463e14i	1.45280	−	1.45280i
$750$	−1.51799e12			−0.00639678
$751$			9.77888e13i			0.409345i	0.978831	+	0.204672i	$0.0656129\pi$
$751$			9.77888e13i			0.409345i	−0.978831	+	0.204672i	$0.934387\pi$
$752$	−8.99068e13	+	8.99068e13i	−0.373855	+	0.373855i
$753$		−	1.28604e14i		−	0.531227i
$754$	4.55588e12	−	1.63813e12i	0.0186946	−	0.00672191i
$755$	2.23743e14			0.912042
$756$	1.78975e14	+	1.78975e14i	0.724741	+	0.724741i
$757$	−3.04144e14			−1.22349			−0.611744	−	0.791056i	$-0.709532\pi$
$757$	−3.04144e14			−1.22349			−0.611744	+	0.791056i	$0.709532\pi$
$758$		−	3.31042e12i		−	0.0132293i
$759$	−7.45320e13	−	7.45320e13i	−0.295893	−	0.295893i
$760$	4.12487e12	+	4.12487e12i	0.0162683	+	0.0162683i
$761$	3.70290e13	−	3.70290e13i	0.145084	−	0.145084i	−0.630834	−	0.775918i	$-0.717287\pi$
$761$	3.70290e13	−	3.70290e13i	0.145084	−	0.145084i	0.775918	+	0.630834i	$0.217287\pi$
$762$	−2.01561e11	+	2.01561e11i	−0.000784569	+	0.000784569i
$763$	1.86177e13			0.0719952
$764$		−	2.95160e14i		−	1.13394i
$765$	5.08846e12	−	5.08846e12i	0.0194213	−	0.0194213i
$766$		−	2.37853e12i		−	0.00901915i
$767$	−9.87461e13	−	2.74627e14i	−0.372000	−	1.03458i
$768$	−1.29140e14			−0.483343
$769$	−3.34451e13	−	3.34451e13i	−0.124366	−	0.124366i	0.642184	−	0.766550i	$-0.278028\pi$
$769$	−3.34451e13	−	3.34451e13i	−0.124366	−	0.124366i	−0.766550	+	0.642184i	$0.778028\pi$
$770$	2.48279e12			0.00917246
$771$			2.13123e14i			0.782275i
$772$	5.06783e13	+	5.06783e13i	0.184814	+	0.184814i
$773$	1.73419e14	+	1.73419e14i	0.628346	+	0.628346i	0.947652	−	0.319306i	$-0.103450\pi$
$773$	1.73419e14	+	1.73419e14i	0.628346	+	0.628346i	−0.319306	+	0.947652i	$0.603450\pi$
$774$	−3.06369e12	+	3.06369e12i	−0.0110291	+	0.0110291i
$775$	2.56148e11	−	2.56148e11i	0.000916183	−	0.000916183i
$776$	2.86801e12			0.0101923
$777$			2.24163e14i			0.791513i
$778$	1.14247e12	−	1.14247e12i	0.00400817	−	0.00400817i
$779$			3.25996e14i			1.13639i
$780$	−3.97502e13	−	1.10551e14i	−0.137679	−	0.382904i
$781$	6.71107e12			0.0230960
$782$	1.23874e11	+	1.23874e11i	0.000423589	+	0.000423589i
$783$	−4.11138e14			−1.39694
$784$			1.29816e14i			0.438276i
$785$	1.53895e14	+	1.53895e14i	0.516270	+	0.516270i
$786$	1.19053e12	+	1.19053e12i	0.00396851	+	0.00396851i
$787$	−1.52597e14	+	1.52597e14i	−0.505443	+	0.505443i	−0.913124	−	0.407681i	$-0.866338\pi$
$787$	−1.52597e14	+	1.52597e14i	−0.505443	+	0.505443i	0.407681	+	0.913124i	$0.366338\pi$
$788$	1.17287e13	−	1.17287e13i	0.0386030	−	0.0386030i
$789$	−1.00156e14			−0.327560
$790$			2.63134e12i			0.00855147i
$791$	−1.22467e14	+	1.22467e14i	−0.395490	+	0.395490i
$792$		−	4.34063e12i		−	0.0139292i
$793$	−1.33325e13	+	2.83033e13i	−0.0425154	+	0.0902550i
$794$	−4.88163e12			−0.0154690
$795$	−6.87764e12	−	6.87764e12i	−0.0216573	−	0.0216573i
$796$	−3.04847e14			−0.953931
$797$			5.57495e13i			0.173360i	0.996236	+	0.0866801i	$0.0276258\pi$
$797$			5.57495e13i			0.173360i	−0.996236	+	0.0866801i	$0.972374\pi$
$798$	1.81781e12	+	1.81781e12i	0.00561739	+	0.00561739i
$799$	5.19654e12	+	5.19654e12i	0.0159581	+	0.0159581i
$800$	−2.47649e12	+	2.47649e12i	−0.00755766	+	0.00755766i
$801$	3.20541e14	−	3.20541e14i	0.972123	−	0.972123i
$802$	3.90681e12			0.0117747
$803$			9.06664e13i			0.271562i
$804$	4.98510e13	−	4.98510e13i	0.148386	−	0.148386i
$805$			3.93743e14i			1.16475i
$806$	−1.65306e10	−	7.78690e9i	−4.85975e−5	−	2.28923e-5i
$807$	1.28242e14			0.374683
$808$	3.56800e12	+	3.56800e12i	0.0103602	+	0.0103602i
$809$	−5.92421e14			−1.70957			−0.854787	−	0.518979i	$-0.826312\pi$
$809$	−5.92421e14			−1.70957			−0.854787	+	0.518979i	$0.826312\pi$
$810$			1.25410e12i			0.00359673i
$811$	2.58585e14	+	2.58585e14i	0.737054	+	0.737054i	0.972007	−	0.234953i	$-0.0754935\pi$
$811$	2.58585e14	+	2.58585e14i	0.737054	+	0.737054i	−0.234953	+	0.972007i	$0.575493\pi$
$812$	−4.89236e14	−	4.89236e14i	−1.38592	−	1.38592i
$813$	−3.22433e13	+	3.22433e13i	−0.0907792	+	0.0907792i
$814$	3.13396e12	−	3.13396e12i	0.00876944	−	0.00876944i
$815$	−2.00492e14			−0.557583
$816$			7.46862e12i			0.0206438i
$817$	4.85623e14	−	4.85623e14i	1.33410	−	1.33410i
$818$		−	1.76763e12i		−	0.00482642i
$819$	1.14498e14	+	3.18434e14i	0.310726	+	0.864171i
$820$	3.14585e14			0.848533
$821$	−1.86466e14	−	1.86466e14i	−0.499901	−	0.499901i	0.411506	−	0.911407i	$-0.365003\pi$
$821$	−1.86466e14	−	1.86466e14i	−0.499901	−	0.499901i	−0.911407	+	0.411506i	$0.865003\pi$
$822$	4.14099e12			0.0110343
$823$		−	3.50652e14i		−	0.928703i	−0.885651	−	0.464352i	$-0.846287\pi$
$823$		−	3.50652e14i		−	0.928703i	0.885651	−	0.464352i	$-0.153713\pi$
$824$	4.16615e12	+	4.16615e12i	0.0109673	+	0.0109673i
$825$	−2.87009e13	−	2.87009e13i	−0.0750975	−	0.0750975i
$826$	4.35767e12	−	4.35767e12i	0.0113332	−	0.0113332i
$827$	3.46239e12	−	3.46239e12i	0.00895052	−	0.00895052i	−0.702617	−	0.711568i	$-0.747985\pi$
$827$	3.46239e12	−	3.46239e12i	0.00895052	−	0.00895052i	0.711568	+	0.702617i	$0.247985\pi$
$828$	3.44163e14			0.884325
$829$			1.02856e14i			0.262699i	0.991336	+	0.131350i	$0.0419311\pi$
$829$			1.02856e14i			0.262699i	−0.991336	+	0.131350i	$0.958069\pi$
$830$	−3.68360e12	+	3.68360e12i	−0.00935151	+	0.00935151i
$831$			2.70789e14i			0.683322i
$832$	−3.60342e14	−	1.69742e14i	−0.903853	−	0.425768i
$833$	7.50326e12			0.0187079
$834$	−2.70815e12	−	2.70815e12i	−0.00671186	−	0.00671186i
$835$	4.94238e14			1.21760
$836$			3.43989e14i			0.842390i
$837$	1.09725e12	+	1.09725e12i	0.00267102	+	0.00267102i
$838$	−6.15829e12	−	6.15829e12i	−0.0149018	−	0.0149018i
$839$	−1.04253e14	+	1.04253e14i	−0.250773	+	0.250773i	−0.821287	−	0.570515i	$-0.806744\pi$
$839$	−1.04253e14	+	1.04253e14i	−0.250773	+	0.250773i	0.570515	+	0.821287i	$0.306744\pi$
$840$	3.50862e12	−	3.50862e12i	0.00838957	−	0.00838957i
$841$	7.03158e14			1.67137
$842$			2.98856e12i			0.00706158i
$843$	2.33414e14	−	2.33414e14i	0.548263	−	0.548263i
$844$		−	2.99541e14i		−	0.699430i
$845$	3.43775e13	−	3.60559e14i	0.0797979	−	0.836938i
$846$	−2.13336e12			−0.00492281
$847$	−1.62638e14	−	1.62638e14i	−0.373082	−	0.373082i
$848$	−3.29875e13			−0.0752264
$849$		−	1.24145e14i		−	0.281443i
$850$	4.77014e10	+	4.77014e10i	0.000107507	+	0.000107507i
$851$	4.97012e14	+	4.97012e14i	1.11357	+	1.11357i
$852$	4.74162e12	−	4.74162e12i	0.0105616	−	0.0105616i
$853$	4.16319e14	−	4.16319e14i	0.921894	−	0.921894i	−0.0752691	−	0.997163i	$-0.523982\pi$
$853$	4.16319e14	−	4.16319e14i	0.921894	−	0.921894i	0.997163	+	0.0752691i	$0.0239816\pi$
$854$	−6.60661e11			−0.00145442
$855$		−	3.31124e14i		−	0.724704i
$856$	−1.35323e13	+	1.35323e13i	−0.0294444	+	0.0294444i
$857$			3.41363e14i			0.738436i	0.929343	+	0.369218i	$0.120374\pi$
$857$			3.41363e14i			0.738436i	−0.929343	+	0.369218i	$0.879626\pi$
$858$	−8.72508e11	+	1.85223e12i	−0.00187643	+	0.00398343i
$859$	−6.78626e14			−1.45099			−0.725495	−	0.688228i	$-0.758389\pi$
$859$	−6.78626e14			−1.45099			−0.725495	+	0.688228i	$0.758389\pi$
$860$	−4.68624e14	−	4.68624e14i	−0.996168	−	0.996168i
$861$	2.77293e14			0.586034
$862$		−	3.65173e12i		−	0.00767294i
$863$	7.74065e12	+	7.74065e12i	0.0161705	+	0.0161705i	0.715146	−	0.698975i	$-0.246360\pi$
$863$	7.74065e12	+	7.74065e12i	0.0161705	+	0.0161705i	−0.698975	+	0.715146i	$0.746360\pi$
$864$	−1.06084e13	−	1.06084e13i	−0.0220335	−	0.0220335i
$865$	−3.86742e14	+	3.86742e14i	−0.798621	+	0.798621i
$866$	−3.04943e12	+	3.04943e12i	−0.00626078	+	0.00626078i
$867$	−2.36702e14			−0.483177
$868$			2.61135e12i			0.00529989i
$869$	−2.19454e14	+	2.19454e14i	−0.442837	+	0.442837i
$870$			4.02967e12i			0.00808488i
$871$	2.04533e14	−	7.35429e13i	0.408012	−	0.146707i
$872$	−7.35672e11			−0.00145916
$873$	−1.15115e14	−	1.15115e14i	−0.227018	−	0.227018i
$874$	8.06089e12			0.0158061
$875$			6.68812e14i			1.30396i
$876$	6.40591e13	+	6.40591e13i	0.124182	+	0.124182i
$877$	−6.01504e14	−	6.01504e14i	−1.15942	−	1.15942i	−0.984600	−	0.174820i	$-0.944066\pi$
$877$	−6.01504e14	−	6.01504e14i	−1.15942	−	1.15942i	−0.174820	−	0.984600i	$-0.555934\pi$
$878$	−5.54194e12	+	5.54194e12i	−0.0106216	+	0.0106216i
$879$	1.52476e14	−	1.52476e14i	0.290574	−	0.290574i
$880$	3.31899e14			0.628916
$881$			6.98125e14i			1.31539i	0.753285	+	0.657694i	$0.228468\pi$
$881$			6.98125e14i			1.31539i	−0.753285	+	0.657694i	$0.771532\pi$
$882$	−1.54017e12	+	1.54017e12i	−0.00288554	+	0.00288554i
$883$		−	2.43888e13i		−	0.0454346i	−0.999742	−	0.0227173i	$-0.992768\pi$
$883$		−	2.43888e13i		−	0.0454346i	0.999742	−	0.0227173i	$-0.00723177\pi$
$884$	−9.81386e12	+	2.08336e13i	−0.0181794	+	0.0385925i
$885$	2.42907e14			0.447429
$886$	2.42997e11	+	2.42997e11i	0.000445074	+	0.000445074i
$887$	4.32476e14			0.787670			0.393835	−	0.919181i	$-0.371148\pi$
$887$	4.32476e14			0.787670			0.393835	+	0.919181i	$0.371148\pi$
$888$		−	8.85769e12i		−	0.0160419i
$889$	8.88060e13	+	8.88060e13i	0.159931	+	0.159931i
$890$	−7.24483e12	−	7.24483e12i	−0.0129741	−	0.0129741i
$891$	−1.04592e14	+	1.04592e14i	−0.186256	+	0.186256i
$892$	−2.65304e14	+	2.65304e14i	−0.469807	+	0.469807i
$893$	3.38157e14			0.595472
$894$			5.92665e12i			0.0103782i
$895$	−1.59124e14	+	1.59124e14i	−0.277090	+	0.277090i
$896$		−	3.36620e13i		−	0.0582909i
$897$	−2.93743e14	−	1.38370e14i	−0.505831	−	0.238276i
$898$	2.01200e12			0.00344545
$899$	−2.99938e12	−	2.99938e12i	−0.00510779	−	0.00510779i
$900$	1.32531e14			0.224442
$901$			1.90665e12i			0.00321105i
$902$	−3.87677e12	−	3.87677e12i	−0.00649288	−	0.00649288i
$903$	−4.13072e14	−	4.13072e14i	−0.687997	−	0.687997i
$904$	4.83922e12	−	4.83922e12i	0.00801555	−	0.00801555i
$905$	−6.60493e14	+	6.60493e14i	−1.08799	+	1.08799i
$906$	−3.89624e12			−0.00638270
$907$			7.00119e13i			0.114061i	0.998372	+	0.0570303i	$0.0181632\pi$
$907$			7.00119e13i			0.114061i	−0.998372	+	0.0570303i	$0.981837\pi$
$908$	−3.20261e14	+	3.20261e14i	−0.518890	+	0.518890i
$909$		−	2.86422e14i		−	0.461516i
$910$	7.19721e12	−	2.58786e12i	0.0115334	−	0.00414700i
$911$	−8.17441e14			−1.30276			−0.651381	−	0.758751i	$-0.725810\pi$
$911$	−8.17441e14			−1.30276			−0.651381	+	0.758751i	$0.725810\pi$
$912$	2.43005e14	+	2.43005e14i	0.385160	+	0.385160i
$913$	−6.14425e14			−0.968534
$914$			9.57502e12i			0.0150110i
$915$	−1.84134e13	−	1.84134e13i	−0.0287098	−	0.0287098i
$916$	6.18276e14	+	6.18276e14i	0.958749	+	0.958749i
$917$	5.24538e14	−	5.24538e14i	0.808966	−	0.808966i
$918$	−2.04336e11	+	2.04336e11i	−0.000313424	+	0.000313424i
$919$	−4.47178e14			−0.682187			−0.341093	−	0.940029i	$-0.610797\pi$
$919$	−4.47178e14			−0.682187			−0.341093	+	0.940029i	$0.610797\pi$
$920$		−	1.55586e13i		−	0.0236065i
$921$	1.89568e14	−	1.89568e14i	0.286066	−	0.286066i
$922$			5.41005e12i			0.00811982i
$923$	1.94543e13	−	6.99509e12i	0.0290408	−	0.0104420i
$924$	2.92597e14			0.434421
$925$	1.91390e14	+	1.91390e14i	0.282625	+	0.282625i
$926$	1.23703e13			0.0181687
$927$		−	3.34438e14i		−	0.488559i
$928$	2.89987e13	+	2.89987e13i	0.0421345	+	0.0421345i
$929$	3.54645e14	+	3.54645e14i	0.512525	+	0.512525i	0.915299	−	0.402774i	$-0.131954\pi$
$929$	3.54645e14	+	3.54645e14i	0.512525	+	0.512525i	−0.402774	+	0.915299i	$0.631954\pi$
$930$	1.07544e10	−	1.07544e10i	1.54587e−5	−	1.54587e-5i
$931$	2.44132e14	−	2.44132e14i	0.349041	−	0.349041i
$932$	−7.67450e14			−1.09137
$933$		−	9.82174e13i		−	0.138925i
$934$	−7.44775e11	+	7.44775e11i	−0.00104783	+	0.00104783i
$935$		−	1.91835e13i		−	0.0268454i
$936$	−4.52433e12	−	1.25828e13i	−0.00629760	−	0.0175145i
$937$	5.17015e14			0.715822			0.357911	−	0.933756i	$-0.383489\pi$
$937$	5.17015e14			0.715822			0.357911	+	0.933756i	$0.383489\pi$
$938$	3.24545e12	+	3.24545e12i	0.00446952	+	0.00446952i
$939$	2.63577e13			0.0361061
$940$		−	3.26320e14i		−	0.444636i
$941$	−2.03237e14	−	2.03237e14i	−0.275458	−	0.275458i	0.555835	−	0.831293i	$-0.312399\pi$
$941$	−2.03237e14	−	2.03237e14i	−0.275458	−	0.275458i	−0.831293	+	0.555835i	$0.812399\pi$
$942$	−2.67992e12	−	2.67992e12i	−0.00361299	−	0.00361299i
$943$	6.14813e14	−	6.14813e14i	0.824488	−	0.824488i
$944$	5.82533e14	−	5.82533e14i	0.777071	−	0.777071i
$945$	−6.49500e14			−0.861827
$946$			1.15501e13i			0.0152451i
$947$	4.72926e14	−	4.72926e14i	0.620931	−	0.620931i	−0.324838	−	0.945770i	$-0.605310\pi$
$947$	4.72926e14	−	4.72926e14i	0.620931	−	0.620931i	0.945770	+	0.324838i	$0.105310\pi$
$948$			3.10104e14i			0.405010i
$949$	9.45035e13	+	2.62827e14i	0.122777	+	0.341460i
$950$	3.10410e12			0.00401160
$951$	3.50812e14	+	3.50812e14i	0.450995	+	0.450995i
$952$	−9.72676e11			−0.00124389
$953$			6.27042e14i			0.797687i	0.917019	+	0.398843i	$0.130588\pi$
$953$			6.27042e14i			0.797687i	−0.917019	+	0.398843i	$0.869412\pi$
$954$	−3.91374e11	−	3.91374e11i	−0.000495279	−	0.000495279i
$955$	5.35569e14	+	5.35569e14i	0.674215	+	0.674215i
$956$	3.29219e14	−	3.29219e14i	0.412283	−	0.412283i
$957$	−3.36075e14	+	3.36075e14i	−0.418675	+	0.418675i
$958$	5.92888e12			0.00734760
$959$		−	1.82449e15i		−	2.24930i
$960$	2.34429e14	−	2.34429e14i	0.287512	−	0.287512i
$961$		−	8.19612e14i		−	0.999980i
$962$	5.81827e12	−	1.23515e13i	0.00706185	−	0.0149914i
$963$	1.08631e15			1.31166
$964$	3.67399e14	+	3.67399e14i	0.441319	+	0.441319i
$965$	−1.83912e14			−0.219772
$966$		−	6.85660e12i		−	0.00815123i
$967$	−6.54396e14	−	6.54396e14i	−0.773941	−	0.773941i	0.204852	−	0.978793i	$-0.434329\pi$
$967$	−6.54396e14	−	6.54396e14i	−0.773941	−	0.773941i	−0.978793	+	0.204852i	$0.934329\pi$
$968$	6.42657e12	+	6.42657e12i	0.00756141	+	0.00756141i
$969$	1.40455e13	−	1.40455e13i	0.0164406	−	0.0164406i
$970$	−2.60181e12	+	2.60181e12i	−0.00302982	+	0.00302982i
$971$	2.41117e14			0.279339			0.139670	−	0.990198i	$-0.455396\pi$
$971$	2.41117e14			0.279339			0.139670	+	0.990198i	$0.455396\pi$
$972$			8.89241e14i			1.02492i
$973$	−1.19319e15	+	1.19319e15i	−1.36819	+	1.36819i
$974$		−	5.75595e12i		−	0.00656632i
$975$	−1.13115e14	−	5.32838e13i	−0.128380	−	0.0604745i
$976$	−8.83172e13			−0.0997232
$977$	5.09990e14	+	5.09990e14i	0.572913	+	0.572913i	0.932941	−	0.360028i	$-0.117233\pi$
$977$	5.09990e14	+	5.09990e14i	0.572913	+	0.572913i	−0.360028	+	0.932941i	$0.617233\pi$
$978$	3.49135e12			0.00390211
$979$		−	1.20844e15i		−	1.34373i
$980$	−2.35586e14	−	2.35586e14i	−0.260627	−	0.260627i
$981$	2.95281e13	+	2.95281e13i	0.0325005	+	0.0325005i
$982$	−7.16608e12	+	7.16608e12i	−0.00784737	+	0.00784737i
$983$	−4.13029e14	+	4.13029e14i	−0.450000	+	0.450000i	−0.895355	−	0.445354i	$-0.853078\pi$
$983$	−4.13029e14	+	4.13029e14i	−0.450000	+	0.450000i	0.445354	+	0.895355i	$0.353078\pi$
$984$	−1.09571e13			−0.0118774
$985$			4.25637e13i			0.0459048i
$986$	5.58563e11	−	5.58563e11i	0.000599359	−	0.000599359i
$987$		−	2.87637e14i		−	0.307085i
$988$	3.58547e14	+	9.97170e14i	0.380857	+	1.05922i
$989$	−1.83172e15			−1.93588
$990$	3.93775e12	+	3.93775e12i	0.00414068	+	0.00414068i
$991$	1.64407e14			0.172009			0.0860047	−	0.996295i	$-0.472590\pi$
$991$	1.64407e14			0.172009			0.0860047	+	0.996295i	$0.472590\pi$
$992$		−	1.54784e11i		−	0.000161127i
$993$	−6.11949e14	−	6.11949e14i	−0.633825	−	0.633825i
$994$	3.08694e11	+	3.08694e11i	0.000318124	+	0.000318124i
$995$	5.53146e14	−	5.53146e14i	0.567184	−	0.567184i
$996$	−4.34113e14	+	4.34113e14i	−0.442901	+	0.442901i
$997$	−1.13965e14			−0.115690			−0.0578449	−	0.998326i	$-0.518423\pi$
$997$	−1.13965e14			−0.115690			−0.0578449	+	0.998326i	$0.518423\pi$
$998$			1.22342e13i			0.0123573i
$999$	−8.19849e14	+	8.19849e14i	−0.823960	+	0.823960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.11.d.a.8.6	yes	20
13.5	odd	4	inner	13.11.d.a.5.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.11.d.a.5.6	✓	20	13.5	odd	4	inner
13.11.d.a.8.6	yes	20	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.275033 + 0.275033i) q^{2} -117.626 q^{3} -1023.85i q^{4} +(1857.78 + 1857.78i) q^{5} +(-32.3511 - 32.3511i) q^{6} +(-14253.6 + 14253.6i) q^{7} +(563.227 - 563.227i) q^{8} -45213.1 q^{9} +1021.90i q^{10} +(-85226.6 + 85226.6i) q^{11} +120431. i q^{12} +(-158225. + 335892. i) q^{13} -7840.45 q^{14} +(-218523. - 218523. i) q^{15} -1.04811e6 q^{16} +60580.0i q^{17} +(-12435.1 - 12435.1i) q^{18} +(1.97108e6 + 1.97108e6i) q^{19} +(1.90208e6 - 1.90208e6i) q^{20} +(1.67660e6 - 1.67660e6i) q^{21} -46880.3 q^{22} -7.43471e6i q^{23} +(-66250.2 + 66250.2i) q^{24} -2.86297e6i q^{25} +(-135899. + 48864.4i) q^{26} +1.22639e7 q^{27} +(1.45936e7 + 1.45936e7i) q^{28} -3.35241e7 q^{29} -120202. i q^{30} +(89469.4 + 89469.4i) q^{31} +(-865010. - 865010. i) q^{32} +(1.00249e7 - 1.00249e7i) q^{33} +(-16661.5 + 16661.5i) q^{34} -5.29601e7 q^{35} +4.62914e7i q^{36} +(-6.68503e7 + 6.68503e7i) q^{37} +1.08422e6i q^{38} +(1.86114e7 - 3.95097e7i) q^{39} +2.09270e6 q^{40} +(8.26950e7 + 8.26950e7i) q^{41} +922242. q^{42} -2.46375e8i q^{43} +(8.72591e7 + 8.72591e7i) q^{44} +(-8.39958e7 - 8.39958e7i) q^{45} +(2.04479e6 - 2.04479e6i) q^{46} +(8.57798e7 - 8.57798e7i) q^{47} +1.23285e8 q^{48} -1.23857e8i q^{49} +(787411. - 787411. i) q^{50} -7.12579e6i q^{51} +(3.43902e8 + 1.61998e8i) q^{52} +3.14733e7 q^{53} +(3.37300e6 + 3.37300e6i) q^{54} -3.16664e8 q^{55} +1.60561e7i q^{56} +(-2.31850e8 - 2.31850e8i) q^{57} +(-9.22025e6 - 9.22025e6i) q^{58} +(-5.55793e8 + 5.55793e8i) q^{59} +(-2.23734e8 + 2.23734e8i) q^{60} +8.42632e7 q^{61} +49214.1i q^{62} +(6.44451e8 - 6.44451e8i) q^{63} +1.07279e9i q^{64} +(-9.17958e8 + 3.30065e8i) q^{65} +5.51435e6 q^{66} +(-4.13937e8 - 4.13937e8i) q^{67} +6.20248e7 q^{68} +8.74516e8i q^{69} +(-1.45658e7 - 1.45658e7i) q^{70} +(-3.93719e7 - 3.93719e7i) q^{71} +(-2.54652e7 + 2.54652e7i) q^{72} +(5.31914e8 - 5.31914e8i) q^{73} -3.67721e7 q^{74} +3.36760e8i q^{75} +(2.01809e9 - 2.01809e9i) q^{76} -2.42958e9i q^{77} +(1.59852e7 - 5.74773e6i) q^{78} +2.57494e9 q^{79} +(-1.94716e9 - 1.94716e9i) q^{80} +1.22723e9 q^{81} +4.54878e7i q^{82} +(3.60465e9 + 3.60465e9i) q^{83} +(-1.71659e9 - 1.71659e9i) q^{84} +(-1.12544e8 + 1.12544e8i) q^{85} +(6.77612e7 - 6.77612e7i) q^{86} +3.94331e9 q^{87} +9.60038e7i q^{88} +(-7.08957e9 + 7.08957e9i) q^{89} -4.62033e7i q^{90} +(-2.53240e9 - 7.04296e9i) q^{91} -7.61201e9 q^{92} +(-1.05239e7 - 1.05239e7i) q^{93} +4.71846e7 q^{94} +7.32364e9i q^{95} +(1.01748e8 + 1.01748e8i) q^{96} +(2.54605e9 + 2.54605e9i) q^{97} +(3.40648e7 - 3.40648e7i) q^{98} +(3.85336e9 - 3.85336e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 34 q^{2} - 4 q^{3} - 7792 q^{5} - 19264 q^{6} - 38312 q^{7} - 1200 q^{8} + 236192 q^{9} + 331856 q^{11} - 445380 q^{13} + 2007244 q^{14} + 379412 q^{15} - 1736492 q^{16} - 5990914 q^{18} - 2277428 q^{19}+ \cdots + 64175005436 q^{99}+O(q^{100}) \) 20 * q - 34 * q^2 - 4 * q^3 - 7792 * q^5 - 19264 * q^6 - 38312 * q^7 - 1200 * q^8 + 236192 * q^9 + 331856 * q^11 - 445380 * q^13 + 2007244 * q^14 + 379412 * q^15 - 1736492 * q^16 - 5990914 * q^18 - 2277428 * q^19 + 3611836 * q^20 - 9480856 * q^21 + 5001216 * q^22 + 41307672 * q^24 + 6769646 * q^26 - 4427116 * q^27 - 113669380 * q^28 + 37095424 * q^29 + 17376308 * q^31 - 1963204 * q^32 - 118752028 * q^33 - 32678040 * q^34 + 283757932 * q^35 + 138434576 * q^37 - 180959428 * q^39 - 8799876 * q^40 - 431088064 * q^41 + 1089534556 * q^42 + 102766076 * q^44 - 551620384 * q^45 - 682329276 * q^46 - 316356304 * q^47 - 332833468 * q^48 + 653613022 * q^50 - 1360524100 * q^52 + 882722032 * q^53 + 206912984 * q^54 - 1205505576 * q^55 + 2161977296 * q^57 + 450412980 * q^58 + 1130230868 * q^59 + 4118247964 * q^60 - 1735259352 * q^61 - 3186516460 * q^63 + 2833033736 * q^65 + 1165082704 * q^66 - 626922128 * q^67 - 11230951788 * q^68 - 3144181512 * q^70 - 196931776 * q^71 + 614552052 * q^72 + 5765831656 * q^73 + 10475267944 * q^74 - 5350301912 * q^76 + 8069244872 * q^78 + 1110987384 * q^79 + 870087872 * q^80 - 21624920380 * q^81 + 13391403584 * q^83 - 25726991224 * q^84 + 1992219096 * q^85 + 32878542048 * q^86 + 194656048 * q^87 + 5940615128 * q^89 + 670762144 * q^91 - 12619717320 * q^92 - 27707434216 * q^93 - 31866209148 * q^94 + 34182859808 * q^96 - 14392811236 * q^97 - 58567835410 * q^98 + 64175005436 * q^99

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