LMFDB - Embedded newform 13.11.d.a.8.1

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			8.1
Root			$-37.3633 + 37.3633i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.11.d.a.5.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-39.3633 - 39.3633i) q^{2} +361.049 q^{3} +2074.94i q^{4} +(-2244.35 - 2244.35i) q^{5} +(-14212.1 - 14212.1i) q^{6} +(-23343.5 + 23343.5i) q^{7} +(41368.4 - 41368.4i) q^{8} +71307.4 q^{9} +176690. i q^{10} +(-27522.6 + 27522.6i) q^{11} +749154. i q^{12} +(-365595. + 64798.4i) q^{13} +1.83775e6 q^{14} +(-810320. - 810320. i) q^{15} -1.13205e6 q^{16} +740598. i q^{17} +(-2.80689e6 - 2.80689e6i) q^{18} +(988674. + 988674. i) q^{19} +(4.65689e6 - 4.65689e6i) q^{20} +(-8.42815e6 + 8.42815e6i) q^{21} +2.16676e6 q^{22} -202139. i q^{23} +(1.49360e7 - 1.49360e7i) q^{24} +308590. i q^{25} +(1.69417e7 + 1.18403e7i) q^{26} +4.42588e6 q^{27} +(-4.84363e7 - 4.84363e7i) q^{28} -1.63488e7 q^{29} +6.37938e7i q^{30} +(-7.27830e6 - 7.27830e6i) q^{31} +(2.20017e6 + 2.20017e6i) q^{32} +(-9.93701e6 + 9.93701e6i) q^{33} +(2.91524e7 - 2.91524e7i) q^{34} +1.04782e8 q^{35} +1.47958e8i q^{36} +(-5.12833e6 + 5.12833e6i) q^{37} -7.78349e7i q^{38} +(-1.31998e8 + 2.33954e7i) q^{39} -1.85690e8 q^{40} +(-7.57766e7 - 7.57766e7i) q^{41} +6.63519e8 q^{42} +2.09402e8i q^{43} +(-5.71077e7 - 5.71077e7i) q^{44} +(-1.60039e8 - 1.60039e8i) q^{45} +(-7.95685e6 + 7.95685e6i) q^{46} +(-9.07574e7 + 9.07574e7i) q^{47} -4.08727e8 q^{48} -8.07363e8i q^{49} +(1.21471e7 - 1.21471e7i) q^{50} +2.67392e8i q^{51} +(-1.34453e8 - 7.58587e8i) q^{52} +1.61443e8 q^{53} +(-1.74217e8 - 1.74217e8i) q^{54} +1.23541e8 q^{55} +1.93137e9i q^{56} +(3.56960e8 + 3.56960e8i) q^{57} +(6.43542e8 + 6.43542e8i) q^{58} +(3.49915e8 - 3.49915e8i) q^{59} +(1.68136e9 - 1.68136e9i) q^{60} -1.34441e9 q^{61} +5.72996e8i q^{62} +(-1.66456e9 + 1.66456e9i) q^{63} +9.86011e8i q^{64} +(9.65953e8 + 6.75093e8i) q^{65} +7.82307e8 q^{66} +(-6.85456e8 - 6.85456e8i) q^{67} -1.53669e9 q^{68} -7.29821e7i q^{69} +(-4.12456e9 - 4.12456e9i) q^{70} +(4.57383e8 + 4.57383e8i) q^{71} +(2.94987e9 - 2.94987e9i) q^{72} +(6.61963e8 - 6.61963e8i) q^{73} +4.03736e8 q^{74} +1.11416e8i q^{75} +(-2.05144e9 + 2.05144e9i) q^{76} -1.28495e9i q^{77} +(6.11678e9 + 4.27494e9i) q^{78} +1.70621e9 q^{79} +(2.54073e9 + 2.54073e9i) q^{80} -2.61267e9 q^{81} +5.96564e9i q^{82} +(4.64465e9 + 4.64465e9i) q^{83} +(-1.74879e10 - 1.74879e10i) q^{84} +(1.66216e9 - 1.66216e9i) q^{85} +(8.24276e9 - 8.24276e9i) q^{86} -5.90271e9 q^{87} +2.27713e9i q^{88} +(-3.09504e9 + 3.09504e9i) q^{89} +1.25993e10i q^{90} +(7.02165e9 - 1.00469e10i) q^{91} +4.19426e8 q^{92} +(-2.62782e9 - 2.62782e9i) q^{93} +7.14502e9 q^{94} -4.43786e9i q^{95} +(7.94370e8 + 7.94370e8i) q^{96} +(1.01614e10 + 1.01614e10i) q^{97} +(-3.17805e10 + 3.17805e10i) q^{98} +(-1.96256e9 + 1.96256e9i) 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 $

$2$	−39.3633	−	39.3633i	−1.23010	−	1.23010i	−0.963924	−	0.266179i	$-0.914239\pi$
$2$	−39.3633	−	39.3633i	−1.23010	−	1.23010i	−0.266179	−	0.963924i	$-0.585761\pi$
$3$	361.049			1.48580			0.742899	−	0.669403i	$-0.233450\pi$
$3$	361.049			1.48580			0.742899	+	0.669403i	$0.233450\pi$
$4$			2074.94i			2.02631i
$5$	−2244.35	−	2244.35i	−0.718192	−	0.718192i	0.250043	−	0.968235i	$-0.419555\pi$
$5$	−2244.35	−	2244.35i	−0.718192	−	0.718192i	−0.968235	+	0.250043i	$0.919555\pi$
$6$	−14212.1	−	14212.1i	−1.82768	−	1.82768i
$7$	−23343.5	+	23343.5i	−1.38892	+	1.38892i	−0.561310	+	0.827605i	$0.689703\pi$
$7$	−23343.5	+	23343.5i	−1.38892	+	1.38892i	−0.827605	+	0.561310i	$0.810297\pi$
$8$	41368.4	−	41368.4i	1.26246	−	1.26246i
$9$	71307.4			1.20760
$10$			176690.i			1.76690i
$11$	−27522.6	+	27522.6i	−0.170894	+	0.170894i	−0.787372	−	0.616478i	$-0.788559\pi$
$11$	−27522.6	+	27522.6i	−0.170894	+	0.170894i	0.616478	+	0.787372i	$0.288559\pi$
$12$			749154.i			3.01068i
$13$	−365595.	+	64798.4i	−0.984653	+	0.174521i
$13$	−365595.	+	64798.4i	−0.984653	+	0.174521i
$14$	1.83775e6			3.41702
$15$	−810320.	−	810320.i	−1.06709	−	1.06709i
$16$	−1.13205e6			−1.07961
$17$			740598.i			0.521600i	0.965393	+	0.260800i	$0.0839863\pi$
$17$			740598.i			0.521600i	−0.965393	+	0.260800i	$0.916014\pi$
$18$	−2.80689e6	−	2.80689e6i	−1.48547	−	1.48547i
$19$	988674.	+	988674.i	0.399287	+	0.399287i	0.877981	−	0.478695i	$-0.158890\pi$
$19$	988674.	+	988674.i	0.399287	+	0.399287i	−0.478695	+	0.877981i	$0.658890\pi$
$20$	4.65689e6	−	4.65689e6i	1.45528	−	1.45528i
$21$	−8.42815e6	+	8.42815e6i	−2.06365	+	2.06365i
$22$	2.16676e6			0.420434
$23$		−	202139.i		−	0.0314059i	−0.999877	−	0.0157029i	$-0.995001\pi$
$23$		−	202139.i		−	0.0314059i	0.999877	−	0.0157029i	$-0.00499860\pi$
$24$	1.49360e7	−	1.49360e7i	1.87576	−	1.87576i
$25$			308590.i			0.0315996i
$26$	1.69417e7	+	1.18403e7i	1.42590	+	0.996546i
$27$	4.42588e6			0.308447
$28$	−4.84363e7	−	4.84363e7i	−2.81437	−	2.81437i
$29$	−1.63488e7			−0.797068			−0.398534	−	0.917154i	$-0.630481\pi$
$29$	−1.63488e7			−0.797068			−0.398534	+	0.917154i	$0.630481\pi$
$30$			6.37938e7i			2.62526i
$31$	−7.27830e6	−	7.27830e6i	−0.254227	−	0.254227i	0.568474	−	0.822701i	$-0.307534\pi$
$31$	−7.27830e6	−	7.27830e6i	−0.254227	−	0.254227i	−0.822701	+	0.568474i	$0.807534\pi$
$32$	2.20017e6	+	2.20017e6i	0.0655702	+	0.0655702i
$33$	−9.93701e6	+	9.93701e6i	−0.253914	+	0.253914i
$34$	2.91524e7	−	2.91524e7i	0.641622	−	0.641622i
$35$	1.04782e8			1.99502
$36$			1.47958e8i			2.44696i
$37$	−5.12833e6	+	5.12833e6i	−0.0739550	+	0.0739550i	−0.743117	−	0.669162i	$-0.766653\pi$
$37$	−5.12833e6	+	5.12833e6i	−0.0739550	+	0.0739550i	0.669162	+	0.743117i	$0.266653\pi$
$38$		−	7.78349e7i		−	0.982328i
$39$	−1.31998e8	+	2.33954e7i	−1.46300	+	0.259303i
$40$	−1.85690e8			−1.81338
$41$	−7.57766e7	−	7.57766e7i	−0.654058	−	0.654058i	0.299910	−	0.953968i	$-0.403043\pi$
$41$	−7.57766e7	−	7.57766e7i	−0.654058	−	0.654058i	−0.953968	+	0.299910i	$0.903043\pi$
$42$	6.63519e8			5.07700
$43$			2.09402e8i			1.42442i	0.701965	+	0.712212i	$0.252306\pi$
$43$			2.09402e8i			1.42442i	−0.701965	+	0.712212i	$0.747694\pi$
$44$	−5.71077e7	−	5.71077e7i	−0.346283	−	0.346283i
$45$	−1.60039e8	−	1.60039e8i	−0.867286	−	0.867286i
$46$	−7.95685e6	+	7.95685e6i	−0.0386325	+	0.0386325i
$47$	−9.07574e7	+	9.07574e7i	−0.395724	+	0.395724i	−0.876722	−	0.480998i	$-0.840275\pi$
$47$	−9.07574e7	+	9.07574e7i	−0.395724	+	0.395724i	0.480998	+	0.876722i	$0.340275\pi$
$48$	−4.08727e8			−1.60408
$49$		−	8.07363e8i		−	2.85817i
$50$	1.21471e7	−	1.21471e7i	0.0388707	−	0.0388707i
$51$			2.67392e8i			0.774993i
$52$	−1.34453e8	−	7.58587e8i	−0.353633	−	1.99521i
$53$	1.61443e8			0.386047			0.193023	−	0.981194i	$-0.438171\pi$
$53$	1.61443e8			0.386047			0.193023	+	0.981194i	$0.438171\pi$
$54$	−1.74217e8	−	1.74217e8i	−0.379422	−	0.379422i
$55$	1.23541e8			0.245469
$56$			1.93137e9i			3.50691i
$57$	3.56960e8	+	3.56960e8i	0.593260	+	0.593260i
$58$	6.43542e8	+	6.43542e8i	0.980476	+	0.980476i
$59$	3.49915e8	−	3.49915e8i	0.489443	−	0.489443i	−0.418687	−	0.908131i	$-0.637510\pi$
$59$	3.49915e8	−	3.49915e8i	0.489443	−	0.489443i	0.908131	+	0.418687i	$0.137510\pi$
$60$	1.68136e9	−	1.68136e9i	2.16225	−	2.16225i
$61$	−1.34441e9			−1.59178			−0.795891	−	0.605440i	$-0.792997\pi$
$61$	−1.34441e9			−1.59178			−0.795891	+	0.605440i	$0.792997\pi$
$62$			5.72996e8i			0.625450i
$63$	−1.66456e9	+	1.66456e9i	−1.67725	+	1.67725i
$64$			9.86011e8i			0.918295i
$65$	9.65953e8	+	6.75093e8i	0.832510	+	0.581831i
$66$	7.82307e8			0.624680
$67$	−6.85456e8	−	6.85456e8i	−0.507698	−	0.507698i	0.406121	−	0.913819i	$-0.366881\pi$
$67$	−6.85456e8	−	6.85456e8i	−0.507698	−	0.507698i	−0.913819	+	0.406121i	$0.866881\pi$
$68$	−1.53669e9			−1.05692
$69$		−	7.29821e7i		−	0.0466628i
$70$	−4.12456e9	−	4.12456e9i	−2.45408	−	2.45408i
$71$	4.57383e8	+	4.57383e8i	0.253506	+	0.253506i	0.822406	−	0.568901i	$-0.192631\pi$
$71$	4.57383e8	+	4.57383e8i	0.253506	+	0.253506i	−0.568901	+	0.822406i	$0.692631\pi$
$72$	2.94987e9	−	2.94987e9i	1.52455	−	1.52455i
$73$	6.61963e8	−	6.61963e8i	0.319315	−	0.319315i	−0.529189	−	0.848504i	$-0.677504\pi$
$73$	6.61963e8	−	6.61963e8i	0.319315	−	0.319315i	0.848504	+	0.529189i	$0.177504\pi$
$74$	4.03736e8			0.181945
$75$			1.11416e8i			0.0469506i
$76$	−2.05144e9	+	2.05144e9i	−0.809077	+	0.809077i
$77$		−	1.28495e9i		−	0.474714i
$78$	6.11678e9	+	4.27494e9i	2.11861	+	1.48067i
$79$	1.70621e9			0.554495			0.277248	−	0.960798i	$-0.410578\pi$
$79$	1.70621e9			0.554495			0.277248	+	0.960798i	$0.410578\pi$
$80$	2.54073e9	+	2.54073e9i	0.775368	+	0.775368i
$81$	−2.61267e9			−0.749307
$82$			5.96564e9i			1.60912i
$83$	4.64465e9	+	4.64465e9i	1.17913	+	1.17913i	0.979966	+	0.199167i	$0.0638236\pi$
$83$	4.64465e9	+	4.64465e9i	1.17913	+	1.17913i	0.199167	+	0.979966i	$0.436176\pi$
$84$	−1.74879e10	−	1.74879e10i	−4.18158	−	4.18158i
$85$	1.66216e9	−	1.66216e9i	0.374609	−	0.374609i
$86$	8.24276e9	−	8.24276e9i	1.75219	−	1.75219i
$87$	−5.90271e9			−1.18428
$88$			2.27713e9i			0.431494i
$89$	−3.09504e9	+	3.09504e9i	−0.554264	+	0.554264i	−0.927669	−	0.373405i	$-0.878190\pi$
$89$	−3.09504e9	+	3.09504e9i	−0.554264	+	0.554264i	0.373405	+	0.927669i	$0.378190\pi$
$90$			1.25993e10i			2.13370i
$91$	7.02165e9	−	1.00469e10i	1.12521	−	1.61000i
$92$	4.19426e8			0.0636379
$93$	−2.62782e9	−	2.62782e9i	−0.377730	−	0.377730i
$94$	7.14502e9			0.973563
$95$		−	4.43786e9i		−	0.573529i
$96$	7.94370e8	+	7.94370e8i	0.0974241	+	0.0974241i
$97$	1.01614e10	+	1.01614e10i	1.18330	+	1.18330i	0.978885	+	0.204412i	$0.0655284\pi$
$97$	1.01614e10	+	1.01614e10i	1.18330	+	1.18330i	0.204412	+	0.978885i	$0.434472\pi$
$98$	−3.17805e10	+	3.17805e10i	−3.51585	+	3.51585i
$99$	−1.96256e9	+	1.96256e9i	−0.206371	+	0.206371i
$100$	−6.40304e8			−0.0640304
$101$		−	1.30639e10i		−	1.24298i	−0.783422	−	0.621491i	$-0.786527\pi$
$101$		−	1.30639e10i		−	1.24298i	0.783422	−	0.621491i	$-0.213473\pi$
$102$	1.05254e10	−	1.05254e10i	0.953321	−	0.953321i
$103$		−	1.30384e9i		−	0.112471i	−0.998418	−	0.0562353i	$-0.982090\pi$
$103$		−	1.30384e9i		−	0.112471i	0.998418	−	0.0562353i	$-0.0179097\pi$
$104$	−1.24435e10	+	1.78047e10i	−1.02276	+	1.46341i
$105$	3.78314e10			2.96419
$106$	−6.35493e9	−	6.35493e9i	−0.474877	−	0.474877i
$107$	1.57084e10			1.11999			0.559993	−	0.828497i	$-0.310804\pi$
$107$	1.57084e10			1.11999			0.559993	+	0.828497i	$0.310804\pi$
$108$			9.18342e9i			0.625008i
$109$	9.67212e8	+	9.67212e8i	0.0628621	+	0.0628621i	0.737839	−	0.674977i	$-0.235846\pi$
$109$	9.67212e8	+	9.67212e8i	0.0628621	+	0.0628621i	−0.674977	+	0.737839i	$0.735846\pi$
$110$	−4.86297e9	−	4.86297e9i	−0.301952	−	0.301952i
$111$	−1.85158e9	+	1.85158e9i	−0.109882	+	0.109882i
$112$	2.64261e10	−	2.64261e10i	1.49949	−	1.49949i
$113$	−2.31950e10			−1.25893			−0.629465	−	0.777029i	$-0.716726\pi$
$113$	−2.31950e10			−1.25893			−0.629465	+	0.777029i	$0.716726\pi$
$114$		−	2.81022e10i		−	1.45954i
$115$	−4.53671e8	+	4.53671e8i	−0.0225554	+	0.0225554i
$116$		−	3.39227e10i		−	1.61510i
$117$	−2.60696e10	+	4.62061e9i	−1.18906	+	0.210751i
$118$	−2.75476e10			−1.20413
$119$	−1.72881e10	−	1.72881e10i	−0.724459	−	0.724459i
$120$	−6.70433e10			−2.69432
$121$			2.44224e10i			0.941591i
$122$	5.29205e10	+	5.29205e10i	1.95806	+	1.95806i
$123$	−2.73591e10	−	2.73591e10i	−0.971798	−	0.971798i
$124$	1.51020e10	−	1.51020e10i	0.515142	−	0.515142i
$125$	−2.12249e10	+	2.12249e10i	−0.695497	+	0.695497i
$126$	1.31045e11			4.12638
$127$			2.93321e10i			0.887818i	0.896072	+	0.443909i	$0.146409\pi$
$127$			2.93321e10i			0.887818i	−0.896072	+	0.443909i	$0.853591\pi$
$128$	4.10656e10	−	4.10656e10i	1.19517	−	1.19517i
$129$			7.56045e10i			2.11641i
$130$	−1.14492e10	−	6.45970e10i	−0.308361	−	1.73978i
$131$	−7.96070e8			−0.0206345			−0.0103173	−	0.999947i	$-0.503284\pi$
$131$	−7.96070e8			−0.0206345			−0.0103173	+	0.999947i	$0.503284\pi$
$132$	−2.06187e10	−	2.06187e10i	−0.514507	−	0.514507i
$133$	−4.61582e10			−1.10915
$134$			5.39636e10i			1.24904i
$135$	−9.93322e9	−	9.93322e9i	−0.221524	−	0.221524i
$136$	3.06373e10	+	3.06373e10i	0.658501	+	0.658501i
$137$	5.17587e10	−	5.17587e10i	1.07246	−	1.07246i	0.0752973	−	0.997161i	$-0.476009\pi$
$137$	5.17587e10	−	5.17587e10i	1.07246	−	1.07246i	0.997161	−	0.0752973i	$-0.0239906\pi$
$138$	−2.87281e9	+	2.87281e9i	−0.0574000	+	0.0574000i
$139$	−1.29480e10			−0.249532			−0.124766	−	0.992186i	$-0.539818\pi$
$139$	−1.29480e10			−0.249532			−0.124766	+	0.992186i	$0.539818\pi$
$140$			2.17416e11i			4.04251i
$141$	−3.27679e10	+	3.27679e10i	−0.587966	+	0.587966i
$142$		−	3.60082e10i		−	0.623676i
$143$	8.27870e9	−	1.18455e10i	0.138447	−	0.198096i
$144$	−8.07238e10			−1.30373
$145$	3.66924e10	+	3.66924e10i	0.572448	+	0.572448i
$146$	−5.21141e10			−0.785581
$147$		−	2.91498e11i		−	4.24667i
$148$	−1.06410e10	−	1.06410e10i	−0.149856	−	0.149856i
$149$	6.10112e10	+	6.10112e10i	0.830765	+	0.830765i	0.987621	−	0.156857i	$-0.0501360\pi$
$149$	6.10112e10	+	6.10112e10i	0.830765	+	0.830765i	−0.156857	+	0.987621i	$0.550136\pi$
$150$	4.38570e9	−	4.38570e9i	0.0577541	−	0.0577541i
$151$	−6.89662e9	+	6.89662e9i	−0.0878520	+	0.0878520i	−0.749667	−	0.661815i	$-0.769786\pi$
$151$	−6.89662e9	+	6.89662e9i	−0.0878520	+	0.0878520i	0.661815	+	0.749667i	$0.269786\pi$
$152$	8.17996e10			1.00817
$153$			5.28101e10i			0.629883i
$154$	−5.05798e10	+	5.05798e10i	−0.583947	+	0.583947i
$155$			3.26701e10i			0.365167i
$156$	−4.85440e10	−	2.73887e11i	−0.525427	−	2.96448i
$157$	−1.03122e11			−1.08107			−0.540536	−	0.841321i	$-0.681778\pi$
$157$	−1.03122e11			−1.08107			−0.540536	+	0.841321i	$0.681778\pi$
$158$	−6.71622e10	−	6.71622e10i	−0.682086	−	0.682086i
$159$	5.82888e10			0.573587
$160$		−	9.87591e9i		−	0.0941840i
$161$	4.71863e9	+	4.71863e9i	0.0436201	+	0.0436201i
$162$	1.02843e11	+	1.02843e11i	0.921724	+	0.921724i
$163$	−6.77250e10	+	6.77250e10i	−0.588588	+	0.588588i	−0.937249	−	0.348661i	$-0.886636\pi$
$163$	−6.77250e10	+	6.77250e10i	−0.588588	+	0.588588i	0.348661	+	0.937249i	$0.386636\pi$
$164$	1.57232e11	−	1.57232e11i	1.32532	−	1.32532i
$165$	4.46042e10			0.364717
$166$		−	3.65657e11i		−	2.90091i
$167$	5.28048e10	−	5.28048e10i	0.406529	−	0.406529i	−0.473997	−	0.880526i	$-0.657189\pi$
$167$	5.28048e10	−	5.28048e10i	0.406529	−	0.406529i	0.880526	+	0.473997i	$0.157189\pi$
$168$			6.97318e11i			5.21056i
$169$	1.29461e11	−	4.73800e10i	0.939085	−	0.343685i
$170$	−1.30856e11			−0.921615
$171$	7.04997e10	+	7.04997e10i	0.482178	+	0.482178i
$172$	−4.34497e11			−2.88632
$173$			2.87473e10i			0.185510i	0.995689	+	0.0927548i	$0.0295673\pi$
$173$			2.87473e10i			0.185510i	−0.995689	+	0.0927548i	$0.970433\pi$
$174$	2.32350e11	+	2.32350e11i	1.45679	+	1.45679i
$175$	−7.20356e9	−	7.20356e9i	−0.0438892	−	0.0438892i
$176$	3.11571e10	−	3.11571e10i	0.184499	−	0.184499i
$177$	1.26336e11	−	1.26336e11i	0.727214	−	0.727214i
$178$	2.43662e11			1.36360
$179$			1.88955e10i			0.102824i	0.998678	+	0.0514120i	$0.0163722\pi$
$179$			1.88955e10i			0.102824i	−0.998678	+	0.0514120i	$0.983628\pi$
$180$	3.32070e11	−	3.32070e11i	1.75739	−	1.75739i
$181$		−	1.53199e11i		−	0.788611i	−0.918979	−	0.394305i	$-0.870985\pi$
$181$		−	1.53199e11i		−	0.788611i	0.918979	−	0.394305i	$-0.129015\pi$
$182$	−6.71874e11	+	1.19084e11i	−3.36458	+	0.596342i
$183$	−4.85399e11			−2.36507
$184$	−8.36216e9	−	8.36216e9i	−0.0396487	−	0.0396487i
$185$	2.30196e10			0.106228
$186$			2.06880e11i			0.929293i
$187$	−2.03832e10	−	2.03832e10i	−0.0891382	−	0.0891382i
$188$	−1.88316e11	−	1.88316e11i	−0.801859	−	0.801859i
$189$	−1.03316e11	+	1.03316e11i	−0.428407	+	0.428407i
$190$	−1.74689e11	+	1.74689e11i	−0.705500	+	0.705500i
$191$	8.66906e10			0.341040			0.170520	−	0.985354i	$-0.445455\pi$
$191$	8.66906e10			0.341040			0.170520	+	0.985354i	$0.445455\pi$
$192$			3.55998e11i			1.36440i
$193$	−2.19963e11	+	2.19963e11i	−0.821417	+	0.821417i	−0.986311	−	0.164894i	$-0.947272\pi$
$193$	−2.19963e11	+	2.19963e11i	−0.821417	+	0.821417i	0.164894	+	0.986311i	$0.447272\pi$
$194$		−	7.99970e11i		−	2.91115i
$195$	3.48757e11	+	2.43742e11i	1.23694	+	0.864483i
$196$	1.67523e12			5.79154
$197$	2.02435e11	+	2.02435e11i	0.682267	+	0.682267i	0.960511	−	0.278244i	$-0.0897523\pi$
$197$	2.02435e11	+	2.02435e11i	0.682267	+	0.682267i	−0.278244	+	0.960511i	$0.589752\pi$
$198$	1.54506e11			0.507714
$199$			2.44019e11i			0.781912i	0.920409	+	0.390956i	$0.127856\pi$
$199$			2.44019e11i			0.781912i	−0.920409	+	0.390956i	$0.872144\pi$
$200$	1.27658e10	+	1.27658e10i	0.0398933	+	0.0398933i
$201$	−2.47483e11	−	2.47483e11i	−0.754337	−	0.754337i
$202$	−5.14236e11	+	5.14236e11i	−1.52899	+	1.52899i
$203$	3.81638e11	−	3.81638e11i	1.10706	−	1.10706i
$204$	−5.54822e11			−1.57037
$205$			3.40139e11i			0.939478i
$206$	−5.13235e10	+	5.13235e10i	−0.138350	+	0.138350i
$207$		−	1.44140e10i		−	0.0379256i
$208$	4.13873e11	−	7.33553e10i	1.06304	−	0.188415i
$209$	−5.44217e10			−0.136471
$210$	−1.48917e12	−	1.48917e12i	−3.64626	−	3.64626i
$211$	−2.20706e11			−0.527719			−0.263860	−	0.964561i	$-0.584996\pi$
$211$	−2.20706e11			−0.527719			−0.263860	+	0.964561i	$0.584996\pi$
$212$			3.34984e11i			0.782249i
$213$	1.65138e11	+	1.65138e11i	0.376659	+	0.376659i
$214$	−6.18334e11	−	6.18334e11i	−1.37770	−	1.37770i
$215$	4.69972e11	−	4.69972e11i	1.02301	−	1.02301i
$216$	1.83091e11	−	1.83091e11i	0.389403	−	0.389403i
$217$	3.39802e11			0.706199
$218$		−	7.61453e10i		−	0.154654i
$219$	2.39001e11	−	2.39001e11i	0.474438	−	0.474438i
$220$			2.56339e11i			0.497395i
$221$	−4.79896e10	−	2.70759e11i	−0.0910302	−	0.513595i
$222$	1.45769e11			0.270333
$223$	1.89560e11	+	1.89560e11i	0.343733	+	0.343733i	0.857769	−	0.514036i	$-0.171850\pi$
$223$	1.89560e11	+	1.89560e11i	0.343733	+	0.343733i	−0.514036	+	0.857769i	$0.671850\pi$
$224$	−1.02719e11			−0.182143
$225$			2.20047e10i			0.0381596i
$226$	9.13031e11	+	9.13031e11i	1.54861	+	1.54861i
$227$	−7.08590e11	−	7.08590e11i	−1.17562	−	1.17562i	−0.980850	−	0.194766i	$-0.937605\pi$
$227$	−7.08590e11	−	7.08590e11i	−1.17562	−	1.17562i	−0.194766	−	0.980850i	$-0.562395\pi$
$228$	−7.40669e11	+	7.40669e11i	−1.20213	+	1.20213i
$229$	−5.34735e11	+	5.34735e11i	−0.849104	+	0.849104i	−0.990021	−	0.140917i	$-0.954995\pi$
$229$	−5.34735e11	+	5.34735e11i	−0.849104	+	0.849104i	0.140917	+	0.990021i	$0.454995\pi$
$230$	3.57159e10			0.0554910
$231$		−	4.63929e11i		−	0.705329i
$232$	−6.76322e11	+	6.76322e11i	−1.00627	+	1.00627i
$233$		−	9.61049e10i		−	0.139948i	−0.997549	−	0.0699739i	$-0.977708\pi$
$233$		−	9.61049e10i		−	0.139948i	0.997549	−	0.0699739i	$-0.0222916\pi$
$234$	1.20807e12	+	8.44304e11i	1.72192	+	1.20343i
$235$	4.07383e11			0.568412
$236$	7.26052e11	+	7.26052e11i	0.991762	+	0.991762i
$237$	6.16027e11			0.823868
$238$			1.36104e12i			1.78232i
$239$	−3.84436e11	−	3.84436e11i	−0.492986	−	0.492986i	0.416260	−	0.909246i	$-0.363341\pi$
$239$	−3.84436e11	−	3.84436e11i	−0.492986	−	0.492986i	−0.909246	+	0.416260i	$0.863341\pi$
$240$	9.17327e11	+	9.17327e11i	1.15204	+	1.15204i
$241$	3.05051e11	−	3.05051e11i	0.375221	−	0.375221i	−0.494154	−	0.869374i	$-0.664522\pi$
$241$	3.05051e11	−	3.05051e11i	0.375221	−	0.375221i	0.869374	+	0.494154i	$0.164522\pi$
$242$	9.61348e11	−	9.61348e11i	1.15825	−	1.15825i
$243$	−1.20465e12			−1.42177
$244$		−	2.78957e12i		−	3.22544i
$245$	−1.81201e12	+	1.81201e12i	−2.05272	+	2.05272i
$246$			2.15389e12i			2.39082i
$247$	−4.25519e11	−	2.97390e11i	−0.462843	−	0.323475i
$248$	−6.02183e11			−0.641904
$249$	1.67695e12	+	1.67695e12i	1.75195	+	1.75195i
$250$	1.67096e12			1.71107
$251$		−	1.98196e12i		−	1.98942i	−0.102721	−	0.994710i	$-0.532755\pi$
$251$		−	1.98196e12i		−	1.98942i	0.102721	−	0.994710i	$-0.467245\pi$
$252$	−3.45387e12	−	3.45387e12i	−3.39862	−	3.39862i
$253$	5.56339e9	+	5.56339e9i	0.00536706	+	0.00536706i
$254$	1.15461e12	−	1.15461e12i	1.09211	−	1.09211i
$255$	6.00121e11	−	6.00121e11i	0.556594	−	0.556594i
$256$	−2.22328e12			−2.02206
$257$			1.54314e12i			1.37638i	0.725530	+	0.688190i	$0.241595\pi$
$257$			1.54314e12i			1.37638i	−0.725530	+	0.688190i	$0.758405\pi$
$258$	2.97604e12	−	2.97604e12i	2.60340	−	2.60340i
$259$		−	2.39427e11i		−	0.205435i
$260$	−1.40078e12	+	2.00429e12i	−1.17897	+	1.68692i
$261$	−1.16579e12			−0.962537
$262$	3.13359e10	+	3.13359e10i	0.0253826	+	0.0253826i
$263$	−1.20204e12			−0.955299			−0.477650	−	0.878550i	$-0.658511\pi$
$263$	−1.20204e12			−0.955299			−0.477650	+	0.878550i	$0.658511\pi$
$264$			8.22156e11i			0.641113i
$265$	−3.62335e11	−	3.62335e11i	−0.277256	−	0.277256i
$266$	1.81694e12	+	1.81694e12i	1.36437	+	1.36437i
$267$	−1.11746e12	+	1.11746e12i	−0.823524	+	0.823524i
$268$	1.42228e12	−	1.42228e12i	1.02875	−	1.02875i
$269$	3.65500e11			0.259493			0.129747	−	0.991547i	$-0.458584\pi$
$269$	3.65500e11			0.259493			0.129747	+	0.991547i	$0.458584\pi$
$270$			7.82009e11i			0.544995i
$271$	−1.29180e12	+	1.29180e12i	−0.883791	+	0.883791i	−0.993918	−	0.110127i	$-0.964874\pi$
$271$	−1.29180e12	+	1.29180e12i	−0.883791	+	0.883791i	0.110127	+	0.993918i	$0.464874\pi$
$272$		−	8.38397e11i		−	0.563125i
$273$	2.53516e12	−	3.62742e12i	1.67183	−	2.39213i
$274$	−4.07479e12			−2.63847
$275$	−8.49319e9	−	8.49319e9i	−0.00540017	−	0.00540017i
$276$	1.51433e11			0.0945531
$277$			1.60395e12i			0.983539i	0.870725	+	0.491770i	$0.163650\pi$
$277$			1.60395e12i			0.983539i	−0.870725	+	0.491770i	$0.836350\pi$
$278$	5.09674e11	+	5.09674e11i	0.306951	+	0.306951i
$279$	−5.18997e11	−	5.18997e11i	−0.307004	−	0.307004i
$280$	4.33466e12	−	4.33466e12i	2.51863	−	2.51863i
$281$	−7.62141e11	+	7.62141e11i	−0.435015	+	0.435015i	−0.890330	−	0.455315i	$-0.849526\pi$
$281$	−7.62141e11	+	7.62141e11i	−0.435015	+	0.435015i	0.455315	+	0.890330i	$0.349526\pi$
$282$	2.57970e12			1.44652
$283$			1.44931e12i			0.798413i	0.916861	+	0.399207i	$0.130714\pi$
$283$			1.44931e12i			0.798413i	−0.916861	+	0.399207i	$0.869286\pi$
$284$	−9.49040e11	+	9.49040e11i	−0.513680	+	0.513680i
$285$		−	1.60228e12i		−	0.852149i
$286$	−7.92157e11	+	1.40403e11i	−0.413981	+	0.0733745i
$287$	3.53778e12			1.81686
$288$	1.56889e11	+	1.56889e11i	0.0791824	+	0.0791824i
$289$	1.46751e12			0.727933
$290$		−	2.88867e12i		−	1.40834i
$291$	3.66875e12	+	3.66875e12i	1.75814	+	1.75814i
$292$	1.37353e12	+	1.37353e12i	0.647031	+	0.647031i
$293$	−1.69798e12	+	1.69798e12i	−0.786310	+	0.786310i	−0.980887	−	0.194577i	$-0.937667\pi$
$293$	−1.69798e12	+	1.69798e12i	−0.786310	+	0.786310i	0.194577	+	0.980887i	$0.437667\pi$
$294$	−1.14743e13	+	1.14743e13i	−5.22384	+	5.22384i
$295$	−1.57066e12			−0.703029
$296$			4.24302e11i			0.186731i
$297$	−1.21812e11	+	1.21812e11i	−0.0527117	+	0.0527117i
$298$		−	4.80320e12i		−	2.04385i
$299$	1.30983e10	+	7.39010e10i	0.00548098	+	0.0309239i
$300$	−2.31181e11			−0.0951363
$301$	−4.88818e12	−	4.88818e12i	−1.97840	−	1.97840i
$302$	5.42947e11			0.216134
$303$		−	4.71669e12i		−	1.84682i
$304$	−1.11923e12	−	1.11923e12i	−0.431074	−	0.431074i
$305$	3.01733e12	+	3.01733e12i	1.14321	+	1.14321i
$306$	2.07878e12	−	2.07878e12i	0.774821	−	0.774821i
$307$	−1.40395e12	+	1.40395e12i	−0.514824	+	0.514824i	−0.916001	−	0.401177i	$-0.868601\pi$
$307$	−1.40395e12	+	1.40395e12i	−0.514824	+	0.514824i	0.401177	+	0.916001i	$0.368601\pi$
$308$	2.66619e12			0.961916
$309$		−	4.70751e11i		−	0.167109i
$310$	1.28600e12	−	1.28600e12i	0.449194	−	0.449194i
$311$		−	1.13854e12i		−	0.391333i	−0.980670	−	0.195667i	$-0.937313\pi$
$311$		−	1.13854e12i		−	0.391333i	0.980670	−	0.195667i	$-0.0626871\pi$
$312$	−4.49270e12	+	6.42836e12i	−1.51962	+	2.17434i
$313$	−6.79111e9			−0.00226057			−0.00113029	−	0.999999i	$-0.500360\pi$
$313$	−6.79111e9			−0.00226057			−0.00113029	+	0.999999i	$0.500360\pi$
$314$	4.05924e12	+	4.05924e12i	1.32983	+	1.32983i
$315$	7.47173e12			2.40918
$316$			3.54029e12i			1.12358i
$317$	−4.03254e12	−	4.03254e12i	−1.25974	−	1.25974i	−0.951214	−	0.308530i	$-0.900163\pi$
$317$	−4.03254e12	−	4.03254e12i	−1.25974	−	1.25974i	−0.308530	−	0.951214i	$-0.599837\pi$
$318$	−2.29444e12	−	2.29444e12i	−0.705572	−	0.705572i
$319$	4.49961e11	−	4.49961e11i	0.136214	−	0.136214i
$320$	2.21295e12	−	2.21295e12i	0.659512	−	0.659512i
$321$	5.67150e12			1.66407
$322$		−	3.71482e11i		−	0.107314i
$323$	−7.32209e11	+	7.32209e11i	−0.208268	+	0.208268i
$324$		−	5.42113e12i		−	1.51832i
$325$	−1.99961e10	−	1.12819e11i	−0.00551479	−	0.0311146i
$326$	5.33176e12			1.44805
$327$	3.49211e11	+	3.49211e11i	0.0934005	+	0.0934005i
$328$	−6.26951e12			−1.65145
$329$		−	4.23719e12i		−	1.09926i
$330$	−1.75577e12	−	1.75577e12i	−0.448640	−	0.448640i
$331$	−6.96159e11	−	6.96159e11i	−0.175214	−	0.175214i	0.614052	−	0.789266i	$-0.289539\pi$
$331$	−6.96159e11	−	6.96159e11i	−0.175214	−	0.175214i	−0.789266	+	0.614052i	$0.789539\pi$
$332$	−9.63736e12	+	9.63736e12i	−2.38928	+	2.38928i
$333$	−3.65688e11	+	3.65688e11i	−0.0893079	+	0.0893079i
$334$	−4.15714e12			−1.00014
$335$			3.07681e12i			0.729250i
$336$	9.54112e12	−	9.54112e12i	2.22794	−	2.22794i
$337$			6.35908e11i			0.146300i	0.997321	+	0.0731501i	$0.0233052\pi$
$337$			6.35908e11i			0.146300i	−0.997321	+	0.0731501i	$0.976695\pi$
$338$	−6.96104e12	−	3.23097e12i	−1.57794	−	0.732403i
$339$	−8.37452e12			−1.87052
$340$	3.44888e12	+	3.44888e12i	0.759073	+	0.759073i
$341$	4.00635e11			0.0868915
$342$		−	5.55020e12i		−	1.18626i
$343$	1.22527e13	+	1.22527e13i	2.58085	+	2.58085i
$344$	8.66263e12	+	8.66263e12i	1.79828	+	1.79828i
$345$	−1.63797e11	+	1.63797e11i	−0.0335128	+	0.0335128i
$346$	1.13159e12	−	1.13159e12i	0.228196	−	0.228196i
$347$	−3.97892e12			−0.790894			−0.395447	−	0.918489i	$-0.629410\pi$
$347$	−3.97892e12			−0.790894			−0.395447	+	0.918489i	$0.629410\pi$
$348$		−	1.22478e13i		−	2.39972i
$349$	5.91251e12	−	5.91251e12i	1.14194	−	1.14194i	0.153849	−	0.988094i	$-0.450833\pi$
$349$	5.91251e12	−	5.91251e12i	1.14194	−	1.14194i	0.988094	−	0.153849i	$-0.0491669\pi$
$350$			5.67112e11i			0.107976i
$351$	−1.61808e12	+	2.86790e11i	−0.303714	+	0.0538305i
$352$	−1.21109e11			−0.0224111
$353$	1.76509e11	+	1.76509e11i	0.0322028	+	0.0322028i	0.723025	−	0.690822i	$-0.242751\pi$
$353$	1.76509e11	+	1.76509e11i	0.0322028	+	0.0322028i	−0.690822	+	0.723025i	$0.742751\pi$
$354$	−9.94604e12			−1.78910
$355$		−	2.05305e12i		−	0.364132i
$356$	−6.42202e12	−	6.42202e12i	−1.12311	−	1.12311i
$357$	−6.24187e12	−	6.24187e12i	−1.07640	−	1.07640i
$358$	7.43791e11	−	7.43791e11i	0.126484	−	0.126484i
$359$	−3.01299e12	+	3.01299e12i	−0.505272	+	0.505272i	−0.913071	−	0.407800i	$-0.866296\pi$
$359$	−3.01299e12	+	3.01299e12i	−0.505272	+	0.505272i	0.407800	+	0.913071i	$0.366296\pi$
$360$	−1.32411e13			−2.18983
$361$		−	4.17611e12i		−	0.681140i
$362$	−6.03041e12	+	6.03041e12i	−0.970073	+	0.970073i
$363$			8.81770e12i			1.39901i
$364$	2.08467e13	+	1.45695e13i	3.26234	+	2.28001i
$365$	−2.97136e12			−0.458659
$366$	1.91069e13	+	1.91069e13i	2.90928	+	2.90928i
$367$	8.76565e12			1.31660			0.658300	−	0.752756i	$-0.271276\pi$
$367$	8.76565e12			1.31660			0.658300	+	0.752756i	$0.271276\pi$
$368$			2.28832e11i			0.0339061i
$369$	−5.40343e12	−	5.40343e12i	−0.789838	−	0.789838i
$370$	−9.06125e11	−	9.06125e11i	−0.130671	−	0.130671i
$371$	−3.76864e12	+	3.76864e12i	−0.536186	+	0.536186i
$372$	5.45257e12	−	5.45257e12i	0.765396	−	0.765396i
$373$	4.87487e12			0.675179			0.337589	−	0.941294i	$-0.390389\pi$
$373$	4.87487e12			0.675179			0.337589	+	0.941294i	$0.390389\pi$
$374$			1.60470e12i			0.219298i
$375$	−7.66323e12	+	7.66323e12i	−1.03337	+	1.03337i
$376$			7.50897e12i			0.999174i
$377$	5.97703e12	−	1.05938e12i	0.784836	−	0.139105i
$378$	8.13368e12			1.05397
$379$	−5.99975e12	−	5.99975e12i	−0.767250	−	0.767250i	0.210371	−	0.977622i	$-0.432533\pi$
$379$	−5.99975e12	−	5.99975e12i	−0.767250	−	0.767250i	−0.977622	+	0.210371i	$0.932533\pi$
$380$	9.20828e12			1.16215
$381$			1.05903e13i			1.31912i
$382$	−3.41243e12	−	3.41243e12i	−0.419514	−	0.419514i
$383$	−6.34228e12	−	6.34228e12i	−0.769577	−	0.769577i	0.208455	−	0.978032i	$-0.433156\pi$
$383$	−6.34228e12	−	6.34228e12i	−0.769577	−	0.769577i	−0.978032	+	0.208455i	$0.933156\pi$
$384$	1.48267e13	−	1.48267e13i	1.77578	−	1.77578i
$385$	−2.88387e12	+	2.88387e12i	−0.340936	+	0.340936i
$386$	1.73170e13			2.02086
$387$			1.49319e13i			1.72013i
$388$	−2.10842e13	+	2.10842e13i	−2.39772	+	2.39772i
$389$		−	1.02856e13i		−	1.15474i	−0.816484	−	0.577368i	$-0.804080\pi$
$389$		−	1.02856e13i		−	1.15474i	0.816484	−	0.577368i	$-0.195920\pi$
$390$	−4.13374e12	−	2.33227e13i	−0.458163	−	2.58497i
$391$	1.49704e11			0.0163813
$392$	−3.33993e13	−	3.33993e13i	−3.60834	−	3.60834i
$393$	−2.87420e11			−0.0306588
$394$		−	1.59370e13i		−	1.67852i
$395$	−3.82934e12	−	3.82934e12i	−0.398234	−	0.398234i
$396$	−4.07220e12	−	4.07220e12i	−0.418170	−	0.418170i
$397$	−3.58089e11	+	3.58089e11i	−0.0363110	+	0.0363110i	−0.725029	−	0.688718i	$-0.758174\pi$
$397$	−3.58089e11	+	3.58089e11i	−0.0363110	+	0.0363110i	0.688718	+	0.725029i	$0.258174\pi$
$398$	9.60539e12	−	9.60539e12i	0.961833	−	0.961833i
$399$	−1.66654e13			−1.64798
$400$		−	3.49340e11i		−	0.0341153i
$401$	−6.44535e12	+	6.44535e12i	−0.621620	+	0.621620i	−0.945945	−	0.324326i	$-0.894863\pi$
$401$	−6.44535e12	+	6.44535e12i	−0.621620	+	0.621620i	0.324326	+	0.945945i	$0.394863\pi$
$402$			1.94835e13i			1.85583i
$403$	3.13253e12	+	2.18929e12i	0.294693	+	0.205957i
$404$	2.71067e13			2.51866
$405$	5.86375e12	+	5.86375e12i	0.538146	+	0.538146i
$406$	−3.00451e13			−2.72360
$407$		−	2.82290e11i		−	0.0252769i
$408$	1.10616e13	+	1.10616e13i	0.978399	+	0.978399i
$409$	−1.21566e13	−	1.21566e13i	−1.06218	−	1.06218i	−0.997934	−	0.0642439i	$-0.979536\pi$
$409$	−1.21566e13	−	1.21566e13i	−1.06218	−	1.06218i	−0.0642439	−	0.997934i	$-0.520464\pi$
$410$	1.33890e13	−	1.33890e13i	1.15565	−	1.15565i
$411$	1.86874e13	−	1.86874e13i	1.59346	−	1.59346i
$412$	2.70539e12			0.227900
$413$			1.63365e13i			1.35959i
$414$	−5.67383e11	+	5.67383e11i	−0.0466524	+	0.0466524i
$415$		−	2.08484e13i		−	1.69369i
$416$	−9.46939e11	−	6.61804e11i	−0.0760073	−	0.0531206i
$417$	−4.67484e12			−0.370755
$418$	2.14222e12	+	2.14222e12i	0.167874	+	0.167874i
$419$	1.57207e13			1.21731			0.608654	−	0.793435i	$-0.291710\pi$
$419$	1.57207e13			1.21731			0.608654	+	0.793435i	$0.291710\pi$
$420$			7.84979e13i			6.00636i
$421$	4.35699e12	+	4.35699e12i	0.329440	+	0.329440i	0.852373	−	0.522934i	$-0.175162\pi$
$421$	4.35699e12	+	4.35699e12i	0.329440	+	0.329440i	−0.522934	+	0.852373i	$0.675162\pi$
$422$	8.68773e12	+	8.68773e12i	0.649149	+	0.649149i
$423$	−6.47167e12	+	6.47167e12i	−0.477875	+	0.477875i
$424$	6.67863e12	−	6.67863e12i	0.487369	−	0.487369i
$425$	−2.28541e11			−0.0164823
$426$		−	1.30007e13i		−	0.926657i
$427$	3.13833e13	−	3.13833e13i	2.21085	−	2.21085i
$428$			3.25939e13i			2.26944i
$429$	2.98902e12	−	4.27682e12i	0.205704	−	0.294330i
$430$	−3.69993e13			−2.51681
$431$	−2.05322e12	−	2.05322e12i	−0.138054	−	0.138054i	0.634703	−	0.772756i	$-0.281123\pi$
$431$	−2.05322e12	−	2.05322e12i	−0.138054	−	0.138054i	−0.772756	+	0.634703i	$0.781123\pi$
$432$	−5.01034e12			−0.333003
$433$			2.85014e13i			1.87252i	0.351306	+	0.936261i	$0.385738\pi$
$433$			2.85014e13i			1.87252i	−0.351306	+	0.936261i	$0.614262\pi$
$434$	−1.33757e13	−	1.33757e13i	−0.868698	−	0.868698i
$435$	1.32478e13	+	1.32478e13i	0.850542	+	0.850542i
$436$	−2.00690e12	+	2.00690e12i	−0.127378	+	0.127378i
$437$	1.99849e11	−	1.99849e11i	0.0125400	−	0.0125400i
$438$	−1.88158e13			−1.16722
$439$			3.12644e12i			0.191746i	0.995394	+	0.0958732i	$0.0305643\pi$
$439$			3.12644e12i			0.191746i	−0.995394	+	0.0958732i	$0.969436\pi$
$440$	5.11068e12	−	5.11068e12i	0.309895	−	0.309895i
$441$		−	5.75710e13i		−	3.45152i
$442$	−8.76893e12	+	1.25470e13i	−0.519799	+	0.743752i
$443$	−1.39314e13			−0.816540			−0.408270	−	0.912861i	$-0.633868\pi$
$443$	−1.39314e13			−0.816540			−0.408270	+	0.912861i	$0.633868\pi$
$444$	−3.84191e12	−	3.84191e12i	−0.222655	−	0.222655i
$445$	1.38927e13			0.796136
$446$		−	1.49234e13i		−	0.845654i
$447$	2.20280e13	+	2.20280e13i	1.23435	+	1.23435i
$448$	−2.30170e13	−	2.30170e13i	−1.27543	−	1.27543i
$449$	−1.34857e13	+	1.34857e13i	−0.738993	+	0.738993i	−0.972383	−	0.233390i	$-0.925018\pi$
$449$	−1.34857e13	+	1.34857e13i	−0.738993	+	0.738993i	0.233390	+	0.972383i	$0.425018\pi$
$450$	8.66178e11	−	8.66178e11i	0.0469402	−	0.0469402i
$451$	4.17114e12			0.223549
$452$		−	4.81281e13i		−	2.55098i
$453$	−2.49002e12	+	2.49002e12i	−0.130530	+	0.130530i
$454$			5.57848e13i			2.89226i
$455$	−3.83078e13	+	6.78971e12i	−1.96440	+	0.348172i
$456$	2.95337e13			1.49794
$457$	−1.20981e13	−	1.20981e13i	−0.606924	−	0.606924i	0.335217	−	0.942141i	$-0.391190\pi$
$457$	−1.20981e13	−	1.20981e13i	−0.606924	−	0.606924i	−0.942141	+	0.335217i	$0.891190\pi$
$458$	4.20978e13			2.08897
$459$			3.27780e12i			0.160886i
$460$	−9.41338e11	−	9.41338e11i	−0.0457042	−	0.0457042i
$461$	2.13254e13	+	2.13254e13i	1.02422	+	1.02422i	0.999699	+	0.0245194i	$0.00780556\pi$
$461$	2.13254e13	+	2.13254e13i	1.02422	+	1.02422i	0.0245194	+	0.999699i	$0.492194\pi$
$462$	−1.82618e13	+	1.82618e13i	−0.867627	+	0.867627i
$463$	1.17072e13	−	1.17072e13i	0.550237	−	0.550237i	−0.376272	−	0.926509i	$-0.622794\pi$
$463$	1.17072e13	−	1.17072e13i	0.550237	−	0.550237i	0.926509	+	0.376272i	$0.122794\pi$
$464$	1.85077e13			0.860524
$465$			1.17955e13i			0.542565i
$466$	−3.78301e12	+	3.78301e12i	−0.172150	+	0.172150i
$467$			4.01325e13i			1.80681i	0.428792	+	0.903403i	$0.358939\pi$
$467$			4.01325e13i			1.80681i	−0.428792	+	0.903403i	$0.641061\pi$
$468$	−9.58747e12	−	5.40928e13i	−0.427046	−	2.40941i
$469$	3.20019e13			1.41030
$470$	−1.60359e13	−	1.60359e13i	−0.699205	−	0.699205i
$471$	−3.72322e13			−1.60625
$472$		−	2.89508e13i		−	1.23581i
$473$	−5.76330e12	−	5.76330e12i	−0.243425	−	0.243425i
$474$	−2.42488e13	−	2.42488e13i	−1.01344	−	1.01344i
$475$	−3.05094e11	+	3.05094e11i	−0.0126173	+	0.0126173i
$476$	3.58718e13	−	3.58718e13i	1.46798	−	1.46798i
$477$	1.15121e13			0.466189
$478$			3.02653e13i			1.21285i
$479$	−1.39096e13	+	1.39096e13i	−0.551618	+	0.551618i	−0.926908	−	0.375290i	$-0.877543\pi$
$479$	−1.39096e13	+	1.39096e13i	−0.551618	+	0.551618i	0.375290	+	0.926908i	$0.377543\pi$
$480$		−	3.56569e12i		−	0.139938i
$481$	1.54258e12	−	2.20720e12i	0.0599134	−	0.0857268i
$482$	−2.40156e13			−0.923120
$483$	1.70366e12	+	1.70366e12i	0.0648107	+	0.0648107i
$484$	−5.06750e13			−1.90795
$485$		−	4.56114e13i		−	1.69967i
$486$	4.74188e13	+	4.74188e13i	1.74892	+	1.74892i
$487$	2.15285e13	+	2.15285e13i	0.785903	+	0.785903i	0.980820	−	0.194917i	$-0.0624436\pi$
$487$	2.15285e13	+	2.15285e13i	0.785903	+	0.785903i	−0.194917	+	0.980820i	$0.562444\pi$
$488$	−5.56162e13	+	5.56162e13i	−2.00957	+	2.00957i
$489$	−2.44520e13	+	2.44520e13i	−0.874522	+	0.874522i
$490$	1.42653e14			5.05011
$491$		−	4.60482e13i		−	1.61363i	−0.590802	−	0.806817i	$-0.701189\pi$
$491$		−	4.60482e13i		−	1.61363i	0.590802	−	0.806817i	$-0.298811\pi$
$492$	5.67684e13	−	5.67684e13i	1.96916	−	1.96916i
$493$		−	1.21079e13i		−	0.415751i
$494$	5.04358e12	+	2.84560e13i	0.171437	+	0.967252i
$495$	8.80936e12			0.296428
$496$	8.23943e12	+	8.23943e12i	0.274466	+	0.274466i
$497$	−2.13538e13			−0.704196
$498$		−	1.32020e14i		−	4.31017i
$499$	−2.54340e13	−	2.54340e13i	−0.822076	−	0.822076i	0.164329	−	0.986406i	$-0.447454\pi$
$499$	−2.54340e13	−	2.54340e13i	−0.822076	−	0.822076i	−0.986406	+	0.164329i	$0.947454\pi$
$500$	−4.40403e13	−	4.40403e13i	−1.40929	−	1.40929i
$501$	1.90651e13	−	1.90651e13i	0.604020	−	0.604020i
$502$	−7.80165e13	+	7.80165e13i	−2.44719	+	2.44719i
$503$	−2.55274e13			−0.792806			−0.396403	−	0.918077i	$-0.629742\pi$
$503$	−2.55274e13			−0.792806			−0.396403	+	0.918077i	$0.629742\pi$
$504$			1.37721e14i			4.23493i
$505$	−2.93199e13	+	2.93199e13i	−0.892699	+	0.892699i
$506$		−	4.37987e11i		−	0.0132041i
$507$	4.67417e13	−	1.71065e13i	1.39529	−	0.510647i
$508$	−6.08622e13			−1.79899
$509$	2.24826e13	+	2.24826e13i	0.658047	+	0.658047i	0.954918	−	0.296870i	$-0.0959429\pi$
$509$	2.24826e13	+	2.24826e13i	0.658047	+	0.658047i	−0.296870	+	0.954918i	$0.595943\pi$
$510$	−4.72455e13			−1.36933
$511$			3.09051e13i			0.887004i
$512$	4.54645e13	+	4.54645e13i	1.29218	+	1.29218i
$513$	4.37575e12	+	4.37575e12i	0.123159	+	0.123159i
$514$	6.07429e13	−	6.07429e13i	1.69309	−	1.69309i
$515$	−2.92628e12	+	2.92628e12i	−0.0807754	+	0.0807754i
$516$	−1.56875e14			−4.28849
$517$		−	4.99576e12i		−	0.135254i
$518$	−9.42462e12	+	9.42462e12i	−0.252706	+	0.252706i
$519$			1.03792e13i			0.275630i
$520$	6.78874e13	−	1.20324e13i	1.78555	−	0.316473i
$521$	4.76679e11			0.0124176			0.00620879	−	0.999981i	$-0.498024\pi$
$521$	4.76679e11			0.0124176			0.00620879	+	0.999981i	$0.498024\pi$
$522$	4.58893e13	+	4.58893e13i	1.18402	+	1.18402i
$523$	−3.19097e12			−0.0815481			−0.0407740	−	0.999168i	$-0.512982\pi$
$523$	−3.19097e12			−0.0815481			−0.0407740	+	0.999168i	$0.512982\pi$
$524$		−	1.65180e12i		−	0.0418119i
$525$	−2.60084e12	−	2.60084e12i	−0.0652104	−	0.0652104i
$526$	4.73162e13	+	4.73162e13i	1.17512	+	1.17512i
$527$	5.39029e12	−	5.39029e12i	0.132605	−	0.132605i
$528$	1.12492e13	−	1.12492e13i	0.274128	−	0.274128i
$529$	4.13857e13			0.999014
$530$			2.85254e13i			0.682106i
$531$	2.49515e13	−	2.49515e13i	0.591050	−	0.591050i
$532$		−	9.57754e13i		−	2.24748i
$533$	3.26138e13	+	2.27933e13i	0.758167	+	0.529873i
$534$	8.79740e13			2.02604
$535$	−3.52551e13	−	3.52551e13i	−0.804365	−	0.804365i
$536$	−5.67124e13			−1.28190
$537$			6.82222e12i			0.152776i
$538$	−1.43873e13	−	1.43873e13i	−0.319203	−	0.319203i
$539$	2.22207e13	+	2.22207e13i	0.488444	+	0.488444i
$540$	2.06108e13	−	2.06108e13i	0.448876	−	0.448876i
$541$	−1.89743e13	+	1.89743e13i	−0.409429	+	0.409429i	−0.881540	−	0.472110i	$-0.843492\pi$
$541$	−1.89743e13	+	1.89743e13i	−0.409429	+	0.409429i	0.472110	+	0.881540i	$0.343492\pi$
$542$	1.01699e14			2.17431
$543$		−	5.53123e13i		−	1.17172i
$544$	−1.62944e12	+	1.62944e12i	−0.0342014	+	0.0342014i
$545$		−	4.34152e12i		−	0.0902942i
$546$	−2.42579e14	+	4.29950e13i	−4.99909	+	0.886043i
$547$	−2.17998e13			−0.445160			−0.222580	−	0.974914i	$-0.571448\pi$
$547$	−2.17998e13			−0.445160			−0.222580	+	0.974914i	$0.571448\pi$
$548$	1.07396e14	+	1.07396e14i	2.17313	+	2.17313i
$549$	−9.58666e13			−1.92223
$550$			6.68640e11i			0.0132855i
$551$	−1.61636e13	−	1.61636e13i	−0.318259	−	0.318259i
$552$	−3.01915e12	−	3.01915e12i	−0.0589100	−	0.0589100i
$553$	−3.98290e13	+	3.98290e13i	−0.770147	+	0.770147i
$554$	6.31367e13	−	6.31367e13i	1.20985	−	1.20985i
$555$	8.31119e12			0.157833
$556$		−	2.68662e13i		−	0.505629i
$557$	4.51494e13	−	4.51494e13i	0.842125	−	0.842125i	−0.147010	−	0.989135i	$-0.546965\pi$
$557$	4.51494e13	−	4.51494e13i	0.842125	−	0.842125i	0.989135	+	0.147010i	$0.0469650\pi$
$558$			4.08588e13i			0.755292i
$559$	−1.35689e13	−	7.65564e13i	−0.248592	−	1.40256i
$560$	−1.18619e14			−2.15384
$561$	−7.35932e12	−	7.35932e12i	−0.132441	−	0.132441i
$562$	6.00008e13			1.07023
$563$		−	6.50123e13i		−	1.14935i	−0.818381	−	0.574677i	$-0.805128\pi$
$563$		−	6.50123e13i		−	1.14935i	0.818381	−	0.574677i	$-0.194872\pi$
$564$	−6.79913e13	−	6.79913e13i	−1.19140	−	1.19140i
$565$	5.20577e13	+	5.20577e13i	0.904154	+	0.904154i
$566$	5.70494e13	−	5.70494e13i	0.982131	−	0.982131i
$567$	6.09889e13	−	6.09889e13i	1.04072	−	1.04072i
$568$	3.78423e13			0.640083
$569$			3.34305e13i			0.560508i	0.959926	+	0.280254i	$0.0904187\pi$
$569$			3.34305e13i			0.560508i	−0.959926	+	0.280254i	$0.909581\pi$
$570$	−6.30712e13	+	6.30712e13i	−1.04823	+	1.04823i
$571$			7.17316e13i			1.18176i	0.806759	+	0.590881i	$0.201220\pi$
$571$			7.17316e13i			1.18176i	−0.806759	+	0.590881i	$0.798780\pi$
$572$	2.45788e13	+	1.71778e13i	0.401402	+	0.280535i
$573$	3.12995e13			0.506716
$574$	−1.39259e14	−	1.39259e14i	−2.23493	−	2.23493i
$575$	6.23780e10			0.000992412
$576$			7.03099e13i			1.10893i
$577$	4.00303e12	+	4.00303e12i	0.0625906	+	0.0625906i	0.737709	−	0.675119i	$-0.235908\pi$
$577$	4.00303e12	+	4.00303e12i	0.0625906	+	0.0625906i	−0.675119	+	0.737709i	$0.735908\pi$
$578$	−5.77660e13	−	5.77660e13i	−0.895433	−	0.895433i
$579$	−7.94175e13	+	7.94175e13i	−1.22046	+	1.22046i
$580$	−7.61344e13	+	7.61344e13i	−1.15995	+	1.15995i
$581$	−2.16845e14			−3.27543
$582$		−	2.88829e14i		−	4.32539i
$583$	−4.44333e12	+	4.44333e12i	−0.0659729	+	0.0659729i
$584$		−	5.47687e13i		−	0.806247i
$585$	6.88796e13	+	4.81391e13i	1.00534	+	0.702617i
$586$	1.33676e14			1.93448
$587$	9.94597e12	+	9.94597e12i	0.142711	+	0.142711i	0.774853	−	0.632142i	$-0.217824\pi$
$587$	9.94597e12	+	9.94597e12i	0.142711	+	0.142711i	−0.632142	+	0.774853i	$0.717824\pi$
$588$	6.04840e14			8.60506
$589$		−	1.43917e13i		−	0.203019i
$590$	6.18265e13	+	6.18265e13i	0.864798	+	0.864798i
$591$	7.30889e13	+	7.30889e13i	1.01371	+	1.01371i
$592$	5.80555e12	−	5.80555e12i	0.0798427	−	0.0798427i
$593$	−6.16000e13	+	6.16000e13i	−0.840054	+	0.840054i	−0.988866	−	0.148812i	$-0.952455\pi$
$593$	−6.16000e13	+	6.16000e13i	−0.840054	+	0.840054i	0.148812	+	0.988866i	$0.452455\pi$
$594$	9.58982e12			0.129682
$595$			7.76013e13i			1.04060i
$596$	−1.26594e14	+	1.26594e14i	−1.68338	+	1.68338i
$597$			8.81028e13i			1.16176i
$598$	2.39339e12	−	3.42458e12i	0.0312974	−	0.0447817i
$599$	−1.18057e14			−1.53094			−0.765468	−	0.643474i	$-0.777493\pi$
$599$	−1.18057e14			−1.53094			−0.765468	+	0.643474i	$0.777493\pi$
$600$	4.60910e12	+	4.60910e12i	0.0592734	+	0.0592734i
$601$	−7.19997e13			−0.918244			−0.459122	−	0.888373i	$-0.651836\pi$
$601$	−7.19997e13			−0.918244			−0.459122	+	0.888373i	$0.651836\pi$
$602$			3.84830e14i			4.86728i
$603$	−4.88781e13	−	4.88781e13i	−0.613095	−	0.613095i
$604$	−1.43101e13	−	1.43101e13i	−0.178015	−	0.178015i
$605$	5.48125e13	−	5.48125e13i	0.676243	−	0.676243i
$606$	−1.85665e14	+	1.85665e14i	−2.27178	+	2.27178i
$607$	−7.59156e13			−0.921271			−0.460636	−	0.887589i	$-0.652378\pi$
$607$	−7.59156e13			−0.921271			−0.460636	+	0.887589i	$0.652378\pi$
$608$			4.35050e12i			0.0523627i
$609$	1.37790e14	−	1.37790e14i	1.64487	−	1.64487i
$610$		−	2.37544e14i		−	2.81252i
$611$	2.72995e13	−	3.90614e13i	0.320589	−	0.458713i
$612$	−1.09578e14			−1.27634
$613$	−4.76111e13	−	4.76111e13i	−0.550054	−	0.550054i	0.376402	−	0.926456i	$-0.377161\pi$
$613$	−4.76111e13	−	4.76111e13i	−0.550054	−	0.550054i	−0.926456	+	0.376402i	$0.877161\pi$
$614$	1.10528e14			1.26657
$615$			1.22807e14i			1.39587i
$616$	−5.31562e13	−	5.31562e13i	−0.599308	−	0.599308i
$617$	1.02141e14	+	1.02141e14i	1.14228	+	1.14228i	0.988032	+	0.154252i	$0.0492968\pi$
$617$	1.02141e14	+	1.02141e14i	1.14228	+	1.14228i	0.154252	+	0.988032i	$0.450703\pi$
$618$	−1.85303e13	+	1.85303e13i	−0.205561	+	0.205561i
$619$	1.21165e14	−	1.21165e14i	1.33328	−	1.33328i	0.430870	−	0.902414i	$-0.358207\pi$
$619$	1.21165e14	−	1.21165e14i	1.33328	−	1.33328i	0.902414	−	0.430870i	$-0.141793\pi$
$620$	−6.77884e13			−0.739941
$621$		−	8.94643e11i		−	0.00968705i
$622$	−4.48167e13	+	4.48167e13i	−0.481380	+	0.481380i
$623$		−	1.44498e14i		−	1.53965i
$624$	1.49429e14	−	2.64849e13i	1.57947	−	0.279946i
$625$	9.82858e13			1.03060
$626$	2.67320e11	+	2.67320e11i	0.00278074	+	0.00278074i
$627$	−1.96489e13			−0.202769
$628$		−	2.13972e14i		−	2.19058i
$629$	−3.79803e12	−	3.79803e12i	−0.0385750	−	0.0385750i
$630$	−2.94112e14	−	2.94112e14i	−2.96353	−	2.96353i
$631$	5.86923e13	−	5.86923e13i	0.586725	−	0.586725i	−0.350018	−	0.936743i	$-0.613825\pi$
$631$	5.86923e13	−	5.86923e13i	0.586725	−	0.586725i	0.936743	+	0.350018i	$0.113825\pi$
$632$	7.05833e13	−	7.05833e13i	0.700030	−	0.700030i
$633$	−7.96858e13			−0.784084
$634$			3.17468e14i			3.09923i
$635$	6.58314e13	−	6.58314e13i	0.637624	−	0.637624i
$636$			1.20946e14i			1.16226i
$637$	5.23159e13	+	2.95168e14i	0.498811	+	2.81431i
$638$	−3.54239e13			−0.335114
$639$	3.26148e13	+	3.26148e13i	0.306133	+	0.306133i
$640$	−1.84331e14			−1.71672
$641$			1.82058e13i			0.168236i	0.996456	+	0.0841180i	$0.0268073\pi$
$641$			1.82058e13i			0.168236i	−0.996456	+	0.0841180i	$0.973193\pi$
$642$	−2.23249e14	−	2.23249e14i	−2.04698	−	2.04698i
$643$	−1.04911e14	−	1.04911e14i	−0.954476	−	0.954476i	0.0445322	−	0.999008i	$-0.485820\pi$
$643$	−1.04911e14	−	1.04911e14i	−0.954476	−	0.954476i	−0.999008	+	0.0445322i	$0.985820\pi$
$644$	−9.79087e12	+	9.79087e12i	−0.0883877	+	0.0883877i
$645$	1.69683e14	−	1.69683e14i	1.51999	−	1.51999i
$646$	5.76444e13			0.512382
$647$		−	8.86062e13i		−	0.781525i	−0.920492	−	0.390762i	$-0.872211\pi$
$647$		−	8.86062e13i		−	0.781525i	0.920492	−	0.390762i	$-0.127789\pi$
$648$	−1.08082e14	+	1.08082e14i	−0.945971	+	0.945971i
$649$			1.92611e13i			0.167286i
$650$	−3.65381e12	+	5.22803e12i	−0.0314904	+	0.0450580i
$651$	1.22685e14			1.04927
$652$	−1.40525e14	−	1.40525e14i	−1.19266	−	1.19266i
$653$	8.55997e13			0.720952			0.360476	−	0.932769i	$-0.382614\pi$
$653$	8.55997e13			0.720952			0.360476	+	0.932769i	$0.382614\pi$
$654$		−	2.74922e13i		−	0.229784i
$655$	1.78666e12	+	1.78666e12i	0.0148196	+	0.0148196i
$656$	8.57833e13	+	8.57833e13i	0.706128	+	0.706128i
$657$	4.72029e13	−	4.72029e13i	0.385604	−	0.385604i
$658$	−1.66790e14	+	1.66790e14i	−1.35220	+	1.35220i
$659$	1.90445e14			1.53229			0.766146	−	0.642666i	$-0.222172\pi$
$659$	1.90445e14			1.53229			0.766146	+	0.642666i	$0.222172\pi$
$660$			9.25510e13i			0.739029i
$661$	−5.62537e13	+	5.62537e13i	−0.445804	+	0.445804i	−0.893957	−	0.448153i	$-0.852082\pi$
$661$	−5.62537e13	+	5.62537e13i	−0.445804	+	0.445804i	0.448153	+	0.893957i	$0.352082\pi$
$662$			5.48062e13i			0.431062i
$663$	−1.73266e13	−	9.77572e13i	−0.135253	−	0.763099i
$664$	3.84283e14			2.97722
$665$	1.03595e14	+	1.03595e14i	0.796584	+	0.796584i
$666$	2.87894e13			0.219716
$667$			3.30473e12i			0.0250326i
$668$	1.09567e14	+	1.09567e14i	0.823752	+	0.823752i
$669$	6.84403e13	+	6.84403e13i	0.510718	+	0.510718i
$670$	1.21113e14	−	1.21113e14i	0.897052	−	0.897052i
$671$	3.70018e13	−	3.70018e13i	0.272026	−	0.272026i
$672$	−3.70868e13			−0.270628
$673$			9.27884e13i			0.672076i	0.941848	+	0.336038i	$0.109087\pi$
$673$			9.27884e13i			0.672076i	−0.941848	+	0.336038i	$0.890913\pi$
$674$	2.50314e13	−	2.50314e13i	0.179964	−	0.179964i
$675$			1.36578e12i			0.00974680i
$676$	9.83104e13	+	2.68623e14i	0.696412	+	1.90287i
$677$	−2.04769e14			−1.43986			−0.719931	−	0.694045i	$-0.755827\pi$
$677$	−2.04769e14			−1.43986			−0.719931	+	0.694045i	$0.755827\pi$
$678$	3.29649e14	+	3.29649e14i	2.30093	+	2.30093i
$679$	−4.74404e14			−3.28700
$680$		−	1.37522e14i		−	0.945860i
$681$	−2.55836e14	−	2.55836e14i	−1.74673	−	1.74673i
$682$	−1.57703e13	−	1.57703e13i	−0.106886	−	0.106886i
$683$	1.27460e13	−	1.27460e13i	0.0857573	−	0.0857573i	−0.662927	−	0.748684i	$-0.730686\pi$
$683$	1.27460e13	−	1.27460e13i	0.0857573	−	0.0857573i	0.748684	+	0.662927i	$0.230686\pi$
$684$	−1.46283e14	+	1.46283e14i	−0.977039	+	0.977039i
$685$	−2.32329e14			−1.54046
$686$		−	9.64616e14i		−	6.34942i
$687$	−1.93065e14	+	1.93065e14i	−1.26160	+	1.26160i
$688$		−	2.37055e14i		−	1.53782i
$689$	−5.90227e13	+	1.04612e13i	−0.380122	+	0.0673732i
$690$	1.28952e13			0.0824485
$691$	1.86203e14	+	1.86203e14i	1.18194	+	1.18194i	0.979240	+	0.202705i	$0.0649731\pi$
$691$	1.86203e14	+	1.86203e14i	1.18194	+	1.18194i	0.202705	+	0.979240i	$0.435027\pi$
$692$	−5.96488e13			−0.375899
$693$		−	9.16263e13i		−	0.573263i
$694$	1.56624e14	+	1.56624e14i	0.972881	+	0.972881i
$695$	2.90597e13	+	2.90597e13i	0.179212	+	0.179212i
$696$	−2.44186e14	+	2.44186e14i	−1.49511	+	1.49511i
$697$	5.61200e13	−	5.61200e13i	0.341157	−	0.341157i
$698$	−4.65472e14			−2.80942
$699$		−	3.46986e13i		−	0.207934i
$700$	1.49469e13	−	1.49469e13i	0.0889329	−	0.0889329i
$701$		−	8.82869e13i		−	0.521562i	−0.965398	−	0.260781i	$-0.916020\pi$
$701$		−	8.82869e13i		−	0.521562i	0.965398	−	0.260781i	$-0.0839801\pi$
$702$	7.49819e13	+	5.24039e13i	0.439816	+	0.307382i
$703$	−1.01405e13			−0.0590585
$704$	−2.71376e13	−	2.71376e13i	−0.156931	−	0.156931i
$705$	1.47085e14			0.844546
$706$		−	1.38960e13i		−	0.0792255i
$707$	3.04956e14	+	3.04956e14i	1.72640	+	1.72640i
$708$	2.62140e14	+	2.62140e14i	1.47356	+	1.47356i
$709$	1.95709e14	−	1.95709e14i	1.09239	−	1.09239i	0.0971193	−	0.995273i	$-0.469037\pi$
$709$	1.95709e14	−	1.95709e14i	1.09239	−	1.09239i	0.995273	−	0.0971193i	$-0.0309628\pi$
$710$	−8.08149e13	+	8.08149e13i	−0.447919	+	0.447919i
$711$	1.21666e14			0.669607
$712$			2.56074e14i			1.39947i
$713$	−1.47123e12	+	1.47123e12i	−0.00798422	+	0.00798422i
$714$			4.91401e14i			2.64816i
$715$	−4.51659e13	+	8.00524e12i	−0.241702	+	0.0428395i
$716$	−3.92071e13			−0.208353
$717$	−1.38800e14	−	1.38800e14i	−0.732478	−	0.732478i
$718$	2.37202e14			1.24307
$719$			8.85803e13i			0.460991i	0.973073	+	0.230496i	$0.0740348\pi$
$719$			8.85803e13i			0.460991i	−0.973073	+	0.230496i	$0.925965\pi$
$720$	1.81173e14	+	1.81173e14i	0.936332	+	0.936332i
$721$	3.04362e13	+	3.04362e13i	0.156212	+	0.156212i
$722$	−1.64386e14	+	1.64386e14i	−0.837872	+	0.837872i
$723$	1.10138e14	−	1.10138e14i	0.557502	−	0.557502i
$724$	3.17878e14			1.59797
$725$		−	5.04506e12i		−	0.0251870i
$726$	3.47094e14	−	3.47094e14i	1.72093	−	1.72093i
$727$		−	4.11488e13i		−	0.202621i	−0.994855	−	0.101311i	$-0.967696\pi$
$727$		−	4.11488e13i		−	0.202621i	0.994855	−	0.101311i	$-0.0323036\pi$
$728$	−1.25149e14	−	7.06097e14i	−0.612029	−	3.45309i
$729$	−2.80661e14			−1.36315
$730$	1.16962e14	+	1.16962e14i	0.564198	+	0.564198i
$731$	−1.55083e14			−0.742980
$732$		−	1.00717e15i		−	4.79235i
$733$	1.29972e14	+	1.29972e14i	0.614227	+	0.614227i	0.944045	−	0.329818i	$-0.106987\pi$
$733$	1.29972e14	+	1.29972e14i	0.614227	+	0.614227i	−0.329818	+	0.944045i	$0.606987\pi$
$734$	−3.45045e14	−	3.45045e14i	−1.61955	−	1.61955i
$735$	−6.54223e14	+	6.54223e14i	−3.04992	+	3.04992i
$736$	4.44740e11	−	4.44740e11i	0.00205929	−	0.00205929i
$737$	3.77311e13			0.173525
$738$			4.25394e14i			1.94316i
$739$	7.94465e13	−	7.94465e13i	0.360456	−	0.360456i	−0.503525	−	0.863981i	$-0.667964\pi$
$739$	7.94465e13	−	7.94465e13i	0.360456	−	0.360456i	0.863981	+	0.503525i	$0.167964\pi$
$740$			4.77641e13i			0.215250i
$741$	−1.53633e14	−	1.07372e14i	−0.687692	−	0.480619i
$742$	2.96693e14			1.31913
$743$	−1.55933e14	−	1.55933e14i	−0.688641	−	0.688641i	0.273290	−	0.961932i	$-0.411888\pi$
$743$	−1.55933e14	−	1.55933e14i	−0.688641	−	0.688641i	−0.961932	+	0.273290i	$0.911888\pi$
$744$	−2.17417e14			−0.953740
$745$		−	2.73861e14i		−	1.19330i
$746$	−1.91891e14	−	1.91891e14i	−0.830539	−	0.830539i
$747$	3.31198e14	+	3.31198e14i	1.42392	+	1.42392i
$748$	4.22938e13	−	4.22938e13i	0.180621	−	0.180621i
$749$	−3.66689e14	+	3.66689e14i	−1.55557	+	1.55557i
$750$	6.03300e14			2.54230
$751$			4.04683e14i			1.69401i	0.531588	+	0.847003i	$0.321596\pi$
$751$			4.04683e14i			1.69401i	−0.531588	+	0.847003i	$0.678404\pi$
$752$	1.02742e14	−	1.02742e14i	0.427228	−	0.427228i
$753$		−	7.15585e14i		−	2.95588i
$754$	−2.76976e14	−	1.93575e14i	−1.13654	−	0.794315i
$755$	3.09568e13			0.126189
$756$	−2.14373e14	−	2.14373e14i	−0.868084	−	0.868084i
$757$	2.40838e14			0.968827			0.484414	−	0.874839i	$-0.339033\pi$
$757$	2.40838e14			0.968827			0.484414	+	0.874839i	$0.339033\pi$
$758$			4.72340e14i			1.88759i
$759$	2.00866e12	+	2.00866e12i	0.00797438	+	0.00797438i
$760$	−1.83587e14	−	1.83587e14i	−0.724059	−	0.724059i
$761$	1.91707e14	−	1.91707e14i	0.751128	−	0.751128i	−0.223562	−	0.974690i	$-0.571769\pi$
$761$	1.91707e14	−	1.91707e14i	0.751128	−	0.751128i	0.974690	+	0.223562i	$0.0717686\pi$
$762$	4.16870e14	−	4.16870e14i	1.62265	−	1.62265i
$763$	−4.51562e13			−0.174620
$764$			1.79877e14i			0.691051i
$765$	1.18524e14	−	1.18524e14i	0.452377	−	0.452377i
$766$			4.99306e14i			1.89332i
$767$	−1.05253e14	+	1.50601e14i	−0.396514	+	0.567350i
$768$	−8.02714e14			−3.00438
$769$	−1.70241e14	−	1.70241e14i	−0.633043	−	0.633043i	0.315787	−	0.948830i	$-0.397732\pi$
$769$	−1.70241e14	−	1.70241e14i	−0.633043	−	0.633043i	−0.948830	+	0.315787i	$0.897732\pi$
$770$	2.27037e14			0.838772
$771$			5.57148e14i			2.04502i
$772$	−4.56410e14	−	4.56410e14i	−1.66444	−	1.66444i
$773$	−4.83418e13	−	4.83418e13i	−0.175156	−	0.175156i	0.614084	−	0.789240i	$-0.289525\pi$
$773$	−4.83418e13	−	4.83418e13i	−0.175156	−	0.175156i	−0.789240	+	0.614084i	$0.789525\pi$
$774$	5.87770e14	−	5.87770e14i	2.11594	−	2.11594i
$775$	2.24601e12	−	2.24601e12i	0.00803346	−	0.00803346i
$776$	8.40719e14			2.98774
$777$		−	8.64447e13i		−	0.305234i
$778$	−4.04876e14	+	4.04876e14i	−1.42044	+	1.42044i
$779$		−	1.49837e14i		−	0.522313i
$780$	−5.05749e14	+	7.23648e14i	−1.75171	+	2.50642i
$781$	−2.51767e13			−0.0866451
$782$	−5.89283e12	−	5.89283e12i	−0.0201507	−	0.0201507i
$783$	−7.23577e13			−0.245853
$784$			9.13979e14i			3.08572i
$785$	2.31443e14	+	2.31443e14i	0.776417	+	0.776417i
$786$	1.13138e13	+	1.13138e13i	0.0377134	+	0.0377134i
$787$	2.46494e14	−	2.46494e14i	0.816455	−	0.816455i	−0.169137	−	0.985592i	$-0.554098\pi$
$787$	2.46494e14	−	2.46494e14i	0.816455	−	0.816455i	0.985592	+	0.169137i	$0.0540981\pi$
$788$	−4.20040e14	+	4.20040e14i	−1.38248	+	1.38248i
$789$	−4.33995e14			−1.41938
$790$			3.01471e14i			0.979738i
$791$	5.41452e14	−	5.41452e14i	1.74855	−	1.74855i
$792$			1.62376e14i			0.521070i
$793$	4.91511e14	−	8.71159e13i	1.56735	−	0.277799i
$794$	2.81911e13			0.0893326
$795$	−1.30821e14	−	1.30821e14i	−0.411946	−	0.411946i
$796$	−5.06324e14			−1.58439
$797$		−	2.18337e14i		−	0.678948i	−0.940615	−	0.339474i	$-0.889751\pi$
$797$		−	2.18337e14i		−	0.678948i	0.940615	−	0.339474i	$-0.110249\pi$
$798$	6.56004e14	+	6.56004e14i	2.02718	+	2.02718i
$799$	−6.72147e13	−	6.72147e13i	−0.206410	−	0.206410i
$800$	−6.78950e11	+	6.78950e11i	−0.00207199	+	0.00207199i
$801$	−2.20699e14	+	2.20699e14i	−0.669327	+	0.669327i
$802$	5.07421e14			1.52931
$803$			3.64379e13i			0.109138i
$804$	5.13512e14	−	5.13512e14i	1.52852	−	1.52852i
$805$		−	2.11805e13i		−	0.0626552i
$806$	−3.71292e13	−	2.09484e14i	−0.109154	−	0.615852i
$807$	1.31963e14			0.385554
$808$	−5.40430e14	−	5.40430e14i	−1.56922	−	1.56922i
$809$	4.58568e14			1.32331			0.661654	−	0.749809i	$-0.269855\pi$
$809$	4.58568e14			1.32331			0.661654	+	0.749809i	$0.269855\pi$
$810$		−	4.61633e14i		−	1.32395i
$811$	−2.23869e14	−	2.23869e14i	−0.638101	−	0.638101i	0.311985	−	0.950087i	$-0.399006\pi$
$811$	−2.23869e14	−	2.23869e14i	−0.638101	−	0.638101i	−0.950087	+	0.311985i	$0.899006\pi$
$812$	7.91875e14	+	7.91875e14i	2.24324	+	2.24324i
$813$	−4.66404e14	+	4.66404e14i	−1.31313	+	1.31313i
$814$	−1.11119e13	+	1.11119e13i	−0.0310932	+	0.0310932i
$815$	3.03997e14			0.845438
$816$		−	3.02702e14i		−	0.836691i
$817$	−2.07031e14	+	2.07031e14i	−0.568754	+	0.568754i
$818$			9.57051e14i			2.61318i
$819$	5.00695e14	−	7.16418e14i	1.35879	−	1.94423i
$820$	−7.05766e14			−1.90367
$821$	−3.96999e13	−	3.96999e13i	−0.106432	−	0.106432i	0.651885	−	0.758318i	$-0.273978\pi$
$821$	−3.96999e13	−	3.96999e13i	−0.106432	−	0.106432i	−0.758318	+	0.651885i	$0.773978\pi$
$822$	−1.47120e15			−3.92023
$823$			1.18183e14i			0.313009i	0.987677	+	0.156505i	$0.0500226\pi$
$823$			1.18183e14i			0.313009i	−0.987677	+	0.156505i	$0.949977\pi$
$824$	−5.39378e13	−	5.39378e13i	−0.141990	−	0.141990i
$825$	−3.06646e12	−	3.06646e12i	−0.00802356	−	0.00802356i
$826$	6.43058e14	−	6.43058e14i	1.67244	−	1.67244i
$827$	2.17639e14	−	2.17639e14i	0.562611	−	0.562611i	−0.367437	−	0.930048i	$-0.619765\pi$
$827$	2.17639e14	−	2.17639e14i	0.562611	−	0.562611i	0.930048	+	0.367437i	$0.119765\pi$
$828$	2.99082e13			0.0768489
$829$		−	1.16292e14i		−	0.297015i	−0.988911	−	0.148507i	$-0.952553\pi$
$829$		−	1.16292e14i		−	0.297015i	0.988911	−	0.148507i	$-0.0474469\pi$
$830$	−8.20663e14	+	8.20663e14i	−2.08341	+	2.08341i
$831$			5.79104e14i			1.46134i
$832$	−6.38920e13	−	3.60481e14i	−0.160262	−	0.904202i
$833$	5.97931e14			1.49082
$834$	1.84017e14	+	1.84017e14i	0.456067	+	0.456067i
$835$	−2.37025e14			−0.583931
$836$		−	1.12922e14i		−	0.276532i
$837$	−3.22129e13	−	3.22129e13i	−0.0784156	−	0.0784156i
$838$	−6.18817e14	−	6.18817e14i	−1.49742	−	1.49742i
$839$	−5.72221e14	+	5.72221e14i	−1.37643	+	1.37643i	−0.525853	+	0.850575i	$0.676254\pi$
$839$	−5.72221e14	+	5.72221e14i	−1.37643	+	1.37643i	−0.850575	+	0.525853i	$0.823746\pi$
$840$	1.56502e15	−	1.56502e15i	3.74218	−	3.74218i
$841$	−1.53425e14			−0.364682
$842$		−	3.43011e14i		−	0.810489i
$843$	−2.75170e14	+	2.75170e14i	−0.646344	+	0.646344i
$844$		−	4.57952e14i		−	1.06932i
$845$	−3.96893e14	−	1.84218e14i	−0.921275	−	0.427611i
$846$	5.09493e14			1.17567
$847$	−5.70105e14	−	5.70105e14i	−1.30779	−	1.30779i
$848$	−1.82762e14			−0.416780
$849$			5.23270e14i			1.18628i
$850$	8.99612e12	+	8.99612e12i	0.0202750	+	0.0202750i
$851$	1.03664e12	+	1.03664e12i	0.00232262	+	0.00232262i
$852$	−3.42650e14	+	3.42650e14i	−0.763226	+	0.763226i
$853$	2.42886e13	−	2.42886e13i	0.0537845	−	0.0537845i	−0.679703	−	0.733487i	$-0.737891\pi$
$853$	2.42886e13	−	2.42886e13i	0.0537845	−	0.0537845i	0.733487	+	0.679703i	$0.237891\pi$
$854$	−2.47070e15			−5.43915
$855$		−	3.16452e14i		−	0.692592i
$856$	6.49830e14	−	6.49830e14i	1.41394	−	1.41394i
$857$			1.88792e14i			0.408393i	0.978930	+	0.204197i	$0.0654582\pi$
$857$			1.88792e14i			0.408393i	−0.978930	+	0.204197i	$0.934542\pi$
$858$	−2.86007e14	+	5.06922e13i	−0.615093	+	0.109020i
$859$	5.85568e14			1.25202			0.626011	−	0.779815i	$-0.284687\pi$
$859$	5.85568e14			1.25202			0.626011	+	0.779815i	$0.284687\pi$
$860$	9.75163e14	+	9.75163e14i	2.07293	+	2.07293i
$861$	1.27731e15			2.69949
$862$			1.61643e14i			0.339641i
$863$	−1.04587e13	−	1.04587e13i	−0.0218485	−	0.0218485i	0.696098	−	0.717947i	$-0.254918\pi$
$863$	−1.04587e13	−	1.04587e13i	−0.0218485	−	0.0218485i	−0.717947	+	0.696098i	$0.754918\pi$
$864$	9.73770e12	+	9.73770e12i	0.0202250	+	0.0202250i
$865$	6.45190e13	−	6.45190e13i	0.133231	−	0.133231i
$866$	1.12191e15	−	1.12191e15i	2.30339	−	2.30339i
$867$	5.29843e14			1.08156
$868$			7.05068e14i			1.43098i
$869$	−4.69594e13	+	4.69594e13i	−0.0947598	+	0.0947598i
$870$		−	1.04295e15i		−	2.09251i
$871$	2.95016e14	+	2.06183e14i	0.588511	+	0.411303i
$872$	8.00239e13			0.158722
$873$	7.24581e14	+	7.24581e14i	1.42895	+	1.42895i
$874$	−1.57335e13			−0.0308509
$875$		−	9.90927e14i		−	1.93197i
$876$	4.95913e14	+	4.95913e14i	0.961357	+	0.961357i
$877$	1.66818e14	+	1.66818e14i	0.321547	+	0.321547i	0.849360	−	0.527814i	$-0.176988\pi$
$877$	1.66818e14	+	1.66818e14i	0.321547	+	0.321547i	−0.527814	+	0.849360i	$0.676988\pi$
$878$	1.23067e14	−	1.23067e14i	0.235868	−	0.235868i
$879$	−6.13053e14	+	6.13053e14i	−1.16830	+	1.16830i
$880$	−1.39855e14			−0.265011
$881$			3.51848e14i			0.662942i	0.943465	+	0.331471i	$0.107545\pi$
$881$			3.51848e14i			0.662942i	−0.943465	+	0.331471i	$0.892455\pi$
$882$	−2.26618e15	+	2.26618e15i	−4.24573	+	4.24573i
$883$			4.93314e14i			0.919009i	0.888175	+	0.459505i	$0.151973\pi$
$883$			4.93314e14i			0.919009i	−0.888175	+	0.459505i	$0.848027\pi$
$884$	5.61808e14	−	9.95753e13i	1.04070	−	0.184455i
$885$	−5.67086e14			−1.04456
$886$	5.48388e14	+	5.48388e14i	1.00443	+	1.00443i
$887$	5.61718e14			1.02306			0.511529	−	0.859266i	$-0.329079\pi$
$887$	5.61718e14			1.02306			0.511529	+	0.859266i	$0.329079\pi$
$888$			1.53194e14i			0.277444i
$889$	−6.84713e14	−	6.84713e14i	−1.23310	−	1.23310i
$890$	−5.46863e14	−	5.46863e14i	−0.979329	−	0.979329i
$891$	7.19075e13	−	7.19075e13i	0.128052	−	0.128052i
$892$	−3.93324e14	+	3.93324e14i	−0.696509	+	0.696509i
$893$	−1.79459e14			−0.316015
$894$		−	1.73419e15i		−	3.03675i
$895$	4.24082e13	−	4.24082e13i	0.0738474	−	0.0738474i
$896$			1.91723e15i			3.31997i
$897$	4.72912e12	+	2.66819e13i	0.00814364	+	0.0459467i
$898$	1.06168e15			1.81808
$899$	1.18991e14	+	1.18991e14i	0.202636	+	0.202636i
$900$	−4.56584e13			−0.0773229
$901$			1.19564e14i			0.201362i
$902$	−1.64190e14	−	1.64190e14i	−0.274988	−	0.274988i
$903$	−1.76487e15	−	1.76487e15i	−2.93951	−	2.93951i
$904$	−9.59539e14	+	9.59539e14i	−1.58935	+	1.58935i
$905$	−3.43832e14	+	3.43832e14i	−0.566374	+	0.566374i
$906$	1.96031e14			0.321131
$907$			4.77987e14i			0.778717i	0.921086	+	0.389358i	$0.127303\pi$
$907$			4.77987e14i			0.778717i	−0.921086	+	0.389358i	$0.872697\pi$
$908$	1.47028e15	−	1.47028e15i	2.38216	−	2.38216i
$909$		−	9.31549e14i		−	1.50102i
$910$	1.77519e15	+	1.24065e15i	2.84470	+	1.98813i
$911$	−1.15629e15			−1.84279			−0.921393	−	0.388632i	$-0.872948\pi$
$911$	−1.15629e15			−1.84279			−0.921393	+	0.388632i	$0.872948\pi$
$912$	−4.04098e14	−	4.04098e14i	−0.640490	−	0.640490i
$913$	−2.55666e14			−0.403013
$914$			9.52439e14i			1.49316i
$915$	1.08941e15	+	1.08941e15i	1.69857	+	1.69857i
$916$	−1.10954e15	−	1.10954e15i	−1.72054	−	1.72054i
$917$	1.85831e13	−	1.85831e13i	0.0286596	−	0.0286596i
$918$	1.29025e14	−	1.29025e14i	0.197906	−	0.197906i
$919$	3.00060e14			0.457753			0.228876	−	0.973455i	$-0.426495\pi$
$919$	3.00060e14			0.457753			0.228876	+	0.973455i	$0.426495\pi$
$920$			3.75352e13i			0.0569508i
$921$	−5.06893e14	+	5.06893e14i	−0.764924	+	0.764924i
$922$		−	1.67888e15i		−	2.51979i
$923$	−1.96854e14	−	1.37579e14i	−0.293857	−	0.205373i
$924$	9.62624e14			1.42921
$925$	−1.58255e12	−	1.58255e12i	−0.00233695	−	0.00233695i
$926$	−9.21671e14			−1.35370
$927$		−	9.29736e13i		−	0.135819i
$928$	−3.59701e13	−	3.59701e13i	−0.0522639	−	0.0522639i
$929$	5.86713e14	+	5.86713e14i	0.847905	+	0.847905i	0.989871	−	0.141966i	$-0.0453425\pi$
$929$	5.86713e14	+	5.86713e14i	0.847905	+	0.847905i	−0.141966	+	0.989871i	$0.545342\pi$
$930$	4.64310e14	−	4.64310e14i	0.667411	−	0.667411i
$931$	7.98219e14	−	7.98219e14i	1.14123	−	1.14123i
$932$	1.99412e14			0.283577
$933$		−	4.11069e14i		−	0.581443i
$934$	1.57975e15	−	1.57975e15i	2.22256	−	2.22256i
$935$			9.14940e13i			0.128037i
$936$	−8.87311e14	+	1.26960e15i	−1.23508	+	1.76721i
$937$	−3.20780e14			−0.444129			−0.222065	−	0.975032i	$-0.571280\pi$
$937$	−3.20780e14			−0.444129			−0.222065	+	0.975032i	$0.571280\pi$
$938$	−1.25970e15	−	1.25970e15i	−1.73481	−	1.73481i
$939$	−2.45192e12			−0.00335876
$940$			8.45294e14i			1.15178i
$941$	−1.24296e14	−	1.24296e14i	−0.168464	−	0.168464i	0.617840	−	0.786304i	$-0.288008\pi$
$941$	−1.24296e14	−	1.24296e14i	−0.168464	−	0.168464i	−0.786304	+	0.617840i	$0.788008\pi$
$942$	1.46558e15	+	1.46558e15i	1.97586	+	1.97586i
$943$	−1.53174e13	+	1.53174e13i	−0.0205412	+	0.0205412i
$944$	−3.96123e14	+	3.96123e14i	−0.528408	+	0.528408i
$945$	4.63753e14			0.615357
$946$			4.53725e14i			0.598876i
$947$	−7.37354e14	+	7.37354e14i	−0.968113	+	0.968113i	−0.999507	−	0.0313942i	$-0.990005\pi$
$947$	−7.37354e14	+	7.37354e14i	−0.968113	+	0.968113i	0.0313942	+	0.999507i	$0.490005\pi$
$948$			1.27822e15i			1.66941i
$949$	−1.99116e14	+	2.84905e14i	−0.258688	+	0.370142i
$950$	2.40190e13			0.0310411
$951$	−1.45595e15	−	1.45595e15i	−1.87173	−	1.87173i
$952$	−1.43036e15			−1.82920
$953$		−	3.95362e14i		−	0.502957i	−0.967863	−	0.251478i	$-0.919083\pi$
$953$		−	3.95362e14i		−	0.502957i	0.967863	−	0.251478i	$-0.0809168\pi$
$954$	−4.53153e14	−	4.53153e14i	−0.573460	−	0.573460i
$955$	−1.94564e14	−	1.94564e14i	−0.244932	−	0.244932i
$956$	7.97681e14	−	7.97681e14i	0.998941	−	0.998941i
$957$	1.62458e14	−	1.62458e14i	0.202386	−	0.202386i
$958$	1.09506e15			1.35709
$959$			2.41646e15i			2.97911i
$960$	7.98985e14	−	7.98985e14i	0.979902	−	0.979902i
$961$		−	7.13681e14i		−	0.870737i
$962$	−1.47604e14	+	2.61615e13i	−0.179152	+	0.0317531i
$963$	1.12012e15			1.35249
$964$	6.32961e14	+	6.32961e14i	0.760312	+	0.760312i
$965$	9.87349e14			1.17987
$966$		−	1.34123e14i		−	0.159448i
$967$	7.70380e14	+	7.70380e14i	0.911114	+	0.911114i	0.996360	−	0.0852457i	$-0.0271675\pi$
$967$	7.70380e14	+	7.70380e14i	0.911114	+	0.911114i	−0.0852457	+	0.996360i	$0.527168\pi$
$968$	1.01032e15	+	1.01032e15i	1.18872	+	1.18872i
$969$	−2.64363e14	+	2.64363e14i	−0.309444	+	0.309444i
$970$	−1.79541e15	+	1.79541e15i	−2.09077	+	2.09077i
$971$	−4.46025e14			−0.516729			−0.258365	−	0.966047i	$-0.583184\pi$
$971$	−4.46025e14			−0.516729			−0.258365	+	0.966047i	$0.583184\pi$
$972$		−	2.49957e15i		−	2.88093i
$973$	3.02251e14	−	3.02251e14i	0.346580	−	0.346580i
$974$		−	1.69487e15i		−	1.93348i
$975$	−7.21958e12	−	4.07331e13i	−0.00819387	−	0.0462301i
$976$	1.52195e15			1.71851
$977$	−5.45379e14	−	5.45379e14i	−0.612669	−	0.612669i	0.330972	−	0.943641i	$-0.392624\pi$
$977$	−5.45379e14	−	5.45379e14i	−0.612669	−	0.612669i	−0.943641	+	0.330972i	$0.892624\pi$
$978$	1.92503e15			2.15151
$979$		−	1.70367e14i		−	0.189440i
$980$	−3.75980e15	−	3.75980e15i	−4.15944	−	4.15944i
$981$	6.89693e13	+	6.89693e13i	0.0759121	+	0.0759121i
$982$	−1.81261e15	+	1.81261e15i	−1.98493	+	1.98493i
$983$	1.20317e15	−	1.20317e15i	1.31087	−	1.31087i	0.390102	−	0.920771i	$-0.372440\pi$
$983$	1.20317e15	−	1.20317e15i	1.31087	−	1.31087i	0.920771	−	0.390102i	$-0.127560\pi$
$984$	−2.26360e15			−2.45372
$985$		−	9.08670e14i		−	0.979997i
$986$	−4.76606e14	+	4.76606e14i	−0.511416	+	0.511416i
$987$		−	1.52983e15i		−	1.63327i
$988$	6.17065e14	−	8.82925e14i	0.655460	−	0.937862i
$989$	4.23284e13			0.0447353
$990$	−3.46766e14	−	3.46766e14i	−0.364636	−	0.364636i
$991$	7.49496e14			0.784153			0.392077	−	0.919933i	$-0.371757\pi$
$991$	7.49496e14			0.784153			0.392077	+	0.919933i	$0.371757\pi$
$992$		−	3.20270e13i		−	0.0333394i
$993$	−2.51348e14	−	2.51348e14i	−0.260333	−	0.260333i
$994$	8.40557e14	+	8.40557e14i	0.866234	+	0.866234i
$995$	5.47664e14	−	5.47664e14i	0.561563	−	0.561563i
$996$	−3.47956e15	+	3.47956e15i	−3.54999	+	3.54999i
$997$	−1.40277e15			−1.42401			−0.712003	−	0.702177i	$-0.752212\pi$
$997$	−1.40277e15			−1.42401			−0.712003	+	0.702177i	$0.752212\pi$
$998$			2.00233e15i			2.02248i
$999$	−2.26974e13	+	2.26974e13i	−0.0228112	+	0.0228112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.11.d.a.8.1	yes	20
13.5	odd	4	inner	13.11.d.a.5.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.11.d.a.5.1	✓	20	13.5	odd	4	inner
13.11.d.a.8.1	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+(-39.3633 - 39.3633i) q^{2} +361.049 q^{3} +2074.94i q^{4} +(-2244.35 - 2244.35i) q^{5} +(-14212.1 - 14212.1i) q^{6} +(-23343.5 + 23343.5i) q^{7} +(41368.4 - 41368.4i) q^{8} +71307.4 q^{9} +176690. i q^{10} +(-27522.6 + 27522.6i) q^{11} +749154. i q^{12} +(-365595. + 64798.4i) q^{13} +1.83775e6 q^{14} +(-810320. - 810320. i) q^{15} -1.13205e6 q^{16} +740598. i q^{17} +(-2.80689e6 - 2.80689e6i) q^{18} +(988674. + 988674. i) q^{19} +(4.65689e6 - 4.65689e6i) q^{20} +(-8.42815e6 + 8.42815e6i) q^{21} +2.16676e6 q^{22} -202139. i q^{23} +(1.49360e7 - 1.49360e7i) q^{24} +308590. i q^{25} +(1.69417e7 + 1.18403e7i) q^{26} +4.42588e6 q^{27} +(-4.84363e7 - 4.84363e7i) q^{28} -1.63488e7 q^{29} +6.37938e7i q^{30} +(-7.27830e6 - 7.27830e6i) q^{31} +(2.20017e6 + 2.20017e6i) q^{32} +(-9.93701e6 + 9.93701e6i) q^{33} +(2.91524e7 - 2.91524e7i) q^{34} +1.04782e8 q^{35} +1.47958e8i q^{36} +(-5.12833e6 + 5.12833e6i) q^{37} -7.78349e7i q^{38} +(-1.31998e8 + 2.33954e7i) q^{39} -1.85690e8 q^{40} +(-7.57766e7 - 7.57766e7i) q^{41} +6.63519e8 q^{42} +2.09402e8i q^{43} +(-5.71077e7 - 5.71077e7i) q^{44} +(-1.60039e8 - 1.60039e8i) q^{45} +(-7.95685e6 + 7.95685e6i) q^{46} +(-9.07574e7 + 9.07574e7i) q^{47} -4.08727e8 q^{48} -8.07363e8i q^{49} +(1.21471e7 - 1.21471e7i) q^{50} +2.67392e8i q^{51} +(-1.34453e8 - 7.58587e8i) q^{52} +1.61443e8 q^{53} +(-1.74217e8 - 1.74217e8i) q^{54} +1.23541e8 q^{55} +1.93137e9i q^{56} +(3.56960e8 + 3.56960e8i) q^{57} +(6.43542e8 + 6.43542e8i) q^{58} +(3.49915e8 - 3.49915e8i) q^{59} +(1.68136e9 - 1.68136e9i) q^{60} -1.34441e9 q^{61} +5.72996e8i q^{62} +(-1.66456e9 + 1.66456e9i) q^{63} +9.86011e8i q^{64} +(9.65953e8 + 6.75093e8i) q^{65} +7.82307e8 q^{66} +(-6.85456e8 - 6.85456e8i) q^{67} -1.53669e9 q^{68} -7.29821e7i q^{69} +(-4.12456e9 - 4.12456e9i) q^{70} +(4.57383e8 + 4.57383e8i) q^{71} +(2.94987e9 - 2.94987e9i) q^{72} +(6.61963e8 - 6.61963e8i) q^{73} +4.03736e8 q^{74} +1.11416e8i q^{75} +(-2.05144e9 + 2.05144e9i) q^{76} -1.28495e9i q^{77} +(6.11678e9 + 4.27494e9i) q^{78} +1.70621e9 q^{79} +(2.54073e9 + 2.54073e9i) q^{80} -2.61267e9 q^{81} +5.96564e9i q^{82} +(4.64465e9 + 4.64465e9i) q^{83} +(-1.74879e10 - 1.74879e10i) q^{84} +(1.66216e9 - 1.66216e9i) q^{85} +(8.24276e9 - 8.24276e9i) q^{86} -5.90271e9 q^{87} +2.27713e9i q^{88} +(-3.09504e9 + 3.09504e9i) q^{89} +1.25993e10i q^{90} +(7.02165e9 - 1.00469e10i) q^{91} +4.19426e8 q^{92} +(-2.62782e9 - 2.62782e9i) q^{93} +7.14502e9 q^{94} -4.43786e9i q^{95} +(7.94370e8 + 7.94370e8i) q^{96} +(1.01614e10 + 1.01614e10i) q^{97} +(-3.17805e10 + 3.17805e10i) q^{98} +(-1.96256e9 + 1.96256e9i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more