LMFDB - Embedded newform 6.29.b.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,29,Mod(5,6)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 29, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 29);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 29 $
Character orbit:	$[\chi]$	$=$	6.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$29.8010845489$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + \cdots + 25\!\cdots\!00 $ x^10 + 1705783760982651862x^8 + 928446040842895947812958762752087500x^6 + 192279697556936840917094366284139303458724287578125000x^4 + 13933851855624639308979728606211838856393321594391853802539062500000000x^2 + 258326581163817503228670067061734240671687781917458198380304371494262695312500000000000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{85}\cdot 3^{50}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.7
Root			$-9.36298e8i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.29.b.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11585.2i q^{2} +(-4.35859e6 + 1.96965e6i) q^{3} -1.34218e8 q^{4} -1.12356e10i q^{5} +(-2.28189e10 - 5.04953e10i) q^{6} -1.18961e12 q^{7} -1.55494e12i q^{8} +(1.51177e13 - 1.71698e13i) q^{9} +O(q^{10})$	\(q+11585.2i q^{2} +(-4.35859e6 + 1.96965e6i) q^{3} -1.34218e8 q^{4} -1.12356e10i q^{5} +(-2.28189e10 - 5.04953e10i) q^{6} -1.18961e12 q^{7} -1.55494e12i q^{8} +(1.51177e13 - 1.71698e13i) q^{9} +1.30167e14 q^{10} -7.26184e13i q^{11} +(5.84999e14 - 2.64362e14i) q^{12} +6.18816e13 q^{13} -1.37819e16i q^{14} +(2.21302e16 + 4.89712e16i) q^{15} +1.80144e16 q^{16} -1.78815e16i q^{17} +(1.98916e17 + 1.75143e17i) q^{18} -6.53439e17 q^{19} +1.50801e18i q^{20} +(5.18502e18 - 2.34312e18i) q^{21} +8.41301e17 q^{22} -4.84413e18i q^{23} +(3.06270e18 + 6.77736e18i) q^{24} -8.89854e19 q^{25} +7.16913e17i q^{26} +(-3.20736e19 + 1.04613e20i) q^{27} +1.59667e20 q^{28} +7.23820e19i q^{29} +(-5.67344e20 + 2.56383e20i) q^{30} +5.33611e20 q^{31} +2.08701e20i q^{32} +(1.43033e20 + 3.16513e20i) q^{33} +2.07161e20 q^{34} +1.33660e22i q^{35} +(-2.02907e21 + 2.30449e21i) q^{36} -1.51306e22 q^{37} -7.57025e21i q^{38} +(-2.69716e20 + 1.21885e20i) q^{39} -1.74707e22 q^{40} +1.91635e22i q^{41} +(2.71456e22 + 6.00697e22i) q^{42} +6.04146e22 q^{43} +9.74667e21i q^{44} +(-1.92912e23 - 1.69857e23i) q^{45} +5.61204e22 q^{46} +1.56986e23i q^{47} +(-7.85173e22 + 3.54821e22i) q^{48} +9.55188e23 q^{49} -1.03092e24i q^{50} +(3.52203e22 + 7.79380e22i) q^{51} -8.30560e21 q^{52} -2.41519e24i q^{53} +(-1.21196e24 - 3.71580e23i) q^{54} -8.15910e23 q^{55} +1.84978e24i q^{56} +(2.84807e24 - 1.28705e24i) q^{57} -8.38562e23 q^{58} +7.50433e24i q^{59} +(-2.97026e24 - 6.57281e24i) q^{60} +1.13291e25 q^{61} +6.18202e24i q^{62} +(-1.79842e25 + 2.04254e25i) q^{63} -2.41785e24 q^{64} -6.95275e23i q^{65} +(-3.66688e24 + 1.65707e24i) q^{66} +3.22479e25 q^{67} +2.40001e24i q^{68} +(9.54125e24 + 2.11136e25i) q^{69} -1.54848e26 q^{70} +9.01137e25i q^{71} +(-2.66980e25 - 2.35073e25i) q^{72} -3.71878e25 q^{73} -1.75292e26i q^{74} +(3.87851e26 - 1.75270e26i) q^{75} +8.77032e25 q^{76} +8.63876e25i q^{77} +(-1.41207e24 - 3.12472e24i) q^{78} +3.19573e26 q^{79} -2.02402e26i q^{80} +(-6.62549e25 - 5.19137e26i) q^{81} -2.22014e26 q^{82} -7.54394e25i q^{83} +(-6.95922e26 + 3.14488e26i) q^{84} -2.00909e26 q^{85} +6.99918e26i q^{86} +(-1.42567e26 - 3.15483e26i) q^{87} -1.12918e26 q^{88} +2.01092e27i q^{89} +(1.96783e27 - 2.23494e27i) q^{90} -7.36150e25 q^{91} +6.50169e26i q^{92} +(-2.32579e27 + 1.05103e27i) q^{93} -1.81872e27 q^{94} +7.34177e27i q^{95} +(-4.11068e26 - 9.09642e26i) q^{96} -6.38716e26 q^{97} +1.10661e28i q^{98} +(-1.24684e27 - 1.09783e27i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8805966 q^{3} - 1342177280 q^{4} - 105213788160 q^{6} - 640581497308 q^{7} + 27322446020490 q^{9}+O(q^{10}) $ 10 * q - 8805966 * q^3 - 1342177280 * q^4 - 105213788160 * q^6 - 640581497308 * q^7 + 27322446020490 * q^9	$ 10 q - 8805966 q^{3} - 1342177280 q^{4} - 105213788160 q^{6} - 640581497308 q^{7} + 27322446020490 q^{9} - 27967405817856 q^{10} + 11\!\cdots\!48 q^{12}+ \cdots - 23\!\cdots\!60 q^{99}+O(q^{100}) $ 10 * q - 8805966 * q^3 - 1342177280 * q^4 - 105213788160 * q^6 - 640581497308 * q^7 + 27322446020490 * q^9 - 27967405817856 * q^10 + 1181916749365248 * q^12 - 12482103411068620 * q^13 + 61319980558590048 * q^15 + 180143985094819840 * q^16 - 211642157524451328 * q^18 + 1498633795842086180 * q^19 - 2708280323934164940 * q^21 + 1023106116785405952 * q^22 + 14121555601108500480 * q^24 - 118736693316812330006 * q^25 - 129985199891557730478 * q^27 + 85977393167517876224 * q^28 - 714377425121915830272 * q^30 - 1023485060491138610140 * q^31 - 810380893747609058976 * q^33 - 3702565864316094382080 * q^34 - 3667156628272809246720 * q^36 - 15135414444725138913292 * q^37 - 90527454224201364861180 * q^39 + 3753721666926614151168 * q^40 - 83782317508213524529152 * q^42 + 197073485543953049687396 * q^43 - 353765338722291397174848 * q^45 + 360592317150577993973760 * q^46 - 158634180784949028716544 * q^48 + 3984185807056499345366430 * q^49 - 4562801433917127503049600 * q^51 + 1675319560494680228495360 * q^52 - 6215034612836859467857920 * q^54 + 16657974515766806205279552 * q^55 - 11868576742254344957945292 * q^57 + 6219704509741016298946560 * q^58 - 8230228471578127125970944 * q^60 + 26578327776203381143621940 * q^61 - 61528988659547989966678236 * q^63 - 24178516392292583494123520 * q^64 - 30776817485090369488158720 * q^66 - 16154878707937381443394972 * q^67 + 181226188204376873380361280 * q^69 - 257896094107734027347951616 * q^70 + 28406129531949961690742784 * q^72 - 331445702470743781613732140 * q^73 + 1054668864238007063534780178 * q^75 - 201143223181940653859799040 * q^76 + 415048527147123554842705920 * q^78 + 264192536445434377129602980 * q^79 + 1925492182685962075308092490 * q^81 - 1026212980364810668034752512 * q^82 + 363499231865547639824056320 * q^84 - 2969528244247922277988161792 * q^85 + 341427023984652036115514400 * q^87 - 137318978497839850435117056 * q^88 - 3202489169155688742678822912 * q^90 + 4475257581880995451850106760 * q^91 - 23261530114293985837100615628 * q^93 + 6585642783869668160671580160 * q^94 - 1895363108606457215912509440 * q^96 + 25466607638754754885505536724 * q^97 - 23060446172911946696379370560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$			11585.2i			0.707107i
$2$			11585.2i			0.707107i
$3$	−4.35859e6	+	1.96965e6i	−0.911272	+	0.411805i
$3$	−4.35859e6	+	1.96965e6i	−0.911272	+	0.411805i
$4$	−1.34218e8			−0.500000
$5$		−	1.12356e10i		−	1.84084i	−0.390934	−	0.920419i	$-0.627848\pi$
$5$		−	1.12356e10i		−	1.84084i	0.390934	−	0.920419i	$-0.372152\pi$
$6$	−2.28189e10	−	5.04953e10i	−0.291190	−	0.644367i
$7$	−1.18961e12			−1.75401			−0.877006	−	0.480480i	$-0.840463\pi$
$7$	−1.18961e12			−1.75401			−0.877006	+	0.480480i	$0.840463\pi$
$8$		−	1.55494e12i		−	0.353553i
$9$	1.51177e13	−	1.71698e13i	0.660833	−	0.750533i
$10$	1.30167e14			1.30167
$11$		−	7.26184e13i		−	0.191227i	−0.995419	−	0.0956135i	$-0.969519\pi$
$11$		−	7.26184e13i		−	0.191227i	0.995419	−	0.0956135i	$-0.0304813\pi$
$12$	5.84999e14	−	2.64362e14i	0.455636	−	0.205902i
$13$	6.18816e13			0.0157164			0.00785822	−	0.999969i	$-0.497499\pi$
$13$	6.18816e13			0.0157164			0.00785822	+	0.999969i	$0.497499\pi$
$14$		−	1.37819e16i		−	1.24027i
$15$	2.21302e16	+	4.89712e16i	0.758066	+	1.67750i
$16$	1.80144e16			0.250000
$17$		−	1.78815e16i		−	0.106199i	−0.998589	−	0.0530993i	$-0.983090\pi$
$17$		−	1.78815e16i		−	0.106199i	0.998589	−	0.0530993i	$-0.0169100\pi$
$18$	1.98916e17	+	1.75143e17i	0.530707	+	0.467280i
$19$	−6.53439e17			−0.817815			−0.408907	−	0.912576i	$-0.634090\pi$
$19$	−6.53439e17			−0.817815			−0.408907	+	0.912576i	$0.634090\pi$
$20$			1.50801e18i			0.920419i
$21$	5.18502e18	−	2.34312e18i	1.59838	−	0.722311i
$22$	8.41301e17			0.135218
$23$		−	4.84413e18i		−	0.417856i	−0.977931	−	0.208928i	$-0.933003\pi$
$23$		−	4.84413e18i		−	0.417856i	0.977931	−	0.208928i	$-0.0669974\pi$
$24$	3.06270e18	+	6.77736e18i	0.145595	+	0.322183i
$25$	−8.89854e19			−2.38868
$26$			7.16913e17i			0.0111132i
$27$	−3.20736e19	+	1.04613e20i	−0.293126	+	0.956074i
$28$	1.59667e20			0.877006
$29$			7.23820e19i			0.243253i	0.992576	+	0.121627i	$0.0388110\pi$
$29$			7.23820e19i			0.243253i	−0.992576	+	0.121627i	$0.961189\pi$
$30$	−5.67344e20	+	2.56383e20i	−1.18617	+	0.536034i
$31$	5.33611e20			0.704955			0.352478	−	0.935820i	$-0.385339\pi$
$31$	5.33611e20			0.704955			0.352478	+	0.935820i	$0.385339\pi$
$32$			2.08701e20i			0.176777i
$33$	1.43033e20	+	3.16513e20i	0.0787482	+	0.174260i
$34$	2.07161e20			0.0750937
$35$			1.33660e22i			3.22885i
$36$	−2.02907e21	+	2.30449e21i	−0.330417	+	0.375266i
$37$	−1.51306e22			−1.67893			−0.839464	−	0.543416i	$-0.817131\pi$
$37$	−1.51306e22			−1.67893			−0.839464	+	0.543416i	$0.817131\pi$
$38$		−	7.57025e21i		−	0.578282i
$39$	−2.69716e20	+	1.21885e20i	−0.0143220	+	0.00647211i
$40$	−1.74707e22			−0.650834
$41$			1.91635e22i			0.505245i	0.967565	+	0.252622i	$0.0812930\pi$
$41$			1.91635e22i			0.505245i	−0.967565	+	0.252622i	$0.918707\pi$
$42$	2.71456e22	+	6.00697e22i	0.510751	+	1.13023i
$43$	6.04146e22			0.817681			0.408840	−	0.912606i	$-0.365933\pi$
$43$	6.04146e22			0.817681			0.408840	+	0.912606i	$0.365933\pi$
$44$			9.74667e21i			0.0956135i
$45$	−1.92912e23	−	1.69857e23i	−1.38161	−	1.21649i
$46$	5.61204e22			0.295469
$47$			1.56986e23i			0.611632i	0.952091	+	0.305816i	$0.0989293\pi$
$47$			1.56986e23i			0.611632i	−0.952091	+	0.305816i	$0.901071\pi$
$48$	−7.85173e22	+	3.54821e22i	−0.227818	+	0.102951i
$49$	9.55188e23			2.07656
$50$		−	1.03092e24i		−	1.68905i
$51$	3.52203e22	+	7.79380e22i	0.0437331	+	0.0967758i
$52$	−8.30560e21			−0.00785822
$53$		−	2.41519e24i		−	1.75021i	−0.483937	−	0.875103i	$-0.660794\pi$
$53$		−	2.41519e24i		−	1.75021i	0.483937	−	0.875103i	$-0.339206\pi$
$54$	−1.21196e24	−	3.71580e23i	−0.676046	−	0.207271i
$55$	−8.15910e23			−0.352018
$56$			1.84978e24i			0.620137i
$57$	2.84807e24	−	1.28705e24i	0.745252	−	0.336780i
$58$	−8.38562e23			−0.172006
$59$			7.50433e24i			1.21167i	0.795591	+	0.605834i	$0.207161\pi$
$59$			7.50433e24i			1.21167i	−0.795591	+	0.605834i	$0.792839\pi$
$60$	−2.97026e24	−	6.57281e24i	−0.379033	−	0.838752i
$61$	1.13291e25			1.14704			0.573520	−	0.819191i	$-0.305577\pi$
$61$	1.13291e25			1.14704			0.573520	+	0.819191i	$0.305577\pi$
$62$			6.18202e24i			0.498478i
$63$	−1.79842e25	+	2.04254e25i	−1.15911	+	1.31644i
$64$	−2.41785e24			−0.125000
$65$		−	6.95275e23i		−	0.0289314i
$66$	−3.66688e24	+	1.65707e24i	−0.123220	+	0.0556834i
$67$	3.22479e25			0.877919			0.438960	−	0.898507i	$-0.355347\pi$
$67$	3.22479e25			0.877919			0.438960	+	0.898507i	$0.355347\pi$
$68$			2.40001e24i			0.0530993i
$69$	9.54125e24	+	2.11136e25i	0.172075	+	0.380780i
$70$	−1.54848e26			−2.28314
$71$			9.01137e25i			1.08937i	0.838642	+	0.544683i	$0.183350\pi$
$71$			9.01137e25i			1.08937i	−0.838642	+	0.544683i	$0.816650\pi$
$72$	−2.66980e25	−	2.35073e25i	−0.265353	−	0.233640i
$73$	−3.71878e25			−0.304705			−0.152353	−	0.988326i	$-0.548685\pi$
$73$	−3.71878e25			−0.304705			−0.152353	+	0.988326i	$0.548685\pi$
$74$		−	1.75292e26i		−	1.18718i
$75$	3.87851e26	−	1.75270e26i	2.17674	−	0.983672i
$76$	8.77032e25			0.408907
$77$			8.63876e25i			0.335414i
$78$	−1.41207e24	−	3.12472e24i	−0.00457647	−	0.0101272i
$79$	3.19573e26			0.866544			0.433272	−	0.901263i	$-0.357359\pi$
$79$	3.19573e26			0.866544			0.433272	+	0.901263i	$0.357359\pi$
$80$		−	2.02402e26i		−	0.460209i
$81$	−6.62549e25	−	5.19137e26i	−0.126598	−	0.991954i
$82$	−2.22014e26			−0.357262
$83$		−	7.54394e25i		−	0.102448i	−0.998687	−	0.0512242i	$-0.983688\pi$
$83$		−	7.54394e25i		−	0.102448i	0.998687	−	0.0512242i	$-0.0163123\pi$
$84$	−6.95922e26	+	3.14488e26i	−0.799191	+	0.361155i
$85$	−2.00909e26			−0.195494
$86$			6.99918e26i			0.578188i
$87$	−1.42567e26	−	3.15483e26i	−0.100173	−	0.221670i
$88$	−1.12918e26			−0.0676089
$89$			2.01092e27i			1.02786i	0.857832	+	0.513930i	$0.171811\pi$
$89$			2.01092e27i			1.02786i	−0.857832	+	0.513930i	$0.828189\pi$
$90$	1.96783e27	−	2.23494e27i	0.860186	−	0.976945i
$91$	−7.36150e25			−0.0275668
$92$			6.50169e26i			0.208928i
$93$	−2.32579e27	+	1.05103e27i	−0.642406	+	0.290304i
$94$	−1.81872e27			−0.432489
$95$			7.34177e27i			1.50546i
$96$	−4.11068e26	−	9.09642e26i	−0.0727975	−	0.161092i
$97$	−6.38716e26			−0.0978371			−0.0489185	−	0.998803i	$-0.515577\pi$
$97$	−6.38716e26			−0.0978371			−0.0489185	+	0.998803i	$0.515577\pi$
$98$			1.10661e28i			1.46835i
$99$	−1.24684e27	−	1.09783e27i	−0.143522	−	0.126369i
$100$	1.19434e28			1.19434
$101$		−	1.50287e28i		−	1.30744i	−0.756737	−	0.653720i	$-0.773207\pi$
$101$		−	1.50287e28i		−	1.30744i	0.756737	−	0.653720i	$-0.226793\pi$
$102$	−9.02930e26	+	4.08035e26i	−0.0684308	+	0.0309240i
$103$	−5.77006e27			−0.381469			−0.190734	−	0.981642i	$-0.561087\pi$
$103$	−5.77006e27			−0.381469			−0.190734	+	0.981642i	$0.561087\pi$
$104$		−	9.62224e25i		−	0.00555660i
$105$	−2.63263e28	−	5.82567e28i	−1.32966	−	2.94236i
$106$	2.79806e28			1.23758
$107$			3.90697e28i			1.51519i	0.652726	+	0.757594i	$0.273625\pi$
$107$			3.90697e28i			1.51519i	−0.652726	+	0.757594i	$0.726375\pi$
$108$	4.30484e27	−	1.40409e28i	0.146563	−	0.478037i
$109$	−5.36045e27			−0.160410			−0.0802048	−	0.996778i	$-0.525557\pi$
$109$	−5.36045e27			−0.160410			−0.0802048	+	0.996778i	$0.525557\pi$
$110$		−	9.45251e27i		−	0.248914i
$111$	6.59480e28	−	2.98020e28i	1.52996	−	0.691391i
$112$	−2.14301e28			−0.438503
$113$			4.13550e28i			0.747188i	0.927592	+	0.373594i	$0.121875\pi$
$113$			4.13550e28i			0.747188i	−0.927592	+	0.373594i	$0.878125\pi$
$114$	1.49107e28	+	3.29956e28i	0.238140	+	0.526973i
$115$	−5.44267e28			−0.769205
$116$		−	9.71495e27i		−	0.121627i
$117$	9.35510e26	−	1.06249e27i	0.0103860	−	0.0117957i
$118$	−8.69395e28			−0.856779
$119$			2.12720e28i			0.186273i
$120$	7.61476e28	−	3.44112e28i	0.593087	−	0.268017i
$121$	1.38937e29			0.963432
$122$			1.31251e29i			0.811080i
$123$	−3.77455e28	−	8.35259e28i	−0.208062	−	0.460415i
$124$	−7.16201e28			−0.352478
$125$			5.81245e29i			2.55634i
$126$	−2.36633e29	−	2.08352e29i	−0.930866	−	0.819614i
$127$	−2.33569e29			−0.822551			−0.411276	−	0.911511i	$-0.634917\pi$
$127$	−2.33569e29			−0.822551			−0.411276	+	0.911511i	$0.634917\pi$
$128$		−	2.80114e28i		−	0.0883883i
$129$	−2.63322e29	+	1.18996e29i	−0.745130	+	0.336725i
$130$	8.05493e27			0.0204576
$131$		−	7.14747e29i		−	1.63063i	−0.579021	−	0.815313i	$-0.696565\pi$
$131$		−	7.14747e29i		−	1.63063i	0.579021	−	0.815313i	$-0.303435\pi$
$132$	−1.91975e28	−	4.24817e28i	−0.0393741	−	0.0871299i
$133$	7.77339e29			1.43446
$134$			3.73600e29i			0.620783i
$135$	1.17538e30	+	3.60365e29i	1.75998	+	0.539597i
$136$	−2.78047e28			−0.0375469
$137$		−	5.49591e29i		−	0.669810i	−0.942252	−	0.334905i	$-0.891296\pi$
$137$		−	5.49591e29i		−	0.669810i	0.942252	−	0.334905i	$-0.108704\pi$
$138$	−2.44606e29	+	1.10538e29i	−0.269252	+	0.121675i
$139$	3.73371e29			0.371478			0.185739	−	0.982599i	$-0.440532\pi$
$139$	3.73371e29			0.371478			0.185739	+	0.982599i	$0.440532\pi$
$140$		−	1.79395e30i		−	1.61443i
$141$	−3.09207e29	−	6.84236e29i	−0.251873	−	0.557363i
$142$	−1.04399e30			−0.770298
$143$		−	4.49374e27i		−	0.00300541i
$144$	2.72337e29	−	3.09303e29i	0.165208	−	0.187633i
$145$	8.13254e29			0.447790
$146$		−	4.30829e29i		−	0.215459i
$147$	−4.16327e30	+	1.88139e30i	−1.89231	+	0.855136i
$148$	2.03079e30			0.839464
$149$		−	2.20879e29i		−	0.0830898i	−0.999137	−	0.0415449i	$-0.986772\pi$
$149$		−	2.20879e29i		−	0.0830898i	0.999137	−	0.0415449i	$-0.0132280\pi$
$150$	2.03055e30	+	4.49334e30i	0.695561	+	1.53919i
$151$	−1.58187e30			−0.493735			−0.246868	−	0.969049i	$-0.579401\pi$
$151$	−1.58187e30			−0.493735			−0.246868	+	0.969049i	$0.579401\pi$
$152$			1.01606e30i			0.289141i
$153$	−3.07021e29	−	2.70328e29i	−0.0797055	−	0.0701795i
$154$	−1.00082e30			−0.237174
$155$		−	5.99544e30i		−	1.29771i
$156$	3.62007e28	−	1.63591e28i	0.00716098	−	0.00323605i
$157$	−2.40704e30			−0.435400			−0.217700	−	0.976016i	$-0.569855\pi$
$157$	−2.40704e30			−0.435400			−0.217700	+	0.976016i	$0.569855\pi$
$158$			3.70233e30i			0.612739i
$159$	4.75708e30	+	1.05268e31i	0.720743	+	1.59491i
$160$	2.34488e30			0.325417
$161$			5.76263e30i			0.732924i
$162$	6.01432e30	−	7.67579e29i	0.701417	−	0.0895186i
$163$	−1.12567e31			−1.20444			−0.602218	−	0.798332i	$-0.705716\pi$
$163$	−1.12567e31			−1.20444			−0.602218	+	0.798332i	$0.705716\pi$
$164$		−	2.57209e30i		−	0.252622i
$165$	3.55621e30	−	1.60706e30i	0.320784	−	0.144963i
$166$	8.73983e29			0.0724419
$167$		−	1.74273e31i		−	1.32801i	−0.747729	−	0.664004i	$-0.768856\pi$
$167$		−	1.74273e31i		−	1.32801i	0.747729	−	0.664004i	$-0.231144\pi$
$168$	−3.64342e30	−	8.06242e30i	−0.255375	−	0.565113i
$169$	−1.54991e31			−0.999753
$170$		−	2.32758e30i		−	0.138235i
$171$	−9.87853e30	+	1.12194e31i	−0.540439	+	0.613797i
$172$	−8.10871e30			−0.408840
$173$		−	2.02028e31i		−	0.939218i	−0.882874	−	0.469609i	$-0.844395\pi$
$173$		−	2.02028e31i		−	0.939218i	0.882874	−	0.469609i	$-0.155605\pi$
$174$	3.65495e30	−	1.65167e30i	0.156744	−	0.0708329i
$175$	1.05858e32			4.18978
$176$		−	1.30818e30i		−	0.0478067i
$177$	−1.47809e31	−	3.27083e31i	−0.498971	−	1.10416i
$178$	−2.32969e31			−0.726806
$179$		−	2.01141e31i		−	0.580174i	−0.957000	−	0.290087i	$-0.906316\pi$
$179$		−	2.01141e31i		−	0.580174i	0.957000	−	0.290087i	$-0.0936843\pi$
$180$	2.58923e31	+	2.27978e31i	0.690804	+	0.608244i
$181$	−2.30163e31			−0.568245			−0.284122	−	0.958788i	$-0.591702\pi$
$181$	−2.30163e31			−0.568245			−0.284122	+	0.958788i	$0.591702\pi$
$182$		−	8.52847e29i		−	0.0194927i
$183$	−4.93790e31	+	2.23144e31i	−1.04527	+	0.472357i
$184$	−7.53236e30			−0.147734
$185$			1.70001e32i			3.09063i
$186$	−1.21764e31	−	2.69448e31i	−0.205276	−	0.454250i
$187$	−1.29852e30			−0.0203080
$188$		−	2.10703e31i		−	0.305816i
$189$	3.81551e31	−	1.24448e32i	0.514146	−	1.67696i
$190$	−8.50562e31			−1.06452
$191$			1.50815e32i			1.75379i	0.480682	+	0.876895i	$0.340389\pi$
$191$			1.50815e32i			1.75379i	−0.480682	+	0.876895i	$0.659611\pi$
$192$	1.05384e31	−	4.76232e30i	0.113909	−	0.0514756i
$193$	1.17307e32			1.17902			0.589511	−	0.807760i	$-0.299320\pi$
$193$	1.17307e32			1.17902			0.589511	+	0.807760i	$0.299320\pi$
$194$		−	7.39968e30i		−	0.0691813i
$195$	1.36945e30	+	3.03042e30i	0.0119141	+	0.0263644i
$196$	−1.28203e32			−1.03828
$197$		−	8.64009e31i		−	0.651615i	−0.945436	−	0.325808i	$-0.894364\pi$
$197$		−	8.64009e31i		−	0.651615i	0.945436	−	0.325808i	$-0.105636\pi$
$198$	1.27186e31	−	1.44450e31i	0.0893565	−	0.101485i
$199$	−1.14537e32			−0.749902			−0.374951	−	0.927045i	$-0.622340\pi$
$199$	−1.14537e32			−0.749902			−0.374951	+	0.927045i	$0.622340\pi$
$200$			1.38367e32i			0.844527i
$201$	−1.40555e32	+	6.35171e31i	−0.800023	+	0.361531i
$202$	1.74111e32			0.924500
$203$		−	8.61064e31i		−	0.426669i
$204$	−4.72718e30	−	1.04607e31i	−0.0218665	−	0.0483879i
$205$	2.15313e32			0.930073
$206$		−	6.68475e31i		−	0.269739i
$207$	−8.31727e31	−	7.32324e31i	−0.313614	−	0.276133i
$208$	1.11476e30			0.00392911
$209$			4.74517e31i			0.156388i
$210$	6.74918e32	−	3.04996e32i	2.08056	−	0.940209i
$211$	1.97044e32			0.568342			0.284171	−	0.958774i	$-0.408282\pi$
$211$	1.97044e32			0.568342			0.284171	+	0.958774i	$0.408282\pi$
$212$			3.24161e32i			0.875103i
$213$	−1.77492e32	−	3.92768e32i	−0.448606	−	0.992709i
$214$	−4.52631e32			−1.07140
$215$		−	6.78794e32i		−	1.50522i
$216$	1.62667e32	+	4.98726e31i	0.338023	+	0.103636i
$217$	−6.34790e32			−1.23650
$218$		−	6.21021e31i		−	0.113427i
$219$	1.62086e32	−	7.32469e31i	0.277669	−	0.125479i
$220$	1.09510e32			0.176009
$221$		−	1.10653e30i		−	0.00166906i
$222$	3.45263e32	+	7.64023e32i	0.488887	+	1.08184i
$223$	1.54709e32			0.205706			0.102853	−	0.994697i	$-0.467203\pi$
$223$	1.54709e32			0.205706			0.102853	+	0.994697i	$0.467203\pi$
$224$		−	2.48273e32i		−	0.310068i
$225$	−1.34526e33	+	1.52786e33i	−1.57852	+	1.79278i
$226$	−4.79108e32			−0.528342
$227$			1.07480e33i			1.11421i	0.830442	+	0.557105i	$0.188088\pi$
$227$			1.07480e33i			1.11421i	−0.830442	+	0.557105i	$0.811912\pi$
$228$	−3.82262e32	+	1.72745e32i	−0.372626	+	0.168390i
$229$	1.15263e33			1.05680			0.528398	−	0.848997i	$-0.322793\pi$
$229$	1.15263e33			1.05680			0.528398	+	0.848997i	$0.322793\pi$
$230$		−	6.30546e32i		−	0.543910i
$231$	−1.70153e32	−	3.76528e32i	−0.138125	−	0.305654i
$232$	1.12550e32			0.0860030
$233$			1.22762e31i			0.00883241i	0.999990	+	0.00441621i	$0.00140573\pi$
$233$			1.22762e31i			0.00883241i	−0.999990	+	0.00441621i	$0.998594\pi$
$234$	1.23092e31	+	1.08381e31i	0.00834082	+	0.00734398i
$235$	1.76383e33			1.12592
$236$		−	1.00721e33i		−	0.605834i
$237$	−1.39289e33	+	6.29447e32i	−0.789658	+	0.356847i
$238$	−2.46441e32			−0.131715
$239$			1.04695e33i			0.527662i	0.964569	+	0.263831i	$0.0849861\pi$
$239$			1.04695e33i			0.527662i	−0.964569	+	0.263831i	$0.915014\pi$
$240$	3.98662e32	+	8.82188e32i	0.189517	+	0.419376i
$241$	4.90866e32			0.220153			0.110077	−	0.993923i	$-0.464890\pi$
$241$	4.90866e32			0.220153			0.110077	+	0.993923i	$0.464890\pi$
$242$			1.60961e33i			0.681249i
$243$	1.31130e33	+	2.13220e33i	0.523857	+	0.851806i
$244$	−1.52057e33			−0.573520
$245$		−	1.07321e34i		−	3.82260i
$246$	9.67668e32	−	4.37290e32i	0.325563	−	0.147122i
$247$	−4.04358e31			−0.0128531
$248$		−	8.29736e32i		−	0.249239i
$249$	1.48589e32	+	3.28809e32i	0.0421887	+	0.0933583i
$250$	−6.73386e33			−1.80761
$251$			3.88273e33i			0.985611i	0.870140	+	0.492805i	$0.164029\pi$
$251$			3.88273e33i			0.985611i	−0.870140	+	0.492805i	$0.835971\pi$
$252$	2.41380e33	−	2.74145e33i	0.579555	−	0.658221i
$253$	−3.51773e32			−0.0799053
$254$		−	2.70595e33i		−	0.581632i
$255$	8.75678e32	−	3.95720e32i	0.178148	−	0.0805055i
$256$	3.24519e32			0.0625000
$257$			1.26561e33i			0.230801i	0.993319	+	0.115400i	$0.0368151\pi$
$257$			1.26561e33i			0.230801i	−0.993319	+	0.115400i	$0.963185\pi$
$258$	−1.37859e33	−	3.05065e33i	−0.238100	−	0.526886i
$259$	1.79995e34			2.94486
$260$			9.33183e31i			0.0144657i
$261$	1.24278e33	+	1.09425e33i	0.182569	+	0.160750i
$262$	8.28051e33			1.15303
$263$			9.29154e33i			1.22661i	0.789845	+	0.613306i	$0.210161\pi$
$263$			9.29154e33i			1.22661i	−0.789845	+	0.613306i	$0.789839\pi$
$264$	4.92161e32	−	2.22408e32i	0.0616101	−	0.0278417i
$265$	−2.71361e34			−3.22185
$266$			9.00566e33i			1.01431i
$267$	−3.96080e33	−	8.76475e33i	−0.423278	−	0.936659i
$268$	−4.32824e33			−0.438960
$269$		−	5.33998e31i		−	0.00514053i	−0.999997	−	0.00257027i	$-0.999182\pi$
$269$		−	5.33998e31i		−	0.00514053i	0.999997	−	0.00257027i	$-0.000818142\pi$
$270$	−4.17491e33	+	1.36171e34i	−0.381553	+	1.24449i
$271$	−6.49866e32			−0.0563967			−0.0281983	−	0.999602i	$-0.508977\pi$
$271$	−6.49866e32			−0.0563967			−0.0281983	+	0.999602i	$0.508977\pi$
$272$		−	3.22124e32i		−	0.0265496i
$273$	3.20857e32	−	1.44996e32i	0.0251209	−	0.0113522i
$274$	6.36714e33			0.473627
$275$			6.46198e33i			0.456781i
$276$	−1.28060e33	−	2.83382e33i	−0.0860375	−	0.190390i
$277$	−1.45602e34			−0.929934			−0.464967	−	0.885328i	$-0.653934\pi$
$277$	−1.45602e34			−0.929934			−0.464967	+	0.885328i	$0.653934\pi$
$278$			4.32559e33i			0.262675i
$279$	8.06700e33	−	9.16199e33i	0.465858	−	0.529092i
$280$	2.07833e34			1.14157
$281$			2.36139e34i			1.23390i	0.787004	+	0.616948i	$0.211631\pi$
$281$			2.36139e34i			1.23390i	−0.787004	+	0.616948i	$0.788369\pi$
$282$	7.92704e33	−	3.58224e33i	0.394115	−	0.178101i
$283$	−1.69012e34			−0.799666			−0.399833	−	0.916588i	$-0.630932\pi$
$283$	−1.69012e34			−0.799666			−0.399833	+	0.916588i	$0.630932\pi$
$284$		−	1.20949e34i		−	0.544683i
$285$	−1.44607e34	−	3.19997e34i	−0.619958	−	1.37189i
$286$	5.20610e31			0.00212514
$287$		−	2.27972e34i		−	0.886205i
$288$	3.58335e33	+	3.15509e33i	0.132677	+	0.116820i
$289$	2.80313e34			0.988722
$290$			9.42174e33i			0.316635i
$291$	2.78390e33	−	1.25805e33i	0.0891562	−	0.0402898i
$292$	4.99126e33			0.152353
$293$			1.15438e34i			0.335894i	0.985796	+	0.167947i	$0.0537137\pi$
$293$			1.15438e34i			0.335894i	−0.985796	+	0.167947i	$0.946286\pi$
$294$	−2.17963e34	−	4.82325e34i	−0.604673	−	1.33806i
$295$	8.43155e34			2.23049
$296$			2.35272e34i			0.593591i
$297$	7.59680e33	+	2.32913e33i	0.182827	+	0.0560536i
$298$	2.55894e33			0.0587533
$299$		−	2.99762e32i		−	0.00656721i
$300$	−5.20564e34	+	2.35244e34i	−1.08837	+	0.491836i
$301$	−7.18699e34			−1.43422
$302$		−	1.83264e34i		−	0.349123i
$303$	2.96013e34	+	6.55038e34i	0.538410	+	1.19143i
$304$	−1.17713e34			−0.204454
$305$		−	1.27289e35i		−	2.11152i
$306$	3.13181e33	−	3.55691e33i	0.0496244	−	0.0563603i
$307$	−7.77942e34			−1.17763			−0.588816	−	0.808267i	$-0.700406\pi$
$307$	−7.77942e34			−1.17763			−0.588816	+	0.808267i	$0.700406\pi$
$308$		−	1.15948e34i		−	0.167707i
$309$	2.51493e34	−	1.13650e34i	0.347622	−	0.157091i
$310$	6.94585e34			0.917618
$311$			4.60627e34i			0.581707i	0.956768	+	0.290854i	$0.0939393\pi$
$311$			4.60627e34i			0.581707i	−0.956768	+	0.290854i	$0.906061\pi$
$312$	1.89524e32	+	4.19393e32i	0.00228824	+	0.00506358i
$313$	−1.01682e35			−1.17388			−0.586940	−	0.809630i	$-0.699668\pi$
$313$	−1.01682e35			−1.17388			−0.586940	+	0.809630i	$0.699668\pi$
$314$		−	2.78861e34i		−	0.307874i
$315$	2.29491e35	+	2.02063e35i	2.42336	+	2.13373i
$316$	−4.28924e34			−0.433272
$317$			1.77674e35i			1.71709i	0.512735	+	0.858547i	$0.328632\pi$
$317$			1.77674e35i			1.71709i	−0.512735	+	0.858547i	$0.671368\pi$
$318$	−1.21956e35	+	5.51119e34i	−1.12777	+	0.509643i
$319$	5.25626e33			0.0465166
$320$			2.71660e34i			0.230105i
$321$	−7.69536e34	−	1.70288e35i	−0.623962	−	1.38075i
$322$	−6.67615e34			−0.518255
$323$			1.16845e34i			0.0868507i
$324$	8.89259e33	+	6.96774e34i	0.0632992	+	0.495977i
$325$	−5.50656e33			−0.0375416
$326$		−	1.30411e35i		−	0.851664i
$327$	2.33640e34	−	1.05582e34i	0.146177	−	0.0660575i
$328$	2.97982e34			0.178631
$329$		−	1.86752e35i		−	1.07281i
$330$	1.86181e34	+	4.11996e34i	0.102504	+	0.226828i
$331$	3.00578e35			1.58622			0.793112	−	0.609076i	$-0.208459\pi$
$331$	3.00578e35			1.58622			0.793112	+	0.609076i	$0.208459\pi$
$332$			1.01253e34i			0.0512242i
$333$	−2.28741e35	+	2.59789e35i	−1.10949	+	1.26009i
$334$	2.01900e35			0.939043
$335$		−	3.62324e35i		−	1.61611i
$336$	9.34051e34	−	4.22099e34i	0.399595	−	0.180578i
$337$	7.94950e34			0.326228			0.163114	−	0.986607i	$-0.447846\pi$
$337$	7.94950e34			0.326228			0.163114	+	0.986607i	$0.447846\pi$
$338$		−	1.79561e35i		−	0.706932i
$339$	−8.14549e34	−	1.80249e35i	−0.307696	−	0.680891i
$340$	2.69655e34			0.0977471
$341$		−	3.87500e34i		−	0.134806i
$342$	−1.29980e35	−	1.14445e35i	−0.434020	−	0.382148i
$343$	−5.89098e35			−1.88829
$344$		−	9.39414e34i		−	0.289094i
$345$	2.37223e35	−	1.07201e35i	0.700955	−	0.316762i
$346$	2.34055e35			0.664128
$347$			1.09794e35i			0.299203i	0.988746	+	0.149601i	$0.0477990\pi$
$347$			1.09794e35i			0.299203i	−0.988746	+	0.149601i	$0.952201\pi$
$348$	1.91350e34	+	4.23434e34i	0.0500864	+	0.110835i
$349$	−5.32192e35			−1.33817			−0.669087	−	0.743184i	$-0.733315\pi$
$349$	−5.32192e35			−1.33817			−0.669087	+	0.743184i	$0.733315\pi$
$350$			1.22639e36i			2.96262i
$351$	−1.98476e33	+	6.47359e33i	−0.00460690	+	0.0150261i
$352$	1.51555e34			0.0338045
$353$		−	1.09696e35i		−	0.235150i	−0.993064	−	0.117575i	$-0.962488\pi$
$353$		−	1.09696e35i		−	0.235150i	0.993064	−	0.117575i	$-0.0375121\pi$
$354$	3.78933e35	−	1.71240e35i	0.780759	−	0.352826i
$355$	1.01248e36			2.00535
$356$		−	2.69900e35i		−	0.513930i
$357$	−4.18984e34	−	9.27159e34i	−0.0767083	−	0.169746i
$358$	2.33027e35			0.410245
$359$			1.82069e35i			0.308258i	0.988051	+	0.154129i	$0.0492572\pi$
$359$			1.82069e35i			0.308258i	−0.988051	+	0.154129i	$0.950743\pi$
$360$	−2.64118e35	+	2.99968e35i	−0.430093	+	0.488472i
$361$	−2.11429e35			−0.331179
$362$		−	2.66649e35i		−	0.401810i
$363$	−6.05567e35	+	2.73656e35i	−0.877949	+	0.396746i
$364$	9.88044e33			0.0137834
$365$			4.17826e35i			0.560913i
$366$	−2.58518e35	−	5.72067e35i	−0.334007	−	0.739115i
$367$	−8.45017e35			−1.05085			−0.525425	−	0.850840i	$-0.676094\pi$
$367$	−8.45017e35			−1.05085			−0.525425	+	0.850840i	$0.676094\pi$
$368$		−	8.72641e34i		−	0.104464i
$369$	3.29034e35	+	2.89710e35i	0.379203	+	0.333883i
$370$	−1.96950e36			−2.18541
$371$			2.87314e36i			3.06988i
$372$	3.12162e35	−	1.41067e35i	0.321203	−	0.145152i
$373$	1.83618e36			1.81967			0.909834	−	0.414973i	$-0.136209\pi$
$373$	1.83618e36			1.81967			0.909834	+	0.414973i	$0.136209\pi$
$374$		−	1.50437e34i		−	0.0143599i
$375$	−1.14485e36	−	2.53340e36i	−1.05271	−	2.32952i
$376$	2.44104e35			0.216245
$377$			4.47911e33i			0.00382307i
$378$	1.44176e36	+	4.42035e35i	1.18579	+	0.363556i
$379$	1.45479e35			0.115306			0.0576530	−	0.998337i	$-0.481638\pi$
$379$	1.45479e35			0.115306			0.0576530	+	0.998337i	$0.481638\pi$
$380$		−	9.85396e35i		−	0.752732i
$381$	1.01803e36	−	4.60049e35i	0.749568	−	0.338731i
$382$	−1.74723e36			−1.24012
$383$		−	1.90800e36i		−	1.30556i	−0.757549	−	0.652779i	$-0.773603\pi$
$383$		−	1.90800e36i		−	1.30556i	0.757549	−	0.652779i	$-0.226397\pi$
$384$	5.51726e34	+	1.22090e35i	0.0363988	+	0.0805458i
$385$	9.70615e35			0.617443
$386$			1.35903e36i			0.833695i
$387$	9.13333e35	−	1.03731e36i	0.540351	−	0.613696i
$388$	8.57270e34			0.0489185
$389$		−	4.28572e35i		−	0.235901i	−0.993020	−	0.117950i	$-0.962368\pi$
$389$		−	4.28572e35i		−	0.235901i	0.993020	−	0.117950i	$-0.0376323\pi$
$390$	−3.51081e34	+	1.58654e34i	−0.0186424	+	0.00842454i
$391$	−8.66203e34			−0.0443757
$392$		−	1.48526e36i		−	0.734174i
$393$	1.40780e36	+	3.11529e36i	0.671500	+	1.48594i
$394$	1.00098e36			0.460762
$395$		−	3.59059e36i		−	1.59517i
$396$	1.67348e35	+	1.47348e35i	0.0717610	+	0.0631846i
$397$	2.51529e36			1.04117			0.520585	−	0.853810i	$-0.325714\pi$
$397$	2.51529e36			1.04117			0.520585	+	0.853810i	$0.325714\pi$
$398$		−	1.32694e36i		−	0.530261i
$399$	−3.38810e36	+	1.53109e36i	−1.30718	+	0.590716i
$400$	−1.60302e36			−0.597171
$401$			4.03167e36i			1.45032i	0.688580	+	0.725160i	$0.258234\pi$
$401$			4.03167e36i			1.45032i	−0.688580	+	0.725160i	$0.741766\pi$
$402$	−7.35861e35	−	1.62837e36i	−0.255641	−	0.565702i
$403$	3.30207e34			0.0110794
$404$			2.01712e36i			0.653720i
$405$	−5.83280e36	+	7.44413e35i	−1.82603	+	0.233047i
$406$	9.97563e35			0.301700
$407$			1.09876e36i			0.321056i
$408$	1.21189e35	−	5.47655e34i	0.0342154	−	0.0154620i
$409$	−2.15348e36			−0.587508			−0.293754	−	0.955881i	$-0.594905\pi$
$409$	−2.15348e36			−0.587508			−0.293754	+	0.955881i	$0.594905\pi$
$410$			2.49446e36i			0.657661i
$411$	1.08250e36	+	2.39544e36i	0.275831	+	0.610379i
$412$	7.74444e35			0.190734
$413$		−	8.92724e36i		−	2.12528i
$414$	8.48415e35	−	9.63575e35i	0.195256	−	0.221759i
$415$	−8.47605e35			−0.188591
$416$			1.29147e34i			0.00277830i
$417$	−1.62737e36	+	7.35411e35i	−0.338518	+	0.152977i
$418$	−5.49739e35			−0.110583
$419$			4.28586e36i			0.833761i	0.908961	+	0.416880i	$0.136877\pi$
$419$			4.28586e36i			0.833761i	−0.908961	+	0.416880i	$0.863123\pi$
$420$	3.53346e36	+	7.81909e36i	0.664828	+	1.47118i
$421$	9.04826e36			1.64670			0.823352	−	0.567531i	$-0.192101\pi$
$421$	9.04826e36			1.64670			0.823352	+	0.567531i	$0.192101\pi$
$422$			2.28280e36i			0.401878i
$423$	2.69541e36	+	2.37327e36i	0.459050	+	0.404187i
$424$	−3.75549e36			−0.618791
$425$			1.59119e36i			0.253675i
$426$	4.55031e36	−	2.05629e36i	0.701951	−	0.317212i
$427$	−1.34773e37			−2.01192
$428$		−	5.24384e36i		−	0.757594i
$429$	8.85109e33	+	1.95863e34i	0.00123764	+	0.00273874i
$430$	7.86398e36			1.06435
$431$		−	1.32908e37i		−	1.74128i	−0.491921	−	0.870640i	$-0.663705\pi$
$431$		−	1.32908e37i		−	1.74128i	0.491921	−	0.870640i	$-0.336295\pi$
$432$	−5.77786e35	+	1.88453e36i	−0.0732815	+	0.239018i
$433$	−5.35638e36			−0.657720			−0.328860	−	0.944379i	$-0.606664\pi$
$433$	−5.35638e36			−0.657720			−0.328860	+	0.944379i	$0.606664\pi$
$434$		−	7.35419e36i		−	0.874337i
$435$	−3.54464e36	+	1.60183e36i	−0.408058	+	0.184402i
$436$	7.19468e35			0.0802048
$437$			3.16535e36i			0.341729i
$438$	8.48582e35	+	1.87781e36i	0.0887271	+	0.196342i
$439$	−5.76571e36			−0.583915			−0.291957	−	0.956431i	$-0.594307\pi$
$439$	−5.76571e36			−0.583915			−0.291957	+	0.956431i	$0.594307\pi$
$440$			1.26869e36i			0.124457i
$441$	1.44403e37	−	1.64004e37i	1.37226	−	1.55852i
$442$	1.28195e34			0.00118021
$443$		−	6.56591e36i		−	0.585656i	−0.956165	−	0.292828i	$-0.905404\pi$
$443$		−	6.56591e36i		−	0.585656i	0.956165	−	0.292828i	$-0.0945964\pi$
$444$	−8.85139e36	+	3.99995e36i	−0.764980	+	0.345695i
$445$	2.25938e37			1.89212
$446$			1.79234e36i			0.145456i
$447$	4.35055e35	+	9.62722e35i	0.0342168	+	0.0757174i
$448$	2.87630e36			0.219251
$449$			1.52957e37i			1.13011i	0.825054	+	0.565054i	$0.191145\pi$
$449$			1.52957e37i			1.13011i	−0.825054	+	0.565054i	$0.808855\pi$
$450$	−1.77006e37	−	1.55851e37i	−1.26769	−	1.11618i
$451$	1.39163e36			0.0966164
$452$		−	5.55057e36i		−	0.373594i
$453$	6.89472e36	−	3.11573e36i	0.449927	−	0.203323i
$454$	−1.24518e37			−0.787865
$455$			8.27107e35i			0.0507461i
$456$	−2.00129e36	−	4.42859e36i	−0.119070	−	0.263486i
$457$	−1.00425e37			−0.579447			−0.289724	−	0.957110i	$-0.593563\pi$
$457$	−1.00425e37			−0.579447			−0.289724	+	0.957110i	$0.593563\pi$
$458$			1.33534e37i			0.747268i
$459$	1.87063e36	+	5.73523e35i	0.101534	+	0.0311296i
$460$	7.30502e36			0.384602
$461$			3.68289e37i			1.88094i	0.339875	+	0.940471i	$0.389615\pi$
$461$			3.68289e37i			1.88094i	−0.339875	+	0.940471i	$0.610385\pi$
$462$	4.36217e36	−	1.97127e36i	0.216130	−	0.0976693i
$463$	−6.09514e36			−0.292988			−0.146494	−	0.989212i	$-0.546799\pi$
$463$	−6.09514e36			−0.292988			−0.146494	+	0.989212i	$0.546799\pi$
$464$			1.30392e36i			0.0608133i
$465$	1.18089e37	+	2.61316e37i	0.534402	+	1.18256i
$466$	−1.42222e35			−0.00624546
$467$			1.10412e37i			0.470521i	0.971932	+	0.235261i	$0.0755944\pi$
$467$			1.10412e37i			0.470521i	−0.971932	+	0.235261i	$0.924406\pi$
$468$	−1.25562e35	+	1.42605e35i	−0.00519298	+	0.00589785i
$469$	−3.83625e37			−1.53988
$470$			2.04344e37i			0.796143i
$471$	1.04913e37	−	4.74103e36i	0.396768	−	0.179300i
$472$	1.16688e37			0.428390
$473$		−	4.38721e36i		−	0.156363i
$474$	−7.29229e36	−	1.61369e37i	−0.252329	−	0.558372i
$475$	5.81466e37			1.95350
$476$		−	2.85508e36i		−	0.0931367i
$477$	−4.14683e37	−	3.65122e37i	−1.31359	−	1.15659i
$478$	−1.21292e37			−0.373113
$479$		−	2.37669e37i		−	0.710028i	−0.934861	−	0.355014i	$-0.884476\pi$
$479$		−	2.37669e37i		−	0.710028i	0.934861	−	0.355014i	$-0.115524\pi$
$480$	−1.02204e37	+	4.61859e36i	−0.296544	+	0.134008i
$481$	−9.36305e35			−0.0263868
$482$			5.68680e36i			0.155672i
$483$	−1.13504e37	−	2.51169e37i	−0.301822	−	0.667893i
$484$	−1.86477e37			−0.481716
$485$			7.17634e36i			0.180102i
$486$	−2.47021e37	+	1.51917e37i	−0.602318	+	0.370423i
$487$	−3.98700e37			−0.944585			−0.472293	−	0.881442i	$-0.656573\pi$
$487$	−3.98700e37			−0.944585			−0.472293	+	0.881442i	$0.656573\pi$
$488$		−	1.76162e37i		−	0.405540i
$489$	4.90632e37	−	2.21717e37i	1.09757	−	0.495992i
$490$	1.24334e38			2.70299
$491$			2.84077e37i			0.600199i	0.953908	+	0.300099i	$0.0970199\pi$
$491$			2.84077e37i			0.600199i	−0.953908	+	0.300099i	$0.902980\pi$
$492$	5.06611e36	+	1.12107e37i	0.104031	+	0.230208i
$493$	1.29430e36			0.0258331
$494$		−	4.68459e35i		−	0.00908854i
$495$	−1.23347e37	+	1.40090e37i	−0.232625	+	0.264201i
$496$	9.61269e36			0.176239
$497$		−	1.07200e38i		−	1.91076i
$498$	−3.80933e36	+	1.72144e36i	−0.0660143	+	0.0298319i
$499$	1.39450e37			0.234969			0.117484	−	0.993075i	$-0.462517\pi$
$499$	1.39450e37			0.234969			0.117484	+	0.993075i	$0.462517\pi$
$500$		−	7.80133e37i		−	1.27817i
$501$	3.43258e37	+	7.59586e37i	0.546880	+	1.21018i
$502$	−4.49824e37			−0.696932
$503$			8.78316e37i			1.32342i	0.749758	+	0.661712i	$0.230170\pi$
$503$			8.78316e37i			1.32342i	−0.749758	+	0.661712i	$0.769830\pi$
$504$	3.17603e37	+	2.79645e37i	0.465433	+	0.409807i
$505$	−1.68856e38			−2.40678
$506$		−	4.07538e36i		−	0.0565015i
$507$	6.75542e37	−	3.05278e37i	0.911047	−	0.411703i
$508$	3.13491e37			0.411276
$509$		−	1.24194e38i		−	1.58508i	−0.609818	−	0.792541i	$-0.708758\pi$
$509$		−	1.24194e38i		−	1.58508i	0.609818	−	0.792541i	$-0.291242\pi$
$510$	4.58451e36	+	1.01449e37i	0.0569260	+	0.125970i
$511$	4.42390e37			0.534457
$512$			3.75962e36i			0.0441942i
$513$	2.09581e37	−	6.83580e37i	0.239723	−	0.781891i
$514$	−1.46624e37			−0.163201
$515$			6.48300e37i			0.702222i
$516$	3.53425e37	−	1.59713e37i	0.372565	−	0.168362i
$517$	1.14001e37			0.116961
$518$			2.08529e38i			2.08233i
$519$	3.97925e37	+	8.80557e37i	0.386775	+	0.855884i
$520$	−1.08111e36			−0.0102288
$521$		−	8.71882e37i		−	0.803026i	−0.915853	−	0.401513i	$-0.868484\pi$
$521$		−	8.71882e37i		−	0.803026i	0.915853	−	0.401513i	$-0.131516\pi$
$522$	−1.26772e37	+	1.43979e37i	−0.113667	+	0.129096i
$523$	−1.39727e38			−1.21971			−0.609854	−	0.792513i	$-0.708772\pi$
$523$	−1.39727e38			−1.21971			−0.609854	+	0.792513i	$0.708772\pi$
$524$			9.59317e37i			0.815313i
$525$	−4.61391e38	+	2.08503e38i	−3.81803	+	1.72537i
$526$	−1.07645e38			−0.867346
$527$		−	9.54176e36i		−	0.0748652i
$528$	2.57665e36	+	5.70180e36i	0.0196870	+	0.0435649i
$529$	1.10928e38			0.825397
$530$		−	3.14378e38i		−	2.27819i
$531$	1.28848e38	+	1.13449e38i	0.909397	+	0.800711i
$532$	−1.04333e38			−0.717228
$533$			1.18587e36i			0.00794065i
$534$	1.01542e38	−	4.58868e37i	0.662318	−	0.299302i
$535$	4.38970e38			2.78922
$536$		−	5.01437e37i		−	0.310391i
$537$	3.96178e37	+	8.76691e37i	0.238919	+	0.528697i
$538$	6.18650e35			0.00363490
$539$		−	6.93642e37i		−	0.397094i
$540$	−1.57757e38	−	4.83674e37i	−0.879988	−	0.269799i
$541$	2.09262e38			1.13744			0.568720	−	0.822531i	$-0.307439\pi$
$541$	2.09262e38			1.13744			0.568720	+	0.822531i	$0.307439\pi$
$542$		−	7.52885e36i		−	0.0398785i
$543$	1.00319e38	−	4.53341e37i	0.517826	−	0.234006i
$544$	3.73188e36			0.0187734
$545$			6.02278e37i			0.295288i
$546$	1.67981e36	+	3.71721e36i	0.00802719	+	0.0177631i
$547$	2.73645e37			0.127457			0.0637286	−	0.997967i	$-0.479701\pi$
$547$	2.73645e37			0.127457			0.0637286	+	0.997967i	$0.479701\pi$
$548$			7.37648e37i			0.334905i
$549$	1.71271e38	−	1.94519e38i	0.758003	−	0.860892i
$550$	−7.48635e37			−0.322993
$551$		−	4.72972e37i		−	0.198936i
$552$	3.28304e37	−	1.48361e37i	0.134626	−	0.0608377i
$553$	−3.80168e38			−1.51993
$554$		−	1.68684e38i		−	0.657562i
$555$	−3.34843e38	−	7.40964e38i	−1.27274	−	2.81641i
$556$	−5.01130e37			−0.185739
$557$			3.61739e38i			1.30744i	0.756735	+	0.653722i	$0.226793\pi$
$557$			3.61739e38i			1.30744i	−0.756735	+	0.653722i	$0.773207\pi$
$558$	1.06144e38	+	9.34582e37i	0.374124	+	0.329411i
$559$	3.73855e36			0.0128510
$560$			2.40780e38i			0.807213i
$561$	5.65973e36	−	2.55764e36i	0.0185061	−	0.00836294i
$562$	−2.73572e38			−0.872497
$563$		−	8.51518e37i		−	0.264897i	−0.991190	−	0.132448i	$-0.957716\pi$
$563$		−	8.51518e37i		−	0.264897i	0.991190	−	0.132448i	$-0.0422839\pi$
$564$	4.15011e37	+	9.18366e37i	0.125937	+	0.278682i
$565$	4.64648e38			1.37545
$566$		−	1.95805e38i		−	0.565449i
$567$	7.88176e37	+	6.17571e38i	0.222055	+	1.73990i
$568$	1.40122e38			0.385149
$569$			1.42664e37i			0.0382598i	0.999817	+	0.0191299i	$0.00608961\pi$
$569$			1.42664e37i			0.0382598i	−0.999817	+	0.0191299i	$0.993910\pi$
$570$	3.70725e38	−	1.67531e38i	0.970071	−	0.438376i
$571$	−4.50557e38			−1.15039			−0.575194	−	0.818017i	$-0.695073\pi$
$571$	−4.50557e38			−1.15039			−0.575194	+	0.818017i	$0.695073\pi$
$572$			6.03139e35i			0.00150270i
$573$	−2.97053e38	−	6.57340e38i	−0.722219	−	1.59818i
$574$	2.64110e38			0.626642
$575$			4.31057e38i			0.998125i
$576$	−3.65525e37	+	4.15140e37i	−0.0826042	+	0.0938166i
$577$	3.41383e38			0.752976			0.376488	−	0.926422i	$-0.377132\pi$
$577$	3.41383e38			0.752976			0.376488	+	0.926422i	$0.377132\pi$
$578$			3.24750e38i			0.699132i
$579$	−5.11293e38	+	2.31054e38i	−1.07441	+	0.485527i
$580$	−1.09153e38			−0.223895
$581$			8.97435e37i			0.179696i
$582$	1.45748e37	+	3.22521e37i	0.0284892	+	0.0630429i
$583$	−1.75387e38			−0.334686
$584$			5.78249e37i			0.107730i
$585$	−1.19377e37	−	1.05110e37i	−0.0217140	−	0.0191189i
$586$	−1.33738e38			−0.237513
$587$			9.49435e37i			0.164639i	0.996606	+	0.0823194i	$0.0262327\pi$
$587$			9.49435e37i			0.164639i	−0.996606	+	0.0823194i	$0.973767\pi$
$588$	5.58785e38	−	2.52515e38i	0.946154	−	0.427568i
$589$	−3.48683e38			−0.576523
$590$			9.76816e38i			1.57719i
$591$	1.70180e38	+	3.76586e38i	0.268338	+	0.593799i
$592$	−2.72569e38			−0.419732
$593$			8.13998e38i			1.22422i	0.790775	+	0.612108i	$0.209678\pi$
$593$			8.13998e38i			1.22422i	−0.790775	+	0.612108i	$0.790322\pi$
$594$	−2.69835e37	+	8.80107e37i	−0.0396359	+	0.129278i
$595$	2.39003e38			0.342899
$596$			2.96459e37i			0.0415449i
$597$	4.99221e38	−	2.25599e38i	0.683364	−	0.308813i
$598$	3.47282e36			0.00464372
$599$		−	1.12165e39i		−	1.46514i	−0.680690	−	0.732571i	$-0.738320\pi$
$599$		−	1.12165e39i		−	1.46514i	0.680690	−	0.732571i	$-0.261680\pi$
$600$	−2.72535e38	−	6.03086e38i	−0.347780	−	0.769594i
$601$	−1.32774e39			−1.65528			−0.827641	−	0.561258i	$-0.810318\pi$
$601$	−1.32774e39			−1.65528			−0.827641	+	0.561258i	$0.810318\pi$
$602$		−	8.32630e38i		−	1.01415i
$603$	4.87516e38	−	5.53690e38i	0.580158	−	0.658907i
$604$	2.12315e38			0.246868
$605$		−	1.56103e39i		−	1.77352i
$606$	−7.58877e38	+	3.42938e38i	−0.842471	+	0.380714i
$607$	−3.04155e37			−0.0329953			−0.0164977	−	0.999864i	$-0.505252\pi$
$607$	−3.04155e37			−0.0329953			−0.0164977	+	0.999864i	$0.505252\pi$
$608$		−	1.36374e38i		−	0.144571i
$609$	1.69600e38	+	3.75302e38i	0.175704	+	0.388811i
$610$	1.47468e39			1.49307
$611$			9.71453e36i			0.00961268i
$612$	4.12077e37	+	3.62828e37i	0.0398527	+	0.0350898i
$613$	7.27558e38			0.687734			0.343867	−	0.939018i	$-0.388263\pi$
$613$	7.27558e38			0.687734			0.343867	+	0.939018i	$0.388263\pi$
$614$		−	9.01264e38i		−	0.832712i
$615$	−9.38462e38	+	4.24092e38i	−0.847550	+	0.383009i
$616$	1.34328e38			0.118587
$617$			1.26579e39i			1.09237i	0.837666	+	0.546183i	$0.183920\pi$
$617$			1.26579e39i			1.09237i	−0.837666	+	0.546183i	$0.816080\pi$
$618$	1.31666e38	+	2.91361e38i	0.111080	+	0.245806i
$619$	4.59321e38			0.378833			0.189416	−	0.981897i	$-0.439340\pi$
$619$	4.59321e38			0.378833			0.189416	+	0.981897i	$0.439340\pi$
$620$			8.04694e38i			0.648854i
$621$	5.06757e38	+	1.55369e38i	0.399501	+	0.122484i
$622$	−5.33648e38			−0.411329
$623$		−	2.39221e39i		−	1.80288i
$624$	−4.85877e36	+	2.19569e36i	−0.00358049	+	0.00161803i
$625$	3.21566e39			2.31713
$626$		−	1.17801e39i		−	0.830059i
$627$	−9.34633e37	−	2.06822e38i	−0.0644014	−	0.142512i
$628$	3.23067e38			0.217700
$629$			2.70557e38i			0.178300i
$630$	−2.34095e39	+	2.65871e39i	−1.50878	+	1.71357i
$631$	−1.16761e39			−0.736015			−0.368007	−	0.929823i	$-0.619960\pi$
$631$	−1.16761e39			−0.736015			−0.368007	+	0.929823i	$0.619960\pi$
$632$		−	4.96918e38i		−	0.306370i
$633$	−8.58834e38	+	3.88108e38i	−0.517914	+	0.234046i
$634$	−2.05839e39			−1.21417
$635$			2.62428e39i			1.51418i
$636$	−6.38484e38	−	1.41288e39i	−0.360372	−	0.797457i
$637$	5.91085e37			0.0326361
$638$			6.08951e37i			0.0328922i
$639$	1.54723e39	+	1.36232e39i	0.817605	+	0.719889i
$640$	−3.14724e38			−0.162709
$641$			1.11988e39i			0.566445i	0.959054	+	0.283223i	$0.0914035\pi$
$641$			1.11988e39i			0.566445i	−0.959054	+	0.283223i	$0.908596\pi$
$642$	1.97283e39	−	8.91525e38i	0.976337	−	0.441208i
$643$	−2.66712e39			−1.29149			−0.645743	−	0.763555i	$-0.723452\pi$
$643$	−2.66712e39			−1.29149			−0.645743	+	0.763555i	$0.723452\pi$
$644$		−	7.73448e38i		−	0.366462i
$645$	1.33699e39	+	2.95858e39i	0.619856	+	1.37166i
$646$	−1.35367e38			−0.0614127
$647$		−	2.20603e39i		−	0.979379i	−0.871897	−	0.489690i	$-0.837110\pi$
$647$		−	2.20603e39i		−	0.979379i	0.871897	−	0.489690i	$-0.162890\pi$
$648$	−8.07229e38	+	1.03023e38i	−0.350709	+	0.0447593i
$649$	5.44953e38			0.231704
$650$		−	6.37947e37i		−	0.0265459i
$651$	2.76679e39	−	1.25031e39i	1.12679	−	0.509197i
$652$	1.51084e39			0.602218
$653$		−	9.07740e38i		−	0.354142i	−0.984198	−	0.177071i	$-0.943338\pi$
$653$		−	9.07740e38i		−	0.354142i	0.984198	−	0.177071i	$-0.0566622\pi$
$654$	1.22319e38	+	2.70677e38i	0.0467097	+	0.103363i
$655$	−8.03060e39			−3.00172
$656$			3.45220e38i			0.126311i
$657$	−5.62195e38	+	6.38506e38i	−0.201359	+	0.228691i
$658$	2.16357e39			0.758591
$659$			3.87881e39i			1.33138i	0.746227	+	0.665691i	$0.231863\pi$
$659$			3.87881e39i			1.33138i	−0.746227	+	0.665691i	$0.768137\pi$
$660$	−4.77307e38	+	2.15696e38i	−0.160392	+	0.0724813i
$661$	1.29123e39			0.424797			0.212399	−	0.977183i	$-0.431872\pi$
$661$	1.29123e39			0.424797			0.212399	+	0.977183i	$0.431872\pi$
$662$			3.48226e39i			1.12163i
$663$	2.17948e36	+	4.82292e36i	0.000687328	+	0.00152097i
$664$	−1.17304e38			−0.0362209
$665$		−	8.73385e39i		−	2.64060i
$666$	−3.00972e39	−	2.65001e39i	−0.891018	−	0.784529i
$667$	3.50628e38			0.101645
$668$			2.33906e39i			0.664004i
$669$	−6.74311e38	+	3.04722e38i	−0.187454	+	0.0847107i
$670$	4.19761e39			1.14276
$671$		−	8.22703e38i		−	0.219345i
$672$	4.89011e38	+	1.08212e39i	0.127688	+	0.282557i
$673$	4.99566e39			1.27756			0.638781	−	0.769389i	$-0.279439\pi$
$673$	4.99566e39			1.27756			0.638781	+	0.769389i	$0.279439\pi$
$674$			9.20968e38i			0.230678i
$675$	2.85408e39	−	9.30900e39i	0.700185	−	2.28376i
$676$	2.08025e39			0.499876
$677$			6.54865e39i			1.54138i	0.637209	+	0.770691i	$0.280089\pi$
$677$			6.54865e39i			1.54138i	−0.637209	+	0.770691i	$0.719911\pi$
$678$	2.08823e39	−	9.43674e38i	0.481463	−	0.217574i
$679$	7.59824e38			0.171607
$680$			3.12402e38i			0.0691177i
$681$	−2.11699e39	−	4.68462e39i	−0.458837	−	1.01535i
$682$	4.48928e38			0.0953225
$683$			1.24017e39i			0.257983i	0.991646	+	0.128991i	$0.0411740\pi$
$683$			1.24017e39i			0.257983i	−0.991646	+	0.128991i	$0.958826\pi$
$684$	1.32587e39	−	1.50584e39i	0.270220	−	0.306898i
$685$	−6.17497e39			−1.23301
$686$		−	6.82484e39i		−	1.33523i
$687$	−5.02382e39	+	2.27027e39i	−0.963029	+	0.435194i
$688$	1.08833e39			0.204420
$689$		−	1.49456e38i		−	0.0275070i
$690$	1.24195e39	+	2.74829e39i	0.223985	+	0.495650i
$691$	−2.18575e39			−0.386286			−0.193143	−	0.981171i	$-0.561868\pi$
$691$	−2.18575e39			−0.386286			−0.193143	+	0.981171i	$0.561868\pi$
$692$			2.71158e39i			0.469609i
$693$	1.48326e39	+	1.30599e39i	0.251739	+	0.221653i
$694$	−1.27199e39			−0.211568
$695$		−	4.19504e39i		−	0.683832i
$696$	−4.90559e38	+	2.21684e38i	−0.0783721	+	0.0354165i
$697$	3.42672e38			0.0536562
$698$		−	6.16557e39i		−	0.946232i
$699$	−2.41797e37	−	5.35067e37i	−0.00363723	−	0.00804873i
$700$	−1.42080e40			−2.09489
$701$			1.04737e40i			1.51373i	0.653569	+	0.756867i	$0.273271\pi$
$701$			1.04737e40i			1.51373i	−0.653569	+	0.756867i	$0.726729\pi$
$702$	−7.49981e37	−	2.29939e37i	−0.0106250	−	0.00325757i
$703$	9.88693e39			1.37305
$704$			1.75580e38i			0.0239034i
$705$	−7.68779e39	+	3.47412e39i	−1.02602	+	0.463658i
$706$	1.27086e39			0.166276
$707$			1.78783e40i			2.29327i
$708$	1.98386e39	+	4.39003e39i	0.249486	+	0.552080i
$709$	1.73802e39			0.214292			0.107146	−	0.994243i	$-0.465829\pi$
$709$	1.73802e39			0.214292			0.107146	+	0.994243i	$0.465829\pi$
$710$			1.17298e40i			1.41799i
$711$	4.83122e39	−	5.48700e39i	0.572641	−	0.650370i
$712$	3.12686e39			0.363403
$713$		−	2.58488e39i		−	0.294569i
$714$	1.07414e39	−	4.85403e38i	0.120028	−	0.0542410i
$715$	−5.04898e37			−0.00553247
$716$			2.69967e39i			0.290087i
$717$	−2.06213e39	−	4.56322e39i	−0.217294	−	0.480843i
$718$	−2.10932e39			−0.217972
$719$		−	7.63464e39i		−	0.773721i	−0.922138	−	0.386860i	$-0.873559\pi$
$719$		−	7.63464e39i		−	0.773721i	0.922138	−	0.386860i	$-0.126441\pi$
$720$	−3.47520e39	−	3.05987e39i	−0.345402	−	0.304122i
$721$	6.86413e39			0.669101
$722$		−	2.44945e39i		−	0.234179i
$723$	−2.13948e39	+	9.66835e38i	−0.200619	+	0.0906601i
$724$	3.08920e39			0.284122
$725$		−	6.44094e39i		−	0.581055i
$726$	−3.17037e39	−	7.01563e39i	−0.280542	−	0.620804i
$727$	1.22865e40			1.06647			0.533233	−	0.845968i	$-0.320977\pi$
$727$	1.22865e40			1.06647			0.533233	+	0.845968i	$0.320977\pi$
$728$			1.14467e38i			0.00974635i
$729$	−9.91509e39	−	6.71060e39i	−0.828154	−	0.560500i
$730$	−4.84061e39			−0.396625
$731$		−	1.08030e39i		−	0.0868365i
$732$	6.62754e39	−	2.99499e39i	0.522633	−	0.236179i
$733$	−2.22752e40			−1.72332			−0.861660	−	0.507487i	$-0.830575\pi$
$733$	−2.22752e40			−1.72332			−0.861660	+	0.507487i	$0.830575\pi$
$734$		−	9.78972e39i		−	0.743063i
$735$	2.11385e40	+	4.67768e40i	1.57417	+	3.48343i
$736$	1.01098e39			0.0738672
$737$		−	2.34179e39i		−	0.167882i
$738$	−3.35635e39	+	3.81193e39i	−0.236091	+	0.268137i
$739$	2.27106e40			1.56749			0.783747	−	0.621080i	$-0.213306\pi$
$739$	2.27106e40			1.56749			0.783747	+	0.621080i	$0.213306\pi$
$740$		−	2.28172e40i		−	1.54532i
$741$	1.76243e38	−	7.96445e37i	0.0117127	−	0.00529299i
$742$	−3.32860e40			−2.17073
$743$		−	2.39598e40i		−	1.53334i	−0.642039	−	0.766672i	$-0.721911\pi$
$743$		−	2.39598e40i		−	1.53334i	0.642039	−	0.766672i	$-0.278089\pi$
$744$	1.63429e39	+	3.61648e39i	0.102638	+	0.227125i
$745$	−2.48171e39			−0.152955
$746$			2.12726e40i			1.28670i
$747$	−1.29528e39	−	1.14047e39i	−0.0768908	−	0.0677013i
$748$	1.74285e38			0.0101540
$749$		−	4.64777e40i		−	2.65766i
$750$	2.93501e40	−	1.32633e40i	1.64722	−	0.744381i

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 29 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+11585.2i q^{2} +(-4.35859e6 + 1.96965e6i) q^{3} -1.34218e8 q^{4} -1.12356e10i q^{5} +(-2.28189e10 - 5.04953e10i) q^{6} -1.18961e12 q^{7} -1.55494e12i q^{8} +(1.51177e13 - 1.71698e13i) q^{9} +O(q^{10})\)	\(q+11585.2i q^{2} +(-4.35859e6 + 1.96965e6i) q^{3} -1.34218e8 q^{4} -1.12356e10i q^{5} +(-2.28189e10 - 5.04953e10i) q^{6} -1.18961e12 q^{7} -1.55494e12i q^{8} +(1.51177e13 - 1.71698e13i) q^{9} +1.30167e14 q^{10} -7.26184e13i q^{11} +(5.84999e14 - 2.64362e14i) q^{12} +6.18816e13 q^{13} -1.37819e16i q^{14} +(2.21302e16 + 4.89712e16i) q^{15} +1.80144e16 q^{16} -1.78815e16i q^{17} +(1.98916e17 + 1.75143e17i) q^{18} -6.53439e17 q^{19} +1.50801e18i q^{20} +(5.18502e18 - 2.34312e18i) q^{21} +8.41301e17 q^{22} -4.84413e18i q^{23} +(3.06270e18 + 6.77736e18i) q^{24} -8.89854e19 q^{25} +7.16913e17i q^{26} +(-3.20736e19 + 1.04613e20i) q^{27} +1.59667e20 q^{28} +7.23820e19i q^{29} +(-5.67344e20 + 2.56383e20i) q^{30} +5.33611e20 q^{31} +2.08701e20i q^{32} +(1.43033e20 + 3.16513e20i) q^{33} +2.07161e20 q^{34} +1.33660e22i q^{35} +(-2.02907e21 + 2.30449e21i) q^{36} -1.51306e22 q^{37} -7.57025e21i q^{38} +(-2.69716e20 + 1.21885e20i) q^{39} -1.74707e22 q^{40} +1.91635e22i q^{41} +(2.71456e22 + 6.00697e22i) q^{42} +6.04146e22 q^{43} +9.74667e21i q^{44} +(-1.92912e23 - 1.69857e23i) q^{45} +5.61204e22 q^{46} +1.56986e23i q^{47} +(-7.85173e22 + 3.54821e22i) q^{48} +9.55188e23 q^{49} -1.03092e24i q^{50} +(3.52203e22 + 7.79380e22i) q^{51} -8.30560e21 q^{52} -2.41519e24i q^{53} +(-1.21196e24 - 3.71580e23i) q^{54} -8.15910e23 q^{55} +1.84978e24i q^{56} +(2.84807e24 - 1.28705e24i) q^{57} -8.38562e23 q^{58} +7.50433e24i q^{59} +(-2.97026e24 - 6.57281e24i) q^{60} +1.13291e25 q^{61} +6.18202e24i q^{62} +(-1.79842e25 + 2.04254e25i) q^{63} -2.41785e24 q^{64} -6.95275e23i q^{65} +(-3.66688e24 + 1.65707e24i) q^{66} +3.22479e25 q^{67} +2.40001e24i q^{68} +(9.54125e24 + 2.11136e25i) q^{69} -1.54848e26 q^{70} +9.01137e25i q^{71} +(-2.66980e25 - 2.35073e25i) q^{72} -3.71878e25 q^{73} -1.75292e26i q^{74} +(3.87851e26 - 1.75270e26i) q^{75} +8.77032e25 q^{76} +8.63876e25i q^{77} +(-1.41207e24 - 3.12472e24i) q^{78} +3.19573e26 q^{79} -2.02402e26i q^{80} +(-6.62549e25 - 5.19137e26i) q^{81} -2.22014e26 q^{82} -7.54394e25i q^{83} +(-6.95922e26 + 3.14488e26i) q^{84} -2.00909e26 q^{85} +6.99918e26i q^{86} +(-1.42567e26 - 3.15483e26i) q^{87} -1.12918e26 q^{88} +2.01092e27i q^{89} +(1.96783e27 - 2.23494e27i) q^{90} -7.36150e25 q^{91} +6.50169e26i q^{92} +(-2.32579e27 + 1.05103e27i) q^{93} -1.81872e27 q^{94} +7.34177e27i q^{95} +(-4.11068e26 - 9.09642e26i) q^{96} -6.38716e26 q^{97} +1.10661e28i q^{98} +(-1.24684e27 - 1.09783e27i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8805966 q^{3} - 1342177280 q^{4} - 105213788160 q^{6} - 640581497308 q^{7} + 27322446020490 q^{9}+O(q^{10}) \) 10 * q - 8805966 * q^3 - 1342177280 * q^4 - 105213788160 * q^6 - 640581497308 * q^7 + 27322446020490 * q^9	\( 10 q - 8805966 q^{3} - 1342177280 q^{4} - 105213788160 q^{6} - 640581497308 q^{7} + 27322446020490 q^{9} - 27967405817856 q^{10} + 11\!\cdots\!48 q^{12}+ \cdots - 23\!\cdots\!60 q^{99}+O(q^{100}) \) 10 * q - 8805966 * q^3 - 1342177280 * q^4 - 105213788160 * q^6 - 640581497308 * q^7 + 27322446020490 * q^9 - 27967405817856 * q^10 + 1181916749365248 * q^12 - 12482103411068620 * q^13 + 61319980558590048 * q^15 + 180143985094819840 * q^16 - 211642157524451328 * q^18 + 1498633795842086180 * q^19 - 2708280323934164940 * q^21 + 1023106116785405952 * q^22 + 14121555601108500480 * q^24 - 118736693316812330006 * q^25 - 129985199891557730478 * q^27 + 85977393167517876224 * q^28 - 714377425121915830272 * q^30 - 1023485060491138610140 * q^31 - 810380893747609058976 * q^33 - 3702565864316094382080 * q^34 - 3667156628272809246720 * q^36 - 15135414444725138913292 * q^37 - 90527454224201364861180 * q^39 + 3753721666926614151168 * q^40 - 83782317508213524529152 * q^42 + 197073485543953049687396 * q^43 - 353765338722291397174848 * q^45 + 360592317150577993973760 * q^46 - 158634180784949028716544 * q^48 + 3984185807056499345366430 * q^49 - 4562801433917127503049600 * q^51 + 1675319560494680228495360 * q^52 - 6215034612836859467857920 * q^54 + 16657974515766806205279552 * q^55 - 11868576742254344957945292 * q^57 + 6219704509741016298946560 * q^58 - 8230228471578127125970944 * q^60 + 26578327776203381143621940 * q^61 - 61528988659547989966678236 * q^63 - 24178516392292583494123520 * q^64 - 30776817485090369488158720 * q^66 - 16154878707937381443394972 * q^67 + 181226188204376873380361280 * q^69 - 257896094107734027347951616 * q^70 + 28406129531949961690742784 * q^72 - 331445702470743781613732140 * q^73 + 1054668864238007063534780178 * q^75 - 201143223181940653859799040 * q^76 + 415048527147123554842705920 * q^78 + 264192536445434377129602980 * q^79 + 1925492182685962075308092490 * q^81 - 1026212980364810668034752512 * q^82 + 363499231865547639824056320 * q^84 - 2969528244247922277988161792 * q^85 + 341427023984652036115514400 * q^87 - 137318978497839850435117056 * q^88 - 3202489169155688742678822912 * q^90 + 4475257581880995451850106760 * q^91 - 23261530114293985837100615628 * q^93 + 6585642783869668160671580160 * q^94 - 1895363108606457215912509440 * q^96 + 25466607638754754885505536724 * q^97 - 23060446172911946696379370560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more