LMFDB - Embedded newform 6.29.b.a.5.9

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			5.9
Root			$-3.05333e8i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.29.b.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11585.2i q^{2} +(1.23098e6 + 4.62185e6i) q^{3} -1.34218e8 q^{4} -3.66400e9i q^{5} +(-5.35452e10 + 1.42612e10i) q^{6} +1.09838e12 q^{7} -1.55494e12i q^{8} +(-1.98462e13 + 1.13788e13i) q^{9} +O(q^{10})$	\(q+11585.2i q^{2} +(1.23098e6 + 4.62185e6i) q^{3} -1.34218e8 q^{4} -3.66400e9i q^{5} +(-5.35452e10 + 1.42612e10i) q^{6} +1.09838e12 q^{7} -1.55494e12i q^{8} +(-1.98462e13 + 1.13788e13i) q^{9} +4.24483e13 q^{10} +7.13577e14i q^{11} +(-1.65220e14 - 6.20334e14i) q^{12} -5.47598e15 q^{13} +1.27250e16i q^{14} +(1.69344e16 - 4.51032e15i) q^{15} +1.80144e16 q^{16} +1.36813e17i q^{17} +(-1.31827e17 - 2.29922e17i) q^{18} -1.19960e17 q^{19} +4.91773e17i q^{20} +(1.35208e18 + 5.07653e18i) q^{21} -8.26696e18 q^{22} -9.88762e18i q^{23} +(7.18671e18 - 1.91411e18i) q^{24} +2.38280e19 q^{25} -6.34406e19i q^{26} +(-7.70215e19 - 7.77187e19i) q^{27} -1.47422e20 q^{28} +7.51680e19i q^{29} +(5.22531e19 + 1.96189e20i) q^{30} -5.84712e20 q^{31} +2.08701e20i q^{32} +(-3.29804e21 + 8.78401e20i) q^{33} -1.58501e21 q^{34} -4.02445e21i q^{35} +(2.66371e21 - 1.52724e21i) q^{36} -1.46417e22 q^{37} -1.38976e21i q^{38} +(-6.74084e21 - 2.53092e22i) q^{39} -5.69731e21 q^{40} +3.27052e22i q^{41} +(-5.88128e22 + 1.56642e22i) q^{42} -5.08348e21 q^{43} -9.57747e22i q^{44} +(4.16920e22 + 7.27162e22i) q^{45} +1.14550e23 q^{46} +4.16191e22i q^{47} +(2.21754e22 + 8.32598e22i) q^{48} +7.46446e23 q^{49} +2.76054e23i q^{50} +(-6.32328e23 + 1.68414e23i) q^{51} +7.34974e23 q^{52} +3.94998e23i q^{53} +(9.00390e23 - 8.92313e23i) q^{54} +2.61454e24 q^{55} -1.70792e24i q^{56} +(-1.47668e23 - 5.54435e23i) q^{57} -8.70839e23 q^{58} +3.88384e24i q^{59} +(-2.27290e24 + 6.05365e23i) q^{60} -3.03902e24 q^{61} -6.77403e24i q^{62} +(-2.17986e25 + 1.24983e25i) q^{63} -2.41785e24 q^{64} +2.00640e25i q^{65} +(-1.01765e25 - 3.82086e25i) q^{66} -4.60298e25 q^{67} -1.83627e25i q^{68} +(4.56991e25 - 1.21715e25i) q^{69} +4.66242e25 q^{70} -4.64902e25i q^{71} +(1.76935e25 + 3.08597e25i) q^{72} -9.93420e25 q^{73} -1.69628e26i q^{74} +(2.93319e25 + 1.10130e26i) q^{75} +1.61007e25 q^{76} +7.83776e26i q^{77} +(2.93213e26 - 7.80943e25i) q^{78} +4.12927e26 q^{79} -6.60047e25i q^{80} +(2.64392e26 - 4.51652e26i) q^{81} -3.78897e26 q^{82} +6.50901e25i q^{83} +(-1.81474e26 - 6.81361e26i) q^{84} +5.01282e26 q^{85} -5.88933e25i q^{86} +(-3.47415e26 + 9.25305e25i) q^{87} +1.10957e27 q^{88} +3.06844e25i q^{89} +(-8.42435e26 + 4.83012e26i) q^{90} -6.01469e27 q^{91} +1.32709e27i q^{92} +(-7.19771e26 - 2.70245e27i) q^{93} -4.82167e26 q^{94} +4.39531e26i q^{95} +(-9.64585e26 + 2.56908e26i) q^{96} +5.86519e27 q^{97} +8.64775e27i q^{98} +(-8.11967e27 - 1.41618e28i) 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
$3$	1.23098e6	+	4.62185e6i	0.257368	+	0.966313i
$3$	1.23098e6	+	4.62185e6i	0.257368	+	0.966313i
$4$	−1.34218e8			−0.500000
$5$		−	3.66400e9i		−	0.600309i	−0.953891	−	0.300154i	$-0.902962\pi$
$5$		−	3.66400e9i		−	0.600309i	0.953891	−	0.300154i	$-0.0970382\pi$
$6$	−5.35452e10	+	1.42612e10i	−0.683287	+	0.181987i
$7$	1.09838e12			1.61949			0.809746	−	0.586780i	$-0.199605\pi$
$7$	1.09838e12			1.61949			0.809746	+	0.586780i	$0.199605\pi$
$8$		−	1.55494e12i		−	0.353553i
$9$	−1.98462e13	+	1.13788e13i	−0.867523	+	0.497396i
$10$	4.24483e13			0.424483
$11$			7.13577e14i			1.87907i	0.342452	+	0.939535i	$0.388743\pi$
$11$			7.13577e14i			1.87907i	−0.342452	+	0.939535i	$0.611257\pi$
$12$	−1.65220e14	−	6.20334e14i	−0.128684	−	0.483157i
$13$	−5.47598e15			−1.39077			−0.695385	−	0.718638i	$-0.744766\pi$
$13$	−5.47598e15			−1.39077			−0.695385	+	0.718638i	$0.744766\pi$
$14$			1.27250e16i			1.14515i
$15$	1.69344e16	−	4.51032e15i	0.580087	−	0.154500i
$16$	1.80144e16			0.250000
$17$			1.36813e17i			0.812535i	0.913754	+	0.406267i	$0.133170\pi$
$17$			1.36813e17i			0.812535i	−0.913754	+	0.406267i	$0.866830\pi$
$18$	−1.31827e17	−	2.29922e17i	−0.351712	−	0.613432i
$19$	−1.19960e17			−0.150136			−0.0750679	−	0.997178i	$-0.523917\pi$
$19$	−1.19960e17			−0.150136			−0.0750679	+	0.997178i	$0.523917\pi$
$20$			4.91773e17i			0.300154i
$21$	1.35208e18	+	5.07653e18i	0.416806	+	1.56494i
$22$	−8.26696e18			−1.32870
$23$		−	9.88762e18i		−	0.852908i	−0.904509	−	0.426454i	$-0.859763\pi$
$23$		−	9.88762e18i		−	0.852908i	0.904509	−	0.426454i	$-0.140237\pi$
$24$	7.18671e18	−	1.91411e18i	0.341643	−	0.0909933i
$25$	2.38280e19			0.639629
$26$		−	6.34406e19i		−	0.983423i
$27$	−7.70215e19	−	7.77187e19i	−0.703914	−	0.710286i
$28$	−1.47422e20			−0.809746
$29$			7.51680e19i			0.252616i	0.991991	+	0.126308i	$0.0403128\pi$
$29$			7.51680e19i			0.252616i	−0.991991	+	0.126308i	$0.959687\pi$
$30$	5.22531e19	+	1.96189e20i	0.109248	+	0.410183i
$31$	−5.84712e20			−0.772465			−0.386232	−	0.922402i	$-0.626224\pi$
$31$	−5.84712e20			−0.772465			−0.386232	+	0.922402i	$0.626224\pi$
$32$			2.08701e20i			0.176777i
$33$	−3.29804e21	+	8.78401e20i	−1.81577	+	0.483613i
$34$	−1.58501e21			−0.574549
$35$		−	4.02445e21i		−	0.972196i
$36$	2.66371e21	−	1.52724e21i	0.433762	−	0.248698i
$37$	−1.46417e22			−1.62468			−0.812341	−	0.583183i	$-0.801807\pi$
$37$	−1.46417e22			−1.62468			−0.812341	+	0.583183i	$0.801807\pi$
$38$		−	1.38976e21i		−	0.106162i
$39$	−6.74084e21	−	2.53092e22i	−0.357940	−	1.34392i
$40$	−5.69731e21			−0.212241
$41$			3.27052e22i			0.862269i	0.902288	+	0.431134i	$0.141887\pi$
$41$			3.27052e22i			0.862269i	−0.902288	+	0.431134i	$0.858113\pi$
$42$	−5.88128e22	+	1.56642e22i	−1.10658	+	0.294726i
$43$	−5.08348e21			−0.0688023			−0.0344011	−	0.999408i	$-0.510952\pi$
$43$	−5.08348e21			−0.0688023			−0.0344011	+	0.999408i	$0.510952\pi$
$44$		−	9.57747e22i		−	0.939535i
$45$	4.16920e22	+	7.27162e22i	0.298592	+	0.520782i
$46$	1.14550e23			0.603097
$47$			4.16191e22i			0.162152i	0.996708	+	0.0810760i	$0.0258357\pi$
$47$			4.16191e22i			0.162152i	−0.996708	+	0.0810760i	$0.974164\pi$
$48$	2.21754e22	+	8.32598e22i	0.0643420	+	0.241578i
$49$	7.46446e23			1.62276
$50$			2.76054e23i			0.452286i
$51$	−6.32328e23	+	1.68414e23i	−0.785163	+	0.209121i
$52$	7.34974e23			0.695385
$53$			3.94998e23i			0.286241i	0.989705	+	0.143121i	$0.0457137\pi$
$53$			3.94998e23i			0.286241i	−0.989705	+	0.143121i	$0.954286\pi$
$54$	9.00390e23	−	8.92313e23i	0.502248	−	0.497742i
$55$	2.61454e24			1.12802
$56$		−	1.70792e24i		−	0.572577i
$57$	−1.47668e23	−	5.54435e23i	−0.0386402	−	0.145078i
$58$	−8.70839e23			−0.178626
$59$			3.88384e24i			0.627095i	0.949573	+	0.313547i	$0.101517\pi$
$59$			3.88384e24i			0.627095i	−0.949573	+	0.313547i	$0.898483\pi$
$60$	−2.27290e24	+	6.05365e23i	−0.290043	+	0.0772502i
$61$	−3.03902e24			−0.307692			−0.153846	−	0.988095i	$-0.549166\pi$
$61$	−3.03902e24			−0.307692			−0.153846	+	0.988095i	$0.549166\pi$
$62$		−	6.77403e24i		−	0.546215i
$63$	−2.17986e25	+	1.24983e25i	−1.40495	+	0.805530i
$64$	−2.41785e24			−0.125000
$65$			2.00640e25i			0.834891i
$66$	−1.01765e25	−	3.82086e25i	−0.341966	−	1.28394i
$67$	−4.60298e25			−1.25312			−0.626559	−	0.779374i	$-0.715537\pi$
$67$	−4.60298e25			−1.25312			−0.626559	+	0.779374i	$0.715537\pi$
$68$		−	1.83627e25i		−	0.406267i
$69$	4.56991e25	−	1.21715e25i	0.824177	−	0.219511i
$70$	4.66242e25			0.687446
$71$		−	4.64902e25i		−	0.562011i	−0.959706	−	0.281005i	$-0.909332\pi$
$71$		−	4.64902e25i		−	0.562011i	0.959706	−	0.281005i	$-0.0906679\pi$
$72$	1.76935e25	+	3.08597e25i	0.175856	+	0.306716i
$73$	−9.93420e25			−0.813978			−0.406989	−	0.913433i	$-0.633421\pi$
$73$	−9.93420e25			−0.813978			−0.406989	+	0.913433i	$0.633421\pi$
$74$		−	1.69628e26i		−	1.14882i
$75$	2.93319e25	+	1.10130e26i	0.164620	+	0.618082i
$76$	1.61007e25			0.0750679
$77$			7.83776e26i			3.04314i
$78$	2.93213e26	−	7.80943e25i	0.950294	−	0.253102i
$79$	4.12927e26			1.11968			0.559840	−	0.828601i	$-0.310863\pi$
$79$	4.12927e26			1.11968			0.559840	+	0.828601i	$0.310863\pi$
$80$		−	6.60047e25i		−	0.150077i
$81$	2.64392e26	−	4.51652e26i	0.505194	−	0.863006i
$82$	−3.78897e26			−0.609716
$83$			6.50901e25i			0.0883938i	0.999023	+	0.0441969i	$0.0140729\pi$
$83$			6.50901e25i			0.0883938i	−0.999023	+	0.0441969i	$0.985927\pi$
$84$	−1.81474e26	−	6.81361e26i	−0.208403	−	0.782469i
$85$	5.01282e26			0.487772
$86$		−	5.88933e25i		−	0.0486505i
$87$	−3.47415e26	+	9.25305e25i	−0.244106	+	0.0650153i
$88$	1.10957e27			0.664352
$89$			3.06844e25i			0.0156840i	0.999969	+	0.00784202i	$0.00249622\pi$
$89$			3.06844e25i			0.0156840i	−0.999969	+	0.00784202i	$0.997504\pi$
$90$	−8.42435e26	+	4.83012e26i	−0.368249	+	0.211136i
$91$	−6.01469e27			−2.25234
$92$			1.32709e27i			0.426454i
$93$	−7.19771e26	−	2.70245e27i	−0.198808	−	0.746443i
$94$	−4.82167e26			−0.114659
$95$			4.39531e26i			0.0901279i
$96$	−9.64585e26	+	2.56908e26i	−0.170822	+	0.0454967i
$97$	5.86519e27			0.898417			0.449209	−	0.893427i	$-0.351706\pi$
$97$	5.86519e27			0.898417			0.449209	+	0.893427i	$0.351706\pi$
$98$			8.64775e27i			1.14746i
$99$	−8.11967e27	−	1.41618e28i	−0.934643	−	1.63014i
$100$	−3.19815e27			−0.319815
$101$			8.58961e27i			0.747264i	0.927577	+	0.373632i	$0.121888\pi$
$101$			8.58961e27i			0.747264i	−0.927577	+	0.373632i	$0.878112\pi$
$102$	−1.95112e27	−	7.32567e27i	−0.147871	−	0.555194i
$103$	2.18592e28			1.44515			0.722576	−	0.691292i	$-0.242958\pi$
$103$	2.18592e28			1.44515			0.722576	+	0.691292i	$0.242958\pi$
$104$			8.51485e27i			0.491711i
$105$	1.86004e28	−	4.95403e27i	0.939446	−	0.250212i
$106$	−4.57614e27			−0.202403
$107$			1.45967e27i			0.0566086i	0.999599	+	0.0283043i	$0.00901075\pi$
$107$			1.45967e27i			0.0566086i	−0.999599	+	0.0283043i	$0.990989\pi$
$108$	1.03377e28	+	1.04312e28i	0.351957	+	0.355143i
$109$	1.80787e28			0.540998			0.270499	−	0.962720i	$-0.412811\pi$
$109$	1.80787e28			0.540998			0.270499	+	0.962720i	$0.412811\pi$
$110$			3.02901e28i			0.797633i
$111$	−1.80237e28	−	6.76719e28i	−0.418141	−	1.56995i
$112$	1.97866e28			0.404873
$113$			5.98855e28i			1.08199i	0.841026	+	0.540995i	$0.181952\pi$
$113$			5.98855e28i			1.08199i	−0.841026	+	0.540995i	$0.818048\pi$
$114$	6.42326e27	−	1.71077e27i	0.102586	−	0.0273227i
$115$	−3.62282e28			−0.512008
$116$		−	1.00889e28i		−	0.126308i
$117$	1.08677e29	−	6.23103e28i	1.20653	−	0.691764i
$118$	−4.49952e28			−0.443423
$119$			1.50272e29i			1.31589i
$120$	−7.01329e27	−	2.63321e28i	−0.0546241	−	0.205092i
$121$	−3.64982e29			−2.53091
$122$		−	3.52078e28i		−	0.217571i
$123$	−1.51158e29	+	4.02595e28i	−0.833222	+	0.221920i
$124$	7.84788e28			0.386232
$125$		−	2.23800e29i		−	0.984284i
$126$	−1.44795e29	−	2.52541e29i	−0.569596	−	0.993448i
$127$	4.38953e29			1.54584			0.772922	−	0.634501i	$-0.218794\pi$
$127$	4.38953e29			1.54584			0.772922	+	0.634501i	$0.218794\pi$
$128$		−	2.80114e28i		−	0.0883883i
$129$	−6.25768e27	−	2.34951e28i	−0.0177075	−	0.0664846i
$130$	−2.32446e29			−0.590357
$131$			5.48900e29i			1.25226i	0.779718	+	0.626131i	$0.215363\pi$
$131$			5.48900e29i			1.25226i	−0.779718	+	0.626131i	$0.784637\pi$
$132$	4.42656e29	−	1.17897e29i	0.907886	−	0.241806i
$133$	−1.31761e29			−0.243144
$134$		−	5.33266e29i		−	0.886088i
$135$	−2.84761e29	+	2.82206e29i	−0.426391	+	0.422566i
$136$	2.12736e29			0.287274
$137$			1.36787e30i			1.66708i	0.552456	+	0.833542i	$0.313691\pi$
$137$			1.36787e30i			1.66708i	−0.552456	+	0.833542i	$0.686309\pi$
$138$	1.41010e29	+	5.29435e29i	0.155218	+	0.582781i
$139$	1.29192e30			1.28537			0.642685	−	0.766130i	$-0.277820\pi$
$139$	1.29192e30			1.28537			0.642685	+	0.766130i	$0.277820\pi$
$140$			5.40152e29i			0.486098i
$141$	−1.92357e29	+	5.12324e28i	−0.156690	+	0.0417328i
$142$	5.38600e29			0.397402
$143$		−	3.90753e30i		−	2.61335i
$144$	−3.57516e29	+	2.04983e29i	−0.216881	+	0.124349i
$145$	2.75415e29			0.151648
$146$		−	1.15090e30i		−	0.575570i
$147$	9.18862e29	+	3.44996e30i	0.417645	+	1.56809i
$148$	1.96518e30			0.812341
$149$		−	2.43293e30i		−	0.915213i	−0.889155	−	0.457607i	$-0.848707\pi$
$149$		−	2.43293e30i		−	0.915213i	0.889155	−	0.457607i	$-0.151293\pi$
$150$	−1.27588e30	+	3.39817e29i	−0.437050	+	0.116404i
$151$	−2.42875e30			−0.758063			−0.379032	−	0.925384i	$-0.623743\pi$
$151$	−2.42875e30			−0.758063			−0.379032	+	0.925384i	$0.623743\pi$
$152$			1.86530e29i			0.0530810i
$153$	−1.55677e30	−	2.71521e30i	−0.404152	−	0.704893i
$154$	−9.08024e30			−2.15183
$155$			2.14238e30i			0.463717i
$156$	9.04741e29	+	3.39694e30i	0.178970	+	0.671960i
$157$	7.20044e29			0.130246			0.0651229	−	0.997877i	$-0.479256\pi$
$157$	7.20044e29			0.130246			0.0651229	+	0.997877i	$0.479256\pi$
$158$			4.78385e30i			0.791733i
$159$	−1.82562e30	+	4.86236e29i	−0.276599	+	0.0736694i
$160$	7.64680e29			0.106121
$161$		−	1.08603e31i		−	1.38128i
$162$	5.23250e30	+	3.06304e30i	0.610237	+	0.357226i
$163$	−6.07467e30			−0.649974			−0.324987	−	0.945718i	$-0.605360\pi$
$163$	−6.07467e30			−0.649974			−0.324987	+	0.945718i	$0.605360\pi$
$164$		−	4.38962e30i		−	0.431134i
$165$	3.21846e30	+	1.20840e31i	0.290317	+	1.09002i
$166$	−7.54084e29			−0.0625038
$167$		−	2.17069e31i		−	1.65412i	−0.562114	−	0.827060i	$-0.690012\pi$
$167$		−	2.17069e31i		−	1.65412i	0.562114	−	0.827060i	$-0.309988\pi$
$168$	7.89372e30	−	2.10242e30i	0.553289	−	0.147363i
$169$	1.44835e31			0.934240
$170$			5.80747e30i			0.344907i
$171$	2.38073e30	−	1.36500e30i	0.130246	−	0.0746770i
$172$	6.82293e29			0.0344011
$173$			1.83592e31i			0.853511i	0.904367	+	0.426756i	$0.140344\pi$
$173$			1.83592e31i			0.853511i	−0.904367	+	0.426756i	$0.859656\pi$
$174$	−1.07199e30	−	4.02488e30i	−0.0459727	−	0.172609i
$175$	2.61722e31			1.03587
$176$			1.28547e31i			0.469768i
$177$	−1.79505e31	+	4.78094e30i	−0.605970	+	0.161394i
$178$	−3.55486e29			−0.0110903
$179$			4.92795e31i			1.42143i	0.703482	+	0.710713i	$0.251627\pi$
$179$			4.92795e31i			1.42143i	−0.703482	+	0.710713i	$0.748373\pi$
$180$	−5.59580e30	−	9.75980e30i	−0.149296	−	0.260391i
$181$	3.63021e31			0.896256			0.448128	−	0.893969i	$-0.352091\pi$
$181$	3.63021e31			0.896256			0.448128	+	0.893969i	$0.352091\pi$
$182$		−	6.96817e31i		−	1.59265i
$183$	−3.74099e30	−	1.40459e31i	−0.0791901	−	0.297327i
$184$	−1.53747e31			−0.301549
$185$			5.36472e31i			0.975311i
$186$	3.13085e31	−	8.33872e30i	0.527815	−	0.140578i
$187$	−9.76265e31			−1.52681
$188$		−	5.58602e30i		−	0.0810760i
$189$	−8.45987e31	−	8.53645e31i	−1.13998	−	1.15030i
$190$	−5.09207e30			−0.0637300
$191$			7.96600e30i			0.0926346i	0.998927	+	0.0463173i	$0.0147485\pi$
$191$			7.96600e30i			0.0926346i	−0.998927	+	0.0463173i	$0.985251\pi$
$192$	−2.97634e30	−	1.11749e31i	−0.0321710	−	0.120789i
$193$	5.49449e31			0.552236			0.276118	−	0.961124i	$-0.410952\pi$
$193$	5.49449e31			0.552236			0.276118	+	0.961124i	$0.410952\pi$
$194$			6.79496e31i			0.635277i
$195$	−9.27326e31	+	2.46984e31i	−0.806767	+	0.214874i
$196$	−1.00186e32			−0.811378
$197$			6.19271e31i			0.467040i	0.972352	+	0.233520i	$0.0750244\pi$
$197$			6.19271e31i			0.467040i	−0.972352	+	0.233520i	$0.924976\pi$
$198$	1.64067e32	−	9.40683e31i	1.15268	−	0.660892i
$199$	6.34877e31			0.415668			0.207834	−	0.978164i	$-0.433359\pi$
$199$	6.34877e31			0.415668			0.207834	+	0.978164i	$0.433359\pi$
$200$		−	3.70513e31i		−	0.226143i
$201$	−5.66619e31	−	2.12743e32i	−0.322512	−	1.21090i
$202$	−9.95127e31			−0.528396
$203$			8.25628e31i			0.409110i
$204$	8.48696e31	−	2.26042e31i	0.392582	−	0.104560i
$205$	1.19832e32			0.517628
$206$			2.53244e32i			1.02188i
$207$	1.12510e32	+	1.96231e32i	0.424233	+	0.739918i
$208$	−9.86465e31			−0.347692
$209$		−	8.56003e31i		−	0.282116i
$210$	5.73936e31	+	2.15490e32i	0.176927	+	0.664289i
$211$	6.30653e32			1.81901			0.909507	−	0.415688i	$-0.136459\pi$
$211$	6.30653e32			1.81901			0.909507	+	0.415688i	$0.136459\pi$
$212$		−	5.30157e31i		−	0.143121i
$213$	2.14871e32	−	5.72287e31i	0.543079	−	0.144644i
$214$	−1.69107e31			−0.0400283
$215$			1.86258e31i			0.0413026i
$216$	−1.20848e32	+	1.19764e32i	−0.251124	+	0.248871i
$217$	−6.42235e32			−1.25100
$218$			2.09446e32i			0.382543i
$219$	−1.22288e32	−	4.59144e32i	−0.209492	−	0.786558i
$220$	−3.50918e32			−0.564012
$221$		−	7.49185e32i		−	1.13005i
$222$	7.83995e32	−	2.08809e32i	1.11012	−	0.295671i
$223$	5.13642e32			0.682955			0.341478	−	0.939890i	$-0.389073\pi$
$223$	5.13642e32			0.682955			0.341478	+	0.939890i	$0.389073\pi$
$224$			2.29232e32i			0.286289i
$225$	−4.72895e32	+	2.71135e32i	−0.554893	+	0.318149i
$226$	−6.93788e32			−0.765083
$227$		−	2.02364e32i		−	0.209783i	−0.994484	−	0.104892i	$-0.966550\pi$
$227$		−	2.02364e32i		−	0.209783i	0.994484	−	0.104892i	$-0.0334495\pi$
$228$	1.98197e31	+	7.44149e31i	0.0193201	+	0.0725391i
$229$	6.08798e32			0.558183			0.279091	−	0.960265i	$-0.409967\pi$
$229$	6.08798e32			0.558183			0.279091	+	0.960265i	$0.409967\pi$
$230$		−	4.19712e32i		−	0.362045i
$231$	−3.62250e33	+	9.64816e32i	−2.94063	+	0.783207i
$232$	1.16882e32			0.0893132
$233$		−	2.00104e33i		−	1.43970i	−0.694127	−	0.719852i	$-0.744210\pi$
$233$		−	2.00104e33i		−	1.43970i	0.694127	−	0.719852i	$-0.255790\pi$
$234$	7.21880e32	+	1.25905e33i	0.489151	+	0.853142i
$235$	1.52492e32			0.0973414
$236$		−	5.21280e32i		−	0.313547i
$237$	5.08306e32	+	1.90848e33i	0.288170	+	1.08196i
$238$	−1.74094e33			−0.930478
$239$			3.61406e33i			1.82148i	0.412980	+	0.910740i	$0.364488\pi$
$239$			3.61406e33i			1.82148i	−0.412980	+	0.910740i	$0.635512\pi$
$240$	3.05064e32	−	8.12507e31i	0.145022	−	0.0386251i
$241$	1.13193e33			0.507668			0.253834	−	0.967248i	$-0.418308\pi$
$241$	1.13193e33			0.507668			0.253834	+	0.967248i	$0.418308\pi$
$242$		−	4.22840e33i		−	1.78962i
$243$	2.41293e33	+	6.66003e32i	0.963955	+	0.266065i
$244$	4.07891e32			0.153846
$245$		−	2.73497e33i		−	0.974155i
$246$	−4.66416e32	−	1.75121e33i	−0.156921	−	0.589177i
$247$	6.56896e32			0.208804
$248$			9.09195e32i			0.273107i
$249$	−3.00836e32	+	8.01248e31i	−0.0854161	+	0.0227497i
$250$	2.59278e33			0.695994
$251$		−	6.13332e32i		−	0.155691i	−0.996965	−	0.0778455i	$-0.975196\pi$
$251$		−	6.13332e32i		−	0.155691i	0.996965	−	0.0778455i	$-0.0248041\pi$
$252$	2.92575e33	−	1.67749e33i	0.702474	−	0.402765i
$253$	7.05558e33			1.60267
$254$			5.08537e33i			1.09308i
$255$	6.17069e32	+	2.31685e33i	0.125537	+	0.471341i
$256$	3.24519e32			0.0625000
$257$			4.72984e33i			0.862547i	0.902221	+	0.431273i	$0.141936\pi$
$257$			4.72984e33i			0.862547i	−0.902221	+	0.431273i	$0.858064\pi$
$258$	2.72196e32	−	7.24967e31i	0.0470117	−	0.0125211i
$259$	−1.60821e34			−2.63116
$260$		−	2.69294e33i		−	0.417446i
$261$	−8.55324e32	−	1.49179e33i	−0.125650	−	0.219150i
$262$	−6.35914e33			−0.885483
$263$			3.25330e33i			0.429481i	0.976671	+	0.214740i	$0.0688905\pi$
$263$			3.25330e33i			0.429481i	−0.976671	+	0.214740i	$0.931109\pi$
$264$	1.36586e33	+	5.12827e33i	0.170983	+	0.641972i
$265$	1.44727e33			0.171833
$266$		−	1.52648e33i		−	0.171929i
$267$	−1.41819e32	+	3.77720e31i	−0.0151557	+	0.00403657i
$268$	6.17801e33			0.626559
$269$		−	1.31083e34i		−	1.26186i	−0.775838	−	0.630932i	$-0.782673\pi$
$269$		−	1.31083e34i		−	1.26186i	0.775838	−	0.630932i	$-0.217327\pi$
$270$	−3.26943e33	−	3.29902e33i	−0.298799	−	0.301504i
$271$	1.04769e34			0.909207			0.454603	−	0.890694i	$-0.349781\pi$
$271$	1.04769e34			0.909207			0.454603	+	0.890694i	$0.349781\pi$
$272$			2.46460e33i			0.203134i
$273$	−7.40399e33	−	2.77990e34i	−0.579681	−	2.17647i
$274$	−1.58471e34			−1.17881
$275$			1.70031e34i			1.20191i
$276$	−6.13363e33	+	1.63363e33i	−0.412088	+	0.109756i
$277$	−1.11299e34			−0.710841			−0.355421	−	0.934706i	$-0.615662\pi$
$277$	−1.11299e34			−0.710841			−0.355421	+	0.934706i	$0.615662\pi$
$278$			1.49672e34i			0.908894i
$279$	1.16043e34	−	6.65335e33i	0.670131	−	0.384221i
$280$	−6.25779e33			−0.343723
$281$		−	1.07604e34i		−	0.562264i	−0.959669	−	0.281132i	$-0.909290\pi$
$281$		−	1.07604e34i		−	0.562264i	0.959669	−	0.281132i	$-0.0907099\pi$
$282$	−5.93540e32	−	2.22850e33i	−0.0295095	−	0.110796i
$283$	−8.63341e32			−0.0408481			−0.0204241	−	0.999791i	$-0.506502\pi$
$283$	−8.63341e32			−0.0408481			−0.0204241	+	0.999791i	$0.506502\pi$
$284$			6.23981e33i			0.281005i
$285$	−2.03145e33	+	5.41055e32i	−0.0870918	+	0.0231960i
$286$	4.52697e34			1.84792
$287$			3.59226e34i			1.39644i
$288$	−2.37478e33	−	4.14191e33i	−0.0879281	−	0.153358i
$289$	9.63334e33			0.339787
$290$			3.19075e33i			0.107231i
$291$	7.21995e33	+	2.71080e34i	0.231224	+	0.868152i
$292$	1.33335e34			0.406989
$293$		−	4.43941e34i		−	1.29175i	−0.763443	−	0.645875i	$-0.776493\pi$
$293$		−	4.43941e34i		−	1.29175i	0.763443	−	0.645875i	$-0.223507\pi$
$294$	−3.99686e34	+	1.06452e34i	−1.10881	+	0.295320i
$295$	1.42304e34			0.376450
$296$			2.27671e34i			0.574412i
$297$	5.54583e34	−	5.49608e34i	1.33468	−	1.32270i
$298$	2.81861e34			0.647154
$299$			5.41445e34i			1.18620i
$300$	−3.93686e33	−	1.47813e34i	−0.0823101	−	0.309041i
$301$	−5.58358e33			−0.111425
$302$		−	2.81376e34i		−	0.536032i
$303$	−3.96999e34	+	1.05737e34i	−0.722091	+	0.192322i
$304$	−2.16100e33			−0.0375339
$305$			1.11350e34i			0.184710i
$306$	3.14563e34	−	1.80356e34i	0.498435	−	0.285779i
$307$	−9.16606e34			−1.38754			−0.693770	−	0.720196i	$-0.744052\pi$
$307$	−9.16606e34			−1.38754			−0.693770	+	0.720196i	$0.744052\pi$
$308$		−	1.05197e35i		−	1.52157i
$309$	2.69083e34	+	1.01030e35i	0.371936	+	1.39647i
$310$	−2.48200e34			−0.327898
$311$		−	3.28284e34i		−	0.414576i	−0.978280	−	0.207288i	$-0.933536\pi$
$311$		−	3.28284e34i		−	0.414576i	0.978280	−	0.207288i	$-0.0664636\pi$
$312$	−3.93543e34	+	1.04816e34i	−0.475147	+	0.126551i
$313$	−5.95564e34			−0.687555			−0.343778	−	0.939051i	$-0.611707\pi$
$313$	−5.95564e34			−0.687555			−0.343778	+	0.939051i	$0.611707\pi$
$314$			8.34188e33i			0.0920977i
$315$	4.57935e34	+	7.98698e34i	0.483567	+	0.843403i
$316$	−5.54221e34			−0.559840
$317$		−	1.15310e35i		−	1.11439i	−0.830383	−	0.557194i	$-0.811878\pi$
$317$		−	1.15310e35i		−	1.11439i	0.830383	−	0.557194i	$-0.188122\pi$
$318$	−5.63316e33	−	2.11502e34i	−0.0520921	−	0.195585i
$319$	−5.36381e34			−0.474683
$320$			8.85900e33i			0.0750386i
$321$	−6.74639e33	+	1.79683e33i	−0.0547017	+	0.0145693i
$322$	1.25820e35			0.976711
$323$		−	1.64120e34i		−	0.121991i
$324$	−3.54861e34	+	6.06197e34i	−0.252597	+	0.431503i
$325$	−1.30482e35			−0.889577
$326$		−	7.03765e34i		−	0.459601i
$327$	2.22545e34	+	8.35568e34i	0.139236	+	0.522773i
$328$	5.08547e34			0.304858
$329$			4.57135e34i			0.262604i
$330$	−1.39996e35	+	3.72866e34i	−0.770763	+	0.205285i
$331$	−7.41386e34			−0.391248			−0.195624	−	0.980679i	$-0.562673\pi$
$331$	−7.41386e34			−0.391248			−0.195624	+	0.980679i	$0.562673\pi$
$332$		−	8.73625e33i		−	0.0441969i
$333$	2.90582e35	−	1.66606e35i	1.40945	−	0.808111i
$334$	2.51479e35			1.16964
$335$			1.68653e35i			0.752258i
$336$	2.43570e34	+	9.14507e34i	0.104201	+	0.391234i
$337$	4.05523e35			1.66417			0.832084	−	0.554649i	$-0.187147\pi$
$337$	4.05523e35			1.66417			0.832084	+	0.554649i	$0.187147\pi$
$338$			1.67794e35i			0.660607i
$339$	−2.76782e35	+	7.37181e34i	−1.04554	+	0.278470i
$340$	−6.72809e34			−0.243886
$341$		−	4.17237e35i		−	1.45152i
$342$	1.58138e34	+	2.75814e34i	0.0528046	+	0.0920981i
$343$	3.14640e35			1.00855
$344$			7.90453e33i			0.0243253i
$345$	−4.45963e34	−	1.67441e35i	−0.131775	−	0.494761i
$346$	−2.12696e35			−0.603523
$347$		−	5.70947e35i		−	1.55591i	−0.628322	−	0.777953i	$-0.716258\pi$
$347$		−	5.70947e35i		−	1.55591i	0.628322	−	0.777953i	$-0.283742\pi$
$348$	4.66292e34	−	1.24192e34i	0.122053	−	0.0325076i
$349$	5.57835e34			0.140265			0.0701326	−	0.997538i	$-0.477658\pi$
$349$	5.57835e34			0.140265			0.0701326	+	0.997538i	$0.477658\pi$
$350$			3.03211e35i			0.732474i
$351$	4.21769e35	+	4.25586e35i	0.978982	+	0.987843i
$352$	−1.48924e35			−0.332176
$353$			5.51281e35i			1.18175i	0.806761	+	0.590877i	$0.201218\pi$
$353$			5.51281e35i			1.18175i	−0.806761	+	0.590877i	$0.798782\pi$
$354$	−5.53883e34	−	2.07961e35i	−0.114123	−	0.428485i
$355$	−1.70340e35			−0.337380
$356$		−	4.11839e33i		−	0.00784202i
$357$	−6.94535e35	+	1.84982e35i	−1.27157	+	0.338669i
$358$	−5.70915e35			−1.00510
$359$			3.97393e35i			0.672818i	0.941716	+	0.336409i	$0.109212\pi$
$359$			3.97393e35i			0.672818i	−0.941716	+	0.336409i	$0.890788\pi$
$360$	1.13070e35	−	6.48287e34i	0.184124	−	0.105568i
$361$	−6.24021e35			−0.977459
$362$			4.20569e35i			0.633749i
$363$	−4.49287e35	−	1.68689e36i	−0.651375	−	2.44565i
$364$	8.07279e35			1.12617
$365$			3.63989e35i			0.488639i
$366$	1.62725e35	−	4.33402e34i	0.210242	−	0.0559958i
$367$	1.68599e35			0.209667			0.104833	−	0.994490i	$-0.466569\pi$
$367$	1.68599e35			0.209667			0.104833	+	0.994490i	$0.466569\pi$
$368$		−	1.78120e35i		−	0.213227i
$369$	−3.72147e35	−	6.49072e35i	−0.428889	−	0.748038i
$370$	−6.21516e35			−0.689649
$371$			4.33857e35i			0.463566i
$372$	9.66061e34	+	3.62717e35i	0.0994039	+	0.373221i
$373$	−2.54308e35			−0.252021			−0.126010	−	0.992029i	$-0.540217\pi$
$373$	−2.54308e35			−0.252021			−0.126010	+	0.992029i	$0.540217\pi$
$374$		−	1.13103e36i		−	1.07962i
$375$	1.03437e36	−	2.75494e35i	0.951127	−	0.253323i
$376$	6.47154e34			0.0573294
$377$		−	4.11618e35i		−	0.351331i
$378$	9.88968e35	−	9.80096e35i	0.813386	−	0.806090i
$379$	−7.20174e35			−0.570806			−0.285403	−	0.958408i	$-0.592127\pi$
$379$	−7.20174e35			−0.570806			−0.285403	+	0.958408i	$0.592127\pi$
$380$		−	5.89929e34i		−	0.0450639i
$381$	5.40343e35	+	2.02877e36i	0.397851	+	1.49377i
$382$	−9.22880e34			−0.0655026
$383$			2.70532e36i			1.85113i	0.378591	+	0.925564i	$0.376409\pi$
$383$			2.70532e36i			1.85113i	−0.378591	+	0.925564i	$0.623591\pi$
$384$	1.29464e35	−	3.44816e34i	0.0854108	−	0.0227483i
$385$	2.87175e36			1.82682
$386$			6.36550e35i			0.390490i
$387$	1.00888e35	−	5.78441e34i	0.0596876	−	0.0342220i
$388$	−7.87213e35			−0.449209
$389$			9.65921e35i			0.531676i	0.964018	+	0.265838i	$0.0856486\pi$
$389$			9.65921e35i			0.531676i	−0.964018	+	0.265838i	$0.914351\pi$
$390$	−2.86137e35	−	1.07433e36i	−0.151939	−	0.570470i
$391$	1.35275e36			0.693018
$392$		−	1.16068e36i		−	0.573731i
$393$	−2.53693e36	+	6.75687e35i	−1.21008	+	0.322292i
$394$	−7.17440e35			−0.330247
$395$		−	1.51296e36i		−	0.672153i
$396$	1.08980e36	+	1.90076e36i	0.467322	+	0.815069i
$397$	−4.39924e35			−0.182100			−0.0910502	−	0.995846i	$-0.529022\pi$
$397$	−4.39924e35			−0.182100			−0.0910502	+	0.995846i	$0.529022\pi$
$398$			7.35520e35i			0.293921i
$399$	−1.62195e35	−	6.08978e35i	−0.0625774	−	0.234953i
$400$	4.29248e35			0.159907
$401$			7.56520e35i			0.272144i	0.990699	+	0.136072i	$0.0434479\pi$
$401$			7.56520e35i			0.272144i	−0.990699	+	0.136072i	$0.956552\pi$
$402$	2.46467e36	−	6.56442e35i	0.856239	−	0.228051i
$403$	3.20188e36			1.07432
$404$		−	1.15288e36i		−	0.373632i
$405$	−1.65485e36	−	9.68731e35i	−0.518070	−	0.303272i
$406$	−9.56509e35			−0.289284
$407$		−	1.04480e37i		−	3.05289i
$408$	2.61875e35	+	9.83235e35i	0.0739353	+	0.277597i
$409$	−2.45828e36			−0.670665			−0.335332	−	0.942100i	$-0.608849\pi$
$409$	−2.45828e36			−0.670665			−0.335332	+	0.942100i	$0.608849\pi$
$410$			1.38828e36i			0.366018i
$411$	−6.32210e36	+	1.68383e36i	−1.61093	+	0.429054i
$412$	−2.93389e36			−0.722576
$413$			4.26592e36i			1.01557i
$414$	−2.27339e36	+	1.30345e36i	−0.523201	+	0.299978i
$415$	2.38490e35			0.0530636
$416$		−	1.14284e36i		−	0.245856i
$417$	1.59033e36	+	5.97106e36i	0.330813	+	1.24207i
$418$	9.91700e35			0.199486
$419$		−	8.80782e36i		−	1.71345i	−0.515772	−	0.856726i	$-0.672495\pi$
$419$		−	8.80782e36i		−	1.71345i	0.515772	−	0.856726i	$-0.327505\pi$
$420$	−2.49650e36	+	6.64919e35i	−0.469723	+	0.125106i
$421$	−2.04908e36			−0.372915			−0.186457	−	0.982463i	$-0.559701\pi$
$421$	−2.04908e36			−0.372915			−0.186457	+	0.982463i	$0.559701\pi$
$422$			7.30626e36i			1.28624i
$423$	−4.73577e35	−	8.25979e35i	−0.0806539	−	0.140671i
$424$	6.14200e35			0.101202
$425$			3.25998e36i			0.519721i
$426$	6.63008e35	+	2.48933e36i	0.102279	+	0.384015i
$427$	−3.33799e36			−0.498305
$428$		−	1.95914e35i		−	0.0283043i
$429$	1.80600e37	−	4.81011e36i	2.52532	−	0.672594i
$430$	−2.15785e35			−0.0292054
$431$		−	2.61055e36i		−	0.342020i	−0.985269	−	0.171010i	$-0.945297\pi$
$431$		−	2.61055e36i		−	0.342020i	0.985269	−	0.171010i	$-0.0547030\pi$
$432$	−1.38750e36	−	1.40006e36i	−0.175978	−	0.177571i
$433$	6.96750e35			0.0855552			0.0427776	−	0.999085i	$-0.486379\pi$
$433$	6.96750e35			0.0855552			0.0427776	+	0.999085i	$0.486379\pi$
$434$		−	7.44044e36i		−	0.884591i
$435$	3.39031e35	+	1.27293e36i	0.0390293	+	0.146539i
$436$	−2.42648e36			−0.270499
$437$			1.18611e36i			0.128052i
$438$	5.31929e36	−	1.41674e36i	0.556181	−	0.148133i
$439$	1.66834e37			1.68959			0.844793	−	0.535093i	$-0.179723\pi$
$439$	1.66834e37			1.68959			0.844793	+	0.535093i	$0.179723\pi$
$440$		−	4.06547e36i		−	0.398816i
$441$	−1.48141e37	+	8.49368e36i	−1.40778	+	0.807153i
$442$	8.67948e36			0.799065
$443$			8.18446e36i			0.730025i	0.931003	+	0.365012i	$0.118935\pi$
$443$			8.18446e36i			0.730025i	−0.931003	+	0.365012i	$0.881065\pi$
$444$	2.41910e36	+	9.08276e36i	0.209071	+	0.784976i
$445$	1.12428e35			0.00941527
$446$			5.95066e36i			0.482922i
$447$	1.12446e37	−	2.99490e36i	0.884383	−	0.235547i
$448$	−2.65571e36			−0.202437
$449$		−	1.20927e37i		−	0.893456i	−0.894670	−	0.446728i	$-0.852589\pi$
$449$		−	1.20927e37i		−	0.893456i	0.894670	−	0.446728i	$-0.147411\pi$
$450$	−3.14117e36	−	5.47860e36i	−0.224965	−	0.392369i
$451$	−2.33377e37			−1.62026
$452$		−	8.03770e36i		−	0.540995i
$453$	−2.98975e36	−	1.12253e37i	−0.195101	−	0.732527i
$454$	2.34443e36			0.148339
$455$			2.20378e37i			1.35210i
$456$	−8.62115e35	+	2.29616e35i	−0.0512929	+	0.0136614i
$457$	−2.89674e36			−0.167141			−0.0835705	−	0.996502i	$-0.526632\pi$
$457$	−2.89674e36			−0.167141			−0.0835705	+	0.996502i	$0.526632\pi$
$458$			7.05307e36i			0.394695i
$459$	1.06329e37	−	1.05375e37i	0.577132	−	0.571954i
$460$	4.86247e36			0.256004
$461$			3.73081e37i			1.90542i	0.303885	+	0.952709i	$0.401716\pi$
$461$			3.73081e37i			1.90542i	−0.303885	+	0.952709i	$0.598284\pi$
$462$	−1.11776e37	−	4.19675e37i	−0.553811	−	2.07934i
$463$	−3.75803e36			−0.180645			−0.0903227	−	0.995913i	$-0.528790\pi$
$463$	−3.75803e36			−0.180645			−0.0903227	+	0.995913i	$0.528790\pi$
$464$			1.35411e36i			0.0631540i
$465$	−9.90177e36	+	2.63724e36i	−0.448096	+	0.119346i
$466$	2.31825e37			1.01802
$467$		−	1.01778e37i		−	0.433728i	−0.976202	−	0.216864i	$-0.930417\pi$
$467$		−	1.01778e37i		−	0.433728i	0.976202	−	0.216864i	$-0.0695827\pi$
$468$	−1.45864e37	+	8.36315e36i	−0.603263	+	0.345882i
$469$	−5.05581e37			−2.02941
$470$			1.76666e36i			0.0688307i
$471$	8.86362e35	+	3.32793e36i	0.0335211	+	0.125858i
$472$	6.03915e36			0.221711
$473$		−	3.62745e36i		−	0.129284i
$474$	−2.21102e37	+	5.88884e36i	−0.765062	+	0.203767i
$475$	−2.85840e36			−0.0960312
$476$		−	2.01692e37i		−	0.657947i
$477$	−4.49462e36	−	7.83919e36i	−0.142375	−	0.248321i
$478$	−4.18697e37			−1.28798
$479$			7.21284e36i			0.215481i	0.994179	+	0.107741i	$0.0343616\pi$
$479$			7.21284e36i			0.215481i	−0.994179	+	0.107741i	$0.965638\pi$
$480$	9.41308e35	+	3.53423e36i	0.0273121	+	0.102546i
$481$	8.01779e37			2.25956
$482$			1.31136e37i			0.358975i
$483$	5.01948e37	−	1.33689e37i	1.33475	−	0.355497i
$484$	4.89871e37			1.26545
$485$		−	2.14900e37i		−	0.539328i
$486$	−7.71580e36	+	2.79544e37i	−0.188137	+	0.681619i
$487$	−1.52282e37			−0.360781			−0.180390	−	0.983595i	$-0.557736\pi$
$487$	−1.52282e37			−0.360781			−0.180390	+	0.983595i	$0.557736\pi$
$488$			4.72551e36i			0.108786i
$489$	−7.47782e36	−	2.80762e37i	−0.167283	−	0.628079i
$490$	3.16853e37			0.688831
$491$			3.09297e37i			0.653483i	0.945114	+	0.326742i	$0.105951\pi$
$491$			3.09297e37i			0.653483i	−0.945114	+	0.326742i	$0.894049\pi$
$492$	2.02881e37	−	5.40354e36i	0.416611	−	0.110960i
$493$	−1.02839e37			−0.205259
$494$			7.61030e36i			0.147647i
$495$	−5.18886e37	+	2.97504e37i	−0.978586	+	0.561075i
$496$	−1.05332e37			−0.193116
$497$		−	5.10638e37i		−	0.910173i
$498$	−9.28265e35	−	3.48526e36i	−0.0160865	−	0.0603983i
$499$	2.68468e36			0.0452361			0.0226181	−	0.999744i	$-0.492800\pi$
$499$	2.68468e36			0.0452361			0.0226181	+	0.999744i	$0.492800\pi$
$500$			3.00380e37i			0.492142i
$501$	1.00326e38	−	2.67208e37i	1.59840	−	0.425718i
$502$	7.10559e36			0.110090
$503$			2.07679e37i			0.312925i	0.987684	+	0.156462i	$0.0500090\pi$
$503$			2.07679e37i			0.312925i	−0.987684	+	0.156462i	$0.949991\pi$
$504$	1.94341e37	+	3.38955e37i	0.284798	+	0.496724i
$505$	3.14723e37			0.448589
$506$			8.17406e37i			1.13326i
$507$	1.78289e37	+	6.69403e37i	0.240443	+	0.902768i
$508$	−5.89152e37			−0.772922
$509$		−	8.36963e37i		−	1.06821i	−0.845418	−	0.534106i	$-0.820648\pi$
$509$		−	8.36963e37i		−	1.06821i	0.845418	−	0.534106i	$-0.179352\pi$
$510$	−2.68412e37	+	7.14890e36i	−0.333288	+	0.0887680i
$511$	−1.09115e38			−1.31823
$512$			3.75962e36i			0.0441942i
$513$	9.23946e36	+	9.32310e36i	0.105683	+	0.106639i
$514$	−5.47963e37			−0.609913
$515$		−	8.00921e37i		−	0.867538i
$516$	8.39892e35	+	3.15345e36i	0.00885375	+	0.0332423i
$517$	−2.96984e37			−0.304695
$518$		−	1.86315e38i		−	1.86051i
$519$	−8.48536e37	+	2.25999e37i	−0.824759	+	0.219666i
$520$	3.11984e37			0.295179
$521$			1.27657e37i			0.117575i	0.998271	+	0.0587876i	$0.0187235\pi$
$521$			1.27657e37i			0.117575i	−0.998271	+	0.0587876i	$0.981277\pi$
$522$	1.72828e37	−	9.90913e36i	0.154963	−	0.0888482i
$523$	2.50358e37			0.218543			0.109272	−	0.994012i	$-0.465148\pi$
$523$	2.50358e37			0.218543			0.109272	+	0.994012i	$0.465148\pi$
$524$		−	7.36722e37i		−	0.626131i
$525$	3.22175e37	+	1.20964e38i	0.266601	+	1.00098i
$526$	−3.76903e37			−0.303689
$527$		−	7.99962e37i		−	0.627654i
$528$	−5.94123e37	+	1.58239e37i	−0.453943	+	0.120903i
$529$	3.66287e37			0.272548
$530$			1.67670e37i			0.121505i
$531$	−4.41936e37	−	7.70793e37i	−0.311915	−	0.544019i
$532$	1.76846e37			0.121572
$533$		−	1.79093e38i		−	1.19922i
$534$	−4.37598e35	−	1.64300e36i	−0.00285429	−	0.0107167i
$535$	5.34823e36			0.0339827
$536$			7.15738e37i			0.443044i
$537$	−2.27762e38	+	6.06623e37i	−1.37354	+	0.365830i
$538$	1.51862e38			0.892273
$539$			5.32646e38i			3.04927i
$540$	3.82200e37	−	3.78771e37i	0.213195	−	0.211283i
$541$	−1.95753e38			−1.06401			−0.532006	−	0.846741i	$-0.678561\pi$
$541$	−1.95753e38			−1.06401			−0.532006	+	0.846741i	$0.678561\pi$
$542$			1.21377e38i			0.642906i
$543$	4.46873e37	+	1.67783e38i	0.230668	+	0.866064i
$544$	−2.85530e37			−0.143637
$545$		−	6.62402e37i		−	0.324766i
$546$	3.22058e38	−	8.57770e37i	1.53899	−	0.409896i
$547$	4.18199e38			1.94787			0.973935	−	0.226828i	$-0.0728355\pi$
$547$	4.18199e38			1.94787			0.973935	+	0.226828i	$0.0728355\pi$
$548$		−	1.83593e38i		−	0.833542i
$549$	6.03129e37	−	3.45805e37i	0.266930	−	0.153045i
$550$	−1.96985e38			−0.849878
$551$		−	9.01711e36i		−	0.0379267i
$552$	−1.89260e37	−	7.10595e37i	−0.0776090	−	0.291390i
$553$	4.53549e38			1.81331
$554$		−	1.28942e38i		−	0.502641i
$555$	−2.47949e38	+	6.60389e37i	−0.942456	+	0.251014i
$556$	−1.73399e38			−0.642685
$557$		−	1.15367e38i		−	0.416973i	−0.978025	−	0.208487i	$-0.933146\pi$
$557$		−	1.15367e38i		−	0.416973i	0.978025	−	0.208487i	$-0.0668537\pi$
$558$	7.70806e37	+	1.34438e38i	0.271685	+	0.473854i
$559$	2.78370e37			0.0956881
$560$		−	7.24980e37i		−	0.243049i
$561$	−1.20177e38	−	4.51215e38i	−0.392952	−	1.47538i
$562$	1.24662e38			0.397581
$563$			3.30770e38i			1.02898i	0.857495	+	0.514492i	$0.172019\pi$
$563$			3.30770e38i			1.02898i	−0.857495	+	0.514492i	$0.827981\pi$
$564$	2.58177e37	−	6.87630e36i	0.0783449	−	0.0208664i
$565$	2.19420e38			0.649529
$566$		−	1.00020e37i		−	0.0288840i
$567$	2.90402e38	−	4.96084e38i	0.818157	−	1.39763i
$568$	−7.22897e37			−0.198701
$569$			4.81727e38i			1.29190i	0.763379	+	0.645951i	$0.223539\pi$
$569$			4.81727e38i			1.29190i	−0.763379	+	0.645951i	$0.776461\pi$
$570$	−6.26826e36	−	2.35348e37i	−0.0164021	−	0.0615832i
$571$	−3.55952e38			−0.908836			−0.454418	−	0.890789i	$-0.650153\pi$
$571$	−3.55952e38			−0.908836			−0.454418	+	0.890789i	$0.650153\pi$
$572$			5.24460e38i			1.30668i
$573$	−3.68176e37	+	9.80602e36i	−0.0895141	+	0.0238412i
$574$	−4.16172e38			−0.987431
$575$		−	2.35603e38i		−	0.545545i
$576$	4.79851e37	−	2.75123e37i	0.108440	−	0.0621746i
$577$	−7.66112e38			−1.68978			−0.844892	−	0.534938i	$-0.820335\pi$
$577$	−7.66112e38			−1.68978			−0.844892	+	0.534938i	$0.820335\pi$
$578$			1.11604e38i			0.240266i
$579$	6.76362e37	+	2.53947e38i	0.142128	+	0.533633i
$580$	−3.69656e37			−0.0758238
$581$			7.14935e37i			0.143153i
$582$	−3.14053e38	+	8.36449e37i	−0.613876	+	0.163500i
$583$	−2.81861e38			−0.537868
$584$			1.54471e38i			0.287785i
$585$	−2.28305e38	−	3.98193e38i	−0.415272	−	0.724288i
$586$	5.14316e38			0.913406
$587$		−	6.16052e38i		−	1.06828i	−0.845397	−	0.534138i	$-0.820636\pi$
$587$		−	6.16052e38i		−	1.06828i	0.845397	−	0.534138i	$-0.179364\pi$
$588$	−1.23328e38	−	4.63046e38i	−0.208823	−	0.784045i
$589$	7.01418e37			0.115975
$590$			1.64862e38i			0.266191i
$591$	−2.86218e38	+	7.62313e37i	−0.451307	+	0.120201i
$592$	−2.63762e38			−0.406171
$593$		−	2.79930e38i		−	0.421001i	−0.977594	−	0.210501i	$-0.932491\pi$
$593$		−	2.79930e38i		−	0.421001i	0.977594	−	0.210501i	$-0.0675094\pi$
$594$	6.36734e38	+	6.42497e38i	0.935293	+	0.943759i
$595$	5.50596e38			0.789943
$596$			3.26543e38i			0.457607i
$597$	7.81523e37	+	2.93430e38i	0.106980	+	0.401665i
$598$	−6.27276e38			−0.838769
$599$		−	1.07262e39i		−	1.40110i	−0.713604	−	0.700549i	$-0.752938\pi$
$599$		−	1.07262e39i		−	1.40110i	0.713604	−	0.700549i	$-0.247062\pi$
$600$	1.71245e38	−	4.56095e37i	0.218525	−	0.0582020i
$601$	9.44393e38			1.17736			0.588681	−	0.808365i	$-0.299647\pi$
$601$	9.44393e38			1.17736			0.588681	+	0.808365i	$0.299647\pi$
$602$		−	6.46871e37i		−	0.0787892i
$603$	9.13514e38	−	5.23765e38i	1.08711	−	0.623296i
$604$	3.25981e38			0.379032
$605$			1.33729e39i			1.51933i
$606$	−1.22498e38	−	4.59932e38i	−0.135992	−	0.510596i
$607$	−1.28830e39			−1.39757			−0.698787	−	0.715330i	$-0.746277\pi$
$607$	−1.28830e39			−1.39757			−0.698787	+	0.715330i	$0.746277\pi$
$608$		−	2.50357e37i		−	0.0265405i
$609$	−3.81593e38	+	1.01633e38i	−0.395328	+	0.105292i
$610$	−1.29001e38			−0.130610
$611$		−	2.27905e38i		−	0.225516i
$612$	2.08946e38	+	3.64429e38i	0.202076	+	0.352446i
$613$	1.60791e39			1.51990			0.759952	−	0.649979i	$-0.225222\pi$
$613$	1.60791e39			1.51990			0.759952	+	0.649979i	$0.225222\pi$
$614$		−	1.06191e39i		−	0.981139i
$615$	1.47511e38	+	5.53844e38i	0.133221	+	0.500191i
$616$	1.21873e39			1.07591
$617$			2.07882e39i			1.79401i	0.442018	+	0.897006i	$0.354263\pi$
$617$			2.07882e39i			1.79401i	−0.442018	+	0.897006i	$0.645737\pi$
$618$	−1.17046e39	+	3.11739e38i	−0.987453	+	0.262998i
$619$	6.27890e38			0.517863			0.258931	−	0.965896i	$-0.416630\pi$
$619$	6.27890e38			0.517863			0.258931	+	0.965896i	$0.416630\pi$
$620$		−	2.87546e38i		−	0.231859i
$621$	−7.68454e38	+	7.61560e38i	−0.605808	+	0.600374i
$622$	3.80324e38			0.293149
$623$			3.37031e37i			0.0254002i
$624$	−1.21432e38	−	4.55929e38i	−0.0894849	−	0.335980i
$625$	6.76605e37			0.0487546
$626$		−	6.89975e38i		−	0.486175i
$627$	3.95632e38	−	1.05373e38i	0.272612	−	0.0726076i
$628$	−9.66427e37			−0.0651229
$629$		−	2.00318e39i		−	1.32011i
$630$	−9.25311e38	+	5.30529e38i	−0.596376	+	0.341933i
$631$	−2.08681e38			−0.131544			−0.0657722	−	0.997835i	$-0.520951\pi$
$631$	−2.08681e38			−0.131544			−0.0657722	+	0.997835i	$0.520951\pi$
$632$		−	6.42078e38i		−	0.395866i
$633$	7.76323e38	+	2.91478e39i	0.468156	+	1.75774i
$634$	1.33589e39			0.787991
$635$		−	1.60832e39i		−	0.927984i
$636$	2.45031e38	−	6.52615e37i	0.138299	−	0.0368347i
$637$	−4.08752e39			−2.25688
$638$		−	6.21410e38i		−	0.335652i
$639$	5.29005e38	+	9.22652e38i	0.279542	+	0.487558i
$640$	−1.02634e38			−0.0530603
$641$		−	2.91357e39i		−	1.47372i	−0.676048	−	0.736858i	$-0.736309\pi$
$641$		−	2.91357e39i		−	1.47372i	0.676048	−	0.736858i	$-0.263691\pi$
$642$	−2.08167e37	−	7.81585e37i	−0.0103020	−	0.0386799i
$643$	−2.74812e39			−1.33071			−0.665354	−	0.746528i	$-0.731719\pi$
$643$	−2.74812e39			−1.33071			−0.665354	+	0.746528i	$0.731719\pi$
$644$			1.45765e39i			0.690639i
$645$	−8.60858e37	+	2.29281e37i	−0.0399113	+	0.0106300i
$646$	1.90137e38			0.0862604
$647$			2.18990e39i			0.972220i	0.873898	+	0.486110i	$0.161585\pi$
$647$			2.18990e39i			0.972220i	−0.873898	+	0.486110i	$0.838415\pi$
$648$	−7.02294e38	−	4.11115e38i	−0.305119	−	0.178613i
$649$	−2.77142e39			−1.17836
$650$		−	1.51166e39i		−	0.629026i
$651$	−7.90580e38	−	2.96831e39i	−0.321968	−	1.20886i
$652$	8.15328e38			0.324987
$653$			4.05184e39i			1.58077i	0.612612	+	0.790384i	$0.290119\pi$
$653$			4.05184e39i			1.58077i	−0.612612	+	0.790384i	$0.709881\pi$
$654$	−9.68026e38	+	2.57824e38i	−0.369657	+	0.0984544i
$655$	2.01117e39			0.751744
$656$			5.89164e38i			0.215567i
$657$	1.97156e39	−	1.13040e39i	0.706145	−	0.404870i
$658$	−5.29601e38			−0.185689
$659$		−	2.53757e39i		−	0.871008i	−0.900187	−	0.435504i	$-0.856570\pi$
$659$		−	2.53757e39i		−	0.871008i	0.900187	−	0.435504i	$-0.143430\pi$
$660$	−4.31974e38	−	1.62189e39i	−0.145159	−	0.545012i
$661$	2.66323e39			0.876168			0.438084	−	0.898934i	$-0.355657\pi$
$661$	2.66323e39			0.876168			0.438084	+	0.898934i	$0.355657\pi$
$662$		−	8.58913e38i		−	0.276654i
$663$	3.46262e39	−	9.22234e38i	1.09198	−	0.290838i
$664$	1.01211e38			0.0312519
$665$			4.82771e38i			0.145961i
$666$	1.93017e39	+	3.36646e39i	0.571421	+	0.996631i
$667$	7.43233e38			0.215458
$668$			2.91345e39i			0.827060i
$669$	6.32284e38	+	2.37397e39i	0.175771	+	0.659949i
$670$	−1.95388e39			−0.531926
$671$		−	2.16858e39i		−	0.578175i
$672$	−1.05948e39	+	2.82181e38i	−0.276644	+	0.0736815i
$673$	−1.05870e39			−0.270745			−0.135373	−	0.990795i	$-0.543223\pi$
$673$	−1.05870e39			−0.270745			−0.135373	+	0.990795i	$0.543223\pi$
$674$			4.69809e39i			1.17675i
$675$	−1.83527e39	−	1.85189e39i	−0.450244	−	0.454319i
$676$	−1.94394e39			−0.467120
$677$			4.09319e38i			0.0963430i	0.998839	+	0.0481715i	$0.0153394\pi$
$677$			4.09319e38i			0.0963430i	−0.998839	+	0.0481715i	$0.984661\pi$
$678$	−8.54041e38	−	3.20658e39i	−0.196908	−	0.739310i
$679$	6.44219e39			1.45498
$680$		−	7.79465e38i		−	0.172453i
$681$	9.35294e38	−	2.49106e38i	0.202716	−	0.0539915i
$682$	4.83379e39			1.02638
$683$			6.84805e39i			1.42455i	0.701901	+	0.712274i	$0.252335\pi$
$683$			6.84805e39i			1.42455i	−0.701901	+	0.712274i	$0.747665\pi$
$684$	−3.19537e38	+	1.83207e38i	−0.0651232	+	0.0373385i
$685$	5.01188e39			1.00077
$686$			3.64518e39i			0.713151i
$687$	7.49420e38	+	2.81377e39i	0.143658	+	0.539380i
$688$	−9.15758e37			−0.0172006
$689$		−	2.16300e39i		−	0.398096i
$690$	1.93985e39	−	5.16659e38i	0.349849	−	0.0931787i
$691$	−9.99115e39			−1.76572			−0.882862	−	0.469633i	$-0.844386\pi$
$691$	−9.99115e39			−1.76572			−0.882862	+	0.469633i	$0.844386\pi$
$692$		−	2.46413e39i		−	0.426756i
$693$	−8.91846e39	−	1.55549e40i	−1.51365	−	2.64000i
$694$	6.61456e39			1.10019
$695$		−	4.73359e39i		−	0.771619i
$696$	1.43880e38	+	5.40211e38i	0.0229864	+	0.0863046i
$697$	−4.47449e39			−0.700623
$698$			6.46265e38i			0.0991824i
$699$	9.24851e39	−	2.46325e39i	1.39121	−	0.370534i
$700$	−3.51277e39			−0.517937
$701$			2.12852e38i			0.0307628i	0.999882	+	0.0153814i	$0.00489624\pi$
$701$			2.12852e38i			0.0307628i	−0.999882	+	0.0153814i	$0.995104\pi$
$702$	−4.93052e39	+	4.88629e39i	−0.698511	+	0.692245i
$703$	1.75642e39			0.243923
$704$		−	1.72532e39i		−	0.234884i
$705$	1.87715e38	+	7.04795e38i	0.0250526	+	0.0940623i
$706$	−6.38672e39			−0.835627
$707$			9.43463e39i			1.21019i
$708$	2.40928e39	−	6.41687e38i	0.302985	−	0.0806970i
$709$	5.05202e39			0.622900			0.311450	−	0.950263i	$-0.399185\pi$
$709$	5.05202e39			0.622900			0.311450	+	0.950263i	$0.399185\pi$
$710$		−	1.97343e39i		−	0.238564i
$711$	−8.19500e39	+	4.69862e39i	−0.971348	+	0.556924i
$712$	4.77126e37			0.00554514
$713$			5.78142e39i			0.658841i
$714$	−2.14307e39	−	8.04635e39i	−0.239475	−	0.899133i
$715$	−1.43172e40			−1.56882
$716$		−	6.61419e39i		−	0.710713i
$717$	−1.67036e40	+	4.44885e39i	−1.76012	+	0.468791i
$718$	−4.60389e39			−0.475754
$719$			2.95353e39i			0.299320i	0.988737	+	0.149660i	$0.0478180\pi$
$719$			2.95353e39i			0.299320i	−0.988737	+	0.149660i	$0.952182\pi$
$720$	7.51056e38	+	1.30994e39i	0.0746479	+	0.130196i
$721$	2.40097e40			2.34041
$722$		−	7.22944e39i		−	0.691168i
$723$	1.39338e39	+	5.23159e39i	0.130658	+	0.490566i
$724$	−4.87239e39			−0.448128
$725$			1.79111e39i			0.161581i
$726$	1.95430e40	−	5.20509e39i	1.72934	−	0.460591i
$727$	−1.38473e40			−1.20195			−0.600973	−	0.799269i	$-0.705220\pi$
$727$	−1.38473e40			−1.20195			−0.600973	+	0.799269i	$0.705220\pi$
$728$			9.35251e39i			0.796323i
$729$	−1.07886e38	+	1.19720e40i	−0.00901115	+	0.999959i
$730$	−4.21689e39			−0.345520
$731$		−	6.95485e38i		−	0.0559042i
$732$	5.02107e38	+	1.88521e39i	0.0395950	+	0.148663i
$733$	2.45542e40			1.89964			0.949819	−	0.312800i	$-0.101267\pi$
$733$	2.45542e40			1.89964			0.949819	+	0.312800i	$0.101267\pi$
$734$			1.95326e39i			0.148257i
$735$	1.26406e40	−	3.36671e39i	0.941339	−	0.250716i
$736$	2.06356e39			0.150774
$737$		−	3.28458e40i		−	2.35470i
$738$	7.51965e39	−	4.31141e39i	0.528943	−	0.303271i
$739$	1.37159e39			0.0946675			0.0473338	−	0.998879i	$-0.484928\pi$
$739$	1.37159e39			0.0946675			0.0473338	+	0.998879i	$0.484928\pi$
$740$		−	7.20041e39i		−	0.487656i
$741$	8.08628e38	+	3.03607e39i	0.0537396	+	0.201770i
$742$	−5.02633e39			−0.327791
$743$			5.17409e39i			0.331124i	0.986199	+	0.165562i	$0.0529437\pi$
$743$			5.17409e39i			0.331124i	−0.986199	+	0.165562i	$0.947056\pi$
$744$	−4.20216e39	+	1.11920e39i	−0.263907	+	0.0702891i
$745$	−8.91426e39			−0.549411
$746$		−	2.94622e39i		−	0.178206i
$747$	−7.40649e38	−	1.29179e39i	−0.0439667	−	0.0766837i
$748$	1.31032e40			0.763405
$749$			1.60327e39i			0.0916772i
$750$	3.19167e39	+	1.19834e40i	0.179127	+	0.672548i

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)

\(f(q)\)	\(=\)	\(q+11585.2i q^{2} +(1.23098e6 + 4.62185e6i) q^{3} -1.34218e8 q^{4} -3.66400e9i q^{5} +(-5.35452e10 + 1.42612e10i) q^{6} +1.09838e12 q^{7} -1.55494e12i q^{8} +(-1.98462e13 + 1.13788e13i) q^{9} +O(q^{10})\)	\(q+11585.2i q^{2} +(1.23098e6 + 4.62185e6i) q^{3} -1.34218e8 q^{4} -3.66400e9i q^{5} +(-5.35452e10 + 1.42612e10i) q^{6} +1.09838e12 q^{7} -1.55494e12i q^{8} +(-1.98462e13 + 1.13788e13i) q^{9} +4.24483e13 q^{10} +7.13577e14i q^{11} +(-1.65220e14 - 6.20334e14i) q^{12} -5.47598e15 q^{13} +1.27250e16i q^{14} +(1.69344e16 - 4.51032e15i) q^{15} +1.80144e16 q^{16} +1.36813e17i q^{17} +(-1.31827e17 - 2.29922e17i) q^{18} -1.19960e17 q^{19} +4.91773e17i q^{20} +(1.35208e18 + 5.07653e18i) q^{21} -8.26696e18 q^{22} -9.88762e18i q^{23} +(7.18671e18 - 1.91411e18i) q^{24} +2.38280e19 q^{25} -6.34406e19i q^{26} +(-7.70215e19 - 7.77187e19i) q^{27} -1.47422e20 q^{28} +7.51680e19i q^{29} +(5.22531e19 + 1.96189e20i) q^{30} -5.84712e20 q^{31} +2.08701e20i q^{32} +(-3.29804e21 + 8.78401e20i) q^{33} -1.58501e21 q^{34} -4.02445e21i q^{35} +(2.66371e21 - 1.52724e21i) q^{36} -1.46417e22 q^{37} -1.38976e21i q^{38} +(-6.74084e21 - 2.53092e22i) q^{39} -5.69731e21 q^{40} +3.27052e22i q^{41} +(-5.88128e22 + 1.56642e22i) q^{42} -5.08348e21 q^{43} -9.57747e22i q^{44} +(4.16920e22 + 7.27162e22i) q^{45} +1.14550e23 q^{46} +4.16191e22i q^{47} +(2.21754e22 + 8.32598e22i) q^{48} +7.46446e23 q^{49} +2.76054e23i q^{50} +(-6.32328e23 + 1.68414e23i) q^{51} +7.34974e23 q^{52} +3.94998e23i q^{53} +(9.00390e23 - 8.92313e23i) q^{54} +2.61454e24 q^{55} -1.70792e24i q^{56} +(-1.47668e23 - 5.54435e23i) q^{57} -8.70839e23 q^{58} +3.88384e24i q^{59} +(-2.27290e24 + 6.05365e23i) q^{60} -3.03902e24 q^{61} -6.77403e24i q^{62} +(-2.17986e25 + 1.24983e25i) q^{63} -2.41785e24 q^{64} +2.00640e25i q^{65} +(-1.01765e25 - 3.82086e25i) q^{66} -4.60298e25 q^{67} -1.83627e25i q^{68} +(4.56991e25 - 1.21715e25i) q^{69} +4.66242e25 q^{70} -4.64902e25i q^{71} +(1.76935e25 + 3.08597e25i) q^{72} -9.93420e25 q^{73} -1.69628e26i q^{74} +(2.93319e25 + 1.10130e26i) q^{75} +1.61007e25 q^{76} +7.83776e26i q^{77} +(2.93213e26 - 7.80943e25i) q^{78} +4.12927e26 q^{79} -6.60047e25i q^{80} +(2.64392e26 - 4.51652e26i) q^{81} -3.78897e26 q^{82} +6.50901e25i q^{83} +(-1.81474e26 - 6.81361e26i) q^{84} +5.01282e26 q^{85} -5.88933e25i q^{86} +(-3.47415e26 + 9.25305e25i) q^{87} +1.10957e27 q^{88} +3.06844e25i q^{89} +(-8.42435e26 + 4.83012e26i) q^{90} -6.01469e27 q^{91} +1.32709e27i q^{92} +(-7.19771e26 - 2.70245e27i) q^{93} -4.82167e26 q^{94} +4.39531e26i q^{95} +(-9.64585e26 + 2.56908e26i) q^{96} +5.86519e27 q^{97} +8.64775e27i q^{98} +(-8.11967e27 - 1.41618e28i) 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

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