LMFDB - Embedded newform 3.33.b.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,33,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 33, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 33);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 33 $
Character orbit:	$[\chi]$	$=$	3.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:	$19.4599965427$
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} + 954745942 x^{8} + \cdots + 31\!\cdots\!00 $ x^10 + 954745942x^8 + 302468338607088448x^6 + 37939920124077893929140224x^4 + 1938513915962148831841211918581760x^2 + 31225030372218346257929044634944667648000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{61}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.2
Root			$-17303.1i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.33.b.a.2.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-103819. i q^{2} +(-2.32547e7 + 3.62248e7i) q^{3} -6.48340e9 q^{4} +2.49832e11i q^{5} +(3.76082e12 + 2.41428e12i) q^{6} -3.04380e13 q^{7} +2.27200e14i q^{8} +(-7.71458e14 - 1.68480e15i) q^{9} +O(q^{10})$	\(q-103819. i q^{2} +(-2.32547e7 + 3.62248e7i) q^{3} -6.48340e9 q^{4} +2.49832e11i q^{5} +(3.76082e12 + 2.41428e12i) q^{6} -3.04380e13 q^{7} +2.27200e14i q^{8} +(-7.71458e14 - 1.68480e15i) q^{9} +2.59372e16 q^{10} -4.78234e16i q^{11} +(1.50769e17 - 2.34860e17i) q^{12} +5.67246e17 q^{13} +3.16003e18i q^{14} +(-9.05011e18 - 5.80976e18i) q^{15} -4.25830e18 q^{16} -9.91887e18i q^{17} +(-1.74914e20 + 8.00919e19i) q^{18} +3.55318e20 q^{19} -1.61976e21i q^{20} +(7.07826e20 - 1.10261e21i) q^{21} -4.96497e21 q^{22} -3.07553e20i q^{23} +(-8.23029e21 - 5.28347e21i) q^{24} -3.91328e22 q^{25} -5.88909e22i q^{26} +(7.89715e22 + 1.12335e22i) q^{27} +1.97341e23 q^{28} -3.31674e23i q^{29} +(-6.03163e23 + 9.39573e23i) q^{30} +3.59216e23 q^{31} +1.41791e24i q^{32} +(1.73239e24 + 1.11212e24i) q^{33} -1.02977e24 q^{34} -7.60436e24i q^{35} +(5.00167e24 + 1.09232e25i) q^{36} +3.31930e24 q^{37} -3.68887e25i q^{38} +(-1.31911e25 + 2.05484e25i) q^{39} -5.67618e25 q^{40} -3.35484e25i q^{41} +(-1.14472e26 - 7.34857e25i) q^{42} +1.34260e26 q^{43} +3.10058e26i q^{44} +(4.20915e26 - 1.92735e26i) q^{45} -3.19298e25 q^{46} +9.71468e23i q^{47} +(9.90254e25 - 1.54256e26i) q^{48} -1.77959e26 q^{49} +4.06272e27i q^{50} +(3.59310e26 + 2.30660e26i) q^{51} -3.67768e27 q^{52} -5.82182e27i q^{53} +(1.16625e27 - 8.19873e27i) q^{54} +1.19478e28 q^{55} -6.91551e27i q^{56} +(-8.26280e27 + 1.28713e28i) q^{57} -3.44340e28 q^{58} -1.32634e28i q^{59} +(5.86755e28 + 3.76670e28i) q^{60} -6.55279e28 q^{61} -3.72934e28i q^{62} +(2.34816e28 + 5.12817e28i) q^{63} +1.28917e29 q^{64} +1.41716e29i q^{65} +(1.15459e29 - 1.79855e29i) q^{66} -8.95668e28 q^{67} +6.43080e28i q^{68} +(1.11410e28 + 7.15205e27i) q^{69} -7.89477e29 q^{70} -4.59368e28i q^{71} +(3.82786e29 - 1.75275e29i) q^{72} +2.56589e28 q^{73} -3.44606e29i q^{74} +(9.10022e29 - 1.41758e30i) q^{75} -2.30366e30 q^{76} +1.45565e30i q^{77} +(2.13331e30 + 1.36949e30i) q^{78} +3.75026e30 q^{79} -1.06386e30i q^{80} +(-2.24339e30 + 2.59950e30i) q^{81} -3.48296e30 q^{82} +1.44084e30i q^{83} +(-4.58911e30 + 7.14866e30i) q^{84} +2.47805e30 q^{85} -1.39387e31i q^{86} +(1.20148e31 + 7.71297e30i) q^{87} +1.08655e31 q^{88} -4.42071e30i q^{89} +(-2.00095e31 - 4.36990e31i) q^{90} -1.72658e31 q^{91} +1.99399e30i q^{92} +(-8.35346e30 + 1.30125e31i) q^{93} +1.00857e29 q^{94} +8.87696e31i q^{95} +(-5.13635e31 - 3.29731e31i) q^{96} +7.67762e31 q^{97} +1.84755e31i q^{98} +(-8.05726e31 + 3.68937e31i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9}+O(q^{10}) $ 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9	$ 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9} - 70\!\cdots\!40 q^{10}+ \cdots - 33\!\cdots\!60 q^{99}+O(q^{100}) $ 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9 - 7003812786596640 * q^10 - 279007424380502640 * q^12 + 567697557679805780 * q^13 - 20342205597863242080 * q^15 + 93452609752238437504 * q^16 - 546532439317269948000 * q^18 + 571007688520350419876 * q^19 - 202809296674597359852 * q^21 - 7726803521259943913760 * q^22 + 40966888307328818303616 * q^24 - 68909708350780834128950 * q^25 - 72967926462080465281230 * q^27 + 205937256056975756717600 * q^28 - 1107420825536697507876000 * q^30 + 2337947500037502285593540 * q^31 + 2522449071689961111334560 * q^33 - 6060358314194999366692224 * q^34 + 19880961335883894024618192 * q^36 - 35307903416851790686359340 * q^37 - 31624005377757923978634972 * q^39 + 103824872020641394026996480 * q^40 - 141365101025586253616004960 * q^42 + 20133134465218107006792740 * q^43 + 324508325822765233105320000 * q^45 - 1081312096716791246752963776 * q^46 + 3981901930430244196770990720 * q^48 - 2767041101974767237639509154 * q^49 + 1958591008210563208705802112 * q^51 - 5054272042223836449280397920 * q^52 + 8609682620485865645134310448 * q^54 - 11870374622399979665591304000 * q^55 + 40568829971233106153298510900 * q^57 - 126691224865576416891245282400 * q^58 + 279833341447916827662753642240 * q^60 - 196667345182223458343232398380 * q^61 + 349775312774222889759843110340 * q^63 - 738816306154787409411488427008 * q^64 + 939413077861687418842822458720 * q^66 - 442550741350999501345614861340 * q^67 + 1096443581430237499419700598208 * q^69 - 3084260511067452830890360584000 * q^70 + 5478956649034785201935062114560 * q^72 - 4530286149796751043896742263020 * q^73 + 5689646867484953837977805651250 * q^75 - 10804853453030293252172855440096 * q^76 + 9245617327241370897996048982560 * q^78 - 2115110787448996851533482223164 * q^79 - 454653247801524309158818752630 * q^81 + 6754240700896495824250705604160 * q^82 - 10589261014798101343390846457952 * q^84 + 8783873758902640422771709896960 * q^85 - 12893796544943502316879779198240 * q^87 + 15416255855088684041150976480000 * q^88 - 76437416541013126109366518121760 * q^90 + 59544256621898576615810233543816 * q^91 - 105131728169400940473110940107820 * q^93 + 301803894289991891760064059517056 * q^94 - 522680019947351351608967407401984 * q^96 + 390148965222370670128665882607700 * q^97 - 333895893109019690643343683610560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	103819.i		−	1.58415i	−0.610423	−	0.792075i	$-0.709001\pi$
$2$		−	103819.i		−	1.58415i	0.610423	−	0.792075i	$-0.290999\pi$
$3$	−2.32547e7	+	3.62248e7i	−0.540220	+	0.841524i
$3$	−2.32547e7	+	3.62248e7i	−0.540220	+	0.841524i
$4$	−6.48340e9			−1.50953
$5$			2.49832e11i			1.63730i	0.574295	+	0.818648i	$0.305276\pi$
$5$			2.49832e11i			1.63730i	−0.574295	+	0.818648i	$0.694724\pi$
$6$	3.76082e12	+	2.41428e12i	1.33310	+	0.855790i
$7$	−3.04380e13			−0.915897			−0.457949	−	0.888979i	$-0.651416\pi$
$7$	−3.04380e13			−0.915897			−0.457949	+	0.888979i	$0.651416\pi$
$8$			2.27200e14i			0.807177i
$9$	−7.71458e14	−	1.68480e15i	−0.416324	−	0.909216i
$10$	2.59372e16			2.59372
$11$		−	4.78234e16i		−	1.04078i	−0.853930	−	0.520388i	$-0.825787\pi$
$11$		−	4.78234e16i		−	1.04078i	0.853930	−	0.520388i	$-0.174213\pi$
$12$	1.50769e17	−	2.34860e17i	0.815480	−	1.27031i
$13$	5.67246e17			0.852468			0.426234	−	0.904613i	$-0.359840\pi$
$13$	5.67246e17			0.852468			0.426234	+	0.904613i	$0.359840\pi$
$14$			3.16003e18i			1.45092i
$15$	−9.05011e18	−	5.80976e18i	−1.37782	−	0.884501i
$16$	−4.25830e18			−0.230843
$17$		−	9.91887e18i		−	0.203835i	−0.994793	−	0.101918i	$-0.967502\pi$
$17$		−	9.91887e18i		−	0.203835i	0.994793	−	0.101918i	$-0.0324978\pi$
$18$	−1.74914e20	+	8.00919e19i	−1.44034	+	0.659521i
$19$	3.55318e20			1.23185			0.615927	−	0.787803i	$-0.288782\pi$
$19$	3.55318e20			1.23185			0.615927	+	0.787803i	$0.288782\pi$
$20$		−	1.61976e21i		−	2.47155i
$21$	7.07826e20	−	1.10261e21i	0.494786	−	0.770749i
$22$	−4.96497e21			−1.64875
$23$		−	3.07553e20i		−	0.0501504i	−0.999686	−	0.0250752i	$-0.992017\pi$
$23$		−	3.07553e20i		−	0.0501504i	0.999686	−	0.0250752i	$-0.00798252\pi$
$24$	−8.23029e21	−	5.28347e21i	−0.679259	−	0.436053i
$25$	−3.91328e22			−1.68074
$26$		−	5.88909e22i		−	1.35044i
$27$	7.89715e22	+	1.12335e22i	0.990034	+	0.140830i
$28$	1.97341e23			1.38258
$29$		−	3.31674e23i		−	1.32539i	−0.748890	−	0.662694i	$-0.769413\pi$
$29$		−	3.31674e23i		−	1.32539i	0.748890	−	0.662694i	$-0.230587\pi$
$30$	−6.03163e23	+	9.39573e23i	−1.40118	+	2.18268i
$31$	3.59216e23			0.493820			0.246910	−	0.969038i	$-0.420585\pi$
$31$	3.59216e23			0.493820			0.246910	+	0.969038i	$0.420585\pi$
$32$			1.41791e24i			1.17287i
$33$	1.73239e24	+	1.11212e24i	0.875838	+	0.562248i
$34$	−1.02977e24			−0.322906
$35$		−	7.60436e24i		−	1.49960i
$36$	5.00167e24	+	1.09232e25i	0.628456	+	1.37249i
$37$	3.31930e24			0.269041			0.134520	−	0.990911i	$-0.457051\pi$
$37$	3.31930e24			0.269041			0.134520	+	0.990911i	$0.457051\pi$
$38$		−	3.68887e25i		−	1.95144i
$39$	−1.31911e25	+	2.05484e25i	−0.460520	+	0.717372i
$40$	−5.67618e25			−1.32159
$41$		−	3.35484e25i		−	0.526175i	−0.964772	−	0.263087i	$-0.915259\pi$
$41$		−	3.35484e25i		−	0.526175i	0.964772	−	0.263087i	$-0.0847408\pi$
$42$	−1.14472e26	−	7.34857e25i	−1.22098	−	0.783816i
$43$	1.34260e26			0.982767			0.491384	−	0.870943i	$-0.336491\pi$
$43$	1.34260e26			0.982767			0.491384	+	0.870943i	$0.336491\pi$
$44$			3.10058e26i			1.57109i
$45$	4.20915e26	−	1.92735e26i	1.48866	−	0.681647i
$46$	−3.19298e25			−0.0794457
$47$			9.71468e23i			0.00171342i	1.00000		0.000856708i	$0.000272699\pi$
$47$			9.71468e23i			0.00171342i	−1.00000		0.000856708i	$0.999727\pi$
$48$	9.90254e25	−	1.54256e26i	0.124706	−	0.194260i
$49$	−1.77959e26			−0.161132
$50$			4.06272e27i			2.66255i
$51$	3.59310e26	+	2.30660e26i	0.171532	+	0.110116i
$52$	−3.67768e27			−1.28683
$53$		−	5.82182e27i		−	1.50191i	−0.660351	−	0.750957i	$-0.729592\pi$
$53$		−	5.82182e27i		−	1.50191i	0.660351	−	0.750957i	$-0.270408\pi$
$54$	1.16625e27	−	8.19873e27i	0.223096	−	1.56836i
$55$	1.19478e28			1.70406
$56$		−	6.91551e27i		−	0.739292i
$57$	−8.26280e27	+	1.28713e28i	−0.665472	+	1.03663i
$58$	−3.44340e28			−2.09961
$59$		−	1.32634e28i		−	0.615208i	−0.951514	−	0.307604i	$-0.900473\pi$
$59$		−	1.32634e28i		−	0.615208i	0.951514	−	0.307604i	$-0.0995272\pi$
$60$	5.86755e28	+	3.76670e28i	2.07987	+	1.33518i
$61$	−6.55279e28			−1.78299			−0.891494	−	0.453032i	$-0.850342\pi$
$61$	−6.55279e28			−1.78299			−0.891494	+	0.453032i	$0.850342\pi$
$62$		−	3.72934e28i		−	0.782285i
$63$	2.34816e28	+	5.12817e28i	0.381310	+	0.832749i
$64$	1.28917e29			1.62716
$65$			1.41716e29i			1.39574i
$66$	1.15459e29	−	1.79855e29i	0.890686	−	1.38746i
$67$	−8.95668e28			−0.543188			−0.271594	−	0.962412i	$-0.587551\pi$
$67$	−8.95668e28			−0.543188			−0.271594	+	0.962412i	$0.587551\pi$
$68$			6.43080e28i			0.307696i
$69$	1.11410e28	+	7.15205e27i	0.0422027	+	0.0270922i
$70$	−7.89477e29			−2.37559
$71$		−	4.59368e28i		−	0.110161i	−0.998482	−	0.0550805i	$-0.982458\pi$
$71$		−	4.59368e28i		−	0.110161i	0.998482	−	0.0550805i	$-0.0175415\pi$
$72$	3.82786e29	−	1.75275e29i	0.733899	−	0.336048i
$73$	2.56589e28			0.0394524			0.0197262	−	0.999805i	$-0.493721\pi$
$73$	2.56589e28			0.0394524			0.0197262	+	0.999805i	$0.493721\pi$
$74$		−	3.44606e29i		−	0.426201i
$75$	9.10022e29	−	1.41758e30i	0.907970	−	1.41438i
$76$	−2.30366e30			−1.85952
$77$			1.45565e30i			0.953244i
$78$	2.13331e30	+	1.36949e30i	1.13642	+	0.729533i
$79$	3.75026e30			1.62940			0.814700	−	0.579883i	$-0.196902\pi$
$79$	3.75026e30			1.62940			0.814700	+	0.579883i	$0.196902\pi$
$80$		−	1.06386e30i		−	0.377958i
$81$	−2.24339e30	+	2.59950e30i	−0.653348	+	0.757058i
$82$	−3.48296e30			−0.833540
$83$			1.44084e30i			0.284032i	0.989864	+	0.142016i	$0.0453585\pi$
$83$			1.44084e30i			0.284032i	−0.989864	+	0.142016i	$0.954642\pi$
$84$	−4.58911e30	+	7.14866e30i	−0.746896	+	1.16347i
$85$	2.47805e30			0.333739
$86$		−	1.39387e31i		−	1.55685i
$87$	1.20148e31	+	7.71297e30i	1.11535	+	0.716001i
$88$	1.08655e31			0.840091
$89$		−	4.42071e30i		−	0.285268i	−0.989776	−	0.142634i	$-0.954443\pi$
$89$		−	4.42071e30i		−	0.285268i	0.989776	−	0.142634i	$-0.0455571\pi$
$90$	−2.00095e31	−	4.36990e31i	−1.07983	−	2.35826i
$91$	−1.72658e31			−0.780773
$92$			1.99399e30i			0.0757036i
$93$	−8.35346e30	+	1.30125e31i	−0.266771	+	0.415561i
$94$	1.00857e29			0.00271431
$95$			8.87696e31i			2.01691i
$96$	−5.13635e31	−	3.29731e31i	−0.986995	−	0.633606i
$97$	7.67762e31			1.24991			0.624955	−	0.780661i	$-0.285117\pi$
$97$	7.67762e31			1.24991			0.624955	+	0.780661i	$0.285117\pi$
$98$			1.84755e31i			0.255257i
$99$	−8.05726e31	+	3.68937e31i	−0.946291	+	0.433301i
$100$	2.53713e32			2.53713
$101$		−	1.25779e32i		−	1.07267i	−0.844006	−	0.536334i	$-0.819809\pi$
$101$		−	1.25779e32i		−	1.07267i	0.844006	−	0.536334i	$-0.180191\pi$
$102$	2.39469e31	−	3.73031e31i	0.174440	−	0.271733i
$103$	−5.21843e31			−0.325195			−0.162598	−	0.986692i	$-0.551987\pi$
$103$	−5.21843e31			−0.325195			−0.162598	+	0.986692i	$0.551987\pi$
$104$			1.28878e32i			0.688093i
$105$	2.75467e32	+	1.76837e32i	1.26195	+	0.810112i
$106$	−6.04415e32			−2.37926
$107$			1.50915e32i			0.511200i	0.966783	+	0.255600i	$0.0822731\pi$
$107$			1.50915e32i			0.511200i	−0.966783	+	0.255600i	$0.917727\pi$
$108$	−5.12003e32	−	7.28312e31i	−1.49449	−	0.212587i
$109$	2.44952e32			0.616961			0.308481	−	0.951231i	$-0.400180\pi$
$109$	2.44952e32			0.616961			0.308481	+	0.951231i	$0.400180\pi$
$110$		−	1.24041e33i		−	2.69949i
$111$	−7.71893e31	+	1.20241e32i	−0.145341	+	0.226404i
$112$	1.29614e32			0.211428
$113$		−	7.51269e32i		−	1.06302i	−0.847053	−	0.531509i	$-0.821625\pi$
$113$		−	7.51269e32i		−	1.06302i	0.847053	−	0.531509i	$-0.178375\pi$
$114$	1.33629e33	+	8.57835e32i	1.64218	+	1.05421i
$115$	7.68364e31			0.0821110
$116$			2.15037e33i			2.00072i
$117$	−4.37606e32	−	9.55694e32i	−0.354903	−	0.775077i
$118$	−1.37699e33			−0.974582
$119$			3.01910e32i			0.186692i
$120$	1.31998e33	−	2.05619e33i	0.713949	−	1.11215i
$121$	−1.75699e32			−0.0832153
$122$			6.80303e33i			2.82452i
$123$	1.21529e33	+	7.80158e32i	0.442789	+	0.284250i
$124$	−2.32894e33			−0.745437
$125$		−	3.95977e33i		−	1.11458i
$126$	5.32401e33	−	2.43783e33i	1.31920	−	0.604053i
$127$	−5.93082e33			−1.29496			−0.647479	−	0.762084i	$-0.724176\pi$
$127$	−5.93082e33			−1.29496			−0.647479	+	0.762084i	$0.724176\pi$
$128$		−	7.29410e33i		−	1.40479i
$129$	−3.12217e33	+	4.86354e33i	−0.530911	+	0.827022i
$130$	1.47128e34			2.21107
$131$		−	6.98819e33i		−	0.929018i	−0.885568	−	0.464509i	$-0.846231\pi$
$131$		−	6.98819e33i		−	0.929018i	0.885568	−	0.464509i	$-0.153769\pi$
$132$	−1.12318e34	−	7.21031e33i	−1.32211	−	0.848732i
$133$	−1.08151e34			−1.12825
$134$			9.29872e33i			0.860491i
$135$	−2.80648e33	+	1.97296e34i	−0.230580	+	1.62098i
$136$	2.25357e33			0.164531
$137$		−	2.45169e34i		−	1.59198i	−0.605312	−	0.795989i	$-0.706952\pi$
$137$		−	2.45169e34i		−	1.59198i	0.605312	−	0.795989i	$-0.293048\pi$
$138$	7.42518e32	−	1.15665e33i	0.0429182	−	0.0668555i
$139$	1.85811e34			0.956828			0.478414	−	0.878134i	$-0.341212\pi$
$139$	1.85811e34			0.956828			0.478414	+	0.878134i	$0.341212\pi$
$140$			4.93021e34i			2.26369i
$141$	−3.51913e31	−	2.25912e31i	−0.00144188	−	0.000925622i
$142$	−4.76911e33			−0.174512
$143$		−	2.71276e34i		−	0.887228i
$144$	3.28509e33	+	7.17436e33i	0.0961054	+	0.209886i
$145$	8.28626e34			2.17005
$146$		−	2.66388e33i		−	0.0624985i
$147$	4.13838e33	−	6.44653e33i	0.0870468	−	0.135596i
$148$	−2.15203e34			−0.406126
$149$			1.74564e34i			0.295784i	0.989004	+	0.147892i	$0.0472488\pi$
$149$			1.74564e34i			0.295784i	−0.989004	+	0.147892i	$0.952751\pi$
$150$	−1.47172e35	−	9.44775e34i	−2.24060	−	1.43836i
$151$	−1.31115e35			−1.79482			−0.897410	−	0.441197i	$-0.854554\pi$
$151$	−1.31115e35			−1.79482			−0.897410	+	0.441197i	$0.854554\pi$
$152$			8.07282e34i			0.994324i
$153$	−1.67113e34	+	7.65199e33i	−0.185330	+	0.0848617i
$154$	1.51124e35			1.51008
$155$			8.97435e34i			0.808530i
$156$	8.55234e34	−	1.33223e35i	0.695170	−	1.08290i
$157$	5.79275e34			0.425099			0.212549	−	0.977150i	$-0.431823\pi$
$157$	5.79275e34			0.425099			0.212549	+	0.977150i	$0.431823\pi$
$158$		−	3.89348e35i		−	2.58121i
$159$	2.10895e35	+	1.35385e35i	1.26390	+	0.811364i
$160$	−3.54239e35			−1.92033
$161$			9.36127e33i			0.0459326i
$162$	2.69877e35	+	2.32906e35i	1.19929	+	1.03500i
$163$	−3.16517e34			−0.127466			−0.0637332	−	0.997967i	$-0.520301\pi$
$163$	−3.16517e34			−0.127466			−0.0637332	+	0.997967i	$0.520301\pi$
$164$			2.17508e35i			0.794278i
$165$	−2.77843e35	+	4.32807e35i	−0.920567	+	1.43401i
$166$	1.49587e35			0.449950
$167$			5.63562e34i			0.153985i	0.997032	+	0.0769925i	$0.0245317\pi$
$167$			5.63562e34i			0.153985i	−0.997032	+	0.0769925i	$0.975468\pi$
$168$	2.50513e35	+	1.60818e35i	0.622131	+	0.399380i
$169$	−1.21011e35			−0.273299
$170$		−	2.57268e35i		−	0.528693i
$171$	−2.74112e35	−	5.98638e35i	−0.512851	−	1.12002i
$172$	−8.70459e35			−1.48352
$173$		−	1.61709e34i		−	0.0251186i	−0.999921	−	0.0125593i	$-0.996002\pi$
$173$		−	1.61709e34i		−	0.0251186i	0.999921	−	0.0125593i	$-0.00399786\pi$
$174$	8.00752e35	−	1.24737e36i	1.13425	−	1.76687i
$175$	1.19112e36			1.53939
$176$			2.03646e35i			0.240256i
$177$	4.80464e35	+	3.08436e35i	0.517712	+	0.332348i
$178$	−4.58954e35			−0.451907
$179$		−	8.90367e35i		−	0.801532i	−0.916180	−	0.400766i	$-0.868744\pi$
$179$		−	8.90367e35i		−	0.801532i	0.916180	−	0.400766i	$-0.131256\pi$
$180$	−2.72896e36	+	1.24957e36i	−2.24718	+	1.02897i
$181$	−1.19270e36			−0.898826			−0.449413	−	0.893324i	$-0.648367\pi$
$181$	−1.19270e36			−0.898826			−0.449413	+	0.893324i	$0.648367\pi$
$182$			1.79252e36i			1.23686i
$183$	1.52383e36	−	2.37374e36i	0.963206	−	1.50043i
$184$	6.98760e34			0.0404802
$185$			8.29265e35i			0.440500i
$186$	1.35095e36	+	8.67247e35i	0.658311	+	0.422606i
$187$	−4.74354e35			−0.212147
$188$		−	6.29841e33i		−	0.00258646i
$189$	−2.40373e36	−	3.41925e35i	−0.906769	−	0.128986i
$190$	9.21596e36			3.19509
$191$			3.89653e36i			1.24207i	0.783784	+	0.621033i	$0.213287\pi$
$191$			3.89653e36i			1.24207i	−0.783784	+	0.621033i	$0.786713\pi$
$192$	−2.99792e36	+	4.66998e36i	−0.879022	+	1.36929i
$193$	1.90013e36			0.512703			0.256351	−	0.966584i	$-0.417480\pi$
$193$	1.90013e36			0.512703			0.256351	+	0.966584i	$0.417480\pi$
$194$		−	7.97082e36i		−	1.98005i
$195$	−5.13364e36	−	3.29556e36i	−1.17455	−	0.754008i
$196$	1.15378e36			0.243234
$197$		−	3.35666e36i		−	0.652300i	−0.945318	−	0.326150i	$-0.894248\pi$
$197$		−	3.35666e36i		−	0.652300i	0.945318	−	0.326150i	$-0.105752\pi$
$198$	3.83027e36	+	8.36496e36i	0.686413	+	1.49907i
$199$	−7.69959e36			−1.27297			−0.636485	−	0.771289i	$-0.719612\pi$
$199$	−7.69959e36			−1.27297			−0.636485	+	0.771289i	$0.719612\pi$
$200$		−	8.89098e36i		−	1.35666i
$201$	2.08285e36	−	3.24454e36i	0.293441	−	0.457105i
$202$	−1.30582e37			−1.69927
$203$			1.00955e37i			1.21392i
$204$	−2.32955e36	−	1.49546e36i	−0.258934	−	0.166224i
$205$	8.38145e36			0.861504
$206$			5.41772e36i			0.515158i
$207$	−5.18163e35	+	2.37264e35i	−0.0455975	+	0.0208788i
$208$	−2.41550e36			−0.196786
$209$		−	1.69925e37i		−	1.28208i
$210$	1.83590e37	−	2.85987e37i	1.28334	−	1.99911i
$211$	6.84634e36			0.443546			0.221773	−	0.975098i	$-0.428816\pi$
$211$	6.84634e36			0.443546			0.221773	+	0.975098i	$0.428816\pi$
$212$			3.77452e37i			2.26719i
$213$	1.66405e36	+	1.06825e36i	0.0927030	+	0.0595111i
$214$	1.56678e37			0.809818
$215$			3.35424e37i			1.60908i
$216$	−2.55225e36	+	1.79423e37i	−0.113675	+	0.799133i
$217$	−1.09338e37			−0.452288
$218$		−	2.54307e37i		−	0.977359i
$219$	−5.96691e35	+	9.29491e35i	−0.0213130	+	0.0332001i
$220$	−7.74623e37			−2.57233
$221$		−	5.62644e36i		−	0.173763i
$222$	1.24833e37	+	8.01370e36i	0.358659	+	0.230243i
$223$	5.43018e37			1.45190			0.725950	−	0.687748i	$-0.241401\pi$
$223$	5.43018e37			1.45190			0.725950	+	0.687748i	$0.241401\pi$
$224$		−	4.31583e37i		−	1.07423i
$225$	3.01893e37	+	6.59308e37i	0.699734	+	1.52816i
$226$	−7.79960e37			−1.68398
$227$		−	4.49436e37i		−	0.904178i	−0.891973	−	0.452089i	$-0.850679\pi$
$227$		−	4.49436e37i		−	0.904178i	0.891973	−	0.452089i	$-0.149321\pi$
$228$	5.35710e37	−	8.34499e37i	1.00455	−	1.56483i
$229$	2.48444e37			0.434372			0.217186	−	0.976130i	$-0.430312\pi$
$229$	2.48444e37			0.434372			0.217186	+	0.976130i	$0.430312\pi$
$230$		−	7.97707e36i		−	0.130076i
$231$	−5.27305e37	−	3.38506e37i	−0.802178	−	0.514962i
$232$	7.53563e37			1.06982
$233$		−	8.15150e37i		−	1.08030i	−0.841570	−	0.540148i	$-0.818368\pi$
$233$		−	8.15150e37i		−	1.08030i	0.841570	−	0.540148i	$-0.181632\pi$
$234$	−9.92191e37	+	4.54318e37i	−1.22784	+	0.562220i
$235$	−2.42704e35			−0.00280537
$236$			8.59917e37i			0.928677i
$237$	−8.72111e37	+	1.35852e38i	−0.880234	+	1.37118i
$238$	3.13440e37			0.295749
$239$			1.65146e38i			1.45714i	0.684971	+	0.728570i	$0.259815\pi$
$239$			1.65146e38i			1.45714i	−0.684971	+	0.728570i	$0.740185\pi$
$240$	3.85381e37	+	2.47397e37i	0.318061	+	0.204180i
$241$	−1.04519e38			−0.807092			−0.403546	−	0.914959i	$-0.632222\pi$
$241$	−1.04519e38			−0.807092			−0.403546	+	0.914959i	$0.632222\pi$
$242$			1.82409e37i			0.131826i
$243$	−4.19970e37	−	1.41717e38i	−0.284130	−	0.958786i
$244$	4.24843e38			2.69148
$245$		−	4.44597e37i		−	0.263821i
$246$	8.09951e37	−	1.26170e38i	0.450295	−	0.701444i
$247$	2.01552e38			1.05012
$248$			8.16139e37i			0.398600i
$249$	−5.21943e37	−	3.35064e37i	−0.239020	−	0.153440i
$250$	−4.11099e38			−1.76566
$251$		−	5.56329e37i		−	0.224157i	−0.993699	−	0.112079i	$-0.964249\pi$
$251$		−	5.56329e37i		−	0.224157i	0.993699	−	0.112079i	$-0.0357508\pi$
$252$	−1.52240e38	−	3.32480e38i	−0.575601	−	1.25706i
$253$	−1.47082e37			−0.0521953
$254$			6.15731e38i			2.05141i
$255$	−5.76263e37	+	8.97669e37i	−0.180293	+	0.280849i
$256$	−2.03573e38			−0.598247
$257$		−	4.70854e38i		−	1.30004i	−0.759917	−	0.650020i	$-0.774761\pi$
$257$		−	4.70854e38i		−	1.30004i	0.759917	−	0.650020i	$-0.225239\pi$
$258$	5.04927e38	+	3.24140e38i	1.31013	+	0.841043i
$259$	−1.01033e38			−0.246414
$260$		−	9.18801e38i		−	2.10692i
$261$	−5.58802e38	+	2.55872e38i	−1.20506	+	0.551791i
$262$	−7.25506e38			−1.47170
$263$		−	8.36358e38i		−	1.59625i	−0.602494	−	0.798124i	$-0.705826\pi$
$263$		−	8.36358e38i		−	1.59625i	0.602494	−	0.798124i	$-0.294174\pi$
$264$	−2.52674e38	+	3.93600e38i	−0.453834	+	0.706957i
$265$	1.45448e39			2.45908
$266$			1.12282e39i			1.78732i
$267$	1.60140e38	+	1.02802e38i	0.240059	+	0.154107i
$268$	5.80697e38			0.819960
$269$			1.11243e38i			0.147992i	0.997259	+	0.0739960i	$0.0235752\pi$
$269$			1.11243e38i			0.147992i	−0.997259	+	0.0739960i	$0.976425\pi$
$270$	2.04830e39	+	2.91366e38i	2.56788	+	0.365274i
$271$	−6.87434e38			−0.812311			−0.406156	−	0.913804i	$-0.633131\pi$
$271$	−6.87434e38			−0.812311			−0.406156	+	0.913804i	$0.633131\pi$
$272$			4.22375e37i			0.0470539i
$273$	4.01511e38	−	6.25451e38i	0.421789	−	0.657039i
$274$	−2.54532e39			−2.52193
$275$			1.87146e39i			1.74928i
$276$	−7.22318e37	−	4.63695e37i	−0.0637064	−	0.0408966i
$277$	−1.52657e39			−1.27070			−0.635348	−	0.772226i	$-0.719143\pi$
$277$	−1.52657e39			−1.27070			−0.635348	+	0.772226i	$0.719143\pi$
$278$		−	1.92907e39i		−	1.51576i
$279$	−2.77120e38	−	6.05206e38i	−0.205589	−	0.448989i
$280$	1.72771e39			1.21044
$281$			1.62418e39i			1.07481i	0.843324	+	0.537405i	$0.180595\pi$
$281$			1.62418e39i			1.07481i	−0.843324	+	0.537405i	$0.819405\pi$
$282$	−2.34539e36	+	3.65352e36i	−0.00146632	+	0.00228416i
$283$	2.63488e39			1.55661			0.778303	−	0.627889i	$-0.216081\pi$
$283$	2.63488e39			1.55661			0.778303	+	0.627889i	$0.216081\pi$
$284$			2.97827e38i			0.166292i
$285$	−3.21566e39	−	2.06431e39i	−1.69728	−	1.08958i
$286$	−2.81636e39			−1.40550
$287$			1.02114e39i			0.481922i
$288$	2.38889e39	−	1.09386e39i	1.06639	−	0.488293i
$289$	2.26953e39			0.958451
$290$		−	8.60270e39i		−	3.43769i
$291$	−1.78541e39	+	2.78121e39i	−0.675227	+	1.05183i
$292$	−1.66357e38			−0.0595547
$293$			5.48987e39i			1.86072i	0.366651	+	0.930359i	$0.380504\pi$
$293$			5.48987e39i			1.86072i	−0.366651	+	0.930359i	$0.619496\pi$
$294$	−6.69271e38	−	4.29642e38i	−0.214805	−	0.137895i
$295$	3.31361e39			1.00728
$296$			7.54145e38i			0.217164i
$297$	5.37224e38	−	3.77668e39i	0.146572	−	1.03040i
$298$	1.81231e39			0.468567
$299$		−	1.74458e38i		−	0.0427516i
$300$	−5.90003e39	+	9.19073e39i	−1.37061	+	2.13506i
$301$	−4.08659e39			−0.900114
$302$			1.36122e40i			2.84327i
$303$	4.55631e39	+	2.92495e39i	0.902675	+	0.579476i
$304$	−1.51305e39			−0.284364
$305$		−	1.63709e40i		−	2.91928i
$306$	7.94421e38	+	1.73495e39i	0.134434	+	0.293591i
$307$	4.15729e39			0.667724			0.333862	−	0.942622i	$-0.391648\pi$
$307$	4.15729e39			0.667724			0.333862	+	0.942622i	$0.391648\pi$
$308$		−	9.43753e39i		−	1.43895i
$309$	1.21353e39	−	1.89037e39i	0.175677	−	0.273660i
$310$	9.31707e39			1.28083
$311$			4.12881e39i			0.539087i	0.962988	+	0.269543i	$0.0868728\pi$
$311$			4.12881e39i			0.539087i	−0.962988	+	0.269543i	$0.913127\pi$
$312$	−4.66860e39	−	2.99703e39i	−0.579046	−	0.371721i
$313$	1.51328e40			1.78324			0.891618	−	0.452788i	$-0.149570\pi$
$313$	1.51328e40			1.78324			0.891618	+	0.452788i	$0.149570\pi$
$314$		−	6.01397e39i		−	0.673421i
$315$	−1.28118e40	+	5.86645e39i	−1.36346	+	0.624318i
$316$	−2.43144e40			−2.45963
$317$			1.30044e39i			0.125067i	0.998043	+	0.0625336i	$0.0199181\pi$
$317$			1.30044e39i			0.125067i	−0.998043	+	0.0625336i	$0.980082\pi$
$318$	1.40555e40	−	2.18948e40i	1.28532	−	2.00220i
$319$	−1.58618e40			−1.37943
$320$			3.22074e40i			2.66414i
$321$	−5.46686e39	−	3.50948e39i	−0.430187	−	0.276161i
$322$	9.71877e38			0.0727641
$323$		−	3.52435e39i		−	0.251095i
$324$	1.45448e40	−	1.68536e40i	0.986250	−	1.14280i
$325$	−2.21979e40			−1.43278
$326$			3.28605e39i			0.201926i
$327$	−5.69630e39	+	8.87336e39i	−0.333295	+	0.519187i
$328$	7.62220e39			0.424716
$329$		−	2.95695e37i		−	0.00156931i
$330$	4.49335e40	+	2.88453e40i	2.27168	+	1.45832i
$331$	3.01231e40			1.45095			0.725475	−	0.688249i	$-0.241620\pi$
$331$	3.01231e40			1.45095			0.725475	+	0.688249i	$0.241620\pi$
$332$		−	9.34156e39i		−	0.428756i
$333$	−2.56070e39	−	5.59234e39i	−0.112008	−	0.244616i
$334$	5.85084e39			0.243935
$335$		−	2.23766e40i		−	0.889360i
$336$	−3.01413e39	+	4.69524e39i	−0.114218	+	0.177922i
$337$	−4.23569e40			−1.53054			−0.765272	−	0.643707i	$-0.777396\pi$
$337$	−4.23569e40			−1.53054			−0.765272	+	0.643707i	$0.777396\pi$
$338$			1.25632e40i			0.432947i
$339$	2.72146e40	+	1.74705e40i	0.894555	+	0.574264i
$340$	−1.60662e40			−0.503790
$341$		−	1.71789e40i		−	0.513956i
$342$	−6.21499e40	+	2.84580e40i	−1.77428	+	0.812433i
$343$	3.90332e40			1.06348
$344$			3.05039e40i			0.793268i
$345$	−1.78681e39	+	2.78339e39i	−0.0443580	+	0.0690984i
$346$	−1.67884e39			−0.0397917
$347$			1.86252e40i			0.421530i	0.977537	+	0.210765i	$0.0675954\pi$
$347$			1.86252e40i			0.421530i	−0.977537	+	0.210765i	$0.932405\pi$
$348$	−7.78969e40	−	5.00063e40i	−1.68365	−	1.08083i
$349$	−2.35818e40			−0.486822			−0.243411	−	0.969923i	$-0.578266\pi$
$349$	−2.35818e40			−0.486822			−0.243411	+	0.969923i	$0.578266\pi$
$350$		−	1.23661e41i		−	2.43862i
$351$	4.47963e40	+	6.37216e39i	0.843972	+	0.120053i
$352$	6.78092e40			1.22069
$353$		−	4.50171e40i		−	0.774430i	−0.921989	−	0.387215i	$-0.873437\pi$
$353$		−	4.50171e40i		−	0.774430i	0.921989	−	0.387215i	$-0.126563\pi$
$354$	3.20215e40	−	4.98812e40i	0.526489	−	0.820134i
$355$	1.14765e40			0.180366
$356$			2.86612e40i			0.430621i
$357$	−1.09366e40	−	7.02083e39i	−0.157106	−	0.100855i
$358$	−9.24370e40			−1.26975
$359$			9.66820e40i			1.27009i	0.772475	+	0.635045i	$0.219019\pi$
$359$			9.66820e40i			1.27009i	−0.772475	+	0.635045i	$0.780981\pi$
$360$	4.37893e40	+	9.56321e40i	0.550210	+	1.20161i
$361$	4.30521e40			0.517463
$362$			1.23825e41i			1.42388i
$363$	4.08583e39	−	6.36467e39i	0.0449546	−	0.0700277i
$364$	1.11941e41			1.17860
$365$			6.41042e39i			0.0645952i
$366$	−2.46439e41	−	1.58202e41i	−2.37690	−	1.52586i
$367$	7.40639e40			0.683832			0.341916	−	0.939730i	$-0.388924\pi$
$367$	7.40639e40			0.683832			0.341916	+	0.939730i	$0.388924\pi$
$368$			1.30965e39i			0.0115768i
$369$	−5.65222e40	+	2.58812e40i	−0.478407	+	0.219059i
$370$	8.60934e40			0.697818
$371$			1.77204e41i			1.37560i
$372$	5.41588e40	−	8.43654e40i	0.402700	−	0.627303i
$373$	−8.48695e40			−0.604519			−0.302260	−	0.953226i	$-0.597741\pi$
$373$	−8.48695e40			−0.604519			−0.302260	+	0.953226i	$0.597741\pi$
$374$			4.92469e40i			0.336073i
$375$	1.43442e41	+	9.20832e40i	0.937942	+	0.602116i
$376$	−2.20718e38			−0.00138303
$377$		−	1.88141e41i		−	1.12985i
$378$	−3.54983e40	+	2.49553e41i	−0.204333	+	1.43646i
$379$	−2.86987e41			−1.58356			−0.791781	−	0.610805i	$-0.790846\pi$
$379$	−2.86987e41			−1.58356			−0.791781	+	0.610805i	$0.790846\pi$
$380$		−	5.75528e41i		−	3.04459i
$381$	1.37920e41	−	2.14843e41i	0.699562	−	1.08974i
$382$	4.04534e41			1.96762
$383$			2.93471e41i			1.36894i	0.729041	+	0.684470i	$0.239966\pi$
$383$			2.93471e41i			1.36894i	−0.729041	+	0.684470i	$0.760034\pi$
$384$	2.64228e41	+	1.69622e41i	1.18217	+	0.758897i
$385$	−3.63666e41			−1.56074
$386$		−	1.97269e41i		−	0.812199i
$387$	−1.03576e41	−	2.26200e41i	−0.409150	−	0.893548i
$388$	−4.97770e41			−1.88678
$389$		−	5.36936e41i		−	1.95312i	−0.215245	−	0.976560i	$-0.569055\pi$
$389$		−	5.36936e41i		−	1.95312i	0.215245	−	0.976560i	$-0.430945\pi$
$390$	−3.42142e41	+	5.32969e41i	−1.19446	+	1.86066i
$391$	−3.05058e39			−0.0102224
$392$		−	4.04323e40i		−	0.130062i
$393$	2.53146e41	+	1.62508e41i	0.781790	+	0.501874i
$394$	−3.48485e41			−1.03334
$395$			9.36933e41i			2.66781i
$396$	5.22384e41	−	2.39197e41i	1.42846	−	0.654082i
$397$	4.82964e41			1.26843			0.634216	−	0.773156i	$-0.281323\pi$
$397$	4.82964e41			1.26843			0.634216	+	0.773156i	$0.281323\pi$
$398$			7.99363e41i			2.01658i
$399$	2.51503e41	−	3.91777e41i	0.609504	−	0.949450i
$400$	1.66639e41			0.387987
$401$		−	6.81584e41i		−	1.52479i	−0.647114	−	0.762394i	$-0.724024\pi$
$401$		−	6.81584e41i		−	1.52479i	0.647114	−	0.762394i	$-0.275976\pi$
$402$	−3.36845e41	−	2.16239e41i	−0.724124	−	0.464855i
$403$	2.03764e41			0.420965
$404$			8.15473e41i			1.61923i
$405$	−6.49437e41	−	5.60470e41i	−1.23953	−	1.06972i
$406$	1.04810e42			1.92303
$407$		−	1.58740e41i		−	0.280011i
$408$	−5.24061e40	+	8.16352e40i	−0.0888831	+	0.138457i
$409$	−9.34417e41			−1.52394			−0.761970	−	0.647613i	$-0.775767\pi$
$409$	−9.34417e41			−1.52394			−0.761970	+	0.647613i	$0.775767\pi$
$410$		−	8.70153e41i		−	1.36475i
$411$	8.88121e41	+	5.70134e41i	1.33969	+	0.860018i
$412$	3.38331e41			0.490893
$413$			4.03710e41i			0.563467i
$414$	2.46325e40	+	5.37952e40i	0.0330752	+	0.0722333i
$415$	−3.59968e41			−0.465045
$416$			8.04303e41i			0.999831i
$417$	−4.32097e41	+	6.73096e41i	−0.516898	+	0.805194i
$418$	−1.76414e42			−2.03101
$419$		−	1.19503e42i		−	1.32421i	−0.749412	−	0.662104i	$-0.769664\pi$
$419$		−	1.19503e42i		−	1.32421i	0.749412	−	0.662104i	$-0.230336\pi$
$420$	−1.78596e42	−	1.14651e42i	−1.90495	−	1.22289i
$421$	−1.01400e41			−0.104118			−0.0520590	−	0.998644i	$-0.516578\pi$
$421$	−1.01400e41			−0.104118			−0.0520590	+	0.998644i	$0.516578\pi$
$422$		−	7.10779e41i		−	0.702644i
$423$	1.63673e39	−	7.49447e38i	0.00155787	−	0.000713337i
$424$	1.32272e42			1.21231
$425$			3.88153e41i			0.342595i
$426$	1.10904e41	−	1.72760e41i	0.0942746	−	0.146856i
$427$	1.99453e42			1.63303
$428$		−	9.78440e41i		−	0.771674i
$429$	9.82694e41	+	6.30845e41i	0.746624	+	0.479298i
$430$	3.48233e42			2.54903
$431$		−	1.23004e42i		−	0.867524i	−0.901028	−	0.433762i	$-0.857186\pi$
$431$		−	1.23004e42i		−	0.867524i	0.901028	−	0.433762i	$-0.142814\pi$
$432$	−3.36284e41	−	4.78356e40i	−0.228542	−	0.0325096i
$433$	−1.88664e42			−1.23561			−0.617806	−	0.786330i	$-0.711978\pi$
$433$	−1.88664e42			−1.23561			−0.617806	+	0.786330i	$0.711978\pi$
$434$			1.13513e42i			0.716493i
$435$	−1.92694e42	+	3.00168e42i	−1.17231	+	1.82615i
$436$	−1.58812e42			−0.931323
$437$		−	1.09279e41i		−	0.0617779i
$438$	9.64987e40	+	6.19478e40i	0.0525940	+	0.0337629i
$439$	8.54191e41			0.448872			0.224436	−	0.974489i	$-0.427946\pi$
$439$	8.54191e41			0.448872			0.224436	+	0.974489i	$0.427946\pi$
$440$			2.71454e42i			1.37548i
$441$	1.37288e41	+	2.99824e41i	0.0670832	+	0.146504i
$442$	−5.84131e41			−0.275267
$443$			2.00522e42i			0.911384i	0.890137	+	0.455692i	$0.150608\pi$
$443$			2.00522e42i			0.911384i	−0.890137	+	0.455692i	$0.849392\pi$
$444$	5.00449e41	−	7.79570e41i	0.219398	−	0.341765i
$445$	1.10443e42			0.467068
$446$		−	5.63755e42i		−	2.30003i
$447$	−6.32356e41	−	4.05944e41i	−0.248909	−	0.159789i
$448$	−3.92395e42			−1.49031
$449$			3.93631e42i			1.44261i	0.692619	+	0.721304i	$0.256457\pi$
$449$			3.93631e42i			1.44261i	−0.692619	+	0.721304i	$0.743543\pi$
$450$	6.84486e42	−	3.13422e42i	2.42083	−	1.10848i
$451$	−1.60440e42			−0.547630
$452$			4.87078e42i			1.60466i
$453$	3.04904e42	−	4.74962e42i	0.969598	−	1.51038i
$454$	−4.66599e42			−1.43235
$455$		−	4.31355e42i		−	1.27836i
$456$	−2.92437e42	−	1.87731e42i	−0.836747	−	0.537154i
$457$	4.01009e42			1.10789			0.553943	−	0.832554i	$-0.313122\pi$
$457$	4.01009e42			1.10789			0.553943	+	0.832554i	$0.313122\pi$
$458$		−	2.57932e42i		−	0.688110i
$459$	1.11424e41	−	7.83308e41i	0.0287061	−	0.201804i
$460$	−4.98161e41			−0.123949
$461$		−	1.44532e42i		−	0.347335i	−0.984804	−	0.173668i	$-0.944438\pi$
$461$		−	1.44532e42i		−	0.347335i	0.984804	−	0.173668i	$-0.0555619\pi$
$462$	−3.51433e42	+	5.47443e42i	−0.815777	+	1.27077i
$463$	4.37917e42			0.981964			0.490982	−	0.871170i	$-0.336638\pi$
$463$	4.37917e42			0.981964			0.490982	+	0.871170i	$0.336638\pi$
$464$			1.41236e42i			0.305956i
$465$	−3.25094e42	−	2.08696e42i	−0.680397	−	0.436784i
$466$	−8.46280e42			−1.71135
$467$			4.22719e42i			0.826002i	0.910731	+	0.413001i	$0.135519\pi$
$467$			4.22719e42i			0.826002i	−0.910731	+	0.413001i	$0.864481\pi$
$468$	2.83718e42	+	6.19614e42i	0.535738	+	1.17000i
$469$	2.72623e42			0.497504
$470$			2.51972e40i			0.00444413i
$471$	−1.34709e42	+	2.09841e42i	−0.229647	+	0.357731i
$472$	3.01344e42			0.496582
$473$		−	6.42076e42i		−	1.02284i
$474$	1.41041e43	+	9.05416e42i	2.17215	+	1.39442i
$475$	−1.39046e43			−2.07043
$476$		−	1.95740e42i		−	0.281818i
$477$	−9.80859e42	+	4.49129e42i	−1.36556	+	0.625284i
$478$	1.71453e43			2.30833
$479$		−	1.09686e43i		−	1.42818i	−0.700054	−	0.714090i	$-0.746841\pi$
$479$		−	1.09686e43i		−	1.42818i	0.700054	−	0.714090i	$-0.253159\pi$
$480$	8.23771e42	−	1.28322e43i	1.03740	−	1.61600i
$481$	1.88286e42			0.229349
$482$			1.08511e43i			1.27856i
$483$	−3.39111e41	−	2.17694e41i	−0.0386534	−	0.0248137i
$484$	1.13913e42			0.125616
$485$			1.91811e43i			2.04647i
$486$	−1.47129e43	+	4.36008e42i	−1.51886	+	0.450105i
$487$	9.98519e42			0.997454			0.498727	−	0.866759i	$-0.333801\pi$
$487$	9.98519e42			0.997454			0.498727	+	0.866759i	$0.333801\pi$
$488$		−	1.48879e43i		−	1.43919i
$489$	7.36052e41	−	1.14658e42i	0.0688599	−	0.107266i
$490$	−4.61576e42			−0.417932
$491$			4.39197e42i			0.384907i	0.981306	+	0.192453i	$0.0616444\pi$
$491$			4.39197e42i			0.384907i	−0.981306	+	0.192453i	$0.938356\pi$
$492$	−7.87918e42	−	5.05807e42i	−0.668404	−	0.429085i
$493$	−3.28983e42			−0.270161
$494$		−	2.09250e43i		−	1.66354i
$495$	−9.21722e42	−	2.01296e43i	−0.709442	−	1.54936i
$496$	−1.52965e42			−0.113995
$497$			1.39822e42i			0.100896i
$498$	−3.47860e42	+	5.41876e42i	−0.243072	+	0.378643i
$499$	−9.63135e42			−0.651746			−0.325873	−	0.945414i	$-0.605658\pi$
$499$	−9.63135e42			−0.651746			−0.325873	+	0.945414i	$0.605658\pi$
$500$			2.56727e43i			1.68249i
$501$	−2.04150e42	−	1.31055e42i	−0.129582	−	0.0831858i
$502$	−5.77575e42			−0.355099
$503$		−	2.08881e42i		−	0.124397i	−0.998064	−	0.0621986i	$-0.980189\pi$
$503$		−	2.08881e42i		−	0.124397i	0.998064	−	0.0621986i	$-0.0198112\pi$
$504$	−1.16512e43	+	5.33502e42i	−0.672176	+	0.307785i
$505$	3.14235e43			1.75627
$506$			1.52699e42i			0.0826852i
$507$	2.81408e42	−	4.38361e42i	0.147642	−	0.229988i
$508$	3.84519e43			1.95478
$509$			1.42164e43i			0.700335i	0.936687	+	0.350167i	$0.113875\pi$
$509$			1.42164e43i			0.700335i	−0.936687	+	0.350167i	$0.886125\pi$
$510$	9.31950e42	+	5.98270e42i	0.444908	+	0.285611i
$511$	−7.81006e41			−0.0361343
$512$		−	1.01932e43i		−	0.457079i
$513$	2.80600e43	+	3.99146e42i	1.21958	+	0.173482i
$514$	−4.88836e43			−2.05946
$515$		−	1.30373e43i		−	0.532441i
$516$	2.02423e43	−	3.15323e43i	0.801427	−	1.24842i
$517$	4.64589e40			0.00178328
$518$			1.04891e43i			0.390357i
$519$	5.85788e41	+	3.76049e41i	0.0211379	+	0.0135696i
$520$	−3.21979e43			−1.12661
$521$			4.58192e42i			0.155469i	0.996974	+	0.0777345i	$0.0247686\pi$
$521$			4.58192e42i			0.155469i	−0.996974	+	0.0777345i	$0.975231\pi$
$522$	2.65644e43	+	5.80142e43i	0.874121	+	1.90900i
$523$	1.51005e43			0.481907			0.240953	−	0.970537i	$-0.422540\pi$
$523$	1.51005e43			0.481907			0.240953	+	0.970537i	$0.422540\pi$
$524$			4.53072e43i			1.40238i
$525$	−2.76992e43	+	4.31482e43i	−0.831607	+	1.29543i
$526$	−8.68297e43			−2.52870
$527$		−	3.56302e42i		−	0.100658i
$528$	−7.37705e42	−	4.73573e42i	−0.202181	−	0.129791i
$529$	3.75143e43			0.997485
$530$		−	1.51002e44i		−	3.89555i
$531$	−2.23461e43	+	1.02321e43i	−0.559357	+	0.256126i
$532$	7.01188e43			1.70313
$533$		−	1.90302e43i		−	0.448547i
$534$	1.06728e43	−	1.66255e43i	0.244129	−	0.380290i
$535$	−3.77033e43			−0.836987
$536$		−	2.03496e43i		−	0.438449i
$537$	3.22534e43	+	2.07052e43i	0.674508	+	0.433004i
$538$	1.15492e43			0.234442
$539$			8.51059e42i			0.167702i
$540$	1.81955e43	−	1.27915e44i	0.348069	−	2.44692i
$541$	−5.59972e43			−1.03994			−0.519972	−	0.854183i	$-0.674058\pi$
$541$	−5.59972e43			−1.03994			−0.519972	+	0.854183i	$0.674058\pi$
$542$			7.13687e43i			1.28682i
$543$	2.77360e43	−	4.32055e43i	0.485564	−	0.756383i
$544$	1.40641e43			0.239072
$545$			6.11969e43i			1.01015i
$546$	−6.49337e43	−	4.16845e43i	−1.04085	−	0.668178i
$547$	−8.07963e43			−1.25775			−0.628875	−	0.777506i	$-0.716484\pi$
$547$	−8.07963e43			−1.25775			−0.628875	+	0.777506i	$0.716484\pi$
$548$			1.58953e44i			2.40314i
$549$	5.05520e43	+	1.10401e44i	0.742302	+	1.62112i
$550$	1.94293e44			2.77112
$551$		−	1.17849e44i		−	1.63268i
$552$	−1.62495e42	+	2.53125e42i	−0.0218682	+	0.0340651i
$553$	−1.14150e44			−1.49236
$554$			1.58487e44i			2.01297i
$555$	−3.00400e43	−	1.92843e43i	−0.370691	−	0.237967i
$556$	−1.20468e44			−1.44436
$557$		−	6.48513e43i		−	0.755501i	−0.925907	−	0.377751i	$-0.876698\pi$
$557$		−	6.48513e43i		−	0.755501i	0.925907	−	0.377751i	$-0.123302\pi$
$558$	−6.28318e43	+	2.87703e43i	−0.711266	+	0.325684i
$559$	7.61584e43			0.837777
$560$			3.23816e43i			0.346171i
$561$	1.10310e43	−	1.71834e43i	0.114606	−	0.178527i
$562$	1.68620e44			1.70266
$563$		−	1.87769e41i		−	0.00184285i	−1.00000		0.000921424i	$-0.999707\pi$
$563$		−	1.87769e41i		−	0.00184285i	1.00000		0.000921424i	$-0.000293298\pi$
$564$	2.28159e41	+	1.46468e41i	0.00217657	+	0.00139726i
$565$	1.87691e44			1.74048
$566$		−	2.73551e44i		−	2.46590i
$567$	6.82842e43	−	7.91234e43i	0.598400	−	0.693387i
$568$	1.04369e43			0.0889194
$569$		−	1.01006e44i		−	0.836661i	−0.908295	−	0.418330i	$-0.862615\pi$
$569$		−	1.01006e44i		−	0.836661i	0.908295	−	0.418330i	$-0.137385\pi$
$570$	−2.14314e44	+	3.33847e44i	−1.72605	+	2.68874i
$571$	1.16891e44			0.915385			0.457692	−	0.889111i	$-0.348676\pi$
$571$	1.16891e44			0.915385			0.457692	+	0.889111i	$0.348676\pi$
$572$			1.75879e44i			1.33930i
$573$	−1.41151e44	−	9.06128e43i	−1.04523	−	0.670989i
$574$	1.06014e44			0.763437
$575$			1.20354e43i			0.0842898i
$576$	−9.94536e43	−	2.17198e44i	−0.677425	−	1.47944i
$577$	−2.29862e44			−1.52284			−0.761421	−	0.648258i	$-0.775498\pi$
$577$	−2.29862e44			−1.52284			−0.761421	+	0.648258i	$0.775498\pi$
$578$		−	2.35620e44i		−	1.51833i
$579$	−4.41869e43	+	6.88318e43i	−0.276972	+	0.431452i
$580$	−5.37231e44			−3.27577
$581$		−	4.38563e43i		−	0.260144i
$582$	2.88742e44	+	1.85359e44i	1.66626	+	1.06966i
$583$	−2.78419e44			−1.56316
$584$			5.82972e42i			0.0318451i
$585$	2.38763e44	−	1.09328e44i	1.26903	−	0.581082i
$586$	5.69953e44			2.94766
$587$			3.36020e44i			1.69105i	0.533937	+	0.845524i	$0.320712\pi$
$587$			3.36020e44i			1.69105i	−0.533937	+	0.845524i	$0.679288\pi$
$588$	−2.68307e43	+	4.17954e43i	−0.131400	+	0.204687i
$589$	1.27636e44			0.608314
$590$		−	3.44016e44i		−	1.59568i
$591$	1.21594e44	+	7.80581e43i	0.548926	+	0.352386i
$592$	−1.41345e43			−0.0621061
$593$			2.81908e44i			1.20568i	0.797862	+	0.602840i	$0.205964\pi$
$593$			2.81908e44i			1.20568i	−0.797862	+	0.602840i	$0.794036\pi$
$594$	−3.92091e44	−	5.57740e43i	−1.63231	−	0.232193i
$595$	−7.54267e43			−0.305671
$596$		−	1.13177e44i		−	0.446496i
$597$	1.79052e44	−	2.78916e44i	0.687684	−	1.07123i
$598$	−1.81120e43			−0.0677249
$599$			1.15173e44i			0.419296i	0.977777	+	0.209648i	$0.0672318\pi$
$599$			1.15173e44i			0.419296i	−0.977777	+	0.209648i	$0.932768\pi$
$600$	3.22074e44	+	2.06757e44i	1.14166	+	0.732893i
$601$	−3.44390e44			−1.18866			−0.594332	−	0.804220i	$-0.702583\pi$
$601$	−3.44390e44			−1.18866			−0.594332	+	0.804220i	$0.702583\pi$
$602$			4.24266e44i			1.42592i
$603$	6.90970e43	+	1.50902e44i	0.226142	+	0.493875i
$604$	8.50070e44			2.70934
$605$		−	4.38952e43i		−	0.136248i
$606$	3.03665e44	−	4.73031e44i	0.917978	−	1.42997i
$607$	9.80874e43			0.288798			0.144399	−	0.989520i	$-0.453875\pi$
$607$	9.80874e43			0.288798			0.144399	+	0.989520i	$0.453875\pi$
$608$			5.03808e44i			1.44480i
$609$	−3.65707e44	−	2.34767e44i	−1.02154	−	0.655784i
$610$	−1.69961e45			−4.62458
$611$			5.51062e41i			0.00146063i
$612$	1.08346e44	−	4.96109e43i	0.279762	−	0.128101i
$613$	4.37991e44			1.10179			0.550893	−	0.834576i	$-0.314287\pi$
$613$	4.37991e44			1.10179			0.550893	+	0.834576i	$0.314287\pi$
$614$		−	4.31606e44i		−	1.05777i
$615$	−1.94908e44	+	3.03617e44i	−0.465402	+	0.724976i
$616$	−3.30723e44			−0.769437
$617$			5.00298e43i			0.113414i	0.998391	+	0.0567069i	$0.0180601\pi$
$617$			5.00298e43i			0.113414i	−0.998391	+	0.0567069i	$0.981940\pi$
$618$	−1.96256e44	−	1.25987e44i	−0.433518	−	0.278299i
$619$	1.56567e44			0.337015			0.168508	−	0.985700i	$-0.446105\pi$
$619$	1.56567e44			0.337015			0.168508	+	0.985700i	$0.446105\pi$
$620$		−	5.81843e44i		−	1.22050i
$621$	3.45489e42	−	2.42879e43i	0.00706267	−	0.0496506i
$622$	4.28649e44			0.853995
$623$			1.34558e44i			0.261276i
$624$	5.61718e43	−	8.75012e43i	0.106308	−	0.165600i
$625$	7.81436e43			0.144149
$626$		−	1.57107e45i		−	2.82492i
$627$	6.15550e44	+	3.95155e44i	1.07890	+	0.692607i
$628$	−3.75567e44			−0.641701
$629$		−	3.29237e43i		−	0.0548401i
$630$	6.09048e44	+	1.33011e45i	0.989014	+	2.15992i
$631$	7.55460e43			0.119603			0.0598015	−	0.998210i	$-0.480953\pi$
$631$	7.55460e43			0.119603			0.0598015	+	0.998210i	$0.480953\pi$
$632$			8.52059e44i			1.31521i
$633$	−1.59210e44	+	2.48007e44i	−0.239613	+	0.373255i
$634$	1.35011e44			0.198125
$635$		−	1.48171e45i		−	2.12023i
$636$	−1.36731e45	−	8.77753e44i	−1.90789	−	1.22478i
$637$	−1.00946e44			−0.137360
$638$			1.64675e45i			2.18523i
$639$	−7.73942e43	+	3.54383e43i	−0.100160	+	0.0458627i
$640$	1.82230e45			2.30006
$641$			5.20543e44i			0.640808i	0.947281	+	0.320404i	$0.103819\pi$
$641$			5.20543e44i			0.640808i	−0.947281	+	0.320404i	$0.896181\pi$
$642$	−3.64350e44	+	5.67563e44i	−0.437480	+	0.681481i
$643$	7.31934e44			0.857229			0.428614	−	0.903488i	$-0.359002\pi$
$643$	7.31934e44			0.857229			0.428614	+	0.903488i	$0.359002\pi$
$644$		−	6.06928e43i		−	0.0693368i
$645$	−1.21507e45	−	7.80017e44i	−1.35408	−	0.869258i
$646$	−3.65894e44			−0.397773
$647$			9.70518e44i			1.02928i	0.857405	+	0.514642i	$0.172075\pi$
$647$			9.70518e44i			1.02928i	−0.857405	+	0.514642i	$0.827925\pi$
$648$	−5.90606e44	−	5.09699e44i	−0.611080	−	0.527368i
$649$	−6.34300e44			−0.640294
$650$			2.30456e45i			2.26974i
$651$	2.54262e44	−	3.96075e44i	0.244335	−	0.380611i
$652$	2.05211e44			0.192415
$653$		−	1.23878e45i		−	1.13340i	−0.823923	−	0.566702i	$-0.808219\pi$
$653$		−	1.23878e45i		−	1.13340i	0.823923	−	0.566702i	$-0.191781\pi$
$654$	9.21223e44	+	5.91383e44i	0.822471	+	0.527989i
$655$	1.74587e45			1.52108
$656$			1.42859e44i			0.121464i
$657$	−1.97948e43	−	4.32301e43i	−0.0164250	−	0.0358707i
$658$	−3.06987e42			−0.00248603
$659$		−	2.31547e43i		−	0.0183009i	−0.999958	−	0.00915045i	$-0.997087\pi$
$659$		−	2.31547e43i		−	0.0183009i	0.999958	−	0.00915045i	$-0.00291272\pi$
$660$	1.80136e45	−	2.80606e45i	1.38963	−	2.16468i
$661$	−2.39852e45			−1.80601			−0.903004	−	0.429632i	$-0.858643\pi$
$661$	−2.39852e45			−1.80601			−0.903004	+	0.429632i	$0.858643\pi$
$662$		−	3.12735e45i		−	2.29852i
$663$	2.03817e44	+	1.30841e44i	0.146226	+	0.0938703i
$664$	−3.27360e44			−0.229264
$665$		−	2.70196e45i		−	1.84728i
$666$	−5.80590e44	+	2.65849e44i	−0.387509	+	0.177438i
$667$	−1.02007e44			−0.0664687
$668$		−	3.65380e44i		−	0.232445i
$669$	−1.26277e45	+	1.96707e45i	−0.784345	+	1.22181i
$670$	−2.32312e45			−1.40888
$671$			3.13376e45i			1.85569i
$672$	1.56340e45	+	1.00363e45i	0.903986	+	0.580318i
$673$	7.52414e44			0.424831			0.212415	−	0.977179i	$-0.431867\pi$
$673$	7.52414e44			0.424831			0.212415	+	0.977179i	$0.431867\pi$
$674$			4.39745e45i			2.42461i
$675$	−3.09038e45	−	4.39598e44i	−1.66399	−	0.236699i
$676$	7.84563e44			0.412554
$677$		−	1.36007e44i		−	0.0698464i	−0.999390	−	0.0349232i	$-0.988881\pi$
$677$		−	1.36007e44i		−	0.0698464i	0.999390	−	0.0349232i	$-0.0111187\pi$
$678$	1.81377e45	−	2.82539e45i	0.909720	−	1.41711i
$679$	−2.33691e45			−1.14479
$680$			5.63013e44i			0.269387i
$681$	1.62807e45	+	1.04515e45i	0.760887	+	0.488455i
$682$	−1.78350e45			−0.814184
$683$		−	2.47049e45i		−	1.10167i	−0.834614	−	0.550835i	$-0.814309\pi$
$683$		−	2.47049e45i		−	1.10167i	0.834614	−	0.550835i	$-0.185691\pi$
$684$	1.77718e45	+	3.88120e45i	0.774165	+	1.69071i
$685$	6.12510e45			2.60654
$686$		−	4.05239e45i		−	1.68471i
$687$	−5.77750e44	+	8.99986e44i	−0.234656	+	0.365534i
$688$	−5.71718e44			−0.226865
$689$		−	3.30241e45i		−	1.28033i
$690$	2.88968e44	+	1.85504e44i	0.109462	+	0.0702698i
$691$	−2.79704e43			−0.0103526			−0.00517631	−	0.999987i	$-0.501648\pi$
$691$	−2.79704e43			−0.0103526			−0.00517631	+	0.999987i	$0.501648\pi$
$692$			1.04842e44i			0.0379174i
$693$	2.45247e45	−	1.12297e45i	0.866705	−	0.396859i
$694$	1.93364e45			0.667767
$695$			4.64214e45i			1.56661i
$696$	−1.75239e45	+	2.72977e45i	−0.577940	+	0.900282i
$697$	−3.32762e44			−0.107253
$698$			2.44824e45i			0.771199i
$699$	2.95287e45	+	1.89561e45i	0.909095	+	0.583598i
$700$	−7.72252e45			−2.32375
$701$			1.62599e45i			0.478224i	0.970992	+	0.239112i	$0.0768562\pi$
$701$			1.62599e45i			0.478224i	−0.970992	+	0.239112i	$0.923144\pi$
$702$	6.61551e44	−	4.65070e45i	0.190182	−	1.33698i
$703$	1.17940e45			0.331419
$704$		−	6.16522e45i		−	1.69350i
$705$	5.64400e42	−	8.79190e42i	0.00151552	−	0.00236079i
$706$	−4.67362e45			−1.22681
$707$			3.82844e45i			0.982453i
$708$	−3.11504e45	−	1.99971e45i	−0.781504	−	0.501690i
$709$	−3.85475e45			−0.945488			−0.472744	−	0.881200i	$-0.656736\pi$
$709$	−3.85475e45			−0.945488			−0.472744	+	0.881200i	$0.656736\pi$
$710$		−	1.19148e45i		−	0.285727i
$711$	−2.89316e45	−	6.31842e45i	−0.678359	−	1.48148i
$712$	1.00439e45			0.230262
$713$		−	1.10478e44i		−	0.0247652i
$714$	−7.28895e44	+	1.13543e45i	−0.159769	+	0.248880i
$715$	6.77734e45			1.45266
$716$			5.77260e45i			1.20994i
$717$	−5.98239e45	−	3.84042e45i	−1.22622	−	0.787177i
$718$	1.00374e46			2.01201
$719$		−	2.74164e45i		−	0.537462i	−0.963215	−	0.268731i	$-0.913396\pi$
$719$		−	2.74164e45i		−	0.537462i	0.963215	−	0.268731i	$-0.0866043\pi$
$720$	−1.79238e45	+	8.20721e44i	−0.343645	+	0.157353i
$721$	1.58838e45			0.297845
$722$		−	4.46962e45i		−	0.819739i
$723$	2.43056e45	−	3.78619e45i	0.436007	−	0.679187i
$724$	7.73277e45			1.35681
$725$			1.29793e46i			2.22763i
$726$	−6.60773e44	−	4.24186e44i	−0.110934	−	0.0712148i
$727$	−2.80128e45			−0.460050			−0.230025	−	0.973185i	$-0.573881\pi$
$727$	−2.80128e45			−0.460050			−0.230025	+	0.973185i	$0.573881\pi$
$728$		−	3.92280e45i		−	0.630222i
$729$	6.11030e45	+	1.77425e45i	0.960334	+	0.278853i
$730$	6.65522e44			0.102329
$731$		−	1.33171e45i		−	0.200323i
$732$	−9.87960e45	+	1.53899e46i	−1.45399	+	2.26495i
$733$	−1.89755e45			−0.273231			−0.136616	−	0.990624i	$-0.543622\pi$
$733$	−1.89755e45			−0.273231			−0.136616	+	0.990624i	$0.543622\pi$
$734$		−	7.68923e45i		−	1.08329i
$735$	1.61055e45	+	1.03390e45i	0.222012	+	0.142521i
$736$	4.36082e44			0.0588197
$737$			4.28339e45i			0.565337i
$738$	2.68695e45	+	5.86807e45i	0.347023	+	0.757868i
$739$	−1.43939e46			−1.81915			−0.909573	−	0.415544i	$-0.863591\pi$
$739$	−1.43939e46			−1.81915			−0.909573	+	0.415544i	$0.863591\pi$
$740$		−	5.37646e45i		−	0.664949i
$741$	−4.68704e45	+	7.30121e45i	−0.567293	+	0.883697i
$742$	1.83972e46			2.17916
$743$		−	2.04644e45i		−	0.237234i	−0.992940	−	0.118617i	$-0.962154\pi$
$743$		−	2.04644e45i		−	0.237234i	0.992940	−	0.118617i	$-0.0378461\pi$
$744$	−2.95645e45	−	1.89791e45i	−0.335432	−	0.215332i
$745$	−4.36117e45			−0.484286
$746$			8.81105e45i			0.957650i
$747$	2.42753e45	−	1.11155e45i	0.258247	−	0.118250i
$748$	3.07543e45			0.320243
$749$		−	4.59353e45i		−	0.468207i
$750$	9.55998e45	−	1.48920e46i	0.953842	−	1.48584i
$751$	−5.69616e45			−0.556344			−0.278172	−	0.960531i	$-0.589729\pi$
$751$	−5.69616e45			−0.556344			−0.278172	+	0.960531i	$0.589729\pi$
$752$		−	4.13680e42i		−	0.000395530i
$753$	2.01529e45	+	1.29373e45i	0.188633	+	0.121094i
$754$	−1.95325e46			−1.78985
$755$		−	3.27567e46i		−	2.93865i
$756$	1.55843e46	+	2.21683e45i	1.36880	+	0.194708i
$757$	1.09110e46			0.938272			0.469136	−	0.883126i	$-0.344565\pi$
$757$	1.09110e46			0.938272			0.469136	+	0.883126i	$0.344565\pi$
$758$			2.97947e46i			2.50860i
$759$	3.42035e44	−	5.32803e44i	0.0281970	−	0.0439236i
$760$	−2.01685e46			−1.62800
$761$			5.51472e45i			0.435882i	0.975962	+	0.217941i	$0.0699341\pi$
$761$			5.51472e45i			0.435882i	−0.975962	+	0.217941i	$0.930066\pi$
$762$	−2.23048e46	−	1.43187e46i	−1.72631	−	1.10821i
$763$	−7.45585e45			−0.565073
$764$		−	2.52628e46i		−	1.87494i
$765$	−1.91171e45	−	4.17501e45i	−0.138944	−	0.303441i
$766$	3.04678e46			2.16861
$767$		−	7.52360e45i		−	0.524445i
$768$	4.73403e45	−	7.37440e45i	0.323185	−	0.503439i
$769$	2.37357e46			1.58702			0.793508	−	0.608560i	$-0.208253\pi$
$769$	2.37357e46			1.58702			0.793508	+	0.608560i	$0.208253\pi$
$770$			3.77555e46i			2.47245i
$771$	1.70566e46	+	1.09496e46i	1.09401	+	0.702308i
$772$	−1.23193e46			−0.773942
$773$			4.02656e45i			0.247778i	0.992296	+	0.123889i	$0.0395366\pi$
$773$			4.02656e45i			0.247778i	−0.992296	+	0.123889i	$0.960463\pi$
$774$	−2.34839e46	+	1.07531e46i	−1.41551	+	0.648155i
$775$	−1.40571e46			−0.829983
$776$			1.74436e46i			1.00890i
$777$	2.34948e45	−	3.65989e45i	0.133118	−	0.207363i
$778$	−5.57441e46			−3.09404
$779$		−	1.19203e46i		−	0.648170i
$780$	3.32834e46	+	2.13665e46i	1.77302	+	1.13820i
$781$	−2.19686e45			−0.114653
$782$			3.16707e44i			0.0161939i
$783$	3.72586e45	−	2.61928e46i	0.186654	−	1.31218i
$784$	7.57801e44			0.0371962
$785$			1.44721e46i			0.696013i
$786$	1.68714e46	−	2.62813e46i	0.795044	−	1.23847i
$787$	−5.78760e45			−0.267241			−0.133620	−	0.991033i	$-0.542660\pi$
$787$	−5.78760e45			−0.267241			−0.133620	+	0.991033i	$0.542660\pi$
$788$			2.17626e46i			0.984669i
$789$	3.02969e46	+	1.94493e46i	1.34328	+	0.862325i
$790$	9.72714e46			4.22621
$791$			2.28671e46i			0.973615i
$792$	−8.38226e45	−	1.83061e46i	−0.349750	−	0.763824i
$793$	−3.71704e46			−1.51994
$794$		−	5.01408e46i		−	2.00939i
$795$	−3.38234e46	+	5.26882e46i	−1.32844	+	2.06937i
$796$	4.99195e46			1.92159
$797$		−	1.60304e46i		−	0.604797i	−0.953182	−	0.302399i	$-0.902213\pi$
$797$		−	1.60304e46i		−	0.604797i	0.953182	−	0.302399i	$-0.0977874\pi$
$798$	−4.06738e46	−	2.61107e46i	−1.50407	−	0.965546i
$799$	9.63587e42			0.000349255
$800$		−	5.54868e46i		−	1.97129i
$801$	−7.44800e45	+	3.41039e45i	−0.259370	+	0.118764i
$802$	−7.07613e46			−2.41549
$803$		−	1.22710e45i		−	0.0410611i
$804$	−1.35039e46	+	2.10356e46i	−0.442959	+	0.690016i
$805$	−2.33874e45			−0.0752053
$806$		−	2.11545e46i		−	0.666873i
$807$	−4.02978e45	−	2.58693e45i	−0.124539	−	0.0799482i
$808$	2.85769e46			0.865833
$809$			3.31969e46i			0.986102i	0.870000	+	0.493051i	$0.164118\pi$
$809$			3.31969e46i			0.986102i	−0.870000	+	0.493051i	$0.835882\pi$
$810$	−5.81874e46	+	6.74238e46i	−1.69460	+	1.96360i
$811$	1.78101e46			0.508549			0.254275	−	0.967132i	$-0.418163\pi$
$811$	1.78101e46			0.508549			0.254275	+	0.967132i	$0.418163\pi$
$812$		−	6.54529e46i		−	1.83245i
$813$	1.59861e46	−	2.49022e46i	0.438827	−	0.683579i
$814$	−1.64802e46			−0.443580
$815$		−	7.90761e45i		−	0.208700i
$816$	−1.53005e45	−	9.82220e44i	−0.0395970	−	0.0254195i
$817$	4.77049e46			1.21063
$818$			9.70101e46i			2.41415i
$819$	1.33198e46	+	2.90894e46i	0.325055	+	0.709891i
$820$	−5.43403e46			−1.30047
$821$			1.00347e46i			0.235514i	0.993042	+	0.117757i	$0.0375703\pi$
$821$			1.00347e46i			0.235514i	−0.993042	+	0.117757i	$0.962430\pi$
$822$	5.91906e46	−	9.22038e46i	1.36240	−	2.12227i
$823$	2.83736e46			0.640497			0.320249	−	0.947334i	$-0.396234\pi$
$823$	2.83736e46			0.640497			0.320249	+	0.947334i	$0.396234\pi$
$824$		−	1.18563e46i		−	0.262490i
$825$	−6.77935e46	−	4.35203e46i	−1.47206	−	0.944994i
$826$	4.19127e46			0.892617
$827$		−	3.50954e45i		−	0.0733098i	−0.999328	−	0.0366549i	$-0.988330\pi$
$827$		−	3.50954e45i		−	0.0733098i	0.999328	−	0.0366549i	$-0.0116702\pi$
$828$	3.35946e45	−	1.53828e45i	0.0688310	−	0.0315173i
$829$	1.92501e46			0.386866			0.193433	−	0.981113i	$-0.438038\pi$
$829$	1.92501e46			0.386866			0.193433	+	0.981113i	$0.438038\pi$
$830$			3.73715e46i			0.736701i
$831$	3.55000e46	−	5.52999e46i	0.686455	−	1.06932i
$832$	7.31274e46			1.38710
$833$			1.76515e45i			0.0328444i
$834$	6.98801e46	+	4.48599e46i	1.27555	+	0.818844i
$835$	−1.40796e46			−0.252119
$836$			1.10169e47i			1.93535i
$837$	2.83678e46	+	4.03525e45i	0.488898	+	0.0695446i
$838$	−1.24067e47			−2.09775
$839$			2.15724e46i			0.357855i	0.983862	+	0.178928i	$0.0572628\pi$
$839$			2.15724e46i			0.357855i	−0.983862	+	0.178928i	$0.942737\pi$
$840$	−4.01775e46	+	6.25861e46i	−0.653904	+	1.01861i
$841$	−4.73841e46			−0.756653
$842$			1.05273e46i			0.164939i
$843$	−5.88355e46	−	3.77697e46i	−0.904478	−	0.580634i
$844$	−4.43875e46			−0.669548
$845$		−	3.02324e46i		−	0.447472i
$846$	−7.78067e43	−	1.69923e44i	−0.00113003	−	0.00246789i
$847$	5.34792e45			0.0762167
$848$			2.47910e46i			0.346706i
$849$	−6.12735e46	+	9.54483e46i	−0.840910	+	1.30992i
$850$	4.02976e46			0.542721
$851$		−	1.02086e45i		−	0.0134925i
$852$	−1.07887e46	−	6.92587e45i	−0.139938	−	0.0898341i
$853$	8.01950e46			1.02085			0.510426	−	0.859922i	$-0.329488\pi$
$853$	8.01950e46			1.02085			0.510426	+	0.859922i	$0.329488\pi$
$854$		−	2.07070e47i		−	2.58697i
$855$	1.49559e47	−	6.84820e46i	1.83381	−	0.839689i
$856$	−3.42879e46			−0.412629
$857$		−	1.07502e47i		−	1.26976i	−0.772610	−	0.634880i	$-0.781049\pi$
$857$		−	1.07502e47i		−	1.26976i	0.772610	−	0.634880i	$-0.218951\pi$
$858$	6.54936e46	−	1.02022e47i	0.759281	−	1.18276i
$859$	−6.14759e46			−0.699543			−0.349772	−	0.936835i	$-0.613741\pi$
$859$	−6.14759e46			−0.699543			−0.349772	+	0.936835i	$0.613741\pi$
$860$		−	2.17468e47i		−	2.42896i
$861$	−3.69908e46	−	2.37464e46i	−0.405549	−	0.260344i
$862$	−1.27701e47			−1.37429
$863$			1.62772e47i			1.71952i	0.510698	+	0.859760i	$0.329387\pi$
$863$			1.62772e47i			1.71952i	−0.510698	+	0.859760i	$0.670613\pi$
$864$	−1.59281e46	+	1.11974e47i	−0.165175	+	1.16118i
$865$	4.04000e45			0.0411267
$866$			1.95869e47i			1.95740i
$867$	−5.27772e46	+	8.22133e46i	−0.517775	+	0.806559i
$868$	7.08881e46			0.682744
$869$		−	1.79350e47i		−	1.69584i
$870$	3.11631e47	+	2.00053e47i	2.89290	+	1.85711i
$871$	−5.08064e46			−0.463050
$872$			5.56533e46i			0.497997i
$873$	−5.92296e46	−	1.29352e47i	−0.520368	−	1.13644i
$874$	−1.13452e46			−0.0978655
$875$			1.20527e47i			1.02084i
$876$	3.86859e45	−	6.02626e45i	0.0321726	−	0.0501167i
$877$	−1.21911e47			−0.995520			−0.497760	−	0.867315i	$-0.665844\pi$
$877$	−1.21911e47			−0.995520			−0.497760	+	0.867315i	$0.665844\pi$
$878$		−	8.86812e46i		−	0.711081i
$879$	−1.98870e47	−	1.27665e47i	−1.56584	−	1.00520i
$880$	−5.08773e46			−0.393370
$881$			1.52849e47i			1.16051i	0.814435	+	0.580254i	$0.197047\pi$
$881$			1.52849e47i			1.16051i	−0.814435	+	0.580254i	$0.802953\pi$
$882$	3.11274e46	−	1.42530e46i	0.232084	−	0.106270i
$883$	1.12145e47			0.821121			0.410561	−	0.911833i	$-0.365333\pi$
$883$	1.12145e47			0.821121			0.410561	+	0.911833i	$0.365333\pi$
$884$			3.64785e46i			0.262301i
$885$	−7.70571e46	+	1.20035e47i	−0.544152	+	0.847649i
$886$	2.08179e47			1.44377
$887$			4.57609e46i			0.311685i	0.987782	+	0.155843i	$0.0498093\pi$
$887$			4.57609e46i			0.311685i	−0.987782	+	0.155843i	$0.950191\pi$
$888$	−2.73188e46	−	1.75374e46i	−0.182749	−	0.117316i
$889$	1.80522e47			1.18605
$890$		−	1.14661e47i		−	0.739906i
$891$	1.24317e47	+	1.07287e47i	0.787928	+	0.679989i
$892$	−3.52060e47			−2.19169
$893$			3.45180e44i			0.00211068i
$894$	−4.21446e46	+	6.56505e46i	−0.253129	+	0.394310i
$895$	2.22442e47			1.31235
$896$			2.22017e47i			1.28665i
$897$	6.31971e45	+	4.05697e45i	0.0359765	+	0.0230953i
$898$	4.08664e47			2.28531
$899$		−	1.19142e47i		−	0.654503i
$900$	−1.95729e47	−	4.27455e47i	−1.05627	−	2.30680i
$901$	−5.77459e46			−0.306143
$902$			1.66567e47i			0.867529i
$903$	9.50325e46	−	1.48036e47i	0.486260	−	0.757467i
$904$	1.70689e47			0.858044
$905$		−	2.97975e47i		−	1.47164i
$906$	−4.93100e47	−	3.16548e47i	−2.39268	−	1.53599i
$907$	1.96956e46			0.0938970			0.0469485	−	0.998897i	$-0.485050\pi$
$907$	1.96956e46			0.0938970			0.0469485	+	0.998897i	$0.485050\pi$
$908$			2.91387e47i			1.36489i
$909$	−2.11911e47	+	9.70329e46i	−0.975286	+	0.446578i
$910$	−4.47828e47			−2.02511
$911$			2.69386e46i			0.119696i	0.998207	+	0.0598481i	$0.0190616\pi$
$911$			2.69386e46i			0.119696i	−0.998207	+	0.0598481i	$0.980938\pi$
$912$	3.51855e46	−	5.48099e46i	0.153619	−	0.239299i
$913$	6.89060e46			0.295614
$914$		−	4.16324e47i		−	1.75506i
$915$	5.93034e47	+	3.80701e47i	2.45665	+	1.57705i
$916$	−1.61076e47			−0.655698
$917$			2.12706e47i			0.850885i
$918$	−8.13222e46	−	1.15679e46i	−0.319688	−	0.0454748i
$919$	−2.40970e47			−0.930924			−0.465462	−	0.885068i	$-0.654112\pi$
$919$	−2.40970e47			−0.930924			−0.465462	+	0.885068i	$0.654112\pi$
$920$			1.74572e46i			0.0662782i
$921$	−9.66767e46	+	1.50597e47i	−0.360718	+	0.561905i
$922$	−1.50052e47			−0.550232
$923$		−	2.60575e46i		−	0.0939086i
$924$	3.41873e47	+	2.19467e47i	1.21091	+	0.777352i
$925$	−1.29893e47			−0.452188
$926$		−	4.54640e47i		−	1.55558i
$927$	4.02580e46	+	8.79199e46i	0.135387	+	0.295673i
$928$	4.70283e47			1.55450
$929$		−	3.65634e47i		−	1.18794i	−0.804486	−	0.593971i	$-0.797559\pi$
$929$		−	3.65634e47i		−	1.18794i	0.804486	−	0.593971i	$-0.202441\pi$
$930$	−2.16666e47	+	3.37509e47i	−0.691932	+	1.07785i
$931$	−6.32319e46			−0.198491
$932$			5.28494e47i			1.63074i
$933$	−1.49566e47	−	9.60143e46i	−0.453654	−	0.291226i
$934$	4.38862e47			1.30851
$935$		−	1.18509e47i		−	0.347348i
$936$	2.17134e47	−	9.94243e46i	0.625625	−	0.286470i
$937$	5.54359e47			1.57021			0.785104	−	0.619364i	$-0.212609\pi$
$937$	5.54359e47			1.57021			0.785104	+	0.619364i	$0.212609\pi$
$938$		−	2.83034e47i		−	0.788122i
$939$	−3.51908e47	+	5.48182e47i	−0.963340	+	1.50064i
$940$	1.57354e45			0.00423480
$941$			2.48801e47i			0.658291i	0.944279	+	0.329146i	$0.106761\pi$
$941$			2.48801e47i			0.658291i	−0.944279	+	0.329146i	$0.893239\pi$
$942$	2.17855e47	+	1.39853e47i	0.566700	+	0.363795i
$943$	−1.03179e46			−0.0263879
$944$			5.64794e46i			0.142016i
$945$	8.54236e46	−	6.00528e47i	0.211188	−	1.48465i
$946$	−6.66596e47			−1.62033
$947$		−	1.57355e47i		−	0.376080i	−0.982161	−	0.188040i	$-0.939787\pi$
$947$		−	1.57355e47i		−	0.376080i	0.982161	−	0.188040i	$-0.0602134\pi$
$948$	5.65424e47	−	8.80785e47i	1.32874	−	2.06984i
$949$	1.45549e46			0.0336319
$950$			1.44356e48i			3.27987i
$951$	−4.71084e46	−	3.02414e46i	−0.105247	−	0.0675638i
$952$	−6.85941e46			−0.150694
$953$		−	9.60355e46i		−	0.207465i	−0.994605	−	0.103733i	$-0.966921\pi$
$953$		−	9.60355e46i		−	0.207465i	0.994605	−	0.103733i	$-0.0330786\pi$
$954$	4.66281e47	+	1.01832e48i	0.990544	+	2.16326i
$955$	−9.73478e47			−2.03363
$956$		−	1.07071e48i		−	2.19960i
$957$	3.68860e47	−	5.74590e47i	0.745197	−	1.16082i
$958$	−1.13875e48			−2.26245
$959$			7.46245e47i			1.45809i
$960$	−1.16671e48	−	7.48974e47i	−2.24193	−	1.43922i
$961$	−4.00108e47			−0.756142
$962$		−	1.95476e47i		−	0.363323i
$963$	2.54260e47	−	1.16424e47i	0.464792	−	0.212825i
$964$	6.77639e47			1.21833
$965$			4.74712e47i			0.839447i
$966$	−2.26007e46	+	3.52061e46i	−0.0393086	+	0.0612327i
$967$	−2.92514e47			−0.500407			−0.250203	−	0.968193i	$-0.580498\pi$
$967$	−2.92514e47			−0.500407			−0.250203	+	0.968193i	$0.580498\pi$
$968$		−	3.99188e46i		−	0.0671695i
$969$	1.27669e47	+	8.19577e46i	0.211303	+	0.135647i
$970$	1.99136e48			3.24192
$971$		−	1.19954e48i		−	1.92092i	−0.278423	−	0.960459i	$-0.589812\pi$
$971$		−	1.19954e48i		−	1.92092i	0.278423	−	0.960459i	$-0.410188\pi$
$972$	2.72283e47	+	9.18807e47i	0.428904	+	1.44732i
$973$	−5.65570e47			−0.876356
$974$		−	1.03665e48i		−	1.58012i
$975$	5.16206e47	−	8.04116e47i	0.774015	−	1.20572i
$976$	2.79037e47			0.411590
$977$			3.06016e47i			0.444049i	0.975041	+	0.222024i	$0.0712664\pi$
$977$			3.06016e47i			0.444049i	−0.975041	+	0.222024i	$0.928734\pi$
$978$	−1.19037e47	−	7.64161e46i	−0.169926	−	0.109084i
$979$	−2.11414e47			−0.296900
$980$			2.88250e47i			0.398247i
$981$	−1.88970e47	−	4.12695e47i	−0.256856	−	0.560951i
$982$	4.55970e47			0.609751
$983$			1.51512e48i			1.99338i	0.0813053	+	0.996689i	$0.474091\pi$
$983$			1.51512e48i			1.99338i	−0.0813053	+	0.996689i	$0.525909\pi$
$984$	−1.77252e47	+	2.76113e47i	−0.229440	+	0.357409i
$985$	8.38600e47			1.06801
$986$			3.41546e47i			0.427976i
$987$	1.07115e45	+	6.87630e44i	0.00132061	+	0.000847775i
$988$	−1.30674e48			−1.58518
$989$		−	4.12920e46i		−	0.0492861i
$990$	−2.08983e48	+	9.56922e47i	−2.45442	+	1.12386i
$991$	3.37053e47			0.389511			0.194756	−	0.980852i	$-0.437609\pi$
$991$	3.37053e47			0.389511			0.194756	+	0.980852i	$0.437609\pi$
$992$			5.09336e47i			0.579185i
$993$	−7.00504e47	+	1.09121e48i	−0.783832	+	1.22101i
$994$	1.45162e47			0.159835
$995$		−	1.92360e48i		−	2.08423i
$996$	3.38397e47	+	2.17235e47i	0.360808	+	0.231623i
$997$	1.52934e48			1.60466			0.802329	−	0.596882i	$-0.203594\pi$
$997$	1.52934e48			1.60466			0.802329	+	0.596882i	$0.203594\pi$
$998$			9.99916e47i			1.03246i
$999$	2.62130e47	+	3.72873e46i	0.266360	+	0.0378890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.33.b.a.2.2	✓	10
3.2	odd	2	inner	3.33.b.a.2.9	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.33.b.a.2.2	✓	10	1.1	even	1	trivial
3.33.b.a.2.9	yes	10	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-103819. i q^{2} +(-2.32547e7 + 3.62248e7i) q^{3} -6.48340e9 q^{4} +2.49832e11i q^{5} +(3.76082e12 + 2.41428e12i) q^{6} -3.04380e13 q^{7} +2.27200e14i q^{8} +(-7.71458e14 - 1.68480e15i) q^{9} +O(q^{10})\)	\(q-103819. i q^{2} +(-2.32547e7 + 3.62248e7i) q^{3} -6.48340e9 q^{4} +2.49832e11i q^{5} +(3.76082e12 + 2.41428e12i) q^{6} -3.04380e13 q^{7} +2.27200e14i q^{8} +(-7.71458e14 - 1.68480e15i) q^{9} +2.59372e16 q^{10} -4.78234e16i q^{11} +(1.50769e17 - 2.34860e17i) q^{12} +5.67246e17 q^{13} +3.16003e18i q^{14} +(-9.05011e18 - 5.80976e18i) q^{15} -4.25830e18 q^{16} -9.91887e18i q^{17} +(-1.74914e20 + 8.00919e19i) q^{18} +3.55318e20 q^{19} -1.61976e21i q^{20} +(7.07826e20 - 1.10261e21i) q^{21} -4.96497e21 q^{22} -3.07553e20i q^{23} +(-8.23029e21 - 5.28347e21i) q^{24} -3.91328e22 q^{25} -5.88909e22i q^{26} +(7.89715e22 + 1.12335e22i) q^{27} +1.97341e23 q^{28} -3.31674e23i q^{29} +(-6.03163e23 + 9.39573e23i) q^{30} +3.59216e23 q^{31} +1.41791e24i q^{32} +(1.73239e24 + 1.11212e24i) q^{33} -1.02977e24 q^{34} -7.60436e24i q^{35} +(5.00167e24 + 1.09232e25i) q^{36} +3.31930e24 q^{37} -3.68887e25i q^{38} +(-1.31911e25 + 2.05484e25i) q^{39} -5.67618e25 q^{40} -3.35484e25i q^{41} +(-1.14472e26 - 7.34857e25i) q^{42} +1.34260e26 q^{43} +3.10058e26i q^{44} +(4.20915e26 - 1.92735e26i) q^{45} -3.19298e25 q^{46} +9.71468e23i q^{47} +(9.90254e25 - 1.54256e26i) q^{48} -1.77959e26 q^{49} +4.06272e27i q^{50} +(3.59310e26 + 2.30660e26i) q^{51} -3.67768e27 q^{52} -5.82182e27i q^{53} +(1.16625e27 - 8.19873e27i) q^{54} +1.19478e28 q^{55} -6.91551e27i q^{56} +(-8.26280e27 + 1.28713e28i) q^{57} -3.44340e28 q^{58} -1.32634e28i q^{59} +(5.86755e28 + 3.76670e28i) q^{60} -6.55279e28 q^{61} -3.72934e28i q^{62} +(2.34816e28 + 5.12817e28i) q^{63} +1.28917e29 q^{64} +1.41716e29i q^{65} +(1.15459e29 - 1.79855e29i) q^{66} -8.95668e28 q^{67} +6.43080e28i q^{68} +(1.11410e28 + 7.15205e27i) q^{69} -7.89477e29 q^{70} -4.59368e28i q^{71} +(3.82786e29 - 1.75275e29i) q^{72} +2.56589e28 q^{73} -3.44606e29i q^{74} +(9.10022e29 - 1.41758e30i) q^{75} -2.30366e30 q^{76} +1.45565e30i q^{77} +(2.13331e30 + 1.36949e30i) q^{78} +3.75026e30 q^{79} -1.06386e30i q^{80} +(-2.24339e30 + 2.59950e30i) q^{81} -3.48296e30 q^{82} +1.44084e30i q^{83} +(-4.58911e30 + 7.14866e30i) q^{84} +2.47805e30 q^{85} -1.39387e31i q^{86} +(1.20148e31 + 7.71297e30i) q^{87} +1.08655e31 q^{88} -4.42071e30i q^{89} +(-2.00095e31 - 4.36990e31i) q^{90} -1.72658e31 q^{91} +1.99399e30i q^{92} +(-8.35346e30 + 1.30125e31i) q^{93} +1.00857e29 q^{94} +8.87696e31i q^{95} +(-5.13635e31 - 3.29731e31i) q^{96} +7.67762e31 q^{97} +1.84755e31i q^{98} +(-8.05726e31 + 3.68937e31i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9}+O(q^{10}) \) 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9	\( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9} - 70\!\cdots\!40 q^{10}+ \cdots - 33\!\cdots\!60 q^{99}+O(q^{100}) \) 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9 - 7003812786596640 * q^10 - 279007424380502640 * q^12 + 567697557679805780 * q^13 - 20342205597863242080 * q^15 + 93452609752238437504 * q^16 - 546532439317269948000 * q^18 + 571007688520350419876 * q^19 - 202809296674597359852 * q^21 - 7726803521259943913760 * q^22 + 40966888307328818303616 * q^24 - 68909708350780834128950 * q^25 - 72967926462080465281230 * q^27 + 205937256056975756717600 * q^28 - 1107420825536697507876000 * q^30 + 2337947500037502285593540 * q^31 + 2522449071689961111334560 * q^33 - 6060358314194999366692224 * q^34 + 19880961335883894024618192 * q^36 - 35307903416851790686359340 * q^37 - 31624005377757923978634972 * q^39 + 103824872020641394026996480 * q^40 - 141365101025586253616004960 * q^42 + 20133134465218107006792740 * q^43 + 324508325822765233105320000 * q^45 - 1081312096716791246752963776 * q^46 + 3981901930430244196770990720 * q^48 - 2767041101974767237639509154 * q^49 + 1958591008210563208705802112 * q^51 - 5054272042223836449280397920 * q^52 + 8609682620485865645134310448 * q^54 - 11870374622399979665591304000 * q^55 + 40568829971233106153298510900 * q^57 - 126691224865576416891245282400 * q^58 + 279833341447916827662753642240 * q^60 - 196667345182223458343232398380 * q^61 + 349775312774222889759843110340 * q^63 - 738816306154787409411488427008 * q^64 + 939413077861687418842822458720 * q^66 - 442550741350999501345614861340 * q^67 + 1096443581430237499419700598208 * q^69 - 3084260511067452830890360584000 * q^70 + 5478956649034785201935062114560 * q^72 - 4530286149796751043896742263020 * q^73 + 5689646867484953837977805651250 * q^75 - 10804853453030293252172855440096 * q^76 + 9245617327241370897996048982560 * q^78 - 2115110787448996851533482223164 * q^79 - 454653247801524309158818752630 * q^81 + 6754240700896495824250705604160 * q^82 - 10589261014798101343390846457952 * q^84 + 8783873758902640422771709896960 * q^85 - 12893796544943502316879779198240 * q^87 + 15416255855088684041150976480000 * q^88 - 76437416541013126109366518121760 * q^90 + 59544256621898576615810233543816 * q^91 - 105131728169400940473110940107820 * q^93 + 301803894289991891760064059517056 * q^94 - 522680019947351351608967407401984 * q^96 + 390148965222370670128665882607700 * q^97 - 333895893109019690643343683610560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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