LMFDB - Embedded newform 3.27.b.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,27,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, 27, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 27);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 27 $
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:	$12.8487876219$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2728193x^{6} + 2071419806976x^{4} + 503906274711956480x^{2} + 26754716118873014272000 $ x^8 + 2728193x^6 + 2071419806976x^4 + 503906274711956480*x^2 + 26754716118873014272000
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{33}\cdot 3^{38}\cdot 5^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.8
Root			$1286.17i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.27.b.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+15434.0i q^{2} +(-1.57937e6 - 217880. i) q^{3} -1.71101e8 q^{4} +7.56364e8i q^{5} +(3.36276e9 - 2.43760e10i) q^{6} -6.43856e10 q^{7} -1.60501e12i q^{8} +(2.44692e12 + 6.88223e11i) q^{9} +O(q^{10})$	\(q+15434.0i q^{2} +(-1.57937e6 - 217880. i) q^{3} -1.71101e8 q^{4} +7.56364e8i q^{5} +(3.36276e9 - 2.43760e10i) q^{6} -6.43856e10 q^{7} -1.60501e12i q^{8} +(2.44692e12 + 6.88223e11i) q^{9} -1.16738e13 q^{10} +4.53285e13i q^{11} +(2.70230e14 + 3.72794e13i) q^{12} -1.22189e14 q^{13} -9.93730e14i q^{14} +(1.64796e14 - 1.19458e15i) q^{15} +1.32894e16 q^{16} -8.44454e14i q^{17} +(-1.06221e16 + 3.77659e16i) q^{18} +1.38890e16 q^{19} -1.29414e17i q^{20} +(1.01688e17 + 1.40283e16i) q^{21} -6.99601e17 q^{22} -6.13136e17i q^{23} +(-3.49700e17 + 2.53490e18i) q^{24} +9.18029e17 q^{25} -1.88586e18i q^{26} +(-3.71463e18 - 1.62009e18i) q^{27} +1.10164e19 q^{28} -1.18072e19i q^{29} +(1.84371e19 + 2.54347e18i) q^{30} -2.12418e19 q^{31} +9.73993e19i q^{32} +(9.87616e18 - 7.15902e19i) q^{33} +1.30333e19 q^{34} -4.86990e19i q^{35} +(-4.18670e20 - 1.17755e20i) q^{36} +2.40487e19 q^{37} +2.14363e20i q^{38} +(1.92980e20 + 2.66224e19i) q^{39} +1.21397e21 q^{40} +2.62573e20i q^{41} +(-2.16514e20 + 1.56946e21i) q^{42} -8.46691e20 q^{43} -7.75573e21i q^{44} +(-5.20548e20 + 1.85076e21i) q^{45} +9.46316e21 q^{46} +8.66938e21i q^{47} +(-2.09889e22 - 2.89550e21i) q^{48} -5.24197e21 q^{49} +1.41689e22i q^{50} +(-1.83990e20 + 1.33370e21i) q^{51} +2.09065e22 q^{52} -3.15687e22i q^{53} +(2.50045e22 - 5.73318e22i) q^{54} -3.42848e22 q^{55} +1.03340e23i q^{56} +(-2.19357e22 - 3.02612e21i) q^{57} +1.82234e23 q^{58} -4.46845e22i q^{59} +(-2.81968e22 + 2.04393e23i) q^{60} -8.62736e22 q^{61} -3.27847e23i q^{62} +(-1.57547e23 - 4.43117e22i) q^{63} -6.11424e23 q^{64} -9.24190e22i q^{65} +(1.10493e24 + 1.52429e23i) q^{66} -7.14670e23 q^{67} +1.44487e23i q^{68} +(-1.33590e23 + 9.68365e23i) q^{69} +7.51622e23 q^{70} +1.40204e24i q^{71} +(1.10461e24 - 3.92734e24i) q^{72} +1.49986e24 q^{73} +3.71168e23i q^{74} +(-1.44990e24 - 2.00020e23i) q^{75} -2.37641e24 q^{76} -2.91850e24i q^{77} +(-4.10891e23 + 2.97846e24i) q^{78} -1.64771e24 q^{79} +1.00517e25i q^{80} +(5.51378e24 + 3.36806e24i) q^{81} -4.05257e24 q^{82} -1.43170e25i q^{83} +(-1.73989e25 - 2.40025e24i) q^{84} +6.38715e23 q^{85} -1.30679e25i q^{86} +(-2.57256e24 + 1.86480e25i) q^{87} +7.27528e25 q^{88} -2.88024e25i q^{89} +(-2.85648e25 - 8.03415e24i) q^{90} +7.86718e24 q^{91} +1.04908e26i q^{92} +(3.35486e25 + 4.62816e24i) q^{93} -1.33803e26 q^{94} +1.05051e25i q^{95} +(2.12213e25 - 1.53829e26i) q^{96} +9.43022e25 q^{97} -8.09048e25i q^{98} +(-3.11961e25 + 1.10915e26i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9}+O(q^{10}) $ 8 * q - 1261080 * q^3 - 248848672 * q^4 + 4268261088 * q^6 - 83723264240 * q^7 + 3535237525320 * q^9	$ 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9} - 19160376580800 q^{10} + 361652147111520 q^{12} - 397915354631600 q^{13} - 719893807027200 q^{15} + 14\!\cdots\!24 q^{16}+ \cdots + 12\!\cdots\!20 q^{99}+O(q^{100}) $ 8 * q - 1261080 * q^3 - 248848672 * q^4 + 4268261088 * q^6 - 83723264240 * q^7 + 3535237525320 * q^9 - 19160376580800 * q^10 + 361652147111520 * q^12 - 397915354631600 * q^13 - 719893807027200 * q^15 + 14708338775335424 * q^16 - 21900893760832320 * q^18 + 16320401555362000 * q^19 + 194580840365988048 * q^21 - 772248680481769920 * q^22 - 462343148304920064 * q^24 + 1971388854053049800 * q^25 - 7894649015962792920 * q^27 + 15321751531929304000 * q^28 + 7398480599799681600 * q^30 - 9272518953250081904 * q^31 - 65168600178932490240 * q^33 + 221246262521511042816 * q^34 - 1016435634925989724704 * q^36 + 879374467120740709840 * q^37 - 1582238541124790450928 * q^39 + 4129217584783179033600 * q^40 - 6703469261814514512960 * q^42 + 6748593942335676212560 * q^43 - 16831420952659929907200 * q^45 + 36160927581299221074816 * q^46 - 66488551077760679646720 * q^48 + 45841873858091621647512 * q^49 - 62114113806050924347392 * q^51 + 99815113130579384624320 * q^52 - 65423424830500017302112 * q^54 + 31541176921532063385600 * q^55 - 68601650728105742286960 * q^57 + 179274146475296123858880 * q^58 + 132515345363297827507200 * q^60 - 319050283467071524566704 * q^61 + 658789337835295522626960 * q^63 - 1937027849517856838066176 * q^64 + 3327191890146340029253440 * q^66 - 3016122636770760226629680 * q^67 + 2874694883813365556256768 * q^69 - 3079956143630742638371200 * q^70 + 4816528692447953902187520 * q^72 - 1734362529074066854728560 * q^73 + 551279759153288953055400 * q^75 - 4252629668197637559664448 * q^76 - 2905541033044787133422400 * q^78 + 5851464318766097144790160 * q^79 - 7387002303358032367832952 * q^81 + 19281076716095151109326720 * q^82 - 58831332525651421466918208 * q^84 + 36766362882842005714329600 * q^85 - 66105320167985812595481600 * q^87 + 166743215953906759732730880 * q^88 - 112582289830354559315755200 * q^90 + 57658591275235919126596256 * q^91 - 721851591602497641585840 * q^93 - 128592383810221185199398144 * q^94 + 66451111218720743421763584 * q^96 + 87088434574088023884109840 * q^97 + 126385397236902706353285120 * 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 $

$2$			15434.0i			1.88404i	0.335560	+	0.942019i	$0.391074\pi$
$2$			15434.0i			1.88404i	−0.335560	+	0.942019i	$0.608926\pi$
$3$	−1.57937e6	−	217880.i	−0.990618	−	0.136660i
$3$	−1.57937e6	−	217880.i	−0.990618	−	0.136660i
$4$	−1.71101e8			−2.54960
$5$			7.56364e8i			0.619614i	0.950800	+	0.309807i	$0.100264\pi$
$5$			7.56364e8i			0.619614i	−0.950800	+	0.309807i	$0.899736\pi$
$6$	3.36276e9	−	2.43760e10i	0.257472	−	1.86636i
$7$	−6.43856e10			−0.664529			−0.332265	−	0.943186i	$-0.607813\pi$
$7$	−6.43856e10			−0.664529			−0.332265	+	0.943186i	$0.607813\pi$
$8$		−	1.60501e12i		−	2.91950i
$9$	2.44692e12	+	6.88223e11i	0.962648	+	0.270755i
$10$	−1.16738e13			−1.16738
$11$			4.53285e13i			1.31300i	0.754324	+	0.656502i	$0.227965\pi$
$11$			4.53285e13i			1.31300i	−0.754324	+	0.656502i	$0.772035\pi$
$12$	2.70230e14	+	3.72794e13i	2.52568	+	0.348427i
$13$	−1.22189e14			−0.403429			−0.201714	−	0.979444i	$-0.564651\pi$
$13$	−1.22189e14			−0.403429			−0.201714	+	0.979444i	$0.564651\pi$
$14$		−	9.93730e14i		−	1.25200i
$15$	1.64796e14	−	1.19458e15i	0.0846762	−	0.613800i
$16$	1.32894e16			2.95085
$17$		−	8.44454e14i		−	0.0852590i	−0.999091	−	0.0426295i	$-0.986426\pi$
$17$		−	8.44454e14i		−	0.0852590i	0.999091	−	0.0426295i	$-0.0135735\pi$
$18$	−1.06221e16	+	3.77659e16i	−0.510113	+	1.81367i
$19$	1.38890e16			0.330273			0.165136	−	0.986271i	$-0.447194\pi$
$19$	1.38890e16			0.330273			0.165136	+	0.986271i	$0.447194\pi$
$20$		−	1.29414e17i		−	1.57977i
$21$	1.01688e17	+	1.40283e16i	0.658295	+	0.0908144i
$22$	−6.99601e17			−2.47375
$23$		−	6.13136e17i		−	1.21645i	−0.793764	−	0.608226i	$-0.791882\pi$
$23$		−	6.13136e17i		−	1.21645i	0.793764	−	0.608226i	$-0.208118\pi$
$24$	−3.49700e17	+	2.53490e18i	−0.398978	+	2.89211i
$25$	9.18029e17			0.616079
$26$		−	1.88586e18i		−	0.760075i
$27$	−3.71463e18	−	1.62009e18i	−0.916615	−	0.399770i
$28$	1.10164e19			1.69428
$29$		−	1.18072e19i		−	1.15073i	−0.817896	−	0.575367i	$-0.804859\pi$
$29$		−	1.18072e19i		−	1.15073i	0.817896	−	0.575367i	$-0.195141\pi$
$30$	1.84371e19	+	2.54347e18i	1.15642	+	0.159533i
$31$	−2.12418e19			−0.869940			−0.434970	−	0.900445i	$-0.643241\pi$
$31$	−2.12418e19			−0.869940			−0.434970	+	0.900445i	$0.643241\pi$
$32$			9.73993e19i			2.64001i
$33$	9.87616e18	−	7.15902e19i	0.179435	−	1.30069i
$34$	1.30333e19			0.160631
$35$		−	4.86990e19i		−	0.411751i
$36$	−4.18670e20	−	1.17755e20i	−2.45437	−	0.690317i
$37$	2.40487e19			0.0987345			0.0493673	−	0.998781i	$-0.484280\pi$
$37$	2.40487e19			0.0987345			0.0493673	+	0.998781i	$0.484280\pi$
$38$			2.14363e20i			0.622247i
$39$	1.92980e20	+	2.66224e19i	0.399644	+	0.0551325i
$40$	1.21397e21			1.80896
$41$			2.62573e20i			0.283831i	0.989879	+	0.141916i	$0.0453262\pi$
$41$			2.62573e20i			0.283831i	−0.989879	+	0.141916i	$0.954674\pi$
$42$	−2.16514e20	+	1.56946e21i	−0.171098	+	1.24025i
$43$	−8.46691e20			−0.492759			−0.246380	−	0.969173i	$-0.579241\pi$
$43$	−8.46691e20			−0.492759			−0.246380	+	0.969173i	$0.579241\pi$
$44$		−	7.75573e21i		−	3.34763i
$45$	−5.20548e20	+	1.85076e21i	−0.167764	+	0.596470i
$46$	9.46316e21			2.29184
$47$			8.66938e21i			1.58751i	0.608239	+	0.793754i	$0.291876\pi$
$47$			8.66938e21i			1.58751i	−0.608239	+	0.793754i	$0.708124\pi$
$48$	−2.09889e22	−	2.89550e21i	−2.92317	−	0.403262i
$49$	−5.24197e21			−0.558401
$50$			1.41689e22i			1.16072i
$51$	−1.83990e20	+	1.33370e21i	−0.0116515	+	0.0844591i
$52$	2.09065e22			1.02858
$53$		−	3.15687e22i		−	1.21247i	−0.795286	−	0.606234i	$-0.792680\pi$
$53$		−	3.15687e22i		−	1.21247i	0.795286	−	0.606234i	$-0.207320\pi$
$54$	2.50045e22	−	5.73318e22i	0.753182	−	1.72694i
$55$	−3.42848e22			−0.813555
$56$			1.03340e23i			1.94009i
$57$	−2.19357e22	−	3.02612e21i	−0.327174	−	0.0451350i
$58$	1.82234e23			2.16803
$59$		−	4.46845e22i		−	0.425677i	−0.977087	−	0.212839i	$-0.931729\pi$
$59$		−	4.46845e22i		−	0.425677i	0.977087	−	0.212839i	$-0.0682709\pi$
$60$	−2.81968e22	+	2.04393e23i	−0.215890	+	1.56494i
$61$	−8.62736e22			−0.532831			−0.266416	−	0.963858i	$-0.585839\pi$
$61$	−8.62736e22			−0.532831			−0.266416	+	0.963858i	$0.585839\pi$
$62$		−	3.27847e23i		−	1.63900i
$63$	−1.57547e23	−	4.43117e22i	−0.639708	−	0.179925i
$64$	−6.11424e23			−2.02303
$65$		−	9.24190e22i		−	0.249970i
$66$	1.10493e24	+	1.52429e23i	2.45054	+	0.338062i
$67$	−7.14670e23			−1.30357			−0.651783	−	0.758405i	$-0.725979\pi$
$67$	−7.14670e23			−1.30357			−0.651783	+	0.758405i	$0.725979\pi$
$68$			1.44487e23i			0.217376i
$69$	−1.33590e23	+	9.68365e23i	−0.166240	+	1.20504i
$70$	7.51622e23			0.775755
$71$			1.40204e24i			1.20338i	0.798730	+	0.601689i	$0.205505\pi$
$71$			1.40204e24i			1.20338i	−0.798730	+	0.601689i	$0.794495\pi$
$72$	1.10461e24	−	3.92734e24i	0.790470	−	2.81045i
$73$	1.49986e24			0.897125			0.448563	−	0.893751i	$-0.351936\pi$
$73$	1.49986e24			0.897125			0.448563	+	0.893751i	$0.351936\pi$
$74$			3.71168e23i			0.186020i
$75$	−1.44990e24	−	2.00020e23i	−0.610299	−	0.0841932i
$76$	−2.37641e24			−0.842063
$77$		−	2.91850e24i		−	0.872530i
$78$	−4.10891e23	+	2.97846e24i	−0.103872	+	0.752944i
$79$	−1.64771e24			−0.352962			−0.176481	−	0.984304i	$-0.556471\pi$
$79$	−1.64771e24			−0.352962			−0.176481	+	0.984304i	$0.556471\pi$
$80$			1.00517e25i			1.82839i
$81$	5.51378e24	+	3.36806e24i	0.853383	+	0.521284i
$82$	−4.05257e24			−0.534749
$83$		−	1.43170e25i		−	1.61375i	−0.590721	−	0.806876i	$-0.701156\pi$
$83$		−	1.43170e25i		−	1.61375i	0.590721	−	0.806876i	$-0.298844\pi$
$84$	−1.73989e25	−	2.40025e24i	−1.67839	−	0.231540i
$85$	6.38715e23			0.0528276
$86$		−	1.30679e25i		−	0.928377i
$87$	−2.57256e24	+	1.86480e25i	−0.157259	+	1.13994i
$88$	7.27528e25			3.83332
$89$		−	2.88024e25i		−	1.31026i	−0.755515	−	0.655132i	$-0.772613\pi$
$89$		−	2.88024e25i		−	1.31026i	0.755515	−	0.655132i	$-0.227387\pi$
$90$	−2.85648e25	−	8.03415e24i	−1.12377	−	0.316073i
$91$	7.86718e24			0.268090
$92$			1.04908e26i			3.10146i
$93$	3.35486e25	+	4.62816e24i	0.861779	+	0.118886i
$94$	−1.33803e26			−2.99092
$95$			1.05051e25i			0.204642i
$96$	2.12213e25	−	1.53829e26i	0.360783	−	2.61524i
$97$	9.43022e25			1.40116			0.700582	−	0.713572i	$-0.252924\pi$
$97$	9.43022e25			1.40116			0.700582	+	0.713572i	$0.252924\pi$
$98$		−	8.09048e25i		−	1.05205i
$99$	−3.11961e25	+	1.10915e26i	−0.355503	+	1.26396i
$100$	−1.57075e26			−1.57075
$101$			2.88995e25i			0.253929i	0.991907	+	0.126965i	$0.0405235\pi$
$101$			2.88995e25i			0.253929i	−0.991907	+	0.126965i	$0.959477\pi$
$102$	−2.05844e25	−	2.83970e24i	−0.159124	−	0.0219518i
$103$	−2.36365e25			−0.160953			−0.0804767	−	0.996756i	$-0.525644\pi$
$103$	−2.36365e25			−0.160953			−0.0804767	+	0.996756i	$0.525644\pi$
$104$			1.96114e26i			1.17781i
$105$	−1.06105e25	+	7.69134e25i	−0.0562699	+	0.407888i
$106$	4.87232e26			2.28433
$107$		−	3.73318e26i		−	1.54914i	−0.632491	−	0.774568i	$-0.717968\pi$
$107$		−	3.73318e26i		−	1.54914i	0.632491	−	0.774568i	$-0.282032\pi$
$108$	6.35576e26	+	2.77199e26i	2.33700	+	1.01925i
$109$	−5.14103e26			−1.67689			−0.838447	−	0.544983i	$-0.816536\pi$
$109$	−5.14103e26			−1.67689			−0.838447	+	0.544983i	$0.816536\pi$
$110$		−	5.29153e26i		−	1.53277i
$111$	−3.79817e25	−	5.23972e24i	−0.0978082	−	0.0134930i
$112$	−8.55649e26			−1.96093
$113$		−	1.57160e26i		−	0.320866i	−0.987047	−	0.160433i	$-0.948711\pi$
$113$		−	1.57160e26i		−	0.320866i	0.987047	−	0.160433i	$-0.0512890\pi$
$114$	4.67053e25	−	3.38557e26i	0.0850361	−	0.616409i
$115$	4.63754e26			0.753730
$116$			2.02023e27i			2.93391i
$117$	−2.98986e26	−	8.40930e25i	−0.388360	−	0.109230i
$118$	6.89662e26			0.801992
$119$			5.43707e25i			0.0566571i
$120$	−1.91731e27	−	2.64500e26i	−1.79199	−	0.247212i
$121$	−8.62854e26			−0.723981
$122$		−	1.33155e27i		−	1.00387i
$123$	5.72094e25	−	4.14699e26i	0.0387883	−	0.281169i
$124$	3.63449e27			2.21800
$125$			1.82143e27i			1.00134i
$126$	6.83908e26	−	2.43158e27i	0.338985	−	1.20523i
$127$	−8.92136e26			−0.399009			−0.199505	−	0.979897i	$-0.563933\pi$
$127$	−8.92136e26			−0.399009			−0.199505	+	0.979897i	$0.563933\pi$
$128$		−	2.90039e27i		−	1.17146i
$129$	1.33723e27	+	1.84477e26i	0.488136	+	0.0673404i
$130$	1.42640e27			0.470953
$131$			4.35795e27i			1.30243i	0.758892	+	0.651217i	$0.225741\pi$
$131$			4.35795e27i			1.30243i	−0.758892	+	0.651217i	$0.774259\pi$
$132$	−1.68982e27	+	1.22491e28i	−0.457487	+	3.31623i
$133$	−8.94249e26			−0.219476
$134$		−	1.10302e28i		−	2.45597i
$135$	1.22538e27	−	2.80962e27i	0.247703	−	0.567947i
$136$	−1.35536e27			−0.248914
$137$			3.72366e25i			0.00621732i	0.999995	+	0.00310866i	$0.000989519\pi$
$137$			3.72366e25i			0.00621732i	−0.999995	+	0.00310866i	$0.999010\pi$
$138$	−1.49458e28	−	2.06183e27i	−2.27034	−	0.313202i
$139$	6.17990e27			0.854652			0.427326	−	0.904098i	$-0.359456\pi$
$139$	6.17990e27			0.854652			0.427326	+	0.904098i	$0.359456\pi$
$140$			8.33242e27i			1.04980i
$141$	1.88888e27	−	1.36921e28i	0.216948	−	1.57261i
$142$	−2.16391e28			−2.26721
$143$		−	5.53862e27i		−	0.529704i
$144$	3.25182e28	+	9.14611e27i	2.84063	+	0.798958i
$145$	8.93058e27			0.713010
$146$			2.31489e28i			1.69022i
$147$	8.27899e27	+	1.14212e27i	0.553162	+	0.0763109i
$148$	−4.11475e27			−0.251733
$149$			1.14194e28i			0.640064i	0.947407	+	0.320032i	$0.103694\pi$
$149$			1.14194e28i			0.640064i	−0.947407	+	0.320032i	$0.896306\pi$
$150$	3.08712e27	−	2.23779e28i	0.158623	−	1.14983i
$151$	−2.99898e28			−1.41343			−0.706713	−	0.707501i	$-0.749823\pi$
$151$	−2.99898e28			−1.41343			−0.706713	+	0.707501i	$0.749823\pi$
$152$		−	2.22920e28i		−	0.964232i
$153$	5.81173e26	−	2.06631e27i	0.0230843	−	0.0820744i
$154$	4.50443e28			1.64388
$155$		−	1.60665e28i		−	0.539027i
$156$	−3.30190e28	−	4.55511e27i	−1.01893	−	0.140566i
$157$	2.76145e28			0.784226			0.392113	−	0.919917i	$-0.371744\pi$
$157$	2.76145e28			0.784226			0.392113	+	0.919917i	$0.371744\pi$
$158$		−	2.54308e28i		−	0.664994i
$159$	−6.87818e27	+	4.98585e28i	−0.165696	+	1.20109i
$160$	−7.36693e28			−1.63579
$161$			3.94771e28i			0.808368i
$162$	−5.19827e28	+	8.50999e28i	−0.982119	+	1.60781i
$163$	−8.18364e28			−1.42728			−0.713638	−	0.700515i	$-0.752954\pi$
$163$	−8.18364e28			−1.42728			−0.713638	+	0.700515i	$0.752954\pi$
$164$		−	4.49264e28i		−	0.723656i
$165$	5.41483e28	+	7.46997e27i	0.805923	+	0.111180i
$166$	2.20969e29			3.04037
$167$		−	2.88328e27i		−	0.0366921i	−0.999832	−	0.0183461i	$-0.994160\pi$
$167$		−	2.88328e27i		−	0.0366921i	0.999832	−	0.0183461i	$-0.00584006\pi$
$168$	2.25156e28	−	1.63211e29i	0.265133	−	1.92189i
$169$	−7.68033e28			−0.837245
$170$			9.85795e27i			0.0995292i
$171$	3.39852e28	+	9.55871e27i	0.317937	+	0.0894231i
$172$	1.44869e29			1.25634
$173$		−	1.95703e29i		−	1.57398i	−0.616968	−	0.786988i	$-0.711639\pi$
$173$		−	1.95703e29i		−	1.57398i	0.616968	−	0.786988i	$-0.288361\pi$
$174$	−2.87813e29	−	3.97050e28i	−2.14768	−	0.296282i
$175$	−5.91079e28			−0.409403
$176$			6.02390e29i			3.87448i
$177$	−9.73584e27	+	7.05731e28i	−0.0581730	+	0.421684i
$178$	4.44537e29			2.46859
$179$		−	1.31094e29i		−	0.676849i	−0.940994	−	0.338424i	$-0.890106\pi$
$179$		−	1.31094e29i		−	0.676849i	0.940994	−	0.338424i	$-0.109894\pi$
$180$	8.90660e28	−	3.16667e29i	0.427730	−	1.52076i
$181$	−1.90225e29			−0.850054			−0.425027	−	0.905181i	$-0.639735\pi$
$181$	−1.90225e29			−0.850054			−0.425027	+	0.905181i	$0.639735\pi$
$182$			1.21422e29i			0.505092i
$183$	1.36257e29	+	1.87973e28i	0.527832	+	0.0728166i
$184$	−9.84090e29			−3.55143
$185$			1.81896e28i			0.0611773i
$186$	−7.14312e28	+	5.17790e29i	−0.223985	+	1.62362i
$187$	3.82778e28			0.111945
$188$		−	1.48334e30i		−	4.04750i
$189$	2.39169e29	+	1.04311e29i	0.609118	+	0.265659i
$190$	−1.62136e29			−0.385552
$191$			1.16985e29i			0.259833i	0.991525	+	0.129917i	$0.0414710\pi$
$191$			1.16985e29i			0.259833i	−0.991525	+	0.129917i	$0.958529\pi$
$192$	9.65662e29	+	1.33217e29i	2.00405	+	0.276467i
$193$	2.85826e29			0.554443			0.277221	−	0.960806i	$-0.410586\pi$
$193$	2.85826e29			0.554443			0.277221	+	0.960806i	$0.410586\pi$
$194$			1.45546e30i			2.63985i
$195$	−2.01362e28	+	1.45963e29i	−0.0341608	+	0.247625i
$196$	8.96905e29			1.42370
$197$			7.75872e28i			0.115273i	0.998338	+	0.0576367i	$0.0183565\pi$
$197$			7.75872e28i			0.115273i	−0.998338	+	0.0576367i	$0.981643\pi$
$198$	−1.71187e30	−	4.81482e29i	−2.38135	−	0.669781i
$199$	3.66878e28			0.0478005			0.0239002	−	0.999714i	$-0.492392\pi$
$199$	3.66878e28			0.0478005			0.0239002	+	0.999714i	$0.492392\pi$
$200$		−	1.47345e30i		−	1.79864i
$201$	1.12872e30	+	1.55712e29i	1.29134	+	0.178145i
$202$	−4.46036e29			−0.478412
$203$			7.60217e29i			0.764696i
$204$	3.14807e28	−	2.28197e29i	0.0297066	−	0.215337i
$205$	−1.98601e29			−0.175866
$206$		−	3.64807e29i		−	0.303242i
$207$	4.21974e29	−	1.50030e30i	0.329361	−	1.17101i
$208$	−1.62382e30			−1.19046
$209$			6.29566e29i			0.433650i
$210$	−1.18708e30	−	1.63763e29i	−0.768477	−	0.106015i
$211$	−2.52317e30			−1.53559			−0.767793	−	0.640699i	$-0.778645\pi$
$211$	−2.52317e30			−1.53559			−0.767793	+	0.640699i	$0.778645\pi$
$212$			5.40142e30i			3.09130i
$213$	3.05476e29	−	2.21433e30i	0.164453	−	1.19209i
$214$	5.76180e30			2.91863
$215$		−	6.40407e29i		−	0.305320i
$216$	−2.60027e30	+	5.96203e30i	−1.16713	+	2.67606i
$217$	1.36767e30			0.578101
$218$		−	7.93468e30i		−	3.15933i
$219$	−2.36882e30	−	3.26789e29i	−0.888709	−	0.122601i
$220$	5.86616e30			2.07424
$221$			1.03183e29i			0.0343959i
$222$	8.08701e28	−	5.86210e29i	0.0254214	−	0.184274i
$223$	−5.39481e30			−1.59960			−0.799802	−	0.600263i	$-0.795062\pi$
$223$	−5.39481e30			−1.59960			−0.799802	+	0.600263i	$0.795062\pi$
$224$		−	6.27111e30i		−	1.75437i
$225$	2.24635e30	+	6.31809e29i	0.593067	+	0.166807i
$226$	2.42562e30			0.604523
$227$			4.37641e30i			1.02987i	0.857229	+	0.514935i	$0.172184\pi$
$227$			4.37641e30i			1.02987i	−0.857229	+	0.514935i	$0.827816\pi$
$228$	3.75322e30	+	5.17772e29i	0.834163	+	0.115076i
$229$	5.23211e30			1.09854			0.549270	−	0.835645i	$-0.314906\pi$
$229$	5.23211e30			1.09854			0.549270	+	0.835645i	$0.314906\pi$
$230$			7.15759e30i			1.42005i
$231$	−6.35883e29	+	4.60938e30i	−0.119240	+	0.864344i
$232$	−1.89508e31			−3.35957
$233$		−	4.10091e30i		−	0.687469i	−0.939067	−	0.343735i	$-0.888308\pi$
$233$		−	4.10091e30i		−	0.687469i	0.939067	−	0.343735i	$-0.111692\pi$
$234$	1.29789e30	−	4.61456e30i	0.205794	−	0.731685i
$235$	−6.55721e30			−0.983641
$236$			7.64554e30i			1.08531i
$237$	2.60233e30	+	3.59002e29i	0.349651	+	0.0482357i
$238$	−8.39159e29			−0.106744
$239$			6.18375e30i			0.744868i	0.928059	+	0.372434i	$0.121477\pi$
$239$			6.18375e30i			0.744868i	−0.928059	+	0.372434i	$0.878523\pi$
$240$	2.19005e30	−	1.58752e31i	0.249867	−	1.81123i
$241$	6.70018e30			0.724211			0.362105	−	0.932137i	$-0.382058\pi$
$241$	6.70018e30			0.724211			0.362105	+	0.932137i	$0.382058\pi$
$242$		−	1.33173e31i		−	1.36401i
$243$	−7.97444e30	−	6.52074e30i	−0.774138	−	0.633017i
$244$	1.47615e31			1.35851
$245$		−	3.96484e30i		−	0.345993i
$246$	6.40048e30	+	8.82972e29i	0.529732	+	0.0730787i
$247$	−1.69707e30			−0.133242
$248$			3.40934e31i			2.53979i
$249$	−3.11939e30	+	2.26118e31i	−0.220535	+	1.59861i
$250$	−2.81121e31			−1.88657
$251$		−	2.03891e31i		−	1.29909i	−0.760322	−	0.649547i	$-0.774959\pi$
$251$		−	2.03891e31i		−	1.29909i	0.760322	−	0.649547i	$-0.225041\pi$
$252$	2.69563e31	+	7.58176e30i	1.63100	+	0.458736i
$253$	2.77925e31			1.59721
$254$		−	1.37693e31i		−	0.751748i
$255$	−1.00876e30	−	1.39163e29i	−0.0523320	−	0.00721941i
$256$	3.73269e30			0.184036
$257$		−	2.66641e31i		−	1.24967i	−0.780755	−	0.624837i	$-0.785165\pi$
$257$		−	2.66641e31i		−	1.24967i	0.780755	−	0.624837i	$-0.214835\pi$
$258$	−2.84722e30	+	2.06389e31i	−0.126872	+	0.919667i
$259$	−1.54839e30			−0.0656120
$260$			1.58129e31i			0.637323i
$261$	8.12603e30	−	2.88914e31i	0.311567	−	1.10775i
$262$	−6.72608e31			−2.45383
$263$		−	1.77891e31i		−	0.617631i	−0.951122	−	0.308815i	$-0.900067\pi$
$263$		−	1.77891e31i		−	0.617631i	0.951122	−	0.308815i	$-0.0999325\pi$
$264$	−1.14903e32	−	1.58514e31i	−3.79735	−	0.523860i
$265$	2.38774e31			0.751261
$266$		−	1.38019e31i		−	0.413501i
$267$	−6.27546e30	+	4.54895e31i	−0.179060	+	1.29797i
$268$	1.22280e32			3.32357
$269$			6.43690e31i			1.66685i	0.552631	+	0.833426i	$0.313624\pi$
$269$			6.43690e31i			1.66685i	−0.552631	+	0.833426i	$0.686376\pi$
$270$	4.33637e31	+	1.89125e31i	1.07003	+	0.466682i
$271$	−1.23255e29			−0.00289871			−0.00144935	−	0.999999i	$-0.500461\pi$
$271$	−1.23255e29			−0.00289871			−0.00144935	+	0.999999i	$0.500461\pi$
$272$		−	1.12223e31i		−	0.251586i
$273$	−1.24252e31	−	1.71410e30i	−0.265575	−	0.0366372i
$274$	−5.74712e29			−0.0117137
$275$			4.16129e31i			0.808915i
$276$	2.28573e31	−	1.65688e32i	0.423845	−	3.07236i
$277$	−4.19607e30			−0.0742346			−0.0371173	−	0.999311i	$-0.511818\pi$
$277$	−4.19607e30			−0.0742346			−0.0371173	+	0.999311i	$0.511818\pi$
$278$			9.53808e31i			1.61020i
$279$	−5.19771e31	−	1.46191e31i	−0.837447	−	0.235541i
$280$	−7.81624e31			−1.20211
$281$		−	8.93137e30i		−	0.131140i	−0.997848	−	0.0655701i	$-0.979113\pi$
$281$		−	8.93137e30i		−	0.131140i	0.997848	−	0.0655701i	$-0.0208866\pi$
$282$	2.11325e32	+	2.91531e31i	2.96286	+	0.408739i
$283$	−6.97738e31			−0.934262			−0.467131	−	0.884188i	$-0.654712\pi$
$283$	−6.97738e31			−0.934262			−0.467131	+	0.884188i	$0.654712\pi$
$284$		−	2.39890e32i		−	3.06813i
$285$	2.28885e30	−	1.65914e31i	0.0279663	−	0.202722i
$286$	8.54833e31			0.997982
$287$		−	1.69059e31i		−	0.188614i
$288$	−6.70325e31	+	2.38328e32i	−0.714797	+	2.54140i
$289$	9.73876e31			0.992731
$290$			1.37835e32i			1.34334i
$291$	−1.48938e32	−	2.05465e31i	−1.38802	−	0.191483i
$292$	−2.56627e32			−2.28731
$293$			1.57236e31i			0.134052i	0.997751	+	0.0670259i	$0.0213510\pi$
$293$			1.57236e31i			0.134052i	−0.997751	+	0.0670259i	$0.978649\pi$
$294$	−1.76275e31	+	1.27778e32i	−0.143773	+	1.04218i
$295$	3.37977e31			0.263755
$296$		−	3.85984e31i		−	0.288255i
$297$	7.34363e31	−	1.68379e32i	0.524900	−	1.20352i
$298$	−1.76248e32			−1.20590
$299$			7.49181e31i			0.490751i
$300$	2.48079e32	+	3.42236e31i	1.55602	+	0.214659i
$301$	5.45147e31			0.327453
$302$		−	4.62863e32i		−	2.66295i
$303$	6.29662e30	−	4.56429e31i	0.0347019	−	0.251547i
$304$	1.84577e32			0.974586
$305$		−	6.52542e31i		−	0.330150i
$306$	3.18916e31	+	8.96985e30i	0.154631	+	0.0434917i
$307$	−2.66329e32			−1.23771			−0.618856	−	0.785505i	$-0.712403\pi$
$307$	−2.66329e32			−1.23771			−0.618856	+	0.785505i	$0.712403\pi$
$308$			4.99357e32i			2.22460i
$309$	3.73307e31	+	5.14993e30i	0.159443	+	0.0219958i
$310$	2.47972e32			1.01555
$311$			8.37175e31i			0.328800i	0.986394	+	0.164400i	$0.0525687\pi$
$311$			8.37175e31i			0.328800i	−0.986394	+	0.164400i	$0.947431\pi$
$312$	4.27293e31	−	3.09736e32i	0.160959	−	1.16676i
$313$	5.08239e31			0.183650			0.0918251	−	0.995775i	$-0.470730\pi$
$313$	5.08239e31			0.183650			0.0918251	+	0.995775i	$0.470730\pi$
$314$			4.26203e32i			1.47751i
$315$	3.35158e31	−	1.19163e32i	0.111484	−	0.396372i
$316$	2.81924e32			0.899911
$317$			2.99132e32i			0.916417i	0.888845	+	0.458208i	$0.151509\pi$
$317$			2.99132e32i			0.916417i	−0.888845	+	0.458208i	$0.848491\pi$
$318$	−7.69518e32	−	1.06158e32i	−2.26290	−	0.312177i
$319$	5.35205e32			1.51092
$320$		−	4.62459e32i		−	1.25350i
$321$	−8.13384e31	+	5.89605e32i	−0.211704	+	1.53460i
$322$	−6.09291e32			−1.52300
$323$		−	1.17286e31i		−	0.0281587i
$324$	−9.43411e32	−	5.76277e32i	−2.17578	−	1.32906i
$325$	−1.12173e32			−0.248544
$326$		−	1.26307e33i		−	2.68904i
$327$	8.11956e32	+	1.12013e32i	1.66116	+	0.229164i
$328$	4.21433e32			0.828646
$329$		−	5.58183e32i		−	1.05495i
$330$	−1.15292e32	+	8.35726e32i	−0.209468	+	1.51839i
$331$	−2.78561e32			−0.486583			−0.243292	−	0.969953i	$-0.578227\pi$
$331$	−2.78561e32			−0.486583			−0.243292	+	0.969953i	$0.578227\pi$
$332$			2.44965e33i			4.11442i
$333$	5.88453e31	+	1.65509e31i	0.0950466	+	0.0267329i
$334$	4.45007e31			0.0691293
$335$		−	5.40551e32i		−	0.807707i
$336$	1.35138e33	+	1.86429e32i	1.94253	+	0.267980i
$337$	−7.29911e32			−1.00944			−0.504721	−	0.863283i	$-0.668405\pi$
$337$	−7.29911e32			−1.00944			−0.504721	+	0.863283i	$0.668405\pi$
$338$		−	1.18538e33i		−	1.57740i
$339$	−3.42421e31	+	2.48214e32i	−0.0438494	+	0.317855i
$340$	−1.09285e32			−0.134689
$341$		−	9.62859e32i		−	1.14224i
$342$	−1.47529e32	+	5.24529e32i	−0.168477	+	0.599005i
$343$	9.41926e32			1.03560
$344$			1.35895e33i			1.43861i
$345$	−7.32437e32	−	1.01043e32i	−0.746658	−	0.103005i
$346$	3.02049e33			2.96543
$347$		−	1.30904e32i		−	0.123785i	−0.998083	−	0.0618927i	$-0.980286\pi$
$347$		−	1.30904e32i		−	0.123785i	0.998083	−	0.0618927i	$-0.0197137\pi$
$348$	4.40167e32	−	3.19068e33i	0.400947	−	2.90638i
$349$	−1.55440e33			−1.36406			−0.682030	−	0.731324i	$-0.738903\pi$
$349$	−1.55440e33			−1.36406			−0.682030	+	0.731324i	$0.738903\pi$
$350$		−	9.12273e32i		−	0.771330i
$351$	4.53886e32	+	1.97957e32i	0.369789	+	0.161279i
$352$	−4.41496e33			−3.46635
$353$			1.39321e33i			1.05426i	0.849785	+	0.527129i	$0.176732\pi$
$353$			1.39321e33i			1.05426i	−0.849785	+	0.527129i	$0.823268\pi$
$354$	−1.08923e33	−	1.50263e32i	−0.794468	−	0.109600i
$355$	−1.06045e33			−0.745629
$356$			4.92811e33i			3.34064i
$357$	1.18463e31	−	8.58712e31i	0.00774275	−	0.0561256i
$358$	2.02330e33			1.27521
$359$		−	4.86706e32i		−	0.295828i	−0.989000	−	0.147914i	$-0.952744\pi$
$359$		−	4.86706e32i		−	0.295828i	0.989000	−	0.147914i	$-0.0472559\pi$
$360$	2.97050e33	+	8.35485e32i	1.74139	+	0.489786i
$361$	−1.57555e33			−0.890920
$362$		−	2.93594e33i		−	1.60153i
$363$	1.36276e33	+	1.87998e32i	0.717189	+	0.0989391i
$364$	−1.34608e33			−0.683522
$365$			1.13444e33i			0.555871i
$366$	−2.90118e32	+	2.10300e33i	−0.137189	+	0.994456i
$367$	2.49772e33			1.13995			0.569974	−	0.821663i	$-0.306953\pi$
$367$	2.49772e33			1.13995			0.569974	+	0.821663i	$0.306953\pi$
$368$		−	8.14823e33i		−	3.58957i
$369$	−1.80709e32	+	6.42497e32i	−0.0768488	+	0.273230i
$370$	−2.80738e32			−0.115260
$371$			2.03257e33i			0.805721i
$372$	−5.74018e33	−	7.91881e32i	−2.19719	−	0.303111i
$373$	−2.22041e33			−0.820765			−0.410383	−	0.911913i	$-0.634605\pi$
$373$	−2.22041e33			−0.820765			−0.410383	+	0.911913i	$0.634605\pi$
$374$			5.90781e32i			0.210909i
$375$	3.96854e32	−	2.87671e33i	0.136843	−	0.991950i
$376$	1.39145e34			4.63473
$377$			1.44271e33i			0.464239i
$378$	−1.60993e33	+	3.69134e33i	−0.500512	+	1.14760i
$379$	1.36618e33			0.410392			0.205196	−	0.978721i	$-0.434217\pi$
$379$	1.36618e33			0.410392			0.205196	+	0.978721i	$0.434217\pi$
$380$		−	1.79743e33i		−	0.521754i
$381$	1.40901e33	+	1.94378e32i	0.395266	+	0.0545285i
$382$	−1.80554e33			−0.489536
$383$			6.09447e32i			0.159717i	0.996806	+	0.0798586i	$0.0254469\pi$
$383$			6.09447e32i			0.159717i	−0.996806	+	0.0798586i	$0.974553\pi$
$384$	−6.31935e32	+	4.58077e33i	−0.160091	+	1.16047i
$385$	2.20745e33			0.540632
$386$			4.41145e33i			1.04459i
$387$	−2.07179e33	−	5.82713e32i	−0.474354	−	0.133417i
$388$	−1.61352e34			−3.57241
$389$		−	5.78437e33i		−	1.23854i	−0.785177	−	0.619272i	$-0.787428\pi$
$389$		−	5.78437e33i		−	1.23854i	0.785177	−	0.619272i	$-0.212572\pi$
$390$	−2.25280e33	−	3.10783e32i	−0.466534	−	0.0643603i
$391$	−5.17765e32			−0.103713
$392$			8.41343e33i			1.63025i
$393$	9.49510e32	−	6.88280e33i	0.177990	−	1.29021i
$394$	−1.19748e33			−0.217179
$395$		−	1.24627e33i		−	0.218700i
$396$	5.33768e33	−	1.89777e34i	0.906389	−	3.22259i
$397$	1.63919e33			0.269372			0.134686	−	0.990888i	$-0.456997\pi$
$397$	1.63919e33			0.269372			0.134686	+	0.990888i	$0.456997\pi$
$398$			5.66241e32i			0.0900579i
$399$	1.41235e33	+	1.94839e32i	0.217417	+	0.0299936i
$400$	1.22001e34			1.81796
$401$			6.56795e33i			0.947443i	0.880675	+	0.473721i	$0.157090\pi$
$401$			6.56795e33i			0.947443i	−0.880675	+	0.473721i	$0.842910\pi$
$402$	−2.40327e33	+	1.74208e34i	−0.335632	+	2.43293i
$403$	2.59551e33			0.350959
$404$		−	4.94472e33i		−	0.647417i
$405$	−2.54748e33	+	4.17042e33i	−0.322995	+	0.528768i
$406$	−1.17332e34			−1.44072
$407$			1.09009e33i			0.129639i
$408$	2.14061e33	+	2.95305e32i	0.246578	+	0.0340165i
$409$	2.39163e33			0.266864			0.133432	−	0.991058i	$-0.457400\pi$
$409$	2.39163e33			0.266864			0.133432	+	0.991058i	$0.457400\pi$
$410$		−	3.06522e33i		−	0.331338i
$411$	8.11311e30	−	5.88103e31i	0.000849657	−	0.00615899i
$412$	4.04423e33			0.410366
$413$			2.87704e33i			0.282875i
$414$	2.31556e34	+	6.51277e33i	2.20624	+	0.620528i
$415$	1.08289e34			0.999903
$416$		−	1.19011e34i		−	1.06506i
$417$	−9.76032e33	−	1.34648e33i	−0.846633	−	0.116796i
$418$	−9.71674e33			−0.817013
$419$		−	2.86768e33i		−	0.233748i	−0.993147	−	0.116874i	$-0.962713\pi$
$419$		−	2.86768e33i		−	0.233748i	0.993147	−	0.116874i	$-0.0372874\pi$
$420$	1.81547e33	−	1.31599e34i	0.143465	−	1.03995i
$421$	−1.43806e34			−1.10182			−0.550908	−	0.834566i	$-0.685718\pi$
$421$	−1.43806e34			−1.10182			−0.550908	+	0.834566i	$0.685718\pi$
$422$		−	3.89426e34i		−	2.89310i
$423$	−5.96647e33	+	2.12133e34i	−0.429826	+	1.52821i
$424$	−5.06681e34			−3.53980
$425$		−	7.75234e32i		−	0.0525263i
$426$	3.41761e34	+	4.71473e33i	2.24594	+	0.309836i
$427$	5.55478e33			0.354082
$428$			6.38749e34i			3.94967i
$429$	−1.20675e33	+	8.74750e33i	−0.0723892	+	0.524734i
$430$	9.88406e33			0.575235
$431$		−	1.54654e34i		−	0.873288i	−0.899634	−	0.436644i	$-0.856167\pi$
$431$		−	1.54654e34i		−	0.873288i	0.899634	−	0.436644i	$-0.143833\pi$
$432$	−4.93654e34	−	2.15301e34i	−2.70479	−	1.17966i
$433$	1.26710e34			0.673705			0.336852	−	0.941557i	$-0.390638\pi$
$433$	1.26710e34			0.673705			0.336852	+	0.941557i	$0.390638\pi$
$434$			2.11086e34i			1.08916i
$435$	−1.41046e34	−	1.94579e33i	−0.706321	−	0.0974398i
$436$	8.79633e34			4.27540
$437$		−	8.51582e33i		−	0.401761i
$438$	5.04367e33	−	3.65605e34i	0.230985	−	1.67436i
$439$	−3.61999e34			−1.60942			−0.804709	−	0.593670i	$-0.797679\pi$
$439$	−3.61999e34			−1.60942			−0.804709	+	0.593670i	$0.797679\pi$
$440$			5.50276e34i			2.37517i
$441$	−1.28267e34	−	3.60765e33i	−0.537543	−	0.151190i
$442$	−1.59252e33			−0.0648032
$443$		−	1.20051e34i		−	0.474371i	−0.971464	−	0.237186i	$-0.923775\pi$
$443$		−	1.20051e34i		−	0.474371i	0.971464	−	0.237186i	$-0.0762250\pi$
$444$	6.49869e33	+	8.96520e32i	0.249372	+	0.0344018i
$445$	2.17851e34			0.811857
$446$		−	8.32637e34i		−	3.01372i
$447$	2.48806e33	−	1.80355e34i	0.0874710	−	0.634059i
$448$	3.93669e34			1.34436
$449$		−	1.65389e34i		−	0.548662i	−0.961635	−	0.274331i	$-0.911544\pi$
$449$		−	1.65389e34i		−	0.548662i	0.961635	−	0.274331i	$-0.0884563\pi$
$450$	−9.75137e33	+	3.46702e34i	−0.314270	+	1.11736i
$451$	−1.19020e34			−0.372672
$452$			2.68902e34i			0.818078i
$453$	4.73648e34	+	6.53417e33i	1.40016	+	0.193158i
$454$	−6.75457e34			−1.94031
$455$			5.95045e33i			0.166112i
$456$	−4.85697e33	+	3.52071e34i	−0.131772	+	0.955185i
$457$	3.92198e34			1.03418			0.517088	−	0.855932i	$-0.327016\pi$
$457$	3.92198e34			1.03418			0.517088	+	0.855932i	$0.327016\pi$
$458$			8.07526e34i			2.06969i
$459$	−1.36809e33	+	3.13684e33i	−0.0340840	+	0.0781497i
$460$	−7.93486e34			−1.92171
$461$			1.19774e34i			0.282000i	0.990010	+	0.141000i	$0.0450318\pi$
$461$			1.19774e34i			0.282000i	−0.990010	+	0.141000i	$0.954968\pi$
$462$	−7.11413e34	−	9.81423e33i	−1.62846	−	0.224652i
$463$	−6.00206e33			−0.133582			−0.0667909	−	0.997767i	$-0.521276\pi$
$463$	−6.00206e33			−0.133582			−0.0667909	+	0.997767i	$0.521276\pi$
$464$		−	1.56912e35i		−	3.39564i
$465$	−3.50058e33	+	2.53749e34i	−0.0736633	+	0.533970i
$466$	6.32936e34			1.29522
$467$			7.71241e34i			1.53487i	0.641128	+	0.767434i	$0.278467\pi$
$467$			7.71241e34i			1.53487i	−0.641128	+	0.767434i	$0.721533\pi$
$468$	5.11567e34	+	1.43884e34i	0.990162	+	0.278494i
$469$	4.60145e34			0.866258
$470$		−	1.01204e35i		−	1.85322i
$471$	−4.36133e34	−	6.01664e33i	−0.776869	−	0.107172i
$472$	−7.17191e34			−1.24276
$473$		−	3.83792e34i		−	0.646995i
$474$	−5.54085e33	+	4.01645e34i	−0.0908779	+	0.658755i
$475$	1.27505e34			0.203474
$476$		−	9.30286e33i		−	0.144453i
$477$	2.17263e34	−	7.72461e34i	0.328282	−	1.16718i
$478$	−9.54402e34			−1.40336
$479$			9.39293e34i			1.34412i	0.740495	+	0.672062i	$0.234591\pi$
$479$			9.39293e34i			1.34412i	−0.740495	+	0.672062i	$0.765409\pi$
$480$	1.16351e35	+	1.60511e34i	1.62044	+	0.223546i
$481$	−2.93847e33			−0.0398323
$482$			1.03411e35i			1.36444i
$483$	8.60127e33	−	6.23488e34i	0.110471	−	0.800784i
$484$	1.47635e35			1.84586
$485$			7.13268e34i			0.868181i
$486$	1.00641e35	−	1.23078e35i	1.19263	−	1.45851i
$487$	−1.26082e35			−1.45471			−0.727356	−	0.686260i	$-0.759251\pi$
$487$	−1.26082e35			−1.45471			−0.727356	+	0.686260i	$0.759251\pi$
$488$			1.38470e35i			1.55560i
$489$	1.29250e35	+	1.78305e34i	1.41388	+	0.195051i
$490$	6.11935e34			0.651863
$491$		−	4.80809e34i		−	0.498785i	−0.968403	−	0.249392i	$-0.919769\pi$
$491$		−	4.80809e34i		−	0.498785i	0.968403	−	0.249392i	$-0.0802309\pi$
$492$	−9.78857e33	+	7.09553e34i	−0.0988946	+	0.716867i
$493$	−9.97068e33			−0.0981104
$494$		−	2.61927e34i		−	0.251032i
$495$	−8.38923e34	−	2.35956e34i	−0.783168	−	0.220274i
$496$	−2.82292e35			−2.56706
$497$		−	9.02712e34i		−	0.799680i
$498$	−3.48991e35	−	4.81447e34i	−3.01185	−	0.415496i
$499$	−8.42930e32			−0.00708736			−0.00354368	−	0.999994i	$-0.501128\pi$
$499$	−8.42930e32			−0.00708736			−0.00354368	+	0.999994i	$0.501128\pi$
$500$		−	3.11649e35i		−	2.55303i
$501$	−6.28209e32	+	4.55375e33i	−0.00501434	+	0.0363479i
$502$	3.14687e35			2.44754
$503$		−	1.44535e35i		−	1.09544i	−0.836661	−	0.547722i	$-0.815495\pi$
$503$		−	1.44535e35i		−	1.09544i	0.836661	−	0.547722i	$-0.184505\pi$
$504$	−7.11208e34	+	2.52864e35i	−0.525291	+	1.86763i
$505$	−2.18586e34			−0.157338
$506$			4.28951e35i			3.00920i
$507$	1.21300e35	+	1.67339e34i	0.829390	+	0.114418i
$508$	1.52645e35			1.01731
$509$			4.92853e33i			0.0320174i	0.999872	+	0.0160087i	$0.00509594\pi$
$509$			4.92853e33i			0.0320174i	−0.999872	+	0.0160087i	$0.994904\pi$
$510$	2.14785e33	−	1.55693e34i	0.0136016	−	0.0985954i
$511$	−9.65693e34			−0.596166
$512$		−	1.37031e35i		−	0.824726i
$513$	−5.15924e34	−	2.25014e34i	−0.302733	−	0.132033i
$514$	4.11535e35			2.35443
$515$		−	1.78778e34i		−	0.0997289i
$516$	−2.28802e35	−	3.15641e34i	−1.24455	−	0.171691i
$517$	−3.92970e35			−2.08440
$518$		−	2.38979e34i		−	0.123616i
$519$	−4.26397e34	+	3.09087e35i	−0.215099	+	1.55921i
$520$	−1.48334e35			−0.729787
$521$			2.96233e35i			1.42149i	0.703451	+	0.710744i	$0.251642\pi$
$521$			2.96233e35i			1.42149i	−0.703451	+	0.710744i	$0.748358\pi$
$522$	4.45911e35	+	1.25417e35i	2.08705	+	0.587004i
$523$	2.24702e35			1.02585			0.512927	−	0.858432i	$-0.328561\pi$
$523$	2.24702e35			1.02585			0.512927	+	0.858432i	$0.328561\pi$
$524$		−	7.45648e35i		−	3.32068i
$525$	9.33529e34	+	1.28784e34i	0.405562	+	0.0559489i
$526$	2.74557e35			1.16364
$527$			1.79377e34i			0.0741702i
$528$	1.31249e35	−	9.51394e35i	0.529485	−	3.83813i
$529$	−1.21883e35			−0.479754
$530$			3.68525e35i			1.41540i
$531$	3.07529e34	−	1.09339e35i	0.115254	−	0.409777i
$532$	1.53007e35			0.559576
$533$		−	3.20834e34i		−	0.114506i
$534$	−7.02087e35	−	9.68557e34i	−2.44543	−	0.337356i
$535$	2.82364e35			0.959865
$536$			1.14705e36i			3.80576i
$537$	−2.85626e34	+	2.07045e35i	−0.0924980	+	0.670499i
$538$	−9.93473e35			−3.14041
$539$		−	2.37611e35i		−	0.733182i
$540$	−2.09663e35	+	4.80727e35i	−0.631543	+	1.44804i
$541$	8.30656e34			0.244263			0.122131	−	0.992514i	$-0.461027\pi$
$541$	8.30656e34			0.244263			0.122131	+	0.992514i	$0.461027\pi$
$542$		−	1.90232e33i		−	0.00546127i
$543$	3.00435e35	+	4.14462e34i	0.842079	+	0.116168i
$544$	8.22492e34			0.225085
$545$		−	3.88849e35i		−	1.03903i
$546$	2.64555e34	−	1.91770e35i	0.0690258	−	0.500353i
$547$	2.26776e35			0.577779			0.288890	−	0.957362i	$-0.406714\pi$
$547$	2.26776e35			0.577779			0.288890	+	0.957362i	$0.406714\pi$
$548$		−	6.37121e33i		−	0.0158517i
$549$	−2.11105e35	−	5.93755e34i	−0.512929	−	0.144267i
$550$	−6.42255e35			−1.52403
$551$		−	1.63990e35i		−	0.380056i
$552$	1.55424e36	+	2.14413e35i	3.51811	+	0.485337i
$553$	1.06089e35			0.234554
$554$		−	6.47624e34i		−	0.139861i
$555$	3.96314e33	−	2.87280e34i	0.00836047	−	0.0606033i
$556$	−1.05738e36			−2.17902
$557$		−	4.42912e35i		−	0.891662i	−0.895117	−	0.445831i	$-0.852908\pi$
$557$		−	4.42912e35i		−	0.891662i	0.895117	−	0.445831i	$-0.147092\pi$
$558$	2.25632e35	−	8.02216e35i	0.443768	−	1.57778i
$559$	1.03456e35			0.198793
$560$		−	6.47182e35i		−	1.21502i
$561$	−6.04547e34	−	8.33997e33i	−0.110895	−	0.0152984i
$562$	1.37847e35			0.247073
$563$			6.73030e35i			1.17876i	0.807856	+	0.589380i	$0.200628\pi$
$563$			6.73030e35i			1.17876i	−0.807856	+	0.589380i	$0.799372\pi$
$564$	−3.23189e35	+	2.34273e36i	−0.553131	+	4.00953i
$565$	1.18870e35			0.198813
$566$		−	1.07689e36i		−	1.76019i
$567$	−3.55008e35	−	2.16855e35i	−0.567098	−	0.346409i
$568$	2.25029e36			3.51326
$569$			3.02745e35i			0.461975i	0.972957	+	0.230987i	$0.0741956\pi$
$569$			3.02745e35i			0.461975i	−0.972957	+	0.230987i	$0.925804\pi$
$570$	2.56072e35	+	3.53262e34i	0.381935	+	0.0526895i
$571$	3.40373e34			0.0496234			0.0248117	−	0.999692i	$-0.492101\pi$
$571$	3.40373e34			0.0496234			0.0248117	+	0.999692i	$0.492101\pi$
$572$			9.47661e35i			1.35053i
$573$	2.54886e34	−	1.84761e35i	0.0355087	−	0.257395i
$574$	2.60927e35			0.355356
$575$		−	5.62877e35i		−	0.749430i
$576$	−1.49611e36	−	4.20796e35i	−1.94747	−	0.547747i
$577$	−9.39165e35			−1.19524			−0.597621	−	0.801778i	$-0.703887\pi$
$577$	−9.39165e35			−1.19524			−0.597621	+	0.801778i	$0.703887\pi$
$578$			1.50308e36i			1.87034i
$579$	−4.51423e35	−	6.22757e34i	−0.549241	−	0.0757700i
$580$	−1.52803e36			−1.81789
$581$			9.21809e35i			1.07239i
$582$	3.17116e35	−	2.29871e36i	0.360761	−	2.61508i
$583$	1.43096e36			1.59198
$584$		−	2.40729e36i		−	2.61916i
$585$	6.36049e34	−	2.26142e35i	0.0676807	−	0.240633i
$586$	−2.42679e35			−0.252559
$587$			1.03983e36i			1.05844i	0.848484	+	0.529222i	$0.177516\pi$
$587$			1.03983e36i			1.05844i	−0.848484	+	0.529222i	$0.822484\pi$
$588$	−1.41654e36	−	1.95417e35i	−1.41034	−	0.194562i
$589$	−2.95027e35			−0.287318
$590$			5.21635e35i			0.496925i
$591$	1.69047e34	−	1.22539e35i	0.0157532	−	0.114192i
$592$	3.19594e35			0.291351
$593$			1.70525e36i			1.52082i	0.649445	+	0.760409i	$0.275001\pi$
$593$			1.70525e36i			1.52082i	−0.649445	+	0.760409i	$0.724999\pi$
$594$	2.59876e36	+	1.13342e36i	2.26748	+	0.988932i
$595$	−4.11240e34			−0.0351055
$596$		−	1.95387e36i		−	1.63190i
$597$	−5.79435e34	−	7.99354e33i	−0.0473520	−	0.00653240i
$598$	−1.15629e36			−0.924594
$599$		−	3.19697e35i		−	0.250144i	−0.992148	−	0.125072i	$-0.960084\pi$
$599$		−	3.19697e35i		−	0.250144i	0.992148	−	0.125072i	$-0.0399162\pi$
$600$	−3.21035e35	+	2.32711e36i	−0.245802	+	1.78177i
$601$	−8.59736e35			−0.644165			−0.322082	−	0.946712i	$-0.604383\pi$
$601$	−8.59736e35			−0.644165			−0.322082	+	0.946712i	$0.604383\pi$
$602$			8.41382e35i			0.616934i
$603$	−1.74874e36	−	4.91853e35i	−1.25488	−	0.352947i
$604$	5.13127e36			3.60367
$605$		−	6.52631e35i		−	0.448588i
$606$	7.04454e35	+	9.71822e34i	0.473924	+	0.0653797i
$607$	1.57024e36			1.03398			0.516990	−	0.855991i	$-0.327052\pi$
$607$	1.57024e36			1.03398			0.516990	+	0.855991i	$0.327052\pi$
$608$			1.35277e36i			0.871925i
$609$	1.65636e35	−	1.20066e36i	0.104503	−	0.757522i
$610$	1.00714e36			0.622014
$611$		−	1.05930e36i		−	0.640446i
$612$	−9.94391e34	+	3.53548e35i	−0.0588557	+	0.209257i
$613$	−1.50442e36			−0.871734			−0.435867	−	0.900011i	$-0.643558\pi$
$613$	−1.50442e36			−0.871734			−0.435867	+	0.900011i	$0.643558\pi$
$614$		−	4.11053e36i		−	2.33190i
$615$	3.13664e35	+	4.32712e34i	0.174216	+	0.0240338i
$616$	−4.68423e36			−2.54735
$617$		−	3.46870e36i		−	1.84697i	−0.383634	−	0.923485i	$-0.625328\pi$
$617$		−	3.46870e36i		−	1.84697i	0.383634	−	0.923485i	$-0.374672\pi$
$618$	−7.94841e34	+	5.76164e35i	−0.0414410	+	0.300397i
$619$	−1.86858e34			−0.00953968			−0.00476984	−	0.999989i	$-0.501518\pi$
$619$	−1.86858e34			−0.00953968			−0.00476984	+	0.999989i	$0.501518\pi$
$620$			2.74900e36i			1.37430i
$621$	−9.93336e35	+	2.27757e36i	−0.486301	+	1.11502i
$622$	−1.29210e36			−0.619471
$623$			1.85446e36i			0.870709i
$624$	2.56460e36	+	3.53797e35i	1.17929	+	0.162688i
$625$	−9.69762e33			−0.00436742
$626$			7.84418e35i			0.346004i
$627$	1.37170e35	−	9.94314e35i	0.0592625	−	0.429581i
$628$	−4.72485e36			−1.99946
$629$		−	2.03080e34i		−	0.00841801i
$630$	1.83916e36	+	5.17284e35i	0.746779	+	0.210040i
$631$	2.53086e36			1.00667			0.503334	−	0.864092i	$-0.332106\pi$
$631$	2.53086e36			1.00667			0.503334	+	0.864092i	$0.332106\pi$
$632$			2.64459e36i			1.03047i
$633$	3.98500e36	+	5.49747e35i	1.52118	+	0.209853i
$634$	−4.61682e36			−1.72656
$635$		−	6.74780e35i		−	0.247231i
$636$	1.17686e36	−	8.53082e36i	0.422457	−	3.06230i
$637$	6.40509e35			0.225275
$638$			8.26037e36i			2.84663i
$639$	−9.64917e35	+	3.43069e36i	−0.325821	+	1.15843i
$640$	2.19375e36			0.725850
$641$			1.14525e36i			0.371318i	0.982614	+	0.185659i	$0.0594420\pi$
$641$			1.14525e36i			0.371318i	−0.982614	+	0.185659i	$0.940558\pi$
$642$	−9.09998e36	−	1.25538e36i	−2.89125	−	0.398859i
$643$	1.31385e36			0.409076			0.204538	−	0.978859i	$-0.434431\pi$
$643$	1.31385e36			0.409076			0.204538	+	0.978859i	$0.434431\pi$
$644$		−	6.75456e36i		−	2.06101i
$645$	−1.39532e35	+	1.01144e36i	−0.0417250	+	0.302456i
$646$	1.81020e35			0.0530521
$647$		−	4.88372e36i		−	1.40280i	−0.712768	−	0.701400i	$-0.752559\pi$
$647$		−	4.88372e36i		−	1.40280i	0.712768	−	0.701400i	$-0.247441\pi$
$648$	5.40578e36	−	8.84968e36i	1.52189	−	2.49145i
$649$	2.02548e36			0.558916
$650$		−	1.73128e36i		−	0.468266i
$651$	−2.16005e36	−	2.97987e35i	−0.572677	−	0.0790032i
$652$	1.40023e37			3.63898
$653$		−	7.49065e35i		−	0.190831i	−0.995438	−	0.0954153i	$-0.969582\pi$
$653$		−	7.49065e35i		−	0.190831i	0.995438	−	0.0954153i	$-0.0304179\pi$
$654$	−1.72881e36	+	1.25318e37i	−0.431753	+	3.12969i
$655$	−3.29620e36			−0.807005
$656$			3.48945e36i			0.837544i
$657$	3.67004e36	+	1.03224e36i	0.863616	+	0.242901i
$658$	8.61502e36			1.98756
$659$			8.20579e36i			1.85614i	0.372409	+	0.928069i	$0.378532\pi$
$659$			8.20579e36i			1.85614i	−0.372409	+	0.928069i	$0.621468\pi$
$660$	−9.26480e36	−	1.27812e36i	−2.05478	−	0.283465i
$661$	−1.11276e35			−0.0241981			−0.0120990	−	0.999927i	$-0.503851\pi$
$661$	−1.11276e35			−0.0241981			−0.0120990	+	0.999927i	$0.503851\pi$
$662$		−	4.29933e36i		−	0.916741i
$663$	2.24814e34	−	1.62963e35i	0.00470054	−	0.0340732i
$664$	−2.29790e37			−4.71135
$665$		−	6.76378e35i		−	0.135990i
$666$	−2.55447e35	+	9.08220e35i	−0.0503658	+	0.179071i
$667$	−7.23945e36			−1.39981
$668$			4.93331e35i			0.0935501i
$669$	8.52037e36	+	1.17542e36i	1.58460	+	0.218602i
$670$	8.34288e36			1.52175
$671$		−	3.91065e36i		−	0.699610i
$672$	−1.36635e36	+	9.90437e36i	−0.239751	+	1.73791i
$673$	−3.71183e36			−0.638841			−0.319420	−	0.947613i	$-0.603488\pi$
$673$	−3.71183e36			−0.638841			−0.319420	+	0.947613i	$0.603488\pi$
$674$		−	1.12655e37i		−	1.90183i
$675$	−3.41014e36	−	1.48729e36i	−0.564708	−	0.246290i
$676$	1.31411e37			2.13464
$677$		−	4.08735e36i		−	0.651312i	−0.945488	−	0.325656i	$-0.894415\pi$
$677$		−	4.08735e36i		−	0.651312i	0.945488	−	0.325656i	$-0.105585\pi$
$678$	−3.83094e36	−	5.28493e35i	−0.598851	−	0.0826139i
$679$	−6.07170e36			−0.931115
$680$		−	1.02515e36i		−	0.154230i
$681$	9.53532e35	−	6.91195e36i	0.140742	−	1.02021i
$682$	1.48608e37			2.15202
$683$		−	3.02236e36i		−	0.429416i	−0.976678	−	0.214708i	$-0.931120\pi$
$683$		−	3.02236e36i		−	0.429416i	0.976678	−	0.214708i	$-0.0688799\pi$
$684$	−5.81489e36	−	1.63550e36i	−0.810610	−	0.227993i
$685$	−2.81645e34			−0.00385233
$686$			1.45377e37i			1.95112i
$687$	−8.26342e36	−	1.13997e36i	−1.08823	−	0.150126i
$688$	−1.12521e37			−1.45406
$689$			3.85733e36i			0.489144i
$690$	1.55949e36	−	1.13045e37i	0.194064	−	1.40673i
$691$	3.54345e36			0.432725			0.216362	−	0.976313i	$-0.430581\pi$
$691$	3.54345e36			0.432725			0.216362	+	0.976313i	$0.430581\pi$
$692$			3.34849e37i			4.01301i
$693$	2.00858e36	−	7.14135e36i	0.236242	−	0.839940i
$694$	2.02038e36			0.233216
$695$			4.67426e36i			0.529554i
$696$	2.99302e37	+	4.12899e36i	3.32805	+	0.459118i
$697$	2.21731e35			0.0241992
$698$		−	2.39907e37i		−	2.56994i
$699$	−8.93506e35	+	6.47684e36i	−0.0939494	+	0.681020i
$700$	1.01134e37			1.04381
$701$			1.11647e37i			1.13113i	0.824704	+	0.565565i	$0.191342\pi$
$701$			1.11647e37i			1.13113i	−0.824704	+	0.565565i	$0.808658\pi$
$702$	−3.05527e36	+	7.00529e36i	−0.303855	+	0.696696i
$703$	3.34011e35			0.0326093
$704$		−	2.77149e37i		−	2.65625i
$705$	1.03562e37	+	1.42868e36i	0.974413	+	0.134424i
$706$	−2.15029e37			−1.98626
$707$		−	1.86071e36i		−	0.168743i
$708$	1.66581e36	−	1.20751e37i	0.148318	−	1.07512i
$709$	−3.51818e36			−0.307551			−0.153775	−	0.988106i	$-0.549143\pi$
$709$	−3.51818e36			−0.307551			−0.153775	+	0.988106i	$0.549143\pi$
$710$		−	1.63671e37i		−	1.40479i
$711$	−4.03181e36	−	1.13399e36i	−0.339778	−	0.0955663i
$712$	−4.62282e37			−3.82531
$713$			1.30241e37i			1.05824i
$714$	1.32534e36	+	1.82836e35i	0.105743	+	0.0145876i
$715$	4.18921e36			0.328212
$716$			2.24302e37i			1.72569i
$717$	1.34731e36	−	9.76640e36i	0.101793	−	0.737880i
$718$	7.51184e36			0.557351
$719$			1.06482e37i			0.775890i	0.921682	+	0.387945i	$0.126815\pi$
$719$			1.06482e37i			0.775890i	−0.921682	+	0.387945i	$0.873185\pi$
$720$	−6.91779e36	+	2.45956e37i	−0.495045	+	1.76009i
$721$	1.52185e36			0.106958
$722$		−	2.43171e37i		−	1.67853i
$723$	−1.05820e37	−	1.45983e36i	−0.717416	−	0.0989705i
$724$	3.25477e37			2.16730
$725$		−	1.08394e37i		−	0.708943i
$726$	−2.90157e36	+	2.10329e37i	−0.186405	+	1.35121i
$727$	1.97297e37			1.24501			0.622506	−	0.782615i	$-0.286115\pi$
$727$	1.97297e37			1.24501			0.622506	+	0.782615i	$0.286115\pi$
$728$		−	1.26269e37i		−	0.782690i
$729$	1.11738e37	+	1.20361e37i	0.680367	+	0.732871i
$730$	−1.75090e37			−1.04728
$731$			7.14992e35i			0.0420122i
$732$	−2.33137e37	−	3.21622e36i	−1.34576	−	0.185653i
$733$	−2.92530e37			−1.65890			−0.829448	−	0.558584i	$-0.811345\pi$
$733$	−2.92530e37			−1.65890			−0.829448	+	0.558584i	$0.811345\pi$
$734$			3.85499e37i			2.14770i
$735$	−8.63859e35	+	6.26193e36i	−0.0472833	+	0.342746i
$736$	5.97190e37			3.21145
$737$		−	3.23949e37i		−	1.71159i
$738$	−9.91631e36	−	2.78907e36i	−0.514775	−	0.144786i
$739$	3.22318e37			1.64402			0.822009	−	0.569474i	$-0.192853\pi$
$739$	3.22318e37			1.64402			0.822009	+	0.569474i	$0.192853\pi$
$740$		−	3.11225e36i		−	0.155977i
$741$	2.68030e36	+	3.69758e35i	0.131992	+	0.0182088i
$742$	−3.13707e37			−1.51801
$743$		−	1.03473e37i		−	0.492009i	−0.969269	−	0.246004i	$-0.920882\pi$
$743$		−	1.03473e37i		−	0.492009i	0.969269	−	0.246004i	$-0.0791178\pi$
$744$	7.42825e36	−	5.38459e37i	0.347087	−	2.51596i
$745$	−8.63725e36			−0.396592
$746$		−	3.42699e37i		−	1.54635i
$747$	9.85330e36	−	3.50326e37i	0.436932	−	1.55348i
$748$	−6.54936e36			−0.285416
$749$			2.40363e37i			1.02945i
$750$	4.43993e37	+	6.12506e36i	1.86887	+	0.257818i
$751$	3.01520e37			1.24737			0.623687	−	0.781674i	$-0.285634\pi$
$751$	3.01520e37			1.24737			0.623687	+	0.781674i	$0.285634\pi$
$752$			1.15211e38i			4.68450i
$753$	−4.44238e36	+	3.22019e37i	−0.177534	+	1.28691i
$754$	−2.22668e37			−0.874644
$755$		−	2.26832e37i		−	0.875777i
$756$	−4.09220e37	−	1.78476e37i	−1.55301	−	0.677324i
$757$	−2.94589e37			−1.09893			−0.549465	−	0.835517i	$-0.685168\pi$
$757$	−2.94589e37			−1.09893			−0.549465	+	0.835517i	$0.685168\pi$
$758$			2.10857e37i			0.773194i
$759$	−4.38945e37	−	6.05543e36i	−1.58222	−	0.218274i
$760$	1.68608e37			0.597451
$761$		−	2.58816e37i		−	0.901550i	−0.892638	−	0.450775i	$-0.851148\pi$
$761$		−	2.58816e37i		−	0.901550i	0.892638	−	0.450775i	$-0.148852\pi$
$762$	−3.00004e36	+	2.17467e37i	−0.102734	+	0.744695i
$763$	3.31008e37			1.11435
$764$		−	2.00161e37i		−	0.662470i
$765$	1.56289e36	+	4.39579e35i	0.0508544	+	0.0143034i
$766$	−9.40622e36			−0.300913
$767$			5.45993e36i			0.171730i
$768$	−5.89527e36	−	8.13277e35i	−0.182309	−	0.0251503i
$769$	1.64070e37			0.498869			0.249435	−	0.968392i	$-0.419755\pi$
$769$	1.64070e37			0.498869			0.249435	+	0.968392i	$0.419755\pi$
$770$			3.40699e37i			1.01857i
$771$	−5.80958e36	+	4.21124e37i	−0.170780	+	1.23795i
$772$	−4.89050e37			−1.41361
$773$			1.17016e37i			0.332592i	0.986076	+	0.166296i	$0.0531807\pi$
$773$			1.17016e37i			0.332592i	−0.986076	+	0.166296i	$0.946819\pi$
$774$	8.99361e36	−	3.19760e37i	0.251363	−	0.893701i
$775$	−1.95006e37			−0.535952
$776$		−	1.51356e38i		−	4.09070i
$777$	2.44547e36	+	3.37363e35i	0.0649964	+	0.00896652i
$778$	8.92762e37			2.33346
$779$			3.64687e36i			0.0937418i
$780$	3.44532e36	−	2.49744e37i	0.0870963	−	0.631343i
$781$	−6.35524e37			−1.58004
$782$		−	7.99120e36i		−	0.195400i
$783$	−1.91288e37	+	4.38596e37i	−0.460029	+	1.05478i
$784$	−6.96629e37			−1.64776
$785$			2.08866e37i			0.485917i
$786$	1.06229e38	+	1.46548e37i	2.43081	+	0.335340i
$787$	2.20060e37			0.495302			0.247651	−	0.968849i	$-0.420341\pi$
$787$	2.20060e37			0.495302			0.247651	+	0.968849i	$0.420341\pi$
$788$		−	1.32752e37i		−	0.293901i
$789$	−3.87588e36	+	2.80955e37i	−0.0844053	+	0.611836i
$790$	1.92349e37			0.412039
$791$			1.01189e37i			0.213225i
$792$	1.78020e38	+	5.00702e37i	3.69014	+	1.03789i
$793$	1.05416e37			0.214960
$794$			2.52993e37i			0.507506i
$795$	−3.77112e37	−	5.20241e36i	−0.744213	−	0.102667i
$796$	−6.27731e36			−0.121872
$797$		−	6.59991e37i		−	1.26061i	−0.776349	−	0.630304i	$-0.782930\pi$
$797$		−	6.59991e37i		−	1.26061i	0.776349	−	0.630304i	$-0.217070\pi$
$798$	−3.00715e36	+	2.17982e37i	−0.0565090	+	0.409622i
$799$	7.32089e36			0.135349
$800$			8.94154e37i			1.62646i
$801$	1.98225e37	−	7.04772e37i	0.354761	−	1.26132i
$802$	−1.01370e38			−1.78502
$803$			6.79863e37i			1.17793i
$804$	−1.93125e38	−	2.66424e37i	−3.29239	−	0.454198i
$805$	−2.98591e37			−0.500876
$806$			4.00591e37i			0.661220i
$807$	1.40247e37	−	1.01662e38i	0.227792	−	1.65121i
$808$	4.63841e37			0.741346
$809$			2.57683e37i			0.405280i	0.979253	+	0.202640i	$0.0649522\pi$
$809$			2.57683e37i			0.405280i	−0.979253	+	0.202640i	$0.935048\pi$
$810$	−6.43665e37	−	3.93179e37i	−0.996218	−	0.608534i
$811$	1.07165e38			1.63224			0.816118	−	0.577885i	$-0.196122\pi$
$811$	1.07165e38			1.63224			0.816118	+	0.577885i	$0.196122\pi$
$812$		−	1.30074e38i		−	1.94967i
$813$	1.94665e35	+	2.68548e34i	0.00287151	+	0.000396136i
$814$	−1.68245e37			−0.244245
$815$		−	6.18981e37i		−	0.884359i
$816$	−2.44512e36	+	1.77242e37i	−0.0343817	+	0.249226i
$817$	−1.17597e37			−0.162745
$818$			3.69124e37i			0.502782i
$819$	1.92504e37	+	5.41438e36i	0.258077	+	0.0725868i
$820$	3.39808e37			0.448387
$821$			1.13885e38i			1.47913i	0.673084	+	0.739566i	$0.264969\pi$
$821$			1.13885e38i			1.47913i	−0.673084	+	0.739566i	$0.735031\pi$
$822$	9.07680e35	+	1.25218e35i	0.0116038	+	0.00160079i
$823$	1.25928e37			0.158462			0.0792308	−	0.996856i	$-0.474754\pi$
$823$	1.25928e37			0.158462			0.0792308	+	0.996856i	$0.474754\pi$
$824$			3.79369e37i			0.469903i
$825$	9.06661e36	−	6.57219e37i	0.110546	−	0.801326i
$826$	−4.44043e37			−0.532947
$827$		−	1.16233e38i		−	1.37328i	−0.726999	−	0.686638i	$-0.759086\pi$
$827$		−	1.16233e38i		−	1.37328i	0.726999	−	0.686638i	$-0.240914\pi$
$828$	−7.22001e37	+	2.56701e38i	−0.839737	+	2.98562i
$829$	−9.32435e37			−1.06760			−0.533802	−	0.845610i	$-0.679237\pi$
$829$	−9.32435e37			−1.06760			−0.533802	+	0.845610i	$0.679237\pi$
$830$			1.67133e38i			1.88385i
$831$	6.62713e36	+	9.14240e35i	0.0735381	+	0.0101449i
$832$	7.47090e37			0.816149
$833$			4.42661e36i			0.0476087i
$834$	2.07816e37	−	1.50641e38i	0.220049	−	1.59509i
$835$	2.18081e36			0.0227349
$836$		−	1.07719e38i		−	1.10563i
$837$	7.89056e37	+	3.44137e37i	0.797401	+	0.347776i
$838$	4.42599e37			0.440390
$839$			1.62318e38i			1.59023i	0.606458	+	0.795116i	$0.292590\pi$
$839$			1.62318e38i			1.59023i	−0.606458	+	0.795116i	$0.707410\pi$
$840$	1.23447e38	+	1.70300e37i	1.19083	+	0.164280i
$841$	−3.41306e37			−0.324188
$842$		−	2.21950e38i		−	2.07586i
$843$	−1.94597e36	+	1.41059e37i	−0.0179216	+	0.129910i
$844$	4.31715e38			3.91512
$845$		−	5.80913e37i		−	0.518768i
$846$	−3.27407e38	−	9.20867e37i	−2.87921	−	0.809808i
$847$	5.55553e37			0.481107
$848$		−	4.19530e38i		−	3.57781i
$849$	1.10198e38	+	1.52023e37i	0.925497	+	0.127676i
$850$	1.19650e37			0.0989615
$851$		−	1.47451e37i		−	0.120106i
$852$	−5.22672e37	+	3.78874e38i	−0.419290	+	3.03934i
$853$	−6.26827e37			−0.495233			−0.247617	−	0.968858i	$-0.579647\pi$
$853$	−6.26827e37			−0.495233			−0.247617	+	0.968858i	$0.579647\pi$
$854$			8.57326e37i			0.667104i
$855$	−7.22987e36	+	2.57052e37i	−0.0554078	+	0.196998i
$856$	−5.99179e38			−4.52270
$857$			1.31009e38i			0.973980i	0.873407	+	0.486990i	$0.161905\pi$
$857$			1.31009e38i			0.973980i	−0.873407	+	0.486990i	$0.838095\pi$
$858$	−1.35009e38	−	1.86251e37i	−0.988619	−	0.136384i
$859$	−1.51682e37			−0.109402			−0.0547008	−	0.998503i	$-0.517420\pi$
$859$	−1.51682e37			−0.109402			−0.0547008	+	0.998503i	$0.517420\pi$
$860$			1.09574e38i			0.778444i
$861$	−3.68346e36	+	2.67007e37i	−0.0257760	+	0.186845i
$862$	2.38694e38			1.64531
$863$			8.19066e37i			0.556133i	0.960562	+	0.278067i	$0.0896936\pi$
$863$			8.19066e37i			0.556133i	−0.960562	+	0.278067i	$0.910306\pi$
$864$	1.57796e38	−	3.61803e38i	1.05540	−	2.41988i
$865$	1.48023e38			0.975257
$866$			1.95565e38i			1.26929i
$867$	−1.53811e38	−	2.12188e37i	−0.983417	−	0.135666i
$868$	−2.34009e38			−1.47393
$869$		−	7.46881e37i		−	0.463441i
$870$	3.00314e37	−	2.17692e38i	0.183580	−	1.33073i
$871$	8.73245e37			0.525896
$872$			8.25141e38i			4.89569i
$873$	2.30750e38	+	6.49010e37i	1.34883	+	0.379373i
$874$	1.31433e38			0.756933
$875$		−	1.17274e38i		−	0.665423i
$876$	4.05307e38	+	5.59138e37i	2.26585	+	0.312583i
$877$	−3.27529e38			−1.80408			−0.902039	−	0.431655i	$-0.857930\pi$
$877$	−3.27529e38			−1.80408			−0.902039	+	0.431655i	$0.857930\pi$
$878$		−	5.58711e38i		−	3.03220i
$879$	3.42585e36	−	2.48333e37i	0.0183195	−	0.132794i
$880$	−4.55627e38			−2.40068
$881$		−	2.58631e38i		−	1.34275i	−0.741119	−	0.671374i	$-0.765705\pi$
$881$		−	2.58631e38i		−	1.34275i	0.741119	−	0.671374i	$-0.234295\pi$
$882$	5.56806e37	−	1.97968e38i	0.284847	−	1.01275i
$883$	−3.80240e38			−1.91676			−0.958381	−	0.285492i	$-0.907843\pi$
$883$	−3.80240e38			−1.91676			−0.958381	+	0.285492i	$0.907843\pi$
$884$		−	1.76546e37i		−	0.0876958i
$885$	−5.33790e37	−	7.36384e36i	−0.261281	−	0.0360447i
$886$	1.85288e38			0.893733
$887$		−	3.39306e38i		−	1.61281i	−0.591361	−	0.806407i	$-0.701409\pi$
$887$		−	3.39306e38i		−	1.61281i	0.591361	−	0.806407i	$-0.298591\pi$
$888$	−8.40982e36	+	6.09610e37i	−0.0393929	+	0.285551i
$889$	5.74407e37			0.265153
$890$			3.36232e38i			1.52957i
$891$	−1.52669e38	+	2.49931e38i	−0.684448	+	1.12050i
$892$	9.23055e38			4.07835
$893$			1.20409e38i			0.524311i
$894$	2.78360e38	+	3.84009e37i	1.19459	+	0.164799i
$895$	9.91544e37			0.419385
$896$			1.86743e38i			0.778467i
$897$	1.63231e37	−	1.18323e38i	0.0670660	−	0.486147i
$898$	2.55262e38			1.03370
$899$			2.50807e38i			1.00107i
$900$	−3.84351e38	−	1.08103e38i	−1.51208	−	0.425290i
$901$	−2.66583e37			−0.103374
$902$		−	1.83697e38i		−	0.702128i
$903$	−8.60986e37	−	1.18777e37i	−0.324381	−	0.0447497i
$904$	−2.52244e38			−0.936767
$905$		−	1.43880e38i		−	0.526705i
$906$	−1.00849e38	+	7.31030e38i	−0.363918	+	2.63796i
$907$	−2.48670e38			−0.884562			−0.442281	−	0.896877i	$-0.645831\pi$
$907$	−2.48670e38			−0.884562			−0.442281	+	0.896877i	$0.645831\pi$
$908$		−	7.48807e38i		−	2.62575i
$909$	−1.98893e37	+	7.07149e37i	−0.0687527	+	0.244444i
$910$	−9.18395e37			−0.312962
$911$			1.82157e38i			0.611937i	0.952042	+	0.305968i	$0.0989802\pi$
$911$			1.82157e38i			0.611937i	−0.952042	+	0.305968i	$0.901020\pi$
$912$	−2.91514e38	−	4.02155e37i	−0.965442	−	0.133187i
$913$	6.48968e38			2.11886
$914$			6.05320e38i			1.94843i
$915$	−1.42176e37	+	1.03060e38i	−0.0451182	+	0.327052i
$916$	−8.95218e38			−2.80084
$917$		−	2.80589e38i		−	0.865506i
$918$	−4.84141e37	−	2.11152e37i	−0.147237	−	0.0642156i
$919$	−1.99483e38			−0.598141			−0.299070	−	0.954231i	$-0.596677\pi$
$919$	−1.99483e38			−0.598141			−0.299070	+	0.954231i	$0.596677\pi$
$920$		−	7.44331e38i		−	2.20051i
$921$	4.20631e38	+	5.80277e37i	1.22610	+	0.169145i
$922$	−1.84859e38			−0.531299
$923$		−	1.71313e38i		−	0.485477i
$924$	1.08800e38	−	7.88668e38i	0.304013	−	2.20373i
$925$	2.20774e37			0.0608283
$926$		−	9.26360e37i		−	0.251673i
$927$	−5.78368e37	−	1.62672e37i	−0.154941	−	0.0435790i
$928$	1.15002e39			3.03795
$929$			6.60756e38i			1.72122i	0.509263	+	0.860611i	$0.329918\pi$
$929$			6.60756e38i			1.72122i	−0.509263	+	0.860611i	$0.670082\pi$
$930$	−3.91638e38	−	5.40280e37i	−1.00602	−	0.138784i
$931$	−7.28056e37			−0.184425
$932$			7.01668e38i			1.75277i
$933$	1.82403e37	−	1.32220e38i	0.0449337	−	0.325715i
$934$	−1.19034e39			−2.89175
$935$			2.89520e37i			0.0693629i
$936$	−1.34970e38	+	4.79876e38i	−0.318898	+	1.13382i
$937$	7.73152e38			1.80157			0.900783	−	0.434269i	$-0.142993\pi$
$937$	7.73152e38			1.80157			0.900783	+	0.434269i	$0.142993\pi$
$938$			7.10189e38i			1.63206i
$939$	−8.02695e37	−	1.10735e37i	−0.181927	−	0.0250976i
$940$	1.12194e39			2.50789
$941$			2.03187e38i			0.447952i	0.974595	+	0.223976i	$0.0719038\pi$
$941$			2.03187e38i			0.447952i	−0.974595	+	0.223976i	$0.928096\pi$
$942$	9.28610e37	−	6.73130e38i	0.201916	−	1.46365i
$943$	1.60993e38			0.345267
$944$		−	5.93832e38i		−	1.25611i
$945$	−7.88968e37	+	1.80899e38i	−0.164606	+	0.377418i
$946$	5.92346e38			1.21896
$947$			4.38067e38i			0.889183i	0.895734	+	0.444591i	$0.146651\pi$
$947$			4.38067e38i			0.889183i	−0.895734	+	0.444591i	$0.853349\pi$
$948$	−4.45261e38	−	6.14255e37i	−0.891468	−	0.122982i
$949$	−1.83265e38			−0.361926
$950$			1.96791e38i			0.383353i
$951$	6.51749e37	−	4.72439e38i	0.125237	−	0.907819i
$952$	8.72656e37			0.165410
$953$		−	7.13804e38i		−	1.33466i	−0.744761	−	0.667331i	$-0.767437\pi$
$953$		−	7.13804e38i		−	1.33466i	0.744761	−	0.667331i	$-0.232563\pi$
$954$	1.19222e39	+	3.35325e38i	2.19901	+	0.618496i
$955$	−8.84829e37			−0.160996
$956$		−	1.05804e39i		−	1.89911i
$957$	−8.45284e38	−	1.16610e38i	−1.49674	−	0.206482i
$958$	−1.44971e39			−2.53238
$959$		−	2.39750e36i		−	0.00413159i
$960$	−1.00761e38	+	7.30392e38i	−0.171303	+	1.24174i
$961$	−1.45002e38			−0.243204
$962$		−	4.53525e37i		−	0.0750456i
$963$	2.56926e38	−	9.13479e38i	0.419436	−	1.49127i
$964$	−1.14641e39			−1.84645
$965$			2.16188e38i			0.343540i
$966$	9.62293e38	+	1.32752e38i	1.50871	+	0.208132i
$967$	5.57724e38			0.862730			0.431365	−	0.902177i	$-0.358032\pi$
$967$	5.57724e38			0.862730			0.431365	+	0.902177i	$0.358032\pi$
$968$			1.38489e39i			2.11366i
$969$	−2.55542e36	+	1.85237e37i	−0.00384817	+	0.0278946i
$970$	−1.10086e39			−1.63568
$971$		−	3.37407e38i		−	0.494656i	−0.968932	−	0.247328i	$-0.920447\pi$
$971$		−	3.37407e38i		−	0.494656i	0.968932	−	0.247328i	$-0.0795526\pi$
$972$	1.36443e39	+	1.11570e39i	1.97374	+	1.61394i
$973$	−3.97897e38			−0.567941
$974$		−	1.94596e39i		−	2.74073i
$975$	1.77162e38	+	2.44402e37i	0.246212	+	0.0339660i
$976$	−1.14653e39			−1.57231
$977$		−	3.47100e38i		−	0.469705i	−0.972031	−	0.234853i	$-0.924539\pi$
$977$		−	3.47100e38i		−	0.469705i	0.972031	−	0.234853i	$-0.0754608\pi$
$978$	−2.75197e38	+	1.99484e39i	−0.367484	+	2.66381i
$979$	1.30557e39			1.72038
$980$			6.78387e38i			0.882142i
$981$	−1.25797e39	−	3.53818e38i	−1.61426	−	0.454028i
$982$	7.42082e38			0.939729
$983$			9.14447e38i			1.14278i	0.820679	+	0.571390i	$0.193596\pi$
$983$			9.14447e38i			1.14278i	−0.820679	+	0.571390i	$0.806404\pi$
$984$	−6.65597e38	−	9.18218e37i	−0.820871	−	0.113243i
$985$	−5.86842e37			−0.0714250
$986$		−	1.53888e38i		−	0.184844i
$987$	−1.21617e38	+	8.81575e38i	−0.144169	+	1.04505i
$988$	2.90370e38			0.339712
$989$			5.19136e38i			0.599418i
$990$	3.64176e38	−	1.29480e39i	0.415005	−	1.47552i
$991$	−8.31021e38			−0.934662			−0.467331	−	0.884083i	$-0.654784\pi$
$991$	−8.31021e38			−0.934662			−0.467331	+	0.884083i	$0.654784\pi$
$992$		−	2.06894e39i		−	2.29665i
$993$	4.39950e38	+	6.06929e37i	0.482018	+	0.0664963i
$994$	1.39325e39			1.50663
$995$			2.77494e37i			0.0296178i
$996$	5.33729e38	−	3.86889e39i	0.562275	−	4.07582i
$997$	−7.04940e38			−0.733019			−0.366510	−	0.930414i	$-0.619447\pi$
$997$	−7.04940e38			−0.733019			−0.366510	+	0.930414i	$0.619447\pi$
$998$		−	1.30098e37i		−	0.0133529i
$999$	−8.93321e37	−	3.89611e37i	−0.0905016	−	0.0394711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.27.b.a.2.8	yes	8
3.2	odd	2	inner	3.27.b.a.2.1	✓	8
4.3	odd	2		48.27.e.d.17.8		8
12.11	even	2		48.27.e.d.17.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.27.b.a.2.1	✓	8	3.2	odd	2	inner
3.27.b.a.2.8	yes	8	1.1	even	1	trivial
48.27.e.d.17.7		8	12.11	even	2
48.27.e.d.17.8		8	4.3	odd	2

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:	\( k \)	\(=\)	\( 27 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+15434.0i q^{2} +(-1.57937e6 - 217880. i) q^{3} -1.71101e8 q^{4} +7.56364e8i q^{5} +(3.36276e9 - 2.43760e10i) q^{6} -6.43856e10 q^{7} -1.60501e12i q^{8} +(2.44692e12 + 6.88223e11i) q^{9} +O(q^{10})\)	\(q+15434.0i q^{2} +(-1.57937e6 - 217880. i) q^{3} -1.71101e8 q^{4} +7.56364e8i q^{5} +(3.36276e9 - 2.43760e10i) q^{6} -6.43856e10 q^{7} -1.60501e12i q^{8} +(2.44692e12 + 6.88223e11i) q^{9} -1.16738e13 q^{10} +4.53285e13i q^{11} +(2.70230e14 + 3.72794e13i) q^{12} -1.22189e14 q^{13} -9.93730e14i q^{14} +(1.64796e14 - 1.19458e15i) q^{15} +1.32894e16 q^{16} -8.44454e14i q^{17} +(-1.06221e16 + 3.77659e16i) q^{18} +1.38890e16 q^{19} -1.29414e17i q^{20} +(1.01688e17 + 1.40283e16i) q^{21} -6.99601e17 q^{22} -6.13136e17i q^{23} +(-3.49700e17 + 2.53490e18i) q^{24} +9.18029e17 q^{25} -1.88586e18i q^{26} +(-3.71463e18 - 1.62009e18i) q^{27} +1.10164e19 q^{28} -1.18072e19i q^{29} +(1.84371e19 + 2.54347e18i) q^{30} -2.12418e19 q^{31} +9.73993e19i q^{32} +(9.87616e18 - 7.15902e19i) q^{33} +1.30333e19 q^{34} -4.86990e19i q^{35} +(-4.18670e20 - 1.17755e20i) q^{36} +2.40487e19 q^{37} +2.14363e20i q^{38} +(1.92980e20 + 2.66224e19i) q^{39} +1.21397e21 q^{40} +2.62573e20i q^{41} +(-2.16514e20 + 1.56946e21i) q^{42} -8.46691e20 q^{43} -7.75573e21i q^{44} +(-5.20548e20 + 1.85076e21i) q^{45} +9.46316e21 q^{46} +8.66938e21i q^{47} +(-2.09889e22 - 2.89550e21i) q^{48} -5.24197e21 q^{49} +1.41689e22i q^{50} +(-1.83990e20 + 1.33370e21i) q^{51} +2.09065e22 q^{52} -3.15687e22i q^{53} +(2.50045e22 - 5.73318e22i) q^{54} -3.42848e22 q^{55} +1.03340e23i q^{56} +(-2.19357e22 - 3.02612e21i) q^{57} +1.82234e23 q^{58} -4.46845e22i q^{59} +(-2.81968e22 + 2.04393e23i) q^{60} -8.62736e22 q^{61} -3.27847e23i q^{62} +(-1.57547e23 - 4.43117e22i) q^{63} -6.11424e23 q^{64} -9.24190e22i q^{65} +(1.10493e24 + 1.52429e23i) q^{66} -7.14670e23 q^{67} +1.44487e23i q^{68} +(-1.33590e23 + 9.68365e23i) q^{69} +7.51622e23 q^{70} +1.40204e24i q^{71} +(1.10461e24 - 3.92734e24i) q^{72} +1.49986e24 q^{73} +3.71168e23i q^{74} +(-1.44990e24 - 2.00020e23i) q^{75} -2.37641e24 q^{76} -2.91850e24i q^{77} +(-4.10891e23 + 2.97846e24i) q^{78} -1.64771e24 q^{79} +1.00517e25i q^{80} +(5.51378e24 + 3.36806e24i) q^{81} -4.05257e24 q^{82} -1.43170e25i q^{83} +(-1.73989e25 - 2.40025e24i) q^{84} +6.38715e23 q^{85} -1.30679e25i q^{86} +(-2.57256e24 + 1.86480e25i) q^{87} +7.27528e25 q^{88} -2.88024e25i q^{89} +(-2.85648e25 - 8.03415e24i) q^{90} +7.86718e24 q^{91} +1.04908e26i q^{92} +(3.35486e25 + 4.62816e24i) q^{93} -1.33803e26 q^{94} +1.05051e25i q^{95} +(2.12213e25 - 1.53829e26i) q^{96} +9.43022e25 q^{97} -8.09048e25i q^{98} +(-3.11961e25 + 1.10915e26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9}+O(q^{10}) \) 8 * q - 1261080 * q^3 - 248848672 * q^4 + 4268261088 * q^6 - 83723264240 * q^7 + 3535237525320 * q^9	\( 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9} - 19160376580800 q^{10} + 361652147111520 q^{12} - 397915354631600 q^{13} - 719893807027200 q^{15} + 14\!\cdots\!24 q^{16}+ \cdots + 12\!\cdots\!20 q^{99}+O(q^{100}) \) 8 * q - 1261080 * q^3 - 248848672 * q^4 + 4268261088 * q^6 - 83723264240 * q^7 + 3535237525320 * q^9 - 19160376580800 * q^10 + 361652147111520 * q^12 - 397915354631600 * q^13 - 719893807027200 * q^15 + 14708338775335424 * q^16 - 21900893760832320 * q^18 + 16320401555362000 * q^19 + 194580840365988048 * q^21 - 772248680481769920 * q^22 - 462343148304920064 * q^24 + 1971388854053049800 * q^25 - 7894649015962792920 * q^27 + 15321751531929304000 * q^28 + 7398480599799681600 * q^30 - 9272518953250081904 * q^31 - 65168600178932490240 * q^33 + 221246262521511042816 * q^34 - 1016435634925989724704 * q^36 + 879374467120740709840 * q^37 - 1582238541124790450928 * q^39 + 4129217584783179033600 * q^40 - 6703469261814514512960 * q^42 + 6748593942335676212560 * q^43 - 16831420952659929907200 * q^45 + 36160927581299221074816 * q^46 - 66488551077760679646720 * q^48 + 45841873858091621647512 * q^49 - 62114113806050924347392 * q^51 + 99815113130579384624320 * q^52 - 65423424830500017302112 * q^54 + 31541176921532063385600 * q^55 - 68601650728105742286960 * q^57 + 179274146475296123858880 * q^58 + 132515345363297827507200 * q^60 - 319050283467071524566704 * q^61 + 658789337835295522626960 * q^63 - 1937027849517856838066176 * q^64 + 3327191890146340029253440 * q^66 - 3016122636770760226629680 * q^67 + 2874694883813365556256768 * q^69 - 3079956143630742638371200 * q^70 + 4816528692447953902187520 * q^72 - 1734362529074066854728560 * q^73 + 551279759153288953055400 * q^75 - 4252629668197637559664448 * q^76 - 2905541033044787133422400 * q^78 + 5851464318766097144790160 * q^79 - 7387002303358032367832952 * q^81 + 19281076716095151109326720 * q^82 - 58831332525651421466918208 * q^84 + 36766362882842005714329600 * q^85 - 66105320167985812595481600 * q^87 + 166743215953906759732730880 * q^88 - 112582289830354559315755200 * q^90 + 57658591275235919126596256 * q^91 - 721851591602497641585840 * q^93 - 128592383810221185199398144 * q^94 + 66451111218720743421763584 * q^96 + 87088434574088023884109840 * q^97 + 126385397236902706353285120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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