LMFDB - Embedded newform 3.27.b.a.2.2

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			2.2
Root			$-818.442i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.27.b.a.2.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9821.30i q^{2} +(1.39737e6 - 767608. i) q^{3} -2.93491e7 q^{4} -1.01800e9i q^{5} +(-7.53891e9 - 1.37240e10i) q^{6} +1.32967e11 q^{7} -3.70850e11i q^{8} +(1.36342e12 - 2.14527e12i) q^{9} +O(q^{10})$	\(q-9821.30i q^{2} +(1.39737e6 - 767608. i) q^{3} -2.93491e7 q^{4} -1.01800e9i q^{5} +(-7.53891e9 - 1.37240e10i) q^{6} +1.32967e11 q^{7} -3.70850e11i q^{8} +(1.36342e12 - 2.14527e12i) q^{9} -9.99808e12 q^{10} +2.72582e13i q^{11} +(-4.10116e13 + 2.25286e13i) q^{12} -3.10985e14 q^{13} -1.30591e15i q^{14} +(-7.81425e14 - 1.42252e15i) q^{15} -5.61181e15 q^{16} +6.64865e15i q^{17} +(-2.10693e16 - 1.33906e16i) q^{18} -5.27648e15 q^{19} +2.98774e16i q^{20} +(1.85804e17 - 1.02067e17i) q^{21} +2.67711e17 q^{22} +7.91861e17i q^{23} +(-2.84667e17 - 5.18215e17i) q^{24} +4.53793e17 q^{25} +3.05428e18i q^{26} +(2.58482e17 - 4.04430e18i) q^{27} -3.90246e18 q^{28} -1.83420e19i q^{29} +(-1.39710e19 + 7.67461e18i) q^{30} -8.35120e18 q^{31} +3.02280e19i q^{32} +(2.09236e19 + 3.80898e19i) q^{33} +6.52984e19 q^{34} -1.35360e20i q^{35} +(-4.00152e19 + 6.29617e19i) q^{36} +3.99842e20 q^{37} +5.18219e19i q^{38} +(-4.34561e20 + 2.38714e20i) q^{39} -3.77525e20 q^{40} +5.66138e20i q^{41} +(-1.00243e21 - 1.82484e21i) q^{42} +1.91808e19 q^{43} -8.00004e20i q^{44} +(-2.18388e21 - 1.38796e21i) q^{45} +7.77710e21 q^{46} +5.72628e21i q^{47} +(-7.84178e21 + 4.30767e21i) q^{48} +8.29274e21 q^{49} -4.45684e21i q^{50} +(5.10356e21 + 9.29063e21i) q^{51} +9.12713e21 q^{52} -1.57151e22i q^{53} +(-3.97203e22 - 2.53863e21i) q^{54} +2.77488e22 q^{55} -4.93108e22i q^{56} +(-7.37320e21 + 4.05027e21i) q^{57} -1.80142e23 q^{58} +7.56199e22i q^{59} +(2.29341e22 + 4.17498e22i) q^{60} +2.63456e23 q^{61} +8.20197e22i q^{62} +(1.81290e23 - 2.85249e23i) q^{63} -7.97240e22 q^{64} +3.16582e23i q^{65} +(3.74091e23 - 2.05497e23i) q^{66} -4.96439e23 q^{67} -1.95132e23i q^{68} +(6.07839e23 + 1.10652e24i) q^{69} -1.32941e24 q^{70} -2.95164e23i q^{71} +(-7.95571e23 - 5.05625e23i) q^{72} -1.62457e23 q^{73} -3.92697e24i q^{74} +(6.34117e23 - 3.48335e23i) q^{75} +1.54860e23 q^{76} +3.62444e24i q^{77} +(2.34449e24 + 4.26795e24i) q^{78} +1.76023e24 q^{79} +5.71283e24i q^{80} +(-2.74324e24 - 5.84980e24i) q^{81} +5.56021e24 q^{82} -3.14800e24i q^{83} +(-5.45319e24 + 2.99556e24i) q^{84} +6.76832e24 q^{85} -1.88380e23i q^{86} +(-1.40795e25 - 2.56306e25i) q^{87} +1.01087e25 q^{88} +1.04549e25i q^{89} +(-1.36316e25 + 2.14485e25i) q^{90} -4.13507e25 q^{91} -2.32404e25i q^{92} +(-1.16697e25 + 6.41045e24i) q^{93} +5.62395e25 q^{94} +5.37146e24i q^{95} +(2.32033e25 + 4.22397e25i) q^{96} +4.46410e25 q^{97} -8.14455e25i q^{98} +(5.84760e25 + 3.71644e25i) 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 $

$2$		−	9821.30i		−	1.19889i	−0.800416	−	0.599445i	$-0.795388\pi$
$2$		−	9821.30i		−	1.19889i	0.800416	−	0.599445i	$-0.204612\pi$
$3$	1.39737e6	−	767608.i	0.876466	−	0.481463i
$3$	1.39737e6	−	767608.i	0.876466	−	0.481463i
$4$	−2.93491e7			−0.437336
$5$		−	1.01800e9i		−	0.833945i	−0.908919	−	0.416973i	$-0.863091\pi$
$5$		−	1.01800e9i		−	0.833945i	0.908919	−	0.416973i	$-0.136909\pi$
$6$	−7.53891e9	−	1.37240e10i	−0.577221	−	1.05079i
$7$	1.32967e11			1.37236			0.686182	−	0.727430i	$-0.259285\pi$
$7$	1.32967e11			1.37236			0.686182	+	0.727430i	$0.259285\pi$
$8$		−	3.70850e11i		−	0.674572i
$9$	1.36342e12	−	2.14527e12i	0.536386	−	0.843973i
$10$	−9.99808e12			−0.999808
$11$			2.72582e13i			0.789573i	0.918773	+	0.394786i	$0.129181\pi$
$11$			2.72582e13i			0.789573i	−0.918773	+	0.394786i	$0.870819\pi$
$12$	−4.10116e13	+	2.25286e13i	−0.383310	+	0.210561i
$13$	−3.10985e14			−1.02678			−0.513388	−	0.858157i	$-0.671610\pi$
$13$	−3.10985e14			−1.02678			−0.513388	+	0.858157i	$0.671610\pi$
$14$		−	1.30591e15i		−	1.64531i
$15$	−7.81425e14	−	1.42252e15i	−0.401514	−	0.730925i
$16$	−5.61181e15			−1.24607
$17$			6.64865e15i			0.671270i	0.941992	+	0.335635i	$0.108951\pi$
$17$			6.64865e15i			0.671270i	−0.941992	+	0.335635i	$0.891049\pi$
$18$	−2.10693e16	−	1.33906e16i	−1.01183	−	0.643068i
$19$	−5.27648e15			−0.125472			−0.0627361	−	0.998030i	$-0.519983\pi$
$19$	−5.27648e15			−0.125472			−0.0627361	+	0.998030i	$0.519983\pi$
$20$			2.98774e16i			0.364714i
$21$	1.85804e17	−	1.02067e17i	1.20283	−	0.660743i
$22$	2.67711e17			0.946610
$23$			7.91861e17i			1.57104i	0.618837	+	0.785519i	$0.287604\pi$
$23$			7.91861e17i			1.57104i	−0.618837	+	0.785519i	$0.712396\pi$
$24$	−2.84667e17	−	5.18215e17i	−0.324782	−	0.591240i
$25$	4.53793e17			0.304535
$26$			3.05428e18i			1.23099i
$27$	2.58482e17	−	4.04430e18i	0.0637826	−	0.997964i
$28$	−3.90246e18			−0.600184
$29$		−	1.83420e19i		−	1.78761i	−0.448455	−	0.893806i	$-0.648025\pi$
$29$		−	1.83420e19i		−	1.78761i	0.448455	−	0.893806i	$-0.351975\pi$
$30$	−1.39710e19	+	7.67461e18i	−0.876298	+	0.481371i
$31$	−8.35120e18			−0.342016			−0.171008	−	0.985270i	$-0.554702\pi$
$31$	−8.35120e18			−0.342016			−0.171008	+	0.985270i	$0.554702\pi$
$32$			3.02280e19i			0.819332i
$33$	2.09236e19	+	3.80898e19i	0.380150	+	0.692034i
$34$	6.52984e19			0.804779
$35$		−	1.35360e20i		−	1.14448i
$36$	−4.00152e19	+	6.29617e19i	−0.234581	+	0.369100i
$37$	3.99842e20			1.64159			0.820797	−	0.571220i	$-0.193530\pi$
$37$	3.99842e20			1.64159			0.820797	+	0.571220i	$0.193530\pi$
$38$			5.18219e19i			0.150427i
$39$	−4.34561e20	+	2.38714e20i	−0.899934	+	0.494355i
$40$	−3.77525e20			−0.562556
$41$			5.66138e20i			0.611973i	0.952036	+	0.305986i	$0.0989862\pi$
$41$			5.66138e20i			0.611973i	−0.952036	+	0.305986i	$0.901014\pi$
$42$	−1.00243e21	−	1.82484e21i	−0.792158	−	1.44206i
$43$	1.91808e19			0.0111629			0.00558144	−	0.999984i	$-0.498223\pi$
$43$	1.91808e19			0.0111629			0.00558144	+	0.999984i	$0.498223\pi$
$44$		−	8.00004e20i		−	0.345309i
$45$	−2.18388e21	−	1.38796e21i	−0.703827	−	0.447317i
$46$	7.77710e21			1.88350
$47$			5.72628e21i			1.04858i	0.851541	+	0.524288i	$0.175669\pi$
$47$			5.72628e21i			1.04858i	−0.851541	+	0.524288i	$0.824331\pi$
$48$	−7.84178e21	+	4.30767e21i	−1.09214	+	0.599939i
$49$	8.29274e21			0.883383
$50$		−	4.45684e21i		−	0.365104i
$51$	5.10356e21	+	9.29063e21i	0.323192	+	0.588346i
$52$	9.12713e21			0.449046
$53$		−	1.57151e22i		−	0.603573i	−0.953376	−	0.301786i	$-0.902417\pi$
$53$		−	1.57151e22i		−	0.603573i	0.953376	−	0.301786i	$-0.0975829\pi$
$54$	−3.97203e22	−	2.53863e21i	−1.19645	−	0.0764683i
$55$	2.77488e22			0.658460
$56$		−	4.93108e22i		−	0.925758i
$57$	−7.37320e21	+	4.05027e21i	−0.109972	+	0.0604103i
$58$	−1.80142e23			−2.14315
$59$			7.56199e22i			0.720377i	0.932880	+	0.360188i	$0.117288\pi$
$59$			7.56199e22i			0.720377i	−0.932880	+	0.360188i	$0.882712\pi$
$60$	2.29341e22	+	4.17498e22i	0.175597	+	0.319660i
$61$	2.63456e23			1.62712			0.813562	−	0.581479i	$-0.197526\pi$
$61$	2.63456e23			1.62712			0.813562	+	0.581479i	$0.197526\pi$
$62$			8.20197e22i			0.410040i
$63$	1.81290e23	−	2.85249e23i	0.736117	−	1.15824i
$64$	−7.97240e22			−0.263785
$65$			3.16582e23i			0.856275i
$66$	3.74091e23	−	2.05497e23i	0.829672	−	0.455758i
$67$	−4.96439e23			−0.905510			−0.452755	−	0.891635i	$-0.649559\pi$
$67$	−4.96439e23			−0.905510			−0.452755	+	0.891635i	$0.649559\pi$
$68$		−	1.95132e23i		−	0.293571i
$69$	6.07839e23	+	1.10652e24i	0.756397	+	1.37696i
$70$	−1.32941e24			−1.37210
$71$		−	2.95164e23i		−	0.253341i	−0.991945	−	0.126670i	$-0.959571\pi$
$71$		−	2.95164e23i		−	0.253341i	0.991945	−	0.126670i	$-0.0404290\pi$
$72$	−7.95571e23	−	5.05625e23i	−0.569320	−	0.361831i
$73$	−1.62457e23			−0.0971719			−0.0485859	−	0.998819i	$-0.515471\pi$
$73$	−1.62457e23			−0.0971719			−0.0485859	+	0.998819i	$0.515471\pi$
$74$		−	3.92697e24i		−	1.96809i
$75$	6.34117e23	−	3.48335e23i	0.266915	−	0.146622i
$76$	1.54860e23			0.0548735
$77$			3.62444e24i			1.08358i
$78$	2.34449e24	+	4.26795e24i	0.592677	+	1.07892i
$79$	1.76023e24			0.377066			0.188533	−	0.982067i	$-0.439627\pi$
$79$	1.76023e24			0.377066			0.188533	+	0.982067i	$0.439627\pi$
$80$			5.71283e24i			1.03916i
$81$	−2.74324e24	−	5.84980e24i	−0.424580	−	0.905391i
$82$	5.56021e24			0.733688
$83$		−	3.14800e24i		−	0.354829i	−0.984136	−	0.177415i	$-0.943227\pi$
$83$		−	3.14800e24i		−	0.354829i	0.984136	−	0.177415i	$-0.0567734\pi$
$84$	−5.45319e24	+	2.99556e24i	−0.526041	+	0.288967i
$85$	6.76832e24			0.559803
$86$		−	1.88380e23i		−	0.0133831i
$87$	−1.40795e25	−	2.56306e25i	−0.860669	−	1.56678i
$88$	1.01087e25			0.532624
$89$			1.04549e25i			0.475608i	0.971313	+	0.237804i	$0.0764276\pi$
$89$			1.04549e25i			0.475608i	−0.971313	+	0.237804i	$0.923572\pi$
$90$	−1.36316e25	+	2.14485e25i	−0.536283	+	0.843811i
$91$	−4.13507e25			−1.40911
$92$		−	2.32404e25i		−	0.687072i
$93$	−1.16697e25	+	6.41045e24i	−0.299766	+	0.164668i
$94$	5.62395e25			1.25713
$95$			5.37146e24i			0.104637i
$96$	2.32033e25	+	4.22397e25i	0.394478	+	0.718117i
$97$	4.46410e25			0.663286			0.331643	−	0.943405i	$-0.392397\pi$
$97$	4.46410e25			0.663286			0.331643	+	0.943405i	$0.392397\pi$
$98$		−	8.14455e25i		−	1.05908i
$99$	5.84760e25	+	3.71644e25i	0.666378	+	0.423516i
$100$	−1.33184e25			−0.133184
$101$			7.44415e25i			0.654089i	0.945009	+	0.327045i	$0.106053\pi$
$101$			7.44415e25i			0.654089i	−0.945009	+	0.327045i	$0.893947\pi$
$102$	9.12461e25	−	5.01236e25i	0.705362	−	0.387472i
$103$	−2.01837e26			−1.37441			−0.687205	−	0.726464i	$-0.741162\pi$
$103$	−2.01837e26			−1.37441			−0.687205	+	0.726464i	$0.741162\pi$
$104$			1.15329e26i			0.692634i
$105$	−1.03904e26	−	1.89149e26i	−0.551023	−	1.00310i
$106$	−1.54342e26			−0.723617
$107$			6.30534e25i			0.261649i	0.991406	+	0.130825i	$0.0417625\pi$
$107$			6.30534e25i			0.261649i	−0.991406	+	0.130825i	$0.958238\pi$
$108$	−7.58623e24	+	1.18697e26i	−0.0278944	+	0.436445i
$109$	8.06943e25			0.263208			0.131604	−	0.991302i	$-0.457987\pi$
$109$	8.06943e25			0.263208			0.131604	+	0.991302i	$0.457987\pi$
$110$		−	2.72530e26i		−	0.789421i
$111$	5.58727e26	−	3.06922e26i	1.43880	−	0.790367i
$112$	−7.46186e26			−1.71007
$113$		−	6.82343e25i		−	0.139310i	−0.997571	−	0.0696551i	$-0.977810\pi$
$113$		−	6.82343e25i		−	0.139310i	0.997571	−	0.0696551i	$-0.0221899\pi$
$114$	3.97789e25	+	7.24144e25i	0.0724252	+	0.131845i
$115$	8.06114e26			1.31016
$116$			5.38322e26i			0.781787i
$117$	−4.24003e26	+	6.67145e26i	−0.550748	+	0.866570i
$118$	7.42685e26			0.863652
$119$			8.84051e26i			0.921227i
$120$	−5.27542e26	+	2.89791e26i	−0.493061	+	0.270850i
$121$	4.48809e26			0.376575
$122$		−	2.58748e27i		−	1.95074i
$123$	4.34572e26	+	7.91105e26i	0.294643	+	0.536374i
$124$	2.45100e26			0.149576
$125$		−	1.97890e27i		−	1.08791i
$126$	−2.80152e27	−	1.78050e27i	−1.38860	−	0.882523i
$127$	−2.05621e27			−0.919644			−0.459822	−	0.888011i	$-0.652087\pi$
$127$	−2.05621e27			−0.919644			−0.459822	+	0.888011i	$0.652087\pi$
$128$			2.81156e27i			1.13558i
$129$	2.68027e25	−	1.47233e25i	0.00978389	−	0.00537452i
$130$	3.10925e27			1.02658
$131$			1.91991e27i			0.573792i	0.957962	+	0.286896i	$0.0926234\pi$
$131$			1.91991e27i			0.573792i	−0.957962	+	0.286896i	$0.907377\pi$
$132$	−6.14089e26	−	1.11790e27i	−0.166253	−	0.302651i
$133$	−7.01598e26			−0.172194
$134$			4.87567e27i			1.08561i
$135$	−4.11710e27	−	2.63135e26i	−0.832247	−	0.0531912i
$136$	2.46565e27			0.452820
$137$		−	5.21428e27i		−	0.870616i	−0.900282	−	0.435308i	$-0.856639\pi$
$137$		−	5.21428e27i		−	0.870616i	0.900282	−	0.435308i	$-0.143361\pi$
$138$	1.08675e28	−	5.96977e27i	1.65083	−	0.906837i
$139$	4.54845e27			0.629030			0.314515	−	0.949253i	$-0.398158\pi$
$139$	4.54845e27			0.629030			0.314515	+	0.949253i	$0.398158\pi$
$140$			3.97271e27i			0.500521i
$141$	4.39554e27	+	8.00173e27i	0.504851	+	0.919042i
$142$	−2.89889e27			−0.303727
$143$		−	8.47688e27i		−	0.810714i
$144$	−7.65127e27	+	1.20388e28i	−0.668377	+	1.05165i
$145$	−1.86722e28			−1.49077
$146$			1.59554e27i			0.116498i
$147$	1.15880e28	−	6.36557e27i	0.774255	−	0.425316i
$148$	−1.17350e28			−0.717928
$149$		−	1.56449e28i		−	0.876904i	−0.898755	−	0.438452i	$-0.855527\pi$
$149$		−	1.56449e28i		−	0.876904i	0.898755	−	0.438452i	$-0.144473\pi$
$150$	−3.42110e27	−	6.22785e27i	−0.175784	−	0.320001i
$151$	−2.51467e28			−1.18517			−0.592585	−	0.805508i	$-0.701893\pi$
$151$	−2.51467e28			−1.18517			−0.592585	+	0.805508i	$0.701893\pi$
$152$			1.95678e27i			0.0846401i
$153$	1.42631e28	+	9.06492e27i	0.566534	+	0.360060i
$154$	3.55967e28			1.29909
$155$			8.50152e27i			0.285223i
$156$	1.27540e28	−	7.00606e27i	0.393574	−	0.216199i
$157$	1.00685e27			0.0285936			0.0142968	−	0.999898i	$-0.495449\pi$
$157$	1.00685e27			0.0285936			0.0142968	+	0.999898i	$0.495449\pi$
$158$		−	1.72878e28i		−	0.452061i
$159$	−1.20630e28	−	2.19597e28i	−0.290598	−	0.529011i
$160$	3.07721e28			0.683278
$161$			1.05291e29i			2.15604i
$162$	−5.74527e28	+	2.69422e28i	−1.08546	+	0.509024i
$163$	4.27656e28			0.745857			0.372929	−	0.927860i	$-0.378354\pi$
$163$	4.27656e28			0.745857			0.372929	+	0.927860i	$0.378354\pi$
$164$		−	1.66157e28i		−	0.267638i
$165$	3.87754e28	−	2.13002e28i	0.577118	−	0.317025i
$166$	−3.09175e28			−0.425401
$167$			4.14044e27i			0.0526905i	0.999653	+	0.0263453i	$0.00838693\pi$
$167$			4.14044e27i			0.0526905i	−0.999653	+	0.0263453i	$0.991613\pi$
$168$	−3.78514e28	−	6.89054e28i	−0.445719	−	0.811396i
$169$	4.97817e27			0.0542678
$170$		−	6.64738e28i		−	0.671142i
$171$	−7.19407e27	+	1.13195e28i	−0.0673016	+	0.105895i
$172$	−5.62939e26			−0.00488193
$173$		−	1.40388e29i		−	1.12909i	−0.825401	−	0.564546i	$-0.809051\pi$
$173$		−	1.40388e29i		−	1.12909i	0.825401	−	0.564546i	$-0.190949\pi$
$174$	−2.51726e29	+	1.38279e29i	−1.87840	+	1.03185i
$175$	6.03395e28			0.417933
$176$		−	1.52968e29i		−	0.983865i
$177$	5.80464e28	+	1.05669e29i	0.346835	+	0.631386i
$178$	1.02681e29			0.570201
$179$			2.19088e29i			1.13118i	0.824688	+	0.565588i	$0.191351\pi$
$179$			2.19088e29i			1.13118i	−0.824688	+	0.565588i	$0.808649\pi$
$180$	6.40949e28	+	4.07355e28i	0.307809	+	0.195628i
$181$	−2.43966e29			−1.09021			−0.545103	−	0.838369i	$-0.683509\pi$
$181$	−2.43966e29			−1.09021			−0.545103	+	0.838369i	$0.683509\pi$
$182$			4.06118e29i			1.68937i
$183$	3.68146e29	−	2.02231e29i	1.42612	−	0.783400i
$184$	2.93661e29			1.05978
$185$		−	4.07039e29i		−	1.36900i
$186$	6.29589e28	+	1.14612e29i	0.197419	+	0.359386i
$187$	−1.81230e29			−0.530017
$188$		−	1.68061e29i		−	0.458580i
$189$	3.43696e28	−	5.37759e29i	0.0875329	−	1.36957i
$190$	5.27547e28			0.125448
$191$			7.98026e29i			1.77249i	0.463220	+	0.886243i	$0.346694\pi$
$191$			7.98026e29i			1.77249i	−0.463220	+	0.886243i	$0.653306\pi$
$192$	−1.11404e29	+	6.11968e28i	−0.231198	+	0.127003i
$193$	−8.82731e29			−1.71231			−0.856156	−	0.516717i	$-0.827154\pi$
$193$	−8.82731e29			−1.71231			−0.856156	+	0.516717i	$0.827154\pi$
$194$		−	4.38432e29i		−	0.795207i
$195$	2.43011e29	+	4.42383e29i	0.412265	+	0.750496i
$196$	−2.43385e29			−0.386335
$197$			4.70466e29i			0.698985i	0.936939	+	0.349492i	$0.113646\pi$
$197$			4.70466e29i			0.698985i	−0.936939	+	0.349492i	$0.886354\pi$
$198$	3.65003e29	−	5.74311e29i	0.507749	−	0.798913i
$199$	−5.61846e29			−0.732028			−0.366014	−	0.930609i	$-0.619278\pi$
$199$	−5.61846e29			−0.732028			−0.366014	+	0.930609i	$0.619278\pi$
$200$		−	1.68289e29i		−	0.205431i
$201$	−6.93709e29	+	3.81070e29i	−0.793649	+	0.435970i
$202$	7.31112e29			0.784181
$203$		−	2.43888e30i		−	2.45325i
$204$	−1.49785e29	−	2.72672e29i	−0.141344	−	0.257305i
$205$	5.76328e29			0.510352
$206$			1.98230e30i			1.64777i
$207$	1.69875e30	+	1.07964e30i	1.32591	+	0.842683i
$208$	1.74519e30			1.27944
$209$		−	1.43827e29i		−	0.0990695i
$210$	−1.85769e30	+	1.02047e30i	−1.20260	+	0.660616i
$211$	−2.68178e28			−0.0163212			−0.00816058	−	0.999967i	$-0.502598\pi$
$211$	−2.68178e28			−0.0163212			−0.00816058	+	0.999967i	$0.502598\pi$
$212$			4.61223e29i			0.263964i
$213$	−2.26570e29	−	4.12453e29i	−0.121974	−	0.222044i
$214$	6.19267e29			0.313689
$215$		−	1.95260e28i		−	0.00930924i
$216$	−1.49983e30	−	9.58582e28i	−0.673198	−	0.0430259i
$217$	−1.11043e30			−0.469371
$218$		−	7.92523e29i		−	0.315557i
$219$	−2.27012e29	+	1.24703e29i	−0.0851679	+	0.0467847i
$220$	−8.14404e29			−0.287968
$221$		−	2.06763e30i		−	0.689244i
$222$	−3.01437e30	−	5.48743e30i	−0.947563	−	1.72496i
$223$	4.54840e30			1.34864			0.674318	−	0.738441i	$-0.264438\pi$
$223$	4.54840e30			1.34864			0.674318	+	0.738441i	$0.264438\pi$
$224$			4.01933e30i			1.12442i
$225$	6.18711e29	−	9.73506e29i	0.163348	−	0.257019i
$226$	−6.70150e29			−0.167018
$227$			4.89758e30i			1.15251i	0.817269	+	0.576256i	$0.195487\pi$
$227$			4.89758e30i			1.15251i	−0.817269	+	0.576256i	$0.804513\pi$
$228$	2.16397e29	−	1.18872e29i	0.0480948	−	0.0264196i
$229$	−3.85737e30			−0.809897			−0.404948	−	0.914340i	$-0.632711\pi$
$229$	−3.85737e30			−0.809897			−0.404948	+	0.914340i	$0.632711\pi$
$230$		−	7.91709e30i		−	1.57074i
$231$	2.78215e30	+	5.06468e30i	0.521704	+	0.949722i
$232$	−6.80213e30			−1.20587
$233$			5.54626e30i			0.929765i	0.885372	+	0.464882i	$0.153903\pi$
$233$			5.54626e30i			0.929765i	−0.885372	+	0.464882i	$0.846097\pi$
$234$	6.55223e30	+	4.16427e30i	1.03892	+	0.660286i
$235$	5.82935e30			0.874456
$236$		−	2.21938e30i		−	0.315047i
$237$	2.45970e30	−	1.35117e30i	0.330486	−	0.181544i
$238$	8.68253e30			1.10445
$239$		−	2.87890e30i		−	0.346780i	−0.984853	−	0.173390i	$-0.944528\pi$
$239$		−	2.87890e30i		−	0.346780i	0.984853	−	0.173390i	$-0.0554720\pi$
$240$	4.38521e30	+	7.98293e30i	0.500316	+	0.910786i
$241$	−8.88512e30			−0.960377			−0.480189	−	0.877165i	$-0.659432\pi$
$241$	−8.88512e30			−0.960377			−0.480189	+	0.877165i	$0.659432\pi$
$242$		−	4.40789e30i		−	0.451472i
$243$	−8.32368e30	−	6.06860e30i	−0.808042	−	0.589125i
$244$	−7.73221e30			−0.711600
$245$		−	8.44201e30i		−	0.736693i
$246$	7.76968e30	−	4.26806e30i	0.643053	−	0.353244i
$247$	1.64091e30			0.128832
$248$			3.09704e30i			0.230715i
$249$	−2.41643e30	−	4.39892e30i	−0.170837	−	0.310996i
$250$	−1.94354e31			−1.30429
$251$			1.02784e31i			0.654889i	0.944870	+	0.327444i	$0.106187\pi$
$251$			1.02784e31i			0.654889i	−0.944870	+	0.327444i	$0.893813\pi$
$252$	−5.32070e30	+	8.37182e30i	−0.321931	+	0.506539i
$253$	−2.15847e31			−1.24045
$254$			2.01947e31i			1.10255i
$255$	9.45786e30	−	5.19542e30i	0.490648	−	0.269525i
$256$	2.22630e31			1.09765
$257$		−	2.02228e31i		−	0.947786i	−0.880582	−	0.473893i	$-0.842848\pi$
$257$		−	2.02228e31i		−	0.947786i	0.880582	−	0.473893i	$-0.157152\pi$
$258$	−1.44602e29	−	2.63237e29i	−0.00644345	−	0.0117298i
$259$	5.31657e31			2.25286
$260$		−	9.29141e30i		−	0.374480i
$261$	−3.93485e31	−	2.50079e31i	−1.50869	−	0.958850i
$262$	1.88560e31			0.687913
$263$			3.76536e31i			1.30732i	0.756789	+	0.653660i	$0.226767\pi$
$263$			3.76536e31i			1.30732i	−0.756789	+	0.653660i	$0.773233\pi$
$264$	1.41256e31	−	7.75952e30i	0.466827	−	0.256439i
$265$	−1.59979e31			−0.503347
$266$			6.89061e30i			0.206441i
$267$	8.02525e30	+	1.46093e31i	0.228988	+	0.416854i
$268$	1.45700e31			0.396012
$269$		−	4.67554e30i		−	0.121074i	−0.998166	−	0.0605372i	$-0.980719\pi$
$269$		−	4.67554e30i		−	0.121074i	0.998166	−	0.0605372i	$-0.0192814\pi$
$270$	−2.58433e30	+	4.04353e31i	−0.0637704	+	0.997773i
$271$	2.37338e31			0.558171			0.279085	−	0.960266i	$-0.409969\pi$
$271$	2.37338e31			0.558171			0.279085	+	0.960266i	$0.409969\pi$
$272$		−	3.73110e31i		−	0.836452i
$273$	−5.77822e31	+	3.17411e31i	−1.23504	+	0.678435i
$274$	−5.12110e31			−1.04377
$275$			1.23696e31i			0.240453i
$276$	−1.78395e31	−	3.24755e31i	−0.330800	−	0.602195i
$277$	2.93898e31			0.519948			0.259974	−	0.965616i	$-0.416286\pi$
$277$	2.93898e31			0.519948			0.259974	+	0.965616i	$0.416286\pi$
$278$		−	4.46717e31i		−	0.754137i
$279$	−1.13862e31	+	1.79155e31i	−0.183453	+	0.288652i
$280$	−5.01984e31			−0.772032
$281$		−	1.08883e32i		−	1.59874i	−0.600839	−	0.799370i	$-0.705167\pi$
$281$		−	1.08883e32i		−	1.59874i	0.600839	−	0.799370i	$-0.294833\pi$
$282$	7.85874e31	−	4.31699e31i	1.10183	−	0.605261i
$283$	1.36069e30			0.0182195			0.00910976	−	0.999959i	$-0.497100\pi$
$283$	1.36069e30			0.0182195			0.00910976	+	0.999959i	$0.497100\pi$
$284$			8.66280e30i			0.110795i
$285$	4.12317e30	+	7.50592e30i	0.0503789	+	0.0917108i
$286$	−8.32540e31			−0.971956
$287$			7.52777e31i			0.839850i
$288$	6.48471e31	+	4.12135e31i	0.691494	+	0.439478i
$289$	5.38961e31			0.549396
$290$			1.83385e32i			1.78727i
$291$	6.23800e31	−	3.42668e31i	0.581348	−	0.319348i
$292$	4.76796e30			0.0424968
$293$			2.01206e32i			1.71539i	0.514161	+	0.857694i	$0.328103\pi$
$293$			2.01206e32i			1.71539i	−0.514161	+	0.857694i	$0.671897\pi$
$294$	−6.25182e31	−	1.13810e32i	−0.509907	−	0.928246i
$295$	7.69810e31			0.600755
$296$		−	1.48281e32i		−	1.10737i
$297$	1.10240e32	+	7.04576e30i	0.787965	+	0.0503610i
$298$	−1.53654e32			−1.05131
$299$		−	2.46257e32i		−	1.61310i
$300$	−1.86108e31	+	1.02233e31i	−0.116731	+	0.0641233i
$301$	2.55041e30			0.0153195
$302$			2.46973e32i			1.42089i
$303$	5.71419e31	+	1.04022e32i	0.314920	+	0.573287i
$304$	2.96106e31			0.156348
$305$		−	2.68198e32i		−	1.35693i
$306$	8.90293e31	−	1.40082e32i	0.431672	−	0.679212i
$307$	−2.39482e32			−1.11295			−0.556474	−	0.830865i	$-0.687846\pi$
$307$	−2.39482e32			−1.11295			−0.556474	+	0.830865i	$0.687846\pi$
$308$		−	1.06374e32i		−	0.473889i
$309$	−2.82041e32	+	1.54931e32i	−1.20462	+	0.661728i
$310$	8.34960e31			0.341951
$311$			8.51135e31i			0.334282i	0.985933	+	0.167141i	$0.0534535\pi$
$311$			8.51135e31i			0.334282i	−0.985933	+	0.167141i	$0.946546\pi$
$312$	8.85272e31	+	1.61157e32i	0.333478	+	0.607070i
$313$	−1.23111e32			−0.444858			−0.222429	−	0.974949i	$-0.571399\pi$
$313$	−1.23111e32			−0.444858			−0.222429	+	0.974949i	$0.571399\pi$
$314$		−	9.88857e30i		−	0.0342806i
$315$	−2.90384e32	−	1.84553e32i	−0.965907	−	0.613881i
$316$	−5.16613e31			−0.164905
$317$		−	1.01595e31i		−	0.0311245i	−0.999879	−	0.0155623i	$-0.995046\pi$
$317$		−	1.01595e31i		−	0.0311245i	0.999879	−	0.0155623i	$-0.00495382\pi$
$318$	−2.15673e32	+	1.18474e32i	−0.634226	+	0.348395i
$319$	4.99970e32			1.41145
$320$			8.11590e31i			0.219982i
$321$	4.84003e31	+	8.81090e31i	0.125975	+	0.229327i
$322$	1.03410e33			2.58485
$323$		−	3.50815e31i		−	0.0842258i
$324$	8.05118e31	+	1.71687e32i	0.185684	+	0.395960i
$325$	−1.41123e32			−0.312689
$326$		−	4.20014e32i		−	0.894200i
$327$	1.12760e32	−	6.19416e31i	0.230693	−	0.126725i
$328$	2.09952e32			0.412820
$329$			7.61406e32i			1.43903i
$330$	−2.09196e32	−	3.80825e32i	−0.380077	−	0.691901i
$331$	−9.96549e32			−1.74074			−0.870372	−	0.492396i	$-0.836121\pi$
$331$	−9.96549e32			−1.74074			−0.870372	+	0.492396i	$0.836121\pi$
$332$			9.23910e31i			0.155180i
$333$	5.45153e32	−	8.57766e32i	0.880528	−	1.38546i
$334$	4.06645e31			0.0631701
$335$			5.05374e32i			0.755146i
$336$	−1.04270e33	+	5.72778e32i	−1.49882	+	0.823334i
$337$	−5.30778e31			−0.0734048			−0.0367024	−	0.999326i	$-0.511685\pi$
$337$	−5.30778e31			−0.0734048			−0.0367024	+	0.999326i	$0.511685\pi$
$338$		−	4.88921e31i		−	0.0650611i
$339$	−5.23772e31	−	9.53486e31i	−0.0670727	−	0.122101i
$340$	−1.98644e32			−0.244822
$341$		−	2.27639e32i		−	0.270047i
$342$	1.11172e32	+	7.06551e31i	0.126957	+	0.0806872i
$343$	−1.45564e32			−0.160041
$344$		−	7.11319e30i		−	0.00753017i
$345$	1.12644e33	−	6.18779e32i	1.14831	−	0.630794i
$346$	−1.37879e33			−1.35366
$347$		−	1.68116e33i		−	1.58974i	−0.606778	−	0.794871i	$-0.707538\pi$
$347$		−	1.68116e33i		−	1.58974i	0.606778	−	0.794871i	$-0.292462\pi$
$348$	4.13220e32	+	7.52235e32i	0.376402	+	0.685210i
$349$	1.05841e33			0.928802			0.464401	−	0.885625i	$-0.346270\pi$
$349$	1.05841e33			0.928802			0.464401	+	0.885625i	$0.346270\pi$
$350$		−	5.92612e32i		−	0.501056i
$351$	−8.03841e31	+	1.25772e33i	−0.0654904	+	1.02468i
$352$	−8.23961e32			−0.646922
$353$			4.82102e32i			0.364811i	0.983223	+	0.182405i	$0.0583883\pi$
$353$			4.82102e32i			0.364811i	−0.983223	+	0.182405i	$0.941612\pi$
$354$	1.03781e33	−	5.70091e32i	0.756962	−	0.415817i
$355$	−3.00477e32			−0.211272
$356$		−	3.06842e32i		−	0.208000i
$357$	6.78605e32	+	1.23535e33i	0.443537	+	0.807425i
$358$	2.15173e33			1.35615
$359$			1.76867e33i			1.07503i	0.843255	+	0.537513i	$0.180636\pi$
$359$			1.76867e33i			1.07503i	−0.843255	+	0.537513i	$0.819364\pi$
$360$	−5.14726e32	+	8.09891e32i	−0.301747	+	0.474782i
$361$	−1.74061e33			−0.984257
$362$			2.39607e33i			1.30704i
$363$	6.27152e32	−	3.44509e32i	0.330055	−	0.181307i
$364$	1.21361e33			0.616254
$365$			1.65381e32i			0.0810360i
$366$	−1.98617e33	−	3.61567e33i	−0.939210	−	1.70976i
$367$	−3.37558e32			−0.154060			−0.0770300	−	0.997029i	$-0.524544\pi$
$367$	−3.37558e32			−0.154060			−0.0770300	+	0.997029i	$0.524544\pi$
$368$		−	4.44377e33i		−	1.95763i
$369$	1.21452e33	+	7.71885e32i	0.516488	+	0.328254i
$370$	−3.99765e33			−1.64128
$371$		−	2.08958e33i		−	0.828321i
$372$	3.42496e32	−	1.88141e32i	0.131098	−	0.0720154i
$373$	3.36348e33			1.24329			0.621647	−	0.783298i	$-0.286464\pi$
$373$	3.36348e33			1.24329			0.621647	+	0.783298i	$0.286464\pi$
$374$			1.77992e33i			0.635432i
$375$	−1.51902e33	−	2.76525e33i	−0.523789	−	0.953517i
$376$	2.12359e33			0.707341
$377$			5.70409e33i			1.83548i
$378$	−5.28149e33	−	3.37555e32i	−1.64196	−	0.104942i
$379$	−5.03589e33			−1.51275			−0.756373	−	0.654140i	$-0.773031\pi$
$379$	−5.03589e33			−1.51275			−0.756373	+	0.654140i	$0.773031\pi$
$380$		−	1.57648e32i		−	0.0457615i
$381$	−2.87329e33	+	1.57837e33i	−0.806037	+	0.442775i
$382$	7.83765e33			2.12502
$383$		−	5.57030e33i		−	1.45980i	−0.683552	−	0.729901i	$-0.739566\pi$
$383$		−	5.57030e33i		−	1.45980i	0.683552	−	0.729901i	$-0.260434\pi$
$384$	2.15818e33	+	3.92879e33i	0.546740	+	0.995298i
$385$	3.68968e33			0.903647
$386$			8.66956e33i			2.05287i
$387$	2.61515e31	−	4.11479e31i	0.00598762	−	0.00942117i
$388$	−1.31017e33			−0.290079
$389$		−	5.26058e33i		−	1.12639i	−0.826324	−	0.563195i	$-0.809572\pi$
$389$		−	5.26058e33i		−	1.12639i	0.826324	−	0.563195i	$-0.190428\pi$
$390$	4.34478e33	−	2.38669e33i	0.899762	−	0.494260i
$391$	−5.26480e33			−1.05459
$392$		−	3.07536e33i		−	0.595905i
$393$	1.47374e33	+	2.68283e33i	0.276260	+	0.502909i
$394$	4.62059e33			0.838006
$395$		−	1.79192e33i		−	0.314453i
$396$	−1.71622e33	−	1.09074e33i	−0.291431	−	0.185219i
$397$	6.24834e33			1.02681			0.513403	−	0.858148i	$-0.328385\pi$
$397$	6.24834e33			1.02681			0.513403	+	0.858148i	$0.328385\pi$
$398$			5.51806e33i			0.877621i
$399$	−9.80392e32	+	5.38552e32i	−0.150922	+	0.0829049i
$400$	−2.54660e33			−0.379473
$401$		−	1.04454e34i		−	1.50677i	−0.657580	−	0.753385i	$-0.728420\pi$
$401$		−	1.04454e34i		−	1.50677i	0.657580	−	0.753385i	$-0.271580\pi$
$402$	3.74261e33	+	6.81312e33i	0.522680	+	0.951497i
$403$	2.59710e33			0.351174
$404$		−	2.18479e33i		−	0.286057i
$405$	−5.95510e33	+	2.79262e33i	−0.755046	+	0.354076i
$406$	−2.39530e34			−2.94118
$407$			1.08990e34i			1.29616i
$408$	3.44543e33	−	1.89265e33i	0.396882	−	0.218016i
$409$	−6.33865e33			−0.707284			−0.353642	−	0.935381i	$-0.615057\pi$
$409$	−6.33865e33			−0.707284			−0.353642	+	0.935381i	$0.615057\pi$
$410$		−	5.66030e33i		−	0.611856i
$411$	−4.00252e33	−	7.28628e33i	−0.419170	−	0.763066i
$412$	5.92373e33			0.601079
$413$			1.00549e34i			0.988619i
$414$	1.06035e34	−	1.66839e34i	1.01028	−	1.58962i
$415$	−3.20466e33			−0.295908
$416$		−	9.40045e33i		−	0.841270i
$417$	6.35587e33	−	3.49143e33i	0.551324	−	0.302855i
$418$	−1.41257e33			−0.118773
$419$			1.59146e34i			1.29722i	0.761123	+	0.648608i	$0.224648\pi$
$419$			1.59146e34i			1.29722i	−0.761123	+	0.648608i	$0.775352\pi$
$420$	3.04948e33	+	5.55134e33i	0.240982	+	0.438690i
$421$	2.20427e33			0.168888			0.0844439	−	0.996428i	$-0.473089\pi$
$421$	2.20427e33			0.168888			0.0844439	+	0.996428i	$0.473089\pi$
$422$			2.63386e32i			0.0195673i
$423$	1.22844e34	+	7.80733e33i	0.884970	+	0.562442i
$424$	−5.82792e33			−0.407153
$425$			3.01711e33i			0.204425i
$426$	−4.05083e33	+	2.22521e33i	−0.266207	+	0.146234i
$427$	3.50310e34			2.23301
$428$		−	1.85056e33i		−	0.114429i
$429$	−6.50692e33	−	1.18453e34i	−0.390329	−	0.710563i
$430$	−1.91771e32			−0.0111607
$431$		−	1.58601e34i		−	0.895573i	−0.894140	−	0.447787i	$-0.852212\pi$
$431$		−	1.58601e34i		−	0.895573i	0.894140	−	0.447787i	$-0.147788\pi$
$432$	−1.45056e33	+	2.26959e34i	−0.0794778	+	1.24354i
$433$	−2.82131e34			−1.50006			−0.750029	−	0.661405i	$-0.769960\pi$
$433$	−2.82131e34			−1.50006			−0.750029	+	0.661405i	$0.769960\pi$
$434$			1.09059e34i			0.562724i
$435$	−2.60919e34	+	1.43329e34i	−1.30661	+	0.717751i
$436$	−2.36831e33			−0.115110
$437$		−	4.17824e33i		−	0.197122i
$438$	1.22475e33	+	2.22956e33i	0.0560897	+	0.102107i
$439$	4.25615e34			1.89225			0.946123	−	0.323807i	$-0.104963\pi$
$439$	4.25615e34			1.89225			0.946123	+	0.323807i	$0.104963\pi$
$440$		−	1.02906e34i		−	0.444179i
$441$	1.13065e34	−	1.77901e34i	0.473834	−	0.745551i
$442$	−2.03068e34			−0.826327
$443$			4.48620e33i			0.177268i	0.996064	+	0.0886339i	$0.0282501\pi$
$443$			4.48620e33i			0.177268i	−0.996064	+	0.0886339i	$0.971750\pi$
$444$	−1.63981e34	+	9.00788e33i	−0.629240	+	0.345656i
$445$	1.06431e34			0.396631
$446$		−	4.46712e34i		−	1.61687i
$447$	−1.20092e34	−	2.18618e34i	−0.422197	−	0.768577i
$448$	−1.06007e34			−0.362008
$449$		−	6.46927e33i		−	0.214611i	−0.994226	−	0.107306i	$-0.965778\pi$
$449$		−	6.46927e33i		−	0.214611i	0.994226	−	0.107306i	$-0.0342223\pi$
$450$	−9.56110e33	−	6.07655e33i	−0.308138	−	0.195837i
$451$	−1.54319e34			−0.483197
$452$			2.00262e33i			0.0609254i
$453$	−3.51392e34	+	1.93028e34i	−1.03876	+	0.570616i
$454$	4.81006e34			1.38174
$455$			4.20950e34i			1.17512i
$456$	1.50204e33	+	2.73435e33i	0.0407511	+	0.0741842i
$457$	1.10525e34			0.291440			0.145720	−	0.989326i	$-0.453450\pi$
$457$	1.10525e34			0.291440			0.145720	+	0.989326i	$0.453450\pi$
$458$			3.78844e34i			0.970977i
$459$	2.68892e34	+	1.71856e33i	0.669904	+	0.0428154i
$460$	−2.36587e34			−0.572980
$461$		−	1.02644e34i		−	0.241670i	−0.992673	−	0.120835i	$-0.961443\pi$
$461$		−	1.02644e34i		−	0.241670i	0.992673	−	0.120835i	$-0.0385572\pi$
$462$	4.97418e34	−	2.73243e34i	1.13861	−	0.625466i
$463$	−1.65260e33			−0.0367802			−0.0183901	−	0.999831i	$-0.505854\pi$
$463$	−1.65260e33			−0.0367802			−0.0183901	+	0.999831i	$0.505854\pi$
$464$			1.02932e35i			2.22749i
$465$	6.52583e33	+	1.18798e34i	0.137324	+	0.249988i
$466$	5.44715e34			1.11469
$467$		−	4.76284e34i		−	0.947865i	−0.880561	−	0.473933i	$-0.842834\pi$
$467$		−	4.76284e34i		−	0.947865i	0.880561	−	0.473933i	$-0.157166\pi$
$468$	1.24441e34	−	1.95801e34i	0.240862	−	0.378982i
$469$	−6.60100e34			−1.24269
$470$		−	5.72518e34i		−	1.04838i
$471$	1.40694e33	−	7.72865e32i	0.0250613	−	0.0137668i
$472$	2.80436e34			0.485946
$473$			5.22833e32i			0.00881391i
$474$	−1.32702e34	−	2.41574e34i	−0.217651	−	0.396216i
$475$	−2.39443e33			−0.0382107
$476$		−	2.59461e34i		−	0.402886i
$477$	−3.37130e34	−	2.14262e34i	−0.509399	−	0.323748i
$478$	−2.82745e34			−0.415750
$479$		−	4.00194e34i		−	0.572676i	−0.958129	−	0.286338i	$-0.907562\pi$
$479$		−	4.00194e34i		−	0.572676i	0.958129	−	0.286338i	$-0.0924381\pi$
$480$	4.30000e34	−	2.36209e34i	0.598870	−	0.328973i
$481$	−1.24345e35			−1.68555
$482$			8.72635e34i			1.15139i
$483$	8.08225e34	+	1.47131e35i	1.03805	+	1.88969i
$484$	−1.31721e34			−0.164690
$485$		−	4.54445e34i		−	0.553144i
$486$	−5.96016e34	+	8.17494e34i	−0.706296	+	0.968753i
$487$	−8.99987e34			−1.03839			−0.519194	−	0.854656i	$-0.673768\pi$
$487$	−8.99987e34			−1.03839			−0.519194	+	0.854656i	$0.673768\pi$
$488$		−	9.77027e34i		−	1.09761i
$489$	5.97594e34	−	3.28272e34i	0.653719	−	0.359103i
$490$	−8.29115e34			−0.883213
$491$			2.38716e34i			0.247641i	0.992305	+	0.123820i	$0.0395147\pi$
$491$			2.38716e34i			0.247641i	−0.992305	+	0.123820i	$0.960485\pi$
$492$	−1.27543e34	−	2.32182e34i	−0.128858	−	0.234576i
$493$	1.21950e35			1.19997
$494$		−	1.61158e34i		−	0.154455i
$495$	3.78334e34	−	5.95286e34i	0.353189	−	0.555723i
$496$	4.68654e34			0.426177
$497$		−	3.92471e34i		−	0.347675i
$498$	−4.32031e34	+	2.37325e34i	−0.372850	+	0.204815i
$499$	1.63831e35			1.37749			0.688745	−	0.725003i	$-0.258162\pi$
$499$	1.63831e35			1.37749			0.688745	+	0.725003i	$0.258162\pi$
$500$			5.80789e34i			0.475783i
$501$	3.17824e33	+	5.78573e33i	0.0253685	+	0.0461815i
$502$	1.00947e35			0.785139
$503$		−	3.74539e34i		−	0.283866i	−0.989876	−	0.141933i	$-0.954668\pi$
$503$		−	3.74539e34i		−	0.283866i	0.989876	−	0.141933i	$-0.0453317\pi$
$504$	−1.05785e35	−	6.72314e34i	−0.781315	−	0.496564i
$505$	7.57814e34			0.545475
$506$			2.11990e35i			1.48716i
$507$	6.95634e33	−	3.82128e33i	0.0475639	−	0.0261280i
$508$	6.03480e34			0.402193
$509$			2.22492e35i			1.44539i	0.691169	+	0.722694i	$0.257096\pi$
$509$			2.22492e35i			1.44539i	−0.691169	+	0.722694i	$0.742904\pi$
$510$	−5.10258e34	−	9.28885e34i	−0.323130	−	0.588233i
$511$	−2.16014e34			−0.133355
$512$		−	2.99711e34i		−	0.180382i
$513$	−1.36388e33	+	2.13397e34i	−0.00800294	+	0.125217i
$514$	−1.98614e35			−1.13629
$515$			2.05470e35i			1.14618i
$516$	−7.86634e32	+	4.32117e32i	−0.00427885	+	0.00235047i
$517$	−1.56088e35			−0.827928
$518$		−	5.22157e35i		−	2.70093i
$519$	−1.07763e35	−	1.96174e35i	−0.543617	−	0.989612i
$520$	1.17405e35			0.577619
$521$		−	1.01413e35i		−	0.486633i	−0.969947	−	0.243316i	$-0.921765\pi$
$521$		−	1.01413e35i		−	0.486633i	0.969947	−	0.243316i	$-0.0782354\pi$
$522$	−2.45610e35	+	3.86453e35i	−1.14956	+	1.80876i
$523$	5.15100e34			0.235163			0.117582	−	0.993063i	$-0.462486\pi$
$523$	5.15100e34			0.235163			0.117582	+	0.993063i	$0.462486\pi$
$524$		−	5.63477e34i		−	0.250940i
$525$	8.43166e34	−	4.63170e34i	0.366304	−	0.201219i
$526$	3.69807e35			1.56733
$527$		−	5.55242e34i		−	0.229585i
$528$	−1.17419e35	−	2.13753e35i	−0.473695	−	0.862325i
$529$	−3.72991e35			−1.46816
$530$			1.57120e35i			0.603457i
$531$	1.62225e35	+	1.03102e35i	0.607978	+	0.386400i
$532$	2.05913e34			0.0753065
$533$		−	1.76060e35i		−	0.628359i
$534$	1.43483e35	−	7.88184e34i	0.499762	−	0.274531i
$535$	6.41884e34			0.218201
$536$			1.84104e35i			0.610832i
$537$	1.68174e35	+	3.06148e35i	0.544619	+	0.991437i
$538$	−4.59199e34			−0.145155
$539$			2.26045e35i			0.697495i
$540$	1.20833e35	+	7.72278e33i	0.363972	+	0.0232624i
$541$	2.34330e35			0.689071			0.344536	−	0.938773i	$-0.388036\pi$
$541$	2.34330e35			0.689071			0.344536	+	0.938773i	$0.388036\pi$
$542$		−	2.33097e35i		−	0.669185i
$543$	−3.40911e35	+	1.87270e35i	−0.955528	+	0.524894i
$544$	−2.00976e35			−0.549993
$545$		−	8.21468e34i		−	0.219501i
$546$	3.11739e35	+	5.67497e35i	0.813368	+	1.48067i
$547$	−4.74802e35			−1.20970			−0.604850	−	0.796340i	$-0.706767\pi$
$547$	−4.74802e35			−1.20970			−0.604850	+	0.796340i	$0.706767\pi$
$548$			1.53034e35i			0.380752i
$549$	3.59202e35	−	5.65183e35i	0.872767	−	1.37325i
$550$	1.21485e35			0.288276
$551$			9.67813e34i			0.224296i
$552$	4.10354e35	−	2.25417e35i	0.928860	−	0.510244i
$553$	2.34053e35			0.517472
$554$		−	2.88646e35i		−	0.623360i
$555$	−3.12446e35	−	5.68784e35i	−0.659123	−	1.19988i
$556$	−1.33493e35			−0.275097
$557$			1.55393e35i			0.312833i	0.987691	+	0.156417i	$0.0499943\pi$
$557$			1.55393e35i			0.312833i	−0.987691	+	0.156417i	$0.950006\pi$
$558$	1.75954e35	+	1.11827e35i	0.346062	+	0.219940i
$559$	−5.96493e33			−0.0114618
$560$			7.59617e35i			1.42610i
$561$	−2.53246e35	+	1.39114e35i	−0.464542	+	0.255184i
$562$	−1.06937e36			−1.91671
$563$		−	1.00441e36i		−	1.75915i	−0.475757	−	0.879577i	$-0.657826\pi$
$563$		−	1.00441e36i		−	1.75915i	0.475757	−	0.879577i	$-0.342174\pi$
$564$	−1.29005e35	−	2.34844e35i	−0.220790	−	0.401930i
$565$	−6.94625e34			−0.116177
$566$		−	1.33638e34i		−	0.0218432i
$567$	−3.64761e35	−	7.77831e35i	−0.582678	−	1.24253i
$568$	−1.09461e35			−0.170896
$569$			7.27698e35i			1.11043i	0.831706	+	0.555216i	$0.187364\pi$
$569$			7.27698e35i			1.11043i	−0.831706	+	0.555216i	$0.812636\pi$
$570$	7.37179e34	−	4.04949e34i	0.109951	−	0.0603987i
$571$	−2.35764e35			−0.343723			−0.171861	−	0.985121i	$-0.554978\pi$
$571$	−2.35764e35			−0.343723			−0.171861	+	0.985121i	$0.554978\pi$
$572$			2.48789e35i			0.354554i
$573$	6.12571e35	+	1.11514e36i	0.853387	+	1.55353i
$574$	7.39325e35			1.00689
$575$			3.59341e35i			0.478436i
$576$	−1.08697e35	+	1.71029e35i	−0.141490	+	0.222627i
$577$	9.36803e35			1.19224			0.596119	−	0.802896i	$-0.296709\pi$
$577$	9.36803e35			1.19224			0.596119	+	0.802896i	$0.296709\pi$
$578$		−	5.29330e35i		−	0.658665i
$579$	−1.23350e36	+	6.77591e35i	−1.50078	+	0.824416i
$580$	5.48012e35			0.651967
$581$		−	4.18580e35i		−	0.486955i
$582$	−3.36544e35	−	6.12652e35i	−0.382863	−	0.696972i
$583$	4.28364e35			0.476564
$584$			6.02471e34i			0.0655494i
$585$	6.79153e35	+	4.31635e35i	0.722672	+	0.459294i
$586$	1.97611e36			2.05656
$587$		−	1.72700e36i		−	1.75791i	−0.476903	−	0.878956i	$-0.658241\pi$
$587$		−	1.72700e36i		−	1.75791i	0.476903	−	0.878956i	$-0.341759\pi$
$588$	−3.40098e35	+	1.86824e35i	−0.338610	+	0.186006i
$589$	4.40650e34			0.0429136
$590$		−	7.56054e35i		−	0.720239i
$591$	3.61134e35	+	6.57416e35i	0.336536	+	0.612637i
$592$	−2.24384e36			−2.04555
$593$			1.36893e36i			1.22087i	0.792066	+	0.610436i	$0.209006\pi$
$593$			1.36893e36i			1.22087i	−0.792066	+	0.610436i	$0.790994\pi$
$594$	6.91986e34	−	1.08270e36i	0.0603773	−	0.944683i
$595$	8.99964e35			0.768253
$596$			4.59165e35i			0.383502i
$597$	−7.85108e35	+	4.31278e35i	−0.641598	+	0.352445i
$598$	−2.41856e36			−1.93393
$599$			1.52803e36i			1.19559i	0.801648	+	0.597797i	$0.203957\pi$
$599$			1.52803e36i			1.19559i	−0.801648	+	0.597797i	$0.796043\pi$
$600$	−1.29180e35	−	2.35162e35i	−0.0989074	−	0.180053i
$601$	9.58852e35			0.718428			0.359214	−	0.933255i	$-0.383045\pi$
$601$	9.58852e35			0.718428			0.359214	+	0.933255i	$0.383045\pi$
$602$		−	2.50484e34i		−	0.0183664i
$603$	−6.76855e35	+	1.06499e36i	−0.485703	+	0.764226i
$604$	7.38033e35			0.518317
$605$		−	4.56887e35i		−	0.314043i
$606$	1.02163e36	−	5.61208e35i	0.687308	−	0.377554i
$607$	1.05330e36			0.693586			0.346793	−	0.937942i	$-0.387271\pi$
$607$	1.05330e36			0.693586			0.346793	+	0.937942i	$0.387271\pi$
$608$		−	1.59498e35i		−	0.102803i
$609$	−1.87211e36	−	3.40802e36i	−1.18115	−	2.15019i
$610$	−2.63406e36			−1.62681
$611$		−	1.78079e36i		−	1.07665i
$612$	−4.18610e35	−	2.66047e35i	−0.247766	−	0.157467i
$613$	−6.97196e35			−0.403988			−0.201994	−	0.979387i	$-0.564742\pi$
$613$	−6.97196e35			−0.403988			−0.201994	+	0.979387i	$0.564742\pi$
$614$			2.35203e36i			1.33430i
$615$	8.05344e35	−	4.42394e35i	0.447306	−	0.245716i
$616$	1.34412e36			0.730953
$617$		−	1.77378e36i		−	0.944480i	−0.881470	−	0.472240i	$-0.843446\pi$
$617$		−	1.77378e36i		−	0.944480i	0.881470	−	0.472240i	$-0.156554\pi$
$618$	1.52163e36	+	2.77001e36i	0.793338	+	1.44421i
$619$	−8.64227e35			−0.441214			−0.220607	−	0.975363i	$-0.570804\pi$
$619$	−8.64227e35			−0.441214			−0.220607	+	0.975363i	$0.570804\pi$
$620$		−	2.49512e35i		−	0.124738i
$621$	3.20252e36	+	2.04682e35i	1.56784	+	0.100205i
$622$	8.35925e35			0.400767
$623$			1.39015e36i			0.652707i
$624$	2.43867e36	−	1.33962e36i	1.12138	−	0.616002i
$625$	−1.33831e36			−0.602723
$626$			1.20911e36i			0.533335i
$627$	−1.10403e35	−	2.00980e35i	−0.0476983	−	0.0868310i
$628$	−2.95501e34			−0.0125050
$629$			2.65841e36i			1.10195i
$630$	−1.81255e36	+	2.85195e36i	−0.735976	+	1.15802i
$631$	−7.08607e34			−0.0281854			−0.0140927	−	0.999901i	$-0.504486\pi$
$631$	−7.08607e34			−0.0281854			−0.0140927	+	0.999901i	$0.504486\pi$
$632$		−	6.52782e35i		−	0.254358i
$633$	−3.74744e34	+	2.05855e34i	−0.0143049	+	0.00785804i
$634$	−9.97797e34			−0.0373149
$635$			2.09322e36i			0.766933i
$636$	3.54038e35	+	6.44499e35i	0.127089	+	0.231356i
$637$	−2.57892e36			−0.907036
$638$		−	4.91036e36i		−	1.69217i
$639$	−6.33205e35	−	4.02433e35i	−0.213812	−	0.135888i
$640$	2.86217e36			0.947012
$641$		−	4.08993e36i		−	1.32605i	−0.748595	−	0.663027i	$-0.769271\pi$
$641$		−	4.08993e36i		−	1.32605i	0.748595	−	0.663027i	$-0.230729\pi$
$642$	8.65345e35	−	4.75354e35i	0.274937	−	0.151030i
$643$	−4.64791e35			−0.144716			−0.0723578	−	0.997379i	$-0.523052\pi$
$643$	−4.64791e35			−0.144716			−0.0723578	+	0.997379i	$0.523052\pi$
$644$		−	3.09021e36i		−	0.942912i
$645$	−1.49883e34	−	2.72851e34i	−0.00448205	−	0.00815923i
$646$	−3.44546e35			−0.100977
$647$		−	2.17559e35i		−	0.0624915i	−0.999512	−	0.0312457i	$-0.990053\pi$
$647$		−	2.17559e35i		−	0.0624915i	0.999512	−	0.0312457i	$-0.00994744\pi$
$648$	−2.16940e36	+	1.01733e36i	−0.610751	+	0.286410i
$649$	−2.06126e36			−0.568790
$650$			1.38601e36i			0.374880i
$651$	−1.55169e36	+	8.52378e35i	−0.411388	+	0.225985i
$652$	−1.25513e36			−0.326190
$653$			2.28233e36i			0.581442i	0.956808	+	0.290721i	$0.0938952\pi$
$653$			2.28233e36i			0.581442i	−0.956808	+	0.290721i	$0.906105\pi$
$654$	−6.08347e35	−	1.10745e36i	−0.151929	−	0.276575i
$655$	1.95447e36			0.478511
$656$		−	3.17706e36i		−	0.762563i
$657$	−2.21497e35	+	3.48513e35i	−0.0521216	+	0.0820104i
$658$	7.47800e36			1.72524
$659$			1.01213e36i			0.228943i	0.993427	+	0.114471i	$0.0365174\pi$
$659$			1.01213e36i			0.228943i	−0.993427	+	0.114471i	$0.963483\pi$
$660$	−1.13802e36	+	6.25143e35i	−0.252395	+	0.138646i
$661$	−8.35151e36			−1.81613			−0.908064	−	0.418832i	$-0.862439\pi$
$661$	−8.35151e36			−1.81613			−0.908064	+	0.418832i	$0.862439\pi$
$662$			9.78741e36i			2.08696i
$663$	−1.58713e36	−	2.88924e36i	−0.331846	−	0.604099i
$664$	−1.16743e36			−0.239358
$665$			7.14227e35i			0.143600i
$666$	−8.42438e36	−	5.35411e36i	−1.66101	−	1.05566i
$667$	1.45243e37			2.80841
$668$		−	1.21518e35i		−	0.0230435i
$669$	6.35579e36	−	3.49138e36i	1.18203	−	0.649319i
$670$	4.96344e36			0.905336
$671$			7.18134e36i			1.28473i
$672$	3.08527e36	+	5.61649e36i	0.541368	+	0.985518i
$673$	−4.52128e36			−0.778154			−0.389077	−	0.921205i	$-0.627206\pi$
$673$	−4.52128e36			−0.778154			−0.389077	+	0.921205i	$0.627206\pi$
$674$			5.21293e35i			0.0880042i
$675$	1.17297e35	−	1.83528e36i	0.0194240	−	0.303915i
$676$	−1.46105e35			−0.0237333
$677$		−	7.24871e36i		−	1.15507i	−0.816366	−	0.577534i	$-0.804015\pi$
$677$		−	7.24871e36i		−	1.15507i	0.816366	−	0.577534i	$-0.195985\pi$
$678$	−9.36447e35	+	5.14412e35i	−0.146385	+	0.0804128i
$679$	5.93577e36			0.910270
$680$		−	2.51003e36i		−	0.377627i
$681$	3.75942e36	+	6.84374e36i	0.554892	+	1.01014i
$682$	−2.23571e36			−0.323756
$683$		−	1.01540e37i		−	1.44267i	−0.692588	−	0.721334i	$-0.743529\pi$
$683$		−	1.01540e37i		−	1.44267i	0.692588	−	0.721334i	$-0.256471\pi$
$684$	2.11140e35	−	3.32216e35i	0.0294334	−	0.0463118i
$685$	−5.30813e36			−0.726046
$686$			1.42963e36i			0.191872i
$687$	−5.39017e36	+	2.96095e36i	−0.709847	+	0.389936i
$688$	−1.07639e35			−0.0139098
$689$			4.88714e36i			0.619733i
$690$	−6.07722e36	−	1.10631e37i	−0.756252	−	1.37670i
$691$	−8.61391e35			−0.105193			−0.0525964	−	0.998616i	$-0.516750\pi$
$691$	−8.61391e35			−0.105193			−0.0525964	+	0.998616i	$0.516750\pi$
$692$			4.12025e36i			0.493793i
$693$	7.77538e36	+	4.94164e36i	0.914513	+	0.581218i
$694$	−1.65112e37			−1.90593
$695$		−	4.63032e36i		−	0.524577i
$696$	−9.50510e36	+	5.22137e36i	−1.05691	+	0.580583i
$697$	−3.76405e36			−0.410799
$698$		−	1.03950e37i		−	1.11353i
$699$	4.25735e36	+	7.75018e36i	0.447648	+	0.814908i
$700$	−1.77091e36			−0.182777
$701$		−	2.89323e35i		−	0.0293122i	−0.999893	−	0.0146561i	$-0.995335\pi$
$701$		−	2.89323e35i		−	0.0293122i	0.999893	−	0.0146561i	$-0.00466535\pi$
$702$	1.23524e37	+	7.89476e35i	1.22848	+	0.0785157i
$703$	−2.10976e36			−0.205974
$704$		−	2.17313e36i		−	0.208277i
$705$	8.14576e36	−	4.47466e36i	0.766431	−	0.421018i
$706$	4.73487e36			0.437368
$707$			9.89826e36i			0.897649i
$708$	−1.70361e36	−	3.10129e36i	−0.151683	−	0.276128i
$709$	2.43137e36			0.212544			0.106272	−	0.994337i	$-0.466109\pi$
$709$	2.43137e36			0.212544			0.106272	+	0.994337i	$0.466109\pi$
$710$			2.95107e36i			0.253292i
$711$	2.39994e36	−	3.77616e36i	0.202253	−	0.318234i
$712$	3.87719e36			0.320832
$713$		−	6.61299e36i		−	0.537321i
$714$	1.21327e37	−	6.66478e36i	0.968013	−	0.531752i
$715$	−8.62946e36			−0.676091
$716$		−	6.43005e36i		−	0.494704i
$717$	−2.20986e36	−	4.02289e36i	−0.166962	−	0.303941i
$718$	1.73707e37			1.28884
$719$			1.59188e37i			1.15994i	0.814638	+	0.579969i	$0.196935\pi$
$719$			1.59188e37i			1.15994i	−0.814638	+	0.579969i	$0.803065\pi$
$720$	1.22555e37	+	7.78899e36i	0.877020	+	0.557389i
$721$	−2.68376e37			−1.88619
$722$			1.70951e37i			1.18002i
$723$	−1.24158e37	+	6.82029e36i	−0.841738	+	0.462386i
$724$	7.16020e36			0.476786
$725$		−	8.32347e36i		−	0.544390i
$726$	−3.38353e36	−	6.15945e36i	−0.217367	−	0.395700i
$727$	2.16227e37			1.36447			0.682234	−	0.731134i	$-0.261008\pi$
$727$	2.16227e37			1.36447			0.682234	+	0.731134i	$0.261008\pi$
$728$			1.53349e37i			0.950546i
$729$	−1.62896e37	−	2.09076e36i	−0.991864	−	0.127305i
$730$	1.62426e36			0.0971532
$731$			1.27526e35i			0.00749331i
$732$	−1.08048e37	+	5.93530e36i	−0.623693	+	0.342609i
$733$	1.82244e37			1.03348			0.516740	−	0.856142i	$-0.327145\pi$
$733$	1.82244e37			1.03348			0.516740	+	0.856142i	$0.327145\pi$
$734$			3.31526e36i			0.184701i
$735$	−6.48015e36	−	1.17966e37i	−0.354691	−	0.645687i
$736$	−2.39364e37			−1.28720
$737$		−	1.35320e37i		−	0.714966i
$738$	7.58092e36	−	1.19281e37i	0.393540	−	0.619213i
$739$	7.55053e36			0.385123			0.192562	−	0.981285i	$-0.438320\pi$
$739$	7.55053e36			0.385123			0.192562	+	0.981285i	$0.438320\pi$
$740$			1.19462e37i			0.598713i
$741$	2.29295e36	−	1.25957e36i	0.112917	−	0.0620278i
$742$	−2.05224e37			−0.993066
$743$		−	3.58577e37i		−	1.70501i	−0.522716	−	0.852507i	$-0.675081\pi$
$743$		−	3.58577e37i		−	1.70501i	0.522716	−	0.852507i	$-0.324919\pi$
$744$	2.37731e36	+	4.32771e36i	0.111081	+	0.202214i
$745$	−1.59265e37			−0.731290
$746$		−	3.30337e37i		−	1.49057i
$747$	−6.75329e36	−	4.29205e36i	−0.299466	−	0.190326i
$748$	5.31895e36			0.231795
$749$			8.38402e36i			0.359078i
$750$	−2.71584e37	+	1.49187e37i	−1.14316	+	0.627965i
$751$	8.95135e36			0.370313			0.185157	−	0.982709i	$-0.440721\pi$
$751$	8.95135e36			0.370313			0.185157	+	0.982709i	$0.440721\pi$
$752$		−	3.21348e37i		−	1.30660i
$753$	7.88979e36	+	1.43627e37i	0.315305	+	0.573988i
$754$	5.60216e37			2.20053
$755$			2.55993e37i			0.988367i
$756$	−1.00872e36	+	1.57827e37i	−0.0382813	+	0.598962i
$757$	1.18563e37			0.442285			0.221143	−	0.975241i	$-0.429021\pi$
$757$	1.18563e37			0.442285			0.221143	+	0.975241i	$0.429021\pi$
$758$			4.94590e37i			1.81362i
$759$	−3.01618e37	+	1.65686e37i	−1.08721	+	0.597231i
$760$	1.99200e36			0.0705852
$761$			2.47764e37i			0.863054i	0.902100	+	0.431527i	$0.142025\pi$
$761$			2.47764e37i			0.863054i	−0.902100	+	0.431527i	$0.857975\pi$
$762$	1.55016e37	+	2.82195e37i	0.530838	+	0.966349i
$763$	1.07297e37			0.361217
$764$		−	2.34214e37i		−	0.775172i
$765$	9.22808e36	−	1.45199e37i	0.300271	−	0.472458i
$766$	−5.47076e37			−1.75014
$767$		−	2.35166e37i		−	0.739665i
$768$	3.11097e37	−	1.70893e37i	0.962054	−	0.528479i
$769$	2.42146e37			0.736265			0.368133	−	0.929773i	$-0.379997\pi$
$769$	2.42146e37			0.736265			0.368133	+	0.929773i	$0.379997\pi$
$770$		−	3.62374e37i		−	1.08337i
$771$	−1.55232e37	−	2.82587e37i	−0.456324	−	0.830702i
$772$	2.59074e37			0.748856
$773$			6.61916e37i			1.88135i	0.339308	+	0.940675i	$0.389807\pi$
$773$			6.61916e37i			1.88135i	−0.339308	+	0.940675i	$0.610193\pi$
$774$	−4.04126e35	−	2.56842e35i	−0.0112949	−	0.00717849i
$775$	−3.78971e36			−0.104156
$776$		−	1.65551e37i		−	0.447434i
$777$	7.42922e37	−	4.08104e37i	1.97456	−	1.08467i
$778$	−5.16657e37			−1.35042
$779$		−	2.98722e36i		−	0.0767856i
$780$	−7.13216e36	−	1.29835e37i	−0.180298	−	0.328219i
$781$	8.04563e36			0.200031
$782$			5.17072e37i			1.26434i
$783$	−7.41807e37	−	4.74109e36i	−1.78397	−	0.114018i
$784$	−4.65373e37			−1.10076
$785$		−	1.02497e36i		−	0.0238455i
$786$	2.63489e37	−	1.44740e37i	0.602933	−	0.331205i
$787$	2.16041e37			0.486256			0.243128	−	0.969994i	$-0.421827\pi$
$787$	2.16041e37			0.486256			0.243128	+	0.969994i	$0.421827\pi$
$788$		−	1.38078e37i		−	0.305691i
$789$	2.89032e37	+	5.26160e37i	0.629426	+	1.14582i
$790$	−1.75989e37			−0.376994
$791$		−	9.07291e36i		−	0.191184i
$792$	1.37824e37	−	2.16858e37i	0.285692	−	0.449520i
$793$	−8.19308e37			−1.67069
$794$		−	6.13669e37i		−	1.23103i
$795$	−2.23550e37	+	1.22801e37i	−0.441166	+	0.242343i
$796$	1.64897e37			0.320142
$797$			4.96216e37i			0.947792i	0.880581	+	0.473896i	$0.157153\pi$
$797$			4.96216e37i			0.947792i	−0.880581	+	0.473896i	$0.842847\pi$
$798$	5.28928e36	+	9.62873e36i	0.0993938	+	0.180939i
$799$	−3.80720e37			−0.703879
$800$			1.37173e37i			0.249515i
$801$	2.24285e37	+	1.42544e37i	0.401400	+	0.255109i
$802$	−1.02587e38			−1.80645
$803$		−	4.42828e36i		−	0.0767242i
$804$	2.03597e37	−	1.11841e37i	0.347091	−	0.190665i
$805$	1.07187e38			1.79802
$806$		−	2.55069e37i		−	0.421019i
$807$	−3.58898e36	−	6.53346e36i	−0.0582929	−	0.106118i
$808$	2.76066e37			0.441230
$809$		−	7.62198e37i		−	1.19877i	−0.800460	−	0.599387i	$-0.795411\pi$
$809$		−	7.62198e37i		−	1.19877i	0.800460	−	0.599387i	$-0.204589\pi$
$810$	2.74272e37	+	5.84868e37i	0.424498	+	0.905217i
$811$	1.03256e38			1.57269			0.786347	−	0.617785i	$-0.211970\pi$
$811$	1.03256e38			1.57269			0.786347	+	0.617785i	$0.211970\pi$
$812$			7.15791e37i			1.07290i
$813$	3.31649e37	−	1.82183e37i	0.489218	−	0.268739i
$814$	1.07042e38			1.55395
$815$		−	4.35354e37i		−	0.622004i
$816$	−2.86402e37	−	5.21373e37i	−0.402721	−	0.733122i
$817$	−1.01207e35			−0.00140063
$818$			6.22538e37i			0.847956i
$819$	−5.63784e37	+	8.87082e37i	−0.755827	+	1.18925i
$820$	−1.69147e37			−0.223195
$821$		−	6.64924e37i		−	0.863596i	−0.901970	−	0.431798i	$-0.857879\pi$
$821$		−	6.64924e37i		−	0.863596i	0.901970	−	0.431798i	$-0.142121\pi$
$822$	−7.15607e37	+	3.93100e37i	−0.914832	+	0.502538i
$823$	−5.40322e37			−0.679915			−0.339957	−	0.940441i	$-0.610413\pi$
$823$	−5.40322e37			−0.679915			−0.339957	+	0.940441i	$0.610413\pi$
$824$			7.48511e37i			0.927138i
$825$	9.49498e36	+	1.72849e37i	0.115769	+	0.210749i
$826$	9.87526e37			1.18524
$827$		−	9.42640e37i		−	1.11372i	−0.830608	−	0.556858i	$-0.812007\pi$
$827$		−	9.42640e37i		−	1.11372i	0.830608	−	0.556858i	$-0.187993\pi$
$828$	−4.98568e37	−	3.16865e37i	−0.579870	−	0.368536i
$829$	−1.56605e38			−1.79307			−0.896535	−	0.442972i	$-0.853924\pi$
$829$	−1.56605e38			−1.79307			−0.896535	+	0.442972i	$0.853924\pi$
$830$			3.14740e37i			0.354761i
$831$	4.10685e37	−	2.25599e37i	0.455717	−	0.250336i
$832$	2.47929e37			0.270848
$833$			5.51355e37i			0.592989i
$834$	−3.42904e37	−	6.24230e37i	−0.363089	−	0.660976i
$835$	4.21497e36			0.0439410
$836$			4.22121e36i			0.0433266i
$837$	−2.15864e36	+	3.37748e37i	−0.0218147	+	0.341320i
$838$	1.56302e38			1.55522
$839$		−	3.66313e37i		−	0.358878i	−0.983769	−	0.179439i	$-0.942572\pi$
$839$		−	3.66313e37i		−	0.358878i	0.983769	−	0.179439i	$-0.0574282\pi$
$840$	−7.01457e37	+	3.85327e37i	−0.676660	+	0.371705i
$841$	−2.31149e38			−2.19555
$842$		−	2.16488e37i		−	0.202478i
$843$	−8.35794e37	−	1.52150e38i	−0.769735	−	1.40124i
$844$	7.87079e35			0.00713783
$845$		−	5.06777e36i		−	0.0452564i
$846$	7.66782e37	−	1.20649e38i	0.674306	−	1.06098i
$847$	5.96767e37			0.516798
$848$			8.81900e37i			0.752096i
$849$	1.90139e36	−	1.04448e36i	0.0159688	−	0.00877203i
$850$	2.96319e37			0.245084
$851$			3.16619e38i			2.57901i
$852$	6.64963e36	+	1.21051e37i	0.0533437	+	0.0971080i
$853$	2.38455e38			1.88395			0.941976	−	0.335682i	$-0.108967\pi$
$853$	2.38455e38			1.88395			0.941976	+	0.335682i	$0.108967\pi$
$854$		−	3.44050e38i		−	2.67713i
$855$	1.15232e37	+	7.32356e36i	0.0883108	+	0.0561258i
$856$	2.33834e37			0.176501
$857$		−	1.86626e38i		−	1.38746i	−0.720234	−	0.693731i	$-0.755966\pi$
$857$		−	1.86626e38i		−	1.38746i	0.720234	−	0.693731i	$-0.244034\pi$
$858$	−1.16337e38	+	6.39064e37i	−0.851887	+	0.467961i
$859$	−4.02625e37			−0.290395			−0.145198	−	0.989403i	$-0.546382\pi$
$859$	−4.02625e37			−0.290395			−0.145198	+	0.989403i	$0.546382\pi$
$860$			5.73072e35i			0.00407126i
$861$	5.77837e37	+	1.05191e38i	0.404357	+	0.736100i
$862$	−1.55767e38			−1.07369
$863$			2.22122e38i			1.50817i	0.656774	+	0.754087i	$0.271920\pi$
$863$			2.22122e38i			1.50817i	−0.656774	+	0.754087i	$0.728080\pi$
$864$	1.22251e38	+	7.81341e36i	0.817664	+	0.0522591i
$865$	−1.42915e38			−0.941602
$866$			2.77089e38i			1.79840i
$867$	7.53128e37	−	4.13711e37i	0.481527	−	0.264514i
$868$	3.25903e37			0.205273
$869$			4.79807e37i			0.297721i
$870$	1.40768e38	+	2.56257e38i	0.860504	+	1.56648i
$871$	1.54385e38			0.929755
$872$		−	2.99255e37i		−	0.177552i
$873$	6.08645e37	−	9.57667e37i	0.355778	−	0.559795i
$874$	−4.10357e37			−0.236327
$875$		−	2.63128e38i		−	1.49301i
$876$	6.66261e36	−	3.65993e36i	0.0372470	−	0.0204606i
$877$	−1.26570e38			−0.697166			−0.348583	−	0.937278i	$-0.613337\pi$
$877$	−1.26570e38			−0.697166			−0.348583	+	0.937278i	$0.613337\pi$
$878$		−	4.18009e38i		−	2.26859i
$879$	1.54447e38	+	2.81159e38i	0.825896	+	1.50348i
$880$	−1.55721e38			−0.820490
$881$		−	7.05999e37i		−	0.366536i	−0.983063	−	0.183268i	$-0.941332\pi$
$881$		−	7.05999e37i		−	0.366536i	0.983063	−	0.183268i	$-0.0586677\pi$
$882$	−1.74722e38	−	1.11045e38i	−0.893833	−	0.568075i
$883$	−2.14992e37			−0.108376			−0.0541880	−	0.998531i	$-0.517257\pi$
$883$	−2.14992e37			−0.108376			−0.0541880	+	0.998531i	$0.517257\pi$
$884$			6.06831e37i			0.301431i
$885$	1.07571e38	−	5.90912e37i	0.526541	−	0.289241i
$886$	4.40603e37			0.212525
$887$			4.16578e37i			0.198011i	0.995087	+	0.0990054i	$0.0315661\pi$
$887$			4.16578e37i			0.198011i	−0.995087	+	0.0990054i	$0.968434\pi$
$888$	−1.13822e38	−	2.07204e38i	−0.533159	−	0.970575i
$889$	−2.73408e38			−1.26209
$890$		−	1.04529e38i		−	0.475517i
$891$	1.59455e38	−	7.47759e37i	0.714872	−	0.335236i
$892$	−1.33491e38			−0.589807
$893$		−	3.02146e37i		−	0.131567i
$894$	−2.14711e38	+	1.17946e38i	−0.921439	+	0.506168i
$895$	2.23032e38			0.943339
$896$			3.73845e38i			1.55843i
$897$	−1.89028e38	−	3.44112e38i	−0.776650	−	1.41383i
$898$	−6.35366e37			−0.257295
$899$			1.53178e38i			0.611392i
$900$	−1.81586e37	+	2.85715e37i	−0.0714382	+	0.112404i
$901$	1.04484e38			0.405160
$902$			1.51561e38i			0.579300i
$903$	3.56387e36	−	1.95772e36i	0.0134271	−	0.00737580i
$904$	−2.53047e37			−0.0939748
$905$			2.48358e38i			0.909172i
$906$	1.89579e38	+	3.45113e38i	0.684105	+	1.24536i
$907$	−2.13252e38			−0.758576			−0.379288	−	0.925279i	$-0.623831\pi$
$907$	−2.13252e38			−0.758576			−0.379288	+	0.925279i	$0.623831\pi$
$908$		−	1.43740e38i		−	0.504035i
$909$	1.59697e38	+	1.01495e38i	0.552034	+	0.350845i
$910$	4.13428e38			1.40884
$911$		−	1.41080e38i		−	0.473944i	−0.971516	−	0.236972i	$-0.923845\pi$
$911$		−	1.41080e38i		−	0.473944i	0.971516	−	0.236972i	$-0.0761550\pi$
$912$	4.13770e37	−	2.27294e37i	0.137033	−	0.0752756i
$913$	8.58088e37			0.280163
$914$		−	1.08550e38i		−	0.349405i
$915$	−2.05871e38	−	3.74772e38i	−0.653313	−	1.18931i
$916$	1.13210e38			0.354197
$917$			2.55285e38i			0.787451i
$918$	1.68785e37	−	2.64087e38i	0.0513309	−	0.803140i
$919$	5.37999e38			1.61317			0.806584	−	0.591119i	$-0.201314\pi$
$919$	5.37999e38			1.61317			0.806584	+	0.591119i	$0.201314\pi$
$920$		−	2.98947e38i		−	0.883797i
$921$	−3.34646e38	+	1.83829e38i	−0.975461	+	0.535843i
$922$	−1.00810e38			−0.289736
$923$			9.17915e37i			0.260124i
$924$	−8.16536e37	−	1.48644e38i	−0.228160	−	0.415348i
$925$	1.81445e38			0.499923
$926$			1.62306e37i			0.0440954i
$927$	−2.75188e38	+	4.32993e38i	−0.737214	+	1.15996i
$928$	5.54443e38			1.46465
$929$		−	1.30794e38i		−	0.340708i	−0.985383	−	0.170354i	$-0.945509\pi$
$929$		−	1.30794e38i		−	0.340708i	0.985383	−	0.170354i	$-0.0544911\pi$
$930$	1.16675e38	−	6.40922e37i	0.299708	−	0.164637i
$931$	−4.37565e37			−0.110840
$932$		−	1.62778e38i		−	0.406620i
$933$	6.53338e37	+	1.18935e38i	0.160945	+	0.292987i
$934$	−4.67773e38			−1.13639
$935$			1.84492e38i			0.442005i
$936$	2.47411e38	+	1.57242e38i	0.584564	+	0.371519i
$937$	−5.08832e38			−1.18566			−0.592829	−	0.805328i	$-0.701989\pi$
$937$	−5.08832e38			−1.18566			−0.592829	+	0.805328i	$0.701989\pi$
$938$			6.48304e38i			1.48985i
$939$	−1.72032e38	+	9.45012e37i	−0.389903	+	0.214183i
$940$	−1.71086e38			−0.382431
$941$		−	3.62933e38i		−	0.800131i	−0.916487	−	0.400065i	$-0.868987\pi$
$941$		−	3.62933e38i		−	0.800131i	0.916487	−	0.400065i	$-0.131013\pi$
$942$	−7.59055e36	−	1.38180e37i	−0.0165048	−	0.0300458i
$943$	−4.48302e38			−0.961433
$944$		−	4.24365e38i		−	0.897642i
$945$	−5.47438e38	−	3.49883e37i	−1.14215	−	0.0729977i
$946$	5.13491e36			0.0105669
$947$		−	7.76470e38i		−	1.57607i	−0.615632	−	0.788034i	$-0.711099\pi$
$947$		−	7.76470e38i		−	1.57607i	0.615632	−	0.788034i	$-0.288901\pi$
$948$	−7.21899e37	+	3.96556e37i	−0.144533	+	0.0793955i
$949$	5.05216e37			0.0997737
$950$			2.35164e37i			0.0458104i
$951$	−7.79853e36	−	1.41966e37i	−0.0149853	−	0.0272796i
$952$	3.27850e38			0.621434
$953$		−	2.70486e38i		−	0.505752i	−0.967499	−	0.252876i	$-0.918624\pi$
$953$		−	2.70486e38i		−	0.505752i	0.967499	−	0.252876i	$-0.0813765\pi$
$954$	−2.10434e38	+	3.31105e38i	−0.388138	+	0.610713i
$955$	8.12390e38			1.47816
$956$			8.44931e37i			0.151659i
$957$	6.98643e38	−	3.83781e38i	1.23709	−	0.679561i
$958$	−3.93043e38			−0.686576
$959$		−	6.93327e38i		−	1.19480i
$960$	6.22983e37	+	1.13409e38i	0.105913	+	0.192807i
$961$	−5.26474e38			−0.883025
$962$			1.22123e39i			2.02079i
$963$	1.35266e38	+	8.59684e37i	0.220825	+	0.140345i
$964$	2.60771e38			0.420008
$965$			8.98619e38i			1.42798i
$966$	1.44502e39	−	7.93782e38i	2.26553	−	1.24451i
$967$	7.91968e37			0.122508			0.0612539	−	0.998122i	$-0.480490\pi$
$967$	7.91968e37			0.122508			0.0612539	+	0.998122i	$0.480490\pi$
$968$		−	1.66441e38i		−	0.254027i
$969$	−2.69288e37	−	4.90218e37i	−0.0405516	−	0.0738211i
$970$	−4.46324e38			−0.663159
$971$			7.71283e38i			1.13074i	0.824836	+	0.565371i	$0.191267\pi$
$971$			7.71283e38i			1.13074i	−0.824836	+	0.565371i	$0.808733\pi$
$972$	2.44293e38	+	1.78108e38i	0.353386	+	0.257645i
$973$	6.04794e38			0.863258
$974$			8.83904e38i			1.24491i
$975$	−1.97201e38	+	1.08327e38i	−0.274062	+	0.150548i
$976$	−1.47847e39			−2.02751
$977$		−	9.30448e38i		−	1.25911i	−0.776957	−	0.629554i	$-0.783238\pi$
$977$		−	9.30448e38i		−	1.25911i	0.776957	−	0.629554i	$-0.216762\pi$
$978$	−3.22406e38	−	5.86915e38i	−0.430525	−	0.783736i
$979$	−2.84981e38			−0.375527
$980$			2.47765e38i			0.322182i
$981$	1.10020e38	−	1.73111e38i	0.141181	−	0.222140i
$982$	2.34450e38			0.296894
$983$			5.85688e38i			0.731932i	0.930628	+	0.365966i	$0.119261\pi$
$983$			5.85688e38i			0.731932i	−0.930628	+	0.365966i	$0.880739\pi$
$984$	2.93381e38	−	1.61161e38i	0.361823	−	0.198758i
$985$	4.78935e38			0.582915
$986$		−	1.19770e39i		−	1.43863i
$987$	5.84461e38	+	1.06397e39i	0.692840	+	1.26126i
$988$	−4.81591e37			−0.0563428
$989$			1.51885e37i			0.0175373i
$990$	−5.84648e38	−	3.71573e38i	−0.666250	−	0.423435i
$991$	−4.02151e37			−0.0452305			−0.0226153	−	0.999744i	$-0.507199\pi$
$991$	−4.02151e37			−0.0452305			−0.0226153	+	0.999744i	$0.507199\pi$
$992$		−	2.52440e38i		−	0.280225i
$993$	−1.39255e39	+	7.64959e38i	−1.52570	+	0.838104i
$994$	−3.85457e38			−0.416824
$995$			5.71960e38i			0.610471i
$996$	7.09201e37	+	1.29104e38i	0.0747133	+	0.136010i
$997$	1.33202e39			1.38507			0.692536	−	0.721383i	$-0.256493\pi$
$997$	1.33202e39			1.38507			0.692536	+	0.721383i	$0.256493\pi$
$998$		−	1.60903e39i		−	1.65146i
$999$	1.03352e38	−	1.61708e39i	0.104705	−	1.63825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.27.b.a.2.2	✓	8
3.2	odd	2	inner	3.27.b.a.2.7	yes	8
4.3	odd	2		48.27.e.d.17.2		8
12.11	even	2		48.27.e.d.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.27.b.a.2.2	✓	8	1.1	even	1	trivial
3.27.b.a.2.7	yes	8	3.2	odd	2	inner
48.27.e.d.17.1		8	12.11	even	2
48.27.e.d.17.2		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)

\(f(q)\)	\(=\)	\(q-9821.30i q^{2} +(1.39737e6 - 767608. i) q^{3} -2.93491e7 q^{4} -1.01800e9i q^{5} +(-7.53891e9 - 1.37240e10i) q^{6} +1.32967e11 q^{7} -3.70850e11i q^{8} +(1.36342e12 - 2.14527e12i) q^{9} +O(q^{10})\)	\(q-9821.30i q^{2} +(1.39737e6 - 767608. i) q^{3} -2.93491e7 q^{4} -1.01800e9i q^{5} +(-7.53891e9 - 1.37240e10i) q^{6} +1.32967e11 q^{7} -3.70850e11i q^{8} +(1.36342e12 - 2.14527e12i) q^{9} -9.99808e12 q^{10} +2.72582e13i q^{11} +(-4.10116e13 + 2.25286e13i) q^{12} -3.10985e14 q^{13} -1.30591e15i q^{14} +(-7.81425e14 - 1.42252e15i) q^{15} -5.61181e15 q^{16} +6.64865e15i q^{17} +(-2.10693e16 - 1.33906e16i) q^{18} -5.27648e15 q^{19} +2.98774e16i q^{20} +(1.85804e17 - 1.02067e17i) q^{21} +2.67711e17 q^{22} +7.91861e17i q^{23} +(-2.84667e17 - 5.18215e17i) q^{24} +4.53793e17 q^{25} +3.05428e18i q^{26} +(2.58482e17 - 4.04430e18i) q^{27} -3.90246e18 q^{28} -1.83420e19i q^{29} +(-1.39710e19 + 7.67461e18i) q^{30} -8.35120e18 q^{31} +3.02280e19i q^{32} +(2.09236e19 + 3.80898e19i) q^{33} +6.52984e19 q^{34} -1.35360e20i q^{35} +(-4.00152e19 + 6.29617e19i) q^{36} +3.99842e20 q^{37} +5.18219e19i q^{38} +(-4.34561e20 + 2.38714e20i) q^{39} -3.77525e20 q^{40} +5.66138e20i q^{41} +(-1.00243e21 - 1.82484e21i) q^{42} +1.91808e19 q^{43} -8.00004e20i q^{44} +(-2.18388e21 - 1.38796e21i) q^{45} +7.77710e21 q^{46} +5.72628e21i q^{47} +(-7.84178e21 + 4.30767e21i) q^{48} +8.29274e21 q^{49} -4.45684e21i q^{50} +(5.10356e21 + 9.29063e21i) q^{51} +9.12713e21 q^{52} -1.57151e22i q^{53} +(-3.97203e22 - 2.53863e21i) q^{54} +2.77488e22 q^{55} -4.93108e22i q^{56} +(-7.37320e21 + 4.05027e21i) q^{57} -1.80142e23 q^{58} +7.56199e22i q^{59} +(2.29341e22 + 4.17498e22i) q^{60} +2.63456e23 q^{61} +8.20197e22i q^{62} +(1.81290e23 - 2.85249e23i) q^{63} -7.97240e22 q^{64} +3.16582e23i q^{65} +(3.74091e23 - 2.05497e23i) q^{66} -4.96439e23 q^{67} -1.95132e23i q^{68} +(6.07839e23 + 1.10652e24i) q^{69} -1.32941e24 q^{70} -2.95164e23i q^{71} +(-7.95571e23 - 5.05625e23i) q^{72} -1.62457e23 q^{73} -3.92697e24i q^{74} +(6.34117e23 - 3.48335e23i) q^{75} +1.54860e23 q^{76} +3.62444e24i q^{77} +(2.34449e24 + 4.26795e24i) q^{78} +1.76023e24 q^{79} +5.71283e24i q^{80} +(-2.74324e24 - 5.84980e24i) q^{81} +5.56021e24 q^{82} -3.14800e24i q^{83} +(-5.45319e24 + 2.99556e24i) q^{84} +6.76832e24 q^{85} -1.88380e23i q^{86} +(-1.40795e25 - 2.56306e25i) q^{87} +1.01087e25 q^{88} +1.04549e25i q^{89} +(-1.36316e25 + 2.14485e25i) q^{90} -4.13507e25 q^{91} -2.32404e25i q^{92} +(-1.16697e25 + 6.41045e24i) q^{93} +5.62395e25 q^{94} +5.37146e24i q^{95} +(2.32033e25 + 4.22397e25i) q^{96} +4.46410e25 q^{97} -8.14455e25i q^{98} +(5.84760e25 + 3.71644e25i) 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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