LMFDB - Embedded newform 3.69.b.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,69,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, 69, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 69);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 69 $
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:	$87.8517980619$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	3.2
Dual form			3.69.b.a.2.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.19205e9i q^{2} +(3.18264e15 + 1.63707e16i) q^{3} +2.28038e20 q^{4} +5.93220e23i q^{5} +(1.34109e26 - 2.60723e25i) q^{6} -6.83050e28 q^{7} -4.28597e30i q^{8} +(-2.57870e32 + 1.04204e32i) q^{9} +O(q^{10})$	\(q-8.19205e9i q^{2} +(3.18264e15 + 1.63707e16i) q^{3} +2.28038e20 q^{4} +5.93220e23i q^{5} +(1.34109e26 - 2.60723e25i) q^{6} -6.83050e28 q^{7} -4.28597e30i q^{8} +(-2.57870e32 + 1.04204e32i) q^{9} +4.85968e33 q^{10} +1.91225e35i q^{11} +(7.25764e35 + 3.73314e36i) q^{12} +3.76084e37 q^{13} +5.59558e38i q^{14} +(-9.71141e39 + 1.88800e39i) q^{15} +3.21942e40 q^{16} -1.23600e42i q^{17} +(8.53644e41 + 2.11248e42i) q^{18} -5.74305e43 q^{19} +1.35277e44i q^{20} +(-2.17390e44 - 1.11820e45i) q^{21} +1.56652e45 q^{22} -1.67308e46i q^{23} +(7.01642e46 - 1.36407e46i) q^{24} -1.30966e46 q^{25} -3.08090e47i q^{26} +(-2.52660e48 - 3.88986e48i) q^{27} -1.55762e49 q^{28} +2.38728e49i q^{29} +(1.54666e49 + 7.95563e49i) q^{30} -4.91081e50 q^{31} -1.52873e51i q^{32} +(-3.13048e51 + 6.08599e50i) q^{33} -1.01253e52 q^{34} -4.05199e52i q^{35} +(-5.88042e52 + 2.37625e52i) q^{36} +2.86719e53 q^{37} +4.70473e53i q^{38} +(1.19694e53 + 6.15675e53i) q^{39} +2.54252e54 q^{40} -3.97717e54i q^{41} +(-9.16035e54 + 1.78087e54i) q^{42} +4.99962e55 q^{43} +4.36065e55i q^{44} +(-6.18159e55 - 1.52974e56i) q^{45} -1.37059e56 q^{46} +2.90470e56i q^{47} +(1.02462e56 + 5.27041e56i) q^{48} +1.73693e57 q^{49} +1.07288e56i q^{50} +(2.02341e58 - 3.93373e57i) q^{51} +8.57615e57 q^{52} +1.15078e58i q^{53} +(-3.18659e58 + 2.06980e58i) q^{54} -1.13438e59 q^{55} +2.92753e59i q^{56} +(-1.82780e59 - 9.40176e59i) q^{57} +1.95567e59 q^{58} +1.83603e59i q^{59} +(-2.21457e60 + 4.30537e59i) q^{60} -1.75550e60 q^{61} +4.02296e60i q^{62} +(1.76138e61 - 7.11766e60i) q^{63} -3.02138e60 q^{64} +2.23100e61i q^{65} +(4.98567e60 + 2.56450e61i) q^{66} -8.48314e61 q^{67} -2.81854e62i q^{68} +(2.73894e62 - 5.32481e61i) q^{69} -3.31941e62 q^{70} +6.37727e62i q^{71} +(4.46615e62 + 1.10522e63i) q^{72} +2.74025e63 q^{73} -2.34881e63i q^{74} +(-4.16817e61 - 2.14400e62i) q^{75} -1.30963e64 q^{76} -1.30616e64i q^{77} +(5.04364e63 - 9.80538e62i) q^{78} -2.32401e64 q^{79} +1.90982e64i q^{80} +(5.56385e64 - 5.37421e64i) q^{81} -3.25812e64 q^{82} +7.50701e64i q^{83} +(-4.95733e64 - 2.54992e65i) q^{84} +7.33217e65 q^{85} -4.09572e65i q^{86} +(-3.90813e65 + 7.59784e64i) q^{87} +8.19582e65 q^{88} -3.38095e66i q^{89} +(-1.25317e66 + 5.06398e65i) q^{90} -2.56884e66 q^{91} -3.81526e66i q^{92} +(-1.56293e66 - 8.03933e66i) q^{93} +2.37955e66 q^{94} -3.40689e67i q^{95} +(2.50264e67 - 4.86540e66i) q^{96} +2.46680e67 q^{97} -1.42290e67i q^{98} +(-1.99264e67 - 4.93111e67i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 18\!\cdots\!78 q^{3}+ \cdots + 84\!\cdots\!78 q^{9}+O(q^{10}) $ 22 * q + 18789723640115478 * q^3 - 2943217790812903705616 * q^4 + 606827522425378326847120944 * q^6 - 3605688981734492610233621044 * q^7 + 84409856735558666343023488765878 * q^9	$ 22 q + 18\!\cdots\!78 q^{3}+ \cdots - 11\!\cdots\!00 q^{99}+O(q^{100}) $ 22 * q + 18789723640115478 * q^3 - 2943217790812903705616 * q^4 + 606827522425378326847120944 * q^6 - 3605688981734492610233621044 * q^7 + 84409856735558666343023488765878 * q^9 + 2045888067334428934113988216421280 * q^10 - 6488396126470402148347182126675194832 * q^12 - 10813885710533400837304817444785935604 * q^13 + 14557528184647372428101554053003296612160 * q^15 + 373601084063432865853473918269277812744320 * q^16 + 17941511735214427632488941901617371491816160 * q^18 - 79553650357260974891342027178031915087354324 * q^19 - 1298400323255969952377913185067359758477401780 * q^21 + 6768843564804724477092404017437690309759833760 * q^22 - 75879178936902674847903860248712590469230731648 * q^24 - 1290406322757665049559021767067242780449078031050 * q^25 + 2674086297347577939313596696269044232072283756918 * q^27 + 42745403006807704515598614320469990457621586593376 * q^28 + 30776582876805533479749631919828742635540596749600 * q^30 - 464825674673310587378006994001777182420658601801716 * q^31 + 2043086192437245889755473926491971918230943629550400 * q^33 + 13079915711847249768451590870017502856673640042982272 * q^34 - 65327203493646647902060088267317231087935232974706704 * q^36 - 167279080426229420846594751930892532669536008046545844 * q^37 + 1637357069222228057847981309081425400083650534736779020 * q^39 + 6053556854890611145141953130785126755317199579733738240 * q^40 - 12457262572316255979922798677909127605820549100734736160 * q^42 - 18628500859740527128618324584150040016275591666233599764 * q^43 + 367822789535544680671556018223028621483838265619669430400 * q^45 + 1476449543055130371522242587937584327352337186768013053888 * q^46 + 202405740838876412041865477434740772123701917763236585088 * q^48 + 4681199846498689520635057982286342899995310041595285382018 * q^49 + 21407584156868532008405510905089022165080050053906507325184 * q^51 + 24391763772592576034526261030318526583680683849133477696736 * q^52 - 112285817002635953902674086392140195155054790343667891881584 * q^54 + 274409579794012893709322560718339246575325740160175650620800 * q^55 + 101758997342686912720089366682761957082398853447685074732716 * q^57 - 2020457744766163498170953106059196558756720252448185539243040 * q^58 - 13276219488047015535811467987165558930747748946804017101031680 * q^60 + 6331070401548027780910089309848838040805985031947773629039244 * q^61 - 11540105667000326350766773710482957857389205527747058022198004 * q^63 + 74144666416333808948332900789778080404085337330317362556926976 * q^64 - 388082670987835008027383208260911873599566866107012006022495200 * q^66 + 690968797068657030373143885315519666504759571640550029794509356 * q^67 - 1027093066405255275213825064853644794250194801896401414490868864 * q^69 + 4371068227635884746027518083549441915821247332843741516741992000 * q^70 - 8830670280256061265338935058781406802503181323103646058149000960 * q^72 + 8806696028067195590640304057094157167006086961761378058824984556 * q^73 - 35720155285864881642804474725062955577201898766624893474579682250 * q^75 + 50989416920172911215005579159200646780346206610233430042766798432 * q^76 - 79580143447707181310585996419552144412335647108094050067906050720 * q^78 - 3083981169532008720747546215983788345611378750423096573576219764 * q^79 - 88762224122457647598561491684821377170571566383688244793770736938 * q^81 + 416784948027081086888539461807826070456316776812312199920865653440 * q^82 + 990441228134853667871418956670095117692984404086848036534801693920 * q^84 - 866637175758839171101071739839460554945096683648478422830993681920 * q^85 + 3620458445475290511813570050310517312523781688405496711995676422080 * q^87 - 4669471445324986882088763579042561683455173004052019441103363626240 * q^88 + 14582942989396685328395597316366348010236984461538262603110152917920 * q^90 - 6998978018734113734240448628263170029174504049408988631375576481960 * q^91 + 22631183723253759871940463881283634110336753405922973132310746358156 * q^93 - 49667911598354463153752845875961955186127772502753374451274725501568 * q^94 - 5532425547839977216491807518703626514248108709732237368596820947968 * q^96 + 90182295908350258367379728070466489774210357027997619180945877805996 * q^97 - 111427931124550204447734414473904809051459145283833102653529748809600 * 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 $

$2$		−	8.19205e9i		−	0.476840i	−0.971162	−	0.238420i	$-0.923371\pi$
$2$		−	8.19205e9i		−	0.476840i	0.971162	−	0.238420i	$-0.0766295\pi$
$3$	3.18264e15	+	1.63707e16i	0.190838	+	0.981622i
$3$	3.18264e15	+	1.63707e16i	0.190838	+	0.981622i
$4$	2.28038e20			0.772624
$5$			5.93220e23i			1.01914i	0.860428	+	0.509572i	$0.170196\pi$
$5$			5.93220e23i			1.01914i	−0.860428	+	0.509572i	$0.829804\pi$
$6$	1.34109e26	−	2.60723e25i	0.468076	−	0.0909992i
$7$	−6.83050e28			−1.26217			−0.631087	−	0.775712i	$-0.717391\pi$
$7$	−6.83050e28			−1.26217			−0.631087	+	0.775712i	$0.717391\pi$
$8$		−	4.28597e30i		−	0.845258i
$9$	−2.57870e32	+	1.04204e32i	−0.927162	+	0.374661i
$10$	4.85968e33			0.485968
$11$			1.91225e35i			0.748501i	0.927328	+	0.374251i	$0.122100\pi$
$11$			1.91225e35i			0.748501i	−0.927328	+	0.374251i	$0.877900\pi$
$12$	7.25764e35	+	3.73314e36i	0.147446	+	0.758424i
$13$	3.76084e37			0.502586			0.251293	−	0.967911i	$-0.419144\pi$
$13$	3.76084e37			0.502586			0.251293	+	0.967911i	$0.419144\pi$
$14$			5.59558e38i			0.601855i
$15$	−9.71141e39	+	1.88800e39i	−1.00041	+	0.194491i
$16$	3.21942e40			0.369571
$17$		−	1.23600e42i		−	1.80615i	−0.429485	−	0.903074i	$-0.641305\pi$
$17$		−	1.23600e42i		−	1.80615i	0.429485	−	0.903074i	$-0.358695\pi$
$18$	8.53644e41	+	2.11248e42i	0.178653	+	0.442108i
$19$	−5.74305e43			−1.91214			−0.956071	−	0.293137i	$-0.905301\pi$
$19$	−5.74305e43			−1.91214			−0.956071	+	0.293137i	$0.905301\pi$
$20$			1.35277e44i			0.787415i
$21$	−2.17390e44	−	1.11820e45i	−0.240871	−	1.23898i
$22$	1.56652e45			0.356915
$23$		−	1.67308e46i		−	0.840950i	−0.907304	−	0.420475i	$-0.861863\pi$
$23$		−	1.67308e46i		−	0.840950i	0.907304	−	0.420475i	$-0.138137\pi$
$24$	7.01642e46	−	1.36407e46i	0.829723	−	0.161307i
$25$	−1.30966e46			−0.0386543
$26$		−	3.08090e47i		−	0.239653i
$27$	−2.52660e48	−	3.88986e48i	−0.544713	−	0.838622i
$28$	−1.55762e49			−0.975186
$29$			2.38728e49i			0.453284i	0.973978	+	0.226642i	$0.0727748\pi$
$29$			2.38728e49i			0.453284i	−0.973978	+	0.226642i	$0.927225\pi$
$30$	1.54666e49	+	7.95563e49i	0.0927412	+	0.477037i
$31$	−4.91081e50			−0.965729			−0.482865	−	0.875695i	$-0.660404\pi$
$31$	−4.91081e50			−0.965729			−0.482865	+	0.875695i	$0.660404\pi$
$32$		−	1.52873e51i		−	1.02148i
$33$	−3.13048e51	+	6.08599e50i	−0.734745	+	0.142842i
$34$	−1.01253e52			−0.861244
$35$		−	4.05199e52i		−	1.28634i
$36$	−5.88042e52	+	2.37625e52i	−0.716347	+	0.289472i
$37$	2.86719e53			1.37593			0.687967	−	0.725742i	$-0.258503\pi$
$37$	2.86719e53			1.37593			0.687967	+	0.725742i	$0.258503\pi$
$38$			4.70473e53i			0.911785i
$39$	1.19694e53	+	6.15675e53i	0.0959125	+	0.493349i
$40$	2.54252e54			0.861439
$41$		−	3.97717e54i		−	0.582000i	−0.956723	−	0.291000i	$-0.906012\pi$
$41$		−	3.97717e54i		−	0.582000i	0.956723	−	0.291000i	$-0.0939880\pi$
$42$	−9.16035e54	+	1.78087e54i	−0.590794	+	0.114857i
$43$	4.99962e55			1.44880			0.724402	−	0.689377i	$-0.242116\pi$
$43$	4.99962e55			1.44880			0.724402	+	0.689377i	$0.242116\pi$
$44$			4.36065e55i			0.578310i
$45$	−6.18159e55	−	1.52974e56i	−0.381834	−	0.944911i
$46$	−1.37059e56			−0.400998
$47$			2.90470e56i			0.409048i	0.978862	+	0.204524i	$0.0655647\pi$
$47$			2.90470e56i			0.409048i	−0.978862	+	0.204524i	$0.934435\pi$
$48$	1.02462e56	+	5.27041e56i	0.0705282	+	0.362779i
$49$	1.73693e57			0.593085
$50$			1.07288e56i			0.0184319i
$51$	2.02341e58	−	3.93373e57i	1.77295	−	0.344682i
$52$	8.57615e57			0.388310
$53$			1.15078e58i			0.272654i	0.990664	+	0.136327i	$0.0435297\pi$
$53$			1.15078e58i			0.272654i	−0.990664	+	0.136327i	$0.956470\pi$
$54$	−3.18659e58	+	2.06980e58i	−0.399889	+	0.259741i
$55$	−1.13438e59			−0.762830
$56$			2.92753e59i			1.06686i
$57$	−1.82780e59	−	9.40176e59i	−0.364909	−	1.87700i
$58$	1.95567e59			0.216144
$59$			1.83603e59i			0.113478i	0.998389	+	0.0567388i	$0.0180702\pi$
$59$			1.83603e59i			0.113478i	−0.998389	+	0.0567388i	$0.981930\pi$
$60$	−2.21457e60	+	4.30537e59i	−0.772943	+	0.150269i
$61$	−1.75550e60			−0.349290			−0.174645	−	0.984631i	$-0.555878\pi$
$61$	−1.75550e60			−0.349290			−0.174645	+	0.984631i	$0.555878\pi$
$62$			4.02296e60i			0.460498i
$63$	1.76138e61	−	7.11766e60i	1.17024	−	0.472888i
$64$	−3.02138e60			−0.117513
$65$			2.23100e61i			0.512208i
$66$	4.98567e60	+	2.56450e61i	0.0681130	+	0.350356i
$67$	−8.48314e61			−0.695046			−0.347523	−	0.937672i	$-0.612977\pi$
$67$	−8.48314e61			−0.695046			−0.347523	+	0.937672i	$0.612977\pi$
$68$		−	2.81854e62i		−	1.39547i
$69$	2.73894e62	−	5.32481e61i	0.825494	−	0.160485i
$70$	−3.31941e62			−0.613377
$71$			6.37727e62i			0.727531i	0.931491	+	0.363765i	$0.118509\pi$
$71$			6.37727e62i			0.727531i	−0.931491	+	0.363765i	$0.881491\pi$
$72$	4.46615e62	+	1.10522e63i	0.316685	+	0.783691i
$73$	2.74025e63			1.21566			0.607832	−	0.794066i	$-0.292039\pi$
$73$	2.74025e63			1.21566			0.607832	+	0.794066i	$0.292039\pi$
$74$		−	2.34881e63i		−	0.656100i
$75$	−4.16817e61	−	2.14400e62i	−0.00737671	−	0.0379439i
$76$	−1.30963e64			−1.47737
$77$		−	1.30616e64i		−	0.944739i
$78$	5.04364e63	−	9.80538e62i	0.235249	−	0.0457349i
$79$	−2.32401e64			−0.702937			−0.351469	−	0.936200i	$-0.614318\pi$
$79$	−2.32401e64			−0.702937			−0.351469	+	0.936200i	$0.614318\pi$
$80$			1.90982e64i			0.376646i
$81$	5.56385e64	−	5.37421e64i	0.719258	−	0.694743i
$82$	−3.25812e64			−0.277521
$83$			7.50701e64i			0.423460i	0.977328	+	0.211730i	$0.0679097\pi$
$83$			7.50701e64i			0.423460i	−0.977328	+	0.211730i	$0.932090\pi$
$84$	−4.95733e64	−	2.54992e65i	−0.186103	−	0.957264i
$85$	7.33217e65			1.84073
$86$		−	4.09572e65i		−	0.690848i
$87$	−3.90813e65	+	7.59784e64i	−0.444954	+	0.0865039i
$88$	8.19582e65			0.632676
$89$		−	3.38095e66i		−	1.77737i	−0.458517	−	0.888685i	$-0.651619\pi$
$89$		−	3.38095e66i		−	1.77737i	0.458517	−	0.888685i	$-0.348381\pi$
$90$	−1.25317e66	+	5.06398e65i	−0.450571	+	0.182074i
$91$	−2.56884e66			−0.634351
$92$		−	3.81526e66i		−	0.649738i
$93$	−1.56293e66	−	8.03933e66i	−0.184298	−	0.947981i
$94$	2.37955e66			0.195050
$95$		−	3.40689e67i		−	1.94875i
$96$	2.50264e67	−	4.86540e66i	1.00271	−	0.194938i
$97$	2.46680e67			0.694857			0.347429	−	0.937706i	$-0.387055\pi$
$97$	2.46680e67			0.694857			0.347429	+	0.937706i	$0.387055\pi$
$98$		−	1.42290e67i		−	0.282806i
$99$	−1.99264e67	−	4.93111e67i	−0.280434	−	0.693982i
$100$	−2.98652e66			−0.0298652
$101$		−	1.80210e68i		−	1.28485i	−0.766350	−	0.642423i	$-0.777929\pi$
$101$		−	1.80210e68i		−	1.28485i	0.766350	−	0.642423i	$-0.222071\pi$
$102$	−3.22253e67	−	1.65759e68i	−0.164358	−	0.845415i
$103$	−2.10095e67			−0.0769041			−0.0384520	−	0.999260i	$-0.512243\pi$
$103$	−2.10095e67			−0.0769041			−0.0384520	+	0.999260i	$0.512243\pi$
$104$		−	1.61188e68i		−	0.424815i
$105$	6.63338e68	−	1.28960e68i	1.26270	−	0.245482i
$106$	9.42721e67			0.130012
$107$		−	3.39397e68i		−	0.340141i	−0.985432	−	0.170071i	$-0.945600\pi$
$107$		−	3.39397e68i		−	0.340141i	0.985432	−	0.170071i	$-0.0543996\pi$
$108$	−5.76161e68	−	8.87038e68i	−0.420858	−	0.647939i
$109$	−6.88384e68			−0.367561			−0.183781	−	0.982967i	$-0.558834\pi$
$109$	−6.88384e68			−0.367561			−0.183781	+	0.982967i	$0.558834\pi$
$110$			9.29291e68i			0.363748i
$111$	9.12522e68	+	4.69378e69i	0.262580	+	1.35065i
$112$	−2.19903e69			−0.466463
$113$		−	3.39840e69i		−	0.532853i	−0.963855	−	0.266426i	$-0.914157\pi$
$113$		−	3.39840e69i		−	0.532853i	0.963855	−	0.266426i	$-0.0858429\pi$
$114$	−7.70196e69	+	1.49735e69i	−0.895028	+	0.174003i
$115$	9.92504e69			0.857049
$116$			5.44390e69i			0.350218i
$117$	−9.69807e69	+	3.91894e69i	−0.465979	+	0.188300i
$118$	1.50408e69			0.0541107
$119$			8.44247e70i			2.27967i
$120$	8.09192e69	+	4.16228e70i	0.164395	+	0.845607i
$121$	2.87015e70			0.439746
$122$			1.43811e70i			0.166556i
$123$	6.51090e70	−	1.26579e70i	0.571304	−	0.111068i
$124$	−1.11985e71			−0.746145
$125$			1.93222e71i			0.979750i
$126$	−5.83082e70	−	1.44293e71i	−0.225492	−	0.558017i
$127$	−5.42996e71			−1.60498			−0.802491	−	0.596664i	$-0.796492\pi$
$127$	−5.42996e71			−1.60498			−0.802491	+	0.596664i	$0.796492\pi$
$128$		−	4.26450e71i		−	0.965449i
$129$	1.59120e71	+	8.18472e71i	0.276487	+	1.42218i
$130$	1.82765e71			0.244241
$131$		−	1.37816e72i		−	1.41931i	−0.704551	−	0.709653i	$-0.748852\pi$
$131$		−	1.37816e72i		−	1.41931i	0.704551	−	0.709653i	$-0.251148\pi$
$132$	−7.13869e71	+	1.38784e71i	−0.567681	+	0.110363i
$133$	3.92279e72			2.41346
$134$			6.94943e71i			0.331425i
$135$	2.30754e72	−	1.49883e72i	0.854677	−	0.555141i
$136$	−5.29743e72			−1.52666
$137$		−	7.44823e72i		−	1.67322i	−0.547797	−	0.836611i	$-0.684533\pi$
$137$		−	7.44823e72i		−	1.67322i	0.547797	−	0.836611i	$-0.315467\pi$
$138$	−4.36211e71	−	2.24376e72i	−0.0765257	−	0.393629i
$139$	3.45318e72			0.473933			0.236966	−	0.971518i	$-0.423847\pi$
$139$	3.45318e72			0.473933			0.236966	+	0.971518i	$0.423847\pi$
$140$		−	9.24009e72i		−	0.993855i
$141$	−4.75519e72	+	9.24462e71i	−0.401530	+	0.0780619i
$142$	5.22429e72			0.346916
$143$			7.19165e72i			0.376186i
$144$	−8.30191e72	+	3.35476e72i	−0.342652	+	0.138464i
$145$	−1.41618e73			−0.461962
$146$		−	2.24483e73i		−	0.579677i
$147$	5.52804e72	+	2.84348e73i	0.113183	+	0.582185i
$148$	6.53828e73			1.06308
$149$		−	1.58359e73i		−	0.204791i	−0.994744	−	0.102395i	$-0.967349\pi$
$149$		−	1.58359e73i		−	0.204791i	0.994744	−	0.102395i	$-0.0326507\pi$
$150$	−1.75638e72	+	3.41459e71i	−0.0180932	+	0.00351751i
$151$	−1.29265e74			−1.06234			−0.531171	−	0.847264i	$-0.678248\pi$
$151$	−1.29265e74			−1.06234			−0.531171	+	0.847264i	$0.678248\pi$
$152$			2.46145e74i			1.61625i
$153$	1.28796e74	+	3.18726e74i	0.676694	+	1.67459i
$154$	−1.07001e74			−0.450489
$155$		−	2.91319e74i		−	0.984217i
$156$	2.72948e73	+	1.40397e74i	0.0741043	+	0.381173i
$157$	−2.91880e74			−0.637700			−0.318850	−	0.947805i	$-0.603297\pi$
$157$	−2.91880e74			−0.637700			−0.318850	+	0.947805i	$0.603297\pi$
$158$			1.90384e74i			0.335188i
$159$	−1.88390e74	+	3.66251e73i	−0.267643	+	0.0520327i
$160$	9.06873e74			1.04104
$161$			1.14280e75i			1.06143i
$162$	−4.40258e74	−	4.55793e74i	−0.331281	−	0.342971i
$163$	2.24726e74			0.137175			0.0685875	−	0.997645i	$-0.478151\pi$
$163$	2.24726e74			0.137175			0.0685875	+	0.997645i	$0.478151\pi$
$164$		−	9.06947e74i		−	0.449667i
$165$	−3.61033e74	−	1.85706e75i	−0.145577	−	0.748811i
$166$	6.14978e74			0.201922
$167$		−	2.27559e75i		−	0.609163i	−0.952486	−	0.304581i	$-0.901483\pi$
$167$		−	2.27559e75i		−	0.609163i	0.952486	−	0.304581i	$-0.0985166\pi$
$168$	−4.79257e75	+	9.31728e74i	−1.04726	+	0.203598i
$169$	−4.18509e75			−0.747407
$170$		−	6.00655e75i		−	0.877731i
$171$	1.48096e76	−	5.98448e75i	1.77286	−	0.716405i
$172$	1.14011e76			1.11938
$173$		−	1.01809e76i		−	0.820766i	−0.911913	−	0.410383i	$-0.865395\pi$
$173$		−	1.01809e76i		−	0.820766i	0.911913	−	0.410383i	$-0.134605\pi$
$174$	6.22419e74	+	3.20156e75i	0.0412485	+	0.212172i
$175$	8.94563e74			0.0487885
$176$			6.15632e75i			0.276624i
$177$	−3.00570e75	+	5.84341e74i	−0.111392	+	0.0216559i
$178$	−2.76969e76			−0.847521
$179$			3.32763e76i			0.841651i	0.907142	+	0.420826i	$0.138260\pi$
$179$			3.32763e76i			0.841651i	−0.907142	+	0.420826i	$0.861740\pi$
$180$	−1.40964e76	−	3.48838e76i	−0.295014	−	0.730061i
$181$	−1.98284e75			−0.0343730			−0.0171865	−	0.999852i	$-0.505471\pi$
$181$	−1.98284e75			−0.0343730			−0.0171865	+	0.999852i	$0.505471\pi$
$182$			2.10441e76i			0.302484i
$183$	−5.58712e75	−	2.87387e76i	−0.0666578	−	0.342871i
$184$	−7.17076e76			−0.710819
$185$			1.70087e77i			1.40227i
$186$	−6.58586e76	+	1.28036e76i	−0.452035	+	0.0878806i
$187$	2.36353e77			1.35190
$188$			6.62383e76i			0.316040i
$189$	1.72579e77	+	2.65697e77i	0.687523	+	1.05849i
$190$	−2.79094e77			−0.929240
$191$			2.68512e77i			0.747875i	0.927454	+	0.373938i	$0.121993\pi$
$191$			2.68512e77i			0.747875i	−0.927454	+	0.373938i	$0.878007\pi$
$192$	−9.61597e75	−	4.94621e76i	−0.0224260	−	0.115353i
$193$	3.07235e77			0.600513			0.300256	−	0.953859i	$-0.402928\pi$
$193$	3.07235e77			0.600513			0.300256	+	0.953859i	$0.402928\pi$
$194$		−	2.02082e77i		−	0.331336i
$195$	−3.65230e77	+	7.10048e76i	−0.502794	+	0.0977487i
$196$	3.96087e77			0.458231
$197$		−	1.66648e78i		−	1.62162i	−0.585312	−	0.810808i	$-0.699028\pi$
$197$		−	1.66648e78i		−	1.62162i	0.585312	−	0.810808i	$-0.300972\pi$
$198$	−4.03959e77	+	1.63238e77i	−0.330918	+	0.133722i
$199$	−9.51089e77			−0.656472			−0.328236	−	0.944596i	$-0.606454\pi$
$199$	−9.51089e77			−0.656472			−0.328236	+	0.944596i	$0.606454\pi$
$200$			5.61316e76i			0.0326729i
$201$	−2.69988e77	−	1.38875e78i	−0.132641	−	0.682272i
$202$	−1.47629e78			−0.612666
$203$		−	1.63063e78i		−	0.572124i
$204$	4.61414e78	−	8.97040e77i	1.36983	−	0.266309i
$205$	2.35934e78			0.593142
$206$			1.72111e77i			0.0366709i
$207$	1.74341e78	+	4.31437e78i	0.315071	+	0.779696i
$208$	1.21077e78			0.185741
$209$		−	1.09821e79i		−	1.43124i
$210$	−1.05645e78	−	5.43410e78i	−0.117056	−	0.602104i
$211$	−3.84824e78			−0.362793			−0.181396	−	0.983410i	$-0.558062\pi$
$211$	−3.84824e78			−0.362793			−0.181396	+	0.983410i	$0.558062\pi$
$212$			2.62421e78i			0.210659i
$213$	−1.04400e79	+	2.02966e78i	−0.714160	+	0.138840i
$214$	−2.78036e78			−0.162193
$215$			2.96588e79i			1.47654i
$216$	−1.66718e79	+	1.08289e79i	−0.708852	+	0.460423i
$217$	3.35433e79			1.21892
$218$			5.63927e78i			0.175268i
$219$	8.72124e78	+	4.48598e79i	0.231995	+	1.19332i
$220$	−2.58683e79			−0.589381
$221$		−	4.64838e79i		−	0.907745i
$222$	3.84517e79	−	7.47543e78i	0.644042	−	0.125209i
$223$	−6.16603e79			−0.886422			−0.443211	−	0.896417i	$-0.646161\pi$
$223$	−6.16603e79			−0.886422			−0.443211	+	0.896417i	$0.646161\pi$
$224$			1.04420e80i			1.28929i
$225$	3.37722e78	−	1.36472e78i	0.0358388	−	0.0144823i
$226$	−2.78398e79			−0.254085
$227$			1.39685e80i			1.09716i	0.836098	+	0.548580i	$0.184831\pi$
$227$			1.39685e80i			1.09716i	−0.836098	+	0.548580i	$0.815169\pi$
$228$	−4.16809e79	−	2.14396e80i	−0.281937	−	1.45021i
$229$	−5.02936e78			−0.0293161			−0.0146581	−	0.999893i	$-0.504666\pi$
$229$	−5.02936e78			−0.0293161			−0.0146581	+	0.999893i	$0.504666\pi$
$230$		−	8.13064e79i		−	0.408675i
$231$	2.13827e80	−	4.15704e79i	0.927376	−	0.180292i
$232$	1.02318e80			0.383142
$233$		−	1.98293e80i		−	0.641513i	−0.947162	−	0.320756i	$-0.896063\pi$
$233$		−	1.98293e80i		−	0.641513i	0.947162	−	0.320756i	$-0.103937\pi$
$234$	3.21041e79	+	7.94470e79i	0.0897888	+	0.222197i
$235$	−1.72313e80			−0.416879
$236$			4.18684e79i			0.0876755i
$237$	−7.39648e79	−	3.80456e80i	−0.134147	−	0.690018i
$238$	6.91611e80			1.08704
$239$		−	1.20451e81i		−	1.64166i	−0.571175	−	0.820828i	$-0.693512\pi$
$239$		−	1.20451e81i		−	1.64166i	0.571175	−	0.820828i	$-0.306488\pi$
$240$	−3.12651e80	+	6.07828e79i	−0.369724	+	0.0718784i
$241$	−8.95909e80			−0.919781			−0.459891	−	0.887976i	$-0.652111\pi$
$241$	−8.95909e80			−0.919781			−0.459891	+	0.887976i	$0.652111\pi$
$242$		−	2.35124e80i		−	0.209688i
$243$	1.05687e81	+	7.39798e80i	0.819237	+	0.573455i
$244$	−4.00321e80			−0.269870
$245$			1.03038e81i			0.604439i
$246$	−1.03694e80	−	5.33376e80i	−0.0529615	−	0.272420i
$247$	−2.15987e81			−0.961016
$248$			2.10476e81i			0.816290i
$249$	−1.22895e81	+	2.38921e80i	−0.415677	+	0.0808122i
$250$	1.58288e81			0.467184
$251$		−	3.98396e80i		−	0.102662i	−0.998682	−	0.0513308i	$-0.983654\pi$
$251$		−	3.98396e80i		−	0.102662i	0.998682	−	0.0513308i	$-0.0163463\pi$
$252$	4.01663e81	−	1.62310e81i	0.904155	−	0.365364i
$253$	3.19934e81			0.629452
$254$			4.44825e81i			0.765319i
$255$	2.33356e81	+	1.20033e82i	0.351280	+	1.80690i
$256$	−4.38525e81			−0.577878
$257$			2.63576e81i			0.304215i	0.988364	+	0.152107i	$0.0486060\pi$
$257$			2.63576e81i			0.304215i	−0.988364	+	0.152107i	$0.951394\pi$
$258$	6.70497e81	−	1.30352e81i	0.678151	−	0.131840i
$259$	−1.95843e82			−1.73667
$260$			5.08754e81i			0.395744i
$261$	−2.48764e81	−	6.15607e81i	−0.169828	−	0.420268i
$262$	−1.12900e82			−0.676782
$263$		−	3.36999e82i		−	1.77473i	−0.461064	−	0.887367i	$-0.652532\pi$
$263$		−	3.36999e82i		−	1.77473i	0.461064	−	0.887367i	$-0.347468\pi$
$264$	2.60843e81	+	1.34171e82i	0.120739	+	0.621049i
$265$	−6.82663e81			−0.277873
$266$		−	3.21357e82i		−	1.15083i
$267$	5.53484e82	−	1.07603e82i	1.74471	−	0.339190i
$268$	−1.93448e82			−0.537009
$269$			5.20464e82i			1.27296i	0.771295	+	0.636478i	$0.219610\pi$
$269$			5.20464e82i			1.27296i	−0.771295	+	0.636478i	$0.780390\pi$
$270$	−1.22785e82	−	1.89035e82i	−0.264714	−	0.407544i
$271$	9.45755e82			1.79814			0.899069	−	0.437808i	$-0.144245\pi$
$271$	9.45755e82			1.79814			0.899069	+	0.437808i	$0.144245\pi$
$272$		−	3.97919e82i		−	0.667500i
$273$	−8.17570e81	−	4.20537e82i	−0.121058	−	0.622693i
$274$	−6.10162e82			−0.797859
$275$		−	2.50439e81i		−	0.0289328i
$276$	6.24584e82	−	1.21426e82i	0.637797	−	0.123995i
$277$	−8.56867e82			−0.773751			−0.386875	−	0.922132i	$-0.626446\pi$
$277$	−8.56867e82			−0.773751			−0.386875	+	0.922132i	$0.626446\pi$
$278$		−	2.82886e82i		−	0.225990i
$279$	1.26635e83	−	5.11726e82i	0.895387	−	0.361822i
$280$	−1.73667e83			−1.08729
$281$			1.23628e83i			0.685651i	0.939399	+	0.342825i	$0.111384\pi$
$281$			1.23628e83i			0.685651i	−0.939399	+	0.342825i	$0.888616\pi$
$282$	7.57323e81	+	3.89548e82i	0.0372230	+	0.191466i
$283$	−3.59308e83			−1.56577			−0.782886	−	0.622165i	$-0.786253\pi$
$283$	−3.59308e83			−1.56577			−0.782886	+	0.622165i	$0.786253\pi$
$284$			1.45426e83i			0.562107i
$285$	5.57731e83	−	1.08429e83i	1.91293	−	0.371895i
$286$	5.89143e82			0.179381
$287$			2.71661e83i			0.734586i
$288$	1.59300e83	+	3.94214e83i	0.382711	+	0.947081i
$289$	−1.05938e84			−2.26217
$290$			1.16014e83i			0.220282i
$291$	7.85095e82	+	4.03832e83i	0.132605	+	0.682087i
$292$	6.24883e83			0.939251
$293$			3.95110e83i			0.528712i	0.964425	+	0.264356i	$0.0851594\pi$
$293$			3.95110e83i			0.528712i	−0.964425	+	0.264356i	$0.914841\pi$
$294$	2.32939e83	−	4.52859e82i	0.277609	−	0.0539702i
$295$	−1.08917e83			−0.115650
$296$		−	1.22887e84i		−	1.16302i
$297$	7.43838e83	−	4.83148e83i	0.627710	−	0.407719i
$298$	−1.29729e83			−0.0976524
$299$		−	6.29218e83i		−	0.422650i
$300$	−9.50503e81	−	4.88914e82i	−0.00569942	−	0.0293164i
$301$	−3.41500e84			−1.82864
$302$			1.05894e84i			0.506567i
$303$	2.95015e84	−	5.73542e83i	1.26123	−	0.245198i
$304$	−1.84893e84			−0.706672
$305$		−	1.04140e84i		−	0.355977i
$306$	2.61102e84	−	1.05510e84i	0.798512	−	0.322675i
$307$	3.34105e84			0.914488			0.457244	−	0.889341i	$-0.348837\pi$
$307$	3.34105e84			0.914488			0.457244	+	0.889341i	$0.348837\pi$
$308$		−	2.97855e84i		−	0.729928i
$309$	−6.68656e82	−	3.43939e83i	−0.0146762	−	0.0754907i
$310$	−2.38650e84			−0.469314
$311$		−	6.98964e84i		−	1.23197i	−0.787756	−	0.615987i	$-0.788757\pi$
$311$		−	6.98964e84i		−	1.23197i	0.787756	−	0.615987i	$-0.211243\pi$
$312$	2.63876e84	−	5.13004e83i	0.417007	−	0.0810708i
$313$	−7.83413e84			−1.11041			−0.555205	−	0.831713i	$-0.687360\pi$
$313$	−7.83413e84			−1.11041			−0.555205	+	0.831713i	$0.687360\pi$
$314$			2.39110e84i			0.304081i
$315$	4.22233e84	+	1.04489e85i	0.481941	+	1.19264i
$316$	−5.29963e84			−0.543106
$317$		−	3.41876e84i		−	0.314668i	−0.987545	−	0.157334i	$-0.949710\pi$
$317$		−	3.41876e84i		−	0.314668i	0.987545	−	0.157334i	$-0.0502900\pi$
$318$	3.00034e83	+	1.54330e84i	0.0248113	+	0.127623i
$319$	−4.56506e84			−0.339284
$320$		−	1.79234e84i		−	0.119763i
$321$	5.55616e84	−	1.08018e84i	0.333890	−	0.0649119i
$322$	9.36185e84			0.506130
$323$			7.09838e85i			3.45361i
$324$	1.26877e85	−	1.22553e85i	0.555716	−	0.536775i
$325$	−4.92541e83			−0.0194271
$326$		−	1.84097e84i		−	0.0654105i
$327$	−2.19088e84	−	1.12693e85i	−0.0701446	−	0.360806i
$328$	−1.70460e85			−0.491940
$329$		−	1.98406e85i		−	0.516290i
$330$	−1.52131e85	+	2.95760e84i	−0.357063	+	0.0694169i
$331$	1.16427e85			0.246549			0.123274	−	0.992373i	$-0.460660\pi$
$331$	1.16427e85			0.246549			0.123274	+	0.992373i	$0.460660\pi$
$332$			1.71189e85i			0.327175i
$333$	−7.39362e85	+	2.98772e85i	−1.27571	+	0.515509i
$334$	−1.86417e85			−0.290473
$335$		−	5.03237e85i		−	0.708351i
$336$	−6.99870e84	−	3.59995e85i	−0.0890189	−	0.457890i
$337$	2.76940e85			0.318397			0.159199	−	0.987247i	$-0.449109\pi$
$337$	2.76940e85			0.318397			0.159199	+	0.987247i	$0.449109\pi$
$338$			3.42845e85i			0.356394i
$339$	5.56341e85	−	1.08159e85i	0.523060	−	0.101688i
$340$	1.67201e86			1.42219
$341$		−	9.39068e85i		−	0.722850i
$342$	−4.90252e85	−	1.21321e86i	−0.341611	−	0.845372i
$343$	8.13999e85			0.513598
$344$		−	2.14282e86i		−	1.22461i
$345$	3.15878e85	+	1.62480e86i	0.163557	+	0.841298i
$346$	−8.34026e85			−0.391374
$347$		−	6.68082e85i		−	0.284202i	−0.989852	−	0.142101i	$-0.954614\pi$
$347$		−	6.68082e85i		−	0.284202i	0.989852	−	0.142101i	$-0.0453859\pi$
$348$	−8.91204e85	+	1.73260e85i	−0.343782	+	0.0668350i
$349$	5.59528e85			0.195775			0.0978875	−	0.995197i	$-0.468791\pi$
$349$	5.59528e85			0.195775			0.0978875	+	0.995197i	$0.468791\pi$
$350$		−	7.32831e84i		−	0.0232643i
$351$	−9.50212e85	−	1.46291e86i	−0.273765	−	0.421480i
$352$	2.92331e86			0.764582
$353$			6.91304e86i			1.64183i	0.571048	+	0.820916i	$0.306537\pi$
$353$			6.91304e86i			1.64183i	−0.571048	+	0.820916i	$0.693463\pi$
$354$	4.78695e84	+	2.46228e85i	0.0103264	+	0.0531162i
$355$	−3.78313e86			−0.741458
$356$		−	7.70985e86i		−	1.37324i
$357$	−1.38209e87	+	2.68693e86i	−2.23778	+	0.435048i
$358$	2.72601e86			0.401333
$359$			6.95174e86i			0.930856i	0.885086	+	0.465428i	$0.154100\pi$
$359$			6.95174e86i			0.930856i	−0.885086	+	0.465428i	$0.845900\pi$
$360$	−6.55640e86	+	2.64941e86i	−0.798694	+	0.322748i
$361$	2.39618e87			2.65628
$362$			1.62436e85i			0.0163904i
$363$	9.13465e85	+	4.69863e86i	0.0839202	+	0.431664i
$364$	−5.85794e86			−0.490115
$365$			1.62557e87i			1.23894i
$366$	−2.35429e86	+	4.57700e85i	−0.163494	+	0.0317851i
$367$	8.66835e86			0.548644			0.274322	−	0.961638i	$-0.411547\pi$
$367$	8.66835e86			0.548644			0.274322	+	0.961638i	$0.411547\pi$
$368$		−	5.38634e86i		−	0.310791i
$369$	4.14437e86	+	1.02559e87i	0.218053	+	0.539608i
$370$	1.39336e87			0.668660
$371$		−	7.86038e86i		−	0.344137i
$372$	−3.56409e86	−	1.83327e87i	−0.142393	−	0.732432i
$373$	−3.64379e87			−1.32878			−0.664390	−	0.747386i	$-0.731309\pi$
$373$	−3.64379e87			−1.32878			−0.664390	+	0.747386i	$0.731309\pi$
$374$		−	1.93621e87i		−	0.644642i
$375$	−3.16317e87	+	6.14955e86i	−0.961743	+	0.186973i
$376$	1.24495e87			0.345751
$377$			8.97816e86i			0.227815i
$378$	2.17660e87	−	1.41378e87i	0.504729	−	0.327839i
$379$	8.23520e85			0.0174558			0.00872792	−	0.999962i	$-0.497222\pi$
$379$	8.23520e85			0.0174558			0.00872792	+	0.999962i	$0.497222\pi$
$380$		−	7.76901e87i		−	1.50565i
$381$	−1.72816e87	−	8.88921e87i	−0.306291	−	1.57548i
$382$	2.19966e87			0.356617
$383$			8.82152e87i			1.30853i	0.756263	+	0.654267i	$0.227023\pi$
$383$			8.82152e87i			1.30853i	−0.756263	+	0.654267i	$0.772977\pi$
$384$	6.98128e87	−	1.35724e87i	0.947706	−	0.184244i
$385$	7.74840e87			0.962825
$386$		−	2.51688e87i		−	0.286348i
$387$	−1.28925e88	+	5.20981e87i	−1.34328	+	0.542811i
$388$	5.62526e87			0.536863
$389$			1.06148e88i			0.928164i	0.885792	+	0.464082i	$0.153616\pi$
$389$			1.06148e88i			0.928164i	−0.885792	+	0.464082i	$0.846384\pi$
$390$	5.81675e86	+	2.99198e87i	0.0466105	+	0.239752i
$391$	−2.06792e88			−1.51888
$392$		−	7.44444e87i		−	0.501309i
$393$	2.25614e88	−	4.38619e87i	1.39322	−	0.270857i
$394$	−1.36519e88			−0.773251
$395$		−	1.37865e88i		−	0.716394i
$396$	−4.54397e87	−	1.12448e88i	−0.216670	−	0.536187i
$397$	6.35762e87			0.278239			0.139119	−	0.990276i	$-0.455573\pi$
$397$	6.35762e87			0.278239			0.139119	+	0.990276i	$0.455573\pi$
$398$			7.79136e87i			0.313032i
$399$	1.24848e88	+	6.42188e88i	0.460579	+	2.36910i
$400$	−4.21634e86			−0.0142855
$401$			4.52104e88i			1.40712i	0.710638	+	0.703558i	$0.248407\pi$
$401$			4.52104e88i			1.40712i	−0.710638	+	0.703558i	$0.751593\pi$
$402$	−1.13767e88	+	2.21175e87i	−0.325334	+	0.0632486i
$403$	−1.84688e88			−0.485362
$404$		−	4.10947e88i		−	0.992703i
$405$	3.18809e88	+	3.30058e88i	0.708043	+	0.733027i
$406$	−1.33582e88			−0.272812
$407$			5.48277e88i			1.02989i
$408$	−1.68598e88	−	8.67226e88i	−0.291345	−	1.49860i
$409$	−8.73035e88			−1.38816			−0.694079	−	0.719899i	$-0.744188\pi$
$409$	−8.73035e88			−1.38816			−0.694079	+	0.719899i	$0.744188\pi$
$410$		−	1.93278e88i		−	0.282834i
$411$	1.21933e89	−	2.37050e88i	1.64247	−	0.319314i
$412$	−4.79096e87			−0.0594179
$413$		−	1.25410e88i		−	0.143229i
$414$	3.53435e88	−	1.42821e88i	0.371790	−	0.150239i
$415$	−4.45331e88			−0.431566
$416$		−	5.74930e88i		−	0.513384i
$417$	1.09902e88	+	5.65310e88i	0.0904443	+	0.465222i
$418$	−8.99660e88			−0.682472
$419$		−	2.09439e89i		−	1.46481i	−0.680871	−	0.732403i	$-0.738399\pi$
$419$		−	2.09439e89i		−	1.46481i	0.680871	−	0.732403i	$-0.261601\pi$
$420$	1.51267e89	−	2.94079e88i	0.975589	−	0.189665i
$421$	1.66583e88			0.0990920			0.0495460	−	0.998772i	$-0.484223\pi$
$421$	1.66583e88			0.0990920			0.0495460	+	0.998772i	$0.484223\pi$
$422$			3.15250e88i			0.172994i
$423$	−3.02681e88	−	7.49035e88i	−0.153254	−	0.379254i
$424$	4.93219e88			0.230463
$425$			1.61873e88i			0.0698154i
$426$	1.66270e88	+	8.55252e88i	0.0662047	+	0.340540i
$427$	1.19909e89			0.440865
$428$		−	7.73955e88i		−	0.262801i
$429$	−1.17732e89	+	2.28884e88i	−0.369273	+	0.0717906i
$430$	2.42966e89			0.704073
$431$			3.39501e89i			0.909104i	0.890720	+	0.454552i	$0.150201\pi$
$431$			3.39501e89i			0.909104i	−0.890720	+	0.454552i	$0.849799\pi$
$432$	−8.13417e88	−	1.25231e89i	−0.201310	−	0.309931i
$433$	−5.61075e89			−1.28361			−0.641805	−	0.766868i	$-0.721814\pi$
$433$	−5.61075e89			−1.28361			−0.641805	+	0.766868i	$0.721814\pi$
$434$		−	2.74788e89i		−	0.581229i
$435$	−4.50719e88	−	2.31838e89i	−0.0881599	−	0.453472i
$436$	−1.56978e89			−0.283986
$437$			9.60857e89i			1.60801i
$438$	3.67494e89	−	7.14448e88i	0.569023	−	0.110624i
$439$	−5.04687e89			−0.723150			−0.361575	−	0.932343i	$-0.617761\pi$
$439$	−5.04687e89			−0.723150			−0.361575	+	0.932343i	$0.617761\pi$
$440$			4.86192e89i			0.644788i
$441$	−4.47903e89	+	1.80995e89i	−0.549885	+	0.222206i
$442$	−3.80797e89			−0.432849
$443$			1.83604e89i			0.193266i	0.995320	+	0.0966328i	$0.0308073\pi$
$443$			1.83604e89i			0.193266i	−0.995320	+	0.0966328i	$0.969193\pi$
$444$	2.08090e89	+	1.07036e90i	0.202876	+	1.04354i
$445$	2.00564e90			1.81140
$446$			5.05124e89i			0.422681i
$447$	2.59245e89	−	5.04000e88i	0.201027	−	0.0390818i
$448$	2.06376e89			0.148322
$449$		−	1.00220e90i		−	0.667697i	−0.942627	−	0.333848i	$-0.891653\pi$
$449$		−	1.00220e90i		−	0.667697i	0.942627	−	0.333848i	$-0.108347\pi$
$450$	−1.11798e88	−	2.76663e88i	−0.00690573	−	0.0170894i
$451$	7.60533e89			0.435628
$452$		−	7.74965e89i		−	0.411694i
$453$	−4.11404e89	−	2.11616e90i	−0.202735	−	1.04282i
$454$	1.14430e90			0.523169
$455$		−	1.52389e90i		−	0.646495i
$456$	−4.02956e90	+	7.83391e89i	−1.58655	+	0.308442i
$457$	−1.02726e90			−0.375431			−0.187716	−	0.982223i	$-0.560108\pi$
$457$	−1.02726e90			−0.375431			−0.187716	+	0.982223i	$0.560108\pi$
$458$			4.12008e88i			0.0139791i
$459$	−4.80785e90	+	3.12286e90i	−1.51468	+	0.983833i
$460$	2.26329e90			0.662176
$461$		−	6.74220e90i		−	1.83219i	−0.400964	−	0.916094i	$-0.631325\pi$
$461$		−	6.74220e90i		−	1.83219i	0.400964	−	0.916094i	$-0.368675\pi$
$462$	−3.40547e89	−	1.75168e90i	−0.0859705	−	0.442210i
$463$	5.15318e90			1.20871			0.604354	−	0.796716i	$-0.293431\pi$
$463$	5.15318e90			1.20871			0.604354	+	0.796716i	$0.293431\pi$
$464$			7.68564e89i			0.167521i
$465$	4.76909e90	−	9.27163e89i	0.966129	−	0.187826i
$466$	−1.62442e90			−0.305899
$467$		−	2.09529e90i		−	0.366834i	−0.983035	−	0.183417i	$-0.941284\pi$
$467$		−	2.09529e90i		−	0.366834i	0.983035	−	0.183417i	$-0.0587159\pi$
$468$	−2.21153e90	+	8.93668e89i	−0.360026	+	0.145485i
$469$	5.79441e90			0.877269
$470$			1.41159e90i			0.198784i
$471$	−9.28950e89	−	4.77828e90i	−0.121697	−	0.625980i
$472$	7.86914e89			0.0959179
$473$			9.56051e90i			1.08443i
$474$	−3.11671e90	+	6.05923e89i	−0.329028	+	0.0639667i
$475$	7.52143e89			0.0739125
$476$			1.92521e91i			1.76133i
$477$	−1.19915e90	−	2.96751e90i	−0.102153	−	0.252794i
$478$	−9.86742e90			−0.782807
$479$		−	1.65410e91i		−	1.22224i	−0.791540	−	0.611118i	$-0.790720\pi$
$479$		−	1.65410e91i		−	1.22224i	0.791540	−	0.611118i	$-0.209280\pi$
$480$	2.88625e90	+	1.48461e91i	0.198670	+	1.02191i
$481$	1.07830e91			0.691525
$482$			7.33933e90i			0.438588i
$483$	−1.87084e91	+	3.63711e90i	−1.04192	+	0.202560i
$484$	6.54504e90			0.339758
$485$			1.46336e91i			0.708159i
$486$	6.06046e90	−	8.65795e90i	0.273446	−	0.390645i
$487$	−3.95444e91			−1.66380			−0.831898	−	0.554928i	$-0.812746\pi$
$487$	−3.95444e91			−1.66380			−0.831898	+	0.554928i	$0.812746\pi$
$488$			7.52401e90i			0.295240i
$489$	7.15222e89	+	3.67892e90i	0.0261782	+	0.134654i
$490$	8.44095e90			0.288220
$491$		−	2.99751e91i		−	0.954971i	−0.878640	−	0.477485i	$-0.841548\pi$
$491$		−	2.99751e91i		−	0.954971i	0.878640	−	0.477485i	$-0.158452\pi$
$492$	1.48473e91	−	2.88649e90i	0.441403	−	0.0858135i
$493$	2.95066e91			0.818699
$494$			1.76937e91i			0.458251i
$495$	2.92523e91	−	1.18207e91i	0.707267	−	0.285803i
$496$	−1.58100e91			−0.356906
$497$		−	4.35600e91i		−	0.918271i
$498$	1.95725e90	+	1.00676e91i	0.0385345	+	0.198211i
$499$	−4.35825e91			−0.801482			−0.400741	−	0.916191i	$-0.631247\pi$
$499$	−4.35825e91			−0.801482			−0.400741	+	0.916191i	$0.631247\pi$
$500$			4.40619e91i			0.756978i
$501$	3.72529e91	−	7.24237e90i	0.597967	−	0.116251i
$502$	−3.26368e90			−0.0489532
$503$		−	5.94450e91i		−	0.833304i	−0.909066	−	0.416652i	$-0.863203\pi$
$503$		−	5.94450e91i		−	0.833304i	0.909066	−	0.416652i	$-0.136797\pi$
$504$	−3.05060e91	−	7.54922e91i	−0.399712	−	0.989154i
$505$	1.06904e92			1.30944
$506$		−	2.62091e91i		−	0.300148i
$507$	−1.33196e91	−	6.85128e91i	−0.142634	−	0.733671i
$508$	−1.23824e92			−1.24005
$509$		−	1.20619e91i		−	0.112983i	−0.998403	−	0.0564915i	$-0.982009\pi$
$509$		−	1.20619e91i		−	0.112983i	0.998403	−	0.0564915i	$-0.0179914\pi$
$510$	9.83313e91	−	1.91167e91i	0.861600	−	0.167504i
$511$	−1.87173e92			−1.53438
$512$		−	8.99417e91i		−	0.689894i
$513$	1.45104e92	+	2.23397e92i	1.04157	+	1.60356i
$514$	2.15923e91			0.145062
$515$		−	1.24632e91i		−	0.0783763i
$516$	3.62855e91	+	1.86643e92i	0.213620	+	1.09881i
$517$	−5.55450e91			−0.306173
$518$			1.60436e92i			0.828113i
$519$	1.66669e92	−	3.24022e91i	0.805682	−	0.156633i
$520$	9.56200e91			0.432947
$521$			1.07695e92i			0.456784i	0.973569	+	0.228392i	$0.0733468\pi$
$521$			1.07695e92i			0.456784i	−0.973569	+	0.228392i	$0.926653\pi$
$522$	−5.04308e91	+	2.03788e91i	−0.200401	+	0.0809809i
$523$	−4.83393e92			−1.79988			−0.899939	−	0.436016i	$-0.856389\pi$
$523$	−4.83393e92			−1.79988			−0.899939	+	0.436016i	$0.856389\pi$
$524$		−	3.14274e92i		−	1.09659i
$525$	2.84707e90	+	1.46446e91i	0.00931070	+	0.0478918i
$526$	−2.76071e92			−0.846264
$527$			6.06974e92i			1.74425i
$528$	−1.00783e92	+	1.95933e91i	−0.271540	+	0.0527904i
$529$	1.15896e92			0.292803
$530$			5.59241e91i			0.132501i
$531$	−1.91321e91	−	4.73456e91i	−0.0425157	−	0.105212i
$532$	8.94546e92			1.86469
$533$		−	1.49575e92i		−	0.292505i
$534$	−8.81492e91	−	4.53417e92i	−0.161739	−	0.831945i
$535$	2.01337e92			0.346653
$536$			3.63584e92i			0.587493i
$537$	−5.44756e92	+	1.05907e92i	−0.826183	+	0.160619i
$538$	4.26367e92			0.606996
$539$			3.32145e92i			0.443924i
$540$	5.26208e92	−	3.41790e92i	0.660344	−	0.428915i
$541$	1.54063e92			0.181548			0.0907741	−	0.995872i	$-0.471066\pi$
$541$	1.54063e92			0.181548			0.0907741	+	0.995872i	$0.471066\pi$
$542$		−	7.74767e92i		−	0.857424i
$543$	−6.31068e90	−	3.24605e91i	−0.00655967	−	0.0337413i
$544$	−1.88950e93			−1.84495
$545$		−	4.08363e92i		−	0.374598i
$546$	−3.44506e92	+	6.69757e91i	−0.296925	+	0.0577254i
$547$	5.71786e92			0.463089			0.231544	−	0.972824i	$-0.425622\pi$
$547$	5.71786e92			0.463089			0.231544	+	0.972824i	$0.425622\pi$
$548$		−	1.69848e93i		−	1.29277i
$549$	4.52691e92	−	1.82930e92i	0.323849	−	0.130866i
$550$	−2.05161e91			−0.0137963
$551$		−	1.37102e93i		−	0.866744i
$552$	−2.28219e92	−	1.17390e93i	−0.135651	−	0.697756i
$553$	1.58741e93			0.887229
$554$			7.01949e92i			0.368955i
$555$	−2.78444e93	+	5.41326e92i	−1.37650	+	0.267607i
$556$	7.87458e92			0.366172
$557$			4.03173e93i			1.76366i	0.471568	+	0.881829i	$0.343688\pi$
$557$			4.03173e93i			1.76366i	−0.471568	+	0.881829i	$0.656312\pi$
$558$	−4.19208e92	−	1.03740e93i	−0.172531	−	0.426956i
$559$	1.88028e93			0.728149
$560$		−	1.30451e93i		−	0.475393i
$561$	7.52225e92	+	3.86925e93i	0.257995	+	1.32706i
$562$	1.01277e93			0.326946
$563$			6.67962e92i			0.202986i	0.994836	+	0.101493i	$0.0323620\pi$
$563$			6.67962e92i			0.202986i	−0.994836	+	0.101493i	$0.967638\pi$
$564$	−1.08437e93	+	2.10813e92i	−0.310232	+	0.0603125i
$565$	2.01600e93			0.543053
$566$			2.94347e93i			0.746623i
$567$	−3.80039e93	+	3.67086e93i	−0.907829	+	0.876887i
$568$	2.73328e93			0.614951
$569$		−	2.51900e93i		−	0.533840i	−0.963719	−	0.266920i	$-0.913994\pi$
$569$		−	2.51900e93i		−	0.533840i	0.963719	−	0.266920i	$-0.0860059\pi$
$570$	−8.88256e92	−	4.56896e93i	−0.177334	−	0.912162i
$571$	−1.07467e93			−0.202138			−0.101069	−	0.994879i	$-0.532226\pi$
$571$	−1.07467e93			−0.202138			−0.101069	+	0.994879i	$0.532226\pi$
$572$			1.63997e93i			0.290650i
$573$	−4.39572e93	+	8.54577e92i	−0.734131	+	0.142723i
$574$	2.22546e93			0.350280
$575$			2.19116e92i			0.0325063i
$576$	7.79124e92	−	3.14840e92i	0.108954	−	0.0440277i
$577$	−8.20977e93			−1.08231			−0.541157	−	0.840922i	$-0.682013\pi$
$577$	−8.20977e93			−1.08231			−0.541157	+	0.840922i	$0.682013\pi$
$578$			8.67850e93i			1.07869i
$579$	9.77819e92	+	5.02965e93i	0.114601	+	0.589476i
$580$	−3.22943e93			−0.356923
$581$		−	5.12767e93i		−	0.534480i
$582$	3.30821e93	−	6.43153e92i	0.325246	−	0.0632314i
$583$	−2.20057e93			−0.204082
$584$		−	1.17446e94i		−	1.02755i
$585$	−2.32479e93	−	5.75309e93i	−0.191904	−	0.474899i
$586$	3.23676e93			0.252111
$587$		−	1.94848e94i		−	1.43219i	−0.698004	−	0.716094i	$-0.745928\pi$
$587$		−	1.94848e94i		−	1.43219i	0.698004	−	0.716094i	$-0.254072\pi$
$588$	1.26060e93	+	6.48422e93i	0.0874479	+	0.449810i
$589$	2.82030e94			1.84661
$590$			8.92251e92i			0.0551466i
$591$	2.72814e94	−	5.30380e93i	1.59181	−	0.309466i
$592$	9.23068e93			0.508505
$593$			1.63246e94i			0.849145i	0.905394	+	0.424573i	$0.139576\pi$
$593$			1.63246e94i			0.849145i	−0.905394	+	0.424573i	$0.860424\pi$
$594$	−3.95797e93	−	6.09355e93i	−0.194416	−	0.299317i
$595$	−5.00824e94			−2.32332
$596$		−	3.61120e93i		−	0.158226i
$597$	−3.02697e93	−	1.55700e94i	−0.125280	−	0.644407i
$598$	−5.15458e93			−0.201536
$599$		−	3.03043e94i		−	1.11942i	−0.828689	−	0.559709i	$-0.810913\pi$
$599$		−	3.03043e94i		−	1.11942i	0.828689	−	0.559709i	$-0.189087\pi$
$600$	−9.18912e92	+	1.78646e92i	−0.0320724	+	0.00623522i
$601$	−9.84996e93			−0.324865			−0.162432	−	0.986720i	$-0.551934\pi$
$601$	−9.84996e93			−0.324865			−0.162432	+	0.986720i	$0.551934\pi$
$602$			2.79758e94i			0.871971i
$603$	2.18755e94	−	8.83977e93i	0.644420	−	0.260407i
$604$	−2.94774e94			−0.820791
$605$			1.70263e94i			0.448165i
$606$	−4.69849e93	−	2.41678e94i	−0.116920	−	0.601406i
$607$	−1.22552e94			−0.288340			−0.144170	−	0.989553i	$-0.546051\pi$
$607$	−1.22552e94			−0.288340			−0.144170	+	0.989553i	$0.546051\pi$
$608$			8.77957e94i			1.95322i
$609$	2.66945e94	−	5.18971e93i	0.561609	−	0.109183i
$610$	−8.53118e93			−0.169744
$611$			1.09241e94i			0.205582i
$612$	2.93703e94	+	7.26817e94i	0.522830	+	1.29383i
$613$	2.77461e94			0.467246			0.233623	−	0.972327i	$-0.424942\pi$
$613$	2.77461e94			0.467246			0.233623	+	0.972327i	$0.424942\pi$
$614$		−	2.73700e94i		−	0.436064i
$615$	7.50892e93	+	3.86239e94i	0.113194	+	0.582241i
$616$	−5.59816e94			−0.798548
$617$		−	8.76735e94i		−	1.18351i	−0.806117	−	0.591756i	$-0.798435\pi$
$617$		−	8.76735e94i		−	1.18351i	0.806117	−	0.591756i	$-0.201565\pi$
$618$	−2.81757e93	+	5.47766e92i	−0.0359970	+	0.00699821i
$619$	9.12032e94			1.10288			0.551440	−	0.834215i	$-0.314079\pi$
$619$	9.12032e94			1.10288			0.551440	+	0.834215i	$0.314079\pi$
$620$		−	6.64319e94i		−	0.760430i
$621$	−6.50805e94	+	4.22720e94i	−0.705239	+	0.458077i
$622$	−5.72595e94			−0.587454
$623$			2.30936e95i			2.24335i
$624$	3.85345e93	+	1.98211e94i	0.0354465	+	0.182328i
$625$	−1.19060e95			−1.03716
$626$			6.41776e94i			0.529488i
$627$	1.79785e95	−	3.49521e94i	1.40494	−	0.273135i
$628$	−6.65599e94			−0.492702
$629$		−	3.54383e95i		−	2.48514i
$630$	8.55976e94	−	3.45896e94i	0.568700	−	0.229809i
$631$	3.92999e94			0.247396			0.123698	−	0.992320i	$-0.460525\pi$
$631$	3.92999e94			0.247396			0.123698	+	0.992320i	$0.460525\pi$
$632$			9.96062e94i			0.594163i
$633$	−1.22476e94	−	6.29983e94i	−0.0692347	−	0.356125i
$634$	−2.80066e94			−0.150046
$635$		−	3.22116e95i		−	1.63571i
$636$	−4.29601e94	+	8.35192e93i	−0.206787	+	0.0402017i
$637$	6.53233e94			0.298076
$638$			3.73972e94i			0.161784i
$639$	−6.64537e94	−	1.64451e95i	−0.272578	−	0.674539i
$640$	2.52979e95			0.983931
$641$			8.20363e94i			0.302575i	0.988490	+	0.151288i	$0.0483419\pi$
$641$			8.20363e94i			0.302575i	−0.988490	+	0.151288i	$0.951658\pi$
$642$	−8.84887e93	−	4.55163e94i	−0.0309526	−	0.159212i
$643$	−2.10538e95			−0.698486			−0.349243	−	0.937032i	$-0.613561\pi$
$643$	−2.10538e95			−0.698486			−0.349243	+	0.937032i	$0.613561\pi$
$644$			2.60602e95i			0.820082i
$645$	−4.85534e95	+	9.43931e94i	−1.44940	+	0.281780i
$646$	5.81502e95			1.64682
$647$		−	2.27494e95i		−	0.611259i	−0.952151	−	0.305629i	$-0.901133\pi$
$647$		−	2.27494e95i		−	0.611259i	0.952151	−	0.305629i	$-0.0988668\pi$
$648$	−2.30337e95	−	2.38465e95i	−0.587237	−	0.607958i
$649$	−3.51093e94			−0.0849382
$650$			4.03492e93i			0.00926363i
$651$	1.06756e95	+	5.49127e95i	0.232616	+	1.19652i
$652$	5.12461e94			0.105985
$653$		−	2.30439e95i		−	0.452385i	−0.974083	−	0.226192i	$-0.927372\pi$
$653$		−	2.30439e95i		−	0.452385i	0.974083	−	0.226192i	$-0.0726278\pi$
$654$	−9.23187e94	+	1.79478e94i	−0.172047	+	0.0334478i
$655$	8.17553e95			1.44648
$656$		−	1.28042e95i		−	0.215090i
$657$	−7.06629e95	+	2.85545e95i	−1.12712	+	0.455462i
$658$	−1.62535e95			−0.246188
$659$			1.04580e96i			1.50433i	0.658976	+	0.752164i	$0.270990\pi$
$659$			1.04580e96i			1.50433i	−0.658976	+	0.752164i	$0.729010\pi$
$660$	−8.23293e94	−	4.23481e95i	−0.112476	−	0.578549i
$661$	−7.64921e95			−0.992584			−0.496292	−	0.868156i	$-0.665305\pi$
$661$	−7.64921e95			−0.992584			−0.496292	+	0.868156i	$0.665305\pi$
$662$		−	9.53778e94i		−	0.117564i
$663$	7.60971e95	−	1.47941e95i	0.891062	−	0.173232i
$664$	3.21748e95			0.357933
$665$			2.32708e96i			2.45966i
$666$	2.44756e95	+	6.05689e95i	0.245815	+	0.608311i
$667$	3.99410e95			0.381189
$668$		−	5.18921e95i		−	0.470654i
$669$	−1.96243e95	−	1.00942e96i	−0.169163	−	0.870131i
$670$	−4.12254e95			−0.337770
$671$		−	3.35695e95i		−	0.261444i
$672$	−1.70943e96	+	3.32331e95i	−1.26560	+	0.246046i
$673$	1.96971e96			1.38641			0.693203	−	0.720743i	$-0.256199\pi$
$673$	1.96971e96			1.38641			0.693203	+	0.720743i	$0.256199\pi$
$674$		−	2.26871e95i		−	0.151824i
$675$	3.30898e94	+	5.09440e94i	0.0210555	+	0.0324164i
$676$	−9.54362e95			−0.577465
$677$		−	8.09429e95i		−	0.465762i	−0.972505	−	0.232881i	$-0.925185\pi$
$677$		−	8.09429e95i		−	0.465762i	0.972505	−	0.232881i	$-0.0748153\pi$
$678$	−8.86041e94	−	4.55757e95i	−0.0484891	−	0.249416i
$679$	−1.68495e96			−0.877031
$680$		−	3.14254e96i		−	1.55589i
$681$	−2.28673e96	+	4.44566e95i	−1.07700	+	0.209380i
$682$	−7.69289e95			−0.344684
$683$		−	1.60948e95i		−	0.0686090i	−0.999411	−	0.0343045i	$-0.989078\pi$
$683$		−	1.60948e95i		−	0.0686090i	0.999411	−	0.0343045i	$-0.0109216\pi$
$684$	3.37715e96	−	1.36469e96i	1.36976	−	0.553512i
$685$	4.41844e96			1.70525
$686$		−	6.66832e95i		−	0.244904i
$687$	−1.60066e94	−	8.23341e94i	−0.00559463	−	0.0287773i
$688$	1.60959e96			0.535436
$689$			4.32788e95i			0.137032i
$690$	1.33104e96	−	2.58769e95i	0.401164	−	0.0779907i
$691$	−6.37742e95			−0.182975			−0.0914874	−	0.995806i	$-0.529162\pi$
$691$	−6.37742e95			−0.182975			−0.0914874	+	0.995806i	$0.529162\pi$
$692$		−	2.32164e96i		−	0.634144i
$693$	1.36107e96	+	3.36820e96i	0.353957	+	0.875926i
$694$	−5.47296e95			−0.135519
$695$			2.04850e96i			0.483005i
$696$	3.25641e95	+	1.67501e96i	0.0731181	+	0.376101i
$697$	−4.91576e96			−1.05118
$698$		−	4.58368e95i		−	0.0933533i
$699$	3.24619e96	−	6.31094e95i	0.629723	−	0.122425i
$700$	2.03995e95			0.0376952
$701$		−	4.51130e96i		−	0.794126i	−0.917791	−	0.397063i	$-0.870030\pi$
$701$		−	4.51130e96i		−	0.794126i	0.917791	−	0.397063i	$-0.129970\pi$
$702$	−1.19843e96	+	7.78418e95i	−0.200978	+	0.130542i
$703$	−1.64664e97			−2.63098
$704$		−	5.77763e95i		−	0.0879588i
$705$	−5.48409e95	−	2.82088e96i	−0.0795563	−	0.409217i
$706$	5.66319e96			0.782891
$707$			1.23092e97i			1.62170i
$708$	−6.85415e95	+	1.33252e95i	−0.0860642	+	0.0167318i
$709$	6.05199e96			0.724313			0.362156	−	0.932117i	$-0.382041\pi$
$709$	6.05199e96			0.724313			0.362156	+	0.932117i	$0.382041\pi$
$710$			3.09915e96i			0.353557i
$711$	5.99292e96	−	2.42171e96i	0.651736	−	0.263363i
$712$	−1.44906e97			−1.50234
$713$			8.21617e96i			0.812130i
$714$	2.20115e96	+	1.13221e97i	0.207448	+	1.06706i
$715$	−4.26623e96			−0.383388
$716$			7.58827e96i			0.650280i
$717$	1.97187e97	−	3.83353e96i	1.61149	−	0.313290i
$718$	5.69490e96			0.443869
$719$			9.41989e96i			0.700266i	0.936700	+	0.350133i	$0.113864\pi$
$719$			9.41989e96i			0.700266i	−0.936700	+	0.350133i	$0.886136\pi$
$720$	−1.99011e96	−	4.92486e96i	−0.141115	−	0.349212i
$721$	1.43505e96			0.0970664
$722$		−	1.96296e97i		−	1.26662i
$723$	−2.85136e96	−	1.46666e97i	−0.175529	−	0.902877i
$724$	−4.52165e95			−0.0265574
$725$		−	3.12652e95i		−	0.0175214i
$726$	3.84914e96	−	7.48315e95i	0.205835	−	0.0400165i
$727$	−1.51113e97			−0.771135			−0.385568	−	0.922680i	$-0.625994\pi$
$727$	−1.51113e97			−0.771135			−0.385568	+	0.922680i	$0.625994\pi$
$728$			1.10100e97i			0.536190i
$729$	−8.74735e96	+	1.96562e97i	−0.406575	+	0.913617i
$730$	1.33168e97			0.590774
$731$		−	6.17951e97i		−	2.61676i
$732$	−1.27408e96	−	6.55353e96i	−0.0515014	−	0.264910i
$733$	2.26903e97			0.875600			0.437800	−	0.899072i	$-0.355758\pi$
$733$	2.26903e97			0.875600			0.437800	+	0.899072i	$0.355758\pi$
$734$		−	7.10115e96i		−	0.261615i
$735$	−1.68681e97	+	3.27934e96i	−0.593330	+	0.115350i
$736$	−2.55769e97			−0.859017
$737$		−	1.62218e97i		−	0.520242i
$738$	8.40170e96	−	3.39509e96i	0.257307	−	0.103976i
$739$	1.52107e97			0.444875			0.222438	−	0.974947i	$-0.428599\pi$
$739$	1.52107e97			0.444875			0.222438	+	0.974947i	$0.428599\pi$
$740$			3.87864e97i			1.08343i
$741$	−6.87408e96	−	3.53585e97i	−0.183398	−	0.943354i
$742$	−6.43926e96			−0.164098
$743$		−	4.82235e96i		−	0.117392i	−0.998276	−	0.0586960i	$-0.981306\pi$
$743$		−	4.82235e96i		−	0.117392i	0.998276	−	0.0586960i	$-0.0186943\pi$
$744$	−3.44563e97	+	6.69868e96i	−0.801288	+	0.155779i
$745$	9.39418e96			0.208711
$746$			2.98501e97i			0.633616i
$747$	−7.82261e96	−	1.93583e97i	−0.158654	−	0.392616i
$748$	5.38975e97			1.04451
$749$			2.31825e97i			0.429318i
$750$	5.03774e96	+	2.59128e97i	0.0891564	+	0.458598i
$751$	5.21049e97			0.881294			0.440647	−	0.897681i	$-0.354749\pi$
$751$	5.21049e97			0.881294			0.440647	+	0.897681i	$0.354749\pi$
$752$			9.35145e96i			0.151172i
$753$	6.52201e96	−	1.26795e96i	0.100775	−	0.0195917i
$754$	7.35495e96			0.108631
$755$		−	7.66826e97i		−	1.08268i
$756$	3.93547e97	+	6.05892e97i	0.531197	+	0.817813i
$757$	−4.81136e97			−0.620880			−0.310440	−	0.950593i	$-0.600476\pi$
$757$	−4.81136e97			−0.620880			−0.310440	+	0.950593i	$0.600476\pi$
$758$		−	6.74631e95i		−	0.00832364i
$759$	1.01823e97	+	5.23754e97i	0.120123	+	0.617884i
$760$	−1.46018e98			−1.64719
$761$			1.02636e98i			1.10718i	0.832788	+	0.553592i	$0.186743\pi$
$761$			1.02636e98i			1.10718i	−0.832788	+	0.553592i	$0.813257\pi$
$762$	−7.28209e97	+	1.41572e97i	−0.751254	+	0.146052i
$763$	4.70201e97			0.463926
$764$			6.12310e97i			0.577826i
$765$	−1.89075e98	+	7.64041e97i	−1.70665	+	0.689649i
$766$	7.22663e97			0.623962
$767$			6.90499e96i			0.0570323i
$768$	−1.39567e97	−	7.17896e97i	−0.110281	−	0.567257i
$769$	2.38317e98			1.80161			0.900804	−	0.434227i	$-0.142978\pi$
$769$	2.38317e98			1.80161			0.900804	+	0.434227i	$0.142978\pi$
$770$		−	6.34753e97i		−	0.459113i
$771$	−4.31493e97	+	8.38869e96i	−0.298624	+	0.0580557i
$772$	7.00614e97			0.463970
$773$		−	1.42743e98i		−	0.904591i	−0.891868	−	0.452296i	$-0.850605\pi$
$773$		−	1.42743e98i		−	0.904591i	0.891868	−	0.452296i	$-0.149395\pi$
$774$	4.26790e97	+	1.05616e98i	0.258834	+	0.640528i
$775$	6.43149e96			0.0373296
$776$		−	1.05726e98i		−	0.587333i
$777$	−6.23299e97	−	3.20609e98i	−0.331422	−	1.70475i
$778$	8.69568e97			0.442586
$779$			2.28411e98i			1.11287i
$780$	−8.32865e97	+	1.61918e97i	−0.388471	+	0.0755229i
$781$	−1.21949e98			−0.544558
$782$			1.69405e98i			0.724263i
$783$	9.28618e97	−	6.03169e97i	0.380134	−	0.246910i
$784$	5.59192e97			0.219187
$785$		−	1.73149e98i		−	0.649908i
$786$	−3.59319e97	−	1.84824e98i	−0.129156	−	0.664343i
$787$	−2.96998e98			−1.02238			−0.511191	−	0.859467i	$-0.670795\pi$
$787$	−2.96998e98			−1.02238			−0.511191	+	0.859467i	$0.670795\pi$
$788$		−	3.80021e98i		−	1.25290i
$789$	5.51690e98	−	1.07255e98i	1.74212	−	0.338687i
$790$	−1.12939e98			−0.341605
$791$			2.32128e98i			0.672553i
$792$	−2.11346e98	+	8.54037e97i	−0.586593	+	0.237039i
$793$	−6.60215e97			−0.175548
$794$		−	5.20820e97i		−	0.132675i
$795$	−2.17267e97	−	1.11757e98i	−0.0530288	−	0.272766i
$796$	−2.16885e98			−0.507206
$797$		−	1.89173e98i		−	0.423913i	−0.977279	−	0.211957i	$-0.932016\pi$
$797$		−	1.89173e98i		−	0.423913i	0.977279	−	0.211957i	$-0.0679835\pi$
$798$	5.26083e98	−	1.02276e98i	1.12968	−	0.219622i
$799$	3.59020e98			0.738801
$800$			2.00212e97i			0.0394848i
$801$	3.52308e98	+	8.71845e98i	0.665912	+	1.64791i
$802$	3.70366e98			0.670969
$803$			5.24004e98i			0.909926i
$804$	−6.15675e97	−	3.16688e98i	−0.102482	−	0.527139i
$805$	−6.77930e98			−1.08175
$806$			1.51297e98i			0.231440i
$807$	−8.52036e98	+	1.65645e98i	−1.24956	+	0.242928i
$808$	−7.72372e98			−1.08603
$809$			1.28530e98i			0.173282i	0.996240	+	0.0866411i	$0.0276133\pi$
$809$			1.28530e98i			0.173282i	−0.996240	+	0.0866411i	$0.972387\pi$
$810$	2.70385e98	−	2.61170e98i	0.349537	−	0.337623i
$811$	−3.71102e97			−0.0460028			−0.0230014	−	0.999735i	$-0.507322\pi$
$811$	−3.71102e97			−0.0460028			−0.0230014	+	0.999735i	$0.507322\pi$
$812$		−	3.71846e98i		−	0.442037i
$813$	3.01000e98	+	1.54827e99i	0.343153	+	1.76509i
$814$	4.49151e98			0.491092
$815$			1.33312e98i			0.139801i
$816$	6.51420e98	−	1.26643e98i	0.655233	−	0.127384i
$817$	−2.87131e99			−2.77032
$818$			7.15194e98i			0.661929i
$819$	6.62427e98	−	2.67683e98i	0.588146	−	0.237667i
$820$	5.38019e98			0.458275
$821$			4.02368e98i			0.328818i	0.986392	+	0.164409i	$0.0525717\pi$
$821$			4.02368e98i			0.328818i	−0.986392	+	0.164409i	$0.947428\pi$
$822$	−1.94193e98	−	9.98877e98i	−0.152262	−	0.783196i
$823$	1.85802e99			1.39784			0.698919	−	0.715201i	$-0.253665\pi$
$823$	1.85802e99			1.39784			0.698919	+	0.715201i	$0.253665\pi$
$824$			9.00458e97i			0.0650038i
$825$	4.09986e97	−	7.97057e96i	0.0284011	−	0.00552148i
$826$	−1.02736e98			−0.0682971
$827$		−	1.60698e99i		−	1.02524i	−0.858617	−	0.512618i	$-0.828676\pi$
$827$		−	1.60698e99i		−	1.02524i	0.858617	−	0.512618i	$-0.171324\pi$
$828$	3.97565e98	+	9.83841e98i	0.243432	+	0.602412i
$829$	−1.89945e98			−0.111628			−0.0558141	−	0.998441i	$-0.517775\pi$
$829$	−1.89945e98			−0.111628			−0.0558141	+	0.998441i	$0.517775\pi$
$830$			3.64817e98i			0.205788i
$831$	−2.72710e98	−	1.40275e99i	−0.147661	−	0.759531i
$832$	−1.13629e98			−0.0590605
$833$		−	2.14684e99i		−	1.07120i
$834$	4.63104e98	−	9.00326e97i	0.221837	−	0.0431275i
$835$	1.34992e99			0.620825
$836$		−	2.50434e99i		−	1.10581i
$837$	1.24076e99	+	1.91024e99i	0.526046	+	0.809882i
$838$	−1.71573e99			−0.698478
$839$			4.34293e99i			1.69776i	0.528587	+	0.848879i	$0.322722\pi$
$839$			4.34293e99i			1.69776i	−0.528587	+	0.848879i	$0.677278\pi$
$840$	−5.52719e98	−	2.84305e99i	−0.207496	−	1.06730i
$841$	2.20382e99			0.794533
$842$		−	1.36465e98i		−	0.0472510i
$843$	−2.02388e99	+	3.93464e98i	−0.673049	+	0.130848i
$844$	−8.77546e98			−0.280302
$845$		−	2.48268e99i		−	0.761715i
$846$	−6.13613e98	+	2.47958e98i	−0.180843	+	0.0730779i
$847$	−1.96046e99			−0.555036
$848$			3.70483e98i			0.100765i
$849$	−1.14355e99	−	5.88212e99i	−0.298809	−	1.53700i
$850$	1.32607e98			0.0332908
$851$		−	4.79703e99i		−	1.15709i
$852$	−2.38073e99	+	4.62839e98i	−0.551777	+	0.107271i
$853$	1.54300e98			0.0343636			0.0171818	−	0.999852i	$-0.494531\pi$
$853$	1.54300e98			0.0343636			0.0171818	+	0.999852i	$0.494531\pi$
$854$		−	9.82304e98i		−	0.210222i
$855$	3.55011e99	+	8.78535e99i	0.730120	+	1.80680i
$856$	−1.45464e99			−0.287507
$857$			5.00578e99i			0.950876i	0.879749	+	0.475438i	$0.157710\pi$
$857$			5.00578e99i			0.950876i	−0.879749	+	0.475438i	$0.842290\pi$
$858$	1.87503e98	+	9.64467e98i	0.0342326	+	0.176084i
$859$	9.60442e99			1.68540			0.842701	−	0.538381i	$-0.180964\pi$
$859$	9.60442e99			1.68540			0.842701	+	0.538381i	$0.180964\pi$
$860$			6.76333e99i			1.14081i
$861$	−4.44727e99	+	8.64598e98i	−0.721085	+	0.140187i
$862$	2.78121e99			0.433497
$863$			1.26659e100i			1.89788i	0.315451	+	0.948942i	$0.397844\pi$
$863$			1.26659e100i			1.89788i	−0.315451	+	0.948942i	$0.602156\pi$
$864$	−5.94655e99	+	3.86248e99i	−0.856639	+	0.556416i
$865$	6.03952e99			0.836479
$866$			4.59636e99i			0.612076i
$867$	−3.37163e99	−	1.73428e100i	−0.431708	−	2.22060i
$868$	7.64916e99			0.941766
$869$		−	4.44407e99i		−	0.526149i
$870$	−1.89923e99	+	3.69231e98i	−0.216234	+	0.0420382i
$871$	−3.19037e99			−0.349320
$872$			2.95039e99i			0.310684i
$873$	−6.36115e99	+	2.57051e99i	−0.644245	+	0.260336i
$874$	7.87139e99			0.766765
$875$		−	1.31980e100i		−	1.23661i
$876$	1.98878e99	+	1.02298e100i	0.179245	+	0.921989i
$877$	−2.10584e100			−1.82574			−0.912872	−	0.408247i	$-0.866140\pi$
$877$	−2.10584e100			−1.82574			−0.912872	+	0.408247i	$0.866140\pi$
$878$			4.13442e99i			0.344827i
$879$	−6.46822e99	+	1.25749e99i	−0.518995	+	0.100898i
$880$	−3.65205e99			−0.281920
$881$		−	1.41283e100i		−	1.04933i	−0.851310	−	0.524663i	$-0.824191\pi$
$881$		−	1.41283e100i		−	1.04933i	0.851310	−	0.524663i	$-0.175809\pi$
$882$	1.48272e99	+	3.66924e99i	0.105957	+	0.262207i
$883$	−3.37692e99			−0.232197			−0.116098	−	0.993238i	$-0.537039\pi$
$883$	−3.37692e99			−0.232197			−0.116098	+	0.993238i	$0.537039\pi$
$884$		−	1.06001e100i		−	0.701345i
$885$	−3.46643e98	−	1.78304e99i	−0.0220704	−	0.113525i
$886$	1.50409e99			0.0921568
$887$		−	9.30365e98i		−	0.0548593i	−0.999624	−	0.0274296i	$-0.991268\pi$
$887$		−	9.30365e98i		−	0.0548593i	0.999624	−	0.0274296i	$-0.00873222\pi$
$888$	2.01174e100	−	3.91104e99i	1.14164	−	0.221948i
$889$	3.70894e100			2.02577
$890$		−	1.64303e100i		−	0.863746i
$891$	1.02768e100	+	1.06394e100i	0.520016	+	0.538365i
$892$	−1.40609e100			−0.684870
$893$		−	1.66818e100i		−	0.782158i
$894$	−4.12879e98	−	2.12375e99i	−0.0186358	−	0.0958577i
$895$	−1.97402e100			−0.857764
$896$			2.91287e100i			1.21857i
$897$	1.03007e100	−	2.00257e99i	0.414882	−	0.0806576i
$898$	−8.21008e99			−0.318385
$899$		−	1.17235e100i		−	0.437750i
$900$	7.70135e98	−	3.11208e98i	0.0276899	−	0.0111894i
$901$	1.42235e100			0.492453
$902$		−	6.23032e99i		−	0.207725i
$903$	−1.08687e100	−	5.59058e100i	−0.348975	−	1.79504i
$904$	−1.45654e100			−0.450398
$905$		−	1.17626e99i		−	0.0350310i
$906$	−1.73356e100	+	3.37024e99i	−0.497258	+	0.0966723i
$907$	1.48707e100			0.410851			0.205425	−	0.978673i	$-0.434142\pi$
$907$	1.48707e100			0.410851			0.205425	+	0.978673i	$0.434142\pi$
$908$			3.18535e100i			0.847691i
$909$	1.87786e100	+	4.64707e100i	0.481382	+	1.19126i
$910$	−1.24838e100			−0.308275
$911$			1.95604e100i			0.465321i	0.972558	+	0.232661i	$0.0747431\pi$
$911$			1.95604e100i			0.465321i	−0.972558	+	0.232661i	$0.925257\pi$
$912$	−5.88447e99	−	3.02682e100i	−0.134860	−	0.693685i
$913$	−1.43553e100			−0.316960
$914$			8.41538e99i			0.179021i
$915$	1.70484e100	−	3.31439e99i	0.349435	−	0.0679339i
$916$	−1.14689e99			−0.0226503
$917$			9.41354e100i			1.79141i
$918$	2.55826e100	+	3.93862e100i	0.469131	+	0.722258i
$919$	−6.14715e100			−1.08629			−0.543146	−	0.839638i	$-0.682767\pi$
$919$	−6.14715e100			−1.08629			−0.543146	+	0.839638i	$0.682767\pi$
$920$		−	4.25384e100i		−	0.724427i
$921$	1.06334e100	+	5.46952e100i	0.174519	+	0.897681i
$922$	−5.52324e100			−0.873660
$923$			2.39839e100i			0.365647i
$924$	4.87608e100	−	9.47964e99i	0.716513	−	0.139298i
$925$	−3.75504e99			−0.0531858
$926$		−	4.22151e100i		−	0.576361i
$927$	5.41771e99	−	2.18927e99i	0.0713025	−	0.0288130i
$928$	3.64950e100			0.463023
$929$		−	7.24167e99i		−	0.0885736i	−0.999019	−	0.0442868i	$-0.985898\pi$
$929$		−	7.24167e99i		−	0.0885736i	0.999019	−	0.0442868i	$-0.0141015\pi$
$930$	−7.59537e99	−	3.90686e100i	−0.0895630	−	0.460689i
$931$	−9.97529e100			−1.13406
$932$		−	4.52183e100i		−	0.495648i
$933$	1.14425e101	−	2.22455e100i	1.20933	−	0.235107i
$934$	−1.71647e100			−0.174921
$935$			1.40209e101i			1.37778i
$936$	1.67964e100	+	4.15656e100i	0.159162	+	0.393872i
$937$	1.13174e101			1.03419			0.517095	−	0.855928i	$-0.327013\pi$
$937$	1.13174e101			1.03419			0.517095	+	0.855928i	$0.327013\pi$
$938$		−	4.74681e100i		−	0.418317i
$939$	−2.49332e100	−	1.28250e101i	−0.211908	−	1.09000i
$940$	−3.92939e100			−0.322090
$941$		−	1.53739e101i		−	1.21545i	−0.794149	−	0.607723i	$-0.792083\pi$
$941$		−	1.53739e101i		−	1.21545i	0.794149	−	0.607723i	$-0.207917\pi$
$942$	−3.91439e100	+	7.61000e99i	−0.298492	+	0.0580302i
$943$	−6.65412e100			−0.489433
$944$			5.91094e99i			0.0419381i
$945$	−1.57617e101	+	1.02377e101i	−1.07875	+	0.700685i
$946$	7.83202e100			0.517100
$947$		−	2.87880e100i		−	0.183363i	−0.995788	−	0.0916816i	$-0.970776\pi$
$947$		−	2.87880e100i		−	0.183363i	0.995788	−	0.0916816i	$-0.0292242\pi$
$948$	−1.68668e100	−	8.67585e100i	−0.103645	−	0.533124i
$949$	1.03056e101			0.610976
$950$		−	6.16159e99i		−	0.0352444i
$951$	5.59674e100	−	1.08807e100i	0.308885	−	0.0600507i
$952$	3.61841e101			1.92691
$953$		−	2.08995e101i		−	1.07393i	−0.843604	−	0.536966i	$-0.819570\pi$
$953$		−	2.08995e101i		−	1.07393i	0.843604	−	0.536966i	$-0.180430\pi$
$954$	−2.43100e100	+	9.82353e99i	−0.120542	+	0.0487105i
$955$	−1.59287e101			−0.762193
$956$		−	2.74675e101i		−	1.26838i
$957$	−1.45289e100	−	7.47332e100i	−0.0647483	−	0.333048i
$958$	−1.35505e101			−0.582811
$959$			5.08752e101i			2.11190i
$960$	2.93419e100	−	5.70439e99i	0.117562	−	0.0228553i
$961$	−1.74197e100			−0.0673666
$962$		−	8.83350e100i		−	0.329747i
$963$	3.53665e100	+	8.75203e100i	0.127438	+	0.315366i
$964$	−2.04302e101			−0.710645
$965$			1.82258e101i			0.612009i
$966$	2.97954e100	+	1.53260e101i	0.0965888	+	0.496828i
$967$	5.82381e101			1.82267			0.911333	−	0.411670i	$-0.135054\pi$
$967$	5.82381e101			1.82267			0.911333	+	0.411670i	$0.135054\pi$
$968$		−	1.23014e101i		−	0.371699i
$969$	−1.16205e102	+	2.25916e101i	−3.39014	+	0.659080i
$970$	1.19879e101			0.337679
$971$		−	3.18036e101i		−	0.865013i	−0.901631	−	0.432507i	$-0.857629\pi$
$971$		−	3.18036e101i		−	0.865013i	0.901631	−	0.432507i	$-0.142371\pi$
$972$	2.41007e101	+	1.68702e101i	0.632962	+	0.443065i
$973$	−2.35870e101			−0.598186
$974$			3.23949e101i			0.793365i
$975$	−1.56758e99	−	8.06324e99i	−0.00370743	−	0.0190701i
$976$	−5.65169e100			−0.129088
$977$			3.65416e101i			0.806070i	0.915185	+	0.403035i	$0.132045\pi$
$977$			3.65416e101i			0.806070i	−0.915185	+	0.403035i	$0.867955\pi$
$978$	3.01379e100	−	5.85913e99i	0.0642084	−	0.0124828i
$979$	6.46520e101			1.33036
$980$			2.34967e101i			0.467004i
$981$	1.77513e101	−	7.17323e100i	0.340789	−	0.137711i
$982$	−2.45558e101			−0.455368
$983$			6.46268e101i			1.15769i	0.815437	+	0.578846i	$0.196497\pi$
$983$			6.46268e101i			1.15769i	−0.815437	+	0.578846i	$0.803503\pi$
$984$	−5.42513e100	−	2.79055e101i	−0.0938808	−	0.482899i
$985$	9.88588e101			1.65266
$986$		−	2.41720e101i		−	0.390388i
$987$	3.24804e101	−	6.31454e100i	0.506801	−	0.0985277i
$988$	−4.92532e101			−0.742503
$989$		−	8.36477e101i		−	1.21837i
$990$	−9.68358e100	−	2.39636e101i	−0.136282	−	0.337253i
$991$	−4.49474e100			−0.0611224			−0.0305612	−	0.999533i	$-0.509729\pi$
$991$	−4.49474e100			−0.0611224			−0.0305612	+	0.999533i	$0.509729\pi$
$992$			7.50730e101i			0.986477i
$993$	3.70546e100	+	1.90599e101i	0.0470509	+	0.242018i
$994$	−3.56846e101			−0.437868
$995$		−	5.64205e101i		−	0.669040i
$996$	−2.80247e101	+	5.44832e100i	−0.321162	+	0.0624374i
$997$	−1.61126e102			−1.78456			−0.892281	−	0.451481i	$-0.850896\pi$
$997$	−1.61126e102			−1.78456			−0.892281	+	0.451481i	$0.850896\pi$
$998$			3.57030e101i			0.382179i
$999$	−7.24423e101	−	1.11530e102i	−0.749489	−	1.15389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.69.b.a.2.10	✓	22
3.2	odd	2	inner	3.69.b.a.2.13	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.69.b.a.2.10	✓	22	1.1	even	1	trivial
3.69.b.a.2.13	yes	22	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 69 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.19205e9i q^{2} +(3.18264e15 + 1.63707e16i) q^{3} +2.28038e20 q^{4} +5.93220e23i q^{5} +(1.34109e26 - 2.60723e25i) q^{6} -6.83050e28 q^{7} -4.28597e30i q^{8} +(-2.57870e32 + 1.04204e32i) q^{9} +O(q^{10})\)	\(q-8.19205e9i q^{2} +(3.18264e15 + 1.63707e16i) q^{3} +2.28038e20 q^{4} +5.93220e23i q^{5} +(1.34109e26 - 2.60723e25i) q^{6} -6.83050e28 q^{7} -4.28597e30i q^{8} +(-2.57870e32 + 1.04204e32i) q^{9} +4.85968e33 q^{10} +1.91225e35i q^{11} +(7.25764e35 + 3.73314e36i) q^{12} +3.76084e37 q^{13} +5.59558e38i q^{14} +(-9.71141e39 + 1.88800e39i) q^{15} +3.21942e40 q^{16} -1.23600e42i q^{17} +(8.53644e41 + 2.11248e42i) q^{18} -5.74305e43 q^{19} +1.35277e44i q^{20} +(-2.17390e44 - 1.11820e45i) q^{21} +1.56652e45 q^{22} -1.67308e46i q^{23} +(7.01642e46 - 1.36407e46i) q^{24} -1.30966e46 q^{25} -3.08090e47i q^{26} +(-2.52660e48 - 3.88986e48i) q^{27} -1.55762e49 q^{28} +2.38728e49i q^{29} +(1.54666e49 + 7.95563e49i) q^{30} -4.91081e50 q^{31} -1.52873e51i q^{32} +(-3.13048e51 + 6.08599e50i) q^{33} -1.01253e52 q^{34} -4.05199e52i q^{35} +(-5.88042e52 + 2.37625e52i) q^{36} +2.86719e53 q^{37} +4.70473e53i q^{38} +(1.19694e53 + 6.15675e53i) q^{39} +2.54252e54 q^{40} -3.97717e54i q^{41} +(-9.16035e54 + 1.78087e54i) q^{42} +4.99962e55 q^{43} +4.36065e55i q^{44} +(-6.18159e55 - 1.52974e56i) q^{45} -1.37059e56 q^{46} +2.90470e56i q^{47} +(1.02462e56 + 5.27041e56i) q^{48} +1.73693e57 q^{49} +1.07288e56i q^{50} +(2.02341e58 - 3.93373e57i) q^{51} +8.57615e57 q^{52} +1.15078e58i q^{53} +(-3.18659e58 + 2.06980e58i) q^{54} -1.13438e59 q^{55} +2.92753e59i q^{56} +(-1.82780e59 - 9.40176e59i) q^{57} +1.95567e59 q^{58} +1.83603e59i q^{59} +(-2.21457e60 + 4.30537e59i) q^{60} -1.75550e60 q^{61} +4.02296e60i q^{62} +(1.76138e61 - 7.11766e60i) q^{63} -3.02138e60 q^{64} +2.23100e61i q^{65} +(4.98567e60 + 2.56450e61i) q^{66} -8.48314e61 q^{67} -2.81854e62i q^{68} +(2.73894e62 - 5.32481e61i) q^{69} -3.31941e62 q^{70} +6.37727e62i q^{71} +(4.46615e62 + 1.10522e63i) q^{72} +2.74025e63 q^{73} -2.34881e63i q^{74} +(-4.16817e61 - 2.14400e62i) q^{75} -1.30963e64 q^{76} -1.30616e64i q^{77} +(5.04364e63 - 9.80538e62i) q^{78} -2.32401e64 q^{79} +1.90982e64i q^{80} +(5.56385e64 - 5.37421e64i) q^{81} -3.25812e64 q^{82} +7.50701e64i q^{83} +(-4.95733e64 - 2.54992e65i) q^{84} +7.33217e65 q^{85} -4.09572e65i q^{86} +(-3.90813e65 + 7.59784e64i) q^{87} +8.19582e65 q^{88} -3.38095e66i q^{89} +(-1.25317e66 + 5.06398e65i) q^{90} -2.56884e66 q^{91} -3.81526e66i q^{92} +(-1.56293e66 - 8.03933e66i) q^{93} +2.37955e66 q^{94} -3.40689e67i q^{95} +(2.50264e67 - 4.86540e66i) q^{96} +2.46680e67 q^{97} -1.42290e67i q^{98} +(-1.99264e67 - 4.93111e67i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 18\!\cdots\!78 q^{3}+ \cdots + 84\!\cdots\!78 q^{9}+O(q^{10}) \) 22 * q + 18789723640115478 * q^3 - 2943217790812903705616 * q^4 + 606827522425378326847120944 * q^6 - 3605688981734492610233621044 * q^7 + 84409856735558666343023488765878 * q^9	\( 22 q + 18\!\cdots\!78 q^{3}+ \cdots - 11\!\cdots\!00 q^{99}+O(q^{100}) \) 22 * q + 18789723640115478 * q^3 - 2943217790812903705616 * q^4 + 606827522425378326847120944 * q^6 - 3605688981734492610233621044 * q^7 + 84409856735558666343023488765878 * q^9 + 2045888067334428934113988216421280 * q^10 - 6488396126470402148347182126675194832 * q^12 - 10813885710533400837304817444785935604 * q^13 + 14557528184647372428101554053003296612160 * q^15 + 373601084063432865853473918269277812744320 * q^16 + 17941511735214427632488941901617371491816160 * q^18 - 79553650357260974891342027178031915087354324 * q^19 - 1298400323255969952377913185067359758477401780 * q^21 + 6768843564804724477092404017437690309759833760 * q^22 - 75879178936902674847903860248712590469230731648 * q^24 - 1290406322757665049559021767067242780449078031050 * q^25 + 2674086297347577939313596696269044232072283756918 * q^27 + 42745403006807704515598614320469990457621586593376 * q^28 + 30776582876805533479749631919828742635540596749600 * q^30 - 464825674673310587378006994001777182420658601801716 * q^31 + 2043086192437245889755473926491971918230943629550400 * q^33 + 13079915711847249768451590870017502856673640042982272 * q^34 - 65327203493646647902060088267317231087935232974706704 * q^36 - 167279080426229420846594751930892532669536008046545844 * q^37 + 1637357069222228057847981309081425400083650534736779020 * q^39 + 6053556854890611145141953130785126755317199579733738240 * q^40 - 12457262572316255979922798677909127605820549100734736160 * q^42 - 18628500859740527128618324584150040016275591666233599764 * q^43 + 367822789535544680671556018223028621483838265619669430400 * q^45 + 1476449543055130371522242587937584327352337186768013053888 * q^46 + 202405740838876412041865477434740772123701917763236585088 * q^48 + 4681199846498689520635057982286342899995310041595285382018 * q^49 + 21407584156868532008405510905089022165080050053906507325184 * q^51 + 24391763772592576034526261030318526583680683849133477696736 * q^52 - 112285817002635953902674086392140195155054790343667891881584 * q^54 + 274409579794012893709322560718339246575325740160175650620800 * q^55 + 101758997342686912720089366682761957082398853447685074732716 * q^57 - 2020457744766163498170953106059196558756720252448185539243040 * q^58 - 13276219488047015535811467987165558930747748946804017101031680 * q^60 + 6331070401548027780910089309848838040805985031947773629039244 * q^61 - 11540105667000326350766773710482957857389205527747058022198004 * q^63 + 74144666416333808948332900789778080404085337330317362556926976 * q^64 - 388082670987835008027383208260911873599566866107012006022495200 * q^66 + 690968797068657030373143885315519666504759571640550029794509356 * q^67 - 1027093066405255275213825064853644794250194801896401414490868864 * q^69 + 4371068227635884746027518083549441915821247332843741516741992000 * q^70 - 8830670280256061265338935058781406802503181323103646058149000960 * q^72 + 8806696028067195590640304057094157167006086961761378058824984556 * q^73 - 35720155285864881642804474725062955577201898766624893474579682250 * q^75 + 50989416920172911215005579159200646780346206610233430042766798432 * q^76 - 79580143447707181310585996419552144412335647108094050067906050720 * q^78 - 3083981169532008720747546215983788345611378750423096573576219764 * q^79 - 88762224122457647598561491684821377170571566383688244793770736938 * q^81 + 416784948027081086888539461807826070456316776812312199920865653440 * q^82 + 990441228134853667871418956670095117692984404086848036534801693920 * q^84 - 866637175758839171101071739839460554945096683648478422830993681920 * q^85 + 3620458445475290511813570050310517312523781688405496711995676422080 * q^87 - 4669471445324986882088763579042561683455173004052019441103363626240 * q^88 + 14582942989396685328395597316366348010236984461538262603110152917920 * q^90 - 6998978018734113734240448628263170029174504049408988631375576481960 * q^91 + 22631183723253759871940463881283634110336753405922973132310746358156 * q^93 - 49667911598354463153752845875961955186127772502753374451274725501568 * q^94 - 5532425547839977216491807518703626514248108709732237368596820947968 * q^96 + 90182295908350258367379728070466489774210357027997619180945877805996 * q^97 - 111427931124550204447734414473904809051459145283833102653529748809600 * q^99

Introduction

L-functions

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