LMFDB - Embedded newform 3.69.b.a.2.12

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			2.12
Character	$\chi$	$=$	3.2
Dual form			3.69.b.a.2.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.69746e9i q^{2} +(-1.51595e16 + 6.95107e15i) q^{3} +2.50292e20 q^{4} +7.66457e23i q^{5} +(-4.65545e25 - 1.01530e26i) q^{6} +4.76233e28 q^{7} +3.65306e30i q^{8} +(1.81494e32 - 2.10750e32i) q^{9} +O(q^{10})$	\(q+6.69746e9i q^{2} +(-1.51595e16 + 6.95107e15i) q^{3} +2.50292e20 q^{4} +7.66457e23i q^{5} +(-4.65545e25 - 1.01530e26i) q^{6} +4.76233e28 q^{7} +3.65306e30i q^{8} +(1.81494e32 - 2.10750e32i) q^{9} -5.13331e33 q^{10} -1.05183e35i q^{11} +(-3.79431e36 + 1.73980e36i) q^{12} -2.29850e37 q^{13} +3.18955e38i q^{14} +(-5.32770e39 - 1.16191e40i) q^{15} +4.94069e40 q^{16} +9.58998e41i q^{17} +(1.41149e42 + 1.21555e42i) q^{18} -4.30737e43 q^{19} +1.91838e44i q^{20} +(-7.21946e44 + 3.31033e44i) q^{21} +7.04462e44 q^{22} -2.39008e46i q^{23} +(-2.53927e46 - 5.53786e46i) q^{24} -2.48643e47 q^{25} -1.53941e47i q^{26} +(-1.28642e48 + 4.45644e48i) q^{27} +1.19197e49 q^{28} +5.15317e49i q^{29} +(7.78186e49 - 3.56820e49i) q^{30} +8.13675e50 q^{31} +1.40909e51i q^{32} +(7.31138e50 + 1.59453e51i) q^{33} -6.42285e51 q^{34} +3.65012e52i q^{35} +(4.54264e52 - 5.27490e52i) q^{36} -2.30116e52 q^{37} -2.88484e53i q^{38} +(3.48441e53 - 1.59770e53i) q^{39} -2.79991e54 q^{40} +2.46731e54i q^{41} +(-2.21708e54 - 4.83520e54i) q^{42} -2.77116e55 q^{43} -2.63266e55i q^{44} +(1.61531e56 + 1.39107e56i) q^{45} +1.60075e56 q^{46} +1.17852e57i q^{47} +(-7.48985e56 + 3.43431e56i) q^{48} -6.60670e56 q^{49} -1.66528e57i q^{50} +(-6.66606e57 - 1.45379e58i) q^{51} -5.75295e57 q^{52} +5.27828e58i q^{53} +(-2.98468e58 - 8.61574e57i) q^{54} +8.06186e58 q^{55} +1.73971e59i q^{56} +(6.52976e59 - 2.99408e59i) q^{57} -3.45132e59 q^{58} +2.37147e59i q^{59} +(-1.33348e60 - 2.90817e60i) q^{60} -2.42748e60 q^{61} +5.44955e60i q^{62} +(8.64332e60 - 1.00366e61i) q^{63} +5.14500e60 q^{64} -1.76170e61i q^{65} +(-1.06793e61 + 4.89677e60i) q^{66} -5.51342e61 q^{67} +2.40029e62i q^{68} +(1.66136e62 + 3.62325e62i) q^{69} -2.44465e62 q^{70} -1.62802e63i q^{71} +(7.69882e62 + 6.63007e62i) q^{72} -1.89849e63 q^{73} -1.54119e62i q^{74} +(3.76931e63 - 1.72834e63i) q^{75} -1.07810e64 q^{76} -5.00918e63i q^{77} +(1.07005e63 + 2.33367e63i) q^{78} +2.45788e64 q^{79} +3.78683e64i q^{80} +(-1.14755e64 - 7.64995e64i) q^{81} -1.65247e64 q^{82} -1.04823e64i q^{83} +(-1.80697e65 + 8.28548e64i) q^{84} -7.35031e65 q^{85} -1.85598e65i q^{86} +(-3.58201e65 - 7.81196e65i) q^{87} +3.84242e65 q^{88} +3.23918e65i q^{89} +(-9.31664e65 + 1.08184e66i) q^{90} -1.09462e66 q^{91} -5.98219e66i q^{92} +(-1.23349e67 + 5.65591e66i) q^{93} -7.89311e66 q^{94} -3.30141e67i q^{95} +(-9.79471e66 - 2.13612e67i) q^{96} -6.81578e67 q^{97} -4.42481e66i q^{98} +(-2.21674e67 - 1.90901e67i) 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 $

$2$			6.69746e9i			0.389843i	0.980819	+	0.194922i	$0.0624453\pi$
$2$			6.69746e9i			0.389843i	−0.980819	+	0.194922i	$0.937555\pi$
$3$	−1.51595e16	+	6.95107e15i	−0.908998	+	0.416801i
$3$	−1.51595e16	+	6.95107e15i	−0.908998	+	0.416801i
$4$	2.50292e20			0.848022
$5$			7.66457e23i			1.31676i	0.752684	+	0.658381i	$0.228759\pi$
$5$			7.66457e23i			1.31676i	−0.752684	+	0.658381i	$0.771241\pi$
$6$	−4.65545e25	−	1.01530e26i	−0.162487	−	0.354367i
$7$	4.76233e28			0.880006			0.440003	−	0.897996i	$-0.354977\pi$
$7$	4.76233e28			0.880006			0.440003	+	0.897996i	$0.354977\pi$
$8$			3.65306e30i			0.720439i
$9$	1.81494e32	−	2.10750e32i	0.652553	−	0.757743i
$10$	−5.13331e33			−0.513331
$11$		−	1.05183e35i		−	0.411715i	−0.978582	−	0.205857i	$-0.934002\pi$
$11$		−	1.05183e35i		−	0.411715i	0.978582	−	0.205857i	$-0.0659983\pi$
$12$	−3.79431e36	+	1.73980e36i	−0.770850	+	0.353457i
$13$	−2.29850e37			−0.307164			−0.153582	−	0.988136i	$-0.549081\pi$
$13$	−2.29850e37			−0.307164			−0.153582	+	0.988136i	$0.549081\pi$
$14$			3.18955e38i			0.343065i
$15$	−5.32770e39	−	1.16191e40i	−0.548829	−	1.19693i
$16$	4.94069e40			0.567164
$17$			9.58998e41i			1.40137i	0.713468	+	0.700687i	$0.247123\pi$
$17$			9.58998e41i			1.40137i	−0.713468	+	0.700687i	$0.752877\pi$
$18$	1.41149e42	+	1.21555e42i	0.295401	+	0.254394i
$19$	−4.30737e43			−1.43413			−0.717066	−	0.697005i	$-0.754516\pi$
$19$	−4.30737e43			−1.43413			−0.717066	+	0.697005i	$0.754516\pi$
$20$			1.91838e44i			1.11664i
$21$	−7.21946e44	+	3.31033e44i	−0.799924	+	0.366788i
$22$	7.04462e44			0.160504
$23$		−	2.39008e46i		−	1.20134i	−0.799496	−	0.600671i	$-0.794900\pi$
$23$		−	2.39008e46i		−	1.20134i	0.799496	−	0.600671i	$-0.205100\pi$
$24$	−2.53927e46	−	5.53786e46i	−0.300280	−	0.654878i
$25$	−2.48643e47			−0.733865
$26$		−	1.53941e47i		−	0.119746i
$27$	−1.28642e48	+	4.45644e48i	−0.277341	+	0.960771i
$28$	1.19197e49			0.746265
$29$			5.15317e49i			0.978460i	0.872155	+	0.489230i	$0.162722\pi$
$29$			5.15317e49i			0.978460i	−0.872155	+	0.489230i	$0.837278\pi$
$30$	7.78186e49	−	3.56820e49i	0.466617	−	0.213957i
$31$	8.13675e50			1.60012			0.800061	−	0.599919i	$-0.204800\pi$
$31$	8.13675e50			1.60012			0.800061	+	0.599919i	$0.204800\pi$
$32$			1.40909e51i			0.941544i
$33$	7.31138e50	+	1.59453e51i	0.171603	+	0.374248i
$34$	−6.42285e51			−0.546317
$35$			3.65012e52i			1.15876i
$36$	4.54264e52	−	5.27490e52i	0.553380	−	0.642583i
$37$	−2.30116e52			−0.110430			−0.0552151	−	0.998474i	$-0.517584\pi$
$37$	−2.30116e52			−0.110430			−0.0552151	+	0.998474i	$0.517584\pi$
$38$		−	2.88484e53i		−	0.559087i
$39$	3.48441e53	−	1.59770e53i	0.279211	−	0.128026i
$40$	−2.79991e54			−0.948648
$41$			2.46731e54i			0.361054i	0.983570	+	0.180527i	$0.0577804\pi$
$41$			2.46731e54i			0.361054i	−0.983570	+	0.180527i	$0.942220\pi$
$42$	−2.21708e54	−	4.83520e54i	−0.142990	−	0.311845i
$43$	−2.77116e55			−0.803035			−0.401518	−	0.915851i	$-0.631517\pi$
$43$	−2.77116e55			−0.803035			−0.401518	+	0.915851i	$0.631517\pi$
$44$		−	2.63266e55i		−	0.349143i
$45$	1.61531e56	+	1.39107e56i	0.997768	+	0.859258i
$46$	1.60075e56			0.468335
$47$			1.17852e57i			1.65963i	0.558039	+	0.829815i	$0.311554\pi$
$47$			1.17852e57i			1.65963i	−0.558039	+	0.829815i	$0.688446\pi$
$48$	−7.48985e56	+	3.43431e56i	−0.515550	+	0.236395i
$49$	−6.60670e56			−0.225589
$50$		−	1.66528e57i		−	0.286092i
$51$	−6.66606e57	−	1.45379e58i	−0.584095	−	1.27385i
$52$	−5.75295e57			−0.260482
$53$			5.27828e58i			1.25058i	0.780391	+	0.625292i	$0.215020\pi$
$53$			5.27828e58i			1.25058i	−0.780391	+	0.625292i	$0.784980\pi$
$54$	−2.98468e58	−	8.61574e57i	−0.374550	−	0.108120i
$55$	8.06186e58			0.542131
$56$			1.73971e59i			0.633991i
$57$	6.52976e59	−	2.99408e59i	1.30362	−	0.597748i
$58$	−3.45132e59			−0.381446
$59$			2.37147e59i			0.146571i	0.997311	+	0.0732856i	$0.0233485\pi$
$59$			2.37147e59i			0.146571i	−0.997311	+	0.0732856i	$0.976652\pi$
$60$	−1.33348e60	−	2.90817e60i	−0.465419	−	1.01503i
$61$	−2.42748e60			−0.482994			−0.241497	−	0.970402i	$-0.577638\pi$
$61$	−2.42748e60			−0.482994			−0.241497	+	0.970402i	$0.577638\pi$
$62$			5.44955e60i			0.623797i
$63$	8.64332e60	−	1.00366e61i	0.574251	−	0.666818i
$64$	5.14500e60			0.200109
$65$		−	1.76170e61i		−	0.404462i
$66$	−1.06793e61	+	4.89677e60i	−0.145898	+	0.0668984i
$67$	−5.51342e61			−0.451729			−0.225864	−	0.974159i	$-0.572521\pi$
$67$	−5.51342e61			−0.451729			−0.225864	+	0.974159i	$0.572521\pi$
$68$			2.40029e62i			1.18840i
$69$	1.66136e62	+	3.62325e62i	0.500721	+	1.09202i
$70$	−2.44465e62			−0.451735
$71$		−	1.62802e63i		−	1.85727i	−0.370991	−	0.928636i	$-0.620982\pi$
$71$		−	1.62802e63i		−	1.85727i	0.370991	−	0.928636i	$-0.379018\pi$
$72$	7.69882e62	+	6.63007e62i	0.545908	+	0.470125i
$73$	−1.89849e63			−0.842230			−0.421115	−	0.907007i	$-0.638361\pi$
$73$	−1.89849e63			−0.842230			−0.421115	+	0.907007i	$0.638361\pi$
$74$		−	1.54119e62i		−	0.0430504i
$75$	3.76931e63	−	1.72834e63i	0.667081	−	0.305876i
$76$	−1.07810e64			−1.21618
$77$		−	5.00918e63i		−	0.362311i
$78$	1.07005e63	+	2.33367e63i	0.0499102	+	0.108849i
$79$	2.45788e64			0.743430			0.371715	−	0.928347i	$-0.378770\pi$
$79$	2.45788e64			0.743430			0.371715	+	0.928347i	$0.378770\pi$
$80$			3.78683e64i			0.746820i
$81$	−1.14755e64	−	7.64995e64i	−0.148348	−	0.988935i
$82$	−1.65247e64			−0.140755
$83$		−	1.04823e64i		−	0.0591291i	−0.999563	−	0.0295645i	$-0.990588\pi$
$83$		−	1.04823e64i		−	0.0591291i	0.999563	−	0.0295645i	$-0.00941205\pi$
$84$	−1.80697e65	+	8.28548e64i	−0.678353	+	0.311044i
$85$	−7.35031e65			−1.84528
$86$		−	1.85598e65i		−	0.313058i
$87$	−3.58201e65	−	7.81196e65i	−0.407823	−	0.889417i
$88$	3.84242e65			0.296615
$89$			3.23918e65i			0.170284i	0.996369	+	0.0851422i	$0.0271345\pi$
$89$			3.23918e65i			0.170284i	−0.996369	+	0.0851422i	$0.972866\pi$
$90$	−9.31664e65	+	1.08184e66i	−0.334976	+	0.388973i
$91$	−1.09462e66			−0.270306
$92$		−	5.98219e66i		−	1.01876i
$93$	−1.23349e67	+	5.65591e66i	−1.45451	+	0.666933i
$94$	−7.89311e66			−0.646995
$95$		−	3.30141e67i		−	1.88841i
$96$	−9.79471e66	−	2.13612e67i	−0.392437	−	0.855861i
$97$	−6.81578e67			−1.91989			−0.959945	−	0.280188i	$-0.909603\pi$
$97$	−6.81578e67			−1.91989			−0.959945	+	0.280188i	$0.909603\pi$
$98$		−	4.42481e66i		−	0.0879444i
$99$	−2.21674e67	−	1.90901e67i	−0.311974	−	0.268666i
$100$	−6.22333e67			−0.622333
$101$			1.71713e68i			1.22427i	0.790755	+	0.612133i	$0.209688\pi$
$101$			1.71713e68i			1.22427i	−0.790755	+	0.612133i	$0.790312\pi$
$102$	9.73673e67	−	4.46457e67i	0.496601	−	0.227706i
$103$	−4.61738e68			−1.69017			−0.845084	−	0.534633i	$-0.820450\pi$
$103$	−4.61738e68			−1.69017			−0.845084	+	0.534633i	$0.820450\pi$
$104$		−	8.39655e67i		−	0.221293i
$105$	−2.53722e68	−	5.53340e68i	−0.482973	−	1.05331i
$106$	−3.53511e68			−0.487532
$107$		−	1.14849e69i		−	1.15101i	−0.817798	−	0.575505i	$-0.804806\pi$
$107$		−	1.14849e69i		−	1.15101i	0.817798	−	0.575505i	$-0.195194\pi$
$108$	−3.21980e68	+	1.11541e69i	−0.235191	+	0.814755i
$109$	3.91325e68			0.208947			0.104474	−	0.994528i	$-0.466684\pi$
$109$	3.91325e68			0.208947			0.104474	+	0.994528i	$0.466684\pi$
$110$			5.39940e68i			0.211346i
$111$	3.48844e68	−	1.59955e68i	0.100381	−	0.0460274i
$112$	2.35292e69			0.499108
$113$		−	3.24352e69i		−	0.508568i	−0.967130	−	0.254284i	$-0.918160\pi$
$113$		−	3.24352e69i		−	0.508568i	0.967130	−	0.254284i	$-0.0818398\pi$
$114$	2.00527e69	+	4.37328e69i	0.233028	+	0.508209i
$115$	1.83190e70			1.58188
$116$			1.28980e70i			0.829755i
$117$	−4.17162e69	+	4.84408e69i	−0.200441	+	0.232751i
$118$	−1.58828e69			−0.0571398
$119$			4.56706e70i			1.23322i
$120$	4.24453e70	−	1.94624e70i	0.862318	−	0.395398i
$121$	5.42048e70			0.830491
$122$		−	1.62580e70i		−	0.188292i
$123$	−1.71505e70	−	3.74032e70i	−0.150488	−	0.328198i
$124$	2.03656e71			1.35694
$125$			6.91116e70i			0.350437i
$126$	6.72197e70	+	5.78883e70i	0.259955	+	0.223868i
$127$	−3.53909e71			−1.04608			−0.523040	−	0.852308i	$-0.675202\pi$
$127$	−3.53909e71			−1.04608			−0.523040	+	0.852308i	$0.675202\pi$
$128$			4.50350e71i			1.01956i
$129$	4.20095e71	−	1.92626e71i	0.729957	−	0.334706i
$130$	1.17989e71			0.157677
$131$		−	1.44435e72i		−	1.48747i	−0.668473	−	0.743737i	$-0.733052\pi$
$131$		−	1.44435e72i		−	1.48747i	0.668473	−	0.743737i	$-0.266948\pi$
$132$	1.82998e71	+	3.99098e71i	0.145523	+	0.317370i
$133$	−2.05131e72			−1.26205
$134$		−	3.69259e71i		−	0.176104i
$135$	−3.41567e72	−	9.85985e71i	−1.26511	−	0.365193i
$136$	−3.50328e72			−1.00961
$137$		−	2.48851e71i		−	0.0559037i	−0.999609	−	0.0279519i	$-0.991101\pi$
$137$		−	2.48851e71i		−	0.0559037i	0.999609	−	0.0279519i	$-0.00889851\pi$
$138$	−2.42666e72	+	1.11269e72i	−0.425716	+	0.195203i
$139$	3.15760e72			0.433365			0.216682	−	0.976242i	$-0.430476\pi$
$139$	3.15760e72			0.433365			0.216682	+	0.976242i	$0.430476\pi$
$140$			9.13595e72i			0.982654i
$141$	−8.19200e72	−	1.78658e73i	−0.691736	−	1.50860i
$142$	1.09036e73			0.724046
$143$			2.41764e72i			0.126464i
$144$	8.96704e72	−	1.04125e73i	0.370105	−	0.429764i
$145$	−3.94969e73			−1.28840
$146$		−	1.27151e73i		−	0.328338i
$147$	1.00154e73	−	4.59236e72i	0.205060	−	0.0940258i
$148$	−5.75961e72			−0.0936472
$149$			6.83241e73i			0.883569i	0.897121	+	0.441785i	$0.145654\pi$
$149$			6.83241e73i			0.883569i	−0.897121	+	0.441785i	$0.854346\pi$
$150$	1.15755e73	+	2.52448e73i	0.119244	+	0.260057i
$151$	1.61210e74			1.32487			0.662437	−	0.749118i	$-0.269522\pi$
$151$	1.61210e74			1.32487			0.662437	+	0.749118i	$0.269522\pi$
$152$		−	1.57351e74i		−	1.03321i
$153$	2.02109e74	+	1.74052e74i	1.06188	+	0.914472i
$154$	3.35488e73			0.141245
$155$			6.23646e74i			2.10698i
$156$	8.72120e73	−	3.99892e73i	0.236777	−	0.108569i
$157$	5.51080e74			1.20400			0.602000	−	0.798496i	$-0.294371\pi$
$157$	5.51080e74			1.20400			0.602000	+	0.798496i	$0.294371\pi$
$158$			1.64616e74i			0.289821i
$159$	−3.66897e74	−	8.00162e74i	−0.521245	−	1.13678i
$160$	−1.08001e75			−1.23979
$161$		−	1.13824e75i		−	1.05719i
$162$	5.12352e74	−	7.68570e73i	0.385530	−	0.0578326i
$163$	1.37678e75			0.840397			0.420199	−	0.907432i	$-0.361960\pi$
$163$	1.37678e75			0.840397			0.420199	+	0.907432i	$0.361960\pi$
$164$			6.17548e74i			0.306182i
$165$	−1.22214e75	+	5.60386e74i	−0.492795	+	0.225961i
$166$	7.02047e73			0.0230511
$167$			2.48387e75i			0.664918i	0.943118	+	0.332459i	$0.107878\pi$
$167$			2.48387e75i			0.664918i	−0.943118	+	0.332459i	$0.892122\pi$
$168$	−1.20928e75	−	2.63731e75i	−0.264248	−	0.576296i
$169$	−5.07117e75			−0.905650
$170$		−	4.92284e75i		−	0.719370i
$171$	−7.81759e75	+	9.07776e75i	−0.935848	+	1.08670i
$172$	−6.93600e75			−0.680992
$173$		−	1.78249e76i		−	1.43701i	−0.695522	−	0.718505i	$-0.744827\pi$
$173$		−	1.78249e76i		−	1.43701i	0.695522	−	0.718505i	$-0.255173\pi$
$174$	5.23203e75	−	2.39904e75i	0.346734	−	0.158987i
$175$	−1.18412e76			−0.645805
$176$		−	5.19679e75i		−	0.233510i
$177$	−1.64842e75	−	3.59503e75i	−0.0610911	−	0.133233i
$178$	−2.16943e75			−0.0663843
$179$			2.47957e76i			0.627152i	0.949563	+	0.313576i	$0.101527\pi$
$179$			2.47957e76i			0.627152i	−0.949563	+	0.313576i	$0.898473\pi$
$180$	4.04298e76	+	3.48174e76i	0.846129	+	0.728670i
$181$	1.59028e76			0.275677			0.137839	−	0.990455i	$-0.455984\pi$
$181$	1.59028e76			0.275677			0.137839	+	0.990455i	$0.455984\pi$
$182$		−	7.33117e75i		−	0.105377i
$183$	3.67995e76	−	1.68736e76i	0.439041	−	0.201313i
$184$	8.73112e76			0.865494
$185$		−	1.76374e76i		−	0.145410i
$186$	−3.78802e76	−	8.26126e76i	−0.259999	−	0.567030i
$187$	1.00871e77			0.576967
$188$			2.94975e77i			1.40740i
$189$	−6.12635e76	+	2.12230e77i	−0.244062	+	0.845485i
$190$	2.21111e77			0.736185
$191$		−	1.67179e77i		−	0.465636i	−0.972520	−	0.232818i	$-0.925205\pi$
$191$		−	1.67179e77i		−	0.465636i	0.972520	−	0.232818i	$-0.0747947\pi$
$192$	−7.79957e76	+	3.57633e76i	−0.181898	+	0.0834056i
$193$	1.33711e77			0.261348			0.130674	−	0.991425i	$-0.458286\pi$
$193$	1.33711e77			0.261348			0.130674	+	0.991425i	$0.458286\pi$
$194$		−	4.56484e77i		−	0.748457i
$195$	1.22457e77	+	2.67065e77i	0.168580	+	0.367655i
$196$	−1.65360e77			−0.191304
$197$			1.90817e77i			0.185680i	0.995681	+	0.0928398i	$0.0295945\pi$
$197$			1.90817e77i			0.185680i	−0.995681	+	0.0928398i	$0.970406\pi$
$198$	1.27855e77	−	1.48465e77i	0.104738	−	0.121621i
$199$	−1.85648e78			−1.28140			−0.640700	−	0.767791i	$-0.721356\pi$
$199$	−1.85648e78			−1.28140			−0.640700	+	0.767791i	$0.721356\pi$
$200$		−	9.08308e77i		−	0.528705i
$201$	8.35808e77	−	3.83242e77i	0.410620	−	0.188281i
$202$	−1.15004e78			−0.477272
$203$			2.45411e78i			0.861051i
$204$	−1.66846e78	−	3.63873e78i	−0.495325	−	1.08025i
$205$	−1.89109e78			−0.475423
$206$		−	3.09247e78i		−	0.658901i
$207$	−5.03710e78	−	4.33785e78i	−0.910308	−	0.783940i
$208$	−1.13562e78			−0.174212
$209$			4.53064e78i			0.590453i
$210$	3.70597e78	−	1.69929e78i	0.410626	−	0.188284i
$211$	−2.69464e78			−0.254038			−0.127019	−	0.991900i	$-0.540541\pi$
$211$	−2.69464e78			−0.254038			−0.127019	+	0.991900i	$0.540541\pi$
$212$			1.32111e79i			1.06052i
$213$	1.13165e79	+	2.46800e79i	0.774114	+	1.68826i
$214$	7.69197e78			0.448714
$215$		−	2.12398e79i		−	1.05741i
$216$	−1.62796e79	−	4.69937e78i	−0.692177	−	0.199807i
$217$	3.87498e79			1.40812
$218$			2.62088e78i			0.0814567i
$219$	2.87802e79	−	1.31965e79i	0.765585	−	0.351043i
$220$	2.01782e79			0.459739
$221$		−	2.20425e79i		−	0.430451i
$222$	1.07129e78	+	2.33637e78i	0.0179435	+	0.0391328i
$223$	−3.61682e79			−0.519950			−0.259975	−	0.965615i	$-0.583714\pi$
$223$	−3.61682e79			−0.519950			−0.259975	+	0.965615i	$0.583714\pi$
$224$			6.71057e79i			0.828565i
$225$	−4.51271e79	+	5.24015e79i	−0.478886	+	0.556081i
$226$	2.17233e79			0.198262
$227$			5.82028e78i			0.0457156i	0.999739	+	0.0228578i	$0.00727650\pi$
$227$			5.82028e78i			0.0457156i	−0.999739	+	0.0228578i	$0.992724\pi$
$228$	1.63435e80	−	7.49394e79i	1.10550	−	0.506904i
$229$	3.09595e79			0.180463			0.0902314	−	0.995921i	$-0.471239\pi$
$229$	3.09595e79			0.180463			0.0902314	+	0.995921i	$0.471239\pi$
$230$			1.22691e80i			0.616687i
$231$	3.48192e79	+	7.59368e79i	0.151012	+	0.329340i
$232$	−1.88249e80			−0.704921
$233$		−	4.06017e80i		−	1.31354i	−0.754091	−	0.656770i	$-0.771922\pi$
$233$		−	4.06017e80i		−	1.31354i	0.754091	−	0.656770i	$-0.228078\pi$
$234$	−3.24430e79	−	2.79393e79i	−0.0907365	−	0.0781405i
$235$	−9.03287e80			−2.18534
$236$			5.93559e79i			0.124296i
$237$	−3.72603e80	+	1.70849e80i	−0.675776	+	0.309863i
$238$	−3.05877e80			−0.480762
$239$		−	1.03782e81i		−	1.41447i	−0.706977	−	0.707236i	$-0.749942\pi$
$239$		−	1.03782e81i		−	1.41447i	0.706977	−	0.707236i	$-0.250058\pi$
$240$	−2.63225e80	−	5.74065e80i	−0.311276	−	0.678858i
$241$	1.34466e81			1.38049			0.690243	−	0.723577i	$-0.257504\pi$
$241$	1.34466e81			1.38049			0.690243	+	0.723577i	$0.257504\pi$
$242$			3.63034e80i			0.323761i
$243$	7.05717e80	+	1.07993e81i	0.547038	+	0.837108i
$244$	−6.07580e80			−0.409590
$245$		−	5.06375e80i		−	0.297047i
$246$	2.50507e80	−	1.14864e80i	0.127946	−	0.0586667i
$247$	9.90047e80			0.440513
$248$			2.97240e81i			1.15279i
$249$	7.28631e79	+	1.58906e80i	0.0246451	+	0.0537482i
$250$	−4.62872e80			−0.136616
$251$			3.01240e81i			0.776257i	0.921605	+	0.388128i	$0.126878\pi$
$251$			3.01240e81i			0.776257i	−0.921605	+	0.388128i	$0.873122\pi$
$252$	2.16335e81	−	2.51208e81i	0.486978	−	0.565477i
$253$	−2.51397e81			−0.494610
$254$		−	2.37029e81i		−	0.407807i
$255$	1.11427e82	−	5.10925e81i	1.67735	−	0.769115i
$256$	−1.49766e81			−0.197358
$257$			9.84189e81i			1.13593i	0.823052	+	0.567966i	$0.192270\pi$
$257$			9.84189e81i			1.13593i	−0.823052	+	0.567966i	$0.807730\pi$
$258$	1.29010e81	+	2.81357e81i	0.130483	+	0.284569i
$259$	−1.09589e81			−0.0971792
$260$		−	4.40939e81i		−	0.342993i
$261$	1.08603e82	+	9.35268e81i	0.741421	+	0.638497i
$262$	9.67349e81			0.579882
$263$		−	4.05916e81i		−	0.213767i	−0.994272	−	0.106884i	$-0.965913\pi$
$263$		−	4.05916e81i		−	0.213767i	0.994272	−	0.106884i	$-0.0340872\pi$
$264$	−5.82492e81	+	2.67089e81i	−0.269623	+	0.123630i
$265$	−4.04558e82			−1.64672
$266$		−	1.37386e82i		−	0.492000i
$267$	−2.25158e81	−	4.91044e81i	−0.0709748	−	0.154788i
$268$	−1.37996e82			−0.383076
$269$		−	5.25452e82i		−	1.28516i	−0.766221	−	0.642578i	$-0.777865\pi$
$269$		−	5.25452e82i		−	1.28516i	0.766221	−	0.642578i	$-0.222135\pi$
$270$	6.60359e81	−	2.28763e82i	0.142368	−	0.493194i
$271$	−8.61663e82			−1.63825			−0.819127	−	0.573612i	$-0.805542\pi$
$271$	−8.61663e82			−1.63825			−0.819127	+	0.573612i	$0.805542\pi$
$272$			4.73811e82i			0.794809i
$273$	1.65939e82	−	7.60877e81i	0.245707	−	0.112664i
$274$	1.66667e81			0.0217937
$275$			2.61531e82i			0.302143i
$276$	4.15826e82	+	9.06871e82i	0.424623	+	0.926055i
$277$	−1.16498e83			−1.05198			−0.525990	−	0.850491i	$-0.676305\pi$
$277$	−1.16498e83			−1.05198			−0.525990	+	0.850491i	$0.676305\pi$
$278$			2.11479e82i			0.168944i
$279$	1.47677e83	−	1.71482e83i	1.04416	−	1.21248i
$280$	−1.33341e83			−0.834816
$281$			9.87472e82i			0.547659i	0.961778	+	0.273829i	$0.0882904\pi$
$281$			9.87472e82i			0.547659i	−0.961778	+	0.273829i	$0.911710\pi$
$282$	1.19656e83	−	5.48656e82i	0.588117	−	0.269669i
$283$	1.65575e83			0.721531			0.360766	−	0.932656i	$-0.382515\pi$
$283$	1.65575e83			0.721531			0.360766	+	0.932656i	$0.382515\pi$
$284$		−	4.07480e83i		−	1.57501i
$285$	2.29483e83	+	5.00478e83i	0.787093	+	1.71656i
$286$	−1.61920e82			−0.0493011
$287$			1.17501e83i			0.317730i
$288$	2.96966e83	+	2.55742e83i	0.713448	+	0.614408i
$289$	−4.51374e83			−0.963852
$290$		−	2.64529e83i		−	0.502274i
$291$	1.03324e84	−	4.73770e83i	1.74518	−	0.800213i
$292$	−4.75176e83			−0.714230
$293$			8.66232e83i			1.15914i	0.814923	+	0.579569i	$0.196779\pi$
$293$			8.66232e83i			1.15914i	−0.814923	+	0.579569i	$0.803221\pi$
$294$	3.07572e82	+	6.70780e82i	0.0366553	+	0.0799412i
$295$	−1.81763e83			−0.193000
$296$		−	8.40626e82i		−	0.0795582i
$297$	4.68744e83	+	1.35310e83i	0.395564	+	0.114185i
$298$	−4.57598e83			−0.344454
$299$			5.49360e83i			0.369009i
$300$	9.43428e83	−	4.32588e83i	0.565700	−	0.259389i
$301$	−1.31972e84			−0.706676
$302$			1.07969e84i			0.516493i
$303$	−1.19359e84	−	2.60308e84i	−0.510276	−	1.11285i
$304$	−2.12814e84			−0.813388
$305$		−	1.86056e84i		−	0.635989i
$306$	−1.16571e84	+	1.35361e84i	−0.356501	+	0.413968i
$307$	−3.09619e84			−0.847466			−0.423733	−	0.905787i	$-0.639281\pi$
$307$	−3.09619e84			−0.847466			−0.423733	+	0.905787i	$0.639281\pi$
$308$		−	1.25376e84i		−	0.307248i
$309$	6.99973e84	−	3.20957e84i	1.53636	−	0.704465i
$310$	−4.17685e84			−0.821393
$311$		−	6.96561e84i		−	1.22774i	−0.789408	−	0.613869i	$-0.789612\pi$
$311$		−	6.96561e84i		−	1.22774i	0.789408	−	0.613869i	$-0.210388\pi$
$312$	5.83650e83	+	1.27288e84i	0.0922351	+	0.201155i
$313$	−1.23850e85			−1.75545			−0.877727	−	0.479161i	$-0.840941\pi$
$313$	−1.23850e85			−1.75545			−0.877727	+	0.479161i	$0.840941\pi$
$314$			3.69083e84i			0.469371i
$315$	7.69262e84	+	6.62473e84i	0.878042	+	0.756152i
$316$	6.15188e84			0.630445
$317$			1.78763e85i			1.64537i	0.568501	+	0.822683i	$0.307524\pi$
$317$			1.78763e85i			1.64537i	−0.568501	+	0.822683i	$0.692476\pi$
$318$	5.35905e84	−	2.45728e84i	0.443165	−	0.203204i
$319$	5.42029e84			0.402846
$320$			3.94342e84i			0.263496i
$321$	7.98324e84	+	1.74106e85i	0.479742	+	1.04627i
$322$	7.62329e84			0.412138
$323$		−	4.13076e85i		−	2.00976i
$324$	−2.87224e84	−	1.91472e85i	−0.125803	−	0.838639i
$325$	5.71505e84			0.225417
$326$			9.22090e84i			0.327623i
$327$	−5.93230e84	+	2.72013e84i	−0.189932	+	0.0870894i
$328$	−9.01324e84			−0.260118
$329$			5.61251e85i			1.46048i
$330$	−3.75316e84	−	8.18523e84i	−0.0880893	−	0.192113i
$331$	6.32889e85			1.34022			0.670109	−	0.742262i	$-0.266247\pi$
$331$	6.32889e85			1.34022			0.670109	+	0.742262i	$0.266247\pi$
$332$		−	2.62363e84i		−	0.0501427i
$333$	−4.17645e84	+	4.84968e84i	−0.0720615	+	0.0836776i
$334$	−1.66356e85			−0.259214
$335$		−	4.22580e85i		−	0.594820i
$336$	−3.56691e85	+	1.63553e85i	−0.453688	+	0.208029i
$337$	7.70740e85			0.886117			0.443059	−	0.896493i	$-0.353893\pi$
$337$	7.70740e85			0.886117			0.443059	+	0.896493i	$0.353893\pi$
$338$		−	3.39640e85i		−	0.353062i
$339$	2.25459e85	+	4.91701e85i	0.211972	+	0.462287i
$340$	−1.83972e86			−1.56484
$341$		−	8.55851e85i		−	0.658794i
$342$	−6.07980e85	−	5.23580e85i	−0.423644	−	0.364834i
$343$	−1.70935e86			−1.07853
$344$		−	1.01232e86i		−	0.578538i
$345$	−2.77707e86	+	1.27336e86i	−1.43793	+	0.659331i
$346$	1.19382e86			0.560209
$347$			1.44828e86i			0.616098i	0.951370	+	0.308049i	$0.0996761\pi$
$347$			1.44828e86i			0.616098i	−0.951370	+	0.308049i	$0.900324\pi$
$348$	−8.96548e85	−	1.95527e86i	−0.345843	−	0.754246i
$349$	1.58500e86			0.554579			0.277290	−	0.960786i	$-0.410564\pi$
$349$	1.58500e86			0.554579			0.277290	+	0.960786i	$0.410564\pi$
$350$		−	7.93059e85i		−	0.251763i
$351$	2.95683e85	−	1.02431e86i	0.0851891	−	0.295114i
$352$	1.48213e86			0.387648
$353$			4.37795e86i			1.03975i	0.854241	+	0.519877i	$0.174022\pi$
$353$			4.37795e86i			1.03975i	−0.854241	+	0.519877i	$0.825978\pi$
$354$	2.40776e85	−	1.10403e85i	0.0519400	−	0.0238160i
$355$	1.24781e87			2.44559
$356$			8.10741e85i			0.144405i
$357$	−3.17460e86	−	6.92344e86i	−0.514007	−	1.12099i
$358$	−1.66068e86			−0.244491
$359$			6.75199e86i			0.904108i	0.891990	+	0.452054i	$0.149309\pi$
$359$			6.75199e86i			0.904108i	−0.891990	+	0.452054i	$0.850691\pi$
$360$	−5.08166e86	+	5.90081e86i	−0.619043	+	0.718831i
$361$	9.53261e86			1.05674
$362$			1.06508e86i			0.107471i
$363$	−8.21718e86	+	3.76781e86i	−0.754914	+	0.346150i
$364$	−2.73974e86			−0.229225
$365$		−	1.45511e87i		−	1.10902i
$366$	1.13010e86	+	2.46463e86i	0.0784804	+	0.171157i
$367$	2.65891e87			1.68290			0.841448	−	0.540339i	$-0.181704\pi$
$367$	2.65891e87			1.68290			0.841448	+	0.540339i	$0.181704\pi$
$368$		−	1.18087e87i		−	0.681358i
$369$	5.19985e86	+	4.47801e86i	0.273586	+	0.235607i
$370$	1.18126e86			0.0566872
$371$			2.51369e87i			1.10052i
$372$	−3.08733e87	+	1.41563e87i	−1.23345	+	0.565574i
$373$	2.42013e87			0.882546			0.441273	−	0.897373i	$-0.354527\pi$
$373$	2.42013e87			0.882546			0.441273	+	0.897373i	$0.354527\pi$
$374$			6.75578e86i			0.224927i
$375$	−4.80399e86	−	1.04770e87i	−0.146063	−	0.318547i
$376$	−4.30522e87			−1.19566
$377$		−	1.18446e87i		−	0.300547i
$378$	−1.42140e87	−	4.10309e86i	−0.329607	−	0.0951460i
$379$	−7.02346e87			−1.48874			−0.744369	−	0.667769i	$-0.767250\pi$
$379$	−7.02346e87			−1.48874			−0.744369	+	0.667769i	$0.767250\pi$
$380$		−	8.26316e87i		−	1.60142i
$381$	5.36508e87	−	2.46004e87i	0.950884	−	0.436007i
$382$	1.11967e87			0.181525
$383$			3.26500e87i			0.484312i	0.970237	+	0.242156i	$0.0778546\pi$
$383$			3.26500e87i			0.484312i	−0.970237	+	0.242156i	$0.922145\pi$
$384$	−3.13041e87	−	6.82708e87i	−0.424952	−	0.926773i
$385$	3.83932e87			0.477078
$386$			8.95524e86i			0.101885i
$387$	−5.02948e87	+	5.84022e87i	−0.524023	+	0.608494i
$388$	−1.70593e88			−1.62811
$389$			4.74444e86i			0.0414857i	0.999785	+	0.0207429i	$0.00660313\pi$
$389$			4.74444e86i			0.0414857i	−0.999785	+	0.0207429i	$0.993397\pi$
$390$	−1.78866e87	+	8.20150e86i	−0.143328	+	0.0657199i
$391$	2.29209e88			1.68353
$392$		−	2.41347e87i		−	0.162523i
$393$	1.00398e88	+	2.18957e88i	0.619981	+	1.35211i
$394$	−1.27799e87			−0.0723860
$395$			1.88386e88i			0.978921i
$396$	−5.54832e87	−	4.77811e87i	−0.264561	−	0.227834i
$397$	1.84404e88			0.807036			0.403518	−	0.914972i	$-0.367787\pi$
$397$	1.84404e88			0.807036			0.403518	+	0.914972i	$0.367787\pi$
$398$		−	1.24337e88i		−	0.499545i
$399$	3.10968e88	−	1.42588e88i	1.14720	−	0.526022i
$400$	−1.22847e88			−0.416221
$401$		−	1.24748e88i		−	0.388261i	−0.980976	−	0.194131i	$-0.937811\pi$
$401$		−	1.24748e88i		−	0.388261i	0.980976	−	0.194131i	$-0.0621886\pi$
$402$	2.56675e87	+	5.59779e87i	0.0734002	+	0.160078i
$403$	−1.87023e88			−0.491499
$404$			4.29783e88i			1.03820i
$405$	5.86336e88	−	8.79551e87i	1.30219	−	0.195340i
$406$	−1.64363e88			−0.335675
$407$			2.42044e87i			0.0454657i
$408$	5.31080e88	−	2.43515e88i	0.917729	−	0.420805i
$409$	−4.33673e88			−0.689556			−0.344778	−	0.938684i	$-0.612046\pi$
$409$	−4.33673e88			−0.689556			−0.344778	+	0.938684i	$0.612046\pi$
$410$		−	1.26655e88i		−	0.185341i
$411$	1.72978e87	+	3.77247e87i	0.0233007	+	0.0508163i
$412$	−1.15569e89			−1.43330
$413$			1.12937e88i			0.128984i
$414$	2.90526e88	−	3.37358e88i	0.305614	−	0.354878i
$415$	8.03422e87			0.0778590
$416$		−	3.23880e88i		−	0.289208i
$417$	−4.78677e88	+	2.19487e88i	−0.393928	+	0.180627i
$418$	−3.03438e88			−0.230184
$419$			1.21051e89i			0.846627i	0.905983	+	0.423314i	$0.139133\pi$
$419$			1.21051e89i			0.846627i	−0.905983	+	0.423314i	$0.860867\pi$
$420$	−6.35046e88	−	1.38497e89i	−0.409571	−	0.893230i
$421$	−1.33215e89			−0.792433			−0.396217	−	0.918157i	$-0.629677\pi$
$421$	−1.33215e89			−0.792433			−0.396217	+	0.918157i	$0.629677\pi$
$422$		−	1.80473e88i		−	0.0990349i
$423$	2.48374e89	+	2.13894e89i	1.25757	+	1.08300i
$424$	−1.92819e89			−0.900970
$425$		−	2.38448e89i		−	1.02842i
$426$	−1.65293e89	+	7.57916e88i	−0.658156	+	0.301783i
$427$	−1.15605e89			−0.425038
$428$		−	2.87458e89i		−	0.976082i
$429$	−1.68052e88	−	3.66502e88i	−0.0527103	−	0.114955i
$430$	1.42253e89			0.412223
$431$		−	3.33681e89i		−	0.893520i	−0.894654	−	0.446760i	$-0.852578\pi$
$431$		−	3.33681e89i		−	0.893520i	0.894654	−	0.446760i	$-0.147422\pi$
$432$	−6.35580e88	+	2.20179e89i	−0.157298	+	0.544915i
$433$	2.53243e89			0.579360			0.289680	−	0.957124i	$-0.406451\pi$
$433$	2.53243e89			0.579360			0.289680	+	0.957124i	$0.406451\pi$
$434$			2.59525e89i			0.548945i
$435$	5.98753e89	−	2.74545e89i	1.17115	−	0.537007i
$436$	9.79455e88			0.177192
$437$			1.02950e90i			1.72288i
$438$	8.83832e88	+	1.92754e89i	0.136852	+	0.298458i
$439$	8.17890e89			1.17193			0.585965	−	0.810337i	$-0.300716\pi$
$439$	8.17890e89			1.17193			0.585965	+	0.810337i	$0.300716\pi$
$440$			2.94505e89i			0.390572i
$441$	−1.19907e89	+	1.39236e89i	−0.147209	+	0.170938i
$442$	1.47629e89			0.167809
$443$			1.01735e88i			0.0107089i	0.999986	+	0.00535444i	$0.00170438\pi$
$443$			1.01735e88i			0.0107089i	−0.999986	+	0.00535444i	$0.998296\pi$
$444$	8.73129e88	−	4.00355e88i	0.0851251	−	0.0390323i
$445$	−2.48269e89			−0.224224
$446$		−	2.42235e89i		−	0.202699i
$447$	−4.74925e89	−	1.03576e90i	−0.368273	−	0.803162i
$448$	2.45022e89			0.176097
$449$			2.89294e88i			0.0192737i	0.999954	+	0.00963683i	$0.00306755\pi$
$449$			2.89294e88i			0.0192737i	−0.999954	+	0.00963683i	$0.996932\pi$
$450$	−3.50957e89	−	3.02237e89i	−0.216784	−	0.186690i
$451$	2.59520e89			0.148651
$452$		−	8.11826e89i		−	0.431277i
$453$	−2.44386e90	+	1.12058e90i	−1.20431	+	0.552209i
$454$	−3.89811e88			−0.0178219
$455$		−	8.38978e89i		−	0.355929i
$456$	1.09376e90	+	2.38536e90i	0.430641	+	0.939181i
$457$	−2.69119e89			−0.0983545			−0.0491772	−	0.998790i	$-0.515660\pi$
$457$	−2.69119e89			−0.0983545			−0.0491772	+	0.998790i	$0.515660\pi$
$458$			2.07350e89i			0.0703523i
$459$	−4.27372e90	−	1.23367e90i	−1.34640	−	0.388659i
$460$	4.58509e90			1.34147
$461$		−	2.20696e90i		−	0.599741i	−0.953980	−	0.299870i	$-0.903057\pi$
$461$		−	2.20696e90i		−	0.599741i	0.953980	−	0.299870i	$-0.0969435\pi$
$462$	−5.08583e89	+	2.33200e89i	−0.128391	+	0.0588710i
$463$	−1.43368e90			−0.336278			−0.168139	−	0.985763i	$-0.553776\pi$
$463$	−1.43368e90			−0.336278			−0.168139	+	0.985763i	$0.553776\pi$
$464$			2.54602e90i			0.554947i
$465$	−4.33501e90	−	9.45418e90i	−0.878193	−	1.91524i
$466$	2.71928e90			0.512075
$467$			2.89873e90i			0.507497i	0.967270	+	0.253749i	$0.0816636\pi$
$467$			2.89873e90i			0.507497i	−0.967270	+	0.253749i	$0.918336\pi$
$468$	−1.04412e90	+	1.21243e90i	−0.169978	+	0.197378i
$469$	−2.62567e90			−0.397524
$470$		−	6.04973e90i		−	0.851940i
$471$	−8.35411e90	+	3.83060e90i	−1.09443	+	0.501829i
$472$	−8.66311e89			−0.105596
$473$			2.91481e90i			0.330621i
$474$	−1.14426e90	−	2.49549e90i	−0.120798	−	0.263447i
$475$	1.07100e91			1.05246
$476$			1.14310e91i			1.04580i
$477$	1.11240e91	+	9.57974e90i	0.947621	+	0.816073i
$478$	6.95077e90			0.551423
$479$			4.81572e90i			0.355839i	0.984045	+	0.177920i	$0.0569367\pi$
$479$			4.81572e90i			0.355839i	−0.984045	+	0.177920i	$0.943063\pi$
$480$	1.63724e91	−	7.50723e90i	1.12697	−	0.516746i
$481$	5.28920e89			0.0339201
$482$			9.00579e90i			0.538174i
$483$	7.91196e90	+	1.72551e91i	0.440638	+	0.960982i
$484$	1.35670e91			0.704275
$485$		−	5.22400e91i		−	2.52804i
$486$	−7.23277e90	+	4.72651e90i	−0.326341	+	0.213259i
$487$	−4.72904e90			−0.198970			−0.0994852	−	0.995039i	$-0.531720\pi$
$487$	−4.72904e90			−0.198970			−0.0994852	+	0.995039i	$0.531720\pi$
$488$		−	8.86774e90i		−	0.347968i
$489$	−2.08713e91	+	9.57007e90i	−0.763919	+	0.350279i
$490$	3.39143e90			0.115802
$491$			4.35588e91i			1.38773i	0.720105	+	0.693865i	$0.244093\pi$
$491$			4.35588e91i			1.38773i	−0.720105	+	0.693865i	$0.755907\pi$
$492$	−4.29262e90	−	9.36173e90i	−0.127617	−	0.278319i
$493$	−4.94188e91			−1.37119
$494$			6.63080e90i			0.171731i
$495$	1.46318e91	−	1.69904e91i	0.353769	−	0.410796i
$496$	4.02012e91			0.907531
$497$		−	7.75316e91i		−	1.63441i
$498$	−1.06427e90	+	4.87998e89i	−0.0209534	+	0.00960772i
$499$	−3.28448e91			−0.604016			−0.302008	−	0.953305i	$-0.597657\pi$
$499$	−3.28448e91			−0.604016			−0.302008	+	0.953305i	$0.597657\pi$
$500$			1.72981e91i			0.297178i
$501$	−1.72655e91	−	3.76542e91i	−0.277139	−	0.604409i
$502$	−2.01754e91			−0.302619
$503$			1.04665e92i			1.46720i	0.679583	+	0.733598i	$0.262161\pi$
$503$			1.04665e92i			1.46720i	−0.679583	+	0.733598i	$0.737839\pi$
$504$	3.66643e91	+	3.15746e91i	0.480402	+	0.413713i
$505$	−1.31610e92			−1.61207
$506$		−	1.68372e91i		−	0.192821i
$507$	7.68766e91	−	3.52501e91i	0.823234	−	0.377476i
$508$	−8.85805e91			−0.887098
$509$		−	2.32586e91i		−	0.217861i	−0.994049	−	0.108930i	$-0.965257\pi$
$509$		−	2.32586e91i		−	0.217861i	0.994049	−	0.108930i	$-0.0347426\pi$
$510$	3.42190e91	+	7.46278e91i	0.299834	+	0.653905i
$511$	−9.04122e91			−0.741168
$512$			1.22889e92i			0.942617i
$513$	5.54108e91	−	1.91955e92i	0.397744	−	1.37787i
$514$	−6.59157e91			−0.442836
$515$		−	3.53902e92i		−	2.22555i
$516$	1.05146e92	−	4.82126e91i	0.619020	−	0.283838i
$517$	1.23961e92			0.683294
$518$		−	7.33965e90i		−	0.0378847i
$519$	1.23902e92	+	2.70217e92i	0.598947	+	1.30624i
$520$	6.43559e91			0.291390
$521$			4.10587e92i			1.74150i	0.491729	+	0.870748i	$0.336365\pi$
$521$			4.10587e92i			1.74150i	−0.491729	+	0.870748i	$0.663635\pi$
$522$	−6.26392e91	+	7.27364e91i	−0.248914	+	0.289038i
$523$	2.42810e92			0.904083			0.452042	−	0.891997i	$-0.350696\pi$
$523$	2.42810e92			0.904083			0.452042	+	0.891997i	$0.350696\pi$
$524$		−	3.61510e92i		−	1.26141i
$525$	1.79507e92	−	8.23090e91i	0.587036	−	0.269173i
$526$	2.71861e91			0.0833357
$527$			7.80312e92i			2.24237i
$528$	3.61233e91	+	7.87809e91i	0.0973271	+	0.212260i
$529$	−1.75435e92			−0.443223
$530$		−	2.70951e92i		−	0.641964i
$531$	4.99786e91	+	4.30406e91i	0.111063	+	0.0956455i
$532$	−5.13426e92			−1.07024
$533$		−	5.67110e91i		−	0.110903i
$534$	3.28875e91	−	1.50798e91i	0.0603431	−	0.0276690i
$535$	8.80269e92			1.51561
$536$		−	2.01409e92i		−	0.325443i
$537$	−1.72356e92	−	3.75890e92i	−0.261398	−	0.570079i
$538$	3.51919e92			0.501009
$539$			6.94916e91i			0.0928783i
$540$	−8.54915e92	−	2.46784e92i	−1.07284	−	0.309691i
$541$	−7.68290e92			−0.905354			−0.452677	−	0.891675i	$-0.649531\pi$
$541$	−7.68290e92			−0.905354			−0.452677	+	0.891675i	$0.649531\pi$
$542$		−	5.77095e92i		−	0.638663i
$543$	−2.41078e92	+	1.10541e92i	−0.250590	+	0.114903i
$544$	−1.35132e93			−1.31946
$545$			2.99934e92i			0.275134i
$546$	5.09595e91	+	1.11137e92i	0.0439213	+	0.0957874i
$547$	9.64189e92			0.780896			0.390448	−	0.920625i	$-0.372320\pi$
$547$	9.64189e92			0.780896			0.390448	+	0.920625i	$0.372320\pi$
$548$		−	6.22855e91i		−	0.0474076i
$549$	−4.40573e92	+	5.11592e92i	−0.315179	+	0.365985i
$550$	−1.75160e92			−0.117788
$551$		−	2.21966e93i		−	1.40324i
$552$	−1.32360e93	+	6.06907e92i	−0.786732	+	0.360739i
$553$	1.17052e93			0.654223
$554$		−	7.80243e92i		−	0.410108i
$555$	1.22599e92	+	2.67374e92i	0.0606072	+	0.132178i
$556$	7.90321e92			0.367503
$557$			3.21266e91i			0.0140536i	0.999975	+	0.00702681i	$0.00223672\pi$
$557$			3.21266e91i			0.0140536i	−0.999975	+	0.00702681i	$0.997763\pi$
$558$	1.14849e93	+	9.89059e92i	0.472678	+	0.407061i
$559$	6.36951e92			0.246663
$560$			1.80341e93i			0.657206i
$561$	−1.52915e93	+	7.01160e92i	−0.524461	+	0.240480i
$562$	−6.61356e92			−0.213501
$563$			5.87549e93i			1.78549i	0.450558	+	0.892747i	$0.351225\pi$
$563$			5.87549e93i			1.78549i	−0.450558	+	0.892747i	$0.648775\pi$
$564$	−2.05039e93	−	4.47168e93i	−0.586607	−	1.27933i
$565$	2.48602e93			0.669663
$566$			1.10893e93i			0.281284i
$567$	−5.46503e92	−	3.64315e93i	−0.130547	−	0.870269i
$568$	5.94725e93			1.33805
$569$		−	3.33910e93i		−	0.707640i	−0.935314	−	0.353820i	$-0.884883\pi$
$569$		−	3.33910e93i		−	0.707640i	0.935314	−	0.353820i	$-0.115117\pi$
$570$	−3.35193e93	+	1.53696e93i	−0.669191	+	0.306843i
$571$	8.66772e93			1.63034			0.815168	−	0.579225i	$-0.196645\pi$
$571$	8.66772e93			1.63034			0.815168	+	0.579225i	$0.196645\pi$
$572$			6.05116e92i			0.107244i
$573$	1.16207e93	+	2.53435e93i	0.194078	+	0.423262i
$574$	−7.86961e92			−0.123865
$575$			5.94278e93i			0.881623i
$576$	9.33785e92	−	1.08431e93i	0.130582	−	0.151631i
$577$	4.11821e93			0.542914			0.271457	−	0.962451i	$-0.412495\pi$
$577$	4.11821e93			0.542914			0.271457	+	0.962451i	$0.412495\pi$
$578$		−	3.02306e93i		−	0.375751i
$579$	−2.02699e93	+	9.29434e92i	−0.237564	+	0.108930i
$580$	−9.88575e93			−1.09259
$581$		−	4.99201e92i		−	0.0520339i
$582$	3.17305e93	+	6.92008e93i	0.311958	+	0.680345i
$583$	5.55188e93			0.514884
$584$		−	6.93530e93i		−	0.606776i
$585$	−3.71278e93	−	3.19737e93i	−0.306478	−	0.263933i
$586$	−5.80155e93			−0.451882
$587$		−	8.90006e93i		−	0.654181i	−0.944993	−	0.327090i	$-0.893932\pi$
$587$		−	8.90006e93i		−	0.654181i	0.944993	−	0.327090i	$-0.106068\pi$
$588$	2.50678e93	−	1.14943e93i	0.173895	−	0.0797359i
$589$	−3.50479e94			−2.29479
$590$		−	1.21735e93i		−	0.0752396i
$591$	−1.32638e93	−	2.89269e93i	−0.0773915	−	0.168782i
$592$	−1.13693e93			−0.0626319
$593$		−	1.91214e94i		−	0.994627i	−0.867571	−	0.497313i	$-0.834320\pi$
$593$		−	1.91214e94i		−	0.994627i	0.867571	−	0.497313i	$-0.165680\pi$
$594$	−9.06233e92	+	3.13939e93i	−0.0445144	+	0.154208i
$595$	−3.50046e94			−1.62386
$596$			1.71010e94i			0.749286i
$597$	2.81433e94	−	1.29045e94i	1.16479	−	0.534089i
$598$	−3.67932e93			−0.143856
$599$			2.64373e94i			0.976572i	0.872684	+	0.488286i	$0.162378\pi$
$599$			2.64373e94i			0.976572i	−0.872684	+	0.488286i	$0.837622\pi$
$600$	6.31371e93	+	1.37695e94i	0.220365	+	0.480591i
$601$	3.86706e94			1.27541			0.637704	−	0.770282i	$-0.279884\pi$
$601$	3.86706e94			1.27541			0.637704	+	0.770282i	$0.279884\pi$
$602$		−	8.83876e93i		−	0.275493i
$603$	−1.00065e94	+	1.16195e94i	−0.294777	+	0.342294i
$604$	4.03495e94			1.12352
$605$			4.15456e94i			1.09356i
$606$	1.74340e94	−	7.99400e93i	0.433839	−	0.198928i
$607$	−4.51675e94			−1.06270			−0.531350	−	0.847152i	$-0.678315\pi$
$607$	−4.51675e94			−1.06270			−0.531350	+	0.847152i	$0.678315\pi$
$608$		−	6.06948e94i		−	1.35030i
$609$	−1.70587e94	−	3.72031e94i	−0.358887	−	0.782693i
$610$	1.24610e94			0.247936
$611$		−	2.70883e94i		−	0.509778i
$612$	5.05862e94	+	4.35638e94i	0.900499	+	0.775492i
$613$	−2.50255e94			−0.421432			−0.210716	−	0.977547i	$-0.567579\pi$
$613$	−2.50255e94			−0.421432			−0.210716	+	0.977547i	$0.567579\pi$
$614$		−	2.07366e94i		−	0.330379i
$615$	2.86680e94	−	1.31451e94i	0.432158	−	0.198157i
$616$	1.82988e94			0.261023
$617$			1.40782e94i			0.190043i	0.995475	+	0.0950217i	$0.0302921\pi$
$617$			1.40782e94i			0.190043i	−0.995475	+	0.0950217i	$0.969708\pi$
$618$	2.14960e94	+	4.68804e94i	0.274631	+	0.598940i
$619$	−5.55167e94			−0.671338			−0.335669	−	0.941980i	$-0.608962\pi$
$619$	−5.55167e94			−0.671338			−0.335669	+	0.941980i	$0.608962\pi$
$620$			1.56094e95i			1.78677i
$621$	1.06513e95	+	3.07465e94i	1.15422	+	0.333182i
$622$	4.66519e94			0.478626
$623$			1.54260e94i			0.149851i
$624$	1.72154e94	−	7.89375e93i	0.158358	−	0.0726118i
$625$	−1.37215e95			−1.19531
$626$		−	8.29482e94i		−	0.684352i
$627$	−3.14928e94	−	6.86823e94i	−0.246102	−	0.536721i
$628$	1.37931e95			1.02102
$629$		−	2.20680e94i		−	0.154754i
$630$	−4.43689e94	+	5.15210e94i	−0.294781	+	0.342299i
$631$	−1.12738e95			−0.709698			−0.354849	−	0.934924i	$-0.615468\pi$
$631$	−1.12738e95			−0.709698			−0.354849	+	0.934924i	$0.615468\pi$
$632$			8.97880e94i			0.535596i
$633$	4.08495e94	−	1.87307e94i	0.230920	−	0.105883i
$634$	−1.19726e95			−0.641435
$635$		−	2.71256e95i		−	1.37744i
$636$	−9.18314e94	−	2.00274e95i	−0.442027	−	0.964013i
$637$	1.51855e94			0.0692927
$638$			3.63022e94i			0.157047i
$639$	−3.43105e95	−	2.95475e95i	−1.40734	−	1.21197i
$640$	−3.45174e95			−1.34251
$641$			4.27561e95i			1.57698i	0.615050	+	0.788488i	$0.289136\pi$
$641$			4.27561e95i			1.57698i	−0.615050	+	0.788488i	$0.710864\pi$
$642$	−1.16607e95	+	5.34674e94i	−0.407880	+	0.187024i
$643$	3.00026e95			0.995374			0.497687	−	0.867357i	$-0.334183\pi$
$643$	3.00026e95			0.995374			0.497687	+	0.867357i	$0.334183\pi$
$644$		−	2.84891e95i		−	0.896519i
$645$	1.47639e95	+	3.21985e95i	0.440729	+	0.961181i
$646$	2.76656e95			0.783491
$647$		−	2.82123e95i		−	0.758042i	−0.925388	−	0.379021i	$-0.876261\pi$
$647$		−	2.82123e95i		−	0.758042i	0.925388	−	0.379021i	$-0.123739\pi$
$648$	2.79457e95	−	4.19209e94i	0.712468	−	0.106876i
$649$	2.49439e94			0.0603455
$650$			3.82763e94i			0.0878772i
$651$	−5.87429e95	+	2.69353e95i	−1.27998	+	0.586905i
$652$	3.44596e95			0.712675
$653$			3.02469e95i			0.593790i	0.954910	+	0.296895i	$0.0959512\pi$
$653$			3.02469e95i			0.593790i	−0.954910	+	0.296895i	$0.904049\pi$
$654$	−1.82179e94	−	3.97313e94i	−0.0339512	−	0.0740439i
$655$	1.10703e96			1.95865
$656$			1.21902e95i			0.204777i
$657$	−3.44564e95	+	4.00106e95i	−0.549600	+	0.638194i
$658$	−3.75896e95			−0.569360
$659$		−	2.14111e95i		−	0.307988i	−0.988072	−	0.153994i	$-0.950786\pi$
$659$		−	2.14111e95i		−	0.307988i	0.988072	−	0.153994i	$-0.0492137\pi$
$660$	−3.05892e95	+	1.40260e95i	−0.417901	+	0.191620i
$661$	2.26156e95			0.293466			0.146733	−	0.989176i	$-0.453124\pi$
$661$	2.26156e95			0.293466			0.146733	+	0.989176i	$0.453124\pi$
$662$			4.23875e95i			0.522475i
$663$	1.53219e95	+	3.34154e95i	0.179413	+	0.391279i
$664$	3.82924e94			0.0425989
$665$		−	1.57224e96i		−	1.66182i
$666$	−3.24805e94	−	2.79716e94i	−0.0326212	−	0.0280927i
$667$	1.23165e96			1.17546
$668$			6.21692e95i			0.563865i
$669$	5.48293e95	−	2.51408e95i	0.472633	−	0.216716i
$670$	2.83021e95			0.231887
$671$			2.55331e95i			0.198856i
$672$	−4.66456e95	−	1.01729e96i	−0.345347	−	0.753163i
$673$	8.08039e95			0.568748			0.284374	−	0.958713i	$-0.408214\pi$
$673$	8.08039e95			0.568748			0.284374	+	0.958713i	$0.408214\pi$
$674$			5.16200e95i			0.345447i
$675$	3.19859e95	−	1.10806e96i	0.203531	−	0.705076i
$676$	−1.26927e96			−0.768012
$677$			2.77813e96i			1.59859i	0.600937	+	0.799296i	$0.294794\pi$
$677$			2.77813e96i			1.59859i	−0.600937	+	0.799296i	$0.705206\pi$
$678$	−3.29315e95	+	1.51000e95i	−0.180220	+	0.0826358i
$679$	−3.24590e96			−1.68952
$680$		−	2.68511e96i		−	1.32941i
$681$	−4.04571e94	−	8.82326e94i	−0.0190543	−	0.0415554i
$682$	5.73203e95			0.256826
$683$			7.06957e95i			0.301363i	0.988582	+	0.150681i	$0.0481467\pi$
$683$			7.06957e95i			0.301363i	−0.988582	+	0.150681i	$0.951853\pi$
$684$	−1.95668e96	+	2.27209e96i	−0.793620	+	0.921549i
$685$	1.90734e95			0.0736119
$686$		−	1.14483e96i		−	0.420456i
$687$	−4.69331e95	+	2.15202e95i	−0.164040	+	0.0752172i
$688$	−1.36915e96			−0.455452
$689$		−	1.21321e96i		−	0.384134i
$690$	−8.52830e95	−	1.85993e96i	−0.257036	−	0.560567i
$691$	1.49114e96			0.427824			0.213912	−	0.976853i	$-0.431379\pi$
$691$	1.49114e96			0.427824			0.213912	+	0.976853i	$0.431379\pi$
$692$		−	4.46143e96i		−	1.21862i
$693$	−1.05568e96	−	9.09134e95i	−0.274539	−	0.236428i
$694$	−9.69978e95			−0.240182
$695$			2.42016e96i			0.570639i
$696$	2.85376e96	−	1.30853e96i	0.640771	−	0.293812i
$697$	−2.36615e96			−0.505973
$698$			1.06154e96i			0.216199i
$699$	2.82225e96	+	6.15502e96i	0.547485	+	1.19400i
$700$	−2.96375e96			−0.547657
$701$			3.85880e96i			0.679265i	0.940558	+	0.339633i	$0.110303\pi$
$701$			3.85880e96i			0.679265i	−0.940558	+	0.339633i	$0.889697\pi$
$702$	6.86028e95	+	1.98032e95i	0.115048	+	0.0332104i
$703$	9.91192e95			0.158371
$704$		−	5.41169e95i		−	0.0823877i
$705$	1.36934e97	−	6.27881e96i	1.98647	−	0.910852i
$706$	−2.93211e96			−0.405341
$707$			8.17752e96i			1.07736i
$708$	−4.12587e95	−	8.99807e95i	−0.0518066	−	0.112984i
$709$	6.98464e96			0.835934			0.417967	−	0.908462i	$-0.362743\pi$
$709$	6.98464e96			0.835934			0.417967	+	0.908462i	$0.362743\pi$
$710$			8.35713e96i			0.953396i
$711$	4.46090e96	−	5.17998e96i	0.485128	−	0.563329i
$712$	−1.18329e96			−0.122680
$713$		−	1.94475e97i		−	1.92229i
$714$	4.63695e96	−	2.12617e96i	0.437012	−	0.200382i
$715$	−1.85302e96			−0.166523
$716$			6.20615e96i			0.531838i
$717$	7.21398e96	+	1.57329e97i	0.589554	+	1.28575i
$718$	−4.52212e96			−0.352461
$719$		−	2.97161e96i		−	0.220907i	−0.993881	−	0.110454i	$-0.964770\pi$
$719$		−	2.97161e96i		−	0.220907i	0.993881	−	0.110454i	$-0.0352304\pi$
$720$	7.98073e96	+	6.87285e96i	0.565898	+	0.487340i
$721$	−2.19895e97			−1.48736
$722$			6.38442e96i			0.411962i
$723$	−2.03844e97	+	9.34681e96i	−1.25486	+	0.575389i
$724$	3.98033e96			0.233780
$725$		−	1.28130e97i		−	0.718057i
$726$	−2.52348e96	−	5.50342e96i	−0.134944	−	0.294298i
$727$	1.16440e97			0.594201			0.297101	−	0.954846i	$-0.403980\pi$
$727$	1.16440e97			0.594201			0.297101	+	0.954846i	$0.403980\pi$
$728$		−	3.99871e96i		−	0.194739i
$729$	−1.82050e97	−	1.14657e97i	−0.846164	−	0.532923i
$730$	9.74554e96			0.432343
$731$		−	2.65754e97i		−	1.12535i
$732$	9.21061e96	−	4.22333e96i	0.372316	−	0.170718i
$733$	−4.54501e97			−1.75388			−0.876940	−	0.480599i	$-0.840419\pi$
$733$	−4.54501e97			−1.75388			−0.876940	+	0.480599i	$0.840419\pi$
$734$			1.78079e97i			0.656066i
$735$	3.51985e96	+	7.67640e96i	0.123810	+	0.270015i
$736$	3.36785e97			1.13112
$737$			5.79921e96i			0.185983i
$738$	−2.99913e96	+	3.48258e96i	−0.0918499	+	0.106656i
$739$	1.16422e97			0.340504			0.170252	−	0.985401i	$-0.445542\pi$
$739$	1.16422e97			0.340504			0.170252	+	0.985401i	$0.445542\pi$
$740$		−	4.41449e96i		−	0.123311i
$741$	−1.50086e97	+	6.88188e96i	−0.400426	+	0.183607i
$742$	−1.68353e97			−0.429031
$743$		−	4.35557e96i		−	0.106029i	−0.998594	−	0.0530146i	$-0.983117\pi$
$743$		−	4.35557e96i		−	0.106029i	0.998594	−	0.0530146i	$-0.0168830\pi$
$744$	−2.06614e97	−	4.50602e97i	−0.480485	−	1.04788i
$745$	−5.23675e97			−1.16345
$746$			1.62087e97i			0.344055i
$747$	−2.20914e96	−	1.90247e96i	−0.0448046	−	0.0385849i
$748$	2.52471e97			0.489280
$749$		−	5.46949e97i		−	1.01290i
$750$	7.01691e96	−	3.21745e96i	0.124183	−	0.0569416i
$751$	4.92302e97			0.832671			0.416335	−	0.909211i	$-0.363314\pi$
$751$	4.92302e97			0.832671			0.416335	+	0.909211i	$0.363314\pi$
$752$			5.82272e97i			0.941281i
$753$	−2.09394e97	−	4.56665e97i	−0.323545	−	0.705616i
$754$	7.93284e96			0.117166
$755$			1.23560e98i			1.74455i
$756$	−1.53338e97	+	5.31195e97i	−0.206970	+	0.716990i
$757$	1.10038e98			1.41998			0.709990	−	0.704211i	$-0.248699\pi$
$757$	1.10038e98			1.41998			0.709990	+	0.704211i	$0.248699\pi$
$758$		−	4.70394e97i		−	0.580375i
$759$	3.81106e97	−	1.74748e97i	0.449599	−	0.206154i
$760$	1.20603e98			1.36049
$761$			5.72960e97i			0.618082i	0.951049	+	0.309041i	$0.100008\pi$
$761$			5.72960e97i			0.618082i	−0.951049	+	0.309041i	$0.899992\pi$
$762$	1.64760e97	+	3.59324e97i	0.169975	+	0.370696i
$763$	1.86362e97			0.183875
$764$		−	4.18435e97i		−	0.394870i
$765$	−1.33403e98	+	1.54908e98i	−1.20414	+	1.39825i
$766$	−2.18672e97			−0.188806
$767$		−	5.45081e96i		−	0.0450214i
$768$	2.27038e97	−	1.04104e97i	0.179398	−	0.0822591i
$769$	1.35142e98			1.02163			0.510815	−	0.859691i	$-0.329344\pi$
$769$	1.35142e98			1.02163			0.510815	+	0.859691i	$0.329344\pi$
$770$			2.57137e97i			0.185986i
$771$	−6.84117e97	−	1.49198e98i	−0.473458	−	1.03256i
$772$	3.34668e97			0.221629
$773$		−	1.39471e98i		−	0.883854i	−0.897051	−	0.441927i	$-0.854295\pi$
$773$		−	1.39471e98i		−	0.883854i	0.897051	−	0.441927i	$-0.145705\pi$
$774$	−3.91146e97	−	3.36848e97i	−0.237217	−	0.204287i
$775$	−2.02314e98			−1.17427
$776$		−	2.48984e98i		−	1.38316i
$777$	1.66131e97	−	7.61758e96i	0.0883356	−	0.0405044i
$778$	−3.17757e96			−0.0161729
$779$		−	1.06276e98i		−	0.517800i
$780$	3.06500e97	+	6.68442e97i	0.142960	+	0.311779i
$781$	−1.71241e98			−0.764666
$782$			1.53511e98i			0.656313i
$783$	−2.29648e98	−	6.62914e97i	−0.940076	−	0.271367i
$784$	−3.26417e97			−0.127946
$785$			4.22379e98i			1.58538i
$786$	−1.46646e98	+	6.72412e97i	−0.527111	+	0.241696i
$787$	2.63767e98			0.907987			0.453993	−	0.891005i	$-0.349999\pi$
$787$	2.63767e98			0.907987			0.453993	+	0.891005i	$0.349999\pi$
$788$			4.77598e97i			0.157460i
$789$	2.82155e97	+	6.15349e97i	0.0890984	+	0.194314i
$790$	−1.26171e98			−0.381626
$791$		−	1.54467e98i		−	0.447543i
$792$	6.97374e97	−	8.09789e97i	0.193557	−	0.224758i
$793$	5.57956e97			0.148358
$794$			1.23504e98i			0.314618i
$795$	6.13290e98	−	2.81211e98i	1.49687	−	0.686356i
$796$	−4.64661e98			−1.08666
$797$		−	3.97147e98i		−	0.889956i	−0.895541	−	0.444978i	$-0.853211\pi$
$797$		−	3.97147e98i		−	0.889956i	0.895541	−	0.444978i	$-0.146789\pi$
$798$	9.54977e97	+	2.08270e98i	0.205066	+	0.447227i
$799$	−1.13020e99			−2.32576
$800$		−	3.50361e98i		−	0.690966i
$801$	6.82657e97	+	5.87891e97i	0.129032	+	0.111120i
$802$	8.35493e97			0.151361
$803$			1.99690e98i			0.346758i
$804$	2.09196e98	−	9.59223e97i	0.348215	−	0.159667i
$805$	8.72409e98			1.39207
$806$		−	1.25258e98i		−	0.191608i
$807$	3.65245e98	+	7.96560e98i	0.535654	+	1.16820i
$808$	−6.27277e98			−0.882009
$809$		−	3.92185e98i		−	0.528739i	−0.964421	−	0.264370i	$-0.914836\pi$
$809$		−	3.92185e98i		−	0.528739i	0.964421	−	0.264370i	$-0.0851639\pi$
$810$	5.89076e97	+	3.92696e98i	0.0761519	+	0.507651i
$811$	9.88493e98			1.22536			0.612681	−	0.790330i	$-0.290091\pi$
$811$	9.88493e98			1.22536			0.612681	+	0.790330i	$0.290091\pi$
$812$			6.14244e98i			0.730190i
$813$	1.30624e99	−	5.98948e98i	1.48917	−	0.682827i
$814$	−1.62108e97			−0.0177245
$815$			1.05524e99i			1.10660i
$816$	−3.29350e98	−	7.18275e98i	−0.331277	−	0.722479i
$817$	1.19364e99			1.15166
$818$		−	2.90451e98i		−	0.268819i
$819$	−1.98666e98	+	2.30691e98i	−0.176389	+	0.204822i
$820$	−4.73324e98			−0.403169
$821$			1.68698e99i			1.37862i	0.724468	+	0.689309i	$0.242086\pi$
$821$			1.68698e99i			1.37862i	−0.724468	+	0.689309i	$0.757914\pi$
$822$	−2.52659e97	+	1.15851e97i	−0.0198104	+	0.00908364i
$823$	−9.47488e98			−0.712819			−0.356409	−	0.934330i	$-0.615999\pi$
$823$	−9.47488e98			−0.712819			−0.356409	+	0.934330i	$0.615999\pi$
$824$		−	1.68676e99i		−	1.21766i
$825$	−1.81792e98	−	3.96469e98i	−0.125934	−	0.274647i
$826$	−7.56391e97			−0.0502834
$827$			1.20826e99i			0.770858i	0.922738	+	0.385429i	$0.125946\pi$
$827$			1.20826e99i			0.770858i	−0.922738	+	0.385429i	$0.874054\pi$
$828$	−1.26074e99	−	1.08573e99i	−0.771962	−	0.664798i
$829$	−2.17989e99			−1.28109			−0.640547	−	0.767919i	$-0.721292\pi$
$829$	−2.17989e99			−1.28109			−0.640547	+	0.767919i	$0.721292\pi$
$830$			5.38089e97i			0.0303528i
$831$	1.76606e99	−	8.09788e98i	0.956247	−	0.438467i
$832$	−1.18258e98			−0.0614662
$833$		−	6.33581e98i		−	0.316135i
$834$	−1.47000e98	−	3.20592e98i	−0.0704163	−	0.153570i
$835$	−1.90378e99			−0.875539
$836$			1.13398e99i			0.500718i
$837$	−1.04673e99	+	3.62609e99i	−0.443780	+	1.53735i
$838$	−8.10735e98			−0.330052
$839$		−	4.17628e99i		−	1.63261i	−0.577621	−	0.816305i	$-0.696019\pi$
$839$		−	4.17628e99i		−	1.63261i	0.577621	−	0.816305i	$-0.303981\pi$
$840$	2.02139e99	−	9.26863e98i	0.758846	−	0.347952i
$841$	1.18207e98			0.0426168
$842$		−	8.92204e98i		−	0.308925i
$843$	−6.86399e98	−	1.49696e99i	−0.228265	−	0.497821i
$844$	−6.74448e98			−0.215429
$845$		−	3.88684e99i		−	1.19253i
$846$	−1.43255e99	+	1.66347e99i	−0.422199	+	0.490256i
$847$	2.58141e99			0.730837
$848$			2.60784e99i			0.709286i
$849$	−2.51003e99	+	1.15092e99i	−0.655870	+	0.300735i
$850$	1.59700e99			0.400923
$851$			5.49996e98i			0.132664i
$852$	2.83242e99	+	6.17720e99i	0.656466	+	1.43168i
$853$	2.87935e99			0.641249			0.320624	−	0.947206i	$-0.396107\pi$
$853$	2.87935e99			0.641249			0.320624	+	0.947206i	$0.396107\pi$
$854$		−	7.74258e98i		−	0.165698i
$855$	−6.95772e99	−	5.99185e99i	−1.43093	−	1.23229i
$856$	4.19551e99			0.829233
$857$			7.85669e99i			1.49242i	0.665709	+	0.746211i	$0.268129\pi$
$857$			7.85669e99i			1.49242i	−0.665709	+	0.746211i	$0.731871\pi$
$858$	2.45463e98	−	1.12552e98i	0.0448146	−	0.0205488i
$859$	−2.23718e99			−0.392586			−0.196293	−	0.980545i	$-0.562890\pi$
$859$	−2.23718e99			−0.392586			−0.196293	+	0.980545i	$0.562890\pi$
$860$		−	5.31614e99i		−	0.896705i
$861$	−8.16760e98	−	1.78126e99i	−0.132430	−	0.288816i
$862$	2.23481e99			0.348333
$863$			5.08165e99i			0.761444i	0.924690	+	0.380722i	$0.124324\pi$
$863$			5.08165e99i			0.761444i	−0.924690	+	0.380722i	$0.875676\pi$
$864$	−6.27954e99	−	1.81269e99i	−0.904609	−	0.261129i
$865$	1.36620e100			1.89220
$866$			1.69608e99i			0.225860i
$867$	6.84262e99	−	3.13754e99i	0.876139	−	0.401735i
$868$	9.69877e99			1.19411
$869$		−	2.58529e99i		−	0.306081i
$870$	1.83876e99	+	4.01013e99i	0.209348	+	0.456566i
$871$	1.26726e99			0.138755
$872$			1.42953e99i			0.150534i
$873$	−1.23702e100	+	1.43642e100i	−1.25283	+	1.45478i
$874$	−6.89501e99			−0.671655
$875$			3.29132e99i			0.308387i
$876$	7.20345e99	−	3.30299e99i	0.649233	−	0.297692i
$877$	−9.17253e99			−0.795249			−0.397624	−	0.917548i	$-0.630165\pi$
$877$	−9.17253e99			−0.795249			−0.397624	+	0.917548i	$0.630165\pi$
$878$			5.47779e99i			0.456869i
$879$	−6.02124e99	−	1.31317e100i	−0.483130	−	1.05365i
$880$	3.98312e99			0.307477
$881$		−	8.59759e99i		−	0.638552i	−0.947662	−	0.319276i	$-0.896560\pi$
$881$		−	8.59759e99i		−	0.638552i	0.947662	−	0.319276i	$-0.103440\pi$
$882$	−9.32528e98	−	8.03075e98i	−0.0666392	−	0.0573884i
$883$	5.87117e99			0.403702			0.201851	−	0.979416i	$-0.435304\pi$
$883$	5.87117e99			0.403702			0.201851	+	0.979416i	$0.435304\pi$
$884$		−	5.51707e99i		−	0.365032i
$885$	2.75544e99	−	1.26345e99i	0.175436	−	0.0804425i
$886$	−6.81367e97			−0.00417479
$887$			1.79676e99i			0.105946i	0.998596	+	0.0529732i	$0.0168698\pi$
$887$			1.79676e99i			0.105946i	−0.998596	+	0.0529732i	$0.983130\pi$
$888$	5.84325e98	+	1.27435e99i	0.0331600	+	0.0723182i
$889$	−1.68543e100			−0.920556
$890$		−	1.66277e99i		−	0.0874123i
$891$	−8.04648e99	+	1.20704e99i	−0.407159	+	0.0610772i
$892$	−9.05261e99			−0.440929
$893$		−	5.07633e100i		−	2.38013i
$894$	6.93696e99	−	3.18079e99i	0.313108	−	0.143569i
$895$	−1.90048e100			−0.825810
$896$			2.14471e100i			0.897215i
$897$	−3.81864e99	−	8.32803e99i	−0.153803	−	0.335428i
$898$	−1.93754e98			−0.00751371
$899$			4.19301e100i			1.56565i
$900$	−1.12950e100	+	1.31157e100i	−0.406106	+	0.471569i
$901$	−5.06186e100			−1.75254
$902$			1.73813e99i			0.0579508i
$903$	2.00063e100	−	9.17346e99i	0.642367	−	0.294544i
$904$	1.18488e100			0.366392
$905$			1.21888e100i			0.363002i
$906$	−7.50503e99	−	1.63676e100i	−0.215275	−	0.469491i
$907$	5.46134e100			1.50887			0.754434	−	0.656376i	$-0.227911\pi$
$907$	5.46134e100			1.50887			0.754434	+	0.656376i	$0.227911\pi$
$908$			1.45677e99i			0.0387678i
$909$	3.61884e100	+	3.11648e100i	0.927679	+	0.798899i
$910$	5.61902e99			0.138757
$911$		−	5.30808e98i		−	0.0126274i	−0.999980	−	0.00631368i	$-0.997990\pi$
$911$		−	5.30808e98i		−	0.0126274i	0.999980	−	0.00631368i	$-0.00200972\pi$
$912$	3.22615e100	−	1.47928e100i	0.739368	−	0.339021i
$913$	−1.10256e99			−0.0243443
$914$		−	1.80242e99i		−	0.0383428i
$915$	1.29329e100	+	2.82052e100i	0.265081	+	0.578112i
$916$	7.74892e99			0.153036
$917$		−	6.87848e100i		−	1.30899i
$918$	8.26247e99	−	2.86230e100i	0.151516	−	0.524886i
$919$	−3.08385e100			−0.544962			−0.272481	−	0.962161i	$-0.587844\pi$
$919$	−3.08385e100			−0.544962			−0.272481	+	0.962161i	$0.587844\pi$
$920$			6.69203e100i			1.13965i
$921$	4.69367e100	−	2.15218e100i	0.770345	−	0.353225i
$922$	1.47810e100			0.233805
$923$			3.74200e100i			0.570487i
$924$	8.71496e99	+	1.90064e100i	0.128061	+	0.279288i
$925$	5.72166e99			0.0810408
$926$		−	9.60202e99i		−	0.131096i
$927$	−8.38025e100	+	9.73112e100i	−1.10293	+	1.28071i
$928$	−7.26131e100			−0.921263
$929$		−	1.22362e101i		−	1.49663i	−0.663345	−	0.748314i	$-0.730864\pi$
$929$		−	1.22362e101i		−	1.49663i	0.663345	−	0.748314i	$-0.269136\pi$
$930$	6.33190e100	−	2.90336e100i	0.746644	−	0.342358i
$931$	2.84575e100			0.323525
$932$		−	1.01623e101i		−	1.11391i
$933$	4.84184e100	+	1.05595e101i	0.511723	+	1.11601i
$934$	−1.94141e100			−0.197844
$935$			7.73131e100i			0.759728i
$936$	−1.76957e100	−	1.52392e100i	−0.167683	−	0.144405i
$937$	−9.41927e99			−0.0860738			−0.0430369	−	0.999073i	$-0.513703\pi$
$937$	−9.41927e99			−0.0860738			−0.0430369	+	0.999073i	$0.513703\pi$
$938$		−	1.75853e100i		−	0.154972i
$939$	1.87751e101	−	8.60892e100i	1.59570	−	0.731676i
$940$	−2.26086e101			−1.85321
$941$			1.93977e101i			1.53357i	0.641903	+	0.766786i	$0.278145\pi$
$941$			1.93977e101i			1.53357i	−0.641903	+	0.766786i	$0.721855\pi$
$942$	−2.56553e100	−	5.59513e100i	−0.195635	−	0.426657i
$943$	5.89708e100			0.433750
$944$			1.17167e100i			0.0831299i
$945$	−1.62665e101	−	4.69558e100i	−1.11330	−	0.321372i
$946$	−1.95218e100			−0.128891
$947$			2.50660e100i			0.159656i	0.996809	+	0.0798281i	$0.0254371\pi$
$947$			2.50660e100i			0.159656i	−0.996809	+	0.0798281i	$0.974563\pi$
$948$	−9.32596e100	+	4.27622e100i	−0.573073	+	0.262770i
$949$	4.36367e100			0.258703
$950$			7.17295e100i			0.410294i
$951$	−1.24259e101	−	2.70996e101i	−0.685790	−	1.49563i
$952$	−1.66838e101			−0.888459
$953$		−	1.36354e101i		−	0.700666i	−0.936625	−	0.350333i	$-0.886068\pi$
$953$		−	1.36354e101i		−	0.700666i	0.936625	−	0.350333i	$-0.113932\pi$
$954$	−6.41599e100	+	7.45023e100i	−0.318141	+	0.369424i
$955$	1.28135e101			0.613133
$956$		−	2.59759e101i		−	1.19950i
$957$	−8.21690e100	+	3.76768e100i	−0.366186	+	0.167907i
$958$	−3.22531e100			−0.138722
$959$		−	1.18511e100i		−	0.0491956i
$960$	−2.74110e100	−	5.97804e100i	−0.109825	−	0.239517i
$961$	4.03486e101			1.56039
$962$			3.54242e99i			0.0132235i
$963$	−2.42044e101	−	2.08444e101i	−0.872169	−	0.751095i
$964$	3.36557e101			1.17068
$965$			1.02484e101i			0.344133i
$966$	−1.15565e101	+	5.29900e100i	−0.374633	+	0.171780i
$967$	6.74425e100			0.211073			0.105537	−	0.994415i	$-0.466344\pi$
$967$	6.74425e100			0.211073			0.105537	+	0.994415i	$0.466344\pi$
$968$			1.98013e101i			0.598318i
$969$	2.87132e101	+	6.26203e101i	0.837670	+	1.82686i
$970$	3.49875e101			0.985540
$971$			5.70283e101i			1.55109i	0.631294	+	0.775544i	$0.282524\pi$
$971$			5.70283e101i			1.55109i	−0.631294	+	0.775544i	$0.717476\pi$
$972$	1.76635e101	+	2.70297e101i	0.463900	+	0.709886i
$973$	1.50375e101			0.381364
$974$		−	3.16725e100i		−	0.0775673i
$975$	−8.66374e100	+	3.97257e100i	−0.204903	+	0.0939539i
$976$	−1.19934e101			−0.273937
$977$		−	7.30301e101i		−	1.61097i	−0.592618	−	0.805483i	$-0.701906\pi$
$977$		−	7.30301e101i		−	1.61097i	0.592618	−	0.805483i	$-0.298094\pi$
$978$	−6.40951e100	−	1.39784e101i	−0.136554	−	0.297809i
$979$	3.40708e100			0.0701086
$980$		−	1.26742e101i		−	0.251903i
$981$	7.10229e100	−	8.24716e100i	0.136349	−	0.158328i
$982$	−2.91733e101			−0.540997
$983$			1.45035e101i			0.259809i	0.991527	+	0.129904i	$0.0414670\pi$
$983$			1.45035e101i			0.259809i	−0.991527	+	0.129904i	$0.958533\pi$
$984$	1.36636e101	−	6.26516e100i	0.236446	−	0.108417i
$985$	−1.46253e101			−0.244496
$986$		−	3.30981e101i		−	0.534549i
$987$	−3.90130e101	−	8.50830e101i	−0.608732	−	1.32758i
$988$	2.47801e101			0.373565
$989$			6.62331e101i			0.964720i
$990$	1.13792e101	+	9.79956e100i	0.160146	+	0.137915i
$991$	5.40363e101			0.734821			0.367410	−	0.930059i	$-0.380244\pi$
$991$	5.40363e101			0.734821			0.367410	+	0.930059i	$0.380244\pi$
$992$			1.14654e102i			1.50659i
$993$	−9.59429e101	+	4.39926e101i	−1.21826	+	0.558605i
$994$	5.19265e101			0.637165
$995$		−	1.42291e102i		−	1.68730i
$996$	1.82371e100	+	3.97730e100i	0.0208996	+	0.0455796i
$997$	−8.16389e101			−0.904194			−0.452097	−	0.891969i	$-0.649324\pi$
$997$	−8.16389e101			−0.904194			−0.452097	+	0.891969i	$0.649324\pi$
$998$		−	2.19977e101i		−	0.235472i
$999$	2.96025e100	−	1.02550e101i	0.0306268	−	0.106098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.69.b.a.2.12	yes	22
3.2	odd	2	inner	3.69.b.a.2.11	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.69.b.a.2.11	✓	22	3.2	odd	2	inner
3.69.b.a.2.12	yes	22	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+6.69746e9i q^{2} +(-1.51595e16 + 6.95107e15i) q^{3} +2.50292e20 q^{4} +7.66457e23i q^{5} +(-4.65545e25 - 1.01530e26i) q^{6} +4.76233e28 q^{7} +3.65306e30i q^{8} +(1.81494e32 - 2.10750e32i) q^{9} +O(q^{10})\)	\(q+6.69746e9i q^{2} +(-1.51595e16 + 6.95107e15i) q^{3} +2.50292e20 q^{4} +7.66457e23i q^{5} +(-4.65545e25 - 1.01530e26i) q^{6} +4.76233e28 q^{7} +3.65306e30i q^{8} +(1.81494e32 - 2.10750e32i) q^{9} -5.13331e33 q^{10} -1.05183e35i q^{11} +(-3.79431e36 + 1.73980e36i) q^{12} -2.29850e37 q^{13} +3.18955e38i q^{14} +(-5.32770e39 - 1.16191e40i) q^{15} +4.94069e40 q^{16} +9.58998e41i q^{17} +(1.41149e42 + 1.21555e42i) q^{18} -4.30737e43 q^{19} +1.91838e44i q^{20} +(-7.21946e44 + 3.31033e44i) q^{21} +7.04462e44 q^{22} -2.39008e46i q^{23} +(-2.53927e46 - 5.53786e46i) q^{24} -2.48643e47 q^{25} -1.53941e47i q^{26} +(-1.28642e48 + 4.45644e48i) q^{27} +1.19197e49 q^{28} +5.15317e49i q^{29} +(7.78186e49 - 3.56820e49i) q^{30} +8.13675e50 q^{31} +1.40909e51i q^{32} +(7.31138e50 + 1.59453e51i) q^{33} -6.42285e51 q^{34} +3.65012e52i q^{35} +(4.54264e52 - 5.27490e52i) q^{36} -2.30116e52 q^{37} -2.88484e53i q^{38} +(3.48441e53 - 1.59770e53i) q^{39} -2.79991e54 q^{40} +2.46731e54i q^{41} +(-2.21708e54 - 4.83520e54i) q^{42} -2.77116e55 q^{43} -2.63266e55i q^{44} +(1.61531e56 + 1.39107e56i) q^{45} +1.60075e56 q^{46} +1.17852e57i q^{47} +(-7.48985e56 + 3.43431e56i) q^{48} -6.60670e56 q^{49} -1.66528e57i q^{50} +(-6.66606e57 - 1.45379e58i) q^{51} -5.75295e57 q^{52} +5.27828e58i q^{53} +(-2.98468e58 - 8.61574e57i) q^{54} +8.06186e58 q^{55} +1.73971e59i q^{56} +(6.52976e59 - 2.99408e59i) q^{57} -3.45132e59 q^{58} +2.37147e59i q^{59} +(-1.33348e60 - 2.90817e60i) q^{60} -2.42748e60 q^{61} +5.44955e60i q^{62} +(8.64332e60 - 1.00366e61i) q^{63} +5.14500e60 q^{64} -1.76170e61i q^{65} +(-1.06793e61 + 4.89677e60i) q^{66} -5.51342e61 q^{67} +2.40029e62i q^{68} +(1.66136e62 + 3.62325e62i) q^{69} -2.44465e62 q^{70} -1.62802e63i q^{71} +(7.69882e62 + 6.63007e62i) q^{72} -1.89849e63 q^{73} -1.54119e62i q^{74} +(3.76931e63 - 1.72834e63i) q^{75} -1.07810e64 q^{76} -5.00918e63i q^{77} +(1.07005e63 + 2.33367e63i) q^{78} +2.45788e64 q^{79} +3.78683e64i q^{80} +(-1.14755e64 - 7.64995e64i) q^{81} -1.65247e64 q^{82} -1.04823e64i q^{83} +(-1.80697e65 + 8.28548e64i) q^{84} -7.35031e65 q^{85} -1.85598e65i q^{86} +(-3.58201e65 - 7.81196e65i) q^{87} +3.84242e65 q^{88} +3.23918e65i q^{89} +(-9.31664e65 + 1.08184e66i) q^{90} -1.09462e66 q^{91} -5.98219e66i q^{92} +(-1.23349e67 + 5.65591e66i) q^{93} -7.89311e66 q^{94} -3.30141e67i q^{95} +(-9.79471e66 - 2.13612e67i) q^{96} -6.81578e67 q^{97} -4.42481e66i q^{98} +(-2.21674e67 - 1.90901e67i) 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

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