LMFDB - Embedded newform 3.69.b.a.2.14

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			2.14
Character	$\chi$	$=$	3.2
Dual form			3.69.b.a.2.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.08296e9i q^{2} +(-6.37287e15 + 1.54115e16i) q^{3} +2.12648e20 q^{4} -8.19633e23i q^{5} +(-1.39982e26 - 5.78846e25i) q^{6} -1.46000e28 q^{7} +4.61229e30i q^{8} +(-1.96901e32 - 1.96431e32i) q^{9} +O(q^{10})$	\(q+9.08296e9i q^{2} +(-6.37287e15 + 1.54115e16i) q^{3} +2.12648e20 q^{4} -8.19633e23i q^{5} +(-1.39982e26 - 5.78846e25i) q^{6} -1.46000e28 q^{7} +4.61229e30i q^{8} +(-1.96901e32 - 1.96431e32i) q^{9} +7.44469e33 q^{10} +9.57569e34i q^{11} +(-1.35518e36 + 3.27722e36i) q^{12} -4.01379e37 q^{13} -1.32611e38i q^{14} +(1.26318e40 + 5.22341e39i) q^{15} +2.08693e40 q^{16} -9.03733e40i q^{17} +(1.78418e42 - 1.78845e42i) q^{18} +5.00561e43 q^{19} -1.74293e44i q^{20} +(9.30438e43 - 2.25008e44i) q^{21} -8.69756e44 q^{22} -1.67236e45i q^{23} +(-7.10824e46 - 2.93935e46i) q^{24} -3.32985e47 q^{25} -3.64571e47i q^{26} +(4.28213e48 - 1.78272e48i) q^{27} -3.10465e48 q^{28} +6.61119e49i q^{29} +(-4.74441e49 + 1.14734e50i) q^{30} -7.76836e50 q^{31} +1.55086e51i q^{32} +(-1.47576e51 - 6.10246e50i) q^{33} +8.20857e50 q^{34} +1.19666e52i q^{35} +(-4.18706e52 - 4.17706e52i) q^{36} -5.29571e52 q^{37} +4.54658e53i q^{38} +(2.55794e53 - 6.18586e53i) q^{39} +3.78038e54 q^{40} -7.25162e54i q^{41} +(2.04374e54 + 8.45114e53i) q^{42} -4.70196e55 q^{43} +2.03625e55i q^{44} +(-1.61001e56 + 1.61387e56i) q^{45} +1.51900e55 q^{46} +3.33636e56i q^{47} +(-1.32997e56 + 3.21627e56i) q^{48} -2.71549e57 q^{49} -3.02449e57i q^{50} +(1.39279e57 + 5.75937e56i) q^{51} -8.53523e57 q^{52} -2.18859e58i q^{53} +(1.61924e58 + 3.88944e58i) q^{54} +7.84855e58 q^{55} -6.73394e58i q^{56} +(-3.19001e59 + 7.71440e59i) q^{57} -6.00492e59 q^{58} -2.70885e60i q^{59} +(2.68612e60 + 1.11075e60i) q^{60} +5.80460e60 q^{61} -7.05597e60i q^{62} +(2.87476e60 + 2.86789e60i) q^{63} -7.92691e60 q^{64} +3.28983e61i q^{65} +(5.54284e60 - 1.34043e61i) q^{66} -1.64188e62 q^{67} -1.92177e61i q^{68} +(2.57737e61 + 1.06578e61i) q^{69} -1.08692e62 q^{70} +8.24659e62i q^{71} +(9.05998e62 - 9.08166e62i) q^{72} -1.92603e63 q^{73} -4.81008e62i q^{74} +(2.12207e63 - 5.13180e63i) q^{75} +1.06443e64 q^{76} -1.39805e63i q^{77} +(5.61859e63 + 2.32336e63i) q^{78} -6.09106e64 q^{79} -1.71051e64i q^{80} +(1.84940e62 + 7.73552e64i) q^{81} +6.58662e64 q^{82} -2.89288e65i q^{83} +(1.97856e64 - 4.78474e64i) q^{84} -7.40729e64 q^{85} -4.27078e65i q^{86} +(-1.01888e66 - 4.21322e65i) q^{87} -4.41658e65 q^{88} +1.30346e65i q^{89} +(-1.46587e66 - 1.46237e66i) q^{90} +5.86013e65 q^{91} -3.55624e65i q^{92} +(4.95068e66 - 1.19722e67i) q^{93} -3.03040e66 q^{94} -4.10276e67i q^{95} +(-2.39011e67 - 9.88344e66i) q^{96} -4.75457e66 q^{97} -2.46647e67i q^{98} +(1.88096e67 - 1.88547e67i) 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 $

$2$			9.08296e9i			0.528698i	0.964427	+	0.264349i	$0.0851571\pi$
$2$			9.08296e9i			0.528698i	−0.964427	+	0.264349i	$0.914843\pi$
$3$	−6.37287e15	+	1.54115e16i	−0.382131	+	0.924108i
$3$	−6.37287e15	+	1.54115e16i	−0.382131	+	0.924108i
$4$	2.12648e20			0.720478
$5$		−	8.19633e23i		−	1.40812i	−0.710141	−	0.704059i	$-0.751369\pi$
$5$		−	8.19633e23i		−	1.40812i	0.710141	−	0.704059i	$-0.248631\pi$
$6$	−1.39982e26	−	5.78846e25i	−0.488574	−	0.202032i
$7$	−1.46000e28			−0.269786			−0.134893	−	0.990860i	$-0.543069\pi$
$7$	−1.46000e28			−0.269786			−0.134893	+	0.990860i	$0.543069\pi$
$8$			4.61229e30i			0.909614i
$9$	−1.96901e32	−	1.96431e32i	−0.707952	−	0.706261i
$10$	7.44469e33			0.744469
$11$			9.57569e34i			0.374816i	0.982282	+	0.187408i	$0.0600087\pi$
$11$			9.57569e34i			0.374816i	−0.982282	+	0.187408i	$0.939991\pi$
$12$	−1.35518e36	+	3.27722e36i	−0.275317	+	0.665800i
$13$	−4.01379e37			−0.536390			−0.268195	−	0.963365i	$-0.586427\pi$
$13$	−4.01379e37			−0.536390			−0.268195	+	0.963365i	$0.586427\pi$
$14$		−	1.32611e38i		−	0.142635i
$15$	1.26318e40	+	5.22341e39i	1.30125	+	0.538086i
$16$	2.08693e40			0.239567
$17$		−	9.03733e40i		−	0.132062i	−0.997818	−	0.0660308i	$-0.978966\pi$
$17$		−	9.03733e40i		−	0.132062i	0.997818	−	0.0660308i	$-0.0210336\pi$
$18$	1.78418e42	−	1.78845e42i	0.373399	−	0.374293i
$19$	5.00561e43			1.66661			0.833306	−	0.552812i	$-0.186445\pi$
$19$	5.00561e43			1.66661			0.833306	+	0.552812i	$0.186445\pi$
$20$		−	1.74293e44i		−	1.01452i
$21$	9.30438e43	−	2.25008e44i	0.103094	−	0.249311i
$22$	−8.69756e44			−0.198165
$23$		−	1.67236e45i		−	0.0840590i	−0.999116	−	0.0420295i	$-0.986618\pi$
$23$		−	1.67236e45i		−	0.0840590i	0.999116	−	0.0420295i	$-0.0133823\pi$
$24$	−7.10824e46	−	2.93935e46i	−0.840581	−	0.347592i
$25$	−3.32985e47			−0.982797
$26$		−	3.64571e47i		−	0.283588i
$27$	4.28213e48	−	1.78272e48i	0.923192	−	0.384339i
$28$	−3.10465e48			−0.194375
$29$			6.61119e49i			1.25530i	0.778496	+	0.627650i	$0.215983\pi$
$29$			6.61119e49i			1.25530i	−0.778496	+	0.627650i	$0.784017\pi$
$30$	−4.74441e49	+	1.14734e50i	−0.284485	+	0.687970i
$31$	−7.76836e50			−1.52768			−0.763839	−	0.645407i	$-0.776688\pi$
$31$	−7.76836e50			−1.52768			−0.763839	+	0.645407i	$0.776688\pi$
$32$			1.55086e51i			1.03627i
$33$	−1.47576e51	−	6.10246e50i	−0.346371	−	0.143229i
$34$	8.20857e50			0.0698208
$35$			1.19666e52i			0.379890i
$36$	−4.18706e52	−	4.17706e52i	−0.510064	−	0.508846i
$37$	−5.29571e52			−0.254136			−0.127068	−	0.991894i	$-0.540557\pi$
$37$	−5.29571e52			−0.254136			−0.127068	+	0.991894i	$0.540557\pi$
$38$			4.54658e53i			0.881135i
$39$	2.55794e53	−	6.18586e53i	0.204971	−	0.495682i
$40$	3.78038e54			1.28084
$41$		−	7.25162e54i		−	1.06117i	−0.847632	−	0.530584i	$-0.821973\pi$
$41$		−	7.25162e54i		−	1.06117i	0.847632	−	0.530584i	$-0.178027\pi$
$42$	2.04374e54	+	8.45114e53i	0.131810	+	0.0545054i
$43$	−4.70196e55			−1.36255			−0.681274	−	0.732029i	$-0.738574\pi$
$43$	−4.70196e55			−1.36255			−0.681274	+	0.732029i	$0.738574\pi$
$44$			2.03625e55i			0.270047i
$45$	−1.61001e56	+	1.61387e56i	−0.994499	+	0.996880i
$46$	1.51900e55			0.0444418
$47$			3.33636e56i			0.469835i	0.972015	+	0.234918i	$0.0754820\pi$
$47$			3.33636e56i			0.469835i	−0.972015	+	0.234918i	$0.924518\pi$
$48$	−1.32997e56	+	3.21627e56i	−0.0915462	+	0.221386i
$49$	−2.71549e57			−0.927216
$50$		−	3.02449e57i		−	0.519603i
$51$	1.39279e57	+	5.75937e56i	0.122039	+	0.0504649i
$52$	−8.53523e57			−0.386457
$53$		−	2.18859e58i		−	0.518542i	−0.965805	−	0.259271i	$-0.916518\pi$
$53$		−	2.18859e58i		−	0.518542i	0.965805	−	0.259271i	$-0.0834823\pi$
$54$	1.61924e58	+	3.88944e58i	0.203200	+	0.488090i
$55$	7.84855e58			0.527786
$56$		−	6.73394e58i		−	0.245401i
$57$	−3.19001e59	+	7.71440e59i	−0.636864	+	1.54013i
$58$	−6.00492e59			−0.663675
$59$		−	2.70885e60i		−	1.67423i	−0.547024	−	0.837117i	$-0.684239\pi$
$59$		−	2.70885e60i		−	1.67423i	0.547024	−	0.837117i	$-0.315761\pi$
$60$	2.68612e60	+	1.11075e60i	0.937525	+	0.387679i
$61$	5.80460e60			1.15494			0.577468	−	0.816414i	$-0.304041\pi$
$61$	5.80460e60			1.15494			0.577468	+	0.816414i	$0.304041\pi$
$62$		−	7.05597e60i		−	0.807680i
$63$	2.87476e60	+	2.86789e60i	0.190995	+	0.190539i
$64$	−7.92691e60			−0.308308
$65$			3.28983e61i			0.755301i
$66$	5.54284e60	−	1.34043e61i	0.0757249	−	0.183126i
$67$	−1.64188e62			−1.34523			−0.672617	−	0.739990i	$-0.734830\pi$
$67$	−1.64188e62			−1.34523			−0.672617	+	0.739990i	$0.734830\pi$
$68$		−	1.92177e61i		−	0.0951476i
$69$	2.57737e61	+	1.06578e61i	0.0776796	+	0.0321216i
$70$	−1.08692e62			−0.200847
$71$			8.24659e62i			0.940785i	0.882457	+	0.470392i	$0.155888\pi$
$71$			8.24659e62i			0.940785i	−0.882457	+	0.470392i	$0.844112\pi$
$72$	9.05998e62	−	9.08166e62i	0.642425	−	0.643962i
$73$	−1.92603e63			−0.854449			−0.427224	−	0.904146i	$-0.640509\pi$
$73$	−1.92603e63			−0.854449			−0.427224	+	0.904146i	$0.640509\pi$
$74$		−	4.81008e62i		−	0.134361i
$75$	2.12207e63	−	5.13180e63i	0.375557	−	0.908211i
$76$	1.06443e64			1.20076
$77$		−	1.39805e63i		−	0.101120i
$78$	5.61859e63	+	2.32336e63i	0.262066	+	0.108368i
$79$	−6.09106e64			−1.84235			−0.921174	−	0.389151i	$-0.872768\pi$
$79$	−6.09106e64			−1.84235			−0.921174	+	0.389151i	$0.872768\pi$
$80$		−	1.71051e64i		−	0.337339i
$81$	1.84940e62	+	7.73552e64i	0.00239078	+	0.999997i
$82$	6.58662e64			0.561037
$83$		−	2.89288e65i		−	1.63183i	−0.578169	−	0.815917i	$-0.696233\pi$
$83$		−	2.89288e65i		−	1.63183i	0.578169	−	0.815917i	$-0.303767\pi$
$84$	1.97856e64	−	4.78474e64i	0.0742767	−	0.179623i
$85$	−7.40729e64			−0.185958
$86$		−	4.27078e65i		−	0.720376i
$87$	−1.01888e66	−	4.21322e65i	−1.16003	−	0.479689i
$88$	−4.41658e65			−0.340938
$89$			1.30346e65i			0.0685234i	0.999413	+	0.0342617i	$0.0109080\pi$
$89$			1.30346e65i			0.0685234i	−0.999413	+	0.0342617i	$0.989092\pi$
$90$	−1.46587e66	−	1.46237e66i	−0.527048	−	0.525790i
$91$	5.86013e65			0.144710
$92$		−	3.55624e65i		−	0.0605627i
$93$	4.95068e66	−	1.19722e67i	0.583773	−	1.41174i
$94$	−3.03040e66			−0.248401
$95$		−	4.10276e67i		−	2.34679i
$96$	−2.39011e67	−	9.88344e66i	−0.957628	−	0.395992i
$97$	−4.75457e66			−0.133928			−0.0669642	−	0.997755i	$-0.521331\pi$
$97$	−4.75457e66			−0.133928			−0.0669642	+	0.997755i	$0.521331\pi$
$98$		−	2.46647e67i		−	0.490217i
$99$	1.88096e67	−	1.88547e67i	0.264718	−	0.265352i
$100$	−7.08084e67			−0.708084
$101$		−	1.73350e68i		−	1.23594i	−0.786203	−	0.617969i	$-0.787956\pi$
$101$		−	1.73350e68i		−	1.23594i	0.786203	−	0.617969i	$-0.212044\pi$
$102$	−5.23122e66	+	1.26507e67i	−0.0266807	+	0.0645219i
$103$	−4.99704e68			−1.82914			−0.914571	−	0.404426i	$-0.867471\pi$
$103$	−4.99704e68			−1.82914			−0.914571	+	0.404426i	$0.867471\pi$
$104$		−	1.85128e68i		−	0.487908i
$105$	−1.84424e68	−	7.62618e67i	−0.351060	−	0.145168i
$106$	1.98789e68			0.274152
$107$		−	1.18998e69i		−	1.19259i	−0.802764	−	0.596296i	$-0.796638\pi$
$107$		−	1.18998e69i		−	1.19259i	0.802764	−	0.596296i	$-0.203362\pi$
$108$	9.10585e68	−	3.79091e68i	0.665140	−	0.276908i
$109$	1.69136e69			0.903098			0.451549	−	0.892246i	$-0.350872\pi$
$109$	1.69136e69			0.903098			0.451549	+	0.892246i	$0.350872\pi$
$110$			7.12881e68i			0.279039i
$111$	3.37489e68	−	8.16150e68i	0.0971132	−	0.234849i
$112$	−3.04691e68			−0.0646319
$113$			1.16324e70i			1.82390i	0.410297	+	0.911952i	$0.365425\pi$
$113$			1.16324e70i			1.82390i	−0.410297	+	0.911952i	$0.634575\pi$
$114$	−7.00696e69	−	2.89747e69i	−0.814264	−	0.336709i
$115$	−1.37072e69			−0.118365
$116$			1.40585e70i			0.904416i
$117$	7.90321e69	+	7.88434e69i	0.379738	+	0.378831i
$118$	2.46044e70			0.885164
$119$			1.31945e69i			0.0356284i
$120$	−2.40919e70	+	5.82614e70i	−0.489450	+	1.18364i
$121$	5.60990e70			0.859513
$122$			5.27229e70i			0.610612i
$123$	1.11758e71	+	4.62136e70i	0.980634	+	0.405505i
$124$	−1.65192e71			−1.10066
$125$		−	4.77723e69i		−	0.0242234i
$126$	−2.60490e70	+	2.61113e70i	−0.100738	+	0.100979i
$127$	2.44833e71			0.723674			0.361837	−	0.932241i	$-0.382150\pi$
$127$	2.44833e71			0.723674			0.361837	+	0.932241i	$0.382150\pi$
$128$			3.85734e71i			0.873271i
$129$	2.99650e71	−	7.24644e71i	0.520672	−	1.25914i
$130$	−2.98814e71			−0.399326
$131$			3.87599e71i			0.399171i	0.979880	+	0.199585i	$0.0639595\pi$
$131$			3.87599e71i			0.399171i	−0.979880	+	0.199585i	$0.936040\pi$
$132$	−3.13817e71	−	1.29767e71i	−0.249553	−	0.103193i
$133$	−7.30818e71			−0.449628
$134$		−	1.49131e72i		−	0.711223i
$135$	−1.46117e72	−	3.50977e72i	−0.541195	−	1.29996i
$136$	4.16828e71			0.120125
$137$		−	4.30312e72i		−	0.966684i	−0.875432	−	0.483342i	$-0.839423\pi$
$137$		−	4.30312e72i		−	0.966684i	0.875432	−	0.483342i	$-0.160577\pi$
$138$	−9.68040e70	+	2.34101e71i	−0.0169826	+	0.0410691i
$139$	−4.51849e72			−0.620141			−0.310070	−	0.950714i	$-0.600353\pi$
$139$	−4.51849e72			−0.620141			−0.310070	+	0.950714i	$0.600353\pi$
$140$			2.54468e72i			0.273703i
$141$	−5.14183e72	−	2.12622e72i	−0.434178	−	0.179539i
$142$	−7.49034e72			−0.497391
$143$		−	3.84348e72i		−	0.201048i
$144$	−4.10919e72	−	4.09938e72i	−0.169602	−	0.169197i
$145$	5.41875e73			1.76761
$146$		−	1.74941e73i		−	0.451745i
$147$	1.73054e73	−	4.18498e73i	0.354318	−	0.856847i
$148$	−1.12612e73			−0.183099
$149$			9.45597e73i			1.22285i	0.791303	+	0.611425i	$0.209403\pi$
$149$			9.45597e73i			1.22285i	−0.791303	+	0.611425i	$0.790597\pi$
$150$	4.66120e73	+	1.92747e73i	0.480169	+	0.198557i
$151$	−1.26564e74			−1.04014			−0.520072	−	0.854123i	$-0.674095\pi$
$151$	−1.26564e74			−1.04014			−0.520072	+	0.854123i	$0.674095\pi$
$152$			2.30873e74i			1.51597i
$153$	−1.77521e73	+	1.77946e73i	−0.0932700	+	0.0934933i
$154$	1.26984e73			0.0534620
$155$			6.36720e74i			2.15115i
$156$	5.43939e73	−	1.31541e74i	0.147677	−	0.357128i
$157$	8.58159e73			0.187491			0.0937453	−	0.995596i	$-0.470116\pi$
$157$	8.58159e73			0.187491			0.0937453	+	0.995596i	$0.470116\pi$
$158$		−	5.53249e74i		−	0.974046i
$159$	3.37294e74	+	1.39476e74i	0.479189	+	0.198151i
$160$	1.27114e75			1.45919
$161$			2.44165e73i			0.0226779i
$162$	−7.02614e74	+	1.67980e72i	−0.528697	+	0.00126400i
$163$	−1.76601e75			−1.07799			−0.538994	−	0.842309i	$-0.681196\pi$
$163$	−1.76601e75			−1.07799			−0.538994	+	0.842309i	$0.681196\pi$
$164$		−	1.54204e75i		−	0.764548i
$165$	−5.00178e74	+	1.20958e75i	−0.201683	+	0.487731i
$166$	2.62760e75			0.862747
$167$		−	2.30236e75i		−	0.616331i	−0.951333	−	0.308165i	$-0.900285\pi$
$167$		−	2.30236e75i		−	0.616331i	0.951333	−	0.308165i	$-0.0997150\pi$
$168$	1.03780e75	+	4.29145e74i	0.226777	+	0.0937753i
$169$	−3.98843e75			−0.712286
$170$		−	6.72802e74i		−	0.0983159i
$171$	−9.85612e75	−	9.83258e75i	−1.17988	−	1.17706i
$172$	−9.99862e75			−0.981686
$173$		−	7.23576e75i		−	0.583333i	−0.956520	−	0.291666i	$-0.905790\pi$
$173$		−	7.23576e75i		−	0.583333i	0.956520	−	0.291666i	$-0.0942097\pi$
$174$	3.82686e75	−	9.25449e75i	0.253611	−	0.613307i
$175$	4.86157e75			0.265145
$176$			1.99838e75i			0.0897938i
$177$	4.17475e76	+	1.72631e76i	1.54717	+	0.639777i
$178$	−1.18393e75			−0.0362282
$179$		−	3.52676e76i		−	0.892016i	−0.895029	−	0.446008i	$-0.852845\pi$
$179$		−	3.52676e76i		−	0.892016i	0.895029	−	0.446008i	$-0.147155\pi$
$180$	−3.42366e76	+	3.43185e76i	−0.716515	+	0.718230i
$181$	1.47978e76			0.256523			0.128262	−	0.991740i	$-0.459060\pi$
$181$	1.47978e76			0.256523			0.128262	+	0.991740i	$0.459060\pi$
$182$			5.32273e75i			0.0765081i
$183$	−3.69919e76	+	8.94577e76i	−0.441337	+	1.06729i
$184$	7.71342e75			0.0764612
$185$			4.34054e76i			0.357853i
$186$	1.08743e77	+	4.49668e76i	0.746384	+	0.308640i
$187$	8.65386e75			0.0494989
$188$			7.09469e76i			0.338506i
$189$	−6.25191e76	+	2.60277e76i	−0.249064	+	0.103689i
$190$	3.72652e77			1.24074
$191$			3.43607e77i			0.957035i	0.878078	+	0.478517i	$0.158826\pi$
$191$			3.43607e77i			0.957035i	−0.878078	+	0.478517i	$0.841174\pi$
$192$	5.05171e76	−	1.22166e77i	0.117814	−	0.284910i
$193$	−2.74541e77			−0.536610			−0.268305	−	0.963334i	$-0.586463\pi$
$193$	−2.74541e77			−0.536610			−0.268305	+	0.963334i	$0.586463\pi$
$194$		−	4.31856e76i		−	0.0708077i
$195$	−5.07013e77	−	2.09657e77i	−0.697979	−	0.288624i
$196$	−5.77442e77			−0.668039
$197$			2.88152e77i			0.280395i	0.990124	+	0.140197i	$0.0447737\pi$
$197$			2.88152e77i			0.280395i	−0.990124	+	0.140197i	$0.955226\pi$
$198$	1.71256e77	+	1.70847e77i	0.140291	+	0.139956i
$199$	2.69586e77			0.186077			0.0930385	−	0.995663i	$-0.470342\pi$
$199$	2.69586e77			0.186077			0.0930385	+	0.995663i	$0.470342\pi$
$200$		−	1.53582e78i		−	0.893966i
$201$	1.04635e78	−	2.53039e78i	0.514056	−	1.24314i
$202$	1.57453e78			0.653438
$203$		−	9.65232e77i		−	0.338662i
$204$	2.96174e77	+	1.22472e77i	0.0879267	+	0.0363589i
$205$	−5.94367e78			−1.49425
$206$		−	4.53879e78i		−	0.967063i
$207$	−3.28504e77	+	3.29291e77i	−0.0593676	+	0.0595097i
$208$	−8.37648e77			−0.128502
$209$			4.79321e78i			0.624674i
$210$	6.92683e77	−	1.67512e78i	0.0767500	−	0.185605i
$211$	−1.67422e78			−0.157837			−0.0789185	−	0.996881i	$-0.525147\pi$
$211$	−1.67422e78			−0.157837			−0.0789185	+	0.996881i	$0.525147\pi$
$212$		−	4.65398e78i		−	0.373598i
$213$	−1.27092e79	−	5.25544e78i	−0.869387	−	0.359503i
$214$	1.08086e79			0.630522
$215$			3.85388e79i			1.91863i
$216$	8.22242e78	+	1.97504e79i	0.349600	+	0.839748i
$217$	1.13418e79			0.412146
$218$			1.53626e79i			0.477466i
$219$	1.22743e79	−	2.96831e79i	0.326511	−	0.789603i
$220$	1.66898e79			0.380258
$221$			3.62739e78i			0.0708366i
$222$	7.41306e78	+	3.06540e78i	0.124164	+	0.0513436i
$223$	4.47746e79			0.643675			0.321837	−	0.946795i	$-0.395700\pi$
$223$	4.47746e79			0.643675			0.321837	+	0.946795i	$0.395700\pi$
$224$		−	2.26426e79i		−	0.279572i
$225$	6.55652e79	+	6.54086e79i	0.695773	+	0.694111i
$226$	−1.05657e80			−0.964295
$227$		−	3.31012e79i		−	0.259994i	−0.991514	−	0.129997i	$-0.958503\pi$
$227$		−	3.31012e79i		−	0.259994i	0.991514	−	0.129997i	$-0.0414968\pi$
$228$	−6.78348e79	+	1.64045e80i	−0.458847	+	1.10963i
$229$	−7.40925e79			−0.431885			−0.215942	−	0.976406i	$-0.569282\pi$
$229$	−7.40925e79			−0.431885			−0.215942	+	0.976406i	$0.569282\pi$
$230$		−	1.24502e79i		−	0.0625794i
$231$	2.15461e79	+	8.90959e78i	0.0934460	+	0.0386412i
$232$	−3.04927e80			−1.14184
$233$		−	3.45185e80i		−	1.11674i	−0.829593	−	0.558368i	$-0.811428\pi$
$233$		−	3.45185e80i		−	1.11674i	0.829593	−	0.558368i	$-0.188572\pi$
$234$	−7.16131e79	+	7.17846e79i	−0.200287	+	0.200767i
$235$	2.73459e80			0.661583
$236$		−	5.76030e80i		−	1.20625i
$237$	3.88175e80	−	9.38725e80i	0.704019	−	1.70253i
$238$	−1.19845e79			−0.0188367
$239$			2.32883e79i			0.0317401i	0.999874	+	0.0158701i	$0.00505181\pi$
$239$			2.32883e79i			0.0317401i	−0.999874	+	0.0158701i	$0.994948\pi$
$240$	2.63616e80	+	1.09009e80i	0.311738	+	0.128908i
$241$	−6.76913e80			−0.694950			−0.347475	−	0.937689i	$-0.612961\pi$
$241$	−6.76913e80			−0.694950			−0.347475	+	0.937689i	$0.612961\pi$
$242$			5.09545e80i			0.454423i
$243$	−1.19334e81	−	4.90124e80i	−0.925019	−	0.379921i
$244$	1.23433e81			0.832106
$245$			2.22570e81i			1.30563i
$246$	−4.19757e80	+	1.01510e81i	−0.214390	+	0.518459i
$247$	−2.00915e81			−0.893954
$248$		−	3.58299e81i		−	1.38960i
$249$	4.45837e81	+	1.84360e81i	1.50799	+	0.623574i
$250$	4.33914e79			0.0128069
$251$			3.03059e81i			0.780944i	0.920615	+	0.390472i	$0.127688\pi$
$251$			3.03059e81i			0.780944i	−0.920615	+	0.390472i	$0.872312\pi$
$252$	6.11311e80	+	6.09851e80i	0.137608	+	0.137279i
$253$	1.60140e80			0.0315067
$254$			2.22381e81i			0.382605i
$255$	4.72057e80	−	1.14158e81i	0.0710605	−	0.171846i
$256$	−5.84322e81			−0.770004
$257$			9.37707e81i			1.08228i	0.840932	+	0.541142i	$0.182008\pi$
$257$			9.37707e81i			1.08228i	−0.840932	+	0.541142i	$0.817992\pi$
$258$	6.58192e81	+	2.72171e81i	0.665706	+	0.275278i
$259$	7.73173e80			0.0685622
$260$			6.99575e81i			0.544178i
$261$	1.29864e82	−	1.30175e82i	0.886569	−	0.888692i
$262$	−3.52055e81			−0.211041
$263$		−	2.54001e81i		−	0.133764i	−0.997761	−	0.0668821i	$-0.978695\pi$
$263$		−	2.54001e81i		−	0.133764i	0.997761	−	0.0668821i	$-0.0213051\pi$
$264$	2.81463e81	−	6.80663e81i	0.130283	−	0.315064i
$265$	−1.79384e82			−0.730169
$266$		−	6.63800e81i		−	0.237718i
$267$	−2.00884e81	−	8.30681e80i	−0.0633231	−	0.0261849i
$268$	−3.49142e82			−0.969212
$269$		−	6.20171e82i		−	1.51682i	−0.651778	−	0.758410i	$-0.725976\pi$
$269$		−	6.20171e82i		−	1.51682i	0.651778	−	0.758410i	$-0.274024\pi$
$270$	3.18792e82	−	1.32718e82i	0.687288	−	0.286129i
$271$	−2.54954e82			−0.484737			−0.242369	−	0.970184i	$-0.577924\pi$
$271$	−2.54954e82			−0.484737			−0.242369	+	0.970184i	$0.577924\pi$
$272$		−	1.88602e81i		−	0.0316377i
$273$	−3.73458e81	+	9.03135e81i	−0.0552984	+	0.133728i
$274$	3.90851e82			0.511084
$275$		−	3.18856e82i		−	0.368369i
$276$	5.48071e81	+	2.26635e81i	0.0559665	+	0.0231429i
$277$	−1.64475e83			−1.48521			−0.742605	−	0.669729i	$-0.766410\pi$
$277$	−1.64475e83			−1.48521			−0.742605	+	0.669729i	$0.766410\pi$
$278$		−	4.10413e82i		−	0.327867i
$279$	1.52960e83	+	1.52595e83i	1.08152	+	1.07894i
$280$	−5.51935e82			−0.345553
$281$		−	7.05244e82i		−	0.391133i	−0.980690	−	0.195566i	$-0.937345\pi$
$281$		−	7.05244e82i		−	0.391133i	0.980690	−	0.195566i	$-0.0626545\pi$
$282$	1.93124e82	−	4.67031e82i	0.0949217	−	0.229549i
$283$	−3.57018e83			−1.55579			−0.777896	−	0.628392i	$-0.783713\pi$
$283$	−3.57018e83			−1.55579			−0.777896	+	0.628392i	$0.783713\pi$
$284$			1.75362e83i			0.677815i
$285$	6.32298e83	+	2.61464e83i	2.16868	+	0.896780i
$286$	3.49102e82			0.106294
$287$			1.05874e83i			0.286288i
$288$	3.04638e83	−	3.05367e83i	0.731879	−	0.733631i
$289$	4.60135e83			0.982560
$290$			4.92183e83i			0.934532i
$291$	3.03003e82	−	7.32752e82i	0.0511782	−	0.123764i
$292$	−4.09566e83			−0.615612
$293$			4.54675e83i			0.608418i	0.952605	+	0.304209i	$0.0983922\pi$
$293$			4.54675e83i			0.608418i	−0.952605	+	0.304209i	$0.901608\pi$
$294$	3.80120e83	+	1.57185e83i	0.453014	+	0.187327i
$295$	−2.22026e84			−2.35752
$296$		−	2.44254e83i		−	0.231165i
$297$	1.70708e83	+	4.10043e83i	0.144057	+	0.346027i
$298$	−8.58882e83			−0.646518
$299$			6.71251e82i			0.0450884i
$300$	4.51253e83	−	1.09127e84i	0.270581	−	0.654346i
$301$	6.86486e83			0.367596
$302$		−	1.14957e84i		−	0.549922i
$303$	2.67158e84	+	1.10474e84i	1.14214	+	0.472290i
$304$	1.04463e84			0.399266
$305$		−	4.75764e84i		−	1.62629i
$306$	−1.61628e83	−	1.61242e83i	−0.0494297	−	0.0493117i
$307$	−5.94012e84			−1.62589			−0.812943	−	0.582343i	$-0.802136\pi$
$307$	−5.94012e84			−1.62589			−0.812943	+	0.582343i	$0.802136\pi$
$308$		−	2.97292e83i		−	0.0728549i
$309$	3.18455e84	−	7.70120e84i	0.698972	−	1.69032i
$310$	−5.78331e84			−1.13731
$311$			4.46362e84i			0.786745i	0.919379	+	0.393373i	$0.128692\pi$
$311$			4.46362e84i			0.786745i	−0.919379	+	0.393373i	$0.871308\pi$
$312$	2.85310e84	+	1.17979e84i	0.450879	+	0.186445i
$313$	6.27395e84			0.889270			0.444635	−	0.895712i	$-0.353333\pi$
$313$	6.27395e84			0.889270			0.444635	+	0.895712i	$0.353333\pi$
$314$			7.79462e83i			0.0991259i
$315$	2.35062e84	−	2.35625e84i	0.268302	−	0.268944i
$316$	−1.29525e85			−1.32737
$317$			1.17488e85i			1.08138i	0.841221	+	0.540691i	$0.181837\pi$
$317$			1.17488e85i			1.08138i	−0.841221	+	0.540691i	$0.818163\pi$
$318$	−1.26685e84	+	3.06363e84i	−0.104762	+	0.253346i
$319$	−6.33067e84			−0.470507
$320$			6.49715e84i			0.434134i
$321$	1.83394e85	+	7.58361e84i	1.10208	+	0.455727i
$322$	−2.21774e83			−0.0119898
$323$		−	4.52373e84i		−	0.220096i
$324$	3.93270e82	+	1.64494e85i	0.00172251	+	0.720476i
$325$	1.33653e85			0.527163
$326$		−	1.60406e85i		−	0.569931i
$327$	−1.07788e85	+	2.60664e85i	−0.345102	+	0.834560i
$328$	3.34466e85			0.965252
$329$		−	4.87108e84i		−	0.126755i
$330$	−1.09866e85	−	4.54310e84i	−0.257863	−	0.106630i
$331$	9.12286e84			0.193188			0.0965938	−	0.995324i	$-0.469205\pi$
$331$	9.12286e84			0.193188			0.0965938	+	0.995324i	$0.469205\pi$
$332$		−	6.15165e85i		−	1.17570i
$333$	1.04273e85	+	1.04024e85i	0.179916	+	0.179486i
$334$	2.09123e85			0.325853
$335$			1.34574e86i			1.89425i
$336$	1.94176e84	−	4.69575e84i	0.0246979	−	0.0597269i
$337$	−8.08867e85			−0.929952			−0.464976	−	0.885323i	$-0.653937\pi$
$337$	−8.08867e85			−0.929952			−0.464976	+	0.885323i	$0.653937\pi$
$338$		−	3.62268e85i		−	0.376584i
$339$	−1.79273e86	−	7.41317e85i	−1.68548	−	0.696971i
$340$	−1.57514e85			−0.133979
$341$		−	7.43874e85i		−	0.572599i
$342$	8.93090e85	−	8.95227e85i	0.622311	−	0.623801i
$343$	8.24042e85			0.519935
$344$		−	2.16868e86i		−	1.23939i
$345$	8.73545e84	−	2.11249e85i	0.0452310	−	0.109382i
$346$	6.57221e85			0.308407
$347$		−	1.20898e85i		−	0.0514300i	−0.999669	−	0.0257150i	$-0.991814\pi$
$347$		−	1.20898e85i		−	0.0514300i	0.999669	−	0.0257150i	$-0.00818624\pi$
$348$	−2.16663e86	−	8.95932e85i	−0.835779	−	0.345606i
$349$	1.15297e86			0.403417			0.201708	−	0.979446i	$-0.435351\pi$
$349$	1.15297e86			0.403417			0.201708	+	0.979446i	$0.435351\pi$
$350$			4.41575e85i			0.140182i
$351$	−1.71876e86	+	7.15546e85i	−0.495191	+	0.206156i
$352$	−1.48506e86			−0.388412
$353$			5.33284e86i			1.26654i	0.773931	+	0.633270i	$0.218288\pi$
$353$			5.33284e86i			1.26654i	−0.773931	+	0.633270i	$0.781712\pi$
$354$	−1.56800e86	+	3.79191e86i	−0.338249	+	0.817988i
$355$	6.75917e86			1.32474
$356$			2.77179e85i			0.0493696i
$357$	−2.03347e85	−	8.40868e84i	−0.0329245	−	0.0136147i
$358$	3.20334e86			0.471607
$359$		−	7.66568e85i		−	0.102645i	−0.998682	−	0.0513227i	$-0.983656\pi$
$359$		−	7.66568e85i		−	0.102645i	0.998682	−	0.0513227i	$-0.0163437\pi$
$360$	−7.44363e86	−	7.42585e86i	−0.906775	−	0.904610i
$361$	1.60353e87			1.77760
$362$			1.34408e86i			0.135623i
$363$	−3.57511e86	+	8.64570e86i	−0.328447	+	0.794283i
$364$	1.24614e86			0.104261
$365$			1.57864e87i			1.20316i
$366$	−8.12541e86	−	3.35997e86i	−0.564272	−	0.233334i
$367$	1.05645e87			0.668657			0.334328	−	0.942457i	$-0.391491\pi$
$367$	1.05645e87			0.668657			0.334328	+	0.942457i	$0.391491\pi$
$368$		−	3.49010e85i		−	0.0201378i
$369$	−1.42444e87	+	1.42785e87i	−0.749461	+	0.751255i
$370$	−3.94250e86			−0.189196
$371$			3.19533e86i			0.139895i
$372$	1.05275e87	−	2.54587e87i	0.420596	−	1.01713i
$373$	−2.11211e87			−0.770223			−0.385112	−	0.922870i	$-0.625837\pi$
$373$	−2.11211e87			−0.770223			−0.385112	+	0.922870i	$0.625837\pi$
$374$			7.86027e85i			0.0261700i
$375$	7.36243e85	+	3.04446e85i	0.0223850	+	0.00925652i
$376$	−1.53882e87			−0.427368
$377$		−	2.65359e87i		−	0.673330i
$378$	−2.36408e86	−	5.67858e86i	−0.0548203	−	0.131680i
$379$	7.33660e87			1.55511			0.777556	−	0.628814i	$-0.216459\pi$
$379$	7.33660e87			1.55511			0.777556	+	0.628814i	$0.216459\pi$
$380$		−	8.72443e87i		−	1.69081i
$381$	−1.56029e87	+	3.77324e87i	−0.276538	+	0.668753i
$382$	−3.12097e87			−0.505983
$383$		−	7.00895e87i		−	1.03967i	−0.854267	−	0.519834i	$-0.825994\pi$
$383$		−	7.00895e87i		−	1.03967i	0.854267	−	0.519834i	$-0.174006\pi$
$384$	−5.94475e87	−	2.45823e87i	−0.806996	−	0.333704i
$385$	−1.14589e87			−0.142389
$386$		−	2.49365e87i		−	0.283705i
$387$	9.25823e87	+	9.23613e87i	0.964618	+	0.962314i
$388$	−1.01105e87			−0.0964925
$389$			9.91047e87i			0.866578i	0.901255	+	0.433289i	$0.142647\pi$
$389$			9.91047e87i			0.866578i	−0.901255	+	0.433289i	$0.857353\pi$
$390$	1.90431e87	−	4.60518e87i	0.152595	−	0.369020i
$391$	−1.51137e86			−0.0111010
$392$		−	1.25246e88i		−	0.843408i
$393$	−5.97349e87	−	2.47012e87i	−0.368877	−	0.152536i
$394$	−2.61728e87			−0.148244
$395$			4.99243e88i			2.59424i
$396$	3.99983e87	−	4.00940e87i	0.190724	−	0.191180i
$397$	−2.05156e88			−0.897858			−0.448929	−	0.893567i	$-0.648194\pi$
$397$	−2.05156e88			−0.897858			−0.448929	+	0.893567i	$0.648194\pi$
$398$			2.44864e87i			0.0983785i
$399$	4.65741e87	−	1.12630e88i	0.171817	−	0.415505i
$400$	−6.94915e87			−0.235446
$401$			4.63698e88i			1.44320i	0.692311	+	0.721599i	$0.256593\pi$
$401$			4.63698e88i			1.44320i	−0.692311	+	0.721599i	$0.743407\pi$
$402$	2.29834e88	+	9.50395e87i	0.657247	+	0.271780i
$403$	3.11806e88			0.819431
$404$		−	3.68624e88i		−	0.890466i
$405$	6.34028e88	−	1.51583e86i	1.40811	−	0.00336650i
$406$	8.76717e87			0.179050
$407$		−	5.07101e87i		−	0.0952542i
$408$	−2.65639e87	+	6.42395e87i	−0.0459035	+	0.111009i
$409$	−2.10550e88			−0.334783			−0.167391	−	0.985891i	$-0.553534\pi$
$409$	−2.10550e88			−0.334783			−0.167391	+	0.985891i	$0.553534\pi$
$410$		−	5.39861e88i		−	0.790007i
$411$	6.63177e88	+	2.74233e88i	0.893321	+	0.369400i
$412$	−1.06261e89			−1.31786
$413$			3.95491e88i			0.451685i
$414$	−2.99094e87	−	2.98379e87i	−0.0314627	−	0.0313875i
$415$	−2.37110e89			−2.29781
$416$		−	6.22483e88i		−	0.555846i
$417$	2.87958e88	−	6.96368e88i	0.236975	−	0.573077i
$418$	−4.35366e88			−0.330264
$419$		−	3.22634e88i		−	0.225649i	−0.993615	−	0.112824i	$-0.964010\pi$
$419$		−	3.22634e88i		−	0.225649i	0.993615	−	0.112824i	$-0.0359898\pi$
$420$	−3.92173e88	−	1.62169e88i	−0.252931	−	0.104590i
$421$	1.38729e89			0.825233			0.412617	−	0.910905i	$-0.364615\pi$
$421$	1.38729e89			0.825233			0.412617	+	0.910905i	$0.364615\pi$
$422$		−	1.52069e88i		−	0.0834481i
$423$	6.55365e88	−	6.56934e88i	0.331826	−	0.332620i
$424$	1.00944e89			0.471673
$425$			3.00929e88i			0.129790i
$426$	4.77350e88	−	1.15438e89i	0.190069	−	0.459643i
$427$	−8.47470e88			−0.311585
$428$		−	2.53047e89i		−	0.859237i
$429$	5.92338e88	+	2.44940e88i	0.185790	+	0.0768266i
$430$	−3.50047e89			−1.01438
$431$			1.16765e89i			0.312670i	0.987704	+	0.156335i	$0.0499680\pi$
$431$			1.16765e89i			0.312670i	−0.987704	+	0.156335i	$0.950032\pi$
$432$	8.93649e88	−	3.72040e88i	0.221167	−	0.0920752i
$433$	2.83468e89			0.648508			0.324254	−	0.945970i	$-0.394887\pi$
$433$	2.83468e89			0.648508			0.324254	+	0.945970i	$0.394887\pi$
$434$			1.03017e89i			0.217901i
$435$	−3.45330e89	+	8.35111e89i	−0.675459	+	1.63346i
$436$	3.59664e89			0.650662
$437$		−	8.37120e88i		−	0.140094i
$438$	2.69610e89	+	1.11487e89i	0.417462	+	0.172626i
$439$	−8.14797e88			−0.116750			−0.0583749	−	0.998295i	$-0.518592\pi$
$439$	−8.14797e88			−0.116750			−0.0583749	+	0.998295i	$0.518592\pi$
$440$			3.61998e89i			0.480081i
$441$	5.34683e89	+	5.33406e89i	0.656424	+	0.654856i
$442$	−3.29475e88			−0.0374512
$443$			6.70892e89i			0.706197i	0.935586	+	0.353098i	$0.114872\pi$
$443$			6.70892e89i			0.706197i	−0.935586	+	0.353098i	$0.885128\pi$
$444$	7.17662e88	−	1.73552e89i	0.0699679	−	0.169204i
$445$	1.06836e89			0.0964891
$446$			4.06686e89i			0.340310i
$447$	−1.45731e90	−	6.02617e89i	−1.13004	−	0.467289i
$448$	1.15733e89			0.0831771
$449$		−	2.46441e90i		−	1.64186i	−0.571028	−	0.820931i	$-0.693455\pi$
$449$		−	2.46441e90i		−	1.64186i	0.571028	−	0.820931i	$-0.306545\pi$
$450$	−5.94104e89	+	5.95526e89i	−0.366975	+	0.367854i
$451$	6.94393e89			0.397743
$452$			2.47360e90i			1.31408i
$453$	8.06575e89	−	1.95054e90i	0.397471	−	0.961205i
$454$	3.00657e89			0.137459
$455$		−	4.80315e89i		−	0.203769i
$456$	−3.55811e90	−	1.47132e90i	−1.40092	−	0.579300i
$457$	3.66366e90			1.33895			0.669475	−	0.742834i	$-0.266519\pi$
$457$	3.66366e90			1.33895			0.669475	+	0.742834i	$0.266519\pi$
$458$		−	6.72980e89i		−	0.228337i
$459$	−1.61110e89	−	3.86990e89i	−0.0507565	−	0.121918i
$460$	−2.91481e89			−0.0852794
$461$		−	3.17203e89i		−	0.0861996i	−0.999071	−	0.0430998i	$-0.986277\pi$
$461$		−	3.17203e89i		−	0.0861996i	0.999071	−	0.0430998i	$-0.0137233\pi$
$462$	−8.09254e88	+	1.95702e89i	−0.0204295	+	0.0494047i
$463$	−1.06268e90			−0.249258			−0.124629	−	0.992203i	$-0.539774\pi$
$463$	−1.06268e90			−0.249258			−0.124629	+	0.992203i	$0.539774\pi$
$464$			1.37971e90i			0.300729i
$465$	−9.81283e90	−	4.05774e90i	−1.98790	−	0.822022i
$466$	3.13530e90			0.590417
$467$		−	7.14158e90i		−	1.25032i	−0.780497	−	0.625159i	$-0.785034\pi$
$467$		−	7.14158e90i		−	1.25032i	0.780497	−	0.625159i	$-0.214966\pi$
$468$	1.68060e90	+	1.67659e90i	0.273593	+	0.272940i
$469$	2.39714e90			0.362925
$470$			2.48382e90i			0.349778i
$471$	−5.46893e89	+	1.32255e90i	−0.0716460	+	0.173262i
$472$	1.24940e91			1.52291
$473$		−	4.50245e90i		−	0.510705i
$474$	8.52640e90	+	3.52578e90i	0.900124	+	0.372213i
$475$	−1.66679e91			−1.63794
$476$			2.80578e89i			0.0256695i
$477$	−4.29907e90	+	4.30936e90i	−0.366226	+	0.367103i
$478$	−2.11527e89			−0.0167809
$479$			2.51302e91i			1.85690i	0.371461	+	0.928449i	$0.378857\pi$
$479$			2.51302e91i			1.85690i	−0.371461	+	0.928449i	$0.621143\pi$
$480$	−8.10079e90	+	1.95902e91i	−0.557604	+	1.34845i
$481$	2.12559e90			0.136316
$482$		−	6.14838e90i		−	0.367419i
$483$	−3.76295e89	−	1.55603e89i	−0.0209569	−	0.00866594i
$484$	1.19293e91			0.619260
$485$			3.89700e90i			0.188587i
$486$	4.45178e90	−	1.08391e91i	0.200863	−	0.489056i
$487$	2.41409e91			1.01571			0.507853	−	0.861443i	$-0.330439\pi$
$487$	2.41409e91			1.01571			0.507853	+	0.861443i	$0.330439\pi$
$488$			2.67725e91i			1.05054i
$489$	1.12545e91	−	2.72169e91i	0.411933	−	0.996178i
$490$	−2.02160e91			−0.690284
$491$		−	3.87907e91i		−	1.23582i	−0.786247	−	0.617912i	$-0.787979\pi$
$491$		−	3.87907e91i		−	1.23582i	0.786247	−	0.617912i	$-0.212021\pi$
$492$	2.37652e91	+	9.82722e90i	0.706525	+	0.292158i
$493$	5.97475e90			0.165777
$494$		−	1.82490e91i		−	0.472632i
$495$	−1.54539e91	−	1.54170e91i	−0.373647	−	0.372755i
$496$	−1.62120e91			−0.365982
$497$		−	1.20400e91i		−	0.253810i
$498$	−1.67453e91	+	4.04952e91i	−0.329683	+	0.797272i
$499$	−4.88641e91			−0.898611			−0.449305	−	0.893378i	$-0.648328\pi$
$499$	−4.88641e91			−0.898611			−0.449305	+	0.893378i	$0.648328\pi$
$500$		−	1.01587e90i		−	0.0174524i
$501$	3.54829e91	+	1.46727e91i	0.569556	+	0.235519i
$502$	−2.75267e91			−0.412884
$503$		−	3.56615e91i		−	0.499906i	−0.968258	−	0.249953i	$-0.919585\pi$
$503$		−	3.56615e91i		−	0.499906i	0.968258	−	0.249953i	$-0.0804151\pi$
$504$	−1.32276e91	+	1.32592e91i	−0.173317	+	0.173732i
$505$	−1.42083e92			−1.74035
$506$			1.45455e90i			0.0166575i
$507$	2.54178e91	−	6.14678e91i	0.272187	−	0.658229i
$508$	5.20631e91			0.521391
$509$		−	1.93719e92i		−	1.81454i	−0.420544	−	0.907272i	$-0.638161\pi$
$509$		−	1.93719e92i		−	1.81454i	0.420544	−	0.907272i	$-0.361839\pi$
$510$	1.03689e91	+	4.28768e90i	0.0908545	+	0.0375696i
$511$	2.81200e91			0.230518
$512$			6.07748e91i			0.466171i
$513$	2.14347e92	−	8.92359e91i	1.53860	−	0.640545i
$514$	−8.51716e91			−0.572201
$515$			4.09574e92i			2.57565i
$516$	6.37199e91	−	1.54094e92i	0.375133	−	0.907184i
$517$	−3.19479e91			−0.176102
$518$			7.02270e90i			0.0362487i
$519$	1.11514e92	+	4.61125e91i	0.539063	+	0.222910i
$520$	−1.51737e92			−0.687032
$521$			9.28879e91i			0.393982i	0.980405	+	0.196991i	$0.0631170\pi$
$521$			9.28879e91i			0.393982i	−0.980405	+	0.196991i	$0.936883\pi$
$522$	1.18238e92	+	1.17955e92i	0.469850	+	0.468728i
$523$	3.11264e91			0.115897			0.0579485	−	0.998320i	$-0.481544\pi$
$523$	3.11264e91			0.115897			0.0579485	+	0.998320i	$0.481544\pi$
$524$			8.24220e91i			0.287594i
$525$	−3.09822e91	+	7.49242e91i	−0.101320	+	0.245022i
$526$	2.30708e91			0.0707209
$527$			7.02052e91i			0.201748i
$528$	−3.07980e91	−	1.27354e91i	−0.0829792	−	0.0343130i
$529$	3.93019e92			0.992934
$530$		−	1.62934e92i		−	0.386039i
$531$	−5.32102e92	+	5.33376e92i	−1.18245	+	1.18528i
$532$	−1.55407e92			−0.323947
$533$			2.91065e92i			0.569200i
$534$	7.54505e90	−	1.82462e91i	0.0138439	−	0.0334788i
$535$	−9.75349e92			−1.67931
$536$		−	7.57282e92i		−	1.22364i
$537$	5.43527e92	+	2.24756e92i	0.824320	+	0.340867i
$538$	5.63299e92			0.801940
$539$		−	2.60026e92i		−	0.347536i
$540$	−3.10715e92	−	7.46345e92i	−0.389920	−	0.936595i
$541$	1.43860e93			1.69524			0.847622	−	0.530600i	$-0.178033\pi$
$541$	1.43860e93			1.69524			0.847622	+	0.530600i	$0.178033\pi$
$542$		−	2.31574e92i		−	0.256280i
$543$	−9.43047e91	+	2.28057e92i	−0.0980255	+	0.237055i
$544$	1.40157e92			0.136852
$545$		−	1.38629e93i		−	1.27167i
$546$	−8.20314e91	−	3.39211e91i	−0.0707018	−	0.0292361i
$547$	−1.65019e93			−1.33649			−0.668244	−	0.743942i	$-0.732954\pi$
$547$	−1.65019e93			−1.33649			−0.668244	+	0.743942i	$0.732954\pi$
$548$		−	9.15049e92i		−	0.696475i
$549$	−1.14293e93	−	1.14020e93i	−0.817638	−	0.815686i
$550$	2.89615e92			0.194756
$551$			3.30930e93i			2.09210i
$552$	−4.91566e91	+	1.18876e92i	−0.0292182	+	0.0706584i
$553$	8.89294e92			0.497039
$554$		−	1.49392e93i		−	0.785228i
$555$	−6.68943e92	−	2.76617e92i	−0.330695	−	0.136747i
$556$	−9.60846e92			−0.446798
$557$			2.14664e91i			0.00939038i	0.999989	+	0.00469519i	$0.00149453\pi$
$557$			2.14664e91i			0.00939038i	−0.999989	+	0.00469519i	$0.998505\pi$
$558$	−1.38601e93	+	1.38933e93i	−0.570433	+	0.571798i
$559$	1.88727e93			0.730857
$560$			2.49735e92i			0.0910093i
$561$	−5.51500e91	+	1.33369e92i	−0.0189151	+	0.0457423i
$562$	6.40570e92			0.206791
$563$			3.65650e93i			1.11117i	0.831460	+	0.555585i	$0.187506\pi$
$563$			3.65650e93i			1.11117i	−0.831460	+	0.555585i	$0.812494\pi$
$564$	−1.09340e93	−	4.52135e92i	−0.312816	−	0.129354i
$565$	9.53429e93			2.56827
$566$		−	3.24279e93i		−	0.822545i
$567$	−2.70012e90	−	1.12938e93i	−0.000644999	−	0.269785i
$568$	−3.80356e93			−0.855751
$569$			5.88769e93i			1.24775i	0.781524	+	0.623876i	$0.214443\pi$
$569$			5.88769e93i			1.24775i	−0.781524	+	0.623876i	$0.785557\pi$
$570$	−2.37486e93	+	5.74314e93i	−0.474126	+	1.14658i
$571$	2.43734e93			0.458446			0.229223	−	0.973374i	$-0.426381\pi$
$571$	2.43734e93			0.458446			0.229223	+	0.973374i	$0.426381\pi$
$572$		−	8.17307e92i		−	0.144851i
$573$	−5.29551e93	−	2.18976e93i	−0.884404	−	0.365713i
$574$	−9.61646e92			−0.151360
$575$			5.56871e92i			0.0826130i
$576$	1.56082e93	+	1.55709e93i	0.218267	+	0.217746i
$577$	−2.28235e93			−0.300888			−0.150444	−	0.988619i	$-0.548070\pi$
$577$	−2.28235e93			−0.300888			−0.150444	+	0.988619i	$0.548070\pi$
$578$			4.17939e93i			0.519477i
$579$	1.74961e93	−	4.23109e93i	0.205055	−	0.495886i
$580$	1.15228e94			1.27353
$581$			4.22361e93i			0.440246i
$582$	6.65556e92	+	2.75216e92i	0.0654340	+	0.0270578i
$583$	2.09572e93			0.194358
$584$		−	8.88341e93i		−	0.777218i
$585$	6.46226e93	−	6.47773e93i	0.533439	−	0.534716i
$586$	−4.12980e93			−0.321670
$587$		−	4.68789e93i		−	0.344574i	−0.985047	−	0.172287i	$-0.944884\pi$
$587$		−	4.68789e93i		−	0.344574i	0.985047	−	0.172287i	$-0.0551156\pi$
$588$	3.67996e93	−	8.89925e93i	0.255278	−	0.617340i
$589$	−3.88854e94			−2.54605
$590$		−	2.01665e94i		−	1.24642i
$591$	−4.44086e93	−	1.83636e93i	−0.259115	−	0.107148i
$592$	−1.10518e93			−0.0608826
$593$			2.87435e93i			0.149514i	0.997202	+	0.0747568i	$0.0238181\pi$
$593$			2.87435e93i			0.149514i	−0.997202	+	0.0747568i	$0.976182\pi$
$594$	−3.72441e93	+	1.55053e93i	−0.182944	+	0.0761625i
$595$	1.08146e93			0.0501690
$596$			2.01079e94i			0.881036i
$597$	−1.71804e93	+	4.15473e93i	−0.0711058	+	0.171955i
$598$	−6.09695e92			−0.0238382
$599$		−	3.85679e94i		−	1.42467i	−0.701840	−	0.712335i	$-0.747638\pi$
$599$		−	3.85679e94i		−	1.42467i	0.701840	−	0.712335i	$-0.252362\pi$
$600$	2.36693e94	+	9.78759e93i	0.826121	+	0.341612i
$601$	−3.35142e91			−0.00110534			−0.000552671	−	1.00000i	$-0.500176\pi$
$601$	−3.35142e91			−0.00110534			−0.000552671		1.00000i	$0.500176\pi$
$602$			6.23533e93i			0.194347i
$603$	3.23288e94	+	3.22516e94i	0.952361	+	0.950087i
$604$	−2.69135e94			−0.749401
$605$		−	4.59806e94i		−	1.21030i
$606$	−1.00343e94	+	2.42659e94i	−0.249699	+	0.603847i
$607$	−6.09765e92			−0.0143465			−0.00717326	−	0.999974i	$-0.502283\pi$
$607$	−6.09765e92			−0.0143465			−0.00717326	+	0.999974i	$0.502283\pi$
$608$			7.76301e94i			1.72706i
$609$	1.48757e94	+	6.15130e93i	0.312960	+	0.129413i
$610$	4.32135e94			0.859814
$611$		−	1.33914e94i		−	0.252015i
$612$	−3.77495e93	+	3.78399e93i	−0.0671990	+	0.0673599i
$613$	−3.81354e94			−0.642202			−0.321101	−	0.947045i	$-0.604053\pi$
$613$	−3.81354e94			−0.642202			−0.321101	+	0.947045i	$0.604053\pi$
$614$		−	5.39539e94i		−	0.859603i
$615$	3.78782e94	−	9.16009e94i	0.570999	−	1.38085i
$616$	6.44821e93			0.0919803
$617$			1.17291e95i			1.58332i	0.610962	+	0.791660i	$0.290783\pi$
$617$			1.17291e95i			1.58332i	−0.610962	+	0.791660i	$0.709217\pi$
$618$	6.99497e94	+	2.89251e94i	0.893671	+	0.369545i
$619$	2.91667e93			0.0352700			0.0176350	−	0.999844i	$-0.494386\pi$
$619$	2.91667e93			0.0352700			0.0176350	+	0.999844i	$0.494386\pi$
$620$			1.35397e95i			1.54986i
$621$	−2.98135e93	−	7.16128e93i	−0.0323072	−	0.0776026i
$622$	−4.05429e94			−0.415951
$623$		−	1.90306e93i		−	0.0184866i
$624$	5.33822e93	−	1.29094e94i	0.0491044	−	0.118749i
$625$	−1.16735e95			−1.01691
$626$			5.69861e94i			0.470155i
$627$	−7.38707e94	−	3.05465e94i	−0.577266	−	0.238707i
$628$	1.82485e94			0.135083
$629$			4.78591e93i			0.0335616i
$630$	2.14017e94	+	2.13506e94i	0.142190	+	0.141851i
$631$	−9.73216e94			−0.612648			−0.306324	−	0.951927i	$-0.599099\pi$
$631$	−9.73216e94			−0.612648			−0.306324	+	0.951927i	$0.599099\pi$
$632$		−	2.80937e95i		−	1.67582i
$633$	1.06696e94	−	2.58023e94i	0.0603144	−	0.145858i
$634$	−1.06714e95			−0.571724
$635$		−	2.00673e95i		−	1.01902i
$636$	7.17249e94	+	2.96592e94i	0.345245	+	0.142764i
$637$	1.08994e95			0.497349
$638$		−	5.75012e94i		−	0.248756i
$639$	1.61989e95	−	1.62376e95i	0.664440	−	0.666030i
$640$	3.16160e95			1.22967
$641$		−	3.06760e95i		−	1.13142i	−0.824603	−	0.565712i	$-0.808601\pi$
$641$		−	3.06760e95i		−	1.13142i	0.824603	−	0.565712i	$-0.191399\pi$
$642$	−6.88816e94	+	1.66576e95i	−0.240942	+	0.582670i
$643$	1.23270e95			0.408963			0.204481	−	0.978870i	$-0.434449\pi$
$643$	1.23270e95			0.408963			0.204481	+	0.978870i	$0.434449\pi$
$644$			5.19211e93i			0.0163390i
$645$	−5.93942e95	−	2.45603e95i	−1.77302	−	0.733168i
$646$	4.10889e94			0.116364
$647$			5.24329e95i			1.40883i	0.709789	+	0.704414i	$0.248790\pi$
$647$			5.24329e95i			1.40883i	−0.709789	+	0.704414i	$0.751210\pi$
$648$	−3.56784e95	+	8.52996e92i	−0.909611	+	0.00217469i
$649$	2.59391e95			0.627531
$650$			1.21397e95i			0.278710i
$651$	−7.22798e94	+	1.74794e95i	−0.157494	+	0.380867i
$652$	−3.75538e95			−0.776668
$653$			6.88409e95i			1.35145i	0.737156	+	0.675723i	$0.236168\pi$
$653$			6.88409e95i			1.35145i	−0.737156	+	0.675723i	$0.763832\pi$
$654$	−2.36760e95	−	9.79036e94i	−0.441230	−	0.182455i
$655$	3.17689e95			0.562080
$656$		−	1.51336e95i		−	0.254221i
$657$	3.79238e95	+	3.78333e95i	0.604908	+	0.603464i
$658$	4.42438e94			0.0670150
$659$		−	6.02302e95i		−	0.866384i	−0.901302	−	0.433192i	$-0.857387\pi$
$659$		−	6.02302e95i		−	0.866384i	0.901302	−	0.433192i	$-0.142613\pi$
$660$	−1.06362e95	+	2.57214e95i	−0.145309	+	0.351400i
$661$	4.84500e95			0.628702			0.314351	−	0.949307i	$-0.398213\pi$
$661$	4.84500e95			0.628702			0.314351	+	0.949307i	$0.398213\pi$
$662$			8.28626e94i			0.102138i
$663$	−5.59037e94	−	2.31169e94i	−0.0654606	−	0.0270689i
$664$	1.33428e96			1.48434
$665$			5.99003e95i			0.633130i
$666$	−9.44849e94	+	9.47111e94i	−0.0948940	+	0.0951211i
$667$	1.10563e95			0.105519
$668$		−	4.89592e95i		−	0.444053i
$669$	−2.85343e95	+	6.90045e95i	−0.245968	+	0.594825i
$670$	−1.22233e96			−1.00149
$671$			5.55830e95i			0.432889i
$672$	3.48956e95	+	1.44298e95i	0.258354	+	0.106833i
$673$	1.53779e96			1.08240			0.541198	−	0.840895i	$-0.317971\pi$
$673$	1.53779e96			1.08240			0.541198	+	0.840895i	$0.317971\pi$
$674$		−	7.34691e95i		−	0.491664i
$675$	−1.42588e96	+	5.93618e95i	−0.907310	+	0.377728i
$676$	−8.48131e95			−0.513187
$677$		−	6.70718e95i		−	0.385945i	−0.981204	−	0.192972i	$-0.938187\pi$
$677$		−	6.70718e95i		−	0.385945i	0.981204	−	0.192972i	$-0.0618128\pi$
$678$	6.73336e95	−	1.62833e96i	0.368487	−	0.891112i
$679$	6.94167e94			0.0361320
$680$		−	3.41646e95i		−	0.169150i
$681$	5.10139e95	+	2.10949e95i	0.240263	+	0.0993520i
$682$	6.75658e95			0.302732
$683$		−	1.50667e96i		−	0.642264i	−0.947035	−	0.321132i	$-0.895937\pi$
$683$		−	1.50667e96i		−	0.642264i	0.947035	−	0.321132i	$-0.104063\pi$
$684$	−2.09588e96	−	2.09088e96i	−0.850078	−	0.848048i
$685$	−3.52698e96			−1.36121
$686$			7.48475e95i			0.274889i
$687$	4.72182e95	−	1.14188e96i	0.165037	−	0.399108i
$688$	−9.81265e95			−0.326422
$689$			8.78453e95i			0.278141i
$690$	1.91877e95	+	7.93437e94i	0.0578301	+	0.0239135i
$691$	1.43250e96			0.410999			0.205500	−	0.978657i	$-0.434118\pi$
$691$	1.43250e96			0.410999			0.205500	+	0.978657i	$0.434118\pi$
$692$		−	1.53867e96i		−	0.420279i
$693$	−2.74621e95	+	2.75278e95i	−0.0714172	+	0.0715882i
$694$	1.09811e95			0.0271909
$695$			3.70350e96i			0.873231i
$696$	1.94326e96	−	4.69939e96i	0.436332	−	1.05518i
$697$	−6.55353e95			−0.140140
$698$			1.04724e96i			0.213286i
$699$	5.31983e96	+	2.19982e96i	1.03199	+	0.426740i
$700$	1.03380e96			0.191031
$701$		−	6.48706e95i		−	0.114192i	−0.998369	−	0.0570960i	$-0.981816\pi$
$701$		−	6.48706e95i		−	0.114192i	0.998369	−	0.0570960i	$-0.0181841\pi$
$702$	−6.49928e95	−	1.56114e96i	−0.108994	−	0.261806i
$703$	−2.65083e96			−0.423546
$704$		−	7.59056e95i		−	0.115559i
$705$	−1.74272e96	+	4.21442e96i	−0.252812	+	0.611375i
$706$	−4.84380e96			−0.669617
$707$			2.53090e96i			0.333438i
$708$	8.87750e96	+	3.67097e96i	1.11471	+	0.460946i
$709$	−5.06378e96			−0.606043			−0.303021	−	0.952984i	$-0.597995\pi$
$709$	−5.06378e96			−0.606043			−0.303021	+	0.952984i	$0.597995\pi$
$710$			6.13933e96i			0.700386i
$711$	1.19934e97	+	1.19647e97i	1.30429	+	1.30118i
$712$	−6.01196e95			−0.0623298
$713$			1.29915e96i			0.128415i
$714$	7.63757e94	−	1.84699e95i	0.00719807	−	0.0174071i
$715$	−3.15024e96			−0.283099
$716$		−	7.49957e96i		−	0.642679i
$717$	−3.58908e95	−	1.48413e95i	−0.0293313	−	0.0121289i
$718$	6.96271e95			0.0542684
$719$		−	8.31216e96i		−	0.617919i	−0.951075	−	0.308959i	$-0.900019\pi$
$719$		−	8.31216e96i		−	0.617919i	0.951075	−	0.308959i	$-0.0999807\pi$
$720$	−3.35998e96	+	3.36802e96i	−0.238250	+	0.238820i
$721$	7.29567e96			0.493476
$722$			1.45648e97i			0.939811i
$723$	4.31388e96	−	1.04323e97i	0.265562	−	0.642209i
$724$	3.14672e96			0.184819
$725$		−	2.20142e97i		−	1.23371i
$726$	−7.85286e96	−	3.24726e96i	−0.419936	−	0.173649i
$727$	−2.57974e97			−1.31645			−0.658226	−	0.752820i	$-0.728693\pi$
$727$	−2.57974e97			−1.31645			−0.658226	+	0.752820i	$0.728693\pi$
$728$			2.70286e96i			0.131631i
$729$	1.51586e97	−	1.52677e97i	0.704566	−	0.709638i
$730$	−1.43387e97			−0.636111
$731$			4.24932e96i			0.179940i
$732$	−7.86625e96	+	1.90230e97i	−0.317974	+	0.768956i
$733$	6.84734e96			0.264233			0.132116	−	0.991234i	$-0.457823\pi$
$733$	6.84734e96			0.264233			0.132116	+	0.991234i	$0.457823\pi$
$734$			9.59571e96i			0.353517i
$735$	−3.43014e97	−	1.41841e97i	−1.20654	−	0.498922i
$736$	2.59360e96			0.0871080
$737$		−	1.57221e97i		−	0.504216i
$738$	−1.29692e97	−	1.29382e97i	−0.397187	−	0.396239i
$739$	2.82328e97			0.825740			0.412870	−	0.910790i	$-0.364526\pi$
$739$	2.82328e97			0.825740			0.412870	+	0.910790i	$0.364526\pi$
$740$			9.23005e96i			0.257825i
$741$	1.28040e97	−	3.09640e97i	0.341608	−	0.826110i
$742$	−2.90231e96			−0.0739624
$743$		−	6.85759e97i		−	1.66937i	−0.550730	−	0.834684i	$-0.685650\pi$
$743$		−	6.85759e97i		−	1.66937i	0.550730	−	0.834684i	$-0.314350\pi$
$744$	5.52193e97	+	2.28339e97i	1.28414	+	0.531008i
$745$	7.75042e97			1.72192
$746$		−	1.91842e97i		−	0.407216i
$747$	−5.68253e97	+	5.69613e97i	−1.15250	+	1.15526i
$748$	1.84022e96			0.0356629
$749$			1.73737e97i			0.321745i
$750$	−2.76528e95	+	6.68727e95i	−0.00489390	+	0.0118349i
$751$	−8.29163e97			−1.40243			−0.701217	−	0.712948i	$-0.747359\pi$
$751$	−8.29163e97			−1.40243			−0.701217	+	0.712948i	$0.747359\pi$
$752$			6.96273e96i			0.112557i
$753$	−4.67059e97	−	1.93135e97i	−0.721677	−	0.298423i
$754$	2.41025e97			0.355988
$755$			1.03736e98i			1.46465i
$756$	−1.32945e97	+	5.53472e96i	−0.179445	+	0.0747059i
$757$	−6.24041e97			−0.805292			−0.402646	−	0.915356i	$-0.631909\pi$
$757$	−6.24041e97			−0.805292			−0.402646	+	0.915356i	$0.631909\pi$
$758$			6.66380e97i			0.822184i
$759$	−1.02055e96	+	2.46800e96i	−0.0120397	+	0.0291156i
$760$	1.89231e98			2.13467
$761$			4.82269e97i			0.520249i	0.965575	+	0.260124i	$0.0837635\pi$
$761$			4.82269e97i			0.520249i	−0.965575	+	0.260124i	$0.916236\pi$
$762$	−3.42722e97	−	1.41720e97i	−0.353568	−	0.146205i
$763$	−2.46938e97			−0.243643
$764$			7.30673e97i			0.689523i
$765$	1.45851e97	+	1.45502e97i	0.131650	+	0.131335i
$766$	6.36620e97			0.549670
$767$			1.08727e98i			0.898042i
$768$	3.72381e97	−	9.00528e97i	0.294243	−	0.711567i
$769$	1.15847e98			0.875769			0.437885	−	0.899031i	$-0.355728\pi$
$769$	1.15847e98			0.875769			0.437885	+	0.899031i	$0.355728\pi$
$770$		−	1.04080e97i		−	0.0752809i
$771$	−1.44515e98	−	5.97588e97i	−1.00015	−	0.413574i
$772$	−5.83805e97			−0.386616
$773$		−	2.64286e98i		−	1.67483i	−0.546564	−	0.837417i	$-0.684065\pi$
$773$		−	2.64286e98i		−	1.67483i	0.546564	−	0.837417i	$-0.315935\pi$
$774$	−8.38914e97	+	8.40922e97i	−0.508774	+	0.509992i
$775$	2.58674e98			1.50140
$776$		−	2.19295e97i		−	0.121823i
$777$	−4.92733e96	+	1.19158e97i	−0.0261998	+	0.0633589i
$778$	−9.00164e97			−0.458158
$779$		−	3.62988e98i		−	1.76855i
$780$	−1.07815e98	−	4.45830e97i	−0.502879	−	0.207947i
$781$	−7.89667e97			−0.352622
$782$		−	1.37277e96i		−	0.00586906i
$783$	1.17859e98	+	2.83100e98i	0.482461	+	1.15888i
$784$	−5.66702e97			−0.222131
$785$		−	7.03375e97i		−	0.264009i
$786$	2.24360e97	−	5.42570e97i	0.0806453	−	0.195024i
$787$	−7.26046e97			−0.249933			−0.124966	−	0.992161i	$-0.539882\pi$
$787$	−7.26046e97			−0.249933			−0.124966	+	0.992161i	$0.539882\pi$
$788$			6.12749e97i			0.202019i
$789$	3.91454e97	+	1.61872e97i	0.123613	+	0.0511155i
$790$	−4.53461e98			−1.37157
$791$		−	1.69833e98i		−	0.492064i
$792$	8.69632e97	+	8.67555e97i	0.241368	+	0.240791i
$793$	−2.32984e98			−0.619496
$794$		−	1.86343e98i		−	0.474696i
$795$	1.14319e98	−	2.76458e98i	0.279020	−	0.674755i
$796$	5.73268e97			0.134064
$797$			8.08800e98i			1.81242i	0.422832	+	0.906208i	$0.361036\pi$
$797$			8.08800e98i			1.81242i	−0.422832	+	0.906208i	$0.638964\pi$
$798$	1.02302e98	+	4.23031e97i	0.219677	+	0.0908393i
$799$	3.01518e97			0.0620472
$800$		−	5.16413e98i		−	1.01845i
$801$	2.56041e97	−	2.56654e97i	0.0483954	−	0.0485113i
$802$	−4.21175e98			−0.763016
$803$		−	1.84431e98i		−	0.320261i
$804$	2.22504e98	−	5.38081e98i	0.370366	−	0.895657i
$805$	2.00126e97			0.0319332
$806$			2.83212e98i			0.433232i
$807$	9.55778e98	+	3.95227e98i	1.40171	+	0.579624i
$808$	7.99539e98			1.12423
$809$			1.07949e99i			1.45536i	0.685919	+	0.727678i	$0.259400\pi$
$809$			1.07949e99i			1.45536i	−0.685919	+	0.727678i	$0.740600\pi$
$810$	1.37682e96	+	5.75886e98i	0.00177986	+	0.744467i
$811$	7.71105e98			0.955882			0.477941	−	0.878392i	$-0.341383\pi$
$811$	7.71105e98			0.955882			0.477941	+	0.878392i	$0.341383\pi$
$812$		−	2.05254e98i		−	0.243999i
$813$	1.62479e98	−	3.92923e98i	0.185233	−	0.447950i
$814$	4.60598e97			0.0503607
$815$			1.44748e99i			1.51794i
$816$	2.90665e97	+	1.20194e97i	0.0292366	+	0.0120897i
$817$	−2.35362e99			−2.27084
$818$		−	1.91242e98i		−	0.176999i
$819$	−1.15387e98	−	1.15111e98i	−0.102448	−	0.102203i
$820$	−1.26391e99			−1.07657
$821$			1.14547e99i			0.936089i	0.883705	+	0.468044i	$0.155041\pi$
$821$			1.14547e99i			0.936089i	−0.883705	+	0.468044i	$0.844959\pi$
$822$	−2.49084e98	+	6.02361e98i	−0.195301	+	0.472297i
$823$	3.66245e98			0.275535			0.137768	−	0.990465i	$-0.456007\pi$
$823$	3.66245e98			0.275535			0.137768	+	0.990465i	$0.456007\pi$
$824$		−	2.30478e99i		−	1.66381i
$825$	4.91405e98	+	2.03203e98i	0.340412	+	0.140765i
$826$	−3.59223e98			−0.238805
$827$			2.31639e98i			0.147783i	0.997266	+	0.0738915i	$0.0235419\pi$
$827$			2.31639e98i			0.147783i	−0.997266	+	0.0738915i	$0.976458\pi$
$828$	−6.98557e97	+	7.00229e97i	−0.0427731	+	0.0428754i
$829$	2.18604e99			1.28471			0.642354	−	0.766408i	$-0.277958\pi$
$829$	2.18604e99			1.28471			0.642354	+	0.766408i	$0.277958\pi$
$830$		−	2.15366e99i		−	1.21485i
$831$	1.04818e99	−	2.53481e99i	0.567545	−	1.37250i
$832$	3.18169e98			0.165373
$833$			2.45407e98i			0.122450i
$834$	6.32508e98	+	2.61551e98i	0.302985	+	0.125288i
$835$	−1.88709e99			−0.867866
$836$			1.01927e99i			0.450064i
$837$	−3.32651e99	+	1.38488e99i	−1.41034	+	0.587147i
$838$	2.93047e98			0.119300
$839$		−	5.05927e99i		−	1.97779i	−0.148607	−	0.988896i	$-0.547479\pi$
$839$		−	5.05927e99i		−	1.97779i	0.148607	−	0.988896i	$-0.452521\pi$
$840$	3.51741e98	−	8.50616e98i	0.132047	−	0.319329i
$841$	−1.59705e99			−0.575778
$842$			1.26007e99i			0.436299i
$843$	1.08689e99	+	4.49443e98i	0.361449	+	0.149464i
$844$	−3.56019e98			−0.113718
$845$			3.26905e99i			1.00298i
$846$	5.96690e98	+	5.95265e98i	0.175856	+	0.175436i
$847$	−8.19044e98			−0.231884
$848$		−	4.56742e98i		−	0.124226i
$849$	2.27523e99	−	5.50220e99i	0.594517	−	1.43772i
$850$	−2.73333e98			−0.0686197
$851$			8.85635e97i			0.0213624i
$852$	−2.70259e99	−	1.11756e99i	−0.626374	−	0.259014i
$853$	4.86752e99			1.08403			0.542014	−	0.840370i	$-0.317662\pi$
$853$	4.86752e99			1.08403			0.542014	+	0.840370i	$0.317662\pi$
$854$		−	7.69754e98i		−	0.164734i
$855$	−8.05910e99	+	8.07839e99i	−1.65744	+	1.66141i
$856$	5.48854e99			1.08480
$857$		−	3.24034e99i		−	0.615521i	−0.951464	−	0.307761i	$-0.900420\pi$
$857$		−	3.24034e99i		−	0.615521i	0.951464	−	0.307761i	$-0.0995796\pi$
$858$	−2.22478e98	+	5.38019e98i	−0.0406181	+	0.0982267i
$859$	8.61110e99			1.51109			0.755547	−	0.655095i	$-0.227371\pi$
$859$	8.61110e99			1.51109			0.755547	+	0.655095i	$0.227371\pi$
$860$			8.19519e99i			1.38233i
$861$	−1.63167e99	−	6.74719e98i	−0.264561	−	0.109400i
$862$	−1.06058e99			−0.165308
$863$		−	2.57814e99i		−	0.386313i	−0.981168	−	0.193156i	$-0.938128\pi$
$863$		−	2.57814e99i		−	0.386313i	0.981168	−	0.193156i	$-0.0618725\pi$
$864$	2.76475e99	+	6.64099e99i	0.398280	+	0.956678i
$865$	−5.93066e99			−0.821402
$866$			2.57473e99i			0.342865i
$867$	−2.93238e99	+	7.09138e99i	−0.375467	+	0.907991i
$868$	2.41181e99			0.296942
$869$		−	5.83261e99i		−	0.690542i
$870$	−7.58528e99	−	3.13662e99i	−0.863609	−	0.357114i
$871$	6.59016e99			0.721570
$872$			7.80104e99i			0.821470i
$873$	9.36182e98	+	9.33947e98i	0.0948148	+	0.0945884i
$874$	7.60353e98			0.0740673
$875$			6.97474e97i			0.00653513i
$876$	2.61011e99	−	6.31203e99i	0.235244	−	0.568892i
$877$	1.11623e100			0.967763			0.483881	−	0.875134i	$-0.339227\pi$
$877$	1.11623e100			0.967763			0.483881	+	0.875134i	$0.339227\pi$
$878$		−	7.40078e98i		−	0.0617254i
$879$	−7.00724e99	−	2.89759e99i	−0.562244	−	0.232496i
$880$	1.63793e99			0.126440
$881$			4.23363e99i			0.314435i	0.987564	+	0.157218i	$0.0502524\pi$
$881$			4.23363e99i			0.314435i	−0.987564	+	0.157218i	$0.949748\pi$
$882$	−4.84491e99	+	4.85651e99i	−0.346221	+	0.347050i
$883$	−1.42280e100			−0.978321			−0.489161	−	0.872194i	$-0.662697\pi$
$883$	−1.42280e100			−0.978321			−0.489161	+	0.872194i	$0.662697\pi$
$884$			7.71357e98i			0.0510362i
$885$	1.41494e100	−	3.42176e100i	0.900882	−	2.17860i
$886$	−6.09368e99			−0.373365
$887$		−	9.46018e99i		−	0.557823i	−0.960317	−	0.278911i	$-0.910026\pi$
$887$		−	9.46018e99i		−	0.557823i	0.960317	−	0.278911i	$-0.0899736\pi$
$888$	3.76432e99	+	1.55660e99i	0.213622	+	0.0883355i
$889$	−3.57455e99			−0.195237
$890$			9.70390e98i			0.0510136i
$891$	−7.40729e99	+	1.77093e97i	−0.374815	+	0.000896104i
$892$	9.52121e99			0.463754
$893$			1.67005e100i			0.783033i
$894$	5.47355e99	−	1.32367e100i	0.247055	−	0.597453i
$895$	−2.89065e100			−1.25606
$896$		−	5.63171e99i		−	0.235596i
$897$	−1.03450e99	−	4.27780e98i	−0.0416666	−	0.0172297i
$898$	2.23841e100			0.868049
$899$		−	5.13581e100i		−	1.91769i
$900$	1.39423e100	+	1.39090e100i	0.501289	+	0.500092i
$901$	−1.97790e99			−0.0684796
$902$			6.30714e99i			0.210286i
$903$	−4.37489e99	+	1.05798e100i	−0.140470	+	0.339699i
$904$	−5.36520e100			−1.65905
$905$		−	1.21288e100i		−	0.361215i
$906$	1.77167e100	+	7.32609e99i	0.508187	+	0.210142i
$907$	−1.12114e100			−0.309750			−0.154875	−	0.987934i	$-0.549497\pi$
$907$	−1.12114e100			−0.309750			−0.154875	+	0.987934i	$0.549497\pi$
$908$		−	7.03888e99i		−	0.187320i
$909$	−3.40513e100	+	3.41328e100i	−0.872894	+	0.874984i
$910$	4.36269e99			0.107732
$911$			6.05838e100i			1.44122i	0.693339	+	0.720612i	$0.256139\pi$
$911$			6.05838e100i			1.44122i	−0.693339	+	0.720612i	$0.743861\pi$
$912$	−6.65732e99	+	1.60994e100i	−0.152572	+	0.368965i
$913$	2.77013e100			0.611638
$914$			3.32769e100i			0.707901i
$915$	7.33224e100	+	3.03198e100i	1.50286	+	0.621454i
$916$	−1.57556e100			−0.311164
$917$		−	5.65894e99i		−	0.107691i
$918$	3.51502e99	−	1.46336e99i	0.0644580	−	0.0268349i
$919$	6.07334e100			1.07325			0.536624	−	0.843821i	$-0.319699\pi$
$919$	6.07334e100			1.07325			0.536624	+	0.843821i	$0.319699\pi$
$920$		−	6.32217e99i		−	0.107666i
$921$	3.78556e100	−	9.15462e100i	0.621302	−	1.50249i
$922$	2.88114e99			0.0455736
$923$		−	3.31001e100i		−	0.504628i
$924$	4.58172e99	+	1.89460e99i	0.0673258	+	0.0278401i
$925$	1.76339e100			0.249764
$926$		−	9.65229e99i		−	0.131782i
$927$	9.83924e100	+	9.81575e100i	1.29494	+	1.29185i
$928$	−1.02530e101			−1.30083
$929$			1.39549e101i			1.70684i	0.521223	+	0.853421i	$0.325476\pi$
$929$			1.39549e101i			1.70684i	−0.521223	+	0.853421i	$0.674524\pi$
$930$	3.68563e100	−	8.91295e100i	0.434601	−	1.05100i
$931$	−1.35927e101			−1.54531
$932$		−	7.34028e100i		−	0.804585i
$933$	−6.87912e100	−	2.84461e100i	−0.727038	−	0.300640i
$934$	6.48668e100			0.661041
$935$		−	7.09299e99i		−	0.0697003i
$936$	−3.63648e100	+	3.64519e100i	−0.344590	+	0.345415i
$937$	−1.52916e101			−1.39736			−0.698679	−	0.715435i	$-0.746228\pi$
$937$	−1.52916e101			−1.39736			−0.698679	+	0.715435i	$0.746228\pi$
$938$			2.17732e100i			0.191878i
$939$	−3.99831e100	+	9.66911e100i	−0.339818	+	0.821782i
$940$	5.81504e100			0.476656
$941$		−	3.19174e100i		−	0.252337i	−0.992009	−	0.126168i	$-0.959732\pi$
$941$		−	3.19174e100i		−	0.252337i	0.992009	−	0.126168i	$-0.0402679\pi$
$942$	−1.20127e100	−	4.96741e99i	−0.0916030	−	0.0378791i
$943$	−1.21273e100			−0.0892007
$944$		−	5.65317e100i		−	0.401092i
$945$	2.13331e100	+	5.12427e100i	0.146007	+	0.350712i
$946$	4.08956e100			0.270009
$947$		−	1.88837e101i		−	1.20278i	−0.798954	−	0.601392i	$-0.794613\pi$
$947$		−	1.88837e101i		−	1.20278i	0.798954	−	0.601392i	$-0.205387\pi$
$948$	8.25446e100	−	1.99618e101i	0.507230	−	1.22664i
$949$	7.73068e100			0.458318
$950$		−	1.51394e101i		−	0.865977i
$951$	−1.81067e101	−	7.48737e100i	−0.999314	−	0.413230i
$952$	−6.08568e99			−0.0324081
$953$			9.62265e100i			0.494465i	0.968956	+	0.247233i	$0.0795212\pi$
$953$			9.62265e100i			0.494465i	−0.968956	+	0.247233i	$0.920479\pi$
$954$	−3.91417e100	−	3.90483e100i	−0.194087	−	0.193623i
$955$	2.81632e101			1.34762
$956$			4.95220e99i			0.0228681i
$957$	4.03445e100	−	9.75652e100i	0.179795	−	0.434799i
$958$	−2.28256e101			−0.981738
$959$			6.28256e100i			0.260798i
$960$	−1.00131e101	−	4.14055e100i	−0.401187	−	0.165896i
$961$	3.44894e101			1.33380
$962$			1.93066e100i			0.0720699i
$963$	−2.33750e101	+	2.34309e101i	−0.842282	+	0.844298i
$964$	−1.43944e101			−0.500697
$965$			2.25023e101i			0.755610i
$966$	1.41334e99	−	3.41787e99i	0.00458167	−	0.0110798i
$967$	3.59442e101			1.12494			0.562468	−	0.826819i	$-0.309852\pi$
$967$	3.59442e101			1.12494			0.562468	+	0.826819i	$0.309852\pi$
$968$			2.58745e101i			0.781824i
$969$	6.97176e100	+	2.88292e100i	0.203392	+	0.0841054i
$970$	−3.53964e100			−0.0997056
$971$			1.77859e101i			0.483751i	0.970307	+	0.241876i	$0.0777626\pi$
$971$			1.77859e101i			0.483751i	−0.970307	+	0.241876i	$0.922237\pi$
$972$	−2.53761e101	−	1.04224e101i	−0.666456	−	0.273725i
$973$	6.59699e100			0.167305
$974$			2.19271e101i			0.537002i
$975$	−8.51754e100	+	2.05980e101i	−0.201445	+	0.487155i
$976$	1.21138e101			0.276685
$977$			5.28819e100i			0.116652i	0.998298	+	0.0583259i	$0.0185763\pi$
$977$			5.28819e100i			0.116652i	−0.998298	+	0.0583259i	$0.981424\pi$
$978$	2.47210e101	+	1.02225e101i	0.526677	+	0.217788i
$979$	−1.24816e100			−0.0256837
$980$			4.73290e101i			0.940678i
$981$	−3.33031e101	−	3.32236e101i	−0.639350	−	0.637823i
$982$	3.52335e101			0.653378
$983$		−	8.79036e101i		−	1.57466i	−0.616531	−	0.787331i	$-0.711463\pi$
$983$		−	8.79036e101i		−	1.57466i	0.616531	−	0.787331i	$-0.288537\pi$
$984$	−2.13151e101	+	5.15462e101i	−0.368853	+	0.891998i
$985$	2.36179e101			0.394829
$986$			5.42684e100i			0.0876460i
$987$	7.50707e100	+	3.10427e100i	0.117135	+	0.0484370i
$988$	−4.27240e101			−0.644074
$989$			7.86339e100i			0.114534i
$990$	1.40032e101	−	1.40367e101i	0.197075	−	0.197546i
$991$	−3.57662e101			−0.486371			−0.243186	−	0.969980i	$-0.578192\pi$
$991$	−3.57662e101			−0.486371			−0.243186	+	0.969980i	$0.578192\pi$
$992$		−	1.20477e102i		−	1.58309i
$993$	−5.81388e100	+	1.40597e101i	−0.0738230	+	0.178526i
$994$	1.09359e101			0.134189
$995$		−	2.20961e101i		−	0.262018i
$996$	9.48063e101	+	3.92037e101i	1.08647	+	0.449272i
$997$	6.81894e101			0.755234			0.377617	−	0.925962i	$-0.376744\pi$
$997$	6.81894e101			0.755234			0.377617	+	0.925962i	$0.376744\pi$
$998$		−	4.43831e101i		−	0.475094i
$999$	−2.26769e101	+	9.44077e100i	−0.234616	+	0.0976744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.69.b.a.2.14	yes	22
3.2	odd	2	inner	3.69.b.a.2.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.69.b.a.2.9	✓	22	3.2	odd	2	inner
3.69.b.a.2.14	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)

\(f(q)\)	\(=\)	\(q+9.08296e9i q^{2} +(-6.37287e15 + 1.54115e16i) q^{3} +2.12648e20 q^{4} -8.19633e23i q^{5} +(-1.39982e26 - 5.78846e25i) q^{6} -1.46000e28 q^{7} +4.61229e30i q^{8} +(-1.96901e32 - 1.96431e32i) q^{9} +O(q^{10})\)	\(q+9.08296e9i q^{2} +(-6.37287e15 + 1.54115e16i) q^{3} +2.12648e20 q^{4} -8.19633e23i q^{5} +(-1.39982e26 - 5.78846e25i) q^{6} -1.46000e28 q^{7} +4.61229e30i q^{8} +(-1.96901e32 - 1.96431e32i) q^{9} +7.44469e33 q^{10} +9.57569e34i q^{11} +(-1.35518e36 + 3.27722e36i) q^{12} -4.01379e37 q^{13} -1.32611e38i q^{14} +(1.26318e40 + 5.22341e39i) q^{15} +2.08693e40 q^{16} -9.03733e40i q^{17} +(1.78418e42 - 1.78845e42i) q^{18} +5.00561e43 q^{19} -1.74293e44i q^{20} +(9.30438e43 - 2.25008e44i) q^{21} -8.69756e44 q^{22} -1.67236e45i q^{23} +(-7.10824e46 - 2.93935e46i) q^{24} -3.32985e47 q^{25} -3.64571e47i q^{26} +(4.28213e48 - 1.78272e48i) q^{27} -3.10465e48 q^{28} +6.61119e49i q^{29} +(-4.74441e49 + 1.14734e50i) q^{30} -7.76836e50 q^{31} +1.55086e51i q^{32} +(-1.47576e51 - 6.10246e50i) q^{33} +8.20857e50 q^{34} +1.19666e52i q^{35} +(-4.18706e52 - 4.17706e52i) q^{36} -5.29571e52 q^{37} +4.54658e53i q^{38} +(2.55794e53 - 6.18586e53i) q^{39} +3.78038e54 q^{40} -7.25162e54i q^{41} +(2.04374e54 + 8.45114e53i) q^{42} -4.70196e55 q^{43} +2.03625e55i q^{44} +(-1.61001e56 + 1.61387e56i) q^{45} +1.51900e55 q^{46} +3.33636e56i q^{47} +(-1.32997e56 + 3.21627e56i) q^{48} -2.71549e57 q^{49} -3.02449e57i q^{50} +(1.39279e57 + 5.75937e56i) q^{51} -8.53523e57 q^{52} -2.18859e58i q^{53} +(1.61924e58 + 3.88944e58i) q^{54} +7.84855e58 q^{55} -6.73394e58i q^{56} +(-3.19001e59 + 7.71440e59i) q^{57} -6.00492e59 q^{58} -2.70885e60i q^{59} +(2.68612e60 + 1.11075e60i) q^{60} +5.80460e60 q^{61} -7.05597e60i q^{62} +(2.87476e60 + 2.86789e60i) q^{63} -7.92691e60 q^{64} +3.28983e61i q^{65} +(5.54284e60 - 1.34043e61i) q^{66} -1.64188e62 q^{67} -1.92177e61i q^{68} +(2.57737e61 + 1.06578e61i) q^{69} -1.08692e62 q^{70} +8.24659e62i q^{71} +(9.05998e62 - 9.08166e62i) q^{72} -1.92603e63 q^{73} -4.81008e62i q^{74} +(2.12207e63 - 5.13180e63i) q^{75} +1.06443e64 q^{76} -1.39805e63i q^{77} +(5.61859e63 + 2.32336e63i) q^{78} -6.09106e64 q^{79} -1.71051e64i q^{80} +(1.84940e62 + 7.73552e64i) q^{81} +6.58662e64 q^{82} -2.89288e65i q^{83} +(1.97856e64 - 4.78474e64i) q^{84} -7.40729e64 q^{85} -4.27078e65i q^{86} +(-1.01888e66 - 4.21322e65i) q^{87} -4.41658e65 q^{88} +1.30346e65i q^{89} +(-1.46587e66 - 1.46237e66i) q^{90} +5.86013e65 q^{91} -3.55624e65i q^{92} +(4.95068e66 - 1.19722e67i) q^{93} -3.03040e66 q^{94} -4.10276e67i q^{95} +(-2.39011e67 - 9.88344e66i) q^{96} -4.75457e66 q^{97} -2.46647e67i q^{98} +(1.88096e67 - 1.88547e67i) 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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