LMFDB - Embedded newform 3.69.b.a.2.7

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			2.7
Character	$\chi$	$=$	3.2
Dual form			3.69.b.a.2.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12696e10i q^{2} +(1.62840e16 - 3.59996e15i) q^{3} +1.68144e20 q^{4} -1.29685e23i q^{5} +(-4.05701e25 - 1.83514e26i) q^{6} -3.11566e28 q^{7} -5.22111e30i q^{8} +(2.52209e32 - 1.17244e32i) q^{9} +O(q^{10})$	\(q-1.12696e10i q^{2} +(1.62840e16 - 3.59996e15i) q^{3} +1.68144e20 q^{4} -1.29685e23i q^{5} +(-4.05701e25 - 1.83514e26i) q^{6} -3.11566e28 q^{7} -5.22111e30i q^{8} +(2.52209e32 - 1.17244e32i) q^{9} -1.46150e33 q^{10} +4.93471e35i q^{11} +(2.73806e36 - 6.05313e35i) q^{12} -1.12213e38 q^{13} +3.51122e38i q^{14} +(-4.66861e38 - 2.11179e39i) q^{15} -9.21231e39 q^{16} +1.07342e42i q^{17} +(-1.32129e42 - 2.84229e42i) q^{18} +1.55304e43 q^{19} -2.18058e43i q^{20} +(-5.07353e44 + 1.12162e44i) q^{21} +5.56121e45 q^{22} +1.90341e46i q^{23} +(-1.87958e46 - 8.50206e46i) q^{24} +3.21995e47 q^{25} +1.26459e48i q^{26} +(3.68490e48 - 2.81714e48i) q^{27} -5.23880e48 q^{28} +4.45224e49i q^{29} +(-2.37990e49 + 5.26133e48i) q^{30} +7.16854e50 q^{31} -1.43718e51i q^{32} +(1.77647e51 + 8.03568e51i) q^{33} +1.20970e52 q^{34} +4.04054e51i q^{35} +(4.24075e52 - 1.97138e52i) q^{36} -8.21451e52 q^{37} -1.75021e53i q^{38} +(-1.82727e54 + 4.03962e53i) q^{39} -6.77101e53 q^{40} -2.89455e54i q^{41} +(1.26402e54 + 5.71766e54i) q^{42} +9.24062e54 q^{43} +8.29743e55i q^{44} +(-1.52047e55 - 3.27078e55i) q^{45} +2.14507e56 q^{46} +1.23297e57i q^{47} +(-1.50013e56 + 3.31640e55i) q^{48} -1.95791e57 q^{49} -3.62875e57i q^{50} +(3.86426e57 + 1.74796e58i) q^{51} -1.88680e58 q^{52} -1.29728e56i q^{53} +(-3.17480e58 - 4.15273e58i) q^{54} +6.39958e58 q^{55} +1.62672e59i q^{56} +(2.52897e59 - 5.59088e58i) q^{57} +5.01749e59 q^{58} -1.45054e60i q^{59} +(-7.85001e58 - 3.55086e59i) q^{60} -9.36955e59 q^{61} -8.07865e60i q^{62} +(-7.85796e60 + 3.65290e60i) q^{63} -1.89154e61 q^{64} +1.45523e61i q^{65} +(9.05588e61 - 2.00201e61i) q^{66} +1.40560e60 q^{67} +1.80489e62i q^{68} +(6.85221e61 + 3.09952e62i) q^{69} +4.55352e61 q^{70} +5.41869e61i q^{71} +(-6.12141e62 - 1.31681e63i) q^{72} -2.26140e63 q^{73} +9.25742e62i q^{74} +(5.24337e63 - 1.15917e63i) q^{75} +2.61135e63 q^{76} -1.53748e64i q^{77} +(4.55248e63 + 2.05926e64i) q^{78} +2.20373e64 q^{79} +1.19470e63i q^{80} +(4.98633e64 - 5.91397e64i) q^{81} -3.26204e64 q^{82} +2.06010e65i q^{83} +(-8.53086e64 + 1.88595e64i) q^{84} +1.39206e65 q^{85} -1.04138e65i q^{86} +(1.60279e65 + 7.25003e65i) q^{87} +2.57647e66 q^{88} -1.94994e65i q^{89} +(-3.68603e65 + 1.71351e65i) q^{90} +3.49617e66 q^{91} +3.20048e66i q^{92} +(1.16733e67 - 2.58065e66i) q^{93} +1.38951e67 q^{94} -2.01406e66i q^{95} +(-5.17380e66 - 2.34031e67i) q^{96} +3.82289e67 q^{97} +2.20649e67i q^{98} +(5.78562e67 + 1.24458e68i) 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 $

$2$		−	1.12696e10i		−	0.655976i	−0.944682	−	0.327988i	$-0.893629\pi$
$2$		−	1.12696e10i		−	0.655976i	0.944682	−	0.327988i	$-0.106371\pi$
$3$	1.62840e16	−	3.59996e15i	0.976424	−	0.215861i
$3$	1.62840e16	−	3.59996e15i	0.976424	−	0.215861i
$4$	1.68144e20			0.569695
$5$		−	1.29685e23i		−	0.222797i	−0.993776	−	0.111399i	$-0.964467\pi$
$5$		−	1.29685e23i		−	0.222797i	0.993776	−	0.111399i	$-0.0355331\pi$
$6$	−4.05701e25	−	1.83514e26i	−0.141600	−	0.640511i
$7$	−3.11566e28			−0.575726			−0.287863	−	0.957672i	$-0.592945\pi$
$7$	−3.11566e28			−0.575726			−0.287863	+	0.957672i	$0.592945\pi$
$8$		−	5.22111e30i		−	1.02968i
$9$	2.52209e32	−	1.17244e32i	0.906808	−	0.421545i
$10$	−1.46150e33			−0.146150
$11$			4.93471e35i			1.93157i	0.259347	+	0.965784i	$0.416493\pi$
$11$			4.93471e35i			1.93157i	−0.259347	+	0.965784i	$0.583507\pi$
$12$	2.73806e36	−	6.05313e35i	0.556264	−	0.122975i
$13$	−1.12213e38			−1.49958			−0.749788	−	0.661678i	$-0.769845\pi$
$13$	−1.12213e38			−1.49958			−0.749788	+	0.661678i	$0.769845\pi$
$14$			3.51122e38i			0.377663i
$15$	−4.66861e38	−	2.11179e39i	−0.0480934	−	0.217545i
$16$	−9.21231e39			−0.105752
$17$			1.07342e42i			1.56858i	0.620396	+	0.784288i	$0.286972\pi$
$17$			1.07342e42i			1.56858i	−0.620396	+	0.784288i	$0.713028\pi$
$18$	−1.32129e42	−	2.84229e42i	−0.276523	−	0.594844i
$19$	1.55304e43			0.517083			0.258541	−	0.966000i	$-0.416758\pi$
$19$	1.55304e43			0.517083			0.258541	+	0.966000i	$0.416758\pi$
$20$		−	2.18058e43i		−	0.126927i
$21$	−5.07353e44	+	1.12162e44i	−0.562153	+	0.124277i
$22$	5.56121e45			1.26706
$23$			1.90341e46i			0.956724i	0.878163	+	0.478362i	$0.158769\pi$
$23$			1.90341e46i			0.956724i	−0.878163	+	0.478362i	$0.841231\pi$
$24$	−1.87958e46	−	8.50206e46i	−0.222269	−	1.00541i
$25$	3.21995e47			0.950361
$26$			1.26459e48i			0.983687i
$27$	3.68490e48	−	2.81714e48i	0.794434	−	0.607351i
$28$	−5.23880e48			−0.327989
$29$			4.45224e49i			0.845370i	0.906277	+	0.422685i	$0.138912\pi$
$29$			4.45224e49i			0.845370i	−0.906277	+	0.422685i	$0.861088\pi$
$30$	−2.37990e49	+	5.26133e48i	−0.142704	+	0.0315481i
$31$	7.16854e50			1.40972			0.704861	−	0.709346i	$-0.251009\pi$
$31$	7.16854e50			1.40972			0.704861	+	0.709346i	$0.251009\pi$
$32$		−	1.43718e51i		−	0.960312i
$33$	1.77647e51	+	8.03568e51i	0.416951	+	1.88603i
$34$	1.20970e52			1.02895
$35$			4.04054e51i			0.128270i
$36$	4.24075e52	−	1.97138e52i	0.516604	−	0.240152i
$37$	−8.21451e52			−0.394206			−0.197103	−	0.980383i	$-0.563153\pi$
$37$	−8.21451e52			−0.394206			−0.197103	+	0.980383i	$0.563153\pi$
$38$		−	1.75021e53i		−	0.339194i
$39$	−1.82727e54	+	4.03962e53i	−1.46422	+	0.323701i
$40$	−6.77101e53			−0.229411
$41$		−	2.89455e54i		−	0.423575i	−0.977316	−	0.211787i	$-0.932072\pi$
$41$		−	2.89455e54i		−	0.423575i	0.977316	−	0.211787i	$-0.0679285\pi$
$42$	1.26402e54	+	5.71766e54i	0.0815228	+	0.368759i
$43$	9.24062e54			0.267777			0.133889	−	0.990996i	$-0.457254\pi$
$43$	9.24062e54			0.267777			0.133889	+	0.990996i	$0.457254\pi$
$44$			8.29743e55i			1.10041i
$45$	−1.52047e55	−	3.27078e55i	−0.0939190	−	0.202034i
$46$	2.14507e56			0.627588
$47$			1.23297e57i			1.73631i	0.496297	+	0.868153i	$0.334693\pi$
$47$			1.23297e57i			1.73631i	−0.496297	+	0.868153i	$0.665307\pi$
$48$	−1.50013e56	+	3.31640e55i	−0.103259	+	0.0228278i
$49$	−1.95791e57			−0.668539
$50$		−	3.62875e57i		−	0.623414i
$51$	3.86426e57	+	1.74796e58i	0.338595	+	1.53160i
$52$	−1.88680e58			−0.854302
$53$		−	1.29728e56i		−	0.00307365i	−0.999999	−	0.00153683i	$-0.999511\pi$
$53$		−	1.29728e56i		−	0.00307365i	0.999999	−	0.00153683i	$-0.000489187\pi$
$54$	−3.17480e58	−	4.15273e58i	−0.398408	−	0.521130i
$55$	6.39958e58			0.430348
$56$			1.62672e59i			0.592816i
$57$	2.52897e59	−	5.59088e58i	0.504892	−	0.111618i
$58$	5.01749e59			0.554542
$59$		−	1.45054e60i		−	0.896521i	−0.893903	−	0.448260i	$-0.852044\pi$
$59$		−	1.45054e60i		−	0.896521i	0.893903	−	0.448260i	$-0.147956\pi$
$60$	−7.85001e58	−	3.55086e59i	−0.0273986	−	0.123934i
$61$	−9.36955e59			−0.186425			−0.0932125	−	0.995646i	$-0.529714\pi$
$61$	−9.36955e59			−0.186425			−0.0932125	+	0.995646i	$0.529714\pi$
$62$		−	8.07865e60i		−	0.924744i
$63$	−7.85796e60	+	3.65290e60i	−0.522073	+	0.242694i
$64$	−1.89154e61			−0.735694
$65$			1.45523e61i			0.334102i
$66$	9.05588e61	−	2.00201e61i	1.23719	−	0.273510i
$67$	1.40560e60			0.0115164			0.00575822	−	0.999983i	$-0.498167\pi$
$67$	1.40560e60			0.0115164			0.00575822	+	0.999983i	$0.498167\pi$
$68$			1.80489e62i			0.893611i
$69$	6.85221e61	+	3.09952e62i	0.206520	+	0.934168i
$70$	4.55352e61			0.0841423
$71$			5.41869e61i			0.0618174i	0.999522	+	0.0309087i	$0.00984011\pi$
$71$			5.41869e61i			0.0618174i	−0.999522	+	0.0309087i	$0.990160\pi$
$72$	−6.12141e62	−	1.31681e63i	−0.434057	−	0.933724i
$73$	−2.26140e63			−1.00323			−0.501615	−	0.865091i	$-0.667261\pi$
$73$	−2.26140e63			−1.00323			−0.501615	+	0.865091i	$0.667261\pi$
$74$			9.25742e62i			0.258590i
$75$	5.24337e63	−	1.15917e63i	0.927956	−	0.205146i
$76$	2.61135e63			0.294580
$77$		−	1.53748e64i		−	1.11205i
$78$	4.55248e63	+	2.05926e64i	0.212340	+	0.960495i
$79$	2.20373e64			0.666558			0.333279	−	0.942828i	$-0.391845\pi$
$79$	2.20373e64			0.666558			0.333279	+	0.942828i	$0.391845\pi$
$80$			1.19470e63i			0.0235613i
$81$	4.98633e64	−	5.91397e64i	0.644600	−	0.764520i
$82$	−3.26204e64			−0.277855
$83$			2.06010e65i			1.16207i	0.813878	+	0.581036i	$0.197353\pi$
$83$			2.06010e65i			1.16207i	−0.813878	+	0.581036i	$0.802647\pi$
$84$	−8.53086e64	+	1.88595e64i	−0.320256	+	0.0708001i
$85$	1.39206e65			0.349475
$86$		−	1.04138e65i		−	0.175655i
$87$	1.60279e65	+	7.25003e65i	0.182483	+	0.825439i
$88$	2.57647e66			1.98890
$89$		−	1.94994e65i		−	0.102509i	−0.998686	−	0.0512543i	$-0.983678\pi$
$89$		−	1.94994e65i		−	0.102509i	0.998686	−	0.0512543i	$-0.0163219\pi$
$90$	−3.68603e65	+	1.71351e65i	−0.132530	+	0.0616086i
$91$	3.49617e66			0.863346
$92$			3.20048e66i			0.545041i
$93$	1.16733e67	−	2.58065e66i	1.37649	−	0.304304i
$94$	1.38951e67			1.13898
$95$		−	2.01406e66i		−	0.115205i
$96$	−5.17380e66	−	2.34031e67i	−0.207294	−	0.937672i
$97$	3.82289e67			1.07684			0.538421	−	0.842676i	$-0.319021\pi$
$97$	3.82289e67			1.07684			0.538421	+	0.842676i	$0.319021\pi$
$98$			2.20649e67i			0.438546i
$99$	5.78562e67	+	1.24458e68i	0.814242	+	1.75156i
$100$	5.41416e67			0.541416
$101$		−	3.45341e67i		−	0.246219i	−0.992393	−	0.123110i	$-0.960713\pi$
$101$		−	3.45341e67i		−	0.246219i	0.992393	−	0.123110i	$-0.0392866\pi$
$102$	1.96987e68	−	4.35487e67i	1.00469	−	0.222110i
$103$	4.05509e68			1.48434			0.742172	−	0.670209i	$-0.233796\pi$
$103$	4.05509e68			1.48434			0.742172	+	0.670209i	$0.233796\pi$
$104$			5.85876e68i			1.54409i
$105$	1.45458e67	+	6.57962e67i	0.0276886	+	0.125246i
$106$	−1.46198e66			−0.00201624
$107$		−	1.05558e69i		−	1.05790i	−0.848654	−	0.528948i	$-0.822587\pi$
$107$		−	1.05558e69i		−	1.05790i	0.848654	−	0.528948i	$-0.177413\pi$
$108$	6.19595e68	−	4.73685e68i	0.452585	−	0.346005i
$109$	−1.16218e69			−0.620544			−0.310272	−	0.950648i	$-0.600420\pi$
$109$	−1.16218e69			−0.620544			−0.310272	+	0.950648i	$0.600420\pi$
$110$		−	7.21206e68i		−	0.282298i
$111$	−1.33765e69	+	2.95719e68i	−0.384912	+	0.0850939i
$112$	2.87024e68			0.0608843
$113$		−	1.72362e68i		−	0.0270256i	−0.999909	−	0.0135128i	$-0.995699\pi$
$113$		−	1.72362e68i		−	0.0270256i	0.999909	−	0.0135128i	$-0.00430139\pi$
$114$	−6.30069e68	−	2.85004e69i	−0.0732189	−	0.331197i
$115$	2.46844e69			0.213156
$116$			7.48619e69i			0.481603i
$117$	−2.83011e70	+	1.31562e70i	−1.35983	+	0.632138i
$118$	−1.63470e70			−0.588096
$119$		−	3.34440e70i		−	0.903071i
$120$	−1.10259e70	+	2.43754e69i	−0.224002	+	0.0495209i
$121$	−1.78245e71			−2.73096
$122$			1.05591e70i			0.122290i
$123$	−1.04203e70	−	4.71349e70i	−0.0914335	−	0.413589i
$124$	1.20535e71			0.803112
$125$		−	8.56970e70i		−	0.434535i
$126$	4.11667e70	+	8.85560e70i	0.159202	+	0.342468i
$127$	−8.15420e70			−0.241021			−0.120511	−	0.992712i	$-0.538453\pi$
$127$	−8.15420e70			−0.241021			−0.120511	+	0.992712i	$0.538453\pi$
$128$		−	2.11012e71i		−	0.477714i
$129$	1.50474e71	−	3.32659e70i	0.261464	−	0.0578028i
$130$	1.63999e71			0.219163
$131$		−	3.75994e71i		−	0.387219i	−0.981079	−	0.193610i	$-0.937980\pi$
$131$		−	3.75994e71i		−	0.387219i	0.981079	−	0.193610i	$-0.0620195\pi$
$132$	2.98704e71	+	1.35115e72i	0.237535	+	1.07446i
$133$	−4.83874e71			−0.297698
$134$		−	1.58405e70i		−	0.00755451i
$135$	−3.65341e71	−	4.77877e71i	−0.135316	−	0.176998i
$136$	5.60444e72			1.61514
$137$			4.27475e72i			0.960309i	0.877184	+	0.480155i	$0.159419\pi$
$137$			4.27475e72i			0.960309i	−0.877184	+	0.480155i	$0.840581\pi$
$138$	3.49303e72	−	7.72216e71i	0.612792	−	0.135472i
$139$	7.56419e72			1.03815			0.519074	−	0.854729i	$-0.326277\pi$
$139$	7.56419e72			1.03815			0.519074	+	0.854729i	$0.326277\pi$
$140$			6.79394e71i			0.0730750i
$141$	4.43865e72	+	2.00777e73i	0.374801	+	1.69537i
$142$	6.10664e71			0.0405507
$143$		−	5.53738e73i		−	2.89654i
$144$	−2.32343e72	+	1.08008e72i	−0.0958969	+	0.0445793i
$145$	5.77389e72			0.188346
$146$			2.54851e73i			0.658095i
$147$	−3.18827e73	+	7.04841e72i	−0.652778	+	0.144312i
$148$	−1.38122e73			−0.224577
$149$			1.10154e73i			0.142452i	0.997460	+	0.0712261i	$0.0226912\pi$
$149$			1.10154e73i			0.142452i	−0.997460	+	0.0712261i	$0.977309\pi$
$150$	−1.30634e73	−	5.90906e73i	−0.134571	−	0.608717i
$151$	−1.62140e74			−1.33252			−0.666258	−	0.745721i	$-0.732105\pi$
$151$	−1.62140e74			−1.33252			−0.666258	+	0.745721i	$0.732105\pi$
$152$		−	8.10859e73i		−	0.532431i
$153$	1.25851e74	+	2.70726e74i	0.661225	+	1.42240i
$154$	−1.73268e74			−0.729482
$155$		−	9.29654e73i		−	0.314082i
$156$	−3.07246e74	+	6.79239e73i	−0.834161	+	0.184411i
$157$	−2.18959e74			−0.478381			−0.239191	−	0.970973i	$-0.576882\pi$
$157$	−2.18959e74			−0.478381			−0.239191	+	0.970973i	$0.576882\pi$
$158$		−	2.48352e74i		−	0.437246i
$159$	−4.67016e71	−	2.11249e72i	−0.000663483	−	0.00300119i
$160$	−1.86381e74			−0.213955
$161$		−	5.93038e74i		−	0.550811i
$162$	−6.66480e74	−	5.61939e74i	−0.501507	−	0.422843i
$163$	7.37125e74			0.449949			0.224974	−	0.974365i	$-0.427770\pi$
$163$	7.37125e74			0.449949			0.224974	+	0.974365i	$0.427770\pi$
$164$		−	4.86703e74i		−	0.241309i
$165$	1.04211e75	−	2.30382e74i	0.420202	−	0.0928956i
$166$	2.32165e75			0.762292
$167$			4.44121e75i			1.18889i	0.804137	+	0.594444i	$0.202628\pi$
$167$			4.44121e75i			1.18889i	−0.804137	+	0.594444i	$0.797372\pi$
$168$	5.85612e74	+	2.64895e75i	0.127966	+	0.578839i
$169$	6.99225e75			1.24873
$170$		−	1.56880e75i		−	0.229247i
$171$	3.91690e75	−	1.82084e75i	0.468895	−	0.217973i
$172$	1.55376e75			0.152551
$173$			1.36427e76i			1.09985i	0.835216	+	0.549923i	$0.185343\pi$
$173$			1.36427e76i			1.09985i	−0.835216	+	0.549923i	$0.814657\pi$
$174$	8.17048e75	−	1.80628e75i	0.541469	−	0.119704i
$175$	−1.00323e76			−0.547148
$176$		−	4.54601e75i		−	0.204268i
$177$	−5.22188e75	−	2.36205e76i	−0.193524	−	0.875385i
$178$	−2.19750e75			−0.0672432
$179$			2.15430e76i			0.544882i	0.962173	+	0.272441i	$0.0878309\pi$
$179$			2.15430e76i			0.544882i	−0.962173	+	0.272441i	$0.912169\pi$
$180$	−2.55659e75	−	5.49962e75i	−0.0535052	−	0.115098i
$181$	−1.56144e75			−0.0270678			−0.0135339	−	0.999908i	$-0.504308\pi$
$181$	−1.56144e75			−0.0270678			−0.0135339	+	0.999908i	$0.504308\pi$
$182$		−	3.94004e76i		−	0.566334i
$183$	−1.52574e76	+	3.37300e75i	−0.182030	+	0.0402420i
$184$	9.93793e76			0.985122
$185$			1.06530e76i			0.0878281i
$186$	−2.90828e76	−	1.31553e77i	−0.199617	−	0.902942i
$187$	−5.29701e77			−3.02981
$188$			2.07317e77i			0.989165i
$189$	−1.14809e77	+	8.77723e76i	−0.457376	+	0.349668i
$190$	−2.26976e76			−0.0755715
$191$		−	2.30993e77i		−	0.643375i	−0.946846	−	0.321688i	$-0.895750\pi$
$191$		−	2.30993e77i		−	0.643375i	0.946846	−	0.321688i	$-0.104250\pi$
$192$	−3.08019e77	+	6.80948e76i	−0.718349	+	0.158808i
$193$	5.56331e77			1.08739			0.543694	−	0.839283i	$-0.317025\pi$
$193$	5.56331e77			1.08739			0.543694	+	0.839283i	$0.317025\pi$
$194$		−	4.30823e77i		−	0.706383i
$195$	5.23879e76	+	2.36970e77i	0.0721197	+	0.326225i
$196$	−3.29212e77			−0.380864
$197$			1.64483e78i			1.60055i	0.599635	+	0.800274i	$0.295313\pi$
$197$			1.64483e78i			1.60055i	−0.599635	+	0.800274i	$0.704687\pi$
$198$	1.40259e78	−	6.52016e77i	1.14898	−	0.534123i
$199$	1.99949e78			1.38011			0.690056	−	0.723756i	$-0.257586\pi$
$199$	1.99949e78			1.38011			0.690056	+	0.723756i	$0.257586\pi$
$200$		−	1.68117e78i		−	0.978571i
$201$	2.28888e76	−	5.06010e75i	0.0112449	−	0.00248596i
$202$	−3.89185e77			−0.161514
$203$		−	1.38716e78i		−	0.486702i
$204$	6.49754e77	+	2.93909e78i	0.192896	+	0.872543i
$205$	−3.75380e77			−0.0943714
$206$		−	4.56992e78i		−	0.973694i
$207$	2.23163e78	+	4.80058e78i	0.403302	+	0.867565i
$208$	1.03374e78			0.158584
$209$			7.66379e78i			0.998781i
$210$	7.41496e77	−	1.63925e77i	0.0821585	−	0.0181631i
$211$	9.04800e78			0.853001			0.426500	−	0.904487i	$-0.359746\pi$
$211$	9.04800e78			0.853001			0.426500	+	0.904487i	$0.359746\pi$
$212$		−	2.18131e76i		−	0.00175104i
$213$	1.95071e77	+	8.82380e77i	0.0133440	+	0.0603600i
$214$	−1.18960e79			−0.693955
$215$		−	1.19837e78i		−	0.0596601i
$216$	−1.47086e79	−	1.92393e79i	−0.625379	−	0.818015i
$217$	−2.23347e79			−0.811614
$218$			1.30973e79i			0.407062i
$219$	−3.68247e79	+	8.14096e78i	−0.979578	+	0.216559i
$220$	1.07605e79			0.245167
$221$		−	1.20451e80i		−	2.35220i
$222$	3.33263e78	+	1.50748e79i	0.0558196	+	0.252493i
$223$	−1.01193e80			−1.45473			−0.727367	−	0.686248i	$-0.759256\pi$
$223$	−1.01193e80			−1.45473			−0.727367	+	0.686248i	$0.759256\pi$
$224$			4.47776e79i			0.552877i
$225$	8.12100e79	−	3.77518e79i	0.861795	−	0.400620i
$226$	−1.94245e78			−0.0177282
$227$			2.28649e80i			1.79593i	0.440065	+	0.897966i	$0.354956\pi$
$227$			2.28649e80i			1.79593i	−0.440065	+	0.897966i	$0.645044\pi$
$228$	4.25232e79	−	9.40075e78i	0.287635	−	0.0635884i
$229$	−1.45853e78			−0.00850179			−0.00425089	−	0.999991i	$-0.501353\pi$
$229$	−1.45853e78			−0.00850179			−0.00425089	+	0.999991i	$0.501353\pi$
$230$		−	2.78183e79i		−	0.139825i
$231$	−5.53488e79	−	2.50364e80i	−0.240050	−	1.08584i
$232$	2.32456e80			0.870463
$233$			3.48854e80i			1.12861i	0.825567	+	0.564304i	$0.190855\pi$
$233$			3.48854e80i			1.12861i	−0.825567	+	0.564304i	$0.809145\pi$
$234$	1.48265e80	+	3.18942e80i	0.414668	+	0.892015i
$235$	1.59898e80			0.386844
$236$		−	2.43900e80i		−	0.510744i
$237$	3.58856e80	−	7.93335e79i	0.650843	−	0.143884i
$238$	−3.76900e80			−0.592393
$239$		−	1.04589e81i		−	1.42547i	−0.701434	−	0.712734i	$-0.747457\pi$
$239$		−	1.04589e81i		−	1.42547i	0.701434	−	0.712734i	$-0.252543\pi$
$240$	4.30087e78	+	1.94545e79i	0.00508598	+	0.0230058i
$241$	1.11686e81			1.14662			0.573310	−	0.819338i	$-0.305659\pi$
$241$	1.11686e81			1.14662			0.573310	+	0.819338i	$0.305659\pi$
$242$			2.00875e81i			1.79144i
$243$	5.99074e80	−	1.14254e81i	0.464373	−	0.885640i
$244$	−1.57544e80			−0.106205
$245$			2.53912e80i			0.148949i
$246$	−5.31191e80	+	1.17432e80i	−0.271304	+	0.0599782i
$247$	−1.74271e81			−0.775405
$248$		−	3.74278e81i		−	1.45157i
$249$	7.41628e80	+	3.35467e81i	0.250847	+	1.13468i
$250$	−9.65770e80			−0.285045
$251$			1.91479e81i			0.493417i	0.969090	+	0.246708i	$0.0793490\pi$
$251$			1.91479e81i			0.493417i	−0.969090	+	0.246708i	$0.920651\pi$
$252$	−1.32127e81	+	6.14215e80i	−0.297423	+	0.138262i
$253$	−9.39279e81			−1.84798
$254$			9.18945e80i			0.158104i
$255$	2.26684e81	−	5.01138e80i	0.341236	−	0.0754381i
$256$	−7.96087e81			−1.04906
$257$		−	1.34158e82i		−	1.54842i	−0.632928	−	0.774211i	$-0.718147\pi$
$257$		−	1.34158e82i		−	1.54842i	0.632928	−	0.774211i	$-0.281853\pi$
$258$	−3.74892e80	−	1.69578e81i	−0.0379172	−	0.171514i
$259$	2.55936e81			0.226955
$260$			2.44689e81i			0.190336i
$261$	5.21996e81	+	1.12289e82i	0.356361	+	0.766588i
$262$	−4.23730e81			−0.254007
$263$			1.92750e81i			0.101507i	0.998711	+	0.0507537i	$0.0161624\pi$
$263$			1.92750e81i			0.101507i	−0.998711	+	0.0507537i	$0.983838\pi$
$264$	4.19552e82	−	9.27517e81i	1.94201	−	0.429327i
$265$	−1.68238e79			−0.000684802
$266$			5.45306e81i			0.195283i
$267$	−7.01969e80	−	3.17528e81i	−0.0221276	−	0.100092i
$268$	2.36344e80			0.00656086
$269$			1.11710e81i			0.0273221i	0.999907	+	0.0136611i	$0.00434858\pi$
$269$			1.11710e81i			0.0273221i	−0.999907	+	0.0136611i	$0.995651\pi$
$270$	−5.38547e81	+	4.11724e81i	−0.116106	+	0.0887642i
$271$	−7.88993e81			−0.150009			−0.0750045	−	0.997183i	$-0.523897\pi$
$271$	−7.88993e81			−0.150009			−0.0750045	+	0.997183i	$0.523897\pi$
$272$		−	9.88867e81i		−	0.165880i
$273$	5.69316e82	−	1.25861e82i	0.842992	−	0.186363i
$274$	4.81746e82			0.629940
$275$			1.58895e83i			1.83569i
$276$	1.15216e82	+	5.21166e82i	0.117653	+	0.532191i
$277$	−1.43040e83			−1.29165			−0.645827	−	0.763483i	$-0.723487\pi$
$277$	−1.43040e83			−1.29165			−0.645827	+	0.763483i	$0.723487\pi$
$278$		−	8.52453e82i		−	0.681001i
$279$	1.80797e83	−	8.40465e82i	1.27835	−	0.594260i
$280$	2.10961e82			0.132078
$281$		−	5.80561e82i		−	0.321983i	−0.986956	−	0.160992i	$-0.948531\pi$
$281$		−	5.80561e82i		−	0.321983i	0.986956	−	0.160992i	$-0.0514692\pi$
$282$	2.26268e83	−	5.00218e82i	1.11212	−	0.245861i
$283$	−2.77184e83			−1.20789			−0.603947	−	0.797025i	$-0.706406\pi$
$283$	−2.77184e83			−1.20789			−0.603947	+	0.797025i	$0.706406\pi$
$284$			9.11122e81i			0.0352171i
$285$	−7.25054e81	−	3.27970e82i	−0.0248682	−	0.112489i
$286$	−6.24039e83			−1.90006
$287$			9.01843e82i			0.243863i
$288$	−1.68500e83	−	3.62470e83i	−0.404814	−	0.870818i
$289$	−6.83925e83			−1.46043
$290$		−	6.50694e82i		−	0.123551i
$291$	6.22519e83	−	1.37622e83i	1.05146	−	0.232449i
$292$	−3.80242e83			−0.571535
$293$			8.12201e82i			0.108684i	0.998522	+	0.0543418i	$0.0173061\pi$
$293$			8.12201e82i			0.108684i	−0.998522	+	0.0543418i	$0.982694\pi$
$294$	7.94327e82	+	3.59304e83i	0.0946651	+	0.428207i
$295$	−1.88113e83			−0.199743
$296$			4.28889e83i			0.405907i
$297$	1.39017e84	+	1.81839e84i	1.17314	+	1.53450i
$298$	1.24140e83			0.0934452
$299$		−	2.13587e84i		−	1.43468i
$300$	8.81642e83	−	1.94908e83i	0.528652	−	0.116871i
$301$	−2.87906e83			−0.154166
$302$			1.82725e84i			0.874099i
$303$	−1.24321e83	−	5.62354e83i	−0.0531492	−	0.240414i
$304$	−1.43071e83			−0.0546826
$305$			1.21509e83i			0.0415350i
$306$	3.05097e84	−	1.41829e84i	0.933059	−	0.433748i
$307$	−1.94768e84			−0.533106			−0.266553	−	0.963820i	$-0.585885\pi$
$307$	−1.94768e84			−0.533106			−0.266553	+	0.963820i	$0.585885\pi$
$308$		−	2.58519e84i		−	0.633532i
$309$	6.60330e84	−	1.45982e84i	1.44935	−	0.320413i
$310$	−1.04768e84			−0.206030
$311$		−	3.25431e84i		−	0.573595i	−0.957991	−	0.286797i	$-0.907409\pi$
$311$		−	3.25431e84i		−	0.573595i	0.957991	−	0.286797i	$-0.0925907\pi$
$312$	2.10913e84	+	9.54041e84i	0.333309	+	1.50769i
$313$	−7.98846e83			−0.113228			−0.0566142	−	0.998396i	$-0.518031\pi$
$313$	−7.98846e83			−0.113228			−0.0566142	+	0.998396i	$0.518031\pi$
$314$			2.46758e84i			0.313807i
$315$	4.73727e83	+	1.01906e84i	0.0540717	+	0.116317i
$316$	3.70545e84			0.379735
$317$			2.74873e84i			0.252998i	0.991967	+	0.126499i	$0.0403741\pi$
$317$			2.74873e84i			0.252998i	−0.991967	+	0.126499i	$0.959626\pi$
$318$	−2.38069e82	+	5.26308e81i	−0.00196871	+	0.000435229i
$319$	−2.19705e85			−1.63289
$320$			2.45305e84i			0.163911i
$321$	−3.80005e84	−	1.71891e85i	−0.228359	−	1.03295i
$322$	−6.68329e84			−0.361319
$323$			1.66706e85i			0.811084i
$324$	8.38424e84	−	9.94401e84i	0.367226	−	0.435543i
$325$	−3.61320e85			−1.42514
$326$		−	8.30710e84i		−	0.295156i
$327$	−1.89249e85	+	4.18380e84i	−0.605914	+	0.133951i
$328$	−1.51128e85			−0.436148
$329$		−	3.84152e85i		−	0.999637i
$330$	−2.59631e84	−	1.17441e85i	−0.0609373	−	0.275643i
$331$	6.94166e85			1.46998			0.734991	−	0.678077i	$-0.237187\pi$
$331$	6.94166e85			1.46998			0.734991	+	0.678077i	$0.237187\pi$
$332$			3.46394e85i			0.662027i
$333$	−2.07177e85	+	9.63098e84i	−0.357469	+	0.166175i
$334$	5.00505e85			0.779882
$335$		−	1.82285e83i		−	0.00256583i
$336$	4.67390e84	−	1.03328e84i	0.0594489	−	0.0131426i
$337$	1.63440e85			0.187907			0.0939534	−	0.995577i	$-0.470050\pi$
$337$	1.63440e85			0.187907			0.0939534	+	0.995577i	$0.470050\pi$
$338$		−	7.87997e85i		−	0.819138i
$339$	−6.20498e83	−	2.80675e84i	−0.00583379	−	0.0263885i
$340$	2.34068e85			0.199094
$341$			3.53747e86i			2.72297i
$342$	−2.05201e85	−	4.41419e85i	−0.142985	−	0.307584i
$343$	1.52248e86			0.960622
$344$		−	4.82463e85i		−	0.275726i
$345$	4.01961e85	−	8.88630e84i	0.208130	−	0.0460121i
$346$	1.53747e86			0.721472
$347$		−	3.47787e86i		−	1.47949i	−0.672890	−	0.739743i	$-0.734947\pi$
$347$		−	3.47787e86i		−	1.47949i	0.672890	−	0.739743i	$-0.265053\pi$
$348$	2.69500e85	+	1.21905e86i	0.103960	+	0.470249i
$349$	−2.50638e86			−0.876965			−0.438483	−	0.898740i	$-0.644484\pi$
$349$	−2.50638e86			−0.876965			−0.438483	+	0.898740i	$0.644484\pi$
$350$			1.13059e86i			0.358916i
$351$	−4.13493e86	+	3.16119e86i	−1.19131	+	0.910770i
$352$	7.09207e86			1.85491
$353$		−	3.27684e86i		−	0.778244i	−0.921186	−	0.389122i	$-0.872778\pi$
$353$		−	3.27684e86i		−	0.778244i	0.921186	−	0.389122i	$-0.127222\pi$
$354$	−2.66194e86	+	5.88484e85i	−0.574231	+	0.126947i
$355$	7.02724e84			0.0137727
$356$		−	3.27871e85i		−	0.0583986i
$357$	−1.20397e86	−	5.44603e86i	−0.194938	−	0.881780i
$358$	2.42780e86			0.357430
$359$		−	3.73183e86i		−	0.499701i	−0.968284	−	0.249851i	$-0.919618\pi$
$359$		−	3.73183e86i		−	0.499701i	0.968284	−	0.249851i	$-0.0803815\pi$
$360$	−1.70771e86	+	7.93857e85i	−0.208031	+	0.0967068i
$361$	−6.60886e86			−0.732625
$362$			1.75968e85i			0.0177559i
$363$	−2.90254e87	+	6.41675e86i	−2.66657	+	0.589508i
$364$	5.87861e86			0.491844
$365$			2.93270e86i			0.223517i
$366$	3.80123e85	+	1.71944e86i	0.0263978	+	0.119407i
$367$	2.79611e86			0.176973			0.0884866	−	0.996077i	$-0.471797\pi$
$367$	2.79611e86			0.176973			0.0884866	+	0.996077i	$0.471797\pi$
$368$		−	1.75348e86i		−	0.101176i
$369$	−3.39367e86	−	7.30032e86i	−0.178556	−	0.384101i
$370$	1.20055e86			0.0576131
$371$			4.04188e84i			0.00176958i
$372$	1.96279e87	−	4.33921e86i	0.784177	−	0.173361i
$373$	−8.43245e86			−0.307506			−0.153753	−	0.988109i	$-0.549136\pi$
$373$	−8.43245e86			−0.307506			−0.153753	+	0.988109i	$0.549136\pi$
$374$			5.96951e87i			1.98749i
$375$	−3.08506e86	−	1.39549e87i	−0.0937994	−	0.424291i
$376$	6.43749e87			1.78784
$377$		−	4.99599e87i		−	1.26770i
$378$	9.89157e86	+	1.29385e87i	0.229374	+	0.300028i
$379$	5.42437e87			1.14978			0.574892	−	0.818229i	$-0.305044\pi$
$379$	5.42437e87			1.14978			0.574892	+	0.818229i	$0.305044\pi$
$380$		−	3.38653e86i		−	0.0656316i
$381$	−1.32783e87	+	2.93548e86i	−0.235339	+	0.0520271i
$382$	−2.60320e87			−0.422039
$383$			1.40979e87i			0.209121i	0.994519	+	0.104560i	$0.0333435\pi$
$383$			1.40979e87i			0.209121i	−0.994519	+	0.104560i	$0.966656\pi$
$384$	−7.59635e86	−	3.43612e87i	−0.103120	−	0.466452i
$385$	−1.99389e87			−0.247763
$386$		−	6.26962e87i		−	0.713301i
$387$	2.33057e87	−	1.08340e87i	0.242822	−	0.112880i
$388$	6.42797e87			0.613472
$389$			1.55769e88i			1.36205i	0.732259	+	0.681026i	$0.238466\pi$
$389$			1.55769e88i			1.36205i	−0.732259	+	0.681026i	$0.761534\pi$
$390$	2.67056e87	−	5.90389e86i	0.213996	−	0.0473088i
$391$	−2.04316e88			−1.50070
$392$			1.02225e88i			0.688383i
$393$	−1.35356e87	−	6.12269e87i	−0.0835857	−	0.378090i
$394$	1.85365e88			1.04992
$395$		−	2.85791e87i		−	0.148507i
$396$	9.72820e87	+	2.09269e88i	0.463870	+	0.997856i
$397$	−2.91340e88			−1.27504			−0.637519	−	0.770435i	$-0.720039\pi$
$397$	−2.91340e88			−1.27504			−0.637519	+	0.770435i	$0.720039\pi$
$398$		−	2.25334e88i		−	0.905320i
$399$	−7.87940e87	+	1.74193e87i	−0.290680	+	0.0642616i
$400$	−2.96632e87			−0.100503
$401$		−	2.43916e88i		−	0.759158i	−0.925159	−	0.379579i	$-0.876069\pi$
$401$		−	2.43916e88i		−	0.759158i	0.925159	−	0.379579i	$-0.123931\pi$
$402$	−5.70253e85	−	2.57947e86i	−0.00163073	−	0.00737641i
$403$	−8.04403e88			−2.11399
$404$		−	5.80672e87i		−	0.140270i
$405$	−7.66954e87	−	6.46653e87i	−0.170333	−	0.143615i
$406$	−1.56328e88			−0.319265
$407$		−	4.05362e88i		−	0.761436i
$408$	9.12627e88	−	2.01758e88i	1.57706	−	0.348646i
$409$	−5.95013e88			−0.946093			−0.473047	−	0.881037i	$-0.656846\pi$
$409$	−5.95013e88			−0.946093			−0.473047	+	0.881037i	$0.656846\pi$
$410$			4.23038e87i			0.0619054i
$411$	1.53889e88	+	6.96100e88i	0.207294	+	0.937669i
$412$	6.81840e88			0.845624
$413$			4.51937e88i			0.516151i
$414$	5.41005e88	−	2.51495e88i	0.569102	−	0.264556i
$415$	2.67164e88			0.258907
$416$			1.61270e89i			1.44006i
$417$	1.23175e89	−	2.72308e88i	1.01367	−	0.224096i
$418$	8.63678e88			0.655176
$419$		−	1.64761e89i		−	1.15233i	−0.817332	−	0.576167i	$-0.804548\pi$
$419$		−	1.64761e89i		−	1.15233i	0.817332	−	0.576167i	$-0.195452\pi$
$420$	2.44579e87	+	1.10633e88i	0.0157741	+	0.0713522i
$421$	−2.10118e89			−1.24989			−0.624944	−	0.780669i	$-0.714878\pi$
$421$	−2.10118e89			−1.24989			−0.624944	+	0.780669i	$0.714878\pi$
$422$		−	1.01967e89i		−	0.559548i
$423$	1.44558e89	+	3.10967e89i	0.731930	+	1.57450i
$424$	−6.77325e86			−0.00316489
$425$			3.45635e89i			1.49071i
$426$	9.94405e87	−	2.19837e87i	0.0395947	−	0.00875334i
$427$	2.91923e88			0.107330
$428$		−	1.77490e89i		−	0.602678i
$429$	−1.99343e89	−	9.01707e89i	−0.625250	−	2.82825i
$430$	−1.35051e88			−0.0391356
$431$			3.34093e88i			0.0894624i	0.998999	+	0.0447312i	$0.0142431\pi$
$431$			3.34093e88i			0.0894624i	−0.998999	+	0.0447312i	$0.985757\pi$
$432$	−3.39464e88	+	2.59523e88i	−0.0840131	+	0.0642287i
$433$	2.69868e89			0.617395			0.308697	−	0.951160i	$-0.400107\pi$
$433$	2.69868e89			0.617395			0.308697	+	0.951160i	$0.400107\pi$
$434$			2.51703e89i			0.532399i
$435$	9.40221e88	−	2.07858e88i	0.183906	−	0.0406567i
$436$	−1.95414e89			−0.353521
$437$			2.95608e89i			0.494705i
$438$	9.17452e88	+	4.14999e89i	0.142057	+	0.642580i
$439$	−4.57998e89			−0.656252			−0.328126	−	0.944634i	$-0.606417\pi$
$439$	−4.57998e89			−0.656252			−0.328126	+	0.944634i	$0.606417\pi$
$440$		−	3.34129e89i		−	0.443122i
$441$	−4.93803e89	+	2.29553e89i	−0.606236	+	0.281819i
$442$	−1.35744e90			−1.54299
$443$		−	1.66192e90i		−	1.74938i	−0.484684	−	0.874689i	$-0.661065\pi$
$443$		−	1.66192e90i		−	1.74938i	0.484684	−	0.874689i	$-0.338935\pi$
$444$	−2.24919e89	+	4.97235e88i	−0.219283	+	0.0484776i
$445$	−2.52878e88			−0.0228386
$446$			1.14040e90i			0.954271i
$447$	3.96552e88	+	1.79376e89i	0.0307499	+	0.139094i
$448$	5.89340e89			0.423558
$449$			1.15837e90i			0.771740i	0.922553	+	0.385870i	$0.126099\pi$
$449$			1.15837e90i			0.771740i	−0.922553	+	0.385870i	$0.873901\pi$
$450$	−4.25447e89	−	9.15203e89i	−0.262797	−	0.565317i
$451$	1.42838e90			0.818164
$452$		−	2.89818e88i		−	0.0153964i
$453$	−2.64028e90	+	5.83696e89i	−1.30110	+	0.287639i
$454$	2.57678e90			1.17809
$455$		−	4.53401e89i		−	0.192351i
$456$	−2.91906e89	−	1.32040e90i	−0.114931	−	0.519879i
$457$	3.95192e90			1.44430			0.722150	−	0.691736i	$-0.243154\pi$
$457$	3.95192e90			1.44430			0.722150	+	0.691736i	$0.243154\pi$
$458$			1.64371e88i			0.00557697i
$459$	3.02397e90	+	3.95544e90i	0.952677	+	1.24613i
$460$	4.15055e89			0.121434
$461$		−	4.86071e90i		−	1.32089i	−0.750872	−	0.660447i	$-0.770367\pi$
$461$		−	4.86071e90i		−	1.32089i	0.750872	−	0.660447i	$-0.229633\pi$
$462$	−2.82150e90	+	6.23759e89i	−0.712283	+	0.157467i
$463$	4.56465e90			1.07066			0.535332	−	0.844641i	$-0.320186\pi$
$463$	4.56465e90			1.07066			0.535332	+	0.844641i	$0.320186\pi$
$464$		−	4.10154e89i		−	0.0893997i
$465$	−3.34672e89	−	1.51385e90i	−0.0677982	−	0.306677i
$466$	3.93144e90			0.740339
$467$			4.12349e90i			0.721923i	0.932581	+	0.360961i	$0.117551\pi$
$467$			4.12349e90i			0.721923i	−0.932581	+	0.360961i	$0.882449\pi$
$468$	−4.75867e90	+	2.21215e90i	−0.774687	+	0.360126i
$469$	−4.37937e88			−0.00663032
$470$		−	1.80199e90i		−	0.253761i
$471$	−3.56553e90	+	7.88243e89i	−0.467103	+	0.103264i
$472$	−7.57342e90			−0.923132
$473$			4.55997e90i			0.517230i
$474$	−8.94056e89	−	4.04416e90i	−0.0943846	−	0.426938i
$475$	5.00071e90			0.491415
$476$		−	5.62343e90i		−	0.514475i
$477$	−1.52098e88	−	3.27186e88i	−0.00129568	−	0.00278721i
$478$	−1.17867e91			−0.935073
$479$			1.76017e91i			1.30061i	0.759672	+	0.650306i	$0.225360\pi$
$479$			1.76017e91i			1.30061i	−0.759672	+	0.650306i	$0.774640\pi$
$480$	−3.03503e90	+	6.70964e89i	−0.208911	+	0.0461846i
$481$	9.21774e90			0.591142
$482$		−	1.25866e91i		−	0.752156i
$483$	−2.13491e90	−	9.65703e90i	−0.118899	−	0.537825i
$484$	−2.99709e91			−1.55581
$485$		−	4.95771e90i		−	0.239918i
$486$	−1.28759e91	−	6.75131e90i	−0.580959	−	0.304618i
$487$	2.80143e91			1.17868			0.589339	−	0.807886i	$-0.299388\pi$
$487$	2.80143e91			1.17868			0.589339	+	0.807886i	$0.299388\pi$
$488$			4.89194e90i			0.191959i
$489$	1.20034e91	−	2.65362e90i	0.439341	−	0.0971265i
$490$	2.86149e90			0.0977069
$491$		−	5.02508e90i		−	0.160093i	−0.996791	−	0.0800465i	$-0.974493\pi$
$491$		−	5.02508e90i		−	0.160093i	0.996791	−	0.0800465i	$-0.0255069\pi$
$492$	−1.75211e90	−	7.92546e90i	−0.0520892	−	0.235620i
$493$	−4.77912e91			−1.32603
$494$			1.96396e91i			0.508647i
$495$	1.61403e91	−	7.50309e90i	0.390243	−	0.181411i
$496$	−6.60389e90			−0.149081
$497$		−	1.68828e90i		−	0.0355899i
$498$	3.78057e91	−	8.35784e90i	0.744320	−	0.164549i
$499$	5.30460e91			0.975515			0.487758	−	0.872979i	$-0.337815\pi$
$499$	5.30460e91			0.975515			0.487758	+	0.872979i	$0.337815\pi$
$500$		−	1.44095e91i		−	0.247553i
$501$	1.59882e91	+	7.23206e91i	0.256635	+	1.16086i
$502$	2.15789e91			0.323670
$503$			3.66028e91i			0.513101i	0.966531	+	0.256550i	$0.0825860\pi$
$503$			3.66028e91i			0.513101i	−0.966531	+	0.256550i	$0.917414\pi$
$504$	1.90722e91	+	4.10273e91i	0.249898	+	0.537570i
$505$	−4.47856e90			−0.0548570
$506$			1.05853e92i			1.21223i
$507$	1.13862e92	−	2.51718e91i	1.21929	−	0.269553i
$508$	−1.37108e91			−0.137309
$509$		−	1.78704e92i		−	1.67390i	−0.547281	−	0.836949i	$-0.684337\pi$
$509$		−	1.78704e92i		−	1.67390i	0.547281	−	0.836949i	$-0.315663\pi$
$510$	−5.64761e90	−	2.55463e91i	−0.0494856	−	0.223842i
$511$	7.04575e91			0.577586
$512$			2.74359e91i			0.210446i
$513$	5.72279e91	−	4.37512e91i	0.410788	−	0.314051i
$514$	−1.51190e92			−1.01573
$515$		−	5.25885e91i		−	0.330708i
$516$	2.53014e91	−	5.59347e90i	0.148955	−	0.0329300i
$517$	−6.08436e92			−3.35379
$518$		−	2.88429e91i		−	0.148877i
$519$	4.91130e91	+	2.22157e92i	0.237414	+	1.07392i
$520$	7.59794e91			0.344019
$521$		−	4.09269e92i		−	1.73591i	−0.496646	−	0.867953i	$-0.665435\pi$
$521$		−	4.09269e92i		−	1.73591i	0.496646	−	0.867953i	$-0.334565\pi$
$522$	1.26546e92	−	5.88268e91i	0.502863	−	0.233764i
$523$	2.57942e91			0.0960429			0.0480215	−	0.998846i	$-0.484708\pi$
$523$	2.57942e91			0.0960429			0.0480215	+	0.998846i	$0.484708\pi$
$524$		−	6.32213e91i		−	0.220597i
$525$	−1.63365e92	+	3.61157e91i	−0.534249	+	0.118108i
$526$	2.17221e91			0.0665865
$527$			7.69485e92i			2.21126i
$528$	−1.63654e91	−	7.40272e91i	−0.0440935	−	0.199452i
$529$	3.35174e91			0.0846794
$530$			1.89597e89i			0.000449214i
$531$	−1.70066e92	−	3.65838e92i	−0.377924	−	0.812972i
$532$	−8.13606e91			−0.169597
$533$			3.24806e92i			0.635183i
$534$	−3.57840e91	+	7.91090e90i	−0.0656578	+	0.0145152i
$535$	−1.36893e92			−0.235696
$536$		−	7.33879e90i		−	0.0118583i
$537$	7.75538e91	+	3.50806e92i	0.117619	+	0.532036i
$538$	1.25892e91			0.0179227
$539$		−	9.66173e92i		−	1.29133i
$540$	−6.14300e91	−	8.03523e91i	−0.0770890	−	0.100835i
$541$	3.10964e92			0.366440			0.183220	−	0.983072i	$-0.441348\pi$
$541$	3.10964e92			0.366440			0.183220	+	0.983072i	$0.441348\pi$
$542$			8.89162e91i			0.0984023i
$543$	−2.54265e91	+	5.62112e90i	−0.0264297	+	0.00584290i
$544$	1.54270e93			1.50632
$545$			1.50717e92i			0.138256i
$546$	−1.41840e92	−	6.41595e92i	−0.122250	−	0.552983i
$547$	4.40474e92			0.356739			0.178370	−	0.983964i	$-0.442918\pi$
$547$	4.40474e92			0.356739			0.178370	+	0.983964i	$0.442918\pi$
$548$			7.18774e92i			0.547084i
$549$	−2.36308e92	+	1.09852e92i	−0.169052	+	0.0785864i
$550$	1.79068e93			1.20417
$551$			6.91450e92i			0.437126i
$552$	1.61829e93	−	3.57762e92i	0.961897	−	0.212650i
$553$	−6.86607e92			−0.383755
$554$			1.61201e93i			0.847295i
$555$	3.83504e91	+	1.73474e92i	0.0189587	+	0.0857574i
$556$	1.27188e93			0.591428
$557$		−	1.25347e93i		−	0.548322i	−0.961684	−	0.274161i	$-0.911600\pi$
$557$		−	1.25347e93i		−	0.548322i	0.961684	−	0.274161i	$-0.0884001\pi$
$558$	−9.47169e92	−	2.03751e93i	−0.389821	−	0.838565i
$559$	−1.03692e93			−0.401552
$560$		−	3.72228e91i		−	0.0135649i
$561$	−8.62565e93	+	1.90690e93i	−2.95838	+	0.654020i
$562$	−6.54268e92			−0.211213
$563$		−	3.13769e93i		−	0.953508i	−0.879037	−	0.476754i	$-0.841813\pi$
$563$		−	3.13769e93i		−	0.953508i	0.879037	−	0.476754i	$-0.158187\pi$
$564$	7.46334e92	+	3.37595e93i	0.213523	+	0.965844i
$565$	−2.23529e91			−0.00602124
$566$			3.12374e93i			0.792349i
$567$	−1.55357e93	+	1.84259e93i	−0.371113	+	0.440154i
$568$	2.82916e92			0.0636523
$569$		−	4.97175e93i		−	1.05364i	−0.849977	−	0.526820i	$-0.823384\pi$
$569$		−	4.97175e93i		−	1.05364i	0.849977	−	0.526820i	$-0.176616\pi$
$570$	−3.69608e92	+	8.17106e91i	−0.0737899	+	0.0163130i
$571$	2.41408e93			0.454072			0.227036	−	0.973886i	$-0.427097\pi$
$571$	2.41408e93			0.454072			0.227036	+	0.973886i	$0.427097\pi$
$572$		−	9.31079e93i		−	1.65014i
$573$	−8.31565e92	−	3.76149e93i	−0.138880	−	0.628207i
$574$	1.01634e93			0.159968
$575$			6.12889e93i			0.909233i
$576$	−4.77064e93	+	2.21771e93i	−0.667133	+	0.310128i
$577$	−2.10461e93			−0.277456			−0.138728	−	0.990330i	$-0.544301\pi$
$577$	−2.10461e93			−0.277456			−0.138728	+	0.990330i	$0.544301\pi$
$578$			7.70755e93i			0.958010i
$579$	9.05929e93	−	2.00277e93i	1.06175	−	0.234725i
$580$	9.70848e92			0.107300
$581$		−	6.41856e93i		−	0.669036i
$582$	−1.55095e93	−	7.01553e93i	−0.152481	−	0.689730i
$583$	6.40170e91			0.00593697
$584$			1.18070e94i			1.03301i
$585$	1.70617e93	+	3.67023e93i	0.140839	+	0.302966i
$586$	9.15317e92			0.0712939
$587$		−	1.48771e94i		−	1.09351i	−0.837292	−	0.546756i	$-0.815863\pi$
$587$		−	1.48771e94i		−	1.09351i	0.837292	−	0.546756i	$-0.184137\pi$
$588$	−5.36089e93	+	1.18515e93i	−0.371884	+	0.0822137i
$589$	1.11330e94			0.728943
$590$			2.11996e93i			0.131026i
$591$	5.92131e93	+	2.67844e94i	0.345496	+	1.56281i
$592$	7.56747e92			0.0416881
$593$			1.29572e94i			0.673985i	0.941507	+	0.336993i	$0.109410\pi$
$593$			1.29572e94i			0.673985i	−0.941507	+	0.336993i	$0.890590\pi$
$594$	2.04925e94	−	1.56667e94i	1.00660	−	0.769552i
$595$	−4.33719e93			−0.201202
$596$			1.85218e93i			0.0811543i
$597$	3.25597e94	−	7.19808e93i	1.34757	−	0.297913i
$598$	−2.40704e94			−0.941117
$599$			2.21515e94i			0.818259i	0.912476	+	0.409129i	$0.134168\pi$
$599$			2.21515e94i			0.818259i	−0.912476	+	0.409129i	$0.865832\pi$
$600$	−6.05215e93	−	2.73762e94i	−0.211236	−	0.955500i
$601$	2.81177e94			0.927360			0.463680	−	0.886003i	$-0.346529\pi$
$601$	2.81177e94			0.927360			0.463680	+	0.886003i	$0.346529\pi$
$602$			3.24458e93i			0.101129i
$603$	3.54505e92	−	1.64797e92i	0.0104432	−	0.00485469i
$604$	−2.72628e94			−0.759128
$605$			2.31157e94i			0.608450i
$606$	−6.33749e93	+	1.40105e93i	−0.157706	+	0.0348646i
$607$	−4.12425e94			−0.970351			−0.485176	−	0.874417i	$-0.661244\pi$
$607$	−4.12425e94			−0.970351			−0.485176	+	0.874417i	$0.661244\pi$
$608$		−	2.23200e94i		−	0.496561i
$609$	−4.99374e93	−	2.25886e94i	−0.105060	−	0.475227i
$610$	1.36936e93			0.0272460
$611$		−	1.38355e95i		−	2.60372i
$612$	2.11612e94	+	4.55210e94i	0.376697	+	0.810333i
$613$	−6.02065e94			−1.01388			−0.506941	−	0.861981i	$-0.669224\pi$
$613$	−6.02065e94			−1.01388			−0.506941	+	0.861981i	$0.669224\pi$
$614$			2.19496e94i			0.349705i
$615$	−6.11269e93	+	1.35135e93i	−0.0921465	+	0.0203711i
$616$	−8.02738e94			−1.14506
$617$			1.29178e95i			1.74379i	0.489692	+	0.871896i	$0.337109\pi$
$617$			1.29178e95i			1.74379i	−0.489692	+	0.871896i	$0.662891\pi$
$618$	−1.64515e94	−	7.44165e94i	−0.210183	−	0.950739i
$619$	−3.01219e94			−0.364251			−0.182125	−	0.983275i	$-0.558298\pi$
$619$	−3.01219e94			−0.364251			−0.182125	+	0.983275i	$0.558298\pi$
$620$		−	1.56316e94i		−	0.178931i
$621$	5.36217e94	+	7.01388e94i	0.581067	+	0.760054i
$622$	−3.66747e94			−0.376265
$623$			6.07533e93i			0.0590169i
$624$	1.68334e94	−	3.72142e93i	0.154845	−	0.0342321i
$625$	9.79825e94			0.853548
$626$			9.00267e93i			0.0742752i
$627$	2.75894e94	+	1.24797e95i	0.215598	+	0.975233i
$628$	−3.68167e94			−0.272532
$629$		−	8.81761e94i		−	0.618342i
$630$	1.14844e94	−	5.33871e93i	0.0763009	−	0.0354697i
$631$	6.31103e94			0.397285			0.198642	−	0.980072i	$-0.436347\pi$
$631$	6.31103e94			0.397285			0.198642	+	0.980072i	$0.436347\pi$
$632$		−	1.15059e95i		−	0.686343i
$633$	1.47338e95	−	3.25725e94i	0.832890	−	0.184130i
$634$	3.09771e94			0.165961
$635$			1.05748e94i			0.0536989i
$636$	−7.85261e91	−	3.55204e92i	−0.000377983	−	0.00170976i
$637$	2.19703e95			1.00253
$638$			2.47598e95i			1.07114i
$639$	6.35306e93	+	1.36664e94i	0.0260588	+	0.0560565i
$640$	−2.73651e94			−0.106433
$641$		−	2.81005e95i		−	1.03643i	−0.855249	−	0.518217i	$-0.826596\pi$
$641$		−	2.81005e95i		−	1.03643i	0.855249	−	0.518217i	$-0.173404\pi$
$642$	−1.93714e95	+	4.28250e94i	−0.677594	+	0.149798i
$643$	−2.32161e94			−0.0770224			−0.0385112	−	0.999258i	$-0.512262\pi$
$643$	−2.32161e94			−0.0770224			−0.0385112	+	0.999258i	$0.512262\pi$
$644$		−	9.97160e94i		−	0.313794i
$645$	−4.31409e93	−	1.95143e94i	−0.0128783	−	0.0582535i
$646$	1.87871e95			0.532052
$647$		−	3.50068e94i		−	0.0940604i	−0.998893	−	0.0470302i	$-0.985024\pi$
$647$		−	3.50068e94i		−	0.0940604i	0.998893	−	0.0470302i	$-0.0149757\pi$
$648$	−3.08775e95	−	2.60342e95i	−0.787213	−	0.663734i
$649$	7.15798e95			1.73169
$650$			4.07192e95i			0.934858i
$651$	−3.63698e95	+	8.04041e94i	−0.792479	+	0.175196i
$652$	1.23943e95			0.256334
$653$			3.30159e95i			0.648149i	0.946032	+	0.324075i	$0.105053\pi$
$653$			3.30159e95i			0.648149i	−0.946032	+	0.324075i	$0.894947\pi$
$654$	4.71497e94	+	2.13276e95i	0.0878690	+	0.397465i
$655$	−4.87608e94			−0.0862714
$656$			2.66655e94i			0.0447940i
$657$	−5.70346e95	+	2.65135e95i	−0.909737	+	0.422906i
$658$	−4.32923e95			−0.655738
$659$			2.86734e95i			0.412453i	0.978504	+	0.206227i	$0.0661184\pi$
$659$			2.86734e95i			0.412453i	−0.978504	+	0.206227i	$0.933882\pi$
$660$	1.75225e95	−	3.87375e94i	0.239387	−	0.0529222i
$661$	−1.32784e96			−1.72304			−0.861522	−	0.507721i	$-0.830488\pi$
$661$	−1.32784e96			−1.72304			−0.861522	+	0.507721i	$0.830488\pi$
$662$		−	7.82297e95i		−	0.964273i
$663$	−4.33620e95	−	1.96143e96i	−0.507750	−	2.29675i
$664$	1.07560e96			1.19657
$665$			6.27512e94i			0.0663264i
$666$	1.08537e95	+	2.33480e95i	0.109007	+	0.234491i
$667$	−8.47445e95			−0.808785
$668$			7.46764e95i			0.677304i
$669$	−1.64782e96	+	3.64290e95i	−1.42044	+	0.314021i
$670$	−2.05428e93			−0.00168313
$671$		−	4.62360e95i		−	0.360093i
$672$	1.61198e95	+	7.29159e95i	0.119345	+	0.539842i
$673$	1.69326e96			1.19182			0.595910	−	0.803051i	$-0.296791\pi$
$673$	1.69326e96			1.19182			0.595910	+	0.803051i	$0.296791\pi$
$674$		−	1.84191e95i		−	0.123262i
$675$	1.18652e96	−	9.07103e95i	0.754999	−	0.577203i
$676$	1.17571e96			0.711396
$677$		−	1.43236e96i		−	0.824210i	−0.911136	−	0.412105i	$-0.864794\pi$
$677$		−	1.43236e96i		−	0.824210i	0.911136	−	0.412105i	$-0.135206\pi$
$678$	−3.16309e94	+	6.99276e93i	−0.0173102	+	0.00382683i
$679$	−1.19108e96			−0.619967
$680$		−	7.26812e95i		−	0.359848i
$681$	8.23127e95	+	3.72332e96i	0.387673	+	1.75359i
$682$	3.98658e96			1.78621
$683$			3.72120e96i			1.58628i	0.609041	+	0.793139i	$0.291555\pi$
$683$			3.72120e96i			1.58628i	−0.609041	+	0.793139i	$0.708445\pi$
$684$	6.58605e95	−	3.06164e95i	0.267127	−	0.124178i
$685$	5.54371e95			0.213954
$686$		−	1.71578e96i		−	0.630145i
$687$	−2.37508e94	+	5.25066e93i	−0.00830135	+	0.00183521i
$688$	−8.51275e94			−0.0283180
$689$			1.45572e94i			0.00460918i
$690$	−1.00145e95	−	4.52994e95i	−0.0301828	−	0.136528i
$691$	−3.35289e96			−0.961978			−0.480989	−	0.876727i	$-0.659722\pi$
$691$	−3.35289e96			−0.961978			−0.480989	+	0.876727i	$0.659722\pi$
$692$			2.29394e96i			0.626577i
$693$	−1.80260e96	−	3.87767e96i	−0.468781	−	1.00842i
$694$	−3.91941e96			−0.970508
$695$		−	9.80964e95i		−	0.231297i
$696$	3.78532e96	−	8.36834e95i	0.849941	−	0.187899i
$697$	3.10707e96			0.664410
$698$			2.82459e96i			0.575268i
$699$	1.25586e96	+	5.68074e96i	0.243623	+	1.10200i
$700$	−1.68687e96			−0.311708
$701$		−	7.03536e96i		−	1.23844i	−0.785219	−	0.619218i	$-0.787450\pi$
$701$		−	7.03536e96i		−	1.23844i	0.785219	−	0.619218i	$-0.212550\pi$
$702$	3.56253e96	+	4.65990e96i	0.597443	+	0.781474i
$703$	−1.27575e96			−0.203837
$704$		−	9.33421e96i		−	1.42104i
$705$	2.60378e96	−	5.75627e95i	0.377724	−	0.0835048i
$706$	−3.69287e96			−0.510510
$707$			1.07596e96i			0.141755i
$708$	−8.78029e95	−	3.97166e96i	−0.110250	−	0.498702i
$709$	−1.51154e97			−1.80904			−0.904518	−	0.426435i	$-0.859769\pi$
$709$	−1.51154e97			−1.80904			−0.904518	+	0.426435i	$0.859769\pi$
$710$		−	7.91940e94i		−	0.00903459i
$711$	5.55801e96	−	2.58373e96i	0.604440	−	0.280984i
$712$	−1.01808e96			−0.105551
$713$			1.36447e97i			1.34871i
$714$	−6.13745e96	+	1.35683e96i	−0.578427	+	0.127875i
$715$	−7.18116e96			−0.645340
$716$			3.62233e96i			0.310417i
$717$	−3.76516e96	−	1.70313e97i	−0.307704	−	1.39186i
$718$	−4.20562e96			−0.327792
$719$		−	3.33859e96i		−	0.248188i	−0.992270	−	0.124094i	$-0.960398\pi$
$719$		−	3.33859e96i		−	0.248188i	0.992270	−	0.124094i	$-0.0396024\pi$
$720$	1.40071e95	+	3.01314e95i	0.00993214	+	0.0213656i
$721$	−1.26343e97			−0.854576
$722$			7.44792e96i			0.480585i
$723$	1.81870e97	−	4.02066e96i	1.11959	−	0.247511i
$724$	−2.62547e95			−0.0154204
$725$			1.43360e97i			0.803407i
$726$	7.23141e96	+	3.27104e97i	0.386703	+	1.74921i
$727$	2.64567e97			1.35010			0.675050	−	0.737772i	$-0.264122\pi$
$727$	2.64567e97			1.35010			0.675050	+	0.737772i	$0.264122\pi$
$728$		−	1.82539e97i		−	0.888972i
$729$	5.64223e96	−	2.07617e97i	0.262249	−	0.965000i
$730$	3.30503e96			0.146622
$731$			9.91905e96i			0.420029i
$732$	−2.56544e96	+	5.67151e95i	−0.103702	+	0.0229257i
$733$	1.90872e97			0.736557			0.368279	−	0.929715i	$-0.379947\pi$
$733$	1.90872e97			0.736557			0.368279	+	0.929715i	$0.379947\pi$
$734$		−	3.15110e96i		−	0.116090i
$735$	9.14074e95	+	4.13471e96i	0.0321523	+	0.145437i
$736$	2.73555e97			0.918753
$737$			6.93622e95i			0.0222448i
$738$	−8.22716e96	+	3.82453e96i	−0.251961	+	0.117128i
$739$	3.21964e97			0.941665			0.470833	−	0.882223i	$-0.343954\pi$
$739$	3.21964e97			0.941665			0.470833	+	0.882223i	$0.343954\pi$
$740$			1.79124e96i			0.0500352i
$741$	−2.83783e97	+	6.27369e96i	−0.757124	+	0.167380i
$742$	4.55503e94			0.00116080
$743$		−	4.53457e97i		−	1.10387i	−0.833888	−	0.551934i	$-0.813890\pi$
$743$		−	4.53457e97i		−	1.10387i	0.833888	−	0.551934i	$-0.186110\pi$
$744$	−1.34738e97	−	6.09474e97i	−0.313337	−	1.41734i
$745$	1.42854e96			0.0317380
$746$			9.50303e96i			0.201717i
$747$	2.41533e97	+	5.19576e97i	0.489865	+	1.05378i
$748$	−8.90662e97			−1.72607
$749$			3.28883e97i			0.609059i
$750$	−1.57266e97	+	3.47673e96i	−0.278325	+	0.0615302i
$751$	4.42531e97			0.748490			0.374245	−	0.927330i	$-0.377902\pi$
$751$	4.42531e97			0.748490			0.374245	+	0.927330i	$0.377902\pi$
$752$		−	1.13585e97i		−	0.183618i
$753$	6.89316e96	+	3.11804e97i	0.106510	+	0.481784i
$754$	−5.63027e97			−0.831579
$755$			2.10271e97i			0.296881i
$756$	−1.93044e97	+	1.47584e97i	−0.260565	+	0.199204i
$757$	8.64862e97			1.11606			0.558029	−	0.829821i	$-0.311558\pi$
$757$	8.64862e97			1.11606			0.558029	+	0.829821i	$0.311558\pi$
$758$		−	6.11304e97i		−	0.754231i
$759$	−1.52952e98	+	3.38137e97i	−1.80441	+	0.398907i
$760$	−1.05156e97			−0.118624
$761$		−	7.73871e97i		−	0.834815i	−0.908719	−	0.417408i	$-0.862939\pi$
$761$		−	7.73871e97i		−	0.834815i	0.908719	−	0.417408i	$-0.137061\pi$
$762$	3.30816e96	+	1.49641e97i	0.0341286	+	0.154377i
$763$	3.62095e97			0.357263
$764$		−	3.88402e97i		−	0.366528i
$765$	3.51091e97	−	1.63211e97i	0.316906	−	0.147319i
$766$	1.58878e97			0.137178
$767$			1.62769e98i			1.34440i
$768$	−1.29635e98	+	2.86588e97i	−1.02433	+	0.226452i
$769$	−1.64728e98			−1.24529			−0.622647	−	0.782503i	$-0.713943\pi$
$769$	−1.64728e98			−1.24529			−0.622647	+	0.782503i	$0.713943\pi$
$770$			2.24703e97i			0.162527i
$771$	−4.82962e97	−	2.18462e98i	−0.334244	−	1.51192i
$772$	9.35439e97			0.619480
$773$			9.95759e96i			0.0631032i	0.999502	+	0.0315516i	$0.0100449\pi$
$773$			9.95759e96i			0.0631032i	−0.999502	+	0.0315516i	$0.989955\pi$
$774$	−1.22095e97	−	2.62645e97i	−0.0740466	−	0.159286i
$775$	2.30823e98			1.33974
$776$		−	1.99597e98i		−	1.10881i
$777$	4.16766e97	−	9.21359e96i	0.221604	−	0.0489908i
$778$	1.75545e98			0.893474
$779$		−	4.49535e97i		−	0.219023i
$780$	8.80872e96	+	3.98452e97i	0.0410862	+	0.185849i
$781$	−2.67396e97			−0.119404
$782$			2.30256e98i			0.984420i
$783$	1.25426e98	+	1.64061e98i	0.513436	+	0.671590i
$784$	1.80369e97			0.0706995
$785$			2.83957e97i			0.106582i
$786$	−6.90001e97	+	1.52541e97i	−0.248018	+	0.0548302i
$787$	4.08387e97			0.140582			0.0702911	−	0.997527i	$-0.477607\pi$
$787$	4.08387e97			0.140582			0.0702911	+	0.997527i	$0.477607\pi$
$788$			2.76568e98i			0.911824i
$789$	6.93891e96	+	3.13873e97i	0.0219115	+	0.0991143i
$790$	−3.22075e97			−0.0974173
$791$			5.37022e96i			0.0155594i
$792$	6.49808e98	−	3.02074e98i	1.80355	−	0.838411i
$793$	1.05138e98			0.279559
$794$			3.28328e98i			0.836394i
$795$	−2.73959e95	+	6.05651e94i	−0.000668657	+	0.000147822i
$796$	3.36203e98			0.786243
$797$			1.44401e98i			0.323584i	0.986825	+	0.161792i	$0.0517274\pi$
$797$			1.44401e98i			0.323584i	−0.986825	+	0.161792i	$0.948273\pi$
$798$	1.96308e97	+	8.87976e97i	0.0421541	+	0.190679i
$799$	−1.32350e99			−2.72353
$800$		−	4.62765e98i		−	0.912643i
$801$	−2.28617e97	−	4.91791e97i	−0.0432119	−	0.0929555i
$802$	−2.74884e98			−0.497990
$803$		−	1.11594e99i		−	1.93781i
$804$	3.84862e96	−	8.50828e95i	0.00640618	−	0.00141624i
$805$	−7.69082e97			−0.122719
$806$			9.06529e98i			1.38672i
$807$	4.02151e96	+	1.81908e97i	0.00589779	+	0.0266780i
$808$	−1.80306e98			−0.253528
$809$		−	5.25307e98i		−	0.708212i	−0.935205	−	0.354106i	$-0.884785\pi$
$809$		−	5.25307e98i		−	0.708212i	0.935205	−	0.354106i	$-0.115215\pi$
$810$	−7.28751e97	+	8.64326e97i	−0.0942082	+	0.111734i
$811$	−5.33000e98			−0.660721			−0.330360	−	0.943855i	$-0.607170\pi$
$811$	−5.33000e98			−0.660721			−0.330360	+	0.943855i	$0.607170\pi$
$812$		−	2.33244e98i		−	0.277272i
$813$	−1.28480e98	+	2.84034e97i	−0.146472	+	0.0323811i
$814$	−4.56826e98			−0.499484
$815$		−	9.55942e97i		−	0.100247i
$816$	−3.55988e97	−	1.61027e98i	−0.0358072	−	0.161970i
$817$	1.43510e98			0.138463
$818$			6.70555e98i			0.620615i
$819$	8.81765e98	−	4.09903e98i	0.782889	−	0.363939i
$820$	−6.31181e97			−0.0537629
$821$			3.23125e98i			0.264060i	0.991246	+	0.132030i	$0.0421496\pi$
$821$			3.23125e98i			0.264060i	−0.991246	+	0.132030i	$0.957850\pi$
$822$	7.84476e98	−	1.73427e98i	0.615089	−	0.135980i
$823$	−1.67330e99			−1.25887			−0.629434	−	0.777054i	$-0.716713\pi$
$823$	−1.67330e99			−1.25887			−0.629434	+	0.777054i	$0.716713\pi$
$824$		−	2.11721e99i		−	1.52840i
$825$	5.72016e98	+	2.58745e99i	0.396254	+	1.79241i
$826$	5.09315e98			0.338583
$827$			1.73504e99i			1.10694i	0.832870	+	0.553468i	$0.186696\pi$
$827$			1.73504e99i			1.10694i	−0.832870	+	0.553468i	$0.813304\pi$
$828$	3.75236e98	+	8.07190e98i	0.229759	+	0.494247i
$829$	3.29128e98			0.193424			0.0967122	−	0.995312i	$-0.469167\pi$
$829$	3.29128e98			0.193424			0.0967122	+	0.995312i	$0.469167\pi$
$830$		−	3.01083e98i		−	0.169837i
$831$	−2.32927e99	+	5.14940e98i	−1.26120	+	0.278818i
$832$	2.12256e99			1.10323
$833$		−	2.10166e99i		−	1.04866i
$834$	−3.06880e98	−	1.38814e99i	−0.147002	−	0.664945i
$835$	5.75958e98			0.264881
$836$			1.28862e99i			0.569001i
$837$	2.64154e99	−	2.01948e99i	1.11993	−	0.856196i
$838$	−1.85679e99			−0.755903
$839$			1.64906e99i			0.644658i	0.946628	+	0.322329i	$0.104466\pi$
$839$			1.64906e99i			0.644658i	−0.946628	+	0.322329i	$0.895534\pi$
$840$	3.43529e98	−	7.59452e97i	0.128964	−	0.0285105i
$841$	7.91484e98			0.285350
$842$			2.36794e99i			0.819897i
$843$	−2.09000e98	−	9.45386e98i	−0.0695037	−	0.314392i
$844$	1.52137e99			0.485950
$845$		−	9.06791e98i		−	0.278214i
$846$	3.50447e99	−	1.62911e99i	1.03283	−	0.480129i
$847$	5.55350e99			1.57228
$848$			1.19510e96i			0.000325045i
$849$	−4.51366e99	+	9.97850e98i	−1.17942	+	0.260738i
$850$	3.89517e99			0.977874
$851$		−	1.56356e99i		−	0.377146i
$852$	3.28000e97	+	1.48367e98i	0.00760200	+	0.0343868i
$853$	−5.09261e99			−1.13416			−0.567078	−	0.823664i	$-0.691926\pi$
$853$	−5.09261e99			−1.13416			−0.567078	+	0.823664i	$0.691926\pi$
$854$		−	3.28985e98i		−	0.0704058i
$855$	−2.36136e98	−	5.07964e98i	−0.0485639	−	0.104468i
$856$	−5.51130e99			−1.08930
$857$			5.78252e99i			1.09842i	0.835683	+	0.549211i	$0.185072\pi$
$857$			5.78252e99i			1.09842i	−0.835683	+	0.549211i	$0.814928\pi$
$858$	−1.01619e100	+	2.24652e99i	−1.85526	+	0.410149i
$859$	1.74352e99			0.305956			0.152978	−	0.988230i	$-0.451114\pi$
$859$	1.74352e99			0.305956			0.152978	+	0.988230i	$0.451114\pi$
$860$		−	2.01499e98i		−	0.0339880i
$861$	3.24660e98	+	1.46856e99i	0.0526407	+	0.238114i
$862$	3.76509e98			0.0586852
$863$		−	1.04917e100i		−	1.57209i	−0.618167	−	0.786047i	$-0.712124\pi$
$863$		−	1.04917e100i		−	1.57209i	0.618167	−	0.786047i	$-0.287876\pi$
$864$	−4.04873e99	−	5.29587e99i	−0.583246	−	0.762904i
$865$	1.76925e99			0.245043
$866$		−	3.04130e99i		−	0.404996i
$867$	−1.11370e100	+	2.46210e99i	−1.42600	+	0.315251i
$868$	−3.75546e99			−0.462373
$869$			1.08748e100i			1.28750i
$870$	−2.34247e98	−	1.05959e99i	−0.0266698	−	0.120638i
$871$	−1.57726e98			−0.0172698
$872$			6.06787e99i			0.638963i
$873$	9.64166e99	−	4.48208e99i	0.976489	−	0.453937i
$874$	3.33137e99			0.324515
$875$			2.67002e99i			0.250173i
$876$	−6.19186e99	+	1.36886e99i	−0.558061	+	0.123372i
$877$	1.81116e100			1.57025			0.785127	−	0.619335i	$-0.212598\pi$
$877$	1.81116e100			1.57025			0.785127	+	0.619335i	$0.212598\pi$
$878$			5.16145e99i			0.430485i
$879$	2.92389e98	+	1.32259e99i	0.0234606	+	0.106121i
$880$	−5.89550e98			−0.0455103
$881$		−	2.15686e100i		−	1.60192i	−0.598719	−	0.800959i	$-0.704323\pi$
$881$		−	2.15686e100i		−	1.60192i	0.598719	−	0.800959i	$-0.295677\pi$
$882$	2.58696e99	+	5.56496e99i	0.184867	+	0.397677i
$883$	1.76511e100			1.21369			0.606844	−	0.794821i	$-0.292435\pi$
$883$	1.76511e100			1.21369			0.606844	+	0.794821i	$0.292435\pi$
$884$		−	2.02532e100i		−	1.34004i
$885$	−3.06323e99	+	6.77200e98i	−0.195033	+	0.0431167i
$886$	−1.87292e100			−1.14755
$887$		−	5.71135e99i		−	0.336772i	−0.985721	−	0.168386i	$-0.946145\pi$
$887$		−	5.71135e99i		−	0.336772i	0.985721	−	0.168386i	$-0.0538555\pi$
$888$	1.54398e99	+	6.98403e99i	0.0876197	+	0.396337i
$889$	2.54057e99			0.138762
$890$			2.84983e98i			0.0149816i
$891$	2.91837e100	+	2.46061e100i	1.47672	+	1.24509i
$892$	−1.70150e100			−0.828755
$893$			1.91485e100i			0.897814i
$894$	2.02149e99	−	4.46897e98i	0.0912421	−	0.0201712i
$895$	2.79380e99			0.121398
$896$			6.57441e99i			0.275033i
$897$	−7.68906e99	−	3.47806e100i	−0.309692	−	1.40086i
$898$	1.30543e100			0.506243
$899$			3.19161e100i			1.19174i
$900$	1.36550e100	−	6.34775e99i	0.490960	−	0.228231i
$901$	1.39253e98			0.00482126
$902$		−	1.60972e100i		−	0.536696i
$903$	−4.68826e99	+	1.03645e99i	−0.150532	+	0.0332786i
$904$	−8.99924e98			−0.0278278
$905$			2.02495e98i			0.00603064i
$906$	6.57801e99	+	2.97549e100i	0.188684	+	0.853492i
$907$	3.64389e100			1.00674			0.503370	−	0.864071i	$-0.332093\pi$
$907$	3.64389e100			1.00674			0.503370	+	0.864071i	$0.332093\pi$
$908$			3.84460e100i			1.02313i
$909$	−4.04890e99	−	8.70981e99i	−0.103792	−	0.223273i
$910$	−5.10964e99			−0.126178
$911$		−	3.68044e100i		−	0.875538i	−0.899088	−	0.437769i	$-0.855769\pi$
$911$		−	3.68044e100i		−	0.875538i	0.899088	−	0.437769i	$-0.144231\pi$
$912$	−2.32977e99	+	5.15049e98i	−0.0533934	+	0.0118039i
$913$	−1.01660e101			−2.24462
$914$		−	4.45365e100i		−	0.947427i
$915$	4.37428e98	+	1.97865e99i	0.00896580	+	0.0405558i
$916$	−2.45244e98			−0.00484343
$917$			1.17147e100i			0.222932i
$918$	4.45762e100	−	3.40788e100i	0.817432	−	0.624933i
$919$	−1.03919e101			−1.83640			−0.918199	−	0.396120i	$-0.870356\pi$
$919$	−1.03919e101			−1.83640			−0.918199	+	0.396120i	$0.870356\pi$
$920$		−	1.28880e100i		−	0.219483i
$921$	−3.17161e100	+	7.01158e99i	−0.520538	+	0.115077i
$922$	−5.47782e100			−0.866476
$923$		−	6.08047e99i		−	0.0926999i
$924$	−9.30660e99	−	4.20973e100i	−0.136755	−	0.618596i
$925$	−2.64503e100			−0.374638
$926$		−	5.14417e100i		−	0.702331i
$927$	1.02273e101	−	4.75433e100i	1.34601	−	0.625717i
$928$	6.39868e100			0.811818
$929$			1.30360e101i			1.59445i	0.603682	+	0.797225i	$0.293700\pi$
$929$			1.30360e101i			1.59445i	−0.603682	+	0.797225i	$0.706300\pi$
$930$	−1.70604e100	+	3.77161e99i	−0.201173	+	0.0444740i
$931$	−3.04072e100			−0.345690
$932$			5.86579e100i			0.642962i
$933$	−1.17154e100	−	5.29931e100i	−0.123817	−	0.560072i
$934$	4.64700e100			0.473564
$935$			6.86943e100i			0.675035i
$936$	6.86902e100	+	1.47763e101i	0.650902	+	1.40019i
$937$	−8.43079e99			−0.0770410			−0.0385205	−	0.999258i	$-0.512264\pi$
$937$	−8.43079e99			−0.0770410			−0.0385205	+	0.999258i	$0.512264\pi$
$938$			4.93536e98i			0.00434933i
$939$	−1.30084e100	+	2.87581e99i	−0.110559	+	0.0244417i
$940$	2.68860e100			0.220383
$941$		−	2.09479e101i		−	1.65613i	−0.560633	−	0.828064i	$-0.689442\pi$
$941$		−	2.09479e101i		−	1.65613i	0.560633	−	0.828064i	$-0.310558\pi$
$942$	8.88317e99	+	4.01820e100i	0.0677388	+	0.306409i
$943$	5.50953e100			0.405244
$944$			1.33628e100i			0.0948090i
$945$	1.13828e100	+	1.48890e100i	0.0779051	+	0.101902i
$946$	5.13890e100			0.339291
$947$			1.72153e101i			1.09651i	0.836310	+	0.548257i	$0.184709\pi$
$947$			1.72153e101i			1.09651i	−0.836310	+	0.548257i	$0.815291\pi$
$948$	6.03396e100	−	1.33395e100i	0.370782	−	0.0819701i
$949$	2.53758e101			1.50442
$950$		−	5.63559e100i		−	0.322357i
$951$	9.89533e99	+	4.47604e100i	0.0546126	+	0.247034i
$952$	−1.74615e101			−0.929877
$953$		−	8.97791e100i		−	0.461335i	−0.973033	−	0.230668i	$-0.925909\pi$
$953$		−	8.97791e100i		−	0.461335i	0.973033	−	0.230668i	$-0.0740910\pi$
$954$	−3.68725e98	+	1.71408e98i	−0.00182834	+	0.000849936i
$955$	−2.99564e100			−0.143342
$956$		−	1.75861e101i		−	0.812082i
$957$	−3.57768e101	+	7.90929e100i	−1.59439	+	0.352478i
$958$	1.98364e101			0.853171
$959$		−	1.33186e101i		−	0.552875i
$960$	8.83088e99	+	3.99455e100i	0.0353820	+	0.160046i
$961$	2.55300e101			0.987315
$962$		−	1.03880e101i		−	0.387775i
$963$	−1.23760e101	−	2.66227e101i	−0.445950	−	0.959308i
$964$	1.87794e101			0.653224
$965$		−	7.21479e100i		−	0.242267i
$966$	−1.08831e101	+	2.40596e100i	−0.352801	+	0.0779948i
$967$	−3.10706e101			−0.972410			−0.486205	−	0.873845i	$-0.661619\pi$
$967$	−3.10706e101			−0.972410			−0.486205	+	0.873845i	$0.661619\pi$
$968$			9.30637e101i			2.81202i
$969$	6.00136e100	+	2.71464e101i	0.175082	+	0.791962i
$970$	−5.58714e100			−0.157380
$971$		−	3.19885e101i		−	0.870043i	−0.900420	−	0.435021i	$-0.856741\pi$
$971$		−	3.19885e101i		−	0.870043i	0.900420	−	0.435021i	$-0.143259\pi$
$972$	1.00731e101	−	1.92111e101i	0.264551	−	0.504545i
$973$	−2.35674e101			−0.597689
$974$		−	3.15710e101i		−	0.773185i
$975$	−5.88373e101	+	1.30074e101i	−1.39154	+	0.307633i
$976$	8.63152e99			0.0197149
$977$		−	1.33887e101i		−	0.295341i	−0.989037	−	0.147670i	$-0.952823\pi$
$977$		−	1.33887e101i		−	0.295341i	0.989037	−	0.147670i	$-0.0471774\pi$
$978$	−2.99052e100	−	1.35273e101i	−0.0637127	−	0.288197i
$979$	9.62236e100			0.198002
$980$			4.26939e100i			0.0848554i
$981$	−2.93112e101	+	1.36258e101i	−0.562714	+	0.261587i
$982$	−5.66306e100			−0.105017
$983$			3.90746e101i			0.699963i	0.936757	+	0.349982i	$0.113812\pi$
$983$			3.90746e101i			0.699963i	−0.936757	+	0.349982i	$0.886188\pi$
$984$	−2.46097e101	+	5.44054e100i	−0.425865	+	0.0941475i
$985$	2.13310e101			0.356598
$986$			5.38587e101i			0.869842i
$987$	−1.38293e101	−	6.25553e101i	−0.215783	−	0.976069i
$988$	−2.93027e101			−0.441745
$989$			1.75887e101i			0.256189i
$990$	−8.45568e100	−	1.81895e101i	−0.119001	−	0.255990i
$991$	3.97933e101			0.541135			0.270567	−	0.962701i	$-0.412789\pi$
$991$	3.97933e101			0.541135			0.270567	+	0.962701i	$0.412789\pi$
$992$		−	1.03025e102i		−	1.35377i
$993$	1.13038e102	−	2.49897e101i	1.43532	−	0.317312i
$994$	−1.90262e100			−0.0233461
$995$		−	2.59304e101i		−	0.307485i
$996$	1.24701e101	+	5.64068e101i	0.142906	+	0.646419i
$997$	4.54258e101			0.503115			0.251557	−	0.967842i	$-0.419057\pi$
$997$	4.54258e101			0.503115			0.251557	+	0.967842i	$0.419057\pi$
$998$		−	5.97806e101i		−	0.639915i
$999$	−3.02697e101	+	2.31414e101i	−0.313171	+	0.239421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.69.b.a.2.7	✓	22
3.2	odd	2	inner	3.69.b.a.2.16	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.69.b.a.2.7	✓	22	1.1	even	1	trivial
3.69.b.a.2.16	yes	22	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.12696e10i q^{2} +(1.62840e16 - 3.59996e15i) q^{3} +1.68144e20 q^{4} -1.29685e23i q^{5} +(-4.05701e25 - 1.83514e26i) q^{6} -3.11566e28 q^{7} -5.22111e30i q^{8} +(2.52209e32 - 1.17244e32i) q^{9} +O(q^{10})\)	\(q-1.12696e10i q^{2} +(1.62840e16 - 3.59996e15i) q^{3} +1.68144e20 q^{4} -1.29685e23i q^{5} +(-4.05701e25 - 1.83514e26i) q^{6} -3.11566e28 q^{7} -5.22111e30i q^{8} +(2.52209e32 - 1.17244e32i) q^{9} -1.46150e33 q^{10} +4.93471e35i q^{11} +(2.73806e36 - 6.05313e35i) q^{12} -1.12213e38 q^{13} +3.51122e38i q^{14} +(-4.66861e38 - 2.11179e39i) q^{15} -9.21231e39 q^{16} +1.07342e42i q^{17} +(-1.32129e42 - 2.84229e42i) q^{18} +1.55304e43 q^{19} -2.18058e43i q^{20} +(-5.07353e44 + 1.12162e44i) q^{21} +5.56121e45 q^{22} +1.90341e46i q^{23} +(-1.87958e46 - 8.50206e46i) q^{24} +3.21995e47 q^{25} +1.26459e48i q^{26} +(3.68490e48 - 2.81714e48i) q^{27} -5.23880e48 q^{28} +4.45224e49i q^{29} +(-2.37990e49 + 5.26133e48i) q^{30} +7.16854e50 q^{31} -1.43718e51i q^{32} +(1.77647e51 + 8.03568e51i) q^{33} +1.20970e52 q^{34} +4.04054e51i q^{35} +(4.24075e52 - 1.97138e52i) q^{36} -8.21451e52 q^{37} -1.75021e53i q^{38} +(-1.82727e54 + 4.03962e53i) q^{39} -6.77101e53 q^{40} -2.89455e54i q^{41} +(1.26402e54 + 5.71766e54i) q^{42} +9.24062e54 q^{43} +8.29743e55i q^{44} +(-1.52047e55 - 3.27078e55i) q^{45} +2.14507e56 q^{46} +1.23297e57i q^{47} +(-1.50013e56 + 3.31640e55i) q^{48} -1.95791e57 q^{49} -3.62875e57i q^{50} +(3.86426e57 + 1.74796e58i) q^{51} -1.88680e58 q^{52} -1.29728e56i q^{53} +(-3.17480e58 - 4.15273e58i) q^{54} +6.39958e58 q^{55} +1.62672e59i q^{56} +(2.52897e59 - 5.59088e58i) q^{57} +5.01749e59 q^{58} -1.45054e60i q^{59} +(-7.85001e58 - 3.55086e59i) q^{60} -9.36955e59 q^{61} -8.07865e60i q^{62} +(-7.85796e60 + 3.65290e60i) q^{63} -1.89154e61 q^{64} +1.45523e61i q^{65} +(9.05588e61 - 2.00201e61i) q^{66} +1.40560e60 q^{67} +1.80489e62i q^{68} +(6.85221e61 + 3.09952e62i) q^{69} +4.55352e61 q^{70} +5.41869e61i q^{71} +(-6.12141e62 - 1.31681e63i) q^{72} -2.26140e63 q^{73} +9.25742e62i q^{74} +(5.24337e63 - 1.15917e63i) q^{75} +2.61135e63 q^{76} -1.53748e64i q^{77} +(4.55248e63 + 2.05926e64i) q^{78} +2.20373e64 q^{79} +1.19470e63i q^{80} +(4.98633e64 - 5.91397e64i) q^{81} -3.26204e64 q^{82} +2.06010e65i q^{83} +(-8.53086e64 + 1.88595e64i) q^{84} +1.39206e65 q^{85} -1.04138e65i q^{86} +(1.60279e65 + 7.25003e65i) q^{87} +2.57647e66 q^{88} -1.94994e65i q^{89} +(-3.68603e65 + 1.71351e65i) q^{90} +3.49617e66 q^{91} +3.20048e66i q^{92} +(1.16733e67 - 2.58065e66i) q^{93} +1.38951e67 q^{94} -2.01406e66i q^{95} +(-5.17380e66 - 2.34031e67i) q^{96} +3.82289e67 q^{97} +2.20649e67i q^{98} +(5.78562e67 + 1.24458e68i) 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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