LMFDB - Embedded newform 3.65.b.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,65,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, 65, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 65);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 65 $
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:	$77.8210007872$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + \cdots + 16\!\cdots\!00 $ x^20 + 7311620310544130870x^18 + 22358487980721272907183916295956311360x^16 + 37151477629356825732703787880242169529959327824546365440x^14 + 36577181937810097505802558725609391305997892024084599011051392566432890880x^12 + 21935641171547673670160171082705160741656638588244077191486011854728032463189461160295399424x^10 + 7987590380643085516837715299239509687511714431882675077252129349944354353324495609058844076954843300338073600x^8 + 1710143772340434230497591035020629235004345720649150432831527862605417826076987625088696459955931505107452119767981124013260800x^6 + 199559493966567753586460823054432425913919626315388689256905837099260296596989625340870411494788613678146935690514294992985875052698640842752000x^4 + 10702784460042876021719901360844959671777640009115178231708236016838731916069031254098710374341157066177328971282822479332468235994068983580479110003870924800000*x^2 + 167568134216338749789449630379565687313704071449349934396227509090519869920154785147318672798791670461429330519185506832081715257764352465938683107924227686312105507553280000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{190}\cdot 3^{282}\cdot 5^{19}\cdot 7^{8}\cdot 11^{4}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.4
Root			$-1.15913e9i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.65.b.a.2.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.95479e9i q^{2} +(1.80867e15 - 4.02985e14i) q^{3} -2.99223e19 q^{4} -4.26608e21i q^{5} +(-2.80268e24 - 1.25789e25i) q^{6} -1.59304e27 q^{7} +7.98101e28i q^{8} +(3.10889e30 - 1.45773e30i) q^{9} +O(q^{10})$	\(q-6.95479e9i q^{2} +(1.80867e15 - 4.02985e14i) q^{3} -2.99223e19 q^{4} -4.26608e21i q^{5} +(-2.80268e24 - 1.25789e25i) q^{6} -1.59304e27 q^{7} +7.98101e28i q^{8} +(3.10889e30 - 1.45773e30i) q^{9} -2.96697e31 q^{10} -1.95522e33i q^{11} +(-5.41196e34 + 1.20583e34i) q^{12} -4.09446e35 q^{13} +1.10793e37i q^{14} +(-1.71917e36 - 7.71594e36i) q^{15} +3.09321e36 q^{16} +1.60359e39i q^{17} +(-1.01382e40 - 2.16217e40i) q^{18} -4.25866e40 q^{19} +1.27651e41i q^{20} +(-2.88129e42 + 6.41973e41i) q^{21} -1.35982e43 q^{22} -6.67799e43i q^{23} +(3.21623e43 + 1.44350e44i) q^{24} +5.23902e44 q^{25} +2.84761e45i q^{26} +(5.03551e45 - 3.88940e45i) q^{27} +4.76675e46 q^{28} +3.89949e46i q^{29} +(-5.36627e46 + 1.19565e46i) q^{30} -3.52667e47 q^{31} +1.45072e48i q^{32} +(-7.87927e47 - 3.53636e48i) q^{33} +1.11526e49 q^{34} +6.79605e48i q^{35} +(-9.30252e49 + 4.36188e49i) q^{36} -1.20138e49 q^{37} +2.96181e50i q^{38} +(-7.40553e50 + 1.65001e50i) q^{39} +3.40477e50 q^{40} +7.11845e51i q^{41} +(4.46478e51 + 2.00387e52i) q^{42} +1.24729e52 q^{43} +5.85048e52i q^{44} +(-6.21882e51 - 1.32628e52i) q^{45} -4.64440e53 q^{46} +5.35217e53i q^{47} +(5.59460e51 - 1.24652e51i) q^{48} +1.31802e54 q^{49} -3.64362e54i q^{50} +(6.46224e53 + 2.90037e54i) q^{51} +1.22516e55 q^{52} -1.42076e55i q^{53} +(-2.70499e55 - 3.50209e55i) q^{54} -8.34115e54 q^{55} -1.27141e56i q^{56} +(-7.70251e55 + 1.71618e55i) q^{57} +2.71201e56 q^{58} +6.80375e56i q^{59} +(5.14415e55 + 2.30879e56i) q^{60} -3.82753e56 q^{61} +2.45273e57i q^{62} +(-4.95259e57 + 2.32223e57i) q^{63} +1.01465e58 q^{64} +1.74673e57i q^{65} +(-2.45946e58 + 5.47986e57i) q^{66} +4.35199e58 q^{67} -4.79832e58i q^{68} +(-2.69113e58 - 1.20783e59i) q^{69} +4.72651e58 q^{70} -6.48041e58i q^{71} +(1.16342e59 + 2.48121e59i) q^{72} +1.90649e59 q^{73} +8.35533e58i q^{74} +(9.47565e59 - 2.11125e59i) q^{75} +1.27429e60 q^{76} +3.11476e60i q^{77} +(1.14754e60 + 5.15039e60i) q^{78} -9.64097e60 q^{79} -1.31959e58i q^{80} +(7.54020e60 - 9.06387e60i) q^{81} +4.95073e61 q^{82} +1.66247e61i q^{83} +(8.62148e61 - 1.92093e61i) q^{84} +6.84105e60 q^{85} -8.67464e61i q^{86} +(1.57144e61 + 7.05288e61i) q^{87} +1.56047e62 q^{88} -1.95845e62i q^{89} +(-9.22398e61 + 4.32506e61i) q^{90} +6.52265e62 q^{91} +1.99821e63i q^{92} +(-6.37859e62 + 1.42120e62i) q^{93} +3.72232e63 q^{94} +1.81678e62i q^{95} +(5.84621e62 + 2.62388e63i) q^{96} -2.35055e63 q^{97} -9.16658e63i q^{98} +(-2.85020e63 - 6.07858e63i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14\!\cdots\!92 q^{3}+ \cdots - 22\!\cdots\!00 q^{9}+O(q^{10}) $ 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9	$ 20 q - 14\!\cdots\!92 q^{3}+ \cdots + 31\!\cdots\!00 q^{99}+O(q^{100}) $ 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9 + 331029217205387677806996511116000 * q^10 + 6534659062821156745233165595144848 * q^12 - 751508903297384088692483175344422424 * q^13 + 38547509823020584674418593740816815200 * q^15 + 333898239622199115079798041399657464960 * q^16 - 3676009515412490831675032229198156934240 * q^18 + 109286088964872656413026262415428611794200 * q^19 - 1311511276150890256934838463853331394769880 * q^21 - 8079025213365934710514462143494926255299360 * q^22 + 371409898348173331095205935880826344773509760 * q^24 - 1408933246315215357541047632909406493714979500 * q^25 + 5130931947084052629864823829892614277399503148 * q^27 - 38556600155873290275414028639950032296787869664 * q^28 - 141541842553229550692763020870574637255687216800 * q^30 + 458034135616019870141982361360522347620359726840 * q^31 - 2882270174679362228632701138961802589863549285280 * q^33 - 787058086714062550476148644876342688312553235840 * q^34 + 75759088962200911205216155020070755577873854233040 * q^36 - 167241277488128791881901510734045117370850836062104 * q^37 + 458879560232529079697344976545706436533594974010520 * q^39 - 3172271879697225400792978571433360199916055661804800 * q^40 - 22013931366996449796115743111552261520406610644630880 * q^42 + 10353394041775726307362489381794503494462017586072216 * q^43 + 37622210359250231761078599539977430954460378542462400 * q^45 - 297398119355935548173345475928562088559055731847559360 * q^46 - 127296049249148961420276393789708282996205874832565632 * q^48 + 2035505279477569607000808808313462872867812749377748220 * q^49 - 8993599813445960529795685588193052695282052910939102080 * q^51 + 12450863873285726446941747254985680826918117392844470176 * q^52 + 1380721489513428759527937305946915244571081819618418480 * q^54 + 86716751505127419669577189864656813143075791367545723200 * q^55 - 410655148353071807815217561752202738362370559954491547384 * q^57 + 1171127646996109205778370152132525033757099595854063443360 * q^58 - 4554593355431768584543074712701226261422872417617275398400 * q^60 + 4552152490922647485493920930203353370116723196876970427240 * q^61 - 18340670222945277450481852597884877177550760958776639152904 * q^63 + 30281219638275425893507737167512138061029087969644636247040 * q^64 - 73446637659820047047259347339723389117534541697924310768800 * q^66 + 108802231400777081380268556166029877921173626685759369971416 * q^67 - 255718829710356626829923504360603133388502621634044634870720 * q^69 + 559303866272797397220431985027879540776975892234361655006400 * q^70 - 561110698242036073669580259260779527574289380077856046595840 * q^72 - 569085806526237236378057540729119438030642048917813502604504 * q^73 + 2290039066363366330022806756651688579736177808604861676211500 * q^75 - 5532330994825480968263901289000933629970925314426608479594720 * q^76 + 9655803402636036605327159547820723686984585271634655943687200 * q^78 - 22640121063621617622122249693012788180804867706114977596801800 * q^79 + 37075761484886132865783336331999338158569856937859957696374420 * q^81 - 69993225281309073377388502634775301823581628014590259964399040 * q^82 + 62923532655099413129084384942812878939798728172266572844745120 * q^84 - 142181474118416523657627044760532405955688084516779285440262400 * q^85 + 23785411541262749066239132616113250012236593481925882591047200 * q^87 + 345107275964501391166111220047509272448066379695588836103893760 * q^88 - 1925479853343216377261941955721474942915647264800935046773530400 * q^90 + 1225124508801982757577911377627409097047306370806522445345728240 * q^91 - 2776404525956613483290023288082668840477640965472850083253548184 * q^93 + 1658662465458978832407333757013771498132481417946327912207224960 * q^94 - 3771017263293375391290634333996451541183976624371029742095907840 * q^96 + 818755932265886448325223871671724131911117159175492830487918056 * q^97 + 3118093180125811439250837213823663221313339534064003298574718400 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	6.95479e9i		−	1.61929i	−0.586922	−	0.809644i	$-0.699660\pi$
$2$		−	6.95479e9i		−	1.61929i	0.586922	−	0.809644i	$-0.300340\pi$
$3$	1.80867e15	−	4.02985e14i	0.976066	−	0.217475i
$3$	1.80867e15	−	4.02985e14i	0.976066	−	0.217475i
$4$	−2.99223e19			−1.62209
$5$		−	4.26608e21i		−	0.183227i	−0.995795	−	0.0916135i	$-0.970798\pi$
$5$		−	4.26608e21i		−	0.183227i	0.995795	−	0.0916135i	$-0.0292024\pi$
$6$	−2.80268e24	−	1.25789e25i	−0.352154	−	1.58053i
$7$	−1.59304e27			−1.44241			−0.721207	−	0.692719i	$-0.756412\pi$
$7$	−1.59304e27			−1.44241			−0.721207	+	0.692719i	$0.756412\pi$
$8$			7.98101e28i			1.00735i
$9$	3.10889e30	−	1.45773e30i	0.905409	−	0.424540i
$10$	−2.96697e31			−0.296697
$11$		−	1.95522e33i		−	0.926042i	−0.886347	−	0.463021i	$-0.846765\pi$
$11$		−	1.95522e33i		−	0.926042i	0.886347	−	0.463021i	$-0.153235\pi$
$12$	−5.41196e34	+	1.20583e34i	−1.58327	+	0.352764i
$13$	−4.09446e35			−0.924718			−0.462359	−	0.886693i	$-0.652997\pi$
$13$	−4.09446e35			−0.924718			−0.462359	+	0.886693i	$0.652997\pi$
$14$			1.10793e37i			2.33568i
$15$	−1.71917e36	−	7.71594e36i	−0.0398472	−	0.178842i
$16$	3.09321e36			0.00909013
$17$			1.60359e39i			0.677217i	0.940927	+	0.338609i	$0.109956\pi$
$17$			1.60359e39i			0.677217i	−0.940927	+	0.338609i	$0.890044\pi$
$18$	−1.01382e40	−	2.16217e40i	−0.687452	−	1.46612i
$19$	−4.25866e40			−0.511867			−0.255934	−	0.966694i	$-0.582383\pi$
$19$	−4.25866e40			−0.511867			−0.255934	+	0.966694i	$0.582383\pi$
$20$			1.27651e41i			0.297211i
$21$	−2.88129e42	+	6.41973e41i	−1.40789	+	0.313689i
$22$	−1.35982e43			−1.49953
$23$		−	6.67799e43i		−	1.77564i	−0.460190	−	0.887821i	$-0.652219\pi$
$23$		−	6.67799e43i		−	1.77564i	0.460190	−	0.887821i	$-0.347781\pi$
$24$	3.21623e43	+	1.44350e44i	0.219072	+	0.983236i
$25$	5.23902e44			0.966428
$26$			2.84761e45i			1.49738i
$27$	5.03551e45	−	3.88940e45i	0.791413	−	0.611282i
$28$	4.76675e46			2.33973
$29$			3.89949e46i			0.622689i	0.950297	+	0.311345i	$0.100779\pi$
$29$			3.89949e46i			0.622689i	−0.950297	+	0.311345i	$0.899221\pi$
$30$	−5.36627e46	+	1.19565e46i	−0.289596	+	0.0645241i
$31$	−3.52667e47			−0.666486			−0.333243	−	0.942841i	$-0.608143\pi$
$31$	−3.52667e47			−0.666486			−0.333243	+	0.942841i	$0.608143\pi$
$32$			1.45072e48i			0.992626i
$33$	−7.87927e47	−	3.53636e48i	−0.201391	−	0.903878i
$34$	1.11526e49			1.09661
$35$			6.79605e48i			0.264289i
$36$	−9.30252e49	+	4.36188e49i	−1.46866	+	0.688642i
$37$	−1.20138e49			−0.0789268			−0.0394634	−	0.999221i	$-0.512565\pi$
$37$	−1.20138e49			−0.0789268			−0.0394634	+	0.999221i	$0.512565\pi$
$38$			2.96181e50i			0.828860i
$39$	−7.40553e50	+	1.65001e50i	−0.902586	+	0.201103i
$40$	3.40477e50			0.184573
$41$			7.11845e51i			1.75106i	0.483160	+	0.875532i	$0.339489\pi$
$41$			7.11845e51i			1.75106i	−0.483160	+	0.875532i	$0.660511\pi$
$42$	4.46478e51	+	2.00387e52i	0.507953	+	2.27978i
$43$	1.24729e52			0.668309			0.334154	−	0.942518i	$-0.391549\pi$
$43$	1.24729e52			0.668309			0.334154	+	0.942518i	$0.391549\pi$
$44$			5.85048e52i			1.50213i
$45$	−6.21882e51	−	1.32628e52i	−0.0777871	−	0.165895i
$46$	−4.64440e53			−2.87527
$47$			5.35217e53i			1.66494i	0.554070	+	0.832470i	$0.313074\pi$
$47$			5.35217e53i			1.66494i	−0.554070	+	0.832470i	$0.686926\pi$
$48$	5.59460e51	−	1.24652e51i	0.00887256	−	0.00197687i
$49$	1.31802e54			1.08056
$50$		−	3.64362e54i		−	1.56492i
$51$	6.46224e53	+	2.90037e54i	0.147278	+	0.661009i
$52$	1.22516e55			1.49998
$53$		−	1.42076e55i		−	0.945570i	−0.881178	−	0.472785i	$-0.843249\pi$
$53$		−	1.42076e55i		−	0.945570i	0.881178	−	0.472785i	$-0.156751\pi$
$54$	−2.70499e55	−	3.50209e55i	−0.989842	−	1.28152i
$55$	−8.34115e54			−0.169676
$56$		−	1.27141e56i		−	1.45301i
$57$	−7.70251e55	+	1.71618e55i	−0.499616	+	0.111318i
$58$	2.71201e56			1.00831
$59$			6.80375e56i			1.46381i	0.681409	+	0.731903i	$0.261368\pi$
$59$			6.80375e56i			1.46381i	−0.681409	+	0.731903i	$0.738632\pi$
$60$	5.14415e55	+	2.30879e56i	0.0646359	+	0.290097i
$61$	−3.82753e56			−0.283376			−0.141688	−	0.989911i	$-0.545253\pi$
$61$	−3.82753e56			−0.283376			−0.141688	+	0.989911i	$0.545253\pi$
$62$			2.45273e57i			1.07923i
$63$	−4.95259e57	+	2.32223e57i	−1.30598	+	0.612362i
$64$	1.01465e58			1.61644
$65$			1.74673e57i			0.169433i
$66$	−2.45946e58	+	5.47986e57i	−1.46364	+	0.326110i
$67$	4.35199e58			1.60064			0.800321	−	0.599571i	$-0.204662\pi$
$67$	4.35199e58			1.60064			0.800321	+	0.599571i	$0.204662\pi$
$68$		−	4.79832e58i		−	1.09851i
$69$	−2.69113e58	−	1.20783e59i	−0.386157	−	1.73314i
$70$	4.72651e58			0.427960
$71$		−	6.48041e58i		−	0.372679i	−0.982485	−	0.186340i	$-0.940337\pi$
$71$		−	6.48041e58i		−	0.372679i	0.982485	−	0.186340i	$-0.0596625\pi$
$72$	1.16342e59	+	2.48121e59i	0.427658	+	0.912060i
$73$	1.90649e59			0.450717			0.225359	−	0.974276i	$-0.427645\pi$
$73$	1.90649e59			0.450717			0.225359	+	0.974276i	$0.427645\pi$
$74$			8.35533e58i			0.127805i
$75$	9.47565e59	−	2.11125e59i	0.943297	−	0.210174i
$76$	1.27429e60			0.830296
$77$			3.11476e60i			1.33574i
$78$	1.14754e60	+	5.15039e60i	0.325643	+	1.46155i
$79$	−9.64097e60			−1.81993			−0.909964	−	0.414688i	$-0.863891\pi$
$79$	−9.64097e60			−1.81993			−0.909964	+	0.414688i	$0.863891\pi$
$80$		−	1.31959e58i		−	0.00166556i
$81$	7.54020e60	−	9.06387e60i	0.639532	−	0.768764i
$82$	4.95073e61			2.83548
$83$			1.66247e61i			0.646033i	0.946393	+	0.323016i	$0.104697\pi$
$83$			1.66247e61i			0.646033i	−0.946393	+	0.323016i	$0.895303\pi$
$84$	8.62148e61	−	1.92093e61i	2.28373	−	0.508832i
$85$	6.84105e60			0.124084
$86$		−	8.67464e61i		−	1.08218i
$87$	1.57144e61	+	7.05288e61i	0.135419	+	0.607786i
$88$	1.56047e62			0.932844
$89$		−	1.95845e62i		−	0.815518i	−0.913090	−	0.407759i	$-0.866310\pi$
$89$		−	1.95845e62i		−	0.815518i	0.913090	−	0.407759i	$-0.133690\pi$
$90$	−9.22398e61	+	4.32506e61i	−0.268632	+	0.125960i
$91$	6.52265e62			1.33383
$92$			1.99821e63i			2.88025i
$93$	−6.37859e62	+	1.42120e62i	−0.650534	+	0.144944i
$94$	3.72232e63			2.69602
$95$			1.81678e62i			0.0937879i
$96$	5.84621e62	+	2.62388e63i	0.215871	+	0.968868i
$97$	−2.35055e63			−0.622980			−0.311490	−	0.950249i	$-0.600828\pi$
$97$	−2.35055e63			−0.622980			−0.311490	+	0.950249i	$0.600828\pi$
$98$		−	9.16658e63i		−	1.74974i
$99$	−2.85020e63	−	6.07858e63i	−0.393141	−	0.838447i
$100$	−1.56763e64			−1.56763
$101$		−	2.35492e63i		−	0.171274i	−0.996326	−	0.0856372i	$-0.972707\pi$
$101$		−	2.35492e63i		−	0.171274i	0.996326	−	0.0856372i	$-0.0272926\pi$
$102$	2.01714e64	−	4.49435e63i	1.07036	−	0.238485i
$103$	−3.65887e63			−0.142087			−0.0710437	−	0.997473i	$-0.522633\pi$
$103$	−3.65887e63			−0.142087			−0.0710437	+	0.997473i	$0.522633\pi$
$104$		−	3.26779e64i		−	0.931511i
$105$	2.73871e63	+	1.22918e64i	0.0574762	+	0.257964i
$106$	−9.88110e64			−1.53115
$107$			7.03619e64i			0.807340i	0.914905	+	0.403670i	$0.132266\pi$
$107$			7.03619e64i			0.807340i	−0.914905	+	0.403670i	$0.867734\pi$
$108$	−1.50674e65	+	1.16380e65i	−1.28374	+	0.991556i
$109$	−1.81505e65			−1.15144			−0.575718	−	0.817649i	$-0.695277\pi$
$109$	−1.81505e65			−1.15144			−0.575718	+	0.817649i	$0.695277\pi$
$110$			5.80109e64i			0.274754i
$111$	−2.17290e64	+	4.84138e63i	−0.0770378	+	0.0171646i
$112$	−4.92762e63			−0.0131117
$113$		−	9.26370e65i		−	1.85470i	−0.374192	−	0.927351i	$-0.622080\pi$
$113$		−	9.26370e65i		−	1.85470i	0.374192	−	0.927351i	$-0.377920\pi$
$114$	1.19356e65	+	5.35693e65i	0.180256	+	0.809022i
$115$	−2.84889e65			−0.325345
$116$		−	1.16682e66i		−	1.01006i
$117$	−1.27292e66	+	5.96864e65i	−0.837248	+	0.392579i
$118$	4.73186e66			2.37032
$119$		−	2.55459e66i		−	0.976828i
$120$	6.15810e65	−	1.37207e65i	0.180155	−	0.0401399i
$121$	6.35014e65			0.142446
$122$			2.66196e66i			0.458868i
$123$	2.86863e66	+	1.28749e67i	0.380813	+	1.70915i
$124$	1.05526e67			1.08110
$125$		−	4.54766e66i		−	0.360302i
$126$	1.61506e67	+	3.44442e67i	0.991590	+	2.11475i
$127$	−3.35689e67			−1.60036			−0.800180	−	0.599761i	$-0.795262\pi$
$127$	−3.35689e67			−1.60036			−0.800180	+	0.599761i	$0.795262\pi$
$128$		−	4.38059e67i		−	1.62485i
$129$	2.25594e67	−	5.02640e66i	0.652313	−	0.145340i
$130$	1.21481e67			0.274361
$131$		−	1.53804e67i		−	0.271822i	−0.990721	−	0.135911i	$-0.956604\pi$
$131$		−	1.53804e67i		−	0.271822i	0.990721	−	0.135911i	$-0.0433961\pi$
$132$	2.35766e67	+	1.05816e68i	0.326674	+	1.46617i
$133$	6.78422e67			0.738325
$134$		−	3.02672e68i		−	2.59190i
$135$	−1.65925e67	−	2.14819e67i	−0.112003	−	0.145008i
$136$	−1.27983e68			−0.682192
$137$		−	1.10350e68i		−	0.465279i	−0.972563	−	0.232640i	$-0.925264\pi$
$137$		−	1.10350e68i		−	0.465279i	0.972563	−	0.232640i	$-0.0747362\pi$
$138$	−8.40019e68	+	1.87163e68i	−2.80646	+	0.625300i
$139$	−1.55182e68			−0.411498			−0.205749	−	0.978605i	$-0.565963\pi$
$139$	−1.55182e68			−0.411498			−0.205749	+	0.978605i	$0.565963\pi$
$140$		−	2.03354e68i		−	0.428701i
$141$	2.15685e68	+	9.68031e68i	0.362083	+	1.62509i
$142$	−4.50699e68			−0.603475
$143$			8.00559e68i			0.856328i
$144$	9.61645e66	−	4.50908e66i	0.00823029	−	0.00385912i
$145$	1.66355e68			0.114093
$146$		−	1.32593e69i		−	0.729841i
$147$	2.38387e69	−	5.31144e68i	1.05470	−	0.234995i
$148$	3.59480e68			0.128027
$149$			7.59968e68i			0.218190i	0.994031	+	0.109095i	$0.0347952\pi$
$149$			7.59968e68i			0.218190i	−0.994031	+	0.109095i	$0.965205\pi$
$150$	−1.46833e69	−	6.59011e69i	−0.340332	−	1.52747i
$151$	−6.43520e69			−1.20587			−0.602934	−	0.797791i	$-0.706002\pi$
$151$	−6.43520e69			−1.20587			−0.602934	+	0.797791i	$0.706002\pi$
$152$		−	3.39884e69i		−	0.515627i
$153$	2.33761e69	+	4.98539e69i	0.287506	+	0.613159i
$154$	2.16625e70			2.16294
$155$			1.50451e69i			0.122118i
$156$	2.21590e70	−	4.93720e69i	1.46408	−	0.326207i
$157$	7.96152e69			0.428753			0.214376	−	0.976751i	$-0.431228\pi$
$157$	7.96152e69			0.428753			0.214376	+	0.976751i	$0.431228\pi$
$158$			6.70509e70i			2.94699i
$159$	−5.72546e69	−	2.56969e70i	−0.205638	−	0.922938i
$160$	6.18891e69			0.181876
$161$			1.06383e71i			2.56121i
$162$	−6.30373e70	−	5.24405e70i	−1.24485	−	1.03559i
$163$	−6.64959e70			−1.07843			−0.539214	−	0.842169i	$-0.681279\pi$
$163$	−6.64959e70			−1.07843			−0.539214	+	0.842169i	$0.681279\pi$
$164$		−	2.13001e71i		−	2.84039i
$165$	−1.50864e70	+	3.36136e69i	−0.165615	+	0.0369002i
$166$	1.15621e71			1.04611
$167$			1.63718e71i			1.22228i	0.791523	+	0.611140i	$0.209289\pi$
$167$			1.63718e71i			1.22228i	−0.791523	+	0.611140i	$0.790711\pi$
$168$	−5.12359e70	−	2.29956e71i	−0.315993	−	1.41823i
$169$	−2.84075e70			−0.144896
$170$		−	4.75781e70i		−	0.200928i
$171$	−1.32397e71	+	6.20799e70i	−0.463450	+	0.217308i
$172$	−3.73218e71			−1.08406
$173$		−	1.85013e71i		−	0.446402i	−0.974772	−	0.223201i	$-0.928349\pi$
$173$		−	1.85013e71i		−	0.446402i	0.974772	−	0.223201i	$-0.0716507\pi$
$174$	4.90513e71	−	1.09290e71i	0.984180	−	0.219283i
$175$	−8.34598e71			−1.39399
$176$		−	6.04792e69i		−	0.00841784i
$177$	2.74181e71	+	1.23057e72i	0.318341	+	1.42877i
$178$	−1.36206e72			−1.32056
$179$			1.89544e72i			1.53607i	0.640405	+	0.768037i	$0.278766\pi$
$179$			1.89544e72i			1.53607i	−0.640405	+	0.768037i	$0.721234\pi$
$180$	1.86081e71	+	3.96853e71i	0.126178	+	0.269098i
$181$	3.10607e72			1.76399			0.881997	−	0.471256i	$-0.156199\pi$
$181$	3.10607e72			1.76399			0.881997	+	0.471256i	$0.156199\pi$
$182$		−	4.53636e72i		−	2.15985i
$183$	−6.92273e71	+	1.54244e71i	−0.276594	+	0.0616272i
$184$	5.32972e72			1.78868
$185$			5.12518e70i			0.0144615i
$186$	9.88413e71	+	4.43617e72i	0.234706	+	1.05340i
$187$	3.13538e72			0.627132
$188$		−	1.60149e73i		−	2.70069i
$189$	−8.02178e72	+	6.19598e72i	−1.14155	+	0.881723i
$190$	1.26353e72			0.151870
$191$			7.00777e72i			0.712052i	0.934476	+	0.356026i	$0.115869\pi$
$191$			7.00777e72i			0.712052i	−0.934476	+	0.356026i	$0.884131\pi$
$192$	1.83517e73	−	4.08891e72i	1.57775	−	0.351534i
$193$	2.51854e72			0.183364			0.0916821	−	0.995788i	$-0.470776\pi$
$193$	2.51854e72			0.183364			0.0916821	+	0.995788i	$0.470776\pi$
$194$			1.63476e73i			1.00878i
$195$	7.03907e71	+	3.15926e72i	0.0368475	+	0.165378i
$196$	−3.94383e73			−1.75277
$197$		−	1.19886e73i		−	0.452741i	−0.974041	−	0.226370i	$-0.927314\pi$
$197$		−	1.19886e73i		−	0.452741i	0.974041	−	0.226370i	$-0.0726859\pi$
$198$	−4.22752e73	+	1.98225e73i	−1.35769	+	0.636609i
$199$	−4.42627e73			−1.20987			−0.604936	−	0.796274i	$-0.706801\pi$
$199$	−4.42627e73			−1.20987			−0.604936	+	0.796274i	$0.706801\pi$
$200$			4.18127e73i			0.973527i
$201$	7.87132e73	−	1.75379e73i	1.56233	−	0.348100i
$202$	−1.63780e73			−0.277342
$203$		−	6.21205e73i		−	0.898176i
$204$	−1.93365e73	−	8.67857e73i	−0.238898	−	1.07222i
$205$	3.03679e73			0.320842
$206$			2.54467e73i			0.230080i
$207$	−9.73474e73	−	2.07611e74i	−0.753830	−	1.60768i
$208$	−1.26650e72			−0.00840580
$209$			8.32663e73i			0.474011i
$210$	8.54870e73	−	1.90471e73i	0.417717	−	0.0930706i
$211$	−2.39039e74			−1.00330			−0.501650	−	0.865071i	$-0.667273\pi$
$211$	−2.39039e74			−1.00330			−0.501650	+	0.865071i	$0.667273\pi$
$212$			4.25125e74i			1.53380i
$213$	−2.61151e73	−	1.17209e74i	−0.0810484	−	0.363760i
$214$	4.89352e74			1.30732
$215$		−	5.32105e73i		−	0.122452i
$216$	3.10413e74	+	4.01885e74i	0.615773	+	0.797226i
$217$	5.61814e74			0.961349
$218$			1.26233e75i			1.86450i
$219$	3.44822e74	−	7.68289e73i	0.439930	−	0.0980196i
$220$	2.49587e74			0.275230
$221$		−	6.56584e74i		−	0.626235i
$222$	3.36708e73	+	1.51120e74i	0.0277944	+	0.124746i
$223$	−4.24805e73			−0.0303693			−0.0151846	−	0.999885i	$-0.504834\pi$
$223$	−4.24805e73			−0.0303693			−0.0151846	+	0.999885i	$0.504834\pi$
$224$		−	2.31107e75i		−	1.43178i
$225$	1.62875e75	−	7.63710e74i	0.875013	−	0.410287i
$226$	−6.44271e75			−3.00330
$227$		−	3.85160e75i		−	1.55888i	−0.626474	−	0.779442i	$-0.715503\pi$
$227$		−	3.85160e75i		−	1.55888i	0.626474	−	0.779442i	$-0.284497\pi$
$228$	2.30477e75	−	5.13520e74i	0.810424	−	0.180568i
$229$	−4.68035e74			−0.143068			−0.0715341	−	0.997438i	$-0.522789\pi$
$229$	−4.68035e74			−0.143068			−0.0715341	+	0.997438i	$0.522789\pi$
$230$			1.98134e75i			0.526827i
$231$	1.25520e75	+	5.63356e75i	0.290489	+	1.30377i
$232$	−3.11219e75			−0.627263
$233$			1.84384e75i			0.323842i	0.986804	+	0.161921i	$0.0517690\pi$
$233$			1.84384e75i			0.323842i	−0.986804	+	0.161921i	$0.948231\pi$
$234$	4.15106e75	+	8.85290e75i	0.635699	+	1.35575i
$235$	2.28328e75			0.305062
$236$		−	2.03584e76i		−	2.37443i
$237$	−1.74373e76	+	3.88517e75i	−1.77637	+	0.395788i
$238$	−1.77666e76			−1.58177
$239$			2.07276e76i			1.61367i	0.590774	+	0.806837i	$0.298823\pi$
$239$			2.07276e76i			1.61367i	−0.590774	+	0.806837i	$0.701177\pi$
$240$	−5.31775e72	−	2.38670e73i	−0.000362217	−	0.00162569i
$241$	−4.95072e75			−0.295205			−0.147602	−	0.989047i	$-0.547156\pi$
$241$	−4.95072e75			−0.295205			−0.147602	+	0.989047i	$0.547156\pi$
$242$		−	4.41639e75i		−	0.230662i
$243$	9.98513e75	−	1.94321e76i	0.457039	−	0.889447i
$244$	1.14528e76			0.459662
$245$		−	5.62280e75i		−	0.197988i
$246$	8.95424e76	−	1.99507e76i	2.76761	−	0.616645i
$247$	1.74369e76			0.473333
$248$		−	2.81464e76i		−	0.671382i
$249$	6.69951e75	+	3.00686e76i	0.140496	+	0.630571i
$250$	−3.16280e76			−0.583433
$251$			2.86400e76i			0.464958i	0.972601	+	0.232479i	$0.0746837\pi$
$251$			2.86400e76i			0.464958i	−0.972601	+	0.232479i	$0.925316\pi$
$252$	1.48193e77	−	6.94866e76i	2.11841	−	0.993308i
$253$	−1.30570e77			−1.64432
$254$			2.33464e77i			2.59144i
$255$	1.23732e76	−	2.75684e75i	0.121115	−	0.0269852i
$256$	−1.17490e77			−1.01466
$257$			4.17752e76i			0.318462i	0.987241	+	0.159231i	$0.0509015\pi$
$257$			4.17752e76i			0.318462i	−0.987241	+	0.159231i	$0.949098\pi$
$258$	−3.49575e76	−	1.56896e77i	−0.235348	−	1.05628i
$259$	1.91385e76			0.113845
$260$		−	5.22662e76i		−	0.274836i
$261$	5.68442e76	+	1.21231e77i	0.264356	+	0.563789i
$262$	−1.06967e77			−0.440158
$263$			2.60812e77i			0.950044i	0.879974	+	0.475022i	$0.157560\pi$
$263$			2.60812e77i			0.950044i	−0.879974	+	0.475022i	$0.842440\pi$
$264$	2.82237e77	−	6.28845e76i	0.910517	−	0.202870i
$265$	−6.06109e76			−0.173254
$266$		−	4.71828e77i		−	1.19556i
$267$	−7.89228e76	−	3.54220e77i	−0.177355	−	0.795999i
$268$	−1.30222e78			−2.59639
$269$		−	6.55025e77i		−	1.15927i	−0.814876	−	0.579635i	$-0.803195\pi$
$269$		−	6.55025e77i		−	1.15927i	0.814876	−	0.579635i	$-0.196805\pi$
$270$	−1.49402e77	+	1.15397e77i	−0.234810	+	0.181366i
$271$	1.42286e77			0.198675			0.0993377	−	0.995054i	$-0.468328\pi$
$271$	1.42286e77			0.198675			0.0993377	+	0.995054i	$0.468328\pi$
$272$			4.96024e75i			0.00615599i
$273$	1.17973e78	−	2.62853e77i	1.30190	−	0.290074i
$274$	−7.67460e77			−0.753421
$275$		−	1.02435e78i		−	0.894953i
$276$	8.05249e77	+	3.61410e78i	0.626383	+	2.81132i
$277$	3.53902e77			0.245206			0.122603	−	0.992456i	$-0.460876\pi$
$277$	3.53902e77			0.245206			0.122603	+	0.992456i	$0.460876\pi$
$278$			1.07926e78i			0.666333i
$279$	−1.09640e78	+	5.14096e77i	−0.603443	+	0.282950i
$280$	−5.42394e77			−0.266231
$281$			8.60394e77i			0.376786i	0.982094	+	0.188393i	$0.0603279\pi$
$281$			8.60394e77i			0.376786i	−0.982094	+	0.188393i	$0.939672\pi$
$282$	6.73245e78	−	1.50004e78i	2.63149	−	0.586316i
$283$	−3.66218e78			−1.27813			−0.639064	−	0.769154i	$-0.720678\pi$
$283$	−3.66218e78			−1.27813			−0.639064	+	0.769154i	$0.720678\pi$
$284$			1.93909e78i			0.604520i
$285$	7.32135e76	+	3.28595e77i	0.0203965	+	0.0915432i
$286$	5.56771e78			1.38664
$287$		−	1.13400e79i		−	2.52576i
$288$	2.11477e78	+	4.51014e78i	0.421409	+	0.898733i
$289$	3.03550e78			0.541377
$290$		−	1.15697e78i		−	0.184750i
$291$	−4.25137e78	+	9.47237e77i	−0.608069	+	0.135482i
$292$	−5.70467e78			−0.731105
$293$			5.76961e78i			0.662801i	0.943490	+	0.331400i	$0.107521\pi$
$293$			5.76961e78i			0.662801i	−0.943490	+	0.331400i	$0.892479\pi$
$294$	−3.69400e78	−	1.65793e79i	−0.380524	−	1.70786i
$295$	2.90253e78			0.268209
$296$		−	9.58822e77i		−	0.0795066i
$297$	−7.60464e78	−	9.84555e78i	−0.566073	−	0.732881i
$298$	5.28541e78			0.353312
$299$			2.73428e79i			1.64197i
$300$	−2.83533e79	+	6.31734e78i	−1.53011	+	0.340921i
$301$	−1.98699e79			−0.963978
$302$			4.47554e79i			1.95265i
$303$	−9.48998e77	−	4.25927e78i	−0.0372479	−	0.167175i
$304$	−1.31729e77			−0.00465294
$305$			1.63285e78i			0.0519222i
$306$	3.46723e79	−	1.62576e79i	0.992881	−	0.465554i
$307$	6.96433e78			0.179660			0.0898300	−	0.995957i	$-0.471368\pi$
$307$	6.96433e78			0.179660			0.0898300	+	0.995957i	$0.471368\pi$
$308$		−	9.32007e79i		−	2.16669i
$309$	−6.61769e78	+	1.47447e78i	−0.138687	+	0.0309005i
$310$	1.04635e79			0.197744
$311$			4.34085e79i			0.740018i	0.929028	+	0.370009i	$0.120645\pi$
$311$			4.34085e79i			0.740018i	−0.929028	+	0.370009i	$0.879355\pi$
$312$	−1.31687e79	−	5.91036e79i	−0.202580	−	0.909216i
$313$	−9.69112e79			−1.34572			−0.672861	−	0.739769i	$-0.734935\pi$
$313$	−9.69112e79			−1.34572			−0.672861	+	0.739769i	$0.734935\pi$
$314$		−	5.53707e79i		−	0.694274i
$315$	9.90684e78	+	2.11282e79i	0.112201	+	0.239290i
$316$	2.88480e80			2.95209
$317$			5.89871e79i			0.545583i	0.962073	+	0.272791i	$0.0879469\pi$
$317$			5.89871e79i			0.545583i	−0.962073	+	0.272791i	$0.912053\pi$
$318$	−1.78716e80	+	3.98194e79i	−1.49450	+	0.332986i
$319$	7.62437e79			0.576637
$320$		−	4.32860e79i		−	0.296175i
$321$	2.83548e79	+	1.27261e80i	0.175576	+	0.788018i
$322$	7.39873e80			4.14734
$323$		−	6.82914e79i		−	0.346646i
$324$	−2.25620e80	+	2.71212e80i	−1.03738	+	1.24701i
$325$	−2.14509e80			−0.893673
$326$			4.62465e80i			1.74629i
$327$	−3.28282e80	+	7.31437e79i	−1.12388	+	0.250408i
$328$	−5.68125e80			−1.76393
$329$		−	8.52624e80i		−	2.40153i
$330$	2.33775e79	+	1.04923e80i	0.0597521	+	0.268178i
$331$	−4.12509e80			−0.957058			−0.478529	−	0.878072i	$-0.658830\pi$
$331$	−4.12509e80			−0.957058			−0.478529	+	0.878072i	$0.658830\pi$
$332$		−	4.97449e80i		−	1.04792i
$333$	−3.73495e79	+	1.75129e79i	−0.0714611	+	0.0335076i
$334$	1.13863e81			1.97922
$335$		−	1.85660e80i		−	0.293281i
$336$	−8.91243e78	+	1.98576e78i	−0.0127979	+	0.00285147i
$337$	−5.19926e80			−0.678867			−0.339433	−	0.940630i	$-0.610235\pi$
$337$	−5.19926e80			−0.678867			−0.339433	+	0.940630i	$0.610235\pi$
$338$			1.97568e80i			0.234629i
$339$	−3.73313e80	−	1.67550e81i	−0.403351	−	1.81031i
$340$	−2.04700e80			−0.201276
$341$			6.89544e80i			0.617194i
$342$	4.31753e80	+	9.20793e80i	0.351884	+	0.750458i
$343$	−1.56539e80			−0.116201
$344$			9.95464e80i			0.673218i
$345$	−5.15270e80	+	1.14806e80i	−0.317558	+	0.0707544i
$346$	−1.28672e81			−0.722853
$347$		−	2.82503e80i		−	0.144704i	−0.997379	−	0.0723520i	$-0.976950\pi$
$347$		−	2.82503e80i		−	0.144704i	0.997379	−	0.0723520i	$-0.0230505\pi$
$348$	−4.70210e80	−	2.11039e81i	−0.219663	−	0.985885i
$349$	3.96335e80			0.168908			0.0844538	−	0.996427i	$-0.473085\pi$
$349$	3.96335e80			0.168908			0.0844538	+	0.996427i	$0.473085\pi$
$350$			5.80445e81i			2.25727i
$351$	−2.06177e81	+	1.59250e81i	−0.731833	+	0.565264i
$352$	2.83649e81			0.919213
$353$		−	2.51928e81i		−	0.745566i	−0.927919	−	0.372783i	$-0.878404\pi$
$353$		−	2.51928e81i		−	0.745566i	0.927919	−	0.372783i	$-0.121596\pi$
$354$	8.55837e81	−	1.90687e81i	2.31359	−	0.515486i
$355$	−2.76460e80			−0.0682849
$356$			5.86015e81i			1.32284i
$357$	−1.02946e81	−	4.62041e81i	−0.212436	−	0.953449i
$358$	1.31824e82			2.48735
$359$			2.32720e81i			0.401617i	0.979631	+	0.200808i	$0.0643568\pi$
$359$			2.32720e81i			0.401617i	−0.979631	+	0.200808i	$0.935643\pi$
$360$	1.05850e81	−	4.96325e80i	0.167114	−	0.0783585i
$361$	−5.10837e81			−0.737992
$362$		−	2.16021e82i		−	2.85641i
$363$	1.14853e81	−	2.55901e80i	0.139037	−	0.0309785i
$364$	−1.95173e82			−2.16359
$365$		−	8.13327e80i		−	0.0825835i
$366$	1.07273e81	+	4.81461e81i	0.0997922	+	0.447885i
$367$	−1.71983e82			−1.46613			−0.733064	−	0.680160i	$-0.761911\pi$
$367$	−1.71983e82			−1.46613			−0.733064	+	0.680160i	$0.761911\pi$
$368$		−	2.06564e80i		−	0.0161408i
$369$	1.03768e82	+	2.21305e82i	0.743396	+	1.58543i
$370$	3.56445e80			0.0234174
$371$			2.26333e82i			1.36390i
$372$	1.90862e82	−	4.25255e81i	1.05523	−	0.235112i
$373$	−2.28264e82			−1.15812			−0.579061	−	0.815285i	$-0.696581\pi$
$373$	−2.28264e82			−1.15812			−0.579061	+	0.815285i	$0.696581\pi$
$374$		−	2.18059e82i		−	1.01551i
$375$	−1.83264e81	−	8.22521e81i	−0.0783567	−	0.351679i
$376$	−4.27158e82			−1.67717
$377$		−	1.59663e82i		−	0.575812i
$378$	4.30917e82	+	5.57898e82i	1.42776	+	1.84849i
$379$	−1.63074e82			−0.496511			−0.248256	−	0.968695i	$-0.579857\pi$
$379$	−1.63074e82			−0.496511			−0.248256	+	0.968695i	$0.579857\pi$
$380$		−	5.43622e81i		−	0.152133i
$381$	−6.07150e82	+	1.35278e82i	−1.56206	+	0.348038i
$382$	4.87375e82			1.15302
$383$		−	3.32574e82i		−	0.723647i	−0.932247	−	0.361824i	$-0.882154\pi$
$383$		−	3.32574e82i		−	0.723647i	0.932247	−	0.361824i	$-0.117846\pi$
$384$	−1.76531e82	−	7.92304e82i	−0.353364	−	1.58596i
$385$	1.32878e82			0.244743
$386$		−	1.75159e82i		−	0.296919i
$387$	3.87769e82	−	1.81822e82i	0.605093	−	0.283723i
$388$	7.03339e82			1.01053
$389$		−	2.21303e82i		−	0.292819i	−0.989224	−	0.146409i	$-0.953228\pi$
$389$		−	2.21303e82i		−	0.292819i	0.989224	−	0.146409i	$-0.0467717\pi$
$390$	2.19720e82	−	4.89552e81i	0.267795	−	0.0596666i
$391$	1.07088e83			1.20250
$392$			1.05192e83i			1.08850i
$393$	−6.19806e81	−	2.78180e82i	−0.0591145	−	0.265316i
$394$	−8.33782e82			−0.733117
$395$			4.11292e82i			0.333460i
$396$	8.52845e82	+	1.81885e83i	0.637712	+	1.36004i
$397$	−9.77323e82			−0.674128			−0.337064	−	0.941482i	$-0.609434\pi$
$397$	−9.77323e82			−0.674128			−0.337064	+	0.941482i	$0.609434\pi$
$398$			3.07837e83i			1.95913i
$399$	1.22704e83	−	2.73394e82i	0.720654	−	0.160567i
$400$	1.62054e81			0.00878495
$401$			7.90722e82i			0.395734i	0.980229	+	0.197867i	$0.0634015\pi$
$401$			7.90722e82i			0.395734i	−0.980229	+	0.197867i	$0.936599\pi$
$402$	−1.21972e83	−	5.47433e83i	−0.563673	−	2.52987i
$403$	1.44398e83			0.616312
$404$			7.04647e82i			0.277823i
$405$	−3.86672e82	−	3.21671e82i	−0.140858	−	0.117180i
$406$	−4.32035e83			−1.45441
$407$			2.34896e82i			0.0730895i
$408$	−2.31479e83	+	5.15752e82i	−0.665864	+	0.148360i
$409$	4.29348e83			1.14199			0.570997	−	0.820952i	$-0.306557\pi$
$409$	4.29348e83			1.14199			0.570997	+	0.820952i	$0.306557\pi$
$410$		−	2.11202e83i		−	0.519536i
$411$	−4.44694e82	−	1.99586e83i	−0.101186	−	0.454143i
$412$	1.09482e83			0.230479
$413$		−	1.08387e84i		−	2.11142i
$414$	−1.44389e84	+	6.77031e83i	−2.60330	+	1.22067i
$415$	7.09223e82			0.118371
$416$		−	5.93993e83i		−	0.917899i
$417$	−2.80673e83	+	6.25360e82i	−0.401649	+	0.0894904i
$418$	5.79099e83			0.767560
$419$			3.73885e83i			0.459081i	0.973299	+	0.229541i	$0.0737224\pi$
$419$			3.73885e83i			0.459081i	−0.973299	+	0.229541i	$0.926278\pi$
$420$	−8.19485e82	−	3.67800e83i	−0.0932318	−	0.418441i
$421$	3.17104e83			0.334329			0.167165	−	0.985929i	$-0.446539\pi$
$421$	3.17104e83			0.334329			0.167165	+	0.985929i	$0.446539\pi$
$422$			1.66247e84i			1.62463i
$423$	7.80205e83	+	1.66393e84i	0.706833	+	1.50745i
$424$	1.13391e84			0.952515
$425$			8.40124e83i			0.654482i
$426$	−8.15165e83	+	1.81625e83i	−0.589032	+	0.131241i
$427$	6.09741e83			0.408746
$428$		−	2.10539e84i		−	1.30958i
$429$	3.22613e83	+	1.44795e84i	0.186230	+	0.835832i
$430$	−3.70067e83			−0.198285
$431$		−	1.26083e84i		−	0.627166i	−0.949561	−	0.313583i	$-0.898471\pi$
$431$		−	1.26083e84i		−	0.627166i	0.949561	−	0.313583i	$-0.101529\pi$
$432$	1.55759e82	−	1.20307e82i	0.00719404	−	0.00555663i
$433$	−1.75564e84			−0.753049			−0.376525	−	0.926407i	$-0.622881\pi$
$433$	−1.75564e84			−0.753049			−0.376525	+	0.926407i	$0.622881\pi$
$434$		−	3.90730e84i		−	1.55670i
$435$	3.00882e83	−	6.70388e82i	0.111363	−	0.0248125i
$436$	5.43104e84			1.86773
$437$			2.84393e84i			0.908893i
$438$	−5.34329e83	−	2.39816e84i	−0.158722	−	0.712373i
$439$	2.72120e84			0.751443			0.375721	−	0.926733i	$-0.377395\pi$
$439$	2.72120e84			0.751443			0.375721	+	0.926733i	$0.377395\pi$
$440$		−	6.65708e83i		−	0.170922i
$441$	4.09759e84	−	1.92133e84i	0.978349	−	0.458740i
$442$	−4.56640e84			−1.01405
$443$			5.76876e84i			1.19169i	0.803100	+	0.595844i	$0.203183\pi$
$443$			5.76876e84i			1.19169i	−0.803100	+	0.595844i	$0.796817\pi$
$444$	6.50181e83	−	1.44865e83i	0.124962	−	0.0278426i
$445$	−8.35493e83			−0.149425
$446$			2.95443e83i			0.0491766i
$447$	3.06256e83	+	1.37453e84i	0.0474508	+	0.212968i
$448$	−1.61639e85			−2.33157
$449$		−	5.65724e84i		−	0.759840i	−0.925019	−	0.379920i	$-0.875952\pi$
$449$		−	5.65724e84i		−	0.759840i	0.925019	−	0.379920i	$-0.124048\pi$
$450$	−5.31144e84	−	1.13276e85i	−0.664372	−	1.41690i
$451$	1.39182e85			1.62156
$452$			2.77191e85i			3.00850i
$453$	−1.16391e85	+	2.59329e84i	−1.17701	+	0.262246i
$454$	−2.67871e85			−2.52428
$455$		−	2.78262e84i		−	0.244393i
$456$	−1.36968e84	−	6.14738e84i	−0.112136	−	0.503286i
$457$	−7.76570e83			−0.0592737			−0.0296369	−	0.999561i	$-0.509435\pi$
$457$	−7.76570e83			−0.0592737			−0.0296369	+	0.999561i	$0.509435\pi$
$458$			3.25509e84i			0.231669i
$459$	6.23700e84	+	8.07490e84i	0.413971	+	0.535958i
$460$	8.52453e84			0.527740
$461$		−	2.82696e85i		−	1.63264i	−0.577602	−	0.816318i	$-0.696012\pi$
$461$		−	2.82696e85i		−	1.63264i	0.577602	−	0.816318i	$-0.303988\pi$
$462$	3.91802e85	−	8.72965e84i	2.11117	−	0.470385i
$463$	2.04160e85			1.02655			0.513273	−	0.858226i	$-0.328433\pi$
$463$	2.04160e85			1.02655			0.513273	+	0.858226i	$0.328433\pi$
$464$			1.20619e83i			0.00566033i
$465$	6.06295e83	+	2.72116e84i	0.0265576	+	0.119195i
$466$	1.28235e85			0.524393
$467$			1.71624e84i			0.0655295i	0.999463	+	0.0327648i	$0.0104312\pi$
$467$			1.71624e84i			0.0655295i	−0.999463	+	0.0327648i	$0.989569\pi$
$468$	3.80888e85	−	1.78595e85i	1.35809	−	0.636800i
$469$	−6.93291e85			−2.30879
$470$		−	1.58797e85i		−	0.493983i
$471$	1.43998e85	−	3.20837e84i	0.418491	−	0.0932429i
$472$	−5.43008e85			−1.47456
$473$		−	2.43873e85i		−	0.618882i
$474$	2.70205e85	+	1.21273e86i	0.640895	+	2.87645i
$475$	−2.23112e85			−0.494683
$476$			7.64392e85i			1.58451i
$477$	−2.07109e85	−	4.41699e85i	−0.401432	−	0.856128i
$478$	1.44156e86			2.61300
$479$		−	1.01724e86i		−	1.72459i	−0.506404	−	0.862297i	$-0.669025\pi$
$479$		−	1.01724e86i		−	1.72459i	0.506404	−	0.862297i	$-0.330975\pi$
$480$	1.11937e85	−	2.49404e84i	0.177523	−	0.0395534i
$481$	4.91900e84			0.0729851
$482$			3.44312e85i			0.478021i
$483$	4.28709e85	+	1.92412e86i	0.556999	+	2.49991i
$484$	−1.90011e85			−0.231061
$485$			1.00276e85i			0.114147i
$486$	−1.35146e86	−	6.94445e85i	−1.44027	−	0.740077i
$487$	2.63004e85			0.262443			0.131222	−	0.991353i	$-0.458110\pi$
$487$	2.63004e85			0.262443			0.131222	+	0.991353i	$0.458110\pi$
$488$		−	3.05475e85i		−	0.285458i
$489$	−1.20269e86	+	2.67969e85i	−1.05262	+	0.234531i
$490$	−3.91054e85			−0.320599
$491$		−	1.06937e86i		−	0.821334i	−0.911785	−	0.410667i	$-0.865296\pi$
$491$		−	1.06937e86i		−	0.821334i	0.911785	−	0.410667i	$-0.134704\pi$
$492$	−8.58361e85	−	3.85248e86i	−0.617713	−	2.77241i
$493$	−6.25318e85			−0.421696
$494$		−	1.21270e86i		−	0.766462i
$495$	−2.59317e85	+	1.21592e85i	−0.153626	+	0.0720341i
$496$	−1.09087e84			−0.00605844
$497$			1.03236e86i			0.537558i
$498$	2.09121e86	−	4.65936e85i	1.02108	−	0.227503i
$499$	−2.98169e86			−1.36535			−0.682676	−	0.730721i	$-0.739184\pi$
$499$	−2.98169e86			−1.36535			−0.682676	+	0.730721i	$0.739184\pi$
$500$			1.36076e86i			0.584444i
$501$	6.59761e85	+	2.96113e86i	0.265815	+	1.19303i
$502$	1.99185e86			0.752900
$503$			1.54929e86i			0.549485i	0.961518	+	0.274743i	$0.0885926\pi$
$503$			1.54929e86i			0.549485i	−0.961518	+	0.274743i	$0.911407\pi$
$504$	−1.85338e86	−	3.95267e86i	−0.616860	−	1.31557i
$505$	−1.00463e85			−0.0313821
$506$			9.08085e86i			2.66262i
$507$	−5.13797e85	+	1.14478e85i	−0.141429	+	0.0315113i
$508$	1.00446e87			2.59593
$509$		−	2.04370e86i		−	0.495962i	−0.968765	−	0.247981i	$-0.920233\pi$
$509$		−	2.04370e86i		−	0.495962i	0.968765	−	0.247981i	$-0.0797670\pi$
$510$	−1.91733e85	−	8.60530e85i	−0.0436969	−	0.196119i
$511$	−3.03713e86			−0.650121
$512$			9.04133e84i			0.0181800i
$513$	−2.14445e86	+	1.65636e86i	−0.405098	+	0.312896i
$514$	2.90537e86			0.515682
$515$			1.56090e85i			0.0260343i
$516$	−6.75028e86	+	1.50401e86i	−1.05811	+	0.235755i
$517$	1.04647e87			1.54180
$518$		−	1.33104e86i		−	0.184348i
$519$	−7.45574e85	−	3.34627e86i	−0.0970812	−	0.435718i
$520$	−1.39407e86			−0.170678
$521$		−	1.62638e87i		−	1.87247i	−0.351371	−	0.936236i	$-0.614284\pi$
$521$		−	1.62638e87i		−	1.87247i	0.351371	−	0.936236i	$-0.385716\pi$
$522$	8.43134e86	−	3.95339e86i	0.912936	−	0.428069i
$523$	9.63062e86			0.980845			0.490422	−	0.871485i	$-0.336842\pi$
$523$	9.63062e86			0.980845			0.490422	+	0.871485i	$0.336842\pi$
$524$			4.60216e86i			0.440921i
$525$	−1.50951e87	+	3.36331e86i	−1.36063	+	0.303158i
$526$	1.81389e87			1.53839
$527$		−	5.65534e86i		−	0.451356i
$528$	−2.43722e84	−	1.09387e85i	−0.00183067	−	0.00821637i
$529$	−3.04513e87			−2.15290
$530$			4.21536e86i			0.280548i
$531$	9.91806e86	+	2.11521e87i	0.621444	+	1.32534i
$532$	−2.03000e87			−1.19763
$533$		−	2.91462e87i		−	1.61924i
$534$	−2.46352e87	+	5.48892e86i	−1.28895	+	0.287188i
$535$	3.00170e86			0.147926
$536$			3.47333e87i			1.61240i
$537$	7.63833e86	+	3.42822e87i	0.334058	+	1.49931i
$538$	−4.55556e87			−1.87719
$539$		−	2.57703e87i		−	1.00064i
$540$	4.96486e86	+	6.42788e86i	0.181680	+	0.235216i
$541$	4.25393e87			1.46716			0.733581	−	0.679602i	$-0.237848\pi$
$541$	4.25393e87			1.46716			0.733581	+	0.679602i	$0.237848\pi$
$542$		−	9.89567e86i		−	0.321712i
$543$	5.61786e87	−	1.25170e87i	1.72177	−	0.383624i
$544$	−2.32637e87			−0.672224
$545$			7.74314e86i			0.210974i
$546$	−1.82809e87	−	8.20478e87i	−0.469713	−	2.10816i
$547$	−5.44089e87			−1.31849			−0.659243	−	0.751930i	$-0.729123\pi$
$547$	−5.44089e87			−1.31849			−0.659243	+	0.751930i	$0.729123\pi$
$548$			3.30192e87i			0.754725i
$549$	−1.18994e87	+	5.57952e86i	−0.256572	+	0.120304i
$550$	−7.12410e87			−1.44919
$551$		−	1.66066e87i		−	0.318734i
$552$	9.63970e87	−	2.14780e87i	1.74587	−	0.388994i
$553$	1.53585e88			2.62509
$554$		−	2.46131e87i		−	0.397058i
$555$	2.06537e85	+	9.26976e85i	0.00314502	+	0.0141154i
$556$	4.64340e87			0.667487
$557$			3.43898e87i			0.466727i	0.972390	+	0.233363i	$0.0749732\pi$
$557$			3.43898e87i			0.466727i	−0.972390	+	0.233363i	$0.925027\pi$
$558$	3.57542e87	+	7.62526e87i	0.458177	+	0.977147i
$559$	−5.10698e87			−0.617997
$560$			2.10216e85i			0.00240242i
$561$	5.67087e87	−	1.26351e87i	0.612122	−	0.136385i
$562$	5.98386e87			0.610125
$563$			1.07417e88i			1.03467i	0.855782	+	0.517336i	$0.173076\pi$
$563$			1.07417e88i			1.03467i	−0.855782	+	0.517336i	$0.826924\pi$
$564$	−6.45378e87	−	2.89657e88i	−0.587331	−	2.63605i
$565$	−3.95197e87			−0.339831
$566$			2.54697e88i			2.06966i
$567$	−1.20119e88	+	1.44391e88i	−0.922471	+	1.10888i
$568$	5.17203e87			0.375417
$569$			2.06276e88i			1.41532i	0.706551	+	0.707662i	$0.250250\pi$
$569$			2.06276e88i			1.41532i	−0.706551	+	0.707662i	$0.749750\pi$
$570$	2.28531e87	−	5.09184e86i	0.148235	−	0.0330278i
$571$	−6.60073e87			−0.404796			−0.202398	−	0.979303i	$-0.564874\pi$
$571$	−6.60073e87			−0.404796			−0.202398	+	0.979303i	$0.564874\pi$
$572$		−	2.39546e88i		−	1.38904i
$573$	2.82403e87	+	1.26747e88i	0.154853	+	0.695010i
$574$	−7.88673e88			−4.08993
$575$		−	3.49861e88i		−	1.71603i
$576$	3.15445e88	−	1.47910e88i	1.46354	−	0.686241i
$577$	3.68927e88			1.61925			0.809625	−	0.586947i	$-0.199670\pi$
$577$	3.68927e88			1.61925			0.809625	+	0.586947i	$0.199670\pi$
$578$		−	2.11113e88i		−	0.876644i
$579$	4.55520e87	−	1.01493e87i	0.178976	−	0.0398771i
$580$	−4.97774e87			−0.185070
$581$		−	2.64838e88i		−	0.931847i
$582$	6.58783e87	+	2.95674e88i	0.219385	+	0.984639i
$583$	−2.77791e88			−0.875637
$584$			1.52158e88i			0.454028i
$585$	2.54627e87	+	5.43039e87i	0.0719311	+	0.153406i
$586$	4.01264e88			1.07326
$587$		−	1.32150e88i		−	0.334693i	−0.985898	−	0.167346i	$-0.946480\pi$
$587$		−	1.32150e88i		−	0.334693i	0.985898	−	0.167346i	$-0.0535198\pi$
$588$	−7.13309e88	+	1.58931e88i	−1.71082	+	0.381183i
$589$	1.50189e88			0.341153
$590$		−	2.01865e88i		−	0.434307i
$591$	−4.83123e87	−	2.16834e88i	−0.0984597	−	0.441905i
$592$	−3.71612e85			−0.000717455
$593$		−	1.06877e88i		−	0.195494i	−0.995211	−	0.0977469i	$-0.968836\pi$
$593$		−	1.06877e88i		−	0.195494i	0.995211	−	0.0977469i	$-0.0311635\pi$
$594$	−6.84737e88	+	5.28887e88i	−1.18675	+	0.916635i
$595$	−1.08981e88			−0.178981
$596$		−	2.27400e88i		−	0.353924i
$597$	−8.00566e88	+	1.78372e88i	−1.18091	+	0.263117i
$598$	1.90163e89			2.65882
$599$			8.75600e88i			1.16051i	0.814436	+	0.580253i	$0.197046\pi$
$599$			8.75600e88i			1.16051i	−0.814436	+	0.580253i	$0.802954\pi$
$600$	1.68499e88	+	7.56253e88i	0.211718	+	0.950226i
$601$	9.04709e87			0.107777			0.0538885	−	0.998547i	$-0.482838\pi$
$601$	9.04709e87			0.107777			0.0538885	+	0.998547i	$0.482838\pi$
$602$			1.38191e89i			1.56096i
$603$	1.35299e89	−	6.34405e88i	1.44924	−	0.679536i
$604$	1.92556e89			1.95603
$605$		−	2.70902e87i		−	0.0261000i
$606$	−2.96223e88	+	6.60008e87i	−0.270704	+	0.0603150i
$607$	−2.55280e87			−0.0221299			−0.0110649	−	0.999939i	$-0.503522\pi$
$607$	−2.55280e87			−0.0221299			−0.0110649	+	0.999939i	$0.503522\pi$
$608$		−	6.17814e88i		−	0.508093i
$609$	−2.50336e88	−	1.12355e89i	−0.195331	−	0.876679i
$610$	1.13562e88			0.0840769
$611$		−	2.19143e89i		−	1.53960i
$612$	−6.99467e88	−	1.49174e89i	−0.466360	−	0.994600i
$613$	−4.28601e88			−0.271218			−0.135609	−	0.990762i	$-0.543299\pi$
$613$	−4.28601e88			−0.271218			−0.135609	+	0.990762i	$0.543299\pi$
$614$		−	4.84355e88i		−	0.290921i
$615$	5.49255e88	−	1.22378e88i	0.313163	−	0.0697751i
$616$	−2.48589e89			−1.34555
$617$			2.34422e89i			1.20468i	0.798238	+	0.602342i	$0.205766\pi$
$617$			2.34422e89i			1.20468i	−0.798238	+	0.602342i	$0.794234\pi$
$618$	1.02546e88	+	4.60246e88i	0.0500367	+	0.224574i
$619$	−3.80937e89			−1.76503			−0.882515	−	0.470284i	$-0.844152\pi$
$619$	−3.80937e89			−1.76503			−0.882515	+	0.470284i	$0.844152\pi$
$620$		−	4.50184e88i		−	0.198087i
$621$	−2.59734e89	−	3.36271e89i	−1.08542	−	1.40526i
$622$	3.01897e89			1.19830
$623$			3.11990e89i			1.17631i
$624$	−2.29068e87	+	5.10382e86i	−0.00820462	+	0.00182805i
$625$	2.64607e89			0.900411
$626$			6.73997e89i			2.17911i
$627$	3.35551e88	+	1.50601e89i	0.103085	+	0.462666i
$628$	−2.38227e89			−0.695476
$629$		−	1.92652e88i		−	0.0534506i
$630$	1.46942e89	−	6.89000e88i	0.387479	−	0.181686i
$631$	−2.45607e89			−0.615605			−0.307802	−	0.951450i	$-0.599594\pi$
$631$	−2.45607e89			−0.615605			−0.307802	+	0.951450i	$0.599594\pi$
$632$		−	7.69448e89i		−	1.83330i
$633$	−4.32343e89	+	9.63293e88i	−0.979286	+	0.218192i
$634$	4.10243e89			0.883455
$635$			1.43208e89i			0.293229i
$636$	1.71319e89	+	7.68910e89i	0.333563	+	1.49709i
$637$	−5.39660e89			−0.999213
$638$		−	5.30259e89i		−	0.933740i
$639$	−9.44672e88	−	2.01469e89i	−0.158217	−	0.337428i
$640$	−1.86880e89			−0.297716
$641$			8.12214e89i			1.23087i	0.788186	+	0.615437i	$0.211020\pi$
$641$			8.12214e89i			1.23087i	−0.788186	+	0.615437i	$0.788980\pi$
$642$	8.85076e89	−	1.97202e89i	1.27603	−	0.284308i
$643$	9.70369e88			0.133102			0.0665512	−	0.997783i	$-0.478800\pi$
$643$	9.70369e88			0.133102			0.0665512	+	0.997783i	$0.478800\pi$
$644$		−	3.18323e90i		−	4.15452i
$645$	−2.14430e88	−	9.62401e88i	−0.0266303	−	0.119521i
$646$	−4.74952e89			−0.561319
$647$			4.21513e89i			0.474105i	0.971497	+	0.237052i	$0.0761813\pi$
$647$			4.21513e89i			0.474105i	−0.971497	+	0.237052i	$0.923819\pi$
$648$	7.23389e89	+	6.01785e89i	0.774411	+	0.644230i
$649$	1.33028e90			1.35555
$650$			1.49187e90i			1.44711i
$651$	1.01614e90	−	2.26403e89i	0.938340	−	0.209069i
$652$	1.98971e90			1.74931
$653$		−	9.27096e89i		−	0.776073i	−0.921644	−	0.388037i	$-0.873153\pi$
$653$		−	9.27096e89i		−	0.776073i	0.921644	−	0.388037i	$-0.126847\pi$
$654$	5.08699e89	+	2.28313e90i	0.405483	+	1.81988i
$655$	−6.56139e88			−0.0498051
$656$			2.20189e88i			0.0159174i
$657$	5.92708e89	−	2.77916e89i	0.408084	−	0.191347i
$658$	−5.92982e90			−3.88877
$659$			1.40061e90i			0.874954i	0.899230	+	0.437477i	$0.144128\pi$
$659$			1.40061e90i			0.874954i	−0.899230	+	0.437477i	$0.855872\pi$
$660$	4.51420e89	−	1.00580e89i	0.268642	−	0.0598555i
$661$	−1.30054e90			−0.737356			−0.368678	−	0.929557i	$-0.620189\pi$
$661$	−1.30054e90			−0.737356			−0.368678	+	0.929557i	$0.620189\pi$
$662$			2.86891e90i			1.54975i
$663$	−2.64594e89	−	1.18754e90i	−0.136190	−	0.611247i
$664$	−1.32682e90			−0.650778
$665$		−	2.89421e89i		−	0.135281i
$666$	1.21799e89	+	2.59758e89i	0.0542584	+	0.115716i
$667$	2.60407e90			1.10567
$668$		−	4.89883e90i		−	1.98265i
$669$	−7.68332e88	+	1.71190e88i	−0.0296424	+	0.00660455i
$670$	−1.29122e90			−0.474906
$671$			7.48367e89i			0.262418i
$672$	−9.31326e89	−	4.17996e90i	−0.311376	−	1.39751i
$673$	−1.44699e90			−0.461300			−0.230650	−	0.973037i	$-0.574085\pi$
$673$	−1.44699e90			−0.461300			−0.230650	+	0.973037i	$0.574085\pi$
$674$			3.61597e90i			1.09928i
$675$	2.63811e90	−	2.03766e90i	0.764843	−	0.590760i
$676$	8.50017e89			0.235035
$677$		−	1.76222e90i		−	0.464753i	−0.972626	−	0.232376i	$-0.925350\pi$
$677$		−	1.76222e90i		−	0.464753i	0.972626	−	0.232376i	$-0.0746501\pi$
$678$	−1.16527e91	+	2.59632e90i	−2.93142	+	0.653142i
$679$	3.74452e90			0.898595
$680$			5.45985e89i			0.124996i
$681$	−1.55214e90	−	6.96627e90i	−0.339018	−	1.52157i
$682$	4.79563e90			0.999415
$683$			1.55068e90i			0.308362i	0.988043	+	0.154181i	$0.0492739\pi$
$683$			1.55068e90i			0.308362i	−0.988043	+	0.154181i	$0.950726\pi$
$684$	3.96162e90	−	1.85758e90i	0.751758	−	0.352494i
$685$	−4.70762e89			−0.0852516
$686$			1.08869e90i			0.188163i
$687$	−8.46521e89	+	1.88611e89i	−0.139644	+	0.0311137i
$688$	3.85813e88			0.00607501
$689$			5.81725e90i			0.874385i
$690$	7.98451e89	+	3.58359e90i	0.114572	+	0.514218i
$691$	7.49880e90			1.02729			0.513647	−	0.858002i	$-0.328294\pi$
$691$	7.49880e90			1.02729			0.513647	+	0.858002i	$0.328294\pi$
$692$			5.53601e90i			0.724105i
$693$	4.54049e90	+	9.68343e90i	0.567073	+	1.20939i
$694$	−1.96475e90			−0.234317
$695$			6.62019e89i			0.0753974i
$696$	−5.62892e90	+	1.25417e90i	−0.612251	+	0.136414i
$697$	−1.14151e91			−1.18585
$698$		−	2.75643e90i		−	0.273510i
$699$	7.43040e89	+	3.33489e90i	0.0704275	+	0.316091i
$700$	2.49731e91			2.26118
$701$		−	1.40957e91i		−	1.21930i	−0.792672	−	0.609648i	$-0.791311\pi$
$701$		−	1.40957e91i		−	1.21930i	0.792672	−	0.609648i	$-0.208689\pi$
$702$	1.10755e91	+	1.43392e91i	0.915325	+	1.18505i
$703$	5.11626e89			0.0404001
$704$		−	1.98388e91i		−	1.49689i
$705$	4.12970e90	−	9.20129e89i	0.297760	−	0.0663433i
$706$	−1.75211e91			−1.20729
$707$			3.75149e90i			0.247049i
$708$	−8.20413e90	−	3.68216e91i	−0.516379	−	2.31760i
$709$	2.26807e91			1.36451			0.682255	−	0.731114i	$-0.260999\pi$
$709$	2.26807e91			1.36451			0.682255	+	0.731114i	$0.260999\pi$
$710$			1.92272e90i			0.110573i
$711$	−2.99727e91	+	1.40540e91i	−1.64778	+	0.772631i
$712$	1.56305e91			0.821508
$713$			2.35511e91i			1.18344i
$714$	−3.21340e91	+	7.15969e90i	−1.54391	+	0.343994i
$715$	3.41525e90			0.156902
$716$		−	5.67159e91i		−	2.49165i
$717$	8.35291e90	+	3.74894e91i	0.350934	+	1.57505i
$718$	1.61852e91			0.650333
$719$		−	4.16861e91i		−	1.60201i	−0.598655	−	0.801007i	$-0.704298\pi$
$719$		−	4.16861e91i		−	1.60201i	0.598655	−	0.801007i	$-0.295702\pi$
$720$	−1.92361e88	−	4.10246e88i	−0.000707094	−	0.00150801i
$721$	5.82874e90			0.204949
$722$			3.55276e91i			1.19502i
$723$	−8.95423e90	+	1.99507e90i	−0.288139	+	0.0641996i
$724$	−9.29408e91			−2.86136
$725$			2.04295e91i			0.601784i
$726$	−1.77974e90	−	7.98779e90i	−0.0501631	−	0.225141i
$727$	−2.36138e91			−0.636890			−0.318445	−	0.947941i	$-0.603161\pi$
$727$	−2.36138e91			−0.636890			−0.318445	+	0.947941i	$0.603161\pi$
$728$			5.20574e91i			1.34362i
$729$	1.02289e91	−	3.91702e91i	0.252668	−	0.967553i
$730$	−5.65651e90			−0.133726
$731$			2.00014e91i			0.452590i
$732$	2.07144e91	−	4.61533e90i	0.448661	−	0.0999650i
$733$	−6.31771e91			−1.30988			−0.654941	−	0.755680i	$-0.727307\pi$
$733$	−6.31771e91			−1.30988			−0.654941	+	0.755680i	$0.727307\pi$
$734$			1.19611e92i			2.37408i
$735$	−2.26591e90	−	1.01698e91i	−0.0430573	−	0.193249i
$736$	9.68793e91			1.76255
$737$		−	8.50912e91i		−	1.48226i
$738$	1.53913e92	−	7.21685e91i	2.56727	−	1.20377i
$739$	−5.36414e91			−0.856797			−0.428399	−	0.903590i	$-0.640922\pi$
$739$	−5.36414e91			−0.856797			−0.428399	+	0.903590i	$0.640922\pi$
$740$		−	1.53357e90i		−	0.0234579i
$741$	3.15376e91	−	7.02682e90i	0.462004	−	0.102938i
$742$	1.57410e92			2.20855
$743$		−	1.13699e92i		−	1.52797i	−0.645236	−	0.763983i	$-0.723241\pi$
$743$		−	1.13699e92i		−	1.52797i	0.645236	−	0.763983i	$-0.276759\pi$
$744$	−1.13426e91	−	5.09076e91i	−0.146009	−	0.655313i
$745$	3.24209e90			0.0399782
$746$			1.58752e92i			1.87533i
$747$	2.42344e91	+	5.16843e91i	0.274267	+	0.584924i
$748$	−9.38178e91			−1.01727
$749$		−	1.12090e92i		−	1.16452i
$750$	−5.72046e91	+	1.27456e91i	−0.569469	+	0.126882i
$751$	−1.18620e92			−1.13156			−0.565781	−	0.824556i	$-0.691425\pi$
$751$	−1.18620e92			−1.13156			−0.565781	+	0.824556i	$0.691425\pi$
$752$			1.65554e90i			0.0151345i
$753$	1.15415e91	+	5.18003e91i	0.101117	+	0.453829i
$754$	−1.11042e92			−0.932406
$755$			2.74531e91i			0.220947i
$756$	2.40030e92	−	1.85398e92i	1.85169	−	1.43024i
$757$	7.76434e91			0.574165			0.287082	−	0.957906i	$-0.407315\pi$
$757$	7.76434e91			0.574165			0.287082	+	0.957906i	$0.407315\pi$
$758$			1.13414e92i			0.803994i
$759$	−2.36158e92	+	5.26177e91i	−1.60496	+	0.357598i
$760$	−1.44997e91			−0.0944768
$761$			2.02785e92i			1.26685i	0.773802	+	0.633427i	$0.218352\pi$
$761$			2.02785e92i			1.26685i	−0.773802	+	0.633427i	$0.781648\pi$
$762$	9.40826e91	+	4.22260e92i	0.563573	+	2.52942i
$763$	2.89144e92			1.66085
$764$		−	2.09689e92i		−	1.15501i
$765$	2.12681e91	−	9.97244e90i	0.112347	−	0.0526788i
$766$	−2.31298e92			−1.17179
$767$		−	2.78577e92i		−	1.35361i
$768$	−2.12500e92	+	4.73467e91i	−0.990377	+	0.220664i
$769$	−1.19041e92			−0.532172			−0.266086	−	0.963949i	$-0.585731\pi$
$769$	−1.19041e92			−0.532172			−0.266086	+	0.963949i	$0.585731\pi$
$770$		−	9.24139e91i		−	0.396309i
$771$	1.68348e91	+	7.55575e91i	0.0692576	+	0.310840i
$772$	−7.53605e91			−0.297434
$773$			1.03481e92i			0.391846i	0.980619	+	0.195923i	$0.0627702\pi$
$773$			1.03481e92i			0.391846i	−0.980619	+	0.195923i	$0.937230\pi$
$774$	−1.26453e92	−	2.69685e92i	−0.459430	−	0.979819i
$775$	−1.84763e92			−0.644111
$776$		−	1.87598e92i		−	0.627556i
$777$	3.46152e91	−	7.71252e90i	0.111120	−	0.0247585i
$778$	−1.53911e92			−0.474158
$779$		−	3.03151e92i		−	0.896313i
$780$	−2.10625e91	−	9.45324e91i	−0.0597700	−	0.268258i
$781$	−1.26707e92			−0.345117
$782$		−	7.44772e92i		−	1.94719i
$783$	1.51667e92	+	1.96359e92i	0.380639	+	0.492804i
$784$	4.07693e90			0.00982243
$785$		−	3.39645e91i		−	0.0785590i
$786$	−1.93468e92	+	4.31062e91i	−0.429623	+	0.0957233i
$787$	8.52091e92			1.81675			0.908373	−	0.418160i	$-0.137325\pi$
$787$	8.52091e92			1.81675			0.908373	+	0.418160i	$0.137325\pi$
$788$			3.58727e92i			0.734387i
$789$	1.05103e92	+	4.71723e92i	0.206611	+	0.927306i
$790$	2.86045e92			0.539967
$791$			1.47575e93i			2.67525i
$792$	4.85132e92	−	2.27475e92i	0.844606	−	0.396029i
$793$	1.56717e92			0.262043
$794$			6.79708e92i			1.09161i
$795$	−1.09625e92	+	2.44253e91i	−0.169107	+	0.0376783i
$796$	1.32444e93			1.96252
$797$			2.25575e92i			0.321089i	0.987029	+	0.160544i	$0.0513250\pi$
$797$			2.25575e92i			0.321089i	−0.987029	+	0.160544i	$0.948675\pi$
$798$	−1.90140e92	−	8.53381e92i	−0.260004	−	1.16695i
$799$	−8.58270e92			−1.12753
$800$			7.60037e92i			0.959301i
$801$	−2.85491e92	−	6.08862e92i	−0.346220	−	0.738377i
$802$	5.49930e92			0.640808
$803$		−	3.72762e92i		−	0.417383i
$804$	−2.35528e93	+	5.24774e92i	−2.53425	+	0.564649i
$805$	4.53840e92			0.469283
$806$		−	1.00426e93i		−	0.997986i
$807$	−2.63965e92	−	1.18472e93i	−0.252112	−	1.13152i
$808$	1.87947e92			0.172532
$809$		−	7.00949e92i		−	0.618492i	−0.950982	−	0.309246i	$-0.899923\pi$
$809$		−	7.00949e92i		−	0.618492i	0.950982	−	0.309246i	$-0.100077\pi$
$810$	−2.23716e92	+	2.68922e92i	−0.189747	+	0.228090i
$811$	1.78150e93			1.45251			0.726253	−	0.687428i	$-0.241260\pi$
$811$	1.78150e93			1.45251			0.726253	+	0.687428i	$0.241260\pi$
$812$			1.85879e93i			1.45692i
$813$	2.57348e92	−	5.73390e91i	0.193920	−	0.0432069i
$814$	1.63365e92			0.118353
$815$			2.83677e92i			0.197597i
$816$	1.99891e90	+	8.97144e90i	0.00133877	+	0.00600865i
$817$	−5.31178e92			−0.342085
$818$		−	2.98602e93i		−	1.84922i
$819$	2.02782e93	−	9.50829e92i	1.20766	−	0.566262i
$820$	−9.08678e92			−0.520435
$821$		−	8.76497e92i		−	0.482802i	−0.970425	−	0.241401i	$-0.922393\pi$
$821$		−	8.76497e92i		−	0.482802i	0.970425	−	0.241401i	$-0.0776070\pi$
$822$	−1.38808e93	+	3.09275e92i	−0.735388	+	0.163850i
$823$	−1.29955e93			−0.662215			−0.331108	−	0.943593i	$-0.607422\pi$
$823$	−1.29955e93			−0.662215			−0.331108	+	0.943593i	$0.607422\pi$
$824$		−	2.92015e92i		−	0.143131i
$825$	−4.12796e92	−	1.85270e93i	−0.194630	−	0.873533i
$826$	−7.53805e93			−3.41899
$827$			2.89065e93i			1.26130i	0.776067	+	0.630650i	$0.217212\pi$
$827$			2.89065e93i			1.26130i	−0.776067	+	0.630650i	$0.782788\pi$
$828$	2.91286e93	+	6.21221e93i	1.22278	+	2.60781i
$829$	2.34600e93			0.947509			0.473754	−	0.880657i	$-0.342898\pi$
$829$	2.34600e93			0.947509			0.473754	+	0.880657i	$0.342898\pi$
$830$		−	4.93250e92i		−	0.191676i
$831$	6.40092e92	−	1.42617e92i	0.239337	−	0.0533261i
$832$	−4.15446e93			−1.49475
$833$			2.11357e93i			0.731774i
$834$	4.34925e92	+	1.95202e93i	0.144911	+	0.650385i
$835$	6.98436e92			0.223954
$836$		−	2.49152e93i		−	0.768889i
$837$	−1.77586e93	+	1.37166e93i	−0.527466	+	0.407411i
$838$	2.60029e93			0.743384
$839$		−	4.39968e93i		−	1.21071i	−0.795957	−	0.605353i	$-0.793032\pi$
$839$		−	4.39968e93i		−	1.21071i	0.795957	−	0.605353i	$-0.206968\pi$
$840$	−9.81012e92	+	2.18577e92i	−0.259859	+	0.0578984i
$841$	2.40108e93			0.612258
$842$		−	2.20539e93i		−	0.541375i
$843$	3.46726e92	+	1.55617e93i	0.0819415	+	0.367768i
$844$	7.15260e93			1.62744
$845$			1.21189e92i			0.0265489i
$846$	1.15723e94	−	5.42616e93i	2.44100	−	1.14457i
$847$	−1.01160e93			−0.205467
$848$		−	4.39471e91i		−	0.00859535i
$849$	−6.62368e93	+	1.47581e93i	−1.24754	+	0.277961i
$850$	5.84288e93			1.05979
$851$			8.02280e92i			0.140146i
$852$	7.81424e92	+	3.50717e93i	0.131468	+	0.590052i
$853$	−7.51274e93			−1.21739			−0.608694	−	0.793405i	$-0.708306\pi$
$853$	−7.51274e93			−1.21739			−0.608694	+	0.793405i	$0.708306\pi$
$854$		−	4.24062e93i		−	0.661877i
$855$	2.64838e92	+	5.64816e92i	0.0398167	+	0.0849164i
$856$	−5.61559e93			−0.813271
$857$			2.80325e93i			0.391088i	0.980695	+	0.195544i	$0.0626473\pi$
$857$			2.80325e93i			0.391088i	−0.980695	+	0.195544i	$0.937353\pi$
$858$	1.00702e94	−	2.24371e93i	1.35345	−	0.301559i
$859$	6.05967e93			0.784635			0.392318	−	0.919830i	$-0.371673\pi$
$859$	6.05967e93			0.784635			0.392318	+	0.919830i	$0.371673\pi$
$860$			1.59218e93i			0.198629i
$861$	−4.56985e93	−	2.05103e94i	−0.549290	−	2.46531i
$862$	−8.76878e93			−1.01556
$863$			9.98281e93i			1.11406i	0.830493	+	0.557029i	$0.188059\pi$
$863$			9.98281e93i			1.11406i	−0.830493	+	0.557029i	$0.811941\pi$
$864$	5.64244e93	+	7.30514e93i	0.606775	+	0.785577i
$865$	−7.89280e92			−0.0817929
$866$			1.22101e94i			1.21940i
$867$	5.49022e93	−	1.22326e93i	0.528419	−	0.117736i
$868$	−1.68108e94			−1.55940
$869$			1.88503e94i			1.68533i
$870$	−4.66240e92	−	2.09257e93i	−0.0401785	−	0.180328i
$871$	−1.78191e94			−1.48014
$872$		−	1.44859e94i		−	1.15989i
$873$	−7.30760e93	+	3.42648e93i	−0.564052	+	0.264479i
$874$	1.97789e94			1.47176
$875$			7.24461e93i			0.519706i
$876$	−1.03179e94	+	2.29890e93i	−0.713606	+	0.158997i
$877$	−9.58776e93			−0.639338			−0.319669	−	0.947529i	$-0.603572\pi$
$877$	−9.58776e93			−0.639338			−0.319669	+	0.947529i	$0.603572\pi$
$878$		−	1.89254e94i		−	1.21680i
$879$	2.32507e93	+	1.04353e94i	0.144142	+	0.646937i
$880$	−2.58009e91			−0.00154237
$881$		−	9.87540e93i		−	0.569279i	−0.958635	−	0.284640i	$-0.908126\pi$
$881$		−	9.87540e93i		−	0.569279i	0.958635	−	0.284640i	$-0.0918739\pi$
$882$	−1.33624e94	−	2.84979e94i	−0.742833	−	1.58423i
$883$	−2.70632e94			−1.45090			−0.725448	−	0.688277i	$-0.758367\pi$
$883$	−2.70632e94			−1.45090			−0.725448	+	0.688277i	$0.758367\pi$
$884$			1.96465e94i			1.01581i
$885$	5.24973e93	−	1.16968e93i	0.261789	−	0.0583287i
$886$	4.01205e94			1.92969
$887$		−	3.51632e94i		−	1.63129i	−0.578550	−	0.815647i	$-0.696381\pi$
$887$		−	3.51632e94i		−	1.63129i	0.578550	−	0.815647i	$-0.303619\pi$
$888$	−3.86391e92	−	1.73419e93i	−0.0172907	−	0.0776037i
$889$	5.34766e94			2.30838
$890$			5.81068e93i			0.241962i
$891$	−1.77219e94	−	1.47428e94i	−0.711908	−	0.592234i
$892$	1.27112e93			0.0492617
$893$		−	2.27931e94i		−	0.852229i
$894$	9.55957e93	−	2.12994e93i	0.344856	−	0.0768365i
$895$	8.08609e93			0.281450
$896$			6.97846e94i			2.34371i
$897$	1.10187e94	+	4.94541e94i	0.357087	+	1.60267i
$898$	−3.93449e94			−1.23040
$899$		−	1.37522e94i		−	0.415014i
$900$	−4.87360e94	+	2.28520e94i	−1.41935	+	0.665523i
$901$	2.27832e94			0.640356
$902$		−	9.67979e94i		−	2.62577i
$903$	−3.59380e94	+	8.00727e93i	−0.940906	+	0.209641i
$904$	7.39337e94			1.86833
$905$		−	1.32508e94i		−	0.323211i
$906$	1.80358e94	+	8.09478e94i	0.424651	+	1.90591i
$907$	4.44922e94			1.01123			0.505616	−	0.862759i	$-0.331265\pi$
$907$	4.44922e94			1.01123			0.505616	+	0.862759i	$0.331265\pi$
$908$			1.15249e95i			2.52865i
$909$	−3.43285e93	−	7.32119e93i	−0.0727127	−	0.155073i
$910$	−1.93525e94			−0.395742
$911$		−	5.81726e94i		−	1.14850i	−0.818680	−	0.574250i	$-0.805294\pi$
$911$		−	5.81726e94i		−	1.14850i	0.818680	−	0.574250i	$-0.194706\pi$
$912$	−2.38255e92	+	5.30849e91i	−0.00454158	+	0.00101190i
$913$	3.25050e94			0.598254
$914$			5.40088e93i			0.0959812i
$915$	6.58016e92	+	2.95330e93i	0.0112918	+	0.0506794i
$916$	1.40047e94			0.232070
$917$			2.45016e94i			0.392080i
$918$	5.61592e94	−	4.33770e94i	0.867871	−	0.670338i
$919$	−2.90922e93			−0.0434191			−0.0217095	−	0.999764i	$-0.506911\pi$
$919$	−2.90922e93			−0.0434191			−0.0217095	+	0.999764i	$0.506911\pi$
$920$		−	2.27370e94i		−	0.327735i
$921$	1.25962e94	−	2.80652e93i	0.175360	−	0.0390715i
$922$	−1.96609e95			−2.64371
$923$			2.65338e94i			0.344623i
$924$	−3.75585e94	−	1.68569e95i	−0.471200	−	2.11483i
$925$	−6.29404e93			−0.0762771
$926$		−	1.41989e95i		−	1.66227i
$927$	−1.13750e94	+	5.33366e93i	−0.128647	+	0.0603218i
$928$	−5.65708e94			−0.618098
$929$		−	4.47551e92i		−	0.00472432i	−0.999997	−	0.00236216i	$-0.999248\pi$
$929$		−	4.47551e92i		−	0.00472432i	0.999997	−	0.00236216i	$-0.000751900\pi$
$930$	1.89251e94	−	4.21665e93i	0.193012	−	0.0430044i
$931$	−5.61301e94			−0.553103
$932$		−	5.51719e94i		−	0.525302i
$933$	1.74930e94	+	7.85116e94i	0.160935	+	0.722306i
$934$	1.19361e94			0.106111
$935$		−	1.33758e94i		−	0.114907i
$936$	−4.76358e94	−	1.01592e95i	−0.395463	−	0.843398i
$937$	−3.36818e94			−0.270227			−0.135113	−	0.990830i	$-0.543140\pi$
$937$	−3.36818e94			−0.270227			−0.135113	+	0.990830i	$0.543140\pi$
$938$			4.82169e95i			3.73860i
$939$	−1.75280e95	+	3.90538e94i	−1.31351	+	0.292661i
$940$	−6.83211e94			−0.494838
$941$			5.44927e94i			0.381479i	0.981641	+	0.190739i	$0.0610886\pi$
$941$			5.44927e94i			0.381479i	−0.981641	+	0.190739i	$0.938911\pi$
$942$	−2.23136e94	−	1.00147e95i	−0.150987	−	0.677657i
$943$	4.75370e95			3.10926
$944$			2.10454e93i			0.0133062i
$945$	2.64326e94	+	3.42216e94i	0.161555	+	0.209162i
$946$	−1.69609e95			−1.00215
$947$			1.44318e95i			0.824370i	0.911100	+	0.412185i	$0.135234\pi$
$947$			1.44318e95i			0.824370i	−0.911100	+	0.412185i	$0.864766\pi$
$948$	5.21766e95	−	1.16253e95i	2.88143	−	0.642005i
$949$	−7.80607e94			−0.416786
$950$			1.55169e95i			0.801034i
$951$	2.37709e94	+	1.06688e95i	0.118651	+	0.532525i
$952$	2.03882e95			0.984004
$953$		−	2.43542e95i		−	1.13658i	−0.822827	−	0.568292i	$-0.807604\pi$
$953$		−	2.43542e95i		−	1.13658i	0.822827	−	0.568292i	$-0.192396\pi$
$954$	−3.07192e95	+	1.44040e95i	−1.38632	+	0.650033i
$955$	2.98957e94			0.130467
$956$		−	6.20217e95i		−	2.61753i
$957$	1.37900e95	−	3.07251e94i	0.562835	−	0.125404i
$958$	−7.07468e95			−2.79261
$959$			1.75792e95i			0.671125i
$960$	−1.74436e94	−	7.82901e94i	−0.0644106	−	0.289086i
$961$	−1.55619e95			−0.555796
$962$		−	3.42106e94i		−	0.118184i
$963$	1.02569e95	+	2.18747e95i	0.342748	+	0.730974i
$964$	1.48137e95			0.478849
$965$		−	1.07443e94i		−	0.0335973i
$966$	1.33819e96	−	2.98158e95i	4.04807	−	0.901941i
$967$	1.10613e95			0.323712			0.161856	−	0.986814i	$-0.448252\pi$
$967$	1.10613e95			0.323712			0.161856	+	0.986814i	$0.448252\pi$
$968$			5.06806e94i			0.143493i
$969$	−2.75204e94	−	1.23517e95i	−0.0753867	−	0.338349i
$970$	6.97401e94			0.184836
$971$		−	6.88700e95i		−	1.76610i	−0.469282	−	0.883049i	$-0.655487\pi$
$971$		−	6.88700e95i		−	1.76610i	0.469282	−	0.883049i	$-0.344513\pi$
$972$	−2.98778e95	+	5.81455e95i	−0.741359	+	1.44276i
$973$	2.47211e95			0.593550
$974$		−	1.82914e95i		−	0.424971i
$975$	−3.87977e95	+	8.64441e94i	−0.872284	+	0.194351i
$976$	−1.18393e93			−0.00257593
$977$			3.16282e95i			0.665961i	0.942934	+	0.332980i	$0.108054\pi$
$977$			3.16282e95i			0.665961i	−0.942934	+	0.332980i	$0.891946\pi$
$978$	1.86366e95	+	8.36446e95i	0.379773	+	1.70449i
$979$	−3.82922e95			−0.755203
$980$			1.68247e95i			0.321154i
$981$	−5.64278e95	+	2.64585e95i	−1.04252	+	0.488830i
$982$	−7.43723e95			−1.32998
$983$			3.10446e95i			0.537370i	0.963228	+	0.268685i	$0.0865891\pi$
$983$			3.10446e95i			0.537370i	−0.963228	+	0.268685i	$0.913411\pi$
$984$	−1.02755e96	+	2.28946e95i	−1.72171	+	0.383610i
$985$	−5.11444e94			−0.0829542
$986$			4.34895e95i			0.682847i
$987$	−3.43595e95	−	1.54212e96i	−0.522273	−	2.34406i
$988$	−5.21752e95			−0.767790
$989$		−	8.32940e95i		−	1.18668i
$990$	8.45645e94	+	1.80350e95i	0.116644	+	0.248765i
$991$	1.03606e96			1.38366			0.691829	−	0.722061i	$-0.256805\pi$
$991$	1.03606e96			1.38366			0.691829	+	0.722061i	$0.256805\pi$
$992$		−	5.11623e95i		−	0.661572i
$993$	−7.46093e95	+	1.66235e95i	−0.934151	+	0.208136i
$994$	7.17983e95			0.870461
$995$			1.88828e95i			0.221681i
$996$	−2.00465e95	−	8.99721e95i	−0.227897	−	1.02284i
$997$	8.38120e95			0.922701			0.461351	−	0.887218i	$-0.347365\pi$
$997$	8.38120e95			0.922701			0.461351	+	0.887218i	$0.347365\pi$
$998$			2.07370e96i			2.21090i
$999$	−6.04955e94	+	4.67264e94i	−0.0624637	+	0.0482466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.65.b.a.2.4	✓	20
3.2	odd	2	inner	3.65.b.a.2.17	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.65.b.a.2.4	✓	20	1.1	even	1	trivial
3.65.b.a.2.17	yes	20	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:	\( k \)	\(=\)	\( 65 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.95479e9i q^{2} +(1.80867e15 - 4.02985e14i) q^{3} -2.99223e19 q^{4} -4.26608e21i q^{5} +(-2.80268e24 - 1.25789e25i) q^{6} -1.59304e27 q^{7} +7.98101e28i q^{8} +(3.10889e30 - 1.45773e30i) q^{9} +O(q^{10})\)	\(q-6.95479e9i q^{2} +(1.80867e15 - 4.02985e14i) q^{3} -2.99223e19 q^{4} -4.26608e21i q^{5} +(-2.80268e24 - 1.25789e25i) q^{6} -1.59304e27 q^{7} +7.98101e28i q^{8} +(3.10889e30 - 1.45773e30i) q^{9} -2.96697e31 q^{10} -1.95522e33i q^{11} +(-5.41196e34 + 1.20583e34i) q^{12} -4.09446e35 q^{13} +1.10793e37i q^{14} +(-1.71917e36 - 7.71594e36i) q^{15} +3.09321e36 q^{16} +1.60359e39i q^{17} +(-1.01382e40 - 2.16217e40i) q^{18} -4.25866e40 q^{19} +1.27651e41i q^{20} +(-2.88129e42 + 6.41973e41i) q^{21} -1.35982e43 q^{22} -6.67799e43i q^{23} +(3.21623e43 + 1.44350e44i) q^{24} +5.23902e44 q^{25} +2.84761e45i q^{26} +(5.03551e45 - 3.88940e45i) q^{27} +4.76675e46 q^{28} +3.89949e46i q^{29} +(-5.36627e46 + 1.19565e46i) q^{30} -3.52667e47 q^{31} +1.45072e48i q^{32} +(-7.87927e47 - 3.53636e48i) q^{33} +1.11526e49 q^{34} +6.79605e48i q^{35} +(-9.30252e49 + 4.36188e49i) q^{36} -1.20138e49 q^{37} +2.96181e50i q^{38} +(-7.40553e50 + 1.65001e50i) q^{39} +3.40477e50 q^{40} +7.11845e51i q^{41} +(4.46478e51 + 2.00387e52i) q^{42} +1.24729e52 q^{43} +5.85048e52i q^{44} +(-6.21882e51 - 1.32628e52i) q^{45} -4.64440e53 q^{46} +5.35217e53i q^{47} +(5.59460e51 - 1.24652e51i) q^{48} +1.31802e54 q^{49} -3.64362e54i q^{50} +(6.46224e53 + 2.90037e54i) q^{51} +1.22516e55 q^{52} -1.42076e55i q^{53} +(-2.70499e55 - 3.50209e55i) q^{54} -8.34115e54 q^{55} -1.27141e56i q^{56} +(-7.70251e55 + 1.71618e55i) q^{57} +2.71201e56 q^{58} +6.80375e56i q^{59} +(5.14415e55 + 2.30879e56i) q^{60} -3.82753e56 q^{61} +2.45273e57i q^{62} +(-4.95259e57 + 2.32223e57i) q^{63} +1.01465e58 q^{64} +1.74673e57i q^{65} +(-2.45946e58 + 5.47986e57i) q^{66} +4.35199e58 q^{67} -4.79832e58i q^{68} +(-2.69113e58 - 1.20783e59i) q^{69} +4.72651e58 q^{70} -6.48041e58i q^{71} +(1.16342e59 + 2.48121e59i) q^{72} +1.90649e59 q^{73} +8.35533e58i q^{74} +(9.47565e59 - 2.11125e59i) q^{75} +1.27429e60 q^{76} +3.11476e60i q^{77} +(1.14754e60 + 5.15039e60i) q^{78} -9.64097e60 q^{79} -1.31959e58i q^{80} +(7.54020e60 - 9.06387e60i) q^{81} +4.95073e61 q^{82} +1.66247e61i q^{83} +(8.62148e61 - 1.92093e61i) q^{84} +6.84105e60 q^{85} -8.67464e61i q^{86} +(1.57144e61 + 7.05288e61i) q^{87} +1.56047e62 q^{88} -1.95845e62i q^{89} +(-9.22398e61 + 4.32506e61i) q^{90} +6.52265e62 q^{91} +1.99821e63i q^{92} +(-6.37859e62 + 1.42120e62i) q^{93} +3.72232e63 q^{94} +1.81678e62i q^{95} +(5.84621e62 + 2.62388e63i) q^{96} -2.35055e63 q^{97} -9.16658e63i q^{98} +(-2.85020e63 - 6.07858e63i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14\!\cdots\!92 q^{3}+ \cdots - 22\!\cdots\!00 q^{9}+O(q^{10}) \) 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9	\( 20 q - 14\!\cdots\!92 q^{3}+ \cdots + 31\!\cdots\!00 q^{99}+O(q^{100}) \) 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9 + 331029217205387677806996511116000 * q^10 + 6534659062821156745233165595144848 * q^12 - 751508903297384088692483175344422424 * q^13 + 38547509823020584674418593740816815200 * q^15 + 333898239622199115079798041399657464960 * q^16 - 3676009515412490831675032229198156934240 * q^18 + 109286088964872656413026262415428611794200 * q^19 - 1311511276150890256934838463853331394769880 * q^21 - 8079025213365934710514462143494926255299360 * q^22 + 371409898348173331095205935880826344773509760 * q^24 - 1408933246315215357541047632909406493714979500 * q^25 + 5130931947084052629864823829892614277399503148 * q^27 - 38556600155873290275414028639950032296787869664 * q^28 - 141541842553229550692763020870574637255687216800 * q^30 + 458034135616019870141982361360522347620359726840 * q^31 - 2882270174679362228632701138961802589863549285280 * q^33 - 787058086714062550476148644876342688312553235840 * q^34 + 75759088962200911205216155020070755577873854233040 * q^36 - 167241277488128791881901510734045117370850836062104 * q^37 + 458879560232529079697344976545706436533594974010520 * q^39 - 3172271879697225400792978571433360199916055661804800 * q^40 - 22013931366996449796115743111552261520406610644630880 * q^42 + 10353394041775726307362489381794503494462017586072216 * q^43 + 37622210359250231761078599539977430954460378542462400 * q^45 - 297398119355935548173345475928562088559055731847559360 * q^46 - 127296049249148961420276393789708282996205874832565632 * q^48 + 2035505279477569607000808808313462872867812749377748220 * q^49 - 8993599813445960529795685588193052695282052910939102080 * q^51 + 12450863873285726446941747254985680826918117392844470176 * q^52 + 1380721489513428759527937305946915244571081819618418480 * q^54 + 86716751505127419669577189864656813143075791367545723200 * q^55 - 410655148353071807815217561752202738362370559954491547384 * q^57 + 1171127646996109205778370152132525033757099595854063443360 * q^58 - 4554593355431768584543074712701226261422872417617275398400 * q^60 + 4552152490922647485493920930203353370116723196876970427240 * q^61 - 18340670222945277450481852597884877177550760958776639152904 * q^63 + 30281219638275425893507737167512138061029087969644636247040 * q^64 - 73446637659820047047259347339723389117534541697924310768800 * q^66 + 108802231400777081380268556166029877921173626685759369971416 * q^67 - 255718829710356626829923504360603133388502621634044634870720 * q^69 + 559303866272797397220431985027879540776975892234361655006400 * q^70 - 561110698242036073669580259260779527574289380077856046595840 * q^72 - 569085806526237236378057540729119438030642048917813502604504 * q^73 + 2290039066363366330022806756651688579736177808604861676211500 * q^75 - 5532330994825480968263901289000933629970925314426608479594720 * q^76 + 9655803402636036605327159547820723686984585271634655943687200 * q^78 - 22640121063621617622122249693012788180804867706114977596801800 * q^79 + 37075761484886132865783336331999338158569856937859957696374420 * q^81 - 69993225281309073377388502634775301823581628014590259964399040 * q^82 + 62923532655099413129084384942812878939798728172266572844745120 * q^84 - 142181474118416523657627044760532405955688084516779285440262400 * q^85 + 23785411541262749066239132616113250012236593481925882591047200 * q^87 + 345107275964501391166111220047509272448066379695588836103893760 * q^88 - 1925479853343216377261941955721474942915647264800935046773530400 * q^90 + 1225124508801982757577911377627409097047306370806522445345728240 * q^91 - 2776404525956613483290023288082668840477640965472850083253548184 * q^93 + 1658662465458978832407333757013771498132481417946327912207224960 * q^94 - 3771017263293375391290634333996451541183976624371029742095907840 * q^96 + 818755932265886448325223871671724131911117159175492830487918056 * q^97 + 3118093180125811439250837213823663221313339534064003298574718400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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