LMFDB - Embedded newform 3.65.b.a.2.15

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			2.15
Root			$6.71940e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.65.b.a.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.03164e9i q^{2} +(5.57989e14 + 1.76701e15i) q^{3} +2.19261e18 q^{4} +2.91915e22i q^{5} +(-7.12396e24 + 2.24961e24i) q^{6} +6.92352e26 q^{7} +8.32105e28i q^{8} +(-2.81098e30 + 1.97195e30i) q^{9} +O(q^{10})$	\(q+4.03164e9i q^{2} +(5.57989e14 + 1.76701e15i) q^{3} +2.19261e18 q^{4} +2.91915e22i q^{5} +(-7.12396e24 + 2.24961e24i) q^{6} +6.92352e26 q^{7} +8.32105e28i q^{8} +(-2.81098e30 + 1.97195e30i) q^{9} -1.17690e32 q^{10} -2.05319e33i q^{11} +(1.22345e33 + 3.87437e33i) q^{12} -9.38974e34 q^{13} +2.79131e36i q^{14} +(-5.15818e37 + 1.62885e37i) q^{15} -2.95028e38 q^{16} -1.29532e39i q^{17} +(-7.95018e39 - 1.13329e40i) q^{18} -2.23545e40 q^{19} +6.40057e40i q^{20} +(3.86325e41 + 1.22339e42i) q^{21} +8.27774e42 q^{22} -4.35116e43i q^{23} +(-1.47034e44 + 4.64305e43i) q^{24} -3.10044e44 q^{25} -3.78561e44i q^{26} +(-5.05295e45 - 3.86671e45i) q^{27} +1.51806e45 q^{28} +1.55583e45i q^{29} +(-6.56695e46 - 2.07959e47i) q^{30} -9.94186e47 q^{31} +3.45514e47i q^{32} +(3.62802e48 - 1.14566e48i) q^{33} +5.22226e48 q^{34} +2.02108e49i q^{35} +(-6.16339e48 + 4.32371e48i) q^{36} -6.98898e49 q^{37} -9.01252e49i q^{38} +(-5.23937e49 - 1.65918e50i) q^{39} -2.42904e51 q^{40} -4.06020e51i q^{41} +(-4.93229e51 + 1.55752e51i) q^{42} -3.69152e52 q^{43} -4.50186e51i q^{44} +(-5.75641e52 - 8.20568e52i) q^{45} +1.75423e53 q^{46} +5.97972e53i q^{47} +(-1.64622e53 - 5.21319e53i) q^{48} -7.40409e53 q^{49} -1.24999e54i q^{50} +(2.28884e54 - 7.22773e53i) q^{51} -2.05880e53 q^{52} +1.81495e55i q^{53} +(1.55892e55 - 2.03717e55i) q^{54} +5.99358e55 q^{55} +5.76109e55i q^{56} +(-1.24735e55 - 3.95006e55i) q^{57} -6.27257e54 q^{58} +1.74464e56i q^{59} +(-1.13099e56 + 3.57144e55i) q^{60} -1.21233e57 q^{61} -4.00820e57i q^{62} +(-1.94619e57 + 1.36528e57i) q^{63} -6.83530e57 q^{64} -2.74101e57i q^{65} +(4.61888e57 + 1.46269e58i) q^{66} +4.80588e58 q^{67} -2.84013e57i q^{68} +(7.68856e58 - 2.42790e58i) q^{69} -8.14827e58 q^{70} +4.77800e58i q^{71} +(-1.64087e59 - 2.33903e59i) q^{72} +3.60721e59 q^{73} -2.81771e59i q^{74} +(-1.73001e59 - 5.47851e59i) q^{75} -4.90147e58 q^{76} -1.42153e60i q^{77} +(6.68921e59 - 2.11233e59i) q^{78} -3.79967e60 q^{79} -8.61232e60i q^{80} +(4.01304e60 - 1.10862e61i) q^{81} +1.63693e61 q^{82} -2.93347e61i q^{83} +(8.47060e59 + 2.68243e60i) q^{84} +3.78123e61 q^{85} -1.48829e62i q^{86} +(-2.74918e60 + 8.68138e59i) q^{87} +1.70847e62 q^{88} -1.74845e62i q^{89} +(3.30824e62 - 2.32078e62i) q^{90} -6.50100e61 q^{91} -9.54041e61i q^{92} +(-5.54745e62 - 1.75674e63i) q^{93} -2.41081e63 q^{94} -6.52561e62i q^{95} +(-6.10528e62 + 1.92793e62i) q^{96} +6.41265e63 q^{97} -2.98506e63i q^{98} +(4.04879e63 + 5.77149e63i) 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 $

$2$			4.03164e9i			0.938690i	0.883015	+	0.469345i	$0.155510\pi$
$2$			4.03164e9i			0.938690i	−0.883015	+	0.469345i	$0.844490\pi$
$3$	5.57989e14	+	1.76701e15i	0.301124	+	0.953585i
$3$	5.57989e14	+	1.76701e15i	0.301124	+	0.953585i
$4$	2.19261e18			0.118862
$5$			2.91915e22i			1.25377i	0.779113	+	0.626883i	$0.215670\pi$
$5$			2.91915e22i			1.25377i	−0.779113	+	0.626883i	$0.784330\pi$
$6$	−7.12396e24	+	2.24961e24i	−0.895120	+	0.282662i
$7$	6.92352e26			0.626888			0.313444	−	0.949607i	$-0.398517\pi$
$7$	6.92352e26			0.626888			0.313444	+	0.949607i	$0.398517\pi$
$8$			8.32105e28i			1.05026i
$9$	−2.81098e30	+	1.97195e30i	−0.818649	+	0.574294i
$10$	−1.17690e32			−1.17690
$11$		−	2.05319e33i		−	0.972442i	−0.873836	−	0.486221i	$-0.838375\pi$
$11$		−	2.05319e33i		−	0.972442i	0.873836	−	0.486221i	$-0.161625\pi$
$12$	1.22345e33	+	3.87437e33i	0.0357921	+	0.113345i
$13$	−9.38974e34			−0.212064			−0.106032	−	0.994363i	$-0.533815\pi$
$13$	−9.38974e34			−0.212064			−0.106032	+	0.994363i	$0.533815\pi$
$14$			2.79131e36i			0.588453i
$15$	−5.15818e37	+	1.62885e37i	−1.19557	+	0.377539i
$16$	−2.95028e38			−0.867010
$17$		−	1.29532e39i		−	0.547030i	−0.961868	−	0.273515i	$-0.911814\pi$
$17$		−	1.29532e39i		−	0.547030i	0.961868	−	0.273515i	$-0.0881863\pi$
$18$	−7.95018e39	−	1.13329e40i	−0.539084	−	0.768457i
$19$	−2.23545e40			−0.268688			−0.134344	−	0.990935i	$-0.542893\pi$
$19$	−2.23545e40			−0.268688			−0.134344	+	0.990935i	$0.542893\pi$
$20$			6.40057e40i			0.149025i
$21$	3.86325e41	+	1.22339e42i	0.188771	+	0.597791i
$22$	8.27774e42			0.912822
$23$		−	4.35116e43i		−	1.15695i	−0.815700	−	0.578475i	$-0.803648\pi$
$23$		−	4.35116e43i		−	1.15695i	0.815700	−	0.578475i	$-0.196352\pi$
$24$	−1.47034e44	+	4.64305e43i	−1.00152	+	0.316260i
$25$	−3.10044e44			−0.571930
$26$		−	3.78561e44i		−	0.199062i
$27$	−5.05295e45	−	3.86671e45i	−0.794153	−	0.607717i
$28$	1.51806e45			0.0745129
$29$			1.55583e45i			0.0248443i	0.999923	+	0.0124222i	$0.00395420\pi$
$29$			1.55583e45i			0.0248443i	−0.999923	+	0.0124222i	$0.996046\pi$
$30$	−6.56695e46	−	2.07959e47i	−0.354392	−	1.12227i
$31$	−9.94186e47			−1.87886			−0.939428	−	0.342745i	$-0.888643\pi$
$31$	−9.94186e47			−1.87886			−0.939428	+	0.342745i	$0.888643\pi$
$32$			3.45514e47i			0.236410i
$33$	3.62802e48	−	1.14566e48i	0.927306	−	0.292826i
$34$	5.22226e48			0.513491
$35$			2.02108e49i			0.785970i
$36$	−6.16339e48	+	4.32371e48i	−0.0973060	+	0.0682616i
$37$	−6.98898e49			−0.459154			−0.229577	−	0.973290i	$-0.573734\pi$
$37$	−6.98898e49			−0.459154			−0.229577	+	0.973290i	$0.573734\pi$
$38$		−	9.01252e49i		−	0.252215i
$39$	−5.23937e49	−	1.65918e50i	−0.0638574	−	0.202221i
$40$	−2.42904e51			−1.31679
$41$		−	4.06020e51i		−	0.998767i	−0.866381	−	0.499384i	$-0.833560\pi$
$41$		−	4.06020e51i		−	0.998767i	0.866381	−	0.499384i	$-0.166440\pi$
$42$	−4.93229e51	+	1.55752e51i	−0.561140	+	0.177197i
$43$	−3.69152e52			−1.97795			−0.988974	−	0.148088i	$-0.952688\pi$
$43$	−3.69152e52			−1.97795			−0.988974	+	0.148088i	$0.952688\pi$
$44$		−	4.50186e51i		−	0.115586i
$45$	−5.75641e52	−	8.20568e52i	−0.720031	−	1.02639i
$46$	1.75423e53			1.08602
$47$			5.97972e53i			1.86016i	0.367363	+	0.930078i	$0.380261\pi$
$47$			5.97972e53i			1.86016i	−0.367363	+	0.930078i	$0.619739\pi$
$48$	−1.64622e53	−	5.21319e53i	−0.261077	−	0.826768i
$49$	−7.40409e53			−0.607012
$50$		−	1.24999e54i		−	0.536865i
$51$	2.28884e54	−	7.22773e53i	0.521639	−	0.164724i
$52$	−2.05880e53			−0.0252062
$53$			1.81495e55i			1.20791i	0.797017	+	0.603957i	$0.206410\pi$
$53$			1.81495e55i			1.20791i	−0.797017	+	0.603957i	$0.793590\pi$
$54$	1.55892e55	−	2.03717e55i	0.570458	−	0.745464i
$55$	5.99358e55			1.21922
$56$			5.76109e55i			0.658397i
$57$	−1.24735e55	−	3.95006e55i	−0.0809085	−	0.256217i
$58$	−6.27257e54			−0.0233211
$59$			1.74464e56i			0.375354i	0.982231	+	0.187677i	$0.0600958\pi$
$59$			1.74464e56i			0.375354i	−0.982231	+	0.187677i	$0.939904\pi$
$60$	−1.13099e56	+	3.57144e55i	−0.142108	+	0.0448749i
$61$	−1.21233e57			−0.897569			−0.448784	−	0.893640i	$-0.648143\pi$
$61$	−1.21233e57			−0.897569			−0.448784	+	0.893640i	$0.648143\pi$
$62$		−	4.00820e57i		−	1.76366i
$63$	−1.94619e57	+	1.36528e57i	−0.513201	+	0.360018i
$64$	−6.83530e57			−1.08893
$65$		−	2.74101e57i		−	0.265878i
$66$	4.61888e57	+	1.46269e58i	0.274872	+	0.870453i
$67$	4.80588e58			1.76758			0.883791	−	0.467883i	$-0.154983\pi$
$67$	4.80588e58			1.76758			0.883791	+	0.467883i	$0.154983\pi$
$68$		−	2.84013e57i		−	0.0650209i
$69$	7.68856e58	−	2.42790e58i	1.10325	−	0.348385i
$70$	−8.14827e58			−0.737782
$71$			4.77800e58i			0.274776i	0.990517	+	0.137388i	$0.0438707\pi$
$71$			4.77800e58i			0.274776i	−0.990517	+	0.137388i	$0.956129\pi$
$72$	−1.64087e59	−	2.33903e59i	−0.603161	−	0.859797i
$73$	3.60721e59			0.852785			0.426392	−	0.904538i	$-0.359784\pi$
$73$	3.60721e59			0.852785			0.426392	+	0.904538i	$0.359784\pi$
$74$		−	2.81771e59i		−	0.431003i
$75$	−1.73001e59	−	5.47851e59i	−0.172222	−	0.545384i
$76$	−4.90147e58			−0.0319368
$77$		−	1.42153e60i		−	0.609612i
$78$	6.68921e59	−	2.11233e59i	0.189822	−	0.0599423i
$79$	−3.79967e60			−0.717264			−0.358632	−	0.933479i	$-0.616757\pi$
$79$	−3.79967e60			−0.717264			−0.358632	+	0.933479i	$0.616757\pi$
$80$		−	8.61232e60i		−	1.08703i
$81$	4.01304e60	−	1.10862e61i	0.340372	−	0.940291i
$82$	1.63693e61			0.937533
$83$		−	2.93347e61i		−	1.13994i	−0.821665	−	0.569971i	$-0.806955\pi$
$83$		−	2.93347e61i		−	1.13994i	0.821665	−	0.569971i	$-0.193045\pi$
$84$	8.47060e59	+	2.68243e60i	0.0224376	+	0.0710544i
$85$	3.78123e61			0.685847
$86$		−	1.48829e62i		−	1.85668i
$87$	−2.74918e60	+	8.68138e59i	−0.0236912	+	0.00748123i
$88$	1.70847e62			1.02132
$89$		−	1.74845e62i		−	0.728071i	−0.931385	−	0.364036i	$-0.881399\pi$
$89$		−	1.74845e62i		−	0.728071i	0.931385	−	0.364036i	$-0.118601\pi$
$90$	3.30824e62	−	2.32078e62i	0.963466	−	0.675886i
$91$	−6.50100e61			−0.132940
$92$		−	9.54041e61i		−	0.137517i
$93$	−5.54745e62	−	1.75674e63i	−0.565769	−	1.79165i
$94$	−2.41081e63			−1.74611
$95$		−	6.52561e62i		−	0.336873i
$96$	−6.10528e62	+	1.92793e62i	−0.225437	+	0.0711888i
$97$	6.41265e63			1.69958			0.849791	−	0.527119i	$-0.176728\pi$
$97$	6.41265e63			1.69958			0.849791	+	0.527119i	$0.176728\pi$
$98$		−	2.98506e63i		−	0.569796i
$99$	4.04879e63	+	5.77149e63i	0.558468	+	0.796089i
$100$	−6.79806e62			−0.0679806
$101$			1.93229e64i			1.40536i	0.711506	+	0.702680i	$0.248013\pi$
$101$			1.93229e64i			1.40536i	−0.711506	+	0.702680i	$0.751987\pi$
$102$	2.91396e63	+	9.22779e63i	0.154624	+	0.489657i
$103$	7.58837e63			0.294684			0.147342	−	0.989086i	$-0.452928\pi$
$103$	7.58837e63			0.294684			0.147342	+	0.989086i	$0.452928\pi$
$104$		−	7.81325e63i		−	0.222723i
$105$	−3.57127e64	+	1.12774e64i	−0.749490	+	0.236674i
$106$	−7.31722e64			−1.13386
$107$			1.22724e65i			1.40815i	0.710127	+	0.704073i	$0.248637\pi$
$107$			1.22724e65i			1.40815i	−0.710127	+	0.704073i	$0.751363\pi$
$108$	−1.10792e64	−	8.47820e63i	−0.0943944	−	0.0722343i
$109$	−6.72712e64			−0.426757			−0.213379	−	0.976970i	$-0.568447\pi$
$109$	−6.72712e64			−0.426757			−0.213379	+	0.976970i	$0.568447\pi$
$110$			2.41640e65i			1.14446i
$111$	−3.89977e64	−	1.23496e65i	−0.138262	−	0.437843i
$112$	−2.04263e65			−0.543518
$113$			5.33474e65i			1.06808i	0.845460	+	0.534039i	$0.179326\pi$
$113$			5.33474e65i			1.06808i	−0.845460	+	0.534039i	$0.820674\pi$
$114$	1.59252e65	−	5.02888e64i	0.240509	−	0.0759480i
$115$	1.27017e66			1.45054
$116$			3.41134e63i			0.00295304i
$117$	2.63944e65	−	1.85161e65i	0.173606	−	0.121787i
$118$	−7.03376e65			−0.352341
$119$		−	8.96816e65i		−	0.342926i
$120$	−1.35538e66	−	4.29214e66i	−0.396516	−	1.25567i
$121$	2.42314e65			0.0543558
$122$		−	4.88770e66i		−	0.842538i
$123$	7.17443e66	−	2.26555e66i	0.952410	−	0.300753i
$124$	−2.17986e66			−0.223324
$125$			6.77410e66i			0.536700i
$126$	−5.50432e66	−	7.84633e66i	−0.337945	−	0.481736i
$127$	8.61373e66			0.410650			0.205325	−	0.978694i	$-0.434175\pi$
$127$	8.61373e66			0.410650			0.205325	+	0.978694i	$0.434175\pi$
$128$		−	2.11839e67i		−	0.785753i
$129$	−2.05983e67	−	6.52297e67i	−0.595607	−	1.88614i
$130$	1.10508e67			0.249577
$131$			8.49022e67i			1.50051i	0.661151	+	0.750253i	$0.270068\pi$
$131$			8.49022e67i			1.50051i	−0.661151	+	0.750253i	$0.729932\pi$
$132$	7.95483e66	−	2.51198e66i	0.110221	−	0.0348058i
$133$	−1.54772e67			−0.168437
$134$			1.93756e68i			1.65921i
$135$	1.12875e68	−	1.47503e68i	0.761936	−	0.995683i
$136$	1.07784e68			0.574526
$137$			1.71793e68i			0.724349i	0.932110	+	0.362175i	$0.117966\pi$
$137$			1.71793e68i			0.724349i	−0.932110	+	0.362175i	$0.882034\pi$
$138$	9.78842e67	+	3.09975e68i	0.327026	+	1.03561i
$139$	−4.51374e68			−1.19691			−0.598457	−	0.801155i	$-0.704219\pi$
$139$	−4.51374e68			−1.19691			−0.598457	+	0.801155i	$0.704219\pi$
$140$			4.43144e67i			0.0934218i
$141$	−1.05662e69	+	3.33662e68i	−1.77382	+	0.560137i
$142$	−1.92632e68			−0.257929
$143$			1.92789e68i			0.206220i
$144$	8.29319e68	−	5.81780e68i	0.709777	−	0.497919i
$145$	−4.54172e67			−0.0311490
$146$			1.45430e69i			0.800500i
$147$	−4.13140e68	−	1.30831e69i	−0.182786	−	0.578838i
$148$	−1.53241e68			−0.0545759
$149$		−	6.14972e67i		−	0.0176561i	−0.999961	−	0.00882804i	$-0.997190\pi$
$149$		−	6.14972e67i		−	0.0176561i	0.999961	−	0.00882804i	$-0.00281009\pi$
$150$	2.20874e69	−	6.97478e68i	0.511946	−	0.161663i
$151$	6.05213e69			1.13409			0.567043	−	0.823688i	$-0.308087\pi$
$151$	6.05213e69			1.13409			0.567043	+	0.823688i	$0.308087\pi$
$152$		−	1.86013e69i		−	0.282194i
$153$	2.55430e69	+	3.64111e69i	0.314156	+	0.447825i
$154$	5.73111e69			0.572236
$155$		−	2.90218e70i		−	2.35565i
$156$	−1.14879e68	−	3.63793e68i	−0.00759020	−	0.0240363i
$157$	−1.96305e70			−1.05716			−0.528582	−	0.848883i	$-0.677276\pi$
$157$	−1.96305e70			−1.05716			−0.528582	+	0.848883i	$0.677276\pi$
$158$		−	1.53189e70i		−	0.673288i
$159$	−3.20703e70	+	1.01272e70i	−1.15185	+	0.363732i
$160$	−1.00861e70			−0.296403
$161$		−	3.01254e70i		−	0.725278i
$162$	4.46956e70	+	1.61792e70i	0.882641	+	0.319503i
$163$	1.06209e70			0.172249			0.0861245	−	0.996284i	$-0.472552\pi$
$163$	1.06209e70			0.172249			0.0861245	+	0.996284i	$0.472552\pi$
$164$		−	8.90245e69i		−	0.118715i
$165$	3.34435e70	+	1.05907e71i	0.367135	+	1.16263i
$166$	1.18267e71			1.07005
$167$			1.34253e71i			1.00230i	0.865361	+	0.501149i	$0.167089\pi$
$167$			1.34253e71i			1.00230i	−0.865361	+	0.501149i	$0.832911\pi$
$168$	−1.01799e71	+	3.21463e70i	−0.627838	+	0.198259i
$169$	−1.87237e71			−0.955029
$170$			1.52446e71i			0.643798i
$171$	6.28380e70	−	4.40818e70i	0.219962	−	0.154306i
$172$	−8.09407e70			−0.235102
$173$			3.96208e70i			0.0955977i	0.998857	+	0.0477989i	$0.0152206\pi$
$173$			3.96208e70i			0.0955977i	−0.998857	+	0.0477989i	$0.984779\pi$
$174$	−3.50002e69	−	1.10837e70i	−0.00702255	−	0.0222387i
$175$	−2.14659e71			−0.358536
$176$			6.05750e71i			0.843117i
$177$	−3.08280e71	+	9.73489e70i	−0.357932	+	0.113028i
$178$	7.04914e71			0.683433
$179$		−	8.90068e71i		−	0.721317i	−0.932698	−	0.360659i	$-0.882552\pi$
$179$		−	8.90068e71i		−	0.721317i	0.932698	−	0.360659i	$-0.117448\pi$
$180$	−1.26216e71	−	1.79919e71i	−0.0855841	−	0.121999i
$181$	−1.48768e72			−0.844881			−0.422441	−	0.906391i	$-0.638827\pi$
$181$	−1.48768e72			−0.844881			−0.422441	+	0.906391i	$0.638827\pi$
$182$		−	2.62097e71i		−	0.124789i
$183$	−6.76469e71	−	2.14221e72i	−0.270279	−	0.855908i
$184$	3.62062e72			1.21510
$185$		−	2.04019e72i		−	0.575672i
$186$	7.08254e72	−	2.23653e72i	1.68180	−	0.531081i
$187$	−2.65954e72			−0.531955
$188$			1.31112e72i			0.221101i
$189$	−3.49842e72	−	2.67713e72i	−0.497845	−	0.380970i
$190$	2.63089e72			0.316219
$191$			1.28776e72i			0.130848i	0.997858	+	0.0654238i	$0.0208399\pi$
$191$			1.28776e72i			0.130848i	−0.997858	+	0.0654238i	$0.979160\pi$
$192$	−3.81402e72	−	1.20781e73i	−0.327902	−	1.03838i
$193$	2.25674e72			0.164304			0.0821518	−	0.996620i	$-0.473821\pi$
$193$	2.25674e72			0.164304			0.0821518	+	0.996620i	$0.473821\pi$
$194$			2.58535e73i			1.59538i
$195$	4.84339e72	−	1.52945e72i	0.253537	−	0.0800623i
$196$	−1.62343e72			−0.0721505
$197$		−	7.61719e72i		−	0.287658i	−0.989603	−	0.143829i	$-0.954059\pi$
$197$		−	7.61719e72i		−	0.287658i	0.989603	−	0.143829i	$-0.0459415\pi$
$198$	−2.32686e73	+	1.63233e73i	−0.747280	+	0.524228i
$199$	−3.07876e73			−0.841544			−0.420772	−	0.907166i	$-0.638241\pi$
$199$	−3.07876e73			−0.841544			−0.420772	+	0.907166i	$0.638241\pi$
$200$		−	2.57989e73i		−	0.600677i
$201$	2.68163e73	+	8.49205e73i	0.532261	+	1.68554i
$202$	−7.79029e73			−1.31920
$203$			1.07719e72i			0.0155746i
$204$	5.01854e72	−	1.58476e72i	0.0620029	−	0.0195793i
$205$	1.18524e74			1.25222
$206$			3.05936e73i			0.276617i
$207$	8.58026e73	+	1.22310e74i	0.664430	+	0.947136i
$208$	2.77024e73			0.183861
$209$			4.58980e73i			0.261284i
$210$	−4.54664e73	−	1.43981e74i	−0.222164	−	0.703538i
$211$	1.48249e74			0.622234			0.311117	−	0.950372i	$-0.399297\pi$
$211$	1.48249e74			0.622234			0.311117	+	0.950372i	$0.399297\pi$
$212$			3.97948e73i			0.143575i
$213$	−8.44278e73	+	2.66607e73i	−0.262022	+	0.0827416i
$214$	−4.94778e74			−1.32181
$215$		−	1.07761e75i		−	2.47988i
$216$	3.21751e74	−	4.20458e74i	0.638264	−	0.834071i
$217$	−6.88327e74			−1.17783
$218$		−	2.71213e74i		−	0.400593i
$219$	2.01278e74	+	6.37398e74i	0.256794	+	0.813203i
$220$	1.31416e74			0.144918
$221$			1.21627e74i			0.116005i
$222$	4.97892e74	−	1.57225e74i	0.410998	−	0.129785i
$223$	2.42586e75			1.73424			0.867122	−	0.498097i	$-0.165968\pi$
$223$	2.42586e75			1.73424			0.867122	+	0.498097i	$0.165968\pi$
$224$			2.39217e74i			0.148203i
$225$	8.71527e74	−	6.11390e74i	0.468210	−	0.328456i
$226$	−2.15078e75			−1.00259
$227$			1.10669e75i			0.447917i	0.974599	+	0.223959i	$0.0718980\pi$
$227$			1.10669e75i			0.447917i	−0.974599	+	0.223959i	$0.928102\pi$
$228$	−2.73496e73	−	8.66095e73i	−0.00961693	−	0.0304544i
$229$	−2.23301e75			−0.682581			−0.341291	−	0.939958i	$-0.610864\pi$
$229$	−2.23301e75			−0.682581			−0.341291	+	0.939958i	$0.610864\pi$
$230$			5.12087e75i			1.36161i
$231$	2.51186e75	−	7.93199e74i	0.581317	−	0.183569i
$232$	−1.29462e74			−0.0260931
$233$			3.19241e75i			0.560698i	0.959898	+	0.280349i	$0.0904502\pi$
$233$			3.19241e75i			0.560698i	−0.959898	+	0.280349i	$0.909550\pi$
$234$	7.46501e74	+	1.06413e75i	0.114320	+	0.162962i
$235$	−1.74557e76			−2.33220
$236$			3.82532e74i			0.0446152i
$237$	−2.12017e75	−	6.71406e75i	−0.215985	−	0.683972i
$238$	3.61564e75			0.321901
$239$			1.70002e76i			1.32349i	0.749730	+	0.661744i	$0.230184\pi$
$239$			1.70002e76i			1.32349i	−0.749730	+	0.661744i	$0.769816\pi$
$240$	1.52181e76	−	4.80558e75i	1.03657	−	0.327330i
$241$	−9.50971e75			−0.567051			−0.283525	−	0.958965i	$-0.591504\pi$
$241$	−9.50971e75			−0.567051			−0.283525	+	0.958965i	$0.591504\pi$
$242$			9.76922e74i			0.0510232i
$243$	2.18287e76	+	9.05123e74i	0.999141	+	0.0414292i
$244$	−2.65818e75			−0.106687
$245$		−	2.16137e76i		−	0.761051i
$246$	9.13387e75	+	2.89247e76i	0.282313	+	0.894017i
$247$	2.09903e75			0.0569791
$248$		−	8.27267e76i		−	1.97330i
$249$	5.18348e76	−	1.63684e76i	1.08703	−	0.343264i
$250$	−2.73108e76			−0.503795
$251$		−	5.86102e76i		−	0.951512i	−0.879577	−	0.475756i	$-0.842174\pi$
$251$		−	5.86102e76i		−	0.951512i	0.879577	−	0.475756i	$-0.157826\pi$
$252$	−4.26723e75	+	2.99353e75i	−0.0609999	+	0.0427924i
$253$	−8.93378e76			−1.12507
$254$			3.47275e76i			0.385473i
$255$	2.10988e76	+	6.68148e76i	0.206525	+	0.654014i
$256$	−4.06833e76			−0.351348
$257$		−	2.80888e76i		−	0.214128i	−0.994252	−	0.107064i	$-0.965855\pi$
$257$		−	2.80888e76i		−	0.214128i	0.994252	−	0.107064i	$-0.0341450\pi$
$258$	2.62983e77	−	8.30449e76i	1.77050	−	0.559091i
$259$	−4.83883e76			−0.287838
$260$		−	6.00996e75i		−	0.0316027i
$261$	−3.06802e75	−	4.37342e75i	−0.0142680	−	0.0203388i
$262$	−3.42295e77			−1.40851
$263$			3.49339e77i			1.27251i	0.771477	+	0.636257i	$0.219518\pi$
$263$			3.49339e77i			1.27251i	−0.771477	+	0.636257i	$0.780482\pi$
$264$	9.53308e76	+	3.01889e77i	0.307544	+	0.973917i
$265$	−5.29811e77			−1.51444
$266$		−	6.23984e76i		−	0.158111i
$267$	3.08954e77	−	9.75618e76i	0.694278	−	0.219240i
$268$	1.05374e77			0.210098
$269$			6.61485e76i			0.117070i	0.998285	+	0.0585352i	$0.0186430\pi$
$269$			6.61485e76i			0.117070i	−0.998285	+	0.0585352i	$0.981357\pi$
$270$	5.94680e77	+	4.55073e77i	0.934637	+	0.715221i
$271$	6.35626e77			0.887533			0.443767	−	0.896142i	$-0.353642\pi$
$271$	6.35626e77			0.887533			0.443767	+	0.896142i	$0.353642\pi$
$272$			3.82155e77i			0.474280i
$273$	−3.62749e76	−	1.14874e77i	−0.0400314	−	0.126770i
$274$	−6.92609e77			−0.679939
$275$			6.36580e77i			0.556169i
$276$	1.68580e77	−	5.32344e76i	0.131134	−	0.0414097i
$277$	−2.86999e78			−1.98851			−0.994255	−	0.107040i	$-0.965863\pi$
$277$	−2.86999e78			−1.98851			−0.994255	+	0.107040i	$0.965863\pi$
$278$		−	1.81978e78i		−	1.12353i
$279$	2.79464e78	−	1.96048e78i	1.53812	−	1.07902i
$280$	−1.68175e78			−0.825476
$281$			1.64781e78i			0.721613i	0.932641	+	0.360807i	$0.117499\pi$
$281$			1.64781e78i			0.721613i	−0.932641	+	0.360807i	$0.882501\pi$
$282$	−1.34520e78	−	4.25993e78i	−0.525795	−	1.66506i
$283$	2.98655e78			1.04233			0.521163	−	0.853457i	$-0.325498\pi$
$283$	2.98655e78			1.04233			0.521163	+	0.853457i	$0.325498\pi$
$284$			1.04763e77i			0.0326603i
$285$	1.15308e78	−	3.64122e77i	0.321237	−	0.101440i
$286$	−7.77258e77			−0.193576
$287$		−	2.81109e78i		−	0.626115i
$288$	−6.81335e77	−	9.71234e77i	−0.135769	−	0.193537i
$289$	3.92916e78			0.700759
$290$		−	1.83106e77i		−	0.0292392i
$291$	3.57819e78	+	1.13312e79i	0.511785	+	1.62070i
$292$	7.90920e77			0.101363
$293$			8.14901e77i			0.0936141i	0.998904	+	0.0468070i	$0.0149046\pi$
$293$			8.14901e77i			0.0936141i	−0.998904	+	0.0468070i	$0.985095\pi$
$294$	5.27465e78	−	1.66563e78i	0.543349	−	0.171579i
$295$	−5.09287e78			−0.470606
$296$		−	5.81556e78i		−	0.482233i
$297$	−7.93911e78	+	1.03747e79i	−0.590970	+	0.772268i
$298$	2.47934e77			0.0165736
$299$			4.08563e78i			0.245347i
$300$	−3.79324e77	−	1.20123e78i	−0.0204706	−	0.0648253i
$301$	−2.55583e79			−1.23995
$302$			2.44000e79i			1.06456i
$303$	−3.41437e79	+	1.07819e79i	−1.34013	+	0.423188i
$304$	6.59520e78			0.232956
$305$		−	3.53899e79i		−	1.12534i
$306$	−1.46797e79	+	1.02980e79i	−0.420369	+	0.294895i
$307$	2.30771e79			0.595324			0.297662	−	0.954671i	$-0.403793\pi$
$307$	2.30771e79			0.595324			0.297662	+	0.954671i	$0.403793\pi$
$308$		−	3.11687e78i		−	0.0724595i
$309$	4.23422e78	+	1.34087e79i	0.0887365	+	0.281007i
$310$	1.17006e80			2.21122
$311$			7.16854e79i			1.22208i	0.791601	+	0.611038i	$0.209248\pi$
$311$			7.16854e79i			1.22208i	−0.791601	+	0.611038i	$0.790752\pi$
$312$	1.38061e79	−	4.35970e78i	0.212385	−	0.0670672i
$313$	2.75726e79			0.382877			0.191438	−	0.981505i	$-0.438685\pi$
$313$	2.75726e79			0.382877			0.191438	+	0.981505i	$0.438685\pi$
$314$		−	7.91430e79i		−	0.992348i
$315$	−3.98546e79	−	5.68122e79i	−0.451379	−	0.643434i
$316$	−8.33120e78			−0.0852552
$317$		−	4.63917e77i		−	0.00429085i	−0.999998	−	0.00214543i	$-0.999317\pi$
$317$		−	4.63917e77i		−	0.00429085i	0.999998	−	0.00214543i	$-0.000682911\pi$
$318$	−4.08292e79	−	1.29296e80i	−0.341431	−	1.08123i
$319$	3.19443e78			0.0241597
$320$		−	1.99533e80i		−	1.36526i
$321$	−2.16854e80	+	6.84785e79i	−1.34279	+	0.424027i
$322$	1.21455e80			0.680811
$323$			2.89561e79i			0.146981i
$324$	8.79905e78	−	2.43077e79i	0.0404572	−	0.111765i
$325$	2.91123e79			0.121286
$326$			4.28195e79i			0.161688i
$327$	−3.75365e79	−	1.18869e80i	−0.128507	−	0.406949i
$328$	3.37851e80			1.04897
$329$			4.14007e80i			1.16611i
$330$	−4.26980e80	+	1.34832e80i	−1.09134	+	0.344626i
$331$	7.82463e79			0.181538			0.0907691	−	0.995872i	$-0.471067\pi$
$331$	7.82463e79			0.181538			0.0907691	+	0.995872i	$0.471067\pi$
$332$		−	6.43196e79i		−	0.135495i
$333$	1.96459e80	−	1.37819e80i	0.375886	−	0.263690i
$334$	−5.41259e80			−0.940846
$335$			1.40291e81i			2.21613i
$336$	−1.13977e80	−	3.60936e80i	−0.163666	−	0.518290i
$337$	1.40682e81			1.83688			0.918441	−	0.395558i	$-0.129449\pi$
$337$	1.40682e81			1.83688			0.918441	+	0.395558i	$0.129449\pi$
$338$		−	7.54871e80i		−	0.896476i
$339$	−9.42655e80	+	2.97672e80i	−1.01850	+	0.321624i
$340$	8.29077e79			0.0815210
$341$			2.04126e81i			1.82708i
$342$	1.77722e80	+	2.53340e80i	0.144846	+	0.206476i
$343$	−1.35713e81			−1.00742
$344$		−	3.07173e81i		−	2.07737i
$345$	7.08741e80	+	2.24441e81i	0.436794	+	1.38322i
$346$	−1.59737e80			−0.0897366
$347$		−	2.15437e81i		−	1.10351i	−0.834006	−	0.551755i	$-0.813958\pi$
$347$		−	2.15437e81i		−	1.10351i	0.834006	−	0.551755i	$-0.186042\pi$
$348$	−6.02788e78	+	1.90349e78i	−0.00281598	+	0.000889231i
$349$	−3.32585e80			−0.141739			−0.0708695	−	0.997486i	$-0.522577\pi$
$349$	−3.32585e80			−0.141739			−0.0708695	+	0.997486i	$0.522577\pi$
$350$		−	8.65430e80i		−	0.336554i
$351$	4.74459e80	+	3.63074e80i	0.168411	+	0.128875i
$352$	7.09407e80			0.229896
$353$		−	3.13929e81i		−	0.929055i	−0.885559	−	0.464528i	$-0.846224\pi$
$353$		−	3.13929e81i		−	0.929055i	0.885559	−	0.464528i	$-0.153776\pi$
$354$	−3.92476e80	−	1.24287e81i	−0.106098	−	0.335987i
$355$	−1.39477e81			−0.344505
$356$		−	3.83368e80i		−	0.0865398i
$357$	1.58468e81	−	5.00413e80i	0.327009	−	0.103263i
$358$	3.58844e81			0.677093
$359$			2.41993e81i			0.417619i	0.977956	+	0.208809i	$0.0669588\pi$
$359$			2.41993e81i			0.417619i	−0.977956	+	0.208809i	$0.933041\pi$
$360$	6.82799e81	−	4.78994e81i	1.07798	−	0.756223i
$361$	−6.42226e81			−0.927806
$362$		−	5.99780e81i		−	0.793081i
$363$	1.35208e80	+	4.28171e80i	0.0163678	+	0.0518329i
$364$	−1.42542e80			−0.0158015
$365$			1.05300e82i			1.06919i
$366$	8.63662e81	−	2.72728e81i	0.803432	−	0.253708i
$367$	−1.52534e82			−1.30032			−0.650161	−	0.759796i	$-0.725299\pi$
$367$	−1.52534e82			−1.30032			−0.650161	+	0.759796i	$0.725299\pi$
$368$			1.28372e82i			1.00309i
$369$	8.00650e81	+	1.14132e82i	0.573587	+	0.817640i
$370$	8.22531e81			0.540377
$371$			1.25658e82i			0.757227i
$372$	−1.21634e81	−	3.85185e81i	−0.0672482	−	0.212959i
$373$	−1.77178e82			−0.898931			−0.449465	−	0.893298i	$-0.648386\pi$
$373$	−1.77178e82			−0.898931			−0.449465	+	0.893298i	$0.648386\pi$
$374$		−	1.07223e82i		−	0.499340i
$375$	−1.19699e82	+	3.77987e81i	−0.511789	+	0.161613i
$376$	−4.97575e82			−1.95365
$377$		−	1.46089e80i		−	0.00526858i
$378$	1.07932e82	−	1.41044e82i	0.357613	−	0.467322i
$379$	1.32298e82			0.402808			0.201404	−	0.979508i	$-0.435450\pi$
$379$	1.32298e82			0.402808			0.201404	+	0.979508i	$0.435450\pi$
$380$		−	1.43081e81i		−	0.0400413i
$381$	4.80636e81	+	1.52206e82i	0.123657	+	0.391590i
$382$	−5.19177e81			−0.122825
$383$			6.77011e82i			1.47311i	0.676378	+	0.736555i	$0.263549\pi$
$383$			6.77011e82i			1.47311i	−0.676378	+	0.736555i	$0.736451\pi$
$384$	3.74322e82	−	1.18204e82i	0.749283	−	0.236609i
$385$	4.14967e82			0.764311
$386$			9.09835e81i			0.154230i
$387$	1.03768e83	−	7.27948e82i	1.61924	−	1.13592i
$388$	1.40605e82			0.202015
$389$		−	8.55613e82i		−	1.13211i	−0.824366	−	0.566057i	$-0.808468\pi$
$389$		−	8.55613e82i		−	1.13211i	0.824366	−	0.566057i	$-0.191532\pi$
$390$	6.16620e81	+	1.95268e82i	0.0751536	+	0.237993i
$391$	−5.63614e82			−0.632886
$392$		−	6.16098e82i		−	0.637523i
$393$	−1.50023e83	+	4.73745e82i	−1.43086	+	0.451838i
$394$	3.07098e82			0.270021
$395$		−	1.10918e83i		−	0.899281i
$396$	8.87741e81	+	1.26546e82i	0.0663805	+	0.0946245i
$397$	−6.71946e82			−0.463488			−0.231744	−	0.972777i	$-0.574443\pi$
$397$	−6.71946e82			−0.463488			−0.231744	+	0.972777i	$0.574443\pi$
$398$		−	1.24124e83i		−	0.789949i
$399$	−8.63608e81	−	2.73483e82i	−0.0507205	−	0.160619i
$400$	9.14717e82			0.495869
$401$		−	6.20773e82i		−	0.310680i	−0.987861	−	0.155340i	$-0.950353\pi$
$401$		−	6.20773e82i		−	0.310680i	0.987861	−	0.155340i	$-0.0496473\pi$
$402$	−3.42369e83	+	1.08114e83i	−1.58220	+	0.499628i
$403$	9.33515e82			0.398437
$404$			4.23675e82i			0.167044i
$405$	3.23623e83	+	1.17147e83i	1.17891	+	0.426747i
$406$	−4.34282e81			−0.0146197
$407$			1.43497e83i			0.446501i
$408$	6.01423e82	+	1.90456e83i	0.173003	+	0.547859i
$409$	1.71390e83			0.455870			0.227935	−	0.973676i	$-0.426803\pi$
$409$	1.71390e83			0.455870			0.227935	+	0.973676i	$0.426803\pi$
$410$			4.77844e83i			1.17545i
$411$	−3.03561e83	+	9.58587e82i	−0.690729	+	0.218119i
$412$	1.66383e82			0.0350267
$413$			1.20790e83i			0.235305i
$414$	−4.93112e83	+	3.45925e83i	−0.889067	+	0.623694i
$415$	8.56324e83			1.42922
$416$		−	3.24429e82i		−	0.0501341i
$417$	−2.51862e83	−	7.97583e83i	−0.360419	−	1.14136i
$418$	−1.85044e83			−0.245265
$419$			2.07793e83i			0.255142i	0.991829	+	0.127571i	$0.0407181\pi$
$419$			2.07793e83i			0.255142i	−0.991829	+	0.127571i	$0.959282\pi$
$420$	−7.83042e82	+	2.47270e82i	−0.0890856	+	0.0281315i
$421$	7.29102e83			0.768708			0.384354	−	0.923186i	$-0.374424\pi$
$421$	7.29102e83			0.768708			0.384354	+	0.923186i	$0.374424\pi$
$422$			5.97688e83i			0.584085i
$423$	−1.17917e84	−	1.68089e84i	−1.06828	−	1.52281i
$424$	−1.51023e84			−1.26863
$425$			4.01605e83i			0.312863i
$426$	−1.07486e83	−	3.40383e83i	−0.0776687	−	0.245958i
$427$	−8.39362e83			−0.562675
$428$			2.69086e83i			0.167375i
$429$	−3.40661e83	+	1.07574e83i	−0.196648	+	0.0620977i
$430$	4.34454e84			2.32784
$431$		−	3.36771e84i		−	1.67518i	−0.546299	−	0.837590i	$-0.683964\pi$
$431$		−	3.36771e84i		−	1.67518i	0.546299	−	0.837590i	$-0.316036\pi$
$432$	1.49076e84	+	1.14079e84i	0.688539	+	0.526897i
$433$	3.05000e84			1.30824			0.654119	−	0.756391i	$-0.273039\pi$
$433$	3.05000e84			1.30824			0.654119	+	0.756391i	$0.273039\pi$
$434$		−	2.77509e84i		−	1.10562i
$435$	−2.53423e82	−	8.02527e82i	−0.00937971	−	0.0297032i
$436$	−1.47500e83			−0.0507251
$437$			9.72679e83i			0.310859i
$438$	−2.56976e84	+	8.11481e83i	−0.763345	+	0.241050i
$439$	−5.46827e84			−1.51003			−0.755014	−	0.655708i	$-0.772370\pi$
$439$	−5.46827e84			−1.51003			−0.755014	+	0.655708i	$0.772370\pi$
$440$			4.98729e84i			1.28050i
$441$	2.08128e84	−	1.46005e84i	0.496930	−	0.348604i
$442$	−4.90356e83			−0.108893
$443$		−	8.93153e84i		−	1.84504i	−0.385946	−	0.922521i	$-0.626125\pi$
$443$		−	8.93153e84i		−	1.84504i	0.385946	−	0.922521i	$-0.373875\pi$
$444$	−8.55068e82	−	2.70779e83i	−0.0164341	−	0.0520427i
$445$	5.10400e84			0.912832
$446$			9.78019e84i			1.62792i
$447$	1.08666e83	−	3.43147e82i	0.0168366	−	0.00531667i
$448$	−4.73243e84			−0.682634
$449$			5.16344e84i			0.693516i	0.937955	+	0.346758i	$0.112718\pi$
$449$			5.16344e84i			0.693516i	−0.937955	+	0.346758i	$0.887282\pi$
$450$	2.46490e84	+	3.51369e84i	0.308318	+	0.439504i
$451$	−8.33638e84			−0.971244
$452$			1.16970e84i			0.126954i
$453$	3.37702e84	+	1.06942e85i	0.341501	+	1.08145i
$454$	−4.46177e84			−0.420455
$455$		−	1.89774e84i		−	0.166676i
$456$	3.28687e84	−	1.03793e84i	0.269096	−	0.0849753i
$457$	−9.25266e84			−0.706233			−0.353117	−	0.935579i	$-0.614878\pi$
$457$	−9.25266e84			−0.706233			−0.353117	+	0.935579i	$0.614878\pi$
$458$		−	9.00268e84i		−	0.640732i
$459$	−5.00862e84	+	6.54517e84i	−0.332439	+	0.434425i
$460$	2.78499e84			0.172414
$461$		−	1.64845e85i		−	0.952018i	−0.879441	−	0.476009i	$-0.842083\pi$
$461$		−	1.64845e85i		−	0.952018i	0.879441	−	0.476009i	$-0.157917\pi$
$462$	3.19789e84	+	1.01269e85i	0.172314	+	0.545676i
$463$	−1.00569e85			−0.505678			−0.252839	−	0.967508i	$-0.581364\pi$
$463$	−1.00569e85			−0.505678			−0.252839	+	0.967508i	$0.581364\pi$
$464$		−	4.59015e83i		−	0.0215403i
$465$	5.12819e85	−	1.61938e85i	2.24631	−	0.709342i
$466$	−1.28707e85			−0.526322
$467$			3.16877e85i			1.20990i	0.796263	+	0.604951i	$0.206807\pi$
$467$			3.16877e85i			1.20990i	−0.796263	+	0.604951i	$0.793193\pi$
$468$	5.78726e83	−	4.05985e83i	0.0206351	−	0.0144758i
$469$	3.32736e85			1.10807
$470$		−	7.03752e85i		−	2.18921i
$471$	−1.09536e85	−	3.46873e85i	−0.318337	−	1.00809i
$472$	−1.45172e85			−0.394221
$473$			7.57941e85i			1.92344i
$474$	2.70687e85	−	8.54778e84i	0.642038	−	0.202743i
$475$	6.93086e84			0.153671
$476$		−	1.96637e84i		−	0.0407608i
$477$	−3.57898e85	−	5.10178e85i	−0.693699	−	0.988858i
$478$	−6.85386e85			−1.24235
$479$		−	3.25020e85i		−	0.551029i	−0.961297	−	0.275514i	$-0.911152\pi$
$479$		−	3.25020e85i		−	0.551029i	0.961297	−	0.275514i	$-0.0888482\pi$
$480$	−5.62792e84	−	1.78222e85i	−0.0892542	−	0.282646i
$481$	6.56247e84			0.0973699
$482$		−	3.83397e85i		−	0.532285i
$483$	5.32319e85	−	1.68096e85i	0.691614	−	0.218398i
$484$	5.31300e83			0.00646082
$485$			1.87195e86i			2.13088i
$486$	−3.64913e84	+	8.80055e85i	−0.0388892	+	0.937884i
$487$	−1.16139e86			−1.15892			−0.579459	−	0.815001i	$-0.696736\pi$
$487$	−1.16139e86			−1.15892			−0.579459	+	0.815001i	$0.696736\pi$
$488$		−	1.00879e86i		−	0.942684i
$489$	5.92632e84	+	1.87672e85i	0.0518683	+	0.164254i
$490$	8.71386e85			0.714391
$491$			9.03597e85i			0.694012i	0.937863	+	0.347006i	$0.112802\pi$
$491$			9.03597e85i			0.694012i	−0.937863	+	0.347006i	$0.887198\pi$
$492$	1.57307e85	−	4.96747e84i	0.113205	−	0.0357480i
$493$	2.01530e84			0.0135906
$494$			8.46252e84i			0.0534857i
$495$	−1.68478e86	+	1.18190e86i	−0.998109	+	0.700189i
$496$	2.93313e86			1.62899
$497$			3.30805e85i			0.172254i
$498$	6.59916e85	+	2.08979e86i	0.322218	+	1.02038i
$499$	7.67339e85			0.351374			0.175687	−	0.984446i	$-0.443785\pi$
$499$	7.67339e85			0.351374			0.175687	+	0.984446i	$0.443785\pi$
$500$			1.48530e85i			0.0637931i
$501$	−2.37226e86	+	7.49116e85i	−0.955776	+	0.301816i
$502$	2.36295e86			0.893175
$503$		−	7.07583e85i		−	0.250959i	−0.992096	−	0.125479i	$-0.959953\pi$
$503$		−	7.07583e85i		−	0.250959i	0.992096	−	0.125479i	$-0.0400469\pi$
$504$	−1.13606e86	−	1.61943e86i	−0.378114	−	0.538996i
$505$	−5.64064e86			−1.76199
$506$		−	3.60178e86i		−	1.05609i
$507$	−1.04476e86	−	3.30850e86i	−0.287582	−	0.910701i
$508$	1.88866e85			0.0488106
$509$		−	1.33731e86i		−	0.324537i	−0.986747	−	0.162268i	$-0.948119\pi$
$509$		−	1.33731e86i		−	0.324537i	0.986747	−	0.162268i	$-0.0518810\pi$
$510$	−2.69373e86	+	8.50629e85i	−0.613916	+	0.193863i
$511$	2.49746e86			0.534600
$512$		−	5.54794e86i		−	1.11556i
$513$	1.12956e86	+	8.64383e85i	0.213380	+	0.163287i
$514$	1.13244e86			0.201000
$515$			2.21516e86i			0.369465i
$516$	−4.51640e85	−	1.43023e86i	−0.0707949	−	0.224190i
$517$	1.22775e87			1.80889
$518$		−	1.95084e86i		−	0.270191i
$519$	−7.00104e85	+	2.21079e85i	−0.0911605	+	0.0287868i
$520$	2.28081e86			0.279242
$521$			5.10044e86i			0.587220i	0.955925	+	0.293610i	$0.0948567\pi$
$521$			5.10044e86i			0.587220i	−0.955925	+	0.293610i	$0.905143\pi$
$522$	1.76321e85	−	1.23692e85i	0.0190918	−	0.0133932i
$523$	1.44838e87			1.47512			0.737560	−	0.675282i	$-0.235978\pi$
$523$	1.44838e87			1.47512			0.737560	+	0.675282i	$0.235978\pi$
$524$			1.86158e86i			0.178353i
$525$	−1.19778e86	−	3.79306e86i	−0.107964	−	0.341894i
$526$	−1.40841e87			−1.19450
$527$			1.28779e87i			1.02779i
$528$	−1.07037e87	+	3.38002e86i	−0.803984	+	0.253883i
$529$	−4.78832e86			−0.338533
$530$		−	2.13601e87i		−	1.42159i
$531$	−3.44033e86	−	4.90415e86i	−0.215564	−	0.307283i
$532$	−3.39354e85			−0.0200208
$533$			3.81242e86i			0.211802i
$534$	3.93334e86	+	1.24559e87i	0.205798	+	0.651712i
$535$	−3.58249e87			−1.76549
$536$			3.99900e87i			1.85643i
$537$	1.57276e87	−	4.96648e86i	0.687837	−	0.217206i
$538$	−2.66687e86			−0.109893
$539$			1.52020e87i			0.590284i
$540$	2.47492e86	−	3.23417e86i	0.0905650	−	0.118349i
$541$	1.76616e87			0.609140			0.304570	−	0.952490i	$-0.401487\pi$
$541$	1.76616e87			0.609140			0.304570	+	0.952490i	$0.401487\pi$
$542$			2.56262e87i			0.833118i
$543$	−8.30110e86	−	2.62875e87i	−0.254414	−	0.805666i
$544$	4.47551e86			0.129324
$545$		−	1.96375e87i		−	0.535054i
$546$	4.63129e86	−	1.46247e86i	0.118997	−	0.0375771i
$547$	5.33603e86			0.129307			0.0646537	−	0.997908i	$-0.479406\pi$
$547$	5.33603e86			0.129307			0.0646537	+	0.997908i	$0.479406\pi$
$548$			3.76676e86i			0.0860974i
$549$	3.40785e87	−	2.39066e87i	0.734794	−	0.515469i
$550$	−2.56646e87			−0.522070
$551$		−	3.47799e85i		−	0.00667539i
$552$	2.02027e87	+	6.39769e87i	0.365897	+	1.15870i
$553$	−2.63071e87			−0.449644
$554$		−	1.15708e88i		−	1.86659i
$555$	3.60504e87	−	1.13840e87i	0.548952	−	0.173349i
$556$	−9.89688e86			−0.142267
$557$		−	1.00171e88i		−	1.35949i	−0.733449	−	0.679744i	$-0.762091\pi$
$557$		−	1.00171e88i		−	1.35949i	0.733449	−	0.679744i	$-0.237909\pi$
$558$	7.90396e87	+	1.12670e88i	1.01286	+	1.44382i
$559$	3.46624e87			0.419451
$560$		−	5.96276e87i		−	0.681444i
$561$	−1.48399e87	−	4.69944e87i	−0.160184	−	0.507264i
$562$	−6.64337e87			−0.677371
$563$		−	1.01582e88i		−	0.978475i	−0.872151	−	0.489238i	$-0.837275\pi$
$563$		−	1.01582e88i		−	0.978475i	0.872151	−	0.489238i	$-0.162725\pi$
$564$	−2.31677e87	+	7.31590e86i	−0.210839	+	0.0665789i
$565$	−1.55729e88			−1.33912
$566$			1.20407e88i			0.978421i
$567$	2.77844e87	−	7.67555e87i	0.213375	−	0.589457i
$568$	−3.97579e87			−0.288587
$569$			1.74501e88i			1.19731i	0.801008	+	0.598654i	$0.204298\pi$
$569$			1.74501e88i			1.19731i	−0.801008	+	0.598654i	$0.795702\pi$
$570$	1.46801e87	+	4.64882e87i	0.0952210	+	0.301542i
$571$	1.31556e88			0.806780			0.403390	−	0.915028i	$-0.367832\pi$
$571$	1.31556e88			0.806780			0.403390	+	0.915028i	$0.367832\pi$
$572$			4.22712e86i			0.0245116i
$573$	−2.27548e87	+	7.18553e86i	−0.124774	+	0.0394013i
$574$	1.13333e88			0.587727
$575$			1.34905e88i			0.661694i
$576$	1.92139e88	−	1.34788e88i	0.891448	−	0.625364i
$577$	−3.70656e88			−1.62684			−0.813421	−	0.581675i	$-0.802398\pi$
$577$	−3.70656e88			−1.62684			−0.813421	+	0.581675i	$0.802398\pi$
$578$			1.58410e88i			0.657795i
$579$	1.25923e87	+	3.98768e87i	0.0494757	+	0.156677i
$580$	−9.95822e85			−0.00370242
$581$		−	2.03099e88i		−	0.714615i
$582$	−4.56835e88	+	1.44260e88i	−1.52133	+	0.480407i
$583$	3.72644e88			1.17463
$584$			3.00157e88i			0.895649i
$585$	5.40512e87	+	7.70492e87i	0.152692	+	0.217661i
$586$	−3.28539e87			−0.0878746
$587$			4.84133e88i			1.22616i	0.790023	+	0.613078i	$0.210069\pi$
$587$			4.84133e88i			1.22616i	−0.790023	+	0.613078i	$0.789931\pi$
$588$	−9.05856e86	−	2.86862e87i	−0.0217262	−	0.0688016i
$589$	2.22245e88			0.504827
$590$		−	2.05326e88i		−	0.441753i
$591$	1.34597e88	−	4.25031e87i	0.274306	−	0.0866206i
$592$	2.06195e88			0.398091
$593$		−	4.05836e88i		−	0.742335i	−0.928566	−	0.371168i	$-0.878958\pi$
$593$		−	4.05836e88i		−	0.742335i	0.928566	−	0.371168i	$-0.121042\pi$
$594$	−4.18270e88	−	3.20077e88i	−0.724920	−	0.554738i
$595$	2.61794e88			0.429949
$596$		−	1.34839e86i		−	0.00209863i
$597$	−1.71791e88	−	5.44020e88i	−0.253409	−	0.802484i
$598$	−1.64718e88			−0.230305
$599$		−	1.42376e88i		−	0.188702i	−0.995539	−	0.0943511i	$-0.969922\pi$
$599$		−	1.42376e88i		−	0.188702i	0.995539	−	0.0943511i	$-0.0300776\pi$
$600$	4.55870e88	−	1.43955e88i	0.572797	−	0.180878i
$601$	−5.94108e88			−0.707754			−0.353877	−	0.935292i	$-0.615137\pi$
$601$	−5.94108e88			−0.707754			−0.353877	+	0.935292i	$0.615137\pi$
$602$		−	1.03042e89i		−	1.16393i
$603$	−1.35092e89	+	9.47694e88i	−1.44703	+	1.01511i
$604$	1.32700e88			0.134799
$605$			7.07350e87i			0.0681495i
$606$	−4.34689e88	−	1.37655e89i	−0.397242	−	1.25797i
$607$	1.33450e89			1.15686			0.578428	−	0.815733i	$-0.303666\pi$
$607$	1.33450e89			1.15686			0.578428	+	0.815733i	$0.303666\pi$
$608$		−	7.72379e87i		−	0.0635208i
$609$	−1.90340e87	+	6.01057e86i	−0.0148517	+	0.00468989i
$610$	1.42679e89			1.05635
$611$		−	5.61480e88i		−	0.394471i
$612$	5.60058e87	+	7.98355e87i	0.0373411	+	0.0532293i
$613$	1.81992e89			1.15164			0.575822	−	0.817575i	$-0.304682\pi$
$613$	1.81992e89			1.15164			0.575822	+	0.817575i	$0.304682\pi$
$614$			9.30386e88i			0.558825i
$615$	6.61348e88	+	2.09432e89i	0.377074	+	1.19410i
$616$	1.18286e89			0.640253
$617$			1.12960e89i			0.580499i	0.956951	+	0.290249i	$0.0937383\pi$
$617$			1.12960e89i			0.580499i	−0.956951	+	0.290249i	$0.906262\pi$
$618$	−5.40592e88	+	1.70709e88i	−0.263778	+	0.0832961i
$619$	−9.79850e88			−0.454003			−0.227002	−	0.973894i	$-0.572892\pi$
$619$	−9.79850e88			−0.454003			−0.227002	+	0.973894i	$0.572892\pi$
$620$		−	6.36336e88i		−	0.279996i
$621$	−1.68247e89	+	2.19862e89i	−0.703099	+	0.918796i
$622$	−2.89010e89			−1.14715
$623$		−	1.21055e89i		−	0.456419i
$624$	1.54576e88	+	4.89504e88i	0.0553650	+	0.175327i
$625$	−3.65822e89			−1.24483
$626$			1.11163e89i			0.359402i
$627$	−8.11024e88	+	2.56106e88i	−0.249157	+	0.0786789i
$628$	−4.30420e88			−0.125656
$629$			9.05295e88i			0.251171i
$630$	2.29046e89	−	1.60680e89i	0.603985	−	0.423704i
$631$	−3.31504e88			−0.0830901			−0.0415451	−	0.999137i	$-0.513228\pi$
$631$	−3.31504e88			−0.0830901			−0.0415451	+	0.999137i	$0.513228\pi$
$632$		−	3.16172e89i		−	0.753316i
$633$	8.27214e88	+	2.61958e89i	0.187370	+	0.593353i
$634$	1.87035e87			0.00402778
$635$			2.51448e89i			0.514860i
$636$	−7.03178e88	+	2.22050e88i	−0.136911	+	0.0432338i
$637$	6.95225e88			0.128725
$638$			1.28788e88i			0.0226785i
$639$	−9.42195e88	−	1.34309e89i	−0.157802	−	0.224945i
$640$	6.18389e89			0.985151
$641$			6.93161e89i			1.05045i	0.850962	+	0.525227i	$0.176020\pi$
$641$			6.93161e89i			1.05045i	−0.850962	+	0.525227i	$0.823980\pi$
$642$	−2.76081e89	−	8.74279e89i	−0.398029	−	1.26046i
$643$	−6.09792e89			−0.836432			−0.418216	−	0.908348i	$-0.637344\pi$
$643$	−6.09792e89			−0.836432			−0.418216	+	0.908348i	$0.637344\pi$
$644$		−	6.60532e88i		−	0.0862077i
$645$	1.90415e90	−	6.01295e89i	2.36478	−	0.746753i
$646$	−1.16741e89			−0.137969
$647$		−	4.05302e89i		−	0.455871i	−0.973676	−	0.227935i	$-0.926803\pi$
$647$		−	4.05302e89i		−	0.455871i	0.973676	−	0.227935i	$-0.0731975\pi$
$648$	9.22488e89	+	3.33927e89i	0.987554	+	0.357480i
$649$	3.58208e89			0.365010
$650$			1.17370e89i			0.113849i
$651$	−3.84079e89	−	1.21628e90i	−0.354673	−	1.12316i
$652$	2.32874e88			0.0204738
$653$		−	7.91821e89i		−	0.662835i	−0.943484	−	0.331417i	$-0.892473\pi$
$653$		−	7.91821e89i		−	0.662835i	0.943484	−	0.331417i	$-0.107527\pi$
$654$	4.79237e89	−	1.51334e89i	0.381999	−	0.120628i
$655$	−2.47842e90			−1.88128
$656$			1.19787e90i			0.865941i
$657$	−1.01398e90	+	7.11321e89i	−0.698131	+	0.489750i
$658$	−1.66913e90			−1.09461
$659$		−	2.26922e90i		−	1.41756i	−0.705427	−	0.708782i	$-0.749245\pi$
$659$		−	2.26922e90i		−	1.41756i	0.705427	−	0.708782i	$-0.250755\pi$
$660$	7.33286e88	+	2.32214e89i	0.0436383	+	0.138192i
$661$	2.86139e89			0.162230			0.0811149	−	0.996705i	$-0.474152\pi$
$661$	2.86139e89			0.162230			0.0811149	+	0.996705i	$0.474152\pi$
$662$			3.15461e89i			0.170408i
$663$	−2.14916e89	+	6.78665e88i	−0.110621	+	0.0349319i
$664$	2.44095e90			1.19724
$665$		−	4.51802e89i		−	0.211181i
$666$	5.55636e89	+	7.92052e89i	0.247523	+	0.352840i
$667$	6.76969e88			0.0287437
$668$			2.94364e89i			0.119135i
$669$	1.35360e90	+	4.28652e90i	0.522222	+	1.65375i
$670$	−5.65603e90			−2.08026
$671$			2.48916e90i			0.872834i
$672$	−4.22700e89	+	1.33481e89i	−0.141324	+	0.0446274i
$673$	5.80761e90			1.85147			0.925733	−	0.378179i	$-0.123450\pi$
$673$	5.80761e90			1.85147			0.925733	+	0.378179i	$0.123450\pi$
$674$			5.67179e90i			1.72426i
$675$	1.56664e90	+	1.19885e90i	0.454200	+	0.347572i
$676$	−4.10537e89			−0.113516
$677$		−	6.66468e90i		−	1.75769i	−0.477109	−	0.878844i	$-0.658315\pi$
$677$		−	6.66468e90i		−	1.75769i	0.477109	−	0.878844i	$-0.341685\pi$
$678$	−1.20011e90	−	3.80045e90i	−0.301905	−	0.956058i
$679$	4.43981e90			1.06545
$680$			3.14638e90i			0.720321i
$681$	−1.95553e90	+	6.17519e89i	−0.427127	+	0.134879i
$682$	−8.22962e90			−1.71506
$683$			1.47127e90i			0.292570i	0.989242	+	0.146285i	$0.0467317\pi$
$683$			1.47127e90i			0.292570i	−0.989242	+	0.146285i	$0.953268\pi$
$684$	1.37779e89	−	9.66543e88i	0.0261450	−	0.0183411i
$685$	−5.01491e90			−0.908165
$686$		−	5.47145e90i		−	0.945651i
$687$	−1.24599e90	−	3.94575e90i	−0.205542	−	0.650899i
$688$	1.08910e91			1.71490
$689$		−	1.70419e90i		−	0.256155i
$690$	−9.04865e90	+	2.85739e90i	−1.29841	+	0.410014i
$691$	7.02981e90			0.963044			0.481522	−	0.876434i	$-0.340084\pi$
$691$	7.02981e90			0.963044			0.481522	+	0.876434i	$0.340084\pi$
$692$			8.68729e88i			0.0113629i
$693$	2.80318e90	+	3.99590e90i	0.350097	+	0.499058i
$694$	8.68563e90			1.03585
$695$		−	1.31763e91i		−	1.50065i
$696$	−7.22382e88	−	2.28760e89i	−0.00785726	−	0.0248820i
$697$	−5.25925e90			−0.546355
$698$		−	1.34086e90i		−	0.133049i
$699$	−5.64103e90	+	1.78133e90i	−0.534673	+	0.168840i
$700$	−4.70665e89			−0.0426162
$701$		−	9.17626e90i		−	0.793760i	−0.917871	−	0.396880i	$-0.870093\pi$
$701$		−	9.17626e90i		−	0.793760i	0.917871	−	0.396880i	$-0.129907\pi$
$702$	−1.46379e90	+	1.91285e90i	−0.120973	+	0.158086i
$703$	1.56235e90			0.123369
$704$			1.40342e91i			1.05892i
$705$	−9.74009e90	−	3.08445e91i	−0.702281	−	2.22395i
$706$	1.26565e91			0.872094
$707$			1.33782e91i			0.881003i
$708$	−6.75938e89	+	2.13448e89i	−0.0425444	+	0.0134347i
$709$	1.61343e90			0.0970669			0.0485334	−	0.998822i	$-0.484545\pi$
$709$	1.61343e90			0.0970669			0.0485334	+	0.998822i	$0.484545\pi$
$710$		−	5.62321e90i		−	0.323383i
$711$	1.06808e91	−	7.49274e90i	0.587187	−	0.411921i
$712$	1.45490e91			0.764667
$713$			4.32587e91i			2.17374i
$714$	2.01749e90	+	6.38888e90i	0.0969321	+	0.306960i
$715$	−5.62782e90			−0.258551
$716$		−	1.95157e90i		−	0.0857370i
$717$	−3.00395e91	+	9.48590e90i	−1.26206	+	0.398534i
$718$	−9.75628e90			−0.392014
$719$			2.11167e91i			0.811524i	0.913979	+	0.405762i	$0.132994\pi$
$719$			2.11167e91i			0.811524i	−0.913979	+	0.405762i	$0.867006\pi$
$720$	1.69830e91	+	2.42091e91i	0.624274	+	0.889894i
$721$	5.25382e90			0.184734
$722$		−	2.58922e91i		−	0.870922i
$723$	−5.30631e90	−	1.68038e91i	−0.170752	−	0.540731i
$724$	−3.26191e90			−0.100424
$725$		−	4.82377e89i		−	0.0142092i
$726$	−1.72623e90	+	5.45111e89i	−0.0486550	+	0.0153643i
$727$	−4.26565e91			−1.15049			−0.575247	−	0.817980i	$-0.695094\pi$
$727$	−4.26565e91			−1.15049			−0.575247	+	0.817980i	$0.695094\pi$
$728$		−	5.40952e90i		−	0.139622i
$729$	1.05808e91	+	3.90766e91i	0.261359	+	0.965242i
$730$	−4.24531e91			−1.00364
$731$			4.78169e91i			1.08200i
$732$	−1.48323e90	−	4.69703e90i	−0.0321259	−	0.101735i
$733$	2.29332e91			0.475486			0.237743	−	0.971328i	$-0.423592\pi$
$733$	2.29332e91			0.475486			0.237743	+	0.971328i	$0.423592\pi$
$734$		−	6.14960e91i		−	1.22060i
$735$	3.81916e91	−	1.20602e91i	0.725727	−	0.229171i
$736$	1.50339e91			0.273515
$737$		−	9.86740e91i		−	1.71887i
$738$	−4.60137e91	+	3.22793e91i	−0.767510	+	0.538420i
$739$	4.37716e91			0.699150			0.349575	−	0.936908i	$-0.386326\pi$
$739$	4.37716e91			0.699150			0.349575	+	0.936908i	$0.386326\pi$
$740$		−	4.47334e90i		−	0.0684254i
$741$	1.17123e90	+	3.70900e90i	0.0171578	+	0.0543344i
$742$	−5.06609e91			−0.710801
$743$		−	9.54033e89i		−	0.0128210i	−0.999979	−	0.00641049i	$-0.997959\pi$
$743$		−	9.54033e89i		−	0.0128210i	0.999979	−	0.00641049i	$-0.00204054\pi$
$744$	1.46179e92	−	4.61606e91i	1.88170	−	0.594206i
$745$	1.79520e90			0.0221366
$746$		−	7.14317e91i		−	0.843817i
$747$	5.78464e91	+	8.24592e91i	0.654662	+	0.933212i
$748$	−5.83133e90			−0.0632291
$749$			8.49680e91i			0.882749i
$750$	−1.52391e91	−	4.82584e91i	−0.151705	−	0.480411i
$751$	−4.95401e91			−0.472584			−0.236292	−	0.971682i	$-0.575932\pi$
$751$	−4.95401e91			−0.472584			−0.236292	+	0.971682i	$0.575932\pi$
$752$		−	1.76419e92i		−	1.61277i
$753$	1.03565e92	−	3.27038e91i	0.907348	−	0.286523i
$754$	5.88978e89			0.00494556
$755$			1.76671e92i			1.42188i
$756$	−7.67067e90	−	5.86990e90i	−0.0591747	−	0.0452828i
$757$	−1.26297e92			−0.933955			−0.466977	−	0.884269i	$-0.654657\pi$
$757$	−1.26297e92			−0.933955			−0.466977	+	0.884269i	$0.654657\pi$
$758$			5.33377e91i			0.378112i
$759$	−4.98495e91	−	1.57861e92i	−0.338785	−	1.07285i
$760$	5.42999e91			0.353805
$761$			6.11994e91i			0.382330i	0.981558	+	0.191165i	$0.0612265\pi$
$761$			6.11994e91i			0.382330i	−0.981558	+	0.191165i	$0.938773\pi$
$762$	−6.13639e91	+	1.93775e91i	−0.367582	+	0.116075i
$763$	−4.65753e91			−0.267529
$764$			2.82355e90i			0.0155528i
$765$	−1.06290e92	+	7.45638e91i	−0.561468	+	0.393878i
$766$	−2.72947e92			−1.38279
$767$		−	1.63817e91i		−	0.0795990i
$768$	−2.27008e91	−	7.18879e91i	−0.105799	−	0.335040i
$769$	−6.72049e91			−0.300440			−0.150220	−	0.988653i	$-0.547998\pi$
$769$	−6.72049e91			−0.300440			−0.150220	+	0.988653i	$0.547998\pi$
$770$			1.67300e92i			0.717451i
$771$	4.96333e91	−	1.56733e91i	0.204190	−	0.0644791i
$772$	4.94815e90			0.0195294
$773$		−	3.14630e90i		−	0.0119140i	−0.999982	−	0.00595698i	$-0.998104\pi$
$773$		−	3.14630e90i		−	0.0119140i	0.999982	−	0.00595698i	$-0.00189618\pi$
$774$	2.93483e92	+	4.18355e92i	1.06628	+	1.51997i
$775$	3.08241e92			1.07457
$776$			5.33600e92i			1.78501i
$777$	−2.70001e91	−	8.55028e91i	−0.0866749	−	0.274478i
$778$	3.44953e92			1.06270
$779$			9.07637e91i			0.268357i
$780$	1.06197e91	−	3.35349e90i	0.0301359	−	0.00951634i
$781$	9.81015e91			0.267204
$782$		−	2.27229e92i		−	0.594084i
$783$	6.01597e90	−	7.86155e90i	0.0150983	−	0.0197302i
$784$	2.18442e92			0.526286
$785$		−	5.73043e92i		−	1.32544i
$786$	−1.90997e92	−	6.04840e92i	−0.424136	−	1.34313i
$787$	−6.49555e92			−1.38492			−0.692460	−	0.721456i	$-0.743473\pi$
$787$	−6.49555e92			−1.38492			−0.692460	+	0.721456i	$0.743473\pi$
$788$		−	1.67015e91i		−	0.0341915i
$789$	−6.17286e92	+	1.94927e92i	−1.21345	+	0.383185i
$790$	4.47182e92			0.844146
$791$			3.69352e92i			0.669565i
$792$	−4.80248e92	+	3.36901e92i	−0.836103	+	0.586539i
$793$	1.13835e92			0.190342
$794$		−	2.70905e92i		−	0.435071i
$795$	−2.95628e92	−	9.36182e92i	−0.456035	−	1.44415i
$796$	−6.75052e91			−0.100027
$797$		−	9.48826e92i		−	1.35058i	−0.737552	−	0.675290i	$-0.764018\pi$
$797$		−	9.48826e92i		−	1.35058i	0.737552	−	0.675290i	$-0.235982\pi$
$798$	1.10259e92	−	3.48176e91i	0.150772	−	0.0476109i
$799$	7.74564e92			1.01756
$800$		−	1.07125e92i		−	0.135210i
$801$	3.44786e92	+	4.91487e92i	0.418127	+	0.596035i
$802$	2.50273e92			0.291632
$803$		−	7.40629e92i		−	0.829284i
$804$	5.87977e91	+	1.86198e92i	0.0632655	+	0.200346i
$805$	8.79405e92			0.909329
$806$			3.76360e92i			0.374009i
$807$	−1.16885e92	+	3.69101e91i	−0.111637	+	0.0352527i
$808$	−1.60787e93			−1.47600
$809$		−	1.73106e92i		−	0.152743i	−0.997079	−	0.0763713i	$-0.975667\pi$
$809$		−	1.73106e92i		−	0.152743i	0.997079	−	0.0763713i	$-0.0243334\pi$
$810$	−4.72294e92	+	1.30473e93i	−0.400583	+	1.10663i
$811$	1.59212e93			1.29810			0.649049	−	0.760747i	$-0.275167\pi$
$811$	1.59212e93			1.29810			0.649049	+	0.760747i	$0.275167\pi$
$812$			2.36185e90i			0.00185122i
$813$	3.54672e92	+	1.12316e93i	0.267257	+	0.846338i
$814$	−5.78529e92			−0.419126
$815$			3.10039e92i			0.215960i
$816$	−6.75273e92	+	2.13238e92i	−0.452267	+	0.142817i
$817$	8.25220e92			0.531452
$818$			6.90985e92i			0.427920i
$819$	1.82742e92	−	1.28196e92i	0.108831	−	0.0763467i
$820$	2.59876e92			0.148841
$821$		−	6.31906e92i		−	0.348074i	−0.984739	−	0.174037i	$-0.944319\pi$
$821$		−	6.31906e92i		−	0.348074i	0.984739	−	0.174037i	$-0.0556813\pi$
$822$	−3.86468e92	−	1.22385e93i	−0.204746	−	0.648380i
$823$	7.46483e91			0.0380387			0.0190193	−	0.999819i	$-0.493946\pi$
$823$	7.46483e91			0.0380387			0.0190193	+	0.999819i	$0.493946\pi$
$824$			6.31432e92i			0.309496i
$825$	−1.12484e93	+	3.55204e92i	−0.530354	+	0.167476i
$826$	−4.86984e92			−0.220878
$827$			2.98896e93i			1.30420i	0.758133	+	0.652100i	$0.226112\pi$
$827$			2.98896e93i			1.30420i	−0.758133	+	0.652100i	$0.773888\pi$
$828$	1.88132e92	+	2.68179e92i	0.0789753	+	0.112578i
$829$	−3.47656e93			−1.40412			−0.702060	−	0.712117i	$-0.747736\pi$
$829$	−3.47656e93			−1.40412			−0.702060	+	0.712117i	$0.747736\pi$
$830$			3.45239e93i			1.34159i
$831$	−1.60142e93	−	5.07131e93i	−0.598788	−	1.89621i
$832$	6.41817e92			0.230922
$833$			9.59065e92i			0.332054i
$834$	3.21557e93	−	1.01542e93i	1.07138	−	0.338322i
$835$	−3.91905e93			−1.25665
$836$			1.00637e92i			0.0310567i
$837$	5.02357e93	+	3.84424e93i	1.49210	+	1.14181i
$838$	−8.37747e92			−0.239499
$839$		−	4.79104e93i		−	1.31840i	−0.751968	−	0.659200i	$-0.770895\pi$
$839$		−	4.79104e93i		−	1.31840i	0.751968	−	0.659200i	$-0.229105\pi$
$840$	−9.38398e92	−	2.97167e93i	−0.248571	−	0.787162i
$841$	3.91926e93			0.999383
$842$			2.93948e93i			0.721578i
$843$	−2.91170e93	+	9.19458e92i	−0.688119	+	0.217295i
$844$	3.25053e92			0.0739598
$845$		−	5.46573e93i		−	1.19738i
$846$	6.77674e93	−	4.75398e93i	1.42945	−	1.00278i
$847$	1.67766e92			0.0340750
$848$		−	5.35461e93i		−	1.04727i
$849$	1.66646e93	+	5.27727e93i	0.313869	+	0.993947i
$850$	−1.61913e93			−0.293681
$851$			3.04102e93i			0.531218i
$852$	−1.85117e92	+	5.84565e91i	−0.0311444	+	0.00983481i
$853$	2.81943e93			0.456870			0.228435	−	0.973559i	$-0.426639\pi$
$853$	2.81943e93			0.456870			0.228435	+	0.973559i	$0.426639\pi$
$854$		−	3.38401e93i		−	0.528177i
$855$	1.28681e93	+	1.83434e93i	0.193464	+	0.275780i
$856$	−1.02119e94			−1.47893
$857$		−	4.84459e93i		−	0.675882i	−0.941167	−	0.337941i	$-0.890270\pi$
$857$		−	4.84459e93i		−	0.675882i	0.941167	−	0.337941i	$-0.109730\pi$
$858$	−4.33701e92	−	1.37342e93i	−0.0582904	−	0.184591i
$859$	−9.15442e93			−1.18536			−0.592679	−	0.805439i	$-0.701930\pi$
$859$	−9.15442e93			−1.18536			−0.592679	+	0.805439i	$0.701930\pi$
$860$		−	2.36278e93i		−	0.294763i
$861$	4.96723e93	−	1.56856e93i	0.597054	−	0.188538i
$862$	1.35774e94			1.57247
$863$			3.42152e93i			0.381833i	0.981606	+	0.190916i	$0.0611459\pi$
$863$			3.42152e93i			0.381833i	−0.981606	+	0.190916i	$0.938854\pi$
$864$	1.33601e93	−	1.74587e93i	0.143671	−	0.187746i
$865$	−1.15659e93			−0.119857
$866$			1.22965e94i			1.22803i
$867$	2.19243e93	+	6.94287e93i	0.211015	+	0.668233i
$868$	−1.50923e93			−0.139999
$869$			7.80146e93i			0.697498i
$870$	3.23550e92	−	1.02171e92i	0.0278821	−	0.00880464i
$871$	−4.51260e93			−0.374840
$872$		−	5.59767e93i		−	0.448208i
$873$	−1.80259e94	+	1.26454e94i	−1.39136	+	0.976061i
$874$	−3.92149e93			−0.291800
$875$			4.69006e93i			0.336450i
$876$	4.41325e92	+	1.39757e93i	0.0305230	+	0.0966587i
$877$	−1.31321e94			−0.875684			−0.437842	−	0.899052i	$-0.644257\pi$
$877$	−1.31321e94			−0.875684			−0.437842	+	0.899052i	$0.644257\pi$
$878$		−	2.20461e94i		−	1.41745i
$879$	−1.43994e93	+	4.54706e92i	−0.0892690	+	0.0281894i
$880$	−1.76828e94			−1.05707
$881$			7.05859e93i			0.406901i	0.979085	+	0.203451i	$0.0652157\pi$
$881$			7.05859e93i			0.406901i	−0.979085	+	0.203451i	$0.934784\pi$
$882$	5.88639e93	+	8.39096e93i	0.327231	+	0.466463i
$883$	2.67231e94			1.43266			0.716332	−	0.697759i	$-0.245819\pi$
$883$	2.67231e94			1.43266			0.716332	+	0.697759i	$0.245819\pi$
$884$			2.66681e92i			0.0137886i
$885$	−2.84176e93	−	8.99916e93i	−0.141711	−	0.448763i
$886$	3.60087e94			1.73192
$887$			1.85073e94i			0.858595i	0.903163	+	0.429297i	$0.141239\pi$
$887$			1.85073e94i			0.858595i	−0.903163	+	0.429297i	$0.858761\pi$
$888$	1.02762e94	−	3.24502e93i	0.459850	−	0.145212i
$889$	5.96373e93			0.257432
$890$			2.05775e94i			0.856865i
$891$	−2.27621e94	−	8.23956e93i	−0.914379	−	0.330992i
$892$	5.31897e93			0.206135
$893$		−	1.33673e94i		−	0.499802i
$894$	1.38345e92	+	4.38103e92i	0.00499070	+	0.0158043i
$895$	2.59824e94			0.904363
$896$		−	1.46667e94i		−	0.492579i
$897$	−7.21935e93	+	2.27973e93i	−0.233959	+	0.0738799i
$898$	−2.08172e94			−0.650996
$899$		−	1.54679e93i		−	0.0466790i
$900$	1.91092e93	−	1.34054e93i	0.0556522	−	0.0390409i
$901$	2.35093e94			0.660765
$902$		−	3.36093e94i		−	0.911696i
$903$	−1.42613e94	−	4.51619e94i	−0.373379	−	1.18240i
$904$	−4.43906e94			−1.12176
$905$		−	4.34277e94i		−	1.05928i
$906$	−4.31152e94	+	1.36149e94i	−1.01514	+	0.320563i
$907$	7.13098e94			1.62075			0.810375	−	0.585912i	$-0.199263\pi$
$907$	7.13098e94			1.62075			0.810375	+	0.585912i	$0.199263\pi$
$908$			2.42654e93i			0.0532402i
$909$	−3.81036e94	−	5.43162e94i	−0.807091	−	1.15050i
$910$	7.65101e93			0.156457
$911$			7.27359e94i			1.43602i	0.696032	+	0.718010i	$0.254947\pi$
$911$			7.27359e94i			1.43602i	−0.696032	+	0.718010i	$0.745053\pi$
$912$	3.68005e93	+	1.16538e94i	0.0701485	+	0.222143i
$913$	−6.02298e94			−1.10853
$914$		−	3.73034e94i		−	0.662934i
$915$	6.25344e94	−	1.97472e94i	1.07311	−	0.338867i
$916$	−4.89611e93			−0.0811328
$917$			5.87822e94i			0.940648i
$918$	−2.63878e94	−	2.01930e94i	−0.407791	−	0.312057i
$919$	3.08336e94			0.460180			0.230090	−	0.973169i	$-0.426098\pi$
$919$	3.08336e94			0.460180			0.230090	+	0.973169i	$0.426098\pi$
$920$			1.05692e95i			1.52346i
$921$	1.28768e94	+	4.07775e94i	0.179266	+	0.567692i
$922$	6.64594e94			0.893649
$923$		−	4.48641e93i		−	0.0582700i
$924$	5.50754e93	−	1.73918e93i	0.0690963	−	0.0218193i
$925$	2.16689e94			0.262604
$926$		−	4.05459e94i		−	0.474674i
$927$	−2.13308e94	+	1.49638e94i	−0.241243	+	0.169236i
$928$	−5.37563e92			−0.00587346
$929$		−	2.95605e94i		−	0.312039i	−0.987754	−	0.156020i	$-0.950134\pi$
$929$		−	2.95605e94i		−	0.312039i	0.987754	−	0.156020i	$-0.0498663\pi$
$930$	6.52878e94	+	2.06750e95i	0.665852	+	2.10859i
$931$	1.65515e94			0.163097
$932$			6.99971e93i			0.0666455i
$933$	−1.26669e95	+	3.99997e94i	−1.16535	+	0.367996i
$934$	−1.27753e95			−1.13572
$935$		−	7.76360e94i		−	0.666947i
$936$	1.54073e94	+	2.19629e94i	0.127908	+	0.182332i
$937$	4.44512e94			0.356629			0.178315	−	0.983974i	$-0.442936\pi$
$937$	4.44512e94			0.356629			0.178315	+	0.983974i	$0.442936\pi$
$938$			1.34147e95i			1.04014i
$939$	1.53852e94	+	4.87211e94i	0.115293	+	0.365105i
$940$	−3.82736e94			−0.277209
$941$		−	2.35848e95i		−	1.65106i	−0.564355	−	0.825532i	$-0.690875\pi$
$941$		−	2.35848e95i		−	1.65106i	0.564355	−	0.825532i	$-0.309125\pi$
$942$	1.39847e95	−	4.41609e94i	0.946288	−	0.298820i
$943$	−1.76666e95			−1.15552
$944$		−	5.14718e94i		−	0.325436i
$945$	7.81494e94	−	1.02124e95i	0.477648	−	0.624181i
$946$	−3.05575e95			−1.80551
$947$		−	1.86527e94i		−	0.106548i	−0.998580	−	0.0532738i	$-0.983034\pi$
$947$		−	1.86527e94i		−	0.106548i	0.998580	−	0.0532738i	$-0.0169656\pi$
$948$	−4.64872e93	−	1.47213e94i	−0.0256724	−	0.0812981i
$949$	−3.38707e94			−0.180845
$950$			2.79428e94i			0.144249i
$951$	8.19747e92	−	2.58860e92i	0.00409169	−	0.00129208i
$952$	7.46245e94			0.360163
$953$		−	5.42713e94i		−	0.253278i	−0.991949	−	0.126639i	$-0.959581\pi$
$953$		−	5.42713e94i		−	0.253278i	0.991949	−	0.126639i	$-0.0404189\pi$
$954$	2.05686e95	−	1.44292e95i	0.928231	−	0.651168i
$955$	−3.75916e94			−0.164052
$956$			3.72748e94i			0.157312i
$957$	1.78246e93	+	5.64460e93i	0.00727506	+	0.0230383i
$958$	1.31037e95			0.517245
$959$			1.18941e95i			0.454085i
$960$	3.52577e95	−	1.11337e95i	1.30189	−	0.411112i
$961$	7.08413e95			2.53010
$962$			2.64575e94i			0.0914001i
$963$	−2.42005e95	−	3.44974e95i	−0.808691	−	1.15278i
$964$	−2.08511e94			−0.0674006
$965$			6.58776e94i			0.205998i
$966$	6.77703e94	+	2.14612e95i	0.205008	+	0.649211i
$967$	−1.76197e95			−0.515646			−0.257823	−	0.966192i	$-0.583005\pi$
$967$	−1.76197e95			−0.515646			−0.257823	+	0.966192i	$0.583005\pi$
$968$			2.01630e94i			0.0570879i
$969$	−5.11659e94	+	1.61572e94i	−0.140158	+	0.0442594i
$970$	−7.54704e95			−2.00023
$971$		−	2.02883e95i		−	0.520273i	−0.965572	−	0.260136i	$-0.916232\pi$
$971$		−	2.02883e95i		−	0.520273i	0.965572	−	0.260136i	$-0.0837675\pi$
$972$	4.78618e94	+	1.98458e93i	0.118760	+	0.00492435i
$973$	−3.12510e95			−0.750330
$974$		−	4.68233e95i		−	1.08786i
$975$	1.62443e94	+	5.14418e94i	0.0365220	+	0.115656i
$976$	3.57673e95			0.778201
$977$			6.80631e95i			1.43313i	0.697520	+	0.716566i	$0.254287\pi$
$977$			6.80631e95i			1.43313i	−0.697520	+	0.716566i	$0.745713\pi$
$978$	−7.56626e94	+	2.38928e94i	−0.154184	+	0.0486882i
$979$	−3.58991e95			−0.708008
$980$		−	4.73904e94i		−	0.0904599i
$981$	1.89098e95	−	1.32655e95i	0.349364	−	0.245084i
$982$	−3.64298e95			−0.651462
$983$			3.52900e95i			0.610857i	0.952215	+	0.305428i	$0.0987997\pi$
$983$			3.52900e95i			0.610857i	−0.952215	+	0.305428i	$0.901200\pi$
$984$	1.88517e95	+	5.96988e95i	0.315870	+	1.00028i
$985$	2.22358e95			0.360655
$986$			8.12497e93i			0.0127573i
$987$	−7.31555e95	+	2.31011e95i	−1.11198	+	0.351143i
$988$	4.60235e93			0.00677263
$989$			1.60624e96i			2.28839i
$990$	−4.76501e95	−	6.79245e95i	−0.657260	−	0.936915i
$991$	1.22601e96			1.63733			0.818665	−	0.574272i	$-0.194715\pi$
$991$	1.22601e96			1.63733			0.818665	+	0.574272i	$0.194715\pi$
$992$		−	3.43506e95i		−	0.444181i
$993$	4.36606e94	+	1.38262e95i	0.0546655	+	0.173112i
$994$	−1.33369e95			−0.161693
$995$		−	8.98736e95i		−	1.05510i
$996$	1.13653e95	−	3.58896e94i	0.129206	−	0.0408009i
$997$	6.56589e95			0.722851			0.361425	−	0.932401i	$-0.382290\pi$
$997$	6.56589e95			0.722851			0.361425	+	0.932401i	$0.382290\pi$
$998$			3.09364e95i			0.329831i
$999$	3.53149e95	+	2.70244e95i	0.364639	+	0.279036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.65.b.a.2.15	yes	20
3.2	odd	2	inner	3.65.b.a.2.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.65.b.a.2.6	✓	20	3.2	odd	2	inner
3.65.b.a.2.15	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 65 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.03164e9i q^{2} +(5.57989e14 + 1.76701e15i) q^{3} +2.19261e18 q^{4} +2.91915e22i q^{5} +(-7.12396e24 + 2.24961e24i) q^{6} +6.92352e26 q^{7} +8.32105e28i q^{8} +(-2.81098e30 + 1.97195e30i) q^{9} +O(q^{10})\)	\(q+4.03164e9i q^{2} +(5.57989e14 + 1.76701e15i) q^{3} +2.19261e18 q^{4} +2.91915e22i q^{5} +(-7.12396e24 + 2.24961e24i) q^{6} +6.92352e26 q^{7} +8.32105e28i q^{8} +(-2.81098e30 + 1.97195e30i) q^{9} -1.17690e32 q^{10} -2.05319e33i q^{11} +(1.22345e33 + 3.87437e33i) q^{12} -9.38974e34 q^{13} +2.79131e36i q^{14} +(-5.15818e37 + 1.62885e37i) q^{15} -2.95028e38 q^{16} -1.29532e39i q^{17} +(-7.95018e39 - 1.13329e40i) q^{18} -2.23545e40 q^{19} +6.40057e40i q^{20} +(3.86325e41 + 1.22339e42i) q^{21} +8.27774e42 q^{22} -4.35116e43i q^{23} +(-1.47034e44 + 4.64305e43i) q^{24} -3.10044e44 q^{25} -3.78561e44i q^{26} +(-5.05295e45 - 3.86671e45i) q^{27} +1.51806e45 q^{28} +1.55583e45i q^{29} +(-6.56695e46 - 2.07959e47i) q^{30} -9.94186e47 q^{31} +3.45514e47i q^{32} +(3.62802e48 - 1.14566e48i) q^{33} +5.22226e48 q^{34} +2.02108e49i q^{35} +(-6.16339e48 + 4.32371e48i) q^{36} -6.98898e49 q^{37} -9.01252e49i q^{38} +(-5.23937e49 - 1.65918e50i) q^{39} -2.42904e51 q^{40} -4.06020e51i q^{41} +(-4.93229e51 + 1.55752e51i) q^{42} -3.69152e52 q^{43} -4.50186e51i q^{44} +(-5.75641e52 - 8.20568e52i) q^{45} +1.75423e53 q^{46} +5.97972e53i q^{47} +(-1.64622e53 - 5.21319e53i) q^{48} -7.40409e53 q^{49} -1.24999e54i q^{50} +(2.28884e54 - 7.22773e53i) q^{51} -2.05880e53 q^{52} +1.81495e55i q^{53} +(1.55892e55 - 2.03717e55i) q^{54} +5.99358e55 q^{55} +5.76109e55i q^{56} +(-1.24735e55 - 3.95006e55i) q^{57} -6.27257e54 q^{58} +1.74464e56i q^{59} +(-1.13099e56 + 3.57144e55i) q^{60} -1.21233e57 q^{61} -4.00820e57i q^{62} +(-1.94619e57 + 1.36528e57i) q^{63} -6.83530e57 q^{64} -2.74101e57i q^{65} +(4.61888e57 + 1.46269e58i) q^{66} +4.80588e58 q^{67} -2.84013e57i q^{68} +(7.68856e58 - 2.42790e58i) q^{69} -8.14827e58 q^{70} +4.77800e58i q^{71} +(-1.64087e59 - 2.33903e59i) q^{72} +3.60721e59 q^{73} -2.81771e59i q^{74} +(-1.73001e59 - 5.47851e59i) q^{75} -4.90147e58 q^{76} -1.42153e60i q^{77} +(6.68921e59 - 2.11233e59i) q^{78} -3.79967e60 q^{79} -8.61232e60i q^{80} +(4.01304e60 - 1.10862e61i) q^{81} +1.63693e61 q^{82} -2.93347e61i q^{83} +(8.47060e59 + 2.68243e60i) q^{84} +3.78123e61 q^{85} -1.48829e62i q^{86} +(-2.74918e60 + 8.68138e59i) q^{87} +1.70847e62 q^{88} -1.74845e62i q^{89} +(3.30824e62 - 2.32078e62i) q^{90} -6.50100e61 q^{91} -9.54041e61i q^{92} +(-5.54745e62 - 1.75674e63i) q^{93} -2.41081e63 q^{94} -6.52561e62i q^{95} +(-6.10528e62 + 1.92793e62i) q^{96} +6.41265e63 q^{97} -2.98506e63i q^{98} +(4.04879e63 + 5.77149e63i) 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

Related objects

Downloads

Learn more