LMFDB - Embedded newform 3.65.b.a.2.20

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			2.20
Root			$1.25990e9i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.65.b.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.55940e9i q^{2} +(-2.98618e14 + 1.82880e15i) q^{3} -3.86978e19 q^{4} -3.78912e22i q^{5} +(-1.38246e25 - 2.25737e24i) q^{6} +1.61394e27 q^{7} -1.53086e29i q^{8} +(-3.25534e30 - 1.09222e30i) q^{9} +O(q^{10})$	\(q+7.55940e9i q^{2} +(-2.98618e14 + 1.82880e15i) q^{3} -3.86978e19 q^{4} -3.78912e22i q^{5} +(-1.38246e25 - 2.25737e24i) q^{6} +1.61394e27 q^{7} -1.53086e29i q^{8} +(-3.25534e30 - 1.09222e30i) q^{9} +2.86435e32 q^{10} +1.51478e33i q^{11} +(1.15558e34 - 7.07705e34i) q^{12} -1.60143e35 q^{13} +1.22004e37i q^{14} +(6.92955e37 + 1.13150e37i) q^{15} +4.43388e38 q^{16} +1.42356e39i q^{17} +(8.25656e39 - 2.46084e40i) q^{18} +7.62287e40 q^{19} +1.46631e42i q^{20} +(-4.81951e41 + 2.95158e42i) q^{21} -1.14509e43 q^{22} +3.71581e43i q^{23} +(2.79963e44 + 4.57141e43i) q^{24} -8.93643e44 q^{25} -1.21058e45i q^{26} +(2.96956e45 - 5.62721e45i) q^{27} -6.24559e46 q^{28} -6.21817e46i q^{29} +(-8.55345e46 + 5.23832e47i) q^{30} +5.53593e47 q^{31} +5.27813e47i q^{32} +(-2.77024e48 - 4.52341e47i) q^{33} -1.07612e49 q^{34} -6.11542e49i q^{35} +(1.25974e50 + 4.22666e49i) q^{36} -2.20964e50 q^{37} +5.76243e50i q^{38} +(4.78214e49 - 2.92869e50i) q^{39} -5.80060e51 q^{40} +4.47120e51i q^{41} +(-2.23121e52 - 3.64326e51i) q^{42} -1.29318e52 q^{43} -5.86188e52i q^{44} +(-4.13857e52 + 1.23349e53i) q^{45} -2.80893e53 q^{46} +1.54561e53i q^{47} +(-1.32403e53 + 8.10868e53i) q^{48} +1.38504e54 q^{49} -6.75540e54i q^{50} +(-2.60340e54 - 4.25099e53i) q^{51} +6.19716e54 q^{52} +2.62991e55i q^{53} +(4.25383e55 + 2.24481e55i) q^{54} +5.73970e55 q^{55} -2.47071e56i q^{56} +(-2.27632e55 + 1.39407e56i) q^{57} +4.70056e56 q^{58} +6.43195e55i q^{59} +(-2.68158e57 - 4.37865e56i) q^{60} -8.05548e56 q^{61} +4.18483e57i q^{62} +(-5.25392e57 - 1.76278e57i) q^{63} +4.18911e57 q^{64} +6.06800e57i q^{65} +(3.41943e57 - 2.09413e58i) q^{66} +1.17745e58 q^{67} -5.50885e58i q^{68} +(-6.79547e58 - 1.10961e58i) q^{69} +4.62289e59 q^{70} +6.05922e58i q^{71} +(-1.67204e59 + 4.98346e59i) q^{72} -5.83550e59 q^{73} -1.67036e60i q^{74} +(2.66857e59 - 1.63429e60i) q^{75} -2.94988e60 q^{76} +2.44477e60i q^{77} +(2.21391e60 + 3.61501e59i) q^{78} -3.50375e60 q^{79} -1.68005e61i q^{80} +(9.40428e60 + 7.11112e60i) q^{81} -3.37996e61 q^{82} -5.79358e60i q^{83} +(1.86504e61 - 1.14219e62i) q^{84} +5.39403e61 q^{85} -9.77566e61i q^{86} +(1.13718e62 + 1.85685e61i) q^{87} +2.31892e62 q^{88} -5.84896e61i q^{89} +(-9.32442e62 - 3.12851e62i) q^{90} -2.58461e62 q^{91} -1.43793e63i q^{92} +(-1.65312e62 + 1.01241e63i) q^{93} -1.16839e63 q^{94} -2.88840e63i q^{95} +(-9.65264e62 - 1.57614e62i) q^{96} -1.93918e63 q^{97} +1.04701e64i q^{98} +(1.65448e63 - 4.93114e63i) 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 $

$2$			7.55940e9i			1.76006i	0.474918	+	0.880030i	$0.342478\pi$
$2$			7.55940e9i			1.76006i	−0.474918	+	0.880030i	$0.657522\pi$
$3$	−2.98618e14	+	1.82880e15i	−0.161152	+	0.986930i
$3$	−2.98618e14	+	1.82880e15i	−0.161152	+	0.986930i
$4$	−3.86978e19			−2.09781
$5$		−	3.78912e22i		−	1.62742i	−0.581274	−	0.813708i	$-0.697446\pi$
$5$		−	3.78912e22i		−	1.62742i	0.581274	−	0.813708i	$-0.302554\pi$
$6$	−1.38246e25	−	2.25737e24i	−1.73706	−	0.283637i
$7$	1.61394e27			1.46134			0.730668	−	0.682733i	$-0.239209\pi$
$7$	1.61394e27			1.46134			0.730668	+	0.682733i	$0.239209\pi$
$8$		−	1.53086e29i		−	1.93221i
$9$	−3.25534e30	−	1.09222e30i	−0.948060	−	0.318091i
$10$	2.86435e32			2.86435
$11$			1.51478e33i			0.717439i	0.933445	+	0.358719i	$0.116786\pi$
$11$			1.51478e33i			0.717439i	−0.933445	+	0.358719i	$0.883214\pi$
$12$	1.15558e34	−	7.07705e34i	0.338066	−	2.07039i
$13$	−1.60143e35			−0.361676			−0.180838	−	0.983513i	$-0.557881\pi$
$13$	−1.60143e35			−0.361676			−0.180838	+	0.983513i	$0.557881\pi$
$14$			1.22004e37i			2.57204i
$15$	6.92955e37	+	1.13150e37i	1.60614	+	0.262261i
$16$	4.43388e38			1.30300
$17$			1.42356e39i			0.601187i	0.953752	+	0.300594i	$0.0971848\pi$
$17$			1.42356e39i			0.601187i	−0.953752	+	0.300594i	$0.902815\pi$
$18$	8.25656e39	−	2.46084e40i	0.559859	−	1.66864i
$19$	7.62287e40			0.916227			0.458114	−	0.888894i	$-0.348525\pi$
$19$	7.62287e40			0.916227			0.458114	+	0.888894i	$0.348525\pi$
$20$			1.46631e42i			3.41401i
$21$	−4.81951e41	+	2.95158e42i	−0.235497	+	1.44224i
$22$	−1.14509e43			−1.26274
$23$			3.71581e43i			0.988013i	0.869458	+	0.494006i	$0.164468\pi$
$23$			3.71581e43i			0.988013i	−0.869458	+	0.494006i	$0.835532\pi$
$24$	2.79963e44	+	4.57141e43i	1.90696	+	0.311380i
$25$	−8.93643e44			−1.64848
$26$		−	1.21058e45i		−	0.636571i
$27$	2.96956e45	−	5.62721e45i	0.466715	−	0.884408i
$28$	−6.24559e46			−3.06561
$29$		−	6.21817e46i		−	0.992948i	−0.868052	−	0.496474i	$-0.834628\pi$
$29$		−	6.21817e46i		−	0.992948i	0.868052	−	0.496474i	$-0.165372\pi$
$30$	−8.55345e46	+	5.23832e47i	−0.461595	+	2.82691i
$31$	5.53593e47			1.04620			0.523102	−	0.852270i	$-0.324775\pi$
$31$	5.53593e47			1.04620			0.523102	+	0.852270i	$0.324775\pi$
$32$			5.27813e47i			0.361144i
$33$	−2.77024e48	−	4.52341e47i	−0.708062	−	0.115617i
$34$	−1.07612e49			−1.05813
$35$		−	6.11542e49i		−	2.37820i
$36$	1.25974e50	+	4.22666e49i	1.98885	+	0.667295i
$37$	−2.20964e50			−1.45166			−0.725832	−	0.687872i	$-0.758545\pi$
$37$	−2.20964e50			−1.45166			−0.725832	+	0.687872i	$0.758545\pi$
$38$			5.76243e50i			1.61261i
$39$	4.78214e49	−	2.92869e50i	0.0582847	−	0.356949i
$40$	−5.80060e51			−3.14451
$41$			4.47120e51i			1.09987i	0.835208	+	0.549934i	$0.185347\pi$
$41$			4.47120e51i			1.09987i	−0.835208	+	0.549934i	$0.814653\pi$
$42$	−2.23121e52	−	3.64326e51i	−2.53842	−	0.414489i
$43$	−1.29318e52			−0.692897			−0.346448	−	0.938069i	$-0.612612\pi$
$43$	−1.29318e52			−0.692897			−0.346448	+	0.938069i	$0.612612\pi$
$44$		−	5.86188e52i		−	1.50505i
$45$	−4.13857e52	+	1.23349e53i	−0.517666	+	1.54289i
$46$	−2.80893e53			−1.73896
$47$			1.54561e53i			0.480804i	0.970673	+	0.240402i	$0.0772792\pi$
$47$			1.54561e53i			0.480804i	−0.970673	+	0.240402i	$0.922721\pi$
$48$	−1.32403e53	+	8.10868e53i	−0.209981	+	1.28597i
$49$	1.38504e54			1.13551
$50$		−	6.75540e54i		−	2.90142i
$51$	−2.60340e54	−	4.25099e53i	−0.593329	−	0.0968824i
$52$	6.19716e54			0.758728
$53$			2.62991e55i			1.75030i	0.483848	+	0.875152i	$0.339239\pi$
$53$			2.62991e55i			1.75030i	−0.483848	+	0.875152i	$0.660761\pi$
$54$	4.25383e55	+	2.24481e55i	1.55661	+	0.821446i
$55$	5.73970e55			1.16757
$56$		−	2.47071e56i		−	2.82361i
$57$	−2.27632e55	+	1.39407e56i	−0.147652	+	0.904252i
$58$	4.70056e56			1.74765
$59$			6.43195e55i			0.138382i	0.997603	+	0.0691908i	$0.0220417\pi$
$59$			6.43195e55i			0.138382i	−0.997603	+	0.0691908i	$0.977958\pi$
$60$	−2.68158e57	−	4.37865e56i	−3.36939	−	0.550174i
$61$	−8.05548e56			−0.596398			−0.298199	−	0.954504i	$-0.596386\pi$
$61$	−8.05548e56			−0.596398			−0.298199	+	0.954504i	$0.596386\pi$
$62$			4.18483e57i			1.84138i
$63$	−5.25392e57	−	1.76278e57i	−1.38544	−	0.464838i
$64$	4.18911e57			0.667364
$65$			6.06800e57i			0.588597i
$66$	3.41943e57	−	2.09413e58i	0.203492	−	1.24623i
$67$	1.17745e58			0.433061			0.216530	−	0.976276i	$-0.430526\pi$
$67$	1.17745e58			0.433061			0.216530	+	0.976276i	$0.430526\pi$
$68$		−	5.50885e58i		−	1.26118i
$69$	−6.79547e58	−	1.10961e58i	−0.975099	−	0.159220i
$70$	4.62289e59			4.18578
$71$			6.05922e58i			0.348457i	0.984705	+	0.174229i	$0.0557432\pi$
$71$			6.05922e58i			0.348457i	−0.984705	+	0.174229i	$0.944257\pi$
$72$	−1.67204e59	+	4.98346e59i	−0.614619	+	1.83185i
$73$	−5.83550e59			−1.37958			−0.689789	−	0.724010i	$-0.742297\pi$
$73$	−5.83550e59			−1.37958			−0.689789	+	0.724010i	$0.742297\pi$
$74$		−	1.67036e60i		−	2.55502i
$75$	2.66857e59	−	1.63429e60i	0.265656	−	1.62693i
$76$	−2.94988e60			−1.92207
$77$			2.44477e60i			1.04842i
$78$	2.21391e60	+	3.61501e59i	0.628251	+	0.102585i
$79$	−3.50375e60			−0.661404			−0.330702	−	0.943735i	$-0.607285\pi$
$79$	−3.50375e60			−0.661404			−0.330702	+	0.943735i	$0.607285\pi$
$80$		−	1.68005e61i		−	2.12052i
$81$	9.40428e60	+	7.11112e60i	0.797636	+	0.603139i
$82$	−3.37996e61			−1.93583
$83$		−	5.79358e60i		−	0.225137i	−0.993644	−	0.112569i	$-0.964092\pi$
$83$		−	5.79358e60i		−	0.225137i	0.993644	−	0.112569i	$-0.0359079\pi$
$84$	1.86504e61	−	1.14219e62i	0.494028	−	3.02554i
$85$	5.39403e61			0.978381
$86$		−	9.77566e61i		−	1.21954i
$87$	1.13718e62	+	1.85685e61i	0.979969	+	0.160015i
$88$	2.31892e62			1.38624
$89$		−	5.84896e61i		−	0.243556i	−0.992557	−	0.121778i	$-0.961140\pi$
$89$		−	5.84896e61i		−	0.243556i	0.992557	−	0.121778i	$-0.0388595\pi$
$90$	−9.32442e62	−	3.12851e62i	−2.71557	−	0.911123i
$91$	−2.58461e62			−0.528530
$92$		−	1.43793e63i		−	2.07266i
$93$	−1.65312e62	+	1.01241e63i	−0.168598	+	1.03253i
$94$	−1.16839e63			−0.846243
$95$		−	2.88840e63i		−	1.49108i
$96$	−9.65264e62	−	1.57614e62i	−0.356424	−	0.0581990i
$97$	−1.93918e63			−0.513953			−0.256977	−	0.966418i	$-0.582726\pi$
$97$	−1.93918e63			−0.513953			−0.256977	+	0.966418i	$0.582726\pi$
$98$			1.04701e64i			1.99856i
$99$	1.65448e63	−	4.93114e63i	0.228211	−	0.680175i
$100$	3.45820e64			3.45820
$101$			7.72968e63i			0.562183i	0.959681	+	0.281092i	$0.0906965\pi$
$101$			7.72968e63i			0.562183i	−0.959681	+	0.281092i	$0.909304\pi$
$102$	3.21350e63	−	1.96802e64i	0.170519	−	1.04430i
$103$	−2.25389e64			−0.875268			−0.437634	−	0.899153i	$-0.644183\pi$
$103$	−2.25389e64			−0.875268			−0.437634	+	0.899153i	$0.644183\pi$
$104$			2.45155e64i			0.698835i
$105$	1.11839e65	+	1.82617e64i	2.34712	+	0.383251i
$106$	−1.98806e65			−3.08064
$107$			1.21071e65i			1.38918i	0.719406	+	0.694590i	$0.244414\pi$
$107$			1.21071e65i			1.38918i	−0.719406	+	0.694590i	$0.755586\pi$
$108$	−1.14915e65	+	2.17760e65i	−0.979080	+	1.85532i
$109$	−7.42636e64			−0.471116			−0.235558	−	0.971860i	$-0.575692\pi$
$109$	−7.42636e64			−0.471116			−0.235558	+	0.971860i	$0.575692\pi$
$110$			4.33887e65i			2.05499i
$111$	6.59837e64	−	4.04099e65i	0.233938	−	1.43269i
$112$	7.15601e65			1.90412
$113$		−	8.83933e65i		−	1.76974i	−0.465840	−	0.884869i	$-0.654248\pi$
$113$		−	8.83933e65i		−	1.76974i	0.465840	−	0.884869i	$-0.345752\pi$
$114$	−1.05383e66	−	1.72076e65i	−1.59154	−	0.259876i
$115$	1.40796e66			1.60791
$116$			2.40629e66i			2.08302i
$117$	5.21319e65	+	1.74912e65i	0.342891	+	0.115046i
$118$	−4.86217e65			−0.243560
$119$			2.29754e66i			0.878537i
$120$	1.73216e66	−	1.06081e67i	0.506744	−	3.10341i
$121$	2.16334e66			0.485282
$122$		−	6.08946e66i		−	1.04970i
$123$	−8.17693e66	−	1.33518e66i	−1.08549	−	0.177246i
$124$	−2.14228e67			−2.19474
$125$			1.33203e67i			1.05535i
$126$	1.33256e67	−	3.97165e67i	0.818143	−	2.43845i
$127$	−2.53945e66			−0.121066			−0.0605329	−	0.998166i	$-0.519280\pi$
$127$	−2.53945e66			−0.121066			−0.0605329	+	0.998166i	$0.519280\pi$
$128$			4.14036e67i			1.53574i
$129$	3.86166e66	−	2.36497e67i	0.111662	−	0.683840i
$130$	−4.58704e67			−1.03597
$131$		−	2.29758e67i		−	0.406059i	−0.979173	−	0.203030i	$-0.934921\pi$
$131$		−	2.29758e67i		−	0.406059i	0.979173	−	0.203030i	$-0.0650788\pi$
$132$	1.07202e68	+	1.75046e67i	1.48538	+	0.242542i
$133$	1.23029e68			1.33892
$134$			8.90081e67i			0.762213i
$135$	−2.13222e68	−	1.12520e68i	−1.43930	−	0.759539i
$136$	2.17926e68			1.16162
$137$			2.49184e68i			1.05066i	0.850899	+	0.525329i	$0.176058\pi$
$137$			2.49184e68i			1.05066i	−0.850899	+	0.525329i	$0.823942\pi$
$138$	8.38795e67	−	5.13697e68i	0.280237	−	1.71623i
$139$	8.30549e67			0.220238			0.110119	−	0.993918i	$-0.464877\pi$
$139$	8.30549e67			0.220238			0.110119	+	0.993918i	$0.464877\pi$
$140$			2.36653e69i			4.98902i
$141$	−2.82661e68	−	4.61545e67i	−0.474519	−	0.0774824i
$142$	−4.58041e68			−0.613306
$143$		−	2.42582e68i		−	0.259480i
$144$	−1.44338e69	−	4.84279e68i	−1.23532	−	0.414472i
$145$	−2.35614e69			−1.61594
$146$		−	4.41129e69i		−	2.42814i
$147$	−4.13598e68	+	2.53297e69i	−0.182989	+	1.12066i
$148$	8.55082e69			3.04532
$149$			3.72672e69i			1.06996i	0.844866	+	0.534979i	$0.179680\pi$
$149$			3.72672e69i			1.06996i	−0.844866	+	0.534979i	$0.820320\pi$
$150$	1.23543e70	+	2.01728e69i	2.86350	+	0.467570i
$151$	−5.56742e69			−1.04326			−0.521629	−	0.853173i	$-0.674675\pi$
$151$	−5.56742e69			−1.04326			−0.521629	+	0.853173i	$0.674675\pi$
$152$		−	1.16695e70i		−	1.77035i
$153$	1.55484e69	−	4.63416e69i	0.191232	−	0.569962i
$154$	−1.84810e70			−1.84528
$155$		−	2.09763e70i		−	1.70261i
$156$	−1.85058e69	+	1.13334e70i	−0.122270	+	0.748811i
$157$	−4.89424e69			−0.263570			−0.131785	−	0.991278i	$-0.542071\pi$
$157$	−4.89424e69			−0.263570			−0.131785	+	0.991278i	$0.542071\pi$
$158$		−	2.64863e70i		−	1.16411i
$159$	−4.80959e70	−	7.85338e69i	−1.72743	−	0.282065i
$160$	1.99995e70			0.587731
$161$			5.99709e70i			1.44382i
$162$	−5.37558e70	+	7.10907e70i	−1.06156	+	1.40389i
$163$	8.48189e70			1.37559			0.687796	−	0.725904i	$-0.258578\pi$
$163$	8.48189e70			1.37559			0.687796	+	0.725904i	$0.258578\pi$
$164$		−	1.73025e71i		−	2.30732i
$165$	−1.71398e70	+	1.04968e71i	−0.188156	+	1.15231i
$166$	4.37960e70			0.396255
$167$		−	6.91432e70i		−	0.516205i	−0.966117	−	0.258103i	$-0.916903\pi$
$167$		−	6.91432e70i		−	0.516205i	0.966117	−	0.258103i	$-0.0830973\pi$
$168$	4.51844e71	+	7.37798e70i	2.78671	+	0.455030i
$169$	−1.70408e71			−0.869190
$170$			4.07757e71i			1.72201i
$171$	−2.48150e71	−	8.32588e70i	−0.868638	−	0.291444i
$172$	5.00432e71			1.45357
$173$		−	2.44676e71i		−	0.590359i	−0.955442	−	0.295180i	$-0.904621\pi$
$173$		−	2.44676e71i		−	0.590359i	0.955442	−	0.295180i	$-0.0953795\pi$
$174$	−1.40367e71	+	8.59639e71i	−0.281636	+	1.72480i
$175$	−1.44229e72			−2.40898
$176$			6.71637e71i			0.934822i
$177$	−1.17627e71	−	1.92069e70i	−0.136573	−	0.0223004i
$178$	4.42146e71			0.428672
$179$			8.78496e71i			0.711939i	0.934498	+	0.355970i	$0.115849\pi$
$179$			8.78496e71i			0.711939i	−0.934498	+	0.355970i	$0.884151\pi$
$180$	1.60153e72	−	4.77332e72i	1.08597	−	3.23669i
$181$	−2.62948e72			−1.49333			−0.746665	−	0.665200i	$-0.768346\pi$
$181$	−2.62948e72			−1.49333			−0.746665	+	0.665200i	$0.768346\pi$
$182$		−	1.95381e72i		−	0.930245i
$183$	2.40551e71	−	1.47319e72i	0.0961107	−	0.588603i
$184$	5.68837e72			1.90905
$185$			8.37259e72i			2.36246i
$186$	−7.65321e72	−	1.24966e72i	−1.81731	−	0.296742i
$187$	−2.15638e72			−0.431315
$188$		−	5.98116e72i		−	1.00863i
$189$	4.79269e72	−	9.08198e72i	0.682028	−	1.29242i
$190$	2.18345e73			2.62439
$191$		−	3.78485e72i		−	0.384575i	−0.981339	−	0.192288i	$-0.938409\pi$
$191$		−	3.78485e72i		−	0.384575i	0.981339	−	0.192288i	$-0.0615906\pi$
$192$	−1.25094e72	+	7.66105e72i	−0.107547	+	0.658641i
$193$	−1.58706e73			−1.15547			−0.577735	−	0.816225i	$-0.696063\pi$
$193$	−1.58706e73			−1.15547			−0.577735	+	0.816225i	$0.696063\pi$
$194$		−	1.46591e73i		−	0.904588i
$195$	−1.10972e73	−	1.81201e72i	−0.580904	−	0.0948535i
$196$	−5.35981e73			−2.38207
$197$			3.01743e73i			1.13951i	0.821815	+	0.569755i	$0.192962\pi$
$197$			3.01743e73i			1.13951i	−0.821815	+	0.569755i	$0.807038\pi$
$198$	3.72764e73	+	1.25069e73i	1.19715	+	0.401665i
$199$	9.99232e72			0.273129			0.136565	−	0.990631i	$-0.456394\pi$
$199$	9.99232e72			0.273129			0.136565	+	0.990631i	$0.456394\pi$
$200$			1.36804e74i			3.18521i
$201$	−3.51607e72	+	2.15332e73i	−0.0697885	+	0.427400i
$202$	−5.84318e73			−0.989476
$203$		−	1.00358e74i		−	1.45103i
$204$	1.00746e74	+	1.64504e73i	1.24469	+	0.203241i
$205$	1.69419e74			1.78994
$206$		−	1.70380e74i		−	1.54052i
$207$	4.05849e73	−	1.20962e74i	0.314278	−	0.936695i
$208$	−7.10053e73			−0.471264
$209$			1.15470e74i			0.657337i
$210$	−1.38048e74	+	8.45434e74i	−0.674546	+	4.13107i
$211$	4.26345e74			1.78946			0.894730	−	0.446607i	$-0.147368\pi$
$211$	4.26345e74			1.78946			0.894730	+	0.446607i	$0.147368\pi$
$212$		−	1.01772e75i		−	3.67181i
$213$	−1.10811e74	−	1.80939e73i	−0.343903	−	0.0561545i
$214$	−9.15223e74			−2.44504
$215$			4.90002e74i			1.12763i
$216$	−8.61445e74	−	4.54597e74i	−1.70886	−	0.901793i
$217$	8.93466e74			1.52886
$218$		−	5.61388e74i		−	0.829193i
$219$	1.74258e74	−	1.06720e75i	0.222322	−	1.36155i
$220$	−2.22114e75			−2.44934
$221$		−	2.27972e74i		−	0.217435i
$222$	3.05475e75	+	4.98797e74i	2.52162	+	0.411746i
$223$	−2.17737e75			−1.55660			−0.778300	−	0.627892i	$-0.783918\pi$
$223$	−2.17737e75			−1.55660			−0.778300	+	0.627892i	$0.783918\pi$
$224$			8.51858e74i			0.527753i
$225$	2.90911e75	+	9.76058e74i	1.56286	+	0.524367i
$226$	6.68200e75			3.11485
$227$			1.02491e74i			0.0414819i	0.999785	+	0.0207409i	$0.00660252\pi$
$227$			1.02491e74i			0.0414819i	−0.999785	+	0.0207409i	$0.993397\pi$
$228$	8.80886e74	−	5.39474e75i	0.309745	−	1.89695i
$229$	−3.41982e75			−1.04536			−0.522682	−	0.852527i	$-0.675069\pi$
$229$	−3.41982e75			−1.04536			−0.522682	+	0.852527i	$0.675069\pi$
$230$			1.06434e76i			2.83001i
$231$	−4.47100e75	−	7.30052e74i	−1.03472	−	0.168955i
$232$	−9.51912e75			−1.91859
$233$			2.57001e75i			0.451383i	0.974199	+	0.225691i	$0.0724641\pi$
$233$			2.57001e75i			0.451383i	−0.974199	+	0.225691i	$0.927536\pi$
$234$	−1.32223e75	+	3.94086e75i	−0.202488	+	0.603508i
$235$	5.85649e75			0.782467
$236$		−	2.48902e75i		−	0.290298i
$237$	1.04628e75	−	6.40766e75i	0.106586	−	0.652759i
$238$	−1.73680e76			−1.54628
$239$			1.35982e76i			1.05864i	0.848423	+	0.529319i	$0.177552\pi$
$239$			1.35982e76i			1.05864i	−0.848423	+	0.529319i	$0.822448\pi$
$240$	3.07248e76	+	5.01692e75i	2.09280	+	0.341726i
$241$	−2.07574e75			−0.123773			−0.0618867	−	0.998083i	$-0.519712\pi$
$241$	−2.07574e75			−0.123773			−0.0618867	+	0.998083i	$0.519712\pi$
$242$			1.63536e76i			0.854125i
$243$	−1.58131e76	+	1.50750e76i	−0.723796	+	0.690014i
$244$	3.11729e76			1.25113
$245$		−	5.24810e76i		−	1.84794i
$246$	1.00931e76	−	6.18127e76i	0.311963	−	1.91053i
$247$	−1.22075e76			−0.331377
$248$		−	8.47471e76i		−	2.02149i
$249$	1.05953e76	+	1.73006e75i	0.222195	+	0.0362813i
$250$	−1.00694e77			−1.85747
$251$			6.68465e76i			1.08523i	0.839983	+	0.542613i	$0.182565\pi$
$251$			6.68465e76i			1.08523i	−0.839983	+	0.542613i	$0.817435\pi$
$252$	2.03315e77	+	6.82158e76i	2.90638	+	0.975142i
$253$	−5.62865e76			−0.708838
$254$		−	1.91967e76i		−	0.213083i
$255$	−1.61075e76	+	9.86461e76i	−0.157668	+	0.965593i
$256$	−2.35711e77			−2.03564
$257$		−	2.14539e77i		−	1.63549i	−0.575584	−	0.817743i	$-0.695225\pi$
$257$		−	2.14539e77i		−	1.63549i	0.575584	−	0.817743i	$-0.304775\pi$
$258$	1.78777e77	+	2.91918e76i	1.20360	+	0.196531i
$259$	−3.56623e77			−2.12137
$260$		−	2.34818e77i		−	1.23477i
$261$	−6.79163e76	+	2.02422e77i	−0.315848	+	0.941374i
$262$	1.73683e77			0.714689
$263$		−	1.76058e77i		−	0.641316i	−0.947195	−	0.320658i	$-0.896096\pi$
$263$		−	1.76058e77i		−	0.641316i	0.947195	−	0.320658i	$-0.103904\pi$
$264$	−6.92469e76	+	4.24084e77i	−0.223396	+	1.36813i
$265$	9.96506e77			2.84847
$266$			9.30022e77i			2.35657i
$267$	1.06966e77	+	1.74660e76i	0.240372	+	0.0392494i
$268$	−4.55647e77			−0.908479
$269$			1.03294e78i			1.82811i	0.405585	+	0.914057i	$0.367068\pi$
$269$			1.03294e78i			1.82811i	−0.405585	+	0.914057i	$0.632932\pi$
$270$	8.50586e77	−	1.61183e78i	1.33683	−	2.53325i
$271$	−5.92773e77			−0.827696			−0.413848	−	0.910346i	$-0.635816\pi$
$271$	−5.92773e77			−0.827696			−0.413848	+	0.910346i	$0.635816\pi$
$272$			6.31188e77i			0.783347i
$273$	7.71809e76	−	4.72673e77i	0.0851736	−	0.521622i
$274$	−1.88368e78			−1.84922
$275$		−	1.35368e78i		−	1.18268i
$276$	2.62970e78	+	4.29393e77i	2.04557	+	0.334013i
$277$	2.66355e78			1.84548			0.922739	−	0.385426i	$-0.125946\pi$
$277$	2.66355e78			1.84548			0.922739	+	0.385426i	$0.125946\pi$
$278$			6.27845e77i			0.387632i
$279$	−1.80213e78	−	6.04647e77i	−0.991864	−	0.332788i
$280$	−9.36183e78			−4.59519
$281$			1.44256e77i			0.0631729i	0.999501	+	0.0315865i	$0.0100560\pi$
$281$			1.44256e77i			0.0631729i	−0.999501	+	0.0315865i	$0.989944\pi$
$282$	3.48901e77	−	2.13675e78i	0.136374	−	0.835182i
$283$	−9.30510e77			−0.324754			−0.162377	−	0.986729i	$-0.551916\pi$
$283$	−9.30510e77			−0.324754			−0.162377	+	0.986729i	$0.551916\pi$
$284$		−	2.34478e78i		−	0.730998i
$285$	5.28230e78	+	8.62526e77i	1.47159	+	0.240291i
$286$	1.83377e78			0.456701
$287$			7.21625e78i			1.60728i
$288$	5.76490e77	−	1.71821e78i	0.114877	−	0.342386i
$289$	3.58049e78			0.638574
$290$		−	1.78110e79i		−	2.84415i
$291$	5.79074e77	−	3.54638e78i	0.0828245	−	0.507236i
$292$	2.25821e79			2.89410
$293$			4.39663e77i			0.0505075i	0.999681	+	0.0252537i	$0.00803937\pi$
$293$			4.39663e77i			0.0505075i	−0.999681	+	0.0252537i	$0.991961\pi$
$294$	−1.91477e79	−	3.12656e78i	−1.97244	−	0.322071i
$295$	2.43714e78			0.225204
$296$			3.38264e79i			2.80493i
$297$	8.52401e78	+	4.49824e78i	0.634508	+	0.334839i
$298$	−2.81718e79			−1.88319
$299$		−	5.95059e78i		−	0.357340i
$300$	−1.03268e79	+	6.32436e79i	−0.557295	+	3.41300i
$301$	−2.08712e79			−1.01256
$302$		−	4.20863e79i		−	1.83620i
$303$	−1.41361e79	−	2.30822e78i	−0.554835	−	0.0905968i
$304$	3.37989e79			1.19384
$305$			3.05232e79i			0.970588i
$306$	3.50315e79	+	1.17537e79i	1.00317	+	0.336580i
$307$	−5.79060e79			−1.49381			−0.746906	−	0.664930i	$-0.768461\pi$
$307$	−5.79060e79			−1.49381			−0.746906	+	0.664930i	$0.768461\pi$
$308$		−	9.46072e79i		−	2.19939i
$309$	6.73050e78	−	4.12191e79i	0.141051	−	0.863828i
$310$	1.58568e80			2.99669
$311$			6.89508e79i			1.17546i	0.809058	+	0.587728i	$0.199978\pi$
$311$			6.89508e79i			1.17546i	−0.809058	+	0.587728i	$0.800022\pi$
$312$	−4.48340e79	−	7.32077e78i	−0.689701	−	0.112619i
$313$	−2.38152e79			−0.330700			−0.165350	−	0.986235i	$-0.552875\pi$
$313$	−2.38152e79			−0.330700			−0.165350	+	0.986235i	$0.552875\pi$
$314$		−	3.69975e79i		−	0.463900i
$315$	−6.67940e79	+	1.99078e80i	−0.756484	+	2.25468i
$316$	1.35587e80			1.38750
$317$		−	4.15524e78i		−	0.0384326i	−0.999815	−	0.0192163i	$-0.993883\pi$
$317$		−	4.15524e78i		−	0.0384326i	0.999815	−	0.0192163i	$-0.00611711\pi$
$318$	5.93668e79	−	3.63576e80i	0.496451	−	3.04038i
$319$	9.41918e79			0.712379
$320$		−	1.58731e80i		−	1.08608i
$321$	−2.21414e80	−	3.61539e79i	−1.37102	−	0.223869i
$322$	−4.53344e80			−2.54121
$323$			1.08516e80i			0.550824i
$324$	−3.63925e80	−	2.75184e80i	−1.67329	−	1.26527i
$325$	1.43110e80			0.596216
$326$			6.41180e80i			2.42112i
$327$	2.21764e79	−	1.35813e80i	0.0759212	−	0.464958i
$328$	6.84477e80			2.12518
$329$			2.49452e80i			0.702616i
$330$	−7.93493e80	−	1.29566e80i	−2.02813	−	0.331166i
$331$	7.49653e80			1.73926			0.869630	−	0.493704i	$-0.164357\pi$
$331$	7.49653e80			1.73926			0.869630	+	0.493704i	$0.164357\pi$
$332$			2.24199e80i			0.472296i
$333$	7.19313e80	+	2.41342e80i	1.37627	+	0.461761i
$334$	5.22681e80			0.908552
$335$		−	4.46150e80i		−	0.704769i
$336$	−2.13691e80	+	1.30869e81i	−0.306852	+	1.87923i
$337$	−9.07971e80			−1.18554			−0.592768	−	0.805373i	$-0.701965\pi$
$337$	−9.07971e80			−1.18554			−0.592768	+	0.805373i	$0.701965\pi$
$338$		−	1.28818e81i		−	1.52983i
$339$	1.61654e81	+	2.63958e80i	1.74661	+	0.285196i
$340$	−2.08737e81			−2.05246
$341$			8.38573e80i			0.750587i
$342$	6.29386e80	−	1.87587e81i	0.512958	−	1.52886i
$343$	2.66758e80			0.198019
$344$			1.97967e81i			1.33882i
$345$	−4.20443e80	+	2.57489e81i	−0.259117	+	1.58689i
$346$	1.84960e81			1.03907
$347$			2.03273e81i			1.04120i	0.853799	+	0.520602i	$0.174292\pi$
$347$			2.03273e81i			1.04120i	−0.853799	+	0.520602i	$0.825708\pi$
$348$	−4.40063e81	−	7.18561e80i	−2.05579	−	0.335682i
$349$	2.39840e80			0.102214			0.0511068	−	0.998693i	$-0.483725\pi$
$349$	2.39840e80			0.102214			0.0511068	+	0.998693i	$0.483725\pi$
$350$		−	1.09028e82i		−	4.23996i
$351$	−4.75553e80	+	9.01156e80i	−0.168800	+	0.319869i
$352$	−7.99522e80			−0.259099
$353$		−	2.78172e79i		−	0.00823232i	−0.999992	−	0.00411616i	$-0.998690\pi$
$353$		−	2.78172e79i		−	0.00823232i	0.999992	−	0.00411616i	$-0.00131022\pi$
$354$	1.45193e80	−	8.89193e80i	0.0392501	−	0.240376i
$355$	2.29591e81			0.567085
$356$			2.26342e81i			0.510934i
$357$	−4.20174e81	−	6.86085e80i	−0.867054	−	0.141578i
$358$	−6.64090e81			−1.25306
$359$		−	6.32102e81i		−	1.09085i	−0.838160	−	0.545425i	$-0.816368\pi$
$359$		−	6.32102e81i		−	1.09085i	0.838160	−	0.545425i	$-0.183632\pi$
$360$	1.88829e82	+	6.33555e81i	2.98119	+	1.00024i
$361$	−1.11117e81			−0.160528
$362$		−	1.98773e82i		−	2.62835i
$363$	−6.46013e80	+	3.95633e81i	−0.0782040	+	0.478939i
$364$	1.00019e82			1.10876
$365$			2.21114e82i			2.24515i
$366$	1.11364e82	+	1.81842e81i	1.03598	+	0.169161i
$367$	2.24465e81			0.191353			0.0956765	−	0.995412i	$-0.469499\pi$
$367$	2.24465e81			0.191353			0.0956765	+	0.995412i	$0.469499\pi$
$368$			1.64754e82i			1.28738i
$369$	4.88355e81	−	1.45553e82i	0.349858	−	1.04274i
$370$	−6.32918e82			−4.15807
$371$			4.24452e82i			2.55778i
$372$	6.39722e81	−	3.91780e82i	0.353686	−	2.16605i
$373$	−1.01265e82			−0.513780			−0.256890	−	0.966441i	$-0.582698\pi$
$373$	−1.01265e82			−0.513780			−0.256890	+	0.966441i	$0.582698\pi$
$374$		−	1.63010e82i		−	0.759140i
$375$	−2.43603e82	−	3.97769e81i	−1.04155	−	0.170071i
$376$	2.36610e82			0.929015
$377$			9.95793e81i			0.359125i
$378$	6.86543e82	+	3.62299e82i	2.27473	+	1.20041i
$379$	−4.58134e82			−1.39488			−0.697442	−	0.716641i	$-0.745679\pi$
$379$	−4.58134e82			−1.39488			−0.697442	+	0.716641i	$0.745679\pi$
$380$			1.11775e83i			3.12801i
$381$	7.58325e80	−	4.64415e81i	0.0195100	−	0.119483i
$382$	2.86112e82			0.676875
$383$		−	6.27655e82i		−	1.36572i	−0.730551	−	0.682858i	$-0.760737\pi$
$383$		−	6.27655e82i		−	1.36572i	0.730551	−	0.682858i	$-0.239263\pi$
$384$	−7.57189e82	−	1.23638e82i	−1.51567	−	0.247488i
$385$	9.26354e82			1.70621
$386$		−	1.19972e83i		−	2.03370i
$387$	4.20974e82	+	1.41244e82i	0.656908	+	0.220404i
$388$	7.50421e82			1.07818
$389$		−	3.51579e82i		−	0.465196i	−0.972573	−	0.232598i	$-0.925277\pi$
$389$		−	3.51579e82i		−	0.465196i	0.972573	−	0.232598i	$-0.0747226\pi$
$390$	1.36977e82	−	8.38879e82i	0.166948	−	1.02243i
$391$	−5.28967e82			−0.593980
$392$		−	2.12030e83i		−	2.19404i
$393$	4.20182e82	+	6.86098e81i	0.400752	+	0.0654372i
$394$	−2.28100e83			−2.00561
$395$			1.32761e83i			1.07638i
$396$	−6.40248e82	+	1.90824e83i	−0.478743	+	1.42688i
$397$	8.40245e82			0.579575			0.289788	−	0.957091i	$-0.406415\pi$
$397$	8.40245e82			0.579575			0.289788	+	0.957091i	$0.406415\pi$
$398$			7.55360e82i			0.480724i
$399$	−3.67385e82	+	2.24995e83i	−0.215769	+	1.32142i
$400$	−3.96230e83			−2.14797
$401$		−	1.30012e83i		−	0.650676i	−0.945598	−	0.325338i	$-0.894522\pi$
$401$		−	1.30012e83i		−	0.650676i	0.945598	−	0.325338i	$-0.105478\pi$
$402$	−1.62778e83	−	2.65794e82i	−0.752250	−	0.122832i
$403$	−8.86538e82			−0.378387
$404$		−	2.99122e83i		−	1.17935i
$405$	2.69449e83	−	3.56340e83i	0.981557	−	1.29809i
$406$	7.58643e83			2.55390
$407$		−	3.34713e83i		−	1.04148i
$408$	−6.50766e82	+	3.98544e83i	−0.187197	+	1.14644i
$409$	3.51294e83			0.934383			0.467191	−	0.884156i	$-0.345266\pi$
$409$	3.51294e83			0.934383			0.467191	+	0.884156i	$0.345266\pi$
$410$			1.28071e84i			3.15041i
$411$	−4.55707e83	−	7.44106e82i	−1.03693	−	0.169315i
$412$	8.72205e83			1.83615
$413$			1.03808e83i			0.202222i
$414$	9.14401e83	+	3.06798e83i	1.64864	+	0.553148i
$415$	−2.19526e83			−0.366392
$416$		−	8.45253e82i		−	0.130617i
$417$	−2.48017e82	+	1.51891e83i	−0.0354917	+	0.217359i
$418$	−8.72884e83			−1.15695
$419$		−	7.41803e83i		−	0.910836i	−0.890278	−	0.455418i	$-0.849490\pi$
$419$		−	7.41803e83i		−	0.910836i	0.890278	−	0.455418i	$-0.150510\pi$
$420$	−4.32791e84	−	7.06688e83i	−4.92381	−	0.803989i
$421$	3.82256e83			0.403020			0.201510	−	0.979486i	$-0.435415\pi$
$421$	3.82256e83			0.403020			0.201510	+	0.979486i	$0.435415\pi$
$422$			3.22291e84i			3.14956i
$423$	1.68815e83	−	5.03148e83i	0.152939	−	0.455831i
$424$	4.02602e84			3.38196
$425$		−	1.27215e84i		−	0.991045i
$426$	1.36779e83	−	8.37665e83i	0.0988353	−	0.605290i
$427$	−1.30011e84			−0.871539
$428$		−	4.68517e84i		−	2.91424i
$429$	4.43633e83	+	7.24391e82i	0.256089	+	0.0418157i
$430$	−3.70412e84			−1.98470
$431$			1.63796e84i			0.814762i	0.913258	+	0.407381i	$0.133558\pi$
$431$			1.63796e84i			0.814762i	−0.913258	+	0.407381i	$0.866442\pi$
$432$	1.31667e84	−	2.49504e84i	0.608129	−	1.15238i
$433$	−1.16487e84			−0.499647			−0.249823	−	0.968291i	$-0.580373\pi$
$433$	−1.16487e84			−0.499647			−0.249823	+	0.968291i	$0.580373\pi$
$434$			6.75406e84i			2.69088i
$435$	7.03584e83	−	4.30891e84i	0.260411	−	1.59482i
$436$	2.87384e84			0.988312
$437$			2.83251e84i			0.905244i
$438$	8.06737e84	+	1.31729e84i	2.39640	+	0.391299i
$439$	−2.06964e83			−0.0571518			−0.0285759	−	0.999592i	$-0.509097\pi$
$439$	−2.06964e83			−0.0571518			−0.0285759	+	0.999592i	$0.509097\pi$
$440$		−	8.78666e84i		−	2.25600i
$441$	−4.50879e84	−	1.51278e84i	−1.07653	−	0.361194i
$442$	1.72333e84			0.382699
$443$		−	2.43106e83i		−	0.0502200i	−0.999685	−	0.0251100i	$-0.992006\pi$
$443$		−	2.43106e83i		−	0.0502200i	0.999685	−	0.0251100i	$-0.00799359\pi$
$444$	−2.55342e84	+	1.56377e85i	−0.490758	+	3.00551i
$445$	−2.21624e84			−0.396366
$446$		−	1.64596e85i		−	2.73971i
$447$	−6.81543e84	−	1.11286e84i	−1.05597	−	0.172426i
$448$	6.76098e84			0.975244
$449$		−	7.02025e84i		−	0.942908i	−0.881891	−	0.471454i	$-0.843729\pi$
$449$		−	7.02025e84i		−	0.942908i	0.881891	−	0.471454i	$-0.156271\pi$
$450$	−7.37841e84	+	2.19911e85i	−0.922917	+	2.75072i
$451$	−6.77290e84			−0.789088
$452$			3.42062e85i			3.71258i
$453$	1.66253e84	−	1.01817e85i	0.168123	−	1.02962i
$454$	−7.74770e83			−0.0730105
$455$			9.79339e84i			0.860138i
$456$	2.13412e85	+	3.48472e84i	1.74721	+	0.285294i
$457$	7.31607e84			0.558418			0.279209	−	0.960230i	$-0.409928\pi$
$457$	7.31607e84			0.558418			0.279209	+	0.960230i	$0.409928\pi$
$458$		−	2.58518e85i		−	1.83990i
$459$	8.01066e84	+	4.22734e84i	0.531695	+	0.280583i
$460$	−5.44851e85			−3.37308
$461$			4.98286e84i			0.287773i	0.989594	+	0.143886i	$0.0459600\pi$
$461$			4.98286e84i			0.287773i	−0.989594	+	0.143886i	$0.954040\pi$
$462$	5.51875e84	−	3.37981e85i	0.297370	−	1.82116i
$463$	2.94859e85			1.48260			0.741298	−	0.671176i	$-0.234211\pi$
$463$	2.94859e85			1.48260			0.741298	+	0.671176i	$0.234211\pi$
$464$		−	2.75706e85i		−	1.29381i
$465$	3.83615e85	+	6.26389e84i	1.68035	+	0.274378i
$466$	−1.94277e85			−0.794461
$467$			1.26047e85i			0.481273i	0.970615	+	0.240637i	$0.0773562\pi$
$467$			1.26047e85i			0.481273i	−0.970615	+	0.240637i	$0.922644\pi$
$468$	−2.01739e85	−	6.76869e84i	−0.719320	−	0.241344i
$469$	1.90033e85			0.632847
$470$			4.42716e85i			1.37719i
$471$	1.46151e84	−	8.95059e84i	0.0424748	−	0.260125i
$472$	9.84639e84			0.267383
$473$		−	1.95889e85i		−	0.497111i
$474$	4.84381e85	+	7.90926e84i	1.14889	+	0.187598i
$475$	−6.81212e85			−1.51038
$476$		−	8.89096e85i		−	1.84300i
$477$	2.87245e85	−	8.56126e85i	0.556756	−	1.65939i
$478$	−1.02794e86			−1.86326
$479$			8.86072e85i			1.50222i	0.660179	+	0.751109i	$0.270481\pi$
$479$			8.86072e85i			1.50222i	−0.660179	+	0.751109i	$0.729519\pi$
$480$	−5.97219e84	+	3.65750e85i	−0.0947140	+	0.580050i
$481$	3.53858e85			0.525032
$482$		−	1.56913e85i		−	0.217849i
$483$	−1.09675e86	−	1.79084e85i	−1.42495	−	0.232674i
$484$	−8.37166e85			−1.01803
$485$			7.34780e85i			0.836415i
$486$	−1.13958e86	−	1.19538e86i	−1.21447	−	1.27392i
$487$	7.95385e85			0.793689			0.396845	−	0.917886i	$-0.370105\pi$
$487$	7.95385e85			0.793689			0.396845	+	0.917886i	$0.370105\pi$
$488$			1.23318e86i			1.15237i
$489$	−2.53284e85	+	1.55117e86i	−0.221679	+	1.35761i
$490$	3.96725e86			3.25248
$491$			1.39862e86i			1.07422i	0.843513	+	0.537109i	$0.180484\pi$
$491$			1.39862e86i			1.07422i	−0.843513	+	0.537109i	$0.819516\pi$
$492$	3.16429e86	+	5.16684e85i	2.27716	+	0.371828i
$493$	8.85192e85			0.596947
$494$		−	9.22811e85i		−	0.583244i
$495$	−1.86847e86	−	6.26904e85i	−1.10693	−	0.371394i
$496$	2.45456e86			1.36320
$497$			9.77923e85i			0.509214i
$498$	−1.30782e85	+	8.00941e85i	−0.0638573	+	0.391076i
$499$	−4.05627e86			−1.85742			−0.928708	−	0.370811i	$-0.879080\pi$
$499$	−4.05627e86			−1.85742			−0.928708	+	0.370811i	$0.879080\pi$
$500$		−	5.15468e86i		−	2.21392i
$501$	1.26449e86	+	2.06474e85i	0.509458	+	0.0831874i
$502$	−5.05320e86			−1.91006
$503$		−	1.02023e86i		−	0.361846i	−0.983497	−	0.180923i	$-0.942092\pi$
$503$		−	1.02023e86i		−	0.361846i	0.983497	−	0.180923i	$-0.0579084\pi$
$504$	−2.69857e86	+	8.04300e86i	−0.898166	+	2.67696i
$505$	2.92887e86			0.914905
$506$		−	4.25492e86i		−	1.24760i
$507$	5.08868e85	−	3.11642e86i	0.140072	−	0.857830i
$508$	9.82712e85			0.253973
$509$			7.76149e86i			1.88355i	0.336250	+	0.941773i	$0.390841\pi$
$509$			7.76149e86i			1.88355i	−0.336250	+	0.941773i	$0.609159\pi$
$510$	−7.45706e86	−	1.21763e86i	−1.69950	−	0.277505i
$511$	−9.41815e86			−2.01603
$512$		−	1.01807e87i		−	2.04710i
$513$	2.26366e86	−	4.28955e86i	0.427617	−	0.810318i
$514$	1.62179e87			2.87855
$515$			8.54026e86i			1.42442i
$516$	−1.49438e86	+	9.15190e86i	−0.234245	+	1.43457i
$517$	−2.34126e86			−0.344947
$518$		−	2.69585e87i		−	3.73374i
$519$	4.47464e86	+	7.30646e85i	0.582643	+	0.0951374i
$520$	9.28924e86			1.13729
$521$			4.19964e86i			0.483510i	0.970337	+	0.241755i	$0.0777230\pi$
$521$			4.19964e86i			0.483510i	−0.970337	+	0.241755i	$0.922277\pi$
$522$	−1.53019e87	−	5.13406e86i	−1.65687	−	0.555911i
$523$	1.53903e87			1.56744			0.783721	−	0.621112i	$-0.213319\pi$
$523$	1.53903e87			1.56744			0.783721	+	0.621112i	$0.213319\pi$
$524$			8.89113e86i			0.851836i
$525$	4.30692e86	−	2.63765e87i	0.388212	−	2.37750i
$526$	1.33089e87			1.12875
$527$			7.88071e86i			0.628964i
$528$	−1.22829e87	−	2.00562e86i	−0.922604	−	0.150648i
$529$	3.37077e85			0.0238313
$530$			7.53299e87i			5.01348i
$531$	7.02513e85	−	2.09382e86i	0.0440179	−	0.131194i
$532$	−4.76093e87			−2.80879
$533$		−	7.16030e86i		−	0.397796i
$534$	−1.32033e86	+	8.08597e86i	−0.0690813	+	0.423070i
$535$	4.58752e87			2.26077
$536$		−	1.80251e87i		−	0.836765i
$537$	−1.60659e87	−	2.62334e86i	−0.702634	−	0.114730i
$538$	−7.80843e87			−3.21759
$539$			2.09804e87i			0.814655i
$540$	8.25121e87	+	4.35428e87i	3.01938	+	1.59337i
$541$	−4.84908e87			−1.67242			−0.836212	−	0.548406i	$-0.815235\pi$
$541$	−4.84908e87			−1.67242			−0.836212	+	0.548406i	$0.815235\pi$
$542$		−	4.48101e87i		−	1.45680i
$543$	7.85209e86	−	4.80880e87i	0.240653	−	1.47381i
$544$	−7.51372e86			−0.217115
$545$			2.81394e87i			0.766701i
$546$	3.57312e87	+	5.83441e86i	0.918087	+	0.149911i
$547$	5.56417e87			1.34836			0.674180	−	0.738567i	$-0.264497\pi$
$547$	5.56417e87			1.34836			0.674180	+	0.738567i	$0.264497\pi$
$548$		−	9.64285e87i		−	2.20408i
$549$	2.62233e87	+	8.79838e86i	0.565422	+	0.189709i
$550$	1.02330e88			2.08159
$551$		−	4.74003e87i		−	0.909766i
$552$	−1.69865e87	+	1.04029e88i	−0.307647	+	1.88410i
$553$	−5.65485e87			−0.966533
$554$			2.01349e88i			3.24815i
$555$	−1.53118e88	−	2.50020e87i	−2.33158	−	0.380715i
$556$	−3.21404e87			−0.462017
$557$		−	5.69643e87i		−	0.773101i	−0.922268	−	0.386551i	$-0.873666\pi$
$557$		−	5.69643e87i		−	0.773101i	0.922268	−	0.386551i	$-0.126334\pi$
$558$	4.57077e87	−	1.36230e88i	0.585726	−	1.74574i
$559$	2.07093e87			0.250604
$560$		−	2.71150e88i		−	3.09880i
$561$	6.43934e86	−	3.94360e87i	0.0695072	−	0.425678i
$562$	−1.09049e87			−0.111188
$563$		−	6.64952e87i		−	0.640504i	−0.947332	−	0.320252i	$-0.896232\pi$
$563$		−	6.64952e87i		−	0.640504i	0.947332	−	0.320252i	$-0.103768\pi$
$564$	1.09383e88	+	1.78608e87i	0.995452	+	0.162543i
$565$	−3.34933e88			−2.88010
$566$		−	7.03409e87i		−	0.571587i
$567$	1.51779e88	+	1.14769e88i	1.16562	+	0.881389i
$568$	9.27580e87			0.673294
$569$			2.58787e88i			1.77562i	0.460214	+	0.887808i	$0.347773\pi$
$569$			2.58787e88i			1.77562i	−0.460214	+	0.887808i	$0.652227\pi$
$570$	−6.52018e87	+	3.99310e88i	−0.422926	+	2.59009i
$571$	1.09002e88			0.668467			0.334234	−	0.942490i	$-0.391523\pi$
$571$	1.09002e88			0.668467			0.334234	+	0.942490i	$0.391523\pi$
$572$			9.38737e87i			0.544341i
$573$	6.92174e87	+	1.13022e87i	0.379549	+	0.0619750i
$574$	−5.45505e88			−2.82891
$575$		−	3.32061e88i		−	1.62872i
$576$	−1.36370e88	−	4.57545e87i	−0.632701	−	0.212282i
$577$	2.06897e88			0.908088			0.454044	−	0.890979i	$-0.349981\pi$
$577$	2.06897e88			0.908088			0.454044	+	0.890979i	$0.349981\pi$
$578$			2.70663e88i			1.12393i
$579$	4.73923e87	−	2.90241e88i	0.186206	−	1.14037i
$580$	9.11773e88			3.38993
$581$		−	9.35049e87i		−	0.329002i
$582$	2.68085e88	+	4.37745e87i	0.892765	+	0.145776i
$583$	−3.98375e88			−1.25574
$584$			8.93331e88i			2.66564i
$585$	6.62761e87	−	1.97534e88i	0.187227	−	0.558025i
$586$	−3.32359e87			−0.0888962
$587$			3.30533e88i			0.837135i	0.908186	+	0.418568i	$0.137468\pi$
$587$			3.30533e88i			0.837135i	−0.908186	+	0.418568i	$0.862532\pi$
$588$	1.60053e88	−	9.80203e88i	0.383876	−	2.35094i
$589$	4.21996e88			0.958560
$590$			1.84233e88i			0.396373i
$591$	−5.51828e88	−	9.01057e87i	−1.12462	−	0.183634i
$592$	−9.79727e88			−1.89152
$593$			2.30640e88i			0.421876i	0.977499	+	0.210938i	$0.0676518\pi$
$593$			2.30640e88i			0.421876i	−0.977499	+	0.210938i	$0.932348\pi$
$594$	−3.40040e88	+	6.44364e88i	−0.589337	+	1.11677i
$595$	8.70565e88			1.42974
$596$		−	1.44216e89i		−	2.24457i
$597$	−2.98388e87	+	1.82740e88i	−0.0440152	+	0.269559i
$598$	4.49829e88			0.628940
$599$			1.28055e89i			1.69722i	0.529015	+	0.848612i	$0.322561\pi$
$599$			1.28055e89i			1.69722i	−0.529015	+	0.848612i	$0.677439\pi$
$600$	−2.50187e89	−	4.08521e88i	−3.14358	−	0.513303i
$601$	−1.18181e89			−1.40788			−0.703938	−	0.710261i	$-0.748577\pi$
$601$	−1.18181e89			−1.40788			−0.703938	+	0.710261i	$0.748577\pi$
$602$		−	1.57773e89i		−	1.78216i
$603$	−3.83300e88	−	1.28604e88i	−0.410567	−	0.137753i
$604$	2.15447e89			2.18856
$605$		−	8.19718e88i		−	0.789755i
$606$	1.74488e88	−	1.06860e89i	0.159456	−	0.976543i
$607$	2.13761e89			1.85306			0.926532	−	0.376217i	$-0.122775\pi$
$607$	2.13761e89			1.85306			0.926532	+	0.376217i	$0.122775\pi$
$608$			4.02345e88i			0.330890i
$609$	1.83534e89	+	2.99685e88i	1.43207	+	0.233836i
$610$	−2.30737e89			−1.70829
$611$		−	2.47518e88i		−	0.173895i
$612$	−6.01690e88	+	1.79332e89i	−0.401169	+	1.19567i
$613$	−8.21117e88			−0.519601			−0.259800	−	0.965662i	$-0.583657\pi$
$613$	−8.21117e88			−0.519601			−0.259800	+	0.965662i	$0.583657\pi$
$614$		−	4.37735e89i		−	2.62920i
$615$	−5.05915e88	+	3.09834e89i	−0.288452	+	1.76655i
$616$	3.74260e89			2.02577
$617$		−	8.38040e88i		−	0.430665i	−0.976541	−	0.215333i	$-0.930916\pi$
$617$		−	8.38040e88i		−	0.430665i	0.976541	−	0.215333i	$-0.0690835\pi$
$618$	3.11592e89	+	5.08786e88i	1.52039	+	0.248258i
$619$	6.36627e87			0.0294974			0.0147487	−	0.999891i	$-0.495305\pi$
$619$	6.36627e87			0.0294974			0.0147487	+	0.999891i	$0.495305\pi$
$620$			8.11736e89i			3.57175i
$621$	2.09096e89	+	1.10343e89i	0.873806	+	0.461120i
$622$	−5.21226e89			−2.06887
$623$		−	9.43987e88i		−	0.355917i
$624$	2.12034e88	−	1.29854e89i	0.0759450	−	0.465104i
$625$	2.02794e88			0.0690072
$626$		−	1.80028e89i		−	0.582053i
$627$	−2.11172e89	−	3.44814e88i	−0.648745	−	0.105931i
$628$	1.89396e89			0.552921
$629$		−	3.14555e89i		−	0.872722i
$630$	−1.50491e90	−	5.04923e89i	−3.96837	−	1.33146i
$631$	−4.95209e89			−1.24122			−0.620611	−	0.784119i	$-0.713115\pi$
$631$	−4.95209e89			−1.24122			−0.620611	+	0.784119i	$0.713115\pi$
$632$			5.36374e89i			1.27797i
$633$	−1.27314e89	+	7.79699e89i	−0.288375	+	1.76607i
$634$	3.14111e88			0.0676437
$635$			9.62230e88i			0.197024i
$636$	1.86120e90	+	3.03908e89i	3.62382	+	0.591718i
$637$	−2.21805e89			−0.410685
$638$			7.12033e89i			1.25383i
$639$	6.61803e88	−	1.97248e89i	0.110841	−	0.330359i
$640$	1.56883e90			2.49929
$641$			1.01898e90i			1.54422i	0.635489	+	0.772110i	$0.280799\pi$
$641$			1.01898e90i			1.54422i	−0.635489	+	0.772110i	$0.719201\pi$
$642$	2.73302e89	−	1.67376e90i	0.394023	−	2.41308i
$643$	7.51327e89			1.03057			0.515285	−	0.857019i	$-0.327686\pi$
$643$	7.51327e89			1.03057			0.515285	+	0.857019i	$0.327686\pi$
$644$		−	2.32074e90i		−	3.02886i
$645$	−8.96115e89	−	1.46323e89i	−1.11289	−	0.181720i
$646$	−8.20315e89			−0.969483
$647$		−	1.63174e90i		−	1.83532i	−0.397362	−	0.917662i	$-0.630074\pi$
$647$		−	1.63174e90i		−	1.83532i	0.397362	−	0.917662i	$-0.369926\pi$
$648$	1.08861e90	−	1.43966e90i	1.16539	−	1.54120i
$649$	−9.74301e88			−0.0992803
$650$			1.08183e90i			1.04938i
$651$	−2.66804e89	+	1.63397e90i	−0.246378	+	1.50887i
$652$	−3.28230e90			−2.88573
$653$		−	2.94932e89i		−	0.246888i	−0.992352	−	0.123444i	$-0.960606\pi$
$653$		−	2.94932e89i		−	0.246888i	0.992352	−	0.123444i	$-0.0393939\pi$
$654$	1.02667e90	+	1.67640e89i	0.818355	+	0.133626i
$655$	−8.70581e89			−0.660827
$656$			1.98247e90i			1.43313i
$657$	1.89965e90	+	6.37367e89i	1.30792	+	0.438832i
$658$	−1.88571e90			−1.23665
$659$		−	4.54952e89i		−	0.284205i	−0.989852	−	0.142103i	$-0.954614\pi$
$659$		−	4.54952e89i		−	0.284205i	0.989852	−	0.142103i	$-0.0453863\pi$
$660$	6.63270e89	−	4.06202e90i	0.394716	−	2.41733i
$661$	−1.64254e90			−0.931258			−0.465629	−	0.884980i	$-0.654172\pi$
$661$	−1.64254e90			−0.931258			−0.465629	+	0.884980i	$0.654172\pi$
$662$			5.66693e90i			3.06120i
$663$	4.16916e89	+	6.80765e88i	0.214593	+	0.0350400i
$664$	−8.86914e89			−0.435013
$665$		−	4.66170e90i		−	2.17897i
$666$	−1.82440e90	+	5.43757e90i	−0.812728	+	2.42231i
$667$	2.31055e90			0.981045
$668$			2.67569e90i			1.08290i
$669$	6.50202e89	−	3.98198e90i	0.250849	−	1.53626i
$670$	3.37263e90			1.24044
$671$		−	1.22023e90i		−	0.427879i
$672$	−1.55788e90	−	2.54380e89i	−0.520855	−	0.0850484i
$673$	4.58309e90			1.46109			0.730544	−	0.682866i	$-0.239267\pi$
$673$	4.58309e90			1.46109			0.730544	+	0.682866i	$0.239267\pi$
$674$		−	6.86371e90i		−	2.08662i
$675$	−2.65373e90	+	5.02872e90i	−0.769370	+	1.45793i
$676$	6.59440e90			1.82340
$677$			4.89782e90i			1.29171i	0.763460	+	0.645855i	$0.223499\pi$
$677$			4.89782e90i			1.29171i	−0.763460	+	0.645855i	$0.776501\pi$
$678$	−1.99536e90	+	1.22200e91i	−0.501963	+	3.07413i
$679$	−3.12973e90			−0.751058
$680$		−	8.25749e90i		−	1.89044i
$681$	−1.87436e89	−	3.06056e88i	−0.0409397	−	0.00668488i
$682$	−6.33911e90			−1.32108
$683$		−	1.00931e90i		−	0.200708i	−0.994952	−	0.100354i	$-0.968003\pi$
$683$		−	1.00931e90i		−	0.200708i	0.994952	−	0.100354i	$-0.0319975\pi$
$684$	9.60286e90	+	3.22193e90i	1.82224	+	0.611393i
$685$	9.44187e90			1.70986
$686$			2.01653e90i			0.348524i
$687$	1.02122e90	−	6.25417e90i	0.168462	−	1.03170i
$688$	−5.73380e90			−0.902844
$689$		−	4.21161e90i		−	0.633043i
$690$	−1.94646e91	−	3.17830e90i	−2.79302	−	0.456061i
$691$	−5.11815e90			−0.701157			−0.350579	−	0.936533i	$-0.614015\pi$
$691$	−5.11815e90			−0.701157			−0.350579	+	0.936533i	$0.614015\pi$
$692$			9.46842e90i			1.23846i
$693$	2.67024e90	−	7.95856e90i	0.333493	−	0.993965i
$694$	−1.53662e91			−1.83258
$695$		−	3.14705e90i		−	0.358418i
$696$	2.84258e90	−	1.74086e91i	0.309184	−	1.89351i
$697$	−6.36501e90			−0.661227
$698$			1.81305e90i			0.179902i
$699$	−4.70003e90	−	7.67449e89i	−0.445483	−	0.0727411i
$700$	5.58133e91			5.05359
$701$		−	9.51428e90i		−	0.822999i	−0.911410	−	0.411499i	$-0.865005\pi$
$701$		−	9.51428e90i		−	0.822999i	0.911410	−	0.411499i	$-0.134995\pi$
$702$	−6.81220e90	−	3.59490e90i	−0.562989	−	0.297097i
$703$	−1.68438e91			−1.33005
$704$			6.34560e90i			0.478793i
$705$	−1.74885e90	+	1.07104e91i	−0.126096	+	0.772240i
$706$	2.10281e89			0.0144894
$707$			1.24753e91i			0.821539i
$708$	4.55192e90	+	7.43265e89i	0.286504	+	0.0467821i
$709$	1.21885e91			0.733281			0.366641	−	0.930363i	$-0.380508\pi$
$709$	1.21885e91			0.733281			0.366641	+	0.930363i	$0.380508\pi$
$710$			1.73557e91i			0.998103i
$711$	1.14059e91	+	3.82688e90i	0.627050	+	0.210386i
$712$	−8.95391e90			−0.470601
$713$			2.05704e91i			1.03366i
$714$	5.18639e90	−	3.17626e91i	0.249185	−	1.52607i
$715$	−9.19171e90			−0.422282
$716$		−	3.39958e91i		−	1.49351i
$717$	−2.48683e91	−	4.06065e90i	−1.04480	−	0.170601i
$718$	4.77831e91			1.91996
$719$		−	3.50945e90i		−	0.134870i	−0.997724	−	0.0674349i	$-0.978519\pi$
$719$		−	3.50945e90i		−	0.134870i	0.997724	−	0.0674349i	$-0.0214815\pi$
$720$	−1.83499e91	+	5.46913e91i	−0.674519	+	2.01038i
$721$	−3.63764e91			−1.27906
$722$		−	8.39978e90i		−	0.282539i
$723$	6.19852e89	−	3.79611e90i	0.0199463	−	0.122156i
$724$	1.01755e92			3.13272
$725$			5.55682e91i			1.63685i
$726$	−2.99074e91	−	4.88347e90i	−0.842961	−	0.137644i
$727$	5.75909e90			0.155329			0.0776645	−	0.996980i	$-0.475254\pi$
$727$	5.75909e90			0.155329			0.0776645	+	0.996980i	$0.475254\pi$
$728$			3.95666e91i			1.02123i
$729$	−2.28472e91	−	3.34207e91i	−0.564354	−	0.825533i
$730$	−1.67149e92			−3.95159
$731$		−	1.84092e91i		−	0.416561i
$732$	−9.30877e90	+	5.70090e91i	−0.201622	+	1.23478i
$733$	−1.72966e91			−0.358620			−0.179310	−	0.983793i	$-0.557387\pi$
$733$	−1.72966e91			−0.358620			−0.179310	+	0.983793i	$0.557387\pi$
$734$			1.69682e91i			0.336793i
$735$	9.59773e91	+	1.56717e91i	1.82379	+	0.297799i
$736$	−1.96125e91			−0.356815
$737$			1.78358e91i			0.310694i
$738$	1.10029e92	+	3.69167e91i	1.83529	+	0.615771i
$739$	9.17504e91			1.46550			0.732750	−	0.680498i	$-0.238236\pi$
$739$	9.17504e91			1.46550			0.732750	+	0.680498i	$0.238236\pi$
$740$		−	3.24001e92i		−	4.95600i
$741$	3.64536e90	−	2.23250e91i	0.0534021	−	0.327046i
$742$	−3.20861e92			−4.50185
$743$		−	8.00381e91i		−	1.07561i	−0.843069	−	0.537805i	$-0.819254\pi$
$743$		−	8.00381e91i		−	1.07561i	0.843069	−	0.537805i	$-0.180746\pi$
$744$	1.54986e92	+	2.53070e91i	1.99507	+	0.325766i
$745$	1.41210e92			1.74126
$746$		−	7.65503e91i		−	0.904283i
$747$	−6.32788e90	+	1.88601e91i	−0.0716142	+	0.213444i
$748$	8.34472e91			0.904817
$749$			1.95401e92i			2.03006i
$750$	3.00689e91	−	1.84149e92i	0.299335	−	1.83320i
$751$	1.65978e92			1.58333			0.791667	−	0.610953i	$-0.209214\pi$
$751$	1.65978e92			1.58333			0.791667	+	0.610953i	$0.209214\pi$
$752$			6.85303e91i			0.626487i
$753$	−1.22249e92	−	1.99615e91i	−1.07104	−	0.174886i
$754$	−7.52760e91			−0.632082
$755$			2.10956e92i			1.69781i
$756$	−1.85467e92	+	3.51452e92i	−1.43077	+	2.71125i
$757$	−2.28153e91			−0.168717			−0.0843585	−	0.996435i	$-0.526884\pi$
$757$	−2.28153e91			−0.168717			−0.0843585	+	0.996435i	$0.526884\pi$
$758$		−	3.46322e92i		−	2.45508i
$759$	1.68081e91	−	1.02937e92i	0.114231	−	0.699574i
$760$	−4.42172e92			−2.88109
$761$		−	2.90799e91i		−	0.181670i	−0.995866	−	0.0908351i	$-0.971046\pi$
$761$		−	2.90799e91i		−	0.181670i	0.995866	−	0.0908351i	$-0.0289536\pi$
$762$	3.51070e91	+	5.73248e90i	0.210298	+	0.0343387i
$763$	−1.19857e92			−0.688459
$764$			1.46465e92i			0.806766i
$765$	−1.75594e92	−	5.89149e91i	−0.927564	−	0.311214i
$766$	4.74470e92			2.40374
$767$		−	1.03003e91i		−	0.0500493i
$768$	7.03874e91	−	4.31068e92i	0.328047	−	2.00903i
$769$	−2.60713e92			−1.16552			−0.582760	−	0.812644i	$-0.698027\pi$
$769$	−2.60713e92			−1.16552			−0.582760	+	0.812644i	$0.698027\pi$
$770$			7.00268e92i			3.00304i
$771$	3.92349e92	+	6.40652e91i	1.61411	+	0.263561i
$772$	6.14156e92			2.42396
$773$			1.76946e92i			0.670034i	0.942212	+	0.335017i	$0.108742\pi$
$773$			1.76946e92i			0.670034i	−0.942212	+	0.335017i	$0.891258\pi$
$774$	−1.06772e92	+	3.18231e92i	−0.387924	+	1.15620i
$775$	−4.94714e92			−1.72465
$776$			2.96861e92i			0.993067i
$777$	1.06494e92	−	6.52192e92i	0.341863	−	2.09364i
$778$	2.65773e92			0.818773
$779$			3.40834e92i			1.00773i
$780$	4.29435e92	+	7.01208e91i	1.21863	+	0.198985i
$781$	−9.17841e91			−0.249997
$782$		−	3.99867e92i		−	1.04544i
$783$	−3.49909e92	−	1.84652e92i	−0.878171	−	0.463424i
$784$	6.14112e92			1.47956
$785$			1.85449e92i			0.428938i
$786$	−5.18649e91	+	3.17632e92i	−0.115173	+	0.705347i
$787$	4.11840e91			0.0878086			0.0439043	−	0.999036i	$-0.486020\pi$
$787$	4.11840e91			0.0878086			0.0439043	+	0.999036i	$0.486020\pi$
$788$		−	1.16768e93i		−	2.39048i
$789$	3.21975e92	+	5.25740e91i	0.632933	+	0.103349i
$790$	−1.00360e93			−1.89449
$791$		−	1.42662e93i		−	2.58618i
$792$	−7.54886e92	−	2.53278e92i	−1.31424	−	0.440952i
$793$	1.29002e92			0.215703
$794$			6.35175e92i			1.02009i
$795$	−2.97574e92	+	1.82241e93i	−0.459036	+	2.81124i
$796$	−3.86681e92			−0.572973
$797$			7.85770e91i			0.111848i	0.998435	+	0.0559241i	$0.0178105\pi$
$797$			7.85770e91i			0.111848i	−0.998435	+	0.0559241i	$0.982190\pi$
$798$	−1.70082e93	−	2.77721e92i	−2.32577	−	0.379766i
$799$	−2.20026e92			−0.289053
$800$		−	4.71676e92i		−	0.595339i
$801$	−6.38837e91	+	1.90403e92i	−0.0774728	+	0.230905i
$802$	9.82816e92			1.14523
$803$		−	8.83952e92i		−	0.989763i
$804$	1.36064e92	−	8.33287e92i	0.146403	−	0.896605i
$805$	2.27237e93			2.34969
$806$		−	6.70169e92i		−	0.665983i
$807$	−1.88905e93	−	3.08455e92i	−1.80422	−	0.294604i
$808$	1.18330e93			1.08626
$809$		−	4.07022e92i		−	0.359141i	−0.983745	−	0.179570i	$-0.942529\pi$
$809$		−	4.07022e92i		−	0.359141i	0.983745	−	0.179570i	$-0.0574708\pi$
$810$	2.69371e93	+	2.03687e93i	2.28471	+	1.72760i
$811$	−5.40998e91			−0.0441091			−0.0220546	−	0.999757i	$-0.507021\pi$
$811$	−5.40998e91			−0.0441091			−0.0220546	+	0.999757i	$0.507021\pi$
$812$			3.88361e93i			3.04399i
$813$	1.77012e92	−	1.08406e93i	0.133385	−	0.816878i
$814$	2.53023e93			1.83307
$815$		−	3.21389e93i		−	2.23866i
$816$	−1.15432e93	−	1.88484e92i	−0.773108	−	0.126238i
$817$	−9.85774e92			−0.634851
$818$			2.65557e93i			1.64457i
$819$	8.41377e92	+	2.82297e92i	0.501079	+	0.168121i
$820$	−6.55615e93			−3.75496
$821$		−	1.43917e93i		−	0.792740i	−0.918091	−	0.396370i	$-0.870270\pi$
$821$		−	1.43917e93i		−	0.792740i	0.918091	−	0.396370i	$-0.129730\pi$
$822$	5.62499e92	−	3.44487e93i	0.298005	−	1.82505i
$823$	1.83249e93			0.933787			0.466893	−	0.884314i	$-0.345373\pi$
$823$	1.83249e93			0.933787			0.466893	+	0.884314i	$0.345373\pi$
$824$			3.45038e93i			1.69120i
$825$	2.47560e93	+	4.04231e92i	1.16723	+	0.190592i
$826$	−7.84725e92			−0.355923
$827$			3.41447e93i			1.48987i	0.667139	+	0.744933i	$0.267519\pi$
$827$			3.41447e93i			1.48987i	−0.667139	+	0.744933i	$0.732481\pi$
$828$	−1.57055e93	+	4.68097e93i	−0.659295	+	1.96501i
$829$	−1.38672e92			−0.0560074			−0.0280037	−	0.999608i	$-0.508915\pi$
$829$	−1.38672e92			−0.0560074			−0.0280037	+	0.999608i	$0.508915\pi$
$830$		−	1.65948e93i		−	0.644872i
$831$	−7.95384e92	+	4.87111e93i	−0.297402	+	1.82136i
$832$	−6.70855e92			−0.241370
$833$			1.97169e93i			0.682651i
$834$	−1.14820e93	−	1.87486e92i	−0.382565	−	0.0624675i
$835$	−2.61992e93			−0.840080
$836$		−	4.46843e93i		−	1.37897i
$837$	1.64393e93	−	3.11518e93i	0.488279	−	0.925270i
$838$	5.60759e93			1.60313
$839$		−	5.52754e93i		−	1.52107i	−0.649297	−	0.760535i	$-0.724937\pi$
$839$		−	5.52754e93i		−	1.52107i	0.649297	−	0.760535i	$-0.275063\pi$
$840$	2.79561e93	−	1.71209e94i	0.740523	−	4.53513i
$841$	5.51190e91			0.0140550
$842$			2.88962e93i			0.709340i
$843$	−2.63815e92	−	4.30773e91i	−0.0623472	−	0.0101804i
$844$	−1.64986e94			−3.75395
$845$			6.45696e93i			1.41453i
$846$	3.80349e93	+	1.27614e93i	0.802289	+	0.269182i
$847$	3.49151e93			0.709160
$848$			1.16607e94i			2.28065i
$849$	2.77866e92	−	1.70172e93i	0.0523347	−	0.320510i
$850$	9.61671e93			1.74430
$851$		−	8.21060e93i		−	1.43426i
$852$	4.28814e93	+	7.00194e92i	0.721443	+	0.117802i
$853$	−7.73765e93			−1.25383			−0.626917	−	0.779086i	$-0.715683\pi$
$853$	−7.73765e93			−1.25383			−0.626917	+	0.779086i	$0.715683\pi$
$854$		−	9.82802e93i		−	1.53396i
$855$	−3.15478e93	+	9.40271e93i	−0.474300	+	1.41364i
$856$	1.85342e94			2.68419
$857$			3.42764e93i			0.478200i	0.970995	+	0.239100i	$0.0768523\pi$
$857$			3.42764e93i			0.478200i	−0.970995	+	0.239100i	$0.923148\pi$
$858$	−5.47596e92	+	3.35360e93i	−0.0735982	+	0.450732i
$859$	8.85002e93			1.14594			0.572972	−	0.819575i	$-0.305790\pi$
$859$	8.85002e93			1.14594			0.572972	+	0.819575i	$0.305790\pi$
$860$		−	1.89620e94i		−	2.36556i
$861$	−1.31971e94	−	2.15490e93i	−1.58627	−	0.259016i
$862$	−1.23820e94			−1.43403
$863$			5.71192e93i			0.637436i	0.947850	+	0.318718i	$0.103252\pi$
$863$			5.71192e93i			0.637436i	−0.947850	+	0.318718i	$0.896748\pi$
$864$	2.97011e93	+	1.56737e93i	0.319399	+	0.168551i
$865$	−9.27108e93			−0.960760
$866$		−	8.80569e93i		−	0.879409i
$867$	−1.06920e93	+	6.54800e93i	−0.102907	+	0.630228i
$868$	−3.45751e94			−3.20725
$869$		−	5.30743e93i		−	0.474517i
$870$	3.25728e94	+	5.31867e93i	2.80697	+	0.458340i
$871$	−1.88560e93			−0.156628
$872$			1.13687e94i			0.910296i
$873$	6.31270e93	+	2.11802e93i	0.487258	+	0.163484i
$874$	−2.14121e94			−1.59328
$875$			2.14983e94i			1.54222i
$876$	−6.74341e93	+	4.12981e94i	−0.466389	+	2.85627i
$877$	2.69014e94			1.79386			0.896930	−	0.442172i	$-0.145792\pi$
$877$	2.69014e94			1.79386			0.896930	+	0.442172i	$0.145792\pi$
$878$		−	1.56452e93i		−	0.100591i
$879$	−8.04055e92	−	1.31291e92i	−0.0498473	−	0.00813937i
$880$	2.54491e94			1.52134
$881$		−	1.87151e93i		−	0.107885i	−0.998544	−	0.0539427i	$-0.982821\pi$
$881$		−	1.87151e93i		−	0.107885i	0.998544	−	0.0539427i	$-0.0171788\pi$
$882$	1.14357e94	−	3.40837e94i	0.635723	−	1.89475i
$883$	−9.67878e92			−0.0518893			−0.0259447	−	0.999663i	$-0.508259\pi$
$883$	−9.67878e92			−0.0518893			−0.0259447	+	0.999663i	$0.508259\pi$
$884$			8.82202e93i			0.456137i
$885$	−7.27774e92	+	4.45705e93i	−0.0362921	+	0.222261i
$886$	1.83773e93			0.0883901
$887$		−	2.79661e94i		−	1.29741i	−0.761041	−	0.648704i	$-0.775311\pi$
$887$		−	2.79661e94i		−	1.29741i	0.761041	−	0.648704i	$-0.224689\pi$
$888$	−6.18618e94	−	1.01012e94i	−2.76826	−	0.452019i
$889$	−4.09853e93			−0.176918
$890$		−	1.67534e94i		−	0.697628i
$891$	−1.07718e94	+	1.42455e94i	−0.432715	+	0.572255i
$892$	8.42595e94			3.26545
$893$			1.17820e94i			0.440525i
$894$	8.41259e93	−	5.15206e94i	0.303479	−	1.85857i
$895$	3.32873e94			1.15862
$896$			6.68230e94i			2.24424i
$897$	1.08824e94	+	1.77695e93i	0.352670	+	0.0575860i
$898$	5.30689e94			1.65958
$899$		−	3.44233e94i		−	1.03882i
$900$	−1.12576e95	−	3.77713e94i	−3.27858	−	1.10002i
$901$	−3.74383e94			−1.05226
$902$		−	5.11991e94i		−	1.38884i
$903$	6.23249e93	−	3.81692e94i	0.163175	−	0.999321i
$904$	−1.35317e95			−3.41951
$905$			9.96343e94i			2.43027i
$906$	7.69675e94	+	1.25677e94i	1.81220	+	0.295906i
$907$	9.77359e93			0.222137			0.111068	−	0.993813i	$-0.464573\pi$
$907$	9.77359e93			0.222137			0.111068	+	0.993813i	$0.464573\pi$
$908$		−	3.96617e93i		−	0.0870211i
$909$	8.44254e93	−	2.51627e94i	0.178825	−	0.532983i
$910$	−7.40321e94			−1.51390
$911$		−	1.55170e94i		−	0.306352i	−0.988199	−	0.153176i	$-0.951050\pi$
$911$		−	1.55170e94i		−	0.306352i	0.988199	−	0.153176i	$-0.0489501\pi$
$912$	−1.00929e94	+	6.18114e94i	−0.192390	+	1.17824i
$913$	8.77602e93			0.161522
$914$			5.53051e94i			0.982849i
$915$	−5.58208e94	−	9.11475e93i	−0.957902	−	0.156412i
$916$	1.32339e95			2.19298
$917$		−	3.70816e94i		−	0.593389i
$918$	−3.19562e94	+	6.05558e94i	−0.493843	+	0.935814i
$919$	−3.50719e94			−0.523436			−0.261718	−	0.965144i	$-0.584289\pi$
$919$	−3.50719e94			−0.523436			−0.261718	+	0.965144i	$0.584289\pi$
$920$		−	2.15539e95i		−	3.10682i
$921$	1.72918e94	−	1.05899e95i	0.240730	−	1.47429i
$922$	−3.76675e94			−0.506497
$923$		−	9.70340e93i		−	0.126029i
$924$	1.73018e95	+	2.82514e94i	2.17064	+	0.354435i
$925$	1.97463e95			2.39304
$926$			2.22896e95i			2.60946i
$927$	7.33717e94	+	2.46175e94i	0.829807	+	0.278415i
$928$	3.28203e94			0.358597
$929$			6.14035e94i			0.648172i	0.946028	+	0.324086i	$0.105057\pi$
$929$			6.14035e94i			0.648172i	−0.946028	+	0.324086i	$0.894943\pi$
$930$	−4.73512e94	+	2.89990e95i	−0.482922	+	2.95752i
$931$	1.05580e95			1.04038
$932$		−	9.94536e94i		−	0.946916i
$933$	−1.26097e95	−	2.05899e94i	−1.16009	−	0.189427i
$934$	−9.52838e94			−0.847069
$935$			8.17080e94i			0.701929i
$936$	2.67765e94	−	7.98064e94i	0.222293	−	0.662538i
$937$	−2.00459e95			−1.60827			−0.804136	−	0.594446i	$-0.797371\pi$
$937$	−2.00459e95			−1.60827			−0.804136	+	0.594446i	$0.797371\pi$
$938$			1.43654e95i			1.11385i
$939$	7.11162e93	−	4.35532e94i	0.0532930	−	0.326378i
$940$	−2.26633e95			−1.64147
$941$		−	1.86552e95i		−	1.30597i	−0.757372	−	0.652984i	$-0.773517\pi$
$941$		−	1.86552e95i		−	1.30597i	0.757372	−	0.652984i	$-0.226483\pi$
$942$	6.76611e94	+	1.10481e94i	0.457836	+	0.0747582i
$943$	−1.66141e95			−1.08668
$944$			2.85185e94i			0.180311i
$945$	−3.44127e95	−	1.81601e95i	−2.10330	−	1.10994i
$946$	1.48080e95			0.874945
$947$			9.92817e93i			0.0567113i	0.999598	+	0.0283557i	$0.00902710\pi$
$947$			9.92817e93i			0.0567113i	−0.999598	+	0.0283557i	$0.990973\pi$
$948$	−4.04888e94	+	2.47962e95i	−0.223598	+	1.36936i
$949$	9.34512e94			0.498961
$950$		−	5.14956e95i		−	2.65836i
$951$	7.59910e93	+	1.24083e93i	0.0379303	+	0.00619348i
$952$	3.51720e95			1.69752
$953$		−	9.94290e94i		−	0.464024i	−0.972713	−	0.232012i	$-0.925469\pi$
$953$		−	9.94290e94i		−	0.464024i	0.972713	−	0.232012i	$-0.0745308\pi$
$954$	6.47180e95	+	2.17140e95i	2.92063	+	0.979924i
$955$	−1.43413e95			−0.625864
$956$		−	5.26218e95i		−	2.22082i
$957$	−2.81273e94	+	1.72258e95i	−0.114801	+	0.703068i
$958$	−6.69818e95			−2.64399
$959$			4.02168e95i			1.53537i
$960$	2.90287e95	+	4.73997e94i	1.07188	+	0.175023i
$961$	2.64709e94			0.0945411
$962$			2.67495e95i			0.924088i
$963$	1.32236e95	−	3.94127e95i	0.441886	−	1.31703i
$964$	8.03265e94			0.259653
$965$			6.01355e95i			1.88043i
$966$	1.35377e95	−	8.29076e95i	0.409520	−	2.50799i
$967$	3.77518e95			1.10482			0.552408	−	0.833574i	$-0.313709\pi$
$967$	3.77518e95			1.10482			0.552408	+	0.833574i	$0.313709\pi$
$968$		−	3.31177e95i		−	0.937667i
$969$	−1.98454e95	−	3.24048e94i	−0.543625	−	0.0887663i
$970$	−5.55450e95			−1.47214
$971$		−	2.49418e95i		−	0.639607i	−0.947484	−	0.319803i	$-0.896383\pi$
$971$		−	2.49418e95i		−	0.639607i	0.947484	−	0.319803i	$-0.103617\pi$
$972$	6.11932e95	−	5.83371e95i	1.51839	−	1.44752i
$973$	1.34046e95			0.321841
$974$			6.01263e95i			1.39694i
$975$	−4.27353e94	+	2.61720e95i	−0.0960812	+	0.588423i
$976$	−3.57170e95			−0.777107
$977$		−	2.78916e95i		−	0.587282i	−0.955916	−	0.293641i	$-0.905133\pi$
$977$		−	2.78916e95i		−	0.587282i	0.955916	−	0.293641i	$-0.0948671\pi$
$978$	−1.17259e96	−	1.91468e95i	−2.38948	−	0.390168i
$979$	8.85991e94			0.174736
$980$			2.03090e96i			3.87662i
$981$	2.41753e95	+	8.11124e94i	0.446646	+	0.149858i
$982$	−1.05727e96			−1.89069
$983$		−	3.05689e95i		−	0.529136i	−0.964367	−	0.264568i	$-0.914771\pi$
$983$		−	3.05689e95i		−	0.529136i	0.964367	−	0.264568i	$-0.0852294\pi$
$984$	−2.04397e95	+	1.25177e96i	−0.342476	+	2.09740i
$985$	1.14334e96			1.85446
$986$			6.69152e95i			1.05066i
$987$	−4.56198e95	−	7.44907e94i	−0.693432	−	0.113228i
$988$	4.72402e95			0.695167
$989$		−	4.80521e95i		−	0.684590i
$990$	4.73902e95	−	1.41245e96i	0.653675	−	1.94826i
$991$	6.14199e95			0.820261			0.410131	−	0.912027i	$-0.365483\pi$
$991$	6.14199e95			0.820261			0.410131	+	0.912027i	$0.365483\pi$
$992$			2.92193e95i			0.377830i
$993$	−2.23860e95	+	1.37097e96i	−0.280285	+	1.71653i
$994$	−7.39251e95			−0.896247
$995$		−	3.78621e95i		−	0.444495i
$996$	−4.10014e95	−	6.69496e94i	−0.466123	−	0.0761113i
$997$	1.23710e96			1.36194			0.680970	−	0.732311i	$-0.261558\pi$
$997$	1.23710e96			1.36194			0.680970	+	0.732311i	$0.261558\pi$
$998$		−	3.06630e96i		−	3.26916i
$999$	−6.56166e95	+	1.24341e96i	−0.677514	+	1.28386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.65.b.a.2.20	yes	20
3.2	odd	2	inner	3.65.b.a.2.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.65.b.a.2.1	✓	20	3.2	odd	2	inner
3.65.b.a.2.20	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)

\(f(q)\)	\(=\)	\(q+7.55940e9i q^{2} +(-2.98618e14 + 1.82880e15i) q^{3} -3.86978e19 q^{4} -3.78912e22i q^{5} +(-1.38246e25 - 2.25737e24i) q^{6} +1.61394e27 q^{7} -1.53086e29i q^{8} +(-3.25534e30 - 1.09222e30i) q^{9} +O(q^{10})\)	\(q+7.55940e9i q^{2} +(-2.98618e14 + 1.82880e15i) q^{3} -3.86978e19 q^{4} -3.78912e22i q^{5} +(-1.38246e25 - 2.25737e24i) q^{6} +1.61394e27 q^{7} -1.53086e29i q^{8} +(-3.25534e30 - 1.09222e30i) q^{9} +2.86435e32 q^{10} +1.51478e33i q^{11} +(1.15558e34 - 7.07705e34i) q^{12} -1.60143e35 q^{13} +1.22004e37i q^{14} +(6.92955e37 + 1.13150e37i) q^{15} +4.43388e38 q^{16} +1.42356e39i q^{17} +(8.25656e39 - 2.46084e40i) q^{18} +7.62287e40 q^{19} +1.46631e42i q^{20} +(-4.81951e41 + 2.95158e42i) q^{21} -1.14509e43 q^{22} +3.71581e43i q^{23} +(2.79963e44 + 4.57141e43i) q^{24} -8.93643e44 q^{25} -1.21058e45i q^{26} +(2.96956e45 - 5.62721e45i) q^{27} -6.24559e46 q^{28} -6.21817e46i q^{29} +(-8.55345e46 + 5.23832e47i) q^{30} +5.53593e47 q^{31} +5.27813e47i q^{32} +(-2.77024e48 - 4.52341e47i) q^{33} -1.07612e49 q^{34} -6.11542e49i q^{35} +(1.25974e50 + 4.22666e49i) q^{36} -2.20964e50 q^{37} +5.76243e50i q^{38} +(4.78214e49 - 2.92869e50i) q^{39} -5.80060e51 q^{40} +4.47120e51i q^{41} +(-2.23121e52 - 3.64326e51i) q^{42} -1.29318e52 q^{43} -5.86188e52i q^{44} +(-4.13857e52 + 1.23349e53i) q^{45} -2.80893e53 q^{46} +1.54561e53i q^{47} +(-1.32403e53 + 8.10868e53i) q^{48} +1.38504e54 q^{49} -6.75540e54i q^{50} +(-2.60340e54 - 4.25099e53i) q^{51} +6.19716e54 q^{52} +2.62991e55i q^{53} +(4.25383e55 + 2.24481e55i) q^{54} +5.73970e55 q^{55} -2.47071e56i q^{56} +(-2.27632e55 + 1.39407e56i) q^{57} +4.70056e56 q^{58} +6.43195e55i q^{59} +(-2.68158e57 - 4.37865e56i) q^{60} -8.05548e56 q^{61} +4.18483e57i q^{62} +(-5.25392e57 - 1.76278e57i) q^{63} +4.18911e57 q^{64} +6.06800e57i q^{65} +(3.41943e57 - 2.09413e58i) q^{66} +1.17745e58 q^{67} -5.50885e58i q^{68} +(-6.79547e58 - 1.10961e58i) q^{69} +4.62289e59 q^{70} +6.05922e58i q^{71} +(-1.67204e59 + 4.98346e59i) q^{72} -5.83550e59 q^{73} -1.67036e60i q^{74} +(2.66857e59 - 1.63429e60i) q^{75} -2.94988e60 q^{76} +2.44477e60i q^{77} +(2.21391e60 + 3.61501e59i) q^{78} -3.50375e60 q^{79} -1.68005e61i q^{80} +(9.40428e60 + 7.11112e60i) q^{81} -3.37996e61 q^{82} -5.79358e60i q^{83} +(1.86504e61 - 1.14219e62i) q^{84} +5.39403e61 q^{85} -9.77566e61i q^{86} +(1.13718e62 + 1.85685e61i) q^{87} +2.31892e62 q^{88} -5.84896e61i q^{89} +(-9.32442e62 - 3.12851e62i) q^{90} -2.58461e62 q^{91} -1.43793e63i q^{92} +(-1.65312e62 + 1.01241e63i) q^{93} -1.16839e63 q^{94} -2.88840e63i q^{95} +(-9.65264e62 - 1.57614e62i) q^{96} -1.93918e63 q^{97} +1.04701e64i q^{98} +(1.65448e63 - 4.93114e63i) 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

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