LMFDB - Embedded newform 3.65.b.a.2.14

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			2.14
Root			$5.00631e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.65.b.a.2.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.00379e9i q^{2} +(1.81065e15 - 3.93978e14i) q^{3} +9.42400e18 q^{4} -2.20086e22i q^{5} +(1.18343e24 + 5.43882e24i) q^{6} +9.43770e26 q^{7} +8.37178e28i q^{8} +(3.12325e30 - 1.42671e30i) q^{9} +O(q^{10})$	\(q+3.00379e9i q^{2} +(1.81065e15 - 3.93978e14i) q^{3} +9.42400e18 q^{4} -2.20086e22i q^{5} +(1.18343e24 + 5.43882e24i) q^{6} +9.43770e26 q^{7} +8.37178e28i q^{8} +(3.12325e30 - 1.42671e30i) q^{9} +6.61093e31 q^{10} -1.69655e33i q^{11} +(1.70636e34 - 3.71285e33i) q^{12} +2.86301e35 q^{13} +2.83489e36i q^{14} +(-8.67092e36 - 3.98500e37i) q^{15} -7.76285e37 q^{16} +3.89724e39i q^{17} +(4.28555e39 + 9.38157e39i) q^{18} -1.08676e40 q^{19} -2.07409e41i q^{20} +(1.70884e42 - 3.71825e41i) q^{21} +5.09607e42 q^{22} -1.19572e43i q^{23} +(3.29830e43 + 1.51584e44i) q^{24} +5.77211e43 q^{25} +8.59988e44i q^{26} +(5.09302e45 - 3.81378e45i) q^{27} +8.89409e45 q^{28} +6.29558e46i q^{29} +(1.19701e47 - 2.60456e46i) q^{30} +6.35077e47 q^{31} +1.31114e48i q^{32} +(-6.68403e47 - 3.07186e48i) q^{33} -1.17065e49 q^{34} -2.07711e49i q^{35} +(2.94335e49 - 1.34454e49i) q^{36} -1.98298e50 q^{37} -3.26439e49i q^{38} +(5.18392e50 - 1.12796e50i) q^{39} +1.84251e51 q^{40} -6.64278e51i q^{41} +(1.11688e51 + 5.13300e51i) q^{42} +2.64805e51 q^{43} -1.59883e52i q^{44} +(-3.14000e52 - 6.87384e52i) q^{45} +3.59168e52 q^{46} -3.26664e53i q^{47} +(-1.40558e53 + 3.05839e52i) q^{48} -3.29058e53 q^{49} +1.73382e53i q^{50} +(1.53543e54 + 7.05656e54i) q^{51} +2.69810e54 q^{52} -1.07005e55i q^{53} +(1.14558e55 + 1.52984e55i) q^{54} -3.73387e55 q^{55} +7.90104e55i q^{56} +(-1.96774e55 + 4.28159e54i) q^{57} -1.89106e56 q^{58} -5.16286e56i q^{59} +(-8.17147e55 - 3.75546e56i) q^{60} +1.92706e57 q^{61} +1.90764e57i q^{62} +(2.94763e57 - 1.34649e57i) q^{63} -5.37039e57 q^{64} -6.30110e57i q^{65} +(9.22722e57 - 2.00774e57i) q^{66} -2.61319e58 q^{67} +3.67276e58i q^{68} +(-4.71086e57 - 2.16503e58i) q^{69} +6.23920e58 q^{70} +1.40259e59i q^{71} +(1.19441e59 + 2.61471e59i) q^{72} +5.03853e59 q^{73} -5.95645e59i q^{74} +(1.04513e59 - 2.27408e58i) q^{75} -1.02416e59 q^{76} -1.60115e60i q^{77} +(3.38816e59 + 1.55714e60i) q^{78} +7.40798e60 q^{79} +1.70850e60i q^{80} +(7.71915e60 - 8.91196e60i) q^{81} +1.99535e61 q^{82} +4.72747e61i q^{83} +(1.61041e61 - 3.50408e60i) q^{84} +8.57730e61 q^{85} +7.95419e60i q^{86} +(2.48032e61 + 1.13991e62i) q^{87} +1.42031e62 q^{88} -5.97669e61i q^{89} +(2.06476e62 - 9.43191e61i) q^{90} +2.70203e62 q^{91} -1.12684e62i q^{92} +(1.14990e63 - 2.50206e62i) q^{93} +9.81230e62 q^{94} +2.39181e62i q^{95} +(5.16561e62 + 2.37402e63i) q^{96} -5.26812e62 q^{97} -9.88420e62i q^{98} +(-2.42049e63 - 5.29874e63i) 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 $

$2$			3.00379e9i			0.699374i	0.936867	+	0.349687i	$0.113712\pi$
$2$			3.00379e9i			0.699374i	−0.936867	+	0.349687i	$0.886288\pi$
$3$	1.81065e15	−	3.93978e14i	0.977136	−	0.212614i
$3$	1.81065e15	−	3.93978e14i	0.977136	−	0.212614i
$4$	9.42400e18			0.510876
$5$		−	2.20086e22i		−	0.945264i	−0.881260	−	0.472632i	$-0.843304\pi$
$5$		−	2.20086e22i		−	0.945264i	0.881260	−	0.472632i	$-0.156696\pi$
$6$	1.18343e24	+	5.43882e24i	0.148697	+	0.683384i
$7$	9.43770e26			0.854533			0.427267	−	0.904126i	$-0.359477\pi$
$7$	9.43770e26			0.854533			0.427267	+	0.904126i	$0.359477\pi$
$8$			8.37178e28i			1.05667i
$9$	3.12325e30	−	1.42671e30i	0.909591	−	0.415506i
$10$	6.61093e31			0.661093
$11$		−	1.69655e33i		−	0.803527i	−0.915743	−	0.401763i	$-0.868397\pi$
$11$		−	1.69655e33i		−	0.803527i	0.915743	−	0.401763i	$-0.131603\pi$
$12$	1.70636e34	−	3.71285e33i	0.499195	−	0.108619i
$13$	2.86301e35			0.646600			0.323300	−	0.946296i	$-0.395208\pi$
$13$	2.86301e35			0.646600			0.323300	+	0.946296i	$0.395208\pi$
$14$			2.83489e36i			0.597638i
$15$	−8.67092e36	−	3.98500e37i	−0.200976	−	0.923651i
$16$	−7.76285e37			−0.228130
$17$			3.89724e39i			1.64586i	0.568145	+	0.822929i	$0.307661\pi$
$17$			3.89724e39i			1.64586i	−0.568145	+	0.822929i	$0.692339\pi$
$18$	4.28555e39	+	9.38157e39i	0.290594	+	0.636144i
$19$	−1.08676e40			−0.130622			−0.0653112	−	0.997865i	$-0.520804\pi$
$19$	−1.08676e40			−0.130622			−0.0653112	+	0.997865i	$0.520804\pi$
$20$		−	2.07409e41i		−	0.482913i
$21$	1.70884e42	−	3.71825e41i	0.834996	−	0.181686i
$22$	5.09607e42			0.561966
$23$		−	1.19572e43i		−	0.317934i	−0.987284	−	0.158967i	$-0.949184\pi$
$23$		−	1.19572e43i		−	0.317934i	0.987284	−	0.158967i	$-0.0508164\pi$
$24$	3.29830e43	+	1.51584e44i	0.224662	+	1.03251i
$25$	5.77211e43			0.106477
$26$			8.59988e44i			0.452215i
$27$	5.09302e45	−	3.81378e45i	0.800452	−	0.599397i
$28$	8.89409e45			0.436561
$29$			6.29558e46i			1.00531i	0.864487	+	0.502654i	$0.167643\pi$
$29$			6.29558e46i			1.00531i	−0.864487	+	0.502654i	$0.832357\pi$
$30$	1.19701e47	−	2.60456e46i	0.645978	−	0.140558i
$31$	6.35077e47			1.20020			0.600098	−	0.799926i	$-0.295128\pi$
$31$	6.35077e47			1.20020			0.600098	+	0.799926i	$0.295128\pi$
$32$			1.31114e48i			0.897119i
$33$	−6.68403e47	−	3.07186e48i	−0.170841	−	0.785155i
$34$	−1.17065e49			−1.15107
$35$		−	2.07711e49i		−	0.807759i
$36$	2.94335e49	−	1.34454e49i	0.464688	−	0.212272i
$37$	−1.98298e50			−1.30276			−0.651378	−	0.758754i	$-0.725809\pi$
$37$	−1.98298e50			−1.30276			−0.651378	+	0.758754i	$0.725809\pi$
$38$		−	3.26439e49i		−	0.0913539i
$39$	5.18392e50	−	1.12796e50i	0.631816	−	0.137476i
$40$	1.84251e51			0.998829
$41$		−	6.64278e51i		−	1.63405i	−0.576600	−	0.817027i	$-0.695621\pi$
$41$		−	6.64278e51i		−	1.63405i	0.576600	−	0.817027i	$-0.304379\pi$
$42$	1.11688e51	+	5.13300e51i	0.127066	+	0.583974i
$43$	2.64805e51			0.141885			0.0709424	−	0.997480i	$-0.477399\pi$
$43$	2.64805e51			0.141885			0.0709424	+	0.997480i	$0.477399\pi$
$44$		−	1.59883e52i		−	0.410503i
$45$	−3.14000e52	−	6.87384e52i	−0.392762	−	0.859803i
$46$	3.59168e52			0.222355
$47$		−	3.26664e53i		−	1.01618i	−0.861305	−	0.508089i	$-0.830352\pi$
$47$		−	3.26664e53i		−	1.01618i	0.861305	−	0.508089i	$-0.169648\pi$
$48$	−1.40558e53	+	3.05839e52i	−0.222914	+	0.0485036i
$49$	−3.29058e53			−0.269773
$50$			1.73382e53i			0.0744669i
$51$	1.53543e54	+	7.05656e54i	0.349932	+	1.60823i
$52$	2.69810e54			0.330333
$53$		−	1.07005e55i		−	0.712157i	−0.934456	−	0.356078i	$-0.884114\pi$
$53$		−	1.07005e55i		−	0.712157i	0.934456	−	0.356078i	$-0.115886\pi$
$54$	1.14558e55	+	1.52984e55i	0.419203	+	0.559815i
$55$	−3.73387e55			−0.759545
$56$			7.90104e55i			0.902958i
$57$	−1.96774e55	+	4.28159e54i	−0.127636	+	0.0277721i
$58$	−1.89106e56			−0.703087
$59$		−	5.16286e56i		−	1.11077i	−0.831592	−	0.555387i	$-0.812570\pi$
$59$		−	5.16286e56i		−	1.11077i	0.831592	−	0.555387i	$-0.187430\pi$
$60$	−8.17147e55	−	3.75546e56i	−0.102674	−	0.471871i
$61$	1.92706e57			1.42672			0.713362	−	0.700796i	$-0.247172\pi$
$61$	1.92706e57			1.42672			0.713362	+	0.700796i	$0.247172\pi$
$62$			1.90764e57i			0.839386i
$63$	2.94763e57	−	1.34649e57i	0.777276	−	0.355063i
$64$	−5.37039e57			−0.855552
$65$		−	6.30110e57i		−	0.611208i
$66$	9.22722e57	−	2.00774e57i	0.549117	−	0.119482i
$67$	−2.61319e58			−0.961120			−0.480560	−	0.876962i	$-0.659567\pi$
$67$	−2.61319e58			−0.961120			−0.480560	+	0.876962i	$0.659567\pi$
$68$			3.67276e58i			0.840829i
$69$	−4.71086e57	−	2.16503e58i	−0.0675973	−	0.310665i
$70$	6.23920e58			0.564926
$71$			1.40259e59i			0.806611i	0.915065	+	0.403306i	$0.132139\pi$
$71$			1.40259e59i			0.806611i	−0.915065	+	0.403306i	$0.867861\pi$
$72$	1.19441e59	+	2.61471e59i	0.439051	+	0.961135i
$73$	5.03853e59			1.19117			0.595583	−	0.803294i	$-0.296921\pi$
$73$	5.03853e59			1.19117			0.595583	+	0.803294i	$0.296921\pi$
$74$		−	5.95645e59i		−	0.911113i
$75$	1.04513e59	−	2.27408e58i	0.104042	−	0.0226384i
$76$	−1.02416e59			−0.0667319
$77$		−	1.60115e60i		−	0.686641i
$78$	3.38816e59	+	1.55714e60i	0.0961473	+	0.441876i
$79$	7.40798e60			1.39840			0.699202	−	0.714924i	$-0.253539\pi$
$79$	7.40798e60			1.39840			0.699202	+	0.714924i	$0.253539\pi$
$80$			1.70850e60i			0.215643i
$81$	7.71915e60	−	8.91196e60i	0.654710	−	0.755880i
$82$	1.99535e61			1.14281
$83$			4.72747e61i			1.83709i	0.395321	+	0.918543i	$0.370633\pi$
$83$			4.72747e61i			1.83709i	−0.395321	+	0.918543i	$0.629367\pi$
$84$	1.61041e61	−	3.50408e60i	0.426579	−	0.0928189i
$85$	8.57730e61			1.55577
$86$			7.95419e60i			0.0992306i
$87$	2.48032e61	+	1.13991e62i	0.213743	+	0.982324i
$88$	1.42031e62			0.849061
$89$		−	5.97669e61i		−	0.248875i	−0.992227	−	0.124437i	$-0.960287\pi$
$89$		−	5.97669e61i		−	0.248875i	0.992227	−	0.124437i	$-0.0397126\pi$
$90$	2.06476e62	−	9.43191e61i	0.601324	−	0.274688i
$91$	2.70203e62			0.552541
$92$		−	1.12684e62i		−	0.162425i
$93$	1.14990e63	−	2.50206e62i	1.17276	−	0.255178i
$94$	9.81230e62			0.710689
$95$			2.39181e62i			0.123473i
$96$	5.16561e62	+	2.37402e63i	0.190740	+	0.876608i
$97$	−5.26812e62			−0.139624			−0.0698120	−	0.997560i	$-0.522240\pi$
$97$	−5.26812e62			−0.139624			−0.0698120	+	0.997560i	$0.522240\pi$
$98$		−	9.88420e62i		−	0.188672i
$99$	−2.42049e63	−	5.29874e63i	−0.333870	−	0.730881i
$100$	5.43963e62			0.0543963
$101$			7.25824e63i			0.527895i	0.964537	+	0.263947i	$0.0850245\pi$
$101$			7.25824e63i			0.527895i	−0.964537	+	0.263947i	$0.914975\pi$
$102$	−2.11964e64	+	4.61210e63i	−1.12475	+	0.244733i
$103$	−3.71701e64			−1.44345			−0.721726	−	0.692179i	$-0.756651\pi$
$103$	−3.71701e64			−1.44345			−0.721726	+	0.692179i	$0.756651\pi$
$104$			2.39685e64i			0.683241i
$105$	−8.18336e63	−	3.76093e64i	−0.171741	−	0.789291i
$106$	3.21420e64			0.498064
$107$		−	6.50232e64i		−	0.746084i	−0.927815	−	0.373042i	$-0.878315\pi$
$107$		−	6.50232e64i		−	0.746084i	0.927815	−	0.373042i	$-0.121685\pi$
$108$	4.79966e64	−	3.59410e64i	0.408932	−	0.306218i
$109$	−2.74560e65			−1.74177			−0.870883	−	0.491491i	$-0.836452\pi$
$109$	−2.74560e65			−1.74177			−0.870883	+	0.491491i	$0.836452\pi$
$110$		−	1.12158e65i		−	0.531206i
$111$	−3.59049e65	+	7.81250e64i	−1.27297	+	0.276984i
$112$	−7.32635e64			−0.194944
$113$		−	3.80274e64i		−	0.0761354i	−0.999275	−	0.0380677i	$-0.987880\pi$
$113$		−	3.80274e64i		−	0.0761354i	0.999275	−	0.0380677i	$-0.0121203\pi$
$114$	−1.28610e64	−	5.91068e64i	−0.0194231	−	0.0892652i
$115$	−2.63161e65			−0.300532
$116$			5.93295e65i			0.513588i
$117$	8.94189e65	−	4.08470e65i	0.588141	−	0.268666i
$118$	1.55081e66			0.776847
$119$			3.67810e66i			1.40644i
$120$	3.33616e66	−	7.25910e65i	0.975992	−	0.212365i
$121$	1.57964e66			0.354345
$122$			5.78847e66i			0.997814i
$123$	−2.61711e66	−	1.20278e67i	−0.347423	−	1.59669i
$124$	5.98496e66			0.613151
$125$		−	1.32013e67i		−	1.04591i
$126$	4.04458e66	+	8.85405e66i	0.248322	+	0.543606i
$127$	2.30410e67			1.09845			0.549227	−	0.835673i	$-0.314922\pi$
$127$	2.30410e67			1.09845			0.549227	+	0.835673i	$0.314922\pi$
$128$			8.05479e66i			0.298769i
$129$	4.79471e66	−	1.04327e66i	0.138641	−	0.0301667i
$130$	1.89272e67			0.427463
$131$			1.01099e68i			1.78676i	0.449305	+	0.893379i	$0.351672\pi$
$131$			1.01099e68i			1.78676i	−0.449305	+	0.893379i	$0.648328\pi$
$132$	−6.29903e66	−	2.89492e67i	−0.0872786	−	0.401117i
$133$	−1.02565e67			−0.111621
$134$		−	7.84948e67i		−	0.672182i
$135$	−8.39360e67	−	1.12090e68i	−0.566588	−	0.756638i
$136$	−3.26269e68			−1.73912
$137$			2.52515e68i			1.06470i	0.846523	+	0.532352i	$0.178692\pi$
$137$			2.52515e68i			1.06470i	−0.846523	+	0.532352i	$0.821308\pi$
$138$	6.50328e67	−	1.41504e67i	0.217271	−	0.0472758i
$139$	−2.67044e68			−0.708125			−0.354062	−	0.935222i	$-0.615200\pi$
$139$	−2.67044e68			−0.708125			−0.354062	+	0.935222i	$0.615200\pi$
$140$		−	1.95747e68i		−	0.412665i
$141$	−1.28698e68	−	5.91475e68i	−0.216054	−	0.992945i
$142$	−4.21309e68			−0.564123
$143$		−	4.85724e68i		−	0.519561i
$144$	−2.42453e68	+	1.10754e68i	−0.207505	+	0.0947892i
$145$	1.38557e69			0.950282
$146$			1.51347e69i			0.833070i
$147$	−5.95810e68	+	1.29642e68i	−0.263605	+	0.0573574i
$148$	−1.86876e69			−0.665547
$149$		−	2.63296e68i		−	0.0755932i	−0.999285	−	0.0377966i	$-0.987966\pi$
$149$		−	2.63296e68i		−	0.0755932i	0.999285	−	0.0377966i	$-0.0120339\pi$
$150$	6.83086e67	+	3.13934e68i	0.0158327	+	0.0727643i
$151$	4.17653e69			0.782624			0.391312	−	0.920258i	$-0.372021\pi$
$151$	4.17653e69			0.782624			0.391312	+	0.920258i	$0.372021\pi$
$152$		−	9.09810e68i		−	0.138024i
$153$	5.56026e69	+	1.21721e70i	0.683863	+	1.49706i
$154$	4.80952e69			0.480219
$155$		−	1.39772e70i		−	1.13450i
$156$	4.88533e69	−	1.06299e69i	0.322780	−	0.0702333i
$157$	1.62964e70			0.877610			0.438805	−	0.898582i	$-0.355402\pi$
$157$	1.62964e70			0.877610			0.438805	+	0.898582i	$0.355402\pi$
$158$			2.22520e70i			0.978007i
$159$	−4.21575e69	−	1.93749e70i	−0.151414	−	0.695874i
$160$	2.88564e70			0.848014
$161$		−	1.12848e70i		−	0.271685i
$162$	2.67697e70	+	2.31867e70i	0.528643	+	0.457887i
$163$	−5.27386e70			−0.855313			−0.427657	−	0.903941i	$-0.640661\pi$
$163$	−5.27386e70			−0.855313			−0.427657	+	0.903941i	$0.640661\pi$
$164$		−	6.26015e70i		−	0.834799i
$165$	−6.76075e70	+	1.47106e70i	−0.742179	+	0.161490i
$166$	−1.42003e71			−1.28481
$167$		−	8.70575e70i		−	0.649948i	−0.945723	−	0.324974i	$-0.894644\pi$
$167$		−	8.70575e70i		−	0.649948i	0.945723	−	0.324974i	$-0.105356\pi$
$168$	3.11284e70	+	1.43060e71i	0.191981	+	0.882313i
$169$	−1.14085e71			−0.581908
$170$			2.57644e71i			1.08806i
$171$	−3.39421e70	+	1.55049e70i	−0.118813	+	0.0542743i
$172$	2.49552e70			0.0724856
$173$		−	5.70396e71i		−	1.37626i	−0.725586	−	0.688132i	$-0.758431\pi$
$173$		−	5.70396e71i		−	1.37626i	0.725586	−	0.688132i	$-0.241569\pi$
$174$	−3.42405e71	+	7.45035e70i	−0.687012	+	0.149486i
$175$	5.44754e70			0.0909878
$176$			1.31701e71i			0.183308i
$177$	−2.03405e71	−	9.34815e71i	−0.236166	−	1.08538i
$178$	1.79527e71			0.174057
$179$			6.69504e71i			0.542571i	0.962499	+	0.271285i	$0.0874487\pi$
$179$			6.69504e71i			0.542571i	−0.962499	+	0.271285i	$0.912551\pi$
$180$	−2.95914e71	−	6.47791e71i	−0.200653	−	0.439253i
$181$	−1.60659e71			−0.0912410			−0.0456205	−	0.998959i	$-0.514527\pi$
$181$	−1.60659e71			−0.0912410			−0.0456205	+	0.998959i	$0.514527\pi$
$182$			8.11631e71i			0.386433i
$183$	3.48923e72	−	7.59218e71i	1.39410	−	0.303341i
$184$	1.00103e72			0.335951
$185$			4.36427e72i			1.23145i
$186$	7.51567e71	+	3.45407e72i	0.178465	+	0.820194i
$187$	6.61186e72			1.32249
$188$		−	3.07848e72i		−	0.519141i
$189$	4.80664e72	−	3.59933e72i	0.684013	−	0.512205i
$190$	−7.18448e71			−0.0863535
$191$			6.05000e72i			0.614734i	0.951591	+	0.307367i	$0.0994480\pi$
$191$			6.05000e72i			0.614734i	−0.951591	+	0.307367i	$0.900552\pi$
$192$	−9.72391e72	+	2.11581e72i	−0.835991	+	0.181902i
$193$	−1.20982e73			−0.880819			−0.440409	−	0.897797i	$-0.645167\pi$
$193$	−1.20982e73			−0.880819			−0.440409	+	0.897797i	$0.645167\pi$
$194$		−	1.58243e72i		−	0.0976494i
$195$	−2.48249e72	−	1.14091e73i	−0.129951	−	0.597233i
$196$	−3.10104e72			−0.137820
$197$		−	2.79807e73i		−	1.05667i	−0.849036	−	0.528335i	$-0.822817\pi$
$197$		−	2.79807e73i		−	1.05667i	0.849036	−	0.528335i	$-0.177183\pi$
$198$	1.59163e73	−	7.27064e72i	0.511159	−	0.233500i
$199$	4.99164e72			0.136441			0.0682205	−	0.997670i	$-0.478268\pi$
$199$	4.99164e72			0.136441			0.0682205	+	0.997670i	$0.478268\pi$
$200$			4.83228e72i			0.112510i
$201$	−4.73159e73	+	1.02954e73i	−0.939145	+	0.204348i
$202$	−2.18022e73			−0.369196
$203$			5.94158e73i			0.859070i
$204$	1.44699e73	+	6.65010e73i	0.178772	+	0.821604i
$205$	−1.46198e74			−1.54461
$206$		−	1.11651e74i		−	1.00951i
$207$	−1.70595e73	−	3.73452e73i	−0.132103	−	0.289190i
$208$	−2.22251e73			−0.147509
$209$			1.84374e73i			0.104959i
$210$	1.12970e74	−	2.45811e73i	0.552010	−	0.120111i
$211$	7.71407e73			0.323776			0.161888	−	0.986809i	$-0.448242\pi$
$211$	7.71407e73			0.323776			0.161888	+	0.986809i	$0.448242\pi$
$212$		−	1.00841e74i		−	0.363824i
$213$	5.52590e73	+	2.53961e74i	0.171497	+	0.788169i
$214$	1.95316e74			0.521791
$215$		−	5.82800e73i		−	0.134119i
$216$	3.19281e74	+	4.26377e74i	0.633364	+	0.845811i
$217$	5.99367e74			1.02561
$218$		−	8.24721e74i		−	1.21815i
$219$	9.12303e74	−	1.98507e74i	1.16393	−	0.253258i
$220$	−3.51880e74			−0.388033
$221$			1.11579e75i			1.06421i
$222$	−2.34671e74	−	1.07851e75i	−0.193715	−	0.890282i
$223$	−1.39031e75			−0.993933			−0.496967	−	0.867770i	$-0.665553\pi$
$223$	−1.39031e75			−0.993933			−0.496967	+	0.867770i	$0.665553\pi$
$224$			1.23742e75i			0.766619i
$225$	1.80277e74	−	8.23515e73i	0.0968501	−	0.0442416i
$226$	1.14226e74			0.0532471
$227$			2.04976e75i			0.829615i	0.909909	+	0.414807i	$0.136151\pi$
$227$			2.04976e75i			0.829615i	−0.909909	+	0.414807i	$0.863849\pi$
$228$	−1.85440e74	+	4.03497e73i	−0.0652061	+	0.0141881i
$229$	−6.22854e74			−0.190393			−0.0951965	−	0.995458i	$-0.530348\pi$
$229$	−6.22854e74			−0.190393			−0.0951965	+	0.995458i	$0.530348\pi$
$230$		−	7.90479e74i		−	0.210184i
$231$	−6.30819e74	−	2.89913e75i	−0.145989	−	0.670941i
$232$	−5.27052e75			−1.06228
$233$		−	3.79308e75i		−	0.666196i	−0.942892	−	0.333098i	$-0.891906\pi$
$233$		−	3.79308e75i		−	0.666196i	0.942892	−	0.333098i	$-0.108094\pi$
$234$	1.22696e75	+	2.68595e75i	0.187898	+	0.411331i
$235$	−7.18943e75			−0.960556
$236$		−	4.86548e75i		−	0.567468i
$237$	1.34133e76	−	2.91858e75i	1.36643	−	0.297320i
$238$	−1.10482e76			−0.983628
$239$			5.27100e75i			0.410356i	0.978725	+	0.205178i	$0.0657773\pi$
$239$			5.27100e75i			0.410356i	−0.978725	+	0.205178i	$0.934223\pi$
$240$	6.73110e74	+	3.09350e75i	0.0458487	+	0.210712i
$241$	−2.40326e76			−1.43303			−0.716515	−	0.697571i	$-0.754264\pi$
$241$	−2.40326e76			−1.43303			−0.716515	+	0.697571i	$0.754264\pi$
$242$			4.74490e75i			0.247819i
$243$	1.04656e76	−	1.91777e76i	0.479030	−	0.877798i
$244$	1.81606e76			0.728879
$245$			7.24212e75i			0.255006i
$246$	3.61289e76	−	7.86124e75i	1.11669	−	0.242978i
$247$	−3.11140e75			−0.0844605
$248$			5.31673e76i			1.26821i
$249$	1.86252e76	+	8.55980e76i	0.390590	+	1.79508i
$250$	3.96538e76			0.731484
$251$		−	9.45755e76i		−	1.53539i	−0.640814	−	0.767696i	$-0.721403\pi$
$251$		−	9.45755e76i		−	1.53539i	0.640814	−	0.767696i	$-0.278597\pi$
$252$	2.77784e76	−	1.26893e76i	0.397091	−	0.181393i
$253$	−2.02859e76			−0.255469
$254$			6.92103e76i			0.768231i
$255$	1.55305e77	−	3.37927e76i	1.52020	−	0.330778i
$256$	−1.23261e77			−1.06450
$257$		−	2.39711e77i		−	1.82738i	−0.406416	−	0.913688i	$-0.633222\pi$
$257$		−	2.39711e77i		−	1.82738i	0.406416	−	0.913688i	$-0.366778\pi$
$258$	3.13378e75	+	1.44023e76i	0.0210978	+	0.0969618i
$259$	−1.87148e77			−1.11325
$260$		−	5.93815e76i		−	0.312251i
$261$	8.98199e76	+	1.96626e77i	0.417711	+	0.914420i
$262$	−3.03680e77			−1.24961
$263$			1.44644e77i			0.526885i	0.964675	+	0.263442i	$0.0848579\pi$
$263$			1.44644e77i			0.526885i	−0.964675	+	0.263442i	$0.915142\pi$
$264$	2.57170e77	−	5.59572e76i	0.829648	−	0.180522i
$265$	−2.35503e77			−0.673176
$266$		−	3.08084e76i		−	0.0780650i
$267$	−2.35469e76	−	1.08217e77i	−0.0529142	−	0.243185i
$268$	−2.46267e77			−0.491013
$269$			6.24330e77i			1.10495i	0.833530	+	0.552474i	$0.186316\pi$
$269$			6.24330e77i			1.10495i	−0.833530	+	0.552474i	$0.813684\pi$
$270$	3.36696e77	−	2.52126e77i	0.529173	−	0.396257i
$271$	−9.98441e77			−1.39414			−0.697068	−	0.717005i	$-0.745512\pi$
$271$	−9.98441e77			−1.39414			−0.697068	+	0.717005i	$0.745512\pi$
$272$		−	3.02537e77i		−	0.375469i
$273$	4.89243e77	−	1.06454e77i	0.539908	−	0.117478i
$274$	−7.58501e77			−0.744626
$275$		−	9.79266e76i		−	0.0855568i
$276$	−4.43951e76	−	2.04032e77i	−0.0345338	−	0.158711i
$277$	−5.45601e77			−0.378027			−0.189013	−	0.981974i	$-0.560529\pi$
$277$	−5.45601e77			−0.378027			−0.189013	+	0.981974i	$0.560529\pi$
$278$		−	8.02145e77i		−	0.495244i
$279$	1.98350e78	−	9.06074e77i	1.09169	−	0.498688i
$280$	1.73891e78			0.853533
$281$			3.12224e78i			1.36730i	0.729810	+	0.683650i	$0.239608\pi$
$281$			3.12224e78i			1.36730i	−0.729810	+	0.683650i	$0.760392\pi$
$282$	1.77667e78	−	3.86583e77i	0.694440	−	0.151102i
$283$	3.41329e78			1.19126			0.595631	−	0.803258i	$-0.296902\pi$
$283$	3.41329e78			1.19126			0.595631	+	0.803258i	$0.296902\pi$
$284$			1.32180e78i			0.412078i
$285$	9.42319e76	+	4.33073e77i	0.0262520	+	0.120650i
$286$	1.45901e78			0.363367
$287$		−	6.26926e78i		−	1.39635i
$288$	1.87063e78	+	4.09502e78i	0.372758	+	0.816011i
$289$	−9.58151e78			−1.70885
$290$			4.16196e78i			0.664603i
$291$	−9.53873e77	+	2.07552e77i	−0.136432	+	0.0296860i
$292$	4.74831e78			0.608538
$293$			9.58092e78i			1.10063i	0.834956	+	0.550317i	$0.185493\pi$
$293$			9.58092e78i			1.10063i	−0.834956	+	0.550317i	$0.814507\pi$
$294$	−3.89416e77	−	1.78969e78i	−0.0401143	−	0.184358i
$295$	−1.13627e79			−1.04997
$296$		−	1.66011e79i		−	1.37658i
$297$	−6.47026e78	−	8.64056e78i	−0.481632	−	0.643184i
$298$	7.90884e77			0.0528679
$299$		−	3.42335e78i		−	0.205576i
$300$	9.84929e77	−	2.14309e77i	0.0531526	−	0.0115654i
$301$	2.49915e78			0.121245
$302$			1.25454e79i			0.547347i
$303$	2.85959e78	+	1.31422e79i	0.112238	+	0.515825i
$304$	8.43634e77			0.0297989
$305$		−	4.24119e79i		−	1.34863i
$306$	−3.65623e79	+	1.67018e79i	−1.04700	+	0.478276i
$307$	−1.70461e79			−0.439742			−0.219871	−	0.975529i	$-0.570564\pi$
$307$	−1.70461e79			−0.439742			−0.219871	+	0.975529i	$0.570564\pi$
$308$		−	1.50893e79i		−	0.350788i
$309$	−6.73021e79	+	1.46442e79i	−1.41045	+	0.306898i
$310$	4.19845e79			0.793441
$311$		−	1.37737e79i		−	0.234811i	−0.993084	−	0.117405i	$-0.962542\pi$
$311$		−	1.37737e79i		−	0.234811i	0.993084	−	0.117405i	$-0.0374577\pi$
$312$	9.44306e78	+	4.33987e79i	0.145267	+	0.667620i
$313$	1.21679e80			1.68965			0.844823	−	0.535046i	$-0.179706\pi$
$313$	1.21679e80			1.68965			0.844823	+	0.535046i	$0.179706\pi$
$314$			4.89508e79i			0.613778i
$315$	−2.96344e79	−	6.48733e79i	−0.335629	−	0.734730i
$316$	6.98128e79			0.714411
$317$			1.14263e80i			1.05684i	0.848983	+	0.528420i	$0.177215\pi$
$317$			1.14263e80i			1.05684i	−0.848983	+	0.528420i	$0.822785\pi$
$318$	5.81980e79	−	1.26632e79i	0.486676	−	0.105895i
$319$	1.06808e80			0.807793
$320$			1.18195e80i			0.808722i
$321$	−2.56177e79	−	1.17734e80i	−0.158628	−	0.729025i
$322$	3.38972e79			0.190010
$323$		−	4.23536e79i		−	0.214986i
$324$	7.27453e79	−	8.39863e79i	0.334476	−	0.386161i
$325$	1.65256e79			0.0688478
$326$		−	1.58416e80i		−	0.598184i
$327$	−4.97133e80	+	1.08171e80i	−1.70194	+	0.370324i
$328$	5.56119e80			1.72665
$329$		−	3.08296e80i		−	0.868358i
$330$	−4.41876e79	−	2.03079e80i	−0.112942	−	0.519061i
$331$	−6.06082e80			−1.40616			−0.703081	−	0.711110i	$-0.748193\pi$
$331$	−6.06082e80			−1.40616			−0.703081	+	0.711110i	$0.748193\pi$
$332$			4.45516e80i			0.938523i
$333$	−6.19333e80	+	2.82915e80i	−1.18497	+	0.541302i
$334$	2.61502e80			0.454557
$335$			5.75128e80i			0.908512i
$336$	−1.32655e80	+	2.88642e79i	−0.190487	+	0.0414479i
$337$	−4.93595e80			−0.644487			−0.322244	−	0.946657i	$-0.604437\pi$
$337$	−4.93595e80			−0.644487			−0.322244	+	0.946657i	$0.604437\pi$
$338$		−	3.42688e80i		−	0.406971i
$339$	−1.49820e79	−	6.88545e79i	−0.0161875	−	0.0743947i
$340$	8.08325e80			0.794805
$341$		−	1.07744e81i		−	0.964390i
$342$	−4.65736e79	−	1.01955e80i	−0.0379581	−	0.0830947i
$343$	−1.46173e81			−1.08506
$344$			2.21689e80i			0.149925i
$345$	−4.76493e80	+	1.03680e80i	−0.293660	+	0.0638972i
$346$	1.71335e81			0.962523
$347$			4.05410e79i			0.0207659i	0.999946	+	0.0103830i	$0.00330506\pi$
$347$			4.05410e79i			0.0207659i	−0.999946	+	0.0103830i	$0.996695\pi$
$348$	2.33745e80	+	1.07425e81i	0.109196	+	0.501846i
$349$	−1.48309e81			−0.632054			−0.316027	−	0.948750i	$-0.602349\pi$
$349$	−1.48309e81			−0.632054			−0.316027	+	0.948750i	$0.602349\pi$
$350$			1.63633e80i			0.0636345i
$351$	1.45814e81	−	1.09189e81i	0.517572	−	0.387570i
$352$	2.22442e81			0.720860
$353$		−	3.79531e81i		−	1.12320i	−0.827409	−	0.561599i	$-0.810186\pi$
$353$		−	3.79531e81i		−	1.12320i	0.827409	−	0.561599i	$-0.189814\pi$
$354$	2.80799e81	−	6.10986e80i	0.759085	−	0.165168i
$355$	3.08691e81			0.762460
$356$		−	5.63244e80i		−	0.127144i
$357$	1.44909e81	+	6.65977e81i	0.299029	+	1.37428i
$358$	−2.01105e81			−0.379460
$359$			1.12325e82i			1.93845i	0.246176	+	0.969225i	$0.420826\pi$
$359$			1.12325e82i			1.93845i	−0.246176	+	0.969225i	$0.579174\pi$
$360$	5.75463e81	−	2.62874e81i	0.908526	−	0.415019i
$361$	−6.80388e81			−0.982938
$362$		−	4.82585e80i		−	0.0638116i
$363$	2.86018e81	−	6.22343e80i	0.346243	−	0.0753386i
$364$	2.54639e81			0.282280
$365$		−	1.10891e82i		−	1.12597i
$366$	2.28053e81	+	1.04809e82i	0.212149	+	0.975000i
$367$	−1.47721e82			−1.25930			−0.629650	−	0.776879i	$-0.716802\pi$
$367$	−1.47721e82			−1.25930			−0.629650	+	0.776879i	$0.716802\pi$
$368$			9.28217e80i			0.0725303i
$369$	−9.47735e81	−	2.07470e82i	−0.678958	−	1.48632i
$370$	−1.31093e82			−0.861242
$371$		−	1.00988e82i		−	0.608562i
$372$	1.08367e82	−	2.35794e81i	0.599132	−	0.130365i
$373$	−2.73165e82			−1.38593			−0.692966	−	0.720970i	$-0.743697\pi$
$373$	−2.73165e82			−1.38593			−0.692966	+	0.720970i	$0.743697\pi$
$374$			1.98606e82i			0.924915i
$375$	−5.20101e81	−	2.39029e82i	−0.222376	−	1.02200i
$376$	2.73476e82			1.07376
$377$			1.80243e82i			0.650033i
$378$	1.08116e82	+	1.44381e82i	0.358223	+	0.478381i
$379$	−2.85759e82			−0.870052			−0.435026	−	0.900418i	$-0.643261\pi$
$379$	−2.85759e82			−0.870052			−0.435026	+	0.900418i	$0.643261\pi$
$380$			2.25404e81i			0.0630792i
$381$	4.17193e82	−	9.07765e81i	1.07334	−	0.233547i
$382$	−1.81729e82			−0.429929
$383$			4.39047e81i			0.0955324i	0.998859	+	0.0477662i	$0.0152102\pi$
$383$			4.39047e81i			0.0955324i	−0.998859	+	0.0477662i	$0.984790\pi$
$384$	3.17341e81	+	1.45844e82i	0.0635224	+	0.291938i
$385$	−3.52392e82			−0.649056
$386$		−	3.63404e82i		−	0.616022i
$387$	8.27052e81	−	3.77802e81i	0.129057	−	0.0589540i
$388$	−4.96467e81			−0.0713305
$389$			6.31137e82i			0.835096i	0.908655	+	0.417548i	$0.137110\pi$
$389$			6.31137e82i			0.835096i	−0.908655	+	0.417548i	$0.862890\pi$
$390$	3.42705e82	−	7.45689e81i	0.417689	−	0.0908845i
$391$	4.66000e82			0.523274
$392$		−	2.75480e82i		−	0.285060i
$393$	3.98308e82	+	1.83055e83i	0.379889	+	1.74591i
$394$	8.40481e82			0.739007
$395$		−	1.63039e83i		−	1.32186i
$396$	−2.28107e82	−	4.99353e82i	−0.170566	−	0.373389i
$397$	1.83354e83			1.26472			0.632359	−	0.774676i	$-0.282087\pi$
$397$	1.83354e83			1.26472			0.632359	+	0.774676i	$0.282087\pi$
$398$			1.49938e82i			0.0954233i
$399$	−1.85710e82	+	4.04084e81i	−0.109069	+	0.0237322i
$400$	−4.48080e81			−0.0242905
$401$			1.54834e82i			0.0774900i	0.999249	+	0.0387450i	$0.0123360\pi$
$401$			1.54834e82i			0.0774900i	−0.999249	+	0.0387450i	$0.987664\pi$
$402$	−3.09252e82	−	1.42127e83i	−0.142915	−	0.656814i
$403$	1.81823e83			0.776047
$404$			6.84016e82i			0.269689i
$405$	−1.96140e83	−	1.69888e83i	−0.714506	−	0.618874i
$406$	−1.78472e83			−0.600811
$407$			3.36422e83i			1.04680i
$408$	−5.90760e83	+	1.28543e83i	−1.69936	+	0.369762i
$409$	−4.50712e83			−1.19882			−0.599408	−	0.800443i	$-0.704597\pi$
$409$	−4.50712e83			−1.19882			−0.599408	+	0.800443i	$0.704597\pi$
$410$		−	4.39149e83i		−	1.08026i
$411$	9.94852e82	+	4.57217e83i	0.226371	+	1.04036i
$412$	−3.50291e83			−0.737425
$413$		−	4.87255e83i		−	0.949194i
$414$	1.12177e83	−	5.12430e82i	0.202252	−	0.0923897i
$415$	1.04045e84			1.73653
$416$			3.75381e83i			0.580078i
$417$	−4.83525e83	+	1.05210e83i	−0.691935	+	0.150557i
$418$	−5.53820e82			−0.0734053
$419$			2.55052e83i			0.313169i	0.987665	+	0.156585i	$0.0500484\pi$
$419$			2.55052e83i			0.313169i	−0.987665	+	0.156585i	$0.949952\pi$
$420$	−7.71199e82	−	3.54430e83i	−0.0877383	−	0.403230i
$421$	1.83943e83			0.193935			0.0969674	−	0.995288i	$-0.469086\pi$
$421$	1.83943e83			0.193935			0.0969674	+	0.995288i	$0.469086\pi$
$422$			2.31714e83i			0.226441i
$423$	−4.66056e83	−	1.02025e84i	−0.422228	−	0.924306i
$424$	8.95821e83			0.752513
$425$			2.24953e83i			0.175245i
$426$	−7.62845e83	+	1.65986e83i	−0.551225	+	0.119940i
$427$	1.81870e84			1.21918
$428$		−	6.12779e83i		−	0.381156i
$429$	−1.91364e83	−	8.79477e83i	−0.110466	−	0.507682i
$430$	1.75061e83			0.0937991
$431$			1.27681e84i			0.635117i	0.948239	+	0.317559i	$0.102863\pi$
$431$			1.27681e84i			0.635117i	−0.948239	+	0.317559i	$0.897137\pi$
$432$	−3.95364e83	+	2.96058e83i	−0.182607	+	0.136740i
$433$	2.00177e84			0.858620			0.429310	−	0.903157i	$-0.358757\pi$
$433$	2.00177e84			0.858620			0.429310	+	0.903157i	$0.358757\pi$
$434$			1.80037e84i			0.717283i
$435$	2.50879e84	−	5.45884e83i	0.928555	−	0.202043i
$436$	−2.58746e84			−0.889826
$437$			1.29945e83i			0.0415293i
$438$	5.96273e83	+	2.74036e84i	0.177122	+	0.814023i
$439$	5.71642e84			1.57855			0.789277	−	0.614038i	$-0.210456\pi$
$439$	5.71642e84			1.57855			0.789277	+	0.614038i	$0.210456\pi$
$440$		−	3.12592e84i		−	0.802586i
$441$	−1.02773e84	+	4.69472e83i	−0.245383	+	0.112092i
$442$	−3.35158e84			−0.744282
$443$			5.89301e84i			1.21736i	0.793417	+	0.608678i	$0.208300\pi$
$443$			5.89301e84i			1.21736i	−0.793417	+	0.608678i	$0.791700\pi$
$444$	−3.38367e84	+	7.36250e83i	−0.650330	+	0.141504i
$445$	−1.31539e84			−0.235252
$446$		−	4.17621e84i		−	0.695131i
$447$	−1.03733e83	−	4.76737e83i	−0.0160722	−	0.0738649i
$448$	−5.06841e84			−0.731098
$449$		−	1.30049e85i		−	1.74672i	−0.487076	−	0.873360i	$-0.661937\pi$
$449$		−	1.30049e85i		−	1.74672i	0.487076	−	0.873360i	$-0.338063\pi$
$450$	2.47366e83	+	5.41514e83i	0.0309414	+	0.0677344i
$451$	−1.12698e85			−1.31301
$452$		−	3.58370e83i		−	0.0388958i
$453$	7.56225e84	−	1.64546e84i	0.764731	−	0.166397i
$454$	−6.15706e84			−0.580211
$455$		−	5.94679e84i		−	0.522297i
$456$	−3.58445e83	−	1.64735e84i	−0.0293459	−	0.134869i
$457$	−1.30998e85			−0.999875			−0.499937	−	0.866062i	$-0.666644\pi$
$457$	−1.30998e85			−0.999875			−0.499937	+	0.866062i	$0.666644\pi$
$458$		−	1.87092e84i		−	0.133156i
$459$	1.48632e85	+	1.98488e85i	0.986522	+	1.31743i
$460$	−2.48003e84			−0.153534
$461$			2.44752e85i			1.41350i	0.707463	+	0.706751i	$0.249840\pi$
$461$			2.44752e85i			1.41350i	−0.707463	+	0.706751i	$0.750160\pi$
$462$	8.70838e84	−	1.89485e84i	0.469239	−	0.102101i
$463$	7.97897e84			0.401195			0.200597	−	0.979674i	$-0.435712\pi$
$463$	7.97897e84			0.401195			0.200597	+	0.979674i	$0.435712\pi$
$464$		−	4.88716e84i		−	0.229341i
$465$	−5.50670e84	−	2.53078e85i	−0.241211	−	1.10856i
$466$	1.13936e85			0.465920
$467$			3.35614e85i			1.28145i	0.767772	+	0.640723i	$0.221365\pi$
$467$			3.35614e85i			1.28145i	−0.767772	+	0.640723i	$0.778635\pi$
$468$	8.42684e84	−	3.84942e84i	0.300467	−	0.137255i
$469$	−2.46625e85			−0.821309
$470$		−	2.15955e85i		−	0.671788i
$471$	2.95070e85	−	6.42040e84i	0.857545	−	0.186592i
$472$	4.32223e85			1.17372
$473$		−	4.49255e84i		−	0.114008i
$474$	8.76680e84	+	4.02906e85i	0.207938	+	0.955647i
$475$	−6.27288e83			−0.0139082
$476$			3.46624e85i			0.718516i
$477$	−1.52665e85	−	3.34203e85i	−0.295905	−	0.647771i
$478$	−1.58330e85			−0.286992
$479$		−	2.55240e85i		−	0.432725i	−0.976313	−	0.216363i	$-0.930581\pi$
$479$		−	2.55240e85i		−	0.432725i	0.976313	−	0.216363i	$-0.0694194\pi$
$480$	5.22490e85	−	1.13688e85i	0.828626	−	0.180300i
$481$	−5.67729e85			−0.842362
$482$		−	7.21889e85i		−	1.00222i
$483$	−4.44597e84	−	2.04329e85i	−0.0577641	−	0.265474i
$484$	1.48865e85			0.181026
$485$			1.15944e85i			0.131981i
$486$	5.76056e85	+	3.14364e85i	0.613909	+	0.335021i
$487$	2.25012e85			0.224533			0.112266	−	0.993678i	$-0.464189\pi$
$487$	2.25012e85			0.224533			0.112266	+	0.993678i	$0.464189\pi$
$488$			1.61329e86i			1.50757i
$489$	−9.54913e85	+	2.07778e85i	−0.835757	+	0.181852i
$490$	−2.17538e85			−0.178345
$491$		−	5.80827e85i		−	0.446107i	−0.974806	−	0.223053i	$-0.928398\pi$
$491$		−	5.80827e85i		−	0.446107i	0.974806	−	0.223053i	$-0.0716024\pi$
$492$	−2.46636e85	−	1.13350e86i	−0.177490	−	0.815712i
$493$	−2.45354e86			−1.65459
$494$		−	9.34599e84i		−	0.0590695i
$495$	−1.16618e86	+	5.32717e85i	−0.690875	+	0.315595i
$496$	−4.93001e85			−0.273800
$497$			1.32373e86i			0.689276i
$498$	−2.57118e86	+	5.59461e85i	−1.25543	+	0.273169i
$499$	2.16296e86			0.990446			0.495223	−	0.868766i	$-0.335086\pi$
$499$	2.16296e86			0.990446			0.495223	+	0.868766i	$0.335086\pi$
$500$		−	1.24409e86i		−	0.534331i
$501$	−3.42987e85	−	1.57631e86i	−0.138188	−	0.635088i
$502$	2.84085e86			1.07381
$503$		−	3.76417e86i		−	1.33504i	−0.744593	−	0.667518i	$-0.767357\pi$
$503$		−	3.76417e86i		−	1.33504i	0.744593	−	0.667518i	$-0.232643\pi$
$504$	1.12725e86	+	2.46769e86i	0.375184	+	0.821322i
$505$	1.59744e86			0.499000
$506$		−	6.09346e85i		−	0.178668i
$507$	−2.06569e86	+	4.49470e85i	−0.568604	+	0.123722i
$508$	2.17138e86			0.561174
$509$		−	1.20319e85i		−	0.0291987i	−0.999893	−	0.0145993i	$-0.995353\pi$
$509$		−	1.20319e85i		−	0.0291987i	0.999893	−	0.0145993i	$-0.00464728\pi$
$510$	1.01506e86	+	4.66504e86i	0.231338	+	1.06319i
$511$	4.75521e86			1.01789
$512$		−	2.21665e86i		−	0.445717i
$513$	−5.53488e85	+	4.14465e85i	−0.104557	+	0.0782947i
$514$	7.20041e86			1.27802
$515$			8.18062e86i			1.36444i
$516$	4.51853e85	−	9.83182e84i	0.0708283	−	0.0154114i
$517$	−5.54201e86			−0.816527
$518$		−	5.62152e86i		−	0.778577i
$519$	−2.24724e86	−	1.03279e87i	−0.292613	−	1.34480i
$520$	5.27514e86			0.645843
$521$		−	1.39133e86i		−	0.160185i	−0.996787	−	0.0800927i	$-0.974478\pi$
$521$		−	1.39133e86i		−	0.160185i	0.996787	−	0.0800927i	$-0.0255216\pi$
$522$	−5.90624e86	+	2.69800e86i	−0.639521	+	0.292137i
$523$	−4.68668e86			−0.477321			−0.238661	−	0.971103i	$-0.576708\pi$
$523$	−4.68668e86			−0.477321			−0.238661	+	0.971103i	$0.576708\pi$
$524$			9.52757e86i			0.912811i
$525$	9.86361e85	−	2.14621e85i	0.0889075	−	0.0193453i
$526$	−4.34479e86			−0.368490
$527$			2.47505e87i			1.97535i
$528$	5.18871e85	+	2.38464e86i	0.0389739	+	0.179117i
$529$	1.27146e87			0.898918
$530$		−	7.07401e86i		−	0.470802i
$531$	−7.36593e86	−	1.61249e87i	−0.461533	−	1.01035i
$532$	−9.66573e85			−0.0570246
$533$		−	1.90183e87i		−	1.05658i
$534$	3.25062e86	−	7.07298e85i	0.170077	−	0.0370068i
$535$	−1.43107e87			−0.705246
$536$		−	2.18771e87i		−	1.01558i
$537$	2.63770e86	+	1.21224e87i	0.115358	+	0.530166i
$538$	−1.87536e87			−0.772771
$539$			5.58263e86i			0.216769i
$540$	−7.91013e86	−	1.05634e87i	−0.289456	−	0.386548i
$541$	−1.82160e87			−0.628262			−0.314131	−	0.949380i	$-0.601713\pi$
$541$	−1.82160e87			−0.628262			−0.314131	+	0.949380i	$0.601713\pi$
$542$		−	2.99911e87i		−	0.975022i
$543$	−2.90897e86	+	6.32960e85i	−0.0891549	+	0.0193991i
$544$	−5.10984e87			−1.47653
$545$			6.04270e87i			1.64643i
$546$	3.19765e86	+	1.46958e87i	0.0821611	+	0.377598i
$547$	3.84542e87			0.931858			0.465929	−	0.884822i	$-0.345720\pi$
$547$	3.84542e87			0.931858			0.465929	+	0.884822i	$0.345720\pi$
$548$			2.37970e87i			0.543931i
$549$	6.01868e87	−	2.74936e87i	1.29773	−	0.592812i
$550$	2.94151e86			0.0598362
$551$		−	6.84177e86i		−	0.131316i
$552$	1.81251e87	−	3.94383e86i	0.328270	−	0.0714278i
$553$	6.99143e87			1.19498
$554$		−	1.63887e87i		−	0.264382i
$555$	1.71942e87	+	7.90217e87i	0.261823	+	1.20329i
$556$	−2.51663e87			−0.361764
$557$		−	3.12705e87i		−	0.424394i	−0.977227	−	0.212197i	$-0.931938\pi$
$557$		−	3.12705e87i		−	0.424394i	0.977227	−	0.212197i	$-0.0680619\pi$
$558$	2.72165e87	+	5.95802e87i	0.348770	+	0.763498i
$559$	7.58141e86			0.0917428
$560$			1.61243e87i			0.184274i
$561$	1.19718e88	−	2.60493e87i	1.29225	−	0.281180i
$562$	−9.37854e87			−0.956253
$563$		−	8.62106e87i		−	0.830409i	−0.909728	−	0.415205i	$-0.863710\pi$
$563$		−	8.62106e87i		−	0.830409i	0.909728	−	0.415205i	$-0.136290\pi$
$564$	−1.21285e87	−	5.57406e87i	−0.110377	−	0.507272i
$565$	−8.36932e86			−0.0719680
$566$			1.02528e88i			0.833137i
$567$	7.28511e87	−	8.41085e87i	0.559472	−	0.645925i
$568$	−1.17422e88			−0.852320
$569$		−	8.16750e87i		−	0.560398i	−0.959942	−	0.280199i	$-0.909600\pi$
$569$		−	8.16750e87i		−	0.560398i	0.959942	−	0.280199i	$-0.0904004\pi$
$570$	−1.30086e87	+	2.83053e86i	−0.0843792	+	0.0183600i
$571$	−1.62833e88			−0.998589			−0.499294	−	0.866432i	$-0.666407\pi$
$571$	−1.62833e88			−0.998589			−0.499294	+	0.866432i	$0.666407\pi$
$572$		−	4.57746e87i		−	0.265431i
$573$	2.38357e87	+	1.09544e88i	0.130701	+	0.600679i
$574$	1.88315e88			0.976573
$575$		−	6.90180e86i		−	0.0338525i
$576$	−1.67730e88	+	7.66201e87i	−0.778202	+	0.355487i
$577$	−1.41418e87			−0.0620696			−0.0310348	−	0.999518i	$-0.509880\pi$
$577$	−1.41418e87			−0.0620696			−0.0310348	+	0.999518i	$0.509880\pi$
$578$		−	2.87808e88i		−	1.19512i
$579$	−2.19056e88	+	4.76642e87i	−0.860680	+	0.187274i
$580$	1.30576e88			0.485476
$581$			4.46164e88i			1.56985i
$582$	−6.23443e86	−	2.86523e87i	−0.0207616	−	0.0954167i
$583$	−1.81539e88			−0.572237
$584$			4.21815e88i			1.25867i
$585$	−8.98987e87	−	1.96799e88i	−0.253960	−	0.555949i
$586$	−2.87790e88			−0.769755
$587$		−	2.31354e88i		−	0.585946i	−0.956121	−	0.292973i	$-0.905355\pi$
$587$		−	2.31354e88i		−	0.585946i	0.956121	−	0.292973i	$-0.0946447\pi$
$588$	−5.61491e87	+	1.22174e87i	−0.134669	+	0.0293025i
$589$	−6.90175e87			−0.156773
$590$		−	3.41313e88i		−	0.734325i
$591$	−1.10238e88	−	5.06633e88i	−0.224663	−	1.03251i
$592$	1.53936e88			0.297197
$593$			3.63960e88i			0.665737i	0.942973	+	0.332869i	$0.108017\pi$
$593$			3.63960e88i			0.665737i	−0.942973	+	0.332869i	$0.891983\pi$
$594$	2.59544e88	−	1.94353e88i	0.449826	−	0.336841i
$595$	8.09500e88			1.32946
$596$		−	2.48130e87i		−	0.0386188i
$597$	9.03813e87	−	1.96660e87i	0.133321	−	0.0290093i
$598$	1.02830e88			0.143775
$599$			3.96764e88i			0.525864i	0.964814	+	0.262932i	$0.0846895\pi$
$599$			3.96764e88i			0.525864i	−0.964814	+	0.262932i	$0.915310\pi$
$600$	1.90381e87	+	8.74958e87i	0.0239213	+	0.109938i
$601$	1.20610e89			1.43681			0.718407	−	0.695623i	$-0.244871\pi$
$601$	1.20610e89			1.43681			0.718407	+	0.695623i	$0.244871\pi$
$602$			7.50693e87i			0.0847959i
$603$	−8.16164e88	+	3.72828e88i	−0.874226	+	0.399351i
$604$	3.93596e88			0.399824
$605$		−	3.47657e88i		−	0.334949i
$606$	−3.94763e88	+	8.58959e87i	−0.360755	+	0.0784962i
$607$	1.05122e89			0.911288			0.455644	−	0.890162i	$-0.349409\pi$
$607$	1.05122e89			0.911288			0.455644	+	0.890162i	$0.349409\pi$
$608$		−	1.42489e88i		−	0.117184i
$609$	2.34085e88	+	1.07581e89i	0.182650	+	0.839429i
$610$	1.27396e89			0.943197
$611$		−	9.35243e88i		−	0.657061i
$612$	5.23998e88	+	1.14709e89i	0.349369	+	0.764810i
$613$	−2.26552e89			−1.43362			−0.716808	−	0.697271i	$-0.754398\pi$
$613$	−2.26552e89			−1.43362			−0.716808	+	0.697271i	$0.754398\pi$
$614$		−	5.12030e88i		−	0.307544i
$615$	−2.64715e89	+	5.75990e88i	−1.50930	+	0.328406i
$616$	1.34045e89			0.725551
$617$			1.38264e89i			0.710534i	0.934765	+	0.355267i	$0.115610\pi$
$617$			1.38264e89i			0.710534i	−0.934765	+	0.355267i	$0.884390\pi$
$618$	−4.39880e88	−	2.02161e89i	−0.214636	−	0.986431i
$619$	−2.11754e89			−0.981139			−0.490570	−	0.871402i	$-0.663211\pi$
$619$	−2.11754e89			−0.981139			−0.490570	+	0.871402i	$0.663211\pi$
$620$		−	1.31721e89i		−	0.579590i
$621$	−4.56019e88	−	6.08981e88i	−0.190569	−	0.254491i
$622$	4.13733e88			0.164221
$623$		−	5.64063e88i		−	0.212672i
$624$	−4.02420e88	+	8.75621e87i	−0.144136	+	0.0313624i
$625$	−2.59251e89			−0.882186
$626$			3.65497e89i			1.18169i
$627$	7.26392e87	+	3.33837e88i	0.0223157	+	0.102559i
$628$	1.53577e89			0.448350
$629$		−	7.72815e89i		−	2.14415i
$630$	1.94866e89	−	8.90156e88i	0.513851	−	0.234730i
$631$	−1.18487e89			−0.296983			−0.148491	−	0.988914i	$-0.547442\pi$
$631$	−1.18487e89			−0.296983			−0.148491	+	0.988914i	$0.547442\pi$
$632$			6.20180e89i			1.47765i
$633$	1.39675e89	−	3.03917e88i	0.316374	−	0.0688394i
$634$	−3.43222e89			−0.739126
$635$		−	5.07101e89i		−	1.03833i
$636$	−3.97293e88	−	1.82589e89i	−0.0773540	−	0.355505i
$637$	−9.42097e88			−0.174435
$638$			3.20827e89i			0.564949i
$639$	2.00110e89	+	4.38064e89i	0.335152	+	0.733686i
$640$	1.77275e89			0.282415
$641$			2.19125e89i			0.332075i	0.986119	+	0.166037i	$0.0530972\pi$
$641$			2.19125e89i			0.332075i	−0.986119	+	0.166037i	$0.946903\pi$
$642$	3.53649e89	−	7.69502e88i	0.509861	−	0.110940i
$643$	−6.86281e87			−0.00941350			−0.00470675	−	0.999989i	$-0.501498\pi$
$643$	−6.86281e87			−0.00941350			−0.00470675	+	0.999989i	$0.501498\pi$
$644$		−	1.06348e89i		−	0.138798i
$645$	−2.29610e88	−	1.05525e89i	−0.0285155	−	0.131052i
$646$	1.27221e89			0.150356
$647$			9.77475e89i			1.09943i	0.835351	+	0.549716i	$0.185264\pi$
$647$			9.77475e89i			1.09943i	−0.835351	+	0.549716i	$0.814736\pi$
$648$	7.46090e89	+	6.46231e89i	0.798714	+	0.691811i
$649$	−8.75904e89			−0.892537
$650$			4.96394e88i			0.0481503i
$651$	1.08525e90	−	2.36137e89i	1.00216	−	0.218059i
$652$	−4.97008e89			−0.436959
$653$		−	7.24783e89i		−	0.606717i	−0.952877	−	0.303358i	$-0.901892\pi$
$653$		−	7.24783e89i		−	0.606717i	0.952877	−	0.303358i	$-0.0981079\pi$
$654$	−3.24922e89	−	1.49328e90i	−0.258995	−	1.19029i
$655$	2.22505e90			1.68896
$656$			5.15669e89i			0.372776i
$657$	1.57366e90	−	7.18854e89i	1.08347	−	0.494936i
$658$	9.26056e89			0.607307
$659$			1.65302e90i			1.03263i	0.856399	+	0.516314i	$0.172696\pi$
$659$			1.65302e90i			1.03263i	−0.856399	+	0.516314i	$0.827304\pi$
$660$	−6.37133e89	+	1.38633e89i	−0.379161	+	0.0825013i
$661$	−1.51173e90			−0.857089			−0.428545	−	0.903521i	$-0.640974\pi$
$661$	−1.51173e90			−0.857089			−0.428545	+	0.903521i	$0.640974\pi$
$662$		−	1.82054e90i		−	0.983433i
$663$	4.39595e89	+	2.02030e90i	0.226266	+	1.03988i
$664$	−3.95773e90			−1.94119
$665$			2.25732e89i			0.105511i
$666$	−8.49816e89	−	1.86035e90i	−0.378573	−	0.828740i
$667$	7.52772e89			0.319622
$668$		−	8.20429e89i		−	0.332043i
$669$	−2.51738e90	+	5.47753e89i	−0.971208	+	0.211324i
$670$	−1.72756e90			−0.635390
$671$		−	3.26935e90i		−	1.14641i
$672$	4.87515e89	+	2.24053e90i	0.162994	+	0.749091i
$673$	−1.78961e90			−0.570526			−0.285263	−	0.958449i	$-0.592081\pi$
$673$	−1.78961e90			−0.570526			−0.285263	+	0.958449i	$0.592081\pi$
$674$		−	1.48266e90i		−	0.450737i
$675$	2.93975e89	−	2.20135e89i	0.0852293	−	0.0638218i
$676$	−1.07514e90			−0.297283
$677$			9.63887e89i			0.254208i	0.991889	+	0.127104i	$0.0405682\pi$
$677$			9.63887e89i			0.254208i	−0.991889	+	0.127104i	$0.959432\pi$
$678$	2.06824e89	−	4.50027e88i	0.0520297	−	0.0113211i
$679$	−4.97189e89			−0.119313
$680$			7.18073e90i			1.64393i
$681$	8.07562e89	+	3.71141e90i	0.176388	+	0.810647i
$682$	3.23640e90			0.674469
$683$		−	1.20111e90i		−	0.238847i	−0.992843	−	0.119423i	$-0.961895\pi$
$683$		−	1.20111e90i		−	0.238847i	0.992843	−	0.119423i	$-0.0381046\pi$
$684$	−3.19871e89	+	1.46119e89i	−0.0606987	+	0.0277275i
$685$	5.55750e90			1.00643
$686$		−	4.39072e90i		−	0.758865i
$687$	−1.12777e90	+	2.45391e89i	−0.186040	+	0.0404802i
$688$	−2.05564e89			−0.0323682
$689$		−	3.06356e90i		−	0.460481i
$690$	−3.11431e89	−	1.43128e90i	−0.0446881	−	0.205378i
$691$	2.21386e90			0.303286			0.151643	−	0.988435i	$-0.451544\pi$
$691$	2.21386e90			0.303286			0.151643	+	0.988435i	$0.451544\pi$
$692$		−	5.37541e90i		−	0.703100i
$693$	−2.28439e90	−	5.00079e90i	−0.285303	−	0.624562i
$694$	−1.21776e89			−0.0145231
$695$			5.87728e90i			0.669365i
$696$	−9.54308e90	+	2.07647e90i	−1.03799	+	0.225855i
$697$	2.58885e91			2.68942
$698$		−	4.45489e90i		−	0.442042i
$699$	−1.49439e90	−	6.86795e90i	−0.141643	−	0.650964i
$700$	5.13376e89			0.0464835
$701$			1.39626e91i			1.20779i	0.797065	+	0.603893i	$0.206385\pi$
$701$			1.39626e91i			1.20779i	−0.797065	+	0.603893i	$0.793615\pi$
$702$	3.27980e90	+	4.37994e90i	0.271057	+	0.361977i
$703$	2.15502e90			0.170169
$704$			9.11112e90i			0.687459i
$705$	−1.30176e91	+	2.83248e90i	−0.938594	+	0.204228i
$706$	1.14003e91			0.785536
$707$			6.85011e90i			0.451104i
$708$	−1.91689e90	−	8.80969e90i	−0.120652	−	0.554494i
$709$	−8.01883e90			−0.482427			−0.241213	−	0.970472i	$-0.577545\pi$
$709$	−8.01883e90			−0.482427			−0.241213	+	0.970472i	$0.577545\pi$
$710$			9.27244e90i			0.533245i
$711$	2.31369e91	−	1.05691e91i	1.27198	−	0.581045i
$712$	5.00356e90			0.262978
$713$		−	7.59372e90i		−	0.381583i
$714$	−2.00045e91	+	4.35277e90i	−0.961138	+	0.209133i
$715$	−1.06901e91			−0.491122
$716$			6.30941e90i			0.277186i
$717$	2.07666e90	+	9.54396e90i	0.0872473	+	0.400973i
$718$	−3.37401e91			−1.35570
$719$		−	4.53411e91i		−	1.74248i	−0.490857	−	0.871240i	$-0.663316\pi$
$719$		−	4.53411e91i		−	1.74248i	0.490857	−	0.871240i	$-0.336684\pi$
$720$	2.43754e90	+	5.33606e90i	0.0896008	+	0.196147i
$721$	−3.50800e91			−1.23348
$722$		−	2.04374e91i		−	0.687441i
$723$	−4.35147e91	+	9.46832e90i	−1.40027	+	0.304682i
$724$	−1.51405e90			−0.0466129
$725$			3.63387e90i			0.107042i
$726$	1.86939e90	+	8.59137e90i	0.0526899	+	0.242153i
$727$	1.56066e91			0.420927			0.210464	−	0.977602i	$-0.432503\pi$
$727$	1.56066e91			0.420927			0.210464	+	0.977602i	$0.432503\pi$
$728$			2.26208e91i			0.583853i
$729$	1.13940e91	−	3.88473e91i	0.281446	−	0.959577i
$730$	3.33094e91			0.787471
$731$			1.03201e91i			0.233522i
$732$	3.28825e91	−	7.15487e90i	0.712214	−	0.154970i
$733$	2.11193e91			0.437877			0.218939	−	0.975739i	$-0.429741\pi$
$733$	2.11193e91			0.437877			0.218939	+	0.975739i	$0.429741\pi$
$734$		−	4.43723e91i		−	0.880721i
$735$	2.85323e90	+	1.31130e91i	0.0542179	+	0.249176i
$736$	1.56775e91			0.285225
$737$			4.43341e91i			0.772286i
$738$	6.23197e91	−	2.84680e91i	1.03949	−	0.474846i
$739$	−1.08882e92			−1.73914			−0.869571	−	0.493809i	$-0.835604\pi$
$739$	−1.08882e92			−1.73914			−0.869571	+	0.493809i	$0.835604\pi$
$740$			4.11288e91i			0.629117i
$741$	−5.63367e90	+	1.22582e90i	−0.0825294	+	0.0179575i
$742$	3.03347e91			0.425612
$743$			4.25743e91i			0.572144i	0.958208	+	0.286072i	$0.0923496\pi$
$743$			4.25743e91i			0.572144i	−0.958208	+	0.286072i	$0.907650\pi$
$744$	2.09467e91	+	9.62675e91i	0.269639	+	1.23921i
$745$	−5.79478e90			−0.0714555
$746$		−	8.20529e91i		−	0.969285i
$747$	6.74475e91	+	1.47650e92i	0.763320	+	1.67100i
$748$	6.23102e91			0.675629
$749$		−	6.13670e91i		−	0.637553i
$750$	7.17993e91	−	1.56227e91i	0.714759	−	0.155524i
$751$	−8.96458e91			−0.855169			−0.427585	−	0.903975i	$-0.640635\pi$
$751$	−8.96458e91			−0.855169			−0.427585	+	0.903975i	$0.640635\pi$
$752$			2.53584e91i			0.231820i
$753$	−3.72606e91	−	1.71243e92i	−0.326446	−	1.50029i
$754$	−5.41412e91			−0.454616
$755$		−	9.19198e91i		−	0.739786i
$756$	4.52978e91	−	3.39201e91i	0.349446	−	0.261673i
$757$	1.23748e92			0.915106			0.457553	−	0.889182i	$-0.348726\pi$
$757$	1.23748e92			0.915106			0.457553	+	0.889182i	$0.348726\pi$
$758$		−	8.58360e91i		−	0.608492i
$759$	−3.67307e91	+	7.99220e90i	−0.249628	+	0.0543162i
$760$	−2.00237e91			−0.130470
$761$			2.65722e92i			1.66004i	0.557732	+	0.830021i	$0.311672\pi$
$761$			2.65722e92i			1.66004i	−0.557732	+	0.830021i	$0.688328\pi$
$762$	2.72673e91	+	1.25316e92i	0.163337	+	0.750666i
$763$	−2.59122e92			−1.48840
$764$			5.70152e91i			0.314053i
$765$	2.67890e92	−	1.22374e92i	1.41511	−	0.646431i
$766$	−1.31881e91			−0.0668129
$767$		−	1.47813e92i		−	0.718227i
$768$	−2.23183e92	+	4.85621e91i	−1.04016	+	0.226328i
$769$	−1.28157e92			−0.572929			−0.286464	−	0.958091i	$-0.592480\pi$
$769$	−1.28157e92			−0.572929			−0.286464	+	0.958091i	$0.592480\pi$
$770$		−	1.05851e92i		−	0.453933i
$771$	−9.44408e91	−	4.34033e92i	−0.388526	−	1.78560i
$772$	−1.14013e92			−0.449989
$773$			4.35940e92i			1.65076i	0.564581	+	0.825378i	$0.309038\pi$
$773$			4.35940e92i			1.65076i	−0.564581	+	0.825378i	$0.690962\pi$
$774$	1.13484e91	+	2.48429e91i	0.0412309	+	0.0902592i
$775$	3.66573e91			0.127793
$776$		−	4.41035e91i		−	0.147536i
$777$	−3.38860e92	+	7.37321e91i	−1.08780	+	0.236692i
$778$	−1.89580e92			−0.584045
$779$			7.21909e91i			0.213444i
$780$	−2.33950e91	−	1.07519e92i	−0.0663890	−	0.305112i
$781$	2.37957e92			0.648134
$782$			1.39976e92i			0.365964i
$783$	2.40099e92	+	3.20635e92i	0.602579	+	0.804701i
$784$	2.55443e91			0.0615431
$785$		−	3.58660e92i		−	0.829573i
$786$	−5.49859e92	+	1.19643e92i	−1.22104	+	0.265685i
$787$	5.03676e92			1.07389			0.536945	−	0.843617i	$-0.319578\pi$
$787$	5.03676e92			1.07389			0.536945	+	0.843617i	$0.319578\pi$
$788$		−	2.63690e92i		−	0.539827i
$789$	5.69865e91	+	2.61900e92i	0.112023	+	0.514838i
$790$	4.89736e92			0.924475
$791$		−	3.58892e91i		−	0.0650603i
$792$	4.43599e92	−	2.02638e92i	0.772298	−	0.352789i
$793$	5.51719e92			0.922520
$794$			5.50756e92i			0.884511i
$795$	−4.26414e92	+	9.27830e91i	−0.657785	+	0.143127i
$796$	4.70412e91			0.0697044
$797$		−	6.37568e92i		−	0.907528i	−0.891122	−	0.453764i	$-0.850081\pi$
$797$		−	6.37568e92i		−	0.907528i	0.891122	−	0.453764i	$-0.149919\pi$
$798$	−1.21378e91	−	5.57833e91i	−0.0165977	−	0.0762801i
$799$	1.27309e93			1.67248
$800$			7.56805e91i			0.0955222i
$801$	−8.52704e91	−	1.86667e92i	−0.103409	−	0.226374i
$802$	−4.65088e91			−0.0541945
$803$		−	8.54811e92i		−	0.957134i
$804$	−4.45905e92	+	9.70239e91i	−0.479787	+	0.104396i
$805$	−2.48363e92			−0.256814
$806$			5.46159e92i			0.542747i
$807$	2.45972e92	+	1.13045e93i	0.234927	+	1.07968i
$808$	−6.07644e92			−0.557809
$809$		−	2.06899e92i		−	0.182560i	−0.995825	−	0.0912801i	$-0.970904\pi$
$809$		−	2.06899e92i		−	0.182560i	0.995825	−	0.0912801i	$-0.0290959\pi$
$810$	5.10308e92	−	5.89164e92i	0.432824	−	0.499707i
$811$	4.23288e91			0.0345119			0.0172559	−	0.999851i	$-0.494507\pi$
$811$	4.23288e91			0.0345119			0.0172559	+	0.999851i	$0.494507\pi$
$812$			5.59934e92i			0.438878i
$813$	−1.80783e93	+	3.93364e92i	−1.36226	+	0.296413i
$814$	−1.01054e93			−0.732104
$815$			1.16070e93i			0.808496i
$816$	−1.19193e92	−	5.47790e92i	−0.0798299	−	0.366884i
$817$	−2.87779e91			−0.0185333
$818$		−	1.35384e93i		−	0.838421i
$819$	8.43909e92	−	3.85502e92i	0.502587	−	0.229584i
$820$	−1.37777e93			−0.789105
$821$			2.25902e93i			1.24434i	0.782882	+	0.622171i	$0.213749\pi$
$821$			2.25902e93i			1.24434i	−0.782882	+	0.622171i	$0.786251\pi$
$822$	−1.37338e93	+	2.98833e92i	−0.727601	+	0.158318i
$823$	2.59326e93			1.32145			0.660725	−	0.750628i	$-0.270249\pi$
$823$	2.59326e93			1.32145			0.660725	+	0.750628i	$0.270249\pi$
$824$		−	3.11180e93i		−	1.52525i
$825$	−3.85809e91	−	1.77311e92i	−0.0181906	−	0.0836006i
$826$	1.46361e93			0.663842
$827$		−	1.26269e93i		−	0.550959i	−0.961307	−	0.275480i	$-0.911163\pi$
$827$		−	1.26269e93i		−	0.550959i	0.961307	−	0.275480i	$-0.0888367\pi$
$828$	−1.60768e92	−	3.51941e92i	−0.0674885	−	0.147740i
$829$	−2.90349e93			−1.17267			−0.586335	−	0.810069i	$-0.699430\pi$
$829$	−2.90349e93			−1.17267			−0.586335	+	0.810069i	$0.699430\pi$
$830$			3.12529e93i			1.21448i
$831$	−9.87895e92	+	2.14955e92i	−0.369384	+	0.0803738i
$832$	−1.53755e93			−0.553200
$833$		−	1.28242e93i		−	0.444007i
$834$	−3.16027e92	−	1.45241e93i	−0.105296	−	0.483921i
$835$	−1.91602e93			−0.614373
$836$			1.73754e92i			0.0536208i
$837$	3.23446e93	−	2.42204e93i	0.960699	−	0.719394i
$838$	−7.66121e92			−0.219022
$839$		−	7.69153e92i		−	0.211656i	−0.994384	−	0.105828i	$-0.966251\pi$
$839$		−	7.69153e92i		−	0.211656i	0.994384	−	0.105828i	$-0.0337493\pi$
$840$	3.14856e93	−	6.85093e92i	0.834018	−	0.181473i
$841$	−4.17498e91			−0.0106459
$842$			5.52526e92i			0.135633i
$843$	1.23009e93	+	5.65329e93i	0.290707	+	1.33604i
$844$	7.26974e92			0.165410
$845$			2.51086e93i			0.550057i
$846$	3.06462e93	−	1.39994e93i	0.646436	−	0.295295i
$847$	1.49082e93			0.302799
$848$			8.30663e92i			0.162464i
$849$	6.18028e93	−	1.34476e93i	1.16402	−	0.253279i
$850$	−6.75711e92			−0.122562
$851$			2.37108e93i			0.414191i
$852$	5.20761e92	+	2.39333e93i	0.0876136	+	0.402657i
$853$	−5.08124e91			−0.00823381			−0.00411690	−	0.999992i	$-0.501310\pi$
$853$	−5.08124e91			−0.00823381			−0.00411690	+	0.999992i	$0.501310\pi$
$854$			5.46299e93i			0.852665i
$855$	3.41243e92	+	7.47020e92i	0.0513036	+	0.112310i
$856$	5.44360e93			0.788362
$857$			8.80044e92i			0.122777i	0.998114	+	0.0613886i	$0.0195529\pi$
$857$			8.80044e92i			0.122777i	−0.998114	+	0.0613886i	$0.980447\pi$
$858$	2.64176e93	−	5.74818e92i	0.355059	−	0.0772569i
$859$	−4.36970e93			−0.565810			−0.282905	−	0.959148i	$-0.591298\pi$
$859$	−4.36970e93			−0.565810			−0.282905	+	0.959148i	$0.591298\pi$
$860$		−	5.49231e92i		−	0.0685180i
$861$	−2.46995e93	−	1.13514e94i	−0.296884	−	1.36443i
$862$	−3.83527e93			−0.444184
$863$		−	1.24505e94i		−	1.38944i	−0.719280	−	0.694720i	$-0.755528\pi$
$863$		−	1.24505e94i		−	1.38944i	0.719280	−	0.694720i	$-0.244472\pi$
$864$	5.00040e93	+	6.67767e93i	0.537731	+	0.718101i
$865$	−1.25536e94			−1.30093
$866$			6.01289e93i			0.600496i
$867$	−1.73488e94	+	3.77490e93i	−1.66977	+	0.363324i
$868$	5.64843e93			0.523958
$869$		−	1.25680e94i		−	1.12366i
$870$	1.63972e93	+	7.53587e93i	0.141304	+	0.649407i
$871$	−7.48160e93			−0.621460
$872$		−	2.29856e94i		−	1.84047i
$873$	−1.64536e93	+	7.51610e92i	−0.127001	+	0.0580145i
$874$	−3.90329e92			−0.0290445
$875$		−	1.24590e94i		−	0.893767i
$876$	8.59754e93	−	1.87073e93i	0.594625	−	0.129384i
$877$	−8.35673e93			−0.557249			−0.278624	−	0.960400i	$-0.589878\pi$
$877$	−8.35673e93			−0.557249			−0.278624	+	0.960400i	$0.589878\pi$
$878$			1.71709e94i			1.10400i
$879$	3.77467e93	+	1.73477e94i	0.234010	+	1.07547i
$880$	2.89855e93			0.173275
$881$			2.50810e94i			1.44583i	0.690939	+	0.722913i	$0.257197\pi$
$881$			2.50810e94i			1.44583i	−0.690939	+	0.722913i	$0.742803\pi$
$882$	−1.41019e93	−	3.08708e93i	−0.0783942	−	0.171614i
$883$	1.97496e94			1.05881			0.529403	−	0.848371i	$-0.322416\pi$
$883$	1.97496e94			1.05881			0.529403	+	0.848371i	$0.322416\pi$
$884$			1.05152e94i			0.543680i
$885$	−2.05740e94	+	4.47667e93i	−1.02597	+	0.223239i
$886$	−1.77013e94			−0.851387
$887$		−	4.18323e93i		−	0.194069i	−0.995281	−	0.0970346i	$-0.969064\pi$
$887$		−	4.18323e93i		−	0.194069i	0.995281	−	0.0970346i	$-0.0309357\pi$
$888$	−6.54045e93	−	3.00588e94i	−0.292680	−	1.34511i
$889$	2.17454e94			0.938666
$890$		−	3.95115e93i		−	0.164529i
$891$	−1.51196e94	−	1.30959e94i	−0.607370	−	0.526077i
$892$	−1.31023e94			−0.507777
$893$			3.55005e93i			0.132736i
$894$	1.43202e93	−	3.11591e92i	0.0516592	−	0.0112405i
$895$	1.47349e94			0.512872
$896$			7.60187e93i			0.255308i
$897$	−1.34872e93	−	6.19850e93i	−0.0437084	−	0.200876i
$898$	3.90639e94			1.22161
$899$			3.99818e94i			1.20657i
$900$	1.69893e93	−	7.76080e92i	0.0494784	−	0.0226020i
$901$	4.17024e94			1.17211
$902$		−	3.38521e94i		−	0.918282i
$903$	4.52510e93	−	9.84611e92i	0.118473	−	0.0257785i
$904$	3.18357e93			0.0804498
$905$			3.53588e93i			0.0862468i
$906$	4.94262e93	+	2.27154e94i	0.116374	+	0.534833i
$907$	−7.53609e93			−0.171283			−0.0856413	−	0.996326i	$-0.527294\pi$
$907$	−7.53609e93			−0.171283			−0.0856413	+	0.996326i	$0.527294\pi$
$908$			1.93170e94i			0.423830i
$909$	1.03554e94	+	2.26693e94i	0.219343	+	0.480168i
$910$	1.78629e94			0.365281
$911$		−	6.46595e94i		−	1.27657i	−0.769800	−	0.638285i	$-0.779644\pi$
$911$		−	6.46595e94i		−	1.27657i	0.769800	−	0.638285i	$-0.220356\pi$
$912$	1.52753e93	−	3.32373e92i	0.0291175	−	0.00633565i
$913$	8.02038e94			1.47615
$914$		−	3.93490e94i		−	0.699286i
$915$	−1.67094e94	−	7.67933e94i	−0.286738	−	1.31780i
$916$	−5.86978e93			−0.0972672
$917$			9.54143e94i			1.52684i
$918$	−5.96214e94	+	4.46460e94i	−0.921376	+	0.689948i
$919$	−2.44807e94			−0.365365			−0.182683	−	0.983172i	$-0.558478\pi$
$919$	−2.44807e94			−0.365365			−0.182683	+	0.983172i	$0.558478\pi$
$920$		−	2.20312e94i		−	0.317562i
$921$	−3.08646e94	+	6.71580e93i	−0.429688	+	0.0934953i
$922$	−7.35182e94			−0.988566
$923$			4.01564e94i			0.521555i
$924$	−5.94484e93	−	2.73214e94i	−0.0745825	−	0.342768i
$925$	−1.14460e94			−0.138713
$926$			2.39671e94i			0.280585i
$927$	−1.16091e95	+	5.30311e94i	−1.31295	+	0.599762i
$928$	−8.25439e94			−0.901882
$929$			1.06080e94i			0.111977i	0.998431	+	0.0559886i	$0.0178310\pi$
$929$			1.06080e94i			0.111977i	−0.998431	+	0.0559886i	$0.982169\pi$
$930$	7.60193e94	−	1.65410e94i	0.775300	−	0.168697i
$931$	3.57606e93			0.0352383
$932$		−	3.57460e94i		−	0.340344i
$933$	−5.42654e93	−	2.49394e94i	−0.0499241	−	0.229442i
$934$	−1.00811e95			−0.896210
$935$		−	1.45518e95i		−	1.25010i
$936$	3.41962e94	+	7.48596e94i	0.283891	+	0.621470i
$937$	6.88352e94			0.552260			0.276130	−	0.961120i	$-0.410948\pi$
$937$	6.88352e94			0.552260			0.276130	+	0.961120i	$0.410948\pi$
$938$		−	7.40810e94i		−	0.574402i
$939$	2.20318e95	−	4.79387e94i	1.65101	−	0.359242i
$940$	−6.77532e94			−0.490725
$941$		−	1.24282e94i		−	0.0870040i	−0.999053	−	0.0435020i	$-0.986149\pi$
$941$		−	1.24282e94i		−	0.0870040i	0.999053	−	0.0435020i	$-0.0138515\pi$
$942$	1.92855e94	+	8.86329e94i	0.130498	+	0.599744i
$943$	−7.94288e94			−0.519522
$944$			4.00785e94i			0.253401i
$945$	−7.92163e94	−	1.05788e95i	−0.484169	−	0.646572i
$946$	1.34947e94			0.0797344
$947$			1.74651e95i			0.997634i	0.866707	+	0.498817i	$0.166232\pi$
$947$			1.74651e95i			0.997634i	−0.866707	+	0.498817i	$0.833768\pi$
$948$	1.26407e95	−	2.75047e94i	0.698077	−	0.151894i
$949$	1.44254e95			0.770208
$950$		−	1.88424e93i		−	0.00972705i
$951$	4.50171e94	+	2.06891e95i	0.224699	+	1.03268i
$952$	−3.07923e95			−1.48614
$953$		−	3.17381e95i		−	1.48118i	−0.671957	−	0.740590i	$-0.734546\pi$
$953$		−	3.17381e95i		−	1.48118i	0.671957	−	0.740590i	$-0.265454\pi$
$954$	1.00387e95	−	4.58575e94i	0.453034	−	0.206948i
$955$	1.33152e95			0.581086
$956$			4.96739e94i			0.209641i
$957$	1.93391e95	−	4.20798e94i	0.789324	−	0.171748i
$958$	7.66687e94			0.302637
$959$			2.38316e95i			0.909824i
$960$	4.65662e94	+	2.14010e95i	0.171946	+	0.790232i
$961$	1.23329e95			0.440470
$962$		−	1.70534e95i		−	0.589126i
$963$	−9.27696e94	−	2.03084e95i	−0.310002	−	0.678631i
$964$	−2.26483e95			−0.732101
$965$			2.66265e95i			0.832606i
$966$	6.13761e94	−	1.33547e94i	0.185665	−	0.0403987i
$967$	3.14502e95			0.920400			0.460200	−	0.887815i	$-0.347778\pi$
$967$	3.14502e95			0.920400			0.460200	+	0.887815i	$0.347778\pi$
$968$			1.32244e95i			0.374424i
$969$	−1.66864e94	−	7.66877e94i	−0.0457090	−	0.210070i
$970$	−3.48271e94			−0.0923044
$971$			4.01654e95i			1.03000i	0.857190	+	0.515000i	$0.172208\pi$
$971$			4.01654e95i			1.03000i	−0.857190	+	0.515000i	$0.827792\pi$
$972$	9.86277e94	−	1.80730e95i	0.244725	−	0.448446i
$973$	−2.52029e95			−0.605116
$974$			6.75890e94i			0.157032i
$975$	2.99221e94	−	6.51072e93i	0.0672736	−	0.0146380i
$976$	−1.49595e95			−0.325478
$977$		−	2.68247e95i		−	0.564818i	−0.959294	−	0.282409i	$-0.908866\pi$
$977$		−	2.68247e95i		−	0.564818i	0.959294	−	0.282409i	$-0.0911336\pi$
$978$	−6.24122e94	−	2.86836e95i	−0.127182	−	0.584507i
$979$	−1.01398e95			−0.199978
$980$			6.82497e94i			0.130277i
$981$	−8.57519e95	+	3.91719e95i	−1.58429	+	0.723713i
$982$	1.74468e95			0.311996
$983$		−	4.17603e95i		−	0.722856i	−0.932400	−	0.361428i	$-0.882289\pi$
$983$		−	4.17603e95i		−	0.722856i	0.932400	−	0.361428i	$-0.117711\pi$
$984$	1.00694e96	−	2.19099e95i	1.68717	−	0.367110i
$985$	−6.15817e95			−0.998831
$986$		−	7.36991e95i		−	1.15718i
$987$	−1.21462e95	−	5.58217e95i	−0.184625	−	0.848504i
$988$	−2.93218e94			−0.0431488
$989$		−	3.16632e94i		−	0.0451101i
$990$	−1.60017e95	−	3.50296e95i	−0.220719	−	0.483180i
$991$	−7.33843e95			−0.980046			−0.490023	−	0.871710i	$-0.663012\pi$
$991$	−7.33843e95			−0.980046			−0.490023	+	0.871710i	$0.663012\pi$
$992$			8.32676e95i			1.07672i
$993$	−1.09740e96	+	2.38783e95i	−1.37401	+	0.298970i
$994$	−3.97619e95			−0.482062
$995$		−	1.09859e95i		−	0.128973i
$996$	1.75524e95	+	8.06676e95i	0.199543	+	0.917065i
$997$	4.20965e95			0.463448			0.231724	−	0.972782i	$-0.425563\pi$
$997$	4.20965e95			0.463448			0.231724	+	0.972782i	$0.425563\pi$
$998$			6.49707e95i			0.692692i
$999$	−1.00994e96	+	7.56264e95i	−1.04279	+	0.780868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.65.b.a.2.14	yes	20
3.2	odd	2	inner	3.65.b.a.2.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.65.b.a.2.7	✓	20	3.2	odd	2	inner
3.65.b.a.2.14	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)

\(f(q)\)	\(=\)	\(q+3.00379e9i q^{2} +(1.81065e15 - 3.93978e14i) q^{3} +9.42400e18 q^{4} -2.20086e22i q^{5} +(1.18343e24 + 5.43882e24i) q^{6} +9.43770e26 q^{7} +8.37178e28i q^{8} +(3.12325e30 - 1.42671e30i) q^{9} +O(q^{10})\)	\(q+3.00379e9i q^{2} +(1.81065e15 - 3.93978e14i) q^{3} +9.42400e18 q^{4} -2.20086e22i q^{5} +(1.18343e24 + 5.43882e24i) q^{6} +9.43770e26 q^{7} +8.37178e28i q^{8} +(3.12325e30 - 1.42671e30i) q^{9} +6.61093e31 q^{10} -1.69655e33i q^{11} +(1.70636e34 - 3.71285e33i) q^{12} +2.86301e35 q^{13} +2.83489e36i q^{14} +(-8.67092e36 - 3.98500e37i) q^{15} -7.76285e37 q^{16} +3.89724e39i q^{17} +(4.28555e39 + 9.38157e39i) q^{18} -1.08676e40 q^{19} -2.07409e41i q^{20} +(1.70884e42 - 3.71825e41i) q^{21} +5.09607e42 q^{22} -1.19572e43i q^{23} +(3.29830e43 + 1.51584e44i) q^{24} +5.77211e43 q^{25} +8.59988e44i q^{26} +(5.09302e45 - 3.81378e45i) q^{27} +8.89409e45 q^{28} +6.29558e46i q^{29} +(1.19701e47 - 2.60456e46i) q^{30} +6.35077e47 q^{31} +1.31114e48i q^{32} +(-6.68403e47 - 3.07186e48i) q^{33} -1.17065e49 q^{34} -2.07711e49i q^{35} +(2.94335e49 - 1.34454e49i) q^{36} -1.98298e50 q^{37} -3.26439e49i q^{38} +(5.18392e50 - 1.12796e50i) q^{39} +1.84251e51 q^{40} -6.64278e51i q^{41} +(1.11688e51 + 5.13300e51i) q^{42} +2.64805e51 q^{43} -1.59883e52i q^{44} +(-3.14000e52 - 6.87384e52i) q^{45} +3.59168e52 q^{46} -3.26664e53i q^{47} +(-1.40558e53 + 3.05839e52i) q^{48} -3.29058e53 q^{49} +1.73382e53i q^{50} +(1.53543e54 + 7.05656e54i) q^{51} +2.69810e54 q^{52} -1.07005e55i q^{53} +(1.14558e55 + 1.52984e55i) q^{54} -3.73387e55 q^{55} +7.90104e55i q^{56} +(-1.96774e55 + 4.28159e54i) q^{57} -1.89106e56 q^{58} -5.16286e56i q^{59} +(-8.17147e55 - 3.75546e56i) q^{60} +1.92706e57 q^{61} +1.90764e57i q^{62} +(2.94763e57 - 1.34649e57i) q^{63} -5.37039e57 q^{64} -6.30110e57i q^{65} +(9.22722e57 - 2.00774e57i) q^{66} -2.61319e58 q^{67} +3.67276e58i q^{68} +(-4.71086e57 - 2.16503e58i) q^{69} +6.23920e58 q^{70} +1.40259e59i q^{71} +(1.19441e59 + 2.61471e59i) q^{72} +5.03853e59 q^{73} -5.95645e59i q^{74} +(1.04513e59 - 2.27408e58i) q^{75} -1.02416e59 q^{76} -1.60115e60i q^{77} +(3.38816e59 + 1.55714e60i) q^{78} +7.40798e60 q^{79} +1.70850e60i q^{80} +(7.71915e60 - 8.91196e60i) q^{81} +1.99535e61 q^{82} +4.72747e61i q^{83} +(1.61041e61 - 3.50408e60i) q^{84} +8.57730e61 q^{85} +7.95419e60i q^{86} +(2.48032e61 + 1.13991e62i) q^{87} +1.42031e62 q^{88} -5.97669e61i q^{89} +(2.06476e62 - 9.43191e61i) q^{90} +2.70203e62 q^{91} -1.12684e62i q^{92} +(1.14990e63 - 2.50206e62i) q^{93} +9.81230e62 q^{94} +2.39181e62i q^{95} +(5.16561e62 + 2.37402e63i) q^{96} -5.26812e62 q^{97} -9.88420e62i q^{98} +(-2.42049e63 - 5.29874e63i) 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