LMFDB - Embedded newform 3.65.b.a.2.10

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			2.10
Root			$-1.58953e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.65.b.a.2.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.53717e8i q^{2} +(8.49626e14 + 1.64676e15i) q^{3} +1.75372e19 q^{4} -2.45445e22i q^{5} +(1.57054e24 - 8.10302e23i) q^{6} -1.16039e27 q^{7} -3.43185e28i q^{8} +(-1.98996e30 + 2.79826e30i) q^{9} +O(q^{10})$	\(q-9.53717e8i q^{2} +(8.49626e14 + 1.64676e15i) q^{3} +1.75372e19 q^{4} -2.45445e22i q^{5} +(1.57054e24 - 8.10302e23i) q^{6} -1.16039e27 q^{7} -3.43185e28i q^{8} +(-1.98996e30 + 2.79826e30i) q^{9} -2.34085e31 q^{10} +6.76641e32i q^{11} +(1.49000e34 + 2.88795e34i) q^{12} -2.73244e35 q^{13} +1.10668e36i q^{14} +(4.04189e37 - 2.08536e37i) q^{15} +2.90774e38 q^{16} +1.54455e39i q^{17} +(2.66875e39 + 1.89786e39i) q^{18} +8.35664e40 q^{19} -4.30441e41i q^{20} +(-9.85894e41 - 1.91088e42i) q^{21} +6.45324e41 q^{22} -2.80644e43i q^{23} +(5.65143e43 - 2.91578e43i) q^{24} -6.03301e43 q^{25} +2.60597e44i q^{26} +(-6.29878e45 - 8.99509e44i) q^{27} -2.03499e46 q^{28} -9.86394e46i q^{29} +(-1.98884e46 - 3.85482e46i) q^{30} +2.10152e47 q^{31} -9.10380e47i q^{32} +(-1.11427e48 + 5.74892e47i) q^{33} +1.47306e48 q^{34} +2.84811e49i q^{35} +(-3.48982e49 + 4.90736e49i) q^{36} +2.82385e50 q^{37} -7.96986e49i q^{38} +(-2.32155e50 - 4.49967e50i) q^{39} -8.42329e50 q^{40} -1.43063e51i q^{41} +(-1.82244e51 + 9.40263e50i) q^{42} +4.26558e51 q^{43} +1.18664e52i q^{44} +(6.86818e52 + 4.88424e52i) q^{45} -2.67655e52 q^{46} -2.67862e53i q^{47} +(2.47049e53 + 4.78834e53i) q^{48} +1.26735e53 q^{49} +5.75379e52i q^{50} +(-2.54350e54 + 1.31229e54i) q^{51} -4.79192e54 q^{52} -2.54583e55i q^{53} +(-8.57877e53 + 6.00725e54i) q^{54} +1.66078e55 q^{55} +3.98227e55i q^{56} +(7.10001e55 + 1.37614e56i) q^{57} -9.40741e55 q^{58} -2.49843e55i q^{59} +(7.08833e56 - 3.65713e56i) q^{60} -2.06291e57 q^{61} -2.00425e56i q^{62} +(2.30912e57 - 3.24706e57i) q^{63} +4.49558e57 q^{64} +6.70662e57i q^{65} +(5.48284e56 + 1.06269e57i) q^{66} -2.49683e58 q^{67} +2.70870e58i q^{68} +(4.62153e58 - 2.38442e58i) q^{69} +2.71629e58 q^{70} -3.22236e59i q^{71} +(9.60320e58 + 6.82923e58i) q^{72} -3.78481e59 q^{73} -2.69315e59i q^{74} +(-5.12580e58 - 9.93493e58i) q^{75} +1.46552e60 q^{76} -7.85165e59i q^{77} +(-4.29141e59 + 2.21410e59i) q^{78} +1.02816e61 q^{79} -7.13688e60i q^{80} +(-3.87033e60 - 1.11368e61i) q^{81} -1.36442e60 q^{82} -3.30630e61i q^{83} +(-1.72898e61 - 3.35114e61i) q^{84} +3.79101e61 q^{85} -4.06816e60i q^{86} +(1.62436e62 - 8.38066e61i) q^{87} +2.32213e61 q^{88} -3.88161e62i q^{89} +(4.65819e61 - 6.55030e61i) q^{90} +3.17068e62 q^{91} -4.92170e62i q^{92} +(1.78550e62 + 3.46070e62i) q^{93} -2.55464e62 q^{94} -2.05109e63i q^{95} +(1.49918e63 - 7.73482e62i) q^{96} -5.25219e62 q^{97} -1.20870e62i q^{98} +(-1.89342e63 - 1.34649e63i) 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 $

$2$		−	9.53717e8i		−	0.222055i	−0.993817	−	0.111027i	$-0.964586\pi$
$2$		−	9.53717e8i		−	0.222055i	0.993817	−	0.111027i	$-0.0354141\pi$
$3$	8.49626e14	+	1.64676e15i	0.458509	+	0.888690i
$3$	8.49626e14	+	1.64676e15i	0.458509	+	0.888690i
$4$	1.75372e19			0.950692
$5$		−	2.45445e22i		−	1.05418i	−0.849810	−	0.527089i	$-0.823284\pi$
$5$		−	2.45445e22i		−	1.05418i	0.849810	−	0.527089i	$-0.176716\pi$
$6$	1.57054e24	−	8.10302e23i	0.197338	−	0.101814i
$7$	−1.16039e27			−1.05067			−0.525334	−	0.850896i	$-0.676059\pi$
$7$	−1.16039e27			−1.05067			−0.525334	+	0.850896i	$0.676059\pi$
$8$		−	3.43185e28i		−	0.433160i
$9$	−1.98996e30	+	2.79826e30i	−0.579540	+	0.814944i
$10$	−2.34085e31			−0.234085
$11$			6.76641e32i			0.320474i	0.987079	+	0.160237i	$0.0512258\pi$
$11$			6.76641e32i			0.320474i	−0.987079	+	0.160237i	$0.948774\pi$
$12$	1.49000e34	+	2.88795e34i	0.435900	+	0.844870i
$13$	−2.73244e35			−0.617110			−0.308555	−	0.951206i	$-0.599845\pi$
$13$	−2.73244e35			−0.617110			−0.308555	+	0.951206i	$0.599845\pi$
$14$			1.10668e36i			0.233305i
$15$	4.04189e37	−	2.08536e37i	0.936837	−	0.483349i
$16$	2.90774e38			0.854507
$17$			1.54455e39i			0.652282i	0.945321	+	0.326141i	$0.105748\pi$
$17$			1.54455e39i			0.652282i	−0.945321	+	0.326141i	$0.894252\pi$
$18$	2.66875e39	+	1.89786e39i	0.180962	+	0.128689i
$19$	8.35664e40			1.00442			0.502211	−	0.864745i	$-0.332520\pi$
$19$	8.35664e40			1.00442			0.502211	+	0.864745i	$0.332520\pi$
$20$		−	4.30441e41i		−	1.00220i
$21$	−9.85894e41	−	1.91088e42i	−0.481740	−	0.933718i
$22$	6.45324e41			0.0711626
$23$		−	2.80644e43i		−	0.746216i	−0.927788	−	0.373108i	$-0.878292\pi$
$23$		−	2.80644e43i		−	0.746216i	0.927788	−	0.373108i	$-0.121708\pi$
$24$	5.65143e43	−	2.91578e43i	0.384945	−	0.198608i
$25$	−6.03301e43			−0.111289
$26$			2.60597e44i			0.137032i
$27$	−6.29878e45	−	8.99509e44i	−0.989956	−	0.141373i
$28$	−2.03499e46			−0.998861
$29$		−	9.86394e46i		−	1.57512i	−0.616236	−	0.787562i	$-0.711343\pi$
$29$		−	9.86394e46i		−	1.57512i	0.616236	−	0.787562i	$-0.288657\pi$
$30$	−1.98884e46	−	3.85482e46i	−0.107330	−	0.208029i
$31$	2.10152e47			0.397154			0.198577	−	0.980085i	$-0.436368\pi$
$31$	2.10152e47			0.397154			0.198577	+	0.980085i	$0.436368\pi$
$32$		−	9.10380e47i		−	0.622907i
$33$	−1.11427e48	+	5.74892e47i	−0.284802	+	0.146940i
$34$	1.47306e48			0.144842
$35$			2.84811e49i			1.10759i
$36$	−3.48982e49	+	4.90736e49i	−0.550964	+	0.774760i
$37$	2.82385e50			1.85518			0.927590	−	0.373601i	$-0.121877\pi$
$37$	2.82385e50			1.85518			0.927590	+	0.373601i	$0.121877\pi$
$38$		−	7.96986e49i		−	0.223036i
$39$	−2.32155e50	−	4.49967e50i	−0.282950	−	0.548420i
$40$	−8.42329e50			−0.456627
$41$		−	1.43063e51i		−	0.351920i	−0.984397	−	0.175960i	$-0.943697\pi$
$41$		−	1.43063e51i		−	0.351920i	0.984397	−	0.175960i	$-0.0563030\pi$
$42$	−1.82244e51	+	9.40263e50i	−0.207336	+	0.106973i
$43$	4.26558e51			0.228553			0.114277	−	0.993449i	$-0.463545\pi$
$43$	4.26558e51			0.228553			0.114277	+	0.993449i	$0.463545\pi$
$44$			1.18664e52i			0.304672i
$45$	6.86818e52	+	4.88424e52i	0.859095	+	0.610938i
$46$	−2.67655e52			−0.165701
$47$		−	2.67862e53i		−	0.833258i	−0.909077	−	0.416629i	$-0.863211\pi$
$47$		−	2.67862e53i		−	0.833258i	0.909077	−	0.416629i	$-0.136789\pi$
$48$	2.47049e53	+	4.78834e53i	0.391799	+	0.759392i
$49$	1.26735e53			0.103902
$50$			5.75379e52i			0.0247123i
$51$	−2.54350e54	+	1.31229e54i	−0.579677	+	0.299077i
$52$	−4.79192e54			−0.586681
$53$		−	2.54583e55i		−	1.69434i	−0.531320	−	0.847171i	$-0.678304\pi$
$53$		−	2.54583e55i		−	1.69434i	0.531320	−	0.847171i	$-0.321696\pi$
$54$	−8.57877e53	+	6.00725e54i	−0.0313924	+	0.219824i
$55$	1.66078e55			0.337836
$56$			3.98227e55i			0.455107i
$57$	7.10001e55	+	1.37614e56i	0.460536	+	0.892620i
$58$	−9.40741e55			−0.349763
$59$		−	2.49843e55i		−	0.0537530i	−0.999639	−	0.0268765i	$-0.991444\pi$
$59$		−	2.49843e55i		−	0.0537530i	0.999639	−	0.0268765i	$-0.00855609\pi$
$60$	7.08833e56	−	3.65713e56i	0.890643	−	0.459516i
$61$	−2.06291e57			−1.52731			−0.763654	−	0.645626i	$-0.776596\pi$
$61$	−2.06291e57			−1.52731			−0.763654	+	0.645626i	$0.776596\pi$
$62$		−	2.00425e56i		−	0.0881898i
$63$	2.30912e57	−	3.24706e57i	0.608904	−	0.856235i
$64$	4.49558e57			0.716187
$65$			6.70662e57i			0.650543i
$66$	5.48284e56	+	1.06269e57i	0.0326287	+	0.0632415i
$67$	−2.49683e58			−0.918322			−0.459161	−	0.888353i	$-0.651850\pi$
$67$	−2.49683e58			−0.918322			−0.459161	+	0.888353i	$0.651850\pi$
$68$			2.70870e58i			0.620119i
$69$	4.62153e58	−	2.38442e58i	0.663155	−	0.342146i
$70$	2.71629e58			0.245945
$71$		−	3.22236e59i		−	1.85313i	−0.376130	−	0.926567i	$-0.622745\pi$
$71$		−	3.22236e59i		−	1.85313i	0.376130	−	0.926567i	$-0.377255\pi$
$72$	9.60320e58	+	6.82923e58i	0.353001	+	0.251033i
$73$	−3.78481e59			−0.894772			−0.447386	−	0.894341i	$-0.647645\pi$
$73$	−3.78481e59			−0.894772			−0.447386	+	0.894341i	$0.647645\pi$
$74$		−	2.69315e59i		−	0.411951i
$75$	−5.12580e58	−	9.93493e58i	−0.0510272	−	0.0989018i
$76$	1.46552e60			0.954896
$77$		−	7.85165e59i		−	0.336711i
$78$	−4.29141e59	+	2.21410e59i	−0.121779	+	0.0628304i
$79$	1.02816e61			1.94086			0.970430	−	0.241382i	$-0.0776007\pi$
$79$	1.02816e61			1.94086			0.970430	+	0.241382i	$0.0776007\pi$
$80$		−	7.13688e60i		−	0.900801i
$81$	−3.87033e60	−	1.11368e61i	−0.328267	−	0.944585i
$82$	−1.36442e60			−0.0781455
$83$		−	3.30630e61i		−	1.28482i	−0.766360	−	0.642411i	$-0.777934\pi$
$83$		−	3.30630e61i		−	1.28482i	0.766360	−	0.642411i	$-0.222066\pi$
$84$	−1.72898e61	−	3.35114e61i	−0.457986	−	0.887678i
$85$	3.79101e61			0.687621
$86$		−	4.06816e60i		−	0.0507513i
$87$	1.62436e62	−	8.38066e61i	1.39980	−	0.722208i
$88$	2.32213e61			0.138816
$89$		−	3.88161e62i		−	1.61634i	−0.588952	−	0.808168i	$-0.700459\pi$
$89$		−	3.88161e62i		−	1.61634i	0.588952	−	0.808168i	$-0.299541\pi$
$90$	4.65819e61	−	6.55030e61i	0.135661	−	0.190766i
$91$	3.17068e62			0.648377
$92$		−	4.92170e62i		−	0.709421i
$93$	1.78550e62	+	3.46070e62i	0.182098	+	0.352947i
$94$	−2.55464e62			−0.185029
$95$		−	2.05109e63i		−	1.05884i
$96$	1.49918e63	−	7.73482e62i	0.553571	−	0.285608i
$97$	−5.25219e62			−0.139202			−0.0696010	−	0.997575i	$-0.522173\pi$
$97$	−5.25219e62			−0.139202			−0.0696010	+	0.997575i	$0.522173\pi$
$98$		−	1.20870e62i		−	0.0230719i
$99$	−1.89342e63	−	1.34649e63i	−0.261168	−	0.185727i
$100$	−1.05802e63			−0.105802
$101$			2.41346e64i			1.75532i	0.479282	+	0.877661i	$0.340897\pi$
$101$			2.41346e64i			1.75532i	−0.479282	+	0.877661i	$0.659103\pi$
$102$	1.25155e63	+	2.42578e63i	0.0664114	+	0.128720i
$103$	−1.22328e63			−0.0475044			−0.0237522	−	0.999718i	$-0.507561\pi$
$103$	−1.22328e63			−0.0475044			−0.0237522	+	0.999718i	$0.507561\pi$
$104$			9.37730e63i			0.267307i
$105$	−4.69015e64	+	2.41982e64i	−0.984304	+	0.507839i
$106$	−2.42800e64			−0.376236
$107$			5.22329e64i			0.599326i	0.954045	+	0.299663i	$0.0968743\pi$
$107$			5.22329e64i			0.599326i	−0.954045	+	0.299663i	$0.903126\pi$
$108$	−1.10463e65	−	1.57748e64i	−0.941143	−	0.134402i
$109$	1.03661e65			0.657609			0.328805	−	0.944398i	$-0.393354\pi$
$109$	1.03661e65			0.657609			0.328805	+	0.944398i	$0.393354\pi$
$110$		−	1.58391e64i		−	0.0750180i
$111$	2.39921e65	+	4.65020e65i	0.850615	+	1.64868i
$112$	−3.37410e65			−0.897802
$113$			7.55936e65i			1.51347i	0.653719	+	0.756737i	$0.273208\pi$
$113$			7.55936e65i			1.51347i	−0.653719	+	0.756737i	$0.726792\pi$
$114$	1.31245e65	−	6.77140e64i	0.198210	−	0.102264i
$115$	−6.88825e65			−0.786644
$116$		−	1.72986e66i		−	1.49746i
$117$	5.43743e65	−	7.64606e65i	0.357640	−	0.502910i
$118$	−2.38279e64			−0.0119361
$119$		−	1.79227e66i		−	0.685331i
$120$	−7.15664e65	−	1.38711e66i	−0.209368	−	0.405800i
$121$	4.00007e66			0.897297
$122$			1.96744e66i			0.339145i
$123$	2.35591e66	−	1.21550e66i	0.312748	−	0.161358i
$124$	3.68547e66			0.377571
$125$		−	1.18248e67i		−	0.936858i
$126$	−3.09678e66	−	2.20224e66i	−0.190131	−	0.135210i
$127$	1.68169e67			0.801728			0.400864	−	0.916138i	$-0.368710\pi$
$127$	1.68169e67			0.801728			0.400864	+	0.916138i	$0.368710\pi$
$128$		−	2.10811e67i		−	0.781940i
$129$	3.62415e66	+	7.02439e66i	0.104794	+	0.203113i
$130$	6.39622e66			0.144456
$131$		−	4.54308e67i		−	0.802914i	−0.915878	−	0.401457i	$-0.868504\pi$
$131$		−	4.54308e67i		−	0.802914i	0.915878	−	0.401457i	$-0.131496\pi$
$132$	−1.95411e67	+	1.00820e67i	−0.270759	+	0.139695i
$133$	−9.69692e67			−1.05531
$134$			2.38127e67i			0.203918i
$135$	−2.20780e67	+	1.54600e68i	−0.149032	+	1.04359i
$136$	5.30065e67			0.282542
$137$			3.02184e68i			1.27413i	0.770810	+	0.637065i	$0.219852\pi$
$137$			3.02184e68i			1.27413i	−0.770810	+	0.637065i	$0.780148\pi$
$138$	−2.27406e67	−	4.40763e67i	−0.0759751	−	0.147256i
$139$	−1.10502e68			−0.293020			−0.146510	−	0.989209i	$-0.546804\pi$
$139$	−1.10502e68			−0.293020			−0.146510	+	0.989209i	$0.546804\pi$
$140$			4.99477e68i			1.05298i
$141$	4.41104e68	−	2.27582e68i	0.740508	−	0.382056i
$142$	−3.07322e68			−0.411497
$143$		−	1.84888e68i		−	0.197768i
$144$	−5.78627e68	+	8.13660e68i	−0.495221	+	0.696375i
$145$	−2.42105e69			−1.66046
$146$			3.60964e68i			0.198688i
$147$	1.07678e68	+	2.08703e68i	0.0476399	+	0.0923366i
$148$	4.95223e69			1.76370
$149$		−	2.96553e69i		−	0.851415i	−0.904861	−	0.425707i	$-0.860025\pi$
$149$		−	2.96553e69i		−	0.851415i	0.904861	−	0.425707i	$-0.139975\pi$
$150$	−9.47511e67	+	4.88856e67i	−0.0219616	+	0.0113308i
$151$	4.20890e69			0.788690			0.394345	−	0.918962i	$-0.370972\pi$
$151$	4.20890e69			0.788690			0.394345	+	0.918962i	$0.370972\pi$
$152$		−	2.86787e69i		−	0.435075i
$153$	−4.32204e69	−	3.07358e69i	−0.531573	−	0.378023i
$154$	−7.48825e68			−0.0747683
$155$		−	5.15806e69i		−	0.418671i
$156$	−4.07134e69	−	7.89114e69i	−0.268998	−	0.521378i
$157$	7.24486e69			0.390159			0.195079	−	0.980787i	$-0.437504\pi$
$157$	7.24486e69			0.390159			0.195079	+	0.980787i	$0.437504\pi$
$158$		−	9.80575e69i		−	0.430977i
$159$	4.19237e70	−	2.16300e70i	1.50575	−	0.776870i
$160$	−2.23448e70			−0.656654
$161$			3.25655e70i			0.784025i
$162$	−1.06214e70	+	3.69120e69i	−0.209749	+	0.0728932i
$163$	7.30770e69			0.118516			0.0592580	−	0.998243i	$-0.481127\pi$
$163$	7.30770e69			0.118516			0.0592580	+	0.998243i	$0.481127\pi$
$164$		−	2.50892e70i		−	0.334568i
$165$	1.41104e70	+	2.73491e70i	0.154901	+	0.300232i
$166$	−3.15327e70			−0.285301
$167$			1.99179e71i			1.48702i	0.668727	+	0.743508i	$0.266840\pi$
$167$			1.99179e71i			1.48702i	−0.668727	+	0.743508i	$0.733160\pi$
$168$	−6.55784e70	+	3.38344e70i	−0.404449	+	0.208670i
$169$	−1.21391e71			−0.619175
$170$		−	3.61555e70i		−	0.152689i
$171$	−1.66293e71	+	2.33840e71i	−0.582103	+	0.818548i
$172$	7.48063e70			0.217284
$173$		−	9.57534e70i		−	0.231036i	−0.993305	−	0.115518i	$-0.963147\pi$
$173$		−	9.57534e70i		−	0.231036i	0.993305	−	0.115518i	$-0.0368527\pi$
$174$	−7.99277e70	−	1.54917e71i	−0.160369	−	0.310831i
$175$	7.00062e70			0.116928
$176$			1.96749e71i			0.273847i
$177$	4.11432e70	−	2.12273e70i	0.0477698	−	0.0246462i
$178$	−3.70196e71			−0.358915
$179$			9.29489e71i			0.753264i	0.926363	+	0.376632i	$0.122918\pi$
$179$			9.29489e71i			0.753264i	−0.926363	+	0.376632i	$0.877082\pi$
$180$	1.20448e72	+	8.56558e71i	0.816735	+	0.580813i
$181$	1.98369e72			1.12658			0.563288	−	0.826261i	$-0.309536\pi$
$181$	1.98369e72			1.12658			0.563288	+	0.826261i	$0.309536\pi$
$182$		−	3.02393e71i		−	0.143975i
$183$	−1.75270e72	−	3.39713e72i	−0.700283	−	1.35730i
$184$	−9.63126e71			−0.323231
$185$		−	6.93098e72i		−	1.95569i
$186$	3.30052e71	−	1.70286e71i	0.0783734	−	0.0404358i
$187$	−1.04510e72			−0.209039
$188$		−	4.69754e72i		−	0.792171i
$189$	7.30902e72	+	1.04378e72i	1.04011	+	0.148535i
$190$	−1.95616e72			−0.235120
$191$			4.55191e72i			0.462515i	0.972893	+	0.231258i	$0.0742841\pi$
$191$			4.55191e72i			0.462515i	−0.972893	+	0.231258i	$0.925716\pi$
$192$	3.81956e72	+	7.40315e72i	0.328378	+	0.636469i
$193$	3.39108e72			0.246890			0.123445	−	0.992351i	$-0.460606\pi$
$193$	3.39108e72			0.246890			0.123445	+	0.992351i	$0.460606\pi$
$194$			5.00911e71i			0.0309104i
$195$	−1.10442e73	+	5.69812e72i	−0.578131	+	0.298280i
$196$	2.22258e72			0.0987787
$197$			1.30228e73i			0.491794i	0.969296	+	0.245897i	$0.0790826\pi$
$197$			1.30228e73i			0.491794i	−0.969296	+	0.245897i	$0.920917\pi$
$198$	−1.28417e72	+	1.80578e72i	−0.0412416	+	0.0579936i
$199$	−2.32319e73			−0.635017			−0.317509	−	0.948255i	$-0.602846\pi$
$199$	−2.32319e73			−0.635017			−0.317509	+	0.948255i	$0.602846\pi$
$200$			2.07044e72i			0.0482061i
$201$	−2.12137e73	−	4.11168e73i	−0.421059	−	0.816104i
$202$	2.30176e73			0.389777
$203$			1.14460e74i			1.65493i
$204$	−4.46057e73	+	2.30138e73i	−0.551094	+	0.284330i
$205$	−3.51141e73			−0.370986
$206$			1.16666e72i			0.0105486i
$207$	7.85314e73	+	5.58469e73i	0.608124	+	0.432462i
$208$	−7.94520e73			−0.527325
$209$			5.65444e73i			0.321891i
$210$	2.30783e73	+	4.47307e73i	0.112768	+	0.218569i
$211$	−6.94514e73			−0.291503			−0.145751	−	0.989321i	$-0.546560\pi$
$211$	−6.94514e73			−0.291503			−0.145751	+	0.989321i	$0.546560\pi$
$212$		−	4.46466e74i		−	1.61080i
$213$	5.30645e74	−	2.73780e74i	1.64686	−	0.849678i
$214$	4.98154e73			0.133083
$215$		−	1.04697e74i		−	0.240936i
$216$	−3.08698e73	+	2.16165e74i	−0.0612369	+	0.428809i
$217$	−2.43857e74			−0.417277
$218$		−	9.88633e73i		−	0.146025i
$219$	−3.21567e74	−	6.23267e74i	−0.410261	−	0.795175i
$220$	2.91254e74			0.321178
$221$		−	4.22037e74i		−	0.402530i
$222$	4.43497e74	−	2.28817e74i	0.366097	−	0.188883i
$223$	4.46055e74			0.318884			0.159442	−	0.987207i	$-0.449030\pi$
$223$	4.46055e74			0.318884			0.159442	+	0.987207i	$0.449030\pi$
$224$			1.05639e75i			0.654468i
$225$	1.20054e74	−	1.68819e74i	0.0644967	−	0.0906946i
$226$	7.20949e74			0.336074
$227$		−	1.51806e74i		−	0.0614413i	−0.999528	−	0.0307207i	$-0.990220\pi$
$227$		−	1.51806e74i		−	0.0614413i	0.999528	−	0.0307207i	$-0.00978023\pi$
$228$	1.24514e75	+	2.41336e75i	0.437828	+	0.848606i
$229$	−5.66043e75			−1.73027			−0.865136	−	0.501538i	$-0.832768\pi$
$229$	−5.66043e75			−1.73027			−0.865136	+	0.501538i	$0.832768\pi$
$230$			6.56944e74i			0.174678i
$231$	1.29298e75	−	6.67096e74i	0.299232	−	0.154385i
$232$	−3.38515e75			−0.682280
$233$			3.03138e75i			0.532415i	0.963916	+	0.266208i	$0.0857707\pi$
$233$			3.03138e75i			0.532415i	−0.963916	+	0.266208i	$0.914229\pi$
$234$	−7.29218e74	−	5.18577e74i	−0.111673	−	0.0794155i
$235$	−6.57453e75			−0.878401
$236$		−	4.38154e74i		−	0.0511026i
$237$	8.73552e75	+	1.69314e76i	0.889901	+	1.72482i
$238$	−1.70932e75			−0.152181
$239$			2.53282e75i			0.197184i	0.995128	+	0.0985921i	$0.0314339\pi$
$239$			2.53282e75i			0.197184i	−0.995128	+	0.0985921i	$0.968566\pi$
$240$	1.17527e76	−	6.06368e75i	0.800533	−	0.413025i
$241$	4.40252e75			0.262516			0.131258	−	0.991348i	$-0.458098\pi$
$241$	4.40252e75			0.262516			0.131258	+	0.991348i	$0.458098\pi$
$242$		−	3.81494e75i		−	0.199249i
$243$	1.50514e76	−	1.58356e76i	0.688930	−	0.724828i
$244$	−3.61777e76			−1.45200
$245$		−	3.11065e75i		−	0.109531i
$246$	−1.15924e75	−	2.24687e75i	−0.0358304	−	0.0694471i
$247$	−2.28340e76			−0.619839
$248$		−	7.21208e75i		−	0.172031i
$249$	5.44468e76	−	2.80912e76i	1.14181	−	0.589102i
$250$	−1.12775e76			−0.208034
$251$		−	5.22172e76i		−	0.847723i	−0.905727	−	0.423862i	$-0.860674\pi$
$251$		−	5.22172e76i		−	0.847723i	0.905727	−	0.423862i	$-0.139326\pi$
$252$	4.04954e76	−	5.69443e76i	0.578880	−	0.814016i
$253$	1.89895e76			0.239143
$254$		−	1.60386e76i		−	0.178027i
$255$	3.22094e76	+	6.24288e76i	0.315280	+	0.611082i
$256$	6.28235e76			0.542554
$257$			3.71123e76i			0.282916i	0.989944	+	0.141458i	$0.0451790\pi$
$257$			3.71123e76i			0.282916i	−0.989944	+	0.141458i	$0.954821\pi$
$258$	6.69928e75	−	3.45641e75i	0.0451022	−	0.0232699i
$259$	−3.27675e77			−1.94918
$260$			1.17615e77i			0.618466i
$261$	2.76019e77	+	1.96288e77i	1.28364	+	0.912847i
$262$	−4.33281e76			−0.178291
$263$		−	4.25885e76i		−	0.155134i	−0.996987	−	0.0775672i	$-0.975285\pi$
$263$		−	4.25885e76i		−	0.155134i	0.996987	−	0.0775672i	$-0.0247152\pi$
$264$	1.97294e76	+	3.82399e76i	0.0636485	+	0.123365i
$265$	−6.24860e77			−1.78614
$266$			9.24812e76i			0.234337i
$267$	6.39208e77	−	3.29791e77i	1.43642	−	0.741104i
$268$	−4.37873e77			−0.873041
$269$			3.80654e77i			0.673686i	0.941561	+	0.336843i	$0.109359\pi$
$269$			3.80654e77i			0.673686i	−0.941561	+	0.336843i	$0.890641\pi$
$270$	1.47445e77	+	2.10561e76i	0.231734	+	0.0330932i
$271$	−9.77952e77			−1.36553			−0.682764	−	0.730639i	$-0.739222\pi$
$271$	−9.77952e77			−1.36553			−0.682764	+	0.730639i	$0.739222\pi$
$272$			4.49113e77i			0.557379i
$273$	2.69389e77	+	5.22135e77i	0.297287	+	0.576207i
$274$	2.88198e77			0.282926
$275$		−	4.08218e76i		−	0.0356653i
$276$	8.10485e77	−	4.18160e77i	0.630456	−	0.325276i
$277$	1.10155e78			0.763221			0.381611	−	0.924323i	$-0.375370\pi$
$277$	1.10155e78			0.763221			0.381611	+	0.924323i	$0.375370\pi$
$278$			1.05388e77i			0.0650664i
$279$	−4.18193e77	+	5.88059e77i	−0.230166	+	0.323658i
$280$	9.77426e77			0.479763
$281$		−	3.54456e78i		−	1.55224i	−0.630582	−	0.776122i	$-0.717184\pi$
$281$		−	3.54456e78i		−	1.55224i	0.630582	−	0.776122i	$-0.282816\pi$
$282$	−2.17049e77	−	4.20689e77i	−0.0848372	−	0.164433i
$283$	−3.70973e78			−1.29472			−0.647360	−	0.762184i	$-0.724127\pi$
$283$	−3.70973e78			−1.29472			−0.647360	+	0.762184i	$0.724127\pi$
$284$		−	5.65110e78i		−	1.76176i
$285$	3.37766e78	−	1.74266e78i	0.940979	−	0.485487i
$286$	−1.76331e77			−0.0439152
$287$			1.66008e78i			0.369751i
$288$	2.54748e78	+	1.81162e78i	0.507634	+	0.360999i
$289$	3.22138e78			0.574528
$290$			2.30900e78i			0.368712i
$291$	−4.46240e77	−	8.64911e77i	−0.0638253	−	0.123707i
$292$	−6.63748e78			−0.850652
$293$			1.59018e79i			1.82676i	0.407106	+	0.913381i	$0.366538\pi$
$293$			1.59018e79i			1.82676i	−0.407106	+	0.913381i	$0.633462\pi$
$294$	1.99043e77	−	1.02694e77i	0.0205037	−	0.0105787i
$295$	−6.13227e77			−0.0566652
$296$		−	9.69101e78i		−	0.803589i
$297$	6.08645e77	−	4.26201e78i	0.0453062	−	0.317255i
$298$	−2.82827e78			−0.189061
$299$			7.66841e78i			0.460497i
$300$	−8.98920e77	−	1.74230e78i	−0.0485111	−	0.0940251i
$301$	−4.94972e78			−0.240134
$302$		−	4.01410e78i		−	0.175132i
$303$	−3.97440e79	+	2.05054e79i	−1.55994	+	0.804830i
$304$	2.42989e79			0.858285
$305$			5.06331e79i			1.61005i
$306$	−2.93132e78	+	4.12200e78i	−0.0839418	+	0.118038i
$307$	2.76867e79			0.714238			0.357119	−	0.934059i	$-0.383759\pi$
$307$	2.76867e79			0.714238			0.357119	+	0.934059i	$0.383759\pi$
$308$		−	1.37696e79i		−	0.320109i
$309$	−1.03933e78	−	2.01444e78i	−0.0217812	−	0.0422167i
$310$	−4.91933e78			−0.0929677
$311$		−	5.59973e79i		−	0.954629i	−0.878733	−	0.477314i	$-0.841610\pi$
$311$		−	5.59973e79i		−	0.954629i	0.878733	−	0.477314i	$-0.158390\pi$
$312$	−1.54422e79	+	7.96719e78i	−0.237553	+	0.122563i
$313$	7.30818e78			0.101482			0.0507412	−	0.998712i	$-0.483842\pi$
$313$	7.30818e78			0.101482			0.0507412	+	0.998712i	$0.483842\pi$
$314$		−	6.90955e78i		−	0.0866365i
$315$	−7.96974e79	−	5.66761e79i	−0.902623	−	0.641892i
$316$	1.80310e80			1.84516
$317$		−	7.76625e79i		−	0.718315i	−0.933277	−	0.359158i	$-0.883064\pi$
$317$		−	7.76625e79i		−	0.718315i	0.933277	−	0.359158i	$-0.116936\pi$
$318$	−2.06289e79	−	3.99833e79i	−0.172508	−	0.334357i
$319$	6.67435e79			0.504786
$320$		−	1.10342e80i		−	0.754988i
$321$	−8.60151e79	+	4.43784e79i	−0.532615	+	0.274796i
$322$	3.10583e79			0.174096
$323$			1.29072e80i			0.655166i
$324$	−6.78746e79	−	1.95308e80i	−0.312081	−	0.898009i
$325$	1.64848e79			0.0686778
$326$		−	6.96948e78i		−	0.0263170i
$327$	8.80731e79	+	1.70705e80i	0.301519	+	0.584411i
$328$	−4.90971e79			−0.152438
$329$			3.10823e80i			0.875477i
$330$	2.60833e79	−	1.34573e79i	0.0666678	−	0.0343964i
$331$	5.11103e80			1.18580			0.592902	−	0.805275i	$-0.297982\pi$
$331$	5.11103e80			1.18580			0.592902	+	0.805275i	$0.297982\pi$
$332$		−	5.79831e80i		−	1.22147i
$333$	−5.61933e80	+	7.90185e80i	−1.07515	+	1.51187i
$334$	1.89960e80			0.330199
$335$			6.12833e80i			0.968074i
$336$	−2.86672e80	−	5.55633e80i	−0.411650	−	0.797868i
$337$	−1.08166e81			−1.41232			−0.706159	−	0.708053i	$-0.749574\pi$
$337$	−1.08166e81			−1.41232			−0.706159	+	0.708053i	$0.749574\pi$
$338$			1.15773e80i			0.137491i
$339$	−1.24485e81	+	6.42263e80i	−1.34501	+	0.693941i
$340$	6.64835e80			0.653715
$341$			1.42197e80i			0.127277i
$342$	2.23018e80	+	1.58597e80i	0.181762	+	0.129259i
$343$	1.26833e81			0.941501
$344$		−	1.46388e80i		−	0.0990002i
$345$	−5.85243e80	−	1.13433e81i	−0.360683	−	0.699082i
$346$	−9.13217e79			−0.0513025
$347$			1.61695e81i			0.828235i	0.910224	+	0.414117i	$0.135910\pi$
$347$			1.61695e81i			0.828235i	−0.910224	+	0.414117i	$0.864090\pi$
$348$	2.84866e81	−	1.46973e81i	1.33077	−	0.686597i
$349$	−5.34005e79			−0.0227579			−0.0113789	−	0.999935i	$-0.503622\pi$
$349$	−5.34005e79			−0.0227579			−0.0113789	+	0.999935i	$0.503622\pi$
$350$		−	6.67661e79i		−	0.0259644i
$351$	1.72110e81	+	2.45785e80i	0.610912	+	0.0872424i
$352$	6.16000e80			0.199625
$353$		−	8.20881e80i		−	0.242935i	−0.992595	−	0.121467i	$-0.961240\pi$
$353$		−	8.20881e80i		−	0.242935i	0.992595	−	0.121467i	$-0.0387600\pi$
$354$	−2.02448e79	−	3.92389e79i	−0.00547280	−	0.0106075i
$355$	−7.90911e81			−1.95353
$356$		−	6.80724e81i		−	1.53664i
$357$	2.95144e81	−	1.52276e81i	0.609047	−	0.314230i
$358$	8.86469e80			0.167266
$359$		−	2.15067e81i		−	0.371151i	−0.982630	−	0.185576i	$-0.940585\pi$
$359$		−	2.15067e81i		−	0.371151i	0.982630	−	0.185576i	$-0.0594150\pi$
$360$	1.67620e81	−	2.35705e81i	0.264634	−	0.372126i
$361$	6.13544e79			0.00886370
$362$		−	1.89188e81i		−	0.250161i
$363$	3.39856e81	+	6.58716e81i	0.411418	+	0.797419i
$364$	5.56047e81			0.616407
$365$			9.28961e81i			0.943248i
$366$	−3.23990e81	+	1.67158e81i	−0.301395	+	0.155501i
$367$	−9.21335e81			−0.785423			−0.392711	−	0.919662i	$-0.628463\pi$
$367$	−9.21335e81			−0.785423			−0.392711	+	0.919662i	$0.628463\pi$
$368$		−	8.16038e81i		−	0.637647i
$369$	4.00328e81	+	2.84689e81i	0.286795	+	0.203952i
$370$	−6.61019e81			−0.434269
$371$			2.95414e82i			1.78019i
$372$	3.13127e81	+	6.06908e81i	0.173119	+	0.335543i
$373$	−2.05816e82			−1.04423			−0.522115	−	0.852875i	$-0.674857\pi$
$373$	−2.05816e82			−1.04423			−0.522115	+	0.852875i	$0.674857\pi$
$374$			9.96733e80i			0.0464181i
$375$	1.94726e82	−	1.00467e82i	0.832577	−	0.429558i
$376$	−9.19261e81			−0.360934
$377$			2.69526e82i			0.972025i
$378$	9.95468e80	−	6.97073e81i	0.0329830	−	0.230962i
$379$	−2.69187e82			−0.819596			−0.409798	−	0.912176i	$-0.634401\pi$
$379$	−2.69187e82			−0.819596			−0.409798	+	0.912176i	$0.634401\pi$
$380$		−	3.59704e82i		−	1.00663i
$381$	1.42881e82	+	2.76934e82i	0.367599	+	0.712488i
$382$	4.34124e81			0.102704
$383$		−	4.23433e82i		−	0.921348i	−0.887569	−	0.460674i	$-0.847608\pi$
$383$		−	4.23433e82i		−	0.921348i	0.887569	−	0.460674i	$-0.152392\pi$
$384$	3.47154e82	−	1.79110e82i	0.694902	−	0.358526i
$385$	−1.92715e82			−0.354953
$386$		−	3.23413e81i		−	0.0548231i
$387$	−8.48833e81	+	1.19362e82i	−0.132456	+	0.186258i
$388$	−9.21086e81			−0.132338
$389$			5.23339e82i			0.692462i	0.938149	+	0.346231i	$0.112539\pi$
$389$			5.23339e82i			0.692462i	−0.938149	+	0.346231i	$0.887461\pi$
$390$	5.43439e81	+	1.05330e82i	0.0662343	+	0.128377i
$391$	4.33467e82			0.486743
$392$		−	4.34936e81i		−	0.0450061i
$393$	7.48137e82	−	3.85992e82i	0.713542	−	0.368143i
$394$	1.24200e82			0.109205
$395$		−	2.52357e83i		−	2.04601i
$396$	−3.32052e82	−	2.36136e82i	−0.248290	−	0.176569i
$397$	1.07524e83			0.741665			0.370832	−	0.928700i	$-0.379072\pi$
$397$	1.07524e83			0.741665			0.370832	+	0.928700i	$0.379072\pi$
$398$			2.21566e82i			0.141008i
$399$	−8.23875e82	−	1.59685e83i	−0.483870	−	0.937847i
$400$	−1.75424e82			−0.0950976
$401$			9.93395e81i			0.0497167i	0.999691	+	0.0248583i	$0.00791347\pi$
$401$			9.93395e81i			0.0497167i	−0.999691	+	0.0248583i	$0.992087\pi$
$402$	−3.92138e82	+	2.02319e82i	−0.181219	+	0.0934979i
$403$	−5.74226e82			−0.245088
$404$			4.23253e83i			1.66877i
$405$	−2.73348e83	+	9.49952e82i	−0.995760	+	0.346052i
$406$	1.09162e83			0.367485
$407$			1.91073e83i			0.594536i
$408$	4.50356e82	+	8.72889e82i	0.129548	+	0.251093i
$409$	5.82645e83			1.54974			0.774868	−	0.632123i	$-0.217816\pi$
$409$	5.82645e83			1.54974			0.774868	+	0.632123i	$0.217816\pi$
$410$			3.34889e82i			0.0823792i
$411$	−4.97625e83	+	2.56744e83i	−1.13231	+	0.584200i
$412$	−2.14528e82			−0.0451620
$413$			2.89914e82i			0.0564765i
$414$	5.32621e82	−	7.48967e82i	0.0960301	−	0.135037i
$415$	−8.11513e83			−1.35443
$416$			2.48755e83i			0.384402i
$417$	−9.38854e82	−	1.81971e83i	−0.134352	−	0.260404i
$418$	5.39274e82			0.0714773
$419$		−	1.14567e84i		−	1.40673i	−0.710827	−	0.703367i	$-0.751679\pi$
$419$		−	1.14567e84i		−	1.40673i	0.710827	−	0.703367i	$-0.248321\pi$
$420$	−8.22519e83	+	4.24369e83i	−0.935769	+	0.482799i
$421$	1.29529e84			1.36565			0.682824	−	0.730583i	$-0.260752\pi$
$421$	1.29529e84			1.36565			0.682824	+	0.730583i	$0.260752\pi$
$422$			6.62370e82i			0.0647295i
$423$	7.49547e83	+	5.33033e83i	0.679058	+	0.482906i
$424$	−8.73689e83			−0.733921
$425$		−	9.31827e82i		−	0.0725921i
$426$	−2.61108e83	−	5.06085e83i	−0.188675	−	0.365693i
$427$	2.39378e84			1.60469
$428$			9.16017e83i			0.569775i
$429$	3.04466e83	−	1.57085e83i	0.175754	−	0.0906781i
$430$	−9.98508e82			−0.0535009
$431$		−	1.80704e84i		−	0.898868i	−0.893313	−	0.449434i	$-0.851626\pi$
$431$		−	1.80704e84i		−	0.898868i	0.893313	−	0.449434i	$-0.148374\pi$
$432$	−1.83152e84	−	2.61553e83i	−0.845924	−	0.120804i
$433$	2.34410e84			1.00546			0.502729	−	0.864444i	$-0.332329\pi$
$433$	2.34410e84			1.00546			0.502729	+	0.864444i	$0.332329\pi$
$434$			2.32571e83i			0.0926582i
$435$	−2.05699e84	−	3.98689e84i	−0.761335	−	1.47563i
$436$	1.81792e84			0.625183
$437$		−	2.34524e84i		−	0.749516i
$438$	−5.94421e83	+	3.06684e83i	−0.176572	+	0.0911002i
$439$	−1.70979e83			−0.0472147			−0.0236074	−	0.999721i	$-0.507515\pi$
$439$	−1.70979e83			−0.0472147			−0.0236074	+	0.999721i	$0.507515\pi$
$440$		−	5.69954e83i		−	0.146337i
$441$	−2.52198e83	+	3.54639e83i	−0.0602153	+	0.0846742i
$442$	−4.02504e83			−0.0893836
$443$			4.11444e84i			0.849946i	0.905206	+	0.424973i	$0.139716\pi$
$443$			4.11444e84i			0.849946i	−0.905206	+	0.424973i	$0.860284\pi$
$444$	4.20754e84	+	8.15513e84i	0.808673	+	1.56739i
$445$	−9.52720e84			−1.70390
$446$		−	4.25410e83i		−	0.0708097i
$447$	4.88351e84	−	2.51959e84i	0.756644	−	0.390381i
$448$	−5.21661e84			−0.752475
$449$			1.84879e83i			0.0248316i	0.999923	+	0.0124158i	$0.00395217\pi$
$449$			1.84879e83i			0.0248316i	−0.999923	+	0.0124158i	$0.996048\pi$
$450$	−1.61006e83	−	1.14498e83i	−0.0201392	−	0.0143218i
$451$	9.68024e83			0.112781
$452$			1.32570e85i			1.43885i
$453$	3.57599e84	+	6.93105e84i	0.361621	+	0.700901i
$454$	−1.44780e83			−0.0136433
$455$		−	7.78227e84i		−	0.683505i
$456$	4.72269e84	−	2.43661e84i	0.386647	−	0.199486i
$457$	−1.46215e84			−0.111602			−0.0558011	−	0.998442i	$-0.517771\pi$
$457$	−1.46215e84			−0.111602			−0.0558011	+	0.998442i	$0.517771\pi$
$458$			5.39845e84i			0.384215i
$459$	1.38933e84	−	9.72876e84i	0.0922147	−	0.645731i
$460$	−1.20800e85			−0.747856
$461$			2.71625e85i			1.56870i	0.620319	+	0.784349i	$0.287003\pi$
$461$			2.71625e85i			1.56870i	−0.620319	+	0.784349i	$0.712997\pi$
$462$	−6.36221e83	−	1.23314e84i	−0.0342819	−	0.0664458i
$463$	−2.41218e85			−1.21288			−0.606441	−	0.795129i	$-0.707403\pi$
$463$	−2.41218e85			−1.21288			−0.606441	+	0.795129i	$0.707403\pi$
$464$		−	2.86817e85i		−	1.34595i
$465$	8.49410e84	−	4.38242e84i	0.372068	−	0.191964i
$466$	2.89108e84			0.118225
$467$		−	3.53384e85i		−	1.34929i	−0.738141	−	0.674647i	$-0.764296\pi$
$467$		−	3.53384e85i		−	1.34929i	0.738141	−	0.674647i	$-0.235704\pi$
$468$	9.53571e84	−	1.34090e85i	0.340005	−	0.478112i
$469$	2.89729e85			0.964851
$470$			6.27024e84i			0.195053i
$471$	6.15542e84	+	1.19306e85i	0.178891	+	0.346730i
$472$	−8.57423e83			−0.0232837
$473$			2.88627e84i			0.0732454i
$474$	1.61477e85	−	8.33121e84i	0.383005	−	0.197607i
$475$	−5.04157e84			−0.111782
$476$		−	3.14313e85i		−	0.651539i
$477$	7.12389e85	+	5.06609e85i	1.38079	+	0.981939i
$478$	2.41560e84			0.0437856
$479$		−	2.28274e85i		−	0.387008i	−0.981099	−	0.193504i	$-0.938015\pi$
$479$		−	2.28274e85i		−	0.387008i	0.981099	−	0.193504i	$-0.0619852\pi$
$480$	−1.89847e85	−	3.67965e85i	−0.301082	−	0.583562i
$481$	−7.71598e85			−1.14485
$482$		−	4.19876e84i		−	0.0582929i
$483$	−5.36276e85	+	2.76685e85i	−0.696755	+	0.359482i
$484$	7.01499e85			0.853053
$485$			1.28912e85i			0.146744i
$486$	−1.51027e85	−	1.43547e85i	−0.160951	−	0.152980i
$487$	−1.43402e86			−1.43096			−0.715482	−	0.698631i	$-0.753793\pi$
$487$	−1.43402e86			−1.43096			−0.715482	+	0.698631i	$0.753793\pi$
$488$			7.07960e85i			0.661568i
$489$	6.20881e84	+	1.20340e85i	0.0543406	+	0.105324i
$490$	−2.96668e84			−0.0243218
$491$			5.62860e85i			0.432308i	0.976359	+	0.216154i	$0.0693513\pi$
$491$			5.62860e85i			0.432308i	−0.976359	+	0.216154i	$0.930649\pi$
$492$	4.13159e85	−	2.13164e85i	0.297327	−	0.153402i
$493$	1.52353e86			1.02742
$494$			2.17771e85i			0.137638i
$495$	−3.30488e85	+	4.64729e85i	−0.195789	+	0.275317i
$496$	6.11066e85			0.339371
$497$			3.73918e86i			1.94703i
$498$	−2.67910e85	−	5.19268e85i	−0.130813	−	0.253544i
$499$	−1.88472e86			−0.863038			−0.431519	−	0.902104i	$-0.642022\pi$
$499$	−1.88472e86			−0.863038			−0.431519	+	0.902104i	$0.642022\pi$
$500$		−	2.07374e86i		−	0.890664i
$501$	−3.28000e86	+	1.69227e86i	−1.32150	+	0.681810i
$502$	−4.98004e85			−0.188241
$503$		−	4.29486e85i		−	0.152326i	−0.997095	−	0.0761629i	$-0.975733\pi$
$503$		−	4.29486e85i		−	0.152326i	0.997095	−	0.0761629i	$-0.0242669\pi$
$504$	−1.11434e86	−	7.92454e85i	−0.370887	−	0.263753i
$505$	5.92372e86			1.85042
$506$		−	1.81106e85i		−	0.0531027i
$507$	−1.03137e86	−	1.99903e86i	−0.283897	−	0.550255i
$508$	2.94921e86			0.762197
$509$		−	4.96777e86i		−	1.20557i	−0.797903	−	0.602785i	$-0.794058\pi$
$509$		−	4.96777e86i		−	1.20557i	0.797903	−	0.602785i	$-0.205942\pi$
$510$	5.95394e85	−	3.07186e85i	0.135693	−	0.0700093i
$511$	4.39184e86			0.940108
$512$		−	4.48793e86i		−	0.902416i
$513$	−5.26366e86	−	7.51687e85i	−0.994334	−	0.141998i
$514$	3.53946e85			0.0628228
$515$			3.00247e85i			0.0500780i
$516$	6.35573e85	+	1.23188e86i	0.0996265	+	0.193098i
$517$	1.81246e86			0.267037
$518$			3.12509e86i			0.432823i
$519$	1.57683e86	−	8.13546e85i	0.205319	−	0.105932i
$520$	2.30161e86			0.281789
$521$			5.67587e86i			0.653469i	0.945116	+	0.326735i	$0.105948\pi$
$521$			5.67587e86i			0.653469i	−0.945116	+	0.326735i	$0.894052\pi$
$522$	1.87203e86	−	2.63244e86i	0.202702	−	0.285037i
$523$	−9.06529e86			−0.923268			−0.461634	−	0.887070i	$-0.652737\pi$
$523$	−9.06529e86			−0.923268			−0.461634	+	0.887070i	$0.652737\pi$
$524$		−	7.96728e86i		−	0.763324i
$525$	5.94791e85	+	1.15284e86i	0.0536126	+	0.103913i
$526$	−4.06173e85			−0.0344483
$527$			3.24589e86i			0.259056i
$528$	−3.23999e86	+	1.67163e86i	−0.243365	+	0.125561i
$529$	6.26821e86			0.443162
$530$			5.95939e86i			0.396620i
$531$	6.99126e85	+	4.97177e85i	0.0438057	+	0.0311520i
$532$	−1.70057e87			−1.00328
$533$			3.90911e86i			0.217174i
$534$	−3.14528e86	−	6.09623e86i	−0.164565	−	0.318964i
$535$	1.28203e87			0.631796
$536$			8.56873e86i			0.397780i
$537$	−1.53065e87	+	7.89717e86i	−0.669418	+	0.345378i
$538$	3.63036e86			0.149595
$539$			8.57544e85i			0.0332978i
$540$	−3.87185e86	+	2.71125e87i	−0.141683	+	0.992132i
$541$	−2.28893e87			−0.789443			−0.394721	−	0.918801i	$-0.629159\pi$
$541$	−2.28893e87			−0.789443			−0.394721	+	0.918801i	$0.629159\pi$
$542$			9.32690e86i			0.303221i
$543$	1.68540e87	+	3.26667e87i	0.516544	+	1.00118i
$544$	1.40612e87			0.406311
$545$		−	2.54431e87i		−	0.693236i
$546$	4.97969e86	−	2.56921e86i	0.127949	−	0.0660138i
$547$	7.03957e86			0.170589			0.0852946	−	0.996356i	$-0.472817\pi$
$547$	7.03957e86			0.170589			0.0852946	+	0.996356i	$0.472817\pi$
$548$			5.29946e87i			1.21131i
$549$	4.10511e87	−	5.77257e87i	0.885135	−	1.24467i
$550$	−3.89325e85			−0.00791965
$551$		−	8.24294e87i		−	1.58209i
$552$	−8.18297e86	−	1.58604e87i	−0.148204	−	0.287252i
$553$	−1.19306e88			−2.03920
$554$		−	1.05056e87i		−	0.169477i
$555$	1.14137e88	−	5.88874e87i	1.73800	−	0.896699i
$556$	−1.93789e87			−0.278572
$557$		−	1.12052e88i		−	1.52074i	−0.649492	−	0.760368i	$-0.725018\pi$
$557$		−	1.12052e88i		−	1.52074i	0.649492	−	0.760368i	$-0.274982\pi$
$558$	5.60842e86	+	3.98838e86i	0.0718697	+	0.0511095i
$559$	−1.16554e87			−0.141043
$560$			8.28154e87i			0.946443i
$561$	−8.87946e86	−	1.72103e87i	−0.0958463	−	0.185771i
$562$	−3.38051e87			−0.344683
$563$			1.63354e88i			1.57348i	0.617283	+	0.786741i	$0.288233\pi$
$563$			1.63354e88i			1.57348i	−0.617283	+	0.786741i	$0.711767\pi$
$564$	7.73572e87	−	3.99115e87i	0.703995	−	0.363217i
$565$	1.85541e88			1.59547
$566$			3.53803e87i			0.287499i
$567$	4.49108e87	+	1.29230e88i	0.344900	+	0.992445i
$568$	−1.10586e88			−0.802703
$569$		−	2.04932e88i		−	1.40610i	−0.711140	−	0.703051i	$-0.751821\pi$
$569$		−	2.04932e88i		−	1.40610i	0.711140	−	0.703051i	$-0.248179\pi$
$570$	−1.66200e87	−	3.22133e87i	−0.107804	−	0.208949i
$571$	−5.29180e87			−0.324525			−0.162262	−	0.986748i	$-0.551879\pi$
$571$	−5.29180e87			−0.324525			−0.162262	+	0.986748i	$0.551879\pi$
$572$		−	3.24241e87i		−	0.188016i
$573$	−7.49591e87	+	3.86742e87i	−0.411033	+	0.212067i
$574$	1.58325e87			0.0821049
$575$			1.69313e87i			0.0830460i
$576$	−8.94601e87	+	1.25798e88i	−0.415059	+	0.583653i
$577$	−2.20259e87			−0.0966734			−0.0483367	−	0.998831i	$-0.515392\pi$
$577$	−2.20259e87			−0.0966734			−0.0483367	+	0.998831i	$0.515392\pi$
$578$		−	3.07229e87i		−	0.127577i
$579$	2.88115e87	+	5.58429e87i	0.113201	+	0.219409i
$580$	−4.24584e88			−1.57858
$581$			3.83658e88i			1.34992i
$582$	−8.24880e86	+	4.25587e86i	−0.0274698	+	0.0141727i
$583$	1.72261e88			0.542992
$584$			1.29889e88i			0.387579i
$585$	−1.87669e88	−	1.33459e88i	−0.530156	−	0.377016i
$586$	1.51658e88			0.405641
$587$		−	1.04302e87i		−	0.0264163i	−0.999913	−	0.0132081i	$-0.995796\pi$
$587$		−	1.04302e87i		−	0.0264163i	0.999913	−	0.0132081i	$-0.00420441\pi$
$588$	1.88836e87	+	3.66006e87i	0.0452909	+	0.0877836i
$589$	1.75616e88			0.398910
$590$			5.84845e86i			0.0125828i
$591$	−2.14454e88	+	1.10645e88i	−0.437053	+	0.225492i
$592$	8.21100e88			1.58526
$593$		−	4.08942e87i		−	0.0748016i	−0.999300	−	0.0374008i	$-0.988092\pi$
$593$		−	4.08942e87i		−	0.0748016i	0.999300	−	0.0374008i	$-0.0119078\pi$
$594$	−4.06475e87	−	5.80475e86i	−0.0704479	−	0.0100604i
$595$	−4.39903e88			−0.722461
$596$		−	5.20069e88i		−	0.809433i
$597$	−1.97384e88	−	3.82573e88i	−0.291161	−	0.564333i
$598$	7.31349e87			0.102256
$599$		−	1.90595e88i		−	0.252611i	−0.991991	−	0.126305i	$-0.959688\pi$
$599$		−	1.90595e88i		−	0.252611i	0.991991	−	0.126305i	$-0.0403120\pi$
$600$	−3.40951e87	+	1.75910e87i	−0.0428403	+	0.0221029i
$601$	7.41298e88			0.883100			0.441550	−	0.897237i	$-0.354429\pi$
$601$	7.41298e88			0.883100			0.441550	+	0.897237i	$0.354429\pi$
$602$			4.72063e87i			0.0533228i
$603$	4.96858e88	−	6.98677e88i	0.532204	−	0.748381i
$604$	7.38122e88			0.749801
$605$		−	9.81797e88i		−	0.945910i
$606$	1.95564e88	+	3.79045e88i	0.178716	+	0.346391i
$607$	−1.19845e89			−1.03892			−0.519458	−	0.854496i	$-0.673866\pi$
$607$	−1.19845e89			−1.03892			−0.519458	+	0.854496i	$0.673866\pi$
$608$		−	7.60771e88i		−	0.625662i
$609$	−1.88488e89	+	9.72480e88i	−1.47072	+	0.758800i
$610$	4.82897e88			0.357519
$611$			7.31915e88i			0.514212i
$612$	−7.57964e88	−	5.39019e88i	−0.505362	−	0.359384i
$613$	1.90300e89			1.20421			0.602107	−	0.798416i	$-0.294328\pi$
$613$	1.90300e89			1.20421			0.602107	+	0.798416i	$0.294328\pi$
$614$		−	2.64053e88i		−	0.158600i
$615$	−2.98338e88	−	5.78245e88i	−0.170100	−	0.329692i
$616$	−2.69457e88			−0.145850
$617$			1.89339e89i			0.973003i	0.873680	+	0.486501i	$0.161727\pi$
$617$			1.89339e89i			0.973003i	−0.873680	+	0.486501i	$0.838273\pi$
$618$	−1.92121e87	+	9.91224e86i	−0.00937440	+	0.00483660i
$619$	2.38275e89			1.10402			0.552012	−	0.833836i	$-0.313860\pi$
$619$	2.38275e89			1.10402			0.552012	+	0.833836i	$0.313860\pi$
$620$		−	9.04578e88i		−	0.398027i
$621$	−2.52441e88	+	1.76771e89i	−0.105494	+	0.738721i
$622$	−5.34055e88			−0.211980
$623$			4.50416e89i			1.69823i
$624$	−6.75044e88	−	1.30838e89i	−0.241783	−	0.468628i
$625$	−3.22939e89			−1.09890
$626$		−	6.96994e87i		−	0.0225346i
$627$	−9.31151e88	+	4.80416e88i	−0.286061	+	0.147590i
$628$	1.27054e89			0.370921
$629$			4.36156e89i			1.21010i
$630$	−5.40529e88	+	7.60088e88i	−0.142535	+	0.200432i
$631$	−4.60162e89			−1.15338			−0.576688	−	0.816964i	$-0.695655\pi$
$631$	−4.60162e89			−1.15338			−0.576688	+	0.816964i	$0.695655\pi$
$632$		−	3.52849e89i		−	0.840703i
$633$	−5.90077e88	−	1.14370e89i	−0.133656	−	0.259055i
$634$	−7.40680e88			−0.159505
$635$		−	4.12762e89i		−	0.845164i
$636$	7.35223e89	−	3.79329e89i	1.43150	−	0.738564i
$637$	−3.46296e88			−0.0641189
$638$		−	6.36544e88i		−	0.112090i
$639$	9.01700e89	+	6.41235e89i	1.51020	+	1.07396i
$640$	−5.17423e89			−0.824303
$641$		−	1.11661e89i		−	0.169217i	−0.996414	−	0.0846086i	$-0.973036\pi$
$641$		−	1.11661e89i		−	0.169217i	0.996414	−	0.0846086i	$-0.0269640\pi$
$642$	4.23244e88	+	8.20340e88i	0.0610197	+	0.118270i
$643$	1.50372e89			0.206261			0.103130	−	0.994668i	$-0.467114\pi$
$643$	1.50372e89			0.206261			0.103130	+	0.994668i	$0.467114\pi$
$644$			5.71107e89i			0.745366i
$645$	1.72410e89	−	8.89528e88i	0.214117	−	0.110471i
$646$	1.23098e89			0.145483
$647$		−	1.45740e90i		−	1.63924i	−0.572908	−	0.819620i	$-0.694185\pi$
$647$		−	1.45740e90i		−	1.63924i	0.572908	−	0.819620i	$-0.305815\pi$
$648$	−3.82199e89	+	1.32824e89i	−0.409156	+	0.142192i
$649$	1.69054e88			0.0172264
$650$		−	1.57218e88i		−	0.0152502i
$651$	−2.07187e89	−	4.01574e89i	−0.191325	−	0.370830i
$652$	1.28156e89			0.112672
$653$		−	1.19434e90i		−	0.999785i	−0.866087	−	0.499892i	$-0.833373\pi$
$653$		−	1.19434e90i		−	0.999785i	0.866087	−	0.499892i	$-0.166627\pi$
$654$	1.62804e89	−	8.39968e88i	0.129771	−	0.0669537i
$655$	−1.11508e90			−0.846414
$656$		−	4.15990e89i		−	0.300718i
$657$	7.53160e89	−	1.05909e90i	0.518556	−	0.729189i
$658$	2.96437e89			0.194404
$659$			1.68310e90i			1.05142i	0.850664	+	0.525709i	$0.176200\pi$
$659$			1.68310e90i			1.05142i	−0.850664	+	0.525709i	$0.823800\pi$
$660$	2.47457e89	+	4.79625e89i	0.147263	+	0.285428i
$661$	1.42114e90			0.805728			0.402864	−	0.915260i	$-0.368015\pi$
$661$	1.42114e90			0.805728			0.402864	+	0.915260i	$0.368015\pi$
$662$		−	4.87448e89i		−	0.263313i
$663$	6.94994e89	−	3.58574e89i	0.357724	−	0.184563i
$664$	−1.13467e90			−0.556533
$665$			2.38006e90i			1.11249i
$666$	7.53613e89	+	5.35925e89i	0.335717	+	0.238742i
$667$	−2.76825e90			−1.17538
$668$			3.49303e90i			1.41369i
$669$	3.78980e89	+	7.34546e89i	0.146211	+	0.283389i
$670$	5.84470e89			0.214965
$671$		−	1.39585e90i		−	0.489462i
$672$	−1.73962e90	+	8.97538e89i	−0.581619	+	0.300079i
$673$	−2.16576e90			−0.690443			−0.345221	−	0.938521i	$-0.612196\pi$
$673$	−2.16576e90			−0.690443			−0.345221	+	0.938521i	$0.612196\pi$
$674$			1.03159e90i			0.313612i
$675$	3.80006e89	+	5.42675e88i	0.110172	+	0.0157333i
$676$	−2.12886e90			−0.588645
$677$			7.83268e89i			0.206573i	0.994652	+	0.103286i	$0.0329358\pi$
$677$			7.83268e89i			0.206573i	−0.994652	+	0.103286i	$0.967064\pi$
$678$	6.12537e89	+	1.18723e90i	0.154093	+	0.298665i
$679$	6.09457e89			0.146255
$680$		−	1.30102e90i		−	0.297850i
$681$	2.49988e89	−	1.28978e89i	0.0546023	−	0.0281714i
$682$	1.35616e89			0.0282625
$683$		−	7.62378e90i		−	1.51603i	−0.652237	−	0.758015i	$-0.726169\pi$
$683$		−	7.62378e90i		−	1.51603i	0.652237	−	0.758015i	$-0.273831\pi$
$684$	−2.91632e90	+	4.10090e90i	−0.553400	+	0.778187i
$685$	7.41696e90			1.34316
$686$		−	1.20963e90i		−	0.209065i
$687$	−4.80925e90	−	9.32138e90i	−0.793344	−	1.53767i
$688$	1.24032e90			0.195300
$689$			6.95631e90i			1.04560i
$690$	−1.08183e90	+	5.58157e89i	−0.155234	+	0.0800913i
$691$	6.84008e90			0.937052			0.468526	−	0.883450i	$-0.344785\pi$
$691$	6.84008e90			0.937052			0.468526	+	0.883450i	$0.344785\pi$
$692$		−	1.67924e90i		−	0.219644i
$693$	2.19710e90	+	1.56244e90i	0.274401	+	0.195138i
$694$	1.54211e90			0.183913
$695$			2.71222e90i			0.308895i
$696$	−2.87611e90	−	5.57454e90i	−0.312831	−	0.606336i
$697$	2.20968e90			0.229551
$698$			5.09290e88i			0.00505349i
$699$	−4.99195e90	+	2.57554e90i	−0.473152	+	0.244117i
$700$	1.22771e90			0.111163
$701$		−	6.87165e90i		−	0.594408i	−0.954814	−	0.297204i	$-0.903946\pi$
$701$		−	6.87165e90i		−	0.594408i	0.954814	−	0.297204i	$-0.0960542\pi$
$702$	2.34409e89	−	1.64144e90i	0.0193726	−	0.135656i
$703$	2.35979e91			1.86338
$704$			3.04189e90i			0.229519i
$705$	−5.58589e90	−	1.08267e91i	−0.402754	−	0.780626i
$706$	−7.82888e89			−0.0539448
$707$		−	2.80055e91i		−	1.84426i
$708$	7.21535e89	−	3.72267e89i	0.0454143	−	0.0234310i
$709$	−7.11775e90			−0.428216			−0.214108	−	0.976810i	$-0.568685\pi$
$709$	−7.11775e90			−0.428216			−0.214108	+	0.976810i	$0.568685\pi$
$710$			7.54305e90i			0.433790i
$711$	−2.04600e91	+	2.87706e91i	−1.12481	+	1.58169i
$712$	−1.33211e91			−0.700132
$713$		−	5.89778e90i		−	0.296363i
$714$	−1.45228e90	−	2.81484e90i	−0.0697763	−	0.135242i
$715$	−4.53797e90			−0.208482
$716$			1.63006e91i			0.716122i
$717$	−4.17095e90	+	2.15195e90i	−0.175236	+	0.0904106i
$718$	−2.05113e90			−0.0824158
$719$			4.47395e91i			1.71936i	0.510833	+	0.859680i	$0.329337\pi$
$719$			4.47395e91i			1.71936i	−0.510833	+	0.859680i	$0.670663\pi$
$720$	1.99709e91	+	1.42021e91i	0.734103	+	0.522050i
$721$	1.41947e90			0.0499113
$722$		−	5.85147e88i		−	0.00196822i
$723$	3.74049e90	+	7.24990e90i	0.120366	+	0.233295i
$724$	3.47884e91			1.07103
$725$			5.95093e90i			0.175295i
$726$	6.28229e90	−	3.24127e90i	0.177070	−	0.0913573i
$727$	−6.15097e91			−1.65898			−0.829492	−	0.558519i	$-0.811370\pi$
$727$	−6.15097e91			−1.65898			−0.829492	+	0.558519i	$0.811370\pi$
$728$		−	1.08813e91i		−	0.280851i
$729$	3.88655e91	+	1.13316e91i	0.960028	+	0.279905i
$730$	8.85966e90			0.209453
$731$			6.58839e90i			0.149081i
$732$	−3.07375e91	−	5.95760e91i	−0.665754	−	1.29038i
$733$	−4.48703e91			−0.930319			−0.465159	−	0.885227i	$-0.654003\pi$
$733$	−4.48703e91			−0.930319			−0.465159	+	0.885227i	$0.654003\pi$
$734$			8.78693e90i			0.174407i
$735$	5.12250e90	−	2.64289e90i	0.0973391	−	0.0502209i
$736$	−2.55492e91			−0.464823
$737$		−	1.68946e91i		−	0.294298i
$738$	2.71513e90	−	3.81799e90i	0.0452884	−	0.0636842i
$739$	9.39146e91			1.50007			0.750034	−	0.661399i	$-0.230037\pi$
$739$	9.39146e91			1.50007			0.750034	+	0.661399i	$0.230037\pi$
$740$		−	1.21550e92i		−	1.85926i
$741$	−1.94003e91	−	3.76021e91i	−0.284201	−	0.550845i
$742$	2.81742e91			0.395299
$743$			1.10818e92i			1.48926i	0.667478	+	0.744629i	$0.267374\pi$
$743$			1.10818e92i			1.48926i	−0.667478	+	0.744629i	$0.732626\pi$
$744$	1.18766e91	−	6.12757e90i	0.152882	−	0.0788777i
$745$	−7.27873e91			−0.897542
$746$			1.96290e91i			0.231876i
$747$	9.25188e91	+	6.57939e91i	1.04706	+	0.744606i
$748$	−1.83282e91			−0.198732
$749$		−	6.06103e91i		−	0.629693i
$750$	−9.58167e90	−	1.85714e91i	−0.0953852	−	0.184877i
$751$	5.70439e91			0.544166			0.272083	−	0.962274i	$-0.412288\pi$
$751$	5.70439e91			0.544166			0.272083	+	0.962274i	$0.412288\pi$
$752$		−	7.78871e91i		−	0.712024i
$753$	8.59892e91	−	4.43650e91i	0.753363	−	0.388688i
$754$	2.57051e91			0.215842
$755$		−	1.03305e92i		−	0.831419i
$756$	1.28179e92	+	1.83049e91i	0.988829	+	0.141211i
$757$	−2.59685e92			−1.92035			−0.960173	−	0.279407i	$-0.909862\pi$
$757$	−2.59685e92			−1.92035			−0.960173	+	0.279407i	$0.909862\pi$
$758$			2.56728e91i			0.181995i
$759$	1.61340e91	+	3.12712e91i	0.109649	+	0.212524i
$760$	−7.03903e91			−0.458647
$761$			1.10774e92i			0.692037i	0.938228	+	0.346019i	$0.112467\pi$
$761$			1.10774e92i			0.692037i	−0.938228	+	0.346019i	$0.887533\pi$
$762$	2.64117e91	−	1.36268e91i	0.158211	−	0.0816271i
$763$	−1.20287e92			−0.690928
$764$			7.98277e91i			0.439710i
$765$	−7.54394e91	+	1.06082e92i	−0.398504	+	0.560372i
$766$	−4.03835e91			−0.204589
$767$			6.82680e90i			0.0331715i
$768$	5.33764e91	+	1.03455e92i	0.248766	+	0.482162i
$769$	9.32917e91			0.417062			0.208531	−	0.978016i	$-0.433132\pi$
$769$	9.32917e91			0.417062			0.208531	+	0.978016i	$0.433132\pi$
$770$			1.83795e91i			0.0788190i
$771$	−6.11150e91	+	3.15315e91i	−0.251425	+	0.129719i
$772$	5.94699e91			0.234716
$773$			4.03518e92i			1.52799i	0.645224	+	0.763993i	$0.276764\pi$
$773$			4.03518e92i			1.52799i	−0.645224	+	0.763993i	$0.723236\pi$
$774$	1.13838e91	+	8.09546e90i	0.0413595	+	0.0294124i
$775$	−1.26785e91			−0.0441990
$776$			1.80247e91i			0.0602967i
$777$	−2.78401e92	−	5.39603e92i	−0.893714	−	1.73221i
$778$	4.99118e91			0.153764
$779$		−	1.19553e92i		−	0.353476i
$780$	−1.93684e92	+	9.99288e91i	−0.549625	+	0.283572i
$781$	2.18038e92			0.593881
$782$		−	4.13405e91i		−	0.108084i
$783$	−8.87270e91	+	6.21308e92i	−0.222679	+	1.55930i
$784$	3.68513e91			0.0887848
$785$		−	1.77821e92i		−	0.411296i
$786$	−3.68127e91	−	7.13511e91i	−0.0817478	−	0.158445i
$787$	5.69914e92			1.21512			0.607558	−	0.794275i	$-0.292149\pi$
$787$	5.69914e92			1.21512			0.607558	+	0.794275i	$0.292149\pi$
$788$			2.28382e92i			0.467545i
$789$	7.01330e91	−	3.61842e91i	0.137866	−	0.0711304i
$790$	−2.40677e92			−0.454326
$791$		−	8.77178e92i		−	1.59016i
$792$	−4.62093e91	+	6.49792e91i	−0.0804496	+	0.113128i
$793$	5.63678e92			0.942517
$794$		−	1.02547e92i		−	0.164690i
$795$	−5.30897e92	−	1.02899e93i	−0.818959	−	1.58732i
$796$	−4.07421e92			−0.603706
$797$		−	3.68371e92i		−	0.524347i	−0.965021	−	0.262174i	$-0.915561\pi$
$797$		−	3.68371e92i		−	0.524347i	0.965021	−	0.262174i	$-0.0844393\pi$
$798$	−1.52294e92	+	7.85744e91i	−0.208253	+	0.107446i
$799$	4.13725e92			0.543519
$800$			5.49233e91i			0.0693230i
$801$	1.08617e93	+	7.72423e92i	1.31722	+	0.936731i
$802$	9.47417e90			0.0110398
$803$		−	2.56096e92i		−	0.286751i
$804$	−3.72028e92	−	7.21072e92i	−0.400297	−	0.775863i
$805$	7.99303e92			0.826501
$806$			5.47649e91i			0.0544228i
$807$	−6.26846e92	+	3.23413e92i	−0.598698	+	0.308891i
$808$	8.28264e92			0.760335
$809$			8.35717e92i			0.737406i	0.929547	+	0.368703i	$0.120198\pi$
$809$			8.35717e92i			0.737406i	−0.929547	+	0.368703i	$0.879802\pi$
$810$	9.05986e91	+	2.60696e92i	0.0768424	+	0.221113i
$811$	−7.27132e92			−0.592852			−0.296426	−	0.955056i	$-0.595795\pi$
$811$	−7.27132e92			−0.592852			−0.296426	+	0.955056i	$0.595795\pi$
$812$			2.00730e93i			1.57333i
$813$	−8.30893e92	−	1.61045e93i	−0.626106	−	1.21353i
$814$	1.82230e92			0.132019
$815$		−	1.79364e92i		−	0.124937i
$816$	−7.39582e92	+	3.81578e92i	−0.495337	+	0.255563i
$817$	3.56459e92			0.229564
$818$		−	5.55678e92i		−	0.344126i
$819$	−6.30952e92	+	8.87239e92i	−0.375761	+	0.528391i
$820$	−6.15802e92			−0.352694
$821$			9.98238e92i			0.549861i	0.961464	+	0.274930i	$0.0886548\pi$
$821$			9.98238e92i			0.549861i	−0.961464	+	0.274930i	$0.911345\pi$
$822$	2.44861e92	+	4.74594e92i	0.129724	+	0.251434i
$823$	−3.66859e93			−1.86941			−0.934704	−	0.355427i	$-0.884336\pi$
$823$	−3.66859e93			−1.86941			−0.934704	+	0.355427i	$0.884336\pi$
$824$			4.19810e91i			0.0205770i
$825$	6.72238e91	−	3.46833e91i	0.0316954	−	0.0163529i
$826$	2.76496e91			0.0125409
$827$		−	2.27403e93i		−	0.992249i	−0.868251	−	0.496124i	$-0.834756\pi$
$827$		−	2.27403e93i		−	0.992249i	0.868251	−	0.496124i	$-0.165244\pi$
$828$	1.37722e93	+	9.79396e92i	0.578139	+	0.411138i
$829$	2.91684e93			1.17806			0.589031	−	0.808110i	$-0.299510\pi$
$829$	2.91684e93			1.17806			0.589031	+	0.808110i	$0.299510\pi$
$830$			7.73954e92i			0.300757i
$831$	9.35902e92	+	1.81398e93i	0.349943	+	0.678267i
$832$	−1.22839e93			−0.441966
$833$			1.95749e92i			0.0677733i
$834$	−1.73548e92	+	8.95401e91i	−0.0578238	+	0.0298335i
$835$	4.88874e93			1.56758
$836$			9.91629e92i			0.306019i
$837$	−1.32370e93	−	1.89033e92i	−0.393165	−	0.0561466i
$838$	−1.09265e93			−0.312372
$839$		−	5.69847e92i		−	0.156811i	−0.996922	−	0.0784054i	$-0.975017\pi$
$839$		−	5.69847e92i		−	0.156811i	0.996922	−	0.0784054i	$-0.0249828\pi$
$840$	8.30447e92	+	1.60959e93i	0.219976	+	0.426361i
$841$	−5.80806e93			−1.48101
$842$		−	1.23534e93i		−	0.303248i
$843$	5.83704e93	−	3.01155e93i	1.37946	−	0.711718i
$844$	−1.21798e93			−0.277129
$845$			2.97949e93i			0.652720i
$846$	5.08363e92	−	7.14856e92i	0.107231	−	0.150788i
$847$	−4.64163e93			−0.942760
$848$		−	7.40259e93i		−	1.44783i
$849$	−3.15188e93	−	6.10903e93i	−0.593640	−	1.15061i
$850$	−8.88699e91			−0.0161194
$851$		−	7.92495e93i		−	1.38436i
$852$	9.30602e93	−	4.80132e93i	1.56566	−	0.807781i
$853$	1.80379e93			0.292291			0.146146	−	0.989263i	$-0.453313\pi$
$853$	1.80379e93			0.292291			0.146146	+	0.989263i	$0.453313\pi$
$854$		−	2.28299e93i		−	0.356329i
$855$	5.73949e93	+	4.08158e93i	0.862894	+	0.613639i
$856$	1.79255e93			0.259604
$857$			1.36904e94i			1.90998i	0.296636	+	0.954991i	$0.404135\pi$
$857$			1.36904e94i			1.90998i	−0.296636	+	0.954991i	$0.595865\pi$
$858$	−1.49815e92	−	2.90374e92i	−0.0201355	−	0.0390270i
$859$	−5.92234e93			−0.766853			−0.383426	−	0.923571i	$-0.625256\pi$
$859$	−5.92234e93			−0.766853			−0.383426	+	0.923571i	$0.625256\pi$
$860$		−	1.83608e93i		−	0.229056i
$861$	−2.73376e93	+	1.41045e93i	−0.328594	+	0.169534i
$862$	−1.72341e93			−0.199598
$863$			4.51449e93i			0.503806i	0.967753	+	0.251903i	$0.0810563\pi$
$863$			4.51449e93i			0.503806i	−0.967753	+	0.251903i	$0.918944\pi$
$864$	−8.18894e92	+	5.73428e93i	−0.0880619	+	0.616651i
$865$	−2.35022e93			−0.243553
$866$		−	2.23561e93i		−	0.223266i
$867$	2.73697e93	+	5.30485e93i	0.263426	+	0.510577i
$868$	−4.27656e93			−0.396701
$869$			6.95696e93i			0.621995i
$870$	−3.80237e93	+	1.96178e93i	−0.327671	+	0.169058i
$871$	6.82242e93			0.566706
$872$		−	3.55749e93i		−	0.284850i
$873$	1.04516e93	−	1.46970e93i	0.0806731	−	0.113442i
$874$	−2.23669e93			−0.166433
$875$			1.37214e94i			0.984326i
$876$	−5.63937e93	−	1.09303e94i	−0.390031	−	0.755966i
$877$	1.81082e94			1.20750			0.603751	−	0.797173i	$-0.293672\pi$
$877$	1.81082e94			1.20750			0.603751	+	0.797173i	$0.293672\pi$
$878$			1.63065e92i			0.0104842i
$879$	−2.61864e94	+	1.35106e94i	−1.62342	+	0.837586i
$880$	4.82911e93			0.288683
$881$		−	9.39464e93i		−	0.541566i	−0.962640	−	0.270783i	$-0.912717\pi$
$881$		−	9.39464e93i		−	0.541566i	0.962640	−	0.270783i	$-0.0872825\pi$
$882$	3.38225e92	+	2.40525e92i	0.0188023	+	0.0133711i
$883$	−1.88153e94			−1.00871			−0.504357	−	0.863495i	$-0.668270\pi$
$883$	−1.88153e94			−1.00871			−0.504357	+	0.863495i	$0.668270\pi$
$884$		−	7.40134e93i		−	0.382682i
$885$	−5.21013e92	−	1.00984e93i	−0.0259815	−	0.0503578i
$886$	3.92401e93			0.188734
$887$			1.48994e94i			0.691216i	0.938379	+	0.345608i	$0.112327\pi$
$887$			1.48994e94i			0.691216i	−0.938379	+	0.345608i	$0.887673\pi$
$888$	1.59588e94	−	8.23373e93i	0.714142	−	0.368453i
$889$	−1.95141e94			−0.842350
$890$			9.08626e93i			0.378360i
$891$	7.53564e93	−	2.61882e93i	0.302715	−	0.105201i
$892$	7.82255e93			0.303161
$893$		−	2.23842e94i		−	0.836942i
$894$	−2.40297e93	−	4.65749e93i	−0.0866859	−	0.168016i
$895$	2.28138e94			0.794073
$896$			2.44622e94i			0.821558i
$897$	−1.26280e94	+	6.51528e93i	−0.409239	+	0.211142i
$898$	1.76322e92			0.00551397
$899$		−	2.07292e94i		−	0.625566i
$900$	2.10541e93	−	2.96061e93i	0.0613164	−	0.0862227i
$901$	3.93215e94			1.10519
$902$		−	9.23220e92i		−	0.0250436i
$903$	−4.20541e93	−	8.15101e93i	−0.110103	−	0.213404i
$904$	2.59426e94			0.655576
$905$		−	4.86887e94i		−	1.18761i
$906$	6.61026e93	−	3.41048e93i	0.155638	−	0.0802996i
$907$	4.20546e94			0.955828			0.477914	−	0.878407i	$-0.341393\pi$
$907$	4.20546e94			0.955828			0.477914	+	0.878407i	$0.341393\pi$
$908$		−	2.66224e93i		−	0.0584118i
$909$	−6.75350e94	−	4.80269e94i	−1.43049	−	1.01728i
$910$	−7.42208e93			−0.151775
$911$		−	7.49440e94i		−	1.47962i	−0.672818	−	0.739808i	$-0.734916\pi$
$911$		−	7.49440e94i		−	1.47962i	0.672818	−	0.739808i	$-0.265084\pi$
$912$	2.06450e94	+	4.00144e94i	0.393531	+	0.762750i
$913$	2.23718e94			0.411752
$914$			1.39447e93i			0.0247818i
$915$	−8.33807e94	+	4.30192e94i	−1.43084	+	0.738223i
$916$	−9.92680e94			−1.64495
$917$			5.27173e94i			0.843596i
$918$	−9.27848e93	−	1.32503e93i	−0.143387	−	0.0204767i
$919$	9.66474e94			1.44243			0.721213	−	0.692713i	$-0.243585\pi$
$919$	9.66474e94			1.44243			0.721213	+	0.692713i	$0.243585\pi$
$920$			2.36394e94i			0.340743i
$921$	2.35233e94	+	4.55933e94i	0.327484	+	0.634736i
$922$	2.59053e94			0.348337
$923$			8.80489e94i			1.14359i
$924$	2.26752e94	−	1.16990e94i	0.284477	−	0.146773i
$925$	−1.70363e94			−0.206462
$926$			2.30054e94i			0.269326i
$927$	2.43427e93	−	3.42305e93i	0.0275307	−	0.0387134i
$928$	−8.97993e94			−0.981155
$929$			3.75027e93i			0.0395877i	0.999804	+	0.0197938i	$0.00630098\pi$
$929$			3.75027e93i			0.0395877i	−0.999804	+	0.0197938i	$0.993699\pi$
$930$	−4.17959e93	−	8.10096e93i	−0.0426265	−	0.0826194i
$931$	1.05908e94			0.104361
$932$			5.31618e94i			0.506163i
$933$	9.22141e94	−	4.75767e94i	0.848369	−	0.437705i
$934$	−3.37028e94			−0.299617
$935$			2.56515e94i			0.220364i
$936$	−2.62401e94	−	1.86604e94i	−0.217840	−	0.154915i
$937$	−9.22861e94			−0.740405			−0.370202	−	0.928951i	$-0.620712\pi$
$937$	−9.22861e94			−0.740405			−0.370202	+	0.928951i	$0.620712\pi$
$938$		−	2.76319e94i		−	0.214250i
$939$	6.20922e93	+	1.20348e94i	0.0465305	+	0.0901864i
$940$	−1.15299e95			−0.835089
$941$			9.64595e94i			0.675269i	0.941277	+	0.337635i	$0.109627\pi$
$941$			9.64595e94i			0.675269i	−0.941277	+	0.337635i	$0.890373\pi$
$942$	1.13784e94	−	5.87053e93i	0.0769930	−	0.0397236i
$943$	−4.01498e94			−0.262608
$944$		−	7.26477e93i		−	0.0459323i
$945$	2.56190e94	−	1.79396e95i	0.156583	−	1.09647i
$946$	2.75268e93			0.0162645
$947$		−	1.31295e95i		−	0.749979i	−0.927029	−	0.374989i	$-0.877646\pi$
$947$		−	1.31295e95i		−	0.749979i	0.927029	−	0.374989i	$-0.122354\pi$
$948$	1.53196e95	+	2.96928e95i	0.846022	+	1.63978i
$949$	1.03417e95			0.552173
$950$			4.80823e93i			0.0248216i
$951$	1.27892e95	−	6.59840e94i	0.638359	−	0.329354i
$952$	−6.15079e94			−0.296858
$953$		−	2.21633e95i		−	1.03434i	−0.855884	−	0.517168i	$-0.826986\pi$
$953$		−	2.21633e95i		−	1.03434i	0.855884	−	0.517168i	$-0.173014\pi$
$954$	4.83161e94	−	6.79417e94i	0.218044	−	0.306612i
$955$	1.11724e95			0.487573
$956$			4.44185e94i			0.187461i
$957$	5.67070e94	+	1.09911e95i	0.231449	+	0.448598i
$958$	−2.17709e94			−0.0859369
$959$		−	3.50651e95i		−	1.33869i
$960$	1.81706e95	−	9.37491e94i	0.670951	−	0.346169i
$961$	−2.35830e95			−0.842269
$962$			7.35886e94i			0.254219i
$963$	−1.46161e95	−	1.03941e95i	−0.488417	−	0.347333i
$964$	7.72077e94			0.249572
$965$		−	8.32322e94i		−	0.260266i
$966$	2.63879e94	+	5.11455e94i	0.0798246	+	0.154718i
$967$	−8.32070e94			−0.243508			−0.121754	−	0.992560i	$-0.538852\pi$
$967$	−8.32070e94			−0.243508			−0.121754	+	0.992560i	$0.538852\pi$
$968$		−	1.37276e95i		−	0.388673i
$969$	−2.12551e95	+	1.09663e95i	−0.582240	+	0.300399i
$970$	1.22946e94			0.0325851
$971$			3.61501e95i			0.927032i	0.886089	+	0.463516i	$0.153412\pi$
$971$			3.61501e95i			0.927032i	−0.886089	+	0.463516i	$0.846588\pi$
$972$	2.63958e95	−	2.77712e95i	0.654960	−	0.689088i
$973$	1.28225e95			0.307866
$974$			1.36765e95i			0.317752i
$975$	1.40059e94	+	2.71465e94i	0.0314894	+	0.0610333i
$976$	−5.99841e95			−1.30509
$977$			1.73814e95i			0.365981i	0.983115	+	0.182991i	$0.0585778\pi$
$977$			1.73814e95i			0.365981i	−0.983115	+	0.182991i	$0.941422\pi$
$978$	1.14771e94	−	5.92144e93i	0.0233877	−	0.0120666i
$979$	2.62646e95			0.517993
$980$		−	5.45521e94i		−	0.104130i
$981$	−2.06281e95	+	2.90071e95i	−0.381111	+	0.535914i
$982$	5.36809e94			0.0959959
$983$			7.41358e95i			1.28326i	0.767013	+	0.641631i	$0.221742\pi$
$983$			7.41358e95i			1.28326i	−0.767013	+	0.641631i	$0.778258\pi$
$984$	−4.17141e94	−	8.08511e94i	−0.0698940	−	0.135470i
$985$	3.19637e95			0.518438
$986$		−	1.45302e95i		−	0.228144i
$987$	−5.11851e95	+	2.64083e95i	−0.778027	+	0.401414i
$988$	−4.00443e95			−0.589276
$989$		−	1.19711e95i		−	0.170550i
$990$	4.43220e94	+	3.15192e94i	0.0611355	+	0.0434759i
$991$	9.53822e94			0.127383			0.0636913	−	0.997970i	$-0.479713\pi$
$991$	9.53822e94			0.127383			0.0636913	+	0.997970i	$0.479713\pi$
$992$		−	1.91318e95i		−	0.247390i
$993$	4.34247e95	+	8.41665e95i	0.543701	+	1.05381i
$994$	3.56612e95			0.432346
$995$			5.70214e95i			0.669421i
$996$	9.54843e95	−	4.92639e95i	1.08551	−	0.560054i
$997$	−9.29879e94			−0.102372			−0.0511860	−	0.998689i	$-0.516300\pi$
$997$	−9.29879e94			−0.102372			−0.0511860	+	0.998689i	$0.516300\pi$
$998$			1.79749e95i			0.191642i
$999$	−1.77868e96	−	2.54007e95i	−1.83655	−	0.262271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.65.b.a.2.10	✓	20
3.2	odd	2	inner	3.65.b.a.2.11	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.65.b.a.2.10	✓	20	1.1	even	1	trivial
3.65.b.a.2.11	yes	20	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-9.53717e8i q^{2} +(8.49626e14 + 1.64676e15i) q^{3} +1.75372e19 q^{4} -2.45445e22i q^{5} +(1.57054e24 - 8.10302e23i) q^{6} -1.16039e27 q^{7} -3.43185e28i q^{8} +(-1.98996e30 + 2.79826e30i) q^{9} +O(q^{10})\)	\(q-9.53717e8i q^{2} +(8.49626e14 + 1.64676e15i) q^{3} +1.75372e19 q^{4} -2.45445e22i q^{5} +(1.57054e24 - 8.10302e23i) q^{6} -1.16039e27 q^{7} -3.43185e28i q^{8} +(-1.98996e30 + 2.79826e30i) q^{9} -2.34085e31 q^{10} +6.76641e32i q^{11} +(1.49000e34 + 2.88795e34i) q^{12} -2.73244e35 q^{13} +1.10668e36i q^{14} +(4.04189e37 - 2.08536e37i) q^{15} +2.90774e38 q^{16} +1.54455e39i q^{17} +(2.66875e39 + 1.89786e39i) q^{18} +8.35664e40 q^{19} -4.30441e41i q^{20} +(-9.85894e41 - 1.91088e42i) q^{21} +6.45324e41 q^{22} -2.80644e43i q^{23} +(5.65143e43 - 2.91578e43i) q^{24} -6.03301e43 q^{25} +2.60597e44i q^{26} +(-6.29878e45 - 8.99509e44i) q^{27} -2.03499e46 q^{28} -9.86394e46i q^{29} +(-1.98884e46 - 3.85482e46i) q^{30} +2.10152e47 q^{31} -9.10380e47i q^{32} +(-1.11427e48 + 5.74892e47i) q^{33} +1.47306e48 q^{34} +2.84811e49i q^{35} +(-3.48982e49 + 4.90736e49i) q^{36} +2.82385e50 q^{37} -7.96986e49i q^{38} +(-2.32155e50 - 4.49967e50i) q^{39} -8.42329e50 q^{40} -1.43063e51i q^{41} +(-1.82244e51 + 9.40263e50i) q^{42} +4.26558e51 q^{43} +1.18664e52i q^{44} +(6.86818e52 + 4.88424e52i) q^{45} -2.67655e52 q^{46} -2.67862e53i q^{47} +(2.47049e53 + 4.78834e53i) q^{48} +1.26735e53 q^{49} +5.75379e52i q^{50} +(-2.54350e54 + 1.31229e54i) q^{51} -4.79192e54 q^{52} -2.54583e55i q^{53} +(-8.57877e53 + 6.00725e54i) q^{54} +1.66078e55 q^{55} +3.98227e55i q^{56} +(7.10001e55 + 1.37614e56i) q^{57} -9.40741e55 q^{58} -2.49843e55i q^{59} +(7.08833e56 - 3.65713e56i) q^{60} -2.06291e57 q^{61} -2.00425e56i q^{62} +(2.30912e57 - 3.24706e57i) q^{63} +4.49558e57 q^{64} +6.70662e57i q^{65} +(5.48284e56 + 1.06269e57i) q^{66} -2.49683e58 q^{67} +2.70870e58i q^{68} +(4.62153e58 - 2.38442e58i) q^{69} +2.71629e58 q^{70} -3.22236e59i q^{71} +(9.60320e58 + 6.82923e58i) q^{72} -3.78481e59 q^{73} -2.69315e59i q^{74} +(-5.12580e58 - 9.93493e58i) q^{75} +1.46552e60 q^{76} -7.85165e59i q^{77} +(-4.29141e59 + 2.21410e59i) q^{78} +1.02816e61 q^{79} -7.13688e60i q^{80} +(-3.87033e60 - 1.11368e61i) q^{81} -1.36442e60 q^{82} -3.30630e61i q^{83} +(-1.72898e61 - 3.35114e61i) q^{84} +3.79101e61 q^{85} -4.06816e60i q^{86} +(1.62436e62 - 8.38066e61i) q^{87} +2.32213e61 q^{88} -3.88161e62i q^{89} +(4.65819e61 - 6.55030e61i) q^{90} +3.17068e62 q^{91} -4.92170e62i q^{92} +(1.78550e62 + 3.46070e62i) q^{93} -2.55464e62 q^{94} -2.05109e63i q^{95} +(1.49918e63 - 7.73482e62i) q^{96} -5.25219e62 q^{97} -1.20870e62i q^{98} +(-1.89342e63 - 1.34649e63i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14\!\cdots\!92 q^{3}+ \cdots - 22\!\cdots\!00 q^{9}+O(q^{10}) \) 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9	\( 20 q - 14\!\cdots\!92 q^{3}+ \cdots + 31\!\cdots\!00 q^{99}+O(q^{100}) \) 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9 + 331029217205387677806996511116000 * q^10 + 6534659062821156745233165595144848 * q^12 - 751508903297384088692483175344422424 * q^13 + 38547509823020584674418593740816815200 * q^15 + 333898239622199115079798041399657464960 * q^16 - 3676009515412490831675032229198156934240 * q^18 + 109286088964872656413026262415428611794200 * q^19 - 1311511276150890256934838463853331394769880 * q^21 - 8079025213365934710514462143494926255299360 * q^22 + 371409898348173331095205935880826344773509760 * q^24 - 1408933246315215357541047632909406493714979500 * q^25 + 5130931947084052629864823829892614277399503148 * q^27 - 38556600155873290275414028639950032296787869664 * q^28 - 141541842553229550692763020870574637255687216800 * q^30 + 458034135616019870141982361360522347620359726840 * q^31 - 2882270174679362228632701138961802589863549285280 * q^33 - 787058086714062550476148644876342688312553235840 * q^34 + 75759088962200911205216155020070755577873854233040 * q^36 - 167241277488128791881901510734045117370850836062104 * q^37 + 458879560232529079697344976545706436533594974010520 * q^39 - 3172271879697225400792978571433360199916055661804800 * q^40 - 22013931366996449796115743111552261520406610644630880 * q^42 + 10353394041775726307362489381794503494462017586072216 * q^43 + 37622210359250231761078599539977430954460378542462400 * q^45 - 297398119355935548173345475928562088559055731847559360 * q^46 - 127296049249148961420276393789708282996205874832565632 * q^48 + 2035505279477569607000808808313462872867812749377748220 * q^49 - 8993599813445960529795685588193052695282052910939102080 * q^51 + 12450863873285726446941747254985680826918117392844470176 * q^52 + 1380721489513428759527937305946915244571081819618418480 * q^54 + 86716751505127419669577189864656813143075791367545723200 * q^55 - 410655148353071807815217561752202738362370559954491547384 * q^57 + 1171127646996109205778370152132525033757099595854063443360 * q^58 - 4554593355431768584543074712701226261422872417617275398400 * q^60 + 4552152490922647485493920930203353370116723196876970427240 * q^61 - 18340670222945277450481852597884877177550760958776639152904 * q^63 + 30281219638275425893507737167512138061029087969644636247040 * q^64 - 73446637659820047047259347339723389117534541697924310768800 * q^66 + 108802231400777081380268556166029877921173626685759369971416 * q^67 - 255718829710356626829923504360603133388502621634044634870720 * q^69 + 559303866272797397220431985027879540776975892234361655006400 * q^70 - 561110698242036073669580259260779527574289380077856046595840 * q^72 - 569085806526237236378057540729119438030642048917813502604504 * q^73 + 2290039066363366330022806756651688579736177808604861676211500 * q^75 - 5532330994825480968263901289000933629970925314426608479594720 * q^76 + 9655803402636036605327159547820723686984585271634655943687200 * q^78 - 22640121063621617622122249693012788180804867706114977596801800 * q^79 + 37075761484886132865783336331999338158569856937859957696374420 * q^81 - 69993225281309073377388502634775301823581628014590259964399040 * q^82 + 62923532655099413129084384942812878939798728172266572844745120 * q^84 - 142181474118416523657627044760532405955688084516779285440262400 * q^85 + 23785411541262749066239132616113250012236593481925882591047200 * q^87 + 345107275964501391166111220047509272448066379695588836103893760 * q^88 - 1925479853343216377261941955721474942915647264800935046773530400 * q^90 + 1225124508801982757577911377627409097047306370806522445345728240 * q^91 - 2776404525956613483290023288082668840477640965472850083253548184 * q^93 + 1658662465458978832407333757013771498132481417946327912207224960 * q^94 - 3771017263293375391290634333996451541183976624371029742095907840 * q^96 + 818755932265886448325223871671724131911117159175492830487918056 * q^97 + 3118093180125811439250837213823663221313339534064003298574718400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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