LMFDB - Embedded newform 3.65.b.a.2.5

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			2.5
Root			$-7.41715e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.65.b.a.2.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.45029e9i q^{2} +(-9.93580e14 + 1.56412e15i) q^{3} -1.35835e18 q^{4} +4.47337e22i q^{5} +(6.96081e24 + 4.42172e24i) q^{6} -9.42280e26 q^{7} -7.60483e28i q^{8} +(-1.45928e30 - 3.10816e30i) q^{9} +O(q^{10})$	\(q-4.45029e9i q^{2} +(-9.93580e14 + 1.56412e15i) q^{3} -1.35835e18 q^{4} +4.47337e22i q^{5} +(6.96081e24 + 4.42172e24i) q^{6} -9.42280e26 q^{7} -7.60483e28i q^{8} +(-1.45928e30 - 3.10816e30i) q^{9} +1.99078e32 q^{10} +1.15249e33i q^{11} +(1.34963e33 - 2.12463e33i) q^{12} -4.26655e35 q^{13} +4.19342e36i q^{14} +(-6.99691e37 - 4.44465e37i) q^{15} -3.63494e38 q^{16} +4.50536e39i q^{17} +(-1.38322e40 + 6.49423e39i) q^{18} -8.89583e39 q^{19} -6.07642e40i q^{20} +(9.36230e41 - 1.47384e42i) q^{21} +5.12893e42 q^{22} +1.53732e43i q^{23} +(1.18949e44 + 7.55601e43i) q^{24} -1.45901e45 q^{25} +1.89874e45i q^{26} +(6.31147e45 + 8.05709e44i) q^{27} +1.27995e45 q^{28} +5.61451e45i q^{29} +(-1.97800e47 + 3.11383e47i) q^{30} -1.62659e47 q^{31} +2.14812e47i q^{32} +(-1.80264e48 - 1.14509e48i) q^{33} +2.00502e49 q^{34} -4.21517e49i q^{35} +(1.98222e48 + 4.22198e48i) q^{36} -4.66147e49 q^{37} +3.95890e49i q^{38} +(4.23915e50 - 6.67341e50i) q^{39} +3.40193e51 q^{40} +1.59791e51i q^{41} +(-6.55903e51 - 4.16650e51i) q^{42} +1.19528e52 q^{43} -1.56549e51i q^{44} +(1.39040e53 - 6.52792e52i) q^{45} +6.84151e52 q^{46} -3.71384e53i q^{47} +(3.61161e53 - 5.68550e53i) q^{48} -3.31869e53 q^{49} +6.49301e54i q^{50} +(-7.04694e54 - 4.47644e54i) q^{51} +5.79548e53 q^{52} +2.17040e55i q^{53} +(3.58564e54 - 2.80879e55i) q^{54} -5.15553e55 q^{55} +7.16588e55i q^{56} +(8.83871e54 - 1.39142e55i) q^{57} +2.49862e55 q^{58} -6.31862e56i q^{59} +(9.50428e55 + 6.03741e55i) q^{60} +1.65631e57 q^{61} +7.23880e56i q^{62} +(1.37505e57 + 2.92876e57i) q^{63} -5.74931e57 q^{64} -1.90859e58i q^{65} +(-5.09600e57 + 8.02228e57i) q^{66} +3.39229e58 q^{67} -6.11987e57i q^{68} +(-2.40455e58 - 1.52745e58i) q^{69} -1.87587e59 q^{70} +1.19897e59i q^{71} +(-2.36371e59 + 1.10976e59i) q^{72} -9.39044e58 q^{73} +2.07449e59i q^{74} +(1.44964e60 - 2.28207e60i) q^{75} +1.20837e58 q^{76} -1.08597e60i q^{77} +(-2.96986e60 - 1.88655e60i) q^{78} +1.16542e59 q^{79} -1.62605e61i q^{80} +(-7.53117e60 + 9.07138e60i) q^{81} +7.11118e60 q^{82} -2.45126e61i q^{83} +(-1.27173e60 + 2.00200e60i) q^{84} -2.01542e62 q^{85} -5.31936e61i q^{86} +(-8.78180e60 - 5.57847e60i) q^{87} +8.76452e61 q^{88} -3.73131e62i q^{89} +(-2.90511e62 - 6.18768e62i) q^{90} +4.02028e62 q^{91} -2.08822e61i q^{92} +(1.61615e62 - 2.54419e62i) q^{93} -1.65277e63 q^{94} -3.97944e62i q^{95} +(-3.35993e62 - 2.13433e62i) q^{96} +6.84980e62 q^{97} +1.47691e63i q^{98} +(3.58214e63 - 1.68181e63i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14\!\cdots\!92 q^{3}+ \cdots - 22\!\cdots\!00 q^{9}+O(q^{10}) $ 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9	$ 20 q - 14\!\cdots\!92 q^{3}+ \cdots + 31\!\cdots\!00 q^{99}+O(q^{100}) $ 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9 + 331029217205387677806996511116000 * q^10 + 6534659062821156745233165595144848 * q^12 - 751508903297384088692483175344422424 * q^13 + 38547509823020584674418593740816815200 * q^15 + 333898239622199115079798041399657464960 * q^16 - 3676009515412490831675032229198156934240 * q^18 + 109286088964872656413026262415428611794200 * q^19 - 1311511276150890256934838463853331394769880 * q^21 - 8079025213365934710514462143494926255299360 * q^22 + 371409898348173331095205935880826344773509760 * q^24 - 1408933246315215357541047632909406493714979500 * q^25 + 5130931947084052629864823829892614277399503148 * q^27 - 38556600155873290275414028639950032296787869664 * q^28 - 141541842553229550692763020870574637255687216800 * q^30 + 458034135616019870141982361360522347620359726840 * q^31 - 2882270174679362228632701138961802589863549285280 * q^33 - 787058086714062550476148644876342688312553235840 * q^34 + 75759088962200911205216155020070755577873854233040 * q^36 - 167241277488128791881901510734045117370850836062104 * q^37 + 458879560232529079697344976545706436533594974010520 * q^39 - 3172271879697225400792978571433360199916055661804800 * q^40 - 22013931366996449796115743111552261520406610644630880 * q^42 + 10353394041775726307362489381794503494462017586072216 * q^43 + 37622210359250231761078599539977430954460378542462400 * q^45 - 297398119355935548173345475928562088559055731847559360 * q^46 - 127296049249148961420276393789708282996205874832565632 * q^48 + 2035505279477569607000808808313462872867812749377748220 * q^49 - 8993599813445960529795685588193052695282052910939102080 * q^51 + 12450863873285726446941747254985680826918117392844470176 * q^52 + 1380721489513428759527937305946915244571081819618418480 * q^54 + 86716751505127419669577189864656813143075791367545723200 * q^55 - 410655148353071807815217561752202738362370559954491547384 * q^57 + 1171127646996109205778370152132525033757099595854063443360 * q^58 - 4554593355431768584543074712701226261422872417617275398400 * q^60 + 4552152490922647485493920930203353370116723196876970427240 * q^61 - 18340670222945277450481852597884877177550760958776639152904 * q^63 + 30281219638275425893507737167512138061029087969644636247040 * q^64 - 73446637659820047047259347339723389117534541697924310768800 * q^66 + 108802231400777081380268556166029877921173626685759369971416 * q^67 - 255718829710356626829923504360603133388502621634044634870720 * q^69 + 559303866272797397220431985027879540776975892234361655006400 * q^70 - 561110698242036073669580259260779527574289380077856046595840 * q^72 - 569085806526237236378057540729119438030642048917813502604504 * q^73 + 2290039066363366330022806756651688579736177808604861676211500 * q^75 - 5532330994825480968263901289000933629970925314426608479594720 * q^76 + 9655803402636036605327159547820723686984585271634655943687200 * q^78 - 22640121063621617622122249693012788180804867706114977596801800 * q^79 + 37075761484886132865783336331999338158569856937859957696374420 * q^81 - 69993225281309073377388502634775301823581628014590259964399040 * q^82 + 62923532655099413129084384942812878939798728172266572844745120 * q^84 - 142181474118416523657627044760532405955688084516779285440262400 * q^85 + 23785411541262749066239132616113250012236593481925882591047200 * q^87 + 345107275964501391166111220047509272448066379695588836103893760 * q^88 - 1925479853343216377261941955721474942915647264800935046773530400 * q^90 + 1225124508801982757577911377627409097047306370806522445345728240 * q^91 - 2776404525956613483290023288082668840477640965472850083253548184 * q^93 + 1658662465458978832407333757013771498132481417946327912207224960 * q^94 - 3771017263293375391290634333996451541183976624371029742095907840 * q^96 + 818755932265886448325223871671724131911117159175492830487918056 * q^97 + 3118093180125811439250837213823663221313339534064003298574718400 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	4.45029e9i		−	1.03616i	−0.855331	−	0.518082i	$-0.826646\pi$
$2$		−	4.45029e9i		−	1.03616i	0.855331	−	0.518082i	$-0.173354\pi$
$3$	−9.93580e14	+	1.56412e15i	−0.536195	+	0.844094i
$3$	−9.93580e14	+	1.56412e15i	−0.536195	+	0.844094i
$4$	−1.35835e18			−0.0736365
$5$			4.47337e22i			1.92130i	0.277762	+	0.960650i	$0.410407\pi$
$5$			4.47337e22i			1.92130i	−0.277762	+	0.960650i	$0.589593\pi$
$6$	6.96081e24	+	4.42172e24i	0.874620	+	0.555586i
$7$	−9.42280e26			−0.853184			−0.426592	−	0.904444i	$-0.640286\pi$
$7$	−9.42280e26			−0.853184			−0.426592	+	0.904444i	$0.640286\pi$
$8$		−	7.60483e28i		−	0.959865i
$9$	−1.45928e30	−	3.10816e30i	−0.424990	−	0.905198i
$10$	1.99078e32			1.99078
$11$			1.15249e33i			0.545849i	0.962035	+	0.272924i	$0.0879909\pi$
$11$			1.15249e33i			0.545849i	−0.962035	+	0.272924i	$0.912009\pi$
$12$	1.34963e33	−	2.12463e33i	0.0394835	−	0.0621561i
$13$	−4.26655e35			−0.963583			−0.481792	−	0.876286i	$-0.660014\pi$
$13$	−4.26655e35			−0.963583			−0.481792	+	0.876286i	$0.660014\pi$
$14$			4.19342e36i			0.884039i
$15$	−6.99691e37	−	4.44465e37i	−1.62176	−	1.03019i
$16$	−3.63494e38			−1.06821
$17$			4.50536e39i			1.90267i	0.308154	+	0.951336i	$0.400289\pi$
$17$			4.50536e39i			1.90267i	−0.308154	+	0.951336i	$0.599711\pi$
$18$	−1.38322e40	+	6.49423e39i	−0.937934	+	0.440360i
$19$	−8.89583e39			−0.106923			−0.0534615	−	0.998570i	$-0.517025\pi$
$19$	−8.89583e39			−0.106923			−0.0534615	+	0.998570i	$0.517025\pi$
$20$		−	6.07642e40i		−	0.141478i
$21$	9.36230e41	−	1.47384e42i	0.457473	−	0.720168i
$22$	5.12893e42			0.565589
$23$			1.53732e43i			0.408764i	0.978891	+	0.204382i	$0.0655184\pi$
$23$			1.53732e43i			0.408764i	−0.978891	+	0.204382i	$0.934482\pi$
$24$	1.18949e44	+	7.55601e43i	0.810216	+	0.514674i
$25$	−1.45901e45			−2.69139
$26$			1.89874e45i			0.998431i
$27$	6.31147e45	+	8.05709e44i	0.991950	+	0.126630i
$28$	1.27995e45			0.0628255
$29$			5.61451e45i			0.0896554i	0.998995	+	0.0448277i	$0.0142739\pi$
$29$			5.61451e45i			0.0896554i	−0.998995	+	0.0448277i	$0.985726\pi$
$30$	−1.97800e47	+	3.11383e47i	−1.06745	+	1.68041i
$31$	−1.62659e47			−0.307400			−0.153700	−	0.988118i	$-0.549119\pi$
$31$	−1.62659e47			−0.307400			−0.153700	+	0.988118i	$0.549119\pi$
$32$			2.14812e47i			0.146981i
$33$	−1.80264e48	−	1.14509e48i	−0.460748	−	0.292681i
$34$	2.00502e49			1.97148
$35$		−	4.21517e49i		−	1.63922i
$36$	1.98222e48	+	4.22198e48i	0.0312948	+	0.0666556i
$37$	−4.66147e49			−0.306244			−0.153122	−	0.988207i	$-0.548933\pi$
$37$	−4.66147e49			−0.306244			−0.153122	+	0.988207i	$0.548933\pi$
$38$			3.95890e49i			0.110790i
$39$	4.23915e50	−	6.67341e50i	0.516668	−	0.813355i
$40$	3.40193e51			1.84419
$41$			1.59791e51i			0.393070i	0.980497	+	0.196535i	$0.0629689\pi$
$41$			1.59791e51i			0.393070i	−0.980497	+	0.196535i	$0.937031\pi$
$42$	−6.55903e51	−	4.16650e51i	−0.746212	−	0.474017i
$43$	1.19528e52			0.640442			0.320221	−	0.947343i	$-0.396243\pi$
$43$	1.19528e52			0.640442			0.320221	+	0.947343i	$0.396243\pi$
$44$		−	1.56549e51i		−	0.0401944i
$45$	1.39040e53	−	6.52792e52i	1.73916	−	0.816534i
$46$	6.84151e52			0.423546
$47$		−	3.71384e53i		−	1.15529i	−0.816288	−	0.577645i	$-0.803972\pi$
$47$		−	3.71384e53i		−	1.15529i	0.816288	−	0.577645i	$-0.196028\pi$
$48$	3.61161e53	−	5.68550e53i	0.572771	−	0.901673i
$49$	−3.31869e53			−0.272077
$50$			6.49301e54i			2.78872i
$51$	−7.04694e54	−	4.47644e54i	−1.60604	−	1.02020i
$52$	5.79548e53			0.0709549
$53$			2.17040e55i			1.44448i	0.691643	+	0.722240i	$0.256887\pi$
$53$			2.17040e55i			1.44448i	−0.691643	+	0.722240i	$0.743113\pi$
$54$	3.58564e54	−	2.80879e55i	0.131210	−	1.02782i
$55$	−5.15553e55			−1.04874
$56$			7.16588e55i			0.818941i
$57$	8.83871e54	−	1.39142e55i	0.0573316	−	0.0902531i
$58$	2.49862e55			0.0928977
$59$		−	6.31862e56i		−	1.35943i	−0.733475	−	0.679717i	$-0.762103\pi$
$59$		−	6.31862e56i		−	1.35943i	0.733475	−	0.679717i	$-0.237897\pi$
$60$	9.50428e55	+	6.03741e55i	0.119421	+	0.0758596i
$61$	1.65631e57			1.22627			0.613136	−	0.789978i	$-0.289908\pi$
$61$	1.65631e57			1.22627			0.613136	+	0.789978i	$0.289908\pi$
$62$			7.23880e56i			0.318517i
$63$	1.37505e57	+	2.92876e57i	0.362595	+	0.772300i
$64$	−5.74931e57			−0.915918
$65$		−	1.90859e58i		−	1.85133i
$66$	−5.09600e57	+	8.02228e57i	−0.303266	+	0.477410i
$67$	3.39229e58			1.24767			0.623834	−	0.781557i	$-0.285574\pi$
$67$	3.39229e58			1.24767			0.623834	+	0.781557i	$0.285574\pi$
$68$		−	6.11987e57i		−	0.140106i
$69$	−2.40455e58	−	1.52745e58i	−0.345035	−	0.219177i
$70$	−1.87587e59			−1.69850
$71$			1.19897e59i			0.689510i	0.938693	+	0.344755i	$0.112038\pi$
$71$			1.19897e59i			0.689510i	−0.938693	+	0.344755i	$0.887962\pi$
$72$	−2.36371e59	+	1.10976e59i	−0.868868	+	0.407933i
$73$	−9.39044e58			−0.222001			−0.111000	−	0.993820i	$-0.535405\pi$
$73$	−9.39044e58			−0.222001			−0.111000	+	0.993820i	$0.535405\pi$
$74$			2.07449e59i			0.317319i
$75$	1.44964e60	−	2.28207e60i	1.44311	−	2.27179i
$76$	1.20837e58			0.00787343
$77$		−	1.08597e60i		−	0.465709i
$78$	−2.96986e60	−	1.88655e60i	−0.842770	−	0.535353i
$79$	1.16542e59			0.0219997			0.0109999	−	0.999939i	$-0.496499\pi$
$79$	1.16542e59			0.0219997			0.0109999	+	0.999939i	$0.496499\pi$
$80$		−	1.62605e61i		−	2.05236i
$81$	−7.53117e60	+	9.07138e60i	−0.638766	+	0.769401i
$82$	7.11118e60			0.407285
$83$		−	2.45126e61i		−	0.952555i	−0.879295	−	0.476278i	$-0.841986\pi$
$83$		−	2.45126e61i		−	0.952555i	0.879295	−	0.476278i	$-0.158014\pi$
$84$	−1.27173e60	+	2.00200e60i	−0.0336867	+	0.0530306i
$85$	−2.01542e62			−3.65560
$86$		−	5.31936e61i		−	0.663603i
$87$	−8.78180e60	−	5.57847e60i	−0.0756776	−	0.0480727i
$88$	8.76452e61			0.523941
$89$		−	3.73131e62i		−	1.55375i	−0.629654	−	0.776876i	$-0.716803\pi$
$89$		−	3.73131e62i		−	1.55375i	0.629654	−	0.776876i	$-0.283197\pi$
$90$	−2.90511e62	−	6.18768e62i	−0.846063	−	1.80205i
$91$	4.02028e62			0.822114
$92$		−	2.08822e61i		−	0.0300999i
$93$	1.61615e62	−	2.54419e62i	0.164826	−	0.259475i
$94$	−1.65277e63			−1.19707
$95$		−	3.97944e62i		−	0.205431i
$96$	−3.35993e62	−	2.13433e62i	−0.124065	−	0.0788102i
$97$	6.84980e62			0.181544			0.0907721	−	0.995872i	$-0.471067\pi$
$97$	6.84980e62			0.181544			0.0907721	+	0.995872i	$0.471067\pi$
$98$			1.47691e63i			0.281917i
$99$	3.58214e63	−	1.68181e63i	0.494101	−	0.231981i
$100$	1.98185e63			0.198185
$101$		−	9.63597e63i		−	0.700828i	−0.936595	−	0.350414i	$-0.886041\pi$
$101$		−	9.63597e63i		−	0.700828i	0.936595	−	0.350414i	$-0.113959\pi$
$102$	−1.99214e64	+	3.13610e64i	−1.05710	+	1.66412i
$103$	−1.83306e64			−0.711846			−0.355923	−	0.934515i	$-0.615833\pi$
$103$	−1.83306e64			−0.711846			−0.355923	+	0.934515i	$0.615833\pi$
$104$			3.24464e64i			0.924910i
$105$	6.59305e64	+	4.18811e64i	1.38366	+	0.878942i
$106$	9.65890e64			1.49672
$107$		−	2.56162e63i		−	0.0293924i	−0.999892	−	0.0146962i	$-0.995322\pi$
$107$		−	2.56162e63i		−	0.0293924i	0.999892	−	0.0146962i	$-0.00467811\pi$
$108$	−8.57320e63	−	1.09444e63i	−0.0730437	−	0.00932461i
$109$	7.51919e64			0.477006			0.238503	−	0.971142i	$-0.423343\pi$
$109$	7.51919e64			0.477006			0.238503	+	0.971142i	$0.423343\pi$
$110$			2.29436e65i			1.08667i
$111$	4.63155e64	−	7.29112e64i	0.164207	−	0.258499i
$112$	3.42514e65			0.911383
$113$			5.79483e64i			0.116019i	0.998316	+	0.0580097i	$0.0184754\pi$
$113$			5.79483e64i			0.116019i	−0.998316	+	0.0580097i	$0.981525\pi$
$114$	−6.19222e64	−	3.93349e64i	−0.0935170	−	0.0594049i
$115$	−6.87699e65			−0.785358
$116$		−	7.62649e63i		−	0.00660190i
$117$	6.22610e65	+	1.32611e66i	0.409514	+	0.872234i
$118$	−2.81197e66			−1.40860
$119$		−	4.24531e66i		−	1.62333i
$120$	−3.38008e66	+	5.32103e66i	−0.988844	+	1.55667i
$121$	3.12968e66			0.702049
$122$		−	7.37106e66i		−	1.27062i
$123$	−2.49933e66	−	1.58765e66i	−0.331788	−	0.210762i
$124$	2.20948e65			0.0226359
$125$		−	4.10166e67i		−	3.24967i
$126$	1.30338e67	−	6.11939e66i	0.800230	−	0.375708i
$127$	7.66708e66			0.365520			0.182760	−	0.983158i	$-0.441497\pi$
$127$	7.66708e66			0.365520			0.182760	+	0.983158i	$0.441497\pi$
$128$			2.95487e67i			1.09602i
$129$	−1.18761e67	+	1.86957e67i	−0.343402	+	0.540594i
$130$	−8.49377e67			−1.91828
$131$			3.09184e67i			0.546431i	0.961953	+	0.273216i	$0.0880873\pi$
$131$			3.09184e67i			0.546431i	−0.961953	+	0.273216i	$0.911913\pi$
$132$	2.44862e66	+	1.55544e66i	0.0339278	+	0.0215520i
$133$	8.38236e66			0.0912250
$134$		−	1.50967e68i		−	1.29279i
$135$	−3.60424e67	+	2.82335e68i	−0.243295	+	1.90583i
$136$	3.42625e68			1.82631
$137$			5.35724e66i			0.0225883i	0.999936	+	0.0112941i	$0.00359511\pi$
$137$			5.35724e66i			0.0225883i	−0.999936	+	0.0112941i	$0.996405\pi$
$138$	−6.79758e67	+	1.07010e68i	−0.227103	+	0.357513i
$139$	−1.30567e68			−0.346225			−0.173113	−	0.984902i	$-0.555382\pi$
$139$	−1.30567e68			−0.346225			−0.173113	+	0.984902i	$0.555382\pi$
$140$			5.72569e67i			0.120707i
$141$	5.80890e68	+	3.68999e68i	0.975174	+	0.619461i
$142$	5.33576e68			0.714445
$143$		−	4.91717e68i		−	0.525971i
$144$	5.30441e68	+	1.12980e69i	0.453981	+	0.966945i
$145$	−2.51158e68			−0.172255
$146$			4.17902e68i			0.230029i
$147$	3.29738e68	−	5.19084e68i	0.145886	−	0.229659i
$148$	6.33193e67			0.0225508
$149$			2.63224e69i			0.755726i	0.925861	+	0.377863i	$0.123341\pi$
$149$			2.63224e69i			0.755726i	−0.925861	+	0.377863i	$0.876659\pi$
$150$	−1.01559e70	−	6.45132e69i	−2.35395	−	1.49530i
$151$	−3.68262e69			−0.690072			−0.345036	−	0.938589i	$-0.612133\pi$
$151$	−3.68262e69			−0.690072			−0.345036	+	0.938589i	$0.612133\pi$
$152$			6.76513e68i			0.102632i
$153$	1.40034e70	−	6.57460e69i	1.72230	−	0.808618i
$154$	−4.83289e69			−0.482551
$155$		−	7.27635e69i		−	0.590608i
$156$	−5.75827e68	+	9.06485e68i	−0.0380456	+	0.0598926i
$157$	−1.92659e69			−0.103753			−0.0518765	−	0.998654i	$-0.516520\pi$
$157$	−1.92659e69			−0.103753			−0.0518765	+	0.998654i	$0.516520\pi$
$158$		−	5.18647e68i		−	0.0227953i
$159$	−3.39477e70	−	2.15646e70i	−1.21928	−	0.774522i
$160$	−9.60936e69			−0.282394
$161$		−	1.44858e70i		−	0.348751i
$162$	4.03703e70	+	3.35159e70i	0.797226	+	0.661867i
$163$	9.41141e70			1.52634			0.763170	−	0.646198i	$-0.223642\pi$
$163$	9.41141e70			1.52634			0.763170	+	0.646198i	$0.223642\pi$
$164$		−	2.17053e69i		−	0.0289443i
$165$	5.12243e70	−	8.06389e70i	0.562328	−	0.885235i
$166$	−1.09088e71			−0.987004
$167$			1.55765e71i			1.16290i	0.813581	+	0.581451i	$0.197515\pi$
$167$			1.55765e71i			1.16290i	−0.813581	+	0.581451i	$0.802485\pi$
$168$	−1.12083e71	−	7.11987e70i	−0.691264	−	0.439112i
$169$	−1.40192e70			−0.0715070
$170$			8.96919e71i			3.78781i
$171$	1.29815e70	+	2.76497e70i	0.0454413	+	0.0967865i
$172$	−1.62362e70			−0.0471599
$173$		−	5.19272e71i		−	1.25291i	−0.779458	−	0.626454i	$-0.784505\pi$
$173$		−	5.19272e71i		−	1.25291i	0.779458	−	0.626454i	$-0.215495\pi$
$174$	−2.48258e70	+	3.90816e70i	−0.0498112	+	0.0784144i
$175$	1.37479e72			2.29625
$176$		−	4.18925e71i		−	0.583083i
$177$	9.88311e71	+	6.27805e71i	1.14749	+	0.728921i
$178$	−1.66054e72			−1.60994
$179$		−	1.83548e72i		−	1.48749i	−0.668464	−	0.743745i	$-0.733048\pi$
$179$		−	1.83548e72i		−	1.48749i	0.668464	−	0.743745i	$-0.266952\pi$
$180$	−1.88865e71	+	8.86722e70i	−0.128065	+	0.0601267i
$181$	−5.80142e71			−0.329473			−0.164737	−	0.986338i	$-0.552677\pi$
$181$	−5.80142e71			−0.329473			−0.164737	+	0.986338i	$0.552677\pi$
$182$		−	1.78914e72i		−	0.851845i
$183$	−1.64567e72	+	2.59067e72i	−0.657520	+	1.03509i
$184$	1.16910e72			0.392358
$185$		−	2.08525e72i		−	0.588387i
$186$	−1.13224e72	−	7.19232e71i	−0.268858	−	0.170787i
$187$	−5.19240e72			−1.03857
$188$			5.04470e71i			0.0850715i
$189$	−5.94717e72	−	7.59203e71i	−0.846316	−	0.108039i
$190$	−1.77097e72			−0.212860
$191$		−	1.09467e72i		−	0.111228i	−0.998452	−	0.0556140i	$-0.982288\pi$
$191$		−	1.09467e72i		−	0.111228i	0.998452	−	0.0556140i	$-0.0177116\pi$
$192$	5.71240e72	−	8.99263e72i	0.491110	−	0.773121i
$193$	1.97045e71			0.0143460			0.00717300	−	0.999974i	$-0.497717\pi$
$193$	1.97045e71			0.0143460			0.00717300	+	0.999974i	$0.497717\pi$
$194$		−	3.04836e72i		−	0.188110i
$195$	2.98527e73	+	1.89633e73i	1.56270	+	0.992675i
$196$	4.50795e71			0.0200348
$197$		−	3.38094e73i		−	1.27679i	−0.769711	−	0.638393i	$-0.779600\pi$
$197$		−	3.38094e73i		−	1.27679i	0.769711	−	0.638393i	$-0.220400\pi$
$198$	−7.48456e72	−	1.59416e73i	−0.240370	−	0.511970i
$199$	6.27810e73			1.71605			0.858025	−	0.513608i	$-0.171691\pi$
$199$	6.27810e73			1.71605			0.858025	+	0.513608i	$0.171691\pi$
$200$			1.10955e74i			2.58337i
$201$	−3.37051e73	+	5.30596e73i	−0.668993	+	1.05315i
$202$	−4.28829e73			−0.726173
$203$		−	5.29044e72i		−	0.0764925i
$204$	9.57224e72	+	6.08058e72i	0.118263	+	0.0751242i
$205$	−7.14806e73			−0.755205
$206$			8.15766e73i			0.737589i
$207$	4.77823e73	−	2.24338e73i	0.370012	−	0.173721i
$208$	1.55087e74			1.02931
$209$		−	1.02524e73i		−	0.0583638i
$210$	1.86383e74	−	2.93410e74i	0.910728	−	1.43370i
$211$	−3.79458e74			−1.59267			−0.796335	−	0.604856i	$-0.793230\pi$
$211$	−3.79458e74			−1.59267			−0.796335	+	0.604856i	$0.793230\pi$
$212$		−	2.94816e73i		−	0.106366i
$213$	−1.87533e74	−	1.19127e74i	−0.582011	−	0.369711i
$214$	−1.14000e73			−0.0304553
$215$			5.34695e74i			1.23048i
$216$	6.12728e73	−	4.79976e74i	0.121548	−	0.952138i
$217$	1.53270e74			0.262269
$218$		−	3.34626e74i		−	0.494256i
$219$	9.33015e73	−	1.46878e74i	0.119036	−	0.187390i
$220$	7.00303e73			0.0772255
$221$		−	1.92223e75i		−	1.83338i
$222$	−3.24476e74	−	2.06117e74i	−0.267848	−	0.170145i
$223$	−2.28308e75			−1.63217			−0.816084	−	0.577933i	$-0.803860\pi$
$223$	−2.28308e75			−1.63217			−0.816084	+	0.577933i	$0.803860\pi$
$224$		−	2.02413e74i		−	0.125401i
$225$	2.12910e75	+	4.53483e75i	1.14382	+	2.43624i
$226$	2.57887e74			0.120215
$227$		−	1.28280e75i		−	0.519197i	−0.965717	−	0.259598i	$-0.916410\pi$
$227$		−	1.28280e75i		−	0.519197i	0.965717	−	0.259598i	$-0.0835902\pi$
$228$	−1.20061e73	+	1.89004e73i	−0.00422169	+	0.00664592i
$229$	−3.56410e75			−1.08947			−0.544734	−	0.838609i	$-0.683369\pi$
$229$	−3.56410e75			−1.08947			−0.544734	+	0.838609i	$0.683369\pi$
$230$			3.06046e75i			0.813760i
$231$	1.69859e75	+	1.07900e75i	0.393103	+	0.249711i
$232$	4.26974e74			0.0860570
$233$			4.98290e75i			0.875170i	0.899177	+	0.437585i	$0.144166\pi$
$233$			4.98290e75i			0.875170i	−0.899177	+	0.437585i	$0.855834\pi$
$234$	5.90159e75	−	2.77080e75i	0.903777	−	0.424324i
$235$	1.66134e76			2.21966
$236$			8.58292e74i			0.100104i
$237$	−1.15794e74	+	1.82287e74i	−0.0117961	+	0.0185698i
$238$	−1.88929e76			−1.68204
$239$		−	4.16333e75i		−	0.324122i	−0.986781	−	0.162061i	$-0.948186\pi$
$239$		−	4.16333e75i		−	0.324122i	0.986781	−	0.162061i	$-0.0518141\pi$
$240$	2.54334e76	+	1.61561e76i	1.73239	+	1.10046i
$241$	−2.11645e76			−1.26201			−0.631005	−	0.775779i	$-0.717357\pi$
$241$	−2.11645e76			−1.26201			−0.631005	+	0.775779i	$0.717357\pi$
$242$		−	1.39280e76i		−	0.727438i
$243$	−6.70594e75	−	2.07928e76i	−0.306944	−	0.951728i
$244$	−2.24985e75			−0.0902983
$245$		−	1.48457e76i		−	0.522742i
$246$	−7.06552e75	+	1.11228e76i	−0.218384	+	0.343787i
$247$	3.79545e75			0.103029
$248$			1.23699e76i			0.295062i
$249$	3.83407e76	+	2.43552e76i	0.804046	+	0.510755i
$250$	−1.82536e77			−3.36719
$251$		−	2.64818e74i		−	0.00429920i	−0.999998	−	0.00214960i	$-0.999316\pi$
$251$		−	2.64818e74i		−	0.00429920i	0.999998	−	0.00214960i	$-0.000684240\pi$
$252$	−1.86781e75	−	3.97829e75i	−0.0267002	−	0.0568695i
$253$	−1.77175e76			−0.223123
$254$		−	3.41207e76i		−	0.378739i
$255$	2.00248e77	−	3.15236e77i	1.96012	−	3.08568i
$256$	2.54443e76			0.219741
$257$			1.03069e77i			0.785724i	0.919597	+	0.392862i	$0.128515\pi$
$257$			1.03069e77i			0.785724i	−0.919597	+	0.392862i	$0.871485\pi$
$258$	8.32013e76	+	5.28520e76i	0.560144	+	0.355821i
$259$	4.39241e76			0.261283
$260$			2.59253e76i			0.136326i
$261$	1.74508e76	−	8.19316e75i	0.0811558	−	0.0381027i
$262$	1.37596e77			0.566193
$263$			3.84716e77i			1.40138i	0.713465	+	0.700691i	$0.247125\pi$
$263$			3.84716e77i			1.40138i	−0.713465	+	0.700691i	$0.752875\pi$
$264$	−8.70824e76	+	1.37088e77i	−0.280934	+	0.442256i
$265$	−9.70900e77			−2.77528
$266$		−	3.73040e76i		−	0.0945241i
$267$	5.83623e77	+	3.70736e77i	1.31151	+	0.833113i
$268$	−4.60793e76			−0.0918739
$269$			9.31472e77i			1.64853i	0.566204	+	0.824265i	$0.308412\pi$
$269$			9.31472e77i			1.64853i	−0.566204	+	0.824265i	$0.691588\pi$
$270$	1.25648e78	+	1.60399e77i	1.97476	+	0.252093i
$271$	−3.06688e77			−0.428233			−0.214116	−	0.976808i	$-0.568687\pi$
$271$	−3.06688e77			−0.428233			−0.214116	+	0.976808i	$0.568687\pi$
$272$		−	1.63767e78i		−	2.03246i
$273$	−3.99447e77	+	6.28822e77i	−0.440813	+	0.693942i
$274$	2.38413e76			0.0234052
$275$		−	1.68150e78i		−	1.46909i
$276$	3.26623e76	+	2.07481e76i	0.0254072	+	0.0161394i
$277$	3.70755e77			0.256882			0.128441	−	0.991717i	$-0.459003\pi$
$277$	3.70755e77			0.256882			0.128441	+	0.991717i	$0.459003\pi$
$278$			5.81059e77i			0.358746i
$279$	2.37365e77	+	5.05571e77i	0.130642	+	0.278258i
$280$	−3.20557e78			−1.57343
$281$		−	1.20055e78i		−	0.525749i	−0.964830	−	0.262875i	$-0.915329\pi$
$281$		−	1.20055e78i		−	0.525749i	0.964830	−	0.262875i	$-0.0846706\pi$
$282$	1.64215e78	−	2.58513e78i	0.641863	−	1.01044i
$283$	2.01387e78			0.702856			0.351428	−	0.936215i	$-0.385696\pi$
$283$	2.01387e78			0.702856			0.351428	+	0.936215i	$0.385696\pi$
$284$		−	1.62862e77i		−	0.0507731i
$285$	6.22433e77	+	3.95389e77i	0.173403	+	0.110151i
$286$	−2.18828e78			−0.544992
$287$		−	1.50568e78i		−	0.335361i
$288$	6.67672e77	−	3.13472e77i	0.133046	−	0.0624653i
$289$	−1.46913e79			−2.62016
$290$			1.11773e78i			0.178484i
$291$	−6.80582e77	+	1.07139e78i	−0.0973430	+	0.153240i
$292$	1.27555e77			0.0163473
$293$			1.53608e78i			0.176462i	0.996100	+	0.0882310i	$0.0281214\pi$
$293$			1.53608e78i			0.176462i	−0.996100	+	0.0882310i	$0.971879\pi$
$294$	−2.31008e78	−	1.46743e78i	−0.237964	−	0.151162i
$295$	2.82656e79			2.61188
$296$			3.54497e78i			0.293953i
$297$	−9.28574e77	+	7.27392e78i	−0.0691210	+	0.541455i
$298$	1.17142e79			0.783057
$299$		−	6.55903e78i		−	0.393878i
$300$	−1.96912e78	+	3.09985e78i	−0.106266	+	0.167287i
$301$	−1.12629e79			−0.546415
$302$			1.63887e79i			0.715028i
$303$	1.50718e79	+	9.57410e78i	0.591565	+	0.375780i
$304$	3.23358e78			0.114217
$305$			7.40929e79i			2.35603i
$306$	−2.92589e79	−	6.23192e79i	−0.837861	−	1.78458i
$307$	4.63784e79			1.19643			0.598215	−	0.801335i	$-0.295877\pi$
$307$	4.63784e79			1.19643			0.598215	+	0.801335i	$0.295877\pi$
$308$			1.47513e78i			0.0342932i
$309$	1.82129e79	−	2.86714e79i	0.381688	−	0.600865i
$310$	−3.23819e79			−0.611966
$311$		−	4.13989e79i		−	0.705759i	−0.935669	−	0.352879i	$-0.885203\pi$
$311$		−	4.13989e79i		−	0.705759i	0.935669	−	0.352879i	$-0.114797\pi$
$312$	−5.07502e79	−	3.22381e79i	−0.780711	−	0.495932i
$313$	4.71839e79			0.655202			0.327601	−	0.944816i	$-0.393760\pi$
$313$	4.71839e79			0.655202			0.327601	+	0.944816i	$0.393760\pi$
$314$			8.57390e78i			0.107505i
$315$	−1.31014e80	+	6.15113e79i	−1.48382	+	0.696654i
$316$	−1.58306e77			−0.00161998
$317$		−	6.66446e79i		−	0.616409i	−0.951320	−	0.308204i	$-0.900272\pi$
$317$		−	6.66446e79i		−	0.616409i	0.951320	−	0.308204i	$-0.0997280\pi$
$318$	−9.59688e79	+	1.51077e80i	−0.802532	+	1.26337i
$319$	−6.47069e78			−0.0489383
$320$		−	2.57188e80i		−	1.75975i
$321$	4.00670e78	+	2.54518e78i	0.0248099	+	0.0157600i
$322$	−6.44661e79			−0.361363
$323$		−	4.00789e79i		−	0.203440i
$324$	1.02300e79	−	1.23221e79i	0.0470365	−	0.0566560i
$325$	6.22492e80			2.59338
$326$		−	4.18835e80i		−	1.58154i
$327$	−7.47092e79	+	1.17610e80i	−0.255768	+	0.402638i
$328$	1.21519e80			0.377294
$329$			3.49947e80i			0.985675i
$330$	−3.58867e80	−	2.27963e80i	−0.917249	−	0.582665i
$331$	−3.64537e80			−0.845757			−0.422878	−	0.906186i	$-0.638980\pi$
$331$	−3.64537e80			−0.845757			−0.422878	+	0.906186i	$0.638980\pi$
$332$			3.32968e79i			0.0701428i
$333$	6.80241e79	+	1.44886e80i	0.130151	+	0.277212i
$334$	6.93200e80			1.20496
$335$			1.51750e81i			2.39714i
$336$	−3.40314e80	+	5.35734e80i	−0.488679	+	0.769293i
$337$	−3.45562e80			−0.451200			−0.225600	−	0.974220i	$-0.572434\pi$
$337$	−3.45562e80			−0.451200			−0.225600	+	0.974220i	$0.572434\pi$
$338$			6.23895e79i			0.0740930i
$339$	−9.06383e79	−	5.75763e79i	−0.0979313	−	0.0622090i
$340$	2.73765e80			0.269186
$341$		−	1.87463e80i		−	0.167794i
$342$	1.23049e80	−	5.77716e79i	0.100287	−	0.0470846i
$343$	1.46207e81			1.08532
$344$		−	9.08992e80i		−	0.614738i
$345$	6.83284e80	−	1.07565e81i	0.421105	−	0.662916i
$346$	−2.31091e81			−1.29822
$347$			2.65632e81i			1.36062i	0.732925	+	0.680310i	$0.238155\pi$
$347$			2.65632e81i			1.36062i	−0.732925	+	0.680310i	$0.761845\pi$
$348$	1.19288e79	+	7.57753e78i	0.00557263	+	0.00353991i
$349$	3.06807e81			1.30753			0.653764	−	0.756698i	$-0.273189\pi$
$349$	3.06807e81			1.30753			0.653764	+	0.756698i	$0.273189\pi$
$350$		−	6.11823e81i		−	2.37930i
$351$	−2.69282e81	−	3.43759e80i	−0.955827	−	0.122019i
$352$	−2.47570e80			−0.0802292
$353$			1.19948e80i			0.0354978i	0.999842	+	0.0177489i	$0.00564995\pi$
$353$			1.19948e80i			0.0354978i	−0.999842	+	0.0177489i	$0.994350\pi$
$354$	2.79392e81	−	4.39827e81i	0.755282	−	1.18899i
$355$	−5.36343e81			−1.32475
$356$			5.06844e80i			0.114413i
$357$	6.64019e81	+	4.21805e81i	1.37024	+	0.870421i
$358$	−8.16844e81			−1.54128
$359$			9.06134e81i			1.56376i	0.623429	+	0.781880i	$0.285739\pi$
$359$			9.06134e81i			1.56376i	−0.623429	+	0.781880i	$0.714261\pi$
$360$	−4.96437e81	−	1.05737e82i	−0.783762	−	1.66935i
$361$	−6.84285e81			−0.988567
$362$			2.58180e81i			0.341388i
$363$	−3.10958e81	+	4.89520e81i	−0.376435	+	0.592596i
$364$	−5.46096e80			−0.0605376
$365$		−	4.20069e81i		−	0.426530i
$366$	1.15292e82	+	7.32373e81i	1.07252	+	0.681299i
$367$	2.01616e82			1.71874			0.859370	−	0.511354i	$-0.170856\pi$
$367$	2.01616e82			1.71874			0.859370	+	0.511354i	$0.170856\pi$
$368$		−	5.58806e81i		−	0.436647i
$369$	4.96657e81	−	2.33181e81i	0.355806	−	0.167051i
$370$	−9.27998e81			−0.609666
$371$		−	2.04512e82i		−	1.23241i
$372$	−2.19530e80	+	3.45591e80i	−0.0121372	+	0.0191068i
$373$	5.41003e81			0.274484			0.137242	−	0.990538i	$-0.456176\pi$
$373$	5.41003e81			0.274484			0.137242	+	0.990538i	$0.456176\pi$
$374$			2.31077e82i			1.07613i
$375$	6.41551e82	+	4.07533e82i	2.74303	+	1.74246i
$376$	−2.82431e82			−1.10892
$377$		−	2.39546e81i		−	0.0863904i
$378$	−3.37868e81	+	2.64666e82i	−0.111946	+	0.876922i
$379$	−3.79560e82			−1.15565			−0.577824	−	0.816162i	$-0.696098\pi$
$379$	−3.79560e82			−1.15565			−0.577824	+	0.816162i	$0.696098\pi$
$380$			5.40548e80i			0.0151272i
$381$	−7.61785e81	+	1.19923e82i	−0.195990	+	0.308533i
$382$	−4.87159e81			−0.115251
$383$		−	5.25936e82i		−	1.14438i	−0.820119	−	0.572192i	$-0.806093\pi$
$383$		−	5.25936e82i		−	1.14438i	0.820119	−	0.572192i	$-0.193907\pi$
$384$	−4.62178e82	−	2.93590e82i	−0.925146	−	0.587681i
$385$	4.85795e82			0.894767
$386$		−	8.76906e80i		−	0.0148648i
$387$	−1.74425e82	−	3.71513e82i	−0.272182	−	0.579727i
$388$	−9.30445e80			−0.0133683
$389$			9.10818e82i			1.20516i	0.798059	+	0.602580i	$0.205860\pi$
$389$			9.10818e82i			1.20516i	−0.798059	+	0.602580i	$0.794140\pi$
$390$	8.43923e82	−	1.32853e83i	1.02857	−	1.61921i
$391$	−6.92616e82			−0.777744
$392$			2.52381e82i			0.261157i
$393$	−4.83602e82	−	3.07199e82i	−0.461240	−	0.292994i
$394$	−1.50462e83			−1.32296
$395$			5.21338e81i			0.0422680i
$396$	−4.86581e81	+	2.28450e81i	−0.0363839	+	0.0170822i
$397$	−1.22482e83			−0.844842			−0.422421	−	0.906400i	$-0.638820\pi$
$397$	−1.22482e83			−0.844842			−0.422421	+	0.906400i	$0.638820\pi$
$398$		−	2.79394e83i		−	1.77811i
$399$	−8.32854e81	+	1.31111e82i	−0.0489144	+	0.0770025i
$400$	5.30341e83			2.87498
$401$			1.96139e83i			0.981621i	0.871266	+	0.490811i	$0.163299\pi$
$401$			1.96139e83i			0.981621i	−0.871266	+	0.490811i	$0.836701\pi$
$402$	2.36131e83	+	1.49997e83i	1.09124	+	0.693187i
$403$	6.93992e82			0.296206
$404$			1.30890e82i			0.0516065i
$405$	−4.05797e83	−	3.36898e83i	−1.47825	−	1.22726i
$406$	−2.35440e82			−0.0792588
$407$		−	5.37232e82i		−	0.167163i
$408$	−3.40425e83	+	5.35908e83i	−0.979257	+	1.54158i
$409$	−1.17638e82			−0.0312897			−0.0156449	−	0.999878i	$-0.504980\pi$
$409$	−1.17638e82			−0.0312897			−0.0156449	+	0.999878i	$0.504980\pi$
$410$			3.18110e83i			0.782516i
$411$	−8.37939e81	−	5.32285e81i	−0.0190666	−	0.0121117i
$412$	2.48994e82			0.0524178
$413$			5.95391e83i			1.15985i
$414$	−9.98369e82	−	2.12645e83i	−0.180003	−	0.383393i
$415$	1.09654e84			1.83014
$416$		−	9.16507e82i		−	0.141628i
$417$	1.29728e83	−	2.04222e83i	0.185644	−	0.292247i
$418$	−4.56261e82			−0.0604745
$419$			5.47932e83i			0.672787i	0.941721	+	0.336394i	$0.109207\pi$
$419$			5.47932e83i			0.672787i	−0.941721	+	0.336394i	$0.890793\pi$
$420$	−8.95569e82	−	5.68893e82i	−0.101888	−	0.0647222i
$421$	−3.12031e83			−0.328981			−0.164490	−	0.986379i	$-0.552598\pi$
$421$	−3.12031e83			−0.328981			−0.164490	+	0.986379i	$0.552598\pi$
$422$			1.68870e84i			1.65027i
$423$	−1.15432e84	+	5.41954e83i	−1.04577	+	0.490987i
$424$	1.65055e84			1.38650
$425$		−	6.57335e84i		−	5.12084i
$426$	−5.30150e83	+	8.34578e83i	−0.383082	+	0.603059i
$427$	−1.56071e84			−1.04623
$428$			3.47959e81i			0.00216435i
$429$	7.69106e83	+	4.88560e83i	0.443969	+	0.282023i
$430$	2.37955e84			1.27498
$431$		−	6.65764e83i		−	0.331168i	−0.986196	−	0.165584i	$-0.947049\pi$
$431$		−	6.65764e83i		−	0.331168i	0.986196	−	0.165584i	$-0.0529508\pi$
$432$	−2.29418e84	−	2.92871e83i	−1.05962	−	0.135268i
$433$	−8.41711e82			−0.0361036			−0.0180518	−	0.999837i	$-0.505746\pi$
$433$	−8.41711e82			−0.0361036			−0.0180518	+	0.999837i	$0.505746\pi$
$434$		−	6.82098e83i		−	0.271754i
$435$	2.49546e83	−	3.92843e83i	0.0923621	−	0.145399i
$436$	−1.02137e83			−0.0351250
$437$		−	1.36757e83i		−	0.0437063i
$438$	−6.53650e83	−	4.15219e83i	−0.194166	−	0.123340i
$439$	−6.14244e84			−1.69620			−0.848099	−	0.529838i	$-0.822253\pi$
$439$	−6.14244e84			−1.69620			−0.848099	+	0.529838i	$0.822253\pi$
$440$			3.92070e84i			1.00665i
$441$	4.84291e83	+	1.03150e84i	0.115630	+	0.246284i
$442$	−8.55450e84			−1.89969
$443$			2.38885e84i			0.493479i	0.969082	+	0.246740i	$0.0793592\pi$
$443$			2.38885e84i			0.493479i	−0.969082	+	0.246740i	$0.920641\pi$
$444$	−6.29127e82	+	9.90392e82i	−0.0120916	+	0.0190350i
$445$	1.66916e85			2.98522
$446$			1.01604e85i			1.69119i
$447$	−4.11715e84	−	2.61534e84i	−0.637904	−	0.405216i
$448$	5.41746e84			0.781447
$449$		−	7.91551e84i		−	1.06315i	−0.847010	−	0.531577i	$-0.821600\pi$
$449$		−	7.91551e84i		−	1.06315i	0.847010	−	0.531577i	$-0.178400\pi$
$450$	2.01813e85	−	9.47513e84i	2.52435	−	1.18518i
$451$	−1.84158e84			−0.214557
$452$		−	7.87143e82i		−	0.00854326i
$453$	3.65898e84	−	5.76007e84i	0.370013	−	0.582486i
$454$	−5.70884e84			−0.537973
$455$			1.79842e85i			1.57953i
$456$	−1.05815e84	−	6.72169e83i	−0.0866308	−	0.0550305i
$457$	−1.07755e85			−0.822467			−0.411234	−	0.911530i	$-0.634902\pi$
$457$	−1.07755e85			−0.822467			−0.411234	+	0.911530i	$0.634902\pi$
$458$			1.58613e85i			1.12887i
$459$	−3.63001e84	+	2.84354e85i	−0.240936	+	1.88736i
$460$	9.34138e83			0.0578310
$461$		−	2.73671e85i		−	1.58052i	−0.612772	−	0.790260i	$-0.709946\pi$
$461$		−	2.73671e85i		−	1.58052i	0.612772	−	0.790260i	$-0.290054\pi$
$462$	4.80186e84	−	7.55923e84i	0.258742	−	0.407319i
$463$	−3.30765e85			−1.66314			−0.831569	−	0.555422i	$-0.812557\pi$
$463$	−3.30765e85			−1.66314			−0.831569	+	0.555422i	$0.812557\pi$
$464$		−	2.04084e84i		−	0.0957711i
$465$	1.13811e85	+	7.22963e84i	0.498528	+	0.316681i
$466$	2.21754e85			0.906820
$467$			3.08268e84i			0.117703i	0.998267	+	0.0588515i	$0.0187439\pi$
$467$			3.08268e84i			0.117703i	−0.998267	+	0.0588515i	$0.981256\pi$
$468$	−8.45724e83	−	1.80133e84i	−0.0301551	−	0.0642282i
$469$	−3.19649e85			−1.06449
$470$		−	7.39344e85i		−	2.29993i
$471$	1.91422e84	−	3.01343e84i	0.0556318	−	0.0875774i
$472$	−4.80521e85			−1.30487
$473$			1.37755e85i			0.349585i
$474$	8.11229e83	+	5.15318e83i	0.0192414	+	0.0122227i
$475$	1.29791e85			0.287772
$476$			5.76663e84i			0.119536i
$477$	6.74595e85	−	3.16722e85i	1.30754	−	0.613890i
$478$	−1.85280e85			−0.335843
$479$		−	7.47563e85i		−	1.26739i	−0.773582	−	0.633697i	$-0.781537\pi$
$479$		−	7.47563e85i		−	1.26739i	0.773582	−	0.633697i	$-0.218463\pi$
$480$	9.54766e84	−	1.50302e85i	0.151418	−	0.238367i
$481$	1.98884e85			0.295092
$482$			9.41883e85i			1.30765i
$483$	2.26576e85	+	1.43928e85i	0.294378	+	0.186998i
$484$	−4.25121e84			−0.0516964
$485$			3.06417e85i			0.348801i
$486$	−9.25341e85	+	2.98434e85i	−0.986146	+	0.318044i
$487$	1.55661e86			1.55329			0.776646	−	0.629937i	$-0.216919\pi$
$487$	1.55661e86			1.55329			0.776646	+	0.629937i	$0.216919\pi$
$488$		−	1.25959e86i		−	1.17705i
$489$	−9.35099e85	+	1.47206e86i	−0.818416	+	1.28838i
$490$	−6.60679e85			−0.541647
$491$			2.33110e86i			1.79041i	0.445651	+	0.895207i	$0.352972\pi$
$491$			2.33110e86i			1.79041i	−0.445651	+	0.895207i	$0.647028\pi$
$492$	3.39498e84	+	2.15659e84i	0.0244317	+	0.0155198i
$493$	−2.52954e85			−0.170585
$494$		−	1.68908e85i		−	0.106755i
$495$	7.52338e85	+	1.60242e86i	0.445704	+	0.949316i
$496$	5.91256e85			0.328369
$497$		−	1.12976e86i		−	0.588278i
$498$	1.08388e86	−	1.70627e86i	0.529226	−	0.833124i
$499$	3.61369e85			0.165475			0.0827376	−	0.996571i	$-0.473634\pi$
$499$	3.61369e85			0.165475			0.0827376	+	0.996571i	$0.473634\pi$
$500$			5.57151e85i			0.239294i
$501$	−2.43636e86	−	1.54765e86i	−0.981599	−	0.623542i
$502$	−1.17852e84			−0.00445468
$503$			1.74045e86i			0.617287i	0.951178	+	0.308643i	$0.0998750\pi$
$503$			1.74045e86i			0.617287i	−0.951178	+	0.308643i	$0.900125\pi$
$504$	2.22727e86	−	1.04570e86i	0.741304	−	0.348042i
$505$	4.31053e86			1.34650
$506$			7.88479e85i			0.231192i
$507$	1.39292e85	−	2.19278e85i	0.0383417	−	0.0603587i
$508$	−1.04146e85			−0.0269156
$509$			2.21649e86i			0.537893i	0.963155	+	0.268947i	$0.0866755\pi$
$509$			2.21649e86i			0.537893i	−0.963155	+	0.268947i	$0.913325\pi$
$510$	−1.40289e87	−	8.91161e86i	−3.19727	−	2.03100i
$511$	8.84842e85			0.189407
$512$			4.31843e86i			0.868334i
$513$	−5.61457e85	−	7.16745e84i	−0.106062	−	0.0135397i
$514$	4.58689e86			0.814139
$515$		−	8.19997e86i		−	1.36767i
$516$	1.61319e85	−	2.53954e85i	0.0252869	−	0.0398074i
$517$	4.28017e86			0.630614
$518$		−	1.95475e86i		−	0.270732i
$519$	8.12206e86	+	5.15938e86i	1.05757	+	0.671803i
$520$	−1.45145e87			−1.77703
$521$		−	1.55380e87i		−	1.78891i	−0.447158	−	0.894455i	$-0.647564\pi$
$521$		−	1.55380e87i		−	1.78891i	0.447158	−	0.894455i	$-0.352436\pi$
$522$	−3.64620e85	−	7.76613e85i	−0.0394806	−	0.0840908i
$523$	−1.14059e87			−1.16165			−0.580827	−	0.814027i	$-0.697271\pi$
$523$	−1.14059e87			−1.16165			−0.580827	+	0.814027i	$0.697271\pi$
$524$		−	4.19981e85i		−	0.0402373i
$525$	−1.36597e87	+	2.15035e87i	−1.23124	+	1.93825i
$526$	1.71210e87			1.45206
$527$		−	7.32837e86i		−	0.584882i
$528$	6.55250e86	+	4.16235e86i	0.492177	+	0.312646i
$529$	1.17810e87			0.832912
$530$			4.32079e87i			2.87564i
$531$	−1.96393e87	+	9.22066e86i	−1.23056	+	0.577746i
$532$	−1.13862e85			−0.00671749
$533$		−	6.81757e86i		−	0.378755i
$534$	1.64988e87	−	2.59729e87i	0.863242	−	1.35894i
$535$	1.14591e86			0.0564715
$536$		−	2.57978e87i		−	1.19759i
$537$	2.87093e87	+	1.82370e87i	1.25558	+	0.797584i
$538$	4.14532e87			1.70815
$539$		−	3.82477e86i		−	0.148513i
$540$	4.89583e85	−	3.83511e86i	0.0179154	−	0.140339i
$541$	−2.83429e87			−0.977534			−0.488767	−	0.872414i	$-0.662553\pi$
$541$	−2.83429e87			−0.977534			−0.488767	+	0.872414i	$0.662553\pi$
$542$			1.36485e87i			0.443720i
$543$	5.76417e86	−	9.07414e86i	0.176662	−	0.278106i
$544$	−9.67807e86			−0.279656
$545$			3.36362e87i			0.916471i
$546$	2.79844e87	+	1.77766e87i	0.719038	+	0.456755i
$547$	−4.63869e87			−1.12409			−0.562045	−	0.827107i	$-0.689985\pi$
$547$	−4.63869e87			−1.12409			−0.562045	+	0.827107i	$0.689985\pi$
$548$		−	7.27703e84i		−	0.00166332i
$549$	−2.41702e87	−	5.14808e87i	−0.521154	−	1.11002i
$550$	−7.48314e87			−1.52222
$551$		−	4.99458e85i		−	0.00958622i
$552$	−1.16160e87	+	1.82862e87i	−0.210380	+	0.331187i
$553$	−1.09816e86			−0.0187698
$554$		−	1.64997e87i		−	0.266172i
$555$	3.26159e87	+	2.07186e87i	0.496654	+	0.315490i
$556$	1.77356e86			0.0254948
$557$		−	1.14607e88i		−	1.55542i	−0.628626	−	0.777708i	$-0.716382\pi$
$557$		−	1.14607e88i		−	1.55542i	0.628626	−	0.777708i	$-0.283618\pi$
$558$	2.24994e87	−	1.05635e87i	0.288321	−	0.135367i
$559$	−5.09973e87			−0.617119
$560$			1.53219e88i			1.75104i
$561$	5.15906e87	−	8.12155e87i	0.556877	−	0.876652i
$562$	−5.34281e87			−0.544763
$563$		−	1.23867e88i		−	1.19313i	−0.802564	−	0.596566i	$-0.796531\pi$
$563$		−	1.23867e88i		−	1.19313i	0.802564	−	0.596566i	$-0.203469\pi$
$564$	−7.89054e86	−	5.01231e86i	−0.0718084	−	0.0456149i
$565$	−2.59225e87			−0.222908
$566$		−	8.96233e87i		−	0.728274i
$567$	7.09647e87	−	8.54778e87i	0.544985	−	0.656440i
$568$	9.11795e87			0.661836
$569$			2.07953e88i			1.42683i	0.700741	+	0.713416i	$0.252853\pi$
$569$			2.07953e88i			1.42683i	−0.700741	+	0.713416i	$0.747147\pi$
$570$	1.75960e87	−	2.77001e87i	0.114135	−	0.179674i
$571$	4.93529e87			0.302661			0.151331	−	0.988483i	$-0.451644\pi$
$571$	4.93529e87			0.302661			0.151331	+	0.988483i	$0.451644\pi$
$572$			6.67925e86i			0.0387306i
$573$	1.71219e87	+	1.08764e87i	0.0938870	+	0.0596399i
$574$	−6.70072e87			−0.347489
$575$		−	2.24295e88i		−	1.10014i
$576$	8.38987e87	+	1.78698e88i	0.389256	+	0.829087i
$577$	8.52130e87			0.374007			0.187004	−	0.982359i	$-0.440122\pi$
$577$	8.52130e87			0.374007			0.187004	+	0.982359i	$0.440122\pi$
$578$			6.53805e88i			2.71492i
$579$	−1.95780e86	+	3.08202e86i	−0.00769225	+	0.0121094i
$580$	3.41162e86			0.0126842
$581$			2.30977e88i			0.812705i
$582$	4.76801e87	+	3.02879e87i	0.158782	+	0.100863i
$583$	−2.50137e88			−0.788467
$584$			7.14127e87i			0.213091i
$585$	−5.93220e88	+	2.78517e88i	−1.67582	+	0.786799i
$586$	6.83602e87			0.182844
$587$		−	1.86769e88i		−	0.473028i	−0.971628	−	0.236514i	$-0.923995\pi$
$587$		−	1.86769e88i		−	0.473028i	0.971628	−	0.236514i	$-0.0760048\pi$
$588$	−4.47901e86	+	7.05100e86i	−0.0107426	+	0.0169113i
$589$	1.44699e87			0.0328681
$590$		−	1.25790e89i		−	2.70634i
$591$	5.28821e88	+	3.35923e88i	1.07773	+	0.684606i
$592$	1.69442e88			0.327135
$593$		−	6.95614e88i		−	1.27238i	−0.771531	−	0.636192i	$-0.780509\pi$
$593$		−	6.95614e88i		−	1.27238i	0.771531	−	0.636192i	$-0.219491\pi$
$594$	3.23711e88	+	4.13242e87i	0.561036	+	0.0716207i
$595$	1.89909e89			3.11890
$596$		−	3.57551e87i		−	0.0556490i
$597$	−6.23780e88	+	9.81973e88i	−0.920137	+	1.44851i
$598$	−2.91896e88			−0.408122
$599$		−	4.63119e88i		−	0.613810i	−0.951740	−	0.306905i	$-0.900707\pi$
$599$		−	4.63119e88i		−	0.613810i	0.951740	−	0.306905i	$-0.0992934\pi$
$600$	−1.73547e89	−	1.10243e89i	−2.18061	−	1.38519i
$601$	−1.03838e89			−1.23701			−0.618506	−	0.785780i	$-0.712262\pi$
$601$	−1.03838e89			−1.23701			−0.618506	+	0.785780i	$0.712262\pi$
$602$			5.01232e88i			0.566176i
$603$	−4.95031e88	−	1.05438e89i	−0.530247	−	1.12939i
$604$	5.00230e87			0.0508145
$605$			1.40002e89i			1.34885i
$606$	4.26076e88	−	6.70741e88i	0.389370	−	0.612958i
$607$	−1.53098e89			−1.32719			−0.663594	−	0.748093i	$-0.730970\pi$
$607$	−1.53098e89			−1.32719			−0.663594	+	0.748093i	$0.730970\pi$
$608$		−	1.91093e87i		−	0.0157156i
$609$	8.27491e87	+	5.25648e87i	0.0645669	+	0.0410149i
$610$	3.29735e89			2.44124
$611$			1.58453e89i			1.11322i
$612$	−1.90216e88	+	8.93062e87i	−0.126824	+	0.0595438i
$613$	−7.84427e88			−0.496384			−0.248192	−	0.968711i	$-0.579836\pi$
$613$	−7.84427e88			−0.496384			−0.248192	+	0.968711i	$0.579836\pi$
$614$		−	2.06397e89i		−	1.23970i
$615$	7.10217e88	−	1.11805e89i	0.404937	−	0.637464i
$616$	−8.25863e88			−0.447018
$617$			1.89994e89i			0.976369i	0.872741	+	0.488184i	$0.162341\pi$
$617$			1.89994e89i			0.976369i	−0.872741	+	0.488184i	$0.837659\pi$
$618$	−1.27596e89	−	8.10528e88i	−0.622595	−	0.395491i
$619$	2.09845e88			0.0972293			0.0486146	−	0.998818i	$-0.484519\pi$
$619$	2.09845e88			0.0972293			0.0486146	+	0.998818i	$0.484519\pi$
$620$			9.88385e87i			0.0434903i
$621$	−1.23863e88	+	9.70272e88i	−0.0517619	+	0.405473i
$622$	−1.84237e89			−0.731282
$623$			3.51594e89i			1.32564i
$624$	−1.54091e89	+	2.42575e89i	−0.551912	+	0.868838i
$625$	1.04390e90			3.55220
$626$		−	2.09982e89i		−	0.678897i
$627$	1.60360e88	+	1.01866e88i	0.0492645	+	0.0312944i
$628$	2.61699e87			0.00764001
$629$		−	2.10016e89i		−	0.582683i
$630$	2.73743e89	+	5.83052e89i	0.721848	+	1.53748i
$631$	−3.25521e89			−0.815905			−0.407953	−	0.913003i	$-0.633757\pi$
$631$	−3.25521e89			−0.815905			−0.407953	+	0.913003i	$0.633757\pi$
$632$		−	8.86285e87i		−	0.0211167i
$633$	3.77022e89	−	5.93520e89i	0.853981	−	1.34436i
$634$	−2.96588e89			−0.638701
$635$			3.42977e89i			0.702273i
$636$	4.61130e88	+	2.92924e88i	0.0897832	+	0.0570331i
$637$	1.41594e89			0.262169
$638$			2.87964e88i			0.0507081i
$639$	3.72659e89	−	1.74963e89i	0.624143	−	0.293035i
$640$	−1.32182e90			−2.10579
$641$		−	6.81807e89i		−	1.03325i	−0.856212	−	0.516624i	$-0.827189\pi$
$641$		−	6.81807e89i		−	1.03325i	0.856212	−	0.516624i	$-0.172811\pi$
$642$	1.13268e88	−	1.78310e88i	0.0163300	−	0.0257072i
$643$	−6.95255e89			−0.953658			−0.476829	−	0.878996i	$-0.658214\pi$
$643$	−6.95255e89			−0.953658			−0.476829	+	0.878996i	$0.658214\pi$
$644$			1.96769e88i			0.0256808i
$645$	−8.36328e89	−	5.31262e89i	−1.03864	−	0.659778i
$646$	−1.78363e89			−0.210797
$647$			1.32368e90i			1.48883i	0.667717	+	0.744416i	$0.267272\pi$
$647$			1.32368e90i			1.48883i	−0.667717	+	0.744416i	$0.732728\pi$
$648$	6.89863e89	+	5.72733e89i	0.738521	+	0.613129i
$649$	7.28217e89			0.742045
$650$		−	2.77027e90i		−	2.68717i
$651$	−1.52286e89	+	2.39734e89i	−0.140627	+	0.221380i
$652$	−1.27840e89			−0.112394
$653$		−	3.91385e89i		−	0.327629i	−0.986491	−	0.163814i	$-0.947620\pi$
$653$		−	3.91385e89i		−	0.327629i	0.986491	−	0.163814i	$-0.0523798\pi$
$654$	5.23397e89	+	3.32478e89i	0.417199	+	0.265018i
$655$	−1.38310e90			−1.04986
$656$		−	5.80832e89i		−	0.419883i
$657$	1.37033e89	+	2.91870e89i	0.0943482	+	0.200955i
$658$	1.55737e90			1.02132
$659$		−	7.08423e89i		−	0.442547i	−0.975212	−	0.221274i	$-0.928979\pi$
$659$		−	7.08423e89i		−	0.442547i	0.975212	−	0.221274i	$-0.0710214\pi$
$660$	−6.95807e88	+	1.09536e89i	−0.0414079	+	0.0651856i
$661$	−2.11424e90			−1.19869			−0.599346	−	0.800490i	$-0.704573\pi$
$661$	−2.11424e90			−1.19869			−0.599346	+	0.800490i	$0.704573\pi$
$662$			1.62230e90i			0.876343i
$663$	3.00661e90	+	1.90989e90i	1.54755	+	0.983051i
$664$	−1.86414e90			−0.914324
$665$			3.74974e89i			0.175271i
$666$	6.44786e89	−	3.02727e89i	0.287237	−	0.134858i
$667$	−8.63128e88			−0.0366479
$668$		−	2.11584e89i		−	0.0856320i
$669$	2.26842e90	−	3.57102e90i	0.875160	−	1.37770i
$670$	6.75331e90			2.48384
$671$			1.90888e90i			0.669359i
$672$	3.16600e89	+	2.01114e89i	0.105851	+	0.0672396i
$673$	−1.64317e90			−0.523843			−0.261922	−	0.965089i	$-0.584356\pi$
$673$	−1.64317e90			−0.523843			−0.261922	+	0.965089i	$0.584356\pi$
$674$			1.53785e90i			0.467517i
$675$	−9.20847e90	−	1.17553e90i	−2.66973	−	0.340812i
$676$	1.90430e88			0.00526553
$677$			2.67116e90i			0.704469i	0.935912	+	0.352235i	$0.114578\pi$
$677$			2.67116e90i			0.704469i	−0.935912	+	0.352235i	$0.885422\pi$
$678$	−2.56231e89	+	4.03367e89i	−0.0644587	+	0.101473i
$679$	−6.45443e89			−0.154891
$680$			1.53269e91i			3.50889i
$681$	2.00646e90	+	1.27457e90i	0.438251	+	0.278391i
$682$	−8.34267e89			−0.173862
$683$		−	4.19752e90i		−	0.834700i	−0.908746	−	0.417350i	$-0.862959\pi$
$683$		−	4.19752e90i		−	0.834700i	0.908746	−	0.417350i	$-0.137041\pi$
$684$	−1.76335e88	−	3.75580e88i	−0.00334613	−	0.00712702i
$685$	−2.39650e89			−0.0433989
$686$		−	6.50664e90i		−	1.12457i
$687$	3.54122e90	−	5.57469e90i	0.584167	−	0.919614i
$688$	−4.34478e90			−0.684129
$689$		−	9.26010e90i		−	1.39188i
$690$	−4.78694e90	−	3.04081e90i	−0.686890	−	0.436334i
$691$	1.22695e91			1.68086			0.840429	−	0.541922i	$-0.182303\pi$
$691$	1.22695e91			1.68086			0.840429	+	0.541922i	$0.182303\pi$
$692$			7.05355e89i			0.0922598i
$693$	−3.37537e90	+	1.58474e90i	−0.421559	+	0.197922i
$694$	1.18214e91			1.40983
$695$		−	5.84073e90i		−	0.665202i
$696$	−4.24233e89	+	6.67841e89i	−0.0461433	+	0.0726402i
$697$	−7.19917e90			−0.747883
$698$		−	1.36538e91i		−	1.35481i
$699$	−7.79387e90	−	4.95091e90i	−0.738726	−	0.469262i
$700$	−1.86745e90			−0.169088
$701$		−	7.06145e90i		−	0.610825i	−0.952220	−	0.305413i	$-0.901206\pi$
$701$		−	7.06145e90i		−	0.610825i	0.952220	−	0.305413i	$-0.0987944\pi$
$702$	−1.52983e90	+	1.19838e91i	−0.126432	+	0.990393i
$703$	4.14677e89			0.0327446
$704$		−	6.62604e90i		−	0.499953i
$705$	−1.65067e91	+	2.59854e91i	−1.19017	+	1.87360i
$706$	5.33803e89			0.0367816
$707$			9.07978e90i			0.597935i
$708$	−1.34248e90	−	8.52782e89i	−0.0844971	−	0.0536752i
$709$	5.74071e90			0.345371			0.172686	−	0.984977i	$-0.444756\pi$
$709$	5.74071e90			0.345371			0.172686	+	0.984977i	$0.444756\pi$
$710$			2.38688e91i			1.37266i
$711$	−1.70068e89	−	3.62233e89i	−0.00934966	−	0.0199141i
$712$	−2.83760e91			−1.49139
$713$		−	2.50058e90i		−	0.125654i
$714$	1.87716e91	−	2.95508e91i	0.901899	−	1.41980i
$715$	2.19963e91			1.01055
$716$			2.49324e90i			0.109533i
$717$	6.51196e90	+	4.13660e90i	0.273589	+	0.173792i
$718$	4.03256e91			1.62031
$719$			7.52232e90i			0.289086i	0.989499	+	0.144543i	$0.0461712\pi$
$719$			7.52232e90i			0.289086i	−0.989499	+	0.144543i	$0.953829\pi$
$720$	−5.05402e91	+	2.37286e91i	−1.85779	+	0.872233i
$721$	1.72726e91			0.607335
$722$			3.04527e91i			1.02432i
$723$	2.10286e91	−	3.31039e91i	0.676683	−	1.06526i
$724$	7.88038e89			0.0242612
$725$		−	8.19161e90i		−	0.241298i
$726$	2.17851e91	+	1.38385e91i	0.614026	+	0.390049i
$727$	−1.10857e91			−0.298994			−0.149497	−	0.988762i	$-0.547765\pi$
$727$	−1.10857e91			−0.298994			−0.149497	+	0.988762i	$0.547765\pi$
$728$		−	3.05736e91i		−	0.789118i
$729$	3.91854e91	+	1.01704e91i	0.967930	+	0.251222i
$730$	−1.86943e91			−0.441955
$731$			5.38518e91i			1.21855i
$732$	2.23541e90	−	3.51905e90i	0.0484175	−	0.0762203i
$733$	−2.09892e91			−0.435179			−0.217589	−	0.976040i	$-0.569819\pi$
$733$	−2.09892e91			−0.435179			−0.217589	+	0.976040i	$0.569819\pi$
$734$		−	8.97248e91i		−	1.78090i
$735$	2.32206e91	+	1.47504e91i	0.441244	+	0.280291i
$736$	−3.30234e90			−0.0600803
$737$			3.90959e91i			0.681038i
$738$	−1.03772e91	−	2.21027e91i	−0.173092	−	0.368673i
$739$	−2.38419e91			−0.380819			−0.190409	−	0.981705i	$-0.560982\pi$
$739$	−2.38419e91			−0.380819			−0.190409	+	0.981705i	$0.560982\pi$
$740$			2.83251e90i			0.0433268i
$741$	−3.77108e90	+	5.93655e90i	−0.0552437	+	0.0869664i
$742$	−9.10139e91			−1.27698
$743$			5.70479e90i			0.0766651i	0.999265	+	0.0383326i	$0.0122046\pi$
$743$			5.70479e90i			0.0766651i	−0.999265	+	0.0383326i	$0.987795\pi$
$744$	−1.93481e91	−	1.22905e91i	−0.249061	−	0.158211i
$745$	−1.17750e92			−1.45198
$746$		−	2.40762e91i		−	0.284411i
$747$	−7.61891e91	+	3.57708e91i	−0.862251	+	0.404827i
$748$	7.05311e90			0.0764768
$749$			2.41377e90i			0.0250771i
$750$	1.81364e92	−	2.85509e92i	1.80547	−	2.84223i
$751$	6.71100e90			0.0640190			0.0320095	−	0.999488i	$-0.489809\pi$
$751$	6.71100e90			0.0640190			0.0320095	+	0.999488i	$0.489809\pi$
$752$			1.34996e92i			1.23410i
$753$	4.14208e89	+	2.63117e89i	0.00362893	+	0.00230521i
$754$	−1.06605e91			−0.0895147
$755$		−	1.64737e92i		−	1.32584i
$756$	8.07835e90	+	1.03127e90i	0.0623197	+	0.00795560i
$757$	1.48031e92			1.09467			0.547336	−	0.836913i	$-0.315642\pi$
$757$	1.48031e92			1.09467			0.547336	+	0.836913i	$0.315642\pi$
$758$			1.68915e92i			1.19744i
$759$	1.76037e91	−	2.77123e91i	0.119637	−	0.188337i
$760$	−3.02630e91			−0.197186
$761$		−	2.23825e92i		−	1.39830i	−0.714976	−	0.699149i	$-0.753562\pi$
$761$		−	2.23825e92i		−	1.39830i	0.714976	−	0.699149i	$-0.246438\pi$
$762$	5.33691e91	+	3.39017e91i	0.319691	+	0.203078i
$763$	−7.08519e91			−0.406973
$764$			1.48694e90i			0.00819044i
$765$	2.94106e92	+	6.26424e92i	1.55360	+	3.30905i
$766$	−2.34057e92			−1.18577
$767$			2.69587e92i			1.30993i
$768$	−2.52809e91	+	3.97980e91i	−0.117824	+	0.185482i
$769$	1.33361e92			0.596194			0.298097	−	0.954536i	$-0.403648\pi$
$769$	1.33361e92			0.596194			0.298097	+	0.954536i	$0.403648\pi$
$770$		−	2.16193e92i		−	0.927126i
$771$	−1.61213e92	−	1.02408e92i	−0.663225	−	0.421301i
$772$	−2.67656e89			−0.00105639
$773$		−	1.54232e92i		−	0.584024i	−0.956415	−	0.292012i	$-0.905675\pi$
$773$		−	1.54232e92i		−	0.584024i	0.956415	−	0.292012i	$-0.0943247\pi$
$774$	−1.65334e92	+	7.76244e91i	−0.600692	+	0.282025i
$775$	2.37321e92			0.827334
$776$		−	5.20916e91i		−	0.174258i
$777$	−4.36421e91	+	6.87028e91i	−0.140098	+	0.220547i
$778$	4.05341e92			1.24874
$779$		−	1.42148e91i		−	0.0420282i
$780$	−4.05504e91	−	2.57589e91i	−0.115072	−	0.0730971i
$781$	−1.38180e92			−0.376368
$782$			3.08235e92i			0.805870i
$783$	−4.52366e90	+	3.54358e91i	−0.0113531	+	0.0889336i
$784$	1.20633e92			0.290637
$785$		−	8.61837e91i		−	0.199341i
$786$	−1.36712e92	+	2.15217e92i	−0.303589	+	0.477920i
$787$	−3.00831e92			−0.641404			−0.320702	−	0.947180i	$-0.603919\pi$
$787$	−3.00831e92			−0.641404			−0.320702	+	0.947180i	$0.603919\pi$
$788$			4.59251e91i			0.0940180i
$789$	−6.01744e92	−	3.82246e92i	−1.18290	−	0.751414i
$790$	2.32010e91			0.0437966
$791$		−	5.46035e91i		−	0.0989859i
$792$	−1.27899e92	−	2.72415e92i	−0.222670	−	0.474270i
$793$	−7.06672e92			−1.18161
$794$			5.45080e92i			0.875395i
$795$	9.64666e92	−	1.51861e93i	1.48809	−	2.34260i
$796$	−8.52788e91			−0.126364
$797$		−	3.79850e92i		−	0.540687i	−0.962764	−	0.270343i	$-0.912863\pi$
$797$		−	3.79850e92i		−	0.540687i	0.962764	−	0.270343i	$-0.0871372\pi$
$798$	5.83480e91	+	3.70644e91i	0.0797872	+	0.0506833i
$799$	1.67322e93			2.19814
$800$		−	3.13413e92i		−	0.395582i
$801$	−1.15975e93	+	5.44504e92i	−1.40645	+	0.660329i
$802$	8.72876e92			1.01712
$803$		−	1.08224e92i		−	0.121179i
$804$	4.57834e91	−	7.20737e91i	0.0492623	−	0.0775502i
$805$	6.48005e92			0.670055
$806$		−	3.08847e92i		−	0.306918i
$807$	−1.45694e93	−	9.25492e92i	−1.39152	−	0.883933i
$808$	−7.32799e92			−0.672700
$809$		−	8.20725e92i		−	0.724177i	−0.932144	−	0.362089i	$-0.882064\pi$
$809$		−	8.20725e92i		−	0.724177i	0.932144	−	0.362089i	$-0.117936\pi$
$810$	−1.49929e93	+	1.80591e93i	−1.27164	+	1.53171i
$811$	−6.63964e92			−0.541349			−0.270674	−	0.962671i	$-0.587247\pi$
$811$	−6.63964e92			−0.541349			−0.270674	+	0.962671i	$0.587247\pi$
$812$			7.18629e90i			0.00563264i
$813$	3.04719e92	−	4.79699e92i	0.229616	−	0.361469i
$814$	−2.39084e92			−0.173208
$815$			4.21008e93i			2.93256i
$816$	2.56152e93	+	1.62716e93i	1.71559	+	1.08980i
$817$	−1.06330e92			−0.0684780
$818$			5.23524e91i			0.0324213i
$819$	−5.86673e92	−	1.24957e93i	−0.349391	−	0.744176i
$820$	9.70959e91			0.0556106
$821$		−	2.20446e93i		−	1.21428i	−0.794593	−	0.607142i	$-0.792316\pi$
$821$		−	2.20446e93i		−	1.21428i	0.794593	−	0.607142i	$-0.207684\pi$
$822$	−2.36882e91	+	3.72907e91i	−0.0125497	+	0.0197562i
$823$	6.10757e92			0.311224			0.155612	−	0.987818i	$-0.450265\pi$
$823$	6.10757e92			0.311224			0.155612	+	0.987818i	$0.450265\pi$
$824$			1.39401e93i			0.683276i
$825$	2.63007e93	+	1.67070e93i	1.24005	+	0.787720i
$826$	2.64966e93			1.20179
$827$			3.53510e93i			1.54250i	0.636531	+	0.771251i	$0.280369\pi$
$827$			3.53510e93i			1.54250i	−0.636531	+	0.771251i	$0.719631\pi$
$828$	−6.49052e91	+	3.04730e91i	−0.0272464	+	0.0127922i
$829$	−1.81199e93			−0.731829			−0.365915	−	0.930648i	$-0.619244\pi$
$829$	−1.81199e93			−0.731829			−0.365915	+	0.930648i	$0.619244\pi$
$830$		−	4.87992e93i		−	1.89633i
$831$	−3.68374e92	+	5.79906e92i	−0.137739	+	0.216833i
$832$	2.45297e93			0.882564
$833$		−	1.49519e93i		−	0.517674i
$834$	−9.08849e92	−	5.77329e92i	−0.302816	−	0.192358i
$835$	−6.96796e93			−2.23428
$836$			1.39264e91i			0.00429770i
$837$	−1.02662e93	−	1.31056e92i	−0.304925	−	0.0389261i
$838$	2.43846e93			0.697118
$839$		−	1.66799e93i		−	0.458998i	−0.973309	−	0.229499i	$-0.926291\pi$
$839$		−	1.66799e93i		−	0.458998i	0.973309	−	0.229499i	$-0.0737088\pi$
$840$	3.18499e93	−	5.01390e93i	0.843666	−	1.32812i
$841$	3.89015e93			0.991962
$842$			1.38863e93i			0.340878i
$843$	1.87781e93	+	1.19284e93i	0.443782	+	0.281904i
$844$	5.15438e92			0.117279
$845$		−	6.27131e92i		−	0.137386i
$846$	2.41185e93	+	5.13706e93i	0.508744	+	1.08359i
$847$	−2.94903e93			−0.598977
$848$		−	7.88927e93i		−	1.54301i
$849$	−2.00094e93	+	3.14995e93i	−0.376868	+	0.593277i
$850$	−2.92533e94			−5.30603
$851$		−	7.16616e92i		−	0.125182i
$852$	2.54737e92	+	1.61817e92i	0.0428572	+	0.0272242i
$853$	4.88530e93			0.791630			0.395815	−	0.918330i	$-0.370462\pi$
$853$	4.88530e93			0.791630			0.395815	+	0.918330i	$0.370462\pi$
$854$			6.94560e93i			1.08407i
$855$	−1.23687e93	+	5.80712e92i	−0.185956	+	0.0873063i
$856$	−1.94807e92			−0.0282127
$857$		−	8.38821e93i		−	1.17026i	−0.810939	−	0.585131i	$-0.801043\pi$
$857$		−	8.38821e93i		−	1.17026i	0.810939	−	0.585131i	$-0.198957\pi$
$858$	2.17423e93	−	3.42274e93i	0.292222	−	0.460025i
$859$	7.79141e93			1.00887			0.504435	−	0.863450i	$-0.331701\pi$
$859$	7.79141e93			1.00887			0.504435	+	0.863450i	$0.331701\pi$
$860$		−	7.26304e92i		−	0.0906083i
$861$	2.35507e93	+	1.49601e93i	0.283076	+	0.179819i
$862$	−2.96284e93			−0.343144
$863$			1.08047e94i			1.20578i	0.797824	+	0.602891i	$0.205985\pi$
$863$			1.08047e94i			1.20578i	−0.797824	+	0.602891i	$0.794015\pi$
$864$	−1.73076e92	+	1.35578e93i	−0.0186122	+	0.145797i
$865$	2.32290e94			2.40721
$866$			3.74586e92i			0.0374092i
$867$	1.45969e94	−	2.29790e94i	1.40492	−	2.21167i
$868$	−2.08195e92			−0.0193125
$869$			1.34314e92i			0.0120085i
$870$	−1.74826e93	−	1.11055e93i	−0.150658	−	0.0957023i
$871$	−1.44734e94			−1.20223
$872$		−	5.71822e93i		−	0.457861i
$873$	−9.99580e92	−	2.12903e93i	−0.0771546	−	0.164333i
$874$	−6.08609e92			−0.0452869
$875$			3.86491e94i			2.77257i
$876$	−1.26736e92	+	1.99512e92i	−0.00876536	+	0.0137987i
$877$	−6.87049e92			−0.0458143			−0.0229071	−	0.999738i	$-0.507292\pi$
$877$	−6.87049e92			−0.0458143			−0.0229071	+	0.999738i	$0.507292\pi$
$878$			2.73357e94i			1.75754i
$879$	−2.40263e93	−	1.52622e93i	−0.148951	−	0.0946180i
$880$	1.87401e94			1.12028
$881$			1.50103e93i			0.0865288i	0.999064	+	0.0432644i	$0.0137758\pi$
$881$			1.50103e93i			0.0865288i	−0.999064	+	0.0432644i	$0.986224\pi$
$882$	4.59049e93	−	2.15524e93i	0.255190	−	0.119812i
$883$	−1.42363e94			−0.763227			−0.381614	−	0.924322i	$-0.624632\pi$
$883$	−1.42363e94			−0.763227			−0.381614	+	0.924322i	$0.624632\pi$
$884$			2.61107e93i			0.135004i
$885$	−2.80841e94	+	4.42108e94i	−1.40048	+	2.20467i
$886$	1.06311e94			0.511325
$887$		−	1.89377e94i		−	0.878558i	−0.898351	−	0.439279i	$-0.855234\pi$
$887$		−	1.89377e94i		−	0.878558i	0.898351	−	0.439279i	$-0.144766\pi$
$888$	−5.54478e93	−	3.52221e93i	−0.248124	−	0.157616i
$889$	−7.22453e93			−0.311856
$890$		−	7.42823e94i		−	3.09318i
$891$	−1.04547e94	−	8.67962e93i	−0.419977	−	0.348670i
$892$	3.10123e93			0.120187
$893$			3.30376e93i			0.123527i
$894$	−1.16390e94	+	1.83225e94i	−0.419871	+	0.660974i
$895$	8.21081e94			2.85791
$896$		−	2.78431e94i		−	0.935109i
$897$	1.02591e94	+	6.51692e93i	0.332470	+	0.211195i
$898$	−3.52263e94			−1.10160
$899$		−	9.13251e92i		−	0.0275601i
$900$	−2.89207e93	−	6.15990e93i	−0.0842266	−	0.179396i
$901$	−9.77842e94			−2.74837
$902$			8.19558e93i			0.222316i
$903$	1.11906e94	−	1.76166e94i	0.292985	−	0.461226i
$904$	4.40687e93			0.111363
$905$		−	2.59519e94i		−	0.633016i
$906$	−2.56340e94	−	1.62835e94i	−0.603551	−	0.383394i
$907$	7.60067e94			1.72750			0.863751	−	0.503919i	$-0.168109\pi$
$907$	7.60067e94			1.72750			0.863751	+	0.503919i	$0.168109\pi$
$908$			1.74250e93i			0.0382318i
$909$	−2.99502e94	+	1.40616e94i	−0.634388	+	0.297845i
$910$	8.00351e94			1.63665
$911$		−	2.57568e93i		−	0.0508515i	−0.999677	−	0.0254257i	$-0.991906\pi$
$911$		−	2.57568e93i		−	0.0508515i	0.999677	−	0.0254257i	$-0.00809414\pi$
$912$	−3.21282e93	+	5.05773e93i	−0.0612424	+	0.0964096i
$913$	2.82506e94			0.519951
$914$			4.79541e94i			0.852211i
$915$	−1.15890e95	−	7.36172e94i	−1.98872	−	1.26329i
$916$	4.84131e93			0.0802246
$917$		−	2.91338e94i		−	0.466206i
$918$	1.26546e95	+	1.61546e94i	1.95561	+	0.249649i
$919$	−3.80796e94			−0.568323			−0.284162	−	0.958776i	$-0.591715\pi$
$919$	−3.80796e94			−0.568323			−0.284162	+	0.958776i	$0.591715\pi$
$920$			5.22984e94i			0.753837i
$921$	−4.60806e94	+	7.25415e94i	−0.641520	+	1.00990i
$922$	−1.21792e95			−1.63768
$923$		−	5.11545e94i		−	0.664400i
$924$	−2.30729e93	−	1.46566e93i	−0.0289467	−	0.0183878i
$925$	6.80112e94			0.824224
$926$			1.47200e95i			1.72328i
$927$	2.67496e94	+	5.69745e94i	0.302528	+	0.644361i
$928$	−1.20607e93			−0.0131776
$929$			6.14225e94i			0.648373i	0.945993	+	0.324186i	$0.105091\pi$
$929$			6.14225e94i			0.648373i	−0.945993	+	0.324186i	$0.894909\pi$
$930$	3.21740e94	−	5.06492e94i	0.328133	−	0.516557i
$931$	2.95225e93			0.0290913
$932$		−	6.76854e93i		−	0.0644445i
$933$	6.47530e94	+	4.11331e94i	0.595727	+	0.378424i
$934$	1.37188e94			0.121960
$935$		−	2.32275e95i		−	1.99541i
$936$	1.00849e95	−	4.73484e94i	0.837226	−	0.393078i
$937$	1.41423e94			0.113463			0.0567314	−	0.998389i	$-0.481932\pi$
$937$	1.41423e94			0.113463			0.0567314	+	0.998389i	$0.481932\pi$
$938$			1.42253e95i			1.10299i
$939$	−4.68810e94	+	7.38015e94i	−0.351316	+	0.553052i
$940$	−2.25668e94			−0.163448
$941$			3.82385e94i			0.267691i	0.991002	+	0.133845i	$0.0427325\pi$
$941$			3.82385e94i			0.267691i	−0.991002	+	0.133845i	$0.957267\pi$
$942$	−1.34106e94	−	8.51885e93i	−0.0907445	−	0.0576437i
$943$	−2.45650e94			−0.160673
$944$			2.29678e95i			1.45217i
$945$	3.39620e94	−	2.66039e95i	0.207575	−	1.62603i
$946$	6.13052e94			0.362227
$947$			5.16290e93i			0.0294913i	0.999891	+	0.0147457i	$0.00469386\pi$
$947$			5.16290e93i			0.0294913i	−0.999891	+	0.0147457i	$0.995306\pi$
$948$	1.57289e92	−	2.47610e92i	0.000868625	−	0.00136742i
$949$	4.00647e94			0.213916
$950$		−	5.77607e94i		−	0.298179i
$951$	1.04240e95	+	6.62167e94i	0.520307	+	0.330515i
$952$	−3.22849e95			−1.55818
$953$		−	3.74439e95i		−	1.74747i	−0.486406	−	0.873733i	$-0.661692\pi$
$953$		−	3.74439e95i		−	1.74747i	0.486406	−	0.873733i	$-0.338308\pi$
$954$	−1.40951e95	−	3.00214e95i	−0.636091	−	1.35483i
$955$	4.89686e94			0.213702
$956$			5.65527e93i			0.0238672i
$957$	6.42914e93	−	1.01210e94i	0.0262404	−	0.0413085i
$958$	−3.32687e95			−1.31323
$959$		−	5.04802e93i		−	0.0192720i
$960$	4.02274e95	+	2.55537e95i	1.48540	+	0.943570i
$961$	−2.53536e95			−0.905505
$962$		−	8.85092e94i		−	0.305764i
$963$	−7.96195e93	+	3.73813e93i	−0.0266059	+	0.0124915i
$964$	2.87489e94			0.0929300
$965$			8.81455e93i			0.0275630i
$966$	6.40522e94	−	1.00833e95i	0.193761	−	0.305024i
$967$	−3.46601e95			−1.01434			−0.507169	−	0.861847i	$-0.669308\pi$
$967$	−3.46601e95			−1.01434			−0.507169	+	0.861847i	$0.669308\pi$
$968$		−	2.38007e95i		−	0.673872i
$969$	6.26884e94	+	3.98216e94i	0.171722	+	0.109083i
$970$	1.36365e95			0.361415
$971$			5.65920e95i			1.45124i	0.688095	+	0.725621i	$0.258447\pi$
$971$			5.65920e95i			1.45124i	−0.688095	+	0.725621i	$0.741553\pi$
$972$	9.10903e93	+	2.82440e94i	0.0226023	+	0.0700819i
$973$	1.23030e95			0.295394
$974$		−	6.92737e95i		−	1.60947i
$975$	−6.18496e95	+	9.73655e95i	−1.39056	+	2.18906i
$976$	−6.02059e95			−1.30992
$977$			3.99920e95i			0.842069i	0.907045	+	0.421034i	$0.138333\pi$
$977$			3.99920e95i			0.842069i	−0.907045	+	0.421034i	$0.861667\pi$
$978$	6.55110e95	+	4.16146e95i	1.33497	+	0.848013i
$979$	4.30031e95			0.848113
$980$			2.01658e94i			0.0384929i
$981$	−1.09726e95	−	2.33709e95i	−0.202723	−	0.431784i
$982$	1.03741e96			1.85516
$983$		−	1.08763e96i		−	1.88264i	−0.337512	−	0.941321i	$-0.609585\pi$
$983$		−	1.08763e96i		−	1.88264i	0.337512	−	0.941321i	$-0.390415\pi$
$984$	−1.20738e95	+	1.90070e95i	−0.202303	+	0.318472i
$985$	1.51242e96			2.45309
$986$			1.12572e95i			0.176754i
$987$	−5.47361e95	−	3.47700e95i	−0.832003	−	0.528514i
$988$	−5.15556e93			−0.00758671
$989$			1.83753e95i			0.261790i
$990$	7.13125e95	−	3.34812e95i	0.983648	−	0.461823i
$991$	−4.08828e95			−0.545989			−0.272995	−	0.962016i	$-0.588014\pi$
$991$	−4.08828e95			−0.545989			−0.272995	+	0.962016i	$0.588014\pi$
$992$		−	3.49412e94i		−	0.0451818i
$993$	3.62196e95	−	5.70181e95i	0.453490	−	0.713899i
$994$	−5.02778e95			−0.609553
$995$			2.80843e96i			3.29705i
$996$	−5.20802e94	−	3.30830e94i	−0.0592071	−	0.0376102i
$997$	−2.98957e95			−0.329127			−0.164563	−	0.986366i	$-0.552622\pi$
$997$	−2.98957e95			−0.329127			−0.164563	+	0.986366i	$0.552622\pi$
$998$		−	1.60820e95i		−	0.171459i
$999$	−2.94207e95	−	3.75579e94i	−0.303779	−	0.0387798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.65.b.a.2.5	✓	20
3.2	odd	2	inner	3.65.b.a.2.16	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.65.b.a.2.5	✓	20	1.1	even	1	trivial
3.65.b.a.2.16	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)

\(f(q)\)	\(=\)	\(q-4.45029e9i q^{2} +(-9.93580e14 + 1.56412e15i) q^{3} -1.35835e18 q^{4} +4.47337e22i q^{5} +(6.96081e24 + 4.42172e24i) q^{6} -9.42280e26 q^{7} -7.60483e28i q^{8} +(-1.45928e30 - 3.10816e30i) q^{9} +O(q^{10})\)	\(q-4.45029e9i q^{2} +(-9.93580e14 + 1.56412e15i) q^{3} -1.35835e18 q^{4} +4.47337e22i q^{5} +(6.96081e24 + 4.42172e24i) q^{6} -9.42280e26 q^{7} -7.60483e28i q^{8} +(-1.45928e30 - 3.10816e30i) q^{9} +1.99078e32 q^{10} +1.15249e33i q^{11} +(1.34963e33 - 2.12463e33i) q^{12} -4.26655e35 q^{13} +4.19342e36i q^{14} +(-6.99691e37 - 4.44465e37i) q^{15} -3.63494e38 q^{16} +4.50536e39i q^{17} +(-1.38322e40 + 6.49423e39i) q^{18} -8.89583e39 q^{19} -6.07642e40i q^{20} +(9.36230e41 - 1.47384e42i) q^{21} +5.12893e42 q^{22} +1.53732e43i q^{23} +(1.18949e44 + 7.55601e43i) q^{24} -1.45901e45 q^{25} +1.89874e45i q^{26} +(6.31147e45 + 8.05709e44i) q^{27} +1.27995e45 q^{28} +5.61451e45i q^{29} +(-1.97800e47 + 3.11383e47i) q^{30} -1.62659e47 q^{31} +2.14812e47i q^{32} +(-1.80264e48 - 1.14509e48i) q^{33} +2.00502e49 q^{34} -4.21517e49i q^{35} +(1.98222e48 + 4.22198e48i) q^{36} -4.66147e49 q^{37} +3.95890e49i q^{38} +(4.23915e50 - 6.67341e50i) q^{39} +3.40193e51 q^{40} +1.59791e51i q^{41} +(-6.55903e51 - 4.16650e51i) q^{42} +1.19528e52 q^{43} -1.56549e51i q^{44} +(1.39040e53 - 6.52792e52i) q^{45} +6.84151e52 q^{46} -3.71384e53i q^{47} +(3.61161e53 - 5.68550e53i) q^{48} -3.31869e53 q^{49} +6.49301e54i q^{50} +(-7.04694e54 - 4.47644e54i) q^{51} +5.79548e53 q^{52} +2.17040e55i q^{53} +(3.58564e54 - 2.80879e55i) q^{54} -5.15553e55 q^{55} +7.16588e55i q^{56} +(8.83871e54 - 1.39142e55i) q^{57} +2.49862e55 q^{58} -6.31862e56i q^{59} +(9.50428e55 + 6.03741e55i) q^{60} +1.65631e57 q^{61} +7.23880e56i q^{62} +(1.37505e57 + 2.92876e57i) q^{63} -5.74931e57 q^{64} -1.90859e58i q^{65} +(-5.09600e57 + 8.02228e57i) q^{66} +3.39229e58 q^{67} -6.11987e57i q^{68} +(-2.40455e58 - 1.52745e58i) q^{69} -1.87587e59 q^{70} +1.19897e59i q^{71} +(-2.36371e59 + 1.10976e59i) q^{72} -9.39044e58 q^{73} +2.07449e59i q^{74} +(1.44964e60 - 2.28207e60i) q^{75} +1.20837e58 q^{76} -1.08597e60i q^{77} +(-2.96986e60 - 1.88655e60i) q^{78} +1.16542e59 q^{79} -1.62605e61i q^{80} +(-7.53117e60 + 9.07138e60i) q^{81} +7.11118e60 q^{82} -2.45126e61i q^{83} +(-1.27173e60 + 2.00200e60i) q^{84} -2.01542e62 q^{85} -5.31936e61i q^{86} +(-8.78180e60 - 5.57847e60i) q^{87} +8.76452e61 q^{88} -3.73131e62i q^{89} +(-2.90511e62 - 6.18768e62i) q^{90} +4.02028e62 q^{91} -2.08822e61i q^{92} +(1.61615e62 - 2.54419e62i) q^{93} -1.65277e63 q^{94} -3.97944e62i q^{95} +(-3.35993e62 - 2.13433e62i) q^{96} +6.84980e62 q^{97} +1.47691e63i q^{98} +(3.58214e63 - 1.68181e63i) 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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