LMFDB - Embedded newform 3.65.b.a.2.2

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			2.2
Root			$-1.17774e9i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.65.b.a.2.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.06644e9i q^{2} +(-1.85210e15 - 5.82746e13i) q^{3} -3.14879e19 q^{4} -1.76003e22i q^{5} +(-4.11794e23 + 1.30878e25i) q^{6} -6.88028e26 q^{7} +9.21545e28i q^{8} +(3.42689e30 + 2.15861e29i) q^{9} +O(q^{10})$	\(q-7.06644e9i q^{2} +(-1.85210e15 - 5.82746e13i) q^{3} -3.14879e19 q^{4} -1.76003e22i q^{5} +(-4.11794e23 + 1.30878e25i) q^{6} -6.88028e26 q^{7} +9.21545e28i q^{8} +(3.42689e30 + 2.15861e29i) q^{9} -1.24372e32 q^{10} +3.27443e33i q^{11} +(5.83188e34 + 1.83494e33i) q^{12} -2.24307e35 q^{13} +4.86191e36i q^{14} +(-1.02565e36 + 3.25976e37i) q^{15} +7.03557e37 q^{16} -2.36955e39i q^{17} +(1.52537e39 - 2.42159e40i) q^{18} +1.24001e41 q^{19} +5.54197e41i q^{20} +(1.27430e42 + 4.00945e40i) q^{21} +2.31386e43 q^{22} +8.69868e42i q^{23} +(5.37027e42 - 1.70680e44i) q^{24} +2.32330e44 q^{25} +1.58506e45i q^{26} +(-6.33438e45 - 5.99498e44i) q^{27} +2.16645e46 q^{28} -3.59991e46i q^{29} +(2.30349e47 + 7.24771e45i) q^{30} +8.41027e47 q^{31} +1.20279e48i q^{32} +(1.90816e47 - 6.06459e48i) q^{33} -1.67443e49 q^{34} +1.21095e49i q^{35} +(-1.07906e50 - 6.79701e48i) q^{36} +1.15440e50 q^{37} -8.76244e50i q^{38} +(4.15441e50 + 1.30714e49i) q^{39} +1.62195e51 q^{40} -5.56698e51i q^{41} +(2.83326e50 - 9.00476e51i) q^{42} -1.84892e52 q^{43} -1.03105e53i q^{44} +(3.79922e51 - 6.03144e52i) q^{45} +6.14687e52 q^{46} -8.60352e52i q^{47} +(-1.30306e53 - 4.09995e51i) q^{48} -7.46378e53 q^{49} -1.64175e54i q^{50} +(-1.38085e53 + 4.38865e54i) q^{51} +7.06297e54 q^{52} +2.63619e55i q^{53} +(-4.23632e54 + 4.47615e55i) q^{54} +5.76311e55 q^{55} -6.34048e55i q^{56} +(-2.29662e56 - 7.22609e54i) q^{57} -2.54386e56 q^{58} +5.74665e56i q^{59} +(3.22956e55 - 1.02643e57i) q^{60} +2.11842e57 q^{61} -5.94307e57i q^{62} +(-2.35780e57 - 1.48518e56i) q^{63} +9.79725e57 q^{64} +3.94788e57i q^{65} +(-4.28551e58 - 1.34839e57i) q^{66} -8.44916e57 q^{67} +7.46121e58i q^{68} +(5.06912e56 - 1.61109e58i) q^{69} +8.55711e58 q^{70} +1.22668e59i q^{71} +(-1.98926e58 + 3.15804e59i) q^{72} +1.04982e59 q^{73} -8.15749e59i q^{74} +(-4.30299e59 - 1.35389e58i) q^{75} -3.90452e60 q^{76} -2.25290e60i q^{77} +(9.23685e58 - 2.93569e60i) q^{78} -3.38074e60 q^{79} -1.23828e60i q^{80} +(1.16970e61 + 1.47947e60i) q^{81} -3.93387e61 q^{82} +2.79817e61i q^{83} +(-4.01250e61 - 1.26249e60i) q^{84} -4.17048e61 q^{85} +1.30653e62i q^{86} +(-2.09783e60 + 6.66741e61i) q^{87} -3.01754e62 q^{88} -3.41392e62i q^{89} +(-4.26208e62 - 2.68470e61i) q^{90} +1.54330e62 q^{91} -2.73903e62i q^{92} +(-1.55767e63 - 4.90105e61i) q^{93} -6.07963e62 q^{94} -2.18245e63i q^{95} +(7.00919e61 - 2.22768e63i) q^{96} +4.56300e63 q^{97} +5.27424e63i q^{98} +(-7.06823e62 + 1.12211e64i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14\!\cdots\!92 q^{3}+ \cdots - 22\!\cdots\!00 q^{9}+O(q^{10}) $ 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9	$ 20 q - 14\!\cdots\!92 q^{3}+ \cdots + 31\!\cdots\!00 q^{99}+O(q^{100}) $ 20 * q - 1420757969558292 * q^3 - 157501780884986390320 * q^4 - 7007663926080441102858480 * q^6 + 682116984600047763945825976 * q^7 - 2289432393664418080316877857100 * q^9 + 331029217205387677806996511116000 * q^10 + 6534659062821156745233165595144848 * q^12 - 751508903297384088692483175344422424 * q^13 + 38547509823020584674418593740816815200 * q^15 + 333898239622199115079798041399657464960 * q^16 - 3676009515412490831675032229198156934240 * q^18 + 109286088964872656413026262415428611794200 * q^19 - 1311511276150890256934838463853331394769880 * q^21 - 8079025213365934710514462143494926255299360 * q^22 + 371409898348173331095205935880826344773509760 * q^24 - 1408933246315215357541047632909406493714979500 * q^25 + 5130931947084052629864823829892614277399503148 * q^27 - 38556600155873290275414028639950032296787869664 * q^28 - 141541842553229550692763020870574637255687216800 * q^30 + 458034135616019870141982361360522347620359726840 * q^31 - 2882270174679362228632701138961802589863549285280 * q^33 - 787058086714062550476148644876342688312553235840 * q^34 + 75759088962200911205216155020070755577873854233040 * q^36 - 167241277488128791881901510734045117370850836062104 * q^37 + 458879560232529079697344976545706436533594974010520 * q^39 - 3172271879697225400792978571433360199916055661804800 * q^40 - 22013931366996449796115743111552261520406610644630880 * q^42 + 10353394041775726307362489381794503494462017586072216 * q^43 + 37622210359250231761078599539977430954460378542462400 * q^45 - 297398119355935548173345475928562088559055731847559360 * q^46 - 127296049249148961420276393789708282996205874832565632 * q^48 + 2035505279477569607000808808313462872867812749377748220 * q^49 - 8993599813445960529795685588193052695282052910939102080 * q^51 + 12450863873285726446941747254985680826918117392844470176 * q^52 + 1380721489513428759527937305946915244571081819618418480 * q^54 + 86716751505127419669577189864656813143075791367545723200 * q^55 - 410655148353071807815217561752202738362370559954491547384 * q^57 + 1171127646996109205778370152132525033757099595854063443360 * q^58 - 4554593355431768584543074712701226261422872417617275398400 * q^60 + 4552152490922647485493920930203353370116723196876970427240 * q^61 - 18340670222945277450481852597884877177550760958776639152904 * q^63 + 30281219638275425893507737167512138061029087969644636247040 * q^64 - 73446637659820047047259347339723389117534541697924310768800 * q^66 + 108802231400777081380268556166029877921173626685759369971416 * q^67 - 255718829710356626829923504360603133388502621634044634870720 * q^69 + 559303866272797397220431985027879540776975892234361655006400 * q^70 - 561110698242036073669580259260779527574289380077856046595840 * q^72 - 569085806526237236378057540729119438030642048917813502604504 * q^73 + 2290039066363366330022806756651688579736177808604861676211500 * q^75 - 5532330994825480968263901289000933629970925314426608479594720 * q^76 + 9655803402636036605327159547820723686984585271634655943687200 * q^78 - 22640121063621617622122249693012788180804867706114977596801800 * q^79 + 37075761484886132865783336331999338158569856937859957696374420 * q^81 - 69993225281309073377388502634775301823581628014590259964399040 * q^82 + 62923532655099413129084384942812878939798728172266572844745120 * q^84 - 142181474118416523657627044760532405955688084516779285440262400 * q^85 + 23785411541262749066239132616113250012236593481925882591047200 * q^87 + 345107275964501391166111220047509272448066379695588836103893760 * q^88 - 1925479853343216377261941955721474942915647264800935046773530400 * q^90 + 1225124508801982757577911377627409097047306370806522445345728240 * q^91 - 2776404525956613483290023288082668840477640965472850083253548184 * q^93 + 1658662465458978832407333757013771498132481417946327912207224960 * q^94 - 3771017263293375391290634333996451541183976624371029742095907840 * q^96 + 818755932265886448325223871671724131911117159175492830487918056 * q^97 + 3118093180125811439250837213823663221313339534064003298574718400 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	7.06644e9i		−	1.64528i	−0.568559	−	0.822642i	$-0.692499\pi$
$2$		−	7.06644e9i		−	1.64528i	0.568559	−	0.822642i	$-0.307501\pi$
$3$	−1.85210e15	−	5.82746e13i	−0.999505	−	0.0314484i
$3$	−1.85210e15	−	5.82746e13i	−0.999505	−	0.0314484i
$4$	−3.14879e19			−1.70696
$5$		−	1.76003e22i		−	0.755928i	−0.925820	−	0.377964i	$-0.876624\pi$
$5$		−	1.76003e22i		−	0.755928i	0.925820	−	0.377964i	$-0.123376\pi$
$6$	−4.11794e23	+	1.30878e25i	−0.0517416	+	1.64447i
$7$	−6.88028e26			−0.622972			−0.311486	−	0.950251i	$-0.600827\pi$
$7$	−6.88028e26			−0.622972			−0.311486	+	0.950251i	$0.600827\pi$
$8$			9.21545e28i			1.16315i
$9$	3.42689e30	+	2.15861e29i	0.998022	+	0.0628658i
$10$	−1.24372e32			−1.24372
$11$			3.27443e33i			1.55085i	0.631438	+	0.775426i	$0.282465\pi$
$11$			3.27443e33i			1.55085i	−0.631438	+	0.775426i	$0.717535\pi$
$12$	5.83188e34	+	1.83494e33i	1.70612	+	0.0536813i
$13$	−2.24307e35			−0.506590			−0.253295	−	0.967389i	$-0.581514\pi$
$13$	−2.24307e35			−0.506590			−0.253295	+	0.967389i	$0.581514\pi$
$14$			4.86191e36i			1.02497i
$15$	−1.02565e36	+	3.25976e37i	−0.0237728	+	0.755554i
$16$	7.03557e37			0.206757
$17$		−	2.36955e39i		−	1.00069i	−0.865826	−	0.500346i	$-0.833206\pi$
$17$		−	2.36955e39i		−	1.00069i	0.865826	−	0.500346i	$-0.166794\pi$
$18$	1.52537e39	−	2.42159e40i	0.103432	−	1.64203i
$19$	1.24001e41			1.49042			0.745210	−	0.666830i	$-0.232349\pi$
$19$	1.24001e41			1.49042			0.745210	+	0.666830i	$0.232349\pi$
$20$			5.54197e41i			1.29034i
$21$	1.27430e42	+	4.00945e40i	0.622664	+	0.0195915i
$22$	2.31386e43			2.55159
$23$			8.69868e42i			0.231293i	0.993290	+	0.115646i	$0.0368940\pi$
$23$			8.69868e42i			0.231293i	−0.993290	+	0.115646i	$0.963106\pi$
$24$	5.37027e42	−	1.70680e44i	0.0365794	−	1.16258i
$25$	2.32330e44			0.428573
$26$			1.58506e45i			0.833485i
$27$	−6.33438e45	−	5.99498e44i	−0.995551	−	0.0942209i
$28$	2.16645e46			1.06339
$29$		−	3.59991e46i		−	0.574852i	−0.957803	−	0.287426i	$-0.907200\pi$
$29$		−	3.59991e46i		−	0.574852i	0.957803	−	0.287426i	$-0.0927995\pi$
$30$	2.30349e47	+	7.24771e45i	1.24310	+	0.0391129i
$31$	8.41027e47			1.58941			0.794705	−	0.606996i	$-0.207626\pi$
$31$	8.41027e47			1.58941			0.794705	+	0.606996i	$0.207626\pi$
$32$			1.20279e48i			0.822980i
$33$	1.90816e47	−	6.06459e48i	0.0487719	−	1.55008i
$34$	−1.67443e49			−1.64642
$35$			1.21095e49i			0.470922i
$36$	−1.07906e50	−	6.79701e48i	−1.70359	−	0.107309i
$37$	1.15440e50			0.758404			0.379202	−	0.925314i	$-0.376199\pi$
$37$	1.15440e50			0.758404			0.379202	+	0.925314i	$0.376199\pi$
$38$		−	8.76244e50i		−	2.45217i
$39$	4.15441e50	+	1.30714e49i	0.506339	+	0.0159315i
$40$	1.62195e51			0.879260
$41$		−	5.56698e51i		−	1.36942i	−0.728816	−	0.684709i	$-0.759929\pi$
$41$		−	5.56698e51i		−	1.36942i	0.728816	−	0.684709i	$-0.240071\pi$
$42$	2.83326e50	−	9.00476e51i	0.0322336	−	1.02446i
$43$	−1.84892e52			−0.990666			−0.495333	−	0.868703i	$-0.664954\pi$
$43$	−1.84892e52			−0.990666			−0.495333	+	0.868703i	$0.664954\pi$
$44$		−	1.03105e53i		−	2.64725i
$45$	3.79922e51	−	6.03144e52i	0.0475220	−	0.754433i
$46$	6.14687e52			0.380543
$47$		−	8.60352e52i		−	0.267636i	−0.991006	−	0.133818i	$-0.957276\pi$
$47$		−	8.60352e52i		−	0.267636i	0.991006	−	0.133818i	$-0.0427238\pi$
$48$	−1.30306e53	−	4.09995e51i	−0.206654	−	0.00650218i
$49$	−7.46378e53			−0.611906
$50$		−	1.64175e54i		−	0.705125i
$51$	−1.38085e53	+	4.38865e54i	−0.0314702	+	1.00020i
$52$	7.06297e54			0.864730
$53$			2.63619e55i			1.75448i	0.480053	+	0.877240i	$0.340617\pi$
$53$			2.63619e55i			1.75448i	−0.480053	+	0.877240i	$0.659383\pi$
$54$	−4.23632e54	+	4.47615e55i	−0.155020	+	1.63797i
$55$	5.76311e55			1.17233
$56$		−	6.34048e55i		−	0.724612i
$57$	−2.29662e56	−	7.22609e54i	−1.48968	−	0.0468714i
$58$	−2.54386e56			−0.945795
$59$			5.74665e56i			1.23638i	0.786030	+	0.618188i	$0.212133\pi$
$59$			5.74665e56i			1.23638i	−0.786030	+	0.618188i	$0.787867\pi$
$60$	3.22956e55	−	1.02643e57i	0.0405792	−	1.28970i
$61$	2.11842e57			1.56840			0.784200	−	0.620508i	$-0.213073\pi$
$61$	2.11842e57			1.56840			0.784200	+	0.620508i	$0.213073\pi$
$62$		−	5.94307e57i		−	2.61503i
$63$	−2.35780e57	−	1.48518e56i	−0.621740	−	0.0391636i
$64$	9.79725e57			1.56079
$65$			3.94788e57i			0.382945i
$66$	−4.28551e58	−	1.34839e57i	−2.55033	−	0.0802436i
$67$	−8.44916e57			−0.310756			−0.155378	−	0.987855i	$-0.549660\pi$
$67$	−8.44916e57			−0.310756			−0.155378	+	0.987855i	$0.549660\pi$
$68$			7.46121e58i			1.70814i
$69$	5.06912e56	−	1.61109e58i	0.00727380	−	0.231179i
$70$	8.55711e58			0.774801
$71$			1.22668e59i			0.705446i	0.935728	+	0.352723i	$0.114744\pi$
$71$			1.22668e59i			0.705446i	−0.935728	+	0.352723i	$0.885256\pi$
$72$	−1.98926e58	+	3.15804e59i	−0.0731225	+	1.16085i
$73$	1.04982e59			0.248190			0.124095	−	0.992270i	$-0.460397\pi$
$73$	1.04982e59			0.248190			0.124095	+	0.992270i	$0.460397\pi$
$74$		−	8.15749e59i		−	1.24779i
$75$	−4.30299e59	−	1.35389e58i	−0.428361	−	0.0134779i
$76$	−3.90452e60			−2.54409
$77$		−	2.25290e60i		−	0.966138i
$78$	9.23685e58	−	2.93569e60i	0.0262118	−	0.833072i
$79$	−3.38074e60			−0.638182			−0.319091	−	0.947724i	$-0.603378\pi$
$79$	−3.38074e60			−0.638182			−0.319091	+	0.947724i	$0.603378\pi$
$80$		−	1.23828e60i		−	0.156293i
$81$	1.16970e61	+	1.47947e60i	0.992096	+	0.125483i
$82$	−3.93387e61			−2.25308
$83$			2.79817e61i			1.08736i	0.839291	+	0.543682i	$0.182970\pi$
$83$			2.79817e61i			1.08736i	−0.839291	+	0.543682i	$0.817030\pi$
$84$	−4.01250e61	−	1.26249e60i	−1.06286	−	0.0334419i
$85$	−4.17048e61			−0.756451
$86$			1.30653e62i			1.62993i
$87$	−2.09783e60	+	6.66741e61i	−0.0180782	+	0.574568i
$88$	−3.01754e62			−1.80388
$89$		−	3.41392e62i		−	1.42159i	−0.703400	−	0.710794i	$-0.748336\pi$
$89$		−	3.41392e62i		−	1.42159i	0.703400	−	0.710794i	$-0.251664\pi$
$90$	−4.26208e62	−	2.68470e61i	−1.24126	−	0.0781872i
$91$	1.54330e62			0.315591
$92$		−	2.73903e62i		−	0.394808i
$93$	−1.55767e63	−	4.90105e61i	−1.58862	−	0.0499844i
$94$	−6.07963e62			−0.440338
$95$		−	2.18245e63i		−	1.12665i
$96$	7.00919e61	−	2.22768e63i	0.0258814	−	0.822573i
$97$	4.56300e63			1.20936			0.604679	−	0.796469i	$-0.293301\pi$
$97$	4.56300e63			1.20936			0.604679	+	0.796469i	$0.293301\pi$
$98$			5.27424e63i			1.00676i
$99$	−7.06823e62	+	1.12211e64i	−0.0974955	+	1.54778i
$100$	−7.31558e63			−0.731558
$101$			1.12115e64i			0.815417i	0.913112	+	0.407709i	$0.133672\pi$
$101$			1.12115e64i			0.815417i	−0.913112	+	0.407709i	$0.866328\pi$
$102$	3.10122e64	+	9.75767e62i	1.64561	+	0.0517774i
$103$	−3.20773e64			−1.24568			−0.622841	−	0.782349i	$-0.714022\pi$
$103$	−3.20773e64			−1.24568			−0.622841	+	0.782349i	$0.714022\pi$
$104$		−	2.06709e64i		−	0.589242i
$105$	7.05676e62	−	2.24281e64i	0.0148098	−	0.470689i
$106$	1.86285e65			2.88662
$107$		−	1.01725e64i		−	0.116720i	−0.998296	−	0.0583600i	$-0.981413\pi$
$107$		−	1.01725e64i		−	0.116720i	0.998296	−	0.0583600i	$-0.0185871\pi$
$108$	1.99456e65	+	1.88769e64i	1.69937	+	0.160831i
$109$	4.91565e63			0.0311841			0.0155920	−	0.999878i	$-0.495037\pi$
$109$	4.91565e63			0.0311841			0.0155920	+	0.999878i	$0.495037\pi$
$110$		−	4.07247e65i		−	1.92882i
$111$	−2.13807e65	−	6.72721e63i	−0.758029	−	0.0238506i
$112$	−4.84066e64			−0.128804
$113$		−	5.09276e65i		−	1.01963i	−0.860284	−	0.509815i	$-0.829714\pi$
$113$		−	5.09276e65i		−	1.01963i	0.860284	−	0.509815i	$-0.170286\pi$
$114$	−5.10627e64	+	1.62289e66i	−0.0771168	+	2.45095i
$115$	1.53099e65			0.174841
$116$			1.13354e66i			0.981250i
$117$	−7.68678e65	−	4.84193e64i	−0.505588	−	0.0318472i
$118$	4.06084e66			2.03419
$119$			1.63032e66i			0.623403i
$120$	−3.00402e66	−	9.45184e64i	−0.878825	−	0.0276514i
$121$	−6.26401e66			−1.40514
$122$		−	1.49697e67i		−	2.58047i
$123$	−3.24413e65	+	1.03106e67i	−0.0430661	+	1.36874i
$124$	−2.64822e67			−2.71306
$125$		−	1.36302e67i		−	1.07990i
$126$	−1.04950e66	+	1.66612e67i	−0.0644353	+	1.02294i
$127$	−6.23145e66			−0.297078			−0.148539	−	0.988907i	$-0.547457\pi$
$127$	−6.23145e66			−0.297078			−0.148539	+	0.988907i	$0.547457\pi$
$128$		−	4.70443e67i		−	1.74497i
$129$	3.42439e67	+	1.07745e66i	0.990176	+	0.0311549i
$130$	2.78975e67			0.630054
$131$		−	1.53504e67i		−	0.271293i	−0.990757	−	0.135647i	$-0.956689\pi$
$131$		−	1.53504e67i		−	0.271293i	0.990757	−	0.135647i	$-0.0433112\pi$
$132$	−6.00840e66	+	1.90961e68i	−0.0832517	+	2.64594i
$133$	−8.53159e67			−0.928490
$134$			5.97055e67i			0.511282i
$135$	−1.05514e67	+	1.11487e68i	−0.0712242	+	0.752565i
$136$	2.18365e68			1.16396
$137$		−	4.01489e68i		−	1.69284i	−0.532517	−	0.846419i	$-0.678754\pi$
$137$		−	4.01489e68i		−	1.69284i	0.532517	−	0.846419i	$-0.321246\pi$
$138$	−1.13846e68	−	3.58206e66i	−0.380355	−	0.0119675i
$139$	6.81905e68			1.80821			0.904107	−	0.427305i	$-0.140537\pi$
$139$	6.81905e68			1.80821			0.904107	+	0.427305i	$0.140537\pi$
$140$		−	3.81303e68i		−	0.803846i
$141$	−5.01366e66	+	1.59346e68i	−0.00841674	+	0.267504i
$142$	8.66826e68			1.16066
$143$		−	7.34480e68i		−	0.785646i
$144$	2.41101e68	+	1.51871e67i	0.206348	+	0.0129979i
$145$	−6.33596e68			−0.434547
$146$		−	7.41851e68i		−	0.408343i
$147$	1.38237e69	+	4.34949e67i	0.611603	+	0.0192435i
$148$	−3.63496e69			−1.29457
$149$			4.38583e69i			1.25919i	0.776923	+	0.629595i	$0.216779\pi$
$149$			4.38583e69i			1.25919i	−0.776923	+	0.629595i	$0.783221\pi$
$150$	−9.56721e67	+	3.04068e69i	−0.0221751	+	0.704776i
$151$	−2.01022e67			−0.00376688			−0.00188344	−	0.999998i	$-0.500600\pi$
$151$	−2.01022e67			−0.00376688			−0.00188344	+	0.999998i	$0.500600\pi$
$152$			1.14272e70i			1.73359i
$153$	5.11494e68	−	8.12019e69i	0.0629093	−	0.998713i
$154$	−1.59200e70			−1.58957
$155$		−	1.48023e70i		−	1.20148i
$156$	−1.30813e70	−	4.11592e68i	−0.864302	−	0.0271944i
$157$	−7.19315e69			−0.387374			−0.193687	−	0.981063i	$-0.562045\pi$
$157$	−7.19315e69			−0.387374			−0.193687	+	0.981063i	$0.562045\pi$
$158$			2.38898e70i			1.04999i
$159$	1.53623e69	−	4.88249e70i	0.0551756	−	1.75361i
$160$	2.11694e70			0.622113
$161$		−	5.98493e69i		−	0.144089i
$162$	1.04546e70	−	8.26561e70i	0.206455	−	1.63228i
$163$	−7.32357e69			−0.118773			−0.0593867	−	0.998235i	$-0.518915\pi$
$163$	−7.32357e69			−0.118773			−0.0593867	+	0.998235i	$0.518915\pi$
$164$			1.75292e71i			2.33754i
$165$	−1.06739e71	−	3.35843e69i	−1.17175	−	0.0368680i
$166$	1.97731e71			1.78902
$167$		−	3.68517e70i		−	0.275126i	−0.990493	−	0.137563i	$-0.956073\pi$
$167$		−	3.68517e70i		−	0.275126i	0.990493	−	0.137563i	$-0.0439269\pi$
$168$	−3.69489e69	+	1.17432e71i	−0.0227879	+	0.724254i
$169$	−1.45740e71			−0.743367
$170$			2.94705e71i			1.24458i
$171$	4.24937e71	+	2.67669e70i	1.48747	+	0.0936964i
$172$	5.82185e71			1.69103
$173$		−	6.77611e71i		−	1.63495i	−0.575962	−	0.817477i	$-0.695372\pi$
$173$		−	6.77611e71i		−	1.63495i	0.575962	−	0.817477i	$-0.304628\pi$
$174$	4.71149e71	+	1.48242e70i	0.945327	+	0.0297438i
$175$	−1.59849e71			−0.266989
$176$			2.30375e71i			0.320649i
$177$	3.34884e70	−	1.06434e72i	0.0388821	−	1.23576i
$178$	−2.41243e72			−2.33892
$179$		−	1.23837e72i		−	1.00358i	−0.864989	−	0.501790i	$-0.832675\pi$
$179$		−	1.23837e72i		−	1.00358i	0.864989	−	0.501790i	$-0.167325\pi$
$180$	−1.19630e71	+	1.89917e72i	−0.0811182	+	1.28779i
$181$	9.81550e71			0.557440			0.278720	−	0.960372i	$-0.410090\pi$
$181$	9.81550e71			0.557440			0.278720	+	0.960372i	$0.410090\pi$
$182$		−	1.09056e72i		−	0.519238i
$183$	−3.92353e72	−	1.23450e71i	−1.56763	−	0.0493238i
$184$	−8.01622e71			−0.269029
$185$		−	2.03178e72i		−	0.573299i
$186$	−3.46330e71	+	1.10072e73i	−0.0822386	+	2.61374i
$187$	7.75894e72			1.55193
$188$			2.70907e72i			0.456845i
$189$	4.35823e72	+	4.12471e71i	0.620201	+	0.0586970i
$190$	−1.54222e73			−1.85366
$191$		−	1.19942e72i		−	0.121872i	−0.998142	−	0.0609362i	$-0.980591\pi$
$191$		−	1.19942e72i		−	0.121872i	0.998142	−	0.0609362i	$-0.0194086\pi$
$192$	−1.81455e73	−	5.70931e71i	−1.56002	−	0.0490845i
$193$	−7.83184e72			−0.570203			−0.285102	−	0.958497i	$-0.592027\pi$
$193$	−7.83184e72			−0.570203			−0.285102	+	0.958497i	$0.592027\pi$
$194$		−	3.22442e73i		−	1.98974i
$195$	2.30061e71	−	7.31189e72i	0.0120430	−	0.382756i
$196$	2.35019e73			1.04450
$197$			7.61155e71i			0.0287444i	0.999897	+	0.0143722i	$0.00457498\pi$
$197$			7.61155e71i			0.0287444i	−0.999897	+	0.0143722i	$0.995425\pi$
$198$	7.92935e73	+	4.99473e72i	2.54655	+	0.160408i
$199$	−1.03989e73			−0.284243			−0.142121	−	0.989849i	$-0.545392\pi$
$199$	−1.03989e73			−0.284243			−0.142121	+	0.989849i	$0.545392\pi$
$200$			2.14102e73i			0.498496i
$201$	1.56487e73	+	4.92371e71i	0.310602	+	0.00977279i
$202$	7.92255e73			1.34159
$203$			2.47684e73i			0.358117i
$204$	4.34799e72	−	1.38189e74i	0.0537184	−	1.70730i
$205$	−9.79806e73			−1.03518
$206$			2.26673e74i			2.04950i
$207$	−1.87771e72	+	2.98094e73i	−0.0145404	+	0.230835i
$208$	−1.57813e73			−0.104741
$209$			4.06032e74i			2.31142i
$210$	−1.58487e74	−	4.98662e72i	−0.774418	−	0.0243663i
$211$	1.73184e74			0.726891			0.363445	−	0.931616i	$-0.381600\pi$
$211$	1.73184e74			0.726891			0.363445	+	0.931616i	$0.381600\pi$
$212$		−	8.30079e74i		−	2.99483i
$213$	7.14842e72	−	2.27194e74i	0.0221852	−	0.705097i
$214$	−7.18832e73			−0.192038
$215$			3.25416e74i			0.748872i
$216$	5.52464e73	−	5.83742e74i	0.109593	−	1.15798i
$217$	−5.78650e74			−0.990158
$218$		−	3.47362e73i		−	0.0513067i
$219$	−1.94438e74	−	6.11780e72i	−0.248067	−	0.00780519i
$220$	−1.81468e75			−2.00113
$221$			5.31508e74i			0.506940i
$222$	−4.75374e73	+	1.51085e75i	−0.0392411	+	1.24717i
$223$	1.65273e75			1.18153			0.590766	−	0.806843i	$-0.298826\pi$
$223$	1.65273e75			1.18153			0.590766	+	0.806843i	$0.298826\pi$
$224$		−	8.27550e74i		−	0.512693i
$225$	7.96169e74	+	5.01510e73i	0.427725	+	0.0269426i
$226$	−3.59877e75			−1.67758
$227$			2.24582e75i			0.908967i	0.890755	+	0.454484i	$0.150176\pi$
$227$			2.24582e75i			0.908967i	−0.890755	+	0.454484i	$0.849824\pi$
$228$	7.23157e75	+	2.27534e74i	2.54283	+	0.0800077i
$229$	−1.92120e74			−0.0587268			−0.0293634	−	0.999569i	$-0.509348\pi$
$229$	−1.92120e74			−0.0587268			−0.0293634	+	0.999569i	$0.509348\pi$
$230$		−	1.08187e75i		−	0.287663i
$231$	−1.31287e74	+	4.17261e75i	−0.0303835	+	0.965660i
$232$	3.31748e75			0.668641
$233$		−	9.12742e75i		−	1.60309i	−0.597933	−	0.801546i	$-0.704011\pi$
$233$		−	9.12742e75i		−	1.60309i	0.597933	−	0.801546i	$-0.295989\pi$
$234$	−3.42152e74	+	5.43182e75i	−0.0523976	+	0.831836i
$235$	−1.51425e75			−0.202314
$236$		−	1.80950e76i		−	2.11045i
$237$	6.26148e75	+	1.97011e74i	0.637866	+	0.0200698i
$238$	1.15205e76			1.02568
$239$		−	1.42167e76i		−	1.10679i	−0.832918	−	0.553396i	$-0.813332\pi$
$239$		−	1.42167e76i		−	1.10679i	0.832918	−	0.553396i	$-0.186668\pi$
$240$	−7.21604e73	+	2.29343e75i	−0.00491518	+	0.156216i
$241$	6.54074e75			0.390015			0.195008	−	0.980802i	$-0.437527\pi$
$241$	6.54074e75			0.390015			0.195008	+	0.980802i	$0.437527\pi$
$242$			4.42642e76i			2.31186i
$243$	−2.15778e76	−	3.42176e75i	−0.987659	−	0.156621i
$244$	−6.67045e76			−2.67720
$245$			1.31365e76i			0.462557i
$246$	7.28594e76	+	2.29245e75i	2.25197	+	0.0708559i
$247$	−2.78143e76			−0.755032
$248$			7.75044e76i			1.84873i
$249$	1.63062e75	−	5.18250e76i	0.0341959	−	1.08683i
$250$	−9.63173e76			−1.77674
$251$		−	7.72380e76i		−	1.25393i	−0.779049	−	0.626963i	$-0.784298\pi$
$251$		−	7.72380e76i		−	1.25393i	0.779049	−	0.626963i	$-0.215702\pi$
$252$	7.42420e76	+	4.67653e75i	1.06129	+	0.0668508i
$253$	−2.84832e76			−0.358701
$254$			4.40342e76i			0.488778i
$255$	7.72417e76	+	2.43033e75i	0.756077	+	0.0237892i
$256$	−1.51708e77			−1.31018
$257$			2.04483e76i			0.155883i	0.996958	+	0.0779414i	$0.0248347\pi$
$257$			2.04483e76i			0.155883i	−0.996958	+	0.0779414i	$0.975165\pi$
$258$	7.61374e75	−	2.41983e77i	0.0512587	−	1.62912i
$259$	−7.94258e76			−0.472464
$260$		−	1.24310e77i		−	0.653673i
$261$	7.77081e75	−	1.23365e77i	0.0361385	−	0.573715i
$262$	−1.08473e77			−0.446355
$263$			2.89478e77i			1.05446i	0.849722	+	0.527231i	$0.176770\pi$
$263$			2.89478e77i			1.05446i	−0.849722	+	0.527231i	$0.823230\pi$
$264$	5.58879e77	+	1.75846e76i	1.80299	+	0.0567292i
$265$	4.63977e77			1.32626
$266$			6.02880e77i			1.52763i
$267$	−1.98945e76	+	6.32294e77i	−0.0447067	+	1.42088i
$268$	2.66046e77			0.530449
$269$		−	7.92776e77i		−	1.40306i	−0.712638	−	0.701532i	$-0.752500\pi$
$269$		−	7.92776e77i		−	1.40306i	0.712638	−	0.701532i	$-0.247500\pi$
$270$	7.87817e77	+	7.45606e76i	1.23818	+	0.117184i
$271$	4.00863e77			0.559730			0.279865	−	0.960039i	$-0.409710\pi$
$271$	4.00863e77			0.559730			0.279865	+	0.960039i	$0.409710\pi$
$272$		−	1.66711e77i		−	0.206900i
$273$	−2.85835e77	−	8.99350e75i	−0.315435	−	0.00992485i
$274$	−2.83710e78			−2.78520
$275$			7.60749e77i			0.664653i
$276$	−1.59616e76	+	5.07297e77i	−0.0124161	+	0.394613i
$277$	−1.73172e78			−1.19984			−0.599922	−	0.800058i	$-0.704802\pi$
$277$	−1.73172e78			−1.19984			−0.599922	+	0.800058i	$0.704802\pi$
$278$		−	4.81864e78i		−	2.97503i
$279$	2.88211e78	+	1.81545e77i	1.58627	+	0.0999194i
$280$	−1.11595e78			−0.547755
$281$			7.80902e77i			0.341975i	0.985273	+	0.170988i	$0.0546958\pi$
$281$			7.80902e77i			0.341975i	−0.985273	+	0.170988i	$0.945304\pi$
$282$	1.12601e78	+	3.54288e76i	0.440120	+	0.0138479i
$283$	1.32431e77			0.0462193			0.0231097	−	0.999733i	$-0.492643\pi$
$283$	1.32431e77			0.0462193			0.0231097	+	0.999733i	$0.492643\pi$
$284$		−	3.86255e78i		−	1.20417i
$285$	−1.27181e77	+	4.04213e78i	−0.0354314	+	1.12609i
$286$	−5.19016e78			−1.29261
$287$			3.83023e78i			0.853109i
$288$	−2.59635e77	+	4.12182e78i	−0.0517372	+	0.821352i
$289$	−7.76162e75			−0.00138427
$290$			4.47727e78i			0.714953i
$291$	−8.45115e78	−	2.65907e77i	−1.20876	−	0.0380324i
$292$	−3.30567e78			−0.423651
$293$			3.74809e78i			0.430573i	0.976551	+	0.215286i	$0.0690685\pi$
$293$			3.74809e78i			0.430573i	−0.976551	+	0.215286i	$0.930932\pi$
$294$	3.07354e77	−	9.76844e78i	0.0316610	−	1.00626i
$295$	1.01143e79			0.934611
$296$			1.06383e79i			0.882140i
$297$	1.96302e78	−	2.07415e79i	0.146123	−	1.54395i
$298$	3.09922e79			2.07173
$299$		−	1.95118e78i		−	0.117171i
$300$	1.35492e79	+	4.26312e77i	0.731196	+	0.0230063i
$301$	1.27211e79			0.617157
$302$			1.42051e77i			0.00619760i
$303$	6.53346e77	−	2.07649e79i	0.0256436	−	0.815014i
$304$	8.72415e78			0.308154
$305$		−	3.72848e79i		−	1.18560i
$306$	−5.73809e79	−	3.61444e78i	−1.64317	−	0.103504i
$307$	1.66304e77			0.00429017			0.00214509	−	0.999998i	$-0.499317\pi$
$307$	1.66304e77			0.00429017			0.00214509	+	0.999998i	$0.499317\pi$
$308$			7.09391e79i			1.64916i
$309$	5.94105e79	+	1.86929e78i	1.24507	+	0.0391747i
$310$	−1.04600e80			−1.97677
$311$			2.92070e79i			0.497914i	0.968515	+	0.248957i	$0.0800877\pi$
$311$			2.92070e79i			0.497914i	−0.968515	+	0.248957i	$0.919912\pi$
$312$	−1.20459e78	+	3.82847e79i	−0.0185307	+	0.588950i
$313$	3.99598e79			0.554887			0.277443	−	0.960742i	$-0.410513\pi$
$313$	3.99598e79			0.554887			0.277443	+	0.960742i	$0.410513\pi$
$314$			5.08300e79i			0.637340i
$315$	−2.61397e78	+	4.14980e79i	−0.0296049	+	0.469991i
$316$	1.06452e80			1.08935
$317$		−	2.37805e79i		−	0.219950i	−0.993934	−	0.109975i	$-0.964923\pi$
$317$		−	2.37805e79i		−	0.219950i	0.993934	−	0.109975i	$-0.0350771\pi$
$318$	−3.45018e80	−	1.08557e79i	−2.88519	−	0.0907796i
$319$	1.17877e80			0.891510
$320$		−	1.72435e80i		−	1.17985i
$321$	−5.92797e77	+	1.88405e79i	−0.00367066	+	0.116662i
$322$	−4.22922e79			−0.237068
$323$		−	2.93826e80i		−	1.49145i
$324$	−3.68314e80	−	4.65852e79i	−1.69347	−	0.214194i
$325$	−5.21133e79			−0.217111
$326$			5.17516e79i			0.195416i
$327$	−9.10429e78	−	2.86457e77i	−0.0311687	−	0.000980691i
$328$	5.13022e80			1.59284
$329$			5.91946e79i			0.166730i
$330$	−2.37321e79	+	7.54263e80i	−0.0606584	+	1.92787i
$331$	4.05680e80			0.941212			0.470606	−	0.882343i	$-0.344035\pi$
$331$	4.05680e80			0.941212			0.470606	+	0.882343i	$0.344035\pi$
$332$		−	8.81085e80i		−	1.85609i
$333$	3.95600e80	+	2.49190e79i	0.756904	+	0.0476776i
$334$	−2.60411e80			−0.452660
$335$			1.48708e80i			0.234909i
$336$	8.96541e79	+	2.82088e78i	0.128740	+	0.00405067i
$337$	8.62053e79			0.112558			0.0562791	−	0.998415i	$-0.482076\pi$
$337$	8.62053e79			0.112558			0.0562791	+	0.998415i	$0.482076\pi$
$338$			1.02986e81i			1.22305i
$339$	−2.96778e79	+	9.43231e80i	−0.0320658	+	1.01913i
$340$	1.31320e81			1.29123
$341$			2.75389e81i			2.46494i
$342$	1.89147e80	−	3.00279e81i	0.154157	−	2.44732i
$343$	1.35276e81			1.00417
$344$		−	1.70386e81i		−	1.15230i
$345$	−2.83556e80	−	8.92181e78i	−0.174754	−	0.00549847i
$346$	−4.78830e81			−2.68996
$347$		−	2.86768e81i		−	1.46889i	−0.678671	−	0.734443i	$-0.737444\pi$
$347$		−	2.86768e81i		−	1.46889i	0.678671	−	0.734443i	$-0.262556\pi$
$348$	6.60564e79	−	2.09943e81i	0.0308588	−	0.980765i
$349$	2.57258e81			1.09636			0.548182	−	0.836359i	$-0.315320\pi$
$349$	2.57258e81			1.09636			0.548182	+	0.836359i	$0.315320\pi$
$350$			1.12957e81i			0.439273i
$351$	1.42085e81	+	1.34472e80i	0.504336	+	0.0477313i
$352$	−3.93844e81			−1.27632
$353$			1.07659e81i			0.318611i	0.987229	+	0.159306i	$0.0509255\pi$
$353$			1.07659e81i			0.318611i	−0.987229	+	0.159306i	$0.949075\pi$
$354$	−7.52109e81	−	2.36644e80i	−2.03318	−	0.0639721i
$355$	2.15899e81			0.533266
$356$			1.07497e82i			2.42660i
$357$	9.50060e79	−	3.01951e81i	0.0196051	−	0.623095i
$358$	−8.75085e81			−1.65118
$359$			8.47028e80i			0.146176i	0.997326	+	0.0730879i	$0.0232854\pi$
$359$			8.47028e80i			0.146176i	−0.997326	+	0.0730879i	$0.976715\pi$
$360$	5.55824e81	+	3.50116e80i	0.877521	+	0.0552754i
$361$	8.45418e81			1.22135
$362$		−	6.93607e81i		−	0.917147i
$363$	1.16016e82	+	3.65032e80i	1.40445	+	0.0441895i
$364$	−4.85952e81			−0.538702
$365$		−	1.84772e81i		−	0.187614i
$366$	−8.72352e80	+	2.77254e82i	−0.0811516	+	2.57919i
$367$	−1.28466e82			−1.09515			−0.547576	−	0.836756i	$-0.684449\pi$
$367$	−1.28466e82			−1.09515			−0.547576	+	0.836756i	$0.684449\pi$
$368$			6.12001e80i			0.0478214i
$369$	1.20169e81	−	1.90774e82i	0.0860895	−	1.36671i
$370$	−1.43574e82			−0.943239
$371$		−	1.81377e82i		−	1.09299i
$372$	4.90477e82	+	1.54324e81i	2.71172	+	0.0853215i
$373$	−1.09578e82			−0.555959			−0.277979	−	0.960587i	$-0.589665\pi$
$373$	−1.09578e82			−0.555959			−0.277979	+	0.960587i	$0.589665\pi$
$374$		−	5.48281e82i		−	2.55336i
$375$	−7.94296e80	+	2.52446e82i	−0.0339611	+	1.07936i
$376$	7.92853e81			0.311302
$377$			8.07487e81i			0.291214i
$378$	2.91470e81	−	3.07972e82i	0.0965733	−	1.02041i
$379$	6.44052e82			1.96095			0.980474	−	0.196648i	$-0.0630057\pi$
$379$	6.44052e82			1.96095			0.980474	+	0.196648i	$0.0630057\pi$
$380$			6.87208e82i			1.92315i
$381$	1.15413e82	+	3.63135e80i	0.296931	+	0.00934263i
$382$	−8.47567e81			−0.200515
$383$		−	3.58961e82i		−	0.781064i	−0.920589	−	0.390532i	$-0.872291\pi$
$383$		−	3.58961e82i		−	0.781064i	0.920589	−	0.390532i	$-0.127709\pi$
$384$	−2.74148e81	+	8.71308e82i	−0.0548765	+	1.74411i
$385$	−3.96518e82			−0.730330
$386$			5.53432e82i			0.938147i
$387$	−6.33604e82	−	3.99110e81i	−0.988706	−	0.0622790i
$388$	−1.43679e83			−2.06433
$389$		−	1.77327e82i		−	0.234632i	−0.993095	−	0.117316i	$-0.962571\pi$
$389$		−	1.77327e82i		−	0.234632i	0.993095	−	0.117316i	$-0.0374290\pi$
$390$	−5.16691e82	−	1.62571e81i	−0.629743	−	0.0198142i
$391$	2.06119e82			0.231453
$392$		−	6.87821e82i		−	0.711740i
$393$	−8.94540e80	+	2.84306e82i	−0.00853175	+	0.271159i
$394$	5.37866e81			0.0472928
$395$			5.95021e82i			0.482420i
$396$	2.22564e82	−	3.53330e83i	0.166421	−	2.64201i
$397$	3.50644e82			0.241863			0.120932	−	0.992661i	$-0.461412\pi$
$397$	3.50644e82			0.241863			0.120932	+	0.992661i	$0.461412\pi$
$398$			7.34833e82i			0.467660i
$399$	1.58014e83	+	4.97175e81i	0.928031	+	0.0291996i
$400$	1.63457e82			0.0886103
$401$			2.39956e83i			1.20091i	0.799658	+	0.600456i	$0.205014\pi$
$401$			2.39956e83i			1.20091i	−0.799658	+	0.600456i	$0.794986\pi$
$402$	3.47931e81	−	1.10581e83i	0.0160790	−	0.511029i
$403$	−1.88649e83			−0.805178
$404$		−	3.53027e83i		−	1.39189i
$405$	2.60391e82	−	2.05871e83i	0.0948560	−	0.749953i
$406$	1.75024e83			0.589204
$407$			3.78000e83i			1.17617i
$408$	−4.04434e83	−	1.27251e82i	−1.16338	−	0.0366047i
$409$	−1.04818e83			−0.278799			−0.139399	−	0.990236i	$-0.544517\pi$
$409$	−1.04818e83			−0.278799			−0.139399	+	0.990236i	$0.544517\pi$
$410$			6.92374e83i			1.70317i
$411$	−2.33966e82	+	7.43599e83i	−0.0532371	+	1.69200i
$412$	1.01005e84			2.12633
$413$		−	3.95386e83i		−	0.770228i
$414$	2.10647e83	+	1.32687e82i	0.379790	+	0.0239231i
$415$	4.92487e83			0.821969
$416$		−	2.69794e83i		−	0.416913i
$417$	−1.26296e84	−	3.97377e82i	−1.80732	−	0.0568655i
$418$	2.86920e84			3.80295
$419$		−	8.99370e83i		−	1.10431i	−0.833743	−	0.552153i	$-0.813806\pi$
$419$		−	8.99370e83i		−	1.10431i	0.833743	−	0.552153i	$-0.186194\pi$
$420$	−2.22203e82	+	7.06212e83i	−0.0252797	+	0.803448i
$421$	−9.14931e83			−0.964631			−0.482315	−	0.875998i	$-0.660204\pi$
$421$	−9.14931e83			−0.964631			−0.482315	+	0.875998i	$0.660204\pi$
$422$		−	1.22379e84i		−	1.19594i
$423$	1.85717e82	−	2.94833e83i	0.0168251	−	0.267107i
$424$	−2.42936e84			−2.04073
$425$		−	5.50517e83i		−	0.428869i
$426$	−1.60545e84	−	5.05139e82i	−1.16009	−	0.0365009i
$427$	−1.45753e84			−0.977070
$428$			3.20310e83i			0.199237i
$429$	−4.28015e82	+	1.36033e84i	−0.0247073	+	0.785257i
$430$	2.29953e84			1.23211
$431$		−	3.01835e84i		−	1.50140i	−0.660641	−	0.750702i	$-0.729716\pi$
$431$		−	3.01835e84i		−	1.50140i	0.660641	−	0.750702i	$-0.270284\pi$
$432$	−4.45660e83	−	4.21781e82i	−0.205837	−	0.0194808i
$433$	−2.31324e84			−0.992220			−0.496110	−	0.868260i	$-0.665239\pi$
$433$	−2.31324e84			−0.992220			−0.496110	+	0.868260i	$0.665239\pi$
$434$			4.08900e84i			1.62909i
$435$	1.17349e84	+	3.69225e82i	0.434332	+	0.0136658i
$436$	−1.54783e83			−0.0532300
$437$			1.07864e84i			0.344724i
$438$	−4.32311e82	+	1.37399e84i	−0.0128418	+	0.408141i
$439$	5.74244e83			0.158574			0.0792870	−	0.996852i	$-0.474736\pi$
$439$	5.74244e83			0.158574			0.0792870	+	0.996852i	$0.474736\pi$
$440$			5.31096e84i			1.36360i
$441$	−2.55776e84	−	1.61114e83i	−0.610695	−	0.0384679i
$442$	3.75587e84			0.834061
$443$			6.39557e83i			0.132118i	0.997816	+	0.0660588i	$0.0210425\pi$
$443$			6.39557e83i			0.132118i	−0.997816	+	0.0660588i	$0.978958\pi$
$444$	6.73232e84	+	2.11826e83i	1.29393	+	0.0407121i
$445$	−6.00862e84			−1.07462
$446$		−	1.16789e85i		−	1.94396i
$447$	2.55583e83	−	8.12302e84i	0.0395996	−	1.25857i
$448$	−6.74078e84			−0.972330
$449$			1.48336e84i			0.199234i	0.995026	+	0.0996170i	$0.0317617\pi$
$449$			1.48336e84i			0.199234i	−0.995026	+	0.0996170i	$0.968238\pi$
$450$	3.54389e83	−	5.62609e84i	0.0443282	−	0.703730i
$451$	1.82287e85			2.12376
$452$			1.60360e85i			1.74047i
$453$	3.72314e82	+	1.17145e81i	0.00376502	+	0.000118463i
$454$	1.58700e85			1.49551
$455$		−	2.71625e84i		−	0.238564i
$456$	6.65916e83	−	2.11644e85i	0.0545186	−	1.73273i
$457$	−1.21811e85			−0.929755			−0.464877	−	0.885375i	$-0.653902\pi$
$457$	−1.21811e85			−0.929755			−0.464877	+	0.885375i	$0.653902\pi$
$458$			1.35760e84i			0.0966223i
$459$	−1.42054e84	+	1.50096e85i	−0.0942861	+	0.996240i
$460$	−4.82078e84			−0.298447
$461$		−	2.02716e84i		−	0.117074i	−0.998285	−	0.0585369i	$-0.981356\pi$
$461$		−	2.02716e84i		−	0.117074i	0.998285	−	0.0585369i	$-0.0186435\pi$
$462$	2.94855e85	+	9.27732e83i	1.58879	+	0.0499895i
$463$	−1.40714e85			−0.707529			−0.353764	−	0.935335i	$-0.615099\pi$
$463$	−1.40714e85			−0.707529			−0.353764	+	0.935335i	$0.615099\pi$
$464$		−	2.53274e84i		−	0.118855i
$465$	−8.62600e83	+	2.74155e85i	−0.0377846	+	1.20088i
$466$	−6.44984e85			−2.63754
$467$			4.26310e85i			1.62774i	0.581046	+	0.813871i	$0.302644\pi$
$467$			4.26310e85i			1.62774i	−0.581046	+	0.813871i	$0.697356\pi$
$468$	2.42040e85	+	1.52462e84i	0.863019	+	0.0543619i
$469$	5.81325e84			0.193592
$470$			1.07003e85i			0.332863i
$471$	1.33225e85	+	4.19178e83i	0.387182	+	0.0121823i
$472$	−5.29580e85			−1.43809
$473$		−	6.05416e85i		−	1.53638i
$474$	1.39217e84	−	4.42464e85i	0.0330206	−	1.04947i
$475$	2.88091e85			0.638754
$476$		−	5.13352e85i		−	1.06413i
$477$	−5.69050e84	+	9.03392e85i	−0.110297	+	1.75101i
$478$	−1.00462e86			−1.82099
$479$		−	9.39329e85i		−	1.59251i	−0.604964	−	0.796253i	$-0.706812\pi$
$479$		−	9.39329e85i		−	1.59251i	0.604964	−	0.796253i	$-0.293188\pi$
$480$	−3.92080e85	−	1.23364e84i	−0.621806	−	0.0195645i
$481$	−2.58940e85			−0.384200
$482$		−	4.62198e85i		−	0.641686i
$483$	−3.48769e83	+	1.10847e85i	−0.00453138	+	0.144018i
$484$	1.97240e86			2.39852
$485$		−	8.03102e85i		−	0.914187i
$486$	−2.41797e85	+	1.52479e86i	−0.257686	+	1.62498i
$487$	1.26485e86			1.26216			0.631078	−	0.775719i	$-0.282613\pi$
$487$	1.26485e86			1.26216			0.631078	+	0.775719i	$0.282613\pi$
$488$			1.95222e86i			1.82429i
$489$	1.35640e85	+	4.26778e83i	0.118715	+	0.00373524i
$490$	9.28283e85			0.761037
$491$			1.12653e86i			0.865234i	0.901578	+	0.432617i	$0.142410\pi$
$491$			1.12653e86i			0.865234i	−0.901578	+	0.432617i	$0.857590\pi$
$492$	1.02151e85	−	3.24660e86i	0.0735121	−	2.33639i
$493$	−8.53017e85			−0.575250
$494$			1.96548e86i			1.24224i
$495$	1.97496e86	+	1.24403e85i	1.17001	+	0.0736996i
$496$	5.91710e85			0.328621
$497$		−	8.43989e85i		−	0.439473i
$498$	−3.66218e86	−	1.15227e85i	−1.78814	−	0.0562620i
$499$	2.79155e86			1.27828			0.639142	−	0.769089i	$-0.279290\pi$
$499$	2.79155e86			1.27828			0.639142	+	0.769089i	$0.279290\pi$
$500$			4.29187e86i			1.84334i
$501$	−2.14752e84	+	6.82532e85i	−0.00865227	+	0.274989i
$502$	−5.45798e86			−2.06307
$503$		−	5.22622e86i		−	1.85358i	−0.375575	−	0.926792i	$-0.622555\pi$
$503$		−	5.22622e86i		−	1.85358i	0.375575	−	0.926792i	$-0.377445\pi$
$504$	1.36866e85	−	2.17282e86i	0.0455533	−	0.723179i
$505$	1.97326e86			0.616397
$506$			2.01275e86i			0.590166i
$507$	2.69925e86	+	8.49292e84i	0.742999	+	0.0233777i
$508$	1.96215e86			0.507100
$509$		−	6.81243e86i		−	1.65323i	−0.562768	−	0.826615i	$-0.690264\pi$
$509$		−	6.81243e86i		−	1.65323i	0.562768	−	0.826615i	$-0.309736\pi$
$510$	1.71738e85	−	5.45824e86i	0.0391400	−	1.24396i
$511$	−7.22307e85			−0.154616
$512$			2.04224e86i			0.410646i
$513$	−7.85467e86	−	7.43381e85i	−1.48379	−	0.140429i
$514$	1.44497e86			0.256471
$515$			5.64571e86i			0.941645i
$516$	−1.07827e87	−	3.39266e85i	−1.69019	−	0.0531802i
$517$	2.81717e86			0.415064
$518$			5.61258e86i			0.777339i
$519$	−3.94875e85	+	1.25501e87i	−0.0514167	+	1.63414i
$520$	−3.63815e86			−0.445424
$521$			7.33280e86i			0.844234i	0.906541	+	0.422117i	$0.138713\pi$
$521$			7.33280e86i			0.844234i	−0.906541	+	0.422117i	$0.861287\pi$
$522$	−8.71753e86	−	5.49120e85i	−0.943924	−	0.0594581i
$523$	−9.23075e86			−0.940119			−0.470060	−	0.882635i	$-0.655768\pi$
$523$	−9.23075e86			−0.940119			−0.470060	+	0.882635i	$0.655768\pi$
$524$			4.83353e86i			0.463087i
$525$	2.96058e86	+	9.31516e84i	0.266857	+	0.00839639i
$526$	2.04558e87			1.73489
$527$		−	1.99286e87i		−	1.59051i
$528$	1.34250e85	−	4.26678e86i	0.0100839	−	0.320491i
$529$	1.33876e87			0.946504
$530$		−	3.27867e87i		−	2.18207i
$531$	−1.24048e86	+	1.96932e87i	−0.0777257	+	1.23393i
$532$	2.68642e87			1.58490
$533$			1.24871e87i			0.693733i
$534$	4.46807e87	+	1.40583e86i	2.33776	+	0.0735553i
$535$	−1.79039e86			−0.0882320
$536$		−	7.78628e86i		−	0.361457i
$537$	−7.21653e85	+	2.29358e87i	−0.0315610	+	1.00308i
$538$	−5.60211e87			−2.30844
$539$		−	2.44397e87i		−	0.948975i
$540$	3.32240e86	−	3.51049e87i	0.121577	−	1.28460i
$541$	−1.69599e87			−0.584939			−0.292470	−	0.956275i	$-0.594477\pi$
$541$	−1.69599e87			−0.584939			−0.292470	+	0.956275i	$0.594477\pi$
$542$		−	2.83268e87i		−	0.920916i
$543$	−1.81793e87	−	5.71994e85i	−0.557164	−	0.0175306i
$544$	2.85006e87			0.823549
$545$		−	8.65170e85i		−	0.0235729i
$546$	−6.35521e85	+	2.01983e87i	−0.0163292	+	0.518981i
$547$	−7.32048e87			−1.77397			−0.886983	−	0.461803i	$-0.847203\pi$
$547$	−7.32048e87			−1.77397			−0.886983	+	0.461803i	$0.847203\pi$
$548$			1.26420e88i			2.88961i
$549$	7.25959e87	+	4.57284e86i	1.56530	+	0.0985987i
$550$	5.37579e87			1.09354
$551$		−	4.46391e87i		−	0.856771i
$552$	1.48469e87	+	4.67142e85i	0.268896	+	0.00846055i
$553$	2.32604e87			0.397570
$554$			1.22371e88i			1.97409i
$555$	−1.18401e86	+	3.76306e87i	−0.0180293	+	0.573015i
$556$	−2.14717e88			−3.08655
$557$		−	3.63261e86i		−	0.0493006i	−0.999696	−	0.0246503i	$-0.992153\pi$
$557$		−	3.63261e86i		−	0.0493006i	0.999696	−	0.0246503i	$-0.00784724\pi$
$558$	1.28288e87	−	2.03663e88i	0.164396	−	2.60986i
$559$	4.14726e87			0.501861
$560$			8.51972e86i			0.0973663i
$561$	−1.43704e88	−	4.52149e86i	−1.55116	−	0.0488056i
$562$	5.51820e87			0.562646
$563$		−	2.64669e87i		−	0.254938i	−0.991843	−	0.127469i	$-0.959315\pi$
$563$		−	2.64669e87i		−	0.254938i	0.991843	−	0.127469i	$-0.0406853\pi$
$564$	1.57870e86	−	5.01747e87i	0.0143670	−	0.456619i
$565$	−8.96341e87			−0.770767
$566$		−	9.35816e86i		−	0.0760440i
$567$	−8.04785e87	−	1.01791e87i	−0.618048	−	0.0781723i
$568$	−1.13044e88			−0.820542
$569$		−	2.12600e88i		−	1.45872i	−0.684131	−	0.729359i	$-0.739818\pi$
$569$		−	2.12600e88i		−	1.45872i	0.684131	−	0.729359i	$-0.260182\pi$
$570$	2.85635e88	+	8.98720e86i	1.85274	+	0.0582947i
$571$	−2.05532e87			−0.126045			−0.0630224	−	0.998012i	$-0.520074\pi$
$571$	−2.05532e87			−0.126045			−0.0630224	+	0.998012i	$0.520074\pi$
$572$			2.31272e88i			1.34107i
$573$	−6.98960e85	+	2.22146e87i	−0.00383269	+	0.121812i
$574$	2.70661e88			1.40361
$575$			2.02096e87i			0.0991259i
$576$	3.35741e88	+	2.11485e87i	1.55771	+	0.0981204i
$577$	5.70211e87			0.250271			0.125135	−	0.992140i	$-0.460063\pi$
$577$	5.70211e87			0.250271			0.125135	+	0.992140i	$0.460063\pi$
$578$			5.48471e85i			0.00227752i
$579$	1.45054e88	+	4.56397e86i	0.569921	+	0.0179320i
$580$	1.99506e88			0.741755
$581$		−	1.92522e88i		−	0.677398i
$582$	−1.87902e87	+	5.97196e88i	−0.0625742	+	1.98875i
$583$	−8.63202e88			−2.72094
$584$			9.67459e87i			0.288683i
$585$	−8.52195e86	+	1.35290e88i	−0.0240742	+	0.382188i
$586$	2.64857e88			0.708415
$587$			9.55021e87i			0.241877i	0.992660	+	0.120938i	$0.0385903\pi$
$587$			9.55021e87i			0.241877i	−0.992660	+	0.120938i	$0.961410\pi$
$588$	−4.35279e88	−	1.36956e87i	−1.04398	−	0.0328479i
$589$	1.04288e89			2.36889
$590$		−	7.14721e88i		−	1.53770i
$591$	4.43560e85	−	1.40974e87i	0.000903968	−	0.0287302i
$592$	8.12185e87			0.156805
$593$			2.51652e88i			0.460310i	0.973154	+	0.230155i	$0.0739233\pi$
$593$			2.51652e88i			0.460310i	−0.973154	+	0.230155i	$0.926077\pi$
$594$	−1.46569e89	−	1.38715e88i	−2.54024	−	0.240413i
$595$	2.86941e88			0.471248
$596$		−	1.38101e89i		−	2.14939i
$597$	1.92599e88	+	6.05992e86i	0.284102	+	0.00893899i
$598$	−1.37879e88			−0.192779
$599$			8.74373e88i			1.15888i	0.815015	+	0.579440i	$0.196729\pi$
$599$			8.74373e88i			1.15888i	−0.815015	+	0.579440i	$0.803271\pi$
$600$	1.24767e87	−	3.96540e88i	0.0156769	−	0.498250i
$601$	−4.98556e88			−0.593923			−0.296962	−	0.954889i	$-0.595973\pi$
$601$	−4.98556e88			−0.593923			−0.296962	+	0.954889i	$0.595973\pi$
$602$		−	8.98927e88i		−	1.01540i
$603$	−2.89543e88	−	1.82384e87i	−0.310141	−	0.0195359i
$604$	6.32977e86			0.00642993
$605$			1.10248e89i			1.06219i
$606$	−1.46734e89	−	4.61683e87i	−1.34093	−	0.0421910i
$607$	1.06920e89			0.926874			0.463437	−	0.886130i	$-0.346616\pi$
$607$	1.06920e89			0.926874			0.463437	+	0.886130i	$0.346616\pi$
$608$			1.49146e89i			1.22659i
$609$	1.44337e87	−	4.58736e88i	0.0112622	−	0.357940i
$610$	−2.63471e89			−1.95065
$611$			1.92983e88i			0.135582i
$612$	−1.61059e88	+	2.55688e89i	−0.107384	+	1.70476i
$613$	2.54739e89			1.61198			0.805992	−	0.591927i	$-0.201633\pi$
$613$	2.54739e89			1.61198			0.805992	+	0.591927i	$0.201633\pi$
$614$		−	1.17518e87i		−	0.00705856i
$615$	1.81470e89	+	5.70978e87i	1.03467	+	0.0325548i
$616$	2.07615e89			1.12377
$617$		−	8.77237e88i		−	0.450808i	−0.974265	−	0.225404i	$-0.927630\pi$
$617$		−	8.77237e88i		−	0.450808i	0.974265	−	0.225404i	$-0.0723702\pi$
$618$	1.32093e88	−	4.19821e89i	0.0644536	−	2.04849i
$619$	−3.20453e89			−1.48479			−0.742393	−	0.669965i	$-0.766309\pi$
$619$	−3.20453e89			−1.48479			−0.742393	+	0.669965i	$0.766309\pi$
$620$			4.66094e89i			2.05088i
$621$	5.21484e87	−	5.51007e88i	0.0217926	−	0.230264i
$622$	2.06389e89			0.819210
$623$			2.34887e89i			0.885609i
$624$	2.92286e88	+	9.19649e86i	0.104689	+	0.00329394i
$625$	−1.13950e89			−0.387752
$626$		−	2.82374e89i		−	0.912946i
$627$	2.36613e88	−	7.52013e89i	0.0726906	−	2.31028i
$628$	2.26497e89			0.661232
$629$		−	2.73540e89i		−	0.758929i
$630$	2.93243e89	+	1.84715e88i	0.773268	+	0.0487084i
$631$	6.14803e89			1.54098			0.770489	−	0.637454i	$-0.220012\pi$
$631$	6.14803e89			1.54098			0.770489	+	0.637454i	$0.220012\pi$
$632$		−	3.11550e89i		−	0.742304i
$633$	−3.20755e89	−	1.00922e88i	−0.726531	−	0.0228596i
$634$	−1.68044e89			−0.361881
$635$			1.09676e89i			0.224569i
$636$	−4.83725e88	+	1.53739e90i	−0.0941827	+	2.99335i
$637$	1.67418e89			0.309985
$638$		−	8.32970e89i		−	1.46679i
$639$	−2.64792e88	+	4.20370e89i	−0.0443484	+	0.704051i
$640$	−8.27994e89			−1.31907
$641$			9.19083e89i			1.39283i	0.717640	+	0.696414i	$0.245222\pi$
$641$			9.19083e89i			1.39283i	−0.717640	+	0.696414i	$0.754778\pi$
$642$	1.33135e89	+	4.18896e87i	0.191943	+	0.00603929i
$643$	4.86884e89			0.667843			0.333921	−	0.942601i	$-0.391628\pi$
$643$	4.86884e89			0.667843			0.333921	+	0.942601i	$0.391628\pi$
$644$			1.88453e89i			0.245955i
$645$	1.89635e88	−	6.02703e89i	0.0235509	−	0.748502i
$646$	−2.07630e90			−2.45386
$647$		−	9.37107e89i		−	1.05403i	−0.849857	−	0.527014i	$-0.823311\pi$
$647$		−	9.37107e89i		−	1.05403i	0.849857	−	0.527014i	$-0.176689\pi$
$648$	−1.36339e89	+	1.07793e90i	−0.145956	+	1.15396i
$649$	−1.88170e90			−1.91744
$650$			3.68256e89i			0.357209i
$651$	1.07172e90	+	3.37206e88i	0.989668	+	0.0311389i
$652$	2.30604e89			0.202742
$653$			1.40404e89i			0.117533i	0.998272	+	0.0587664i	$0.0187167\pi$
$653$			1.40404e89i			0.117533i	−0.998272	+	0.0587664i	$0.981283\pi$
$654$	−2.02424e87	+	6.43350e88i	−0.00161352	+	0.0512813i
$655$	−2.70172e89			−0.205078
$656$		−	3.91668e89i		−	0.283136i
$657$	3.59763e89	+	2.26616e88i	0.247699	+	0.0156027i
$658$	4.18295e89			0.274318
$659$		−	1.84260e90i		−	1.15106i	−0.817780	−	0.575531i	$-0.804796\pi$
$659$		−	1.84260e90i		−	1.15106i	0.817780	−	0.575531i	$-0.195204\pi$
$660$	3.36098e90	+	1.05750e89i	2.00014	+	0.0629323i
$661$	9.56930e89			0.542542			0.271271	−	0.962503i	$-0.412556\pi$
$661$	9.56930e89			0.542542			0.271271	+	0.962503i	$0.412556\pi$
$662$		−	2.86671e90i		−	1.54856i
$663$	3.09734e88	−	9.84407e89i	0.0159425	−	0.506690i
$664$	−2.57864e90			−1.26477
$665$			1.50159e90i			0.701872i
$666$	1.76089e89	−	2.79548e90i	0.0784433	−	1.24532i
$667$	3.13145e89			0.132959
$668$			1.16038e90i			0.469629i
$669$	−3.06102e90	−	9.63120e88i	−1.18095	−	0.0371573i
$670$	1.05084e90			0.386493
$671$			6.93662e90i			2.43236i
$672$	−4.82251e88	+	1.53271e90i	−0.0161234	+	0.512440i
$673$	9.35762e89			0.298321			0.149160	−	0.988813i	$-0.452343\pi$
$673$	9.35762e89			0.298321			0.149160	+	0.988813i	$0.452343\pi$
$674$		−	6.09165e89i		−	0.185190i
$675$	−1.47167e90	−	1.39281e89i	−0.426666	−	0.0403805i
$676$	4.58903e90			1.26890
$677$			7.41772e90i			1.95629i	0.207923	+	0.978145i	$0.433329\pi$
$677$			7.41772e90i			1.95629i	−0.207923	+	0.978145i	$0.566671\pi$
$678$	6.66529e90	+	2.09717e89i	1.67675	+	0.0527573i
$679$	−3.13947e90			−0.753396
$680$		−	3.84329e90i		−	0.879869i
$681$	1.30874e89	−	4.15950e90i	0.0285856	−	0.908518i
$682$	1.94602e91			4.05553
$683$			3.27108e90i			0.650471i	0.945633	+	0.325236i	$0.105444\pi$
$683$			3.27108e90i			0.650471i	−0.945633	+	0.325236i	$0.894556\pi$
$684$	−1.33804e91	−	8.42834e89i	−2.53906	−	0.159936i
$685$	−7.06633e90			−1.27966
$686$		−	9.55919e90i		−	1.65215i
$687$	3.55826e89	+	1.11957e88i	0.0586978	+	0.00184687i
$688$	−1.30082e90			−0.204827
$689$		−	5.91316e90i		−	0.888801i
$690$	−6.30455e88	+	2.00373e90i	−0.00904655	+	0.287521i
$691$	−1.10295e90			−0.151098			−0.0755491	−	0.997142i	$-0.524071\pi$
$691$	−1.10295e90			−0.151098			−0.0755491	+	0.997142i	$0.524071\pi$
$692$			2.13366e91i			2.79080i
$693$	4.86314e89	−	7.72045e90i	0.0607370	−	0.964227i
$694$	−2.02643e91			−2.41674
$695$		−	1.20017e91i		−	1.36688i
$696$	−6.14432e90	−	1.93325e89i	−0.668310	−	0.0210277i
$697$	−1.31912e91			−1.37037
$698$		−	1.81790e91i		−	1.80383i
$699$	−5.31896e89	+	1.69049e91i	−0.0504147	+	1.60230i
$700$	5.03332e90			0.455740
$701$		−	1.17159e91i		−	1.01344i	−0.862109	−	0.506722i	$-0.830857\pi$
$701$		−	1.17159e91i		−	1.01344i	0.862109	−	0.506722i	$-0.169143\pi$
$702$	9.50238e89	−	1.00403e91i	0.0785317	−	0.829777i
$703$	1.43146e91			1.13034
$704$			3.20805e91i			2.42056i
$705$	2.80454e90	+	8.82421e88i	0.202214	+	0.00636245i
$706$	7.60768e90			0.524206
$707$		−	7.71382e90i		−	0.507982i
$708$	−1.05448e90	+	3.35138e91i	−0.0663702	+	2.10940i
$709$	1.98341e91			1.19325			0.596626	−	0.802519i	$-0.296507\pi$
$709$	1.98341e91			1.19325			0.596626	+	0.802519i	$0.296507\pi$
$710$		−	1.52564e91i		−	0.877375i
$711$	−1.15854e91	−	7.29770e89i	−0.636920	−	0.0401198i
$712$	3.14608e91			1.65352
$713$			7.31582e90i			0.367619i
$714$	−2.13372e91	−	6.71354e89i	−1.02517	−	0.0322559i
$715$	−1.29271e91			−0.593892
$716$			3.89935e91i			1.71307i
$717$	−8.28473e89	+	2.63308e91i	−0.0348069	+	1.10624i
$718$	5.98548e90			0.240501
$719$		−	4.53670e91i		−	1.74347i	−0.489975	−	0.871736i	$-0.662994\pi$
$719$		−	4.53670e91i		−	1.74347i	0.489975	−	0.871736i	$-0.337006\pi$
$720$	2.67297e89	−	4.24346e90i	0.00982549	−	0.155984i
$721$	2.20701e91			0.776025
$722$		−	5.97410e91i		−	2.00947i
$723$	−1.21141e91	−	3.81159e89i	−0.389822	−	0.0122654i
$724$	−3.09069e91			−0.951529
$725$		−	8.36367e90i		−	0.246366i
$726$	2.57948e90	−	8.19820e91i	0.0727043	−	2.31072i
$727$	4.83390e91			1.30376			0.651879	−	0.758323i	$-0.273981\pi$
$727$	4.83390e91			1.30376			0.651879	+	0.758323i	$0.273981\pi$
$728$			1.42222e91i			0.367081i
$729$	3.97650e91	+	7.59490e90i	0.982245	+	0.187603i
$730$	−1.30568e91			−0.308678
$731$			4.38111e91i			0.991351i
$732$	1.23544e92	+	3.88718e90i	2.67588	+	0.0841938i
$733$	−4.40162e91			−0.912610			−0.456305	−	0.889823i	$-0.650827\pi$
$733$	−4.40162e91			−0.912610			−0.456305	+	0.889823i	$0.650827\pi$
$734$			9.07798e91i			1.80184i
$735$	7.65524e89	−	2.43302e91i	0.0145467	−	0.462328i
$736$	−1.04626e91			−0.190349
$737$		−	2.76662e91i		−	0.481937i
$738$	−1.34810e92	−	8.49170e90i	−2.24863	−	0.141642i
$739$	−5.65534e91			−0.903310			−0.451655	−	0.892193i	$-0.649166\pi$
$739$	−5.65534e91			−0.903310			−0.451655	+	0.892193i	$0.649166\pi$
$740$			6.39764e91i			0.978599i
$741$	5.15149e91	+	1.62087e90i	0.754658	+	0.0237446i
$742$	−1.28169e92			−1.79828
$743$			3.62322e91i			0.486914i	0.969912	+	0.243457i	$0.0782814\pi$
$743$			3.62322e91i			0.486914i	−0.969912	+	0.243457i	$0.921719\pi$
$744$	4.51654e90	−	1.43546e92i	0.0581396	−	1.84781i
$745$	7.71920e91			0.951857
$746$			7.74330e91i			0.914710i
$747$	−6.04016e90	+	9.58903e91i	−0.0683580	+	1.08521i
$748$	−2.44312e92			−2.64908
$749$			6.99894e90i			0.0727134i
$750$	1.78390e92	+	5.61285e90i	1.77586	+	0.0558757i
$751$	−7.52766e91			−0.718095			−0.359048	−	0.933319i	$-0.616898\pi$
$751$	−7.52766e91			−0.718095			−0.359048	+	0.933319i	$0.616898\pi$
$752$		−	6.05306e90i		−	0.0553356i
$753$	−4.50101e90	+	1.43053e92i	−0.0394340	+	1.25331i
$754$	5.70606e91			0.479130
$755$			3.53806e89i			0.00284749i
$756$	−1.37231e92	−	1.29878e91i	−1.05866	−	0.100194i
$757$	1.39010e92			1.02796			0.513980	−	0.857802i	$-0.328170\pi$
$757$	1.39010e92			1.02796			0.513980	+	0.857802i	$0.328170\pi$
$758$		−	4.55116e92i		−	3.22632i
$759$	5.27539e91	+	1.65985e90i	0.358524	+	0.0112806i
$760$	2.01123e92			1.31047
$761$		−	8.22600e91i		−	0.513901i	−0.966425	−	0.256951i	$-0.917282\pi$
$761$		−	8.22600e91i		−	0.513901i	0.966425	−	0.256951i	$-0.0827178\pi$
$762$	2.56608e90	−	8.15559e91i	0.0153713	−	0.488536i
$763$	−3.38210e90			−0.0194268
$764$			3.77673e91i			0.208031i
$765$	−1.42918e92	−	9.00245e90i	−0.754955	−	0.0475549i
$766$	−2.53658e92			−1.28507
$767$		−	1.28902e92i		−	0.626335i
$768$	2.80979e92	+	8.84073e90i	1.30953	+	0.0412030i
$769$	2.17695e92			0.973207			0.486604	−	0.873623i	$-0.338236\pi$
$769$	2.17695e92			0.973207			0.486604	+	0.873623i	$0.338236\pi$
$770$			2.80197e92i			1.20160i
$771$	1.19162e90	−	3.78724e91i	0.00490227	−	0.155806i
$772$	2.46608e92			0.973315
$773$			8.90702e91i			0.337278i	0.985678	+	0.168639i	$0.0539373\pi$
$773$			8.90702e91i			0.337278i	−0.985678	+	0.168639i	$0.946063\pi$
$774$	−2.82029e91	+	4.47733e92i	−0.102467	+	1.62670i
$775$	1.95396e92			0.681178
$776$			4.20501e92i			1.40667i
$777$	1.47105e92	+	4.62851e90i	0.472231	+	0.0148583i
$778$	−1.25307e92			−0.386036
$779$		−	6.90309e92i		−	2.04101i
$780$	−7.24414e90	+	2.30236e92i	−0.0205570	+	0.653350i
$781$	−4.01668e92			−1.09404
$782$		−	1.45653e92i		−	0.380806i
$783$	−2.15814e91	+	2.28032e92i	−0.0541631	+	0.572295i
$784$	−5.25120e91			−0.126516
$785$			1.26602e92i			0.292827i
$786$	2.00903e92	+	6.32122e90i	0.446134	+	0.0140372i
$787$	−8.13055e91			−0.173352			−0.0866760	−	0.996237i	$-0.527624\pi$
$787$	−8.13055e91			−0.173352			−0.0866760	+	0.996237i	$0.527624\pi$
$788$		−	2.39672e91i		−	0.0490657i
$789$	1.68692e91	−	5.36142e92i	0.0331612	−	1.05394i
$790$	4.20468e92			0.793718
$791$			3.50396e92i			0.635201i
$792$	−1.03408e93	−	6.51369e91i	−1.80031	−	0.113402i
$793$	−4.75177e92			−0.794536
$794$		−	2.47781e92i		−	0.397934i
$795$	−8.59334e92	−	2.70381e91i	−1.32560	−	0.0417088i
$796$	3.27440e92			0.485192
$797$		−	2.65703e92i		−	0.378208i	−0.981957	−	0.189104i	$-0.939442\pi$
$797$		−	2.65703e92i		−	0.378208i	0.981957	−	0.189104i	$-0.0605583\pi$
$798$	3.51326e91	−	1.11660e93i	0.0480416	−	1.52688i
$799$	−2.03865e92			−0.267821
$800$			2.79443e92i			0.352707i
$801$	7.36934e91	−	1.16991e93i	0.0893692	−	1.41878i
$802$	1.69563e93			1.97584
$803$			3.43758e92i			0.384906i
$804$	−4.92745e92	−	1.55037e91i	−0.530186	−	0.0166818i
$805$	−1.05337e92			−0.108921
$806$			1.33307e93i			1.32475i
$807$	−4.61987e91	+	1.46830e93i	−0.0441242	+	1.40237i
$808$	−1.03319e93			−0.948455
$809$			8.75139e92i			0.772190i	0.922459	+	0.386095i	$0.126176\pi$
$809$			8.75139e92i			0.772190i	−0.922459	+	0.386095i	$0.873824\pi$
$810$	−1.45477e93	−	1.84004e92i	−1.23389	−	0.156065i
$811$	4.01094e92			0.327023			0.163512	−	0.986541i	$-0.447718\pi$
$811$	4.01094e92			0.327023			0.163512	+	0.986541i	$0.447718\pi$
$812$		−	7.79904e92i		−	0.611292i
$813$	−7.42440e92	−	2.33601e91i	−0.559453	−	0.0176026i
$814$	2.67112e93			1.93514
$815$			1.28897e92i			0.0897842i
$816$	−9.71503e90	+	3.08767e92i	−0.00650667	+	0.206797i
$817$	−2.29267e93			−1.47651
$818$			7.40692e92i			0.458703i
$819$	5.28871e92	+	3.33138e91i	0.314967	+	0.0198399i
$820$	3.08520e93			1.76702
$821$			2.95542e93i			1.62794i	0.580906	+	0.813971i	$0.302698\pi$
$821$			2.95542e93i			1.62794i	−0.580906	+	0.813971i	$0.697302\pi$
$822$	5.25460e93	+	1.65331e92i	2.78382	+	0.0875902i
$823$	1.27974e93			0.652118			0.326059	−	0.945349i	$-0.394279\pi$
$823$	1.27974e93			0.652118			0.326059	+	0.945349i	$0.394279\pi$
$824$		−	2.95607e93i		−	1.44892i
$825$	4.43323e91	−	1.40899e93i	0.0209023	−	0.664324i
$826$	−2.79397e93			−1.26724
$827$		−	2.08973e93i		−	0.911832i	−0.890023	−	0.455916i	$-0.849312\pi$
$827$		−	2.08973e93i		−	0.911832i	0.890023	−	0.455916i	$-0.150688\pi$
$828$	5.91250e91	−	9.38636e92i	0.0248199	−	0.394027i
$829$	4.02995e92			0.162762			0.0813812	−	0.996683i	$-0.474067\pi$
$829$	4.02995e92			0.162762			0.0813812	+	0.996683i	$0.474067\pi$
$830$		−	3.48013e93i		−	1.35237i
$831$	3.20733e93	+	1.00915e92i	1.19925	+	0.0377332i
$832$	−2.19760e93			−0.790682
$833$			1.76858e93i			0.612329i
$834$	−2.80804e92	+	8.92462e93i	−0.0935600	+	2.97356i
$835$	−6.48602e92			−0.207975
$836$		−	1.27851e94i		−	3.94551i
$837$	−5.32738e93	−	5.04194e92i	−1.58234	−	0.149756i
$838$	−6.35535e93			−1.81690
$839$			1.64864e93i			0.453673i	0.973933	+	0.226836i	$0.0728383\pi$
$839$			1.64864e93i			0.453673i	−0.973933	+	0.226836i	$0.927162\pi$
$840$	2.06685e93	+	6.50313e91i	0.547484	+	0.0172260i
$841$	2.62574e93			0.669545
$842$			6.46531e93i			1.58709i
$843$	4.55067e91	−	1.44631e93i	0.0107546	−	0.341806i
$844$	−5.45320e93			−1.24077
$845$			2.56506e93i			0.561932i
$846$	−2.08342e93	−	1.31236e92i	−0.439467	−	0.0276822i
$847$	4.30981e93			0.875364
$848$			1.85471e93i			0.362750i
$849$	−2.45276e92	−	7.71736e90i	−0.0461965	−	0.00145353i
$850$	−3.89020e93			−0.705612
$851$			1.00417e93i			0.175413i
$852$	−2.25089e92	+	7.15385e93i	−0.0378692	+	1.20357i
$853$	9.48398e93			1.53682			0.768408	−	0.639961i	$-0.221049\pi$
$853$	9.48398e93			1.53682			0.768408	+	0.639961i	$0.221049\pi$
$854$			1.02996e94i			1.60756i
$855$	4.71106e92	−	7.47902e93i	0.0708277	−	1.12442i
$856$	9.37439e92			0.135763
$857$			1.53334e93i			0.213920i	0.994263	+	0.106960i	$0.0341117\pi$
$857$			1.53334e93i			0.213920i	−0.994263	+	0.106960i	$0.965888\pi$
$858$	9.61272e93	+	3.02455e92i	1.29197	+	0.0406506i
$859$	−9.18561e93			−1.18940			−0.594699	−	0.803949i	$-0.702729\pi$
$859$	−9.18561e93			−1.18940			−0.594699	+	0.803949i	$0.702729\pi$
$860$		−	1.02466e94i		−	1.27830i
$861$	2.23205e92	−	7.09399e93i	0.0268290	−	0.852687i
$862$	−2.13290e94			−2.47024
$863$		−	7.11614e93i		−	0.794143i	−0.917788	−	0.397072i	$-0.870026\pi$
$863$		−	7.11614e93i		−	0.794143i	0.917788	−	0.397072i	$-0.129974\pi$
$864$	7.21068e92	−	7.61890e93i	0.0775419	−	0.819319i
$865$	−1.19262e94			−1.23591
$866$			1.63464e94i			1.63248i
$867$	1.43753e91	+	4.52305e89i	0.00138359	+	4.35332e-5i
$868$	1.82205e94			1.69016
$869$		−	1.10700e94i		−	0.989726i
$870$	2.60911e92	−	8.29237e93i	0.0224842	−	0.714599i
$871$	1.89521e93			0.157426
$872$			4.52999e92i			0.0362719i
$873$	1.56369e94	+	9.84974e92i	1.20697	+	0.0760272i
$874$	7.62216e93			0.567169
$875$			9.37798e93i			0.672746i
$876$	6.12244e93	+	1.92637e92i	0.423442	+	0.0133232i
$877$	1.95395e94			1.30295			0.651473	−	0.758672i	$-0.274151\pi$
$877$	1.95395e94			1.30295			0.651473	+	0.758672i	$0.274151\pi$
$878$		−	4.05787e93i		−	0.260899i
$879$	2.18419e92	−	6.94186e93i	0.0135408	−	0.430360i
$880$	4.05467e93			0.242388
$881$			1.40838e94i			0.811879i	0.913900	+	0.405940i	$0.133056\pi$
$881$			1.40838e94i			0.811879i	−0.913900	+	0.405940i	$0.866944\pi$
$882$	−1.13850e93	+	1.80743e94i	−0.0632907	+	1.00477i
$883$	2.21973e94			1.19003			0.595016	−	0.803714i	$-0.297146\pi$
$883$	2.21973e94			1.19003			0.595016	+	0.803714i	$0.297146\pi$
$884$		−	1.67361e94i		−	0.865328i
$885$	−1.87327e94	−	5.89406e92i	−0.934149	−	0.0293921i
$886$	4.51940e93			0.217371
$887$			7.60737e93i			0.352922i	0.984308	+	0.176461i	$0.0564650\pi$
$887$			7.60737e93i			0.352922i	−0.984308	+	0.176461i	$0.943535\pi$
$888$	6.19943e92	−	1.97032e94i	0.0277419	−	0.881704i
$889$	4.28741e93			0.185071
$890$			4.24595e94i			1.76805i
$891$	−4.84441e93	+	3.83010e94i	−0.194605	+	1.53859i
$892$	−5.20409e94			−2.01683
$893$		−	1.06684e94i		−	0.398890i
$894$	−5.74008e94	−	1.80606e93i	−2.07070	−	0.0651526i
$895$	−2.17956e94			−0.758634
$896$			3.23678e94i			1.08707i
$897$	−1.13704e92	+	3.61378e93i	−0.00368483	+	0.117113i
$898$	1.04821e94			0.327797
$899$		−	3.02762e94i		−	0.913675i
$900$	−2.50697e94	−	1.57915e93i	−0.730111	−	0.0459899i
$901$	6.24657e94			1.75569
$902$		−	1.28812e95i		−	3.49420i
$903$	−2.35607e94	−	7.41315e92i	−0.616852	−	0.0194086i
$904$	4.69320e94			1.18599
$905$		−	1.72756e94i		−	0.421384i
$906$	8.27799e90	−	2.63094e92i	0.000194905	−	0.00619453i
$907$	1.39392e94			0.316815			0.158407	−	0.987374i	$-0.449364\pi$
$907$	1.39392e94			0.316815			0.158407	+	0.987374i	$0.449364\pi$
$908$		−	7.07163e94i		−	1.55157i
$909$	−2.42013e93	+	3.84206e94i	−0.0512618	+	0.813804i
$910$	−1.91942e94			−0.392506
$911$			1.85422e94i			0.366078i	0.983106	+	0.183039i	$0.0585935\pi$
$911$			1.85422e94i			0.366078i	−0.983106	+	0.183039i	$0.941406\pi$
$912$	−1.61580e94	−	5.08396e92i	−0.308002	−	0.00969097i
$913$	−9.16242e94			−1.68634
$914$			8.60771e94i			1.52971i
$915$	−2.17276e93	+	6.90554e94i	−0.0372852	+	1.18501i
$916$	6.04944e93			0.100244
$917$			1.05615e94i			0.169008i
$918$	1.06065e95	+	1.00382e94i	1.63910	+	0.155127i
$919$	1.05125e94			0.156895			0.0784476	−	0.996918i	$-0.475004\pi$
$919$	1.05125e94			0.156895			0.0784476	+	0.996918i	$0.475004\pi$
$920$			1.41088e94i			0.203367i
$921$	−3.08012e92	−	9.69130e90i	−0.00428805	−	0.000134919i
$922$	−1.43248e94			−0.192620
$923$		−	2.75153e94i		−	0.357372i
$924$	4.13395e93	−	1.31387e95i	0.0518635	−	1.64834i
$925$	2.68201e94			0.325031
$926$			9.94344e94i			1.16409i
$927$	−1.09926e95	−	6.92425e93i	−1.24322	−	0.0783107i
$928$	4.32992e94			0.473091
$929$			2.92925e94i			0.309210i	0.987976	+	0.154605i	$0.0494105\pi$
$929$			2.92925e94i			0.309210i	−0.987976	+	0.154605i	$0.950589\pi$
$930$	1.93730e95	+	6.09552e93i	1.97580	+	0.0621665i
$931$	−9.25514e94			−0.911997
$932$			2.87403e95i			2.73642i
$933$	1.70202e93	−	5.40943e94i	0.0156586	−	0.497667i
$934$	3.01250e95			2.67810
$935$		−	1.36560e95i		−	1.17314i
$936$	4.46205e93	−	7.08371e94i	0.0370431	−	0.588076i
$937$	3.31046e93			0.0265596			0.0132798	−	0.999912i	$-0.495773\pi$
$937$	3.31046e93			0.0265596			0.0132798	+	0.999912i	$0.495773\pi$
$938$		−	4.10790e94i		−	0.318515i
$939$	−7.40096e94	−	2.32864e93i	−0.554612	−	0.0174503i
$940$	4.76804e94			0.345342
$941$		−	8.86848e94i		−	0.620842i	−0.950599	−	0.310421i	$-0.899530\pi$
$941$		−	8.86848e94i		−	0.620842i	0.950599	−	0.310421i	$-0.100470\pi$
$942$	2.96210e93	−	9.41424e94i	0.0200434	−	0.637025i
$943$	4.84253e94			0.316737
$944$			4.04310e94i			0.255629i
$945$	7.25962e93	−	7.67062e94i	0.0443707	−	0.468827i
$946$	−4.27814e95			−2.52778
$947$		−	7.50594e94i		−	0.428752i	−0.976751	−	0.214376i	$-0.931228\pi$
$947$		−	7.50594e94i		−	0.428752i	0.976751	−	0.214376i	$-0.0687717\pi$
$948$	−1.97161e95	−	6.20346e93i	−1.08881	−	0.0342584i
$949$	−2.35483e94			−0.125731
$950$		−	2.03578e95i		−	1.05093i
$951$	−1.38580e93	+	4.40439e94i	−0.00691709	+	0.219841i
$952$	−1.50241e95			−0.725113
$953$		−	1.62509e95i		−	0.758411i	−0.925313	−	0.379205i	$-0.876197\pi$
$953$		−	1.62509e95i		−	0.758411i	0.925313	−	0.379205i	$-0.123803\pi$
$954$	6.38377e95	+	4.02116e94i	2.88091	+	0.181469i
$955$	−2.11103e94			−0.0921267
$956$			4.47654e95i			1.88925i
$957$	−2.18320e95	−	6.86922e93i	−0.891069	−	0.0280366i
$958$	−6.63771e95			−2.62013
$959$			2.76235e95i			1.05459i
$960$	−1.00486e94	+	3.19367e95i	−0.0371043	+	1.17926i
$961$	4.27332e95			1.52622
$962$			1.82979e95i			0.632118i
$963$	2.19584e93	−	3.48600e94i	0.00733770	−	0.116489i
$964$	−2.05954e95			−0.665741
$965$			1.37843e95i			0.431033i
$966$	7.83295e94	+	2.46456e93i	0.236950	+	0.00745540i
$967$	5.96870e93			0.0174676			0.00873379	−	0.999962i	$-0.497220\pi$
$967$	5.96870e93			0.0174676			0.00873379	+	0.999962i	$0.497220\pi$
$968$		−	5.77256e95i		−	1.63440i
$969$	−1.71226e94	+	5.44196e95i	−0.0469038	+	1.49071i
$970$	−5.67508e95			−1.50410
$971$		−	3.73965e95i		−	0.958995i	−0.877543	−	0.479497i	$-0.840819\pi$
$971$		−	3.73965e95i		−	0.958995i	0.877543	−	0.479497i	$-0.159181\pi$
$972$	6.79440e95	+	1.07744e95i	1.68590	+	0.267345i
$973$	−4.69169e95			−1.12647
$974$		−	8.93801e95i		−	2.07661i
$975$	9.65193e94	+	3.03688e93i	0.217003	+	0.00682779i
$976$	1.49043e95			0.324277
$977$			4.62747e95i			0.974356i	0.873303	+	0.487178i	$0.161974\pi$
$977$			4.62747e95i			0.974356i	−0.873303	+	0.487178i	$0.838026\pi$
$978$	3.01580e93	−	9.58493e94i	0.00614553	−	0.195319i
$979$	1.11787e96			2.20467
$980$		−	4.13641e95i		−	0.789567i
$981$	1.68454e94	+	1.06110e93i	0.0311224	+	0.00196041i
$982$	7.96054e95			1.42356
$983$		−	2.81108e95i		−	0.486587i	−0.969953	−	0.243293i	$-0.921772\pi$
$983$		−	2.81108e95i		−	0.486587i	0.969953	−	0.243293i	$-0.0782277\pi$
$984$	−9.50170e95	−	2.98962e94i	−1.59206	−	0.0500924i
$985$	1.33966e94			0.0217287
$986$			6.02780e95i			0.946450i
$987$	3.44954e93	−	1.09635e95i	0.00524339	−	0.166647i
$988$	8.75813e95			1.28881
$989$		−	1.60831e95i		−	0.229134i
$990$	8.79088e94	−	1.39559e96i	0.121257	−	1.92501i
$991$	6.64242e95			0.887094			0.443547	−	0.896251i	$-0.353720\pi$
$991$	6.64242e95			0.887094			0.443547	+	0.896251i	$0.353720\pi$
$992$			1.01158e96i			1.30805i
$993$	−7.51361e95	−	2.36408e94i	−0.940746	−	0.0295996i
$994$	−5.96400e95			−0.723058
$995$			1.83024e95i			0.214867i
$996$	−5.13448e94	+	1.63186e96i	−0.0583711	+	1.85517i
$997$	−8.56321e95			−0.942740			−0.471370	−	0.881936i	$-0.656240\pi$
$997$	−8.56321e95			−0.942740			−0.471370	+	0.881936i	$0.656240\pi$
$998$		−	1.97263e96i		−	2.10314i
$999$	−7.31240e95	−	6.92059e94i	−0.755030	−	0.0714575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.65.b.a.2.2	✓	20
3.2	odd	2	inner	3.65.b.a.2.19	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.65.b.a.2.2	✓	20	1.1	even	1	trivial
3.65.b.a.2.19	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)

\(f(q)\)	\(=\)	\(q-7.06644e9i q^{2} +(-1.85210e15 - 5.82746e13i) q^{3} -3.14879e19 q^{4} -1.76003e22i q^{5} +(-4.11794e23 + 1.30878e25i) q^{6} -6.88028e26 q^{7} +9.21545e28i q^{8} +(3.42689e30 + 2.15861e29i) q^{9} +O(q^{10})\)	\(q-7.06644e9i q^{2} +(-1.85210e15 - 5.82746e13i) q^{3} -3.14879e19 q^{4} -1.76003e22i q^{5} +(-4.11794e23 + 1.30878e25i) q^{6} -6.88028e26 q^{7} +9.21545e28i q^{8} +(3.42689e30 + 2.15861e29i) q^{9} -1.24372e32 q^{10} +3.27443e33i q^{11} +(5.83188e34 + 1.83494e33i) q^{12} -2.24307e35 q^{13} +4.86191e36i q^{14} +(-1.02565e36 + 3.25976e37i) q^{15} +7.03557e37 q^{16} -2.36955e39i q^{17} +(1.52537e39 - 2.42159e40i) q^{18} +1.24001e41 q^{19} +5.54197e41i q^{20} +(1.27430e42 + 4.00945e40i) q^{21} +2.31386e43 q^{22} +8.69868e42i q^{23} +(5.37027e42 - 1.70680e44i) q^{24} +2.32330e44 q^{25} +1.58506e45i q^{26} +(-6.33438e45 - 5.99498e44i) q^{27} +2.16645e46 q^{28} -3.59991e46i q^{29} +(2.30349e47 + 7.24771e45i) q^{30} +8.41027e47 q^{31} +1.20279e48i q^{32} +(1.90816e47 - 6.06459e48i) q^{33} -1.67443e49 q^{34} +1.21095e49i q^{35} +(-1.07906e50 - 6.79701e48i) q^{36} +1.15440e50 q^{37} -8.76244e50i q^{38} +(4.15441e50 + 1.30714e49i) q^{39} +1.62195e51 q^{40} -5.56698e51i q^{41} +(2.83326e50 - 9.00476e51i) q^{42} -1.84892e52 q^{43} -1.03105e53i q^{44} +(3.79922e51 - 6.03144e52i) q^{45} +6.14687e52 q^{46} -8.60352e52i q^{47} +(-1.30306e53 - 4.09995e51i) q^{48} -7.46378e53 q^{49} -1.64175e54i q^{50} +(-1.38085e53 + 4.38865e54i) q^{51} +7.06297e54 q^{52} +2.63619e55i q^{53} +(-4.23632e54 + 4.47615e55i) q^{54} +5.76311e55 q^{55} -6.34048e55i q^{56} +(-2.29662e56 - 7.22609e54i) q^{57} -2.54386e56 q^{58} +5.74665e56i q^{59} +(3.22956e55 - 1.02643e57i) q^{60} +2.11842e57 q^{61} -5.94307e57i q^{62} +(-2.35780e57 - 1.48518e56i) q^{63} +9.79725e57 q^{64} +3.94788e57i q^{65} +(-4.28551e58 - 1.34839e57i) q^{66} -8.44916e57 q^{67} +7.46121e58i q^{68} +(5.06912e56 - 1.61109e58i) q^{69} +8.55711e58 q^{70} +1.22668e59i q^{71} +(-1.98926e58 + 3.15804e59i) q^{72} +1.04982e59 q^{73} -8.15749e59i q^{74} +(-4.30299e59 - 1.35389e58i) q^{75} -3.90452e60 q^{76} -2.25290e60i q^{77} +(9.23685e58 - 2.93569e60i) q^{78} -3.38074e60 q^{79} -1.23828e60i q^{80} +(1.16970e61 + 1.47947e60i) q^{81} -3.93387e61 q^{82} +2.79817e61i q^{83} +(-4.01250e61 - 1.26249e60i) q^{84} -4.17048e61 q^{85} +1.30653e62i q^{86} +(-2.09783e60 + 6.66741e61i) q^{87} -3.01754e62 q^{88} -3.41392e62i q^{89} +(-4.26208e62 - 2.68470e61i) q^{90} +1.54330e62 q^{91} -2.73903e62i q^{92} +(-1.55767e63 - 4.90105e61i) q^{93} -6.07963e62 q^{94} -2.18245e63i q^{95} +(7.00919e61 - 2.22768e63i) q^{96} +4.56300e63 q^{97} +5.27424e63i q^{98} +(-7.06823e62 + 1.12211e64i) 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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