LMFDB - Embedded newform 3.67.b.b.2.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,67,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, 67, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 67);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 67 $
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:	$82.7604085389$
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 + 56\!\cdots\!00 $ x^20 + 906717684887249855x^18 + 344606158489511664696698228332738560x^16 + 71652971665901614605371772053696816281967289983887360x^14 + 8921702771745764004349589391487877757784958676037438882928369158062080x^12 + 683403379594951632563697758305810601419154166308878019955226233819915447649058345189376x^10 + 31772957367677271365415732215028927227037755531987823390235825210012529727999274511693739707490264678400x^8 + 847964773053274963652827780310639028120086491835670486067065232524144747514188148844364201186425789578281808007738163200x^6 + 11506211018221614217869179366991618199482201012751276612182882363431530293525433274689836274264163709469073141596829595134065631035392000x^4 + 60607531838376195456599500642331923018616851910965149510682392060466386164945809665702677714428674778241564538431592184046417165018463941554706841600000*x^2 + 562967847204053425511937299454033818405377210070880712980208780397371469949095783773485167746826255963506772441456393084506064672971373387205630483863961600000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{216}\cdot 3^{291}\cdot 5^{20}\cdot 7^{10}\cdot 11^{6}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.12
Root			$1.26111e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.67.b.b.2.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.54000e9i q^{2} +(5.46530e15 + 1.01669e15i) q^{3} +5.31753e19 q^{4} +1.75307e23i q^{5} +(-4.61577e24 + 2.48125e25i) q^{6} -8.19169e27 q^{7} +5.76409e29i q^{8} +(2.88358e31 + 1.11130e31i) q^{9} -7.95893e32 q^{10} +2.37945e34i q^{11} +(2.90619e35 + 5.40628e34i) q^{12} +7.13046e36 q^{13} -3.71903e37i q^{14} +(-1.78232e38 + 9.58103e38i) q^{15} +1.30675e39 q^{16} +5.94349e40i q^{17} +(-5.04531e40 + 1.30915e41i) q^{18} +8.13114e41 q^{19} +9.32199e42i q^{20} +(-4.47700e43 - 8.32840e42i) q^{21} -1.08027e44 q^{22} -1.37490e45i q^{23} +(-5.86029e44 + 3.15025e45i) q^{24} -1.71799e46 q^{25} +3.23723e46i q^{26} +(1.46298e47 + 9.00531e46i) q^{27} -4.35596e47 q^{28} -9.76720e47i q^{29} +(-4.34979e48 - 8.09175e47i) q^{30} -1.85675e49 q^{31} +4.84641e49i q^{32} +(-2.41916e49 + 1.30044e50i) q^{33} -2.69835e50 q^{34} -1.43606e51i q^{35} +(1.53336e51 + 5.90939e50i) q^{36} +6.12483e51 q^{37} +3.69154e51i q^{38} +(3.89701e52 + 7.24946e51i) q^{39} -1.01048e53 q^{40} +1.20825e53i q^{41} +(3.78110e52 - 2.03256e53i) q^{42} -2.91666e53 q^{43} +1.26528e54i q^{44} +(-1.94819e54 + 5.05512e54i) q^{45} +6.24205e54 q^{46} -1.66827e54i q^{47} +(7.14177e54 + 1.32856e54i) q^{48} +7.33550e54 q^{49} -7.79968e55i q^{50} +(-6.04268e55 + 3.24830e56i) q^{51} +3.79165e56 q^{52} -6.92806e56i q^{53} +(-4.08841e56 + 6.64194e56i) q^{54} -4.17133e57 q^{55} -4.72177e57i q^{56} +(4.44391e57 + 8.26684e56i) q^{57} +4.43431e57 q^{58} -2.60594e58i q^{59} +(-9.47757e57 + 5.09475e58i) q^{60} +1.11009e59 q^{61} -8.42964e58i q^{62} +(-2.36214e59 - 9.10344e58i) q^{63} -1.23606e59 q^{64} +1.25002e60i q^{65} +(-5.90399e59 - 1.09830e59i) q^{66} +3.96041e59 q^{67} +3.16047e60i q^{68} +(1.39785e60 - 7.51425e60i) q^{69} +6.51971e60 q^{70} -1.42835e61i q^{71} +(-6.40565e60 + 1.66212e61i) q^{72} -2.22307e61 q^{73} +2.78068e61i q^{74} +(-9.38933e61 - 1.74666e61i) q^{75} +4.32376e61 q^{76} -1.94917e62i q^{77} +(-3.29126e61 + 1.76924e62i) q^{78} -3.86775e62 q^{79} +2.29082e62i q^{80} +(7.08007e62 + 6.40906e62i) q^{81} -5.48546e62 q^{82} +9.18639e62i q^{83} +(-2.38066e63 - 4.42866e62i) q^{84} -1.04193e64 q^{85} -1.32416e63i q^{86} +(9.93021e62 - 5.33807e63i) q^{87} -1.37153e64 q^{88} +3.59677e64i q^{89} +(-2.29502e64 - 8.84477e63i) q^{90} -5.84105e64 q^{91} -7.31108e64i q^{92} +(-1.01477e65 - 1.88773e64i) q^{93} +7.57396e63 q^{94} +1.42544e65i q^{95} +(-4.92730e64 + 2.64871e65i) q^{96} -5.76248e65 q^{97} +3.33032e64i q^{98} +(-2.64428e65 + 6.86133e65i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 48\!\cdots\!16 q^{3} - 87\!\cdots\!80 q^{4} - 36\!\cdots\!80 q^{6} + 12\!\cdots\!88 q^{7} + 15\!\cdots\!00 q^{9} - 78\!\cdots\!00 q^{10} + 72\!\cdots\!64 q^{12} + 18\!\cdots\!12 q^{13} + 29\!\cdots\!00 q^{15}+ \cdots + 13\!\cdots\!00 q^{99}+O(q^{100}) $ 20 * q + 4870975596954516 * q^3 - 874472713330987494880 * q^4 - 36458623571791371420365280 * q^6 + 12757412570419684480800346888 * q^7 + 15089557305995766698320873638900 * q^9 - 783798592344000703899756417518400 * q^10 + 723313252400516086588885120719010464 * q^12 + 18091739616075205076630659610294803912 * q^13 + 291841906843973945390453919652713854400 * q^15 + 35169907781372839393817803526848507036160 * q^16 - 1327598375030727473316959111629621787325120 * q^18 - 2193455295604677957336968896648577476247000 * q^19 + 8465393426583554489761097856455177936278920 * q^21 - 19209253722854761211546865955725969475475520 * q^22 - 8536939678857788536491103872952212579880680960 * q^24 - 30700488848472932976681231276090805532106633100 * q^25 + 558391355065775903739609435927472633730508278964 * q^27 + 144501040816005166289020822469679267340863318592 * q^28 - 13469561117532417280775174235598750536019791067200 * q^30 + 6175065418525787560244925992300120132476837130440 * q^31 + 76031443883614128882573745917963369573166525959360 * q^33 - 607578292754219603165333260413176675880514014447360 * q^34 - 3175274131330481643421765009589425373421119877953760 * q^36 + 27435708863590762009354808934891346302092239434849928 * q^37 + 5521526696977593923927147874084291303373365890875080 * q^39 - 164157270356735970397207190518038139497893424374707200 * q^40 - 362475530834094311762041222130355899146344066985844160 * q^42 + 2995923276457113198574378450730231874677434142901437032 * q^43 + 2893961767142107219663835709681578507068881328379222400 * q^45 - 9354105762324374445425328051923657080564209708616152960 * q^46 + 44083933305287886033485048811587957889306840899931818496 * q^48 + 35901948198185324872729610934124248147969595380066179580 * q^49 + 244898096463243383440025305755038369424109352434412094720 * q^51 - 707065170108353883018319930521496060001554914206203205312 * q^52 - 386962012382976993771518038850875450617071434969909598880 * q^54 + 1313751320608480207642793301222628514163843327983665564800 * q^55 + 14469858017237851043428899294433298407417456132214681222568 * q^57 - 100361163480954821917122043432794223233970822326053950441920 * q^58 + 188095594234899922680776576921513155518384075353356847385600 * q^60 + 36618251899234461407858901457296968011564547062158638752840 * q^61 + 1345036046130625400347897603264169586395820510566342530416072 * q^63 - 4235878925879978009146455436735085155393347326504147849175040 * q^64 + 8309681532541455738248790801869091701653966958238676467844800 * q^66 - 6285867272675020649645690828535183608121600074432515838268632 * q^67 + 26395268384310228436148510386607667671115625880708467370286720 * q^69 - 53673269104481250134670425876769459429788829882429608923689600 * q^70 + 135607917285688125946137613885497485690645144416066370695173120 * q^72 - 234584045940242428610177340241689807173326553683343804321823128 * q^73 + 123839979253809259811223462461211616240588739801286415169843700 * q^75 - 88416171262693699731320177563519953392160098165342187898838720 * q^76 + 42333034554100439516880814575759716324771014654582144994836800 * q^78 - 180033150591234061548131792670437122720422789571688775376700600 * q^79 - 2669759984009083569841876166867012798635236563858567744127147180 * q^81 + 9780548955253740491517774427483475844287869484539284101189512320 * q^82 - 29550683862870558945501681808473602755499090201740971929153891520 * q^84 + 15725476767553808561610465539289169056529282358913795578981260800 * q^85 - 20361537149674837364457194316410702650457831770981879709222020800 * q^87 + 43127341602231234631198337877354797375008485566513397535855918080 * q^88 - 68986845993042571618317468832763287342807845905185213796199009600 * q^90 - 166695697853283961323776703924127811908080973516544145788509117360 * q^91 + 50074015382338903474492727100775024610496294621525101240240943432 * q^93 - 243292275786183398644891798798613800120302016678942850492866824960 * q^94 + 1707340756716414995397633331453898170371668874444383803046536028160 * q^96 - 2044564925167962718092629881048800142635399871213696847289077976152 * q^97 + 1311784025950014883691036763145966005164166837426590048709685526400 * q^99

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 $

$2$			4.54000e9i			0.528526i	0.964451	+	0.264263i	$0.0851287\pi$
$2$			4.54000e9i			0.528526i	−0.964451	+	0.264263i	$0.914871\pi$
$3$	5.46530e15	+	1.01669e15i	0.983134	+	0.182889i
$3$	5.46530e15	+	1.01669e15i	0.983134	+	0.182889i
$4$	5.31753e19			0.720660
$5$			1.75307e23i			1.50587i	0.658093	+	0.752936i	$0.271363\pi$
$5$			1.75307e23i			1.50587i	−0.658093	+	0.752936i	$0.728637\pi$
$6$	−4.61577e24	+	2.48125e25i	−0.0966614	+	0.519612i
$7$	−8.19169e27			−1.05959			−0.529795	−	0.848126i	$-0.677731\pi$
$7$	−8.19169e27			−1.05959			−0.529795	+	0.848126i	$0.677731\pi$
$8$			5.76409e29i			0.909414i
$9$	2.88358e31	+	1.11130e31i	0.933104	+	0.359608i
$10$	−7.95893e32			−0.795893
$11$			2.37945e34i			1.02451i	0.858833	+	0.512256i	$0.171190\pi$
$11$			2.37945e34i			1.02451i	−0.858833	+	0.512256i	$0.828810\pi$
$12$	2.90619e35	+	5.40628e34i	0.708505	+	0.131801i
$13$	7.13046e36			1.23876			0.619380	−	0.785092i	$-0.287384\pi$
$13$	7.13046e36			1.23876			0.619380	+	0.785092i	$0.287384\pi$
$14$		−	3.71903e37i		−	0.560021i
$15$	−1.78232e38	+	9.58103e38i	−0.275407	+	1.48047i
$16$	1.30675e39			0.240012
$17$			5.94349e40i			1.47648i	0.674539	+	0.738239i	$0.264342\pi$
$17$			5.94349e40i			1.47648i	−0.674539	+	0.738239i	$0.735658\pi$
$18$	−5.04531e40	+	1.30915e41i	−0.190062	+	0.493169i
$19$	8.13114e41			0.514378			0.257189	−	0.966361i	$-0.417204\pi$
$19$	8.13114e41			0.514378			0.257189	+	0.966361i	$0.417204\pi$
$20$			9.32199e42i			1.08522i
$21$	−4.47700e43	−	8.32840e42i	−1.04172	−	0.193787i
$22$	−1.08027e44			−0.541481
$23$		−	1.37490e45i		−	1.58947i	−0.606955	−	0.794736i	$-0.707609\pi$
$23$		−	1.37490e45i		−	1.58947i	0.606955	−	0.794736i	$-0.292391\pi$
$24$	−5.86029e44	+	3.15025e45i	−0.166321	+	0.894075i
$25$	−1.71799e46			−1.26765
$26$			3.23723e46i			0.654717i
$27$	1.46298e47	+	9.00531e46i	0.851597	+	0.524197i
$28$	−4.35596e47			−0.763605
$29$		−	9.76720e47i		−	0.537819i	−0.963165	−	0.268910i	$-0.913337\pi$
$29$		−	9.76720e47i		−	0.537819i	0.963165	−	0.268910i	$-0.0866633\pi$
$30$	−4.34979e48	−	8.09175e47i	−0.782469	−	0.145560i
$31$	−1.85675e49			−1.13192			−0.565961	−	0.824432i	$-0.691495\pi$
$31$	−1.85675e49			−1.13192			−0.565961	+	0.824432i	$0.691495\pi$
$32$			4.84641e49i			1.03627i
$33$	−2.41916e49	+	1.30044e50i	−0.187372	+	1.00723i
$34$	−2.69835e50			−0.780357
$35$		−	1.43606e51i		−	1.59561i
$36$	1.53336e51	+	5.90939e50i	0.672451	+	0.259155i
$37$	6.12483e51			1.08752			0.543760	−	0.839241i	$-0.317000\pi$
$37$	6.12483e51			1.08752			0.543760	+	0.839241i	$0.317000\pi$
$38$			3.69154e51i			0.271862i
$39$	3.89701e52	+	7.24946e51i	1.21787	+	0.226555i
$40$	−1.01048e53			−1.36946
$41$			1.20825e53i			0.724920i	0.931999	+	0.362460i	$0.118063\pi$
$41$			1.20825e53i			0.724920i	−0.931999	+	0.362460i	$0.881937\pi$
$42$	3.78110e52	−	2.03256e53i	0.102421	−	0.550576i
$43$	−2.91666e53			−0.363435			−0.181717	−	0.983351i	$-0.558166\pi$
$43$	−2.91666e53			−0.363435			−0.181717	+	0.983351i	$0.558166\pi$
$44$			1.26528e54i			0.738325i
$45$	−1.94819e54	+	5.05512e54i	−0.541524	+	1.40514i
$46$	6.24205e54			0.840077
$47$		−	1.66827e54i		−	0.110417i	−0.998475	−	0.0552087i	$-0.982418\pi$
$47$		−	1.66827e54i		−	0.110417i	0.998475	−	0.0552087i	$-0.0175824\pi$
$48$	7.14177e54	+	1.32856e54i	0.235964	+	0.0438954i
$49$	7.33550e54			0.122732
$50$		−	7.79968e55i		−	0.669987i
$51$	−6.04268e55	+	3.24830e56i	−0.270031	+	1.45158i
$52$	3.79165e56			0.892725
$53$		−	6.92806e56i		−	0.869977i	−0.900436	−	0.434989i	$-0.856752\pi$
$53$		−	6.92806e56i		−	0.869977i	0.900436	−	0.434989i	$-0.143248\pi$
$54$	−4.08841e56	+	6.64194e56i	−0.277052	+	0.450091i
$55$	−4.17133e57			−1.54279
$56$		−	4.72177e57i		−	0.963606i
$57$	4.44391e57	+	8.26684e56i	0.505703	+	0.0940740i
$58$	4.43431e57			0.284251
$59$		−	2.60594e58i		−	0.950271i	−0.879913	−	0.475136i	$-0.842399\pi$
$59$		−	2.60594e58i		−	0.950271i	0.879913	−	0.475136i	$-0.157601\pi$
$60$	−9.47757e57	+	5.09475e58i	−0.198475	+	1.06692i
$61$	1.11009e59			1.34732			0.673662	−	0.739040i	$-0.264720\pi$
$61$	1.11009e59			1.34732			0.673662	+	0.739040i	$0.264720\pi$
$62$		−	8.42964e58i		−	0.598251i
$63$	−2.36214e59	−	9.10344e58i	−0.988708	−	0.381037i
$64$	−1.23606e59			−0.307682
$65$			1.25002e60i			1.86541i
$66$	−5.90399e59	−	1.09830e59i	−0.532349	−	0.0990308i
$67$	3.96041e59			0.217406			0.108703	−	0.994074i	$-0.465330\pi$
$67$	3.96041e59			0.217406			0.108703	+	0.994074i	$0.465330\pi$
$68$			3.16047e60i			1.06404i
$69$	1.39785e60	−	7.51425e60i	0.290696	−	1.56266i
$70$	6.51971e60			0.843321
$71$		−	1.42835e61i		−	1.15694i	−0.815704	−	0.578469i	$-0.803650\pi$
$71$		−	1.42835e61i		−	1.15694i	0.815704	−	0.578469i	$-0.196350\pi$
$72$	−6.40565e60	+	1.66212e61i	−0.327032	+	0.848577i
$73$	−2.22307e61			−0.719945			−0.359973	−	0.932963i	$-0.617214\pi$
$73$	−2.22307e61			−0.719945			−0.359973	+	0.932963i	$0.617214\pi$
$74$			2.78068e61i			0.574783i
$75$	−9.38933e61	−	1.74666e61i	−1.24627	−	0.231839i
$76$	4.32376e61			0.370692
$77$		−	1.94917e62i		−	1.08556i
$78$	−3.29126e61	+	1.76924e62i	−0.119740	+	0.643674i
$79$	−3.86775e62			−0.924196			−0.462098	−	0.886829i	$-0.652903\pi$
$79$	−3.86775e62			−0.924196			−0.462098	+	0.886829i	$0.652903\pi$
$80$			2.29082e62i			0.361427i
$81$	7.08007e62	+	6.40906e62i	0.741364	+	0.671103i
$82$	−5.48546e62			−0.383139
$83$			9.18639e62i			0.430099i	0.976603	+	0.215049i	$0.0689912\pi$
$83$			9.18639e62i			0.430099i	−0.976603	+	0.215049i	$0.931009\pi$
$84$	−2.38066e63	−	4.42866e62i	−0.750726	−	0.139655i
$85$	−1.04193e64			−2.22339
$86$		−	1.32416e63i		−	0.192085i
$87$	9.93021e62	−	5.33807e63i	0.0983610	−	0.528748i
$88$	−1.37153e64			−0.931705
$89$			3.59677e64i			1.68284i	0.540384	+	0.841419i	$0.318279\pi$
$89$			3.59677e64i			1.68284i	−0.540384	+	0.841419i	$0.681721\pi$
$90$	−2.29502e64	−	8.84477e63i	−0.742650	−	0.286209i
$91$	−5.84105e64			−1.31258
$92$		−	7.31108e64i		−	1.14547i
$93$	−1.01477e65	−	1.88773e64i	−1.11283	−	0.207016i
$94$	7.57396e63			0.0583584
$95$			1.42544e65i			0.774588i
$96$	−4.92730e64	+	2.64871e65i	−0.189521	+	1.01879i
$97$	−5.76248e65			−1.57450			−0.787249	−	0.616635i	$-0.788496\pi$
$97$	−5.76248e65			−1.57450			−0.787249	+	0.616635i	$0.788496\pi$
$98$			3.33032e64i			0.0648673i
$99$	−2.64428e65	+	6.86133e65i	−0.368423	+	0.955976i
$100$	−9.13547e65			−0.913547
$101$		−	1.62683e66i		−	1.17149i	−0.810496	−	0.585744i	$-0.800802\pi$
$101$		−	1.62683e66i		−	1.17149i	0.810496	−	0.585744i	$-0.199198\pi$
$102$	−1.47473e66	−	2.74338e65i	−0.767195	−	0.142718i
$103$	3.15392e66			1.18911			0.594555	−	0.804055i	$-0.297328\pi$
$103$	3.15392e66			1.18911			0.594555	+	0.804055i	$0.297328\pi$
$104$			4.11006e66i			1.12654i
$105$	1.46002e66	−	7.84849e66i	0.291819	−	1.56870i
$106$	3.14534e66			0.459806
$107$			1.08079e66i			0.115899i	0.998320	+	0.0579493i	$0.0184562\pi$
$107$			1.08079e66i			0.115899i	−0.998320	+	0.0579493i	$0.981544\pi$
$108$	7.77945e66	+	4.78860e66i	0.613712	+	0.377768i
$109$	−4.38346e66			−0.255119			−0.127559	−	0.991831i	$-0.540714\pi$
$109$	−4.38346e66			−0.255119			−0.127559	+	0.991831i	$0.540714\pi$
$110$		−	1.89378e67i		−	0.815402i
$111$	3.34740e67	+	6.22705e66i	1.06918	+	0.198895i
$112$	−1.07045e67			−0.254314
$113$			2.63153e67i			0.466250i	0.972447	+	0.233125i	$0.0748951\pi$
$113$			2.63153e67i			0.466250i	−0.972447	+	0.233125i	$0.925105\pi$
$114$	−3.75315e66	+	2.01754e67i	−0.0497205	+	0.267277i
$115$	2.41029e68			2.39354
$116$		−	5.19374e67i		−	0.387585i
$117$	2.05613e68	+	7.92409e67i	1.15589	+	0.445468i
$118$	1.18310e68			0.502243
$119$		−	4.86872e68i		−	1.56446i
$120$	−5.52260e68	−	1.02735e68i	−1.34636	−	0.250459i
$121$	−2.67684e67			−0.0496255
$122$			5.03979e68i			0.712095i
$123$	−1.22842e68	+	6.60345e68i	−0.132580	+	0.712693i
$124$	−9.87332e68			−0.815732
$125$		−	6.35902e68i		−	0.403051i
$126$	4.13296e68	−	1.07241e69i	0.201388	−	0.522558i
$127$	−2.32803e68			−0.0873907			−0.0436954	−	0.999045i	$-0.513913\pi$
$127$	−2.32803e68			−0.0873907			−0.0436954	+	0.999045i	$0.513913\pi$
$128$			3.01485e69i			0.873648i
$129$	−1.59404e69	−	2.96533e68i	−0.357305	−	0.0664681i
$130$	−5.67508e69			−0.985920
$131$		−	3.02547e69i		−	0.408169i	−0.978953	−	0.204084i	$-0.934578\pi$
$131$		−	3.02547e69i		−	0.408169i	0.978953	−	0.204084i	$-0.0654217\pi$
$132$	−1.28639e69	+	6.91513e69i	−0.135031	+	0.725873i
$133$	−6.66078e69			−0.545031
$134$			1.79803e69i			0.114905i
$135$	−1.57869e70	+	2.56470e70i	−0.789373	+	1.28240i
$136$	−3.42588e70			−1.34273
$137$		−	5.04414e70i		−	1.55242i	−0.630477	−	0.776208i	$-0.717141\pi$
$137$		−	5.04414e70i		−	1.55242i	0.630477	−	0.776208i	$-0.282859\pi$
$138$	3.41147e70	+	6.34623e69i	0.825908	+	0.153641i
$139$	4.91774e70			0.938160			0.469080	−	0.883156i	$-0.344586\pi$
$139$	4.91774e70			0.938160			0.469080	+	0.883156i	$0.344586\pi$
$140$		−	7.63629e70i		−	1.14989i
$141$	1.69611e69	−	9.11760e69i	0.0201941	−	0.108555i
$142$	6.48473e70			0.611472
$143$			1.69665e71i			1.26912i
$144$	3.76812e70	+	1.45219e70i	0.223956	+	0.0863101i
$145$	1.71226e71			0.809887
$146$		−	1.00928e71i		−	0.380510i
$147$	4.00907e70	+	7.45793e69i	0.120662	+	0.0224464i
$148$	3.25690e71			0.783733
$149$		−	5.41414e70i		−	0.104324i	−0.998639	−	0.0521618i	$-0.983389\pi$
$149$		−	5.41414e70i		−	0.104324i	0.998639	−	0.0521618i	$-0.0166112\pi$
$150$	7.92985e70	−	4.26276e71i	0.122533	−	0.658687i
$151$	2.78382e71			0.345463			0.172732	−	0.984969i	$-0.444741\pi$
$151$	2.78382e71			0.345463			0.172732	+	0.984969i	$0.444741\pi$
$152$			4.68687e71i			0.467783i
$153$	−6.60501e71	+	1.71386e72i	−0.530953	+	1.37771i
$154$	8.84923e71			0.573749
$155$		−	3.25500e72i		−	1.70453i
$156$	2.07225e72	+	3.85493e71i	0.877668	+	0.163269i
$157$	−3.95465e72			−1.35650			−0.678249	−	0.734832i	$-0.737261\pi$
$157$	−3.95465e72			−1.35650			−0.678249	+	0.734832i	$0.737261\pi$
$158$		−	1.75596e72i		−	0.488461i
$159$	7.04368e71	−	3.78639e72i	0.159109	−	0.855304i
$160$	−8.49609e72			−1.56048
$161$			1.12628e73i			1.68419i
$162$	−2.90972e72	+	3.21435e72i	−0.354695	+	0.391830i
$163$	1.54007e72			0.153232			0.0766161	−	0.997061i	$-0.475588\pi$
$163$	1.54007e72			0.153232			0.0766161	+	0.997061i	$0.475588\pi$
$164$			6.42492e72i			0.522421i
$165$	−2.27976e73	−	4.24094e72i	−1.51676	−	0.282158i
$166$	−4.17063e72			−0.227318
$167$			2.38387e73i			1.06571i	0.846207	+	0.532854i	$0.178880\pi$
$167$			2.38387e73i			1.06571i	−0.846207	+	0.532854i	$0.821120\pi$
$168$	4.80057e72	−	2.58059e73i	0.176233	−	0.947354i
$169$	1.77104e73			0.534525
$170$		−	4.73038e73i		−	1.17512i
$171$	2.34468e73	+	9.03615e72i	0.479968	+	0.184975i
$172$	−1.55094e73			−0.261913
$173$			4.37187e73i			0.609742i	0.952394	+	0.304871i	$0.0986133\pi$
$173$			4.37187e73i			0.609742i	−0.952394	+	0.304871i	$0.901387\pi$
$174$	2.42349e73	+	4.50832e72i	0.279457	+	0.0519863i
$175$	1.40732e74			1.34319
$176$			3.10933e73i			0.245895i
$177$	2.64943e73	−	1.42422e74i	0.173794	−	0.934243i
$178$	−1.63293e74			−0.889423
$179$		−	1.98526e74i		−	0.898811i	−0.893328	−	0.449405i	$-0.851636\pi$
$179$		−	1.98526e74i		−	0.898811i	0.893328	−	0.449405i	$-0.148364\pi$
$180$	−1.03595e74	+	2.68807e74i	−0.390255	+	1.01263i
$181$	3.22841e74			1.01297			0.506483	−	0.862250i	$-0.330945\pi$
$181$	3.22841e74			1.01297			0.506483	+	0.862250i	$0.330945\pi$
$182$		−	2.65184e74i		−	0.693732i
$183$	6.06695e74	+	1.12861e74i	1.32460	+	0.246410i
$184$	7.92506e74			1.44549
$185$			1.07372e75i			1.63767i
$186$	8.57032e73	−	4.60705e74i	0.109413	−	0.588160i
$187$	−1.41422e75			−1.51267
$188$		−	8.87109e73i		−	0.0795734i
$189$	−1.19843e75	−	7.37687e74i	−0.902345	−	0.555434i
$190$	−6.47152e74			−0.409390
$191$		−	3.66795e73i		−	0.0195129i	−0.999952	−	0.00975646i	$-0.996894\pi$
$191$		−	3.66795e73i		−	0.0195129i	0.999952	−	0.00975646i	$-0.00310563\pi$
$192$	−6.75546e74	−	1.25669e74i	−0.302492	−	0.0562715i
$193$	−2.82897e75			−1.06718			−0.533589	−	0.845744i	$-0.679157\pi$
$193$	−2.82897e75			−1.06718			−0.533589	+	0.845744i	$0.679157\pi$
$194$		−	2.61617e75i		−	0.832163i
$195$	−1.27088e75	+	6.83172e75i	−0.341163	+	1.83395i
$196$	3.90068e74			0.0884484
$197$		−	4.32318e74i		−	0.0828739i	−0.999141	−	0.0414370i	$-0.986806\pi$
$197$		−	4.32318e74i		−	0.0828739i	0.999141	−	0.0414370i	$-0.0131936\pi$
$198$	−3.11505e75	−	1.20051e75i	−0.505258	−	0.194721i
$199$	3.57850e75			0.491530			0.245765	−	0.969329i	$-0.420961\pi$
$199$	3.57850e75			0.491530			0.245765	+	0.969329i	$0.420961\pi$
$200$		−	9.90265e75i		−	1.15282i
$201$	2.16449e75	+	4.02651e74i	0.213739	+	0.0397611i
$202$	7.38583e75			0.619162
$203$			8.00099e75i			0.569868i
$204$	−3.21322e75	+	1.72729e76i	−0.194601	+	1.04609i
$205$	−2.11814e76			−1.09164
$206$			1.43188e76i			0.628476i
$207$	1.52793e76	−	3.96464e76i	0.571587	−	1.48314i
$208$	9.31771e75			0.297317
$209$			1.93476e76i			0.526987i
$210$	3.56321e76	+	6.62851e75i	0.829097	+	0.154234i
$211$	7.36918e76			1.46588			0.732940	−	0.680293i	$-0.238148\pi$
$211$	7.36918e76			1.46588			0.732940	+	0.680293i	$0.238148\pi$
$212$		−	3.68402e76i		−	0.626958i
$213$	1.45219e76	−	7.80638e76i	0.211591	−	1.13742i
$214$	−4.90681e75			−0.0612555
$215$		−	5.11310e76i		−	0.547287i
$216$	−5.19074e76	+	8.43276e76i	−0.476712	+	0.774454i
$217$	1.52099e77			1.19938
$218$		−	1.99009e76i		−	0.134837i
$219$	−1.21498e77	−	2.26017e76i	−0.707802	−	0.131670i
$220$	−2.21812e77			−1.11182
$221$			4.23798e77i			1.82900i
$222$	−2.82708e76	+	1.51972e77i	−0.105121	+	0.565088i
$223$	9.48336e76			0.304020			0.152010	−	0.988379i	$-0.451425\pi$
$223$	9.48336e76			0.304020			0.152010	+	0.988379i	$0.451425\pi$
$224$		−	3.97003e77i		−	1.09802i
$225$	−4.95397e77	−	1.90921e77i	−1.18285	−	0.455858i
$226$	−1.19471e77			−0.246425
$227$			1.35674e77i			0.241905i	0.992658	+	0.120952i	$0.0385948\pi$
$227$			1.35674e77i			0.241905i	−0.992658	+	0.120952i	$0.961405\pi$
$228$	2.36307e77	+	4.39592e76i	0.364440	+	0.0677954i
$229$	−9.43956e77			−1.26003			−0.630015	−	0.776583i	$-0.716951\pi$
$229$	−9.43956e77			−1.26003			−0.630015	+	0.776583i	$0.716951\pi$
$230$			1.09427e78i			1.26505i
$231$	1.98170e77	−	1.06528e78i	0.198537	−	1.06725i
$232$	5.62991e77			0.489100
$233$		−	6.05594e77i		−	0.456495i	−0.973603	−	0.228248i	$-0.926700\pi$
$233$		−	6.05594e77i		−	0.456495i	0.973603	−	0.228248i	$-0.0732996\pi$
$234$	−3.59754e77	+	9.33483e77i	−0.235441	+	0.610918i
$235$	2.92459e77			0.166275
$236$		−	1.38572e78i		−	0.684823i
$237$	−2.11384e78	−	3.93230e77i	−0.908608	−	0.169025i
$238$	2.21040e78			0.826859
$239$		−	7.14432e77i		−	0.232718i	−0.993207	−	0.116359i	$-0.962878\pi$
$239$		−	7.14432e77i		−	0.232718i	0.993207	−	0.116359i	$-0.0371223\pi$
$240$	−2.32905e77	+	1.25200e78i	−0.0661009	+	0.355331i
$241$	3.67033e78			0.908118			0.454059	−	0.890972i	$-0.349975\pi$
$241$	3.67033e78			0.908118			0.454059	+	0.890972i	$0.349975\pi$
$242$		−	1.21529e77i		−	0.0262284i
$243$	3.21787e78	+	4.22257e78i	0.606123	+	0.795371i
$244$	5.90292e78			0.970963
$245$			1.28596e78i			0.184819i
$246$	−2.99797e78	−	5.57701e77i	−0.376677	−	0.0700717i
$247$	5.79788e78			0.637191
$248$		−	1.07025e79i		−	1.02939i
$249$	−9.33970e77	+	5.02064e78i	−0.0786601	+	0.422844i
$250$	2.88700e78			0.213023
$251$		−	5.76326e78i		−	0.372765i	−0.982477	−	0.186383i	$-0.940324\pi$
$251$		−	5.76326e78i		−	0.372765i	0.982477	−	0.186383i	$-0.0596764\pi$
$252$	−1.25608e79	−	4.84079e78i	−0.712522	−	0.274598i
$253$	3.27150e79			1.62843
$254$		−	1.05693e78i		−	0.0461883i
$255$	−5.69448e79	−	1.05932e79i	−2.18589	−	0.406632i
$256$	−2.28080e79			−0.769428
$257$			4.77843e79i			1.41740i	0.705510	+	0.708700i	$0.250718\pi$
$257$			4.77843e79i			1.41740i	−0.705510	+	0.708700i	$0.749282\pi$
$258$	1.34626e78	−	7.23695e78i	0.0351301	−	0.188845i
$259$	−5.01727e79			−1.15233
$260$			6.64701e79i			1.34433i
$261$	1.08543e79	−	2.81646e79i	0.193404	−	0.501841i
$262$	1.37356e79			0.215728
$263$		−	1.18969e80i		−	1.64776i	−0.566762	−	0.823881i	$-0.691804\pi$
$263$		−	1.18969e80i		−	1.64776i	0.566762	−	0.823881i	$-0.308196\pi$
$264$	−7.49585e79	−	1.39442e79i	−0.915991	−	0.170398i
$265$	1.21453e80			1.31008
$266$		−	3.02400e79i		−	0.288063i
$267$	−3.65679e79	+	1.96574e80i	−0.307772	+	1.65445i
$268$	2.10596e79			0.156676
$269$			1.36204e80i			0.896117i	0.894004	+	0.448059i	$0.147884\pi$
$269$			1.36204e80i			0.896117i	−0.894004	+	0.448059i	$0.852116\pi$
$270$	−1.16438e80	−	7.16726e79i	−0.677780	−	0.417204i
$271$	2.12724e80			1.09605			0.548025	−	0.836462i	$-0.315380\pi$
$271$	2.12724e80			1.09605			0.548025	+	0.836462i	$0.315380\pi$
$272$			7.76664e79i			0.354372i
$273$	−3.19231e80	−	5.93853e79i	−1.29044	−	0.240056i
$274$	2.29004e80			0.820492
$275$		−	4.08786e80i		−	1.29873i
$276$	7.43310e79	−	3.99573e80i	0.209493	−	1.12615i
$277$	5.29134e80			1.32353			0.661764	−	0.749712i	$-0.269808\pi$
$277$	5.29134e80			1.32353			0.661764	+	0.749712i	$0.269808\pi$
$278$			2.23266e80i			0.495842i
$279$	−5.35409e80	−	2.06341e80i	−1.05620	−	0.407048i
$280$	8.27757e80			1.45107
$281$			8.19545e80i			1.27722i	0.769533	+	0.638608i	$0.220489\pi$
$281$			8.19545e80i			1.27722i	−0.769533	+	0.638608i	$0.779511\pi$
$282$	4.13940e79	+	7.70036e78i	0.0573742	+	0.0106731i
$283$	1.37616e81			1.69714			0.848569	−	0.529084i	$-0.177464\pi$
$283$	1.37616e81			1.69714			0.848569	+	0.529084i	$0.177464\pi$
$284$		−	7.59532e80i		−	0.833759i
$285$	−1.44923e80	+	7.79048e80i	−0.141663	+	0.761524i
$286$	−7.70282e80			−0.670765
$287$		−	9.89762e80i		−	0.768118i
$288$	−5.38583e80	+	1.39750e81i	−0.372649	+	0.966943i
$289$	−1.91208e81			−1.17999
$290$			7.77365e80i			0.428046i
$291$	−3.14937e81	−	5.85865e80i	−1.54794	−	0.287958i
$292$	−1.18213e81			−0.518836
$293$		−	1.46139e81i		−	0.572972i	−0.958084	−	0.286486i	$-0.907513\pi$
$293$		−	1.46139e81i		−	0.572972i	0.958084	−	0.286486i	$-0.0924873\pi$
$294$	−3.38590e79	+	1.82012e80i	−0.0118635	+	0.0637732i
$295$	4.56838e81			1.43099
$296$			3.53041e81i			0.989006i
$297$	−2.14276e81	+	3.48108e81i	−0.537046	+	0.872472i
$298$	2.45802e80			0.0551377
$299$		−	9.80368e81i		−	1.96897i
$300$	−4.99281e81	−	9.28793e80i	−0.898139	−	0.167077i
$301$	2.38924e81			0.385092
$302$			1.26386e81i			0.182586i
$303$	1.65398e81	−	8.89113e81i	0.214252	−	1.15173i
$304$	1.06254e81			0.123457
$305$			1.94605e82i			2.02890i
$306$	−7.78091e81	−	2.99868e81i	−0.728154	−	0.280623i
$307$	−4.16161e81			−0.349699			−0.174850	−	0.984595i	$-0.555944\pi$
$307$	−4.16161e81			−0.349699			−0.174850	+	0.984595i	$0.555944\pi$
$308$		−	1.03648e82i		−	0.782323i
$309$	1.72371e82	+	3.20655e81i	1.16905	+	0.217475i
$310$	1.47777e82			0.900889
$311$			1.88584e82i			1.03374i	0.856063	+	0.516872i	$0.172904\pi$
$311$			1.88584e82i			1.03374i	−0.856063	+	0.516872i	$0.827096\pi$
$312$	−4.17866e81	+	2.24627e82i	−0.206032	+	1.10754i
$313$	2.82273e82			1.25230			0.626148	−	0.779704i	$-0.284631\pi$
$313$	2.82273e82			1.25230			0.626148	+	0.779704i	$0.284631\pi$
$314$		−	1.79541e82i		−	0.716944i
$315$	1.59589e82	−	4.14099e82i	0.573794	−	1.48887i
$316$	−2.05669e82			−0.666031
$317$		−	1.78011e82i		−	0.519387i	−0.965691	−	0.259693i	$-0.916378\pi$
$317$		−	1.78011e82i		−	0.519387i	0.965691	−	0.259693i	$-0.0836215\pi$
$318$	1.71902e82	+	3.19783e81i	0.452050	+	0.0840932i
$319$	2.32405e82			0.551002
$320$		−	2.16690e82i		−	0.463330i
$321$	−1.09883e81	+	5.90687e81i	−0.0211965	+	0.113944i
$322$	−5.11330e82			−0.890138
$323$			4.83274e82i			0.759469i
$324$	3.76485e82	+	3.40804e82i	0.534272	+	0.483637i
$325$	−1.22501e83			−1.57032
$326$			6.99193e81i			0.0809872i
$327$	−2.39569e82	−	4.45661e81i	−0.250816	−	0.0466583i
$328$	−6.96447e82			−0.659252
$329$			1.36660e82i			0.116997i
$330$	1.92539e82	−	1.03501e83i	0.149128	−	0.801649i
$331$	−1.55622e83			−1.09080			−0.545401	−	0.838175i	$-0.683623\pi$
$331$	−1.55622e83			−1.09080			−0.545401	+	0.838175i	$0.683623\pi$
$332$			4.88490e82i			0.309955i
$333$	1.76615e83	+	6.80654e82i	1.01477	+	0.391081i
$334$	−1.08228e83			−0.563254
$335$			6.94287e82i			0.327386i
$336$	−5.85031e82	−	1.08831e82i	−0.250025	−	0.0465112i
$337$	2.95048e83			1.14316			0.571579	−	0.820547i	$-0.306331\pi$
$337$	2.95048e83			1.14316			0.571579	+	0.820547i	$0.306331\pi$
$338$			8.04054e82i			0.282510i
$339$	−2.67544e82	+	1.43821e83i	−0.0852718	+	0.458386i
$340$	−5.54052e83			−1.60231
$341$		−	4.41803e83i		−	1.15967i
$342$	−4.10242e82	+	1.06449e83i	−0.0977638	+	0.253676i
$343$	4.29513e83			0.929545
$344$		−	1.68119e83i		−	0.330513i
$345$	1.31730e84	+	2.45052e83i	2.35317	+	0.437752i
$346$	−1.98483e83			−0.322264
$347$		−	9.67641e83i		−	1.42837i	−0.699955	−	0.714186i	$-0.746797\pi$
$347$		−	9.67641e83i		−	1.42837i	0.699955	−	0.714186i	$-0.253203\pi$
$348$	5.28042e82	−	2.83854e83i	0.0708849	−	0.381048i
$349$	−8.88966e83			−1.08554			−0.542770	−	0.839881i	$-0.682625\pi$
$349$	−8.88966e83			−1.08554			−0.542770	+	0.839881i	$0.682625\pi$
$350$			6.38926e83i			0.709912i
$351$	1.04317e84	+	6.42120e83i	1.05492	+	0.649354i
$352$	−1.15318e84			−1.06167
$353$		−	3.94336e83i		−	0.330599i	−0.986243	−	0.165300i	$-0.947141\pi$
$353$		−	3.94336e83i		−	0.330599i	0.986243	−	0.165300i	$-0.0528591\pi$
$354$	6.46597e83	+	1.20284e83i	0.493772	+	0.0918545i
$355$	2.50400e84			1.74220
$356$			1.91259e84i			1.21275i
$357$	4.94998e83	−	2.66090e84i	0.286122	−	1.53808i
$358$	9.01311e83			0.475045
$359$			1.95436e84i			0.939483i	0.882804	+	0.469741i	$0.155653\pi$
$359$			1.95436e84i			0.939483i	−0.882804	+	0.469741i	$0.844347\pi$
$360$	−2.91382e84	−	1.12295e84i	−1.27785	−	0.492469i
$361$	−1.83768e84			−0.735415
$362$			1.46570e84i			0.535379i
$363$	−1.46297e83	−	2.72151e82i	−0.0487885	−	0.00907595i
$364$	−3.10600e84			−0.945923
$365$		−	3.89720e84i		−	1.08415i
$366$	−5.12390e83	+	2.75440e84i	−0.130234	+	0.700085i
$367$	−1.73953e84			−0.404066			−0.202033	−	0.979379i	$-0.564755\pi$
$367$	−1.73953e84			−0.404066			−0.202033	+	0.979379i	$0.564755\pi$
$368$		−	1.79665e84i		−	0.381492i
$369$	−1.34273e84	+	3.48409e84i	−0.260687	+	0.676425i
$370$	−4.87471e84			−0.865550
$371$			5.67525e84i			0.921820i
$372$	−5.39606e84	−	1.00381e84i	−0.801974	−	0.149188i
$373$	7.27452e84			0.989493			0.494746	−	0.869037i	$-0.335261\pi$
$373$	7.27452e84			0.989493			0.494746	+	0.869037i	$0.335261\pi$
$374$		−	6.42057e84i		−	0.799486i
$375$	6.46515e83	−	3.47540e84i	0.0737134	−	0.396253i
$376$	9.61607e83			0.100415
$377$		−	6.96447e84i		−	0.666229i
$378$	3.34910e84	−	5.44087e84i	0.293561	−	0.476912i
$379$	1.39620e85			1.12164			0.560820	−	0.827938i	$-0.310486\pi$
$379$	1.39620e85			1.12164			0.560820	+	0.827938i	$0.310486\pi$
$380$			7.57984e84i			0.558215i
$381$	−1.27234e84	−	2.36688e83i	−0.0859168	−	0.0159828i
$382$	1.66525e83			0.0103131
$383$			2.54135e85i			1.44380i	0.692000	+	0.721898i	$0.256730\pi$
$383$			2.54135e85i			1.44380i	−0.692000	+	0.721898i	$0.743270\pi$
$384$	−3.06516e84	+	1.64771e85i	−0.159780	+	0.858913i
$385$	3.41702e85			1.63472
$386$		−	1.28435e85i		−	0.564031i
$387$	−8.41043e84	−	3.24129e84i	−0.339122	−	0.130694i
$388$	−3.06422e85			−1.13468
$389$		−	2.10388e85i		−	0.715624i	−0.933794	−	0.357812i	$-0.883523\pi$
$389$		−	2.10388e85i		−	0.715624i	0.933794	−	0.357812i	$-0.116477\pi$
$390$	−3.10160e85	−	5.76979e84i	−0.969291	−	0.180314i
$391$	8.17171e85			2.34682
$392$			4.22825e84i			0.111615i
$393$	3.07596e84	−	1.65351e85i	0.0746494	−	0.401284i
$394$	1.96273e84			0.0438010
$395$		−	6.78042e85i		−	1.39172i
$396$	−1.40611e85	+	3.64854e85i	−0.265508	+	0.688934i
$397$	7.10170e85			1.23389			0.616944	−	0.787007i	$-0.288371\pi$
$397$	7.10170e85			1.23389			0.616944	+	0.787007i	$0.288371\pi$
$398$			1.62464e85i			0.259786i
$399$	−3.64032e85	−	6.77194e84i	−0.535838	−	0.0996799i
$400$	−2.24498e85			−0.304251
$401$			6.07889e85i			0.758682i	0.925257	+	0.379341i	$0.123849\pi$
$401$			6.07889e85i			0.758682i	−0.925257	+	0.379341i	$0.876151\pi$
$402$	−1.82804e84	+	9.82677e84i	−0.0210148	+	0.112967i
$403$	−1.32395e86			−1.40218
$404$		−	8.65074e85i		−	0.844245i
$405$	−1.12355e86	+	1.24118e86i	−1.01060	+	1.11640i
$406$	−3.63245e85			−0.301190
$407$			1.45737e86i			1.11418i
$408$	−1.87235e86	−	3.48306e85i	−1.32008	−	0.245570i
$409$	8.72186e84			0.0567205			0.0283603	−	0.999598i	$-0.490971\pi$
$409$	8.72186e84			0.0567205			0.0283603	+	0.999598i	$0.490971\pi$
$410$		−	9.61638e85i		−	0.576958i
$411$	5.12832e85	−	2.75677e86i	0.283919	−	1.52623i
$412$	1.67711e86			0.856945
$413$			2.13470e86i			1.00690i
$414$	1.79995e86	+	6.93681e85i	0.783879	+	0.302098i
$415$	−1.61044e86			−0.647674
$416$			3.45572e86i			1.28368i
$417$	2.68769e86	+	4.99981e85i	0.922337	+	0.171579i
$418$	−8.78382e85			−0.278526
$419$		−	4.48845e86i		−	1.31533i	−0.753313	−	0.657663i	$-0.771545\pi$
$419$		−	4.48845e86i		−	1.31533i	0.753313	−	0.657663i	$-0.228455\pi$
$420$	7.76373e85	−	4.17346e86i	0.210302	−	1.13050i
$421$	1.61509e86			0.404471			0.202236	−	0.979337i	$-0.435179\pi$
$421$	1.61509e86			0.404471			0.202236	+	0.979337i	$0.435179\pi$
$422$			3.34561e86i			0.774756i
$423$	1.85395e85	−	4.81060e85i	0.0397070	−	0.103031i
$424$	3.99340e86			0.791169
$425$		−	1.02109e87i		−	1.87166i
$426$	3.54410e86	+	6.59295e85i	0.601158	+	0.111831i
$427$	−9.09348e86			−1.42761
$428$			5.74716e85i			0.0835236i
$429$	−1.72497e86	+	9.27272e86i	−0.232108	+	1.24772i
$430$	2.32135e86			0.289255
$431$			5.75168e86i			0.663811i	0.943313	+	0.331906i	$0.107692\pi$
$431$			5.75168e86i			0.663811i	−0.943313	+	0.331906i	$0.892308\pi$
$432$	1.91175e86	+	1.17677e86i	0.204393	+	0.125813i
$433$	1.40876e87			1.39552			0.697759	−	0.716332i	$-0.254180\pi$
$433$	1.40876e87			1.39552			0.697759	+	0.716332i	$0.254180\pi$
$434$			6.90530e86i			0.633901i
$435$	9.35799e86	+	1.74083e86i	0.796227	+	0.148119i
$436$	−2.33092e86			−0.183854
$437$		−	1.11795e87i		−	0.817590i
$438$	1.02612e86	−	5.51600e86i	0.0695909	−	0.374092i
$439$	−2.16131e87			−1.35953			−0.679764	−	0.733431i	$-0.737918\pi$
$439$	−2.16131e87			−1.35953			−0.679764	+	0.733431i	$0.737918\pi$
$440$		−	2.40439e87i		−	1.40303i
$441$	2.11525e86	+	8.15196e85i	0.114522	+	0.0441356i
$442$	−1.92405e87			−0.966675
$443$			3.15309e87i			1.47033i	0.677890	+	0.735163i	$0.262895\pi$
$443$			3.15309e87i			1.47033i	−0.677890	+	0.735163i	$0.737105\pi$
$444$	1.77999e87	+	3.31126e86i	0.770514	+	0.143336i
$445$	−6.30537e87			−2.53414
$446$			4.30545e86i			0.160682i
$447$	5.50449e85	−	2.95899e86i	0.0190796	−	0.102564i
$448$	1.01255e87			0.326017
$449$			2.32824e87i			0.696465i	0.937408	+	0.348233i	$0.113218\pi$
$449$			2.32824e87i			0.696465i	−0.937408	+	0.348233i	$0.886782\pi$
$450$	8.66780e86	−	2.24910e87i	0.240933	−	0.625168i
$451$	−2.87497e87			−0.742689
$452$			1.39932e87i			0.336008i
$453$	1.52144e87	+	2.83028e86i	0.339637	+	0.0631813i
$454$	−6.15962e86			−0.127853
$455$		−	1.02398e88i		−	1.97658i
$456$	−4.76509e86	+	2.56151e87i	−0.0855521	+	0.459893i
$457$	7.36037e86			0.122932			0.0614660	−	0.998109i	$-0.480422\pi$
$457$	7.36037e86			0.122932			0.0614660	+	0.998109i	$0.480422\pi$
$458$		−	4.28556e87i		−	0.665958i
$459$	−5.35229e87	+	8.69521e87i	−0.773965	+	1.25736i
$460$	1.28168e88			1.72493
$461$			6.91242e87i			0.865963i	0.901403	+	0.432982i	$0.142538\pi$
$461$			6.91242e87i			0.865963i	−0.901403	+	0.432982i	$0.857462\pi$
$462$	4.83637e87	+	8.99691e86i	0.564072	+	0.104932i
$463$	5.24019e87			0.569081			0.284541	−	0.958664i	$-0.408159\pi$
$463$	5.24019e87			0.569081			0.284541	+	0.958664i	$0.408159\pi$
$464$		−	1.27633e87i		−	0.129083i
$465$	3.30932e87	−	1.77896e88i	0.311739	−	1.67578i
$466$	2.74940e87			0.241270
$467$			1.75715e88i			1.43665i	0.695706	+	0.718327i	$0.255092\pi$
$467$			1.75715e88i			1.43665i	−0.695706	+	0.718327i	$0.744908\pi$
$468$	1.09335e88	+	4.21366e87i	0.833005	+	0.321031i
$469$	−3.24425e87			−0.230362
$470$			1.32777e87i			0.0878804i
$471$	−2.16133e88	−	4.02064e87i	−1.33362	−	0.248088i
$472$	1.50209e88			0.864189
$473$		−	6.94003e87i		−	0.372343i
$474$	1.78526e87	−	9.59684e87i	0.0893340	−	0.480223i
$475$	−1.39692e88			−0.652053
$476$		−	2.58896e88i		−	1.12745i
$477$	7.69917e87	−	1.99776e88i	0.312851	−	0.811779i
$478$	3.24352e87			0.122997
$479$			5.02717e88i			1.77931i	0.456633	+	0.889655i	$0.349055\pi$
$479$			5.02717e88i			1.77931i	−0.456633	+	0.889655i	$0.650945\pi$
$480$	−4.64337e88	−	8.63788e87i	−1.53417	−	0.285395i
$481$	4.36729e88			1.34718
$482$			1.66633e88i			0.479964i
$483$	−1.14507e88	+	6.15544e88i	−0.308019	+	1.65578i
$484$	−1.42342e87			−0.0357632
$485$		−	1.01020e89i		−	2.37099i
$486$	−1.91705e88	+	1.46091e88i	−0.420374	+	0.320352i
$487$	−6.36381e88			−1.30395			−0.651976	−	0.758239i	$-0.726060\pi$
$487$	−6.36381e88			−1.30395			−0.651976	+	0.758239i	$0.726060\pi$
$488$			6.39864e88i			1.22527i
$489$	8.41695e87	+	1.56577e87i	0.150648	+	0.0280244i
$490$	−5.83828e87			−0.0976819
$491$		−	6.69541e88i		−	1.04734i	−0.851921	−	0.523670i	$-0.824562\pi$
$491$		−	6.69541e88i		−	1.04734i	0.851921	−	0.523670i	$-0.175438\pi$
$492$	−6.53214e87	+	3.51141e88i	−0.0955448	+	0.513609i
$493$	5.80513e88			0.794078
$494$			2.63224e88i			0.336772i
$495$	−1.20284e89	−	4.63560e88i	−1.43958	−	0.554798i
$496$	−2.42630e88			−0.271675
$497$			1.17006e89i			1.22588i
$498$	−2.27937e88	−	4.24023e87i	−0.223484	−	0.0415739i
$499$	8.74967e88			0.802922			0.401461	−	0.915876i	$-0.368502\pi$
$499$	8.74967e88			0.802922			0.401461	+	0.915876i	$0.368502\pi$
$500$		−	3.38143e88i		−	0.290463i
$501$	−2.42365e88	+	1.30285e89i	−0.194906	+	1.04773i
$502$	2.61652e88			0.197016
$503$		−	2.67710e89i		−	1.88765i	−0.330451	−	0.943823i	$-0.607201\pi$
$503$		−	2.67710e89i		−	1.88765i	0.330451	−	0.943823i	$-0.392799\pi$
$504$	5.24731e88	−	1.36156e89i	0.346520	−	0.899144i
$505$	2.85195e89			1.76411
$506$			1.48526e89i			0.860669i
$507$	9.67928e88	+	1.80060e88i	0.525509	+	0.0977585i
$508$	−1.23794e88			−0.0629790
$509$		−	1.95321e89i		−	0.931242i	−0.884984	−	0.465621i	$-0.845831\pi$
$509$		−	1.95321e89i		−	0.931242i	0.884984	−	0.465621i	$-0.154169\pi$
$510$	4.80933e88	−	2.58529e89i	0.214916	−	1.15530i
$511$	1.82107e89			0.762847
$512$			1.18908e89i			0.466986i
$513$	1.18957e89	+	7.32234e88i	0.438043	+	0.269635i
$514$	−2.16941e89			−0.749132
$515$			5.52903e89i			1.79065i
$516$	−8.47637e88	−	1.57683e88i	−0.257496	−	0.0479009i
$517$	3.96956e88			0.113124
$518$		−	2.27784e89i		−	0.609034i
$519$	−4.44483e88	+	2.38936e89i	−0.111515	+	0.599458i
$520$	−7.20522e89			−1.69643
$521$			2.08568e89i			0.460896i	0.973085	+	0.230448i	$0.0740191\pi$
$521$			2.08568e89i			0.460896i	−0.973085	+	0.230448i	$0.925981\pi$
$522$	1.27867e89	+	4.92786e88i	0.265236	+	0.102219i
$523$	−5.33913e89			−1.03972			−0.519858	−	0.854252i	$-0.674015\pi$
$523$	−5.33913e89			−1.03972			−0.519858	+	0.854252i	$0.674015\pi$
$524$		−	1.60880e89i		−	0.294151i
$525$	7.69145e89	+	1.43081e89i	1.32054	+	0.245655i
$526$	5.40120e89			0.870885
$527$		−	1.10356e90i		−	1.67126i
$528$	−3.16123e88	+	1.69934e89i	−0.0449714	+	0.241748i
$529$	−1.14212e90			−1.52642
$530$			5.51399e89i			0.692409i
$531$	2.89598e89	−	7.51444e89i	0.341725	−	0.886701i
$532$	−3.54189e89			−0.392782
$533$			8.61539e89i			0.898001i
$534$	−8.92447e89	−	1.66019e89i	−0.874422	−	0.162665i
$535$	−1.89470e89			−0.174529
$536$			2.28282e89i			0.197712i
$537$	2.01840e89	−	1.08501e90i	0.164382	−	0.883651i
$538$	−6.18367e89			−0.473621
$539$			1.74544e89i			0.125741i
$540$	−8.39474e89	+	1.36379e90i	−0.568870	+	0.924173i
$541$	1.75875e90			1.12123			0.560616	−	0.828076i	$-0.310564\pi$
$541$	1.75875e90			1.12123			0.560616	+	0.828076i	$0.310564\pi$
$542$			9.65768e89i			0.579291i
$543$	1.76442e90	+	3.28229e89i	0.995882	+	0.185260i
$544$	−2.88046e90			−1.53002
$545$		−	7.68450e89i		−	0.384177i
$546$	2.69610e89	−	1.44931e90i	0.126876	−	0.682031i
$547$	−5.47604e89			−0.242596			−0.121298	−	0.992616i	$-0.538706\pi$
$547$	−5.47604e89			−0.242596			−0.121298	+	0.992616i	$0.538706\pi$
$548$		−	2.68224e90i		−	1.11877i
$549$	3.20103e90	+	1.23364e90i	1.25719	+	0.484508i
$550$	1.85589e90			0.686410
$551$		−	7.94185e89i		−	0.276643i
$552$	4.33128e90	+	8.05732e89i	1.42111	+	0.264363i
$553$	3.16834e90			0.979269
$554$			2.40227e90i			0.699519i
$555$	−1.09164e90	+	5.86822e90i	−0.299511	+	1.61005i
$556$	2.61502e90			0.676095
$557$		−	4.58557e90i		−	1.11731i	−0.829401	−	0.558653i	$-0.811318\pi$
$557$		−	4.58557e90i		−	1.11731i	0.829401	−	0.558653i	$-0.188682\pi$
$558$	9.36787e89	−	2.43076e90i	0.215136	−	0.558230i
$559$	−2.07971e90			−0.450208
$560$		−	1.87656e90i		−	0.382965i
$561$	−7.72914e90	−	1.43782e90i	−1.48716	−	0.276650i
$562$	−3.72074e90			−0.675041
$563$		−	8.36332e89i		−	0.143088i	−0.997437	−	0.0715438i	$-0.977207\pi$
$563$		−	8.36332e89i		−	0.143088i	0.997437	−	0.0715438i	$-0.0227926\pi$
$564$	9.01914e88	−	4.84832e89i	0.0145531	−	0.0782313i
$565$	−4.61324e90			−0.702113
$566$			6.24778e90i			0.896982i
$567$	−5.79977e90	−	5.25011e90i	−0.785543	−	0.711094i
$568$	8.23316e90			1.05214
$569$		−	4.17107e90i		−	0.502971i	−0.967861	−	0.251485i	$-0.919081\pi$
$569$		−	4.17107e90i		−	0.502971i	0.967861	−	0.251485i	$-0.0809190\pi$
$570$	−3.53688e90	−	6.57952e89i	−0.402485	−	0.0748728i
$571$	3.02971e90			0.325394			0.162697	−	0.986676i	$-0.447981\pi$
$571$	3.02971e90			0.325394			0.162697	+	0.986676i	$0.447981\pi$
$572$			9.02202e90i			0.914608i
$573$	3.72916e88	−	2.00464e89i	0.00356869	−	0.0191838i
$574$	4.49352e90			0.405970
$575$			2.36207e91i			2.01490i
$576$	−3.56430e90	−	1.37364e90i	−0.287099	−	0.110645i
$577$	−1.64270e91			−1.24956			−0.624779	−	0.780802i	$-0.714811\pi$
$577$	−1.64270e91			−1.24956			−0.624779	+	0.780802i	$0.714811\pi$
$578$		−	8.68086e90i		−	0.623655i
$579$	−1.54611e91	−	2.87618e90i	−1.04918	−	0.195175i
$580$	9.10498e90			0.583654
$581$		−	7.52521e90i		−	0.455728i
$582$	2.65983e90	−	1.42981e91i	0.152193	−	0.818128i
$583$	1.64849e91			0.891302
$584$		−	1.28140e91i		−	0.654728i
$585$	−1.38915e91	+	3.60453e91i	−0.670818	+	1.74062i
$586$	6.63470e90			0.302831
$587$		−	1.15474e91i		−	0.498228i	−0.968474	−	0.249114i	$-0.919861\pi$
$587$		−	1.15474e91i		−	0.498228i	0.968474	−	0.249114i	$-0.0801394\pi$
$588$	2.13184e90	+	3.96578e89i	0.0869566	+	0.0161762i
$589$	−1.50975e91			−0.582237
$590$			2.07405e91i			0.756314i
$591$	4.39533e89	−	2.36275e90i	0.0151567	−	0.0814761i
$592$	8.00361e90			0.261018
$593$		−	1.00698e91i		−	0.310611i	−0.987866	−	0.155306i	$-0.950364\pi$
$593$		−	1.00698e91i		−	0.310611i	0.987866	−	0.155306i	$-0.0496363\pi$
$594$	−1.58041e91	−	9.72815e90i	−0.461124	−	0.283843i
$595$	8.53519e91			2.35588
$596$		−	2.87899e90i		−	0.0751819i
$597$	1.95576e91	+	3.63823e90i	0.483240	+	0.0898952i
$598$	4.45087e91			1.04065
$599$		−	2.21628e91i		−	0.490388i	−0.969474	−	0.245194i	$-0.921148\pi$
$599$		−	2.21628e91i		−	0.490388i	0.969474	−	0.245194i	$-0.0788517\pi$
$600$	1.00679e91	−	5.41210e91i	0.210838	−	1.13338i
$601$	−9.31219e91			−1.84584			−0.922920	−	0.384991i	$-0.874205\pi$
$601$	−9.31219e91			−1.84584			−0.922920	+	0.384991i	$0.874205\pi$
$602$			1.08471e91i			0.203531i
$603$	1.14202e91	+	4.40122e90i	0.202863	+	0.0781810i
$604$	1.48031e91			0.248962
$605$		−	4.69268e90i		−	0.0747297i
$606$	4.03658e91	+	7.50909e90i	0.608719	+	0.113238i
$607$	6.55193e91			0.935713			0.467856	−	0.883805i	$-0.345026\pi$
$607$	6.55193e91			0.935713			0.467856	+	0.883805i	$0.345026\pi$
$608$			3.94069e91i			0.533033i
$609$	−8.13452e90	+	4.37278e91i	−0.104222	+	0.560257i
$610$	−8.83509e91			−1.07233
$611$		−	1.18955e91i		−	0.136781i
$612$	−3.51224e91	+	9.11348e91i	−0.382637	+	0.992859i
$613$	−7.42051e91			−0.766017			−0.383008	−	0.923745i	$-0.625112\pi$
$613$	−7.42051e91			−0.766017			−0.383008	+	0.923745i	$0.625112\pi$
$614$		−	1.88937e91i		−	0.184825i
$615$	−1.15763e92	−	2.15349e91i	−1.07322	−	0.199648i
$616$	1.12352e92			0.987226
$617$			1.60829e92i			1.33954i	0.742570	+	0.669768i	$0.233607\pi$
$617$			1.60829e92i			1.33954i	−0.742570	+	0.669768i	$0.766393\pi$
$618$	−1.45578e91	+	7.82565e91i	−0.114941	+	0.617876i
$619$	−2.09973e92			−1.57171			−0.785853	−	0.618414i	$-0.787776\pi$
$619$	−2.09973e92			−1.57171			−0.785853	+	0.618414i	$0.787776\pi$
$620$		−	1.73086e92i		−	1.22839i
$621$	1.23814e92	−	2.01145e92i	0.833196	−	1.35359i
$622$	−8.56174e91			−0.546361
$623$		−	2.94636e92i		−	1.78312i
$624$	5.09241e91	+	9.47322e90i	0.292302	+	0.0543758i
$625$	−1.21353e92			−0.660709
$626$			1.28152e92i			0.661871i
$627$	−1.96705e91	+	1.05740e92i	−0.0963799	+	0.518099i
$628$	−2.10290e92			−0.977574
$629$			3.64029e92i			1.60570i
$630$	1.88001e92	+	7.24536e91i	0.786905	+	0.303265i
$631$	6.08271e91			0.241617			0.120809	−	0.992676i	$-0.461451\pi$
$631$	6.08271e91			0.241617			0.120809	+	0.992676i	$0.461451\pi$
$632$		−	2.22941e92i		−	0.840476i
$633$	4.02748e92	+	7.49217e91i	1.44116	+	0.268093i
$634$	8.08170e91			0.274509
$635$		−	4.08119e91i		−	0.131599i
$636$	3.74550e91	−	2.01343e92i	0.114663	−	0.616384i
$637$	5.23055e91			0.152036
$638$			1.05512e92i			0.291219i
$639$	1.58733e92	−	4.11878e92i	0.416044	−	1.07954i
$640$	−5.28523e92			−1.31560
$641$			9.26976e91i			0.219156i	0.993978	+	0.109578i	$0.0349500\pi$
$641$			9.26976e91i			0.219156i	−0.993978	+	0.109578i	$0.965050\pi$
$642$	−2.68172e91	−	4.98870e90i	−0.0602223	−	0.0112029i
$643$	6.09661e92			1.30055			0.650274	−	0.759700i	$-0.274654\pi$
$643$	6.09661e92			1.30055			0.650274	+	0.759700i	$0.274654\pi$
$644$			5.98901e92i			1.21373i
$645$	5.19843e91	−	2.79446e92i	0.100092	−	0.538056i
$646$	−2.19406e92			−0.401399
$647$			3.89881e92i			0.677782i	0.940826	+	0.338891i	$0.110052\pi$
$647$			3.89881e92i			0.677782i	−0.940826	+	0.338891i	$0.889948\pi$
$648$	−3.69425e92	+	4.08102e92i	−0.610310	+	0.674207i
$649$	6.20069e92			0.973564
$650$		−	5.56153e92i		−	0.829953i
$651$	8.31266e92	+	1.54637e92i	1.17915	+	0.219352i
$652$	8.18938e91			0.110428
$653$		−	7.68912e92i		−	0.985693i	−0.870116	−	0.492847i	$-0.835956\pi$
$653$		−	7.68912e92i		−	0.985693i	0.870116	−	0.492847i	$-0.164044\pi$
$654$	2.02330e91	−	1.08764e92i	0.0246601	−	0.132563i
$655$	5.30385e92			0.614650
$656$			1.57888e92i			0.173989i
$657$	−6.41042e92	−	2.47051e92i	−0.671783	−	0.258898i
$658$	−6.20435e91			−0.0618361
$659$		−	7.50602e92i		−	0.711527i	−0.934576	−	0.355763i	$-0.884221\pi$
$659$		−	7.50602e92i		−	0.711527i	0.934576	−	0.355763i	$-0.115779\pi$
$660$	−1.21227e93	−	2.25514e92i	−1.09307	−	0.203340i
$661$	−7.79686e92			−0.668762			−0.334381	−	0.942438i	$-0.608527\pi$
$661$	−7.79686e92			−0.668762			−0.334381	+	0.942438i	$0.608527\pi$
$662$		−	7.06523e92i		−	0.576517i
$663$	−4.30871e92	+	2.31618e93i	−0.334504	+	1.79815i
$664$	−5.29512e92			−0.391137
$665$		−	1.16768e93i		−	0.820747i
$666$	−3.09017e92	+	8.01831e92i	−0.206696	+	0.536332i
$667$	−1.34289e93			−0.854848
$668$			1.26763e93i			0.768013i
$669$	5.18294e92	+	9.64163e91i	0.298892	+	0.0556018i
$670$	−3.15207e92			−0.173032
$671$			2.64139e93i			1.38035i
$672$	4.03629e92	−	2.16974e93i	0.200815	−	1.07950i
$673$	−9.94314e92			−0.471006			−0.235503	−	0.971874i	$-0.575674\pi$
$673$	−9.94314e92			−0.471006			−0.235503	+	0.971874i	$0.575674\pi$
$674$			1.33952e93i			0.604188i
$675$	−2.51339e93	−	1.54710e93i	−1.07953	−	0.664499i
$676$	9.41759e92			0.385211
$677$			3.05087e93i			1.18849i	0.804282	+	0.594247i	$0.202550\pi$
$677$			3.05087e93i			1.18849i	−0.804282	+	0.594247i	$0.797450\pi$
$678$	−6.52947e92	−	1.21465e92i	−0.242269	−	0.0450684i
$679$	4.72045e93			1.66832
$680$		−	6.00580e93i		−	2.02198i
$681$	−1.37939e92	+	7.41501e92i	−0.0442416	+	0.237825i
$682$	2.00579e93			0.612915
$683$		−	2.29995e93i		−	0.669629i	−0.942284	−	0.334815i	$-0.891326\pi$
$683$		−	2.29995e93i		−	0.669629i	0.942284	−	0.334815i	$-0.108674\pi$
$684$	1.24679e93	+	4.80501e92i	0.345894	+	0.133304i
$685$	8.84271e93			2.33774
$686$			1.94999e93i			0.491288i
$687$	−5.15900e93	−	9.59709e92i	−1.23878	−	0.230445i
$688$	−3.81134e92			−0.0872286
$689$		−	4.94003e93i		−	1.07769i
$690$	−1.11254e93	+	5.98053e93i	−0.231363	+	1.24371i
$691$	−5.47360e93			−1.08517			−0.542585	−	0.840001i	$-0.682554\pi$
$691$	−5.47360e93			−1.08517			−0.542585	+	0.840001i	$0.682554\pi$
$692$			2.32476e93i			0.439417i
$693$	2.16611e93	−	5.62059e93i	0.390377	−	1.01294i
$694$	4.39309e93			0.754932
$695$			8.62112e93i			1.41275i
$696$	3.07691e93	+	5.72386e92i	0.480851	+	0.0894508i
$697$	−7.18123e93			−1.07033
$698$		−	4.03591e93i		−	0.573736i
$699$	6.15701e92	−	3.30975e93i	0.0834878	−	0.448796i
$700$	7.48349e93			0.967986
$701$		−	9.81125e93i		−	1.21068i	−0.795966	−	0.605341i	$-0.793037\pi$
$701$		−	9.81125e93i		−	1.21068i	0.795966	−	0.605341i	$-0.206963\pi$
$702$	−2.91523e93	+	4.73601e93i	−0.343200	+	0.557555i
$703$	4.98019e93			0.559397
$704$		−	2.94115e93i		−	0.315224i
$705$	1.59838e93	+	2.97340e92i	0.163470	+	0.0304097i
$706$	1.79029e93			0.174730
$707$			1.33265e94i			1.24130i
$708$	1.40884e93	−	7.57335e93i	0.125246	−	0.673272i
$709$	4.95259e93			0.420249			0.210125	−	0.977675i	$-0.432613\pi$
$709$	4.95259e93			0.420249			0.210125	+	0.977675i	$0.432613\pi$
$710$			1.13682e94i			0.920799i
$711$	−1.11530e94	−	4.29823e93i	−0.862370	−	0.332348i
$712$	−2.07321e94			−1.53039
$713$			2.55284e94i			1.79916i
$714$	1.20805e94	+	2.24729e93i	0.812913	+	0.151223i
$715$	−2.97435e94			−1.91114
$716$		−	1.05567e94i		−	0.647737i
$717$	7.26355e92	−	3.90458e93i	0.0425615	−	0.228793i
$718$	−8.87282e93			−0.496541
$719$		−	2.75992e94i		−	1.47517i	−0.675253	−	0.737586i	$-0.735965\pi$
$719$		−	2.75992e94i		−	1.47517i	0.675253	−	0.737586i	$-0.264035\pi$
$720$	−2.54579e93	+	6.60576e93i	−0.129972	+	0.337249i
$721$	−2.58359e94			−1.25997
$722$		−	8.34308e93i		−	0.388686i
$723$	2.00594e94	+	3.73158e93i	0.892802	+	0.166085i
$724$	1.71672e94			0.730005
$725$			1.67800e94i			0.681768i
$726$	1.23557e92	−	6.64190e92i	0.00479687	−	0.0257860i
$727$	−2.93602e94			−1.08924			−0.544619	−	0.838683i	$-0.683326\pi$
$727$	−2.93602e94			−1.08924			−0.544619	+	0.838683i	$0.683326\pi$
$728$		−	3.36684e94i		−	1.19368i
$729$	1.32936e94	+	2.63492e94i	0.450436	+	0.892809i
$730$	1.76933e94			0.572999
$731$		−	1.73351e94i		−	0.536604i
$732$	3.22612e94	+	6.00143e93i	0.954586	+	0.177578i
$733$	1.05409e94			0.298159			0.149079	−	0.988825i	$-0.452369\pi$
$733$	1.05409e94			0.298159			0.149079	+	0.988825i	$0.452369\pi$
$734$		−	7.89749e93i		−	0.213560i
$735$	−1.30742e93	+	7.02817e93i	−0.0338014	+	0.181702i
$736$	6.66334e94			1.64712
$737$			9.42359e93i			0.222735i
$738$	−1.58178e94	−	6.09601e93i	−0.357508	−	0.137780i
$739$	1.00758e93			0.0217777			0.0108888	−	0.999941i	$-0.496534\pi$
$739$	1.00758e93			0.0217777			0.0108888	+	0.999941i	$0.496534\pi$
$740$			5.70956e94i			1.18020i
$741$	3.16871e94	+	5.89464e93i	0.626444	+	0.116535i
$742$	−2.57657e94			−0.487206
$743$		−	4.62951e94i		−	0.837345i	−0.908137	−	0.418672i	$-0.862496\pi$
$743$		−	4.62951e94i		−	0.837345i	0.908137	−	0.418672i	$-0.137504\pi$
$744$	1.08811e94	−	5.84922e94i	0.188263	−	1.01202i
$745$	9.49134e93			0.157098
$746$			3.30263e94i			0.522973i
$747$	−1.02089e94	+	2.64897e94i	−0.154667	+	0.401326i
$748$	−7.52017e94			−1.09012
$749$		−	8.85353e93i		−	0.122805i
$750$	1.57783e94	+	2.93518e93i	0.209430	+	0.0389595i
$751$	4.99844e94			0.634917			0.317458	−	0.948272i	$-0.397171\pi$
$751$	4.99844e94			0.634917			0.317458	+	0.948272i	$0.397171\pi$
$752$		−	2.18001e93i		−	0.0265015i
$753$	5.85944e93	−	3.14979e94i	0.0681745	−	0.366478i
$754$	3.16187e94			0.352119
$755$			4.88022e94i			0.520224i
$756$	−6.37268e94	−	3.92267e94i	−0.650284	−	0.400279i
$757$	−9.29550e94			−0.908047			−0.454024	−	0.890990i	$-0.650012\pi$
$757$	−9.29550e94			−0.908047			−0.454024	+	0.890990i	$0.650012\pi$
$758$			6.33875e94i			0.592816i
$759$	1.78797e95	+	3.32610e94i	1.60097	+	0.297822i
$760$	−8.21639e94			−0.704421
$761$		−	6.66223e94i		−	0.546922i	−0.961883	−	0.273461i	$-0.911831\pi$
$761$		−	6.66223e94i		−	0.546922i	0.961883	−	0.273461i	$-0.0881685\pi$
$762$	1.07456e93	−	5.77641e93i	0.00844731	−	0.0454092i
$763$	3.59079e94			0.270322
$764$		−	1.95044e93i		−	0.0140622i
$765$	−3.00450e95	−	1.15790e95i	−2.07465	−	0.799548i
$766$	−1.15378e95			−0.763083
$767$		−	1.85815e95i		−	1.17716i
$768$	−1.24652e95	−	2.31886e94i	−0.756450	−	0.140720i
$769$	1.96905e95			1.14469			0.572344	−	0.820014i	$-0.306034\pi$
$769$	1.96905e95			1.14469			0.572344	+	0.820014i	$0.306034\pi$
$770$			1.55133e95i			0.863992i
$771$	−4.85818e94	+	2.61156e95i	−0.259226	+	1.39349i
$772$	−1.50431e95			−0.769072
$773$			3.13593e95i			1.53618i	0.640341	+	0.768091i	$0.278793\pi$
$773$			3.13593e95i			1.53618i	−0.640341	+	0.768091i	$0.721207\pi$
$774$	1.47155e94	−	3.81834e94i	0.0690752	−	0.179235i
$775$	3.18987e95			1.43489
$776$		−	3.32155e95i		−	1.43187i
$777$	−2.74209e95	−	5.10101e94i	−1.13289	−	0.210747i
$778$	9.55164e94			0.378226
$779$			9.82446e94i			0.372883i
$780$	−6.75794e94	+	3.63279e95i	−0.245863	+	1.32166i
$781$	3.39869e95			1.18530
$782$			3.70996e95i			1.24036i
$783$	8.79566e94	−	1.42892e95i	0.281923	−	0.458005i
$784$	9.58565e93			0.0294572
$785$		−	6.93276e95i		−	2.04271i
$786$	7.50693e94	+	1.39649e94i	0.212089	+	0.0394541i
$787$	−2.55070e95			−0.691023			−0.345512	−	0.938414i	$-0.612295\pi$
$787$	−2.55070e95			−0.691023			−0.345512	+	0.938414i	$0.612295\pi$
$788$		−	2.29887e94i		−	0.0597239i
$789$	1.20955e95	−	6.50202e95i	0.301357	−	1.61997i
$790$	3.07831e95			0.735561
$791$		−	2.15566e95i		−	0.494034i
$792$	−3.95494e95	−	1.52419e95i	−0.869378	−	0.335049i
$793$	7.91542e95			1.66901
$794$			3.22417e95i			0.652142i
$795$	6.63780e95	+	1.23480e95i	1.28798	+	0.239598i
$796$	1.90288e95			0.354226
$797$			1.02512e96i			1.83083i	0.402507	+	0.915417i	$0.368139\pi$
$797$			1.02512e96i			1.83083i	−0.402507	+	0.915417i	$0.631861\pi$
$798$	3.07446e94	−	1.65270e95i	0.0526834	−	0.283204i
$799$	9.91535e94			0.163029
$800$		−	8.32609e95i		−	1.31363i
$801$	−3.99709e95	+	1.03716e96i	−0.605162	+	1.57026i
$802$	−2.75982e95			−0.400983
$803$		−	5.28968e95i		−	0.737593i
$804$	1.15097e95	+	2.14111e94i	0.154034	+	0.0286543i
$805$	−1.97444e96			−2.53618
$806$		−	6.01072e95i		−	0.741089i
$807$	−1.38477e95	+	7.44396e95i	−0.163890	+	0.881003i
$808$	9.37722e95			1.06537
$809$		−	6.06638e94i		−	0.0661650i	−0.999453	−	0.0330825i	$-0.989468\pi$
$809$		−	6.06638e94i		−	0.0661650i	0.999453	−	0.0330825i	$-0.0105324\pi$
$810$	−5.63497e95	−	5.10093e95i	−0.590047	−	0.534126i
$811$	−3.09599e95			−0.311251			−0.155626	−	0.987816i	$-0.549739\pi$
$811$	−3.09599e95			−0.311251			−0.155626	+	0.987816i	$0.549739\pi$
$812$			4.25455e95i			0.410681i
$813$	1.16260e96	+	2.16274e95i	1.07756	+	0.200455i
$814$	−6.61647e95			−0.588872
$815$			2.69985e95i			0.230748i
$816$	−7.89626e94	+	4.24470e95i	−0.0648106	+	0.348395i
$817$	−2.37158e95			−0.186943
$818$			3.95973e94i			0.0299783i
$819$	−1.68432e96	−	6.49117e95i	−1.22477	−	0.472013i
$820$	−1.12633e96			−0.786699
$821$			1.48891e96i			0.998952i	0.866328	+	0.499476i	$0.166474\pi$
$821$			1.48891e96i			0.998952i	−0.866328	+	0.499476i	$0.833526\pi$
$822$	1.25158e96	+	2.32826e95i	0.806654	+	0.150059i
$823$	7.60471e95			0.470856			0.235428	−	0.971892i	$-0.424351\pi$
$823$	7.60471e95			0.470856			0.235428	+	0.971892i	$0.424351\pi$
$824$			1.81795e96i			1.08139i
$825$	4.15609e95	−	2.23414e96i	0.237522	−	1.27682i
$826$	−9.69156e95			−0.532172
$827$		−	1.47753e96i		−	0.779569i	−0.920906	−	0.389785i	$-0.872549\pi$
$827$		−	1.47753e96i		−	0.779569i	0.920906	−	0.389785i	$-0.127451\pi$
$828$	8.12482e95	−	2.10821e96i	0.411920	−	1.06884i
$829$	−5.31196e95			−0.258794			−0.129397	−	0.991593i	$-0.541304\pi$
$829$	−5.31196e95			−0.258794			−0.129397	+	0.991593i	$0.541304\pi$
$830$		−	7.31138e95i		−	0.342312i
$831$	2.89188e96	+	5.37965e95i	1.30121	+	0.242058i
$832$	−8.81371e95			−0.381144
$833$			4.35985e95i			0.181212i
$834$	−2.26992e95	+	1.22021e96i	−0.0906839	+	0.487479i
$835$	−4.17907e96			−1.60482
$836$			1.02882e96i			0.379779i
$837$	−2.71638e96	−	1.67206e96i	−0.963942	−	0.593350i
$838$	2.03776e96			0.695184
$839$		−	2.54405e96i		−	0.834414i	−0.908812	−	0.417207i	$-0.863009\pi$
$839$		−	2.54405e96i		−	0.834414i	0.908812	−	0.417207i	$-0.136991\pi$
$840$	4.52394e96	+	8.41571e95i	1.42659	+	0.265384i
$841$	2.34415e96			0.710751
$842$			7.33252e95i			0.213774i
$843$	−8.33222e95	+	4.47906e96i	−0.233588	+	1.25567i
$844$	3.91859e96			1.05640
$845$			3.10476e96i			0.804927i
$846$	2.18401e95	+	8.41695e94i	0.0544545	+	0.0209862i
$847$	2.19278e95			0.0525828
$848$		−	9.05322e95i		−	0.208805i
$849$	7.52114e96	+	1.39913e96i	1.66851	+	0.310387i
$850$	4.63573e96			0.989222
$851$		−	8.42104e96i		−	1.72858i
$852$	7.72208e95	−	4.15107e96i	0.152485	−	0.819697i
$853$	−5.87163e96			−1.11543			−0.557713	−	0.830034i	$-0.688321\pi$
$853$	−5.87163e96			−1.11543			−0.557713	+	0.830034i	$0.688321\pi$
$854$		−	4.12844e96i		−	0.754530i
$855$	−1.58410e96	+	4.11039e96i	−0.278548	+	0.722771i
$856$	−6.22980e95			−0.105400
$857$			7.32825e96i			1.19298i	0.802621	+	0.596490i	$0.203438\pi$
$857$			7.32825e96i			1.19298i	−0.802621	+	0.596490i	$0.796562\pi$
$858$	−4.20982e96	−	7.83137e95i	−0.659452	−	0.122675i
$859$	−5.35107e96			−0.806615			−0.403308	−	0.915064i	$-0.632140\pi$
$859$	−5.35107e96			−0.806615			−0.403308	+	0.915064i	$0.632140\pi$
$860$		−	2.71891e96i		−	0.394408i
$861$	1.00628e96	−	5.40934e96i	0.140480	−	0.755163i
$862$	−2.61126e96			−0.350841
$863$			7.13263e96i			0.922345i	0.887310	+	0.461173i	$0.152571\pi$
$863$			7.13263e96i			0.922345i	−0.887310	+	0.461173i	$0.847429\pi$
$864$	−4.36434e96	+	7.09021e96i	−0.543207	+	0.882481i
$865$	−7.66418e96			−0.918194
$866$			6.39576e96i			0.737568i
$867$	−1.04501e97	−	1.94399e96i	−1.16009	−	0.215806i
$868$	8.08791e96			0.864342
$869$		−	9.20309e96i		−	0.946850i
$870$	−7.90338e95	+	4.24853e96i	−0.0782848	+	0.420827i
$871$	2.82396e96			0.269314
$872$		−	2.52667e96i		−	0.232009i
$873$	−1.66166e97	−	6.40386e96i	−1.46917	−	0.566202i
$874$	5.07550e96			0.432118
$875$			5.20911e96i			0.427069i
$876$	−6.46068e96	−	1.20186e96i	−0.510085	−	0.0948892i
$877$	2.42393e97			1.84304			0.921519	−	0.388334i	$-0.126949\pi$
$877$	2.42393e97			1.84304			0.921519	+	0.388334i	$0.126949\pi$
$878$		−	9.81236e96i		−	0.718546i
$879$	1.48578e96	−	7.98692e96i	0.104790	−	0.563308i
$880$	−5.45087e96			−0.370286
$881$		−	3.60825e96i		−	0.236097i	−0.993008	−	0.118049i	$-0.962336\pi$
$881$		−	3.60825e96i		−	0.236097i	0.993008	−	0.118049i	$-0.0376639\pi$
$882$	−3.70099e95	+	9.60326e95i	−0.0233268	+	0.0605279i
$883$	4.38928e95			0.0266496			0.0133248	−	0.999911i	$-0.495758\pi$
$883$	4.38928e95			0.0266496			0.0133248	+	0.999911i	$0.495758\pi$
$884$			2.25356e97i			1.31809i
$885$	2.49676e97	+	4.64462e96i	1.40685	+	0.261711i
$886$	−1.43151e97			−0.777106
$887$			1.93289e97i			1.01094i	0.862843	+	0.505472i	$0.168682\pi$
$887$			1.93289e97i			1.01094i	−0.862843	+	0.505472i	$0.831318\pi$
$888$	−3.58933e96	+	1.92948e97i	−0.180878	+	0.972325i
$889$	1.90705e96			0.0925984
$890$		−	2.86264e97i		−	1.33936i
$891$	−1.52500e97	+	1.68466e97i	−0.687553	+	0.759537i
$892$	5.04281e96			0.219095
$893$		−	1.35650e96i		−	0.0567963i
$894$	1.34338e96	+	2.49904e95i	0.0542077	+	0.0100841i
$895$	3.48030e97			1.35349
$896$		−	2.46967e97i		−	0.925709i
$897$	9.96729e96	−	5.35800e97i	0.360103	−	1.93576i
$898$	−1.05702e97			−0.368100
$899$			1.81352e97i			0.608770i
$900$	−2.63429e97	−	1.01523e97i	−0.852434	−	0.328519i
$901$	4.11768e97			1.28450
$902$		−	1.30524e97i		−	0.392530i
$903$	1.30579e97	+	2.42911e96i	0.378597	+	0.0704290i
$904$	−1.51684e97			−0.424014
$905$			5.65961e97i			1.52540i
$906$	−1.28495e96	+	6.90735e96i	−0.0333930	+	0.179507i
$907$	3.13441e97			0.785443			0.392722	−	0.919657i	$-0.371534\pi$
$907$	3.13441e97			0.785443			0.392722	+	0.919657i	$0.371534\pi$
$908$			7.21453e96i			0.174331i
$909$	1.80790e97	−	4.69111e97i	0.421276	−	1.09312i
$910$	4.64885e97			1.04467
$911$		−	7.88305e97i		−	1.70839i	−0.519951	−	0.854196i	$-0.674050\pi$
$911$		−	7.88305e97i		−	1.70839i	0.519951	−	0.854196i	$-0.325950\pi$
$912$	5.80707e96	+	1.08027e96i	0.121375	+	0.0225788i
$913$	−2.18585e97			−0.440641
$914$			3.34161e96i			0.0649727i
$915$	−1.97853e97	+	1.06358e98i	−0.371062	+	1.99468i
$916$	−5.01952e97			−0.908053
$917$			2.47837e97i			0.432492i
$918$	−3.94763e97	−	2.42994e97i	−0.664550	−	0.409061i
$919$	−1.08019e98			−1.75424			−0.877118	−	0.480274i	$-0.840537\pi$
$919$	−1.08019e98			−1.75424			−0.877118	+	0.480274i	$0.840537\pi$
$920$			1.38932e98i			2.17672i
$921$	−2.27444e97	−	4.23106e96i	−0.343801	−	0.0639560i
$922$	−3.13824e97			−0.457684
$923$		−	1.01848e98i		−	1.43317i
$924$	1.05377e97	−	5.66466e97i	0.143078	−	0.769128i
$925$	−1.05224e98			−1.37860
$926$			2.37905e97i			0.300774i
$927$	9.09459e97	+	3.50496e97i	1.10956	+	0.427613i
$928$	4.73359e97			0.557324
$929$		−	4.22603e96i		−	0.0480192i	−0.999712	−	0.0240096i	$-0.992357\pi$
$929$		−	4.22603e96i		−	0.0480192i	0.999712	−	0.0240096i	$-0.00764322\pi$
$930$	8.07647e97	+	1.50243e97i	0.885695	+	0.164762i
$931$	5.96460e96			0.0631309
$932$		−	3.22027e97i		−	0.328978i
$933$	−1.91732e97	+	1.03067e98i	−0.189060	+	1.01631i
$934$	−7.97747e97			−0.759308
$935$		−	2.47922e98i		−	2.27789i
$936$	−4.56752e97	+	1.18517e98i	−0.405114	+	1.05118i
$937$	−1.26917e98			−1.08671			−0.543354	−	0.839504i	$-0.682846\pi$
$937$	−1.26917e98			−1.08671			−0.543354	+	0.839504i	$0.682846\pi$
$938$		−	1.47289e97i		−	0.121752i
$939$	1.54271e98	+	2.86984e97i	1.23117	+	0.229031i
$940$	1.55516e97			0.119827
$941$			2.33685e98i			1.73850i	0.494376	+	0.869248i	$0.335397\pi$
$941$			2.33685e98i			1.73850i	−0.494376	+	0.869248i	$0.664603\pi$
$942$	1.82537e97	−	9.81246e97i	0.131121	−	0.704852i
$943$	1.66123e98			1.15224
$944$		−	3.40530e97i		−	0.228076i
$945$	1.29321e98	−	2.10092e98i	0.836413	−	1.35882i
$946$	3.15078e97			0.196793
$947$		−	1.63376e98i		−	0.985463i	−0.870181	−	0.492731i	$-0.835999\pi$
$947$		−	1.63376e98i		−	0.985463i	0.870181	−	0.492731i	$-0.164001\pi$
$948$	−1.12404e98	−	2.09101e97i	−0.654798	−	0.121810i
$949$	−1.58515e98			−0.891839
$950$		−	6.34203e97i		−	0.344627i
$951$	1.80982e97	−	9.72883e97i	0.0949899	−	0.510627i
$952$	2.80638e98			1.42274
$953$			3.71425e98i			1.81888i	0.415831	+	0.909442i	$0.363491\pi$
$953$			3.71425e98i			1.81888i	−0.415831	+	0.909442i	$0.636509\pi$
$954$	9.06986e97	+	3.49542e97i	0.429046	+	0.165350i
$955$	6.43016e96			0.0293840
$956$		−	3.79901e97i		−	0.167711i
$957$	1.27016e98	+	2.36284e97i	0.541709	+	0.100772i
$958$	−2.28234e98			−0.940412
$959$			4.13200e98i			1.64493i
$960$	2.20307e97	−	1.18428e98i	0.0847377	−	0.455515i
$961$	7.56770e97			0.281250
$962$			1.98275e98i			0.712017i
$963$	−1.20109e97	+	3.11656e97i	−0.0416781	+	0.108145i
$964$	1.95171e98			0.654445
$965$		−	4.95937e98i		−	1.60703i
$966$	−2.79457e98	−	5.19863e97i	−0.875124	−	0.162796i
$967$	−2.71236e97			−0.0820868			−0.0410434	−	0.999157i	$-0.513068\pi$
$967$	−2.71236e97			−0.0820868			−0.0410434	+	0.999157i	$0.513068\pi$
$968$		−	1.54296e97i		−	0.0451301i
$969$	−4.91339e97	+	2.64123e98i	−0.138898	+	0.746659i
$970$	4.58632e98			1.25313
$971$		−	2.62149e98i		−	0.692330i	−0.938174	−	0.346165i	$-0.887484\pi$
$971$		−	2.62149e98i		−	0.692330i	0.938174	−	0.346165i	$-0.112516\pi$
$972$	1.71111e98	+	2.24537e98i	0.436809	+	0.573192i
$973$	−4.02846e98			−0.994066
$974$		−	2.88917e98i		−	0.689173i
$975$	−6.69502e98	−	1.24545e98i	−1.54383	−	0.287193i
$976$	1.45060e98			0.323373
$977$		−	2.83972e98i		−	0.612004i	−0.952031	−	0.306002i	$-0.901009\pi$
$977$		−	2.83972e98i		−	0.612004i	0.952031	−	0.306002i	$-0.0989915\pi$
$978$	−7.10862e96	+	3.82130e97i	−0.0148116	+	0.0796212i
$979$	−8.55831e98			−1.72409
$980$			6.83815e97i			0.133192i
$981$	−1.26401e98	−	4.87135e97i	−0.238052	−	0.0917428i
$982$	3.03972e98			0.553547
$983$			8.51874e98i			1.50006i	0.661402	+	0.750031i	$0.269962\pi$
$983$			8.51874e98i			1.50006i	−0.661402	+	0.750031i	$0.730038\pi$
$984$	−3.80629e98	−	7.08070e97i	−0.648133	−	0.120570i
$985$	7.57882e97			0.124798
$986$			2.63553e98i			0.419691i
$987$	−1.38940e97	+	7.46886e97i	−0.0213975	+	0.115024i
$988$	3.08304e98			0.459198
$989$			4.01012e98i			0.577669i
$990$	2.10457e98	−	5.46088e98i	0.293225	−	0.760854i
$991$	−1.12831e98			−0.152054			−0.0760272	−	0.997106i	$-0.524224\pi$
$991$	−1.12831e98			−0.152054			−0.0760272	+	0.997106i	$0.524224\pi$
$992$		−	8.99857e98i		−	1.17297i
$993$	−8.50519e98	−	1.58219e98i	−1.07240	−	0.199495i
$994$	−5.31209e98			−0.647910
$995$			6.27336e98i			0.740182i
$996$	−4.96642e97	+	2.66974e98i	−0.0566872	+	0.304727i
$997$	7.88342e98			0.870512			0.435256	−	0.900307i	$-0.356658\pi$
$997$	7.88342e98			0.870512			0.435256	+	0.900307i	$0.356658\pi$
$998$			3.97235e98i			0.424365i
$999$	8.96051e98	+	5.51560e98i	0.926129	+	0.570074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.67.b.b.2.12	yes	20
3.2	odd	2	inner	3.67.b.b.2.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.67.b.b.2.9	✓	20	3.2	odd	2	inner
3.67.b.b.2.12	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 67 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.54000e9i q^{2} +(5.46530e15 + 1.01669e15i) q^{3} +5.31753e19 q^{4} +1.75307e23i q^{5} +(-4.61577e24 + 2.48125e25i) q^{6} -8.19169e27 q^{7} +5.76409e29i q^{8} +(2.88358e31 + 1.11130e31i) q^{9} -7.95893e32 q^{10} +2.37945e34i q^{11} +(2.90619e35 + 5.40628e34i) q^{12} +7.13046e36 q^{13} -3.71903e37i q^{14} +(-1.78232e38 + 9.58103e38i) q^{15} +1.30675e39 q^{16} +5.94349e40i q^{17} +(-5.04531e40 + 1.30915e41i) q^{18} +8.13114e41 q^{19} +9.32199e42i q^{20} +(-4.47700e43 - 8.32840e42i) q^{21} -1.08027e44 q^{22} -1.37490e45i q^{23} +(-5.86029e44 + 3.15025e45i) q^{24} -1.71799e46 q^{25} +3.23723e46i q^{26} +(1.46298e47 + 9.00531e46i) q^{27} -4.35596e47 q^{28} -9.76720e47i q^{29} +(-4.34979e48 - 8.09175e47i) q^{30} -1.85675e49 q^{31} +4.84641e49i q^{32} +(-2.41916e49 + 1.30044e50i) q^{33} -2.69835e50 q^{34} -1.43606e51i q^{35} +(1.53336e51 + 5.90939e50i) q^{36} +6.12483e51 q^{37} +3.69154e51i q^{38} +(3.89701e52 + 7.24946e51i) q^{39} -1.01048e53 q^{40} +1.20825e53i q^{41} +(3.78110e52 - 2.03256e53i) q^{42} -2.91666e53 q^{43} +1.26528e54i q^{44} +(-1.94819e54 + 5.05512e54i) q^{45} +6.24205e54 q^{46} -1.66827e54i q^{47} +(7.14177e54 + 1.32856e54i) q^{48} +7.33550e54 q^{49} -7.79968e55i q^{50} +(-6.04268e55 + 3.24830e56i) q^{51} +3.79165e56 q^{52} -6.92806e56i q^{53} +(-4.08841e56 + 6.64194e56i) q^{54} -4.17133e57 q^{55} -4.72177e57i q^{56} +(4.44391e57 + 8.26684e56i) q^{57} +4.43431e57 q^{58} -2.60594e58i q^{59} +(-9.47757e57 + 5.09475e58i) q^{60} +1.11009e59 q^{61} -8.42964e58i q^{62} +(-2.36214e59 - 9.10344e58i) q^{63} -1.23606e59 q^{64} +1.25002e60i q^{65} +(-5.90399e59 - 1.09830e59i) q^{66} +3.96041e59 q^{67} +3.16047e60i q^{68} +(1.39785e60 - 7.51425e60i) q^{69} +6.51971e60 q^{70} -1.42835e61i q^{71} +(-6.40565e60 + 1.66212e61i) q^{72} -2.22307e61 q^{73} +2.78068e61i q^{74} +(-9.38933e61 - 1.74666e61i) q^{75} +4.32376e61 q^{76} -1.94917e62i q^{77} +(-3.29126e61 + 1.76924e62i) q^{78} -3.86775e62 q^{79} +2.29082e62i q^{80} +(7.08007e62 + 6.40906e62i) q^{81} -5.48546e62 q^{82} +9.18639e62i q^{83} +(-2.38066e63 - 4.42866e62i) q^{84} -1.04193e64 q^{85} -1.32416e63i q^{86} +(9.93021e62 - 5.33807e63i) q^{87} -1.37153e64 q^{88} +3.59677e64i q^{89} +(-2.29502e64 - 8.84477e63i) q^{90} -5.84105e64 q^{91} -7.31108e64i q^{92} +(-1.01477e65 - 1.88773e64i) q^{93} +7.57396e63 q^{94} +1.42544e65i q^{95} +(-4.92730e64 + 2.64871e65i) q^{96} -5.76248e65 q^{97} +3.33032e64i q^{98} +(-2.64428e65 + 6.86133e65i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 48\!\cdots\!16 q^{3} - 87\!\cdots\!80 q^{4} - 36\!\cdots\!80 q^{6} + 12\!\cdots\!88 q^{7} + 15\!\cdots\!00 q^{9} - 78\!\cdots\!00 q^{10} + 72\!\cdots\!64 q^{12} + 18\!\cdots\!12 q^{13} + 29\!\cdots\!00 q^{15}+ \cdots + 13\!\cdots\!00 q^{99}+O(q^{100}) \) 20 * q + 4870975596954516 * q^3 - 874472713330987494880 * q^4 - 36458623571791371420365280 * q^6 + 12757412570419684480800346888 * q^7 + 15089557305995766698320873638900 * q^9 - 783798592344000703899756417518400 * q^10 + 723313252400516086588885120719010464 * q^12 + 18091739616075205076630659610294803912 * q^13 + 291841906843973945390453919652713854400 * q^15 + 35169907781372839393817803526848507036160 * q^16 - 1327598375030727473316959111629621787325120 * q^18 - 2193455295604677957336968896648577476247000 * q^19 + 8465393426583554489761097856455177936278920 * q^21 - 19209253722854761211546865955725969475475520 * q^22 - 8536939678857788536491103872952212579880680960 * q^24 - 30700488848472932976681231276090805532106633100 * q^25 + 558391355065775903739609435927472633730508278964 * q^27 + 144501040816005166289020822469679267340863318592 * q^28 - 13469561117532417280775174235598750536019791067200 * q^30 + 6175065418525787560244925992300120132476837130440 * q^31 + 76031443883614128882573745917963369573166525959360 * q^33 - 607578292754219603165333260413176675880514014447360 * q^34 - 3175274131330481643421765009589425373421119877953760 * q^36 + 27435708863590762009354808934891346302092239434849928 * q^37 + 5521526696977593923927147874084291303373365890875080 * q^39 - 164157270356735970397207190518038139497893424374707200 * q^40 - 362475530834094311762041222130355899146344066985844160 * q^42 + 2995923276457113198574378450730231874677434142901437032 * q^43 + 2893961767142107219663835709681578507068881328379222400 * q^45 - 9354105762324374445425328051923657080564209708616152960 * q^46 + 44083933305287886033485048811587957889306840899931818496 * q^48 + 35901948198185324872729610934124248147969595380066179580 * q^49 + 244898096463243383440025305755038369424109352434412094720 * q^51 - 707065170108353883018319930521496060001554914206203205312 * q^52 - 386962012382976993771518038850875450617071434969909598880 * q^54 + 1313751320608480207642793301222628514163843327983665564800 * q^55 + 14469858017237851043428899294433298407417456132214681222568 * q^57 - 100361163480954821917122043432794223233970822326053950441920 * q^58 + 188095594234899922680776576921513155518384075353356847385600 * q^60 + 36618251899234461407858901457296968011564547062158638752840 * q^61 + 1345036046130625400347897603264169586395820510566342530416072 * q^63 - 4235878925879978009146455436735085155393347326504147849175040 * q^64 + 8309681532541455738248790801869091701653966958238676467844800 * q^66 - 6285867272675020649645690828535183608121600074432515838268632 * q^67 + 26395268384310228436148510386607667671115625880708467370286720 * q^69 - 53673269104481250134670425876769459429788829882429608923689600 * q^70 + 135607917285688125946137613885497485690645144416066370695173120 * q^72 - 234584045940242428610177340241689807173326553683343804321823128 * q^73 + 123839979253809259811223462461211616240588739801286415169843700 * q^75 - 88416171262693699731320177563519953392160098165342187898838720 * q^76 + 42333034554100439516880814575759716324771014654582144994836800 * q^78 - 180033150591234061548131792670437122720422789571688775376700600 * q^79 - 2669759984009083569841876166867012798635236563858567744127147180 * q^81 + 9780548955253740491517774427483475844287869484539284101189512320 * q^82 - 29550683862870558945501681808473602755499090201740971929153891520 * q^84 + 15725476767553808561610465539289169056529282358913795578981260800 * q^85 - 20361537149674837364457194316410702650457831770981879709222020800 * q^87 + 43127341602231234631198337877354797375008485566513397535855918080 * q^88 - 68986845993042571618317468832763287342807845905185213796199009600 * q^90 - 166695697853283961323776703924127811908080973516544145788509117360 * q^91 + 50074015382338903474492727100775024610496294621525101240240943432 * q^93 - 243292275786183398644891798798613800120302016678942850492866824960 * q^94 + 1707340756716414995397633331453898170371668874444383803046536028160 * q^96 - 2044564925167962718092629881048800142635399871213696847289077976152 * q^97 + 1311784025950014883691036763145966005164166837426590048709685526400 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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