LMFDB - Embedded newform 3.67.b.b.2.4

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			2.4
Root			$-3.39530e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.67.b.b.2.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22231e10i q^{2} +(1.27232e15 - 5.41150e15i) q^{3} -7.56171e19 q^{4} +1.11898e23i q^{5} +(-6.61453e25 - 1.55517e25i) q^{6} -1.34063e28 q^{7} +2.23699e28i q^{8} +(-2.76656e31 - 1.37703e31i) q^{9} +O(q^{10})$	\(q-1.22231e10i q^{2} +(1.27232e15 - 5.41150e15i) q^{3} -7.56171e19 q^{4} +1.11898e23i q^{5} +(-6.61453e25 - 1.55517e25i) q^{6} -1.34063e28 q^{7} +2.23699e28i q^{8} +(-2.76656e31 - 1.37703e31i) q^{9} +1.36774e33 q^{10} +2.93013e34i q^{11} +(-9.62092e34 + 4.09202e35i) q^{12} +3.87614e36 q^{13} +1.63867e38i q^{14} +(6.05537e38 + 1.42370e38i) q^{15} -5.30613e39 q^{16} -2.37940e40i q^{17} +(-1.68316e41 + 3.38159e41i) q^{18} -1.19889e42 q^{19} -8.46141e42i q^{20} +(-1.70571e43 + 7.25484e43i) q^{21} +3.58153e44 q^{22} +1.09383e45i q^{23} +(1.21055e44 + 2.84617e43i) q^{24} +1.03135e45 q^{25} -4.73785e46i q^{26} +(-1.09718e47 + 1.32192e47i) q^{27} +1.01375e48 q^{28} -2.55829e48i q^{29} +(1.74020e48 - 7.40153e48i) q^{30} +1.47668e49 q^{31} +6.65079e49i q^{32} +(1.58564e50 + 3.72806e49i) q^{33} -2.90837e50 q^{34} -1.50014e51i q^{35} +(2.09199e51 + 1.04127e51i) q^{36} -5.97408e51 q^{37} +1.46542e52i q^{38} +(4.93169e51 - 2.09758e52i) q^{39} -2.50315e51 q^{40} -4.97073e52i q^{41} +(8.86766e53 + 2.08491e53i) q^{42} +1.15764e54 q^{43} -2.21568e54i q^{44} +(1.54087e54 - 3.09572e54i) q^{45} +1.33700e55 q^{46} -2.00509e54i q^{47} +(-6.75109e54 + 2.87141e55i) q^{48} +1.19962e56 q^{49} -1.26063e55i q^{50} +(-1.28761e56 - 3.02736e55i) q^{51} -2.93103e56 q^{52} -1.00051e57i q^{53} +(1.61580e57 + 1.34109e57i) q^{54} -3.27876e57 q^{55} -2.99898e56i q^{56} +(-1.52537e57 + 6.48780e57i) q^{57} -3.12703e58 q^{58} +1.54437e58i q^{59} +(-4.57889e58 - 1.07656e58i) q^{60} +2.11015e58 q^{61} -1.80496e59i q^{62} +(3.70894e59 + 1.84610e59i) q^{63} +4.21410e59 q^{64} +4.33733e59i q^{65} +(4.55685e59 - 1.93814e60i) q^{66} +7.76951e59 q^{67} +1.79924e60i q^{68} +(5.91925e60 + 1.39170e60i) q^{69} -1.83364e61 q^{70} -1.19531e61i q^{71} +(3.08041e59 - 6.18875e59i) q^{72} -4.94610e61 q^{73} +7.30217e61i q^{74} +(1.31221e60 - 5.58115e60i) q^{75} +9.06566e61 q^{76} -3.92823e62i q^{77} +(-2.56389e62 - 6.02806e61i) q^{78} +3.63937e62 q^{79} -5.93746e62i q^{80} +(5.75761e62 + 7.61928e62i) q^{81} -6.07577e62 q^{82} +6.01832e62i q^{83} +(1.28981e63 - 5.48590e63i) q^{84} +2.66251e63 q^{85} -1.41499e64i q^{86} +(-1.38442e64 - 3.25497e63i) q^{87} -6.55467e62 q^{88} +3.58687e63i q^{89} +(-3.78393e64 - 1.88342e64i) q^{90} -5.19649e64 q^{91} -8.27121e64i q^{92} +(1.87881e64 - 7.99105e64i) q^{93} -2.45084e64 q^{94} -1.34154e65i q^{95} +(3.59908e65 + 8.46194e64i) q^{96} -2.58963e64 q^{97} -1.46630e66i q^{98} +(4.03489e65 - 8.10637e65i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 48\!\cdots\!16 q^{3}+ \cdots + 15\!\cdots\!00 q^{9}+O(q^{10}) $ 20 * q + 4870975596954516 * q^3 - 874472713330987494880 * q^4 - 36458623571791371420365280 * q^6 + 12757412570419684480800346888 * q^7 + 15089557305995766698320873638900 * q^9	$ 20 q + 48\!\cdots\!16 q^{3}+ \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

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 $

$2$		−	1.22231e10i		−	1.42296i	−0.702709	−	0.711478i	$-0.748026\pi$
$2$		−	1.22231e10i		−	1.42296i	0.702709	−	0.711478i	$-0.251974\pi$
$3$	1.27232e15	−	5.41150e15i	0.228873	−	0.973456i
$3$	1.27232e15	−	5.41150e15i	0.228873	−	0.973456i
$4$	−7.56171e19			−1.02480
$5$			1.11898e23i			0.961197i	0.876941	+	0.480599i	$0.159581\pi$
$5$			1.11898e23i			0.961197i	−0.876941	+	0.480599i	$0.840419\pi$
$6$	−6.61453e25	−	1.55517e25i	−1.38519	−	0.325676i
$7$	−1.34063e28			−1.73410			−0.867051	−	0.498219i	$-0.833988\pi$
$7$	−1.34063e28			−1.73410			−0.867051	+	0.498219i	$0.833988\pi$
$8$			2.23699e28i			0.0352935i
$9$	−2.76656e31	−	1.37703e31i	−0.895234	−	0.445596i
$10$	1.36774e33			1.36774
$11$			2.93013e34i			1.26162i	0.775938	+	0.630810i	$0.217277\pi$
$11$			2.93013e34i			1.26162i	−0.775938	+	0.630810i	$0.782723\pi$
$12$	−9.62092e34	+	4.09202e35i	−0.234550	+	0.997601i
$13$	3.87614e36			0.673394			0.336697	−	0.941613i	$-0.390690\pi$
$13$	3.87614e36			0.673394			0.336697	+	0.941613i	$0.390690\pi$
$14$			1.63867e38i			2.46755i
$15$	6.05537e38	+	1.42370e38i	0.935683	+	0.219992i
$16$	−5.30613e39			−0.974582
$17$		−	2.37940e40i		−	0.591090i	−0.955329	−	0.295545i	$-0.904499\pi$
$17$		−	2.37940e40i		−	0.591090i	0.955329	−	0.295545i	$-0.0955012\pi$
$18$	−1.68316e41	+	3.38159e41i	−0.634064	+	1.27388i
$19$	−1.19889e42			−0.758422			−0.379211	−	0.925310i	$-0.623804\pi$
$19$	−1.19889e42			−0.758422			−0.379211	+	0.925310i	$0.623804\pi$
$20$		−	8.46141e42i		−	0.985038i
$21$	−1.70571e43	+	7.25484e43i	−0.396890	+	1.68807i
$22$	3.58153e44			1.79523
$23$			1.09383e45i			1.26453i	0.774751	+	0.632267i	$0.217875\pi$
$23$			1.09383e45i			1.26453i	−0.774751	+	0.632267i	$0.782125\pi$
$24$	1.21055e44	+	2.84617e43i	0.0343566	+	0.00807773i
$25$	1.03135e45			0.0761002
$26$		−	4.73785e46i		−	0.958209i
$27$	−1.09718e47	+	1.32192e47i	−0.638663	+	0.769486i
$28$	1.01375e48			1.77711
$29$		−	2.55829e48i		−	1.40869i	−0.709856	−	0.704347i	$-0.751240\pi$
$29$		−	2.55829e48i		−	1.40869i	0.709856	−	0.704347i	$-0.248760\pi$
$30$	1.74020e48	−	7.40153e48i	0.313039	−	1.33144i
$31$	1.47668e49			0.900223			0.450112	−	0.892972i	$-0.351384\pi$
$31$	1.47668e49			0.900223			0.450112	+	0.892972i	$0.351384\pi$
$32$			6.65079e49i			1.42208i
$33$	1.58564e50	+	3.72806e49i	1.22813	+	0.288751i
$34$	−2.90837e50			−0.841095
$35$		−	1.50014e51i		−	1.66681i
$36$	2.09199e51	+	1.04127e51i	0.917439	+	0.456648i
$37$	−5.97408e51			−1.06075			−0.530376	−	0.847762i	$-0.677949\pi$
$37$	−5.97408e51			−1.06075			−0.530376	+	0.847762i	$0.677949\pi$
$38$			1.46542e52i			1.07920i
$39$	4.93169e51	−	2.09758e52i	0.154122	−	0.655519i
$40$	−2.50315e51			−0.0339240
$41$		−	4.97073e52i		−	0.298231i	−0.988820	−	0.149115i	$-0.952357\pi$
$41$		−	4.97073e52i		−	0.298231i	0.988820	−	0.149115i	$-0.0476426\pi$
$42$	8.86766e53	+	2.08491e53i	2.40205	+	0.564756i
$43$	1.15764e54			1.44249			0.721247	−	0.692678i	$-0.243569\pi$
$43$	1.15764e54			1.44249			0.721247	+	0.692678i	$0.243569\pi$
$44$		−	2.21568e54i		−	1.29291i
$45$	1.54087e54	−	3.09572e54i	0.428306	−	0.860496i
$46$	1.33700e55			1.79938
$47$		−	2.00509e54i		−	0.132710i	−0.997796	−	0.0663552i	$-0.978863\pi$
$47$		−	2.00509e54i		−	0.132710i	0.997796	−	0.0663552i	$-0.0211371\pi$
$48$	−6.75109e54	+	2.87141e55i	−0.223056	+	0.948713i
$49$	1.19962e56			2.00711
$50$		−	1.26063e55i		−	0.108287i
$51$	−1.28761e56	−	3.02736e55i	−0.575400	−	0.135285i
$52$	−2.93103e56			−0.690096
$53$		−	1.00051e57i		−	1.25637i	−0.778065	−	0.628184i	$-0.783799\pi$
$53$		−	1.00051e57i		−	1.25637i	0.778065	−	0.628184i	$-0.216201\pi$
$54$	1.61580e57	+	1.34109e57i	1.09494	+	0.908790i
$55$	−3.27876e57			−1.21267
$56$		−	2.99898e56i		−	0.0612025i
$57$	−1.52537e57	+	6.48780e57i	−0.173582	+	0.738290i
$58$	−3.12703e58			−2.00451
$59$			1.54437e58i			0.563165i	0.959537	+	0.281583i	$0.0908594\pi$
$59$			1.54437e58i			0.563165i	−0.959537	+	0.281583i	$0.909141\pi$
$60$	−4.57889e58	−	1.07656e58i	−0.958891	−	0.225449i
$61$	2.11015e58			0.256111			0.128056	−	0.991767i	$-0.459126\pi$
$61$	2.11015e58			0.256111			0.128056	+	0.991767i	$0.459126\pi$
$62$		−	1.80496e59i		−	1.28098i
$63$	3.70894e59	+	1.84610e59i	1.55243	+	0.772709i
$64$	4.21410e59			1.04898
$65$			4.33733e59i			0.647264i
$66$	4.55685e59	−	1.93814e60i	0.410880	−	1.74758i
$67$	7.76951e59			0.426506			0.213253	−	0.976997i	$-0.431594\pi$
$67$	7.76951e59			0.426506			0.213253	+	0.976997i	$0.431594\pi$
$68$			1.79924e60i			0.605751i
$69$	5.91925e60	+	1.39170e60i	1.23097	+	0.289418i
$70$	−1.83364e61			−2.37180
$71$		−	1.19531e61i		−	0.968174i	−0.875020	−	0.484087i	$-0.839152\pi$
$71$		−	1.19531e61i		−	0.968174i	0.875020	−	0.484087i	$-0.160848\pi$
$72$	3.08041e59	−	6.18875e59i	0.0157266	−	0.0315959i
$73$	−4.94610e61			−1.60180			−0.800900	−	0.598798i	$-0.795645\pi$
$73$	−4.94610e61			−1.60180			−0.800900	+	0.598798i	$0.795645\pi$
$74$			7.30217e61i			1.50940i
$75$	1.31221e60	−	5.58115e60i	0.0174173	−	0.0740802i
$76$	9.06566e61			0.777233
$77$		−	3.92823e62i		−	2.18778i
$78$	−2.56389e62	−	6.02806e61i	−0.932775	−	0.219308i
$79$	3.63937e62			0.869626			0.434813	−	0.900521i	$-0.356815\pi$
$79$	3.63937e62			0.869626			0.434813	+	0.900521i	$0.356815\pi$
$80$		−	5.93746e62i		−	0.936765i
$81$	5.75761e62	+	7.61928e62i	0.602888	+	0.797826i
$82$	−6.07577e62			−0.424369
$83$			6.01832e62i			0.281772i	0.990026	+	0.140886i	$0.0449952\pi$
$83$			6.01832e62i			0.281772i	−0.990026	+	0.140886i	$0.955005\pi$
$84$	1.28981e63	−	5.48590e63i	0.406734	−	1.72994i
$85$	2.66251e63			0.568154
$86$		−	1.41499e64i		−	2.05260i
$87$	−1.38442e64	−	3.25497e63i	−1.37130	−	0.322412i
$88$	−6.55467e62			−0.0445269
$89$			3.58687e63i			0.167820i	0.996473	+	0.0839102i	$0.0267409\pi$
$89$			3.58687e63i			0.167820i	−0.996473	+	0.0839102i	$0.973259\pi$
$90$	−3.78393e64	−	1.88342e64i	−1.22445	−	0.609460i
$91$	−5.19649e64			−1.16773
$92$		−	8.27121e64i		−	1.29590i
$93$	1.87881e64	−	7.99105e64i	0.206037	−	0.876328i
$94$	−2.45084e64			−0.188841
$95$		−	1.34154e65i		−	0.728993i
$96$	3.59908e65	+	8.46194e64i	1.38433	+	0.325476i
$97$	−2.58963e64			−0.0707571			−0.0353785	−	0.999374i	$-0.511264\pi$
$97$	−2.58963e64			−0.0707571			−0.0353785	+	0.999374i	$0.511264\pi$
$98$		−	1.46630e66i		−	2.85603i
$99$	4.03489e65	−	8.10637e65i	0.562173	−	1.12944i
$100$	−7.79877e64			−0.0779877
$101$			1.64889e66i			1.18737i	0.804698	+	0.593684i	$0.202327\pi$
$101$			1.64889e66i			1.18737i	−0.804698	+	0.593684i	$0.797673\pi$
$102$	−3.70038e65	+	1.57386e66i	−0.192504	+	0.818769i
$103$	1.63871e65			0.0617836			0.0308918	−	0.999523i	$-0.490165\pi$
$103$	1.63871e65			0.0617836			0.0308918	+	0.999523i	$0.490165\pi$
$104$			8.67089e64i			0.0237664i
$105$	−8.11803e66	−	1.90866e66i	−1.62257	−	0.381489i
$106$	−1.22293e67			−1.78776
$107$			8.01513e66i			0.859500i	0.902948	+	0.429750i	$0.141398\pi$
$107$			8.01513e66i			0.859500i	−0.902948	+	0.429750i	$0.858602\pi$
$108$	8.29653e66	−	9.99597e66i	0.654504	−	0.788572i
$109$	3.05399e67			1.77743			0.888716	−	0.458458i	$-0.151598\pi$
$109$	3.05399e67			1.77743			0.888716	+	0.458458i	$0.151598\pi$
$110$			4.00766e67i			1.72557i
$111$	−7.60094e66	+	3.23287e67i	−0.242778	+	1.03260i
$112$	7.11357e67			1.69002
$113$		−	1.94618e67i		−	0.344822i	−0.985025	−	0.172411i	$-0.944844\pi$
$113$		−	1.94618e67i		−	0.344822i	0.985025	−	0.172411i	$-0.0551557\pi$
$114$	7.93010e67	+	1.86448e67i	1.05055	+	0.247000i
$115$	−1.22397e68			−1.21547
$116$			1.93451e68i			1.44363i
$117$	−1.07236e68	−	5.33757e67i	−0.602845	−	0.300062i
$118$	1.88770e68			0.801360
$119$			3.18991e68i			1.02501i
$120$	−3.18480e66	+	1.35458e67i	−0.00776429	+	0.0330235i
$121$	−3.19159e68			−0.591684
$122$		−	2.57926e68i		−	0.364435i
$123$	−2.68991e68	−	6.32436e67i	−0.290315	−	0.0682571i
$124$	−1.11662e69			−0.922551
$125$			1.63191e69i			1.03434i
$126$	2.25650e69	−	4.53347e69i	1.09953	−	2.20904i
$127$	−2.01001e69			−0.754528			−0.377264	−	0.926106i	$-0.623135\pi$
$127$	−2.01001e69			−0.754528			−0.377264	+	0.926106i	$0.623135\pi$
$128$		−	2.43512e68i		−	0.0705652i
$129$	1.47289e69	−	6.26456e69i	0.330148	−	1.40420i
$130$	5.30156e69			0.921028
$131$			5.66022e68i			0.0763625i	0.999271	+	0.0381813i	$0.0121564\pi$
$131$			5.66022e68i			0.0763625i	−0.999271	+	0.0381813i	$0.987844\pi$
$132$	−1.19902e70	−	2.81905e69i	−1.25859	−	0.295913i
$133$	1.60727e70			1.31518
$134$		−	9.49674e69i		−	0.606899i
$135$	−1.47920e70	−	1.22772e70i	−0.739628	−	0.613881i
$136$	5.32270e68			0.0208616
$137$			3.11806e70i			0.959635i	0.877368	+	0.479817i	$0.159297\pi$
$137$			3.11806e70i			0.959635i	−0.877368	+	0.479817i	$0.840703\pi$
$138$	1.70109e70	−	7.23516e70i	0.411829	−	1.75161i
$139$	−6.89209e70			−1.31481			−0.657404	−	0.753538i	$-0.728345\pi$
$139$	−6.89209e70			−1.31481			−0.657404	+	0.753538i	$0.728345\pi$
$140$			1.13436e71i			1.70816i
$141$	−1.08506e70	−	2.55112e69i	−0.129188	−	0.0303739i
$142$	−1.46103e71			−1.37767
$143$			1.13576e71i			0.849567i
$144$	1.46797e71	+	7.30671e70i	0.872479	+	0.434270i
$145$	2.86268e71			1.35403
$146$			6.04567e71i			2.27929i
$147$	1.52629e71	−	6.49172e71i	0.459374	−	1.95383i
$148$	4.51743e71			1.08706
$149$			2.05968e71i			0.396874i	0.980114	+	0.198437i	$0.0635866\pi$
$149$			2.05968e71i			0.396874i	−0.980114	+	0.198437i	$0.936413\pi$
$150$	−6.82190e70	−	1.60392e70i	−0.105413	−	0.0247840i
$151$	8.60865e71			1.06831			0.534153	−	0.845388i	$-0.320631\pi$
$151$	8.60865e71			1.06831			0.534153	+	0.845388i	$0.320631\pi$
$152$		−	2.68190e70i		−	0.0267673i
$153$	−3.27652e71	+	6.58275e71i	−0.263387	+	0.529164i
$154$	−4.80152e72			−3.11311
$155$			1.65238e72i			0.865292i
$156$	−3.72920e71	+	1.58613e72i	−0.157944	+	0.671778i
$157$	4.73363e72			1.62370			0.811850	−	0.583866i	$-0.198461\pi$
$157$	4.73363e72			1.62370			0.811850	+	0.583866i	$0.198461\pi$
$158$		−	4.44844e72i		−	1.23744i
$159$	−5.41425e72	−	1.27297e72i	−1.22302	−	0.287549i
$160$	−7.44211e72			−1.36690
$161$		−	1.46642e73i		−	2.19283i
$162$	9.31311e72	−	7.03758e72i	1.13527	−	0.857883i
$163$	1.63451e73			1.62629			0.813145	−	0.582062i	$-0.197754\pi$
$163$	1.63451e73			1.62629			0.813145	+	0.582062i	$0.197754\pi$
$164$			3.75872e72i			0.305628i
$165$	−4.17163e72	+	1.77430e73i	−0.277547	+	1.18048i
$166$	7.35626e72			0.400950
$167$		−	3.15012e73i		−	1.40826i	−0.710071	−	0.704131i	$-0.751337\pi$
$167$		−	3.15012e73i		−	1.40826i	0.710071	−	0.704131i	$-0.248663\pi$
$168$	−1.62290e72	−	3.81566e71i	−0.0595779	−	0.0140076i
$169$	−1.81086e73			−0.546541
$170$		−	3.25441e73i		−	0.808458i
$171$	3.31680e73	+	1.65091e73i	0.678965	+	0.337950i
$172$	−8.75373e73			−1.47827
$173$			7.33202e73i			1.02259i	0.859405	+	0.511296i	$0.170834\pi$
$173$			7.33202e73i			1.02259i	−0.859405	+	0.511296i	$0.829166\pi$
$174$	−3.97858e73	+	1.69219e74i	−0.458778	+	1.95130i
$175$	−1.38266e73			−0.131965
$176$		−	1.55477e74i		−	1.22955i
$177$	8.35738e73	+	1.96494e73i	0.548217	+	0.128894i
$178$	4.38426e73			0.238801
$179$			8.52176e73i			0.385815i	0.981217	+	0.192908i	$0.0617918\pi$
$179$			8.52176e73i			0.385815i	−0.981217	+	0.192908i	$0.938208\pi$
$180$	−1.16516e74	+	2.34090e74i	−0.438929	+	0.881839i
$181$	5.82996e74			1.82925			0.914625	−	0.404304i	$-0.132486\pi$
$181$	5.82996e74			1.82925			0.914625	+	0.404304i	$0.132486\pi$
$182$			6.35171e74i			1.66163i
$183$	2.68479e73	−	1.14191e74i	0.0586170	−	0.249313i
$184$	−2.44688e73			−0.0446298
$185$		−	6.68488e74i		−	1.01959i
$186$	−9.76754e74	−	2.29649e74i	−1.24698	−	0.293182i
$187$	6.97196e74			0.745731
$188$			1.51619e74i			0.136002i
$189$	1.47091e75	−	1.77221e75i	1.10751	−	1.33437i
$190$	−1.63977e75			−1.03732
$191$			2.33048e75i			1.23978i	0.784688	+	0.619891i	$0.212823\pi$
$191$			2.33048e75i			1.23978i	−0.784688	+	0.619891i	$0.787177\pi$
$192$	5.36168e74	−	2.28046e75i	0.240082	−	1.02113i
$193$	−2.03031e75			−0.765899			−0.382949	−	0.923769i	$-0.625092\pi$
$193$	−2.03031e75			−0.765899			−0.382949	+	0.923769i	$0.625092\pi$
$194$			3.16532e74i			0.100684i
$195$	2.34715e75	+	5.51847e74i	0.630083	+	0.148141i
$196$	−9.07114e75			−2.05689
$197$		−	8.50392e75i		−	1.63017i	−0.579340	−	0.815086i	$-0.696690\pi$
$197$		−	8.50392e75i		−	1.63017i	0.579340	−	0.815086i	$-0.303310\pi$
$198$	−9.90849e75	−	4.93188e75i	−1.60715	−	0.799947i
$199$	1.04884e76			1.44065			0.720326	−	0.693636i	$-0.243992\pi$
$199$	1.04884e76			1.44065			0.720326	+	0.693636i	$0.243992\pi$
$200$			2.30712e73i			0.00268584i
$201$	9.88530e74	−	4.20447e75i	0.0976158	−	0.415185i
$202$	2.01545e76			1.68957
$203$			3.42973e76i			2.44282i
$204$	9.73657e75	+	2.28920e75i	0.589672	+	0.138640i
$205$	5.56215e75			0.286659
$206$		−	2.00301e75i		−	0.0879154i
$207$	1.50624e76	−	3.02614e76i	0.563471	−	1.13205i
$208$	−2.05673e76			−0.656277
$209$		−	3.51291e76i		−	0.956840i
$210$	−2.33298e76	+	9.92274e76i	−0.542842	+	2.30885i
$211$	−2.83385e76			−0.563709			−0.281855	−	0.959457i	$-0.590950\pi$
$211$	−2.83385e76			−0.563709			−0.281855	+	0.959457i	$0.590950\pi$
$212$			7.56555e76i			1.28753i
$213$	−6.46840e76	−	1.52081e76i	−0.942475	−	0.221589i
$214$	9.79698e76			1.22303
$215$			1.29537e77i			1.38652i
$216$	−2.95712e75	−	2.45437e75i	−0.0271578	−	0.0225406i
$217$	−1.97969e77			−1.56108
$218$		−	3.73292e77i		−	2.52921i
$219$	−6.29302e76	+	2.67658e77i	−0.366609	+	1.55928i
$220$	2.47930e77			1.24274
$221$		−	9.22291e76i		−	0.398036i
$222$	3.95157e77	+	9.29070e76i	1.46934	+	0.345462i
$223$	2.30583e77			0.739209			0.369605	−	0.929189i	$-0.379493\pi$
$223$	2.30583e77			0.739209			0.369605	+	0.929189i	$0.379493\pi$
$224$		−	8.91627e77i		−	2.46603i
$225$	−2.85329e76	−	1.42020e76i	−0.0681275	−	0.0339099i
$226$	−2.37884e77			−0.490666
$227$		−	3.50513e77i		−	0.624958i	−0.949925	−	0.312479i	$-0.898841\pi$
$227$		−	3.50513e77i		−	0.624958i	0.949925	−	0.312479i	$-0.101159\pi$
$228$	1.15344e77	−	4.90589e77i	0.177888	−	0.756602i
$229$	−4.45168e77			−0.594228			−0.297114	−	0.954842i	$-0.596024\pi$
$229$	−4.45168e77			−0.594228			−0.297114	+	0.954842i	$0.596024\pi$
$230$			1.49607e78i			1.72955i
$231$	−2.12576e78	−	4.99797e77i	−2.12971	−	0.500724i
$232$	5.72287e76			0.0497177
$233$			9.03528e76i			0.0681077i	0.999420	+	0.0340539i	$0.0108418\pi$
$233$			9.03528e76i			0.0681077i	−0.999420	+	0.0340539i	$0.989158\pi$
$234$	−6.52417e77	+	1.31075e78i	−0.426974	+	0.857822i
$235$	2.24366e77			0.127561
$236$		−	1.16781e78i		−	0.577134i
$237$	4.63045e77	−	1.96945e78i	0.199034	−	0.846543i
$238$	3.89906e78			1.45854
$239$			2.90634e78i			0.946706i	0.880873	+	0.473353i	$0.156956\pi$
$239$			2.90634e78i			0.946706i	−0.880873	+	0.473353i	$0.843044\pi$
$240$	−3.21306e78	−	7.55434e77i	−0.911900	−	0.214400i
$241$	5.13136e78			1.26961			0.634804	−	0.772673i	$-0.281081\pi$
$241$	5.13136e78			1.26961			0.634804	+	0.772673i	$0.281081\pi$
$242$			3.90111e78i			0.841940i
$243$	4.85572e78	−	2.14632e78i	0.914633	−	0.404284i
$244$	−1.59563e78			−0.262464
$245$			1.34235e79i			1.92923i
$246$	−7.73032e77	+	3.28790e78i	−0.0971268	+	0.413105i
$247$	−4.64707e78			−0.510716
$248$			3.30331e77i			0.0317720i
$249$	3.25682e78	+	7.65723e77i	0.274293	+	0.0644902i
$250$	1.99470e79			1.47183
$251$		−	1.41302e79i		−	0.913937i	−0.889483	−	0.456969i	$-0.848935\pi$
$251$		−	1.41302e79i		−	0.913937i	0.889483	−	0.456969i	$-0.151065\pi$
$252$	−2.80459e79	−	1.39596e79i	−1.59093	−	0.791875i
$253$	−3.20506e79			−1.59536
$254$			2.45686e79i			1.07366i
$255$	3.38756e78	−	1.44082e79i	0.130035	−	0.553073i
$256$	2.81181e79			0.948564
$257$		−	2.72517e79i		−	0.808352i	−0.914681	−	0.404176i	$-0.867558\pi$
$257$		−	2.72517e79i		−	0.808352i	0.914681	−	0.404176i	$-0.132442\pi$
$258$	−7.65723e79	−	1.80032e79i	−1.99812	−	0.469786i
$259$	8.00905e79			1.83945
$260$		−	3.27976e79i		−	0.663318i
$261$	−3.52285e79	+	7.07766e79i	−0.627708	+	1.26111i
$262$	6.91854e78			0.108660
$263$		−	6.05932e79i		−	0.839236i	−0.907701	−	0.419618i	$-0.862164\pi$
$263$		−	6.05932e79i		−	0.839236i	0.907701	−	0.419618i	$-0.137836\pi$
$264$	−8.33964e77	+	3.54706e78i	−0.0101910	+	0.0433450i
$265$	1.11955e80			1.20762
$266$		−	1.96458e80i		−	1.87144i
$267$	1.94103e79	+	4.56364e78i	0.163366	+	0.0384096i
$268$	−5.87508e79			−0.437084
$269$		−	1.65958e79i		−	0.109188i	−0.998509	−	0.0545939i	$-0.982614\pi$
$269$		−	1.65958e79i		−	0.109188i	0.998509	−	0.0545939i	$-0.0173864\pi$
$270$	−1.50065e80	+	1.80804e80i	−0.873526	+	1.05246i
$271$	1.68420e80			0.867773			0.433887	−	0.900967i	$-0.357142\pi$
$271$	1.68420e80			0.867773			0.433887	+	0.900967i	$0.357142\pi$
$272$			1.26254e80i			0.576066i
$273$	−6.61159e79	+	2.81208e80i	−0.267263	+	1.13674i
$274$	3.81124e80			1.36552
$275$			3.02199e79i			0.0960095i
$276$	−4.47597e80	−	1.05236e80i	−1.26150	−	0.296596i
$277$	−1.61975e80			−0.405150			−0.202575	−	0.979267i	$-0.564931\pi$
$277$	−1.61975e80			−0.405150			−0.202575	+	0.979267i	$0.564931\pi$
$278$			8.42426e80i			1.87091i
$279$	−4.08532e80	−	2.03344e80i	−0.805911	−	0.401136i
$280$	3.35580e79			0.0588276
$281$		−	4.07271e80i		−	0.634710i	−0.948307	−	0.317355i	$-0.897205\pi$
$281$		−	4.07271e80i		−	0.634710i	0.948307	−	0.317355i	$-0.102795\pi$
$282$	−3.11826e79	+	1.32628e80i	−0.0432207	+	0.183829i
$283$	6.34627e80			0.782647			0.391323	−	0.920253i	$-0.372017\pi$
$283$	6.34627e80			0.782647			0.391323	+	0.920253i	$0.372017\pi$
$284$			9.03856e80i			0.992188i
$285$	−7.25972e80	−	1.70686e80i	−0.709642	−	0.166847i
$286$	1.38825e81			1.20890
$287$			6.66392e80i			0.517163i
$288$	9.15836e80	−	1.83998e81i	0.633674	−	1.27309i
$289$	1.05427e81			0.650612
$290$		−	3.49908e81i		−	1.92673i
$291$	−3.29483e79	+	1.40138e80i	−0.0161944	+	0.0688789i
$292$	3.74010e81			1.64153
$293$			1.98609e81i			0.778695i	0.921091	+	0.389347i	$0.127299\pi$
$293$			1.98609e81i			0.778695i	−0.921091	+	0.389347i	$0.872701\pi$
$294$	−7.93489e81	−	1.86560e81i	−2.78022	−	0.653669i
$295$	−1.72812e81			−0.541313
$296$		−	1.33639e80i		−	0.0374376i
$297$	−3.87340e81	−	3.21487e81i	−0.970799	−	0.805750i
$298$	2.51757e81			0.564735
$299$			4.23983e81i			0.851529i
$300$	−9.92253e79	+	4.22031e80i	−0.0178493	+	0.0759176i
$301$	−1.55197e82			−2.50143
$302$		−	1.05224e82i		−	1.52015i
$303$	8.92296e81	+	2.09791e81i	1.15585	+	0.271757i
$304$	6.36147e81			0.739144
$305$			2.36122e81i			0.246174i
$306$	8.04616e81	+	4.00492e81i	0.752977	+	0.374789i
$307$	1.04478e82			0.877928			0.438964	−	0.898505i	$-0.355346\pi$
$307$	1.04478e82			0.877928			0.438964	+	0.898505i	$0.355346\pi$
$308$			2.97042e82i			2.24204i
$309$	2.08496e80	−	8.86788e80i	0.0141406	−	0.0601437i
$310$	2.01971e82			1.23127
$311$		−	8.64391e81i		−	0.473824i	−0.971531	−	0.236912i	$-0.923865\pi$
$311$		−	8.64391e81i		−	0.473824i	0.971531	−	0.236912i	$-0.0761354\pi$
$312$	4.69225e80	+	1.10321e80i	0.0231355	+	0.00543949i
$313$	−2.19377e81			−0.0973258			−0.0486629	−	0.998815i	$-0.515496\pi$
$313$	−2.19377e81			−0.0973258			−0.0486629	+	0.998815i	$0.515496\pi$
$314$		−	5.78596e82i		−	2.31045i
$315$	−2.06575e82	+	4.15023e82i	−0.742726	+	1.49219i
$316$	−2.75199e82			−0.891195
$317$			3.95328e81i			0.115346i	0.998336	+	0.0576730i	$0.0183681\pi$
$317$			3.95328e81i			0.115346i	−0.998336	+	0.0576730i	$0.981632\pi$
$318$	−1.55596e82	+	6.61789e82i	−0.409169	+	1.74030i
$319$	7.49614e82			1.77724
$320$			4.71549e82i			1.00827i
$321$	4.33739e82	+	1.01978e82i	0.836686	+	0.196717i
$322$	−1.79242e83			−3.12030
$323$			2.85264e82i			0.448296i
$324$	−4.35374e82	−	5.76148e82i	−0.617842	−	0.817614i
$325$	3.99766e81			0.0512454
$326$		−	1.99788e83i		−	2.31414i
$327$	3.88565e82	−	1.65267e83i	0.406807	−	1.73025i
$328$	1.11195e81			0.0105256
$329$			2.68809e82i			0.230134i
$330$	2.16875e83	+	5.09903e82i	1.67977	+	0.394936i
$331$	5.80049e82			0.406575			0.203288	−	0.979119i	$-0.434837\pi$
$331$	5.80049e82			0.406575			0.203288	+	0.979119i	$0.434837\pi$
$332$		−	4.55088e82i		−	0.288761i
$333$	1.65276e83	+	8.22650e82i	0.949622	+	0.472667i
$334$	−3.85042e83			−2.00389
$335$			8.69393e82i			0.409956i
$336$	9.05074e82	−	3.84951e83i	0.386801	−	1.64517i
$337$	1.39279e83			0.539633			0.269816	−	0.962912i	$-0.413037\pi$
$337$	1.39279e83			0.539633			0.269816	+	0.962912i	$0.413037\pi$
$338$			2.21343e83i			0.777704i
$339$	−1.05318e83	−	2.47617e82i	−0.335669	−	0.0789205i
$340$	−2.01331e83			−0.582246
$341$			4.32686e83i			1.13574i
$342$	2.01793e83	−	4.05415e83i	0.480888	−	0.966137i
$343$	−8.06971e83			−1.74643
$344$			2.58962e82i			0.0509106i
$345$	−1.55728e83	+	6.62353e83i	−0.278188	+	1.18320i
$346$	8.96200e83			1.45510
$347$			1.03739e82i			0.0153133i	0.999971	+	0.00765665i	$0.00243721\pi$
$347$			1.03739e82i			0.0153133i	−0.999971	+	0.00765665i	$0.997563\pi$
$348$	1.04686e84	+	2.46131e83i	1.40531	+	0.330409i
$349$	−3.78947e83			−0.462742			−0.231371	−	0.972866i	$-0.574321\pi$
$349$	−3.78947e83			−0.462742			−0.231371	+	0.972866i	$0.574321\pi$
$350$			1.69004e83i			0.187781i
$351$	−4.25281e83	+	5.12395e83i	−0.430072	+	0.518167i
$352$	−1.94877e84			−1.79412
$353$			1.31899e84i			1.10580i	0.833248	+	0.552900i	$0.186479\pi$
$353$			1.31899e84i			1.10580i	−0.833248	+	0.552900i	$0.813521\pi$
$354$	2.40176e83	−	1.02153e84i	0.183410	−	0.780088i
$355$	1.33752e84			0.930606
$356$		−	2.71228e83i		−	0.171983i
$357$	1.72622e84	+	4.05858e83i	0.997803	+	0.234598i
$358$	1.04162e84			0.548998
$359$			1.63953e84i			0.788137i	0.919081	+	0.394069i	$0.128933\pi$
$359$			1.63953e84i			0.788137i	−0.919081	+	0.394069i	$0.871067\pi$
$360$	6.92510e82	+	3.44692e82i	0.0303699	+	0.0151164i
$361$	−1.06150e84			−0.424797
$362$		−	7.12602e84i		−	2.60294i
$363$	−4.06072e83	+	1.72713e84i	−0.135421	+	0.575978i
$364$	3.92943e84			1.19670
$365$		−	5.53459e84i		−	1.53965i
$366$	−1.39577e84	−	3.28164e83i	−0.354762	−	0.0834094i
$367$	−5.86884e84			−1.36324			−0.681620	−	0.731706i	$-0.738724\pi$
$367$	−5.86884e84			−1.36324			−0.681620	+	0.731706i	$0.738724\pi$
$368$		−	5.80399e84i		−	1.23239i
$369$	−6.84485e83	+	1.37518e84i	−0.132891	+	0.266987i
$370$	−8.17099e84			−1.45083
$371$			1.34131e85i			2.17867i
$372$	−1.42070e84	+	6.04260e84i	−0.211147	+	0.898063i
$373$	1.59521e84			0.216983			0.108492	−	0.994097i	$-0.465398\pi$
$373$	1.59521e84			0.216983			0.108492	+	0.994097i	$0.465398\pi$
$374$		−	8.52190e84i		−	1.06114i
$375$	8.83107e84	+	2.07631e84i	1.00689	+	0.236734i
$376$	4.48537e82			0.00468381
$377$		−	9.91631e84i		−	0.948605i
$378$	−2.16619e85	−	1.79791e85i	−1.89875	−	1.57593i
$379$	1.29573e85			1.04093			0.520463	−	0.853884i	$-0.325759\pi$
$379$	1.29573e85			1.04093			0.520463	+	0.853884i	$0.325759\pi$
$380$			1.01443e85i			0.747074i
$381$	−2.55738e84	+	1.08772e85i	−0.172691	+	0.734500i
$382$	2.84857e85			1.76415
$383$			1.99600e85i			1.13397i	0.823730	+	0.566983i	$0.191889\pi$
$383$			1.99600e85i			1.13397i	−0.823730	+	0.566983i	$0.808111\pi$
$384$	−1.31776e84	−	3.09825e83i	−0.0686921	−	0.0161505i
$385$	4.39562e85			2.10289
$386$			2.48167e85i			1.08984i
$387$	−3.20267e85	−	1.59411e85i	−1.29137	−	0.642769i
$388$	1.95820e84			0.0725120
$389$			4.04352e85i			1.37538i	0.726004	+	0.687691i	$0.241375\pi$
$389$			4.04352e85i			1.37538i	−0.726004	+	0.687691i	$0.758625\pi$
$390$	6.74528e84	−	2.86894e85i	0.210799	−	0.896581i
$391$	2.60266e85			0.747453
$392$			2.68353e84i			0.0708379i
$393$	3.06303e84	+	7.20161e83i	0.0743356	+	0.0174773i
$394$	−1.03944e86			−2.31966
$395$			4.07239e85i			0.835882i
$396$	−3.05106e85	+	6.12980e85i	−0.576116	+	1.15746i
$397$	−4.80321e85			−0.834536			−0.417268	−	0.908784i	$-0.637012\pi$
$397$	−4.80321e85			−0.834536			−0.417268	+	0.908784i	$0.637012\pi$
$398$		−	1.28201e86i		−	2.04998i
$399$	2.04497e85	−	8.69776e85i	0.301010	−	1.28027i
$400$	−5.47247e84			−0.0741659
$401$			1.05588e86i			1.31780i	0.752230	+	0.658901i	$0.228978\pi$
$401$			1.05588e86i			1.31780i	−0.752230	+	0.658901i	$0.771022\pi$
$402$	−5.13916e85	−	1.20829e85i	−0.590789	−	0.138903i
$403$	5.72382e85			0.606205
$404$		−	1.24684e86i		−	1.21682i
$405$	−8.52582e85	+	6.44266e85i	−0.766868	+	0.579494i
$406$	4.19220e86			3.47602
$407$		−	1.75048e86i		−	1.33827i
$408$	6.77218e83	−	2.88038e84i	0.00477467	−	0.0203079i
$409$	−5.38262e85			−0.350045			−0.175023	−	0.984564i	$-0.556000\pi$
$409$	−5.38262e85			−0.350045			−0.175023	+	0.984564i	$0.556000\pi$
$410$		−	6.79867e85i		−	0.407903i
$411$	1.68734e86	+	3.96717e85i	0.934162	+	0.219635i
$412$	−1.23914e85			−0.0633160
$413$		−	2.07044e86i		−	0.976587i
$414$	−3.69887e86	−	1.84109e86i	−1.61086	−	0.801795i
$415$	−6.73439e85			−0.270839
$416$			2.57794e86i			0.957620i
$417$	−8.76894e85	+	3.72965e86i	−0.300924	+	1.27991i
$418$	−4.29386e86			−1.36154
$419$			5.52553e85i			0.161924i	0.996717	+	0.0809620i	$0.0257992\pi$
$419$			5.52553e85i			0.161924i	−0.996717	+	0.0809620i	$0.974201\pi$
$420$	6.13862e86	+	1.44328e86i	1.66282	+	0.390951i
$421$	−2.74501e86			−0.687440			−0.343720	−	0.939072i	$-0.611687\pi$
$421$	−2.74501e86			−0.687440			−0.343720	+	0.939072i	$0.611687\pi$
$422$			3.46384e86i			0.802133i
$423$	−2.76108e85	+	5.54720e85i	−0.0591353	+	0.118807i
$424$	2.23812e85			0.0443416
$425$		−	2.45400e85i		−	0.0449821i
$426$	−1.85890e86	+	7.90639e86i	−0.315312	+	1.34110i
$427$	−2.82894e86			−0.444123
$428$		−	6.06081e86i		−	0.880819i
$429$	6.14617e86	+	1.44505e86i	0.827016	+	0.194443i
$430$	1.58335e87			1.97296
$431$		−	7.36293e85i		−	0.0849769i	−0.999097	−	0.0424884i	$-0.986471\pi$
$431$		−	7.36293e85i		−	0.0849769i	0.999097	−	0.0424884i	$-0.0135286\pi$
$432$	5.82176e86	−	7.01428e86i	0.622430	−	0.749927i
$433$	−1.31665e87			−1.30428			−0.652138	−	0.758100i	$-0.726128\pi$
$433$	−1.31665e87			−1.30428			−0.652138	+	0.758100i	$0.726128\pi$
$434$			2.41979e87i			2.22135i
$435$	3.64225e86	−	1.54914e87i	0.309902	−	1.31809i
$436$	−2.30934e87			−1.82152
$437$		−	1.31138e87i		−	0.959050i
$438$	3.27161e87	+	7.69202e86i	2.21879	+	0.521669i
$439$	1.74404e87			1.09705			0.548526	−	0.836134i	$-0.315189\pi$
$439$	1.74404e87			1.09705			0.548526	+	0.836134i	$0.315189\pi$
$440$		−	7.33455e85i		−	0.0427991i
$441$	−3.31880e87	−	1.65191e87i	−1.79683	−	0.894361i
$442$	−1.12732e87			−0.566388
$443$			2.32567e87i			1.08449i	0.840221	+	0.542244i	$0.182425\pi$
$443$			2.32567e87i			1.08449i	−0.840221	+	0.542244i	$0.817575\pi$
$444$	5.74761e86	−	2.44461e87i	0.248799	−	1.05821i
$445$	−4.01363e86			−0.161309
$446$		−	2.81844e87i		−	1.05186i
$447$	1.11460e87	+	2.62057e86i	0.386340	+	0.0908339i
$448$	−5.64956e87			−1.81903
$449$			7.28143e86i			0.217815i	0.994052	+	0.108907i	$0.0347352\pi$
$449$			7.28143e86i			0.217815i	−0.994052	+	0.108907i	$0.965265\pi$
$450$	−1.73593e86	+	3.48760e86i	−0.0482524	+	0.0969424i
$451$	1.45649e87			0.376254
$452$			1.47165e87i			0.353374i
$453$	1.09530e87	−	4.65857e87i	0.244507	−	1.03995i
$454$	−4.28436e87			−0.889288
$455$		−	5.81477e87i		−	1.12242i
$456$	−1.45131e86	−	3.41224e85i	−0.0260568	−	0.00612632i
$457$	4.04717e87			0.675954			0.337977	−	0.941154i	$-0.390257\pi$
$457$	4.04717e87			0.675954			0.337977	+	0.941154i	$0.390257\pi$
$458$			5.44134e87i			0.845561i
$459$	3.14538e87	+	2.61062e87i	0.454836	+	0.377508i
$460$	9.25532e87			1.24561
$461$		−	7.39518e87i		−	0.926442i	−0.886243	−	0.463221i	$-0.846694\pi$
$461$		−	7.39518e87i		−	0.926442i	0.886243	−	0.463221i	$-0.153306\pi$
$462$	−6.10906e87	+	2.59834e88i	−0.712508	+	3.03048i
$463$	−3.70147e86			−0.0401978			−0.0200989	−	0.999798i	$-0.506398\pi$
$463$	−3.70147e86			−0.0401978			−0.0200989	+	0.999798i	$0.506398\pi$
$464$			1.35746e88i			1.37289i
$465$	8.94183e87	+	2.10235e87i	0.842324	+	0.198042i
$466$	1.10439e87			0.0969143
$467$		−	2.02503e88i		−	1.65568i	−0.560967	−	0.827838i	$-0.689571\pi$
$467$		−	2.02503e88i		−	1.65568i	0.560967	−	0.827838i	$-0.310429\pi$
$468$	8.10885e87	+	4.03612e87i	0.617797	+	0.307504i
$469$	−1.04161e88			−0.739605
$470$		−	2.74245e87i		−	0.181514i
$471$	6.02269e87	−	2.56160e88i	0.371621	−	1.58060i
$472$	−3.45475e86			−0.0198761
$473$			3.39203e88i			1.81988i
$474$	−2.40727e88	−	5.65984e87i	−1.20459	−	0.283217i
$475$	−1.23648e87			−0.0577160
$476$		−	2.41212e88i		−	1.05043i
$477$	−1.37773e88	+	2.76796e88i	−0.559833	+	1.12474i
$478$	3.55244e88			1.34712
$479$			2.97840e88i			1.05417i	0.849812	+	0.527085i	$0.176715\pi$
$479$			2.97840e88i			1.05417i	−0.849812	+	0.527085i	$0.823285\pi$
$480$	−9.46874e87	+	4.02730e88i	−0.312847	+	1.33062i
$481$	−2.31564e88			−0.714304
$482$		−	6.27211e88i		−	1.80660i
$483$	−7.93555e88	−	1.86576e88i	−2.13462	−	0.501880i
$484$	2.41339e88			0.606359
$485$		−	2.89774e87i		−	0.0680115i
$486$	−2.62346e88	−	5.93520e88i	−0.575279	−	1.30148i
$487$	3.36136e88			0.688746			0.344373	−	0.938833i	$-0.388091\pi$
$487$	3.36136e88			0.688746			0.344373	+	0.938833i	$0.388091\pi$
$488$			4.72038e86i			0.00903906i
$489$	2.07963e88	−	8.84518e88i	0.372214	−	1.58312i
$490$	1.64076e89			2.74521
$491$		−	6.16349e88i		−	0.964133i	−0.876135	−	0.482067i	$-0.839886\pi$
$491$		−	6.16349e88i		−	0.964133i	0.876135	−	0.482067i	$-0.160114\pi$
$492$	2.03403e88	+	4.78230e87i	0.297515	+	0.0699501i
$493$	−6.08721e88			−0.832665
$494$			5.68016e88i			0.726727i
$495$	9.07087e88	+	4.51496e88i	1.08562	+	0.540359i
$496$	−7.83545e88			−0.877341
$497$			1.60247e89i			1.67891i
$498$	9.35951e87	−	3.98084e88i	0.0917667	−	0.390307i
$499$	6.71565e88			0.616269			0.308134	−	0.951343i	$-0.400295\pi$
$499$	6.71565e88			0.616269			0.308134	+	0.951343i	$0.400295\pi$
$500$		−	1.23400e89i		−	1.06000i
$501$	−1.70469e89	−	4.00796e88i	−1.37088	−	0.322313i
$502$	−1.72715e89			−1.30049
$503$			5.22801e88i			0.368632i	0.982867	+	0.184316i	$0.0590069\pi$
$503$			5.22801e88i			0.368632i	−0.982867	+	0.184316i	$0.940993\pi$
$504$	−4.12970e87	+	8.29685e87i	−0.0272716	+	0.0547905i
$505$	−1.84507e89			−1.14130
$506$			3.91757e89i			2.27013i
$507$	−2.30399e88	+	9.79945e88i	−0.125089	+	0.532034i
$508$	1.51991e89			0.773243
$509$			2.87661e89i			1.37150i	0.727839	+	0.685748i	$0.240525\pi$
$509$			2.87661e89i			1.37150i	−0.727839	+	0.685748i	$0.759475\pi$
$510$	−1.76112e89	−	4.14065e88i	−0.786999	−	0.185034i
$511$	6.63091e89			2.77769
$512$		−	3.61658e89i		−	1.42033i
$513$	1.31539e89	−	1.58484e89i	0.484376	−	0.583595i
$514$	−3.33100e89			−1.15025
$515$			1.83368e88i			0.0593862i
$516$	−1.11375e89	+	4.73708e89i	−0.338337	+	1.43903i
$517$	5.87519e88			0.167430
$518$		−	9.78954e89i		−	2.61746i
$519$	3.96772e89	+	9.32867e88i	0.995448	+	0.234044i
$520$	−9.70255e87			−0.0228442
$521$			2.17928e89i			0.481581i	0.970577	+	0.240790i	$0.0774066\pi$
$521$			2.17928e89i			0.481581i	−0.970577	+	0.240790i	$0.922593\pi$
$522$	8.65109e89	+	4.30602e89i	1.79450	+	0.893201i
$523$	9.29637e88			0.181033			0.0905165	−	0.995895i	$-0.471148\pi$
$523$	9.29637e88			0.181033			0.0905165	+	0.995895i	$0.471148\pi$
$524$		−	4.28009e88i		−	0.0782565i
$525$	−1.75919e88	+	7.48228e88i	−0.0302034	+	0.128463i
$526$	−7.40636e89			−1.19420
$527$		−	3.51362e89i		−	0.532113i
$528$	−8.41361e89	−	1.97816e89i	−1.19691	−	0.281411i
$529$	−4.48226e89			−0.599045
$530$		−	1.36844e90i		−	1.71839i
$531$	2.12665e89	−	4.27260e89i	0.250944	−	0.504165i
$532$	−1.21537e90			−1.34780
$533$		−	1.92672e89i		−	0.200827i
$534$	5.57818e88	−	2.37254e89i	0.0546552	−	0.232462i
$535$	−8.96878e89			−0.826149
$536$			1.73803e88i			0.0150529i
$537$	4.61155e89	+	1.08424e89i	0.375574	+	0.0883028i
$538$	−2.02853e89			−0.155369
$539$			3.51503e90i			2.53221i
$540$	1.11853e90	+	9.28365e89i	0.757973	+	0.629108i
$541$	−2.16785e88			−0.0138204			−0.00691020	−	0.999976i	$-0.502200\pi$
$541$	−2.16785e88			−0.0138204			−0.00691020	+	0.999976i	$0.502200\pi$
$542$		−	2.05861e90i		−	1.23480i
$543$	7.41758e89	−	3.15489e90i	0.418666	−	1.78069i
$544$	1.58249e90			0.840578
$545$			3.41735e90i			1.70846i
$546$	3.43723e90	+	8.08141e89i	1.61753	+	0.380303i
$547$	−1.88414e88			−0.00834701			−0.00417351	−	0.999991i	$-0.501328\pi$
$547$	−1.88414e88			−0.00834701			−0.00417351	+	0.999991i	$0.501328\pi$
$548$		−	2.35779e90i		−	0.983436i
$549$	−5.83785e89	−	2.90575e89i	−0.229280	−	0.114122i
$550$	3.69381e89			0.136617
$551$			3.06711e90i			1.06838i
$552$	−3.11322e88	+	1.32413e89i	−0.0102146	+	0.0434451i
$553$	−4.87906e90			−1.50802
$554$			1.97984e90i			0.576511i
$555$	−3.61752e90	−	8.50531e89i	−0.992528	−	0.233357i
$556$	5.21160e90			1.34742
$557$			1.07089e90i			0.260929i	0.991453	+	0.130465i	$0.0416469\pi$
$557$			1.07089e90i			0.260929i	−0.991453	+	0.130465i	$0.958353\pi$
$558$	−2.48549e90	+	4.99352e90i	−0.570799	+	1.14678i
$559$	4.48717e90			0.971366
$560$			7.95995e90i			1.62445i
$561$	8.87057e89	−	3.77288e90i	0.170678	−	0.725936i
$562$	−4.97811e90			−0.903164
$563$		−	4.06558e90i		−	0.695577i	−0.937573	−	0.347789i	$-0.886933\pi$
$563$		−	4.06558e90i		−	0.695577i	0.937573	−	0.347789i	$-0.113067\pi$
$564$	8.20488e89	+	1.92908e89i	0.132392	+	0.0311272i
$565$	2.17774e90			0.331442
$566$		−	7.75710e90i		−	1.11367i
$567$	−7.71885e90	−	1.02147e91i	−1.04547	−	1.38351i
$568$	2.67389e89			0.0341702
$569$		−	4.32914e90i		−	0.522031i	−0.965335	−	0.261016i	$-0.915943\pi$
$569$		−	4.32914e90i		−	0.522031i	0.965335	−	0.261016i	$-0.0840574\pi$
$570$	−2.08631e90	+	8.87363e90i	−0.237416	+	1.00979i
$571$	−1.15273e91			−1.23805			−0.619023	−	0.785373i	$-0.712471\pi$
$571$	−1.15273e91			−1.23805			−0.619023	+	0.785373i	$0.712471\pi$
$572$		−	8.58829e90i		−	0.870638i
$573$	1.26114e91	+	2.96512e90i	1.20687	+	0.283753i
$574$	8.14538e90			0.735900
$575$			1.12812e90i			0.0962312i
$576$	−1.16585e91	−	5.80295e90i	−0.939079	−	0.467419i
$577$	1.94270e91			1.47776			0.738878	−	0.673839i	$-0.235356\pi$
$577$	1.94270e91			1.47776			0.738878	+	0.673839i	$0.235356\pi$
$578$		−	1.28864e91i		−	0.925793i
$579$	−2.58320e90	+	1.09870e91i	−0.175294	+	0.745569i
$580$	−2.16468e91			−1.38762
$581$		−	8.06837e90i		−	0.488622i
$582$	1.71292e90	+	4.02731e89i	0.0980116	+	0.0230439i
$583$	2.93162e91			1.58506
$584$		−	1.10644e90i		−	0.0565331i
$585$	5.97264e90	−	1.19995e91i	0.288418	−	0.579453i
$586$	2.42762e91			1.10805
$587$		−	6.18587e90i		−	0.266897i	−0.991056	−	0.133448i	$-0.957395\pi$
$587$		−	6.18587e90i		−	0.266897i	0.991056	−	0.133448i	$-0.0426051\pi$
$588$	−1.15414e91	+	4.90885e91i	−0.470768	+	2.00230i
$589$	−1.77038e91			−0.682749
$590$			2.11230e91i			0.770264i
$591$	−4.60190e91	−	1.08197e91i	−1.58690	−	0.373103i
$592$	3.16992e91			1.03379
$593$		−	2.76895e91i		−	0.854103i	−0.904227	−	0.427051i	$-0.859552\pi$
$593$		−	2.76895e91i		−	0.854103i	0.904227	−	0.427051i	$-0.140448\pi$
$594$	−3.92957e91	+	4.73449e91i	−1.14655	+	1.38140i
$595$	−3.56945e91			−0.985237
$596$		−	1.55747e91i		−	0.406718i
$597$	1.33446e91	−	5.67582e91i	0.329727	−	1.40241i
$598$	5.18239e91			1.21169
$599$			8.44653e91i			1.86893i	0.356055	+	0.934465i	$0.384121\pi$
$599$			8.44653e91i			1.86893i	−0.356055	+	0.934465i	$0.615879\pi$
$600$	1.24850e89	+	2.93539e88i	0.00261455	+	0.000614717i
$601$	1.42953e91			0.283358			0.141679	−	0.989913i	$-0.454750\pi$
$601$	1.42953e91			0.283358			0.141679	+	0.989913i	$0.454750\pi$
$602$			1.89699e92i			3.55943i
$603$	−2.14948e91	−	1.06989e91i	−0.381823	−	0.190049i
$604$	−6.50961e91			−1.09480
$605$		−	3.57133e91i		−	0.568725i
$606$	2.56430e91	−	1.09066e92i	0.386698	−	1.64473i
$607$	3.12704e91			0.446587			0.223294	−	0.974751i	$-0.428319\pi$
$607$	3.12704e91			0.446587			0.223294	+	0.974751i	$0.428319\pi$
$608$		−	7.97357e91i		−	1.07854i
$609$	1.85600e92	+	4.36372e91i	2.37798	+	0.559096i
$610$	2.88614e91			0.350294
$611$		−	7.77203e90i		−	0.0893664i
$612$	2.47761e91	−	4.97769e91i	0.269920	−	0.542289i
$613$	−1.80195e92			−1.86015			−0.930073	−	0.367376i	$-0.880256\pi$
$613$	−1.80195e92			−1.86015			−0.930073	+	0.367376i	$0.880256\pi$
$614$		−	1.27705e92i		−	1.24925i
$615$	7.07683e90	−	3.00996e91i	0.0656085	−	0.279050i
$616$	8.78741e90			0.0772142
$617$			9.03100e91i			0.752186i	0.926582	+	0.376093i	$0.122733\pi$
$617$			9.03100e91i			0.752186i	−0.926582	+	0.376093i	$0.877267\pi$
$618$	−1.08393e91	−	2.54847e90i	−0.0855818	−	0.0201215i
$619$	2.02351e92			1.51465			0.757327	−	0.653036i	$-0.226505\pi$
$619$	2.02351e92			1.51465			0.757327	+	0.653036i	$0.226505\pi$
$620$		−	1.24948e92i		−	0.886754i
$621$	−1.44595e92	−	1.20012e92i	−0.973041	−	0.807611i
$622$	−1.05655e92			−0.674231
$623$		−	4.80867e91i		−	0.291018i
$624$	−2.61682e91	+	1.11300e92i	−0.150204	+	0.638857i
$625$	−1.68630e92			−0.918109
$626$			2.68147e91i			0.138490i
$627$	−1.90101e92	−	4.46954e91i	−0.931441	−	0.218995i
$628$	−3.57943e92			−1.66397
$629$			1.42147e92i			0.627000i
$630$	5.07286e92	+	2.52498e92i	2.12332	+	1.05687i
$631$	−2.57647e92			−1.02342			−0.511712	−	0.859157i	$-0.670989\pi$
$631$	−2.57647e92			−1.02342			−0.511712	+	0.859157i	$0.670989\pi$
$632$			8.14123e90i			0.0306921i
$633$	−3.60556e91	+	1.53354e92i	−0.129018	+	0.548746i
$634$	4.83214e91			0.164132
$635$		−	2.24916e92i		−	0.725251i
$636$	4.09410e92	+	9.62580e91i	1.25335	+	0.294681i
$637$	4.64988e92			1.35158
$638$		−	9.16260e92i		−	2.52893i
$639$	−1.64598e92	+	3.30688e92i	−0.431415	+	0.866743i
$640$	2.72485e91			0.0678271
$641$			3.91266e92i			0.925032i	0.886611	+	0.462516i	$0.153053\pi$
$641$			3.91266e92i			0.925032i	−0.886611	+	0.462516i	$0.846947\pi$
$642$	1.24649e92	−	5.30164e92i	0.279919	−	1.19057i
$643$	3.48247e92			0.742892			0.371446	−	0.928455i	$-0.378862\pi$
$643$	3.48247e92			0.742892			0.371446	+	0.928455i	$0.378862\pi$
$644$			1.10887e93i			2.24722i
$645$	7.00992e92	+	1.64813e92i	1.34972	+	0.317337i
$646$	3.48681e92			0.637905
$647$			4.47442e92i			0.777849i	0.921270	+	0.388924i	$0.127153\pi$
$647$			4.47442e92i			0.777849i	−0.921270	+	0.388924i	$0.872847\pi$
$648$	−1.70442e91	+	1.28797e91i	−0.0281580	+	0.0212780i
$649$	−4.52522e92			−0.710501
$650$		−	4.88638e91i		−	0.0729199i
$651$	−2.51879e92	+	1.07131e93i	−0.357289	+	1.51964i
$652$	−1.23597e93			−1.66663
$653$		−	7.54715e92i		−	0.967493i	−0.875208	−	0.483746i	$-0.839276\pi$
$653$		−	7.54715e92i		−	0.967493i	0.875208	−	0.483746i	$-0.160724\pi$
$654$	−2.02007e93	−	4.74947e92i	−2.46207	−	0.578868i
$655$	−6.33367e91			−0.0733994
$656$			2.63753e92i			0.290650i
$657$	1.36837e93	+	6.81094e92i	1.43399	+	0.713756i
$658$	3.28568e92			0.327470
$659$		−	1.82446e93i		−	1.72948i	−0.502220	−	0.864740i	$-0.667483\pi$
$659$		−	1.82446e93i		−	1.72948i	0.502220	−	0.864740i	$-0.332517\pi$
$660$	3.15447e92	−	1.34168e93i	0.284431	−	1.20976i
$661$	−1.64655e93			−1.41230			−0.706150	−	0.708063i	$-0.749569\pi$
$661$	−1.64655e93			−1.41230			−0.706150	+	0.708063i	$0.749569\pi$
$662$		−	7.08999e92i		−	0.578538i
$663$	−4.99098e92	−	1.17345e92i	−0.387471	−	0.0910999i
$664$	−1.34629e91			−0.00994472
$665$			1.79851e93i			1.26415i
$666$	1.00553e93	−	2.02019e93i	0.672585	−	1.35127i
$667$	2.79833e93			1.78134
$668$			2.38203e93i			1.44319i
$669$	2.93376e92	−	1.24780e93i	0.169185	−	0.719588i
$670$	1.06267e93			0.583349
$671$			6.18302e92i			0.323115i
$672$	−4.82504e93	−	1.13444e93i	−2.40057	−	0.564409i
$673$	2.33912e93			1.10804			0.554019	−	0.832504i	$-0.313093\pi$
$673$	2.33912e93			1.10804			0.554019	+	0.832504i	$0.313093\pi$
$674$		−	1.70242e93i		−	0.767874i
$675$	−1.13157e92	+	1.36336e92i	−0.0486024	+	0.0585580i
$676$	1.36932e93			0.560097
$677$		−	3.69813e93i		−	1.44064i	−0.693640	−	0.720321i	$-0.743994\pi$
$677$		−	3.69813e93i		−	1.44064i	0.693640	−	0.720321i	$-0.256006\pi$
$678$	−3.02664e92	+	1.28731e93i	−0.112300	+	0.477642i
$679$	3.47174e92			0.122700
$680$			5.95600e91i			0.0200521i
$681$	−1.89680e93	−	4.45965e92i	−0.608369	−	0.143036i
$682$	5.28877e93			1.61611
$683$			4.78206e93i			1.39230i	0.717899	+	0.696148i	$0.245104\pi$
$683$			4.78206e93i			1.39230i	−0.717899	+	0.696148i	$0.754896\pi$
$684$	−2.50807e93	−	1.24837e93i	−0.695805	−	0.346332i
$685$	−3.48905e93			−0.922398
$686$			9.86368e93i			2.48510i
$687$	−5.66397e92	+	2.40903e93i	−0.136003	+	0.578455i
$688$	−6.14258e93			−1.40583
$689$		−	3.87811e93i		−	0.846030i
$690$	8.09600e93	+	1.90348e93i	1.68365	+	0.395849i
$691$	9.45872e92			0.187524			0.0937620	−	0.995595i	$-0.470111\pi$
$691$	9.45872e92			0.187524			0.0937620	+	0.995595i	$0.470111\pi$
$692$		−	5.54426e93i		−	1.04795i
$693$	−5.40930e93	+	1.08677e94i	−0.974865	+	1.95857i
$694$	1.26801e92			0.0217902
$695$		−	7.71211e93i		−	1.26379i
$696$	7.28133e91	−	3.09693e92i	0.0113790	−	0.0483980i
$697$	−1.18274e93			−0.176281
$698$			4.63190e93i			0.658462i
$699$	4.88945e92	+	1.14958e92i	0.0662999	+	0.0155880i
$700$	1.04553e93			0.135239
$701$		−	4.29448e93i		−	0.529927i	−0.964258	−	0.264964i	$-0.914640\pi$
$701$		−	4.29448e93i		−	0.529927i	0.964258	−	0.264964i	$-0.0853599\pi$
$702$	6.26305e93	+	5.19825e93i	0.737329	+	0.611973i
$703$	7.16227e93			0.804498
$704$			1.23479e94i			1.32341i
$705$	2.85465e92	−	1.21416e93i	0.0291953	−	0.124175i
$706$	1.61222e94			1.57350
$707$		−	2.21055e94i		−	2.05902i
$708$	−6.31961e93	−	1.48583e93i	−0.561814	−	0.132090i
$709$	−1.78704e94			−1.51638			−0.758190	−	0.652033i	$-0.773916\pi$
$709$	−1.78704e94			−1.51638			−0.758190	+	0.652033i	$0.773916\pi$
$710$		−	1.63487e94i		−	1.32421i
$711$	−1.00685e94	−	5.01153e93i	−0.778519	−	0.387502i
$712$	−8.02378e91			−0.00592296
$713$			1.61523e94i			1.13836i
$714$	4.96085e93	−	2.10997e94i	0.333822	−	1.41983i
$715$	−1.27089e94			−0.816601
$716$		−	6.44391e93i		−	0.395385i
$717$	1.57276e94	+	3.69779e93i	0.921577	+	0.216676i
$718$	2.00401e94			1.12148
$719$			8.06091e93i			0.430855i	0.976520	+	0.215427i	$0.0691144\pi$
$719$			8.06091e93i			0.430855i	−0.976520	+	0.215427i	$0.930886\pi$
$720$	−8.17607e93	+	1.64263e94i	−0.417419	+	0.838624i
$721$	−2.19691e93			−0.107139
$722$			1.29748e94i			0.604467i
$723$	6.52873e93	−	2.77684e94i	0.290580	−	1.23591i
$724$	−4.40845e94			−1.87462
$725$		−	2.63850e93i		−	0.107202i
$726$	2.11109e94	+	4.96346e93i	0.819592	+	0.192698i
$727$	3.76356e92			0.0139625			0.00698124	−	0.999976i	$-0.497778\pi$
$727$	3.76356e92			0.0139625			0.00698124	+	0.999976i	$0.497778\pi$
$728$		−	1.16245e93i		−	0.0412134i
$729$	−5.43676e93	−	2.90076e94i	−0.184218	−	0.982885i
$730$	−6.76498e94			−2.19085
$731$		−	2.75449e94i		−	0.852644i
$732$	−2.03016e93	+	8.63478e93i	−0.0600709	+	0.255497i
$733$	1.65121e94			0.467059			0.233530	−	0.972350i	$-0.424972\pi$
$733$	1.65121e94			0.467059			0.233530	+	0.972350i	$0.424972\pi$
$734$			7.17354e94i			1.93983i
$735$	7.26411e94	+	1.70789e94i	1.87802	+	0.441549i
$736$	−7.27482e94			−1.79827
$737$			2.27657e94i			0.538088i
$738$	1.68090e94	+	8.36653e93i	0.379910	+	0.189097i
$739$	5.89743e94			1.27467			0.637333	−	0.770589i	$-0.280038\pi$
$739$	5.89743e94			1.27467			0.637333	+	0.770589i	$0.280038\pi$
$740$			5.05491e94i			1.04488i
$741$	−5.91256e93	+	2.51476e94i	−0.116889	+	0.497160i
$742$	1.63950e95			3.10015
$743$			2.89608e94i			0.523817i	0.965093	+	0.261908i	$0.0843518\pi$
$743$			2.89608e94i			0.523817i	−0.965093	+	0.261908i	$0.915648\pi$
$744$	1.78759e93	+	4.20287e92i	0.0309286	+	0.00727176i
$745$	−2.30474e94			−0.381474
$746$		−	1.94984e94i		−	0.308758i
$747$	8.28743e93	−	1.66500e94i	0.125557	−	0.252252i
$748$	−5.27200e94			−0.764227
$749$		−	1.07454e95i		−	1.49046i
$750$	2.53789e94	−	1.07943e95i	0.336862	−	1.43276i
$751$	1.57997e94			0.200692			0.100346	−	0.994953i	$-0.468005\pi$
$751$	1.57997e94			0.200692			0.100346	+	0.994953i	$0.468005\pi$
$752$			1.06393e94i			0.129337i
$753$	−7.64658e94	−	1.79782e94i	−0.889678	−	0.209176i
$754$	−1.21208e95			−1.34982
$755$			9.63292e94i			1.02685i
$756$	−1.11226e95	+	1.34009e95i	−1.13498	+	1.36746i
$757$	8.08015e94			0.789325			0.394662	−	0.918826i	$-0.370862\pi$
$757$	8.08015e94			0.789325			0.394662	+	0.918826i	$0.370862\pi$
$758$		−	1.58378e95i		−	1.48119i
$759$	−4.07786e94	+	1.73442e95i	−0.365135	+	1.55301i
$760$	3.00100e93			0.0257287
$761$		−	1.81683e94i		−	0.149149i	−0.997215	−	0.0745746i	$-0.976240\pi$
$761$		−	1.81683e94i		−	0.149149i	0.997215	−	0.0745746i	$-0.0237599\pi$
$762$	1.32953e95	+	3.12591e94i	1.04516	+	0.245732i
$763$	−4.09428e95			−3.08225
$764$		−	1.76224e95i		−	1.27053i
$765$	−7.36597e94	−	3.66636e94i	−0.508631	−	0.253167i
$766$	2.43972e95			1.61358
$767$			5.98621e94i			0.379232i
$768$	3.57752e94	−	1.52161e95i	0.217101	−	0.923386i
$769$	2.56981e95			1.49393			0.746966	−	0.664862i	$-0.231510\pi$
$769$	2.56981e95			1.49393			0.746966	+	0.664862i	$0.231510\pi$
$770$		−	5.37280e95i		−	2.99231i
$771$	−1.47473e95	−	3.46729e94i	−0.786895	−	0.185010i
$772$	1.53526e95			0.784895
$773$			3.10010e95i			1.51863i	0.650722	+	0.759316i	$0.274466\pi$
$773$			3.10010e95i			1.51863i	−0.650722	+	0.759316i	$0.725534\pi$
$774$	−1.94849e95	+	3.91466e95i	−0.914633	+	1.83756i
$775$	1.52297e94			0.0685072
$776$		−	5.79296e92i		−	0.00249726i
$777$	1.01901e95	−	4.33410e95i	0.421002	−	1.79063i
$778$	4.94244e95			1.95711
$779$			5.95936e94i			0.226185i
$780$	−1.77484e95	−	4.17291e94i	−0.645711	−	0.151816i
$781$	3.50240e95			1.22147
$782$		−	3.18125e95i		−	1.06359i
$783$	3.38186e95	+	2.80690e95i	1.08397	+	0.899681i
$784$	−6.36531e95			−1.95609
$785$			5.29684e95i			1.56070i
$786$	8.80259e93	−	3.74397e94i	0.0248695	−	0.105776i
$787$	−6.03069e95			−1.63381			−0.816904	−	0.576774i	$-0.804311\pi$
$787$	−6.03069e95			−1.63381			−0.816904	+	0.576774i	$0.804311\pi$
$788$			6.43042e95i			1.67061i
$789$	−3.27900e95	−	7.70939e94i	−0.816959	−	0.192079i
$790$	4.97772e95			1.18942
$791$			2.60912e95i			0.597956i
$792$	1.81339e94	+	9.02599e93i	0.0398620	+	0.0198410i
$793$	8.17924e94			0.172464
$794$			5.87101e95i			1.18751i
$795$	1.42442e95	−	6.05844e95i	0.276391	−	1.17556i
$796$	−7.93105e95			−1.47638
$797$			8.65932e95i			1.54653i	0.634081	+	0.773267i	$0.281379\pi$
$797$			8.65932e95i			1.54653i	−0.634081	+	0.773267i	$0.718621\pi$
$798$	−1.06314e96	−	2.49958e95i	−1.82177	−	0.428323i
$799$	−4.77093e94			−0.0784439
$800$			6.85929e94i			0.108221i
$801$	4.93923e94	−	9.92326e94i	0.0747801	−	0.150239i
$802$	1.29061e96			1.87517
$803$		−	1.44927e96i		−	2.02086i
$804$	−7.47498e94	+	3.17930e95i	−0.100037	+	0.425483i
$805$	1.64090e96			2.10774
$806$		−	6.99628e95i		−	0.862602i
$807$	−8.98084e94	−	2.11152e94i	−0.106290	−	0.0249902i
$808$	−3.68854e94			−0.0419063
$809$			1.08403e95i			0.118234i	0.998251	+	0.0591168i	$0.0188284\pi$
$809$			1.08403e95i			0.118234i	−0.998251	+	0.0591168i	$0.981172\pi$
$810$	7.87492e95	+	1.04212e96i	0.824595	+	1.09122i
$811$	4.30165e95			0.432461			0.216230	−	0.976342i	$-0.430624\pi$
$811$	4.30165e95			0.432461			0.216230	+	0.976342i	$0.430624\pi$
$812$		−	2.59347e96i		−	2.50341i
$813$	2.14284e95	−	9.11403e95i	0.198610	−	0.844739i
$814$	−2.13963e96			−1.90429
$815$			1.82899e96i			1.56318i
$816$	6.83225e95	+	1.60636e95i	0.560775	+	0.131846i
$817$	−1.38788e96			−1.09402
$818$			6.57922e95i			0.498099i
$819$	1.43764e96	+	7.15573e95i	1.04539	+	0.520338i
$820$	−4.20594e95			−0.293769
$821$		−	1.29186e96i		−	0.866747i	−0.901214	−	0.433374i	$-0.857323\pi$
$821$		−	1.29186e96i		−	0.866747i	0.901214	−	0.433374i	$-0.142677\pi$
$822$	4.84911e95	−	2.06245e96i	0.312530	−	1.32927i
$823$	−1.66682e96			−1.03203			−0.516016	−	0.856579i	$-0.672586\pi$
$823$	−1.66682e96			−1.03203			−0.516016	+	0.856579i	$0.672586\pi$
$824$			3.66577e93i			0.00218056i
$825$	1.63535e95	+	3.84494e94i	0.0934610	+	0.0219740i
$826$	−2.53072e96			−1.38964
$827$		−	2.74780e96i		−	1.44979i	−0.688862	−	0.724893i	$-0.741889\pi$
$827$		−	2.74780e96i		−	1.44979i	0.688862	−	0.724893i	$-0.258111\pi$
$828$	−1.13897e96	+	2.28828e96i	−0.577447	+	1.16013i
$829$	−2.06929e96			−1.00814			−0.504070	−	0.863663i	$-0.668165\pi$
$829$	−2.06929e96			−1.00814			−0.504070	+	0.863663i	$0.668165\pi$
$830$			8.23151e95i			0.385392i
$831$	−2.06084e95	+	8.76529e95i	−0.0927280	+	0.394396i
$832$	1.63344e96			0.706373
$833$		−	2.85437e96i		−	1.18638i
$834$	4.55879e96	+	1.07184e96i	1.82125	+	0.428202i
$835$	3.52492e96			1.35362
$836$			2.65636e96i			0.980572i
$837$	−1.62018e96	+	1.95205e96i	−0.574940	+	0.692709i
$838$	6.75391e95			0.230411
$839$			2.95428e96i			0.968964i	0.874801	+	0.484482i	$0.160992\pi$
$839$			2.95428e96i			0.968964i	−0.874801	+	0.484482i	$0.839008\pi$
$840$	4.26966e94	−	1.81599e95i	0.0134641	−	0.0572661i
$841$	−3.24674e96			−0.984417
$842$			3.35525e96i			0.978197i
$843$	−2.20395e96	−	5.18179e95i	−0.617862	−	0.145268i
$844$	2.14287e96			0.577691
$845$		−	2.02631e96i		−	0.525334i
$846$	6.78040e95	+	3.37489e95i	0.169057	+	0.0841469i
$847$	4.27875e96			1.02604
$848$			5.30882e96i			1.22443i
$849$	8.07448e95	−	3.43428e96i	0.179127	−	0.761872i
$850$	−2.99954e95			−0.0640075
$851$		−	6.53461e96i		−	1.34136i
$852$	4.89122e96	+	1.14999e96i	0.965851	+	0.227085i
$853$	−2.17566e96			−0.413307			−0.206653	−	0.978414i	$-0.566257\pi$
$853$	−2.17566e96			−0.413307			−0.206653	+	0.978414i	$0.566257\pi$
$854$			3.45784e96i			0.631968i
$855$	−1.84734e96	+	3.71143e96i	−0.324836	+	0.652619i
$856$	−1.79298e95			−0.0303347
$857$			4.42484e96i			0.720328i	0.932889	+	0.360164i	$0.117279\pi$
$857$			4.42484e96i			0.720328i	−0.932889	+	0.360164i	$0.882721\pi$
$858$	1.76630e96	−	7.51252e96i	0.276684	−	1.17681i
$859$	−5.20225e96			−0.784183			−0.392091	−	0.919926i	$-0.628248\pi$
$859$	−5.20225e96			−0.784183			−0.392091	+	0.919926i	$0.628248\pi$
$860$		−	9.79525e96i		−	1.42091i
$861$	3.60618e96	+	8.47864e95i	0.503436	+	0.118365i
$862$	−8.99978e95			−0.120918
$863$		−	1.69983e96i		−	0.219811i	−0.993942	−	0.109905i	$-0.964945\pi$
$863$		−	1.69983e96i		−	0.219811i	0.993942	−	0.109905i	$-0.0350548\pi$
$864$	−8.79181e96	−	7.29709e96i	−1.09427	−	0.908231i
$865$	−8.20439e96			−0.982912
$866$			1.60935e97i			1.85593i
$867$	1.34137e96	−	5.70518e96i	0.148908	−	0.633343i
$868$	1.49698e97			1.59980
$869$			1.06638e97i			1.09714i
$870$	−1.89353e97	−	4.45195e96i	−1.87558	−	0.440976i
$871$	3.01157e96			0.287206
$872$			6.83174e95i			0.0627317i
$873$	7.16434e95	+	3.56600e95i	0.0633441	+	0.0315291i
$874$	−1.60291e97			−1.36469
$875$		−	2.18779e97i		−	1.79366i
$876$	4.75860e96	−	2.02395e97i	0.375702	−	1.59796i
$877$	−1.84878e96			−0.140572			−0.0702859	−	0.997527i	$-0.522391\pi$
$877$	−1.84878e96			−0.140572			−0.0702859	+	0.997527i	$0.522391\pi$
$878$		−	2.13176e97i		−	1.56106i
$879$	1.07477e97	+	2.52694e96i	0.758025	+	0.178222i
$880$	1.73975e97			1.18184
$881$		−	3.70612e96i		−	0.242501i	−0.992622	−	0.121251i	$-0.961310\pi$
$881$		−	3.70612e96i		−	0.242501i	0.992622	−	0.121251i	$-0.0386905\pi$
$882$	−2.01914e97	+	4.05660e97i	−1.27264	+	2.55682i
$883$	1.61100e97			0.978117			0.489059	−	0.872251i	$-0.337340\pi$
$883$	1.61100e97			0.978117			0.489059	+	0.872251i	$0.337340\pi$
$884$			6.97409e96i			0.407909i
$885$	−2.19873e96	+	9.35175e96i	−0.123892	+	0.526945i
$886$	2.84269e97			1.54318
$887$			7.71534e96i			0.403530i	0.979434	+	0.201765i	$0.0646677\pi$
$887$			7.71534e96i			0.403530i	−0.979434	+	0.201765i	$0.935332\pi$
$888$	−7.23190e95	−	1.70032e95i	−0.0364439	−	0.00856847i
$889$	2.69469e97			1.30843
$890$			4.90590e96i			0.229535i
$891$	−2.23255e97	+	1.68706e97i	−1.00655	+	0.760615i
$892$	−1.74360e97			−0.757544
$893$			2.40389e96i			0.100651i
$894$	3.20315e96	−	1.36238e97i	0.129253	−	0.549744i
$895$	−9.53569e96			−0.370844
$896$			3.26460e96i			0.122367i
$897$	2.29439e97	+	5.39442e96i	0.828926	+	0.194892i
$898$	8.90017e96			0.309941
$899$		−	3.77778e97i		−	1.26814i
$900$	2.15757e96	+	1.07392e96i	0.0698172	+	0.0347510i
$901$	−2.38061e97			−0.742626
$902$		−	1.78028e97i		−	0.535393i
$903$	−1.97460e97	+	8.39848e97i	−0.572511	+	2.43503i
$904$	4.35359e95			0.0121700
$905$			6.52362e97i			1.75827i
$906$	−5.69422e97	−	1.33879e97i	−1.47980	−	0.347922i
$907$	2.01602e97			0.505189			0.252595	−	0.967572i	$-0.418716\pi$
$907$	2.01602e97			0.505189			0.252595	+	0.967572i	$0.418716\pi$
$908$			2.65048e97i			0.640459i
$909$	2.27057e97	−	4.56174e97i	0.529087	−	1.06297i
$910$	−7.10745e97			−1.59716
$911$			2.00570e97i			0.434669i	0.976097	+	0.217335i	$0.0697363\pi$
$911$			2.00570e97i			0.434669i	−0.976097	+	0.217335i	$0.930264\pi$
$912$	8.09382e96	−	3.44251e97i	0.169170	−	0.719524i
$913$	−1.76345e97			−0.355490
$914$		−	4.94690e97i		−	0.961852i
$915$	1.27777e97	+	3.00422e96i	0.239639	+	0.0563425i
$916$	3.36624e97			0.608967
$917$		−	7.58827e96i		−	0.132420i
$918$	3.19099e97	−	3.84463e97i	0.537177	−	0.647211i
$919$	7.20468e97			1.17005			0.585023	−	0.811017i	$-0.301085\pi$
$919$	7.20468e97			1.17005			0.585023	+	0.811017i	$0.301085\pi$
$920$		−	2.73801e96i		−	0.0428980i
$921$	1.32930e97	−	5.65384e97i	0.200934	−	0.854625i
$922$	−9.03921e97			−1.31829
$923$		−	4.63318e97i		−	0.651962i
$924$	1.60744e98	+	3.77932e97i	2.18253	+	0.513143i
$925$	−6.16136e96			−0.0807235
$926$			4.52435e96i			0.0571996i
$927$	−4.53358e96	−	2.25656e96i	−0.0553108	−	0.0275305i
$928$	1.70147e98			2.00328
$929$		−	7.02283e97i		−	0.797983i	−0.916955	−	0.398992i	$-0.869360\pi$
$929$		−	7.02283e97i		−	0.797983i	0.916955	−	0.398992i	$-0.130640\pi$
$930$	2.56972e97	−	1.09297e98i	0.281805	−	1.19859i
$931$	−1.43821e98			−1.52224
$932$		−	6.83222e96i		−	0.0697970i
$933$	−4.67765e97	−	1.09978e97i	−0.461247	−	0.108446i
$934$	−2.47522e98			−2.35595
$935$			7.80149e97i			0.716794i
$936$	1.19401e96	−	2.39885e96i	0.0105902	−	0.0212765i
$937$	−1.05965e98			−0.907309			−0.453655	−	0.891178i	$-0.649880\pi$
$937$	−1.05965e98			−0.907309			−0.453655	+	0.891178i	$0.649880\pi$
$938$			1.27316e98i			1.05242i
$939$	−2.79118e96	+	1.18716e97i	−0.0222753	+	0.0947424i
$940$	−1.69659e97			−0.130725
$941$			8.09811e97i			0.602457i	0.953552	+	0.301228i	$0.0973967\pi$
$941$			8.09811e97i			0.602457i	−0.953552	+	0.301228i	$0.902603\pi$
$942$	−3.13107e98	−	7.36160e97i	−2.24913	−	0.528801i
$943$	5.43712e97			0.377123
$944$		−	8.19465e97i		−	0.548851i
$945$	1.98307e98	+	1.64592e98i	1.28259	+	1.06453i
$946$	4.14611e98			2.58961
$947$			2.17413e98i			1.31140i	0.755021	+	0.655701i	$0.227627\pi$
$947$			2.17413e98i			1.31140i	−0.755021	+	0.655701i	$0.772373\pi$
$948$	−3.50141e97	+	1.48924e98i	−0.203971	+	0.867539i
$949$	−1.91718e98			−1.07864
$950$			1.51136e97i			0.0821273i
$951$	2.13932e97	+	5.02984e96i	0.112284	+	0.0263996i
$952$	−7.13579e96			−0.0361762
$953$			1.22952e98i			0.602102i	0.953608	+	0.301051i	$0.0973374\pi$
$953$			1.22952e98i			0.602102i	−0.953608	+	0.301051i	$0.902663\pi$
$954$	3.38330e98	+	1.68401e98i	1.60046	+	0.796617i
$955$	−2.60777e98			−1.19167
$956$		−	2.19769e98i		−	0.970187i
$957$	9.53748e97	−	4.05654e98i	0.406762	−	1.73006i
$958$	3.64052e98			1.50004
$959$		−	4.18018e98i		−	1.66410i
$960$	2.55179e98	+	5.99962e97i	0.981509	+	0.230766i
$961$	−5.10159e97			−0.189598
$962$			2.83043e98i			1.01642i
$963$	1.10371e98	−	2.21743e98i	0.382990	−	0.769454i
$964$	−3.88019e98			−1.30110
$965$		−	2.27188e98i		−	0.736179i
$966$	−2.28053e98	+	9.69970e98i	−0.714153	+	3.03748i
$967$	−1.05764e98			−0.320083			−0.160042	−	0.987110i	$-0.551163\pi$
$967$	−1.05764e98			−0.320083			−0.160042	+	0.987110i	$0.551163\pi$
$968$		−	7.13955e96i		−	0.0208826i
$969$	1.54371e98	+	3.62948e97i	0.436396	+	0.102603i
$970$	−3.54194e97			−0.0967773
$971$			1.72623e98i			0.455895i	0.973673	+	0.227948i	$0.0732015\pi$
$971$			1.72623e98i			0.455895i	−0.973673	+	0.227948i	$0.926799\pi$
$972$	−3.67176e98	+	1.62298e98i	−0.937319	+	0.414312i
$973$	9.23976e98			2.28001
$974$		−	4.10862e98i		−	0.980055i
$975$	5.08630e96	−	2.16333e97i	0.0117287	−	0.0498851i
$976$	−1.11967e98			−0.249602
$977$		−	1.30299e97i		−	0.0280815i	−0.999901	−	0.0140408i	$-0.995531\pi$
$977$		−	1.30299e97i		−	0.0280815i	0.999901	−	0.0140408i	$-0.00446946\pi$
$978$	−1.08115e99	−	2.54195e98i	−2.25271	−	0.529644i
$979$	−1.05100e98			−0.211726
$980$		−	1.01504e99i		−	1.97708i
$981$	−8.44903e98	−	4.20544e98i	−1.59122	−	0.792017i
$982$	−7.53369e98			−1.37192
$983$		−	9.87142e98i		−	1.73826i	−0.494587	−	0.869128i	$-0.664681\pi$
$983$		−	9.87142e98i		−	1.73826i	0.494587	−	0.869128i	$-0.335319\pi$
$984$	1.41475e96	−	6.01730e96i	0.00240903	−	0.0102462i
$985$	9.51572e98			1.56692
$986$			7.44046e98i			1.18485i
$987$	1.45466e98	+	3.42012e97i	0.224025	+	0.0526714i
$988$	3.51398e98			0.523384
$989$			1.26626e99i			1.82408i
$990$	5.51868e98	−	1.10874e99i	0.768907	−	1.54479i
$991$	−4.06315e98			−0.547560			−0.273780	−	0.961792i	$-0.588274\pi$
$991$	−4.06315e98			−0.547560			−0.273780	+	0.961792i	$0.588274\pi$
$992$			9.82109e98i			1.28019i
$993$	7.38008e97	−	3.13894e98i	0.0930541	−	0.395783i
$994$	1.95871e99			2.38902
$995$			1.17364e99i			1.38475i
$996$	−2.46271e98	−	5.79018e97i	−0.281096	−	0.0660897i
$997$	−6.76976e98			−0.747538			−0.373769	−	0.927522i	$-0.621935\pi$
$997$	−6.76976e98			−0.747538			−0.373769	+	0.927522i	$0.621935\pi$
$998$		−	8.20861e98i		−	0.876923i
$999$	6.55462e98	−	7.89725e98i	0.677464	−	0.816234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.67.b.b.2.4	✓	20
3.2	odd	2	inner	3.67.b.b.2.17	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.67.b.b.2.4	✓	20	1.1	even	1	trivial
3.67.b.b.2.17	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:	\( k \)	\(=\)	\( 67 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.22231e10i q^{2} +(1.27232e15 - 5.41150e15i) q^{3} -7.56171e19 q^{4} +1.11898e23i q^{5} +(-6.61453e25 - 1.55517e25i) q^{6} -1.34063e28 q^{7} +2.23699e28i q^{8} +(-2.76656e31 - 1.37703e31i) q^{9} +O(q^{10})\)	\(q-1.22231e10i q^{2} +(1.27232e15 - 5.41150e15i) q^{3} -7.56171e19 q^{4} +1.11898e23i q^{5} +(-6.61453e25 - 1.55517e25i) q^{6} -1.34063e28 q^{7} +2.23699e28i q^{8} +(-2.76656e31 - 1.37703e31i) q^{9} +1.36774e33 q^{10} +2.93013e34i q^{11} +(-9.62092e34 + 4.09202e35i) q^{12} +3.87614e36 q^{13} +1.63867e38i q^{14} +(6.05537e38 + 1.42370e38i) q^{15} -5.30613e39 q^{16} -2.37940e40i q^{17} +(-1.68316e41 + 3.38159e41i) q^{18} -1.19889e42 q^{19} -8.46141e42i q^{20} +(-1.70571e43 + 7.25484e43i) q^{21} +3.58153e44 q^{22} +1.09383e45i q^{23} +(1.21055e44 + 2.84617e43i) q^{24} +1.03135e45 q^{25} -4.73785e46i q^{26} +(-1.09718e47 + 1.32192e47i) q^{27} +1.01375e48 q^{28} -2.55829e48i q^{29} +(1.74020e48 - 7.40153e48i) q^{30} +1.47668e49 q^{31} +6.65079e49i q^{32} +(1.58564e50 + 3.72806e49i) q^{33} -2.90837e50 q^{34} -1.50014e51i q^{35} +(2.09199e51 + 1.04127e51i) q^{36} -5.97408e51 q^{37} +1.46542e52i q^{38} +(4.93169e51 - 2.09758e52i) q^{39} -2.50315e51 q^{40} -4.97073e52i q^{41} +(8.86766e53 + 2.08491e53i) q^{42} +1.15764e54 q^{43} -2.21568e54i q^{44} +(1.54087e54 - 3.09572e54i) q^{45} +1.33700e55 q^{46} -2.00509e54i q^{47} +(-6.75109e54 + 2.87141e55i) q^{48} +1.19962e56 q^{49} -1.26063e55i q^{50} +(-1.28761e56 - 3.02736e55i) q^{51} -2.93103e56 q^{52} -1.00051e57i q^{53} +(1.61580e57 + 1.34109e57i) q^{54} -3.27876e57 q^{55} -2.99898e56i q^{56} +(-1.52537e57 + 6.48780e57i) q^{57} -3.12703e58 q^{58} +1.54437e58i q^{59} +(-4.57889e58 - 1.07656e58i) q^{60} +2.11015e58 q^{61} -1.80496e59i q^{62} +(3.70894e59 + 1.84610e59i) q^{63} +4.21410e59 q^{64} +4.33733e59i q^{65} +(4.55685e59 - 1.93814e60i) q^{66} +7.76951e59 q^{67} +1.79924e60i q^{68} +(5.91925e60 + 1.39170e60i) q^{69} -1.83364e61 q^{70} -1.19531e61i q^{71} +(3.08041e59 - 6.18875e59i) q^{72} -4.94610e61 q^{73} +7.30217e61i q^{74} +(1.31221e60 - 5.58115e60i) q^{75} +9.06566e61 q^{76} -3.92823e62i q^{77} +(-2.56389e62 - 6.02806e61i) q^{78} +3.63937e62 q^{79} -5.93746e62i q^{80} +(5.75761e62 + 7.61928e62i) q^{81} -6.07577e62 q^{82} +6.01832e62i q^{83} +(1.28981e63 - 5.48590e63i) q^{84} +2.66251e63 q^{85} -1.41499e64i q^{86} +(-1.38442e64 - 3.25497e63i) q^{87} -6.55467e62 q^{88} +3.58687e63i q^{89} +(-3.78393e64 - 1.88342e64i) q^{90} -5.19649e64 q^{91} -8.27121e64i q^{92} +(1.87881e64 - 7.99105e64i) q^{93} -2.45084e64 q^{94} -1.34154e65i q^{95} +(3.59908e65 + 8.46194e64i) q^{96} -2.58963e64 q^{97} -1.46630e66i q^{98} +(4.03489e65 - 8.10637e65i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 48\!\cdots\!16 q^{3}+ \cdots + 15\!\cdots\!00 q^{9}+O(q^{10}) \) 20 * q + 4870975596954516 * q^3 - 874472713330987494880 * q^4 - 36458623571791371420365280 * q^6 + 12757412570419684480800346888 * q^7 + 15089557305995766698320873638900 * q^9	\( 20 q + 48\!\cdots\!16 q^{3}+ \cdots + 13\!\cdots\!00 q^{99}+O(q^{100}) \) 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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Groups

Database

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