LMFDB - Embedded newform 3.67.b.b.2.19

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			2.19
Root			$4.43955e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.67.b.b.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.59824e10i q^{2} +(5.28212e15 + 1.73274e15i) q^{3} -1.81649e20 q^{4} +8.56960e22i q^{5} +(-2.76933e25 + 8.44208e25i) q^{6} +1.24551e28 q^{7} -1.72390e30i q^{8} +(2.48984e31 + 1.83050e31i) q^{9} -1.36963e33 q^{10} -3.23641e34i q^{11} +(-9.59494e35 - 3.14751e35i) q^{12} +4.92454e36 q^{13} +1.99063e38i q^{14} +(-1.48489e38 + 4.52656e38i) q^{15} +1.41486e40 q^{16} -1.87651e40i q^{17} +(-2.92558e41 + 3.97936e41i) q^{18} +1.55238e42 q^{19} -1.55666e43i q^{20} +(6.57896e43 + 2.15815e43i) q^{21} +5.17256e44 q^{22} +2.71494e44i q^{23} +(2.98706e45 - 9.10584e45i) q^{24} +6.20872e45 q^{25} +7.87059e46i q^{26} +(9.97984e46 + 1.39832e47i) q^{27} -2.26247e48 q^{28} +1.13044e48i q^{29} +(-7.23453e48 - 2.37320e48i) q^{30} +1.24010e49 q^{31} +9.89276e49i q^{32} +(5.60786e49 - 1.70951e50i) q^{33} +2.99912e50 q^{34} +1.06736e51i q^{35} +(-4.52278e51 - 3.32510e51i) q^{36} +3.41856e51 q^{37} +2.48107e52i q^{38} +(2.60120e52 + 8.53294e51i) q^{39} +1.47731e53 q^{40} -2.61816e53i q^{41} +(-3.44924e53 + 1.05147e54i) q^{42} +4.27712e53 q^{43} +5.87893e54i q^{44} +(-1.56867e54 + 2.13369e54i) q^{45} -4.33912e54 q^{46} +1.98170e55i q^{47} +(7.47348e55 + 2.45159e55i) q^{48} +9.53625e55 q^{49} +9.92301e55i q^{50} +(3.25151e55 - 9.91197e55i) q^{51} -8.94541e56 q^{52} -6.52528e55i q^{53} +(-2.23484e57 + 1.59502e57i) q^{54} +2.77348e57 q^{55} -2.14714e58i q^{56} +(8.19985e57 + 2.68986e57i) q^{57} -1.80671e58 q^{58} +6.23201e57i q^{59} +(2.69729e58 - 8.22248e58i) q^{60} -9.12777e58 q^{61} +1.98198e59i q^{62} +(3.10113e59 + 2.27992e59i) q^{63} -5.37113e59 q^{64} +4.22014e59i q^{65} +(2.73221e60 + 8.96269e59i) q^{66} -1.10057e60 q^{67} +3.40868e60i q^{68} +(-4.70428e59 + 1.43406e60i) q^{69} -1.70589e61 q^{70} -2.12124e61i q^{71} +(3.15560e61 - 4.29223e61i) q^{72} -5.91057e60 q^{73} +5.46368e61i q^{74} +(3.27952e61 + 1.07581e61i) q^{75} -2.81989e62 q^{76} -4.03100e62i q^{77} +(-1.36377e62 + 4.15734e62i) q^{78} -3.17730e62 q^{79} +1.21248e63i q^{80} +(2.84855e62 + 9.11533e62i) q^{81} +4.18444e63 q^{82} +1.29266e63i q^{83} +(-1.19506e64 - 3.92027e63i) q^{84} +1.60810e63 q^{85} +6.83585e63i q^{86} +(-1.95875e63 + 5.97111e63i) q^{87} -5.57925e64 q^{88} -1.78551e64i q^{89} +(-3.41015e64 - 2.50711e64i) q^{90} +6.13359e64 q^{91} -4.93168e64i q^{92} +(6.55036e64 + 2.14877e64i) q^{93} -3.16723e65 q^{94} +1.33033e65i q^{95} +(-1.71416e65 + 5.22547e65i) q^{96} -5.99167e65 q^{97} +1.52412e66i q^{98} +(5.92427e65 - 8.05815e65i) 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 $

$2$			1.59824e10i			1.86059i	0.366808	+	0.930297i	$0.380451\pi$
$2$			1.59824e10i			1.86059i	−0.366808	+	0.930297i	$0.619549\pi$
$3$	5.28212e15	+	1.73274e15i	0.950182	+	0.311696i
$3$	5.28212e15	+	1.73274e15i	0.950182	+	0.311696i
$4$	−1.81649e20			−2.46181
$5$			8.56960e22i			0.736123i	0.929801	+	0.368062i	$0.119978\pi$
$5$			8.56960e22i			0.736123i	−0.929801	+	0.368062i	$0.880022\pi$
$6$	−2.76933e25	+	8.44208e25i	−0.579940	+	1.76790i
$7$	1.24551e28			1.61107			0.805533	−	0.592550i	$-0.201879\pi$
$7$	1.24551e28			1.61107			0.805533	+	0.592550i	$0.201879\pi$
$8$		−	1.72390e30i		−	2.71983i
$9$	2.48984e31	+	1.83050e31i	0.805691	+	0.592336i
$10$	−1.36963e33			−1.36963
$11$		−	3.23641e34i		−	1.39350i	−0.717316	−	0.696748i	$-0.754630\pi$
$11$		−	3.23641e34i		−	1.39350i	0.717316	−	0.696748i	$-0.245370\pi$
$12$	−9.59494e35	−	3.14751e35i	−2.33917	−	0.767336i
$13$	4.92454e36			0.855530			0.427765	−	0.903890i	$-0.359301\pi$
$13$	4.92454e36			0.855530			0.427765	+	0.903890i	$0.359301\pi$
$14$			1.99063e38i			2.99754i
$15$	−1.48489e38	+	4.52656e38i	−0.229447	+	0.699451i
$16$	1.41486e40			2.59869
$17$		−	1.87651e40i		−	0.466162i	−0.972457	−	0.233081i	$-0.925119\pi$
$17$		−	1.87651e40i		−	0.466162i	0.972457	−	0.233081i	$-0.0748808\pi$
$18$	−2.92558e41	+	3.97936e41i	−1.10210	+	1.49906i
$19$	1.55238e42			0.982039			0.491020	−	0.871149i	$-0.336624\pi$
$19$	1.55238e42			0.982039			0.491020	+	0.871149i	$0.336624\pi$
$20$		−	1.55666e43i		−	1.81219i
$21$	6.57896e43	+	2.15815e43i	1.53081	+	0.502163i
$22$	5.17256e44			2.59273
$23$			2.71494e44i			0.313864i	0.987609	+	0.156932i	$0.0501604\pi$
$23$			2.71494e44i			0.313864i	−0.987609	+	0.156932i	$0.949840\pi$
$24$	2.98706e45	−	9.10584e45i	0.847761	−	2.58434i
$25$	6.20872e45			0.458123
$26$			7.87059e46i			1.59179i
$27$	9.97984e46	+	1.39832e47i	0.580924	+	0.813958i
$28$	−2.26247e48			−3.96614
$29$			1.13044e48i			0.622463i	0.950334	+	0.311231i	$0.100741\pi$
$29$			1.13044e48i			0.622463i	−0.950334	+	0.311231i	$0.899259\pi$
$30$	−7.23453e48	−	2.37320e48i	−1.30139	−	0.426907i
$31$	1.24010e49			0.755999			0.378000	−	0.925806i	$-0.376612\pi$
$31$	1.24010e49			0.755999			0.378000	+	0.925806i	$0.376612\pi$
$32$			9.89276e49i			2.11528i
$33$	5.60786e49	−	1.70951e50i	0.434347	−	1.32407i
$34$	2.99912e50			0.867339
$35$			1.06736e51i			1.18594i
$36$	−4.52278e51	−	3.32510e51i	−1.98346	−	1.45822i
$37$	3.41856e51			0.606997			0.303499	−	0.952832i	$-0.401845\pi$
$37$	3.41856e51			0.606997			0.303499	+	0.952832i	$0.401845\pi$
$38$			2.48107e52i			1.82718i
$39$	2.60120e52	+	8.53294e51i	0.812910	+	0.266665i
$40$	1.47731e53			2.00213
$41$		−	2.61816e53i		−	1.57083i	−0.618970	−	0.785415i	$-0.712450\pi$
$41$		−	2.61816e53i		−	1.57083i	0.618970	−	0.785415i	$-0.287550\pi$
$42$	−3.44924e53	+	1.05147e54i	−0.934322	+	2.84821i
$43$	4.27712e53			0.532957			0.266478	−	0.963841i	$-0.414140\pi$
$43$	4.27712e53			0.532957			0.266478	+	0.963841i	$0.414140\pi$
$44$			5.87893e54i			3.43052i
$45$	−1.56867e54	+	2.13369e54i	−0.436032	+	0.593088i
$46$	−4.33912e54			−0.583974
$47$			1.98170e55i			1.31162i	0.754925	+	0.655811i	$0.227673\pi$
$47$			1.98170e55i			1.31162i	−0.754925	+	0.655811i	$0.772327\pi$
$48$	7.47348e55	+	2.45159e55i	2.46923	+	0.810003i
$49$	9.53625e55			1.59554
$50$			9.92301e55i			0.852380i
$51$	3.25151e55	−	9.91197e55i	0.145301	−	0.442939i
$52$	−8.94541e56			−2.10615
$53$		−	6.52528e55i		−	0.0819400i	−0.999160	−	0.0409700i	$-0.986955\pi$
$53$		−	6.52528e55i		−	0.0819400i	0.999160	−	0.0409700i	$-0.0130448\pi$
$54$	−2.23484e57	+	1.59502e57i	−1.51444	+	1.08086i
$55$	2.77348e57			1.02578
$56$		−	2.14714e58i		−	4.38183i
$57$	8.19985e57	+	2.68986e57i	0.933116	+	0.306098i
$58$	−1.80671e58			−1.15815
$59$			6.23201e57i			0.227254i	0.993523	+	0.113627i	$0.0362469\pi$
$59$			6.23201e57i			0.227254i	−0.993523	+	0.113627i	$0.963753\pi$
$60$	2.69729e58	−	8.22248e58i	0.564854	−	1.72191i
$61$	−9.12777e58			−1.10785			−0.553924	−	0.832567i	$-0.686870\pi$
$61$	−9.12777e58			−1.10785			−0.553924	+	0.832567i	$0.686870\pi$
$62$			1.98198e59i			1.40661i
$63$	3.10113e59	+	2.27992e59i	1.29802	+	0.954293i
$64$	−5.37113e59			−1.33699
$65$			4.22014e59i			0.629776i
$66$	2.73221e60	+	8.96269e59i	2.46356	+	0.808143i
$67$	−1.10057e60			−0.604155			−0.302078	−	0.953283i	$-0.597680\pi$
$67$	−1.10057e60			−0.604155			−0.302078	+	0.953283i	$0.597680\pi$
$68$			3.40868e60i			1.14760i
$69$	−4.70428e59	+	1.43406e60i	−0.0978303	+	0.298228i
$70$	−1.70589e61			−2.20656
$71$		−	2.12124e61i		−	1.71816i	−0.511839	−	0.859082i	$-0.671035\pi$
$71$		−	2.12124e61i		−	1.71816i	0.511839	−	0.859082i	$-0.328965\pi$
$72$	3.15560e61	−	4.29223e61i	1.61105	−	2.19134i
$73$	−5.91057e60			−0.191415			−0.0957073	−	0.995410i	$-0.530511\pi$
$73$	−5.91057e60			−0.191415			−0.0957073	+	0.995410i	$0.530511\pi$
$74$			5.46368e61i			1.12938i
$75$	3.27952e61	+	1.07581e61i	0.435300	+	0.142795i
$76$	−2.81989e62			−2.41759
$77$		−	4.03100e62i		−	2.24501i
$78$	−1.36377e62	+	4.15734e62i	−0.496156	+	1.51249i
$79$	−3.17730e62			−0.759213			−0.379607	−	0.925148i	$-0.623941\pi$
$79$	−3.17730e62			−0.759213			−0.379607	+	0.925148i	$0.623941\pi$
$80$			1.21248e63i			1.91296i
$81$	2.84855e62	+	9.11533e62i	0.298276	+	0.954480i
$82$	4.18444e63			2.92268
$83$			1.29266e63i			0.605210i	0.953116	+	0.302605i	$0.0978563\pi$
$83$			1.29266e63i			0.605210i	−0.953116	+	0.302605i	$0.902144\pi$
$84$	−1.19506e64	−	3.92027e63i	−3.76855	−	1.23623i
$85$	1.60810e63			0.343153
$86$			6.83585e63i			0.991616i
$87$	−1.95875e63	+	5.97111e63i	−0.194019	+	0.591453i
$88$	−5.57925e64			−3.79007
$89$		−	1.78551e64i		−	0.835394i	−0.908586	−	0.417697i	$-0.862837\pi$
$89$		−	1.78551e64i		−	0.835394i	0.908586	−	0.417697i	$-0.137163\pi$
$90$	−3.41015e64	−	2.50711e64i	−1.10350	−	0.811279i
$91$	6.13359e64			1.37832
$92$		−	4.93168e64i		−	0.772674i
$93$	6.55036e64	+	2.14877e64i	0.718337	+	0.235642i
$94$	−3.16723e65			−2.44040
$95$			1.33033e65i			0.722902i
$96$	−1.71416e65	+	5.22547e65i	−0.659325	+	2.00990i
$97$	−5.99167e65			−1.63712			−0.818561	−	0.574420i	$-0.805228\pi$
$97$	−5.99167e65			−1.63712			−0.818561	+	0.574420i	$0.805228\pi$
$98$			1.52412e66i			2.96865i
$99$	5.92427e65	−	8.05815e65i	0.825417	−	1.12273i
$100$	−1.12781e66			−1.12781
$101$		−	1.42406e66i		−	1.02547i	−0.858547	−	0.512735i	$-0.828632\pi$
$101$		−	1.42406e66i		−	1.02547i	0.858547	−	0.512735i	$-0.171368\pi$
$102$	1.58417e66	+	5.19668e65i	0.824130	+	0.270346i
$103$	4.14299e65			0.156202			0.0781008	−	0.996945i	$-0.475114\pi$
$103$	4.14299e65			0.156202			0.0781008	+	0.996945i	$0.475114\pi$
$104$		−	8.48942e66i		−	2.32690i
$105$	−1.84945e66	+	5.63790e66i	−0.369654	+	1.12686i
$106$	1.04290e66			0.152457
$107$		−	4.06185e66i		−	0.435571i	−0.975997	−	0.217786i	$-0.930117\pi$
$107$		−	4.06185e66i		−	0.435571i	0.975997	−	0.217786i	$-0.0698834\pi$
$108$	−1.81283e67	−	2.54004e67i	−1.43012	−	2.00381i
$109$	1.22254e67			0.711523			0.355762	−	0.934577i	$-0.384221\pi$
$109$	1.22254e67			0.711523			0.355762	+	0.934577i	$0.384221\pi$
$110$			4.43268e67i			1.90857i
$111$	1.80573e67	+	5.92347e66i	0.576758	+	0.189199i
$112$	1.76223e68			4.18667
$113$		−	2.96386e67i		−	0.525132i	−0.964914	−	0.262566i	$-0.915431\pi$
$113$		−	2.96386e67i		−	0.525132i	0.964914	−	0.262566i	$-0.0845688\pi$
$114$	−4.29904e67	+	1.31053e68i	−0.569524	+	1.73615i
$115$	−2.32660e67			−0.231043
$116$		−	2.05344e68i		−	1.53238i
$117$	1.22613e68	+	9.01440e67i	0.689293	+	0.506761i
$118$	−9.96024e67			−0.422828
$119$		−	2.33723e68i		−	0.751019i
$120$	7.80334e68	+	2.55979e68i	1.90239	+	0.624057i
$121$	−5.08030e68			−0.941829
$122$		−	1.45883e69i		−	2.06125i
$123$	4.53659e68	−	1.38294e69i	0.489621	−	1.49257i
$124$	−2.25264e69			−1.86113
$125$			1.69346e69i			1.07336i
$126$	−3.64386e69	+	4.95635e69i	−1.77555	+	2.41509i
$127$	2.87260e69			1.07833			0.539166	−	0.842200i	$-0.318740\pi$
$127$	2.87260e69			1.07833			0.539166	+	0.842200i	$0.318740\pi$
$128$		−	1.28478e69i		−	0.372306i
$129$	2.25922e69	+	7.41112e68i	0.506406	+	0.166121i
$130$	−6.74478e69			−1.17176
$131$		−	7.52575e69i		−	1.01531i	−0.861561	−	0.507653i	$-0.830513\pi$
$131$		−	7.52575e69i		−	1.01531i	0.861561	−	0.507653i	$-0.169487\pi$
$132$	−1.01866e70	+	3.10532e70i	−1.06928	+	3.25962i
$133$	1.93351e70			1.58213
$134$		−	1.75897e70i		−	1.12409i
$135$	−1.19830e70	+	8.55233e69i	−0.599173	+	0.427632i
$136$	−3.23492e70			−1.26788
$137$		−	1.46118e70i		−	0.449703i	−0.974393	−	0.224852i	$-0.927810\pi$
$137$		−	1.46118e70i		−	0.449703i	0.974393	−	0.224852i	$-0.0721898\pi$
$138$	−2.29198e70	−	7.51856e69i	−0.554881	−	0.182022i
$139$	−6.53744e70			−1.24715			−0.623576	−	0.781763i	$-0.714321\pi$
$139$	−6.53744e70			−1.24715			−0.623576	+	0.781763i	$0.714321\pi$
$140$		−	1.93885e71i		−	2.91957i
$141$	−3.43377e70	+	1.04676e71i	−0.408828	+	1.24628i
$142$	3.39025e71			3.19680
$143$		−	1.59379e71i		−	1.19218i
$144$	3.52278e71	+	2.58992e71i	2.09375	+	1.53930i
$145$	−9.68741e70			−0.458209
$146$		−	9.44650e70i		−	0.356145i
$147$	5.03716e71	+	1.65238e71i	1.51605	+	0.497323i
$148$	−6.20980e71			−1.49431
$149$			9.45091e71i			1.82107i	0.413432	+	0.910535i	$0.364330\pi$
$149$			9.45091e71i			1.82107i	−0.413432	+	0.910535i	$0.635670\pi$
$150$	−1.71940e71	+	5.24145e71i	−0.265684	+	0.809916i
$151$	−6.02201e71			−0.747313			−0.373656	−	0.927567i	$-0.621896\pi$
$151$	−6.02201e71			−0.747313			−0.373656	+	0.927567i	$0.621896\pi$
$152$		−	2.67614e72i		−	2.67098i
$153$	3.43497e71	−	4.67222e71i	0.276125	−	0.375583i
$154$	6.44250e72			4.17706
$155$			1.06272e72i			0.556508i
$156$	−4.72507e72	−	1.55000e72i	−2.00123	−	0.656479i
$157$	−4.04655e72			−1.38802			−0.694012	−	0.719964i	$-0.744158\pi$
$157$	−4.04655e72			−1.38802			−0.694012	+	0.719964i	$0.744158\pi$
$158$		−	5.07808e72i		−	1.41259i
$159$	1.13066e71	−	3.44673e71i	0.0255404	−	0.0778579i
$160$	−8.47770e72			−1.55711
$161$			3.38150e72i			0.505656i
$162$	−1.45685e73	+	4.55267e72i	−1.77590	+	0.554971i
$163$	8.48532e72			0.844262			0.422131	−	0.906535i	$-0.361282\pi$
$163$	8.48532e72			0.844262			0.422131	+	0.906535i	$0.361282\pi$
$164$			4.75588e73i			3.86708i
$165$	1.46498e73	+	4.80571e72i	0.974681	+	0.319733i
$166$	−2.06597e73			−1.12605
$167$			1.30002e73i			0.581177i	0.956848	+	0.290588i	$0.0938510\pi$
$167$			1.30002e73i			0.581177i	−0.956848	+	0.290588i	$0.906149\pi$
$168$	3.72043e73	−	1.13415e74i	1.36580	−	4.16354i
$169$	−8.88189e72			−0.268068
$170$			2.57012e73i			0.638468i
$171$	3.86517e73	+	2.84164e73i	0.791220	+	0.581697i
$172$	−7.76936e73			−1.31204
$173$			7.95155e73i			1.10900i	0.832185	+	0.554499i	$0.187090\pi$
$173$			7.95155e73i			1.10900i	−0.832185	+	0.554499i	$0.812910\pi$
$174$	−9.54326e73	−	3.13056e73i	−1.10045	−	0.360991i
$175$	7.73306e73			0.738067
$176$		−	4.57909e74i		−	3.62127i
$177$	−1.07984e73	+	3.29182e73i	−0.0708343	+	0.215933i
$178$	2.85366e74			1.55433
$179$			2.99507e74i			1.35599i	0.735066	+	0.677996i	$0.237151\pi$
$179$			2.99507e74i			1.35599i	−0.735066	+	0.677996i	$0.762849\pi$
$180$	2.84948e74	−	3.87584e74i	1.07343	−	1.46007i
$181$	3.81264e74			1.19628			0.598140	−	0.801391i	$-0.295907\pi$
$181$	3.81264e74			1.19628			0.598140	+	0.801391i	$0.295907\pi$
$182$			9.80294e74i			2.56449i
$183$	−4.82139e74	−	1.58160e74i	−1.05266	−	0.345312i
$184$	4.68028e74			0.853658
$185$			2.92957e74i			0.446825i
$186$	−3.43424e74	+	1.04690e75i	−0.438434	+	1.33653i
$187$	−6.07317e74			−0.649595
$188$		−	3.59975e75i		−	3.22896i
$189$	1.24300e75	+	1.74163e75i	0.935908	+	1.31134i
$190$	−2.12618e75			−1.34503
$191$			2.30040e75i			1.22378i	0.790944	+	0.611888i	$0.209590\pi$
$191$			2.30040e75i			1.22378i	−0.790944	+	0.611888i	$0.790410\pi$
$192$	−2.83710e75	−	9.30676e74i	−1.27038	−	0.416733i
$193$	3.80178e75			1.43415			0.717076	−	0.696995i	$-0.245480\pi$
$193$	3.80178e75			1.43415			0.717076	+	0.696995i	$0.245480\pi$
$194$		−	9.57612e75i		−	3.04602i
$195$	−7.31239e74	+	2.22913e75i	−0.196299	+	0.598401i
$196$	−1.73225e76			−3.92791
$197$			5.24955e75i			1.00632i	0.864193	+	0.503160i	$0.167830\pi$
$197$			5.24955e75i			1.00632i	−0.864193	+	0.503160i	$0.832170\pi$
$198$	1.28788e76	+	9.46839e75i	2.08894	+	1.53577i
$199$	−5.99925e75			−0.824035			−0.412017	−	0.911176i	$-0.635176\pi$
$199$	−5.99925e75			−0.824035			−0.412017	+	0.911176i	$0.635176\pi$
$200$		−	1.07032e76i		−	1.24602i
$201$	−5.81333e75	−	1.90700e75i	−0.574058	−	0.188313i
$202$	2.27599e76			1.90798
$203$			1.40798e76i			1.00283i
$204$	−5.90634e75	+	1.80050e76i	−0.357703	+	1.09043i
$205$	2.24366e76			1.15632
$206$			6.62149e75i			0.290628i
$207$	−4.96971e75	+	6.75977e75i	−0.185913	+	0.252878i
$208$	6.96756e76			2.22326
$209$		−	5.02414e76i		−	1.36847i
$210$	−9.01071e76	−	2.95586e76i	−2.09663	−	0.687776i
$211$	−6.52623e76			−1.29820			−0.649099	−	0.760704i	$-0.724854\pi$
$211$	−6.52623e76			−1.29820			−0.649099	+	0.760704i	$0.724854\pi$
$212$			1.18531e76i			0.201721i
$213$	3.67555e76	−	1.12046e77i	0.535545	−	1.63257i
$214$	6.49180e76			0.810421
$215$			3.66532e76i			0.392322i
$216$	2.41056e77	−	1.72042e77i	2.21383	−	1.58002i
$217$	1.54456e77			1.21797
$218$			1.95391e77i			1.32386i
$219$	−3.12204e76	−	1.02415e76i	−0.181879	−	0.0596632i
$220$	−5.03801e77			−2.52528
$221$		−	9.24098e76i		−	0.398816i
$222$	−9.46712e76	+	2.88598e77i	−0.352022	+	1.07311i
$223$	−3.77171e77			−1.20914			−0.604572	−	0.796550i	$-0.706656\pi$
$223$	−3.77171e77			−1.20914			−0.604572	+	0.796550i	$0.706656\pi$
$224$			1.23216e78i			3.40786i
$225$	1.54587e77	+	1.13651e77i	0.369105	+	0.271363i
$226$	4.73695e77			0.977058
$227$		−	4.75811e77i		−	0.848362i	−0.905577	−	0.424181i	$-0.860562\pi$
$227$		−	4.75811e77i		−	0.848362i	0.905577	−	0.424181i	$-0.139438\pi$
$228$	−1.48950e78	−	4.88612e77i	−2.29715	−	0.753554i
$229$	−1.88017e77			−0.250973			−0.125486	−	0.992095i	$-0.540049\pi$
$229$	−1.88017e77			−0.250973			−0.125486	+	0.992095i	$0.540049\pi$
$230$		−	3.71845e77i		−	0.429877i
$231$	6.98467e77	−	2.12922e78i	0.699762	−	2.13317i
$232$	1.94876e78			1.69299
$233$		−	2.01626e77i		−	0.151985i	−0.997108	−	0.0759925i	$-0.975788\pi$
$233$		−	2.01626e77i		−	0.151985i	0.997108	−	0.0759925i	$-0.0242125\pi$
$234$	−1.44072e78	+	1.95965e78i	−0.942877	+	1.28249i
$235$	−1.69824e78			−0.965516
$236$		−	1.13204e78i		−	0.559457i
$237$	−1.67829e78	−	5.50542e77i	−0.721391	−	0.236644i
$238$	3.73544e78			1.39734
$239$		−	1.07288e78i		−	0.349478i	−0.984615	−	0.174739i	$-0.944092\pi$
$239$		−	1.07288e78i		−	0.349478i	0.984615	−	0.174739i	$-0.0559082\pi$
$240$	−2.10091e78	+	6.40447e78i	−0.596262	+	1.81766i
$241$	−1.96459e78			−0.486082			−0.243041	−	0.970016i	$-0.578145\pi$
$241$	−1.96459e78			−0.486082			−0.243041	+	0.970016i	$0.578145\pi$
$242$		−	8.11952e78i		−	1.75236i
$243$	−7.48067e76	+	5.30840e78i	−0.0140907	+	0.999901i
$244$	1.65805e79			2.72731
$245$			8.17218e78i			1.17451i
$246$	2.21027e79	+	7.25054e78i	2.77707	+	0.910987i
$247$	7.64476e78			0.840165
$248$		−	2.13781e79i		−	2.05619i
$249$	−2.23984e78	+	6.82797e78i	−0.188642	+	0.575060i
$250$	−2.70655e79			−1.99708
$251$		−	7.44822e78i		−	0.481748i	−0.970556	−	0.240874i	$-0.922566\pi$
$251$		−	7.44822e78i		−	0.481748i	0.970556	−	0.240874i	$-0.0774340\pi$
$252$	−5.63319e79	−	4.14146e79i	−3.19548	−	2.34929i
$253$	8.78668e78			0.437368
$254$			4.59110e79i			2.00634i
$255$	8.49416e78	+	2.78641e78i	0.326058	+	0.106959i
$256$	−1.90981e79			−0.644276
$257$		−	2.59001e79i		−	0.768259i	−0.923279	−	0.384129i	$-0.874502\pi$
$257$		−	2.59001e79i		−	0.768259i	0.923279	−	0.384129i	$-0.125498\pi$
$258$	−1.18447e79	+	3.61078e79i	−0.309083	+	0.942215i
$259$	4.25787e79			0.977913
$260$		−	7.66586e79i		−	1.55039i
$261$	−2.06927e79	+	2.81461e79i	−0.368707	+	0.501513i
$262$	1.20279e80			1.88907
$263$			1.30436e80i			1.80658i	0.429029	+	0.903291i	$0.358856\pi$
$263$			1.30436e80i			1.80658i	−0.429029	+	0.903291i	$0.641144\pi$
$264$	−2.94703e80	−	9.66737e79i	−3.60126	−	1.18135i
$265$	5.59191e78			0.0603179
$266$			3.09021e80i			2.94370i
$267$	3.09381e79	−	9.43126e79i	0.260389	−	0.793776i
$268$	1.99918e80			1.48732
$269$			1.72367e80i			1.13404i	0.823703	+	0.567022i	$0.191905\pi$
$269$			1.72367e80i			1.13404i	−0.823703	+	0.567022i	$0.808095\pi$
$270$	−1.36687e80	−	1.91517e80i	−0.795649	−	1.11482i
$271$	−5.01889e79			−0.258595			−0.129298	−	0.991606i	$-0.541272\pi$
$271$	−5.01889e79			−0.258595			−0.129298	+	0.991606i	$0.541272\pi$
$272$		−	2.65501e80i		−	1.21141i
$273$	3.23984e80	+	1.06279e80i	1.30965	+	0.429616i
$274$	2.33532e80			0.836715
$275$		−	2.00940e80i		−	0.638392i
$276$	8.54530e79	−	2.60497e80i	0.240839	−	0.734181i
$277$	−7.17984e80			−1.79590			−0.897950	−	0.440097i	$-0.854944\pi$
$277$	−7.17984e80			−1.79590			−0.897950	+	0.440097i	$0.854944\pi$
$278$		−	1.04484e81i		−	2.32044i
$279$	3.08765e80	+	2.27001e80i	0.609102	+	0.447805i
$280$	1.84001e81			3.22557
$281$			9.08058e78i			0.0141516i	0.999975	+	0.00707579i	$0.00225231\pi$
$281$			9.08058e78i			0.0141516i	−0.999975	+	0.00707579i	$0.997748\pi$
$282$	−1.67297e81	−	5.48798e80i	−2.31882	−	0.760662i
$283$	−3.06529e80			−0.378024			−0.189012	−	0.981975i	$-0.560529\pi$
$283$	−3.06529e80			−0.378024			−0.189012	+	0.981975i	$0.560529\pi$
$284$			3.85322e81i			4.22979i
$285$	−2.30511e80	+	7.02694e80i	−0.225326	+	0.686888i
$286$	2.54725e81			2.21816
$287$		−	3.26096e81i		−	2.53071i
$288$	−1.81087e81	+	2.46314e81i	−1.25296	+	1.70426i
$289$	1.26829e81			0.782693
$290$		−	1.54828e81i		−	0.852541i
$291$	−3.16487e81	−	1.03820e81i	−1.55556	−	0.510284i
$292$	1.07365e81			0.471226
$293$			4.55847e80i			0.178726i	0.995999	+	0.0893630i	$0.0284831\pi$
$293$			4.55847e80i			0.178726i	−0.995999	+	0.0893630i	$0.971517\pi$
$294$	−2.64090e81	+	8.05058e81i	−0.925315	+	2.82075i
$295$	−5.34059e80			−0.167287
$296$		−	5.89326e81i		−	1.65093i
$297$	4.52554e81	−	3.22989e81i	1.13425	−	0.809515i
$298$	−1.51048e82			−3.38827
$299$			1.33699e81i			0.268520i
$300$	−5.95723e81	−	1.95420e81i	−1.07163	−	0.351534i
$301$	5.32721e81			0.858629
$302$		−	9.62461e81i		−	1.39045i
$303$	2.46752e81	−	7.52205e81i	0.319635	−	0.974383i
$304$	2.19640e82			2.55202
$305$		−	7.82213e81i		−	0.815512i
$306$	7.46732e81	+	5.48989e81i	0.698807	+	0.513756i
$307$	−3.38069e81			−0.284079			−0.142039	−	0.989861i	$-0.545366\pi$
$307$	−3.38069e81			−0.284079			−0.142039	+	0.989861i	$0.545366\pi$
$308$			7.32229e82i			5.52680i
$309$	2.18838e81	+	7.17872e80i	0.148420	+	0.0486874i
$310$	−1.69847e82			−1.03544
$311$			8.74144e81i			0.479171i	0.970875	+	0.239585i	$0.0770115\pi$
$311$			8.74144e81i			0.479171i	−0.970875	+	0.239585i	$0.922989\pi$
$312$	1.47099e82	−	4.48421e82i	0.725285	−	2.21098i
$313$	1.89077e80			0.00838834			0.00419417	−	0.999991i	$-0.498665\pi$
$313$	1.89077e80			0.00838834			0.00419417	+	0.999991i	$0.498665\pi$
$314$		−	6.46736e82i		−	2.58255i
$315$	−1.95380e82	+	2.65755e82i	−0.702477	+	0.955504i
$316$	5.77154e82			1.86904
$317$			3.20279e82i			0.934487i	0.884129	+	0.467244i	$0.154753\pi$
$317$			3.20279e82i			0.934487i	−0.884129	+	0.467244i	$0.845247\pi$
$318$	5.50870e81	+	1.80706e81i	0.144862	+	0.0475202i
$319$	3.65857e82			0.867399
$320$		−	4.60285e82i		−	0.984186i
$321$	7.03812e81	−	2.14552e82i	0.135766	−	0.413872i
$322$	−5.40444e82			−0.940821
$323$		−	2.91306e82i		−	0.457790i
$324$	−5.17438e82	−	1.65579e83i	−0.734299	−	2.34975i
$325$	3.05751e82			0.391938
$326$			1.35616e83i			1.57083i
$327$	6.45761e82	+	2.11834e82i	0.676077	+	0.221779i
$328$	−4.51344e83			−4.27239
$329$			2.46824e83i			2.11311i
$330$	−7.68066e82	+	2.34139e83i	−0.594893	+	1.81349i
$331$	1.24989e83			0.876090			0.438045	−	0.898953i	$-0.355671\pi$
$331$	1.24989e83			0.876090			0.438045	+	0.898953i	$0.355671\pi$
$332$		−	2.34810e83i		−	1.48991i
$333$	8.51167e82	+	6.25770e82i	0.489052	+	0.359546i
$334$	−2.07775e83			−1.08133
$335$		−	9.43143e82i		−	0.444733i
$336$	9.30833e83	+	3.05349e83i	3.97810	+	1.30497i
$337$	−1.53455e83			−0.594557			−0.297279	−	0.954791i	$-0.596079\pi$
$337$	−1.53455e83			−0.594557			−0.297279	+	0.954791i	$0.596079\pi$
$338$		−	1.41954e83i		−	0.498765i
$339$	5.13559e82	−	1.56554e83i	0.163682	−	0.498971i
$340$	−2.92110e83			−0.844777
$341$		−	4.01348e83i		−	1.05348i
$342$	−4.54161e83	+	6.17747e83i	−1.08230	+	1.47214i
$343$	4.43331e83			0.959450
$344$		−	7.37331e83i		−	1.44955i
$345$	−1.22894e83	−	4.03138e82i	−0.219533	−	0.0720151i
$346$	−1.27085e84			−2.06339
$347$		−	3.48722e83i		−	0.514763i	−0.966310	−	0.257381i	$-0.917140\pi$
$347$		−	3.48722e83i		−	0.514763i	0.966310	−	0.257381i	$-0.0828597\pi$
$348$	3.55807e83	−	1.08465e84i	0.477638	−	1.45604i
$349$	5.29896e83			0.647070			0.323535	−	0.946216i	$-0.395129\pi$
$349$	5.29896e83			0.647070			0.323535	+	0.946216i	$0.395129\pi$
$350$			1.23593e84i			1.37324i
$351$	4.91462e83	+	6.88608e83i	0.496998	+	0.696366i
$352$	3.20171e84			2.94764
$353$		−	1.95479e84i		−	1.63883i	−0.573200	−	0.819415i	$-0.694298\pi$
$353$		−	1.95479e84i		−	1.63883i	0.573200	−	0.819415i	$-0.305702\pi$
$354$	−5.26112e83	−	1.72585e83i	−0.401763	−	0.131794i
$355$	1.81782e84			1.26478
$356$			3.24336e84i			2.05658i
$357$	4.04980e83	−	1.23455e84i	0.234090	−	0.713605i
$358$	−4.78683e84			−2.52295
$359$		−	6.24760e83i		−	0.300328i	−0.988661	−	0.150164i	$-0.952020\pi$
$359$		−	6.24760e83i		−	0.300328i	0.988661	−	0.150164i	$-0.0479802\pi$
$360$	3.67827e84	+	2.70423e84i	1.61310	+	1.18593i
$361$	−8.89558e82			−0.0355989
$362$			6.09351e84i			2.22579i
$363$	−2.68347e84	−	8.80282e83i	−0.894909	−	0.293564i
$364$	−1.11416e85			−3.39315
$365$		−	5.06513e83i		−	0.140905i
$366$	2.52778e84	−	7.70573e84i	0.642485	−	1.95857i
$367$	4.49725e83			0.104464			0.0522320	−	0.998635i	$-0.483366\pi$
$367$	4.49725e83			0.104464			0.0522320	+	0.998635i	$0.483366\pi$
$368$			3.84127e84i			0.815637i
$369$	4.79256e84	−	6.51880e84i	0.930459	−	1.26560i
$370$	−4.68215e84			−0.831359
$371$		−	8.12734e83i		−	0.132011i
$372$	−1.18987e85	−	3.90323e84i	−1.76841	−	0.580105i
$373$	6.13960e84			0.835120			0.417560	−	0.908649i	$-0.362885\pi$
$373$	6.13960e84			0.835120			0.417560	+	0.908649i	$0.362885\pi$
$374$		−	9.70638e84i		−	1.20863i
$375$	−2.93432e84	+	8.94506e84i	−0.334561	+	1.01989i
$376$	3.41625e85			3.56739
$377$			5.56690e84i			0.532536i
$378$	−2.78353e85	+	1.98662e85i	−2.43987	+	1.74134i
$379$	1.98477e84			0.159447			0.0797235	−	0.996817i	$-0.474596\pi$
$379$	1.98477e84			0.159447			0.0797235	+	0.996817i	$0.474596\pi$
$380$		−	2.41653e85i		−	1.77965i
$381$	1.51734e85	+	4.97746e84i	1.02461	+	0.336112i
$382$	−3.67658e85			−2.27695
$383$			7.51779e84i			0.427101i	0.976932	+	0.213550i	$0.0685028\pi$
$383$			7.51779e84i			0.427101i	−0.976932	+	0.213550i	$0.931497\pi$
$384$	2.22619e84	−	6.78636e84i	0.116046	−	0.353758i
$385$	3.45441e85			1.65261
$386$			6.07614e85i			2.66837i
$387$	1.06493e85	+	7.82928e84i	0.429398	+	0.315689i
$388$	1.08838e86			4.03028
$389$			5.04150e84i			0.171484i	0.996317	+	0.0857419i	$0.0273261\pi$
$389$			5.04150e84i			0.171484i	−0.996317	+	0.0857419i	$0.972674\pi$
$390$	−3.56268e85	−	1.16869e85i	−1.11338	−	0.365232i
$391$	5.09463e84			0.146312
$392$		−	1.64395e86i		−	4.33959i
$393$	1.30402e85	−	3.97519e85i	0.316467	−	0.964726i
$394$	−8.39003e85			−1.87235
$395$		−	2.72282e85i		−	0.558875i
$396$	−1.07614e86	+	1.46376e86i	−2.03202	+	2.76394i
$397$	−8.88518e85			−1.54376			−0.771880	−	0.635769i	$-0.780683\pi$
$397$	−8.88518e85			−1.54376			−0.771880	+	0.635769i	$0.780683\pi$
$398$		−	9.58823e85i		−	1.53319i
$399$	1.02130e86	+	3.35027e85i	1.50331	+	0.493144i
$400$	8.78450e85			1.19052
$401$			7.27457e85i			0.907911i	0.891024	+	0.453956i	$0.149988\pi$
$401$			7.27457e85i			0.907911i	−0.891024	+	0.453956i	$0.850012\pi$
$402$	3.04783e85	−	9.29109e85i	0.350374	−	1.06809i
$403$	6.10693e85			0.646780
$404$			2.58680e86i			2.52451i
$405$	−7.81147e85	+	2.44110e85i	−0.702614	+	0.219568i
$406$	−2.25029e86			−1.86586
$407$		−	1.10639e86i		−	0.845848i
$408$	−1.70872e86	−	5.60527e85i	−1.20472	−	0.395194i
$409$	2.28263e86			1.48445			0.742227	−	0.670148i	$-0.233769\pi$
$409$	2.28263e86			1.48445			0.742227	+	0.670148i	$0.233769\pi$
$410$			3.58590e86i			2.15145i
$411$	2.53185e85	−	7.71815e85i	0.140171	−	0.427300i
$412$	−7.52572e85			−0.384539
$413$			7.76207e85i			0.366122i
$414$	−1.08037e86	−	7.94278e85i	−0.470503	−	0.345909i
$415$	−1.10776e86			−0.445509
$416$			4.87174e86i			1.80969i
$417$	−3.45315e86	−	1.13277e86i	−1.18502	−	0.388732i
$418$	8.02977e86			2.54616
$419$		−	3.53899e86i		−	1.03709i	−0.855050	−	0.518545i	$-0.826474\pi$
$419$		−	3.53899e86i		−	1.03709i	0.855050	−	0.518545i	$-0.173526\pi$
$420$	3.35951e86	−	1.02412e87i	0.910017	−	2.77412i
$421$	2.28494e85			0.0572224			0.0286112	−	0.999591i	$-0.490892\pi$
$421$	2.28494e85			0.0572224			0.0286112	+	0.999591i	$0.490892\pi$
$422$		−	1.04305e87i		−	2.41542i
$423$	−3.62751e86	+	4.93412e86i	−0.776921	+	1.05676i
$424$	−1.12489e86			−0.222863
$425$		−	1.16508e86i		−	0.213560i
$426$	1.79077e87	+	5.87441e86i	3.03754	+	0.996431i
$427$	−1.13688e87			−1.78482
$428$			7.37833e86i			1.07229i
$429$	2.76161e86	−	8.41857e86i	0.371597	−	1.13279i
$430$	−5.85805e86			−0.729951
$431$		−	8.35213e86i		−	0.963934i	−0.876189	−	0.481967i	$-0.839922\pi$
$431$		−	8.35213e86i		−	0.963934i	0.876189	−	0.481967i	$-0.160078\pi$
$432$	1.41201e87	+	1.97843e87i	1.50964	+	2.11523i
$433$	1.87212e86			0.185453			0.0927264	−	0.995692i	$-0.470442\pi$
$433$	1.87212e86			0.185453			0.0927264	+	0.995692i	$0.470442\pi$
$434$			2.46858e87i			2.26614i
$435$	−5.11701e86	−	1.67857e86i	−0.435382	−	0.142822i
$436$	−2.22074e87			−1.75163
$437$			4.21462e86i			0.308227i
$438$	1.63683e86	−	4.98975e86i	0.111009	−	0.338403i
$439$	6.13531e86			0.385929			0.192964	−	0.981206i	$-0.438190\pi$
$439$	6.13531e86			0.385929			0.192964	+	0.981206i	$0.438190\pi$
$440$		−	4.78119e87i		−	2.78996i
$441$	2.37437e87	+	1.74561e87i	1.28551	+	0.945094i
$442$	1.47693e87			0.742035
$443$			2.38507e87i			1.11219i	0.831120	+	0.556093i	$0.187700\pi$
$443$			2.38507e87i			1.11219i	−0.831120	+	0.556093i	$0.812300\pi$
$444$	−3.28009e87	−	1.07600e87i	−1.41987	−	0.465771i
$445$	1.53011e87			0.614953
$446$		−	6.02810e87i		−	2.24973i
$447$	−1.63759e87	+	4.99208e87i	−0.567620	+	1.73035i
$448$	−6.68983e87			−2.15397
$449$		−	3.52036e87i		−	1.05307i	−0.850153	−	0.526535i	$-0.823491\pi$
$449$		−	3.52036e87i		−	1.05307i	0.850153	−	0.526535i	$-0.176509\pi$
$450$	−1.81641e87	+	2.47067e87i	−0.504896	+	0.686755i
$451$	−8.47345e87			−2.18894
$452$			5.38383e87i			1.29278i
$453$	−3.18090e87	−	1.04346e87i	−0.710083	−	0.232935i
$454$	7.60459e87			1.57846
$455$			5.25625e87i			1.01461i
$456$	4.63705e87	−	1.41357e88i	0.832535	−	2.53792i
$457$	1.60352e86			0.0267817			0.0133909	−	0.999910i	$-0.495737\pi$
$457$	1.60352e86			0.0267817			0.0133909	+	0.999910i	$0.495737\pi$
$458$		−	3.00496e87i		−	0.466958i
$459$	2.62396e87	−	1.87273e87i	0.379436	−	0.270805i
$460$	4.22625e87			0.568783
$461$			1.70468e87i			0.213556i	0.994283	+	0.106778i	$0.0340534\pi$
$461$			1.70468e87i			0.213556i	−0.994283	+	0.106778i	$0.965947\pi$
$462$	3.40300e88	+	1.11632e88i	3.96897	+	1.30197i
$463$	2.15247e87			0.233756			0.116878	−	0.993146i	$-0.462711\pi$
$463$	2.15247e87			0.233756			0.116878	+	0.993146i	$0.462711\pi$
$464$			1.59942e88i			1.61759i
$465$	−1.84141e87	+	5.61340e87i	−0.173461	+	0.528784i
$466$	3.22246e87			0.282782
$467$			1.53271e88i			1.25315i	0.779360	+	0.626576i	$0.215544\pi$
$467$			1.53271e88i			1.25315i	−0.779360	+	0.626576i	$0.784456\pi$
$468$	−2.22726e88	−	1.63746e88i	−1.69691	−	1.24755i
$469$	−1.37077e88			−0.973335
$470$		−	2.71419e88i		−	1.79643i
$471$	−2.13744e88	−	7.01162e87i	−1.31887	−	0.432642i
$472$	1.07434e88			0.618094
$473$		−	1.38425e88i		−	0.742673i
$474$	8.79897e87	−	2.68230e88i	0.440298	−	1.34222i
$475$	9.63829e87			0.449895
$476$			4.24556e88i			1.84887i
$477$	1.19446e87	−	1.62469e87i	0.0485360	−	0.0660183i
$478$	1.71471e88			0.650236
$479$			2.97597e87i			0.105331i	0.998612	+	0.0526655i	$0.0167717\pi$
$479$			2.97597e87i			0.105331i	−0.998612	+	0.0526655i	$0.983228\pi$
$480$	−4.47802e88	−	1.46896e88i	−1.47954	−	0.485344i
$481$	1.68349e88			0.519305
$482$		−	3.13988e88i		−	0.904400i
$483$	−5.85925e87	+	1.78615e88i	−0.157611	+	0.480466i
$484$	9.22833e88			2.31860
$485$		−	5.13462e88i		−	1.20512i
$486$	−8.48409e88	−	1.19559e87i	−1.86041	−	0.0262171i
$487$	−6.09769e88			−1.24942			−0.624712	−	0.780855i	$-0.714784\pi$
$487$	−6.09769e88			−1.24942			−0.624712	+	0.780855i	$0.714784\pi$
$488$			1.57353e89i			3.01316i
$489$	4.48204e88	+	1.47028e88i	0.802202	+	0.263153i
$490$	−1.30611e89			−2.18529
$491$		−	1.18921e89i		−	1.86024i	−0.367251	−	0.930122i	$-0.619701\pi$
$491$		−	1.18921e89i		−	1.86024i	0.367251	−	0.930122i	$-0.380299\pi$
$492$	−8.24068e88	+	2.51211e89i	−1.20535	+	3.67443i
$493$	2.12128e88			0.290169
$494$			1.22181e89i			1.56320i
$495$	6.90551e88	+	5.07686e88i	0.826465	+	0.607609i
$496$	1.75457e89			1.96461
$497$		−	2.64204e89i		−	2.76808i
$498$	−1.09127e89	−	3.57979e88i	−1.06995	−	0.350985i
$499$	−4.16945e88			−0.382614			−0.191307	−	0.981530i	$-0.561273\pi$
$499$	−4.16945e88			−0.382614			−0.191307	+	0.981530i	$0.561273\pi$
$500$		−	3.07616e89i		−	2.64240i
$501$	−2.25260e88	+	6.86689e88i	−0.181150	+	0.552224i
$502$	1.19040e89			0.896336
$503$			2.22826e89i			1.57117i	0.618754	+	0.785585i	$0.287638\pi$
$503$			2.22826e89i			1.57117i	−0.618754	+	0.785585i	$0.712362\pi$
$504$	3.93035e89	−	5.34604e89i	2.59552	−	3.53040i
$505$	1.22036e89			0.754872
$506$			1.40432e89i			0.813765i
$507$	−4.69152e88	−	1.53900e88i	−0.254713	−	0.0835556i
$508$	−5.21806e89			−2.65465
$509$			1.08847e89i			0.518957i	0.965749	+	0.259478i	$0.0835506\pi$
$509$			1.08847e89i			0.518957i	−0.965749	+	0.259478i	$0.916449\pi$
$510$	−4.45335e88	+	1.35757e89i	−0.199008	+	0.606661i
$511$	−7.36171e88			−0.308382
$512$		−	4.00034e89i		−	1.57104i
$513$	1.54925e89	+	2.17072e89i	0.570490	+	0.799338i
$514$	4.13944e89			1.42942
$515$			3.55038e88i			0.114984i
$516$	−4.10387e89	−	1.34623e89i	−1.24667	−	0.408957i
$517$	6.41361e89			1.82774
$518$			6.80509e89i			1.81950i
$519$	−1.37780e89	+	4.20010e89i	−0.345670	+	1.05375i
$520$	7.27509e89			1.71288
$521$		−	1.04134e89i		−	0.230117i	−0.993359	−	0.115059i	$-0.963294\pi$
$521$		−	1.04134e89i		−	0.230117i	0.993359	−	0.115059i	$-0.0367056\pi$
$522$	−4.49842e89	−	3.30719e89i	−0.933111	−	0.686014i
$523$	−3.10110e89			−0.603893			−0.301947	−	0.953325i	$-0.597636\pi$
$523$	−3.10110e89			−0.603893			−0.301947	+	0.953325i	$0.597636\pi$
$524$			1.36705e90i			2.49949i
$525$	4.08469e89	+	1.33994e89i	0.701297	+	0.230052i
$526$	−2.08468e90			−3.36131
$527$		−	2.32707e89i		−	0.352418i
$528$	7.93435e89	−	2.41873e90i	1.12874	−	3.44086i
$529$	6.74524e89			0.901489
$530$			8.93720e88i			0.112227i
$531$	−1.14077e89	+	1.55167e89i	−0.134611	+	0.183097i
$532$	−3.51221e90			−3.89490
$533$		−	1.28933e90i		−	1.34389i
$534$	1.50734e90	+	4.94465e89i	1.47689	+	0.484478i
$535$	3.48084e89			0.320634
$536$			1.89727e90i			1.64320i
$537$	−5.18967e89	+	1.58203e90i	−0.422657	+	1.28844i
$538$	−2.75484e90			−2.10999
$539$		−	3.08632e90i		−	2.22337i
$540$	2.17671e90	−	1.55353e90i	1.47505	−	1.05275i
$541$	1.93782e90			1.23539			0.617694	−	0.786418i	$-0.288067\pi$
$541$	1.93782e90			1.23539			0.617694	+	0.786418i	$0.288067\pi$
$542$		−	8.02138e89i		−	0.481141i
$543$	2.01388e90	+	6.60631e89i	1.13668	+	0.372876i
$544$	1.85639e90			0.986065
$545$			1.04767e90i			0.523769i
$546$	−1.69859e90	+	5.17803e90i	−0.799341	+	2.43673i
$547$	−6.14579e89			−0.272268			−0.136134	−	0.990690i	$-0.543468\pi$
$547$	−6.14579e89			−0.272268			−0.136134	+	0.990690i	$0.543468\pi$
$548$			2.65423e90i			1.10708i
$549$	−2.27267e90	−	1.67084e90i	−0.892583	−	0.656218i
$550$	3.21150e90			1.18779
$551$			1.75487e90i			0.611283i
$552$	2.47218e90	+	8.10970e89i	0.811131	+	0.266082i
$553$	−3.95737e90			−1.22314
$554$		−	1.14751e91i		−	3.34144i
$555$	−5.07618e89	+	1.54743e90i	−0.139273	+	0.424565i
$556$	1.18752e91			3.07025
$557$		−	7.14969e90i		−	1.74207i	−0.491221	−	0.871035i	$-0.663449\pi$
$557$		−	7.14969e90i		−	1.74207i	0.491221	−	0.871035i	$-0.336551\pi$
$558$	−3.62802e90	+	4.93480e90i	−0.833184	+	1.13329i
$559$	2.10628e90			0.455961
$560$			1.51016e91i			3.08191i
$561$	−3.20792e90	−	1.05232e90i	−0.617234	−	0.202476i
$562$	−1.45129e89			−0.0263303
$563$		−	8.65237e90i		−	1.48033i	−0.672427	−	0.740164i	$-0.734748\pi$
$563$		−	8.65237e90i		−	1.48033i	0.672427	−	0.740164i	$-0.265252\pi$
$564$	6.23742e90	−	1.90143e91i	1.00646	−	3.06810i
$565$	2.53991e90			0.386562
$566$		−	4.89907e90i		−	0.703350i
$567$	3.54792e90	+	1.13533e91i	0.480543	+	1.53773i
$568$	−3.65680e91			−4.67312
$569$		−	6.71200e90i		−	0.809370i	−0.914456	−	0.404685i	$-0.867381\pi$
$569$		−	6.71200e90i		−	0.809370i	0.914456	−	0.404685i	$-0.132619\pi$
$570$	−1.12307e91	−	3.68411e90i	−1.27802	−	0.419239i
$571$	−1.67460e91			−1.79854			−0.899270	−	0.437395i	$-0.855901\pi$
$571$	−1.67460e91			−1.79854			−0.899270	+	0.437395i	$0.855901\pi$
$572$			2.89510e91i			2.93491i
$573$	−3.98599e90	+	1.21510e91i	−0.381446	+	1.16281i
$574$	5.21179e91			4.70863
$575$			1.68563e90i			0.143788i
$576$	−1.33733e91	−	9.83189e90i	−1.07720	−	0.791945i
$577$	−1.52909e91			−1.16314			−0.581568	−	0.813498i	$-0.697561\pi$
$577$	−1.52909e91			−1.16314			−0.581568	+	0.813498i	$0.697561\pi$
$578$			2.02704e91i			1.45627i
$579$	2.00814e91	+	6.58748e90i	1.36271	+	0.447020i
$580$	1.75971e91			1.12802
$581$			1.61002e91i			0.975034i
$582$	1.65929e91	−	5.05822e91i	0.949432	−	2.89427i
$583$	−2.11185e90			−0.114183
$584$			1.01892e91i			0.520616i
$585$	−7.72498e90	+	1.05075e91i	−0.373039	+	0.507405i
$586$	−7.28552e90			−0.332536
$587$		−	1.88035e91i		−	0.811298i	−0.914029	−	0.405649i	$-0.867046\pi$
$587$		−	1.88035e91i		−	0.811298i	0.914029	−	0.405649i	$-0.132954\pi$
$588$	−9.14997e91	−	3.00154e91i	−3.73223	−	1.22431i
$589$	1.92511e91			0.742421
$590$		−	8.53553e90i		−	0.311253i
$591$	−9.09609e90	+	2.77287e91i	−0.313666	+	0.956188i
$592$	4.83680e91			1.57740
$593$			5.09013e91i			1.57009i	0.619440	+	0.785044i	$0.287360\pi$
$593$			5.09013e91i			1.57009i	−0.619440	+	0.785044i	$0.712640\pi$
$594$	5.16213e91	+	7.23288e91i	1.50618	+	2.11037i
$595$	2.00291e91			0.552842
$596$		−	1.71675e92i		−	4.48313i
$597$	−3.16888e91	−	1.03951e91i	−0.782983	−	0.256848i
$598$	−2.13682e91			−0.499608
$599$		−	6.40912e91i		−	1.41812i	−0.705147	−	0.709061i	$-0.749119\pi$
$599$		−	6.40912e91i		−	1.41812i	0.705147	−	0.709061i	$-0.250881\pi$
$600$	1.85458e91	−	5.65356e91i	0.388379	−	1.18394i
$601$	3.03034e91			0.600667			0.300333	−	0.953834i	$-0.402902\pi$
$601$	3.03034e91			0.600667			0.300333	+	0.953834i	$0.402902\pi$
$602$			8.51415e91i			1.59756i
$603$	−2.74024e91	−	2.01460e91i	−0.486763	−	0.357863i
$604$	1.09390e92			1.83974
$605$		−	4.35361e91i		−	0.693302i
$606$	1.20220e92	+	3.94369e91i	1.81293	+	0.594711i
$607$	−9.87115e91			−1.40975			−0.704873	−	0.709333i	$-0.748996\pi$
$607$	−9.87115e91			−1.40975			−0.704873	+	0.709333i	$0.748996\pi$
$608$			1.53573e92i			2.07729i
$609$	−2.43966e91	+	7.43711e91i	−0.312578	+	0.952870i
$610$	1.25016e92			1.51734
$611$			9.75898e91i			1.12213i
$612$	−6.23960e91	+	8.48706e91i	−0.679766	+	0.924614i
$613$	−8.91984e91			−0.920791			−0.460396	−	0.887714i	$-0.652292\pi$
$613$	−8.91984e91			−0.920791			−0.460396	+	0.887714i	$0.652292\pi$
$614$		−	5.40314e91i		−	0.528555i
$615$	1.18513e92	+	3.88767e91i	1.09872	+	0.360422i
$616$	−6.94904e92			−6.10606
$617$		−	9.63188e91i		−	0.802233i	−0.916027	−	0.401117i	$-0.868622\pi$
$617$		−	9.63188e91i		−	0.802233i	0.916027	−	0.401117i	$-0.131378\pi$
$618$	−1.14733e91	+	3.49755e91i	−0.0905875	+	0.276149i
$619$	1.59150e92			1.19128			0.595642	−	0.803250i	$-0.296898\pi$
$619$	1.59150e92			1.19128			0.595642	+	0.803250i	$0.296898\pi$
$620$		−	1.93042e92i		−	1.37002i
$621$	−3.79635e91	+	2.70947e91i	−0.255472	+	0.182331i
$622$	−1.39709e92			−0.891542
$623$		−	2.22388e92i		−	1.34588i
$624$	3.68035e92	+	1.20730e92i	2.11250	+	0.692982i
$625$	−6.09789e91			−0.332001
$626$			3.02190e90i			0.0156073i
$627$	8.70552e91	−	2.65381e92i	0.426546	−	1.30029i
$628$	7.35054e92			3.41705
$629$		−	6.41498e91i		−	0.282959i
$630$	−4.24739e92	−	3.12264e92i	−1.77781	−	1.30702i
$631$	−1.82313e92			−0.724186			−0.362093	−	0.932142i	$-0.617938\pi$
$631$	−1.82313e92			−0.724186			−0.362093	+	0.932142i	$0.617938\pi$
$632$			5.47734e92i			2.06493i
$633$	−3.44723e92	−	1.13082e92i	−1.23352	−	0.404643i
$634$	−5.11883e92			−1.73870
$635$			2.46170e92i			0.793785i
$636$	−2.05384e91	+	6.26097e91i	−0.0628755	+	0.191671i
$637$	4.69617e92			1.36503
$638$			5.84726e92i			1.61388i
$639$	3.88294e92	−	5.28155e92i	1.01773	−	1.38431i
$640$	1.10100e92			0.274063
$641$			6.84495e92i			1.61829i	0.587612	+	0.809143i	$0.300068\pi$
$641$			6.84495e92i			1.61829i	−0.587612	+	0.809143i	$0.699932\pi$
$642$	3.42905e92	+	1.12486e92i	0.770047	+	0.252605i
$643$	−1.78711e92			−0.381232			−0.190616	−	0.981665i	$-0.561049\pi$
$643$	−1.78711e92			−0.381232			−0.190616	+	0.981665i	$0.561049\pi$
$644$		−	6.14248e92i		−	1.24483i
$645$	−6.35103e91	+	1.93606e92i	−0.122285	+	0.372777i
$646$	4.65576e92			0.851761
$647$		−	1.51743e92i		−	0.263796i	−0.991263	−	0.131898i	$-0.957893\pi$
$647$		−	1.51743e92i		−	0.263796i	0.991263	−	0.131898i	$-0.0421071\pi$
$648$	1.57139e93	−	4.91062e92i	2.59602	−	0.811262i
$649$	2.01694e92			0.316678
$650$			4.88663e92i			0.729237i
$651$	8.15857e92	+	2.67632e92i	1.15729	+	0.379635i
$652$	−1.54135e93			−2.07841
$653$		−	5.90649e92i		−	0.757172i	−0.925566	−	0.378586i	$-0.876411\pi$
$653$		−	5.90649e92i		−	0.757172i	0.925566	−	0.378586i	$-0.123589\pi$
$654$	−3.38562e92	+	1.03208e93i	−0.412641	+	1.25790i
$655$	6.44927e92			0.747391
$656$		−	3.70434e93i		−	4.08211i
$657$	−1.47164e92	−	1.08193e92i	−0.154221	−	0.113382i
$658$	−3.94483e93			−3.93164
$659$			5.09242e92i			0.482732i	0.970434	+	0.241366i	$0.0775954\pi$
$659$			5.09242e92i			0.482732i	−0.970434	+	0.241366i	$0.922405\pi$
$660$	−2.66113e93	−	8.72954e92i	−2.39948	−	0.787121i
$661$	1.93661e93			1.66109			0.830546	−	0.556949i	$-0.188028\pi$
$661$	1.93661e93			1.66109			0.830546	+	0.556949i	$0.188028\pi$
$662$			1.99762e93i			1.63005i
$663$	1.60122e92	−	4.88119e92i	0.124309	−	0.378948i
$664$	2.22841e93			1.64607
$665$			1.65694e93i			1.16464i
$666$	−1.00013e93	+	1.36037e93i	−0.668969	+	0.909928i
$667$	−3.06908e92			−0.195369
$668$		−	2.36149e93i		−	1.43075i
$669$	−1.99226e93	−	6.53539e92i	−1.14891	−	0.376886i
$670$	1.50737e93			0.827467
$671$			2.95412e93i			1.54378i
$672$	−2.13501e93	+	6.50841e93i	−1.06222	+	3.23809i
$673$	2.91428e93			1.38049			0.690246	−	0.723574i	$-0.257502\pi$
$673$	2.91428e93			1.38049			0.690246	+	0.723574i	$0.257502\pi$
$674$		−	2.45257e93i		−	1.10623i
$675$	6.19621e92	+	8.68177e92i	0.266135	+	0.372893i
$676$	1.61339e93			0.659931
$677$		−	4.14164e93i		−	1.61341i	−0.590951	−	0.806707i	$-0.701247\pi$
$677$		−	4.14164e93i		−	1.61341i	0.590951	−	0.806707i	$-0.298753\pi$
$678$	2.50211e93	+	8.20789e92i	0.928382	+	0.304545i
$679$	−7.46272e93			−2.63751
$680$		−	2.77220e93i		−	0.933319i
$681$	8.24456e92	−	2.51329e93i	0.264431	−	0.806098i
$682$	6.41450e93			1.96010
$683$			6.24755e93i			1.81897i	0.415732	+	0.909487i	$0.363525\pi$
$683$			6.24755e93i			1.81897i	−0.415732	+	0.909487i	$0.636475\pi$
$684$	−7.02107e93	−	5.16182e93i	−1.94783	−	1.43203i
$685$	1.25218e93			0.331037
$686$			7.08548e93i			1.78515i
$687$	−9.93129e92	−	3.25784e92i	−0.238470	−	0.0782272i
$688$	6.05154e93			1.38499
$689$		−	3.21341e92i		−	0.0701021i
$690$	6.44311e92	−	1.96413e93i	0.133991	−	0.408461i
$691$	−4.57682e93			−0.907377			−0.453689	−	0.891160i	$-0.649892\pi$
$691$	−4.57682e93			−0.907377			−0.453689	+	0.891160i	$0.649892\pi$
$692$		−	1.44440e94i		−	2.73014i
$693$	7.37877e93	−	1.00365e94i	1.32980	−	1.80879i
$694$	5.57341e93			0.957765
$695$		−	5.60232e93i		−	0.918057i
$696$	1.02936e94	+	3.37669e93i	1.60865	+	0.527700i
$697$	−4.91302e93			−0.732262
$698$			8.46899e93i			1.20393i
$699$	3.49364e92	−	1.06501e93i	0.0473731	−	0.144413i
$700$	−1.40471e94			−1.81698
$701$			1.56969e94i			1.93695i	0.249115	+	0.968474i	$0.419860\pi$
$701$			1.56969e94i			1.93695i	−0.249115	+	0.968474i	$0.580140\pi$
$702$	−1.10056e94	+	7.85473e93i	−1.29565	+	0.924712i
$703$	5.30690e93			0.596095
$704$			1.73832e94i			1.86308i
$705$	−8.97030e93	−	2.94260e93i	−0.917416	−	0.300947i
$706$	3.12421e94			3.04920
$707$		−	1.77369e94i		−	1.65210i
$708$	1.96153e93	−	5.97958e93i	0.174380	−	0.531585i
$709$	−1.48811e94			−1.26272			−0.631362	−	0.775488i	$-0.717504\pi$
$709$	−1.48811e94			−1.26272			−0.631362	+	0.775488i	$0.717504\pi$
$710$			2.90531e94i			2.35324i
$711$	−7.91096e93	−	5.81606e93i	−0.611692	−	0.449709i
$712$	−3.07803e94			−2.27213
$713$			3.36680e93i			0.237281i
$714$	1.97310e94	+	6.47254e93i	1.32773	+	0.435546i
$715$	1.36581e94			0.877589
$716$		−	5.44053e94i		−	3.33819i
$717$	1.85902e93	−	5.66707e93i	0.108931	−	0.332068i
$718$	9.98515e93			0.558789
$719$			3.45601e94i			1.84723i	0.383318	+	0.923617i	$0.374781\pi$
$719$			3.45601e94i			1.84723i	−0.383318	+	0.923617i	$0.625219\pi$
$720$	−2.21945e94	+	3.01889e94i	−1.13311	+	1.54125i
$721$	5.16016e93			0.251651
$722$		−	1.42172e93i		−	0.0662351i
$723$	−1.03772e94	−	3.40412e93i	−0.461866	−	0.151510i
$724$	−6.92564e94			−2.94501
$725$			7.01858e93i			0.285164i
$726$	1.40690e94	−	4.28883e94i	0.546204	−	1.66506i
$727$	−2.52698e94			−0.937489			−0.468744	−	0.883334i	$-0.655293\pi$
$727$	−2.52698e94			−0.937489			−0.468744	+	0.883334i	$0.655293\pi$
$728$		−	1.05737e95i		−	3.74879i
$729$	−9.59321e93	+	2.79100e94i	−0.325054	+	0.945695i
$730$	8.09528e93			0.262167
$731$		−	8.02606e93i		−	0.248444i
$732$	8.75804e94	+	2.87297e94i	2.59144	+	0.850091i
$733$	3.24547e94			0.918009			0.459005	−	0.888434i	$-0.348206\pi$
$733$	3.24547e94			0.918009			0.459005	+	0.888434i	$0.348206\pi$
$734$			7.18767e93i			0.194365i
$735$	−1.41602e94	+	4.31664e94i	−0.366091	+	1.11600i
$736$	−2.68583e94			−0.663912
$737$			3.56190e94i			0.841888i
$738$	1.04186e95	+	7.65965e94i	2.35477	+	1.73121i
$739$	3.56294e94			0.770091			0.385045	−	0.922898i	$-0.374186\pi$
$739$	3.56294e94			0.770091			0.385045	+	0.922898i	$0.374186\pi$
$740$		−	5.32155e94i		−	1.10000i
$741$	4.03805e94	+	1.32464e94i	0.798309	+	0.261876i
$742$	1.29894e94			0.245618
$743$		−	2.21600e94i		−	0.400810i	−0.979713	−	0.200405i	$-0.935774\pi$
$743$		−	2.21600e94i		−	0.400810i	0.979713	−	0.200405i	$-0.0642258\pi$
$744$	3.70426e94	−	1.12922e95i	0.640907	−	1.95376i
$745$	−8.09905e94			−1.34053
$746$			9.81255e94i			1.55382i
$747$	−2.36621e94	+	3.21851e94i	−0.358488	+	0.487613i
$748$	1.10319e95			1.59918
$749$		−	5.05909e94i		−	0.701734i
$750$	−1.42963e95	−	4.68974e94i	−1.89759	−	0.622483i
$751$	−6.16631e94			−0.783262			−0.391631	−	0.920122i	$-0.628089\pi$
$751$	−6.16631e94			−0.783262			−0.391631	+	0.920122i	$0.628089\pi$
$752$			2.80384e95i			3.40851i
$753$	1.29058e94	−	3.93424e94i	0.150159	−	0.457748i
$754$	−8.89723e94			−0.990833
$755$		−	5.16063e94i		−	0.550114i
$756$	−2.25791e95	−	3.16365e95i	−2.30403	−	3.22827i
$757$	2.49483e94			0.243712			0.121856	−	0.992548i	$-0.461115\pi$
$757$	2.49483e94			0.243712			0.121856	+	0.992548i	$0.461115\pi$
$758$			3.17214e94i			0.296666i
$759$	4.64123e94	+	1.52250e94i	0.415580	+	0.136326i
$760$	2.29335e95			1.96617
$761$		−	1.09407e95i		−	0.898158i	−0.893492	−	0.449079i	$-0.851752\pi$
$761$		−	1.09407e95i		−	0.898158i	0.893492	−	0.449079i	$-0.148248\pi$
$762$	−7.95517e94	+	2.42507e95i	−0.625368	+	1.90639i
$763$	1.52269e95			1.14631
$764$		−	4.17866e95i		−	3.01270i
$765$	4.00390e94	+	2.94363e94i	0.276475	+	0.203262i
$766$	−1.20152e95			−0.794661
$767$			3.06898e94i			0.194423i
$768$	−1.00879e95	−	3.30921e94i	−0.612180	−	0.200818i
$769$	2.11016e95			1.22672			0.613361	−	0.789803i	$-0.289817\pi$
$769$	2.11016e95			1.22672			0.613361	+	0.789803i	$0.289817\pi$
$770$			5.52096e95i			3.07483i
$771$	4.48780e94	−	1.36807e95i	0.239463	−	0.729986i
$772$	−6.90590e95			−3.53061
$773$		−	9.91090e94i		−	0.485500i	−0.970089	−	0.242750i	$-0.921950\pi$
$773$		−	9.91090e94i		−	0.485500i	0.970089	−	0.242750i	$-0.0780495\pi$
$774$	−1.25131e95	+	1.70202e95i	−0.587370	+	0.798936i
$775$	7.69944e94			0.346340
$776$			1.03290e96i			4.45270i
$777$	2.24906e95	+	7.37777e94i	0.929195	+	0.304812i
$778$	−8.05752e94			−0.319062
$779$		−	4.06438e95i		−	1.54262i
$780$	1.32829e95	−	4.04920e95i	0.483250	−	1.47315i
$781$	−6.86521e95			−2.39425
$782$			8.14242e94i			0.272227i
$783$	−1.58071e95	+	1.12816e95i	−0.506658	+	0.361604i
$784$	1.34925e96			4.14631
$785$		−	3.46774e95i		−	1.02176i
$786$	6.35330e95	+	2.08413e95i	1.79496	+	0.588817i
$787$	6.29908e95			1.70652			0.853259	−	0.521487i	$-0.174623\pi$
$787$	6.29908e95			1.70652			0.853259	+	0.521487i	$0.174623\pi$
$788$		−	9.53578e95i		−	2.47737i
$789$	−2.26011e95	+	6.88978e95i	−0.563104	+	1.71658i
$790$	4.35171e95			1.03984
$791$		−	3.69153e95i		−	0.846023i
$792$	−1.38914e96	−	1.02128e96i	−3.05363	−	2.24500i
$793$	−4.49501e95			−0.947797
$794$		−	1.42006e96i		−	2.87231i
$795$	2.95371e94	+	9.68931e93i	0.0573130	+	0.0188009i
$796$	1.08976e96			2.02862
$797$			2.01285e95i			0.359490i	0.983713	+	0.179745i	$0.0575273\pi$
$797$			2.01285e95i			0.359490i	−0.983713	+	0.179745i	$0.942473\pi$
$798$	−5.35452e95	+	1.63229e96i	−0.917541	+	2.79705i
$799$	3.71869e95			0.611429
$800$			6.14214e95i			0.969059i
$801$	3.26838e95	−	4.44563e95i	0.494834	−	0.673069i
$802$	−1.16265e96			−1.68925
$803$			1.91291e95i			0.266735i
$804$	1.05599e96	+	3.46405e95i	1.41322	+	0.463590i
$805$	−2.89781e95			−0.372225
$806$			9.76033e95i			1.20340i
$807$	−2.98667e95	+	9.10465e95i	−0.353477	+	1.07755i
$808$	−2.45493e96			−2.78911
$809$			1.22048e96i			1.33116i	0.746328	+	0.665578i	$0.231815\pi$
$809$			1.22048e96i			1.33116i	−0.746328	+	0.665578i	$0.768185\pi$
$810$	−3.90145e95	−	1.24846e96i	−0.408527	−	1.30728i
$811$	1.66203e96			1.67090			0.835452	−	0.549563i	$-0.185206\pi$
$811$	1.66203e96			1.67090			0.835452	+	0.549563i	$0.185206\pi$
$812$		−	2.55759e96i		−	2.46877i
$813$	−2.65104e95	−	8.69642e94i	−0.245713	−	0.0806032i
$814$	1.76827e96			1.57378
$815$			7.27158e95i			0.621481i
$816$	4.60044e95	−	1.40241e96i	0.377593	−	1.15106i
$817$	6.63970e95			0.523384
$818$			3.64819e96i			2.76197i
$819$	1.52717e96	+	1.12276e96i	1.11050	+	0.816427i
$820$	−4.07560e96			−2.84665
$821$			1.11692e96i			0.749371i	0.927152	+	0.374686i	$0.122249\pi$
$821$			1.11692e96i			0.749371i	−0.927152	+	0.374686i	$0.877751\pi$
$822$	1.23354e96	+	4.04650e95i	0.795032	+	0.260801i
$823$	−3.06615e96			−1.89845			−0.949225	−	0.314597i	$-0.898130\pi$
$823$	−3.06615e96			−1.89845			−0.949225	+	0.314597i	$0.898130\pi$
$824$		−	7.14210e95i		−	0.424842i
$825$	3.48176e95	−	1.06139e96i	0.198984	−	0.606588i
$826$	−1.24056e96			−0.681204
$827$		−	3.42279e96i		−	1.80592i	−0.429725	−	0.902960i	$-0.641389\pi$
$827$		−	3.42279e96i		−	1.80592i	0.429725	−	0.902960i	$-0.358611\pi$
$828$	9.02746e95	−	1.22791e96i	0.457683	−	0.622537i
$829$	−2.78401e95			−0.135635			−0.0678173	−	0.997698i	$-0.521604\pi$
$829$	−2.78401e95			−0.135635			−0.0678173	+	0.997698i	$0.521604\pi$
$830$		−	1.77046e96i		−	0.828912i
$831$	−3.79248e96	−	1.24408e96i	−1.70643	−	0.559775i
$832$	−2.64504e96			−1.14383
$833$		−	1.78949e96i		−	0.743779i
$834$	1.81043e96	−	5.51896e96i	0.723273	−	2.20484i
$835$	−1.11407e96			−0.427818
$836$			9.12632e96i			3.36890i
$837$	1.23760e96	+	1.73406e96i	0.439178	+	0.615351i
$838$	5.65615e96			1.92960
$839$			1.20263e96i			0.394447i	0.980359	+	0.197224i	$0.0631925\pi$
$839$			1.20263e96i			0.394447i	−0.980359	+	0.197224i	$0.936807\pi$
$840$	9.71917e96	+	3.18826e96i	3.06488	+	1.00540i
$841$	2.02024e96			0.612540
$842$			3.65188e95i			0.106468i
$843$	−1.57343e94	+	4.79647e94i	−0.00441099	+	0.0134466i
$844$	1.18549e97			3.19592
$845$		−	7.61143e95i		−	0.197331i
$846$	−7.88590e96	−	5.79763e96i	−1.96621	−	1.44553i
$847$	−6.32759e96			−1.51735
$848$		−	9.23239e95i		−	0.212937i
$849$	−1.61912e96	−	5.31135e95i	−0.359192	−	0.117829i
$850$	1.86207e96			0.397348
$851$			9.28120e95i			0.190515i
$852$	−6.67662e96	+	2.03532e97i	−1.31841	+	4.01907i
$853$	2.48273e95			0.0471640			0.0235820	−	0.999722i	$-0.492493\pi$
$853$	2.48273e95			0.0471640			0.0235820	+	0.999722i	$0.492493\pi$
$854$		−	1.81700e97i		−	3.32082i
$855$	−2.43517e96	+	3.31230e96i	−0.428201	+	0.582436i
$856$	−7.00222e96			−1.18468
$857$			6.73838e96i			1.09695i	0.836166	+	0.548477i	$0.184792\pi$
$857$			6.73838e96i			1.09695i	−0.836166	+	0.548477i	$0.815208\pi$
$858$	1.34549e97	+	4.41372e96i	2.10765	+	0.691391i
$859$	−1.86782e96			−0.281553			−0.140777	−	0.990041i	$-0.544960\pi$
$859$	−1.86782e96			−0.281553			−0.140777	+	0.990041i	$0.544960\pi$
$860$		−	6.65803e96i		−	0.965821i
$861$	5.65038e96	−	1.72248e97i	0.788813	−	2.40464i
$862$	1.33487e97			1.79349
$863$		−	6.91247e96i		−	0.893876i	−0.894565	−	0.446938i	$-0.852514\pi$
$863$		−	6.91247e96i		−	0.893876i	0.894565	−	0.446938i	$-0.147486\pi$
$864$	−1.38332e97	+	9.87282e96i	−1.72175	+	1.22882i
$865$	−6.81416e96			−0.816359
$866$			2.99209e96i			0.345052i
$867$	6.69928e96	+	2.19762e96i	0.743700	+	0.243962i
$868$	−2.80569e97			−2.99840
$869$			1.02831e97i			1.05796i
$870$	2.68276e96	−	8.17819e96i	0.265734	−	0.810069i
$871$	−5.41980e96			−0.516873
$872$		−	2.10754e97i		−	1.93522i
$873$	−1.49183e97	−	1.09678e97i	−1.31901	−	0.969726i
$874$	−6.73596e96			−0.573485
$875$			2.10923e97i			1.72925i
$876$	5.67116e96	+	1.86036e96i	0.447751	+	0.146879i
$877$	4.36121e96			0.331605			0.165802	−	0.986159i	$-0.446979\pi$
$877$	4.36121e96			0.331605			0.165802	+	0.986159i	$0.446979\pi$
$878$			9.80568e96i			0.718057i
$879$	−7.89863e95	+	2.40784e96i	−0.0557082	+	0.169822i
$880$	3.92409e97			2.66570
$881$		−	1.04652e97i		−	0.684768i	−0.939560	−	0.342384i	$-0.888766\pi$
$881$		−	1.04652e97i		−	0.684768i	0.939560	−	0.342384i	$-0.111234\pi$
$882$	−2.78991e97	+	3.79481e97i	−1.75844	+	2.39181i
$883$	2.81794e97			1.71091			0.855457	−	0.517874i	$-0.173276\pi$
$883$	2.81794e97			1.71091			0.855457	+	0.517874i	$0.173276\pi$
$884$			1.67862e97i			0.981809i
$885$	−2.82096e96	−	9.25383e95i	−0.158953	−	0.0521427i
$886$	−3.81190e97			−2.06933
$887$		−	9.15895e96i		−	0.479034i	−0.970892	−	0.239517i	$-0.923011\pi$
$887$		−	9.15895e96i		−	0.479034i	0.970892	−	0.239517i	$-0.0769891\pi$
$888$	1.02115e97	−	3.11289e97i	0.514589	−	1.56868i
$889$	3.57787e97			1.73726
$890$			2.44548e97i			1.14418i
$891$	2.95010e97	−	9.21910e96i	1.33006	−	0.415647i
$892$	6.85130e97			2.97668
$893$			3.07635e97i			1.28806i
$894$	−7.97853e97	−	2.61726e97i	−3.21947	−	1.05611i
$895$	−2.56666e97			−0.998177
$896$		−	1.60021e97i		−	0.599809i
$897$	−2.31664e96	+	7.06211e96i	−0.0836968	+	0.255143i
$898$	5.62637e97			1.95934
$899$			1.40186e97i			0.470581i
$900$	−2.80807e97	−	2.06446e97i	−0.908667	−	0.668043i
$901$	−1.22448e96			−0.0381973
$902$		−	1.35426e98i		−	4.07273i
$903$	2.81390e97	+	9.23066e96i	0.815854	+	0.267631i
$904$	−5.10939e97			−1.42827
$905$			3.26728e97i			0.880610i
$906$	1.66769e97	−	5.08383e97i	0.433397	−	1.32118i
$907$	−4.08452e97			−1.02353			−0.511765	−	0.859126i	$-0.671008\pi$
$907$	−4.08452e97			−1.02353			−0.511765	+	0.859126i	$0.671008\pi$
$908$			8.64308e97i			2.08851i
$909$	2.60675e97	−	3.54568e97i	0.607422	−	0.826212i
$910$	−8.40073e97			−1.88778
$911$			6.23708e97i			1.35168i	0.737047	+	0.675841i	$0.236220\pi$
$911$			6.23708e97i			1.35168i	−0.737047	+	0.675841i	$0.763780\pi$
$912$	1.16017e98	+	3.80579e97i	2.42488	+	0.795455i
$913$	4.18357e97			0.843358
$914$			2.56280e96i			0.0498299i
$915$	1.35537e97	−	4.13174e97i	0.254192	−	0.774885i
$916$	3.41532e97			0.617847
$917$		−	9.37344e97i		−	1.63573i
$918$	2.99307e97	+	4.19372e97i	0.503858	+	0.705977i
$919$	−9.79905e97			−1.59137			−0.795687	−	0.605709i	$-0.792890\pi$
$919$	−9.79905e97			−1.59137			−0.795687	+	0.605709i	$0.792890\pi$
$920$			4.01082e97i			0.628398i
$921$	−1.78572e97	−	5.85784e96i	−0.269926	−	0.0885462i
$922$	−2.72448e97			−0.397340
$923$		−	1.04461e98i		−	1.46994i
$924$	−1.26876e98	+	3.86772e98i	−1.72268	+	5.25146i
$925$	2.12249e97			0.278079
$926$			3.44015e97i			0.434926i
$927$	1.03154e97	+	7.58377e96i	0.125850	+	0.0925238i
$928$	−1.11832e98			−1.31668
$929$		−	9.05951e96i		−	0.102940i	−0.998675	−	0.0514702i	$-0.983609\pi$
$929$		−	9.05951e96i		−	0.102940i	0.998675	−	0.0514702i	$-0.0163907\pi$
$930$	−8.97155e97	−	2.94301e97i	−0.983852	−	0.322741i
$931$	1.48039e98			1.56688
$932$			3.66252e97i			0.374158i
$933$	−1.51466e97	+	4.61733e97i	−0.149356	+	0.455299i
$934$	−2.44964e98			−2.33161
$935$		−	5.20447e97i		−	0.478182i
$936$	1.55399e98	−	2.11373e98i	1.37831	−	1.87476i
$937$	−1.02596e98			−0.878467			−0.439234	−	0.898373i	$-0.644750\pi$
$937$	−1.02596e98			−0.878467			−0.439234	+	0.898373i	$0.644750\pi$
$938$		−	2.19082e98i		−	1.81098i
$939$	9.98729e95	+	3.27621e95i	0.00797045	+	0.00261461i
$940$	3.08484e98			2.37692
$941$		−	2.97803e97i		−	0.221550i	−0.993846	−	0.110775i	$-0.964667\pi$
$941$		−	2.97803e97i		−	0.221550i	0.993846	−	0.110775i	$-0.0353333\pi$
$942$	1.12062e98	−	3.41613e98i	0.804970	−	2.45389i
$943$	7.10816e97			0.493027
$944$			8.81745e97i			0.590564i
$945$	−1.49250e98	+	1.06521e98i	−0.965308	+	0.688943i
$946$	2.21236e98			1.38181
$947$		−	2.21213e98i		−	1.33433i	−0.744912	−	0.667163i	$-0.767508\pi$
$947$		−	2.21213e98i		−	1.33433i	0.744912	−	0.667163i	$-0.232492\pi$
$948$	3.04860e98	+	1.00006e98i	1.77593	+	0.582572i
$949$	−2.91069e97			−0.163761
$950$			1.54043e98i			0.837071i
$951$	−5.54960e97	+	1.69175e98i	−0.291276	+	0.887933i
$952$	−4.02914e98			−2.04265
$953$			1.72401e98i			0.844256i	0.906536	+	0.422128i	$0.138717\pi$
$953$			1.72401e98i			0.844256i	−0.906536	+	0.422128i	$0.861283\pi$
$954$	2.59664e97	+	1.90903e97i	0.122833	+	0.0903057i
$955$	−1.97135e98			−0.900850
$956$			1.94888e98i			0.860348i
$957$	1.93250e98	+	6.33934e97i	0.824187	+	0.270365i
$958$	−4.75631e97			−0.195978
$959$		−	1.81993e98i		−	0.724502i
$960$	7.97553e97	−	2.43128e98i	0.306767	−	0.935156i
$961$	−1.15289e98			−0.428465
$962$			2.69061e98i			0.966215i
$963$	7.43523e97	−	1.01134e98i	0.258004	−	0.350936i
$964$	3.56866e98			1.19664
$965$			3.25797e98i			1.05571i
$966$	−2.85469e98	−	9.36448e97i	−0.893951	−	0.293250i
$967$	5.00099e98			1.51350			0.756750	−	0.653705i	$-0.226786\pi$
$967$	5.00099e98			1.51350			0.756750	+	0.653705i	$0.226786\pi$
$968$			8.75792e98i			2.56162i
$969$	5.04757e97	−	1.53871e98i	0.142691	−	0.434984i
$970$	8.20635e98			2.24224
$971$			1.13163e98i			0.298860i	0.988772	+	0.149430i	$0.0477439\pi$
$971$			1.13163e98i			0.298860i	−0.988772	+	0.149430i	$0.952256\pi$
$972$	1.35886e97	−	9.64268e98i	0.0346887	−	2.46156i
$973$	−8.14248e98			−2.00924
$974$		−	9.74556e98i		−	2.32467i
$975$	1.61501e98	+	5.29787e97i	0.372412	+	0.122166i
$976$	−1.29145e99			−2.87896
$977$			1.90139e98i			0.409780i	0.978785	+	0.204890i	$0.0656836\pi$
$977$			1.90139e98i			0.409780i	−0.978785	+	0.204890i	$0.934316\pi$
$978$	−2.34986e98	+	7.16337e98i	−0.489621	+	1.49257i
$979$	−5.77864e98			−1.16412
$980$		−	1.48447e99i		−	2.89142i
$981$	3.04393e98	+	2.23787e98i	0.573268	+	0.421461i
$982$	1.90064e99			3.46116
$983$			1.11584e98i			0.196487i	0.995162	+	0.0982437i	$0.0313225\pi$
$983$			1.11584e98i			0.196487i	−0.995162	+	0.0982437i	$0.968678\pi$
$984$	−2.38405e99	−	7.82061e98i	−4.05955	−	1.33169i
$985$	−4.49865e98			−0.740776
$986$			3.39032e98i			0.539886i
$987$	−4.27681e98	+	1.30375e99i	−0.658649	+	2.00784i
$988$	−1.38867e99			−2.06832
$989$			1.16121e98i			0.167276i
$990$	−8.11404e98	+	1.10367e99i	−1.13051	+	1.53772i
$991$	4.30245e98			0.579809			0.289905	−	0.957056i	$-0.406376\pi$
$991$	4.30245e98			0.579809			0.289905	+	0.957056i	$0.406376\pi$
$992$			1.22680e99i			1.59915i
$993$	6.60208e98	+	2.16573e98i	0.832445	+	0.273074i
$994$	4.22260e99			5.15026
$995$		−	5.14112e98i		−	0.606591i
$996$	4.06865e98	−	1.24030e99i	0.464400	−	1.41569i
$997$	−1.00478e99			−1.10951			−0.554753	−	0.832015i	$-0.687187\pi$
$997$	−1.00478e99			−1.10951			−0.554753	+	0.832015i	$0.687187\pi$
$998$		−	6.66377e98i		−	0.711889i
$999$	3.41167e98	+	4.78024e98i	0.352619	+	0.494070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.67.b.b.2.19	yes	20
3.2	odd	2	inner	3.67.b.b.2.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.67.b.b.2.2	✓	20	3.2	odd	2	inner
3.67.b.b.2.19	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+1.59824e10i q^{2} +(5.28212e15 + 1.73274e15i) q^{3} -1.81649e20 q^{4} +8.56960e22i q^{5} +(-2.76933e25 + 8.44208e25i) q^{6} +1.24551e28 q^{7} -1.72390e30i q^{8} +(2.48984e31 + 1.83050e31i) q^{9} -1.36963e33 q^{10} -3.23641e34i q^{11} +(-9.59494e35 - 3.14751e35i) q^{12} +4.92454e36 q^{13} +1.99063e38i q^{14} +(-1.48489e38 + 4.52656e38i) q^{15} +1.41486e40 q^{16} -1.87651e40i q^{17} +(-2.92558e41 + 3.97936e41i) q^{18} +1.55238e42 q^{19} -1.55666e43i q^{20} +(6.57896e43 + 2.15815e43i) q^{21} +5.17256e44 q^{22} +2.71494e44i q^{23} +(2.98706e45 - 9.10584e45i) q^{24} +6.20872e45 q^{25} +7.87059e46i q^{26} +(9.97984e46 + 1.39832e47i) q^{27} -2.26247e48 q^{28} +1.13044e48i q^{29} +(-7.23453e48 - 2.37320e48i) q^{30} +1.24010e49 q^{31} +9.89276e49i q^{32} +(5.60786e49 - 1.70951e50i) q^{33} +2.99912e50 q^{34} +1.06736e51i q^{35} +(-4.52278e51 - 3.32510e51i) q^{36} +3.41856e51 q^{37} +2.48107e52i q^{38} +(2.60120e52 + 8.53294e51i) q^{39} +1.47731e53 q^{40} -2.61816e53i q^{41} +(-3.44924e53 + 1.05147e54i) q^{42} +4.27712e53 q^{43} +5.87893e54i q^{44} +(-1.56867e54 + 2.13369e54i) q^{45} -4.33912e54 q^{46} +1.98170e55i q^{47} +(7.47348e55 + 2.45159e55i) q^{48} +9.53625e55 q^{49} +9.92301e55i q^{50} +(3.25151e55 - 9.91197e55i) q^{51} -8.94541e56 q^{52} -6.52528e55i q^{53} +(-2.23484e57 + 1.59502e57i) q^{54} +2.77348e57 q^{55} -2.14714e58i q^{56} +(8.19985e57 + 2.68986e57i) q^{57} -1.80671e58 q^{58} +6.23201e57i q^{59} +(2.69729e58 - 8.22248e58i) q^{60} -9.12777e58 q^{61} +1.98198e59i q^{62} +(3.10113e59 + 2.27992e59i) q^{63} -5.37113e59 q^{64} +4.22014e59i q^{65} +(2.73221e60 + 8.96269e59i) q^{66} -1.10057e60 q^{67} +3.40868e60i q^{68} +(-4.70428e59 + 1.43406e60i) q^{69} -1.70589e61 q^{70} -2.12124e61i q^{71} +(3.15560e61 - 4.29223e61i) q^{72} -5.91057e60 q^{73} +5.46368e61i q^{74} +(3.27952e61 + 1.07581e61i) q^{75} -2.81989e62 q^{76} -4.03100e62i q^{77} +(-1.36377e62 + 4.15734e62i) q^{78} -3.17730e62 q^{79} +1.21248e63i q^{80} +(2.84855e62 + 9.11533e62i) q^{81} +4.18444e63 q^{82} +1.29266e63i q^{83} +(-1.19506e64 - 3.92027e63i) q^{84} +1.60810e63 q^{85} +6.83585e63i q^{86} +(-1.95875e63 + 5.97111e63i) q^{87} -5.57925e64 q^{88} -1.78551e64i q^{89} +(-3.41015e64 - 2.50711e64i) q^{90} +6.13359e64 q^{91} -4.93168e64i q^{92} +(6.55036e64 + 2.14877e64i) q^{93} -3.16723e65 q^{94} +1.33033e65i q^{95} +(-1.71416e65 + 5.22547e65i) q^{96} -5.99167e65 q^{97} +1.52412e66i q^{98} +(5.92427e65 - 8.05815e65i) 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

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