LMFDB - Embedded newform 3.67.b.b.2.7

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			2.7
Root			$-2.39059e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.67.b.b.2.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.60612e9i q^{2} +(-5.53379e15 - 5.29477e14i) q^{3} -2.78318e17 q^{4} +1.34902e23i q^{5} +(-4.55674e24 + 4.76244e25i) q^{6} +8.41299e27 q^{7} -6.32624e29i q^{8} +(3.03425e31 + 5.86002e30i) q^{9} +O(q^{10})$	\(q-8.60612e9i q^{2} +(-5.53379e15 - 5.29477e14i) q^{3} -2.78318e17 q^{4} +1.34902e23i q^{5} +(-4.55674e24 + 4.76244e25i) q^{6} +8.41299e27 q^{7} -6.32624e29i q^{8} +(3.03425e31 + 5.86002e30i) q^{9} +1.16098e33 q^{10} +1.80389e34i q^{11} +(1.54015e33 + 1.47363e32i) q^{12} +5.91892e36 q^{13} -7.24032e37i q^{14} +(7.14272e37 - 7.46517e38i) q^{15} -5.46498e39 q^{16} -2.55988e40i q^{17} +(5.04321e40 - 2.61131e41i) q^{18} +6.76409e41 q^{19} -3.75456e40i q^{20} +(-4.65557e43 - 4.45448e42i) q^{21} +1.55245e44 q^{22} +1.41229e44i q^{23} +(-3.34960e44 + 3.50081e45i) q^{24} -4.64591e45 q^{25} -5.09389e46i q^{26} +(-1.64806e47 - 4.84938e46i) q^{27} -2.34149e45 q^{28} +2.70885e48i q^{29} +(-6.42461e48 - 6.14711e47i) q^{30} -1.55874e49 q^{31} +3.52809e47i q^{32} +(9.55119e48 - 9.98236e49i) q^{33} -2.20307e50 q^{34} +1.13493e51i q^{35} +(-8.44487e48 - 1.63095e48i) q^{36} +1.04544e52 q^{37} -5.82125e51i q^{38} +(-3.27541e52 - 3.13393e51i) q^{39} +8.53420e52 q^{40} +2.11573e53i q^{41} +(-3.83358e52 + 4.00664e53i) q^{42} -7.75012e53 q^{43} -5.02057e51i q^{44} +(-7.90526e53 + 4.09325e54i) q^{45} +1.21543e54 q^{46} +2.25610e55i q^{47} +(3.02420e55 + 2.89358e54i) q^{48} +1.10101e55 q^{49} +3.99832e55i q^{50} +(-1.35540e55 + 1.41658e56i) q^{51} -1.64734e54 q^{52} -1.41172e57i q^{53} +(-4.17343e56 + 1.41834e57i) q^{54} -2.43348e57 q^{55} -5.32226e57i q^{56} +(-3.74310e57 - 3.58143e56i) q^{57} +2.33127e58 q^{58} -3.88022e58i q^{59} +(-1.98795e55 + 2.07769e56i) q^{60} -3.61314e58 q^{61} +1.34147e59i q^{62} +(2.55271e59 + 4.93003e58i) q^{63} -4.00208e59 q^{64} +7.98472e59i q^{65} +(-8.59094e59 - 8.21987e58i) q^{66} +1.05899e60 q^{67} +7.12462e57i q^{68} +(7.47772e58 - 7.81529e59i) q^{69} +9.76730e60 q^{70} +8.62453e60i q^{71} +(3.70719e60 - 1.91954e61i) q^{72} -2.48441e61 q^{73} -8.99718e61i q^{74} +(2.57095e61 + 2.45990e60i) q^{75} -1.88257e59 q^{76} +1.51761e62i q^{77} +(-2.69710e61 + 2.81885e62i) q^{78} +3.64608e62 q^{79} -7.37234e62i q^{80} +(8.86325e62 + 3.55615e62i) q^{81} +1.82083e63 q^{82} +1.85595e63i q^{83} +(1.29573e61 + 1.23976e60i) q^{84} +3.45332e63 q^{85} +6.66984e63i q^{86} +(1.43427e63 - 1.49902e64i) q^{87} +1.14119e64 q^{88} -3.49253e64i q^{89} +(3.52270e64 + 6.80336e63i) q^{90} +4.97958e64 q^{91} -3.93065e61i q^{92} +(8.62573e64 + 8.25316e63i) q^{93} +1.94162e65 q^{94} +9.12486e64i q^{95} +(1.86804e62 - 1.95237e63i) q^{96} +3.57760e65 q^{97} -9.47546e64i q^{98} +(-1.05709e65 + 5.47346e65i) 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 $

$2$		−	8.60612e9i		−	1.00188i	−0.865481	−	0.500942i	$-0.832987\pi$
$2$		−	8.60612e9i		−	1.00188i	0.865481	−	0.500942i	$-0.167013\pi$
$3$	−5.53379e15	−	5.29477e14i	−0.995454	−	0.0952457i
$3$	−5.53379e15	−	5.29477e14i	−0.995454	−	0.0952457i
$4$	−2.78318e17			−0.00377192
$5$			1.34902e23i			1.15880i	0.815045	+	0.579398i	$0.196712\pi$
$5$			1.34902e23i			1.15880i	−0.815045	+	0.579398i	$0.803288\pi$
$6$	−4.55674e24	+	4.76244e25i	−0.0954252	+	0.997329i
$7$	8.41299e27			1.08822			0.544108	−	0.839015i	$-0.316868\pi$
$7$	8.41299e27			1.08822			0.544108	+	0.839015i	$0.316868\pi$
$8$		−	6.32624e29i		−	0.998105i
$9$	3.03425e31	+	5.86002e30i	0.981857	+	0.189625i
$10$	1.16098e33			1.16098
$11$			1.80389e34i			0.776698i	0.921512	+	0.388349i	$0.126954\pi$
$11$			1.80389e34i			0.776698i	−0.921512	+	0.388349i	$0.873046\pi$
$12$	1.54015e33	+	1.47363e32i	0.00375477	+	0.000359259i
$13$	5.91892e36			1.02828			0.514141	−	0.857706i	$-0.328111\pi$
$13$	5.91892e36			1.02828			0.514141	+	0.857706i	$0.328111\pi$
$14$		−	7.24032e37i		−	1.09027i
$15$	7.14272e37	−	7.46517e38i	0.110370	−	1.15353i
$16$	−5.46498e39			−1.00376
$17$		−	2.55988e40i		−	0.635924i	−0.948103	−	0.317962i	$-0.897001\pi$
$17$		−	2.55988e40i		−	0.635924i	0.948103	−	0.317962i	$-0.102999\pi$
$18$	5.04321e40	−	2.61131e41i	0.189983	−	0.983707i
$19$	6.76409e41			0.427898			0.213949	−	0.976845i	$-0.431367\pi$
$19$	6.76409e41			0.427898			0.213949	+	0.976845i	$0.431367\pi$
$20$		−	3.75456e40i		−	0.00437088i
$21$	−4.65557e43	−	4.45448e42i	−1.08327	−	0.103648i
$22$	1.55245e44			0.778161
$23$			1.41229e44i			0.163269i	0.996662	+	0.0816345i	$0.0260140\pi$
$23$			1.41229e44i			0.163269i	−0.996662	+	0.0816345i	$0.973986\pi$
$24$	−3.34960e44	+	3.50081e45i	−0.0950652	+	0.993568i
$25$	−4.64591e45			−0.342807
$26$		−	5.09389e46i		−	1.03022i
$27$	−1.64806e47	−	4.84938e46i	−0.959332	−	0.282281i
$28$	−2.34149e45			−0.00410466
$29$			2.70885e48i			1.49160i	0.666173	+	0.745798i	$0.267931\pi$
$29$			2.70885e48i			1.49160i	−0.666173	+	0.745798i	$0.732069\pi$
$30$	−6.42461e48	−	6.14711e47i	−1.15570	−	0.110578i
$31$	−1.55874e49			−0.950249			−0.475124	−	0.879919i	$-0.657597\pi$
$31$	−1.55874e49			−0.950249			−0.475124	+	0.879919i	$0.657597\pi$
$32$			3.52809e47i			0.00754379i
$33$	9.55119e48	−	9.98236e49i	0.0739772	−	0.773167i
$34$	−2.20307e50			−0.637123
$35$			1.13493e51i			1.26102i
$36$	−8.44487e48	−	1.63095e48i	−0.00370348	−	0.000715251i
$37$	1.04544e52			1.85627			0.928137	−	0.372238i	$-0.121409\pi$
$37$	1.04544e52			1.85627			0.928137	+	0.372238i	$0.121409\pi$
$38$		−	5.82125e51i		−	0.428704i
$39$	−3.27541e52	−	3.13393e51i	−1.02361	−	0.0979394i
$40$	8.53420e52			1.15660
$41$			2.11573e53i			1.26939i	0.772764	+	0.634693i	$0.218873\pi$
$41$			2.11573e53i			1.26939i	−0.772764	+	0.634693i	$0.781127\pi$
$42$	−3.83358e52	+	4.00664e53i	−0.103843	+	1.08531i
$43$	−7.75012e53			−0.965715			−0.482858	−	0.875699i	$-0.660401\pi$
$43$	−7.75012e53			−0.965715			−0.482858	+	0.875699i	$0.660401\pi$
$44$		−	5.02057e51i		−	0.00292964i
$45$	−7.90526e53	+	4.09325e54i	−0.219737	+	1.13777i
$46$	1.21543e54			0.163577
$47$			2.25610e55i			1.49324i	0.665253	+	0.746618i	$0.268324\pi$
$47$			2.25610e55i			1.49324i	−0.665253	+	0.746618i	$0.731676\pi$
$48$	3.02420e55	+	2.89358e54i	0.999194	+	0.0956036i
$49$	1.10101e55			0.184214
$50$			3.99832e55i			0.343453i
$51$	−1.35540e55	+	1.41658e56i	−0.0605691	+	0.633033i
$52$	−1.64734e54			−0.00387859
$53$		−	1.41172e57i		−	1.77274i	−0.462981	−	0.886368i	$-0.653220\pi$
$53$		−	1.41172e57i		−	1.77274i	0.462981	−	0.886368i	$-0.346780\pi$
$54$	−4.17343e56	+	1.41834e57i	−0.282813	+	0.961139i
$55$	−2.43348e57			−0.900034
$56$		−	5.32226e57i		−	1.08615i
$57$	−3.74310e57	−	3.58143e56i	−0.425953	−	0.0407555i
$58$	2.33127e58			1.49441
$59$		−	3.88022e58i		−	1.41495i	−0.706740	−	0.707474i	$-0.749835\pi$
$59$		−	3.88022e58i		−	1.41495i	0.706740	−	0.707474i	$-0.250165\pi$
$60$	−1.98795e55	+	2.07769e56i	−0.000416308	+	0.00435101i
$61$	−3.61314e58			−0.438531			−0.219265	−	0.975665i	$-0.570366\pi$
$61$	−3.61314e58			−0.438531			−0.219265	+	0.975665i	$0.570366\pi$
$62$			1.34147e59i			0.952039i
$63$	2.55271e59	+	4.93003e58i	1.06847	+	0.206353i
$64$	−4.00208e59			−0.996200
$65$			7.98472e59i			1.19157i
$66$	−8.59094e59	−	8.21987e58i	−0.774624	−	0.0741165i
$67$	1.05899e60			0.581331			0.290666	−	0.956825i	$-0.406123\pi$
$67$	1.05899e60			0.581331			0.290666	+	0.956825i	$0.406123\pi$
$68$			7.12462e57i			0.00239865i
$69$	7.47772e58	−	7.81529e59i	0.0155507	−	0.162527i
$70$	9.76730e60			1.26340
$71$			8.62453e60i			0.698570i	0.937017	+	0.349285i	$0.113575\pi$
$71$			8.62453e60i			0.698570i	−0.937017	+	0.349285i	$0.886425\pi$
$72$	3.70719e60	−	1.91954e61i	0.189266	−	0.979996i
$73$	−2.48441e61			−0.804581			−0.402290	−	0.915512i	$-0.631786\pi$
$73$	−2.48441e61			−0.804581			−0.402290	+	0.915512i	$0.631786\pi$
$74$		−	8.99718e61i		−	1.85977i
$75$	2.57095e61	+	2.45990e60i	0.341249	+	0.0326509i
$76$	−1.88257e59			−0.00161400
$77$			1.51761e62i			0.845215i
$78$	−2.69710e61	+	2.81885e62i	−0.0981239	+	1.02554i
$79$	3.64608e62			0.871229			0.435615	−	0.900133i	$-0.356531\pi$
$79$	3.64608e62			0.871229			0.435615	+	0.900133i	$0.356531\pi$
$80$		−	7.37234e62i		−	1.16315i
$81$	8.86325e62	+	3.55615e62i	0.928084	+	0.372370i
$82$	1.82083e63			1.27178
$83$			1.85595e63i			0.868938i	0.900687	+	0.434469i	$0.143064\pi$
$83$			1.85595e63i			0.868938i	−0.900687	+	0.434469i	$0.856936\pi$
$84$	1.29573e61	+	1.23976e60i	0.00408600	+	0.000390951i
$85$	3.45332e63			0.736907
$86$			6.66984e63i			0.967535i
$87$	1.43427e63	−	1.49902e64i	0.142068	−	1.48481i
$88$	1.14119e64			0.775226
$89$		−	3.49253e64i		−	1.63407i	−0.576591	−	0.817033i	$-0.695618\pi$
$89$		−	3.49253e64i		−	1.63407i	0.576591	−	0.817033i	$-0.304382\pi$
$90$	3.52270e64	+	6.80336e63i	1.13991	+	0.220151i
$91$	4.97958e64			1.11899
$92$		−	3.93065e61i		−	0.000615837i
$93$	8.62573e64	+	8.25316e63i	0.945929	+	0.0905071i
$94$	1.94162e65			1.49605
$95$			9.12486e64i			0.495847i
$96$	1.86804e62	−	1.95237e63i	0.000718514	−	0.00750950i
$97$	3.57760e65			0.977517			0.488758	−	0.872419i	$-0.337450\pi$
$97$	3.57760e65			0.977517			0.488758	+	0.872419i	$0.337450\pi$
$98$		−	9.47546e64i		−	0.184561i
$99$	−1.05709e65	+	5.47346e65i	−0.147282	+	0.762606i
$100$	1.29304e63			0.00129304
$101$			3.63379e65i			0.261670i	0.991404	+	0.130835i	$0.0417659\pi$
$101$			3.63379e65i			0.261670i	−0.991404	+	0.130835i	$0.958234\pi$
$102$	1.21913e66	+	1.16647e65i	0.634226	+	0.0606832i
$103$	2.78339e66			1.04941			0.524705	−	0.851284i	$-0.324175\pi$
$103$	2.78339e66			1.04941			0.524705	+	0.851284i	$0.324175\pi$
$104$		−	3.74445e66i		−	1.02633i
$105$	6.00917e65	−	6.28044e66i	0.120107	−	1.25529i
$106$	−1.21494e67			−1.77608
$107$			4.60493e66i			0.493808i	0.969040	+	0.246904i	$0.0794133\pi$
$107$			4.60493e66i			0.493808i	−0.969040	+	0.246904i	$0.920587\pi$
$108$	4.58685e64	+	1.34967e64i	0.00361852	+	0.00106474i
$109$	8.13237e65			0.0473307			0.0236653	−	0.999720i	$-0.492466\pi$
$109$	8.13237e65			0.0473307			0.0236653	+	0.999720i	$0.492466\pi$
$110$			2.09428e67i			0.901730i
$111$	−5.78524e67	−	5.53536e66i	−1.84784	−	0.176802i
$112$	−4.59768e67			−1.09231
$113$			3.05190e67i			0.540732i	0.962758	+	0.270366i	$0.0871446\pi$
$113$			3.05190e67i			0.540732i	−0.962758	+	0.270366i	$0.912855\pi$
$114$	−3.08222e66	+	3.22136e67i	−0.0408323	+	0.426755i
$115$	−1.90520e67			−0.189195
$116$		−	7.53923e65i		−	0.00562617i
$117$	1.79595e68	+	3.46850e67i	1.00962	+	0.194988i
$118$	−3.33937e68			−1.41761
$119$		−	2.15363e68i		−	0.692023i
$120$	−4.72265e68	−	4.51866e67i	−1.15134	−	0.110161i
$121$	2.14005e68			0.396740
$122$			3.10951e68i			0.439357i
$123$	1.12023e68	−	1.17080e69i	0.120904	−	1.26361i
$124$	4.33826e66			0.00358426
$125$			1.20152e69i			0.761552i
$126$	4.24284e68	−	2.19689e69i	0.206742	−	1.07049i
$127$	2.96592e69			1.11336			0.556680	−	0.830727i	$-0.312075\pi$
$127$	2.96592e69			1.11336			0.556680	+	0.830727i	$0.312075\pi$
$128$			3.47027e69i			1.00562i
$129$	4.28875e69	+	4.10351e68i	0.961325	+	0.0919802i
$130$	6.87174e69			1.19381
$131$			7.05357e69i			0.951604i	0.879552	+	0.475802i	$0.157842\pi$
$131$			7.05357e69i			0.951604i	−0.879552	+	0.475802i	$0.842158\pi$
$132$	−2.65827e66	+	2.77827e67i	−0.000279036	+	0.00291632i
$133$	5.69062e69			0.465646
$134$		−	9.11380e69i		−	0.582427i
$135$	6.54188e69	−	2.22326e70i	0.327106	−	1.11167i
$136$	−1.61944e70			−0.634720
$137$			2.52298e70i			0.776489i	0.921556	+	0.388244i	$0.126918\pi$
$137$			2.52298e70i			0.776489i	−0.921556	+	0.388244i	$0.873082\pi$
$138$	−6.72593e69	−	6.43542e68i	−0.162833	−	0.0155800i
$139$	−1.06533e69			−0.0203234			−0.0101617	−	0.999948i	$-0.503235\pi$
$139$	−1.06533e69			−0.0203234			−0.0101617	+	0.999948i	$0.503235\pi$
$140$		−	3.15871e68i		−	0.00475646i
$141$	1.19455e70	−	1.24848e71i	0.142224	−	1.48645i
$142$	7.42237e70			0.699886
$143$			1.06771e71i			0.798664i
$144$	−1.65821e71	−	3.20249e70i	−0.985546	−	0.190338i
$145$	−3.65428e71			−1.72845
$146$			2.13812e71i			0.806097i
$147$	−6.09278e70	−	5.82961e69i	−0.183376	−	0.0175456i
$148$	−2.90965e69			−0.00700171
$149$			9.36262e71i			1.80406i	0.431675	+	0.902029i	$0.357923\pi$
$149$			9.36262e71i			1.80406i	−0.431675	+	0.902029i	$0.642077\pi$
$150$	2.11702e70	−	2.21259e71i	0.0327124	−	0.341892i
$151$	−1.51681e72			−1.88232			−0.941159	−	0.337963i	$-0.890262\pi$
$151$	−1.51681e72			−1.88232			−0.941159	+	0.337963i	$0.890262\pi$
$152$		−	4.27913e71i		−	0.427087i
$153$	1.50010e71	−	7.76731e71i	0.120587	−	0.624387i
$154$	1.30608e72			0.846808
$155$		−	2.10276e72i		−	1.10114i
$156$	9.11606e69	+	8.72231e68i	0.00386096	+	0.000369419i
$157$	4.54418e72			1.55872			0.779358	−	0.626578i	$-0.215545\pi$
$157$	4.54418e72			1.55872			0.779358	+	0.626578i	$0.215545\pi$
$158$		−	3.13786e72i		−	0.872871i
$159$	−7.47472e71	+	7.81215e72i	−0.168846	+	1.76468i
$160$	−4.75944e70			−0.00874172
$161$			1.18815e72i			0.177672i
$162$	3.06047e72	−	7.62782e72i	0.373071	−	0.929833i
$163$	−4.62556e71			−0.0460228			−0.0230114	−	0.999735i	$-0.507325\pi$
$163$	−4.62556e71			−0.0460228			−0.0230114	+	0.999735i	$0.507325\pi$
$164$		−	5.88847e70i		−	0.00478802i
$165$	1.34664e73	+	1.28847e72i	0.895943	+	0.0857244i
$166$	1.59725e73			0.870575
$167$			1.82426e73i			0.815534i	0.913086	+	0.407767i	$0.133693\pi$
$167$			1.82426e73i			0.815534i	−0.913086	+	0.407767i	$0.866307\pi$
$168$	−2.81801e72	+	2.94523e73i	−0.103451	+	1.08122i
$169$	1.90060e72			0.0573626
$170$		−	2.97197e73i		−	0.738295i
$171$	2.05239e73	+	3.96377e72i	0.420135	+	0.0811404i
$172$	2.15700e71			0.00364260
$173$		−	1.25662e74i		−	1.75261i	−0.481761	−	0.876303i	$-0.660003\pi$
$173$		−	1.25662e74i		−	1.75261i	0.481761	−	0.876303i	$-0.339997\pi$
$174$	−1.29007e74	−	1.23435e73i	−1.48761	−	0.142336i
$175$	−3.90860e73			−0.373048
$176$		−	9.85823e73i		−	0.779617i
$177$	−2.05449e73	+	2.14723e74i	−0.134768	+	1.40851i
$178$	−3.00571e74			−1.63714
$179$			2.37973e74i			1.07740i	0.842497	+	0.538702i	$0.181085\pi$
$179$			2.37973e74i			1.07740i	−0.842497	+	0.538702i	$0.818915\pi$
$180$	2.20018e71	−	1.13923e72i	0.000828830	−	0.00429158i
$181$	−9.42114e73			−0.295604			−0.147802	−	0.989017i	$-0.547220\pi$
$181$	−9.42114e73			−0.295604			−0.147802	+	0.989017i	$0.547220\pi$
$182$		−	4.28549e74i		−	1.12110i
$183$	1.99943e74	+	1.91307e73i	0.436537	+	0.0417682i
$184$	8.93446e73			0.162960
$185$			1.41031e75i			2.15104i
$186$	7.10276e73	−	7.42340e74i	0.0906776	−	0.947711i
$187$	4.61775e74			0.493921
$188$		−	6.27913e72i		−	0.00563236i
$189$	−1.38651e75	−	4.07977e74i	−1.04396	−	0.307183i
$190$	7.85296e74			0.496781
$191$			2.77206e74i			0.147469i	0.997278	+	0.0737347i	$0.0234918\pi$
$191$			2.77206e74i			0.147469i	−0.997278	+	0.0737347i	$0.976508\pi$
$192$	2.21467e75	+	2.11901e74i	0.991671	+	0.0948837i
$193$	9.53944e74			0.359859			0.179929	−	0.983680i	$-0.442413\pi$
$193$	9.53944e74			0.359859			0.179929	+	0.983680i	$0.442413\pi$
$194$		−	3.07892e75i		−	0.979359i
$195$	4.22772e74	−	4.41857e75i	0.113492	−	1.18615i
$196$	−3.06432e72			−0.000694839
$197$			3.01501e75i			0.577967i	0.957334	+	0.288983i	$0.0933172\pi$
$197$			3.01501e75i			0.577967i	−0.957334	+	0.288983i	$0.906683\pi$
$198$	4.71052e75	+	9.09740e74i	0.764043	+	0.147559i
$199$	9.57674e75			1.31543			0.657713	−	0.753269i	$-0.271524\pi$
$199$	9.57674e75			1.31543			0.657713	+	0.753269i	$0.271524\pi$
$200$			2.93911e75i			0.342158i
$201$	−5.86023e75	−	5.60711e74i	−0.578689	−	0.0553693i
$202$	3.12728e75			0.262163
$203$			2.27895e76i			1.62318i
$204$	3.77232e72	−	3.94261e73i	0.000228462	−	0.00238775i
$205$	−2.85416e76			−1.47096
$206$		−	2.39542e76i		−	1.05139i
$207$	−8.27603e74	+	4.28522e75i	−0.0309600	+	0.160307i
$208$	−3.23468e76			−1.03215
$209$			1.22017e76i			0.332348i
$210$	−5.40502e76	−	5.17156e75i	−1.25765	−	0.120333i
$211$	2.57089e76			0.511402			0.255701	−	0.966756i	$-0.417694\pi$
$211$	2.57089e76			0.511402			0.255701	+	0.966756i	$0.417694\pi$
$212$			3.92907e74i			0.00668661i
$213$	4.56649e75	−	4.77263e76i	0.0665358	−	0.695394i
$214$	3.96306e76			0.494739
$215$		−	1.04550e77i		−	1.11907i
$216$	−3.06783e76	+	1.04260e77i	−0.281746	+	0.957514i
$217$	−1.31136e77			−1.03408
$218$		−	6.99882e75i		−	0.0474199i
$219$	1.37482e77	+	1.31544e76i	0.800923	+	0.0766329i
$220$	6.77282e74			0.00339485
$221$		−	1.51517e77i		−	0.653909i
$222$	−4.76380e76	+	4.97885e77i	−0.177135	+	1.85132i
$223$	3.59276e77			1.15178			0.575888	−	0.817529i	$-0.304657\pi$
$223$	3.59276e77			1.15178			0.575888	+	0.817529i	$0.304657\pi$
$224$			2.96818e75i			0.00820928i
$225$	−1.40968e77	−	2.72251e76i	−0.336588	−	0.0650050i
$226$	2.62650e77			0.541750
$227$		−	9.31799e76i		−	0.166138i	−0.996544	−	0.0830690i	$-0.973528\pi$
$227$		−	9.31799e76i		−	0.166138i	0.996544	−	0.0830690i	$-0.0264722\pi$
$228$	1.04177e75	+	9.96777e73i	0.00160666	+	0.000153726i
$229$	9.34799e77			1.24781			0.623904	−	0.781501i	$-0.285546\pi$
$229$	9.34799e77			1.24781			0.623904	+	0.781501i	$0.285546\pi$
$230$			1.63963e77i			0.189552i
$231$	8.03541e76	−	8.39815e77i	0.0805031	−	0.841373i
$232$	1.71368e78			1.48877
$233$		−	3.85747e77i		−	0.290775i	−0.989375	−	0.145388i	$-0.953557\pi$
$233$		−	3.85747e77i		−	0.290775i	0.989375	−	0.145388i	$-0.0464429\pi$
$234$	2.98503e77	−	1.54561e78i	0.195356	−	1.01153i
$235$	−3.04351e78			−1.73035
$236$			1.07994e76i			0.00533706i
$237$	−2.01766e78	−	1.93052e77i	−0.867269	−	0.0829809i
$238$	−1.85344e78			−0.693327
$239$			3.89998e78i			1.27037i	0.772359	+	0.635186i	$0.219077\pi$
$239$			3.89998e78i			1.27037i	−0.772359	+	0.635186i	$0.780923\pi$
$240$	−3.90348e77	+	4.07970e78i	−0.110785	+	1.15786i
$241$	2.30502e78			0.570310			0.285155	−	0.958481i	$-0.407955\pi$
$241$	2.30502e78			0.570310			0.285155	+	0.958481i	$0.407955\pi$
$242$		−	1.84175e78i		−	0.397488i
$243$	−4.71645e78	−	2.43719e78i	−0.888399	−	0.459073i
$244$	1.00560e76			0.00165410
$245$			1.48528e78i			0.213466i
$246$	−1.00761e79	−	9.64085e77i	−1.26600	−	0.121131i
$247$	4.00361e78			0.440000
$248$			9.86096e78i			0.948448i
$249$	9.82681e77	−	1.02704e79i	0.0827626	−	0.864987i
$250$	1.03404e79			0.762987
$251$			9.17504e78i			0.593438i	0.954965	+	0.296719i	$0.0958924\pi$
$251$			9.17504e78i			0.593438i	−0.954965	+	0.296719i	$0.904108\pi$
$252$	−7.10466e76	−	1.37212e76i	−0.00403019	−	0.000778348i
$253$	−2.54761e78			−0.126811
$254$		−	2.55250e79i		−	1.11546i
$255$	−1.91099e79	−	1.82845e78i	−0.733556	−	0.0701872i
$256$	3.35426e77			0.0113156
$257$		−	1.25559e79i		−	0.372438i	−0.982508	−	0.186219i	$-0.940377\pi$
$257$		−	1.25559e79i		−	0.372438i	0.982508	−	0.186219i	$-0.0596234\pi$
$258$	3.53153e78	−	3.69095e79i	0.0921535	−	0.963136i
$259$	8.79528e79			2.02003
$260$		−	2.22229e77i		−	0.00449450i
$261$	−1.58739e79	+	8.21932e79i	−0.282844	+	1.46453i
$262$	6.07039e79			0.953397
$263$			4.89188e79i			0.677541i	0.940869	+	0.338771i	$0.110011\pi$
$263$			4.89188e79i			0.677541i	−0.940869	+	0.338771i	$0.889989\pi$
$264$	−6.31508e79	−	6.04232e78i	−0.771702	−	0.0738370i
$265$	1.90443e80			2.05424
$266$		−	4.89742e79i		−	0.466523i
$267$	−1.84921e79	+	1.93269e80i	−0.155638	+	1.62664i
$268$	−2.94737e77			−0.00219273
$269$		−	2.53838e80i		−	1.67005i	−0.550209	−	0.835027i	$-0.685452\pi$
$269$		−	2.53838e80i		−	1.67005i	0.550209	−	0.835027i	$-0.314548\pi$
$270$	−1.91336e80	−	5.63002e79i	−1.11376	−	0.327722i
$271$	−2.01057e80			−1.03594			−0.517968	−	0.855400i	$-0.673311\pi$
$271$	−2.01057e80			−1.03594			−0.517968	+	0.855400i	$0.673311\pi$
$272$			1.39897e80i			0.638314i
$273$	−2.75560e80	−	2.63657e79i	−1.11390	−	0.106579i
$274$	2.17131e80			0.777952
$275$		−	8.38072e79i		−	0.266258i
$276$	−2.08119e76	+	2.17514e77i	−5.86559e−5	+	0.000613038i
$277$	−3.28820e80			−0.822480			−0.411240	−	0.911527i	$-0.634904\pi$
$277$	−3.28820e80			−0.822480			−0.411240	+	0.911527i	$0.634904\pi$
$278$			9.16837e78i			0.0203617i
$279$	−4.72960e80	−	9.13424e79i	−0.933008	−	0.180191i
$280$	7.17981e80			1.25863
$281$		−	3.43268e79i		−	0.0534964i	−0.999642	−	0.0267482i	$-0.991485\pi$
$281$		−	3.43268e79i		−	0.0534964i	0.999642	−	0.0267482i	$-0.00851523\pi$
$282$	−1.07445e81	−	1.02804e80i	−1.48925	−	0.142492i
$283$	4.25867e80			0.525197			0.262598	−	0.964905i	$-0.415421\pi$
$283$	4.25867e80			0.525197			0.262598	+	0.964905i	$0.415421\pi$
$284$		−	2.40037e78i		−	0.00263495i
$285$	4.83140e79	−	5.04950e80i	0.0472273	−	0.493592i
$286$	9.18884e80			0.800169
$287$			1.77996e81i			1.38137i
$288$	−2.06747e78	+	1.07051e79i	−0.00143050	+	0.00740692i
$289$	9.65125e80			0.595600
$290$			3.14492e81i			1.73171i
$291$	−1.97977e81	−	1.89425e80i	−0.973073	−	0.0931043i
$292$	6.91458e78			0.00303481
$293$		−	3.14368e81i		−	1.23256i	−0.787529	−	0.616278i	$-0.788640\pi$
$293$		−	3.14368e81i		−	1.23256i	0.787529	−	0.616278i	$-0.211360\pi$
$294$	−5.01703e79	+	5.24352e80i	−0.0175786	+	0.183722i
$295$	5.23448e81			1.63963
$296$		−	6.61371e81i		−	1.85276i
$297$	8.74775e80	−	2.97292e81i	0.219247	−	0.745111i
$298$	8.05758e81			1.80746
$299$			8.35921e80i			0.167887i
$300$	−7.15541e78	−	6.84635e77i	−0.00128716	−	0.000123157i
$301$	−6.52016e81			−1.05091
$302$			1.30539e82i			1.88587i
$303$	1.92401e80	−	2.01086e81i	0.0249230	−	0.260481i
$304$	−3.69656e81			−0.429506
$305$		−	4.87418e81i		−	0.508168i
$306$	−6.68464e81	−	1.29100e81i	−0.625563	−	0.120815i
$307$	9.63518e81			0.809643			0.404821	−	0.914396i	$-0.367334\pi$
$307$	9.63518e81			0.809643			0.404821	+	0.914396i	$0.367334\pi$
$308$		−	4.22380e79i		−	0.00318808i
$309$	−1.54027e82	−	1.47374e81i	−1.04464	−	0.0999519i
$310$	−1.80966e82			−1.10322
$311$			1.86645e82i			1.02311i	0.859250	+	0.511556i	$0.170931\pi$
$311$			1.86645e82i			1.02311i	−0.859250	+	0.511556i	$0.829069\pi$
$312$	−1.98260e81	+	2.07210e82i	−0.0977538	+	1.02167i
$313$	−1.01210e82			−0.449013			−0.224507	−	0.974473i	$-0.572077\pi$
$313$	−1.01210e82			−0.449013			−0.224507	+	0.974473i	$0.572077\pi$
$314$		−	3.91078e82i		−	1.56165i
$315$	−6.65069e81	+	3.44364e82i	−0.239121	+	1.23814i
$316$	−1.01477e80			−0.00328621
$317$		−	1.20335e82i		−	0.351104i	−0.984470	−	0.175552i	$-0.943829\pi$
$317$		−	1.20335e82i		−	0.351104i	0.984470	−	0.175552i	$-0.0561709\pi$
$318$	6.72323e82	+	6.43283e81i	1.76800	+	0.169164i
$319$	−4.88648e82			−1.15852
$320$		−	5.39887e82i		−	1.15439i
$321$	2.43820e81	−	2.54827e82i	0.0470331	−	0.491563i
$322$	1.02254e82			0.178007
$323$		−	1.73153e82i		−	0.272111i
$324$	−2.46681e80	−	9.89742e79i	−0.00350066	−	0.00140455i
$325$	−2.74988e82			−0.352502
$326$			3.98081e81i			0.0461095i
$327$	−4.50028e81	−	4.30590e80i	−0.0471155	−	0.00450804i
$328$	1.33846e83			1.26698
$329$			1.89805e83i			1.62496i
$330$	1.10887e82	−	1.15893e83i	0.0858859	−	0.897631i
$331$	−1.05740e83			−0.741166			−0.370583	−	0.928799i	$-0.620842\pi$
$331$	−1.05740e83			−0.741166			−0.370583	+	0.928799i	$0.620842\pi$
$332$		−	5.16544e80i		−	0.00327756i
$333$	3.17212e83	+	6.12630e82i	1.82260	+	0.351997i
$334$	1.56998e83			0.817071
$335$			1.42860e83i			0.673644i
$336$	2.54426e83	+	2.43436e82i	1.08734	+	0.104037i
$337$	−4.07920e83			−1.58048			−0.790239	−	0.612799i	$-0.790044\pi$
$337$	−4.07920e83			−1.58048			−0.790239	+	0.612799i	$0.790044\pi$
$338$		−	1.63568e82i		−	0.0574707i
$339$	1.61591e82	−	1.68886e83i	0.0515024	−	0.538273i
$340$	−9.61123e80			−0.00277955
$341$		−	2.81180e83i		−	0.738056i
$342$	3.41127e82	−	1.76631e83i	0.0812932	−	0.420926i
$343$	−4.10202e83			−0.887752
$344$			4.90291e83i			0.963885i
$345$	1.05429e83	+	1.00876e82i	0.188335	+	0.0180201i
$346$	−1.08147e84			−1.75591
$347$		−	5.11856e83i		−	0.755570i	−0.925893	−	0.377785i	$-0.876686\pi$
$347$		−	5.11856e83i		−	0.755570i	0.925893	−	0.377785i	$-0.123314\pi$
$348$	−3.99184e80	+	4.17205e81i	−0.000535869	+	0.00560060i
$349$	−3.22129e83			−0.393361			−0.196680	−	0.980468i	$-0.563016\pi$
$349$	−3.22129e83			−0.393361			−0.196680	+	0.980468i	$0.563016\pi$
$350$			3.36378e83i			0.373751i
$351$	−9.75474e83	−	2.87031e83i	−0.986463	−	0.290264i
$352$	−6.36429e81			−0.00585925
$353$		−	5.13730e82i		−	0.0430694i	−0.999768	−	0.0215347i	$-0.993145\pi$
$353$		−	5.13730e82i		−	0.0430694i	0.999768	−	0.0215347i	$-0.00685524\pi$
$354$	1.84793e84	+	1.76812e83i	1.41117	+	0.135022i
$355$	−1.16346e84			−0.809500
$356$			9.72034e81i			0.00616356i
$357$	−1.14029e83	+	1.19177e84i	−0.0659122	+	0.688877i
$358$	2.04803e84			1.07943
$359$			8.48607e83i			0.407934i	0.978978	+	0.203967i	$0.0653835\pi$
$359$			8.48607e83i			0.407934i	−0.978978	+	0.203967i	$0.934616\pi$
$360$	2.58949e84	+	5.00106e83i	1.13562	+	0.219321i
$361$	−2.04131e84			−0.816903
$362$			8.10795e83i			0.296161i
$363$	−1.18426e84	−	1.13311e83i	−0.394937	−	0.0377878i
$364$	−1.38591e82			−0.00422075
$365$		−	3.35151e84i		−	0.932345i
$366$	1.64641e83	−	1.72074e84i	0.0418469	−	0.437360i
$367$	2.16685e84			0.503324			0.251662	−	0.967815i	$-0.419023\pi$
$367$	2.16685e84			0.503324			0.251662	+	0.967815i	$0.419023\pi$
$368$		−	7.71811e83i		−	0.163883i
$369$	−1.23982e84	+	6.41966e84i	−0.240708	+	1.24635i
$370$	1.21373e85			2.15510
$371$		−	1.18768e85i		−	1.92912i
$372$	−2.40070e82	−	2.29700e81i	−0.00356796	−	0.000341385i
$373$	−8.34580e84			−1.13521			−0.567605	−	0.823301i	$-0.692130\pi$
$373$	−8.34580e84			−1.13521			−0.567605	+	0.823301i	$0.692130\pi$
$374$		−	3.97409e84i		−	0.494852i
$375$	6.36175e83	−	6.64894e84i	0.0725346	−	0.758090i
$376$	1.42726e85			1.49041
$377$			1.60335e85i			1.53378i
$378$	−3.51110e84	+	1.19325e85i	−0.307761	+	1.04593i
$379$	−5.15769e84			−0.414344			−0.207172	−	0.978305i	$-0.566426\pi$
$379$	−5.15769e84			−0.414344			−0.207172	+	0.978305i	$0.566426\pi$
$380$		−	2.53962e82i		−	0.00187029i
$381$	−1.64127e85	−	1.57038e84i	−1.10830	−	0.106043i
$382$	2.38567e84			0.147747
$383$			2.43453e85i			1.38311i	0.722326	+	0.691553i	$0.243073\pi$
$383$			2.43453e85i			1.38311i	−0.722326	+	0.691553i	$0.756927\pi$
$384$	1.83743e84	−	1.92037e85i	0.0957810	−	1.00105i
$385$	−2.04728e85			−0.979432
$386$		−	8.20976e84i		−	0.360537i
$387$	−2.35158e85	−	4.54159e84i	−0.948194	−	0.183124i
$388$	−9.95711e82			−0.00368711
$389$			2.73430e85i			0.930056i	0.885296	+	0.465028i	$0.153956\pi$
$389$			2.73430e85i			0.930056i	−0.885296	+	0.465028i	$0.846044\pi$
$390$	−3.80268e85	−	3.63843e84i	−1.18839	−	0.113706i
$391$	3.61528e84			0.103827
$392$		−	6.96528e84i		−	0.183865i
$393$	3.73470e84	−	3.90330e85i	0.0906362	−	0.947278i
$394$	2.59475e85			0.579056
$395$			4.91862e85i			1.00958i
$396$	2.94206e82	−	1.52336e83i	0.000555534	−	0.00287649i
$397$	1.12836e86			1.96048			0.980239	−	0.197816i	$-0.0633850\pi$
$397$	1.12836e86			1.96048			0.980239	+	0.197816i	$0.0633850\pi$
$398$		−	8.24186e85i		−	1.31790i
$399$	−3.14907e85	−	3.01305e84i	−0.463529	−	0.0443507i
$400$	2.53898e85			0.344095
$401$		−	1.27731e86i		−	1.59416i	−0.603872	−	0.797081i	$-0.706376\pi$
$401$		−	1.27731e86i		−	1.59416i	0.603872	−	0.797081i	$-0.293624\pi$
$402$	−4.82555e84	+	5.04339e85i	−0.0554737	+	0.579779i
$403$	−9.22605e85			−0.977123
$404$		−	1.01135e83i		−	0.000986999i
$405$	−4.79730e85	+	1.19567e86i	−0.431501	+	1.07546i
$406$	1.96129e86			1.62624
$407$			1.88586e86i			1.44176i
$408$	8.96166e85	+	8.57458e84i	0.631834	+	0.0604543i
$409$	9.02163e85			0.586700			0.293350	−	0.956005i	$-0.405230\pi$
$409$	9.02163e85			0.586700			0.293350	+	0.956005i	$0.405230\pi$
$410$			2.45632e86i			1.47373i
$411$	1.33586e85	−	1.39616e86i	0.0739572	−	0.772959i
$412$	−7.74668e83			−0.00395829
$413$		−	3.26443e86i		−	1.53977i
$414$	3.68791e85	+	7.12245e84i	0.160609	+	0.0310183i
$415$	−2.50370e86			−1.00692
$416$			2.08825e84i			0.00775714i
$417$	5.89532e84	+	5.64068e83i	0.0202310	+	0.00193572i
$418$	1.05009e86			0.332974
$419$		−	3.89747e86i		−	1.14214i	−0.820900	−	0.571071i	$-0.806528\pi$
$419$		−	3.89747e86i		−	1.14214i	0.820900	−	0.571071i	$-0.193472\pi$
$420$	−1.67246e83	+	1.74796e84i	−0.000453033	+	0.00473484i
$421$	2.12322e86			0.531724			0.265862	−	0.964011i	$-0.414344\pi$
$421$	2.12322e86			0.531724			0.265862	+	0.964011i	$0.414344\pi$
$422$		−	2.21254e86i		−	0.512366i
$423$	−1.32208e86	+	6.84555e86i	−0.283155	+	1.46614i
$424$	−8.93087e86			−1.76938
$425$			1.18930e86i			0.218000i
$426$	−4.10738e86	−	3.92997e85i	−0.696704	−	0.0666612i
$427$	−3.03973e86			−0.477216
$428$		−	1.28164e84i		−	0.00186260i
$429$	5.65328e85	−	5.90848e86i	0.0760693	−	0.795033i
$430$	−8.99772e86			−1.12118
$431$		−	2.41369e85i		−	0.0278568i	−0.999903	−	0.0139284i	$-0.995566\pi$
$431$		−	2.41369e85i		−	0.0278568i	0.999903	−	0.0139284i	$-0.00443369\pi$
$432$	9.00661e86	+	2.65017e86i	0.962937	+	0.283342i
$433$	−1.08391e87			−1.07373			−0.536864	−	0.843669i	$-0.680391\pi$
$433$	−1.08391e87			−1.07373			−0.536864	+	0.843669i	$0.680391\pi$
$434$			1.12858e87i			1.03602i
$435$	2.02220e87	+	1.93486e86i	1.72060	+	0.164628i
$436$	−2.26339e83			−0.000178527
$437$			9.55282e85i			0.0698625i
$438$	1.13208e86	−	1.18319e87i	0.0767773	−	0.802432i
$439$	1.82304e87			1.14674			0.573372	−	0.819295i	$-0.305635\pi$
$439$	1.82304e87			1.14674			0.573372	+	0.819295i	$0.305635\pi$
$440$			1.53948e87i			0.898329i
$441$	3.34075e86	+	6.45197e85i	0.180872	+	0.0349316i
$442$	−1.30398e87			−0.655141
$443$			1.54035e87i			0.718283i	0.933283	+	0.359142i	$0.116931\pi$
$443$			1.54035e87i			0.718283i	−0.933283	+	0.359142i	$0.883069\pi$
$444$	1.61014e85	+	1.54059e84i	0.00696988	+	0.000666883i
$445$	4.71147e87			1.89355
$446$		−	3.09197e87i		−	1.15395i
$447$	4.95729e86	−	5.18108e87i	0.171829	−	1.79586i
$448$	−3.36694e87			−1.08408
$449$		−	1.85001e87i		−	0.553407i	−0.960955	−	0.276703i	$-0.910758\pi$
$449$		−	1.85001e87i		−	0.553407i	0.960955	−	0.276703i	$-0.0892419\pi$
$450$	−2.34303e86	+	1.21319e87i	−0.0651275	+	0.337222i
$451$	−3.81656e87			−0.985929
$452$		−	8.49400e84i		−	0.00203959i
$453$	8.39373e87	+	8.03118e86i	1.87376	+	0.179283i
$454$	−8.01918e86			−0.166451
$455$			6.71754e87i			1.29668i
$456$	−2.26570e86	+	2.36798e87i	−0.0406782	+	0.425146i
$457$	4.05609e85			0.00677443			0.00338722	−	0.999994i	$-0.498922\pi$
$457$	4.05609e85			0.00677443			0.00338722	+	0.999994i	$0.498922\pi$
$458$		−	8.04499e87i		−	1.25016i
$459$	−1.24138e87	+	4.21884e87i	−0.179509	+	0.610063i
$460$	5.30251e84			0.000713630
$461$			1.08534e88i			1.35967i	0.733365	+	0.679835i	$0.237949\pi$
$461$			1.08534e88i			1.35967i	−0.733365	+	0.679835i	$0.762051\pi$
$462$	−7.22755e87	−	6.91537e86i	−0.842958	−	0.0806548i
$463$	−2.90719e87			−0.315719			−0.157859	−	0.987462i	$-0.550459\pi$
$463$	−2.90719e87			−0.315719			−0.157859	+	0.987462i	$0.550459\pi$
$464$		−	1.48038e88i		−	1.49720i
$465$	−1.11336e87	+	1.16362e88i	−0.104879	+	1.09614i
$466$	−3.31979e87			−0.291323
$467$		−	1.36048e88i		−	1.11234i	−0.831069	−	0.556169i	$-0.812271\pi$
$467$		−	1.36048e88i		−	1.11234i	0.831069	−	0.556169i	$-0.187729\pi$
$468$	−4.99845e85	−	9.65348e84i	−0.00380822	−	0.000735480i
$469$	8.90928e87			0.632614
$470$			2.61928e88i			1.73361i
$471$	−2.51465e88	−	2.40604e87i	−1.55163	−	0.148461i
$472$	−2.45472e88			−1.41227
$473$		−	1.39804e88i		−	0.750069i
$474$	−1.66142e87	+	1.73643e88i	−0.0831372	+	0.868903i
$475$	−3.14253e87			−0.146687
$476$			5.99394e85i			0.00261025i
$477$	8.27270e87	−	4.28350e88i	0.336156	−	1.74057i
$478$	3.35637e88			1.27277
$479$		−	1.79469e88i		−	0.635211i	−0.948223	−	0.317606i	$-0.897121\pi$
$479$		−	1.79469e88i		−	0.635211i	0.948223	−	0.317606i	$-0.102879\pi$
$480$	2.63377e86	+	2.52001e85i	0.00870197	+	0.000832611i
$481$	6.18788e88			1.90877
$482$		−	1.98372e88i		−	0.571385i
$483$	6.29100e86	−	6.57499e87i	0.0169225	−	0.176864i
$484$	−5.95615e85			−0.00149647
$485$			4.82623e88i			1.13274i
$486$	−2.09747e88	+	4.05903e88i	−0.459938	+	0.890072i
$487$	3.61703e88			0.741134			0.370567	−	0.928806i	$-0.379163\pi$
$487$	3.61703e88			0.741134			0.370567	+	0.928806i	$0.379163\pi$
$488$			2.28576e88i			0.437700i
$489$	2.55969e87	+	2.44913e86i	0.0458136	+	0.00438348i
$490$	1.27825e88			0.213868
$491$			1.11550e88i			0.174495i	0.996187	+	0.0872473i	$0.0278070\pi$
$491$			1.11550e88i			0.174495i	−0.996187	+	0.0872473i	$0.972193\pi$
$492$	−3.11781e85	+	3.25856e86i	−0.000456038	+	0.00476625i
$493$	6.93434e88			0.948542
$494$		−	3.44556e88i		−	0.440829i
$495$	−7.38378e88	−	1.42602e88i	−0.883705	−	0.170669i
$496$	8.51847e88			0.953819
$497$			7.25581e88i			0.760195i
$498$	−8.83885e88	−	8.45707e87i	−0.866617	−	0.0829185i
$499$	−1.80240e89			−1.65399			−0.826997	−	0.562206i	$-0.809953\pi$
$499$	−1.80240e89			−1.65399			−0.826997	+	0.562206i	$0.809953\pi$
$500$		−	3.34404e86i		−	0.00287251i
$501$	9.65901e87	−	1.00950e89i	0.0776762	−	0.811827i
$502$	7.89615e88			0.594556
$503$			2.13059e88i			0.150230i	0.997175	+	0.0751151i	$0.0239324\pi$
$503$			2.13059e88i			0.150230i	−0.997175	+	0.0751151i	$0.976068\pi$
$504$	3.11886e88	−	1.61491e89i	0.205962	−	1.06645i
$505$	−4.90204e88			−0.303223
$506$			2.19251e88i			0.127050i
$507$	−1.05175e88	−	1.00632e87i	−0.0571018	−	0.00546354i
$508$	−8.25469e86			−0.00419950
$509$		−	2.19379e89i		−	1.04595i	−0.852349	−	0.522973i	$-0.824823\pi$
$509$		−	2.19379e89i		−	1.04595i	0.852349	−	0.522973i	$-0.175177\pi$
$510$	−1.57359e88	+	1.64462e89i	−0.0703194	+	0.734939i
$511$	−2.09014e89			−0.875558
$512$			2.53174e89i			0.994284i
$513$	−1.11476e89	−	3.28016e88i	−0.410496	−	0.120787i
$514$	−1.08057e89			−0.373140
$515$			3.75484e89i			1.21605i
$516$	−1.19364e87	−	1.14208e86i	−0.00362604	−	0.000346942i
$517$	−4.06976e89			−1.15979
$518$		−	7.56932e89i		−	2.02383i
$519$	−6.65353e88	+	6.95389e89i	−0.166928	+	1.74464i
$520$	5.05133e89			1.18931
$521$		−	1.98266e89i		−	0.438131i	−0.975710	−	0.219065i	$-0.929699\pi$
$521$		−	1.98266e89i		−	0.438131i	0.975710	−	0.219065i	$-0.0703008\pi$
$522$	7.07364e89	+	1.36613e89i	1.46729	+	0.283377i
$523$	−3.64322e89			−0.709463			−0.354732	−	0.934968i	$-0.615428\pi$
$523$	−3.64322e89			−0.709463			−0.354732	+	0.934968i	$0.615428\pi$
$524$		−	1.96314e87i		−	0.00358937i
$525$	2.16293e89	+	2.06951e88i	0.371352	+	0.0355313i
$526$	4.21001e89			0.678818
$527$			3.99019e89i			0.604286i
$528$	−5.21970e88	+	5.45534e89i	−0.0742551	+	0.776072i
$529$	7.28288e89			0.973343
$530$		−	1.63897e90i		−	2.05811i
$531$	2.27382e89	−	1.17735e90i	0.268310	−	1.38928i
$532$	−1.58380e87			−0.00175638
$533$			1.25229e90i			1.30529i
$534$	1.66330e90	+	1.59145e89i	1.62970	+	0.155931i
$535$	−6.21212e89			−0.572223
$536$		−	6.69944e89i		−	0.580230i
$537$	1.26001e89	−	1.31689e90i	0.102618	−	1.07251i
$538$	−2.18456e90			−1.67320
$539$			1.98611e89i			0.143078i
$540$	−1.82073e87	+	6.18774e87i	−0.00123382	+	0.00419313i
$541$	−2.03398e89			−0.129669			−0.0648347	−	0.997896i	$-0.520652\pi$
$541$	−2.03398e89			−0.129669			−0.0648347	+	0.997896i	$0.520652\pi$
$542$			1.73032e90i			1.03789i
$543$	5.21346e89	+	4.98827e88i	0.294260	+	0.0281550i
$544$	9.03148e87			0.00479728
$545$			1.09707e89i			0.0548466i
$546$	−2.26907e89	+	2.37150e90i	−0.106780	+	1.11600i
$547$	−2.65890e90			−1.17793			−0.588965	−	0.808159i	$-0.700464\pi$
$547$	−2.65890e90			−1.17793			−0.588965	+	0.808159i	$0.700464\pi$
$548$		−	7.02192e87i		−	0.00292885i
$549$	−1.09632e90	−	2.11731e89i	−0.430574	−	0.0831566i
$550$	−7.21255e89			−0.266759
$551$			1.83229e90i			0.638251i
$552$	−4.94414e89	−	4.73059e88i	−0.162219	−	0.0155212i
$553$	3.06745e90			0.948086
$554$			2.82986e90i			0.824030i
$555$	7.46729e89	−	7.80438e90i	0.204878	−	2.14126i
$556$	2.96501e86			7.66582e−5
$557$		−	4.39739e89i		−	0.107145i	−0.998564	−	0.0535727i	$-0.982939\pi$
$557$		−	4.39739e89i		−	0.107145i	0.998564	−	0.0535727i	$-0.0170609\pi$
$558$	−7.86104e89	+	4.07035e90i	−0.180531	+	0.934766i
$559$	−4.58723e90			−0.993027
$560$		−	6.20234e90i		−	1.26576i
$561$	−2.55537e90	−	2.44499e89i	−0.491676	−	0.0470439i
$562$	−2.95420e89			−0.0535972
$563$			1.94097e90i			0.332079i	0.986119	+	0.166039i	$0.0530979\pi$
$563$			1.94097e90i			0.332079i	−0.986119	+	0.166039i	$0.946902\pi$
$564$	−3.32465e87	+	3.47474e88i	−0.000536458	+	0.00560675i
$565$	−4.11706e90			−0.626597
$566$		−	3.66507e90i		−	0.526186i
$567$	7.45665e90	+	2.99179e90i	1.00996	+	0.405219i
$568$	5.45609e90			0.697246
$569$			1.87470e90i			0.226062i	0.993591	+	0.113031i	$0.0360559\pi$
$569$			1.87470e90i			0.226062i	−0.993591	+	0.113031i	$0.963944\pi$
$570$	−4.34566e90	−	4.15796e89i	−0.494522	−	0.0473162i
$571$	1.13645e91			1.22056			0.610280	−	0.792186i	$-0.291057\pi$
$571$	1.13645e91			1.22056			0.610280	+	0.792186i	$0.291057\pi$
$572$		−	2.97163e88i		−	0.00301250i
$573$	1.46774e89	−	1.53400e90i	0.0140458	−	0.146799i
$574$	1.53186e91			1.38397
$575$		−	6.56134e89i		−	0.0559698i
$576$	−1.21433e91	−	2.34523e90i	−0.978125	−	0.188905i
$577$	1.88890e91			1.43683			0.718417	−	0.695612i	$-0.244867\pi$
$577$	1.88890e91			1.43683			0.718417	+	0.695612i	$0.244867\pi$
$578$		−	8.30598e90i		−	0.596722i
$579$	−5.27893e90	−	5.05091e89i	−0.358223	−	0.0342750i
$580$	1.01705e89			0.00651959
$581$			1.56141e91i			0.945592i
$582$	−1.63022e90	+	1.70381e91i	−0.0932797	+	0.974906i
$583$	2.54659e91			1.37688
$584$			1.57170e91i			0.803056i
$585$	−4.67906e90	+	2.42276e91i	−0.225952	+	1.16995i
$586$	−2.70549e91			−1.23488
$587$		−	3.14443e91i		−	1.35670i	−0.734738	−	0.678351i	$-0.762695\pi$
$587$		−	3.14443e91i		−	1.35670i	0.734738	−	0.678351i	$-0.237305\pi$
$588$	1.69573e88	+	1.62249e87i	0.000691680	+	6.61804e-5i
$589$	−1.05434e91			−0.406610
$590$		−	4.50486e91i		−	1.64272i
$591$	1.59638e90	−	1.66844e91i	0.0550488	−	0.575339i
$592$	−5.71331e91			−1.86325
$593$		−	5.17961e90i		−	0.159769i	−0.996804	−	0.0798845i	$-0.974545\pi$
$593$		−	5.17961e90i		−	0.159769i	0.996804	−	0.0798845i	$-0.0254551\pi$
$594$	−2.55853e91	−	7.52842e90i	−0.746515	−	0.219660i
$595$	2.90528e91			0.801913
$596$		−	2.60579e89i		−	0.00680476i
$597$	−5.29957e91	−	5.07066e90i	−1.30945	−	0.125289i
$598$	7.19403e90			0.168203
$599$			4.07605e91i			0.901892i	0.892551	+	0.450946i	$0.148913\pi$
$599$			4.07605e91i			0.901892i	−0.892551	+	0.450946i	$0.851087\pi$
$600$	1.55619e90	−	1.62644e91i	0.0325891	−	0.340602i
$601$	4.79621e91			0.950693			0.475347	−	0.879799i	$-0.342323\pi$
$601$	4.79621e91			0.950693			0.475347	+	0.879799i	$0.342323\pi$
$602$			5.61133e91i			1.05289i
$603$	3.21324e91	+	6.20571e90i	0.570784	+	0.110235i
$604$	4.22157e89			0.00709995
$605$			2.88696e91i			0.459741i
$606$	−1.73057e91	−	1.65582e90i	−0.260972	−	0.0249699i
$607$	−5.24528e90			−0.0749104			−0.0374552	−	0.999298i	$-0.511925\pi$
$607$	−5.24528e90			−0.0749104			−0.0374552	+	0.999298i	$0.511925\pi$
$608$			2.38643e89i			0.00322798i
$609$	1.20665e91	−	1.26112e92i	0.154601	−	1.61580i
$610$	−4.19478e91			−0.509125
$611$			1.33537e92i			1.53547i
$612$	−4.17505e88	+	2.16179e89i	−0.000454846	+	0.00235513i
$613$	−1.10860e92			−1.14441			−0.572203	−	0.820112i	$-0.693911\pi$
$613$	−1.10860e92			−1.14441			−0.572203	+	0.820112i	$0.693911\pi$
$614$		−	8.29215e91i		−	0.811168i
$615$	1.57943e92	+	1.51121e91i	1.46427	+	0.140103i
$616$	9.60079e91			0.843614
$617$			3.12949e91i			0.260653i	0.991471	+	0.130327i	$0.0416026\pi$
$617$			3.12949e91i			0.260653i	−0.991471	+	0.130327i	$0.958397\pi$
$618$	−1.26832e91	+	1.32557e92i	−0.100140	+	1.04661i
$619$	5.16464e91			0.386588			0.193294	−	0.981141i	$-0.438083\pi$
$619$	5.16464e91			0.386588			0.193294	+	0.981141i	$0.438083\pi$
$620$			5.85237e89i			0.00415342i
$621$	6.84870e90	−	2.32753e91i	0.0460877	−	0.156629i
$622$	1.60629e92			1.02504
$623$		−	2.93826e92i		−	1.77822i
$624$	1.79000e92	+	1.71269e91i	1.02745	+	0.0983074i
$625$	−2.25050e92			−1.22529
$626$			8.71024e91i			0.449860i
$627$	6.46051e90	−	6.75216e91i	0.0316547	−	0.330837i
$628$	−1.26473e90			−0.00587935
$629$		−	2.67620e92i		−	1.18045i
$630$	2.96364e92	+	5.72366e91i	1.24047	+	0.239572i
$631$	−1.42401e92			−0.565645			−0.282823	−	0.959172i	$-0.591271\pi$
$631$	−1.42401e92			−0.565645			−0.282823	+	0.959172i	$0.591271\pi$
$632$		−	2.30660e92i		−	0.869579i
$633$	−1.42268e92	−	1.36123e91i	−0.509077	−	0.0487089i
$634$	−1.03561e92			−0.351765
$635$			4.00107e92i			1.29016i
$636$	2.08035e89	−	2.17426e90i	0.000636871	−	0.00665622i
$637$	6.51681e91			0.189424
$638$			4.20536e92i			1.16070i
$639$	−5.05399e91	+	2.61689e92i	−0.132467	+	0.685895i
$640$	−4.68145e92			−1.16531
$641$			1.37010e92i			0.323920i	0.986797	+	0.161960i	$0.0517816\pi$
$641$			1.37010e92i			0.323920i	−0.986797	+	0.161960i	$0.948218\pi$
$642$	−2.19307e92	−	2.09835e91i	−0.492490	−	0.0471217i
$643$	−8.76906e92			−1.87064			−0.935321	−	0.353799i	$-0.884890\pi$
$643$	−8.76906e92			−1.87064			−0.935321	+	0.353799i	$0.884890\pi$
$644$		−	3.30685e89i		−	0.000670164i
$645$	−5.53569e91	+	5.78559e92i	−0.106586	+	1.11398i
$646$	−1.49017e92			−0.272624
$647$		−	7.56429e92i		−	1.31500i	−0.753453	−	0.657502i	$-0.771613\pi$
$647$		−	7.56429e92i		−	1.31500i	0.753453	−	0.657502i	$-0.228387\pi$
$648$	2.24971e92	−	5.60711e92i	0.371664	−	0.926326i
$649$	6.99951e92			1.09899
$650$			2.36658e92i			0.353167i
$651$	7.25682e92	+	6.94337e91i	1.02937	+	0.0984913i
$652$	1.28738e89			0.000173594
$653$		−	2.53205e92i		−	0.324591i	−0.986742	−	0.162296i	$-0.948110\pi$
$653$		−	2.53205e92i		−	0.324591i	0.986742	−	0.162296i	$-0.0518899\pi$
$654$	−3.70571e90	+	3.87300e91i	−0.00451654	+	0.0472043i
$655$	−9.51538e92			−1.10271
$656$		−	1.15624e93i		−	1.27416i
$657$	−7.53833e92	−	1.45587e92i	−0.789983	−	0.152569i
$658$	1.63349e93			1.62802
$659$			3.29043e92i			0.311913i	0.987764	+	0.155957i	$0.0498460\pi$
$659$			3.29043e92i			0.311913i	−0.987764	+	0.155957i	$0.950154\pi$
$660$	−3.74794e90	−	3.58605e89i	−0.00337942	−	0.000323345i
$661$	3.88346e92			0.333097			0.166548	−	0.986033i	$-0.446738\pi$
$661$	3.88346e92			0.333097			0.166548	+	0.986033i	$0.446738\pi$
$662$			9.10011e92i			0.742562i
$663$	−8.02249e91	+	8.38465e92i	−0.0622821	+	0.650937i
$664$	1.17412e93			0.867291
$665$			7.67674e92i			0.539588i
$666$	5.27237e92	−	2.72997e93i	0.352660	−	1.82603i
$667$	−3.82567e92			−0.243531
$668$		−	5.07724e90i		−	0.00307613i
$669$	−1.98816e93	−	1.90228e92i	−1.14654	−	0.109702i
$670$	1.22947e93			0.674914
$671$		−	6.51772e92i		−	0.340606i
$672$	1.57158e90	−	1.64253e91i	0.000781898	−	0.00817196i
$673$	2.47247e93			1.17121			0.585604	−	0.810597i	$-0.300857\pi$
$673$	2.47247e93			1.17121			0.585604	+	0.810597i	$0.300857\pi$
$674$			3.51061e93i			1.58346i
$675$	7.65673e92	+	2.25297e92i	0.328866	+	0.0967680i
$676$	−5.28971e89			−0.000216367
$677$			3.53336e93i			1.37646i	0.725494	+	0.688228i	$0.241611\pi$
$677$			3.53336e93i			1.37646i	−0.725494	+	0.688228i	$0.758389\pi$
$678$	−1.45345e93	−	1.39067e92i	−0.539287	−	0.0515994i
$679$	3.00983e93			1.06375
$680$		−	2.18465e93i		−	0.735510i
$681$	−4.93366e91	+	5.15638e92i	−0.0158239	+	0.165383i
$682$	−2.41987e93			−0.739447
$683$		−	4.56857e93i		−	1.33014i	−0.746781	−	0.665070i	$-0.768402\pi$
$683$		−	4.56857e93i		−	1.33014i	0.746781	−	0.665070i	$-0.231598\pi$
$684$	−5.71218e90	−	1.10319e90i	−0.00158471	−	0.000306055i
$685$	−3.40354e93			−0.899792
$686$			3.53024e93i			0.889424i
$687$	−5.17298e93	−	4.94954e92i	−1.24213	−	0.118848i
$688$	4.23542e93			0.969344
$689$		−	8.35585e93i		−	1.82287i
$690$	8.68148e91	−	9.07339e92i	0.0180540	−	0.188690i
$691$	−5.96892e93			−1.18337			−0.591685	−	0.806169i	$-0.701537\pi$
$691$	−5.96892e93			−1.18337			−0.591685	+	0.806169i	$0.701537\pi$
$692$			3.49742e91i			0.00661068i
$693$	−8.89325e92	+	4.60481e93i	−0.160274	+	0.829880i
$694$	−4.40509e93			−0.756994
$695$		−	1.43715e92i		−	0.0235507i
$696$	−9.48316e93	−	9.07356e92i	−1.48200	−	0.141799i
$697$	5.41603e93			0.807234
$698$			2.77228e93i			0.394102i
$699$	−2.04244e92	+	2.13464e93i	−0.0276951	+	0.289453i
$700$	1.08783e91			0.00140711
$701$		−	3.39134e93i		−	0.418482i	−0.977864	−	0.209241i	$-0.932901\pi$
$701$		−	3.39134e93i		−	0.418482i	0.977864	−	0.209241i	$-0.0670993\pi$
$702$	−2.47022e93	+	8.39504e93i	−0.290811	+	0.988322i
$703$	7.07145e93			0.794296
$704$		−	7.21932e93i		−	0.773746i
$705$	1.68421e94	+	1.61147e93i	1.72249	+	0.164809i
$706$	−4.42122e92			−0.0431506
$707$			3.05711e93i			0.284754i
$708$	5.71802e90	−	5.97614e91i	0.000508332	−	0.00531280i
$709$	1.64961e94			1.39976			0.699881	−	0.714259i	$-0.253236\pi$
$709$	1.64961e94			1.39976			0.699881	+	0.714259i	$0.253236\pi$
$710$			1.00129e94i			0.811025i
$711$	1.10631e94	+	2.13661e93i	0.855422	+	0.165207i
$712$	−2.20946e94			−1.63097
$713$		−	2.20138e93i		−	0.155146i
$714$	1.02565e94	+	9.81351e92i	0.690175	+	0.0660364i
$715$	−1.44036e94			−0.925488
$716$		−	6.62324e91i		−	0.00406388i
$717$	2.06495e93	−	2.15816e94i	0.120998	−	1.26460i
$718$	7.30322e93			0.408703
$719$			6.50810e93i			0.347857i	0.984758	+	0.173929i	$0.0556462\pi$
$719$			6.50810e93i			0.347857i	−0.984758	+	0.173929i	$0.944354\pi$
$720$	4.32021e93	−	2.23695e94i	0.220563	−	1.14205i
$721$	2.34166e94			1.14199
$722$			1.75677e94i			0.818442i
$723$	−1.27555e94	−	1.22045e93i	−0.567718	−	0.0543196i
$724$	2.62208e91			0.00111499
$725$		−	1.25851e94i		−	0.511330i
$726$	−9.75164e92	+	1.01919e94i	−0.0378590	+	0.395681i
$727$	−1.51277e94			−0.561225			−0.280613	−	0.959821i	$-0.590538\pi$
$727$	−1.51277e94			−0.561225			−0.280613	+	0.959821i	$0.590538\pi$
$728$		−	3.15021e94i		−	1.11687i
$729$	2.48094e94	+	1.59841e94i	0.840635	+	0.541602i
$730$	−2.88435e94			−0.934102
$731$			1.98394e94i			0.614122i
$732$	−5.56479e91	−	5.32443e90i	−0.00164658	−	0.000157546i
$733$	−3.75737e94			−1.06280			−0.531401	−	0.847120i	$-0.678334\pi$
$733$	−3.75737e94			−1.06280			−0.531401	+	0.847120i	$0.678334\pi$
$734$		−	1.86481e94i		−	0.504273i
$735$	7.86424e92	−	8.21925e93i	0.0203317	−	0.212496i
$736$	−4.98266e91			−0.00123167
$737$			1.91031e94i			0.451519i
$738$	5.52483e94	+	1.06701e94i	1.24870	+	0.241161i
$739$	4.28397e94			0.925934			0.462967	−	0.886376i	$-0.346785\pi$
$739$	4.28397e94			0.925934			0.462967	+	0.886376i	$0.346785\pi$
$740$		−	3.92517e92i		−	0.00811356i
$741$	−2.21551e94	−	2.11982e93i	−0.437999	−	0.0419081i
$742$	−1.02213e95			−1.93275
$743$			8.22752e94i			1.48812i	0.668113	+	0.744060i	$0.267102\pi$
$743$			8.22752e94i			1.48812i	−0.668113	+	0.744060i	$0.732898\pi$
$744$	5.22115e93	−	5.45684e94i	0.0903356	−	0.944136i
$745$	−1.26303e95			−2.09054
$746$			7.18249e94i			1.13735i
$747$	−1.08759e94	+	5.63140e94i	−0.164773	+	0.853172i
$748$	−1.28521e92			−0.00186303
$749$			3.87412e94i			0.537370i
$750$	−5.72216e94	−	5.47500e93i	−0.759518	−	0.0726712i
$751$	8.22683e94			1.04500			0.522498	−	0.852641i	$-0.325000\pi$
$751$	8.22683e94			1.04500			0.522498	+	0.852641i	$0.325000\pi$
$752$		−	1.23295e95i		−	1.49885i
$753$	4.85797e93	−	5.07727e94i	0.0565224	−	0.590740i
$754$	1.37986e95			1.53667
$755$		−	2.04621e95i		−	2.18122i
$756$	3.85892e92	+	1.13548e92i	0.00393773	+	0.00115867i
$757$	9.78625e93			0.0955987			0.0477994	−	0.998857i	$-0.484779\pi$
$757$	9.78625e93			0.0955987			0.0477994	+	0.998857i	$0.484779\pi$
$758$			4.43877e94i			0.415125i
$759$	1.40979e94	+	1.34890e93i	0.126234	+	0.0120782i
$760$	5.77261e94			0.494907
$761$		−	2.34148e94i		−	0.192219i	−0.995371	−	0.0961096i	$-0.969360\pi$
$761$		−	2.34148e94i		−	0.192219i	0.995371	−	0.0961096i	$-0.0306399\pi$
$762$	−1.35149e94	+	1.41250e95i	−0.106243	+	1.11039i
$763$	6.84176e93			0.0515060
$764$		−	7.71516e91i		−	0.000556242i
$765$	1.04782e95	+	2.02365e94i	0.723536	+	0.139736i
$766$	2.09518e95			1.38571
$767$		−	2.29667e95i		−	1.45496i
$768$	−1.85617e93	−	1.77600e92i	−0.0112641	−	0.00107776i
$769$	−1.71548e94			−0.0997276			−0.0498638	−	0.998756i	$-0.515879\pi$
$769$	−1.71548e94			−0.0997276			−0.0498638	+	0.998756i	$0.515879\pi$
$770$			1.76192e95i			0.981277i
$771$	−6.64804e93	+	6.94816e94i	−0.0354731	+	0.370745i
$772$	−2.65500e92			−0.00135736
$773$			1.28537e95i			0.629657i	0.949148	+	0.314829i	$0.101947\pi$
$773$			1.28537e95i			0.629657i	−0.949148	+	0.314829i	$0.898053\pi$
$774$	−3.90854e94	+	2.02379e95i	−0.183469	+	0.949980i
$775$	7.24175e94			0.325752
$776$		−	2.26327e95i		−	0.975665i
$777$	−4.86712e95	−	4.65689e94i	−2.01084	−	0.192399i
$778$	2.35317e95			0.931809
$779$			1.43110e95i			0.543168i
$780$	−1.17665e92	+	1.22977e93i	−0.000428081	+	0.00447406i
$781$	−1.55577e95			−0.542578
$782$		−	3.11136e94i		−	0.104022i
$783$	1.31362e95	−	4.46435e95i	0.421049	−	1.43093i
$784$	−6.01701e94			−0.184906
$785$			6.13017e95i			1.80623i
$786$	−3.35922e95	−	3.21413e94i	−0.949063	−	0.0908070i
$787$	−2.46355e95			−0.667414			−0.333707	−	0.942677i	$-0.608300\pi$
$787$	−2.46355e95			−0.667414			−0.333707	+	0.942677i	$0.608300\pi$
$788$		−	8.39132e92i		−	0.00218004i
$789$	2.59013e94	−	2.70706e95i	0.0645329	−	0.674461i
$790$	4.23303e95			1.01148
$791$			2.56756e95i			0.588433i
$792$	3.46264e95	+	6.68738e94i	0.761161	+	0.147003i
$793$	−2.13859e95			−0.450933
$794$		−	9.71082e95i		−	1.96417i
$795$	−1.05387e96	−	1.00835e95i	−2.04490	−	0.195657i
$796$	−2.66538e93			−0.00496168
$797$			3.70283e95i			0.661317i	0.943750	+	0.330659i	$0.107271\pi$
$797$			3.70283e95i			0.661317i	−0.943750	+	0.330659i	$0.892729\pi$
$798$	−2.59307e94	+	2.71013e95i	−0.0444343	+	0.464402i
$799$	5.77534e95			0.949585
$800$		−	1.63912e93i		−	0.00258607i
$801$	2.04663e95	−	1.05972e96i	0.309860	−	1.60442i
$802$	−1.09927e96			−1.59717
$803$		−	4.48162e95i		−	0.624916i
$804$	1.63101e93	+	1.56056e92i	0.00218277	+	0.000208849i
$805$	−1.60284e95			−0.205886
$806$			7.94005e95i			0.978964i
$807$	−1.34401e95	+	1.40468e96i	−0.159066	+	1.66246i
$808$	2.29882e95			0.261175
$809$			9.23799e95i			1.00757i	0.863828	+	0.503786i	$0.168060\pi$
$809$			9.23799e95i			1.00757i	−0.863828	+	0.503786i	$0.831940\pi$
$810$	1.02900e96	+	4.12862e95i	1.07749	+	0.432314i
$811$	−9.43537e94			−0.0948573			−0.0474286	−	0.998875i	$-0.515103\pi$
$811$	−9.43537e94			−0.0948573			−0.0474286	+	0.998875i	$0.515103\pi$
$812$		−	6.34274e93i		−	0.00612249i
$813$	1.11261e96	+	1.06455e95i	1.03123	+	0.0986685i
$814$	1.62300e96			1.44448
$815$		−	6.23995e94i		−	0.0533311i
$816$	7.40722e94	−	7.74160e95i	0.0607967	−	0.635412i
$817$	−5.24225e95			−0.413228
$818$		−	7.76413e95i		−	0.587805i
$819$	1.51093e96	+	2.91805e95i	1.09869	+	0.212189i
$820$	7.94364e93			0.00554833
$821$		−	1.91078e96i		−	1.28199i	−0.767544	−	0.640997i	$-0.778521\pi$
$821$		−	1.91078e96i		−	1.28199i	0.767544	−	0.640997i	$-0.221479\pi$
$822$	−1.20156e96	−	1.14966e95i	−0.774415	−	0.0740966i
$823$	2.08837e96			1.29304			0.646522	−	0.762896i	$-0.276223\pi$
$823$	2.08837e96			1.29304			0.646522	+	0.762896i	$0.276223\pi$
$824$		−	1.76084e96i		−	1.04742i
$825$	−4.43739e94	+	4.63771e95i	−0.0253599	+	0.265047i
$826$	−2.80940e96			−1.54267
$827$			5.70193e95i			0.300843i	0.988622	+	0.150422i	$0.0480631\pi$
$827$			5.70193e95i			0.300843i	−0.988622	+	0.150422i	$0.951937\pi$
$828$	2.30337e92	−	1.19266e93i	0.000116778	−	0.000604664i
$829$	1.05951e96			0.516184			0.258092	−	0.966120i	$-0.416906\pi$
$829$	1.05951e96			0.516184			0.258092	+	0.966120i	$0.416906\pi$
$830$			2.15472e96i			1.00882i
$831$	1.81962e96	+	1.74102e95i	0.818741	+	0.0783377i
$832$	−2.36880e96			−1.02437
$833$		−	2.81847e95i		−	0.117146i
$834$	4.85444e93	−	5.07358e94i	0.00193936	−	0.0202691i
$835$	−2.46095e96			−0.945038
$836$		−	3.39596e93i		−	0.00125359i
$837$	2.56889e96	+	7.55891e95i	0.911604	+	0.268237i
$838$	−3.35421e96			−1.14429
$839$		−	2.14772e96i		−	0.704422i	−0.935921	−	0.352211i	$-0.885430\pi$
$839$		−	2.14772e96i		−	0.704422i	0.935921	−	0.352211i	$-0.114570\pi$
$840$	−3.97316e96	−	3.80154e95i	−1.25291	−	0.119879i
$841$	−4.03974e96			−1.22486
$842$		−	1.82727e96i		−	0.532725i
$843$	−1.81752e94	+	1.89957e95i	−0.00509530	+	0.0532532i
$844$	−7.15526e93			−0.00192897
$845$			2.56394e95i			0.0664715i
$846$	5.89136e96	+	1.13780e96i	1.46891	+	0.283689i
$847$	1.80042e96			0.431739
$848$			7.71500e96i			1.77940i
$849$	−2.35666e96	−	2.25487e95i	−0.522809	−	0.0500227i
$850$	1.02352e96			0.218410
$851$			1.47646e96i			0.303072i
$852$	−1.27094e93	+	1.32831e94i	−0.000250968	+	0.00262297i
$853$	1.68831e96			0.320726			0.160363	−	0.987058i	$-0.448733\pi$
$853$	1.68831e96			0.320726			0.160363	+	0.987058i	$0.448733\pi$
$854$			2.61603e96i			0.478115i
$855$	−5.34719e95	+	2.76871e96i	−0.0940251	+	0.486850i
$856$	2.91319e96			0.492873
$857$		−	5.74950e96i		−	0.935972i	−0.883736	−	0.467986i	$-0.844980\pi$
$857$		−	5.74950e96i		−	0.935972i	0.883736	−	0.467986i	$-0.155020\pi$
$858$	−5.08491e96	−	4.86528e95i	−0.796531	−	0.0762127i
$859$	−7.13093e96			−1.07491			−0.537455	−	0.843293i	$-0.680614\pi$
$859$	−7.13093e96			−1.07491			−0.537455	+	0.843293i	$0.680614\pi$
$860$			2.90983e94i			0.00422103i
$861$	9.42450e95	−	9.84994e96i	0.131569	−	1.37509i
$862$	−2.07725e95			−0.0279093
$863$		−	9.95267e96i		−	1.28701i	−0.765440	−	0.643507i	$-0.777479\pi$
$863$		−	9.95267e96i		−	1.28701i	0.765440	−	0.643507i	$-0.222521\pi$
$864$	1.71090e94	−	5.81450e94i	0.00212947	−	0.00723700i
$865$	1.69521e97			2.03091
$866$			9.32829e96i			1.07575i
$867$	−5.34080e96	−	5.11011e95i	−0.592892	−	0.0567283i
$868$	3.64977e94			0.00390045
$869$			6.57714e96i			0.676682i
$870$	1.66516e96	−	1.74033e97i	0.164938	−	1.72384i
$871$	6.26809e96			0.597772
$872$		−	5.14474e95i		−	0.0472410i
$873$	1.08553e97	+	2.09648e96i	0.959781	+	0.185362i
$874$	8.22127e95			0.0699942
$875$			1.01084e97i			0.828733i
$876$	−3.82638e94	−	3.66111e93i	−0.00302102	−	0.000289053i
$877$	9.81445e96			0.746241			0.373121	−	0.927783i	$-0.378288\pi$
$877$	9.81445e96			0.746241			0.373121	+	0.927783i	$0.378288\pi$
$878$		−	1.56893e97i		−	1.14890i
$879$	−1.66450e96	+	1.73965e97i	−0.117396	+	1.22695i
$880$	1.32989e97			0.903416
$881$			2.30906e97i			1.51088i	0.655217	+	0.755441i	$0.272577\pi$
$881$			2.30906e97i			1.51088i	−0.655217	+	0.755441i	$0.727423\pi$
$882$	5.55264e95	−	2.87509e96i	0.0349974	−	0.181212i
$883$	−2.21529e97			−1.34502			−0.672508	−	0.740090i	$-0.734783\pi$
$883$	−2.21529e97			−1.34502			−0.672508	+	0.740090i	$0.734783\pi$
$884$			4.21701e94i			0.00246649i
$885$	−2.89665e97	−	2.77154e96i	−1.63218	−	0.156168i
$886$	1.32564e97			0.719637
$887$		−	2.90022e97i		−	1.51688i	−0.651744	−	0.758439i	$-0.725962\pi$
$887$		−	2.90022e97i		−	1.51688i	0.651744	−	0.758439i	$-0.274038\pi$
$888$	−3.50180e96	+	3.65989e97i	−0.176467	+	1.84433i
$889$	2.49522e97			1.21158
$890$		−	4.05475e97i		−	1.89712i
$891$	−6.41492e96	+	1.59884e97i	−0.289219	+	0.720841i
$892$	−9.99931e94			−0.00434440
$893$			1.52604e97i			0.638953i
$894$	−4.45890e97	−	4.26630e96i	−1.79924	−	0.172153i
$895$	−3.21030e97			−1.24849
$896$			2.91953e97i			1.09433i
$897$	4.42601e95	−	4.62581e96i	0.0159905	−	0.167123i
$898$	−1.59214e97			−0.554449
$899$		−	4.22239e97i		−	1.41739i
$900$	3.92340e94	+	7.57725e93i	0.00126958	+	0.000245193i
$901$	−3.61383e97			−1.12733
$902$			3.28457e97i			0.987787i
$903$	3.60812e97	+	3.45227e96i	1.04613	+	0.100094i
$904$	1.93071e97			0.539707
$905$		−	1.27093e97i		−	0.342545i
$906$	6.91173e96	−	7.22374e97i	0.179621	−	1.87729i
$907$	−2.91451e96			−0.0730341			−0.0365170	−	0.999333i	$-0.511626\pi$
$907$	−2.91451e96			−0.0730341			−0.0365170	+	0.999333i	$0.511626\pi$
$908$			2.59337e94i			0.000626659i
$909$	−2.12941e96	+	1.10258e97i	−0.0496194	+	0.256923i
$910$	5.78119e97			1.29913
$911$		−	2.51339e97i		−	0.544695i	−0.962199	−	0.272347i	$-0.912200\pi$
$911$		−	2.51339e97i		−	0.544695i	0.962199	−	0.272347i	$-0.0878000\pi$
$912$	2.04560e97	+	1.95724e96i	0.427553	+	0.0409086i
$913$	−3.34793e97			−0.674902
$914$		−	3.49072e95i		−	0.00678720i
$915$	−2.58077e96	+	2.69727e97i	−0.0484008	+	0.505857i
$916$	−2.60172e95			−0.00470663
$917$			5.93416e97i			1.03555i
$918$	3.63078e97	+	1.06835e97i	0.611212	+	0.179848i
$919$	−6.32793e96			−0.102766			−0.0513831	−	0.998679i	$-0.516363\pi$
$919$	−6.32793e96			−0.102766			−0.0513831	+	0.998679i	$0.516363\pi$
$920$			1.20527e97i			0.188837i
$921$	−5.33190e97	−	5.10160e96i	−0.805962	−	0.0771150i
$922$	9.34053e97			1.36223
$923$			5.10479e97i			0.718327i
$924$	−2.23640e94	+	2.33736e95i	−0.000303651	+	0.00317359i
$925$	−4.85702e97			−0.636344
$926$			2.50196e97i			0.316314i
$927$	8.44549e97	+	1.63107e97i	1.03037	+	0.198995i
$928$	−9.55705e95			−0.0112523
$929$		−	5.42272e97i		−	0.616167i	−0.951359	−	0.308083i	$-0.900312\pi$
$929$		−	5.42272e97i		−	0.616167i	0.951359	−	0.308083i	$-0.0996876\pi$
$930$	1.00143e98	+	9.58174e96i	1.09820	+	0.105077i
$931$	7.44735e96			0.0788247
$932$			1.07361e95i			0.00109678i
$933$	9.88240e96	−	1.03285e98i	0.0974470	−	1.01846i
$934$	−1.17085e98			−1.11443
$935$			6.22942e97i			0.572354i
$936$	2.19426e97	−	1.13616e98i	0.194619	−	1.00771i
$937$	−1.46562e96			−0.0125492			−0.00627460	−	0.999980i	$-0.501997\pi$
$937$	−1.46562e96			−0.0125492			−0.00627460	+	0.999980i	$0.501997\pi$
$938$		−	7.66743e97i		−	0.633806i
$939$	5.60074e97	+	5.35882e96i	0.446972	+	0.0427666i
$940$	8.47064e95			0.00652675
$941$		−	1.36903e98i		−	1.01849i	−0.860622	−	0.509244i	$-0.829925\pi$
$941$		−	1.36903e98i		−	1.01849i	0.860622	−	0.509244i	$-0.170075\pi$
$942$	−2.07067e97	+	2.16414e98i	−0.148741	+	1.55455i
$943$	−2.98802e97			−0.207251
$944$			2.12053e98i			1.42026i
$945$	5.50368e97	−	1.87043e98i	0.355962	−	1.20974i
$946$	−1.20317e98			−0.751482
$947$		−	2.43300e98i		−	1.46755i	−0.679392	−	0.733775i	$-0.737756\pi$
$947$		−	2.43300e98i		−	1.46755i	0.679392	−	0.733775i	$-0.262244\pi$
$948$	5.61553e95	+	5.37298e94i	0.00327127	+	0.000312997i
$949$	−1.47051e98			−0.827336
$950$			2.70450e97i			0.146963i
$951$	−6.37144e96	+	6.65907e97i	−0.0334411	+	0.349507i
$952$	−1.36244e98			−0.690712
$953$			3.22439e98i			1.57900i	0.613750	+	0.789500i	$0.289660\pi$
$953$			3.22439e98i			1.57900i	−0.613750	+	0.789500i	$0.710340\pi$
$954$	−3.68643e98	−	7.11958e97i	−1.74385	−	0.336789i
$955$	−3.73956e97			−0.170887
$956$		−	1.08543e96i		−	0.00479174i
$957$	2.70407e98	+	2.58727e97i	1.15325	+	0.110344i
$958$	−1.54453e98			−0.636408
$959$			2.12258e98i			0.844988i
$960$	−2.85857e97	+	2.98762e98i	−0.109951	+	1.14914i
$961$	−2.61075e97			−0.0970274
$962$		−	5.32536e98i		−	1.91237i
$963$	−2.69850e97	+	1.39725e98i	−0.0936386	+	0.484849i
$964$	−6.41528e95			−0.00215116
$965$			1.28689e98i			0.417003i
$966$	−5.65852e97	−	5.41411e96i	−0.177198	−	0.0169544i
$967$	4.27965e98			1.29519			0.647597	−	0.761983i	$-0.275774\pi$
$967$	4.27965e98			1.29519			0.647597	+	0.761983i	$0.275774\pi$
$968$		−	1.35385e98i		−	0.395988i
$969$	−9.16803e96	+	9.58190e97i	−0.0259174	+	0.270874i
$970$	4.15352e98			1.13488
$971$		−	2.53823e98i		−	0.670343i	−0.942157	−	0.335171i	$-0.891206\pi$
$971$		−	2.53823e98i		−	0.670343i	0.942157	−	0.335171i	$-0.108794\pi$
$972$	1.31267e96	+	6.78314e95i	0.00335097	+	0.00173159i
$973$	−8.96263e96			−0.0221163
$974$		−	3.11286e98i		−	0.742530i
$975$	1.52172e98	+	1.45599e97i	0.350900	+	0.0335743i
$976$	1.97457e98			0.440179
$977$			1.94388e98i			0.418938i	0.977815	+	0.209469i	$0.0671735\pi$
$977$			1.94388e98i			0.418938i	−0.977815	+	0.209469i	$0.932827\pi$
$978$	2.10775e96	−	2.20290e97i	0.00439174	−	0.0458999i
$979$	6.30014e98			1.26918
$980$		−	4.13382e95i		−	0.000805177i
$981$	2.46756e97	+	4.76559e96i	0.0464719	+	0.00897510i
$982$	9.60017e97			0.174823
$983$			1.80035e98i			0.317022i	0.987357	+	0.158511i	$0.0506694\pi$
$983$			1.80035e98i			0.317022i	−0.987357	+	0.158511i	$0.949331\pi$
$984$	−7.40678e98	−	7.08686e97i	−1.26122	−	0.120674i
$985$	−4.06729e98			−0.669745
$986$		−	5.96777e98i		−	0.950329i
$987$	1.00497e98	−	1.05034e99i	0.154771	−	1.61757i
$988$	−1.11428e96			−0.00165964
$989$		−	1.09454e98i		−	0.157671i
$990$	−1.22725e98	+	6.35457e98i	−0.170991	+	0.885370i
$991$	1.81816e98			0.245020			0.122510	−	0.992467i	$-0.460906\pi$
$991$	1.81816e98			0.245020			0.122510	+	0.992467i	$0.460906\pi$
$992$		−	5.49936e96i		−	0.00716848i
$993$	5.85142e98	+	5.59868e97i	0.737796	+	0.0705928i
$994$	6.24444e98			0.761627
$995$			1.29192e99i			1.52431i
$996$	−2.73498e95	+	2.85845e96i	−0.000312174	+	0.00326266i
$997$	3.62760e98			0.400571			0.200285	−	0.979738i	$-0.435813\pi$
$997$	3.62760e98			0.400571			0.200285	+	0.979738i	$0.435813\pi$
$998$			1.55117e99i			1.65711i
$999$	−1.72295e99	−	5.06973e98i	−1.78078	−	0.523991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.67.b.b.2.7	✓	20
3.2	odd	2	inner	3.67.b.b.2.14	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.67.b.b.2.7	✓	20	1.1	even	1	trivial
3.67.b.b.2.14	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)

\(f(q)\)	\(=\)	\(q-8.60612e9i q^{2} +(-5.53379e15 - 5.29477e14i) q^{3} -2.78318e17 q^{4} +1.34902e23i q^{5} +(-4.55674e24 + 4.76244e25i) q^{6} +8.41299e27 q^{7} -6.32624e29i q^{8} +(3.03425e31 + 5.86002e30i) q^{9} +O(q^{10})\)	\(q-8.60612e9i q^{2} +(-5.53379e15 - 5.29477e14i) q^{3} -2.78318e17 q^{4} +1.34902e23i q^{5} +(-4.55674e24 + 4.76244e25i) q^{6} +8.41299e27 q^{7} -6.32624e29i q^{8} +(3.03425e31 + 5.86002e30i) q^{9} +1.16098e33 q^{10} +1.80389e34i q^{11} +(1.54015e33 + 1.47363e32i) q^{12} +5.91892e36 q^{13} -7.24032e37i q^{14} +(7.14272e37 - 7.46517e38i) q^{15} -5.46498e39 q^{16} -2.55988e40i q^{17} +(5.04321e40 - 2.61131e41i) q^{18} +6.76409e41 q^{19} -3.75456e40i q^{20} +(-4.65557e43 - 4.45448e42i) q^{21} +1.55245e44 q^{22} +1.41229e44i q^{23} +(-3.34960e44 + 3.50081e45i) q^{24} -4.64591e45 q^{25} -5.09389e46i q^{26} +(-1.64806e47 - 4.84938e46i) q^{27} -2.34149e45 q^{28} +2.70885e48i q^{29} +(-6.42461e48 - 6.14711e47i) q^{30} -1.55874e49 q^{31} +3.52809e47i q^{32} +(9.55119e48 - 9.98236e49i) q^{33} -2.20307e50 q^{34} +1.13493e51i q^{35} +(-8.44487e48 - 1.63095e48i) q^{36} +1.04544e52 q^{37} -5.82125e51i q^{38} +(-3.27541e52 - 3.13393e51i) q^{39} +8.53420e52 q^{40} +2.11573e53i q^{41} +(-3.83358e52 + 4.00664e53i) q^{42} -7.75012e53 q^{43} -5.02057e51i q^{44} +(-7.90526e53 + 4.09325e54i) q^{45} +1.21543e54 q^{46} +2.25610e55i q^{47} +(3.02420e55 + 2.89358e54i) q^{48} +1.10101e55 q^{49} +3.99832e55i q^{50} +(-1.35540e55 + 1.41658e56i) q^{51} -1.64734e54 q^{52} -1.41172e57i q^{53} +(-4.17343e56 + 1.41834e57i) q^{54} -2.43348e57 q^{55} -5.32226e57i q^{56} +(-3.74310e57 - 3.58143e56i) q^{57} +2.33127e58 q^{58} -3.88022e58i q^{59} +(-1.98795e55 + 2.07769e56i) q^{60} -3.61314e58 q^{61} +1.34147e59i q^{62} +(2.55271e59 + 4.93003e58i) q^{63} -4.00208e59 q^{64} +7.98472e59i q^{65} +(-8.59094e59 - 8.21987e58i) q^{66} +1.05899e60 q^{67} +7.12462e57i q^{68} +(7.47772e58 - 7.81529e59i) q^{69} +9.76730e60 q^{70} +8.62453e60i q^{71} +(3.70719e60 - 1.91954e61i) q^{72} -2.48441e61 q^{73} -8.99718e61i q^{74} +(2.57095e61 + 2.45990e60i) q^{75} -1.88257e59 q^{76} +1.51761e62i q^{77} +(-2.69710e61 + 2.81885e62i) q^{78} +3.64608e62 q^{79} -7.37234e62i q^{80} +(8.86325e62 + 3.55615e62i) q^{81} +1.82083e63 q^{82} +1.85595e63i q^{83} +(1.29573e61 + 1.23976e60i) q^{84} +3.45332e63 q^{85} +6.66984e63i q^{86} +(1.43427e63 - 1.49902e64i) q^{87} +1.14119e64 q^{88} -3.49253e64i q^{89} +(3.52270e64 + 6.80336e63i) q^{90} +4.97958e64 q^{91} -3.93065e61i q^{92} +(8.62573e64 + 8.25316e63i) q^{93} +1.94162e65 q^{94} +9.12486e64i q^{95} +(1.86804e62 - 1.95237e63i) q^{96} +3.57760e65 q^{97} -9.47546e64i q^{98} +(-1.05709e65 + 5.47346e65i) 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

Fields

Representations

Groups

Database

Properties

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