LMFDB - Embedded newform 3.67.b.b.2.13

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			2.13
Root			$1.32287e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.67.b.b.2.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.76234e9i q^{2} +(4.09693e15 + 3.75743e15i) q^{3} +5.11071e19 q^{4} -1.11626e23i q^{5} +(-1.78942e25 + 1.95110e25i) q^{6} +1.00296e28 q^{7} +5.94788e29i q^{8} +(2.66653e30 + 3.07879e31i) q^{9} +O(q^{10})$	\(q+4.76234e9i q^{2} +(4.09693e15 + 3.75743e15i) q^{3} +5.11071e19 q^{4} -1.11626e23i q^{5} +(-1.78942e25 + 1.95110e25i) q^{6} +1.00296e28 q^{7} +5.94788e29i q^{8} +(2.66653e30 + 3.07879e31i) q^{9} +5.31601e32 q^{10} +2.71493e34i q^{11} +(2.09382e35 + 1.92031e35i) q^{12} -8.16964e36 q^{13} +4.77642e37i q^{14} +(4.19427e38 - 4.57324e38i) q^{15} +9.38452e38 q^{16} -3.36501e40i q^{17} +(-1.46622e41 + 1.26989e40i) q^{18} -2.59388e42 q^{19} -5.70488e42i q^{20} +(4.10904e43 + 3.76854e43i) q^{21} -1.29294e44 q^{22} +7.82235e44i q^{23} +(-2.23488e45 + 2.43681e45i) q^{24} +1.09216e45 q^{25} -3.89066e46i q^{26} +(-1.04759e47 + 1.36155e47i) q^{27} +5.12581e47 q^{28} +2.09277e48i q^{29} +(2.17793e48 + 1.99746e48i) q^{30} -9.44360e48 q^{31} +4.83568e49i q^{32} +(-1.02012e50 + 1.11229e50i) q^{33} +1.60254e50 q^{34} -1.11956e51i q^{35} +(1.36278e50 + 1.57348e51i) q^{36} +5.25278e51 q^{37} -1.23529e52i q^{38} +(-3.34705e52 - 3.06969e52i) q^{39} +6.63938e52 q^{40} +2.65367e53i q^{41} +(-1.79471e53 + 1.95687e53i) q^{42} +7.04522e53 q^{43} +1.38752e54i q^{44} +(3.43673e54 - 2.97654e53i) q^{45} -3.72527e54 q^{46} +5.54764e54i q^{47} +(3.84477e54 + 3.52617e54i) q^{48} +4.08237e55 q^{49} +5.20122e54i q^{50} +(1.26438e56 - 1.37862e56i) q^{51} -4.17526e56 q^{52} +5.01179e56i q^{53} +(-6.48418e56 - 4.98898e56i) q^{54} +3.03057e57 q^{55} +5.96546e57i q^{56} +(-1.06269e58 - 9.74634e57i) q^{57} -9.96649e57 q^{58} -2.39968e58i q^{59} +(2.14357e58 - 2.33725e58i) q^{60} +5.18967e58 q^{61} -4.49737e58i q^{62} +(2.67441e58 + 3.08789e59i) q^{63} -1.61046e59 q^{64} +9.11945e59i q^{65} +(-5.29710e59 - 4.85815e59i) q^{66} +1.99087e60 q^{67} -1.71976e60i q^{68} +(-2.93920e60 + 3.20476e60i) q^{69} +5.33173e60 q^{70} -1.53185e61i q^{71} +(-1.83123e61 + 1.58602e60i) q^{72} -8.33852e60 q^{73} +2.50155e61i q^{74} +(4.47449e60 + 4.10371e60i) q^{75} -1.32566e62 q^{76} +2.72296e62i q^{77} +(1.46189e62 - 1.59398e62i) q^{78} +2.10112e62 q^{79} -1.04756e62i q^{80} +(-9.40784e62 + 1.64194e62i) q^{81} -1.26377e63 q^{82} +2.23637e63i q^{83} +(2.10001e63 + 1.92599e63i) q^{84} -3.75623e63 q^{85} +3.35518e63i q^{86} +(-7.86345e63 + 8.57394e63i) q^{87} -1.61481e64 q^{88} -2.08278e62i q^{89} +(1.41753e63 + 1.63669e64i) q^{90} -8.19379e64 q^{91} +3.99778e64i q^{92} +(-3.86898e64 - 3.54837e64i) q^{93} -2.64197e64 q^{94} +2.89545e65i q^{95} +(-1.81698e65 + 1.98115e65i) q^{96} +1.02926e65 q^{97} +1.94416e65i q^{98} +(-8.35870e65 + 7.23944e64i) 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 $

$2$			4.76234e9i			0.554410i	0.960811	+	0.277205i	$0.0894080\pi$
$2$			4.76234e9i			0.554410i	−0.960811	+	0.277205i	$0.910592\pi$
$3$	4.09693e15	+	3.75743e15i	0.736983	+	0.675912i
$3$	4.09693e15	+	3.75743e15i	0.736983	+	0.675912i
$4$	5.11071e19			0.692630
$5$		−	1.11626e23i		−	0.958860i	−0.877580	−	0.479430i	$-0.840843\pi$
$5$		−	1.11626e23i		−	0.958860i	0.877580	−	0.479430i	$-0.159157\pi$
$6$	−1.78942e25	+	1.95110e25i	−0.374732	+	0.408590i
$7$	1.00296e28			1.29732			0.648659	−	0.761079i	$-0.275330\pi$
$7$	1.00296e28			1.29732			0.648659	+	0.761079i	$0.275330\pi$
$8$			5.94788e29i			0.938410i
$9$	2.66653e30	+	3.07879e31i	0.0862866	+	0.996270i
$10$	5.31601e32			0.531601
$11$			2.71493e34i			1.16896i	0.811407	+	0.584481i	$0.198702\pi$
$11$			2.71493e34i			1.16896i	−0.811407	+	0.584481i	$0.801298\pi$
$12$	2.09382e35	+	1.92031e35i	0.510456	+	0.468157i
$13$	−8.16964e36			−1.41929			−0.709647	−	0.704558i	$-0.751146\pi$
$13$	−8.16964e36			−1.41929			−0.709647	+	0.704558i	$0.751146\pi$
$14$			4.77642e37i			0.719245i
$15$	4.19427e38	−	4.57324e38i	0.648105	−	0.706663i
$16$	9.38452e38			0.172366
$17$		−	3.36501e40i		−	0.835935i	−0.908462	−	0.417968i	$-0.862743\pi$
$17$		−	3.36501e40i		−	0.835935i	0.908462	−	0.417968i	$-0.137257\pi$
$18$	−1.46622e41	+	1.26989e40i	−0.552342	+	0.0478381i
$19$	−2.59388e42			−1.64090			−0.820448	−	0.571721i	$-0.806276\pi$
$19$	−2.59388e42			−1.64090			−0.820448	+	0.571721i	$0.806276\pi$
$20$		−	5.70488e42i		−	0.664135i
$21$	4.10904e43	+	3.76854e43i	0.956101	+	0.876872i
$22$	−1.29294e44			−0.648084
$23$			7.82235e44i			0.904313i	0.891939	+	0.452157i	$0.149345\pi$
$23$			7.82235e44i			0.904313i	−0.891939	+	0.452157i	$0.850655\pi$
$24$	−2.23488e45	+	2.43681e45i	−0.634283	+	0.691592i
$25$	1.09216e45			0.0805869
$26$		−	3.89066e46i		−	0.786870i
$27$	−1.04759e47	+	1.36155e47i	−0.609799	+	0.792556i
$28$	5.12581e47			0.898561
$29$			2.09277e48i			1.15236i	0.817323	+	0.576180i	$0.195457\pi$
$29$			2.09277e48i			1.15236i	−0.817323	+	0.576180i	$0.804543\pi$
$30$	2.17793e48	+	1.99746e48i	0.391781	+	0.359316i
$31$	−9.44360e48			−0.575707			−0.287854	−	0.957674i	$-0.592942\pi$
$31$	−9.44360e48			−0.575707			−0.287854	+	0.957674i	$0.592942\pi$
$32$			4.83568e49i			1.03397i
$33$	−1.02012e50	+	1.11229e50i	−0.790115	+	0.861504i
$34$	1.60254e50			0.463450
$35$		−	1.11956e51i		−	1.24395i
$36$	1.36278e50	+	1.57348e51i	0.0597647	+	0.690047i
$37$	5.25278e51			0.932679			0.466340	−	0.884606i	$-0.345572\pi$
$37$	5.25278e51			0.932679			0.466340	+	0.884606i	$0.345572\pi$
$38$		−	1.23529e52i		−	0.909729i
$39$	−3.34705e52	−	3.06969e52i	−1.04599	−	0.959317i
$40$	6.63938e52			0.899804
$41$			2.65367e53i			1.59213i	0.605210	+	0.796066i	$0.293089\pi$
$41$			2.65367e53i			1.59213i	−0.605210	+	0.796066i	$0.706911\pi$
$42$	−1.79471e53	+	1.95687e53i	−0.486146	+	0.530071i
$43$	7.04522e53			0.877881			0.438941	−	0.898516i	$-0.355354\pi$
$43$	7.04522e53			0.877881			0.438941	+	0.898516i	$0.355354\pi$
$44$			1.38752e54i			0.809658i
$45$	3.43673e54	−	2.97654e53i	0.955284	−	0.0827368i
$46$	−3.72527e54			−0.501360
$47$			5.54764e54i			0.367180i	0.983003	+	0.183590i	$0.0587718\pi$
$47$			5.54764e54i			0.367180i	−0.983003	+	0.183590i	$0.941228\pi$
$48$	3.84477e54	+	3.52617e54i	0.127031	+	0.116504i
$49$	4.08237e55			0.683033
$50$			5.20122e54i			0.0446782i
$51$	1.26438e56	−	1.37862e56i	0.565018	−	0.616070i
$52$	−4.17526e56			−0.983045
$53$			5.01179e56i			0.629345i	0.949200	+	0.314673i	$0.101895\pi$
$53$			5.01179e56i			0.629345i	−0.949200	+	0.314673i	$0.898105\pi$
$54$	−6.48418e56	−	4.98898e56i	−0.439401	−	0.338078i
$55$	3.03057e57			1.12087
$56$			5.96546e57i			1.21742i
$57$	−1.06269e58	−	9.74634e57i	−1.20931	−	1.10910i
$58$	−9.96649e57			−0.638879
$59$		−	2.39968e58i		−	0.875057i	−0.899205	−	0.437528i	$-0.855854\pi$
$59$		−	2.39968e58i		−	0.875057i	0.899205	−	0.437528i	$-0.144146\pi$
$60$	2.14357e58	−	2.33725e58i	0.448897	−	0.489456i
$61$	5.18967e58			0.629876			0.314938	−	0.949112i	$-0.398016\pi$
$61$	5.18967e58			0.629876			0.314938	+	0.949112i	$0.398016\pi$
$62$		−	4.49737e58i		−	0.319178i
$63$	2.67441e58	+	3.08789e59i	0.111941	+	1.29248i
$64$	−1.61046e59			−0.400878
$65$			9.11945e59i			1.36090i
$66$	−5.29710e59	−	4.85815e59i	−0.477626	−	0.438047i
$67$	1.99087e60			1.09288			0.546442	−	0.837497i	$-0.315982\pi$
$67$	1.99087e60			1.09288			0.546442	+	0.837497i	$0.315982\pi$
$68$		−	1.71976e60i		−	0.578994i
$69$	−2.93920e60	+	3.20476e60i	−0.611236	+	0.666463i
$70$	5.33173e60			0.689656
$71$		−	1.53185e61i		−	1.24077i	−0.784299	−	0.620383i	$-0.786977\pi$
$71$		−	1.53185e61i		−	1.24077i	0.784299	−	0.620383i	$-0.213023\pi$
$72$	−1.83123e61	+	1.58602e60i	−0.934910	+	0.0809723i
$73$	−8.33852e60			−0.270044			−0.135022	−	0.990843i	$-0.543111\pi$
$73$	−8.33852e60			−0.270044			−0.135022	+	0.990843i	$0.543111\pi$
$74$			2.50155e61i			0.517086i
$75$	4.47449e60	+	4.10371e60i	0.0593912	+	0.0544697i
$76$	−1.32566e62			−1.13653
$77$			2.72296e62i			1.51651i
$78$	1.46189e62	−	1.59398e62i	0.531855	−	0.579910i
$79$	2.10112e62			0.502062			0.251031	−	0.967979i	$-0.419230\pi$
$79$	2.10112e62			0.502062			0.251031	+	0.967979i	$0.419230\pi$
$80$		−	1.04756e62i		−	0.165275i
$81$	−9.40784e62	+	1.64194e62i	−0.985109	+	0.171930i
$82$	−1.26377e63			−0.882693
$83$			2.23637e63i			1.04705i	0.852011	+	0.523523i	$0.175383\pi$
$83$			2.23637e63i			1.04705i	−0.852011	+	0.523523i	$0.824617\pi$
$84$	2.10001e63	+	1.92599e63i	0.662224	+	0.607348i
$85$	−3.75623e63			−0.801545
$86$			3.35518e63i			0.486706i
$87$	−7.86345e63	+	8.57394e63i	−0.778893	+	0.849269i
$88$	−1.61481e64			−1.09697
$89$		−	2.08278e62i		−	0.00974479i	−0.999988	−	0.00487240i	$-0.998449\pi$
$89$		−	2.08278e62i		−	0.00974479i	0.999988	−	0.00487240i	$-0.00155094\pi$
$90$	1.41753e63	+	1.63669e64i	0.0458701	+	0.529619i
$91$	−8.19379e64			−1.84128
$92$			3.99778e64i			0.626354i
$93$	−3.86898e64	−	3.54837e64i	−0.424286	−	0.389127i
$94$	−2.64197e64			−0.203568
$95$			2.89545e65i			1.57339i
$96$	−1.81698e65	+	1.98115e65i	−0.698874	+	0.762019i
$97$	1.02926e65			0.281228			0.140614	−	0.990064i	$-0.455092\pi$
$97$	1.02926e65			0.281228			0.140614	+	0.990064i	$0.455092\pi$
$98$			1.94416e65i			0.378680i
$99$	−8.35870e65	+	7.23944e64i	−1.16460	+	0.100866i
$100$	5.58169e64			0.0558169
$101$			1.71518e66i			1.23511i	0.786528	+	0.617554i	$0.211876\pi$
$101$			1.71518e66i			1.23511i	−0.786528	+	0.617554i	$0.788124\pi$
$102$	6.56548e65	+	6.02142e65i	0.341555	+	0.313252i
$103$	−2.35799e66			−0.889023			−0.444511	−	0.895773i	$-0.646623\pi$
$103$	−2.35799e66			−0.889023			−0.444511	+	0.895773i	$0.646623\pi$
$104$		−	4.85921e66i		−	1.33188i
$105$	4.20667e66	−	4.58676e66i	0.840798	−	0.916767i
$106$	−2.38679e66			−0.348915
$107$		−	1.01687e67i		−	1.09043i	−0.838295	−	0.545216i	$-0.816448\pi$
$107$		−	1.01687e67i		−	1.09043i	0.838295	−	0.545216i	$-0.183552\pi$
$108$	−5.35392e66	+	6.95849e66i	−0.422365	+	0.548948i
$109$	2.22359e67			1.29414			0.647070	−	0.762431i	$-0.275994\pi$
$109$	2.22359e67			1.29414			0.647070	+	0.762431i	$0.275994\pi$
$110$			1.44326e67i			0.621422i
$111$	2.15203e67	+	1.97370e67i	0.687368	+	0.630409i
$112$	9.41225e66			0.223614
$113$		−	1.00520e68i		−	1.78099i	−0.454991	−	0.890496i	$-0.650358\pi$
$113$		−	1.00520e68i		−	1.78099i	0.454991	−	0.890496i	$-0.349642\pi$
$114$	4.64154e67	−	5.06092e67i	0.614896	−	0.670454i
$115$	8.73178e67			0.867110
$116$			1.06955e68i			0.798158i
$117$	−2.17846e67	−	2.51526e68i	−0.122466	−	1.41400i
$118$	1.14281e68			0.485140
$119$		−	3.37496e68i		−	1.08447i
$120$	2.72011e68	+	2.49471e68i	0.663140	+	0.608188i
$121$	−1.97678e68			−0.366472
$122$			2.47150e68i			0.349209i
$123$	−9.97098e68	+	1.08719e69i	−1.07614	+	1.17337i
$124$	−4.82635e68			−0.398752
$125$		−	1.63473e69i		−	1.03613i
$126$	−1.47056e69	+	1.27365e68i	−0.716563	+	0.0620613i
$127$	1.97327e69			0.740736			0.370368	−	0.928885i	$-0.379232\pi$
$127$	1.97327e69			0.740736			0.370368	+	0.928885i	$0.379232\pi$
$128$			2.80115e69i			0.811721i
$129$	2.88638e69	+	2.64720e69i	0.646983	+	0.593370i
$130$	−4.34299e69			−0.754498
$131$			4.38140e68i			0.0591099i	0.999563	+	0.0295549i	$0.00940900\pi$
$131$			4.38140e68i			0.0591099i	−0.999563	+	0.0295549i	$0.990591\pi$
$132$	−5.21352e69	+	5.68458e69i	−0.547257	+	0.596704i
$133$	−2.60155e70			−2.12876
$134$			9.48119e69i			0.605905i
$135$	1.51985e70	+	1.16938e70i	0.759951	+	0.584712i
$136$	2.00147e70			0.784450
$137$		−	2.37612e69i		−	0.0731290i	−0.999331	−	0.0365645i	$-0.988359\pi$
$137$		−	2.37612e69i		−	0.0731290i	0.999331	−	0.0365645i	$-0.0116414\pi$
$138$	−1.52622e70	−	1.39975e70i	−0.369494	−	0.338875i
$139$	−2.10404e70			−0.401390			−0.200695	−	0.979654i	$-0.564320\pi$
$139$	−2.10404e70			−0.401390			−0.200695	+	0.979654i	$0.564320\pi$
$140$		−	5.72174e70i		−	0.861595i
$141$	−2.08449e70	+	2.27283e70i	−0.248181	+	0.270605i
$142$	7.29518e70			0.687893
$143$		−	2.21800e71i		−	1.65910i
$144$	2.50241e69	+	2.88929e70i	0.0148729	+	0.171723i
$145$	2.33608e71			1.10495
$146$		−	3.97109e70i		−	0.149715i
$147$	1.67252e71	+	1.53392e71i	0.503384	+	0.461670i
$148$	2.68454e71			0.646002
$149$			1.98769e71i			0.383003i	0.981492	+	0.191501i	$0.0613357\pi$
$149$			1.98769e71i			0.383003i	−0.981492	+	0.191501i	$0.938664\pi$
$150$	−1.95433e70	+	2.13091e70i	−0.0301985	+	0.0329270i
$151$	1.99268e71			0.247286			0.123643	−	0.992327i	$-0.460542\pi$
$151$	1.99268e71			0.247286			0.123643	+	0.992327i	$0.460542\pi$
$152$		−	1.54281e72i		−	1.53983i
$153$	1.03602e72	−	8.97291e70i	0.832817	−	0.0721300i
$154$	−1.29676e72			−0.840770
$155$			1.05415e72i			0.552023i
$156$	−1.71058e72	−	1.56883e72i	−0.724487	−	0.664452i
$157$	−1.78221e72			−0.611322			−0.305661	−	0.952140i	$-0.598877\pi$
$157$	−1.78221e72			−0.611322			−0.305661	+	0.952140i	$0.598877\pi$
$158$			1.00063e72i			0.278348i
$159$	−1.88315e72	+	2.05330e72i	−0.425382	+	0.463817i
$160$	5.39788e72			0.991435
$161$			7.84547e72i			1.17318i
$162$	−7.81946e71	−	4.48034e72i	−0.0953194	−	0.546154i
$163$	−1.88015e73			−1.87069			−0.935344	−	0.353739i	$-0.884910\pi$
$163$	−1.88015e73			−1.87069			−0.935344	+	0.353739i	$0.884910\pi$
$164$			1.35621e73i			1.10276i
$165$	1.24160e73	+	1.13872e73i	0.826062	+	0.757610i
$166$	−1.06503e73			−0.580493
$167$		−	9.45676e72i		−	0.422765i	−0.977403	−	0.211383i	$-0.932203\pi$
$167$		−	9.45676e72i		−	0.422765i	0.977403	−	0.211383i	$-0.0677966\pi$
$168$	−2.24148e73	+	2.44401e73i	−0.822866	+	0.897215i
$169$	3.36100e73			1.01439
$170$		−	1.78885e73i		−	0.444384i
$171$	−6.91666e72	−	7.98601e73i	−0.141587	−	1.63478i
$172$	3.60061e73			0.608047
$173$			2.80759e73i			0.391573i	0.980647	+	0.195786i	$0.0627259\pi$
$173$			2.80759e73i			0.391573i	−0.980647	+	0.195786i	$0.937274\pi$
$174$	−4.08320e73	−	3.74484e73i	−0.470843	−	0.431826i
$175$	1.09538e73			0.104547
$176$			2.54783e73i			0.201490i
$177$	9.01663e73	−	9.83131e73i	0.591461	−	0.644902i
$178$	9.91890e71			0.00540261
$179$			7.97451e73i			0.361039i	0.983571	+	0.180519i	$0.0577779\pi$
$179$			7.97451e73i			0.361039i	−0.983571	+	0.180519i	$0.942222\pi$
$180$	1.75641e74	−	1.52122e73i	0.661658	−	0.0573060i
$181$	2.41480e74			0.757683			0.378841	−	0.925462i	$-0.376323\pi$
$181$	2.41480e74			0.757683			0.378841	+	0.925462i	$0.376323\pi$
$182$		−	3.90216e74i		−	1.02082i
$183$	2.12617e74	+	1.94998e74i	0.464207	+	0.425740i
$184$	−4.65264e74			−0.848617
$185$		−	5.86347e74i		−	0.894309i
$186$	1.68986e74	−	1.84254e74i	0.215736	−	0.235228i
$187$	9.13579e74			0.977176
$188$			2.83523e74i			0.254320i
$189$	−1.05069e75	+	1.36558e75i	−0.791103	+	1.02820i
$190$	−1.37891e75			−0.872303
$191$			2.34298e75i			1.24643i	0.782050	+	0.623215i	$0.214174\pi$
$191$			2.34298e75i			1.24643i	−0.782050	+	0.623215i	$0.785826\pi$
$192$	−6.59796e74	−	6.05121e74i	−0.295440	−	0.270958i
$193$	−1.66241e75			−0.627116			−0.313558	−	0.949569i	$-0.601521\pi$
$193$	−1.66241e75			−0.627116			−0.313558	+	0.949569i	$0.601521\pi$
$194$			4.90170e74i			0.155915i
$195$	−3.42657e75	+	3.73617e75i	−0.919851	+	1.00296i
$196$	2.08638e75			0.473089
$197$		−	6.66851e75i		−	1.27833i	−0.769070	−	0.639165i	$-0.779280\pi$
$197$		−	6.66851e75i		−	1.27833i	0.769070	−	0.639165i	$-0.220720\pi$
$198$	−3.44767e74	−	3.98070e75i	−0.0559210	−	0.645667i
$199$	−3.43455e75			−0.471756			−0.235878	−	0.971783i	$-0.575797\pi$
$199$	−3.43455e75			−0.471756			−0.235878	+	0.971783i	$0.575797\pi$
$200$			6.49602e74i			0.0756236i
$201$	8.15645e75	+	7.48055e75i	0.805436	+	0.738693i
$202$	−8.16829e75			−0.684756
$203$			2.09896e76i			1.49498i
$204$	6.46189e75	−	7.04574e75i	0.391349	−	0.426708i
$205$	2.96218e76			1.52663
$206$		−	1.12295e76i		−	0.492883i
$207$	−2.40834e76	+	2.08585e75i	−0.900940	+	0.0780301i
$208$	−7.66681e75			−0.244638
$209$		−	7.04221e76i		−	1.91815i
$210$	2.18437e76	+	2.00336e76i	0.508264	+	0.466146i
$211$	2.69113e76			0.535321			0.267660	−	0.963513i	$-0.413750\pi$
$211$	2.69113e76			0.535321			0.267660	+	0.963513i	$0.413750\pi$
$212$			2.56138e76i			0.435904i
$213$	5.75582e76	−	6.27587e76i	0.838649	−	0.914423i
$214$	4.84266e76			0.604546
$215$		−	7.86430e76i		−	0.841765i
$216$	−8.09835e76	−	6.23094e76i	−0.743743	−	0.572242i
$217$	−9.47151e76			−0.746875
$218$			1.05895e77i			0.717483i
$219$	−3.41624e76	−	3.13315e76i	−0.199018	−	0.182526i
$220$	1.54884e77			0.776349
$221$			2.74910e77i			1.18644i
$222$	−9.39942e76	+	1.02487e77i	−0.349505	+	0.381084i
$223$	−2.32321e77			−0.744780			−0.372390	−	0.928076i	$-0.621462\pi$
$223$	−2.32321e77			−0.744780			−0.372390	+	0.928076i	$0.621462\pi$
$224$			4.84998e77i			1.34139i
$225$	2.91227e75	+	3.36252e76i	0.00695358	+	0.0802864i
$226$	4.78708e77			0.987399
$227$		−	2.54284e77i		−	0.453383i	−0.973967	−	0.226692i	$-0.927209\pi$
$227$		−	2.54284e77i		−	0.453383i	0.973967	−	0.226692i	$-0.0727909\pi$
$228$	−5.43112e77	−	4.98107e77i	−0.837606	−	0.768197i
$229$	−2.66886e77			−0.356250			−0.178125	−	0.984008i	$-0.557003\pi$
$229$	−2.66886e77			−0.356250			−0.178125	+	0.984008i	$0.557003\pi$
$230$			4.15837e77i			0.480734i
$231$	−1.02313e78	+	1.11558e78i	−1.02503	+	1.11765i
$232$	−1.24476e78			−1.08139
$233$		−	1.67239e78i		−	1.26064i	−0.776335	−	0.630321i	$-0.782923\pi$
$233$		−	1.67239e78i		−	1.26064i	0.776335	−	0.630321i	$-0.217077\pi$
$234$	1.19785e78	−	1.03746e77i	0.783935	−	0.0678964i
$235$	6.19260e77			0.352074
$236$		−	1.22640e78i		−	0.606091i
$237$	8.60816e77	+	7.89484e77i	0.370011	+	0.339350i
$238$	1.60727e78			0.601242
$239$			2.67411e78i			0.871062i	0.900174	+	0.435531i	$0.143439\pi$
$239$			2.67411e78i			0.871062i	−0.900174	+	0.435531i	$0.856561\pi$
$240$	3.93612e77	−	4.29177e77i	0.111711	−	0.121805i
$241$	3.51268e78			0.869112			0.434556	−	0.900645i	$-0.356905\pi$
$241$	3.51268e78			0.869112			0.434556	+	0.900645i	$0.356905\pi$
$242$		−	9.41409e77i		−	0.203175i
$243$	−4.47127e78	−	2.86224e78i	−0.842218	−	0.539138i
$244$	2.65229e78			0.436271
$245$		−	4.55699e78i		−	0.654933i
$246$	−5.17756e78	−	4.74852e78i	−0.650529	−	0.596623i
$247$	2.11911e79			2.32891
$248$		−	5.61694e78i		−	0.540250i
$249$	−8.40300e78	+	9.16224e78i	−0.707711	+	0.771655i
$250$	7.78513e78			0.574441
$251$		−	1.00593e79i		−	0.650632i	−0.945605	−	0.325316i	$-0.894529\pi$
$251$		−	1.00593e79i		−	0.650632i	0.945605	−	0.325316i	$-0.105471\pi$
$252$	1.36681e78	+	1.57813e79i	0.0775338	+	0.895210i
$253$	−2.12372e79			−1.05711
$254$			9.39738e78i			0.410671i
$255$	−1.53890e79	−	1.41138e79i	−0.590725	−	0.541774i
$256$	−2.52231e79			−0.850904
$257$			7.80840e78i			0.231616i	0.993272	+	0.115808i	$0.0369458\pi$
$257$			7.80840e78i			0.231616i	−0.993272	+	0.115808i	$0.963054\pi$
$258$	−1.26069e79	+	1.37459e79i	−0.328970	+	0.358694i
$259$	5.26830e79			1.20998
$260$			4.66068e79i			0.942603i
$261$	−6.44320e79	+	5.58044e78i	−1.14806	+	0.0994332i
$262$	−2.08657e78			−0.0327711
$263$			8.43767e79i			1.16865i	0.811521	+	0.584323i	$0.198640\pi$
$263$			8.43767e79i			1.16865i	−0.811521	+	0.584323i	$0.801360\pi$
$264$	−6.61576e79	−	6.06754e79i	−0.808445	−	0.741452i
$265$	5.59446e79			0.603454
$266$		−	1.23895e80i		−	1.18021i
$267$	7.82590e77	−	8.53300e77i	0.00658662	−	0.00718174i
$268$	1.01747e80			0.756964
$269$			1.40981e80i			0.927543i	0.885955	+	0.463771i	$0.153504\pi$
$269$			1.40981e80i			0.927543i	−0.885955	+	0.463771i	$0.846496\pi$
$270$	−5.56900e79	+	7.23803e79i	−0.324170	+	0.421324i
$271$	2.33299e80			1.20206			0.601031	−	0.799225i	$-0.294757\pi$
$271$	2.33299e80			1.20206			0.601031	+	0.799225i	$0.294757\pi$
$272$		−	3.15790e79i		−	0.144087i
$273$	−3.35694e80	−	3.07876e80i	−1.35699	−	1.24454i
$274$	1.13159e79			0.0405434
$275$			2.96513e79i			0.0942031i
$276$	−1.50214e80	+	1.63786e80i	−0.423360	+	0.461612i
$277$	5.90165e80			1.47619			0.738093	−	0.674698i	$-0.235726\pi$
$277$	5.90165e80			1.47619			0.738093	+	0.674698i	$0.235726\pi$
$278$		−	1.00202e80i		−	0.222534i
$279$	−2.51816e79	−	2.90749e80i	−0.0496758	−	0.573560i
$280$	6.65901e80			1.16733
$281$		−	1.26663e81i		−	1.97397i	−0.160808	−	0.986986i	$-0.551410\pi$
$281$		−	1.26663e81i		−	1.97397i	0.160808	−	0.986986i	$-0.448590\pi$
$282$	−1.08240e80	−	9.92704e79i	−0.150026	−	0.137594i
$283$	1.62778e80			0.200744			0.100372	−	0.994950i	$-0.467997\pi$
$283$	1.62778e80			0.200744			0.100372	+	0.994950i	$0.467997\pi$
$284$		−	7.82883e80i		−	0.859392i
$285$	−1.08794e81	+	1.18624e81i	−1.06347	+	1.15956i
$286$	1.05629e81			0.919821
$287$			2.66151e81i			2.06550i
$288$	−1.48881e81	+	1.28945e80i	−1.03012	+	0.0892179i
$289$	4.88092e80			0.301213
$290$			1.11252e81i			0.612596i
$291$	4.21681e80	+	3.86738e80i	0.207260	+	0.190085i
$292$	−4.26158e80			−0.187041
$293$		−	1.13023e81i		−	0.443133i	−0.975145	−	0.221567i	$-0.928883\pi$
$293$		−	1.13023e81i		−	0.443133i	0.975145	−	0.221567i	$-0.0711170\pi$
$294$	−7.30507e80	+	7.96511e80i	−0.255954	+	0.279081i
$295$	−2.67866e81			−0.839057
$296$			3.12429e81i			0.875236i
$297$	−3.69652e81	−	2.84413e81i	−0.926468	−	0.712832i
$298$	−9.46606e80			−0.212340
$299$		−	6.39058e81i		−	1.28349i
$300$	2.28678e80	+	2.09728e80i	0.0411361	+	0.0377273i
$301$	7.06605e81			1.13889
$302$			9.48984e80i			0.137098i
$303$	−6.44469e81	+	7.02698e81i	−0.834824	+	0.910253i
$304$	−2.43423e81			−0.282835
$305$		−	5.79302e81i		−	0.603963i
$306$	4.27321e80	+	4.93387e81i	0.0399896	+	0.461722i
$307$	2.32712e82			1.95548			0.977738	−	0.209829i	$-0.0672908\pi$
$307$	2.32712e82			1.95548			0.977738	+	0.209829i	$0.0672908\pi$
$308$			1.39162e82i			1.05038i
$309$	−9.66051e81	−	8.85998e81i	−0.655194	−	0.600901i
$310$	−5.02023e81			−0.306047
$311$		−	5.11858e81i		−	0.280580i	−0.990110	−	0.140290i	$-0.955196\pi$
$311$		−	5.11858e81i		−	0.280580i	0.990110	−	0.140290i	$-0.0448035\pi$
$312$	1.82581e82	−	1.99078e82i	0.900233	−	0.981572i
$313$	5.81970e81			0.258189			0.129094	−	0.991632i	$-0.458793\pi$
$313$	5.81970e81			0.258189			0.129094	+	0.991632i	$0.458793\pi$
$314$		−	8.48749e81i		−	0.338923i
$315$	3.44689e82	−	2.98534e81i	1.23931	−	0.107336i
$316$	1.07382e82			0.347743
$317$		−	1.66865e82i		−	0.486867i	−0.969918	−	0.243434i	$-0.921726\pi$
$317$		−	1.66865e82i		−	0.486867i	0.969918	−	0.243434i	$-0.0782738\pi$
$318$	−9.77849e81	−	8.96819e81i	−0.257144	−	0.235836i
$319$	−5.68173e82			−1.34706
$320$			1.79770e82i			0.384386i
$321$	3.82081e82	−	4.16603e82i	0.737036	−	0.803630i
$322$	−3.73628e82			−0.650423
$323$			8.72845e82i			1.37168i
$324$	−4.80807e82	+	8.39146e81i	−0.682316	+	0.119084i
$325$	−8.92253e81			−0.114377
$326$		−	8.95391e82i		−	1.03713i
$327$	9.10991e82	+	8.35501e82i	0.953758	+	0.874724i
$328$	−1.57837e83			−1.49407
$329$			5.56403e82i			0.476349i
$330$	−5.42296e82	+	5.91294e82i	−0.420026	+	0.457977i
$331$	9.56493e82			0.670437			0.335219	−	0.942140i	$-0.391190\pi$
$331$	9.56493e82			0.670437			0.335219	+	0.942140i	$0.391190\pi$
$332$			1.14294e83i			0.725216i
$333$	1.40067e82	+	1.61722e83i	0.0804777	+	0.929201i
$334$	4.50364e82			0.234385
$335$		−	2.22233e83i		−	1.04792i
$336$	3.85613e82	+	3.53659e82i	0.164800	+	0.151143i
$337$	−4.91700e83			−1.90508			−0.952540	−	0.304412i	$-0.901540\pi$
$337$	−4.91700e83			−1.90508			−0.952540	+	0.304412i	$0.901540\pi$
$338$			1.60062e83i			0.562390i
$339$	3.77696e83	−	4.11822e83i	1.20379	−	1.31256i
$340$	−1.91970e83			−0.555174
$341$		−	2.56387e83i		−	0.672980i
$342$	3.80321e83	−	3.29395e82i	0.906336	−	0.0784974i
$343$	−1.90005e83			−0.411207
$344$			4.19042e83i			0.823813i
$345$	3.57735e83	+	3.28091e83i	0.639045	+	0.586090i
$346$	−1.33707e83			−0.217092
$347$		−	1.12779e84i		−	1.66478i	−0.554193	−	0.832388i	$-0.686973\pi$
$347$		−	1.12779e84i		−	1.66478i	0.554193	−	0.832388i	$-0.313027\pi$
$348$	−4.01878e83	+	4.38189e83i	−0.539485	+	0.588229i
$349$	1.60460e84			1.95942			0.979710	−	0.200421i	$-0.0642309\pi$
$349$	1.60460e84			1.95942			0.979710	+	0.200421i	$0.0642309\pi$
$350$			5.21660e82i			0.0579618i
$351$	8.55843e83	−	1.11234e84i	0.865484	−	1.12487i
$352$	−1.31286e84			−1.20867
$353$		−	5.07192e83i		−	0.425214i	−0.977138	−	0.212607i	$-0.931805\pi$
$353$		−	5.07192e83i		−	0.425214i	0.977138	−	0.212607i	$-0.0681954\pi$
$354$	4.68201e83	+	4.29403e83i	0.357540	+	0.327912i
$355$	−1.70994e84			−1.18972
$356$		−	1.06445e82i		−	0.00674954i
$357$	1.26812e84	−	1.38270e84i	0.733008	−	0.799238i
$358$	−3.79773e83			−0.200163
$359$			1.65366e84i			0.794929i	0.917618	+	0.397464i	$0.130110\pi$
$359$			1.65366e84i			0.794929i	−0.917618	+	0.397464i	$0.869890\pi$
$360$	1.77041e83	+	2.04413e84i	0.0776411	+	0.896448i
$361$	4.22938e84			1.69254
$362$			1.15001e84i			0.420067i
$363$	−8.09872e83	−	7.42761e83i	−0.270083	−	0.247702i
$364$	−4.18760e84			−1.27532
$365$			9.30796e83i			0.258935i
$366$	−9.28648e83	+	1.01255e84i	−0.236035	+	0.257361i
$367$	−4.67354e84			−1.08559			−0.542794	−	0.839866i	$-0.682634\pi$
$367$	−4.67354e84			−1.08559			−0.542794	+	0.839866i	$0.682634\pi$
$368$			7.34090e83i			0.155873i
$369$	−8.17008e84	+	7.07608e83i	−1.58619	+	0.137380i
$370$	2.79238e84			0.495813
$371$			5.02660e84i			0.816461i
$372$	−1.97732e84	−	1.81347e84i	−0.293873	−	0.269521i
$373$	3.60604e84			0.490501			0.245250	−	0.969460i	$-0.421130\pi$
$373$	3.60604e84			0.490501			0.245250	+	0.969460i	$0.421130\pi$
$374$			4.35077e84i			0.541756i
$375$	6.14238e84	−	6.69737e84i	0.700334	−	0.763611i
$376$	−3.29967e84			−0.344565
$377$		−	1.70972e85i		−	1.63554i
$378$	−6.50334e84	−	5.00372e84i	−0.570042	−	0.438595i
$379$	1.99630e85			1.60373			0.801866	−	0.597504i	$-0.203841\pi$
$379$	1.99630e85			1.60373			0.801866	+	0.597504i	$0.203841\pi$
$380$			1.47978e85i			1.08978i
$381$	8.08435e84	+	7.41443e84i	0.545910	+	0.500672i
$382$	−1.11581e85			−0.691033
$383$		−	1.29127e85i		−	0.733598i	−0.930300	−	0.366799i	$-0.880454\pi$
$383$		−	1.29127e85i		−	0.733598i	0.930300	−	0.366799i	$-0.119546\pi$
$384$	−1.05251e85	+	1.14761e85i	−0.548652	+	0.598225i
$385$	3.03953e85			1.45413
$386$		−	7.91698e84i		−	0.347679i
$387$	1.87863e84	+	2.16908e85i	0.0757494	+	0.874607i
$388$	5.26025e84			0.194787
$389$		−	4.51592e85i		−	1.53606i	−0.640412	−	0.768032i	$-0.721236\pi$
$389$		−	4.51592e85i		−	1.53606i	0.640412	−	0.768032i	$-0.278764\pi$
$390$	−1.77929e85	−	1.63185e85i	−0.556052	−	0.509974i
$391$	2.63223e85			0.755947
$392$			2.42815e85i			0.640965i
$393$	−1.64628e84	+	1.79503e84i	−0.0399531	+	0.0435630i
$394$	3.17577e85			0.708719
$395$		−	2.34540e85i		−	0.481408i
$396$	−4.27189e85	+	3.69987e84i	−0.806638	+	0.0698627i
$397$	1.54656e85			0.268708			0.134354	−	0.990933i	$-0.457104\pi$
$397$	1.54656e85			0.268708			0.134354	+	0.990933i	$0.457104\pi$
$398$		−	1.63565e85i		−	0.261546i
$399$	−1.06584e86	−	9.77514e85i	−1.56886	−	1.43886i
$400$	1.02494e84			0.0138905
$401$			5.34957e85i			0.667659i	0.942634	+	0.333829i	$0.108341\pi$
$401$			5.34957e85i			0.667659i	−0.942634	+	0.333829i	$0.891659\pi$
$402$	−3.56250e85	+	3.88438e85i	−0.409538	+	0.446541i
$403$	7.71508e85			0.817098
$404$			8.76580e85i			0.855473i
$405$	1.83283e85	+	1.05016e86i	0.164856	+	0.944582i
$406$	−9.99595e85			−0.828829
$407$			1.42609e86i			1.09027i
$408$	8.19989e85	+	7.52040e85i	0.578126	+	0.530219i
$409$	−1.53999e86			−1.00150			−0.500748	−	0.865593i	$-0.666942\pi$
$409$	−1.53999e86			−1.00150			−0.500748	+	0.865593i	$0.666942\pi$
$410$			1.41069e86i			0.846379i
$411$	8.92811e84	−	9.73479e84i	0.0494287	−	0.0538948i
$412$	−1.20510e86			−0.615764
$413$		−	2.40677e86i		−	1.13523i
$414$	−9.93355e84	−	1.14693e86i	−0.0432607	−	0.499490i
$415$	2.49637e86			1.00397
$416$		−	3.95058e86i		−	1.46751i
$417$	−8.62012e85	−	7.90580e85i	−0.295817	−	0.271304i
$418$	3.35374e86			1.06344
$419$			2.41715e86i			0.708339i	0.935181	+	0.354170i	$0.115236\pi$
$419$			2.41715e86i			0.708339i	−0.935181	+	0.354170i	$0.884764\pi$
$420$	2.14991e86	−	2.34416e86i	0.582362	−	0.634980i
$421$	−3.82162e86			−0.957058			−0.478529	−	0.878072i	$-0.658830\pi$
$421$	−3.82162e86			−0.957058			−0.478529	+	0.878072i	$0.658830\pi$
$422$			1.28161e86i			0.296787i
$423$	−1.70800e86	+	1.47929e85i	−0.365810	+	0.0316827i
$424$	−2.98095e86			−0.590584
$425$		−	3.67512e85i		−	0.0673655i
$426$	2.98879e86	+	2.74112e86i	0.506965	+	0.464955i
$427$	5.20500e86			0.817149
$428$		−	5.19690e86i		−	0.755266i
$429$	8.33400e86	−	9.08700e86i	1.12141	−	1.22273i
$430$	3.74525e86			0.466683
$431$			1.00679e87i			1.16196i	0.813918	+	0.580979i	$0.197330\pi$
$431$			1.00679e87i			1.16196i	−0.813918	+	0.580979i	$0.802670\pi$
$432$	−9.83112e85	+	1.27775e86i	−0.105109	+	0.136610i
$433$	−1.35263e87			−1.33992			−0.669962	−	0.742396i	$-0.733690\pi$
$433$	−1.35263e87			−1.33992			−0.669962	+	0.742396i	$0.733690\pi$
$434$		−	4.51066e86i		−	0.414075i
$435$	9.57075e86	+	8.77766e86i	0.814330	+	0.746850i
$436$	1.13641e87			0.896360
$437$		−	2.02903e87i		−	1.48388i
$438$	1.49211e86	−	1.62693e86i	0.101194	−	0.110337i
$439$	−2.91566e87			−1.83403			−0.917017	−	0.398848i	$-0.869410\pi$
$439$	−2.91566e87			−1.83403			−0.917017	+	0.398848i	$0.869410\pi$
$440$			1.80255e87i			1.05184i
$441$	1.08858e86	+	1.25688e87i	0.0589366	+	0.680486i
$442$	−1.30921e87			−0.657772
$443$			2.75569e86i			0.128501i	0.997934	+	0.0642506i	$0.0204657\pi$
$443$			2.75569e86i			0.128501i	−0.997934	+	0.0642506i	$0.979534\pi$
$444$	1.09984e87	+	1.00870e87i	0.476092	+	0.436640i
$445$	−2.32492e85			−0.00934390
$446$		−	1.10639e87i		−	0.412913i
$447$	−7.46862e86	+	8.14343e86i	−0.258876	+	0.282266i
$448$	−1.61522e87			−0.520066
$449$			2.94185e87i			0.880017i	0.897994	+	0.440009i	$0.145025\pi$
$449$			2.94185e87i			0.880017i	−0.897994	+	0.440009i	$0.854975\pi$
$450$	−1.60135e86	+	1.38692e85i	−0.0445115	+	0.00385513i
$451$	−7.20452e87			−1.86114
$452$		−	5.13726e87i		−	1.23357i
$453$	8.16389e86	+	7.48738e86i	0.182245	+	0.167143i
$454$	1.21099e87			0.251360
$455$			9.14640e87i			1.76553i
$456$	5.79701e87	−	6.32078e87i	1.04079	−	1.13483i
$457$	2.81675e87			0.470450			0.235225	−	0.971941i	$-0.424417\pi$
$457$	2.81675e87			0.470450			0.235225	+	0.971941i	$0.424417\pi$
$458$		−	1.27100e87i		−	0.197509i
$459$	4.58164e87	+	3.52515e87i	0.662525	+	0.509752i
$460$	4.46256e87			0.600586
$461$		−	1.02715e88i		−	1.28678i	−0.765539	−	0.643389i	$-0.777528\pi$
$461$		−	1.02715e88i		−	1.28678i	0.765539	−	0.643389i	$-0.222472\pi$
$462$	−5.31276e87	−	4.87251e87i	−0.619633	−	0.568287i
$463$	−2.23256e87			−0.242455			−0.121227	−	0.992625i	$-0.538683\pi$
$463$	−2.23256e87			−0.242455			−0.121227	+	0.992625i	$0.538683\pi$
$464$			1.96396e87i			0.198628i
$465$	−3.96091e87	+	4.31879e87i	−0.373119	+	0.406831i
$466$	7.96448e87			0.698912
$467$			1.05727e86i			0.00864431i	0.999991	+	0.00432216i	$0.00137579\pi$
$467$			1.05727e86i			0.00864431i	−0.999991	+	0.00432216i	$0.998624\pi$
$468$	−1.11335e87	−	1.28548e88i	−0.0848237	−	0.979379i
$469$	1.99675e88			1.41782
$470$			2.94913e87i			0.195193i
$471$	−7.30159e87	−	6.69653e87i	−0.450534	−	0.413200i
$472$	1.42730e88			0.821162
$473$			1.91273e88i			1.02621i
$474$	−3.75979e87	+	4.09950e87i	−0.188139	+	0.205138i
$475$	−2.83292e87			−0.132235
$476$		−	1.72484e88i		−	0.751139i
$477$	−1.54302e88	+	1.33641e87i	−0.626998	+	0.0543041i
$478$	−1.27350e88			−0.482925
$479$		−	3.13406e88i		−	1.10927i	−0.832095	−	0.554633i	$-0.812859\pi$
$479$		−	3.13406e88i		−	1.10927i	0.832095	−	0.554633i	$-0.187141\pi$
$480$	2.21148e88	+	2.02822e88i	0.730670	+	0.670122i
$481$	−4.29133e88			−1.32375
$482$			1.67286e88i			0.481844i
$483$	−2.94788e88	+	3.21424e88i	−0.792967	+	0.864614i
$484$	−1.01027e88			−0.253829
$485$		−	1.14892e88i		−	0.269658i
$486$	1.36310e88	−	2.12937e88i	0.298903	−	0.466934i
$487$	6.55251e88			1.34262			0.671308	−	0.741179i	$-0.265733\pi$
$487$	6.55251e88			1.34262			0.671308	+	0.741179i	$0.265733\pi$
$488$			3.08675e88i			0.591082i
$489$	−7.70284e88	−	7.06454e88i	−1.37866	−	1.26442i
$490$	2.17019e88			0.363101
$491$			1.03456e89i			1.61833i	0.587582	+	0.809165i	$0.300080\pi$
$491$			1.03456e89i			1.61833i	−0.587582	+	0.809165i	$0.699920\pi$
$492$	−5.09587e88	+	5.55630e88i	−0.745367	+	0.812714i
$493$	7.04221e88			0.963297
$494$			1.00919e89i			1.29117i
$495$	8.08110e87	+	9.33049e88i	0.0967162	+	1.11669i
$496$	−8.86236e87			−0.0992326
$497$		−	1.53638e89i		−	1.60967i
$498$	−4.36337e88	−	4.00180e88i	−0.427813	−	0.392362i
$499$	−4.58449e88			−0.420700			−0.210350	−	0.977626i	$-0.567460\pi$
$499$	−4.58449e88			−0.420700			−0.210350	+	0.977626i	$0.567460\pi$
$500$		−	8.35462e88i		−	0.717656i
$501$	3.55332e88	−	3.87437e88i	0.285752	−	0.311570i
$502$	4.79059e88			0.360717
$503$		−	1.87043e89i		−	1.31886i	−0.751767	−	0.659429i	$-0.770798\pi$
$503$		−	1.87043e89i		−	1.31886i	0.751767	−	0.659429i	$-0.229202\pi$
$504$	−1.83664e89	+	1.59071e88i	−1.21288	+	0.105047i
$505$	1.91459e89			1.18430
$506$		−	1.01139e89i		−	0.586071i
$507$	1.37698e89	+	1.26287e89i	0.747591	+	0.685641i
$508$	1.00848e89			0.513056
$509$		−	1.10894e89i		−	0.528714i	−0.964425	−	0.264357i	$-0.914840\pi$
$509$		−	1.10894e89i		−	0.528714i	0.964425	−	0.264357i	$-0.0851598\pi$
$510$	6.72147e88	−	7.32878e88i	0.300365	−	0.327503i
$511$	−8.36317e88			−0.350333
$512$			8.65670e88i			0.339972i
$513$	2.71732e89	−	3.53170e89i	1.00062	−	1.30050i
$514$	−3.71863e88			−0.128410
$515$			2.63213e89i			0.852449i
$516$	1.47514e89	+	1.35290e89i	0.448120	+	0.410986i
$517$	−1.50615e89			−0.429219
$518$			2.50895e89i			0.670825i
$519$	−1.05493e89	+	1.15025e89i	−0.264669	+	0.288582i
$520$	−5.42414e89			−1.27709
$521$			3.29116e89i			0.727284i	0.931539	+	0.363642i	$0.118467\pi$
$521$			3.29116e89i			0.727284i	−0.931539	+	0.363642i	$0.881533\pi$
$522$	−2.65759e88	−	3.06847e89i	−0.0551267	−	0.636496i
$523$	3.94819e89			0.768851			0.384425	−	0.923156i	$-0.374400\pi$
$523$	3.94819e89			0.768851			0.384425	+	0.923156i	$0.374400\pi$
$524$			2.23921e88i			0.0409413i
$525$	4.48772e88	+	4.11584e88i	0.0770492	+	0.0706645i
$526$	−4.01831e89			−0.647908
$527$			3.17779e89i			0.481254i
$528$	−9.57331e88	+	1.04383e89i	−0.136189	+	0.148494i
$529$	1.36341e89			0.182218
$530$			2.66427e89i			0.334561i
$531$	7.38810e89	−	6.39881e88i	0.871793	−	0.0755057i
$532$	−1.32957e90			−1.47445
$533$		−	2.16795e90i		−	2.25970i
$534$	4.06370e87	+	3.72696e87i	0.00398163	+	0.00365169i
$535$	−1.13509e90			−1.04557
$536$			1.18414e90i			1.02557i
$537$	−2.99637e89	+	3.26710e89i	−0.244030	+	0.266079i
$538$	−6.71397e89			−0.514239
$539$			1.10834e90i			0.798440i
$540$	7.76749e89	+	5.97637e89i	0.526365	+	0.404989i
$541$	−6.61490e89			−0.421710			−0.210855	−	0.977517i	$-0.567625\pi$
$541$	−6.61490e89			−0.421710			−0.210855	+	0.977517i	$0.567625\pi$
$542$			1.11105e90i			0.666435i
$543$	9.89325e89	+	9.07344e89i	0.558399	+	0.512127i
$544$	1.62722e90			0.864333
$545$		−	2.48211e90i		−	1.24090i
$546$	1.46621e90	−	1.59869e90i	0.689985	−	0.752327i
$547$	2.03418e90			0.901170			0.450585	−	0.892734i	$-0.351215\pi$
$547$	2.03418e90			0.901170			0.450585	+	0.892734i	$0.351215\pi$
$548$		−	1.21436e89i		−	0.0506513i
$549$	1.38384e89	+	1.59779e90i	0.0543498	+	0.627526i
$550$	−1.41210e89			−0.0522271
$551$		−	5.42840e90i		−	1.89090i
$552$	−1.90616e90	−	1.74820e90i	−0.625416	−	0.573590i
$553$	2.10733e90			0.651334
$554$			2.81057e90i			0.818412i
$555$	2.20316e90	−	2.40222e90i	0.604474	−	0.659090i
$556$	−1.07531e90			−0.278015
$557$		−	6.52629e89i		−	0.159017i	−0.996834	−	0.0795087i	$-0.974665\pi$
$557$		−	6.52629e89i		−	0.159017i	0.996834	−	0.0795087i	$-0.0253352\pi$
$558$	1.38464e90	−	1.19924e89i	0.317987	−	0.0275408i
$559$	−5.75569e90			−1.24597
$560$		−	1.05065e90i		−	0.214414i
$561$	3.74287e90	+	3.43271e90i	0.720162	+	0.660485i
$562$	6.03212e90			1.09439
$563$			8.83877e89i			0.151222i	0.997137	+	0.0756110i	$0.0240907\pi$
$563$			8.83877e89i			0.151222i	−0.997137	+	0.0756110i	$0.975909\pi$
$564$	−1.06532e90	+	1.16158e90i	−0.171898	+	0.187429i
$565$	−1.12206e91			−1.70772
$566$			7.75203e89i			0.111294i
$567$	−9.43565e90	+	1.64679e90i	−1.27800	+	0.223047i
$568$	9.11125e90			1.16435
$569$			1.29091e91i			1.55665i	0.627862	+	0.778325i	$0.283930\pi$
$569$			1.29091e91i			1.55665i	−0.627862	+	0.778325i	$0.716070\pi$
$570$	−5.64930e90	−	5.18117e90i	−0.642872	−	0.589600i
$571$	7.71993e90			0.829128			0.414564	−	0.910020i	$-0.363934\pi$
$571$	7.71993e90			0.829128			0.414564	+	0.910020i	$0.363934\pi$
$572$		−	1.13356e91i		−	1.14914i
$573$	−8.80361e90	+	9.59904e90i	−0.842477	+	0.918598i
$574$	−1.26750e91			−1.14513
$575$			8.54324e89i			0.0728758i
$576$	−4.29435e89	−	4.95828e90i	−0.0345904	−	0.399382i
$577$	2.03705e91			1.54953			0.774766	−	0.632248i	$-0.217867\pi$
$577$	2.03705e91			1.54953			0.774766	+	0.632248i	$0.217867\pi$
$578$			2.32446e90i			0.166995i
$579$	−6.81079e90	−	6.24641e90i	−0.462173	−	0.423875i
$580$	1.19390e91			0.765322
$581$			2.24298e91i			1.35835i
$582$	−1.84178e90	+	2.00819e90i	−0.105385	+	0.114907i
$583$	−1.36067e91			−0.735681
$584$		−	4.95966e90i		−	0.253412i
$585$	−2.80769e91	+	2.43173e90i	−1.35583	+	0.117428i
$586$	5.38253e90			0.245677
$587$			1.91542e91i			0.826431i	0.910633	+	0.413215i	$0.135594\pi$
$587$			1.91542e91i			0.826431i	−0.910633	+	0.413215i	$0.864406\pi$
$588$	8.54776e90	+	7.83944e90i	0.348659	+	0.319767i
$589$	2.44956e91			0.944676
$590$		−	1.27567e91i		−	0.465181i
$591$	2.50565e91	−	2.73204e91i	0.864038	−	0.942107i
$592$	4.92948e90			0.160762
$593$		−	4.05156e91i		−	1.24973i	−0.780731	−	0.624867i	$-0.785153\pi$
$593$		−	4.05156e91i		−	1.24973i	0.780731	−	0.624867i	$-0.214847\pi$
$594$	1.35447e91	−	1.76041e91i	0.395201	−	0.513643i
$595$	−3.76733e91			−1.03986
$596$			1.01585e91i			0.265279i
$597$	−1.40711e91	−	1.29051e91i	−0.347676	−	0.318866i
$598$	3.04341e91			0.711577
$599$		−	5.55907e91i		−	1.23003i	−0.788514	−	0.615017i	$-0.789149\pi$
$599$		−	5.55907e91i		−	1.23003i	0.788514	−	0.615017i	$-0.210851\pi$
$600$	−2.44084e90	+	2.66137e90i	−0.0511149	+	0.0557333i
$601$	5.83160e91			1.15593			0.577963	−	0.816063i	$-0.303848\pi$
$601$	5.83160e91			1.15593			0.577963	+	0.816063i	$0.303848\pi$
$602$			3.36509e91i			0.631412i
$603$	5.30871e90	+	6.12946e91i	0.0943012	+	1.08881i
$604$	1.01840e91			0.171277
$605$			2.20660e91i			0.351395i
$606$	−3.34649e91	−	3.06918e91i	−0.504653	−	0.462835i
$607$	−1.20208e91			−0.171675			−0.0858375	−	0.996309i	$-0.527357\pi$
$607$	−1.20208e91			−0.171675			−0.0858375	+	0.996309i	$0.527357\pi$
$608$		−	1.25432e92i		−	1.69664i
$609$	−7.88669e91	+	8.59928e91i	−1.01047	+	1.10177i
$610$	2.75883e91			0.334843
$611$		−	4.53222e91i		−	0.521136i
$612$	5.29478e91	−	4.58579e90i	0.576834	−	0.0499594i
$613$	2.30231e91			0.237667			0.118833	−	0.992914i	$-0.462085\pi$
$613$	2.30231e91			0.237667			0.118833	+	0.992914i	$0.462085\pi$
$614$			1.10825e92i			1.08413i
$615$	1.21359e92	+	1.11302e92i	1.12510	+	1.03187i
$616$	−1.61958e92			−1.42311
$617$			1.79035e92i			1.49117i	0.666409	+	0.745587i	$0.267831\pi$
$617$			1.79035e92i			1.49117i	−0.666409	+	0.745587i	$0.732169\pi$
$618$	4.21943e91	−	4.60066e91i	0.333145	−	0.363246i
$619$	−2.15496e92			−1.61305			−0.806524	−	0.591201i	$-0.798654\pi$
$619$	−2.15496e92			−1.61305			−0.806524	+	0.591201i	$0.798654\pi$
$620$			5.38746e91i			0.382348i
$621$	−1.06505e92	−	8.19461e91i	−0.716719	−	0.551449i
$622$	2.43764e91			0.155556
$623$		−	2.08893e90i		−	0.0126421i
$624$	−3.14104e91	−	2.88075e91i	−0.180294	−	0.165354i
$625$	−1.67677e92			−0.912919
$626$			2.77154e91i			0.143142i
$627$	2.64606e92	−	2.88514e92i	1.29650	−	1.41364i
$628$	−9.10835e91			−0.423420
$629$		−	1.76757e92i		−	0.779659i
$630$	1.42172e91	+	1.64153e92i	0.0595081	+	0.687084i
$631$	1.80767e91			0.0718044			0.0359022	−	0.999355i	$-0.488570\pi$
$631$	1.80767e91			0.0718044			0.0359022	+	0.999355i	$0.488570\pi$
$632$			1.24972e92i			0.471141i
$633$	1.10254e92	+	1.01118e92i	0.394522	+	0.361829i
$634$	7.94670e91			0.269924
$635$		−	2.20268e92i		−	0.710262i
$636$	−9.62421e91	+	1.04938e92i	−0.294632	+	0.321253i
$637$	−3.33515e92			−0.969425
$638$		−	2.70583e92i		−	0.746825i
$639$	4.71624e92	−	4.08472e91i	1.23614	−	0.107062i
$640$	3.12681e92			0.778327
$641$			1.97841e92i			0.467737i	0.972268	+	0.233868i	$0.0751385\pi$
$641$			1.97841e92i			0.467737i	−0.972268	+	0.233868i	$0.924862\pi$
$642$	1.98400e92	+	1.81960e92i	0.445540	+	0.408620i
$643$	4.43786e92			0.946698			0.473349	−	0.880875i	$-0.343045\pi$
$643$	4.43786e92			0.946698			0.473349	+	0.880875i	$0.343045\pi$
$644$			4.00959e92i			0.812581i
$645$	2.95496e92	−	3.22195e92i	0.568959	−	0.620366i
$646$	−4.15678e92			−0.760474
$647$			9.41682e91i			0.163705i	0.996644	+	0.0818527i	$0.0260837\pi$
$647$			9.41682e91i			0.163705i	−0.996644	+	0.0818527i	$0.973916\pi$
$648$	−9.76604e91	−	5.59567e92i	−0.161341	−	0.924437i
$649$	6.51496e92			1.02291
$650$		−	4.24921e91i		−	0.0634115i
$651$	−3.88041e92	−	3.55886e92i	−0.550434	−	0.504822i
$652$	−9.60889e92			−1.29569
$653$		−	9.87640e92i		−	1.26609i	−0.774116	−	0.633044i	$-0.781805\pi$
$653$		−	9.87640e92i		−	1.26609i	0.774116	−	0.633044i	$-0.218195\pi$
$654$	−3.97894e92	+	4.33845e92i	−0.484955	+	0.528773i
$655$	4.89078e91			0.0566781
$656$			2.49034e92i			0.274430i
$657$	−2.22349e91	−	2.56726e92i	−0.0233012	−	0.269037i
$658$	−2.64978e92			−0.264092
$659$		−	8.84049e92i		−	0.838026i	−0.907980	−	0.419013i	$-0.862376\pi$
$659$		−	8.84049e92i		−	0.838026i	0.907980	−	0.419013i	$-0.137624\pi$
$660$	6.34547e92	+	5.81965e92i	0.572156	+	0.524743i
$661$	2.08708e93			1.79016			0.895080	−	0.445906i	$-0.147118\pi$
$661$	2.08708e93			1.79016			0.895080	+	0.445906i	$0.147118\pi$
$662$			4.55515e92i			0.371697i
$663$	−1.03295e93	+	1.12629e93i	−0.801927	+	0.874384i
$664$	−1.33016e93			−0.982559
$665$			2.90400e93i			2.04119i
$666$	−7.70176e92	+	6.67046e91i	−0.515158	+	0.0446176i
$667$	−1.63704e93			−1.04209
$668$		−	4.83308e92i		−	0.292820i
$669$	−9.51803e92	−	8.72931e92i	−0.548890	−	0.503405i
$670$	1.05835e93			0.580978
$671$			1.40896e93i			0.736301i
$672$	−1.82235e93	+	1.98700e93i	−0.906661	+	0.988581i
$673$	3.12867e92			0.148205			0.0741025	−	0.997251i	$-0.476391\pi$
$673$	3.12867e92			0.148205			0.0741025	+	0.997251i	$0.476391\pi$
$674$		−	2.34164e93i		−	1.05620i
$675$	−1.14413e92	+	1.48703e92i	−0.0491418	+	0.0638697i
$676$	1.71771e93			0.702600
$677$		−	1.53207e93i		−	0.596834i	−0.954436	−	0.298417i	$-0.903541\pi$
$677$		−	1.53207e93i		−	0.596834i	0.954436	−	0.298417i	$-0.0964586\pi$
$678$	1.96124e93	+	1.79872e93i	0.727696	+	0.667394i
$679$	1.03230e93			0.364842
$680$		−	2.23416e93i		−	0.752178i
$681$	9.55454e92	−	1.04178e93i	0.306447	−	0.334135i
$682$	1.22100e93			0.373106
$683$			2.57622e93i			0.750066i	0.927011	+	0.375033i	$0.122369\pi$
$683$			2.57622e93i			0.750066i	−0.927011	+	0.375033i	$0.877631\pi$
$684$	−3.53490e92	−	4.08142e93i	−0.0980677	−	1.13230i
$685$	−2.65237e92			−0.0701204
$686$		−	9.04871e92i		−	0.227977i
$687$	−1.09341e93	−	1.00281e93i	−0.262550	−	0.240794i
$688$	6.61160e92			0.151317
$689$		−	4.09445e93i		−	0.893226i
$690$	−1.56248e93	+	1.70366e93i	−0.324934	+	0.354293i
$691$	4.05213e93			0.803356			0.401678	−	0.915781i	$-0.368427\pi$
$691$	4.05213e93			0.803356			0.401678	+	0.915781i	$0.368427\pi$
$692$			1.43488e93i			0.271215i
$693$	−8.38341e93	+	7.26084e92i	−1.51086	+	0.130855i
$694$	5.37092e93			0.922968
$695$			2.34866e93i			0.384877i
$696$	−5.09968e93	−	4.67709e93i	−0.796962	−	0.730921i
$697$	8.92962e93			1.33092
$698$			7.64165e93i			1.08632i
$699$	6.28389e93	−	6.85166e93i	0.852082	−	0.929071i
$700$	5.59819e92			0.0724123
$701$		−	5.64714e93i		−	0.696842i	−0.937338	−	0.348421i	$-0.886718\pi$
$701$		−	5.64714e93i		−	0.696842i	0.937338	−	0.348421i	$-0.113282\pi$
$702$	5.29734e93	+	4.07582e93i	0.623639	+	0.479833i
$703$	−1.36251e94			−1.53043
$704$		−	4.37230e93i		−	0.468611i
$705$	2.53707e93	+	2.32683e93i	0.259472	+	0.237971i
$706$	2.41542e93			0.235743
$707$			1.72025e94i			1.60233i
$708$	4.60813e93	−	5.02449e93i	0.409664	−	0.446678i
$709$	−1.03680e94			−0.879772			−0.439886	−	0.898054i	$-0.644981\pi$
$709$	−1.03680e94			−0.879772			−0.439886	+	0.898054i	$0.644981\pi$
$710$		−	8.14332e93i		−	0.659593i
$711$	5.60271e92	+	6.46892e93i	0.0433213	+	0.500190i
$712$	1.23881e92			0.00914462
$713$		−	7.38712e93i		−	0.520620i
$714$	6.58488e93	+	6.03922e93i	0.443105	+	0.406387i
$715$	−2.47587e94			−1.59085
$716$			4.07554e93i			0.250066i
$717$	−1.00478e94	+	1.09557e94i	−0.588761	+	0.641958i
$718$	−7.87527e93			−0.440716
$719$			1.26419e94i			0.675709i	0.941198	+	0.337854i	$0.109701\pi$
$719$			1.26419e94i			0.675709i	−0.941198	+	0.337854i	$0.890299\pi$
$720$	3.22521e93	−	2.79334e92i	0.164659	−	0.0142610i
$721$	−2.36496e94			−1.15335
$722$			2.01418e94i			0.938361i
$723$	1.43912e94	+	1.31987e94i	0.640521	+	0.587443i
$724$	1.23413e94			0.524794
$725$			2.28563e93i			0.0928651i
$726$	3.53728e93	−	3.85689e93i	0.137329	−	0.149737i
$727$	2.43739e94			0.904251			0.452126	−	0.891954i	$-0.350666\pi$
$727$	2.43739e94			0.904251			0.452126	+	0.891954i	$0.350666\pi$
$728$		−	4.87357e94i		−	1.72787i
$729$	−7.56381e93	−	2.85269e94i	−0.256290	−	0.966600i
$730$	−4.43277e93			−0.143556
$731$		−	2.37073e94i		−	0.733852i
$732$	1.08662e94	+	9.96579e93i	0.321524	+	0.294881i
$733$	−1.42262e94			−0.402399			−0.201199	−	0.979550i	$-0.564484\pi$
$733$	−1.42262e94			−0.402399			−0.201199	+	0.979550i	$0.564484\pi$
$734$		−	2.22570e94i		−	0.601861i
$735$	1.71226e94	−	1.86697e94i	0.442677	−	0.482675i
$736$	−3.78264e94			−0.935034
$737$			5.40507e94i			1.27754i
$738$	−3.36987e93	−	3.89087e94i	−0.0761646	−	0.879401i
$739$	6.47461e94			1.39942			0.699708	−	0.714429i	$-0.253313\pi$
$739$	6.47461e94			1.39942			0.699708	+	0.714429i	$0.253313\pi$
$740$		−	2.99665e94i		−	0.619425i
$741$	8.68183e94	+	7.96241e94i	1.71637	+	1.57414i
$742$	−2.39384e94			−0.452654
$743$			3.38589e94i			0.612410i	0.951966	+	0.306205i	$0.0990592\pi$
$743$			3.38589e94i			0.612410i	−0.951966	+	0.306205i	$0.900941\pi$
$744$	2.11053e94	−	2.30122e94i	0.365161	−	0.398155i
$745$	2.21878e94			0.367246
$746$			1.71732e94i			0.271938i
$747$	−6.88530e94	+	5.96334e93i	−1.04314	+	0.0903461i
$748$	4.66903e94			0.676822
$749$		−	1.01987e95i		−	1.41464i
$750$	3.18952e94	+	2.92521e94i	0.423353	+	0.388272i
$751$	−1.25300e95			−1.59160			−0.795801	−	0.605559i	$-0.792950\pi$
$751$	−1.25300e95			−1.59160			−0.795801	+	0.605559i	$0.792950\pi$
$752$			5.20619e93i			0.0632894i
$753$	3.77972e94	−	4.12123e94i	0.439770	−	0.479505i
$754$	8.14227e94			0.906757
$755$		−	2.22435e94i		−	0.237112i
$756$	−5.36975e94	+	6.97906e94i	−0.547942	+	0.712160i
$757$	−6.88341e94			−0.672418			−0.336209	−	0.941787i	$-0.609145\pi$
$757$	−6.88341e94			−0.672418			−0.336209	+	0.941787i	$0.609145\pi$
$758$			9.50706e94i			0.889124i
$759$	−8.70072e94	−	7.97972e94i	−0.779070	−	0.714511i
$760$	−1.72218e95			−1.47649
$761$		−	8.72317e94i		−	0.716111i	−0.933700	−	0.358056i	$-0.883440\pi$
$761$		−	8.72317e94i		−	0.716111i	0.933700	−	0.358056i	$-0.116560\pi$
$762$	−3.53100e94	+	3.85004e94i	−0.277577	+	0.302657i
$763$	2.23017e95			1.67891
$764$			1.19743e95i			0.863315i
$765$	−1.00161e94	−	1.15646e95i	−0.0691626	−	0.798555i
$766$	6.14948e94			0.406714
$767$			1.96045e95i			1.24196i
$768$	−1.03337e95	−	9.47743e94i	−0.627101	−	0.575136i
$769$	−8.94550e94			−0.520038			−0.260019	−	0.965603i	$-0.583729\pi$
$769$	−8.94550e94			−0.520038			−0.260019	+	0.965603i	$0.583729\pi$
$770$			1.44753e95i			0.806181i
$771$	−2.93396e94	+	3.19905e94i	−0.156552	+	0.170697i
$772$	−8.49610e94			−0.434359
$773$			1.48435e95i			0.727130i	0.931569	+	0.363565i	$0.118440\pi$
$773$			1.48435e95i			0.727130i	−0.931569	+	0.363565i	$0.881560\pi$
$774$	−1.03299e95	+	8.94667e93i	−0.484890	+	0.0419962i
$775$	−1.03139e94			−0.0463945
$776$			6.12193e94i			0.263907i
$777$	2.15839e95	+	1.97953e95i	0.891735	+	0.817841i
$778$	2.15063e95			0.851608
$779$		−	6.88329e95i		−	2.61252i
$780$	−1.75122e95	+	1.90945e95i	−0.637117	+	0.694682i
$781$	4.15886e95			1.45041
$782$			1.25356e95i			0.419104i
$783$	−2.84942e95	−	2.19236e95i	−0.913309	−	0.702708i
$784$	3.83111e94			0.117732
$785$			1.98941e95i			0.586172i
$786$	−8.54854e93	−	7.84016e93i	−0.0241517	−	0.0221504i
$787$	6.31584e95			1.71106			0.855529	−	0.517754i	$-0.173232\pi$
$787$	6.31584e95			1.71106			0.855529	+	0.517754i	$0.173232\pi$
$788$		−	3.40808e95i		−	0.885410i
$789$	−3.17040e95	+	3.45686e95i	−0.789901	+	0.861271i
$790$	1.11696e95			0.266897
$791$		−	1.00817e96i		−	2.31051i
$792$	−4.30594e94	−	4.97166e95i	−0.0946535	−	1.09287i
$793$	−4.23977e95			−0.893979
$794$			7.36526e94i			0.148974i
$795$	2.29201e95	+	2.10208e95i	0.444735	+	0.407882i
$796$	−1.75530e95			−0.326753
$797$			5.07830e95i			0.906972i	0.891263	+	0.453486i	$0.149820\pi$
$797$			5.07830e95i			0.906972i	−0.891263	+	0.453486i	$0.850180\pi$
$798$	4.65526e95	−	5.07587e95i	0.797716	−	0.869792i
$799$	1.86679e95			0.306938
$800$			5.28133e94i			0.0833246i
$801$	6.41243e93	−	5.55379e92i	0.00970845	−	0.000840846i
$802$	−2.54765e95			−0.370156
$803$		−	2.26385e95i		−	0.315671i
$804$	4.16852e95	+	3.82309e95i	0.557869	+	0.511641i
$805$	8.75759e95			1.12492
$806$			3.67419e95i			0.453007i
$807$	−5.29725e95	+	5.77587e95i	−0.626937	+	0.683583i
$808$	−1.02017e96			−1.15904
$809$		−	2.63427e95i		−	0.287315i	−0.989627	−	0.143658i	$-0.954114\pi$
$809$		−	2.63427e95i		−	0.287315i	0.989627	−	0.143658i	$-0.0458864\pi$
$810$	−5.00122e95	+	8.72856e94i	−0.523685	+	0.0913980i
$811$	−2.78615e95			−0.280102			−0.140051	−	0.990144i	$-0.544727\pi$
$811$	−2.78615e95			−0.280102			−0.140051	+	0.990144i	$0.544727\pi$
$812$			1.07272e96i			1.03547i
$813$	9.55812e95	+	8.76607e95i	0.885899	+	0.812488i
$814$	−6.79155e95			−0.604454
$815$			2.09874e96i			1.79373i
$816$	1.18656e95	−	1.29377e95i	0.0973901	−	0.106190i
$817$	−1.82745e96			−1.44051
$818$		−	7.33397e95i		−	0.555239i
$819$	−2.18490e95	−	2.52269e96i	−0.158877	−	1.83441i
$820$	1.51388e96			1.05739
$821$		−	1.59159e96i		−	1.06784i	−0.845534	−	0.533921i	$-0.820718\pi$
$821$		−	1.59159e96i		−	1.06784i	0.845534	−	0.533921i	$-0.179282\pi$
$822$	4.63604e94	+	4.25187e94i	0.0298798	+	0.0274038i
$823$	−1.01941e96			−0.631181			−0.315591	−	0.948895i	$-0.602203\pi$
$823$	−1.01941e96			−0.631181			−0.315591	+	0.948895i	$0.602203\pi$
$824$		−	1.40250e96i		−	0.834268i
$825$	−1.11413e95	+	1.21479e95i	−0.0636730	+	0.0694260i
$826$	1.14619e96			0.629381
$827$			3.10475e96i			1.63812i	0.573708	+	0.819060i	$0.305504\pi$
$827$			3.10475e96i			1.63812i	−0.573708	+	0.819060i	$0.694496\pi$
$828$	−1.23083e96	+	1.06602e95i	−0.624018	+	0.0540460i
$829$	−2.62690e96			−1.27980			−0.639902	−	0.768456i	$-0.721025\pi$
$829$	−2.62690e96			−1.27980			−0.639902	+	0.768456i	$0.721025\pi$
$830$			1.18886e96i			0.556611i
$831$	2.41787e96	+	2.21751e96i	1.08792	+	0.997772i
$832$	1.31569e96			0.568963
$833$		−	1.37372e96i		−	0.570971i
$834$	3.76501e95	−	4.10520e95i	0.150414	−	0.164004i
$835$	−1.05562e96			−0.405373
$836$		−	3.59907e96i		−	1.32856i
$837$	9.89301e95	−	1.28580e96i	0.351066	−	0.456280i
$838$	−1.15113e96			−0.392710
$839$			3.27888e96i			1.07543i	0.843128	+	0.537713i	$0.180712\pi$
$839$			3.27888e96i			1.07543i	−0.843128	+	0.537713i	$0.819288\pi$
$840$	2.72815e96	+	2.50208e96i	0.860303	+	0.789014i
$841$	−1.08156e96			−0.327932
$842$		−	1.81999e96i		−	0.530602i
$843$	4.75928e96	−	5.18929e96i	1.33423	−	1.45478i
$844$	1.37536e96			0.370779
$845$		−	3.75175e96i		−	0.972663i
$846$	−7.04490e94	−	8.13408e95i	−0.0175652	−	0.202809i
$847$	−1.98262e96			−0.475430
$848$			4.70332e95i			0.108478i
$849$	6.66889e95	+	6.11626e95i	0.147945	+	0.135685i
$850$	1.75022e95			0.0373481
$851$			4.10891e96i			0.843434i
$852$	2.94163e96	−	3.20742e96i	0.580873	−	0.633357i
$853$	4.09685e96			0.778273			0.389136	−	0.921180i	$-0.372773\pi$
$853$	4.09685e96			0.778273			0.389136	+	0.921180i	$0.372773\pi$
$854$			2.47880e96i			0.453035i
$855$	−8.91447e96	+	7.72079e95i	−1.56752	+	0.135763i
$856$	6.04820e96			1.02327
$857$		−	6.48094e96i		−	1.05504i	−0.849541	−	0.527522i	$-0.823121\pi$
$857$		−	6.48094e96i		−	1.05504i	0.849541	−	0.527522i	$-0.176879\pi$
$858$	4.32754e96	+	3.96893e96i	0.677892	+	0.621718i
$859$	−1.57468e96			−0.237366			−0.118683	−	0.992932i	$-0.537867\pi$
$859$	−1.57468e96			−0.237366			−0.118683	+	0.992932i	$0.537867\pi$
$860$		−	4.01921e96i		−	0.583032i
$861$	−1.00004e97	+	1.09040e97i	−1.39610	+	1.52224i
$862$	−4.79470e96			−0.644201
$863$			8.93981e96i			1.15604i	0.816023	+	0.578019i	$0.196174\pi$
$863$			8.93981e96i			1.15604i	−0.816023	+	0.578019i	$0.803826\pi$
$864$	−6.58404e96	−	5.06581e96i	−0.819481	−	0.630515i
$865$	3.13400e96			0.375464
$866$		−	6.44171e96i		−	0.742866i
$867$	1.99968e96	+	1.83397e96i	0.221988	+	0.203593i
$868$	−4.84061e96			−0.517308
$869$			5.70441e96i			0.586892i
$870$	−4.18022e96	+	4.55792e96i	−0.414061	+	0.451472i
$871$	−1.62647e97			−1.55112
$872$			1.32257e97i			1.21443i
$873$	2.74456e95	+	3.16888e96i	0.0242662	+	0.280179i
$874$	9.66291e96			0.822680
$875$		−	1.63956e97i		−	1.34419i
$876$	−1.74594e96	−	1.60126e96i	−0.137846	−	0.126423i
$877$	8.72612e96			0.663490			0.331745	−	0.943369i	$-0.392363\pi$
$877$	8.72612e96			0.663490			0.331745	+	0.943369i	$0.392363\pi$
$878$		−	1.38854e97i		−	1.01681i
$879$	4.24675e96	−	4.63046e96i	0.299519	−	0.326581i
$880$	2.84404e96			0.193200
$881$			3.81448e96i			0.249592i	0.992182	+	0.124796i	$0.0398277\pi$
$881$			3.81448e96i			0.249592i	−0.992182	+	0.124796i	$0.960172\pi$
$882$	−5.98567e96	+	5.18417e95i	−0.377268	+	0.0326750i
$883$	2.47898e97			1.50511			0.752556	−	0.658528i	$-0.228821\pi$
$883$	2.47898e97			1.50511			0.752556	+	0.658528i	$0.228821\pi$
$884$			1.40498e97i			0.821762i
$885$	−1.09743e97	−	1.00649e97i	−0.618371	−	0.567129i
$886$	−1.31235e96			−0.0712424
$887$			2.39028e97i			1.25017i	0.780556	+	0.625085i	$0.214936\pi$
$887$			2.39028e97i			1.25017i	−0.780556	+	0.625085i	$0.785064\pi$
$888$	−1.17393e97	+	1.28000e97i	−0.591582	+	0.645033i
$889$	1.97910e97			0.960970
$890$		−	1.10721e95i		−	0.00518035i
$891$	−4.45775e96	−	2.55416e97i	−0.200979	−	1.15156i
$892$	−1.18732e97			−0.515857
$893$		−	1.43899e97i		−	0.602504i
$894$	−3.87818e96	−	3.55681e96i	−0.156491	−	0.143523i
$895$	8.90163e96			0.346186
$896$			2.80943e97i			1.05306i
$897$	2.40122e97	−	2.61818e97i	0.867523	−	0.945907i
$898$	−1.40101e97			−0.487890
$899$		−	1.97633e97i		−	0.663422i
$900$	1.48837e95	+	1.71849e96i	0.00481626	+	0.0556088i
$901$	1.68647e97			0.526092
$902$		−	3.43104e97i		−	1.03183i
$903$	2.89491e97	+	2.65502e97i	0.839343	+	0.769790i
$904$	5.97878e97			1.67130
$905$		−	2.69554e97i		−	0.726512i
$906$	−3.56574e96	+	3.88792e96i	−0.0926659	+	0.101039i
$907$	−6.60749e96			−0.165575			−0.0827877	−	0.996567i	$-0.526382\pi$
$907$	−6.60749e96			−0.165575			−0.0827877	+	0.996567i	$0.526382\pi$
$908$		−	1.29957e97i		−	0.314027i
$909$	−5.28069e97	+	4.57358e96i	−1.23050	+	0.106573i
$910$	−4.35583e97			−0.978824
$911$		−	9.53247e96i		−	0.206585i	−0.994651	−	0.103293i	$-0.967062\pi$
$911$		−	9.53247e96i		−	0.206585i	0.994651	−	0.103293i	$-0.0329378\pi$
$912$	−9.97288e96	−	9.14646e96i	−0.208445	−	0.191172i
$913$	−6.07158e97			−1.22396
$914$			1.34143e97i			0.260822i
$915$	2.17669e97	−	2.37336e97i	0.408226	−	0.445110i
$916$	−1.36398e97			−0.246750
$917$			4.39435e96i			0.0766843i
$918$	−1.67880e97	+	2.18193e97i	−0.282612	+	0.367310i
$919$	6.29938e96			0.102302			0.0511512	−	0.998691i	$-0.483711\pi$
$919$	6.29938e96			0.102302			0.0511512	+	0.998691i	$0.483711\pi$
$920$			5.19356e97i			0.813705i
$921$	9.53405e97	+	8.74400e97i	1.44115	+	1.32173i
$922$	4.89164e97			0.713402
$923$			1.25146e98i			1.76101i
$924$	−5.22893e97	+	5.70138e97i	−0.709967	+	0.774114i
$925$	5.73686e96			0.0751618
$926$		−	1.06322e97i		−	0.134419i
$927$	−6.28764e96	−	7.25975e97i	−0.0767108	−	0.885707i
$928$	−1.01200e98			−1.19151
$929$			5.56128e97i			0.631912i	0.948774	+	0.315956i	$0.102325\pi$
$929$			5.56128e97i			0.631912i	−0.948774	+	0.315956i	$0.897675\pi$
$930$	−2.05675e97	−	1.88632e97i	−0.225551	−	0.206861i
$931$	−1.05892e98			−1.12079
$932$		−	8.54709e97i		−	0.873158i
$933$	1.92327e97	−	2.09705e97i	0.189647	−	0.206783i
$934$	−5.03510e95			−0.00479249
$935$		−	1.01979e98i		−	0.936975i
$936$	1.49605e98	−	1.29572e97i	1.32691	−	0.114923i
$937$	−4.54606e97			−0.389250			−0.194625	−	0.980878i	$-0.562349\pi$
$937$	−4.54606e97			−0.389250			−0.194625	+	0.980878i	$0.562349\pi$
$938$			9.50921e97i			0.786051i
$939$	2.38429e97	+	2.18671e97i	0.190281	+	0.174513i
$940$	3.16486e97			0.243857
$941$		−	2.46857e98i		−	1.83649i	−0.396015	−	0.918244i	$-0.629607\pi$
$941$		−	2.46857e98i		−	1.83649i	0.396015	−	0.918244i	$-0.370393\pi$
$942$	3.18912e97	−	3.47727e97i	0.229082	−	0.249780i
$943$	−2.07579e98			−1.43979
$944$		−	2.25198e97i		−	0.150830i
$945$	1.52434e98	+	1.17284e98i	0.985897	+	0.758557i
$946$	−9.10907e97			−0.568940
$947$		−	6.48446e97i		−	0.391133i	−0.980690	−	0.195566i	$-0.937345\pi$
$947$		−	6.48446e97i		−	0.391133i	0.980690	−	0.195566i	$-0.0626545\pi$
$948$	4.39938e97	+	4.03482e97i	0.256281	+	0.235044i
$949$	6.81227e97			0.383272
$950$		−	1.34914e97i		−	0.0733123i
$951$	6.26986e97	−	6.83636e97i	0.329079	−	0.358813i
$952$	2.00739e98			1.01768
$953$			1.90568e98i			0.933221i	0.884463	+	0.466610i	$0.154525\pi$
$953$			1.90568e98i			0.933221i	−0.884463	+	0.466610i	$0.845475\pi$
$954$	−6.36443e96	−	7.34841e97i	−0.0301067	−	0.347614i
$955$	2.61538e98			1.19515
$956$			1.36666e98i			0.603324i
$957$	−2.32777e98	−	2.13487e98i	−0.992763	−	0.910496i
$958$	1.49255e98			0.614987
$959$		−	2.38314e97i		−	0.0948715i
$960$	−6.75473e97	+	7.36504e97i	−0.259811	+	0.283285i
$961$	−1.79892e98			−0.668561
$962$		−	2.04368e98i		−	0.733897i
$963$	3.13071e98	−	2.71150e97i	1.08637	−	0.0940898i
$964$	1.79523e98			0.601973
$965$			1.85569e98i			0.601316i
$966$	−1.53073e98	−	1.40388e98i	−0.479350	−	0.439629i
$967$	−7.99314e97			−0.241904			−0.120952	−	0.992658i	$-0.538595\pi$
$967$	−7.99314e97			−0.241904			−0.120952	+	0.992658i	$0.538595\pi$
$968$		−	1.17576e98i		−	0.343901i
$969$	−3.27966e98	+	3.57598e98i	−0.927136	+	1.01091i
$970$	5.47157e97			0.149501
$971$			9.84731e97i			0.260066i	0.991510	+	0.130033i	$0.0415083\pi$
$971$			9.84731e97i			0.260066i	−0.991510	+	0.130033i	$0.958492\pi$
$972$	−2.28514e98	−	1.46281e98i	−0.583345	−	0.373423i
$973$	−2.11026e98			−0.520730
$974$			3.12053e98i			0.744359i
$975$	−3.65550e97	−	3.35258e97i	−0.0842935	−	0.0773085i
$976$	4.87025e97			0.108569
$977$			1.73034e98i			0.372916i	0.982463	+	0.186458i	$0.0597008\pi$
$977$			1.73034e98i			0.372916i	−0.982463	+	0.186458i	$0.940299\pi$
$978$	3.36437e98	−	3.66836e98i	0.701007	−	0.764345i
$979$	5.65460e96			0.0113913
$980$		−	2.32894e98i		−	0.453627i
$981$	5.92928e97	+	6.84598e98i	0.111667	+	1.28931i
$982$	−4.92693e98			−0.897217
$983$		−	2.14187e97i		−	0.0377161i	−0.999822	−	0.0188580i	$-0.993997\pi$
$983$		−	2.14187e97i		−	0.0377161i	0.999822	−	0.0188580i	$-0.00600306\pi$
$984$	−6.46647e98	−	5.93062e98i	−1.10111	−	1.00986i
$985$	−7.44379e98			−1.22574
$986$			3.35374e98i			0.534061i
$987$	−2.09065e98	+	2.27955e98i	−0.321970	+	0.351061i
$988$	1.08301e99			1.61308
$989$			5.51102e98i			0.793879i
$990$	−4.44350e98	+	3.84850e97i	−0.619104	+	0.0536204i
$991$	−1.39208e98			−0.187600			−0.0938001	−	0.995591i	$-0.529901\pi$
$991$	−1.39208e98			−0.187600			−0.0938001	+	0.995591i	$0.529901\pi$
$992$		−	4.56663e98i		−	0.595265i
$993$	3.91869e98	+	3.59396e98i	0.494100	+	0.453156i
$994$	7.31674e98			0.892416
$995$			3.83385e98i			0.452348i
$996$	−4.29453e98	+	4.68255e98i	−0.490182	+	0.534471i
$997$	9.29444e98			1.02632			0.513160	−	0.858293i	$-0.328475\pi$
$997$	9.29444e98			1.02632			0.513160	+	0.858293i	$0.328475\pi$
$998$		−	2.18329e98i		−	0.233240i
$999$	−5.50275e98	+	7.15193e98i	−0.568747	+	0.739200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.67.b.b.2.13	yes	20
3.2	odd	2	inner	3.67.b.b.2.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.67.b.b.2.8	✓	20	3.2	odd	2	inner
3.67.b.b.2.13	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+4.76234e9i q^{2} +(4.09693e15 + 3.75743e15i) q^{3} +5.11071e19 q^{4} -1.11626e23i q^{5} +(-1.78942e25 + 1.95110e25i) q^{6} +1.00296e28 q^{7} +5.94788e29i q^{8} +(2.66653e30 + 3.07879e31i) q^{9} +O(q^{10})\)	\(q+4.76234e9i q^{2} +(4.09693e15 + 3.75743e15i) q^{3} +5.11071e19 q^{4} -1.11626e23i q^{5} +(-1.78942e25 + 1.95110e25i) q^{6} +1.00296e28 q^{7} +5.94788e29i q^{8} +(2.66653e30 + 3.07879e31i) q^{9} +5.31601e32 q^{10} +2.71493e34i q^{11} +(2.09382e35 + 1.92031e35i) q^{12} -8.16964e36 q^{13} +4.77642e37i q^{14} +(4.19427e38 - 4.57324e38i) q^{15} +9.38452e38 q^{16} -3.36501e40i q^{17} +(-1.46622e41 + 1.26989e40i) q^{18} -2.59388e42 q^{19} -5.70488e42i q^{20} +(4.10904e43 + 3.76854e43i) q^{21} -1.29294e44 q^{22} +7.82235e44i q^{23} +(-2.23488e45 + 2.43681e45i) q^{24} +1.09216e45 q^{25} -3.89066e46i q^{26} +(-1.04759e47 + 1.36155e47i) q^{27} +5.12581e47 q^{28} +2.09277e48i q^{29} +(2.17793e48 + 1.99746e48i) q^{30} -9.44360e48 q^{31} +4.83568e49i q^{32} +(-1.02012e50 + 1.11229e50i) q^{33} +1.60254e50 q^{34} -1.11956e51i q^{35} +(1.36278e50 + 1.57348e51i) q^{36} +5.25278e51 q^{37} -1.23529e52i q^{38} +(-3.34705e52 - 3.06969e52i) q^{39} +6.63938e52 q^{40} +2.65367e53i q^{41} +(-1.79471e53 + 1.95687e53i) q^{42} +7.04522e53 q^{43} +1.38752e54i q^{44} +(3.43673e54 - 2.97654e53i) q^{45} -3.72527e54 q^{46} +5.54764e54i q^{47} +(3.84477e54 + 3.52617e54i) q^{48} +4.08237e55 q^{49} +5.20122e54i q^{50} +(1.26438e56 - 1.37862e56i) q^{51} -4.17526e56 q^{52} +5.01179e56i q^{53} +(-6.48418e56 - 4.98898e56i) q^{54} +3.03057e57 q^{55} +5.96546e57i q^{56} +(-1.06269e58 - 9.74634e57i) q^{57} -9.96649e57 q^{58} -2.39968e58i q^{59} +(2.14357e58 - 2.33725e58i) q^{60} +5.18967e58 q^{61} -4.49737e58i q^{62} +(2.67441e58 + 3.08789e59i) q^{63} -1.61046e59 q^{64} +9.11945e59i q^{65} +(-5.29710e59 - 4.85815e59i) q^{66} +1.99087e60 q^{67} -1.71976e60i q^{68} +(-2.93920e60 + 3.20476e60i) q^{69} +5.33173e60 q^{70} -1.53185e61i q^{71} +(-1.83123e61 + 1.58602e60i) q^{72} -8.33852e60 q^{73} +2.50155e61i q^{74} +(4.47449e60 + 4.10371e60i) q^{75} -1.32566e62 q^{76} +2.72296e62i q^{77} +(1.46189e62 - 1.59398e62i) q^{78} +2.10112e62 q^{79} -1.04756e62i q^{80} +(-9.40784e62 + 1.64194e62i) q^{81} -1.26377e63 q^{82} +2.23637e63i q^{83} +(2.10001e63 + 1.92599e63i) q^{84} -3.75623e63 q^{85} +3.35518e63i q^{86} +(-7.86345e63 + 8.57394e63i) q^{87} -1.61481e64 q^{88} -2.08278e62i q^{89} +(1.41753e63 + 1.63669e64i) q^{90} -8.19379e64 q^{91} +3.99778e64i q^{92} +(-3.86898e64 - 3.54837e64i) q^{93} -2.64197e64 q^{94} +2.89545e65i q^{95} +(-1.81698e65 + 1.98115e65i) q^{96} +1.02926e65 q^{97} +1.94416e65i q^{98} +(-8.35870e65 + 7.23944e64i) 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

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Groups

Database

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