LMFDB - Embedded newform 3.67.b.b.2.20

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			2.20
Root			$4.67878e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.67.b.b.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68436e10i q^{2} +(-3.79959e15 - 4.05786e15i) q^{3} -2.09920e20 q^{4} -9.39164e22i q^{5} +(6.83490e25 - 6.39988e25i) q^{6} -5.61847e27 q^{7} -2.29297e30i q^{8} +(-2.02937e30 + 3.08364e31i) q^{9} +O(q^{10})$	\(q+1.68436e10i q^{2} +(-3.79959e15 - 4.05786e15i) q^{3} -2.09920e20 q^{4} -9.39164e22i q^{5} +(6.83490e25 - 6.39988e25i) q^{6} -5.61847e27 q^{7} -2.29297e30i q^{8} +(-2.02937e30 + 3.08364e31i) q^{9} +1.58189e33 q^{10} +3.11598e34i q^{11} +(7.97610e35 + 8.51826e35i) q^{12} +6.10892e35 q^{13} -9.46352e37i q^{14} +(-3.81100e38 + 3.56844e38i) q^{15} +2.31325e40 q^{16} +4.49897e40i q^{17} +(-5.19397e41 - 3.41819e40i) q^{18} -1.04778e42 q^{19} +1.97149e43i q^{20} +(2.13479e43 + 2.27990e43i) q^{21} -5.24843e44 q^{22} +9.46595e44i q^{23} +(-9.30455e45 + 8.71234e45i) q^{24} +4.73223e45 q^{25} +1.02896e46i q^{26} +(1.32841e47 - 1.08931e47i) q^{27} +1.17943e48 q^{28} +8.84525e47i q^{29} +(-6.01054e48 - 6.41910e48i) q^{30} -2.69697e48 q^{31} +2.20443e50i q^{32} +(1.26442e50 - 1.18394e50i) q^{33} -7.57789e50 q^{34} +5.27667e50i q^{35} +(4.26005e50 - 6.47318e51i) q^{36} +8.18894e51 q^{37} -1.76483e52i q^{38} +(-2.32114e51 - 2.47892e51i) q^{39} -2.15347e53 q^{40} -4.96496e52i q^{41} +(-3.84017e53 + 3.59575e53i) q^{42} -5.17684e53 q^{43} -6.54106e54i q^{44} +(2.89605e54 + 1.90591e53i) q^{45} -1.59441e55 q^{46} +5.70835e54i q^{47} +(-8.78940e55 - 9.38685e55i) q^{48} -2.82011e55 q^{49} +7.97078e55i q^{50} +(1.82562e56 - 1.70942e56i) q^{51} -1.28238e56 q^{52} -7.48074e56i q^{53} +(1.83479e57 + 2.23752e57i) q^{54} +2.92642e57 q^{55} +1.28830e58i q^{56} +(3.98112e57 + 4.25173e57i) q^{57} -1.48986e58 q^{58} +1.33209e58i q^{59} +(8.00005e58 - 7.49087e58i) q^{60} +1.11747e59 q^{61} -4.54267e58i q^{62} +(1.14020e58 - 1.73254e59i) q^{63} -2.00618e60 q^{64} -5.73728e58i q^{65} +(1.99419e60 + 2.12974e60i) q^{66} -1.40334e60 q^{67} -9.44423e60i q^{68} +(3.84116e60 - 3.59667e60i) q^{69} -8.88780e60 q^{70} +1.22130e61i q^{71} +(7.07070e61 + 4.65328e60i) q^{72} -4.81444e61 q^{73} +1.37931e62i q^{74} +(-1.79805e61 - 1.92027e61i) q^{75} +2.19949e62 q^{76} -1.75070e62i q^{77} +(4.17539e61 - 3.90964e61i) q^{78} -1.69264e62 q^{79} -2.17252e63i q^{80} +(-9.46768e62 - 1.25157e62i) q^{81} +8.36277e62 q^{82} +3.17029e63i q^{83} +(-4.48135e63 - 4.78596e63i) q^{84} +4.22527e63 q^{85} -8.71966e63i q^{86} +(3.58928e63 - 3.36083e63i) q^{87} +7.14484e64 q^{88} +1.06309e64i q^{89} +(-3.21024e63 + 4.87799e64i) q^{90} -3.43228e63 q^{91} -1.98709e65i q^{92} +(1.02474e64 + 1.09439e64i) q^{93} -9.61491e64 q^{94} +9.84034e64i q^{95} +(8.94529e65 - 8.37594e65i) q^{96} -2.41843e65 q^{97} -4.75008e65i q^{98} +(-9.60857e65 - 6.32348e64i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 48\!\cdots\!16 q^{3}+ \cdots + 15\!\cdots\!00 q^{9}+O(q^{10}) $ 20 * q + 4870975596954516 * q^3 - 874472713330987494880 * q^4 - 36458623571791371420365280 * q^6 + 12757412570419684480800346888 * q^7 + 15089557305995766698320873638900 * q^9	$ 20 q + 48\!\cdots\!16 q^{3}+ \cdots + 13\!\cdots\!00 q^{99}+O(q^{100}) $ 20 * q + 4870975596954516 * q^3 - 874472713330987494880 * q^4 - 36458623571791371420365280 * q^6 + 12757412570419684480800346888 * q^7 + 15089557305995766698320873638900 * q^9 - 783798592344000703899756417518400 * q^10 + 723313252400516086588885120719010464 * q^12 + 18091739616075205076630659610294803912 * q^13 + 291841906843973945390453919652713854400 * q^15 + 35169907781372839393817803526848507036160 * q^16 - 1327598375030727473316959111629621787325120 * q^18 - 2193455295604677957336968896648577476247000 * q^19 + 8465393426583554489761097856455177936278920 * q^21 - 19209253722854761211546865955725969475475520 * q^22 - 8536939678857788536491103872952212579880680960 * q^24 - 30700488848472932976681231276090805532106633100 * q^25 + 558391355065775903739609435927472633730508278964 * q^27 + 144501040816005166289020822469679267340863318592 * q^28 - 13469561117532417280775174235598750536019791067200 * q^30 + 6175065418525787560244925992300120132476837130440 * q^31 + 76031443883614128882573745917963369573166525959360 * q^33 - 607578292754219603165333260413176675880514014447360 * q^34 - 3175274131330481643421765009589425373421119877953760 * q^36 + 27435708863590762009354808934891346302092239434849928 * q^37 + 5521526696977593923927147874084291303373365890875080 * q^39 - 164157270356735970397207190518038139497893424374707200 * q^40 - 362475530834094311762041222130355899146344066985844160 * q^42 + 2995923276457113198574378450730231874677434142901437032 * q^43 + 2893961767142107219663835709681578507068881328379222400 * q^45 - 9354105762324374445425328051923657080564209708616152960 * q^46 + 44083933305287886033485048811587957889306840899931818496 * q^48 + 35901948198185324872729610934124248147969595380066179580 * q^49 + 244898096463243383440025305755038369424109352434412094720 * q^51 - 707065170108353883018319930521496060001554914206203205312 * q^52 - 386962012382976993771518038850875450617071434969909598880 * q^54 + 1313751320608480207642793301222628514163843327983665564800 * q^55 + 14469858017237851043428899294433298407417456132214681222568 * q^57 - 100361163480954821917122043432794223233970822326053950441920 * q^58 + 188095594234899922680776576921513155518384075353356847385600 * q^60 + 36618251899234461407858901457296968011564547062158638752840 * q^61 + 1345036046130625400347897603264169586395820510566342530416072 * q^63 - 4235878925879978009146455436735085155393347326504147849175040 * q^64 + 8309681532541455738248790801869091701653966958238676467844800 * q^66 - 6285867272675020649645690828535183608121600074432515838268632 * q^67 + 26395268384310228436148510386607667671115625880708467370286720 * q^69 - 53673269104481250134670425876769459429788829882429608923689600 * q^70 + 135607917285688125946137613885497485690645144416066370695173120 * q^72 - 234584045940242428610177340241689807173326553683343804321823128 * q^73 + 123839979253809259811223462461211616240588739801286415169843700 * q^75 - 88416171262693699731320177563519953392160098165342187898838720 * q^76 + 42333034554100439516880814575759716324771014654582144994836800 * q^78 - 180033150591234061548131792670437122720422789571688775376700600 * q^79 - 2669759984009083569841876166867012798635236563858567744127147180 * q^81 + 9780548955253740491517774427483475844287869484539284101189512320 * q^82 - 29550683862870558945501681808473602755499090201740971929153891520 * q^84 + 15725476767553808561610465539289169056529282358913795578981260800 * q^85 - 20361537149674837364457194316410702650457831770981879709222020800 * q^87 + 43127341602231234631198337877354797375008485566513397535855918080 * q^88 - 68986845993042571618317468832763287342807845905185213796199009600 * q^90 - 166695697853283961323776703924127811908080973516544145788509117360 * q^91 + 50074015382338903474492727100775024610496294621525101240240943432 * q^93 - 243292275786183398644891798798613800120302016678942850492866824960 * q^94 + 1707340756716414995397633331453898170371668874444383803046536028160 * q^96 - 2044564925167962718092629881048800142635399871213696847289077976152 * q^97 + 1311784025950014883691036763145966005164166837426590048709685526400 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.68436e10i			1.96085i	0.196885	+	0.980427i	$0.436917\pi$
$2$			1.68436e10i			1.96085i	−0.196885	+	0.980427i	$0.563083\pi$
$3$	−3.79959e15	−	4.05786e15i	−0.683495	−	0.729955i
$3$	−3.79959e15	−	4.05786e15i	−0.683495	−	0.729955i
$4$	−2.09920e20			−2.84495
$5$		−	9.39164e22i		−	0.806736i	−0.915038	−	0.403368i	$-0.867839\pi$
$5$		−	9.39164e22i		−	0.806736i	0.915038	−	0.403368i	$-0.132161\pi$
$6$	6.83490e25	−	6.39988e25i	1.43133	−	1.34023i
$7$	−5.61847e27			−0.726746			−0.363373	−	0.931644i	$-0.618375\pi$
$7$	−5.61847e27			−0.726746			−0.363373	+	0.931644i	$0.618375\pi$
$8$		−	2.29297e30i		−	3.61767i
$9$	−2.02937e30	+	3.08364e31i	−0.0656687	+	0.997841i
$10$	1.58189e33			1.58189
$11$			3.11598e34i			1.34164i	0.741620	+	0.670820i	$0.234058\pi$
$11$			3.11598e34i			1.34164i	−0.741620	+	0.670820i	$0.765942\pi$
$12$	7.97610e35	+	8.51826e35i	1.94451	+	2.07668i
$13$	6.10892e35			0.106129			0.0530645	−	0.998591i	$-0.483101\pi$
$13$	6.10892e35			0.106129			0.0530645	+	0.998591i	$0.483101\pi$
$14$		−	9.46352e37i		−	1.42504i
$15$	−3.81100e38	+	3.56844e38i	−0.588881	+	0.551400i
$16$	2.31325e40			4.24877
$17$			4.49897e40i			1.11763i	0.829292	+	0.558816i	$0.188744\pi$
$17$			4.49897e40i			1.11763i	−0.829292	+	0.558816i	$0.811256\pi$
$18$	−5.19397e41	−	3.41819e40i	−1.95662	−	0.128767i
$19$	−1.04778e42			−0.662826			−0.331413	−	0.943486i	$-0.607525\pi$
$19$	−1.04778e42			−0.662826			−0.331413	+	0.943486i	$0.607525\pi$
$20$			1.97149e43i			2.29512i
$21$	2.13479e43	+	2.27990e43i	0.496727	+	0.530492i
$22$	−5.24843e44			−2.63076
$23$			9.46595e44i			1.09432i	0.837027	+	0.547162i	$0.184292\pi$
$23$			9.46595e44i			1.09432i	−0.837027	+	0.547162i	$0.815708\pi$
$24$	−9.30455e45	+	8.71234e45i	−2.64073	+	2.47266i
$25$	4.73223e45			0.349177
$26$			1.02896e46i			0.208103i
$27$	1.32841e47	−	1.08931e47i	0.773264	−	0.634085i
$28$	1.17943e48			2.06755
$29$			8.84525e47i			0.487053i	0.969894	+	0.243526i	$0.0783043\pi$
$29$			8.84525e47i			0.487053i	−0.969894	+	0.243526i	$0.921696\pi$
$30$	−6.01054e48	−	6.41910e48i	−1.08121	−	1.15471i
$31$	−2.69697e48			−0.164415			−0.0822074	−	0.996615i	$-0.526197\pi$
$31$	−2.69697e48			−0.164415			−0.0822074	+	0.996615i	$0.526197\pi$
$32$			2.20443e50i			4.71354i
$33$	1.26442e50	−	1.18394e50i	0.979337	−	0.917004i
$34$	−7.57789e50			−2.19151
$35$			5.27667e50i			0.586292i
$36$	4.26005e50	−	6.47318e51i	0.186824	−	2.83880i
$37$	8.18894e51			1.45402			0.727011	−	0.686626i	$-0.240909\pi$
$37$	8.18894e51			1.45402			0.727011	+	0.686626i	$0.240909\pi$
$38$		−	1.76483e52i		−	1.29970i
$39$	−2.32114e51	−	2.47892e51i	−0.0725387	−	0.0774694i
$40$	−2.15347e53			−2.91850
$41$		−	4.96496e52i		−	0.297885i	−0.988846	−	0.148942i	$-0.952413\pi$
$41$		−	4.96496e52i		−	0.297885i	0.988846	−	0.148942i	$-0.0475869\pi$
$42$	−3.84017e53	+	3.59575e53i	−1.04022	+	0.974009i
$43$	−5.17684e53			−0.645068			−0.322534	−	0.946558i	$-0.604535\pi$
$43$	−5.17684e53			−0.645068			−0.322534	+	0.946558i	$0.604535\pi$
$44$		−	6.54106e54i		−	3.81689i
$45$	2.89605e54	+	1.90591e53i	0.804995	+	0.0529773i
$46$	−1.59441e55			−2.14581
$47$			5.70835e54i			0.377817i	0.981995	+	0.188908i	$0.0604949\pi$
$47$			5.70835e54i			0.377817i	−0.981995	+	0.188908i	$0.939505\pi$
$48$	−8.78940e55	−	9.38685e55i	−2.90401	−	3.10141i
$49$	−2.82011e55			−0.471840
$50$			7.97078e55i			0.684685i
$51$	1.82562e56	−	1.70942e56i	0.815821	−	0.763896i
$52$	−1.28238e56			−0.301931
$53$		−	7.48074e56i		−	0.939378i	−0.882832	−	0.469689i	$-0.844366\pi$
$53$		−	7.48074e56i		−	0.939378i	0.882832	−	0.469689i	$-0.155634\pi$
$54$	1.83479e57	+	2.23752e57i	1.24335	+	1.51626i
$55$	2.92642e57			1.08235
$56$			1.28830e58i			2.62912i
$57$	3.98112e57	+	4.25173e57i	0.453038	+	0.483833i
$58$	−1.48986e58			−0.955039
$59$			1.33209e58i			0.485756i	0.970057	+	0.242878i	$0.0780914\pi$
$59$			1.33209e58i			0.485756i	−0.970057	+	0.242878i	$0.921909\pi$
$60$	8.00005e58	−	7.49087e58i	1.67533	−	1.56870i
$61$	1.11747e59			1.35629			0.678146	−	0.734927i	$-0.262784\pi$
$61$	1.11747e59			1.35629			0.678146	+	0.734927i	$0.262784\pi$
$62$		−	4.54267e58i		−	0.322393i
$63$	1.14020e58	−	1.73254e59i	0.0477245	−	0.725177i
$64$	−2.00618e60			−4.99380
$65$		−	5.73728e58i		−	0.0856181i
$66$	1.99419e60	+	2.12974e60i	1.79811	+	1.92034i
$67$	−1.40334e60			−0.770363			−0.385182	−	0.922841i	$-0.625861\pi$
$67$	−1.40334e60			−0.770363			−0.385182	+	0.922841i	$0.625861\pi$
$68$		−	9.44423e60i		−	3.17960i
$69$	3.84116e60	−	3.59667e60i	0.798807	−	0.747965i
$70$	−8.88780e60			−1.14963
$71$			1.22130e61i			0.989230i	0.869112	+	0.494615i	$0.164691\pi$
$71$			1.22130e61i			0.989230i	−0.869112	+	0.494615i	$0.835309\pi$
$72$	7.07070e61	+	4.65328e60i	3.60986	+	0.237568i
$73$	−4.81444e61			−1.55916			−0.779581	−	0.626302i	$-0.784568\pi$
$73$	−4.81444e61			−1.55916			−0.779581	+	0.626302i	$0.784568\pi$
$74$			1.37931e62i			2.85112i
$75$	−1.79805e61	−	1.92027e61i	−0.238661	−	0.254883i
$76$	2.19949e62			1.88570
$77$		−	1.75070e62i		−	0.975031i
$78$	4.17539e61	−	3.90964e61i	0.151906	−	0.142238i
$79$	−1.69264e62			−0.404455			−0.202227	−	0.979339i	$-0.564818\pi$
$79$	−1.69264e62			−0.404455			−0.202227	+	0.979339i	$0.564818\pi$
$80$		−	2.17252e63i		−	3.42763i
$81$	−9.46768e62	−	1.25157e62i	−0.991375	−	0.131054i
$82$	8.36277e62			0.584108
$83$			3.17029e63i			1.48430i	0.670233	+	0.742151i	$0.266194\pi$
$83$			3.17029e63i			1.48430i	−0.670233	+	0.742151i	$0.733806\pi$
$84$	−4.48135e63	−	4.78596e63i	−1.41316	−	1.50922i
$85$	4.22527e63			0.901634
$86$		−	8.71966e63i		−	1.26488i
$87$	3.58928e63	−	3.36083e63i	0.355527	−	0.332898i
$88$	7.14484e64			4.85361
$89$			1.06309e64i			0.497394i	0.968581	+	0.248697i	$0.0800023\pi$
$89$			1.06309e64i			0.497394i	−0.968581	+	0.248697i	$0.919998\pi$
$90$	−3.21024e63	+	4.87799e64i	−0.103881	+	1.57848i
$91$	−3.43228e63			−0.0771288
$92$		−	1.98709e65i		−	3.11329i
$93$	1.02474e64	+	1.09439e64i	0.112377	+	0.120015i
$94$	−9.61491e64			−0.740843
$95$			9.84034e64i			0.534726i
$96$	8.94529e65	−	8.37594e65i	3.44067	−	3.22168i
$97$	−2.41843e65			−0.660794			−0.330397	−	0.943842i	$-0.607183\pi$
$97$	−2.41843e65			−0.660794			−0.330397	+	0.943842i	$0.607183\pi$
$98$		−	4.75008e65i		−	0.925210i
$99$	−9.60857e65	−	6.32348e64i	−1.33874	−	0.0881038i
$100$	−9.93389e65			−0.993389
$101$		−	1.89207e64i		−	0.0136248i	−0.999977	−	0.00681241i	$-0.997832\pi$
$101$		−	1.89207e64i		−	0.0136248i	0.999977	−	0.00681241i	$-0.00216848\pi$
$102$	2.87929e66	+	3.07500e66i	1.49789	+	1.59971i
$103$	3.32280e65			0.125278			0.0626392	−	0.998036i	$-0.480048\pi$
$103$	3.32280e65			0.125278			0.0626392	+	0.998036i	$0.480048\pi$
$104$		−	1.40076e66i		−	0.383939i
$105$	2.14120e66	−	2.00492e66i	0.427967	−	0.400728i
$106$	1.26003e67			1.84198
$107$		−	3.64325e66i		−	0.390683i	−0.980735	−	0.195342i	$-0.937418\pi$
$107$		−	3.64325e66i		−	0.390683i	0.980735	−	0.195342i	$-0.0625815\pi$
$108$	−2.78859e67	+	2.28668e67i	−2.19989	+	1.80394i
$109$	2.24540e67			1.30683			0.653415	−	0.757000i	$-0.273336\pi$
$109$	2.24540e67			1.30683			0.653415	+	0.757000i	$0.273336\pi$
$110$			4.92914e67i			2.12233i
$111$	−3.11146e67	−	3.32296e67i	−0.993817	−	1.06137i
$112$	−1.29969e68			−3.08777
$113$		−	1.53806e67i		−	0.272511i	−0.990674	−	0.136256i	$-0.956493\pi$
$113$		−	1.53806e67i		−	0.272511i	0.990674	−	0.136256i	$-0.0435069\pi$
$114$	−7.16145e67	+	6.70564e67i	−0.948726	+	0.888342i
$115$	8.89009e67			0.882830
$116$		−	1.85679e68i		−	1.38564i
$117$	−1.23973e66	+	1.88378e67i	−0.00696936	+	0.105900i
$118$	−2.24372e68			−0.952496
$119$		−	2.52773e68i		−	0.812234i
$120$	8.18232e68	+	8.73851e68i	1.99478	+	2.13038i
$121$	−4.31525e68			−0.799997
$122$			1.88223e69i			2.65949i
$123$	−2.01471e68	+	1.88648e68i	−0.217442	+	0.203603i
$124$	5.66148e68			0.467751
$125$		−	1.71724e69i		−	1.08843i
$126$	2.91821e69	+	1.92050e68i	1.42197	+	0.0935807i
$127$	−3.67005e68			−0.137768			−0.0688841	−	0.997625i	$-0.521944\pi$
$127$	−3.67005e68			−0.137768			−0.0688841	+	0.997625i	$0.521944\pi$
$128$		−	1.75255e70i		−	5.07856i
$129$	1.96699e69	+	2.10069e69i	0.440901	+	0.470871i
$130$	9.66365e68			0.167884
$131$		−	7.95631e69i		−	1.07339i	−0.843775	−	0.536697i	$-0.819672\pi$
$131$		−	7.95631e69i		−	1.07339i	0.843775	−	0.536697i	$-0.180328\pi$
$132$	−2.65427e70	+	2.48534e70i	−2.78616	+	2.60883i
$133$	5.88690e69			0.481706
$134$		−	2.36374e70i		−	1.51057i
$135$	−1.02304e70	−	1.24759e70i	−0.511539	−	0.623820i
$136$	1.03160e71			4.04322
$137$			3.60177e70i			1.10850i	0.832349	+	0.554252i	$0.186996\pi$
$137$			3.60177e70i			1.10850i	−0.832349	+	0.554252i	$0.813004\pi$
$138$	6.05810e70	+	6.46989e70i	1.46665	+	1.56634i
$139$	−7.36019e70			−1.40411			−0.702054	−	0.712123i	$-0.747734\pi$
$139$	−7.36019e70			−1.40411			−0.702054	+	0.712123i	$0.747734\pi$
$140$		−	1.10768e71i		−	1.66797i
$141$	2.31637e70	−	2.16894e70i	0.275789	−	0.258236i
$142$	−2.05711e71			−1.93974
$143$			1.90353e70i			0.142387i
$144$	−4.69444e70	+	7.13324e71i	−0.279011	+	4.23960i
$145$	8.30714e70			0.392923
$146$		−	8.10924e71i		−	3.05729i
$147$	1.07153e71	+	1.14436e71i	0.322501	+	0.344422i
$148$	−1.71902e72			−4.13661
$149$		−	2.53981e71i		−	0.489389i	−0.969600	−	0.244695i	$-0.921312\pi$
$149$		−	2.53981e71i		−	0.489389i	0.969600	−	0.244695i	$-0.0786877\pi$
$150$	3.23443e71	−	3.02857e71i	0.499789	−	0.467979i
$151$	1.14348e72			1.41902			0.709509	−	0.704696i	$-0.248917\pi$
$151$	1.14348e72			1.41902			0.709509	+	0.704696i	$0.248917\pi$
$152$			2.40252e72i			2.39788i
$153$	−1.38732e72	−	9.13008e70i	−1.11522	−	0.0733935i
$154$	2.94881e72			1.91189
$155$			2.53290e71i			0.132639i
$156$	4.87254e71	+	5.20374e71i	0.206368	+	0.220396i
$157$	−3.52421e72			−1.20885			−0.604425	−	0.796662i	$-0.706597\pi$
$157$	−3.52421e72			−1.20885			−0.604425	+	0.796662i	$0.706597\pi$
$158$		−	2.85101e72i		−	0.793077i
$159$	−3.03558e72	+	2.84237e72i	−0.685704	+	0.642061i
$160$	2.07032e73			3.80258
$161$		−	5.31842e72i		−	0.795295i
$162$	2.10810e72	−	1.59470e73i	0.256978	−	1.94394i
$163$	1.66617e72			0.165779			0.0828894	−	0.996559i	$-0.473585\pi$
$163$	1.66617e72			0.165779			0.0828894	+	0.996559i	$0.473585\pi$
$164$			1.04224e73i			0.847465i
$165$	−1.11192e73	−	1.18750e73i	−0.739780	−	0.790066i
$166$	−5.33991e73			−2.91050
$167$			8.61108e72i			0.384959i	0.981301	+	0.192479i	$0.0616529\pi$
$167$			8.61108e72i			0.384959i	−0.981301	+	0.192479i	$0.938347\pi$
$168$	5.22773e73	−	4.89500e73i	1.91914	−	1.79699i
$169$	−3.27598e73			−0.988737
$170$			7.11688e73i			1.76797i
$171$	2.12633e72	−	3.23097e73i	0.0435270	−	0.661395i
$172$	1.08672e74			1.83518
$173$		−	1.42973e74i		−	1.99404i	−0.0771601	−	0.997019i	$-0.524585\pi$
$173$		−	1.42973e74i		−	1.99404i	0.0771601	−	0.997019i	$-0.475415\pi$
$174$	5.66085e73	+	6.04564e73i	0.652765	+	0.697136i
$175$	−2.65879e73			−0.253763
$176$			7.20804e74i			5.70032i
$177$	5.40545e73	−	5.06141e73i	0.354580	−	0.332012i
$178$	−1.79063e74			−0.975317
$179$		−	1.57904e74i		−	0.714898i	−0.933933	−	0.357449i	$-0.883647\pi$
$179$		−	1.57904e74i		−	0.714898i	0.933933	−	0.357449i	$-0.116353\pi$
$180$	−6.07938e74	−	4.00089e73i	−2.29017	−	0.150718i
$181$	−4.85598e74			−1.52365			−0.761823	−	0.647785i	$-0.775695\pi$
$181$	−4.85598e74			−1.52365			−0.761823	+	0.647785i	$0.775695\pi$
$182$		−	5.78119e73i		−	0.151238i
$183$	−4.24595e74	−	4.53456e74i	−0.927019	−	0.990032i
$184$	2.17051e75			3.95890
$185$		−	7.69076e74i		−	1.17301i
$186$	−1.84336e74	+	1.72603e74i	−0.235332	+	0.220354i
$187$	−1.40187e75			−1.49946
$188$		−	1.19830e75i		−	1.07487i
$189$	−7.46362e74	+	6.12025e74i	−0.561966	+	0.460818i
$190$	−1.65747e75			−1.04852
$191$		−	4.26222e74i		−	0.226743i	−0.993553	−	0.113372i	$-0.963835\pi$
$191$		−	4.26222e74i		−	0.226743i	0.993553	−	0.113372i	$-0.0361651\pi$
$192$	7.62267e75	+	8.14081e75i	3.41324	+	3.64525i
$193$	2.06591e75			0.779330			0.389665	−	0.920957i	$-0.372591\pi$
$193$	2.06591e75			0.779330			0.389665	+	0.920957i	$0.372591\pi$
$194$		−	4.07350e75i		−	1.29572i
$195$	−2.32811e74	+	2.17993e74i	−0.0624974	+	0.0585195i
$196$	5.91997e75			1.34236
$197$		−	1.42448e75i		−	0.273068i	−0.990635	−	0.136534i	$-0.956404\pi$
$197$		−	1.42448e75i		−	0.273068i	0.990635	−	0.136534i	$-0.0435964\pi$
$198$	1.06510e75	−	1.61843e76i	0.172759	−	2.62508i
$199$	−1.03236e76			−1.41800			−0.709002	−	0.705206i	$-0.750854\pi$
$199$	−1.03236e76			−1.41800			−0.709002	+	0.705206i	$0.750854\pi$
$200$		−	1.08509e76i		−	1.26321i
$201$	5.33213e75	+	5.69458e75i	0.526540	+	0.562331i
$202$	3.18692e74			0.0267163
$203$		−	4.96968e75i		−	0.353964i
$204$	−3.83234e76	+	3.58842e76i	−2.32097	+	2.17324i
$205$	−4.66291e75			−0.240314
$206$			5.59680e75i			0.245652i
$207$	−2.91896e76	−	1.92099e75i	−1.09196	−	0.0718629i
$208$	1.41315e76			0.450917
$209$		−	3.26485e76i		−	0.889274i
$210$	3.37700e76	+	3.60655e76i	0.785768	+	0.839180i
$211$	3.19056e76			0.634667			0.317333	−	0.948314i	$-0.397213\pi$
$211$	3.19056e76			0.634667			0.317333	+	0.948314i	$0.397213\pi$
$212$			1.57036e77i			2.67248i
$213$	4.95588e76	−	4.64045e76i	0.722094	−	0.676134i
$214$	6.13655e76			0.766072
$215$			4.86190e76i			0.520400i
$216$	−2.49775e77	−	3.04600e77i	−2.29391	−	2.79741i
$217$	1.51529e76			0.119488
$218$			3.78206e77i			2.56250i
$219$	1.82929e77	+	1.95363e77i	1.06568	+	1.13812i
$220$	−6.14313e77			−3.07922
$221$			2.74839e76i			0.118613i
$222$	5.59706e77	−	5.24082e77i	2.08119	−	1.94873i
$223$	1.83661e77			0.588784			0.294392	−	0.955685i	$-0.404883\pi$
$223$	1.83661e77			0.588784			0.294392	+	0.955685i	$0.404883\pi$
$224$		−	1.23855e78i		−	3.42555i
$225$	−9.60345e75	+	1.45925e77i	−0.0229300	+	0.348423i
$226$	2.59065e77			0.534355
$227$			1.81417e77i			0.323463i	0.986835	+	0.161732i	$0.0517079\pi$
$227$			1.81417e77i			0.323463i	−0.986835	+	0.161732i	$0.948292\pi$
$228$	−8.35716e77	−	8.92523e77i	−1.28887	−	1.37648i
$229$	7.92613e77			1.05801			0.529006	−	0.848618i	$-0.322565\pi$
$229$	7.92613e77			1.05801			0.529006	+	0.848618i	$0.322565\pi$
$230$			1.49741e78i			1.73110i
$231$	−7.10412e77	+	6.65196e77i	−0.711729	+	0.666429i
$232$	2.02819e78			1.76199
$233$			1.30864e78i			0.986452i	0.869901	+	0.493226i	$0.164182\pi$
$233$			1.30864e78i			0.986452i	−0.869901	+	0.493226i	$0.835818\pi$
$234$	−3.17296e77	−	2.08815e76i	−0.207654	−	0.0136659i
$235$	5.36108e77			0.304798
$236$		−	2.79633e78i		−	1.38195i
$237$	6.43133e77	+	6.86850e77i	0.276443	+	0.295234i
$238$	4.25761e78			1.59267
$239$		−	1.98541e78i		−	0.646726i	−0.946275	−	0.323363i	$-0.895187\pi$
$239$		−	1.98541e78i		−	0.646726i	0.946275	−	0.323363i	$-0.104813\pi$
$240$	−8.81580e78	+	8.25469e78i	−2.50202	+	2.34277i
$241$	−6.74839e77			−0.166970			−0.0834848	−	0.996509i	$-0.526605\pi$
$241$	−6.74839e77			−0.166970			−0.0834848	+	0.996509i	$0.526605\pi$
$242$		−	7.26843e78i		−	1.56868i
$243$	3.08946e78	+	4.31740e78i	0.581937	+	0.813234i
$244$	−2.34580e79			−3.85858
$245$			2.64854e78i			0.380651i
$246$	−3.17751e78	−	3.39350e78i	−0.399235	−	0.426373i
$247$	−6.40078e77			−0.0703451
$248$			6.18407e78i			0.594798i
$249$	1.28646e79	−	1.20458e79i	1.08347	−	1.01451i
$250$	2.89245e79			2.13425
$251$		−	1.14604e79i		−	0.741253i	−0.928782	−	0.370627i	$-0.879143\pi$
$251$		−	1.14604e79i		−	0.741253i	0.928782	−	0.370627i	$-0.120857\pi$
$252$	−2.39350e78	+	3.63694e79i	−0.135774	+	2.06309i
$253$	−2.94957e79			−1.46819
$254$		−	6.18169e78i		−	0.270143i
$255$	−1.60543e79	−	1.71456e79i	−0.616262	−	0.658152i
$256$	1.47162e80			4.96451
$257$			1.85196e79i			0.549336i	0.961539	+	0.274668i	$0.0885679\pi$
$257$			1.85196e79i			0.549336i	−0.961539	+	0.274668i	$0.911432\pi$
$258$	−3.53832e79	+	3.31311e79i	−0.923308	+	0.864542i
$259$	−4.60093e79			−1.05670
$260$			1.20437e79i			0.243579i
$261$	−2.72756e79	−	1.79503e78i	−0.486002	−	0.0319842i
$262$	1.34013e80			2.10477
$263$		−	1.22268e80i		−	1.69345i	−0.532030	−	0.846726i	$-0.678571\pi$
$263$		−	1.22268e80i		−	1.69345i	0.532030	−	0.846726i	$-0.321429\pi$
$264$	−2.71475e80	−	2.89928e80i	−3.31742	−	3.54291i
$265$	−7.02564e79			−0.757830
$266$			9.91565e79i			0.944555i
$267$	4.31388e79	−	4.03931e79i	0.363075	−	0.339966i
$268$	2.94590e80			2.19164
$269$		−	4.22979e79i		−	0.278287i	−0.990272	−	0.139144i	$-0.955565\pi$
$269$		−	4.22979e79i		−	0.278287i	0.990272	−	0.139144i	$-0.0444350\pi$
$270$	2.10140e80	−	1.72317e80i	1.22322	−	1.00305i
$271$	−9.75910e79			−0.502832			−0.251416	−	0.967879i	$-0.580896\pi$
$271$	−9.75910e79			−0.502832			−0.251416	+	0.967879i	$0.580896\pi$
$272$			1.04072e81i			4.74856i
$273$	1.30413e79	+	1.39277e79i	0.0527172	+	0.0563006i
$274$	−6.06667e80			−2.17361
$275$			1.47455e80i			0.468470i
$276$	−8.06335e80	+	7.55014e80i	−2.27256	+	2.12792i
$277$	6.57725e80			1.64517			0.822587	−	0.568639i	$-0.192530\pi$
$277$	6.57725e80			1.64517			0.822587	+	0.568639i	$0.192530\pi$
$278$		−	1.23972e81i		−	2.75325i
$279$	5.47316e78	−	8.31651e79i	0.0107969	−	0.164060i
$280$	1.20992e81			2.12101
$281$			1.04790e81i			1.63309i	0.577279	+	0.816547i	$0.304114\pi$
$281$			1.04790e81i			1.63309i	−0.577279	+	0.816547i	$0.695886\pi$
$282$	3.65327e80	+	3.90160e80i	0.506363	+	0.540782i
$283$	−8.32934e80			−1.02721			−0.513604	−	0.858028i	$-0.671690\pi$
$283$	−8.32934e80			−1.02721			−0.513604	+	0.858028i	$0.671690\pi$
$284$		−	2.56376e81i		−	2.81431i
$285$	3.99308e80	−	3.73893e80i	0.390326	−	0.365482i
$286$	−3.20623e80			−0.279200
$287$			2.78954e80i			0.216486i
$288$	−6.79769e81	−	4.47361e80i	−4.70337	−	0.309532i
$289$	−4.03649e80			−0.249101
$290$			1.39922e81i			0.770465i
$291$	9.18904e80	+	9.81365e80i	0.451649	+	0.482350i
$292$	1.01065e82			4.43573
$293$			1.43612e81i			0.563066i	0.959552	+	0.281533i	$0.0908428\pi$
$293$			1.43612e81i			0.563066i	−0.959552	+	0.281533i	$0.909157\pi$
$294$	−1.92752e81	+	1.80483e81i	−0.675361	+	0.632376i
$295$	1.25105e81			0.391877
$296$		−	1.87770e82i		−	5.26017i
$297$	3.39427e81	+	4.13930e81i	0.850713	+	1.03744i
$298$	4.27795e81			0.959620
$299$			5.78268e80i			0.116139i
$300$	3.77447e81	+	4.03104e81i	0.678977	+	0.725129i
$301$	2.90859e81			0.468801
$302$			1.92603e82i			2.78249i
$303$	−7.67775e79	+	7.18908e79i	−0.00994551	+	0.00931250i
$304$	−2.42377e82			−2.81619
$305$		−	1.04949e82i		−	1.09417i
$306$	1.53783e81	−	2.33675e82i	0.143914	−	2.18678i
$307$	−9.94907e81			−0.836019			−0.418009	−	0.908443i	$-0.637272\pi$
$307$	−9.94907e81			−0.836019			−0.418009	+	0.908443i	$0.637272\pi$
$308$			3.67507e82i			2.77391i
$309$	−1.26253e81	−	1.34835e81i	−0.0856272	−	0.0914476i
$310$	−4.26632e81			−0.260086
$311$			3.33489e81i			0.182805i	0.995814	+	0.0914026i	$0.0291350\pi$
$311$			3.33489e81i			0.182805i	−0.995814	+	0.0914026i	$0.970865\pi$
$312$	−5.68408e81	+	5.32230e81i	−0.280258	+	0.262421i
$313$	3.11280e80			0.0138098			0.00690492	−	0.999976i	$-0.497802\pi$
$313$	3.11280e80			0.0138098			0.00690492	+	0.999976i	$0.497802\pi$
$314$		−	5.93603e82i		−	2.37038i
$315$	−1.62714e82	−	1.07083e81i	−0.585027	−	0.0385011i
$316$	3.55318e82			1.15065
$317$			3.40719e82i			0.994125i	0.867715	+	0.497062i	$0.165588\pi$
$317$			3.40719e82i			0.994125i	−0.867715	+	0.497062i	$0.834412\pi$
$318$	−4.78758e82	−	5.11301e82i	−1.25899	−	1.34456i
$319$	−2.75616e82			−0.653450
$320$			1.88413e83i			4.02868i
$321$	−1.47838e82	+	1.38429e82i	−0.285181	+	0.267030i
$322$	8.95813e82			1.55946
$323$		−	4.71391e82i		−	0.740796i
$324$	1.98745e83	+	2.62730e82i	2.82041	+	0.372841i
$325$	2.89088e81			0.0370578
$326$			2.80643e82i			0.325068i
$327$	−8.53160e82	−	9.11153e82i	−0.893212	−	0.953927i
$328$	−1.13845e83			−1.07765
$329$		−	3.20722e82i		−	0.274577i
$330$	2.00018e83	−	1.87287e83i	1.54920	−	1.45060i
$331$	−7.45530e82			−0.522566			−0.261283	−	0.965262i	$-0.584146\pi$
$331$	−7.45530e82			−0.522566			−0.261283	+	0.965262i	$0.584146\pi$
$332$		−	6.65507e83i		−	4.22276i
$333$	−1.66184e82	+	2.52518e83i	−0.0954838	+	1.45088i
$334$	−1.45042e83			−0.754848
$335$			1.31797e83i			0.621480i
$336$	4.93830e83	+	5.27397e83i	2.11048	+	2.25394i
$337$	−4.71276e83			−1.82595			−0.912974	−	0.408018i	$-0.866220\pi$
$337$	−4.71276e83			−1.82595			−0.912974	+	0.408018i	$0.866220\pi$
$338$		−	5.51794e83i		−	1.93877i
$339$	−6.24124e82	+	5.84400e82i	−0.198921	+	0.186260i
$340$	−8.86969e83			−2.56510
$341$		−	8.40371e82i		−	0.220585i
$342$	5.44212e83	+	3.58150e82i	1.29690	+	0.0853500i
$343$	4.94253e83			1.06965
$344$			1.18703e84i			2.33364i
$345$	−3.37787e83	−	3.60748e83i	−0.603410	−	0.644426i
$346$	2.40818e84			3.91001
$347$			9.31858e83i			1.37555i	0.725923	+	0.687776i	$0.241413\pi$
$347$			9.31858e83i			1.37555i	−0.725923	+	0.687776i	$0.758587\pi$
$348$	−7.53462e83	+	7.05506e83i	−1.01145	+	0.947077i
$349$	5.63203e83			0.687743			0.343871	−	0.939017i	$-0.388262\pi$
$349$	5.63203e83			0.687743			0.343871	+	0.939017i	$0.388262\pi$
$350$		−	4.47836e83i		−	0.497592i
$351$	8.11515e82	−	6.65451e82i	0.0820657	−	0.0672948i
$352$	−6.86896e84			−6.32388
$353$		−	2.07223e83i		−	0.173729i	−0.996220	−	0.0868644i	$-0.972315\pi$
$353$		−	2.07223e83i		−	0.173729i	0.996220	−	0.0868644i	$-0.0276847\pi$
$354$	8.52523e83	+	9.10472e83i	0.651026	+	0.695279i
$355$	1.14700e84			0.798048
$356$		−	2.23164e84i		−	1.41506i
$357$	−1.02572e84	+	9.60435e83i	−0.592895	+	0.555158i
$358$	2.65968e84			1.40181
$359$			3.30238e84i			1.58749i	0.608254	+	0.793743i	$0.291870\pi$
$359$			3.30238e84i			1.58749i	−0.608254	+	0.793743i	$0.708130\pi$
$360$	4.37020e83	−	6.64055e84i	0.191654	−	2.91220i
$361$	−1.40100e84			−0.560661
$362$		−	8.17922e84i		−	2.98765i
$363$	1.63962e84	+	1.75107e84i	0.546794	+	0.583962i
$364$	7.20504e83			0.219427
$365$			4.52155e84i			1.25783i
$366$	7.63783e84	−	7.15170e84i	1.94131	−	1.81775i
$367$	−7.30424e84			−1.69666			−0.848330	−	0.529468i	$-0.822392\pi$
$367$	−7.30424e84			−1.69666			−0.848330	+	0.529468i	$0.822392\pi$
$368$			2.18971e85i			4.64953i
$369$	1.53102e84	+	1.00757e83i	0.297242	+	0.0195617i
$370$	1.29540e85			2.30010
$371$			4.20303e84i			0.682689i
$372$	−2.15113e84	−	2.29735e84i	−0.319705	−	0.341437i
$373$	−2.17116e84			−0.295326			−0.147663	−	0.989038i	$-0.547175\pi$
$373$	−2.17116e84			−0.295326			−0.147663	+	0.989038i	$0.547175\pi$
$374$		−	2.36125e85i		−	2.94022i
$375$	−6.96832e84	+	6.52481e84i	−0.794505	+	0.743936i
$376$	1.30891e85			1.36681
$377$			5.40349e83i			0.0516904i
$378$	−1.03087e85	−	1.25714e85i	−0.903597	−	1.10193i
$379$	4.66866e83			0.0375058			0.0187529	−	0.999824i	$-0.494030\pi$
$379$	4.66866e83			0.0375058			0.0187529	+	0.999824i	$0.494030\pi$
$380$		−	2.06568e85i		−	1.52127i
$381$	1.39447e84	+	1.48926e84i	0.0941639	+	0.100565i
$382$	7.17911e84			0.444610
$383$		−	6.40286e84i		−	0.363759i	−0.983321	−	0.181880i	$-0.941782\pi$
$383$		−	6.40286e84i		−	0.363759i	0.983321	−	0.181880i	$-0.0582181\pi$
$384$	−7.11160e85	+	6.65896e85i	−3.70712	+	3.47117i
$385$	−1.64420e85			−0.786593
$386$			3.47974e85i			1.52815i
$387$	1.05057e84	−	1.59635e85i	0.0423608	−	0.643676i
$388$	5.07676e85			1.87992
$389$		−	4.35740e85i		−	1.48214i	−0.671426	−	0.741072i	$-0.734318\pi$
$389$		−	4.35740e85i		−	1.48214i	0.671426	−	0.741072i	$-0.265682\pi$
$390$	−3.67179e84	−	3.92138e84i	−0.114748	−	0.122548i
$391$	−4.25870e85			−1.22305
$392$			6.46642e85i			1.70696i
$393$	−3.22856e85	+	3.02307e85i	−0.783529	+	0.733659i
$394$	2.39934e85			0.535447
$395$			1.58967e85i			0.326288i
$396$	2.01703e86	+	1.32742e85i	3.80865	+	0.250650i
$397$	−3.65940e85			−0.635803			−0.317902	−	0.948124i	$-0.602978\pi$
$397$	−3.65940e85			−0.635803			−0.317902	+	0.948124i	$0.602978\pi$
$398$		−	1.73886e86i		−	2.78050i
$399$	−2.23678e85	−	2.38882e85i	−0.329244	−	0.351624i
$400$	1.09468e86			1.48357
$401$		−	4.31332e85i		−	0.538329i	−0.963094	−	0.269164i	$-0.913253\pi$
$401$		−	4.31332e85i		−	0.538329i	0.963094	−	0.269164i	$-0.0867475\pi$
$402$	−9.59172e85	+	8.98123e85i	−1.10265	+	1.03247i
$403$	−1.64756e84			−0.0174492
$404$			3.97182e84i			0.0387619i
$405$	−1.17543e85	+	8.89171e85i	−0.105726	+	0.799778i
$406$	8.37072e85			0.694071
$407$			2.55166e86i			1.95077i
$408$	−3.91966e86	−	4.18609e86i	−2.76352	−	2.95137i
$409$	−2.57296e85			−0.167326			−0.0836630	−	0.996494i	$-0.526662\pi$
$409$	−2.57296e85			−0.167326			−0.0836630	+	0.996494i	$0.526662\pi$
$410$		−	7.85402e85i		−	0.471221i
$411$	1.46155e86	−	1.36852e86i	0.809158	−	0.757657i
$412$	−6.97522e85			−0.356410
$413$		−	7.48432e85i		−	0.353021i
$414$	3.23564e85	−	4.91659e86i	0.140913	−	2.14118i
$415$	2.97743e86			1.19744
$416$			1.34667e86i			0.500244i
$417$	2.79657e86	+	2.98667e86i	0.959702	+	1.02494i
$418$	5.49918e86			1.74374
$419$			2.37021e86i			0.694584i	0.937757	+	0.347292i	$0.112899\pi$
$419$			2.37021e86i			0.694584i	−0.937757	+	0.347292i	$0.887101\pi$
$420$	−4.49480e86	+	4.20872e86i	−1.21754	+	1.14005i
$421$	9.99347e85			0.250269			0.125135	−	0.992140i	$-0.460064\pi$
$421$	9.99347e85			0.250269			0.125135	+	0.992140i	$0.460064\pi$
$422$			5.37405e86i			1.24449i
$423$	−1.76025e86	−	1.15844e85i	−0.377001	−	0.0248108i
$424$	−1.71531e87			−3.39836
$425$			2.12902e86i			0.390251i
$426$	7.81618e86	+	8.34748e86i	1.32580	+	1.41592i
$427$	−6.27850e86			−0.985679
$428$			7.64791e86i			1.11147i
$429$	7.72426e85	−	7.23263e85i	0.103936	−	0.0973207i
$430$	−8.18919e86			−1.02043
$431$		−	7.77214e86i		−	0.896996i	−0.893784	−	0.448498i	$-0.851959\pi$
$431$		−	7.77214e86i		−	0.896996i	0.893784	−	0.448498i	$-0.148041\pi$
$432$	3.07294e87	−	2.51984e87i	3.28542	−	2.69408i
$433$	1.81514e87			1.79808			0.899042	−	0.437862i	$-0.144264\pi$
$433$	1.81514e87			1.79808			0.899042	+	0.437862i	$0.144264\pi$
$434$			2.55229e86i			0.234298i
$435$	−3.15637e86	−	3.37093e86i	−0.268561	−	0.286816i
$436$	−4.71354e87			−3.71786
$437$		−	9.91820e86i		−	0.725346i
$438$	−3.29062e87	+	3.08118e87i	−2.23168	+	2.08964i
$439$	7.24172e86			0.455525			0.227763	−	0.973717i	$-0.426859\pi$
$439$	7.24172e86			0.455525			0.227763	+	0.973717i	$0.426859\pi$
$440$		−	6.71018e87i		−	3.91558i
$441$	5.72305e85	−	8.69621e86i	0.0309852	−	0.470822i
$442$	−4.62927e86			−0.232583
$443$			8.13094e86i			0.379156i	0.981866	+	0.189578i	$0.0607120\pi$
$443$			8.13094e86i			0.379156i	−0.981866	+	0.189578i	$0.939288\pi$
$444$	6.53158e87	+	6.97556e87i	2.82735	+	3.01954i
$445$	9.98418e86			0.401266
$446$			3.09351e87i			1.15452i
$447$	−1.03062e87	+	9.65024e86i	−0.357232	+	0.334495i
$448$	1.12717e88			3.62922
$449$		−	6.64975e87i		−	1.98919i	−0.103838	−	0.994594i	$-0.533112\pi$
$449$		−	6.64975e87i		−	1.98919i	0.103838	−	0.994594i	$-0.466888\pi$
$450$	−2.45791e87	−	1.61757e86i	−0.683207	−	0.0449624i
$451$	1.54707e87			0.399654
$452$			3.22869e87i			0.775280i
$453$	−4.34474e87	−	4.64007e87i	−0.969893	−	1.03582i
$454$	−3.05572e87			−0.634264
$455$			3.22347e86i			0.0622226i
$456$	9.74909e87	−	9.12858e87i	1.75035	−	1.63894i
$457$	−9.42675e87			−1.57444			−0.787222	−	0.616670i	$-0.788481\pi$
$457$	−9.42675e87			−1.57444			−0.787222	+	0.616670i	$0.788481\pi$
$458$			1.33505e88i			2.07461i
$459$	4.90077e87	+	5.97647e87i	0.708673	+	0.864224i
$460$	−1.86621e88			−2.51160
$461$		−	1.07613e88i		−	1.34813i	−0.738670	−	0.674067i	$-0.764546\pi$
$461$		−	1.07613e88i		−	1.34813i	0.738670	−	0.674067i	$-0.235454\pi$
$462$	−1.12043e88	−	1.19659e88i	−1.30677	−	1.39560i
$463$	4.74223e87			0.515004			0.257502	−	0.966278i	$-0.417101\pi$
$463$	4.74223e87			0.515004			0.257502	+	0.966278i	$0.417101\pi$
$464$			2.04613e88i			2.06937i
$465$	1.02782e87	−	9.62399e86i	0.0968207	−	0.0906583i
$466$	−2.20423e88			−1.93429
$467$		−	6.47628e87i		−	0.529503i	−0.964317	−	0.264751i	$-0.914710\pi$
$467$		−	6.47628e87i		−	0.529503i	0.964317	−	0.264751i	$-0.0852899\pi$
$468$	2.60243e86	−	3.95442e87i	0.0198274	−	0.301279i
$469$	7.88464e87			0.559858
$470$			9.02998e87i			0.597665i
$471$	1.33905e88	+	1.43007e88i	0.826244	+	0.882407i
$472$	3.05445e88			1.75730
$473$		−	1.61309e88i		−	0.865449i
$474$	−1.15690e88	+	1.08327e88i	−0.578910	+	0.542064i
$475$	−4.95832e87			−0.231444
$476$			5.30621e88i			2.31076i
$477$	2.30679e88	+	1.51812e87i	0.937351	+	0.0616878i
$478$	3.34415e88			1.26813
$479$			2.43318e88i			0.861197i	0.902544	+	0.430598i	$0.141697\pi$
$479$			2.43318e88i			0.861197i	−0.902544	+	0.430598i	$0.858303\pi$
$480$	−7.86638e88	−	8.40109e88i	−2.59905	−	2.77572i
$481$	5.00256e87			0.154314
$482$		−	1.13667e88i		−	0.327403i
$483$	−2.15814e88	+	2.02078e88i	−0.580530	+	0.543580i
$484$	9.05857e88			2.27595
$485$			2.27130e88i			0.533086i
$486$	−7.27206e88	+	5.20376e88i	−1.59463	+	1.14109i
$487$	8.81272e88			1.80574			0.902868	−	0.429919i	$-0.141458\pi$
$487$	8.81272e88			1.80574			0.902868	+	0.429919i	$0.141458\pi$
$488$		−	2.56233e89i		−	4.90661i
$489$	−6.33077e87	−	6.76110e87i	−0.113309	−	0.121011i
$490$	−4.46110e88			−0.746400
$491$		−	5.16852e88i		−	0.808494i	−0.914650	−	0.404247i	$-0.867534\pi$
$491$		−	5.16852e88i		−	0.808494i	0.914650	−	0.404247i	$-0.132466\pi$
$492$	4.22928e88	−	3.96010e88i	0.618612	−	0.579238i
$493$	−3.97945e88			−0.544346
$494$		−	1.07812e88i		−	0.137936i
$495$	−5.93879e87	+	9.02403e88i	−0.0710765	+	1.08001i
$496$	−6.23877e88			−0.698560
$497$		−	6.86185e88i		−	0.718919i
$498$	2.02895e89	+	2.16686e89i	1.98931	+	2.12453i
$499$	−2.02358e89			−1.85696			−0.928480	−	0.371382i	$-0.878884\pi$
$499$	−2.02358e89			−1.85696			−0.928480	+	0.371382i	$0.878884\pi$
$500$			3.60483e89i			3.09652i
$501$	3.49426e88	−	3.27186e88i	0.281003	−	0.263118i
$502$	1.93034e89			1.45349
$503$			1.30405e89i			0.919495i	0.888050	+	0.459748i	$0.152060\pi$
$503$			1.30405e89i			0.919495i	−0.888050	+	0.459748i	$0.847940\pi$
$504$	−3.97265e89	−	2.61443e88i	−2.62345	−	0.172651i
$505$	−1.77696e87			−0.0109916
$506$		−	4.96814e89i		−	2.87890i
$507$	1.24474e89	+	1.32935e89i	0.675797	+	0.721733i
$508$	7.70417e88			0.391943
$509$		−	2.10927e89i		−	1.00564i	−0.864390	−	0.502822i	$-0.832295\pi$
$509$		−	2.10927e89i		−	1.00564i	0.864390	−	0.502822i	$-0.167705\pi$
$510$	2.88793e89	−	2.70412e89i	1.29054	−	1.20840i
$511$	2.70498e89			1.13311
$512$			1.18559e90i			4.65612i
$513$	−1.39188e89	+	1.14135e89i	−0.512539	+	0.420288i
$514$	−3.11936e89			−1.07717
$515$		−	3.12066e88i		−	0.101067i
$516$	−4.12910e89	−	4.40977e89i	−1.25434	−	1.33960i
$517$	−1.77871e89			−0.506894
$518$		−	7.74962e89i		−	2.07204i
$519$	−5.80166e89	+	5.43240e89i	−1.45556	+	1.36291i
$520$	−1.31554e89			−0.309738
$521$		−	3.59671e89i		−	0.794805i	−0.917644	−	0.397403i	$-0.869912\pi$
$521$		−	3.59671e89i		−	0.794805i	0.917644	−	0.397403i	$-0.130088\pi$
$522$	3.02348e88	−	4.59419e89i	0.0627162	−	0.952978i
$523$	−9.90261e89			−1.92839			−0.964193	−	0.265201i	$-0.914562\pi$
$523$	−9.90261e89			−1.92839			−0.964193	+	0.265201i	$0.914562\pi$
$524$			1.67019e90i			3.05375i
$525$	1.01023e89	+	1.07890e89i	0.173446	+	0.185236i
$526$	2.05943e90			3.32061
$527$		−	1.21336e89i		−	0.183755i
$528$	2.92492e90	−	2.73876e90i	4.16097	−	3.89614i
$529$	−1.47809e89			−0.197544
$530$		−	1.18337e90i		−	1.48599i
$531$	−4.10770e89	−	2.70331e88i	−0.484707	−	0.0318990i
$532$	−1.23578e90			−1.37043
$533$		−	3.03305e88i		−	0.0316142i
$534$	6.80366e89	+	7.26613e89i	0.666624	+	0.711937i
$535$	−3.42161e89			−0.315178
$536$			3.21782e90i			2.78692i
$537$	−6.40754e89	+	5.99972e89i	−0.521843	+	0.488629i
$538$	7.12448e89			0.545680
$539$		−	8.78740e89i		−	0.633040i
$540$	2.14757e90	+	2.61895e90i	1.45530	+	1.77473i
$541$	4.48281e89			0.285786			0.142893	−	0.989738i	$-0.454360\pi$
$541$	4.48281e89			0.285786			0.142893	+	0.989738i	$0.454360\pi$
$542$		−	1.64378e90i		−	0.985981i
$543$	1.84507e90	+	1.97049e90i	1.04140	+	1.11219i
$544$	−9.91767e90			−5.26800
$545$		−	2.10880e90i		−	1.05427i
$546$	−2.34593e89	+	2.19662e89i	−0.110397	+	0.103371i
$547$	3.56584e90			1.57972			0.789861	−	0.613287i	$-0.210153\pi$
$547$	3.56584e90			1.57972			0.789861	+	0.613287i	$0.210153\pi$
$548$		−	7.56083e90i		−	3.15363i
$549$	−2.26777e89	+	3.44589e90i	−0.0890660	+	1.35336i
$550$	−2.48368e90			−0.918600
$551$		−	9.26784e89i		−	0.322831i
$552$	−8.24706e90	−	8.80765e90i	−2.70589	−	2.88982i
$553$	9.51004e89			0.293936
$554$			1.10785e91i			3.22595i
$555$	−3.12081e90	+	2.92218e90i	−0.856246	+	0.801748i
$556$	1.54505e91			3.99461
$557$		−	2.48541e90i		−	0.605587i	−0.953056	−	0.302794i	$-0.902081\pi$
$557$		−	2.48541e90i		−	0.605587i	0.953056	−	0.302794i	$-0.0979193\pi$
$558$	1.40080e90	+	9.21877e88i	0.321697	+	0.0211712i
$559$	−3.16249e89			−0.0684604
$560$			1.22062e91i			2.49102i
$561$	5.32653e90	+	5.68860e90i	1.02487	+	1.09454i
$562$	−1.76504e91			−3.20226
$563$		−	3.70318e90i		−	0.633574i	−0.948497	−	0.316787i	$-0.897396\pi$
$563$		−	3.70318e90i		−	0.633574i	0.948497	−	0.316787i	$-0.102604\pi$
$564$	−4.86252e90	+	4.55303e90i	−0.784605	+	0.734667i
$565$	−1.44449e90			−0.219845
$566$		−	1.40296e91i		−	2.01420i
$567$	5.31939e90	+	7.03192e89i	0.720478	+	0.0952430i
$568$	2.80041e91			3.57871
$569$		−	7.92989e89i		−	0.0956230i	−0.998856	−	0.0478115i	$-0.984775\pi$
$569$		−	7.92989e89i		−	0.0956230i	0.998856	−	0.0478115i	$-0.0152247\pi$
$570$	6.29770e90	+	6.72578e90i	0.716657	+	0.765372i
$571$	3.57059e90			0.383485			0.191743	−	0.981445i	$-0.438586\pi$
$571$	3.57059e90			0.383485			0.191743	+	0.981445i	$0.438586\pi$
$572$		−	3.99588e90i		−	0.405083i
$573$	−1.72955e90	+	1.61947e90i	−0.165512	+	0.154978i
$574$	−4.69860e90			−0.424498
$575$			4.47951e90i			0.382113i
$576$	4.07129e90	−	6.18635e91i	0.327936	−	4.98302i
$577$	−1.50114e91			−1.14188			−0.570938	−	0.820993i	$-0.693420\pi$
$577$	−1.50114e91			−1.14188			−0.570938	+	0.820993i	$0.693420\pi$
$578$		−	6.79891e90i		−	0.488450i
$579$	−7.84963e90	−	8.38320e90i	−0.532668	−	0.568876i
$580$	−1.74383e91			−1.11784
$581$		−	1.78122e91i		−	1.07871i
$582$	−1.65297e91	+	1.54776e91i	−0.945817	+	0.885618i
$583$	2.33098e91			1.26031
$584$			1.10394e92i			5.64053i
$585$	1.76917e90	+	1.16431e89i	0.0854333	+	0.00562243i
$586$	−2.41894e91			−1.10409
$587$		−	3.66862e91i		−	1.58287i	−0.611252	−	0.791436i	$-0.709334\pi$
$587$		−	3.66862e91i		−	1.58287i	0.611252	−	0.791436i	$-0.290666\pi$
$588$	−2.24935e91	−	2.40224e91i	−0.917496	−	0.979862i
$589$	2.82582e90			0.108978
$590$			2.10722e91i			0.768412i
$591$	−5.78035e90	+	5.41245e90i	−0.199328	+	0.186641i
$592$	1.89431e92			6.17780
$593$		−	5.08882e91i		−	1.56968i	−0.619697	−	0.784841i	$-0.712744\pi$
$593$		−	5.08882e91i		−	1.56968i	0.619697	−	0.784841i	$-0.287256\pi$
$594$	−6.97206e91	+	5.71717e91i	−2.03427	+	1.66812i
$595$	−2.37396e91			−0.655259
$596$			5.33157e91i			1.39229i
$597$	3.92253e91	+	4.18916e91i	0.969199	+	1.03508i
$598$	−9.74011e90			−0.227732
$599$		−	6.29692e91i		−	1.39329i	−0.717414	−	0.696647i	$-0.754674\pi$
$599$		−	6.29692e91i		−	1.39329i	0.717414	−	0.696647i	$-0.245326\pi$
$600$	−4.40313e91	+	4.12288e91i	−0.922083	+	0.863395i
$601$	−7.75848e90			−0.153787			−0.0768934	−	0.997039i	$-0.524500\pi$
$601$	−7.75848e90			−0.153787			−0.0768934	+	0.997039i	$0.524500\pi$
$602$			4.89911e91i			0.919249i
$603$	2.84791e90	−	4.32741e91i	0.0505888	−	0.768700i
$604$	−2.40039e92			−4.03703
$605$			4.05273e91i			0.645387i
$606$	−1.21090e90	−	1.29321e90i	−0.0182605	−	0.0195017i
$607$	−7.79142e91			−1.11273			−0.556365	−	0.830938i	$-0.687804\pi$
$607$	−7.79142e91			−1.11273			−0.556365	+	0.830938i	$0.687804\pi$
$608$		−	2.30975e92i		−	3.12426i
$609$	−2.01663e91	+	1.88827e91i	−0.258378	+	0.241932i
$610$	1.76772e92			2.14551
$611$			3.48719e90i			0.0400973i
$612$	2.91227e92	+	1.91659e91i	3.17274	+	0.208800i
$613$	1.12273e92			1.15899			0.579496	−	0.814975i	$-0.303249\pi$
$613$	1.12273e92			1.15899			0.579496	+	0.814975i	$0.303249\pi$
$614$		−	1.67578e92i		−	1.63931i
$615$	1.77171e91	+	1.89215e91i	0.164254	+	0.175419i
$616$	−4.01431e92			−3.52734
$617$			1.00909e92i			0.840462i	0.907417	+	0.420231i	$0.138051\pi$
$617$			1.00909e92i			0.840462i	−0.907417	+	0.420231i	$0.861949\pi$
$618$	2.27110e91	−	2.12655e91i	0.179315	−	0.167902i
$619$	1.83201e92			1.37131			0.685655	−	0.727926i	$-0.259516\pi$
$619$	1.83201e92			1.37131			0.685655	+	0.727926i	$0.259516\pi$
$620$		−	5.31706e91i		−	0.377351i
$621$	1.03114e92	+	1.25747e92i	0.693894	+	0.846201i
$622$	−5.61715e91			−0.358454
$623$		−	5.97295e91i		−	0.361479i
$624$	−5.36938e91	−	5.73436e91i	−0.308200	−	0.329149i
$625$	−9.71433e91			−0.528899
$626$			5.24308e90i			0.0270791i
$627$	−1.32483e92	+	1.24051e92i	−0.649130	+	0.607814i
$628$	7.39801e92			3.43911
$629$			3.68418e92i			1.62506i
$630$	1.80367e91	−	2.74068e92i	0.0754949	−	1.14715i
$631$	1.78633e92			0.709565			0.354783	−	0.934949i	$-0.384555\pi$
$631$	1.78633e92			0.709565			0.354783	+	0.934949i	$0.384555\pi$
$632$			3.88117e92i			1.46318i
$633$	−1.21228e92	−	1.29469e92i	−0.433792	−	0.463278i
$634$	−5.73894e92			−1.94933
$635$			3.44678e91i			0.111143i
$636$	6.37229e92	−	5.96671e92i	1.95079	−	1.82663i
$637$	−1.72278e91			−0.0500759
$638$		−	4.64237e92i		−	1.28132i
$639$	−3.76606e92	−	2.47847e91i	−0.987095	−	0.0649615i
$640$	−1.64593e93			−4.09706
$641$			4.26103e92i			1.00740i	0.863880	+	0.503698i	$0.168028\pi$
$641$			4.26103e92i			1.00740i	−0.863880	+	0.503698i	$0.831972\pi$
$642$	−2.33164e92	−	2.49013e92i	−0.523607	−	0.559198i
$643$	6.70124e91			0.142953			0.0714765	−	0.997442i	$-0.477229\pi$
$643$	6.70124e91			0.142953			0.0714765	+	0.997442i	$0.477229\pi$
$644$			1.11644e93i			2.26257i
$645$	1.97289e92	−	1.84732e92i	0.379868	−	0.355691i
$646$	7.93993e92			1.45259
$647$		−	9.15228e92i		−	1.59106i	−0.605911	−	0.795532i	$-0.707191\pi$
$647$		−	9.15228e92i		−	1.59106i	0.605911	−	0.795532i	$-0.292809\pi$
$648$	−2.86982e92	+	2.17091e93i	−0.474110	+	3.58646i
$649$	−4.15077e92			−0.651709
$650$			4.86929e91i			0.0726649i
$651$	−5.75747e91	−	6.14882e91i	−0.0816693	−	0.0872207i
$652$	−3.49763e92			−0.471632
$653$			3.30721e92i			0.423961i	0.977274	+	0.211981i	$0.0679914\pi$
$653$			3.30721e92i			0.423961i	−0.977274	+	0.211981i	$0.932009\pi$
$654$	1.53471e93	−	1.43703e93i	1.87051	−	1.75146i
$655$	−7.47228e92			−0.865945
$656$		−	1.14852e93i		−	1.26564i
$657$	9.77028e91	−	1.48460e93i	0.102388	−	1.55580i
$658$	5.40211e92			0.538405
$659$			1.56475e93i			1.48329i	0.670793	+	0.741645i	$0.265954\pi$
$659$			1.56475e93i			1.48329i	−0.670793	+	0.741645i	$0.734046\pi$
$660$	2.33414e93	+	2.49280e93i	2.10463	+	2.24770i
$661$	−1.03288e93			−0.885936			−0.442968	−	0.896537i	$-0.646075\pi$
$661$	−1.03288e93			−0.885936			−0.442968	+	0.896537i	$0.646075\pi$
$662$		−	1.25574e93i		−	1.02468i
$663$	1.11526e92	−	1.04427e92i	0.0865823	−	0.0810715i
$664$	7.26938e93			5.36971
$665$		−	5.52876e92i		−	0.388610i
$666$	−4.25331e93	−	2.79914e92i	−2.84497	−	0.187230i
$667$	−8.37287e92			−0.532993
$668$		−	1.80764e93i		−	1.09519i
$669$	−6.97836e92	−	7.45271e92i	−0.402431	−	0.429786i
$670$	−2.21994e93			−1.21863
$671$			3.48203e93i			1.81965i
$672$	−5.02588e93	+	4.70600e93i	−2.50050	+	2.34135i
$673$	−2.66944e93			−1.26451			−0.632255	−	0.774760i	$-0.717871\pi$
$673$	−2.66944e93			−1.26451			−0.632255	+	0.774760i	$0.717871\pi$
$674$		−	7.93798e93i		−	3.58042i
$675$	6.28634e92	−	5.15486e92i	0.270006	−	0.221408i
$676$	6.87694e93			2.81290
$677$		−	4.33783e92i		−	0.168985i	−0.996424	−	0.0844923i	$-0.973073\pi$
$677$		−	4.33783e92i		−	0.168985i	0.996424	−	0.0844923i	$-0.0269268\pi$
$678$	−9.84340e92	−	1.05125e93i	−0.365229	−	0.390055i
$679$	1.35879e93			0.480229
$680$		−	9.68842e93i		−	3.26181i
$681$	7.36166e92	−	6.89311e92i	0.236114	−	0.221086i
$682$	1.41549e93			0.432535
$683$			4.16861e93i			1.21369i	0.794819	+	0.606846i	$0.207566\pi$
$683$			4.16861e93i			1.21369i	−0.794819	+	0.606846i	$0.792434\pi$
$684$	−4.46358e92	+	6.78245e93i	−0.123832	+	1.88163i
$685$	3.38265e93			0.894270
$686$			8.32500e93i			2.09743i
$687$	−3.01161e93	−	3.21632e93i	−0.723146	−	0.772301i
$688$	−1.19753e94			−2.74074
$689$		−	4.56992e92i		−	0.0996953i
$690$	6.07629e93	−	5.68955e93i	1.26363	−	1.18320i
$691$	8.73386e93			1.73153			0.865766	−	0.500449i	$-0.166832\pi$
$691$	8.73386e93			1.73153			0.865766	+	0.500449i	$0.166832\pi$
$692$			3.00129e94i			5.67293i
$693$	5.39855e93	+	3.55283e92i	0.972927	+	0.0640291i
$694$	−1.56959e94			−2.69726
$695$			6.91243e93i			1.13275i
$696$	−7.70628e93	−	8.23011e93i	−1.20431	−	1.28618i
$697$	2.23372e93			0.332925
$698$			9.48637e93i			1.34856i
$699$	5.31030e93	−	4.97231e93i	0.720065	−	0.674235i
$700$	5.58133e93			0.721942
$701$		−	7.02428e93i		−	0.866776i	−0.901207	−	0.433388i	$-0.857318\pi$
$701$		−	7.02428e93i		−	0.866776i	0.901207	−	0.433388i	$-0.142682\pi$
$702$	1.12086e93	+	1.36688e93i	0.131955	+	0.160919i
$703$	−8.58018e93			−0.963764
$704$		−	6.25122e94i		−	6.69988i
$705$	−2.03699e93	−	2.17545e93i	−0.208328	−	0.222489i
$706$	3.49037e93			0.340657
$707$			1.06305e92i			0.00990179i
$708$	−1.13471e94	+	1.06249e94i	−1.00876	+	0.944555i
$709$	8.49512e93			0.720848			0.360424	−	0.932789i	$-0.382632\pi$
$709$	8.49512e93			0.720848			0.360424	+	0.932789i	$0.382632\pi$
$710$			1.93197e94i			1.56485i
$711$	3.43499e92	−	5.21950e93i	0.0265601	−	0.403582i
$712$	2.43764e94			1.79941
$713$		−	2.55294e93i		−	0.179923i
$714$	−1.61772e94	−	1.72768e94i	−1.08858	−	1.16258i
$715$	1.78773e93			0.114869
$716$			3.31472e94i			2.03384i
$717$	−8.05654e93	+	7.54376e93i	−0.472081	+	0.442034i
$718$	−5.56239e94			−3.11283
$719$			1.33779e93i			0.0715049i	0.999361	+	0.0357525i	$0.0113828\pi$
$719$			1.33779e93i			0.0715049i	−0.999361	+	0.0357525i	$0.988617\pi$
$720$	6.69928e94	+	4.40885e93i	3.42024	+	0.225088i
$721$	−1.86691e93			−0.0910455
$722$		−	2.35979e94i		−	1.09937i
$723$	2.56411e93	+	2.73840e93i	0.114123	+	0.121880i
$724$	1.01937e95			4.33469
$725$			4.18578e93i			0.170068i
$726$	−2.94943e94	+	2.76171e94i	−1.14506	+	1.07218i
$727$	1.06774e94			0.396124			0.198062	−	0.980189i	$-0.436535\pi$
$727$	1.06774e94			0.396124			0.198062	+	0.980189i	$0.436535\pi$
$728$			7.87011e93i			0.279026i
$729$	5.78075e93	−	2.89410e94i	0.195873	−	0.980629i
$730$	−7.61591e94			−2.46642
$731$		−	2.32904e94i		−	0.720948i
$732$	8.91309e94	+	9.51894e94i	2.63732	+	2.81659i
$733$	−9.84318e93			−0.278423			−0.139211	−	0.990263i	$-0.544457\pi$
$733$	−9.84318e93			−0.278423			−0.139211	+	0.990263i	$0.544457\pi$
$734$		−	1.23030e95i		−	3.32690i
$735$	1.07474e94	−	1.00634e94i	0.277858	−	0.260173i
$736$	−2.08670e95			−5.15814
$737$		−	4.37279e94i		−	1.03355i
$738$	−1.69712e93	+	2.57878e94i	−0.0383576	+	0.582847i
$739$	−5.68256e93			−0.122822			−0.0614112	−	0.998113i	$-0.519560\pi$
$739$	−5.68256e93			−0.122822			−0.0614112	+	0.998113i	$0.519560\pi$
$740$			1.61444e95i			3.33715i
$741$	2.43204e93	+	2.59735e93i	0.0480805	+	0.0513487i
$742$	−7.07941e94			−1.33865
$743$			2.62480e94i			0.474750i	0.971418	+	0.237375i	$0.0762871\pi$
$743$			2.62480e94i			0.474750i	−0.971418	+	0.237375i	$0.923713\pi$
$744$	2.50941e94	−	2.34969e94i	0.434175	−	0.406541i
$745$	−2.38530e94			−0.394808
$746$		−	3.65702e94i		−	0.579090i
$747$	−9.77606e94	−	6.43370e93i	−1.48110	−	0.0974723i
$748$	2.94280e95			4.26588
$749$			2.04695e94i			0.283927i
$750$	−1.09901e95	−	1.17372e95i	−1.45875	−	1.55791i
$751$	−2.26476e94			−0.287676			−0.143838	−	0.989601i	$-0.545944\pi$
$751$	−2.26476e94			−0.287676			−0.143838	+	0.989601i	$0.545944\pi$
$752$			1.32048e95i			1.60526i
$753$	−4.65047e94	+	4.35448e94i	−0.541082	+	0.506643i
$754$	−9.10143e93			−0.101357
$755$		−	1.07391e95i		−	1.14477i
$756$	1.56676e95	−	1.28476e95i	1.59876	−	1.31100i
$757$	1.09032e95			1.06510			0.532548	−	0.846400i	$-0.321235\pi$
$757$	1.09032e95			1.06510			0.532548	+	0.846400i	$0.321235\pi$
$758$			7.86370e93i			0.0735433i
$759$	1.12072e95	+	1.19690e95i	1.00350	+	1.07171i
$760$	2.25636e95			1.93446
$761$			1.26383e95i			1.03752i	0.854921	+	0.518758i	$0.173605\pi$
$761$			1.26383e95i			1.03752i	−0.854921	+	0.518758i	$0.826395\pi$
$762$	−2.50844e94	+	2.34879e94i	−0.197192	+	0.184642i
$763$	−1.26157e95			−0.949734
$764$			8.94724e94i			0.645072i
$765$	−8.57465e93	+	1.30292e95i	−0.0592092	+	0.899688i
$766$	1.07847e95			0.713279
$767$			8.13765e93i			0.0515528i
$768$	−5.59155e95	−	5.97163e95i	−3.39322	−	3.62387i
$769$	1.21254e95			0.704902			0.352451	−	0.935830i	$-0.385348\pi$
$769$	1.21254e95			0.704902			0.352451	+	0.935830i	$0.385348\pi$
$770$		−	2.76942e95i		−	1.54239i
$771$	7.51499e94	−	7.03668e94i	0.400991	−	0.375468i
$772$	−4.33677e95			−2.21715
$773$		−	2.00951e95i		−	0.984388i	−0.870486	−	0.492194i	$-0.836195\pi$
$773$		−	2.00951e95i		−	0.984388i	0.870486	−	0.492194i	$-0.163805\pi$
$774$	2.68883e95	+	1.76954e94i	1.26215	+	0.0830633i
$775$	−1.27627e94			−0.0574098
$776$			5.54538e95i			2.39053i
$777$	1.74817e95	+	1.86700e95i	0.722252	+	0.771347i
$778$	7.33942e95			2.90627
$779$			5.20216e94i			0.197446i
$780$	4.88717e94	−	4.57611e94i	0.177802	−	0.166485i
$781$	−3.80555e95			−1.32719
$782$		−	7.17319e95i		−	2.39822i
$783$	9.63522e94	+	1.17501e95i	0.308833	+	0.376620i
$784$	−6.52361e95			−2.00474
$785$			3.30981e95i			0.975223i
$786$	−5.09194e95	−	5.43806e95i	−1.43860	−	1.53639i
$787$	8.74585e94			0.236939			0.118469	−	0.992958i	$-0.462201\pi$
$787$	8.74585e94			0.236939			0.118469	+	0.992958i	$0.462201\pi$
$788$			2.99027e95i			0.776865i
$789$	−4.96146e95	+	4.64568e95i	−1.23614	+	1.15747i
$790$	−2.67757e95			−0.639804
$791$			8.64154e94i			0.198047i
$792$	−1.44995e95	+	2.20322e96i	−0.318730	+	4.84313i
$793$	6.82657e94			0.143942
$794$		−	6.16374e95i		−	1.24672i
$795$	2.66946e95	+	2.85091e95i	0.517973	+	0.553182i
$796$	2.16712e96			4.03414
$797$		−	7.75142e95i		−	1.38438i	−0.721713	−	0.692192i	$-0.756645\pi$
$797$		−	7.75142e95i		−	1.38438i	0.721713	−	0.692192i	$-0.243355\pi$
$798$	4.02364e95	−	3.76754e95i	0.689483	−	0.645599i
$799$	−2.56817e95			−0.422260
$800$			1.04319e96i			1.64586i
$801$	−3.27820e95	−	2.15741e94i	−0.496320	−	0.0326632i
$802$	7.26518e95			1.05558
$803$		−	1.50017e96i		−	2.09183i
$804$	−1.11932e96	−	1.19541e96i	−1.49798	−	1.59980i
$805$	−4.99487e95			−0.641593
$806$		−	2.77508e94i		−	0.0342153i
$807$	−1.71639e95	+	1.60715e95i	−0.203137	+	0.190208i
$808$	−4.33845e94			−0.0492901
$809$			9.35322e95i			1.02014i	0.860133	+	0.510070i	$0.170381\pi$
$809$			9.35322e95i			1.02014i	−0.860133	+	0.510070i	$0.829619\pi$
$810$	−1.49768e96	−	1.97985e95i	−1.56825	−	0.207313i
$811$	4.43181e95			0.445547			0.222773	−	0.974870i	$-0.428489\pi$
$811$	4.43181e95			0.445547			0.222773	+	0.974870i	$0.428489\pi$
$812$			1.04323e96i			1.00701i
$813$	3.70806e95	+	3.96011e95i	0.343684	+	0.367045i
$814$	−4.29791e96			−3.82518
$815$		−	1.56481e95i		−	0.133740i
$816$	4.22312e96	−	3.95433e96i	3.46623	−	3.24562i
$817$	5.42417e95			0.427568
$818$		−	4.33379e95i		−	0.328102i
$819$	6.96537e93	−	1.05839e95i	0.00506495	−	0.0769623i
$820$	9.78837e95			0.683681
$821$		−	1.92869e96i		−	1.29402i	−0.762484	−	0.647008i	$-0.776020\pi$
$821$		−	1.92869e96i		−	1.29402i	0.762484	−	0.647008i	$-0.223980\pi$
$822$	2.30509e96	+	2.46177e96i	1.48565	+	1.58664i
$823$	−2.27252e96			−1.40706			−0.703530	−	0.710666i	$-0.748394\pi$
$823$	−2.27252e96			−1.40706			−0.703530	+	0.710666i	$0.748394\pi$
$824$		−	7.61908e95i		−	0.453215i
$825$	5.98354e95	−	5.60270e95i	0.341962	−	0.320197i
$826$	1.26063e96			0.692222
$827$			1.47111e95i			0.0776184i	0.999247	+	0.0388092i	$0.0123565\pi$
$827$			1.47111e95i			0.0776184i	−0.999247	+	0.0388092i	$0.987644\pi$
$828$	6.12749e96	+	4.03255e95i	3.10657	+	0.204446i
$829$	1.23297e96			0.600695			0.300348	−	0.953830i	$-0.402897\pi$
$829$	1.23297e96			0.600695			0.300348	+	0.953830i	$0.402897\pi$
$830$			5.01506e96i			2.34800i
$831$	−2.49909e96	−	2.66896e96i	−1.12447	−	1.20090i
$832$	−1.22556e96			−0.529987
$833$		−	1.26876e96i		−	0.527344i
$834$	−5.03062e96	+	4.71043e96i	−2.00975	+	1.88183i
$835$	8.08722e95			0.310560
$836$			6.85357e96i			2.52994i
$837$	−3.58268e95	+	2.93784e95i	−0.127136	+	0.104253i
$838$	−3.99230e96			−1.36198
$839$			1.70729e96i			0.559966i	0.960005	+	0.279983i	$0.0903288\pi$
$839$			1.70729e96i			0.559966i	−0.960005	+	0.279983i	$0.909671\pi$
$840$	−4.59721e96	−	4.90970e96i	−1.44970	−	1.54824i
$841$	2.51575e96			0.762779
$842$			1.68326e96i			0.490741i
$843$	4.25223e96	−	3.98159e96i	1.19208	−	1.11621i
$844$	−6.69762e96			−1.80559
$845$			3.07669e96i			0.797649i
$846$	1.95122e95	−	2.96490e96i	0.0486502	−	0.739244i
$847$	2.42451e96			0.581395
$848$		−	1.73048e97i		−	3.99120i
$849$	3.16481e96	+	3.37993e96i	0.702091	+	0.749815i
$850$	−3.58603e96			−0.765225
$851$			7.75161e96i			1.59117i
$852$	−1.04034e97	+	9.74122e96i	−2.05432	+	1.92356i
$853$	6.76243e96			1.28465			0.642325	−	0.766432i	$-0.277970\pi$
$853$	6.76243e96			1.28465			0.642325	+	0.766432i	$0.277970\pi$
$854$		−	1.05752e97i		−	1.93277i
$855$	−3.03441e96	−	1.99697e95i	−0.533572	−	0.0351148i
$856$	−8.35386e96			−1.41336
$857$		−	9.57408e96i		−	1.55858i	−0.626662	−	0.779291i	$-0.715579\pi$
$857$		−	9.57408e96i		−	1.55858i	0.626662	−	0.779291i	$-0.284421\pi$
$858$	1.21823e96	+	1.30104e96i	0.190832	+	0.203803i
$859$	9.61703e96			1.44966			0.724831	−	0.688927i	$-0.241918\pi$
$859$	9.61703e96			1.44966			0.724831	+	0.688927i	$0.241918\pi$
$860$		−	1.02061e97i		−	1.48051i
$861$	1.13196e96	−	1.05991e96i	0.158025	−	0.147967i
$862$	1.30911e97			1.75888
$863$			1.32977e97i			1.71957i	0.510652	+	0.859787i	$0.329404\pi$
$863$			1.32977e97i			1.71957i	−0.510652	+	0.859787i	$0.670596\pi$
$864$	2.40131e97	+	2.92839e97i	2.98878	+	3.64481i
$865$	−1.34275e97			−1.60866
$866$			3.05735e97i			3.52578i
$867$	1.53370e96	+	1.63795e96i	0.170259	+	0.181832i
$868$	−3.18089e96			−0.339936
$869$		−	5.27423e96i		−	0.542633i
$870$	5.67785e96	−	5.31647e96i	0.562404	−	0.526609i
$871$	−8.57292e95			−0.0817579
$872$		−	5.14863e97i		−	4.72768i
$873$	4.90789e95	−	7.45757e96i	0.0433935	−	0.659367i
$874$	1.67058e97			1.42230
$875$			9.64825e96i			0.791012i
$876$	−3.84004e97	−	4.10106e97i	−3.03180	−	3.23788i
$877$	−2.45649e97			−1.86779			−0.933897	−	0.357541i	$-0.883615\pi$
$877$	−2.45649e97			−1.86779			−0.933897	+	0.357541i	$0.883615\pi$
$878$			1.21977e97i			0.893219i
$879$	5.82758e96	−	5.45666e96i	0.411013	−	0.384853i
$880$	6.76953e97			4.59865
$881$		−	5.69265e96i		−	0.372486i	−0.982504	−	0.186243i	$-0.940369\pi$
$881$		−	5.69265e96i		−	0.372486i	0.982504	−	0.186243i	$-0.0596311\pi$
$882$	1.46475e97	+	9.63967e95i	0.923212	+	0.0607574i
$883$	−1.56652e97			−0.951116			−0.475558	−	0.879684i	$-0.657754\pi$
$883$	−1.56652e97			−0.951116			−0.475558	+	0.879684i	$0.657754\pi$
$884$		−	5.76941e96i		−	0.337448i
$885$	−4.75349e96	−	5.07661e96i	−0.267846	−	0.286052i
$886$	−1.36954e97			−0.743469
$887$			3.97321e96i			0.207808i	0.994587	+	0.103904i	$0.0331335\pi$
$887$			3.97321e96i			0.207808i	−0.994587	+	0.103904i	$0.966867\pi$
$888$	−7.61945e97	+	7.13449e97i	−3.83968	+	3.59530i
$889$	2.06201e96			0.100123
$890$			1.68170e97i			0.786823i
$891$	3.89987e96	−	2.95011e97i	0.175827	−	1.33007i
$892$	−3.85541e97			−1.67506
$893$		−	5.98107e96i		−	0.250427i
$894$	−1.62545e97	−	1.73594e97i	−0.655896	−	0.700480i
$895$	−1.48298e97			−0.576734
$896$			9.84663e97i			3.69082i
$897$	2.34653e96	−	2.19718e96i	0.0847766	−	0.0793808i
$898$	1.12006e98			3.90051
$899$		−	2.38554e96i		−	0.0800787i
$900$	2.01596e96	−	3.06326e97i	0.0652346	−	0.991245i
$901$	3.36556e97			1.04988
$902$			2.60582e97i			0.783663i
$903$	−1.10515e97	−	1.18027e97i	−0.320423	−	0.342203i
$904$	−3.52672e97			−0.985856
$905$			4.56057e97i			1.22918i
$906$	7.81556e97	−	7.31811e97i	2.03109	−	1.90182i
$907$	3.33315e96			0.0835246			0.0417623	−	0.999128i	$-0.486703\pi$
$907$	3.33315e96			0.0835246			0.0417623	+	0.999128i	$0.486703\pi$
$908$		−	3.80831e97i		−	0.920236i
$909$	5.83446e95	+	3.83971e94i	0.0135954	+	0.000894725i
$910$	−5.42949e96			−0.122009
$911$			3.10309e97i			0.672494i	0.941774	+	0.336247i	$0.109158\pi$
$911$			3.10309e97i			0.672494i	−0.941774	+	0.336247i	$0.890842\pi$
$912$	9.20932e97	+	9.83532e97i	1.92486	+	2.05570i
$913$	−9.87857e97			−1.99140
$914$		−	1.58780e98i		−	3.08725i
$915$	−4.25870e97	+	3.98764e97i	−0.798694	+	0.747859i
$916$	−1.66385e98			−3.00999
$917$			4.47023e97i			0.780084i
$918$	−1.00665e98	+	8.25467e97i	−1.69462	+	1.38960i
$919$	5.71753e96			0.0928531			0.0464266	−	0.998922i	$-0.485217\pi$
$919$	5.71753e96			0.0928531			0.0464266	+	0.998922i	$0.485217\pi$
$920$		−	2.03847e98i		−	3.19379i
$921$	3.78024e97	+	4.03720e97i	0.571415	+	0.610256i
$922$	1.81259e98			2.64349
$923$			7.46084e96i			0.104986i
$924$	1.49130e98	−	1.39638e98i	2.02483	−	1.89595i
$925$	3.87520e97			0.507711
$926$			7.98763e97i			1.00985i
$927$	−6.74320e95	+	1.02463e97i	−0.00822687	+	0.125008i
$928$	−1.94987e98			−2.29574
$929$		−	9.02375e97i		−	1.02534i	−0.858585	−	0.512670i	$-0.828656\pi$
$929$		−	9.02375e97i		−	1.02534i	0.858585	−	0.512670i	$-0.171344\pi$
$930$	1.62103e97	+	1.73121e97i	0.177768	+	0.189851i
$931$	2.95484e97			0.312748
$932$		−	2.74710e98i		−	2.80640i
$933$	1.35325e97	−	1.26712e97i	0.133440	−	0.124946i
$934$	1.09084e98			1.03828
$935$			1.31659e98i			1.20967i
$936$	4.31944e97	+	2.84266e96i	0.383111	+	0.0252128i
$937$	1.00504e98			0.860555			0.430278	−	0.902697i	$-0.358416\pi$
$937$	1.00504e98			0.860555			0.430278	+	0.902697i	$0.358416\pi$
$938$			1.32806e98i			1.09780i
$939$	−1.18274e96	−	1.26313e96i	−0.00943896	−	0.0100806i
$940$	−1.12540e98			−0.867135
$941$			2.28849e98i			1.70252i	0.524744	+	0.851260i	$0.324161\pi$
$941$			2.28849e98i			1.70252i	−0.524744	+	0.851260i	$0.675839\pi$
$942$	−2.40876e98	+	2.25545e98i	−1.73027	+	1.62014i
$943$	4.69980e97			0.325982
$944$			3.08146e98i			2.06386i
$945$	5.74792e97	+	7.00957e97i	0.371759	+	0.453358i
$946$	2.71703e98			1.69702
$947$		−	3.30383e98i		−	1.99282i	−0.0846364	−	0.996412i	$-0.526973\pi$
$947$		−	3.30383e98i		−	1.99282i	0.0846364	−	0.996412i	$-0.473027\pi$
$948$	−1.35006e98	−	1.44183e98i	−0.786465	−	0.839924i
$949$	−2.94110e97			−0.165472
$950$		−	8.35159e97i		−	0.453827i
$951$	1.38259e98	−	1.29459e98i	0.725666	−	0.679479i
$952$	−5.79601e98			−2.93839
$953$		−	1.66316e98i		−	0.814457i	−0.913326	−	0.407229i	$-0.866495\pi$
$953$		−	1.66316e98i		−	0.814457i	0.913326	−	0.407229i	$-0.133505\pi$
$954$	−2.55706e97	+	3.88547e98i	−0.120961	+	1.83801i
$955$	−4.00292e97			−0.182922
$956$			4.16778e98i			1.83990i
$957$	1.04723e98	+	1.11841e98i	0.446630	+	0.476989i
$958$	−4.09835e98			−1.68868
$959$		−	2.02364e98i		−	0.805600i
$960$	7.64556e98	−	7.15894e98i	2.94075	−	2.75358i
$961$	−2.61800e98			−0.972968
$962$			8.42611e97i			0.302587i
$963$	1.12345e98	+	7.39351e96i	0.389840	+	0.0256557i
$964$	1.41662e98			0.475019
$965$		−	1.94023e98i		−	0.628713i
$966$	−3.40372e98	−	3.63509e98i	−1.06588	−	1.13833i
$967$	−3.71629e98			−1.12470			−0.562349	−	0.826900i	$-0.690102\pi$
$967$	−3.71629e98			−1.12470			−0.562349	+	0.826900i	$0.690102\pi$
$968$			9.89473e98i			2.89412i
$969$	−1.91284e98	+	1.79109e98i	−0.540748	+	0.506330i
$970$	−3.82569e98			−1.04530
$971$		−	6.23720e98i		−	1.64723i	−0.567147	−	0.823617i	$-0.691953\pi$
$971$		−	6.23720e98i		−	1.64723i	0.567147	−	0.823617i	$-0.308047\pi$
$972$	−6.48539e98	−	9.06309e98i	−1.65558	−	2.31361i
$973$	4.13530e98			1.02043
$974$			1.48438e99i			3.54078i
$975$	−1.09842e97	−	1.17308e97i	−0.0253288	−	0.0270505i
$976$	2.58500e99			5.76257
$977$		−	5.03535e98i		−	1.08520i	−0.839992	−	0.542599i	$-0.817440\pi$
$977$		−	5.03535e98i		−	1.08520i	0.839992	−	0.542599i	$-0.182560\pi$
$978$	1.13881e98	−	1.06633e98i	0.237285	−	0.222182i
$979$	−3.31257e98			−0.667324
$980$		−	5.55982e98i		−	1.08293i
$981$	−4.55675e97	+	6.92401e98i	−0.0858179	+	1.30401i
$982$	8.70565e98			1.58534
$983$		−	4.87316e97i		−	0.0858113i	−0.999079	−	0.0429057i	$-0.986339\pi$
$983$		−	4.87316e97i		−	0.0858113i	0.999079	−	0.0429057i	$-0.0136615\pi$
$984$	4.32564e98	+	4.61967e98i	0.736567	+	0.786634i
$985$	−1.33782e98			−0.220294
$986$		−	6.70283e98i		−	1.06738i
$987$	−1.30145e98	+	1.21861e98i	−0.200429	+	0.187672i
$988$	1.34365e98			0.200128
$989$		−	4.90037e98i		−	0.705913i
$990$	−1.51997e99	−	1.00031e98i	−2.11775	−	0.139371i
$991$	7.03821e98			0.948487			0.474244	−	0.880394i	$-0.342722\pi$
$991$	7.03821e98			0.948487			0.474244	+	0.880394i	$0.342722\pi$
$992$		−	5.94529e98i		−	0.774976i
$993$	2.83271e98	+	3.02526e98i	0.357171	+	0.381450i
$994$	1.15578e99			1.40970
$995$			9.69551e98i			1.14396i
$996$	−2.70054e99	+	2.52866e99i	−3.08242	+	2.88623i
$997$	−3.49568e97			−0.0386003			−0.0193002	−	0.999814i	$-0.506144\pi$
$997$	−3.49568e97			−0.0386003			−0.0193002	+	0.999814i	$0.506144\pi$
$998$		−	3.40844e99i		−	3.64123i
$999$	1.08783e99	−	8.92029e98i	1.12434	−	0.921973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.67.b.b.2.20	yes	20
3.2	odd	2	inner	3.67.b.b.2.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.67.b.b.2.1	✓	20	3.2	odd	2	inner
3.67.b.b.2.20	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.68436e10i q^{2} +(-3.79959e15 - 4.05786e15i) q^{3} -2.09920e20 q^{4} -9.39164e22i q^{5} +(6.83490e25 - 6.39988e25i) q^{6} -5.61847e27 q^{7} -2.29297e30i q^{8} +(-2.02937e30 + 3.08364e31i) q^{9} +O(q^{10})\)	\(q+1.68436e10i q^{2} +(-3.79959e15 - 4.05786e15i) q^{3} -2.09920e20 q^{4} -9.39164e22i q^{5} +(6.83490e25 - 6.39988e25i) q^{6} -5.61847e27 q^{7} -2.29297e30i q^{8} +(-2.02937e30 + 3.08364e31i) q^{9} +1.58189e33 q^{10} +3.11598e34i q^{11} +(7.97610e35 + 8.51826e35i) q^{12} +6.10892e35 q^{13} -9.46352e37i q^{14} +(-3.81100e38 + 3.56844e38i) q^{15} +2.31325e40 q^{16} +4.49897e40i q^{17} +(-5.19397e41 - 3.41819e40i) q^{18} -1.04778e42 q^{19} +1.97149e43i q^{20} +(2.13479e43 + 2.27990e43i) q^{21} -5.24843e44 q^{22} +9.46595e44i q^{23} +(-9.30455e45 + 8.71234e45i) q^{24} +4.73223e45 q^{25} +1.02896e46i q^{26} +(1.32841e47 - 1.08931e47i) q^{27} +1.17943e48 q^{28} +8.84525e47i q^{29} +(-6.01054e48 - 6.41910e48i) q^{30} -2.69697e48 q^{31} +2.20443e50i q^{32} +(1.26442e50 - 1.18394e50i) q^{33} -7.57789e50 q^{34} +5.27667e50i q^{35} +(4.26005e50 - 6.47318e51i) q^{36} +8.18894e51 q^{37} -1.76483e52i q^{38} +(-2.32114e51 - 2.47892e51i) q^{39} -2.15347e53 q^{40} -4.96496e52i q^{41} +(-3.84017e53 + 3.59575e53i) q^{42} -5.17684e53 q^{43} -6.54106e54i q^{44} +(2.89605e54 + 1.90591e53i) q^{45} -1.59441e55 q^{46} +5.70835e54i q^{47} +(-8.78940e55 - 9.38685e55i) q^{48} -2.82011e55 q^{49} +7.97078e55i q^{50} +(1.82562e56 - 1.70942e56i) q^{51} -1.28238e56 q^{52} -7.48074e56i q^{53} +(1.83479e57 + 2.23752e57i) q^{54} +2.92642e57 q^{55} +1.28830e58i q^{56} +(3.98112e57 + 4.25173e57i) q^{57} -1.48986e58 q^{58} +1.33209e58i q^{59} +(8.00005e58 - 7.49087e58i) q^{60} +1.11747e59 q^{61} -4.54267e58i q^{62} +(1.14020e58 - 1.73254e59i) q^{63} -2.00618e60 q^{64} -5.73728e58i q^{65} +(1.99419e60 + 2.12974e60i) q^{66} -1.40334e60 q^{67} -9.44423e60i q^{68} +(3.84116e60 - 3.59667e60i) q^{69} -8.88780e60 q^{70} +1.22130e61i q^{71} +(7.07070e61 + 4.65328e60i) q^{72} -4.81444e61 q^{73} +1.37931e62i q^{74} +(-1.79805e61 - 1.92027e61i) q^{75} +2.19949e62 q^{76} -1.75070e62i q^{77} +(4.17539e61 - 3.90964e61i) q^{78} -1.69264e62 q^{79} -2.17252e63i q^{80} +(-9.46768e62 - 1.25157e62i) q^{81} +8.36277e62 q^{82} +3.17029e63i q^{83} +(-4.48135e63 - 4.78596e63i) q^{84} +4.22527e63 q^{85} -8.71966e63i q^{86} +(3.58928e63 - 3.36083e63i) q^{87} +7.14484e64 q^{88} +1.06309e64i q^{89} +(-3.21024e63 + 4.87799e64i) q^{90} -3.43228e63 q^{91} -1.98709e65i q^{92} +(1.02474e64 + 1.09439e64i) q^{93} -9.61491e64 q^{94} +9.84034e64i q^{95} +(8.94529e65 - 8.37594e65i) q^{96} -2.41843e65 q^{97} -4.75008e65i q^{98} +(-9.60857e65 - 6.32348e64i) 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

Related objects

Downloads

Learn more