LMFDB - Embedded newform 3.67.b.b.2.3

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			2.3
Root			$-3.58413e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.67.b.b.2.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29029e10i q^{2} +(-3.61968e15 - 4.21913e15i) q^{3} -9.26974e19 q^{4} -1.27679e23i q^{5} +(-5.44390e25 + 4.67043e25i) q^{6} +1.78063e27 q^{7} +2.43999e29i q^{8} +(-4.69903e30 + 3.05438e31i) q^{9} +O(q^{10})$	\(q-1.29029e10i q^{2} +(-3.61968e15 - 4.21913e15i) q^{3} -9.26974e19 q^{4} -1.27679e23i q^{5} +(-5.44390e25 + 4.67043e25i) q^{6} +1.78063e27 q^{7} +2.43999e29i q^{8} +(-4.69903e30 + 3.05438e31i) q^{9} -1.64743e33 q^{10} -3.95474e34i q^{11} +(3.35535e35 + 3.91103e35i) q^{12} -6.77923e36 q^{13} -2.29752e37i q^{14} +(-5.38696e38 + 4.62158e38i) q^{15} -3.69157e39 q^{16} +3.35654e40i q^{17} +(3.94103e41 + 6.06310e40i) q^{18} +8.39894e41 q^{19} +1.18355e43i q^{20} +(-6.44529e42 - 7.51270e42i) q^{21} -5.10275e44 q^{22} +1.17555e45i q^{23} +(1.02946e45 - 8.83198e44i) q^{24} -2.74946e45 q^{25} +8.74716e46i q^{26} +(1.45877e47 - 9.07329e46i) q^{27} -1.65059e47 q^{28} -9.23296e47i q^{29} +(5.96317e48 + 6.95073e48i) q^{30} -5.89213e48 q^{31} +6.56358e49i q^{32} +(-1.66856e50 + 1.43149e50i) q^{33} +4.33091e50 q^{34} -2.27349e50i q^{35} +(4.35588e50 - 2.83133e51i) q^{36} -5.07361e50 q^{37} -1.08371e52i q^{38} +(2.45386e52 + 2.86025e52i) q^{39} +3.11536e52 q^{40} +2.10575e53i q^{41} +(-9.69355e52 + 8.31628e52i) q^{42} +1.23727e54 q^{43} +3.66594e54i q^{44} +(3.89981e54 + 5.99968e53i) q^{45} +1.51680e55 q^{46} +1.13848e55i q^{47} +(1.33623e55 + 1.55752e55i) q^{48} -5.65976e55 q^{49} +3.54759e55i q^{50} +(1.41617e56 - 1.21496e56i) q^{51} +6.28417e56 q^{52} +8.31529e56i q^{53} +(-1.17072e57 - 1.88224e57i) q^{54} -5.04938e57 q^{55} +4.34471e56i q^{56} +(-3.04015e57 - 3.54363e57i) q^{57} -1.19132e58 q^{58} -2.93045e58i q^{59} +(4.99357e58 - 4.28408e58i) q^{60} -7.77396e58 q^{61} +7.60254e58i q^{62} +(-8.36721e57 + 5.43871e58i) q^{63} +5.74502e59 q^{64} +8.65566e59i q^{65} +(1.84703e60 + 2.15292e60i) q^{66} -2.37580e60 q^{67} -3.11143e60i q^{68} +(4.95981e60 - 4.25511e60i) q^{69} -2.93346e60 q^{70} -1.49523e61i q^{71} +(-7.45266e60 - 1.14656e60i) q^{72} -3.45775e61 q^{73} +6.54642e60i q^{74} +(9.95215e60 + 1.16003e61i) q^{75} -7.78560e61 q^{76} -7.04190e61i q^{77} +(3.69054e62 - 3.16619e62i) q^{78} +5.34762e62 q^{79} +4.71337e62i q^{80} +(-9.10843e62 - 2.87052e62i) q^{81} +2.71702e63 q^{82} -1.52749e62i q^{83} +(5.97462e62 + 6.96408e62i) q^{84} +4.28561e63 q^{85} -1.59643e64i q^{86} +(-3.89551e63 + 3.34203e63i) q^{87} +9.64952e63 q^{88} -1.34336e64i q^{89} +(7.74132e63 - 5.03188e64i) q^{90} -1.20713e64 q^{91} -1.08971e65i q^{92} +(2.13276e64 + 2.48597e64i) q^{93} +1.46897e65 q^{94} -1.07237e65i q^{95} +(2.76926e65 - 2.37581e65i) q^{96} +3.59974e65 q^{97} +7.30273e65i q^{98} +(1.20793e66 + 1.85834e65i) 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 $

$2$		−	1.29029e10i		−	1.50209i	−0.660249	−	0.751047i	$-0.729549\pi$
$2$		−	1.29029e10i		−	1.50209i	0.660249	−	0.751047i	$-0.270451\pi$
$3$	−3.61968e15	−	4.21913e15i	−0.651131	−	0.758965i
$3$	−3.61968e15	−	4.21913e15i	−0.651131	−	0.758965i
$4$	−9.26974e19			−1.25628
$5$		−	1.27679e23i		−	1.09676i	−0.836231	−	0.548378i	$-0.815245\pi$
$5$		−	1.27679e23i		−	1.09676i	0.836231	−	0.548378i	$-0.184755\pi$
$6$	−5.44390e25	+	4.67043e25i	−1.14004	+	0.978060i
$7$	1.78063e27			0.230323			0.115162	−	0.993347i	$-0.463261\pi$
$7$	1.78063e27			0.230323			0.115162	+	0.993347i	$0.463261\pi$
$8$			2.43999e29i			0.384963i
$9$	−4.69903e30	+	3.05438e31i	−0.152057	+	0.988372i
$10$	−1.64743e33			−1.64743
$11$		−	3.95474e34i		−	1.70278i	−0.524532	−	0.851390i	$-0.675760\pi$
$11$		−	3.95474e34i		−	1.70278i	0.524532	−	0.851390i	$-0.324240\pi$
$12$	3.35535e35	+	3.91103e35i	0.818006	+	0.953476i
$13$	−6.77923e36			−1.17774			−0.588870	−	0.808228i	$-0.700427\pi$
$13$	−6.77923e36			−1.17774			−0.588870	+	0.808228i	$0.700427\pi$
$14$		−	2.29752e37i		−	0.345967i
$15$	−5.38696e38	+	4.62158e38i	−0.832400	+	0.714132i
$16$	−3.69157e39			−0.678034
$17$			3.35654e40i			0.833830i	0.908945	+	0.416915i	$0.136889\pi$
$17$			3.35654e40i			0.833830i	−0.908945	+	0.416915i	$0.863111\pi$
$18$	3.94103e41	+	6.06310e40i	1.48463	+	0.228403i
$19$	8.39894e41			0.531320			0.265660	−	0.964067i	$-0.414410\pi$
$19$	8.39894e41			0.531320			0.265660	+	0.964067i	$0.414410\pi$
$20$			1.18355e43i			1.37784i
$21$	−6.44529e42	−	7.51270e42i	−0.149970	−	0.174807i
$22$	−5.10275e44			−2.55774
$23$			1.17555e45i			1.35901i	0.733671	+	0.679505i	$0.237806\pi$
$23$			1.17555e45i			1.35901i	−0.733671	+	0.679505i	$0.762194\pi$
$24$	1.02946e45	−	8.83198e44i	0.292173	−	0.250661i
$25$	−2.74946e45			−0.202874
$26$			8.74716e46i			1.76908i
$27$	1.45877e47	−	9.07329e46i	0.849149	−	0.528154i
$28$	−1.65059e47			−0.289351
$29$		−	9.23296e47i		−	0.508402i	−0.967151	−	0.254201i	$-0.918188\pi$
$29$		−	9.23296e47i		−	0.508402i	0.967151	−	0.254201i	$-0.0818125\pi$
$30$	5.96317e48	+	6.95073e48i	1.07269	+	1.25034i
$31$	−5.89213e48			−0.359200			−0.179600	−	0.983740i	$-0.557480\pi$
$31$	−5.89213e48			−0.359200			−0.179600	+	0.983740i	$0.557480\pi$
$32$			6.56358e49i			1.40343i
$33$	−1.66856e50	+	1.43149e50i	−1.29235	+	1.10873i
$34$	4.33091e50			1.25249
$35$		−	2.27349e50i		−	0.252608i
$36$	4.35588e50	−	2.83133e51i	0.191026	−	1.24168i
$37$	−5.07361e50			−0.0900866			−0.0450433	−	0.998985i	$-0.514343\pi$
$37$	−5.07361e50			−0.0900866			−0.0450433	+	0.998985i	$0.514343\pi$
$38$		−	1.08371e52i		−	0.798091i
$39$	2.45386e52	+	2.86025e52i	0.766863	+	0.893864i
$40$	3.11536e52			0.422210
$41$			2.10575e53i			1.26339i	0.775215	+	0.631697i	$0.217641\pi$
$41$			2.10575e53i			1.26339i	−0.775215	+	0.631697i	$0.782359\pi$
$42$	−9.69355e52	+	8.31628e52i	−0.262577	+	0.225270i
$43$	1.23727e54			1.54172			0.770858	−	0.637007i	$-0.219828\pi$
$43$	1.23727e54			1.54172			0.770858	+	0.637007i	$0.219828\pi$
$44$			3.66594e54i			2.13918i
$45$	3.89981e54	+	5.99968e53i	1.08400	+	0.166769i
$46$	1.51680e55			2.04136
$47$			1.13848e55i			0.753525i	0.926310	+	0.376762i	$0.122963\pi$
$47$			1.13848e55i			0.753525i	−0.926310	+	0.376762i	$0.877037\pi$
$48$	1.33623e55	+	1.55752e55i	0.441489	+	0.514604i
$49$	−5.65976e55			−0.946951
$50$			3.54759e55i			0.304736i
$51$	1.41617e56	−	1.21496e56i	0.632848	−	0.542933i
$52$	6.28417e56			1.47958
$53$			8.31529e56i			1.04418i	0.852892	+	0.522088i	$0.174847\pi$
$53$			8.31529e56i			1.04418i	−0.852892	+	0.522088i	$0.825153\pi$
$54$	−1.17072e57	−	1.88224e57i	−0.793336	−	1.27550i
$55$	−5.04938e57			−1.86754
$56$			4.34471e56i			0.0886658i
$57$	−3.04015e57	−	3.54363e57i	−0.345959	−	0.403253i
$58$	−1.19132e58			−0.763667
$59$		−	2.93045e58i		−	1.06861i	−0.845292	−	0.534304i	$-0.820574\pi$
$59$		−	2.93045e58i		−	1.06861i	0.845292	−	0.534304i	$-0.179426\pi$
$60$	4.99357e58	−	4.28408e58i	1.04573	−	0.897153i
$61$	−7.77396e58			−0.943535			−0.471767	−	0.881723i	$-0.656384\pi$
$61$	−7.77396e58			−0.943535			−0.471767	+	0.881723i	$0.656384\pi$
$62$			7.60254e58i			0.539552i
$63$	−8.36721e57	+	5.43871e58i	−0.0350221	+	0.227645i
$64$	5.74502e59			1.43005
$65$			8.65566e59i			1.29169i
$66$	1.84703e60	+	2.15292e60i	1.66542	+	1.94123i
$67$	−2.37580e60			−1.30419			−0.652096	−	0.758137i	$-0.726110\pi$
$67$	−2.37580e60			−1.30419			−0.652096	+	0.758137i	$0.726110\pi$
$68$		−	3.11143e60i		−	1.04753i
$69$	4.95981e60	−	4.25511e60i	1.03144	−	0.884894i
$70$	−2.93346e60			−0.379441
$71$		−	1.49523e61i		−	1.21111i	−0.795804	−	0.605555i	$-0.792951\pi$
$71$		−	1.49523e61i		−	1.21111i	0.795804	−	0.605555i	$-0.207049\pi$
$72$	−7.45266e60	−	1.14656e60i	−0.380486	−	0.0585361i
$73$	−3.45775e61			−1.11980			−0.559898	−	0.828561i	$-0.689160\pi$
$73$	−3.45775e61			−1.11980			−0.559898	+	0.828561i	$0.689160\pi$
$74$			6.54642e60i			0.135319i
$75$	9.95215e60	+	1.16003e61i	0.132098	+	0.153974i
$76$	−7.78560e61			−0.667488
$77$		−	7.04190e61i		−	0.392190i
$78$	3.69054e62	−	3.16619e62i	1.34267	−	1.15190i
$79$	5.34762e62			1.27781			0.638906	−	0.769285i	$-0.279387\pi$
$79$	5.34762e62			1.27781			0.638906	+	0.769285i	$0.279387\pi$
$80$			4.71337e62i			0.743638i
$81$	−9.10843e62	−	2.87052e62i	−0.953758	−	0.300577i
$82$	2.71702e63			1.89774
$83$		−	1.52749e62i		−	0.0715158i	−0.999360	−	0.0357579i	$-0.988615\pi$
$83$		−	1.52749e62i		−	0.0715158i	0.999360	−	0.0357579i	$-0.0113845\pi$
$84$	5.97462e62	+	6.96408e62i	0.188406	+	0.219607i
$85$	4.28561e63			0.914509
$86$		−	1.59643e64i		−	2.31580i
$87$	−3.89551e63	+	3.34203e63i	−0.385859	+	0.331036i
$88$	9.64952e63			0.655507
$89$		−	1.34336e64i		−	0.628526i	−0.949336	−	0.314263i	$-0.898243\pi$
$89$		−	1.34336e64i		−	0.628526i	0.949336	−	0.314263i	$-0.101757\pi$
$90$	7.74132e63	−	5.03188e64i	0.250503	−	1.62827i
$91$	−1.20713e64			−0.271261
$92$		−	1.08971e65i		−	1.70730i
$93$	2.13276e64	+	2.48597e64i	0.233886	+	0.272620i
$94$	1.46897e65			1.13186
$95$		−	1.07237e65i		−	0.582728i
$96$	2.76926e65	−	2.37581e65i	1.06516	−	0.913819i
$97$	3.59974e65			0.983567			0.491783	−	0.870718i	$-0.336345\pi$
$97$	3.59974e65			0.983567			0.491783	+	0.870718i	$0.336345\pi$
$98$			7.30273e65i			1.42241i
$99$	1.20793e66	+	1.85834e65i	1.68298	+	0.258919i
$100$	2.54868e65			0.254868
$101$		−	9.55256e65i		−	0.687883i	−0.938991	−	0.343941i	$-0.888238\pi$
$101$		−	9.55256e65i		−	0.687883i	0.938991	−	0.343941i	$-0.111762\pi$
$102$	−1.56765e66	−	1.82727e66i	−0.815536	−	0.950597i
$103$	−5.22788e66			−1.97105			−0.985524	−	0.169534i	$-0.945774\pi$
$103$	−5.22788e66			−1.97105			−0.985524	+	0.169534i	$0.945774\pi$
$104$		−	1.65413e66i		−	0.453386i
$105$	−9.59215e65	+	8.22930e65i	−0.191721	+	0.164481i
$106$	1.07291e67			1.56845
$107$		−	1.41556e67i		−	1.51798i	−0.651105	−	0.758988i	$-0.725694\pi$
$107$		−	1.41556e67i		−	1.51798i	0.651105	−	0.758988i	$-0.274306\pi$
$108$	−1.35225e67	+	8.41070e66i	−1.06677	+	0.663511i
$109$	−2.00798e67			−1.16865			−0.584326	−	0.811519i	$-0.698641\pi$
$109$	−2.00798e67			−1.16865			−0.584326	+	0.811519i	$0.698641\pi$
$110$			6.51515e67i			2.80521i
$111$	1.83648e66	+	2.14062e66i	0.0586582	+	0.0683726i
$112$	−6.57330e66			−0.156167
$113$			7.43791e67i			1.31784i	0.752213	+	0.658920i	$0.228986\pi$
$113$			7.43791e67i			1.31784i	−0.752213	+	0.658920i	$0.771014\pi$
$114$	−4.57230e67	+	3.92266e67i	−0.605724	+	0.519662i
$115$	1.50093e68			1.49050
$116$			8.55872e67i			0.638697i
$117$	3.18558e67	−	2.07063e68i	0.179083	−	1.16405i
$118$	−3.78113e68			−1.60515
$119$			5.97675e67i			0.192050i
$120$	−1.12766e68	−	1.31441e68i	−0.274914	−	0.320443i
$121$	−1.02459e69			−1.89946
$122$			1.00307e69i			1.41728i
$123$	8.88443e68	−	7.62213e68i	0.958873	−	0.822636i
$124$	5.46185e68			0.451257
$125$		−	1.37933e69i		−	0.874253i
$126$	7.01750e68	+	1.07961e68i	0.341944	+	0.0526065i
$127$	2.10830e69			0.791423			0.395712	−	0.918375i	$-0.370498\pi$
$127$	2.10830e69			0.791423			0.395712	+	0.918375i	$0.370498\pi$
$128$		−	2.56966e69i		−	0.744641i
$129$	−4.47851e69	−	5.22020e69i	−1.00386	−	1.17011i
$130$	1.11683e70			1.94024
$131$			1.07828e70i			1.45472i	0.686256	+	0.727361i	$0.259253\pi$
$131$			1.07828e70i			1.45472i	−0.686256	+	0.727361i	$0.740747\pi$
$132$	1.54671e70	−	1.32695e70i	1.62356	−	1.39288i
$133$	1.49554e69			0.122375
$134$			3.06547e70i			1.95902i
$135$	−1.15847e70	−	1.86255e70i	−0.579256	−	0.931309i
$136$	−8.18993e69			−0.320994
$137$		−	2.21903e70i		−	0.682944i	−0.939892	−	0.341472i	$-0.889075\pi$
$137$		−	2.21903e70i		−	0.682944i	0.939892	−	0.341472i	$-0.110925\pi$
$138$	−5.49032e70	−	6.39958e70i	−1.32919	−	1.54932i
$139$	4.42603e70			0.844357			0.422179	−	0.906513i	$-0.361266\pi$
$139$	4.42603e70			0.844357			0.422179	+	0.906513i	$0.361266\pi$
$140$			2.10747e70i			0.317348i
$141$	4.80342e70	−	4.12094e70i	0.571899	−	0.490643i
$142$	−1.92928e71			−1.81920
$143$			2.68100e71i			2.00543i
$144$	1.73468e70	−	1.12755e71i	0.103100	−	0.670150i
$145$	−1.17886e71			−0.557593
$146$			4.46149e71i			1.68204i
$147$	2.04865e71	+	2.38793e71i	0.616589	+	0.718703i
$148$	4.70311e70			0.113174
$149$			3.42827e71i			0.660584i	0.943879	+	0.330292i	$0.107147\pi$
$149$			3.42827e71i			0.660584i	−0.943879	+	0.330292i	$0.892853\pi$
$150$	1.49678e71	−	1.28411e71i	0.231284	−	0.198423i
$151$	1.79057e71			0.222204			0.111102	−	0.993809i	$-0.464562\pi$
$151$	1.79057e71			0.222204			0.111102	+	0.993809i	$0.464562\pi$
$152$			2.04933e71i			0.204538i
$153$	−1.02522e72	−	1.57725e71i	−0.824134	−	0.126789i
$154$	−9.08608e71			−0.589105
$155$			7.52302e71i			0.393955i
$156$	−2.27467e72	−	2.65137e72i	−0.963398	−	1.12295i
$157$	−1.01701e72			−0.348849			−0.174425	−	0.984671i	$-0.555807\pi$
$157$	−1.01701e72			−0.348849			−0.174425	+	0.984671i	$0.555807\pi$
$158$		−	6.89998e72i		−	1.91939i
$159$	3.50833e72	−	3.00987e72i	0.792494	−	0.679896i
$160$	8.38033e72			1.53922
$161$			2.09322e72i			0.313011i
$162$	−3.70380e72	+	1.17525e73i	−0.451495	+	1.43263i
$163$	9.72133e72			0.967241			0.483621	−	0.875278i	$-0.339321\pi$
$163$	9.72133e72			0.967241			0.483621	+	0.875278i	$0.339321\pi$
$164$		−	1.95197e73i		−	1.58718i
$165$	1.82771e73	+	2.13040e73i	1.21601	+	1.41739i
$166$	−1.97091e72			−0.107423
$167$		−	4.42826e72i		−	0.197965i	−0.995089	−	0.0989827i	$-0.968441\pi$
$167$		−	4.42826e72i		−	0.197965i	0.995089	−	0.0989827i	$-0.0315588\pi$
$168$	1.83309e72	−	1.57265e72i	0.0672942	−	0.0577330i
$169$	1.28249e73			0.387072
$170$		−	5.52967e73i		−	1.37368i
$171$	−3.94669e72	+	2.56536e73i	−0.0807906	+	0.525141i
$172$	−1.14691e74			−1.93683
$173$		−	8.37700e73i		−	1.16833i	−0.811633	−	0.584167i	$-0.801421\pi$
$173$		−	8.37700e73i		−	1.16833i	0.811633	−	0.584167i	$-0.198579\pi$
$174$	4.31219e73	+	5.02633e73i	0.497247	+	0.579597i
$175$	−4.89575e72			−0.0467266
$176$			1.45992e74i			1.15454i
$177$	−1.23640e74	+	1.06073e74i	−0.811037	+	0.695804i
$178$	−1.73333e74			−0.944105
$179$			1.22928e74i			0.556547i	0.960502	+	0.278273i	$0.0897621\pi$
$179$			1.22928e74i			0.556547i	−0.960502	+	0.278273i	$0.910238\pi$
$180$	−3.61502e74	−	5.56155e73i	−1.36182	−	0.209509i
$181$	4.83616e74			1.51743			0.758713	−	0.651425i	$-0.225829\pi$
$181$	4.83616e74			1.51743			0.758713	+	0.651425i	$0.225829\pi$
$182$			1.55754e74i			0.407459i
$183$	2.81392e74	+	3.27994e74i	0.614365	+	0.716110i
$184$	−2.86833e74			−0.523168
$185$			6.47795e73i			0.0988031i
$186$	3.20761e74	−	2.75187e74i	0.409501	−	0.351319i
$187$	1.32742e75			1.41983
$188$		−	1.05535e75i		−	0.946641i
$189$	2.59753e74	−	1.61561e74i	0.195578	−	0.121646i
$190$	−1.38367e75			−0.875312
$191$			3.03699e75i			1.61563i	0.589435	+	0.807816i	$0.299350\pi$
$191$			3.03699e75i			1.61563i	−0.589435	+	0.807816i	$0.700650\pi$
$192$	−2.07951e75	−	2.42390e75i	−0.931152	−	1.08536i
$193$	−2.26866e75			−0.855811			−0.427906	−	0.903823i	$-0.640748\pi$
$193$	−2.26866e75			−0.855811			−0.427906	+	0.903823i	$0.640748\pi$
$194$		−	4.64470e75i		−	1.47741i
$195$	3.65194e75	−	3.13307e75i	0.980351	−	0.841062i
$196$	5.24645e75			1.18964
$197$			7.37614e75i			1.41398i	0.707222	+	0.706991i	$0.249948\pi$
$197$			7.37614e75i			1.41398i	−0.707222	+	0.706991i	$0.750052\pi$
$198$	2.39780e75	−	1.55857e76i	0.388921	−	2.52799i
$199$	9.82935e74			0.135012			0.0675062	−	0.997719i	$-0.478496\pi$
$199$	9.82935e74			0.135012			0.0675062	+	0.997719i	$0.478496\pi$
$200$		−	6.70865e74i		−	0.0780990i
$201$	8.59963e75	+	1.00238e76i	0.849200	+	0.989836i
$202$	−1.23256e76			−1.03326
$203$		−	1.64405e75i		−	0.117097i
$204$	−1.31275e76	+	1.12624e76i	−0.795037	+	0.682078i
$205$	2.68860e76			1.38564
$206$			6.74547e76i			2.96070i
$207$	−3.59058e76	−	5.52395e75i	−1.34321	−	0.206647i
$208$	2.50260e76			0.798548
$209$		−	3.32156e76i		−	0.904721i
$210$	1.06182e76	+	1.23766e76i	0.247066	+	0.287983i
$211$	−3.65676e76			−0.727404			−0.363702	−	0.931515i	$-0.618487\pi$
$211$	−3.65676e76			−0.727404			−0.363702	+	0.931515i	$0.618487\pi$
$212$		−	7.70806e76i		−	1.31178i
$213$	−6.30859e76	+	5.41226e76i	−0.919190	+	0.788591i
$214$	−1.82649e77			−2.28014
$215$		−	1.57973e77i		−	1.69089i
$216$	2.21387e76	+	3.55940e76i	0.203320	+	0.326891i
$217$	−1.04917e76			−0.0827320
$218$			2.59088e77i			1.75543i
$219$	1.25159e77	+	1.45887e77i	0.729134	+	0.849887i
$220$	4.68064e77			2.34616
$221$		−	2.27548e77i		−	0.982036i
$222$	2.76202e76	−	2.36959e76i	0.102702	−	0.0881101i
$223$	−2.68892e77			−0.862021			−0.431010	−	0.902347i	$-0.641843\pi$
$223$	−2.68892e77			−0.862021			−0.431010	+	0.902347i	$0.641843\pi$
$224$			1.16873e77i			0.323243i
$225$	1.29198e76	−	8.39789e76i	0.0308483	−	0.200515i
$226$	9.59705e77			1.97952
$227$		−	5.82718e77i		−	1.03898i	−0.854478	−	0.519488i	$-0.826123\pi$
$227$		−	5.82718e77i		−	1.03898i	0.854478	−	0.519488i	$-0.173877\pi$
$228$	2.81814e77	+	3.28485e77i	0.434622	+	0.506600i
$229$	−6.54836e77			−0.874101			−0.437051	−	0.899437i	$-0.643977\pi$
$229$	−6.54836e77			−0.874101			−0.437051	+	0.899437i	$0.643977\pi$
$230$		−	1.93664e78i		−	2.23887i
$231$	−2.97107e77	+	2.54894e77i	−0.297658	+	0.255367i
$232$	2.25284e77			0.195716
$233$			1.29984e77i			0.0979814i	0.998799	+	0.0489907i	$0.0156005\pi$
$233$			1.29984e77i			0.0979814i	−0.998799	+	0.0489907i	$0.984400\pi$
$234$	−2.67171e78	−	4.11031e77i	−1.74850	−	0.269000i
$235$	1.45361e78			0.826433
$236$			2.71645e78i			1.34248i
$237$	−1.93567e78	−	2.25623e78i	−0.832023	−	0.969815i
$238$	7.71172e77			0.288477
$239$			2.12102e77i			0.0690897i	0.999403	+	0.0345449i	$0.0109982\pi$
$239$			2.12102e77i			0.0690897i	−0.999403	+	0.0345449i	$0.989002\pi$
$240$	1.98863e78	−	1.70609e78i	0.564396	−	0.484206i
$241$	−2.09723e78			−0.518901			−0.259450	−	0.965756i	$-0.583541\pi$
$241$	−2.09723e78			−0.518901			−0.259450	+	0.965756i	$0.583541\pi$
$242$			1.32201e79i			2.85317i
$243$	2.08585e78	+	4.88201e78i	0.392894	+	0.919584i
$244$	7.20626e78			1.18535
$245$			7.22634e78i			1.03857i
$246$	−9.83474e78	−	1.14635e79i	−1.23568	−	1.44032i
$247$	−5.69383e78			−0.625756
$248$		−	1.43767e78i		−	0.138279i
$249$	−6.44470e77	+	5.52903e77i	−0.0542780	+	0.0465662i
$250$	−1.77973e79			−1.31321
$251$		−	3.48798e78i		−	0.225601i	−0.993618	−	0.112800i	$-0.964018\pi$
$251$		−	3.48798e78i		−	0.225601i	0.993618	−	0.112800i	$-0.0359821\pi$
$252$	7.75619e77	−	5.04154e78i	0.0439977	−	0.285987i
$253$	4.64899e79			2.31410
$254$		−	2.72031e79i		−	1.18879i
$255$	−1.55125e79	−	1.80816e79i	−0.595465	−	0.694080i
$256$	9.23474e78			0.311534
$257$			1.92460e79i			0.570883i	0.958396	+	0.285442i	$0.0921402\pi$
$257$			1.92460e79i			0.570883i	−0.958396	+	0.285442i	$0.907860\pi$
$258$	−6.73556e79	+	5.77857e79i	−1.75761	+	1.50789i
$259$	−9.03420e77			−0.0207490
$260$		−	8.02358e79i		−	1.62273i
$261$	2.82010e79	+	4.33860e78i	0.502490	+	0.0773059i
$262$	1.39130e80			2.18513
$263$		−	5.04659e79i		−	0.698969i	−0.936942	−	0.349485i	$-0.886357\pi$
$263$		−	5.04659e79i		−	0.698969i	0.936942	−	0.349485i	$-0.113643\pi$
$264$	−3.49281e79	−	4.07126e79i	−0.426821	−	0.497507i
$265$	1.06169e80			1.14521
$266$		−	1.92967e79i		−	0.183819i
$267$	−5.66783e79	+	4.86254e79i	−0.477030	+	0.409253i
$268$	2.20230e80			1.63844
$269$			1.28250e80i			0.843786i	0.906646	+	0.421893i	$0.138634\pi$
$269$			1.28250e80i			0.843786i	−0.906646	+	0.421893i	$0.861366\pi$
$270$	−2.40323e80	+	1.49476e80i	−1.39891	+	0.870097i
$271$	−1.13304e80			−0.583791			−0.291896	−	0.956450i	$-0.594286\pi$
$271$	−1.13304e80			−0.583791			−0.291896	+	0.956450i	$0.594286\pi$
$272$		−	1.23909e80i		−	0.565366i
$273$	4.36941e79	+	5.09303e79i	0.176626	+	0.205877i
$274$	−2.86319e80			−1.02585
$275$			1.08734e80i			0.345450i
$276$	−4.59761e80	+	3.94438e80i	−1.29578	+	1.11168i
$277$	−1.43294e80			−0.358424			−0.179212	−	0.983810i	$-0.557355\pi$
$277$	−1.43294e80			−0.358424			−0.179212	+	0.983810i	$0.557355\pi$
$278$		−	5.71086e80i		−	1.26830i
$279$	2.76873e79	−	1.79968e80i	0.0546187	−	0.355023i
$280$	5.54729e79			0.0972447
$281$			1.88275e80i			0.293416i	0.989180	+	0.146708i	$0.0468677\pi$
$281$			1.88275e80i			0.293416i	−0.989180	+	0.146708i	$0.953132\pi$
$282$	−5.31721e80	−	6.19779e80i	−0.736992	−	0.859046i
$283$	5.15940e80			0.636278			0.318139	−	0.948044i	$-0.396942\pi$
$283$	5.15940e80			0.636278			0.318139	+	0.948044i	$0.396942\pi$
$284$			1.38604e81i			1.52150i
$285$	−4.52447e80	+	3.88163e80i	−0.442270	+	0.379432i
$286$	3.45927e81			3.01235
$287$			3.74955e80i			0.290989i
$288$	−2.00477e81	−	3.08425e80i	−1.38711	−	0.213401i
$289$	4.93787e80			0.304727
$290$			1.52107e81i			0.837557i
$291$	−1.30299e81	−	1.51878e81i	−0.640431	−	0.746493i
$292$	3.20524e81			1.40678
$293$			3.40868e80i			0.133646i	0.997765	+	0.0668228i	$0.0212862\pi$
$293$			3.40868e80i			0.133646i	−0.997765	+	0.0668228i	$0.978714\pi$
$294$	3.08112e81	−	2.64335e81i	1.07956	−	0.926175i
$295$	−3.74158e81			−1.17200
$296$		−	1.23796e80i		−	0.0346800i
$297$	−3.58825e81	−	5.76906e81i	−0.899330	−	1.44591i
$298$	4.42345e81			0.992258
$299$		−	7.96933e81i		−	1.60056i
$300$	−9.22538e80	−	1.07532e81i	−0.165952	−	0.193436i
$301$	2.20311e81			0.355093
$302$		−	2.31035e81i		−	0.333771i
$303$	−4.03035e81	+	3.45772e81i	−0.522079	+	0.447902i
$304$	−3.10053e81			−0.360253
$305$			9.92573e81i			1.03483i
$306$	−2.03511e81	+	1.32282e82i	−0.190450	+	1.23793i
$307$	−1.24752e82			−1.04829			−0.524145	−	0.851629i	$-0.675615\pi$
$307$	−1.24752e82			−1.04829			−0.524145	+	0.851629i	$0.675615\pi$
$308$			6.52766e81i			0.492702i
$309$	1.89232e82	+	2.20571e82i	1.28341	+	1.49596i
$310$	9.70686e81			0.591757
$311$		−	1.27838e82i		−	0.700755i	−0.936609	−	0.350378i	$-0.886053\pi$
$311$		−	1.27838e82i		−	0.700755i	0.936609	−	0.350378i	$-0.113947\pi$
$312$	−6.97898e81	+	5.98740e81i	−0.344104	+	0.295214i
$313$	2.68669e82			1.19194			0.595971	−	0.803006i	$-0.296767\pi$
$313$	2.68669e82			1.19194			0.595971	+	0.803006i	$0.296767\pi$
$314$			1.31224e82i			0.524004i
$315$	6.94410e81	+	1.06832e81i	0.249671	+	0.0384107i
$316$	−4.95711e82			−1.60529
$317$			4.38282e81i			0.127879i	0.997954	+	0.0639393i	$0.0203664\pi$
$317$			4.38282e81i			0.127879i	−0.997954	+	0.0639393i	$0.979634\pi$
$318$	−3.88360e82	−	4.52676e82i	−1.02127	−	1.19040i
$319$	−3.65139e82			−0.865697
$320$		−	7.33520e82i		−	1.56842i
$321$	−5.97245e82	+	5.12388e82i	−1.15209	+	0.988401i
$322$	2.70085e82			0.470172
$323$			2.81914e82i			0.443030i
$324$	8.44328e82	+	2.66090e82i	1.19819	+	0.377610i
$325$	1.86392e82			0.238933
$326$		−	1.25433e83i		−	1.45289i
$327$	7.26825e82	+	8.47195e82i	0.760946	+	0.886967i
$328$	−5.13801e82			−0.486360
$329$			2.02721e82i			0.173554i
$330$	2.74883e83	−	2.35827e83i	2.12906	−	1.82656i
$331$	−2.86351e82			−0.200713			−0.100356	−	0.994952i	$-0.531998\pi$
$331$	−2.86351e82			−0.200713			−0.100356	+	0.994952i	$0.531998\pi$
$332$			1.41595e82i			0.0898442i
$333$	2.38410e81	−	1.54967e82i	0.0136983	−	0.0890391i
$334$	−5.71373e82			−0.297362
$335$			3.03340e83i			1.43038i
$336$	2.37932e82	+	2.77336e82i	0.101685	+	0.118525i
$337$	5.30976e82			0.205725			0.102863	−	0.994696i	$-0.467200\pi$
$337$	5.30976e82			0.205725			0.102863	+	0.994696i	$0.467200\pi$
$338$		−	1.65478e83i		−	0.581419i
$339$	3.13816e83	−	2.69228e83i	1.00019	−	0.858086i
$340$	−3.97265e83			−1.14888
$341$			2.33018e83i			0.611639i
$342$	3.31005e83	+	5.09236e82i	0.788811	+	0.121355i
$343$	−2.07204e83			−0.448428
$344$			3.01892e83i			0.593503i
$345$	−5.43290e83	−	6.33264e83i	−0.970513	−	1.13124i
$346$	−1.08087e84			−1.75495
$347$			7.01358e83i			1.03530i	0.855592	+	0.517651i	$0.173193\pi$
$347$			7.01358e83i			1.03530i	−0.855592	+	0.517651i	$0.826807\pi$
$348$	3.61104e83	−	3.09798e83i	0.484749	−	0.415876i
$349$	−1.14167e84			−1.39412			−0.697060	−	0.717013i	$-0.745509\pi$
$349$	−1.14167e84			−1.39412			−0.697060	+	0.717013i	$0.745509\pi$
$350$			6.31693e82i			0.0701877i
$351$	−9.88936e83	+	6.15099e83i	−1.00008	+	0.622028i
$352$	2.59572e84			2.38974
$353$		−	5.69448e82i		−	0.0477407i	−0.999715	−	0.0238703i	$-0.992401\pi$
$353$		−	5.69448e82i		−	0.0477407i	0.999715	−	0.0238703i	$-0.00759889\pi$
$354$	1.36865e84	+	1.59531e84i	1.04516	+	1.21825i
$355$	−1.90910e84			−1.32829
$356$			1.24526e84i			0.789608i
$357$	2.52167e83	−	2.16339e83i	0.145760	−	0.125050i
$358$	1.58613e84			0.835985
$359$		−	3.13306e84i		−	1.50610i	−0.657966	−	0.753048i	$-0.728583\pi$
$359$		−	3.13306e84i		−	1.50610i	0.657966	−	0.753048i	$-0.271417\pi$
$360$	−1.46392e83	+	9.51550e83i	−0.0641999	+	0.417301i
$361$	−1.79341e84			−0.717700
$362$		−	6.24004e84i		−	2.27931i
$363$	3.70867e84	+	4.32286e84i	1.23680	+	1.44163i
$364$	1.11898e84			0.340781
$365$			4.41483e84i			1.22814i
$366$	4.23207e84	−	3.63077e84i	1.07566	−	0.922833i
$367$	−1.13480e84			−0.263596			−0.131798	−	0.991277i	$-0.542075\pi$
$367$	−1.13480e84			−0.263596			−0.131798	+	0.991277i	$0.542075\pi$
$368$		−	4.33963e84i		−	0.921456i
$369$	−6.43175e84	−	9.89497e83i	−1.24870	−	0.192107i
$370$	8.35842e83			0.148411
$371$			1.48064e84i			0.240498i
$372$	−1.97701e84	−	2.30443e84i	−0.293827	−	0.342488i
$373$	3.11984e83			0.0424366			0.0212183	−	0.999775i	$-0.493245\pi$
$373$	3.11984e83			0.0424366			0.0212183	+	0.999775i	$0.493245\pi$
$374$		−	1.71276e85i		−	2.13272i
$375$	−5.81957e84	+	4.99272e84i	−0.663527	+	0.569253i
$376$	−2.77789e84			−0.290079
$377$			6.25924e84i			0.598765i
$378$	−2.08461e84	−	3.35156e84i	−0.182724	−	0.293777i
$379$	1.67902e85			1.34885			0.674424	−	0.738344i	$-0.264392\pi$
$379$	1.67902e85			1.34885			0.674424	+	0.738344i	$0.264392\pi$
$380$			9.94060e84i			0.732072i
$381$	−7.63135e84	−	8.89519e84i	−0.515320	−	0.600663i
$382$	3.91859e85			2.42683
$383$			2.69958e85i			1.53369i	0.641833	+	0.766844i	$0.278174\pi$
$383$			2.69958e85i			1.53369i	−0.641833	+	0.766844i	$0.721826\pi$
$384$	−1.08417e85	+	9.30134e84i	−0.565156	+	0.484859i
$385$	−8.99105e84			−0.430136
$386$			2.92722e85i			1.28551i
$387$	−5.81395e84	+	3.77909e85i	−0.234428	+	1.52379i
$388$	−3.33687e85			−1.23564
$389$			2.69994e85i			0.918368i	0.888341	+	0.459184i	$0.151858\pi$
$389$			2.69994e85i			0.918368i	−0.888341	+	0.459184i	$0.848142\pi$
$390$	−4.04257e85	−	4.71206e85i	−1.26335	−	1.47258i
$391$	−3.94579e85			−1.13318
$392$		−	1.38098e85i		−	0.364541i
$393$	4.54942e85	−	3.90303e85i	1.10408	−	0.947214i
$394$	9.51735e85			2.12393
$395$		−	6.82781e85i		−	1.40145i
$396$	−1.11972e86	−	1.72263e85i	−2.11430	−	0.325276i
$397$	−1.32289e85			−0.229846			−0.114923	−	0.993374i	$-0.536662\pi$
$397$	−1.32289e85			−0.229846			−0.114923	+	0.993374i	$0.536662\pi$
$398$		−	1.26827e85i		−	0.202801i
$399$	−5.41336e84	−	6.30987e84i	−0.0796822	−	0.0928785i
$400$	1.01498e85			0.137556
$401$			5.78348e85i			0.721813i	0.932602	+	0.360907i	$0.117533\pi$
$401$			5.78348e85i			0.721813i	−0.932602	+	0.360907i	$0.882467\pi$
$402$	1.29336e86	−	1.10960e86i	1.48683	−	1.27558i
$403$	3.99441e85			0.423044
$404$			8.85498e85i			0.864176i
$405$	−3.66506e85	+	1.16296e86i	−0.329660	+	1.04604i
$406$	−2.12129e85			−0.175890
$407$			2.00648e85i			0.153398i
$408$	2.96449e85	+	3.45544e85i	0.209009	+	0.243623i
$409$	1.56636e86			1.01864			0.509322	−	0.860576i	$-0.329896\pi$
$409$	1.56636e86			1.01864			0.509322	+	0.860576i	$0.329896\pi$
$410$		−	3.46907e86i		−	2.08135i
$411$	−9.36240e85	+	8.03218e85i	−0.518331	+	0.444686i
$412$	4.84611e86			2.47620
$413$		−	5.21804e85i		−	0.246125i
$414$	−7.12748e85	+	4.63288e86i	−0.310402	+	2.01762i
$415$	−1.95029e85			−0.0784354
$416$		−	4.44960e86i		−	1.65288i
$417$	−1.60208e86	−	1.86740e86i	−0.549787	−	0.640838i
$418$	−4.28577e86			−1.35897
$419$		−	1.19312e86i		−	0.349641i	−0.984600	−	0.174821i	$-0.944065\pi$
$419$		−	1.19312e86i		−	0.349641i	0.984600	−	0.174821i	$-0.0559345\pi$
$420$	8.89168e85	−	7.62834e85i	0.240856	−	0.206635i
$421$	−7.04583e86			−1.76450			−0.882252	−	0.470777i	$-0.843974\pi$
$421$	−7.04583e86			−1.76450			−0.882252	+	0.470777i	$0.843974\pi$
$422$			4.71828e86i			1.09263i
$423$	−3.47736e86	−	5.34977e85i	−0.744763	−	0.114578i
$424$	−2.02892e86			−0.401969
$425$		−	9.22867e85i		−	0.169163i
$426$	6.98338e86	+	8.13990e86i	1.18454	+	1.38071i
$427$	−1.38425e86			−0.217318
$428$			1.31219e87i			1.90701i
$429$	1.13115e87	−	9.70437e86i	1.52205	−	1.30580i
$430$	−2.03831e87			−2.53987
$431$		−	7.15154e85i		−	0.0825372i	−0.999148	−	0.0412686i	$-0.986860\pi$
$431$		−	7.15154e85i		−	0.0825372i	0.999148	−	0.0412686i	$-0.0131399\pi$
$432$	−5.38516e86	+	3.34947e86i	−0.575752	+	0.358106i
$433$	1.44028e87			1.42675			0.713374	−	0.700784i	$-0.247166\pi$
$433$	1.44028e87			1.42675			0.713374	+	0.700784i	$0.247166\pi$
$434$			1.35373e86i			0.124271i
$435$	4.26708e86	+	4.97376e86i	0.363066	+	0.423194i
$436$	1.86135e87			1.46816
$437$			9.87338e86i			0.722069i
$438$	1.88236e87	−	1.61492e87i	1.27661	−	1.09523i
$439$	−1.07291e87			−0.674895			−0.337447	−	0.941344i	$-0.609564\pi$
$439$	−1.07291e87			−0.674895			−0.337447	+	0.941344i	$0.609564\pi$
$440$		−	1.23204e87i		−	0.718932i
$441$	2.65954e86	−	1.72871e87i	0.143990	−	0.935940i
$442$	−2.93602e87			−1.47511
$443$		−	8.75385e86i		−	0.408203i	−0.978950	−	0.204102i	$-0.934573\pi$
$443$		−	8.75385e86i		−	0.408203i	0.978950	−	0.204102i	$-0.0654273\pi$
$444$	−1.70237e86	−	1.98430e86i	−0.0736914	−	0.0858954i
$445$	−1.71520e87			−0.689340
$446$			3.46949e87i			1.29484i
$447$	1.44643e87	−	1.24092e87i	0.501360	−	0.430127i
$448$	1.02297e87			0.329374
$449$		−	2.32768e87i		−	0.696296i	−0.937440	−	0.348148i	$-0.886811\pi$
$449$		−	2.32768e87i		−	0.696296i	0.937440	−	0.348148i	$-0.113189\pi$
$450$	−1.08357e87	−	1.66702e86i	−0.301192	−	0.0463371i
$451$	8.32767e87			2.15128
$452$		−	6.89475e87i		−	1.65558i
$453$	−6.48128e86	−	7.55465e86i	−0.144684	−	0.168645i
$454$	−7.51874e87			−1.56064
$455$			1.54125e87i			0.297507i
$456$	8.64642e86	−	7.41793e86i	0.155237	−	0.133181i
$457$	3.15899e87			0.527611			0.263806	−	0.964576i	$-0.415022\pi$
$457$	3.15899e87			0.527611			0.263806	+	0.964576i	$0.415022\pi$
$458$			8.44927e87i			1.31298i
$459$	3.04549e87	+	4.89644e87i	0.440391	+	0.708046i
$460$	−1.39133e88			−1.87250
$461$		−	2.08981e87i		−	0.261804i	−0.991395	−	0.130902i	$-0.958213\pi$
$461$		−	2.08981e87i		−	0.261804i	0.991395	−	0.130902i	$-0.0417873\pi$
$462$	3.28887e87	+	3.83354e87i	0.383585	+	0.447111i
$463$	3.18714e87			0.346121			0.173061	−	0.984911i	$-0.444634\pi$
$463$	3.18714e87			0.346121			0.173061	+	0.984911i	$0.444634\pi$
$464$			3.40841e87i			0.344714i
$465$	3.17406e87	−	2.72309e87i	0.298998	−	0.256516i
$466$	1.67716e87			0.147177
$467$			2.01827e88i			1.65015i	0.565026	+	0.825073i	$0.308866\pi$
$467$			2.01827e88i			1.65015i	−0.565026	+	0.825073i	$0.691134\pi$
$468$	−2.95295e87	+	1.91942e88i	−0.224979	+	1.46237i
$469$	−4.23041e87			−0.300385
$470$		−	1.87557e88i		−	1.24138i
$471$	3.68126e87	+	4.29091e87i	0.227147	+	0.264764i
$472$	7.15028e87			0.411374
$473$		−	4.89306e88i		−	2.62521i
$474$	−2.91119e88	+	2.49757e88i	−1.45675	+	1.24978i
$475$	−2.30925e87			−0.107791
$476$		−	5.54029e87i		−	0.241270i
$477$	−2.53981e88	−	3.90738e87i	−1.03203	−	0.158774i
$478$	2.73672e87			0.103779
$479$			1.71410e88i			0.606687i	0.952881	+	0.303344i	$0.0981030\pi$
$479$			1.71410e88i			0.606687i	−0.952881	+	0.303344i	$0.901897\pi$
$480$	−3.03341e88	−	3.53578e88i	−1.00224	−	1.16822i
$481$	3.43952e87			0.106099
$482$			2.70604e88i			0.779438i
$483$	8.83156e87	−	7.57677e87i	0.237565	−	0.203811i
$484$	9.49764e88			2.38627
$485$		−	4.59612e88i		−	1.07873i
$486$	6.29920e88	−	2.69134e88i	1.38130	−	0.590163i
$487$	9.23988e86			0.0189326			0.00946631	−	0.999955i	$-0.496987\pi$
$487$	9.23988e86			0.0189326			0.00946631	+	0.999955i	$0.496987\pi$
$488$		−	1.89684e88i		−	0.363226i
$489$	−3.51881e88	−	4.10156e88i	−0.629801	−	0.734103i
$490$	9.32406e88			1.56004
$491$			1.04493e89i			1.63455i	0.576245	+	0.817277i	$0.304517\pi$
$491$			1.04493e89i			1.63455i	−0.576245	+	0.817277i	$0.695483\pi$
$492$	−8.23564e88	+	7.06551e88i	−1.20462	+	1.03346i
$493$	3.09908e88			0.423921
$494$			7.34669e88i			0.939945i
$495$	2.37272e88	−	1.54227e89i	0.283971	−	1.84582i
$496$	2.17512e88			0.243550
$497$		−	2.66245e88i		−	0.278946i
$498$	7.13404e87	+	8.31551e87i	0.0699467	+	0.0815306i
$499$	−1.10945e89			−1.01810			−0.509048	−	0.860738i	$-0.670002\pi$
$499$	−1.10945e89			−1.01810			−0.509048	+	0.860738i	$0.670002\pi$
$500$			1.27860e89i			1.09831i
$501$	−1.86834e88	+	1.60289e88i	−0.150249	+	0.128901i
$502$	−4.50049e88			−0.338873
$503$			1.45114e89i			1.02321i	0.859220	+	0.511606i	$0.170949\pi$
$503$			1.45114e89i			1.02321i	−0.859220	+	0.511606i	$0.829051\pi$
$504$	−1.32704e88	−	2.04159e87i	−0.0876348	−	0.0134822i
$505$	−1.21966e89			−0.754440
$506$		−	5.99854e89i		−	3.47599i
$507$	−4.64219e88	−	5.41099e88i	−0.252035	−	0.293774i
$508$	−1.95434e89			−0.994253
$509$			2.96132e89i			1.41188i	0.708272	+	0.705940i	$0.249475\pi$
$509$			2.96132e89i			1.41188i	−0.708272	+	0.705940i	$0.750525\pi$
$510$	−2.33304e89	+	2.00156e89i	−1.04257	+	0.894444i
$511$	−6.15696e88			−0.257915
$512$		−	3.08762e89i		−	1.21259i
$513$	1.22522e89	−	7.62060e88i	0.451169	−	0.280618i
$514$	2.48329e89			0.857520
$515$			6.67492e89i			2.16176i
$516$	4.15146e89	+	4.83899e89i	1.26113	+	1.46999i
$517$	4.50240e89			1.28309
$518$			1.16567e88i			0.0311670i
$519$	−3.53437e89	+	3.03220e89i	−0.886725	+	0.760739i
$520$	−2.11197e89			−0.497254
$521$			3.23250e89i			0.714322i	0.934043	+	0.357161i	$0.116255\pi$
$521$			3.23250e89i			0.714322i	−0.934043	+	0.357161i	$0.883745\pi$
$522$	5.59804e88	−	3.63874e89i	0.116121	−	0.754787i
$523$	5.81978e89			1.13331			0.566657	−	0.823954i	$-0.308236\pi$
$523$	5.81978e89			1.13331			0.566657	+	0.823954i	$0.308236\pi$
$524$		−	9.99540e89i		−	1.82754i
$525$	1.77210e88	+	2.06558e88i	0.0304251	+	0.0354639i
$526$	−6.51155e89			−1.04992
$527$		−	1.97772e89i		−	0.299512i
$528$	6.15959e89	−	5.28443e89i	0.876259	−	0.751759i
$529$	−6.33686e89			−0.846910
$530$		−	1.36989e90i		−	1.72021i
$531$	8.95072e89	+	1.37703e89i	1.05618	+	0.162489i
$532$	−1.38632e89			−0.153738
$533$		−	1.42753e90i		−	1.48795i
$534$	6.27408e89	+	7.31314e89i	0.614736	+	0.716543i
$535$	−1.80738e90			−1.66485
$536$		−	5.79693e89i		−	0.502065i
$537$	5.18651e89	−	4.44961e89i	0.422400	−	0.362385i
$538$	1.65480e90			1.26745
$539$			2.23829e90i			1.61245i
$540$	1.07387e90	+	1.72654e90i	0.727710	+	1.16999i
$541$	−2.81679e90			−1.79575			−0.897873	−	0.440256i	$-0.854888\pi$
$541$	−2.81679e90			−1.79575			−0.897873	+	0.440256i	$0.854888\pi$
$542$			1.46194e90i			0.876909i
$543$	−1.75053e90	−	2.04044e90i	−0.988043	−	1.15167i
$544$	−2.20310e90			−1.17023
$545$			2.56378e90i			1.28173i
$546$	6.57148e89	−	5.63780e89i	0.309247	−	0.265309i
$547$	4.13407e90			1.83145			0.915727	−	0.401802i	$-0.131616\pi$
$547$	4.13407e90			1.83145			0.915727	+	0.401802i	$0.131616\pi$
$548$			2.05699e90i			0.857972i
$549$	3.65301e89	−	2.37446e90i	0.143471	−	0.932563i
$550$	1.40298e90			0.518898
$551$		−	7.75471e89i		−	0.270124i
$552$	1.03824e90	+	1.21019e90i	0.340651	+	0.397067i
$553$	9.52212e89			0.294309
$554$			1.84891e90i			0.538386i
$555$	2.73313e89	−	2.34481e89i	0.0749881	−	0.0643337i
$556$	−4.10282e90			−1.06075
$557$			4.32303e90i			1.05334i	0.850071	+	0.526668i	$0.176559\pi$
$557$			4.32303e90i			1.05334i	−0.850071	+	0.526668i	$0.823441\pi$
$558$	−2.32211e90	−	3.57246e89i	−0.533278	−	0.0820424i
$559$	−8.38772e90			−1.81574
$560$			8.39274e89i			0.171277i
$561$	−4.80484e90	−	5.60058e90i	−0.924496	−	1.07760i
$562$	2.42929e90			0.440738
$563$		−	3.78722e90i		−	0.647952i	−0.946065	−	0.323976i	$-0.894980\pi$
$563$		−	3.78722e90i		−	0.647952i	0.946065	−	0.323976i	$-0.105020\pi$
$564$	−4.45264e90	+	3.82001e90i	−0.718468	+	0.616388i
$565$	9.49667e90			1.44535
$566$		−	6.65711e90i		−	0.955749i
$567$	−1.62187e90	−	5.11133e89i	−0.219672	−	0.0692298i
$568$	3.64836e90			0.466232
$569$			7.35457e90i			0.886854i	0.896310	+	0.443427i	$0.146238\pi$
$569$			7.35457e90i			0.886854i	−0.896310	+	0.443427i	$0.853762\pi$
$570$	5.00843e90	+	5.83788e90i	0.569943	+	0.664331i
$571$	3.29694e90			0.354095			0.177048	−	0.984202i	$-0.443345\pi$
$571$	3.29694e90			0.354095			0.177048	+	0.984202i	$0.443345\pi$
$572$		−	2.48522e91i		−	2.51939i
$573$	1.28135e91	−	1.09929e91i	1.22621	−	1.05199i
$574$	4.83800e90			0.437092
$575$		−	3.23213e90i		−	0.275708i
$576$	−2.69960e90	+	1.75475e91i	−0.217449	+	1.41342i
$577$	−8.33796e90			−0.634246			−0.317123	−	0.948384i	$-0.602717\pi$
$577$	−8.33796e90			−0.634246			−0.317123	+	0.948384i	$0.602717\pi$
$578$		−	6.37127e90i		−	0.457728i
$579$	8.21181e90	+	9.57177e90i	0.557245	+	0.649531i
$580$	1.09277e91			0.700495
$581$		−	2.71989e89i		−	0.0164717i
$582$	−1.95966e91	+	1.68123e91i	−1.12130	+	0.961987i
$583$	3.28848e91			1.77800
$584$		−	8.43688e90i		−	0.431080i
$585$	−2.64377e91	−	4.06732e90i	−1.27667	−	0.196411i
$586$	4.39818e90			0.200748
$587$			7.28041e90i			0.314122i	0.987589	+	0.157061i	$0.0502020\pi$
$587$			7.28041e90i			0.314122i	−0.987589	+	0.157061i	$0.949798\pi$
$588$	−1.89905e91	−	2.21355e91i	−0.774612	−	0.902895i
$589$	−4.94876e90			−0.190850
$590$			4.82772e91i			1.76046i
$591$	3.11209e91	−	2.66993e91i	1.07316	−	0.920688i
$592$	1.87296e90			0.0610818
$593$			1.77089e90i			0.0546244i	0.999627	+	0.0273122i	$0.00869482\pi$
$593$			1.77089e90i			0.0546244i	−0.999627	+	0.0273122i	$0.991305\pi$
$594$	−7.44376e91	+	4.62987e91i	−2.17190	+	1.35088i
$595$	7.63106e90			0.210632
$596$		−	3.17791e91i		−	0.829881i
$597$	−3.55791e90	−	4.14714e90i	−0.0879107	−	0.102470i
$598$	−1.02827e92			−2.40419
$599$		−	6.17839e90i		−	0.136707i	−0.997661	−	0.0683534i	$-0.978225\pi$
$599$		−	6.17839e90i		−	0.136707i	0.997661	−	0.0683534i	$-0.0217745\pi$
$600$	−2.83047e90	+	2.42832e90i	−0.0592744	+	0.0508527i
$601$	8.27420e91			1.64009			0.820047	−	0.572297i	$-0.193947\pi$
$601$	8.27420e91			1.64009			0.820047	+	0.572297i	$0.193947\pi$
$602$		−	2.84265e91i		−	0.533382i
$603$	1.11640e91	−	7.25660e91i	0.198311	−	1.28903i
$604$	−1.65981e91			−0.279151
$605$			1.30818e92i			2.08325i
$606$	4.46145e91	+	5.20032e91i	0.672791	+	0.784212i
$607$	−7.85832e91			−1.12228			−0.561142	−	0.827719i	$-0.689638\pi$
$607$	−7.85832e91			−1.12228			−0.561142	+	0.827719i	$0.689638\pi$
$608$			5.51272e91i			0.745672i
$609$	−6.93645e90	+	5.95091e90i	−0.0888723	+	0.0762453i
$610$	1.28071e92			1.55441
$611$		−	7.71804e91i		−	0.887457i
$612$	9.50348e91	+	1.46207e91i	1.03535	+	0.159284i
$613$	7.52986e91			0.777305			0.388653	−	0.921384i	$-0.372941\pi$
$613$	7.52986e91			0.777305			0.388653	+	0.921384i	$0.372941\pi$
$614$			1.60966e92i			1.57463i
$615$	−9.73187e91	−	1.13436e92i	−0.902231	−	1.05165i
$616$	1.71822e91			0.150978
$617$		−	7.18163e91i		−	0.598153i	−0.954229	−	0.299077i	$-0.903321\pi$
$617$		−	7.18163e91i		−	0.598153i	0.954229	−	0.299077i	$-0.0966786\pi$
$618$	2.84601e92	−	2.44164e92i	2.24707	−	1.92780i
$619$	−1.67241e92			−1.25185			−0.625924	−	0.779884i	$-0.715278\pi$
$619$	−1.67241e92			−1.25185			−0.625924	+	0.779884i	$0.715278\pi$
$620$		−	6.97364e91i		−	0.494919i
$621$	1.06661e92	+	1.71486e92i	0.717767	+	1.15400i
$622$	−1.64948e92			−1.05260
$623$		−	2.39203e91i		−	0.144764i
$624$	−9.05860e91	−	1.05588e92i	−0.519960	−	0.606070i
$625$	−2.13374e92			−1.16172
$626$		−	3.46661e92i		−	1.79041i
$627$	−1.40141e92	+	1.20230e92i	−0.686652	+	0.589092i
$628$	9.42744e91			0.438254
$629$		−	1.70298e91i		−	0.0751170i
$630$	1.37844e91	−	8.95989e91i	0.0576965	−	0.375029i
$631$	3.98549e91			0.158312			0.0791559	−	0.996862i	$-0.474778\pi$
$631$	3.98549e91			0.158312			0.0791559	+	0.996862i	$0.474778\pi$
$632$			1.30482e92i			0.491910i
$633$	1.32363e92	+	1.54284e92i	0.473636	+	0.552075i
$634$	5.65510e91			0.192085
$635$		−	2.69186e92i		−	0.867999i
$636$	−3.25213e92	+	2.79007e92i	−0.995597	+	0.854142i
$637$	3.83688e92			1.11526
$638$			4.71135e92i			1.30036i
$639$	4.56701e92	+	7.02614e91i	1.19703	+	0.184157i
$640$	−3.28092e92			−0.816689
$641$		−	1.48472e92i		−	0.351019i	−0.984478	−	0.175509i	$-0.943843\pi$
$641$		−	1.48472e92i		−	0.351019i	0.984478	−	0.175509i	$-0.0561572\pi$
$642$	6.61129e92	+	7.70619e92i	1.48467	+	1.73055i
$643$	−6.69417e92			−1.42802			−0.714011	−	0.700135i	$-0.753123\pi$
$643$	−6.69417e92			−1.42802			−0.714011	+	0.700135i	$0.753123\pi$
$644$		−	1.94036e92i		−	0.393231i
$645$	−6.66511e92	+	5.71812e92i	−1.28332	+	1.10099i
$646$	3.63750e92			0.665473
$647$			5.47780e92i			0.952280i	0.879369	+	0.476140i	$0.157964\pi$
$647$			5.47780e92i			0.952280i	−0.879369	+	0.476140i	$0.842036\pi$
$648$	7.00405e91	−	2.22245e92i	0.115711	−	0.367161i
$649$	−1.15892e93			−1.81961
$650$		−	2.40499e92i		−	0.358900i
$651$	3.79765e91	+	4.42658e91i	0.0538694	+	0.0627907i
$652$	−9.01142e92			−1.21513
$653$			7.06380e91i			0.0905531i	0.998974	+	0.0452766i	$0.0144169\pi$
$653$			7.06380e91i			0.0905531i	−0.998974	+	0.0452766i	$0.985583\pi$
$654$	1.09313e93	−	9.37814e92i	1.33231	−	1.14301i
$655$	1.37674e93			1.59547
$656$		−	7.77351e92i		−	0.856625i
$657$	1.62481e92	−	1.05613e93i	0.170272	−	1.10678i
$658$	2.61569e92			0.260694
$659$			2.02698e92i			0.192145i	0.995374	+	0.0960727i	$0.0306281\pi$
$659$			2.02698e92i			0.192145i	−0.995374	+	0.0960727i	$0.969372\pi$
$660$	−1.69424e93	−	1.97482e93i	−1.52765	−	1.78065i
$661$	−2.57863e92			−0.221178			−0.110589	−	0.993866i	$-0.535274\pi$
$661$	−2.57863e92			−0.221178			−0.110589	+	0.993866i	$0.535274\pi$
$662$			3.69476e92i			0.301489i
$663$	−9.60054e92	+	8.23649e92i	−0.745331	+	0.639434i
$664$	3.72707e91			0.0275309
$665$		−	1.90949e92i		−	0.134216i
$666$	−1.99953e92	−	3.07618e91i	−0.133745	−	0.0205761i
$667$	1.08538e93			0.690924
$668$			4.10488e92i			0.248701i
$669$	9.73303e92	+	1.13449e93i	0.561289	+	0.654244i
$670$	3.91396e93			2.14856
$671$			3.07440e93i			1.60663i
$672$	4.93102e92	−	4.23042e92i	0.245330	−	0.210474i
$673$	2.67058e93			1.26505			0.632527	−	0.774538i	$-0.282018\pi$
$673$	2.67058e93			1.26505			0.632527	+	0.774538i	$0.282018\pi$
$674$		−	6.85112e92i		−	0.309019i
$675$	−4.01084e92	+	2.49466e92i	−0.172270	+	0.107149i
$676$	−1.18883e93			−0.486273
$677$		−	1.89710e93i		−	0.739033i	−0.929224	−	0.369517i	$-0.879523\pi$
$677$		−	1.89710e93i		−	0.739033i	0.929224	−	0.369517i	$-0.120477\pi$
$678$	−3.47382e93	−	4.04912e93i	−1.28893	−	1.50239i
$679$	6.40979e92			0.226538
$680$			1.04568e93i			0.352052i
$681$	−2.45857e93	+	2.10925e93i	−0.788546	+	0.676509i
$682$	3.00660e93			0.918738
$683$		−	1.64032e93i		−	0.477578i	−0.971071	−	0.238789i	$-0.923250\pi$
$683$		−	1.64032e93i		−	0.477578i	0.971071	−	0.238789i	$-0.0767505\pi$
$684$	3.65848e92	−	2.37802e93i	0.101496	−	0.659727i
$685$	−2.83324e93			−0.749023
$686$			2.67353e93i			0.673580i
$687$	2.37030e93	+	2.76284e93i	0.569155	+	0.663413i
$688$	−4.56746e93			−1.04534
$689$		−	5.63713e93i		−	1.22977i
$690$	−8.17093e93	+	7.01000e93i	−1.69923	+	1.45780i
$691$	−6.74466e93			−1.33716			−0.668582	−	0.743639i	$-0.733098\pi$
$691$	−6.74466e93			−1.33716			−0.668582	+	0.743639i	$0.733098\pi$
$692$			7.76527e93i			1.46776i
$693$	2.15087e93	+	3.30901e92i	0.387629	+	0.0596350i
$694$	9.04953e93			1.55512
$695$		−	5.65112e93i		−	0.926054i
$696$	−8.15454e92	−	9.50501e92i	−0.127437	−	0.148541i
$697$	−7.06803e93			−1.05346
$698$			1.47308e94i			2.09410i
$699$	5.48419e92	−	4.70499e92i	0.0743645	−	0.0637987i
$700$	4.53824e92			0.0587019
$701$		−	1.17558e94i		−	1.45063i	−0.688416	−	0.725316i	$-0.741694\pi$
$701$		−	1.17558e94i		−	1.45063i	0.688416	−	0.725316i	$-0.258306\pi$
$702$	7.93655e93	+	1.27601e94i	0.934344	+	1.50221i
$703$	−4.26130e92			−0.0478648
$704$		−	2.27200e94i		−	2.43507i
$705$	−5.26159e93	−	6.13296e93i	−0.538116	−	0.627234i
$706$	−7.34752e92			−0.0717110
$707$		−	1.70095e93i		−	0.158435i
$708$	1.14611e94	−	9.83269e93i	1.01889	−	0.874128i
$709$	2.18006e94			1.84988			0.924940	−	0.380113i	$-0.124115\pi$
$709$	2.18006e94			1.84988			0.924940	+	0.380113i	$0.124115\pi$
$710$			2.46329e94i			1.99522i
$711$	−2.51286e93	+	1.63337e94i	−0.194300	+	1.26295i
$712$	3.27780e93			0.241959
$713$		−	6.92649e93i		−	0.488156i
$714$	−2.79140e93	−	3.25368e93i	−0.187837	−	0.218944i
$715$	3.42309e94			2.19947
$716$		−	1.13951e94i		−	0.699181i
$717$	8.94886e92	−	7.67740e92i	0.0524367	−	0.0449865i
$718$	−4.04255e94			−2.26230
$719$		−	2.80118e94i		−	1.49723i	−0.663006	−	0.748614i	$-0.730720\pi$
$719$		−	2.80118e94i		−	1.49723i	0.663006	−	0.748614i	$-0.269280\pi$
$720$	−1.43964e94	−	2.21482e93i	−0.734991	−	0.113075i
$721$	−9.30890e93			−0.453978
$722$			2.31402e94i			1.07805i
$723$	7.59131e93	+	8.84851e93i	0.337872	+	0.393828i
$724$	−4.48299e94			−1.90632
$725$			2.53856e93i			0.103142i
$726$	5.57774e94	−	4.78525e94i	2.16546	−	1.85779i
$727$	−4.10642e94			−1.52345			−0.761725	−	0.647901i	$-0.775647\pi$
$727$	−4.10642e94			−1.52345			−0.761725	+	0.647901i	$0.775647\pi$
$728$		−	2.94538e93i		−	0.104425i
$729$	1.30478e94	−	2.64718e94i	0.442107	−	0.896962i
$730$	5.69640e94			1.84479
$731$			4.15294e94i			1.28553i
$732$	−2.60843e94	−	3.04042e94i	−0.771817	−	0.899638i
$733$	2.28498e94			0.646325			0.323162	−	0.946344i	$-0.395254\pi$
$733$	2.28498e94			0.646325			0.323162	+	0.946344i	$0.395254\pi$
$734$			1.46422e94i			0.395946i
$735$	3.04889e94	−	2.61570e94i	0.788242	−	0.676248i
$736$	−7.71583e94			−1.90728
$737$			9.39566e94i			2.22075i
$738$	−1.27674e94	+	8.29882e94i	−0.288563	+	1.87567i
$739$	−5.48994e94			−1.18659			−0.593295	−	0.804985i	$-0.702173\pi$
$739$	−5.48994e94			−1.18659			−0.593295	+	0.804985i	$0.702173\pi$
$740$		−	6.00489e93i		−	0.124125i
$741$	2.06098e94	+	2.40230e94i	0.407449	+	0.474927i
$742$	1.91046e94			0.361250
$743$		−	1.08690e91i		−	0.000196589i	−1.00000		9.82945e-5i	$-0.999969\pi$
$743$		−	1.08690e91i		−	0.000196589i	1.00000		9.82945e-5i	$-3.12881e-5\pi$
$744$	−6.06574e93	+	5.20391e93i	−0.104949	+	0.0900375i
$745$	4.37718e94			0.724499
$746$		−	4.02549e93i		−	0.0637437i
$747$	4.66554e93	+	7.17773e92i	0.0706842	+	0.0108744i
$748$	−1.23049e95			−1.78371
$749$		−	2.52059e94i		−	0.349625i
$750$	6.44205e94	+	7.50892e94i	0.855071	+	0.996680i
$751$	9.90024e94			1.25756			0.628779	−	0.777584i	$-0.283555\pi$
$751$	9.90024e94			1.25756			0.628779	+	0.777584i	$0.283555\pi$
$752$		−	4.20279e94i		−	0.510916i
$753$	−1.47162e94	+	1.26253e94i	−0.171223	+	0.146896i
$754$	8.07622e94			0.899402
$755$		−	2.28618e94i		−	0.243703i
$756$	−2.40784e94	+	1.49763e94i	−0.245702	+	0.152822i
$757$	−5.94144e94			−0.580401			−0.290200	−	0.956966i	$-0.593722\pi$
$757$	−5.94144e94			−0.580401			−0.290200	+	0.956966i	$0.593722\pi$
$758$		−	2.16643e95i		−	2.02610i
$759$	−1.68279e95	−	1.96147e95i	−1.50678	−	1.75632i
$760$	2.61657e94			0.224329
$761$		−	1.62197e94i		−	0.133153i	−0.997781	−	0.0665763i	$-0.978792\pi$
$761$		−	1.62197e94i		−	0.133153i	0.997781	−	0.0665763i	$-0.0212076\pi$
$762$	−1.14774e95	+	9.84665e94i	−0.902252	+	0.774059i
$763$	−3.57547e94			−0.269168
$764$		−	2.81521e95i		−	2.02969i
$765$	−2.01382e94	+	1.30899e95i	−0.139057	+	0.903875i
$766$	3.48324e95			2.30374
$767$			1.98662e95i			1.25854i
$768$	−3.34268e94	−	3.89626e94i	−0.202850	−	0.236444i
$769$	−1.43575e95			−0.834657			−0.417329	−	0.908756i	$-0.637034\pi$
$769$	−1.43575e95			−0.834657			−0.417329	+	0.908756i	$0.637034\pi$
$770$			1.16010e95i			0.646105i
$771$	8.12014e94	−	6.96643e94i	0.433280	−	0.371720i
$772$	2.10299e95			1.07514
$773$		−	1.99393e95i		−	0.976759i	−0.872631	−	0.488380i	$-0.837588\pi$
$773$		−	1.99393e95i		−	0.976759i	0.872631	−	0.488380i	$-0.162412\pi$
$774$	4.87611e95	+	7.50168e94i	2.28887	+	0.352133i
$775$	1.62001e94			0.0728723
$776$			8.78333e94i			0.378637i
$777$	3.27009e93	+	3.81165e93i	0.0135103	+	0.0157478i
$778$	3.48370e95			1.37947
$779$			1.76861e95i			0.671266i
$780$	−3.38525e95	+	2.90428e95i	−1.23160	+	1.05661i
$781$	−5.91325e95			−2.06225
$782$			5.09120e95i			1.70215i
$783$	−8.37733e94	−	1.34688e95i	−0.268514	−	0.431709i
$784$	2.08934e95			0.642065
$785$			1.29851e95i			0.382603i
$786$	−5.03604e95	−	5.87006e95i	−1.42280	−	1.65844i
$787$	3.16470e95			0.857367			0.428684	−	0.903455i	$-0.358977\pi$
$787$	3.16470e95			0.857367			0.428684	+	0.903455i	$0.358977\pi$
$788$		−	6.83750e95i		−	1.77636i
$789$	−2.12922e95	+	1.82670e95i	−0.530493	+	0.455120i
$790$	−8.80984e95			−2.10511
$791$			1.32441e95i			0.303529i
$792$	−4.53434e94	+	2.94733e95i	−0.0996742	+	0.647885i
$793$	5.27014e95			1.11124
$794$			1.70691e95i			0.345251i
$795$	−3.84298e95	−	4.47941e95i	−0.745680	−	0.869172i
$796$	−9.11156e94			−0.169614
$797$			3.46937e95i			0.619621i	0.950798	+	0.309811i	$0.100266\pi$
$797$			3.46937e95i			0.619621i	−0.950798	+	0.309811i	$0.899734\pi$
$798$	−8.14155e94	+	6.98480e94i	−0.139512	+	0.119690i
$799$	−3.82137e95			−0.628312
$800$		−	1.80463e95i		−	0.284720i
$801$	4.10315e95	+	6.31251e94i	0.621218	+	0.0955716i
$802$	7.46236e95			1.08423
$803$			1.36745e96i			1.90677i
$804$	−7.97163e95	−	9.29182e95i	−1.06684	−	1.24352i
$805$	2.67260e95			0.343297
$806$		−	5.15393e95i		−	0.635452i
$807$	5.41104e95	−	4.64224e95i	0.640405	−	0.549416i
$808$	2.33082e95			0.264809
$809$			1.02169e96i			1.11435i	0.830397	+	0.557173i	$0.188114\pi$
$809$			1.02169e96i			1.11435i	−0.830397	+	0.557173i	$0.811886\pi$
$810$	1.50055e96	+	4.72899e95i	1.57125	+	0.495179i
$811$	−4.24187e94			−0.0426451			−0.0213226	−	0.999773i	$-0.506788\pi$
$811$	−4.24187e94			−0.0426451			−0.0213226	+	0.999773i	$0.506788\pi$
$812$			1.52399e95i			0.147107i
$813$	4.10123e95	+	4.78044e95i	0.380125	+	0.443077i
$814$	2.58894e95			0.230418
$815$		−	1.24121e96i		−	1.06083i
$816$	−5.22789e95	+	4.48511e95i	−0.429093	+	0.368127i
$817$	1.03917e96			0.819144
$818$		−	2.02105e96i		−	1.53010i
$819$	5.67232e94	−	3.68702e95i	0.0412470	−	0.268106i
$820$	−2.49226e96			−1.74075
$821$		−	9.74293e95i		−	0.653680i	−0.945080	−	0.326840i	$-0.894016\pi$
$821$		−	9.74293e95i		−	0.653680i	0.945080	−	0.326840i	$-0.105984\pi$
$822$	1.03638e96	+	1.20802e96i	0.667960	+	0.778581i
$823$	2.23266e95			0.138238			0.0691190	−	0.997608i	$-0.477981\pi$
$823$	2.23266e95			0.138238			0.0691190	+	0.997608i	$0.477981\pi$
$824$		−	1.27560e96i		−	0.758780i
$825$	4.58762e95	−	3.93581e95i	0.262185	−	0.224933i
$826$	−6.73278e95			−0.369703
$827$		−	2.25485e96i		−	1.18969i	−0.803839	−	0.594847i	$-0.797213\pi$
$827$		−	2.25485e96i		−	1.18969i	0.803839	−	0.594847i	$-0.202787\pi$
$828$	3.32837e96	+	5.12056e95i	1.68745	+	0.259607i
$829$	−1.62128e96			−0.789874			−0.394937	−	0.918708i	$-0.629234\pi$
$829$	−1.62128e96			−0.789874			−0.394937	+	0.918708i	$0.629234\pi$
$830$			2.51644e95i			0.117817i
$831$	5.18680e95	+	6.04579e95i	0.233381	+	0.272031i
$832$	−3.89468e96			−1.68423
$833$		−	1.89972e96i		−	0.789597i
$834$	−2.40949e96	+	2.06715e96i	−0.962598	+	0.825832i
$835$	−5.65396e95			−0.217120
$836$			3.07900e96i			1.13659i
$837$	−8.59528e95	+	5.34610e95i	−0.305014	+	0.189713i
$838$	−1.53947e96			−0.525194
$839$			9.45464e95i			0.310099i	0.987907	+	0.155049i	$0.0495537\pi$
$839$			9.45464e95i			0.310099i	−0.987907	+	0.155049i	$0.950446\pi$
$840$	−2.00794e95	−	2.34048e95i	−0.0633191	−	0.0738054i
$841$	2.44565e96			0.741527
$842$			9.09115e96i			2.65045i
$843$	7.94356e95	−	6.81494e95i	0.222692	−	0.191052i
$844$	3.38973e96			0.913827
$845$		−	1.63747e96i		−	0.424524i
$846$	−6.90274e95	+	4.48680e96i	−0.172107	+	1.11870i
$847$	−1.82440e96			−0.437490
$848$		−	3.06965e96i		−	0.707987i
$849$	−1.86754e96	−	2.17682e96i	−0.414300	−	0.482913i
$850$	−1.19076e96			−0.254098
$851$		−	5.96429e95i		−	0.122429i
$852$	5.84790e96	−	5.01703e96i	1.15476	−	0.990694i
$853$	4.83038e96			0.917620			0.458810	−	0.888534i	$-0.348276\pi$
$853$	4.83038e96			0.917620			0.458810	+	0.888534i	$0.348276\pi$
$854$			1.78608e96i			0.326431i
$855$	3.27543e96	+	5.03910e95i	0.575952	+	0.0886076i
$856$	3.45396e96			0.584364
$857$			7.83213e95i			0.127501i	0.997966	+	0.0637504i	$0.0203062\pi$
$857$			7.83213e95i			0.127501i	−0.997966	+	0.0637504i	$0.979694\pi$
$858$	−1.25214e97	−	1.45951e97i	−1.96143	−	2.28627i
$859$	−7.72879e96			−1.16503			−0.582515	−	0.812820i	$-0.697931\pi$
$859$	−7.72879e96			−1.16503			−0.582515	+	0.812820i	$0.697931\pi$
$860$			1.46437e97i			2.12423i
$861$	1.58198e96	−	1.35722e96i	0.220850	−	0.189472i
$862$	−9.22755e95			−0.123979
$863$			1.09450e97i			1.41533i	0.706547	+	0.707666i	$0.250252\pi$
$863$			1.09450e97i			1.41533i	−0.706547	+	0.707666i	$0.749748\pi$
$864$	5.95533e96	+	9.57479e96i	0.741229	+	1.19172i
$865$	−1.06957e97			−1.28138
$866$		−	1.85838e97i		−	2.14311i
$867$	−1.78735e96	−	2.08335e96i	−0.198417	−	0.231277i
$868$	9.72551e95			0.103935
$869$		−	2.11484e97i		−	2.17583i
$870$	6.41758e96	−	5.50577e96i	0.635676	−	0.545359i
$871$	1.61061e97			1.53600
$872$		−	4.89946e96i		−	0.449888i
$873$	−1.69153e96	+	1.09950e97i	−0.149558	+	0.972130i
$874$	1.27395e97			1.08461
$875$		−	2.45607e96i		−	0.201361i
$876$	−1.16019e97	−	1.35234e97i	−0.916000	−	1.06770i
$877$	−1.81902e96			−0.138309			−0.0691547	−	0.997606i	$-0.522030\pi$
$877$	−1.81902e96			−0.138309			−0.0691547	+	0.997606i	$0.522030\pi$
$878$			1.38437e97i			1.01375i
$879$	1.43817e96	−	1.23383e96i	0.101432	−	0.0870208i
$880$	1.86401e97			1.26625
$881$		−	2.02750e97i		−	1.32665i	−0.748332	−	0.663324i	$-0.769145\pi$
$881$		−	2.02750e97i		−	1.32665i	0.748332	−	0.663324i	$-0.230855\pi$
$882$	−2.23053e97	−	3.43157e96i	−1.40587	−	0.216287i
$883$	7.46010e96			0.452941			0.226470	−	0.974018i	$-0.427281\pi$
$883$	7.46010e96			0.452941			0.226470	+	0.974018i	$0.427281\pi$
$884$			2.10931e97i			1.23372i
$885$	1.35433e97	+	1.57862e97i	0.763127	+	0.889509i
$886$	−1.12950e97			−0.613159
$887$			1.04679e97i			0.547494i	0.961802	+	0.273747i	$0.0882631\pi$
$887$			1.04679e97i			0.547494i	−0.961802	+	0.273747i	$0.911737\pi$
$888$	−5.22311e95	+	4.48100e95i	−0.0263209	+	0.0225812i
$889$	3.75409e96			0.182283
$890$			2.21310e97i			1.03545i
$891$	−1.13522e97	+	3.60214e97i	−0.511817	+	1.62404i
$892$	2.49256e97			1.08294
$893$			9.56206e96i			0.400362i
$894$	−1.60115e97	−	1.86631e97i	−0.646090	−	0.753090i
$895$	1.56954e97			0.610396
$896$		−	4.57560e96i		−	0.171508i
$897$	−3.36237e97	+	2.88464e97i	−1.21477	+	1.04218i
$898$	−3.00338e97			−1.04590
$899$			5.44018e96i			0.182618i
$900$	−1.19763e96	+	7.78463e96i	−0.0387543	+	0.251904i
$901$	−2.79106e97			−0.870666
$902$		−	1.07451e98i		−	3.23143i
$903$	−7.97455e96	−	9.29522e96i	−0.231212	−	0.269503i
$904$	−1.81484e97			−0.507319
$905$		−	6.17477e97i		−	1.66425i
$906$	−9.74767e96	+	8.36272e96i	−0.253321	+	0.217329i
$907$	−2.22303e97			−0.557063			−0.278531	−	0.960427i	$-0.589848\pi$
$907$	−2.22303e97			−0.557063			−0.278531	+	0.960427i	$0.589848\pi$
$908$			5.40164e97i			1.30525i
$909$	2.91772e97	+	4.48878e96i	0.679884	+	0.104597i
$910$	1.98866e97			0.446883
$911$			5.91339e97i			1.28153i	0.767735	+	0.640767i	$0.221384\pi$
$911$			5.91339e97i			1.28153i	−0.767735	+	0.640767i	$0.778616\pi$
$912$	1.12229e97	+	1.30815e97i	0.234572	+	0.273419i
$913$	−6.04083e96			−0.121776
$914$		−	4.07601e97i		−	0.792521i
$915$	4.18780e97	−	3.59280e97i	0.785398	−	0.673808i
$916$	6.07016e97			1.09812
$917$			1.92002e97i			0.335056i
$918$	6.31781e97	−	3.92956e97i	1.06355	−	0.661508i
$919$	−6.03412e97			−0.979947			−0.489973	−	0.871737i	$-0.662993\pi$
$919$	−6.03412e97			−0.979947			−0.489973	+	0.871737i	$0.662993\pi$
$920$			3.66227e97i			0.573788i
$921$	4.51563e97	+	5.26346e97i	0.682575	+	0.795616i
$922$	−2.69646e97			−0.393254
$923$			1.01365e98i			1.42637i
$924$	2.75411e97	−	2.36280e97i	0.373943	−	0.320813i
$925$	1.39497e96			0.0182762
$926$		−	4.11232e97i		−	0.519906i
$927$	2.45660e97	−	1.59679e98i	0.299711	−	1.94813i
$928$	6.06013e97			0.713508
$929$			6.37282e97i			0.724124i	0.932154	+	0.362062i	$0.117927\pi$
$929$			6.37282e97i			0.724124i	−0.932154	+	0.362062i	$0.882073\pi$
$930$	−3.51357e97	−	4.09546e97i	−0.385311	−	0.449123i
$931$	−4.75360e97			−0.503134
$932$		−	1.20492e97i		−	0.123092i
$933$	−5.39365e97	+	4.62731e97i	−0.531849	+	0.456283i
$934$	2.60415e98			2.47867
$935$		−	1.69484e98i		−	1.55721i
$936$	5.05233e97	+	7.77278e96i	0.448114	+	0.0689404i
$937$	−5.48374e97			−0.469538			−0.234769	−	0.972051i	$-0.575433\pi$
$937$	−5.48374e97			−0.469538			−0.234769	+	0.972051i	$0.575433\pi$
$938$			5.45845e97i			0.451207i
$939$	−9.72496e97	−	1.13355e98i	−0.776110	−	0.904642i
$940$	−1.34746e98			−1.03823
$941$			4.15108e97i			0.308818i	0.988007	+	0.154409i	$0.0493474\pi$
$941$			4.15108e97i			0.308818i	−0.988007	+	0.154409i	$0.950653\pi$
$942$	5.53651e97	−	4.74988e97i	0.397701	−	0.341195i
$943$	−2.47541e98			−1.71697
$944$			1.08180e98i			0.724553i
$945$	−2.06280e97	−	3.31651e97i	−0.133416	−	0.214502i
$946$	−6.31346e98			−3.94330
$947$		−	1.95766e97i		−	0.118083i	−0.998256	−	0.0590415i	$-0.981196\pi$
$947$		−	1.95766e97i		−	0.118083i	0.998256	−	0.0590415i	$-0.0188044\pi$
$948$	1.79431e98	+	2.09147e98i	1.04526	+	1.21836i
$949$	2.34409e98			1.31883
$950$			2.97960e97i			0.161912i
$951$	1.84917e97	−	1.58644e97i	0.0970554	−	0.0832657i
$952$	−1.45832e97			−0.0739322
$953$		−	7.42853e97i		−	0.363779i	−0.983319	−	0.181889i	$-0.941779\pi$
$953$		−	7.42853e97i		−	0.363779i	0.983319	−	0.181889i	$-0.0582213\pi$
$954$	−5.04165e97	+	3.27708e98i	−0.238493	+	1.55021i
$955$	3.87761e98			1.77195
$956$		−	1.96613e97i		−	0.0867963i
$957$	1.32169e98	+	1.54057e98i	0.563682	+	0.657034i
$958$	2.21169e98			0.911301
$959$		−	3.95127e97i		−	0.157298i
$960$	−3.09482e98	+	2.65510e98i	−1.19038	+	1.02125i
$961$	−2.34357e98			−0.870976
$962$		−	4.43797e97i		−	0.159370i
$963$	4.32367e98	+	6.65177e97i	1.50032	+	0.230818i
$964$	1.94408e98			0.651887
$965$			2.89661e98i			0.938616i
$966$	−9.77621e97	−	1.13953e98i	−0.306144	−	0.356844i
$967$	−6.91536e96			−0.0209286			−0.0104643	−	0.999945i	$-0.503331\pi$
$967$	−6.91536e96			−0.0209286			−0.0104643	+	0.999945i	$0.503331\pi$
$968$		−	2.49998e98i		−	0.731222i
$969$	1.18943e98	−	1.02044e98i	0.336245	−	0.288471i
$970$	−5.93032e98			−1.62036
$971$		−	1.77252e98i		−	0.468119i	−0.972222	−	0.234059i	$-0.924799\pi$
$971$		−	1.77252e98i		−	0.468119i	0.972222	−	0.234059i	$-0.0752010\pi$
$972$	−1.93353e98	−	4.52549e98i	−0.493586	−	1.15526i
$973$	7.88111e97			0.194475
$974$		−	1.19221e97i		−	0.0284386i
$975$	−6.74679e97	−	7.86413e97i	−0.155577	−	0.181342i
$976$	2.86981e98			0.639749
$977$		−	6.75333e98i		−	1.45545i	−0.685869	−	0.727725i	$-0.740578\pi$
$977$		−	6.75333e98i		−	1.45545i	0.685869	−	0.727725i	$-0.259422\pi$
$978$	−5.29220e98	+	4.54028e98i	−1.10269	+	0.946020i
$979$	−5.31265e98			−1.07024
$980$		−	6.69863e98i		−	1.30474i
$981$	9.43557e97	−	6.13314e98i	0.177701	−	1.15506i
$982$	1.34826e99			2.45525
$983$			4.21083e98i			0.741483i	0.928736	+	0.370742i	$0.120896\pi$
$983$			4.21083e98i			0.741483i	−0.928736	+	0.370742i	$0.879104\pi$
$984$	1.85979e98	+	2.16779e98i	0.316684	+	0.369130i
$985$	9.41780e98			1.55079
$986$		−	3.99871e98i		−	0.636769i
$987$	8.55309e97	−	7.33786e97i	0.131722	−	0.113006i
$988$	5.27804e98			0.786128
$989$			1.45447e99i			2.09521i
$990$	−1.98997e99	−	3.06149e98i	−2.77259	−	0.426551i
$991$	3.23581e98			0.436066			0.218033	−	0.975941i	$-0.430036\pi$
$991$	3.23581e98			0.436066			0.218033	+	0.975941i	$0.430036\pi$
$992$		−	3.86735e98i		−	0.504113i
$993$	1.03650e98	+	1.20815e98i	0.130690	+	0.152334i
$994$	−3.43533e98			−0.419003
$995$		−	1.25500e98i		−	0.148076i
$996$	5.97407e97	−	5.12527e97i	0.0681886	−	0.0585003i
$997$	−1.11383e99			−1.22992			−0.614962	−	0.788557i	$-0.710829\pi$
$997$	−1.11383e99			−1.22992			−0.614962	+	0.788557i	$0.710829\pi$
$998$			1.43151e99i			1.52927i
$999$	−7.40125e97	+	4.60343e97i	−0.0764969	+	0.0475796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.67.b.b.2.3	✓	20
3.2	odd	2	inner	3.67.b.b.2.18	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.67.b.b.2.3	✓	20	1.1	even	1	trivial
3.67.b.b.2.18	yes	20	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.29029e10i q^{2} +(-3.61968e15 - 4.21913e15i) q^{3} -9.26974e19 q^{4} -1.27679e23i q^{5} +(-5.44390e25 + 4.67043e25i) q^{6} +1.78063e27 q^{7} +2.43999e29i q^{8} +(-4.69903e30 + 3.05438e31i) q^{9} +O(q^{10})\)	\(q-1.29029e10i q^{2} +(-3.61968e15 - 4.21913e15i) q^{3} -9.26974e19 q^{4} -1.27679e23i q^{5} +(-5.44390e25 + 4.67043e25i) q^{6} +1.78063e27 q^{7} +2.43999e29i q^{8} +(-4.69903e30 + 3.05438e31i) q^{9} -1.64743e33 q^{10} -3.95474e34i q^{11} +(3.35535e35 + 3.91103e35i) q^{12} -6.77923e36 q^{13} -2.29752e37i q^{14} +(-5.38696e38 + 4.62158e38i) q^{15} -3.69157e39 q^{16} +3.35654e40i q^{17} +(3.94103e41 + 6.06310e40i) q^{18} +8.39894e41 q^{19} +1.18355e43i q^{20} +(-6.44529e42 - 7.51270e42i) q^{21} -5.10275e44 q^{22} +1.17555e45i q^{23} +(1.02946e45 - 8.83198e44i) q^{24} -2.74946e45 q^{25} +8.74716e46i q^{26} +(1.45877e47 - 9.07329e46i) q^{27} -1.65059e47 q^{28} -9.23296e47i q^{29} +(5.96317e48 + 6.95073e48i) q^{30} -5.89213e48 q^{31} +6.56358e49i q^{32} +(-1.66856e50 + 1.43149e50i) q^{33} +4.33091e50 q^{34} -2.27349e50i q^{35} +(4.35588e50 - 2.83133e51i) q^{36} -5.07361e50 q^{37} -1.08371e52i q^{38} +(2.45386e52 + 2.86025e52i) q^{39} +3.11536e52 q^{40} +2.10575e53i q^{41} +(-9.69355e52 + 8.31628e52i) q^{42} +1.23727e54 q^{43} +3.66594e54i q^{44} +(3.89981e54 + 5.99968e53i) q^{45} +1.51680e55 q^{46} +1.13848e55i q^{47} +(1.33623e55 + 1.55752e55i) q^{48} -5.65976e55 q^{49} +3.54759e55i q^{50} +(1.41617e56 - 1.21496e56i) q^{51} +6.28417e56 q^{52} +8.31529e56i q^{53} +(-1.17072e57 - 1.88224e57i) q^{54} -5.04938e57 q^{55} +4.34471e56i q^{56} +(-3.04015e57 - 3.54363e57i) q^{57} -1.19132e58 q^{58} -2.93045e58i q^{59} +(4.99357e58 - 4.28408e58i) q^{60} -7.77396e58 q^{61} +7.60254e58i q^{62} +(-8.36721e57 + 5.43871e58i) q^{63} +5.74502e59 q^{64} +8.65566e59i q^{65} +(1.84703e60 + 2.15292e60i) q^{66} -2.37580e60 q^{67} -3.11143e60i q^{68} +(4.95981e60 - 4.25511e60i) q^{69} -2.93346e60 q^{70} -1.49523e61i q^{71} +(-7.45266e60 - 1.14656e60i) q^{72} -3.45775e61 q^{73} +6.54642e60i q^{74} +(9.95215e60 + 1.16003e61i) q^{75} -7.78560e61 q^{76} -7.04190e61i q^{77} +(3.69054e62 - 3.16619e62i) q^{78} +5.34762e62 q^{79} +4.71337e62i q^{80} +(-9.10843e62 - 2.87052e62i) q^{81} +2.71702e63 q^{82} -1.52749e62i q^{83} +(5.97462e62 + 6.96408e62i) q^{84} +4.28561e63 q^{85} -1.59643e64i q^{86} +(-3.89551e63 + 3.34203e63i) q^{87} +9.64952e63 q^{88} -1.34336e64i q^{89} +(7.74132e63 - 5.03188e64i) q^{90} -1.20713e64 q^{91} -1.08971e65i q^{92} +(2.13276e64 + 2.48597e64i) q^{93} +1.46897e65 q^{94} -1.07237e65i q^{95} +(2.76926e65 - 2.37581e65i) q^{96} +3.59974e65 q^{97} +7.30273e65i q^{98} +(1.20793e66 + 1.85834e65i) 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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