LMFDB - Embedded newform 3.67.b.b.2.15

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			2.15
Root			$2.56585e8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.67.b.b.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.23704e9i q^{2} +(-3.04579e15 - 4.65041e15i) q^{3} -1.15360e19 q^{4} +1.92130e23i q^{5} +(4.29561e25 - 2.81341e25i) q^{6} +2.12741e26 q^{7} +5.75015e29i q^{8} +(-1.23495e31 + 2.83283e31i) q^{9} +O(q^{10})$	\(q+9.23704e9i q^{2} +(-3.04579e15 - 4.65041e15i) q^{3} -1.15360e19 q^{4} +1.92130e23i q^{5} +(4.29561e25 - 2.81341e25i) q^{6} +2.12741e26 q^{7} +5.75015e29i q^{8} +(-1.23495e31 + 2.83283e31i) q^{9} -1.77471e33 q^{10} -2.81881e34i q^{11} +(3.51362e34 + 5.36471e34i) q^{12} +1.93603e36 q^{13} +1.96509e36i q^{14} +(8.93481e38 - 5.85186e38i) q^{15} -6.16265e39 q^{16} -3.10261e40i q^{17} +(-2.61670e41 - 1.14073e41i) q^{18} -2.58430e42 q^{19} -2.21641e42i q^{20} +(-6.47963e41 - 9.89331e41i) q^{21} +2.60375e44 q^{22} +1.28776e45i q^{23} +(2.67406e45 - 1.75137e45i) q^{24} -2.33612e46 q^{25} +1.78832e46i q^{26} +(1.69352e47 - 2.88519e46i) q^{27} -2.45418e45 q^{28} +1.79489e48i q^{29} +(5.40539e48 + 8.25312e48i) q^{30} +2.51287e48 q^{31} -1.44960e49i q^{32} +(-1.31086e50 + 8.58550e49i) q^{33} +2.86589e50 q^{34} +4.08737e49i q^{35} +(1.42464e50 - 3.26796e50i) q^{36} -3.69630e51 q^{37} -2.38713e52i q^{38} +(-5.89673e51 - 9.00333e51i) q^{39} -1.10477e53 q^{40} +3.71828e52i q^{41} +(9.13850e51 - 5.98526e51i) q^{42} +3.83181e53 q^{43} +3.25178e53i q^{44} +(-5.44271e54 - 2.37270e54i) q^{45} -1.18951e55 q^{46} -2.78104e55i q^{47} +(1.87701e55 + 2.86588e55i) q^{48} -5.97230e55 q^{49} -2.15789e56i q^{50} +(-1.44284e56 + 9.44989e55i) q^{51} -2.23340e55 q^{52} +2.47624e56i q^{53} +(2.66506e56 + 1.56432e57i) q^{54} +5.41577e57 q^{55} +1.22329e56i q^{56} +(7.87123e57 + 1.20180e58i) q^{57} -1.65795e58 q^{58} -4.29894e58i q^{59} +(-1.03072e58 + 6.75070e57i) q^{60} +6.76510e58 q^{61} +2.32115e58i q^{62} +(-2.62724e57 + 6.02659e57i) q^{63} -3.20823e59 q^{64} +3.71968e59i q^{65} +(-7.93047e59 - 1.21085e60i) q^{66} -1.21724e60 q^{67} +3.57917e59i q^{68} +(5.98862e60 - 3.92225e60i) q^{69} -3.77553e59 q^{70} +9.25851e60i q^{71} +(-1.62892e61 - 7.10114e60i) q^{72} +3.92715e61 q^{73} -3.41429e61i q^{74} +(7.11533e61 + 1.08639e62i) q^{75} +2.98125e61 q^{76} -5.99676e60i q^{77} +(8.31641e61 - 5.44684e61i) q^{78} -1.61159e62 q^{79} -1.18403e63i q^{80} +(-6.49985e62 - 6.99681e62i) q^{81} -3.43459e62 q^{82} -2.73065e63i q^{83} +(7.47490e60 + 1.14129e61i) q^{84} +5.96102e63 q^{85} +3.53946e63i q^{86} +(8.34699e63 - 5.46686e63i) q^{87} +1.62086e64 q^{88} -9.54368e63i q^{89} +(2.19168e64 - 5.02746e64i) q^{90} +4.11872e62 q^{91} -1.48556e64i q^{92} +(-7.65368e63 - 1.16859e64i) q^{93} +2.56886e65 q^{94} -4.96520e65i q^{95} +(-6.74124e64 + 4.41518e64i) q^{96} -5.23415e65 q^{97} -5.51664e65i q^{98} +(7.98523e65 + 3.48109e65i) 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 $

$2$			9.23704e9i			1.07533i	0.843157	+	0.537667i	$0.180694\pi$
$2$			9.23704e9i			1.07533i	−0.843157	+	0.537667i	$0.819306\pi$
$3$	−3.04579e15	−	4.65041e15i	−0.547896	−	0.836546i
$3$	−3.04579e15	−	4.65041e15i	−0.547896	−	0.836546i
$4$	−1.15360e19			−0.156342
$5$			1.92130e23i			1.65038i	0.564855	+	0.825190i	$0.308932\pi$
$5$			1.92130e23i			1.65038i	−0.564855	+	0.825190i	$0.691068\pi$
$6$	4.29561e25	−	2.81341e25i	0.899566	−	0.589171i
$7$	2.12741e26			0.0275179			0.0137589	−	0.999905i	$-0.495620\pi$
$7$	2.12741e26			0.0275179			0.0137589	+	0.999905i	$0.495620\pi$
$8$			5.75015e29i			0.907214i
$9$	−1.23495e31	+	2.83283e31i	−0.399619	+	0.916681i
$10$	−1.77471e33			−1.77471
$11$		−	2.81881e34i		−	1.21369i	−0.794821	−	0.606845i	$-0.792435\pi$
$11$		−	2.81881e34i		−	1.21369i	0.794821	−	0.606845i	$-0.207565\pi$
$12$	3.51362e34	+	5.36471e34i	0.0856592	+	0.130787i
$13$	1.93603e36			0.336342			0.168171	−	0.985758i	$-0.446214\pi$
$13$	1.93603e36			0.336342			0.168171	+	0.985758i	$0.446214\pi$
$14$			1.96509e36i			0.0295909i
$15$	8.93481e38	−	5.85186e38i	1.38062	−	0.904237i
$16$	−6.16265e39			−1.13190
$17$		−	3.10261e40i		−	0.770748i	−0.922760	−	0.385374i	$-0.874072\pi$
$17$		−	3.10261e40i		−	0.770748i	0.922760	−	0.385374i	$-0.125928\pi$
$18$	−2.61670e41	−	1.14073e41i	−0.985738	−	0.429724i
$19$	−2.58430e42			−1.63483			−0.817417	−	0.576046i	$-0.804595\pi$
$19$	−2.58430e42			−1.63483			−0.817417	+	0.576046i	$0.804595\pi$
$20$		−	2.21641e42i		−	0.258024i
$21$	−6.47963e41	−	9.89331e41i	−0.0150769	−	0.0230200i
$22$	2.60375e44			1.30512
$23$			1.28776e45i			1.48873i	0.667771	+	0.744367i	$0.267249\pi$
$23$			1.28776e45i			1.48873i	−0.667771	+	0.744367i	$0.732751\pi$
$24$	2.67406e45	−	1.75137e45i	0.758926	−	0.497059i
$25$	−2.33612e46			−1.72375
$26$			1.78832e46i			0.361680i
$27$	1.69352e47	−	2.88519e46i	0.985796	−	0.167946i
$28$	−2.45418e45			−0.00430220
$29$			1.79489e48i			0.988336i	0.869366	+	0.494168i	$0.164527\pi$
$29$			1.79489e48i			0.988336i	−0.869366	+	0.494168i	$0.835473\pi$
$30$	5.40539e48	+	8.25312e48i	0.972356	+	1.48463i
$31$	2.51287e48			0.153191			0.0765957	−	0.997062i	$-0.475595\pi$
$31$	2.51287e48			0.153191			0.0765957	+	0.997062i	$0.475595\pi$
$32$		−	1.44960e49i		−	0.309955i
$33$	−1.31086e50	+	8.58550e49i	−1.01531	+	0.664976i
$34$	2.86589e50			0.828811
$35$			4.08737e49i			0.0454150i
$36$	1.42464e50	−	3.26796e50i	0.0624773	−	0.143316i
$37$	−3.69630e51			−0.656312			−0.328156	−	0.944624i	$-0.606427\pi$
$37$	−3.69630e51			−0.656312			−0.328156	+	0.944624i	$0.606427\pi$
$38$		−	2.38713e52i		−	1.75799i
$39$	−5.89673e51	−	9.00333e51i	−0.184281	−	0.281366i
$40$	−1.10477e53			−1.49725
$41$			3.71828e52i			0.223087i	0.993760	+	0.111544i	$0.0355795\pi$
$41$			3.71828e52i			0.223087i	−0.993760	+	0.111544i	$0.964421\pi$
$42$	9.13850e51	−	5.98526e51i	0.0247542	−	0.0162127i
$43$	3.83181e53			0.477469			0.238735	−	0.971085i	$-0.423267\pi$
$43$	3.83181e53			0.477469			0.238735	+	0.971085i	$0.423267\pi$
$44$			3.25178e53i			0.189751i
$45$	−5.44271e54	−	2.37270e54i	−1.51287	−	0.659524i
$46$	−1.18951e55			−1.60088
$47$		−	2.78104e55i		−	1.84068i	−0.391119	−	0.920340i	$-0.627912\pi$
$47$		−	2.78104e55i		−	1.84068i	0.391119	−	0.920340i	$-0.372088\pi$
$48$	1.87701e55	+	2.86588e55i	0.620163	+	0.946886i
$49$	−5.97230e55			−0.999243
$50$		−	2.15789e56i		−	1.85361i
$51$	−1.44284e56	+	9.44989e55i	−0.644766	+	0.422290i
$52$	−2.23340e55			−0.0525844
$53$			2.47624e56i			0.310949i	0.987840	+	0.155475i	$0.0496907\pi$
$53$			2.47624e56i			0.310949i	−0.987840	+	0.155475i	$0.950309\pi$
$54$	2.66506e56	+	1.56432e57i	0.180598	+	1.06006i
$55$	5.41577e57			2.00305
$56$			1.22329e56i			0.0249646i
$57$	7.87123e57	+	1.20180e58i	0.895720	+	1.36761i
$58$	−1.65795e58			−1.06279
$59$		−	4.29894e58i		−	1.56764i	−0.620991	−	0.783818i	$-0.713270\pi$
$59$		−	4.29894e58i		−	1.56764i	0.620991	−	0.783818i	$-0.286730\pi$
$60$	−1.03072e58	+	6.75070e57i	−0.215849	+	0.141370i
$61$	6.76510e58			0.821088			0.410544	−	0.911841i	$-0.365339\pi$
$61$	6.76510e58			0.821088			0.410544	+	0.911841i	$0.365339\pi$
$62$			2.32115e58i			0.164732i
$63$	−2.62724e57	+	6.02659e57i	−0.0109967	+	0.0252251i
$64$	−3.20823e59			−0.798594
$65$			3.71968e59i			0.555092i
$66$	−7.93047e59	−	1.21085e60i	−0.715071	−	1.09179i
$67$	−1.21724e60			−0.668204			−0.334102	−	0.942537i	$-0.608433\pi$
$67$	−1.21724e60			−0.668204			−0.334102	+	0.942537i	$0.608433\pi$
$68$			3.57917e59i			0.120500i
$69$	5.98862e60	−	3.92225e60i	1.24539	−	0.815672i
$70$	−3.77553e59			−0.0488362
$71$			9.25851e60i			0.749921i	0.927041	+	0.374961i	$0.122344\pi$
$71$			9.25851e60i			0.749921i	−0.927041	+	0.374961i	$0.877656\pi$
$72$	−1.62892e61	−	7.10114e60i	−0.831626	−	0.362540i
$73$	3.92715e61			1.27181			0.635906	−	0.771766i	$-0.280627\pi$
$73$	3.92715e61			1.27181			0.635906	+	0.771766i	$0.280627\pi$
$74$		−	3.41429e61i		−	0.705754i
$75$	7.11533e61	+	1.08639e62i	0.944438	+	1.44200i
$76$	2.98125e61			0.255593
$77$		−	5.99676e60i		−	0.0333982i
$78$	8.31641e61	−	5.44684e61i	0.302562	−	0.198163i
$79$	−1.61159e62			−0.385089			−0.192545	−	0.981288i	$-0.561674\pi$
$79$	−1.61159e62			−0.385089			−0.192545	+	0.981288i	$0.561674\pi$
$80$		−	1.18403e63i		−	1.86806i
$81$	−6.49985e62	−	6.99681e62i	−0.680609	−	0.732647i
$82$	−3.43459e62			−0.239893
$83$		−	2.73065e63i		−	1.27847i	−0.769013	−	0.639233i	$-0.779252\pi$
$83$		−	2.73065e63i		−	1.27847i	0.769013	−	0.639233i	$-0.220748\pi$
$84$	7.47490e60	+	1.14129e61i	0.00235716	+	0.00359899i
$85$	5.96102e63			1.27203
$86$			3.53946e63i			0.513439i
$87$	8.34699e63	−	5.46686e63i	0.826789	−	0.541506i
$88$	1.62086e64			1.10108
$89$		−	9.54368e63i		−	0.446525i	−0.974758	−	0.223262i	$-0.928329\pi$
$89$		−	9.54368e63i		−	0.446525i	0.974758	−	0.223262i	$-0.0716707\pi$
$90$	2.19168e64	−	5.02746e64i	0.709208	−	1.62684i
$91$	4.11872e62			0.00925542
$92$		−	1.48556e64i		−	0.232751i
$93$	−7.65368e63	−	1.16859e64i	−0.0839330	−	0.128152i
$94$	2.56886e65			1.97934
$95$		−	4.96520e65i		−	2.69810i
$96$	−6.74124e64	+	4.41518e64i	−0.259292	+	0.169823i
$97$	−5.23415e65			−1.43014			−0.715071	−	0.699052i	$-0.753606\pi$
$97$	−5.23415e65			−1.43014			−0.715071	+	0.699052i	$0.753606\pi$
$98$		−	5.51664e65i		−	1.07452i
$99$	7.98523e65	+	3.48109e65i	1.11257	+	0.485013i
$100$	2.69495e65			0.269495
$101$			5.91938e64i			0.0426257i	0.999773	+	0.0213128i	$0.00678460\pi$
$101$			5.91938e64i			0.0426257i	−0.999773	+	0.0213128i	$0.993215\pi$
$102$	−8.72890e65	−	1.33276e66i	−0.454103	−	0.693339i
$103$	3.07110e66			1.15788			0.578942	−	0.815368i	$-0.303466\pi$
$103$	3.07110e66			1.15788			0.578942	+	0.815368i	$0.303466\pi$
$104$			1.11325e66i			0.305134i
$105$	1.90080e65	−	1.24493e65i	0.0379917	−	0.0248827i
$106$	−2.28732e66			−0.334374
$107$			4.97912e66i			0.533934i	0.963706	+	0.266967i	$0.0860215\pi$
$107$			4.97912e66i			0.533934i	−0.963706	+	0.266967i	$0.913979\pi$
$108$	−1.95365e66	+	3.32836e65i	−0.154121	+	0.0262571i
$109$	−8.73306e66			−0.508267			−0.254134	−	0.967169i	$-0.581790\pi$
$109$	−8.73306e66			−0.508267			−0.254134	+	0.967169i	$0.581790\pi$
$110$			5.00257e67i			2.15394i
$111$	1.12582e67	+	1.71893e67i	0.359591	+	0.549035i
$112$	−1.31104e66			−0.0311475
$113$		−	7.24765e67i		−	1.28413i	−0.766651	−	0.642064i	$-0.778078\pi$
$113$		−	7.24765e67i		−	1.28413i	0.766651	−	0.642064i	$-0.221922\pi$
$114$	−1.11011e68	+	7.27069e67i	−1.47064	+	0.963197i
$115$	−2.47417e68			−2.45698
$116$		−	2.07059e67i		−	0.154518i
$117$	−2.39090e67	+	5.48445e67i	−0.134409	+	0.308318i
$118$	3.97095e68			1.68573
$119$		−	6.60051e66i		−	0.0212094i
$120$	3.36491e68	+	5.13765e68i	0.820336	+	1.25252i
$121$	−2.55162e68			−0.473041
$122$			6.24895e68i			0.882943i
$123$	1.72915e68	−	1.13251e68i	0.186623	−	0.122229i
$124$	−2.89885e67			−0.0239503
$125$		−	1.88454e69i		−	1.19447i
$126$	−5.56679e67	−	2.42679e67i	−0.0271254	−	0.0118251i
$127$	3.24514e69			1.21818			0.609090	−	0.793101i	$-0.291535\pi$
$127$	3.24514e69			1.21818			0.609090	+	0.793101i	$0.291535\pi$
$128$		−	4.03307e69i		−	1.16871i
$129$	−1.16709e69	−	1.78195e69i	−0.261604	−	0.399425i
$130$	−3.43589e69			−0.596909
$131$		−	1.20242e70i		−	1.62220i	−0.584911	−	0.811098i	$-0.698870\pi$
$131$		−	1.20242e70i		−	1.62220i	0.584911	−	0.811098i	$-0.301130\pi$
$132$	1.51221e69	−	9.90424e68i	0.158735	−	0.103964i
$133$	−5.49785e68			−0.0449872
$134$		−	1.12437e70i		−	0.718542i
$135$	5.54330e69	+	3.25376e70i	0.277175	+	1.62694i
$136$	1.78405e70			0.699233
$137$		−	4.79232e70i		−	1.47492i	−0.675393	−	0.737458i	$-0.736026\pi$
$137$		−	4.79232e70i		−	1.47492i	0.675393	−	0.737458i	$-0.263974\pi$
$138$	3.62300e70	+	5.53172e70i	0.877119	+	1.33921i
$139$	5.78156e70			1.10295			0.551476	−	0.834191i	$-0.314065\pi$
$139$	5.78156e70			1.10295			0.551476	+	0.834191i	$0.314065\pi$
$140$		−	4.71519e68i		−	0.00710026i
$141$	−1.29330e71	+	8.47047e70i	−1.53981	+	1.00850i
$142$	−8.55213e70			−0.806415
$143$		−	5.45730e70i		−	0.408215i
$144$	7.61056e70	−	1.74578e71i	0.452329	−	1.03759i
$145$	−3.44852e71			−1.63113
$146$			3.62752e71i			1.36762i
$147$	1.81904e71	+	2.77737e71i	0.547481	+	0.835913i
$148$	4.26405e70			0.102609
$149$			2.26137e71i			0.435737i	0.975978	+	0.217868i	$0.0699104\pi$
$149$			2.26137e71i			0.435737i	−0.975978	+	0.217868i	$0.930090\pi$
$150$	−1.00351e72	+	6.57247e71i	−1.55063	+	1.01559i
$151$	−1.56508e71			−0.194222			−0.0971110	−	0.995274i	$-0.530960\pi$
$151$	−1.56508e71			−0.194222			−0.0971110	+	0.995274i	$0.530960\pi$
$152$		−	1.48601e72i		−	1.48314i
$153$	8.78917e71	+	3.83156e71i	0.706530	+	0.308006i
$154$	5.53923e70			0.0359141
$155$			4.82797e71i			0.252824i
$156$	6.80247e70	+	1.03862e71i	0.0288108	+	0.0439893i
$157$	2.80722e72			0.962916			0.481458	−	0.876469i	$-0.340107\pi$
$157$	2.80722e72			0.962916			0.481458	+	0.876469i	$0.340107\pi$
$158$		−	1.48863e72i		−	0.414099i
$159$	1.15155e72	−	7.54211e71i	0.260123	−	0.170368i
$160$	2.78511e72			0.511544
$161$			2.73959e71i			0.0409668i
$162$	6.46299e72	−	6.00394e72i	0.787840	−	0.731882i
$163$	−9.56493e72			−0.951679			−0.475840	−	0.879532i	$-0.657856\pi$
$163$	−9.56493e72			−0.951679			−0.475840	+	0.879532i	$0.657856\pi$
$164$		−	4.28941e71i		−	0.0348779i
$165$	−1.64953e73	−	2.51856e73i	−1.09746	−	1.67564i
$166$	2.52231e73			1.37478
$167$		−	3.09630e72i		−	0.138420i	−0.997602	−	0.0692101i	$-0.977952\pi$
$167$		−	3.09630e72i		−	0.138420i	0.997602	−	0.0692101i	$-0.0220479\pi$
$168$	5.68880e71	−	3.72588e71i	0.0208840	−	0.0136780i
$169$	−2.93848e73			−0.886874
$170$			5.50622e73i			1.36785i
$171$	3.19148e73	−	7.32089e73i	0.653311	−	1.49862i
$172$	−4.42038e72			−0.0746485
$173$			1.49759e72i			0.0208868i	0.999945	+	0.0104434i	$0.00332430\pi$
$173$			1.49759e72i			0.0208868i	−0.999945	+	0.0104434i	$0.996676\pi$
$174$	5.04977e73	+	7.71015e73i	0.582299	+	0.889073i
$175$	−4.96988e72			−0.0474341
$176$			1.73713e74i			1.37377i
$177$	−1.99918e74	+	1.30937e74i	−1.31140	+	0.858902i
$178$	8.81554e73			0.480163
$179$			1.24682e74i			0.564489i	0.959343	+	0.282244i	$0.0910789\pi$
$179$			1.24682e74i			0.564489i	−0.959343	+	0.282244i	$0.908921\pi$
$180$	6.27871e73	+	2.73715e73i	0.236525	+	0.103111i
$181$	−1.08447e74			−0.340272			−0.170136	−	0.985421i	$-0.554421\pi$
$181$	−1.08447e74			−0.340272			−0.170136	+	0.985421i	$0.554421\pi$
$182$			3.80448e72i			0.00995266i
$183$	−2.06051e74	−	3.14605e74i	−0.449871	−	0.686878i
$184$	−7.40482e74			−1.35060
$185$		−	7.10168e74i		−	1.08316i
$186$	1.07943e74	−	7.06974e73i	0.137806	−	0.0902560i
$187$	−8.74567e74			−0.935448
$188$			3.20821e74i			0.287776i
$189$	3.60281e73	−	6.13797e72i	0.0271270	−	0.00462153i
$190$	4.58638e75			2.90135
$191$			1.16751e75i			0.621096i	0.950558	+	0.310548i	$0.100513\pi$
$191$			1.16751e75i			0.621096i	−0.950558	+	0.310548i	$0.899487\pi$
$192$	9.77158e74	+	1.49196e75i	0.437547	+	0.668061i
$193$	−1.49140e74			−0.0562603			−0.0281302	−	0.999604i	$-0.508955\pi$
$193$	−1.49140e74			−0.0562603			−0.0281302	+	0.999604i	$0.508955\pi$
$194$		−	4.83481e75i		−	1.53788i
$195$	1.72981e75	−	1.13294e75i	0.464360	−	0.304133i
$196$	6.88965e74			0.156224
$197$		−	7.76939e75i		−	1.48937i	−0.667419	−	0.744683i	$-0.732601\pi$
$197$		−	7.76939e75i		−	1.48937i	0.667419	−	0.744683i	$-0.267399\pi$
$198$	−3.21550e75	+	7.37599e75i	−0.521551	+	1.19638i
$199$	−2.75395e75			−0.378272			−0.189136	−	0.981951i	$-0.560569\pi$
$199$	−2.75395e75			−0.378272			−0.189136	+	0.981951i	$0.560569\pi$
$200$		−	1.34331e76i		−	1.56381i
$201$	3.70747e75	+	5.66069e75i	0.366107	+	0.558984i
$202$	−5.46776e74			−0.0458368
$203$			3.81846e74i			0.0271969i
$204$	1.66446e75	−	1.09014e75i	0.100804	−	0.0660216i
$205$	−7.14391e75			−0.368179
$206$			2.83679e76i			1.24511i
$207$	−3.64802e76	−	1.59032e76i	−1.36469	−	0.594927i
$208$	−1.19311e76			−0.380705
$209$			7.28465e76i			1.98418i
$210$	1.14995e75	+	1.75577e75i	0.0267572	+	0.0408538i
$211$	4.92867e76			0.980411			0.490206	−	0.871607i	$-0.336922\pi$
$211$	4.92867e76			0.980411			0.490206	+	0.871607i	$0.336922\pi$
$212$		−	2.85659e75i		−	0.0486144i
$213$	4.30559e76	−	2.81995e76i	0.627344	−	0.410879i
$214$	−4.59923e76			−0.574157
$215$			7.36204e76i			0.788005i
$216$	1.65903e76	+	9.73802e76i	0.152363	+	0.894328i
$217$	5.34590e74			0.00421550
$218$		−	8.06677e76i		−	0.546557i
$219$	−1.19613e77	−	1.82629e77i	−0.696821	−	1.06393i
$220$	−6.24763e76			−0.313160
$221$		−	6.00674e76i		−	0.259235i
$222$	−1.58778e77	+	1.03992e77i	−0.590396	+	0.386680i
$223$	1.70734e77			0.547342			0.273671	−	0.961823i	$-0.411762\pi$
$223$	1.70734e77			0.547342			0.273671	+	0.961823i	$0.411762\pi$
$224$		−	3.08389e75i		−	0.00852931i
$225$	2.88499e77	−	6.61785e77i	0.688845	−	1.58013i
$226$	6.69468e77			1.38087
$227$			5.42472e77i			0.967217i	0.875285	+	0.483608i	$0.160674\pi$
$227$			5.42472e77i			0.967217i	−0.875285	+	0.483608i	$0.839326\pi$
$228$	−9.08025e76	−	1.38640e77i	−0.140039	−	0.213816i
$229$	−3.80836e77			−0.508354			−0.254177	−	0.967158i	$-0.581805\pi$
$229$	−3.80836e77			−0.508354			−0.254177	+	0.967158i	$0.581805\pi$
$230$		−	2.28540e78i		−	2.64207i
$231$	−2.78874e76	+	1.82649e76i	−0.0279391	+	0.0182987i
$232$	−1.03209e78			−0.896632
$233$			2.32549e78i			1.75295i	0.481452	+	0.876473i	$0.340110\pi$
$233$			2.32549e78i			1.75295i	−0.481452	+	0.876473i	$0.659890\pi$
$234$	−5.06601e77	−	2.20848e77i	−0.331545	−	0.144534i
$235$	5.34320e78			3.03782
$236$			4.95926e77i			0.245087i
$237$	4.90857e77	+	7.49457e77i	0.210989	+	0.322145i
$238$	6.09692e76			0.0228071
$239$			1.04894e78i			0.341679i	0.985299	+	0.170840i	$0.0546480\pi$
$239$			1.04894e78i			0.341679i	−0.985299	+	0.170840i	$0.945352\pi$
$240$	−5.50621e78	+	3.60629e78i	−1.56272	+	1.02351i
$241$	−6.25634e78			−1.54795			−0.773976	−	0.633215i	$-0.781735\pi$
$241$	−6.25634e78			−1.54795			−0.773976	+	0.633215i	$0.781735\pi$
$242$		−	2.35694e78i		−	0.508677i
$243$	−1.27409e78	+	5.15378e78i	−0.239990	+	0.970775i
$244$	−7.80422e77			−0.128370
$245$		−	1.14746e79i		−	1.64913i
$246$	1.04610e78	+	1.59723e78i	0.131437	+	0.200682i
$247$	−5.00328e78			−0.549864
$248$			1.44494e78i			0.138977i
$249$	−1.26986e79	+	8.31698e78i	−1.06950	+	0.700467i
$250$	1.74076e79			1.28445
$251$			4.39155e78i			0.284044i	0.989864	+	0.142022i	$0.0453603\pi$
$251$			4.39155e78i			0.284044i	−0.989864	+	0.142022i	$0.954640\pi$
$252$	3.03078e76	−	6.95227e76i	0.00171924	−	0.00394375i
$253$	3.62996e79			1.80686
$254$			2.99755e79i			1.30995i
$255$	−1.81560e79	−	2.77212e79i	−0.696939	−	1.06411i
$256$	1.35811e79			0.458159
$257$		−	2.20601e79i		−	0.654358i	−0.944962	−	0.327179i	$-0.893902\pi$
$257$		−	2.20601e79i		−	0.654358i	0.944962	−	0.327179i	$-0.106098\pi$
$258$	1.64600e79	−	1.07805e79i	0.429515	−	0.281311i
$259$	−7.86353e77			−0.0180603
$260$		−	4.29103e78i		−	0.0867842i
$261$	−5.08463e79	−	2.21660e79i	−0.905989	−	0.394958i
$262$	1.11068e80			1.74440
$263$		−	5.81189e79i		−	0.804967i	−0.915427	−	0.402483i	$-0.868147\pi$
$263$		−	5.81189e79i		−	0.804967i	0.915427	−	0.402483i	$-0.131853\pi$
$264$	−4.93679e79	−	7.53766e79i	−0.603275	−	0.921100i
$265$	−4.75759e79			−0.513184
$266$		−	5.07839e78i		−	0.0483762i
$267$	−4.43820e79	+	2.90680e79i	−0.373539	+	0.244649i
$268$	1.40421e79			0.104468
$269$		−	5.93564e79i		−	0.390519i	−0.980752	−	0.195260i	$-0.937445\pi$
$269$		−	5.93564e79i		−	0.390519i	0.980752	−	0.195260i	$-0.0625550\pi$
$270$	−3.00551e80	+	5.12037e79i	−1.74950	+	0.298056i
$271$	2.55005e80			1.31390			0.656949	−	0.753935i	$-0.271847\pi$
$271$	2.55005e80			1.31390			0.656949	+	0.753935i	$0.271847\pi$
$272$			1.91203e80i			0.872409i
$273$	−1.25447e78	−	1.91537e78i	−0.00507101	−	0.00774259i
$274$	4.42669e80			1.58603
$275$			6.58509e80i			2.09210i
$276$	−6.90847e79	+	4.52471e79i	−0.194707	+	0.127524i
$277$	−4.22713e80			−1.05734			−0.528668	−	0.848829i	$-0.677308\pi$
$277$	−4.22713e80			−1.05734			−0.528668	+	0.848829i	$0.677308\pi$
$278$			5.34045e80i			1.18604i
$279$	−3.10327e79	+	7.11855e79i	−0.0612183	+	0.140428i
$280$	−2.35030e79			−0.0412011
$281$		−	8.12859e80i		−	1.26680i	−0.773826	−	0.633398i	$-0.781660\pi$
$281$		−	8.12859e80i		−	1.26680i	0.773826	−	0.633398i	$-0.218340\pi$
$282$	−7.82421e80	−	1.19463e81i	−1.08448	−	1.65581i
$283$	1.10059e81			1.35729			0.678644	−	0.734468i	$-0.262568\pi$
$283$	1.10059e81			1.35729			0.678644	+	0.734468i	$0.262568\pi$
$284$		−	1.06806e80i		−	0.117244i
$285$	−2.30902e81	+	1.51229e81i	−2.25708	+	1.47828i
$286$	5.04093e80			0.438967
$287$			7.91029e78i			0.00613889i
$288$	4.10648e80	+	1.79018e80i	0.284130	+	0.123864i
$289$	6.57807e80			0.405947
$290$		−	3.18541e81i		−	1.75401i
$291$	1.59421e81	+	2.43410e81i	0.783569	+	1.19638i
$292$	−4.53036e80			−0.198838
$293$		−	2.74781e81i		−	1.07735i	−0.842515	−	0.538673i	$-0.818926\pi$
$293$		−	2.74781e81i		−	1.07735i	0.842515	−	0.538673i	$-0.181074\pi$
$294$	−2.56546e81	+	1.68025e81i	−0.898885	+	0.588725i
$295$	8.25954e81			2.58719
$296$		−	2.12543e81i		−	0.595415i
$297$	−8.13281e80	−	4.77372e81i	−0.203835	−	1.19645i
$298$	−2.08884e81			−0.468562
$299$			2.49314e81i			0.500724i
$300$	−8.20825e80	−	1.25326e81i	−0.147655	−	0.225445i
$301$	8.15182e79			0.0131389
$302$		−	1.44567e81i		−	0.208853i
$303$	2.75276e80	−	1.80292e80i	0.0356583	−	0.0233544i
$304$	1.59261e82			1.85047
$305$			1.29978e82i			1.35511i
$306$	−3.53923e81	+	8.11860e81i	−0.331209	+	0.759756i
$307$	−2.03888e82			−1.71326			−0.856632	−	0.515927i	$-0.827447\pi$
$307$	−2.03888e82			−1.71326			−0.856632	+	0.515927i	$0.827447\pi$
$308$			6.91786e79i			0.00522153i
$309$	−9.35392e81	−	1.42819e82i	−0.634401	−	0.968624i
$310$	−4.45962e81			−0.271870
$311$			6.15503e81i			0.337394i	0.985668	+	0.168697i	$0.0539559\pi$
$311$			6.15503e81i			0.337394i	−0.985668	+	0.168697i	$0.946044\pi$
$312$	5.17705e81	−	3.39071e81i	0.255259	−	0.167182i
$313$	−3.23533e82			−1.43534			−0.717672	−	0.696381i	$-0.754792\pi$
$313$	−3.23533e82			−1.43534			−0.717672	+	0.696381i	$0.754792\pi$
$314$			2.59304e82i			1.03546i
$315$	−1.15789e81	−	5.04770e80i	−0.0416310	−	0.0181487i
$316$	1.85913e81			0.0602056
$317$			2.46101e82i			0.718054i	0.933327	+	0.359027i	$0.116891\pi$
$317$			2.46101e82i			0.718054i	−0.933327	+	0.359027i	$0.883109\pi$
$318$	6.96668e81	+	1.06370e82i	0.183202	+	0.279719i
$319$	5.05946e82			1.19953
$320$		−	6.16395e82i		−	1.31798i
$321$	2.31549e82	−	1.51653e82i	0.446661	−	0.292541i
$322$	−2.53057e81			−0.0440530
$323$			8.01806e82i			1.26005i
$324$	7.49823e81	+	8.07152e81i	0.106408	+	0.114543i
$325$	−4.52280e82			−0.579771
$326$		−	8.83516e82i		−	1.02337i
$327$	2.65991e82	+	4.06123e82i	0.278478	+	0.425189i
$328$	−2.13807e82			−0.202388
$329$		−	5.91641e81i		−	0.0506516i
$330$	2.32640e83	−	1.52368e83i	1.80187	−	1.18014i
$331$	−9.60920e82			−0.673540			−0.336770	−	0.941587i	$-0.609334\pi$
$331$	−9.60920e82			−0.673540			−0.336770	+	0.941587i	$0.609334\pi$
$332$			3.15008e82i			0.199878i
$333$	4.56474e82	−	1.04710e83i	0.262275	−	0.601629i
$334$	2.86007e82			0.148848
$335$		−	2.33868e83i		−	1.10279i
$336$	3.99317e81	+	6.09690e81i	0.0170656	+	0.0260563i
$337$	−3.75584e83			−1.45519			−0.727596	−	0.686005i	$-0.759363\pi$
$337$	−3.75584e83			−1.45519			−0.727596	+	0.686005i	$0.759363\pi$
$338$		−	2.71429e83i		−	0.953685i
$339$	−3.37045e83	+	2.20748e83i	−1.07423	+	0.703569i
$340$	−6.87664e82			−0.198871
$341$		−	7.08331e82i		−	0.185927i
$342$	6.76234e83	+	2.94798e83i	1.61152	+	0.702528i
$343$	−2.54206e82			−0.0550149
$344$			2.20335e83i			0.433167i
$345$	7.53580e83	+	1.15059e84i	1.34617	+	2.05537i
$346$	−1.38333e82			−0.0224603
$347$			3.90342e83i			0.576200i	0.957600	+	0.288100i	$0.0930235\pi$
$347$			3.90342e83i			0.576200i	−0.957600	+	0.288100i	$0.906976\pi$
$348$	−9.62909e82	+	6.30657e82i	−0.129262	+	0.0846600i
$349$	−7.64575e83			−0.933644			−0.466822	−	0.884351i	$-0.654601\pi$
$349$	−7.64575e83			−0.933644			−0.466822	+	0.884351i	$0.654601\pi$
$350$		−	4.59070e82i		−	0.0510074i
$351$	3.27871e83	−	5.58581e82i	0.331565	−	0.0564874i
$352$	−4.08615e83			−0.376189
$353$			9.69523e83i			0.812817i	0.913691	+	0.406409i	$0.133219\pi$
$353$			9.69523e83i			0.812817i	−0.913691	+	0.406409i	$0.866781\pi$
$354$	−1.20947e84	−	1.84666e84i	−0.923606	−	1.41019i
$355$	−1.77883e84			−1.23765
$356$			1.10096e83i			0.0698106i
$357$	−3.06951e82	+	2.01037e82i	−0.0177426	+	0.0116205i
$358$	−1.15170e84			−0.607014
$359$		−	4.72878e83i		−	0.227317i	−0.993520	−	0.113659i	$-0.963743\pi$
$359$		−	4.72878e83i		−	0.227317i	0.993520	−	0.113659i	$-0.0362570\pi$
$360$	1.36434e84	−	3.12964e84i	0.598329	−	1.37250i
$361$	4.17976e84			1.67268
$362$		−	1.00173e84i		−	0.365906i
$363$	7.77170e83	+	1.18661e84i	0.259177	+	0.395721i
$364$	−4.75135e81			−0.00144701
$365$			7.54521e84i			2.09897i
$366$	2.90602e84	−	1.90330e84i	0.738623	−	0.483761i
$367$	−4.10274e84			−0.953002			−0.476501	−	0.879174i	$-0.658095\pi$
$367$	−4.10274e84			−0.953002			−0.476501	+	0.879174i	$0.658095\pi$
$368$		−	7.93602e84i		−	1.68510i
$369$	−1.05333e84	−	4.59189e83i	−0.204500	−	0.0891500i
$370$	6.55986e84			1.16476
$371$			5.26797e82i			0.00855667i
$372$	8.82928e82	+	1.34808e83i	0.0131223	+	0.0200355i
$373$	6.13143e84			0.834008			0.417004	−	0.908905i	$-0.363080\pi$
$373$	6.13143e84			0.834008			0.417004	+	0.908905i	$0.363080\pi$
$374$		−	8.07841e84i		−	1.00592i
$375$	−8.76388e84	+	5.73991e84i	−0.999228	+	0.654445i
$376$	1.59914e85			1.66989
$377$			3.47496e84i			0.332419i
$378$	5.66967e82	+	3.32793e83i	0.00496968	+	0.0291706i
$379$	−1.81844e85			−1.46085			−0.730423	−	0.682995i	$-0.760677\pi$
$379$	−1.81844e85			−1.46085			−0.730423	+	0.682995i	$0.760677\pi$
$380$			5.72785e84i			0.421826i
$381$	−9.88403e84	−	1.50913e85i	−0.667436	−	1.01906i
$382$	−1.07843e85			−0.667886
$383$			6.70270e84i			0.380794i	0.981707	+	0.190397i	$0.0609775\pi$
$383$			6.70270e84i			0.380794i	−0.981707	+	0.190397i	$0.939022\pi$
$384$	−1.87554e85	+	1.22839e85i	−0.977680	+	0.640332i
$385$	1.15215e84			0.0551196
$386$		−	1.37761e84i		−	0.0604986i
$387$	−4.73210e84	+	1.08549e85i	−0.190806	+	0.437687i
$388$	6.03812e84			0.223591
$389$			3.97184e85i			1.35100i	0.737361	+	0.675499i	$0.236072\pi$
$389$			3.97184e85i			1.35100i	−0.737361	+	0.675499i	$0.763928\pi$
$390$	1.04650e85	+	1.59783e85i	0.327044	+	0.499342i
$391$	3.99542e85			1.14744
$392$		−	3.43416e85i		−	0.906527i
$393$	−5.59174e85	+	3.66232e85i	−1.35704	+	0.888795i
$394$	7.17662e85			1.60156
$395$		−	3.09634e85i		−	0.635543i
$396$	−9.21176e84	−	4.01579e84i	−0.173941	−	0.0758280i
$397$	−9.27361e85			−1.61125			−0.805624	−	0.592428i	$-0.798170\pi$
$397$	−9.27361e85			−1.61125			−0.805624	+	0.592428i	$0.798170\pi$
$398$		−	2.54383e85i		−	0.406768i
$399$	1.67453e84	+	2.55673e84i	0.0246483	+	0.0376339i
$400$	1.43967e86			1.95112
$401$		−	8.06534e85i		−	1.00660i	−0.864111	−	0.503302i	$-0.832118\pi$
$401$		−	8.06534e85i		−	1.00660i	0.864111	−	0.503302i	$-0.167882\pi$
$402$	−5.22880e85	+	3.42460e85i	−0.601094	+	0.393687i
$403$	4.86499e84			0.0515247
$404$		−	6.82860e83i		−	0.00666418i
$405$	1.34429e86	−	1.24881e86i	1.20915	−	1.12326i
$406$	−3.52713e84			−0.0292457
$407$			1.04192e86i			0.796559i
$408$	−5.43383e85	−	8.29655e85i	−0.383107	−	0.584941i
$409$	−2.58359e85			−0.168017			−0.0840087	−	0.996465i	$-0.526772\pi$
$409$	−2.58359e85			−0.168017			−0.0840087	+	0.996465i	$0.526772\pi$
$410$		−	6.59886e85i		−	0.395915i
$411$	−2.22863e86	+	1.45964e86i	−1.23384	+	0.808101i
$412$	−3.54282e85			−0.181026
$413$		−	9.14559e84i		−	0.0431380i
$414$	1.46899e86	−	3.36969e86i	0.639744	−	1.46750i
$415$	5.24639e86			2.10995
$416$		−	2.80647e85i		−	0.104251i
$417$	−1.76094e86	−	2.68866e86i	−0.604303	−	0.922670i
$418$	−6.72886e86			−2.13366
$419$			4.62976e86i			1.35674i	0.734722	+	0.678368i	$0.237313\pi$
$419$			4.62976e86i			1.35674i	−0.734722	+	0.678368i	$0.762687\pi$
$420$	−2.19276e84	+	1.43615e84i	−0.00593970	+	0.00389021i
$421$	2.68338e85			0.0672005			0.0336003	−	0.999435i	$-0.489303\pi$
$421$	2.68338e85			0.0672005			0.0336003	+	0.999435i	$0.489303\pi$
$422$			4.55263e86i			1.05427i
$423$	7.87823e86	+	3.43445e86i	1.68732	+	0.735571i
$424$	−1.42388e86			−0.282097
$425$			7.24807e86i			1.32858i
$426$	2.60480e86	+	3.97709e86i	0.441832	+	0.674604i
$427$	1.43921e85			0.0225946
$428$		−	5.74391e85i		−	0.0834763i
$429$	−2.53787e86	+	1.66218e86i	−0.341490	+	0.223659i
$430$	−6.80035e86			−0.847369
$431$		−	1.62004e87i		−	1.86972i	−0.355013	−	0.934861i	$-0.615524\pi$
$431$		−	1.62004e87i		−	1.86972i	0.355013	−	0.934861i	$-0.384476\pi$
$432$	−1.04366e87	+	1.77804e86i	−1.11582	+	0.190098i
$433$	−1.19158e87			−1.18038			−0.590189	−	0.807265i	$-0.700947\pi$
$433$	−1.19158e87			−1.18038			−0.590189	+	0.807265i	$0.700947\pi$
$434$			4.93803e84i			0.00453307i
$435$	1.05035e87	+	1.60370e87i	0.893690	+	1.36452i
$436$	1.00745e86			0.0794635
$437$		−	3.32796e87i		−	2.43383i
$438$	1.68695e87	−	1.10487e87i	1.14408	−	0.749315i
$439$	−1.72003e87			−1.08195			−0.540975	−	0.841039i	$-0.681945\pi$
$439$	−1.72003e87			−1.08195			−0.540975	+	0.841039i	$0.681945\pi$
$440$			3.11415e87i			1.81719i
$441$	7.37549e86	−	1.69185e87i	0.399317	−	0.915987i
$442$	5.54845e86			0.278764
$443$		−	1.05950e87i		−	0.494059i	−0.969008	−	0.247029i	$-0.920546\pi$
$443$		−	1.05950e87i		−	0.494059i	0.969008	−	0.247029i	$-0.0794544\pi$
$444$	−1.29874e86	−	1.98296e86i	−0.0562192	−	0.0858373i
$445$	1.83362e87			0.736936
$446$			1.57707e87i			0.588575i
$447$	1.05163e87	−	6.88765e86i	0.364514	−	0.238739i
$448$	−6.82520e85			−0.0219756
$449$		−	4.41856e87i		−	1.32176i	−0.750493	−	0.660879i	$-0.770184\pi$
$449$		−	4.41856e87i		−	1.32176i	0.750493	−	0.660879i	$-0.229816\pi$
$450$	6.11293e87	+	2.66488e87i	1.69917	+	0.740738i
$451$	1.04811e87			0.270759
$452$			8.36089e86i			0.200763i
$453$	4.76692e86	+	7.27828e86i	0.106414	+	0.162476i
$454$	−5.01083e87			−1.04008
$455$			7.91327e85i			0.0152750i
$456$	−6.91056e87	+	4.52607e87i	−1.24072	+	0.812609i
$457$	2.57474e87			0.430030			0.215015	−	0.976611i	$-0.431020\pi$
$457$	2.57474e87			0.430030			0.215015	+	0.976611i	$0.431020\pi$
$458$		−	3.51780e87i		−	0.546651i
$459$	−8.95162e86	−	5.25434e87i	−0.129444	−	0.759800i
$460$	2.85420e87			0.384128
$461$			5.71780e87i			0.716305i	0.933663	+	0.358153i	$0.116593\pi$
$461$			5.71780e87i			0.716305i	−0.933663	+	0.358153i	$0.883407\pi$
$462$	−1.68713e86	−	2.57597e86i	−0.0196772	−	0.0300438i
$463$	−1.13661e88			−1.23435			−0.617176	−	0.786825i	$-0.711723\pi$
$463$	−1.13661e88			−1.23435			−0.617176	+	0.786825i	$0.711723\pi$
$464$		−	1.10613e88i		−	1.11870i
$465$	2.24520e87	−	1.47050e87i	0.211499	−	0.138521i
$466$	−2.14806e88			−1.88500
$467$			1.47919e88i			1.20939i	0.796456	+	0.604697i	$0.206706\pi$
$467$			1.47919e88i			1.20939i	−0.796456	+	0.604697i	$0.793294\pi$
$468$	2.75814e86	−	6.32686e86i	0.0210137	−	0.0482031i
$469$	−2.58957e86			−0.0183876
$470$			4.93554e88i			3.26667i
$471$	−8.55021e87	−	1.30547e88i	−0.527578	−	0.805524i
$472$	2.47196e88			1.42218
$473$		−	1.08012e88i		−	0.579499i
$474$	−6.92276e87	+	4.53407e87i	−0.346413	+	0.226883i
$475$	6.03724e88			2.81805
$476$			7.61434e85i			0.00331591i
$477$	−7.01479e87	−	3.05804e87i	−0.285041	−	0.124261i
$478$	−9.68908e87			−0.367419
$479$			3.02682e88i			1.07131i	0.844438	+	0.535654i	$0.179935\pi$
$479$			3.02682e88i			1.07131i	−0.844438	+	0.535654i	$0.820065\pi$
$480$	−8.48286e87	−	1.29519e88i	−0.280273	−	0.427930i
$481$	−7.15614e87			−0.220745
$482$		−	5.77900e88i		−	1.66457i
$483$	1.27402e87	−	8.34422e86i	0.0342706	−	0.0224456i
$484$	2.94355e87			0.0739562
$485$		−	1.00564e89i		−	2.36028i
$486$	−4.76057e88	−	1.17688e88i	−1.04391	−	0.258069i
$487$	−3.00428e88			−0.615580			−0.307790	−	0.951454i	$-0.599589\pi$
$487$	−3.00428e88			−0.615580			−0.307790	+	0.951454i	$0.599589\pi$
$488$			3.89003e88i			0.744902i
$489$	2.91327e88	+	4.44808e88i	0.521422	+	0.796124i
$490$	1.05991e89			1.77336
$491$		−	6.34161e88i		−	0.991997i	−0.868323	−	0.495999i	$-0.834802\pi$
$491$		−	6.34161e88i		−	0.991997i	0.868323	−	0.495999i	$-0.165198\pi$
$492$	−1.99475e87	+	1.30646e87i	−0.0291770	+	0.0191095i
$493$	5.56885e88			0.761758
$494$		−	4.62155e88i		−	0.591287i
$495$	−6.68820e88	+	1.53420e89i	−0.800456	+	1.83616i
$496$	−1.54859e88			−0.173397
$497$			1.96966e87i			0.0206362i
$498$	−7.68244e88	−	1.17298e89i	−0.753235	−	1.15006i
$499$	3.18785e88			0.292536			0.146268	−	0.989245i	$-0.453274\pi$
$499$	3.18785e88			0.292536			0.146268	+	0.989245i	$0.453274\pi$
$500$			2.17400e88i			0.186746i
$501$	−1.43991e88	+	9.43068e87i	−0.115795	+	0.0758400i
$502$	−4.05649e88			−0.305442
$503$			5.91261e88i			0.416903i	0.978033	+	0.208452i	$0.0668424\pi$
$503$			5.91261e88i			0.416903i	−0.978033	+	0.208452i	$0.933158\pi$
$504$	−3.46538e87	−	1.51070e87i	−0.0228846	−	0.00997633i
$505$	−1.13729e88			−0.0703485
$506$			3.35301e89i			1.94298i
$507$	8.95000e88	+	1.36652e89i	0.485915	+	0.741911i
$508$	−3.74360e88			−0.190453
$509$		−	1.17109e89i		−	0.558344i	−0.960241	−	0.279172i	$-0.909940\pi$
$509$		−	1.17109e89i		−	0.558344i	0.960241	−	0.279172i	$-0.0900600\pi$
$510$	2.56062e89	−	1.67708e89i	1.14427	−	0.749442i
$511$	8.35464e87			0.0349976
$512$		−	1.72139e89i		−	0.676036i
$513$	−4.37657e89	+	7.45620e88i	−1.61161	+	0.274564i
$514$	2.03771e89			0.703653
$515$			5.90049e89i			1.91095i
$516$	1.34635e88	+	2.05566e88i	0.0408996	+	0.0624469i
$517$	−7.83923e89			−2.23401
$518$		−	7.26358e87i		−	0.0194209i
$519$	6.96441e87	−	4.56135e87i	0.0174728	−	0.0114438i
$520$	−2.13887e89			−0.503587
$521$		−	6.45237e89i		−	1.42585i	−0.701239	−	0.712926i	$-0.747369\pi$
$521$		−	6.45237e89i		−	1.42585i	0.701239	−	0.712926i	$-0.252631\pi$
$522$	2.04748e89	−	4.69670e89i	0.424712	−	0.974240i
$523$	5.42818e89			1.05706			0.528529	−	0.848915i	$-0.322744\pi$
$523$	5.42818e89			1.05706			0.528529	+	0.848915i	$0.322744\pi$
$524$			1.38711e89i			0.253617i
$525$	1.51372e88	+	2.31120e88i	0.0259889	+	0.0396808i
$526$	5.36847e89			0.865607
$527$		−	7.79646e88i		−	0.118072i
$528$	8.07839e89	−	5.29094e89i	1.14923	−	0.752685i
$529$	−9.10097e89			−1.21633
$530$		−	4.39461e89i		−	0.551844i
$531$	1.21782e90	+	5.30898e89i	1.43702	+	0.626457i
$532$	6.34232e87			0.00703338
$533$			7.19870e88i			0.0750336i
$534$	−2.68503e89	−	4.09959e89i	−0.263080	−	0.401679i
$535$	−9.56635e89			−0.881194
$536$		−	6.99934e89i		−	0.606204i
$537$	5.79825e89	−	3.79756e89i	0.472221	−	0.309281i
$538$	5.48278e89			0.419939
$539$			1.68348e90i			1.21277i
$540$	−6.39476e88	−	3.75354e89i	−0.0433341	−	0.254359i
$541$	7.02444e89			0.447818			0.223909	−	0.974610i	$-0.428118\pi$
$541$	7.02444e89			0.447818			0.223909	+	0.974610i	$0.428118\pi$
$542$			2.35549e90i			1.41288i
$543$	3.30308e89	+	5.04325e89i	0.186434	+	0.284653i
$544$	−4.49754e89			−0.238897
$545$		−	1.67788e90i		−	0.838834i
$546$	1.76924e88	−	1.15876e88i	0.00832586	−	0.00545303i
$547$	−1.59613e90			−0.707108			−0.353554	−	0.935414i	$-0.615027\pi$
$547$	−1.59613e90			−0.707108			−0.353554	+	0.935414i	$0.615027\pi$
$548$			5.52842e89i			0.230591i
$549$	−8.35456e89	+	1.91644e90i	−0.328122	+	0.752676i
$550$	−6.08267e90			−2.24971
$551$		−	4.63854e90i		−	1.61577i
$552$	2.25535e90	+	3.44355e90i	0.739988	+	1.12984i
$553$	−3.42851e88			−0.0105968
$554$		−	3.90462e90i		−	1.13699i
$555$	−3.30258e90	+	2.16302e90i	−0.906117	+	0.593462i
$556$	−6.66961e89			−0.172438
$557$			2.81429e90i			0.685721i	0.939386	+	0.342860i	$0.111396\pi$
$557$			2.81429e90i			0.685721i	−0.939386	+	0.342860i	$0.888604\pi$
$558$	−6.57544e89	−	2.86650e89i	−0.151007	−	0.0658300i
$559$	7.41850e89			0.160593
$560$		−	2.51890e89i		−	0.0514052i
$561$	2.66375e90	+	4.06709e90i	0.512529	+	0.782546i
$562$	7.50841e90			1.36223
$563$			1.57052e90i			0.268700i	0.990934	+	0.134350i	$0.0428946\pi$
$563$			1.57052e90i			0.268700i	−0.990934	+	0.134350i	$0.957105\pi$
$564$	1.49195e90	−	9.77153e89i	0.240738	−	0.157671i
$565$	1.39249e91			2.11930
$566$			1.01662e91i			1.45954i
$567$	−1.38278e89	−	1.48851e89i	−0.0187289	−	0.0201609i
$568$	−5.32378e90			−0.680339
$569$			4.03496e90i			0.486557i	0.969956	+	0.243279i	$0.0782230\pi$
$569$			4.03496e90i			0.486557i	−0.969956	+	0.243279i	$0.921777\pi$
$570$	−1.39691e91	−	2.13285e91i	−1.58964	−	2.42712i
$571$	−1.87610e90			−0.201495			−0.100748	−	0.994912i	$-0.532123\pi$
$571$	−1.87610e90			−0.201495			−0.100748	+	0.994912i	$0.532123\pi$
$572$			6.29554e89i			0.0638211i
$573$	5.42939e90	−	3.55598e90i	0.519576	−	0.340296i
$574$	−7.30677e88			−0.00660135
$575$		−	3.00837e91i		−	2.56621i
$576$	3.96200e90	−	9.08838e90i	0.319133	−	0.732056i
$577$	1.81060e90			0.137727			0.0688637	−	0.997626i	$-0.478063\pi$
$577$	1.81060e90			0.137727			0.0688637	+	0.997626i	$0.478063\pi$
$578$			6.07619e90i			0.436529i
$579$	4.54248e89	+	6.93561e89i	0.0308248	+	0.0470644i
$580$	3.97821e90			0.255014
$581$		−	5.80920e89i		−	0.0351807i
$582$	−2.24839e91	+	1.47258e91i	−1.28651	+	0.842598i
$583$	6.98006e90			0.377396
$584$			2.25817e91i			1.15381i
$585$	−1.05372e91	−	4.59362e90i	−0.508842	−	0.221825i
$586$	2.53817e91			1.15851
$587$		−	4.39528e91i		−	1.89640i	−0.317680	−	0.948198i	$-0.602904\pi$
$587$		−	4.39528e91i		−	1.89640i	0.317680	−	0.948198i	$-0.397096\pi$
$588$	−2.09844e90	−	3.20397e90i	−0.0855943	−	0.130688i
$589$	−6.49401e90			−0.250443
$590$			7.62937e91i			2.78210i
$591$	−3.61308e91	+	2.36639e91i	−1.24592	+	0.816018i
$592$	2.27790e91			0.742879
$593$		−	1.12282e90i		−	0.0346341i	−0.999850	−	0.0173171i	$-0.994488\pi$
$593$		−	1.12282e90i		−	0.0346341i	0.999850	−	0.0173171i	$-0.00551246\pi$
$594$	4.40951e91	−	7.51231e90i	1.28658	−	0.219190i
$595$	1.26815e90			0.0350035
$596$		−	2.60871e90i		−	0.0681240i
$597$	8.38794e90	+	1.28070e91i	0.207254	+	0.316442i
$598$	−2.30293e91			−0.538445
$599$			1.12554e91i			0.249045i	0.992217	+	0.124522i	$0.0397399\pi$
$599$			1.12554e91i			0.249045i	−0.992217	+	0.124522i	$0.960260\pi$
$600$	−6.24692e91	+	4.09142e91i	−1.30820	+	0.856807i
$601$	−1.58635e91			−0.314443			−0.157222	−	0.987563i	$-0.550254\pi$
$601$	−1.58635e91			−0.314443			−0.157222	+	0.987563i	$0.550254\pi$
$602$			7.52987e89i			0.0141287i
$603$	1.50323e91	−	3.44825e91i	0.267027	−	0.612530i
$604$	1.80548e90			0.0303650
$605$		−	4.90242e91i		−	0.780697i
$606$	1.66536e90	+	2.54273e90i	0.0251138	+	0.0383446i
$607$	1.24703e91			0.178094			0.0890470	−	0.996027i	$-0.471618\pi$
$607$	1.24703e91			0.178094			0.0890470	+	0.996027i	$0.471618\pi$
$608$			3.74620e91i			0.506726i
$609$	1.77574e90	−	1.16302e90i	0.0227515	−	0.0149011i
$610$	−1.20061e92			−1.45719
$611$		−	5.38418e91i		−	0.619098i
$612$	−1.01392e91	−	4.42009e90i	−0.110460	−	0.0481542i
$613$	6.56391e91			0.677590			0.338795	−	0.940860i	$-0.389981\pi$
$613$	6.56391e91			0.677590			0.338795	+	0.940860i	$0.389981\pi$
$614$		−	1.88332e92i		−	1.84233i
$615$	2.17589e91	+	3.32221e91i	0.201724	+	0.307999i
$616$	3.44822e90			0.0302993
$617$			8.00028e91i			0.666339i	0.942867	+	0.333169i	$0.108118\pi$
$617$			8.00028e91i			0.666339i	−0.942867	+	0.333169i	$0.891882\pi$
$618$	1.31922e92	−	8.64025e91i	1.04159	−	0.682192i
$619$	8.03328e91			0.601314			0.300657	−	0.953732i	$-0.402794\pi$
$619$	8.03328e91			0.601314			0.300657	+	0.953732i	$0.402794\pi$
$620$		−	5.56955e90i		−	0.0395270i
$621$	3.71544e91	+	2.18086e92i	0.250027	+	1.46759i
$622$	−5.68543e91			−0.362811
$623$		−	2.03033e90i		−	0.0122874i
$624$	3.63395e91	+	5.54843e91i	0.208587	+	0.318478i
$625$	4.54720e91			0.247573
$626$		−	2.98849e92i		−	1.54347i
$627$	3.38766e92	−	2.21875e92i	1.65986	−	1.08713i
$628$	−3.23841e91			−0.150544
$629$			1.14682e92i			0.505851i
$630$	4.66258e90	−	1.06954e91i	0.0195159	−	0.0447672i
$631$	−3.20798e92			−1.27428			−0.637138	−	0.770750i	$-0.719882\pi$
$631$	−3.20798e92			−1.27428			−0.637138	+	0.770750i	$0.719882\pi$
$632$		−	9.26690e91i		−	0.349358i
$633$	−1.50117e92	−	2.29203e92i	−0.537164	−	0.820159i
$634$	−2.27324e92			−0.772147
$635$			6.23488e92i			2.01046i
$636$	−1.32843e91	+	8.70058e90i	−0.0406682	+	0.0266357i
$637$	−1.15625e92			−0.336087
$638$			4.67345e92i			1.28990i
$639$	−2.62278e92	−	1.14338e92i	−0.687439	−	0.299683i
$640$	7.74872e92			1.92882
$641$			1.37911e92i			0.326049i	0.986622	+	0.163024i	$0.0521250\pi$
$641$			1.37911e92i			0.326049i	−0.986622	+	0.163024i	$0.947875\pi$
$642$	1.40083e92	+	2.13883e92i	0.314579	+	0.480309i
$643$	−6.95961e92			−1.48465			−0.742323	−	0.670042i	$-0.766276\pi$
$643$	−6.95961e92			−1.48465			−0.742323	+	0.670042i	$0.766276\pi$
$644$		−	3.16039e90i		−	0.00640483i
$645$	3.42365e92	−	2.24232e92i	0.659203	−	0.431745i
$646$	−7.40632e92			−1.35497
$647$			5.83089e92i			1.01366i	0.862045	+	0.506832i	$0.169183\pi$
$647$			5.83089e92i			1.01366i	−0.862045	+	0.506832i	$0.830817\pi$
$648$	4.02327e92	−	3.73751e92i	0.664667	−	0.617458i
$649$	−1.21179e93			−1.90262
$650$		−	4.17773e92i		−	0.623447i
$651$	−1.62825e90	−	2.48606e90i	−0.00230966	−	0.00352646i
$652$	1.10341e92			0.148787
$653$		−	2.57137e92i		−	0.329632i	−0.986324	−	0.164816i	$-0.947297\pi$
$653$		−	2.57137e92i		−	0.329632i	0.986324	−	0.164816i	$-0.0527030\pi$
$654$	−3.75138e92	+	2.45697e92i	−0.457220	+	0.299456i
$655$	2.31020e93			2.67724
$656$		−	2.29144e92i		−	0.252512i
$657$	−4.84983e92	+	1.11250e93i	−0.508241	+	1.16585i
$658$	5.46501e91			0.0544674
$659$		−	8.55397e92i		−	0.810866i	−0.914125	−	0.405433i	$-0.867121\pi$
$659$		−	8.55397e92i		−	0.810866i	0.914125	−	0.405433i	$-0.132879\pi$
$660$	1.90290e92	+	2.90541e92i	0.171579	+	0.261973i
$661$	1.13035e93			0.969535			0.484767	−	0.874643i	$-0.338904\pi$
$661$	1.13035e93			0.969535			0.484767	+	0.874643i	$0.338904\pi$
$662$		−	8.87606e92i		−	0.724280i
$663$	−2.79338e92	+	1.82953e92i	−0.216862	+	0.142034i
$664$	1.57016e93			1.15984
$665$		−	1.05630e92i		−	0.0742459i
$666$	9.67211e92	+	4.21647e92i	0.646952	+	0.282033i
$667$	−2.31139e93			−1.47137
$668$			3.57189e91i			0.0216409i
$669$	−5.20018e92	−	7.93981e92i	−0.299886	−	0.457877i
$670$	2.16025e93			1.18587
$671$		−	1.90695e93i		−	0.996545i
$672$	−1.43413e91	+	9.39287e90i	−0.00713516	+	0.00467318i
$673$	−1.55143e93			−0.734912			−0.367456	−	0.930041i	$-0.619771\pi$
$673$	−1.55143e93			−0.734912			−0.367456	+	0.930041i	$0.619771\pi$
$674$		−	3.46929e93i		−	1.56482i
$675$	−3.95628e93	+	6.74016e92i	−1.69927	+	0.289498i
$676$	3.38983e92			0.138656
$677$			2.55939e93i			0.997036i	0.866879	+	0.498518i	$0.166122\pi$
$677$			2.55939e93i			0.997036i	−0.866879	+	0.498518i	$0.833878\pi$
$678$	−2.03906e93	−	3.11330e93i	−0.756572	−	1.15516i
$679$	−1.11352e92			−0.0393545
$680$			3.42768e93i			1.15400i
$681$	2.52272e93	−	1.65225e93i	0.809121	−	0.529934i
$682$	6.54289e92			0.199933
$683$			1.98103e93i			0.576775i	0.957514	+	0.288388i	$0.0931192\pi$
$683$			1.98103e93i			0.576775i	−0.957514	+	0.288388i	$0.906881\pi$
$684$	−3.68169e92	+	8.44538e92i	−0.102140	+	0.234298i
$685$	9.20747e93			2.43417
$686$		−	2.34812e92i		−	0.0591594i
$687$	1.15994e93	+	1.77104e93i	0.278526	+	0.425262i
$688$	−2.36141e93			−0.540447
$689$			4.79408e92i			0.104585i
$690$	−1.06281e94	+	6.96085e93i	−2.21021	+	1.44758i
$691$	−2.68699e93			−0.532709			−0.266354	−	0.963875i	$-0.585819\pi$
$691$	−2.68699e93			−0.532709			−0.266354	+	0.963875i	$0.585819\pi$
$692$		−	1.72762e91i		−	0.00326548i
$693$	1.69878e92	+	7.40569e91i	0.0306155	+	0.0133465i
$694$	−3.60561e93			−0.619607
$695$			1.11081e94i			1.82029i
$696$	3.14353e93	+	4.79964e93i	0.491261	+	0.750074i
$697$	1.15364e93			0.171944
$698$		−	7.06242e93i		−	1.00398i
$699$	1.08145e94	−	7.08294e93i	1.46642	−	0.960432i
$700$	5.73325e91			0.00741593
$701$		−	8.33635e92i		−	0.102868i	−0.998676	−	0.0514341i	$-0.983621\pi$
$701$		−	8.33635e92i		−	0.102868i	0.998676	−	0.0514341i	$-0.0163792\pi$
$702$	5.15964e92	+	3.02856e93i	0.0607428	+	0.356543i
$703$	9.55234e93			1.07296
$704$			9.04339e93i			0.969245i
$705$	−1.62743e94	−	2.48481e94i	−1.66441	−	2.54128i
$706$	−8.95553e93			−0.874050
$707$			1.25929e91i			0.00117297i
$708$	2.30626e93	−	1.51049e93i	0.205027	−	0.134282i
$709$	−1.61122e94			−1.36719			−0.683595	−	0.729862i	$-0.739584\pi$
$709$	−1.61122e94			−1.36719			−0.683595	+	0.729862i	$0.739584\pi$
$710$		−	1.64312e94i		−	1.33089i
$711$	1.99023e93	−	4.56537e93i	0.153889	−	0.353004i
$712$	5.48776e93			0.405094
$713$			3.23598e93i			0.228061i
$714$	−1.85699e92	−	2.83532e92i	−0.0124959	−	0.0190792i
$715$	1.04851e94			0.673709
$716$		−	1.43834e93i		−	0.0882533i
$717$	4.87799e93	−	3.19484e93i	0.285831	−	0.187205i
$718$	4.36799e93			0.244442
$719$		−	1.68923e94i		−	0.902893i	−0.892298	−	0.451447i	$-0.850908\pi$
$719$		−	1.68923e94i		−	0.902893i	0.892298	−	0.451447i	$-0.149092\pi$
$720$	3.35415e94	+	1.46221e94i	1.71242	+	0.746514i
$721$	6.53347e92			0.0318625
$722$			3.86086e94i			1.79869i
$723$	1.90555e94	+	2.90945e94i	0.848118	+	1.29493i
$724$	1.25105e93			0.0531987
$725$		−	4.19309e94i		−	1.70365i
$726$	−1.09608e94	+	7.17875e93i	−0.425532	+	0.278702i
$727$	1.89497e94			0.703019			0.351510	−	0.936184i	$-0.385668\pi$
$727$	1.89497e94			0.703019			0.351510	+	0.936184i	$0.385668\pi$
$728$			2.36832e92i			0.00839664i
$729$	2.78478e94	−	9.77228e93i	0.943588	−	0.331122i
$730$	−6.96954e94			−2.25710
$731$		−	1.18886e94i		−	0.368008i
$732$	2.37700e93	+	3.62928e93i	0.0703337	+	0.107388i
$733$	−4.52051e94			−1.27866			−0.639332	−	0.768931i	$-0.720789\pi$
$733$	−4.52051e94			−1.27866			−0.639332	+	0.768931i	$0.720789\pi$
$734$		−	3.78972e94i		−	1.02479i
$735$	−5.33614e94	+	3.49491e94i	−1.37957	+	0.903552i
$736$	1.86674e94			0.461441
$737$			3.43118e94i			0.810992i
$738$	4.24155e93	−	9.72963e93i	0.0958659	−	0.219906i
$739$	−2.42681e94			−0.524528			−0.262264	−	0.964996i	$-0.584469\pi$
$739$	−2.42681e94			−0.524528			−0.262264	+	0.964996i	$0.584469\pi$
$740$			8.19250e93i			0.169344i
$741$	1.52389e94	+	2.32673e94i	0.301268	+	0.459986i
$742$	−4.86605e92			−0.00920127
$743$		−	9.95759e93i		−	0.180104i	−0.995937	−	0.0900520i	$-0.971297\pi$
$743$		−	9.95759e93i		−	0.180104i	0.995937	−	0.0900520i	$-0.0287033\pi$
$744$	6.71956e93	−	4.40098e93i	0.116261	−	0.0761452i
$745$	−4.34475e94			−0.719131
$746$			5.66363e94i			0.896837i
$747$	7.73548e94	+	3.37222e94i	1.17195	+	0.510899i
$748$	1.00890e94			0.146250
$749$			1.05926e93i			0.0146927i
$750$	−5.30198e94	−	8.09524e94i	−0.703746	−	1.07450i
$751$	−3.44876e94			−0.438071			−0.219036	−	0.975717i	$-0.570291\pi$
$751$	−3.44876e94			−0.438071			−0.219036	+	0.975717i	$0.570291\pi$
$752$			1.71386e95i			2.08346i
$753$	2.04225e94	−	1.33757e94i	0.237616	−	0.155626i
$754$	−3.20984e94			−0.357461
$755$		−	3.00699e94i		−	0.320540i
$756$	−4.15620e92	+	7.08077e91i	−0.00424109	+	0.000722538i
$757$	8.67449e94			0.847383			0.423692	−	0.905806i	$-0.360734\pi$
$757$	8.67449e94			0.847383			0.423692	+	0.905806i	$0.360734\pi$
$758$		−	1.67970e95i		−	1.57090i
$759$	−1.10561e95	−	1.68808e95i	−0.989972	−	1.51152i
$760$	2.85506e95			2.44775
$761$			8.54347e94i			0.701360i	0.936495	+	0.350680i	$0.114049\pi$
$761$			8.54347e94i			0.701360i	−0.936495	+	0.350680i	$0.885951\pi$
$762$	1.39399e95	−	9.12992e94i	1.09583	−	0.717716i
$763$	−1.85788e93			−0.0139864
$764$		−	1.34684e94i		−	0.0971034i
$765$	−7.36156e94	+	1.68866e95i	−0.508327	+	1.16604i
$766$	−6.19131e94			−0.409480
$767$		−	8.32287e94i		−	0.527262i
$768$	−4.13652e94	−	6.31577e94i	−0.251024	−	0.383271i
$769$	1.67762e95			0.975267			0.487633	−	0.873048i	$-0.337860\pi$
$769$	1.67762e95			0.975267			0.487633	+	0.873048i	$0.337860\pi$
$770$			1.06425e94i			0.0592720i
$771$	−1.02589e95	+	6.71905e94i	−0.547401	+	0.358520i
$772$	1.72048e93			0.00879585
$773$		−	6.04607e94i		−	0.296176i	−0.988974	−	0.148088i	$-0.952688\pi$
$773$		−	6.04607e94i		−	0.296176i	0.988974	−	0.148088i	$-0.0473119\pi$
$774$	−1.00267e95	−	4.37106e94i	−0.470659	−	0.205180i
$775$	−5.87038e94			−0.264064
$776$		−	3.00972e95i		−	1.29744i
$777$	2.39507e93	+	3.65687e93i	0.00989518	+	0.0151083i
$778$	−3.66881e95			−1.45277
$779$		−	9.60914e94i		−	0.364711i
$780$	−1.99550e94	+	1.30696e94i	−0.0725990	+	0.0475487i
$781$	2.60980e95			0.910171
$782$			3.69059e95i			1.23388i
$783$	5.17861e94	+	3.03969e95i	0.165987	+	0.974298i
$784$	3.68052e95			1.13104
$785$			5.39351e95i			1.58918i
$786$	−3.38290e95	−	5.16512e95i	−0.955751	−	1.45927i
$787$	−1.32615e95			−0.359276			−0.179638	−	0.983733i	$-0.557493\pi$
$787$	−1.32615e95			−0.359276			−0.179638	+	0.983733i	$0.557493\pi$
$788$			8.96276e94i			0.232850i
$789$	−2.70277e95	+	1.77018e95i	−0.673392	+	0.441038i
$790$	2.86011e95			0.683421
$791$		−	1.54187e94i		−	0.0353365i
$792$	−2.00168e95	+	4.59162e95i	−0.440011	+	1.00934i
$793$	1.30974e95			0.276166
$794$		−	8.56608e95i		−	1.73263i
$795$	1.44906e95	+	2.21248e95i	0.281172	+	0.429303i
$796$	3.17695e94			0.0591398
$797$			8.42738e95i			1.50511i	0.658530	+	0.752555i	$0.271179\pi$
$797$			8.42738e95i			1.50511i	−0.658530	+	0.752555i	$0.728821\pi$
$798$	−2.36166e94	+	1.54677e94i	−0.0404689	+	0.0265052i
$799$	−8.62848e95			−1.41870
$800$			3.38644e95i			0.534287i
$801$	2.70357e95	+	1.17860e95i	0.409321	+	0.178440i
$802$	7.44999e95			1.08243
$803$		−	1.10699e96i		−	1.54358i
$804$	−4.27694e94	−	6.53017e94i	−0.0572378	−	0.0873926i
$805$	−5.26356e94			−0.0676108
$806$			4.49382e94i			0.0554063i
$807$	−2.76032e95	+	1.80787e95i	−0.326687	+	0.213964i
$808$	−3.40373e94			−0.0386706
$809$		−	4.68558e95i		−	0.511049i	−0.966803	−	0.255524i	$-0.917752\pi$
$809$		−	4.68558e95i		−	0.511049i	0.966803	−	0.255524i	$-0.0822481\pi$
$810$	1.15353e96	+	1.24173e96i	1.20788	+	1.30023i
$811$	5.27219e94			0.0530033			0.0265016	−	0.999649i	$-0.491563\pi$
$811$	5.27219e94			0.0530033			0.0265016	+	0.999649i	$0.491563\pi$
$812$		−	4.40498e93i		−	0.00425202i
$813$	−7.76690e95	−	1.18588e96i	−0.719880	−	1.09914i
$814$	−9.62424e95			−0.856566
$815$		−	1.83770e96i		−	1.57063i
$816$	8.89171e95	−	5.82363e95i	0.729811	−	0.477990i
$817$	−9.90255e95			−0.780583
$818$		−	2.38647e95i		−	0.180675i
$819$	−5.08641e93	+	1.16676e94i	−0.00369864	+	0.00848427i
$820$	8.24122e94			0.0575618
$821$		−	7.84633e95i		−	0.526432i	−0.964737	−	0.263216i	$-0.915217\pi$
$821$		−	7.84633e95i		−	0.526432i	0.964737	−	0.263216i	$-0.0847832\pi$
$822$	−1.34828e96	−	2.05859e96i	−0.868978	−	1.32678i
$823$	2.70958e96			1.67767			0.838837	−	0.544382i	$-0.183236\pi$
$823$	2.70958e96			1.67767			0.838837	+	0.544382i	$0.183236\pi$
$824$			1.76593e96i			1.05045i
$825$	3.06234e96	−	2.00568e96i	1.75014	−	1.14625i
$826$	8.44782e94			0.0463878
$827$			1.84397e96i			0.972911i	0.873705	+	0.486455i	$0.161710\pi$
$827$			1.84397e96i			0.972911i	−0.873705	+	0.486455i	$0.838290\pi$
$828$	4.20835e95	+	1.83459e95i	0.213359	+	0.0930120i
$829$	−2.94745e96			−1.43597			−0.717987	−	0.696057i	$-0.754936\pi$
$829$	−2.94745e96			−1.43597			−0.717987	+	0.696057i	$0.754936\pi$
$830$			4.84611e96i			2.26890i
$831$	1.28749e96	+	1.96579e96i	0.579310	+	0.884510i
$832$	−6.21122e95			−0.268601
$833$			1.85297e96i			0.770164i
$834$	2.48353e96	−	1.62659e96i	0.992178	−	0.649828i
$835$	5.94891e95			0.228446
$836$		−	8.40357e95i		−	0.310211i
$837$	4.25561e95	−	7.25012e94i	0.151016	−	0.0257279i
$838$	−4.27653e96			−1.45894
$839$		−	3.08779e95i		−	0.101275i	−0.998717	−	0.0506376i	$-0.983875\pi$
$839$		−	3.08779e95i		−	0.101275i	0.998717	−	0.0506376i	$-0.0161253\pi$
$840$	7.15852e94	+	1.09299e95i	0.0225739	+	0.0344666i
$841$	7.64910e94			0.0231922
$842$			2.47865e95i			0.0722630i
$843$	−3.78013e96	+	2.47580e96i	−1.05973	+	0.694073i
$844$	−5.68571e95			−0.153279
$845$		−	5.64569e96i		−	1.46368i
$846$	−3.17241e96	+	7.27716e96i	−0.790984	+	1.81443i
$847$	−5.42833e94			−0.0130171
$848$		−	1.52602e96i		−	0.351963i
$849$	−3.35215e96	−	5.11818e96i	−0.743653	−	1.13543i
$850$	−6.69507e96			−1.42867
$851$		−	4.75995e96i		−	0.977074i
$852$	−4.96693e95	+	3.25309e95i	−0.0980802	+	0.0642376i
$853$	2.62395e96			0.498469			0.249234	−	0.968443i	$-0.419821\pi$
$853$	2.62395e96			0.498469			0.249234	+	0.968443i	$0.419821\pi$
$854$			1.32941e95i			0.0242967i
$855$	1.40656e97	+	6.13177e96i	2.47330	+	1.07821i
$856$	−2.86307e96			−0.484392
$857$			9.11913e96i			1.48452i	0.670112	+	0.742260i	$0.266246\pi$
$857$			9.11913e96i			1.48452i	−0.670112	+	0.742260i	$0.733754\pi$
$858$	−1.53536e96	−	2.34424e96i	−0.240508	−	0.367216i
$859$	2.29009e96			0.345205			0.172603	−	0.984992i	$-0.444782\pi$
$859$	2.29009e96			0.345205			0.172603	+	0.984992i	$0.444782\pi$
$860$		−	8.49285e95i		−	0.123198i
$861$	3.67861e94	−	2.40931e94i	0.00513547	−	0.00336348i
$862$	1.49644e97			2.01058
$863$		−	3.37141e94i		−	0.00435968i	−0.999998	−	0.00217984i	$-0.999306\pi$
$863$		−	3.37141e94i		−	0.00435968i	0.999998	−	0.00217984i	$-0.000693866\pi$
$864$	−4.18238e95	−	2.45493e96i	−0.0520558	−	0.305553i
$865$	−2.87731e95			−0.0344711
$866$		−	1.10066e97i		−	1.26930i
$867$	−2.00354e96	−	3.05907e96i	−0.222417	−	0.339594i
$868$	−6.16703e93			−0.000659060
$869$			4.54277e96i			0.467378i
$870$	−1.48135e97	+	9.70209e96i	−1.46731	+	0.961015i
$871$	−2.35662e96			−0.224745
$872$		−	5.02164e96i		−	0.461107i
$873$	6.46391e96	−	1.48275e97i	0.571512	−	1.31098i
$874$	3.07405e97			2.61718
$875$		−	4.00918e95i		−	0.0328692i
$876$	1.37985e96	+	2.10680e96i	0.108942	+	0.166337i
$877$	9.48656e96			0.721310			0.360655	−	0.932699i	$-0.382553\pi$
$877$	9.48656e96			0.721310			0.360655	+	0.932699i	$0.382553\pi$
$878$		−	1.58880e97i		−	1.16346i
$879$	−1.27785e97	+	8.36925e96i	−0.901250	+	0.590274i
$880$	−3.33755e97			−2.26725
$881$			6.47659e96i			0.423781i	0.977293	+	0.211890i	$0.0679620\pi$
$881$			6.47659e96i			0.423781i	−0.977293	+	0.211890i	$0.932038\pi$
$882$	1.56277e97	+	6.81277e96i	0.984992	+	0.429399i
$883$	−5.21882e95			−0.0316861			−0.0158431	−	0.999874i	$-0.505043\pi$
$883$	−5.21882e95			−0.0316861			−0.0158431	+	0.999874i	$0.505043\pi$
$884$			6.92937e95i			0.0405293i
$885$	−2.51568e97	−	3.84102e97i	−1.41751	−	2.16431i
$886$	9.78666e96			0.531278
$887$		−	1.92757e97i		−	1.00816i	−0.863656	−	0.504081i	$-0.831831\pi$
$887$		−	1.92757e97i		−	1.00816i	0.863656	−	0.504081i	$-0.168169\pi$
$888$	−9.88412e96	+	6.47361e96i	−0.498092	+	0.326226i
$889$	6.90374e95			0.0335217
$890$			1.69373e97i			0.792452i
$891$	−1.97227e97	+	1.83218e97i	−0.889206	+	0.826048i
$892$	−1.96958e96			−0.0855725
$893$			7.18704e97i			3.00921i
$894$	6.36215e96	+	9.71394e96i	0.256724	+	0.391974i
$895$	−2.39552e97			−0.931621
$896$		−	8.57998e95i		−	0.0321604i
$897$	1.15941e97	−	7.59359e96i	0.418878	−	0.274345i
$898$	4.08144e97			1.42133
$899$			4.51034e96i			0.151405i
$900$	−3.32813e96	+	7.63435e96i	−0.107695	+	0.247041i
$901$	7.68281e96			0.239664
$902$			9.68147e96i			0.291156i
$903$	−2.48287e95	−	3.79093e95i	−0.00719878	−	0.0109913i
$904$	4.16751e97			1.16498
$905$		−	2.08359e97i		−	0.561578i
$906$	−6.72298e96	+	4.40322e96i	−0.174716	+	0.114430i
$907$	−1.79689e97			−0.450279			−0.225140	−	0.974327i	$-0.572284\pi$
$907$	−1.79689e97			−0.450279			−0.225140	+	0.974327i	$0.572284\pi$
$908$		−	6.25795e96i		−	0.151217i
$909$	−1.67686e96	−	7.31014e95i	−0.0390741	−	0.0170340i
$910$	−7.30952e95			−0.0164257
$911$			3.40072e97i			0.736995i	0.929629	+	0.368498i	$0.120128\pi$
$911$			3.40072e97i			0.736995i	−0.929629	+	0.368498i	$0.879872\pi$
$912$	−4.85076e97	−	7.40630e97i	−1.01386	−	1.54800i
$913$	−7.69719e97			−1.55166
$914$			2.37830e97i			0.462425i
$915$	6.04449e97	−	3.95884e97i	1.13361	−	0.742458i
$916$	4.39332e96			0.0794771
$917$		−	2.55803e96i		−	0.0446394i
$918$	4.85346e97	−	8.26865e96i	0.817039	−	0.139196i
$919$	−4.05829e97			−0.659069			−0.329535	−	0.944143i	$-0.606892\pi$
$919$	−4.05829e97			−0.659069			−0.329535	+	0.944143i	$0.606892\pi$
$920$		−	1.42269e98i		−	2.22900i
$921$	6.20999e97	+	9.48161e97i	0.938691	+	1.43323i
$922$	−5.28155e97			−0.770267
$923$			1.79247e97i			0.252230i
$924$	3.21709e95	−	2.10703e95i	0.00436805	−	0.00286086i
$925$	8.63501e97			1.13132
$926$		−	1.04989e98i		−	1.32734i
$927$	−3.79265e97	+	8.69991e97i	−0.462713	+	1.06141i
$928$	2.60188e97			0.306340
$929$		−	5.09438e96i		−	0.0578860i	−0.999581	−	0.0289430i	$-0.990786\pi$
$929$		−	5.09438e96i		−	0.0578860i	0.999581	−	0.0289430i	$-0.00921412\pi$
$930$	1.35831e97	+	2.07391e97i	0.148957	+	0.227432i
$931$	1.54342e98			1.63360
$932$		−	2.68268e97i		−	0.274059i
$933$	2.86234e97	−	1.87469e97i	0.282246	−	0.184857i
$934$	−1.36634e98			−1.30050
$935$		−	1.68030e98i		−	1.54385i
$936$	−3.15364e97	−	1.37480e97i	−0.279711	−	0.121937i
$937$	−1.88930e98			−1.61769			−0.808844	−	0.588024i	$-0.799906\pi$
$937$	−1.88930e98			−1.61769			−0.808844	+	0.588024i	$0.799906\pi$
$938$		−	2.39200e96i		−	0.0197728i
$939$	9.85414e97	+	1.50456e98i	0.786420	+	1.20073i
$940$	−6.16392e97			−0.474939
$941$			3.76477e97i			0.280079i	0.990146	+	0.140040i	$0.0447230\pi$
$941$			3.76477e97i			0.280079i	−0.990146	+	0.140040i	$0.955277\pi$
$942$	1.20587e98	−	7.89787e97i	0.866207	−	0.567323i
$943$	−4.78826e97			−0.332118
$944$			2.64929e98i			1.77441i
$945$	1.17929e96	+	6.92207e96i	0.00762727	+	0.0447699i
$946$	9.97708e97			0.623155
$947$		−	1.50715e98i		−	0.909090i	−0.890724	−	0.454545i	$-0.849802\pi$
$947$		−	1.50715e98i		−	0.909090i	0.890724	−	0.454545i	$-0.150198\pi$
$948$	−5.66253e96	−	8.64573e96i	−0.0329864	−	0.0503647i
$949$	7.60307e97			0.427764
$950$			5.57662e98i			3.03035i
$951$	1.14447e98	−	7.49570e97i	0.600685	−	0.393419i
$952$	3.79539e96			0.0192414
$953$			1.09009e98i			0.533821i	0.963721	+	0.266910i	$0.0860028\pi$
$953$			1.09009e98i			0.533821i	−0.963721	+	0.266910i	$0.913997\pi$
$954$	2.82472e97	−	6.47959e97i	0.133622	−	0.306515i
$955$	−2.24313e98			−1.02504
$956$		−	1.21005e97i		−	0.0534188i
$957$	−1.54101e98	−	2.35286e98i	−0.657219	−	1.00346i
$958$	−2.79589e98			−1.15201
$959$		−	1.01952e97i		−	0.0405866i
$960$	−2.86649e98	+	1.87741e98i	−1.10255	+	0.722118i
$961$	−2.62760e98			−0.976532
$962$		−	6.61016e97i		−	0.237375i
$963$	−1.41050e98	−	6.14896e97i	−0.489447	−	0.213370i
$964$	7.21731e97			0.242010
$965$		−	2.86541e97i		−	0.0928509i
$966$	7.70759e96	+	1.17682e97i	0.0241365	+	0.0368523i
$967$	1.91439e98			0.579372			0.289686	−	0.957122i	$-0.406449\pi$
$967$	1.91439e98			0.579372			0.289686	+	0.957122i	$0.406449\pi$
$968$		−	1.46722e98i		−	0.429149i
$969$	3.72873e98	−	2.44213e98i	1.05409	−	0.690374i
$970$	9.28910e98			2.53809
$971$		−	1.29650e98i		−	0.342403i	−0.985236	−	0.171202i	$-0.945235\pi$
$971$		−	1.29650e98i		−	0.342403i	0.985236	−	0.171202i	$-0.0547650\pi$
$972$	1.46979e97	−	5.94540e97i	0.0375205	−	0.151773i
$973$	1.22997e97			0.0303509
$974$		−	2.77507e98i		−	0.661954i
$975$	1.37755e98	+	2.10329e98i	0.317654	+	0.485005i
$976$	−4.16909e98			−0.929389
$977$			1.83140e98i			0.394696i	0.980334	+	0.197348i	$0.0632329\pi$
$977$			1.83140e98i			0.394696i	−0.980334	+	0.197348i	$0.936767\pi$
$978$	−4.10871e98	+	2.69100e98i	−0.856099	+	0.560702i
$979$	−2.69018e98			−0.541942
$980$			1.32370e98i			0.257828i
$981$	1.07849e98	−	2.47393e98i	0.203113	−	0.465919i
$982$	5.85778e98			1.06673
$983$		−	1.03702e99i		−	1.82609i	−0.407856	−	0.913046i	$-0.633723\pi$
$983$		−	1.03702e99i		−	1.82609i	0.407856	−	0.913046i	$-0.366277\pi$
$984$	6.51210e97	+	9.94289e97i	0.110888	+	0.169307i
$985$	1.49273e99			2.45802
$986$			5.14397e98i			0.819144i
$987$	−2.75137e97	+	1.80201e97i	−0.0423724	+	0.0277518i
$988$	5.77178e97			0.0859667
$989$			4.93446e98i			0.710824i
$990$	−1.41714e99	−	6.17792e98i	−1.97448	−	0.860758i
$991$	1.98088e98			0.266949			0.133474	−	0.991052i	$-0.457387\pi$
$991$	1.98088e98			0.266949			0.133474	+	0.991052i	$0.457387\pi$
$992$		−	3.64266e97i		−	0.0474825i
$993$	2.92676e98	+	4.46867e98i	0.369030	+	0.563447i
$994$	−1.81938e97			−0.0221908
$995$		−	5.29115e98i		−	0.624292i
$996$	1.46492e98	−	9.59447e97i	0.167207	−	0.109512i
$997$	−1.13429e99			−1.25251			−0.626257	−	0.779617i	$-0.715414\pi$
$997$	−1.13429e99			−1.25251			−0.626257	+	0.779617i	$0.715414\pi$
$998$			2.94463e98i			0.314574i
$999$	−6.25977e98	+	1.06645e98i	−0.646990	+	0.110225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.67.b.b.2.15	yes	20
3.2	odd	2	inner	3.67.b.b.2.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.67.b.b.2.6	✓	20	3.2	odd	2	inner
3.67.b.b.2.15	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)

\(f(q)\)	\(=\)	\(q+9.23704e9i q^{2} +(-3.04579e15 - 4.65041e15i) q^{3} -1.15360e19 q^{4} +1.92130e23i q^{5} +(4.29561e25 - 2.81341e25i) q^{6} +2.12741e26 q^{7} +5.75015e29i q^{8} +(-1.23495e31 + 2.83283e31i) q^{9} +O(q^{10})\)	\(q+9.23704e9i q^{2} +(-3.04579e15 - 4.65041e15i) q^{3} -1.15360e19 q^{4} +1.92130e23i q^{5} +(4.29561e25 - 2.81341e25i) q^{6} +2.12741e26 q^{7} +5.75015e29i q^{8} +(-1.23495e31 + 2.83283e31i) q^{9} -1.77471e33 q^{10} -2.81881e34i q^{11} +(3.51362e34 + 5.36471e34i) q^{12} +1.93603e36 q^{13} +1.96509e36i q^{14} +(8.93481e38 - 5.85186e38i) q^{15} -6.16265e39 q^{16} -3.10261e40i q^{17} +(-2.61670e41 - 1.14073e41i) q^{18} -2.58430e42 q^{19} -2.21641e42i q^{20} +(-6.47963e41 - 9.89331e41i) q^{21} +2.60375e44 q^{22} +1.28776e45i q^{23} +(2.67406e45 - 1.75137e45i) q^{24} -2.33612e46 q^{25} +1.78832e46i q^{26} +(1.69352e47 - 2.88519e46i) q^{27} -2.45418e45 q^{28} +1.79489e48i q^{29} +(5.40539e48 + 8.25312e48i) q^{30} +2.51287e48 q^{31} -1.44960e49i q^{32} +(-1.31086e50 + 8.58550e49i) q^{33} +2.86589e50 q^{34} +4.08737e49i q^{35} +(1.42464e50 - 3.26796e50i) q^{36} -3.69630e51 q^{37} -2.38713e52i q^{38} +(-5.89673e51 - 9.00333e51i) q^{39} -1.10477e53 q^{40} +3.71828e52i q^{41} +(9.13850e51 - 5.98526e51i) q^{42} +3.83181e53 q^{43} +3.25178e53i q^{44} +(-5.44271e54 - 2.37270e54i) q^{45} -1.18951e55 q^{46} -2.78104e55i q^{47} +(1.87701e55 + 2.86588e55i) q^{48} -5.97230e55 q^{49} -2.15789e56i q^{50} +(-1.44284e56 + 9.44989e55i) q^{51} -2.23340e55 q^{52} +2.47624e56i q^{53} +(2.66506e56 + 1.56432e57i) q^{54} +5.41577e57 q^{55} +1.22329e56i q^{56} +(7.87123e57 + 1.20180e58i) q^{57} -1.65795e58 q^{58} -4.29894e58i q^{59} +(-1.03072e58 + 6.75070e57i) q^{60} +6.76510e58 q^{61} +2.32115e58i q^{62} +(-2.62724e57 + 6.02659e57i) q^{63} -3.20823e59 q^{64} +3.71968e59i q^{65} +(-7.93047e59 - 1.21085e60i) q^{66} -1.21724e60 q^{67} +3.57917e59i q^{68} +(5.98862e60 - 3.92225e60i) q^{69} -3.77553e59 q^{70} +9.25851e60i q^{71} +(-1.62892e61 - 7.10114e60i) q^{72} +3.92715e61 q^{73} -3.41429e61i q^{74} +(7.11533e61 + 1.08639e62i) q^{75} +2.98125e61 q^{76} -5.99676e60i q^{77} +(8.31641e61 - 5.44684e61i) q^{78} -1.61159e62 q^{79} -1.18403e63i q^{80} +(-6.49985e62 - 6.99681e62i) q^{81} -3.43459e62 q^{82} -2.73065e63i q^{83} +(7.47490e60 + 1.14129e61i) q^{84} +5.96102e63 q^{85} +3.53946e63i q^{86} +(8.34699e63 - 5.46686e63i) q^{87} +1.62086e64 q^{88} -9.54368e63i q^{89} +(2.19168e64 - 5.02746e64i) q^{90} +4.11872e62 q^{91} -1.48556e64i q^{92} +(-7.65368e63 - 1.16859e64i) q^{93} +2.56886e65 q^{94} -4.96520e65i q^{95} +(-6.74124e64 + 4.41518e64i) q^{96} -5.23415e65 q^{97} -5.51664e65i q^{98} +(7.98523e65 + 3.48109e65i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 48\!\cdots\!16 q^{3}+ \cdots + 15\!\cdots\!00 q^{9}+O(q^{10}) \) 20 * q + 4870975596954516 * q^3 - 874472713330987494880 * q^4 - 36458623571791371420365280 * q^6 + 12757412570419684480800346888 * q^7 + 15089557305995766698320873638900 * q^9	\( 20 q + 48\!\cdots\!16 q^{3}+ \cdots + 13\!\cdots\!00 q^{99}+O(q^{100}) \) 20 * q + 4870975596954516 * q^3 - 874472713330987494880 * q^4 - 36458623571791371420365280 * q^6 + 12757412570419684480800346888 * q^7 + 15089557305995766698320873638900 * q^9 - 783798592344000703899756417518400 * q^10 + 723313252400516086588885120719010464 * q^12 + 18091739616075205076630659610294803912 * q^13 + 291841906843973945390453919652713854400 * q^15 + 35169907781372839393817803526848507036160 * q^16 - 1327598375030727473316959111629621787325120 * q^18 - 2193455295604677957336968896648577476247000 * q^19 + 8465393426583554489761097856455177936278920 * q^21 - 19209253722854761211546865955725969475475520 * q^22 - 8536939678857788536491103872952212579880680960 * q^24 - 30700488848472932976681231276090805532106633100 * q^25 + 558391355065775903739609435927472633730508278964 * q^27 + 144501040816005166289020822469679267340863318592 * q^28 - 13469561117532417280775174235598750536019791067200 * q^30 + 6175065418525787560244925992300120132476837130440 * q^31 + 76031443883614128882573745917963369573166525959360 * q^33 - 607578292754219603165333260413176675880514014447360 * q^34 - 3175274131330481643421765009589425373421119877953760 * q^36 + 27435708863590762009354808934891346302092239434849928 * q^37 + 5521526696977593923927147874084291303373365890875080 * q^39 - 164157270356735970397207190518038139497893424374707200 * q^40 - 362475530834094311762041222130355899146344066985844160 * q^42 + 2995923276457113198574378450730231874677434142901437032 * q^43 + 2893961767142107219663835709681578507068881328379222400 * q^45 - 9354105762324374445425328051923657080564209708616152960 * q^46 + 44083933305287886033485048811587957889306840899931818496 * q^48 + 35901948198185324872729610934124248147969595380066179580 * q^49 + 244898096463243383440025305755038369424109352434412094720 * q^51 - 707065170108353883018319930521496060001554914206203205312 * q^52 - 386962012382976993771518038850875450617071434969909598880 * q^54 + 1313751320608480207642793301222628514163843327983665564800 * q^55 + 14469858017237851043428899294433298407417456132214681222568 * q^57 - 100361163480954821917122043432794223233970822326053950441920 * q^58 + 188095594234899922680776576921513155518384075353356847385600 * q^60 + 36618251899234461407858901457296968011564547062158638752840 * q^61 + 1345036046130625400347897603264169586395820510566342530416072 * q^63 - 4235878925879978009146455436735085155393347326504147849175040 * q^64 + 8309681532541455738248790801869091701653966958238676467844800 * q^66 - 6285867272675020649645690828535183608121600074432515838268632 * q^67 + 26395268384310228436148510386607667671115625880708467370286720 * q^69 - 53673269104481250134670425876769459429788829882429608923689600 * q^70 + 135607917285688125946137613885497485690645144416066370695173120 * q^72 - 234584045940242428610177340241689807173326553683343804321823128 * q^73 + 123839979253809259811223462461211616240588739801286415169843700 * q^75 - 88416171262693699731320177563519953392160098165342187898838720 * q^76 + 42333034554100439516880814575759716324771014654582144994836800 * q^78 - 180033150591234061548131792670437122720422789571688775376700600 * q^79 - 2669759984009083569841876166867012798635236563858567744127147180 * q^81 + 9780548955253740491517774427483475844287869484539284101189512320 * q^82 - 29550683862870558945501681808473602755499090201740971929153891520 * q^84 + 15725476767553808561610465539289169056529282358913795578981260800 * q^85 - 20361537149674837364457194316410702650457831770981879709222020800 * q^87 + 43127341602231234631198337877354797375008485566513397535855918080 * q^88 - 68986845993042571618317468832763287342807845905185213796199009600 * q^90 - 166695697853283961323776703924127811908080973516544145788509117360 * q^91 + 50074015382338903474492727100775024610496294621525101240240943432 * q^93 - 243292275786183398644891798798613800120302016678942850492866824960 * q^94 + 1707340756716414995397633331453898170371668874444383803046536028160 * q^96 - 2044564925167962718092629881048800142635399871213696847289077976152 * q^97 + 1311784025950014883691036763145966005164166837426590048709685526400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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