LMFDB - Embedded newform 3.67.b.b.2.11

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			2.11
Root			$96378.2i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.67.b.b.2.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.46962e6i q^{2} +(-1.28962e15 + 5.40740e15i) q^{3} +7.37870e19 q^{4} +7.05043e22i q^{5} +(-1.87616e22 - 4.47450e21i) q^{6} +2.25837e27 q^{7} +5.12025e26i q^{8} +(-2.75769e31 - 1.39470e31i) q^{9} +O(q^{10})$	\(q+3.46962e6i q^{2} +(-1.28962e15 + 5.40740e15i) q^{3} +7.37870e19 q^{4} +7.05043e22i q^{5} +(-1.87616e22 - 4.47450e21i) q^{6} +2.25837e27 q^{7} +5.12025e26i q^{8} +(-2.75769e31 - 1.39470e31i) q^{9} -2.44623e29 q^{10} -1.85844e34i q^{11} +(-9.51574e34 + 3.98996e35i) q^{12} +3.22617e36 q^{13} +7.83568e33i q^{14} +(-3.81245e38 - 9.09240e37i) q^{15} +5.44452e39 q^{16} -1.45423e39i q^{17} +(4.83909e37 - 9.56812e37i) q^{18} +1.46014e42 q^{19} +5.20230e42i q^{20} +(-2.91245e42 + 1.22119e43i) q^{21} +6.44807e40 q^{22} +1.37479e45i q^{23} +(-2.76873e42 - 6.60319e41i) q^{24} +8.58167e45 q^{25} +1.11936e43i q^{26} +(1.10981e47 - 1.31133e47i) q^{27} +1.66638e47 q^{28} -2.34553e48i q^{29} +(3.15471e44 - 1.32277e45i) q^{30} +2.48306e49 q^{31} +5.66711e46i q^{32} +(1.00493e50 + 2.39669e49i) q^{33} +5.04562e45 q^{34} +1.59225e50i q^{35} +(-2.03482e51 - 1.02911e51i) q^{36} -2.99601e51 q^{37} +5.06614e48i q^{38} +(-4.16054e51 + 1.74452e52i) q^{39} -3.60999e49 q^{40} +5.53989e52i q^{41} +(-4.23707e49 - 1.01051e49i) q^{42} +5.79437e53 q^{43} -1.37128e54i q^{44} +(9.83326e53 - 1.94429e54i) q^{45} -4.76998e51 q^{46} +4.20114e54i q^{47} +(-7.02138e54 + 2.94407e55i) q^{48} -5.46680e55 q^{49} +2.97751e52i q^{50} +(7.86361e54 + 1.87541e54i) q^{51} +2.38049e56 q^{52} -7.32848e56i q^{53} +(4.54981e53 + 3.85062e53i) q^{54} +1.31028e57 q^{55} +1.15634e54i q^{56} +(-1.88304e57 + 7.89559e57i) q^{57} +8.13807e54 q^{58} -7.26572e57i q^{59} +(-2.81309e58 - 6.70901e57i) q^{60} -1.08751e58 q^{61} +8.61525e55i q^{62} +(-6.22788e58 - 3.14976e58i) q^{63} +4.01734e59 q^{64} +2.27459e59i q^{65} +(-8.31558e55 + 3.48673e56i) q^{66} +1.44521e60 q^{67} -1.07303e59i q^{68} +(-7.43403e60 - 1.77296e60i) q^{69} -5.52449e56 q^{70} +1.04157e61i q^{71} +(7.14123e57 - 1.41201e58i) q^{72} +1.98450e61 q^{73} -1.03950e58i q^{74} +(-1.10671e61 + 4.64046e61i) q^{75} +1.07740e62 q^{76} -4.19704e61i q^{77} +(-6.05281e58 - 1.44355e58i) q^{78} -3.79184e62 q^{79} +3.83862e62i q^{80} +(5.65965e62 + 7.69232e62i) q^{81} -1.92213e59 q^{82} +3.32800e63i q^{83} +(-2.14901e62 + 9.01080e62i) q^{84} +1.02529e62 q^{85} +2.01042e60i q^{86} +(1.26832e64 + 3.02485e63i) q^{87} +9.51566e60 q^{88} +3.93657e64i q^{89} +(6.74594e60 + 3.41176e60i) q^{90} +7.28588e63 q^{91} +1.01441e65i q^{92} +(-3.20221e64 + 1.34269e65i) q^{93} -1.45763e61 q^{94} +1.02946e65i q^{95} +(-3.06444e62 - 7.30845e61i) q^{96} +5.02502e65 q^{97} -1.89677e62i q^{98} +(-2.59197e65 + 5.12499e65i) 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 $

$2$			3.46962e6i			0.000403916i	1.00000		0.000201958i	$6.42853e-5\pi$
$2$			3.46962e6i			0.000403916i	−1.00000		0.000201958i	$0.999936\pi$
$3$	−1.28962e15	+	5.40740e15i	−0.231986	+	0.972719i
$3$	−1.28962e15	+	5.40740e15i	−0.231986	+	0.972719i
$4$	7.37870e19			1.00000
$5$			7.05043e22i			0.605627i	0.953050	+	0.302814i	$0.0979260\pi$
$5$			7.05043e22i			0.605627i	−0.953050	+	0.302814i	$0.902074\pi$
$6$	−1.87616e22	−	4.47450e21i	−0.000392897	−	9.37029e-5i
$7$	2.25837e27			0.292119			0.146059	−	0.989276i	$-0.453341\pi$
$7$	2.25837e27			0.292119			0.146059	+	0.989276i	$0.453341\pi$
$8$			5.12025e26i			0.000807833i
$9$	−2.75769e31	−	1.39470e31i	−0.892365	−	0.451314i
$10$	−2.44623e29			−0.000244623
$11$		−	1.85844e34i		−	0.800183i	−0.916475	−	0.400092i	$-0.868978\pi$
$11$		−	1.85844e34i		−	0.800183i	0.916475	−	0.400092i	$-0.131022\pi$
$12$	−9.51574e34	+	3.98996e35i	−0.231986	+	0.972719i
$13$	3.22617e36			0.560475			0.280237	−	0.959931i	$-0.409587\pi$
$13$	3.22617e36			0.560475			0.280237	+	0.959931i	$0.409587\pi$
$14$			7.83568e33i			0.000117992i
$15$	−3.81245e38	−	9.09240e37i	−0.589105	−	0.140497i
$16$	5.44452e39			1.00000
$17$		−	1.45423e39i		−	0.0361259i	−0.999837	−	0.0180629i	$-0.994250\pi$
$17$		−	1.45423e39i		−	0.0361259i	0.999837	−	0.0180629i	$-0.00574993\pi$
$18$	4.83909e37	−	9.56812e37i	0.000182293	−	0.000360441i
$19$	1.46014e42			0.923691			0.461846	−	0.886960i	$-0.347187\pi$
$19$	1.46014e42			0.923691			0.461846	+	0.886960i	$0.347187\pi$
$20$			5.20230e42i			0.605627i
$21$	−2.91245e42	+	1.22119e43i	−0.0677675	+	0.284150i
$22$	6.44807e40			0.000323207
$23$			1.37479e45i			1.58934i	0.607041	+	0.794670i	$0.292356\pi$
$23$			1.37479e45i			1.58934i	−0.607041	+	0.794670i	$0.707644\pi$
$24$	−2.76873e42	−	6.60319e41i	−0.000785794	−	0.000187406i
$25$	8.58167e45			0.633216
$26$			1.11936e43i			0.000226385i
$27$	1.10981e47	−	1.31133e47i	0.646018	−	0.763322i
$28$	1.66638e47			0.292119
$29$		−	2.34553e48i		−	1.29154i	−0.763534	−	0.645768i	$-0.776537\pi$
$29$		−	2.34553e48i		−	1.29154i	0.763534	−	0.645768i	$-0.223463\pi$
$30$	3.15471e44	−	1.32277e45i	5.67490e−5	−	0.000237949i
$31$	2.48306e49			1.51374			0.756869	−	0.653567i	$-0.226728\pi$
$31$	2.48306e49			1.51374			0.756869	+	0.653567i	$0.226728\pi$
$32$			5.66711e46i			0.00121175i
$33$	1.00493e50	+	2.39669e49i	0.778354	+	0.185631i
$34$	5.04562e45			1.45918e−5
$35$			1.59225e50i			0.176915i
$36$	−2.03482e51	−	1.02911e51i	−0.892365	−	0.451314i
$37$	−2.99601e51			−0.531969			−0.265985	−	0.963977i	$-0.585697\pi$
$37$	−2.99601e51			−0.531969			−0.265985	+	0.963977i	$0.585697\pi$
$38$			5.06614e48i			0.000373094i
$39$	−4.16054e51	+	1.74452e52i	−0.130022	+	0.545185i
$40$	−3.60999e49			−0.000489246
$41$			5.53989e52i			0.332379i	0.986094	+	0.166190i	$0.0531464\pi$
$41$			5.53989e52i			0.332379i	−0.986094	+	0.166190i	$0.946854\pi$
$42$	−4.23707e49	−	1.01051e49i	−0.000114773	−	2.73724e-5i
$43$	5.79437e53			0.722016			0.361008	−	0.932563i	$-0.382433\pi$
$43$	5.79437e53			0.722016			0.361008	+	0.932563i	$0.382433\pi$
$44$		−	1.37128e54i		−	0.800183i
$45$	9.83326e53	−	1.94429e54i	0.273328	−	0.540441i
$46$	−4.76998e51			−0.000641961
$47$			4.20114e54i			0.278060i	0.990288	+	0.139030i	$0.0443984\pi$
$47$			4.20114e54i			0.278060i	−0.990288	+	0.139030i	$0.955602\pi$
$48$	−7.02138e54	+	2.94407e55i	−0.231986	+	0.972719i
$49$	−5.46680e55			−0.914667
$50$			2.97751e52i			0.000255766i
$51$	7.86361e54	+	1.87541e54i	0.0351403	+	0.00838070i
$52$	2.38049e56			0.560475
$53$		−	7.32848e56i		−	0.920259i	−0.887852	−	0.460130i	$-0.847803\pi$
$53$		−	7.32848e56i		−	0.920259i	0.887852	−	0.460130i	$-0.152197\pi$
$54$	4.54981e53	+	3.85062e53i	0.000308318	+	0.000260937i
$55$	1.31028e57			0.484613
$56$			1.15634e54i			0.000235983i
$57$	−1.88304e57	+	7.89559e57i	−0.214283	+	0.898492i
$58$	8.13807e54			0.000521672
$59$		−	7.26572e57i		−	0.264949i	−0.991186	−	0.132475i	$-0.957708\pi$
$59$		−	7.26572e57i		−	0.264949i	0.991186	−	0.132475i	$-0.0422923\pi$
$60$	−2.81309e58	−	6.70901e57i	−0.589105	−	0.140497i
$61$	−1.08751e58			−0.131992			−0.0659961	−	0.997820i	$-0.521023\pi$
$61$	−1.08751e58			−0.131992			−0.0659961	+	0.997820i	$0.521023\pi$
$62$			8.61525e55i			0.000611424i
$63$	−6.22788e58	−	3.14976e58i	−0.260677	−	0.131837i
$64$	4.01734e59			0.999999
$65$			2.27459e59i			0.339439i
$66$	−8.31558e55	+	3.48673e56i	−7.49795e−5	+	0.000314390i
$67$	1.44521e60			0.793345			0.396673	−	0.917960i	$-0.370165\pi$
$67$	1.44521e60			0.793345			0.396673	+	0.917960i	$0.370165\pi$
$68$		−	1.07303e59i		−	0.0361259i
$69$	−7.43403e60	−	1.77296e60i	−1.54598	−	0.368705i
$70$	−5.52449e56			−7.14590e−5
$71$			1.04157e61i			0.843653i	0.906676	+	0.421827i	$0.138611\pi$
$71$			1.04157e61i			0.843653i	−0.906676	+	0.421827i	$0.861389\pi$
$72$	7.14123e57	−	1.41201e58i	0.000364586	−	0.000720882i
$73$	1.98450e61			0.642683			0.321342	−	0.946963i	$-0.395866\pi$
$73$	1.98450e61			0.642683			0.321342	+	0.946963i	$0.395866\pi$
$74$		−	1.03950e58i		−	0.000214871i
$75$	−1.10671e61	+	4.64046e61i	−0.146897	+	0.615941i
$76$	1.07740e62			0.923691
$77$		−	4.19704e61i		−	0.233749i
$78$	−6.05281e58	−	1.44355e58i	−0.000220209	−	5.25181e-5i
$79$	−3.79184e62			−0.906058			−0.453029	−	0.891496i	$-0.649657\pi$
$79$	−3.79184e62			−0.906058			−0.453029	+	0.891496i	$0.649657\pi$
$80$			3.83862e62i			0.605627i
$81$	5.65965e62	+	7.69232e62i	0.592631	+	0.805474i
$82$	−1.92213e59			−0.000134253
$83$			3.32800e63i			1.55814i	0.626937	+	0.779070i	$0.284308\pi$
$83$			3.32800e63i			1.55814i	−0.626937	+	0.779070i	$0.715692\pi$
$84$	−2.14901e62	+	9.01080e62i	−0.0677675	+	0.284150i
$85$	1.02529e62			0.0218788
$86$			2.01042e60i			0.000291634i
$87$	1.26832e64	+	3.02485e63i	1.25630	+	0.299618i
$88$	9.51566e60			0.000646414
$89$			3.93657e64i			1.84182i	0.389773	+	0.920911i	$0.372553\pi$
$89$			3.93657e64i			1.84182i	−0.389773	+	0.920911i	$0.627447\pi$
$90$	6.74594e60	+	3.41176e60i	0.000218293	+	0.000110402i
$91$	7.28588e63			0.163725
$92$			1.01441e65i			1.58934i
$93$	−3.20221e64	+	1.34269e65i	−0.351166	+	1.47244i
$94$	−1.45763e61			−0.000112313
$95$			1.02946e65i			0.559413i
$96$	−3.06444e62	−	7.30845e61i	−0.00117869	−	0.000281109i
$97$	5.02502e65			1.37300			0.686501	−	0.727129i	$-0.259146\pi$
$97$	5.02502e65			1.37300			0.686501	+	0.727129i	$0.259146\pi$
$98$		−	1.89677e62i		−	0.000369449i
$99$	−2.59197e65	+	5.12499e65i	−0.361134	+	0.714056i
$100$	6.33216e65			0.633216
$101$			1.59359e66i			1.14755i	0.819013	+	0.573775i	$0.194521\pi$
$101$			1.59359e66i			1.14755i	−0.819013	+	0.573775i	$0.805479\pi$
$102$	−6.50695e60	+	2.72837e61i	−3.38510e−6	+	1.41938e-5i
$103$	−2.16723e66			−0.817101			−0.408551	−	0.912736i	$-0.633966\pi$
$103$	−2.16723e66			−0.817101			−0.408551	+	0.912736i	$0.633966\pi$
$104$			1.65188e63i			0.000452770i
$105$	−8.60993e65	−	2.05340e65i	−0.172089	−	0.0410418i
$106$	2.54270e63			0.000371708
$107$		−	1.01912e67i		−	1.09285i	−0.837508	−	0.546426i	$-0.815988\pi$
$107$		−	1.01912e67i		−	1.09285i	0.837508	−	0.546426i	$-0.184012\pi$
$108$	8.18896e66	−	9.67591e66i	0.646018	−	0.763322i
$109$	−1.19499e67			−0.695486			−0.347743	−	0.937590i	$-0.613052\pi$
$109$	−1.19499e67			−0.695486			−0.347743	+	0.937590i	$0.613052\pi$
$110$			4.54616e63i			0.000195743i
$111$	3.86373e66	−	1.62006e67i	0.123409	−	0.517457i
$112$	1.22957e67			0.292119
$113$		−	6.47013e67i		−	1.14637i	−0.819427	−	0.573184i	$-0.805708\pi$
$113$		−	6.47013e67i		−	1.14637i	0.819427	−	0.573184i	$-0.194292\pi$
$114$	−2.73947e64	−	6.53341e63i	−0.000362916	−	8.65526e-5i
$115$	−9.69284e67			−0.962548
$116$		−	1.73069e68i		−	1.29154i
$117$	−8.89677e67	−	4.49955e67i	−0.500148	−	0.252950i
$118$	2.52093e64			0.000107017
$119$		−	3.28419e66i		−	0.0105531i
$120$	4.65554e64	−	1.95207e65i	0.000113498	−	0.000475898i
$121$	1.94029e68			0.359707
$122$		−	3.77324e64i		−	5.33138e-5i
$123$	−2.99564e68	−	7.14438e67i	−0.323312	−	0.0771073i
$124$	1.83217e69			1.51374
$125$			1.56056e69i			0.989120i
$126$	1.09284e65	−	2.16084e65i	5.32513e−5	−	0.000105292i
$127$	−2.90563e69			−1.09073			−0.545365	−	0.838199i	$-0.683609\pi$
$127$	−2.90563e69			−1.09073			−0.545365	+	0.838199i	$0.683609\pi$
$128$			5.57546e66i			0.00161567i
$129$	−7.47256e68	+	3.13325e69i	−0.167498	+	0.702319i
$130$	−7.89194e65			−0.000137105
$131$			1.42638e70i			1.92435i	0.272435	+	0.962174i	$0.412171\pi$
$131$			1.42638e70i			1.92435i	−0.272435	+	0.962174i	$0.587829\pi$
$132$	7.41509e69	+	1.76844e69i	0.778353	+	0.185631i
$133$	3.29755e69			0.269828
$134$			5.01432e66i			0.000320445i
$135$	9.24544e69	+	7.82464e69i	0.462289	+	0.391246i
$136$	7.44602e65			2.91837e−5
$137$		−	2.50709e70i		−	0.771598i	−0.922583	−	0.385799i	$-0.873926\pi$
$137$		−	2.50709e70i		−	0.771598i	0.922583	−	0.385799i	$-0.126074\pi$
$138$	6.15149e66	−	2.57932e67i	0.000148926	−	0.000624448i
$139$	−2.68185e70			−0.511619			−0.255810	−	0.966727i	$-0.582342\pi$
$139$	−2.68185e70			−0.511619			−0.255810	+	0.966727i	$0.582342\pi$
$140$			1.17487e70i			0.176915i
$141$	−2.27173e70	−	5.41789e69i	−0.270474	−	0.0645059i
$142$	−3.61386e67			−0.000340765
$143$		−	5.99563e70i		−	0.448483i
$144$	−1.50143e71	−	7.59348e70i	−0.892365	−	0.451314i
$145$	1.65370e71			0.782189
$146$			6.88546e67i			0.000259590i
$147$	7.05012e70	−	2.95612e71i	0.212190	−	0.889714i
$148$	−2.21067e71			−0.531969
$149$		−	9.31260e71i		−	1.79442i	−0.441604	−	0.897210i	$-0.645590\pi$
$149$		−	9.31260e71i		−	1.79442i	0.441604	−	0.897210i	$-0.354410\pi$
$150$	−1.61006e68	−	3.83987e67i	−0.000248789	−	5.93342e-5i
$151$	1.77219e71			0.219923			0.109962	−	0.993936i	$-0.464927\pi$
$151$	1.77219e71			0.219923			0.109962	+	0.993936i	$0.464927\pi$
$152$			7.47630e68i			0.000746188i
$153$	−2.02822e70	+	4.01031e70i	−0.0163041	+	0.0322375i
$154$	1.45621e68			9.44149e−5
$155$			1.75066e72i			0.916761i
$156$	−3.06994e71	+	1.28723e72i	−0.130022	+	0.545185i
$157$	−2.65890e72			−0.912038			−0.456019	−	0.889970i	$-0.650725\pi$
$157$	−2.65890e72			−0.912038			−0.456019	+	0.889970i	$0.650725\pi$
$158$		−	1.31562e69i		−	0.000365972i
$159$	3.96281e72	+	9.45098e71i	0.895154	+	0.213487i
$160$	−3.99556e69			−0.000733868
$161$			3.10478e72i			0.464277i
$162$	−2.66894e69	+	1.96368e69i	−0.000325344	+	0.000239373i
$163$	1.14886e73			1.14308			0.571540	−	0.820574i	$-0.306346\pi$
$163$	1.14886e73			1.14308			0.571540	+	0.820574i	$0.306346\pi$
$164$			4.08772e72i			0.332379i
$165$	−1.68977e72	+	7.08520e72i	−0.112423	+	0.471392i
$166$	−1.15469e70			−0.000629359
$167$			3.15179e73i			1.40901i	0.709699	+	0.704505i	$0.248831\pi$
$167$			3.15179e73i			1.40901i	−0.709699	+	0.704505i	$0.751169\pi$
$168$	−6.25281e69	−	1.49125e69i	−0.000229545	−	5.47448e-5i
$169$	−2.27249e73			−0.685868
$170$			3.55738e68i			8.83721e-6i
$171$	−4.02662e73	−	2.03647e73i	−0.824270	−	0.416875i
$172$	4.27549e73			0.722016
$173$		−	9.28662e73i		−	1.29520i	−0.761981	−	0.647599i	$-0.775773\pi$
$173$		−	9.28662e73i		−	1.29520i	0.761981	−	0.647599i	$-0.224227\pi$
$174$	−1.04951e70	+	4.40059e70i	−0.000121021	+	0.000507441i
$175$	1.93806e73			0.184974
$176$		−	1.01183e74i		−	0.800183i
$177$	3.92887e73	+	9.37005e72i	0.257721	+	0.0614645i
$178$	−1.36584e71			−0.000743942
$179$		−	9.24052e73i		−	0.418356i	−0.977878	−	0.209178i	$-0.932921\pi$
$179$		−	9.24052e73i		−	0.418356i	0.977878	−	0.209178i	$-0.0670788\pi$
$180$	7.25566e73	−	1.43463e74i	0.273328	−	0.540440i
$181$	−4.13506e74			−1.29744			−0.648722	−	0.761025i	$-0.724696\pi$
$181$	−4.13506e74			−1.29744			−0.648722	+	0.761025i	$0.724696\pi$
$182$			2.52792e70i			6.61314e-5i
$183$	1.40248e73	−	5.88060e73i	0.0306203	−	0.128391i
$184$	−7.03925e71			−0.00128392
$185$		−	2.11232e74i		−	0.322175i
$186$	−4.65862e71	−	1.11104e71i	−0.000594744	−	0.000141842i
$187$	−2.70259e73			−0.0289073
$188$			3.09989e74i			0.278060i
$189$	2.50636e74	−	2.96147e74i	0.188714	−	0.222981i
$190$	−3.57184e71			−0.000225956
$191$			2.39550e75i			1.27437i	0.770711	+	0.637185i	$0.219901\pi$
$191$			2.39550e75i			1.27437i	−0.770711	+	0.637185i	$0.780099\pi$
$192$	−5.18086e74	+	2.17234e75i	−0.231986	+	0.972718i
$193$	5.27146e75			1.98856			0.994282	−	0.106788i	$-0.0340567\pi$
$193$	5.27146e75			1.98856			0.994282	+	0.106788i	$0.0340567\pi$
$194$			1.74349e72i			0.000554578i
$195$	−1.22996e75	−	2.93336e74i	−0.330179	−	0.0787450i
$196$	−4.03379e75			−0.914666
$197$			2.82492e75i			0.541528i	0.962646	+	0.270764i	$0.0872763\pi$
$197$			2.82492e75i			0.541528i	−0.962646	+	0.270764i	$0.912724\pi$
$198$	−1.77818e72	−	8.99314e71i	−0.000288419	−	0.000145868i
$199$	4.15381e74			0.0570552			0.0285276	−	0.999593i	$-0.490918\pi$
$199$	4.15381e74			0.0570552			0.0285276	+	0.999593i	$0.490918\pi$
$200$			4.39403e72i			0.000511532i
$201$	−1.86378e75	+	7.81483e75i	−0.184045	+	0.771702i
$202$	−5.52914e72			−0.000463514
$203$		−	5.29706e75i		−	0.377282i
$204$	5.80232e74	+	1.38381e74i	0.0351403	+	0.00838070i
$205$	−3.90586e75			−0.201298
$206$		−	7.51944e72i		−	0.000330041i
$207$	1.91742e76	−	3.79124e76i	0.717292	−	1.41827i
$208$	1.75649e76			0.560475
$209$		−	2.71359e76i		−	0.739122i
$210$	7.12451e71	−	2.98731e72i	1.65775e−5	−	6.95095e-5i
$211$	−6.11813e76			−1.21702			−0.608510	−	0.793546i	$-0.708232\pi$
$211$	−6.11813e76			−1.21702			−0.608510	+	0.793546i	$0.708232\pi$
$212$		−	5.40746e76i		−	0.920259i
$213$	−5.63220e76	−	1.34324e76i	−0.820638	−	0.195716i
$214$	3.53596e73			0.000441421
$215$			4.08528e76i			0.437273i
$216$	6.71434e73	+	5.68251e73i	0.000616637	+	0.000521875i
$217$	5.60766e76			0.442192
$218$		−	4.14614e73i		−	0.000280918i
$219$	−2.55926e76	+	1.07310e77i	−0.149093	+	0.625150i
$220$	9.66815e76			0.484613
$221$		−	4.69159e75i		−	0.0202477i
$222$	5.62100e73	+	1.34057e73i	0.000209009	+	4.98471e-5i
$223$	2.95049e77			0.945874			0.472937	−	0.881096i	$-0.343194\pi$
$223$	2.95049e77			0.945874			0.472937	+	0.881096i	$0.343194\pi$
$224$			1.27984e74i			0.000353975i
$225$	−2.36656e77	−	1.19689e77i	−0.565060	−	0.285779i
$226$	2.24489e74			0.000463037
$227$			8.24658e77i			1.47035i	0.677878	+	0.735175i	$0.262900\pi$
$227$			8.24658e77i			1.47035i	−0.677878	+	0.735175i	$0.737100\pi$
$228$	−1.38944e77	+	5.82592e77i	−0.214283	+	0.898492i
$229$	2.26946e76			0.0302937			0.0151469	−	0.999885i	$-0.495178\pi$
$229$	2.26946e76			0.0302937			0.0151469	+	0.999885i	$0.495178\pi$
$230$		−	3.36304e74i		−	0.000388789i
$231$	2.26951e77	+	5.41260e76i	0.227372	+	0.0542264i
$232$	1.20097e75			0.00104334
$233$			1.02606e78i			0.773438i	0.922198	+	0.386719i	$0.126392\pi$
$233$			1.02606e78i			0.773438i	−0.922198	+	0.386719i	$0.873608\pi$
$234$	1.56117e74	−	3.08684e74i	0.000102171	−	0.000202018i
$235$	−2.96198e77			−0.168400
$236$		−	5.36116e77i		−	0.264949i
$237$	4.89005e77	−	2.05040e78i	0.210193	−	0.881340i
$238$	1.13949e73			4.26255e−6
$239$		−	5.08510e78i		−	1.65641i	−0.560423	−	0.828206i	$-0.689361\pi$
$239$		−	5.08510e78i		−	1.65641i	0.560423	−	0.828206i	$-0.310639\pi$
$240$	−2.07570e78	−	4.95037e77i	−0.589105	−	0.140497i
$241$	4.50962e78			1.11578			0.557888	−	0.829916i	$-0.311612\pi$
$241$	4.50962e78			1.11578			0.557888	+	0.829916i	$0.311612\pi$
$242$			6.73205e74i			0.000145292i
$243$	−4.88943e78	+	2.06838e78i	−0.920982	+	0.389605i
$244$	−8.02440e77			−0.131992
$245$		−	3.85433e78i		−	0.553947i
$246$	2.47882e74	−	1.03937e75i	3.11449e−5	−	0.000130591i
$247$	4.71067e78			0.517706
$248$			1.27139e76i			0.00122285i
$249$	−1.79959e79	−	4.29187e78i	−1.51563	−	0.361467i
$250$	−5.41453e75			−0.000399522
$251$			6.24034e76i			0.00403623i	0.999998	+	0.00201811i	$0.000642386\pi$
$251$			6.24034e76i			0.00403623i	−0.999998	+	0.00201811i	$0.999358\pi$
$252$	−4.59537e78	−	2.32411e78i	−0.260677	−	0.131837i
$253$	2.55496e79			1.27176
$254$		−	1.00814e76i		−	0.000440564i
$255$	−1.32224e77	+	5.54418e77i	−0.00507558	+	0.0212819i
$256$	2.96427e79			0.999998
$257$			3.90750e79i			1.15906i	0.814951	+	0.579529i	$0.196764\pi$
$257$			3.90750e79i			1.15906i	−0.814951	+	0.579529i	$0.803236\pi$
$258$	−1.08712e76	−	2.59269e75i	−0.000283678	−	6.76551e-5i
$259$	−6.76610e78			−0.155398
$260$			1.67835e79i			0.339439i
$261$	−3.27131e79	+	6.46823e79i	−0.582888	+	1.15252i
$262$	−4.94900e76			−0.000777276
$263$			4.76552e79i			0.660041i	0.943974	+	0.330020i	$0.107056\pi$
$263$			4.76552e79i			0.660041i	−0.943974	+	0.330020i	$0.892944\pi$
$264$	−1.22716e76	+	5.14550e76i	−0.000149959	+	0.000628779i
$265$	5.16689e79			0.557334
$266$			1.14412e76i			0.000108988i
$267$	−2.12866e80	−	5.07669e79i	−1.79158	−	0.427277i
$268$	1.06638e80			0.793345
$269$		−	1.51294e80i		−	0.995397i	−0.867350	−	0.497698i	$-0.834179\pi$
$269$		−	1.51294e80i		−	0.995397i	0.867350	−	0.497698i	$-0.165821\pi$
$270$	−2.71485e76	+	3.20781e76i	−0.000158031	+	0.000186726i
$271$	2.63554e80			1.35795			0.678975	−	0.734161i	$-0.262424\pi$
$271$	2.63554e80			1.35795			0.678975	+	0.734161i	$0.262424\pi$
$272$		−	7.91757e78i		−	0.0361259i
$273$	−9.39604e78	+	3.93977e79i	−0.0379820	+	0.159259i
$274$	8.69864e76			0.000311661
$275$		−	1.59485e80i		−	0.506689i
$276$	−5.48535e80	−	1.30821e80i	−1.54598	−	0.368705i
$277$	4.59089e80			1.14832			0.574162	−	0.818742i	$-0.305328\pi$
$277$	4.59089e80			1.14832			0.574162	+	0.818742i	$0.305328\pi$
$278$		−	9.30500e76i		−	0.000206651i
$279$	−6.84750e80	−	3.46313e80i	−1.35081	−	0.683172i
$280$	−8.15270e76			−0.000142918
$281$		−	6.86787e80i		−	1.07032i	−0.844751	−	0.535160i	$-0.820251\pi$
$281$		−	6.86787e80i		−	1.07032i	0.844751	−	0.535160i	$-0.179749\pi$
$282$	1.87980e76	−	7.88202e76i	2.60550e−5	−	0.000109249i
$283$	5.03053e80			0.620385			0.310193	−	0.950674i	$-0.399606\pi$
$283$	5.03053e80			0.620385			0.310193	+	0.950674i	$0.399606\pi$
$284$			7.68545e80i			0.843653i
$285$	−5.56673e80	−	1.32762e80i	−0.544151	−	0.129776i
$286$	2.08025e77			0.000181149
$287$			1.25111e80i			0.0970943i
$288$	7.90394e77	−	1.56281e78i	0.000546880	−	0.00108132i
$289$	1.61831e81			0.998695
$290$			5.73769e77i			0.000315939i
$291$	−6.48039e80	+	2.71723e81i	−0.318517	+	1.33554i
$292$	1.46430e81			0.642683
$293$			1.50615e81i			0.590523i	0.955416	+	0.295262i	$0.0954068\pi$
$293$			1.50615e81i			0.590523i	−0.955416	+	0.295262i	$0.904593\pi$
$294$	1.02566e78	+	2.44612e77i	0.000359370	+	8.57069e-5i
$295$	5.12265e80			0.160460
$296$		−	1.53403e78i		−	0.000429742i
$297$	−2.43703e81	−	2.06251e81i	−0.610797	−	0.516933i
$298$	3.23112e78			0.000724796
$299$			4.43529e81i			0.890785i
$300$	−8.16610e80	+	3.42405e81i	−0.146897	+	0.615941i
$301$	1.30858e81			0.210915
$302$			6.14882e77i			8.88306e-5i
$303$	−8.61719e81	−	2.05513e81i	−1.11624	−	0.266215i
$304$	7.94978e81			0.923691
$305$		−	7.66741e80i		−	0.0799381i
$306$	−1.39142e77	−	7.03714e76i	−1.30212e−5	−	6.58551e-6i
$307$	4.78843e81			0.402371			0.201186	−	0.979553i	$-0.435521\pi$
$307$	4.78843e81			0.402371			0.201186	+	0.979553i	$0.435521\pi$
$308$		−	3.09687e81i		−	0.233749i
$309$	2.79491e81	−	1.17191e82i	0.189556	−	0.794810i
$310$	−6.07412e78			−0.000370295
$311$		−	3.02452e82i		−	1.65792i	−0.559308	−	0.828960i	$-0.688933\pi$
$311$		−	3.02452e82i		−	1.65792i	0.559308	−	0.828960i	$-0.311067\pi$
$312$	−8.93237e78	−	2.13030e78i	−0.000440418	−	0.000105036i
$313$	−8.44287e81			−0.374565			−0.187282	−	0.982306i	$-0.559968\pi$
$313$	−8.44287e81			−0.374565			−0.187282	+	0.982306i	$0.559968\pi$
$314$		−	9.22535e78i		−	0.000368387i
$315$	2.22071e81	−	4.39092e81i	0.0798444	−	0.157873i
$316$	−2.79788e82			−0.906058
$317$		−	6.99474e81i		−	0.204087i	−0.994780	−	0.102044i	$-0.967462\pi$
$317$		−	6.99474e81i		−	0.204087i	0.994780	−	0.102044i	$-0.0325382\pi$
$318$	−3.27913e78	+	1.37494e79i	−8.62310e−5	+	0.000361567i
$319$	−4.35901e82			−1.03346
$320$			2.83240e82i			0.605627i
$321$	5.51080e82	+	1.31428e82i	1.06304	+	0.253526i
$322$	−1.07724e79			−0.000187529
$323$		−	2.12338e81i		−	0.0333692i
$324$	4.17609e82	+	5.67593e82i	0.592631	+	0.805474i
$325$	2.76859e82			0.354901
$326$			3.98611e79i			0.000461709i
$327$	1.54108e82	−	6.46177e82i	0.161343	−	0.676513i
$328$	−2.83656e79			−0.000268507
$329$			9.48773e81i			0.0812265i
$330$	−2.45829e79	−	5.86284e78i	−0.000190403	−	4.54096e-5i
$331$	−6.56673e82			−0.460284			−0.230142	−	0.973157i	$-0.573919\pi$
$331$	−6.56673e82			−0.460284			−0.230142	+	0.973157i	$0.573919\pi$
$332$			2.45563e83i			1.55814i
$333$	8.26207e82	+	4.17855e82i	0.474711	+	0.240085i
$334$	−1.09355e80			−0.000569122
$335$			1.01893e83i			0.480472i
$336$	−1.58569e82	+	6.64880e82i	−0.0677675	+	0.284150i
$337$	−3.07993e83			−1.19331			−0.596656	−	0.802497i	$-0.703504\pi$
$337$	−3.07993e83			−1.19331			−0.596656	+	0.802497i	$0.703504\pi$
$338$		−	7.88466e79i		−	0.000277033i
$339$	3.49866e83	+	8.34403e82i	1.11509	+	0.265941i
$340$	7.56533e81			0.0218788
$341$		−	4.61461e83i		−	1.21127i
$342$	7.06576e79	−	1.39708e80i	0.000168383	−	0.000332936i
$343$	−2.58439e83			−0.559310
$344$			2.96686e80i			0.000583269i
$345$	1.25001e83	−	5.24131e83i	0.223298	−	0.936289i
$346$	3.22210e80			0.000523152
$347$		−	9.43820e83i		−	1.39321i	−0.717455	−	0.696605i	$-0.754693\pi$
$347$		−	9.43820e83i		−	1.39321i	0.717455	−	0.696605i	$-0.245307\pi$
$348$	9.35855e83	+	2.23194e83i	1.25630	+	0.299618i
$349$	−1.37870e84			−1.68357			−0.841784	−	0.539815i	$-0.818494\pi$
$349$	−1.37870e84			−1.68357			−0.841784	+	0.539815i	$0.818494\pi$
$350$			6.72432e79i			7.47142e-5i
$351$	3.58043e83	−	4.23057e83i	0.362077	−	0.427823i
$352$	1.05320e81			0.000969621
$353$		−	4.76011e83i		−	0.399073i	−0.979890	−	0.199536i	$-0.936056\pi$
$353$		−	4.76011e83i		−	0.399073i	0.979890	−	0.199536i	$-0.0639436\pi$
$354$	−3.25105e79	+	1.36317e80i	−2.48265e−5	+	0.000104098i
$355$	−7.34353e83			−0.510939
$356$			2.90467e84i			1.84182i
$357$	1.77589e82	+	4.23537e81i	0.0102652	+	0.00244816i
$358$	3.20610e80			0.000168981
$359$		−	2.35167e84i		−	1.13047i	−0.824929	−	0.565236i	$-0.808785\pi$
$359$		−	2.35167e84i		−	1.13047i	0.824929	−	0.565236i	$-0.191215\pi$
$360$	9.95524e80	+	5.03487e80i	0.000436586	+	0.000220803i
$361$	−3.66815e83			−0.146794
$362$		−	1.43471e81i		−	0.000524059i
$363$	−2.50224e83	+	1.04919e84i	−0.0834469	+	0.349894i
$364$	5.37603e83			0.163725
$365$			1.39916e84i			0.389227i
$366$	2.04034e80	+	4.86606e79i	5.18594e−5	+	1.23681e-5i
$367$	7.18311e84			1.66852			0.834262	−	0.551369i	$-0.185894\pi$
$367$	7.18311e84			1.66852			0.834262	+	0.551369i	$0.185894\pi$
$368$			7.48505e84i			1.58934i
$369$	7.72651e83	−	1.52773e84i	0.150008	−	0.296604i
$370$	7.32893e80			0.000130132
$371$		−	1.65504e84i		−	0.268825i
$372$	−2.36281e84	+	9.90730e84i	−0.351166	+	1.47244i
$373$	−2.40641e84			−0.327324			−0.163662	−	0.986516i	$-0.552331\pi$
$373$	−2.40641e84			−0.327324			−0.163662	+	0.986516i	$0.552331\pi$
$374$		−	9.37697e79i		−	1.16761e-5i
$375$	−8.43856e84	−	2.01253e84i	−0.962136	−	0.229462i
$376$	−2.15109e81			−0.000224626
$377$		−	7.56706e84i		−	0.723873i
$378$	1.02752e81	+	8.69612e80i	9.00656e−5	+	7.62248e-5i
$379$	8.54260e83			0.0686272			0.0343136	−	0.999411i	$-0.489075\pi$
$379$	8.54260e83			0.0686272			0.0343136	+	0.999411i	$0.489075\pi$
$380$			7.59610e84i			0.559413i
$381$	3.74717e84	−	1.57119e85i	0.253034	−	1.06097i
$382$	−8.31147e81			−0.000514739
$383$		−	2.26456e85i		−	1.28654i	−0.765639	−	0.643271i	$-0.777577\pi$
$383$		−	2.26456e85i		−	1.28654i	0.765639	−	0.643271i	$-0.222423\pi$
$384$	−3.01487e82	−	7.19024e81i	−0.00157159	−	0.000374812i
$385$	2.95909e84			0.141565
$386$			1.82899e82i			0.000803214i
$387$	−1.59791e85	−	8.08143e84i	−0.644302	−	0.325856i
$388$	3.70781e85			1.37300
$389$		−	1.73194e83i		−	0.00589108i	−0.999996	−	0.00294554i	$-0.999062\pi$
$389$		−	1.73194e83i		−	0.00589108i	0.999996	−	0.00294554i	$-0.000937596\pi$
$390$	1.01776e81	−	4.26749e81i	3.18064e−5	−	0.000133365i
$391$	1.99926e84			0.0574163
$392$		−	2.79914e82i		−	0.000738898i
$393$	−7.71303e85	−	1.83950e85i	−1.87185	−	0.446422i
$394$	−9.80139e81			−0.000218732
$395$		−	2.67341e85i		−	0.548733i
$396$	−1.91254e85	+	3.78158e85i	−0.361134	+	0.714055i
$397$	2.91983e85			0.507307			0.253653	−	0.967295i	$-0.418368\pi$
$397$	2.91983e85			0.507307			0.253653	+	0.967295i	$0.418368\pi$
$398$			1.44121e81i			2.30455e-5i
$399$	−4.25259e84	+	1.78312e85i	−0.0625962	+	0.262467i
$400$	4.67230e85			0.633215
$401$			2.61641e85i			0.326544i	0.986581	+	0.163272i	$0.0522048\pi$
$401$			2.61641e85i			0.326544i	−0.986581	+	0.163272i	$0.947795\pi$
$402$	−2.71145e82	−	6.46659e81i	−0.000311703	−	7.43388e-5i
$403$	8.01075e85			0.848412
$404$			1.17586e86i			1.14755i
$405$	−5.42341e85	+	3.99030e85i	−0.487817	+	0.358913i
$406$	1.83788e82			0.000152390
$407$			5.56790e85i			0.425673i
$408$	−9.60256e80	+	4.02636e81i	−6.77020e−6	+	2.83875e-5i
$409$	1.18255e86			0.769045			0.384522	−	0.923116i	$-0.374366\pi$
$409$	1.18255e86			0.769045			0.384522	+	0.923116i	$0.374366\pi$
$410$		−	1.35518e82i		−	8.13076e-5i
$411$	1.35569e86	+	3.23320e85i	0.750548	+	0.179000i
$412$	−1.59913e86			−0.817101
$413$		−	1.64087e85i		−	0.0773967i
$414$	1.31541e83	+	6.65271e82i	0.000572863	+	0.000289726i
$415$	−2.34638e86			−0.943652
$416$			1.82831e83i			0.000679155i
$417$	3.45858e85	−	1.45019e86i	0.118688	−	0.497662i
$418$	9.41510e82			0.000298544
$419$		−	1.43259e86i		−	0.419817i	−0.977721	−	0.209909i	$-0.932683\pi$
$419$		−	1.43259e86i		−	0.419817i	0.977721	−	0.209909i	$-0.0673167\pi$
$420$	−6.35300e85	−	1.51514e85i	−0.172089	−	0.0410418i
$421$	−5.13400e85			−0.128572			−0.0642861	−	0.997932i	$-0.520477\pi$
$421$	−5.13400e85			−0.128572			−0.0642861	+	0.997932i	$0.520477\pi$
$422$		−	2.12276e83i		−	0.000491574i
$423$	5.85935e85	−	1.15854e86i	0.125492	−	0.248131i
$424$	3.75236e83			0.000743416
$425$		−	1.24797e85i		−	0.0228755i
$426$	4.66052e82	−	1.95416e83i	7.90528e−5	−	0.000331469i
$427$	−2.45600e85			−0.0385574
$428$		−	7.51979e86i		−	1.09285i
$429$	3.24208e86	+	7.73211e85i	0.436248	+	0.104042i
$430$	−1.41743e83			−0.000176622
$431$		−	1.03944e87i		−	1.19964i	−0.800136	−	0.599818i	$-0.795240\pi$
$431$		−	1.03944e87i		−	1.19964i	0.800136	−	0.599818i	$-0.204760\pi$
$432$	6.04238e86	−	7.13956e86i	0.646018	−	0.763322i
$433$	−5.57992e86			−0.552749			−0.276374	−	0.961050i	$-0.589133\pi$
$433$	−5.57992e86			−0.552749			−0.276374	+	0.961050i	$0.589133\pi$
$434$			1.94564e83i			0.000178608i
$435$	−2.13265e86	+	8.94220e86i	−0.181457	+	0.760850i
$436$	−8.81744e86			−0.695486
$437$			2.00739e87i			1.46806i
$438$	−3.72325e83	−	8.87965e82i	−0.000252509	−	6.02213e-5i
$439$	−6.19030e86			−0.389388			−0.194694	−	0.980864i	$-0.562371\pi$
$439$	−6.19030e86			−0.389388			−0.194694	+	0.980864i	$0.562371\pi$
$440$			6.70895e83i			0.000391486i
$441$	1.50757e87	+	7.62457e86i	0.816216	+	0.412802i
$442$	1.62780e82			8.17836e−6
$443$			2.95788e87i			1.37930i	0.724145	+	0.689648i	$0.242235\pi$
$443$			2.95788e87i			1.37930i	−0.724145	+	0.689648i	$0.757765\pi$
$444$	2.85093e86	−	1.19540e87i	0.123409	−	0.517457i
$445$	−2.77545e87			−1.11546
$446$			1.02371e84i			0.000382054i
$447$	5.03570e87	+	1.20098e87i	1.74547	+	0.416280i
$448$	9.07264e86			0.292119
$449$			1.71493e87i			0.513001i	0.966544	+	0.256500i	$0.0825695\pi$
$449$			1.71493e87i			0.513001i	−0.966544	+	0.256500i	$0.917431\pi$
$450$	4.15274e83	−	8.21105e83i	0.000115431	−	0.000228237i
$451$	1.02955e87			0.265964
$452$		−	4.77411e87i		−	1.14637i
$453$	−2.28546e86	+	9.58295e86i	−0.0510191	+	0.213923i
$454$	−2.86125e84			−0.000593898
$455$			5.13686e86i			0.0991565i
$456$	−4.04274e84	−	9.64162e83i	−0.000725832	−	0.000173105i
$457$	−7.31383e87			−1.22155			−0.610774	−	0.791805i	$-0.709142\pi$
$457$	−7.31383e87			−1.22155			−0.610774	+	0.791805i	$0.709142\pi$
$458$			7.87417e82i			1.22361e-5i
$459$	−1.90697e86	−	1.61392e86i	−0.0275757	−	0.0233380i
$460$	−7.15205e87			−0.962548
$461$			6.25168e87i			0.783189i	0.920138	+	0.391594i	$0.128076\pi$
$461$			6.25168e87i			0.783189i	−0.920138	+	0.391594i	$0.871924\pi$
$462$	−1.87797e83	+	7.87433e83i	−2.19029e−5	+	9.18392e-5i
$463$	1.74033e88			1.88998			0.944991	−	0.327095i	$-0.106070\pi$
$463$	1.74033e88			1.88998			0.944991	+	0.327095i	$0.106070\pi$
$464$		−	1.27703e88i		−	1.29153i
$465$	−9.46653e87	−	2.25769e87i	−0.891751	−	0.212676i
$466$	−3.56002e84			−0.000312404
$467$		−	1.03339e88i		−	0.844901i	−0.906386	−	0.422450i	$-0.861170\pi$
$467$		−	1.03339e88i		−	0.844901i	0.906386	−	0.422450i	$-0.138830\pi$
$468$	−6.56465e87	−	3.32008e87i	−0.500148	−	0.252950i
$469$	3.26382e87			0.231751
$470$		−	1.02769e84i		−	6.80197e-5i
$471$	3.42898e87	−	1.43777e88i	0.211580	−	0.887157i
$472$	3.72023e84			0.000214035
$473$		−	1.07685e88i		−	0.577745i
$474$	7.11410e84	+	1.69666e84i	0.000355988	+	8.49003e-5i
$475$	1.25305e88			0.584896
$476$		−	2.42330e86i		−	0.0105531i
$477$	−1.02211e88	+	2.02097e88i	−0.415326	+	0.821207i
$478$	1.76433e85			0.000669052
$479$			4.85976e88i			1.72006i	0.510245	+	0.860029i	$0.329555\pi$
$479$			4.85976e88i			1.72006i	−0.510245	+	0.860029i	$0.670445\pi$
$480$	5.15277e84	−	2.16056e85i	0.000170247	−	0.000713848i
$481$	−9.66563e87			−0.298155
$482$			1.56466e85i			0.000450680i
$483$	−1.67888e88	−	4.00400e87i	−0.451611	−	0.107706i
$484$	1.43168e88			0.359707
$485$			3.54286e88i			0.831527i
$486$	−7.17650e84	−	1.69644e85i	−0.000157368	−	0.000372000i
$487$	4.34878e88			0.891070			0.445535	−	0.895265i	$-0.353014\pi$
$487$	4.34878e88			0.891070			0.445535	+	0.895265i	$0.353014\pi$
$488$		−	5.56832e84i		−	0.000106628i
$489$	−1.48160e88	+	6.21236e88i	−0.265178	+	1.11190i
$490$	1.33730e85			0.000223748
$491$		−	5.44364e88i		−	0.851530i	−0.904834	−	0.425765i	$-0.860005\pi$
$491$		−	5.44364e88i		−	0.851530i	0.904834	−	0.425765i	$-0.139995\pi$
$492$	−2.21039e88	−	5.27162e87i	−0.323312	−	0.0771073i
$493$	−3.41093e87			−0.0466579
$494$			1.63442e85i			0.000209110i
$495$	−3.61334e88	−	1.82745e88i	−0.432451	−	0.218713i
$496$	1.35190e89			1.51374
$497$			2.35226e88i			0.246447i
$498$	1.48911e85	−	6.24387e85i	0.000146002	−	0.000612189i
$499$	9.52228e88			0.873822			0.436911	−	0.899505i	$-0.356072\pi$
$499$	9.52228e88			0.873822			0.436911	+	0.899505i	$0.356072\pi$
$500$			1.15149e89i			0.989120i
$501$	−1.70430e89	−	4.06463e88i	−1.37057	−	0.326870i
$502$	−2.16516e83			−1.63030e−6
$503$		−	1.67359e89i		−	1.18006i	−0.807380	−	0.590031i	$-0.799115\pi$
$503$		−	1.67359e89i		−	1.18006i	0.807380	−	0.590031i	$-0.200885\pi$
$504$	1.61275e85	−	3.18883e85i	0.000106503	−	0.000210583i
$505$	−1.12355e89			−0.694987
$506$			8.86472e85i			0.000513686i
$507$	2.93066e88	−	1.22883e89i	0.159112	−	0.667157i
$508$	−2.14398e89			−1.09073
$509$		−	1.77849e89i		−	0.847941i	−0.905676	−	0.423970i	$-0.860636\pi$
$509$		−	1.77849e89i		−	0.847941i	0.905676	−	0.423970i	$-0.139364\pi$
$510$	−1.92362e84	−	4.58768e83i	−8.59613e−6	−	2.05011e-6i
$511$	4.48174e88			0.187740
$512$			5.14245e86i			0.00201958i
$513$	1.62048e89	−	1.91473e89i	0.596721	−	0.705074i
$514$	−1.35575e86			−0.000468163
$515$		−	1.52799e89i		−	0.494859i
$516$	−5.51377e88	+	2.31193e89i	−0.167498	+	0.702319i
$517$	7.80756e88			0.222499
$518$		−	2.34758e85i		−	6.27679e-5i
$519$	5.02165e89	+	1.19763e89i	1.25986	+	0.300468i
$520$	−1.16464e86			−0.000274210
$521$		−	1.61035e89i		−	0.355858i	−0.984043	−	0.177929i	$-0.943060\pi$
$521$		−	1.61035e89i		−	0.355858i	0.984043	−	0.177929i	$-0.0569397\pi$
$522$	−2.24423e86	−	1.13502e86i	−0.000465522	−	0.000235438i
$523$	−4.32534e89			−0.842296			−0.421148	−	0.906992i	$-0.638373\pi$
$523$	−4.32534e89			−0.842296			−0.421148	+	0.906992i	$0.638373\pi$
$524$			1.05249e90i			1.92435i
$525$	−2.49937e88	+	1.04799e89i	−0.0429114	+	0.179928i
$526$	−1.65345e86			−0.000266601
$527$		−	3.61093e88i		−	0.0546851i
$528$	5.47137e89	+	1.30488e89i	0.778353	+	0.185631i
$529$	−1.14181e90			−1.52600
$530$			1.79271e86i			0.000225116i
$531$	−1.01335e89	+	2.00366e89i	−0.119575	+	0.236431i
$532$	2.43316e89			0.269828
$533$			1.78726e89i			0.186290i
$534$	1.76142e86	−	7.38564e86i	0.000172584	−	0.000723647i
$535$	7.18524e89			0.661861
$536$			7.39983e86i			0.000640890i
$537$	4.99672e89	+	1.19168e89i	0.406943	+	0.0970528i
$538$	5.24932e86			0.000402057
$539$			1.01597e90i			0.731901i
$540$	6.82193e89	+	5.77357e89i	0.462288	+	0.391246i
$541$	−6.54452e88			−0.0417223			−0.0208612	−	0.999782i	$-0.506641\pi$
$541$	−6.54452e88			−0.0417223			−0.0208612	+	0.999782i	$0.506641\pi$
$542$			9.14433e86i			0.000548498i
$543$	5.33267e89	−	2.23599e90i	0.300989	−	1.26205i
$544$	8.24128e85			4.37755e−5
$545$		−	8.42516e89i		−	0.421205i
$546$	−1.36695e86	−	3.26007e85i	−6.43272e−5	−	1.53415e-5i
$547$	−3.76881e90			−1.66964			−0.834819	−	0.550525i	$-0.814428\pi$
$547$	−3.76881e90			−1.66964			−0.834819	+	0.550525i	$0.814428\pi$
$548$		−	1.84991e90i		−	0.771598i
$549$	2.99901e89	+	1.51675e89i	0.117785	+	0.0595700i
$550$	5.53352e86			0.000204660
$551$		−	3.42481e90i		−	1.19298i
$552$	9.07799e86	−	3.80641e87i	0.000297852	−	0.00124889i
$553$	−8.56337e89			−0.264677
$554$			1.59286e87i			0.000463827i
$555$	1.14222e90	+	2.72409e89i	0.313386	+	0.0747401i
$556$	−1.97886e90			−0.511619
$557$			2.66722e89i			0.0649885i	0.999472	+	0.0324943i	$0.0103451\pi$
$557$			2.66722e89i			0.0649885i	−0.999472	+	0.0324943i	$0.989655\pi$
$558$	1.20157e87	−	2.37582e87i	0.000275944	−	0.000545613i
$559$	1.86936e90			0.404672
$560$			8.66902e89i			0.176915i
$561$	3.48533e88	−	1.46140e89i	0.00670609	−	0.0281187i
$562$	2.38289e87			0.000432320
$563$		−	8.57444e89i		−	0.146700i	−0.997306	−	0.0733498i	$-0.976631\pi$
$563$		−	8.57444e89i		−	0.146700i	0.997306	−	0.0733498i	$-0.0233689\pi$
$564$	−1.67624e90	−	3.99770e89i	−0.270474	−	0.0645059i
$565$	4.56172e90			0.694272
$566$			1.74540e87i			0.000250584i
$567$	1.27816e90	+	1.73721e90i	0.173119	+	0.235294i
$568$	−5.33311e87			−0.000681531
$569$			1.13916e91i			1.37366i	0.726818	+	0.686831i	$0.240999\pi$
$569$			1.13916e91i			1.37366i	−0.726818	+	0.686831i	$0.759001\pi$
$570$	4.60634e86	−	1.93144e87i	5.24186e−5	−	0.000219792i
$571$	1.11033e91			1.19251			0.596254	−	0.802796i	$-0.296655\pi$
$571$	1.11033e91			1.19251			0.596254	+	0.802796i	$0.296655\pi$
$572$		−	4.42399e90i		−	0.448483i
$573$	−1.29534e91	−	3.08930e90i	−1.23960	−	0.295636i
$574$	−4.34088e86			−3.92180e−5
$575$			1.17980e91i			1.00640i
$576$	−1.10786e91	−	5.60300e90i	−0.892364	−	0.451314i
$577$	1.00749e91			0.766369			0.383184	−	0.923672i	$-0.374827\pi$
$577$	1.00749e91			0.766369			0.383184	+	0.923672i	$0.374827\pi$
$578$			5.61491e87i			0.000403389i
$579$	−6.79820e90	+	2.85049e91i	−0.461319	+	1.93431i
$580$	1.22021e91			0.782189
$581$			7.51586e90i			0.455162i
$582$	−9.42776e87	−	2.24845e87i	−0.000539448	−	0.000128654i
$583$	−1.36195e91			−0.736376
$584$			1.01611e88i			0.000519181i
$585$	3.17237e90	−	6.27260e90i	0.153194	−	0.302903i
$586$	−5.22577e87			−0.000238522
$587$		−	1.77770e91i		−	0.767008i	−0.923539	−	0.383504i	$-0.874717\pi$
$587$		−	1.77770e91i		−	0.767008i	0.923539	−	0.383504i	$-0.125283\pi$
$588$	5.20207e90	−	2.18123e91i	0.212190	−	0.889713i
$589$	3.62562e91			1.39823
$590$			1.77736e87i			6.48126e-5i
$591$	−1.52755e91	−	3.64309e90i	−0.526755	−	0.125627i
$592$	−1.63118e91			−0.531969
$593$		−	3.37670e91i		−	1.04157i	−0.853689	−	0.520784i	$-0.825640\pi$
$593$		−	3.37670e91i		−	1.04157i	0.853689	−	0.520784i	$-0.174360\pi$
$594$	7.15613e87	−	8.45554e87i	0.000208798	−	0.000246711i
$595$	2.31549e89			0.00639122
$596$		−	6.87149e91i		−	1.79442i
$597$	−5.35686e89	+	2.24614e90i	−0.0132360	+	0.0554987i
$598$	−1.53888e88			−0.000359803
$599$			7.05617e91i			1.56129i	0.624974	+	0.780645i	$0.285109\pi$
$599$			7.05617e91i			1.56129i	−0.624974	+	0.780645i	$0.714891\pi$
$600$	−2.37603e88	−	5.66665e87i	−0.000497577	−	0.000118668i
$601$	−5.28386e91			−1.04735			−0.523677	−	0.851917i	$-0.675440\pi$
$601$	−5.28386e91			−1.04735			−0.523677	+	0.851917i	$0.675440\pi$
$602$			4.54028e87i			8.51919e-5i
$603$	−3.98544e91	−	2.01564e91i	−0.707954	−	0.358048i
$604$	1.30765e91			0.219923
$605$			1.36799e91i			0.217848i
$606$	7.13052e87	−	2.98983e88i	0.000107529	−	0.000450869i
$607$	2.07288e91			0.296037			0.148019	−	0.988985i	$-0.452710\pi$
$607$	2.07288e91			0.296037			0.148019	+	0.988985i	$0.452710\pi$
$608$			8.27480e88i			0.00111928i
$609$	2.86434e91	+	6.83122e90i	0.366989	+	0.0875241i
$610$	2.66030e87			3.22883e−5
$611$			1.35536e91i			0.155845i
$612$	−1.49656e90	+	2.95909e90i	−0.0163041	+	0.0322375i
$613$	1.43428e92			1.48060			0.740300	−	0.672276i	$-0.234683\pi$
$613$	1.43428e92			1.48060			0.740300	+	0.672276i	$0.234683\pi$
$614$			1.66140e88i			0.000162524i
$615$	5.03709e90	−	2.11206e91i	0.0466983	−	0.195806i
$616$	2.14899e88			0.000188830
$617$		−	2.15483e91i		−	0.179475i	−0.995965	−	0.0897373i	$-0.971397\pi$
$617$		−	2.15483e91i		−	0.179475i	0.995965	−	0.0897373i	$-0.0286027\pi$
$618$	4.06607e88	+	9.69725e87i	0.000321037	+	7.65648e-5i
$619$	−2.23458e92			−1.67265			−0.836325	−	0.548234i	$-0.815300\pi$
$619$	−2.23458e92			−1.67265			−0.836325	+	0.548234i	$0.815300\pi$
$620$			1.29176e92i			0.916761i
$621$	1.80280e92	+	1.52575e92i	1.21318	+	1.02674i
$622$	1.04939e89			0.000669661
$623$			8.89023e91i			0.538031i
$624$	−2.26521e91	+	9.49806e91i	−0.130022	+	0.545184i
$625$	6.27747e90			0.0341778
$626$		−	2.92935e88i		−	0.000151293i
$627$	1.46735e92	+	3.49951e91i	0.718958	+	0.171466i
$628$	−1.96192e92			−0.912038
$629$			4.35689e90i			0.0192179i
$630$	1.52348e88	+	7.70502e87i	6.37675e−5	+	3.22504e-5i
$631$	−2.02333e92			−0.803705			−0.401853	−	0.915704i	$-0.631634\pi$
$631$	−2.02333e92			−0.803705			−0.401853	+	0.915704i	$0.631634\pi$
$632$		−	1.94152e89i		−	0.000731943i
$633$	7.89009e91	−	3.30832e92i	0.282331	−	1.18382i
$634$	2.42691e88			8.24342e−5
$635$		−	2.04859e92i		−	0.660576i
$636$	2.92403e92	+	6.97359e91i	0.895154	+	0.213487i
$637$	−1.76368e92			−0.512648
$638$		−	1.51241e89i		−	0.000417433i
$639$	1.45268e92	−	2.87233e92i	0.380753	−	0.752847i
$640$	−3.93093e89			−0.000978491
$641$		−	5.55805e92i		−	1.31404i	−0.753874	−	0.657019i	$-0.771817\pi$
$641$		−	5.55805e92i		−	1.31404i	0.753874	−	0.657019i	$-0.228183\pi$
$642$	−4.56006e88	+	1.91204e89i	−0.000102403	+	0.000429378i
$643$	−1.17876e92			−0.251457			−0.125728	−	0.992065i	$-0.540127\pi$
$643$	−1.17876e92			−0.251457			−0.125728	+	0.992065i	$0.540127\pi$
$644$			2.29092e92i			0.464276i
$645$	−2.20908e92	−	5.26847e91i	−0.425344	−	0.101441i
$646$	7.36733e87			1.34784e−5
$647$		−	2.13609e92i		−	0.371345i	−0.982612	−	0.185673i	$-0.940554\pi$
$647$		−	2.13609e92i		−	0.371345i	0.982612	−	0.185673i	$-0.0594464\pi$
$648$	−3.93866e89	+	2.89788e89i	−0.000650689	+	0.000478747i
$649$	−1.35029e92			−0.212008
$650$			9.60595e88i			0.000143351i
$651$	−7.23177e91	+	3.03229e92i	−0.102582	+	0.430128i
$652$	8.47710e92			1.14308
$653$			1.09435e92i			0.140289i	0.997537	+	0.0701443i	$0.0223460\pi$
$653$			1.09435e92i			0.140289i	−0.997537	+	0.0701443i	$0.977654\pi$
$654$	2.24199e89	+	5.34696e88i	0.000273255	+	6.51691e-5i
$655$	−1.00566e93			−1.16544
$656$			3.01620e92i			0.332379i
$657$	−5.47264e92	−	2.76779e92i	−0.573508	−	0.290052i
$658$	−3.29188e88			−3.28087e−5
$659$		−	2.18887e92i		−	0.207492i	−0.994604	−	0.103746i	$-0.966917\pi$
$659$		−	2.18887e92i		−	0.207492i	0.994604	−	0.103746i	$-0.0330828\pi$
$660$	−1.24683e92	+	5.22796e92i	−0.112423	+	0.471392i
$661$	7.88036e92			0.675924			0.337962	−	0.941160i	$-0.390262\pi$
$661$	7.88036e92			0.675924			0.337962	+	0.941160i	$0.390262\pi$
$662$		−	2.27840e89i		−	0.000185916i
$663$	2.53693e91	+	6.05038e90i	0.0196953	+	0.00469717i
$664$	−1.70402e90			−0.00125872
$665$			2.32491e92i			0.163415i
$666$	−1.44980e89	+	2.86662e89i	−9.69744e−5	+	0.000191744i
$667$	3.22460e93			2.05269
$668$			2.32561e93i			1.40901i
$669$	−3.80502e92	+	1.59545e93i	−0.219429	+	0.920070i
$670$	−3.53531e89			−0.000194070
$671$			2.02107e92i			0.105618i
$672$	−6.92063e89	−	1.65052e89i	−0.000344318	−	8.21172e-5i
$673$	−1.25498e93			−0.594481			−0.297241	−	0.954803i	$-0.596066\pi$
$673$	−1.25498e93			−0.594481			−0.297241	+	0.954803i	$0.596066\pi$
$674$		−	1.06862e90i		−	0.000481998i
$675$	9.52403e92	−	1.12534e93i	0.409069	−	0.483347i
$676$	−1.67680e93			−0.685868
$677$		−	9.84234e91i		−	0.0383418i	−0.999816	−	0.0191709i	$-0.993897\pi$
$677$		−	9.84234e91i		−	0.0383418i	0.999816	−	0.0191709i	$-0.00610266\pi$
$678$	−2.89506e89	+	1.21390e90i	−0.000107418	+	0.000450405i
$679$	1.13484e93			0.401080
$680$			5.24976e88i			1.76744e-5i
$681$	−4.45926e93	−	1.06350e93i	−1.43024	−	0.341100i
$682$	1.60109e90			0.000489251
$683$		−	1.58591e93i		−	0.461737i	−0.972985	−	0.230869i	$-0.925843\pi$
$683$		−	1.58591e93i		−	0.461737i	0.972985	−	0.230869i	$-0.0741568\pi$
$684$	−2.97112e93	−	1.50265e93i	−0.824270	−	0.416875i
$685$	1.76761e93			0.467301
$686$		−	8.96686e89i		−	0.000225915i
$687$	−2.92676e91	+	1.22719e92i	−0.00702771	+	0.0294673i
$688$	3.15475e93			0.722016
$689$		−	2.36429e93i		−	0.515782i
$690$	1.81853e90	+	4.33706e89i	0.000378182	+	9.01936e-5i
$691$	4.39819e93			0.871964			0.435982	−	0.899955i	$-0.356401\pi$
$691$	4.39819e93			0.871964			0.435982	+	0.899955i	$0.356401\pi$
$692$		−	6.85232e93i		−	1.29520i
$693$	−5.85363e92	+	1.15741e93i	−0.105494	+	0.208589i
$694$	3.27469e90			0.000562741
$695$		−	1.89082e93i		−	0.309850i
$696$	−1.54880e90	+	6.49412e90i	−0.000242041	+	0.00101488i
$697$	8.05627e91			0.0120075
$698$		−	4.78356e90i		−	0.000680020i
$699$	−5.54830e93	−	1.32323e93i	−0.752338	−	0.179427i
$700$	1.43004e93			0.184974
$701$			9.31016e93i			1.14885i	0.818558	+	0.574424i	$0.194774\pi$
$701$			9.31016e93i			1.14885i	−0.818558	+	0.574424i	$0.805226\pi$
$702$	1.46784e90	+	1.24227e90i	0.000172805	+	0.000146249i
$703$	−4.37461e93			−0.491375
$704$		−	7.46598e93i		−	0.800182i
$705$	3.81984e92	−	1.60166e93i	0.0390665	−	0.163806i
$706$	1.65158e90			0.000161192
$707$			3.59892e93i			0.335221i
$708$	2.89899e93	+	6.91387e92i	0.257721	+	0.0614644i
$709$	−1.35345e94			−1.14846			−0.574231	−	0.818693i	$-0.694699\pi$
$709$	−1.35345e94			−1.14846			−0.574231	+	0.818693i	$0.694699\pi$
$710$		−	2.54792e90i		−	0.000206377i
$711$	1.04567e94	+	5.28849e93i	0.808534	+	0.408917i
$712$	−2.01562e91			−0.00148788
$713$			3.41368e94i			2.40585i
$714$	−1.46951e88	+	6.16167e88i	−9.88852e−7	+	4.14627e-6i
$715$	4.22718e93			0.271613
$716$		−	6.81830e93i		−	0.418356i
$717$	2.74972e94	+	6.55786e93i	1.61122	+	0.384264i
$718$	8.15940e90			0.000456616
$719$			2.64205e93i			0.141217i	0.997504	+	0.0706085i	$0.0224941\pi$
$719$			2.64205e93i			0.141217i	−0.997504	+	0.0706085i	$0.977506\pi$
$720$	5.35373e93	−	1.05857e94i	0.273328	−	0.540440i
$721$	−4.89440e93			−0.238691
$722$		−	1.27271e90i		−	5.92926e-5i
$723$	−5.81571e93	+	2.43853e94i	−0.258844	+	1.08534i
$724$	−3.05113e94			−1.29744
$725$		−	2.01285e94i		−	0.817820i
$726$	−3.64029e90	−	8.68181e89i	−0.000141328	−	3.37056e-5i
$727$	2.45777e94			0.911813			0.455907	−	0.890028i	$-0.349315\pi$
$727$	2.45777e94			0.911813			0.455907	+	0.890028i	$0.349315\pi$
$728$			3.73055e90i			0.000132263i
$729$	−4.87906e93	−	2.91066e94i	−0.165321	−	0.986240i
$730$	−4.85454e90			−0.000157215
$731$		−	8.42634e92i		−	0.0260835i
$732$	1.03485e93	−	4.33912e93i	0.0306203	−	0.128391i
$733$	−3.20690e94			−0.907098			−0.453549	−	0.891231i	$-0.649842\pi$
$733$	−3.20690e94			−0.907098			−0.453549	+	0.891231i	$0.649842\pi$
$734$			2.49226e91i			0.000673944i
$735$	2.08419e94	+	4.97064e93i	0.538835	+	0.128508i
$736$	−7.79108e91			−0.00192588
$737$		−	2.68583e94i		−	0.634822i
$738$	5.30064e90	+	2.68080e90i	0.000119803	+	6.05905e-5i
$739$	−5.59005e94			−1.20823			−0.604115	−	0.796897i	$-0.706473\pi$
$739$	−5.59005e94			−1.20823			−0.604115	+	0.796897i	$0.706473\pi$
$740$		−	1.55861e94i		−	0.322175i
$741$	−6.07499e93	+	2.54725e94i	−0.120100	+	0.503582i
$742$	5.74236e90			0.000108583
$743$		−	2.25169e94i		−	0.407265i	−0.979047	−	0.203633i	$-0.934725\pi$
$743$		−	2.25169e94i		−	0.407265i	0.979047	−	0.203633i	$-0.0652748\pi$
$744$	−6.87490e91	−	1.63961e91i	−0.00118949	−	0.000283683i
$745$	6.56578e94			1.08675
$746$		−	8.34931e90i		−	0.000132212i
$747$	4.64158e94	−	9.17760e94i	0.703211	−	1.39043i
$748$	−1.99416e93			−0.0289073
$749$		−	2.30155e94i		−	0.319243i
$750$	6.98271e90	−	2.92786e91i	9.26834e−5	−	0.000388622i
$751$	−6.85963e94			−0.871330			−0.435665	−	0.900109i	$-0.643487\pi$
$751$	−6.85963e94			−0.871330			−0.435665	+	0.900109i	$0.643487\pi$
$752$			2.28732e94i			0.278059i
$753$	−3.37441e92	−	8.04770e91i	−0.00392612	−	0.000936348i
$754$	2.62548e91			0.000292384
$755$			1.24947e94i			0.133191i
$756$	1.84937e94	−	2.18518e94i	0.188714	−	0.222981i
$757$	4.22715e94			0.412936			0.206468	−	0.978453i	$-0.433803\pi$
$757$	4.22715e94			0.412936			0.206468	+	0.978453i	$0.433803\pi$
$758$			2.96395e90i			2.77196e-5i
$759$	−3.29493e94	+	1.38157e95i	−0.295031	+	1.23707i
$760$	−5.27111e91			−0.000451912
$761$			1.32705e95i			1.08941i	0.838627	+	0.544707i	$0.183359\pi$
$761$			1.32705e95i			1.08941i	−0.838627	+	0.544707i	$0.816641\pi$
$762$	5.45143e91	+	1.30012e91i	0.000428545	+	0.000102205i
$763$	−2.69872e94			−0.203165
$764$			1.76757e95i			1.27437i
$765$	−2.82744e93	−	1.42998e93i	−0.0195239	−	0.00987422i
$766$	7.85714e91			0.000519655
$767$		−	2.34404e94i		−	0.148497i
$768$	−3.82280e94	+	1.60290e95i	−0.231986	+	0.972718i
$769$	−2.80685e94			−0.163174			−0.0815869	−	0.996666i	$-0.525999\pi$
$769$	−2.80685e94			−0.163174			−0.0815869	+	0.996666i	$0.525999\pi$
$770$			1.02669e91i			5.71803e-5i
$771$	−2.11294e95	−	5.03920e94i	−1.12744	−	0.268885i
$772$	3.88965e95			1.98856
$773$		−	2.58278e95i		−	1.26521i	−0.774473	−	0.632607i	$-0.781985\pi$
$773$		−	2.58278e95i		−	1.26521i	0.774473	−	0.632607i	$-0.218015\pi$
$774$	2.80394e91	−	5.54412e91i	0.000131619	−	0.000260244i
$775$	2.13088e95			0.958523
$776$			2.57294e92i			0.00110916i
$777$	8.72573e93	−	3.65871e94i	0.0360502	−	0.151159i
$778$	6.00915e89			2.37950e−6
$779$			8.08904e94i			0.307016i
$780$	−9.07551e94	−	2.16444e94i	−0.330179	−	0.0787450i
$781$	1.93570e95			0.675077
$782$			6.93665e90i			2.31914e-5i
$783$	−3.07576e95	−	2.60309e95i	−0.985857	−	0.834355i
$784$	−2.97641e95			−0.914666
$785$		−	1.87464e95i		−	0.552355i
$786$	6.38235e91	−	2.67613e92i	0.000180317	−	0.000756071i
$787$	1.07922e95			0.292378			0.146189	−	0.989257i	$-0.453299\pi$
$787$	1.07922e95			0.292378			0.146189	+	0.989257i	$0.453299\pi$
$788$			2.08442e95i			0.541528i
$789$	−2.57691e95	−	6.14573e94i	−0.642034	−	0.153120i
$790$	9.27570e91			0.000221642
$791$		−	1.46119e95i		−	0.334876i
$792$	−2.62412e92	−	1.32715e92i	−0.000576837	−	0.000291736i
$793$	−3.50849e94			−0.0739783
$794$			1.01307e92i			0.000204910i
$795$	−6.66335e94	+	2.79395e95i	−0.129294	+	0.542129i
$796$	3.06497e94			0.0570552
$797$		−	6.80923e95i		−	1.21611i	−0.793895	−	0.608055i	$-0.791950\pi$
$797$		−	6.80923e95i		−	1.21611i	0.793895	−	0.608055i	$-0.208050\pi$
$798$	−6.18673e91	−	1.47549e91i	−0.000106015	−	2.52837e-5i
$799$	6.10942e93			0.0100451
$800$			4.86333e92i			0.000767299i
$801$	5.49035e95	−	1.08558e96i	0.831241	−	1.64358i
$802$	−9.07794e91			−0.000131896
$803$		−	3.68807e95i		−	0.514264i
$804$	−1.37522e95	+	5.76633e95i	−0.184045	+	0.771702i
$805$	−2.18900e95			−0.281178
$806$			2.77942e92i			0.000342688i
$807$	8.18108e95	+	1.95112e95i	0.968242	+	0.230918i
$808$	−8.15958e92			−0.000927028
$809$			1.70617e96i			1.86089i	0.366435	+	0.930444i	$0.380578\pi$
$809$			1.70617e96i			1.86089i	−0.366435	+	0.930444i	$0.619422\pi$
$810$	−1.38448e92	−	1.88172e92i	−0.000144971	−	0.000197037i
$811$	−3.57809e95			−0.359719			−0.179859	−	0.983692i	$-0.557564\pi$
$811$	−3.57809e95			−0.359719			−0.179859	+	0.983692i	$0.557564\pi$
$812$		−	3.90854e95i		−	0.377282i
$813$	−3.39886e95	+	1.42515e96i	−0.315025	+	1.32090i
$814$	−1.93185e92			−0.000171936
$815$			8.09996e95i			0.692280i
$816$	4.28135e94	+	1.02107e94i	0.0351403	+	0.00838069i
$817$	8.46061e95			0.666920
$818$			4.10301e92i			0.000310630i
$819$	−2.00922e95	−	1.01616e95i	−0.146103	−	0.0738916i
$820$	−2.88202e95			−0.201298
$821$			1.04534e96i			0.701348i	0.936498	+	0.350674i	$0.114048\pi$
$821$			1.04534e96i			0.701348i	−0.936498	+	0.350674i	$0.885952\pi$
$822$	−1.12180e92	+	4.70371e92i	−7.23010e−5	+	0.000303159i
$823$	−1.50654e96			−0.932792			−0.466396	−	0.884576i	$-0.654448\pi$
$823$	−1.50654e96			−0.932792			−0.466396	+	0.884576i	$0.654448\pi$
$824$		−	1.10967e93i		−	0.000660081i
$825$	8.62400e95	+	2.05676e95i	0.492866	+	0.117545i
$826$	5.69318e91			3.12618e−5
$827$		−	7.43417e95i		−	0.392239i	−0.980580	−	0.196119i	$-0.937166\pi$
$827$		−	7.43417e95i		−	0.392239i	0.980580	−	0.196119i	$-0.0628340\pi$
$828$	1.41481e96	−	2.79744e96i	0.717292	−	1.41827i
$829$	−3.95956e95			−0.192907			−0.0964535	−	0.995337i	$-0.530750\pi$
$829$	−3.95956e95			−0.192907			−0.0964535	+	0.995337i	$0.530750\pi$
$830$		−	8.14105e92i		−	0.000381157i
$831$	−5.92052e95	+	2.48248e96i	−0.266395	+	1.11700i
$832$	1.29606e96			0.560474
$833$			7.94999e94i			0.0330431i
$834$	5.03159e92	+	1.20000e92i	0.000201014	+	4.79402e-5i
$835$	−2.22215e96			−0.853334
$836$		−	2.00227e96i		−	0.739122i
$837$	2.75572e96	−	3.25611e96i	0.977902	−	1.15547i
$838$	4.97055e92			0.000169571
$839$			1.42821e95i			0.0468434i	0.999726	+	0.0234217i	$0.00745603\pi$
$839$			1.42821e95i			0.0468434i	−0.999726	+	0.0234217i	$0.992544\pi$
$840$	1.05139e92	−	4.40850e92i	3.31549e−5	−	0.000139019i
$841$	−2.20336e96			−0.668064
$842$		−	1.78130e92i		−	5.19324e-5i
$843$	3.71373e96	+	8.85696e95i	1.04112	+	0.248299i
$844$	−4.51438e96			−1.21702
$845$		−	1.60220e96i		−	0.415380i
$846$	4.01970e92	+	2.03297e92i	0.000100224	+	5.06884e-5i
$847$	4.38189e95			0.105077
$848$		−	3.99000e96i		−	0.920259i
$849$	−6.48749e95	+	2.72021e96i	−0.143921	+	0.603460i
$850$	4.32998e91			9.23978e−6
$851$		−	4.11888e96i		−	0.845480i
$852$	−4.15583e96	−	9.91134e95i	−0.820638	−	0.195716i
$853$	−5.31455e96			−1.00960			−0.504799	−	0.863237i	$-0.668433\pi$
$853$	−5.31455e96			−1.00960			−0.504799	+	0.863237i	$0.668433\pi$
$854$		−	8.52137e91i		−	1.55740e-5i
$855$	1.43580e96	−	2.83894e96i	0.252471	−	0.499200i
$856$	5.21815e93			0.000882841
$857$			7.22427e96i			1.17605i	0.808841	+	0.588027i	$0.200095\pi$
$857$			7.22427e96i			1.17605i	−0.808841	+	0.588027i	$0.799905\pi$
$858$	−2.68274e92	+	1.12488e93i	−4.20241e−5	+	0.000176208i
$859$	1.27783e97			1.92619			0.963096	−	0.269159i	$-0.0867456\pi$
$859$	1.27783e97			1.92619			0.963096	+	0.269159i	$0.0867456\pi$
$860$			3.01440e96i			0.437273i
$861$	−6.76527e95	−	1.61346e95i	−0.0944455	−	0.0225245i
$862$	3.60646e93			0.000484553
$863$			3.81632e96i			0.493502i	0.969079	+	0.246751i	$0.0793630\pi$
$863$			3.81632e96i			0.493502i	−0.969079	+	0.246751i	$0.920637\pi$
$864$	7.43146e93	+	6.28942e93i	0.000924955	+	0.000782812i
$865$	6.54747e96			0.784408
$866$		−	1.93602e93i		−	0.000223264i
$867$	−2.08701e96	+	8.75086e96i	−0.231683	+	0.971450i
$868$	4.13772e96			0.442192
$869$			7.04690e96i			0.725012i
$870$	−3.10260e93	−	7.39946e92i	−0.000307320	−	7.32934e-5i
$871$	4.66249e96			0.444650
$872$		−	6.11863e93i		−	0.000561836i
$873$	−1.38575e97	−	7.00842e96i	−1.22522	−	0.619655i
$874$	−6.96486e93			−0.000592974
$875$			3.52431e96i			0.288941i
$876$	−1.88840e96	+	7.91808e96i	−0.149093	+	0.625150i
$877$	−6.01426e96			−0.457294			−0.228647	−	0.973509i	$-0.573430\pi$
$877$	−6.01426e96			−0.457294			−0.228647	+	0.973509i	$0.573430\pi$
$878$		−	2.14780e93i		−	0.000157280i
$879$	−8.14437e96	−	1.94237e96i	−0.574413	−	0.136993i
$880$	7.13383e96			0.484612
$881$			2.31569e96i			0.151522i	0.997126	+	0.0757611i	$0.0241386\pi$
$881$			2.31569e96i			0.151522i	−0.997126	+	0.0757611i	$0.975861\pi$
$882$	−2.64543e93	+	5.23070e93i	−0.000166738	+	0.000329683i
$883$	2.94895e96			0.179046			0.0895229	−	0.995985i	$-0.471466\pi$
$883$	2.94895e96			0.179046			0.0895229	+	0.995985i	$0.471466\pi$
$884$		−	3.46178e95i		−	0.0202476i
$885$	−6.60629e95	+	2.77002e96i	−0.0372245	+	0.156083i
$886$	−1.02627e94			−0.000557120
$887$		−	2.26703e97i		−	1.18571i	−0.805309	−	0.592855i	$-0.798001\pi$
$887$		−	2.26703e97i		−	1.18571i	0.805309	−	0.592855i	$-0.201999\pi$
$888$	8.29513e93	+	1.97832e93i	0.000418019	+	9.96942e-5i
$889$	−6.56198e96			−0.318623
$890$		−	9.62974e93i		−	0.000450552i
$891$	1.42957e97	−	1.05181e97i	0.644527	−	0.474213i
$892$	2.17708e97			0.945874
$893$			6.13427e96i			0.256841i
$894$	−4.16692e93	+	1.74719e94i	−0.000168142	+	0.000705023i
$895$	6.51496e96			0.253368
$896$			1.25914e94i			0.000471966i
$897$	−2.39834e97	−	5.71986e96i	−0.866484	−	0.206650i
$898$	−5.95016e93			−0.000207209
$899$		−	5.82407e97i		−	1.95505i
$900$	−1.74621e97	−	8.83148e96i	−0.565059	−	0.285779i
$901$	−1.06573e96			−0.0332452
$902$			3.57216e93i			0.000107427i
$903$	−1.68758e96	+	7.07604e96i	−0.0489292	+	0.205161i
$904$	3.31287e94			0.000926074
$905$		−	2.91539e97i		−	0.785767i
$906$	−3.32491e93	−	7.92966e92i	−8.64072e−5	−	2.06074e-5i
$907$	−6.06048e97			−1.51868			−0.759340	−	0.650694i	$-0.774478\pi$
$907$	−6.06048e97			−1.51868			−0.759340	+	0.650694i	$0.774478\pi$
$908$			6.08490e97i			1.47035i
$909$	2.22259e97	−	4.39463e97i	0.517905	−	1.02403i
$910$	−1.78229e93			−4.00509e−5
$911$			3.87984e97i			0.840828i	0.907332	+	0.420414i	$0.138115\pi$
$911$			3.87984e97i			0.840828i	−0.907332	+	0.420414i	$0.861885\pi$
$912$	−1.02522e97	+	4.29877e97i	−0.214283	+	0.898492i
$913$	6.18489e97			1.24680
$914$		−	2.53762e94i		−	0.000493403i
$915$	4.14608e96	+	9.88807e95i	0.0777573	+	0.0185445i
$916$	1.67457e96			0.0302937
$917$			3.22130e97i			0.562139i
$918$	5.59968e92	−	6.61647e92i	9.42659e−6	−	1.11383e-5i
$919$	2.01013e97			0.326447			0.163223	−	0.986589i	$-0.447811\pi$
$919$	2.01013e97			0.326447			0.163223	+	0.986589i	$0.447811\pi$
$920$		−	4.96298e94i		−	0.000777578i
$921$	−6.17528e96	+	2.58930e97i	−0.0933445	+	0.391394i
$922$	−2.16909e94			−0.000316343
$923$			3.36029e97i			0.472846i
$924$	1.67460e97	+	3.99380e96i	0.227372	+	0.0542264i
$925$	−2.57108e97			−0.336851
$926$			6.03826e94i			0.000763395i
$927$	5.97654e97	+	3.02264e97i	0.729152	+	0.368769i
$928$	1.32924e95			0.00156502
$929$		−	9.31936e97i		−	1.05893i	−0.848332	−	0.529465i	$-0.822393\pi$
$929$		−	9.31936e97i		−	1.05893i	0.848332	−	0.529465i	$-0.177607\pi$
$930$	7.83333e93	−	3.28452e94i	8.59032e−5	−	0.000360193i
$931$	−7.98232e97			−0.844870
$932$			7.57095e97i			0.773438i
$933$	1.63548e98	+	3.90049e97i	1.61269	+	0.384614i
$934$	3.58545e94			0.000341269
$935$		−	1.90545e96i		−	0.0175071i
$936$	2.30388e94	−	4.55537e94i	0.000204342	−	0.000404036i
$937$	−1.91447e98			−1.63924			−0.819618	−	0.572911i	$-0.805814\pi$
$937$	−1.91447e98			−1.63924			−0.819618	+	0.572911i	$0.805814\pi$
$938$			1.13242e94i			9.36081e-5i
$939$	1.08881e97	−	4.56540e97i	0.0868938	−	0.364347i
$940$	−2.18556e97			−0.168400
$941$			1.65299e97i			0.122974i	0.998108	+	0.0614870i	$0.0195843\pi$
$941$			1.65299e97i			0.122974i	−0.998108	+	0.0614870i	$0.980416\pi$
$942$	4.98852e94	+	1.18972e94i	0.000358337	+	8.54606e-5i
$943$	−7.61617e97			−0.528264
$944$		−	3.95583e97i		−	0.264949i
$945$	2.08796e97	+	1.76709e97i	0.135043	+	0.114290i
$946$	3.73625e94			0.000233361
$947$			3.91189e97i			0.235960i	0.993016	+	0.117980i	$0.0376418\pi$
$947$			3.91189e97i			0.235960i	−0.993016	+	0.117980i	$0.962358\pi$
$948$	3.60822e97	−	1.51293e98i	0.210193	−	0.881339i
$949$	6.40233e97			0.360208
$950$			4.34759e94i			0.000236249i
$951$	3.78234e97	+	9.02059e96i	0.198520	+	0.0473454i
$952$	1.68159e93			8.52510e−6
$953$		−	1.59825e98i		−	0.782673i	−0.920248	−	0.391336i	$-0.872013\pi$
$953$		−	1.59825e98i		−	0.782673i	0.920248	−	0.391336i	$-0.127987\pi$
$954$	−7.01198e94	−	3.54631e94i	−0.000331699	−	0.000167757i
$955$	−1.68893e98			−0.771793
$956$		−	3.75214e98i		−	1.65641i
$957$	5.62149e97	−	2.35710e98i	0.239749	−	1.00527i
$958$	−1.68615e95			−0.000694760
$959$		−	5.66194e97i		−	0.225398i
$960$	−1.53159e98	−	3.65273e97i	−0.589105	−	0.140497i
$961$	3.47483e98			1.29140
$962$		−	3.35360e94i		−	0.000120430i
$963$	−1.42137e98	+	2.81042e98i	−0.493220	+	0.975223i
$964$	3.32751e98			1.11578
$965$			3.71660e98i			1.20433i
$966$	1.38923e94	−	5.82507e94i	4.35041e−5	−	0.000182413i
$967$	−3.78980e98			−1.14694			−0.573472	−	0.819225i	$-0.694404\pi$
$967$	−3.78980e98			−1.14694			−0.573472	+	0.819225i	$0.694404\pi$
$968$			9.93475e94i			0.000290583i
$969$	1.14820e97	+	2.73837e96i	0.0324588	+	0.00774118i
$970$	−1.22924e95			−0.000335867
$971$			3.84929e98i			1.01659i	0.861182	+	0.508296i	$0.169724\pi$
$971$			3.84929e98i			1.01659i	−0.861182	+	0.508296i	$0.830276\pi$
$972$	−3.60776e98	+	1.52620e98i	−0.920982	+	0.389605i
$973$	−6.05662e97			−0.149454
$974$			1.50886e95i			0.000359918i
$975$	−3.57044e97	+	1.49709e98i	−0.0823322	+	0.345219i
$976$	−5.92096e97			−0.131992
$977$			3.94409e98i			0.850014i	0.905190	+	0.425007i	$0.139728\pi$
$977$			3.94409e98i			0.850014i	−0.905190	+	0.425007i	$0.860272\pi$
$978$	−2.15545e95	−	5.14058e94i	−0.000449113	−	0.000107110i
$979$	7.31587e98			1.47379
$980$		−	2.84399e98i		−	0.553947i
$981$	3.29540e98	+	1.66665e98i	0.620627	+	0.313883i
$982$	1.88873e95			0.000343947
$983$		−	4.13146e98i		−	0.727508i	−0.931495	−	0.363754i	$-0.881495\pi$
$983$		−	4.13146e98i		−	0.727508i	0.931495	−	0.363754i	$-0.118505\pi$
$984$	3.65810e94	−	1.53384e95i	6.22898e−5	−	0.000261182i
$985$	−1.99169e98			−0.327964
$986$		−	1.18346e94i		−	1.88459e-5i
$987$	−5.13040e97	−	1.22356e97i	−0.0790105	−	0.0188434i
$988$	3.47586e98			0.517706
$989$			7.96603e98i			1.14753i
$990$	6.34055e94	−	1.25369e95i	8.83416e−5	−	0.000174674i
$991$	4.48334e98			0.604186			0.302093	−	0.953278i	$-0.402315\pi$
$991$	4.48334e98			0.604186			0.302093	+	0.953278i	$0.402315\pi$
$992$			1.40718e96i			0.00183427i
$993$	8.46862e97	−	3.55090e98i	0.106779	−	0.447727i
$994$	−8.16142e94			−9.95440e−5
$995$			2.92862e97i			0.0345542i
$996$	−1.32786e99	−	3.16684e98i	−1.51563	−	0.361467i
$997$	2.02511e98			0.223619			0.111809	−	0.993730i	$-0.464335\pi$
$997$	2.02511e98			0.223619			0.111809	+	0.993730i	$0.464335\pi$
$998$			3.30386e95i			0.000352951i
$999$	−3.32501e98	+	3.92876e98i	−0.343662	+	0.406064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.67.b.b.2.11	yes	20
3.2	odd	2	inner	3.67.b.b.2.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.67.b.b.2.10	✓	20	3.2	odd	2	inner
3.67.b.b.2.11	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)

\(f(q)\)	\(=\)	\(q+3.46962e6i q^{2} +(-1.28962e15 + 5.40740e15i) q^{3} +7.37870e19 q^{4} +7.05043e22i q^{5} +(-1.87616e22 - 4.47450e21i) q^{6} +2.25837e27 q^{7} +5.12025e26i q^{8} +(-2.75769e31 - 1.39470e31i) q^{9} +O(q^{10})\)	\(q+3.46962e6i q^{2} +(-1.28962e15 + 5.40740e15i) q^{3} +7.37870e19 q^{4} +7.05043e22i q^{5} +(-1.87616e22 - 4.47450e21i) q^{6} +2.25837e27 q^{7} +5.12025e26i q^{8} +(-2.75769e31 - 1.39470e31i) q^{9} -2.44623e29 q^{10} -1.85844e34i q^{11} +(-9.51574e34 + 3.98996e35i) q^{12} +3.22617e36 q^{13} +7.83568e33i q^{14} +(-3.81245e38 - 9.09240e37i) q^{15} +5.44452e39 q^{16} -1.45423e39i q^{17} +(4.83909e37 - 9.56812e37i) q^{18} +1.46014e42 q^{19} +5.20230e42i q^{20} +(-2.91245e42 + 1.22119e43i) q^{21} +6.44807e40 q^{22} +1.37479e45i q^{23} +(-2.76873e42 - 6.60319e41i) q^{24} +8.58167e45 q^{25} +1.11936e43i q^{26} +(1.10981e47 - 1.31133e47i) q^{27} +1.66638e47 q^{28} -2.34553e48i q^{29} +(3.15471e44 - 1.32277e45i) q^{30} +2.48306e49 q^{31} +5.66711e46i q^{32} +(1.00493e50 + 2.39669e49i) q^{33} +5.04562e45 q^{34} +1.59225e50i q^{35} +(-2.03482e51 - 1.02911e51i) q^{36} -2.99601e51 q^{37} +5.06614e48i q^{38} +(-4.16054e51 + 1.74452e52i) q^{39} -3.60999e49 q^{40} +5.53989e52i q^{41} +(-4.23707e49 - 1.01051e49i) q^{42} +5.79437e53 q^{43} -1.37128e54i q^{44} +(9.83326e53 - 1.94429e54i) q^{45} -4.76998e51 q^{46} +4.20114e54i q^{47} +(-7.02138e54 + 2.94407e55i) q^{48} -5.46680e55 q^{49} +2.97751e52i q^{50} +(7.86361e54 + 1.87541e54i) q^{51} +2.38049e56 q^{52} -7.32848e56i q^{53} +(4.54981e53 + 3.85062e53i) q^{54} +1.31028e57 q^{55} +1.15634e54i q^{56} +(-1.88304e57 + 7.89559e57i) q^{57} +8.13807e54 q^{58} -7.26572e57i q^{59} +(-2.81309e58 - 6.70901e57i) q^{60} -1.08751e58 q^{61} +8.61525e55i q^{62} +(-6.22788e58 - 3.14976e58i) q^{63} +4.01734e59 q^{64} +2.27459e59i q^{65} +(-8.31558e55 + 3.48673e56i) q^{66} +1.44521e60 q^{67} -1.07303e59i q^{68} +(-7.43403e60 - 1.77296e60i) q^{69} -5.52449e56 q^{70} +1.04157e61i q^{71} +(7.14123e57 - 1.41201e58i) q^{72} +1.98450e61 q^{73} -1.03950e58i q^{74} +(-1.10671e61 + 4.64046e61i) q^{75} +1.07740e62 q^{76} -4.19704e61i q^{77} +(-6.05281e58 - 1.44355e58i) q^{78} -3.79184e62 q^{79} +3.83862e62i q^{80} +(5.65965e62 + 7.69232e62i) q^{81} -1.92213e59 q^{82} +3.32800e63i q^{83} +(-2.14901e62 + 9.01080e62i) q^{84} +1.02529e62 q^{85} +2.01042e60i q^{86} +(1.26832e64 + 3.02485e63i) q^{87} +9.51566e60 q^{88} +3.93657e64i q^{89} +(6.74594e60 + 3.41176e60i) q^{90} +7.28588e63 q^{91} +1.01441e65i q^{92} +(-3.20221e64 + 1.34269e65i) q^{93} -1.45763e61 q^{94} +1.02946e65i q^{95} +(-3.06444e62 - 7.30845e61i) q^{96} +5.02502e65 q^{97} -1.89677e62i q^{98} +(-2.59197e65 + 5.12499e65i) 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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