LMFDB - Embedded newform 3.68.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,68,Mod(1,3)]

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([0]))

N = Newforms(chi, 68, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 68);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 68 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

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:	yes
Analytic conductor:	$85.2871055790$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 80\!\cdots\!00 $ x^6 - 3x^5 - 18265801580559590892x^4 - 7523970115455178716247853536x^3 + 78501261395396048023472482629898922880x^2 + 29605717530431234535889524616359650095893868800*x - 80637078962263575025979556823830075867035962985404800000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{46}\cdot 3^{29}\cdot 5^{6}\cdot 7^{2}\cdot 11^{2}\cdot 13\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.84072e9$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.07551e10 q^{2} -5.55906e15 q^{3} +2.83199e20 q^{4} -8.85856e22 q^{5} +1.15379e26 q^{6} -1.53665e28 q^{7} -2.81491e30 q^{8} +3.09032e31 q^{9} +O(q^{10})$	\(q-2.07551e10 q^{2} -5.55906e15 q^{3} +2.83199e20 q^{4} -8.85856e22 q^{5} +1.15379e26 q^{6} -1.53665e28 q^{7} -2.81491e30 q^{8} +3.09032e31 q^{9} +1.83860e33 q^{10} -9.20436e34 q^{11} -1.57432e36 q^{12} -1.88677e37 q^{13} +3.18934e38 q^{14} +4.92453e38 q^{15} +1.66308e40 q^{16} +2.76163e40 q^{17} -6.41397e41 q^{18} +2.82591e42 q^{19} -2.50874e43 q^{20} +8.54235e43 q^{21} +1.91037e45 q^{22} +6.73636e45 q^{23} +1.56482e46 q^{24} -5.99152e46 q^{25} +3.91601e47 q^{26} -1.71793e47 q^{27} -4.35179e48 q^{28} -1.33382e49 q^{29} -1.02209e49 q^{30} -7.13148e49 q^{31} +7.02332e49 q^{32} +5.11676e50 q^{33} -5.73178e50 q^{34} +1.36125e51 q^{35} +8.75174e51 q^{36} -6.38758e52 q^{37} -5.86519e52 q^{38} +1.04887e53 q^{39} +2.49360e53 q^{40} -5.31882e53 q^{41} -1.77297e54 q^{42} +2.05689e54 q^{43} -2.60666e55 q^{44} -2.73757e54 q^{45} -1.39814e56 q^{46} -1.75883e56 q^{47} -9.24518e55 q^{48} -1.82247e56 q^{49} +1.24354e57 q^{50} -1.53521e56 q^{51} -5.34333e57 q^{52} -7.64647e57 q^{53} +3.56557e57 q^{54} +8.15373e57 q^{55} +4.32554e58 q^{56} -1.57094e58 q^{57} +2.76836e59 q^{58} +2.57564e59 q^{59} +1.39462e59 q^{60} -9.49476e59 q^{61} +1.48014e60 q^{62} -4.74875e59 q^{63} -3.91197e60 q^{64} +1.67141e60 q^{65} -1.06199e61 q^{66} -9.40829e60 q^{67} +7.82091e60 q^{68} -3.74479e61 q^{69} -2.82529e61 q^{70} +6.18909e61 q^{71} -8.69896e61 q^{72} -7.31930e61 q^{73} +1.32575e63 q^{74} +3.33072e62 q^{75} +8.00294e62 q^{76} +1.41439e63 q^{77} -2.17694e63 q^{78} -3.05827e63 q^{79} -1.47325e63 q^{80} +9.55005e62 q^{81} +1.10392e64 q^{82} -1.26115e64 q^{83} +2.41919e64 q^{84} -2.44640e63 q^{85} -4.26909e64 q^{86} +7.41481e64 q^{87} +2.59094e65 q^{88} -1.65742e65 q^{89} +5.68185e64 q^{90} +2.89932e65 q^{91} +1.90773e66 q^{92} +3.96443e65 q^{93} +3.65047e66 q^{94} -2.50335e65 q^{95} -3.90431e65 q^{96} -3.51073e66 q^{97} +3.78255e66 q^{98} -2.84444e66 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 13735355166 q^{2} - 33\!\cdots\!38 q^{3}+ \cdots + 18\!\cdots\!74 q^{9}+O(q^{10}) $ 6 * q + 13735355166 * q^2 - 33354363399333138 * q^3 + 461137328518259214852 * q^4 - 180289059197853505182300 * q^5 - 76355671270945289663881818 * q^6 - 28067678610591277820235434208 * q^7 + 174428717775449559766832729592 * q^8 + 185418926295795674171523850821174 * q^9	$ 6 q + 13735355166 q^{2} - 33\!\cdots\!38 q^{3}+ \cdots + 38\!\cdots\!96 q^{99}+O(q^{100}) $ 6 * q + 13735355166 * q^2 - 33354363399333138 * q^3 + 461137328518259214852 * q^4 - 180289059197853505182300 * q^5 - 76355671270945289663881818 * q^6 - 28067678610591277820235434208 * q^7 + 174428717775449559766832729592 * q^8 + 185418926295795674171523850821174 * q^9 + 7304190735814693245550459325330100 * q^10 + 1253554983811830341203783945028424 * q^11 - 2563490338732614404400323640044227596 * q^12 - 1032427018834954393824819765456935964 * q^13 - 447380929503565966859381489320173353952 * q^14 + 1002237799568181731536569743941186842900 * q^15 - 10777060270558286469269005744606427140080 * q^16 - 22303705201707705421583405421371675716596 * q^17 + 424465801195188392885382149078137607180814 * q^18 - 6709513794502265961382038704145157001302152 * q^19 + 46181758835098395119891481090112367056690200 * q^20 + 156029925358891883498812737570110890845530784 * q^21 + 1406045276258114363650986812146594678084267368 * q^22 + 12239031860950699209155226229708548540686529264 * q^23 - 969659806660344055206631047583378687513136616 * q^24 + 124984998689116279435075553443500491502742646250 * q^25 + 147728325197899719596176944836466085493373208692 * q^26 - 1030755041464022662072922259531242545404215044002 * q^27 - 14712260029031223829746951621139067346976206433344 * q^28 - 18873418589468921842047146695821329699174822684364 * q^29 - 40604438690067631054858099234477451658621953142300 * q^30 - 224044794880051525600176726995317503621741761218704 * q^31 - 647694914760137169573449462765066287313897316284448 * q^32 - 6968588078517493039340379725427973276022009185752 * q^33 + 693429763914603914127075176718731888866377974041404 * q^34 - 6444089679967517736201498858201618112886103095496000 * q^35 + 14250598054794536997029174176783125114340868782812708 * q^36 + 27414420131407696449125644786001907623181109991614452 * q^37 + 12552113658955455007053647987482106208988678055446104 * q^38 + 5739324328251871187904239839929767039225529061529172 * q^39 + 1194094866560066539991934179669093556164670510853198800 * q^40 + 2660548042321177320771169314506367536908331651920652796 * q^41 + 2487017683432229918848259981037750023330134118939476896 * q^42 - 1105961611152903745004520895209354208863582663043308600 * q^43 - 34817398461777279630054811602795668745922518275227441104 * q^44 - 5571500629890857041236058470500559035466867019928336700 * q^45 - 45061363378216725453974438646463842380148485881039366224 * q^46 + 58003762634770246900699775563009450632230835045286599360 * q^47 + 59910330773452765968526051655136782182831882309418661840 * q^48 + 985569916983315185097203394977137449656339808292459655670 * q^49 + 4791887184864825461869475209769884139573386495444648751250 * q^50 + 123987648074892602292236983996852174235365272762446559708 * q^51 - 772447381048143948901083488309399868612217101599766652776 * q^52 - 13674721974185597882029982508413224730588130474226494780636 * q^53 - 2359631097275567979107397504361474172402795777134631335722 * q^54 - 51238754618576674303553172437218137404754442562163094366800 * q^55 - 53382539406310631647595973723370754348378361469563798407040 * q^56 + 37298593555777863535226252514563917312860433886972407385496 * q^57 - 27334542479326918025552783071893481077859694969007500722812 * q^58 + 432173245375539353201786532564121354794334705181731449983112 * q^59 - 256727194434372614254225940479565827463386469783086909974600 * q^60 - 301681480554705175984062079070767927549030780778630557968540 * q^61 + 1319649268553974306953641963470020465251839304368009232497584 * q^62 - 867379805265217479240863693041421061959681291088645541720032 * q^63 - 3306273837825060723687391413275118884560206796975317864472512 * q^64 + 9144509139500418095807614952796559412618850636965585264371800 * q^65 - 7816290850038150086493121040028671432967827865802816749073464 * q^66 - 3659535002024051270225014883853538282826668950514180780948296 * q^67 + 62841982068874697565842994801948402899655187355391437927918088 * q^68 - 68037519391027690940233119583149188606433713409875206220325072 * q^69 - 17848574477080955030302460292958517135297977483696841850120000 * q^70 + 252155511033891103624460277167902994429076906738358010146768272 * q^71 + 5390397594179371118067083948912583358245775647599644848330168 * q^72 + 166779610709719144717689715238124518472612391435088881765181724 * q^73 + 1006325717889854285502211107525082701977251477599580185617852868 * q^74 - 694799177623660043822939209279000567990108449155940880572738750 * q^75 - 517707814526076465205777997582680722788148819042185613752993712 * q^76 + 352534620603367398775736559627568751080150267776772663929922944 * q^77 - 821230707170934959628477544327982939588983807972120804684205916 * q^78 - 4778664108337215079572742262604077882794836667809906425462078640 * q^79 + 22035563788144287210408960904426824039627000323030751017638600800 * q^80 + 5730029704780951421359144210646484071519610833846058779021123046 * q^81 + 64371214133499796977109337023506169313379178165909274002938946284 * q^82 + 36651193288697208236374412380857358965233031511415957283935392632 * q^83 + 81786344572298490402773289071356477096023706633672401039174558912 * q^84 + 251284152586026236911243321213724923566970783996009477585132585800 * q^85 + 109459654412686722699057856511584566836933916033705406023221718504 * q^86 + 104918477036812644409737917778017107986270152063164872212109942372 * q^87 + 294858564158317243888419031127963434466163056120837408554388440992 * q^88 - 24716082341461782003245292062820103472910477446347105193539129092 * q^89 + 225722533949076363264521082786586324992651210993012359817269922900 * q^90 + 1637449943486433383394466120659741425501433624430401587862051946176 * q^91 + 4192506910423434290693315227336082767370233979633693670230439475872 * q^92 + 1245478584359715172598232789326604176943806570590746356443962102192 * q^93 + 10776123537142027626725320636495971787147507990566237758042792171712 * q^94 + 8892438758299572900094061329818154779583617585762349202154337045200 * q^95 + 3600575259801619310258913629904116686086350553857582694711853406304 * q^96 + 3864203546244162410999773872217768224094576263762936458169046609164 * q^97 + 26255683859954817683324025976879398726779583524717348419525625709774 * q^98 + 38738803191855518251318864868786039478244708610819286864528508296 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.07551e10	−1.70852	−0.854259	−	0.519848i	$-0.825989\pi$
$2$	−2.07551e10	−1.70852	−0.854259	+	0.519848i	$0.825989\pi$
$3$	−5.55906e15	−0.577350
$3$	−5.55906e15	−0.577350
$4$	2.83199e20	1.91903
$5$	−8.85856e22	−0.340305	−0.170152	−	0.985418i	$-0.554426\pi$
$5$	−8.85856e22	−0.340305	−0.170152	+	0.985418i	$0.554426\pi$
$6$	1.15379e26	0.986413
$7$	−1.53665e28	−0.751263	−0.375631	−	0.926769i	$-0.622574\pi$
$7$	−1.53665e28	−0.751263	−0.375631	+	0.926769i	$0.622574\pi$
$8$	−2.81491e30	−1.57018
$9$	3.09032e31	0.333333
$10$	1.83860e33	0.581416
$11$	−9.20436e34	−1.19492	−0.597459	−	0.801899i	$-0.703823\pi$
$11$	−9.20436e34	−1.19492	−0.597459	+	0.801899i	$0.703823\pi$
$12$	−1.57432e36	−1.10795
$13$	−1.88677e37	−0.909113	−0.454556	−	0.890718i	$-0.650202\pi$
$13$	−1.88677e37	−0.909113	−0.454556	+	0.890718i	$0.650202\pi$
$14$	3.18934e38	1.28355
$15$	4.92453e38	0.196475
$16$	1.66308e40	0.763650
$17$	2.76163e40	0.166390	0.0831948	−	0.996533i	$-0.473488\pi$
$17$	2.76163e40	0.166390	0.0831948	+	0.996533i	$0.473488\pi$
$18$	−6.41397e41	−0.569506
$19$	2.82591e42	0.410121	0.205061	−	0.978749i	$-0.434261\pi$
$19$	2.82591e42	0.410121	0.205061	+	0.978749i	$0.434261\pi$
$20$	−2.50874e43	−0.653055
$21$	8.54235e43	0.433742
$22$	1.91037e45	2.04154
$23$	6.73636e45	1.62384	0.811920	−	0.583769i	$-0.198423\pi$
$23$	6.73636e45	1.62384	0.811920	+	0.583769i	$0.198423\pi$
$24$	1.56482e46	0.906544
$25$	−5.99152e46	−0.884193
$26$	3.91601e47	1.55323
$27$	−1.71793e47	−0.192450
$28$	−4.35179e48	−1.44170
$29$	−1.33382e49	−1.36385	−0.681923	−	0.731424i	$-0.738856\pi$
$29$	−1.33382e49	−1.36385	−0.681923	+	0.731424i	$0.738856\pi$
$30$	−1.02209e49	−0.335681
$31$	−7.13148e49	−0.780841	−0.390421	−	0.920637i	$-0.627670\pi$
$31$	−7.13148e49	−0.780841	−0.390421	+	0.920637i	$0.627670\pi$
$32$	7.02332e49	0.265472
$33$	5.11676e50	0.689887
$34$	−5.73178e50	−0.284280
$35$	1.36125e51	0.255658
$36$	8.75174e51	0.639677
$37$	−6.38758e52	−1.86457	−0.932285	−	0.361724i	$-0.882188\pi$
$37$	−6.38758e52	−1.86457	−0.932285	+	0.361724i	$0.882188\pi$
$38$	−5.86519e52	−0.700699
$39$	1.04887e53	0.524876
$40$	2.49360e53	0.534340
$41$	−5.31882e53	−0.498375	−0.249187	−	0.968455i	$-0.580163\pi$
$41$	−5.31882e53	−0.498375	−0.249187	+	0.968455i	$0.580163\pi$
$42$	−1.77297e54	−0.741055
$43$	2.05689e54	0.390857	0.195428	−	0.980718i	$-0.437390\pi$
$43$	2.05689e54	0.390857	0.195428	+	0.980718i	$0.437390\pi$
$44$	−2.60666e55	−2.29309
$45$	−2.73757e54	−0.113435
$46$	−1.39814e56	−2.77436
$47$	−1.75883e56	−1.69803	−0.849016	−	0.528367i	$-0.822805\pi$
$47$	−1.75883e56	−1.69803	−0.849016	+	0.528367i	$0.822805\pi$
$48$	−9.24518e55	−0.440894
$49$	−1.82247e56	−0.435604
$50$	1.24354e57	1.51066
$51$	−1.53521e56	−0.0960651
$52$	−5.34333e57	−1.74462
$53$	−7.64647e57	−1.31892	−0.659461	−	0.751739i	$-0.729216\pi$
$53$	−7.64647e57	−1.31892	−0.659461	+	0.751739i	$0.729216\pi$
$54$	3.56557e57	0.328804
$55$	8.15373e57	0.406636
$56$	4.32554e58	1.17962
$57$	−1.57094e58	−0.236783
$58$	2.76836e59	2.33016
$59$	2.57564e59	1.22276	0.611381	−	0.791336i	$-0.290614\pi$
$59$	2.57564e59	1.22276	0.611381	+	0.791336i	$0.290614\pi$
$60$	1.39462e59	0.377042
$61$	−9.49476e59	−1.47548	−0.737742	−	0.675083i	$-0.764108\pi$
$61$	−9.49476e59	−1.47548	−0.737742	+	0.675083i	$0.764108\pi$
$62$	1.48014e60	1.33408
$63$	−4.74875e59	−0.250421
$64$	−3.91197e60	−1.21721
$65$	1.67141e60	0.309375
$66$	−1.06199e61	−1.17868
$67$	−9.40829e60	−0.630964	−0.315482	−	0.948932i	$-0.602166\pi$
$67$	−9.40829e60	−0.630964	−0.315482	+	0.948932i	$0.602166\pi$
$68$	7.82091e60	0.319307
$69$	−3.74479e61	−0.937524
$70$	−2.82529e61	−0.436796
$71$	6.18909e61	0.594938	0.297469	−	0.954731i	$-0.403857\pi$
$71$	6.18909e61	0.594938	0.297469	+	0.954731i	$0.403857\pi$
$72$	−8.69896e61	−0.523394
$73$	−7.31930e61	−0.277430	−0.138715	−	0.990332i	$-0.544297\pi$
$73$	−7.31930e61	−0.277430	−0.138715	+	0.990332i	$0.544297\pi$
$74$	1.32575e63	3.18565
$75$	3.33072e62	0.510489
$76$	8.00294e62	0.787035
$77$	1.41439e63	0.897698
$78$	−2.17694e63	−0.896760
$79$	−3.05827e63	−0.822183	−0.411091	−	0.911594i	$-0.634852\pi$
$79$	−3.05827e63	−0.822183	−0.411091	+	0.911594i	$0.634852\pi$
$80$	−1.47325e63	−0.259874
$81$	9.55005e62	0.111111
$82$	1.10392e64	0.851482
$83$	−1.26115e64	−0.648115	−0.324057	−	0.946037i	$-0.605047\pi$
$83$	−1.26115e64	−0.648115	−0.324057	+	0.946037i	$0.605047\pi$
$84$	2.41919e64	0.832364
$85$	−2.44640e63	−0.0566232
$86$	−4.26909e64	−0.667785
$87$	7.41481e64	0.787417
$88$	2.59094e65	1.87624
$89$	−1.65742e65	−0.821989	−0.410995	−	0.911638i	$-0.634818\pi$
$89$	−1.65742e65	−0.821989	−0.410995	+	0.911638i	$0.634818\pi$
$90$	5.68185e64	0.193805
$91$	2.89932e65	0.682982
$92$	1.90773e66	3.11620
$93$	3.96443e65	0.450819
$94$	3.65047e66	2.90112
$95$	−2.50335e65	−0.139566
$96$	−3.90431e65	−0.153270
$97$	−3.51073e66	−0.973968	−0.486984	−	0.873411i	$-0.661903\pi$
$97$	−3.51073e66	−0.973968	−0.486984	+	0.873411i	$0.661903\pi$
$98$	3.78255e66	0.744238
$99$	−2.84444e66	−0.398306
$100$	−1.69679e67	−1.69679
$101$	1.80884e67	1.29609	0.648044	−	0.761603i	$-0.275587\pi$
$101$	1.80884e67	1.29609	0.648044	+	0.761603i	$0.275587\pi$
$102$	3.18633e66	0.164129
$103$	8.58661e66	0.318988	0.159494	−	0.987199i	$-0.449014\pi$
$103$	8.58661e66	0.318988	0.159494	+	0.987199i	$0.449014\pi$
$104$	5.31110e67	1.42747
$105$	−7.56729e66	−0.147604
$106$	1.58703e68	2.25340
$107$	−3.18795e67	−0.330488	−0.165244	−	0.986253i	$-0.552841\pi$
$107$	−3.18795e67	−0.330488	−0.165244	+	0.986253i	$0.552841\pi$
$108$	−4.86515e67	−0.369318
$109$	−1.77827e68	−0.991314	−0.495657	−	0.868518i	$-0.665073\pi$
$109$	−1.77827e68	−0.991314	−0.495657	+	0.868518i	$0.665073\pi$
$110$	−1.69231e68	−0.694745
$111$	3.55090e68	1.07651
$112$	−2.55558e68	−0.573702
$113$	−5.35090e68	−0.891865	−0.445933	−	0.895066i	$-0.647128\pi$
$113$	−5.35090e68	−0.891865	−0.445933	+	0.895066i	$0.647128\pi$
$114$	3.26049e68	0.404549
$115$	−5.96745e68	−0.552600
$116$	−3.77738e69	−2.61726
$117$	−5.83073e68	−0.303038
$118$	−5.34575e69	−2.08911
$119$	−4.24367e68	−0.125002
$120$	−1.38621e69	−0.308501
$121$	2.53853e69	0.427831
$122$	1.97064e70	2.52089
$123$	2.95676e69	0.287737
$124$	−2.01963e70	−1.49846
$125$	1.13104e70	0.641200
$126$	9.85606e69	0.427848
$127$	−1.65936e70	−0.552734	−0.276367	−	0.961052i	$-0.589130\pi$
$127$	−1.65936e70	−0.552734	−0.276367	+	0.961052i	$0.589130\pi$
$128$	7.08287e70	1.81416
$129$	−1.14344e70	−0.225661
$130$	−3.46902e70	−0.528573
$131$	−1.10439e71	−1.30177	−0.650886	−	0.759176i	$-0.725602\pi$
$131$	−1.10439e71	−1.30177	−0.650886	+	0.759176i	$0.725602\pi$
$132$	1.44906e71	1.32391
$133$	−4.34244e70	−0.308109
$134$	1.95270e71	1.07801
$135$	1.52183e70	0.0654917
$136$	−7.77373e70	−0.261262
$137$	2.19389e71	0.576867	0.288434	−	0.957500i	$-0.406866\pi$
$137$	2.19389e71	0.576867	0.288434	+	0.957500i	$0.406866\pi$
$138$	7.77233e71	1.60178
$139$	−8.81751e71	−1.42676	−0.713379	−	0.700779i	$-0.752836\pi$
$139$	−8.81751e71	−1.42676	−0.713379	+	0.700779i	$0.752836\pi$
$140$	3.85506e71	0.490616
$141$	9.77745e71	0.980359
$142$	−1.28455e72	−1.01646
$143$	1.73665e72	1.08632
$144$	5.13945e71	0.254550
$145$	1.18158e72	0.464123
$146$	1.51913e72	0.473994
$147$	1.01312e72	0.251496
$148$	−1.80896e73	−3.57817
$149$	1.59990e72	0.252553	0.126277	−	0.991995i	$-0.459697\pi$
$149$	1.59990e72	0.252553	0.126277	+	0.991995i	$0.459697\pi$
$150$	−6.91294e72	−0.872179
$151$	−1.96424e73	−1.98365	−0.991827	−	0.127587i	$-0.959277\pi$
$151$	−1.96424e73	−1.98365	−0.991827	+	0.127587i	$0.959277\pi$
$152$	−7.95467e72	−0.643964
$153$	8.53430e71	0.0554632
$154$	−2.93558e73	−1.53373
$155$	6.31746e72	0.265724
$156$	2.97039e73	1.00725
$157$	6.95354e73	1.90356	0.951782	−	0.306775i	$-0.0992500\pi$
$157$	6.95354e73	1.90356	0.951782	+	0.306775i	$0.0992500\pi$
$158$	6.34746e73	1.40471
$159$	4.25072e73	0.761480
$160$	−6.22165e72	−0.0903412
$161$	−1.03515e74	−1.21993
$162$	−1.98212e73	−0.189835
$163$	1.87309e74	1.45973	0.729866	−	0.683590i	$-0.239582\pi$
$163$	1.87309e74	1.45973	0.729866	+	0.683590i	$0.239582\pi$
$164$	−1.50628e74	−0.956397
$165$	−4.53271e73	−0.234772
$166$	2.61753e74	1.10732
$167$	7.91566e73	0.273833	0.136916	−	0.990583i	$-0.456281\pi$
$167$	7.91566e73	0.273833	0.136916	+	0.990583i	$0.456281\pi$
$168$	−2.40459e74	−0.681053
$169$	−7.47378e73	−0.173514
$170$	5.07753e73	0.0967417
$171$	8.73294e73	0.136707
$172$	5.82509e74	0.750066
$173$	1.29497e75	1.37314	0.686572	−	0.727062i	$-0.259115\pi$
$173$	1.29497e75	1.37314	0.686572	+	0.727062i	$0.259115\pi$
$174$	−1.53895e75	−1.34532
$175$	9.20690e74	0.664261
$176$	−1.53076e75	−0.912500
$177$	−1.43181e75	−0.705962
$178$	3.43998e75	1.40438
$179$	−2.23519e75	−0.756378	−0.378189	−	0.925728i	$-0.623453\pi$
$179$	−2.23519e75	−0.756378	−0.378189	+	0.925728i	$0.623453\pi$
$180$	−7.75278e74	−0.217685
$181$	6.38585e75	1.48931	0.744657	−	0.667447i	$-0.232613\pi$
$181$	6.38585e75	1.48931	0.744657	+	0.667447i	$0.232613\pi$
$182$	−6.01756e75	−1.16689
$183$	5.27819e75	0.851871
$184$	−1.89623e76	−2.54972
$185$	5.65848e75	0.634522
$186$	−8.22821e75	−0.770232
$187$	−2.54190e75	−0.198822
$188$	−4.98099e76	−3.25858
$189$	2.63986e75	0.144581
$190$	5.19571e75	0.238451
$191$	1.98873e76	0.765524	0.382762	−	0.923847i	$-0.374973\pi$
$191$	1.98873e76	0.765524	0.382762	+	0.923847i	$0.374973\pi$
$192$	2.17469e76	0.702758
$193$	4.02955e76	1.09418	0.547088	−	0.837075i	$-0.315736\pi$
$193$	4.02955e76	1.09418	0.547088	+	0.837075i	$0.315736\pi$
$194$	7.28655e76	1.66404
$195$	−9.29147e75	−0.178618
$196$	−5.16122e76	−0.835938
$197$	1.29243e77	1.76518	0.882590	−	0.470144i	$-0.155798\pi$
$197$	1.29243e77	1.76518	0.882590	+	0.470144i	$0.155798\pi$
$198$	5.90365e76	0.680513
$199$	−4.65190e76	−0.452952	−0.226476	−	0.974017i	$-0.572720\pi$
$199$	−4.65190e76	−0.452952	−0.226476	+	0.974017i	$0.572720\pi$
$200$	1.68656e77	1.38834
$201$	5.23013e76	0.364287
$202$	−3.75427e77	−2.21439
$203$	2.04963e77	1.02461
$204$	−4.34769e76	−0.184352
$205$	4.71171e76	0.169599
$206$	−1.78216e77	−0.544997
$207$	2.08175e77	0.541280
$208$	−3.13786e77	−0.694244
$209$	−2.60106e77	−0.490061
$210$	1.57060e77	0.252185
$211$	−1.37042e77	−0.187669	−0.0938345	−	0.995588i	$-0.529912\pi$
$211$	−1.37042e77	−0.187669	−0.0938345	+	0.995588i	$0.529912\pi$
$212$	−2.16547e78	−2.53105
$213$	−3.44055e77	−0.343488
$214$	6.61662e77	0.564644
$215$	−1.82211e77	−0.133010
$216$	4.83580e77	0.302181
$217$	1.09586e78	0.586617
$218$	3.69082e78	1.69368
$219$	4.06884e77	0.160174
$220$	2.30913e78	0.780348
$221$	−5.21057e77	−0.151267
$222$	−7.36991e78	−1.83924
$223$	−6.61383e78	−1.41984	−0.709921	−	0.704281i	$-0.751269\pi$
$223$	−6.61383e78	−1.41984	−0.709921	+	0.704281i	$0.751269\pi$
$224$	−1.07924e78	−0.199439
$225$	−1.85157e78	−0.294731
$226$	1.11058e79	1.52377
$227$	−7.88749e78	−0.933410	−0.466705	−	0.884413i	$-0.654559\pi$
$227$	−7.88749e78	−0.933410	−0.466705	+	0.884413i	$0.654559\pi$
$228$	−4.44888e78	−0.454395
$229$	−4.55765e78	−0.402025	−0.201012	−	0.979589i	$-0.564423\pi$
$229$	−4.55765e78	−0.402025	−0.201012	+	0.979589i	$0.564423\pi$
$230$	1.23855e79	0.944127
$231$	−7.86269e78	−0.518286
$232$	3.75459e79	2.14149
$233$	−3.78319e78	−0.186825	−0.0934126	−	0.995627i	$-0.529778\pi$
$233$	−3.78319e78	−0.186825	−0.0934126	+	0.995627i	$0.529778\pi$
$234$	1.21017e79	0.517745
$235$	1.55807e79	0.577848
$236$	7.29418e79	2.34652
$237$	1.70011e79	0.474687
$238$	8.80776e78	0.213569
$239$	−6.03661e79	−1.27193	−0.635965	−	0.771718i	$-0.719398\pi$
$239$	−6.03661e79	−1.27193	−0.635965	+	0.771718i	$0.719398\pi$
$240$	8.18989e78	0.150038
$241$	−1.89141e79	−0.301450	−0.150725	−	0.988576i	$-0.548161\pi$
$241$	−1.89141e79	−0.301450	−0.150725	+	0.988576i	$0.548161\pi$
$242$	−5.26874e79	−0.730957
$243$	−5.30893e78	−0.0641500
$244$	−2.68891e80	−2.83150
$245$	1.61445e79	0.148238
$246$	−6.13678e79	−0.491603
$247$	−5.33185e79	−0.372846
$248$	2.00745e80	1.22606
$249$	7.01083e79	0.374189
$250$	−2.34749e80	−1.09550
$251$	1.36947e80	0.559090	0.279545	−	0.960133i	$-0.409816\pi$
$251$	1.36947e80	0.559090	0.279545	+	0.960133i	$0.409816\pi$
$252$	−1.34484e80	−0.480566
$253$	−6.20039e80	−1.94036
$254$	3.44401e80	0.944355
$255$	1.35997e79	0.0326914
$256$	−8.92749e80	−1.88231
$257$	9.80233e80	1.81372	0.906859	−	0.421434i	$-0.138473\pi$
$257$	9.80233e80	1.81372	0.906859	+	0.421434i	$0.138473\pi$
$258$	2.37321e80	0.385546
$259$	9.81551e80	1.40078
$260$	4.73342e80	0.593701
$261$	−4.12194e80	−0.454616
$262$	2.29217e81	2.22410
$263$	1.93379e80	0.165155	0.0825777	−	0.996585i	$-0.473685\pi$
$263$	1.93379e80	0.165155	0.0825777	+	0.996585i	$0.473685\pi$
$264$	−1.44032e81	−1.08325
$265$	6.77367e80	0.448836
$266$	9.01276e80	0.526409
$267$	9.21367e80	0.474576
$268$	−2.66442e81	−1.21084
$269$	−3.48806e81	−1.39921	−0.699604	−	0.714530i	$-0.746640\pi$
$269$	−3.48806e81	−1.39921	−0.699604	+	0.714530i	$0.746640\pi$
$270$	−3.15858e80	−0.111894
$271$	1.65016e81	0.516480	0.258240	−	0.966081i	$-0.416857\pi$
$271$	1.65016e81	0.516480	0.258240	+	0.966081i	$0.416857\pi$
$272$	4.59282e80	0.127063
$273$	−1.61175e81	−0.394320
$274$	−4.55343e81	−0.985587
$275$	5.51481e81	1.05654
$276$	−1.06052e82	−1.79914
$277$	1.17176e82	1.76103	0.880517	−	0.474014i	$-0.157195\pi$
$277$	1.17176e82	1.76103	0.880517	+	0.474014i	$0.157195\pi$
$278$	1.83008e82	2.43764
$279$	−2.20385e81	−0.260280
$280$	−3.83181e81	−0.401430
$281$	−4.62765e81	−0.430228	−0.215114	−	0.976589i	$-0.569012\pi$
$281$	−4.62765e81	−0.430228	−0.215114	+	0.976589i	$0.569012\pi$
$282$	−2.02932e82	−1.67496
$283$	−3.23243e81	−0.236964	−0.118482	−	0.992956i	$-0.537803\pi$
$283$	−3.23243e81	−0.236964	−0.118482	+	0.992956i	$0.537803\pi$
$284$	1.75274e82	1.14171
$285$	1.39162e81	0.0805785
$286$	−3.60444e82	−1.85599
$287$	8.17319e81	0.374410
$288$	2.17043e81	0.0884905
$289$	−2.67846e82	−0.972314
$290$	−2.45237e82	−0.792963
$291$	1.95164e82	0.562321
$292$	−2.07282e82	−0.532397
$293$	1.17436e82	0.268991	0.134495	−	0.990914i	$-0.457059\pi$
$293$	1.17436e82	0.268991	0.134495	+	0.990914i	$0.457059\pi$
$294$	−2.10274e82	−0.429686
$295$	−2.28164e82	−0.416112
$296$	1.79805e83	2.92771
$297$	1.58124e82	0.229962
$298$	−3.32061e82	−0.431492
$299$	−1.27100e83	−1.47625
$300$	9.43258e82	0.979644
$301$	−3.16073e82	−0.293636
$302$	4.07679e83	3.38911
$303$	−1.00555e83	−0.748297
$304$	4.69971e82	0.313189
$305$	8.41099e82	0.502114
$306$	−1.77130e82	−0.0947599
$307$	−3.87477e82	−0.185828	−0.0929139	−	0.995674i	$-0.529618\pi$
$307$	−3.87477e82	−0.185828	−0.0929139	+	0.995674i	$0.529618\pi$
$308$	4.00554e83	1.72271
$309$	−4.77335e82	−0.184168
$310$	−1.31119e83	−0.453994
$311$	1.43110e83	0.444832	0.222416	−	0.974952i	$-0.428606\pi$
$311$	1.43110e83	0.444832	0.222416	+	0.974952i	$0.428606\pi$
$312$	−2.95247e83	−0.824151
$313$	−4.34597e83	−1.08981	−0.544906	−	0.838497i	$-0.683435\pi$
$313$	−4.34597e83	−1.08981	−0.544906	+	0.838497i	$0.683435\pi$
$314$	−1.44321e84	−3.25227
$315$	4.20670e82	0.0852194
$316$	−8.66099e83	−1.57779
$317$	−2.13833e83	−0.350420	−0.175210	−	0.984531i	$-0.556060\pi$
$317$	−2.13833e83	−0.350420	−0.175210	+	0.984531i	$0.556060\pi$
$318$	−8.82240e83	−1.30100
$319$	1.22770e84	1.62969
$320$	3.46544e83	0.414223
$321$	1.77220e83	0.190807
$322$	2.14845e84	2.08427
$323$	7.80410e82	0.0682399
$324$	2.70456e83	0.213226
$325$	1.13047e84	0.803831
$326$	−3.88761e84	−2.49398
$327$	9.88554e83	0.572335
$328$	1.49720e84	0.782538
$329$	2.70272e84	1.27567
$330$	9.40767e83	0.401111
$331$	6.12296e82	0.0235898	0.0117949	−	0.999930i	$-0.496245\pi$
$331$	6.12296e82	0.0235898	0.0117949	+	0.999930i	$0.496245\pi$
$332$	−3.57158e84	−1.24375
$333$	−1.97396e84	−0.621524
$334$	−1.64290e84	−0.467848
$335$	8.33439e83	0.214720
$336$	1.42066e84	0.331227
$337$	8.82119e83	0.186177	0.0930884	−	0.995658i	$-0.470326\pi$
$337$	8.82119e83	0.186177	0.0930884	+	0.995658i	$0.470326\pi$
$338$	1.55119e84	0.296452
$339$	2.97460e84	0.514919
$340$	−6.92819e83	−0.108662
$341$	6.56407e84	0.933042
$342$	−1.81253e84	−0.233566
$343$	9.22953e84	1.07852
$344$	−5.78995e84	−0.613716
$345$	3.31734e84	0.319044
$346$	−2.68772e85	−2.34604
$347$	6.58341e83	0.0521691	0.0260846	−	0.999660i	$-0.491696\pi$
$347$	6.58341e83	0.0521691	0.0260846	+	0.999660i	$0.491696\pi$
$348$	2.09987e85	1.51108
$349$	3.71999e84	0.243159	0.121579	−	0.992582i	$-0.461204\pi$
$349$	3.71999e84	0.243159	0.121579	+	0.992582i	$0.461204\pi$
$350$	−1.91090e85	−1.13490
$351$	3.24134e84	0.174959
$352$	−6.46451e84	−0.317217
$353$	6.16432e83	0.0275063	0.0137532	−	0.999905i	$-0.495622\pi$
$353$	6.16432e83	0.0275063	0.0137532	+	0.999905i	$0.495622\pi$
$354$	2.97174e85	1.20615
$355$	−5.48264e84	−0.202460
$356$	−4.69378e85	−1.57742
$357$	2.35908e84	0.0721701
$358$	4.63916e85	1.29228
$359$	−2.97156e85	−0.753912	−0.376956	−	0.926231i	$-0.623029\pi$
$359$	−2.97156e85	−0.753912	−0.376956	+	0.926231i	$0.623029\pi$
$360$	7.70602e84	0.178113
$361$	−3.94921e85	−0.831801
$362$	−1.32539e86	−2.54452
$363$	−1.41118e85	−0.247008
$364$	8.21085e85	1.31066
$365$	6.48384e84	0.0944108
$366$	−1.09549e86	−1.45544
$367$	4.89609e85	0.593658	0.296829	−	0.954931i	$-0.404071\pi$
$367$	4.89609e85	0.593658	0.296829	+	0.954931i	$0.404071\pi$
$368$	1.12031e86	1.24005
$369$	−1.64368e85	−0.166125
$370$	−1.17442e86	−1.08409
$371$	1.17500e86	0.990857
$372$	1.12272e86	0.865136
$373$	1.09170e86	0.768879	0.384439	−	0.923150i	$-0.374395\pi$
$373$	1.09170e86	0.768879	0.384439	+	0.923150i	$0.374395\pi$
$374$	5.27573e85	0.339691
$375$	−6.28753e85	−0.370197
$376$	4.95095e86	2.66622
$377$	2.51662e86	1.23989
$378$	−5.47904e85	−0.247018
$379$	3.43926e86	1.41923	0.709613	−	0.704592i	$-0.248870\pi$
$379$	3.43926e86	1.41923	0.709613	+	0.704592i	$0.248870\pi$
$380$	−7.08945e85	−0.267832
$381$	9.22448e85	0.319121
$382$	−4.12763e86	−1.30791
$383$	−6.01883e86	−1.74724	−0.873622	−	0.486606i	$-0.838235\pi$
$383$	−6.01883e86	−1.74724	−0.873622	+	0.486606i	$0.838235\pi$
$384$	−3.93741e86	−1.04740
$385$	−1.25295e86	−0.305491
$386$	−8.36337e86	−1.86942
$387$	6.35643e85	0.130286
$388$	−9.94236e86	−1.86908
$389$	1.14351e87	1.97209	0.986045	−	0.166481i	$-0.0532404\pi$
$389$	1.14351e87	1.97209	0.986045	+	0.166481i	$0.0532404\pi$
$390$	1.92845e86	0.305172
$391$	1.86033e86	0.270190
$392$	5.13009e86	0.683978
$393$	6.13938e86	0.751578
$394$	−2.68245e87	−3.01584
$395$	2.70919e86	0.279793
$396$	−8.05542e86	−0.764362
$397$	6.35437e86	0.554103	0.277051	−	0.960855i	$-0.410643\pi$
$397$	6.35437e86	0.554103	0.277051	+	0.960855i	$0.410643\pi$
$398$	9.65504e86	0.773876
$399$	2.41399e86	0.177887
$400$	−9.96440e86	−0.675214
$401$	2.27798e86	0.141976	0.0709879	−	0.997477i	$-0.477385\pi$
$401$	2.27798e86	0.141976	0.0709879	+	0.997477i	$0.477385\pi$
$402$	−1.08552e87	−0.622391
$403$	1.34555e87	0.709873
$404$	5.12262e87	2.48723
$405$	−8.45997e85	−0.0378116
$406$	−4.25401e87	−1.75056
$407$	5.87936e87	2.22801
$408$	4.32146e86	0.150840
$409$	−1.23545e87	−0.397279	−0.198640	−	0.980073i	$-0.563652\pi$
$409$	−1.23545e87	−0.397279	−0.198640	+	0.980073i	$0.563652\pi$
$410$	−9.77918e86	−0.289763
$411$	−1.21960e87	−0.333054
$412$	2.43172e87	0.612148
$413$	−3.95786e87	−0.918616
$414$	−4.32069e87	−0.924786
$415$	1.11720e87	0.220556
$416$	−1.32514e87	−0.241344
$417$	4.90171e87	0.823739
$418$	5.39853e87	0.837278
$419$	−7.53287e87	−1.07843	−0.539213	−	0.842169i	$-0.681278\pi$
$419$	−7.53287e87	−1.07843	−0.539213	+	0.842169i	$0.681278\pi$
$420$	−2.14305e87	−0.283257
$421$	−3.23043e86	−0.0394285	−0.0197143	−	0.999806i	$-0.506276\pi$
$421$	−3.23043e86	−0.0394285	−0.0197143	+	0.999806i	$0.506276\pi$
$422$	2.84432e87	0.320636
$423$	−5.43534e87	−0.566011
$424$	2.15241e88	2.07095
$425$	−1.65464e87	−0.147121
$426$	7.14089e87	0.586855
$427$	1.45902e88	1.10848
$428$	−9.02825e87	−0.634216
$429$	−9.65417e87	−0.627185
$430$	3.78180e87	0.227250
$431$	2.01582e87	0.112063	0.0560316	−	0.998429i	$-0.482155\pi$
$431$	2.01582e87	0.112063	0.0560316	+	0.998429i	$0.482155\pi$
$432$	−2.85705e87	−0.146965
$433$	−1.29731e88	−0.617589	−0.308794	−	0.951129i	$-0.599925\pi$
$433$	−1.29731e88	−0.617589	−0.308794	+	0.951129i	$0.599925\pi$
$434$	−2.27447e88	−1.00225
$435$	−6.56845e87	−0.267962
$436$	−5.03606e88	−1.90236
$437$	1.90363e88	0.665971
$438$	−8.44491e87	−0.273661
$439$	−4.97438e88	−1.49340	−0.746702	−	0.665159i	$-0.768364\pi$
$439$	−4.97438e88	−1.49340	−0.746702	+	0.665159i	$0.768364\pi$
$440$	−2.29520e88	−0.638493
$441$	−5.63201e87	−0.145201
$442$	1.08146e88	0.258442
$443$	−5.67573e88	−1.25747	−0.628734	−	0.777621i	$-0.716426\pi$
$443$	−5.67573e88	−1.25747	−0.628734	+	0.777621i	$0.716426\pi$
$444$	1.00561e89	2.06586
$445$	1.46823e88	0.279727
$446$	1.37271e89	2.42583
$447$	−8.89395e87	−0.145812
$448$	6.01135e88	0.914447
$449$	−6.31326e88	−0.891254	−0.445627	−	0.895219i	$-0.647019\pi$
$449$	−6.31326e88	−0.891254	−0.445627	+	0.895219i	$0.647019\pi$
$450$	3.84295e88	0.503553
$451$	4.89563e88	0.595517
$452$	−1.51537e89	−1.71152
$453$	1.09193e89	1.14526
$454$	1.63705e89	1.59475
$455$	−2.56838e88	−0.232422
$456$	4.42205e88	0.371793
$457$	−9.61963e88	−0.751563	−0.375782	−	0.926708i	$-0.622626\pi$
$457$	−9.61963e88	−0.751563	−0.375782	+	0.926708i	$0.622626\pi$
$458$	9.45944e88	0.686866
$459$	−4.74427e87	−0.0320217
$460$	−1.68998e89	−1.06046
$461$	1.04223e89	0.608109	0.304055	−	0.952655i	$-0.401659\pi$
$461$	1.04223e89	0.608109	0.304055	+	0.952655i	$0.401659\pi$
$462$	1.63191e89	0.885501
$463$	5.39455e88	0.272265	0.136132	−	0.990691i	$-0.456533\pi$
$463$	5.39455e88	0.272265	0.136132	+	0.990691i	$0.456533\pi$
$464$	−2.21826e89	−1.04150
$465$	−3.51192e88	−0.153416
$466$	7.85205e88	0.319194
$467$	5.85028e88	0.221340	0.110670	−	0.993857i	$-0.464700\pi$
$467$	5.85028e88	0.221340	0.110670	+	0.993857i	$0.464700\pi$
$468$	−1.65126e89	−0.581539
$469$	1.44573e89	0.474020
$470$	−3.23379e89	−0.987264
$471$	−3.86551e89	−1.09902
$472$	−7.25018e89	−1.91996
$473$	−1.89323e89	−0.467042
$474$	−3.52859e89	−0.811012
$475$	−1.69315e89	−0.362626
$476$	−1.20180e89	−0.239883
$477$	−2.36300e89	−0.439641
$478$	1.25290e90	2.17312
$479$	−3.69559e89	−0.597646	−0.298823	−	0.954309i	$-0.596594\pi$
$479$	−3.69559e89	−0.597646	−0.298823	+	0.954309i	$0.596594\pi$
$480$	3.45865e88	0.0521585
$481$	1.20519e90	1.69510
$482$	3.92564e89	0.515032
$483$	5.75444e89	0.704327
$484$	7.18909e89	0.821021
$485$	3.11000e89	0.331446
$486$	1.10187e89	0.109601
$487$	−1.58633e90	−1.47290	−0.736448	−	0.676494i	$-0.763498\pi$
$487$	−1.58633e90	−1.47290	−0.736448	+	0.676494i	$0.763498\pi$
$488$	2.67269e90	2.31678
$489$	−1.04126e90	−0.842777
$490$	−3.35080e89	−0.253268
$491$	−2.19856e90	−1.55206	−0.776030	−	0.630696i	$-0.782769\pi$
$491$	−2.19856e90	−1.55206	−0.776030	+	0.630696i	$0.782769\pi$
$492$	8.37353e89	0.552176
$493$	−3.68353e89	−0.226930
$494$	1.10663e90	0.637014
$495$	2.51976e89	0.135545
$496$	−1.18602e90	−0.596290
$497$	−9.51049e89	−0.446955
$498$	−1.45510e90	−0.639309
$499$	−1.41964e89	−0.0583190	−0.0291595	−	0.999575i	$-0.509283\pi$
$499$	−1.41964e89	−0.0583190	−0.0291595	+	0.999575i	$0.509283\pi$
$500$	3.20310e90	1.23048
$501$	−4.40037e89	−0.158097
$502$	−2.84234e90	−0.955214
$503$	6.15336e89	0.193457	0.0967285	−	0.995311i	$-0.469162\pi$
$503$	6.15336e89	0.193457	0.0967285	+	0.995311i	$0.469162\pi$
$504$	1.33673e90	0.393206
$505$	−1.60237e90	−0.441065
$506$	1.28690e91	3.31513
$507$	4.15472e89	0.100179
$508$	−4.69929e90	−1.06071
$509$	7.01158e89	0.148173	0.0740867	−	0.997252i	$-0.476396\pi$
$509$	7.01158e89	0.148173	0.0740867	+	0.997252i	$0.476396\pi$
$510$	−2.82263e89	−0.0558538
$511$	1.12472e90	0.208423
$512$	8.07660e90	1.40180
$513$	−4.85469e89	−0.0789278
$514$	−2.03448e91	−3.09877
$515$	−7.60650e89	−0.108553
$516$	−3.23820e90	−0.433051
$517$	1.61889e91	2.02901
$518$	−2.03722e91	−2.39326
$519$	−7.19883e90	−0.792785
$520$	−4.70487e90	−0.485775
$521$	3.21205e89	0.0310970	0.0155485	−	0.999879i	$-0.495051\pi$
$521$	3.21205e89	0.0310970	0.0155485	+	0.999879i	$0.495051\pi$
$522$	8.55511e90	0.776719
$523$	1.72524e91	1.46907	0.734535	−	0.678570i	$-0.237400\pi$
$523$	1.72524e91	1.46907	0.734535	+	0.678570i	$0.237400\pi$
$524$	−3.12763e91	−2.49814
$525$	−5.11817e90	−0.383511
$526$	−4.01360e90	−0.282171
$527$	−1.96945e90	−0.129924
$528$	8.50959e90	0.526832
$529$	2.81692e91	1.63685
$530$	−1.40588e91	−0.766843
$531$	7.95953e90	0.407588
$532$	−1.22977e91	−0.591270
$533$	1.00354e91	0.453079
$534$	−1.91230e91	−0.810821
$535$	2.82407e90	0.112466
$536$	2.64835e91	0.990728
$537$	1.24256e91	0.436695
$538$	7.23949e91	2.39057
$539$	1.67747e91	0.520512
$540$	4.30982e90	0.125681
$541$	4.34624e91	1.19126	0.595628	−	0.803260i	$-0.296903\pi$
$541$	4.34624e91	1.19126	0.595628	+	0.803260i	$0.296903\pi$
$542$	−3.42491e91	−0.882415
$543$	−3.54993e91	−0.859856
$544$	1.93958e90	0.0441717
$545$	1.57529e91	0.337349
$546$	3.34520e91	0.673703
$547$	1.18855e91	0.225135	0.112568	−	0.993644i	$-0.464093\pi$
$547$	1.18855e91	0.225135	0.112568	+	0.993644i	$0.464093\pi$
$548$	6.21307e91	1.10703
$549$	−2.93418e91	−0.491828
$550$	−1.14460e92	−1.80511
$551$	−3.76926e91	−0.559342
$552$	1.05412e92	1.47208
$553$	4.69950e91	0.617675
$554$	−2.43200e92	−3.00876
$555$	−3.14558e91	−0.366342
$556$	−2.49711e92	−2.73799
$557$	−1.56222e92	−1.61285	−0.806423	−	0.591339i	$-0.798599\pi$
$557$	−1.56222e92	−1.61285	−0.806423	+	0.591339i	$0.798599\pi$
$558$	4.57411e91	0.444694
$559$	−3.88088e91	−0.355333
$560$	2.26388e91	0.195233
$561$	1.41306e91	0.114790
$562$	9.60471e91	0.735051
$563$	1.86782e92	1.34680	0.673399	−	0.739279i	$-0.264833\pi$
$563$	1.86782e92	1.34680	0.673399	+	0.739279i	$0.264833\pi$
$564$	2.76896e92	1.88134
$565$	4.74013e91	0.303506
$566$	6.70892e91	0.404858
$567$	−1.46751e91	−0.0834736
$568$	−1.74217e92	−0.934161
$569$	−2.54196e92	−1.28502	−0.642508	−	0.766279i	$-0.722106\pi$
$569$	−2.54196e92	−1.28502	−0.642508	+	0.766279i	$0.722106\pi$
$570$	−2.88833e91	−0.137670
$571$	2.37692e92	1.06833	0.534165	−	0.845380i	$-0.320626\pi$
$571$	2.37692e92	1.06833	0.534165	+	0.845380i	$0.320626\pi$
$572$	4.91819e92	2.08467
$573$	−1.10555e92	−0.441976
$574$	−1.69635e92	−0.639686
$575$	−4.03611e92	−1.43579
$576$	−1.20892e92	−0.405738
$577$	−8.92557e91	−0.282648	−0.141324	−	0.989963i	$-0.545136\pi$
$577$	−8.92557e91	−0.282648	−0.141324	+	0.989963i	$0.545136\pi$
$578$	5.55915e92	1.66122
$579$	−2.24005e92	−0.631723
$580$	3.34621e92	0.890667
$581$	1.93796e92	0.486904
$582$	−4.05064e92	−0.960735
$583$	7.03808e92	1.57601
$584$	2.06032e92	0.435615
$585$	5.16518e91	0.103125
$586$	−2.43740e92	−0.459576
$587$	−1.78490e92	−0.317862	−0.158931	−	0.987290i	$-0.550805\pi$
$587$	−1.78490e92	−0.317862	−0.158931	+	0.987290i	$0.550805\pi$
$588$	2.86916e92	0.482629
$589$	−2.01529e92	−0.320239
$590$	4.73557e92	0.710934
$591$	−7.18470e92	−1.01913
$592$	−1.06231e93	−1.42388
$593$	6.32966e91	0.0801768	0.0400884	−	0.999196i	$-0.487236\pi$
$593$	6.32966e91	0.0801768	0.0400884	+	0.999196i	$0.487236\pi$
$594$	−3.28187e92	−0.392894
$595$	3.75928e91	0.0425389
$596$	4.53091e92	0.484658
$597$	2.58602e92	0.261512
$598$	2.63797e93	2.52220
$599$	−1.95886e93	−1.77094	−0.885472	−	0.464692i	$-0.846165\pi$
$599$	−1.95886e93	−1.77094	−0.885472	+	0.464692i	$0.846165\pi$
$600$	−9.37568e92	−0.801560
$601$	2.02258e93	1.63535	0.817676	−	0.575679i	$-0.195262\pi$
$601$	2.02258e93	1.63535	0.817676	+	0.575679i	$0.195262\pi$
$602$	6.56011e92	0.501682
$603$	−2.90746e92	−0.210321
$604$	−5.56270e93	−3.80670
$605$	−2.24877e92	−0.145593
$606$	2.08702e93	1.27848
$607$	2.95342e93	1.71200	0.856001	−	0.516974i	$-0.172942\pi$
$607$	2.95342e93	1.71200	0.856001	+	0.516974i	$0.172942\pi$
$608$	1.98472e92	0.108875
$609$	−1.13940e93	−0.591557
$610$	−1.74571e93	−0.857871
$611$	3.31852e93	1.54370
$612$	2.41691e92	0.106436
$613$	−2.74925e93	−1.14627	−0.573136	−	0.819460i	$-0.694273\pi$
$613$	−2.74925e93	−1.14627	−0.573136	+	0.819460i	$0.694273\pi$
$614$	8.04212e92	0.317490
$615$	−2.61927e92	−0.0979182
$616$	−3.98138e93	−1.40955
$617$	−4.50532e93	−1.51068	−0.755340	−	0.655333i	$-0.772528\pi$
$617$	−4.50532e93	−1.51068	−0.755340	+	0.655333i	$0.772528\pi$
$618$	9.90712e92	0.314654
$619$	−6.55833e93	−1.97314	−0.986568	−	0.163354i	$-0.947769\pi$
$619$	−6.55833e93	−1.97314	−0.986568	+	0.163354i	$0.947769\pi$
$620$	1.78910e93	0.509933
$621$	−1.15726e93	−0.312508
$622$	−2.97025e93	−0.760003
$623$	2.54687e93	0.617530
$624$	1.74436e93	0.400822
$625$	3.05807e93	0.665989
$626$	9.02009e93	1.86196
$627$	1.44595e93	0.282937
$628$	1.96924e94	3.65300
$629$	−1.76401e93	−0.310245
$630$	−8.73105e92	−0.145599
$631$	−2.59380e93	−0.410159	−0.205080	−	0.978745i	$-0.565745\pi$
$631$	−2.59380e93	−0.410159	−0.205080	+	0.978745i	$0.565745\pi$
$632$	8.60875e93	1.29098
$633$	7.61827e92	0.108351
$634$	4.43812e93	0.598699
$635$	1.46995e93	0.188098
$636$	1.20380e94	1.46130
$637$	3.43859e93	0.396013
$638$	−2.54810e94	−2.78435
$639$	1.91262e93	0.198313
$640$	−6.27440e93	−0.617366
$641$	−1.72118e94	−1.60725	−0.803623	−	0.595139i	$-0.797097\pi$
$641$	−1.72118e94	−1.60725	−0.803623	+	0.595139i	$0.797097\pi$
$642$	−3.67822e93	−0.325997
$643$	1.66351e94	1.39945	0.699726	−	0.714411i	$-0.253305\pi$
$643$	1.66351e94	1.39945	0.699726	+	0.714411i	$0.253305\pi$
$644$	−2.93152e94	−2.34108
$645$	1.01292e93	0.0767936
$646$	−1.61975e93	−0.116589
$647$	−3.81637e93	−0.260830	−0.130415	−	0.991460i	$-0.541631\pi$
$647$	−3.81637e93	−0.260830	−0.130415	+	0.991460i	$0.541631\pi$
$648$	−2.68825e93	−0.174465
$649$	−2.37071e94	−1.46110
$650$	−2.34629e94	−1.37336
$651$	−6.09196e93	−0.338684
$652$	5.30456e94	2.80127
$653$	1.80645e94	0.906224	0.453112	−	0.891454i	$-0.350314\pi$
$653$	1.80645e94	0.906224	0.453112	+	0.891454i	$0.350314\pi$
$654$	−2.05175e94	−0.977845
$655$	9.78332e93	0.442999
$656$	−8.84564e93	−0.380584
$657$	−2.26189e93	−0.0924767
$658$	−5.60951e94	−2.17950
$659$	2.68841e94	0.992736	0.496368	−	0.868112i	$-0.334667\pi$
$659$	2.68841e94	0.992736	0.496368	+	0.868112i	$0.334667\pi$
$660$	−1.28366e94	−0.450534
$661$	4.31511e94	1.43960	0.719802	−	0.694179i	$-0.244232\pi$
$661$	4.31511e94	1.43960	0.719802	+	0.694179i	$0.244232\pi$
$662$	−1.27083e93	−0.0403036
$663$	2.89659e93	0.0873340
$664$	3.55003e94	1.01766
$665$	3.84678e93	0.104851
$666$	4.09698e94	1.06188
$667$	−8.98512e94	−2.21467
$668$	2.24171e94	0.525494
$669$	3.67667e94	0.819746
$670$	−1.72981e94	−0.366853
$671$	8.73931e94	1.76308
$672$	5.99957e93	0.115146
$673$	3.80191e94	0.694220	0.347110	−	0.937824i	$-0.387163\pi$
$673$	3.80191e94	0.694220	0.347110	+	0.937824i	$0.387163\pi$
$674$	−1.83084e94	−0.318086
$675$	1.02930e94	0.170163
$676$	−2.11657e94	−0.332980
$677$	−2.23934e94	−0.335274	−0.167637	−	0.985849i	$-0.553614\pi$
$677$	−2.23934e94	−0.335274	−0.167637	+	0.985849i	$0.553614\pi$
$678$	−6.17380e94	−0.879748
$679$	5.39478e94	0.731706
$680$	6.88641e93	0.0889087
$681$	4.38470e94	0.538905
$682$	−1.36238e95	−1.59412
$683$	3.08841e94	0.344066	0.172033	−	0.985091i	$-0.444966\pi$
$683$	3.08841e94	0.344066	0.172033	+	0.985091i	$0.444966\pi$
$684$	2.47316e94	0.262345
$685$	−1.94347e94	−0.196311
$686$	−1.91560e95	−1.84266
$687$	2.53363e94	0.232109
$688$	3.42078e94	0.298478
$689$	1.44272e95	1.19905
$690$	−6.88516e94	−0.545092
$691$	−2.24920e95	−1.69634	−0.848171	−	0.529722i	$-0.822296\pi$
$691$	−2.24920e95	−1.69634	−0.848171	+	0.529722i	$0.822296\pi$
$692$	3.66735e95	2.63511
$693$	4.37091e94	0.299233
$694$	−1.36639e94	−0.0891319
$695$	7.81104e94	0.485532
$696$	−2.08720e95	−1.23639
$697$	−1.46886e94	−0.0829244
$698$	−7.72087e94	−0.415441
$699$	2.10310e94	0.107864
$700$	2.60739e95	1.27474
$701$	−6.52515e94	−0.304115	−0.152057	−	0.988372i	$-0.548590\pi$
$701$	−6.52515e94	−0.304115	−0.152057	+	0.988372i	$0.548590\pi$
$702$	−6.72742e94	−0.298920
$703$	−1.80507e95	−0.764700
$704$	3.60072e95	1.45447
$705$	−8.66141e94	−0.333621
$706$	−1.27941e94	−0.0469950
$707$	−2.77957e95	−0.973703
$708$	−4.05488e95	−1.35476
$709$	−2.48077e95	−0.790564	−0.395282	−	0.918560i	$-0.629353\pi$
$709$	−2.48077e95	−0.790564	−0.395282	+	0.918560i	$0.629353\pi$
$710$	1.13793e95	0.345907
$711$	−9.45102e94	−0.274061
$712$	4.66547e95	1.29067
$713$	−4.80402e95	−1.26796
$714$	−4.89629e94	−0.123304
$715$	−1.53843e95	−0.369678
$716$	−6.33005e95	−1.45151
$717$	3.35579e95	0.734349
$718$	6.16750e95	1.28807
$719$	−2.90423e95	−0.578914	−0.289457	−	0.957191i	$-0.593475\pi$
$719$	−2.90423e95	−0.578914	−0.289457	+	0.957191i	$0.593475\pi$
$720$	−4.55281e94	−0.0866246
$721$	−1.31947e95	−0.239644
$722$	8.19662e95	1.42115
$723$	1.05145e95	0.174042
$724$	1.80847e96	2.85804
$725$	7.99164e95	1.20590
$726$	2.92892e95	0.422018
$727$	−1.44746e95	−0.199160	−0.0995802	−	0.995030i	$-0.531750\pi$
$727$	−1.44746e95	−0.199160	−0.0995802	+	0.995030i	$0.531750\pi$
$728$	−8.16132e95	−1.07241
$729$	2.95127e94	0.0370370
$730$	−1.34573e95	−0.161302
$731$	5.68036e94	0.0650345
$732$	1.49478e96	1.63477
$733$	−1.86189e96	−1.94523	−0.972617	−	0.232414i	$-0.925338\pi$
$733$	−1.86189e96	−1.94523	−0.972617	+	0.232414i	$0.925338\pi$
$734$	−1.01619e96	−1.01428
$735$	−8.97481e94	−0.0855854
$736$	4.73116e95	0.431083
$737$	8.65972e95	0.753951
$738$	3.41148e95	0.283827
$739$	6.65460e95	0.529095	0.264547	−	0.964373i	$-0.414777\pi$
$739$	6.65460e95	0.529095	0.264547	+	0.964373i	$0.414777\pi$
$740$	1.60248e96	1.21767
$741$	2.96401e95	0.215263
$742$	−2.43872e96	−1.69290
$743$	−4.07420e95	−0.270344	−0.135172	−	0.990822i	$-0.543159\pi$
$743$	−4.07420e95	−0.270344	−0.135172	+	0.990822i	$0.543159\pi$
$744$	−1.11595e96	−0.707867
$745$	−1.41728e95	−0.0859451
$746$	−2.26583e96	−1.31364
$747$	−3.89736e95	−0.216038
$748$	−7.19864e95	−0.381546
$749$	4.89878e95	0.248283
$750$	1.30498e96	0.632488
$751$	−7.66752e95	−0.355400	−0.177700	−	0.984085i	$-0.556866\pi$
$751$	−7.66752e95	−0.355400	−0.177700	+	0.984085i	$0.556866\pi$
$752$	−2.92508e96	−1.29670
$753$	−7.61294e95	−0.322791
$754$	−5.22327e96	−2.11837
$755$	1.74003e96	0.675047
$756$	7.47605e95	0.277455
$757$	1.32246e96	0.469537	0.234768	−	0.972051i	$-0.424567\pi$
$757$	1.32246e96	0.469537	0.234768	+	0.972051i	$0.424567\pi$
$758$	−7.13821e96	−2.42477
$759$	3.44683e96	1.12027
$760$	7.04669e95	0.219144
$761$	−2.41001e94	−0.00717186	−0.00358593	−	0.999994i	$-0.501141\pi$
$761$	−2.41001e94	−0.00717186	−0.00358593	+	0.999994i	$0.501141\pi$
$762$	−1.91455e96	−0.545224
$763$	2.73259e96	0.744737
$764$	5.63208e96	1.46907
$765$	−7.56016e94	−0.0188744
$766$	1.24921e97	2.98520
$767$	−4.85964e96	−1.11163
$768$	4.96284e96	1.08675
$769$	7.64601e96	1.60288	0.801442	−	0.598072i	$-0.204066\pi$
$769$	7.64601e96	1.60288	0.801442	+	0.598072i	$0.204066\pi$
$770$	2.60050e96	0.521936
$771$	−5.44917e96	−1.04715
$772$	1.14117e97	2.09976
$773$	−4.79798e96	−0.845367	−0.422683	−	0.906277i	$-0.638912\pi$
$773$	−4.79798e96	−0.845367	−0.422683	+	0.906277i	$0.638912\pi$
$774$	−1.31928e96	−0.222595
$775$	4.27284e96	0.690414
$776$	9.88239e96	1.52931
$777$	−5.45650e96	−0.808742
$778$	−2.37335e97	−3.36935
$779$	−1.50305e96	−0.204394
$780$	−2.63134e96	−0.342773
$781$	−5.69666e96	−0.710903
$782$	−3.86114e96	−0.461624
$783$	2.29141e96	0.262472
$784$	−3.03092e96	−0.332649
$785$	−6.15983e96	−0.647792
$786$	−1.27423e97	−1.28408
$787$	−7.73270e96	−0.746754	−0.373377	−	0.927680i	$-0.621800\pi$
$787$	−7.73270e96	−0.746754	−0.373377	+	0.927680i	$0.621800\pi$
$788$	3.66015e97	3.38743
$789$	−1.07501e96	−0.0953525
$790$	−5.62294e96	−0.478031
$791$	8.22249e96	0.670025
$792$	8.00683e96	0.625413
$793$	1.79145e97	1.34138
$794$	−1.31885e97	−0.946694
$795$	−3.76552e96	−0.259135
$796$	−1.31741e97	−0.869229
$797$	1.82391e97	1.15385	0.576925	−	0.816797i	$-0.304252\pi$
$797$	1.82391e97	1.15385	0.576925	+	0.816797i	$0.304252\pi$
$798$	−5.01025e96	−0.303922
$799$	−4.85724e96	−0.282535
$800$	−4.20804e96	−0.234728
$801$	−5.12194e96	−0.273996
$802$	−4.72797e96	−0.242568
$803$	6.73694e96	0.331506
$804$	1.48117e97	0.699079
$805$	9.16991e96	0.415148
$806$	−2.79270e97	−1.21283
$807$	1.93903e97	0.807833
$808$	−5.09173e97	−2.03509
$809$	−2.27870e97	−0.873799	−0.436899	−	0.899510i	$-0.643923\pi$
$809$	−2.27870e97	−0.873799	−0.436899	+	0.899510i	$0.643923\pi$
$810$	1.75587e96	0.0646018
$811$	3.75079e97	1.32411	0.662056	−	0.749455i	$-0.269684\pi$
$811$	3.75079e97	1.32411	0.662056	+	0.749455i	$0.269684\pi$
$812$	5.80452e97	1.96625
$813$	−9.17332e96	−0.298190
$814$	−1.22027e98	−3.80659
$815$	−1.65929e97	−0.496754
$816$	−2.55317e96	−0.0733601
$817$	5.81257e96	0.160299
$818$	2.56419e97	0.678758
$819$	8.95981e96	0.227661
$820$	1.33435e97	0.325466
$821$	5.87622e96	0.137595	0.0687975	−	0.997631i	$-0.478084\pi$
$821$	5.87622e96	0.137595	0.0687975	+	0.997631i	$0.478084\pi$
$822$	2.53128e97	0.569029
$823$	6.15414e97	1.32823	0.664115	−	0.747631i	$-0.268809\pi$
$823$	6.15414e97	1.32823	0.664115	+	0.747631i	$0.268809\pi$
$824$	−2.41705e97	−0.500869
$825$	−3.06572e97	−0.609993
$826$	8.21457e97	1.56947
$827$	3.50072e97	0.642278	0.321139	−	0.947032i	$-0.395934\pi$
$827$	3.50072e97	0.642278	0.321139	+	0.947032i	$0.395934\pi$
$828$	5.89549e97	1.03873
$829$	−1.73146e97	−0.292978	−0.146489	−	0.989212i	$-0.546797\pi$
$829$	−1.73146e97	−0.292978	−0.146489	+	0.989212i	$0.546797\pi$
$830$	−2.31876e97	−0.376825
$831$	−6.51391e97	−1.01673
$832$	7.38101e97	1.10658
$833$	−5.03299e96	−0.0724801
$834$	−1.01735e98	−1.40737
$835$	−7.01214e96	−0.0931866
$836$	−7.36619e97	−0.940443
$837$	1.22513e97	0.150273
$838$	1.56345e98	1.84251
$839$	8.15447e97	0.923358	0.461679	−	0.887047i	$-0.347247\pi$
$839$	8.15447e97	0.923358	0.461679	+	0.887047i	$0.347247\pi$
$840$	2.13012e97	0.231766
$841$	8.22628e97	0.860078
$842$	6.70479e96	0.0673643
$843$	2.57254e97	0.248392
$844$	−3.88103e97	−0.360143
$845$	6.62069e96	0.0590478
$846$	1.12811e98	0.967039
$847$	−3.90084e97	−0.321414
$848$	−1.27167e98	−1.00720
$849$	1.79692e97	0.136811
$850$	3.43421e97	0.251358
$851$	−4.30291e98	−3.02776
$852$	−9.74361e97	−0.659164
$853$	−1.20360e98	−0.782868	−0.391434	−	0.920206i	$-0.628021\pi$
$853$	−1.20360e98	−0.782868	−0.391434	+	0.920206i	$0.628021\pi$
$854$	−3.02820e98	−1.89385
$855$	−7.73613e96	−0.0465220
$856$	8.97379e97	0.518925
$857$	−1.11656e98	−0.620907	−0.310453	−	0.950589i	$-0.600481\pi$
$857$	−1.11656e98	−0.620907	−0.310453	+	0.950589i	$0.600481\pi$
$858$	2.00373e98	1.07156
$859$	−2.08560e98	−1.07266	−0.536329	−	0.844009i	$-0.680189\pi$
$859$	−2.08560e98	−1.07266	−0.536329	+	0.844009i	$0.680189\pi$
$860$	−5.16019e97	−0.255251
$861$	−4.54352e97	−0.216166
$862$	−4.18385e97	−0.191462
$863$	6.45798e97	0.284272	0.142136	−	0.989847i	$-0.454603\pi$
$863$	6.45798e97	0.284272	0.142136	+	0.989847i	$0.454603\pi$
$864$	−1.20655e97	−0.0510900
$865$	−1.14716e98	−0.467287
$866$	2.69258e98	1.05516
$867$	1.48897e98	0.561366
$868$	3.10347e98	1.12574
$869$	2.81494e98	0.982442
$870$	1.36329e98	0.457817
$871$	1.77513e98	0.573618
$872$	5.00568e98	1.55654
$873$	−1.08493e98	−0.324656
$874$	−3.95100e98	−1.13782
$875$	−1.73802e98	−0.481709
$876$	1.15229e98	0.307380
$877$	−4.10750e98	−1.05461	−0.527304	−	0.849677i	$-0.676797\pi$
$877$	−4.10750e98	−1.05461	−0.527304	+	0.849677i	$0.676797\pi$
$878$	1.03244e99	2.55151
$879$	−6.52836e97	−0.155302
$880$	1.35603e98	0.310528
$881$	3.18229e98	0.701531	0.350765	−	0.936463i	$-0.385921\pi$
$881$	3.18229e98	0.701531	0.350765	+	0.936463i	$0.385921\pi$
$882$	1.16893e98	0.248079
$883$	−9.35951e98	−1.91236	−0.956179	−	0.292782i	$-0.905419\pi$
$883$	−9.35951e98	−1.91236	−0.956179	+	0.292782i	$0.905419\pi$
$884$	−1.47563e98	−0.290286
$885$	1.26838e98	0.240242
$886$	1.17800e99	2.14840
$887$	5.71669e98	1.00393	0.501965	−	0.864888i	$-0.332611\pi$
$887$	5.71669e98	1.00393	0.501965	+	0.864888i	$0.332611\pi$
$888$	−9.99545e98	−1.69032
$889$	2.54986e98	0.415248
$890$	−3.04732e98	−0.477918
$891$	−8.79020e97	−0.132769
$892$	−1.87303e99	−2.72472
$893$	−4.97029e98	−0.696399
$894$	1.84595e98	0.249122
$895$	1.98006e98	0.257399
$896$	−1.08839e99	−1.36291
$897$	7.06557e98	0.852315
$898$	1.31032e99	1.52272
$899$	9.51214e98	1.06495
$900$	−5.24363e98	−0.565598
$901$	−2.11167e98	−0.219455
$902$	−1.01609e99	−1.01745
$903$	1.75707e98	0.169531
$904$	1.50623e99	1.40039
$905$	−5.65694e98	−0.506821
$906$	−2.26631e99	−1.95670
$907$	−8.68137e98	−0.722344	−0.361172	−	0.932499i	$-0.617623\pi$
$907$	−8.68137e98	−0.722344	−0.361172	+	0.932499i	$0.617623\pi$
$908$	−2.23373e99	−1.79124
$909$	5.58989e98	0.432030
$910$	5.33069e98	0.397097
$911$	2.17919e99	1.56469	0.782345	−	0.622845i	$-0.214023\pi$
$911$	2.17919e99	1.56469	0.782345	+	0.622845i	$0.214023\pi$
$912$	−2.61260e98	−0.180820
$913$	1.16081e99	0.774445
$914$	1.99656e99	1.28406
$915$	−4.67572e98	−0.289896
$916$	−1.29072e99	−0.771498
$917$	1.69707e99	0.977973
$918$	9.84677e97	0.0547096
$919$	−8.45205e98	−0.452785	−0.226393	−	0.974036i	$-0.572693\pi$
$919$	−8.45205e98	−0.452785	−0.226393	+	0.974036i	$0.572693\pi$
$920$	1.67978e99	0.867682
$921$	2.15401e98	0.107288
$922$	−2.16315e99	−1.03897
$923$	−1.16774e99	−0.540866
$924$	−2.22671e99	−0.994607
$925$	3.82714e99	1.64864
$926$	−1.11964e99	−0.465169
$927$	2.65353e98	0.106329
$928$	−9.36787e98	−0.362063
$929$	1.35636e99	0.505647	0.252823	−	0.967512i	$-0.418641\pi$
$929$	1.35636e99	0.505647	0.252823	+	0.967512i	$0.418641\pi$
$930$	7.28901e98	0.262114
$931$	−5.15013e98	−0.178651
$932$	−1.07140e99	−0.358523
$933$	−7.95556e98	−0.256824
$934$	−1.21423e99	−0.378164
$935$	2.25176e98	0.0676601
$936$	1.64130e99	0.475824
$937$	−4.52096e99	−1.26460	−0.632302	−	0.774722i	$-0.717890\pi$
$937$	−4.52096e99	−1.26460	−0.632302	+	0.774722i	$0.717890\pi$
$938$	−3.00062e99	−0.809871
$939$	2.41595e99	0.629203
$940$	4.41244e99	1.10891
$941$	−5.01985e99	−1.21742	−0.608708	−	0.793395i	$-0.708312\pi$
$941$	−5.01985e99	−1.21742	−0.608708	+	0.793395i	$0.708312\pi$
$942$	8.02290e99	1.87770
$943$	−3.58295e99	−0.809281
$944$	4.28350e99	0.933763
$945$	−2.33853e98	−0.0492014
$946$	3.92942e99	0.797949
$947$	7.82695e99	1.53415	0.767076	−	0.641557i	$-0.221711\pi$
$947$	7.82695e99	1.53415	0.767076	+	0.641557i	$0.221711\pi$
$948$	4.81470e99	0.910940
$949$	1.38099e99	0.252215
$950$	3.51414e99	0.619553
$951$	1.18871e99	0.202315
$952$	1.19455e99	0.196276
$953$	1.61687e99	0.256485	0.128243	−	0.991743i	$-0.459066\pi$
$953$	1.61687e99	0.256485	0.128243	+	0.991743i	$0.459066\pi$
$954$	4.90442e99	0.751134
$955$	−1.76173e99	−0.260511
$956$	−1.70956e100	−2.44087
$957$	−6.82485e99	−0.940900
$958$	7.67022e99	1.02109
$959$	−3.37125e99	−0.433379
$960$	−1.92646e99	−0.239152
$961$	−3.25550e99	−0.390287
$962$	−2.50139e100	−2.89612
$963$	−9.85178e98	−0.110163
$964$	−5.35646e99	−0.578492
$965$	−3.56960e99	−0.372353
$966$	−1.19434e100	−1.20335
$967$	−3.06187e99	−0.297989	−0.148994	−	0.988838i	$-0.547604\pi$
$967$	−3.06187e99	−0.297989	−0.148994	+	0.988838i	$0.547604\pi$
$968$	−7.14573e99	−0.671772
$969$	−4.33835e98	−0.0393983
$970$	−6.45484e99	−0.566281
$971$	1.12607e99	0.0954376	0.0477188	−	0.998861i	$-0.484805\pi$
$971$	1.12607e99	0.0954376	0.0477188	+	0.998861i	$0.484805\pi$
$972$	−1.50348e99	−0.123106
$973$	1.35495e100	1.07187
$974$	3.29243e100	2.51647
$975$	−6.28432e99	−0.464092
$976$	−1.57906e100	−1.12675
$977$	−4.97624e99	−0.343110	−0.171555	−	0.985175i	$-0.554879\pi$
$977$	−4.97624e99	−0.343110	−0.171555	+	0.985175i	$0.554879\pi$
$978$	2.16114e100	1.43990
$979$	1.52554e100	0.982210
$980$	4.57210e99	0.284474
$981$	−5.49543e99	−0.330438
$982$	4.56313e100	2.65172
$983$	−3.85201e99	−0.216344	−0.108172	−	0.994132i	$-0.534500\pi$
$983$	−3.85201e99	−0.216344	−0.108172	+	0.994132i	$0.534500\pi$
$984$	−8.32302e99	−0.451799
$985$	−1.14491e100	−0.600699
$986$	7.64518e99	0.387714
$987$	−1.50246e100	−0.736507
$988$	−1.50997e100	−0.715503
$989$	1.38560e100	0.634688
$990$	−5.22978e99	−0.231582
$991$	3.14988e100	1.34843	0.674213	−	0.738537i	$-0.264483\pi$
$991$	3.14988e100	1.34843	0.674213	+	0.738537i	$0.264483\pi$
$992$	−5.00866e99	−0.207291
$993$	−3.40379e98	−0.0136196
$994$	1.97391e100	0.763630
$995$	4.12091e99	0.154142
$996$	1.98546e100	0.718081
$997$	8.29567e99	0.290111	0.145055	−	0.989424i	$-0.453664\pi$
$997$	8.29567e99	0.290111	0.145055	+	0.989424i	$0.453664\pi$
$998$	2.94647e99	0.0996390
$999$	1.09734e100	0.358837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.68.a.b.1.1	✓	6
3.2	odd	2		9.68.a.c.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.68.a.b.1.1	✓	6	1.1	even	1	trivial
9.68.a.c.1.6		6	3.2	odd	2

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:	\( k \)	\(=\)	\( 68 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-2.07551e10 q^{2} -5.55906e15 q^{3} +2.83199e20 q^{4} -8.85856e22 q^{5} +1.15379e26 q^{6} -1.53665e28 q^{7} -2.81491e30 q^{8} +3.09032e31 q^{9} +O(q^{10})\)	\(q-2.07551e10 q^{2} -5.55906e15 q^{3} +2.83199e20 q^{4} -8.85856e22 q^{5} +1.15379e26 q^{6} -1.53665e28 q^{7} -2.81491e30 q^{8} +3.09032e31 q^{9} +1.83860e33 q^{10} -9.20436e34 q^{11} -1.57432e36 q^{12} -1.88677e37 q^{13} +3.18934e38 q^{14} +4.92453e38 q^{15} +1.66308e40 q^{16} +2.76163e40 q^{17} -6.41397e41 q^{18} +2.82591e42 q^{19} -2.50874e43 q^{20} +8.54235e43 q^{21} +1.91037e45 q^{22} +6.73636e45 q^{23} +1.56482e46 q^{24} -5.99152e46 q^{25} +3.91601e47 q^{26} -1.71793e47 q^{27} -4.35179e48 q^{28} -1.33382e49 q^{29} -1.02209e49 q^{30} -7.13148e49 q^{31} +7.02332e49 q^{32} +5.11676e50 q^{33} -5.73178e50 q^{34} +1.36125e51 q^{35} +8.75174e51 q^{36} -6.38758e52 q^{37} -5.86519e52 q^{38} +1.04887e53 q^{39} +2.49360e53 q^{40} -5.31882e53 q^{41} -1.77297e54 q^{42} +2.05689e54 q^{43} -2.60666e55 q^{44} -2.73757e54 q^{45} -1.39814e56 q^{46} -1.75883e56 q^{47} -9.24518e55 q^{48} -1.82247e56 q^{49} +1.24354e57 q^{50} -1.53521e56 q^{51} -5.34333e57 q^{52} -7.64647e57 q^{53} +3.56557e57 q^{54} +8.15373e57 q^{55} +4.32554e58 q^{56} -1.57094e58 q^{57} +2.76836e59 q^{58} +2.57564e59 q^{59} +1.39462e59 q^{60} -9.49476e59 q^{61} +1.48014e60 q^{62} -4.74875e59 q^{63} -3.91197e60 q^{64} +1.67141e60 q^{65} -1.06199e61 q^{66} -9.40829e60 q^{67} +7.82091e60 q^{68} -3.74479e61 q^{69} -2.82529e61 q^{70} +6.18909e61 q^{71} -8.69896e61 q^{72} -7.31930e61 q^{73} +1.32575e63 q^{74} +3.33072e62 q^{75} +8.00294e62 q^{76} +1.41439e63 q^{77} -2.17694e63 q^{78} -3.05827e63 q^{79} -1.47325e63 q^{80} +9.55005e62 q^{81} +1.10392e64 q^{82} -1.26115e64 q^{83} +2.41919e64 q^{84} -2.44640e63 q^{85} -4.26909e64 q^{86} +7.41481e64 q^{87} +2.59094e65 q^{88} -1.65742e65 q^{89} +5.68185e64 q^{90} +2.89932e65 q^{91} +1.90773e66 q^{92} +3.96443e65 q^{93} +3.65047e66 q^{94} -2.50335e65 q^{95} -3.90431e65 q^{96} -3.51073e66 q^{97} +3.78255e66 q^{98} -2.84444e66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 13735355166 q^{2} - 33\!\cdots\!38 q^{3}+ \cdots + 18\!\cdots\!74 q^{9}+O(q^{10}) \) 6 * q + 13735355166 * q^2 - 33354363399333138 * q^3 + 461137328518259214852 * q^4 - 180289059197853505182300 * q^5 - 76355671270945289663881818 * q^6 - 28067678610591277820235434208 * q^7 + 174428717775449559766832729592 * q^8 + 185418926295795674171523850821174 * q^9	\( 6 q + 13735355166 q^{2} - 33\!\cdots\!38 q^{3}+ \cdots + 38\!\cdots\!96 q^{99}+O(q^{100}) \) 6 * q + 13735355166 * q^2 - 33354363399333138 * q^3 + 461137328518259214852 * q^4 - 180289059197853505182300 * q^5 - 76355671270945289663881818 * q^6 - 28067678610591277820235434208 * q^7 + 174428717775449559766832729592 * q^8 + 185418926295795674171523850821174 * q^9 + 7304190735814693245550459325330100 * q^10 + 1253554983811830341203783945028424 * q^11 - 2563490338732614404400323640044227596 * q^12 - 1032427018834954393824819765456935964 * q^13 - 447380929503565966859381489320173353952 * q^14 + 1002237799568181731536569743941186842900 * q^15 - 10777060270558286469269005744606427140080 * q^16 - 22303705201707705421583405421371675716596 * q^17 + 424465801195188392885382149078137607180814 * q^18 - 6709513794502265961382038704145157001302152 * q^19 + 46181758835098395119891481090112367056690200 * q^20 + 156029925358891883498812737570110890845530784 * q^21 + 1406045276258114363650986812146594678084267368 * q^22 + 12239031860950699209155226229708548540686529264 * q^23 - 969659806660344055206631047583378687513136616 * q^24 + 124984998689116279435075553443500491502742646250 * q^25 + 147728325197899719596176944836466085493373208692 * q^26 - 1030755041464022662072922259531242545404215044002 * q^27 - 14712260029031223829746951621139067346976206433344 * q^28 - 18873418589468921842047146695821329699174822684364 * q^29 - 40604438690067631054858099234477451658621953142300 * q^30 - 224044794880051525600176726995317503621741761218704 * q^31 - 647694914760137169573449462765066287313897316284448 * q^32 - 6968588078517493039340379725427973276022009185752 * q^33 + 693429763914603914127075176718731888866377974041404 * q^34 - 6444089679967517736201498858201618112886103095496000 * q^35 + 14250598054794536997029174176783125114340868782812708 * q^36 + 27414420131407696449125644786001907623181109991614452 * q^37 + 12552113658955455007053647987482106208988678055446104 * q^38 + 5739324328251871187904239839929767039225529061529172 * q^39 + 1194094866560066539991934179669093556164670510853198800 * q^40 + 2660548042321177320771169314506367536908331651920652796 * q^41 + 2487017683432229918848259981037750023330134118939476896 * q^42 - 1105961611152903745004520895209354208863582663043308600 * q^43 - 34817398461777279630054811602795668745922518275227441104 * q^44 - 5571500629890857041236058470500559035466867019928336700 * q^45 - 45061363378216725453974438646463842380148485881039366224 * q^46 + 58003762634770246900699775563009450632230835045286599360 * q^47 + 59910330773452765968526051655136782182831882309418661840 * q^48 + 985569916983315185097203394977137449656339808292459655670 * q^49 + 4791887184864825461869475209769884139573386495444648751250 * q^50 + 123987648074892602292236983996852174235365272762446559708 * q^51 - 772447381048143948901083488309399868612217101599766652776 * q^52 - 13674721974185597882029982508413224730588130474226494780636 * q^53 - 2359631097275567979107397504361474172402795777134631335722 * q^54 - 51238754618576674303553172437218137404754442562163094366800 * q^55 - 53382539406310631647595973723370754348378361469563798407040 * q^56 + 37298593555777863535226252514563917312860433886972407385496 * q^57 - 27334542479326918025552783071893481077859694969007500722812 * q^58 + 432173245375539353201786532564121354794334705181731449983112 * q^59 - 256727194434372614254225940479565827463386469783086909974600 * q^60 - 301681480554705175984062079070767927549030780778630557968540 * q^61 + 1319649268553974306953641963470020465251839304368009232497584 * q^62 - 867379805265217479240863693041421061959681291088645541720032 * q^63 - 3306273837825060723687391413275118884560206796975317864472512 * q^64 + 9144509139500418095807614952796559412618850636965585264371800 * q^65 - 7816290850038150086493121040028671432967827865802816749073464 * q^66 - 3659535002024051270225014883853538282826668950514180780948296 * q^67 + 62841982068874697565842994801948402899655187355391437927918088 * q^68 - 68037519391027690940233119583149188606433713409875206220325072 * q^69 - 17848574477080955030302460292958517135297977483696841850120000 * q^70 + 252155511033891103624460277167902994429076906738358010146768272 * q^71 + 5390397594179371118067083948912583358245775647599644848330168 * q^72 + 166779610709719144717689715238124518472612391435088881765181724 * q^73 + 1006325717889854285502211107525082701977251477599580185617852868 * q^74 - 694799177623660043822939209279000567990108449155940880572738750 * q^75 - 517707814526076465205777997582680722788148819042185613752993712 * q^76 + 352534620603367398775736559627568751080150267776772663929922944 * q^77 - 821230707170934959628477544327982939588983807972120804684205916 * q^78 - 4778664108337215079572742262604077882794836667809906425462078640 * q^79 + 22035563788144287210408960904426824039627000323030751017638600800 * q^80 + 5730029704780951421359144210646484071519610833846058779021123046 * q^81 + 64371214133499796977109337023506169313379178165909274002938946284 * q^82 + 36651193288697208236374412380857358965233031511415957283935392632 * q^83 + 81786344572298490402773289071356477096023706633672401039174558912 * q^84 + 251284152586026236911243321213724923566970783996009477585132585800 * q^85 + 109459654412686722699057856511584566836933916033705406023221718504 * q^86 + 104918477036812644409737917778017107986270152063164872212109942372 * q^87 + 294858564158317243888419031127963434466163056120837408554388440992 * q^88 - 24716082341461782003245292062820103472910477446347105193539129092 * q^89 + 225722533949076363264521082786586324992651210993012359817269922900 * q^90 + 1637449943486433383394466120659741425501433624430401587862051946176 * q^91 + 4192506910423434290693315227336082767370233979633693670230439475872 * q^92 + 1245478584359715172598232789326604176943806570590746356443962102192 * q^93 + 10776123537142027626725320636495971787147507990566237758042792171712 * q^94 + 8892438758299572900094061329818154779583617585762349202154337045200 * q^95 + 3600575259801619310258913629904116686086350553857582694711853406304 * q^96 + 3864203546244162410999773872217768224094576263762936458169046609164 * q^97 + 26255683859954817683324025976879398726779583524717348419525625709774 * q^98 + 38738803191855518251318864868786039478244708610819286864528508296 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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