LMFDB - Embedded newform 1.62.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,62,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 62, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 62);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 62 $
Character orbit:	$[\chi]$	$=$	1.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:	$23.5656183265$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 180363795469121x^{2} + 166129321978984507920x + 2785609847439483545242446300 $ x^4 - x^3 - 180363795469121x^2 + 166129321978984507920x + 2785609847439483545242446300
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{28}\cdot 3^{8}\cdot 5^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.33086e7$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.84183e9 q^{2} -3.79563e14 q^{3} +5.77017e18 q^{4} -6.89620e20 q^{5} -1.07865e24 q^{6} -9.80127e25 q^{7} +9.84504e27 q^{8} +1.68945e28 q^{9} +O(q^{10})$	\(q+2.84183e9 q^{2} -3.79563e14 q^{3} +5.77017e18 q^{4} -6.89620e20 q^{5} -1.07865e24 q^{6} -9.80127e25 q^{7} +9.84504e27 q^{8} +1.68945e28 q^{9} -1.95979e30 q^{10} -2.74880e31 q^{11} -2.19014e33 q^{12} +2.74592e32 q^{13} -2.78536e35 q^{14} +2.61754e35 q^{15} +1.46728e37 q^{16} -2.27394e37 q^{17} +4.80113e37 q^{18} -1.42689e39 q^{19} -3.97923e39 q^{20} +3.72020e40 q^{21} -7.81164e40 q^{22} +1.13228e41 q^{23} -3.73681e42 q^{24} -3.86123e42 q^{25} +7.80343e41 q^{26} +4.18578e43 q^{27} -5.65550e44 q^{28} +2.20574e44 q^{29} +7.43862e44 q^{30} -7.87465e44 q^{31} +1.89967e46 q^{32} +1.04334e46 q^{33} -6.46217e46 q^{34} +6.75915e46 q^{35} +9.74841e46 q^{36} +5.41627e47 q^{37} -4.05499e48 q^{38} -1.04225e47 q^{39} -6.78934e48 q^{40} +3.44353e48 q^{41} +1.05722e50 q^{42} -2.45361e49 q^{43} -1.58611e50 q^{44} -1.16508e49 q^{45} +3.21774e50 q^{46} +7.88915e50 q^{47} -5.56927e51 q^{48} +6.05033e51 q^{49} -1.09730e52 q^{50} +8.63104e51 q^{51} +1.58444e51 q^{52} +4.85762e52 q^{53} +1.18953e53 q^{54} +1.89563e52 q^{55} -9.64938e53 q^{56} +5.41596e53 q^{57} +6.26833e53 q^{58} -1.37665e54 q^{59} +1.51037e54 q^{60} +4.54704e53 q^{61} -2.23784e54 q^{62} -1.65587e54 q^{63} +2.01520e55 q^{64} -1.89364e53 q^{65} +2.96501e55 q^{66} -8.79176e55 q^{67} -1.31210e56 q^{68} -4.29770e55 q^{69} +1.92084e56 q^{70} +3.27010e56 q^{71} +1.66327e56 q^{72} -6.07880e56 q^{73} +1.53921e57 q^{74} +1.46558e57 q^{75} -8.23342e57 q^{76} +2.69418e57 q^{77} -2.96189e56 q^{78} +1.23160e58 q^{79} -1.01187e58 q^{80} -1.80362e58 q^{81} +9.78594e57 q^{82} -6.61561e58 q^{83} +2.14662e59 q^{84} +1.56816e58 q^{85} -6.97276e58 q^{86} -8.37216e58 q^{87} -2.70621e59 q^{88} -1.38088e59 q^{89} -3.31096e58 q^{90} -2.69135e58 q^{91} +6.53342e59 q^{92} +2.98892e59 q^{93} +2.24196e60 q^{94} +9.84014e59 q^{95} -7.21043e60 q^{96} -3.96687e60 q^{97} +1.71940e61 q^{98} -4.64396e59 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1146312000 q^{2} - 573723599022000 q^{3} + 44\!\cdots\!28 q^{4}+ \cdots + 11\!\cdots\!52 q^{9}+O(q^{10}) $ 4 * q + 1146312000 * q^2 - 573723599022000 * q^3 + 4402997675828604928 * q^4 - 524125996020295237800 * q^5 - 810420388530698747434752 * q^6 - 63338569463385158773180000 * q^7 + 9767868387156674079031296000 * q^8 + 116559153778048577840676094452 * q^9	$ 4 q + 1146312000 q^{2} - 573723599022000 q^{3} + 44\!\cdots\!28 q^{4}+ \cdots - 31\!\cdots\!76 q^{99}+O(q^{100}) $ 4 * q + 1146312000 * q^2 - 573723599022000 * q^3 + 4402997675828604928 * q^4 - 524125996020295237800 * q^5 - 810420388530698747434752 * q^6 - 63338569463385158773180000 * q^7 + 9767868387156674079031296000 * q^8 + 116559153778048577840676094452 * q^9 - 1483353386285070117088509033600 * q^10 - 41554515064513200044500416014352 * q^11 - 997468469175503713040400254976000 * q^12 + 10764994985103189070396812401291000 * q^13 - 211155135436541225684077605177122304 * q^14 + 115082099805150572294379175169983200 * q^15 + 10904646278227442826771588888892801024 * q^16 - 40906325415811699311242283170389539000 * q^17 + 15755547385947548040677485816834728000 * q^18 - 356159749895948464708913853630763435120 * q^19 - 5071632401696432486275641956774663577600 * q^20 - 5584164717140650613271728795305539583872 * q^21 - 172062995599931314756360229299481569056000 * q^22 - 410968880183827232479513482663937487796000 * q^23 - 6122904790572089676121487755102001729372160 * q^24 - 16739487717977510894946357652146107782722500 * q^25 - 49284147216613914166808777620995485562632832 * q^26 - 128445331744621566171958781429920350730764000 * q^27 - 790757236315065917044952859738895406239744000 * q^28 + 6672429803576117328528976307882755467518520 * q^29 + 957801420237120366977197975859498893217318400 * q^30 + 3262752943509002552517145952336046015034252928 * q^31 + 29552482936847865082009297897367834619543552000 * q^32 + 80589779417942769949681652178013443031895736000 * q^33 + 39802528145537101299701822666373970434557030016 * q^34 + 94932144900835792457443003213138857525722942400 * q^35 - 491545590287100270921289917536068279191068430336 * q^36 - 710312106544219153529408139748985993336062057000 * q^37 - 6572443117826428556368685861295549874330331616000 * q^38 - 5385266212680187341486607570713939645234734498976 * q^39 - 6935278763126032494337494583468084555036360704000 * q^40 + 16359554122032268527799184148245398149035867491368 * q^41 + 150386101138325781804352908808507125636957747456000 * q^42 + 75844732497959094206655920598930086763379517030000 * q^43 + 152692943245212279510621538861388707588508390670336 * q^44 + 60471855189024852796163743559032445559203109252600 * q^45 - 150345409740296355038882940983341438053393810381312 * q^46 - 2164761335188781225334544122222333542985932701416000 * q^47 - 8471840837080202754288377889649147778899824869376000 * q^48 + 1523957834189526415441239854498433329172794287478628 * q^49 - 3735723416225956799610935352239535395426733934920000 * q^50 + 20623083900467721702728328179464369078682764374557088 * q^51 + 34115942043101628674837973043915515701891779834880000 * q^52 + 84459499120263342936174700173047508278523729350943000 * q^53 + 205362219171375312837640062328590989381764073364257280 * q^54 - 18917852463295959783361213875825060571992233753013600 * q^55 - 895534119833025861281009767571957442822737699977297920 * q^56 - 485813603178903589098646017006457442516302171963128000 * q^57 - 429363306259072204179262197105630766591459158948624000 * q^58 - 2147121767784312006347793068275982647255821920255956560 * q^59 + 1658171820897328745993674937960453150336599512561254400 * q^60 + 4291528347018103219994434901020564652244372107292350648 * q^61 + 5191805357629316458585917076609024961942995611849984000 * q^62 + 17756655477174334714938166349329711292289832299011892000 * q^63 + 19881300699476524526504677072626341971094030107078033408 * q^64 - 4054154514265281184405976695522203389642082195785626800 * q^65 - 32579846274793617809975626285379717775321739705823437824 * q^66 - 151638661420806044794238226134660440129857438609787534000 * q^67 - 199797070973791372723379406738475848419062088637699072000 * q^68 - 65270530395832676459014735893839800626266812319535206016 * q^69 + 164781406287311752350371419457017830072394299112015948800 * q^70 + 266771587169907679430401079119295396456876119234283837088 * q^71 + 1006655875418141826396652361065366291089164315936882688000 * q^72 + 436772697766954812846449565799176070423143504803837369000 * q^73 + 2727029156290392414014538532434064649250131670424597597056 * q^74 + 2289194205716179194928001449493608972625299546441763790000 * q^75 - 9182670231472830669367329606616577285345108294701612810240 * q^76 - 6239400117692696801885467207245334802759585122139865360000 * q^77 - 6237267939864197833204910438280167481125291167753285440000 * q^78 - 2171516124052566840962201891051143348431163494068568095680 * q^79 - 8149820448667982873535456900485215194289704343083732172800 * q^80 + 1640511243926006283516650766266777082670562411829996387684 * q^81 + 41751906507711557992784780576518459967807480604061450704000 * q^82 - 19301891587488226996497021336363284746717620338719475718000 * q^83 + 268654655987364118570161060572621663532678550361090391146496 * q^84 + 23823437828438802480990474713115034607148974715085027364400 * q^85 - 71538345696620408289043701603344533132955103857012068207872 * q^86 - 259922121232275661156614167150119002145659028099089961092000 * q^87 - 453611870852754620593515203785357874778152109551115829248000 * q^88 - 606362068644618673179710823370293144593411608656909401212440 * q^89 - 125913175325979481569463842346677014059444686232867490908800 * q^90 - 452168126000372891758634520948160370052422021946362710252352 * q^91 + 1607280224434271875135145612458728092411753130630908891136000 * q^92 - 430218455333355948319021852668117857154414287268428877504000 * q^93 + 6446155892605066539979931910636020289279531063064695408331776 * q^94 + 1105507768048183718212260841102299501129184381013780070972000 * q^95 + 1502030317602264351709698333215472188025674435863914750148608 * q^96 - 8084830239737746227548751167926342536453719541548201116411000 * q^97 + 17015397362965438448003410858883076702895502959466609182344000 * q^98 - 31217771142326421061022583768766679122998622357827944348749776 * 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 $

$2$	2.84183e9	1.87147	0.935737	−	0.352699i	$-0.114736\pi$
$2$	2.84183e9	1.87147	0.935737	+	0.352699i	$0.114736\pi$
$3$	−3.79563e14	−1.06435	−0.532176	−	0.846634i	$-0.678626\pi$
$3$	−3.79563e14	−1.06435	−0.532176	+	0.846634i	$0.678626\pi$
$4$	5.77017e18	2.50241
$5$	−6.89620e20	−0.331150	−0.165575	−	0.986197i	$-0.552948\pi$
$5$	−6.89620e20	−0.331150	−0.165575	+	0.986197i	$0.552948\pi$
$6$	−1.07865e24	−1.99191
$7$	−9.80127e25	−1.64358	−0.821792	−	0.569787i	$-0.807026\pi$
$7$	−9.80127e25	−1.64358	−0.821792	+	0.569787i	$0.807026\pi$
$8$	9.84504e27	2.81172
$9$	1.68945e28	0.132846
$10$	−1.95979e30	−0.619738
$11$	−2.74880e31	−0.474971	−0.237485	−	0.971391i	$-0.576323\pi$
$11$	−2.74880e31	−0.474971	−0.237485	+	0.971391i	$0.576323\pi$
$12$	−2.19014e33	−2.66345
$13$	2.74592e32	0.0290680	0.0145340	−	0.999894i	$-0.495374\pi$
$13$	2.74592e32	0.0290680	0.0145340	+	0.999894i	$0.495374\pi$
$14$	−2.78536e35	−3.07592
$15$	2.61754e35	0.352460
$16$	1.46728e37	2.75966
$17$	−2.27394e37	−0.673112	−0.336556	−	0.941663i	$-0.609262\pi$
$17$	−2.27394e37	−0.673112	−0.336556	+	0.941663i	$0.609262\pi$
$18$	4.80113e37	0.248618
$19$	−1.42689e39	−1.42039	−0.710193	−	0.704007i	$-0.751393\pi$
$19$	−1.42689e39	−1.42039	−0.710193	+	0.704007i	$0.751393\pi$
$20$	−3.97923e39	−0.828674
$21$	3.72020e40	1.74935
$22$	−7.81164e40	−0.888895
$23$	1.13228e41	0.332088	0.166044	−	0.986118i	$-0.446901\pi$
$23$	1.13228e41	0.332088	0.166044	+	0.986118i	$0.446901\pi$
$24$	−3.73681e42	−2.99267
$25$	−3.86123e42	−0.890340
$26$	7.80343e41	0.0544000
$27$	4.18578e43	0.922957
$28$	−5.65550e44	−4.11293
$29$	2.20574e44	0.550066	0.275033	−	0.961435i	$-0.411311\pi$
$29$	2.20574e44	0.550066	0.275033	+	0.961435i	$0.411311\pi$
$30$	7.43862e44	0.659620
$31$	−7.87465e44	−0.256862	−0.128431	−	0.991718i	$-0.540994\pi$
$31$	−7.87465e44	−0.256862	−0.128431	+	0.991718i	$0.540994\pi$
$32$	1.89967e46	2.35290
$33$	1.04334e46	0.505536
$34$	−6.46217e46	−1.25971
$35$	6.75915e46	0.544273
$36$	9.74841e46	0.332436
$37$	5.41627e47	0.800843	0.400422	−	0.916331i	$-0.368864\pi$
$37$	5.41627e47	0.800843	0.400422	+	0.916331i	$0.368864\pi$
$38$	−4.05499e48	−2.65822
$39$	−1.04225e47	−0.0309386
$40$	−6.78934e48	−0.931103
$41$	3.44353e48	0.222380	0.111190	−	0.993799i	$-0.464534\pi$
$41$	3.44353e48	0.222380	0.111190	+	0.993799i	$0.464534\pi$
$42$	1.05722e50	3.27387
$43$	−2.45361e49	−0.370696	−0.185348	−	0.982673i	$-0.559341\pi$
$43$	−2.45361e49	−0.370696	−0.185348	+	0.982673i	$0.559341\pi$
$44$	−1.58611e50	−1.18857
$45$	−1.16508e49	−0.0439920
$46$	3.21774e50	0.621494
$47$	7.88915e50	0.790761	0.395381	−	0.918517i	$-0.370613\pi$
$47$	7.88915e50	0.790761	0.395381	+	0.918517i	$0.370613\pi$
$48$	−5.56927e51	−2.93725
$49$	6.05033e51	1.70137
$50$	−1.09730e52	−1.66625
$51$	8.63104e51	0.716429
$52$	1.58444e51	0.0727401
$53$	4.85762e52	1.24741	0.623706	−	0.781659i	$-0.285626\pi$
$53$	4.85762e52	1.24741	0.623706	+	0.781659i	$0.285626\pi$
$54$	1.18953e53	1.72729
$55$	1.89563e52	0.157287
$56$	−9.64938e53	−4.62131
$57$	5.41596e53	1.51179
$58$	6.26833e53	1.02943
$59$	−1.37665e54	−1.34226	−0.671130	−	0.741340i	$-0.734191\pi$
$59$	−1.37665e54	−1.34226	−0.671130	+	0.741340i	$0.734191\pi$
$60$	1.51037e54	0.882001
$61$	4.54704e53	0.160387	0.0801934	−	0.996779i	$-0.474446\pi$
$61$	4.54704e53	0.160387	0.0801934	+	0.996779i	$0.474446\pi$
$62$	−2.23784e54	−0.480710
$63$	−1.65587e54	−0.218344
$64$	2.01520e55	1.64373
$65$	−1.89364e53	−0.00962587
$66$	2.96501e55	0.946097
$67$	−8.79176e55	−1.77335	−0.886675	−	0.462393i	$-0.846991\pi$
$67$	−8.79176e55	−1.77335	−0.886675	+	0.462393i	$0.846991\pi$
$68$	−1.31210e56	−1.68440
$69$	−4.29770e55	−0.353459
$70$	1.92084e56	1.01859
$71$	3.27010e56	1.12508	0.562538	−	0.826772i	$-0.309825\pi$
$71$	3.27010e56	1.12508	0.562538	+	0.826772i	$0.309825\pi$
$72$	1.66327e56	0.373527
$73$	−6.07880e56	−0.896336	−0.448168	−	0.893949i	$-0.647923\pi$
$73$	−6.07880e56	−0.896336	−0.448168	+	0.893949i	$0.647923\pi$
$74$	1.53921e57	1.49876
$75$	1.46558e57	0.947635
$76$	−8.23342e57	−3.55439
$77$	2.69418e57	0.780654
$78$	−2.96189e56	−0.0579007
$79$	1.23160e58	1.63246	0.816229	−	0.577729i	$-0.196061\pi$
$79$	1.23160e58	1.63246	0.816229	+	0.577729i	$0.196061\pi$
$80$	−1.01187e58	−0.913860
$81$	−1.80362e58	−1.11520
$82$	9.78594e57	0.416179
$83$	−6.61561e58	−1.94396	−0.971981	−	0.235058i	$-0.924472\pi$
$83$	−6.61561e58	−1.94396	−0.971981	+	0.235058i	$0.924472\pi$
$84$	2.14662e59	4.37760
$85$	1.56816e58	0.222901
$86$	−6.97276e58	−0.693749
$87$	−8.37216e58	−0.585464
$88$	−2.70621e59	−1.33549
$89$	−1.38088e59	−0.482793	−0.241396	−	0.970427i	$-0.577605\pi$
$89$	−1.38088e59	−0.482793	−0.241396	+	0.970427i	$0.577605\pi$
$90$	−3.31096e58	−0.0823298
$91$	−2.69135e58	−0.0477757
$92$	6.53342e59	0.831021
$93$	2.98892e59	0.273391
$94$	2.24196e60	1.47989
$95$	9.84014e59	0.470361
$96$	−7.21043e60	−2.50431
$97$	−3.96687e60	−1.00441	−0.502204	−	0.864749i	$-0.667477\pi$
$97$	−3.96687e60	−1.00441	−0.502204	+	0.864749i	$0.667477\pi$
$98$	1.71940e61	3.18407
$99$	−4.64396e59	−0.0630980
$100$	−2.22800e61	−2.22800
$101$	−4.90481e60	−0.362093	−0.181047	−	0.983474i	$-0.557949\pi$
$101$	−4.90481e60	−0.362093	−0.181047	+	0.983474i	$0.557949\pi$
$102$	2.45280e61	1.34078
$103$	−2.48884e61	−1.01033	−0.505163	−	0.863024i	$-0.668568\pi$
$103$	−2.48884e61	−1.01033	−0.505163	+	0.863024i	$0.668568\pi$
$104$	2.70337e60	0.0817312
$105$	−2.56552e61	−0.579298
$106$	1.38046e62	2.33450
$107$	−1.15288e62	−1.46413	−0.732063	−	0.681237i	$-0.761442\pi$
$107$	−1.15288e62	−1.46413	−0.732063	+	0.681237i	$0.761442\pi$
$108$	2.41527e62	2.30962
$109$	−6.30613e61	−0.455255	−0.227627	−	0.973748i	$-0.573097\pi$
$109$	−6.30613e61	−0.455255	−0.227627	+	0.973748i	$0.573097\pi$
$110$	5.38706e61	0.294358
$111$	−2.05581e62	−0.852379
$112$	−1.43812e63	−4.53573
$113$	3.81996e62	0.918685	0.459343	−	0.888259i	$-0.348085\pi$
$113$	3.81996e62	0.918685	0.459343	+	0.888259i	$0.348085\pi$
$114$	1.53912e63	2.82928
$115$	−7.80840e61	−0.109971
$116$	1.27275e63	1.37649
$117$	4.63909e60	0.00386157
$118$	−3.91220e63	−2.51200
$119$	2.22875e63	1.10632
$120$	2.57698e63	0.991021
$121$	−2.59371e63	−0.774403
$122$	1.29219e63	0.300160
$123$	−1.30704e63	−0.236691
$124$	−4.54381e63	−0.642774
$125$	5.65353e63	0.625986
$126$	−4.70572e63	−0.408624
$127$	−2.01045e64	−1.37176	−0.685881	−	0.727714i	$-0.740583\pi$
$127$	−2.01045e64	−1.37176	−0.685881	+	0.727714i	$0.740583\pi$
$128$	1.34654e64	0.723296
$129$	9.31301e63	0.394552
$130$	−5.38141e62	−0.0180146
$131$	1.95810e64	0.518872	0.259436	−	0.965760i	$-0.416463\pi$
$131$	1.95810e64	0.518872	0.259436	+	0.965760i	$0.416463\pi$
$132$	6.02027e64	1.26506
$133$	1.39854e65	2.33453
$134$	−2.49847e65	−3.31878
$135$	−2.88660e64	−0.305637
$136$	−2.23871e65	−1.89261
$137$	2.25308e65	1.52335	0.761673	−	0.647962i	$-0.224378\pi$
$137$	2.25308e65	1.52335	0.761673	+	0.647962i	$0.224378\pi$
$138$	−1.22133e65	−0.661488
$139$	−1.19702e65	−0.520174	−0.260087	−	0.965585i	$-0.583751\pi$
$139$	−1.19702e65	−0.520174	−0.260087	+	0.965585i	$0.583751\pi$
$140$	3.90014e65	1.36200
$141$	−2.99443e65	−0.841649
$142$	9.29308e65	2.10555
$143$	−7.54798e63	−0.0138064
$144$	2.47890e65	0.366609
$145$	−1.52112e65	−0.182154
$146$	−1.72749e66	−1.67747
$147$	−2.29648e66	−1.81086
$148$	3.12528e66	2.00404
$149$	8.52805e65	0.445316	0.222658	−	0.974897i	$-0.428527\pi$
$149$	8.52805e65	0.445316	0.222658	+	0.974897i	$0.428527\pi$
$150$	4.16493e66	1.77347
$151$	−5.28415e65	−0.183729	−0.0918646	−	0.995772i	$-0.529283\pi$
$151$	−5.28415e65	−0.183729	−0.0918646	+	0.995772i	$0.529283\pi$
$152$	−1.40478e67	−3.99374
$153$	−3.84171e65	−0.0894203
$154$	7.65640e66	1.46097
$155$	5.43052e65	0.0850598
$156$	−6.01395e65	−0.0774211
$157$	7.85892e66	0.832575	0.416287	−	0.909233i	$-0.363331\pi$
$157$	7.85892e66	0.832575	0.416287	+	0.909233i	$0.363331\pi$
$158$	3.49999e67	3.05510
$159$	−1.84377e67	−1.32769
$160$	−1.31005e67	−0.779162
$161$	−1.10977e67	−0.545815
$162$	−5.12559e67	−2.08706
$163$	4.04897e67	1.36654	0.683270	−	0.730166i	$-0.260557\pi$
$163$	4.04897e67	1.36654	0.683270	+	0.730166i	$0.260557\pi$
$164$	1.98698e67	0.556487
$165$	−7.19511e66	−0.167408
$166$	−1.88004e68	−3.63807
$167$	3.79481e67	0.611417	0.305708	−	0.952125i	$-0.401107\pi$
$167$	3.79481e67	0.611417	0.305708	+	0.952125i	$0.401107\pi$
$168$	3.66255e68	4.91870
$169$	−8.91615e67	−0.999155
$170$	4.45644e67	0.417154
$171$	−2.41066e67	−0.188693
$172$	−1.41578e68	−0.927635
$173$	−2.38020e67	−0.130679	−0.0653397	−	0.997863i	$-0.520813\pi$
$173$	−2.38020e67	−0.130679	−0.0653397	+	0.997863i	$0.520813\pi$
$174$	−2.37923e68	−1.09568
$175$	3.78450e68	1.46335
$176$	−4.03328e68	−1.31076
$177$	5.22524e68	1.42864
$178$	−3.92423e68	−0.903534
$179$	1.05792e68	0.205323	0.102661	−	0.994716i	$-0.467264\pi$
$179$	1.05792e68	0.205323	0.102661	+	0.994716i	$0.467264\pi$
$180$	−6.72270e67	−0.110086
$181$	−4.17583e68	−0.577493	−0.288746	−	0.957406i	$-0.593238\pi$
$181$	−4.17583e68	−0.577493	−0.288746	+	0.957406i	$0.593238\pi$
$182$	−7.64835e67	−0.0894109
$183$	−1.72589e68	−0.170708
$184$	1.11473e69	0.933740
$185$	−3.73517e68	−0.265199
$186$	8.49402e68	0.511645
$187$	6.25062e68	0.319709
$188$	4.55217e69	1.97881
$189$	−4.10260e69	−1.51696
$190$	2.79640e69	0.880268
$191$	−3.75239e69	−1.00644	−0.503222	−	0.864157i	$-0.667852\pi$
$191$	−3.75239e69	−1.00644	−0.503222	+	0.864157i	$0.667852\pi$
$192$	−7.64897e69	−1.74951
$193$	−4.33214e69	−0.845678	−0.422839	−	0.906205i	$-0.638966\pi$
$193$	−4.33214e69	−0.845678	−0.422839	+	0.906205i	$0.638966\pi$
$194$	−1.12732e70	−1.87972
$195$	7.18755e67	0.0102453
$196$	3.49114e70	4.25753
$197$	1.20339e70	1.25657	0.628285	−	0.777983i	$-0.283757\pi$
$197$	1.20339e70	1.25657	0.628285	+	0.777983i	$0.283757\pi$
$198$	−1.31974e69	−0.118086
$199$	−3.29217e69	−0.252618	−0.126309	−	0.991991i	$-0.540313\pi$
$199$	−3.29217e69	−0.252618	−0.126309	+	0.991991i	$0.540313\pi$
$200$	−3.80140e70	−2.50339
$201$	3.33703e70	1.88747
$202$	−1.39387e70	−0.677648
$203$	−2.16190e70	−0.904079
$204$	4.98026e70	1.79280
$205$	−2.37473e69	−0.0736412
$206$	−7.07287e70	−1.89080
$207$	1.91292e69	0.0441166
$208$	4.02904e69	0.0802176
$209$	3.92225e70	0.674642
$210$	−7.29079e70	−1.08414
$211$	1.05468e68	0.00135677	0.000678387	−	1.00000i	$-0.499784\pi$
$211$	1.05468e68	0.00135677	0.000678387		1.00000i	$0.499784\pi$
$212$	2.80293e71	3.12154
$213$	−1.24121e71	−1.19748
$214$	−3.27629e71	−2.74007
$215$	1.69206e70	0.122756
$216$	4.12092e71	2.59510
$217$	7.71815e70	0.422174
$218$	−1.79210e71	−0.851997
$219$	2.30729e71	0.954017
$220$	1.09381e71	0.393596
$221$	−6.24406e69	−0.0195660
$222$	−5.84228e71	−1.59521
$223$	2.72351e71	0.648381	0.324191	−	0.945992i	$-0.394908\pi$
$223$	2.72351e71	0.648381	0.324191	+	0.945992i	$0.394908\pi$
$224$	−1.86191e72	−3.86718
$225$	−6.52336e70	−0.118278
$226$	1.08557e72	1.71929
$227$	−2.72607e71	−0.377354	−0.188677	−	0.982039i	$-0.560420\pi$
$227$	−2.72607e71	−0.377354	−0.188677	+	0.982039i	$0.560420\pi$
$228$	3.12510e72	3.78313
$229$	−1.01160e72	−1.07158	−0.535791	−	0.844351i	$-0.679986\pi$
$229$	−1.01160e72	−1.07158	−0.535791	+	0.844351i	$0.679986\pi$
$230$	−2.21902e71	−0.205808
$231$	−1.02261e72	−0.830891
$232$	2.17156e72	1.54663
$233$	1.13228e72	0.707291	0.353646	−	0.935379i	$-0.384942\pi$
$233$	1.13228e72	0.707291	0.353646	+	0.935379i	$0.384942\pi$
$234$	1.31835e70	0.00722682
$235$	−5.44052e71	−0.261861
$236$	−7.94349e72	−3.35889
$237$	−4.67468e72	−1.73751
$238$	6.33374e72	2.07044
$239$	2.78705e72	0.801695	0.400847	−	0.916145i	$-0.368716\pi$
$239$	2.78705e72	0.801695	0.400847	+	0.916145i	$0.368716\pi$
$240$	3.84068e72	0.972669
$241$	2.43249e72	0.542664	0.271332	−	0.962486i	$-0.412536\pi$
$241$	2.43249e72	0.542664	0.271332	+	0.962486i	$0.412536\pi$
$242$	−7.37088e72	−1.44927
$243$	1.52267e72	0.264006
$244$	2.62372e72	0.401354
$245$	−4.17243e72	−0.563408
$246$	−3.71438e72	−0.442961
$247$	−3.91813e71	−0.0412878
$248$	−7.75262e72	−0.722225
$249$	2.51104e73	2.06906
$250$	1.60664e73	1.17152
$251$	8.38055e72	0.541033	0.270517	−	0.962715i	$-0.412806\pi$
$251$	8.38055e72	0.541033	0.270517	+	0.962715i	$0.412806\pi$
$252$	−9.55468e72	−0.546386
$253$	−3.11240e72	−0.157732
$254$	−5.71335e73	−2.56722
$255$	−5.95214e72	−0.237245
$256$	−8.20094e72	−0.290098
$257$	2.92677e73	0.919239	0.459620	−	0.888116i	$-0.347986\pi$
$257$	2.92677e73	0.919239	0.459620	+	0.888116i	$0.347986\pi$
$258$	2.64660e73	0.738393
$259$	−5.30863e73	−1.31625
$260$	−1.09266e72	−0.0240879
$261$	3.72648e72	0.0730741
$262$	5.56459e73	0.971055
$263$	−5.79108e73	−0.899724	−0.449862	−	0.893098i	$-0.648527\pi$
$263$	−5.79108e73	−0.899724	−0.449862	+	0.893098i	$0.648527\pi$
$264$	1.02718e74	1.42143
$265$	−3.34991e73	−0.413080
$266$	3.97441e74	4.36900
$267$	5.24131e73	0.513862
$268$	−5.07300e74	−4.43765
$269$	−1.60983e74	−1.25700	−0.628499	−	0.777810i	$-0.716330\pi$
$269$	−1.60983e74	−1.25700	−0.628499	+	0.777810i	$0.716330\pi$
$270$	−8.20323e73	−0.571992
$271$	1.09220e74	0.680360	0.340180	−	0.940360i	$-0.389512\pi$
$271$	1.09220e74	0.680360	0.340180	+	0.940360i	$0.389512\pi$
$272$	−3.33652e74	−1.85756
$273$	1.02153e73	0.0508502
$274$	6.40286e74	2.85090
$275$	1.06138e74	0.422885
$276$	−2.47984e74	−0.884499
$277$	2.91497e74	0.931112	0.465556	−	0.885018i	$-0.345854\pi$
$277$	2.91497e74	0.931112	0.465556	+	0.885018i	$0.345854\pi$
$278$	−3.40172e74	−0.973492
$279$	−1.33038e73	−0.0341231
$280$	6.65441e74	1.53035
$281$	−4.21232e74	−0.868917	−0.434458	−	0.900692i	$-0.643060\pi$
$281$	−4.21232e74	−0.868917	−0.434458	+	0.900692i	$0.643060\pi$
$282$	−8.50966e74	−1.57512
$283$	−1.72539e74	−0.286682	−0.143341	−	0.989673i	$-0.545785\pi$
$283$	−1.72539e74	−0.286682	−0.143341	+	0.989673i	$0.545785\pi$
$284$	1.88690e75	2.81540
$285$	−3.73495e74	−0.500630
$286$	−2.14501e73	−0.0258384
$287$	−3.37510e74	−0.365501
$288$	3.20939e74	0.312573
$289$	−6.24177e74	−0.546920
$290$	−4.32277e74	−0.340897
$291$	1.50568e75	1.06904
$292$	−3.50757e75	−2.24300
$293$	2.63304e75	1.51703	0.758517	−	0.651654i	$-0.225924\pi$
$293$	2.63304e75	1.51703	0.758517	+	0.651654i	$0.225924\pi$
$294$	−6.52621e75	−3.38897
$295$	9.49364e74	0.444489
$296$	5.33234e75	2.25175
$297$	−1.15059e75	−0.438378
$298$	2.42353e75	0.833397
$299$	3.10913e73	0.00965313
$300$	8.45665e75	2.37137
$301$	2.40485e75	0.609271
$302$	−1.50167e75	−0.343844
$303$	1.86169e75	0.385395
$304$	−2.09366e76	−3.91978
$305$	−3.13573e74	−0.0531121
$306$	−1.09175e75	−0.167348
$307$	−1.01914e76	−1.41421	−0.707103	−	0.707110i	$-0.749998\pi$
$307$	−1.01914e76	−1.41421	−0.707103	+	0.707110i	$0.749998\pi$
$308$	1.55458e76	1.95352
$309$	9.44671e75	1.07534
$310$	1.54326e75	0.159187
$311$	−1.92950e76	−1.80406	−0.902032	−	0.431669i	$-0.857925\pi$
$311$	−1.92950e76	−1.80406	−0.902032	+	0.431669i	$0.857925\pi$
$312$	−1.02610e75	−0.0869908
$313$	−1.21312e76	−0.932825	−0.466413	−	0.884567i	$-0.654454\pi$
$313$	−1.21312e76	−0.932825	−0.466413	+	0.884567i	$0.654454\pi$
$314$	2.23337e76	1.55814
$315$	1.14192e75	0.0723045
$316$	7.10652e76	4.08508
$317$	−1.56107e76	−0.814918	−0.407459	−	0.913224i	$-0.633585\pi$
$317$	−1.56107e76	−0.814918	−0.407459	+	0.913224i	$0.633585\pi$
$318$	−5.23970e76	−2.48473
$319$	−6.06313e75	−0.261265
$320$	−1.38973e76	−0.544321
$321$	4.37590e76	1.55835
$322$	−3.15379e76	−1.02148
$323$	3.24467e76	0.956080
$324$	−1.04072e77	−2.79069
$325$	−1.06026e75	−0.0258804
$326$	1.15065e77	2.55744
$327$	2.39357e76	0.484551
$328$	3.39017e76	0.625272
$329$	−7.73236e76	−1.29968
$330$	−2.04473e76	−0.313300
$331$	6.24069e76	0.871924	0.435962	−	0.899965i	$-0.356408\pi$
$331$	6.24069e76	0.871924	0.435962	+	0.899965i	$0.356408\pi$
$332$	−3.81732e77	−4.86460
$333$	9.15051e75	0.106389
$334$	1.07842e77	1.14425
$335$	6.06298e76	0.587245
$336$	5.45859e77	4.82761
$337$	1.13017e77	0.912922	0.456461	−	0.889743i	$-0.349117\pi$
$337$	1.13017e77	0.912922	0.456461	+	0.889743i	$0.349117\pi$
$338$	−2.53382e77	−1.86989
$339$	−1.44992e77	−0.977805
$340$	9.04853e76	0.557791
$341$	2.16459e76	0.122002
$342$	−6.85070e76	−0.353134
$343$	−2.44461e77	−1.15276
$344$	−2.41559e77	−1.04230
$345$	2.96378e76	0.117048
$346$	−6.76413e76	−0.244563
$347$	8.92703e76	0.295568	0.147784	−	0.989020i	$-0.452786\pi$
$347$	8.92703e76	0.295568	0.147784	+	0.989020i	$0.452786\pi$
$348$	−4.83088e77	−1.46507
$349$	−2.05483e77	−0.570953	−0.285476	−	0.958386i	$-0.592152\pi$
$349$	−2.05483e77	−0.570953	−0.285476	+	0.958386i	$0.592152\pi$
$350$	1.07549e78	2.73862
$351$	1.14938e76	0.0268285
$352$	−5.22181e77	−1.11756
$353$	7.47126e77	1.46644	0.733222	−	0.679990i	$-0.238016\pi$
$353$	7.47126e77	1.46644	0.733222	+	0.679990i	$0.238016\pi$
$354$	1.48493e78	2.67366
$355$	−2.25513e77	−0.372569
$356$	−7.96791e77	−1.20815
$357$	−8.45952e77	−1.17751
$358$	3.00645e77	0.384256
$359$	−9.45141e77	−1.10947	−0.554736	−	0.832027i	$-0.687181\pi$
$359$	−9.45141e77	−1.10947	−0.554736	+	0.832027i	$0.687181\pi$
$360$	−1.14702e77	−0.123693
$361$	1.02684e78	1.01750
$362$	−1.18670e78	−1.08076
$363$	9.84475e77	0.824238
$364$	−1.55295e77	−0.119554
$365$	4.19206e77	0.296822
$366$	−4.90468e77	−0.319476
$367$	−1.08283e78	−0.649002	−0.324501	−	0.945885i	$-0.605196\pi$
$367$	−1.08283e78	−0.649002	−0.324501	+	0.945885i	$0.605196\pi$
$368$	1.66137e78	0.916448
$369$	5.81767e76	0.0295423
$370$	−1.06147e78	−0.496313
$371$	−4.76109e78	−2.05023
$372$	1.72466e78	0.684138
$373$	3.84170e78	1.40412	0.702059	−	0.712119i	$-0.252264\pi$
$373$	3.84170e78	1.40412	0.702059	+	0.712119i	$0.252264\pi$
$374$	1.77632e78	0.598326
$375$	−2.14587e78	−0.666270
$376$	7.76690e78	2.22340
$377$	6.05677e76	0.0159893
$378$	−1.16589e79	−2.83895
$379$	1.78001e78	0.399876	0.199938	−	0.979809i	$-0.435926\pi$
$379$	1.78001e78	0.399876	0.199938	+	0.979809i	$0.435926\pi$
$380$	5.67793e78	1.17704
$381$	7.63090e78	1.46004
$382$	−1.06637e79	−1.88353
$383$	1.00847e79	1.64475	0.822374	−	0.568947i	$-0.192649\pi$
$383$	1.00847e79	1.64475	0.822374	+	0.568947i	$0.192649\pi$
$384$	−5.11098e78	−0.769842
$385$	−1.85796e78	−0.258514
$386$	−1.23112e79	−1.58266
$387$	−4.14526e77	−0.0492456
$388$	−2.28895e79	−2.51344
$389$	−1.43823e78	−0.146004	−0.0730021	−	0.997332i	$-0.523258\pi$
$389$	−1.43823e78	−0.146004	−0.0730021	+	0.997332i	$0.523258\pi$
$390$	2.04258e77	0.0191738
$391$	−2.57473e78	−0.223533
$392$	5.95657e79	4.78378
$393$	−7.43222e78	−0.552263
$394$	3.41983e79	2.35164
$395$	−8.49333e78	−0.540588
$396$	−2.67965e78	−0.157897
$397$	1.30448e79	0.711751	0.355875	−	0.934533i	$-0.384183\pi$
$397$	1.30448e79	0.711751	0.355875	+	0.934533i	$0.384183\pi$
$398$	−9.35580e78	−0.472767
$399$	−5.30832e79	−2.48476
$400$	−5.66553e79	−2.45703
$401$	−1.11670e79	−0.448778	−0.224389	−	0.974500i	$-0.572039\pi$
$401$	−1.11670e79	−0.448778	−0.224389	+	0.974500i	$0.572039\pi$
$402$	9.48327e79	3.53235
$403$	−2.16231e77	−0.00746646
$404$	−2.83016e79	−0.906107
$405$	1.24381e79	0.369298
$406$	−6.14376e79	−1.69196
$407$	−1.48883e79	−0.380377
$408$	8.49730e79	2.01440
$409$	6.64811e79	1.46264	0.731320	−	0.682035i	$-0.238905\pi$
$409$	6.64811e79	1.46264	0.731320	+	0.682035i	$0.238905\pi$
$410$	−6.74858e78	−0.137818
$411$	−8.55184e79	−1.62138
$412$	−1.43610e80	−2.52825
$413$	1.34929e80	2.20612
$414$	5.43621e78	0.0825630
$415$	4.56226e79	0.643743
$416$	5.21632e78	0.0683940
$417$	4.54343e79	0.553649
$418$	1.11464e80	1.26257
$419$	−1.13113e80	−1.19120	−0.595602	−	0.803279i	$-0.703087\pi$
$419$	−1.13113e80	−1.19120	−0.595602	+	0.803279i	$0.703087\pi$
$420$	−1.48035e80	−1.44964
$421$	−2.50575e78	−0.0228210	−0.0114105	−	0.999935i	$-0.503632\pi$
$421$	−2.50575e78	−0.0228210	−0.0114105	+	0.999935i	$0.503632\pi$
$422$	2.99723e77	0.00253916
$423$	1.33283e79	0.105050
$424$	4.78235e80	3.50738
$425$	8.78022e79	0.599299
$426$	−3.52731e80	−2.24105
$427$	−4.45667e79	−0.263609
$428$	−6.65231e80	−3.66385
$429$	2.86493e78	0.0146949
$430$	4.80856e79	0.229735
$431$	−4.22944e80	−1.88246	−0.941231	−	0.337763i	$-0.890330\pi$
$431$	−4.22944e80	−1.88246	−0.941231	+	0.337763i	$0.890330\pi$
$432$	6.14173e80	2.54704
$433$	4.38659e80	1.69530	0.847650	−	0.530556i	$-0.178017\pi$
$433$	4.38659e80	1.69530	0.847650	+	0.530556i	$0.178017\pi$
$434$	2.19337e80	0.790087
$435$	5.77361e79	0.193876
$436$	−3.63874e80	−1.13924
$437$	−1.61564e80	−0.471693
$438$	6.55692e80	1.78542
$439$	1.27552e80	0.323981	0.161991	−	0.986792i	$-0.448209\pi$
$439$	1.27552e80	0.323981	0.161991	+	0.986792i	$0.448209\pi$
$440$	1.86625e80	0.442246
$441$	1.02217e80	0.226020
$442$	−1.77446e79	−0.0366173
$443$	−3.94931e80	−0.760691	−0.380345	−	0.924845i	$-0.624195\pi$
$443$	−3.94931e80	−0.760691	−0.380345	+	0.924845i	$0.624195\pi$
$444$	−1.18624e81	−2.13300
$445$	9.52283e79	0.159877
$446$	7.73975e80	1.21343
$447$	−3.23693e80	−0.473973
$448$	−1.97516e81	−2.70161
$449$	3.41850e80	0.436840	0.218420	−	0.975855i	$-0.429910\pi$
$449$	3.41850e80	0.436840	0.218420	+	0.975855i	$0.429910\pi$
$450$	−1.85383e80	−0.221354
$451$	−9.46559e79	−0.105624
$452$	2.20418e81	2.29893
$453$	2.00567e80	0.195553
$454$	−7.74704e80	−0.706207
$455$	1.85601e79	0.0158209
$456$	5.33203e81	4.25074
$457$	−1.01306e81	−0.755423	−0.377711	−	0.925923i	$-0.623289\pi$
$457$	−1.01306e81	−0.755423	−0.377711	+	0.925923i	$0.623289\pi$
$458$	−2.87479e81	−2.00544
$459$	−9.51823e80	−0.621254
$460$	−4.50558e80	−0.275193
$461$	−3.55139e80	−0.203011	−0.101506	−	0.994835i	$-0.532366\pi$
$461$	−3.55139e80	−0.203011	−0.101506	+	0.994835i	$0.532366\pi$
$462$	−2.90608e81	−1.55499
$463$	6.17959e80	0.309556	0.154778	−	0.987949i	$-0.450534\pi$
$463$	6.17959e80	0.309556	0.154778	+	0.987949i	$0.450534\pi$
$464$	3.23644e81	1.51799
$465$	−2.06122e80	−0.0905336
$466$	3.21775e81	1.32368
$467$	−2.32266e81	−0.894997	−0.447499	−	0.894285i	$-0.647685\pi$
$467$	−2.32266e81	−0.894997	−0.447499	+	0.894285i	$0.647685\pi$
$468$	2.67683e79	0.00966324
$469$	8.61704e81	2.91465
$470$	−1.54610e81	−0.490065
$471$	−2.98295e81	−0.886153
$472$	−1.35531e82	−3.77406
$473$	6.74450e80	0.176070
$474$	−1.32847e82	−3.25170
$475$	5.50957e81	1.26463
$476$	1.28603e82	2.76846
$477$	8.20671e80	0.165714
$478$	7.92034e81	1.50035
$479$	−6.48492e81	−1.15258	−0.576290	−	0.817245i	$-0.695500\pi$
$479$	−6.48492e81	−1.15258	−0.576290	+	0.817245i	$0.695500\pi$
$480$	4.97245e81	0.829303
$481$	1.48726e80	0.0232789
$482$	6.91272e81	1.01558
$483$	4.21229e81	0.580939
$484$	−1.49661e82	−1.93788
$485$	2.73563e81	0.332610
$486$	4.32717e81	0.494081
$487$	1.13904e82	1.22153	0.610765	−	0.791812i	$-0.290862\pi$
$487$	1.13904e82	1.22153	0.610765	+	0.791812i	$0.290862\pi$
$488$	4.47658e81	0.450964
$489$	−1.53684e82	−1.45448
$490$	−1.18573e82	−1.05440
$491$	−8.43794e81	−0.705101	−0.352550	−	0.935793i	$-0.614685\pi$
$491$	−8.43794e81	−0.705101	−0.352550	+	0.935793i	$0.614685\pi$
$492$	−7.54182e81	−0.592298
$493$	−5.01572e81	−0.370256
$494$	−1.11347e81	−0.0772690
$495$	3.20257e80	0.0208949
$496$	−1.15543e82	−0.708850
$497$	−3.20511e82	−1.84916
$498$	7.13595e82	3.87219
$499$	4.77379e81	0.243667	0.121833	−	0.992551i	$-0.461123\pi$
$499$	4.77379e81	0.243667	0.121833	+	0.992551i	$0.461123\pi$
$500$	3.26219e82	1.56648
$501$	−1.44037e82	−0.650763
$502$	2.38161e82	1.01253
$503$	−7.98855e81	−0.319628	−0.159814	−	0.987147i	$-0.551089\pi$
$503$	−7.98855e81	−0.319628	−0.159814	+	0.987147i	$0.551089\pi$
$504$	−1.63021e82	−0.613922
$505$	3.38246e81	0.119907
$506$	−8.84493e81	−0.295191
$507$	3.38424e82	1.06345
$508$	−1.16006e83	−3.43271
$509$	5.44275e82	1.51679	0.758396	−	0.651794i	$-0.225983\pi$
$509$	5.44275e82	1.51679	0.758396	+	0.651794i	$0.225983\pi$
$510$	−1.69150e82	−0.443998
$511$	5.95800e82	1.47320
$512$	−5.43549e82	−1.26621
$513$	−5.97266e82	−1.31096
$514$	8.31740e82	1.72033
$515$	1.71635e82	0.334570
$516$	5.37376e82	0.987331
$517$	−2.16857e82	−0.375588
$518$	−1.50862e83	−2.46333
$519$	9.03435e81	0.139089
$520$	−1.86429e81	−0.0270653
$521$	3.83339e82	0.524847	0.262424	−	0.964953i	$-0.415478\pi$
$521$	3.83339e82	0.524847	0.262424	+	0.964953i	$0.415478\pi$
$522$	1.05900e82	0.136756
$523$	8.06645e82	0.982609	0.491305	−	0.870988i	$-0.336520\pi$
$523$	8.06645e82	0.982609	0.491305	+	0.870988i	$0.336520\pi$
$524$	1.12986e83	1.29843
$525$	−1.43645e83	−1.55752
$526$	−1.64573e83	−1.68381
$527$	1.79065e82	0.172897
$528$	1.53088e83	1.39511
$529$	−1.03431e83	−0.889718
$530$	−9.51990e82	−0.773069
$531$	−2.32578e82	−0.178314
$532$	8.06979e83	5.84195
$533$	9.45564e80	0.00646415
$534$	1.48949e83	0.961678
$535$	7.95048e82	0.484845
$536$	−8.65553e83	−4.98617
$537$	−4.01549e82	−0.218536
$538$	−4.57486e83	−2.35244
$539$	−1.66312e83	−0.808100
$540$	−1.66562e83	−0.764831
$541$	3.06629e83	1.33075	0.665375	−	0.746509i	$-0.268272\pi$
$541$	3.06629e83	1.33075	0.665375	+	0.746509i	$0.268272\pi$
$542$	3.10385e83	1.27328
$543$	1.58499e83	0.614656
$544$	−4.31973e83	−1.58376
$545$	4.34883e82	0.150758
$546$	2.90303e82	0.0951648
$547$	1.45425e83	0.450842	0.225421	−	0.974261i	$-0.427624\pi$
$547$	1.45425e83	0.450842	0.225421	+	0.974261i	$0.427624\pi$
$548$	1.30006e84	3.81204
$549$	7.68199e81	0.0213068
$550$	3.01626e83	0.791418
$551$	−3.14735e83	−0.781306
$552$	−4.23110e83	−0.993828
$553$	−1.20712e84	−2.68308
$554$	8.28387e83	1.74255
$555$	1.41773e83	0.282265
$556$	−6.90699e83	−1.30169
$557$	3.06138e83	0.546177	0.273089	−	0.961989i	$-0.411955\pi$
$557$	3.06138e83	0.546177	0.273089	+	0.961989i	$0.411955\pi$
$558$	−3.78072e82	−0.0638604
$559$	−6.73742e81	−0.0107754
$560$	9.91760e83	1.50201
$561$	−2.37250e83	−0.340283
$562$	−1.19707e84	−1.62615
$563$	2.96460e83	0.381470	0.190735	−	0.981642i	$-0.438913\pi$
$563$	2.96460e83	0.381470	0.190735	+	0.981642i	$0.438913\pi$
$564$	−1.72784e84	−2.10615
$565$	−2.63432e83	−0.304223
$566$	−4.90327e83	−0.536518
$567$	1.76778e84	1.83292
$568$	3.21943e84	3.16340
$569$	−7.76465e83	−0.723099	−0.361549	−	0.932353i	$-0.617752\pi$
$569$	−7.76465e83	−0.723099	−0.361549	+	0.932353i	$0.617752\pi$
$570$	−1.06141e84	−0.936916
$571$	−3.44139e83	−0.287960	−0.143980	−	0.989581i	$-0.545990\pi$
$571$	−3.44139e83	−0.287960	−0.143980	+	0.989581i	$0.545990\pi$
$572$	−4.35531e82	−0.0345494
$573$	1.42427e84	1.07121
$574$	−9.59146e83	−0.684025
$575$	−4.37198e83	−0.295671
$576$	3.40459e83	0.218363
$577$	−1.84102e84	−1.11995	−0.559973	−	0.828511i	$-0.689189\pi$
$577$	−1.84102e84	−1.11995	−0.559973	+	0.828511i	$0.689189\pi$
$578$	−1.77381e84	−1.02355
$579$	1.64432e84	0.900099
$580$	−8.77712e83	−0.455825
$581$	6.48413e84	3.19507
$582$	4.27888e84	2.00069
$583$	−1.33526e84	−0.592484
$584$	−5.98460e84	−2.52025
$585$	−3.19921e81	−0.00127876
$586$	7.48266e84	2.83909
$587$	−5.03892e84	−1.81500	−0.907498	−	0.420057i	$-0.862010\pi$
$587$	−5.03892e84	−1.81500	−0.907498	+	0.420057i	$0.862010\pi$
$588$	−1.32511e85	−4.53151
$589$	1.12363e84	0.364843
$590$	2.69793e84	0.831850
$591$	−4.56762e84	−1.33743
$592$	7.94720e84	2.21005
$593$	−9.78641e82	−0.0258497	−0.0129248	−	0.999916i	$-0.504114\pi$
$593$	−9.78641e82	−0.0258497	−0.0129248	+	0.999916i	$0.504114\pi$
$594$	−3.26978e84	−0.820412
$595$	−1.53699e84	−0.366357
$596$	4.92083e84	1.11436
$597$	1.24959e84	0.268874
$598$	8.83564e82	0.0180656
$599$	8.94959e83	0.173894	0.0869471	−	0.996213i	$-0.472289\pi$
$599$	8.94959e83	0.173894	0.0869471	+	0.996213i	$0.472289\pi$
$600$	1.44287e85	2.66449
$601$	−4.15804e84	−0.729822	−0.364911	−	0.931042i	$-0.618901\pi$
$601$	−4.15804e84	−0.729822	−0.364911	+	0.931042i	$0.618901\pi$
$602$	6.83419e84	1.14023
$603$	−1.48532e84	−0.235583
$604$	−3.04904e84	−0.459766
$605$	1.78867e84	0.256444
$606$	5.29060e84	0.721257
$607$	−1.10453e85	−1.43193	−0.715966	−	0.698135i	$-0.754014\pi$
$607$	−1.10453e85	−1.43193	−0.715966	+	0.698135i	$0.754014\pi$
$608$	−2.71062e85	−3.34202
$609$	8.20577e84	0.962259
$610$	−8.91122e83	−0.0993979
$611$	2.16629e83	0.0229858
$612$	−2.21673e84	−0.223766
$613$	4.37303e83	0.0419989	0.0209994	−	0.999779i	$-0.493315\pi$
$613$	4.37303e83	0.0419989	0.0209994	+	0.999779i	$0.493315\pi$
$614$	−2.89622e85	−2.64665
$615$	9.01358e83	0.0783802
$616$	2.65243e85	2.19498
$617$	1.63068e85	1.28432	0.642158	−	0.766572i	$-0.278039\pi$
$617$	1.63068e85	1.28432	0.642158	+	0.766572i	$0.278039\pi$
$618$	2.68460e85	2.01248
$619$	2.95589e84	0.210923	0.105462	−	0.994423i	$-0.466368\pi$
$619$	2.95589e84	0.210923	0.105462	+	0.994423i	$0.466368\pi$
$620$	3.13350e84	0.212855
$621$	4.73946e84	0.306503
$622$	−5.48330e85	−3.37626
$623$	1.35344e85	0.793511
$624$	−1.52927e84	−0.0853798
$625$	1.28466e85	0.683044
$626$	−3.44747e85	−1.74576
$627$	−1.48874e85	−0.718057
$628$	4.53473e85	2.08345
$629$	−1.23163e85	−0.539057
$630$	3.24516e84	0.135316
$631$	−2.00789e85	−0.797710	−0.398855	−	0.917014i	$-0.630592\pi$
$631$	−2.00789e85	−0.797710	−0.398855	+	0.917014i	$0.630592\pi$
$632$	1.21251e86	4.59002
$633$	−4.00319e82	−0.00144408
$634$	−4.43629e85	−1.52510
$635$	1.38644e85	0.454259
$636$	−1.06389e86	−3.32242
$637$	1.66137e84	0.0494554
$638$	−1.72304e85	−0.488951
$639$	5.52467e84	0.149462
$640$	−9.28603e84	−0.239520
$641$	−5.74852e85	−1.41379	−0.706897	−	0.707316i	$-0.749906\pi$
$641$	−5.74852e85	−1.41379	−0.706897	+	0.707316i	$0.749906\pi$
$642$	1.24356e86	2.91640
$643$	1.81186e85	0.405219	0.202610	−	0.979260i	$-0.435058\pi$
$643$	1.81186e85	0.405219	0.202610	+	0.979260i	$0.435058\pi$
$644$	−6.40358e85	−1.36585
$645$	−6.42244e84	−0.130656
$646$	9.22082e85	1.78928
$647$	−6.46742e84	−0.119716	−0.0598578	−	0.998207i	$-0.519065\pi$
$647$	−6.46742e84	−0.119716	−0.0598578	+	0.998207i	$0.519065\pi$
$648$	−1.77567e86	−3.13563
$649$	3.78413e85	0.637534
$650$	−3.01309e84	−0.0484345
$651$	−2.92952e85	−0.449342
$652$	2.33632e86	3.41965
$653$	5.18677e85	0.724511	0.362256	−	0.932079i	$-0.382007\pi$
$653$	5.18677e85	0.724511	0.362256	+	0.932079i	$0.382007\pi$
$654$	6.80213e85	0.906825
$655$	−1.35035e85	−0.171825
$656$	5.05264e85	0.613693
$657$	−1.02698e85	−0.119075
$658$	−2.19741e86	−2.43232
$659$	−1.56604e85	−0.165500	−0.0827501	−	0.996570i	$-0.526370\pi$
$659$	−1.56604e85	−0.165500	−0.0827501	+	0.996570i	$0.526370\pi$
$660$	−4.15170e85	−0.418925
$661$	5.66912e85	0.546224	0.273112	−	0.961982i	$-0.411947\pi$
$661$	5.66912e85	0.546224	0.273112	+	0.961982i	$0.411947\pi$
$662$	1.77350e86	1.63178
$663$	2.37001e84	0.0208251
$664$	−6.51309e86	−5.46589
$665$	−9.64459e85	−0.773078
$666$	2.60042e85	0.199104
$667$	2.49750e85	0.182670
$668$	2.18967e86	1.53002
$669$	−1.03374e86	−0.690106
$670$	1.72300e86	1.09901
$671$	−1.24989e85	−0.0761790
$672$	7.06713e86	4.11605
$673$	5.64478e85	0.314186	0.157093	−	0.987584i	$-0.449788\pi$
$673$	5.64478e85	0.314186	0.157093	+	0.987584i	$0.449788\pi$
$674$	3.21177e86	1.70851
$675$	−1.61623e86	−0.821746
$676$	−5.14477e86	−2.50030
$677$	−3.08615e86	−1.43371	−0.716857	−	0.697220i	$-0.754420\pi$
$677$	−3.08615e86	−1.43371	−0.716857	+	0.697220i	$0.754420\pi$
$678$	−4.12042e86	−1.82994
$679$	3.88803e86	1.65083
$680$	1.54386e86	0.626737
$681$	1.03472e86	0.401637
$682$	6.15139e85	0.228323
$683$	2.92712e86	1.03898	0.519491	−	0.854476i	$-0.326121\pi$
$683$	2.92712e86	1.03898	0.519491	+	0.854476i	$0.326121\pi$
$684$	−1.39099e86	−0.472187
$685$	−1.55377e86	−0.504456
$686$	−6.94717e86	−2.15736
$687$	3.83964e86	1.14054
$688$	−3.60015e86	−1.02299
$689$	1.33386e85	0.0362598
$690$	8.42256e85	0.219052
$691$	6.58507e86	1.63863	0.819313	−	0.573347i	$-0.194355\pi$
$691$	6.58507e86	1.63863	0.819313	+	0.573347i	$0.194355\pi$
$692$	−1.37342e86	−0.327014
$693$	4.55167e85	0.103707
$694$	2.53691e86	0.553148
$695$	8.25487e85	0.172256
$696$	−8.24242e86	−1.64616
$697$	−7.83039e85	−0.149687
$698$	−5.83948e86	−1.06852
$699$	−4.29771e86	−0.752807
$700$	2.18372e87	3.66190
$701$	−1.19477e87	−1.91817	−0.959083	−	0.283124i	$-0.908629\pi$
$701$	−1.19477e87	−1.91817	−0.959083	+	0.283124i	$0.908629\pi$
$702$	3.26635e85	0.0502089
$703$	−7.72843e86	−1.13751
$704$	−5.53940e86	−0.780723
$705$	2.06502e86	0.278712
$706$	2.12321e87	2.74441
$707$	4.80734e86	0.595131
$708$	3.01505e87	3.57504
$709$	−8.38841e86	−0.952729	−0.476365	−	0.879248i	$-0.658046\pi$
$709$	−8.38841e86	−0.952729	−0.476365	+	0.879248i	$0.658046\pi$
$710$	−6.40870e86	−0.697253
$711$	2.08072e86	0.216866
$712$	−1.35948e87	−1.35748
$713$	−8.91627e85	−0.0853007
$714$	−2.40405e87	−2.20368
$715$	5.20524e84	0.00457200
$716$	6.10441e86	0.513803
$717$	−1.05786e87	−0.853286
$718$	−2.68593e87	−2.07635
$719$	−1.44491e86	−0.107055	−0.0535277	−	0.998566i	$-0.517047\pi$
$719$	−1.44491e86	−0.107055	−0.0535277	+	0.998566i	$0.517047\pi$
$720$	−1.70950e86	−0.121403
$721$	2.43938e87	1.66056
$722$	2.91811e87	1.90422
$723$	−9.23282e86	−0.577585
$724$	−2.40953e87	−1.44512
$725$	−8.51686e86	−0.489745
$726$	2.79771e87	1.54254
$727$	1.05896e87	0.559861	0.279931	−	0.960020i	$-0.409689\pi$
$727$	1.05896e87	0.559861	0.279931	+	0.960020i	$0.409689\pi$
$728$	−2.64964e86	−0.134332
$729$	1.71578e87	0.834202
$730$	1.19131e87	0.555494
$731$	5.57938e86	0.249520
$732$	−9.95866e86	−0.427182
$733$	6.14850e86	0.252987	0.126493	−	0.991967i	$-0.459628\pi$
$733$	6.14850e86	0.252987	0.126493	+	0.991967i	$0.459628\pi$
$734$	−3.07723e87	−1.21459
$735$	1.58370e87	0.599665
$736$	2.15095e87	0.781369
$737$	2.41668e87	0.842289
$738$	1.65328e86	0.0552877
$739$	−1.06088e87	−0.340417	−0.170209	−	0.985408i	$-0.554444\pi$
$739$	−1.06088e87	−0.340417	−0.170209	+	0.985408i	$0.554444\pi$
$740$	−2.15525e87	−0.663638
$741$	1.48718e86	0.0439448
$742$	−1.35302e88	−3.83694
$743$	−7.11678e87	−1.93698	−0.968490	−	0.249054i	$-0.919880\pi$
$743$	−7.11678e87	−1.93698	−0.968490	+	0.249054i	$0.919880\pi$
$744$	2.94261e87	0.768701
$745$	−5.88111e86	−0.147466
$746$	1.09175e88	2.62777
$747$	−1.11767e87	−0.258248
$748$	3.60672e87	0.800043
$749$	1.12997e88	2.40641
$750$	−6.09821e87	−1.24691
$751$	−2.75527e87	−0.540936	−0.270468	−	0.962729i	$-0.587178\pi$
$751$	−2.75527e87	−0.540936	−0.270468	+	0.962729i	$0.587178\pi$
$752$	1.15756e88	2.18223
$753$	−3.18094e87	−0.575850
$754$	1.72123e86	0.0299236
$755$	3.64406e86	0.0608419
$756$	−2.36727e88	−3.79606
$757$	−5.08599e87	−0.783342	−0.391671	−	0.920105i	$-0.628103\pi$
$757$	−5.08599e87	−0.783342	−0.391671	+	0.920105i	$0.628103\pi$
$758$	5.05848e87	0.748358
$759$	1.18135e87	0.167882
$760$	9.68766e87	1.32253
$761$	−6.17119e87	−0.809351	−0.404675	−	0.914460i	$-0.632615\pi$
$761$	−6.17119e87	−0.809351	−0.404675	+	0.914460i	$0.632615\pi$
$762$	2.16858e88	2.73242
$763$	6.18080e87	0.748250
$764$	−2.16519e88	−2.51854
$765$	2.64932e86	0.0296115
$766$	2.86590e88	3.07810
$767$	−3.78016e86	−0.0390168
$768$	3.11277e87	0.308767
$769$	−9.88338e87	−0.942219	−0.471110	−	0.882075i	$-0.656146\pi$
$769$	−9.88338e87	−0.942219	−0.471110	+	0.882075i	$0.656146\pi$
$770$	−5.28000e87	−0.483801
$771$	−1.11089e88	−0.978395
$772$	−2.49972e88	−2.11623
$773$	1.65349e88	1.34563	0.672816	−	0.739810i	$-0.265085\pi$
$773$	1.65349e88	1.34563	0.672816	+	0.739810i	$0.265085\pi$
$774$	−1.17801e87	−0.0921618
$775$	3.04058e87	0.228694
$776$	−3.90540e88	−2.82412
$777$	2.01496e88	1.40096
$778$	−4.08721e87	−0.273243
$779$	−4.91355e87	−0.315866
$780$	4.14734e86	0.0256380
$781$	−8.98887e87	−0.534378
$782$	−7.31695e87	−0.418335
$783$	9.23273e87	0.507687
$784$	8.87755e88	4.69519
$785$	−5.41967e87	−0.275707
$786$	−2.11211e88	−1.03355
$787$	−3.40866e88	−1.60455	−0.802277	−	0.596952i	$-0.796378\pi$
$787$	−3.40866e88	−1.60455	−0.802277	+	0.596952i	$0.796378\pi$
$788$	6.94377e88	3.14446
$789$	2.19808e88	0.957624
$790$	−2.41366e88	−1.01170
$791$	−3.74405e88	−1.50994
$792$	−4.57200e87	−0.177414
$793$	1.24858e86	0.00466212
$794$	3.70712e88	1.33202
$795$	1.27150e88	0.439663
$796$	−1.89964e88	−0.632153
$797$	5.14649e88	1.64828	0.824142	−	0.566384i	$-0.191658\pi$
$797$	5.14649e88	1.64828	0.824142	+	0.566384i	$0.191658\pi$
$798$	−1.50854e89	−4.65016
$799$	−1.79395e88	−0.532271
$800$	−7.33505e88	−2.09488
$801$	−2.33293e87	−0.0641371
$802$	−3.17346e88	−0.839876
$803$	1.67094e88	0.425733
$804$	1.92552e89	4.72323
$805$	7.65322e87	0.180747
$806$	−6.14493e86	−0.0139733
$807$	6.11031e88	1.33789
$808$	−4.82881e88	−1.01811
$809$	−3.94596e88	−0.801167	−0.400583	−	0.916260i	$-0.631192\pi$
$809$	−3.94596e88	−0.801167	−0.400583	+	0.916260i	$0.631192\pi$
$810$	3.53471e88	0.691131
$811$	5.01413e88	0.944189	0.472095	−	0.881548i	$-0.343498\pi$
$811$	5.01413e88	0.944189	0.472095	+	0.881548i	$0.343498\pi$
$812$	−1.24745e89	−2.26238
$813$	−4.14559e88	−0.724143
$814$	−4.23099e88	−0.711865
$815$	−2.79225e88	−0.452530
$816$	1.26642e89	1.97710
$817$	3.50105e88	0.526532
$818$	1.88928e89	2.73729
$819$	−4.54689e86	−0.00634681
$820$	−1.37026e88	−0.184281
$821$	−2.71849e88	−0.352258	−0.176129	−	0.984367i	$-0.556358\pi$
$821$	−2.71849e88	−0.352258	−0.176129	+	0.984367i	$0.556358\pi$
$822$	−2.43029e89	−3.03436
$823$	1.12457e89	1.35299	0.676493	−	0.736449i	$-0.263499\pi$
$823$	1.12457e89	1.35299	0.676493	+	0.736449i	$0.263499\pi$
$824$	−2.45027e89	−2.84076
$825$	−4.02859e88	−0.450099
$826$	3.83445e89	4.12869
$827$	−7.06235e88	−0.732877	−0.366439	−	0.930442i	$-0.619423\pi$
$827$	−7.06235e88	−0.732877	−0.366439	+	0.930442i	$0.619423\pi$
$828$	1.10379e88	0.110398
$829$	−1.28843e89	−1.24207	−0.621035	−	0.783783i	$-0.713288\pi$
$829$	−1.28843e89	−1.24207	−0.621035	+	0.783783i	$0.713288\pi$
$830$	1.29652e89	1.20475
$831$	−1.10642e89	−0.991031
$832$	5.53358e87	0.0477799
$833$	−1.37581e89	−1.14521
$834$	1.29117e89	1.03614
$835$	−2.61697e88	−0.202471
$836$	2.26320e89	1.68823
$837$	−3.29615e88	−0.237072
$838$	−3.21449e89	−2.22931
$839$	1.19830e89	0.801355	0.400678	−	0.916219i	$-0.368775\pi$
$839$	1.19830e89	0.801355	0.400678	+	0.916219i	$0.368775\pi$
$840$	−2.52577e89	−1.62883
$841$	−1.12144e89	−0.697428
$842$	−7.12093e87	−0.0427089
$843$	1.59884e89	0.924834
$844$	6.08570e86	0.00339521
$845$	6.14876e88	0.330870
$846$	3.78768e88	0.196597
$847$	2.54216e89	1.27280
$848$	7.12751e89	3.44243
$849$	6.54894e88	0.305131
$850$	2.49519e89	1.12157
$851$	6.13271e88	0.265950
$852$	−7.16199e89	−2.99658
$853$	2.72024e89	1.09815	0.549075	−	0.835773i	$-0.314980\pi$
$853$	2.72024e89	1.09815	0.549075	+	0.835773i	$0.314980\pi$
$854$	−1.26651e89	−0.493338
$855$	1.66244e88	0.0624856
$856$	−1.13501e90	−4.11672
$857$	−4.40217e89	−1.54082	−0.770409	−	0.637549i	$-0.779948\pi$
$857$	−4.40217e89	−1.54082	−0.770409	+	0.637549i	$0.779948\pi$
$858$	8.14166e87	0.0275012
$859$	4.73420e89	1.54332	0.771659	−	0.636036i	$-0.219427\pi$
$859$	4.73420e89	1.54332	0.771659	+	0.636036i	$0.219427\pi$
$860$	9.76348e88	0.307186
$861$	1.28106e89	0.389022
$862$	−1.20194e90	−3.52298
$863$	−2.92227e89	−0.826781	−0.413390	−	0.910554i	$-0.635656\pi$
$863$	−2.92227e89	−0.826781	−0.413390	+	0.910554i	$0.635656\pi$
$864$	7.95158e89	2.17162
$865$	1.64143e88	0.0432745
$866$	1.24660e90	3.17271
$867$	2.36914e89	0.582115
$868$	4.45351e89	1.05645
$869$	−3.38541e89	−0.775369
$870$	1.64076e89	0.362834
$871$	−2.41415e88	−0.0515477
$872$	−6.20841e89	−1.28005
$873$	−6.70182e88	−0.133432
$874$	−4.59137e89	−0.882762
$875$	−5.54118e89	−1.02886
$876$	1.33134e90	2.38734
$877$	8.38175e89	1.45160	0.725800	−	0.687905i	$-0.241470\pi$
$877$	8.38175e89	1.45160	0.725800	+	0.687905i	$0.241470\pi$
$878$	3.62482e89	0.606322
$879$	−9.99404e89	−1.61466
$880$	2.78143e89	0.434057
$881$	−4.60933e89	−0.694820	−0.347410	−	0.937713i	$-0.612939\pi$
$881$	−4.60933e89	−0.694820	−0.347410	+	0.937713i	$0.612939\pi$
$882$	2.90484e89	0.422991
$883$	−1.05185e90	−1.47963	−0.739815	−	0.672810i	$-0.765087\pi$
$883$	−1.05185e90	−1.47963	−0.739815	+	0.672810i	$0.765087\pi$
$884$	−3.60293e88	−0.0489623
$885$	−3.60343e89	−0.473093
$886$	−1.12233e90	−1.42361
$887$	1.61456e90	1.97871	0.989357	−	0.145510i	$-0.0464824\pi$
$887$	1.61456e90	1.97871	0.989357	+	0.145510i	$0.0464824\pi$
$888$	−2.02396e90	−2.39666
$889$	1.97049e90	2.25461
$890$	2.70623e89	0.299205
$891$	4.95780e89	0.529686
$892$	1.57151e90	1.62252
$893$	−1.12570e90	−1.12319
$894$	−9.19881e89	−0.887028
$895$	−7.29566e88	−0.0679927
$896$	−1.31978e90	−1.18880
$897$	−1.18011e88	−0.0102743
$898$	9.71480e89	0.817534
$899$	−1.73694e89	−0.141291
$900$	−3.76409e89	−0.295981
$901$	−1.10460e90	−0.839648
$902$	−2.68996e89	−0.197673
$903$	−9.12793e89	−0.648479
$904$	3.76077e90	2.58309
$905$	2.87974e89	0.191237
$906$	5.69977e89	0.365971
$907$	1.02664e90	0.637376	0.318688	−	0.947860i	$-0.396758\pi$
$907$	1.02664e90	0.637376	0.318688	+	0.947860i	$0.396758\pi$
$908$	−1.57299e90	−0.944295
$909$	−8.28644e88	−0.0481027
$910$	5.27446e88	0.0296084
$911$	−1.66692e90	−0.904910	−0.452455	−	0.891787i	$-0.649452\pi$
$911$	−1.66692e90	−0.904910	−0.452455	+	0.891787i	$0.649452\pi$
$912$	7.94675e90	4.17203
$913$	1.81850e90	0.923325
$914$	−2.87894e90	−1.41375
$915$	1.19021e89	0.0565300
$916$	−5.83708e90	−2.68154
$917$	−1.91919e90	−0.852810
$918$	−2.70492e90	−1.16266
$919$	1.08032e90	0.449188	0.224594	−	0.974452i	$-0.427894\pi$
$919$	1.08032e90	0.449188	0.224594	+	0.974452i	$0.427894\pi$
$920$	−7.68740e89	−0.309208
$921$	3.86827e90	1.50521
$922$	−1.00925e90	−0.379930
$923$	8.97943e88	0.0327037
$924$	−5.90063e90	−2.07923
$925$	−2.09135e90	−0.713022
$926$	1.75614e90	0.579326
$927$	−4.20477e89	−0.134218
$928$	4.19016e90	1.29425
$929$	4.46225e90	1.33375	0.666875	−	0.745170i	$-0.267632\pi$
$929$	4.46225e90	1.33375	0.666875	+	0.745170i	$0.267632\pi$
$930$	−5.85765e89	−0.169431
$931$	−8.63317e90	−2.41660
$932$	6.53345e90	1.76993
$933$	7.32365e90	1.92016
$934$	−6.60062e90	−1.67496
$935$	−4.31055e89	−0.105871
$936$	4.56720e88	0.0108577
$937$	−2.19447e89	−0.0504978	−0.0252489	−	0.999681i	$-0.508038\pi$
$937$	−2.19447e89	−0.0504978	−0.0252489	+	0.999681i	$0.508038\pi$
$938$	2.44882e91	5.45469
$939$	4.60454e90	0.992855
$940$	−3.13927e90	−0.655283
$941$	−4.73247e90	−0.956321	−0.478161	−	0.878272i	$-0.658696\pi$
$941$	−4.73247e90	−0.956321	−0.478161	+	0.878272i	$0.658696\pi$
$942$	−8.47705e90	−1.65841
$943$	3.89902e89	0.0738498
$944$	−2.01993e91	−3.70417
$945$	2.82923e90	0.502341
$946$	1.91667e90	0.329510
$947$	−6.68420e90	−1.11269	−0.556346	−	0.830951i	$-0.687797\pi$
$947$	−6.68420e90	−1.11269	−0.556346	+	0.830951i	$0.687797\pi$
$948$	−2.69737e91	−4.34797
$949$	−1.66919e89	−0.0260547
$950$	1.56573e91	2.36672
$951$	5.92523e90	0.867359
$952$	2.19422e91	3.11066
$953$	−8.38193e89	−0.115083	−0.0575414	−	0.998343i	$-0.518326\pi$
$953$	−8.38193e89	−0.115083	−0.0575414	+	0.998343i	$0.518326\pi$
$954$	2.33221e90	0.310129
$955$	2.58772e90	0.333284
$956$	1.60818e91	2.00617
$957$	2.30134e90	0.278078
$958$	−1.84291e91	−2.15702
$959$	−2.20830e91	−2.50375
$960$	5.27488e90	0.579349
$961$	−8.77850e90	−0.934022
$962$	4.22655e89	0.0435658
$963$	−1.94773e90	−0.194503
$964$	1.40359e91	1.35797
$965$	2.98753e90	0.280046
$966$	1.19706e91	1.08721
$967$	5.11590e90	0.450209	0.225105	−	0.974335i	$-0.427728\pi$
$967$	5.11590e90	0.450209	0.225105	+	0.974335i	$0.427728\pi$
$968$	−2.55351e91	−2.17741
$969$	−1.23156e91	−1.01761
$970$	7.77421e90	0.622470
$971$	5.40878e90	0.419675	0.209837	−	0.977736i	$-0.432707\pi$
$971$	5.40878e90	0.419675	0.209837	+	0.977736i	$0.432707\pi$
$972$	8.78606e90	0.660653
$973$	1.17323e91	0.854950
$974$	3.23695e91	2.28606
$975$	4.02436e89	0.0275459
$976$	6.67180e90	0.442612
$977$	−1.46776e90	−0.0943778	−0.0471889	−	0.998886i	$-0.515026\pi$
$977$	−1.46776e90	−0.0943778	−0.0471889	+	0.998886i	$0.515026\pi$
$978$	−4.36743e91	−2.72202
$979$	3.79577e90	0.229312
$980$	−2.40756e91	−1.40988
$981$	−1.06539e90	−0.0604788
$982$	−2.39792e91	−1.31958
$983$	3.29286e91	1.75667	0.878337	−	0.478041i	$-0.158653\pi$
$983$	3.29286e91	1.75667	0.878337	+	0.478041i	$0.158653\pi$
$984$	−1.28678e91	−0.665510
$985$	−8.29882e90	−0.416113
$986$	−1.42538e91	−0.692924
$987$	2.93492e91	1.38332
$988$	−2.26083e90	−0.103319
$989$	−2.77817e90	−0.123104
$990$	9.10117e89	0.0391042
$991$	1.54521e91	0.643785	0.321893	−	0.946776i	$-0.395681\pi$
$991$	1.54521e91	0.643785	0.321893	+	0.946776i	$0.395681\pi$
$992$	−1.49592e91	−0.604369
$993$	−2.36873e91	−0.928034
$994$	−9.10840e91	−3.46065
$995$	2.27035e90	0.0836543
$996$	1.44891e92	5.17764
$997$	−7.52005e90	−0.260626	−0.130313	−	0.991473i	$-0.541598\pi$
$997$	−7.52005e90	−0.260626	−0.130313	+	0.991473i	$0.541598\pi$
$998$	1.35663e91	0.456016
$999$	2.26713e91	0.739144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.62.a.a.1.4	✓	4
3.2	odd	2		9.62.a.a.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.62.a.a.1.4	✓	4	1.1	even	1	trivial
9.62.a.a.1.1		4	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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 62 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.84183e9 q^{2} -3.79563e14 q^{3} +5.77017e18 q^{4} -6.89620e20 q^{5} -1.07865e24 q^{6} -9.80127e25 q^{7} +9.84504e27 q^{8} +1.68945e28 q^{9} +O(q^{10})\)	\(q+2.84183e9 q^{2} -3.79563e14 q^{3} +5.77017e18 q^{4} -6.89620e20 q^{5} -1.07865e24 q^{6} -9.80127e25 q^{7} +9.84504e27 q^{8} +1.68945e28 q^{9} -1.95979e30 q^{10} -2.74880e31 q^{11} -2.19014e33 q^{12} +2.74592e32 q^{13} -2.78536e35 q^{14} +2.61754e35 q^{15} +1.46728e37 q^{16} -2.27394e37 q^{17} +4.80113e37 q^{18} -1.42689e39 q^{19} -3.97923e39 q^{20} +3.72020e40 q^{21} -7.81164e40 q^{22} +1.13228e41 q^{23} -3.73681e42 q^{24} -3.86123e42 q^{25} +7.80343e41 q^{26} +4.18578e43 q^{27} -5.65550e44 q^{28} +2.20574e44 q^{29} +7.43862e44 q^{30} -7.87465e44 q^{31} +1.89967e46 q^{32} +1.04334e46 q^{33} -6.46217e46 q^{34} +6.75915e46 q^{35} +9.74841e46 q^{36} +5.41627e47 q^{37} -4.05499e48 q^{38} -1.04225e47 q^{39} -6.78934e48 q^{40} +3.44353e48 q^{41} +1.05722e50 q^{42} -2.45361e49 q^{43} -1.58611e50 q^{44} -1.16508e49 q^{45} +3.21774e50 q^{46} +7.88915e50 q^{47} -5.56927e51 q^{48} +6.05033e51 q^{49} -1.09730e52 q^{50} +8.63104e51 q^{51} +1.58444e51 q^{52} +4.85762e52 q^{53} +1.18953e53 q^{54} +1.89563e52 q^{55} -9.64938e53 q^{56} +5.41596e53 q^{57} +6.26833e53 q^{58} -1.37665e54 q^{59} +1.51037e54 q^{60} +4.54704e53 q^{61} -2.23784e54 q^{62} -1.65587e54 q^{63} +2.01520e55 q^{64} -1.89364e53 q^{65} +2.96501e55 q^{66} -8.79176e55 q^{67} -1.31210e56 q^{68} -4.29770e55 q^{69} +1.92084e56 q^{70} +3.27010e56 q^{71} +1.66327e56 q^{72} -6.07880e56 q^{73} +1.53921e57 q^{74} +1.46558e57 q^{75} -8.23342e57 q^{76} +2.69418e57 q^{77} -2.96189e56 q^{78} +1.23160e58 q^{79} -1.01187e58 q^{80} -1.80362e58 q^{81} +9.78594e57 q^{82} -6.61561e58 q^{83} +2.14662e59 q^{84} +1.56816e58 q^{85} -6.97276e58 q^{86} -8.37216e58 q^{87} -2.70621e59 q^{88} -1.38088e59 q^{89} -3.31096e58 q^{90} -2.69135e58 q^{91} +6.53342e59 q^{92} +2.98892e59 q^{93} +2.24196e60 q^{94} +9.84014e59 q^{95} -7.21043e60 q^{96} -3.96687e60 q^{97} +1.71940e61 q^{98} -4.64396e59 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1146312000 q^{2} - 573723599022000 q^{3} + 44\!\cdots\!28 q^{4}+ \cdots + 11\!\cdots\!52 q^{9}+O(q^{10}) \) 4 * q + 1146312000 * q^2 - 573723599022000 * q^3 + 4402997675828604928 * q^4 - 524125996020295237800 * q^5 - 810420388530698747434752 * q^6 - 63338569463385158773180000 * q^7 + 9767868387156674079031296000 * q^8 + 116559153778048577840676094452 * q^9	\( 4 q + 1146312000 q^{2} - 573723599022000 q^{3} + 44\!\cdots\!28 q^{4}+ \cdots - 31\!\cdots\!76 q^{99}+O(q^{100}) \) 4 * q + 1146312000 * q^2 - 573723599022000 * q^3 + 4402997675828604928 * q^4 - 524125996020295237800 * q^5 - 810420388530698747434752 * q^6 - 63338569463385158773180000 * q^7 + 9767868387156674079031296000 * q^8 + 116559153778048577840676094452 * q^9 - 1483353386285070117088509033600 * q^10 - 41554515064513200044500416014352 * q^11 - 997468469175503713040400254976000 * q^12 + 10764994985103189070396812401291000 * q^13 - 211155135436541225684077605177122304 * q^14 + 115082099805150572294379175169983200 * q^15 + 10904646278227442826771588888892801024 * q^16 - 40906325415811699311242283170389539000 * q^17 + 15755547385947548040677485816834728000 * q^18 - 356159749895948464708913853630763435120 * q^19 - 5071632401696432486275641956774663577600 * q^20 - 5584164717140650613271728795305539583872 * q^21 - 172062995599931314756360229299481569056000 * q^22 - 410968880183827232479513482663937487796000 * q^23 - 6122904790572089676121487755102001729372160 * q^24 - 16739487717977510894946357652146107782722500 * q^25 - 49284147216613914166808777620995485562632832 * q^26 - 128445331744621566171958781429920350730764000 * q^27 - 790757236315065917044952859738895406239744000 * q^28 + 6672429803576117328528976307882755467518520 * q^29 + 957801420237120366977197975859498893217318400 * q^30 + 3262752943509002552517145952336046015034252928 * q^31 + 29552482936847865082009297897367834619543552000 * q^32 + 80589779417942769949681652178013443031895736000 * q^33 + 39802528145537101299701822666373970434557030016 * q^34 + 94932144900835792457443003213138857525722942400 * q^35 - 491545590287100270921289917536068279191068430336 * q^36 - 710312106544219153529408139748985993336062057000 * q^37 - 6572443117826428556368685861295549874330331616000 * q^38 - 5385266212680187341486607570713939645234734498976 * q^39 - 6935278763126032494337494583468084555036360704000 * q^40 + 16359554122032268527799184148245398149035867491368 * q^41 + 150386101138325781804352908808507125636957747456000 * q^42 + 75844732497959094206655920598930086763379517030000 * q^43 + 152692943245212279510621538861388707588508390670336 * q^44 + 60471855189024852796163743559032445559203109252600 * q^45 - 150345409740296355038882940983341438053393810381312 * q^46 - 2164761335188781225334544122222333542985932701416000 * q^47 - 8471840837080202754288377889649147778899824869376000 * q^48 + 1523957834189526415441239854498433329172794287478628 * q^49 - 3735723416225956799610935352239535395426733934920000 * q^50 + 20623083900467721702728328179464369078682764374557088 * q^51 + 34115942043101628674837973043915515701891779834880000 * q^52 + 84459499120263342936174700173047508278523729350943000 * q^53 + 205362219171375312837640062328590989381764073364257280 * q^54 - 18917852463295959783361213875825060571992233753013600 * q^55 - 895534119833025861281009767571957442822737699977297920 * q^56 - 485813603178903589098646017006457442516302171963128000 * q^57 - 429363306259072204179262197105630766591459158948624000 * q^58 - 2147121767784312006347793068275982647255821920255956560 * q^59 + 1658171820897328745993674937960453150336599512561254400 * q^60 + 4291528347018103219994434901020564652244372107292350648 * q^61 + 5191805357629316458585917076609024961942995611849984000 * q^62 + 17756655477174334714938166349329711292289832299011892000 * q^63 + 19881300699476524526504677072626341971094030107078033408 * q^64 - 4054154514265281184405976695522203389642082195785626800 * q^65 - 32579846274793617809975626285379717775321739705823437824 * q^66 - 151638661420806044794238226134660440129857438609787534000 * q^67 - 199797070973791372723379406738475848419062088637699072000 * q^68 - 65270530395832676459014735893839800626266812319535206016 * q^69 + 164781406287311752350371419457017830072394299112015948800 * q^70 + 266771587169907679430401079119295396456876119234283837088 * q^71 + 1006655875418141826396652361065366291089164315936882688000 * q^72 + 436772697766954812846449565799176070423143504803837369000 * q^73 + 2727029156290392414014538532434064649250131670424597597056 * q^74 + 2289194205716179194928001449493608972625299546441763790000 * q^75 - 9182670231472830669367329606616577285345108294701612810240 * q^76 - 6239400117692696801885467207245334802759585122139865360000 * q^77 - 6237267939864197833204910438280167481125291167753285440000 * q^78 - 2171516124052566840962201891051143348431163494068568095680 * q^79 - 8149820448667982873535456900485215194289704343083732172800 * q^80 + 1640511243926006283516650766266777082670562411829996387684 * q^81 + 41751906507711557992784780576518459967807480604061450704000 * q^82 - 19301891587488226996497021336363284746717620338719475718000 * q^83 + 268654655987364118570161060572621663532678550361090391146496 * q^84 + 23823437828438802480990474713115034607148974715085027364400 * q^85 - 71538345696620408289043701603344533132955103857012068207872 * q^86 - 259922121232275661156614167150119002145659028099089961092000 * q^87 - 453611870852754620593515203785357874778152109551115829248000 * q^88 - 606362068644618673179710823370293144593411608656909401212440 * q^89 - 125913175325979481569463842346677014059444686232867490908800 * q^90 - 452168126000372891758634520948160370052422021946362710252352 * q^91 + 1607280224434271875135145612458728092411753130630908891136000 * q^92 - 430218455333355948319021852668117857154414287268428877504000 * q^93 + 6446155892605066539979931910636020289279531063064695408331776 * q^94 + 1105507768048183718212260841102299501129184381013780070972000 * q^95 + 1502030317602264351709698333215472188025674435863914750148608 * q^96 - 8084830239737746227548751167926342536453719541548201116411000 * q^97 + 17015397362965438448003410858883076702895502959466609182344000 * q^98 - 31217771142326421061022583768766679122998622357827944348749776 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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