LMFDB - Embedded newform 1.62.a.a.1.1

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			1.1
Root			$1.21599e7$ 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)

$f(q)$	$=$	$q-2.04812e9 q^{2} +1.78996e14 q^{3} +1.88894e18 q^{4} -2.27994e20 q^{5} -3.66606e23 q^{6} -4.42559e25 q^{7} +8.53860e26 q^{8} -9.51338e28 q^{9} +O(q^{10})$	\(q-2.04812e9 q^{2} +1.78996e14 q^{3} +1.88894e18 q^{4} -2.27994e20 q^{5} -3.66606e23 q^{6} -4.42559e25 q^{7} +8.53860e26 q^{8} -9.51338e28 q^{9} +4.66958e29 q^{10} +7.45476e31 q^{11} +3.38114e32 q^{12} +1.57894e34 q^{13} +9.06412e34 q^{14} -4.08100e34 q^{15} -6.10441e36 q^{16} -3.16443e37 q^{17} +1.94845e38 q^{18} +4.06426e38 q^{19} -4.30667e38 q^{20} -7.92164e39 q^{21} -1.52682e41 q^{22} +5.44945e40 q^{23} +1.52838e41 q^{24} -4.28483e42 q^{25} -3.23385e43 q^{26} -3.97922e43 q^{27} -8.35968e43 q^{28} +2.13683e44 q^{29} +8.35837e43 q^{30} -2.29937e45 q^{31} +1.05337e46 q^{32} +1.33437e46 q^{33} +6.48113e46 q^{34} +1.00901e46 q^{35} -1.79702e47 q^{36} -1.07009e48 q^{37} -8.32407e47 q^{38} +2.82624e48 q^{39} -1.94675e47 q^{40} -1.40249e49 q^{41} +1.62244e49 q^{42} +5.79966e49 q^{43} +1.40816e50 q^{44} +2.16899e49 q^{45} -1.11611e50 q^{46} -1.51708e51 q^{47} -1.09267e51 q^{48} -1.59757e51 q^{49} +8.77583e51 q^{50} -5.66421e51 q^{51} +2.98252e52 q^{52} -4.58000e52 q^{53} +8.14991e52 q^{54} -1.69964e52 q^{55} -3.77883e52 q^{56} +7.27487e52 q^{57} -4.37649e53 q^{58} -1.78535e54 q^{59} -7.70878e52 q^{60} +4.41900e54 q^{61} +4.70938e54 q^{62} +4.21023e54 q^{63} -7.49842e54 q^{64} -3.59987e54 q^{65} -2.73296e55 q^{66} +2.75737e55 q^{67} -5.97743e55 q^{68} +9.75431e54 q^{69} -2.06656e55 q^{70} +1.08638e56 q^{71} -8.12310e55 q^{72} -1.85098e56 q^{73} +2.19168e57 q^{74} -7.66968e56 q^{75} +7.67715e56 q^{76} -3.29917e57 q^{77} -5.78847e57 q^{78} -4.07387e57 q^{79} +1.39177e57 q^{80} +4.97584e57 q^{81} +2.87246e58 q^{82} +2.46467e58 q^{83} -1.49635e58 q^{84} +7.21470e57 q^{85} -1.18784e59 q^{86} +3.82485e58 q^{87} +6.36532e58 q^{88} -6.63380e57 q^{89} -4.44234e58 q^{90} -6.98772e59 q^{91} +1.02937e59 q^{92} -4.11578e59 q^{93} +3.10715e60 q^{94} -9.26624e58 q^{95} +1.88549e60 q^{96} -2.67905e60 q^{97} +3.27201e60 q^{98} -7.09200e60 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.04812e9	−1.34878	−0.674388	−	0.738377i	$-0.735593\pi$
$2$	−2.04812e9	−1.34878	−0.674388	+	0.738377i	$0.735593\pi$
$3$	1.78996e14	0.501933	0.250967	−	0.967996i	$-0.419252\pi$
$3$	1.78996e14	0.501933	0.250967	+	0.967996i	$0.419252\pi$
$4$	1.88894e18	0.819198
$5$	−2.27994e20	−0.109481	−0.0547403	−	0.998501i	$-0.517433\pi$
$5$	−2.27994e20	−0.109481	−0.0547403	+	0.998501i	$0.517433\pi$
$6$	−3.66606e23	−0.676996
$7$	−4.42559e25	−0.742131	−0.371066	−	0.928607i	$-0.621007\pi$
$7$	−4.42559e25	−0.742131	−0.371066	+	0.928607i	$0.621007\pi$
$8$	8.53860e26	0.243861
$9$	−9.51338e28	−0.748063
$10$	4.66958e29	0.147665
$11$	7.45476e31	1.28812	0.644061	−	0.764974i	$-0.277248\pi$
$11$	7.45476e31	1.28812	0.644061	+	0.764974i	$0.277248\pi$
$12$	3.38114e32	0.411183
$13$	1.57894e34	1.67145	0.835723	−	0.549151i	$-0.185049\pi$
$13$	1.57894e34	1.67145	0.835723	+	0.549151i	$0.185049\pi$
$14$	9.06412e34	1.00097
$15$	−4.08100e34	−0.0549520
$16$	−6.10441e36	−1.14811
$17$	−3.16443e37	−0.936706	−0.468353	−	0.883541i	$-0.655152\pi$
$17$	−3.16443e37	−0.936706	−0.468353	+	0.883541i	$0.655152\pi$
$18$	1.94845e38	1.00897
$19$	4.06426e38	0.404572	0.202286	−	0.979326i	$-0.435163\pi$
$19$	4.06426e38	0.404572	0.202286	+	0.979326i	$0.435163\pi$
$20$	−4.30667e38	−0.0896864
$21$	−7.92164e39	−0.372500
$22$	−1.52682e41	−1.73739
$23$	5.44945e40	0.159828	0.0799141	−	0.996802i	$-0.474535\pi$
$23$	5.44945e40	0.159828	0.0799141	+	0.996802i	$0.474535\pi$
$24$	1.52838e41	0.122402
$25$	−4.28483e42	−0.988014
$26$	−3.23385e43	−2.25441
$27$	−3.97922e43	−0.877411
$28$	−8.35968e43	−0.607953
$29$	2.13683e44	0.532883	0.266442	−	0.963851i	$-0.414152\pi$
$29$	2.13683e44	0.532883	0.266442	+	0.963851i	$0.414152\pi$
$30$	8.35837e43	0.0741179
$31$	−2.29937e45	−0.750027	−0.375013	−	0.927019i	$-0.622362\pi$
$31$	−2.29937e45	−0.750027	−0.375013	+	0.927019i	$0.622362\pi$
$32$	1.05337e46	1.30469
$33$	1.33437e46	0.646551
$34$	6.48113e46	1.26341
$35$	1.00901e46	0.0812490
$36$	−1.79702e47	−0.612812
$37$	−1.07009e48	−1.58223	−0.791114	−	0.611668i	$-0.790499\pi$
$37$	−1.07009e48	−1.58223	−0.791114	+	0.611668i	$0.790499\pi$
$38$	−8.32407e47	−0.545678
$39$	2.82624e48	0.838954
$40$	−1.94675e47	−0.0266980
$41$	−1.40249e49	−0.905714	−0.452857	−	0.891583i	$-0.649595\pi$
$41$	−1.40249e49	−0.905714	−0.452857	+	0.891583i	$0.649595\pi$
$42$	1.62244e49	0.502419
$43$	5.79966e49	0.876223	0.438111	−	0.898921i	$-0.355648\pi$
$43$	5.79966e49	0.876223	0.438111	+	0.898921i	$0.355648\pi$
$44$	1.40816e50	1.05523
$45$	2.16899e49	0.0818984
$46$	−1.11611e50	−0.215573
$47$	−1.51708e51	−1.52063	−0.760314	−	0.649555i	$-0.774955\pi$
$47$	−1.51708e51	−1.52063	−0.760314	+	0.649555i	$0.774955\pi$
$48$	−1.09267e51	−0.576276
$49$	−1.59757e51	−0.449242
$50$	8.77583e51	1.33261
$51$	−5.66421e51	−0.470164
$52$	2.98252e52	1.36925
$53$	−4.58000e52	−1.17612	−0.588060	−	0.808817i	$-0.700108\pi$
$53$	−4.58000e52	−1.17612	−0.588060	+	0.808817i	$0.700108\pi$
$54$	8.14991e52	1.18343
$55$	−1.69964e52	−0.141024
$56$	−3.77883e52	−0.180977
$57$	7.27487e52	0.203068
$58$	−4.37649e53	−0.718740
$59$	−1.78535e54	−1.74075	−0.870374	−	0.492391i	$-0.836123\pi$
$59$	−1.78535e54	−1.74075	−0.870374	+	0.492391i	$0.836123\pi$
$60$	−7.70878e52	−0.0450166
$61$	4.41900e54	1.55871	0.779353	−	0.626585i	$-0.215548\pi$
$61$	4.41900e54	1.55871	0.779353	+	0.626585i	$0.215548\pi$
$62$	4.70938e54	1.01162
$63$	4.21023e54	0.555161
$64$	−7.49842e54	−0.611618
$65$	−3.59987e54	−0.182991
$66$	−2.73296e55	−0.872053
$67$	2.75737e55	0.556178	0.278089	−	0.960555i	$-0.410299\pi$
$67$	2.75737e55	0.556178	0.278089	+	0.960555i	$0.410299\pi$
$68$	−5.97743e55	−0.767348
$69$	9.75431e54	0.0802231
$70$	−2.06656e55	−0.109587
$71$	1.08638e56	0.373768	0.186884	−	0.982382i	$-0.440161\pi$
$71$	1.08638e56	0.373768	0.186884	+	0.982382i	$0.440161\pi$
$72$	−8.12310e55	−0.182423
$73$	−1.85098e56	−0.272932	−0.136466	−	0.990645i	$-0.543574\pi$
$73$	−1.85098e56	−0.272932	−0.136466	+	0.990645i	$0.543574\pi$
$74$	2.19168e57	2.13407
$75$	−7.66968e56	−0.495917
$76$	7.67715e56	0.331425
$77$	−3.29917e57	−0.955955
$78$	−5.78847e57	−1.13156
$79$	−4.07387e57	−0.539984	−0.269992	−	0.962863i	$-0.587021\pi$
$79$	−4.07387e57	−0.539984	−0.269992	+	0.962863i	$0.587021\pi$
$80$	1.39177e57	0.125696
$81$	4.97584e57	0.307662
$82$	2.87246e58	1.22161
$83$	2.46467e58	0.724231	0.362115	−	0.932133i	$-0.382055\pi$
$83$	2.46467e58	0.724231	0.362115	+	0.932133i	$0.382055\pi$
$84$	−1.49635e58	−0.305152
$85$	7.21470e57	0.102551
$86$	−1.18784e59	−1.18183
$87$	3.82485e58	0.267472
$88$	6.36532e58	0.314122
$89$	−6.63380e57	−0.0231936	−0.0115968	−	0.999933i	$-0.503691\pi$
$89$	−6.63380e57	−0.0231936	−0.0115968	+	0.999933i	$0.503691\pi$
$90$	−4.44234e58	−0.110463
$91$	−6.98772e59	−1.24043
$92$	1.02937e59	0.130931
$93$	−4.11578e59	−0.376463
$94$	3.10715e60	2.05099
$95$	−9.26624e58	−0.0442928
$96$	1.88549e60	0.654865
$97$	−2.67905e60	−0.678333	−0.339166	−	0.940726i	$-0.610145\pi$
$97$	−2.67905e60	−0.678333	−0.339166	+	0.940726i	$0.610145\pi$
$98$	3.27201e60	0.605926
$99$	−7.09200e60	−0.963596
$100$	−8.09380e60	−0.809380
$101$	−1.78180e61	−1.31540	−0.657699	−	0.753281i	$-0.728470\pi$
$101$	−1.78180e61	−1.31540	−0.657699	+	0.753281i	$0.728470\pi$
$102$	1.16010e61	0.634146
$103$	2.23869e61	0.908778	0.454389	−	0.890803i	$-0.349858\pi$
$103$	2.23869e61	0.908778	0.454389	+	0.890803i	$0.349858\pi$
$104$	1.34819e61	0.407600
$105$	1.80608e60	0.0407816
$106$	9.38038e61	1.58632
$107$	−1.07119e62	−1.36038	−0.680192	−	0.733034i	$-0.738104\pi$
$107$	−1.07119e62	−1.36038	−0.680192	+	0.733034i	$0.738104\pi$
$108$	−7.51652e61	−0.718774
$109$	1.00368e62	0.724585	0.362292	−	0.932064i	$-0.381994\pi$
$109$	1.00368e62	0.724585	0.362292	+	0.932064i	$0.381994\pi$
$110$	3.48106e61	0.190210
$111$	−1.91543e62	−0.794173
$112$	2.70156e62	0.852050
$113$	−4.77242e62	−1.14775	−0.573874	−	0.818944i	$-0.694560\pi$
$113$	−4.77242e62	−1.14775	−0.573874	+	0.818944i	$0.694560\pi$
$114$	−1.48998e62	−0.273894
$115$	−1.24244e61	−0.0174981
$116$	4.03636e62	0.436537
$117$	−1.50210e63	−1.25035
$118$	3.65660e63	2.34788
$119$	1.40045e63	0.695159
$120$	−3.48460e61	−0.0134006
$121$	2.20805e63	0.659257
$122$	−9.05064e63	−2.10235
$123$	−2.51040e63	−0.454608
$124$	−4.34338e63	−0.614421
$125$	1.96568e63	0.217649
$126$	−8.62304e63	−0.748788
$127$	2.87823e64	1.96386	0.981932	−	0.189235i	$-0.0606007\pi$
$127$	2.87823e64	1.96386	0.981932	+	0.189235i	$0.0606007\pi$
$128$	−8.93139e63	−0.479750
$129$	1.03812e64	0.439805
$130$	7.37297e63	0.246814
$131$	−3.69910e63	−0.0980217	−0.0490108	−	0.998798i	$-0.515607\pi$
$131$	−3.69910e63	−0.0980217	−0.0490108	+	0.998798i	$0.515607\pi$
$132$	2.52056e64	0.529653
$133$	−1.79867e64	−0.300246
$134$	−5.64742e64	−0.750160
$135$	9.07236e63	0.0960595
$136$	−2.70198e64	−0.228426
$137$	4.88169e64	0.330060	0.165030	−	0.986289i	$-0.447228\pi$
$137$	4.88169e64	0.330060	0.165030	+	0.986289i	$0.447228\pi$
$138$	−1.99780e64	−0.108203
$139$	−1.13820e65	−0.494614	−0.247307	−	0.968937i	$-0.579546\pi$
$139$	−1.13820e65	−0.494614	−0.247307	+	0.968937i	$0.579546\pi$
$140$	1.90595e64	0.0665591
$141$	−2.71551e65	−0.763254
$142$	−2.22504e65	−0.504130
$143$	1.17706e66	2.15303
$144$	5.80736e65	0.858861
$145$	−4.87184e64	−0.0583404
$146$	3.79102e65	0.368124
$147$	−2.85959e65	−0.225489
$148$	−2.02135e66	−1.29616
$149$	−2.13216e66	−1.11337	−0.556684	−	0.830724i	$-0.687927\pi$
$149$	−2.13216e66	−1.11337	−0.556684	+	0.830724i	$0.687927\pi$
$150$	1.57084e66	0.668881
$151$	−3.70988e66	−1.28992	−0.644961	−	0.764216i	$-0.723126\pi$
$151$	−3.70988e66	−1.28992	−0.644961	+	0.764216i	$0.723126\pi$
$152$	3.47031e65	0.0986594
$153$	3.01044e66	0.700715
$154$	6.75709e66	1.28937
$155$	5.24241e65	0.0821134
$156$	5.33860e66	0.687270
$157$	−1.01374e67	−1.07396	−0.536979	−	0.843596i	$-0.680435\pi$
$157$	−1.01374e67	−1.07396	−0.536979	+	0.843596i	$0.680435\pi$
$158$	8.34376e66	0.728317
$159$	−8.19803e66	−0.590333
$160$	−2.40161e66	−0.142838
$161$	−2.41170e66	−0.118613
$162$	−1.01911e67	−0.414967
$163$	3.38270e67	1.14167	0.570836	−	0.821064i	$-0.306619\pi$
$163$	3.38270e67	1.14167	0.570836	+	0.821064i	$0.306619\pi$
$164$	−2.64922e67	−0.741959
$165$	−3.04229e66	−0.0707848
$166$	−5.04793e67	−0.976825
$167$	−1.22693e67	−0.197682	−0.0988411	−	0.995103i	$-0.531514\pi$
$167$	−1.22693e67	−0.197682	−0.0988411	+	0.995103i	$0.531514\pi$
$168$	−6.76397e66	−0.0908382
$169$	1.60067e68	1.79373
$170$	−1.47765e67	−0.138319
$171$	−3.86648e67	−0.302646
$172$	1.09552e68	0.717800
$173$	1.07923e68	0.592528	0.296264	−	0.955106i	$-0.404259\pi$
$173$	1.07923e68	0.592528	0.296264	+	0.955106i	$0.404259\pi$
$174$	−7.83375e67	−0.360760
$175$	1.89629e68	0.733236
$176$	−4.55069e68	−1.47891
$177$	−3.19570e68	−0.873739
$178$	1.35868e67	0.0312829
$179$	−6.21601e68	−1.20641	−0.603204	−	0.797587i	$-0.706110\pi$
$179$	−6.21601e68	−1.20641	−0.603204	+	0.797587i	$0.706110\pi$
$180$	4.09710e67	0.0670911
$181$	1.52963e68	0.211539	0.105770	−	0.994391i	$-0.466269\pi$
$181$	1.52963e68	0.211539	0.105770	+	0.994391i	$0.466269\pi$
$182$	1.43117e69	1.67307
$183$	7.90985e68	0.782367
$184$	4.65307e67	0.0389759
$185$	2.43974e68	0.173223
$186$	8.42961e68	0.507765
$187$	−2.35901e69	−1.20659
$188$	−2.86567e69	−1.24570
$189$	1.76104e69	0.651154
$190$	1.89783e68	0.0597411
$191$	2.62596e69	0.704322	0.352161	−	0.935939i	$-0.385447\pi$
$191$	2.62596e69	0.704322	0.352161	+	0.935939i	$0.385447\pi$
$192$	−1.34219e69	−0.306991
$193$	−6.76456e69	−1.32051	−0.660255	−	0.751042i	$-0.729552\pi$
$193$	−6.76456e69	−1.32051	−0.660255	+	0.751042i	$0.729552\pi$
$194$	5.48701e69	0.914919
$195$	−6.44364e68	−0.0918493
$196$	−3.01772e69	−0.368018
$197$	−7.24378e69	−0.756389	−0.378195	−	0.925726i	$-0.623455\pi$
$197$	−7.24378e69	−0.756389	−0.378195	+	0.925726i	$0.623455\pi$
$198$	1.45252e70	1.29968
$199$	9.15268e68	0.0702311	0.0351155	−	0.999383i	$-0.488820\pi$
$199$	9.15268e68	0.0702311	0.0351155	+	0.999383i	$0.488820\pi$
$200$	−3.65864e69	−0.240938
$201$	4.93559e69	0.279164
$202$	3.64934e70	1.77418
$203$	−9.45674e69	−0.395469
$204$	−1.06994e70	−0.385158
$205$	3.19758e69	0.0991581
$206$	−4.58509e70	−1.22574
$207$	−5.18427e69	−0.119562
$208$	−9.63848e70	−1.91901
$209$	3.02981e70	0.521138
$210$	−3.69907e69	−0.0550052
$211$	1.42797e71	1.83698	0.918491	−	0.395443i	$-0.129409\pi$
$211$	1.42797e71	1.83698	0.918491	+	0.395443i	$0.129409\pi$
$212$	−8.65136e70	−0.963475
$213$	1.94458e70	0.187607
$214$	2.19392e71	1.83485
$215$	−1.32228e70	−0.0959294
$216$	−3.39770e70	−0.213966
$217$	1.01761e71	0.556618
$218$	−2.05566e71	−0.977303
$219$	−3.31318e70	−0.136993
$220$	−3.21052e70	−0.115527
$221$	−4.99644e71	−1.56565
$222$	3.92302e71	1.07116
$223$	−7.24022e70	−0.172367	−0.0861834	−	0.996279i	$-0.527467\pi$
$223$	−7.24022e70	−0.172367	−0.0861834	+	0.996279i	$0.527467\pi$
$224$	−4.66177e71	−0.968248
$225$	4.07632e71	0.739097
$226$	9.77448e71	1.54805
$227$	−7.90928e71	−1.09483	−0.547417	−	0.836860i	$-0.684389\pi$
$227$	−7.90928e71	−1.09483	−0.547417	+	0.836860i	$0.684389\pi$
$228$	1.37418e71	0.166353
$229$	−2.69486e71	−0.285466	−0.142733	−	0.989761i	$-0.545589\pi$
$229$	−2.69486e71	−0.285466	−0.142733	+	0.989761i	$0.545589\pi$
$230$	2.54466e70	0.0236010
$231$	−5.90539e71	−0.479825
$232$	1.82456e71	0.129949
$233$	1.65753e72	1.03539	0.517696	−	0.855565i	$-0.326790\pi$
$233$	1.65753e72	1.03539	0.517696	+	0.855565i	$0.326790\pi$
$234$	3.07648e72	1.68644
$235$	3.45884e71	0.166479
$236$	−3.37242e72	−1.42602
$237$	−7.29207e71	−0.271036
$238$	−2.86828e72	−0.937614
$239$	−1.37118e72	−0.394421	−0.197210	−	0.980361i	$-0.563188\pi$
$239$	−1.37118e72	−0.394421	−0.197210	+	0.980361i	$0.563188\pi$
$240$	2.49121e71	0.0630910
$241$	−3.48714e72	−0.777946	−0.388973	−	0.921249i	$-0.627170\pi$
$241$	−3.48714e72	−0.777946	−0.388973	+	0.921249i	$0.627170\pi$
$242$	−4.52234e72	−0.889191
$243$	5.95117e72	1.03184
$244$	8.34725e72	1.27689
$245$	3.64236e71	0.0491833
$246$	5.14159e72	0.613164
$247$	6.41720e72	0.676221
$248$	−1.96334e72	−0.182902
$249$	4.41167e72	0.363515
$250$	−4.02594e72	−0.293560
$251$	−1.53704e73	−0.992283	−0.496142	−	0.868242i	$-0.665250\pi$
$251$	−1.53704e73	−0.992283	−0.496142	+	0.868242i	$0.665250\pi$
$252$	7.95288e72	0.454787
$253$	4.06243e72	0.205878
$254$	−5.89495e73	−2.64881
$255$	1.29140e72	0.0514739
$256$	3.55827e73	1.25869
$257$	7.08695e72	0.222587	0.111293	−	0.993788i	$-0.464501\pi$
$257$	7.08695e72	0.222587	0.111293	+	0.993788i	$0.464501\pi$
$258$	−2.12619e73	−0.593199
$259$	4.73579e73	1.17422
$260$	−6.79996e72	−0.149906
$261$	−2.03285e73	−0.398630
$262$	7.57620e72	0.132209
$263$	2.21707e72	0.0344453	0.0172227	−	0.999852i	$-0.494518\pi$
$263$	2.21707e72	0.0344453	0.0172227	+	0.999852i	$0.494518\pi$
$264$	1.13937e73	0.157668
$265$	1.04421e73	0.128762
$266$	3.68389e73	0.404964
$267$	−1.18743e72	−0.0116416
$268$	5.20852e73	0.455620
$269$	−5.72433e73	−0.446972	−0.223486	−	0.974707i	$-0.571744\pi$
$269$	−5.72433e73	−0.446972	−0.223486	+	0.974707i	$0.571744\pi$
$270$	−1.85813e73	−0.129563
$271$	−1.25491e74	−0.781715	−0.390858	−	0.920451i	$-0.627821\pi$
$271$	−1.25491e74	−0.781715	−0.390858	+	0.920451i	$0.627821\pi$
$272$	1.93170e74	1.07544
$273$	−1.25078e74	−0.622614
$274$	−9.99828e73	−0.445177
$275$	−3.19424e74	−1.27268
$276$	1.84253e73	0.0657186
$277$	−9.29554e73	−0.296922	−0.148461	−	0.988918i	$-0.547432\pi$
$277$	−9.29554e73	−0.296922	−0.148461	+	0.988918i	$0.547432\pi$
$278$	2.33116e74	0.667124
$279$	2.18748e74	0.561068
$280$	8.61549e72	0.0198134
$281$	6.92706e74	1.42891	0.714457	−	0.699680i	$-0.246674\pi$
$281$	6.92706e74	1.42891	0.714457	+	0.699680i	$0.246674\pi$
$282$	5.56169e74	1.02946
$283$	2.76298e73	0.0459083	0.0229542	−	0.999737i	$-0.492693\pi$
$283$	2.76298e73	0.0459083	0.0229542	+	0.999737i	$0.492693\pi$
$284$	2.05211e74	0.306190
$285$	−1.65862e73	−0.0222320
$286$	−2.41076e75	−2.90395
$287$	6.20682e74	0.672158
$288$	−1.00211e75	−0.975988
$289$	−1.39897e74	−0.122581
$290$	9.97811e73	0.0786882
$291$	−4.79540e74	−0.340478
$292$	−3.49639e74	−0.223585
$293$	2.78327e75	1.60359	0.801794	−	0.597601i	$-0.203879\pi$
$293$	2.78327e75	1.60359	0.801794	+	0.597601i	$0.203879\pi$
$294$	5.85679e74	0.304135
$295$	4.07047e74	0.190578
$296$	−9.13710e74	−0.385844
$297$	−2.96641e75	−1.13021
$298$	4.36692e75	1.50169
$299$	8.60433e74	0.267144
$300$	−1.44876e75	−0.406254
$301$	−2.56669e75	−0.650272
$302$	7.59828e75	1.73982
$303$	−3.18936e75	−0.660242
$304$	−2.48099e75	−0.464494
$305$	−1.00750e75	−0.170648
$306$	−6.16574e75	−0.945109
$307$	1.07115e76	1.48637	0.743187	−	0.669084i	$-0.233313\pi$
$307$	1.07115e76	1.48637	0.743187	+	0.669084i	$0.233313\pi$
$308$	−6.23194e75	−0.783117
$309$	4.00716e75	0.456146
$310$	−1.07371e75	−0.110753
$311$	−1.92669e76	−1.80144	−0.900719	−	0.434402i	$-0.856960\pi$
$311$	−1.92669e76	−1.80144	−0.900719	+	0.434402i	$0.856960\pi$
$312$	2.41321e75	0.204588
$313$	−7.23121e75	−0.556043	−0.278022	−	0.960575i	$-0.589679\pi$
$313$	−7.23121e75	−0.556043	−0.278022	+	0.960575i	$0.589679\pi$
$314$	2.07626e76	1.44853
$315$	−9.59905e74	−0.0607794
$316$	−7.69530e75	−0.442354
$317$	2.35562e76	1.22969	0.614847	−	0.788646i	$-0.289218\pi$
$317$	2.35562e76	1.22969	0.614847	+	0.788646i	$0.289218\pi$
$318$	1.67905e76	0.796228
$319$	1.59296e76	0.686418
$320$	1.70959e75	0.0669603
$321$	−1.91739e76	−0.682822
$322$	4.93945e75	0.159983
$323$	−1.28611e76	−0.378965
$324$	9.39908e75	0.252036
$325$	−6.76547e76	−1.65141
$326$	−6.92816e76	−1.53986
$327$	1.79656e76	0.363693
$328$	−1.19753e76	−0.220868
$329$	6.71396e76	1.12851
$330$	6.23096e75	0.0954729
$331$	−4.64715e76	−0.649282	−0.324641	−	0.945837i	$-0.605243\pi$
$331$	−4.64715e76	−0.649282	−0.324641	+	0.945837i	$0.605243\pi$
$332$	4.65562e76	0.593289
$333$	1.01802e77	1.18361
$334$	2.51290e76	0.266629
$335$	−6.28663e75	−0.0608907
$336$	4.83569e76	0.427672
$337$	2.10365e77	1.69927	0.849634	−	0.527372i	$-0.176823\pi$
$337$	2.10365e77	1.69927	0.849634	+	0.527372i	$0.176823\pi$
$338$	−3.27837e77	−2.41935
$339$	−8.54246e76	−0.576092
$340$	1.36282e76	0.0840098
$341$	−1.71412e77	−0.966126
$342$	7.91901e76	0.408201
$343$	2.28083e77	1.07553
$344$	4.95210e76	0.213676
$345$	−2.22392e75	−0.00878288
$346$	−2.21040e77	−0.799188
$347$	−2.00534e76	−0.0663956	−0.0331978	−	0.999449i	$-0.510569\pi$
$347$	−2.00534e76	−0.0663956	−0.0331978	+	0.999449i	$0.510569\pi$
$348$	7.22493e76	0.219112
$349$	−2.60527e76	−0.0723897	−0.0361948	−	0.999345i	$-0.511524\pi$
$349$	−2.60527e76	−0.0723897	−0.0361948	+	0.999345i	$0.511524\pi$
$350$	−3.88382e77	−0.988971
$351$	−6.28293e77	−1.46655
$352$	7.85261e77	1.68059
$353$	1.11807e76	0.0219452	0.0109726	−	0.999940i	$-0.496507\pi$
$353$	1.11807e76	0.0219452	0.0109726	+	0.999940i	$0.496507\pi$
$354$	6.54517e77	1.17848
$355$	−2.47688e76	−0.0409204
$356$	−1.25309e76	−0.0190001
$357$	2.50675e77	0.348923
$358$	1.27311e78	1.62718
$359$	−6.93433e77	−0.813999	−0.407000	−	0.913428i	$-0.633425\pi$
$359$	−6.93433e77	−0.813999	−0.407000	+	0.913428i	$0.633425\pi$
$360$	1.85201e76	0.0199718
$361$	−8.44001e77	−0.836321
$362$	−3.13287e77	−0.285319
$363$	3.95233e77	0.330903
$364$	−1.31994e78	−1.01616
$365$	4.22011e76	0.0298807
$366$	−1.62003e78	−1.05524
$367$	−4.69690e77	−0.281511	−0.140756	−	0.990044i	$-0.544953\pi$
$367$	−4.69690e77	−0.281511	−0.140756	+	0.990044i	$0.544953\pi$
$368$	−3.32657e77	−0.183501
$369$	1.33424e78	0.677531
$370$	−4.99688e77	−0.233640
$371$	2.02692e78	0.872835
$372$	−7.77448e77	−0.308398
$373$	2.32868e78	0.851118	0.425559	−	0.904931i	$-0.360078\pi$
$373$	2.32868e78	0.851118	0.425559	+	0.904931i	$0.360078\pi$
$374$	4.83152e78	1.62742
$375$	3.51849e77	0.109245
$376$	−1.29537e78	−0.370822
$377$	3.37393e78	0.890686
$378$	−3.60681e78	−0.878261
$379$	−7.98852e78	−1.79461	−0.897306	−	0.441409i	$-0.854479\pi$
$379$	−7.98852e78	−1.79461	−0.897306	+	0.441409i	$0.854479\pi$
$380$	−1.75034e77	−0.0362846
$381$	5.15192e78	0.985728
$382$	−5.37828e78	−0.949973
$383$	−3.22231e78	−0.525539	−0.262770	−	0.964859i	$-0.584636\pi$
$383$	−3.22231e78	−0.525539	−0.262770	+	0.964859i	$0.584636\pi$
$384$	−1.59869e78	−0.240802
$385$	7.52189e77	0.104659
$386$	1.38546e79	1.78107
$387$	−5.51743e78	−0.655470
$388$	−5.06057e78	−0.555689
$389$	4.01485e77	0.0407574	0.0203787	−	0.999792i	$-0.493513\pi$
$389$	4.01485e77	0.0407574	0.0203787	+	0.999792i	$0.493513\pi$
$390$	1.31973e78	0.123884
$391$	−1.72444e78	−0.149712
$392$	−1.36410e78	−0.109552
$393$	−6.62126e77	−0.0492003
$394$	1.48361e79	1.02020
$395$	9.28815e77	0.0591178
$396$	−1.33964e79	−0.789377
$397$	1.01434e79	0.553444	0.276722	−	0.960950i	$-0.410752\pi$
$397$	1.01434e79	0.553444	0.276722	+	0.960950i	$0.410752\pi$
$398$	−1.87458e78	−0.0947260
$399$	−3.21956e78	−0.150703
$400$	2.61564e79	1.13435
$401$	3.51734e79	1.41355	0.706775	−	0.707438i	$-0.250149\pi$
$401$	3.51734e79	1.41355	0.706775	+	0.707438i	$0.250149\pi$
$402$	−1.01087e79	−0.376530
$403$	−3.63056e79	−1.25363
$404$	−3.36572e79	−1.07757
$405$	−1.13446e78	−0.0336830
$406$	1.93685e79	0.533399
$407$	−7.97729e79	−2.03810
$408$	−4.83645e78	−0.114655
$409$	−1.93067e78	−0.0424763	−0.0212381	−	0.999774i	$-0.506761\pi$
$409$	−1.93067e78	−0.0424763	−0.0212381	+	0.999774i	$0.506761\pi$
$410$	−6.54901e78	−0.133742
$411$	8.73805e78	0.165668
$412$	4.22875e79	0.744469
$413$	7.90120e79	1.29186
$414$	1.06180e79	0.161262
$415$	−5.61929e78	−0.0792892
$416$	1.66320e80	2.18071
$417$	−2.03733e79	−0.248263
$418$	−6.20540e79	−0.702899
$419$	−4.55786e79	−0.479991	−0.239995	−	0.970774i	$-0.577146\pi$
$419$	−4.55786e79	−0.479991	−0.239995	+	0.970774i	$0.577146\pi$
$420$	3.41159e78	0.0334082
$421$	1.05786e79	0.0963442	0.0481721	−	0.998839i	$-0.484660\pi$
$421$	1.05786e79	0.0963442	0.0481721	+	0.998839i	$0.484660\pi$
$422$	−2.92465e80	−2.47768
$423$	1.44325e80	1.13753
$424$	−3.91068e79	−0.286810
$425$	1.35590e80	0.925479
$426$	−3.98273e79	−0.253040
$427$	−1.95567e80	−1.15676
$428$	−2.02342e80	−1.11442
$429$	2.10689e80	1.08068
$430$	2.70819e79	0.129387
$431$	−9.69521e79	−0.431520	−0.215760	−	0.976446i	$-0.569223\pi$
$431$	−9.69521e79	−0.431520	−0.215760	+	0.976446i	$0.569223\pi$
$432$	2.42908e80	1.00737
$433$	3.23814e80	1.25146	0.625728	−	0.780042i	$-0.284802\pi$
$433$	3.23814e80	1.25146	0.625728	+	0.780042i	$0.284802\pi$
$434$	−2.08418e80	−0.750754
$435$	−8.72042e78	−0.0292830
$436$	1.89590e80	0.593579
$437$	2.21479e79	0.0646621
$438$	6.78578e79	0.184773
$439$	−6.77960e80	−1.72201	−0.861007	−	0.508594i	$-0.830165\pi$
$439$	−6.77960e80	−1.72201	−0.861007	+	0.508594i	$0.830165\pi$
$440$	−1.45125e79	−0.0343903
$441$	1.51983e80	0.336061
$442$	1.02333e81	2.11172
$443$	−3.49885e80	−0.673925	−0.336963	−	0.941518i	$-0.609400\pi$
$443$	−3.49885e80	−0.673925	−0.336963	+	0.941518i	$0.609400\pi$
$444$	−3.61813e80	−0.650585
$445$	1.51246e78	0.00253925
$446$	1.48288e80	0.232484
$447$	−3.81649e80	−0.558836
$448$	3.31849e80	0.453901
$449$	3.39509e80	0.433848	0.216924	−	0.976188i	$-0.430398\pi$
$449$	3.39509e80	0.433848	0.216924	+	0.976188i	$0.430398\pi$
$450$	−8.34878e80	−0.996877
$451$	−1.04552e81	−1.16667
$452$	−9.01483e80	−0.940233
$453$	−6.64055e80	−0.647454
$454$	1.61991e81	1.47669
$455$	1.59316e80	0.135803
$456$	6.21172e79	0.0495204
$457$	1.36423e81	1.01729	0.508643	−	0.860978i	$-0.330147\pi$
$457$	1.36423e81	1.01729	0.508643	+	0.860978i	$0.330147\pi$
$458$	5.51939e80	0.385030
$459$	1.25920e81	0.821876
$460$	−2.34690e79	−0.0143344
$461$	1.28858e81	0.736600	0.368300	−	0.929707i	$-0.379940\pi$
$461$	1.28858e81	0.736600	0.368300	+	0.929707i	$0.379940\pi$
$462$	1.20949e81	0.647177
$463$	−1.15302e81	−0.577588	−0.288794	−	0.957391i	$-0.593254\pi$
$463$	−1.15302e81	−0.577588	−0.288794	+	0.957391i	$0.593254\pi$
$464$	−1.30441e81	−0.611810
$465$	9.38372e79	0.0412155
$466$	−3.39481e81	−1.39651
$467$	1.31873e81	0.508148	0.254074	−	0.967185i	$-0.418229\pi$
$467$	1.31873e81	0.508148	0.254074	+	0.967185i	$0.418229\pi$
$468$	−2.83739e81	−1.02428
$469$	−1.22030e81	−0.412757
$470$	−7.08411e80	−0.224544
$471$	−1.81456e81	−0.539055
$472$	−1.52443e81	−0.424500
$473$	4.32351e81	1.12868
$474$	1.49350e81	0.365567
$475$	−1.74146e81	−0.399723
$476$	2.64536e81	0.569473
$477$	4.35713e81	0.879812
$478$	2.80835e81	0.531986
$479$	5.79250e81	1.02952	0.514758	−	0.857336i	$-0.327882\pi$
$479$	5.79250e81	1.02952	0.514758	+	0.857336i	$0.327882\pi$
$480$	−4.29880e80	−0.0716951
$481$	−1.68961e82	−2.64461
$482$	7.14207e81	1.04928
$483$	−4.31685e80	−0.0595360
$484$	4.17088e81	0.540063
$485$	6.10806e80	0.0742643
$486$	−1.21887e82	−1.39172
$487$	5.48178e81	0.587880	0.293940	−	0.955824i	$-0.405033\pi$
$487$	5.48178e81	0.587880	0.293940	+	0.955824i	$0.405033\pi$
$488$	3.77321e81	0.380108
$489$	6.05490e81	0.573043
$490$	−7.45998e80	−0.0663372
$491$	−3.71140e81	−0.310136	−0.155068	−	0.987904i	$-0.549560\pi$
$491$	−3.71140e81	−0.310136	−0.155068	+	0.987904i	$0.549560\pi$
$492$	−4.74200e81	−0.372414
$493$	−6.76186e81	−0.499155
$494$	−1.31432e82	−0.912071
$495$	1.61693e81	0.105495
$496$	1.40363e82	0.861115
$497$	−4.80787e81	−0.277385
$498$	−9.03561e81	−0.490301
$499$	−2.04541e81	−0.104403	−0.0522016	−	0.998637i	$-0.516624\pi$
$499$	−2.04541e81	−0.104403	−0.0522016	+	0.998637i	$0.516624\pi$
$500$	3.71305e81	0.178298
$501$	−2.19616e81	−0.0992232
$502$	3.14803e82	1.33837
$503$	−7.58593e81	−0.303518	−0.151759	−	0.988417i	$-0.548494\pi$
$503$	−7.58593e81	−0.303518	−0.151759	+	0.988417i	$0.548494\pi$
$504$	3.59495e81	0.135382
$505$	4.06239e81	0.144011
$506$	−8.32034e81	−0.277684
$507$	2.86515e82	0.900334
$508$	5.43680e82	1.60879
$509$	−2.88197e82	−0.803152	−0.401576	−	0.915826i	$-0.631537\pi$
$509$	−2.88197e82	−0.803152	−0.401576	+	0.915826i	$0.631537\pi$
$510$	−2.64495e81	−0.0694267
$511$	8.19166e81	0.202551
$512$	−5.22832e82	−1.21795
$513$	−1.61726e82	−0.354976
$514$	−1.45149e82	−0.300220
$515$	−5.10406e81	−0.0994936
$516$	1.96094e82	0.360288
$517$	−1.13095e83	−1.95875
$518$	−9.69946e82	−1.58376
$519$	1.93179e82	0.297410
$520$	−3.07379e81	−0.0446244
$521$	1.39898e83	1.91541	0.957704	−	0.287755i	$-0.0929087\pi$
$521$	1.39898e83	1.91541	0.957704	+	0.287755i	$0.0929087\pi$
$522$	4.16352e82	0.537663
$523$	1.36677e83	1.66493	0.832463	−	0.554081i	$-0.186930\pi$
$523$	1.36677e83	1.66493	0.832463	+	0.554081i	$0.186930\pi$
$524$	−6.98740e81	−0.0802992
$525$	3.39428e82	0.368035
$526$	−4.54083e81	−0.0464590
$527$	7.27619e82	0.702555
$528$	−8.14557e82	−0.742313
$529$	−1.13282e83	−0.974455
$530$	−2.13867e82	−0.173672
$531$	1.69847e83	1.30219
$532$	−3.39759e82	−0.245961
$533$	−2.21444e83	−1.51385
$534$	2.43199e81	0.0157019
$535$	2.44224e82	0.148936
$536$	2.35441e82	0.135630
$537$	−1.11264e83	−0.605536
$538$	1.17241e83	0.602865
$539$	−1.19095e83	−0.578678
$540$	1.71372e82	0.0786918
$541$	−3.34816e82	−0.145308	−0.0726539	−	0.997357i	$-0.523147\pi$
$541$	−3.34816e82	−0.145308	−0.0726539	+	0.997357i	$0.523147\pi$
$542$	2.57020e83	1.05436
$543$	2.73799e82	0.106178
$544$	−3.33331e83	−1.22211
$545$	−2.28834e82	−0.0793280
$546$	2.56174e83	0.839767
$547$	−2.56243e83	−0.794398	−0.397199	−	0.917733i	$-0.630018\pi$
$547$	−2.56243e83	−0.794398	−0.397199	+	0.917733i	$0.630018\pi$
$548$	9.22124e82	0.270385
$549$	−4.20397e83	−1.16601
$550$	6.54217e83	1.71656
$551$	8.68464e82	0.215590
$552$	8.32882e81	0.0195633
$553$	1.80293e83	0.400739
$554$	1.90384e83	0.400481
$555$	4.36705e82	0.0869466
$556$	−2.14999e83	−0.405187
$557$	3.57336e83	0.637519	0.318759	−	0.947836i	$-0.396734\pi$
$557$	3.57336e83	0.637519	0.318759	+	0.947836i	$0.396734\pi$
$558$	−4.48021e83	−0.756755
$559$	9.15729e83	1.46456
$560$	−6.15938e82	−0.0932830
$561$	−4.22254e83	−0.605628
$562$	−1.41874e84	−1.92729
$563$	−4.27507e83	−0.550094	−0.275047	−	0.961431i	$-0.588693\pi$
$563$	−4.27507e83	−0.550094	−0.275047	+	0.961431i	$0.588693\pi$
$564$	−5.12945e83	−0.625256
$565$	1.08808e83	0.125656
$566$	−5.65891e82	−0.0619200
$567$	−2.20210e83	−0.228325
$568$	9.27617e82	0.0911475
$569$	3.86056e83	0.359522	0.179761	−	0.983710i	$-0.442468\pi$
$569$	3.86056e83	0.359522	0.179761	+	0.983710i	$0.442468\pi$
$570$	3.39705e82	0.0299861
$571$	6.19137e83	0.518066	0.259033	−	0.965868i	$-0.416596\pi$
$571$	6.19137e83	0.518066	0.259033	+	0.965868i	$0.416596\pi$
$572$	2.22340e84	1.76376
$573$	4.70038e83	0.353522
$574$	−1.27123e84	−0.906591
$575$	−2.33499e83	−0.157913
$576$	7.13353e83	0.457529
$577$	2.27749e84	1.38546	0.692731	−	0.721196i	$-0.256408\pi$
$577$	2.27749e84	1.38546	0.692731	+	0.721196i	$0.256408\pi$
$578$	2.86526e83	0.165335
$579$	−1.21083e84	−0.662807
$580$	−9.20264e82	−0.0477924
$581$	−1.09076e84	−0.537474
$582$	9.82154e83	0.459228
$583$	−3.41428e84	−1.51499
$584$	−1.58047e83	−0.0665573
$585$	3.42470e83	0.136889
$586$	−5.70046e84	−2.16288
$587$	3.60186e84	1.29737	0.648687	−	0.761055i	$-0.275318\pi$
$587$	3.60186e84	1.29737	0.648687	+	0.761055i	$0.275318\pi$
$588$	−5.40161e83	−0.184720
$589$	−9.34522e83	−0.303440
$590$	−8.33680e83	−0.257047
$591$	−1.29661e84	−0.379657
$592$	6.53229e84	1.81658
$593$	5.90369e83	0.155939	0.0779696	−	0.996956i	$-0.475156\pi$
$593$	5.90369e83	0.155939	0.0779696	+	0.996956i	$0.475156\pi$
$594$	6.07556e84	1.52440
$595$	−3.19293e83	−0.0761064
$596$	−4.02753e84	−0.912070
$597$	1.63830e83	0.0352513
$598$	−1.76227e84	−0.360318
$599$	−5.66096e84	−1.09995	−0.549973	−	0.835182i	$-0.685362\pi$
$599$	−5.66096e84	−1.09995	−0.549973	+	0.835182i	$0.685362\pi$
$600$	−6.54884e83	−0.120935
$601$	7.05697e84	1.23864	0.619322	−	0.785137i	$-0.287407\pi$
$601$	7.05697e84	1.23864	0.619322	+	0.785137i	$0.287407\pi$
$602$	5.25688e84	0.877072
$603$	−2.62319e84	−0.416056
$604$	−7.00776e84	−1.05670
$605$	−5.03421e83	−0.0721759
$606$	6.53218e84	0.890519
$607$	8.24801e84	1.06929	0.534643	−	0.845078i	$-0.320446\pi$
$607$	8.24801e84	1.06929	0.534643	+	0.845078i	$0.320446\pi$
$608$	4.28116e84	0.527840
$609$	−1.69272e84	−0.198499
$610$	2.06349e84	0.230166
$611$	−2.39537e85	−2.54165
$612$	5.68655e84	0.574025
$613$	6.79006e84	0.652122	0.326061	−	0.945349i	$-0.394278\pi$
$613$	6.79006e84	0.652122	0.326061	+	0.945349i	$0.394278\pi$
$614$	−2.19383e85	−2.00479
$615$	5.72355e83	0.0497707
$616$	−2.81703e84	−0.233120
$617$	−1.10340e84	−0.0869033	−0.0434516	−	0.999056i	$-0.513835\pi$
$617$	−1.10340e84	−0.0869033	−0.0434516	+	0.999056i	$0.513835\pi$
$618$	−8.20714e84	−0.615239
$619$	6.79023e84	0.484529	0.242264	−	0.970210i	$-0.422110\pi$
$619$	6.79023e84	0.484529	0.242264	+	0.970210i	$0.422110\pi$
$620$	9.90262e83	0.0672672
$621$	−2.16845e84	−0.140235
$622$	3.94608e85	2.42974
$623$	2.93585e83	0.0172127
$624$	−1.72525e85	−0.963214
$625$	1.81343e85	0.964186
$626$	1.48104e85	0.749978
$627$	5.42324e84	0.261577
$628$	−1.91490e85	−0.879785
$629$	3.38624e85	1.48208
$630$	1.96600e84	0.0819778
$631$	−3.17635e85	−1.26192	−0.630962	−	0.775814i	$-0.717339\pi$
$631$	−3.17635e85	−1.26192	−0.630962	+	0.775814i	$0.717339\pi$
$632$	−3.47851e84	−0.131681
$633$	2.55602e85	0.922042
$634$	−4.82458e85	−1.65858
$635$	−6.56217e84	−0.215005
$636$	−1.54856e85	−0.483600
$637$	−2.52246e85	−0.750883
$638$	−3.26257e85	−0.925825
$639$	−1.03352e85	−0.279602
$640$	2.03630e84	0.0525234
$641$	3.73749e85	0.919201	0.459600	−	0.888126i	$-0.347993\pi$
$641$	3.73749e85	0.919201	0.459600	+	0.888126i	$0.347993\pi$
$642$	3.92704e85	0.920974
$643$	1.63121e85	0.364817	0.182408	−	0.983223i	$-0.441611\pi$
$643$	1.63121e85	0.364817	0.182408	+	0.983223i	$0.441611\pi$
$644$	−4.55556e84	−0.0971680
$645$	−2.36684e84	−0.0481501
$646$	2.63409e85	0.511140
$647$	3.23904e85	0.599564	0.299782	−	0.954008i	$-0.403086\pi$
$647$	3.23904e85	0.599564	0.299782	+	0.954008i	$0.403086\pi$
$648$	4.24867e84	0.0750266
$649$	−1.33093e86	−2.24229
$650$	1.38565e86	2.22739
$651$	1.82148e85	0.279385
$652$	6.38972e85	0.935256
$653$	−1.07815e86	−1.50601	−0.753003	−	0.658018i	$-0.771395\pi$
$653$	−1.07815e86	−1.50601	−0.753003	+	0.658018i	$0.771395\pi$
$654$	−3.67956e85	−0.490541
$655$	8.43372e83	0.0107315
$656$	8.56135e85	1.03986
$657$	1.76090e85	0.204170
$658$	−1.37510e86	−1.52210
$659$	−6.27013e85	−0.662631	−0.331315	−	0.943520i	$-0.607492\pi$
$659$	−6.27013e85	−0.662631	−0.331315	+	0.943520i	$0.607492\pi$
$660$	−5.74671e84	−0.0579868
$661$	1.19678e86	1.15311	0.576556	−	0.817058i	$-0.304396\pi$
$661$	1.19678e86	1.15311	0.576556	+	0.817058i	$0.304396\pi$
$662$	9.51792e85	0.875736
$663$	−8.94344e85	−0.785854
$664$	2.10448e85	0.176612
$665$	4.10085e84	0.0328711
$666$	−2.08503e86	−1.59642
$667$	1.16446e85	0.0851698
$668$	−2.31760e85	−0.161941
$669$	−1.29597e85	−0.0865166
$670$	1.28758e85	0.0821280
$671$	3.29426e86	2.00780
$672$	−8.34440e85	−0.485996
$673$	−1.68005e86	−0.935111	−0.467555	−	0.883964i	$-0.654865\pi$
$673$	−1.68005e86	−0.935111	−0.467555	+	0.883964i	$0.654865\pi$
$674$	−4.30853e86	−2.29193
$675$	1.70503e86	0.866894
$676$	3.02358e86	1.46942
$677$	6.44384e85	0.299358	0.149679	−	0.988735i	$-0.452176\pi$
$677$	6.44384e85	0.299358	0.149679	+	0.988735i	$0.452176\pi$
$678$	1.74960e86	0.777020
$679$	1.18564e86	0.503412
$680$	6.16034e84	0.0250082
$681$	−1.41573e86	−0.549533
$682$	3.51073e86	1.30309
$683$	3.53739e86	1.25560	0.627800	−	0.778375i	$-0.283956\pi$
$683$	3.53739e86	1.25560	0.627800	+	0.778375i	$0.283956\pi$
$684$	−7.30356e85	−0.247927
$685$	−1.11299e85	−0.0361352
$686$	−4.67140e86	−1.45065
$687$	−4.82370e85	−0.143285
$688$	−3.54035e86	−1.00600
$689$	−7.23153e86	−1.96582
$690$	4.55485e84	0.0118461
$691$	−4.67576e86	−1.16352	−0.581758	−	0.813362i	$-0.697635\pi$
$691$	−4.67576e86	−1.16352	−0.581758	+	0.813362i	$0.697635\pi$
$692$	2.03861e86	0.485398
$693$	3.13862e86	0.715115
$694$	4.10717e85	0.0895528
$695$	2.59502e85	0.0541507
$696$	3.26589e85	0.0652259
$697$	4.43807e86	0.848388
$698$	5.33589e85	0.0976375
$699$	2.96691e86	0.519697
$700$	3.58198e86	0.600666
$701$	−2.70001e86	−0.433476	−0.216738	−	0.976230i	$-0.569542\pi$
$701$	−2.70001e86	−0.433476	−0.216738	+	0.976230i	$0.569542\pi$
$702$	1.28682e87	1.97804
$703$	−4.34913e86	−0.640126
$704$	−5.58989e86	−0.787838
$705$	6.19120e85	0.0835615
$706$	−2.28993e85	−0.0295992
$707$	7.88551e86	0.976198
$708$	−6.03650e86	−0.715766
$709$	−8.12454e86	−0.922759	−0.461380	−	0.887203i	$-0.652645\pi$
$709$	−8.12454e86	−0.922759	−0.461380	+	0.887203i	$0.652645\pi$
$710$	5.07294e85	0.0551925
$711$	3.87562e86	0.403942
$712$	−5.66434e84	−0.00565600
$713$	−1.25303e86	−0.119875
$714$	−5.13411e86	−0.470619
$715$	−2.68362e86	−0.235715
$716$	−1.17417e87	−0.988288
$717$	−2.45437e86	−0.197973
$718$	1.42023e87	1.09790
$719$	2.24300e86	0.166188	0.0830938	−	0.996542i	$-0.473520\pi$
$719$	2.24300e86	0.166188	0.0830938	+	0.996542i	$0.473520\pi$
$720$	−1.32404e86	−0.0940286
$721$	−9.90750e86	−0.674432
$722$	1.72861e87	1.12801
$723$	−6.24185e86	−0.390477
$724$	2.88939e86	0.173292
$725$	−9.15597e86	−0.526496
$726$	−8.09483e86	−0.446314
$727$	1.90000e87	1.00451	0.502255	−	0.864720i	$-0.332504\pi$
$727$	1.90000e87	1.00451	0.502255	+	0.864720i	$0.332504\pi$
$728$	−5.96654e86	−0.302493
$729$	4.32442e86	0.210251
$730$	−8.64327e85	−0.0403024
$731$	−1.83526e87	−0.820763
$732$	1.49413e87	0.640913
$733$	1.78617e87	0.734941	0.367471	−	0.930035i	$-0.380224\pi$
$733$	1.78617e87	0.734941	0.367471	+	0.930035i	$0.380224\pi$
$734$	9.61980e86	0.379696
$735$	6.51969e85	0.0246867
$736$	5.74028e86	0.208526
$737$	2.05555e87	0.716425
$738$	−2.73268e87	−0.913838
$739$	2.67566e87	0.858569	0.429284	−	0.903169i	$-0.358766\pi$
$739$	2.67566e87	0.858569	0.429284	+	0.903169i	$0.358766\pi$
$740$	4.60854e86	0.141904
$741$	1.14866e87	0.339418
$742$	−4.15137e87	−1.17726
$743$	−3.68577e87	−1.00316	−0.501579	−	0.865112i	$-0.667247\pi$
$743$	−3.68577e87	−1.00316	−0.501579	+	0.865112i	$0.667247\pi$
$744$	−3.51430e86	−0.0918047
$745$	4.86119e86	0.121892
$746$	−4.76940e87	−1.14797
$747$	−2.34473e87	−0.541770
$748$	−4.45603e87	−0.988438
$749$	4.74064e87	1.00958
$750$	−7.20628e86	−0.147347
$751$	−6.47968e85	−0.0127214	−0.00636071	−	0.999980i	$-0.502025\pi$
$751$	−6.47968e85	−0.0127214	−0.00636071	+	0.999980i	$0.502025\pi$
$752$	9.26087e87	1.74585
$753$	−2.75124e87	−0.498060
$754$	−6.91020e87	−1.20134
$755$	8.45829e86	0.141221
$756$	3.32650e87	0.533424
$757$	3.85344e87	0.593506	0.296753	−	0.954954i	$-0.404096\pi$
$757$	3.85344e87	0.593506	0.296753	+	0.954954i	$0.404096\pi$
$758$	1.63614e88	2.42053
$759$	7.27161e86	0.103337
$760$	−7.91207e85	−0.0108013
$761$	8.59743e87	1.12755	0.563776	−	0.825928i	$-0.309348\pi$
$761$	8.59743e87	1.12755	0.563776	+	0.825928i	$0.309348\pi$
$762$	−1.05517e88	−1.32953
$763$	−4.44189e87	−0.537737
$764$	4.96030e87	0.576979
$765$	−6.86361e86	−0.0767148
$766$	6.59967e87	0.708835
$767$	−2.81895e88	−2.90957
$768$	6.36917e87	0.631780
$769$	−1.59932e88	−1.52469	−0.762344	−	0.647172i	$-0.775952\pi$
$769$	−1.59932e88	−1.52469	−0.762344	+	0.647172i	$0.775952\pi$
$770$	−1.54057e87	−0.141161
$771$	1.26854e87	0.111724
$772$	−1.27779e88	−1.08176
$773$	6.47128e87	0.526642	0.263321	−	0.964708i	$-0.415182\pi$
$773$	6.47128e87	0.526642	0.263321	+	0.964708i	$0.415182\pi$
$774$	1.13004e88	0.884082
$775$	9.85240e87	0.741037
$776$	−2.28753e87	−0.165419
$777$	8.47689e87	0.589380
$778$	−8.22288e86	−0.0549726
$779$	−5.70006e87	−0.366427
$780$	−1.21717e87	−0.0752428
$781$	8.09871e87	0.481459
$782$	3.53186e87	0.201928
$783$	−8.50293e87	−0.467557
$784$	9.75224e87	0.515780
$785$	2.31126e87	0.117578
$786$	1.35611e87	0.0663602
$787$	−1.25948e88	−0.592871	−0.296436	−	0.955053i	$-0.595798\pi$
$787$	−1.25948e88	−0.592871	−0.296436	+	0.955053i	$0.595798\pi$
$788$	−1.36831e88	−0.619633
$789$	3.96848e86	0.0172892
$790$	−1.90232e87	−0.0797367
$791$	2.11208e88	0.851779
$792$	−6.05557e87	−0.234983
$793$	6.97733e88	2.60530
$794$	−2.07749e88	−0.746472
$795$	1.86910e87	0.0646301
$796$	1.72889e87	0.0575332
$797$	−5.76161e88	−1.84529	−0.922645	−	0.385649i	$-0.873977\pi$
$797$	−5.76161e88	−1.84529	−0.922645	+	0.385649i	$0.873977\pi$
$798$	6.59403e87	0.203265
$799$	4.80069e88	1.42438
$800$	−4.51350e88	−1.28905
$801$	6.31099e86	0.0173502
$802$	−7.20393e88	−1.90656
$803$	−1.37986e88	−0.351569
$804$	9.32305e87	0.228691
$805$	5.49852e86	0.0129859
$806$	7.43581e88	1.69087
$807$	−1.02463e88	−0.224350
$808$	−1.52141e88	−0.320774
$809$	−4.29220e88	−0.871465	−0.435732	−	0.900076i	$-0.643511\pi$
$809$	−4.29220e88	−0.871465	−0.435732	+	0.900076i	$0.643511\pi$
$810$	2.32351e87	0.0454308
$811$	−1.37221e88	−0.258395	−0.129198	−	0.991619i	$-0.541240\pi$
$811$	−1.37221e88	−0.258395	−0.129198	+	0.991619i	$0.541240\pi$
$812$	−1.78633e88	−0.323968
$813$	−2.24624e88	−0.392369
$814$	1.63384e89	2.74895
$815$	−7.71233e87	−0.124991
$816$	3.45767e88	0.539801
$817$	2.35713e88	0.354495
$818$	3.95423e87	0.0572910
$819$	6.64768e88	0.927922
$820$	6.04004e87	0.0812302
$821$	5.04540e87	0.0653777	0.0326888	−	0.999466i	$-0.489593\pi$
$821$	5.04540e87	0.0653777	0.0326888	+	0.999466i	$0.489593\pi$
$822$	−1.78965e88	−0.223449
$823$	−3.45387e88	−0.415538	−0.207769	−	0.978178i	$-0.566620\pi$
$823$	−3.45387e88	−0.415538	−0.207769	+	0.978178i	$0.566620\pi$
$824$	1.91152e88	0.221615
$825$	−5.71757e88	−0.638801
$826$	−1.61826e89	−1.74243
$827$	2.64181e88	0.274147	0.137074	−	0.990561i	$-0.456230\pi$
$827$	2.64181e88	0.274147	0.137074	+	0.990561i	$0.456230\pi$
$828$	−9.79278e87	−0.0979447
$829$	−1.24760e89	−1.20271	−0.601356	−	0.798981i	$-0.705373\pi$
$829$	−1.24760e89	−1.20271	−0.601356	+	0.798981i	$0.705373\pi$
$830$	1.15090e88	0.106943
$831$	−1.66387e88	−0.149035
$832$	−1.18395e89	−1.02229
$833$	5.05540e88	0.420807
$834$	4.17270e88	0.334851
$835$	2.79732e87	0.0216424
$836$	5.72313e88	0.426916
$837$	9.14969e88	0.658082
$838$	9.33503e88	0.647400
$839$	1.14813e89	0.767804	0.383902	−	0.923374i	$-0.374580\pi$
$839$	1.14813e89	0.767804	0.383902	+	0.923374i	$0.374580\pi$
$840$	1.54214e87	0.00994503
$841$	−1.15136e89	−0.716036
$842$	−2.16663e88	−0.129947
$843$	1.23992e89	0.717219
$844$	2.69736e89	1.50485
$845$	−3.64943e88	−0.196379
$846$	−2.95595e89	−1.53427
$847$	−9.77191e88	−0.489255
$848$	2.79582e89	1.35032
$849$	4.94563e87	0.0230429
$850$	−2.77705e89	−1.24826
$851$	−5.83142e88	−0.252885
$852$	3.67320e88	0.153687
$853$	−1.40717e89	−0.568070	−0.284035	−	0.958814i	$-0.591673\pi$
$853$	−1.40717e89	−0.568070	−0.284035	+	0.958814i	$0.591673\pi$
$854$	4.00544e89	1.56022
$855$	8.81532e87	0.0331338
$856$	−9.14647e88	−0.331744
$857$	−2.64572e89	−0.926038	−0.463019	−	0.886348i	$-0.653234\pi$
$857$	−2.64572e89	−0.926038	−0.463019	+	0.886348i	$0.653234\pi$
$858$	−4.31517e89	−1.45759
$859$	4.88791e89	1.59342	0.796712	−	0.604359i	$-0.206571\pi$
$859$	4.88791e89	1.59342	0.796712	+	0.604359i	$0.206571\pi$
$860$	−2.49772e88	−0.0785852
$861$	1.11100e89	0.337378
$862$	1.98569e89	0.582024
$863$	2.17102e89	0.614235	0.307117	−	0.951672i	$-0.400636\pi$
$863$	2.17102e89	0.614235	0.307117	+	0.951672i	$0.400636\pi$
$864$	−4.19158e89	−1.14475
$865$	−2.46058e88	−0.0648704
$866$	−6.63210e89	−1.68793
$867$	−2.50410e88	−0.0615276
$868$	1.92220e89	0.455981
$869$	−3.03697e89	−0.695565
$870$	1.78604e88	0.0394962
$871$	4.35371e89	0.929621
$872$	8.57007e88	0.176698
$873$	2.54868e89	0.507436
$874$	−4.53616e88	−0.0872147
$875$	−8.69927e88	−0.161524
$876$	−6.25841e88	−0.112225
$877$	2.09369e89	0.362598	0.181299	−	0.983428i	$-0.441970\pi$
$877$	2.09369e89	0.362598	0.181299	+	0.983428i	$0.441970\pi$
$878$	1.38854e90	2.32261
$879$	4.98195e89	0.804894
$880$	1.03753e89	0.161912
$881$	3.71437e89	0.559912	0.279956	−	0.960013i	$-0.409680\pi$
$881$	3.71437e89	0.559912	0.279956	+	0.960013i	$0.409680\pi$
$882$	−3.11279e89	−0.453271
$883$	−1.22390e90	−1.72165	−0.860823	−	0.508905i	$-0.830050\pi$
$883$	−1.22390e90	−1.72165	−0.860823	+	0.508905i	$0.830050\pi$
$884$	−9.43798e89	−1.28258
$885$	7.28599e88	0.0956575
$886$	7.16606e89	0.908974
$887$	−1.05036e90	−1.28727	−0.643633	−	0.765334i	$-0.722574\pi$
$887$	−1.05036e90	−1.28727	−0.643633	+	0.765334i	$0.722574\pi$
$888$	−1.63551e89	−0.193668
$889$	−1.27378e90	−1.45744
$890$	−3.09770e87	−0.00342488
$891$	3.70937e89	0.396306
$892$	−1.36764e89	−0.141203
$893$	−6.16579e89	−0.615204
$894$	7.81662e89	0.753745
$895$	1.41721e89	0.132078
$896$	3.95266e89	0.356037
$897$	1.54014e89	0.134089
$898$	−6.95355e89	−0.585165
$899$	−4.91337e89	−0.399677
$900$	7.69993e89	0.605467
$901$	1.44931e90	1.10168
$902$	2.14135e90	1.57358
$903$	−4.59428e89	−0.326393
$904$	−4.07498e89	−0.279891
$905$	−3.48746e88	−0.0231594
$906$	1.36006e90	0.873271
$907$	2.03009e89	0.126035	0.0630177	−	0.998012i	$-0.479928\pi$
$907$	2.03009e89	0.126035	0.0630177	+	0.998012i	$0.479928\pi$
$908$	−1.49402e90	−0.896886
$909$	1.69509e90	0.984001
$910$	−3.26297e89	−0.183168
$911$	−2.13327e90	−1.15807	−0.579036	−	0.815302i	$-0.696571\pi$
$911$	−2.13327e90	−1.15807	−0.579036	+	0.815302i	$0.696571\pi$
$912$	−4.44088e89	−0.233145
$913$	1.83735e90	0.932897
$914$	−2.79410e90	−1.37209
$915$	−1.80340e89	−0.0856540
$916$	−5.09044e89	−0.233853
$917$	1.63707e89	0.0727449
$918$	−2.57898e90	−1.10853
$919$	2.52842e89	0.105130	0.0525649	−	0.998618i	$-0.483260\pi$
$919$	2.52842e89	0.105130	0.0525649	+	0.998618i	$0.483260\pi$
$920$	−1.06087e88	−0.00426710
$921$	1.91731e90	0.746060
$922$	−2.63916e90	−0.993509
$923$	1.71533e90	0.624734
$924$	−1.11549e90	−0.393072
$925$	4.58517e90	1.56326
$926$	2.36153e90	0.779037
$927$	−2.12975e90	−0.679823
$928$	2.25087e90	0.695245
$929$	−4.65955e90	−1.39272	−0.696362	−	0.717691i	$-0.745199\pi$
$929$	−4.65955e90	−1.39272	−0.696362	+	0.717691i	$0.745199\pi$
$930$	−1.92190e89	−0.0555904
$931$	−6.49294e89	−0.181751
$932$	3.13097e90	0.848191
$933$	−3.44870e90	−0.904201
$934$	−2.70091e90	−0.685378
$935$	5.37838e89	0.132098
$936$	−1.28259e90	−0.304911
$937$	7.49140e90	1.72387	0.861937	−	0.507015i	$-0.169251\pi$
$937$	7.49140e90	1.72387	0.861937	+	0.507015i	$0.169251\pi$
$938$	2.49931e90	0.556717
$939$	−1.29436e90	−0.279097
$940$	6.53355e89	0.136380
$941$	1.93054e89	0.0390117	0.0195058	−	0.999810i	$-0.493791\pi$
$941$	1.93054e89	0.0390117	0.0195058	+	0.999810i	$0.493791\pi$
$942$	3.71643e90	0.727065
$943$	−7.64277e89	−0.144759
$944$	1.08985e91	1.99857
$945$	−4.01505e89	−0.0712887
$946$	−8.85505e90	−1.52234
$947$	−1.00121e91	−1.66668	−0.833339	−	0.552762i	$-0.813574\pi$
$947$	−1.00121e91	−1.66668	−0.833339	+	0.552762i	$0.813574\pi$
$948$	−1.37743e90	−0.222032
$949$	−2.92258e90	−0.456190
$950$	3.56672e90	0.539137
$951$	4.21647e90	0.617224
$952$	1.19578e90	0.169522
$953$	−6.15324e90	−0.844832	−0.422416	−	0.906402i	$-0.638818\pi$
$953$	−6.15324e90	−0.844832	−0.422416	+	0.906402i	$0.638818\pi$
$954$	−8.92391e90	−1.18667
$955$	−5.98703e89	−0.0771096
$956$	−2.59009e90	−0.323109
$957$	2.85134e90	0.344536
$958$	−1.18637e91	−1.38859
$959$	−2.16043e90	−0.244948
$960$	3.06010e89	0.0336096
$961$	−4.11151e90	−0.437460
$962$	3.46052e91	3.56699
$963$	1.01906e91	1.01765
$964$	−6.58701e90	−0.637292
$965$	1.54228e90	0.144570
$966$	8.84143e89	0.0803008
$967$	1.38599e91	1.21970	0.609848	−	0.792518i	$-0.291230\pi$
$967$	1.38599e91	1.21970	0.609848	+	0.792518i	$0.291230\pi$
$968$	1.88537e90	0.160767
$969$	−2.30208e90	−0.190215
$970$	−1.25100e90	−0.100166
$971$	−2.49235e90	−0.193385	−0.0966924	−	0.995314i	$-0.530826\pi$
$971$	−2.49235e90	−0.193385	−0.0966924	+	0.995314i	$0.530826\pi$
$972$	1.12414e91	0.845279
$973$	5.03719e90	0.367068
$974$	−1.12273e91	−0.792918
$975$	−1.21099e91	−0.828899
$976$	−2.69754e91	−1.78957
$977$	7.93411e90	0.510169	0.255084	−	0.966919i	$-0.417897\pi$
$977$	7.93411e90	0.510169	0.255084	+	0.966919i	$0.417897\pi$
$978$	−1.24012e91	−0.772907
$979$	−4.94534e89	−0.0298761
$980$	6.88021e89	0.0402908
$981$	−9.54844e90	−0.542035
$982$	7.60138e90	0.418304
$983$	−1.27832e91	−0.681960	−0.340980	−	0.940071i	$-0.610759\pi$
$983$	−1.27832e91	−0.681960	−0.340980	+	0.940071i	$0.610759\pi$
$984$	−2.14353e90	−0.110861
$985$	1.65153e90	0.0828100
$986$	1.38491e91	0.673248
$987$	1.20177e91	0.566434
$988$	1.21217e91	0.553959
$989$	3.16049e90	0.140045
$990$	−3.31166e90	−0.142289
$991$	1.10655e91	0.461023	0.230512	−	0.973070i	$-0.425960\pi$
$991$	1.10655e91	0.461023	0.230512	+	0.973070i	$0.425960\pi$
$992$	−2.42208e91	−0.978550
$993$	−8.31824e90	−0.325896
$994$	9.84709e90	0.374131
$995$	−2.08675e89	−0.00768894
$996$	8.33339e90	0.297791
$997$	−2.30608e90	−0.0799232	−0.0399616	−	0.999201i	$-0.512724\pi$
$997$	−2.30608e90	−0.0799232	−0.0399616	+	0.999201i	$0.512724\pi$
$998$	4.18924e90	0.140817
$999$	4.25814e91	1.38826

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.62.a.a.1.1	✓	4	1.1	even	1	trivial
9.62.a.a.1.4		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)

\(f(q)\)	\(=\)	\(q-2.04812e9 q^{2} +1.78996e14 q^{3} +1.88894e18 q^{4} -2.27994e20 q^{5} -3.66606e23 q^{6} -4.42559e25 q^{7} +8.53860e26 q^{8} -9.51338e28 q^{9} +O(q^{10})\)	\(q-2.04812e9 q^{2} +1.78996e14 q^{3} +1.88894e18 q^{4} -2.27994e20 q^{5} -3.66606e23 q^{6} -4.42559e25 q^{7} +8.53860e26 q^{8} -9.51338e28 q^{9} +4.66958e29 q^{10} +7.45476e31 q^{11} +3.38114e32 q^{12} +1.57894e34 q^{13} +9.06412e34 q^{14} -4.08100e34 q^{15} -6.10441e36 q^{16} -3.16443e37 q^{17} +1.94845e38 q^{18} +4.06426e38 q^{19} -4.30667e38 q^{20} -7.92164e39 q^{21} -1.52682e41 q^{22} +5.44945e40 q^{23} +1.52838e41 q^{24} -4.28483e42 q^{25} -3.23385e43 q^{26} -3.97922e43 q^{27} -8.35968e43 q^{28} +2.13683e44 q^{29} +8.35837e43 q^{30} -2.29937e45 q^{31} +1.05337e46 q^{32} +1.33437e46 q^{33} +6.48113e46 q^{34} +1.00901e46 q^{35} -1.79702e47 q^{36} -1.07009e48 q^{37} -8.32407e47 q^{38} +2.82624e48 q^{39} -1.94675e47 q^{40} -1.40249e49 q^{41} +1.62244e49 q^{42} +5.79966e49 q^{43} +1.40816e50 q^{44} +2.16899e49 q^{45} -1.11611e50 q^{46} -1.51708e51 q^{47} -1.09267e51 q^{48} -1.59757e51 q^{49} +8.77583e51 q^{50} -5.66421e51 q^{51} +2.98252e52 q^{52} -4.58000e52 q^{53} +8.14991e52 q^{54} -1.69964e52 q^{55} -3.77883e52 q^{56} +7.27487e52 q^{57} -4.37649e53 q^{58} -1.78535e54 q^{59} -7.70878e52 q^{60} +4.41900e54 q^{61} +4.70938e54 q^{62} +4.21023e54 q^{63} -7.49842e54 q^{64} -3.59987e54 q^{65} -2.73296e55 q^{66} +2.75737e55 q^{67} -5.97743e55 q^{68} +9.75431e54 q^{69} -2.06656e55 q^{70} +1.08638e56 q^{71} -8.12310e55 q^{72} -1.85098e56 q^{73} +2.19168e57 q^{74} -7.66968e56 q^{75} +7.67715e56 q^{76} -3.29917e57 q^{77} -5.78847e57 q^{78} -4.07387e57 q^{79} +1.39177e57 q^{80} +4.97584e57 q^{81} +2.87246e58 q^{82} +2.46467e58 q^{83} -1.49635e58 q^{84} +7.21470e57 q^{85} -1.18784e59 q^{86} +3.82485e58 q^{87} +6.36532e58 q^{88} -6.63380e57 q^{89} -4.44234e58 q^{90} -6.98772e59 q^{91} +1.02937e59 q^{92} -4.11578e59 q^{93} +3.10715e60 q^{94} -9.26624e58 q^{95} +1.88549e60 q^{96} -2.67905e60 q^{97} +3.27201e60 q^{98} -7.09200e60 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1146312000 q^{2} - 573723599022000 q^{3} + 44\!\cdots\!28 q^{4}+ \cdots + 11\!\cdots\!52 q^{9}+O(q^{10}) \) 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

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Groups

Database

Properties

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