LMFDB - Embedded newform 1.62.a.a.1.3

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			1.3
Root			$-3.61406e6$ 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)

$f(q)$	$=$	$q+9.80478e8 q^{2} +2.49037e14 q^{3} -1.34451e18 q^{4} +1.59503e20 q^{5} +2.44176e23 q^{6} +1.63507e25 q^{7} -3.57909e27 q^{8} -6.51539e28 q^{9} +O(q^{10})$	\(q+9.80478e8 q^{2} +2.49037e14 q^{3} -1.34451e18 q^{4} +1.59503e20 q^{5} +2.44176e23 q^{6} +1.63507e25 q^{7} -3.57909e27 q^{8} -6.51539e28 q^{9} +1.56389e29 q^{10} +1.92532e30 q^{11} -3.34832e32 q^{12} -1.30898e34 q^{13} +1.60315e34 q^{14} +3.97221e34 q^{15} -4.08993e35 q^{16} +2.98908e37 q^{17} -6.38819e37 q^{18} -7.88343e38 q^{19} -2.14452e38 q^{20} +4.07194e39 q^{21} +1.88773e39 q^{22} -4.50060e41 q^{23} -8.91326e41 q^{24} -4.31137e42 q^{25} -1.28343e43 q^{26} -4.78967e43 q^{27} -2.19837e43 q^{28} -5.51506e44 q^{29} +3.89466e43 q^{30} +4.17012e45 q^{31} +7.85180e45 q^{32} +4.79477e44 q^{33} +2.93073e46 q^{34} +2.60798e45 q^{35} +8.75998e46 q^{36} -6.95142e47 q^{37} -7.72953e47 q^{38} -3.25985e48 q^{39} -5.70874e47 q^{40} +1.25327e49 q^{41} +3.99245e48 q^{42} +8.92745e49 q^{43} -2.58861e48 q^{44} -1.03922e49 q^{45} -4.41273e50 q^{46} +1.21258e50 q^{47} -1.01854e50 q^{48} -3.28881e51 q^{49} -4.22720e51 q^{50} +7.44393e51 q^{51} +1.75994e52 q^{52} +5.55328e52 q^{53} -4.69616e52 q^{54} +3.07094e50 q^{55} -5.85207e52 q^{56} -1.96327e53 q^{57} -5.40740e53 q^{58} +4.29424e53 q^{59} -5.34066e52 q^{60} +1.17661e53 q^{61} +4.08871e54 q^{62} -1.06531e54 q^{63} +8.64159e54 q^{64} -2.08786e54 q^{65} +4.70116e53 q^{66} -3.47829e55 q^{67} -4.01884e55 q^{68} -1.12082e56 q^{69} +2.55707e54 q^{70} +3.07606e56 q^{71} +2.33191e56 q^{72} +7.42117e56 q^{73} -6.81572e56 q^{74} -1.07369e57 q^{75} +1.05993e57 q^{76} +3.14804e55 q^{77} -3.19621e57 q^{78} -4.19454e57 q^{79} -6.52354e55 q^{80} -3.64222e57 q^{81} +1.22880e58 q^{82} +3.40233e58 q^{83} -5.47475e57 q^{84} +4.76766e57 q^{85} +8.75316e58 q^{86} -1.37346e59 q^{87} -6.89089e57 q^{88} -3.77146e59 q^{89} -1.01893e58 q^{90} -2.14028e59 q^{91} +6.05108e59 q^{92} +1.03852e60 q^{93} +1.18890e59 q^{94} -1.25743e59 q^{95} +1.95539e60 q^{96} -2.29644e60 q^{97} -3.22460e60 q^{98} -1.25442e59 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.80478e8	0.645688	0.322844	−	0.946452i	$-0.395361\pi$
$2$	9.80478e8	0.645688	0.322844	+	0.946452i	$0.395361\pi$
$3$	2.49037e14	0.698339	0.349169	−	0.937060i	$-0.386464\pi$
$3$	2.49037e14	0.698339	0.349169	+	0.937060i	$0.386464\pi$
$4$	−1.34451e18	−0.583087
$5$	1.59503e20	0.0765919	0.0382959	−	0.999266i	$-0.487807\pi$
$5$	1.59503e20	0.0765919	0.0382959	+	0.999266i	$0.487807\pi$
$6$	2.44176e23	0.450909
$7$	1.63507e25	0.274187	0.137094	−	0.990558i	$-0.456224\pi$
$7$	1.63507e25	0.274187	0.137094	+	0.990558i	$0.456224\pi$
$8$	−3.57909e27	−1.02218
$9$	−6.51539e28	−0.512323
$10$	1.56389e29	0.0494545
$11$	1.92532e30	0.0332680	0.0166340	−	0.999862i	$-0.494705\pi$
$11$	1.92532e30	0.0332680	0.0166340	+	0.999862i	$0.494705\pi$
$12$	−3.34832e32	−0.407192
$13$	−1.30898e34	−1.38568	−0.692838	−	0.721094i	$-0.743640\pi$
$13$	−1.30898e34	−1.38568	−0.692838	+	0.721094i	$0.743640\pi$
$14$	1.60315e34	0.177039
$15$	3.97221e34	0.0534871
$16$	−4.08993e35	−0.0769230
$17$	2.98908e37	0.884801	0.442401	−	0.896818i	$-0.354127\pi$
$17$	2.98908e37	0.884801	0.442401	+	0.896818i	$0.354127\pi$
$18$	−6.38819e37	−0.330801
$19$	−7.88343e38	−0.784748	−0.392374	−	0.919806i	$-0.628346\pi$
$19$	−7.88343e38	−0.784748	−0.392374	+	0.919806i	$0.628346\pi$
$20$	−2.14452e38	−0.0446597
$21$	4.07194e39	0.191476
$22$	1.88773e39	0.0214807
$23$	−4.50060e41	−1.31999	−0.659995	−	0.751270i	$-0.729442\pi$
$23$	−4.50060e41	−1.31999	−0.659995	+	0.751270i	$0.729442\pi$
$24$	−8.91326e41	−0.713828
$25$	−4.31137e42	−0.994134
$26$	−1.28343e43	−0.894714
$27$	−4.78967e43	−1.05611
$28$	−2.19837e43	−0.159875
$29$	−5.51506e44	−1.37534	−0.687672	−	0.726021i	$-0.741367\pi$
$29$	−5.51506e44	−1.37534	−0.687672	+	0.726021i	$0.741367\pi$
$30$	3.89466e43	0.0345360
$31$	4.17012e45	1.36025	0.680123	−	0.733098i	$-0.261926\pi$
$31$	4.17012e45	1.36025	0.680123	+	0.733098i	$0.261926\pi$
$32$	7.85180e45	0.972512
$33$	4.79477e44	0.0232323
$34$	2.93073e46	0.571306
$35$	2.60798e45	0.0210005
$36$	8.75998e46	0.298729
$37$	−6.95142e47	−1.02783	−0.513915	−	0.857841i	$-0.671805\pi$
$37$	−6.95142e47	−1.02783	−0.513915	+	0.857841i	$0.671805\pi$
$38$	−7.72953e47	−0.506703
$39$	−3.25985e48	−0.967671
$40$	−5.70874e47	−0.0782907
$41$	1.25327e49	0.809351	0.404676	−	0.914460i	$-0.367384\pi$
$41$	1.25327e49	0.809351	0.404676	+	0.914460i	$0.367384\pi$
$42$	3.99245e48	0.123633
$43$	8.92745e49	1.34877	0.674387	−	0.738378i	$-0.264408\pi$
$43$	8.92745e49	1.34877	0.674387	+	0.738378i	$0.264408\pi$
$44$	−2.58861e48	−0.0193981
$45$	−1.03922e49	−0.0392398
$46$	−4.41273e50	−0.852303
$47$	1.21258e50	0.121541	0.0607707	−	0.998152i	$-0.480644\pi$
$47$	1.21258e50	0.121541	0.0607707	+	0.998152i	$0.480644\pi$
$48$	−1.01854e50	−0.0537183
$49$	−3.28881e51	−0.924821
$50$	−4.22720e51	−0.641900
$51$	7.44393e51	0.617891
$52$	1.75994e52	0.807969
$53$	5.55328e52	1.42605	0.713026	−	0.701138i	$-0.247324\pi$
$53$	5.55328e52	1.42605	0.713026	+	0.701138i	$0.247324\pi$
$54$	−4.69616e52	−0.681920
$55$	3.07094e50	0.00254806
$56$	−5.85207e52	−0.280269
$57$	−1.96327e53	−0.548020
$58$	−5.40740e53	−0.888044
$59$	4.29424e53	0.418697	0.209348	−	0.977841i	$-0.432866\pi$
$59$	4.29424e53	0.418697	0.209348	+	0.977841i	$0.432866\pi$
$60$	−5.34066e52	−0.0311876
$61$	1.17661e53	0.0415024	0.0207512	−	0.999785i	$-0.493394\pi$
$61$	1.17661e53	0.0415024	0.0207512	+	0.999785i	$0.493394\pi$
$62$	4.08871e54	0.878294
$63$	−1.06531e54	−0.140472
$64$	8.64159e54	0.704863
$65$	−2.08786e54	−0.106131
$66$	4.70116e53	0.0150008
$67$	−3.47829e55	−0.701592	−0.350796	−	0.936452i	$-0.614089\pi$
$67$	−3.47829e55	−0.701592	−0.350796	+	0.936452i	$0.614089\pi$
$68$	−4.01884e55	−0.515916
$69$	−1.12082e56	−0.921801
$70$	2.55707e54	0.0135598
$71$	3.07606e56	1.05831	0.529157	−	0.848524i	$-0.322508\pi$
$71$	3.07606e56	1.05831	0.529157	+	0.848524i	$0.322508\pi$
$72$	2.33191e56	0.523687
$73$	7.42117e56	1.09427	0.547136	−	0.837044i	$-0.315718\pi$
$73$	7.42117e56	1.09427	0.547136	+	0.837044i	$0.315718\pi$
$74$	−6.81572e56	−0.663657
$75$	−1.07369e57	−0.694242
$76$	1.05993e57	0.457576
$77$	3.14804e55	0.00912165
$78$	−3.19621e57	−0.624814
$79$	−4.19454e57	−0.555978	−0.277989	−	0.960584i	$-0.589668\pi$
$79$	−4.19454e57	−0.555978	−0.277989	+	0.960584i	$0.589668\pi$
$80$	−6.52354e55	−0.00589168
$81$	−3.64222e57	−0.225202
$82$	1.22880e58	0.522588
$83$	3.40233e58	0.999758	0.499879	−	0.866095i	$-0.333378\pi$
$83$	3.40233e58	0.999758	0.499879	+	0.866095i	$0.333378\pi$
$84$	−5.47475e57	−0.111647
$85$	4.76766e57	0.0677686
$86$	8.75316e58	0.870888
$87$	−1.37346e59	−0.960457
$88$	−6.89089e57	−0.0340059
$89$	−3.77146e59	−1.31860	−0.659302	−	0.751878i	$-0.729148\pi$
$89$	−3.77146e59	−1.31860	−0.659302	+	0.751878i	$0.729148\pi$
$90$	−1.01893e58	−0.0253367
$91$	−2.14028e59	−0.379934
$92$	6.05108e59	0.769669
$93$	1.03852e60	0.949912
$94$	1.18890e59	0.0784779
$95$	−1.25743e59	−0.0601053
$96$	1.95539e60	0.679143
$97$	−2.29644e60	−0.581457	−0.290728	−	0.956806i	$-0.593898\pi$
$97$	−2.29644e60	−0.581457	−0.290728	+	0.956806i	$0.593898\pi$
$98$	−3.22460e60	−0.597146
$99$	−1.25442e59	−0.0170439
$100$	5.79666e60	0.579666
$101$	−1.42955e61	−1.05535	−0.527675	−	0.849446i	$-0.676936\pi$
$101$	−1.42955e61	−1.05535	−0.527675	+	0.849446i	$0.676936\pi$
$102$	7.29860e60	0.398965
$103$	−4.01328e61	−1.62916	−0.814581	−	0.580051i	$-0.803033\pi$
$103$	−4.01328e61	−1.62916	−0.814581	+	0.580051i	$0.803033\pi$
$104$	4.68496e61	1.41641
$105$	6.49486e59	0.0146655
$106$	5.44486e61	0.920785
$107$	4.31345e61	0.547796	0.273898	−	0.961759i	$-0.411687\pi$
$107$	4.31345e61	0.547796	0.273898	+	0.961759i	$0.411687\pi$
$108$	6.43974e61	0.615806
$109$	−1.94980e62	−1.40761	−0.703805	−	0.710393i	$-0.748517\pi$
$109$	−1.94980e62	−1.40761	−0.703805	+	0.710393i	$0.748517\pi$
$110$	3.01099e59	0.00164525
$111$	−1.73116e62	−0.717773
$112$	−6.68733e60	−0.0210913
$113$	−6.70205e61	−0.161182	−0.0805908	−	0.996747i	$-0.525681\pi$
$113$	−6.70205e61	−0.161182	−0.0805908	+	0.996747i	$0.525681\pi$
$114$	−1.92494e62	−0.353850
$115$	−7.17857e61	−0.101101
$116$	7.41504e62	0.801945
$117$	8.52853e62	0.709913
$118$	4.21040e62	0.270347
$119$	4.88737e62	0.242601
$120$	−1.42169e62	−0.0546734
$121$	−3.34559e63	−0.998893
$122$	1.15364e62	0.0267976
$123$	3.12111e63	0.565201
$124$	−5.60676e63	−0.793141
$125$	−1.37941e63	−0.152734
$126$	−1.04452e63	−0.0907014
$127$	−2.06063e63	−0.140600	−0.0703002	−	0.997526i	$-0.522396\pi$
$127$	−2.06063e63	−0.140600	−0.0703002	+	0.997526i	$0.522396\pi$
$128$	−9.63214e63	−0.517391
$129$	2.22327e64	0.941902
$130$	−2.04710e63	−0.0685278
$131$	6.07543e64	1.60991	0.804957	−	0.593333i	$-0.202188\pi$
$131$	6.07543e64	1.60991	0.804957	+	0.593333i	$0.202188\pi$
$132$	−6.44660e62	−0.0135465
$133$	−1.28900e64	−0.215168
$134$	−3.41039e64	−0.453010
$135$	−7.63965e63	−0.0808897
$136$	−1.06982e65	−0.904426
$137$	−1.12737e65	−0.762238	−0.381119	−	0.924526i	$-0.624461\pi$
$137$	−1.12737e65	−0.762238	−0.381119	+	0.924526i	$0.624461\pi$
$138$	−1.09894e65	−0.595196
$139$	3.26131e65	1.41723	0.708616	−	0.705594i	$-0.249320\pi$
$139$	3.26131e65	1.41723	0.708616	+	0.705594i	$0.249320\pi$
$140$	−3.50645e63	−0.0122451
$141$	3.01977e64	0.0848771
$142$	3.01600e65	0.683341
$143$	−2.52021e64	−0.0460986
$144$	2.66475e64	0.0394094
$145$	−8.79667e64	−0.105340
$146$	7.27630e65	0.706559
$147$	−8.19036e65	−0.645839
$148$	9.34623e65	0.599314
$149$	−2.77156e66	−1.44725	−0.723625	−	0.690194i	$-0.757525\pi$
$149$	−2.77156e66	−1.44725	−0.723625	+	0.690194i	$0.757525\pi$
$150$	−1.05273e66	−0.448264
$151$	−1.14707e65	−0.0398836	−0.0199418	−	0.999801i	$-0.506348\pi$
$151$	−1.14707e65	−0.0398836	−0.0199418	+	0.999801i	$0.506348\pi$
$152$	2.82155e66	0.802154
$153$	−1.94750e66	−0.453304
$154$	3.08659e64	0.00588974
$155$	6.65146e65	0.104184
$156$	4.38290e66	0.564236
$157$	4.92931e66	0.522212	0.261106	−	0.965310i	$-0.415913\pi$
$157$	4.92931e66	0.522212	0.261106	+	0.965310i	$0.415913\pi$
$158$	−4.11265e66	−0.358988
$159$	1.38297e67	0.995867
$160$	1.25238e66	0.0744865
$161$	−7.35880e66	−0.361925
$162$	−3.57111e66	−0.145410
$163$	−5.45632e67	−1.84153	−0.920764	−	0.390121i	$-0.872433\pi$
$163$	−5.45632e67	−1.84153	−0.920764	+	0.390121i	$0.872433\pi$
$164$	−1.68503e67	−0.471922
$165$	7.64778e64	0.00177941
$166$	3.33591e67	0.645532
$167$	4.21801e67	0.679603	0.339801	−	0.940497i	$-0.389640\pi$
$167$	4.21801e67	0.679603	0.339801	+	0.940497i	$0.389640\pi$
$168$	−1.45738e67	−0.195723
$169$	8.21065e67	0.920096
$170$	4.67459e66	0.0437574
$171$	5.13636e67	0.402045
$172$	−1.20030e68	−0.786453
$173$	1.33954e68	0.735443	0.367721	−	0.929936i	$-0.380138\pi$
$173$	1.33954e68	0.735443	0.367721	+	0.929936i	$0.380138\pi$
$174$	−1.34664e68	−0.620155
$175$	−7.04940e67	−0.272579
$176$	−7.87443e65	−0.00255907
$177$	1.06942e68	0.292392
$178$	−3.69784e68	−0.851408
$179$	−1.01313e68	−0.196630	−0.0983150	−	0.995155i	$-0.531345\pi$
$179$	−1.01313e68	−0.196630	−0.0983150	+	0.995155i	$0.531345\pi$
$180$	1.39724e67	0.0228802
$181$	4.25098e67	0.0587885	0.0293943	−	0.999568i	$-0.490642\pi$
$181$	4.25098e67	0.0587885	0.0293943	+	0.999568i	$0.490642\pi$
$182$	−2.09850e68	−0.245319
$183$	2.93020e67	0.0289827
$184$	1.61080e69	1.34927
$185$	−1.10877e68	−0.0787234
$186$	1.01824e69	0.613347
$187$	5.75494e67	0.0294355
$188$	−1.63032e68	−0.0708692
$189$	−7.83146e68	−0.289573
$190$	−1.23288e68	−0.0388093
$191$	−5.32231e69	−1.42752	−0.713761	−	0.700389i	$-0.753010\pi$
$191$	−5.32231e69	−1.42752	−0.713761	+	0.700389i	$0.753010\pi$
$192$	2.15208e69	0.492233
$193$	−2.00291e69	−0.390988	−0.195494	−	0.980705i	$-0.562631\pi$
$193$	−2.00291e69	−0.390988	−0.195494	+	0.980705i	$0.562631\pi$
$194$	−2.25161e69	−0.375440
$195$	−5.19955e68	−0.0741157
$196$	4.42182e69	0.539251
$197$	−2.47637e69	−0.258580	−0.129290	−	0.991607i	$-0.541270\pi$
$197$	−2.47637e69	−0.258580	−0.129290	+	0.991607i	$0.541270\pi$
$198$	−1.22993e68	−0.0110051
$199$	2.26238e70	1.73599	0.867994	−	0.496575i	$-0.165409\pi$
$199$	2.26238e70	1.73599	0.867994	+	0.496575i	$0.165409\pi$
$200$	1.54308e70	1.01618
$201$	−8.66225e69	−0.489949
$202$	−1.40164e70	−0.681427
$203$	−9.01754e69	−0.377102
$204$	−1.00084e70	−0.360284
$205$	1.99900e69	0.0619897
$206$	−3.93493e70	−1.05193
$207$	2.93231e70	0.676262
$208$	5.35364e69	0.106590
$209$	−1.51781e69	−0.0261070
$210$	6.36806e68	0.00946932
$211$	−1.43805e70	−0.184995	−0.0924975	−	0.995713i	$-0.529485\pi$
$211$	−1.43805e70	−0.184995	−0.0924975	+	0.995713i	$0.529485\pi$
$212$	−7.46642e70	−0.831512
$213$	7.66053e70	0.739062
$214$	4.22924e70	0.353706
$215$	1.42395e70	0.103305
$216$	1.71426e71	1.07954
$217$	6.81846e70	0.372962
$218$	−1.91174e71	−0.908877
$219$	1.84815e71	0.764173
$220$	−4.12890e68	−0.00148574
$221$	−3.91265e71	−1.22605
$222$	−1.69737e71	−0.463458
$223$	−3.83507e71	−0.913009	−0.456504	−	0.889721i	$-0.650899\pi$
$223$	−3.83507e71	−0.913009	−0.456504	+	0.889721i	$0.650899\pi$
$224$	1.28383e71	0.266650
$225$	2.80902e71	0.509318
$226$	−6.57121e70	−0.104073
$227$	−4.91476e71	−0.680320	−0.340160	−	0.940368i	$-0.610481\pi$
$227$	−4.91476e71	−0.680320	−0.340160	+	0.940368i	$0.610481\pi$
$228$	2.63963e71	0.319543
$229$	1.61052e72	1.70602	0.853012	−	0.521891i	$-0.174773\pi$
$229$	1.61052e72	1.70602	0.853012	+	0.521891i	$0.174773\pi$
$230$	−7.03842e70	−0.0652794
$231$	7.83980e69	0.00637000
$232$	1.97389e72	1.40585
$233$	−2.97343e72	−1.85739	−0.928693	−	0.370850i	$-0.879066\pi$
$233$	−2.97343e72	−1.85739	−0.928693	+	0.370850i	$0.879066\pi$
$234$	8.36203e71	0.458383
$235$	1.93409e70	0.00930908
$236$	−5.77363e71	−0.244136
$237$	−1.04460e72	−0.388261
$238$	4.79196e71	0.156645
$239$	−5.09144e72	−1.46455	−0.732275	−	0.681009i	$-0.761542\pi$
$239$	−5.09144e72	−1.46455	−0.732275	+	0.681009i	$0.761542\pi$
$240$	−1.62461e70	−0.00411439
$241$	4.14476e72	0.924655	0.462327	−	0.886709i	$-0.347015\pi$
$241$	4.14476e72	0.924655	0.462327	+	0.886709i	$0.347015\pi$
$242$	−3.28028e72	−0.644974
$243$	5.18414e72	0.898846
$244$	−1.58196e71	−0.0241995
$245$	−5.24573e71	−0.0708338
$246$	3.06018e72	0.364944
$247$	1.03193e73	1.08741
$248$	−1.49252e73	−1.39042
$249$	8.47307e72	0.698170
$250$	−1.35248e72	−0.0986188
$251$	3.22599e72	0.208264	0.104132	−	0.994563i	$-0.466794\pi$
$251$	3.22599e72	0.208264	0.104132	+	0.994563i	$0.466794\pi$
$252$	1.43232e72	0.0819076
$253$	−8.66509e71	−0.0439134
$254$	−2.02040e72	−0.0907840
$255$	1.18733e72	0.0473254
$256$	−2.93702e73	−1.03894
$257$	−4.70005e73	−1.47619	−0.738095	−	0.674697i	$-0.764274\pi$
$257$	−4.70005e73	−1.47619	−0.738095	+	0.674697i	$0.764274\pi$
$258$	2.17986e73	0.608175
$259$	−1.13661e73	−0.281818
$260$	2.80714e72	0.0618838
$261$	3.59328e73	0.704621
$262$	5.95683e73	1.03950
$263$	6.53435e73	1.01520	0.507601	−	0.861592i	$-0.330532\pi$
$263$	6.53435e73	1.01520	0.507601	+	0.861592i	$0.330532\pi$
$264$	−1.71609e72	−0.0237476
$265$	8.85762e72	0.109224
$266$	−1.26383e73	−0.138931
$267$	−9.39235e73	−0.920833
$268$	4.67659e73	0.409089
$269$	−7.56525e73	−0.590716	−0.295358	−	0.955387i	$-0.595439\pi$
$269$	−7.56525e73	−0.590716	−0.295358	+	0.955387i	$0.595439\pi$
$270$	−7.49050e72	−0.0522295
$271$	−5.25878e73	−0.327583	−0.163792	−	0.986495i	$-0.552372\pi$
$271$	−5.25878e73	−0.327583	−0.163792	+	0.986495i	$0.552372\pi$
$272$	−1.22251e73	−0.0680615
$273$	−5.33010e73	−0.265323
$274$	−1.10537e74	−0.492168
$275$	−8.30077e72	−0.0330728
$276$	1.50694e74	0.537490
$277$	1.19304e72	0.00381085	0.00190543	−	0.999998i	$-0.499393\pi$
$277$	1.19304e72	0.00381085	0.00190543	+	0.999998i	$0.499393\pi$
$278$	3.19764e74	0.915090
$279$	−2.71700e74	−0.696885
$280$	−9.33420e72	−0.0214663
$281$	5.85184e74	1.20712	0.603559	−	0.797319i	$-0.293749\pi$
$281$	5.85184e74	1.20712	0.603559	+	0.797319i	$0.293749\pi$
$282$	2.96081e73	0.0548041
$283$	1.48848e74	0.247318	0.123659	−	0.992325i	$-0.460537\pi$
$283$	1.48848e74	0.247318	0.123659	+	0.992325i	$0.460537\pi$
$284$	−4.13578e74	−0.617089
$285$	−3.13146e73	−0.0419739
$286$	−2.47101e73	−0.0297653
$287$	2.04919e74	0.221914
$288$	−5.11576e74	−0.498240
$289$	−2.47798e74	−0.217127
$290$	−8.62494e73	−0.0680169
$291$	−5.71899e74	−0.406054
$292$	−9.97782e74	−0.638056
$293$	7.53743e74	0.434271	0.217136	−	0.976141i	$-0.430329\pi$
$293$	7.53743e74	0.434271	0.217136	+	0.976141i	$0.430329\pi$
$294$	−8.03046e74	−0.417010
$295$	6.84942e73	0.0320688
$296$	2.48797e75	1.05063
$297$	−9.22165e73	−0.0351348
$298$	−2.71745e75	−0.934472
$299$	5.89120e75	1.82908
$300$	1.44359e75	0.404803
$301$	1.45970e75	0.369817
$302$	−1.12468e74	−0.0257523
$303$	−3.56010e75	−0.736992
$304$	3.22427e74	0.0603652
$305$	1.87673e73	0.00317875
$306$	−1.90948e75	−0.292693
$307$	−1.13968e76	−1.58147	−0.790735	−	0.612159i	$-0.790301\pi$
$307$	−1.13968e76	−1.58147	−0.790735	+	0.612159i	$0.790301\pi$
$308$	−4.23256e73	−0.00531871
$309$	−9.99456e75	−1.13771
$310$	6.52160e74	0.0672702
$311$	1.39236e76	1.30185	0.650923	−	0.759144i	$-0.274382\pi$
$311$	1.39236e76	1.30185	0.650923	+	0.759144i	$0.274382\pi$
$312$	1.16673e76	0.989134
$313$	−2.81704e75	−0.216616	−0.108308	−	0.994117i	$-0.534543\pi$
$313$	−2.81704e75	−0.216616	−0.108308	+	0.994117i	$0.534543\pi$
$314$	4.83308e75	0.337186
$315$	−1.69920e74	−0.0107590
$316$	5.63958e75	0.324183
$317$	−1.48589e76	−0.775674	−0.387837	−	0.921728i	$-0.626778\pi$
$317$	−1.48589e76	−0.775674	−0.387837	+	0.921728i	$0.626778\pi$
$318$	1.35597e76	0.643020
$319$	−1.06183e75	−0.0457549
$320$	1.37836e75	0.0539867
$321$	1.07421e76	0.382547
$322$	−7.21514e75	−0.233690
$323$	−2.35642e76	−0.694346
$324$	4.89698e75	0.131312
$325$	5.64350e76	1.37755
$326$	−5.34980e76	−1.18905
$327$	−4.85574e76	−0.982989
$328$	−4.48556e76	−0.827303
$329$	1.98265e75	0.0333251
$330$	7.49848e73	0.00114894
$331$	9.37638e76	1.31003	0.655015	−	0.755616i	$-0.272662\pi$
$331$	9.37638e76	1.31003	0.655015	+	0.755616i	$0.272662\pi$
$332$	−4.57446e76	−0.582946
$333$	4.52912e76	0.526581
$334$	4.13566e76	0.438811
$335$	−5.54797e75	−0.0537363
$336$	−1.66540e75	−0.0147289
$337$	4.95449e76	0.400209	0.200105	−	0.979775i	$-0.435872\pi$
$337$	4.95449e76	0.400209	0.200105	+	0.979775i	$0.435872\pi$
$338$	8.05036e76	0.594095
$339$	−1.66906e76	−0.112559
$340$	−6.41015e75	−0.0395150
$341$	8.02883e75	0.0452526
$342$	5.03609e76	0.259595
$343$	−1.11920e77	−0.527761
$344$	−3.19521e77	−1.37869
$345$	−1.78773e76	−0.0706024
$346$	1.31339e77	0.474867
$347$	−4.94026e77	−1.63569	−0.817844	−	0.575440i	$-0.804831\pi$
$347$	−4.94026e77	−1.63569	−0.817844	+	0.575440i	$0.804831\pi$
$348$	1.84662e77	0.560030
$349$	−3.62283e76	−0.100664	−0.0503318	−	0.998733i	$-0.516028\pi$
$349$	−3.62283e76	−0.100664	−0.0503318	+	0.998733i	$0.516028\pi$
$350$	−6.91178e76	−0.176001
$351$	6.26959e77	1.46343
$352$	1.51172e76	0.0323535
$353$	1.78348e77	0.350057	0.175028	−	0.984563i	$-0.443998\pi$
$353$	1.78348e77	0.350057	0.175028	+	0.984563i	$0.443998\pi$
$354$	1.04855e77	0.188794
$355$	4.90639e76	0.0810583
$356$	5.07076e77	0.768861
$357$	1.21714e77	0.169418
$358$	−9.93356e76	−0.126962
$359$	−8.52288e77	−1.00047	−0.500237	−	0.865889i	$-0.666754\pi$
$359$	−8.52288e77	−1.00047	−0.500237	+	0.865889i	$0.666754\pi$
$360$	3.71946e76	0.0401101
$361$	−3.87698e77	−0.384170
$362$	4.16799e76	0.0379591
$363$	−8.33177e77	−0.697566
$364$	2.87762e77	0.221535
$365$	1.18370e77	0.0838124
$366$	2.87300e76	0.0187138
$367$	−1.13900e77	−0.0682664	−0.0341332	−	0.999417i	$-0.510867\pi$
$367$	−1.13900e77	−0.0682664	−0.0341332	+	0.999417i	$0.510867\pi$
$368$	1.84071e77	0.101538
$369$	−8.16554e77	−0.414649
$370$	−1.08712e77	−0.0508308
$371$	9.08002e77	0.391005
$372$	−1.39629e78	−0.553881
$373$	2.11898e78	0.774476	0.387238	−	0.921980i	$-0.373429\pi$
$373$	2.11898e78	0.774476	0.387238	+	0.921980i	$0.373429\pi$
$374$	5.64259e76	0.0190062
$375$	−3.43524e77	−0.106660
$376$	−4.33991e77	−0.124237
$377$	7.21912e78	1.90578
$378$	−7.67857e77	−0.186974
$379$	1.08570e78	0.243902	0.121951	−	0.992536i	$-0.461085\pi$
$379$	1.08570e78	0.243902	0.121951	+	0.992536i	$0.461085\pi$
$380$	1.69062e77	0.0350466
$381$	−5.13174e77	−0.0981867
$382$	−5.21841e78	−0.921734
$383$	−6.68528e78	−1.09033	−0.545164	−	0.838329i	$-0.683533\pi$
$383$	−6.68528e78	−1.09033	−0.545164	+	0.838329i	$0.683533\pi$
$384$	−2.39876e78	−0.361314
$385$	5.02121e75	0.000698644 0
$386$	−1.96381e78	−0.252456
$387$	−5.81658e78	−0.691008
$388$	3.08758e78	0.339040
$389$	1.21345e79	1.23185	0.615926	−	0.787804i	$-0.288782\pi$
$389$	1.21345e79	1.23185	0.615926	+	0.787804i	$0.288782\pi$
$390$	−5.09804e77	−0.0478556
$391$	−1.34526e79	−1.16793
$392$	1.17709e79	0.945334
$393$	1.51301e79	1.12427
$394$	−2.42802e78	−0.166962
$395$	−6.69039e77	−0.0425834
$396$	1.68658e77	0.00993810
$397$	1.96626e77	0.0107283	0.00536414	−	0.999986i	$-0.498293\pi$
$397$	1.96626e77	0.0107283	0.00536414	+	0.999986i	$0.498293\pi$
$398$	2.21821e79	1.12091
$399$	−3.21009e78	−0.150260
$400$	1.76332e78	0.0764717
$401$	−1.33975e79	−0.538417	−0.269209	−	0.963082i	$-0.586762\pi$
$401$	−1.33975e79	−0.538417	−0.269209	+	0.963082i	$0.586762\pi$
$402$	−8.49314e78	−0.316354
$403$	−5.45862e79	−1.88486
$404$	1.92204e79	0.615361
$405$	−5.80943e77	−0.0172487
$406$	−8.84149e78	−0.243490
$407$	−1.33837e78	−0.0341938
$408$	−2.66425e79	−0.631596
$409$	5.24362e79	1.15364	0.576820	−	0.816871i	$-0.304293\pi$
$409$	5.24362e79	1.15364	0.576820	+	0.816871i	$0.304293\pi$
$410$	1.95997e78	0.0400260
$411$	−2.80758e79	−0.532301
$412$	5.39588e79	0.949942
$413$	7.02139e78	0.114801
$414$	2.87507e79	0.436654
$415$	5.42681e78	0.0765733
$416$	−1.02779e80	−1.34759
$417$	8.12188e79	0.989708
$418$	−1.48818e78	−0.0168570
$419$	−1.15357e79	−0.121483	−0.0607417	−	0.998154i	$-0.519347\pi$
$419$	−1.15357e79	−0.121483	−0.0607417	+	0.998154i	$0.519347\pi$
$420$	−8.73238e77	−0.00855124
$421$	1.70015e80	1.54840	0.774201	−	0.632939i	$-0.218152\pi$
$421$	1.70015e80	1.54840	0.774201	+	0.632939i	$0.218152\pi$
$422$	−1.40998e79	−0.119449
$423$	−7.90041e78	−0.0622685
$424$	−1.98757e80	−1.45768
$425$	−1.28870e80	−0.879611
$426$	7.51098e79	0.477203
$427$	1.92385e78	0.0113794
$428$	−5.79946e79	−0.319413
$429$	−6.27627e78	−0.0321924
$430$	1.39615e79	0.0667029
$431$	−3.88868e80	−1.73080	−0.865398	−	0.501085i	$-0.832934\pi$
$431$	−3.88868e80	−1.73080	−0.865398	+	0.501085i	$0.832934\pi$
$432$	1.95894e79	0.0812394
$433$	3.92018e80	1.51505	0.757523	−	0.652809i	$-0.226410\pi$
$433$	3.92018e80	1.51505	0.757523	+	0.652809i	$0.226410\pi$
$434$	6.68535e79	0.240817
$435$	−2.19070e79	−0.0735632
$436$	2.62152e80	0.820759
$437$	3.54801e80	1.03586
$438$	1.81207e80	0.493417
$439$	−1.77739e80	−0.451455	−0.225727	−	0.974191i	$-0.572476\pi$
$439$	−1.77739e80	−0.451455	−0.225727	+	0.974191i	$0.572476\pi$
$440$	−1.09912e78	−0.00260457
$441$	2.14279e80	0.473807
$442$	−3.83627e80	−0.791644
$443$	−5.81258e80	−1.11958	−0.559790	−	0.828635i	$-0.689118\pi$
$443$	−5.81258e80	−1.11958	−0.559790	+	0.828635i	$0.689118\pi$
$444$	2.32756e80	0.418524
$445$	−6.01558e79	−0.100994
$446$	−3.76020e80	−0.589519
$447$	−6.90222e80	−1.01067
$448$	1.41296e80	0.193264
$449$	2.43094e80	0.310642	0.155321	−	0.987864i	$-0.450359\pi$
$449$	2.43094e80	0.310642	0.155321	+	0.987864i	$0.450359\pi$
$450$	2.75419e80	0.328860
$451$	2.41295e79	0.0269255
$452$	9.01096e79	0.0939828
$453$	−2.85664e79	−0.0278522
$454$	−4.81881e80	−0.439275
$455$	−3.41381e79	−0.0290999
$456$	7.02670e80	0.560175
$457$	4.97936e80	0.371304	0.185652	−	0.982616i	$-0.440560\pi$
$457$	4.97936e80	0.371304	0.185652	+	0.982616i	$0.440560\pi$
$458$	1.57908e81	1.10156
$459$	−1.43167e81	−0.934451
$460$	9.65163e79	0.0589504
$461$	1.47837e81	0.845091	0.422546	−	0.906342i	$-0.361137\pi$
$461$	1.47837e81	0.845091	0.422546	+	0.906342i	$0.361137\pi$
$462$	7.68675e78	0.00411304
$463$	−1.44774e80	−0.0725219	−0.0362610	−	0.999342i	$-0.511545\pi$
$463$	−1.44774e80	−0.0725219	−0.0362610	+	0.999342i	$0.511545\pi$
$464$	2.25562e80	0.105796
$465$	1.65646e80	0.0727555
$466$	−2.91538e81	−1.19929
$467$	−7.76500e78	−0.00299210	−0.00149605	−	0.999999i	$-0.500476\pi$
$467$	−7.76500e78	−0.00299210	−0.00149605	+	0.999999i	$0.500476\pi$
$468$	−1.14667e81	−0.413941
$469$	−5.68727e80	−0.192368
$470$	1.89633e79	0.00601077
$471$	1.22758e81	0.364681
$472$	−1.53694e81	−0.427983
$473$	1.71882e80	0.0448710
$474$	−1.02420e81	−0.250695
$475$	3.39884e81	0.780145
$476$	−6.57110e80	−0.141457
$477$	−3.61818e81	−0.730599
$478$	−4.99204e81	−0.945643
$479$	5.86941e81	1.04318	0.521592	−	0.853195i	$-0.325338\pi$
$479$	5.86941e81	1.04318	0.521592	+	0.853195i	$0.325338\pi$
$480$	3.11890e80	0.0520168
$481$	9.09929e81	1.42424
$482$	4.06384e81	0.597039
$483$	−1.83262e81	−0.252746
$484$	4.49817e81	0.582441
$485$	−3.66288e80	−0.0445348
$486$	5.08293e81	0.580374
$487$	−6.11323e81	−0.655597	−0.327799	−	0.944748i	$-0.606307\pi$
$487$	−6.11323e81	−0.655597	−0.327799	+	0.944748i	$0.606307\pi$
$488$	−4.21120e80	−0.0424230
$489$	−1.35883e82	−1.28601
$490$	−5.14332e80	−0.0457365
$491$	−6.46236e81	−0.540015	−0.270008	−	0.962858i	$-0.587026\pi$
$491$	−6.46236e81	−0.540015	−0.270008	+	0.962858i	$0.587026\pi$
$492$	−4.19635e81	−0.329561
$493$	−1.64850e82	−1.21691
$494$	1.01178e82	0.702125
$495$	−2.00084e79	−0.00130543
$496$	−1.70555e81	−0.104634
$497$	5.02958e81	0.290176
$498$	8.30766e81	0.450800
$499$	1.13795e82	0.580838	0.290419	−	0.956900i	$-0.406205\pi$
$499$	1.13795e82	0.580838	0.290419	+	0.956900i	$0.406205\pi$
$500$	1.85462e81	0.0890574
$501$	1.05044e82	0.474593
$502$	3.16301e81	0.134474
$503$	5.18866e80	0.0207602	0.0103801	−	0.999946i	$-0.496696\pi$
$503$	5.18866e80	0.0207602	0.0103801	+	0.999946i	$0.496696\pi$
$504$	3.81285e81	0.143588
$505$	−2.28016e81	−0.0808312
$506$	−8.49593e80	−0.0283544
$507$	2.04476e82	0.642539
$508$	2.77053e81	0.0819822
$509$	−5.17719e82	−1.44279	−0.721393	−	0.692526i	$-0.756498\pi$
$509$	−5.17719e82	−1.44279	−0.721393	+	0.692526i	$0.756498\pi$
$510$	1.16415e81	0.0305575
$511$	1.21342e82	0.300035
$512$	−6.58667e81	−0.153438
$513$	3.77590e82	0.828783
$514$	−4.60830e82	−0.953159
$515$	−6.40128e81	−0.124780
$516$	−2.98920e82	−0.549210
$517$	2.33460e80	0.00404344
$518$	−1.11442e82	−0.181966
$519$	3.33595e82	0.513588
$520$	7.47263e81	0.108485
$521$	−1.12930e83	−1.54617	−0.773087	−	0.634300i	$-0.781288\pi$
$521$	−1.12930e83	−1.54617	−0.773087	+	0.634300i	$0.781288\pi$
$522$	3.52313e82	0.454965
$523$	1.20266e83	1.46501	0.732506	−	0.680761i	$-0.238351\pi$
$523$	1.20266e83	1.46501	0.732506	+	0.680761i	$0.238351\pi$
$524$	−8.16846e82	−0.938720
$525$	−1.75556e82	−0.190352
$526$	6.40679e82	0.655504
$527$	1.24648e83	1.20355
$528$	−1.96103e80	−0.00178710
$529$	8.63022e82	0.742376
$530$	8.68470e81	0.0705246
$531$	−2.79786e82	−0.214508
$532$	1.73307e82	0.125462
$533$	−1.64051e83	−1.12150
$534$	−9.20899e82	−0.594571
$535$	6.88006e81	0.0419567
$536$	1.24491e83	0.717154
$537$	−2.52308e82	−0.137314
$538$	−7.41756e82	−0.381418
$539$	−6.33201e81	−0.0307669
$540$	1.02716e82	0.0471657
$541$	−4.18244e83	−1.81515	−0.907576	−	0.419889i	$-0.862069\pi$
$541$	−4.18244e83	−1.81515	−0.907576	+	0.419889i	$0.862069\pi$
$542$	−5.15612e82	−0.211517
$543$	1.05865e82	0.0410543
$544$	2.34697e83	0.860480
$545$	−3.10999e82	−0.107811
$546$	−5.22604e82	−0.171316
$547$	2.73670e83	0.848426	0.424213	−	0.905563i	$-0.360551\pi$
$547$	2.73670e83	0.848426	0.424213	+	0.905563i	$0.360551\pi$
$548$	1.51576e83	0.444451
$549$	−7.66609e81	−0.0212626
$550$	−8.13872e81	−0.0213547
$551$	4.34776e83	1.07930
$552$	4.01150e83	0.942247
$553$	−6.85837e82	−0.152442
$554$	1.16975e81	0.00246062
$555$	−2.76125e82	−0.0549756
$556$	−4.38486e83	−0.826369
$557$	6.78023e82	0.120965	0.0604826	−	0.998169i	$-0.480736\pi$
$557$	6.78023e82	0.120965	0.0604826	+	0.998169i	$0.480736\pi$
$558$	−2.66396e83	−0.449970
$559$	−1.16859e84	−1.86896
$560$	−1.06665e81	−0.00161542
$561$	1.43320e82	0.0205560
$562$	5.73760e83	0.779421
$563$	6.36301e82	0.0818760	0.0409380	−	0.999162i	$-0.486965\pi$
$563$	6.36301e82	0.0818760	0.0409380	+	0.999162i	$0.486965\pi$
$564$	−4.06010e82	−0.0494907
$565$	−1.06899e82	−0.0123452
$566$	1.45942e83	0.159691
$567$	−5.95529e82	−0.0617475
$568$	−1.10095e84	−1.08179
$569$	1.58075e84	1.47211	0.736054	−	0.676923i	$-0.236687\pi$
$569$	1.58075e84	1.47211	0.736054	+	0.676923i	$0.236687\pi$
$570$	−3.07033e82	−0.0271020
$571$	−2.70603e83	−0.226429	−0.113214	−	0.993571i	$-0.536115\pi$
$571$	−2.70603e83	−0.226429	−0.113214	+	0.993571i	$0.536115\pi$
$572$	3.38844e82	0.0268795
$573$	−1.32545e84	−0.996894
$574$	2.00918e83	0.143287
$575$	1.94037e84	1.31225
$576$	−5.63033e83	−0.361117
$577$	2.52668e84	1.53705	0.768525	−	0.639820i	$-0.220991\pi$
$577$	2.52668e84	1.53705	0.768525	+	0.639820i	$0.220991\pi$
$578$	−2.42961e83	−0.140196
$579$	−4.98799e83	−0.273042
$580$	1.18272e83	0.0614225
$581$	5.56306e83	0.274121
$582$	−5.60735e83	−0.262184
$583$	1.06918e83	0.0474419
$584$	−2.65610e84	−1.11854
$585$	1.36032e83	0.0543736
$586$	7.39028e83	0.280404
$587$	−2.58255e84	−0.930223	−0.465112	−	0.885252i	$-0.653986\pi$
$587$	−2.58255e84	−0.930223	−0.465112	+	0.885252i	$0.653986\pi$
$588$	1.10120e84	0.376580
$589$	−3.28749e84	−1.06745
$590$	6.71570e82	0.0207064
$591$	−6.16708e83	−0.180577
$592$	2.84308e83	0.0790637
$593$	−7.02737e83	−0.185620	−0.0928100	−	0.995684i	$-0.529585\pi$
$593$	−7.02737e83	−0.185620	−0.0928100	+	0.995684i	$0.529585\pi$
$594$	−9.04162e82	−0.0226861
$595$	7.79548e82	0.0185813
$596$	3.72638e84	0.843872
$597$	5.63417e84	1.21231
$598$	5.77619e84	1.18101
$599$	−9.83291e84	−1.91057	−0.955287	−	0.295679i	$-0.904454\pi$
$599$	−9.83291e84	−1.91057	−0.955287	+	0.295679i	$0.904454\pi$
$600$	3.84283e84	0.709641
$601$	2.15831e84	0.378828	0.189414	−	0.981897i	$-0.439341\pi$
$601$	2.15831e84	0.378828	0.189414	+	0.981897i	$0.439341\pi$
$602$	1.43121e84	0.238786
$603$	2.26624e84	0.359442
$604$	1.54225e83	0.0232556
$605$	−5.33630e83	−0.0765071
$606$	−3.49060e84	−0.475867
$607$	−9.71024e83	−0.125885	−0.0629426	−	0.998017i	$-0.520049\pi$
$607$	−9.71024e83	−0.125885	−0.0629426	+	0.998017i	$0.520049\pi$
$608$	−6.18991e84	−0.763177
$609$	−2.24570e84	−0.263345
$610$	1.84009e82	0.00205248
$611$	−1.58724e84	−0.168417
$612$	2.61843e84	0.264316
$613$	−6.21883e84	−0.597261	−0.298630	−	0.954369i	$-0.596530\pi$
$613$	−6.21883e84	−0.597261	−0.298630	+	0.954369i	$0.596530\pi$
$614$	−1.11743e85	−1.02114
$615$	4.97825e83	0.0432898
$616$	−1.12671e83	−0.00932397
$617$	2.26334e85	1.78259	0.891297	−	0.453421i	$-0.149796\pi$
$617$	2.26334e85	1.78259	0.891297	+	0.453421i	$0.149796\pi$
$618$	−9.79944e84	−0.734603
$619$	−1.15292e85	−0.822689	−0.411344	−	0.911480i	$-0.634941\pi$
$619$	−1.15292e85	−0.822689	−0.411344	+	0.911480i	$0.634941\pi$
$620$	−8.94293e83	−0.0607482
$621$	2.15564e85	1.39406
$622$	1.36518e85	0.840587
$623$	−6.16662e84	−0.361545
$624$	1.33326e84	0.0744361
$625$	1.84776e85	0.982435
$626$	−2.76204e84	−0.139866
$627$	−3.77992e83	−0.0182315
$628$	−6.62749e84	−0.304495
$629$	−2.07784e85	−0.909425
$630$	−1.66603e83	−0.00694699
$631$	1.45194e84	0.0576838	0.0288419	−	0.999584i	$-0.490818\pi$
$631$	1.45194e84	0.0576838	0.0288419	+	0.999584i	$0.490818\pi$
$632$	1.50126e85	0.568310
$633$	−3.58129e84	−0.129189
$634$	−1.45688e85	−0.500844
$635$	−3.28676e83	−0.0107688
$636$	−1.85942e85	−0.580677
$637$	4.30499e85	1.28150
$638$	−1.04110e84	−0.0295434
$639$	−2.00417e85	−0.542199
$640$	−1.53635e84	−0.0396279
$641$	−3.93288e85	−0.967254	−0.483627	−	0.875274i	$-0.660681\pi$
$641$	−3.93288e85	−0.967254	−0.483627	+	0.875274i	$0.660681\pi$
$642$	1.05324e85	0.247006
$643$	−6.28047e85	−1.40461	−0.702307	−	0.711874i	$-0.747847\pi$
$643$	−6.28047e85	−1.40461	−0.702307	+	0.711874i	$0.747847\pi$
$644$	9.89396e84	0.211033
$645$	3.54617e84	0.0721420
$646$	−2.31042e85	−0.448331
$647$	8.04540e85	1.48925	0.744624	−	0.667484i	$-0.232629\pi$
$647$	8.04540e85	1.48925	0.744624	+	0.667484i	$0.232629\pi$
$648$	1.30358e85	0.230197
$649$	8.26778e83	0.0139292
$650$	5.53333e85	0.889465
$651$	1.69805e85	0.260454
$652$	7.33606e85	1.07377
$653$	2.27157e85	0.317303	0.158651	−	0.987335i	$-0.449285\pi$
$653$	2.27157e85	0.317303	0.158651	+	0.987335i	$0.449285\pi$
$654$	−4.76094e85	−0.634704
$655$	9.69047e84	0.123306
$656$	−5.12578e84	−0.0622577
$657$	−4.83518e85	−0.560621
$658$	1.94395e84	0.0215176
$659$	−1.63534e84	−0.0172823	−0.00864117	−	0.999963i	$-0.502751\pi$
$659$	−1.63534e84	−0.0172823	−0.00864117	+	0.999963i	$0.502751\pi$
$660$	−1.02825e83	−0.00103755
$661$	−1.97954e86	−1.90730	−0.953649	−	0.300920i	$-0.902706\pi$
$661$	−1.97954e86	−1.90730	−0.953649	+	0.300920i	$0.902706\pi$
$662$	9.19333e85	0.845871
$663$	−9.74397e85	−0.856196
$664$	−1.21772e86	−1.02193
$665$	−2.05599e84	−0.0164801
$666$	4.44070e85	0.340007
$667$	2.48211e86	1.81544
$668$	−5.67114e85	−0.396267
$669$	−9.55075e85	−0.637589
$670$	−5.43966e84	−0.0346969
$671$	2.26536e83	0.00138070
$672$	3.19721e85	0.186212
$673$	−2.07904e85	−0.115719	−0.0578594	−	0.998325i	$-0.518428\pi$
$673$	−2.07904e85	−0.115719	−0.0578594	+	0.998325i	$0.518428\pi$
$674$	4.85777e85	0.258410
$675$	2.06500e86	1.04992
$676$	−1.10393e86	−0.536496
$677$	3.55563e86	1.65182	0.825909	−	0.563803i	$-0.190662\pi$
$677$	3.55563e86	1.65182	0.825909	+	0.563803i	$0.190662\pi$
$678$	−1.63648e85	−0.0726782
$679$	−3.75485e85	−0.159428
$680$	−1.70639e85	−0.0692717
$681$	−1.22396e86	−0.475094
$682$	7.87209e84	0.0292191
$683$	−1.05935e86	−0.376018	−0.188009	−	0.982167i	$-0.560203\pi$
$683$	−1.05935e86	−0.376018	−0.188009	+	0.982167i	$0.560203\pi$
$684$	−6.90587e85	−0.234427
$685$	−1.79819e85	−0.0583813
$686$	−1.09735e86	−0.340769
$687$	4.01081e86	1.19138
$688$	−3.65126e85	−0.103752
$689$	−7.26914e86	−1.97604
$690$	−1.75283e85	−0.0455872
$691$	3.75049e86	0.933271	0.466635	−	0.884450i	$-0.345466\pi$
$691$	3.75049e86	0.933271	0.466635	+	0.884450i	$0.345466\pi$
$692$	−1.80102e86	−0.428827
$693$	−2.05107e84	−0.00467323
$694$	−4.84381e86	−1.05614
$695$	5.20188e85	0.108548
$696$	4.91572e86	0.981760
$697$	3.74613e86	0.716115
$698$	−3.55211e85	−0.0649974
$699$	−7.40495e86	−1.29708
$700$	9.47797e85	0.158937
$701$	1.21524e85	0.0195103	0.00975516	−	0.999952i	$-0.496895\pi$
$701$	1.21524e85	0.0195103	0.00975516	+	0.999952i	$0.496895\pi$
$702$	6.14719e86	0.944920
$703$	5.48011e86	0.806587
$704$	1.66378e85	0.0234494
$705$	4.81661e84	0.00650089
$706$	1.74866e86	0.226028
$707$	−2.33741e86	−0.289363
$708$	−1.43785e86	−0.170490
$709$	1.78732e86	0.202998	0.101499	−	0.994836i	$-0.467636\pi$
$709$	1.78732e86	0.202998	0.101499	+	0.994836i	$0.467636\pi$
$710$	4.81060e85	0.0523384
$711$	2.73290e86	0.284840
$712$	1.34984e87	1.34785
$713$	−1.87680e87	−1.79551
$714$	1.19338e86	0.109391
$715$	−4.01980e84	−0.00353078
$716$	1.36217e86	0.114652
$717$	−1.26796e87	−1.02275
$718$	−8.35649e86	−0.645994
$719$	−1.18320e87	−0.876651	−0.438325	−	0.898816i	$-0.644428\pi$
$719$	−1.18320e87	−0.876651	−0.438325	+	0.898816i	$0.644428\pi$
$720$	4.25034e84	0.00301844
$721$	−6.56201e86	−0.446695
$722$	−3.80129e86	−0.248054
$723$	1.03220e87	0.645722
$724$	−5.71547e85	−0.0342788
$725$	2.37775e87	1.36728
$726$	−8.16911e86	−0.450410
$727$	7.32315e86	0.387167	0.193584	−	0.981084i	$-0.437989\pi$
$727$	7.32315e86	0.387167	0.193584	+	0.981084i	$0.437989\pi$
$728$	7.66025e86	0.388361
$729$	1.75424e87	0.852901
$730$	1.16059e86	0.0541166
$731$	2.66849e87	1.19340
$732$	−3.93968e85	−0.0168995
$733$	−5.10204e86	−0.209929	−0.104965	−	0.994476i	$-0.533473\pi$
$733$	−5.10204e86	−0.209929	−0.104965	+	0.994476i	$0.533473\pi$
$734$	−1.11676e86	−0.0440788
$735$	−1.30638e86	−0.0494660
$736$	−3.53378e87	−1.28371
$737$	−6.69683e85	−0.0233406
$738$	−8.00613e86	−0.267734
$739$	−2.70980e87	−0.869524	−0.434762	−	0.900545i	$-0.643168\pi$
$739$	−2.70980e87	−0.869524	−0.434762	+	0.900545i	$0.643168\pi$
$740$	1.49075e86	0.0459026
$741$	2.56988e87	0.759378
$742$	8.90275e86	0.252467
$743$	6.18077e86	0.168222	0.0841112	−	0.996456i	$-0.473195\pi$
$743$	6.18077e86	0.168222	0.0841112	+	0.996456i	$0.473195\pi$
$744$	−3.71694e87	−0.970982
$745$	−4.42071e86	−0.110848
$746$	2.07762e87	0.500070
$747$	−2.21675e87	−0.512199
$748$	−7.73756e85	−0.0171635
$749$	7.05280e86	0.150199
$750$	−3.36817e86	−0.0688693
$751$	−5.20963e87	−1.02279	−0.511397	−	0.859344i	$-0.670872\pi$
$751$	−5.20963e87	−1.02279	−0.511397	+	0.859344i	$0.670872\pi$
$752$	−4.95935e85	−0.00934933
$753$	8.03392e86	0.145439
$754$	7.07819e87	1.23054
$755$	−1.82961e85	−0.00305476
$756$	1.05295e87	0.168846
$757$	2.22778e87	0.343121	0.171561	−	0.985174i	$-0.445119\pi$
$757$	2.22778e87	0.343121	0.171561	+	0.985174i	$0.445119\pi$
$758$	1.06451e87	0.157485
$759$	−2.15793e86	−0.0306664
$760$	4.50044e86	0.0614385
$761$	5.32204e87	0.697985	0.348992	−	0.937126i	$-0.386524\pi$
$761$	5.32204e87	0.697985	0.348992	+	0.937126i	$0.386524\pi$
$762$	−5.03155e86	−0.0633980
$763$	−3.18807e87	−0.385949
$764$	7.15589e87	0.832369
$765$	−3.10632e86	−0.0347194
$766$	−6.55477e87	−0.704012
$767$	−5.62108e87	−0.580178
$768$	−7.31429e87	−0.725529
$769$	1.48822e88	1.41878	0.709389	−	0.704818i	$-0.248971\pi$
$769$	1.48822e88	1.41878	0.709389	+	0.704818i	$0.248971\pi$
$770$	4.92318e84	0.000451106 0
$771$	−1.17049e88	−1.03088
$772$	2.69293e87	0.227980
$773$	−1.68328e87	−0.136988	−0.0684938	−	0.997652i	$-0.521819\pi$
$773$	−1.68328e87	−0.136988	−0.0684938	+	0.997652i	$0.521819\pi$
$774$	−5.70303e87	−0.446176
$775$	−1.79789e88	−1.35227
$776$	8.21916e87	0.594354
$777$	−2.83058e87	−0.196804
$778$	1.18976e88	0.795392
$779$	−9.88006e87	−0.635137
$780$	6.99083e86	0.0432159
$781$	5.92240e86	0.0352080
$782$	−1.31900e88	−0.754118
$783$	2.64153e88	1.45252
$784$	1.34510e87	0.0711400
$785$	7.86238e86	0.0399972
$786$	1.48347e88	0.725925
$787$	1.03317e88	0.486342	0.243171	−	0.969983i	$-0.421812\pi$
$787$	1.03317e88	0.486342	0.243171	+	0.969983i	$0.421812\pi$
$788$	3.32949e87	0.150775
$789$	1.62730e88	0.708955
$790$	−6.55978e86	−0.0274956
$791$	−1.09584e87	−0.0441939
$792$	4.48968e86	0.0174220
$793$	−1.54016e87	−0.0575089
$794$	1.92787e86	0.00692712
$795$	2.20588e87	0.0762753
$796$	−3.04178e88	−1.01223
$797$	−3.51204e88	−1.12481	−0.562407	−	0.826861i	$-0.690124\pi$
$797$	−3.51204e88	−1.12481	−0.562407	+	0.826861i	$0.690124\pi$
$798$	−3.14742e87	−0.0970211
$799$	3.62449e87	0.107540
$800$	−3.38520e88	−0.966807
$801$	2.45726e88	0.675552
$802$	−1.31359e88	−0.347650
$803$	1.42881e87	0.0364042
$804$	1.16465e88	0.285683
$805$	−1.17375e87	−0.0277205
$806$	−5.35205e88	−1.21703
$807$	−1.88403e88	−0.412520
$808$	5.11647e88	1.07876
$809$	4.70026e88	0.954316	0.477158	−	0.878818i	$-0.341667\pi$
$809$	4.70026e88	0.954316	0.477158	+	0.878818i	$0.341667\pi$
$810$	−5.69601e86	−0.0111373
$811$	7.07672e88	1.33259	0.666294	−	0.745689i	$-0.267880\pi$
$811$	7.07672e88	1.33259	0.666294	+	0.745689i	$0.267880\pi$
$812$	1.21241e88	0.219883
$813$	−1.30963e88	−0.228764
$814$	−1.31224e87	−0.0220785
$815$	−8.70298e87	−0.141046
$816$	−3.04451e87	−0.0475300
$817$	−7.03789e88	−1.05845
$818$	5.14125e88	0.744892
$819$	1.39448e88	0.194649
$820$	−2.68767e87	−0.0361454
$821$	−5.20477e88	−0.674428	−0.337214	−	0.941428i	$-0.609485\pi$
$821$	−5.20477e88	−0.674428	−0.337214	+	0.941428i	$0.609485\pi$
$822$	−2.75277e88	−0.343700
$823$	4.31597e88	0.519258	0.259629	−	0.965708i	$-0.416400\pi$
$823$	4.31597e88	0.519258	0.259629	+	0.965708i	$0.416400\pi$
$824$	1.43639e89	1.66530
$825$	−2.06720e87	−0.0230960
$826$	6.88432e87	0.0741258
$827$	−1.50785e89	−1.56473	−0.782365	−	0.622821i	$-0.785987\pi$
$827$	−1.50785e89	−1.56473	−0.782365	+	0.622821i	$0.785987\pi$
$828$	−3.94251e88	−0.394319
$829$	3.48420e88	0.335885	0.167942	−	0.985797i	$-0.446288\pi$
$829$	3.48420e88	0.335885	0.167942	+	0.985797i	$0.446288\pi$
$830$	5.32086e87	0.0494425
$831$	2.97112e86	0.00266127
$832$	−1.13117e89	−0.976711
$833$	−9.83051e88	−0.818283
$834$	7.96332e88	0.639043
$835$	6.72783e87	0.0520520
$836$	2.04071e87	0.0152226
$837$	−1.99735e89	−1.43657
$838$	−1.13105e88	−0.0784404
$839$	1.17215e89	0.783872	0.391936	−	0.919992i	$-0.371805\pi$
$839$	1.17215e89	0.783872	0.391936	+	0.919992i	$0.371805\pi$
$840$	−2.32456e87	−0.0149908
$841$	1.43362e89	0.891574
$842$	1.66696e89	0.999785
$843$	1.45733e89	0.842977
$844$	1.93347e88	0.107868
$845$	1.30962e88	0.0704719
$846$	−7.74617e87	−0.0402060
$847$	−5.47029e88	−0.273884
$848$	−2.27125e88	−0.109696
$849$	3.70687e88	0.172712
$850$	−1.26354e89	−0.567954
$851$	3.12855e89	1.35673
$852$	−1.02996e89	−0.430937
$853$	−1.25601e89	−0.507045	−0.253523	−	0.967329i	$-0.581589\pi$
$853$	−1.25601e89	−0.507045	−0.253523	+	0.967329i	$0.581589\pi$
$854$	1.88629e87	0.00734756
$855$	8.19263e87	0.0307933
$856$	−1.54382e89	−0.559947
$857$	−1.93234e89	−0.676347	−0.338173	−	0.941084i	$-0.609809\pi$
$857$	−1.93234e89	−0.676347	−0.338173	+	0.941084i	$0.609809\pi$
$858$	−6.15374e87	−0.0207863
$859$	−4.33998e88	−0.141481	−0.0707403	−	0.997495i	$-0.522536\pi$
$859$	−4.33998e88	−0.141481	−0.0707403	+	0.997495i	$0.522536\pi$
$860$	−1.91451e88	−0.0602359
$861$	5.10324e88	0.154971
$862$	−3.81277e89	−1.11755
$863$	1.76145e89	0.498359	0.249179	−	0.968457i	$-0.419839\pi$
$863$	1.76145e89	0.498359	0.249179	+	0.968457i	$0.419839\pi$
$864$	−3.76075e89	−1.02708
$865$	2.13660e88	0.0563289
$866$	3.84365e89	0.978247
$867$	−6.17110e88	−0.151628
$868$	−9.16746e88	−0.217469
$869$	−8.07583e87	−0.0184963
$870$	−2.14793e88	−0.0474989
$871$	4.55302e89	0.972179
$872$	6.97851e89	1.43883
$873$	1.49622e89	0.297894
$874$	3.47875e89	0.668843
$875$	−2.25543e88	−0.0418778
$876$	−2.48485e89	−0.445579
$877$	−1.31068e89	−0.226991	−0.113495	−	0.993539i	$-0.536205\pi$
$877$	−1.31068e89	−0.226991	−0.113495	+	0.993539i	$0.536205\pi$
$878$	−1.74269e89	−0.291499
$879$	1.87710e89	0.303268
$880$	−1.25599e86	−0.000196004 0
$881$	−1.11397e90	−1.67923	−0.839614	−	0.543184i	$-0.817219\pi$
$881$	−1.11397e90	−1.67923	−0.839614	+	0.543184i	$0.817219\pi$
$882$	2.10095e89	0.305932
$883$	2.93644e89	0.413067	0.206533	−	0.978440i	$-0.433782\pi$
$883$	2.93644e89	0.413067	0.206533	+	0.978440i	$0.433782\pi$
$884$	5.26059e89	0.714892
$885$	1.70576e88	0.0223949
$886$	−5.69910e89	−0.722900
$887$	−1.32601e90	−1.62509	−0.812544	−	0.582900i	$-0.801918\pi$
$887$	−1.32601e90	−1.62509	−0.812544	+	0.582900i	$0.801918\pi$
$888$	6.19598e89	0.733694
$889$	−3.36928e88	−0.0385508
$890$	−5.89814e88	−0.0652109
$891$	−7.01244e87	−0.00749202
$892$	5.15628e89	0.532363
$893$	−9.55926e88	−0.0953794
$894$	−6.76748e89	−0.652578
$895$	−1.61598e88	−0.0150603
$896$	−1.57493e89	−0.141862
$897$	1.46713e90	1.27732
$898$	2.38348e89	0.200578
$899$	−2.29985e90	−1.87081
$900$	−3.77675e89	−0.296976
$901$	1.65992e90	1.26177
$902$	2.36584e88	0.0173855
$903$	3.63521e89	0.258257
$904$	2.39872e89	0.164757
$905$	6.78043e87	0.00450272
$906$	−2.80087e88	−0.0179839
$907$	1.13903e90	0.707150	0.353575	−	0.935406i	$-0.384966\pi$
$907$	1.13903e90	0.707150	0.353575	+	0.935406i	$0.384966\pi$
$908$	6.60792e89	0.396686
$909$	9.31405e89	0.540680
$910$	−3.34716e88	−0.0187894
$911$	−4.40257e89	−0.238999	−0.119499	−	0.992834i	$-0.538129\pi$
$911$	−4.40257e89	−0.238999	−0.119499	+	0.992834i	$0.538129\pi$
$912$	8.02962e88	0.0421553
$913$	6.55058e88	0.0332599
$914$	4.88215e89	0.239746
$915$	4.67375e87	0.00221984
$916$	−2.16536e90	−0.994760
$917$	9.93378e89	0.441418
$918$	−1.40372e90	−0.603364
$919$	−2.54886e90	−1.05980	−0.529898	−	0.848061i	$-0.677770\pi$
$919$	−2.54886e90	−1.05980	−0.529898	+	0.848061i	$0.677770\pi$
$920$	2.56927e89	0.103343
$921$	−2.83822e90	−1.10440
$922$	1.44950e90	0.545665
$923$	−4.02650e90	−1.46648
$924$	−1.05407e88	−0.00371426
$925$	2.99701e90	1.02180
$926$	−1.41947e89	−0.0468266
$927$	2.61481e90	0.834657
$928$	−4.33032e90	−1.33754
$929$	2.58810e90	0.773575	0.386788	−	0.922169i	$-0.373585\pi$
$929$	2.58810e90	0.773575	0.386788	+	0.922169i	$0.373585\pi$
$930$	1.62412e89	0.0469774
$931$	2.59271e90	0.725752
$932$	3.99780e90	1.08302
$933$	3.46750e90	0.909130
$934$	−7.61340e87	−0.00193196
$935$	9.17928e87	0.00225452
$936$	−3.05243e90	−0.725659
$937$	1.46131e90	0.336266	0.168133	−	0.985764i	$-0.446226\pi$
$937$	1.46131e90	0.336266	0.168133	+	0.985764i	$0.446226\pi$
$938$	−5.57624e89	−0.124209
$939$	−7.01547e89	−0.151271
$940$	−2.60040e88	−0.00542800
$941$	1.30889e90	0.264496	0.132248	−	0.991217i	$-0.457780\pi$
$941$	1.30889e90	0.264496	0.132248	+	0.991217i	$0.457780\pi$
$942$	1.20362e90	0.235470
$943$	−5.64046e90	−1.06834
$944$	−1.75631e89	−0.0322074
$945$	−1.24914e89	−0.0221789
$946$	1.68527e89	0.0289727
$947$	4.48696e90	0.746927	0.373464	−	0.927645i	$-0.378170\pi$
$947$	4.48696e90	0.746927	0.373464	+	0.927645i	$0.378170\pi$
$948$	1.40447e90	0.226390
$949$	−9.71419e90	−1.51631
$950$	3.33248e90	0.503730
$951$	−3.70042e90	−0.541683
$952$	−1.74923e90	−0.247982
$953$	−7.56718e90	−1.03896	−0.519482	−	0.854481i	$-0.673875\pi$
$953$	−7.56718e90	−1.03896	−0.519482	+	0.854481i	$0.673875\pi$
$954$	−3.54754e90	−0.471739
$955$	−8.48923e89	−0.109337
$956$	6.84547e90	0.853960
$957$	−2.64435e89	−0.0319524
$958$	5.75482e90	0.673572
$959$	−1.84334e90	−0.208996
$960$	3.43262e89	0.0377010
$961$	7.99133e90	0.850268
$962$	8.92165e90	0.919614
$963$	−2.81038e90	−0.280649
$964$	−5.57266e90	−0.539154
$965$	−3.19469e89	−0.0299465
$966$	−1.79684e90	−0.163195
$967$	6.35826e90	0.559539	0.279770	−	0.960067i	$-0.409742\pi$
$967$	6.35826e90	0.559539	0.279770	+	0.960067i	$0.409742\pi$
$968$	1.19742e91	1.02105
$969$	−5.86837e90	−0.484889
$970$	−3.59137e89	−0.0287556
$971$	−3.23669e90	−0.251139	−0.125570	−	0.992085i	$-0.540076\pi$
$971$	−3.23669e90	−0.251139	−0.125570	+	0.992085i	$0.540076\pi$
$972$	−6.97011e90	−0.524105
$973$	5.33248e90	0.388587
$974$	−5.99388e90	−0.423311
$975$	1.40544e91	0.961994
$976$	−4.81226e88	−0.00319249
$977$	−1.41204e90	−0.0907953	−0.0453977	−	0.998969i	$-0.514455\pi$
$977$	−1.41204e90	−0.0907953	−0.0453977	+	0.998969i	$0.514455\pi$
$978$	−1.33230e91	−0.830361
$979$	−7.26128e89	−0.0438673
$980$	7.05292e89	0.0413022
$981$	1.27037e91	0.721151
$982$	−6.33620e90	−0.348681
$983$	−8.68181e89	−0.0463157	−0.0231578	−	0.999732i	$-0.507372\pi$
$983$	−8.68181e89	−0.0463157	−0.0231578	+	0.999732i	$0.507372\pi$
$984$	−1.11707e91	−0.577738
$985$	−3.94987e89	−0.0198051
$986$	−1.61631e91	−0.785742
$987$	4.93754e89	0.0232722
$988$	−1.38743e91	−0.634052
$989$	−4.01788e91	−1.78037
$990$	−1.96177e88	−0.000842899 0
$991$	1.85513e91	0.772907	0.386454	−	0.922309i	$-0.373700\pi$
$991$	1.85513e91	0.772907	0.386454	+	0.922309i	$0.373700\pi$
$992$	3.27430e91	1.32286
$993$	2.33507e91	0.914845
$994$	4.93139e90	0.187363
$995$	3.60855e90	0.132963
$996$	−1.13921e91	−0.407093
$997$	6.39525e90	0.221643	0.110822	−	0.993840i	$-0.464652\pi$
$997$	6.39525e90	0.221643	0.110822	+	0.993840i	$0.464652\pi$
$998$	1.11573e91	0.375040
$999$	3.32950e91	1.08551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.62.a.a.1.3	✓	4
3.2	odd	2		9.62.a.a.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.62.a.a.1.3	✓	4	1.1	even	1	trivial
9.62.a.a.1.2		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)

\(f(q)\)	\(=\)	\(q+9.80478e8 q^{2} +2.49037e14 q^{3} -1.34451e18 q^{4} +1.59503e20 q^{5} +2.44176e23 q^{6} +1.63507e25 q^{7} -3.57909e27 q^{8} -6.51539e28 q^{9} +O(q^{10})\)	\(q+9.80478e8 q^{2} +2.49037e14 q^{3} -1.34451e18 q^{4} +1.59503e20 q^{5} +2.44176e23 q^{6} +1.63507e25 q^{7} -3.57909e27 q^{8} -6.51539e28 q^{9} +1.56389e29 q^{10} +1.92532e30 q^{11} -3.34832e32 q^{12} -1.30898e34 q^{13} +1.60315e34 q^{14} +3.97221e34 q^{15} -4.08993e35 q^{16} +2.98908e37 q^{17} -6.38819e37 q^{18} -7.88343e38 q^{19} -2.14452e38 q^{20} +4.07194e39 q^{21} +1.88773e39 q^{22} -4.50060e41 q^{23} -8.91326e41 q^{24} -4.31137e42 q^{25} -1.28343e43 q^{26} -4.78967e43 q^{27} -2.19837e43 q^{28} -5.51506e44 q^{29} +3.89466e43 q^{30} +4.17012e45 q^{31} +7.85180e45 q^{32} +4.79477e44 q^{33} +2.93073e46 q^{34} +2.60798e45 q^{35} +8.75998e46 q^{36} -6.95142e47 q^{37} -7.72953e47 q^{38} -3.25985e48 q^{39} -5.70874e47 q^{40} +1.25327e49 q^{41} +3.99245e48 q^{42} +8.92745e49 q^{43} -2.58861e48 q^{44} -1.03922e49 q^{45} -4.41273e50 q^{46} +1.21258e50 q^{47} -1.01854e50 q^{48} -3.28881e51 q^{49} -4.22720e51 q^{50} +7.44393e51 q^{51} +1.75994e52 q^{52} +5.55328e52 q^{53} -4.69616e52 q^{54} +3.07094e50 q^{55} -5.85207e52 q^{56} -1.96327e53 q^{57} -5.40740e53 q^{58} +4.29424e53 q^{59} -5.34066e52 q^{60} +1.17661e53 q^{61} +4.08871e54 q^{62} -1.06531e54 q^{63} +8.64159e54 q^{64} -2.08786e54 q^{65} +4.70116e53 q^{66} -3.47829e55 q^{67} -4.01884e55 q^{68} -1.12082e56 q^{69} +2.55707e54 q^{70} +3.07606e56 q^{71} +2.33191e56 q^{72} +7.42117e56 q^{73} -6.81572e56 q^{74} -1.07369e57 q^{75} +1.05993e57 q^{76} +3.14804e55 q^{77} -3.19621e57 q^{78} -4.19454e57 q^{79} -6.52354e55 q^{80} -3.64222e57 q^{81} +1.22880e58 q^{82} +3.40233e58 q^{83} -5.47475e57 q^{84} +4.76766e57 q^{85} +8.75316e58 q^{86} -1.37346e59 q^{87} -6.89089e57 q^{88} -3.77146e59 q^{89} -1.01893e58 q^{90} -2.14028e59 q^{91} +6.05108e59 q^{92} +1.03852e60 q^{93} +1.18890e59 q^{94} -1.25743e59 q^{95} +1.95539e60 q^{96} -2.29644e60 q^{97} -3.22460e60 q^{98} -1.25442e59 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1146312000 q^{2} - 573723599022000 q^{3} + 44\!\cdots\!28 q^{4}+ \cdots + 11\!\cdots\!52 q^{9}+O(q^{10}) \) 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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