LMFDB - Embedded newform 1.58.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,58,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, 58, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 58);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 58 $
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:	$20.5766433651$
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} - 20682206675887x^{2} + 1182366456513663853x + 45927816189452762789055234 $ x^4 - x^3 - 20682206675887x^2 + 1182366456513663853x + 45927816189452762789055234
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{25}\cdot 3^{10}\cdot 5^{2}\cdot 7\cdot 19 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.29777e6$ 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)

$f(q)$	$=$	$q-6.73315e8 q^{2} +5.51192e13 q^{3} +3.09237e17 q^{4} -1.13437e20 q^{5} -3.71126e22 q^{6} +6.16816e23 q^{7} -1.11179e26 q^{8} +1.46809e27 q^{9} +O(q^{10})$	\(q-6.73315e8 q^{2} +5.51192e13 q^{3} +3.09237e17 q^{4} -1.13437e20 q^{5} -3.71126e22 q^{6} +6.16816e23 q^{7} -1.11179e26 q^{8} +1.46809e27 q^{9} +7.63789e28 q^{10} -4.46542e28 q^{11} +1.70449e31 q^{12} -1.50421e31 q^{13} -4.15311e32 q^{14} -6.25257e33 q^{15} +3.02928e34 q^{16} +1.30305e35 q^{17} -9.88484e35 q^{18} +2.11773e36 q^{19} -3.50790e37 q^{20} +3.39984e37 q^{21} +3.00663e37 q^{22} -1.21340e39 q^{23} -6.12811e39 q^{24} +5.92910e39 q^{25} +1.01281e40 q^{26} -5.61981e39 q^{27} +1.90743e41 q^{28} -7.31457e41 q^{29} +4.20995e42 q^{30} -1.88432e42 q^{31} -4.37398e42 q^{32} -2.46130e42 q^{33} -8.77362e43 q^{34} -6.99698e43 q^{35} +4.53987e44 q^{36} +3.72569e44 q^{37} -1.42590e45 q^{38} -8.29111e44 q^{39} +1.26119e46 q^{40} -2.74135e45 q^{41} -2.28916e46 q^{42} -3.58496e46 q^{43} -1.38088e46 q^{44} -1.66535e47 q^{45} +8.16998e47 q^{46} -7.49401e47 q^{47} +1.66972e48 q^{48} -1.10065e48 q^{49} -3.99215e48 q^{50} +7.18230e48 q^{51} -4.65159e48 q^{52} -1.28624e49 q^{53} +3.78390e48 q^{54} +5.06545e48 q^{55} -6.85771e49 q^{56} +1.16728e50 q^{57} +4.92500e50 q^{58} +1.82082e50 q^{59} -1.93353e51 q^{60} -3.13164e50 q^{61} +1.26874e51 q^{62} +9.05538e50 q^{63} -1.42059e51 q^{64} +1.70634e51 q^{65} +1.65723e51 q^{66} -6.22614e51 q^{67} +4.02952e52 q^{68} -6.68815e52 q^{69} +4.71117e52 q^{70} +3.91938e52 q^{71} -1.63221e53 q^{72} -3.35931e51 q^{73} -2.50856e53 q^{74} +3.26807e53 q^{75} +6.54881e53 q^{76} -2.75434e52 q^{77} +5.58252e53 q^{78} +3.32824e53 q^{79} -3.43633e54 q^{80} -2.61472e54 q^{81} +1.84579e54 q^{82} +7.49625e53 q^{83} +1.05136e55 q^{84} -1.47814e55 q^{85} +2.41381e55 q^{86} -4.03173e55 q^{87} +4.96462e54 q^{88} +4.16835e55 q^{89} +1.12131e56 q^{90} -9.27822e54 q^{91} -3.75228e56 q^{92} -1.03862e56 q^{93} +5.04582e56 q^{94} -2.40229e56 q^{95} -2.41090e56 q^{96} +3.60852e56 q^{97} +7.41085e56 q^{98} -6.55562e55 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 217744560 q^{2} + 37475862172560 q^{3} + 29\!\cdots\!28 q^{4}+ \cdots + 80\!\cdots\!32 q^{9}+O(q^{10}) $ 4 * q - 217744560 * q^2 + 37475862172560 * q^3 + 293124896311376128 * q^4 - 106961276207842698600 * q^5 - 33990084162012424888512 * q^6 + 952854504056592488640800 * q^7 - 88551069216810449485639680 * q^8 + 807299095982681497210590132 * q^9	$ 4 q - 217744560 q^{2} + 37475862172560 q^{3} + 29\!\cdots\!28 q^{4}+ \cdots + 12\!\cdots\!04 q^{99}+O(q^{100}) $ 4 * q - 217744560 * q^2 + 37475862172560 * q^3 + 293124896311376128 * q^4 - 106961276207842698600 * q^5 - 33990084162012424888512 * q^6 + 952854504056592488640800 * q^7 - 88551069216810449485639680 * q^8 + 807299095982681497210590132 * q^9 + 44476431289760320477662520800 * q^10 - 462030036788542994175991820112 * q^11 + 10003750272364901761239114286080 * q^12 - 35670303061909387812013418679880 * q^13 + 70403094050531232484583448299136 * q^14 - 3873003953749638547444662603837600 * q^15 + 13566910890781728442321186411577344 * q^16 + 13820011728830480443629140931368520 * q^17 - 1287737321088043352155941276317529840 * q^18 + 336853252899071533902360882896311760 * q^19 - 50382729988973225454329459567578483200 * q^20 - 114908173756075652427942608537020743552 * q^21 - 661915503282569637498974918979285510720 * q^22 - 2975542065258688382050024994957196661920 * q^23 - 10578976944220511671340845604322576875520 * q^24 - 9469406228848045007865812554313674602500 * q^25 - 17469964426099436483582477475571041235872 * q^26 + 76349739563972016366032809192591896661920 * q^27 + 649254606795882967703588744692964385720320 * q^28 + 692903173502123074211699189163367889819640 * q^29 + 5634330080537746852583656641742556105212800 * q^30 - 899836592298317074905406089703577976621952 * q^31 - 14233950964359390830124363997913062975733760 * q^32 - 29363967329346027307019371741967172628226880 * q^33 - 169043128317257524614754408952689830505725024 * q^34 - 229326244292419606493088342114240299318011200 * q^35 + 284785472553153735165042638775100342213281024 * q^36 + 1088031360501840746049603861287321623324833560 * q^37 + 1556247388283245464794907962939214603341474880 * q^38 + 4179255936739867118004084422081931511953729504 * q^39 + 11751904708902009656918381872378671214758912000 * q^40 - 11103291557355181141038304173539140276092022872 * q^41 - 59279988331696939901744072326763120527717946880 * q^42 - 61754953860901881142563948460092952248410491600 * q^43 - 133524603192894473629581294520903680469781443584 * q^44 - 107702873160032711230811245899648546573795049800 * q^45 + 784819010796366200631618785819800311186796983168 * q^46 + 363083109323271524824455302894174707948361522880 * q^47 + 2742506186706372359330741580910160874632313569280 * q^48 + 1216129915477179767594559246649850886387208070628 * q^49 - 5243147625423300757899019878966089303259662130000 * q^50 - 764600229637750496670397948984385624631693707232 * q^51 - 22843788670121162835092909423272591563858567692800 * q^52 - 35290483593822076697173728695179253314838955459240 * q^53 + 12366575839681539833915263850508773584456529324160 * q^54 + 49196225093152182399971681538771907122934246240800 * q^55 + 63731767886683182211705479053660664279663635496960 * q^56 + 207676196582248616809244588606912583584671767915840 * q^57 + 617562539749243989517600779192095966343296224852320 * q^58 + 67768373912933539906296460571320281490527711258480 * q^59 - 1815042162748644358648991332911151647292658713651200 * q^60 - 1547288835446782082478245361946256543823484047403912 * q^61 - 749692944011811307313821057793297922348443552785920 * q^62 - 1569461042763431092010126958426126899190556123563360 * q^63 - 1990114977445631941316528741938069721703684937613312 * q^64 + 8063572248542729948506878297975365372089154570456400 * q^65 + 16489629555376763758820085001622755676656730822766336 * q^66 + 15272577061969964687199674310464241542844062558207120 * q^67 + 41305128999321265264790818598430329317542515380584960 * q^68 - 65786095162933072363901793014646952768970242331074176 * q^69 - 24325103535157938973881571830399397699429009026566400 * q^70 - 73888360588713834794031605853188887812717485611902432 * q^71 - 210328265328797773276338939967226276847978373484605440 * q^72 - 130297268842197178419561798573986372195905283718671320 * q^73 + 7685145516671187561069432006215096921673721366642656 * q^74 + 403928833669880609006163131916358629442839611491110000 * q^75 + 1456086045339107958455546112995861351598648681192657920 * q^76 - 106427745818663343042165176190596036157925407112924800 * q^77 + 2074950811168633790188899303505400649698048509219286400 * q^78 - 828943058463042070981602117491995742498435075805703360 * q^79 - 2284181918093911007938097065798931209886961598847385600 * q^80 - 7963307412965608591332950484302680892196600516966334236 * q^81 - 1883428276461442027198836795157559789817480540746193120 * q^82 - 9840480688986571601216593400698100805429733592804704560 * q^83 + 13541340719968270381664710206581288963145836751957467136 * q^84 - 14840134943015755845177119052592106190913842871494565200 * q^85 + 67988974963281087138264344329950027971018743502811738048 * q^86 - 27365055454269193487844075068414523895320708309490878240 * q^87 + 61847074514255305493001192533786291945351930637515735040 * q^88 - 10663966381455218428814337779016832517355842990125366680 * q^89 + 144098850070698626396745850922715348604587043628376674400 * q^90 - 254422712153651549623482540524255137118230327668042523712 * q^91 - 274534438781355859366149237613545893970204939554260346880 * q^92 - 414128946656565192633171191785208529876343680904079162880 * q^93 + 632898423704876935427548603685166753697821378730383050496 * q^94 - 532156934024946939894578863048125180396162968766201396000 * q^95 + 663745987198780197281626102963422448954448917470231134208 * q^96 - 152729877520747450623636953478949994021736793474425664120 * q^97 + 2296925218269808931776551039888426925574868525366690486480 * q^98 + 123613071571796047703935039848745969833181068960384152304 * 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 $

$2$	−6.73315e8	−1.77363	−0.886815	−	0.462124i	$-0.847088\pi$
$2$	−6.73315e8	−1.77363	−0.886815	+	0.462124i	$0.847088\pi$
$3$	5.51192e13	1.39106	0.695532	−	0.718495i	$-0.255169\pi$
$3$	5.51192e13	1.39106	0.695532	+	0.718495i	$0.255169\pi$
$4$	3.09237e17	2.14577
$5$	−1.13437e20	−1.36179	−0.680895	−	0.732381i	$-0.738409\pi$
$5$	−1.13437e20	−1.36179	−0.680895	+	0.732381i	$0.738409\pi$
$6$	−3.71126e22	−2.46724
$7$	6.16816e23	0.506829	0.253414	−	0.967358i	$-0.418446\pi$
$7$	6.16816e23	0.506829	0.253414	+	0.967358i	$0.418446\pi$
$8$	−1.11179e26	−2.03217
$9$	1.46809e27	0.935061
$10$	7.63789e28	2.41531
$11$	−4.46542e28	−0.0933621	−0.0466811	−	0.998910i	$-0.514864\pi$
$11$	−4.46542e28	−0.0933621	−0.0466811	+	0.998910i	$0.514864\pi$
$12$	1.70449e31	2.98490
$13$	−1.50421e31	−0.269106	−0.134553	−	0.990906i	$-0.542960\pi$
$13$	−1.50421e31	−0.269106	−0.134553	+	0.990906i	$0.542960\pi$
$14$	−4.15311e32	−0.898927
$15$	−6.25257e33	−1.89434
$16$	3.02928e34	1.45855
$17$	1.30305e35	1.11472	0.557361	−	0.830270i	$-0.311814\pi$
$17$	1.30305e35	1.11472	0.557361	+	0.830270i	$0.311814\pi$
$18$	−9.88484e35	−1.65845
$19$	2.11773e36	0.761014	0.380507	−	0.924778i	$-0.375749\pi$
$19$	2.11773e36	0.761014	0.380507	+	0.924778i	$0.375749\pi$
$20$	−3.50790e37	−2.92208
$21$	3.39984e37	0.705032
$22$	3.00663e37	0.165590
$23$	−1.21340e39	−1.88261	−0.941304	−	0.337561i	$-0.890398\pi$
$23$	−1.21340e39	−1.88261	−0.941304	+	0.337561i	$0.890398\pi$
$24$	−6.12811e39	−2.82687
$25$	5.92910e39	0.854474
$26$	1.01281e40	0.477295
$27$	−5.61981e39	−0.0903347
$28$	1.90743e41	1.08754
$29$	−7.31457e41	−1.53407	−0.767036	−	0.641604i	$-0.778269\pi$
$29$	−7.31457e41	−1.53407	−0.767036	+	0.641604i	$0.778269\pi$
$30$	4.20995e42	3.35986
$31$	−1.88432e42	−0.590673	−0.295337	−	0.955393i	$-0.595432\pi$
$31$	−1.88432e42	−0.590673	−0.295337	+	0.955393i	$0.595432\pi$
$32$	−4.37398e42	−0.554756
$33$	−2.46130e42	−0.129873
$34$	−8.77362e43	−1.97710
$35$	−6.99698e43	−0.690195
$36$	4.53987e44	2.00642
$37$	3.72569e44	0.754150	0.377075	−	0.926183i	$-0.376930\pi$
$37$	3.72569e44	0.754150	0.377075	+	0.926183i	$0.376930\pi$
$38$	−1.42590e45	−1.34976
$39$	−8.29111e44	−0.374344
$40$	1.26119e46	2.76738
$41$	−2.74135e45	−0.297594	−0.148797	−	0.988868i	$-0.547540\pi$
$41$	−2.74135e45	−0.297594	−0.148797	+	0.988868i	$0.547540\pi$
$42$	−2.28916e46	−1.25047
$43$	−3.58496e46	−1.00146	−0.500730	−	0.865604i	$-0.666935\pi$
$43$	−3.58496e46	−1.00146	−0.500730	+	0.865604i	$0.666935\pi$
$44$	−1.38088e46	−0.200333
$45$	−1.66535e47	−1.27336
$46$	8.16998e47	3.33905
$47$	−7.49401e47	−1.65930	−0.829650	−	0.558283i	$-0.811460\pi$
$47$	−7.49401e47	−1.65930	−0.829650	+	0.558283i	$0.811460\pi$
$48$	1.66972e48	2.02893
$49$	−1.10065e48	−0.743125
$50$	−3.99215e48	−1.51552
$51$	7.18230e48	1.55065
$52$	−4.65159e48	−0.577439
$53$	−1.28624e49	−0.927813	−0.463906	−	0.885884i	$-0.653553\pi$
$53$	−1.28624e49	−0.927813	−0.463906	+	0.885884i	$0.653553\pi$
$54$	3.78390e48	0.160220
$55$	5.06545e48	0.127140
$56$	−6.85771e49	−1.02996
$57$	1.16728e50	1.05862
$58$	4.92500e50	2.72088
$59$	1.82082e50	0.617995	0.308997	−	0.951063i	$-0.400007\pi$
$59$	1.82082e50	0.617995	0.308997	+	0.951063i	$0.400007\pi$
$60$	−1.93353e51	−4.06481
$61$	−3.13164e50	−0.411028	−0.205514	−	0.978654i	$-0.565887\pi$
$61$	−3.13164e50	−0.411028	−0.205514	+	0.978654i	$0.565887\pi$
$62$	1.26874e51	1.04764
$63$	9.05538e50	0.473916
$64$	−1.42059e51	−0.474613
$65$	1.70634e51	0.366466
$66$	1.65723e51	0.230346
$67$	−6.22614e51	−0.563751	−0.281875	−	0.959451i	$-0.590957\pi$
$67$	−6.22614e51	−0.563751	−0.281875	+	0.959451i	$0.590957\pi$
$68$	4.02952e52	2.39193
$69$	−6.68815e52	−2.61883
$70$	4.71117e52	1.22415
$71$	3.91938e52	0.679758	0.339879	−	0.940469i	$-0.389614\pi$
$71$	3.91938e52	0.679758	0.339879	+	0.940469i	$0.389614\pi$
$72$	−1.63221e53	−1.90020
$73$	−3.35931e51	−0.0263966	−0.0131983	−	0.999913i	$-0.504201\pi$
$73$	−3.35931e51	−0.0263966	−0.0131983	+	0.999913i	$0.504201\pi$
$74$	−2.50856e53	−1.33758
$75$	3.26807e53	1.18863
$76$	6.54881e53	1.63296
$77$	−2.75434e52	−0.0473186
$78$	5.58252e53	0.663948
$79$	3.32824e53	0.275323	0.137661	−	0.990479i	$-0.456041\pi$
$79$	3.32824e53	0.275323	0.137661	+	0.990479i	$0.456041\pi$
$80$	−3.43633e54	−1.98623
$81$	−2.61472e54	−1.06072
$82$	1.84579e54	0.527821
$83$	7.49625e53	0.151746	0.0758732	−	0.997117i	$-0.475826\pi$
$83$	7.49625e53	0.151746	0.0758732	+	0.997117i	$0.475826\pi$
$84$	1.05136e55	1.51283
$85$	−1.47814e55	−1.51802
$86$	2.41381e55	1.77622
$87$	−4.03173e55	−2.13399
$88$	4.96462e54	0.189727
$89$	4.16835e55	1.15438	0.577191	−	0.816609i	$-0.304149\pi$
$89$	4.16835e55	1.15438	0.577191	+	0.816609i	$0.304149\pi$
$90$	1.12131e56	2.25847
$91$	−9.27822e54	−0.136391
$92$	−3.75228e56	−4.03963
$93$	−1.03862e56	−0.821664
$94$	5.04582e56	2.94299
$95$	−2.40229e56	−1.03634
$96$	−2.41090e56	−0.771702
$97$	3.60852e56	0.859676	0.429838	−	0.902906i	$-0.358571\pi$
$97$	3.60852e56	0.859676	0.429838	+	0.902906i	$0.358571\pi$
$98$	7.41085e56	1.31803
$99$	−6.55562e55	−0.0872993
$100$	1.83350e57	1.83350
$101$	−2.23538e57	−1.68342	−0.841710	−	0.539930i	$-0.818451\pi$
$101$	−2.23538e57	−1.68342	−0.841710	+	0.539930i	$0.818451\pi$
$102$	−4.83595e57	−2.75028
$103$	2.48990e57	1.07231	0.536155	−	0.844120i	$-0.319876\pi$
$103$	2.48990e57	1.07231	0.536155	+	0.844120i	$0.319876\pi$
$104$	1.67237e57	0.546869
$105$	−3.85668e57	−0.960105
$106$	8.66046e57	1.64560
$107$	−1.71390e57	−0.249200	−0.124600	−	0.992207i	$-0.539765\pi$
$107$	−1.71390e57	−0.249200	−0.124600	+	0.992207i	$0.539765\pi$
$108$	−1.73786e57	−0.193837
$109$	−5.66694e57	−0.486064	−0.243032	−	0.970018i	$-0.578142\pi$
$109$	−5.66694e57	−0.486064	−0.243032	+	0.970018i	$0.578142\pi$
$110$	−3.41064e57	−0.225499
$111$	2.05357e58	1.04907
$112$	1.86851e58	0.739233
$113$	9.71725e57	0.298406	0.149203	−	0.988807i	$-0.452329\pi$
$113$	9.71725e57	0.298406	0.149203	+	0.988807i	$0.452329\pi$
$114$	−7.85944e58	−1.87760
$115$	1.37644e59	2.56372
$116$	−2.26194e59	−3.29176
$117$	−2.20831e58	−0.251631
$118$	−1.22598e59	−1.09609
$119$	8.03741e58	0.564973
$120$	6.95156e59	3.84961
$121$	−2.26768e59	−0.991284
$122$	2.10858e59	0.729011
$123$	−1.51101e59	−0.413972
$124$	−5.82704e59	−1.26745
$125$	1.14548e59	0.198176
$126$	−6.09712e59	−0.840552
$127$	−2.18734e58	−0.0240719	−0.0120359	−	0.999928i	$-0.503831\pi$
$127$	−2.18734e58	−0.0240719	−0.0120359	+	0.999928i	$0.503831\pi$
$128$	1.58686e60	1.39655
$129$	−1.97600e60	−1.39309
$130$	−1.14890e60	−0.649976
$131$	3.13727e60	1.42666	0.713328	−	0.700830i	$-0.247187\pi$
$131$	3.13727e60	1.42666	0.713328	+	0.700830i	$0.247187\pi$
$132$	−7.61128e59	−0.278677
$133$	1.30625e60	0.385704
$134$	4.19215e60	0.999886
$135$	6.37496e59	0.123017
$136$	−1.44872e61	−2.26530
$137$	−9.99806e60	−1.26876	−0.634380	−	0.773021i	$-0.718745\pi$
$137$	−9.99806e60	−1.26876	−0.634380	+	0.773021i	$0.718745\pi$
$138$	4.50323e61	4.64483
$139$	1.37378e60	0.115344	0.0576719	−	0.998336i	$-0.481632\pi$
$139$	1.37378e60	0.115344	0.0576719	+	0.998336i	$0.481632\pi$
$140$	−2.16373e61	−1.48100
$141$	−4.13064e61	−2.30819
$142$	−2.63897e61	−1.20564
$143$	6.71694e59	0.0251243
$144$	4.44725e61	1.36383
$145$	8.29744e61	2.08908
$146$	2.26187e60	0.0468179
$147$	−6.06671e61	−1.03373
$148$	1.15212e62	1.61823
$149$	8.00246e61	0.927716	0.463858	−	0.885910i	$-0.346465\pi$
$149$	8.00246e61	0.927716	0.463858	+	0.885910i	$0.346465\pi$
$150$	−2.20044e62	−2.10819
$151$	−9.95453e61	−0.789183	−0.394591	−	0.918857i	$-0.629114\pi$
$151$	−9.95453e61	−0.789183	−0.394591	+	0.918857i	$0.629114\pi$
$152$	−2.35448e62	−1.54651
$153$	1.91299e62	1.04233
$154$	1.85454e61	0.0839258
$155$	2.13752e62	0.804373
$156$	−2.56392e62	−0.803255
$157$	6.90998e62	1.80442	0.902208	−	0.431300i	$-0.141945\pi$
$157$	6.90998e62	1.80442	0.902208	+	0.431300i	$0.141945\pi$
$158$	−2.24095e62	−0.488321
$159$	−7.08966e62	−1.29065
$160$	4.96172e62	0.755462
$161$	−7.48443e62	−0.954160
$162$	1.76053e63	1.88133
$163$	3.76476e62	0.337591	0.168795	−	0.985651i	$-0.446012\pi$
$163$	3.76476e62	0.337591	0.168795	+	0.985651i	$0.446012\pi$
$164$	−8.47727e62	−0.638567
$165$	2.79203e62	0.176860
$166$	−5.04733e62	−0.269142
$167$	−1.42463e63	−0.640152	−0.320076	−	0.947392i	$-0.603708\pi$
$167$	−1.42463e63	−0.640152	−0.320076	+	0.947392i	$0.603708\pi$
$168$	−3.77992e63	−1.43274
$169$	−2.89817e63	−0.927582
$170$	9.95255e63	2.69240
$171$	3.10901e63	0.711594
$172$	−1.10860e64	−2.14890
$173$	−7.76140e63	−1.27534	−0.637670	−	0.770310i	$-0.720102\pi$
$173$	−7.76140e63	−1.27534	−0.637670	+	0.770310i	$0.720102\pi$
$174$	2.71462e64	3.78491
$175$	3.65716e63	0.433072
$176$	−1.35270e63	−0.136173
$177$	1.00362e64	0.859670
$178$	−2.80661e64	−2.04745
$179$	6.01501e63	0.374046	0.187023	−	0.982356i	$-0.440116\pi$
$179$	6.01501e63	0.374046	0.187023	+	0.982356i	$0.440116\pi$
$180$	−5.14990e64	−2.73233
$181$	−1.44086e63	−0.0652803	−0.0326402	−	0.999467i	$-0.510392\pi$
$181$	−1.44086e63	−0.0652803	−0.0326402	+	0.999467i	$0.510392\pi$
$182$	6.24716e63	0.241907
$183$	−1.72613e64	−0.571766
$184$	1.34905e65	3.82577
$185$	−4.22632e64	−1.02699
$186$	6.99321e64	1.45733
$187$	−5.81866e63	−0.104073
$188$	−2.31743e65	−3.56047
$189$	−3.46639e63	−0.0457842
$190$	1.61750e65	1.83809
$191$	1.45755e65	1.42617	0.713085	−	0.701077i	$-0.247297\pi$
$191$	1.45755e65	1.42617	0.713085	+	0.701077i	$0.247297\pi$
$192$	−7.83019e64	−0.660218
$193$	7.57197e64	0.550587	0.275293	−	0.961360i	$-0.411225\pi$
$193$	7.57197e64	0.550587	0.275293	+	0.961360i	$0.411225\pi$
$194$	−2.42967e65	−1.52475
$195$	9.40520e64	0.509778
$196$	−3.40363e65	−1.59457
$197$	2.34950e65	0.952113	0.476056	−	0.879415i	$-0.342066\pi$
$197$	2.34950e65	0.952113	0.476056	+	0.879415i	$0.342066\pi$
$198$	4.41399e64	0.154837
$199$	5.43494e63	0.0165151	0.00825757	−	0.999966i	$-0.497372\pi$
$199$	5.43494e63	0.0165151	0.00825757	+	0.999966i	$0.497372\pi$
$200$	−6.59193e65	−1.73643
$201$	−3.43180e65	−0.784214
$202$	1.50512e66	2.98577
$203$	−4.51174e65	−0.777512
$204$	2.22104e66	3.32733
$205$	3.10971e65	0.405260
$206$	−1.67648e66	−1.90188
$207$	−1.78137e66	−1.76035
$208$	−4.55669e65	−0.392504
$209$	−9.45655e64	−0.0710499
$210$	2.59676e66	1.70287
$211$	−2.26585e66	−1.29772	−0.648860	−	0.760907i	$-0.724754\pi$
$211$	−2.26585e66	−1.29772	−0.648860	+	0.760907i	$0.724754\pi$
$212$	−3.97754e66	−1.99087
$213$	2.16033e66	0.945587
$214$	1.15400e66	0.441989
$215$	4.06668e66	1.36378
$216$	6.24807e65	0.183575
$217$	−1.16228e66	−0.299370
$218$	3.81564e66	0.862099
$219$	−1.85163e65	−0.0367194
$220$	1.56643e66	0.272812
$221$	−1.96006e66	−0.299979
$222$	−1.38270e67	−1.86066
$223$	1.71148e66	0.202620	0.101310	−	0.994855i	$-0.467697\pi$
$223$	1.71148e66	0.202620	0.101310	+	0.994855i	$0.467697\pi$
$224$	−2.69794e66	−0.281167
$225$	8.70443e66	0.798985
$226$	−6.54277e66	−0.529262
$227$	1.34941e67	0.962513	0.481257	−	0.876580i	$-0.340180\pi$
$227$	1.34941e67	0.962513	0.481257	+	0.876580i	$0.340180\pi$
$228$	3.60965e67	2.27155
$229$	−1.96981e67	−1.09424	−0.547120	−	0.837054i	$-0.684276\pi$
$229$	−1.96981e67	−1.09424	−0.547120	+	0.837054i	$0.684276\pi$
$230$	−9.26780e67	−4.54709
$231$	−1.51817e66	−0.0658233
$232$	8.13228e67	3.11749
$233$	−4.19358e67	−1.42214	−0.711068	−	0.703124i	$-0.751788\pi$
$233$	−4.19358e67	−1.42214	−0.711068	+	0.703124i	$0.751788\pi$
$234$	1.48689e67	0.446300
$235$	8.50099e67	2.25962
$236$	5.63066e67	1.32607
$237$	1.83450e67	0.382992
$238$	−5.41171e67	−1.00205
$239$	−5.19811e67	−0.854093	−0.427046	−	0.904230i	$-0.640446\pi$
$239$	−5.19811e67	−0.854093	−0.427046	+	0.904230i	$0.640446\pi$
$240$	−1.89408e68	−2.76298
$241$	2.64506e66	0.0342728	0.0171364	−	0.999853i	$-0.494545\pi$
$241$	2.64506e66	0.0342728	0.0171364	+	0.999853i	$0.494545\pi$
$242$	1.52686e68	1.75817
$243$	−1.35298e68	−1.38520
$244$	−9.68419e67	−0.881969
$245$	1.24855e68	1.01198
$246$	1.01738e68	0.734234
$247$	−3.18552e67	−0.204794
$248$	2.09498e68	1.20035
$249$	4.13187e67	0.211089
$250$	−7.71268e67	−0.351492
$251$	−1.67083e67	−0.0679567	−0.0339783	−	0.999423i	$-0.510818\pi$
$251$	−1.67083e67	−0.0679567	−0.0339783	+	0.999423i	$0.510818\pi$
$252$	2.80026e68	1.01691
$253$	5.41833e67	0.175764
$254$	1.47277e67	0.0426946
$255$	−8.14740e68	−2.11166
$256$	−8.63729e68	−2.00234
$257$	2.05427e68	0.426151	0.213075	−	0.977036i	$-0.431652\pi$
$257$	2.05427e68	0.426151	0.213075	+	0.977036i	$0.431652\pi$
$258$	1.33047e69	2.47083
$259$	2.29806e68	0.382225
$260$	5.27663e68	0.786351
$261$	−1.07384e69	−1.43445
$262$	−2.11237e69	−2.53036
$263$	1.10882e69	1.19158	0.595788	−	0.803142i	$-0.296840\pi$
$263$	1.10882e69	1.19158	0.595788	+	0.803142i	$0.296840\pi$
$264$	2.73646e68	0.263923
$265$	1.45908e69	1.26349
$266$	−8.79516e68	−0.684096
$267$	2.29756e69	1.60582
$268$	−1.92536e69	−1.20968
$269$	6.67716e68	0.377270	0.188635	−	0.982047i	$-0.439594\pi$
$269$	6.67716e68	0.377270	0.188635	+	0.982047i	$0.439594\pi$
$270$	−4.29235e68	−0.218187
$271$	−1.77215e69	−0.810727	−0.405363	−	0.914156i	$-0.632855\pi$
$271$	−1.77215e69	−0.810727	−0.405363	+	0.914156i	$0.632855\pi$
$272$	3.94730e69	1.62587
$273$	−5.11408e68	−0.189728
$274$	6.73184e69	2.25031
$275$	−2.64759e68	−0.0797755
$276$	−2.06823e70	−5.61939
$277$	1.76004e69	0.431369	0.215684	−	0.976463i	$-0.430802\pi$
$277$	1.76004e69	0.431369	0.215684	+	0.976463i	$0.430802\pi$
$278$	−9.24984e68	−0.204577
$279$	−2.76635e69	−0.552315
$280$	7.77920e69	1.40259
$281$	−6.01422e69	−0.979600	−0.489800	−	0.871835i	$-0.662930\pi$
$281$	−6.01422e69	−0.979600	−0.489800	+	0.871835i	$0.662930\pi$
$282$	2.78122e70	4.09388
$283$	−1.60599e69	−0.213712	−0.106856	−	0.994275i	$-0.534078\pi$
$283$	−1.60599e69	−0.213712	−0.106856	+	0.994275i	$0.534078\pi$
$284$	1.21202e70	1.45860
$285$	−1.32412e70	−1.44162
$286$	−4.52262e68	−0.0445613
$287$	−1.69091e69	−0.150829
$288$	−6.42138e69	−0.518731
$289$	3.31503e69	0.242605
$290$	−5.58679e70	−3.70526
$291$	1.98899e70	1.19587
$292$	−1.03883e69	−0.0566410
$293$	3.27477e70	1.61977	0.809886	−	0.586587i	$-0.199529\pi$
$293$	3.27477e70	1.61977	0.809886	+	0.586587i	$0.199529\pi$
$294$	4.08480e70	1.83346
$295$	−2.06549e70	−0.841579
$296$	−4.14220e70	−1.53256
$297$	2.50948e68	0.00843384
$298$	−5.38817e70	−1.64542
$299$	1.82521e70	0.506621
$300$	1.01061e71	2.55052
$301$	−2.21126e70	−0.507568
$302$	6.70253e70	1.39972
$303$	−1.23213e71	−2.34175
$304$	6.41520e70	1.10997
$305$	3.55244e70	0.559734
$306$	−1.28804e71	−1.84871
$307$	1.02374e71	1.33890	0.669448	−	0.742859i	$-0.266531\pi$
$307$	1.02374e71	1.33890	0.669448	+	0.742859i	$0.266531\pi$
$308$	−8.51746e69	−0.101535
$309$	1.37241e71	1.49165
$310$	−1.43923e71	−1.42666
$311$	−1.53563e71	−1.38872	−0.694360	−	0.719628i	$-0.744312\pi$
$311$	−1.53563e71	−1.38872	−0.694360	+	0.719628i	$0.744312\pi$
$312$	9.21799e70	0.760730
$313$	1.68290e71	1.26778	0.633891	−	0.773422i	$-0.281457\pi$
$313$	1.68290e71	1.26778	0.633891	+	0.773422i	$0.281457\pi$
$314$	−4.65259e71	−3.20037
$315$	−1.02722e71	−0.645374
$316$	1.02922e71	0.590778
$317$	−4.34592e69	−0.0227978	−0.0113989	−	0.999935i	$-0.503628\pi$
$317$	−4.34592e69	−0.0227978	−0.0113989	+	0.999935i	$0.503628\pi$
$318$	4.77358e71	2.28913
$319$	3.26626e70	0.143224
$320$	1.61148e71	0.646324
$321$	−9.44689e70	−0.346654
$322$	5.03937e71	1.69233
$323$	2.75950e71	0.848319
$324$	−8.08569e71	−2.27606
$325$	−8.91863e70	−0.229944
$326$	−2.53487e71	−0.598761
$327$	−3.12357e71	−0.676147
$328$	3.04781e71	0.604760
$329$	−4.62242e71	−0.840981
$330$	−1.87992e71	−0.313683
$331$	−7.64347e71	−1.17002	−0.585010	−	0.811026i	$-0.698909\pi$
$331$	−7.64347e71	−1.17002	−0.585010	+	0.811026i	$0.698909\pi$
$332$	2.31812e71	0.325612
$333$	5.46963e71	0.705176
$334$	9.59226e71	1.13539
$335$	7.06276e71	0.767711
$336$	1.02991e72	1.02832
$337$	−1.37603e72	−1.26234	−0.631169	−	0.775646i	$-0.717424\pi$
$337$	−1.37603e72	−1.26234	−0.631169	+	0.775646i	$0.717424\pi$
$338$	1.95138e72	1.64519
$339$	5.35607e71	0.415102
$340$	−4.57097e72	−3.25731
$341$	8.41430e70	0.0551465
$342$	−2.09334e72	−1.26211
$343$	−1.59247e72	−0.883466
$344$	3.98573e72	2.03513
$345$	7.58685e72	3.56630
$346$	5.22586e72	2.26198
$347$	−4.11427e72	−1.64022	−0.820111	−	0.572205i	$-0.806088\pi$
$347$	−4.11427e72	−1.64022	−0.820111	+	0.572205i	$0.806088\pi$
$348$	−1.24676e73	−4.57905
$349$	7.58941e71	0.256852	0.128426	−	0.991719i	$-0.459008\pi$
$349$	7.58941e71	0.256852	0.128426	+	0.991719i	$0.459008\pi$
$350$	−2.46242e72	−0.768110
$351$	8.45340e70	0.0243096
$352$	1.95317e71	0.0517932
$353$	7.43237e72	1.81781	0.908904	−	0.417005i	$-0.136920\pi$
$353$	7.43237e72	1.81781	0.908904	+	0.417005i	$0.136920\pi$
$354$	−6.75753e72	−1.52474
$355$	−4.44603e72	−0.925688
$356$	1.28901e73	2.47703
$357$	4.43016e72	0.785914
$358$	−4.05000e72	−0.663420
$359$	−4.18855e72	−0.633683	−0.316841	−	0.948479i	$-0.602622\pi$
$359$	−4.18855e72	−0.633683	−0.316841	+	0.948479i	$0.602622\pi$
$360$	1.85153e73	2.58767
$361$	−3.25905e72	−0.420858
$362$	9.70152e71	0.115783
$363$	−1.24993e73	−1.37894
$364$	−2.86917e72	−0.292663
$365$	3.81071e71	0.0359467
$366$	1.16223e73	1.01410
$367$	−7.05495e72	−0.569523	−0.284762	−	0.958598i	$-0.591914\pi$
$367$	−7.05495e72	−0.569523	−0.284762	+	0.958598i	$0.591914\pi$
$368$	−3.67572e73	−2.74587
$369$	−4.02453e72	−0.278268
$370$	2.84564e73	1.82151
$371$	−7.93374e72	−0.470242
$372$	−3.21182e73	−1.76310
$373$	2.43645e73	1.23895	0.619477	−	0.785015i	$-0.287345\pi$
$373$	2.43645e73	1.23895	0.619477	+	0.785015i	$0.287345\pi$
$374$	3.91779e72	0.184587
$375$	6.31379e72	0.275676
$376$	8.33178e73	3.37197
$377$	1.10027e73	0.412828
$378$	2.33397e72	0.0812043
$379$	−2.04703e73	−0.660550	−0.330275	−	0.943885i	$-0.607142\pi$
$379$	−2.04703e73	−0.660550	−0.330275	+	0.943885i	$0.607142\pi$
$380$	−7.42879e73	−2.22375
$381$	−1.20564e72	−0.0334856
$382$	−9.81388e73	−2.52950
$383$	6.39228e73	1.52929	0.764646	−	0.644450i	$-0.222914\pi$
$383$	6.39228e73	1.52929	0.764646	+	0.644450i	$0.222914\pi$
$384$	8.74666e73	1.94268
$385$	3.12445e72	0.0644381
$386$	−5.09832e73	−0.976537
$387$	−5.26303e73	−0.936425
$388$	1.11589e74	1.84466
$389$	−3.98761e72	−0.0612560	−0.0306280	−	0.999531i	$-0.509751\pi$
$389$	−3.98761e72	−0.0612560	−0.0306280	+	0.999531i	$0.509751\pi$
$390$	−6.33266e73	−0.904159
$391$	−1.58112e74	−2.09858
$392$	1.22370e74	1.51015
$393$	1.72924e74	1.98457
$394$	−1.58195e74	−1.68870
$395$	−3.77546e73	−0.374932
$396$	−2.02724e73	−0.187324
$397$	−5.12847e73	−0.441020	−0.220510	−	0.975385i	$-0.570772\pi$
$397$	−5.12847e73	−0.441020	−0.220510	+	0.975385i	$0.570772\pi$
$398$	−3.65943e72	−0.0292918
$399$	7.19994e73	0.536539
$400$	1.79609e74	1.24629
$401$	1.96631e74	1.27068	0.635342	−	0.772231i	$-0.280859\pi$
$401$	1.96631e74	1.27068	0.635342	+	0.772231i	$0.280859\pi$
$402$	2.31068e74	1.39091
$403$	2.83442e73	0.158954
$404$	−6.91264e74	−3.61223
$405$	2.96606e74	1.44448
$406$	3.03782e74	1.37902
$407$	−1.66368e73	−0.0704090
$408$	−7.98523e74	−3.15118
$409$	−3.70182e74	−1.36239	−0.681194	−	0.732103i	$-0.738539\pi$
$409$	−3.70182e74	−1.36239	−0.681194	+	0.732103i	$0.738539\pi$
$410$	−2.09381e74	−0.718782
$411$	−5.51085e74	−1.76493
$412$	7.69969e74	2.30093
$413$	1.12311e74	0.313217
$414$	1.19942e75	3.12221
$415$	−8.50353e73	−0.206647
$416$	6.57940e73	0.149288
$417$	7.57215e73	0.160451
$418$	6.36723e73	0.126016
$419$	4.89820e74	0.905602	0.452801	−	0.891612i	$-0.350425\pi$
$419$	4.89820e74	0.905602	0.452801	+	0.891612i	$0.350425\pi$
$420$	−1.19263e75	−2.06016
$421$	−9.39625e74	−1.51675	−0.758377	−	0.651817i	$-0.774007\pi$
$421$	−9.39625e74	−1.51675	−0.758377	+	0.651817i	$0.774007\pi$
$422$	1.52563e75	2.30168
$423$	−1.10018e75	−1.55155
$424$	1.43003e75	1.88547
$425$	7.72591e74	0.952500
$426$	−1.45458e75	−1.67712
$427$	−1.93164e74	−0.208321
$428$	−5.30003e74	−0.534725
$429$	3.70233e73	0.0349496
$430$	−2.73815e75	−2.41884
$431$	5.23554e74	0.432872	0.216436	−	0.976297i	$-0.430557\pi$
$431$	5.23554e74	0.432872	0.216436	+	0.976297i	$0.430557\pi$
$432$	−1.70240e74	−0.131757
$433$	2.08385e75	1.50994	0.754972	−	0.655756i	$-0.227650\pi$
$433$	2.08385e75	1.50994	0.754972	+	0.655756i	$0.227650\pi$
$434$	7.82581e74	0.530972
$435$	4.57348e75	2.90605
$436$	−1.75243e75	−1.04298
$437$	−2.56965e75	−1.43269
$438$	1.24673e74	0.0651267
$439$	−1.80835e75	−0.885205	−0.442603	−	0.896718i	$-0.645945\pi$
$439$	−1.80835e75	−0.885205	−0.442603	+	0.896718i	$0.645945\pi$
$440$	−5.63173e74	−0.258369
$441$	−1.61585e75	−0.694867
$442$	1.31974e75	0.532051
$443$	3.02958e75	1.14519	0.572593	−	0.819840i	$-0.305938\pi$
$443$	3.02958e75	1.14519	0.572593	+	0.819840i	$0.305938\pi$
$444$	6.35041e75	2.25106
$445$	−4.72846e75	−1.57203
$446$	−1.15236e75	−0.359373
$447$	4.41089e75	1.29051
$448$	−8.76243e74	−0.240548
$449$	2.69097e74	0.0693247	0.0346624	−	0.999399i	$-0.488964\pi$
$449$	2.69097e74	0.0693247	0.0346624	+	0.999399i	$0.488964\pi$
$450$	−5.86082e75	−1.41710
$451$	1.22413e74	0.0277840
$452$	3.00494e75	0.640310
$453$	−5.48686e75	−1.09780
$454$	−9.08577e75	−1.70714
$455$	1.05250e75	0.185736
$456$	−1.29777e76	−2.15129
$457$	6.67120e74	0.103894	0.0519472	−	0.998650i	$-0.483457\pi$
$457$	6.67120e74	0.103894	0.0519472	+	0.998650i	$0.483457\pi$
$458$	1.32630e76	1.94078
$459$	−7.32289e74	−0.100698
$460$	4.25648e76	5.50114
$461$	−3.30245e75	−0.401199	−0.200599	−	0.979673i	$-0.564289\pi$
$461$	−3.30245e75	−0.401199	−0.200599	+	0.979673i	$0.564289\pi$
$462$	1.02221e75	0.116746
$463$	−1.73652e76	−1.86475	−0.932375	−	0.361493i	$-0.882267\pi$
$463$	−1.73652e76	−1.86475	−0.932375	+	0.361493i	$0.882267\pi$
$464$	−2.21579e76	−2.23751
$465$	1.17819e76	1.11893
$466$	2.82360e76	2.52234
$467$	−8.12538e75	−0.682830	−0.341415	−	0.939913i	$-0.610906\pi$
$467$	−8.12538e75	−0.682830	−0.341415	+	0.939913i	$0.610906\pi$
$468$	−6.82893e75	−0.539941
$469$	−3.84038e75	−0.285725
$470$	−5.72384e76	−4.00773
$471$	3.80873e76	2.51006
$472$	−2.02437e76	−1.25587
$473$	1.60083e75	0.0934984
$474$	−1.23519e76	−0.679286
$475$	1.25562e76	0.650266
$476$	2.48547e76	1.21230
$477$	−1.88831e76	−0.867561
$478$	3.49996e76	1.51485
$479$	6.14165e75	0.250451	0.125226	−	0.992128i	$-0.460035\pi$
$479$	6.14165e75	0.250451	0.125226	+	0.992128i	$0.460035\pi$
$480$	2.73486e76	1.05090
$481$	−5.60423e75	−0.202946
$482$	−1.78096e75	−0.0607873
$483$	−4.12536e76	−1.32730
$484$	−7.01250e76	−2.12706
$485$	−4.09341e76	−1.17070
$486$	9.10980e76	2.45683
$487$	6.93930e76	1.76498	0.882491	−	0.470330i	$-0.155865\pi$
$487$	6.93930e76	1.76498	0.882491	+	0.470330i	$0.155865\pi$
$488$	3.48173e76	0.835276
$489$	2.07511e76	0.469610
$490$	−8.40666e76	−1.79488
$491$	7.55108e76	1.52120	0.760600	−	0.649221i	$-0.224905\pi$
$491$	7.55108e76	1.52120	0.760600	+	0.649221i	$0.224905\pi$
$492$	−4.67260e76	−0.888287
$493$	−9.53124e76	−1.71006
$494$	2.14485e76	0.363228
$495$	7.43651e75	0.118883
$496$	−5.70815e76	−0.861524
$497$	2.41753e76	0.344521
$498$	−2.78205e76	−0.374394
$499$	2.35411e76	0.299200	0.149600	−	0.988747i	$-0.452201\pi$
$499$	2.35411e76	0.299200	0.149600	+	0.988747i	$0.452201\pi$
$500$	3.54225e76	0.425240
$501$	−7.85246e76	−0.890493
$502$	1.12500e76	0.120530
$503$	4.10718e76	0.415773	0.207887	−	0.978153i	$-0.433341\pi$
$503$	4.10718e76	0.415773	0.207887	+	0.978153i	$0.433341\pi$
$504$	−1.00677e77	−0.963076
$505$	2.53575e77	2.29247
$506$	−3.64824e76	−0.311741
$507$	−1.59745e77	−1.29033
$508$	−6.76408e75	−0.0516527
$509$	−1.18534e77	−0.855824	−0.427912	−	0.903820i	$-0.640751\pi$
$509$	−1.18534e77	−0.855824	−0.427912	+	0.903820i	$0.640751\pi$
$510$	5.48577e77	3.74531
$511$	−2.07208e75	−0.0133786
$512$	3.52870e77	2.15487
$513$	−1.19012e76	−0.0687460
$514$	−1.38317e77	−0.755835
$515$	−2.82447e77	−1.46026
$516$	−6.11054e77	−2.98925
$517$	3.34639e76	0.154916
$518$	−1.54732e77	−0.677926
$519$	−4.27802e77	−1.77408
$520$	−1.89709e77	−0.744721
$521$	2.05863e76	0.0765074	0.0382537	−	0.999268i	$-0.487820\pi$
$521$	2.05863e76	0.0765074	0.0382537	+	0.999268i	$0.487820\pi$
$522$	7.23033e77	2.54418
$523$	1.81959e77	0.606284	0.303142	−	0.952945i	$-0.401964\pi$
$523$	1.81959e77	0.606284	0.303142	+	0.952945i	$0.401964\pi$
$524$	9.70160e77	3.06127
$525$	2.01580e77	0.602431
$526$	−7.46584e77	−2.11341
$527$	−2.45537e77	−0.658436
$528$	−7.45599e76	−0.189425
$529$	1.05691e78	2.54421
$530$	−9.82418e77	−2.24096
$531$	2.67312e77	0.577862
$532$	4.03941e77	0.827630
$533$	4.12357e76	0.0800844
$534$	−1.54698e78	−2.84813
$535$	1.94420e77	0.339358
$536$	6.92218e77	1.14564
$537$	3.31543e77	0.520322
$538$	−4.49583e77	−0.669137
$539$	4.91487e76	0.0693797
$540$	1.97138e77	0.263966
$541$	−9.71513e77	−1.23403	−0.617016	−	0.786951i	$-0.711659\pi$
$541$	−9.71513e77	−1.23403	−0.617016	+	0.786951i	$0.711659\pi$
$542$	1.19321e78	1.43793
$543$	−7.94191e76	−0.0908091
$544$	−5.69951e77	−0.618399
$545$	6.42842e77	0.661918
$546$	3.44339e77	0.336508
$547$	−3.90157e77	−0.361910	−0.180955	−	0.983491i	$-0.557919\pi$
$547$	−3.90157e77	−0.361910	−0.180955	+	0.983491i	$0.557919\pi$
$548$	−3.09178e78	−2.72246
$549$	−4.59751e77	−0.384336
$550$	1.78266e77	0.141492
$551$	−1.54903e78	−1.16745
$552$	7.43584e78	5.32189
$553$	2.05291e77	0.139541
$554$	−1.18506e78	−0.765089
$555$	−2.32951e78	−1.42861
$556$	4.24823e77	0.247501
$557$	1.76012e78	0.974249	0.487124	−	0.873333i	$-0.338046\pi$
$557$	1.76012e78	0.974249	0.487124	+	0.873333i	$0.338046\pi$
$558$	1.86262e78	0.979603
$559$	5.39254e77	0.269499
$560$	−2.11958e78	−1.00668
$561$	−3.20720e77	−0.144772
$562$	4.04946e78	1.73745
$563$	3.05776e78	1.24714	0.623568	−	0.781769i	$-0.285683\pi$
$563$	3.05776e78	1.24714	0.623568	+	0.781769i	$0.285683\pi$
$564$	−1.27735e79	−4.95285
$565$	−1.10230e78	−0.406367
$566$	1.08133e78	0.379046
$567$	−1.61280e78	−0.537605
$568$	−4.35753e78	−1.38138
$569$	−2.92197e78	−0.880999	−0.440500	−	0.897753i	$-0.645199\pi$
$569$	−2.92197e78	−0.880999	−0.440500	+	0.897753i	$0.645199\pi$
$570$	8.91553e78	2.55690
$571$	1.92082e78	0.524033	0.262017	−	0.965063i	$-0.415612\pi$
$571$	1.92082e78	0.524033	0.262017	+	0.965063i	$0.415612\pi$
$572$	2.07713e77	0.0539110
$573$	8.03388e78	1.98390
$574$	1.13851e78	0.267515
$575$	−7.19436e78	−1.60864
$576$	−2.08555e78	−0.443792
$577$	−2.25361e78	−0.456424	−0.228212	−	0.973611i	$-0.573288\pi$
$577$	−2.25361e78	−0.456424	−0.228212	+	0.973611i	$0.573288\pi$
$578$	−2.23206e78	−0.430291
$579$	4.17361e78	0.765901
$580$	2.56588e79	4.48269
$581$	4.62380e77	0.0769094
$582$	−1.33922e79	−2.12102
$583$	5.74361e77	0.0866226
$584$	3.73486e77	0.0536424
$585$	2.50505e78	0.342668
$586$	−2.20495e79	−2.87288
$587$	−4.08047e78	−0.506435	−0.253218	−	0.967409i	$-0.581489\pi$
$587$	−4.08047e78	−0.506435	−0.253218	+	0.967409i	$0.581489\pi$
$588$	−1.87605e79	−2.21815
$589$	−3.99049e78	−0.449511
$590$	1.39072e79	1.49265
$591$	1.29503e79	1.32445
$592$	1.12862e79	1.09996
$593$	3.71986e78	0.345515	0.172758	−	0.984964i	$-0.444732\pi$
$593$	3.71986e78	0.345515	0.172758	+	0.984964i	$0.444732\pi$
$594$	−1.68967e77	−0.0149585
$595$	−9.11741e78	−0.769375
$596$	2.47466e79	1.99066
$597$	2.99570e77	0.0229736
$598$	−1.22894e79	−0.898559
$599$	8.06741e78	0.562432	0.281216	−	0.959645i	$-0.409262\pi$
$599$	8.06741e78	0.562432	0.281216	+	0.959645i	$0.409262\pi$
$600$	−3.63342e79	−2.41549
$601$	−1.64963e79	−1.04584	−0.522919	−	0.852383i	$-0.675157\pi$
$601$	−1.64963e79	−1.04584	−0.522919	+	0.852383i	$0.675157\pi$
$602$	1.48887e79	0.900239
$603$	−9.14051e78	−0.527141
$604$	−3.07831e79	−1.69340
$605$	2.57239e79	1.34992
$606$	8.29608e79	4.15339
$607$	2.41424e79	1.15319	0.576597	−	0.817028i	$-0.304380\pi$
$607$	2.41424e79	1.15319	0.576597	+	0.817028i	$0.304380\pi$
$608$	−9.26290e78	−0.422177
$609$	−2.48684e79	−1.08157
$610$	−2.39191e79	−0.992761
$611$	1.12726e79	0.446528
$612$	5.91567e79	2.23660
$613$	−4.65456e79	−1.67979	−0.839895	−	0.542749i	$-0.817383\pi$
$613$	−4.65456e79	−1.67979	−0.839895	+	0.542749i	$0.817383\pi$
$614$	−6.89301e79	−2.37471
$615$	1.71405e79	0.563743
$616$	3.06226e78	0.0961593
$617$	−5.09448e79	−1.52747	−0.763735	−	0.645530i	$-0.776637\pi$
$617$	−5.09448e79	−1.52747	−0.763735	+	0.645530i	$0.776637\pi$
$618$	−9.24065e79	−2.64564
$619$	1.52754e79	0.417646	0.208823	−	0.977953i	$-0.433037\pi$
$619$	1.52754e79	0.417646	0.208823	+	0.977953i	$0.433037\pi$
$620$	6.61002e79	1.72600
$621$	6.81907e78	0.170065
$622$	1.03396e80	2.46308
$623$	2.57111e79	0.585074
$624$	−2.51161e79	−0.545998
$625$	−5.41354e79	−1.12435
$626$	−1.13312e80	−2.24858
$627$	−5.21238e78	−0.0988350
$628$	2.13683e80	3.87186
$629$	4.85476e79	0.840667
$630$	6.91640e79	1.14466
$631$	4.47011e79	0.707101	0.353551	−	0.935415i	$-0.384974\pi$
$631$	4.47011e79	0.707101	0.353551	+	0.935415i	$0.384974\pi$
$632$	−3.70031e79	−0.559501
$633$	−1.24892e80	−1.80521
$634$	2.92617e78	0.0404348
$635$	2.48126e78	0.0327809
$636$	−2.19239e80	−2.76943
$637$	1.65561e79	0.199979
$638$	−2.19922e79	−0.254027
$639$	5.75398e79	0.635615
$640$	−1.80009e80	−1.90180
$641$	1.60553e80	1.62242	0.811212	−	0.584752i	$-0.198808\pi$
$641$	1.60553e80	1.62242	0.811212	+	0.584752i	$0.198808\pi$
$642$	6.36073e79	0.614835
$643$	9.19625e79	0.850350	0.425175	−	0.905111i	$-0.360213\pi$
$643$	9.19625e79	0.850350	0.425175	+	0.905111i	$0.360213\pi$
$644$	−2.31447e80	−2.04740
$645$	2.24152e80	1.89710
$646$	−1.85801e80	−1.50460
$647$	−1.12143e80	−0.868964	−0.434482	−	0.900680i	$-0.643069\pi$
$647$	−1.12143e80	−0.868964	−0.434482	+	0.900680i	$0.643069\pi$
$648$	2.90702e80	2.15556
$649$	−8.13072e78	−0.0576973
$650$	6.00505e79	0.407836
$651$	−6.40640e79	−0.416443
$652$	1.16420e80	0.724391
$653$	3.01530e79	0.179600	0.0897998	−	0.995960i	$-0.471377\pi$
$653$	3.01530e79	0.179600	0.0897998	+	0.995960i	$0.471377\pi$
$654$	2.10315e80	1.19923
$655$	−3.55883e80	−1.94281
$656$	−8.30431e79	−0.434054
$657$	−4.93176e78	−0.0246825
$658$	3.11234e80	1.49159
$659$	−3.56507e80	−1.63619	−0.818095	−	0.575083i	$-0.804970\pi$
$659$	−3.56507e80	−1.63619	−0.818095	+	0.575083i	$0.804970\pi$
$660$	8.63402e79	0.379499
$661$	−1.73982e80	−0.732425	−0.366212	−	0.930531i	$-0.619346\pi$
$661$	−1.73982e80	−0.732425	−0.366212	+	0.930531i	$0.619346\pi$
$662$	5.14646e80	2.07518
$663$	−1.08037e80	−0.417290
$664$	−8.33427e79	−0.308374
$665$	−1.48177e80	−0.525248
$666$	−3.68278e80	−1.25072
$667$	8.87547e80	2.88805
$668$	−4.40550e80	−1.37362
$669$	9.43352e79	0.281857
$670$	−4.75546e80	−1.36164
$671$	1.39841e79	0.0383744
$672$	−1.48708e80	−0.391121
$673$	−3.17354e80	−0.800047	−0.400023	−	0.916505i	$-0.630998\pi$
$673$	−3.17354e80	−0.800047	−0.400023	+	0.916505i	$0.630998\pi$
$674$	9.26501e80	2.23892
$675$	−3.33204e79	−0.0771886
$676$	−8.96222e80	−1.99037
$677$	−4.57291e80	−0.973678	−0.486839	−	0.873492i	$-0.661850\pi$
$677$	−4.57291e80	−0.973678	−0.486839	+	0.873492i	$0.661850\pi$
$678$	−3.60632e80	−0.736238
$679$	2.22579e80	0.435709
$680$	1.64339e81	3.08486
$681$	7.43784e80	1.33892
$682$	−5.66547e79	−0.0978095
$683$	−1.79524e80	−0.297258	−0.148629	−	0.988893i	$-0.547486\pi$
$683$	−1.79524e80	−0.297258	−0.148629	+	0.988893i	$0.547486\pi$
$684$	9.61421e80	1.52692
$685$	1.13415e81	1.72779
$686$	1.07224e81	1.56694
$687$	−1.08574e81	−1.52216
$688$	−1.08599e81	−1.46067
$689$	1.93478e80	0.249680
$690$	−5.10834e81	−6.32529
$691$	4.71836e80	0.560618	0.280309	−	0.959910i	$-0.409563\pi$
$691$	4.71836e80	0.560618	0.280309	+	0.959910i	$0.409563\pi$
$692$	−2.40011e81	−2.73658
$693$	−4.04361e79	−0.0442458
$694$	2.77020e81	2.90915
$695$	−1.55837e80	−0.157074
$696$	4.48245e81	4.33663
$697$	−3.57211e80	−0.331734
$698$	−5.11006e80	−0.455561
$699$	−2.31147e81	−1.97828
$700$	1.13093e81	0.929271
$701$	−5.57380e80	−0.439732	−0.219866	−	0.975530i	$-0.570562\pi$
$701$	−5.57380e80	−0.439732	−0.219866	+	0.975530i	$0.570562\pi$
$702$	−5.69180e79	−0.0431163
$703$	7.89000e80	0.573919
$704$	6.34354e79	0.0443109
$705$	4.68568e81	3.14328
$706$	−5.00432e81	−3.22412
$707$	−1.37882e81	−0.853206
$708$	3.10357e81	1.84465
$709$	−9.03269e80	−0.515703	−0.257851	−	0.966185i	$-0.583015\pi$
$709$	−9.03269e80	−0.515703	−0.257851	+	0.966185i	$0.583015\pi$
$710$	2.99358e81	1.64183
$711$	4.88613e80	0.257443
$712$	−4.63434e81	−2.34589
$713$	2.28643e81	1.11201
$714$	−2.98289e81	−1.39392
$715$	−7.61951e79	−0.0342141
$716$	1.86007e81	0.802616
$717$	−2.86516e81	−1.18810
$718$	2.82021e81	1.12392
$719$	3.56990e80	0.136736	0.0683679	−	0.997660i	$-0.478221\pi$
$719$	3.56990e80	0.136736	0.0683679	+	0.997660i	$0.478221\pi$
$720$	−5.04483e81	−1.85725
$721$	1.53581e81	0.543478
$722$	2.19436e81	0.746446
$723$	1.45793e80	0.0476756
$724$	−4.45568e80	−0.140076
$725$	−4.33688e81	−1.31082
$726$	8.41593e81	2.44573
$727$	−2.76076e81	−0.771432	−0.385716	−	0.922618i	$-0.626046\pi$
$727$	−2.76076e81	−0.771432	−0.385716	+	0.922618i	$0.626046\pi$
$728$	1.03155e81	0.277169
$729$	−3.35229e81	−0.866178
$730$	−2.56581e80	−0.0637562
$731$	−4.67138e81	−1.11635
$732$	−5.33785e81	−1.22688
$733$	3.48453e81	0.770337	0.385169	−	0.922846i	$-0.374143\pi$
$733$	3.48453e81	0.770337	0.385169	+	0.922846i	$0.374143\pi$
$734$	4.75020e81	1.01012
$735$	6.88190e81	1.40773
$736$	5.30737e81	1.04439
$737$	2.78023e80	0.0526330
$738$	2.70977e81	0.493545
$739$	7.13496e81	1.25033	0.625165	−	0.780492i	$-0.285032\pi$
$739$	7.13496e81	1.25033	0.625165	+	0.780492i	$0.285032\pi$
$740$	−1.30694e82	−2.20369
$741$	−1.75583e81	−0.284881
$742$	5.34191e81	0.834036
$743$	−3.85497e81	−0.579215	−0.289607	−	0.957146i	$-0.593525\pi$
$743$	−3.85497e81	−0.579215	−0.289607	+	0.957146i	$0.593525\pi$
$744$	1.15474e82	1.66976
$745$	−9.07776e81	−1.26335
$746$	−1.64050e82	−2.19745
$747$	1.10051e81	0.141892
$748$	−1.79935e81	−0.223316
$749$	−1.05716e81	−0.126302
$750$	−4.25117e81	−0.488948
$751$	1.61769e82	1.79125	0.895627	−	0.444806i	$-0.146727\pi$
$751$	1.61769e82	1.79125	0.895627	+	0.444806i	$0.146727\pi$
$752$	−2.27015e82	−2.42017
$753$	−9.20950e80	−0.0945321
$754$	−7.40826e81	−0.732205
$755$	1.12921e82	1.07470
$756$	−1.07194e81	−0.0982423
$757$	−3.94198e81	−0.347922	−0.173961	−	0.984753i	$-0.555657\pi$
$757$	−3.94198e81	−0.347922	−0.173961	+	0.984753i	$0.555657\pi$
$758$	1.37829e82	1.17157
$759$	2.98654e81	0.244499
$760$	2.67085e82	2.10602
$761$	2.02884e82	1.54094	0.770469	−	0.637478i	$-0.220022\pi$
$761$	2.02884e82	1.54094	0.770469	+	0.637478i	$0.220022\pi$
$762$	8.11778e80	0.0593910
$763$	−3.49546e81	−0.246351
$764$	4.50728e82	3.06023
$765$	−2.17004e82	−1.41944
$766$	−4.30401e82	−2.71240
$767$	−2.73890e81	−0.166306
$768$	−4.76080e82	−2.78539
$769$	−8.05382e81	−0.454047	−0.227024	−	0.973889i	$-0.572899\pi$
$769$	−8.05382e81	−0.454047	−0.227024	+	0.973889i	$0.572899\pi$
$770$	−2.10374e81	−0.114289
$771$	1.13230e82	0.592804
$772$	2.34154e82	1.18143
$773$	−1.77650e82	−0.863871	−0.431936	−	0.901904i	$-0.642169\pi$
$773$	−1.77650e82	−0.863871	−0.431936	+	0.901904i	$0.642169\pi$
$774$	3.54367e82	1.66087
$775$	−1.11723e82	−0.504715
$776$	−4.01193e82	−1.74700
$777$	1.26668e82	0.531699
$778$	2.68492e81	0.108646
$779$	−5.80543e81	−0.226473
$780$	2.90844e82	1.09387
$781$	−1.75017e81	−0.0634636
$782$	1.06459e83	3.72211
$783$	4.11065e81	0.138580
$784$	−3.33418e82	−1.08388
$785$	−7.83849e82	−2.45724
$786$	−1.16432e83	−3.51990
$787$	−3.76337e82	−1.09723	−0.548614	−	0.836076i	$-0.684844\pi$
$787$	−3.76337e82	−1.09723	−0.548614	+	0.836076i	$0.684844\pi$
$788$	7.26554e82	2.04301
$789$	6.11172e82	1.65756
$790$	2.54207e82	0.664991
$791$	5.99375e81	0.151241
$792$	7.28849e81	0.177407
$793$	4.71065e81	0.110610
$794$	3.45307e82	0.782206
$795$	8.04232e82	1.75759
$796$	1.68069e81	0.0354376
$797$	3.36181e82	0.683929	0.341964	−	0.939713i	$-0.388908\pi$
$797$	3.36181e82	0.683929	0.341964	+	0.939713i	$0.388908\pi$
$798$	−4.84782e82	−0.951622
$799$	−9.76506e82	−1.84966
$800$	−2.59338e82	−0.474025
$801$	6.11950e82	1.07942
$802$	−1.32395e83	−2.25372
$803$	1.50007e80	0.00246445
$804$	−1.06124e83	−1.68274
$805$	8.49012e82	1.29937
$806$	−1.90846e82	−0.281925
$807$	3.68040e82	0.524807
$808$	2.48528e83	3.42099
$809$	−6.27719e82	−0.834128	−0.417064	−	0.908877i	$-0.636941\pi$
$809$	−6.27719e82	−0.834128	−0.417064	+	0.908877i	$0.636941\pi$
$810$	−1.99709e83	−2.56198
$811$	8.14307e82	1.00854	0.504271	−	0.863546i	$-0.331761\pi$
$811$	8.14307e82	1.00854	0.504271	+	0.863546i	$0.331761\pi$
$812$	−1.39520e83	−1.66836
$813$	−9.76793e82	−1.12777
$814$	1.12018e82	0.124880
$815$	−4.27064e82	−0.459728
$816$	2.17572e83	2.26169
$817$	−7.59197e82	−0.762124
$818$	2.49249e83	2.41637
$819$	−1.36212e82	−0.127534
$820$	9.61637e82	0.869594
$821$	3.07479e82	0.268556	0.134278	−	0.990944i	$-0.457128\pi$
$821$	3.07479e82	0.268556	0.134278	+	0.990944i	$0.457128\pi$
$822$	3.71054e83	3.13033
$823$	3.23658e82	0.263749	0.131875	−	0.991266i	$-0.457900\pi$
$823$	3.23658e82	0.263749	0.131875	+	0.991266i	$0.457900\pi$
$824$	−2.76825e83	−2.17911
$825$	−1.45933e82	−0.110973
$826$	−7.56207e82	−0.555532
$827$	−2.03672e83	−1.44552	−0.722759	−	0.691100i	$-0.757126\pi$
$827$	−2.03672e83	−1.44552	−0.722759	+	0.691100i	$0.757126\pi$
$828$	−5.50867e83	−3.77730
$829$	1.94301e83	1.28728	0.643638	−	0.765330i	$-0.277424\pi$
$829$	1.94301e83	1.28728	0.643638	+	0.765330i	$0.277424\pi$
$830$	5.72555e82	0.366515
$831$	9.70120e82	0.600062
$832$	2.13687e82	0.127721
$833$	−1.43420e83	−0.828377
$834$	−5.09844e82	−0.284580
$835$	1.61606e83	0.871753
$836$	−2.92432e82	−0.152456
$837$	1.05895e82	0.0533583
$838$	−3.29803e83	−1.60620
$839$	−1.06869e83	−0.503078	−0.251539	−	0.967847i	$-0.580937\pi$
$839$	−1.06869e83	−0.503078	−0.251539	+	0.967847i	$0.580937\pi$
$840$	4.28783e83	1.95109
$841$	3.07683e83	1.35338
$842$	6.32663e83	2.69016
$843$	−3.31499e83	−1.36269
$844$	−7.00686e83	−2.78461
$845$	3.28760e83	1.26317
$846$	7.40770e83	2.75187
$847$	−1.39874e83	−0.502411
$848$	−3.89639e83	−1.35326
$849$	−8.85207e82	−0.297287
$850$	−5.20197e83	−1.68938
$851$	−4.52074e83	−1.41977
$852$	6.68055e83	2.02901
$853$	4.98481e83	1.46420	0.732102	−	0.681195i	$-0.238540\pi$
$853$	4.98481e83	1.46420	0.732102	+	0.681195i	$0.238540\pi$
$854$	1.30060e83	0.369484
$855$	−3.52677e83	−0.969043
$856$	1.90550e83	0.506416
$857$	−6.11692e83	−1.57246	−0.786230	−	0.617934i	$-0.787970\pi$
$857$	−6.11692e83	−1.57246	−0.786230	+	0.617934i	$0.787970\pi$
$858$	−2.49283e82	−0.0619876
$859$	−4.98716e83	−1.19963	−0.599816	−	0.800138i	$-0.704759\pi$
$859$	−4.98716e83	−1.19963	−0.599816	+	0.800138i	$0.704759\pi$
$860$	1.25757e84	2.92635
$861$	−9.32014e82	−0.209813
$862$	−3.52517e83	−0.767755
$863$	5.50260e83	1.15947	0.579736	−	0.814805i	$-0.303156\pi$
$863$	5.50260e83	1.15947	0.579736	+	0.814805i	$0.303156\pi$
$864$	2.45809e82	0.0501138
$865$	8.80431e83	1.73675
$866$	−1.40309e84	−2.67808
$867$	1.82722e83	0.337479
$868$	−3.59421e83	−0.642378
$869$	−1.48620e82	−0.0257047
$870$	−3.07939e84	−5.15426
$871$	9.36545e82	0.151709
$872$	6.30047e83	0.987763
$873$	5.29762e83	0.803850
$874$	1.73018e84	2.54106
$875$	7.06550e82	0.100442
$876$	−5.72592e82	−0.0787913
$877$	−2.09486e82	−0.0279040	−0.0139520	−	0.999903i	$-0.504441\pi$
$877$	−2.09486e82	−0.0279040	−0.0139520	+	0.999903i	$0.504441\pi$
$878$	1.21759e84	1.57003
$879$	1.80503e84	2.25321
$880$	1.53447e83	0.185439
$881$	−1.40341e84	−1.64199	−0.820996	−	0.570933i	$-0.806581\pi$
$881$	−1.40341e84	−1.64199	−0.820996	+	0.570933i	$0.806581\pi$
$882$	1.08798e84	1.23244
$883$	9.46348e83	1.03794	0.518968	−	0.854794i	$-0.326316\pi$
$883$	9.46348e83	1.03794	0.518968	+	0.854794i	$0.326316\pi$
$884$	−6.06125e83	−0.643684
$885$	−1.13848e84	−1.17069
$886$	−2.03986e84	−2.03114
$887$	−2.84152e83	−0.273986	−0.136993	−	0.990572i	$-0.543744\pi$
$887$	−2.84152e83	−0.273986	−0.136993	+	0.990572i	$0.543744\pi$
$888$	−2.28315e84	−2.13189
$889$	−1.34919e82	−0.0122003
$890$	3.18374e84	2.78819
$891$	1.16758e83	0.0990313
$892$	5.29253e83	0.434775
$893$	−1.58703e84	−1.26275
$894$	−2.96992e84	−2.28889
$895$	−6.82326e83	−0.509372
$896$	9.78801e83	0.707809
$897$	1.00604e84	0.704743
$898$	−1.81187e83	−0.122956
$899$	1.37830e84	0.906135
$900$	2.69174e84	1.71443
$901$	−1.67604e84	−1.03425
$902$	−8.24222e82	−0.0492785
$903$	−1.21883e84	−0.706060
$904$	−1.08036e84	−0.606411
$905$	1.63447e83	0.0888981
$906$	3.69438e84	1.94710
$907$	1.58567e84	0.809850	0.404925	−	0.914350i	$-0.367298\pi$
$907$	1.58567e84	0.809850	0.404925	+	0.914350i	$0.367298\pi$
$908$	4.17288e84	2.06533
$909$	−3.28173e84	−1.57410
$910$	−7.08661e83	−0.329427
$911$	−3.09258e84	−1.39331	−0.696655	−	0.717406i	$-0.745329\pi$
$911$	−3.09258e84	−1.39331	−0.696655	+	0.717406i	$0.745329\pi$
$912$	3.53601e84	1.54405
$913$	−3.34739e82	−0.0141674
$914$	−4.49182e83	−0.184270
$915$	1.95808e84	0.778625
$916$	−6.09138e84	−2.34798
$917$	1.93512e84	0.723071
$918$	4.93061e83	0.178601
$919$	−4.51927e83	−0.158700	−0.0793499	−	0.996847i	$-0.525284\pi$
$919$	−4.51927e83	−0.158700	−0.0793499	+	0.996847i	$0.525284\pi$
$920$	−1.53032e85	−5.20990
$921$	5.64279e84	1.86249
$922$	2.22359e84	0.711578
$923$	−5.89558e83	−0.182927
$924$	−4.69476e83	−0.141241
$925$	2.20900e84	0.644401
$926$	1.16922e85	3.30738
$927$	3.65538e84	1.00268
$928$	3.19938e84	0.851036
$929$	9.19664e83	0.237236	0.118618	−	0.992940i	$-0.462154\pi$
$929$	9.19664e83	0.237236	0.118618	+	0.992940i	$0.462154\pi$
$930$	−7.93290e84	−1.98458
$931$	−2.33088e84	−0.565528
$932$	−1.29681e85	−3.05157
$933$	−8.46426e84	−1.93180
$934$	5.47094e84	1.21109
$935$	6.60053e83	0.141725
$936$	2.45519e84	0.511355
$937$	−6.69274e84	−1.35215	−0.676076	−	0.736832i	$-0.736321\pi$
$937$	−6.69274e84	−1.35215	−0.676076	+	0.736832i	$0.736321\pi$
$938$	2.58579e84	0.506771
$939$	9.27601e84	1.76357
$940$	2.62882e85	4.84862
$941$	4.10199e84	0.733991	0.366995	−	0.930223i	$-0.380387\pi$
$941$	4.10199e84	0.733991	0.366995	+	0.930223i	$0.380387\pi$
$942$	−2.56447e85	−4.45192
$943$	3.32634e84	0.560252
$944$	5.51578e84	0.901374
$945$	3.93217e83	0.0623485
$946$	−1.07787e84	−0.165832
$947$	−9.80765e83	−0.146417	−0.0732083	−	0.997317i	$-0.523324\pi$
$947$	−9.80765e83	−0.146417	−0.0732083	+	0.997317i	$0.523324\pi$
$948$	5.67295e84	0.821811
$949$	5.05312e82	0.00710350
$950$	−8.45429e84	−1.15333
$951$	−2.39543e83	−0.0317132
$952$	−8.93594e84	−1.14812
$953$	3.25295e84	0.405630	0.202815	−	0.979217i	$-0.434991\pi$
$953$	3.25295e84	0.405630	0.202815	+	0.979217i	$0.434991\pi$
$954$	1.27143e85	1.53873
$955$	−1.65340e85	−1.94215
$956$	−1.60745e85	−1.83268
$957$	1.80034e84	0.199234
$958$	−4.13527e84	−0.444208
$959$	−6.16696e84	−0.643044
$960$	8.88234e84	0.899078
$961$	−6.62625e84	−0.651105
$962$	3.77341e84	0.359952
$963$	−2.51615e84	−0.233017
$964$	8.17951e83	0.0735414
$965$	−8.58943e84	−0.749784
$966$	2.77766e85	2.35414
$967$	1.35602e85	1.11586	0.557932	−	0.829887i	$-0.311595\pi$
$967$	1.35602e85	1.11586	0.557932	+	0.829887i	$0.311595\pi$
$968$	2.52119e85	2.01445
$969$	1.52102e85	1.18007
$970$	2.75615e85	2.07639
$971$	2.79468e84	0.204449	0.102224	−	0.994761i	$-0.467404\pi$
$971$	2.79468e84	0.204449	0.102224	+	0.994761i	$0.467404\pi$
$972$	−4.18392e85	−2.97231
$973$	8.47367e83	0.0584596
$974$	−4.67233e85	−3.13042
$975$	−4.91588e84	−0.319867
$976$	−9.48661e84	−0.599503
$977$	2.48657e85	1.52618	0.763090	−	0.646292i	$-0.223681\pi$
$977$	2.48657e85	1.52618	0.763090	+	0.646292i	$0.223681\pi$
$978$	−1.39720e85	−0.832915
$979$	−1.86134e84	−0.107775
$980$	3.86098e85	2.17147
$981$	−8.31956e84	−0.454500
$982$	−5.08425e85	−2.69805
$983$	−6.93296e84	−0.357391	−0.178695	−	0.983904i	$-0.557188\pi$
$983$	−6.93296e84	−0.357391	−0.178695	+	0.983904i	$0.557188\pi$
$984$	1.67993e85	0.841260
$985$	−2.66521e85	−1.29658
$986$	6.41752e85	3.03302
$987$	−2.54784e85	−1.16986
$988$	−9.85081e84	−0.439439
$989$	4.34998e85	1.88535
$990$	−5.00711e84	−0.210855
$991$	−6.96234e84	−0.284876	−0.142438	−	0.989804i	$-0.545494\pi$
$991$	−6.96234e84	−0.284876	−0.142438	+	0.989804i	$0.545494\pi$
$992$	8.24199e84	0.327680
$993$	−4.21302e85	−1.62757
$994$	−1.62776e85	−0.611053
$995$	−6.16524e83	−0.0224902
$996$	1.27773e85	0.452948
$997$	3.69726e85	1.27370	0.636852	−	0.770986i	$-0.280236\pi$
$997$	3.69726e85	1.27370	0.636852	+	0.770986i	$0.280236\pi$
$998$	−1.58506e85	−0.530670
$999$	−2.09377e84	−0.0681259

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.58.a.a.1.1	✓	4
3.2	odd	2		9.58.a.b.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.58.a.a.1.1	✓	4	1.1	even	1	trivial
9.58.a.b.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:	\( k \)	\(=\)	\( 58 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-6.73315e8 q^{2} +5.51192e13 q^{3} +3.09237e17 q^{4} -1.13437e20 q^{5} -3.71126e22 q^{6} +6.16816e23 q^{7} -1.11179e26 q^{8} +1.46809e27 q^{9} +O(q^{10})\)	\(q-6.73315e8 q^{2} +5.51192e13 q^{3} +3.09237e17 q^{4} -1.13437e20 q^{5} -3.71126e22 q^{6} +6.16816e23 q^{7} -1.11179e26 q^{8} +1.46809e27 q^{9} +7.63789e28 q^{10} -4.46542e28 q^{11} +1.70449e31 q^{12} -1.50421e31 q^{13} -4.15311e32 q^{14} -6.25257e33 q^{15} +3.02928e34 q^{16} +1.30305e35 q^{17} -9.88484e35 q^{18} +2.11773e36 q^{19} -3.50790e37 q^{20} +3.39984e37 q^{21} +3.00663e37 q^{22} -1.21340e39 q^{23} -6.12811e39 q^{24} +5.92910e39 q^{25} +1.01281e40 q^{26} -5.61981e39 q^{27} +1.90743e41 q^{28} -7.31457e41 q^{29} +4.20995e42 q^{30} -1.88432e42 q^{31} -4.37398e42 q^{32} -2.46130e42 q^{33} -8.77362e43 q^{34} -6.99698e43 q^{35} +4.53987e44 q^{36} +3.72569e44 q^{37} -1.42590e45 q^{38} -8.29111e44 q^{39} +1.26119e46 q^{40} -2.74135e45 q^{41} -2.28916e46 q^{42} -3.58496e46 q^{43} -1.38088e46 q^{44} -1.66535e47 q^{45} +8.16998e47 q^{46} -7.49401e47 q^{47} +1.66972e48 q^{48} -1.10065e48 q^{49} -3.99215e48 q^{50} +7.18230e48 q^{51} -4.65159e48 q^{52} -1.28624e49 q^{53} +3.78390e48 q^{54} +5.06545e48 q^{55} -6.85771e49 q^{56} +1.16728e50 q^{57} +4.92500e50 q^{58} +1.82082e50 q^{59} -1.93353e51 q^{60} -3.13164e50 q^{61} +1.26874e51 q^{62} +9.05538e50 q^{63} -1.42059e51 q^{64} +1.70634e51 q^{65} +1.65723e51 q^{66} -6.22614e51 q^{67} +4.02952e52 q^{68} -6.68815e52 q^{69} +4.71117e52 q^{70} +3.91938e52 q^{71} -1.63221e53 q^{72} -3.35931e51 q^{73} -2.50856e53 q^{74} +3.26807e53 q^{75} +6.54881e53 q^{76} -2.75434e52 q^{77} +5.58252e53 q^{78} +3.32824e53 q^{79} -3.43633e54 q^{80} -2.61472e54 q^{81} +1.84579e54 q^{82} +7.49625e53 q^{83} +1.05136e55 q^{84} -1.47814e55 q^{85} +2.41381e55 q^{86} -4.03173e55 q^{87} +4.96462e54 q^{88} +4.16835e55 q^{89} +1.12131e56 q^{90} -9.27822e54 q^{91} -3.75228e56 q^{92} -1.03862e56 q^{93} +5.04582e56 q^{94} -2.40229e56 q^{95} -2.41090e56 q^{96} +3.60852e56 q^{97} +7.41085e56 q^{98} -6.55562e55 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 217744560 q^{2} + 37475862172560 q^{3} + 29\!\cdots\!28 q^{4}+ \cdots + 80\!\cdots\!32 q^{9}+O(q^{10}) \) 4 * q - 217744560 * q^2 + 37475862172560 * q^3 + 293124896311376128 * q^4 - 106961276207842698600 * q^5 - 33990084162012424888512 * q^6 + 952854504056592488640800 * q^7 - 88551069216810449485639680 * q^8 + 807299095982681497210590132 * q^9	\( 4 q - 217744560 q^{2} + 37475862172560 q^{3} + 29\!\cdots\!28 q^{4}+ \cdots + 12\!\cdots\!04 q^{99}+O(q^{100}) \) 4 * q - 217744560 * q^2 + 37475862172560 * q^3 + 293124896311376128 * q^4 - 106961276207842698600 * q^5 - 33990084162012424888512 * q^6 + 952854504056592488640800 * q^7 - 88551069216810449485639680 * q^8 + 807299095982681497210590132 * q^9 + 44476431289760320477662520800 * q^10 - 462030036788542994175991820112 * q^11 + 10003750272364901761239114286080 * q^12 - 35670303061909387812013418679880 * q^13 + 70403094050531232484583448299136 * q^14 - 3873003953749638547444662603837600 * q^15 + 13566910890781728442321186411577344 * q^16 + 13820011728830480443629140931368520 * q^17 - 1287737321088043352155941276317529840 * q^18 + 336853252899071533902360882896311760 * q^19 - 50382729988973225454329459567578483200 * q^20 - 114908173756075652427942608537020743552 * q^21 - 661915503282569637498974918979285510720 * q^22 - 2975542065258688382050024994957196661920 * q^23 - 10578976944220511671340845604322576875520 * q^24 - 9469406228848045007865812554313674602500 * q^25 - 17469964426099436483582477475571041235872 * q^26 + 76349739563972016366032809192591896661920 * q^27 + 649254606795882967703588744692964385720320 * q^28 + 692903173502123074211699189163367889819640 * q^29 + 5634330080537746852583656641742556105212800 * q^30 - 899836592298317074905406089703577976621952 * q^31 - 14233950964359390830124363997913062975733760 * q^32 - 29363967329346027307019371741967172628226880 * q^33 - 169043128317257524614754408952689830505725024 * q^34 - 229326244292419606493088342114240299318011200 * q^35 + 284785472553153735165042638775100342213281024 * q^36 + 1088031360501840746049603861287321623324833560 * q^37 + 1556247388283245464794907962939214603341474880 * q^38 + 4179255936739867118004084422081931511953729504 * q^39 + 11751904708902009656918381872378671214758912000 * q^40 - 11103291557355181141038304173539140276092022872 * q^41 - 59279988331696939901744072326763120527717946880 * q^42 - 61754953860901881142563948460092952248410491600 * q^43 - 133524603192894473629581294520903680469781443584 * q^44 - 107702873160032711230811245899648546573795049800 * q^45 + 784819010796366200631618785819800311186796983168 * q^46 + 363083109323271524824455302894174707948361522880 * q^47 + 2742506186706372359330741580910160874632313569280 * q^48 + 1216129915477179767594559246649850886387208070628 * q^49 - 5243147625423300757899019878966089303259662130000 * q^50 - 764600229637750496670397948984385624631693707232 * q^51 - 22843788670121162835092909423272591563858567692800 * q^52 - 35290483593822076697173728695179253314838955459240 * q^53 + 12366575839681539833915263850508773584456529324160 * q^54 + 49196225093152182399971681538771907122934246240800 * q^55 + 63731767886683182211705479053660664279663635496960 * q^56 + 207676196582248616809244588606912583584671767915840 * q^57 + 617562539749243989517600779192095966343296224852320 * q^58 + 67768373912933539906296460571320281490527711258480 * q^59 - 1815042162748644358648991332911151647292658713651200 * q^60 - 1547288835446782082478245361946256543823484047403912 * q^61 - 749692944011811307313821057793297922348443552785920 * q^62 - 1569461042763431092010126958426126899190556123563360 * q^63 - 1990114977445631941316528741938069721703684937613312 * q^64 + 8063572248542729948506878297975365372089154570456400 * q^65 + 16489629555376763758820085001622755676656730822766336 * q^66 + 15272577061969964687199674310464241542844062558207120 * q^67 + 41305128999321265264790818598430329317542515380584960 * q^68 - 65786095162933072363901793014646952768970242331074176 * q^69 - 24325103535157938973881571830399397699429009026566400 * q^70 - 73888360588713834794031605853188887812717485611902432 * q^71 - 210328265328797773276338939967226276847978373484605440 * q^72 - 130297268842197178419561798573986372195905283718671320 * q^73 + 7685145516671187561069432006215096921673721366642656 * q^74 + 403928833669880609006163131916358629442839611491110000 * q^75 + 1456086045339107958455546112995861351598648681192657920 * q^76 - 106427745818663343042165176190596036157925407112924800 * q^77 + 2074950811168633790188899303505400649698048509219286400 * q^78 - 828943058463042070981602117491995742498435075805703360 * q^79 - 2284181918093911007938097065798931209886961598847385600 * q^80 - 7963307412965608591332950484302680892196600516966334236 * q^81 - 1883428276461442027198836795157559789817480540746193120 * q^82 - 9840480688986571601216593400698100805429733592804704560 * q^83 + 13541340719968270381664710206581288963145836751957467136 * q^84 - 14840134943015755845177119052592106190913842871494565200 * q^85 + 67988974963281087138264344329950027971018743502811738048 * q^86 - 27365055454269193487844075068414523895320708309490878240 * q^87 + 61847074514255305493001192533786291945351930637515735040 * q^88 - 10663966381455218428814337779016832517355842990125366680 * q^89 + 144098850070698626396745850922715348604587043628376674400 * q^90 - 254422712153651549623482540524255137118230327668042523712 * q^91 - 274534438781355859366149237613545893970204939554260346880 * q^92 - 414128946656565192633171191785208529876343680904079162880 * q^93 + 632898423704876935427548603685166753697821378730383050496 * q^94 - 532156934024946939894578863048125180396162968766201396000 * q^95 + 663745987198780197281626102963422448954448917470231134208 * q^96 - 152729877520747450623636953478949994021736793474425664120 * q^97 + 2296925218269808931776551039888426925574868525366690486480 * q^98 + 123613071571796047703935039848745969833181068960384152304 * q^99

Introduction

L-functions

Modular forms

Varieties

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