LMFDB - Embedded newform 3.38.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,38,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 38, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 38 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$26.0142114374$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2495042360x + 9241471873200 $ x^3 - x^2 - 2495042360*x + 9241471873200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3724.64$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-148328. q^{2} -3.87420e8 q^{3} -1.15438e11 q^{4} +7.60742e11 q^{5} +5.74652e13 q^{6} +2.59260e15 q^{7} +3.75086e16 q^{8} +1.50095e17 q^{9} +O(q^{10})$	\(q-148328. q^{2} -3.87420e8 q^{3} -1.15438e11 q^{4} +7.60742e11 q^{5} +5.74652e13 q^{6} +2.59260e15 q^{7} +3.75086e16 q^{8} +1.50095e17 q^{9} -1.12839e17 q^{10} +3.65505e18 q^{11} +4.47230e19 q^{12} +6.05340e19 q^{13} -3.84554e20 q^{14} -2.94727e20 q^{15} +1.03021e22 q^{16} +5.25799e22 q^{17} -2.22632e22 q^{18} -4.58834e23 q^{19} -8.78185e22 q^{20} -1.00443e24 q^{21} -5.42145e23 q^{22} +6.97213e24 q^{23} -1.45316e25 q^{24} -7.21808e25 q^{25} -8.97887e24 q^{26} -5.81497e25 q^{27} -2.99284e26 q^{28} -2.14090e27 q^{29} +4.37162e25 q^{30} -3.44162e27 q^{31} -6.68323e27 q^{32} -1.41604e27 q^{33} -7.79906e27 q^{34} +1.97230e27 q^{35} -1.73266e28 q^{36} +6.38686e28 q^{37} +6.80578e28 q^{38} -2.34521e28 q^{39} +2.85344e28 q^{40} +5.40269e29 q^{41} +1.48984e29 q^{42} +3.10661e30 q^{43} -4.21931e29 q^{44} +1.14183e29 q^{45} -1.03416e30 q^{46} -1.05785e31 q^{47} -3.99124e30 q^{48} -1.18405e31 q^{49} +1.07064e31 q^{50} -2.03705e31 q^{51} -6.98792e30 q^{52} -5.28675e31 q^{53} +8.62521e30 q^{54} +2.78055e30 q^{55} +9.72449e31 q^{56} +1.77762e32 q^{57} +3.17554e32 q^{58} +1.00018e32 q^{59} +3.40227e31 q^{60} -1.03869e32 q^{61} +5.10487e32 q^{62} +3.89135e32 q^{63} -4.24601e32 q^{64} +4.60508e31 q^{65} +2.10038e32 q^{66} -4.87568e33 q^{67} -6.06972e33 q^{68} -2.70115e33 q^{69} -2.92547e32 q^{70} -1.97222e34 q^{71} +5.62984e33 q^{72} +2.72469e34 q^{73} -9.47348e33 q^{74} +2.79643e34 q^{75} +5.29668e34 q^{76} +9.47609e33 q^{77} +3.47860e33 q^{78} +1.01745e35 q^{79} +7.83724e33 q^{80} +2.25284e34 q^{81} -8.01369e34 q^{82} -4.82762e35 q^{83} +1.15949e35 q^{84} +3.99998e34 q^{85} -4.60797e35 q^{86} +8.29427e35 q^{87} +1.37096e35 q^{88} -2.01920e36 q^{89} -1.69365e34 q^{90} +1.56941e35 q^{91} -8.04848e35 q^{92} +1.33335e36 q^{93} +1.56908e36 q^{94} -3.49054e35 q^{95} +2.58922e36 q^{96} +5.47048e36 q^{97} +1.75628e36 q^{98} +5.48604e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 45\!\cdots\!63 q^{9}+O(q^{10}) $ 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9	$ 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 34\!\cdots\!20 q^{99}+O(q^{100}) $ 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9 + 10698950136741797880 * q^10 + 22673303357139628620 * q^11 - 131132770215589974672 * q^12 - 168270000203795091510 * q^13 + 797101803583223694528 * q^14 + 3730362592143228440310 * q^15 + 32071173863897028608256 * q^16 - 27168549617785276146906 * q^17 - 46665622870919402711868 * q^18 + 582035599719143813745204 * q^19 - 4066256929972106412494880 * q^20 + 1790612692538373730632816 * q^21 - 4486408000290444592999152 * q^22 - 17157197763697459349569272 * q^23 + 36178839725894735603677632 * q^24 - 24896488591542260192608275 * q^25 - 618603181238074545425686344 * q^26 - 174449211009120179071170507 * q^27 - 2033429672978753784958610688 * q^28 + 111201150055901033185229778 * q^29 - 4144992493763124201408763320 * q^30 - 11859842025407507592851987736 * q^31 - 27281435223830339470718352384 * q^32 - 8784102273868376561238795180 * q^33 - 18783445175675019452330905464 * q^34 + 47739964986924083632994534880 * q^35 + 50803521960848503410923854608 * q^36 + 60344578140045347560278093666 * q^37 - 372452605565029151271789397776 * q^38 + 65191245762984394008603948390 * q^39 + 1732463594119923393272610326400 * q^40 + 2087364862188523841295969725934 * q^41 - 308813570526994475930424384192 * q^42 + 2483325896102099669944761791244 * q^43 + 4284309379683814482835899511872 * q^44 - 1445218899595437120383607511590 * q^45 - 4327236604482200607954371165856 * q^46 - 11791379189662012541191082473632 * q^47 - 12425029861155006269057528957184 * q^48 - 22445324860908932271245865545973 * q^49 - 96691457712658313260807892933700 * q^50 + 10525652778343134781834358357034 * q^51 + 43220201443333906987967057359584 * q^52 - 115357757368640109037215455345382 * q^53 + 18079218432141178878219826663452 * q^54 - 129419469300146958823045789059480 * q^55 + 630552391741804501615596905794560 * q^56 - 225492516658598958982491855084756 * q^57 + 580965936186746161132050423512088 * q^58 + 1091721381032593697748326986744236 * q^59 + 1575351248209432222688802119596320 * q^60 + 294380981976352085651508270601002 * q^61 + 248838835694853996733454208986592 * q^62 - 693720044952823401986519854167024 * q^63 - 1064135955800023765084313699610624 * q^64 - 7515875365146923444942971038019860 * q^65 + 1738126381326036186247137444425328 * q^66 + 3824374619785575741360273276519444 * q^67 - 21329399470876894544665401157365216 * q^68 + 6647049947481376149267749297614008 * q^69 - 43059062291480572688803543269144960 * q^70 - 22149353642418626281921550104284744 * q^71 - 14016423778058764430102498387802048 * q^72 + 32759279450923542889398870347665278 * q^73 + 46478870171568672595185044851456728 * q^74 + 9645409784518223707985532085946475 * q^75 + 347061692957154720144564653376455616 * q^76 - 61122141948697926808926153780754368 * q^77 + 239659546972210465807272116553102216 * q^78 + 74649348023552719727334936629819640 * q^79 - 618088038723375449595358546989335040 * q^80 + 67585198634817523235520443624317923 * q^81 + 103937675337495441364448738414881512 * q^82 - 317656267631459020909914460046822604 * q^83 + 787792318252538877979265797505586432 * q^84 + 210972517320554825185658741373302580 * q^85 - 2655243937093032975138251645354123760 * q^86 - 43081603932019555612226948170121442 * q^87 - 1353962196634819912991147659264835328 * q^88 - 1604427814888922862357874180114447026 * q^89 + 1605855018835039028277517574319663480 * q^90 + 459759011513895387754487414763335904 * q^91 - 5426885178857894678398508472745540224 * q^92 + 4594745796946127015893929993303122904 * q^93 + 15155501875748762861069416648677456000 * q^94 - 10713376656166940710475311057833316200 * q^95 + 10569386975038174570781705261883595776 * q^96 + 2690787195739502167683294096108844614 * q^97 - 1675640263817086437903041451354198300 * q^98 + 3403141198368098368991272474406443020 * 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 $

$2$	−148328.	−0.400099	−0.200049	−	0.979786i	$-0.564110\pi$
$2$	−148328.	−0.400099	−0.200049	+	0.979786i	$0.564110\pi$
$3$	−3.87420e8	−0.577350
$3$	−3.87420e8	−0.577350
$4$	−1.15438e11	−0.839921
$5$	7.60742e11	0.0891851	0.0445926	−	0.999005i	$-0.485801\pi$
$5$	7.60742e11	0.0891851	0.0445926	+	0.999005i	$0.485801\pi$
$6$	5.74652e13	0.230997
$7$	2.59260e15	0.601758	0.300879	−	0.953662i	$-0.402720\pi$
$7$	2.59260e15	0.601758	0.300879	+	0.953662i	$0.402720\pi$
$8$	3.75086e16	0.736150
$9$	1.50095e17	0.333333
$10$	−1.12839e17	−0.0356829
$11$	3.65505e18	0.198211	0.0991057	−	0.995077i	$-0.468402\pi$
$11$	3.65505e18	0.198211	0.0991057	+	0.995077i	$0.468402\pi$
$12$	4.47230e19	0.484929
$13$	6.05340e19	0.149296	0.0746479	−	0.997210i	$-0.476217\pi$
$13$	6.05340e19	0.149296	0.0746479	+	0.997210i	$0.476217\pi$
$14$	−3.84554e20	−0.240763
$15$	−2.94727e20	−0.0514911
$16$	1.03021e22	0.545388
$17$	5.25799e22	0.906808	0.453404	−	0.891305i	$-0.350210\pi$
$17$	5.25799e22	0.906808	0.453404	+	0.891305i	$0.350210\pi$
$18$	−2.22632e22	−0.133366
$19$	−4.58834e23	−1.01091	−0.505457	−	0.862852i	$-0.668676\pi$
$19$	−4.58834e23	−1.01091	−0.505457	+	0.862852i	$0.668676\pi$
$20$	−8.78185e22	−0.0749085
$21$	−1.00443e24	−0.347425
$22$	−5.42145e23	−0.0793042
$23$	6.97213e24	0.448126	0.224063	−	0.974575i	$-0.428068\pi$
$23$	6.97213e24	0.448126	0.224063	+	0.974575i	$0.428068\pi$
$24$	−1.45316e25	−0.425016
$25$	−7.21808e25	−0.992046
$26$	−8.97887e24	−0.0597331
$27$	−5.81497e25	−0.192450
$28$	−2.99284e26	−0.505429
$29$	−2.14090e27	−1.88900	−0.944502	−	0.328506i	$-0.893455\pi$
$29$	−2.14090e27	−1.88900	−0.944502	+	0.328506i	$0.893455\pi$
$30$	4.37162e25	0.0206015
$31$	−3.44162e27	−0.884242	−0.442121	−	0.896955i	$-0.645774\pi$
$31$	−3.44162e27	−0.884242	−0.442121	+	0.896955i	$0.645774\pi$
$32$	−6.68323e27	−0.954359
$33$	−1.41604e27	−0.114437
$34$	−7.79906e27	−0.362813
$35$	1.97230e27	0.0536678
$36$	−1.73266e28	−0.279974
$37$	6.38686e28	0.621664	0.310832	−	0.950465i	$-0.399392\pi$
$37$	6.38686e28	0.621664	0.310832	+	0.950465i	$0.399392\pi$
$38$	6.80578e28	0.404465
$39$	−2.34521e28	−0.0861960
$40$	2.85344e28	0.0656536
$41$	5.40269e29	0.787243	0.393622	−	0.919273i	$-0.371222\pi$
$41$	5.40269e29	0.787243	0.393622	+	0.919273i	$0.371222\pi$
$42$	1.48984e29	0.139004
$43$	3.10661e30	1.87552	0.937758	−	0.347288i	$-0.112897\pi$
$43$	3.10661e30	1.87552	0.937758	+	0.347288i	$0.112897\pi$
$44$	−4.21931e29	−0.166482
$45$	1.14183e29	0.0297284
$46$	−1.03416e30	−0.179295
$47$	−1.05785e31	−1.23201	−0.616003	−	0.787744i	$-0.711249\pi$
$47$	−1.05785e31	−1.23201	−0.616003	+	0.787744i	$0.711249\pi$
$48$	−3.99124e30	−0.314880
$49$	−1.18405e31	−0.637887
$50$	1.07064e31	0.396916
$51$	−2.03705e31	−0.523546
$52$	−6.98792e30	−0.125397
$53$	−5.28675e31	−0.666938	−0.333469	−	0.942761i	$-0.608219\pi$
$53$	−5.28675e31	−0.666938	−0.333469	+	0.942761i	$0.608219\pi$
$54$	8.62521e30	0.0769990
$55$	2.78055e30	0.0176775
$56$	9.72449e31	0.442984
$57$	1.77762e32	0.583651
$58$	3.17554e32	0.755788
$59$	1.00018e32	0.173507	0.0867535	−	0.996230i	$-0.472351\pi$
$59$	1.00018e32	0.173507	0.0867535	+	0.996230i	$0.472351\pi$
$60$	3.40227e31	0.0432484
$61$	−1.03869e32	−0.0972490	−0.0486245	−	0.998817i	$-0.515484\pi$
$61$	−1.03869e32	−0.0972490	−0.0486245	+	0.998817i	$0.515484\pi$
$62$	5.10487e32	0.353784
$63$	3.89135e32	0.200586
$64$	−4.24601e32	−0.163550
$65$	4.60508e31	0.0133150
$66$	2.10038e32	0.0457863
$67$	−4.87568e33	−0.804732	−0.402366	−	0.915479i	$-0.631812\pi$
$67$	−4.87568e33	−0.804732	−0.402366	+	0.915479i	$0.631812\pi$
$68$	−6.06972e33	−0.761647
$69$	−2.70115e33	−0.258726
$70$	−2.92547e32	−0.0214724
$71$	−1.97222e34	−1.11346	−0.556732	−	0.830692i	$-0.687945\pi$
$71$	−1.97222e34	−1.11346	−0.556732	+	0.830692i	$0.687945\pi$
$72$	5.62984e33	0.245383
$73$	2.72469e34	0.920118	0.460059	−	0.887888i	$-0.347828\pi$
$73$	2.72469e34	0.920118	0.460059	+	0.887888i	$0.347828\pi$
$74$	−9.47348e33	−0.248727
$75$	2.79643e34	0.572758
$76$	5.29668e34	0.849087
$77$	9.47609e33	0.119275
$78$	3.47860e33	0.0344869
$79$	1.01745e35	0.796915	0.398457	−	0.917187i	$-0.369546\pi$
$79$	1.01745e35	0.796915	0.398457	+	0.917187i	$0.369546\pi$
$80$	7.83724e33	0.0486405
$81$	2.25284e34	0.111111
$82$	−8.01369e34	−0.314975
$83$	−4.82762e35	−1.51631	−0.758155	−	0.652074i	$-0.773899\pi$
$83$	−4.82762e35	−1.51631	−0.758155	+	0.652074i	$0.773899\pi$
$84$	1.15949e35	0.291810
$85$	3.99998e34	0.0808737
$86$	−4.60797e35	−0.750392
$87$	8.29427e35	1.09062
$88$	1.37096e35	0.145913
$89$	−2.01920e36	−1.74367	−0.871837	−	0.489797i	$-0.837071\pi$
$89$	−2.01920e36	−1.74367	−0.871837	+	0.489797i	$0.837071\pi$
$90$	−1.69365e34	−0.0118943
$91$	1.56941e35	0.0898399
$92$	−8.04848e35	−0.376391
$93$	1.33335e36	0.510518
$94$	1.56908e36	0.492924
$95$	−3.49054e35	−0.0901584
$96$	2.58922e36	0.551000
$97$	5.47048e36	0.961056	0.480528	−	0.876979i	$-0.340445\pi$
$97$	5.47048e36	0.961056	0.480528	+	0.876979i	$0.340445\pi$
$98$	1.75628e36	0.255218
$99$	5.48604e35	0.0660705
$100$	8.33240e36	0.833240
$101$	−2.06698e37	−1.71945	−0.859727	−	0.510754i	$-0.829366\pi$
$101$	−2.06698e37	−1.71945	−0.859727	+	0.510754i	$0.829366\pi$
$102$	3.02152e36	0.209470
$103$	−3.10209e36	−0.179542	−0.0897710	−	0.995962i	$-0.528614\pi$
$103$	−3.10209e36	−0.179542	−0.0897710	+	0.995962i	$0.528614\pi$
$104$	2.27055e36	0.109904
$105$	−7.64110e35	−0.0309851
$106$	7.84172e36	0.266841
$107$	−4.27045e37	−1.22145	−0.610723	−	0.791844i	$-0.709121\pi$
$107$	−4.27045e37	−1.22145	−0.610723	+	0.791844i	$0.709121\pi$
$108$	6.71268e36	0.161643
$109$	−6.16065e37	−1.25094	−0.625470	−	0.780248i	$-0.715093\pi$
$109$	−6.16065e37	−1.25094	−0.625470	+	0.780248i	$0.715093\pi$
$110$	−4.12433e35	−0.00707275
$111$	−2.47440e37	−0.358918
$112$	2.67092e37	0.328192
$113$	1.11410e38	1.16138	0.580690	−	0.814124i	$-0.302783\pi$
$113$	1.11410e38	1.16138	0.580690	+	0.814124i	$0.302783\pi$
$114$	−2.63670e37	−0.233518
$115$	5.30399e36	0.0399662
$116$	2.47141e38	1.58661
$117$	9.08583e36	0.0497653
$118$	−1.48355e37	−0.0694199
$119$	1.36319e38	0.545679
$120$	−1.10548e37	−0.0379051
$121$	−3.26680e38	−0.960712
$122$	1.54067e37	0.0389092
$123$	−2.09311e38	−0.454515
$124$	3.97293e38	0.742694
$125$	−1.10262e38	−0.177661
$126$	−5.77195e37	−0.0802542
$127$	−1.01769e39	−1.22249	−0.611245	−	0.791441i	$-0.709331\pi$
$127$	−1.01769e39	−1.22249	−0.611245	+	0.791441i	$0.709331\pi$
$128$	9.81516e38	1.01980
$129$	−1.20357e39	−1.08283
$130$	−6.83060e36	−0.00532730
$131$	−1.20760e38	−0.0817343	−0.0408672	−	0.999165i	$-0.513012\pi$
$131$	−1.20760e38	−0.0817343	−0.0408672	+	0.999165i	$0.513012\pi$
$132$	1.63465e38	0.0961184
$133$	−1.18957e39	−0.608325
$134$	7.23198e38	0.321972
$135$	−4.42370e37	−0.0171637
$136$	1.97220e39	0.667546
$137$	−6.25190e38	−0.184791	−0.0923956	−	0.995722i	$-0.529452\pi$
$137$	−6.25190e38	−0.184791	−0.0923956	+	0.995722i	$0.529452\pi$
$138$	4.00655e38	0.103516
$139$	3.06556e39	0.693005	0.346503	−	0.938049i	$-0.387369\pi$
$139$	3.06556e39	0.693005	0.346503	+	0.938049i	$0.387369\pi$
$140$	−2.27678e38	−0.0450768
$141$	4.09832e39	0.711299
$142$	2.92535e39	0.445495
$143$	2.21255e38	0.0295921
$144$	1.54629e39	0.181796
$145$	−1.62867e39	−0.168471
$146$	−4.04146e39	−0.368138
$147$	4.58727e39	0.368285
$148$	−7.37286e39	−0.522148
$149$	−2.24131e40	−1.40138	−0.700689	−	0.713467i	$-0.747124\pi$
$149$	−2.24131e40	−1.40138	−0.700689	+	0.713467i	$0.747124\pi$
$150$	−4.14788e39	−0.229160
$151$	5.01512e38	0.0245024	0.0122512	−	0.999925i	$-0.496100\pi$
$151$	5.01512e38	0.0245024	0.0122512	+	0.999925i	$0.496100\pi$
$152$	−1.72102e40	−0.744184
$153$	7.89197e39	0.302269
$154$	−1.40557e39	−0.0477219
$155$	−2.61818e39	−0.0788613
$156$	2.70726e39	0.0723978
$157$	3.93108e40	0.934046	0.467023	−	0.884245i	$-0.345326\pi$
$157$	3.93108e40	0.934046	0.467023	+	0.884245i	$0.345326\pi$
$158$	−1.50916e40	−0.318845
$159$	2.04820e40	0.385057
$160$	−5.08422e39	−0.0851147
$161$	1.80759e40	0.269663
$162$	−3.34158e39	−0.0444554
$163$	8.49645e40	1.00871	0.504356	−	0.863496i	$-0.331730\pi$
$163$	8.49645e40	1.00871	0.504356	+	0.863496i	$0.331730\pi$
$164$	−6.23675e40	−0.661222
$165$	−1.07724e39	−0.0102061
$166$	7.16069e40	0.606674
$167$	1.99342e41	1.51128	0.755639	−	0.654989i	$-0.227327\pi$
$167$	1.99342e41	1.51128	0.755639	+	0.654989i	$0.227327\pi$
$168$	−3.76747e40	−0.255757
$169$	−1.60736e41	−0.977711
$170$	−5.93307e39	−0.0323575
$171$	−6.88685e40	−0.336971
$172$	−3.58621e41	−1.57529
$173$	1.62039e41	0.639393	0.319697	−	0.947520i	$-0.396419\pi$
$173$	1.62039e41	0.639393	0.319697	+	0.947520i	$0.396419\pi$
$174$	−1.23027e41	−0.436354
$175$	−1.87136e41	−0.596971
$176$	3.76547e40	0.108102
$177$	−3.87491e40	−0.100174
$178$	2.99504e41	0.697641
$179$	2.10383e41	0.441804	0.220902	−	0.975296i	$-0.429100\pi$
$179$	2.10383e41	0.441804	0.220902	+	0.975296i	$0.429100\pi$
$180$	−1.31811e40	−0.0249695
$181$	−4.66595e41	−0.797785	−0.398893	−	0.916998i	$-0.630605\pi$
$181$	−4.66595e41	−0.797785	−0.398893	+	0.916998i	$0.630605\pi$
$182$	−2.32786e40	−0.0359448
$183$	4.02411e40	0.0561468
$184$	2.61515e41	0.329888
$185$	4.85875e40	0.0554432
$186$	−1.97773e41	−0.204257
$187$	1.92182e41	0.179740
$188$	1.22116e42	1.03479
$189$	−1.50759e41	−0.115808
$190$	5.17744e40	0.0360723
$191$	9.30968e41	0.588596	0.294298	−	0.955714i	$-0.404914\pi$
$191$	9.30968e41	0.588596	0.294298	+	0.955714i	$0.404914\pi$
$192$	1.64499e41	0.0944258
$193$	1.74256e42	0.908611	0.454306	−	0.890846i	$-0.349887\pi$
$193$	1.74256e42	0.908611	0.454306	+	0.890846i	$0.349887\pi$
$194$	−8.11424e41	−0.384517
$195$	−1.78410e40	−0.00768740
$196$	1.36685e42	0.535775
$197$	−4.12934e42	−1.47318	−0.736589	−	0.676341i	$-0.763565\pi$
$197$	−4.12934e42	−1.47318	−0.736589	+	0.676341i	$0.763565\pi$
$198$	−8.13731e40	−0.0264347
$199$	−5.51808e42	−1.63308	−0.816538	−	0.577292i	$-0.804109\pi$
$199$	−5.51808e42	−1.63308	−0.816538	+	0.577292i	$0.804109\pi$
$200$	−2.70740e42	−0.730295
$201$	1.88894e42	0.464612
$202$	3.06590e42	0.687951
$203$	−5.55049e42	−1.13672
$204$	2.35153e42	0.439737
$205$	4.11006e41	0.0702104
$206$	4.60126e41	0.0718345
$207$	1.04648e42	0.149375
$208$	6.23627e41	0.0814242
$209$	−1.67706e42	−0.200375
$210$	1.13339e41	0.0123971
$211$	6.01151e42	0.602224	0.301112	−	0.953589i	$-0.402642\pi$
$211$	6.01151e42	0.602224	0.301112	+	0.953589i	$0.402642\pi$
$212$	6.10291e42	0.560175
$213$	7.64078e42	0.642858
$214$	6.33426e42	0.488699
$215$	2.36333e42	0.167268
$216$	−2.18112e42	−0.141672
$217$	−8.92274e42	−0.532100
$218$	9.13795e42	0.500500
$219$	−1.05560e43	−0.531230
$220$	−3.20981e41	−0.0148477
$221$	3.18288e42	0.135383
$222$	3.67022e42	0.143603
$223$	−2.40052e42	−0.0864302	−0.0432151	−	0.999066i	$-0.513760\pi$
$223$	−2.40052e42	−0.0864302	−0.0432151	+	0.999066i	$0.513760\pi$
$224$	−1.73269e43	−0.574293
$225$	−1.08340e43	−0.330682
$226$	−1.65252e43	−0.464667
$227$	−2.28689e42	−0.0592607	−0.0296304	−	0.999561i	$-0.509433\pi$
$227$	−2.28689e42	−0.0592607	−0.0296304	+	0.999561i	$0.509433\pi$
$228$	−2.05204e43	−0.490221
$229$	3.17158e43	0.698746	0.349373	−	0.936984i	$-0.386395\pi$
$229$	3.17158e43	0.698746	0.349373	+	0.936984i	$0.386395\pi$
$230$	−7.86729e41	−0.0159904
$231$	−3.67123e42	−0.0688636
$232$	−8.03021e43	−1.39059
$233$	6.37790e43	1.01998	0.509992	−	0.860179i	$-0.329648\pi$
$233$	6.37790e43	1.01998	0.509992	+	0.860179i	$0.329648\pi$
$234$	−1.34768e42	−0.0199110
$235$	−8.04749e42	−0.109877
$236$	−1.15459e43	−0.145732
$237$	−3.94181e43	−0.460099
$238$	−2.02198e43	−0.218325
$239$	1.80775e44	1.80625	0.903124	−	0.429380i	$-0.141268\pi$
$239$	1.80775e44	1.80625	0.903124	+	0.429380i	$0.141268\pi$
$240$	−3.03631e42	−0.0280826
$241$	7.69104e43	0.658673	0.329336	−	0.944213i	$-0.393175\pi$
$241$	7.69104e43	0.658673	0.329336	+	0.944213i	$0.393175\pi$
$242$	4.84557e43	0.384380
$243$	−8.72796e42	−0.0641500
$244$	1.19905e43	0.0816815
$245$	−9.00760e42	−0.0568901
$246$	3.10467e43	0.181851
$247$	−2.77751e43	−0.150925
$248$	−1.29090e44	−0.650935
$249$	1.87032e44	0.875442
$250$	1.63549e43	0.0710819
$251$	−2.76498e44	−1.11616	−0.558082	−	0.829786i	$-0.688462\pi$
$251$	−2.76498e44	−1.11616	−0.558082	+	0.829786i	$0.688462\pi$
$252$	−4.49210e43	−0.168476
$253$	2.54835e43	0.0888238
$254$	1.50951e44	0.489117
$255$	−1.54967e43	−0.0466925
$256$	−8.72293e43	−0.244469
$257$	−6.65338e44	−1.73492	−0.867461	−	0.497506i	$-0.834249\pi$
$257$	−6.65338e44	−1.73492	−0.867461	+	0.497506i	$0.834249\pi$
$258$	1.78522e44	0.433239
$259$	1.65586e44	0.374091
$260$	−5.31600e42	−0.0111835
$261$	−3.21337e44	−0.629668
$262$	1.79121e43	0.0327018
$263$	−4.99229e44	−0.849413	−0.424706	−	0.905331i	$-0.639623\pi$
$263$	−4.99229e44	−0.849413	−0.424706	+	0.905331i	$0.639623\pi$
$264$	−5.31138e43	−0.0842431
$265$	−4.02186e43	−0.0594809
$266$	1.76447e44	0.243390
$267$	7.82281e44	1.00671
$268$	5.62838e44	0.675911
$269$	3.89715e44	0.436847	0.218424	−	0.975854i	$-0.429909\pi$
$269$	3.89715e44	0.436847	0.218424	+	0.975854i	$0.429909\pi$
$270$	6.56156e42	0.00686717
$271$	1.32142e45	1.29154	0.645772	−	0.763531i	$-0.276536\pi$
$271$	1.32142e45	1.29154	0.645772	+	0.763531i	$0.276536\pi$
$272$	5.41683e44	0.494562
$273$	−6.08020e43	−0.0518691
$274$	9.27329e43	0.0739347
$275$	−2.63825e44	−0.196635
$276$	3.11814e44	0.217309
$277$	−1.66934e45	−1.08810	−0.544052	−	0.839052i	$-0.683111\pi$
$277$	−1.66934e45	−1.08810	−0.544052	+	0.839052i	$0.683111\pi$
$278$	−4.54708e44	−0.277271
$279$	−5.16568e44	−0.294747
$280$	7.39783e43	0.0395076
$281$	−4.64389e44	−0.232175	−0.116087	−	0.993239i	$-0.537035\pi$
$281$	−4.64389e44	−0.232175	−0.116087	+	0.993239i	$0.537035\pi$
$282$	−6.07894e44	−0.284590
$283$	−2.92223e45	−1.28134	−0.640672	−	0.767815i	$-0.721344\pi$
$283$	−2.92223e45	−1.28134	−0.640672	+	0.767815i	$0.721344\pi$
$284$	2.27669e45	0.935221
$285$	1.35231e44	0.0520530
$286$	−3.28182e43	−0.0118398
$287$	1.40070e45	0.473730
$288$	−1.00312e45	−0.318120
$289$	−5.97445e44	−0.177700
$290$	2.41577e44	0.0674050
$291$	−2.11938e45	−0.554866
$292$	−3.14532e45	−0.772826
$293$	2.43231e45	0.561007	0.280503	−	0.959853i	$-0.409499\pi$
$293$	2.43231e45	0.561007	0.280503	+	0.959853i	$0.409499\pi$
$294$	−6.80419e44	−0.147350
$295$	7.60881e43	0.0154742
$296$	2.39562e45	0.457638
$297$	−2.12540e44	−0.0381458
$298$	3.32448e45	0.560690
$299$	4.22051e44	0.0669034
$300$	−3.22814e45	−0.481071
$301$	8.05421e45	1.12861
$302$	−7.43881e43	−0.00980336
$303$	8.00790e45	0.992727
$304$	−4.72695e45	−0.551340
$305$	−7.90178e43	−0.00867317
$306$	−1.17060e45	−0.120938
$307$	6.20341e45	0.603351	0.301676	−	0.953411i	$-0.402454\pi$
$307$	6.20341e45	0.603351	0.301676	+	0.953411i	$0.402454\pi$
$308$	−1.09390e45	−0.100182
$309$	1.20181e45	0.103659
$310$	3.88349e44	0.0315523
$311$	−7.06086e45	−0.540493	−0.270247	−	0.962791i	$-0.587105\pi$
$311$	−7.06086e45	−0.540493	−0.270247	+	0.962791i	$0.587105\pi$
$312$	−8.79657e44	−0.0634532
$313$	2.19336e45	0.149121	0.0745607	−	0.997216i	$-0.476245\pi$
$313$	2.19336e45	0.149121	0.0745607	+	0.997216i	$0.476245\pi$
$314$	−5.83088e45	−0.373711
$315$	2.96032e44	0.0178893
$316$	−1.17452e46	−0.669345
$317$	−8.77401e45	−0.471631	−0.235815	−	0.971798i	$-0.575776\pi$
$317$	−8.77401e45	−0.471631	−0.235815	+	0.971798i	$0.575776\pi$
$318$	−3.03804e45	−0.154061
$319$	−7.82509e45	−0.374422
$320$	−3.23012e44	−0.0145862
$321$	1.65446e46	0.705202
$322$	−2.68116e45	−0.107892
$323$	−2.41255e46	−0.916704
$324$	−2.60063e45	−0.0933246
$325$	−4.36940e45	−0.148108
$326$	−1.26026e46	−0.403584
$327$	2.38676e46	0.722231
$328$	2.02648e46	0.579529
$329$	−2.74258e46	−0.741369
$330$	1.59785e44	0.00408346
$331$	5.90046e46	1.42583	0.712915	−	0.701250i	$-0.247374\pi$
$331$	5.90046e46	1.42583	0.712915	+	0.701250i	$0.247374\pi$
$332$	5.57290e46	1.27358
$333$	9.58634e45	0.207221
$334$	−2.95679e46	−0.604660
$335$	−3.70913e45	−0.0717701
$336$	−1.03477e46	−0.189482
$337$	5.49552e46	0.952480	0.476240	−	0.879315i	$-0.341999\pi$
$337$	5.49552e46	0.952480	0.476240	+	0.879315i	$0.341999\pi$
$338$	2.38417e46	0.391181
$339$	−4.31627e46	−0.670524
$340$	−4.61749e45	−0.0679276
$341$	−1.25793e46	−0.175267
$342$	1.02151e46	0.134822
$343$	−7.88219e46	−0.985612
$344$	1.16525e47	1.38066
$345$	−2.05488e45	−0.0230745
$346$	−2.40349e46	−0.255820
$347$	−2.08191e46	−0.210071	−0.105036	−	0.994468i	$-0.533496\pi$
$347$	−2.08191e46	−0.210071	−0.105036	+	0.994468i	$0.533496\pi$
$348$	−9.57473e46	−0.916032
$349$	−7.81482e46	−0.709003	−0.354502	−	0.935055i	$-0.615349\pi$
$349$	−7.81482e46	−0.709003	−0.354502	+	0.935055i	$0.615349\pi$
$350$	2.77575e46	0.238848
$351$	−3.52004e45	−0.0287320
$352$	−2.44276e46	−0.189165
$353$	−2.52475e47	−1.85518	−0.927591	−	0.373597i	$-0.878124\pi$
$353$	−2.52475e47	−1.85518	−0.927591	+	0.373597i	$0.878124\pi$
$354$	5.74757e45	0.0400796
$355$	−1.50035e46	−0.0993044
$356$	2.33093e47	1.46455
$357$	−5.28127e46	−0.315048
$358$	−3.12056e46	−0.176765
$359$	1.56169e47	0.840133	0.420066	−	0.907493i	$-0.362007\pi$
$359$	1.56169e47	0.840133	0.420066	+	0.907493i	$0.362007\pi$
$360$	4.28286e45	0.0218845
$361$	4.52102e45	0.0219459
$362$	6.92089e46	0.319193
$363$	1.26563e47	0.554667
$364$	−1.81169e46	−0.0754584
$365$	2.07278e46	0.0820608
$366$	−5.96887e45	−0.0224642
$367$	1.80276e47	0.645083	0.322542	−	0.946555i	$-0.395463\pi$
$367$	1.80276e47	0.645083	0.322542	+	0.946555i	$0.395463\pi$
$368$	7.18275e46	0.244403
$369$	8.10915e46	0.262414
$370$	−7.20688e45	−0.0221827
$371$	−1.37064e47	−0.401335
$372$	−1.53919e47	−0.428794
$373$	5.89590e46	0.156292	0.0781460	−	0.996942i	$-0.475100\pi$
$373$	5.89590e46	0.156292	0.0781460	+	0.996942i	$0.475100\pi$
$374$	−2.85060e46	−0.0719136
$375$	4.27179e46	0.102573
$376$	−3.96784e47	−0.906941
$377$	−1.29597e47	−0.282020
$378$	2.23617e46	0.0463348
$379$	9.01391e47	1.77864	0.889319	−	0.457287i	$-0.151179\pi$
$379$	9.01391e47	1.77864	0.889319	+	0.457287i	$0.151179\pi$
$380$	4.02941e46	0.0757260
$381$	3.94273e47	0.705805
$382$	−1.38088e47	−0.235497
$383$	−7.44373e47	−1.20952	−0.604761	−	0.796407i	$-0.706731\pi$
$383$	−7.44373e47	−1.20952	−0.604761	+	0.796407i	$0.706731\pi$
$384$	−3.80260e47	−0.588779
$385$	7.20886e45	0.0106376
$386$	−2.58470e47	−0.363534
$387$	4.66286e47	0.625172
$388$	−6.31501e47	−0.807211
$389$	−1.42792e48	−1.74035	−0.870173	−	0.492746i	$-0.835993\pi$
$389$	−1.42792e48	−1.74035	−0.870173	+	0.492746i	$0.835993\pi$
$390$	2.64632e45	0.00307572
$391$	3.66594e47	0.406364
$392$	−4.44122e47	−0.469581
$393$	4.67849e46	0.0471893
$394$	6.12495e47	0.589417
$395$	7.74017e46	0.0710729
$396$	−6.33296e46	−0.0554940
$397$	7.57199e47	0.633265	0.316633	−	0.948548i	$-0.397448\pi$
$397$	7.57199e47	0.633265	0.316633	+	0.948548i	$0.397448\pi$
$398$	8.18484e47	0.653391
$399$	4.60865e47	0.351217
$400$	−7.43614e47	−0.541050
$401$	1.48151e48	1.02928	0.514639	−	0.857407i	$-0.327926\pi$
$401$	1.48151e48	1.02928	0.514639	+	0.857407i	$0.327926\pi$
$402$	−2.80182e47	−0.185891
$403$	−2.08335e47	−0.132014
$404$	2.38608e48	1.44421
$405$	1.71383e46	0.00990946
$406$	8.23291e47	0.454801
$407$	2.33443e47	0.123221
$408$	−7.64071e47	−0.385408
$409$	−2.49474e48	−1.20266	−0.601331	−	0.799000i	$-0.705363\pi$
$409$	−2.49474e48	−1.20266	−0.601331	+	0.799000i	$0.705363\pi$
$410$	−6.09635e46	−0.0280911
$411$	2.42211e47	0.106689
$412$	3.58099e47	0.150801
$413$	2.59307e47	0.104409
$414$	−1.55222e47	−0.0597649
$415$	−3.67257e47	−0.135232
$416$	−4.04563e47	−0.142482
$417$	−1.18766e48	−0.400107
$418$	2.48755e47	0.0801696
$419$	3.28563e47	0.101312	0.0506558	−	0.998716i	$-0.483869\pi$
$419$	3.28563e47	0.101312	0.0506558	+	0.998716i	$0.483869\pi$
$420$	8.82072e46	0.0260251
$421$	−2.15044e48	−0.607169	−0.303584	−	0.952805i	$-0.598183\pi$
$421$	−2.15044e48	−0.607169	−0.303584	+	0.952805i	$0.598183\pi$
$422$	−8.91674e47	−0.240949
$423$	−1.58777e48	−0.410669
$424$	−1.98299e48	−0.490966
$425$	−3.79527e48	−0.899595
$426$	−1.13334e48	−0.257207
$427$	−2.69292e47	−0.0585204
$428$	4.92972e48	1.02592
$429$	−8.57187e46	−0.0170850
$430$	−3.50548e47	−0.0669238
$431$	5.34912e48	0.978257	0.489129	−	0.872212i	$-0.337315\pi$
$431$	5.34912e48	0.978257	0.489129	+	0.872212i	$0.337315\pi$
$432$	−5.99064e47	−0.104960
$433$	−5.42893e47	−0.0911357	−0.0455678	−	0.998961i	$-0.514510\pi$
$433$	−5.42893e47	−0.0911357	−0.0455678	+	0.998961i	$0.514510\pi$
$434$	1.32349e48	0.212892
$435$	6.30980e47	0.0972668
$436$	7.11173e48	1.05069
$437$	−3.19905e48	−0.453017
$438$	1.56575e48	0.212545
$439$	7.01666e48	0.913138	0.456569	−	0.889688i	$-0.349078\pi$
$439$	7.01666e48	0.913138	0.456569	+	0.889688i	$0.349078\pi$
$440$	1.04295e47	0.0130133
$441$	−1.77720e48	−0.212629
$442$	−4.72109e47	−0.0541664
$443$	−1.97926e48	−0.217788	−0.108894	−	0.994053i	$-0.534731\pi$
$443$	−1.97926e48	−0.217788	−0.108894	+	0.994053i	$0.534731\pi$
$444$	2.85640e48	0.301463
$445$	−1.53609e48	−0.155510
$446$	3.56064e47	0.0345806
$447$	8.68328e48	0.809086
$448$	−1.10082e48	−0.0984176
$449$	−9.61546e48	−0.824922	−0.412461	−	0.910975i	$-0.635331\pi$
$449$	−9.61546e48	−0.824922	−0.412461	+	0.910975i	$0.635331\pi$
$450$	1.60698e48	0.132305
$451$	1.97471e48	0.156041
$452$	−1.28610e49	−0.975468
$453$	−1.94296e47	−0.0141464
$454$	3.39209e47	0.0237101
$455$	1.19391e47	0.00801238
$456$	6.66760e48	0.429655
$457$	−1.22984e49	−0.761027	−0.380513	−	0.924775i	$-0.624253\pi$
$457$	−1.22984e49	−0.761027	−0.380513	+	0.924775i	$0.624253\pi$
$458$	−4.70433e48	−0.279568
$459$	−3.05751e48	−0.174515
$460$	−6.12281e47	−0.0335684
$461$	−1.44289e49	−0.759915	−0.379958	−	0.925004i	$-0.624061\pi$
$461$	−1.44289e49	−0.759915	−0.379958	+	0.925004i	$0.624061\pi$
$462$	5.44545e47	0.0275523
$463$	1.91092e49	0.928952	0.464476	−	0.885586i	$-0.346243\pi$
$463$	1.91092e49	0.928952	0.464476	+	0.885586i	$0.346243\pi$
$464$	−2.20557e49	−1.03024
$465$	1.01434e48	0.0455306
$466$	−9.46019e48	−0.408094
$467$	3.89111e49	1.61328	0.806642	−	0.591041i	$-0.201283\pi$
$467$	3.89111e49	1.61328	0.806642	+	0.591041i	$0.201283\pi$
$468$	−1.04885e48	−0.0417989
$469$	−1.26407e49	−0.484254
$470$	1.19367e48	0.0439615
$471$	−1.52298e49	−0.539272
$472$	3.75155e48	0.127727
$473$	1.13548e49	0.371749
$474$	5.84679e48	0.184085
$475$	3.31190e49	1.00287
$476$	−1.57363e49	−0.458327
$477$	−7.93513e48	−0.222313
$478$	−2.68139e49	−0.722677
$479$	7.12496e49	1.84746	0.923730	−	0.383043i	$-0.125124\pi$
$479$	7.12496e49	1.84746	0.923730	+	0.383043i	$0.125124\pi$
$480$	1.96973e48	0.0491410
$481$	3.86622e48	0.0928118
$482$	−1.14079e49	−0.263534
$483$	−7.00299e48	−0.155690
$484$	3.77112e49	0.806922
$485$	4.16163e48	0.0857119
$486$	1.29460e48	0.0256663
$487$	2.21439e49	0.422637	0.211318	−	0.977417i	$-0.432224\pi$
$487$	2.21439e49	0.422637	0.211318	+	0.977417i	$0.432224\pi$
$488$	−3.89599e48	−0.0715899
$489$	−3.29170e49	−0.582380
$490$	1.33608e48	0.0227616
$491$	4.50299e49	0.738743	0.369372	−	0.929282i	$-0.379573\pi$
$491$	4.50299e49	0.738743	0.369372	+	0.929282i	$0.379573\pi$
$492$	2.41625e49	0.381757
$493$	−1.12568e50	−1.71296
$494$	4.11981e48	0.0603849
$495$	4.17346e47	0.00589251
$496$	−3.54559e49	−0.482255
$497$	−5.11318e49	−0.670035
$498$	−2.77420e49	−0.350263
$499$	−1.42699e50	−1.73605	−0.868023	−	0.496525i	$-0.834609\pi$
$499$	−1.42699e50	−1.73605	−0.868023	+	0.496525i	$0.834609\pi$
$500$	1.27284e49	0.149221
$501$	−7.72292e49	−0.872537
$502$	4.10123e49	0.446576
$503$	6.05148e49	0.635117	0.317559	−	0.948239i	$-0.397137\pi$
$503$	6.05148e49	0.635117	0.317559	+	0.948239i	$0.397137\pi$
$504$	1.45959e49	0.147661
$505$	−1.57244e49	−0.153350
$506$	−3.77991e48	−0.0355383
$507$	6.22726e49	0.564482
$508$	1.17480e50	1.02680
$509$	6.02162e49	0.507498	0.253749	−	0.967270i	$-0.418336\pi$
$509$	6.02162e49	0.507498	0.253749	+	0.967270i	$0.418336\pi$
$510$	2.29859e48	0.0186816
$511$	7.06402e49	0.553688
$512$	−1.21960e50	−0.921984
$513$	2.66811e49	0.194550
$514$	9.86881e49	0.694140
$515$	−2.35989e48	−0.0160125
$516$	1.38937e50	0.909492
$517$	−3.86649e49	−0.244198
$518$	−2.45609e49	−0.149673
$519$	−6.27774e49	−0.369154
$520$	1.72730e48	0.00980181
$521$	−1.55956e50	−0.854088	−0.427044	−	0.904231i	$-0.640445\pi$
$521$	−1.55956e50	−0.854088	−0.427044	+	0.904231i	$0.640445\pi$
$522$	4.76632e49	0.251929
$523$	2.43674e50	1.24316	0.621581	−	0.783350i	$-0.286491\pi$
$523$	2.43674e50	1.24316	0.621581	+	0.783350i	$0.286491\pi$
$524$	1.39403e49	0.0686504
$525$	7.25003e49	0.344662
$526$	7.40495e49	0.339849
$527$	−1.80960e50	−0.801838
$528$	−1.45882e49	−0.0624128
$529$	−1.93453e50	−0.799183
$530$	5.96552e48	0.0237982
$531$	1.50122e49	0.0578357
$532$	1.37322e50	0.510945
$533$	3.27047e49	0.117532
$534$	−1.16034e50	−0.402783
$535$	−3.24871e49	−0.108935
$536$	−1.82880e50	−0.592403
$537$	−8.15067e49	−0.255076
$538$	−5.78055e49	−0.174782
$539$	−4.32778e49	−0.126437
$540$	5.10662e48	0.0144161
$541$	−2.16130e50	−0.589610	−0.294805	−	0.955557i	$-0.595255\pi$
$541$	−2.16130e50	−0.589610	−0.294805	+	0.955557i	$0.595255\pi$
$542$	−1.96003e50	−0.516745
$543$	1.80768e50	0.460602
$544$	−3.51404e50	−0.865420
$545$	−4.68667e49	−0.111565
$546$	9.01861e48	0.0207528
$547$	1.51748e50	0.337565	0.168782	−	0.985653i	$-0.446016\pi$
$547$	1.51748e50	0.337565	0.168782	+	0.985653i	$0.446016\pi$
$548$	7.21706e49	0.155210
$549$	−1.55902e49	−0.0324163
$550$	3.91325e49	0.0786734
$551$	9.82316e50	1.90962
$552$	−1.01316e50	−0.190461
$553$	2.63784e50	0.479550
$554$	2.47610e50	0.435349
$555$	−1.88238e49	−0.0320101
$556$	−3.53882e50	−0.582070
$557$	−2.93619e50	−0.467157	−0.233578	−	0.972338i	$-0.575044\pi$
$557$	−2.93619e50	−0.467157	−0.233578	+	0.972338i	$0.575044\pi$
$558$	7.66214e49	0.117928
$559$	1.88056e50	0.280007
$560$	2.03188e49	0.0292698
$561$	−7.44554e49	−0.103773
$562$	6.88818e49	0.0928929
$563$	6.27370e50	0.818688	0.409344	−	0.912380i	$-0.365758\pi$
$563$	6.27370e50	0.818688	0.409344	+	0.912380i	$0.365758\pi$
$564$	−4.73101e50	−0.597435
$565$	8.47546e49	0.103578
$566$	4.33448e50	0.512664
$567$	5.84071e49	0.0668620
$568$	−7.39753e50	−0.819676
$569$	8.59023e50	0.921357	0.460678	−	0.887567i	$-0.347606\pi$
$569$	8.59023e50	0.921357	0.460678	+	0.887567i	$0.347606\pi$
$570$	−2.00585e49	−0.0208263
$571$	6.31374e50	0.634627	0.317314	−	0.948321i	$-0.397219\pi$
$571$	6.31374e50	0.634627	0.317314	+	0.948321i	$0.397219\pi$
$572$	−2.55412e49	−0.0248551
$573$	−3.60676e50	−0.339826
$574$	−2.07763e50	−0.189539
$575$	−5.03254e50	−0.444562
$576$	−6.37303e49	−0.0545168
$577$	−1.17734e51	−0.975321	−0.487661	−	0.873033i	$-0.662150\pi$
$577$	−1.17734e51	−0.975321	−0.487661	+	0.873033i	$0.662150\pi$
$578$	8.86176e49	0.0710976
$579$	−6.75104e50	−0.524587
$580$	1.88010e50	0.141502
$581$	−1.25161e51	−0.912451
$582$	3.14362e50	0.222001
$583$	−1.93234e50	−0.132195
$584$	1.02199e51	0.677345
$585$	6.91198e48	0.00443832
$586$	−3.60779e50	−0.224458
$587$	−3.20215e51	−1.93035	−0.965176	−	0.261600i	$-0.915750\pi$
$587$	−3.20215e51	−1.93035	−0.965176	+	0.261600i	$0.915750\pi$
$588$	−5.29544e50	−0.309330
$589$	1.57913e51	0.893892
$590$	−1.12860e49	−0.00619123
$591$	1.59979e51	0.850540
$592$	6.57980e50	0.339048
$593$	−1.84366e51	−0.920807	−0.460404	−	0.887710i	$-0.652295\pi$
$593$	−1.84366e51	−0.920807	−0.460404	+	0.887710i	$0.652295\pi$
$594$	3.15256e49	0.0152621
$595$	1.03703e50	0.0486664
$596$	2.58732e51	1.17705
$597$	2.13782e51	0.942856
$598$	−6.26018e49	−0.0267679
$599$	5.10057e49	0.0211457	0.0105729	−	0.999944i	$-0.496634\pi$
$599$	5.10057e49	0.0211457	0.0105729	+	0.999944i	$0.496634\pi$
$600$	1.04890e51	0.421636
$601$	2.47295e51	0.963911	0.481956	−	0.876196i	$-0.339927\pi$
$601$	2.47295e51	0.963911	0.481956	+	0.876196i	$0.339927\pi$
$602$	−1.19466e51	−0.451554
$603$	−7.31813e50	−0.268244
$604$	−5.78935e49	−0.0205800
$605$	−2.48519e50	−0.0856812
$606$	−1.18779e51	−0.397189
$607$	8.24908e50	0.267556	0.133778	−	0.991011i	$-0.457289\pi$
$607$	8.24908e50	0.267556	0.133778	+	0.991011i	$0.457289\pi$
$608$	3.06649e51	0.964775
$609$	2.15037e51	0.656287
$610$	1.17205e49	0.00347012
$611$	−6.40358e50	−0.183933
$612$	−9.11032e50	−0.253882
$613$	−7.67396e50	−0.207492	−0.103746	−	0.994604i	$-0.533083\pi$
$613$	−7.67396e50	−0.207492	−0.103746	+	0.994604i	$0.533083\pi$
$614$	−9.20137e50	−0.241400
$615$	−1.59232e50	−0.0405360
$616$	3.55435e50	0.0878045
$617$	−3.86196e51	−0.925832	−0.462916	−	0.886402i	$-0.653197\pi$
$617$	−3.86196e51	−0.925832	−0.462916	+	0.886402i	$0.653197\pi$
$618$	−1.78262e50	−0.0414737
$619$	−7.97286e51	−1.80027	−0.900134	−	0.435613i	$-0.856532\pi$
$619$	−7.97286e51	−1.80027	−0.900134	+	0.435613i	$0.856532\pi$
$620$	3.02238e50	0.0662372
$621$	−4.05427e50	−0.0862419
$622$	1.04732e51	0.216251
$623$	−5.23499e51	−1.04927
$624$	−2.41606e50	−0.0470103
$625$	5.16797e51	0.976201
$626$	−3.25336e50	−0.0596633
$627$	6.49728e50	0.115686
$628$	−4.53796e51	−0.784525
$629$	3.35821e51	0.563729
$630$	−4.39097e49	−0.00715748
$631$	3.70656e51	0.586717	0.293358	−	0.956003i	$-0.405227\pi$
$631$	3.70656e51	0.586717	0.293358	+	0.956003i	$0.405227\pi$
$632$	3.81631e51	0.586649
$633$	−2.32898e51	−0.347694
$634$	1.30143e51	0.188699
$635$	−7.74198e50	−0.109028
$636$	−2.36439e51	−0.323417
$637$	−7.16756e50	−0.0952339
$638$	1.16068e51	0.149806
$639$	−2.96020e51	−0.371154
$640$	7.46681e50	0.0909506
$641$	1.56704e52	1.85442	0.927210	−	0.374543i	$-0.122200\pi$
$641$	1.56704e52	1.85442	0.927210	+	0.374543i	$0.122200\pi$
$642$	−2.45402e51	−0.282150
$643$	−6.64937e51	−0.742809	−0.371405	−	0.928471i	$-0.621124\pi$
$643$	−6.64937e51	−0.742809	−0.371405	+	0.928471i	$0.621124\pi$
$644$	−2.08665e51	−0.226496
$645$	−9.15604e50	−0.0965723
$646$	3.57847e51	0.366772
$647$	5.30594e51	0.528485	0.264243	−	0.964456i	$-0.414878\pi$
$647$	5.30594e51	0.528485	0.264243	+	0.964456i	$0.414878\pi$
$648$	8.45009e50	0.0817945
$649$	3.65572e50	0.0343911
$650$	6.48102e50	0.0592579
$651$	3.45685e51	0.307208
$652$	−9.80812e51	−0.847238
$653$	1.78263e52	1.49682	0.748408	−	0.663238i	$-0.230818\pi$
$653$	1.78263e52	1.49682	0.748408	+	0.663238i	$0.230818\pi$
$654$	−3.54023e51	−0.288964
$655$	−9.18673e49	−0.00728949
$656$	5.56591e51	0.429353
$657$	4.08961e51	0.306706
$658$	4.06800e51	0.296621
$659$	−1.76349e52	−1.25024	−0.625120	−	0.780529i	$-0.714950\pi$
$659$	−1.76349e52	−1.25024	−0.625120	+	0.780529i	$0.714950\pi$
$660$	1.24355e50	0.00857233
$661$	1.76495e52	1.18306	0.591529	−	0.806284i	$-0.298524\pi$
$661$	1.76495e52	1.18306	0.591529	+	0.806284i	$0.298524\pi$
$662$	−8.75201e51	−0.570473
$663$	−1.23311e51	−0.0781631
$664$	−1.81077e52	−1.11623
$665$	−9.04958e50	−0.0542535
$666$	−1.42192e51	−0.0829090
$667$	−1.49266e52	−0.846512
$668$	−2.30116e52	−1.26935
$669$	9.30011e50	0.0499005
$670$	5.50167e50	0.0287151
$671$	−3.79648e50	−0.0192759
$672$	6.71281e51	0.331568
$673$	−6.55193e51	−0.314841	−0.157420	−	0.987532i	$-0.550318\pi$
$673$	−6.55193e51	−0.314841	−0.157420	+	0.987532i	$0.550318\pi$
$674$	−8.15138e51	−0.381086
$675$	4.19730e51	0.190919
$676$	1.85551e52	0.821200
$677$	−1.81635e52	−0.782183	−0.391091	−	0.920352i	$-0.627902\pi$
$677$	−1.81635e52	−0.782183	−0.391091	+	0.920352i	$0.627902\pi$
$678$	6.40222e51	0.268276
$679$	1.41828e52	0.578323
$680$	1.50034e51	0.0595352
$681$	8.85988e50	0.0342142
$682$	1.86586e51	0.0701241
$683$	1.58198e51	0.0578653	0.0289327	−	0.999581i	$-0.490789\pi$
$683$	1.58198e51	0.0578653	0.0289327	+	0.999581i	$0.490789\pi$
$684$	7.95003e51	0.283029
$685$	−4.75608e50	−0.0164806
$686$	1.16915e52	0.394342
$687$	−1.22874e52	−0.403421
$688$	3.20046e52	1.02288
$689$	−3.20028e51	−0.0995710
$690$	3.04795e50	0.00923208
$691$	−3.06206e51	−0.0902963	−0.0451482	−	0.998980i	$-0.514376\pi$
$691$	−3.06206e51	−0.0902963	−0.0451482	+	0.998980i	$0.514376\pi$
$692$	−1.87055e52	−0.537040
$693$	1.42231e51	0.0397584
$694$	3.08805e51	0.0840493
$695$	2.33210e51	0.0618058
$696$	3.11107e52	0.802858
$697$	2.84073e52	0.713878
$698$	1.15915e52	0.283671
$699$	−2.47093e52	−0.588888
$700$	2.16026e52	0.501409
$701$	3.61387e52	0.816939	0.408469	−	0.912772i	$-0.366063\pi$
$701$	3.61387e52	0.816939	0.408469	+	0.912772i	$0.366063\pi$
$702$	5.22119e50	0.0114956
$703$	−2.93051e52	−0.628448
$704$	−1.55194e51	−0.0324175
$705$	3.11776e51	0.0634373
$706$	3.74490e52	0.742256
$707$	−5.35885e52	−1.03469
$708$	4.47312e51	0.0841385
$709$	−7.65821e52	−1.40337	−0.701684	−	0.712488i	$-0.747568\pi$
$709$	−7.65821e52	−1.40337	−0.701684	+	0.712488i	$0.747568\pi$
$710$	2.22544e51	0.0397316
$711$	1.52714e52	0.265638
$712$	−7.57376e52	−1.28361
$713$	−2.39954e52	−0.396252
$714$	7.83358e51	0.126050
$715$	1.68318e50	0.00263918
$716$	−2.42862e52	−0.371081
$717$	−7.00360e52	−1.04284
$718$	−2.31642e52	−0.336136
$719$	5.00380e52	0.707644	0.353822	−	0.935313i	$-0.384882\pi$
$719$	5.00380e52	0.707644	0.353822	+	0.935313i	$0.384882\pi$
$720$	1.17633e51	0.0162135
$721$	−8.04248e51	−0.108041
$722$	−6.70593e50	−0.00878053
$723$	−2.97967e52	−0.380285
$724$	5.38627e52	0.670077
$725$	1.54532e53	1.87398
$726$	−1.87727e52	−0.221922
$727$	−1.52054e53	−1.75231	−0.876153	−	0.482033i	$-0.839898\pi$
$727$	−1.52054e53	−1.75231	−0.876153	+	0.482033i	$0.839898\pi$
$728$	5.88662e51	0.0661357
$729$	3.38139e51	0.0370370
$730$	−3.07451e51	−0.0328324
$731$	1.63346e53	1.70073
$732$	−4.64535e51	−0.0471588
$733$	1.66772e53	1.65082	0.825412	−	0.564531i	$-0.190943\pi$
$733$	1.66772e53	1.65082	0.825412	+	0.564531i	$0.190943\pi$
$734$	−2.67399e52	−0.258097
$735$	3.48973e51	0.0328455
$736$	−4.65963e52	−0.427673
$737$	−1.78209e52	−0.159507
$738$	−1.20281e52	−0.104992
$739$	4.00559e52	0.340992	0.170496	−	0.985358i	$-0.445463\pi$
$739$	4.00559e52	0.340992	0.170496	+	0.985358i	$0.445463\pi$
$740$	−5.60884e51	−0.0465679
$741$	1.07606e52	0.0871366
$742$	2.03304e52	0.160574
$743$	−1.70678e52	−0.131488	−0.0657439	−	0.997837i	$-0.520942\pi$
$743$	−1.70678e52	−0.131488	−0.0657439	+	0.997837i	$0.520942\pi$
$744$	5.00122e52	0.375818
$745$	−1.70506e52	−0.124982
$746$	−8.74525e51	−0.0625322
$747$	−7.24599e52	−0.505437
$748$	−2.21851e52	−0.150967
$749$	−1.10716e53	−0.735015
$750$	−6.33624e51	−0.0410392
$751$	3.01808e53	1.90718	0.953592	−	0.301102i	$-0.0973546\pi$
$751$	3.01808e53	1.90718	0.953592	+	0.301102i	$0.0973546\pi$
$752$	−1.08980e53	−0.671921
$753$	1.07121e53	0.644417
$754$	1.92228e52	0.112836
$755$	3.81521e50	0.00218525
$756$	1.74033e52	0.0972699
$757$	−2.38775e53	−1.30231	−0.651157	−	0.758943i	$-0.725716\pi$
$757$	−2.38775e53	−1.30231	−0.651157	+	0.758943i	$0.725716\pi$
$758$	−1.33701e53	−0.711631
$759$	−9.87282e51	−0.0512824
$760$	−1.30925e52	−0.0663701
$761$	5.79897e52	0.286903	0.143451	−	0.989657i	$-0.454180\pi$
$761$	5.79897e52	0.286903	0.143451	+	0.989657i	$0.454180\pi$
$762$	−5.84816e52	−0.282392
$763$	−1.59721e53	−0.752763
$764$	−1.07469e53	−0.494374
$765$	6.00375e51	0.0269579
$766$	1.10411e53	0.483928
$767$	6.05451e51	0.0259039
$768$	3.37944e52	0.141144
$769$	−1.79999e52	−0.0733894	−0.0366947	−	0.999327i	$-0.511683\pi$
$769$	−1.79999e52	−0.0733894	−0.0366947	+	0.999327i	$0.511683\pi$
$770$	−1.06927e51	−0.00425608
$771$	2.57766e53	1.00166
$772$	−2.01158e53	−0.763162
$773$	−3.51229e53	−1.30098	−0.650488	−	0.759516i	$-0.725436\pi$
$773$	−3.51229e53	−1.30098	−0.650488	+	0.759516i	$0.725436\pi$
$774$	−6.91631e52	−0.250131
$775$	2.48419e53	0.877209
$776$	2.05190e53	0.707481
$777$	−6.41513e52	−0.215982
$778$	2.11800e53	0.696311
$779$	−2.47894e53	−0.795835
$780$	2.05953e51	0.00645681
$781$	−7.20857e52	−0.220701
$782$	−5.43760e52	−0.162586
$783$	1.24493e53	0.363539
$784$	−1.21982e53	−0.347896
$785$	2.99054e52	0.0833030
$786$	−6.93950e51	−0.0188804
$787$	3.07133e53	0.816196	0.408098	−	0.912938i	$-0.366192\pi$
$787$	3.07133e53	0.816196	0.408098	+	0.912938i	$0.366192\pi$
$788$	4.76682e53	1.23735
$789$	1.93412e53	0.490409
$790$	−1.14808e52	−0.0284362
$791$	2.88843e53	0.698870
$792$	2.05774e52	0.0486378
$793$	−6.28763e51	−0.0145189
$794$	−1.12314e53	−0.253369
$795$	1.55815e52	0.0343413
$796$	6.36996e53	1.37165
$797$	−2.70059e53	−0.568171	−0.284086	−	0.958799i	$-0.591690\pi$
$797$	−2.70059e53	−0.568171	−0.284086	+	0.958799i	$0.591690\pi$
$798$	−6.83590e52	−0.140521
$799$	−5.56216e53	−1.11719
$800$	4.82401e53	0.946768
$801$	−3.03072e53	−0.581224
$802$	−2.19748e53	−0.411813
$803$	9.95887e52	0.182378
$804$	−2.18055e53	−0.390237
$805$	1.37511e52	0.0240500
$806$	3.09018e52	0.0528185
$807$	−1.50984e53	−0.252214
$808$	−7.75295e53	−1.26578
$809$	−9.43604e53	−1.50571	−0.752856	−	0.658185i	$-0.771325\pi$
$809$	−9.43604e53	−1.50571	−0.752856	+	0.658185i	$0.771325\pi$
$810$	−2.54208e51	−0.00396476
$811$	5.48046e53	0.835471	0.417736	−	0.908569i	$-0.362824\pi$
$811$	5.48046e53	0.835471	0.417736	+	0.908569i	$0.362824\pi$
$812$	6.40737e53	0.954757
$813$	−5.11945e53	−0.745673
$814$	−3.46261e52	−0.0493005
$815$	6.46361e52	0.0899621
$816$	−2.09859e53	−0.285536
$817$	−1.42542e54	−1.89599
$818$	3.70038e53	0.481183
$819$	2.35559e52	0.0299466
$820$	−4.74456e52	−0.0589712
$821$	8.20887e53	0.997551	0.498775	−	0.866731i	$-0.333783\pi$
$821$	8.20887e53	0.997551	0.498775	+	0.866731i	$0.333783\pi$
$822$	−3.59266e52	−0.0426862
$823$	1.02438e54	1.19005	0.595026	−	0.803707i	$-0.297142\pi$
$823$	1.02438e54	1.19005	0.595026	+	0.803707i	$0.297142\pi$
$824$	−1.16355e53	−0.132170
$825$	1.02211e53	0.113527
$826$	−3.84624e52	−0.0417740
$827$	2.29267e53	0.243494	0.121747	−	0.992561i	$-0.461150\pi$
$827$	2.29267e53	0.243494	0.121747	+	0.992561i	$0.461150\pi$
$828$	−1.20803e53	−0.125464
$829$	−4.93570e53	−0.501291	−0.250646	−	0.968079i	$-0.580643\pi$
$829$	−4.93570e53	−0.501291	−0.250646	+	0.968079i	$0.580643\pi$
$830$	5.44744e52	0.0541063
$831$	6.46738e53	0.628217
$832$	−2.57028e52	−0.0244174
$833$	−6.22575e53	−0.578441
$834$	1.76163e53	0.160082
$835$	1.51648e53	0.134783
$836$	1.93596e53	0.168299
$837$	2.00129e53	0.170173
$838$	−4.87350e52	−0.0405346
$839$	−8.65291e52	−0.0703989	−0.0351995	−	0.999380i	$-0.511207\pi$
$839$	−8.65291e52	−0.0703989	−0.0351995	+	0.999380i	$0.511207\pi$
$840$	−2.86607e52	−0.0228097
$841$	3.29896e54	2.56833
$842$	3.18970e53	0.242927
$843$	1.79914e53	0.134046
$844$	−6.93956e53	−0.505821
$845$	−1.22279e53	−0.0871973
$846$	2.35511e53	0.164308
$847$	−8.46951e53	−0.578116
$848$	−5.44646e53	−0.363740
$849$	1.13213e54	0.739784
$850$	5.62943e53	0.359927
$851$	4.45300e53	0.278584
$852$	−8.82036e53	−0.539950
$853$	−1.86556e54	−1.11751	−0.558756	−	0.829332i	$-0.688721\pi$
$853$	−1.86556e54	−1.11751	−0.558756	+	0.829332i	$0.688721\pi$
$854$	3.99434e52	0.0234139
$855$	−5.23912e52	−0.0300528
$856$	−1.60179e54	−0.899167
$857$	−2.68028e54	−1.47243	−0.736214	−	0.676748i	$-0.763388\pi$
$857$	−2.68028e54	−1.47243	−0.736214	+	0.676748i	$0.763388\pi$
$858$	1.27145e52	0.00683570
$859$	2.48268e54	1.30631	0.653156	−	0.757223i	$-0.273444\pi$
$859$	2.48268e54	1.30631	0.653156	+	0.757223i	$0.273444\pi$
$860$	−2.72818e53	−0.140492
$861$	−5.42661e53	−0.273508
$862$	−7.93423e53	−0.391399
$863$	−2.19895e54	−1.06173	−0.530866	−	0.847456i	$-0.678133\pi$
$863$	−2.19895e54	−1.06173	−0.530866	+	0.847456i	$0.678133\pi$
$864$	3.88628e53	0.183667
$865$	1.23270e53	0.0570244
$866$	8.05261e52	0.0364633
$867$	2.31462e53	0.102595
$868$	1.03002e54	0.446922
$869$	3.71883e53	0.157958
$870$	−9.35918e52	−0.0389163
$871$	−2.95144e53	−0.120143
$872$	−2.31078e54	−0.920880
$873$	8.21090e53	0.320352
$874$	4.74507e53	0.181251
$875$	−2.85866e53	−0.106909
$876$	1.21856e54	0.446192
$877$	4.36154e54	1.56368	0.781839	−	0.623480i	$-0.214282\pi$
$877$	4.36154e54	1.56368	0.781839	+	0.623480i	$0.214282\pi$
$878$	−1.04076e54	−0.365346
$879$	−9.42327e53	−0.323898
$880$	2.86455e52	0.00964111
$881$	3.09467e54	1.01991	0.509953	−	0.860202i	$-0.329663\pi$
$881$	3.09467e54	1.01991	0.509953	+	0.860202i	$0.329663\pi$
$882$	2.63608e53	0.0850727
$883$	−2.65487e54	−0.839016	−0.419508	−	0.907752i	$-0.637797\pi$
$883$	−2.65487e54	−0.839016	−0.419508	+	0.907752i	$0.637797\pi$
$884$	−3.67424e53	−0.113711
$885$	−2.94781e52	−0.00893406
$886$	2.93579e53	0.0871368
$887$	4.89218e53	0.142205	0.0711026	−	0.997469i	$-0.477348\pi$
$887$	4.89218e53	0.142205	0.0711026	+	0.997469i	$0.477348\pi$
$888$	−9.28114e53	−0.264217
$889$	−2.63846e54	−0.735643
$890$	2.27845e53	0.0622192
$891$	8.23425e52	0.0220235
$892$	2.77111e53	0.0725946
$893$	4.85376e54	1.24545
$894$	−1.28797e54	−0.323714
$895$	1.60047e53	0.0394024
$896$	2.54468e54	0.613670
$897$	−1.63511e53	−0.0386267
$898$	1.42624e54	0.330050
$899$	7.36815e54	1.67034
$900$	1.25065e54	0.277747
$901$	−2.77977e54	−0.604784
$902$	−2.92904e53	−0.0624317
$903$	−3.12037e54	−0.651602
$904$	4.17885e54	0.854951
$905$	−3.54958e53	−0.0711506
$906$	2.88195e52	0.00565997
$907$	−7.29269e54	−1.40331	−0.701654	−	0.712518i	$-0.747555\pi$
$907$	−7.29269e54	−1.40331	−0.701654	+	0.712518i	$0.747555\pi$
$908$	2.63994e53	0.0497743
$909$	−3.10242e54	−0.573151
$910$	−1.77090e52	−0.00320574
$911$	−5.62240e54	−0.997313	−0.498656	−	0.866800i	$-0.666173\pi$
$911$	−5.62240e54	−0.997313	−0.498656	+	0.866800i	$0.666173\pi$
$912$	1.83132e54	0.318316
$913$	−1.76452e54	−0.300550
$914$	1.82420e54	0.304486
$915$	3.06131e52	0.00500746
$916$	−3.66121e54	−0.586892
$917$	−3.13083e53	−0.0491843
$918$	4.53513e53	0.0698233
$919$	−7.97807e54	−1.20382	−0.601909	−	0.798564i	$-0.705593\pi$
$919$	−7.97807e54	−1.20382	−0.601909	+	0.798564i	$0.705593\pi$
$920$	1.98945e53	0.0294211
$921$	−2.40333e54	−0.348345
$922$	2.14020e54	0.304041
$923$	−1.19386e54	−0.166235
$924$	4.23799e53	0.0578400
$925$	−4.61009e54	−0.616719
$926$	−2.83442e54	−0.371673
$927$	−4.65607e53	−0.0598473
$928$	1.43081e55	1.80279
$929$	1.78826e54	0.220872	0.110436	−	0.993883i	$-0.464775\pi$
$929$	1.78826e54	0.220872	0.110436	+	0.993883i	$0.464775\pi$
$930$	−1.50454e53	−0.0182167
$931$	5.43284e54	0.644849
$932$	−7.36251e54	−0.856706
$933$	2.73552e54	0.312054
$934$	−5.77159e54	−0.645473
$935$	1.46201e53	0.0160301
$936$	3.40797e53	0.0366347
$937$	1.44463e55	1.52256	0.761282	−	0.648421i	$-0.224571\pi$
$937$	1.44463e55	1.52256	0.761282	+	0.648421i	$0.224571\pi$
$938$	1.87496e54	0.193749
$939$	−8.49753e53	−0.0860953
$940$	9.28985e53	0.0922876
$941$	7.66096e54	0.746234	0.373117	−	0.927784i	$-0.378289\pi$
$941$	7.66096e54	0.746234	0.373117	+	0.927784i	$0.378289\pi$
$942$	2.25900e54	0.215762
$943$	3.76683e54	0.352784
$944$	1.03040e54	0.0946287
$945$	−1.14689e53	−0.0103284
$946$	−1.68424e54	−0.148736
$947$	−2.84883e54	−0.246713	−0.123357	−	0.992362i	$-0.539366\pi$
$947$	−2.84883e54	−0.246713	−0.123357	+	0.992362i	$0.539366\pi$
$948$	4.55034e54	0.386447
$949$	1.64936e54	0.137370
$950$	−4.91247e54	−0.401248
$951$	3.39923e54	0.272296
$952$	5.11313e54	0.401701
$953$	7.19336e54	0.554259	0.277130	−	0.960833i	$-0.410617\pi$
$953$	7.19336e54	0.554259	0.277130	+	0.960833i	$0.410617\pi$
$954$	1.17700e54	0.0889470
$955$	7.08226e53	0.0524940
$956$	−2.08683e55	−1.51711
$957$	3.03160e54	0.216173
$958$	−1.05683e55	−0.739167
$959$	−1.62087e54	−0.111200
$960$	1.25141e53	0.00842138
$961$	−3.30422e54	−0.218116
$962$	−5.73468e53	−0.0371339
$963$	−6.40972e54	−0.407149
$964$	−8.87837e54	−0.553233
$965$	1.32564e54	0.0810346
$966$	1.03874e54	0.0622915
$967$	5.29113e54	0.311285	0.155643	−	0.987813i	$-0.450255\pi$
$967$	5.29113e54	0.311285	0.155643	+	0.987813i	$0.450255\pi$
$968$	−1.22533e55	−0.707228
$969$	9.34670e54	0.529259
$970$	−6.17284e53	−0.0342932
$971$	−2.88478e55	−1.57238	−0.786190	−	0.617985i	$-0.787949\pi$
$971$	−2.88478e55	−1.57238	−0.786190	+	0.617985i	$0.787949\pi$
$972$	1.00754e54	0.0538810
$973$	7.94778e54	0.417021
$974$	−3.28455e54	−0.169096
$975$	1.69279e54	0.0855104
$976$	−1.07007e54	−0.0530385
$977$	1.74695e55	0.849633	0.424816	−	0.905280i	$-0.360339\pi$
$977$	1.74695e55	0.849633	0.424816	+	0.905280i	$0.360339\pi$
$978$	4.88250e54	0.233009
$979$	−7.38029e54	−0.345616
$980$	1.03982e54	0.0477832
$981$	−9.24681e54	−0.416980
$982$	−6.67918e54	−0.295570
$983$	6.87276e54	0.298464	0.149232	−	0.988802i	$-0.452320\pi$
$983$	6.87276e54	0.298464	0.149232	+	0.988802i	$0.452320\pi$
$984$	−7.85098e54	−0.334591
$985$	−3.14136e54	−0.131386
$986$	1.66970e55	0.685354
$987$	1.06253e55	0.428030
$988$	3.20629e54	0.126765
$989$	2.16597e55	0.840468
$990$	−6.19039e52	−0.00235758
$991$	−2.63811e55	−0.986121	−0.493061	−	0.869995i	$-0.664122\pi$
$991$	−2.63811e55	−0.986121	−0.493061	+	0.869995i	$0.664122\pi$
$992$	2.30011e55	0.843885
$993$	−2.28596e55	−0.823204
$994$	7.58426e54	0.268080
$995$	−4.19784e54	−0.145646
$996$	−2.15905e55	−0.735302
$997$	4.19948e55	1.40390	0.701948	−	0.712229i	$-0.252314\pi$
$997$	4.19948e55	1.40390	0.701948	+	0.712229i	$0.252314\pi$
$998$	2.11662e55	0.694590
$999$	−3.71394e54	−0.119639

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.38.a.a.1.2	✓	3
3.2	odd	2		9.38.a.b.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.38.a.a.1.2	✓	3	1.1	even	1	trivial
9.38.a.b.1.2		3	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-148328. q^{2} -3.87420e8 q^{3} -1.15438e11 q^{4} +7.60742e11 q^{5} +5.74652e13 q^{6} +2.59260e15 q^{7} +3.75086e16 q^{8} +1.50095e17 q^{9} +O(q^{10})\)	\(q-148328. q^{2} -3.87420e8 q^{3} -1.15438e11 q^{4} +7.60742e11 q^{5} +5.74652e13 q^{6} +2.59260e15 q^{7} +3.75086e16 q^{8} +1.50095e17 q^{9} -1.12839e17 q^{10} +3.65505e18 q^{11} +4.47230e19 q^{12} +6.05340e19 q^{13} -3.84554e20 q^{14} -2.94727e20 q^{15} +1.03021e22 q^{16} +5.25799e22 q^{17} -2.22632e22 q^{18} -4.58834e23 q^{19} -8.78185e22 q^{20} -1.00443e24 q^{21} -5.42145e23 q^{22} +6.97213e24 q^{23} -1.45316e25 q^{24} -7.21808e25 q^{25} -8.97887e24 q^{26} -5.81497e25 q^{27} -2.99284e26 q^{28} -2.14090e27 q^{29} +4.37162e25 q^{30} -3.44162e27 q^{31} -6.68323e27 q^{32} -1.41604e27 q^{33} -7.79906e27 q^{34} +1.97230e27 q^{35} -1.73266e28 q^{36} +6.38686e28 q^{37} +6.80578e28 q^{38} -2.34521e28 q^{39} +2.85344e28 q^{40} +5.40269e29 q^{41} +1.48984e29 q^{42} +3.10661e30 q^{43} -4.21931e29 q^{44} +1.14183e29 q^{45} -1.03416e30 q^{46} -1.05785e31 q^{47} -3.99124e30 q^{48} -1.18405e31 q^{49} +1.07064e31 q^{50} -2.03705e31 q^{51} -6.98792e30 q^{52} -5.28675e31 q^{53} +8.62521e30 q^{54} +2.78055e30 q^{55} +9.72449e31 q^{56} +1.77762e32 q^{57} +3.17554e32 q^{58} +1.00018e32 q^{59} +3.40227e31 q^{60} -1.03869e32 q^{61} +5.10487e32 q^{62} +3.89135e32 q^{63} -4.24601e32 q^{64} +4.60508e31 q^{65} +2.10038e32 q^{66} -4.87568e33 q^{67} -6.06972e33 q^{68} -2.70115e33 q^{69} -2.92547e32 q^{70} -1.97222e34 q^{71} +5.62984e33 q^{72} +2.72469e34 q^{73} -9.47348e33 q^{74} +2.79643e34 q^{75} +5.29668e34 q^{76} +9.47609e33 q^{77} +3.47860e33 q^{78} +1.01745e35 q^{79} +7.83724e33 q^{80} +2.25284e34 q^{81} -8.01369e34 q^{82} -4.82762e35 q^{83} +1.15949e35 q^{84} +3.99998e34 q^{85} -4.60797e35 q^{86} +8.29427e35 q^{87} +1.37096e35 q^{88} -2.01920e36 q^{89} -1.69365e34 q^{90} +1.56941e35 q^{91} -8.04848e35 q^{92} +1.33335e36 q^{93} +1.56908e36 q^{94} -3.49054e35 q^{95} +2.58922e36 q^{96} +5.47048e36 q^{97} +1.75628e36 q^{98} +5.48604e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 45\!\cdots\!63 q^{9}+O(q^{10}) \) 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9	\( 3 q - 310908 q^{2} - 1162261467 q^{3} + 338476600848 q^{4} - 9628717886790 q^{5} + 120452129394012 q^{6} - 46\!\cdots\!44 q^{7}+ \cdots + 34\!\cdots\!20 q^{99}+O(q^{100}) \) 3 * q - 310908 * q^2 - 1162261467 * q^3 + 338476600848 * q^4 - 9628717886790 * q^5 + 120452129394012 * q^6 - 4621884343701744 * q^7 - 93383909093911488 * q^8 + 450283905890997363 * q^9 + 10698950136741797880 * q^10 + 22673303357139628620 * q^11 - 131132770215589974672 * q^12 - 168270000203795091510 * q^13 + 797101803583223694528 * q^14 + 3730362592143228440310 * q^15 + 32071173863897028608256 * q^16 - 27168549617785276146906 * q^17 - 46665622870919402711868 * q^18 + 582035599719143813745204 * q^19 - 4066256929972106412494880 * q^20 + 1790612692538373730632816 * q^21 - 4486408000290444592999152 * q^22 - 17157197763697459349569272 * q^23 + 36178839725894735603677632 * q^24 - 24896488591542260192608275 * q^25 - 618603181238074545425686344 * q^26 - 174449211009120179071170507 * q^27 - 2033429672978753784958610688 * q^28 + 111201150055901033185229778 * q^29 - 4144992493763124201408763320 * q^30 - 11859842025407507592851987736 * q^31 - 27281435223830339470718352384 * q^32 - 8784102273868376561238795180 * q^33 - 18783445175675019452330905464 * q^34 + 47739964986924083632994534880 * q^35 + 50803521960848503410923854608 * q^36 + 60344578140045347560278093666 * q^37 - 372452605565029151271789397776 * q^38 + 65191245762984394008603948390 * q^39 + 1732463594119923393272610326400 * q^40 + 2087364862188523841295969725934 * q^41 - 308813570526994475930424384192 * q^42 + 2483325896102099669944761791244 * q^43 + 4284309379683814482835899511872 * q^44 - 1445218899595437120383607511590 * q^45 - 4327236604482200607954371165856 * q^46 - 11791379189662012541191082473632 * q^47 - 12425029861155006269057528957184 * q^48 - 22445324860908932271245865545973 * q^49 - 96691457712658313260807892933700 * q^50 + 10525652778343134781834358357034 * q^51 + 43220201443333906987967057359584 * q^52 - 115357757368640109037215455345382 * q^53 + 18079218432141178878219826663452 * q^54 - 129419469300146958823045789059480 * q^55 + 630552391741804501615596905794560 * q^56 - 225492516658598958982491855084756 * q^57 + 580965936186746161132050423512088 * q^58 + 1091721381032593697748326986744236 * q^59 + 1575351248209432222688802119596320 * q^60 + 294380981976352085651508270601002 * q^61 + 248838835694853996733454208986592 * q^62 - 693720044952823401986519854167024 * q^63 - 1064135955800023765084313699610624 * q^64 - 7515875365146923444942971038019860 * q^65 + 1738126381326036186247137444425328 * q^66 + 3824374619785575741360273276519444 * q^67 - 21329399470876894544665401157365216 * q^68 + 6647049947481376149267749297614008 * q^69 - 43059062291480572688803543269144960 * q^70 - 22149353642418626281921550104284744 * q^71 - 14016423778058764430102498387802048 * q^72 + 32759279450923542889398870347665278 * q^73 + 46478870171568672595185044851456728 * q^74 + 9645409784518223707985532085946475 * q^75 + 347061692957154720144564653376455616 * q^76 - 61122141948697926808926153780754368 * q^77 + 239659546972210465807272116553102216 * q^78 + 74649348023552719727334936629819640 * q^79 - 618088038723375449595358546989335040 * q^80 + 67585198634817523235520443624317923 * q^81 + 103937675337495441364448738414881512 * q^82 - 317656267631459020909914460046822604 * q^83 + 787792318252538877979265797505586432 * q^84 + 210972517320554825185658741373302580 * q^85 - 2655243937093032975138251645354123760 * q^86 - 43081603932019555612226948170121442 * q^87 - 1353962196634819912991147659264835328 * q^88 - 1604427814888922862357874180114447026 * q^89 + 1605855018835039028277517574319663480 * q^90 + 459759011513895387754487414763335904 * q^91 - 5426885178857894678398508472745540224 * q^92 + 4594745796946127015893929993303122904 * q^93 + 15155501875748762861069416648677456000 * q^94 - 10713376656166940710475311057833316200 * q^95 + 10569386975038174570781705261883595776 * q^96 + 2690787195739502167683294096108844614 * q^97 - 1675640263817086437903041451354198300 * q^98 + 3403141198368098368991272474406443020 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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