LMFDB - Embedded newform 1.38.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,38,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, 38, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 38 $
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:	$8.67140381246$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 15934380 $ x^2 - x - 15934380
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3992.29$ 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)

$f(q)$	$=$	$q-480412. q^{2} +3.45869e7 q^{3} +9.33565e10 q^{4} +1.38267e13 q^{5} -1.66160e13 q^{6} -5.42222e15 q^{7} +2.11777e16 q^{8} -4.49088e17 q^{9} +O(q^{10})$	\(q-480412. q^{2} +3.45869e7 q^{3} +9.33565e10 q^{4} +1.38267e13 q^{5} -1.66160e13 q^{6} -5.42222e15 q^{7} +2.11777e16 q^{8} -4.49088e17 q^{9} -6.64253e18 q^{10} -1.03285e18 q^{11} +3.22892e18 q^{12} -1.23244e19 q^{13} +2.60490e21 q^{14} +4.78225e20 q^{15} -2.30048e22 q^{16} -5.41594e22 q^{17} +2.15747e23 q^{18} -3.08845e23 q^{19} +1.29082e24 q^{20} -1.87538e23 q^{21} +4.96192e23 q^{22} -2.61592e25 q^{23} +7.32473e23 q^{24} +1.18419e26 q^{25} +5.92077e24 q^{26} -3.11065e25 q^{27} -5.06199e26 q^{28} +2.49238e26 q^{29} -2.29745e26 q^{30} -2.34643e27 q^{31} +8.14116e27 q^{32} -3.57230e25 q^{33} +2.60188e28 q^{34} -7.49716e28 q^{35} -4.19253e28 q^{36} +6.21792e28 q^{37} +1.48373e29 q^{38} -4.26262e26 q^{39} +2.92819e29 q^{40} -8.53404e29 q^{41} +9.00954e28 q^{42} +3.53994e29 q^{43} -9.64230e28 q^{44} -6.20942e30 q^{45} +1.25672e31 q^{46} +6.68978e29 q^{47} -7.95667e29 q^{48} +1.08383e31 q^{49} -5.68899e31 q^{50} -1.87321e30 q^{51} -1.15056e30 q^{52} +1.24128e32 q^{53} +1.49439e31 q^{54} -1.42809e31 q^{55} -1.14830e32 q^{56} -1.06820e31 q^{57} -1.19737e32 q^{58} +6.57033e31 q^{59} +4.46454e31 q^{60} -1.06034e33 q^{61} +1.12725e33 q^{62} +2.43505e33 q^{63} -7.49344e32 q^{64} -1.70406e32 q^{65} +1.71618e31 q^{66} -8.44869e33 q^{67} -5.05613e33 q^{68} -9.04768e32 q^{69} +3.60172e34 q^{70} -7.04837e33 q^{71} -9.51066e33 q^{72} +9.36735e33 q^{73} -2.98716e34 q^{74} +4.09575e33 q^{75} -2.88327e34 q^{76} +5.60032e33 q^{77} +2.04781e32 q^{78} +1.51854e35 q^{79} -3.18082e35 q^{80} +2.01141e35 q^{81} +4.09985e35 q^{82} -1.43761e35 q^{83} -1.75079e34 q^{84} -7.48847e35 q^{85} -1.70063e35 q^{86} +8.62039e33 q^{87} -2.18734e34 q^{88} +2.28283e35 q^{89} +2.98308e36 q^{90} +6.68253e34 q^{91} -2.44213e36 q^{92} -8.11557e34 q^{93} -3.21385e35 q^{94} -4.27032e36 q^{95} +2.81578e35 q^{96} +7.07361e36 q^{97} -5.20686e36 q^{98} +4.63839e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 194400 q^{2} + 13991400 q^{3} + 37720269824 q^{4} + 5529584385900 q^{5} - 22506543847296 q^{6} - 34\!\cdots\!00 q^{7}+ \cdots - 89\!\cdots\!14 q^{9}+O(q^{10}) $ 2 * q - 194400 * q^2 + 13991400 * q^3 + 37720269824 * q^4 + 5529584385900 * q^5 - 22506543847296 * q^6 - 3448443953486000 * q^7 - 34044043043635200 * q^8 - 898947378401769414 * q^9	$ 2 q - 194400 q^{2} + 13991400 q^{3} + 37720269824 q^{4} + 5529584385900 q^{5} - 22506543847296 q^{6} - 34\!\cdots\!00 q^{7}+ \cdots + 12\!\cdots\!92 q^{99}+O(q^{100}) $ 2 * q - 194400 * q^2 + 13991400 * q^3 + 37720269824 * q^4 + 5529584385900 * q^5 - 22506543847296 * q^6 - 3448443953486000 * q^7 - 34044043043635200 * q^8 - 898947378401769414 * q^9 - 9015609355013275200 * q^10 - 26734036354848538056 * q^11 + 4374774798370099200 * q^12 + 530581741653933178300 * q^13 + 3169419119584065186048 * q^14 + 649108943683113884400 * q^15 - 31152340106193176363008 * q^16 - 89439073881931767332700 * q^17 + 87081814924495841786400 * q^18 + 373276466572513713706120 * q^19 + 1752437909050980457420800 * q^20 - 228188865811378281195456 * q^21 - 6854650238581457086684800 * q^22 - 26241180149933881945462800 * q^23 + 1869795529093100955893760 * q^24 + 114502199615774855754278750 * q^25 + 161198290271390767044721344 * q^26 - 12567565757525316335881200 * q^27 - 616012501603352544390963200 * q^28 - 1270673827125882417951629220 * q^29 - 180869768268003018176083200 * q^30 + 261420819791418895481545024 * q^31 + 13400499670935825918040473600 * q^32 + 493606999076023001294056800 * q^33 + 15928395480391611359115494208 * q^34 - 91348258395203301140779687200 * q^35 - 16896751657649331450099821568 * q^36 - 68025363793820786588733238100 * q^37 + 343467860448446492149172419200 * q^38 - 11607709470242600846801346768 * q^39 + 751002277177488834411651072000 * q^40 - 1260483295466373133974684841836 * q^41 + 78468780705143776426791244800 * q^42 - 2570241023157918831169581605000 * q^43 + 1333494270055063548163396988928 * q^44 - 2476861984515775772921684271300 * q^45 + 12543759397110220887548257622784 * q^46 + 4252206875568934025158407583200 * q^47 - 627865474342240811187752140800 * q^48 - 3828013658149768338307153838286 * q^49 - 58010169823175993824907262180000 * q^50 - 1146602989088714802084517292976 * q^51 - 31355807203456647433862622464000 * q^52 + 159799736258590810071505678893900 * q^53 + 20246293327921369338050721342720 * q^54 + 198965756266726963295068969294800 * q^55 - 223825491222026073030759257210880 * q^56 - 24730693798747893221767420706400 * q^57 - 554449751247961885353825667003200 * q^58 - 237962459606090128758899369700840 * q^59 + 35138010316774983406295554252800 * q^60 + 101798841373038700200106255199644 * q^61 + 1873125324903360954810571368883200 * q^62 + 1547129676521036250657950915523600 * q^63 + 1874672702019432167416499183550464 * q^64 - 4674979790566994364848214315456600 * q^65 + 168556374577560093117347449548288 * q^66 - 10891923280981358108643809352546200 * q^67 - 3093300961636357481932215727257600 * q^68 - 903079825405531082422221799280448 * q^69 + 31333293246739547087546996653401600 * q^70 - 746133089793832492689962158868016 * q^71 + 15331394897876624646558687016550400 * q^72 + 19639851676496426023909382507487700 * q^73 - 67111659095025202293405215279979072 * q^74 + 4176423071329708963282786324335000 * q^75 - 66783420216030647132134009134018560 * q^76 - 45127994201424729507574115685000000 * q^77 - 2993244266642124681941208094368000 * q^78 + 272401638034095839035647945144674080 * q^79 - 250481015549362947010655598516633600 * q^80 + 403323837550038341003235827350619442 * q^81 + 293555739501144005521394805048475200 * q^82 - 470460275390909929308746217601073400 * q^83 - 15246219975764064504961836760399872 * q^84 - 456126475708535200141442602834276200 * q^85 - 1006428830786982641255996134716471936 * q^86 + 39923812909186495628003917423124400 * q^87 + 1397391845312343171300827514362265600 * q^88 - 1332868921711238117914343978794942860 * q^89 + 4050631020486902745715661556073886400 * q^90 + 1138398786311531726477856383010207584 * q^91 - 2437574081740573687511448195442483200 * q^92 - 134865729229255425577378938731155200 * q^93 + 703460887213042587108786164575999488 * q^94 - 9929993151899196579173099213128626000 * q^95 + 173258625718217609590386311471038464 * q^96 + 6002061888473229973039130090661237700 * q^97 - 9401601645347953932912572443881928800 * q^98 + 12025768918384639461946415841980309592 * 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 $

$2$	−480412.	−1.29586	−0.647931	−	0.761699i	$-0.724365\pi$
$2$	−480412.	−1.29586	−0.647931	+	0.761699i	$0.724365\pi$
$3$	3.45869e7	0.0515429	0.0257715	−	0.999668i	$-0.491796\pi$
$3$	3.45869e7	0.0515429	0.0257715	+	0.999668i	$0.491796\pi$
$4$	9.33565e10	0.679258
$5$	1.38267e13	1.62097	0.810484	−	0.585760i	$-0.199204\pi$
$5$	1.38267e13	1.62097	0.810484	+	0.585760i	$0.199204\pi$
$6$	−1.66160e13	−0.0667925
$7$	−5.42222e15	−1.25853	−0.629264	−	0.777191i	$-0.716644\pi$
$7$	−5.42222e15	−1.25853	−0.629264	+	0.777191i	$0.716644\pi$
$8$	2.11777e16	0.415637
$9$	−4.49088e17	−0.997343
$10$	−6.64253e18	−2.10055
$11$	−1.03285e18	−0.0560108	−0.0280054	−	0.999608i	$-0.508916\pi$
$11$	−1.03285e18	−0.0560108	−0.0280054	+	0.999608i	$0.508916\pi$
$12$	3.22892e18	0.0350109
$13$	−1.23244e19	−0.0303957	−0.0151979	−	0.999885i	$-0.504838\pi$
$13$	−1.23244e19	−0.0303957	−0.0151979	+	0.999885i	$0.504838\pi$
$14$	2.60490e21	1.63088
$15$	4.78225e20	0.0835495
$16$	−2.30048e22	−1.21787
$17$	−5.41594e22	−0.934047	−0.467023	−	0.884245i	$-0.654674\pi$
$17$	−5.41594e22	−0.934047	−0.467023	+	0.884245i	$0.654674\pi$
$18$	2.15747e23	1.29242
$19$	−3.08845e23	−0.680455	−0.340228	−	0.940343i	$-0.610504\pi$
$19$	−3.08845e23	−0.680455	−0.340228	+	0.940343i	$0.610504\pi$
$20$	1.29082e24	1.10106
$21$	−1.87538e23	−0.0648682
$22$	4.96192e23	0.0725822
$23$	−2.61592e25	−1.68136	−0.840678	−	0.541535i	$-0.817844\pi$
$23$	−2.61592e25	−1.68136	−0.840678	+	0.541535i	$0.817844\pi$
$24$	7.32473e23	0.0214232
$25$	1.18419e26	1.62754
$26$	5.92077e24	0.0393886
$27$	−3.11065e25	−0.102949
$28$	−5.06199e26	−0.854866
$29$	2.49238e26	0.219913	0.109957	−	0.993936i	$-0.464929\pi$
$29$	2.49238e26	0.219913	0.109957	+	0.993936i	$0.464929\pi$
$30$	−2.29745e26	−0.108269
$31$	−2.34643e27	−0.602859	−0.301429	−	0.953489i	$-0.597464\pi$
$31$	−2.34643e27	−0.602859	−0.301429	+	0.953489i	$0.597464\pi$
$32$	8.14116e27	1.16255
$33$	−3.57230e25	−0.00288696
$34$	2.60188e28	1.21040
$35$	−7.49716e28	−2.04004
$36$	−4.19253e28	−0.677453
$37$	6.21792e28	0.605220	0.302610	−	0.953114i	$-0.402142\pi$
$37$	6.21792e28	0.605220	0.302610	+	0.953114i	$0.402142\pi$
$38$	1.48373e29	0.881776
$39$	−4.26262e26	−0.00156668
$40$	2.92819e29	0.673735
$41$	−8.53404e29	−1.24352	−0.621761	−	0.783207i	$-0.713582\pi$
$41$	−8.53404e29	−1.24352	−0.621761	+	0.783207i	$0.713582\pi$
$42$	9.00954e28	0.0840603
$43$	3.53994e29	0.213713	0.106856	−	0.994274i	$-0.465922\pi$
$43$	3.53994e29	0.213713	0.106856	+	0.994274i	$0.465922\pi$
$44$	−9.64230e28	−0.0380457
$45$	−6.20942e30	−1.61666
$46$	1.25672e31	2.17881
$47$	6.68978e29	0.0779115	0.0389557	−	0.999241i	$-0.487597\pi$
$47$	6.68978e29	0.0779115	0.0389557	+	0.999241i	$0.487597\pi$
$48$	−7.95667e29	−0.0627724
$49$	1.08383e31	0.583895
$50$	−5.68899e31	−2.10907
$51$	−1.87321e30	−0.0481435
$52$	−1.15056e30	−0.0206465
$53$	1.24128e32	1.56591	0.782956	−	0.622077i	$-0.213711\pi$
$53$	1.24128e32	1.56591	0.782956	+	0.622077i	$0.213711\pi$
$54$	1.49439e31	0.133408
$55$	−1.42809e31	−0.0907917
$56$	−1.14830e32	−0.523092
$57$	−1.06820e31	−0.0350726
$58$	−1.19737e32	−0.284977
$59$	6.57033e31	0.113979	0.0569895	−	0.998375i	$-0.481850\pi$
$59$	6.57033e31	0.113979	0.0569895	+	0.998375i	$0.481850\pi$
$60$	4.46454e31	0.0567516
$61$	−1.06034e33	−0.992758	−0.496379	−	0.868106i	$-0.665337\pi$
$61$	−1.06034e33	−0.992758	−0.496379	+	0.868106i	$0.665337\pi$
$62$	1.12725e33	0.781222
$63$	2.43505e33	1.25519
$64$	−7.49344e32	−0.288637
$65$	−1.70406e32	−0.0492705
$66$	1.71618e31	0.00374110
$67$	−8.44869e33	−1.39446	−0.697229	−	0.716849i	$-0.745584\pi$
$67$	−8.44869e33	−1.39446	−0.697229	+	0.716849i	$0.745584\pi$
$68$	−5.05613e33	−0.634459
$69$	−9.04768e32	−0.0866620
$70$	3.60172e34	2.64360
$71$	−7.04837e33	−0.397932	−0.198966	−	0.980006i	$-0.563758\pi$
$71$	−7.04837e33	−0.397932	−0.198966	+	0.980006i	$0.563758\pi$
$72$	−9.51066e33	−0.414533
$73$	9.36735e33	0.316333	0.158166	−	0.987412i	$-0.449442\pi$
$73$	9.36735e33	0.316333	0.158166	+	0.987412i	$0.449442\pi$
$74$	−2.98716e34	−0.784282
$75$	4.09575e33	0.0838881
$76$	−2.88327e34	−0.462205
$77$	5.60032e33	0.0704911
$78$	2.04781e32	0.00203021
$79$	1.51854e35	1.18940	0.594698	−	0.803949i	$-0.297272\pi$
$79$	1.51854e35	1.18940	0.594698	+	0.803949i	$0.297272\pi$
$80$	−3.18082e35	−1.97412
$81$	2.01141e35	0.992037
$82$	4.09985e35	1.61143
$83$	−1.43761e35	−0.451541	−0.225771	−	0.974180i	$-0.572490\pi$
$83$	−1.43761e35	−0.451541	−0.225771	+	0.974180i	$0.572490\pi$
$84$	−1.75079e34	−0.0440623
$85$	−7.48847e35	−1.51406
$86$	−1.70063e35	−0.276942
$87$	8.62039e33	0.0113350
$88$	−2.18734e34	−0.0232802
$89$	2.28283e35	0.197133	0.0985664	−	0.995130i	$-0.468574\pi$
$89$	2.28283e35	0.197133	0.0985664	+	0.995130i	$0.468574\pi$
$90$	2.98308e36	2.09497
$91$	6.68253e34	0.0382539
$92$	−2.44213e36	−1.14208
$93$	−8.11557e34	−0.0310731
$94$	−3.21385e35	−0.100962
$95$	−4.27032e36	−1.10300
$96$	2.81578e35	0.0599212
$97$	7.07361e36	1.24269	0.621347	−	0.783535i	$-0.286586\pi$
$97$	7.07361e36	1.24269	0.621347	+	0.783535i	$0.286586\pi$
$98$	−5.20686e36	−0.756647
$99$	4.63839e35	0.0558620
$100$	1.10552e37	1.10552
$101$	−1.31355e37	−1.09270	−0.546350	−	0.837557i	$-0.683983\pi$
$101$	−1.31355e37	−1.09270	−0.546350	+	0.837557i	$0.683983\pi$
$102$	8.99911e35	0.0623873
$103$	2.33181e37	1.34960	0.674800	−	0.738000i	$-0.264230\pi$
$103$	2.33181e37	1.34960	0.674800	+	0.738000i	$0.264230\pi$
$104$	−2.61002e35	−0.0126336
$105$	−2.59304e36	−0.105149
$106$	−5.96327e37	−2.02920
$107$	3.01693e36	0.0862909	0.0431454	−	0.999069i	$-0.486262\pi$
$107$	3.01693e36	0.0862909	0.0431454	+	0.999069i	$0.486262\pi$
$108$	−2.90400e36	−0.0699289
$109$	3.05531e37	0.620391	0.310195	−	0.950673i	$-0.399606\pi$
$109$	3.05531e37	0.620391	0.310195	+	0.950673i	$0.399606\pi$
$110$	6.86072e36	0.117653
$111$	2.15059e36	0.0311948
$112$	1.24737e38	1.53272
$113$	4.21983e37	0.439890	0.219945	−	0.975512i	$-0.429412\pi$
$113$	4.21983e37	0.439890	0.219945	+	0.975512i	$0.429412\pi$
$114$	5.13177e36	0.0454493
$115$	−3.61697e38	−2.72543
$116$	2.32680e37	0.149378
$117$	5.53472e36	0.0303150
$118$	−3.15646e37	−0.147701
$119$	2.93664e38	1.17552
$120$	1.01277e37	0.0347263
$121$	−3.38973e38	−0.996863
$122$	5.09400e38	1.28648
$123$	−2.95166e37	−0.0640947
$124$	−2.19054e38	−0.409497
$125$	6.31322e38	1.01722
$126$	−1.16983e39	−1.62655
$127$	1.09656e39	1.31724	0.658619	−	0.752476i	$-0.271141\pi$
$127$	1.09656e39	1.31724	0.658619	+	0.752476i	$0.271141\pi$
$128$	−7.58918e38	−0.788516
$129$	1.22436e37	0.0110154
$130$	8.18649e37	0.0638477
$131$	−2.36928e39	−1.60360	−0.801802	−	0.597590i	$-0.796125\pi$
$131$	−2.36928e39	−1.60360	−0.801802	+	0.597590i	$0.796125\pi$
$132$	−3.33498e36	−0.00196099
$133$	1.67463e39	0.856373
$134$	4.05885e39	1.80702
$135$	−4.30102e38	−0.166877
$136$	−1.14697e39	−0.388225
$137$	2.55274e39	0.754529	0.377265	−	0.926105i	$-0.376865\pi$
$137$	2.55274e39	0.754529	0.377265	+	0.926105i	$0.376865\pi$
$138$	4.34661e38	0.112302
$139$	−6.38958e39	−1.44444	−0.722219	−	0.691665i	$-0.756878\pi$
$139$	−6.38958e39	−1.44444	−0.722219	+	0.691665i	$0.756878\pi$
$140$	−6.99908e39	−1.38571
$141$	2.31379e37	0.00401578
$142$	3.38612e39	0.515665
$143$	1.27292e37	0.00170249
$144$	1.03312e40	1.21463
$145$	3.44615e39	0.356473
$146$	−4.50019e39	−0.409923
$147$	3.74864e38	0.0300956
$148$	5.80483e39	0.411100
$149$	−3.49035e39	−0.218234	−0.109117	−	0.994029i	$-0.534802\pi$
$149$	−3.49035e39	−0.218234	−0.109117	+	0.994029i	$0.534802\pi$
$150$	−1.96765e39	−0.108707
$151$	−1.43880e40	−0.702953	−0.351476	−	0.936197i	$-0.614320\pi$
$151$	−1.43880e40	−0.702953	−0.351476	+	0.936197i	$0.614320\pi$
$152$	−6.54064e39	−0.282823
$153$	2.43223e40	0.931565
$154$	−2.69046e39	−0.0913468
$155$	−3.24434e40	−0.977215
$156$	−3.97943e37	−0.00106418
$157$	3.81842e40	0.907277	0.453639	−	0.891186i	$-0.350126\pi$
$157$	3.81842e40	0.907277	0.453639	+	0.891186i	$0.350126\pi$
$158$	−7.29527e40	−1.54129
$159$	4.29322e39	0.0807116
$160$	1.12566e41	1.88446
$161$	1.41841e41	2.11604
$162$	−9.66305e40	−1.28554
$163$	−7.49639e40	−0.889982	−0.444991	−	0.895535i	$-0.646793\pi$
$163$	−7.49639e40	−0.889982	−0.444991	+	0.895535i	$0.646793\pi$
$164$	−7.96708e40	−0.844672
$165$	−4.93933e38	−0.00467967
$166$	6.90646e40	0.585135
$167$	−1.87857e41	−1.42421	−0.712104	−	0.702074i	$-0.752257\pi$
$167$	−1.87857e41	−1.42421	−0.712104	+	0.702074i	$0.752257\pi$
$168$	−3.97163e39	−0.0269617
$169$	−1.64249e41	−0.999076
$170$	3.59755e41	1.96201
$171$	1.38699e41	0.678648
$172$	3.30477e40	0.145166
$173$	2.98432e41	1.17759	0.588793	−	0.808284i	$-0.299603\pi$
$173$	2.98432e41	1.17759	0.588793	+	0.808284i	$0.299603\pi$
$174$	−4.14134e39	−0.0146886
$175$	−6.42094e41	−2.04830
$176$	2.37605e40	0.0682136
$177$	2.27248e39	0.00587481
$178$	−1.09670e41	−0.255457
$179$	3.46258e41	0.727141	0.363570	−	0.931567i	$-0.381558\pi$
$179$	3.46258e41	0.727141	0.363570	+	0.931567i	$0.381558\pi$
$180$	−5.79689e41	−1.09813
$181$	4.05668e41	0.693613	0.346806	−	0.937937i	$-0.387266\pi$
$181$	4.05668e41	0.693613	0.346806	+	0.937937i	$0.387266\pi$
$182$	−3.21037e40	−0.0495717
$183$	−3.66740e40	−0.0511697
$184$	−5.53993e41	−0.698835
$185$	8.59735e41	0.981043
$186$	3.89882e40	0.0402664
$187$	5.59384e40	0.0523167
$188$	6.24534e40	0.0529220
$189$	1.68666e41	0.129564
$190$	2.05151e42	1.42933
$191$	−1.41675e42	−0.895726	−0.447863	−	0.894102i	$-0.647815\pi$
$191$	−1.41675e42	−0.895726	−0.447863	+	0.894102i	$0.647815\pi$
$192$	−2.59175e40	−0.0148772
$193$	−1.28639e42	−0.670751	−0.335375	−	0.942085i	$-0.608863\pi$
$193$	−1.28639e42	−0.670751	−0.335375	+	0.942085i	$0.608863\pi$
$194$	−3.39825e42	−1.61036
$195$	−5.89381e39	−0.00253954
$196$	1.01183e42	0.396615
$197$	3.68135e41	0.131336	0.0656678	−	0.997842i	$-0.479082\pi$
$197$	3.68135e41	0.131336	0.0656678	+	0.997842i	$0.479082\pi$
$198$	−2.22834e41	−0.0723894
$199$	3.12066e42	0.923557	0.461779	−	0.886995i	$-0.347211\pi$
$199$	3.12066e42	0.923557	0.461779	+	0.886995i	$0.347211\pi$
$200$	2.50785e42	0.676466
$201$	−2.92214e41	−0.0718744
$202$	6.31044e42	1.41599
$203$	−1.35142e42	−0.276767
$204$	−1.74876e41	−0.0327019
$205$	−1.17998e43	−2.01571
$206$	−1.12023e43	−1.74890
$207$	1.17478e43	1.67689
$208$	2.83520e41	0.0370179
$209$	3.18990e41	0.0381128
$210$	1.24573e42	0.136259
$211$	−7.58037e42	−0.759391	−0.379695	−	0.925112i	$-0.623971\pi$
$211$	−7.58037e42	−0.759391	−0.379695	+	0.925112i	$0.623971\pi$
$212$	1.15882e43	1.06366
$213$	−2.43782e41	−0.0205106
$214$	−1.44937e42	−0.111821
$215$	4.89459e42	0.346421
$216$	−6.58765e41	−0.0427894
$217$	1.27228e43	0.758715
$218$	−1.46781e43	−0.803941
$219$	3.23988e41	0.0163047
$220$	−1.33322e42	−0.0616710
$221$	6.67479e41	0.0283910
$222$	−1.03317e42	−0.0404242
$223$	4.00362e43	1.44149	0.720747	−	0.693198i	$-0.243799\pi$
$223$	4.00362e43	1.44149	0.720747	+	0.693198i	$0.243799\pi$
$224$	−4.41431e43	−1.46310
$225$	−5.31805e43	−1.62322
$226$	−2.02726e43	−0.570037
$227$	3.89322e43	1.00886	0.504430	−	0.863453i	$-0.331703\pi$
$227$	3.89322e43	1.00886	0.504430	+	0.863453i	$0.331703\pi$
$228$	−9.97236e41	−0.0238234
$229$	−3.32118e43	−0.731704	−0.365852	−	0.930673i	$-0.619222\pi$
$229$	−3.32118e43	−0.731704	−0.365852	+	0.930673i	$0.619222\pi$
$230$	1.73763e44	3.53178
$231$	1.93698e41	0.00363332
$232$	5.27830e42	0.0914043
$233$	−7.95672e43	−1.27248	−0.636238	−	0.771493i	$-0.719510\pi$
$233$	−7.95672e43	−1.27248	−0.636238	+	0.771493i	$0.719510\pi$
$234$	−2.65894e42	−0.0392840
$235$	9.24978e42	0.126292
$236$	6.13383e42	0.0774211
$237$	5.25218e42	0.0613049
$238$	−1.41080e44	−1.52332
$239$	−1.42241e44	−1.42123	−0.710615	−	0.703581i	$-0.751583\pi$
$239$	−1.42241e44	−1.42123	−0.710615	+	0.703581i	$0.751583\pi$
$240$	−1.10015e43	−0.101752
$241$	1.48641e44	1.27299	0.636494	−	0.771282i	$-0.280384\pi$
$241$	1.48641e44	1.27299	0.636494	+	0.771282i	$0.280384\pi$
$242$	1.62846e44	1.29180
$243$	2.09636e43	0.154081
$244$	−9.89897e43	−0.674339
$245$	1.49859e44	0.946475
$246$	1.41801e43	0.0830579
$247$	3.80632e42	0.0206829
$248$	−4.96920e43	−0.250571
$249$	−4.97227e42	−0.0232738
$250$	−3.03294e44	−1.31818
$251$	1.84398e44	0.744377	0.372189	−	0.928157i	$-0.378607\pi$
$251$	1.84398e44	0.744377	0.372189	+	0.928157i	$0.378607\pi$
$252$	2.27328e44	0.852595
$253$	2.70185e43	0.0941741
$254$	−5.26801e44	−1.70696
$255$	−2.59003e43	−0.0780391
$256$	4.67582e44	1.31044
$257$	−2.92391e44	−0.762433	−0.381216	−	0.924486i	$-0.624495\pi$
$257$	−2.92391e44	−0.762433	−0.381216	+	0.924486i	$0.624495\pi$
$258$	−5.88196e42	−0.0142744
$259$	−3.37149e44	−0.761687
$260$	−1.59085e43	−0.0334674
$261$	−1.11930e44	−0.219329
$262$	1.13823e45	2.07805
$263$	−4.07317e44	−0.693029	−0.346514	−	0.938045i	$-0.612635\pi$
$263$	−4.07317e44	−0.693029	−0.346514	+	0.938045i	$0.612635\pi$
$264$	−7.56533e41	−0.00119993
$265$	1.71629e45	2.53829
$266$	−8.04510e44	−1.10974
$267$	7.89562e42	0.0101608
$268$	−7.88740e44	−0.947196
$269$	−6.06370e44	−0.679705	−0.339853	−	0.940479i	$-0.610377\pi$
$269$	−6.06370e44	−0.679705	−0.339853	+	0.940479i	$0.610377\pi$
$270$	2.06626e44	0.216249
$271$	−1.82672e45	−1.78542	−0.892711	−	0.450630i	$-0.851200\pi$
$271$	−1.82672e45	−1.78542	−0.892711	+	0.450630i	$0.851200\pi$
$272$	1.24593e45	1.13754
$273$	2.31128e42	0.00197172
$274$	−1.22637e45	−0.977766
$275$	−1.22309e44	−0.0911597
$276$	−8.44659e43	−0.0588659
$277$	2.33400e45	1.52134	0.760668	−	0.649141i	$-0.224872\pi$
$277$	2.33400e45	1.52134	0.760668	+	0.649141i	$0.224872\pi$
$278$	3.06963e45	1.87179
$279$	1.05375e45	0.601257
$280$	−1.58773e45	−0.847915
$281$	−1.00137e45	−0.500643	−0.250322	−	0.968163i	$-0.580536\pi$
$281$	−1.00137e45	−0.500643	−0.250322	+	0.968163i	$0.580536\pi$
$282$	−1.11157e43	−0.00520390
$283$	−2.73703e45	−1.20014	−0.600069	−	0.799948i	$-0.704860\pi$
$283$	−2.73703e45	−1.20014	−0.600069	+	0.799948i	$0.704860\pi$
$284$	−6.58011e44	−0.270299
$285$	−1.47697e44	−0.0568517
$286$	−6.11525e42	−0.00220619
$287$	4.62734e45	1.56501
$288$	−3.65609e45	−1.15946
$289$	−4.28857e44	−0.127557
$290$	−1.65557e45	−0.461940
$291$	2.44655e44	0.0640521
$292$	8.74503e44	0.214871
$293$	1.07452e45	0.247836	0.123918	−	0.992292i	$-0.460454\pi$
$293$	1.07452e45	0.247836	0.123918	+	0.992292i	$0.460454\pi$
$294$	−1.80089e44	−0.0389998
$295$	9.08462e44	0.184756
$296$	1.31681e45	0.251552
$297$	3.21283e43	0.00576625
$298$	1.67680e45	0.282801
$299$	3.22396e44	0.0511060
$300$	3.82365e44	0.0569817
$301$	−1.91943e45	−0.268963
$302$	6.91215e45	0.910930
$303$	−4.54316e44	−0.0563209
$304$	7.10494e45	0.828704
$305$	−1.46611e46	−1.60923
$306$	−1.16847e46	−1.20718
$307$	−1.41267e46	−1.37398	−0.686989	−	0.726668i	$-0.741068\pi$
$307$	−1.41267e46	−1.37398	−0.686989	+	0.726668i	$0.741068\pi$
$308$	5.22826e44	0.0478817
$309$	8.06503e44	0.0695624
$310$	1.55862e46	1.26634
$311$	1.21153e46	0.927399	0.463700	−	0.885992i	$-0.346522\pi$
$311$	1.21153e46	0.927399	0.463700	+	0.885992i	$0.346522\pi$
$312$	−9.02726e42	−0.000651172 0
$313$	8.67864e45	0.590040	0.295020	−	0.955491i	$-0.404674\pi$
$313$	8.67864e45	0.590040	0.295020	+	0.955491i	$0.404674\pi$
$314$	−1.83441e46	−1.17571
$315$	3.36688e46	2.03462
$316$	1.41766e46	0.807906
$317$	−2.34417e46	−1.26006	−0.630031	−	0.776570i	$-0.716958\pi$
$317$	−2.34417e46	−1.26006	−0.630031	+	0.776570i	$0.716958\pi$
$318$	−2.06251e45	−0.104591
$319$	−2.57425e44	−0.0123175
$320$	−1.03610e46	−0.467871
$321$	1.04346e44	0.00444768
$322$	−6.81421e46	−2.74209
$323$	1.67269e46	0.635577
$324$	1.87778e46	0.673849
$325$	−1.45944e45	−0.0494702
$326$	3.60135e46	1.15329
$327$	1.05674e45	0.0319768
$328$	−1.80732e46	−0.516854
$329$	−3.62734e45	−0.0980538
$330$	2.37291e44	0.00606420
$331$	5.11187e46	1.23527	0.617635	−	0.786465i	$-0.288091\pi$
$331$	5.11187e46	1.23527	0.617635	+	0.786465i	$0.288091\pi$
$332$	−1.34211e46	−0.306713
$333$	−2.79239e46	−0.603612
$334$	9.02488e46	1.84558
$335$	−1.16818e47	−2.26037
$336$	4.31428e45	0.0790009
$337$	2.29819e46	0.398320	0.199160	−	0.979967i	$-0.436179\pi$
$337$	2.29819e46	0.398320	0.199160	+	0.979967i	$0.436179\pi$
$338$	7.89071e46	1.29466
$339$	1.45951e45	0.0226732
$340$	−6.99098e46	−1.02844
$341$	2.42350e45	0.0337666
$342$	−6.66325e46	−0.879433
$343$	4.18801e46	0.523680
$344$	7.49680e45	0.0888269
$345$	−1.25100e46	−0.140476
$346$	−1.43370e47	−1.52599
$347$	−8.38076e46	−0.845645	−0.422822	−	0.906213i	$-0.638961\pi$
$347$	−8.38076e46	−0.845645	−0.422822	+	0.906213i	$0.638961\pi$
$348$	8.04770e44	0.00769938
$349$	1.33845e47	1.21432	0.607158	−	0.794581i	$-0.292310\pi$
$349$	1.33845e47	1.21432	0.607158	+	0.794581i	$0.292310\pi$
$350$	3.08469e47	2.65432
$351$	3.83368e44	0.00312920
$352$	−8.40857e45	−0.0651153
$353$	1.44127e46	0.105904	0.0529520	−	0.998597i	$-0.483137\pi$
$353$	1.44127e46	0.105904	0.0529520	+	0.998597i	$0.483137\pi$
$354$	−1.09172e45	−0.00761294
$355$	−9.74560e46	−0.645036
$356$	2.13117e46	0.133904
$357$	1.01569e46	0.0605900
$358$	−1.66346e47	−0.942274
$359$	6.57303e46	0.353605	0.176802	−	0.984246i	$-0.443425\pi$
$359$	6.57303e46	0.353605	0.176802	+	0.984246i	$0.443425\pi$
$360$	−1.31501e47	−0.671945
$361$	−1.10622e47	−0.536981
$362$	−1.94888e47	−0.898826
$363$	−1.17240e46	−0.0513812
$364$	6.23858e45	0.0259842
$365$	1.29520e47	0.512765
$366$	1.76186e46	0.0663088
$367$	2.16797e47	0.775768	0.387884	−	0.921708i	$-0.373206\pi$
$367$	2.16797e47	0.775768	0.387884	+	0.921708i	$0.373206\pi$
$368$	6.01789e47	2.04767
$369$	3.83253e47	1.24022
$370$	−4.13027e47	−1.27130
$371$	−6.73051e47	−1.97074
$372$	−7.57641e45	−0.0211066
$373$	2.47528e47	0.656163	0.328081	−	0.944649i	$-0.393598\pi$
$373$	2.47528e47	0.656163	0.328081	+	0.944649i	$0.393598\pi$
$374$	−2.68734e46	−0.0677952
$375$	2.18355e46	0.0524305
$376$	1.41674e46	0.0323829
$377$	−3.07170e45	−0.00668442
$378$	−8.10293e46	−0.167897
$379$	1.02737e47	0.202722	0.101361	−	0.994850i	$-0.467680\pi$
$379$	1.02737e47	0.202722	0.101361	+	0.994850i	$0.467680\pi$
$380$	−3.98663e47	−0.749219
$381$	3.79267e46	0.0678943
$382$	6.80622e47	1.16074
$383$	−1.22188e48	−1.98541	−0.992706	−	0.120559i	$-0.961531\pi$
$383$	−1.22188e48	−1.98541	−0.992706	+	0.120559i	$0.961531\pi$
$384$	−2.62487e46	−0.0406424
$385$	7.74342e46	0.114264
$386$	6.17995e47	0.869200
$387$	−1.58975e47	−0.213145
$388$	6.60368e47	0.844110
$389$	−1.16416e48	−1.41888	−0.709440	−	0.704766i	$-0.751052\pi$
$389$	−1.16416e48	−1.41888	−0.709440	+	0.704766i	$0.751052\pi$
$390$	2.83146e45	0.00329090
$391$	1.41677e48	1.57047
$392$	2.29531e47	0.242688
$393$	−8.19461e46	−0.0826544
$394$	−1.76857e47	−0.170193
$395$	2.09965e48	1.92797
$396$	4.33024e46	0.0379447
$397$	−1.33628e48	−1.11756	−0.558781	−	0.829315i	$-0.688731\pi$
$397$	−1.33628e48	−1.11756	−0.558781	+	0.829315i	$0.688731\pi$
$398$	−1.49920e48	−1.19680
$399$	5.79202e46	0.0441399
$400$	−2.72421e48	−1.98213
$401$	2.54007e47	0.176472	0.0882358	−	0.996100i	$-0.471877\pi$
$401$	2.54007e47	0.176472	0.0882358	+	0.996100i	$0.471877\pi$
$402$	1.40383e47	0.0931393
$403$	2.89182e46	0.0183243
$404$	−1.22628e48	−0.742225
$405$	2.78112e48	1.60806
$406$	6.49240e47	0.358652
$407$	−6.42216e46	−0.0338988
$408$	−3.96703e46	−0.0200102
$409$	−1.33788e48	−0.644967	−0.322484	−	0.946575i	$-0.604518\pi$
$409$	−1.33788e48	−0.644967	−0.322484	+	0.946575i	$0.604518\pi$
$410$	5.66876e48	2.61208
$411$	8.82915e46	0.0388906
$412$	2.17690e48	0.916727
$413$	−3.56257e47	−0.143446
$414$	−5.64377e48	−2.17302
$415$	−1.98775e48	−0.731934
$416$	−1.00334e47	−0.0353365
$417$	−2.20996e47	−0.0744505
$418$	−1.53247e47	−0.0493889
$419$	2.08239e48	0.642101	0.321050	−	0.947062i	$-0.395964\pi$
$419$	2.08239e48	0.642101	0.321050	+	0.947062i	$0.395964\pi$
$420$	−2.42077e47	−0.0714236
$421$	−4.42178e48	−1.24847	−0.624236	−	0.781236i	$-0.714590\pi$
$421$	−4.42178e48	−1.24847	−0.624236	+	0.781236i	$0.714590\pi$
$422$	3.64170e48	0.984065
$423$	−3.00430e47	−0.0777045
$424$	2.62876e48	0.650851
$425$	−6.41350e48	−1.52020
$426$	1.17116e47	0.0265789
$427$	5.74940e48	1.24941
$428$	2.81650e47	0.0586138
$429$	4.40263e44	8.77511e−5 0
$430$	−2.35142e48	−0.448914
$431$	3.37175e48	0.616631	0.308315	−	0.951284i	$-0.400235\pi$
$431$	3.37175e48	0.616631	0.308315	+	0.951284i	$0.400235\pi$
$432$	7.15601e47	0.125378
$433$	2.37577e48	0.398822	0.199411	−	0.979916i	$-0.436097\pi$
$433$	2.37577e48	0.398822	0.199411	+	0.979916i	$0.436097\pi$
$434$	−6.11220e48	−0.983190
$435$	1.19192e47	0.0183736
$436$	2.85233e48	0.421405
$437$	8.07916e48	1.14409
$438$	−1.55648e47	−0.0211286
$439$	−2.31976e48	−0.301890	−0.150945	−	0.988542i	$-0.548232\pi$
$439$	−2.31976e48	−0.301890	−0.150945	+	0.988542i	$0.548232\pi$
$440$	−3.02437e47	−0.0377364
$441$	−4.86736e48	−0.582344
$442$	−3.20665e47	−0.0367908
$443$	−1.52174e49	−1.67444	−0.837222	−	0.546864i	$-0.815822\pi$
$443$	−1.52174e49	−1.67444	−0.837222	+	0.546864i	$0.815822\pi$
$444$	2.00771e47	0.0211893
$445$	3.15641e48	0.319546
$446$	−1.92339e49	−1.86798
$447$	−1.20720e47	−0.0112484
$448$	4.06311e48	0.363258
$449$	1.92781e49	1.65390	0.826948	−	0.562279i	$-0.190075\pi$
$449$	1.92781e49	1.65390	0.826948	+	0.562279i	$0.190075\pi$
$450$	2.55486e49	2.10346
$451$	8.81436e47	0.0696506
$452$	3.93949e48	0.298799
$453$	−4.97636e47	−0.0362322
$454$	−1.87035e49	−1.30734
$455$	9.23976e47	0.0620083
$456$	−2.26221e47	−0.0145775
$457$	1.19646e49	0.740367	0.370183	−	0.928959i	$-0.379295\pi$
$457$	1.19646e49	0.740367	0.370183	+	0.928959i	$0.379295\pi$
$458$	1.59553e49	0.948187
$459$	1.68471e48	0.0961591
$460$	−3.37667e49	−1.85127
$461$	−2.78549e49	−1.46702	−0.733508	−	0.679680i	$-0.762119\pi$
$461$	−2.78549e49	−1.46702	−0.733508	+	0.679680i	$0.762119\pi$
$462$	−9.30548e46	−0.00470828
$463$	−1.11920e49	−0.544075	−0.272038	−	0.962287i	$-0.587697\pi$
$463$	−1.11920e49	−0.544075	−0.272038	+	0.962287i	$0.587697\pi$
$464$	−5.73369e48	−0.267825
$465$	−1.12212e48	−0.0503685
$466$	3.82250e49	1.64895
$467$	−1.63248e49	−0.676840	−0.338420	−	0.940995i	$-0.609892\pi$
$467$	−1.63248e49	−0.676840	−0.338420	+	0.940995i	$0.609892\pi$
$468$	5.16702e47	0.0205917
$469$	4.58106e49	1.75497
$470$	−4.44370e48	−0.163657
$471$	1.32067e48	0.0467637
$472$	1.39145e48	0.0473739
$473$	−3.65622e47	−0.0119702
$474$	−2.52321e48	−0.0794427
$475$	−3.65732e49	−1.10747
$476$	2.74154e49	0.798485
$477$	−5.57445e49	−1.56175
$478$	6.83344e49	1.84172
$479$	2.63654e49	0.683639	0.341820	−	0.939766i	$-0.388957\pi$
$479$	2.63654e49	0.683639	0.341820	+	0.939766i	$0.388957\pi$
$480$	3.89330e48	0.0971304
$481$	−7.66319e47	−0.0183961
$482$	−7.14090e49	−1.64962
$483$	4.90585e48	0.109067
$484$	−3.16453e49	−0.677127
$485$	9.78050e49	2.01437
$486$	−1.00712e49	−0.199668
$487$	−7.78447e49	−1.48574	−0.742871	−	0.669435i	$-0.766536\pi$
$487$	−7.78447e49	−1.48574	−0.742871	+	0.669435i	$0.766536\pi$
$488$	−2.24556e49	−0.412628
$489$	−2.59277e48	−0.0458723
$490$	−7.19938e49	−1.22650
$491$	9.85282e49	1.61642	0.808208	−	0.588897i	$-0.200438\pi$
$491$	9.85282e49	1.61642	0.808208	+	0.588897i	$0.200438\pi$
$492$	−2.75557e48	−0.0435368
$493$	−1.34986e49	−0.205409
$494$	−1.82860e48	−0.0268022
$495$	6.41338e48	0.0905505
$496$	5.39792e49	0.734201
$497$	3.82178e49	0.500809
$498$	2.38874e48	0.0301596
$499$	1.25338e50	1.52483	0.762415	−	0.647088i	$-0.224013\pi$
$499$	1.25338e50	1.52483	0.762415	+	0.647088i	$0.224013\pi$
$500$	5.89380e49	0.690955
$501$	−6.49741e48	−0.0734078
$502$	−8.85871e49	−0.964610
$503$	−1.11020e50	−1.16518	−0.582589	−	0.812767i	$-0.697960\pi$
$503$	−1.11020e50	−1.16518	−0.582589	+	0.812767i	$0.697960\pi$
$504$	5.15688e49	0.521702
$505$	−1.81621e50	−1.77123
$506$	−1.29800e49	−0.122037
$507$	−5.68087e48	−0.0514953
$508$	1.02371e50	0.894745
$509$	−1.38813e50	−1.16991	−0.584955	−	0.811066i	$-0.698888\pi$
$509$	−1.38813e50	−1.16991	−0.584955	+	0.811066i	$0.698888\pi$
$510$	1.24428e49	0.101128
$511$	−5.07918e49	−0.398114
$512$	−1.20327e50	−0.909639
$513$	9.60711e48	0.0700521
$514$	1.40468e50	0.988007
$515$	3.22414e50	2.18766
$516$	1.14302e48	0.00748228
$517$	−6.90952e47	−0.00436388
$518$	1.61970e50	0.987041
$519$	1.03219e49	0.0606962
$520$	−3.60880e48	−0.0204787
$521$	−2.33871e50	−1.28079	−0.640396	−	0.768045i	$-0.721230\pi$
$521$	−2.33871e50	−1.28079	−0.640396	+	0.768045i	$0.721230\pi$
$522$	5.37724e49	0.284220
$523$	−1.30285e50	−0.664679	−0.332340	−	0.943160i	$-0.607838\pi$
$523$	−1.30285e50	−0.664679	−0.332340	+	0.943160i	$0.607838\pi$
$524$	−2.21188e50	−1.08926
$525$	−2.22081e49	−0.105576
$526$	1.95680e50	0.898070
$527$	1.27081e50	0.563098
$528$	8.21803e47	0.00351593
$529$	4.42241e50	1.82696
$530$	−8.24525e50	−3.28928
$531$	−2.95065e49	−0.113676
$532$	1.56337e50	0.581698
$533$	1.05177e49	0.0377977
$534$	−3.79315e48	−0.0131670
$535$	4.17143e49	0.139875
$536$	−1.78924e50	−0.579589
$537$	1.19760e49	0.0374789
$538$	2.91307e50	0.880804
$539$	−1.11943e49	−0.0327044
$540$	−4.01528e49	−0.113352
$541$	−5.31273e50	−1.44933	−0.724667	−	0.689099i	$-0.758007\pi$
$541$	−5.31273e50	−1.44933	−0.724667	+	0.689099i	$0.758007\pi$
$542$	8.77579e50	2.31366
$543$	1.40308e49	0.0357508
$544$	−4.40920e50	−1.08588
$545$	4.22450e50	1.00563
$546$	−1.11037e48	−0.00255507
$547$	−7.47732e49	−0.166334	−0.0831669	−	0.996536i	$-0.526503\pi$
$547$	−7.47732e49	−0.166334	−0.0831669	+	0.996536i	$0.526503\pi$
$548$	2.38315e50	0.512520
$549$	4.76186e50	0.990121
$550$	5.87586e49	0.118130
$551$	−7.69761e49	−0.149641
$552$	−1.91609e49	−0.0360200
$553$	−8.23388e50	−1.49689
$554$	−1.12128e51	−1.97144
$555$	2.97356e49	0.0505658
$556$	−5.96509e50	−0.981146
$557$	3.60496e50	0.573560	0.286780	−	0.957996i	$-0.407415\pi$
$557$	3.60496e50	0.573560	0.286780	+	0.957996i	$0.407415\pi$
$558$	−5.06234e50	−0.779146
$559$	−4.36275e48	−0.00649594
$560$	1.72471e51	2.48449
$561$	1.93474e48	0.00269655
$562$	4.81071e50	0.648764
$563$	−3.94055e50	−0.514223	−0.257112	−	0.966382i	$-0.582771\pi$
$563$	−3.94055e50	−0.514223	−0.257112	+	0.966382i	$0.582771\pi$
$564$	2.16007e48	0.00272775
$565$	5.83465e50	0.713048
$566$	1.31490e51	1.55521
$567$	−1.09063e51	−1.24851
$568$	−1.49268e50	−0.165396
$569$	−1.14686e50	−0.123008	−0.0615040	−	0.998107i	$-0.519590\pi$
$569$	−1.14686e50	−0.123008	−0.0615040	+	0.998107i	$0.519590\pi$
$570$	7.09556e49	0.0736719
$571$	1.48184e51	1.48948	0.744739	−	0.667356i	$-0.232574\pi$
$571$	1.48184e51	1.48948	0.744739	+	0.667356i	$0.232574\pi$
$572$	1.18835e48	0.00115643
$573$	−4.90010e49	−0.0461683
$574$	−2.22303e51	−2.02803
$575$	−3.09775e51	−2.73647
$576$	3.36521e50	0.287870
$577$	1.51306e51	1.25344	0.626722	−	0.779243i	$-0.284396\pi$
$577$	1.51306e51	1.25344	0.626722	+	0.779243i	$0.284396\pi$
$578$	2.06028e50	0.165296
$579$	−4.44922e49	−0.0345725
$580$	3.21721e50	0.242137
$581$	7.79505e50	0.568278
$582$	−1.17535e50	−0.0830027
$583$	−1.28206e50	−0.0877079
$584$	1.98379e50	0.131480
$585$	7.65271e49	0.0491396
$586$	−5.16213e50	−0.321161
$587$	8.72797e50	0.526148	0.263074	−	0.964776i	$-0.415264\pi$
$587$	8.72797e50	0.526148	0.263074	+	0.964776i	$0.415264\pi$
$588$	3.49960e49	0.0204427
$589$	7.24683e50	0.410218
$590$	−4.36436e50	−0.239419
$591$	1.27327e49	0.00676942
$592$	−1.43042e51	−0.737077
$593$	4.58679e49	0.0229085	0.0114543	−	0.999934i	$-0.496354\pi$
$593$	4.58679e49	0.0229085	0.0114543	+	0.999934i	$0.496354\pi$
$594$	−1.54348e49	−0.00747226
$595$	4.06041e51	1.90549
$596$	−3.25846e50	−0.148237
$597$	1.07934e50	0.0476028
$598$	−1.54883e50	−0.0662263
$599$	−2.10919e51	−0.874420	−0.437210	−	0.899360i	$-0.644033\pi$
$599$	−2.10919e51	−0.874420	−0.437210	+	0.899360i	$0.644033\pi$
$600$	8.67388e49	0.0348670
$601$	−2.46594e51	−0.961179	−0.480589	−	0.876946i	$-0.659577\pi$
$601$	−2.46594e51	−0.961179	−0.480589	+	0.876946i	$0.659577\pi$
$602$	9.22119e50	0.348539
$603$	3.79420e51	1.39075
$604$	−1.34321e51	−0.477486
$605$	−4.68689e51	−1.61588
$606$	2.18259e50	0.0729841
$607$	−4.33541e51	−1.40618	−0.703088	−	0.711103i	$-0.748196\pi$
$607$	−4.33541e51	−1.40618	−0.703088	+	0.711103i	$0.748196\pi$
$608$	−2.51436e51	−0.791063
$609$	−4.67416e49	−0.0142654
$610$	7.04334e51	2.08534
$611$	−8.24472e48	−0.00236817
$612$	2.27065e51	0.632773
$613$	−1.36136e51	−0.368091	−0.184046	−	0.982918i	$-0.558919\pi$
$613$	−1.36136e51	−0.368091	−0.184046	+	0.982918i	$0.558919\pi$
$614$	6.78662e51	1.78049
$615$	−4.08119e50	−0.103896
$616$	1.18602e50	0.0292988
$617$	3.77980e51	0.906136	0.453068	−	0.891476i	$-0.350329\pi$
$617$	3.77980e51	0.906136	0.453068	+	0.891476i	$0.350329\pi$
$618$	−3.87454e50	−0.0901432
$619$	6.56261e50	0.148183	0.0740917	−	0.997251i	$-0.476394\pi$
$619$	6.56261e50	0.148183	0.0740917	+	0.997251i	$0.476394\pi$
$620$	−3.02880e51	−0.663781
$621$	8.13722e50	0.173094
$622$	−5.82033e51	−1.20178
$623$	−1.23780e51	−0.248097
$624$	9.80609e48	0.00190801
$625$	1.12996e50	0.0213443
$626$	−4.16932e51	−0.764610
$627$	1.10329e49	0.00196445
$628$	3.56474e51	0.616275
$629$	−3.36759e51	−0.565304
$630$	−1.61749e52	−2.63658
$631$	3.19436e51	0.505640	0.252820	−	0.967513i	$-0.418642\pi$
$631$	3.19436e51	0.505640	0.252820	+	0.967513i	$0.418642\pi$
$632$	3.21593e51	0.494357
$633$	−2.62182e50	−0.0391412
$634$	1.12617e52	1.63287
$635$	1.51619e52	2.13520
$636$	4.00800e50	0.0548240
$637$	−1.33575e50	−0.0177479
$638$	1.23670e50	0.0159618
$639$	3.16534e51	0.396875
$640$	−1.04934e52	−1.27816
$641$	−1.48064e52	−1.75217	−0.876085	−	0.482157i	$-0.839853\pi$
$641$	−1.48064e52	−1.75217	−0.876085	+	0.482157i	$0.839853\pi$
$642$	−5.01292e49	−0.00576358
$643$	6.82003e51	0.761874	0.380937	−	0.924601i	$-0.375601\pi$
$643$	6.82003e51	0.761874	0.380937	+	0.924601i	$0.375601\pi$
$644$	1.32418e52	1.43733
$645$	1.69289e50	0.0178556
$646$	−8.03579e51	−0.823620
$647$	−2.43296e51	−0.242329	−0.121165	−	0.992632i	$-0.538663\pi$
$647$	−2.43296e51	−0.242329	−0.121165	+	0.992632i	$0.538663\pi$
$648$	4.25971e51	0.412328
$649$	−6.78614e49	−0.00638405
$650$	7.01131e50	0.0641065
$651$	4.40044e50	0.0391064
$652$	−6.99837e51	−0.604528
$653$	5.92349e51	0.497375	0.248687	−	0.968584i	$-0.420001\pi$
$653$	5.92349e51	0.497375	0.248687	+	0.968584i	$0.420001\pi$
$654$	−5.07670e50	−0.0414375
$655$	−3.27594e52	−2.59939
$656$	1.96324e52	1.51444
$657$	−4.20676e51	−0.315492
$658$	1.74262e51	0.127064
$659$	2.77432e51	0.196687	0.0983437	−	0.995153i	$-0.468646\pi$
$659$	2.77432e51	0.196687	0.0983437	+	0.995153i	$0.468646\pi$
$660$	−4.61118e49	−0.00317870
$661$	1.53847e52	1.03124	0.515622	−	0.856816i	$-0.327561\pi$
$661$	1.53847e52	1.03124	0.515622	+	0.856816i	$0.327561\pi$
$662$	−2.45580e52	−1.60074
$663$	2.30861e49	0.00146336
$664$	−3.04454e51	−0.187677
$665$	2.31546e52	1.38815
$666$	1.34150e52	0.782198
$667$	−6.51988e51	−0.369753
$668$	−1.75377e52	−0.967404
$669$	1.38473e51	0.0742988
$670$	5.61206e52	2.92913
$671$	1.09517e51	0.0556051
$672$	−1.52678e51	−0.0754125
$673$	−8.54768e50	−0.0410742	−0.0205371	−	0.999789i	$-0.506538\pi$
$673$	−8.54768e50	−0.0410742	−0.0205371	+	0.999789i	$0.506538\pi$
$674$	−1.10408e52	−0.516168
$675$	−3.68360e51	−0.167553
$676$	−1.53337e52	−0.678630
$677$	−3.33629e52	−1.43673	−0.718363	−	0.695669i	$-0.755108\pi$
$677$	−3.33629e52	−1.43673	−0.718363	+	0.695669i	$0.755108\pi$
$678$	−7.01167e50	−0.0293814
$679$	−3.83547e52	−1.56397
$680$	−1.58589e52	−0.629300
$681$	1.34655e51	0.0519996
$682$	−1.16428e51	−0.0437568
$683$	3.41377e52	1.24868	0.624340	−	0.781153i	$-0.285368\pi$
$683$	3.41377e52	1.24868	0.624340	+	0.781153i	$0.285368\pi$
$684$	1.29484e52	0.460977
$685$	3.52961e52	1.22307
$686$	−2.01197e52	−0.678618
$687$	−1.14869e51	−0.0377142
$688$	−8.14359e51	−0.260273
$689$	−1.52980e51	−0.0475970
$690$	6.00994e51	0.182038
$691$	5.92716e52	1.74784	0.873922	−	0.486066i	$-0.161569\pi$
$691$	5.92716e52	1.74784	0.873922	+	0.486066i	$0.161569\pi$
$692$	2.78606e52	0.799884
$693$	−2.51504e51	−0.0703039
$694$	4.02621e52	1.09584
$695$	−8.83471e52	−2.34139
$696$	1.82560e50	0.00471124
$697$	4.62198e52	1.16151
$698$	−6.43007e52	−1.57359
$699$	−2.75199e51	−0.0655871
$700$	−5.99436e52	−1.39133
$701$	4.09077e52	0.924744	0.462372	−	0.886686i	$-0.346998\pi$
$701$	4.09077e52	0.924744	0.462372	+	0.886686i	$0.346998\pi$
$702$	−1.84174e50	−0.00405502
$703$	−1.92038e52	−0.411825
$704$	7.73958e50	0.0161668
$705$	3.19922e50	0.00650946
$706$	−6.92401e51	−0.137237
$707$	7.12235e52	1.37519
$708$	2.12150e50	0.00399051
$709$	−8.44115e52	−1.54684	−0.773422	−	0.633891i	$-0.781457\pi$
$709$	−8.44115e52	−1.54684	−0.773422	+	0.633891i	$0.781457\pi$
$710$	4.68190e52	0.835877
$711$	−6.81960e52	−1.18624
$712$	4.83452e51	0.0819357
$713$	6.13807e52	1.01362
$714$	−4.87951e51	−0.0785162
$715$	1.76003e50	0.00275968
$716$	3.23254e52	0.493916
$717$	−4.91969e51	−0.0732544
$718$	−3.15776e52	−0.458223
$719$	−2.81946e52	−0.398733	−0.199367	−	0.979925i	$-0.563888\pi$
$719$	−2.81946e52	−0.398733	−0.199367	+	0.979925i	$0.563888\pi$
$720$	1.42847e53	1.96888
$721$	−1.26436e53	−1.69851
$722$	5.31442e52	0.695853
$723$	5.14105e51	0.0656135
$724$	3.78717e52	0.471142
$725$	2.95146e52	0.357918
$726$	5.63236e51	0.0665830
$727$	6.98427e52	0.804886	0.402443	−	0.915445i	$-0.368161\pi$
$727$	6.98427e52	0.804886	0.402443	+	0.915445i	$0.368161\pi$
$728$	1.41521e51	0.0158997
$729$	−8.98455e52	−0.984095
$730$	−6.22229e52	−0.664473
$731$	−1.91721e52	−0.199618
$732$	−3.42375e51	−0.0347574
$733$	3.54513e52	0.350921	0.175460	−	0.984487i	$-0.443859\pi$
$733$	3.54513e52	0.350921	0.175460	+	0.984487i	$0.443859\pi$
$734$	−1.04152e53	−1.00529
$735$	5.18315e51	0.0487841
$736$	−2.12966e53	−1.95466
$737$	8.72620e51	0.0781046
$738$	−1.84119e53	−1.60715
$739$	1.51689e53	1.29131	0.645655	−	0.763629i	$-0.276584\pi$
$739$	1.51689e53	1.29131	0.645655	+	0.763629i	$0.276584\pi$
$740$	8.02619e52	0.666381
$741$	1.31649e50	0.00106606
$742$	3.23341e53	2.55381
$743$	1.52901e53	1.17793	0.588964	−	0.808159i	$-0.299536\pi$
$743$	1.52901e53	1.17793	0.588964	+	0.808159i	$0.299536\pi$
$744$	−1.71869e51	−0.0129151
$745$	−4.82601e52	−0.353750
$746$	−1.18916e53	−0.850296
$747$	6.45615e52	0.450342
$748$	5.22221e51	0.0355365
$749$	−1.63584e52	−0.108600
$750$	−1.04900e52	−0.0679427
$751$	1.42568e53	0.900916	0.450458	−	0.892798i	$-0.351261\pi$
$751$	1.42568e53	0.900916	0.450458	+	0.892798i	$0.351261\pi$
$752$	−1.53897e52	−0.0948858
$753$	6.37778e51	0.0383674
$754$	1.47568e51	0.00866209
$755$	−1.98939e53	−1.13946
$756$	1.57461e52	0.0880075
$757$	−2.82784e53	−1.54234	−0.771171	−	0.636628i	$-0.780329\pi$
$757$	−2.82784e53	−1.54234	−0.771171	+	0.636628i	$0.780329\pi$
$758$	−4.93559e52	−0.262699
$759$	9.34487e50	0.00485401
$760$	−9.04358e52	−0.458447
$761$	3.71288e52	0.183694	0.0918470	−	0.995773i	$-0.470723\pi$
$761$	3.71288e52	0.183694	0.0918470	+	0.995773i	$0.470723\pi$
$762$	−1.82204e52	−0.0879817
$763$	−1.65666e53	−0.780780
$764$	−1.32263e53	−0.608429
$765$	3.36298e53	1.51004
$766$	5.87005e53	2.57282
$767$	−8.09750e50	−0.00346447
$768$	1.61722e52	0.0675441
$769$	−6.15158e52	−0.250813	−0.125406	−	0.992105i	$-0.540023\pi$
$769$	−6.15158e52	−0.250813	−0.125406	+	0.992105i	$0.540023\pi$
$770$	−3.72003e52	−0.148070
$771$	−1.01129e52	−0.0392980
$772$	−1.20093e53	−0.455613
$773$	−2.28656e53	−0.846960	−0.423480	−	0.905905i	$-0.639192\pi$
$773$	−2.28656e53	−0.846960	−0.423480	+	0.905905i	$0.639192\pi$
$774$	7.63732e52	0.276206
$775$	−2.77862e53	−0.981176
$776$	1.49803e53	0.516510
$777$	−1.16610e52	−0.0392596
$778$	5.59277e53	1.83867
$779$	2.63570e53	0.846161
$780$	−5.50225e50	−0.00172501
$781$	7.27989e51	0.0222885
$782$	−6.80632e53	−2.03511
$783$	−7.75294e51	−0.0226399
$784$	−2.49334e53	−0.711106
$785$	5.27963e53	1.47067
$786$	3.93679e52	0.107109
$787$	7.05791e52	0.187561	0.0937807	−	0.995593i	$-0.470105\pi$
$787$	7.05791e52	0.187561	0.0937807	+	0.995593i	$0.470105\pi$
$788$	3.43678e52	0.0892108
$789$	−1.40879e52	−0.0357207
$790$	−1.00870e54	−2.49839
$791$	−2.28809e53	−0.553614
$792$	9.82306e51	0.0232183
$793$	1.30680e52	0.0301756
$794$	6.41963e53	1.44821
$795$	5.93612e52	0.130831
$796$	2.91333e53	0.627334
$797$	−8.88567e53	−1.86944	−0.934719	−	0.355387i	$-0.884349\pi$
$797$	−8.88567e53	−1.86944	−0.934719	+	0.355387i	$0.884349\pi$
$798$	−2.78256e52	−0.0571993
$799$	−3.62314e52	−0.0727729
$800$	9.64068e53	1.89209
$801$	−1.02519e53	−0.196609
$802$	−1.22028e53	−0.228683
$803$	−9.67504e51	−0.0177180
$804$	−2.72801e52	−0.0488213
$805$	1.96120e54	3.43003
$806$	−1.38926e52	−0.0237458
$807$	−2.09725e52	−0.0350340
$808$	−2.78180e53	−0.454167
$809$	3.72232e53	0.593972	0.296986	−	0.954882i	$-0.404019\pi$
$809$	3.72232e53	0.593972	0.296986	+	0.954882i	$0.404019\pi$
$810$	−1.33608e54	−2.08382
$811$	−5.96718e53	−0.909668	−0.454834	−	0.890576i	$-0.650301\pi$
$811$	−5.96718e53	−0.909668	−0.454834	+	0.890576i	$0.650301\pi$
$812$	−1.26164e53	−0.187996
$813$	−6.31808e52	−0.0920259
$814$	3.08528e52	0.0439282
$815$	−1.03651e54	−1.44263
$816$	4.30929e52	0.0586324
$817$	−1.09330e53	−0.145422
$818$	6.42736e53	0.835788
$819$	−3.00104e52	−0.0381522
$820$	−1.10159e54	−1.36919
$821$	8.74697e52	0.106294	0.0531471	−	0.998587i	$-0.483075\pi$
$821$	8.74697e52	0.106294	0.0531471	+	0.998587i	$0.483075\pi$
$822$	−4.24163e52	−0.0503969
$823$	1.05135e54	1.22138	0.610692	−	0.791869i	$-0.290892\pi$
$823$	1.05135e54	1.22138	0.610692	+	0.791869i	$0.290892\pi$
$824$	4.93825e53	0.560945
$825$	−4.23029e51	−0.00469864
$826$	1.71150e53	0.185886
$827$	−1.54483e53	−0.164069	−0.0820347	−	0.996629i	$-0.526142\pi$
$827$	−1.54483e53	−0.164069	−0.0820347	+	0.996629i	$0.526142\pi$
$828$	1.09673e54	1.13904
$829$	2.69934e53	0.274156	0.137078	−	0.990560i	$-0.456229\pi$
$829$	2.69934e53	0.274156	0.137078	+	0.990560i	$0.456229\pi$
$830$	9.54939e53	0.948486
$831$	8.07259e52	0.0784141
$832$	9.23518e51	0.00877332
$833$	−5.86997e53	−0.545385
$834$	1.06169e53	0.0964776
$835$	−2.59745e54	−2.30860
$836$	2.97798e52	0.0258884
$837$	7.29891e52	0.0620636
$838$	−1.00041e54	−0.832074
$839$	2.43290e54	1.97937	0.989686	−	0.143252i	$-0.0457561\pi$
$839$	2.43290e54	1.97937	0.989686	+	0.143252i	$0.0457561\pi$
$840$	−5.49146e52	−0.0437040
$841$	−1.22236e54	−0.951638
$842$	2.12428e54	1.61785
$843$	−3.46344e52	−0.0258046
$844$	−7.07677e53	−0.515822
$845$	−2.27103e54	−1.61947
$846$	1.44330e53	0.100694
$847$	1.83798e54	1.25458
$848$	−2.85555e54	−1.90707
$849$	−9.46656e52	−0.0618586
$850$	3.08112e54	1.96997
$851$	−1.62656e54	−1.01759
$852$	−2.27586e52	−0.0139320
$853$	9.59321e53	0.574654	0.287327	−	0.957832i	$-0.407233\pi$
$853$	9.59321e53	0.574654	0.287327	+	0.957832i	$0.407233\pi$
$854$	−2.76208e54	−1.61907
$855$	1.91775e54	1.10007
$856$	6.38917e52	0.0358657
$857$	3.59352e52	0.0197413	0.00987063	−	0.999951i	$-0.496858\pi$
$857$	3.59352e52	0.0197413	0.00987063	+	0.999951i	$0.496858\pi$
$858$	−2.11508e50	−0.000113713 0
$859$	8.55580e53	0.450181	0.225091	−	0.974338i	$-0.427732\pi$
$859$	8.55580e53	0.450181	0.225091	+	0.974338i	$0.427732\pi$
$860$	4.56942e53	0.235309
$861$	1.60046e53	0.0806651
$862$	−1.61983e54	−0.799068
$863$	1.56057e54	0.753502	0.376751	−	0.926315i	$-0.377041\pi$
$863$	1.56057e54	0.753502	0.376751	+	0.926315i	$0.377041\pi$
$864$	−2.53243e53	−0.119683
$865$	4.12634e54	1.90883
$866$	−1.14135e54	−0.516818
$867$	−1.48329e52	−0.00657464
$868$	1.18776e54	0.515363
$869$	−1.56842e53	−0.0666190
$870$	−5.72612e52	−0.0238097
$871$	1.04125e53	0.0423855
$872$	6.47046e53	0.257858
$873$	−3.17667e54	−1.23939
$874$	−3.88132e54	−1.48258
$875$	−3.42316e54	−1.28020
$876$	3.02464e52	0.0110751
$877$	−3.37270e54	−1.20916	−0.604581	−	0.796544i	$-0.706659\pi$
$877$	−3.37270e54	−1.20916	−0.604581	+	0.796544i	$0.706659\pi$
$878$	1.11444e54	0.391208
$879$	3.71644e52	0.0127742
$880$	3.28530e53	0.110572
$881$	1.67513e54	0.552069	0.276034	−	0.961148i	$-0.410980\pi$
$881$	1.67513e54	0.552069	0.276034	+	0.961148i	$0.410980\pi$
$882$	2.33834e54	0.754637
$883$	1.42002e54	0.448767	0.224383	−	0.974501i	$-0.427963\pi$
$883$	1.42002e54	0.448767	0.224383	+	0.974501i	$0.427963\pi$
$884$	6.23135e52	0.0192848
$885$	3.14209e52	0.00952288
$886$	7.31060e54	2.16985
$887$	1.98874e54	0.578085	0.289042	−	0.957316i	$-0.406663\pi$
$887$	1.98874e54	0.578085	0.289042	+	0.957316i	$0.406663\pi$
$888$	4.55446e52	0.0129657
$889$	−5.94580e54	−1.65778
$890$	−1.51638e54	−0.414087
$891$	−2.07748e53	−0.0555647
$892$	3.73764e54	0.979147
$893$	−2.06611e53	−0.0530153
$894$	5.79955e52	0.0145764
$895$	4.78761e54	1.17867
$896$	4.11502e54	0.992370
$897$	1.11507e52	0.00263415
$898$	−9.26145e54	−2.14322
$899$	−5.84819e53	−0.132577
$900$	−4.96475e54	−1.10258
$901$	−6.72271e54	−1.46263
$902$	−4.23452e53	−0.0902575
$903$	−6.63874e52	−0.0138632
$904$	8.93665e53	0.182835
$905$	5.60906e54	1.12432
$906$	2.39070e53	0.0469520
$907$	−6.36503e54	−1.22480	−0.612401	−	0.790547i	$-0.709796\pi$
$907$	−6.36503e54	−1.22480	−0.612401	+	0.790547i	$0.709796\pi$
$908$	3.63458e54	0.685276
$909$	5.89899e54	1.08980
$910$	−4.43889e53	−0.0803542
$911$	2.93922e54	0.521365	0.260683	−	0.965425i	$-0.416052\pi$
$911$	2.93922e54	0.521365	0.260683	+	0.965425i	$0.416052\pi$
$912$	2.45738e53	0.0427138
$913$	1.48484e53	0.0252912
$914$	−5.74791e54	−0.959413
$915$	−5.07081e53	−0.0829444
$916$	−3.10053e54	−0.497016
$917$	1.28467e55	2.01818
$918$	−8.09354e53	−0.124609
$919$	−7.57823e54	−1.14349	−0.571743	−	0.820433i	$-0.693733\pi$
$919$	−7.57823e54	−1.14349	−0.571743	+	0.820433i	$0.693733\pi$
$920$	−7.65991e54	−1.13279
$921$	−4.88598e53	−0.0708189
$922$	1.33818e55	1.90105
$923$	8.68666e52	0.0120954
$924$	1.80830e52	0.00246796
$925$	7.36320e54	0.985019
$926$	5.37676e54	0.705046
$927$	−1.04719e55	−1.34602
$928$	2.02909e54	0.255660
$929$	6.55047e53	0.0809062	0.0404531	−	0.999181i	$-0.487120\pi$
$929$	6.55047e53	0.0809062	0.0404531	+	0.999181i	$0.487120\pi$
$930$	5.39079e53	0.0652706
$931$	−3.34737e54	−0.397314
$932$	−7.42812e54	−0.864340
$933$	4.19031e53	0.0478009
$934$	7.84263e54	0.877091
$935$	7.73445e53	0.0848037
$936$	1.17213e53	0.0126000
$937$	−3.87596e54	−0.408505	−0.204253	−	0.978918i	$-0.565476\pi$
$937$	−3.87596e54	−0.408505	−0.204253	+	0.978918i	$0.565476\pi$
$938$	−2.20080e55	−2.27419
$939$	3.00168e53	0.0304124
$940$	8.63527e53	0.0857849
$941$	−1.38620e55	−1.35027	−0.675133	−	0.737696i	$-0.735914\pi$
$941$	−1.38620e55	−1.35027	−0.675133	+	0.737696i	$0.735914\pi$
$942$	−6.34468e53	−0.0605993
$943$	2.23244e55	2.09080
$944$	−1.51149e54	−0.138811
$945$	2.33210e54	0.210019
$946$	1.75649e53	0.0155117
$947$	−8.86598e53	−0.0767807	−0.0383903	−	0.999263i	$-0.512223\pi$
$947$	−8.86598e53	−0.0767807	−0.0383903	+	0.999263i	$0.512223\pi$
$948$	4.90325e53	0.0416419
$949$	−1.15447e53	−0.00961515
$950$	1.75702e55	1.43512
$951$	−8.10776e53	−0.0649473
$952$	6.21913e54	0.488592
$953$	1.94425e55	1.49807	0.749036	−	0.662530i	$-0.230517\pi$
$953$	1.94425e55	1.49807	0.749036	+	0.662530i	$0.230517\pi$
$954$	2.67803e55	2.02381
$955$	−1.95890e55	−1.45194
$956$	−1.32791e55	−0.965382
$957$	−8.90355e51	−0.000634881 0
$958$	−1.26662e55	−0.885902
$959$	−1.38415e55	−0.949597
$960$	−3.58355e53	−0.0241155
$961$	−9.64324e54	−0.636561
$962$	3.68148e53	0.0238388
$963$	−1.35486e54	−0.0860616
$964$	1.38766e55	0.864687
$965$	−1.77865e55	−1.08727
$966$	−2.35683e54	−0.141335
$967$	6.67380e54	0.392630	0.196315	−	0.980541i	$-0.437103\pi$
$967$	6.67380e54	0.392630	0.196315	+	0.980541i	$0.437103\pi$
$968$	−7.17867e54	−0.414333
$969$	5.78532e53	0.0327595
$970$	−4.69867e55	−2.61034
$971$	−3.90466e52	−0.00212827	−0.00106414	−	0.999999i	$-0.500339\pi$
$971$	−3.90466e52	−0.00212827	−0.00106414	+	0.999999i	$0.500339\pi$
$972$	1.95709e54	0.104661
$973$	3.46457e55	1.81787
$974$	3.73975e55	1.92532
$975$	−5.04775e52	−0.00254984
$976$	2.43930e55	1.20905
$977$	−6.49911e54	−0.316085	−0.158043	−	0.987432i	$-0.550518\pi$
$977$	−6.49911e54	−0.316085	−0.158043	+	0.987432i	$0.550518\pi$
$978$	1.24560e54	0.0594441
$979$	−2.35782e53	−0.0110416
$980$	1.39903e55	0.642901
$981$	−1.37210e55	−0.618743
$982$	−4.73341e55	−2.09465
$983$	1.39076e55	0.603967	0.301984	−	0.953313i	$-0.402351\pi$
$983$	1.39076e55	0.603967	0.301984	+	0.953313i	$0.402351\pi$
$984$	−6.25095e53	−0.0266402
$985$	5.09011e54	0.212891
$986$	6.48488e54	0.266182
$987$	−1.25459e53	−0.00505398
$988$	3.55345e53	0.0140490
$989$	−9.26022e54	−0.359327
$990$	−3.08106e54	−0.117341
$991$	4.28319e55	1.60105	0.800525	−	0.599300i	$-0.204554\pi$
$991$	4.28319e55	1.60105	0.800525	+	0.599300i	$0.204554\pi$
$992$	−1.91026e55	−0.700853
$993$	1.76804e54	0.0636695
$994$	−1.83603e55	−0.648980
$995$	4.31485e55	1.49706
$996$	−4.64193e53	−0.0158089
$997$	−3.24811e55	−1.08585	−0.542925	−	0.839781i	$-0.682683\pi$
$997$	−3.24811e55	−1.08585	−0.542925	+	0.839781i	$0.682683\pi$
$998$	−6.02137e55	−1.97597
$999$	−1.93418e54	−0.0623067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.38.a.a.1.1	✓	2
3.2	odd	2		9.38.a.a.1.2		2
4.3	odd	2		16.38.a.b.1.1		2
5.2	odd	4		25.38.b.a.24.1		4
5.3	odd	4		25.38.b.a.24.4		4
5.4	even	2		25.38.a.a.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.38.a.a.1.1	✓	2	1.1	even	1	trivial
9.38.a.a.1.2		2	3.2	odd	2
16.38.a.b.1.1		2	4.3	odd	2
25.38.a.a.1.2		2	5.4	even	2
25.38.b.a.24.1		4	5.2	odd	4
25.38.b.a.24.4		4	5.3	odd	4

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:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-480412. q^{2} +3.45869e7 q^{3} +9.33565e10 q^{4} +1.38267e13 q^{5} -1.66160e13 q^{6} -5.42222e15 q^{7} +2.11777e16 q^{8} -4.49088e17 q^{9} +O(q^{10})\)	\(q-480412. q^{2} +3.45869e7 q^{3} +9.33565e10 q^{4} +1.38267e13 q^{5} -1.66160e13 q^{6} -5.42222e15 q^{7} +2.11777e16 q^{8} -4.49088e17 q^{9} -6.64253e18 q^{10} -1.03285e18 q^{11} +3.22892e18 q^{12} -1.23244e19 q^{13} +2.60490e21 q^{14} +4.78225e20 q^{15} -2.30048e22 q^{16} -5.41594e22 q^{17} +2.15747e23 q^{18} -3.08845e23 q^{19} +1.29082e24 q^{20} -1.87538e23 q^{21} +4.96192e23 q^{22} -2.61592e25 q^{23} +7.32473e23 q^{24} +1.18419e26 q^{25} +5.92077e24 q^{26} -3.11065e25 q^{27} -5.06199e26 q^{28} +2.49238e26 q^{29} -2.29745e26 q^{30} -2.34643e27 q^{31} +8.14116e27 q^{32} -3.57230e25 q^{33} +2.60188e28 q^{34} -7.49716e28 q^{35} -4.19253e28 q^{36} +6.21792e28 q^{37} +1.48373e29 q^{38} -4.26262e26 q^{39} +2.92819e29 q^{40} -8.53404e29 q^{41} +9.00954e28 q^{42} +3.53994e29 q^{43} -9.64230e28 q^{44} -6.20942e30 q^{45} +1.25672e31 q^{46} +6.68978e29 q^{47} -7.95667e29 q^{48} +1.08383e31 q^{49} -5.68899e31 q^{50} -1.87321e30 q^{51} -1.15056e30 q^{52} +1.24128e32 q^{53} +1.49439e31 q^{54} -1.42809e31 q^{55} -1.14830e32 q^{56} -1.06820e31 q^{57} -1.19737e32 q^{58} +6.57033e31 q^{59} +4.46454e31 q^{60} -1.06034e33 q^{61} +1.12725e33 q^{62} +2.43505e33 q^{63} -7.49344e32 q^{64} -1.70406e32 q^{65} +1.71618e31 q^{66} -8.44869e33 q^{67} -5.05613e33 q^{68} -9.04768e32 q^{69} +3.60172e34 q^{70} -7.04837e33 q^{71} -9.51066e33 q^{72} +9.36735e33 q^{73} -2.98716e34 q^{74} +4.09575e33 q^{75} -2.88327e34 q^{76} +5.60032e33 q^{77} +2.04781e32 q^{78} +1.51854e35 q^{79} -3.18082e35 q^{80} +2.01141e35 q^{81} +4.09985e35 q^{82} -1.43761e35 q^{83} -1.75079e34 q^{84} -7.48847e35 q^{85} -1.70063e35 q^{86} +8.62039e33 q^{87} -2.18734e34 q^{88} +2.28283e35 q^{89} +2.98308e36 q^{90} +6.68253e34 q^{91} -2.44213e36 q^{92} -8.11557e34 q^{93} -3.21385e35 q^{94} -4.27032e36 q^{95} +2.81578e35 q^{96} +7.07361e36 q^{97} -5.20686e36 q^{98} +4.63839e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 194400 q^{2} + 13991400 q^{3} + 37720269824 q^{4} + 5529584385900 q^{5} - 22506543847296 q^{6} - 34\!\cdots\!00 q^{7}+ \cdots - 89\!\cdots\!14 q^{9}+O(q^{10}) \) 2 * q - 194400 * q^2 + 13991400 * q^3 + 37720269824 * q^4 + 5529584385900 * q^5 - 22506543847296 * q^6 - 3448443953486000 * q^7 - 34044043043635200 * q^8 - 898947378401769414 * q^9	\( 2 q - 194400 q^{2} + 13991400 q^{3} + 37720269824 q^{4} + 5529584385900 q^{5} - 22506543847296 q^{6} - 34\!\cdots\!00 q^{7}+ \cdots + 12\!\cdots\!92 q^{99}+O(q^{100}) \) 2 * q - 194400 * q^2 + 13991400 * q^3 + 37720269824 * q^4 + 5529584385900 * q^5 - 22506543847296 * q^6 - 3448443953486000 * q^7 - 34044043043635200 * q^8 - 898947378401769414 * q^9 - 9015609355013275200 * q^10 - 26734036354848538056 * q^11 + 4374774798370099200 * q^12 + 530581741653933178300 * q^13 + 3169419119584065186048 * q^14 + 649108943683113884400 * q^15 - 31152340106193176363008 * q^16 - 89439073881931767332700 * q^17 + 87081814924495841786400 * q^18 + 373276466572513713706120 * q^19 + 1752437909050980457420800 * q^20 - 228188865811378281195456 * q^21 - 6854650238581457086684800 * q^22 - 26241180149933881945462800 * q^23 + 1869795529093100955893760 * q^24 + 114502199615774855754278750 * q^25 + 161198290271390767044721344 * q^26 - 12567565757525316335881200 * q^27 - 616012501603352544390963200 * q^28 - 1270673827125882417951629220 * q^29 - 180869768268003018176083200 * q^30 + 261420819791418895481545024 * q^31 + 13400499670935825918040473600 * q^32 + 493606999076023001294056800 * q^33 + 15928395480391611359115494208 * q^34 - 91348258395203301140779687200 * q^35 - 16896751657649331450099821568 * q^36 - 68025363793820786588733238100 * q^37 + 343467860448446492149172419200 * q^38 - 11607709470242600846801346768 * q^39 + 751002277177488834411651072000 * q^40 - 1260483295466373133974684841836 * q^41 + 78468780705143776426791244800 * q^42 - 2570241023157918831169581605000 * q^43 + 1333494270055063548163396988928 * q^44 - 2476861984515775772921684271300 * q^45 + 12543759397110220887548257622784 * q^46 + 4252206875568934025158407583200 * q^47 - 627865474342240811187752140800 * q^48 - 3828013658149768338307153838286 * q^49 - 58010169823175993824907262180000 * q^50 - 1146602989088714802084517292976 * q^51 - 31355807203456647433862622464000 * q^52 + 159799736258590810071505678893900 * q^53 + 20246293327921369338050721342720 * q^54 + 198965756266726963295068969294800 * q^55 - 223825491222026073030759257210880 * q^56 - 24730693798747893221767420706400 * q^57 - 554449751247961885353825667003200 * q^58 - 237962459606090128758899369700840 * q^59 + 35138010316774983406295554252800 * q^60 + 101798841373038700200106255199644 * q^61 + 1873125324903360954810571368883200 * q^62 + 1547129676521036250657950915523600 * q^63 + 1874672702019432167416499183550464 * q^64 - 4674979790566994364848214315456600 * q^65 + 168556374577560093117347449548288 * q^66 - 10891923280981358108643809352546200 * q^67 - 3093300961636357481932215727257600 * q^68 - 903079825405531082422221799280448 * q^69 + 31333293246739547087546996653401600 * q^70 - 746133089793832492689962158868016 * q^71 + 15331394897876624646558687016550400 * q^72 + 19639851676496426023909382507487700 * q^73 - 67111659095025202293405215279979072 * q^74 + 4176423071329708963282786324335000 * q^75 - 66783420216030647132134009134018560 * q^76 - 45127994201424729507574115685000000 * q^77 - 2993244266642124681941208094368000 * q^78 + 272401638034095839035647945144674080 * q^79 - 250481015549362947010655598516633600 * q^80 + 403323837550038341003235827350619442 * q^81 + 293555739501144005521394805048475200 * q^82 - 470460275390909929308746217601073400 * q^83 - 15246219975764064504961836760399872 * q^84 - 456126475708535200141442602834276200 * q^85 - 1006428830786982641255996134716471936 * q^86 + 39923812909186495628003917423124400 * q^87 + 1397391845312343171300827514362265600 * q^88 - 1332868921711238117914343978794942860 * q^89 + 4050631020486902745715661556073886400 * q^90 + 1138398786311531726477856383010207584 * q^91 - 2437574081740573687511448195442483200 * q^92 - 134865729229255425577378938731155200 * q^93 + 703460887213042587108786164575999488 * q^94 - 9929993151899196579173099213128626000 * q^95 + 173258625718217609590386311471038464 * q^96 + 6002061888473229973039130090661237700 * q^97 - 9401601645347953932912572443881928800 * q^98 + 12025768918384639461946415841980309592 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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