LMFDB - Embedded newform 25.38.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,38,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, 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("25.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 38 $
Character orbit:	$[\chi]$	$=$	25.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:	$216.785095312$
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:	no (minimal twist has level 1)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3991.29$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+480412. q^{2} -3.45869e7 q^{3} +9.33565e10 q^{4} -1.66160e13 q^{6} +5.42222e15 q^{7} -2.11777e16 q^{8} -4.49088e17 q^{9} +O(q^{10})$	\(q+480412. q^{2} -3.45869e7 q^{3} +9.33565e10 q^{4} -1.66160e13 q^{6} +5.42222e15 q^{7} -2.11777e16 q^{8} -4.49088e17 q^{9} -1.03285e18 q^{11} -3.22892e18 q^{12} +1.23244e19 q^{13} +2.60490e21 q^{14} -2.30048e22 q^{16} +5.41594e22 q^{17} -2.15747e23 q^{18} -3.08845e23 q^{19} -1.87538e23 q^{21} -4.96192e23 q^{22} +2.61592e25 q^{23} +7.32473e23 q^{24} +5.92077e24 q^{26} +3.11065e25 q^{27} +5.06199e26 q^{28} +2.49238e26 q^{29} -2.34643e27 q^{31} -8.14116e27 q^{32} +3.57230e25 q^{33} +2.60188e28 q^{34} -4.19253e28 q^{36} -6.21792e28 q^{37} -1.48373e29 q^{38} -4.26262e26 q^{39} -8.53404e29 q^{41} -9.00954e28 q^{42} -3.53994e29 q^{43} -9.64230e28 q^{44} +1.25672e31 q^{46} -6.68978e29 q^{47} +7.95667e29 q^{48} +1.08383e31 q^{49} -1.87321e30 q^{51} +1.15056e30 q^{52} -1.24128e32 q^{53} +1.49439e31 q^{54} -1.14830e32 q^{56} +1.06820e31 q^{57} +1.19737e32 q^{58} +6.57033e31 q^{59} -1.06034e33 q^{61} -1.12725e33 q^{62} -2.43505e33 q^{63} -7.49344e32 q^{64} +1.71618e31 q^{66} +8.44869e33 q^{67} +5.05613e33 q^{68} -9.04768e32 q^{69} -7.04837e33 q^{71} +9.51066e33 q^{72} -9.36735e33 q^{73} -2.98716e34 q^{74} -2.88327e34 q^{76} -5.60032e33 q^{77} -2.04781e32 q^{78} +1.51854e35 q^{79} +2.01141e35 q^{81} -4.09985e35 q^{82} +1.43761e35 q^{83} -1.75079e34 q^{84} -1.70063e35 q^{86} -8.62039e33 q^{87} +2.18734e34 q^{88} +2.28283e35 q^{89} +6.68253e34 q^{91} +2.44213e36 q^{92} +8.11557e34 q^{93} -3.21385e35 q^{94} +2.81578e35 q^{96} -7.07361e36 q^{97} +5.20686e36 q^{98} +4.63839e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 194400 q^{2} - 13991400 q^{3} + 37720269824 q^{4} - 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 - 22506543847296 * q^6 + 3448443953486000 * q^7 + 34044043043635200 * q^8 - 898947378401769414 * q^9	$ 2 q + 194400 q^{2} - 13991400 q^{3} + 37720269824 q^{4} - 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 - 22506543847296 * q^6 + 3448443953486000 * q^7 + 34044043043635200 * q^8 - 898947378401769414 * q^9 - 26734036354848538056 * q^11 - 4374774798370099200 * q^12 - 530581741653933178300 * q^13 + 3169419119584065186048 * q^14 - 31152340106193176363008 * q^16 + 89439073881931767332700 * q^17 - 87081814924495841786400 * q^18 + 373276466572513713706120 * q^19 - 228188865811378281195456 * q^21 + 6854650238581457086684800 * q^22 + 26241180149933881945462800 * q^23 + 1869795529093100955893760 * q^24 + 161198290271390767044721344 * q^26 + 12567565757525316335881200 * q^27 + 616012501603352544390963200 * q^28 - 1270673827125882417951629220 * q^29 + 261420819791418895481545024 * q^31 - 13400499670935825918040473600 * q^32 - 493606999076023001294056800 * q^33 + 15928395480391611359115494208 * q^34 - 16896751657649331450099821568 * q^36 + 68025363793820786588733238100 * q^37 - 343467860448446492149172419200 * q^38 - 11607709470242600846801346768 * q^39 - 1260483295466373133974684841836 * q^41 - 78468780705143776426791244800 * q^42 + 2570241023157918831169581605000 * q^43 + 1333494270055063548163396988928 * q^44 + 12543759397110220887548257622784 * q^46 - 4252206875568934025158407583200 * q^47 + 627865474342240811187752140800 * q^48 - 3828013658149768338307153838286 * q^49 - 1146602989088714802084517292976 * q^51 + 31355807203456647433862622464000 * q^52 - 159799736258590810071505678893900 * q^53 + 20246293327921369338050721342720 * q^54 - 223825491222026073030759257210880 * q^56 + 24730693798747893221767420706400 * q^57 + 554449751247961885353825667003200 * q^58 - 237962459606090128758899369700840 * q^59 + 101798841373038700200106255199644 * q^61 - 1873125324903360954810571368883200 * q^62 - 1547129676521036250657950915523600 * q^63 + 1874672702019432167416499183550464 * q^64 + 168556374577560093117347449548288 * q^66 + 10891923280981358108643809352546200 * q^67 + 3093300961636357481932215727257600 * q^68 - 903079825405531082422221799280448 * q^69 - 746133089793832492689962158868016 * q^71 - 15331394897876624646558687016550400 * q^72 - 19639851676496426023909382507487700 * q^73 - 67111659095025202293405215279979072 * q^74 - 66783420216030647132134009134018560 * q^76 + 45127994201424729507574115685000000 * q^77 + 2993244266642124681941208094368000 * q^78 + 272401638034095839035647945144674080 * q^79 + 403323837550038341003235827350619442 * q^81 - 293555739501144005521394805048475200 * q^82 + 470460275390909929308746217601073400 * q^83 - 15246219975764064504961836760399872 * q^84 - 1006428830786982641255996134716471936 * q^86 - 39923812909186495628003917423124400 * q^87 - 1397391845312343171300827514362265600 * q^88 - 1332868921711238117914343978794942860 * q^89 + 1138398786311531726477856383010207584 * q^91 + 2437574081740573687511448195442483200 * q^92 + 134865729229255425577378938731155200 * q^93 + 703460887213042587108786164575999488 * q^94 + 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	$-0.275635\pi$
$2$	480412.	1.29586	0.647931	+	0.761699i	$0.275635\pi$
$3$	−3.45869e7	−0.0515429	−0.0257715	−	0.999668i	$-0.508204\pi$
$3$	−3.45869e7	−0.0515429	−0.0257715	+	0.999668i	$0.508204\pi$
$4$	9.33565e10	0.679258
$5$	0	0
$5$	0	0
$6$	−1.66160e13	−0.0667925
$7$	5.42222e15	1.25853	0.629264	−	0.777191i	$-0.283356\pi$
$7$	5.42222e15	1.25853	0.629264	+	0.777191i	$0.283356\pi$
$8$	−2.11777e16	−0.415637
$9$	−4.49088e17	−0.997343
$10$	0	0
$11$	−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	$-0.495162\pi$
$13$	1.23244e19	0.0303957	0.0151979	+	0.999885i	$0.495162\pi$
$14$	2.60490e21	1.63088
$15$	0	0
$16$	−2.30048e22	−1.21787
$17$	5.41594e22	0.934047	0.467023	−	0.884245i	$-0.345326\pi$
$17$	5.41594e22	0.934047	0.467023	+	0.884245i	$0.345326\pi$
$18$	−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	$0.610504\pi$
$20$	0	0
$21$	−1.87538e23	−0.0648682
$22$	−4.96192e23	−0.0725822
$23$	2.61592e25	1.68136	0.840678	−	0.541535i	$-0.182156\pi$
$23$	2.61592e25	1.68136	0.840678	+	0.541535i	$0.182156\pi$
$24$	7.32473e23	0.0214232
$25$	0	0
$26$	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	$0.464929\pi$
$30$	0	0
$31$	−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
$35$	0	0
$36$	−4.19253e28	−0.677453
$37$	−6.21792e28	−0.605220	−0.302610	−	0.953114i	$-0.597858\pi$
$37$	−6.21792e28	−0.605220	−0.302610	+	0.953114i	$0.597858\pi$
$38$	−1.48373e29	−0.881776
$39$	−4.26262e26	−0.00156668
$40$	0	0
$41$	−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	$-0.534078\pi$
$43$	−3.53994e29	−0.213713	−0.106856	+	0.994274i	$0.534078\pi$
$44$	−9.64230e28	−0.0380457
$45$	0	0
$46$	1.25672e31	2.17881
$47$	−6.68978e29	−0.0779115	−0.0389557	−	0.999241i	$-0.512403\pi$
$47$	−6.68978e29	−0.0779115	−0.0389557	+	0.999241i	$0.512403\pi$
$48$	7.95667e29	0.0627724
$49$	1.08383e31	0.583895
$50$	0	0
$51$	−1.87321e30	−0.0481435
$52$	1.15056e30	0.0206465
$53$	−1.24128e32	−1.56591	−0.782956	−	0.622077i	$-0.786289\pi$
$53$	−1.24128e32	−1.56591	−0.782956	+	0.622077i	$0.786289\pi$
$54$	1.49439e31	0.133408
$55$	0	0
$56$	−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	$0.481850\pi$
$60$	0	0
$61$	−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
$65$	0	0
$66$	1.71618e31	0.00374110
$67$	8.44869e33	1.39446	0.697229	−	0.716849i	$-0.254416\pi$
$67$	8.44869e33	1.39446	0.697229	+	0.716849i	$0.254416\pi$
$68$	5.05613e33	0.634459
$69$	−9.04768e32	−0.0866620
$70$	0	0
$71$	−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	$-0.550558\pi$
$73$	−9.36735e33	−0.316333	−0.158166	+	0.987412i	$0.550558\pi$
$74$	−2.98716e34	−0.784282
$75$	0	0
$76$	−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	$0.297272\pi$
$80$	0	0
$81$	2.01141e35	0.992037
$82$	−4.09985e35	−1.61143
$83$	1.43761e35	0.451541	0.225771	−	0.974180i	$-0.427510\pi$
$83$	1.43761e35	0.451541	0.225771	+	0.974180i	$0.427510\pi$
$84$	−1.75079e34	−0.0440623
$85$	0	0
$86$	−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	$0.468574\pi$
$90$	0	0
$91$	6.68253e34	0.0382539
$92$	2.44213e36	1.14208
$93$	8.11557e34	0.0310731
$94$	−3.21385e35	−0.100962
$95$	0	0
$96$	2.81578e35	0.0599212
$97$	−7.07361e36	−1.24269	−0.621347	−	0.783535i	$-0.713414\pi$
$97$	−7.07361e36	−1.24269	−0.621347	+	0.783535i	$0.713414\pi$
$98$	5.20686e36	0.756647
$99$	4.63839e35	0.0558620
$100$	0	0
$101$	−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	$-0.735770\pi$
$103$	−2.33181e37	−1.34960	−0.674800	+	0.738000i	$0.735770\pi$
$104$	−2.61002e35	−0.0126336
$105$	0	0
$106$	−5.96327e37	−2.02920
$107$	−3.01693e36	−0.0862909	−0.0431454	−	0.999069i	$-0.513738\pi$
$107$	−3.01693e36	−0.0862909	−0.0431454	+	0.999069i	$0.513738\pi$
$108$	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	$0.399606\pi$
$110$	0	0
$111$	2.15059e36	0.0311948
$112$	−1.24737e38	−1.53272
$113$	−4.21983e37	−0.439890	−0.219945	−	0.975512i	$-0.570588\pi$
$113$	−4.21983e37	−0.439890	−0.219945	+	0.975512i	$0.570588\pi$
$114$	5.13177e36	0.0454493
$115$	0	0
$116$	2.32680e37	0.149378
$117$	−5.53472e36	−0.0303150
$118$	3.15646e37	0.147701
$119$	2.93664e38	1.17552
$120$	0	0
$121$	−3.38973e38	−0.996863
$122$	−5.09400e38	−1.28648
$123$	2.95166e37	0.0640947
$124$	−2.19054e38	−0.409497
$125$	0	0
$126$	−1.16983e39	−1.62655
$127$	−1.09656e39	−1.31724	−0.658619	−	0.752476i	$-0.728859\pi$
$127$	−1.09656e39	−1.31724	−0.658619	+	0.752476i	$0.728859\pi$
$128$	7.58918e38	0.788516
$129$	1.22436e37	0.0110154
$130$	0	0
$131$	−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
$135$	0	0
$136$	−1.14697e39	−0.388225
$137$	−2.55274e39	−0.754529	−0.377265	−	0.926105i	$-0.623135\pi$
$137$	−2.55274e39	−0.754529	−0.377265	+	0.926105i	$0.623135\pi$
$138$	−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	$0.756878\pi$
$140$	0	0
$141$	2.31379e37	0.00401578
$142$	−3.38612e39	−0.515665
$143$	−1.27292e37	−0.00170249
$144$	1.03312e40	1.21463
$145$	0	0
$146$	−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	$0.534802\pi$
$150$	0	0
$151$	−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
$155$	0	0
$156$	−3.97943e37	−0.00106418
$157$	−3.81842e40	−0.907277	−0.453639	−	0.891186i	$-0.649874\pi$
$157$	−3.81842e40	−0.907277	−0.453639	+	0.891186i	$0.649874\pi$
$158$	7.29527e40	1.54129
$159$	4.29322e39	0.0807116
$160$	0	0
$161$	1.41841e41	2.11604
$162$	9.66305e40	1.28554
$163$	7.49639e40	0.889982	0.444991	−	0.895535i	$-0.353207\pi$
$163$	7.49639e40	0.889982	0.444991	+	0.895535i	$0.353207\pi$
$164$	−7.96708e40	−0.844672
$165$	0	0
$166$	6.90646e40	0.585135
$167$	1.87857e41	1.42421	0.712104	−	0.702074i	$-0.247743\pi$
$167$	1.87857e41	1.42421	0.712104	+	0.702074i	$0.247743\pi$
$168$	3.97163e39	0.0269617
$169$	−1.64249e41	−0.999076
$170$	0	0
$171$	1.38699e41	0.678648
$172$	−3.30477e40	−0.145166
$173$	−2.98432e41	−1.17759	−0.588793	−	0.808284i	$-0.700397\pi$
$173$	−2.98432e41	−1.17759	−0.588793	+	0.808284i	$0.700397\pi$
$174$	−4.14134e39	−0.0146886
$175$	0	0
$176$	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	$0.381558\pi$
$180$	0	0
$181$	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
$185$	0	0
$186$	3.89882e40	0.0402664
$187$	−5.59384e40	−0.0523167
$188$	−6.24534e40	−0.0529220
$189$	1.68666e41	0.129564
$190$	0	0
$191$	−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	$-0.391137\pi$
$193$	1.28639e42	0.670751	0.335375	+	0.942085i	$0.391137\pi$
$194$	−3.39825e42	−1.61036
$195$	0	0
$196$	1.01183e42	0.396615
$197$	−3.68135e41	−0.131336	−0.0656678	−	0.997842i	$-0.520918\pi$
$197$	−3.68135e41	−0.131336	−0.0656678	+	0.997842i	$0.520918\pi$
$198$	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	$0.347211\pi$
$200$	0	0
$201$	−2.92214e41	−0.0718744
$202$	−6.31044e42	−1.41599
$203$	1.35142e42	0.276767
$204$	−1.74876e41	−0.0327019
$205$	0	0
$206$	−1.12023e43	−1.74890
$207$	−1.17478e43	−1.67689
$208$	−2.83520e41	−0.0370179
$209$	3.18990e41	0.0381128
$210$	0	0
$211$	−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
$215$	0	0
$216$	−6.58765e41	−0.0427894
$217$	−1.27228e43	−0.758715
$218$	1.46781e43	0.803941
$219$	3.23988e41	0.0163047
$220$	0	0
$221$	6.67479e41	0.0283910
$222$	1.03317e42	0.0404242
$223$	−4.00362e43	−1.44149	−0.720747	−	0.693198i	$-0.756201\pi$
$223$	−4.00362e43	−1.44149	−0.720747	+	0.693198i	$0.756201\pi$
$224$	−4.41431e43	−1.46310
$225$	0	0
$226$	−2.02726e43	−0.570037
$227$	−3.89322e43	−1.00886	−0.504430	−	0.863453i	$-0.668297\pi$
$227$	−3.89322e43	−1.00886	−0.504430	+	0.863453i	$0.668297\pi$
$228$	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	$0.619222\pi$
$230$	0	0
$231$	1.93698e41	0.00363332
$232$	−5.27830e42	−0.0914043
$233$	7.95672e43	1.27248	0.636238	−	0.771493i	$-0.280490\pi$
$233$	7.95672e43	1.27248	0.636238	+	0.771493i	$0.280490\pi$
$234$	−2.65894e42	−0.0392840
$235$	0	0
$236$	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	$0.751583\pi$
$240$	0	0
$241$	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
$245$	0	0
$246$	1.41801e43	0.0830579
$247$	−3.80632e42	−0.0206829
$248$	4.96920e43	0.250571
$249$	−4.97227e42	−0.0232738
$250$	0	0
$251$	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
$255$	0	0
$256$	4.67582e44	1.31044
$257$	2.92391e44	0.762433	0.381216	−	0.924486i	$-0.375505\pi$
$257$	2.92391e44	0.762433	0.381216	+	0.924486i	$0.375505\pi$
$258$	5.88196e42	0.0142744
$259$	−3.37149e44	−0.761687
$260$	0	0
$261$	−1.11930e44	−0.219329
$262$	−1.13823e45	−2.07805
$263$	4.07317e44	0.693029	0.346514	−	0.938045i	$-0.387365\pi$
$263$	4.07317e44	0.693029	0.346514	+	0.938045i	$0.387365\pi$
$264$	−7.56533e41	−0.00119993
$265$	0	0
$266$	−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	$0.610377\pi$
$270$	0	0
$271$	−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
$275$	0	0
$276$	−8.44659e43	−0.0588659
$277$	−2.33400e45	−1.52134	−0.760668	−	0.649141i	$-0.775128\pi$
$277$	−2.33400e45	−1.52134	−0.760668	+	0.649141i	$0.775128\pi$
$278$	−3.06963e45	−1.87179
$279$	1.05375e45	0.601257
$280$	0	0
$281$	−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	$-0.295140\pi$
$283$	2.73703e45	1.20014	0.600069	+	0.799948i	$0.295140\pi$
$284$	−6.58011e44	−0.270299
$285$	0	0
$286$	−6.11525e42	−0.00220619
$287$	−4.62734e45	−1.56501
$288$	3.65609e45	1.15946
$289$	−4.28857e44	−0.127557
$290$	0	0
$291$	2.44655e44	0.0640521
$292$	−8.74503e44	−0.214871
$293$	−1.07452e45	−0.247836	−0.123918	−	0.992292i	$-0.539546\pi$
$293$	−1.07452e45	−0.247836	−0.123918	+	0.992292i	$0.539546\pi$
$294$	−1.80089e44	−0.0389998
$295$	0	0
$296$	1.31681e45	0.251552
$297$	−3.21283e43	−0.00576625
$298$	−1.67680e45	−0.282801
$299$	3.22396e44	0.0511060
$300$	0	0
$301$	−1.91943e45	−0.268963
$302$	−6.91215e45	−0.910930
$303$	4.54316e44	0.0563209
$304$	7.10494e45	0.828704
$305$	0	0
$306$	−1.16847e46	−1.20718
$307$	1.41267e46	1.37398	0.686989	−	0.726668i	$-0.258932\pi$
$307$	1.41267e46	1.37398	0.686989	+	0.726668i	$0.258932\pi$
$308$	−5.22826e44	−0.0478817
$309$	8.06503e44	0.0695624
$310$	0	0
$311$	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	$-0.595326\pi$
$313$	−8.67864e45	−0.590040	−0.295020	+	0.955491i	$0.595326\pi$
$314$	−1.83441e46	−1.17571
$315$	0	0
$316$	1.41766e46	0.807906
$317$	2.34417e46	1.26006	0.630031	−	0.776570i	$-0.283042\pi$
$317$	2.34417e46	1.26006	0.630031	+	0.776570i	$0.283042\pi$
$318$	2.06251e45	0.104591
$319$	−2.57425e44	−0.0123175
$320$	0	0
$321$	1.04346e44	0.00444768
$322$	6.81421e46	2.74209
$323$	−1.67269e46	−0.635577
$324$	1.87778e46	0.673849
$325$	0	0
$326$	3.60135e46	1.15329
$327$	−1.05674e45	−0.0319768
$328$	1.80732e46	0.516854
$329$	−3.62734e45	−0.0980538
$330$	0	0
$331$	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
$335$	0	0
$336$	4.31428e45	0.0790009
$337$	−2.29819e46	−0.398320	−0.199160	−	0.979967i	$-0.563821\pi$
$337$	−2.29819e46	−0.398320	−0.199160	+	0.979967i	$0.563821\pi$
$338$	−7.89071e46	−1.29466
$339$	1.45951e45	0.0226732
$340$	0	0
$341$	2.42350e45	0.0337666
$342$	6.66325e46	0.879433
$343$	−4.18801e46	−0.523680
$344$	7.49680e45	0.0888269
$345$	0	0
$346$	−1.43370e47	−1.52599
$347$	8.38076e46	0.845645	0.422822	−	0.906213i	$-0.361039\pi$
$347$	8.38076e46	0.845645	0.422822	+	0.906213i	$0.361039\pi$
$348$	−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	$0.292310\pi$
$350$	0	0
$351$	3.83368e44	0.00312920
$352$	8.40857e45	0.0651153
$353$	−1.44127e46	−0.105904	−0.0529520	−	0.998597i	$-0.516863\pi$
$353$	−1.44127e46	−0.105904	−0.0529520	+	0.998597i	$0.516863\pi$
$354$	−1.09172e45	−0.00761294
$355$	0	0
$356$	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	$0.443425\pi$
$360$	0	0
$361$	−1.10622e47	−0.536981
$362$	1.94888e47	0.898826
$363$	1.17240e46	0.0513812
$364$	6.23858e45	0.0259842
$365$	0	0
$366$	1.76186e46	0.0663088
$367$	−2.16797e47	−0.775768	−0.387884	−	0.921708i	$-0.626794\pi$
$367$	−2.16797e47	−0.775768	−0.387884	+	0.921708i	$0.626794\pi$
$368$	−6.01789e47	−2.04767
$369$	3.83253e47	1.24022
$370$	0	0
$371$	−6.73051e47	−1.97074
$372$	7.57641e45	0.0211066
$373$	−2.47528e47	−0.656163	−0.328081	−	0.944649i	$-0.606402\pi$
$373$	−2.47528e47	−0.656163	−0.328081	+	0.944649i	$0.606402\pi$
$374$	−2.68734e46	−0.0677952
$375$	0	0
$376$	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	$0.467680\pi$
$380$	0	0
$381$	3.79267e46	0.0678943
$382$	−6.80622e47	−1.16074
$383$	1.22188e48	1.98541	0.992706	−	0.120559i	$-0.0384687\pi$
$383$	1.22188e48	1.98541	0.992706	+	0.120559i	$0.0384687\pi$
$384$	−2.62487e46	−0.0406424
$385$	0	0
$386$	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	$0.751052\pi$
$390$	0	0
$391$	1.41677e48	1.57047
$392$	−2.29531e47	−0.242688
$393$	8.19461e46	0.0826544
$394$	−1.76857e47	−0.170193
$395$	0	0
$396$	4.33024e46	0.0379447
$397$	1.33628e48	1.11756	0.558781	−	0.829315i	$-0.311269\pi$
$397$	1.33628e48	1.11756	0.558781	+	0.829315i	$0.311269\pi$
$398$	1.49920e48	1.19680
$399$	5.79202e46	0.0441399
$400$	0	0
$401$	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
$405$	0	0
$406$	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	$0.604518\pi$
$410$	0	0
$411$	8.82915e46	0.0388906
$412$	−2.17690e48	−0.916727
$413$	3.56257e47	0.143446
$414$	−5.64377e48	−2.17302
$415$	0	0
$416$	−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	$0.395964\pi$
$420$	0	0
$421$	−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
$425$	0	0
$426$	1.17116e47	0.0265789
$427$	−5.74940e48	−1.24941
$428$	−2.81650e47	−0.0586138
$429$	4.40263e44	8.77511e−5 0
$430$	0	0
$431$	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	$-0.563903\pi$
$433$	−2.37577e48	−0.398822	−0.199411	+	0.979916i	$0.563903\pi$
$434$	−6.11220e48	−0.983190
$435$	0	0
$436$	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	$0.548232\pi$
$440$	0	0
$441$	−4.86736e48	−0.582344
$442$	3.20665e47	0.0367908
$443$	1.52174e49	1.67444	0.837222	−	0.546864i	$-0.184178\pi$
$443$	1.52174e49	1.67444	0.837222	+	0.546864i	$0.184178\pi$
$444$	2.00771e47	0.0211893
$445$	0	0
$446$	−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	$0.190075\pi$
$450$	0	0
$451$	8.81436e47	0.0696506
$452$	−3.93949e48	−0.298799
$453$	4.97636e47	0.0362322
$454$	−1.87035e49	−1.30734
$455$	0	0
$456$	−2.26221e47	−0.0145775
$457$	−1.19646e49	−0.740367	−0.370183	−	0.928959i	$-0.620705\pi$
$457$	−1.19646e49	−0.740367	−0.370183	+	0.928959i	$0.620705\pi$
$458$	−1.59553e49	−0.948187
$459$	1.68471e48	0.0961591
$460$	0	0
$461$	−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	$-0.412303\pi$
$463$	1.11920e49	0.544075	0.272038	+	0.962287i	$0.412303\pi$
$464$	−5.73369e48	−0.267825
$465$	0	0
$466$	3.82250e49	1.64895
$467$	1.63248e49	0.676840	0.338420	−	0.940995i	$-0.390108\pi$
$467$	1.63248e49	0.676840	0.338420	+	0.940995i	$0.390108\pi$
$468$	−5.16702e47	−0.0205917
$469$	4.58106e49	1.75497
$470$	0	0
$471$	1.32067e48	0.0467637
$472$	−1.39145e48	−0.0473739
$473$	3.65622e47	0.0119702
$474$	−2.52321e48	−0.0794427
$475$	0	0
$476$	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	$0.388957\pi$
$480$	0	0
$481$	−7.66319e47	−0.0183961
$482$	7.14090e49	1.64962
$483$	−4.90585e48	−0.109067
$484$	−3.16453e49	−0.677127
$485$	0	0
$486$	−1.00712e49	−0.199668
$487$	7.78447e49	1.48574	0.742871	−	0.669435i	$-0.233464\pi$
$487$	7.78447e49	1.48574	0.742871	+	0.669435i	$0.233464\pi$
$488$	2.24556e49	0.412628
$489$	−2.59277e48	−0.0458723
$490$	0	0
$491$	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
$495$	0	0
$496$	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	$0.224013\pi$
$500$	0	0
$501$	−6.49741e48	−0.0734078
$502$	8.85871e49	0.964610
$503$	1.11020e50	1.16518	0.582589	−	0.812767i	$-0.302040\pi$
$503$	1.11020e50	1.16518	0.582589	+	0.812767i	$0.302040\pi$
$504$	5.15688e49	0.521702
$505$	0	0
$506$	−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	$0.698888\pi$
$510$	0	0
$511$	−5.07918e49	−0.398114
$512$	1.20327e50	0.909639
$513$	−9.60711e48	−0.0700521
$514$	1.40468e50	0.988007
$515$	0	0
$516$	1.14302e48	0.00748228
$517$	6.90952e47	0.00436388
$518$	−1.61970e50	−0.987041
$519$	1.03219e49	0.0606962
$520$	0	0
$521$	−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	$-0.392162\pi$
$523$	1.30285e50	0.664679	0.332340	+	0.943160i	$0.392162\pi$
$524$	−2.21188e50	−1.08926
$525$	0	0
$526$	1.95680e50	0.898070
$527$	−1.27081e50	−0.563098
$528$	−8.21803e47	−0.00351593
$529$	4.42241e50	1.82696
$530$	0	0
$531$	−2.95065e49	−0.113676
$532$	−1.56337e50	−0.581698
$533$	−1.05177e49	−0.0377977
$534$	−3.79315e48	−0.0131670
$535$	0	0
$536$	−1.78924e50	−0.579589
$537$	−1.19760e49	−0.0374789
$538$	−2.91307e50	−0.880804
$539$	−1.11943e49	−0.0327044
$540$	0	0
$541$	−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
$545$	0	0
$546$	−1.11037e48	−0.00255507
$547$	7.47732e49	0.166334	0.0831669	−	0.996536i	$-0.473497\pi$
$547$	7.47732e49	0.166334	0.0831669	+	0.996536i	$0.473497\pi$
$548$	−2.38315e50	−0.512520
$549$	4.76186e50	0.990121
$550$	0	0
$551$	−7.69761e49	−0.149641
$552$	1.91609e49	0.0360200
$553$	8.23388e50	1.49689
$554$	−1.12128e51	−1.97144
$555$	0	0
$556$	−5.96509e50	−0.981146
$557$	−3.60496e50	−0.573560	−0.286780	−	0.957996i	$-0.592585\pi$
$557$	−3.60496e50	−0.573560	−0.286780	+	0.957996i	$0.592585\pi$
$558$	5.06234e50	0.779146
$559$	−4.36275e48	−0.00649594
$560$	0	0
$561$	1.93474e48	0.00269655
$562$	−4.81071e50	−0.648764
$563$	3.94055e50	0.514223	0.257112	−	0.966382i	$-0.417229\pi$
$563$	3.94055e50	0.514223	0.257112	+	0.966382i	$0.417229\pi$
$564$	2.16007e48	0.00272775
$565$	0	0
$566$	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	$0.519590\pi$
$570$	0	0
$571$	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
$575$	0	0
$576$	3.36521e50	0.287870
$577$	−1.51306e51	−1.25344	−0.626722	−	0.779243i	$-0.715604\pi$
$577$	−1.51306e51	−1.25344	−0.626722	+	0.779243i	$0.715604\pi$
$578$	−2.06028e50	−0.165296
$579$	−4.44922e49	−0.0345725
$580$	0	0
$581$	7.79505e50	0.568278
$582$	1.17535e50	0.0830027
$583$	1.28206e50	0.0877079
$584$	1.98379e50	0.131480
$585$	0	0
$586$	−5.16213e50	−0.321161
$587$	−8.72797e50	−0.526148	−0.263074	−	0.964776i	$-0.584736\pi$
$587$	−8.72797e50	−0.526148	−0.263074	+	0.964776i	$0.584736\pi$
$588$	−3.49960e49	−0.0204427
$589$	7.24683e50	0.410218
$590$	0	0
$591$	1.27327e49	0.00676942
$592$	1.43042e51	0.737077
$593$	−4.58679e49	−0.0229085	−0.0114543	−	0.999934i	$-0.503646\pi$
$593$	−4.58679e49	−0.0229085	−0.0114543	+	0.999934i	$0.503646\pi$
$594$	−1.54348e49	−0.00747226
$595$	0	0
$596$	−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	$0.644033\pi$
$600$	0	0
$601$	−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
$605$	0	0
$606$	2.18259e50	0.0729841
$607$	4.33541e51	1.40618	0.703088	−	0.711103i	$-0.251804\pi$
$607$	4.33541e51	1.40618	0.703088	+	0.711103i	$0.251804\pi$
$608$	2.51436e51	0.791063
$609$	−4.67416e49	−0.0142654
$610$	0	0
$611$	−8.24472e48	−0.00236817
$612$	−2.27065e51	−0.632773
$613$	1.36136e51	0.368091	0.184046	−	0.982918i	$-0.441081\pi$
$613$	1.36136e51	0.368091	0.184046	+	0.982918i	$0.441081\pi$
$614$	6.78662e51	1.78049
$615$	0	0
$616$	1.18602e50	0.0292988
$617$	−3.77980e51	−0.906136	−0.453068	−	0.891476i	$-0.649671\pi$
$617$	−3.77980e51	−0.906136	−0.453068	+	0.891476i	$0.649671\pi$
$618$	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	$0.476394\pi$
$620$	0	0
$621$	8.13722e50	0.173094
$622$	5.82033e51	1.20178
$623$	1.23780e51	0.248097
$624$	9.80609e48	0.00190801
$625$	0	0
$626$	−4.16932e51	−0.764610
$627$	−1.10329e49	−0.00196445
$628$	−3.56474e51	−0.616275
$629$	−3.36759e51	−0.565304
$630$	0	0
$631$	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
$635$	0	0
$636$	4.00800e50	0.0548240
$637$	1.33575e50	0.0177479
$638$	−1.23670e50	−0.0159618
$639$	3.16534e51	0.396875
$640$	0	0
$641$	−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	$-0.624399\pi$
$643$	−6.82003e51	−0.761874	−0.380937	+	0.924601i	$0.624399\pi$
$644$	1.32418e52	1.43733
$645$	0	0
$646$	−8.03579e51	−0.823620
$647$	2.43296e51	0.242329	0.121165	−	0.992632i	$-0.461337\pi$
$647$	2.43296e51	0.242329	0.121165	+	0.992632i	$0.461337\pi$
$648$	−4.25971e51	−0.412328
$649$	−6.78614e49	−0.00638405
$650$	0	0
$651$	4.40044e50	0.0391064
$652$	6.99837e51	0.604528
$653$	−5.92349e51	−0.497375	−0.248687	−	0.968584i	$-0.579999\pi$
$653$	−5.92349e51	−0.497375	−0.248687	+	0.968584i	$0.579999\pi$
$654$	−5.07670e50	−0.0414375
$655$	0	0
$656$	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	$0.468646\pi$
$660$	0	0
$661$	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
$665$	0	0
$666$	1.34150e52	0.782198
$667$	6.51988e51	0.369753
$668$	1.75377e52	0.967404
$669$	1.38473e51	0.0742988
$670$	0	0
$671$	1.09517e51	0.0556051
$672$	1.52678e51	0.0754125
$673$	8.54768e50	0.0410742	0.0205371	−	0.999789i	$-0.493462\pi$
$673$	8.54768e50	0.0410742	0.0205371	+	0.999789i	$0.493462\pi$
$674$	−1.10408e52	−0.516168
$675$	0	0
$676$	−1.53337e52	−0.678630
$677$	3.33629e52	1.43673	0.718363	−	0.695669i	$-0.244892\pi$
$677$	3.33629e52	1.43673	0.718363	+	0.695669i	$0.244892\pi$
$678$	7.01167e50	0.0293814
$679$	−3.83547e52	−1.56397
$680$	0	0
$681$	1.34655e51	0.0519996
$682$	1.16428e51	0.0437568
$683$	−3.41377e52	−1.24868	−0.624340	−	0.781153i	$-0.714632\pi$
$683$	−3.41377e52	−1.24868	−0.624340	+	0.781153i	$0.714632\pi$
$684$	1.29484e52	0.460977
$685$	0	0
$686$	−2.01197e52	−0.678618
$687$	1.14869e51	0.0377142
$688$	8.14359e51	0.260273
$689$	−1.52980e51	−0.0475970
$690$	0	0
$691$	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
$695$	0	0
$696$	1.82560e50	0.00471124
$697$	−4.62198e52	−1.16151
$698$	6.43007e52	1.57359
$699$	−2.75199e51	−0.0655871
$700$	0	0
$701$	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
$705$	0	0
$706$	−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	$0.781457\pi$
$710$	0	0
$711$	−6.81960e52	−1.18624
$712$	−4.83452e51	−0.0819357
$713$	−6.13807e52	−1.01362
$714$	−4.87951e51	−0.0785162
$715$	0	0
$716$	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	$0.563888\pi$
$720$	0	0
$721$	−1.26436e53	−1.69851
$722$	−5.31442e52	−0.695853
$723$	−5.14105e51	−0.0656135
$724$	3.78717e52	0.471142
$725$	0	0
$726$	5.63236e51	0.0665830
$727$	−6.98427e52	−0.804886	−0.402443	−	0.915445i	$-0.631839\pi$
$727$	−6.98427e52	−0.804886	−0.402443	+	0.915445i	$0.631839\pi$
$728$	−1.41521e51	−0.0158997
$729$	−8.98455e52	−0.984095
$730$	0	0
$731$	−1.91721e52	−0.199618
$732$	3.42375e51	0.0347574
$733$	−3.54513e52	−0.350921	−0.175460	−	0.984487i	$-0.556141\pi$
$733$	−3.54513e52	−0.350921	−0.175460	+	0.984487i	$0.556141\pi$
$734$	−1.04152e53	−1.00529
$735$	0	0
$736$	−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	$0.276584\pi$
$740$	0	0
$741$	1.31649e50	0.00106606
$742$	−3.23341e53	−2.55381
$743$	−1.52901e53	−1.17793	−0.588964	−	0.808159i	$-0.700464\pi$
$743$	−1.52901e53	−1.17793	−0.588964	+	0.808159i	$0.700464\pi$
$744$	−1.71869e51	−0.0129151
$745$	0	0
$746$	−1.18916e53	−0.850296
$747$	−6.45615e52	−0.450342
$748$	−5.22221e51	−0.0355365
$749$	−1.63584e52	−0.108600
$750$	0	0
$751$	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
$755$	0	0
$756$	1.57461e52	0.0880075
$757$	2.82784e53	1.54234	0.771171	−	0.636628i	$-0.219671\pi$
$757$	2.82784e53	1.54234	0.771171	+	0.636628i	$0.219671\pi$
$758$	4.93559e52	0.262699
$759$	9.34487e50	0.00485401
$760$	0	0
$761$	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
$765$	0	0
$766$	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	$0.540023\pi$
$770$	0	0
$771$	−1.01129e52	−0.0392980
$772$	1.20093e53	0.455613
$773$	2.28656e53	0.846960	0.423480	−	0.905905i	$-0.360808\pi$
$773$	2.28656e53	0.846960	0.423480	+	0.905905i	$0.360808\pi$
$774$	7.63732e52	0.276206
$775$	0	0
$776$	1.49803e53	0.516510
$777$	1.16610e52	0.0392596
$778$	−5.59277e53	−1.83867
$779$	2.63570e53	0.846161
$780$	0	0
$781$	7.27989e51	0.0222885
$782$	6.80632e53	2.03511
$783$	7.75294e51	0.0226399
$784$	−2.49334e53	−0.711106
$785$	0	0
$786$	3.93679e52	0.107109
$787$	−7.05791e52	−0.187561	−0.0937807	−	0.995593i	$-0.529895\pi$
$787$	−7.05791e52	−0.187561	−0.0937807	+	0.995593i	$0.529895\pi$
$788$	−3.43678e52	−0.0892108
$789$	−1.40879e52	−0.0357207
$790$	0	0
$791$	−2.28809e53	−0.553614
$792$	−9.82306e51	−0.0232183
$793$	−1.30680e52	−0.0301756
$794$	6.41963e53	1.44821
$795$	0	0
$796$	2.91333e53	0.627334
$797$	8.88567e53	1.86944	0.934719	−	0.355387i	$-0.115651\pi$
$797$	8.88567e53	1.86944	0.934719	+	0.355387i	$0.115651\pi$
$798$	2.78256e52	0.0571993
$799$	−3.62314e52	−0.0727729
$800$	0	0
$801$	−1.02519e53	−0.196609
$802$	1.22028e53	0.228683
$803$	9.67504e51	0.0177180
$804$	−2.72801e52	−0.0488213
$805$	0	0
$806$	−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	$0.404019\pi$
$810$	0	0
$811$	−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
$815$	0	0
$816$	4.30929e52	0.0586324
$817$	1.09330e53	0.145422
$818$	−6.42736e53	−0.835788
$819$	−3.00104e52	−0.0381522
$820$	0	0
$821$	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	$-0.709108\pi$
$823$	−1.05135e54	−1.22138	−0.610692	+	0.791869i	$0.709108\pi$
$824$	4.93825e53	0.560945
$825$	0	0
$826$	1.71150e53	0.185886
$827$	1.54483e53	0.164069	0.0820347	−	0.996629i	$-0.473858\pi$
$827$	1.54483e53	0.164069	0.0820347	+	0.996629i	$0.473858\pi$
$828$	−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	$0.456229\pi$
$830$	0	0
$831$	8.07259e52	0.0784141
$832$	−9.23518e51	−0.00877332
$833$	5.86997e53	0.545385
$834$	1.06169e53	0.0964776
$835$	0	0
$836$	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	$0.0457561\pi$
$840$	0	0
$841$	−1.22236e54	−0.951638
$842$	−2.12428e54	−1.61785
$843$	3.46344e52	0.0258046
$844$	−7.07677e53	−0.515822
$845$	0	0
$846$	1.44330e53	0.100694
$847$	−1.83798e54	−1.25458
$848$	2.85555e54	1.90707
$849$	−9.46656e52	−0.0618586
$850$	0	0
$851$	−1.62656e54	−1.01759
$852$	2.27586e52	0.0139320
$853$	−9.59321e53	−0.574654	−0.287327	−	0.957832i	$-0.592767\pi$
$853$	−9.59321e53	−0.574654	−0.287327	+	0.957832i	$0.592767\pi$
$854$	−2.76208e54	−1.61907
$855$	0	0
$856$	6.38917e52	0.0358657
$857$	−3.59352e52	−0.0197413	−0.00987063	−	0.999951i	$-0.503142\pi$
$857$	−3.59352e52	−0.0197413	−0.00987063	+	0.999951i	$0.503142\pi$
$858$	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	$0.427732\pi$
$860$	0	0
$861$	1.60046e53	0.0806651
$862$	1.61983e54	0.799068
$863$	−1.56057e54	−0.753502	−0.376751	−	0.926315i	$-0.622959\pi$
$863$	−1.56057e54	−0.753502	−0.376751	+	0.926315i	$0.622959\pi$
$864$	−2.53243e53	−0.119683
$865$	0	0
$866$	−1.14135e54	−0.516818
$867$	1.48329e52	0.00657464
$868$	−1.18776e54	−0.515363
$869$	−1.56842e53	−0.0666190
$870$	0	0
$871$	1.04125e53	0.0423855
$872$	−6.47046e53	−0.257858
$873$	3.17667e54	1.23939
$874$	−3.88132e54	−1.48258
$875$	0	0
$876$	3.02464e52	0.0110751
$877$	3.37270e54	1.20916	0.604581	−	0.796544i	$-0.293341\pi$
$877$	3.37270e54	1.20916	0.604581	+	0.796544i	$0.293341\pi$
$878$	−1.11444e54	−0.391208
$879$	3.71644e52	0.0127742
$880$	0	0
$881$	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	$-0.572037\pi$
$883$	−1.42002e54	−0.448767	−0.224383	+	0.974501i	$0.572037\pi$
$884$	6.23135e52	0.0192848
$885$	0	0
$886$	7.31060e54	2.16985
$887$	−1.98874e54	−0.578085	−0.289042	−	0.957316i	$-0.593337\pi$
$887$	−1.98874e54	−0.578085	−0.289042	+	0.957316i	$0.593337\pi$
$888$	−4.55446e52	−0.0129657
$889$	−5.94580e54	−1.65778
$890$	0	0
$891$	−2.07748e53	−0.0555647
$892$	−3.73764e54	−0.979147
$893$	2.06611e53	0.0530153
$894$	5.79955e52	0.0145764
$895$	0	0
$896$	4.11502e54	0.992370
$897$	−1.11507e52	−0.00263415
$898$	9.26145e54	2.14322
$899$	−5.84819e53	−0.132577
$900$	0	0
$901$	−6.72271e54	−1.46263
$902$	4.23452e53	0.0902575
$903$	6.63874e52	0.0138632
$904$	8.93665e53	0.182835
$905$	0	0
$906$	2.39070e53	0.0469520
$907$	6.36503e54	1.22480	0.612401	−	0.790547i	$-0.290204\pi$
$907$	6.36503e54	1.22480	0.612401	+	0.790547i	$0.290204\pi$
$908$	−3.63458e54	−0.685276
$909$	5.89899e54	1.08980
$910$	0	0
$911$	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
$915$	0	0
$916$	−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	$0.693733\pi$
$920$	0	0
$921$	−4.88598e53	−0.0708189
$922$	−1.33818e55	−1.90105
$923$	−8.68666e52	−0.0120954
$924$	1.80830e52	0.00246796
$925$	0	0
$926$	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	$0.487120\pi$
$930$	0	0
$931$	−3.34737e54	−0.397314
$932$	7.42812e54	0.864340
$933$	−4.19031e53	−0.0478009
$934$	7.84263e54	0.877091
$935$	0	0
$936$	1.17213e53	0.0126000
$937$	3.87596e54	0.408505	0.204253	−	0.978918i	$-0.434524\pi$
$937$	3.87596e54	0.408505	0.204253	+	0.978918i	$0.434524\pi$
$938$	2.20080e55	2.27419
$939$	3.00168e53	0.0304124
$940$	0	0
$941$	−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
$945$	0	0
$946$	1.75649e53	0.0155117
$947$	8.86598e53	0.0767807	0.0383903	−	0.999263i	$-0.487777\pi$
$947$	8.86598e53	0.0767807	0.0383903	+	0.999263i	$0.487777\pi$
$948$	−4.90325e53	−0.0416419
$949$	−1.15447e53	−0.00961515
$950$	0	0
$951$	−8.10776e53	−0.0649473
$952$	−6.21913e54	−0.488592
$953$	−1.94425e55	−1.49807	−0.749036	−	0.662530i	$-0.769483\pi$
$953$	−1.94425e55	−1.49807	−0.749036	+	0.662530i	$0.769483\pi$
$954$	2.67803e55	2.02381
$955$	0	0
$956$	−1.32791e55	−0.965382
$957$	8.90355e51	0.000634881 0
$958$	1.26662e55	0.885902
$959$	−1.38415e55	−0.949597
$960$	0	0
$961$	−9.64324e54	−0.636561
$962$	−3.68148e53	−0.0238388
$963$	1.35486e54	0.0860616
$964$	1.38766e55	0.864687
$965$	0	0
$966$	−2.35683e54	−0.141335
$967$	−6.67380e54	−0.392630	−0.196315	−	0.980541i	$-0.562897\pi$
$967$	−6.67380e54	−0.392630	−0.196315	+	0.980541i	$0.562897\pi$
$968$	7.17867e54	0.414333
$969$	5.78532e53	0.0327595
$970$	0	0
$971$	−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
$975$	0	0
$976$	2.43930e55	1.20905
$977$	6.49911e54	0.316085	0.158043	−	0.987432i	$-0.449482\pi$
$977$	6.49911e54	0.316085	0.158043	+	0.987432i	$0.449482\pi$
$978$	−1.24560e54	−0.0594441
$979$	−2.35782e53	−0.0110416
$980$	0	0
$981$	−1.37210e55	−0.618743
$982$	4.73341e55	2.09465
$983$	−1.39076e55	−0.603967	−0.301984	−	0.953313i	$-0.597649\pi$
$983$	−1.39076e55	−0.603967	−0.301984	+	0.953313i	$0.597649\pi$
$984$	−6.25095e53	−0.0266402
$985$	0	0
$986$	6.48488e54	0.266182
$987$	1.25459e53	0.00505398
$988$	−3.55345e53	−0.0140490
$989$	−9.26022e54	−0.359327
$990$	0	0
$991$	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
$995$	0	0
$996$	−4.64193e53	−0.0158089
$997$	3.24811e55	1.08585	0.542925	−	0.839781i	$-0.317317\pi$
$997$	3.24811e55	1.08585	0.542925	+	0.839781i	$0.317317\pi$
$998$	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	25.38.a.a.1.2		2
5.2	odd	4		25.38.b.a.24.4		4
5.3	odd	4		25.38.b.a.24.1		4
5.4	even	2		1.38.a.a.1.1	✓	2
15.14	odd	2		9.38.a.a.1.2		2
20.19	odd	2		16.38.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.38.a.a.1.1	✓	2	5.4	even	2
9.38.a.a.1.2		2	15.14	odd	2
16.38.a.b.1.1		2	20.19	odd	2
25.38.a.a.1.2		2	1.1	even	1	trivial
25.38.b.a.24.1		4	5.3	odd	4
25.38.b.a.24.4		4	5.2	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

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

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