LMFDB - Embedded newform 25.38.a.a.1.1

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			1.1
Root			$3992.29$ 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)

$f(q)$	$=$	$q-286012. q^{2} +2.05955e7 q^{3} -5.56362e10 q^{4} -5.89057e12 q^{6} -1.97377e15 q^{7} +5.52218e16 q^{8} -4.49860e17 q^{9} +O(q^{10})$	\(q-286012. q^{2} +2.05955e7 q^{3} -5.56362e10 q^{4} -5.89057e12 q^{6} -1.97377e15 q^{7} +5.52218e16 q^{8} -4.49860e17 q^{9} -2.57012e19 q^{11} -1.14586e18 q^{12} -5.42906e20 q^{13} +5.64522e20 q^{14} -8.14749e21 q^{16} +3.52797e22 q^{17} +1.28665e23 q^{18} +6.82122e23 q^{19} -4.06509e22 q^{21} +7.35084e24 q^{22} +8.19547e22 q^{23} +1.13732e24 q^{24} +1.55278e26 q^{26} -1.85389e25 q^{27} +1.09813e26 q^{28} -1.51991e27 q^{29} +2.60785e27 q^{31} -5.25934e27 q^{32} -5.29330e26 q^{33} -1.00904e28 q^{34} +2.50285e28 q^{36} +1.30205e29 q^{37} -1.95095e29 q^{38} -1.11814e28 q^{39} -4.07079e29 q^{41} +1.16266e28 q^{42} +2.92424e30 q^{43} +1.42992e30 q^{44} -2.34400e28 q^{46} -3.58323e30 q^{47} -1.67802e29 q^{48} -1.46663e31 q^{49} +7.26605e29 q^{51} +3.02052e31 q^{52} -3.56714e31 q^{53} +5.30236e30 q^{54} -1.08995e32 q^{56} +1.40487e31 q^{57} +4.34713e32 q^{58} -3.03666e32 q^{59} +1.16214e33 q^{61} -7.45875e32 q^{62} +8.87921e32 q^{63} +2.62402e33 q^{64} +1.51395e32 q^{66} +2.44324e33 q^{67} -1.96283e33 q^{68} +1.68790e30 q^{69} +6.30224e33 q^{71} -2.48421e34 q^{72} -1.02725e34 q^{73} -3.72400e34 q^{74} -3.79507e34 q^{76} +5.07283e34 q^{77} +3.19803e33 q^{78} +1.20547e35 q^{79} +2.02183e35 q^{81} +1.16430e35 q^{82} +3.26699e35 q^{83} +2.26166e33 q^{84} -8.36366e35 q^{86} -3.13034e34 q^{87} -1.41927e36 q^{88} -1.56115e36 q^{89} +1.07157e36 q^{91} -4.55965e33 q^{92} +5.37100e34 q^{93} +1.02485e36 q^{94} -1.08319e35 q^{96} +1.07155e36 q^{97} +4.19474e36 q^{98} +1.15619e37 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−286012.	−0.771488	−0.385744	−	0.922606i	$-0.626055\pi$
$2$	−286012.	−0.771488	−0.385744	+	0.922606i	$0.626055\pi$
$3$	2.05955e7	0.0306923	0.0153462	−	0.999882i	$-0.495115\pi$
$3$	2.05955e7	0.0306923	0.0153462	+	0.999882i	$0.495115\pi$
$4$	−5.56362e10	−0.404807
$5$	0	0
$5$	0	0
$6$	−5.89057e12	−0.0236788
$7$	−1.97377e15	−0.458124	−0.229062	−	0.973412i	$-0.573566\pi$
$7$	−1.97377e15	−0.458124	−0.229062	+	0.973412i	$0.573566\pi$
$8$	5.52218e16	1.08379
$9$	−4.49860e17	−0.999058
$10$	0	0
$11$	−2.57012e19	−1.39376	−0.696881	−	0.717187i	$-0.745429\pi$
$11$	−2.57012e19	−1.39376	−0.696881	+	0.717187i	$0.745429\pi$
$12$	−1.14586e18	−0.0124245
$13$	−5.42906e20	−1.33898	−0.669488	−	0.742823i	$-0.733486\pi$
$13$	−5.42906e20	−1.33898	−0.669488	+	0.742823i	$0.733486\pi$
$14$	5.64522e20	0.353437
$15$	0	0
$16$	−8.14749e21	−0.431325
$17$	3.52797e22	0.608443	0.304221	−	0.952601i	$-0.401604\pi$
$17$	3.52797e22	0.608443	0.304221	+	0.952601i	$0.401604\pi$
$18$	1.28665e23	0.770761
$19$	6.82122e23	1.50287	0.751433	−	0.659809i	$-0.229363\pi$
$19$	6.82122e23	1.50287	0.751433	+	0.659809i	$0.229363\pi$
$20$	0	0
$21$	−4.06509e22	−0.0140609
$22$	7.35084e24	1.07527
$23$	8.19547e22	0.00526755	0.00263378	−	0.999997i	$-0.499162\pi$
$23$	8.19547e22	0.00526755	0.00263378	+	0.999997i	$0.499162\pi$
$24$	1.13732e24	0.0332641
$25$	0	0
$26$	1.55278e26	1.03300
$27$	−1.85389e25	−0.0613558
$28$	1.09813e26	0.185452
$29$	−1.51991e27	−1.34108	−0.670541	−	0.741872i	$-0.733938\pi$
$29$	−1.51991e27	−1.34108	−0.670541	+	0.741872i	$0.733938\pi$
$30$	0	0
$31$	2.60785e27	0.670025	0.335012	−	0.942214i	$-0.391260\pi$
$31$	2.60785e27	0.670025	0.335012	+	0.942214i	$0.391260\pi$
$32$	−5.25934e27	−0.751030
$33$	−5.29330e26	−0.0427778
$34$	−1.00904e28	−0.469406
$35$	0	0
$36$	2.50285e28	0.404426
$37$	1.30205e29	1.26734	0.633672	−	0.773602i	$-0.281547\pi$
$37$	1.30205e29	1.26734	0.633672	+	0.773602i	$0.281547\pi$
$38$	−1.95095e29	−1.15944
$39$	−1.11814e28	−0.0410963
$40$	0	0
$41$	−4.07079e29	−0.593168	−0.296584	−	0.955007i	$-0.595847\pi$
$41$	−4.07079e29	−0.593168	−0.296584	+	0.955007i	$0.595847\pi$
$42$	1.16266e28	0.0108478
$43$	2.92424e30	1.76541	0.882706	−	0.469926i	$-0.155719\pi$
$43$	2.92424e30	1.76541	0.882706	+	0.469926i	$0.155719\pi$
$44$	1.42992e30	0.564204
$45$	0	0
$46$	−2.34400e28	−0.00406385
$47$	−3.58323e30	−0.417315	−0.208658	−	0.977989i	$-0.566909\pi$
$47$	−3.58323e30	−0.417315	−0.208658	+	0.977989i	$0.566909\pi$
$48$	−1.67802e29	−0.0132384
$49$	−1.46663e31	−0.790122
$50$	0	0
$51$	7.26605e29	0.0186745
$52$	3.02052e31	0.542027
$53$	−3.56714e31	−0.450005	−0.225002	−	0.974358i	$-0.572239\pi$
$53$	−3.56714e31	−0.450005	−0.225002	+	0.974358i	$0.572239\pi$
$54$	5.30236e30	0.0473352
$55$	0	0
$56$	−1.08995e32	−0.496511
$57$	1.40487e31	0.0461265
$58$	4.34713e32	1.03463
$59$	−3.03666e32	−0.526785	−0.263393	−	0.964689i	$-0.584841\pi$
$59$	−3.03666e32	−0.526785	−0.263393	+	0.964689i	$0.584841\pi$
$60$	0	0
$61$	1.16214e33	1.08807	0.544034	−	0.839063i	$-0.316896\pi$
$61$	1.16214e33	1.08807	0.544034	+	0.839063i	$0.316896\pi$
$62$	−7.45875e32	−0.516916
$63$	8.87921e32	0.457693
$64$	2.62402e33	1.01073
$65$	0	0
$66$	1.51395e32	0.0330026
$67$	2.44324e33	0.403257	0.201628	−	0.979462i	$-0.435377\pi$
$67$	2.44324e33	0.403257	0.201628	+	0.979462i	$0.435377\pi$
$68$	−1.96283e33	−0.246302
$69$	1.68790e30	0.000161673 0
$70$	0	0
$71$	6.30224e33	0.355808	0.177904	−	0.984048i	$-0.443068\pi$
$71$	6.30224e33	0.355808	0.177904	+	0.984048i	$0.443068\pi$
$72$	−2.48421e34	−1.08277
$73$	−1.02725e34	−0.346899	−0.173450	−	0.984843i	$-0.555491\pi$
$73$	−1.02725e34	−0.346899	−0.173450	+	0.984843i	$0.555491\pi$
$74$	−3.72400e34	−0.977740
$75$	0	0
$76$	−3.79507e34	−0.608371
$77$	5.07283e34	0.638516
$78$	3.19803e33	0.0317053
$79$	1.20547e35	0.944182	0.472091	−	0.881550i	$-0.343499\pi$
$79$	1.20547e35	0.944182	0.472091	+	0.881550i	$0.343499\pi$
$80$	0	0
$81$	2.02183e35	0.997175
$82$	1.16430e35	0.457622
$83$	3.26699e35	1.02613	0.513066	−	0.858349i	$-0.328510\pi$
$83$	3.26699e35	1.02613	0.513066	+	0.858349i	$0.328510\pi$
$84$	2.26166e33	0.00569195
$85$	0	0
$86$	−8.36366e35	−1.36199
$87$	−3.13034e34	−0.0411610
$88$	−1.41927e36	−1.51055
$89$	−1.56115e36	−1.34812	−0.674062	−	0.738674i	$-0.735452\pi$
$89$	−1.56115e36	−1.34812	−0.674062	+	0.738674i	$0.735452\pi$
$90$	0	0
$91$	1.07157e36	0.613418
$92$	−4.55965e33	−0.00213234
$93$	5.37100e34	0.0205646
$94$	1.02485e36	0.321954
$95$	0	0
$96$	−1.08319e35	−0.0230509
$97$	1.07155e36	0.188251	0.0941254	−	0.995560i	$-0.469995\pi$
$97$	1.07155e36	0.188251	0.0941254	+	0.995560i	$0.469995\pi$
$98$	4.19474e36	0.609569
$99$	1.15619e37	1.39245
$100$	0	0
$101$	1.29521e37	1.07744	0.538721	−	0.842484i	$-0.318908\pi$
$101$	1.29521e37	1.07744	0.538721	+	0.842484i	$0.318908\pi$
$102$	−2.07817e35	−0.0144072
$103$	3.39568e36	0.196534	0.0982672	−	0.995160i	$-0.468670\pi$
$103$	3.39568e36	0.196534	0.0982672	+	0.995160i	$0.468670\pi$
$104$	−2.99802e37	−1.45117
$105$	0	0
$106$	1.02025e37	0.347173
$107$	1.58608e37	0.453653	0.226827	−	0.973935i	$-0.427165\pi$
$107$	1.58608e37	0.453653	0.226827	+	0.973935i	$0.427165\pi$
$108$	1.03144e36	0.0248372
$109$	−1.06858e36	−0.0216978	−0.0108489	−	0.999941i	$-0.503453\pi$
$109$	−1.06858e36	−0.0216978	−0.0108489	+	0.999941i	$0.503453\pi$
$110$	0	0
$111$	2.68163e36	0.0388977
$112$	1.60813e37	0.197600
$113$	−1.64170e37	−0.171136	−0.0855682	−	0.996332i	$-0.527271\pi$
$113$	−1.64170e37	−0.171136	−0.0855682	+	0.996332i	$0.527271\pi$
$114$	−4.01809e36	−0.0355860
$115$	0	0
$116$	8.45622e37	0.542879
$117$	2.44232e38	1.33771
$118$	8.68520e37	0.406408
$119$	−6.96341e37	−0.278743
$120$	0	0
$121$	3.20512e38	0.942572
$122$	−3.32386e38	−0.839432
$123$	−8.38402e36	−0.0182057
$124$	−1.45091e38	−0.271231
$125$	0	0
$126$	−2.53956e38	−0.353104
$127$	1.42456e39	1.71124	0.855619	−	0.517606i	$-0.173177\pi$
$127$	1.42456e39	1.71124	0.855619	+	0.517606i	$0.173177\pi$
$128$	−2.76609e37	−0.0287397
$129$	6.02262e37	0.0541846
$130$	0	0
$131$	2.12044e39	1.43518	0.717590	−	0.696466i	$-0.245245\pi$
$131$	2.12044e39	1.43518	0.717590	+	0.696466i	$0.245245\pi$
$132$	2.94499e37	0.0173168
$133$	−1.34635e39	−0.688500
$134$	−6.98795e38	−0.311108
$135$	0	0
$136$	1.94821e39	0.659425
$137$	1.25855e39	0.371999	0.185999	−	0.982550i	$-0.440448\pi$
$137$	1.25855e39	0.371999	0.185999	+	0.982550i	$0.440448\pi$
$138$	−4.82760e35	−0.000124729 0
$139$	−3.12966e39	−0.707494	−0.353747	−	0.935341i	$-0.615093\pi$
$139$	−3.12966e39	−0.707494	−0.353747	+	0.935341i	$0.615093\pi$
$140$	0	0
$141$	−7.37986e37	−0.0128084
$142$	−1.80251e39	−0.274501
$143$	1.39533e40	1.86621
$144$	3.66523e39	0.430918
$145$	0	0
$146$	2.93806e39	0.267628
$147$	−3.02061e38	−0.0242507
$148$	−7.24409e39	−0.513029
$149$	2.99066e39	0.186991	0.0934956	−	0.995620i	$-0.470196\pi$
$149$	2.99066e39	0.186991	0.0934956	+	0.995620i	$0.470196\pi$
$150$	0	0
$151$	−7.06984e39	−0.345411	−0.172706	−	0.984973i	$-0.555251\pi$
$151$	−7.06984e39	−0.345411	−0.172706	+	0.984973i	$0.555251\pi$
$152$	3.76680e40	1.62879
$153$	−1.58709e40	−0.607870
$154$	−1.45089e40	−0.492607
$155$	0	0
$156$	6.22094e38	0.0166361
$157$	−7.04676e40	−1.67435	−0.837174	−	0.546937i	$-0.815794\pi$
$157$	−7.04676e40	−1.67435	−0.837174	+	0.546937i	$0.815794\pi$
$158$	−3.44779e40	−0.728425
$159$	−7.34673e38	−0.0138117
$160$	0	0
$161$	−1.61760e38	−0.00241319
$162$	−5.78267e40	−0.769308
$163$	8.16698e40	0.969596	0.484798	−	0.874626i	$-0.338893\pi$
$163$	8.16698e40	0.969596	0.484798	+	0.874626i	$0.338893\pi$
$164$	2.26484e40	0.240119
$165$	0	0
$166$	−9.34397e40	−0.791648
$167$	3.94031e40	0.298728	0.149364	−	0.988782i	$-0.452277\pi$
$167$	3.94031e40	0.298728	0.149364	+	0.988782i	$0.452277\pi$
$168$	−2.24482e39	−0.0152391
$169$	1.30346e41	0.792856
$170$	0	0
$171$	−3.06859e41	−1.50145
$172$	−1.62693e41	−0.714651
$173$	−2.61566e41	−1.03212	−0.516058	−	0.856554i	$-0.672601\pi$
$173$	−2.61566e41	−1.03212	−0.516058	+	0.856554i	$0.672601\pi$
$174$	8.95315e39	0.0317552
$175$	0	0
$176$	2.09400e41	0.601164
$177$	−6.25416e39	−0.0161683
$178$	4.46508e41	1.04006
$179$	−4.21879e41	−0.885946	−0.442973	−	0.896535i	$-0.646076\pi$
$179$	−4.21879e41	−0.885946	−0.442973	+	0.896535i	$0.646076\pi$
$180$	0	0
$181$	−9.51260e40	−0.162647	−0.0813234	−	0.996688i	$-0.525915\pi$
$181$	−9.51260e40	−0.162647	−0.0813234	+	0.996688i	$0.525915\pi$
$182$	−3.06483e41	−0.473244
$183$	2.39349e40	0.0333954
$184$	4.52568e39	0.00570892
$185$	0	0
$186$	−1.53617e40	−0.0158654
$187$	−9.06730e41	−0.848024
$188$	1.99357e41	0.168932
$189$	3.65917e40	0.0281086
$190$	0	0
$191$	−2.61439e41	−0.165292	−0.0826462	−	0.996579i	$-0.526337\pi$
$191$	−2.61439e41	−0.165292	−0.0826462	+	0.996579i	$0.526337\pi$
$192$	5.40431e40	0.0310218
$193$	6.27072e41	0.326969	0.163485	−	0.986546i	$-0.447727\pi$
$193$	6.27072e41	0.326969	0.163485	+	0.986546i	$0.447727\pi$
$194$	−3.06477e41	−0.145233
$195$	0	0
$196$	8.15980e41	0.319847
$197$	1.81081e42	0.646021	0.323010	−	0.946395i	$-0.395305\pi$
$197$	1.81081e42	0.646021	0.323010	+	0.946395i	$0.395305\pi$
$198$	−3.30685e42	−1.07426
$199$	−3.78123e41	−0.111906	−0.0559528	−	0.998433i	$-0.517820\pi$
$199$	−3.78123e41	−0.111906	−0.0559528	+	0.998433i	$0.517820\pi$
$200$	0	0
$201$	5.03198e40	0.0123769
$202$	−3.70445e42	−0.831233
$203$	2.99996e42	0.614383
$204$	−4.04255e40	−0.00755958
$205$	0	0
$206$	−9.71205e41	−0.151624
$207$	−3.68681e40	−0.00526259
$208$	4.42332e42	0.577533
$209$	−1.75313e43	−2.09464
$210$	0	0
$211$	1.66783e43	1.67081	0.835404	−	0.549637i	$-0.185234\pi$
$211$	1.66783e43	1.67081	0.835404	+	0.549637i	$0.185234\pi$
$212$	1.98462e42	0.182165
$213$	1.29798e41	0.0109206
$214$	−4.53636e42	−0.349988
$215$	0	0
$216$	−1.02375e42	−0.0664968
$217$	−5.14730e42	−0.306955
$218$	3.05626e41	0.0167396
$219$	−2.11568e41	−0.0106472
$220$	0	0
$221$	−1.91536e43	−0.814690
$222$	−7.66979e41	−0.0300091
$223$	3.60083e43	1.29647	0.648236	−	0.761439i	$-0.275507\pi$
$223$	3.60083e43	1.29647	0.648236	+	0.761439i	$0.275507\pi$
$224$	1.03808e43	0.344065
$225$	0	0
$226$	4.69546e42	0.132030
$227$	−6.76307e43	−1.75253	−0.876265	−	0.481830i	$-0.839972\pi$
$227$	−6.76307e43	−1.75253	−0.876265	+	0.481830i	$0.839972\pi$
$228$	−7.81615e41	−0.0186723
$229$	−5.09302e43	−1.12207	−0.561033	−	0.827793i	$-0.689596\pi$
$229$	−5.09302e43	−1.12207	−0.561033	+	0.827793i	$0.689596\pi$
$230$	0	0
$231$	1.04478e42	0.0195976
$232$	−8.39322e43	−1.45345
$233$	−1.79375e43	−0.286865	−0.143432	−	0.989660i	$-0.545814\pi$
$233$	−1.79375e43	−0.286865	−0.143432	+	0.989660i	$0.545814\pi$
$234$	−6.98531e43	−1.03203
$235$	0	0
$236$	1.68948e43	0.213246
$237$	2.48273e42	0.0289792
$238$	1.99162e43	0.215046
$239$	−2.86950e43	−0.286711	−0.143356	−	0.989671i	$-0.545789\pi$
$239$	−2.86950e43	−0.286711	−0.143356	+	0.989671i	$0.545789\pi$
$240$	0	0
$241$	−1.12255e44	−0.961372	−0.480686	−	0.876893i	$-0.659612\pi$
$241$	−1.12255e44	−0.961372	−0.480686	+	0.876893i	$0.659612\pi$
$242$	−9.16701e43	−0.727182
$243$	1.25119e43	0.0919614
$244$	−6.46571e43	−0.440458
$245$	0	0
$246$	2.39793e42	0.0140455
$247$	−3.70328e44	−2.01230
$248$	1.44010e44	0.726167
$249$	6.72854e42	0.0314944
$250$	0	0
$251$	−4.02278e44	−1.62391	−0.811955	−	0.583720i	$-0.801597\pi$
$251$	−4.02278e44	−1.62391	−0.811955	+	0.583720i	$0.801597\pi$
$252$	−4.94006e43	−0.185277
$253$	−2.10633e42	−0.00734171
$254$	−4.07440e44	−1.32020
$255$	0	0
$256$	−3.52731e44	−0.988562
$257$	−5.42969e44	−1.41583	−0.707917	−	0.706296i	$-0.750365\pi$
$257$	−5.42969e44	−1.41583	−0.707917	+	0.706296i	$0.750365\pi$
$258$	−1.72254e43	−0.0418028
$259$	−2.56994e44	−0.580601
$260$	0	0
$261$	6.83747e44	1.33982
$262$	−6.06470e44	−1.10722
$263$	7.98181e44	1.35806	0.679031	−	0.734109i	$-0.262400\pi$
$263$	7.98181e44	1.35806	0.679031	+	0.734109i	$0.262400\pi$
$264$	−2.92305e43	−0.0463622
$265$	0	0
$266$	3.85073e44	0.531169
$267$	−3.21528e43	−0.0413771
$268$	−1.35933e44	−0.163241
$269$	−1.02189e45	−1.14548	−0.572739	−	0.819738i	$-0.694119\pi$
$269$	−1.02189e45	−1.14548	−0.572739	+	0.819738i	$0.694119\pi$
$270$	0	0
$271$	−2.63101e44	−0.257152	−0.128576	−	0.991700i	$-0.541041\pi$
$271$	−2.63101e44	−0.257152	−0.128576	+	0.991700i	$0.541041\pi$
$272$	−2.87441e44	−0.262436
$273$	2.20696e43	0.0188272
$274$	−3.59961e44	−0.286992
$275$	0	0
$276$	−9.39085e40	−6.54465e−5 0
$277$	−1.60882e45	−1.04865	−0.524327	−	0.851517i	$-0.675683\pi$
$277$	−1.60882e45	−1.04865	−0.524327	+	0.851517i	$0.675683\pi$
$278$	8.95119e44	0.545823
$279$	−1.17317e45	−0.669393
$280$	0	0
$281$	2.86236e45	1.43106	0.715529	−	0.698583i	$-0.246186\pi$
$281$	2.86236e45	1.43106	0.715529	+	0.698583i	$0.246186\pi$
$282$	2.11073e43	0.00988151
$283$	−7.97480e44	−0.349680	−0.174840	−	0.984597i	$-0.555941\pi$
$283$	−7.97480e44	−0.349680	−0.174840	+	0.984597i	$0.555941\pi$
$284$	−3.50633e44	−0.144033
$285$	0	0
$286$	−3.99082e45	−1.43976
$287$	8.03482e44	0.271745
$288$	2.36597e45	0.750322
$289$	−2.11744e45	−0.629797
$290$	0	0
$291$	2.20692e43	0.00577786
$292$	5.71523e44	0.140427
$293$	−5.17198e44	−0.119290	−0.0596452	−	0.998220i	$-0.518997\pi$
$293$	−5.17198e44	−0.119290	−0.0596452	+	0.998220i	$0.518997\pi$
$294$	8.63931e43	0.0187091
$295$	0	0
$296$	7.19013e45	1.37354
$297$	4.76473e44	0.0855153
$298$	−8.55364e44	−0.144261
$299$	−4.44937e43	−0.00705312
$300$	0	0
$301$	−5.77178e45	−0.808778
$302$	2.02206e45	0.266480
$303$	2.66755e44	0.0330692
$304$	−5.55758e45	−0.648223
$305$	0	0
$306$	4.53927e45	0.468964
$307$	−9.59117e45	−0.932850	−0.466425	−	0.884561i	$-0.654458\pi$
$307$	−9.59117e45	−0.932850	−0.466425	+	0.884561i	$0.654458\pi$
$308$	−2.82233e45	−0.258476
$309$	6.99360e43	0.00603210
$310$	0	0
$311$	−5.05857e45	−0.387222	−0.193611	−	0.981078i	$-0.562020\pi$
$311$	−5.05857e45	−0.387222	−0.193611	+	0.981078i	$0.562020\pi$
$312$	−6.17459e44	−0.0445398
$313$	−5.12462e45	−0.348410	−0.174205	−	0.984709i	$-0.555736\pi$
$313$	−5.12462e45	−0.348410	−0.174205	+	0.984709i	$0.555736\pi$
$314$	2.01546e46	1.29174
$315$	0	0
$316$	−6.70679e45	−0.382211
$317$	2.14514e46	1.15308	0.576541	−	0.817068i	$-0.304402\pi$
$317$	2.14514e46	1.15308	0.576541	+	0.817068i	$0.304402\pi$
$318$	2.10125e44	0.0106556
$319$	3.90635e46	1.86915
$320$	0	0
$321$	3.26661e44	0.0139237
$322$	4.62652e43	0.00186175
$323$	2.40651e46	0.914408
$324$	−1.12487e46	−0.403663
$325$	0	0
$326$	−2.33585e46	−0.748032
$327$	−2.20080e43	−0.000665958 0
$328$	−2.24796e46	−0.642870
$329$	7.07248e45	0.191182
$330$	0	0
$331$	1.85276e46	0.447714	0.223857	−	0.974622i	$-0.428135\pi$
$331$	1.85276e46	0.447714	0.223857	+	0.974622i	$0.428135\pi$
$332$	−1.81763e46	−0.415385
$333$	−5.85738e46	−1.26615
$334$	−1.12698e46	−0.230465
$335$	0	0
$336$	3.31203e44	0.00606482
$337$	9.22947e46	1.59965	0.799823	−	0.600236i	$-0.204927\pi$
$337$	9.22947e46	1.59965	0.799823	+	0.600236i	$0.204927\pi$
$338$	−3.72805e46	−0.611679
$339$	−3.38117e44	−0.00525258
$340$	0	0
$341$	−6.70248e46	−0.933855
$342$	8.77653e46	1.15835
$343$	6.55854e46	0.820099
$344$	1.61481e47	1.91334
$345$	0	0
$346$	7.48110e46	0.796265
$347$	5.27249e46	0.532011	0.266005	−	0.963972i	$-0.414296\pi$
$347$	5.27249e46	0.532011	0.266005	+	0.963972i	$0.414296\pi$
$348$	1.74160e45	0.0166622
$349$	9.71277e46	0.881196	0.440598	−	0.897704i	$-0.354766\pi$
$349$	9.71277e46	0.881196	0.440598	+	0.897704i	$0.354766\pi$
$350$	0	0
$351$	1.00649e46	0.0821539
$352$	1.35171e47	1.04676
$353$	−1.73375e47	−1.27396	−0.636979	−	0.770881i	$-0.719816\pi$
$353$	−1.73375e47	−1.27396	−0.636979	+	0.770881i	$0.719816\pi$
$354$	1.78876e45	0.0124736
$355$	0	0
$356$	8.68566e46	0.545730
$357$	−1.43415e45	−0.00855526
$358$	1.20662e47	0.683497
$359$	−1.13075e47	−0.608301	−0.304150	−	0.952624i	$-0.598373\pi$
$359$	−1.13075e47	−0.608301	−0.304150	+	0.952624i	$0.598373\pi$
$360$	0	0
$361$	2.59283e47	1.25861
$362$	2.72072e46	0.125480
$363$	6.60111e45	0.0289297
$364$	−5.96183e46	−0.248316
$365$	0	0
$366$	−6.84566e45	−0.0257641
$367$	8.74068e46	0.312768	0.156384	−	0.987696i	$-0.450016\pi$
$367$	8.74068e46	0.312768	0.156384	+	0.987696i	$0.450016\pi$
$368$	−6.67725e44	−0.00227202
$369$	1.83129e47	0.592609
$370$	0	0
$371$	7.04073e46	0.206158
$372$	−2.98822e45	−0.00832470
$373$	−2.70122e47	−0.716056	−0.358028	−	0.933711i	$-0.616551\pi$
$373$	−2.70122e47	−0.716056	−0.358028	+	0.933711i	$0.616551\pi$
$374$	2.59335e47	0.654240
$375$	0	0
$376$	−1.97872e47	−0.452283
$377$	8.25170e47	1.79568
$378$	−1.04657e46	−0.0216854
$379$	−4.13508e47	−0.815940	−0.407970	−	0.912995i	$-0.633763\pi$
$379$	−4.13508e47	−0.815940	−0.407970	+	0.912995i	$0.633763\pi$
$380$	0	0
$381$	2.93395e46	0.0525219
$382$	7.47746e46	0.127521
$383$	6.64131e47	1.07914	0.539569	−	0.841942i	$-0.318587\pi$
$383$	6.64131e47	1.07914	0.539569	+	0.841942i	$0.318587\pi$
$384$	−5.69691e44	−0.000882088 0
$385$	0	0
$386$	−1.79350e47	−0.252253
$387$	−1.31550e48	−1.76375
$388$	−5.96172e46	−0.0762052
$389$	4.74132e46	0.0577872	0.0288936	−	0.999582i	$-0.490802\pi$
$389$	4.74132e46	0.0577872	0.0288936	+	0.999582i	$0.490802\pi$
$390$	0	0
$391$	2.89134e45	0.00320500
$392$	−8.09901e47	−0.856327
$393$	4.36716e46	0.0440491
$394$	−5.17912e47	−0.498397
$395$	0	0
$396$	−6.43262e47	−0.563673
$397$	−6.00594e47	−0.502292	−0.251146	−	0.967949i	$-0.580807\pi$
$397$	−6.00594e47	−0.502292	−0.251146	+	0.967949i	$0.580807\pi$
$398$	1.08148e47	0.0863337
$399$	−2.77289e46	−0.0211317
$400$	0	0
$401$	−9.30169e47	−0.646235	−0.323118	−	0.946359i	$-0.604731\pi$
$401$	−9.30169e47	−0.646235	−0.323118	+	0.946359i	$0.604731\pi$
$402$	−1.43921e46	−0.00954863
$403$	−1.41582e48	−0.897147
$404$	−7.20605e47	−0.436156
$405$	0	0
$406$	−8.58024e47	−0.473989
$407$	−3.34641e48	−1.76637
$408$	4.01244e46	0.0202393
$409$	−2.60436e47	−0.125551	−0.0627755	−	0.998028i	$-0.519995\pi$
$409$	−2.60436e47	−0.125551	−0.0627755	+	0.998028i	$0.519995\pi$
$410$	0	0
$411$	2.59206e46	0.0114175
$412$	−1.88923e47	−0.0795585
$413$	5.99367e47	0.241333
$414$	1.05447e46	0.00406002
$415$	0	0
$416$	2.85533e48	1.00561
$417$	−6.44570e46	−0.0217147
$418$	5.01417e48	1.61599
$419$	−3.92255e48	−1.20951	−0.604755	−	0.796412i	$-0.706729\pi$
$419$	−3.92255e48	−1.20951	−0.604755	+	0.796412i	$0.706729\pi$
$420$	0	0
$421$	−3.86983e48	−1.09263	−0.546315	−	0.837580i	$-0.683970\pi$
$421$	−3.86983e48	−1.09263	−0.546315	+	0.837580i	$0.683970\pi$
$422$	−4.77019e48	−1.28901
$423$	1.61195e48	0.416922
$424$	−1.96984e48	−0.487711
$425$	0	0
$426$	−3.71238e46	−0.00842509
$427$	−2.29380e48	−0.498471
$428$	−8.82433e47	−0.183642
$429$	2.87377e47	0.0572785
$430$	0	0
$431$	2.97992e48	0.544973	0.272487	−	0.962160i	$-0.412154\pi$
$431$	2.97992e48	0.544973	0.272487	+	0.962160i	$0.412154\pi$
$432$	1.51046e47	0.0264643
$433$	2.20884e48	0.370798	0.185399	−	0.982663i	$-0.440642\pi$
$433$	2.20884e48	0.370798	0.185399	+	0.982663i	$0.440642\pi$
$434$	1.47219e48	0.236812
$435$	0	0
$436$	5.94517e46	0.00878344
$437$	5.59031e46	0.00791643
$438$	6.05109e46	0.00821414
$439$	−1.14225e49	−1.48650	−0.743252	−	0.669011i	$-0.766718\pi$
$439$	−1.14225e49	−1.48650	−0.743252	+	0.669011i	$0.766718\pi$
$440$	0	0
$441$	6.59779e48	0.789378
$442$	5.47814e48	0.628523
$443$	−8.78568e48	−0.966733	−0.483366	−	0.875418i	$-0.660586\pi$
$443$	−8.78568e48	−0.966733	−0.483366	+	0.875418i	$0.660586\pi$
$444$	−1.49196e47	−0.0157461
$445$	0	0
$446$	−1.02988e49	−1.00021
$447$	6.15943e46	0.00573920
$448$	−5.17921e48	−0.463042
$449$	−8.94932e48	−0.767773	−0.383886	−	0.923380i	$-0.625415\pi$
$449$	−8.94932e48	−0.767773	−0.383886	+	0.923380i	$0.625415\pi$
$450$	0	0
$451$	1.04624e49	0.826735
$452$	9.13380e47	0.0692772
$453$	−1.45607e47	−0.0106015
$454$	1.93432e49	1.35205
$455$	0	0
$456$	7.75793e47	0.0499915
$457$	−3.77717e48	−0.233731	−0.116866	−	0.993148i	$-0.537285\pi$
$457$	−3.77717e48	−0.233731	−0.116866	+	0.993148i	$0.537285\pi$
$458$	1.45666e49	0.865661
$459$	−6.54048e47	−0.0373315
$460$	0	0
$461$	8.89831e48	0.468641	0.234320	−	0.972159i	$-0.424714\pi$
$461$	8.89831e48	0.468641	0.234320	+	0.972159i	$0.424714\pi$
$462$	−2.98819e47	−0.0151193
$463$	3.35423e49	1.63059	0.815294	−	0.579047i	$-0.196575\pi$
$463$	3.35423e49	1.63059	0.815294	+	0.579047i	$0.196575\pi$
$464$	1.23835e49	0.578442
$465$	0	0
$466$	5.13034e48	0.221313
$467$	3.67520e49	1.52377	0.761884	−	0.647714i	$-0.224275\pi$
$467$	3.67520e49	1.52377	0.761884	+	0.647714i	$0.224275\pi$
$468$	−1.35881e49	−0.541516
$469$	−4.82240e48	−0.184742
$470$	0	0
$471$	−1.45132e48	−0.0513897
$472$	−1.67690e49	−0.570925
$473$	−7.51563e49	−2.46056
$474$	−7.10091e47	−0.0223571
$475$	0	0
$476$	3.87418e48	0.112837
$477$	1.60471e49	0.449581
$478$	8.20711e48	0.221194
$479$	4.73384e49	1.22746	0.613730	−	0.789516i	$-0.289669\pi$
$479$	4.73384e49	1.22746	0.613730	+	0.789516i	$0.289669\pi$
$480$	0	0
$481$	−7.06889e49	−1.69694
$482$	3.21063e49	0.741686
$483$	−3.33153e45	−7.40666e−5 0
$484$	−1.78321e49	−0.381560
$485$	0	0
$486$	−3.57854e48	−0.0709471
$487$	−7.97298e48	−0.152172	−0.0760860	−	0.997101i	$-0.524242\pi$
$487$	−7.97298e48	−0.152172	−0.0760860	+	0.997101i	$0.524242\pi$
$488$	6.41754e49	1.17924
$489$	1.68203e48	0.0297592
$490$	0	0
$491$	3.59851e49	0.590358	0.295179	−	0.955442i	$-0.404621\pi$
$491$	3.59851e49	0.590358	0.295179	+	0.955442i	$0.404621\pi$
$492$	4.66455e47	0.00736980
$493$	−5.36220e49	−0.815972
$494$	1.05918e50	1.55247
$495$	0	0
$496$	−2.12474e49	−0.288998
$497$	−1.24392e49	−0.163004
$498$	−1.92444e48	−0.0242975
$499$	7.98372e49	0.971282	0.485641	−	0.874158i	$-0.338586\pi$
$499$	7.98372e49	0.971282	0.485641	+	0.874158i	$0.338586\pi$
$500$	0	0
$501$	8.11529e47	0.00916866
$502$	1.15056e50	1.25283
$503$	−6.32137e49	−0.663443	−0.331721	−	0.943377i	$-0.607629\pi$
$503$	−6.32137e49	−0.663443	−0.331721	+	0.943377i	$0.607629\pi$
$504$	4.90326e49	0.496043
$505$	0	0
$506$	6.02436e47	0.00566404
$507$	2.68455e48	0.0243346
$508$	−7.92569e49	−0.692721
$509$	−1.42477e50	−1.20078	−0.600392	−	0.799706i	$-0.704989\pi$
$509$	−1.42477e50	−1.20078	−0.600392	+	0.799706i	$0.704989\pi$
$510$	0	0
$511$	2.02756e49	0.158923
$512$	1.04687e50	0.791403
$513$	−1.26458e49	−0.0922095
$514$	1.55295e50	1.09230
$515$	0	0
$516$	−3.35076e48	−0.0219343
$517$	9.20932e49	0.581638
$518$	7.35034e49	0.447927
$519$	−5.38710e48	−0.0316781
$520$	0	0
$521$	1.18735e50	0.650251	0.325125	−	0.945671i	$-0.394593\pi$
$521$	1.18735e50	0.650251	0.325125	+	0.945671i	$0.394593\pi$
$522$	−1.95560e50	−1.03365
$523$	−6.66586e49	−0.340075	−0.170038	−	0.985438i	$-0.554389\pi$
$523$	−6.66586e49	−0.340075	−0.170038	+	0.985438i	$0.554389\pi$
$524$	−1.17973e50	−0.580971
$525$	0	0
$526$	−2.28289e50	−1.04773
$527$	9.20040e49	0.407672
$528$	4.31271e48	0.0184511
$529$	−2.42057e50	−0.999972
$530$	0	0
$531$	1.36607e50	0.526289
$532$	7.49061e49	0.278709
$533$	2.21006e50	0.794238
$534$	9.19607e48	0.0319219
$535$	0	0
$536$	1.34920e50	0.437046
$537$	−8.68884e48	−0.0271918
$538$	2.92272e50	0.883722
$539$	3.76942e50	1.10124
$540$	0	0
$541$	7.31652e50	1.99597	0.997987	−	0.0634127i	$-0.0201984\pi$
$541$	7.31652e50	1.99597	0.997987	+	0.0634127i	$0.0201984\pi$
$542$	7.52499e49	0.198390
$543$	−1.95917e48	−0.00499201
$544$	−1.85548e50	−0.456959
$545$	0	0
$546$	−6.31218e48	−0.0145250
$547$	−1.90668e50	−0.424143	−0.212072	−	0.977254i	$-0.568021\pi$
$547$	−1.90668e50	−0.424143	−0.212072	+	0.977254i	$0.568021\pi$
$548$	−7.00212e49	−0.150588
$549$	−5.22800e50	−1.08704
$550$	0	0
$551$	−1.03677e51	−2.01547
$552$	9.32089e46	0.000175220 0
$553$	−2.37933e50	−0.432553
$554$	4.60142e50	0.809024
$555$	0	0
$556$	1.74122e50	0.286399
$557$	−6.78617e50	−1.07970	−0.539851	−	0.841761i	$-0.681519\pi$
$557$	−6.78617e50	−1.07970	−0.539851	+	0.841761i	$0.681519\pi$
$558$	3.35539e50	0.516429
$559$	−1.58759e51	−2.36384
$560$	0	0
$561$	−1.86746e49	−0.0260279
$562$	−8.18669e50	−1.10404
$563$	−6.45010e50	−0.841708	−0.420854	−	0.907128i	$-0.638270\pi$
$563$	−6.45010e50	−0.841708	−0.420854	+	0.907128i	$0.638270\pi$
$564$	4.10587e48	0.00518492
$565$	0	0
$566$	2.28089e50	0.269774
$567$	−3.99063e50	−0.456830
$568$	3.48021e50	0.385621
$569$	2.68168e50	0.287627	0.143814	−	0.989605i	$-0.454063\pi$
$569$	2.68168e50	0.287627	0.143814	+	0.989605i	$0.454063\pi$
$570$	0	0
$571$	−3.44946e50	−0.346724	−0.173362	−	0.984858i	$-0.555463\pi$
$571$	−3.44946e50	−0.346724	−0.173362	+	0.984858i	$0.555463\pi$
$572$	−7.76311e50	−0.755456
$573$	−5.38448e48	−0.00507321
$574$	−2.29805e50	−0.209648
$575$	0	0
$576$	−1.18044e51	−1.00978
$577$	−2.52648e50	−0.209297	−0.104648	−	0.994509i	$-0.533372\pi$
$577$	−2.52648e50	−0.209297	−0.104648	+	0.994509i	$0.533372\pi$
$578$	6.05612e50	0.485881
$579$	1.29149e49	0.0100355
$580$	0	0
$581$	−6.44830e50	−0.470096
$582$	−6.31206e48	−0.00445754
$583$	9.16799e50	0.627199
$584$	−5.67266e50	−0.375966
$585$	0	0
$586$	1.47925e50	0.0920311
$587$	−1.13653e51	−0.685134	−0.342567	−	0.939493i	$-0.611296\pi$
$587$	−1.13653e51	−0.685134	−0.342567	+	0.939493i	$0.611296\pi$
$588$	1.68055e49	0.00981685
$589$	1.77887e51	1.00696
$590$	0	0
$591$	3.72945e49	0.0198279
$592$	−1.06084e51	−0.546636
$593$	1.23614e51	0.617383	0.308692	−	0.951162i	$-0.400109\pi$
$593$	1.23614e51	0.617383	0.308692	+	0.951162i	$0.400109\pi$
$594$	−1.36277e50	−0.0659740
$595$	0	0
$596$	−1.66389e50	−0.0756954
$597$	−7.78766e48	−0.00343464
$598$	1.27257e49	0.00544140
$599$	−4.59427e51	−1.90467	−0.952336	−	0.305052i	$-0.901326\pi$
$599$	−4.59427e51	−1.90467	−0.952336	+	0.305052i	$0.901326\pi$
$600$	0	0
$601$	−1.48401e49	−0.00578442	−0.00289221	−	0.999996i	$-0.500921\pi$
$601$	−1.48401e49	−0.00578442	−0.00289221	+	0.999996i	$0.500921\pi$
$602$	1.65080e51	0.623962
$603$	−1.09911e51	−0.402877
$604$	3.93340e50	0.139825
$605$	0	0
$606$	−7.62951e49	−0.0255125
$607$	−2.59968e51	−0.843198	−0.421599	−	0.906782i	$-0.638531\pi$
$607$	−2.59968e51	−0.843198	−0.421599	+	0.906782i	$0.638531\pi$
$608$	−3.58751e51	−1.12870
$609$	6.17859e49	0.0188568
$610$	0	0
$611$	1.94536e51	0.558775
$612$	8.82998e50	0.246070
$613$	−1.49376e50	−0.0403890	−0.0201945	−	0.999796i	$-0.506429\pi$
$613$	−1.49376e50	−0.0403890	−0.0201945	+	0.999796i	$0.506429\pi$
$614$	2.74319e51	0.719682
$615$	0	0
$616$	2.80131e51	0.692018
$617$	6.30081e51	1.51050	0.755250	−	0.655437i	$-0.227516\pi$
$617$	6.30081e51	1.51050	0.755250	+	0.655437i	$0.227516\pi$
$618$	−2.00025e49	−0.00465369
$619$	5.97852e51	1.34995	0.674974	−	0.737842i	$-0.264155\pi$
$619$	5.97852e51	1.34995	0.674974	+	0.737842i	$0.264155\pi$
$620$	0	0
$621$	−1.51935e48	−0.000323195 0
$622$	1.44681e51	0.298737
$623$	3.08136e51	0.617609
$624$	9.11007e49	0.0177258
$625$	0	0
$626$	1.46570e51	0.268794
$627$	−3.61068e50	−0.0642893
$628$	3.92055e51	0.677787
$629$	4.59358e51	0.771106
$630$	0	0
$631$	−3.17011e51	−0.501800	−0.250900	−	0.968013i	$-0.580727\pi$
$631$	−3.17011e51	−0.501800	−0.250900	+	0.968013i	$0.580727\pi$
$632$	6.65683e51	1.02330
$633$	3.43499e50	0.0512810
$634$	−6.13536e51	−0.889588
$635$	0	0
$636$	4.08744e49	0.00559107
$637$	7.96244e51	1.05795
$638$	−1.11726e52	−1.44203
$639$	−2.83512e51	−0.355473
$640$	0	0
$641$	1.15243e52	1.36377	0.681885	−	0.731459i	$-0.261160\pi$
$641$	1.15243e52	1.36377	0.681885	+	0.731459i	$0.261160\pi$
$642$	−9.34289e49	−0.0107420
$643$	−1.66832e52	−1.86370	−0.931851	−	0.362842i	$-0.881807\pi$
$643$	−1.66832e52	−1.86370	−0.931851	+	0.362842i	$0.881807\pi$
$644$	8.99971e48	0.000976877 0
$645$	0	0
$646$	−6.88289e51	−0.705455
$647$	1.67531e52	1.66865	0.834327	−	0.551270i	$-0.185856\pi$
$647$	1.67531e52	1.66865	0.834327	+	0.551270i	$0.185856\pi$
$648$	1.11649e52	1.08073
$649$	7.80457e51	0.734213
$650$	0	0
$651$	−1.06011e50	−0.00942116
$652$	−4.54380e51	−0.392499
$653$	9.01096e51	0.756619	0.378309	−	0.925679i	$-0.376506\pi$
$653$	9.01096e51	0.756619	0.378309	+	0.925679i	$0.376506\pi$
$654$	6.29454e48	0.000513778 0
$655$	0	0
$656$	3.31668e51	0.255848
$657$	4.62118e51	0.346572
$658$	−2.02281e51	−0.147495
$659$	1.92183e52	1.36249	0.681247	−	0.732054i	$-0.261438\pi$
$659$	1.92183e52	1.36249	0.681247	+	0.732054i	$0.261438\pi$
$660$	0	0
$661$	−1.12368e51	−0.0753213	−0.0376606	−	0.999291i	$-0.511991\pi$
$661$	−1.12368e51	−0.0753213	−0.0376606	+	0.999291i	$0.511991\pi$
$662$	−5.29910e51	−0.345405
$663$	−3.94478e50	−0.0250048
$664$	1.80409e52	1.11211
$665$	0	0
$666$	1.67528e52	0.976819
$667$	−1.24564e50	−0.00706422
$668$	−2.19224e51	−0.120927
$669$	7.41611e50	0.0397918
$670$	0	0
$671$	−2.98684e52	−1.51651
$672$	2.13797e50	0.0105602
$673$	−6.07438e51	−0.291893	−0.145946	−	0.989292i	$-0.546623\pi$
$673$	−6.07438e51	−0.291893	−0.145946	+	0.989292i	$0.546623\pi$
$674$	−2.63974e52	−1.23411
$675$	0	0
$676$	−7.25197e51	−0.320954
$677$	−3.94010e52	−1.69675	−0.848373	−	0.529398i	$-0.822418\pi$
$677$	−3.94010e52	−1.69675	−0.848373	+	0.529398i	$0.822418\pi$
$678$	9.67055e49	0.00405230
$679$	−2.11500e51	−0.0862423
$680$	0	0
$681$	−1.39289e51	−0.0537892
$682$	1.91699e52	0.720457
$683$	2.05041e52	0.749993	0.374996	−	0.927026i	$-0.377644\pi$
$683$	2.05041e52	0.749993	0.374996	+	0.927026i	$0.377644\pi$
$684$	1.70725e52	0.607798
$685$	0	0
$686$	−1.87582e52	−0.632696
$687$	−1.04893e51	−0.0344389
$688$	−2.38252e52	−0.761465
$689$	1.93662e52	0.602545
$690$	0	0
$691$	4.63109e51	0.136565	0.0682825	−	0.997666i	$-0.478248\pi$
$691$	4.63109e51	0.136565	0.0682825	+	0.997666i	$0.478248\pi$
$692$	1.45525e52	0.417808
$693$	−2.28206e52	−0.637915
$694$	−1.50799e52	−0.410440
$695$	0	0
$696$	−1.72863e51	−0.0446099
$697$	−1.43616e52	−0.360909
$698$	−2.77797e52	−0.679832
$699$	−3.69433e50	−0.00880456
$700$	0	0
$701$	−6.34322e51	−0.143392	−0.0716962	−	0.997427i	$-0.522841\pi$
$701$	−6.34322e51	−0.143392	−0.0716962	+	0.997427i	$0.522841\pi$
$702$	−2.87868e51	−0.0633807
$703$	8.88154e52	1.90465
$704$	−6.74404e52	−1.40872
$705$	0	0
$706$	4.95873e52	0.982842
$707$	−2.55645e52	−0.493602
$708$	3.47958e50	0.00654503
$709$	−7.70939e52	−1.41275	−0.706374	−	0.707839i	$-0.749670\pi$
$709$	−7.70939e52	−1.41275	−0.706374	+	0.707839i	$0.749670\pi$
$710$	0	0
$711$	−5.42293e52	−0.943293
$712$	−8.62096e52	−1.46109
$713$	2.13725e50	0.00352939
$714$	4.10184e50	0.00660028
$715$	0	0
$716$	2.34718e52	0.358637
$717$	−5.90989e50	−0.00879985
$718$	3.23407e52	0.469296
$719$	5.22428e52	0.738826	0.369413	−	0.929265i	$-0.379559\pi$
$719$	5.22428e52	0.738826	0.369413	+	0.929265i	$0.379559\pi$
$720$	0	0
$721$	−6.70231e51	−0.0900372
$722$	−7.41579e52	−0.971000
$723$	−2.31196e51	−0.0295068
$724$	5.29245e51	0.0658406
$725$	0	0
$726$	−1.88800e51	−0.0223189
$727$	1.24495e53	1.43471	0.717354	−	0.696708i	$-0.245353\pi$
$727$	1.24495e53	1.43471	0.717354	+	0.696708i	$0.245353\pi$
$728$	5.91742e52	0.664816
$729$	−9.07820e52	−0.994352
$730$	0	0
$731$	1.03166e53	1.07415
$732$	−1.33165e51	−0.0135187
$733$	1.12627e52	0.111485	0.0557427	−	0.998445i	$-0.482247\pi$
$733$	1.12627e52	0.111485	0.0557427	+	0.998445i	$0.482247\pi$
$734$	−2.49994e52	−0.241297
$735$	0	0
$736$	−4.31028e50	−0.00395609
$737$	−6.27941e52	−0.562044
$738$	−5.23769e52	−0.457191
$739$	−2.92067e52	−0.248634	−0.124317	−	0.992243i	$-0.539674\pi$
$739$	−2.92067e52	−0.248634	−0.124317	+	0.992243i	$0.539674\pi$
$740$	0	0
$741$	−7.62711e51	−0.0617623
$742$	−2.01373e52	−0.159048
$743$	−3.47917e52	−0.268029	−0.134015	−	0.990979i	$-0.542787\pi$
$743$	−3.47917e52	−0.268029	−0.134015	+	0.990979i	$0.542787\pi$
$744$	2.96596e51	0.0222878
$745$	0	0
$746$	7.72582e52	0.552429
$747$	−1.46969e53	−1.02516
$748$	5.04470e52	0.343286
$749$	−3.13055e52	−0.207830
$750$	0	0
$751$	1.55213e53	0.980818	0.490409	−	0.871492i	$-0.336847\pi$
$751$	1.55213e53	0.980818	0.490409	+	0.871492i	$0.336847\pi$
$752$	2.91943e52	0.179998
$753$	−8.28513e51	−0.0498416
$754$	−2.36008e53	−1.38534
$755$	0	0
$756$	−2.03582e51	−0.0113785
$757$	1.00018e51	0.00545510	0.00272755	−	0.999996i	$-0.499132\pi$
$757$	1.00018e51	0.00545510	0.00272755	+	0.999996i	$0.499132\pi$
$758$	1.18268e53	0.629488
$759$	−4.33811e49	−0.000225334 0
$760$	0	0
$761$	−3.93324e53	−1.94596	−0.972981	−	0.230886i	$-0.925838\pi$
$761$	−3.93324e53	−1.94596	−0.972981	+	0.230886i	$0.925838\pi$
$762$	−8.39144e51	−0.0405200
$763$	2.10913e51	0.00994031
$764$	1.45455e52	0.0669115
$765$	0	0
$766$	−1.89949e53	−0.832541
$767$	1.64862e53	0.705353
$768$	−7.26468e51	−0.0303413
$769$	4.31322e53	1.75859	0.879295	−	0.476278i	$-0.158015\pi$
$769$	4.31322e53	1.75859	0.879295	+	0.476278i	$0.158015\pi$
$770$	0	0
$771$	−1.11827e52	−0.0434552
$772$	−3.48879e52	−0.132359
$773$	−1.93734e53	−0.717604	−0.358802	−	0.933414i	$-0.616815\pi$
$773$	−1.93734e53	−0.717604	−0.358802	+	0.933414i	$0.616815\pi$
$774$	3.76247e53	1.36071
$775$	0	0
$776$	5.91731e52	0.204024
$777$	−5.29294e51	−0.0178200
$778$	−1.35607e52	−0.0445821
$779$	−2.77678e53	−0.891452
$780$	0	0
$781$	−1.61975e53	−0.495911
$782$	−8.26956e50	−0.00247262
$783$	2.81776e52	0.0822832
$784$	1.19494e53	0.340799
$785$	0	0
$786$	−1.24906e52	−0.0339833
$787$	1.53439e52	0.0407759	0.0203880	−	0.999792i	$-0.493510\pi$
$787$	1.53439e52	0.0407759	0.0203880	+	0.999792i	$0.493510\pi$
$788$	−1.00746e53	−0.261514
$789$	1.64390e52	0.0416821
$790$	0	0
$791$	3.24034e52	0.0784018
$792$	6.38470e53	1.50912
$793$	−6.30933e53	−1.45690
$794$	1.71777e53	0.387512
$795$	0	0
$796$	2.10374e52	0.0453001
$797$	−5.82231e53	−1.22494	−0.612472	−	0.790493i	$-0.709825\pi$
$797$	−5.82231e53	−1.22494	−0.612472	+	0.790493i	$0.709825\pi$
$798$	7.93079e51	0.0163028
$799$	−1.26415e53	−0.253912
$800$	0	0
$801$	7.02299e53	1.34685
$802$	2.66039e53	0.498563
$803$	2.64015e53	0.483495
$804$	−2.79960e51	−0.00501025
$805$	0	0
$806$	4.04940e53	0.692137
$807$	−2.10464e52	−0.0351574
$808$	7.15236e53	1.16772
$809$	7.29683e53	1.16436	0.582179	−	0.813061i	$-0.302200\pi$
$809$	7.29683e53	1.16436	0.582179	+	0.813061i	$0.302200\pi$
$810$	0	0
$811$	−8.04109e53	−1.22583	−0.612914	−	0.790150i	$-0.710003\pi$
$811$	−8.04109e53	−1.22583	−0.612914	+	0.790150i	$0.710003\pi$
$812$	−1.66907e53	−0.248706
$813$	−5.41870e51	−0.00789261
$814$	9.57113e53	1.36274
$815$	0	0
$816$	−5.92000e51	−0.00805479
$817$	1.99469e54	2.65318
$818$	7.44878e52	0.0968611
$819$	−4.82058e53	−0.612840
$820$	0	0
$821$	−1.06873e52	−0.0129873	−0.00649364	−	0.999979i	$-0.502067\pi$
$821$	−1.06873e52	−0.0129873	−0.00649364	+	0.999979i	$0.502067\pi$
$822$	−7.41360e51	−0.00880847
$823$	−1.55439e54	−1.80578	−0.902889	−	0.429874i	$-0.858558\pi$
$823$	−1.55439e54	−1.80578	−0.902889	+	0.429874i	$0.858558\pi$
$824$	1.87516e53	0.213002
$825$	0	0
$826$	−1.71426e53	−0.186186
$827$	1.52865e54	1.62352	0.811759	−	0.583992i	$-0.198510\pi$
$827$	1.52865e54	1.62352	0.811759	+	0.583992i	$0.198510\pi$
$828$	2.05120e51	0.00213033
$829$	4.48559e53	0.455576	0.227788	−	0.973711i	$-0.426851\pi$
$829$	4.48559e53	0.455576	0.227788	+	0.973711i	$0.426851\pi$
$830$	0	0
$831$	−3.31346e52	−0.0321857
$832$	−1.42459e54	−1.35335
$833$	−5.17424e53	−0.480744
$834$	1.84355e52	0.0167526
$835$	0	0
$836$	9.75378e53	0.847924
$837$	−4.83467e52	−0.0411099
$838$	1.12190e54	0.933122
$839$	−1.70786e54	−1.38949	−0.694747	−	0.719254i	$-0.744484\pi$
$839$	−1.70786e54	−1.38949	−0.694747	+	0.719254i	$0.744484\pi$
$840$	0	0
$841$	1.02566e54	0.798502
$842$	1.10682e54	0.842950
$843$	5.89519e52	0.0439226
$844$	−9.27918e53	−0.676354
$845$	0	0
$846$	−4.61037e53	−0.321650
$847$	−6.32617e53	−0.431815
$848$	2.90633e53	0.194098
$849$	−1.64245e52	−0.0107325
$850$	0	0
$851$	1.06709e52	0.00667580
$852$	−7.22147e51	−0.00442072
$853$	1.02278e54	0.612667	0.306334	−	0.951924i	$-0.400898\pi$
$853$	1.02278e54	0.612667	0.306334	+	0.951924i	$0.400898\pi$
$854$	6.56054e53	0.384564
$855$	0	0
$856$	8.75859e53	0.491666
$857$	−7.33586e52	−0.0403001	−0.0201500	−	0.999797i	$-0.506414\pi$
$857$	−7.33586e52	−0.0403001	−0.0201500	+	0.999797i	$0.506414\pi$
$858$	−8.21931e52	−0.0441896
$859$	1.46329e54	0.769938	0.384969	−	0.922929i	$-0.374212\pi$
$859$	1.46329e54	0.769938	0.384969	+	0.922929i	$0.374212\pi$
$860$	0	0
$861$	1.65482e52	0.00834049
$862$	−8.52292e53	−0.420440
$863$	−2.49462e54	−1.20449	−0.602247	−	0.798310i	$-0.705728\pi$
$863$	−2.49462e54	−1.20449	−0.602247	+	0.798310i	$0.705728\pi$
$864$	9.75027e52	0.0460800
$865$	0	0
$866$	−6.31753e53	−0.286066
$867$	−4.36098e52	−0.0193300
$868$	2.86376e53	0.124257
$869$	−3.09821e54	−1.31597
$870$	0	0
$871$	−1.32645e54	−0.539951
$872$	−5.90088e52	−0.0235159
$873$	−4.82049e53	−0.188073
$874$	−1.59889e52	−0.00610742
$875$	0	0
$876$	1.17708e52	0.00431004
$877$	−4.03070e54	−1.44507	−0.722534	−	0.691335i	$-0.757023\pi$
$877$	−4.03070e54	−1.44507	−0.722534	+	0.691335i	$0.757023\pi$
$878$	3.26696e54	1.14682
$879$	−1.06520e52	−0.00366130
$880$	0	0
$881$	−2.32935e54	−0.767679	−0.383840	−	0.923400i	$-0.625398\pi$
$881$	−2.32935e54	−0.767679	−0.383840	+	0.923400i	$0.625398\pi$
$882$	−1.88705e54	−0.608995
$883$	2.99176e54	0.945482	0.472741	−	0.881202i	$-0.343265\pi$
$883$	2.99176e54	0.945482	0.472741	+	0.881202i	$0.343265\pi$
$884$	1.06563e54	0.329792
$885$	0	0
$886$	2.51281e54	0.745822
$887$	−5.34771e54	−1.55447	−0.777233	−	0.629213i	$-0.783377\pi$
$887$	−5.34771e54	−1.55447	−0.777233	+	0.629213i	$0.783377\pi$
$888$	1.48085e53	0.0421570
$889$	−2.81175e54	−0.783960
$890$	0	0
$891$	−5.19634e54	−1.38982
$892$	−2.00337e54	−0.524821
$893$	−2.44420e54	−0.627169
$894$	−1.76167e52	−0.00442772
$895$	0	0
$896$	5.45963e52	0.0131663
$897$	−9.16372e50	−0.000216477 0
$898$	2.55961e54	0.592327
$899$	−3.96370e54	−0.898558
$900$	0	0
$901$	−1.25848e54	−0.273802
$902$	−2.99238e54	−0.637816
$903$	−1.18873e53	−0.0248233
$904$	−9.06576e53	−0.185476
$905$	0	0
$906$	4.16454e52	0.00817891
$907$	6.45044e54	1.24124	0.620618	−	0.784113i	$-0.286882\pi$
$907$	6.45044e54	1.24124	0.620618	+	0.784113i	$0.286882\pi$
$908$	3.76271e54	0.709436
$909$	−5.82662e54	−1.07643
$910$	0	0
$911$	2.81261e54	0.498907	0.249453	−	0.968387i	$-0.419749\pi$
$911$	2.81261e54	0.498907	0.249453	+	0.968387i	$0.419749\pi$
$912$	−1.14461e53	−0.0198955
$913$	−8.39655e54	−1.43018
$914$	1.08031e54	0.180321
$915$	0	0
$916$	2.83356e54	0.454220
$917$	−4.18526e54	−0.657491
$918$	1.87066e53	0.0288008
$919$	5.50843e54	0.831171	0.415586	−	0.909554i	$-0.363577\pi$
$919$	5.50843e54	0.831171	0.415586	+	0.909554i	$0.363577\pi$
$920$	0	0
$921$	−1.97535e53	−0.0286314
$922$	−2.54502e54	−0.361551
$923$	−3.42152e54	−0.476418
$924$	−5.81275e52	−0.00793323
$925$	0	0
$926$	−9.59349e54	−1.25798
$927$	−1.52758e54	−0.196349
$928$	7.99374e54	1.00719
$929$	9.70568e54	1.19877	0.599384	−	0.800461i	$-0.295412\pi$
$929$	9.70568e54	1.19877	0.599384	+	0.800461i	$0.295412\pi$
$930$	0	0
$931$	−1.00042e55	−1.18745
$932$	9.97975e53	0.116125
$933$	−1.04184e53	−0.0118848
$934$	−1.05115e55	−1.17557
$935$	0	0
$936$	1.34869e55	1.44980
$937$	4.05525e54	0.427401	0.213701	−	0.976899i	$-0.431448\pi$
$937$	4.05525e54	0.427401	0.213701	+	0.976899i	$0.431448\pi$
$938$	1.37926e54	0.142526
$939$	−1.05544e53	−0.0106935
$940$	0	0
$941$	4.56539e54	0.444703	0.222351	−	0.974967i	$-0.428627\pi$
$941$	4.56539e54	0.444703	0.222351	+	0.974967i	$0.428627\pi$
$942$	4.15094e53	0.0396465
$943$	−3.33621e52	−0.00312454
$944$	2.47411e54	0.227215
$945$	0	0
$946$	2.14956e55	1.89829
$947$	1.72468e55	1.49360	0.746798	−	0.665051i	$-0.231590\pi$
$947$	1.72468e55	1.49360	0.746798	+	0.665051i	$0.231590\pi$
$948$	−1.38130e53	−0.0117310
$949$	5.57700e54	0.464490
$950$	0	0
$951$	4.41804e53	0.0353908
$952$	−3.84532e54	−0.302099
$953$	−6.30605e52	−0.00485891	−0.00242945	−	0.999997i	$-0.500773\pi$
$953$	−6.30605e52	−0.00485891	−0.00242945	+	0.999997i	$0.500773\pi$
$954$	−4.58967e54	−0.346846
$955$	0	0
$956$	1.59648e54	0.116063
$957$	8.04535e53	0.0573686
$958$	−1.35394e55	−0.946969
$959$	−2.48410e54	−0.170422
$960$	0	0
$961$	−8.34809e54	−0.551067
$962$	2.02178e55	1.30917
$963$	−7.13512e54	−0.453226
$964$	6.24546e54	0.389170
$965$	0	0
$966$	9.52858e50	5.71415e−5 0
$967$	1.73337e55	1.01977	0.509883	−	0.860244i	$-0.329689\pi$
$967$	1.73337e55	1.01977	0.509883	+	0.860244i	$0.329689\pi$
$968$	1.76992e55	1.02155
$969$	4.95633e53	0.0280653
$970$	0	0
$971$	1.04588e55	0.570067	0.285033	−	0.958518i	$-0.407995\pi$
$971$	1.04588e55	0.570067	0.285033	+	0.958518i	$0.407995\pi$
$972$	−6.96112e53	−0.0372266
$973$	6.17723e54	0.324121
$974$	2.28037e54	0.117399
$975$	0	0
$976$	−9.46852e54	−0.469311
$977$	1.65065e55	0.802798	0.401399	−	0.915903i	$-0.368524\pi$
$977$	1.65065e55	0.802798	0.401399	+	0.915903i	$0.368524\pi$
$978$	−4.81082e53	−0.0229588
$979$	4.01235e55	1.87896
$980$	0	0
$981$	4.80711e53	0.0216774
$982$	−1.02922e55	−0.455454
$983$	−3.82232e55	−1.65992	−0.829960	−	0.557823i	$-0.811637\pi$
$983$	−3.82232e55	−1.65992	−0.829960	+	0.557823i	$0.811637\pi$
$984$	−4.62981e53	−0.0197312
$985$	0	0
$986$	1.53365e55	0.629512
$987$	1.45662e53	0.00586783
$988$	2.06037e55	0.814593
$989$	2.39655e53	0.00929939
$990$	0	0
$991$	−4.27417e55	−1.59768	−0.798838	−	0.601546i	$-0.794552\pi$
$991$	−4.27417e55	−1.59768	−0.798838	+	0.601546i	$0.794552\pi$
$992$	−1.37156e55	−0.503208
$993$	3.81585e53	0.0137414
$994$	3.55775e54	0.125756
$995$	0	0
$996$	−3.74351e53	−0.0127491
$997$	3.39750e55	1.13579	0.567896	−	0.823100i	$-0.307757\pi$
$997$	3.39750e55	1.13579	0.567896	+	0.823100i	$0.307757\pi$
$998$	−2.28344e55	−0.749332
$999$	−2.41386e54	−0.0777588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.38.a.a.1.1		2
5.2	odd	4		25.38.b.a.24.2		4
5.3	odd	4		25.38.b.a.24.3		4
5.4	even	2		1.38.a.a.1.2	✓	2
15.14	odd	2		9.38.a.a.1.1		2
20.19	odd	2		16.38.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.38.a.a.1.2	✓	2	5.4	even	2
9.38.a.a.1.1		2	15.14	odd	2
16.38.a.b.1.2		2	20.19	odd	2
25.38.a.a.1.1		2	1.1	even	1	trivial
25.38.b.a.24.2		4	5.2	odd	4
25.38.b.a.24.3		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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-286012. q^{2} +2.05955e7 q^{3} -5.56362e10 q^{4} -5.89057e12 q^{6} -1.97377e15 q^{7} +5.52218e16 q^{8} -4.49860e17 q^{9} +O(q^{10})\)	\(q-286012. q^{2} +2.05955e7 q^{3} -5.56362e10 q^{4} -5.89057e12 q^{6} -1.97377e15 q^{7} +5.52218e16 q^{8} -4.49860e17 q^{9} -2.57012e19 q^{11} -1.14586e18 q^{12} -5.42906e20 q^{13} +5.64522e20 q^{14} -8.14749e21 q^{16} +3.52797e22 q^{17} +1.28665e23 q^{18} +6.82122e23 q^{19} -4.06509e22 q^{21} +7.35084e24 q^{22} +8.19547e22 q^{23} +1.13732e24 q^{24} +1.55278e26 q^{26} -1.85389e25 q^{27} +1.09813e26 q^{28} -1.51991e27 q^{29} +2.60785e27 q^{31} -5.25934e27 q^{32} -5.29330e26 q^{33} -1.00904e28 q^{34} +2.50285e28 q^{36} +1.30205e29 q^{37} -1.95095e29 q^{38} -1.11814e28 q^{39} -4.07079e29 q^{41} +1.16266e28 q^{42} +2.92424e30 q^{43} +1.42992e30 q^{44} -2.34400e28 q^{46} -3.58323e30 q^{47} -1.67802e29 q^{48} -1.46663e31 q^{49} +7.26605e29 q^{51} +3.02052e31 q^{52} -3.56714e31 q^{53} +5.30236e30 q^{54} -1.08995e32 q^{56} +1.40487e31 q^{57} +4.34713e32 q^{58} -3.03666e32 q^{59} +1.16214e33 q^{61} -7.45875e32 q^{62} +8.87921e32 q^{63} +2.62402e33 q^{64} +1.51395e32 q^{66} +2.44324e33 q^{67} -1.96283e33 q^{68} +1.68790e30 q^{69} +6.30224e33 q^{71} -2.48421e34 q^{72} -1.02725e34 q^{73} -3.72400e34 q^{74} -3.79507e34 q^{76} +5.07283e34 q^{77} +3.19803e33 q^{78} +1.20547e35 q^{79} +2.02183e35 q^{81} +1.16430e35 q^{82} +3.26699e35 q^{83} +2.26166e33 q^{84} -8.36366e35 q^{86} -3.13034e34 q^{87} -1.41927e36 q^{88} -1.56115e36 q^{89} +1.07157e36 q^{91} -4.55965e33 q^{92} +5.37100e34 q^{93} +1.02485e36 q^{94} -1.08319e35 q^{96} +1.07155e36 q^{97} +4.19474e36 q^{98} +1.15619e37 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 194400 q^{2} - 13991400 q^{3} + 37720269824 q^{4} - 22506543847296 q^{6} + 34\!\cdots\!00 q^{7}+ \cdots - 89\!\cdots\!14 q^{9}+O(q^{10}) \) 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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