LMFDB - Embedded newform 49.26.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,26,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	49.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:	$194.038422177$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} - 35625342 x^{4} - 2465469952 x^{3} + 282703727994240 x^{2} + \cdots - 21\!\cdots\!72 $ x^6 - 3x^5 - 35625342x^4 - 2465469952x^3 + 282703727994240x^2 - 96039483146256384*x - 2113167510962307072
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{15}\cdot 3^{4}\cdot 5\cdot 7^{3} $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3034.56$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6773.12 q^{2} +409558. q^{3} +1.23207e7 q^{4} +2.95928e8 q^{5} -2.77398e9 q^{6} +1.43819e11 q^{8} -6.79551e11 q^{9} +O(q^{10})$	\(q-6773.12 q^{2} +409558. q^{3} +1.23207e7 q^{4} +2.95928e8 q^{5} -2.77398e9 q^{6} +1.43819e11 q^{8} -6.79551e11 q^{9} -2.00436e12 q^{10} +2.31821e12 q^{11} +5.04603e12 q^{12} -1.47378e14 q^{13} +1.21200e14 q^{15} -1.38751e15 q^{16} -3.82513e15 q^{17} +4.60268e15 q^{18} -4.18000e15 q^{19} +3.64603e15 q^{20} -1.57015e16 q^{22} -6.35551e16 q^{23} +5.89021e16 q^{24} -2.10450e17 q^{25} +9.98209e17 q^{26} -6.25329e17 q^{27} -2.10088e18 q^{29} -8.20900e17 q^{30} -1.11885e18 q^{31} +4.57204e18 q^{32} +9.49441e17 q^{33} +2.59080e19 q^{34} -8.37252e18 q^{36} -5.33251e19 q^{37} +2.83116e19 q^{38} -6.03599e19 q^{39} +4.25600e19 q^{40} +3.82036e19 q^{41} +2.38594e20 q^{43} +2.85619e19 q^{44} -2.01098e20 q^{45} +4.30466e20 q^{46} -6.40416e20 q^{47} -5.68267e20 q^{48} +1.42540e21 q^{50} -1.56661e21 q^{51} -1.81580e21 q^{52} +2.95110e21 q^{53} +4.23543e21 q^{54} +6.86023e20 q^{55} -1.71195e21 q^{57} +1.42295e22 q^{58} +2.38398e22 q^{59} +1.49326e21 q^{60} +3.86405e21 q^{61} +7.57808e21 q^{62} +1.55903e22 q^{64} -4.36133e22 q^{65} -6.43067e21 q^{66} -3.90005e22 q^{67} -4.71281e22 q^{68} -2.60295e22 q^{69} -2.27758e23 q^{71} -9.77322e22 q^{72} +1.25483e23 q^{73} +3.61177e23 q^{74} -8.61914e22 q^{75} -5.15004e22 q^{76} +4.08825e23 q^{78} +7.68905e23 q^{79} -4.10605e23 q^{80} +3.19667e23 q^{81} -2.58757e23 q^{82} -5.33784e22 q^{83} -1.13196e24 q^{85} -1.61603e24 q^{86} -8.60434e23 q^{87} +3.33402e23 q^{88} +1.73696e24 q^{89} +1.36206e24 q^{90} -7.83041e23 q^{92} -4.58233e23 q^{93} +4.33761e24 q^{94} -1.23698e24 q^{95} +1.87251e24 q^{96} -8.77699e24 q^{97} -1.57534e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4230 q^{2} + 72104 q^{3} + 86658324 q^{4} - 110161332 q^{5} + 564962452 q^{6} - 381894066504 q^{8} + 1267694965630 q^{9}+O(q^{10}) $ 6 * q - 4230 * q^2 + 72104 * q^3 + 86658324 * q^4 - 110161332 * q^5 + 564962452 * q^6 - 381894066504 * q^8 + 1267694965630 * q^9	$ 6 q - 4230 q^{2} + 72104 q^{3} + 86658324 q^{4} - 110161332 q^{5} + 564962452 q^{6} - 381894066504 q^{8} + 1267694965630 q^{9} + 7032334098696 q^{10} - 1675999103976 q^{11} - 95344327788584 q^{12} - 5288670743748 q^{13} - 560616671505056 q^{15} + 13\!\cdots\!60 q^{16}+ \cdots + 68\!\cdots\!84 q^{99}+O(q^{100}) $ 6 * q - 4230 * q^2 + 72104 * q^3 + 86658324 * q^4 - 110161332 * q^5 + 564962452 * q^6 - 381894066504 * q^8 + 1267694965630 * q^9 + 7032334098696 * q^10 - 1675999103976 * q^11 - 95344327788584 * q^12 - 5288670743748 * q^13 - 560616671505056 * q^15 + 1309466880268560 * q^16 + 3300624486895572 * q^17 - 182370348755830 * q^18 - 23126727727224696 * q^19 + 7429228318925280 * q^20 - 151927901765810400 * q^22 - 1404739007274528 * q^23 + 574116984726291024 * q^24 - 358878993193236438 * q^25 - 55983697223735232 * q^26 + 3738929114579604272 * q^27 + 677678534303781204 * q^29 - 12333396849097754368 * q^30 + 14968503768754072128 * q^31 - 35397820044484059168 * q^32 + 28780935824255416640 * q^33 + 19031341748646640404 * q^34 - 133338488421715535404 * q^36 - 126677436437888686044 * q^37 + 168472707259280072940 * q^38 - 102293332568222925248 * q^39 + 244096086992012102784 * q^40 + 91172275091591492484 * q^41 + 256279402088758843128 * q^43 + 523240472821275944352 * q^44 - 425954983919737668388 * q^45 + 2793188902962758360160 * q^46 - 1325192902978491024192 * q^47 - 2218094363751553650848 * q^48 + 7093510193073768612174 * q^50 + 4055385291547172339280 * q^51 + 1158627608696168592240 * q^52 + 2430243658723437796644 * q^53 - 9117592238247181727912 * q^54 - 15235004455101638634096 * q^55 + 3144149027814187860784 * q^57 - 34089140824468755883596 * q^58 + 52366113046713140988408 * q^59 - 9058452201647015286784 * q^60 + 61668476505939948975420 * q^61 + 36076135594254562190088 * q^62 - 13681683367648116465600 * q^64 - 135029637414446696704440 * q^65 + 165155753913334928125792 * q^66 + 115555384699848804528264 * q^67 + 210104845567293225023496 * q^68 + 191810761136801340782400 * q^69 - 80949744331498661451408 * q^71 + 349152438285165555743160 * q^72 - 53635395837675567463068 * q^73 - 246393455603963396738364 * q^74 - 872061378794548947318344 * q^75 - 1329587552038733754873624 * q^76 + 1303314117900504997024976 * q^78 + 476522675249578322169600 * q^79 - 2769251653361564242057728 * q^80 + 1586143717126971946065190 * q^81 - 785889226268408247568044 * q^82 + 1138767694807125753084456 * q^83 - 1940596452584677200570360 * q^85 + 991916980058225455218288 * q^86 + 1175811061597622796340688 * q^87 - 3983469164122311567512256 * q^88 + 1342743539637531994392996 * q^89 + 2171364008623222233321448 * q^90 - 15426628722967874342364864 * q^92 - 8693521132310091454934880 * q^93 + 1117239000237980229879000 * q^94 - 11385290599630779530511936 * q^95 + 12455996958672134446553408 * q^96 + 14960201036659658714057172 * q^97 + 681381389460162479299384 * 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 $

$2$	−6773.12	−1.16927	−0.584633	−	0.811298i	$-0.698762\pi$
$2$	−6773.12	−1.16927	−0.584633	+	0.811298i	$0.698762\pi$
$3$	409558.	0.444938	0.222469	−	0.974940i	$-0.428588\pi$
$3$	409558.	0.444938	0.222469	+	0.974940i	$0.428588\pi$
$4$	1.23207e7	0.367185
$5$	2.95928e8	0.542077	0.271039	−	0.962568i	$-0.412633\pi$
$5$	2.95928e8	0.542077	0.271039	+	0.962568i	$0.412633\pi$
$6$	−2.77398e9	−0.520251
$7$	0	0
$7$	0	0
$8$	1.43819e11	0.739930
$9$	−6.79551e11	−0.802030
$10$	−2.00436e12	−0.633833
$11$	2.31821e12	0.222712	0.111356	−	0.993781i	$-0.464481\pi$
$11$	2.31821e12	0.222712	0.111356	+	0.993781i	$0.464481\pi$
$12$	5.04603e12	0.163374
$13$	−1.47378e14	−1.75445	−0.877225	−	0.480079i	$-0.840608\pi$
$13$	−1.47378e14	−1.75445	−0.877225	+	0.480079i	$0.840608\pi$
$14$	0	0
$15$	1.21200e14	0.241191
$16$	−1.38751e15	−1.23236
$17$	−3.82513e15	−1.59233	−0.796167	−	0.605077i	$-0.793142\pi$
$17$	−3.82513e15	−1.59233	−0.796167	+	0.605077i	$0.793142\pi$
$18$	4.60268e15	0.937787
$19$	−4.18000e15	−0.433268	−0.216634	−	0.976253i	$-0.569508\pi$
$19$	−4.18000e15	−0.433268	−0.216634	+	0.976253i	$0.569508\pi$
$20$	3.64603e15	0.199042
$21$	0	0
$22$	−1.57015e16	−0.260410
$23$	−6.35551e16	−0.604717	−0.302359	−	0.953194i	$-0.597774\pi$
$23$	−6.35551e16	−0.604717	−0.302359	+	0.953194i	$0.597774\pi$
$24$	5.89021e16	0.329223
$25$	−2.10450e17	−0.706152
$26$	9.98209e17	2.05142
$27$	−6.25329e17	−0.801792
$28$	0	0
$29$	−2.10088e18	−1.10262	−0.551312	−	0.834299i	$-0.685872\pi$
$29$	−2.10088e18	−1.10262	−0.551312	+	0.834299i	$0.685872\pi$
$30$	−8.20900e17	−0.282017
$31$	−1.11885e18	−0.255123	−0.127561	−	0.991831i	$-0.540715\pi$
$31$	−1.11885e18	−0.255123	−0.127561	+	0.991831i	$0.540715\pi$
$32$	4.57204e18	0.701027
$33$	9.49441e17	0.0990931
$34$	2.59080e19	1.86186
$35$	0	0
$36$	−8.37252e18	−0.294493
$37$	−5.33251e19	−1.33171	−0.665856	−	0.746081i	$-0.731933\pi$
$37$	−5.33251e19	−1.33171	−0.665856	+	0.746081i	$0.731933\pi$
$38$	2.83116e19	0.506606
$39$	−6.03599e19	−0.780622
$40$	4.25600e19	0.401099
$41$	3.82036e19	0.264427	0.132213	−	0.991221i	$-0.457792\pi$
$41$	3.82036e19	0.264427	0.132213	+	0.991221i	$0.457792\pi$
$42$	0	0
$43$	2.38594e20	0.910552	0.455276	−	0.890350i	$-0.349541\pi$
$43$	2.38594e20	0.910552	0.455276	+	0.890350i	$0.349541\pi$
$44$	2.85619e19	0.0817764
$45$	−2.01098e20	−0.434762
$46$	4.30466e20	0.707075
$47$	−6.40416e20	−0.803968	−0.401984	−	0.915647i	$-0.631679\pi$
$47$	−6.40416e20	−0.803968	−0.401984	+	0.915647i	$0.631679\pi$
$48$	−5.68267e20	−0.548324
$49$	0	0
$50$	1.42540e21	0.825680
$51$	−1.56661e21	−0.708490
$52$	−1.81580e21	−0.644207
$53$	2.95110e21	0.825156	0.412578	−	0.910922i	$-0.364628\pi$
$53$	2.95110e21	0.825156	0.412578	+	0.910922i	$0.364628\pi$
$54$	4.23543e21	0.937509
$55$	6.86023e20	0.120727
$56$	0	0
$57$	−1.71195e21	−0.192777
$58$	1.42295e22	1.28926
$59$	2.38398e22	1.74442	0.872212	−	0.489128i	$-0.162685\pi$
$59$	2.38398e22	1.74442	0.872212	+	0.489128i	$0.162685\pi$
$60$	1.49326e21	0.0885616
$61$	3.86405e21	0.186389	0.0931945	−	0.995648i	$-0.470292\pi$
$61$	3.86405e21	0.186389	0.0931945	+	0.995648i	$0.470292\pi$
$62$	7.57808e21	0.298307
$63$	0	0
$64$	1.55903e22	0.412672
$65$	−4.36133e22	−0.951048
$66$	−6.43067e21	−0.115866
$67$	−3.90005e22	−0.582284	−0.291142	−	0.956680i	$-0.594035\pi$
$67$	−3.90005e22	−0.582284	−0.291142	+	0.956680i	$0.594035\pi$
$68$	−4.71281e22	−0.584681
$69$	−2.60295e22	−0.269062
$70$	0	0
$71$	−2.27758e23	−1.64719	−0.823596	−	0.567176i	$-0.808036\pi$
$71$	−2.27758e23	−1.64719	−0.823596	+	0.567176i	$0.808036\pi$
$72$	−9.77322e22	−0.593446
$73$	1.25483e23	0.641282	0.320641	−	0.947201i	$-0.396102\pi$
$73$	1.25483e23	0.641282	0.320641	+	0.947201i	$0.396102\pi$
$74$	3.61177e23	1.55713
$75$	−8.61914e22	−0.314194
$76$	−5.15004e22	−0.159089
$77$	0	0
$78$	4.08825e23	0.912756
$79$	7.68905e23	1.46398	0.731988	−	0.681318i	$-0.238593\pi$
$79$	7.68905e23	1.46398	0.731988	+	0.681318i	$0.238593\pi$
$80$	−4.10605e23	−0.668034
$81$	3.19667e23	0.445282
$82$	−2.58757e23	−0.309186
$83$	−5.33784e22	−0.0548137	−0.0274069	−	0.999624i	$-0.508725\pi$
$83$	−5.33784e22	−0.0548137	−0.0274069	+	0.999624i	$0.508725\pi$
$84$	0	0
$85$	−1.13196e24	−0.863168
$86$	−1.61603e24	−1.06468
$87$	−8.60434e23	−0.490599
$88$	3.33402e23	0.164791
$89$	1.73696e24	0.745444	0.372722	−	0.927943i	$-0.378424\pi$
$89$	1.73696e24	0.745444	0.372722	+	0.927943i	$0.378424\pi$
$90$	1.36206e24	0.508353
$91$	0	0
$92$	−7.83041e23	−0.222043
$93$	−4.58233e23	−0.113514
$94$	4.33761e24	0.940053
$95$	−1.23698e24	−0.234865
$96$	1.87251e24	0.311914
$97$	−8.77699e24	−1.28440	−0.642198	−	0.766539i	$-0.721977\pi$
$97$	−8.77699e24	−1.28440	−0.642198	+	0.766539i	$0.721977\pi$
$98$	0	0
$99$	−1.57534e24	−0.178622
$100$	−2.59288e24	−0.259288
$101$	−9.41054e24	−0.830993	−0.415496	−	0.909595i	$-0.636392\pi$
$101$	−9.41054e24	−0.830993	−0.415496	+	0.909595i	$0.636392\pi$
$102$	1.06108e25	0.828414
$103$	1.46777e24	0.101436	0.0507181	−	0.998713i	$-0.483849\pi$
$103$	1.46777e24	0.101436	0.0507181	+	0.998713i	$0.483849\pi$
$104$	−2.11957e25	−1.29817
$105$	0	0
$106$	−1.99882e25	−0.964828
$107$	−3.21596e25	−1.38043	−0.690213	−	0.723606i	$-0.742483\pi$
$107$	−3.21596e25	−1.38043	−0.690213	+	0.723606i	$0.742483\pi$
$108$	−7.70447e24	−0.294406
$109$	2.45966e25	0.837613	0.418806	−	0.908076i	$-0.362449\pi$
$109$	2.45966e25	0.837613	0.418806	+	0.908076i	$0.362449\pi$
$110$	−4.64651e24	−0.141162
$111$	−2.18397e25	−0.592529
$112$	0	0
$113$	−1.08970e25	−0.236498	−0.118249	−	0.992984i	$-0.537728\pi$
$113$	−1.08970e25	−0.236498	−0.118249	+	0.992984i	$0.537728\pi$
$114$	1.15953e25	0.225408
$115$	−1.88077e25	−0.327803
$116$	−2.58843e25	−0.404866
$117$	1.00151e26	1.40712
$118$	−1.61470e26	−2.03970
$119$	0	0
$120$	1.74308e25	0.178464
$121$	−1.02973e26	−0.950399
$122$	−2.61717e25	−0.217938
$123$	1.56466e25	0.117654
$124$	−1.37849e25	−0.0936772
$125$	−1.50471e26	−0.924866
$126$	0	0
$127$	−3.43790e26	−1.73280	−0.866398	−	0.499355i	$-0.833570\pi$
$127$	−3.43790e26	−1.73280	−0.866398	+	0.499355i	$0.833570\pi$
$128$	−2.59007e26	−1.18355
$129$	9.77183e25	0.405139
$130$	2.95398e26	1.11203
$131$	2.73900e26	0.936917	0.468458	−	0.883486i	$-0.344810\pi$
$131$	2.73900e26	0.936917	0.468458	+	0.883486i	$0.344810\pi$
$132$	1.16977e25	0.0363855
$133$	0	0
$134$	2.64155e26	0.680845
$135$	−1.85053e26	−0.434633
$136$	−5.50125e26	−1.17822
$137$	−3.92342e26	−0.766756	−0.383378	−	0.923591i	$-0.625239\pi$
$137$	−3.92342e26	−0.766756	−0.383378	+	0.923591i	$0.625239\pi$
$138$	1.76301e26	0.314605
$139$	−2.06647e26	−0.336934	−0.168467	−	0.985707i	$-0.553882\pi$
$139$	−2.06647e26	−0.336934	−0.168467	+	0.985707i	$0.553882\pi$
$140$	0	0
$141$	−2.62287e26	−0.357716
$142$	1.54263e27	1.92601
$143$	−3.41653e26	−0.390737
$144$	9.42886e26	0.988390
$145$	−6.21711e26	−0.597707
$146$	−8.49911e26	−0.749830
$147$	0	0
$148$	−6.57001e26	−0.488984
$149$	−1.65904e27	−1.13509	−0.567544	−	0.823343i	$-0.692106\pi$
$149$	−1.65904e27	−1.13509	−0.567544	+	0.823343i	$0.692106\pi$
$150$	5.83784e26	0.367377
$151$	2.47812e27	1.43520	0.717598	−	0.696457i	$-0.245241\pi$
$151$	2.47812e27	1.43520	0.717598	+	0.696457i	$0.245241\pi$
$152$	−6.01163e26	−0.320588
$153$	2.59937e27	1.27710
$154$	0	0
$155$	−3.31098e26	−0.138296
$156$	−7.43674e26	−0.286632
$157$	2.46448e27	0.876959	0.438480	−	0.898741i	$-0.355517\pi$
$157$	2.46448e27	0.876959	0.438480	+	0.898741i	$0.355517\pi$
$158$	−5.20788e27	−1.71178
$159$	1.20865e27	0.367144
$160$	1.35299e27	0.380011
$161$	0	0
$162$	−2.16514e27	−0.520653
$163$	5.16511e27	1.15010	0.575049	−	0.818119i	$-0.304983\pi$
$163$	5.16511e27	1.15010	0.575049	+	0.818119i	$0.304983\pi$
$164$	4.70693e26	0.0970935
$165$	2.80966e26	0.0537161
$166$	3.61538e26	0.0640919
$167$	4.23428e27	0.696345	0.348172	−	0.937431i	$-0.386802\pi$
$167$	4.23428e27	0.696345	0.348172	+	0.937431i	$0.386802\pi$
$168$	0	0
$169$	1.46639e28	2.07810
$170$	7.66691e27	1.00927
$171$	2.84052e27	0.347494
$172$	2.93964e27	0.334340
$173$	8.87389e27	0.938724	0.469362	−	0.883006i	$-0.344484\pi$
$173$	8.87389e27	0.938724	0.469362	+	0.883006i	$0.344484\pi$
$174$	5.82782e27	0.573641
$175$	0	0
$176$	−3.21655e27	−0.274461
$177$	9.76377e27	0.776161
$178$	−1.17646e28	−0.871623
$179$	−7.22853e27	−0.499329	−0.249665	−	0.968332i	$-0.580320\pi$
$179$	−7.22853e27	−0.499329	−0.249665	+	0.968332i	$0.580320\pi$
$180$	−2.47766e27	−0.159638
$181$	2.69085e28	1.61774	0.808869	−	0.587989i	$-0.200080\pi$
$181$	2.69085e28	1.61774	0.808869	+	0.587989i	$0.200080\pi$
$182$	0	0
$183$	1.58255e27	0.0829316
$184$	−9.14041e27	−0.447448
$185$	−1.57804e28	−0.721891
$186$	3.10366e27	0.132728
$187$	−8.86744e27	−0.354632
$188$	−7.89035e27	−0.295205
$189$	0	0
$190$	8.37821e27	0.274619
$191$	3.29712e28	1.01209	0.506043	−	0.862508i	$-0.331108\pi$
$191$	3.29712e28	1.01209	0.506043	+	0.862508i	$0.331108\pi$
$192$	6.38513e27	0.183614
$193$	1.48087e28	0.399071	0.199535	−	0.979891i	$-0.436057\pi$
$193$	1.48087e28	0.399071	0.199535	+	0.979891i	$0.436057\pi$
$194$	5.94475e28	1.50180
$195$	−1.78622e28	−0.423158
$196$	0	0
$197$	−6.51488e28	−1.35856	−0.679280	−	0.733880i	$-0.737708\pi$
$197$	−6.51488e28	−1.35856	−0.679280	+	0.733880i	$0.737708\pi$
$198$	1.06700e28	0.208856
$199$	2.70894e27	0.0497892	0.0248946	−	0.999690i	$-0.492075\pi$
$199$	2.70894e27	0.0497892	0.0248946	+	0.999690i	$0.492075\pi$
$200$	−3.02666e28	−0.522503
$201$	−1.59730e28	−0.259080
$202$	6.37387e28	0.971652
$203$	0	0
$204$	−1.93017e28	−0.260147
$205$	1.13055e28	0.143340
$206$	−9.94138e27	−0.118606
$207$	4.31889e28	0.485001
$208$	2.04489e29	2.16212
$209$	−9.69011e27	−0.0964940
$210$	0	0
$211$	−8.77434e28	−0.775682	−0.387841	−	0.921726i	$-0.626779\pi$
$211$	−8.77434e28	−0.775682	−0.387841	+	0.921726i	$0.626779\pi$
$212$	3.63596e28	0.302985
$213$	−9.32801e28	−0.732899
$214$	2.17821e29	1.61409
$215$	7.06068e28	0.493589
$216$	−8.99341e28	−0.593270
$217$	0	0
$218$	−1.66595e29	−0.979393
$219$	5.13926e28	0.285331
$220$	8.45226e27	0.0443292
$221$	5.63740e29	2.79367
$222$	1.47923e29	0.692825
$223$	−3.67511e29	−1.62727	−0.813634	−	0.581377i	$-0.802514\pi$
$223$	−3.67511e29	−1.62727	−0.813634	+	0.581377i	$0.802514\pi$
$224$	0	0
$225$	1.43011e29	0.566355
$226$	7.38069e28	0.276530
$227$	−8.60145e28	−0.304964	−0.152482	−	0.988306i	$-0.548727\pi$
$227$	−8.60145e28	−0.304964	−0.152482	+	0.988306i	$0.548727\pi$
$228$	−2.10924e28	−0.0707849
$229$	5.23622e29	1.66370	0.831849	−	0.555002i	$-0.187283\pi$
$229$	5.23622e29	1.66370	0.831849	+	0.555002i	$0.187283\pi$
$230$	1.27387e29	0.383290
$231$	0	0
$232$	−3.02147e29	−0.815864
$233$	−2.42182e29	−0.619716	−0.309858	−	0.950783i	$-0.600281\pi$
$233$	−2.42182e29	−0.619716	−0.309858	+	0.950783i	$0.600281\pi$
$234$	−6.78334e29	−1.64530
$235$	−1.89517e29	−0.435813
$236$	2.93722e29	0.640525
$237$	3.14911e29	0.651379
$238$	0	0
$239$	−9.02512e29	−1.68066	−0.840328	−	0.542078i	$-0.817638\pi$
$239$	−9.02512e29	−1.68066	−0.840328	+	0.542078i	$0.817638\pi$
$240$	−1.68166e29	−0.297234
$241$	3.24790e29	0.544992	0.272496	−	0.962157i	$-0.412151\pi$
$241$	3.24790e29	0.544992	0.272496	+	0.962157i	$0.412151\pi$
$242$	6.97448e29	1.11127
$243$	6.60757e29	0.999915
$244$	4.76077e28	0.0684391
$245$	0	0
$246$	−1.05976e29	−0.137568
$247$	6.16041e29	0.760147
$248$	−1.60911e29	−0.188773
$249$	−2.18616e28	−0.0243887
$250$	1.01916e30	1.08142
$251$	3.08728e29	0.311641	0.155821	−	0.987785i	$-0.450198\pi$
$251$	3.08728e29	0.311641	0.155821	+	0.987785i	$0.450198\pi$
$252$	0	0
$253$	−1.47334e29	−0.134678
$254$	2.32853e30	2.02610
$255$	−4.63604e29	−0.384057
$256$	1.23116e30	0.971215
$257$	1.17693e30	0.884276	0.442138	−	0.896947i	$-0.354220\pi$
$257$	1.17693e30	0.884276	0.442138	+	0.896947i	$0.354220\pi$
$258$	−6.61857e29	−0.473716
$259$	0	0
$260$	−5.37346e29	−0.349210
$261$	1.42766e30	0.884337
$262$	−1.85516e30	−1.09551
$263$	−2.31474e30	−1.30333	−0.651667	−	0.758505i	$-0.725930\pi$
$263$	−2.31474e30	−1.30333	−0.651667	+	0.758505i	$0.725930\pi$
$264$	1.36547e29	0.0733220
$265$	8.73315e29	0.447299
$266$	0	0
$267$	7.11386e29	0.331677
$268$	−4.80512e29	−0.213806
$269$	1.42251e30	0.604158	0.302079	−	0.953283i	$-0.402319\pi$
$269$	1.42251e30	0.604158	0.302079	+	0.953283i	$0.402319\pi$
$270$	1.25338e30	0.508202
$271$	−8.30928e28	−0.0321697	−0.0160849	−	0.999871i	$-0.505120\pi$
$271$	−8.30928e28	−0.0321697	−0.0160849	+	0.999871i	$0.505120\pi$
$272$	5.30742e30	1.96233
$273$	0	0
$274$	2.65738e30	0.896543
$275$	−4.87866e29	−0.157269
$276$	−3.20701e29	−0.0987953
$277$	3.48537e30	1.02625	0.513123	−	0.858315i	$-0.328488\pi$
$277$	3.48537e30	1.02625	0.513123	+	0.858315i	$0.328488\pi$
$278$	1.39965e30	0.393966
$279$	7.60313e29	0.204616
$280$	0	0
$281$	2.08868e29	0.0514095	0.0257047	−	0.999670i	$-0.491817\pi$
$281$	2.08868e29	0.0514095	0.0257047	+	0.999670i	$0.491817\pi$
$282$	1.77650e30	0.418266
$283$	6.38331e29	0.143786	0.0718929	−	0.997412i	$-0.477096\pi$
$283$	6.38331e29	0.143786	0.0718929	+	0.997412i	$0.477096\pi$
$284$	−2.80613e30	−0.604824
$285$	−5.06615e29	−0.104500
$286$	2.31406e30	0.456876
$287$	0	0
$288$	−3.10693e30	−0.562245
$289$	8.86096e30	1.53553
$290$	4.21092e30	0.698879
$291$	−3.59468e30	−0.571477
$292$	1.54603e30	0.235469
$293$	8.58653e30	1.25306	0.626531	−	0.779397i	$-0.284474\pi$
$293$	8.58653e30	1.25306	0.626531	+	0.779397i	$0.284474\pi$
$294$	0	0
$295$	7.05486e30	0.945613
$296$	−7.66915e30	−0.985373
$297$	−1.44964e30	−0.178569
$298$	1.12369e31	1.32722
$299$	9.36663e30	1.06095
$300$	−1.06194e30	−0.115367
$301$	0	0
$302$	−1.67846e31	−1.67813
$303$	−3.85416e30	−0.369740
$304$	5.79981e30	0.533942
$305$	1.14348e30	0.101037
$306$	−1.76058e31	−1.49327
$307$	−2.19445e31	−1.78688	−0.893440	−	0.449182i	$-0.851716\pi$
$307$	−2.19445e31	−1.78688	−0.893440	+	0.449182i	$0.851716\pi$
$308$	0	0
$309$	6.01137e29	0.0451328
$310$	2.24257e30	0.161705
$311$	−1.63100e31	−1.12966	−0.564831	−	0.825206i	$-0.691059\pi$
$311$	−1.63100e31	−1.12966	−0.564831	+	0.825206i	$0.691059\pi$
$312$	−8.68088e30	−0.577606
$313$	−1.85387e31	−1.18516	−0.592578	−	0.805513i	$-0.701890\pi$
$313$	−1.85387e31	−1.18516	−0.592578	+	0.805513i	$0.701890\pi$
$314$	−1.66922e31	−1.02540
$315$	0	0
$316$	9.47342e30	0.537549
$317$	−6.92688e30	−0.377830	−0.188915	−	0.981993i	$-0.560497\pi$
$317$	−6.92688e30	−0.377830	−0.188915	+	0.981993i	$0.560497\pi$
$318$	−8.18632e30	−0.429289
$319$	−4.87029e30	−0.245568
$320$	4.61361e30	0.223700
$321$	−1.31712e31	−0.614205
$322$	0	0
$323$	1.59890e31	0.689907
$324$	3.93851e30	0.163501
$325$	3.10157e31	1.23891
$326$	−3.49839e31	−1.34477
$327$	1.00737e31	0.372686
$328$	5.49439e30	0.195657
$329$	0	0
$330$	−1.90302e30	−0.0628085
$331$	−4.10169e31	−1.30351	−0.651753	−	0.758431i	$-0.725966\pi$
$331$	−4.10169e31	−1.30351	−0.651753	+	0.758431i	$0.725966\pi$
$332$	−6.57658e29	−0.0201268
$333$	3.62371e31	1.06807
$334$	−2.86793e31	−0.814212
$335$	−1.15413e31	−0.315643
$336$	0	0
$337$	−5.58003e31	−1.41665	−0.708325	−	0.705886i	$-0.750549\pi$
$337$	−5.58003e31	−1.41665	−0.708325	+	0.705886i	$0.750549\pi$
$338$	−9.93204e31	−2.42985
$339$	−4.46297e30	−0.105227
$340$	−1.39465e31	−0.316942
$341$	−2.59372e30	−0.0568189
$342$	−1.92392e31	−0.406313
$343$	0	0
$344$	3.43144e31	0.673745
$345$	−7.70286e30	−0.145852
$346$	−6.01039e31	−1.09762
$347$	−1.97280e31	−0.347508	−0.173754	−	0.984789i	$-0.555590\pi$
$347$	−1.97280e31	−0.347508	−0.173754	+	0.984789i	$0.555590\pi$
$348$	−1.06011e31	−0.180140
$349$	−7.41920e31	−1.21630	−0.608148	−	0.793823i	$-0.708087\pi$
$349$	−7.41920e31	−1.21630	−0.608148	+	0.793823i	$0.708087\pi$
$350$	0	0
$351$	9.21599e31	1.40670
$352$	1.05989e31	0.156127
$353$	1.23012e32	1.74890	0.874451	−	0.485114i	$-0.161222\pi$
$353$	1.23012e32	1.74890	0.874451	+	0.485114i	$0.161222\pi$
$354$	−6.61311e31	−0.907539
$355$	−6.74000e31	−0.892906
$356$	2.14005e31	0.273716
$357$	0	0
$358$	4.89597e31	0.583849
$359$	8.50447e31	0.979415	0.489707	−	0.871887i	$-0.337104\pi$
$359$	8.50447e31	0.979415	0.489707	+	0.871887i	$0.337104\pi$
$360$	−2.89217e31	−0.321694
$361$	−7.56041e31	−0.812279
$362$	−1.82255e32	−1.89157
$363$	−4.21734e31	−0.422869
$364$	0	0
$365$	3.71340e31	0.347625
$366$	−1.07188e31	−0.0969691
$367$	1.72075e32	1.50450	0.752250	−	0.658878i	$-0.228969\pi$
$367$	1.72075e32	1.50450	0.752250	+	0.658878i	$0.228969\pi$
$368$	8.81835e31	0.745229
$369$	−2.59613e31	−0.212078
$370$	1.06882e32	0.844083
$371$	0	0
$372$	−5.64573e30	−0.0416806
$373$	2.98188e31	0.212878	0.106439	−	0.994319i	$-0.466055\pi$
$373$	2.98188e31	0.212878	0.106439	+	0.994319i	$0.466055\pi$
$374$	6.00602e31	0.414660
$375$	−6.16268e31	−0.411508
$376$	−9.21038e31	−0.594880
$377$	3.09624e32	1.93450
$378$	0	0
$379$	2.12971e31	0.124546	0.0622731	−	0.998059i	$-0.480165\pi$
$379$	2.12971e31	0.124546	0.0622731	+	0.998059i	$0.480165\pi$
$380$	−1.52404e31	−0.0862387
$381$	−1.40802e32	−0.770987
$382$	−2.23318e32	−1.18340
$383$	−2.65945e32	−1.36398	−0.681988	−	0.731363i	$-0.738885\pi$
$383$	−2.65945e32	−1.36398	−0.681988	+	0.731363i	$0.738885\pi$
$384$	−1.06078e32	−0.526607
$385$	0	0
$386$	−1.00301e32	−0.466620
$387$	−1.62137e32	−0.730290
$388$	−1.08138e32	−0.471610
$389$	2.16521e31	0.0914385	0.0457193	−	0.998954i	$-0.485442\pi$
$389$	2.16521e31	0.0914385	0.0457193	+	0.998954i	$0.485442\pi$
$390$	1.20983e32	0.494784
$391$	2.43106e32	0.962912
$392$	0	0
$393$	1.12178e32	0.416870
$394$	4.41260e32	1.58852
$395$	2.27541e32	0.793588
$396$	−1.94092e31	−0.0655871
$397$	4.79226e32	1.56913	0.784566	−	0.620046i	$-0.212886\pi$
$397$	4.79226e32	1.56913	0.784566	+	0.620046i	$0.212886\pi$
$398$	−1.83479e31	−0.0582169
$399$	0	0
$400$	2.92002e32	0.870234
$401$	−1.21193e32	−0.350084	−0.175042	−	0.984561i	$-0.556006\pi$
$401$	−1.21193e32	−0.350084	−0.175042	+	0.984561i	$0.556006\pi$
$402$	1.08187e32	0.302934
$403$	1.64894e32	0.447601
$404$	−1.15944e32	−0.305128
$405$	9.45985e31	0.241377
$406$	0	0
$407$	−1.23619e32	−0.296588
$408$	−2.25308e32	−0.524233
$409$	−2.16039e32	−0.487519	−0.243759	−	0.969836i	$-0.578381\pi$
$409$	−2.16039e32	−0.487519	−0.243759	+	0.969836i	$0.578381\pi$
$410$	−7.65735e31	−0.167603
$411$	−1.60687e32	−0.341159
$412$	1.80839e31	0.0372458
$413$	0	0
$414$	−2.92523e32	−0.567096
$415$	−1.57962e31	−0.0297133
$416$	−6.73818e32	−1.22992
$417$	−8.46340e31	−0.149915
$418$	6.56323e31	0.112827
$419$	−9.26495e32	−1.54585	−0.772926	−	0.634496i	$-0.781208\pi$
$419$	−9.26495e32	−1.54585	−0.772926	+	0.634496i	$0.781208\pi$
$420$	0	0
$421$	4.98353e32	0.783449	0.391724	−	0.920083i	$-0.371879\pi$
$421$	4.98353e32	0.783449	0.391724	+	0.920083i	$0.371879\pi$
$422$	5.94296e32	0.906979
$423$	4.35195e32	0.644807
$424$	4.24424e32	0.610558
$425$	8.04997e32	1.12443
$426$	6.31797e32	0.856954
$427$	0	0
$428$	−3.96228e32	−0.506871
$429$	−1.39927e32	−0.173854
$430$	−4.78228e32	−0.577138
$431$	1.45362e33	1.70407	0.852033	−	0.523488i	$-0.175369\pi$
$431$	1.45362e33	1.70407	0.852033	+	0.523488i	$0.175369\pi$
$432$	8.67653e32	0.988096
$433$	−1.61113e33	−1.78251	−0.891257	−	0.453499i	$-0.850176\pi$
$433$	−1.61113e33	−1.78251	−0.891257	+	0.453499i	$0.850176\pi$
$434$	0	0
$435$	−2.54627e32	−0.265943
$436$	3.03046e32	0.307558
$437$	2.65660e32	0.262004
$438$	−3.48088e32	−0.333628
$439$	7.34841e32	0.684521	0.342260	−	0.939605i	$-0.388807\pi$
$439$	7.34841e32	0.684521	0.342260	+	0.939605i	$0.388807\pi$
$440$	9.86630e31	0.0893297
$441$	0	0
$442$	−3.81828e33	−3.26655
$443$	−9.17044e31	−0.0762683	−0.0381341	−	0.999273i	$-0.512141\pi$
$443$	−9.17044e31	−0.0762683	−0.0381341	+	0.999273i	$0.512141\pi$
$444$	−2.69080e32	−0.217568
$445$	5.14016e32	0.404088
$446$	2.48919e33	1.90271
$447$	−6.79475e32	−0.505044
$448$	0	0
$449$	1.66803e32	0.117253	0.0586266	−	0.998280i	$-0.481328\pi$
$449$	1.66803e32	0.117253	0.0586266	+	0.998280i	$0.481328\pi$
$450$	−9.68632e32	−0.662220
$451$	8.85638e31	0.0588911
$452$	−1.34259e32	−0.0868385
$453$	1.01494e33	0.638574
$454$	5.82586e32	0.356584
$455$	0	0
$456$	−2.46211e32	−0.142642
$457$	−1.43070e33	−0.806486	−0.403243	−	0.915093i	$-0.632117\pi$
$457$	−1.43070e33	−0.806486	−0.403243	+	0.915093i	$0.632117\pi$
$458$	−3.54655e33	−1.94531
$459$	2.39196e33	1.27672
$460$	−2.31724e32	−0.120364
$461$	1.73079e33	0.874950	0.437475	−	0.899231i	$-0.355873\pi$
$461$	1.73079e33	0.874950	0.437475	+	0.899231i	$0.355873\pi$
$462$	0	0
$463$	1.38761e33	0.664514	0.332257	−	0.943189i	$-0.392190\pi$
$463$	1.38761e33	0.664514	0.332257	+	0.943189i	$0.392190\pi$
$464$	2.91501e33	1.35883
$465$	−1.35604e32	−0.0615333
$466$	1.64033e33	0.724613
$467$	−2.65157e33	−1.14036	−0.570180	−	0.821520i	$-0.693127\pi$
$467$	−2.65157e33	−1.14036	−0.570180	+	0.821520i	$0.693127\pi$
$468$	1.23393e33	0.516673
$469$	0	0
$470$	1.28362e33	0.509582
$471$	1.00935e33	0.390193
$472$	3.42861e33	1.29075
$473$	5.53111e32	0.202791
$474$	−2.13293e33	−0.761635
$475$	8.79680e32	0.305953
$476$	0	0
$477$	−2.00543e33	−0.661800
$478$	6.11282e33	1.96514
$479$	−9.98630e32	−0.312760	−0.156380	−	0.987697i	$-0.549982\pi$
$479$	−9.98630e32	−0.312760	−0.156380	+	0.987697i	$0.549982\pi$
$480$	5.54130e32	0.169081
$481$	7.85895e33	2.33642
$482$	−2.19984e33	−0.637241
$483$	0	0
$484$	−1.26870e33	−0.348972
$485$	−2.59736e33	−0.696242
$486$	−4.47538e33	−1.16917
$487$	−3.12212e33	−0.794947	−0.397474	−	0.917614i	$-0.630113\pi$
$487$	−3.12212e33	−0.794947	−0.397474	+	0.917614i	$0.630113\pi$
$488$	5.55723e32	0.137915
$489$	2.11541e33	0.511722
$490$	0	0
$491$	6.14315e33	1.41212	0.706062	−	0.708150i	$-0.250470\pi$
$491$	6.14315e33	1.41212	0.706062	+	0.708150i	$0.250470\pi$
$492$	1.92776e32	0.0432006
$493$	8.03615e33	1.75575
$494$	−4.17252e33	−0.888815
$495$	−4.66188e32	−0.0968268
$496$	1.55242e33	0.314403
$497$	0	0
$498$	1.48071e32	0.0285169
$499$	−2.08122e33	−0.390895	−0.195448	−	0.980714i	$-0.562616\pi$
$499$	−2.08122e33	−0.390895	−0.195448	+	0.980714i	$0.562616\pi$
$500$	−1.85391e33	−0.339597
$501$	1.73419e33	0.309830
$502$	−2.09105e33	−0.364392
$503$	5.57859e33	0.948253	0.474127	−	0.880457i	$-0.342764\pi$
$503$	5.57859e33	0.948253	0.474127	+	0.880457i	$0.342764\pi$
$504$	0	0
$505$	−2.78484e33	−0.450462
$506$	9.97909e32	0.157474
$507$	6.00572e33	0.924625
$508$	−4.23573e33	−0.636256
$509$	−1.09770e34	−1.60884	−0.804420	−	0.594061i	$-0.797524\pi$
$509$	−1.09770e34	−1.60884	−0.804420	+	0.594061i	$0.797524\pi$
$510$	3.14005e33	0.449065
$511$	0	0
$512$	3.52039e32	0.0479420
$513$	2.61388e33	0.347391
$514$	−7.97150e33	−1.03395
$515$	4.34355e32	0.0549863
$516$	1.20395e33	0.148761
$517$	−1.48462e33	−0.179053
$518$	0	0
$519$	3.63437e33	0.417674
$520$	−6.27242e33	−0.703709
$521$	1.28450e34	1.40690	0.703450	−	0.710745i	$-0.251642\pi$
$521$	1.28450e34	1.40690	0.703450	+	0.710745i	$0.251642\pi$
$522$	−9.66969e33	−1.03403
$523$	−6.90601e33	−0.721035	−0.360517	−	0.932752i	$-0.617400\pi$
$523$	−6.90601e33	−0.721035	−0.360517	+	0.932752i	$0.617400\pi$
$524$	3.37463e33	0.344021
$525$	0	0
$526$	1.56780e34	1.52395
$527$	4.27973e33	0.406241
$528$	−1.31736e33	−0.122118
$529$	−7.00652e33	−0.634317
$530$	−5.91506e33	−0.523011
$531$	−1.62003e34	−1.39908
$532$	0	0
$533$	−5.63037e33	−0.463924
$534$	−4.81830e33	−0.387818
$535$	−9.51693e33	−0.748298
$536$	−5.60900e33	−0.430849
$537$	−2.96050e33	−0.222171
$538$	−9.63480e33	−0.706422
$539$	0	0
$540$	−2.27997e33	−0.159591
$541$	−1.68575e34	−1.15300	−0.576498	−	0.817099i	$-0.695581\pi$
$541$	−1.68575e34	−1.15300	−0.576498	+	0.817099i	$0.695581\pi$
$542$	5.62797e32	0.0376150
$543$	1.10206e34	0.719793
$544$	−1.74886e34	−1.11627
$545$	7.27882e33	0.454051
$546$	0	0
$547$	2.42995e34	1.44796	0.723978	−	0.689823i	$-0.242312\pi$
$547$	2.42995e34	1.44796	0.723978	+	0.689823i	$0.242312\pi$
$548$	−4.83391e33	−0.281541
$549$	−2.62582e33	−0.149490
$550$	3.30437e33	0.183889
$551$	8.78170e33	0.477731
$552$	−3.74353e33	−0.199087
$553$	0	0
$554$	−2.36068e34	−1.19996
$555$	−6.46299e33	−0.321197
$556$	−2.54603e33	−0.123717
$557$	8.67800e33	0.412316	0.206158	−	0.978519i	$-0.433904\pi$
$557$	8.67800e33	0.412316	0.206158	+	0.978519i	$0.433904\pi$
$558$	−5.14969e33	−0.239251
$559$	−3.51636e34	−1.59752
$560$	0	0
$561$	−3.63173e33	−0.157789
$562$	−1.41469e33	−0.0601114
$563$	1.59573e34	0.663137	0.331568	−	0.943431i	$-0.392422\pi$
$563$	1.59573e34	0.663137	0.331568	+	0.943431i	$0.392422\pi$
$564$	−3.23156e33	−0.131348
$565$	−3.22474e33	−0.128200
$566$	−4.32349e33	−0.168124
$567$	0	0
$568$	−3.27559e34	−1.21881
$569$	−2.09020e34	−0.760826	−0.380413	−	0.924817i	$-0.624218\pi$
$569$	−2.09020e34	−0.760826	−0.380413	+	0.924817i	$0.624218\pi$
$570$	3.43136e33	0.122189
$571$	−4.60705e33	−0.160499	−0.0802494	−	0.996775i	$-0.525572\pi$
$571$	−4.60705e33	−0.160499	−0.0802494	+	0.996775i	$0.525572\pi$
$572$	−4.20940e33	−0.143473
$573$	1.35036e34	0.450316
$574$	0	0
$575$	1.33751e34	0.427022
$576$	−1.05944e34	−0.330975
$577$	4.00915e34	1.22562	0.612808	−	0.790232i	$-0.290040\pi$
$577$	4.00915e34	1.22562	0.612808	+	0.790232i	$0.290040\pi$
$578$	−6.00163e34	−1.79544
$579$	6.06501e33	0.177562
$580$	−7.65989e33	−0.219469
$581$	0	0
$582$	2.43472e34	0.668209
$583$	6.84127e33	0.183772
$584$	1.80468e34	0.474504
$585$	2.96375e34	0.762769
$586$	−5.81576e34	−1.46516
$587$	−2.22912e34	−0.549740	−0.274870	−	0.961481i	$-0.588635\pi$
$587$	−2.22912e34	−0.549740	−0.274870	+	0.961481i	$0.588635\pi$
$588$	0	0
$589$	4.67678e33	0.110537
$590$	−4.77834e34	−1.10567
$591$	−2.66822e34	−0.604475
$592$	7.39893e34	1.64115
$593$	−1.41069e34	−0.306371	−0.153186	−	0.988197i	$-0.548953\pi$
$593$	−1.41069e34	−0.306371	−0.153186	+	0.988197i	$0.548953\pi$
$594$	9.81860e33	0.208795
$595$	0	0
$596$	−2.04405e34	−0.416787
$597$	1.10947e33	0.0221531
$598$	−6.34413e34	−1.24053
$599$	−2.51658e34	−0.481920	−0.240960	−	0.970535i	$-0.577462\pi$
$599$	−2.51658e34	−0.481920	−0.240960	+	0.970535i	$0.577462\pi$
$600$	−1.23959e34	−0.232482
$601$	−1.69769e34	−0.311837	−0.155919	−	0.987770i	$-0.549834\pi$
$601$	−1.69769e34	−0.311837	−0.155919	+	0.987770i	$0.549834\pi$
$602$	0	0
$603$	2.65028e34	0.467009
$604$	3.05322e34	0.526982
$605$	−3.04726e34	−0.515190
$606$	2.61047e34	0.432325
$607$	1.84653e34	0.299569	0.149785	−	0.988719i	$-0.452142\pi$
$607$	1.84653e34	0.299569	0.149785	+	0.988719i	$0.452142\pi$
$608$	−1.91111e34	−0.303733
$609$	0	0
$610$	−7.74494e33	−0.118139
$611$	9.43833e34	1.41052
$612$	3.20259e34	0.468931
$613$	−1.01915e35	−1.46211	−0.731057	−	0.682316i	$-0.760973\pi$
$613$	−1.01915e35	−1.46211	−0.731057	+	0.682316i	$0.760973\pi$
$614$	1.48633e35	2.08934
$615$	4.63026e33	0.0637774
$616$	0	0
$617$	5.05477e34	0.668554	0.334277	−	0.942475i	$-0.391508\pi$
$617$	5.05477e34	0.668554	0.334277	+	0.942475i	$0.391508\pi$
$618$	−4.07157e33	−0.0527723
$619$	−1.83492e34	−0.233069	−0.116534	−	0.993187i	$-0.537179\pi$
$619$	−1.83492e34	−0.233069	−0.116534	+	0.993187i	$0.537179\pi$
$620$	−4.07935e33	−0.0507803
$621$	3.97428e34	0.484857
$622$	1.10469e35	1.32088
$623$	0	0
$624$	8.37502e34	0.962008
$625$	1.81902e34	0.204803
$626$	1.25565e35	1.38576
$627$	−3.96866e33	−0.0429339
$628$	3.03640e34	0.322006
$629$	2.03975e35	2.12053
$630$	0	0
$631$	−1.95172e35	−1.95008	−0.975038	−	0.222038i	$-0.928729\pi$
$631$	−1.95172e35	−1.95008	−0.975038	+	0.222038i	$0.928729\pi$
$632$	1.10583e35	1.08324
$633$	−3.59360e34	−0.345130
$634$	4.69165e34	0.441784
$635$	−1.01737e35	−0.939309
$636$	1.48914e34	0.134809
$637$	0	0
$638$	3.29870e34	0.287134
$639$	1.54773e35	1.32110
$640$	−7.66475e34	−0.641576
$641$	−7.28392e34	−0.597916	−0.298958	−	0.954266i	$-0.596639\pi$
$641$	−7.28392e34	−0.597916	−0.298958	+	0.954266i	$0.596639\pi$
$642$	8.92102e34	0.718169
$643$	1.96467e35	1.55115	0.775574	−	0.631257i	$-0.217461\pi$
$643$	1.96467e35	1.55115	0.775574	+	0.631257i	$0.217461\pi$
$644$	0	0
$645$	2.89176e34	0.219617
$646$	−1.08296e35	−0.806686
$647$	−9.76080e34	−0.713152	−0.356576	−	0.934266i	$-0.616056\pi$
$647$	−9.76080e34	−0.713152	−0.356576	+	0.934266i	$0.616056\pi$
$648$	4.59741e34	0.329478
$649$	5.52656e34	0.388504
$650$	−2.10073e35	−1.44862
$651$	0	0
$652$	6.36376e34	0.422298
$653$	−8.11963e34	−0.528593	−0.264297	−	0.964441i	$-0.585140\pi$
$653$	−8.11963e34	−0.528593	−0.264297	+	0.964441i	$0.585140\pi$
$654$	−6.82305e34	−0.435769
$655$	8.10547e34	0.507881
$656$	−5.30080e34	−0.325869
$657$	−8.52721e34	−0.514328
$658$	0	0
$659$	−7.01739e34	−0.407482	−0.203741	−	0.979025i	$-0.565310\pi$
$659$	−7.01739e34	−0.407482	−0.203741	+	0.979025i	$0.565310\pi$
$660$	3.46169e33	0.0197237
$661$	3.94655e34	0.220648	0.110324	−	0.993896i	$-0.464811\pi$
$661$	3.94655e34	0.220648	0.110324	+	0.993896i	$0.464811\pi$
$662$	2.77812e35	1.52415
$663$	2.30884e35	1.24301
$664$	−7.67682e33	−0.0405583
$665$	0	0
$666$	−2.45438e35	−1.24886
$667$	1.33522e35	0.666775
$668$	5.21692e34	0.255687
$669$	−1.50517e35	−0.724034
$670$	7.81708e34	0.369071
$671$	8.95768e33	0.0415111
$672$	0	0
$673$	−1.19160e35	−0.532039	−0.266019	−	0.963968i	$-0.585708\pi$
$673$	−1.19160e35	−0.532039	−0.266019	+	0.963968i	$0.585708\pi$
$674$	3.77942e35	1.65644
$675$	1.31600e35	0.566187
$676$	1.80669e35	0.763045
$677$	1.85072e34	0.0767332	0.0383666	−	0.999264i	$-0.487785\pi$
$677$	1.85072e34	0.0767332	0.0383666	+	0.999264i	$0.487785\pi$
$678$	3.02282e34	0.123039
$679$	0	0
$680$	−1.62797e35	−0.638684
$681$	−3.52279e34	−0.135690
$682$	1.75676e34	0.0664365
$683$	4.98233e35	1.85001	0.925005	−	0.379956i	$-0.124061\pi$
$683$	4.98233e35	1.85001	0.925005	+	0.379956i	$0.124061\pi$
$684$	3.49972e34	0.127594
$685$	−1.16105e35	−0.415641
$686$	0	0
$687$	2.14454e35	0.740243
$688$	−3.31053e35	−1.12213
$689$	−4.34928e35	−1.44770
$690$	5.21724e34	0.170540
$691$	3.00683e34	0.0965234	0.0482617	−	0.998835i	$-0.484632\pi$
$691$	3.00683e34	0.0965234	0.0482617	+	0.998835i	$0.484632\pi$
$692$	1.09332e35	0.344685
$693$	0	0
$694$	1.33620e35	0.406330
$695$	−6.11528e34	−0.182644
$696$	−1.23747e35	−0.363009
$697$	−1.46133e35	−0.421056
$698$	5.02511e35	1.42218
$699$	−9.91875e34	−0.275735
$700$	0	0
$701$	−4.63773e35	−1.24403	−0.622014	−	0.783006i	$-0.713685\pi$
$701$	−4.63773e35	−1.24403	−0.622014	+	0.783006i	$0.713685\pi$
$702$	−6.24210e35	−1.64481
$703$	2.22899e35	0.576988
$704$	3.61416e34	0.0919070
$705$	−7.76182e34	−0.193910
$706$	−8.33178e35	−2.04493
$707$	0	0
$708$	1.20296e35	0.284994
$709$	2.12563e35	0.494777	0.247389	−	0.968916i	$-0.420428\pi$
$709$	2.12563e35	0.494777	0.247389	+	0.968916i	$0.420428\pi$
$710$	4.56508e35	1.04405
$711$	−5.22510e35	−1.17415
$712$	2.49808e35	0.551576
$713$	7.11084e34	0.154277
$714$	0	0
$715$	−1.01105e35	−0.211810
$716$	−8.90603e34	−0.183346
$717$	−3.69631e35	−0.747789
$718$	−5.76017e35	−1.14520
$719$	−5.07325e35	−0.991231	−0.495616	−	0.868542i	$-0.665058\pi$
$719$	−5.07325e35	−0.991231	−0.495616	+	0.868542i	$0.665058\pi$
$720$	2.79027e35	0.535784
$721$	0	0
$722$	5.12075e35	0.949771
$723$	1.33020e35	0.242488
$724$	3.31531e35	0.594008
$725$	4.42131e35	0.778620
$726$	2.85645e35	0.494447
$727$	2.56553e35	0.436512	0.218256	−	0.975892i	$-0.429963\pi$
$727$	2.56553e35	0.436512	0.218256	+	0.975892i	$0.429963\pi$
$728$	0	0
$729$	−2.32130e32	−0.000381625 0
$730$	−2.51513e35	−0.406466
$731$	−9.12654e35	−1.44990
$732$	1.94981e34	0.0304512
$733$	−1.16699e36	−1.79171	−0.895854	−	0.444349i	$-0.853435\pi$
$733$	−1.16699e36	−1.79171	−0.895854	+	0.444349i	$0.853435\pi$
$734$	−1.16548e36	−1.75916
$735$	0	0
$736$	−2.90576e35	−0.423923
$737$	−9.04112e34	−0.129682
$738$	1.75839e35	0.247976
$739$	−1.64442e35	−0.228012	−0.114006	−	0.993480i	$-0.536368\pi$
$739$	−1.64442e35	−0.228012	−0.114006	+	0.993480i	$0.536368\pi$
$740$	−1.94425e35	−0.265067
$741$	2.52305e35	0.338219
$742$	0	0
$743$	−2.03968e34	−0.0264364	−0.0132182	−	0.999913i	$-0.504208\pi$
$743$	−2.03968e34	−0.0264364	−0.0132182	+	0.999913i	$0.504208\pi$
$744$	−6.59024e34	−0.0839924
$745$	−4.90958e35	−0.615305
$746$	−2.01967e35	−0.248911
$747$	3.62733e34	0.0439623
$748$	−1.09253e35	−0.130215
$749$	0	0
$750$	4.17405e35	0.481163
$751$	−5.30601e34	−0.0601546	−0.0300773	−	0.999548i	$-0.509575\pi$
$751$	−5.30601e34	−0.0601546	−0.0300773	+	0.999548i	$0.509575\pi$
$752$	8.88586e35	0.990778
$753$	1.26442e35	0.138661
$754$	−2.09712e36	−2.26194
$755$	7.33347e35	0.777987
$756$	0	0
$757$	1.14165e36	1.17175	0.585875	−	0.810401i	$-0.300751\pi$
$757$	1.14165e36	1.17175	0.585875	+	0.810401i	$0.300751\pi$
$758$	−1.44248e35	−0.145628
$759$	−6.03418e34	−0.0599233
$760$	−1.77901e35	−0.173783
$761$	−4.76825e35	−0.458195	−0.229098	−	0.973403i	$-0.573578\pi$
$761$	−4.76825e35	−0.458195	−0.229098	+	0.973403i	$0.573578\pi$
$762$	9.53669e35	0.901489
$763$	0	0
$764$	4.06227e35	0.371623
$765$	7.69226e35	0.692287
$766$	1.80128e36	1.59485
$767$	−3.51346e36	−3.06051
$768$	5.04232e35	0.432131
$769$	1.70413e36	1.43689	0.718446	−	0.695582i	$-0.244854\pi$
$769$	1.70413e36	1.43689	0.718446	+	0.695582i	$0.244854\pi$
$770$	0	0
$771$	4.82022e35	0.393448
$772$	1.82453e35	0.146533
$773$	1.28815e36	1.01794	0.508971	−	0.860783i	$-0.330026\pi$
$773$	1.28815e36	1.01794	0.508971	+	0.860783i	$0.330026\pi$
$774$	1.09817e36	0.853903
$775$	2.35461e35	0.180156
$776$	−1.26230e36	−0.950363
$777$	0	0
$778$	−1.46652e35	−0.106916
$779$	−1.59691e35	−0.114568
$780$	−2.20074e35	−0.155377
$781$	−5.27991e35	−0.366850
$782$	−1.64659e36	−1.12590
$783$	1.31374e36	0.884075
$784$	0	0
$785$	7.29309e35	0.475380
$786$	−7.59794e35	−0.487432
$787$	3.10717e36	1.96192	0.980960	−	0.194212i	$-0.0622149\pi$
$787$	3.10717e36	1.96192	0.980960	+	0.194212i	$0.0622149\pi$
$788$	−8.02677e35	−0.498842
$789$	−9.48022e35	−0.579904
$790$	−1.54116e36	−0.927916
$791$	0	0
$792$	−2.26563e35	−0.132168
$793$	−5.69477e35	−0.327010
$794$	−3.24585e36	−1.83473
$795$	3.57673e35	0.199020
$796$	3.33759e34	0.0182818
$797$	2.72707e35	0.147051	0.0735254	−	0.997293i	$-0.476575\pi$
$797$	2.72707e35	0.147051	0.0735254	+	0.997293i	$0.476575\pi$
$798$	0	0
$799$	2.44967e36	1.28019
$800$	−9.62184e35	−0.495032
$801$	−1.18035e36	−0.597868
$802$	8.20853e35	0.409342
$803$	2.90896e35	0.142821
$804$	−1.96797e35	−0.0951303
$805$	0	0
$806$	−1.11684e36	−0.523364
$807$	5.82599e35	0.268813
$808$	−1.35341e36	−0.614876
$809$	3.10086e36	1.38716	0.693578	−	0.720382i	$-0.256033\pi$
$809$	3.10086e36	1.38716	0.693578	+	0.720382i	$0.256033\pi$
$810$	−6.40727e35	−0.282234
$811$	2.24112e35	0.0972087	0.0486044	−	0.998818i	$-0.484523\pi$
$811$	2.24112e35	0.0972087	0.0486044	+	0.998818i	$0.484523\pi$
$812$	0	0
$813$	−3.40313e34	−0.0143135
$814$	8.37283e35	0.346791
$815$	1.52850e36	0.623442
$816$	2.17369e36	0.873115
$817$	−9.97325e35	−0.394513
$818$	1.46326e36	0.570039
$819$	0	0
$820$	1.39291e35	0.0526322
$821$	1.47674e35	0.0549561	0.0274780	−	0.999622i	$-0.491252\pi$
$821$	1.47674e35	0.0549561	0.0274780	+	0.999622i	$0.491252\pi$
$822$	1.08835e36	0.398906
$823$	−5.05065e36	−1.82326	−0.911632	−	0.411007i	$-0.865177\pi$
$823$	−5.05065e36	−1.82326	−0.911632	+	0.411007i	$0.865177\pi$
$824$	2.11093e35	0.0750557
$825$	−1.99810e35	−0.0699748
$826$	0	0
$827$	−5.13655e36	−1.74523	−0.872615	−	0.488408i	$-0.837578\pi$
$827$	−5.13655e36	−1.74523	−0.872615	+	0.488408i	$0.837578\pi$
$828$	5.32116e35	0.178085
$829$	−3.20083e36	−1.05519	−0.527596	−	0.849495i	$-0.676906\pi$
$829$	−3.20083e36	−1.05519	−0.527596	+	0.849495i	$0.676906\pi$
$830$	1.06989e35	0.0347428
$831$	1.42746e36	0.456616
$832$	−2.29767e36	−0.724013
$833$	0	0
$834$	5.73236e35	0.175290
$835$	1.25304e36	0.377473
$836$	−1.19389e35	−0.0354311
$837$	6.99648e35	0.204555
$838$	6.27526e36	1.80751
$839$	−5.13463e36	−1.45708	−0.728542	−	0.685001i	$-0.759802\pi$
$839$	−5.13463e36	−1.45708	−0.728542	+	0.685001i	$0.759802\pi$
$840$	0	0
$841$	7.83354e35	0.215778
$842$	−3.37540e36	−0.916060
$843$	8.55436e34	0.0228740
$844$	−1.08106e36	−0.284818
$845$	4.33946e36	1.12649
$846$	−2.94763e36	−0.753951
$847$	0	0
$848$	−4.09470e36	−1.01689
$849$	2.61434e35	0.0639758
$850$	−5.45234e36	−1.31476
$851$	3.38908e36	0.805309
$852$	−1.14927e36	−0.269109
$853$	−2.02379e36	−0.466985	−0.233492	−	0.972359i	$-0.575015\pi$
$853$	−2.02379e36	−0.466985	−0.233492	+	0.972359i	$0.575015\pi$
$854$	0	0
$855$	8.40591e35	0.188369
$856$	−4.62515e36	−1.02142
$857$	3.17553e36	0.691124	0.345562	−	0.938396i	$-0.387688\pi$
$857$	3.17553e36	0.691124	0.345562	+	0.938396i	$0.387688\pi$
$858$	9.47740e35	0.203282
$859$	−6.64347e36	−1.40437	−0.702183	−	0.711996i	$-0.747791\pi$
$859$	−6.64347e36	−1.40437	−0.702183	+	0.711996i	$0.747791\pi$
$860$	8.69923e35	0.181238
$861$	0	0
$862$	−9.84557e36	−1.99251
$863$	3.44524e35	0.0687202	0.0343601	−	0.999410i	$-0.489061\pi$
$863$	3.44524e35	0.0687202	0.0343601	+	0.999410i	$0.489061\pi$
$864$	−2.85903e36	−0.562078
$865$	2.62603e36	0.508861
$866$	1.09124e37	2.08423
$867$	3.62908e36	0.683215
$868$	0	0
$869$	1.78248e36	0.326045
$870$	1.72462e36	0.310958
$871$	5.74782e36	1.02159
$872$	3.53745e36	0.619775
$873$	5.96441e36	1.03012
$874$	−1.79935e36	−0.306353
$875$	0	0
$876$	6.33191e35	0.104769
$877$	5.47032e36	0.892314	0.446157	−	0.894955i	$-0.352792\pi$
$877$	5.47032e36	0.892314	0.446157	+	0.894955i	$0.352792\pi$
$878$	−4.97716e36	−0.800387
$879$	3.51668e36	0.557535
$880$	−9.51867e35	−0.148779
$881$	1.00780e37	1.55301	0.776504	−	0.630113i	$-0.216991\pi$
$881$	1.00780e37	1.55301	0.776504	+	0.630113i	$0.216991\pi$
$882$	0	0
$883$	7.97022e36	1.19388	0.596941	−	0.802285i	$-0.296383\pi$
$883$	7.97022e36	1.19388	0.596941	+	0.802285i	$0.296383\pi$
$884$	6.94565e36	1.02579
$885$	2.88937e36	0.420739
$886$	6.21125e35	0.0891779
$887$	1.08006e37	1.52898	0.764492	−	0.644633i	$-0.222990\pi$
$887$	1.08006e37	1.52898	0.764492	+	0.644633i	$0.222990\pi$
$888$	−3.14096e36	−0.438430
$889$	0	0
$890$	−3.48149e36	−0.472487
$891$	7.41055e35	0.0991697
$892$	−4.52798e36	−0.597508
$893$	2.67694e36	0.348334
$894$	4.60216e36	0.590531
$895$	−2.13913e36	−0.270675
$896$	0	0
$897$	3.83618e36	0.472056
$898$	−1.12978e36	−0.137100
$899$	2.35057e36	0.281304
$900$	1.76199e36	0.207957
$901$	−1.12883e37	−1.31392
$902$	−5.99853e35	−0.0688594
$903$	0	0
$904$	−1.56720e36	−0.174992
$905$	7.96300e36	0.876939
$906$	−6.87428e36	−0.746663
$907$	8.85234e35	0.0948346	0.0474173	−	0.998875i	$-0.484901\pi$
$907$	8.85234e35	0.0948346	0.0474173	+	0.998875i	$0.484901\pi$
$908$	−1.05976e36	−0.111978
$909$	6.39494e36	0.666481
$910$	0	0
$911$	5.43422e36	0.551008	0.275504	−	0.961300i	$-0.411155\pi$
$911$	5.43422e36	0.551008	0.275504	+	0.961300i	$0.411155\pi$
$912$	2.37536e36	0.237571
$913$	−1.23742e35	−0.0122077
$914$	9.69031e36	0.942997
$915$	4.68322e35	0.0449553
$916$	6.45137e36	0.610884
$917$	0	0
$918$	−1.62010e37	−1.49283
$919$	6.23496e36	0.566748	0.283374	−	0.959010i	$-0.408546\pi$
$919$	6.23496e36	0.566748	0.283374	+	0.959010i	$0.408546\pi$
$920$	−2.70490e36	−0.242552
$921$	−8.98754e36	−0.795052
$922$	−1.17229e37	−1.02305
$923$	3.35666e37	2.88992
$924$	0	0
$925$	1.12223e37	0.940391
$926$	−9.39842e36	−0.776994
$927$	−9.97425e35	−0.0813549
$928$	−9.60532e36	−0.772969
$929$	−3.48926e36	−0.277036	−0.138518	−	0.990360i	$-0.544234\pi$
$929$	−3.48926e36	−0.277036	−0.138518	+	0.990360i	$0.544234\pi$
$930$	9.18461e35	0.0719489
$931$	0	0
$932$	−2.98384e36	−0.227550
$933$	−6.67989e36	−0.502630
$934$	1.79594e37	1.33339
$935$	−2.62412e36	−0.192238
$936$	1.44036e37	1.04117
$937$	−1.13746e36	−0.0811317	−0.0405658	−	0.999177i	$-0.512916\pi$
$937$	−1.13746e36	−0.0811317	−0.0405658	+	0.999177i	$0.512916\pi$
$938$	0	0
$939$	−7.59269e36	−0.527322
$940$	−2.33498e36	−0.160024
$941$	1.54142e37	1.04244	0.521218	−	0.853424i	$-0.325478\pi$
$941$	1.54142e37	1.04244	0.521218	+	0.853424i	$0.325478\pi$
$942$	−6.83642e36	−0.456239
$943$	−2.42803e36	−0.159903
$944$	−3.30780e37	−2.14976
$945$	0	0
$946$	−3.74629e36	−0.237117
$947$	2.74267e37	1.71316	0.856582	−	0.516011i	$-0.172584\pi$
$947$	2.74267e37	1.71316	0.856582	+	0.516011i	$0.172584\pi$
$948$	3.87991e36	0.239176
$949$	−1.84935e37	−1.12510
$950$	−5.95818e36	−0.357741
$951$	−2.83696e36	−0.168111
$952$	0	0
$953$	1.55355e37	0.896732	0.448366	−	0.893850i	$-0.352006\pi$
$953$	1.55355e37	0.896732	0.448366	+	0.893850i	$0.352006\pi$
$954$	1.35830e37	0.773821
$955$	9.75711e36	0.548629
$956$	−1.11195e37	−0.617111
$957$	−1.99466e36	−0.109262
$958$	6.76384e36	0.365700
$959$	0	0
$960$	1.88954e36	0.0995327
$961$	−1.79810e37	−0.934912
$962$	−5.32296e37	−2.73190
$963$	2.18541e37	1.10714
$964$	4.00163e36	0.200113
$965$	4.38231e36	0.216327
$966$	0	0
$967$	1.86406e37	0.896663	0.448331	−	0.893867i	$-0.352018\pi$
$967$	1.86406e37	0.896663	0.448331	+	0.893867i	$0.352018\pi$
$968$	−1.48094e37	−0.703229
$969$	6.54844e36	0.306966
$970$	1.75922e37	0.814092
$971$	−2.15437e37	−0.984193	−0.492096	−	0.870541i	$-0.663769\pi$
$971$	−2.15437e37	−0.984193	−0.492096	+	0.870541i	$0.663769\pi$
$972$	8.14096e36	0.367153
$973$	0	0
$974$	2.11465e37	0.929505
$975$	1.27027e37	0.551238
$976$	−5.36143e36	−0.229698
$977$	−2.67839e37	−1.13290	−0.566451	−	0.824095i	$-0.691684\pi$
$977$	−2.67839e37	−1.13290	−0.566451	+	0.824095i	$0.691684\pi$
$978$	−1.43279e37	−0.598340
$979$	4.02664e36	0.166019
$980$	0	0
$981$	−1.67146e37	−0.671790
$982$	−4.16083e37	−1.65115
$983$	1.53979e37	0.603315	0.301657	−	0.953416i	$-0.402460\pi$
$983$	1.53979e37	0.603315	0.301657	+	0.953416i	$0.402460\pi$
$984$	2.25027e36	0.0870555
$985$	−1.92794e37	−0.736444
$986$	−5.44298e37	−2.05293
$987$	0	0
$988$	7.59004e36	0.279114
$989$	−1.51639e37	−0.550626
$990$	3.15754e36	0.113216
$991$	−1.87224e37	−0.662889	−0.331444	−	0.943475i	$-0.607536\pi$
$991$	−1.87224e37	−0.662889	−0.331444	+	0.943475i	$0.607536\pi$
$992$	−5.11541e36	−0.178848
$993$	−1.67988e37	−0.579980
$994$	0	0
$995$	8.01651e35	0.0269896
$996$	−2.69349e35	−0.00895516
$997$	1.12441e37	0.369176	0.184588	−	0.982816i	$-0.440905\pi$
$997$	1.12441e37	0.369176	0.184588	+	0.982816i	$0.440905\pi$
$998$	1.40963e37	0.457061
$999$	3.33457e37	1.06776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.c.1.2		6
7.6	odd	2		7.26.a.a.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.26.a.a.1.2	✓	6	7.6	odd	2
49.26.a.c.1.2		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q-6773.12 q^{2} +409558. q^{3} +1.23207e7 q^{4} +2.95928e8 q^{5} -2.77398e9 q^{6} +1.43819e11 q^{8} -6.79551e11 q^{9} +O(q^{10})\)	\(q-6773.12 q^{2} +409558. q^{3} +1.23207e7 q^{4} +2.95928e8 q^{5} -2.77398e9 q^{6} +1.43819e11 q^{8} -6.79551e11 q^{9} -2.00436e12 q^{10} +2.31821e12 q^{11} +5.04603e12 q^{12} -1.47378e14 q^{13} +1.21200e14 q^{15} -1.38751e15 q^{16} -3.82513e15 q^{17} +4.60268e15 q^{18} -4.18000e15 q^{19} +3.64603e15 q^{20} -1.57015e16 q^{22} -6.35551e16 q^{23} +5.89021e16 q^{24} -2.10450e17 q^{25} +9.98209e17 q^{26} -6.25329e17 q^{27} -2.10088e18 q^{29} -8.20900e17 q^{30} -1.11885e18 q^{31} +4.57204e18 q^{32} +9.49441e17 q^{33} +2.59080e19 q^{34} -8.37252e18 q^{36} -5.33251e19 q^{37} +2.83116e19 q^{38} -6.03599e19 q^{39} +4.25600e19 q^{40} +3.82036e19 q^{41} +2.38594e20 q^{43} +2.85619e19 q^{44} -2.01098e20 q^{45} +4.30466e20 q^{46} -6.40416e20 q^{47} -5.68267e20 q^{48} +1.42540e21 q^{50} -1.56661e21 q^{51} -1.81580e21 q^{52} +2.95110e21 q^{53} +4.23543e21 q^{54} +6.86023e20 q^{55} -1.71195e21 q^{57} +1.42295e22 q^{58} +2.38398e22 q^{59} +1.49326e21 q^{60} +3.86405e21 q^{61} +7.57808e21 q^{62} +1.55903e22 q^{64} -4.36133e22 q^{65} -6.43067e21 q^{66} -3.90005e22 q^{67} -4.71281e22 q^{68} -2.60295e22 q^{69} -2.27758e23 q^{71} -9.77322e22 q^{72} +1.25483e23 q^{73} +3.61177e23 q^{74} -8.61914e22 q^{75} -5.15004e22 q^{76} +4.08825e23 q^{78} +7.68905e23 q^{79} -4.10605e23 q^{80} +3.19667e23 q^{81} -2.58757e23 q^{82} -5.33784e22 q^{83} -1.13196e24 q^{85} -1.61603e24 q^{86} -8.60434e23 q^{87} +3.33402e23 q^{88} +1.73696e24 q^{89} +1.36206e24 q^{90} -7.83041e23 q^{92} -4.58233e23 q^{93} +4.33761e24 q^{94} -1.23698e24 q^{95} +1.87251e24 q^{96} -8.77699e24 q^{97} -1.57534e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4230 q^{2} + 72104 q^{3} + 86658324 q^{4} - 110161332 q^{5} + 564962452 q^{6} - 381894066504 q^{8} + 1267694965630 q^{9}+O(q^{10}) \) 6 * q - 4230 * q^2 + 72104 * q^3 + 86658324 * q^4 - 110161332 * q^5 + 564962452 * q^6 - 381894066504 * q^8 + 1267694965630 * q^9	\( 6 q - 4230 q^{2} + 72104 q^{3} + 86658324 q^{4} - 110161332 q^{5} + 564962452 q^{6} - 381894066504 q^{8} + 1267694965630 q^{9} + 7032334098696 q^{10} - 1675999103976 q^{11} - 95344327788584 q^{12} - 5288670743748 q^{13} - 560616671505056 q^{15} + 13\!\cdots\!60 q^{16}+ \cdots + 68\!\cdots\!84 q^{99}+O(q^{100}) \) 6 * q - 4230 * q^2 + 72104 * q^3 + 86658324 * q^4 - 110161332 * q^5 + 564962452 * q^6 - 381894066504 * q^8 + 1267694965630 * q^9 + 7032334098696 * q^10 - 1675999103976 * q^11 - 95344327788584 * q^12 - 5288670743748 * q^13 - 560616671505056 * q^15 + 1309466880268560 * q^16 + 3300624486895572 * q^17 - 182370348755830 * q^18 - 23126727727224696 * q^19 + 7429228318925280 * q^20 - 151927901765810400 * q^22 - 1404739007274528 * q^23 + 574116984726291024 * q^24 - 358878993193236438 * q^25 - 55983697223735232 * q^26 + 3738929114579604272 * q^27 + 677678534303781204 * q^29 - 12333396849097754368 * q^30 + 14968503768754072128 * q^31 - 35397820044484059168 * q^32 + 28780935824255416640 * q^33 + 19031341748646640404 * q^34 - 133338488421715535404 * q^36 - 126677436437888686044 * q^37 + 168472707259280072940 * q^38 - 102293332568222925248 * q^39 + 244096086992012102784 * q^40 + 91172275091591492484 * q^41 + 256279402088758843128 * q^43 + 523240472821275944352 * q^44 - 425954983919737668388 * q^45 + 2793188902962758360160 * q^46 - 1325192902978491024192 * q^47 - 2218094363751553650848 * q^48 + 7093510193073768612174 * q^50 + 4055385291547172339280 * q^51 + 1158627608696168592240 * q^52 + 2430243658723437796644 * q^53 - 9117592238247181727912 * q^54 - 15235004455101638634096 * q^55 + 3144149027814187860784 * q^57 - 34089140824468755883596 * q^58 + 52366113046713140988408 * q^59 - 9058452201647015286784 * q^60 + 61668476505939948975420 * q^61 + 36076135594254562190088 * q^62 - 13681683367648116465600 * q^64 - 135029637414446696704440 * q^65 + 165155753913334928125792 * q^66 + 115555384699848804528264 * q^67 + 210104845567293225023496 * q^68 + 191810761136801340782400 * q^69 - 80949744331498661451408 * q^71 + 349152438285165555743160 * q^72 - 53635395837675567463068 * q^73 - 246393455603963396738364 * q^74 - 872061378794548947318344 * q^75 - 1329587552038733754873624 * q^76 + 1303314117900504997024976 * q^78 + 476522675249578322169600 * q^79 - 2769251653361564242057728 * q^80 + 1586143717126971946065190 * q^81 - 785889226268408247568044 * q^82 + 1138767694807125753084456 * q^83 - 1940596452584677200570360 * q^85 + 991916980058225455218288 * q^86 + 1175811061597622796340688 * q^87 - 3983469164122311567512256 * q^88 + 1342743539637531994392996 * q^89 + 2171364008623222233321448 * q^90 - 15426628722967874342364864 * q^92 - 8693521132310091454934880 * q^93 + 1117239000237980229879000 * q^94 - 11385290599630779530511936 * q^95 + 12455996958672134446553408 * q^96 + 14960201036659658714057172 * q^97 + 681381389460162479299384 * q^99

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