LMFDB - Embedded newform 49.26.a.c.1.6

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			1.6
Root			$-4372.34$ 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)

$f(q)$	$=$	$q+8040.68 q^{2} -902351. q^{3} +3.10981e7 q^{4} +9.26311e8 q^{5} -7.25551e9 q^{6} -1.97508e10 q^{8} -3.30517e10 q^{9} +O(q^{10})$	\(q+8040.68 q^{2} -902351. q^{3} +3.10981e7 q^{4} +9.26311e8 q^{5} -7.25551e9 q^{6} -1.97508e10 q^{8} -3.30517e10 q^{9} +7.44816e12 q^{10} -1.37417e13 q^{11} -2.80614e13 q^{12} -3.23829e13 q^{13} -8.35857e14 q^{15} -1.20229e15 q^{16} +1.03453e15 q^{17} -2.65758e14 q^{18} -1.17351e16 q^{19} +2.88065e16 q^{20} -1.10493e17 q^{22} +1.48049e17 q^{23} +1.78222e16 q^{24} +5.60028e17 q^{25} -2.60381e17 q^{26} +7.94376e17 q^{27} +7.97569e17 q^{29} -6.72086e18 q^{30} +3.05931e18 q^{31} -9.00448e18 q^{32} +1.23999e19 q^{33} +8.31832e18 q^{34} -1.02784e18 q^{36} -6.79802e19 q^{37} -9.43579e19 q^{38} +2.92208e19 q^{39} -1.82954e19 q^{40} +1.95010e20 q^{41} +3.06939e20 q^{43} -4.27341e20 q^{44} -3.06161e19 q^{45} +1.19041e21 q^{46} +4.24801e20 q^{47} +1.08489e21 q^{48} +4.50300e21 q^{50} -9.33508e20 q^{51} -1.00705e21 q^{52} -9.04307e19 q^{53} +6.38732e21 q^{54} -1.27291e22 q^{55} +1.05891e22 q^{57} +6.41300e21 q^{58} +1.41832e22 q^{59} -2.59935e22 q^{60} +5.69533e21 q^{61} +2.45989e22 q^{62} -3.20601e22 q^{64} -2.99967e22 q^{65} +9.97033e22 q^{66} +7.93553e22 q^{67} +3.21719e22 q^{68} -1.33592e23 q^{69} -6.43720e22 q^{71} +6.52797e20 q^{72} -2.03888e23 q^{73} -5.46606e23 q^{74} -5.05342e23 q^{75} -3.64938e23 q^{76} +2.34955e23 q^{78} -3.85500e23 q^{79} -1.11369e24 q^{80} -6.88801e23 q^{81} +1.56801e24 q^{82} +1.53926e24 q^{83} +9.58295e23 q^{85} +2.46800e24 q^{86} -7.19687e23 q^{87} +2.71411e23 q^{88} -1.48876e24 q^{89} -2.46174e23 q^{90} +4.60403e24 q^{92} -2.76057e24 q^{93} +3.41569e24 q^{94} -1.08703e25 q^{95} +8.12520e24 q^{96} +1.19099e25 q^{97} +4.54187e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8040.68	1.38809	0.694045	−	0.719931i	$-0.255827\pi$
$2$	8040.68	1.38809	0.694045	+	0.719931i	$0.255827\pi$
$3$	−902351.	−0.980302	−0.490151	−	0.871638i	$-0.663058\pi$
$3$	−902351.	−0.980302	−0.490151	+	0.871638i	$0.663058\pi$
$4$	3.10981e7	0.926795
$5$	9.26311e8	1.69680	0.848402	−	0.529353i	$-0.177565\pi$
$5$	9.26311e8	1.69680	0.848402	+	0.529353i	$0.177565\pi$
$6$	−7.25551e9	−1.36075
$7$	0	0
$7$	0	0
$8$	−1.97508e10	−0.101616
$9$	−3.30517e10	−0.0390087
$10$	7.44816e12	2.35532
$11$	−1.37417e13	−1.32018	−0.660090	−	0.751187i	$-0.729482\pi$
$11$	−1.37417e13	−1.32018	−0.660090	+	0.751187i	$0.729482\pi$
$12$	−2.80614e13	−0.908538
$13$	−3.23829e13	−0.385500	−0.192750	−	0.981248i	$-0.561741\pi$
$13$	−3.23829e13	−0.385500	−0.192750	+	0.981248i	$0.561741\pi$
$14$	0	0
$15$	−8.35857e14	−1.66338
$16$	−1.20229e15	−1.06785
$17$	1.03453e15	0.430657	0.215328	−	0.976542i	$-0.430918\pi$
$17$	1.03453e15	0.430657	0.215328	+	0.976542i	$0.430918\pi$
$18$	−2.65758e14	−0.0541477
$19$	−1.17351e16	−1.21637	−0.608185	−	0.793796i	$-0.708102\pi$
$19$	−1.17351e16	−1.21637	−0.608185	+	0.793796i	$0.708102\pi$
$20$	2.88065e16	1.57259
$21$	0	0
$22$	−1.10493e17	−1.83253
$23$	1.48049e17	1.40866	0.704332	−	0.709871i	$-0.251247\pi$
$23$	1.48049e17	1.40866	0.704332	+	0.709871i	$0.251247\pi$
$24$	1.78222e16	0.0996139
$25$	5.60028e17	1.87914
$26$	−2.60381e17	−0.535109
$27$	7.94376e17	1.01854
$28$	0	0
$29$	7.97569e17	0.418594	0.209297	−	0.977852i	$-0.432882\pi$
$29$	7.97569e17	0.418594	0.209297	+	0.977852i	$0.432882\pi$
$30$	−6.72086e18	−2.30892
$31$	3.05931e18	0.697593	0.348797	−	0.937198i	$-0.386590\pi$
$31$	3.05931e18	0.697593	0.348797	+	0.937198i	$0.386590\pi$
$32$	−9.00448e18	−1.38065
$33$	1.23999e19	1.29417
$34$	8.31832e18	0.597790
$35$	0	0
$36$	−1.02784e18	−0.0361531
$37$	−6.79802e19	−1.69770	−0.848849	−	0.528635i	$-0.822704\pi$
$37$	−6.79802e19	−1.69770	−0.848849	+	0.528635i	$0.822704\pi$
$38$	−9.43579e19	−1.68843
$39$	2.92208e19	0.377906
$40$	−1.82954e19	−0.172422
$41$	1.95010e20	1.34977	0.674883	−	0.737924i	$-0.264194\pi$
$41$	1.95010e20	1.34977	0.674883	+	0.737924i	$0.264194\pi$
$42$	0	0
$43$	3.06939e20	1.17138	0.585688	−	0.810537i	$-0.300824\pi$
$43$	3.06939e20	1.17138	0.585688	+	0.810537i	$0.300824\pi$
$44$	−4.27341e20	−1.22354
$45$	−3.06161e19	−0.0661902
$46$	1.19041e21	1.95535
$47$	4.24801e20	0.533289	0.266644	−	0.963795i	$-0.414085\pi$
$47$	4.24801e20	0.533289	0.266644	+	0.963795i	$0.414085\pi$
$48$	1.08489e21	1.04681
$49$	0	0
$50$	4.50300e21	2.60842
$51$	−9.33508e20	−0.422173
$52$	−1.00705e21	−0.357279
$53$	−9.04307e19	−0.0252853	−0.0126426	−	0.999920i	$-0.504024\pi$
$53$	−9.04307e19	−0.0252853	−0.0126426	+	0.999920i	$0.504024\pi$
$54$	6.38732e21	1.41383
$55$	−1.27291e22	−2.24009
$56$	0	0
$57$	1.05891e22	1.19241
$58$	6.41300e21	0.581047
$59$	1.41832e22	1.03782	0.518911	−	0.854828i	$-0.326338\pi$
$59$	1.41832e22	1.03782	0.518911	+	0.854828i	$0.326338\pi$
$60$	−2.59935e22	−1.54161
$61$	5.69533e21	0.274723	0.137362	−	0.990521i	$-0.456138\pi$
$61$	5.69533e21	0.274723	0.137362	+	0.990521i	$0.456138\pi$
$62$	2.45989e22	0.968323
$63$	0	0
$64$	−3.20601e22	−0.848623
$65$	−2.99967e22	−0.654118
$66$	9.97033e22	1.79643
$67$	7.93553e22	1.18479	0.592394	−	0.805648i	$-0.298183\pi$
$67$	7.93553e22	1.18479	0.592394	+	0.805648i	$0.298183\pi$
$68$	3.21719e22	0.399130
$69$	−1.33592e23	−1.38091
$70$	0	0
$71$	−6.43720e22	−0.465552	−0.232776	−	0.972530i	$-0.574781\pi$
$71$	−6.43720e22	−0.465552	−0.232776	+	0.972530i	$0.574781\pi$
$72$	6.52797e20	0.00396390
$73$	−2.03888e23	−1.04197	−0.520986	−	0.853565i	$-0.674436\pi$
$73$	−2.03888e23	−1.04197	−0.520986	+	0.853565i	$0.674436\pi$
$74$	−5.46606e23	−2.35656
$75$	−5.05342e23	−1.84213
$76$	−3.64938e23	−1.12732
$77$	0	0
$78$	2.34955e23	0.524568
$79$	−3.85500e23	−0.733982	−0.366991	−	0.930224i	$-0.619612\pi$
$79$	−3.85500e23	−0.733982	−0.366991	+	0.930224i	$0.619612\pi$
$80$	−1.11369e24	−1.81193
$81$	−6.88801e23	−0.959470
$82$	1.56801e24	1.87360
$83$	1.53926e24	1.58065	0.790325	−	0.612687i	$-0.209912\pi$
$83$	1.53926e24	1.58065	0.790325	+	0.612687i	$0.209912\pi$
$84$	0	0
$85$	9.58295e23	0.730740
$86$	2.46800e24	1.62597
$87$	−7.19687e23	−0.410349
$88$	2.71411e23	0.134151
$89$	−1.48876e24	−0.638926	−0.319463	−	0.947599i	$-0.603503\pi$
$89$	−1.48876e24	−0.638926	−0.319463	+	0.947599i	$0.603503\pi$
$90$	−2.46174e23	−0.0918779
$91$	0	0
$92$	4.60403e24	1.30554
$93$	−2.76057e24	−0.683852
$94$	3.41569e24	0.740253
$95$	−1.08703e25	−2.06394
$96$	8.12520e24	1.35345
$97$	1.19099e25	1.74286	0.871429	−	0.490522i	$-0.163194\pi$
$97$	1.19099e25	1.74286	0.871429	+	0.490522i	$0.163194\pi$
$98$	0	0
$99$	4.54187e23	0.0514985
$100$	1.74158e25	1.74158
$101$	−7.70553e24	−0.680433	−0.340216	−	0.940347i	$-0.610500\pi$
$101$	−7.70553e24	−0.680433	−0.340216	+	0.940347i	$0.610500\pi$
$102$	−7.50604e24	−0.586015
$103$	−1.03386e25	−0.714491	−0.357246	−	0.934010i	$-0.616284\pi$
$103$	−1.03386e25	−0.714491	−0.357246	+	0.934010i	$0.616284\pi$
$104$	6.39590e23	0.0391728
$105$	0	0
$106$	−7.27124e23	−0.0350982
$107$	−1.53357e25	−0.658271	−0.329136	−	0.944283i	$-0.606757\pi$
$107$	−1.53357e25	−0.658271	−0.329136	+	0.944283i	$0.606757\pi$
$108$	2.47036e25	0.943979
$109$	5.35067e25	1.82212	0.911061	−	0.412272i	$-0.135265\pi$
$109$	5.35067e25	1.82212	0.911061	+	0.412272i	$0.135265\pi$
$110$	−1.02351e26	−3.10944
$111$	6.13419e25	1.66426
$112$	0	0
$113$	1.85847e25	0.403345	0.201672	−	0.979453i	$-0.435362\pi$
$113$	1.85847e25	0.403345	0.201672	+	0.979453i	$0.435362\pi$
$114$	8.51439e25	1.65517
$115$	1.37139e26	2.39022
$116$	2.48029e25	0.387951
$117$	1.07031e24	0.0150379
$118$	1.14042e26	1.44059
$119$	0	0
$120$	1.65089e25	0.169025
$121$	8.04883e25	0.742874
$122$	4.57943e25	0.381341
$123$	−1.75967e26	−1.32318
$124$	9.51386e25	0.646526
$125$	2.42698e26	1.49173
$126$	0	0
$127$	2.14526e26	1.08127	0.540634	−	0.841258i	$-0.318184\pi$
$127$	2.14526e26	1.08127	0.540634	+	0.841258i	$0.318184\pi$
$128$	4.43557e25	0.202687
$129$	−2.76966e26	−1.14830
$130$	−2.41193e26	−0.907974
$131$	2.48902e26	0.851405	0.425703	−	0.904863i	$-0.360027\pi$
$131$	2.48902e26	0.851405	0.425703	+	0.904863i	$0.360027\pi$
$132$	3.85612e26	1.19943
$133$	0	0
$134$	6.38070e26	1.64459
$135$	7.35839e26	1.72827
$136$	−2.04328e25	−0.0437614
$137$	1.72872e26	0.337845	0.168922	−	0.985629i	$-0.445971\pi$
$137$	1.72872e26	0.337845	0.168922	+	0.985629i	$0.445971\pi$
$138$	−1.07417e27	−1.91683
$139$	7.75075e26	1.26374	0.631872	−	0.775073i	$-0.282287\pi$
$139$	7.75075e26	1.26374	0.631872	+	0.775073i	$0.282287\pi$
$140$	0	0
$141$	−3.83320e26	−0.522784
$142$	−5.17595e26	−0.646228
$143$	4.44998e26	0.508929
$144$	3.97376e25	0.0416553
$145$	7.38797e26	0.710272
$146$	−1.63940e27	−1.44635
$147$	0	0
$148$	−2.11405e27	−1.57342
$149$	−5.38018e26	−0.368102	−0.184051	−	0.982917i	$-0.558921\pi$
$149$	−5.38018e26	−0.368102	−0.184051	+	0.982917i	$0.558921\pi$
$150$	−4.06329e27	−2.55704
$151$	−2.03565e27	−1.17894	−0.589470	−	0.807790i	$-0.700663\pi$
$151$	−2.03565e27	−1.17894	−0.589470	+	0.807790i	$0.700663\pi$
$152$	2.31777e26	0.123602
$153$	−3.41929e25	−0.0167994
$154$	0	0
$155$	2.83387e27	1.18368
$156$	9.08709e26	0.350241
$157$	3.26528e27	1.16192	0.580958	−	0.813933i	$-0.302678\pi$
$157$	3.26528e27	1.16192	0.580958	+	0.813933i	$0.302678\pi$
$158$	−3.09968e27	−1.01883
$159$	8.16002e25	0.0247872
$160$	−8.34095e27	−2.34269
$161$	0	0
$162$	−5.53843e27	−1.33183
$163$	−6.33197e27	−1.40992	−0.704959	−	0.709248i	$-0.749034\pi$
$163$	−6.33197e27	−1.40992	−0.704959	+	0.709248i	$0.749034\pi$
$164$	6.06443e27	1.25096
$165$	1.14861e28	2.19596
$166$	1.23767e28	2.19409
$167$	3.20645e27	0.527313	0.263656	−	0.964617i	$-0.415071\pi$
$167$	3.20645e27	0.527313	0.263656	+	0.964617i	$0.415071\pi$
$168$	0	0
$169$	−6.00776e27	−0.851390
$170$	7.70534e27	1.01433
$171$	3.87863e26	0.0474490
$172$	9.54520e27	1.08562
$173$	6.79740e27	0.719062	0.359531	−	0.933133i	$-0.382937\pi$
$173$	6.79740e27	0.719062	0.359531	+	0.933133i	$0.382937\pi$
$174$	−5.78677e27	−0.569601
$175$	0	0
$176$	1.65215e28	1.40975
$177$	−1.27982e28	−1.01738
$178$	−1.19707e28	−0.886887
$179$	2.80722e28	1.93916	0.969581	−	0.244769i	$-0.0787122\pi$
$179$	2.80722e28	1.93916	0.969581	+	0.244769i	$0.0787122\pi$
$180$	−9.52102e26	−0.0613447
$181$	−1.23995e28	−0.745459	−0.372729	−	0.927940i	$-0.621578\pi$
$181$	−1.23995e28	−0.745459	−0.372729	+	0.927940i	$0.621578\pi$
$182$	0	0
$183$	−5.13918e27	−0.269312
$184$	−2.92409e27	−0.143142
$185$	−6.29707e28	−2.88066
$186$	−2.21969e28	−0.949248
$187$	−1.42162e28	−0.568544
$188$	1.32105e28	0.494249
$189$	0	0
$190$	−8.74047e28	−2.86493
$191$	5.97116e27	0.183291	0.0916456	−	0.995792i	$-0.470787\pi$
$191$	5.97116e27	0.183291	0.0916456	+	0.995792i	$0.470787\pi$
$192$	2.89294e28	0.831906
$193$	6.39070e28	1.72219	0.861097	−	0.508440i	$-0.169778\pi$
$193$	6.39070e28	1.72219	0.861097	+	0.508440i	$0.169778\pi$
$194$	9.57637e28	2.41924
$195$	2.70675e28	0.641233
$196$	0	0
$197$	−3.73504e28	−0.778875	−0.389438	−	0.921053i	$-0.627331\pi$
$197$	−3.73504e28	−0.778875	−0.389438	+	0.921053i	$0.627331\pi$
$198$	3.65197e27	0.0714846
$199$	8.92527e28	1.64043	0.820215	−	0.572055i	$-0.193854\pi$
$199$	8.92527e28	1.64043	0.820215	+	0.572055i	$0.193854\pi$
$200$	−1.10610e28	−0.190950
$201$	−7.16063e28	−1.16145
$202$	−6.19577e28	−0.944502
$203$	0	0
$204$	−2.90303e28	−0.391268
$205$	1.80640e29	2.29029
$206$	−8.31294e28	−0.991778
$207$	−4.89326e27	−0.0549502
$208$	3.89336e28	0.411655
$209$	1.61260e29	1.60583
$210$	0	0
$211$	2.06240e28	0.182323	0.0911616	−	0.995836i	$-0.470942\pi$
$211$	2.06240e28	0.182323	0.0911616	+	0.995836i	$0.470942\pi$
$212$	−2.81222e27	−0.0234342
$213$	5.80862e28	0.456381
$214$	−1.23309e29	−0.913740
$215$	2.84321e29	1.98759
$216$	−1.56896e28	−0.103500
$217$	0	0
$218$	4.30231e29	2.52927
$219$	1.83978e29	1.02145
$220$	−3.95851e29	−2.07610
$221$	−3.35011e28	−0.166018
$222$	4.93231e29	2.31014
$223$	−1.23726e29	−0.547836	−0.273918	−	0.961753i	$-0.588320\pi$
$223$	−1.23726e29	−0.547836	−0.273918	+	0.961753i	$0.588320\pi$
$224$	0	0
$225$	−1.85099e28	−0.0733030
$226$	1.49434e29	0.559879
$227$	2.56841e29	0.910627	0.455314	−	0.890331i	$-0.349527\pi$
$227$	2.56841e29	0.910627	0.455314	+	0.890331i	$0.349527\pi$
$228$	3.29302e29	1.10512
$229$	−3.29384e29	−1.04655	−0.523273	−	0.852165i	$-0.675289\pi$
$229$	−3.29384e29	−1.04655	−0.523273	+	0.852165i	$0.675289\pi$
$230$	1.10269e30	3.31785
$231$	0	0
$232$	−1.57526e28	−0.0425357
$233$	−3.46081e29	−0.885582	−0.442791	−	0.896625i	$-0.646012\pi$
$233$	−3.46081e29	−0.885582	−0.442791	+	0.896625i	$0.646012\pi$
$234$	8.60602e27	0.0208739
$235$	3.93498e29	0.904886
$236$	4.41069e29	0.961848
$237$	3.47856e29	0.719524
$238$	0	0
$239$	−1.74885e29	−0.325670	−0.162835	−	0.986653i	$-0.552064\pi$
$239$	−1.74885e29	−0.325670	−0.162835	+	0.986653i	$0.552064\pi$
$240$	1.00494e30	1.77623
$241$	−5.41242e29	−0.908193	−0.454096	−	0.890953i	$-0.650038\pi$
$241$	−5.41242e29	−0.908193	−0.454096	+	0.890953i	$0.650038\pi$
$242$	6.47180e29	1.03118
$243$	−5.15251e28	−0.0779724
$244$	1.77114e29	0.254612
$245$	0	0
$246$	−1.41490e30	−1.83669
$247$	3.80016e29	0.468910
$248$	−6.04239e28	−0.0708864
$249$	−1.38895e30	−1.54951
$250$	1.95145e30	2.07066
$251$	6.66536e28	0.0672825	0.0336413	−	0.999434i	$-0.489290\pi$
$251$	6.66536e28	0.0672825	0.0336413	+	0.999434i	$0.489290\pi$
$252$	0	0
$253$	−2.03445e30	−1.85969
$254$	1.72494e30	1.50090
$255$	−8.64718e29	−0.716345
$256$	1.43241e30	1.12997
$257$	1.73143e29	0.130089	0.0650446	−	0.997882i	$-0.479281\pi$
$257$	1.73143e29	0.130089	0.0650446	+	0.997882i	$0.479281\pi$
$258$	−2.22700e30	−1.59395
$259$	0	0
$260$	−9.32838e29	−0.606233
$261$	−2.63610e28	−0.0163288
$262$	2.00134e30	1.18183
$263$	2.00644e30	1.12974	0.564870	−	0.825180i	$-0.308926\pi$
$263$	2.00644e30	1.12974	0.564870	+	0.825180i	$0.308926\pi$
$264$	−2.44908e29	−0.131508
$265$	−8.37669e28	−0.0429041
$266$	0	0
$267$	1.34339e30	0.626340
$268$	2.46780e30	1.09806
$269$	−1.37595e30	−0.584385	−0.292193	−	0.956359i	$-0.594385\pi$
$269$	−1.37595e30	−0.584385	−0.292193	+	0.956359i	$0.594385\pi$
$270$	5.91664e30	2.39899
$271$	1.91136e30	0.739991	0.369996	−	0.929034i	$-0.379359\pi$
$271$	1.91136e30	0.739991	0.369996	+	0.929034i	$0.379359\pi$
$272$	−1.24380e30	−0.459875
$273$	0	0
$274$	1.39001e30	0.468959
$275$	−7.69576e30	−2.48081
$276$	−4.15445e30	−1.27982
$277$	2.98028e30	0.877526	0.438763	−	0.898603i	$-0.355417\pi$
$277$	2.98028e30	0.877526	0.438763	+	0.898603i	$0.355417\pi$
$278$	6.23213e30	1.75419
$279$	−1.01115e29	−0.0272122
$280$	0	0
$281$	−5.65416e30	−1.39168	−0.695839	−	0.718198i	$-0.744967\pi$
$281$	−5.65416e30	−1.39168	−0.695839	+	0.718198i	$0.744967\pi$
$282$	−3.08215e30	−0.725671
$283$	−2.91926e30	−0.657570	−0.328785	−	0.944405i	$-0.606639\pi$
$283$	−2.91926e30	−0.657570	−0.328785	+	0.944405i	$0.606639\pi$
$284$	−2.00185e30	−0.431471
$285$	9.80884e30	2.02328
$286$	3.57808e30	0.706440
$287$	0	0
$288$	2.97613e29	0.0538575
$289$	−4.70038e30	−0.814535
$290$	5.94043e30	0.985922
$291$	−1.07469e31	−1.70853
$292$	−6.34052e30	−0.965694
$293$	−1.06610e31	−1.55580	−0.777900	−	0.628389i	$-0.783715\pi$
$293$	−1.06610e31	−1.55580	−0.777900	+	0.628389i	$0.783715\pi$
$294$	0	0
$295$	1.31380e31	1.76098
$296$	1.34266e30	0.172513
$297$	−1.09161e31	−1.34466
$298$	−4.32603e30	−0.510959
$299$	−4.79426e30	−0.543040
$300$	−1.57152e31	−1.70727
$301$	0	0
$302$	−1.63680e31	−1.63648
$303$	6.95309e30	0.667029
$304$	1.41089e31	1.29890
$305$	5.27564e30	0.466152
$306$	−2.74934e29	−0.0233190
$307$	9.30049e30	0.757315	0.378657	−	0.925537i	$-0.376386\pi$
$307$	9.30049e30	0.757315	0.378657	+	0.925537i	$0.376386\pi$
$308$	0	0
$309$	9.32905e30	0.700417
$310$	2.27862e31	1.64305
$311$	4.76521e30	0.330048	0.165024	−	0.986290i	$-0.447230\pi$
$311$	4.76521e30	0.330048	0.165024	+	0.986290i	$0.447230\pi$
$312$	−5.77134e29	−0.0384012
$313$	−1.31266e31	−0.839168	−0.419584	−	0.907717i	$-0.637824\pi$
$313$	−1.31266e31	−0.839168	−0.419584	+	0.907717i	$0.637824\pi$
$314$	2.62551e31	1.61284
$315$	0	0
$316$	−1.19883e31	−0.680251
$317$	1.56934e31	0.856008	0.428004	−	0.903777i	$-0.359217\pi$
$317$	1.56934e31	0.856008	0.428004	+	0.903777i	$0.359217\pi$
$318$	6.56121e29	0.0344068
$319$	−1.09600e31	−0.552620
$320$	−2.96976e31	−1.43995
$321$	1.38381e31	0.645305
$322$	0	0
$323$	−1.21403e31	−0.523838
$324$	−2.14204e31	−0.889231
$325$	−1.81354e31	−0.724409
$326$	−5.09133e31	−1.95709
$327$	−4.82819e31	−1.78623
$328$	−3.85161e30	−0.137157
$329$	0	0
$330$	9.23563e31	3.04819
$331$	3.60603e30	0.114599	0.0572993	−	0.998357i	$-0.481751\pi$
$331$	3.60603e30	0.114599	0.0572993	+	0.998357i	$0.481751\pi$
$332$	4.78680e31	1.46494
$333$	2.24686e30	0.0662251
$334$	2.57820e31	0.731958
$335$	7.35076e31	2.01035
$336$	0	0
$337$	2.83258e31	0.719131	0.359566	−	0.933120i	$-0.382925\pi$
$337$	2.83258e31	0.719131	0.359566	+	0.933120i	$0.382925\pi$
$338$	−4.83064e31	−1.18181
$339$	−1.67700e31	−0.395399
$340$	2.98011e31	0.677246
$341$	−4.20402e31	−0.920949
$342$	3.11868e30	0.0658635
$343$	0	0
$344$	−6.06229e30	−0.119030
$345$	−1.23748e32	−2.34314
$346$	5.46557e31	0.998123
$347$	5.23392e31	0.921952	0.460976	−	0.887413i	$-0.347499\pi$
$347$	5.23392e31	0.921952	0.460976	+	0.887413i	$0.347499\pi$
$348$	−2.23809e31	−0.380309
$349$	1.35820e31	0.222661	0.111331	−	0.993783i	$-0.464489\pi$
$349$	1.35820e31	0.222661	0.111331	+	0.993783i	$0.464489\pi$
$350$	0	0
$351$	−2.57242e31	−0.392648
$352$	1.23737e32	1.82271
$353$	9.70750e31	1.38014	0.690071	−	0.723742i	$-0.257579\pi$
$353$	9.70750e31	1.38014	0.690071	+	0.723742i	$0.257579\pi$
$354$	−1.02906e32	−1.41221
$355$	−5.96285e31	−0.789950
$356$	−4.62977e31	−0.592153
$357$	0	0
$358$	2.25720e32	2.69173
$359$	2.78063e31	0.320231	0.160115	−	0.987098i	$-0.448813\pi$
$359$	2.78063e31	0.320231	0.160115	+	0.987098i	$0.448813\pi$
$360$	6.04693e29	0.00672595
$361$	4.46352e31	0.479554
$362$	−9.97007e31	−1.03476
$363$	−7.26286e31	−0.728241
$364$	0	0
$365$	−1.88864e32	−1.76802
$366$	−4.13225e31	−0.373829
$367$	−4.09808e31	−0.358306	−0.179153	−	0.983821i	$-0.557336\pi$
$367$	−4.09808e31	−0.358306	−0.179153	+	0.983821i	$0.557336\pi$
$368$	−1.77997e32	−1.50424
$369$	−6.44540e30	−0.0526527
$370$	−5.06327e32	−3.99862
$371$	0	0
$372$	−8.58484e31	−0.633790
$373$	−2.71449e31	−0.193789	−0.0968944	−	0.995295i	$-0.530891\pi$
$373$	−2.71449e31	−0.193789	−0.0968944	+	0.995295i	$0.530891\pi$
$374$	−1.14308e32	−0.789191
$375$	−2.18999e32	−1.46235
$376$	−8.39017e30	−0.0541904
$377$	−2.58276e31	−0.161368
$378$	0	0
$379$	−3.10519e32	−1.81592	−0.907962	−	0.419053i	$-0.862362\pi$
$379$	−3.10519e32	−1.81592	−0.907962	+	0.419053i	$0.862362\pi$
$380$	−3.38046e32	−1.91285
$381$	−1.93578e32	−1.05997
$382$	4.80122e31	0.254425
$383$	6.99453e31	0.358735	0.179367	−	0.983782i	$-0.442595\pi$
$383$	6.99453e31	0.358735	0.179367	+	0.983782i	$0.442595\pi$
$384$	−4.00244e31	−0.198694
$385$	0	0
$386$	5.13856e32	2.39056
$387$	−1.01448e31	−0.0456939
$388$	3.70375e32	1.61527
$389$	2.05251e32	0.866791	0.433396	−	0.901204i	$-0.357315\pi$
$389$	2.05251e32	0.866791	0.433396	+	0.901204i	$0.357315\pi$
$390$	2.17641e32	0.890089
$391$	1.53161e32	0.606650
$392$	0	0
$393$	−2.24596e32	−0.834634
$394$	−3.00323e32	−1.08115
$395$	−3.57093e32	−1.24542
$396$	1.41243e31	0.0477286
$397$	−6.80893e31	−0.222945	−0.111473	−	0.993768i	$-0.535557\pi$
$397$	−6.80893e31	−0.222945	−0.111473	+	0.993768i	$0.535557\pi$
$398$	7.17652e32	2.27707
$399$	0	0
$400$	−6.73315e32	−2.00664
$401$	−1.02171e32	−0.295136	−0.147568	−	0.989052i	$-0.547145\pi$
$401$	−1.02171e32	−0.295136	−0.147568	+	0.989052i	$0.547145\pi$
$402$	−5.75763e32	−1.61220
$403$	−9.90694e31	−0.268922
$404$	−2.39627e32	−0.630621
$405$	−6.38044e32	−1.62803
$406$	0	0
$407$	9.34165e32	2.24127
$408$	1.84376e31	0.0428994
$409$	4.10045e32	0.925316	0.462658	−	0.886537i	$-0.346896\pi$
$409$	4.10045e32	0.925316	0.462658	+	0.886537i	$0.346896\pi$
$410$	1.45247e33	3.17913
$411$	−1.55991e32	−0.331190
$412$	−3.21511e32	−0.662187
$413$	0	0
$414$	−3.93451e31	−0.0762758
$415$	1.42583e33	2.68205
$416$	2.91592e32	0.532241
$417$	−6.99390e32	−1.23885
$418$	1.29664e33	2.22903
$419$	4.96775e32	0.828866	0.414433	−	0.910080i	$-0.363980\pi$
$419$	4.96775e32	0.828866	0.414433	+	0.910080i	$0.363980\pi$
$420$	0	0
$421$	4.67846e32	0.735490	0.367745	−	0.929927i	$-0.380130\pi$
$421$	4.67846e32	0.735490	0.367745	+	0.929927i	$0.380130\pi$
$422$	1.65831e32	0.253081
$423$	−1.40404e31	−0.0208029
$424$	1.78608e30	0.00256938
$425$	5.79365e32	0.809265
$426$	4.67052e32	0.633498
$427$	0	0
$428$	−4.76909e32	−0.610083
$429$	−4.01544e32	−0.498904
$430$	2.28613e33	2.75896
$431$	−1.24560e32	−0.146020	−0.0730099	−	0.997331i	$-0.523260\pi$
$431$	−1.24560e32	−0.146020	−0.0730099	+	0.997331i	$0.523260\pi$
$432$	−9.55068e32	−1.08765
$433$	1.13182e33	1.25222	0.626109	−	0.779736i	$-0.284647\pi$
$433$	1.13182e33	1.25222	0.626109	+	0.779736i	$0.284647\pi$
$434$	0	0
$435$	−6.66654e32	−0.696281
$436$	1.66396e33	1.68873
$437$	−1.73736e33	−1.71345
$438$	1.47931e33	1.41786
$439$	−1.08200e32	−0.100791	−0.0503953	−	0.998729i	$-0.516048\pi$
$439$	−1.08200e32	−0.100791	−0.0503953	+	0.998729i	$0.516048\pi$
$440$	2.51410e32	0.227628
$441$	0	0
$442$	−2.69371e32	−0.230448
$443$	7.28331e32	0.605734	0.302867	−	0.953033i	$-0.402056\pi$
$443$	7.28331e32	0.605734	0.302867	+	0.953033i	$0.402056\pi$
$444$	1.90762e33	1.54242
$445$	−1.37906e33	−1.08413
$446$	−9.94842e32	−0.760446
$447$	4.85481e32	0.360851
$448$	0	0
$449$	−2.05485e33	−1.44444	−0.722221	−	0.691662i	$-0.756879\pi$
$449$	−2.05485e33	−1.44444	−0.722221	+	0.691662i	$0.756879\pi$
$450$	−1.48832e32	−0.101751
$451$	−2.67978e33	−1.78193
$452$	5.77950e32	0.373818
$453$	1.83687e33	1.15572
$454$	2.06517e33	1.26403
$455$	0	0
$456$	−2.09144e32	−0.121167
$457$	1.72640e33	0.973170	0.486585	−	0.873633i	$-0.338242\pi$
$457$	1.72640e33	0.973170	0.486585	+	0.873633i	$0.338242\pi$
$458$	−2.64847e33	−1.45270
$459$	8.21805e32	0.438642
$460$	4.26477e33	2.21525
$461$	1.88079e33	0.950776	0.475388	−	0.879776i	$-0.342308\pi$
$461$	1.88079e33	0.950776	0.475388	+	0.879776i	$0.342308\pi$
$462$	0	0
$463$	2.12183e33	1.01613	0.508064	−	0.861319i	$-0.330361\pi$
$463$	2.12183e33	1.01613	0.508064	+	0.861319i	$0.330361\pi$
$464$	−9.58908e32	−0.446994
$465$	−2.55715e33	−1.16036
$466$	−2.78273e33	−1.22927
$467$	−7.63718e32	−0.328452	−0.164226	−	0.986423i	$-0.552513\pi$
$467$	−7.63718e32	−0.328452	−0.164226	+	0.986423i	$0.552513\pi$
$468$	3.32846e31	0.0139370
$469$	0	0
$470$	3.16399e33	1.25606
$471$	−2.94643e33	−1.13903
$472$	−2.80129e32	−0.105459
$473$	−4.21787e33	−1.54643
$474$	2.79700e33	0.998764
$475$	−6.57196e33	−2.28573
$476$	0	0
$477$	2.98888e30	0.000986346 0
$478$	−1.40619e33	−0.452060
$479$	2.15626e32	0.0675315	0.0337658	−	0.999430i	$-0.489250\pi$
$479$	2.15626e32	0.0675315	0.0337658	+	0.999430i	$0.489250\pi$
$480$	7.52646e33	2.29655
$481$	2.20140e33	0.654463
$482$	−4.35195e33	−1.26065
$483$	0	0
$484$	2.50303e33	0.688492
$485$	1.10323e34	2.95729
$486$	−4.14297e32	−0.108233
$487$	3.70121e33	0.942392	0.471196	−	0.882029i	$-0.343822\pi$
$487$	3.70121e33	0.942392	0.471196	+	0.882029i	$0.343822\pi$
$488$	−1.12487e32	−0.0279162
$489$	5.71366e33	1.38214
$490$	0	0
$491$	−6.03472e33	−1.38720	−0.693599	−	0.720361i	$-0.743976\pi$
$491$	−6.03472e33	−1.38720	−0.693599	+	0.720361i	$0.743976\pi$
$492$	−5.47225e33	−1.22631
$493$	8.25108e32	0.180270
$494$	3.05558e33	0.650890
$495$	4.20718e32	0.0873829
$496$	−3.67817e33	−0.744922
$497$	0	0
$498$	−1.11681e34	−2.15087
$499$	3.29465e33	0.618804	0.309402	−	0.950931i	$-0.399871\pi$
$499$	3.29465e33	0.618804	0.309402	+	0.950931i	$0.399871\pi$
$500$	7.54743e33	1.38253
$501$	−2.89334e33	−0.516926
$502$	5.35940e32	0.0933942
$503$	−3.45752e33	−0.587712	−0.293856	−	0.955850i	$-0.594939\pi$
$503$	−3.45752e33	−0.587712	−0.293856	+	0.955850i	$0.594939\pi$
$504$	0	0
$505$	−7.13771e33	−1.15456
$506$	−1.63583e34	−2.58142
$507$	5.42110e33	0.834619
$508$	6.67135e33	1.00211
$509$	−8.89271e33	−1.30335	−0.651676	−	0.758497i	$-0.725934\pi$
$509$	−8.89271e33	−1.30335	−0.651676	+	0.758497i	$0.725934\pi$
$510$	−6.95292e33	−0.994352
$511$	0	0
$512$	1.00292e34	1.36581
$513$	−9.32205e33	−1.23892
$514$	1.39219e33	0.180575
$515$	−9.57676e33	−1.21235
$516$	−8.61312e33	−1.06424
$517$	−5.83750e33	−0.704037
$518$	0	0
$519$	−6.13364e33	−0.704898
$520$	5.92459e32	0.0664686
$521$	4.21507e33	0.461671	0.230836	−	0.972993i	$-0.425854\pi$
$521$	4.21507e33	0.461671	0.230836	+	0.972993i	$0.425854\pi$
$522$	−2.11960e32	−0.0226659
$523$	5.79146e33	0.604668	0.302334	−	0.953202i	$-0.402234\pi$
$523$	5.79146e33	0.604668	0.302334	+	0.953202i	$0.402234\pi$
$524$	7.74036e33	0.789078
$525$	0	0
$526$	1.61331e34	1.56818
$527$	3.16495e33	0.300423
$528$	−1.49082e34	−1.38198
$529$	1.08727e34	0.984332
$530$	−6.73543e32	−0.0595548
$531$	−4.68777e32	−0.0404841
$532$	0	0
$533$	−6.31500e33	−0.520335
$534$	1.08017e34	0.869417
$535$	−1.42056e34	−1.11696
$536$	−1.56733e33	−0.120393
$537$	−2.53310e34	−1.90096
$538$	−1.10636e34	−0.811180
$539$	0	0
$540$	2.28832e34	1.60175
$541$	−1.67436e34	−1.14520	−0.572601	−	0.819834i	$-0.694066\pi$
$541$	−1.67436e34	−1.14520	−0.572601	+	0.819834i	$0.694066\pi$
$542$	1.53686e34	1.02717
$543$	1.11887e34	0.730774
$544$	−9.31540e33	−0.594587
$545$	4.95639e34	3.09178
$546$	0	0
$547$	−4.92521e33	−0.293483	−0.146741	−	0.989175i	$-0.546879\pi$
$547$	−4.92521e33	−0.293483	−0.146741	+	0.989175i	$0.546879\pi$
$548$	5.37598e33	0.313113
$549$	−1.88240e32	−0.0107166
$550$	−6.18791e34	−3.44358
$551$	−9.35952e33	−0.509165
$552$	2.63855e33	0.140322
$553$	0	0
$554$	2.39635e34	1.21809
$555$	5.68217e34	2.82392
$556$	2.41033e34	1.17123
$557$	−3.11531e34	−1.48017	−0.740084	−	0.672514i	$-0.765214\pi$
$557$	−3.11531e34	−1.48017	−0.740084	+	0.672514i	$0.765214\pi$
$558$	−8.13035e32	−0.0377730
$559$	−9.93958e33	−0.451565
$560$	0	0
$561$	1.28280e34	0.557345
$562$	−4.54632e34	−1.93177
$563$	−4.21680e34	−1.75238	−0.876190	−	0.481966i	$-0.839923\pi$
$563$	−4.21680e34	−1.75238	−0.876190	+	0.481966i	$0.839923\pi$
$564$	−1.19205e34	−0.484513
$565$	1.72152e34	0.684396
$566$	−2.34728e34	−0.912766
$567$	0	0
$568$	1.27140e33	0.0473073
$569$	−3.78309e34	−1.37703	−0.688516	−	0.725222i	$-0.741737\pi$
$569$	−3.78309e34	−1.37703	−0.688516	+	0.725222i	$0.741737\pi$
$570$	7.88697e34	2.80850
$571$	−8.30726e33	−0.289405	−0.144703	−	0.989475i	$-0.546223\pi$
$571$	−8.30726e33	−0.289405	−0.144703	+	0.989475i	$0.546223\pi$
$572$	1.38386e34	0.471673
$573$	−5.38808e33	−0.179681
$574$	0	0
$575$	8.29115e34	2.64708
$576$	1.05964e33	0.0331037
$577$	−3.26853e34	−0.999207	−0.499603	−	0.866254i	$-0.666521\pi$
$577$	−3.26853e34	−0.999207	−0.499603	+	0.866254i	$0.666521\pi$
$578$	−3.77942e34	−1.13065
$579$	−5.76665e34	−1.68827
$580$	2.29751e34	0.658277
$581$	0	0
$582$	−8.64125e34	−2.37159
$583$	1.24267e33	0.0333811
$584$	4.02695e33	0.105881
$585$	9.91439e32	0.0255163
$586$	−8.57218e34	−2.15959
$587$	4.82607e34	1.19019	0.595096	−	0.803654i	$-0.297114\pi$
$587$	4.82607e34	1.19019	0.595096	+	0.803654i	$0.297114\pi$
$588$	0	0
$589$	−3.59012e34	−0.848531
$590$	1.05639e35	2.44440
$591$	3.37032e34	0.763533
$592$	8.17317e34	1.81288
$593$	3.09992e34	0.673235	0.336617	−	0.941642i	$-0.390717\pi$
$593$	3.09992e34	0.673235	0.336617	+	0.941642i	$0.390717\pi$
$594$	−8.77729e34	−1.86651
$595$	0	0
$596$	−1.67313e34	−0.341155
$597$	−8.05372e34	−1.60812
$598$	−3.85491e34	−0.753788
$599$	6.87798e33	0.131712	0.0658560	−	0.997829i	$-0.479022\pi$
$599$	6.87798e33	0.131712	0.0658560	+	0.997829i	$0.479022\pi$
$600$	9.98091e33	0.187189
$601$	1.25657e34	0.230810	0.115405	−	0.993319i	$-0.463183\pi$
$601$	1.25657e34	0.230810	0.115405	+	0.993319i	$0.463183\pi$
$602$	0	0
$603$	−2.62282e33	−0.0462171
$604$	−6.33048e34	−1.09264
$605$	7.45571e34	1.26051
$606$	5.59075e34	0.925897
$607$	−2.42338e34	−0.393154	−0.196577	−	0.980488i	$-0.562983\pi$
$607$	−2.42338e34	−0.393154	−0.196577	+	0.980488i	$0.562983\pi$
$608$	1.05668e35	1.67938
$609$	0	0
$610$	4.24197e34	0.647060
$611$	−1.37563e34	−0.205583
$612$	−1.06333e33	−0.0155696
$613$	7.09355e34	1.01767	0.508836	−	0.860864i	$-0.330076\pi$
$613$	7.09355e34	1.01767	0.508836	+	0.860864i	$0.330076\pi$
$614$	7.47823e34	1.05122
$615$	−1.63000e35	−2.24517
$616$	0	0
$617$	4.58937e34	0.607000	0.303500	−	0.952831i	$-0.401845\pi$
$617$	4.58937e34	0.607000	0.303500	+	0.952831i	$0.401845\pi$
$618$	7.50119e34	0.972242
$619$	−1.07191e35	−1.36152	−0.680762	−	0.732505i	$-0.738351\pi$
$619$	−1.07191e35	−1.36152	−0.680762	+	0.732505i	$0.738351\pi$
$620$	8.81279e34	1.09703
$621$	1.17606e35	1.43478
$622$	3.83155e34	0.458137
$623$	0	0
$624$	−3.51318e34	−0.403546
$625$	5.79122e34	0.652033
$626$	−1.05547e35	−1.16484
$627$	−1.45513e35	−1.57419
$628$	1.01544e35	1.07686
$629$	−7.03274e34	−0.731125
$630$	0	0
$631$	−3.88998e34	−0.388670	−0.194335	−	0.980935i	$-0.562255\pi$
$631$	−3.88998e34	−0.388670	−0.194335	+	0.980935i	$0.562255\pi$
$632$	7.61394e33	0.0745841
$633$	−1.86101e34	−0.178732
$634$	1.26186e35	1.18822
$635$	1.98718e35	1.83470
$636$	2.53761e33	0.0229726
$637$	0	0
$638$	−8.81257e34	−0.767086
$639$	2.12760e33	0.0181606
$640$	4.10872e34	0.343919
$641$	−5.21930e34	−0.428437	−0.214219	−	0.976786i	$-0.568720\pi$
$641$	−5.21930e34	−0.428437	−0.214219	+	0.976786i	$0.568720\pi$
$642$	1.11268e35	0.895741
$643$	1.53160e35	1.20923	0.604613	−	0.796519i	$-0.293328\pi$
$643$	1.53160e35	1.20923	0.604613	+	0.796519i	$0.293328\pi$
$644$	0	0
$645$	−2.56557e35	−1.94844
$646$	−9.76160e34	−0.727134
$647$	1.61744e35	1.18175	0.590873	−	0.806764i	$-0.298783\pi$
$647$	1.61744e35	1.18175	0.590873	+	0.806764i	$0.298783\pi$
$648$	1.36044e34	0.0974971
$649$	−1.94901e35	−1.37011
$650$	−1.45821e35	−1.00555
$651$	0	0
$652$	−1.96912e35	−1.30670
$653$	−2.04383e35	−1.33054	−0.665272	−	0.746601i	$-0.731684\pi$
$653$	−2.04383e35	−1.33054	−0.665272	+	0.746601i	$0.731684\pi$
$654$	−3.88219e35	−2.47945
$655$	2.30560e35	1.44467
$656$	−2.34458e35	−1.44134
$657$	6.73884e33	0.0406460
$658$	0	0
$659$	5.06298e34	0.293994	0.146997	−	0.989137i	$-0.453039\pi$
$659$	5.06298e34	0.293994	0.146997	+	0.989137i	$0.453039\pi$
$660$	3.57196e35	2.03520
$661$	−1.42218e35	−0.795125	−0.397563	−	0.917575i	$-0.630144\pi$
$661$	−1.42218e35	−0.795125	−0.397563	+	0.917575i	$0.630144\pi$
$662$	2.89949e34	0.159073
$663$	3.02297e34	0.162748
$664$	−3.04017e34	−0.160619
$665$	0	0
$666$	1.80663e34	0.0919264
$667$	1.18079e35	0.589658
$668$	9.97143e34	0.488711
$669$	1.11644e35	0.537045
$670$	5.91051e35	2.79055
$671$	−7.82637e34	−0.362684
$672$	0	0
$673$	2.58864e35	1.15580	0.577900	−	0.816108i	$-0.303872\pi$
$673$	2.58864e35	1.15580	0.577900	+	0.816108i	$0.303872\pi$
$674$	2.27758e35	0.998219
$675$	4.44873e35	1.91399
$676$	−1.86830e35	−0.789064
$677$	−8.08484e34	−0.335207	−0.167603	−	0.985854i	$-0.553603\pi$
$677$	−8.08484e34	−0.335207	−0.167603	+	0.985854i	$0.553603\pi$
$678$	−1.34842e35	−0.548850
$679$	0	0
$680$	−1.89271e34	−0.0742545
$681$	−2.31760e35	−0.892689
$682$	−3.38032e35	−1.27836
$683$	8.68601e34	0.322524	0.161262	−	0.986912i	$-0.448444\pi$
$683$	8.68601e34	0.322524	0.161262	+	0.986912i	$0.448444\pi$
$684$	1.20618e34	0.0439755
$685$	1.60133e35	0.573256
$686$	0	0
$687$	2.97220e35	1.02593
$688$	−3.69029e35	−1.25085
$689$	2.92841e33	0.00974747
$690$	−9.95015e35	−3.25249
$691$	1.71892e35	0.551798	0.275899	−	0.961187i	$-0.411025\pi$
$691$	1.71892e35	0.551798	0.275899	+	0.961187i	$0.411025\pi$
$692$	2.11386e35	0.666423
$693$	0	0
$694$	4.20842e35	1.27975
$695$	7.17960e35	2.14432
$696$	1.42144e34	0.0416978
$697$	2.01744e35	0.581286
$698$	1.09208e35	0.309074
$699$	3.12286e35	0.868137
$700$	0	0
$701$	−2.37726e35	−0.637678	−0.318839	−	0.947809i	$-0.603293\pi$
$701$	−2.37726e35	−0.637678	−0.318839	+	0.947809i	$0.603293\pi$
$702$	−2.06840e35	−0.545031
$703$	7.97751e35	2.06503
$704$	4.40561e35	1.12033
$705$	−3.55073e35	−0.887061
$706$	7.80549e35	1.91576
$707$	0	0
$708$	−3.97999e35	−0.942901
$709$	1.81615e35	0.422740	0.211370	−	0.977406i	$-0.432208\pi$
$709$	1.81615e35	0.422740	0.211370	+	0.977406i	$0.432208\pi$
$710$	−4.79454e35	−1.09652
$711$	1.27414e34	0.0286317
$712$	2.94043e34	0.0649249
$713$	4.52927e35	0.982674
$714$	0	0
$715$	4.12206e35	0.863553
$716$	8.72993e35	1.79721
$717$	1.57807e35	0.319255
$718$	2.23582e35	0.444509
$719$	1.41561e35	0.276588	0.138294	−	0.990391i	$-0.455838\pi$
$719$	1.41561e35	0.276588	0.138294	+	0.990391i	$0.455838\pi$
$720$	3.68094e34	0.0706809
$721$	0	0
$722$	3.58898e35	0.665665
$723$	4.88390e35	0.890303
$724$	−3.85602e35	−0.690887
$725$	4.46661e35	0.786598
$726$	−5.83984e35	−1.01086
$727$	−8.76569e34	−0.149144	−0.0745720	−	0.997216i	$-0.523759\pi$
$727$	−8.76569e34	−0.149144	−0.0745720	+	0.997216i	$0.523759\pi$
$728$	0	0
$729$	6.30107e35	1.03591
$730$	−1.51859e36	−2.45417
$731$	3.17537e35	0.504461
$732$	−1.59819e35	−0.249597
$733$	−3.80319e35	−0.583914	−0.291957	−	0.956432i	$-0.594306\pi$
$733$	−3.80319e35	−0.583914	−0.291957	+	0.956432i	$0.594306\pi$
$734$	−3.29513e35	−0.497361
$735$	0	0
$736$	−1.33310e36	−1.94487
$737$	−1.09048e36	−1.56413
$738$	−5.18254e34	−0.0730867
$739$	−1.02332e36	−1.41891	−0.709457	−	0.704749i	$-0.751060\pi$
$739$	−1.02332e36	−1.41891	−0.709457	+	0.704749i	$0.751060\pi$
$740$	−1.95827e36	−2.66978
$741$	−3.42908e35	−0.459674
$742$	0	0
$743$	7.39190e35	0.958068	0.479034	−	0.877796i	$-0.340987\pi$
$743$	7.39190e35	0.958068	0.479034	+	0.877796i	$0.340987\pi$
$744$	5.45235e34	0.0694900
$745$	−4.98372e35	−0.624597
$746$	−2.18264e35	−0.268996
$747$	−5.08751e34	−0.0616592
$748$	−4.42097e35	−0.526924
$749$	0	0
$750$	−1.76090e36	−2.02987
$751$	1.26385e36	1.43283	0.716416	−	0.697673i	$-0.245781\pi$
$751$	1.26385e36	1.43283	0.716416	+	0.697673i	$0.245781\pi$
$752$	−5.10733e35	−0.569470
$753$	−6.01450e34	−0.0659572
$754$	−2.07672e35	−0.223993
$755$	−1.88565e36	−2.00043
$756$	0	0
$757$	−3.43908e35	−0.352974	−0.176487	−	0.984303i	$-0.556473\pi$
$757$	−3.43908e35	−0.352974	−0.176487	+	0.984303i	$0.556473\pi$
$758$	−2.49678e36	−2.52067
$759$	1.83579e36	1.82306
$760$	2.14698e35	0.209728
$761$	4.75293e35	0.456724	0.228362	−	0.973576i	$-0.426663\pi$
$761$	4.75293e35	0.456724	0.228362	+	0.973576i	$0.426663\pi$
$762$	−1.55650e36	−1.47133
$763$	0	0
$764$	1.85691e35	0.169873
$765$	−3.16732e34	−0.0285052
$766$	5.62407e35	0.497956
$767$	−4.59292e35	−0.400080
$768$	−1.29253e36	−1.10771
$769$	7.72537e35	0.651389	0.325694	−	0.945475i	$-0.394402\pi$
$769$	7.72537e35	0.651389	0.325694	+	0.945475i	$0.394402\pi$
$770$	0	0
$771$	−1.56236e35	−0.127527
$772$	1.98738e36	1.59612
$773$	−7.31034e35	−0.577688	−0.288844	−	0.957376i	$-0.593271\pi$
$773$	−7.31034e35	−0.577688	−0.288844	+	0.957376i	$0.593271\pi$
$774$	−8.15714e34	−0.0634272
$775$	1.71330e36	1.31088
$776$	−2.35230e35	−0.177101
$777$	0	0
$778$	1.65035e36	1.20318
$779$	−2.28845e36	−1.64181
$780$	8.41747e35	0.594291
$781$	8.84584e35	0.614612
$782$	1.23152e36	0.842085
$783$	6.33569e35	0.426356
$784$	0	0
$785$	3.02466e36	1.97154
$786$	−1.80591e36	−1.15855
$787$	7.61886e35	0.481067	0.240534	−	0.970641i	$-0.422678\pi$
$787$	7.61886e35	0.481067	0.240534	+	0.970641i	$0.422678\pi$
$788$	−1.16153e36	−0.721858
$789$	−1.81051e36	−1.10749
$790$	−2.87127e36	−1.72876
$791$	0	0
$792$	−8.97057e33	−0.00523305
$793$	−1.84431e35	−0.105906
$794$	−5.47484e35	−0.309468
$795$	7.55871e34	0.0420590
$796$	2.77559e36	1.52034
$797$	−4.75437e35	−0.256368	−0.128184	−	0.991750i	$-0.540915\pi$
$797$	−4.75437e35	−0.256368	−0.128184	+	0.991750i	$0.540915\pi$
$798$	0	0
$799$	4.39469e35	0.229664
$800$	−5.04276e36	−2.59444
$801$	4.92061e34	0.0249237
$802$	−8.21523e35	−0.409676
$803$	2.80177e36	1.37559
$804$	−2.22682e36	−1.07643
$805$	0	0
$806$	−7.96585e35	−0.373288
$807$	1.24159e36	0.572874
$808$	1.52190e35	0.0691426
$809$	−3.11465e36	−1.39333	−0.696663	−	0.717399i	$-0.745333\pi$
$809$	−3.11465e36	−1.39333	−0.696663	+	0.717399i	$0.745333\pi$
$810$	−5.13031e36	−2.25985
$811$	9.76747e35	0.423664	0.211832	−	0.977306i	$-0.432057\pi$
$811$	9.76747e35	0.423664	0.211832	+	0.977306i	$0.432057\pi$
$812$	0	0
$813$	−1.72472e36	−0.725415
$814$	7.51132e36	3.11108
$815$	−5.86537e36	−2.39235
$816$	1.12235e36	0.450816
$817$	−3.60195e36	−1.42483
$818$	3.29704e36	1.28442
$819$	0	0
$820$	5.61755e36	2.12263
$821$	−1.43077e36	−0.532451	−0.266225	−	0.963911i	$-0.585777\pi$
$821$	−1.43077e36	−0.532451	−0.266225	+	0.963911i	$0.585777\pi$
$822$	−1.25427e36	−0.459721
$823$	−4.48865e36	−1.62038	−0.810192	−	0.586165i	$-0.800637\pi$
$823$	−4.48865e36	−1.62038	−0.810192	+	0.586165i	$0.800637\pi$
$824$	2.04196e35	0.0726034
$825$	6.94427e36	2.43194
$826$	0	0
$827$	−3.75162e36	−1.27468	−0.637338	−	0.770584i	$-0.719965\pi$
$827$	−3.75162e36	−1.27468	−0.637338	+	0.770584i	$0.719965\pi$
$828$	−1.52171e35	−0.0509275
$829$	−1.79836e36	−0.592849	−0.296425	−	0.955056i	$-0.595794\pi$
$829$	−1.79836e36	−0.592849	−0.296425	+	0.955056i	$0.595794\pi$
$830$	1.14647e37	3.72293
$831$	−2.68926e36	−0.860240
$832$	1.03820e36	0.327144
$833$	0	0
$834$	−5.62357e36	−1.71963
$835$	2.97017e36	0.894746
$836$	5.01488e36	1.48827
$837$	2.43024e36	0.710528
$838$	3.99441e36	1.15054
$839$	−1.51451e36	−0.429780	−0.214890	−	0.976638i	$-0.568939\pi$
$839$	−1.51451e36	−0.429780	−0.214890	+	0.976638i	$0.568939\pi$
$840$	0	0
$841$	−2.99425e36	−0.824779
$842$	3.76180e36	1.02093
$843$	5.10203e36	1.36426
$844$	6.41366e35	0.168976
$845$	−5.56505e36	−1.44464
$846$	−1.12894e35	−0.0288763
$847$	0	0
$848$	1.08724e35	0.0270008
$849$	2.63419e36	0.644617
$850$	4.65849e36	1.12333
$851$	−1.00644e37	−2.39149
$852$	1.80637e36	0.422972
$853$	4.82183e36	1.11263	0.556313	−	0.830973i	$-0.312216\pi$
$853$	4.82183e36	1.11263	0.556313	+	0.830973i	$0.312216\pi$
$854$	0	0
$855$	3.59282e35	0.0805117
$856$	3.02892e35	0.0668906
$857$	5.57333e36	1.21298	0.606492	−	0.795090i	$-0.292576\pi$
$857$	5.57333e36	1.21298	0.606492	+	0.795090i	$0.292576\pi$
$858$	−3.22869e36	−0.692524
$859$	5.08372e36	1.07465	0.537325	−	0.843375i	$-0.319435\pi$
$859$	5.08372e36	1.07465	0.537325	+	0.843375i	$0.319435\pi$
$860$	8.84182e36	1.84209
$861$	0	0
$862$	−1.00155e36	−0.202689
$863$	4.83510e36	0.964430	0.482215	−	0.876053i	$-0.339832\pi$
$863$	4.83510e36	0.964430	0.482215	+	0.876053i	$0.339832\pi$
$864$	−7.15294e36	−1.40625
$865$	6.29650e36	1.22011
$866$	9.10062e36	1.73819
$867$	4.24139e36	0.798490
$868$	0	0
$869$	5.29744e36	0.968989
$870$	−5.36035e36	−0.966501
$871$	−2.56976e36	−0.456736
$872$	−1.05680e36	−0.185156
$873$	−3.93642e35	−0.0679867
$874$	−1.39696e37	−2.37843
$875$	0	0
$876$	5.72138e36	0.946671
$877$	8.79920e36	1.43532	0.717659	−	0.696394i	$-0.245213\pi$
$877$	8.79920e36	1.43532	0.717659	+	0.696394i	$0.245213\pi$
$878$	−8.70000e35	−0.139906
$879$	9.61998e36	1.52515
$880$	1.53041e37	2.39207
$881$	−5.93479e36	−0.914548	−0.457274	−	0.889326i	$-0.651174\pi$
$881$	−5.93479e36	−0.914548	−0.457274	+	0.889326i	$0.651174\pi$
$882$	0	0
$883$	6.82969e36	1.02304	0.511519	−	0.859272i	$-0.329083\pi$
$883$	6.82969e36	1.02304	0.511519	+	0.859272i	$0.329083\pi$
$884$	−1.04182e36	−0.153865
$885$	−1.18551e37	−1.72629
$886$	5.85627e36	0.840814
$887$	−6.98539e36	−0.988884	−0.494442	−	0.869211i	$-0.664627\pi$
$887$	−6.98539e36	−0.988884	−0.494442	+	0.869211i	$0.664627\pi$
$888$	−1.21155e36	−0.169114
$889$	0	0
$890$	−1.10886e37	−1.50487
$891$	9.46533e36	1.26667
$892$	−3.84765e36	−0.507732
$893$	−4.98507e36	−0.648676
$894$	3.90360e36	0.500894
$895$	2.60036e37	3.29038
$896$	0	0
$897$	4.32610e36	0.532343
$898$	−1.65224e37	−2.00502
$899$	2.44001e36	0.292009
$900$	−5.75621e35	−0.0679368
$901$	−9.35532e34	−0.0108893
$902$	−2.15472e37	−2.47349
$903$	0	0
$904$	−3.67064e35	−0.0409861
$905$	−1.14858e37	−1.26490
$906$	1.47697e37	1.60424
$907$	1.10080e37	1.17928	0.589641	−	0.807666i	$-0.299269\pi$
$907$	1.10080e37	1.17928	0.589641	+	0.807666i	$0.299269\pi$
$908$	7.98725e36	0.843964
$909$	2.54680e35	0.0265428
$910$	0	0
$911$	−4.75882e36	−0.482525	−0.241263	−	0.970460i	$-0.577562\pi$
$911$	−4.75882e36	−0.482525	−0.241263	+	0.970460i	$0.577562\pi$
$912$	−1.27312e37	−1.27331
$913$	−2.11521e37	−2.08674
$914$	1.38814e37	1.35085
$915$	−4.76048e36	−0.456969
$916$	−1.02432e37	−0.969934
$917$	0	0
$918$	6.60787e36	0.608875
$919$	1.11217e36	0.101095	0.0505474	−	0.998722i	$-0.483903\pi$
$919$	1.11217e36	0.101095	0.0505474	+	0.998722i	$0.483903\pi$
$920$	−2.70861e36	−0.242884
$921$	−8.39231e36	−0.742397
$922$	1.51228e37	1.31976
$923$	2.08456e36	0.179470
$924$	0	0
$925$	−3.80708e37	−3.19022
$926$	1.70610e37	1.41048
$927$	3.41708e35	0.0278714
$928$	−7.18170e36	−0.577933
$929$	−7.10890e36	−0.564425	−0.282212	−	0.959352i	$-0.591068\pi$
$929$	−7.10890e36	−0.564425	−0.282212	+	0.959352i	$0.591068\pi$
$930$	−2.05612e37	−1.61069
$931$	0	0
$932$	−1.07624e37	−0.820752
$933$	−4.29989e36	−0.323547
$934$	−6.14081e36	−0.455921
$935$	−1.31686e37	−0.964708
$936$	−2.11395e34	−0.00152808
$937$	−1.40367e36	−0.100120	−0.0500600	−	0.998746i	$-0.515941\pi$
$937$	−1.40367e36	−0.100120	−0.0500600	+	0.998746i	$0.515941\pi$
$938$	0	0
$939$	1.18448e37	0.822638
$940$	1.22370e37	0.838644
$941$	−3.93953e36	−0.266425	−0.133212	−	0.991088i	$-0.542529\pi$
$941$	−3.93953e36	−0.266425	−0.133212	+	0.991088i	$0.542529\pi$
$942$	−2.36913e37	−1.58107
$943$	2.88710e37	1.90137
$944$	−1.70522e37	−1.10823
$945$	0	0
$946$	−3.39146e37	−2.14658
$947$	−5.30609e35	−0.0331436	−0.0165718	−	0.999863i	$-0.505275\pi$
$947$	−5.30609e35	−0.0331436	−0.0165718	+	0.999863i	$0.505275\pi$
$948$	1.08177e37	0.666851
$949$	6.60249e36	0.401680
$950$	−5.28431e37	−3.17280
$951$	−1.41610e37	−0.839146
$952$	0	0
$953$	1.07159e37	0.618540	0.309270	−	0.950974i	$-0.399915\pi$
$953$	1.07159e37	0.618540	0.309270	+	0.950974i	$0.399915\pi$
$954$	2.40326e34	0.00136914
$955$	5.53115e36	0.311009
$956$	−5.43858e36	−0.301830
$957$	9.88975e36	0.541734
$958$	1.73378e36	0.0937399
$959$	0	0
$960$	2.67976e37	1.41158
$961$	−9.87342e36	−0.513364
$962$	1.77007e37	0.908453
$963$	5.06869e35	0.0256783
$964$	−1.68316e37	−0.841708
$965$	5.91977e37	2.92223
$966$	0	0
$967$	9.93175e36	0.477744	0.238872	−	0.971051i	$-0.423222\pi$
$967$	9.93175e36	0.477744	0.238872	+	0.971051i	$0.423222\pi$
$968$	−1.58971e36	−0.0754876
$969$	1.09548e37	0.513519
$970$	8.87070e37	4.10498
$971$	−3.18711e37	−1.45599	−0.727993	−	0.685585i	$-0.759547\pi$
$971$	−3.18711e37	−1.45599	−0.727993	+	0.685585i	$0.759547\pi$
$972$	−1.60233e36	−0.0722644
$973$	0	0
$974$	2.97602e37	1.30812
$975$	1.63644e37	0.710140
$976$	−6.84742e36	−0.293362
$977$	−3.31170e37	−1.40078	−0.700389	−	0.713762i	$-0.746990\pi$
$977$	−3.31170e37	−1.40078	−0.700389	+	0.713762i	$0.746990\pi$
$978$	4.59417e37	1.91854
$979$	2.04582e37	0.843497
$980$	0	0
$981$	−1.76849e36	−0.0710787
$982$	−4.85233e37	−1.92556
$983$	5.98710e36	0.234584	0.117292	−	0.993097i	$-0.462579\pi$
$983$	5.98710e36	0.234584	0.117292	+	0.993097i	$0.462579\pi$
$984$	3.47550e36	0.134456
$985$	−3.45981e37	−1.32160
$986$	6.63443e36	0.250232
$987$	0	0
$988$	1.18178e37	0.434584
$989$	4.54420e37	1.65007
$990$	3.38286e36	0.121295
$991$	−1.76802e37	−0.625990	−0.312995	−	0.949755i	$-0.601332\pi$
$991$	−1.76802e37	−0.625990	−0.312995	+	0.949755i	$0.601332\pi$
$992$	−2.75475e37	−0.963133
$993$	−3.25391e36	−0.112341
$994$	0	0
$995$	8.26757e37	2.78349
$996$	−4.31937e37	−1.43608
$997$	4.20971e37	1.38217	0.691087	−	0.722771i	$-0.257132\pi$
$997$	4.20971e37	1.38217	0.691087	+	0.722771i	$0.257132\pi$
$998$	2.64912e37	0.858955
$999$	−5.40018e37	−1.72918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.c.1.6		6
7.6	odd	2		7.26.a.a.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.26.a.a.1.6	✓	6	7.6	odd	2
49.26.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q+8040.68 q^{2} -902351. q^{3} +3.10981e7 q^{4} +9.26311e8 q^{5} -7.25551e9 q^{6} -1.97508e10 q^{8} -3.30517e10 q^{9} +O(q^{10})\)	\(q+8040.68 q^{2} -902351. q^{3} +3.10981e7 q^{4} +9.26311e8 q^{5} -7.25551e9 q^{6} -1.97508e10 q^{8} -3.30517e10 q^{9} +7.44816e12 q^{10} -1.37417e13 q^{11} -2.80614e13 q^{12} -3.23829e13 q^{13} -8.35857e14 q^{15} -1.20229e15 q^{16} +1.03453e15 q^{17} -2.65758e14 q^{18} -1.17351e16 q^{19} +2.88065e16 q^{20} -1.10493e17 q^{22} +1.48049e17 q^{23} +1.78222e16 q^{24} +5.60028e17 q^{25} -2.60381e17 q^{26} +7.94376e17 q^{27} +7.97569e17 q^{29} -6.72086e18 q^{30} +3.05931e18 q^{31} -9.00448e18 q^{32} +1.23999e19 q^{33} +8.31832e18 q^{34} -1.02784e18 q^{36} -6.79802e19 q^{37} -9.43579e19 q^{38} +2.92208e19 q^{39} -1.82954e19 q^{40} +1.95010e20 q^{41} +3.06939e20 q^{43} -4.27341e20 q^{44} -3.06161e19 q^{45} +1.19041e21 q^{46} +4.24801e20 q^{47} +1.08489e21 q^{48} +4.50300e21 q^{50} -9.33508e20 q^{51} -1.00705e21 q^{52} -9.04307e19 q^{53} +6.38732e21 q^{54} -1.27291e22 q^{55} +1.05891e22 q^{57} +6.41300e21 q^{58} +1.41832e22 q^{59} -2.59935e22 q^{60} +5.69533e21 q^{61} +2.45989e22 q^{62} -3.20601e22 q^{64} -2.99967e22 q^{65} +9.97033e22 q^{66} +7.93553e22 q^{67} +3.21719e22 q^{68} -1.33592e23 q^{69} -6.43720e22 q^{71} +6.52797e20 q^{72} -2.03888e23 q^{73} -5.46606e23 q^{74} -5.05342e23 q^{75} -3.64938e23 q^{76} +2.34955e23 q^{78} -3.85500e23 q^{79} -1.11369e24 q^{80} -6.88801e23 q^{81} +1.56801e24 q^{82} +1.53926e24 q^{83} +9.58295e23 q^{85} +2.46800e24 q^{86} -7.19687e23 q^{87} +2.71411e23 q^{88} -1.48876e24 q^{89} -2.46174e23 q^{90} +4.60403e24 q^{92} -2.76057e24 q^{93} +3.41569e24 q^{94} -1.08703e25 q^{95} +8.12520e24 q^{96} +1.19099e25 q^{97} +4.54187e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4230 q^{2} + 72104 q^{3} + 86658324 q^{4} - 110161332 q^{5} + 564962452 q^{6} - 381894066504 q^{8} + 1267694965630 q^{9}+O(q^{10}) \) 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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