LMFDB - Embedded newform 49.26.a.c.1.1

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			1.1
Root			$5095.68$ 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)

$f(q)$	$=$	$q-10895.4 q^{2} -750334. q^{3} +8.51545e7 q^{4} -3.86992e8 q^{5} +8.17517e9 q^{6} -5.62202e11 q^{8} -2.84287e11 q^{9} +O(q^{10})$	\(q-10895.4 q^{2} -750334. q^{3} +8.51545e7 q^{4} -3.86992e8 q^{5} +8.17517e9 q^{6} -5.62202e11 q^{8} -2.84287e11 q^{9} +4.21642e12 q^{10} +7.16092e12 q^{11} -6.38944e13 q^{12} +7.56009e13 q^{13} +2.90373e14 q^{15} +3.26808e15 q^{16} +2.56123e15 q^{17} +3.09741e15 q^{18} -1.41497e16 q^{19} -3.29541e16 q^{20} -7.80208e16 q^{22} -1.63002e17 q^{23} +4.21839e17 q^{24} -1.48260e17 q^{25} -8.23700e17 q^{26} +8.49060e17 q^{27} +3.44080e18 q^{29} -3.16372e18 q^{30} +2.73908e18 q^{31} -1.67426e19 q^{32} -5.37308e18 q^{33} -2.79055e19 q^{34} -2.42083e19 q^{36} +3.95665e19 q^{37} +1.54167e20 q^{38} -5.67260e19 q^{39} +2.17568e20 q^{40} +1.12710e20 q^{41} -1.75585e19 q^{43} +6.09784e20 q^{44} +1.10017e20 q^{45} +1.77597e21 q^{46} +7.32800e20 q^{47} -2.45215e21 q^{48} +1.61535e21 q^{50} -1.92178e21 q^{51} +6.43776e21 q^{52} -4.32666e21 q^{53} -9.25082e21 q^{54} -2.77122e21 q^{55} +1.06170e22 q^{57} -3.74888e22 q^{58} +2.53856e22 q^{59} +2.47266e22 q^{60} +1.76183e22 q^{61} -2.98433e22 q^{62} +7.27577e22 q^{64} -2.92570e22 q^{65} +5.85417e22 q^{66} +8.36822e22 q^{67} +2.18100e23 q^{68} +1.22306e23 q^{69} -1.02690e23 q^{71} +1.59827e23 q^{72} -5.97629e21 q^{73} -4.31091e23 q^{74} +1.11245e23 q^{75} -1.20491e24 q^{76} +6.18050e23 q^{78} -2.43658e23 q^{79} -1.26472e24 q^{80} -3.96206e23 q^{81} -1.22801e24 q^{82} +1.02448e24 q^{83} -9.91175e23 q^{85} +1.91307e23 q^{86} -2.58175e24 q^{87} -4.02588e24 q^{88} -4.59761e23 q^{89} -1.19867e24 q^{90} -1.38804e25 q^{92} -2.05523e24 q^{93} -7.98412e24 q^{94} +5.47584e24 q^{95} +1.25625e25 q^{96} -5.84706e24 q^{97} -2.03576e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10895.4	−1.88090	−0.940452	−	0.339926i	$-0.889598\pi$
$2$	−10895.4	−1.88090	−0.940452	+	0.339926i	$0.889598\pi$
$3$	−750334.	−0.815153	−0.407576	−	0.913171i	$-0.633626\pi$
$3$	−750334.	−0.815153	−0.407576	+	0.913171i	$0.633626\pi$
$4$	8.51545e7	2.53780
$5$	−3.86992e8	−0.708887	−0.354443	−	0.935077i	$-0.615330\pi$
$5$	−3.86992e8	−0.708887	−0.354443	+	0.935077i	$0.615330\pi$
$6$	8.17517e9	1.53323
$7$	0	0
$7$	0	0
$8$	−5.62202e11	−2.89246
$9$	−2.84287e11	−0.335526
$10$	4.21642e12	1.33335
$11$	7.16092e12	0.687955	0.343977	−	0.938978i	$-0.388226\pi$
$11$	7.16092e12	0.687955	0.343977	+	0.938978i	$0.388226\pi$
$12$	−6.38944e13	−2.06870
$13$	7.56009e13	0.899985	0.449992	−	0.893032i	$-0.351427\pi$
$13$	7.56009e13	0.899985	0.449992	+	0.893032i	$0.351427\pi$
$14$	0	0
$15$	2.90373e14	0.577851
$16$	3.26808e15	2.90264
$17$	2.56123e15	1.06620	0.533098	−	0.846054i	$-0.321028\pi$
$17$	2.56123e15	1.06620	0.533098	+	0.846054i	$0.321028\pi$
$18$	3.09741e15	0.631092
$19$	−1.41497e16	−1.46666	−0.733328	−	0.679875i	$-0.762034\pi$
$19$	−1.41497e16	−1.46666	−0.733328	+	0.679875i	$0.762034\pi$
$20$	−3.29541e16	−1.79901
$21$	0	0
$22$	−7.80208e16	−1.29398
$23$	−1.63002e17	−1.55094	−0.775471	−	0.631383i	$-0.782488\pi$
$23$	−1.63002e17	−1.55094	−0.775471	+	0.631383i	$0.782488\pi$
$24$	4.21839e17	2.35780
$25$	−1.48260e17	−0.497479
$26$	−8.23700e17	−1.69279
$27$	8.49060e17	1.08866
$28$	0	0
$29$	3.44080e18	1.80586	0.902931	−	0.429786i	$-0.141411\pi$
$29$	3.44080e18	1.80586	0.902931	+	0.429786i	$0.141411\pi$
$30$	−3.16372e18	−1.08688
$31$	2.73908e18	0.624574	0.312287	−	0.949988i	$-0.398905\pi$
$31$	2.73908e18	0.624574	0.312287	+	0.949988i	$0.398905\pi$
$32$	−1.67426e19	−2.56713
$33$	−5.37308e18	−0.560789
$34$	−2.79055e19	−2.00541
$35$	0	0
$36$	−2.42083e19	−0.851498
$37$	3.95665e19	0.988111	0.494055	−	0.869430i	$-0.335514\pi$
$37$	3.95665e19	0.988111	0.494055	+	0.869430i	$0.335514\pi$
$38$	1.54167e20	2.75864
$39$	−5.67260e19	−0.733625
$40$	2.17568e20	2.05043
$41$	1.12710e20	0.780122	0.390061	−	0.920789i	$-0.372454\pi$
$41$	1.12710e20	0.780122	0.390061	+	0.920789i	$0.372454\pi$
$42$	0	0
$43$	−1.75585e19	−0.0670089	−0.0335044	−	0.999439i	$-0.510667\pi$
$43$	−1.75585e19	−0.0670089	−0.0335044	+	0.999439i	$0.510667\pi$
$44$	6.09784e20	1.74589
$45$	1.10017e20	0.237850
$46$	1.77597e21	2.91717
$47$	7.32800e20	0.919946	0.459973	−	0.887933i	$-0.347859\pi$
$47$	7.32800e20	0.919946	0.459973	+	0.887933i	$0.347859\pi$
$48$	−2.45215e21	−2.36609
$49$	0	0
$50$	1.61535e21	0.935711
$51$	−1.92178e21	−0.869113
$52$	6.43776e21	2.28398
$53$	−4.32666e21	−1.20977	−0.604887	−	0.796311i	$-0.706782\pi$
$53$	−4.32666e21	−1.20977	−0.604887	+	0.796311i	$0.706782\pi$
$54$	−9.25082e21	−2.04766
$55$	−2.77122e21	−0.487682
$56$	0	0
$57$	1.06170e22	1.19555
$58$	−3.74888e22	−3.39665
$59$	2.53856e22	1.85753	0.928767	−	0.370665i	$-0.120870\pi$
$59$	2.53856e22	1.85753	0.928767	+	0.370665i	$0.120870\pi$
$60$	2.47266e22	1.46647
$61$	1.76183e22	0.849849	0.424924	−	0.905229i	$-0.360301\pi$
$61$	1.76183e22	0.849849	0.424924	+	0.905229i	$0.360301\pi$
$62$	−2.98433e22	−1.17476
$63$	0	0
$64$	7.27577e22	1.92588
$65$	−2.92570e22	−0.637987
$66$	5.85417e22	1.05479
$67$	8.36822e22	1.24939	0.624695	−	0.780869i	$-0.285223\pi$
$67$	8.36822e22	1.24939	0.624695	+	0.780869i	$0.285223\pi$
$68$	2.18100e23	2.70579
$69$	1.22306e23	1.26426
$70$	0	0
$71$	−1.02690e23	−0.742677	−0.371339	−	0.928498i	$-0.621101\pi$
$71$	−1.02690e23	−0.742677	−0.371339	+	0.928498i	$0.621101\pi$
$72$	1.59827e23	0.970494
$73$	−5.97629e21	−0.0305419	−0.0152710	−	0.999883i	$-0.504861\pi$
$73$	−5.97629e21	−0.0305419	−0.0152710	+	0.999883i	$0.504861\pi$
$74$	−4.31091e23	−1.85854
$75$	1.11245e23	0.405522
$76$	−1.20491e24	−3.72208
$77$	0	0
$78$	6.18050e23	1.37988
$79$	−2.43658e23	−0.463919	−0.231960	−	0.972725i	$-0.574514\pi$
$79$	−2.43658e23	−0.463919	−0.231960	+	0.972725i	$0.574514\pi$
$80$	−1.26472e24	−2.05764
$81$	−3.96206e23	−0.551897
$82$	−1.22801e24	−1.46733
$83$	1.02448e24	1.05202	0.526012	−	0.850477i	$-0.323687\pi$
$83$	1.02448e24	1.05202	0.526012	+	0.850477i	$0.323687\pi$
$84$	0	0
$85$	−9.91175e23	−0.755812
$86$	1.91307e23	0.126037
$87$	−2.58175e24	−1.47205
$88$	−4.02588e24	−1.98988
$89$	−4.59761e23	−0.197314	−0.0986569	−	0.995122i	$-0.531455\pi$
$89$	−4.59761e23	−0.197314	−0.0986569	+	0.995122i	$0.531455\pi$
$90$	−1.19867e24	−0.447373
$91$	0	0
$92$	−1.38804e25	−3.93599
$93$	−2.05523e24	−0.509124
$94$	−7.98412e24	−1.73033
$95$	5.47584e24	1.03969
$96$	1.25625e25	2.09260
$97$	−5.84706e24	−0.855639	−0.427820	−	0.903864i	$-0.640718\pi$
$97$	−5.84706e24	−0.855639	−0.427820	+	0.903864i	$0.640718\pi$
$98$	0	0
$99$	−2.03576e24	−0.230826
$100$	−1.26250e25	−1.26250
$101$	−5.50733e24	−0.486322	−0.243161	−	0.969986i	$-0.578184\pi$
$101$	−5.50733e24	−0.486322	−0.243161	+	0.969986i	$0.578184\pi$
$102$	2.09385e25	1.63472
$103$	−3.72027e24	−0.257104	−0.128552	−	0.991703i	$-0.541033\pi$
$103$	−3.72027e24	−0.257104	−0.128552	+	0.991703i	$0.541033\pi$
$104$	−4.25030e25	−2.60317
$105$	0	0
$106$	4.71405e25	2.27547
$107$	−3.96743e24	−0.170299	−0.0851494	−	0.996368i	$-0.527137\pi$
$107$	−3.96743e24	−0.170299	−0.0851494	+	0.996368i	$0.527137\pi$
$108$	7.23013e25	2.76280
$109$	−8.12239e24	−0.276600	−0.138300	−	0.990390i	$-0.544164\pi$
$109$	−8.12239e24	−0.276600	−0.138300	+	0.990390i	$0.544164\pi$
$110$	3.01934e25	0.917284
$111$	−2.96881e25	−0.805461
$112$	0	0
$113$	−3.81412e25	−0.827777	−0.413889	−	0.910328i	$-0.635830\pi$
$113$	−3.81412e25	−0.827777	−0.413889	+	0.910328i	$0.635830\pi$
$114$	−1.15676e26	−2.24871
$115$	6.30806e25	1.09944
$116$	2.93000e26	4.58292
$117$	−2.14924e25	−0.301968
$118$	−2.76585e26	−3.49384
$119$	0	0
$120$	−1.63248e26	−1.67141
$121$	−5.70683e25	−0.526718
$122$	−1.91958e26	−1.59848
$123$	−8.45698e25	−0.635919
$124$	2.33245e26	1.58505
$125$	1.72708e26	1.06154
$126$	0	0
$127$	−1.86713e26	−0.941085	−0.470543	−	0.882377i	$-0.655942\pi$
$127$	−1.86713e26	−0.941085	−0.470543	+	0.882377i	$0.655942\pi$
$128$	−2.30935e26	−1.05527
$129$	1.31748e25	0.0546225
$130$	3.18765e26	1.19999
$131$	4.29939e26	1.47067	0.735336	−	0.677703i	$-0.237024\pi$
$131$	4.29939e26	1.47067	0.735336	+	0.677703i	$0.237024\pi$
$132$	−4.57542e26	−1.42317
$133$	0	0
$134$	−9.11748e26	−2.34998
$135$	−3.28579e26	−0.771735
$136$	−1.43993e27	−3.08393
$137$	−5.20472e26	−1.01716	−0.508581	−	0.861014i	$-0.669830\pi$
$137$	−5.20472e26	−1.01716	−0.508581	+	0.861014i	$0.669830\pi$
$138$	−1.33257e27	−2.37794
$139$	−8.11237e26	−1.32270	−0.661352	−	0.750076i	$-0.730017\pi$
$139$	−8.11237e26	−1.32270	−0.661352	+	0.750076i	$0.730017\pi$
$140$	0	0
$141$	−5.49845e26	−0.749896
$142$	1.11885e27	1.39690
$143$	5.41372e26	0.619149
$144$	−9.29073e26	−0.973909
$145$	−1.33156e27	−1.28015
$146$	6.51139e25	0.0574464
$147$	0	0
$148$	3.36926e27	2.50763
$149$	1.54244e27	1.05531	0.527656	−	0.849458i	$-0.323071\pi$
$149$	1.54244e27	1.05531	0.527656	+	0.849458i	$0.323071\pi$
$150$	−1.21205e27	−0.762748
$151$	−6.28001e26	−0.363705	−0.181852	−	0.983326i	$-0.558209\pi$
$151$	−6.28001e26	−0.363705	−0.181852	+	0.983326i	$0.558209\pi$
$152$	7.95501e27	4.24225
$153$	−7.28124e26	−0.357736
$154$	0	0
$155$	−1.06000e27	−0.442753
$156$	−4.83047e27	−1.86180
$157$	1.53541e27	0.546361	0.273180	−	0.961963i	$-0.411924\pi$
$157$	1.53541e27	0.546361	0.273180	+	0.961963i	$0.411924\pi$
$158$	2.65475e27	0.872588
$159$	3.24644e27	0.986151
$160$	6.47924e27	1.81980
$161$	0	0
$162$	4.31681e27	1.03807
$163$	2.67048e27	0.594627	0.297313	−	0.954780i	$-0.403909\pi$
$163$	2.67048e27	0.594627	0.297313	+	0.954780i	$0.403909\pi$
$164$	9.59772e27	1.97979
$165$	2.07934e27	0.397536
$166$	−1.11620e28	−1.97876
$167$	1.70286e27	0.280042	0.140021	−	0.990149i	$-0.455283\pi$
$167$	1.70286e27	0.280042	0.140021	+	0.990149i	$0.455283\pi$
$168$	0	0
$169$	−1.34091e27	−0.190027
$170$	1.07992e28	1.42161
$171$	4.02259e27	0.492101
$172$	−1.49519e27	−0.170055
$173$	−1.78696e28	−1.89033	−0.945164	−	0.326595i	$-0.894099\pi$
$173$	−1.78696e28	−1.89033	−0.945164	+	0.326595i	$0.894099\pi$
$174$	2.81291e28	2.76879
$175$	0	0
$176$	2.34024e28	1.99688
$177$	−1.90477e28	−1.51417
$178$	5.00927e27	0.371128
$179$	−1.41289e28	−0.975990	−0.487995	−	0.872846i	$-0.662272\pi$
$179$	−1.41289e28	−0.975990	−0.487995	+	0.872846i	$0.662272\pi$
$180$	9.36843e27	0.603616
$181$	−1.22306e28	−0.735303	−0.367651	−	0.929964i	$-0.619838\pi$
$181$	−1.22306e28	−0.735303	−0.367651	+	0.929964i	$0.619838\pi$
$182$	0	0
$183$	−1.32196e28	−0.692757
$184$	9.16401e28	4.48604
$185$	−1.53119e28	−0.700459
$186$	2.23925e28	0.957613
$187$	1.83407e28	0.733495
$188$	6.24012e28	2.33464
$189$	0	0
$190$	−5.96612e28	−1.95556
$191$	3.30341e28	1.01402	0.507009	−	0.861941i	$-0.330751\pi$
$191$	3.30341e28	1.01402	0.507009	+	0.861941i	$0.330751\pi$
$192$	−5.45926e28	−1.56989
$193$	−4.45194e28	−1.19973	−0.599864	−	0.800102i	$-0.704779\pi$
$193$	−4.45194e28	−1.19973	−0.599864	+	0.800102i	$0.704779\pi$
$194$	6.37058e28	1.60938
$195$	2.19525e28	0.520057
$196$	0	0
$197$	2.82041e28	0.588145	0.294073	−	0.955783i	$-0.404989\pi$
$197$	2.82041e28	0.588145	0.294073	+	0.955783i	$0.404989\pi$
$198$	2.21803e28	0.434163
$199$	−6.15186e28	−1.13069	−0.565345	−	0.824855i	$-0.691257\pi$
$199$	−6.15186e28	−1.13069	−0.565345	+	0.824855i	$0.691257\pi$
$200$	8.33522e28	1.43894
$201$	−6.27896e28	−1.01844
$202$	6.00044e28	0.914726
$203$	0	0
$204$	−1.63648e29	−2.20564
$205$	−4.36177e28	−0.553018
$206$	4.05337e28	0.483588
$207$	4.63394e28	0.520381
$208$	2.47070e29	2.61233
$209$	−1.01325e29	−1.00899
$210$	0	0
$211$	1.41627e29	1.25204	0.626018	−	0.779809i	$-0.284684\pi$
$211$	1.41627e29	1.25204	0.626018	+	0.779809i	$0.284684\pi$
$212$	−3.68435e29	−3.07017
$213$	7.70521e28	0.605395
$214$	4.32265e28	0.320316
$215$	6.79501e27	0.0475017
$216$	−4.77343e29	−3.14890
$217$	0	0
$218$	8.84964e28	0.520259
$219$	4.48422e27	0.0248963
$220$	−2.35982e29	−1.23764
$221$	1.93631e29	0.959560
$222$	3.23462e29	1.51500
$223$	−1.11226e29	−0.492487	−0.246243	−	0.969208i	$-0.579196\pi$
$223$	−1.11226e29	−0.492487	−0.246243	+	0.969208i	$0.579196\pi$
$224$	0	0
$225$	4.21485e28	0.166917
$226$	4.15562e29	1.55697
$227$	1.10256e29	0.390913	0.195456	−	0.980712i	$-0.437381\pi$
$227$	1.10256e29	0.390913	0.195456	+	0.980712i	$0.437381\pi$
$228$	9.04089e29	3.03407
$229$	3.19297e29	1.01450	0.507249	−	0.861799i	$-0.330662\pi$
$229$	3.19297e29	1.01450	0.507249	+	0.861799i	$0.330662\pi$
$230$	−6.87286e29	−2.06795
$231$	0	0
$232$	−1.93442e30	−5.22338
$233$	−9.72046e28	−0.248735	−0.124368	−	0.992236i	$-0.539690\pi$
$233$	−9.72046e28	−0.248735	−0.124368	+	0.992236i	$0.539690\pi$
$234$	2.34167e29	0.567973
$235$	−2.83588e29	−0.652137
$236$	2.16170e30	4.71405
$237$	1.82825e29	0.378165
$238$	0	0
$239$	3.72387e29	0.693460	0.346730	−	0.937965i	$-0.387292\pi$
$239$	3.72387e29	0.693460	0.346730	+	0.937965i	$0.387292\pi$
$240$	9.48963e29	1.67729
$241$	−9.24159e29	−1.55072	−0.775360	−	0.631519i	$-0.782432\pi$
$241$	−9.24159e29	−1.55072	−0.775360	+	0.631519i	$0.782432\pi$
$242$	6.21780e29	0.990706
$243$	−4.22112e29	−0.638777
$244$	1.50028e30	2.15675
$245$	0	0
$246$	9.21419e29	1.19610
$247$	−1.06973e30	−1.31997
$248$	−1.53992e30	−1.80656
$249$	−7.68699e29	−0.857560
$250$	−1.88172e30	−1.99666
$251$	1.00344e30	1.01291	0.506456	−	0.862266i	$-0.330955\pi$
$251$	1.00344e30	1.01291	0.506456	+	0.862266i	$0.330955\pi$
$252$	0	0
$253$	−1.16725e30	−1.06698
$254$	2.03431e30	1.77009
$255$	7.43713e29	0.616103
$256$	7.47741e28	0.0589864
$257$	−3.04071e28	−0.0228460	−0.0114230	−	0.999935i	$-0.503636\pi$
$257$	−3.04071e28	−0.0228460	−0.0114230	+	0.999935i	$0.503636\pi$
$258$	−1.43544e29	−0.102740
$259$	0	0
$260$	−2.49136e30	−1.61909
$261$	−9.78175e29	−0.605913
$262$	−4.68434e30	−2.76619
$263$	1.61545e30	0.909592	0.454796	−	0.890596i	$-0.349712\pi$
$263$	1.61545e30	0.909592	0.454796	+	0.890596i	$0.349712\pi$
$264$	3.02075e30	1.62206
$265$	1.67438e30	0.857593
$266$	0	0
$267$	3.44975e29	0.160841
$268$	7.12592e30	3.17071
$269$	3.64997e30	1.55020	0.775098	−	0.631842i	$-0.217701\pi$
$269$	3.64997e30	1.55020	0.775098	+	0.631842i	$0.217701\pi$
$270$	3.57999e30	1.45156
$271$	−7.68276e29	−0.297441	−0.148721	−	0.988879i	$-0.547516\pi$
$271$	−7.68276e29	−0.297441	−0.148721	+	0.988879i	$0.547516\pi$
$272$	8.37030e30	3.09478
$273$	0	0
$274$	5.67073e30	1.91318
$275$	−1.06168e30	−0.342243
$276$	1.04149e31	3.20843
$277$	1.72824e29	0.0508871	0.0254435	−	0.999676i	$-0.491900\pi$
$277$	1.72824e29	0.0508871	0.0254435	+	0.999676i	$0.491900\pi$
$278$	8.83872e30	2.48788
$279$	−7.78686e29	−0.209561
$280$	0	0
$281$	3.54659e30	0.872935	0.436467	−	0.899720i	$-0.356229\pi$
$281$	3.54659e30	0.872935	0.436467	+	0.899720i	$0.356229\pi$
$282$	5.99076e30	1.41048
$283$	−6.77141e30	−1.52528	−0.762638	−	0.646825i	$-0.776096\pi$
$283$	−6.77141e30	−1.52528	−0.762638	+	0.646825i	$0.776096\pi$
$284$	−8.74454e30	−1.88477
$285$	−4.10871e30	−0.847510
$286$	−5.89844e30	−1.16456
$287$	0	0
$288$	4.75969e30	0.861336
$289$	7.89269e29	0.136773
$290$	1.45079e31	2.40784
$291$	4.38725e30	0.697477
$292$	−5.08908e29	−0.0775093
$293$	−5.38730e30	−0.786187	−0.393094	−	0.919498i	$-0.628595\pi$
$293$	−5.38730e30	−0.786187	−0.393094	+	0.919498i	$0.628595\pi$
$294$	0	0
$295$	−9.82401e30	−1.31678
$296$	−2.22443e31	−2.85807
$297$	6.08005e30	0.748947
$298$	−1.68055e31	−1.98494
$299$	−1.23231e31	−1.39582
$300$	9.47300e30	1.02913
$301$	0	0
$302$	6.84230e30	0.684094
$303$	4.13234e30	0.396427
$304$	−4.62425e31	−4.25717
$305$	−6.81815e30	−0.602447
$306$	7.93318e30	0.672867
$307$	4.75285e30	0.387012	0.193506	−	0.981099i	$-0.438014\pi$
$307$	4.75285e30	0.387012	0.193506	+	0.981099i	$0.438014\pi$
$308$	0	0
$309$	2.79144e30	0.209579
$310$	1.15491e31	0.832775
$311$	2.27504e30	0.157574	0.0787870	−	0.996891i	$-0.474895\pi$
$311$	2.27504e30	0.157574	0.0787870	+	0.996891i	$0.474895\pi$
$312$	3.18914e31	2.12198
$313$	9.67099e30	0.618254	0.309127	−	0.951021i	$-0.399963\pi$
$313$	9.67099e30	0.618254	0.309127	+	0.951021i	$0.399963\pi$
$314$	−1.67289e31	−1.02765
$315$	0	0
$316$	−2.07486e31	−1.17734
$317$	3.50486e30	0.191174	0.0955872	−	0.995421i	$-0.469527\pi$
$317$	3.50486e30	0.191174	0.0955872	+	0.995421i	$0.469527\pi$
$318$	−3.53712e31	−1.85486
$319$	2.46393e31	1.24235
$320$	−2.81567e31	−1.36523
$321$	2.97690e30	0.138820
$322$	0	0
$323$	−3.62407e31	−1.56374
$324$	−3.37387e31	−1.40061
$325$	−1.12086e31	−0.447724
$326$	−2.90959e31	−1.11844
$327$	6.09451e30	0.225471
$328$	−6.33655e31	−2.25647
$329$	0	0
$330$	−2.26552e31	−0.747727
$331$	−3.96004e31	−1.25849	−0.629244	−	0.777208i	$-0.716635\pi$
$331$	−3.96004e31	−1.25849	−0.629244	+	0.777208i	$0.716635\pi$
$332$	8.72388e31	2.66983
$333$	−1.12482e31	−0.331536
$334$	−1.85533e31	−0.526731
$335$	−3.23844e31	−0.885677
$336$	0	0
$337$	5.23004e31	1.32780	0.663898	−	0.747824i	$-0.268901\pi$
$337$	5.23004e31	1.32780	0.663898	+	0.747824i	$0.268901\pi$
$338$	1.46097e31	0.357423
$339$	2.86186e31	0.674765
$340$	−8.44031e31	−1.91810
$341$	1.96143e31	0.429679
$342$	−4.38276e31	−0.925595
$343$	0	0
$344$	9.87143e30	0.193820
$345$	−4.73315e31	−0.896214
$346$	1.94695e32	3.55553
$347$	3.71525e31	0.654440	0.327220	−	0.944948i	$-0.393888\pi$
$347$	3.71525e31	0.654440	0.327220	+	0.944948i	$0.393888\pi$
$348$	−2.19848e32	−3.73578
$349$	5.96416e30	0.0977758	0.0488879	−	0.998804i	$-0.484432\pi$
$349$	5.96416e30	0.0977758	0.0488879	+	0.998804i	$0.484432\pi$
$350$	0	0
$351$	6.41897e31	0.979775
$352$	−1.19892e32	−1.76607
$353$	−1.19073e32	−1.69289	−0.846444	−	0.532477i	$-0.821261\pi$
$353$	−1.19073e32	−1.69289	−0.846444	+	0.532477i	$0.821261\pi$
$354$	2.07531e32	2.84802
$355$	3.97403e31	0.526474
$356$	−3.91508e31	−0.500743
$357$	0	0
$358$	1.53939e32	1.83574
$359$	−4.72824e31	−0.544527	−0.272263	−	0.962223i	$-0.587772\pi$
$359$	−4.72824e31	−0.544527	−0.272263	+	0.962223i	$0.587772\pi$
$360$	−6.18516e31	−0.687971
$361$	1.07139e32	1.15108
$362$	1.33257e32	1.38303
$363$	4.28203e31	0.429356
$364$	0	0
$365$	2.31278e30	0.0216508
$366$	1.44033e32	1.30301
$367$	1.15323e32	1.00830	0.504150	−	0.863616i	$-0.331806\pi$
$367$	1.15323e32	1.00830	0.504150	+	0.863616i	$0.331806\pi$
$368$	−5.32704e32	−4.50182
$369$	−3.20419e31	−0.261751
$370$	1.66829e32	1.31750
$371$	0	0
$372$	−1.75012e32	−1.29206
$373$	−1.04834e32	−0.748413	−0.374206	−	0.927345i	$-0.622085\pi$
$373$	−1.04834e32	−0.748413	−0.374206	+	0.927345i	$0.622085\pi$
$374$	−1.99829e32	−1.37963
$375$	−1.29589e32	−0.865320
$376$	−4.11981e32	−2.66091
$377$	2.60128e32	1.62525
$378$	0	0
$379$	2.15024e32	1.25747	0.628734	−	0.777620i	$-0.283573\pi$
$379$	2.15024e32	1.25747	0.628734	+	0.777620i	$0.283573\pi$
$380$	4.66292e32	2.63854
$381$	1.40098e32	0.767129
$382$	−3.59919e32	−1.90727
$383$	−1.52997e31	−0.0784689	−0.0392344	−	0.999230i	$-0.512492\pi$
$383$	−1.52997e31	−0.0784689	−0.0392344	+	0.999230i	$0.512492\pi$
$384$	1.73278e32	0.860209
$385$	0	0
$386$	4.85055e32	2.25658
$387$	4.99166e30	0.0224832
$388$	−4.97903e32	−2.17144
$389$	−1.13524e32	−0.479423	−0.239712	−	0.970844i	$-0.577053\pi$
$389$	−1.13524e32	−0.479423	−0.239712	+	0.970844i	$0.577053\pi$
$390$	−2.39180e32	−0.978178
$391$	−4.17486e32	−1.65361
$392$	0	0
$393$	−3.22598e32	−1.19882
$394$	−3.07294e32	−1.10625
$395$	9.42938e31	0.328866
$396$	−1.73354e32	−0.585792
$397$	3.42728e32	1.12220	0.561098	−	0.827749i	$-0.310379\pi$
$397$	3.42728e32	1.12220	0.561098	+	0.827749i	$0.310379\pi$
$398$	6.70268e32	2.12672
$399$	0	0
$400$	−4.84527e32	−1.44400
$401$	2.93356e32	0.847404	0.423702	−	0.905802i	$-0.360730\pi$
$401$	2.93356e32	0.847404	0.423702	+	0.905802i	$0.360730\pi$
$402$	6.84116e32	1.91560
$403$	2.07077e32	0.562107
$404$	−4.68974e32	−1.23419
$405$	1.53328e32	0.391233
$406$	0	0
$407$	2.83332e32	0.679776
$408$	1.08043e33	2.51387
$409$	7.97835e32	1.80041	0.900206	−	0.435464i	$-0.143416\pi$
$409$	7.97835e32	1.80041	0.900206	+	0.435464i	$0.143416\pi$
$410$	4.75231e32	1.04017
$411$	3.90528e32	0.829142
$412$	−3.16797e32	−0.652479
$413$	0	0
$414$	−5.04885e32	−0.978787
$415$	−3.96464e32	−0.745766
$416$	−1.26575e33	−2.31037
$417$	6.08699e32	1.07821
$418$	1.10397e33	1.89782
$419$	−3.49063e32	−0.582410	−0.291205	−	0.956661i	$-0.594056\pi$
$419$	−3.49063e32	−0.582410	−0.291205	+	0.956661i	$0.594056\pi$
$420$	0	0
$421$	3.47880e32	0.546894	0.273447	−	0.961887i	$-0.411836\pi$
$421$	3.47880e32	0.546894	0.273447	+	0.961887i	$0.411836\pi$
$422$	−1.54308e33	−2.35496
$423$	−2.08326e32	−0.308665
$424$	2.43245e33	3.49922
$425$	−3.79729e32	−0.530410
$426$	−8.39510e32	−1.13869
$427$	0	0
$428$	−3.37844e32	−0.432185
$429$	−4.06210e32	−0.504701
$430$	−7.40341e31	−0.0893462
$431$	4.46552e32	0.523488	0.261744	−	0.965137i	$-0.415702\pi$
$431$	4.46552e32	0.523488	0.261744	+	0.965137i	$0.415702\pi$
$432$	2.77480e33	3.15998
$433$	−1.21468e33	−1.34389	−0.671944	−	0.740602i	$-0.734540\pi$
$433$	−1.21468e33	−1.34389	−0.671944	+	0.740602i	$0.734540\pi$
$434$	0	0
$435$	9.99117e32	1.04352
$436$	−6.91658e32	−0.701957
$437$	2.30644e33	2.27470
$438$	−4.88572e31	−0.0468276
$439$	−1.76324e33	−1.64250	−0.821250	−	0.570568i	$-0.806723\pi$
$439$	−1.76324e33	−1.64250	−0.821250	+	0.570568i	$0.806723\pi$
$440$	1.55798e33	1.41060
$441$	0	0
$442$	−2.10968e33	−1.80484
$443$	6.86336e32	0.570808	0.285404	−	0.958407i	$-0.407872\pi$
$443$	6.86336e32	0.570808	0.285404	+	0.958407i	$0.407872\pi$
$444$	−2.52807e33	−2.04410
$445$	1.77924e32	0.139873
$446$	1.21184e33	0.926320
$447$	−1.15735e33	−0.860241
$448$	0	0
$449$	3.56662e32	0.250714	0.125357	−	0.992112i	$-0.459992\pi$
$449$	3.56662e32	0.250714	0.125357	+	0.992112i	$0.459992\pi$
$450$	−4.59223e32	−0.313955
$451$	8.07103e32	0.536689
$452$	−3.24789e33	−2.10074
$453$	4.71211e32	0.296475
$454$	−1.20128e33	−0.735270
$455$	0	0
$456$	−5.96892e33	−3.45808
$457$	−1.13769e33	−0.641315	−0.320657	−	0.947195i	$-0.603904\pi$
$457$	−1.13769e33	−0.641315	−0.320657	+	0.947195i	$0.603904\pi$
$458$	−3.47886e33	−1.90818
$459$	2.17464e33	1.16072
$460$	5.37160e33	2.79017
$461$	−5.79484e32	−0.292941	−0.146470	−	0.989215i	$-0.546791\pi$
$461$	−5.79484e32	−0.292941	−0.146470	+	0.989215i	$0.546791\pi$
$462$	0	0
$463$	−6.37894e32	−0.305482	−0.152741	−	0.988266i	$-0.548810\pi$
$463$	−6.37894e32	−0.305482	−0.152741	+	0.988266i	$0.548810\pi$
$464$	1.12448e34	5.24176
$465$	7.95357e32	0.360911
$466$	1.05908e33	0.467848
$467$	7.97993e32	0.343193	0.171596	−	0.985167i	$-0.445107\pi$
$467$	7.97993e32	0.343193	0.171596	+	0.985167i	$0.445107\pi$
$468$	−1.83017e33	−0.766335
$469$	0	0
$470$	3.08979e33	1.22661
$471$	−1.15207e33	−0.445367
$472$	−1.42718e34	−5.37284
$473$	−1.25735e32	−0.0460991
$474$	−1.99195e33	−0.711293
$475$	2.09785e33	0.729631
$476$	0	0
$477$	1.23001e33	0.405910
$478$	−4.05730e33	−1.30433
$479$	5.19276e33	1.62631	0.813156	−	0.582045i	$-0.197747\pi$
$479$	5.19276e33	1.62631	0.813156	+	0.582045i	$0.197747\pi$
$480$	−4.86159e33	−1.48342
$481$	2.99126e33	0.889285
$482$	1.00690e34	2.91676
$483$	0	0
$484$	−4.85963e33	−1.33671
$485$	2.26276e33	0.606551
$486$	4.59907e33	1.20148
$487$	−1.28989e33	−0.328428	−0.164214	−	0.986425i	$-0.552509\pi$
$487$	−1.28989e33	−0.328428	−0.164214	+	0.986425i	$0.552509\pi$
$488$	−9.90505e33	−2.45815
$489$	−2.00375e33	−0.484712
$490$	0	0
$491$	6.81776e33	1.56720	0.783598	−	0.621269i	$-0.213382\pi$
$491$	6.81776e33	1.56720	0.783598	+	0.621269i	$0.213382\pi$
$492$	−7.20150e33	−1.61384
$493$	8.81268e33	1.92540
$494$	1.16551e34	2.48274
$495$	7.87821e32	0.163630
$496$	8.95154e33	1.81291
$497$	0	0
$498$	8.37526e33	1.61299
$499$	−1.61332e33	−0.303016	−0.151508	−	0.988456i	$-0.548413\pi$
$499$	−1.61332e33	−0.303016	−0.151508	+	0.988456i	$0.548413\pi$
$500$	1.47069e34	2.69399
$501$	−1.27771e33	−0.228277
$502$	−1.09329e34	−1.90519
$503$	−4.01246e33	−0.682041	−0.341021	−	0.940056i	$-0.610773\pi$
$503$	−4.01246e33	−0.682041	−0.341021	+	0.940056i	$0.610773\pi$
$504$	0	0
$505$	2.13129e33	0.344747
$506$	1.27176e34	2.00688
$507$	1.00613e33	0.154901
$508$	−1.58995e34	−2.38829
$509$	1.03139e34	1.51165	0.755825	−	0.654774i	$-0.227236\pi$
$509$	1.03139e34	1.51165	0.755825	+	0.654774i	$0.227236\pi$
$510$	−8.10302e33	−1.15883
$511$	0	0
$512$	6.93419e33	0.944325
$513$	−1.20140e34	−1.59669
$514$	3.31296e32	0.0429712
$515$	1.43971e33	0.182258
$516$	1.12189e33	0.138621
$517$	5.24752e33	0.632881
$518$	0	0
$519$	1.34081e34	1.54091
$520$	1.64483e34	1.84535
$521$	1.96614e33	0.215349	0.107674	−	0.994186i	$-0.465660\pi$
$521$	1.96614e33	0.215349	0.107674	+	0.994186i	$0.465660\pi$
$522$	1.06576e34	1.13966
$523$	6.17171e33	0.644368	0.322184	−	0.946677i	$-0.395583\pi$
$523$	6.17171e33	0.644368	0.322184	+	0.946677i	$0.395583\pi$
$524$	3.66113e34	3.73228
$525$	0	0
$526$	−1.76009e34	−1.71086
$527$	7.01542e33	0.665919
$528$	−1.75597e34	−1.62777
$529$	1.55240e34	1.40542
$530$	−1.82430e34	−1.61305
$531$	−7.21679e33	−0.623250
$532$	0	0
$533$	8.52094e33	0.702098
$534$	−3.75863e33	−0.302526
$535$	1.53536e33	0.120723
$536$	−4.70463e34	−3.61381
$537$	1.06014e34	0.795581
$538$	−3.97678e34	−2.91577
$539$	0	0
$540$	−2.79800e34	−1.95851
$541$	−3.40967e33	−0.233210	−0.116605	−	0.993178i	$-0.537201\pi$
$541$	−3.40967e33	−0.233210	−0.116605	+	0.993178i	$0.537201\pi$
$542$	8.37065e33	0.559459
$543$	9.17705e33	0.599384
$544$	−4.28815e34	−2.73706
$545$	3.14330e33	0.196078
$546$	0	0
$547$	−1.32167e34	−0.787556	−0.393778	−	0.919206i	$-0.628832\pi$
$547$	−1.32167e34	−0.787556	−0.393778	+	0.919206i	$0.628832\pi$
$548$	−4.43205e34	−2.58135
$549$	−5.00866e33	−0.285146
$550$	1.15674e34	0.643727
$551$	−4.86864e34	−2.64858
$552$	−6.87607e34	−3.65681
$553$	0	0
$554$	−1.88298e33	−0.0957138
$555$	1.14890e34	0.570981
$556$	−6.90805e34	−3.35676
$557$	−2.75553e34	−1.30923	−0.654613	−	0.755964i	$-0.727169\pi$
$557$	−2.75553e34	−1.30923	−0.654613	+	0.755964i	$0.727169\pi$
$558$	8.48407e33	0.394164
$559$	−1.32744e33	−0.0603070
$560$	0	0
$561$	−1.37617e34	−0.597910
$562$	−3.86414e34	−1.64191
$563$	6.22994e33	0.258898	0.129449	−	0.991586i	$-0.458679\pi$
$563$	6.22994e33	0.258898	0.129449	+	0.991586i	$0.458679\pi$
$564$	−4.68218e34	−1.90309
$565$	1.47603e34	0.586800
$566$	7.37769e34	2.86890
$567$	0	0
$568$	5.77327e34	2.14816
$569$	−4.22510e34	−1.53792	−0.768960	−	0.639297i	$-0.779225\pi$
$569$	−4.22510e34	−1.53792	−0.768960	+	0.639297i	$0.779225\pi$
$570$	4.47659e34	1.59408
$571$	3.57699e34	1.24614	0.623069	−	0.782167i	$-0.285886\pi$
$571$	3.57699e34	1.24614	0.623069	+	0.782167i	$0.285886\pi$
$572$	4.61003e34	1.57128
$573$	−2.47867e34	−0.826580
$574$	0	0
$575$	2.41668e34	0.771562
$576$	−2.06841e34	−0.646182
$577$	3.62815e34	1.10914	0.554571	−	0.832136i	$-0.312882\pi$
$577$	3.62815e34	1.10914	0.554571	+	0.832136i	$0.312882\pi$
$578$	−8.59937e33	−0.257258
$579$	3.34044e34	0.977962
$580$	−1.13389e35	−3.24877
$581$	0	0
$582$	−4.78007e34	−1.31189
$583$	−3.09828e34	−0.832270
$584$	3.35988e33	0.0883412
$585$	8.31737e33	0.214061
$586$	5.86966e34	1.47874
$587$	−1.32495e34	−0.326757	−0.163378	−	0.986563i	$-0.552239\pi$
$587$	−1.32495e34	−0.326757	−0.163378	+	0.986563i	$0.552239\pi$
$588$	0	0
$589$	−3.87573e34	−0.916036
$590$	1.07036e35	2.47674
$591$	−2.11625e34	−0.479428
$592$	1.29306e35	2.86813
$593$	−2.61230e34	−0.567335	−0.283667	−	0.958923i	$-0.591551\pi$
$593$	−2.61230e34	−0.567335	−0.283667	+	0.958923i	$0.591551\pi$
$594$	−6.62443e34	−1.40870
$595$	0	0
$596$	1.31346e35	2.67818
$597$	4.61596e34	0.921685
$598$	1.34265e35	2.62541
$599$	5.19460e34	0.994756	0.497378	−	0.867534i	$-0.334296\pi$
$599$	5.19460e34	0.994756	0.497378	+	0.867534i	$0.334296\pi$
$600$	−6.25420e34	−1.17296
$601$	3.94393e34	0.724434	0.362217	−	0.932094i	$-0.382020\pi$
$601$	3.94393e34	0.724434	0.362217	+	0.932094i	$0.382020\pi$
$602$	0	0
$603$	−2.37898e34	−0.419203
$604$	−5.34772e34	−0.923010
$605$	2.20850e34	0.373383
$606$	−4.50233e34	−0.745641
$607$	−3.81359e34	−0.618694	−0.309347	−	0.950949i	$-0.600110\pi$
$607$	−3.81359e34	−0.618694	−0.309347	+	0.950949i	$0.600110\pi$
$608$	2.36903e35	3.76509
$609$	0	0
$610$	7.42862e34	1.13314
$611$	5.54004e34	0.827937
$612$	−6.20031e34	−0.907863
$613$	−1.15081e35	−1.65100	−0.825499	−	0.564404i	$-0.809106\pi$
$613$	−1.15081e35	−1.65100	−0.825499	+	0.564404i	$0.809106\pi$
$614$	−5.17841e34	−0.727933
$615$	3.27278e34	0.450794
$616$	0	0
$617$	−3.57411e33	−0.0472720	−0.0236360	−	0.999721i	$-0.507524\pi$
$617$	−3.57411e33	−0.0472720	−0.0236360	+	0.999721i	$0.507524\pi$
$618$	−3.04138e34	−0.394198
$619$	−4.07567e34	−0.517686	−0.258843	−	0.965919i	$-0.583341\pi$
$619$	−4.07567e34	−0.517686	−0.258843	+	0.965919i	$0.583341\pi$
$620$	−9.02641e34	−1.12362
$621$	−1.38399e35	−1.68845
$622$	−2.47874e34	−0.296382
$623$	0	0
$624$	−1.85385e35	−2.12945
$625$	−2.26517e34	−0.255035
$626$	−1.05369e35	−1.16288
$627$	7.60277e34	0.822484
$628$	1.30747e35	1.38656
$629$	1.01339e35	1.05352
$630$	0	0
$631$	4.05406e34	0.405063	0.202532	−	0.979276i	$-0.435083\pi$
$631$	4.05406e34	0.405063	0.202532	+	0.979276i	$0.435083\pi$
$632$	1.36985e35	1.34187
$633$	−1.06268e35	−1.02060
$634$	−3.81867e34	−0.359581
$635$	7.22566e34	0.667123
$636$	2.76449e35	2.50266
$637$	0	0
$638$	−2.68454e35	−2.33674
$639$	2.91935e34	0.249187
$640$	8.93699e34	0.748069
$641$	−1.17713e35	−0.966268	−0.483134	−	0.875546i	$-0.660502\pi$
$641$	−1.17713e35	−0.966268	−0.483134	+	0.875546i	$0.660502\pi$
$642$	−3.24344e34	−0.261106
$643$	6.37069e34	0.502978	0.251489	−	0.967860i	$-0.419080\pi$
$643$	6.37069e34	0.502978	0.251489	+	0.967860i	$0.419080\pi$
$644$	0	0
$645$	−5.09853e33	−0.0387212
$646$	3.94856e35	2.94125
$647$	−2.18737e35	−1.59816	−0.799078	−	0.601227i	$-0.794679\pi$
$647$	−2.18737e35	−1.59816	−0.799078	+	0.601227i	$0.794679\pi$
$648$	2.22748e35	1.59634
$649$	1.81784e35	1.27790
$650$	1.22122e35	0.842126
$651$	0	0
$652$	2.27404e35	1.50905
$653$	2.82601e35	1.83975	0.919875	−	0.392211i	$-0.128290\pi$
$653$	2.82601e35	1.83975	0.919875	+	0.392211i	$0.128290\pi$
$654$	−6.64019e34	−0.424090
$655$	−1.66383e35	−1.04254
$656$	3.68344e35	2.26441
$657$	1.69898e33	0.0102476
$658$	0	0
$659$	2.71586e33	0.0157703	0.00788515	−	0.999969i	$-0.497490\pi$
$659$	2.71586e33	0.0157703	0.00788515	+	0.999969i	$0.497490\pi$
$660$	1.77065e35	1.00887
$661$	3.01183e35	1.68388	0.841942	−	0.539568i	$-0.181412\pi$
$661$	3.01183e35	1.68388	0.841942	+	0.539568i	$0.181412\pi$
$662$	4.31460e35	2.36710
$663$	−1.45288e35	−0.782188
$664$	−5.75962e35	−3.04294
$665$	0	0
$666$	1.22554e35	0.623588
$667$	−5.60858e35	−2.80079
$668$	1.45006e35	0.710690
$669$	8.34565e34	0.401452
$670$	3.52839e35	1.66587
$671$	1.26163e35	0.584658
$672$	0	0
$673$	−1.07936e35	−0.481921	−0.240961	−	0.970535i	$-0.577462\pi$
$673$	−1.07936e35	−0.481921	−0.240961	+	0.970535i	$0.577462\pi$
$674$	−5.69832e35	−2.49746
$675$	−1.25882e35	−0.541585
$676$	−1.14185e35	−0.482252
$677$	−7.76498e34	−0.321945	−0.160973	−	0.986959i	$-0.551463\pi$
$677$	−7.76498e34	−0.321945	−0.160973	+	0.986959i	$0.551463\pi$
$678$	−3.11810e35	−1.26917
$679$	0	0
$680$	5.57240e35	2.18616
$681$	−8.27290e34	−0.318654
$682$	−2.13705e35	−0.808185
$683$	−4.69258e35	−1.74242	−0.871211	−	0.490909i	$-0.836665\pi$
$683$	−4.69258e35	−1.74242	−0.871211	+	0.490909i	$0.836665\pi$
$684$	3.42542e35	1.24885
$685$	2.01418e35	0.721052
$686$	0	0
$687$	−2.39580e35	−0.826972
$688$	−5.73827e34	−0.194503
$689$	−3.27099e35	−1.08878
$690$	5.15694e35	1.68569
$691$	−3.37832e35	−1.08449	−0.542244	−	0.840221i	$-0.682425\pi$
$691$	−3.37832e35	−1.08449	−0.542244	+	0.840221i	$0.682425\pi$
$692$	−1.52167e36	−4.79728
$693$	0	0
$694$	−4.04790e35	−1.23094
$695$	3.13942e35	0.937647
$696$	1.45146e36	4.25786
$697$	2.88675e35	0.831763
$698$	−6.49817e34	−0.183907
$699$	7.29359e34	0.202757
$700$	0	0
$701$	3.22276e35	0.864477	0.432238	−	0.901759i	$-0.357724\pi$
$701$	3.22276e35	0.864477	0.432238	+	0.901759i	$0.357724\pi$
$702$	−6.99370e35	−1.84286
$703$	−5.59855e35	−1.44922
$704$	5.21012e35	1.32492
$705$	2.12786e35	0.531592
$706$	1.29734e36	3.18416
$707$	0	0
$708$	−1.62199e36	−3.84267
$709$	7.03153e35	1.63671	0.818355	−	0.574713i	$-0.194886\pi$
$709$	7.03153e35	1.63671	0.818355	+	0.574713i	$0.194886\pi$
$710$	−4.32985e35	−0.990248
$711$	6.92689e34	0.155657
$712$	2.58479e35	0.570722
$713$	−4.46477e35	−0.968679
$714$	0	0
$715$	−2.09507e35	−0.438907
$716$	−1.20314e36	−2.47687
$717$	−2.79415e35	−0.565276
$718$	5.15159e35	1.02420
$719$	4.29420e35	0.839018	0.419509	−	0.907751i	$-0.362202\pi$
$719$	4.29420e35	0.839018	0.419509	+	0.907751i	$0.362202\pi$
$720$	3.59544e35	0.690392
$721$	0	0
$722$	−1.16731e36	−2.16508
$723$	6.93428e35	1.26407
$724$	−1.04149e36	−1.86605
$725$	−5.10134e35	−0.898379
$726$	−4.66543e35	−0.807577
$727$	−2.18185e35	−0.371231	−0.185615	−	0.982622i	$-0.559428\pi$
$727$	−2.18185e35	−0.371231	−0.185615	+	0.982622i	$0.559428\pi$
$728$	0	0
$729$	6.52426e35	1.07260
$730$	−2.51986e34	−0.0407230
$731$	−4.49714e34	−0.0714446
$732$	−1.12571e36	−1.75808
$733$	−6.22036e35	−0.955028	−0.477514	−	0.878624i	$-0.658462\pi$
$733$	−6.22036e35	−0.955028	−0.477514	+	0.878624i	$0.658462\pi$
$734$	−1.25648e36	−1.89652
$735$	0	0
$736$	2.72908e36	3.98146
$737$	5.99241e35	0.859524
$738$	3.49108e35	0.492328
$739$	−1.20159e36	−1.66610	−0.833052	−	0.553194i	$-0.813409\pi$
$739$	−1.20159e36	−1.66610	−0.833052	+	0.553194i	$0.813409\pi$
$740$	−1.30388e36	−1.77763
$741$	8.02658e35	1.07598
$742$	0	0
$743$	−7.23493e35	−0.937722	−0.468861	−	0.883272i	$-0.655335\pi$
$743$	−7.23493e35	−0.937722	−0.468861	+	0.883272i	$0.655335\pi$
$744$	1.15545e36	1.47262
$745$	−5.96914e35	−0.748097
$746$	1.14220e36	1.40769
$747$	−2.91245e35	−0.352981
$748$	1.56180e36	1.86146
$749$	0	0
$750$	1.41192e36	1.62759
$751$	1.25804e36	1.42625	0.713127	−	0.701035i	$-0.247278\pi$
$751$	1.25804e36	1.42625	0.713127	+	0.701035i	$0.247278\pi$
$752$	2.39485e36	2.67027
$753$	−7.52919e35	−0.825678
$754$	−2.83419e36	−3.05694
$755$	2.43032e35	0.257825
$756$	0	0
$757$	−1.30913e36	−1.34364	−0.671821	−	0.740714i	$-0.734487\pi$
$757$	−1.30913e36	−1.34364	−0.671821	+	0.740714i	$0.734487\pi$
$758$	−2.34277e36	−2.36518
$759$	8.75824e35	0.869751
$760$	−3.07852e36	−3.00727
$761$	7.88081e35	0.757291	0.378645	−	0.925542i	$-0.376390\pi$
$761$	7.88081e35	0.757291	0.378645	+	0.925542i	$0.376390\pi$
$762$	−1.52641e36	−1.44290
$763$	0	0
$764$	2.81301e36	2.57338
$765$	2.81778e35	0.253594
$766$	1.66695e35	0.147592
$767$	1.91917e36	1.67175
$768$	−5.61056e34	−0.0480829
$769$	−8.38400e34	−0.0706923	−0.0353462	−	0.999375i	$-0.511253\pi$
$769$	−8.38400e34	−0.0706923	−0.0353462	+	0.999375i	$0.511253\pi$
$770$	0	0
$771$	2.28155e34	0.0186230
$772$	−3.79103e36	−3.04467
$773$	3.13124e35	0.247442	0.123721	−	0.992317i	$-0.460517\pi$
$773$	3.13124e35	0.247442	0.123721	+	0.992317i	$0.460517\pi$
$774$	−5.43860e34	−0.0422887
$775$	−4.06098e35	−0.310713
$776$	3.28722e36	2.47490
$777$	0	0
$778$	1.23689e36	0.901749
$779$	−1.59481e36	−1.14417
$780$	1.86935e36	1.31980
$781$	−7.35357e35	−0.510928
$782$	4.54866e36	3.11028
$783$	2.92145e36	1.96597
$784$	0	0
$785$	−5.94192e35	−0.387308
$786$	3.51482e36	2.25487
$787$	1.63608e36	1.03305	0.516523	−	0.856273i	$-0.327226\pi$
$787$	1.63608e36	1.03305	0.516523	+	0.856273i	$0.327226\pi$
$788$	2.40171e36	1.49260
$789$	−1.21213e36	−0.741457
$790$	−1.02737e36	−0.618566
$791$	0	0
$792$	1.14451e36	0.667656
$793$	1.33196e36	0.764851
$794$	−3.73415e36	−2.11074
$795$	−1.25635e36	−0.699070
$796$	−5.23859e36	−2.86947
$797$	−1.88764e36	−1.01786	−0.508932	−	0.860807i	$-0.669960\pi$
$797$	−1.88764e36	−1.01786	−0.508932	+	0.860807i	$0.669960\pi$
$798$	0	0
$799$	1.87687e36	0.980842
$800$	2.48226e36	1.27709
$801$	1.30704e35	0.0662038
$802$	−3.19622e36	−1.59389
$803$	−4.27957e34	−0.0210115
$804$	−5.34682e36	−2.58461
$805$	0	0
$806$	−2.25618e36	−1.05727
$807$	−2.73870e36	−1.26365
$808$	3.09623e36	1.40667
$809$	5.90144e34	0.0263999	0.0131999	−	0.999913i	$-0.495798\pi$
$809$	5.90144e34	0.0263999	0.0131999	+	0.999913i	$0.495798\pi$
$810$	−1.67057e36	−0.735871
$811$	4.42598e36	1.91977	0.959885	−	0.280395i	$-0.0904655\pi$
$811$	4.42598e36	1.91977	0.959885	+	0.280395i	$0.0904655\pi$
$812$	0	0
$813$	5.76464e35	0.242460
$814$	−3.08701e36	−1.27859
$815$	−1.03346e36	−0.421523
$816$	−6.28053e36	−2.52272
$817$	2.48449e35	0.0982790
$818$	−8.69270e36	−3.38640
$819$	0	0
$820$	−3.71424e36	−1.40345
$821$	1.55811e36	0.579841	0.289920	−	0.957051i	$-0.406371\pi$
$821$	1.55811e36	0.579841	0.289920	+	0.957051i	$0.406371\pi$
$822$	−4.25494e36	−1.55954
$823$	2.55246e36	0.921428	0.460714	−	0.887549i	$-0.347593\pi$
$823$	2.55246e36	0.921428	0.460714	+	0.887549i	$0.347593\pi$
$824$	2.09154e36	0.743663
$825$	7.96615e35	0.278981
$826$	0	0
$827$	1.12276e36	0.381475	0.190738	−	0.981641i	$-0.438912\pi$
$827$	1.12276e36	0.381475	0.190738	+	0.981641i	$0.438912\pi$
$828$	3.94601e36	1.32062
$829$	2.06206e36	0.679781	0.339890	−	0.940465i	$-0.389610\pi$
$829$	2.06206e36	0.679781	0.339890	+	0.940465i	$0.389610\pi$
$830$	4.31962e36	1.40271
$831$	−1.29676e35	−0.0414808
$832$	5.50055e36	1.73326
$833$	0	0
$834$	−6.63199e36	−2.02800
$835$	−6.58992e35	−0.198518
$836$	−8.62829e36	−2.56063
$837$	2.32565e36	0.679948
$838$	3.80317e36	1.09546
$839$	2.00975e36	0.570319	0.285159	−	0.958480i	$-0.407953\pi$
$839$	2.00975e36	0.570319	0.285159	+	0.958480i	$0.407953\pi$
$840$	0	0
$841$	8.20874e36	2.26114
$842$	−3.79028e36	−1.02866
$843$	−2.66113e36	−0.711575
$844$	1.20602e37	3.17742
$845$	5.18922e35	0.134708
$846$	2.26978e36	0.580570
$847$	0	0
$848$	−1.41399e37	−3.51154
$849$	5.08082e36	1.24333
$850$	4.13728e36	0.997651
$851$	−6.44942e36	−1.53250
$852$	6.56133e36	1.53637
$853$	−4.87838e36	−1.12567	−0.562837	−	0.826568i	$-0.690290\pi$
$853$	−4.87838e36	−1.12567	−0.562837	+	0.826568i	$0.690290\pi$
$854$	0	0
$855$	−1.55671e36	−0.348844
$856$	2.23049e36	0.492582
$857$	3.27765e35	0.0713350	0.0356675	−	0.999364i	$-0.488644\pi$
$857$	3.27765e35	0.0713350	0.0356675	+	0.999364i	$0.488644\pi$
$858$	4.42580e36	0.949295
$859$	2.25858e36	0.477443	0.238721	−	0.971088i	$-0.423272\pi$
$859$	2.25858e36	0.477443	0.238721	+	0.971088i	$0.423272\pi$
$860$	5.78626e35	0.120550
$861$	0	0
$862$	−4.86535e36	−0.984631
$863$	−7.59988e36	−1.51590	−0.757952	−	0.652310i	$-0.773800\pi$
$863$	−7.59988e36	−1.51590	−0.757952	+	0.652310i	$0.773800\pi$
$864$	−1.42154e37	−2.79472
$865$	6.91537e36	1.34003
$866$	1.32344e37	2.52773
$867$	−5.92215e35	−0.111491
$868$	0	0
$869$	−1.74482e36	−0.319156
$870$	−1.08857e37	−1.96276
$871$	6.32645e36	1.12443
$872$	4.56642e36	0.800055
$873$	1.66224e36	0.287089
$874$	−2.51295e37	−4.27849
$875$	0	0
$876$	3.81851e35	0.0631819
$877$	−3.92546e36	−0.640318	−0.320159	−	0.947364i	$-0.603736\pi$
$877$	−3.92546e36	−0.640318	−0.320159	+	0.947364i	$0.603736\pi$
$878$	1.92112e37	3.08939
$879$	4.04228e36	0.640863
$880$	−9.05656e36	−1.41557
$881$	4.99107e36	0.769121	0.384560	−	0.923100i	$-0.374353\pi$
$881$	4.99107e36	0.769121	0.384560	+	0.923100i	$0.374353\pi$
$882$	0	0
$883$	1.17497e37	1.76002	0.880009	−	0.474957i	$-0.157536\pi$
$883$	1.17497e37	1.76002	0.880009	+	0.474957i	$0.157536\pi$
$884$	1.64886e37	2.43517
$885$	7.37129e36	1.07338
$886$	−7.47788e36	−1.07364
$887$	−8.76461e36	−1.24076	−0.620380	−	0.784302i	$-0.713021\pi$
$887$	−8.76461e36	−1.24076	−0.620380	+	0.784302i	$0.713021\pi$
$888$	1.66907e37	2.32976
$889$	0	0
$890$	−1.93855e36	−0.263088
$891$	−2.83720e36	−0.379680
$892$	−9.47137e36	−1.24983
$893$	−1.03689e37	−1.34924
$894$	1.26097e37	1.61803
$895$	5.46777e36	0.691866
$896$	0	0
$897$	9.24646e36	1.13781
$898$	−3.88596e36	−0.471568
$899$	9.42464e36	1.12789
$900$	3.58914e36	0.423602
$901$	−1.10816e37	−1.28986
$902$	−8.79369e36	−1.00946
$903$	0	0
$904$	2.14430e37	2.39431
$905$	4.73315e36	0.521247
$906$	−5.13401e36	−0.557641
$907$	4.08979e36	0.438137	0.219068	−	0.975709i	$-0.429698\pi$
$907$	4.08979e36	0.438137	0.219068	+	0.975709i	$0.429698\pi$
$908$	9.38881e36	0.992059
$909$	1.56566e36	0.163174
$910$	0	0
$911$	8.43541e35	0.0855315	0.0427658	−	0.999085i	$-0.486383\pi$
$911$	8.43541e35	0.0855315	0.0427658	+	0.999085i	$0.486383\pi$
$912$	3.46973e37	3.47025
$913$	7.33619e36	0.723745
$914$	1.23955e37	1.20625
$915$	5.11589e36	0.491086
$916$	2.71896e37	2.57460
$917$	0	0
$918$	−2.36935e37	−2.18321
$919$	1.11927e37	1.01739	0.508697	−	0.860945i	$-0.330127\pi$
$919$	1.11927e37	1.01739	0.508697	+	0.860945i	$0.330127\pi$
$920$	−3.54640e37	−3.18009
$921$	−3.56623e36	−0.315474
$922$	6.31369e36	0.550994
$923$	−7.76348e36	−0.668398
$924$	0	0
$925$	−5.86614e36	−0.491565
$926$	6.95009e36	0.574583
$927$	1.05762e36	0.0862650
$928$	−5.76078e37	−4.63587
$929$	9.22117e36	0.732132	0.366066	−	0.930589i	$-0.380704\pi$
$929$	9.22117e36	0.732132	0.366066	+	0.930589i	$0.380704\pi$
$930$	−8.66570e36	−0.678839
$931$	0	0
$932$	−8.27741e36	−0.631241
$933$	−1.70704e36	−0.128447
$934$	−8.69443e36	−0.645513
$935$	−7.09772e36	−0.519965
$936$	1.20830e37	0.873430
$937$	1.76530e37	1.25914	0.629569	−	0.776944i	$-0.283231\pi$
$937$	1.76530e37	1.25914	0.629569	+	0.776944i	$0.283231\pi$
$938$	0	0
$939$	−7.25648e36	−0.503971
$940$	−2.41488e37	−1.65500
$941$	−1.37456e36	−0.0929597	−0.0464798	−	0.998919i	$-0.514800\pi$
$941$	−1.37456e36	−0.0929597	−0.0464798	+	0.998919i	$0.514800\pi$
$942$	1.25522e37	0.837694
$943$	−1.83719e37	−1.20992
$944$	8.29620e37	5.39175
$945$	0	0
$946$	1.36993e36	0.0867080
$947$	2.62512e36	0.163974	0.0819870	−	0.996633i	$-0.473873\pi$
$947$	2.62512e36	0.163974	0.0819870	+	0.996633i	$0.473873\pi$
$948$	1.55684e37	0.959709
$949$	−4.51813e35	−0.0274872
$950$	−2.28568e37	−1.37237
$951$	−2.62982e36	−0.155836
$952$	0	0
$953$	9.56090e36	0.551871	0.275935	−	0.961176i	$-0.411012\pi$
$953$	9.56090e36	0.551871	0.275935	+	0.961176i	$0.411012\pi$
$954$	−1.34014e37	−0.763478
$955$	−1.27840e37	−0.718825
$956$	3.17105e37	1.75986
$957$	−1.84877e37	−1.01271
$958$	−5.65770e37	−3.05894
$959$	0	0
$960$	2.11269e37	1.11287
$961$	−1.17302e37	−0.609907
$962$	−3.25909e37	−1.67266
$963$	1.12789e36	0.0571396
$964$	−7.86963e37	−3.93542
$965$	1.72287e37	0.850472
$966$	0	0
$967$	2.94127e37	1.41483	0.707415	−	0.706799i	$-0.249861\pi$
$967$	2.94127e37	1.41483	0.707415	+	0.706799i	$0.249861\pi$
$968$	3.20839e37	1.52351
$969$	2.71927e37	1.27469
$970$	−2.46536e37	−1.14087
$971$	3.38671e37	1.54717	0.773585	−	0.633693i	$-0.218462\pi$
$971$	3.38671e37	1.54717	0.773585	+	0.633693i	$0.218462\pi$
$972$	−3.59448e37	−1.62109
$973$	0	0
$974$	1.40538e37	0.617743
$975$	8.41021e36	0.364963
$976$	5.75781e37	2.46680
$977$	−8.62180e36	−0.364683	−0.182342	−	0.983235i	$-0.558368\pi$
$977$	−8.62180e36	−0.364683	−0.182342	+	0.983235i	$0.558368\pi$
$978$	2.18316e37	0.911697
$979$	−3.29231e36	−0.135743
$980$	0	0
$981$	2.30909e36	0.0928064
$982$	−7.42820e37	−2.94774
$983$	2.65217e37	1.03916	0.519579	−	0.854422i	$-0.326089\pi$
$983$	2.65217e37	1.03916	0.519579	+	0.854422i	$0.326089\pi$
$984$	4.75453e37	1.83937
$985$	−1.09148e37	−0.416928
$986$	−9.60173e37	−3.62150
$987$	0	0
$988$	−9.10926e37	−3.34982
$989$	2.86208e36	0.103927
$990$	−8.58360e36	−0.307772
$991$	1.11124e37	0.393448	0.196724	−	0.980459i	$-0.436970\pi$
$991$	1.11124e37	0.393448	0.196724	+	0.980459i	$0.436970\pi$
$992$	−4.58593e37	−1.60336
$993$	2.97135e37	1.02586
$994$	0	0
$995$	2.38072e37	0.801531
$996$	−6.54582e37	−2.17632
$997$	4.21223e37	1.38300	0.691500	−	0.722376i	$-0.256950\pi$
$997$	4.21223e37	1.38300	0.691500	+	0.722376i	$0.256950\pi$
$998$	1.75778e37	0.569944
$999$	3.35943e37	1.07571

Twists

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

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

\(f(q)\)	\(=\)	\(q-10895.4 q^{2} -750334. q^{3} +8.51545e7 q^{4} -3.86992e8 q^{5} +8.17517e9 q^{6} -5.62202e11 q^{8} -2.84287e11 q^{9} +O(q^{10})\)	\(q-10895.4 q^{2} -750334. q^{3} +8.51545e7 q^{4} -3.86992e8 q^{5} +8.17517e9 q^{6} -5.62202e11 q^{8} -2.84287e11 q^{9} +4.21642e12 q^{10} +7.16092e12 q^{11} -6.38944e13 q^{12} +7.56009e13 q^{13} +2.90373e14 q^{15} +3.26808e15 q^{16} +2.56123e15 q^{17} +3.09741e15 q^{18} -1.41497e16 q^{19} -3.29541e16 q^{20} -7.80208e16 q^{22} -1.63002e17 q^{23} +4.21839e17 q^{24} -1.48260e17 q^{25} -8.23700e17 q^{26} +8.49060e17 q^{27} +3.44080e18 q^{29} -3.16372e18 q^{30} +2.73908e18 q^{31} -1.67426e19 q^{32} -5.37308e18 q^{33} -2.79055e19 q^{34} -2.42083e19 q^{36} +3.95665e19 q^{37} +1.54167e20 q^{38} -5.67260e19 q^{39} +2.17568e20 q^{40} +1.12710e20 q^{41} -1.75585e19 q^{43} +6.09784e20 q^{44} +1.10017e20 q^{45} +1.77597e21 q^{46} +7.32800e20 q^{47} -2.45215e21 q^{48} +1.61535e21 q^{50} -1.92178e21 q^{51} +6.43776e21 q^{52} -4.32666e21 q^{53} -9.25082e21 q^{54} -2.77122e21 q^{55} +1.06170e22 q^{57} -3.74888e22 q^{58} +2.53856e22 q^{59} +2.47266e22 q^{60} +1.76183e22 q^{61} -2.98433e22 q^{62} +7.27577e22 q^{64} -2.92570e22 q^{65} +5.85417e22 q^{66} +8.36822e22 q^{67} +2.18100e23 q^{68} +1.22306e23 q^{69} -1.02690e23 q^{71} +1.59827e23 q^{72} -5.97629e21 q^{73} -4.31091e23 q^{74} +1.11245e23 q^{75} -1.20491e24 q^{76} +6.18050e23 q^{78} -2.43658e23 q^{79} -1.26472e24 q^{80} -3.96206e23 q^{81} -1.22801e24 q^{82} +1.02448e24 q^{83} -9.91175e23 q^{85} +1.91307e23 q^{86} -2.58175e24 q^{87} -4.02588e24 q^{88} -4.59761e23 q^{89} -1.19867e24 q^{90} -1.38804e25 q^{92} -2.05523e24 q^{93} -7.98412e24 q^{94} +5.47584e24 q^{95} +1.25625e25 q^{96} -5.84706e24 q^{97} -2.03576e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4230 q^{2} + 72104 q^{3} + 86658324 q^{4} - 110161332 q^{5} + 564962452 q^{6} - 381894066504 q^{8} + 1267694965630 q^{9}+O(q^{10}) \) 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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