LMFDB - Embedded newform 49.24.a.f.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,24,Mod(1,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.1"); S:= CuspForms(chi, 24); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 24, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	49.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,-966,-177148] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$164.249978299$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 7 x^{13} - 21591353 x^{12} - 1736098763 x^{11} + 177925612890704 x^{10} + \cdots - 50\!\cdots\!18 $ x^14 - 7x^13 - 21591353x^12 - 1736098763x^11 + 177925612890704x^10 + 22440638605479136x^9 - 708837141279167425756x^8 - 93001068632447634048566x^7 + 1424565171490650325343339825x^6 + 138068341594650942193443298553x^5 - 1378620080712404619433990278685577x^4 - 54896928867175489851543883496924335x^3 + 543960992554124581410981342517061510574x^2 - 22214950574912968179617333346997657789218*x - 50990028542728296688623812565804153999177618
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{49}\cdot 3^{13}\cdot 5^{3}\cdot 7^{23} $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-319.185$ 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)

$f(q)$	$=$	\(q-708.370 q^{2} +198278. q^{3} -7.88682e6 q^{4} +3.63664e7 q^{5} -1.40454e8 q^{6} +1.15290e10 q^{8} -5.48291e10 q^{9} -2.57609e10 q^{10} -2.09183e11 q^{11} -1.56378e12 q^{12} -1.80194e12 q^{13} +7.21066e12 q^{15} +5.79926e13 q^{16} +6.17559e13 q^{17} +3.88393e13 q^{18} +3.57454e14 q^{19} -2.86816e14 q^{20} +1.48179e14 q^{22} +2.91652e14 q^{23} +2.28595e15 q^{24} -1.05984e16 q^{25} +1.27644e15 q^{26} -2.95379e16 q^{27} +6.50216e16 q^{29} -5.10781e15 q^{30} +1.04056e17 q^{31} -1.37793e17 q^{32} -4.14764e16 q^{33} -4.37460e16 q^{34} +4.32427e17 q^{36} -4.18945e17 q^{37} -2.53210e17 q^{38} -3.57286e17 q^{39} +4.19269e17 q^{40} +6.10198e18 q^{41} -6.48576e18 q^{43} +1.64979e18 q^{44} -1.99394e18 q^{45} -2.06597e17 q^{46} +7.19477e18 q^{47} +1.14987e19 q^{48} +7.50759e18 q^{50} +1.22448e19 q^{51} +1.42116e19 q^{52} -1.00880e20 q^{53} +2.09237e19 q^{54} -7.60725e18 q^{55} +7.08752e19 q^{57} -4.60594e19 q^{58} +3.01840e20 q^{59} -5.68692e19 q^{60} +4.76484e19 q^{61} -7.37098e19 q^{62} -3.88869e20 q^{64} -6.55303e19 q^{65} +2.93806e19 q^{66} +8.72370e20 q^{67} -4.87058e20 q^{68} +5.78280e19 q^{69} -3.00535e21 q^{71} -6.32126e20 q^{72} -4.53197e20 q^{73} +2.96768e20 q^{74} -2.10143e21 q^{75} -2.81918e21 q^{76} +2.53090e20 q^{78} -6.15165e21 q^{79} +2.10899e21 q^{80} -6.94924e20 q^{81} -4.32246e21 q^{82} -6.71780e21 q^{83} +2.24584e21 q^{85} +4.59432e21 q^{86} +1.28923e22 q^{87} -2.41168e21 q^{88} +3.62771e22 q^{89} +1.41245e21 q^{90} -2.30020e21 q^{92} +2.06319e22 q^{93} -5.09656e21 q^{94} +1.29993e22 q^{95} -2.73212e22 q^{96} +1.11533e23 q^{97} +1.14693e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 966 q^{2} - 177148 q^{3} + 55357148 q^{4} - 74771022 q^{5} - 1504608254 q^{6} + 25222400616 q^{8} + 336909608980 q^{9} - 334296297894 q^{10} - 1355476566108 q^{11} - 4984668058916 q^{12} + 427040218556 q^{13}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) $ 14 * q - 966 * q^2 - 177148 * q^3 + 55357148 * q^4 - 74771022 * q^5 - 1504608254 * q^6 + 25222400616 * q^8 + 336909608980 * q^9 - 334296297894 * q^10 - 1355476566108 * q^11 - 4984668058916 * q^12 + 427040218556 * q^13 + 38670810653944 * q^15 + 160538324156336 * q^16 - 130193896130514 * q^17 - 110632655983108 * q^18 - 214771980430396 * q^19 + 48219439281468 * q^20 + 7534772282877126 * q^22 - 6685548913560552 * q^23 - 31330599354826008 * q^24 + 9156874000789424 * q^25 - 48260478025970868 * q^26 - 8477622198540028 * q^27 - 115398975455444604 * q^29 - 4149727265170942 * q^30 + 94821366637509632 * q^31 + 989053585410677472 * q^32 + 471925265098792298 * q^33 - 204665719203916350 * q^34 + 161548642910645480 * q^36 - 228196281955951106 * q^37 + 846979764807573006 * q^38 + 4289472930557071768 * q^39 - 10645750240235319192 * q^40 - 12663069502432601532 * q^41 - 427239519112420616 * q^43 - 11572396920387558444 * q^44 - 9362992784223924004 * q^45 + 33418566325741763586 * q^46 - 61615364375433533424 * q^47 - 158511629928130898960 * q^48 - 93272670392614362552 * q^50 - 84287583500847206172 * q^51 - 90603352071153943672 * q^52 + 282093764343878671758 * q^53 + 13895299932605385046 * q^54 - 237446342744567832720 * q^55 - 425457361374285462782 * q^57 - 339998979132364080060 * q^58 - 283820607003252730116 * q^59 + 701673169918628967164 * q^60 - 870322613357668504870 * q^61 - 282243301452069984966 * q^62 + 2124141067160402139584 * q^64 - 384582138286683330588 * q^65 - 157008004213679191250 * q^66 - 1414046473258733295716 * q^67 + 435228382363177447884 * q^68 + 2663127352907733668682 * q^69 + 213218335956247656048 * q^71 + 10118884230376615693104 * q^72 + 5942494661268692359862 * q^73 - 13389833203328450370642 * q^74 + 14120811240771906960232 * q^75 + 22920526497794398939844 * q^76 + 7201287217205176160828 * q^78 + 3444345943288433723680 * q^79 - 8255607259451726029008 * q^80 - 2565358457232096585122 * q^81 + 34656759475287179918772 * q^82 - 6085375799043077804904 * q^83 - 7680353239558358537262 * q^85 - 743687862046869712056 * q^86 - 7978312766181293835640 * q^87 + 2867657955669848060664 * q^88 - 68609868120257601678426 * q^89 - 17331740036513596551428 * q^90 - 7750847835981686889348 * q^92 - 50628291689744906093838 * q^93 + 18415808745499513811142 * q^94 + 113148862333982926479168 * q^95 - 150237583048546245409696 * q^96 - 230188776588461622952972 * q^97 - 234139240054754764282784 * q^99

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 $

$2$	−708.370	−0.244577	−0.122288	−	0.992495i	$-0.539023\pi$
$2$	−708.370	−0.244577	−0.122288	+	0.992495i	$0.539023\pi$
$3$	198278.	0.646219	0.323109	−	0.946362i	$-0.395272\pi$
$3$	198278.	0.646219	0.323109	+	0.946362i	$0.395272\pi$
$4$	−7.88682e6	−0.940182
$5$	3.63664e7	0.333078	0.166539	−	0.986035i	$-0.446741\pi$
$5$	3.63664e7	0.333078	0.166539	+	0.986035i	$0.446741\pi$
$6$	−1.40454e8	−0.158050
$7$	0	0
$7$	0	0
$8$	1.15290e10	0.474523
$9$	−5.48291e10	−0.582401
$10$	−2.57609e10	−0.0814631
$11$	−2.09183e11	−0.221060	−0.110530	−	0.993873i	$-0.535255\pi$
$11$	−2.09183e11	−0.221060	−0.110530	+	0.993873i	$0.535255\pi$
$12$	−1.56378e12	−0.607564
$13$	−1.80194e12	−0.278864	−0.139432	−	0.990232i	$-0.544528\pi$
$13$	−1.80194e12	−0.278864	−0.139432	+	0.990232i	$0.544528\pi$
$14$	0	0
$15$	7.21066e12	0.215241
$16$	5.79926e13	0.824125
$17$	6.17559e13	0.437035	0.218517	−	0.975833i	$-0.429878\pi$
$17$	6.17559e13	0.437035	0.218517	+	0.975833i	$0.429878\pi$
$18$	3.88393e13	0.142442
$19$	3.57454e14	0.703969	0.351985	−	0.936006i	$-0.385507\pi$
$19$	3.57454e14	0.703969	0.351985	+	0.936006i	$0.385507\pi$
$20$	−2.86816e14	−0.313154
$21$	0	0
$22$	1.48179e14	0.0540662
$23$	2.91652e14	0.0638255	0.0319127	−	0.999491i	$-0.489840\pi$
$23$	2.91652e14	0.0638255	0.0319127	+	0.999491i	$0.489840\pi$
$24$	2.28595e15	0.306646
$25$	−1.05984e16	−0.889059
$26$	1.27644e15	0.0682037
$27$	−2.95379e16	−1.02258
$28$	0	0
$29$	6.50216e16	0.989648	0.494824	−	0.868993i	$-0.335232\pi$
$29$	6.50216e16	0.989648	0.494824	+	0.868993i	$0.335232\pi$
$30$	−5.10781e15	−0.0526430
$31$	1.04056e17	0.735540	0.367770	−	0.929917i	$-0.380121\pi$
$31$	1.04056e17	0.735540	0.367770	+	0.929917i	$0.380121\pi$
$32$	−1.37793e17	−0.676085
$33$	−4.14764e16	−0.142853
$34$	−4.37460e16	−0.106888
$35$	0	0
$36$	4.32427e17	0.547563
$37$	−4.18945e17	−0.387112	−0.193556	−	0.981089i	$-0.562002\pi$
$37$	−4.18945e17	−0.387112	−0.193556	+	0.981089i	$0.562002\pi$
$38$	−2.53210e17	−0.172174
$39$	−3.57286e17	−0.180207
$40$	4.19269e17	0.158053
$41$	6.10198e18	1.73163	0.865817	−	0.500360i	$-0.166799\pi$
$41$	6.10198e18	1.73163	0.865817	+	0.500360i	$0.166799\pi$
$42$	0	0
$43$	−6.48576e18	−1.06432	−0.532162	−	0.846642i	$-0.678620\pi$
$43$	−6.48576e18	−1.06432	−0.532162	+	0.846642i	$0.678620\pi$
$44$	1.64979e18	0.207837
$45$	−1.99394e18	−0.193985
$46$	−2.06597e17	−0.0156102
$47$	7.19477e18	0.424514	0.212257	−	0.977214i	$-0.431919\pi$
$47$	7.19477e18	0.424514	0.212257	+	0.977214i	$0.431919\pi$
$48$	1.14987e19	0.532565
$49$	0	0
$50$	7.50759e18	0.217443
$51$	1.22448e19	0.282420
$52$	1.42116e19	0.262183
$53$	−1.00880e20	−1.49497	−0.747484	−	0.664279i	$-0.768738\pi$
$53$	−1.00880e20	−1.49497	−0.747484	+	0.664279i	$0.768738\pi$
$54$	2.09237e19	0.250099
$55$	−7.60725e18	−0.0736303
$56$	0	0
$57$	7.08752e19	0.454918
$58$	−4.60594e19	−0.242045
$59$	3.01840e20	1.30310	0.651552	−	0.758604i	$-0.274118\pi$
$59$	3.01840e20	1.30310	0.651552	+	0.758604i	$0.274118\pi$
$60$	−5.68692e19	−0.202366
$61$	4.76484e19	0.140202	0.0701011	−	0.997540i	$-0.477668\pi$
$61$	4.76484e19	0.140202	0.0701011	+	0.997540i	$0.477668\pi$
$62$	−7.37098e19	−0.179896
$63$	0	0
$64$	−3.88869e20	−0.658770
$65$	−6.55303e19	−0.0928835
$66$	2.93806e19	0.0349386
$67$	8.72370e20	0.872651	0.436326	−	0.899789i	$-0.356280\pi$
$67$	8.72370e20	0.872651	0.436326	+	0.899789i	$0.356280\pi$
$68$	−4.87058e20	−0.410892
$69$	5.78280e19	0.0412452
$70$	0	0
$71$	−3.00535e21	−1.54321	−0.771603	−	0.636105i	$-0.780545\pi$
$71$	−3.00535e21	−1.54321	−0.771603	+	0.636105i	$0.780545\pi$
$72$	−6.32126e20	−0.276363
$73$	−4.53197e20	−0.169073	−0.0845364	−	0.996420i	$-0.526941\pi$
$73$	−4.53197e20	−0.169073	−0.0845364	+	0.996420i	$0.526941\pi$
$74$	2.96768e20	0.0946786
$75$	−2.10143e21	−0.574527
$76$	−2.81918e21	−0.661859
$77$	0	0
$78$	2.53090e20	0.0440745
$79$	−6.15165e21	−0.925295	−0.462647	−	0.886542i	$-0.653100\pi$
$79$	−6.15165e21	−0.925295	−0.462647	+	0.886542i	$0.653100\pi$
$80$	2.10899e21	0.274498
$81$	−6.94924e20	−0.0784078
$82$	−4.32246e21	−0.423517
$83$	−6.71780e21	−0.572571	−0.286285	−	0.958144i	$-0.592421\pi$
$83$	−6.71780e21	−0.572571	−0.286285	+	0.958144i	$0.592421\pi$
$84$	0	0
$85$	2.24584e21	0.145567
$86$	4.59432e21	0.260309
$87$	1.28923e22	0.639530
$88$	−2.41168e21	−0.104898
$89$	3.62771e22	1.38563	0.692815	−	0.721115i	$-0.256370\pi$
$89$	3.62771e22	1.38563	0.692815	+	0.721115i	$0.256370\pi$
$90$	1.41245e21	0.0474442
$91$	0	0
$92$	−2.30020e21	−0.0600076
$93$	2.06319e22	0.475320
$94$	−5.09656e21	−0.103826
$95$	1.29993e22	0.234477
$96$	−2.73212e22	−0.436899
$97$	1.11533e23	1.58317	0.791584	−	0.611061i	$-0.209257\pi$
$97$	1.11533e23	1.58317	0.791584	+	0.611061i	$0.209257\pi$
$98$	0	0
$99$	1.14693e22	0.128746
$100$	8.35878e22	0.835878
$101$	−1.50339e23	−1.34083	−0.670417	−	0.741984i	$-0.733885\pi$
$101$	−1.50339e23	−1.34083	−0.670417	+	0.741984i	$0.733885\pi$
$102$	−8.67386e21	−0.0690734
$103$	1.51745e23	1.08015	0.540077	−	0.841616i	$-0.318395\pi$
$103$	1.51745e23	1.08015	0.540077	+	0.841616i	$0.318395\pi$
$104$	−2.07747e22	−0.132328
$105$	0	0
$106$	7.14603e22	0.365634
$107$	6.44376e22	0.295955	0.147978	−	0.988991i	$-0.452724\pi$
$107$	6.44376e22	0.295955	0.147978	+	0.988991i	$0.452724\pi$
$108$	2.32960e23	0.961409
$109$	8.38566e22	0.311267	0.155633	−	0.987815i	$-0.450258\pi$
$109$	8.38566e22	0.311267	0.155633	+	0.987815i	$0.450258\pi$
$110$	5.38874e21	0.0180083
$111$	−8.30674e22	−0.250159
$112$	0	0
$113$	−3.30075e22	−0.0809488	−0.0404744	−	0.999181i	$-0.512887\pi$
$113$	−3.30075e22	−0.0809488	−0.0404744	+	0.999181i	$0.512887\pi$
$114$	−5.02058e22	−0.111262
$115$	1.06063e22	0.0212589
$116$	−5.12814e23	−0.930450
$117$	9.87990e22	0.162411
$118$	−2.13814e23	−0.318709
$119$	0	0
$120$	8.31318e22	0.102137
$121$	−8.51673e23	−0.951132
$122$	−3.37527e22	−0.0342902
$123$	1.20989e24	1.11901
$124$	−8.20668e23	−0.691541
$125$	−8.18948e23	−0.629204
$126$	0	0
$127$	−2.22220e24	−1.42246	−0.711231	−	0.702958i	$-0.751862\pi$
$127$	−2.22220e24	−1.42246	−0.711231	+	0.702958i	$0.751862\pi$
$128$	1.43135e24	0.837205
$129$	−1.28598e24	−0.687786
$130$	4.64197e22	0.0227171
$131$	−9.43331e23	−0.422712	−0.211356	−	0.977409i	$-0.567788\pi$
$131$	−9.43331e23	−0.422712	−0.211356	+	0.977409i	$0.567788\pi$
$132$	3.27117e23	0.134308
$133$	0	0
$134$	−6.17961e23	−0.213430
$135$	−1.07419e24	−0.340598
$136$	7.11985e23	0.207383
$137$	−8.60235e23	−0.230319	−0.115160	−	0.993347i	$-0.536738\pi$
$137$	−8.60235e23	−0.230319	−0.115160	+	0.993347i	$0.536738\pi$
$138$	−4.09636e22	−0.0100876
$139$	−8.91816e23	−0.202118	−0.101059	−	0.994880i	$-0.532223\pi$
$139$	−8.91816e23	−0.202118	−0.101059	+	0.994880i	$0.532223\pi$
$140$	0	0
$141$	1.42656e24	0.274329
$142$	2.12890e24	0.377432
$143$	3.76936e23	0.0616458
$144$	−3.17968e24	−0.479971
$145$	2.36461e24	0.329630
$146$	3.21031e23	0.0413513
$147$	0	0
$148$	3.30414e24	0.363956
$149$	4.30284e24	0.438645	0.219322	−	0.975652i	$-0.429615\pi$
$149$	4.30284e24	0.438645	0.219322	+	0.975652i	$0.429615\pi$
$150$	1.48859e24	0.140516
$151$	−1.27154e25	−1.11198	−0.555988	−	0.831191i	$-0.687660\pi$
$151$	−1.27154e25	−1.11198	−0.555988	+	0.831191i	$0.687660\pi$
$152$	4.12109e24	0.334050
$153$	−3.38602e24	−0.254529
$154$	0	0
$155$	3.78413e24	0.244992
$156$	2.81785e24	0.169428
$157$	−2.46086e25	−1.37480	−0.687401	−	0.726278i	$-0.741248\pi$
$157$	−2.46086e25	−1.37480	−0.687401	+	0.726278i	$0.741248\pi$
$158$	4.35764e24	0.226305
$159$	−2.00022e25	−0.966077
$160$	−5.01103e24	−0.225189
$161$	0	0
$162$	4.92263e23	0.0191767
$163$	2.67319e25	0.970224	0.485112	−	0.874452i	$-0.338779\pi$
$163$	2.67319e25	0.970224	0.485112	+	0.874452i	$0.338779\pi$
$164$	−4.81252e25	−1.62805
$165$	−1.50835e24	−0.0475813
$166$	4.75869e24	0.140037
$167$	−4.75377e24	−0.130557	−0.0652783	−	0.997867i	$-0.520794\pi$
$167$	−4.75377e24	−0.130557	−0.0652783	+	0.997867i	$0.520794\pi$
$168$	0	0
$169$	−3.85069e25	−0.922235
$170$	−1.59089e24	−0.0356022
$171$	−1.95989e25	−0.409992
$172$	5.11521e25	1.00066
$173$	−2.73639e25	−0.500782	−0.250391	−	0.968145i	$-0.580559\pi$
$173$	−2.73639e25	−0.500782	−0.250391	+	0.968145i	$0.580559\pi$
$174$	−9.13255e24	−0.156414
$175$	0	0
$176$	−1.21311e25	−0.182181
$177$	5.98482e25	0.842090
$178$	−2.56976e25	−0.338893
$179$	−7.55656e25	−0.934360	−0.467180	−	0.884162i	$-0.654730\pi$
$179$	−7.55656e25	−0.934360	−0.467180	+	0.884162i	$0.654730\pi$
$180$	1.57258e25	0.182381
$181$	−1.80390e26	−1.96295	−0.981475	−	0.191588i	$-0.938636\pi$
$181$	−1.80390e26	−1.96295	−0.981475	+	0.191588i	$0.938636\pi$
$182$	0	0
$183$	9.44761e24	0.0906013
$184$	3.36246e24	0.0302867
$185$	−1.52355e25	−0.128939
$186$	−1.46150e25	−0.116252
$187$	−1.29183e25	−0.0966110
$188$	−5.67439e25	−0.399120
$189$	0	0
$190$	−9.20833e24	−0.0573475
$191$	2.46966e26	1.44795	0.723974	−	0.689827i	$-0.242313\pi$
$191$	2.46966e26	1.44795	0.723974	+	0.689827i	$0.242313\pi$
$192$	−7.71042e25	−0.425710
$193$	−1.66881e26	−0.867956	−0.433978	−	0.900923i	$-0.642891\pi$
$193$	−1.66881e26	−0.867956	−0.433978	+	0.900923i	$0.642891\pi$
$194$	−7.90063e25	−0.387206
$195$	−1.29932e25	−0.0600231
$196$	0	0
$197$	−4.54524e26	−1.86722	−0.933608	−	0.358295i	$-0.883358\pi$
$197$	−4.54524e26	−1.86722	−0.933608	+	0.358295i	$0.883358\pi$
$198$	−8.12452e24	−0.0314882
$199$	−3.83977e26	−1.40441	−0.702206	−	0.711974i	$-0.747801\pi$
$199$	−3.83977e26	−1.40441	−0.702206	+	0.711974i	$0.747801\pi$
$200$	−1.22189e26	−0.421879
$201$	1.72972e26	0.563924
$202$	1.06495e26	0.327937
$203$	0	0
$204$	−9.65727e25	−0.265526
$205$	2.21907e26	0.576769
$206$	−1.07491e26	−0.264181
$207$	−1.59910e25	−0.0371720
$208$	−1.04499e26	−0.229819
$209$	−7.47734e25	−0.155620
$210$	0	0
$211$	−2.85833e26	−0.533169	−0.266584	−	0.963812i	$-0.585895\pi$
$211$	−2.85833e26	−0.533169	−0.266584	+	0.963812i	$0.585895\pi$
$212$	7.95622e26	1.40554
$213$	−5.95894e26	−0.997249
$214$	−4.56457e25	−0.0723837
$215$	−2.35864e26	−0.354503
$216$	−3.40543e26	−0.485237
$217$	0	0
$218$	−5.94015e25	−0.0761286
$219$	−8.98589e25	−0.109258
$220$	5.99970e25	0.0692259
$221$	−1.11281e26	−0.121873
$222$	5.88425e25	0.0611831
$223$	−1.85936e27	−1.83594	−0.917970	−	0.396650i	$-0.870173\pi$
$223$	−1.85936e27	−1.83594	−0.917970	+	0.396650i	$0.870173\pi$
$224$	0	0
$225$	5.81101e26	0.517789
$226$	2.33815e25	0.0197982
$227$	−2.05594e27	−1.65467	−0.827337	−	0.561707i	$-0.810145\pi$
$227$	−2.05594e27	−1.65467	−0.827337	+	0.561707i	$0.810145\pi$
$228$	−5.58980e26	−0.427706
$229$	−1.07872e26	−0.0784877	−0.0392439	−	0.999230i	$-0.512495\pi$
$229$	−1.07872e26	−0.0784877	−0.0392439	+	0.999230i	$0.512495\pi$
$230$	−7.51320e24	−0.00519942
$231$	0	0
$232$	7.49636e26	0.469611
$233$	2.32000e27	1.38323	0.691614	−	0.722267i	$-0.256900\pi$
$233$	2.32000e27	1.38323	0.691614	+	0.722267i	$0.256900\pi$
$234$	−6.99862e25	−0.0397219
$235$	2.61648e26	0.141396
$236$	−2.38056e27	−1.22516
$237$	−1.21974e27	−0.597943
$238$	0	0
$239$	−1.98782e27	−0.884709	−0.442354	−	0.896840i	$-0.645857\pi$
$239$	−1.98782e27	−0.884709	−0.442354	+	0.896840i	$0.645857\pi$
$240$	4.18165e26	0.177386
$241$	−3.46684e27	−1.40197	−0.700984	−	0.713177i	$-0.747256\pi$
$241$	−3.46684e27	−1.40197	−0.700984	+	0.713177i	$0.747256\pi$
$242$	6.03299e26	0.232625
$243$	2.64300e27	0.971909
$244$	−3.75794e26	−0.131816
$245$	0	0
$246$	−8.57047e26	−0.273685
$247$	−6.44112e26	−0.196312
$248$	1.19966e27	0.349031
$249$	−1.33199e27	−0.370006
$250$	5.80118e26	0.153889
$251$	4.95207e27	1.25470	0.627348	−	0.778739i	$-0.284140\pi$
$251$	4.95207e27	1.25470	0.627348	+	0.778739i	$0.284140\pi$
$252$	0	0
$253$	−6.10086e25	−0.0141093
$254$	1.57414e27	0.347901
$255$	4.45301e26	0.0940679
$256$	2.24815e27	0.454010
$257$	−3.34941e27	−0.646752	−0.323376	−	0.946271i	$-0.604818\pi$
$257$	−3.34941e27	−0.646752	−0.323376	+	0.946271i	$0.604818\pi$
$258$	9.10951e26	0.168217
$259$	0	0
$260$	5.16826e26	0.0873274
$261$	−3.56508e27	−0.576372
$262$	6.68227e26	0.103385
$263$	−9.85711e27	−1.45968	−0.729842	−	0.683616i	$-0.760406\pi$
$263$	−9.85711e27	−1.45968	−0.729842	+	0.683616i	$0.760406\pi$
$264$	−4.78182e26	−0.0677873
$265$	−3.66864e27	−0.497941
$266$	0	0
$267$	7.19294e27	0.895420
$268$	−6.88023e27	−0.820451
$269$	1.24725e28	1.42496	0.712481	−	0.701691i	$-0.247571\pi$
$269$	1.24725e28	1.42496	0.712481	+	0.701691i	$0.247571\pi$
$270$	7.60922e26	0.0833023
$271$	3.42236e27	0.359070	0.179535	−	0.983752i	$-0.442541\pi$
$271$	3.42236e27	0.359070	0.179535	+	0.983752i	$0.442541\pi$
$272$	3.58139e27	0.360171
$273$	0	0
$274$	6.09364e26	0.0563308
$275$	2.21701e27	0.196536
$276$	−4.56079e26	−0.0387780
$277$	−5.55393e26	−0.0452985	−0.0226492	−	0.999743i	$-0.507210\pi$
$277$	−5.55393e26	−0.0452985	−0.0226492	+	0.999743i	$0.507210\pi$
$278$	6.31736e26	0.0494334
$279$	−5.70527e27	−0.428379
$280$	0	0
$281$	−1.78549e28	−1.23491	−0.617453	−	0.786608i	$-0.711835\pi$
$281$	−1.78549e28	−1.23491	−0.617453	+	0.786608i	$0.711835\pi$
$282$	−1.01053e27	−0.0670944
$283$	1.38627e28	0.883695	0.441847	−	0.897090i	$-0.354323\pi$
$283$	1.38627e28	0.883695	0.441847	+	0.897090i	$0.354323\pi$
$284$	2.37026e28	1.45089
$285$	2.57748e27	0.151523
$286$	−2.67010e26	−0.0150771
$287$	0	0
$288$	7.55505e27	0.393753
$289$	−1.61538e28	−0.809001
$290$	−1.67501e27	−0.0806198
$291$	2.21144e28	1.02307
$292$	3.57428e27	0.158959
$293$	2.78981e28	1.19288	0.596440	−	0.802658i	$-0.296582\pi$
$293$	2.78981e28	1.19288	0.596440	+	0.802658i	$0.296582\pi$
$294$	0	0
$295$	1.09769e28	0.434035
$296$	−4.83002e27	−0.183694
$297$	6.17883e27	0.226051
$298$	−3.04800e27	−0.107282
$299$	−5.25540e26	−0.0177986
$300$	1.65736e28	0.540160
$301$	0	0
$302$	9.00720e27	0.271963
$303$	−2.98088e28	−0.866473
$304$	2.07297e28	0.580159
$305$	1.73280e27	0.0466983
$306$	2.39855e27	0.0622520
$307$	4.23229e27	0.105800	0.0528998	−	0.998600i	$-0.483154\pi$
$307$	4.23229e27	0.105800	0.0528998	+	0.998600i	$0.483154\pi$
$308$	0	0
$309$	3.00876e28	0.698016
$310$	−2.68056e27	−0.0599193
$311$	5.13859e28	1.10688	0.553438	−	0.832890i	$-0.313315\pi$
$311$	5.13859e28	1.10688	0.553438	+	0.832890i	$0.313315\pi$
$312$	−4.11915e27	−0.0855126
$313$	4.91458e28	0.983392	0.491696	−	0.870767i	$-0.336377\pi$
$313$	4.91458e28	0.983392	0.491696	+	0.870767i	$0.336377\pi$
$314$	1.74320e28	0.336244
$315$	0	0
$316$	4.85170e28	0.869946
$317$	−1.97514e27	−0.0341519	−0.0170760	−	0.999854i	$-0.505436\pi$
$317$	−1.97514e27	−0.0341519	−0.0170760	+	0.999854i	$0.505436\pi$
$318$	1.41690e28	0.236280
$319$	−1.36014e28	−0.218772
$320$	−1.41418e28	−0.219422
$321$	1.27765e28	0.191252
$322$	0	0
$323$	2.20749e28	0.307659
$324$	5.48074e27	0.0737177
$325$	1.90977e28	0.247927
$326$	−1.89361e28	−0.237294
$327$	1.66269e28	0.201146
$328$	7.03498e28	0.821701
$329$	0	0
$330$	1.06847e27	0.0116373
$331$	−1.15555e29	−1.21553	−0.607765	−	0.794117i	$-0.707934\pi$
$331$	−1.15555e29	−1.21553	−0.607765	+	0.794117i	$0.707934\pi$
$332$	5.29821e28	0.538321
$333$	2.29704e28	0.225455
$334$	3.36743e27	0.0319311
$335$	3.17250e28	0.290661
$336$	0	0
$337$	−9.67511e28	−0.827775	−0.413887	−	0.910328i	$-0.635829\pi$
$337$	−9.67511e28	−0.827775	−0.413887	+	0.910328i	$0.635829\pi$
$338$	2.72771e28	0.225557
$339$	−6.54465e27	−0.0523107
$340$	−1.77126e28	−0.136859
$341$	−2.17667e28	−0.162599
$342$	1.38833e28	0.100275
$343$	0	0
$344$	−7.47745e28	−0.505047
$345$	2.10300e27	0.0137379
$346$	1.93838e28	0.122479
$347$	1.64508e29	1.00554	0.502769	−	0.864421i	$-0.332315\pi$
$347$	1.64508e29	1.00554	0.502769	+	0.864421i	$0.332315\pi$
$348$	−1.01680e29	−0.601274
$349$	−4.86435e28	−0.278312	−0.139156	−	0.990270i	$-0.544439\pi$
$349$	−4.86435e28	−0.278312	−0.139156	+	0.990270i	$0.544439\pi$
$350$	0	0
$351$	5.32256e28	0.285160
$352$	2.88239e28	0.149456
$353$	−8.13214e28	−0.408127	−0.204064	−	0.978958i	$-0.565415\pi$
$353$	−8.13214e28	−0.408127	−0.204064	+	0.978958i	$0.565415\pi$
$354$	−4.23947e28	−0.205956
$355$	−1.09294e29	−0.514008
$356$	−2.86111e29	−1.30274
$357$	0	0
$358$	5.35284e28	0.228523
$359$	−1.84559e29	−0.763043	−0.381521	−	0.924360i	$-0.624600\pi$
$359$	−1.84559e29	−0.763043	−0.381521	+	0.924360i	$0.624600\pi$
$360$	−2.29882e28	−0.0920504
$361$	−1.30056e29	−0.504427
$362$	1.27783e29	0.480092
$363$	−1.68868e29	−0.614640
$364$	0	0
$365$	−1.64812e28	−0.0563144
$366$	−6.69240e27	−0.0221590
$367$	−1.10154e29	−0.353459	−0.176730	−	0.984259i	$-0.556552\pi$
$367$	−1.10154e29	−0.353459	−0.176730	+	0.984259i	$0.556552\pi$
$368$	1.69136e28	0.0526002
$369$	−3.34566e29	−1.00851
$370$	1.07924e28	0.0315354
$371$	0	0
$372$	−1.62720e29	−0.446887
$373$	6.84128e29	1.82174	0.910868	−	0.412698i	$-0.135413\pi$
$373$	6.84128e29	1.82174	0.910868	+	0.412698i	$0.135413\pi$
$374$	9.15093e27	0.0236288
$375$	−1.62379e29	−0.406603
$376$	8.29487e28	0.201442
$377$	−1.17165e29	−0.275978
$378$	0	0
$379$	2.90688e28	0.0644282	0.0322141	−	0.999481i	$-0.489744\pi$
$379$	2.90688e28	0.0644282	0.0322141	+	0.999481i	$0.489744\pi$
$380$	−1.02523e29	−0.220451
$381$	−4.40613e29	−0.919222
$382$	−1.74943e29	−0.354135
$383$	6.85880e29	1.34729	0.673647	−	0.739053i	$-0.264727\pi$
$383$	6.85880e29	1.34729	0.673647	+	0.739053i	$0.264727\pi$
$384$	2.83805e29	0.541018
$385$	0	0
$386$	1.18213e29	0.212282
$387$	3.55609e29	0.619864
$388$	−8.79638e29	−1.48847
$389$	8.24271e28	0.135410	0.0677048	−	0.997705i	$-0.478432\pi$
$389$	8.24271e28	0.135410	0.0677048	+	0.997705i	$0.478432\pi$
$390$	9.20399e27	0.0146802
$391$	1.80112e28	0.0278940
$392$	0	0
$393$	−1.87042e29	−0.273164
$394$	3.21971e29	0.456678
$395$	−2.23714e29	−0.308195
$396$	−9.04565e28	−0.121045
$397$	−1.05747e30	−1.37460	−0.687301	−	0.726372i	$-0.741205\pi$
$397$	−1.05747e30	−1.37460	−0.687301	+	0.726372i	$0.741205\pi$
$398$	2.71997e29	0.343486
$399$	0	0
$400$	−6.14630e29	−0.732696
$401$	1.13386e30	1.31341	0.656705	−	0.754148i	$-0.271950\pi$
$401$	1.13386e30	1.31341	0.656705	+	0.754148i	$0.271950\pi$
$402$	−1.22528e29	−0.137923
$403$	−1.87502e29	−0.205116
$404$	1.18569e30	1.26063
$405$	−2.52719e28	−0.0261159
$406$	0	0
$407$	8.76362e28	0.0855752
$408$	1.41171e29	0.134015
$409$	−3.31413e29	−0.305880	−0.152940	−	0.988235i	$-0.548874\pi$
$409$	−3.31413e29	−0.305880	−0.152940	+	0.988235i	$0.548874\pi$
$410$	−1.57192e29	−0.141064
$411$	−1.70566e29	−0.148837
$412$	−1.19678e30	−1.01554
$413$	0	0
$414$	1.13275e28	0.00909141
$415$	−2.44303e29	−0.190711
$416$	2.48295e29	0.188536
$417$	−1.76827e29	−0.130613
$418$	5.29672e28	0.0380609
$419$	−2.21807e30	−1.55065	−0.775326	−	0.631561i	$-0.782415\pi$
$419$	−2.21807e30	−1.55065	−0.775326	+	0.631561i	$0.782415\pi$
$420$	0	0
$421$	−8.95652e29	−0.592782	−0.296391	−	0.955067i	$-0.595783\pi$
$421$	−8.95652e29	−0.592782	−0.296391	+	0.955067i	$0.595783\pi$
$422$	2.02476e29	0.130401
$423$	−3.94483e29	−0.247237
$424$	−1.16305e30	−0.709397
$425$	−6.54514e29	−0.388550
$426$	4.22113e29	0.243904
$427$	0	0
$428$	−5.08208e29	−0.278252
$429$	7.47381e28	0.0398367
$430$	1.67079e29	0.0867031
$431$	1.55948e30	0.787935	0.393967	−	0.919124i	$-0.371102\pi$
$431$	1.55948e30	0.787935	0.393967	+	0.919124i	$0.371102\pi$
$432$	−1.71298e30	−0.842732
$433$	−4.19947e29	−0.201180	−0.100590	−	0.994928i	$-0.532073\pi$
$433$	−4.19947e29	−0.201180	−0.100590	+	0.994928i	$0.532073\pi$
$434$	0	0
$435$	4.68849e29	0.213013
$436$	−6.61362e29	−0.292647
$437$	1.04252e29	0.0449312
$438$	6.36533e28	0.0267220
$439$	−4.20126e29	−0.171806	−0.0859028	−	0.996304i	$-0.527377\pi$
$439$	−4.20126e29	−0.171806	−0.0859028	+	0.996304i	$0.527377\pi$
$440$	−8.77041e28	−0.0349393
$441$	0	0
$442$	7.88279e28	0.0298074
$443$	−2.14366e30	−0.789791	−0.394896	−	0.918726i	$-0.629219\pi$
$443$	−2.14366e30	−0.789791	−0.394896	+	0.918726i	$0.629219\pi$
$444$	6.55138e29	0.235195
$445$	1.31927e30	0.461523
$446$	1.31712e30	0.449028
$447$	8.53157e29	0.283460
$448$	0	0
$449$	−3.14728e30	−0.993349	−0.496675	−	0.867937i	$-0.665446\pi$
$449$	−3.14728e30	−0.993349	−0.496675	+	0.867937i	$0.665446\pi$
$450$	−4.11635e29	−0.126639
$451$	−1.27643e30	−0.382796
$452$	2.60324e29	0.0761066
$453$	−2.52118e30	−0.718579
$454$	1.45636e30	0.404694
$455$	0	0
$456$	8.17121e29	0.215869
$457$	−1.21197e30	−0.312216	−0.156108	−	0.987740i	$-0.549895\pi$
$457$	−1.21197e30	−0.312216	−0.156108	+	0.987740i	$0.549895\pi$
$458$	7.64134e28	0.0191963
$459$	−1.82414e30	−0.446902
$460$	−8.36502e28	−0.0199872
$461$	6.86525e30	1.59991	0.799955	−	0.600060i	$-0.204857\pi$
$461$	6.86525e30	1.59991	0.799955	+	0.600060i	$0.204857\pi$
$462$	0	0
$463$	6.95804e30	1.54279	0.771393	−	0.636360i	$-0.219561\pi$
$463$	6.95804e30	1.54279	0.771393	+	0.636360i	$0.219561\pi$
$464$	3.77078e30	0.815594
$465$	7.50309e29	0.158318
$466$	−1.64341e30	−0.338306
$467$	7.30229e30	1.46661	0.733306	−	0.679899i	$-0.237976\pi$
$467$	7.30229e30	1.46661	0.733306	+	0.679899i	$0.237976\pi$
$468$	−7.79210e29	−0.152696
$469$	0	0
$470$	−1.85344e29	−0.0345822
$471$	−4.87933e30	−0.888423
$472$	3.47992e30	0.618353
$473$	1.35671e30	0.235280
$474$	8.64024e29	0.146243
$475$	−3.78844e30	−0.625870
$476$	0	0
$477$	5.53115e30	0.870671
$478$	1.40811e30	0.216379
$479$	1.02559e31	1.53857	0.769285	−	0.638906i	$-0.220613\pi$
$479$	1.02559e31	1.53857	0.769285	+	0.638906i	$0.220613\pi$
$480$	−9.93576e29	−0.145521
$481$	7.54915e29	0.107952
$482$	2.45581e30	0.342889
$483$	0	0
$484$	6.71699e30	0.894238
$485$	4.05604e30	0.527318
$486$	−1.87222e30	−0.237706
$487$	4.95394e30	0.614282	0.307141	−	0.951664i	$-0.400628\pi$
$487$	4.95394e30	0.614282	0.307141	+	0.951664i	$0.400628\pi$
$488$	5.49339e29	0.0665292
$489$	5.30034e30	0.626977
$490$	0	0
$491$	−1.15464e29	−0.0130320	−0.00651600	−	0.999979i	$-0.502074\pi$
$491$	−1.15464e29	−0.0130320	−0.00651600	+	0.999979i	$0.502074\pi$
$492$	−9.54216e30	−1.05208
$493$	4.01547e30	0.432511
$494$	4.56270e29	0.0480133
$495$	4.17098e29	0.0428824
$496$	6.03446e30	0.606176
$497$	0	0
$498$	9.43542e29	0.0904949
$499$	−1.24141e31	−1.16348	−0.581739	−	0.813376i	$-0.697627\pi$
$499$	−1.24141e31	−1.16348	−0.581739	+	0.813376i	$0.697627\pi$
$500$	6.45890e30	0.591566
$501$	−9.42567e29	−0.0843682
$502$	−3.50789e30	−0.306870
$503$	1.74721e30	0.149387	0.0746935	−	0.997207i	$-0.476202\pi$
$503$	1.74721e30	0.149387	0.0746935	+	0.997207i	$0.476202\pi$
$504$	0	0
$505$	−5.46729e30	−0.446602
$506$	4.32166e28	0.00345080
$507$	−7.63506e30	−0.595966
$508$	1.75261e31	1.33737
$509$	−1.14068e31	−0.850958	−0.425479	−	0.904968i	$-0.639894\pi$
$509$	−1.14068e31	−0.850958	−0.425479	+	0.904968i	$0.639894\pi$
$510$	−3.15438e29	−0.0230068
$511$	0	0
$512$	−1.35996e31	−0.948245
$513$	−1.05584e31	−0.719863
$514$	2.37262e30	0.158181
$515$	5.51842e30	0.359775
$516$	1.01423e31	0.646645
$517$	−1.50503e30	−0.0938432
$518$	0	0
$519$	−5.42566e30	−0.323614
$520$	−7.55500e29	−0.0440754
$521$	2.55131e31	1.45589	0.727945	−	0.685635i	$-0.240475\pi$
$521$	2.55131e31	1.45589	0.727945	+	0.685635i	$0.240475\pi$
$522$	2.52539e30	0.140967
$523$	1.04286e31	0.569450	0.284725	−	0.958609i	$-0.408098\pi$
$523$	1.04286e31	0.569450	0.284725	+	0.958609i	$0.408098\pi$
$524$	7.43989e30	0.397426
$525$	0	0
$526$	6.98248e30	0.357005
$527$	6.42605e30	0.321456
$528$	−2.40532e30	−0.117729
$529$	−2.07954e31	−0.995926
$530$	2.59875e30	0.121785
$531$	−1.65496e31	−0.758929
$532$	0	0
$533$	−1.09954e31	−0.482891
$534$	−5.09526e30	−0.218999
$535$	2.34337e30	0.0985761
$536$	1.00576e31	0.414093
$537$	−1.49830e31	−0.603801
$538$	−8.83516e30	−0.348513
$539$	0	0
$540$	8.47193e30	0.320224
$541$	1.02505e31	0.379294	0.189647	−	0.981852i	$-0.439266\pi$
$541$	1.02505e31	0.379294	0.189647	+	0.981852i	$0.439266\pi$
$542$	−2.42430e30	−0.0878202
$543$	−3.57674e31	−1.26850
$544$	−8.50951e30	−0.295473
$545$	3.04957e30	0.103676
$546$	0	0
$547$	2.63292e31	0.858190	0.429095	−	0.903259i	$-0.358833\pi$
$547$	2.63292e31	0.858190	0.429095	+	0.903259i	$0.358833\pi$
$548$	6.78452e30	0.216542
$549$	−2.61252e30	−0.0816539
$550$	−1.57046e30	−0.0480681
$551$	2.32422e31	0.696682
$552$	6.66701e29	0.0195718
$553$	0	0
$554$	3.93424e29	0.0110789
$555$	−3.02087e30	−0.0833225
$556$	7.03359e30	0.190028
$557$	1.21194e31	0.320736	0.160368	−	0.987057i	$-0.448732\pi$
$557$	1.21194e31	0.320736	0.160368	+	0.987057i	$0.448732\pi$
$558$	4.04144e30	0.104772
$559$	1.16870e31	0.296802
$560$	0	0
$561$	−2.56141e30	−0.0624319
$562$	1.26478e31	0.302029
$563$	−7.32890e31	−1.71472	−0.857358	−	0.514720i	$-0.827896\pi$
$563$	−7.32890e31	−1.71472	−0.857358	+	0.514720i	$0.827896\pi$
$564$	−1.12511e31	−0.257919
$565$	−1.20037e30	−0.0269623
$566$	−9.81988e30	−0.216131
$567$	0	0
$568$	−3.46487e31	−0.732287
$569$	7.34607e31	1.52147	0.760736	−	0.649061i	$-0.224838\pi$
$569$	7.34607e31	1.52147	0.760736	+	0.649061i	$0.224838\pi$
$570$	−1.82581e30	−0.0370590
$571$	1.01603e31	0.202111	0.101056	−	0.994881i	$-0.467778\pi$
$571$	1.01603e31	0.202111	0.101056	+	0.994881i	$0.467778\pi$
$572$	−2.97283e30	−0.0579583
$573$	4.89679e31	0.935692
$574$	0	0
$575$	−3.09104e30	−0.0567446
$576$	2.13214e31	0.383669
$577$	−8.13548e31	−1.43503	−0.717516	−	0.696542i	$-0.754721\pi$
$577$	−8.13548e31	−1.43503	−0.717516	+	0.696542i	$0.754721\pi$
$578$	1.14428e31	0.197863
$579$	−3.30888e31	−0.560890
$580$	−1.86492e31	−0.309912
$581$	0	0
$582$	−1.56652e31	−0.250220
$583$	2.11024e31	0.330478
$584$	−5.22491e30	−0.0802290
$585$	3.59297e30	0.0540954
$586$	−1.97621e31	−0.291750
$587$	−1.28648e32	−1.86237	−0.931185	−	0.364546i	$-0.881224\pi$
$587$	−1.28648e32	−1.86237	−0.931185	+	0.364546i	$0.881224\pi$
$588$	0	0
$589$	3.71951e31	0.517797
$590$	−7.77567e30	−0.106155
$591$	−9.01219e31	−1.20663
$592$	−2.42957e31	−0.319029
$593$	1.39385e31	0.179509	0.0897544	−	0.995964i	$-0.471392\pi$
$593$	1.39385e31	0.179509	0.0897544	+	0.995964i	$0.471392\pi$
$594$	−4.37690e30	−0.0552869
$595$	0	0
$596$	−3.39357e31	−0.412406
$597$	−7.61340e31	−0.907557
$598$	3.72277e29	0.00435313
$599$	−1.06230e32	−1.21854	−0.609270	−	0.792963i	$-0.708537\pi$
$599$	−1.06230e32	−1.21854	−0.609270	+	0.792963i	$0.708537\pi$
$600$	−2.42274e31	−0.272626
$601$	−8.53543e31	−0.942256	−0.471128	−	0.882065i	$-0.656153\pi$
$601$	−8.53543e31	−0.942256	−0.471128	+	0.882065i	$0.656153\pi$
$602$	0	0
$603$	−4.78313e31	−0.508233
$604$	1.00284e32	1.04546
$605$	−3.09723e31	−0.316801
$606$	2.11157e31	0.211919
$607$	−7.59194e31	−0.747623	−0.373812	−	0.927505i	$-0.621949\pi$
$607$	−7.59194e31	−0.747623	−0.373812	+	0.927505i	$0.621949\pi$
$608$	−4.92545e31	−0.475943
$609$	0	0
$610$	−1.22746e30	−0.0114213
$611$	−1.29646e31	−0.118382
$612$	2.67049e31	0.239304
$613$	6.55349e31	0.576338	0.288169	−	0.957580i	$-0.406953\pi$
$613$	6.55349e31	0.576338	0.288169	+	0.957580i	$0.406953\pi$
$614$	−2.99802e30	−0.0258761
$615$	4.39993e31	0.372719
$616$	0	0
$617$	7.78028e31	0.634915	0.317458	−	0.948272i	$-0.397171\pi$
$617$	7.78028e31	0.634915	0.317458	+	0.948272i	$0.397171\pi$
$618$	−2.13132e31	−0.170718
$619$	1.12976e32	0.888269	0.444135	−	0.895960i	$-0.353511\pi$
$619$	1.12976e32	0.888269	0.444135	+	0.895960i	$0.353511\pi$
$620$	−2.98448e31	−0.230337
$621$	−8.61477e30	−0.0652665
$622$	−3.64002e31	−0.270716
$623$	0	0
$624$	−2.07199e31	−0.148513
$625$	9.65607e31	0.679485
$626$	−3.48134e31	−0.240515
$627$	−1.48259e31	−0.100564
$628$	1.94083e32	1.29256
$629$	−2.58723e31	−0.169181
$630$	0	0
$631$	−2.09401e32	−1.32020	−0.660101	−	0.751177i	$-0.729487\pi$
$631$	−2.09401e32	−1.32020	−0.660101	+	0.751177i	$0.729487\pi$
$632$	−7.09225e31	−0.439074
$633$	−5.66744e31	−0.344544
$634$	1.39913e30	0.00835277
$635$	−8.08136e31	−0.473791
$636$	1.57754e32	0.908288
$637$	0	0
$638$	9.63484e30	0.0535065
$639$	1.64780e32	0.898765
$640$	5.20532e31	0.278854
$641$	6.89629e31	0.362867	0.181434	−	0.983403i	$-0.441926\pi$
$641$	6.89629e31	0.362867	0.181434	+	0.983403i	$0.441926\pi$
$642$	−9.05052e30	−0.0467757
$643$	2.36652e32	1.20139	0.600696	−	0.799478i	$-0.294890\pi$
$643$	2.36652e32	1.20139	0.600696	+	0.799478i	$0.294890\pi$
$644$	0	0
$645$	−4.67666e31	−0.229086
$646$	−1.56372e31	−0.0752462
$647$	6.86462e31	0.324502	0.162251	−	0.986750i	$-0.448125\pi$
$647$	6.86462e31	0.324502	0.162251	+	0.986750i	$0.448125\pi$
$648$	−8.01179e30	−0.0372064
$649$	−6.31399e31	−0.288065
$650$	−1.35283e31	−0.0606371
$651$	0	0
$652$	−2.10829e32	−0.912187
$653$	−3.07459e32	−1.30703	−0.653515	−	0.756913i	$-0.726707\pi$
$653$	−3.07459e32	−1.30703	−0.653515	+	0.756913i	$0.726707\pi$
$654$	−1.17780e31	−0.0491957
$655$	−3.43056e31	−0.140796
$656$	3.53870e32	1.42708
$657$	2.48484e31	0.0984682
$658$	0	0
$659$	4.91126e32	1.87936	0.939681	−	0.342053i	$-0.111122\pi$
$659$	4.91126e32	1.87936	0.939681	+	0.342053i	$0.111122\pi$
$660$	1.18961e31	0.0447351
$661$	1.55673e32	0.575303	0.287651	−	0.957735i	$-0.407126\pi$
$661$	1.55673e32	0.575303	0.287651	+	0.957735i	$0.407126\pi$
$662$	8.18554e31	0.297290
$663$	−2.20645e31	−0.0787569
$664$	−7.74497e31	−0.271698
$665$	0	0
$666$	−1.62715e31	−0.0551409
$667$	1.89637e31	0.0631648
$668$	3.74921e31	0.122747
$669$	−3.68671e32	−1.18642
$670$	−2.24730e31	−0.0710888
$671$	−9.96724e30	−0.0309932
$672$	0	0
$673$	4.78075e32	1.43656	0.718278	−	0.695756i	$-0.244930\pi$
$673$	4.78075e32	1.43656	0.718278	+	0.695756i	$0.244930\pi$
$674$	6.85356e31	0.202454
$675$	3.13055e32	0.909132
$676$	3.03697e32	0.867069
$677$	−3.26249e32	−0.915755	−0.457877	−	0.889015i	$-0.651390\pi$
$677$	−3.26249e32	−0.915755	−0.457877	+	0.889015i	$0.651390\pi$
$678$	4.63603e30	0.0127940
$679$	0	0
$680$	2.58924e31	0.0690747
$681$	−4.07646e32	−1.06928
$682$	1.54189e31	0.0397678
$683$	2.96979e32	0.753160	0.376580	−	0.926384i	$-0.377100\pi$
$683$	2.96979e32	0.753160	0.376580	+	0.926384i	$0.377100\pi$
$684$	1.54573e32	0.385468
$685$	−3.12837e31	−0.0767143
$686$	0	0
$687$	−2.13887e31	−0.0507203
$688$	−3.76127e32	−0.877136
$689$	1.81780e32	0.416893
$690$	−1.48970e30	−0.00335996
$691$	1.33631e32	0.296421	0.148210	−	0.988956i	$-0.452649\pi$
$691$	1.33631e32	0.296421	0.148210	+	0.988956i	$0.452649\pi$
$692$	2.15814e32	0.470826
$693$	0	0
$694$	−1.16533e32	−0.245931
$695$	−3.24322e31	−0.0673210
$696$	1.48636e32	0.303472
$697$	3.76833e32	0.756784
$698$	3.44576e31	0.0680687
$699$	4.60004e32	0.893869
$700$	0	0
$701$	3.41548e32	0.642235	0.321118	−	0.947039i	$-0.395942\pi$
$701$	3.41548e32	0.642235	0.321118	+	0.947039i	$0.395942\pi$
$702$	−3.77034e31	−0.0697436
$703$	−1.49753e32	−0.272515
$704$	8.13449e31	0.145628
$705$	5.18791e31	0.0913729
$706$	5.76056e31	0.0998184
$707$	0	0
$708$	−4.72012e32	−0.791718
$709$	−1.92539e32	−0.317751	−0.158875	−	0.987299i	$-0.550787\pi$
$709$	−1.92539e32	−0.317751	−0.158875	+	0.987299i	$0.550787\pi$
$710$	7.74204e31	0.125714
$711$	3.37289e32	0.538893
$712$	4.18239e32	0.657514
$713$	3.03480e31	0.0469462
$714$	0	0
$715$	1.37078e31	0.0205329
$716$	5.95972e32	0.878469
$717$	−3.94140e32	−0.571715
$718$	1.30736e32	0.186622
$719$	−1.36743e33	−1.92098	−0.960488	−	0.278321i	$-0.910222\pi$
$719$	−1.36743e33	−1.92098	−0.960488	+	0.278321i	$0.910222\pi$
$720$	−1.15634e32	−0.159868
$721$	0	0
$722$	9.21279e31	0.123371
$723$	−6.87398e32	−0.905978
$724$	1.42271e33	1.84553
$725$	−6.89126e32	−0.879856
$726$	1.19621e32	0.150327
$727$	2.18056e32	0.269726	0.134863	−	0.990864i	$-0.456941\pi$
$727$	2.18056e32	0.269726	0.134863	+	0.990864i	$0.456941\pi$
$728$	0	0
$729$	5.89471e32	0.706474
$730$	1.16747e31	0.0137732
$731$	−4.00534e32	−0.465147
$732$	−7.45116e31	−0.0851818
$733$	7.16063e32	0.805853	0.402926	−	0.915232i	$-0.367993\pi$
$733$	7.16063e32	0.805853	0.402926	+	0.915232i	$0.367993\pi$
$734$	7.80295e31	0.0864478
$735$	0	0
$736$	−4.01874e31	−0.0431515
$737$	−1.82485e32	−0.192909
$738$	2.36996e32	0.246657
$739$	−1.28228e33	−1.31393	−0.656964	−	0.753922i	$-0.728160\pi$
$739$	−1.28228e33	−1.31393	−0.656964	+	0.753922i	$0.728160\pi$
$740$	1.20160e32	0.121226
$741$	−1.27713e32	−0.126860
$742$	0	0
$743$	−1.14998e32	−0.110744	−0.0553719	−	0.998466i	$-0.517634\pi$
$743$	−1.14998e32	−0.110744	−0.0553719	+	0.998466i	$0.517634\pi$
$744$	2.37866e32	0.225550
$745$	1.56479e32	0.146103
$746$	−4.84615e32	−0.445554
$747$	3.68331e32	0.333466
$748$	1.01884e32	0.0908320
$749$	0	0
$750$	1.15025e32	0.0994457
$751$	−3.96598e32	−0.337669	−0.168835	−	0.985644i	$-0.554000\pi$
$751$	−3.96598e32	−0.337669	−0.168835	+	0.985644i	$0.554000\pi$
$752$	4.17244e32	0.349852
$753$	9.81885e32	0.810809
$754$	8.29964e31	0.0674977
$755$	−4.62414e32	−0.370374
$756$	0	0
$757$	5.00573e32	0.388924	0.194462	−	0.980910i	$-0.437704\pi$
$757$	5.00573e32	0.388924	0.194462	+	0.980910i	$0.437704\pi$
$758$	−2.05914e31	−0.0157576
$759$	−1.20967e31	−0.00911769
$760$	1.49870e32	0.111265
$761$	−6.98031e32	−0.510447	−0.255224	−	0.966882i	$-0.582149\pi$
$761$	−6.98031e32	−0.510447	−0.255224	+	0.966882i	$0.582149\pi$
$762$	3.12117e32	0.224820
$763$	0	0
$764$	−1.94778e33	−1.36134
$765$	−1.23138e32	−0.0847781
$766$	−4.85857e32	−0.329517
$767$	−5.43899e32	−0.363389
$768$	4.45758e32	0.293390
$769$	−1.41258e33	−0.915929	−0.457964	−	0.888971i	$-0.651421\pi$
$769$	−1.41258e33	−0.915929	−0.457964	+	0.888971i	$0.651421\pi$
$770$	0	0
$771$	−6.64115e32	−0.417944
$772$	1.31616e33	0.816037
$773$	−3.00166e33	−1.83357	−0.916785	−	0.399381i	$-0.869225\pi$
$773$	−3.00166e33	−1.83357	−0.916785	+	0.399381i	$0.869225\pi$
$774$	−2.51902e32	−0.151604
$775$	−1.10282e33	−0.653938
$776$	1.28586e33	0.751250
$777$	0	0
$778$	−5.83888e31	−0.0331180
$779$	2.18118e33	1.21902
$780$	1.02475e32	0.0564326
$781$	6.28668e32	0.341142
$782$	−1.27586e31	−0.00682221
$783$	−1.92060e33	−1.01199
$784$	0	0
$785$	−8.94925e32	−0.457916
$786$	1.32495e32	0.0668096
$787$	−2.76711e33	−1.37505	−0.687523	−	0.726162i	$-0.741302\pi$
$787$	−2.76711e33	−1.37505	−0.687523	+	0.726162i	$0.741302\pi$
$788$	3.58475e33	1.75552
$789$	−1.95445e33	−0.943275
$790$	1.58472e32	0.0753773
$791$	0	0
$792$	1.32230e32	0.0610929
$793$	−8.58597e31	−0.0390974
$794$	7.49080e32	0.336196
$795$	−7.27410e32	−0.321779
$796$	3.02835e33	1.32040
$797$	−1.45260e33	−0.624273	−0.312136	−	0.950037i	$-0.601045\pi$
$797$	−1.45260e33	−0.624273	−0.312136	+	0.950037i	$0.601045\pi$
$798$	0	0
$799$	4.44320e32	0.185527
$800$	1.46038e33	0.601080
$801$	−1.98904e33	−0.806992
$802$	−8.03194e32	−0.321229
$803$	9.48011e31	0.0373753
$804$	−1.36420e33	−0.530191
$805$	0	0
$806$	1.32821e32	0.0501665
$807$	2.47303e33	0.920838
$808$	−1.73326e33	−0.636257
$809$	−3.98093e33	−1.44071	−0.720356	−	0.693605i	$-0.756021\pi$
$809$	−3.98093e33	−1.44071	−0.720356	+	0.693605i	$0.756021\pi$
$810$	1.79019e31	0.00638734
$811$	−9.82630e32	−0.345661	−0.172830	−	0.984952i	$-0.555291\pi$
$811$	−9.82630e32	−0.345661	−0.172830	+	0.984952i	$0.555291\pi$
$812$	0	0
$813$	6.78579e32	0.232038
$814$	−6.20788e31	−0.0209297
$815$	9.72143e32	0.323160
$816$	7.10110e32	0.232749
$817$	−2.31836e33	−0.749252
$818$	2.34763e32	0.0748112
$819$	0	0
$820$	−1.75014e33	−0.542268
$821$	−7.16302e32	−0.218852	−0.109426	−	0.993995i	$-0.534901\pi$
$821$	−7.16302e32	−0.218852	−0.109426	+	0.993995i	$0.534901\pi$
$822$	1.20823e32	0.0364020
$823$	−1.75793e33	−0.522281	−0.261141	−	0.965301i	$-0.584099\pi$
$823$	−1.75793e33	−0.522281	−0.261141	+	0.965301i	$0.584099\pi$
$824$	1.74947e33	0.512558
$825$	4.39584e32	0.127005
$826$	0	0
$827$	2.54426e33	0.714904	0.357452	−	0.933932i	$-0.383646\pi$
$827$	2.54426e33	0.714904	0.357452	+	0.933932i	$0.383646\pi$
$828$	1.26118e32	0.0349485
$829$	2.11173e33	0.577113	0.288557	−	0.957463i	$-0.406825\pi$
$829$	2.11173e33	0.577113	0.288557	+	0.957463i	$0.406825\pi$
$830$	1.73057e32	0.0466434
$831$	−1.10122e32	−0.0292727
$832$	7.00721e32	0.183707
$833$	0	0
$834$	1.25259e32	0.0319448
$835$	−1.72878e32	−0.0434855
$836$	5.89724e32	0.146311
$837$	−3.07358e33	−0.752146
$838$	1.57122e33	0.379253
$839$	−2.51003e33	−0.597607	−0.298804	−	0.954315i	$-0.596588\pi$
$839$	−2.51003e33	−0.597607	−0.298804	+	0.954315i	$0.596588\pi$
$840$	0	0
$841$	−8.89076e31	−0.0205961
$842$	6.34453e32	0.144981
$843$	−3.54022e33	−0.798019
$844$	2.25432e33	0.501276
$845$	−1.40036e33	−0.307176
$846$	2.79440e32	0.0604685
$847$	0	0
$848$	−5.85029e33	−1.23204
$849$	2.74866e33	0.571060
$850$	4.63638e32	0.0950302
$851$	−1.22186e32	−0.0247076
$852$	4.69971e33	0.937595
$853$	7.59654e33	1.49521	0.747605	−	0.664144i	$-0.231204\pi$
$853$	7.59654e33	1.49521	0.747605	+	0.664144i	$0.231204\pi$
$854$	0	0
$855$	−7.12741e32	−0.136559
$856$	7.42903e32	0.140438
$857$	−2.82227e33	−0.526404	−0.263202	−	0.964741i	$-0.584779\pi$
$857$	−2.82227e33	−0.526404	−0.263202	+	0.964741i	$0.584779\pi$
$858$	−5.29422e31	−0.00974313
$859$	−8.93357e33	−1.62220	−0.811098	−	0.584910i	$-0.801130\pi$
$859$	−8.93357e33	−1.62220	−0.811098	+	0.584910i	$0.801130\pi$
$860$	1.86022e33	0.333297
$861$	0	0
$862$	−1.10469e33	−0.192710
$863$	−7.98960e33	−1.37531	−0.687656	−	0.726037i	$-0.741360\pi$
$863$	−7.98960e33	−1.37531	−0.687656	+	0.726037i	$0.741360\pi$
$864$	4.07010e33	0.691349
$865$	−9.95129e32	−0.166799
$866$	2.97478e32	0.0492038
$867$	−3.20294e33	−0.522792
$868$	0	0
$869$	1.28682e33	0.204546
$870$	−3.32118e32	−0.0520980
$871$	−1.57196e33	−0.243351
$872$	9.66785e32	0.147703
$873$	−6.11523e33	−0.922038
$874$	−7.38490e31	−0.0109891
$875$	0	0
$876$	7.08701e32	0.102723
$877$	−7.68421e33	−1.09927	−0.549634	−	0.835405i	$-0.685233\pi$
$877$	−7.68421e33	−1.09927	−0.549634	+	0.835405i	$0.685233\pi$
$878$	2.97604e32	0.0420196
$879$	5.53157e33	0.770861
$880$	−4.41164e32	−0.0606806
$881$	−3.64190e33	−0.494430	−0.247215	−	0.968961i	$-0.579515\pi$
$881$	−3.64190e33	−0.494430	−0.247215	+	0.968961i	$0.579515\pi$
$882$	0	0
$883$	8.89916e33	1.17707	0.588533	−	0.808473i	$-0.299706\pi$
$883$	8.89916e33	1.17707	0.588533	+	0.808473i	$0.299706\pi$
$884$	8.77651e32	0.114583
$885$	2.17647e33	0.280482
$886$	1.51850e33	0.193165
$887$	9.99033e33	1.25446	0.627232	−	0.778832i	$-0.284188\pi$
$887$	9.99033e33	1.25446	0.627232	+	0.778832i	$0.284188\pi$
$888$	−9.57686e32	−0.118706
$889$	0	0
$890$	−9.34530e32	−0.112878
$891$	1.45366e32	0.0173329
$892$	1.46645e34	1.72612
$893$	2.57180e33	0.298845
$894$	−6.04351e32	−0.0693278
$895$	−2.74805e33	−0.311215
$896$	0	0
$897$	−1.04203e32	−0.0115018
$898$	2.22943e33	0.242950
$899$	6.76587e33	0.727925
$900$	−4.58304e33	−0.486816
$901$	−6.22993e33	−0.653353
$902$	9.04185e32	0.0936229
$903$	0	0
$904$	−3.80544e32	−0.0384121
$905$	−6.56015e33	−0.653815
$906$	1.78593e33	0.175748
$907$	1.04545e34	1.01583	0.507915	−	0.861407i	$-0.330416\pi$
$907$	1.04545e34	1.01583	0.507915	+	0.861407i	$0.330416\pi$
$908$	1.62148e34	1.55569
$909$	8.24294e33	0.780904
$910$	0	0
$911$	1.54151e34	1.42391	0.711957	−	0.702223i	$-0.247809\pi$
$911$	1.54151e34	1.42391	0.711957	+	0.702223i	$0.247809\pi$
$912$	4.11024e33	0.374909
$913$	1.40525e33	0.126573
$914$	8.58521e32	0.0763607
$915$	3.43576e32	0.0301773
$916$	8.50769e32	0.0737928
$917$	0	0
$918$	1.29217e33	0.109302
$919$	−1.42600e34	−1.19122	−0.595611	−	0.803273i	$-0.703090\pi$
$919$	−1.42600e34	−1.19122	−0.595611	+	0.803273i	$0.703090\pi$
$920$	1.22281e32	0.0100878
$921$	8.39168e32	0.0683696
$922$	−4.86313e33	−0.391301
$923$	5.41547e33	0.430345
$924$	0	0
$925$	4.44015e33	0.344166
$926$	−4.92886e33	−0.377329
$927$	−8.32003e33	−0.629083
$928$	−8.95950e33	−0.669086
$929$	2.53657e33	0.187096	0.0935482	−	0.995615i	$-0.470179\pi$
$929$	2.53657e33	0.187096	0.0935482	+	0.995615i	$0.470179\pi$
$930$	−5.31496e32	−0.0387210
$931$	0	0
$932$	−1.82974e34	−1.30049
$933$	1.01887e34	0.715285
$934$	−5.17272e33	−0.358699
$935$	−4.69792e32	−0.0321790
$936$	1.13906e33	0.0770677
$937$	2.63986e34	1.76431	0.882157	−	0.470956i	$-0.156091\pi$
$937$	2.63986e34	1.76431	0.882157	+	0.470956i	$0.156091\pi$
$938$	0	0
$939$	9.74452e33	0.635486
$940$	−2.06357e33	−0.132938
$941$	8.54613e33	0.543862	0.271931	−	0.962317i	$-0.412338\pi$
$941$	8.54613e33	0.543862	0.271931	+	0.962317i	$0.412338\pi$
$942$	3.45637e33	0.217287
$943$	1.77965e33	0.110522
$944$	1.75045e34	1.07392
$945$	0	0
$946$	−9.61054e32	−0.0575440
$947$	9.16236e33	0.541979	0.270990	−	0.962582i	$-0.412649\pi$
$947$	9.16236e33	0.541979	0.270990	+	0.962582i	$0.412649\pi$
$948$	9.61984e33	0.562175
$949$	8.16635e32	0.0471484
$950$	2.68362e33	0.153073
$951$	−3.91625e32	−0.0220696
$952$	0	0
$953$	1.38393e33	0.0761283	0.0380642	−	0.999275i	$-0.487881\pi$
$953$	1.38393e33	0.0761283	0.0380642	+	0.999275i	$0.487881\pi$
$954$	−3.91810e33	−0.212946
$955$	8.98127e33	0.482280
$956$	1.56775e34	0.831787
$957$	−2.69686e33	−0.141375
$958$	−7.26500e33	−0.376298
$959$	0	0
$960$	−2.80400e33	−0.141795
$961$	−9.18574e33	−0.458982
$962$	−5.34759e32	−0.0264025
$963$	−3.53306e33	−0.172365
$964$	2.73424e34	1.31811
$965$	−6.06887e33	−0.289097
$966$	0	0
$967$	6.65131e32	0.0309387	0.0154694	−	0.999880i	$-0.495076\pi$
$967$	6.65131e32	0.0309387	0.0154694	+	0.999880i	$0.495076\pi$
$968$	−9.81895e33	−0.451334
$969$	4.37696e33	0.198815
$970$	−2.87318e33	−0.128970
$971$	−1.55122e34	−0.688103	−0.344052	−	0.938951i	$-0.611799\pi$
$971$	−1.55122e34	−0.688103	−0.344052	+	0.938951i	$0.611799\pi$
$972$	−2.08449e34	−0.913772
$973$	0	0
$974$	−3.50922e33	−0.150239
$975$	3.78666e33	0.160215
$976$	2.76325e33	0.115544
$977$	−3.03575e34	−1.25452	−0.627260	−	0.778810i	$-0.715824\pi$
$977$	−3.03575e34	−1.25452	−0.627260	+	0.778810i	$0.715824\pi$
$978$	−3.75460e33	−0.153344
$979$	−7.58855e33	−0.306308
$980$	0	0
$981$	−4.59778e33	−0.181282
$982$	8.17915e31	0.00318732
$983$	2.57708e34	0.992574	0.496287	−	0.868158i	$-0.334696\pi$
$983$	2.57708e34	0.992574	0.496287	+	0.868158i	$0.334696\pi$
$984$	1.39488e34	0.530999
$985$	−1.65294e34	−0.621929
$986$	−2.84444e33	−0.105782
$987$	0	0
$988$	5.08000e33	0.184569
$989$	−1.89158e33	−0.0679310
$990$	−2.95460e32	−0.0104880
$991$	−1.23176e34	−0.432193	−0.216097	−	0.976372i	$-0.569333\pi$
$991$	−1.23176e34	−0.432193	−0.216097	+	0.976372i	$0.569333\pi$
$992$	−1.43381e34	−0.497287
$993$	−2.29119e34	−0.785498
$994$	0	0
$995$	−1.39639e34	−0.467778
$996$	1.05052e34	0.347873
$997$	−3.78133e34	−1.23780	−0.618900	−	0.785470i	$-0.712421\pi$
$997$	−3.78133e34	−1.23780	−0.618900	+	0.785470i	$0.712421\pi$
$998$	8.79375e33	0.284559
$999$	1.23747e34	0.395852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.24.a.f.1.7		14
7.3	odd	6		7.24.c.a.2.8	✓	28
7.5	odd	6		7.24.c.a.4.8	yes	28
7.6	odd	2		49.24.a.g.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.24.c.a.2.8	✓	28	7.3	odd	6
7.24.c.a.4.8	yes	28	7.5	odd	6
49.24.a.f.1.7		14	1.1	even	1	trivial
49.24.a.g.1.7		14	7.6	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q-708.370 q^{2} +198278. q^{3} -7.88682e6 q^{4} +3.63664e7 q^{5} -1.40454e8 q^{6} +1.15290e10 q^{8} -5.48291e10 q^{9} -2.57609e10 q^{10} -2.09183e11 q^{11} -1.56378e12 q^{12} -1.80194e12 q^{13} +7.21066e12 q^{15} +5.79926e13 q^{16} +6.17559e13 q^{17} +3.88393e13 q^{18} +3.57454e14 q^{19} -2.86816e14 q^{20} +1.48179e14 q^{22} +2.91652e14 q^{23} +2.28595e15 q^{24} -1.05984e16 q^{25} +1.27644e15 q^{26} -2.95379e16 q^{27} +6.50216e16 q^{29} -5.10781e15 q^{30} +1.04056e17 q^{31} -1.37793e17 q^{32} -4.14764e16 q^{33} -4.37460e16 q^{34} +4.32427e17 q^{36} -4.18945e17 q^{37} -2.53210e17 q^{38} -3.57286e17 q^{39} +4.19269e17 q^{40} +6.10198e18 q^{41} -6.48576e18 q^{43} +1.64979e18 q^{44} -1.99394e18 q^{45} -2.06597e17 q^{46} +7.19477e18 q^{47} +1.14987e19 q^{48} +7.50759e18 q^{50} +1.22448e19 q^{51} +1.42116e19 q^{52} -1.00880e20 q^{53} +2.09237e19 q^{54} -7.60725e18 q^{55} +7.08752e19 q^{57} -4.60594e19 q^{58} +3.01840e20 q^{59} -5.68692e19 q^{60} +4.76484e19 q^{61} -7.37098e19 q^{62} -3.88869e20 q^{64} -6.55303e19 q^{65} +2.93806e19 q^{66} +8.72370e20 q^{67} -4.87058e20 q^{68} +5.78280e19 q^{69} -3.00535e21 q^{71} -6.32126e20 q^{72} -4.53197e20 q^{73} +2.96768e20 q^{74} -2.10143e21 q^{75} -2.81918e21 q^{76} +2.53090e20 q^{78} -6.15165e21 q^{79} +2.10899e21 q^{80} -6.94924e20 q^{81} -4.32246e21 q^{82} -6.71780e21 q^{83} +2.24584e21 q^{85} +4.59432e21 q^{86} +1.28923e22 q^{87} -2.41168e21 q^{88} +3.62771e22 q^{89} +1.41245e21 q^{90} -2.30020e21 q^{92} +2.06319e22 q^{93} -5.09656e21 q^{94} +1.29993e22 q^{95} -2.73212e22 q^{96} +1.11533e23 q^{97} +1.14693e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 966 q^{2} - 177148 q^{3} + 55357148 q^{4} - 74771022 q^{5} - 1504608254 q^{6} + 25222400616 q^{8} + 336909608980 q^{9} - 334296297894 q^{10} - 1355476566108 q^{11} - 4984668058916 q^{12} + 427040218556 q^{13}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) \) 14 * q - 966 * q^2 - 177148 * q^3 + 55357148 * q^4 - 74771022 * q^5 - 1504608254 * q^6 + 25222400616 * q^8 + 336909608980 * q^9 - 334296297894 * q^10 - 1355476566108 * q^11 - 4984668058916 * q^12 + 427040218556 * q^13 + 38670810653944 * q^15 + 160538324156336 * q^16 - 130193896130514 * q^17 - 110632655983108 * q^18 - 214771980430396 * q^19 + 48219439281468 * q^20 + 7534772282877126 * q^22 - 6685548913560552 * q^23 - 31330599354826008 * q^24 + 9156874000789424 * q^25 - 48260478025970868 * q^26 - 8477622198540028 * q^27 - 115398975455444604 * q^29 - 4149727265170942 * q^30 + 94821366637509632 * q^31 + 989053585410677472 * q^32 + 471925265098792298 * q^33 - 204665719203916350 * q^34 + 161548642910645480 * q^36 - 228196281955951106 * q^37 + 846979764807573006 * q^38 + 4289472930557071768 * q^39 - 10645750240235319192 * q^40 - 12663069502432601532 * q^41 - 427239519112420616 * q^43 - 11572396920387558444 * q^44 - 9362992784223924004 * q^45 + 33418566325741763586 * q^46 - 61615364375433533424 * q^47 - 158511629928130898960 * q^48 - 93272670392614362552 * q^50 - 84287583500847206172 * q^51 - 90603352071153943672 * q^52 + 282093764343878671758 * q^53 + 13895299932605385046 * q^54 - 237446342744567832720 * q^55 - 425457361374285462782 * q^57 - 339998979132364080060 * q^58 - 283820607003252730116 * q^59 + 701673169918628967164 * q^60 - 870322613357668504870 * q^61 - 282243301452069984966 * q^62 + 2124141067160402139584 * q^64 - 384582138286683330588 * q^65 - 157008004213679191250 * q^66 - 1414046473258733295716 * q^67 + 435228382363177447884 * q^68 + 2663127352907733668682 * q^69 + 213218335956247656048 * q^71 + 10118884230376615693104 * q^72 + 5942494661268692359862 * q^73 - 13389833203328450370642 * q^74 + 14120811240771906960232 * q^75 + 22920526497794398939844 * q^76 + 7201287217205176160828 * q^78 + 3444345943288433723680 * q^79 - 8255607259451726029008 * q^80 - 2565358457232096585122 * q^81 + 34656759475287179918772 * q^82 - 6085375799043077804904 * q^83 - 7680353239558358537262 * q^85 - 743687862046869712056 * q^86 - 7978312766181293835640 * q^87 + 2867657955669848060664 * q^88 - 68609868120257601678426 * q^89 - 17331740036513596551428 * q^90 - 7750847835981686889348 * q^92 - 50628291689744906093838 * q^93 + 18415808745499513811142 * q^94 + 113148862333982926479168 * q^95 - 150237583048546245409696 * q^96 - 230188776588461622952972 * q^97 - 234139240054754764282784 * q^99

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