LMFDB - Embedded newform 49.24.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,24,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, 24, names="a")

//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);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 24 $
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:	$164.249978299$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{144169}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 36042 $ x^2 - x - 36042
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$190.348$ 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)

$f(q)$	$=$	$q-4016.35 q^{2} -388445. q^{3} +7.74247e6 q^{4} -1.05062e8 q^{5} +1.56013e9 q^{6} +2.59512e9 q^{8} +5.67462e10 q^{9} +O(q^{10})$	\(q-4016.35 q^{2} -388445. q^{3} +7.74247e6 q^{4} -1.05062e8 q^{5} +1.56013e9 q^{6} +2.59512e9 q^{8} +5.67462e10 q^{9} +4.21966e11 q^{10} +2.52200e11 q^{11} -3.00752e12 q^{12} +3.59099e12 q^{13} +4.08108e13 q^{15} -7.53715e13 q^{16} -2.34190e14 q^{17} -2.27913e14 q^{18} +6.23086e14 q^{19} -8.13439e14 q^{20} -1.01292e15 q^{22} -3.58786e15 q^{23} -1.00806e15 q^{24} -8.82898e14 q^{25} -1.44227e16 q^{26} +1.45267e16 q^{27} -2.05923e16 q^{29} -1.63911e17 q^{30} -1.36357e17 q^{31} +2.80949e17 q^{32} -9.79656e16 q^{33} +9.40588e17 q^{34} +4.39356e17 q^{36} -1.23898e18 q^{37} -2.50253e18 q^{38} -1.39490e18 q^{39} -2.72649e17 q^{40} -1.40074e18 q^{41} +2.18793e17 q^{43} +1.95265e18 q^{44} -5.96187e18 q^{45} +1.44101e19 q^{46} +8.67836e18 q^{47} +2.92777e19 q^{48} +3.54603e18 q^{50} +9.09698e19 q^{51} +2.78032e19 q^{52} -7.63436e19 q^{53} -5.83441e19 q^{54} -2.64966e19 q^{55} -2.42034e20 q^{57} +8.27059e19 q^{58} +1.01862e18 q^{59} +3.15976e20 q^{60} -2.87337e20 q^{61} +5.47658e20 q^{62} -4.96127e20 q^{64} -3.77277e20 q^{65} +3.93464e20 q^{66} +1.47683e21 q^{67} -1.81321e21 q^{68} +1.39369e21 q^{69} +7.64346e20 q^{71} +1.47263e20 q^{72} +3.49433e21 q^{73} +4.97617e21 q^{74} +3.42957e20 q^{75} +4.82422e21 q^{76} +5.60242e21 q^{78} +1.02350e22 q^{79} +7.91868e21 q^{80} -1.09851e22 q^{81} +5.62587e21 q^{82} +7.71597e21 q^{83} +2.46044e22 q^{85} -8.78750e20 q^{86} +7.99897e21 q^{87} +6.54489e20 q^{88} -4.58518e21 q^{89} +2.39450e22 q^{90} -2.77789e22 q^{92} +5.29672e22 q^{93} -3.48553e22 q^{94} -6.54627e22 q^{95} -1.09133e23 q^{96} +1.13703e23 q^{97} +1.43114e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 1080 q^{2} - 339480 q^{3} + 25326656 q^{4} - 73069020 q^{5} + 1809673056 q^{6} + 49459023360 q^{8} - 34999394166 q^{9}+O(q^{10}) $ 2 * q + 1080 * q^2 - 339480 * q^3 + 25326656 * q^4 - 73069020 * q^5 + 1809673056 * q^6 + 49459023360 * q^8 - 34999394166 * q^9	$ 2 q + 1080 q^{2} - 339480 q^{3} + 25326656 q^{4} - 73069020 q^{5} + 1809673056 q^{6} + 49459023360 q^{8} - 34999394166 q^{9} + 585013636080 q^{10} + 856801968264 q^{11} - 2146514952960 q^{12} - 4376109322060 q^{13} + 42377338985040 q^{15} + 15956586401792 q^{16} - 254028147597540 q^{17} - 695480683916520 q^{18} - 4260600979960 q^{19} - 250868387468160 q^{20} + 20\!\cdots\!60 q^{22}+ \cdots - 41\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 1080 * q^2 - 339480 * q^3 + 25326656 * q^4 - 73069020 * q^5 + 1809673056 * q^6 + 49459023360 * q^8 - 34999394166 * q^9 + 585013636080 * q^10 + 856801968264 * q^11 - 2146514952960 * q^12 - 4376109322060 * q^13 + 42377338985040 * q^15 + 15956586401792 * q^16 - 254028147597540 * q^17 - 695480683916520 * q^18 - 4260600979960 * q^19 - 250868387468160 * q^20 + 2068343882177760 * q^22 - 8144713079008560 * q^23 + 1286622315141120 * q^24 - 11780274628800850 * q^25 - 55025854658735184 * q^26 + 5424634982716560 * q^27 + 20818433601623340 * q^29 - 155926924188644160 * q^30 - 137714017177000384 * q^31 + 353265663781601280 * q^32 - 68361366766001760 * q^33 + 839483655961325328 * q^34 - 1173916300077574848 * q^36 - 897721264408967780 * q^37 - 5699708971590961440 * q^38 - 1785011473665029232 * q^39 + 1226668524414336000 * q^40 + 2294435477168314956 * q^41 - 1750760768619855800 * q^43 + 12584088840033038592 * q^44 - 8897092690294206540 * q^45 - 8813206018050221376 * q^46 - 15759744217656780960 * q^47 + 33749519399576616960 * q^48 - 51990825483785316600 * q^50 + 89998362845078292144 * q^51 - 112291883783912022400 * q^52 - 140287253401646796420 * q^53 - 104731223417039799360 * q^54 - 7153550955060182640 * q^55 - 272752401448627175520 * q^57 + 293749486923568689360 * q^58 - 280872989971340771880 * q^59 + 343522601114937592320 * q^60 + 180452892516502223636 * q^61 + 540743475843874103040 * q^62 - 893690254469352914944 * q^64 - 632168834809440380760 * q^65 + 544338140913651883392 * q^66 + 1754233163431557625240 * q^67 - 2162050190142944330880 * q^68 + 1170560672172404223552 * q^69 + 3055033510194143328624 * q^71 - 4152294352103038548480 * q^72 + 8063408253877606149260 * q^73 + 6715344283148807757072 * q^74 - 190631089350520885800 * q^75 - 6207154294513080590080 * q^76 + 3614293948840808587200 * q^78 + 6244916814559639980640 * q^79 + 10840537585501794017280 * q^80 - 2793528580929833975598 * q^81 + 24457792891615712450640 * q^82 - 6875994082418498976120 * q^83 + 23969743087870314902520 * q^85 - 10916288812918999243296 * q^86 + 10026640653837674384880 * q^87 + 28988514668199273707520 * q^88 - 6395093086173070004820 * q^89 + 8986073954327865866160 * q^90 - 107907439017191756981760 * q^92 + 52900811441357852079360 * q^93 - 159400518006534931827072 * q^94 - 85533361066700858502000 * q^95 - 105592121669584394256384 * q^96 + 31147288846254030500540 * q^97 - 41158245132312135981912 * 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 $

$2$	−4016.35	−1.38671	−0.693357	−	0.720595i	$-0.743869\pi$
$2$	−4016.35	−1.38671	−0.693357	+	0.720595i	$0.743869\pi$
$3$	−388445.	−1.26600	−0.633002	−	0.774150i	$-0.718177\pi$
$3$	−388445.	−1.26600	−0.633002	+	0.774150i	$0.718177\pi$
$4$	7.74247e6	0.922974
$5$	−1.05062e8	−0.962256	−0.481128	−	0.876650i	$-0.659773\pi$
$5$	−1.05062e8	−0.962256	−0.481128	+	0.876650i	$0.659773\pi$
$6$	1.56013e9	1.75558
$7$	0	0
$7$	0	0
$8$	2.59512e9	0.106813
$9$	5.67462e10	0.602765
$10$	4.21966e11	1.33437
$11$	2.52200e11	0.266519	0.133260	−	0.991081i	$-0.457456\pi$
$11$	2.52200e11	0.266519	0.133260	+	0.991081i	$0.457456\pi$
$12$	−3.00752e12	−1.16849
$13$	3.59099e12	0.555733	0.277867	−	0.960620i	$-0.410373\pi$
$13$	3.59099e12	0.555733	0.277867	+	0.960620i	$0.410373\pi$
$14$	0	0
$15$	4.08108e13	1.21822
$16$	−7.53715e13	−1.07109
$17$	−2.34190e14	−1.65731	−0.828657	−	0.559756i	$-0.810895\pi$
$17$	−2.34190e14	−1.65731	−0.828657	+	0.559756i	$0.810895\pi$
$18$	−2.27913e14	−0.835863
$19$	6.23086e14	1.22710	0.613552	−	0.789654i	$-0.289740\pi$
$19$	6.23086e14	1.22710	0.613552	+	0.789654i	$0.289740\pi$
$20$	−8.13439e14	−0.888138
$21$	0	0
$22$	−1.01292e15	−0.369586
$23$	−3.58786e15	−0.785173	−0.392587	−	0.919715i	$-0.628420\pi$
$23$	−3.58786e15	−0.785173	−0.392587	+	0.919715i	$0.628420\pi$
$24$	−1.00806e15	−0.135225
$25$	−8.82898e14	−0.0740629
$26$	−1.44227e16	−0.770642
$27$	1.45267e16	0.502901
$28$	0	0
$29$	−2.05923e16	−0.313421	−0.156710	−	0.987645i	$-0.550089\pi$
$29$	−2.05923e16	−0.313421	−0.156710	+	0.987645i	$0.550089\pi$
$30$	−1.63911e17	−1.68932
$31$	−1.36357e17	−0.963870	−0.481935	−	0.876207i	$-0.660066\pi$
$31$	−1.36357e17	−0.963870	−0.481935	+	0.876207i	$0.660066\pi$
$32$	2.80949e17	1.37849
$33$	−9.79656e16	−0.337414
$34$	9.40588e17	2.29822
$35$	0	0
$36$	4.39356e17	0.556337
$37$	−1.23898e18	−1.14484	−0.572419	−	0.819961i	$-0.693995\pi$
$37$	−1.23898e18	−1.14484	−0.572419	+	0.819961i	$0.693995\pi$
$38$	−2.50253e18	−1.70164
$39$	−1.39490e18	−0.703560
$40$	−2.72649e17	−0.102781
$41$	−1.40074e18	−0.397506	−0.198753	−	0.980050i	$-0.563689\pi$
$41$	−1.40074e18	−0.397506	−0.198753	+	0.980050i	$0.563689\pi$
$42$	0	0
$43$	2.18793e17	0.0359043	0.0179522	−	0.999839i	$-0.494285\pi$
$43$	2.18793e17	0.0359043	0.0179522	+	0.999839i	$0.494285\pi$
$44$	1.95265e18	0.245990
$45$	−5.96187e18	−0.580015
$46$	1.44101e19	1.08881
$47$	8.67836e18	0.512050	0.256025	−	0.966670i	$-0.417587\pi$
$47$	8.67836e18	0.512050	0.256025	+	0.966670i	$0.417587\pi$
$48$	2.92777e19	1.35601
$49$	0	0
$50$	3.54603e18	0.102704
$51$	9.09698e19	2.09817
$52$	2.78032e19	0.512927
$53$	−7.63436e19	−1.13136	−0.565679	−	0.824626i	$-0.691386\pi$
$53$	−7.63436e19	−1.13136	−0.565679	+	0.824626i	$0.691386\pi$
$54$	−5.83441e19	−0.697379
$55$	−2.64966e19	−0.256460
$56$	0	0
$57$	−2.42034e20	−1.55352
$58$	8.27059e19	0.434625
$59$	1.01862e18	0.00439760	0.00219880	−	0.999998i	$-0.499300\pi$
$59$	1.01862e18	0.00439760	0.00219880	+	0.999998i	$0.499300\pi$
$60$	3.15976e20	1.12439
$61$	−2.87337e20	−0.845472	−0.422736	−	0.906253i	$-0.638930\pi$
$61$	−2.87337e20	−0.845472	−0.422736	+	0.906253i	$0.638930\pi$
$62$	5.47658e20	1.33661
$63$	0	0
$64$	−4.96127e20	−0.840472
$65$	−3.77277e20	−0.534758
$66$	3.93464e20	0.467897
$67$	1.47683e21	1.47730	0.738652	−	0.674088i	$-0.235463\pi$
$67$	1.47683e21	1.47730	0.738652	+	0.674088i	$0.235463\pi$
$68$	−1.81321e21	−1.52966
$69$	1.39369e21	0.994032
$70$	0	0
$71$	7.64346e20	0.392481	0.196241	−	0.980556i	$-0.437127\pi$
$71$	7.64346e20	0.392481	0.196241	+	0.980556i	$0.437127\pi$
$72$	1.47263e20	0.0643830
$73$	3.49433e21	1.30362	0.651810	−	0.758382i	$-0.274010\pi$
$73$	3.49433e21	1.30362	0.651810	+	0.758382i	$0.274010\pi$
$74$	4.97617e21	1.58756
$75$	3.42957e20	0.0937639
$76$	4.82422e21	1.13259
$77$	0	0
$78$	5.60242e21	0.975636
$79$	1.02350e22	1.53948	0.769742	−	0.638356i	$-0.220385\pi$
$79$	1.02350e22	1.53948	0.769742	+	0.638356i	$0.220385\pi$
$80$	7.91868e21	1.03067
$81$	−1.09851e22	−1.23944
$82$	5.62587e21	0.551227
$83$	7.71597e21	0.657646	0.328823	−	0.944392i	$-0.393348\pi$
$83$	7.71597e21	0.657646	0.328823	+	0.944392i	$0.393348\pi$
$84$	0	0
$85$	2.46044e22	1.59476
$86$	−8.78750e20	−0.0497890
$87$	7.99897e21	0.396792
$88$	6.54489e20	0.0284676
$89$	−4.58518e21	−0.175134	−0.0875672	−	0.996159i	$-0.527909\pi$
$89$	−4.58518e21	−0.175134	−0.0875672	+	0.996159i	$0.527909\pi$
$90$	2.39450e22	0.804314
$91$	0	0
$92$	−2.77789e22	−0.724695
$93$	5.29672e22	1.22026
$94$	−3.48553e22	−0.710067
$95$	−6.54627e22	−1.18079
$96$	−1.09133e23	−1.74517
$97$	1.13703e23	1.61398	0.806991	−	0.590564i	$-0.201095\pi$
$97$	1.13703e23	1.61398	0.806991	+	0.590564i	$0.201095\pi$
$98$	0	0
$99$	1.43114e22	0.160648
$100$	−6.83581e21	−0.0683581
$101$	−1.36243e23	−1.21512	−0.607558	−	0.794275i	$-0.707851\pi$
$101$	−1.36243e23	−1.21512	−0.607558	+	0.794275i	$0.707851\pi$
$102$	−3.65366e23	−2.90956
$103$	−1.41401e22	−0.100653	−0.0503264	−	0.998733i	$-0.516026\pi$
$103$	−1.41401e22	−0.100653	−0.0503264	+	0.998733i	$0.516026\pi$
$104$	9.31907e21	0.0593594
$105$	0	0
$106$	3.06623e23	1.56887
$107$	6.02971e22	0.276938	0.138469	−	0.990367i	$-0.455782\pi$
$107$	6.02971e22	0.276938	0.138469	+	0.990367i	$0.455782\pi$
$108$	1.12472e23	0.464164
$109$	−5.58169e22	−0.207186	−0.103593	−	0.994620i	$-0.533034\pi$
$109$	−5.58169e22	−0.207186	−0.103593	+	0.994620i	$0.533034\pi$
$110$	1.06420e23	0.355636
$111$	4.81275e23	1.44937
$112$	0	0
$113$	3.51523e23	0.862089	0.431044	−	0.902331i	$-0.358145\pi$
$113$	3.51523e23	0.862089	0.431044	+	0.902331i	$0.358145\pi$
$114$	9.72095e23	2.15428
$115$	3.76948e23	0.755538
$116$	−1.59435e23	−0.289279
$117$	2.03775e23	0.334976
$118$	−4.09115e21	−0.00609821
$119$	0	0
$120$	1.05909e23	0.130121
$121$	−8.31826e23	−0.928968
$122$	1.15405e24	1.17243
$123$	5.44111e23	0.503244
$124$	−1.05574e24	−0.889627
$125$	1.34520e24	1.03352
$126$	0	0
$127$	2.32044e24	1.48535	0.742674	−	0.669653i	$-0.233557\pi$
$127$	2.32044e24	1.48535	0.742674	+	0.669653i	$0.233557\pi$
$128$	−3.64148e23	−0.212992
$129$	−8.49891e22	−0.0454550
$130$	1.51528e24	0.741556
$131$	−8.70825e23	−0.390221	−0.195111	−	0.980781i	$-0.562507\pi$
$131$	−8.70825e23	−0.390221	−0.195111	+	0.980781i	$0.562507\pi$
$132$	−7.58496e23	−0.311425
$133$	0	0
$134$	−5.93146e24	−2.04860
$135$	−1.52620e24	−0.483919
$136$	−6.07751e23	−0.177022
$137$	4.43869e24	1.18841	0.594207	−	0.804312i	$-0.297466\pi$
$137$	4.43869e24	1.18841	0.594207	+	0.804312i	$0.297466\pi$
$138$	−5.59753e24	−1.37844
$139$	4.97229e23	0.112690	0.0563452	−	0.998411i	$-0.482055\pi$
$139$	4.97229e23	0.112690	0.0563452	+	0.998411i	$0.482055\pi$
$140$	0	0
$141$	−3.37106e24	−0.648257
$142$	−3.06988e24	−0.544259
$143$	9.05647e23	0.148114
$144$	−4.27705e24	−0.645617
$145$	2.16347e24	0.301591
$146$	−1.40345e25	−1.80775
$147$	0	0
$148$	−9.59276e24	−1.05666
$149$	1.10598e24	0.112748	0.0563738	−	0.998410i	$-0.482046\pi$
$149$	1.10598e24	0.112748	0.0563738	+	0.998410i	$0.482046\pi$
$150$	−1.37744e24	−0.130024
$151$	3.76304e24	0.329082	0.164541	−	0.986370i	$-0.447386\pi$
$151$	3.76304e24	0.329082	0.164541	+	0.986370i	$0.447386\pi$
$152$	1.61698e24	0.131070
$153$	−1.32894e25	−0.998972
$154$	0	0
$155$	1.43260e25	0.927490
$156$	−1.08000e25	−0.649368
$157$	−1.50090e25	−0.838504	−0.419252	−	0.907870i	$-0.637708\pi$
$157$	−1.50090e25	−0.838504	−0.419252	+	0.907870i	$0.637708\pi$
$158$	−4.11072e25	−2.13482
$159$	2.96553e25	1.43230
$160$	−2.95170e25	−1.32646
$161$	0	0
$162$	4.41199e25	1.71875
$163$	−2.61170e25	−0.947907	−0.473953	−	0.880550i	$-0.657173\pi$
$163$	−2.61170e25	−0.947907	−0.473953	+	0.880550i	$0.657173\pi$
$164$	−1.08452e25	−0.366888
$165$	1.02925e25	0.324679
$166$	−3.09900e25	−0.911967
$167$	−1.77408e25	−0.487230	−0.243615	−	0.969872i	$-0.578333\pi$
$167$	−1.77408e25	−0.487230	−0.243615	+	0.969872i	$0.578333\pi$
$168$	0	0
$169$	−2.88587e25	−0.691161
$170$	−9.88201e25	−2.21148
$171$	3.53578e25	0.739656
$172$	1.69400e24	0.0331387
$173$	−1.04109e26	−1.90528	−0.952640	−	0.304100i	$-0.901644\pi$
$173$	−1.04109e26	−1.90528	−0.952640	+	0.304100i	$0.901644\pi$
$174$	−3.21267e25	−0.550237
$175$	0	0
$176$	−1.90087e25	−0.285467
$177$	−3.95679e23	−0.00556737
$178$	1.84157e25	0.242861
$179$	−1.00142e25	−0.123824	−0.0619122	−	0.998082i	$-0.519720\pi$
$179$	−1.00142e25	−0.123824	−0.0619122	+	0.998082i	$0.519720\pi$
$180$	−4.61596e25	−0.535338
$181$	5.17169e25	0.562768	0.281384	−	0.959595i	$-0.409207\pi$
$181$	5.17169e25	0.562768	0.281384	+	0.959595i	$0.409207\pi$
$182$	0	0
$183$	1.11615e26	1.07037
$184$	−9.31094e24	−0.0838665
$185$	1.30170e26	1.10163
$186$	−2.12735e26	−1.69216
$187$	−5.90625e25	−0.441706
$188$	6.71919e25	0.472609
$189$	0	0
$190$	2.62921e26	1.63742
$191$	3.10126e26	1.81825	0.909127	−	0.416520i	$-0.136750\pi$
$191$	3.10126e26	1.81825	0.909127	+	0.416520i	$0.136750\pi$
$192$	1.92718e26	1.06404
$193$	−1.28183e26	−0.666687	−0.333344	−	0.942805i	$-0.608177\pi$
$193$	−1.28183e26	−0.666687	−0.333344	+	0.942805i	$0.608177\pi$
$194$	−4.56673e26	−2.23813
$195$	1.46551e26	0.677005
$196$	0	0
$197$	−3.89967e26	−1.60201	−0.801007	−	0.598655i	$-0.795702\pi$
$197$	−3.89967e26	−1.60201	−0.801007	+	0.598655i	$0.795702\pi$
$198$	−5.74795e25	−0.222773
$199$	1.25611e26	0.459426	0.229713	−	0.973258i	$-0.426221\pi$
$199$	1.25611e26	0.459426	0.229713	+	0.973258i	$0.426221\pi$
$200$	−2.29123e24	−0.00791086
$201$	−5.73666e26	−1.87027
$202$	5.47199e26	1.68502
$203$	0	0
$204$	7.04330e26	1.93655
$205$	1.47165e26	0.382503
$206$	5.67918e25	0.139577
$207$	−2.03598e26	−0.473275
$208$	−2.70658e26	−0.595242
$209$	1.57142e26	0.327047
$210$	0	0
$211$	5.88286e26	1.09734	0.548669	−	0.836040i	$-0.315135\pi$
$211$	5.88286e26	1.09734	0.548669	+	0.836040i	$0.315135\pi$
$212$	−5.91088e26	−1.04421
$213$	−2.96906e26	−0.496883
$214$	−2.42174e26	−0.384034
$215$	−2.29869e25	−0.0345491
$216$	3.76984e25	0.0537162
$217$	0	0
$218$	2.24180e26	0.287308
$219$	−1.35735e27	−1.65039
$220$	−2.05149e26	−0.236706
$221$	−8.40974e26	−0.921025
$222$	−1.93297e27	−2.00986
$223$	−1.38821e27	−1.37072	−0.685361	−	0.728203i	$-0.740356\pi$
$223$	−1.38821e27	−1.37072	−0.685361	+	0.728203i	$0.740356\pi$
$224$	0	0
$225$	−5.01012e25	−0.0446425
$226$	−1.41184e27	−1.19547
$227$	2.14958e27	1.73004	0.865022	−	0.501734i	$-0.167304\pi$
$227$	2.14958e27	1.73004	0.865022	+	0.501734i	$0.167304\pi$
$228$	−1.87394e27	−1.43386
$229$	6.39851e26	0.465554	0.232777	−	0.972530i	$-0.425219\pi$
$229$	6.39851e26	0.465554	0.232777	+	0.972530i	$0.425219\pi$
$230$	−1.51396e27	−1.04771
$231$	0	0
$232$	−5.34395e25	−0.0334773
$233$	2.19149e27	1.30661	0.653306	−	0.757094i	$-0.273381\pi$
$233$	2.19149e27	1.30661	0.653306	+	0.757094i	$0.273381\pi$
$234$	−8.18434e26	−0.464516
$235$	−9.11766e26	−0.492723
$236$	7.88666e24	0.00405887
$237$	−3.97572e27	−1.94899
$238$	0	0
$239$	1.09944e27	0.489322	0.244661	−	0.969609i	$-0.421323\pi$
$239$	1.09944e27	0.489322	0.244661	+	0.969609i	$0.421323\pi$
$240$	−3.07597e27	−1.30483
$241$	1.44651e27	0.584961	0.292480	−	0.956272i	$-0.405519\pi$
$241$	1.44651e27	0.584961	0.292480	+	0.956272i	$0.405519\pi$
$242$	3.34090e27	1.28821
$243$	2.89951e27	1.06623
$244$	−2.22470e27	−0.780349
$245$	0	0
$246$	−2.18534e27	−0.697855
$247$	2.23750e27	0.681942
$248$	−3.53864e26	−0.102954
$249$	−2.99723e27	−0.832582
$250$	−5.40278e27	−1.43320
$251$	−2.24453e26	−0.0568693	−0.0284346	−	0.999596i	$-0.509052\pi$
$251$	−2.24453e26	−0.0568693	−0.0284346	+	0.999596i	$0.509052\pi$
$252$	0	0
$253$	−9.04857e26	−0.209264
$254$	−9.31972e27	−2.05975
$255$	−9.55747e27	−2.01897
$256$	5.62436e27	1.13583
$257$	3.95005e27	0.762732	0.381366	−	0.924424i	$-0.375454\pi$
$257$	3.95005e27	0.762732	0.381366	+	0.924424i	$0.375454\pi$
$258$	3.41346e26	0.0630330
$259$	0	0
$260$	−2.92106e27	−0.493567
$261$	−1.16853e27	−0.188919
$262$	3.49754e27	0.541125
$263$	2.01521e27	0.298420	0.149210	−	0.988805i	$-0.452327\pi$
$263$	2.01521e27	0.298420	0.149210	+	0.988805i	$0.452327\pi$
$264$	−2.54233e26	−0.0360401
$265$	8.02081e27	1.08866
$266$	0	0
$267$	1.78109e27	0.221721
$268$	1.14343e28	1.36351
$269$	−5.72063e27	−0.653571	−0.326785	−	0.945099i	$-0.605965\pi$
$269$	−5.72063e27	−0.653571	−0.326785	+	0.945099i	$0.605965\pi$
$270$	6.12975e27	0.671058
$271$	−5.18050e27	−0.543531	−0.271766	−	0.962363i	$-0.587608\pi$
$271$	−5.18050e27	−0.543531	−0.271766	+	0.962363i	$0.587608\pi$
$272$	1.76512e28	1.77514
$273$	0	0
$274$	−1.78273e28	−1.64799
$275$	−2.22667e26	−0.0197392
$276$	1.07906e28	0.917466
$277$	1.29611e28	1.05712	0.528560	−	0.848896i	$-0.322732\pi$
$277$	1.29611e28	1.05712	0.528560	+	0.848896i	$0.322732\pi$
$278$	−1.99705e27	−0.156269
$279$	−7.73776e27	−0.580987
$280$	0	0
$281$	1.24154e28	0.858691	0.429346	−	0.903140i	$-0.358744\pi$
$281$	1.24154e28	0.858691	0.429346	+	0.903140i	$0.358744\pi$
$282$	1.35394e28	0.898947
$283$	2.15031e28	1.37074	0.685372	−	0.728193i	$-0.259640\pi$
$283$	2.15031e28	1.37074	0.685372	+	0.728193i	$0.259640\pi$
$284$	5.91792e27	0.362250
$285$	2.54286e28	1.49488
$286$	−3.63740e27	−0.205391
$287$	0	0
$288$	1.59428e28	0.830903
$289$	3.48772e28	1.74669
$290$	−8.68925e27	−0.418220
$291$	−4.41675e28	−2.04331
$292$	2.70547e28	1.20321
$293$	1.20307e28	0.514416	0.257208	−	0.966356i	$-0.417197\pi$
$293$	1.20307e28	0.514416	0.257208	+	0.966356i	$0.417197\pi$
$294$	0	0
$295$	−1.07019e26	−0.00423161
$296$	−3.21530e27	−0.122283
$297$	3.66362e27	0.134033
$298$	−4.44202e27	−0.156349
$299$	−1.28840e28	−0.436347
$300$	2.65534e27	0.0865416
$301$	0	0
$302$	−1.51137e28	−0.456342
$303$	5.29228e28	1.53834
$304$	−4.69629e28	−1.31434
$305$	3.01883e28	0.813560
$306$	5.33748e28	1.38529
$307$	4.70428e28	1.17598	0.587992	−	0.808867i	$-0.299919\pi$
$307$	4.70428e28	1.17598	0.587992	+	0.808867i	$0.299919\pi$
$308$	0	0
$309$	5.49267e27	0.127427
$310$	−5.75381e28	−1.28616
$311$	8.99672e26	0.0193794	0.00968968	−	0.999953i	$-0.496916\pi$
$311$	8.99672e26	0.0193794	0.00968968	+	0.999953i	$0.496916\pi$
$312$	−3.61994e27	−0.0751492
$313$	1.13525e28	0.227159	0.113579	−	0.993529i	$-0.463768\pi$
$313$	1.13525e28	0.227159	0.113579	+	0.993529i	$0.463768\pi$
$314$	6.02814e28	1.16277
$315$	0	0
$316$	7.92439e28	1.42090
$317$	1.37896e28	0.238436	0.119218	−	0.992868i	$-0.461961\pi$
$317$	1.37896e28	0.238436	0.119218	+	0.992868i	$0.461961\pi$
$318$	−1.19106e29	−1.98619
$319$	−5.19337e27	−0.0835326
$320$	5.21241e28	0.808750
$321$	−2.34221e28	−0.350605
$322$	0	0
$323$	−1.45920e29	−2.03370
$324$	−8.50516e28	−1.14397
$325$	−3.17048e27	−0.0411592
$326$	1.04895e29	1.31448
$327$	2.16818e28	0.262298
$328$	−3.63510e27	−0.0424587
$329$	0	0
$330$	−4.13382e28	−0.450237
$331$	1.62668e29	1.71112	0.855559	−	0.517706i	$-0.173214\pi$
$331$	1.62668e29	1.71112	0.855559	+	0.517706i	$0.173214\pi$
$332$	5.97406e28	0.606990
$333$	−7.03074e28	−0.690069
$334$	7.12534e28	0.675649
$335$	−1.55159e29	−1.42154
$336$	0	0
$337$	−1.64138e29	−1.40432	−0.702160	−	0.712019i	$-0.747781\pi$
$337$	−1.64138e29	−1.40432	−0.702160	+	0.712019i	$0.747781\pi$
$338$	1.15907e29	0.958442
$339$	−1.36547e29	−1.09141
$340$	1.90499e29	1.47192
$341$	−3.43892e28	−0.256890
$342$	−1.42009e29	−1.02569
$343$	0	0
$344$	5.67795e26	0.00383504
$345$	−1.46424e29	−0.956514
$346$	4.18139e29	2.64208
$347$	1.45586e29	0.889876	0.444938	−	0.895561i	$-0.353226\pi$
$347$	1.45586e29	0.889876	0.444938	+	0.895561i	$0.353226\pi$
$348$	6.19318e28	0.366229
$349$	−2.22110e28	−0.127080	−0.0635398	−	0.997979i	$-0.520239\pi$
$349$	−2.22110e28	−0.127080	−0.0635398	+	0.997979i	$0.520239\pi$
$350$	0	0
$351$	5.21651e28	0.279479
$352$	7.08552e28	0.367393
$353$	−2.57166e28	−0.129064	−0.0645320	−	0.997916i	$-0.520555\pi$
$353$	−2.57166e28	−0.129064	−0.0645320	+	0.997916i	$0.520555\pi$
$354$	1.58919e27	0.00772035
$355$	−8.03037e28	−0.377668
$356$	−3.55006e28	−0.161644
$357$	0	0
$358$	4.02205e28	0.171709
$359$	−3.34157e29	−1.38154	−0.690771	−	0.723074i	$-0.742729\pi$
$359$	−3.34157e29	−1.38154	−0.690771	+	0.723074i	$0.742729\pi$
$360$	−1.54718e28	−0.0619529
$361$	1.30406e29	0.505785
$362$	−2.07713e29	−0.780398
$363$	3.23118e29	1.17608
$364$	0	0
$365$	−3.67122e29	−1.25442
$366$	−4.48284e29	−1.48430
$367$	−1.62664e29	−0.521954	−0.260977	−	0.965345i	$-0.584045\pi$
$367$	−1.62664e29	−0.521954	−0.260977	+	0.965345i	$0.584045\pi$
$368$	2.70422e29	0.840994
$369$	−7.94868e28	−0.239603
$370$	−5.22807e29	−1.52764
$371$	0	0
$372$	4.10097e29	1.12627
$373$	1.03540e29	0.275712	0.137856	−	0.990452i	$-0.455979\pi$
$373$	1.03540e29	0.275712	0.137856	+	0.990452i	$0.455979\pi$
$374$	2.37216e29	0.612520
$375$	−5.22535e29	−1.30844
$376$	2.25214e28	0.0546935
$377$	−7.39468e28	−0.174178
$378$	0	0
$379$	6.62210e29	1.46772	0.733862	−	0.679298i	$-0.237716\pi$
$379$	6.62210e29	1.46772	0.733862	+	0.679298i	$0.237716\pi$
$380$	−5.06843e29	−1.08984
$381$	−9.01364e29	−1.88046
$382$	−1.24557e30	−2.52140
$383$	−2.96585e29	−0.582591	−0.291295	−	0.956633i	$-0.594086\pi$
$383$	−2.96585e29	−0.582591	−0.291295	+	0.956633i	$0.594086\pi$
$384$	1.41451e29	0.269648
$385$	0	0
$386$	5.14829e29	0.924504
$387$	1.24157e28	0.0216419
$388$	8.80345e29	1.48966
$389$	−1.06609e30	−1.75134	−0.875672	−	0.482906i	$-0.839581\pi$
$389$	−1.06609e30	−1.75134	−0.875672	+	0.482906i	$0.839581\pi$
$390$	−5.88602e29	−0.938812
$391$	8.40240e29	1.30128
$392$	0	0
$393$	3.38267e29	0.494021
$394$	1.56624e30	2.22153
$395$	−1.07531e30	−1.48138
$396$	1.10805e29	0.148274
$397$	−1.67462e28	−0.0217683	−0.0108842	−	0.999941i	$-0.503465\pi$
$397$	−1.67462e28	−0.0217683	−0.0108842	+	0.999941i	$0.503465\pi$
$398$	−5.04496e29	−0.637093
$399$	0	0
$400$	6.65453e28	0.0793282
$401$	3.87121e29	0.448421	0.224211	−	0.974541i	$-0.428020\pi$
$401$	3.87121e29	0.448421	0.224211	+	0.974541i	$0.428020\pi$
$402$	2.30404e30	2.59353
$403$	−4.89658e29	−0.535654
$404$	−1.05486e30	−1.12152
$405$	1.15411e30	1.19266
$406$	0	0
$407$	−3.12470e29	−0.305121
$408$	2.36078e29	0.224111
$409$	−5.00511e29	−0.461950	−0.230975	−	0.972960i	$-0.574192\pi$
$409$	−5.00511e29	−0.461950	−0.230975	+	0.972960i	$0.574192\pi$
$410$	−5.91065e29	−0.530422
$411$	−1.72418e30	−1.50454
$412$	−1.09480e29	−0.0928999
$413$	0	0
$414$	8.17719e29	0.656297
$415$	−8.10655e29	−0.632824
$416$	1.00889e30	0.766070
$417$	−1.93146e29	−0.142666
$418$	−6.31137e29	−0.453520
$419$	−1.70760e30	−1.19378	−0.596891	−	0.802322i	$-0.703598\pi$
$419$	−1.70760e30	−1.19378	−0.596891	+	0.802322i	$0.703598\pi$
$420$	0	0
$421$	−5.97218e29	−0.395265	−0.197633	−	0.980276i	$-0.563325\pi$
$421$	−5.97218e29	−0.395265	−0.197633	+	0.980276i	$0.563325\pi$
$422$	−2.36276e30	−1.52169
$423$	4.92464e29	0.308646
$424$	−1.98121e29	−0.120843
$425$	2.06766e29	0.122746
$426$	1.19248e30	0.689034
$427$	0	0
$428$	4.66848e29	0.255607
$429$	−3.51794e29	−0.187512
$430$	9.23233e28	0.0479098
$431$	1.91854e30	0.969353	0.484676	−	0.874694i	$-0.338937\pi$
$431$	1.91854e30	0.969353	0.484676	+	0.874694i	$0.338937\pi$
$432$	−1.09490e30	−0.538653
$433$	2.68456e30	1.28606	0.643032	−	0.765839i	$-0.277676\pi$
$433$	2.68456e30	1.28606	0.643032	+	0.765839i	$0.277676\pi$
$434$	0	0
$435$	−8.40388e29	−0.381815
$436$	−4.32160e29	−0.191228
$437$	−2.23555e30	−0.963489
$438$	5.45161e30	2.28862
$439$	−2.11168e29	−0.0863549	−0.0431775	−	0.999067i	$-0.513748\pi$
$439$	−2.11168e29	−0.0863549	−0.0431775	+	0.999067i	$0.513748\pi$
$440$	−6.87619e28	−0.0273932
$441$	0	0
$442$	3.37765e30	1.27720
$443$	−8.12623e29	−0.299396	−0.149698	−	0.988732i	$-0.547830\pi$
$443$	−8.12623e29	−0.299396	−0.149698	+	0.988732i	$0.547830\pi$
$444$	3.72626e30	1.33773
$445$	4.81728e29	0.168524
$446$	5.57554e30	1.90080
$447$	−4.29614e29	−0.142739
$448$	0	0
$449$	−3.76596e30	−1.18862	−0.594310	−	0.804236i	$-0.702575\pi$
$449$	−3.76596e30	−1.18862	−0.594310	+	0.804236i	$0.702575\pi$
$450$	2.01224e29	0.0619064
$451$	−3.53267e29	−0.105943
$452$	2.72166e30	0.795686
$453$	−1.46173e30	−0.416619
$454$	−8.63348e30	−2.39907
$455$	0	0
$456$	−6.28109e29	−0.165936
$457$	2.14090e30	0.551518	0.275759	−	0.961227i	$-0.411071\pi$
$457$	2.14090e30	0.551518	0.275759	+	0.961227i	$0.411071\pi$
$458$	−2.56986e30	−0.645591
$459$	−3.40199e30	−0.833465
$460$	2.91851e30	0.697342
$461$	−4.76379e30	−1.11018	−0.555088	−	0.831792i	$-0.687315\pi$
$461$	−4.76379e30	−1.11018	−0.555088	+	0.831792i	$0.687315\pi$
$462$	0	0
$463$	−7.67574e30	−1.70192	−0.850959	−	0.525232i	$-0.823979\pi$
$463$	−7.67574e30	−1.70192	−0.850959	+	0.525232i	$0.823979\pi$
$464$	1.55207e30	0.335703
$465$	−5.56485e30	−1.17421
$466$	−8.80180e30	−1.81190
$467$	2.87884e30	0.578194	0.289097	−	0.957300i	$-0.406645\pi$
$467$	2.87884e30	0.578194	0.289097	+	0.957300i	$0.406645\pi$
$468$	1.57772e30	0.309175
$469$	0	0
$470$	3.66197e30	0.683266
$471$	5.83016e30	1.06155
$472$	2.64345e27	0.000469719 0
$473$	5.51796e28	0.00956919
$474$	1.59679e31	2.70269
$475$	−5.50121e29	−0.0908829
$476$	0	0
$477$	−4.33221e30	−0.681943
$478$	−4.41573e30	−0.678549
$479$	−6.82143e30	−1.02333	−0.511666	−	0.859184i	$-0.670972\pi$
$479$	−6.82143e30	−1.02333	−0.511666	+	0.859184i	$0.670972\pi$
$480$	1.14657e31	1.67930
$481$	−4.44917e30	−0.636224
$482$	−5.80971e30	−0.811173
$483$	0	0
$484$	−6.44038e30	−0.857413
$485$	−1.19459e31	−1.55306
$486$	−1.16455e31	−1.47856
$487$	8.59361e29	0.106560	0.0532798	−	0.998580i	$-0.483032\pi$
$487$	8.59361e29	0.106560	0.0532798	+	0.998580i	$0.483032\pi$
$488$	−7.45676e29	−0.0903071
$489$	1.01450e31	1.20005
$490$	0	0
$491$	−7.15140e30	−0.807149	−0.403575	−	0.914947i	$-0.632232\pi$
$491$	−7.15140e30	−0.807149	−0.403575	+	0.914947i	$0.632232\pi$
$492$	4.21276e30	0.464481
$493$	4.82250e30	0.519437
$494$	−8.98658e30	−0.945659
$495$	−1.50358e30	−0.154585
$496$	1.02774e31	1.03239
$497$	0	0
$498$	1.20379e31	1.15455
$499$	1.77913e31	1.66744	0.833722	−	0.552185i	$-0.186206\pi$
$499$	1.77913e31	1.66744	0.833722	+	0.552185i	$0.186206\pi$
$500$	1.04151e31	0.953916
$501$	6.89133e30	0.616835
$502$	9.01483e29	0.0788614
$503$	−6.56155e30	−0.561015	−0.280507	−	0.959852i	$-0.590503\pi$
$503$	−6.56155e30	−0.561015	−0.280507	+	0.959852i	$0.590503\pi$
$504$	0	0
$505$	1.43139e31	1.16925
$506$	3.63422e30	0.290189
$507$	1.12100e31	0.875012
$508$	1.79660e31	1.37094
$509$	1.19826e31	0.893917	0.446959	−	0.894555i	$-0.352507\pi$
$509$	1.19826e31	0.893917	0.446959	+	0.894555i	$0.352507\pi$
$510$	3.83861e31	2.79974
$511$	0	0
$512$	−1.95347e31	−1.36208
$513$	9.05135e30	0.617112
$514$	−1.58648e31	−1.05769
$515$	1.48559e30	0.0968537
$516$	−6.58025e29	−0.0419538
$517$	2.18868e30	0.136471
$518$	0	0
$519$	4.04407e31	2.41209
$520$	−9.79080e29	−0.0571189
$521$	2.26240e31	1.29103	0.645514	−	0.763749i	$-0.276643\pi$
$521$	2.26240e31	1.29103	0.645514	+	0.763749i	$0.276643\pi$
$522$	4.69325e30	0.261977
$523$	3.41914e31	1.86702	0.933508	−	0.358557i	$-0.116731\pi$
$523$	3.41914e31	1.86702	0.933508	+	0.358557i	$0.116731\pi$
$524$	−6.74233e30	−0.360164
$525$	0	0
$526$	−8.09378e30	−0.413824
$527$	3.19334e31	1.59744
$528$	7.38381e30	0.361402
$529$	−8.00772e30	−0.383503
$530$	−3.22144e31	−1.50965
$531$	5.78030e28	0.00265072
$532$	0	0
$533$	−5.03006e30	−0.220907
$534$	−7.15348e30	−0.307463
$535$	−6.33494e30	−0.266486
$536$	3.83255e30	0.157795
$537$	3.88996e30	0.156762
$538$	2.29761e31	0.906315
$539$	0	0
$540$	−1.18166e31	−0.446645
$541$	−2.75024e30	−0.101766	−0.0508829	−	0.998705i	$-0.516204\pi$
$541$	−2.75024e30	−0.101766	−0.0508829	+	0.998705i	$0.516204\pi$
$542$	2.08067e31	0.753722
$543$	−2.00892e31	−0.712466
$544$	−6.57953e31	−2.28459
$545$	5.86424e30	0.199366
$546$	0	0
$547$	−1.03197e31	−0.336367	−0.168184	−	0.985756i	$-0.553790\pi$
$547$	−1.03197e31	−0.336367	−0.168184	+	0.985756i	$0.553790\pi$
$548$	3.43664e31	1.09688
$549$	−1.63053e31	−0.509621
$550$	8.94307e29	0.0273726
$551$	−1.28308e31	−0.384600
$552$	3.61679e30	0.106175
$553$	0	0
$554$	−5.20563e31	−1.46592
$555$	−5.05637e31	−1.39466
$556$	3.84978e30	0.104010
$557$	1.36262e31	0.360613	0.180307	−	0.983610i	$-0.442291\pi$
$557$	1.36262e31	0.360613	0.180307	+	0.983610i	$0.442291\pi$
$558$	3.10775e31	0.805663
$559$	7.85685e29	0.0199532
$560$	0	0
$561$	2.29425e31	0.559202
$562$	−4.98645e31	−1.19076
$563$	−3.09091e31	−0.723169	−0.361585	−	0.932339i	$-0.617764\pi$
$563$	−3.09091e31	−0.723169	−0.361585	+	0.932339i	$0.617764\pi$
$564$	−2.61004e31	−0.598325
$565$	−3.69317e31	−0.829550
$566$	−8.63638e31	−1.90083
$567$	0	0
$568$	1.98357e30	0.0419220
$569$	−6.93051e31	−1.43540	−0.717702	−	0.696350i	$-0.754806\pi$
$569$	−6.93051e31	−1.43540	−0.717702	+	0.696350i	$0.754806\pi$
$570$	−1.02130e32	−2.07297
$571$	−6.24961e30	−0.124319	−0.0621595	−	0.998066i	$-0.519799\pi$
$571$	−6.24961e30	−0.124319	−0.0621595	+	0.998066i	$0.519799\pi$
$572$	7.01195e30	0.136705
$573$	−1.20467e32	−2.30192
$574$	0	0
$575$	3.16772e30	0.0581522
$576$	−2.81534e31	−0.506607
$577$	1.59740e31	0.281768	0.140884	−	0.990026i	$-0.455006\pi$
$577$	1.59740e31	0.281768	0.140884	+	0.990026i	$0.455006\pi$
$578$	−1.40079e32	−2.42216
$579$	4.97921e31	0.844029
$580$	1.67506e31	0.278361
$581$	0	0
$582$	1.77392e32	2.83348
$583$	−1.92538e31	−0.301529
$584$	9.06822e30	0.139243
$585$	−2.14091e31	−0.322333
$586$	−4.83197e31	−0.713348
$587$	−8.16635e31	−1.18220	−0.591099	−	0.806599i	$-0.701306\pi$
$587$	−8.16635e31	−1.18220	−0.591099	+	0.806599i	$0.701306\pi$
$588$	0	0
$589$	−8.49622e31	−1.18277
$590$	4.29824e29	0.00586804
$591$	1.51481e32	2.02816
$592$	9.33837e31	1.22623
$593$	5.61370e30	0.0722970	0.0361485	−	0.999346i	$-0.488491\pi$
$593$	5.61370e30	0.0722970	0.0361485	+	0.999346i	$0.488491\pi$
$594$	−1.47144e31	−0.185865
$595$	0	0
$596$	8.56305e30	0.104063
$597$	−4.87928e31	−0.581635
$598$	5.17466e31	0.605088
$599$	1.60231e32	1.83797	0.918985	−	0.394293i	$-0.129010\pi$
$599$	1.60231e32	1.83797	0.918985	+	0.394293i	$0.129010\pi$
$600$	8.90016e29	0.0100152
$601$	−8.47641e31	−0.935741	−0.467870	−	0.883797i	$-0.654979\pi$
$601$	−8.47641e31	−0.935741	−0.467870	+	0.883797i	$0.654979\pi$
$602$	0	0
$603$	8.38044e31	0.890467
$604$	2.91352e31	0.303734
$605$	8.73933e31	0.893905
$606$	−2.12557e32	−2.13324
$607$	1.63793e31	0.161296	0.0806481	−	0.996743i	$-0.474301\pi$
$607$	1.63793e31	0.161296	0.0806481	+	0.996743i	$0.474301\pi$
$608$	1.75055e32	1.69155
$609$	0	0
$610$	−1.21247e32	−1.12818
$611$	3.11639e31	0.284563
$612$	−1.02893e32	−0.922025
$613$	1.93558e31	0.170222	0.0851110	−	0.996371i	$-0.472876\pi$
$613$	1.93558e31	0.170222	0.0851110	+	0.996371i	$0.472876\pi$
$614$	−1.88940e32	−1.63075
$615$	−5.71654e31	−0.484250
$616$	0	0
$617$	5.25618e31	0.428934	0.214467	−	0.976731i	$-0.431199\pi$
$617$	5.25618e31	0.428934	0.214467	+	0.976731i	$0.431199\pi$
$618$	−2.20605e31	−0.176704
$619$	9.42009e31	0.740650	0.370325	−	0.928902i	$-0.379246\pi$
$619$	9.42009e31	0.740650	0.370325	+	0.928902i	$0.379246\pi$
$620$	1.10918e32	0.856049
$621$	−5.21196e31	−0.394864
$622$	−3.61340e30	−0.0268736
$623$	0	0
$624$	1.05136e32	0.753578
$625$	−1.30804e32	−0.920452
$626$	−4.55954e31	−0.315004
$627$	−6.10410e31	−0.414042
$628$	−1.16207e32	−0.773918
$629$	2.90156e32	1.89736
$630$	0	0
$631$	−2.22784e32	−1.40458	−0.702288	−	0.711892i	$-0.747838\pi$
$631$	−2.22784e32	−1.40458	−0.702288	+	0.711892i	$0.747838\pi$
$632$	2.65610e31	0.164436
$633$	−2.28517e32	−1.38923
$634$	−5.53840e31	−0.330642
$635$	−2.43790e32	−1.42929
$636$	2.29605e32	1.32198
$637$	0	0
$638$	2.08584e31	0.115836
$639$	4.33738e31	0.236574
$640$	3.82581e31	0.204953
$641$	1.38602e32	0.729295	0.364648	−	0.931146i	$-0.381189\pi$
$641$	1.38602e32	0.729295	0.364648	+	0.931146i	$0.381189\pi$
$642$	9.40714e31	0.486188
$643$	−3.71401e31	−0.188546	−0.0942729	−	0.995546i	$-0.530053\pi$
$643$	−3.71401e31	−0.188546	−0.0942729	+	0.995546i	$0.530053\pi$
$644$	0	0
$645$	8.92913e30	0.0437393
$646$	5.86067e32	2.82016
$647$	3.77554e32	1.78476	0.892379	−	0.451286i	$-0.149035\pi$
$647$	3.77554e32	1.78476	0.892379	+	0.451286i	$0.149035\pi$
$648$	−2.85076e31	−0.132388
$649$	2.56896e29	0.00117204
$650$	1.27338e31	0.0570760
$651$	0	0
$652$	−2.02210e32	−0.874893
$653$	−8.58042e31	−0.364760	−0.182380	−	0.983228i	$-0.558380\pi$
$653$	−8.58042e31	−0.364760	−0.182380	+	0.983228i	$0.558380\pi$
$654$	−8.70816e31	−0.363733
$655$	9.14906e31	0.375493
$656$	1.05576e32	0.425766
$657$	1.98290e32	0.785777
$658$	0	0
$659$	1.46687e32	0.561319	0.280660	−	0.959807i	$-0.409447\pi$
$659$	1.46687e32	0.561319	0.280660	+	0.959807i	$0.409447\pi$
$660$	7.96891e31	0.299670
$661$	−2.02066e32	−0.746752	−0.373376	−	0.927680i	$-0.621800\pi$
$661$	−2.02066e32	−0.746752	−0.373376	+	0.927680i	$0.621800\pi$
$662$	−6.53331e32	−2.37283
$663$	3.26672e32	1.16602
$664$	2.00239e31	0.0702450
$665$	0	0
$666$	2.82379e32	0.956927
$667$	7.38823e31	0.246090
$668$	−1.37358e32	−0.449701
$669$	5.39243e32	1.73534
$670$	6.23171e32	1.97127
$671$	−7.24664e31	−0.225334
$672$	0	0
$673$	5.34692e32	1.60668	0.803341	−	0.595519i	$-0.203053\pi$
$673$	5.34692e32	1.60668	0.803341	+	0.595519i	$0.203053\pi$
$674$	6.59237e32	1.94739
$675$	−1.28256e31	−0.0372463
$676$	−2.23437e32	−0.637924
$677$	−1.10049e32	−0.308899	−0.154449	−	0.988001i	$-0.549360\pi$
$677$	−1.10049e32	−0.308899	−0.154449	+	0.988001i	$0.549360\pi$
$678$	5.48422e32	1.51347
$679$	0	0
$680$	6.38515e31	0.170341
$681$	−8.34995e32	−2.19024
$682$	1.38119e32	0.356233
$683$	−2.97297e32	−0.753967	−0.376983	−	0.926220i	$-0.623039\pi$
$683$	−2.97297e32	−0.753967	−0.376983	+	0.926220i	$0.623039\pi$
$684$	2.73756e32	0.682683
$685$	−4.66337e32	−1.14356
$686$	0	0
$687$	−2.48547e32	−0.589394
$688$	−1.64908e31	−0.0384568
$689$	−2.74149e32	−0.628733
$690$	5.88088e32	1.32641
$691$	7.18838e32	1.59453	0.797266	−	0.603628i	$-0.206279\pi$
$691$	7.18838e32	1.59453	0.797266	+	0.603628i	$0.206279\pi$
$692$	−8.06062e32	−1.75852
$693$	0	0
$694$	−5.84723e32	−1.23400
$695$	−5.22399e31	−0.108437
$696$	2.07583e31	0.0423824
$697$	3.28039e32	0.658793
$698$	8.92072e31	0.176223
$699$	−8.51274e32	−1.65418
$700$	0	0
$701$	−1.02832e33	−1.93362	−0.966810	−	0.255497i	$-0.917761\pi$
$701$	−1.02832e33	−1.93362	−0.966810	+	0.255497i	$0.917761\pi$
$702$	−2.09513e32	−0.387557
$703$	−7.71990e32	−1.40484
$704$	−1.25123e32	−0.224002
$705$	3.54171e32	0.623790
$706$	1.03287e32	0.178975
$707$	0	0
$708$	−3.06353e30	−0.00513854
$709$	−2.50942e32	−0.414134	−0.207067	−	0.978327i	$-0.566392\pi$
$709$	−2.50942e32	−0.414134	−0.207067	+	0.978327i	$0.566392\pi$
$710$	3.22528e32	0.523717
$711$	5.80796e32	0.927947
$712$	−1.18991e31	−0.0187066
$713$	4.89231e32	0.756805
$714$	0	0
$715$	−9.51492e31	−0.142523
$716$	−7.75346e31	−0.114287
$717$	−4.27071e32	−0.619483
$718$	1.34209e33	1.91580
$719$	−7.09247e32	−0.996358	−0.498179	−	0.867074i	$-0.665998\pi$
$719$	−7.09247e32	−0.996358	−0.498179	+	0.867074i	$0.665998\pi$
$720$	4.49355e32	0.621249
$721$	0	0
$722$	−5.23757e32	−0.701378
$723$	−5.61891e32	−0.740562
$724$	4.00417e32	0.519420
$725$	1.81809e31	0.0232128
$726$	−1.29776e33	−1.63088
$727$	−4.63712e32	−0.573591	−0.286795	−	0.957992i	$-0.592590\pi$
$727$	−4.63712e32	−0.573591	−0.286795	+	0.957992i	$0.592590\pi$
$728$	0	0
$729$	−9.21300e31	−0.110417
$730$	1.47449e33	1.73952
$731$	−5.12391e31	−0.0595047
$732$	8.64174e32	0.987924
$733$	1.54780e33	1.74188	0.870941	−	0.491387i	$-0.163510\pi$
$733$	1.54780e33	1.74188	0.870941	+	0.491387i	$0.163510\pi$
$734$	6.53317e32	0.723801
$735$	0	0
$736$	−1.00801e33	−1.08235
$737$	3.72455e32	0.393730
$738$	3.19247e32	0.332260
$739$	−1.49249e33	−1.52932	−0.764662	−	0.644431i	$-0.777094\pi$
$739$	−1.49249e33	−1.52932	−0.764662	+	0.644431i	$0.777094\pi$
$740$	1.00783e33	1.01677
$741$	−8.69144e32	−0.863341
$742$	0	0
$743$	1.19934e32	0.115497	0.0577487	−	0.998331i	$-0.481608\pi$
$743$	1.19934e32	0.115497	0.0577487	+	0.998331i	$0.481608\pi$
$744$	1.37456e32	0.130340
$745$	−1.16197e32	−0.108492
$746$	−4.15852e32	−0.382334
$747$	4.37852e32	0.396406
$748$	−4.57290e32	−0.407683
$749$	0	0
$750$	2.09868e33	1.81444
$751$	1.42812e33	1.21592	0.607959	−	0.793969i	$-0.291989\pi$
$751$	1.42812e33	1.21592	0.607959	+	0.793969i	$0.291989\pi$
$752$	−6.54101e32	−0.548453
$753$	8.71877e31	0.0719967
$754$	2.96996e32	0.241535
$755$	−3.95352e32	−0.316661
$756$	0	0
$757$	−1.56208e33	−1.21367	−0.606835	−	0.794828i	$-0.707561\pi$
$757$	−1.56208e33	−1.21367	−0.606835	+	0.794828i	$0.707561\pi$
$758$	−2.65967e33	−2.03531
$759$	3.51487e32	0.264929
$760$	−1.69884e32	−0.126123
$761$	−1.92115e33	−1.40488	−0.702439	−	0.711744i	$-0.747906\pi$
$761$	−1.92115e33	−1.40488	−0.702439	+	0.711744i	$0.747906\pi$
$762$	3.62020e33	2.60765
$763$	0	0
$764$	2.40114e33	1.67820
$765$	1.39621e33	0.961267
$766$	1.19119e33	0.807886
$767$	3.65787e30	0.00244389
$768$	−2.18475e33	−1.43797
$769$	−1.22615e33	−0.795044	−0.397522	−	0.917593i	$-0.630130\pi$
$769$	−1.22615e33	−0.795044	−0.397522	+	0.917593i	$0.630130\pi$
$770$	0	0
$771$	−1.53438e33	−0.965621
$772$	−9.92455e32	−0.615335
$773$	8.43914e32	0.515507	0.257753	−	0.966211i	$-0.417018\pi$
$773$	8.43914e32	0.515507	0.257753	+	0.966211i	$0.417018\pi$
$774$	−4.98658e31	−0.0300111
$775$	1.20390e32	0.0713870
$776$	2.95074e32	0.172394
$777$	0	0
$778$	4.28177e33	2.42861
$779$	−8.72782e32	−0.487781
$780$	1.13467e33	0.624858
$781$	1.92768e32	0.104604
$782$	−3.37470e33	−1.80450
$783$	−2.99137e32	−0.157620
$784$	0	0
$785$	1.57687e33	0.806856
$786$	−1.35860e33	−0.685066
$787$	−1.37027e33	−0.680919	−0.340460	−	0.940259i	$-0.610583\pi$
$787$	−1.37027e33	−0.680919	−0.340460	+	0.940259i	$0.610583\pi$
$788$	−3.01931e33	−1.47862
$789$	−7.82797e32	−0.377801
$790$	4.31881e33	2.05425
$791$	0	0
$792$	3.71398e31	0.0171593
$793$	−1.03183e33	−0.469857
$794$	6.72586e31	0.0301865
$795$	−3.11564e33	−1.37824
$796$	9.72536e32	0.424039
$797$	−1.57462e33	−0.676714	−0.338357	−	0.941018i	$-0.609871\pi$
$797$	−1.57462e33	−0.676714	−0.338357	+	0.941018i	$0.609871\pi$
$798$	0	0
$799$	−2.03238e33	−0.848628
$800$	−2.48049e32	−0.102095
$801$	−2.60192e32	−0.105565
$802$	−1.55481e33	−0.621832
$803$	8.81269e32	0.347440
$804$	−4.44159e33	−1.72621
$805$	0	0
$806$	1.96664e33	0.742799
$807$	2.22215e33	0.827423
$808$	−3.53567e32	−0.129790
$809$	−2.56942e33	−0.929882	−0.464941	−	0.885342i	$-0.653924\pi$
$809$	−2.56942e33	−0.929882	−0.464941	+	0.885342i	$0.653924\pi$
$810$	−4.63533e33	−1.65388
$811$	−1.25770e33	−0.442423	−0.221212	−	0.975226i	$-0.571001\pi$
$811$	−1.25770e33	−0.442423	−0.221212	+	0.975226i	$0.571001\pi$
$812$	0	0
$813$	2.01234e33	0.688112
$814$	1.25499e33	0.423116
$815$	2.74390e33	0.912129
$816$	−6.85652e33	−2.24733
$817$	1.36327e32	0.0440583
$818$	2.01023e33	0.640593
$819$	0	0
$820$	1.13942e33	0.353040
$821$	−2.38117e32	−0.0727519	−0.0363759	−	0.999338i	$-0.511581\pi$
$821$	−2.38117e32	−0.0727519	−0.0363759	+	0.999338i	$0.511581\pi$
$822$	6.92493e33	2.08636
$823$	5.82453e33	1.73047	0.865233	−	0.501370i	$-0.167170\pi$
$823$	5.82453e33	1.73047	0.865233	+	0.501370i	$0.167170\pi$
$824$	−3.66954e31	−0.0107510
$825$	8.64937e31	0.0249899
$826$	0	0
$827$	−3.61128e33	−1.01472	−0.507362	−	0.861733i	$-0.669379\pi$
$827$	−3.61128e33	−1.01472	−0.507362	+	0.861733i	$0.669379\pi$
$828$	−1.57635e33	−0.436821
$829$	−6.27935e33	−1.71608	−0.858040	−	0.513584i	$-0.828318\pi$
$829$	−6.27935e33	−1.71608	−0.858040	+	0.513584i	$0.828318\pi$
$830$	3.25588e33	0.877546
$831$	−5.03467e33	−1.33832
$832$	−1.78159e33	−0.467078
$833$	0	0
$834$	7.75743e32	0.197837
$835$	1.86389e33	0.468841
$836$	1.21667e33	0.301856
$837$	−1.98081e33	−0.484731
$838$	6.85832e33	1.65543
$839$	−7.51696e32	−0.178970	−0.0894849	−	0.995988i	$-0.528522\pi$
$839$	−7.51696e32	−0.178970	−0.0894849	+	0.995988i	$0.528522\pi$
$840$	0	0
$841$	−3.89268e33	−0.901767
$842$	2.39864e33	0.548120
$843$	−4.82269e33	−1.08711
$844$	4.55478e33	1.01281
$845$	3.03195e33	0.665074
$846$	−1.97791e33	−0.428003
$847$	0	0
$848$	5.75412e33	1.21179
$849$	−8.35275e33	−1.73537
$850$	−8.30443e32	−0.170213
$851$	4.44528e33	0.898896
$852$	−2.29879e33	−0.458610
$853$	9.11290e33	1.79367	0.896836	−	0.442364i	$-0.145860\pi$
$853$	9.11290e33	1.79367	0.896836	+	0.442364i	$0.145860\pi$
$854$	0	0
$855$	−3.71476e33	−0.711738
$856$	1.56478e32	0.0295805
$857$	−6.17423e33	−1.15160	−0.575802	−	0.817589i	$-0.695310\pi$
$857$	−6.17423e33	−1.15160	−0.575802	+	0.817589i	$0.695310\pi$
$858$	1.41293e33	0.260026
$859$	1.86175e33	0.338065	0.169033	−	0.985610i	$-0.445936\pi$
$859$	1.86175e33	0.338065	0.169033	+	0.985610i	$0.445936\pi$
$860$	−1.77975e32	−0.0318880
$861$	0	0
$862$	−7.70552e33	−1.34421
$863$	−5.22144e33	−0.898806	−0.449403	−	0.893329i	$-0.648363\pi$
$863$	−5.22144e33	−0.898806	−0.449403	+	0.893329i	$0.648363\pi$
$864$	4.08125e33	0.693242
$865$	1.09379e34	1.83337
$866$	−1.07821e34	−1.78340
$867$	−1.35479e34	−2.21132
$868$	0	0
$869$	2.58126e33	0.410302
$870$	3.37529e33	0.529469
$871$	5.30328e33	0.820986
$872$	−1.44852e32	−0.0221301
$873$	6.45224e33	0.972852
$874$	8.97874e33	1.33608
$875$	0	0
$876$	−1.05093e34	−1.52327
$877$	−6.73800e32	−0.0963908	−0.0481954	−	0.998838i	$-0.515347\pi$
$877$	−6.73800e32	−0.0963908	−0.0481954	+	0.998838i	$0.515347\pi$
$878$	8.48127e32	0.119750
$879$	−4.67328e33	−0.651253
$880$	1.99709e33	0.274692
$881$	−1.36978e34	−1.85963	−0.929815	−	0.368028i	$-0.880033\pi$
$881$	−1.36978e34	−1.85963	−0.929815	+	0.368028i	$0.880033\pi$
$882$	0	0
$883$	1.49590e33	0.197859	0.0989294	−	0.995094i	$-0.468458\pi$
$883$	1.49590e33	0.197859	0.0989294	+	0.995094i	$0.468458\pi$
$884$	−6.51121e33	−0.850082
$885$	4.15708e31	0.00535724
$886$	3.26378e33	0.415177
$887$	6.44904e33	0.809792	0.404896	−	0.914363i	$-0.367308\pi$
$887$	6.44904e33	0.809792	0.404896	+	0.914363i	$0.367308\pi$
$888$	1.24897e33	0.154811
$889$	0	0
$890$	−1.93479e33	−0.233695
$891$	−2.77043e33	−0.330334
$892$	−1.07482e34	−1.26514
$893$	5.40736e33	0.628339
$894$	1.72548e33	0.197938
$895$	1.05211e33	0.119151
$896$	0	0
$897$	5.00472e33	0.552417
$898$	1.51254e34	1.64827
$899$	2.80791e33	0.302097
$900$	−3.87907e32	−0.0412039
$901$	1.78789e34	1.87502
$902$	1.41884e33	0.146913
$903$	0	0
$904$	9.12246e32	0.0920820
$905$	−5.43349e33	−0.541527
$906$	5.87083e33	0.577731
$907$	6.42282e33	0.624083	0.312041	−	0.950069i	$-0.398987\pi$
$907$	6.42282e33	0.624083	0.312041	+	0.950069i	$0.398987\pi$
$908$	1.66431e34	1.59679
$909$	−7.73126e33	−0.732430
$910$	0	0
$911$	−1.48932e34	−1.37571	−0.687855	−	0.725848i	$-0.741447\pi$
$911$	−1.48932e34	−1.37571	−0.687855	+	0.725848i	$0.741447\pi$
$912$	1.82425e34	1.66396
$913$	1.94596e33	0.175275
$914$	−8.59859e33	−0.764797
$915$	−1.17265e34	−1.02997
$916$	4.95402e33	0.429695
$917$	0	0
$918$	1.36636e34	1.15578
$919$	3.10701e33	0.259546	0.129773	−	0.991544i	$-0.458575\pi$
$919$	3.10701e33	0.259546	0.129773	+	0.991544i	$0.458575\pi$
$920$	9.78226e32	0.0807011
$921$	−1.82735e34	−1.48880
$922$	1.91330e34	1.53950
$923$	2.74476e33	0.218115
$924$	0	0
$925$	1.09389e33	0.0847900
$926$	3.08285e34	2.36007
$927$	−8.02400e32	−0.0606700
$928$	−5.78538e33	−0.432046
$929$	−1.72846e34	−1.27490	−0.637452	−	0.770490i	$-0.720012\pi$
$929$	−1.72846e34	−1.27490	−0.637452	+	0.770490i	$0.720012\pi$
$930$	2.23504e34	1.62829
$931$	0	0
$932$	1.69676e34	1.20597
$933$	−3.49473e32	−0.0245343
$934$	−1.15624e34	−0.801790
$935$	6.20523e33	0.425035
$936$	5.28822e32	0.0357797
$937$	1.61548e34	1.07969	0.539843	−	0.841766i	$-0.318484\pi$
$937$	1.61548e34	1.07969	0.539843	+	0.841766i	$0.318484\pi$
$938$	0	0
$939$	−4.40980e33	−0.287584
$940$	−7.05932e33	−0.454771
$941$	−7.69275e33	−0.489554	−0.244777	−	0.969579i	$-0.578715\pi$
$941$	−7.69275e33	−0.489554	−0.244777	+	0.969579i	$0.578715\pi$
$942$	−2.34160e34	−1.47206
$943$	5.02567e33	0.312111
$944$	−7.67751e31	−0.00471023
$945$	0	0
$946$	−2.21620e32	−0.0132697
$947$	−2.94332e34	−1.74106	−0.870528	−	0.492119i	$-0.836222\pi$
$947$	−2.94332e34	−1.74106	−0.870528	+	0.492119i	$0.836222\pi$
$948$	−3.07819e34	−1.79887
$949$	1.25481e34	0.724465
$950$	2.20948e33	0.126029
$951$	−5.35651e33	−0.301860
$952$	0	0
$953$	1.97292e34	1.08528	0.542641	−	0.839965i	$-0.317425\pi$
$953$	1.97292e34	1.08528	0.542641	+	0.839965i	$0.317425\pi$
$954$	1.73997e34	0.945659
$955$	−3.25825e34	−1.74963
$956$	8.51236e33	0.451632
$957$	2.01734e33	0.105753
$958$	2.73973e34	1.41907
$959$	0	0
$960$	−2.02474e34	−1.02388
$961$	−1.42003e33	−0.0709542
$962$	1.78694e34	0.882261
$963$	3.42163e33	0.166929
$964$	1.11996e34	0.539904
$965$	1.34672e34	0.641524
$966$	0	0
$967$	−2.03266e34	−0.945496	−0.472748	−	0.881198i	$-0.656738\pi$
$967$	−2.03266e34	−0.945496	−0.472748	+	0.881198i	$0.656738\pi$
$968$	−2.15869e33	−0.0992255
$969$	5.66820e34	2.57467
$970$	4.79790e34	2.15365
$971$	−3.40470e34	−1.51028	−0.755141	−	0.655563i	$-0.772431\pi$
$971$	−3.40470e34	−1.51028	−0.755141	+	0.655563i	$0.772431\pi$
$972$	2.24494e34	0.984106
$973$	0	0
$974$	−3.45150e33	−0.147768
$975$	1.23156e33	0.0521077
$976$	2.16570e34	0.905579
$977$	−3.68167e32	−0.0152145	−0.00760725	−	0.999971i	$-0.502421\pi$
$977$	−3.68167e32	−0.0152145	−0.00760725	+	0.999971i	$0.502421\pi$
$978$	−4.07459e34	−1.66413
$979$	−1.15638e33	−0.0466767
$980$	0	0
$981$	−3.16740e33	−0.124885
$982$	2.87225e34	1.11928
$983$	8.23724e33	0.317261	0.158630	−	0.987338i	$-0.449292\pi$
$983$	8.23724e33	0.317261	0.158630	+	0.987338i	$0.449292\pi$
$984$	1.41203e33	0.0537529
$985$	4.09707e34	1.54155
$986$	−1.93689e34	−0.720310
$987$	0	0
$988$	1.73238e34	0.629415
$989$	−7.85000e32	−0.0281911
$990$	6.03891e33	0.214365
$991$	2.70349e33	0.0948590	0.0474295	−	0.998875i	$-0.484897\pi$
$991$	2.70349e33	0.0948590	0.0474295	+	0.998875i	$0.484897\pi$
$992$	−3.83094e34	−1.32868
$993$	−6.31875e34	−2.16628
$994$	0	0
$995$	−1.31969e34	−0.442086
$996$	−2.32059e34	−0.768452
$997$	4.64692e33	0.152115	0.0760573	−	0.997103i	$-0.475767\pi$
$997$	4.64692e33	0.152115	0.0760573	+	0.997103i	$0.475767\pi$
$998$	−7.14561e34	−2.31227
$999$	−1.79982e34	−0.575740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.24.a.b.1.1		2
7.6	odd	2		1.24.a.a.1.1	✓	2
21.20	even	2		9.24.a.b.1.2		2
28.27	even	2		16.24.a.b.1.1		2
35.13	even	4		25.24.b.a.24.3		4
35.27	even	4		25.24.b.a.24.2		4
35.34	odd	2		25.24.a.a.1.2		2
56.13	odd	2		64.24.a.d.1.1		2
56.27	even	2		64.24.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.24.a.a.1.1	✓	2	7.6	odd	2
9.24.a.b.1.2		2	21.20	even	2
16.24.a.b.1.1		2	28.27	even	2
25.24.a.a.1.2		2	35.34	odd	2
25.24.b.a.24.2		4	35.27	even	4
25.24.b.a.24.3		4	35.13	even	4
49.24.a.b.1.1		2	1.1	even	1	trivial
64.24.a.d.1.1		2	56.13	odd	2
64.24.a.g.1.2		2	56.27	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-4016.35 q^{2} -388445. q^{3} +7.74247e6 q^{4} -1.05062e8 q^{5} +1.56013e9 q^{6} +2.59512e9 q^{8} +5.67462e10 q^{9} +O(q^{10})\)	\(q-4016.35 q^{2} -388445. q^{3} +7.74247e6 q^{4} -1.05062e8 q^{5} +1.56013e9 q^{6} +2.59512e9 q^{8} +5.67462e10 q^{9} +4.21966e11 q^{10} +2.52200e11 q^{11} -3.00752e12 q^{12} +3.59099e12 q^{13} +4.08108e13 q^{15} -7.53715e13 q^{16} -2.34190e14 q^{17} -2.27913e14 q^{18} +6.23086e14 q^{19} -8.13439e14 q^{20} -1.01292e15 q^{22} -3.58786e15 q^{23} -1.00806e15 q^{24} -8.82898e14 q^{25} -1.44227e16 q^{26} +1.45267e16 q^{27} -2.05923e16 q^{29} -1.63911e17 q^{30} -1.36357e17 q^{31} +2.80949e17 q^{32} -9.79656e16 q^{33} +9.40588e17 q^{34} +4.39356e17 q^{36} -1.23898e18 q^{37} -2.50253e18 q^{38} -1.39490e18 q^{39} -2.72649e17 q^{40} -1.40074e18 q^{41} +2.18793e17 q^{43} +1.95265e18 q^{44} -5.96187e18 q^{45} +1.44101e19 q^{46} +8.67836e18 q^{47} +2.92777e19 q^{48} +3.54603e18 q^{50} +9.09698e19 q^{51} +2.78032e19 q^{52} -7.63436e19 q^{53} -5.83441e19 q^{54} -2.64966e19 q^{55} -2.42034e20 q^{57} +8.27059e19 q^{58} +1.01862e18 q^{59} +3.15976e20 q^{60} -2.87337e20 q^{61} +5.47658e20 q^{62} -4.96127e20 q^{64} -3.77277e20 q^{65} +3.93464e20 q^{66} +1.47683e21 q^{67} -1.81321e21 q^{68} +1.39369e21 q^{69} +7.64346e20 q^{71} +1.47263e20 q^{72} +3.49433e21 q^{73} +4.97617e21 q^{74} +3.42957e20 q^{75} +4.82422e21 q^{76} +5.60242e21 q^{78} +1.02350e22 q^{79} +7.91868e21 q^{80} -1.09851e22 q^{81} +5.62587e21 q^{82} +7.71597e21 q^{83} +2.46044e22 q^{85} -8.78750e20 q^{86} +7.99897e21 q^{87} +6.54489e20 q^{88} -4.58518e21 q^{89} +2.39450e22 q^{90} -2.77789e22 q^{92} +5.29672e22 q^{93} -3.48553e22 q^{94} -6.54627e22 q^{95} -1.09133e23 q^{96} +1.13703e23 q^{97} +1.43114e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 1080 q^{2} - 339480 q^{3} + 25326656 q^{4} - 73069020 q^{5} + 1809673056 q^{6} + 49459023360 q^{8} - 34999394166 q^{9}+O(q^{10}) \) 2 * q + 1080 * q^2 - 339480 * q^3 + 25326656 * q^4 - 73069020 * q^5 + 1809673056 * q^6 + 49459023360 * q^8 - 34999394166 * q^9	\( 2 q + 1080 q^{2} - 339480 q^{3} + 25326656 q^{4} - 73069020 q^{5} + 1809673056 q^{6} + 49459023360 q^{8} - 34999394166 q^{9} + 585013636080 q^{10} + 856801968264 q^{11} - 2146514952960 q^{12} - 4376109322060 q^{13} + 42377338985040 q^{15} + 15956586401792 q^{16} - 254028147597540 q^{17} - 695480683916520 q^{18} - 4260600979960 q^{19} - 250868387468160 q^{20} + 20\!\cdots\!60 q^{22}+ \cdots - 41\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 1080 * q^2 - 339480 * q^3 + 25326656 * q^4 - 73069020 * q^5 + 1809673056 * q^6 + 49459023360 * q^8 - 34999394166 * q^9 + 585013636080 * q^10 + 856801968264 * q^11 - 2146514952960 * q^12 - 4376109322060 * q^13 + 42377338985040 * q^15 + 15956586401792 * q^16 - 254028147597540 * q^17 - 695480683916520 * q^18 - 4260600979960 * q^19 - 250868387468160 * q^20 + 2068343882177760 * q^22 - 8144713079008560 * q^23 + 1286622315141120 * q^24 - 11780274628800850 * q^25 - 55025854658735184 * q^26 + 5424634982716560 * q^27 + 20818433601623340 * q^29 - 155926924188644160 * q^30 - 137714017177000384 * q^31 + 353265663781601280 * q^32 - 68361366766001760 * q^33 + 839483655961325328 * q^34 - 1173916300077574848 * q^36 - 897721264408967780 * q^37 - 5699708971590961440 * q^38 - 1785011473665029232 * q^39 + 1226668524414336000 * q^40 + 2294435477168314956 * q^41 - 1750760768619855800 * q^43 + 12584088840033038592 * q^44 - 8897092690294206540 * q^45 - 8813206018050221376 * q^46 - 15759744217656780960 * q^47 + 33749519399576616960 * q^48 - 51990825483785316600 * q^50 + 89998362845078292144 * q^51 - 112291883783912022400 * q^52 - 140287253401646796420 * q^53 - 104731223417039799360 * q^54 - 7153550955060182640 * q^55 - 272752401448627175520 * q^57 + 293749486923568689360 * q^58 - 280872989971340771880 * q^59 + 343522601114937592320 * q^60 + 180452892516502223636 * q^61 + 540743475843874103040 * q^62 - 893690254469352914944 * q^64 - 632168834809440380760 * q^65 + 544338140913651883392 * q^66 + 1754233163431557625240 * q^67 - 2162050190142944330880 * q^68 + 1170560672172404223552 * q^69 + 3055033510194143328624 * q^71 - 4152294352103038548480 * q^72 + 8063408253877606149260 * q^73 + 6715344283148807757072 * q^74 - 190631089350520885800 * q^75 - 6207154294513080590080 * q^76 + 3614293948840808587200 * q^78 + 6244916814559639980640 * q^79 + 10840537585501794017280 * q^80 - 2793528580929833975598 * q^81 + 24457792891615712450640 * q^82 - 6875994082418498976120 * q^83 + 23969743087870314902520 * q^85 - 10916288812918999243296 * q^86 + 10026640653837674384880 * q^87 + 28988514668199273707520 * q^88 - 6395093086173070004820 * q^89 + 8986073954327865866160 * q^90 - 107907439017191756981760 * q^92 + 52900811441357852079360 * q^93 - 159400518006534931827072 * q^94 - 85533361066700858502000 * q^95 - 105592121669584394256384 * q^96 + 31147288846254030500540 * q^97 - 41158245132312135981912 * q^99

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