LMFDB - Embedded newform 98.11.b.c.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,11,Mod(97,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("98.97");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	98.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$62.2650107620$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 7168 x^{10} - 191104 x^{9} + 39872585 x^{8} - 837614684 x^{7} + 83400850488 x^{6} + \cdots + 16\!\cdots\!56 $ x^12 + 7168x^10 - 191104x^9 + 39872585x^8 - 837614684x^7 + 83400850488x^6 - 1089499860800x^5 + 117569881085905x^4 - 972128975671236x^3 + 70590565447335180x^2 + 627290085157877232x + 16876036055394640656
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{4}\cdot 7^{12} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.3
Root			$26.6851 + 46.2199i$ of defining polynomial
Character	$\chi$	$=$	98.97
Dual form			98.11.b.c.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.6274 q^{2} -118.013i q^{3} +512.000 q^{4} -37.1782i q^{5} +2670.32i q^{6} -11585.2 q^{8} +45122.0 q^{9} +O(q^{10})$	\(q-22.6274 q^{2} -118.013i q^{3} +512.000 q^{4} -37.1782i q^{5} +2670.32i q^{6} -11585.2 q^{8} +45122.0 q^{9} +841.247i q^{10} -134080. q^{11} -60422.4i q^{12} +182276. i q^{13} -4387.50 q^{15} +262144. q^{16} -1.61330e6i q^{17} -1.02100e6 q^{18} +1.62752e6i q^{19} -19035.3i q^{20} +3.03388e6 q^{22} -5.87288e6 q^{23} +1.36720e6i q^{24} +9.76424e6 q^{25} -4.12444e6i q^{26} -1.22935e7i q^{27} +4.34134e6 q^{29} +99277.7 q^{30} -2.71871e7i q^{31} -5.93164e6 q^{32} +1.58231e7i q^{33} +3.65047e7i q^{34} +2.31025e7 q^{36} +3.97532e7 q^{37} -3.68265e7i q^{38} +2.15109e7 q^{39} +430719. i q^{40} +1.69868e8i q^{41} +1.87794e8 q^{43} -6.86490e7 q^{44} -1.67756e6i q^{45} +1.32888e8 q^{46} -2.00807e7i q^{47} -3.09363e7i q^{48} -2.20940e8 q^{50} -1.90389e8 q^{51} +9.33255e7i q^{52} -1.79045e8 q^{53} +2.78170e8i q^{54} +4.98486e6i q^{55} +1.92067e8 q^{57} -9.82332e7 q^{58} -4.79819e8i q^{59} -2.24640e6 q^{60} -6.31025e8i q^{61} +6.15173e8i q^{62} +1.34218e8 q^{64} +6.77671e6 q^{65} -3.58036e8i q^{66} -1.02259e9 q^{67} -8.26007e8i q^{68} +6.93074e8i q^{69} -1.95589e9 q^{71} -5.22750e8 q^{72} -2.35872e9i q^{73} -8.99513e8 q^{74} -1.15230e9i q^{75} +8.33288e8i q^{76} -4.86736e8 q^{78} -5.73586e9 q^{79} -9.74605e6i q^{80} +1.21363e9 q^{81} -3.84367e9i q^{82} -5.54809e9i q^{83} -5.99795e7 q^{85} -4.24929e9 q^{86} -5.12332e8i q^{87} +1.55335e9 q^{88} -7.86098e9i q^{89} +3.79588e7i q^{90} -3.00692e9 q^{92} -3.20842e9 q^{93} +4.54375e8i q^{94} +6.05082e7 q^{95} +7.00008e8i q^{96} +1.40393e10i q^{97} -6.04996e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6144 q^{4} + 91056 q^{9}+O(q^{10}) $ 12 * q + 6144 * q^4 + 91056 * q^9	$ 12 q + 6144 q^{4} + 91056 q^{9} + 222420 q^{11} + 1065684 q^{15} + 3145728 q^{16} - 1430784 q^{18} - 1922688 q^{22} - 1706148 q^{23} - 33811608 q^{25} + 60157248 q^{29} + 74818944 q^{30} + 46620672 q^{36} + 15333012 q^{37} + 143256168 q^{39} + 1066803336 q^{43} + 113879040 q^{44} + 336490368 q^{46} + 1764094464 q^{50} + 638862780 q^{51} + 1200045108 q^{53} + 3357095652 q^{57} + 589196544 q^{58} + 545630208 q^{60} + 1610612736 q^{64} - 3072256152 q^{65} + 3180116652 q^{67} - 7739561160 q^{71} - 732561408 q^{72} - 2084616192 q^{74} - 8450806272 q^{78} - 4621124484 q^{79} - 15124682844 q^{81} - 39581743596 q^{85} + 9848173824 q^{86} - 984416256 q^{88} - 873547776 q^{92} + 15672528540 q^{93} - 58048533180 q^{95} - 13213951200 q^{99}+O(q^{100}) $ 12 * q + 6144 * q^4 + 91056 * q^9 + 222420 * q^11 + 1065684 * q^15 + 3145728 * q^16 - 1430784 * q^18 - 1922688 * q^22 - 1706148 * q^23 - 33811608 * q^25 + 60157248 * q^29 + 74818944 * q^30 + 46620672 * q^36 + 15333012 * q^37 + 143256168 * q^39 + 1066803336 * q^43 + 113879040 * q^44 + 336490368 * q^46 + 1764094464 * q^50 + 638862780 * q^51 + 1200045108 * q^53 + 3357095652 * q^57 + 589196544 * q^58 + 545630208 * q^60 + 1610612736 * q^64 - 3072256152 * q^65 + 3180116652 * q^67 - 7739561160 * q^71 - 732561408 * q^72 - 2084616192 * q^74 - 8450806272 * q^78 - 4621124484 * q^79 - 15124682844 * q^81 - 39581743596 * q^85 + 9848173824 * q^86 - 984416256 * q^88 - 873547776 * q^92 + 15672528540 * q^93 - 58048533180 * q^95 - 13213951200 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−22.6274	−0.707107
$2$	−22.6274	−0.707107
$3$	− 118.013i	− 0.485648i	−0.970070	−	0.242824i	$-0.921926\pi$
$3$	− 118.013i	− 0.485648i	0.970070	−	0.242824i	$-0.0780738\pi$
$4$	512.000	0.500000
$5$	− 37.1782i	− 0.0118970i	−0.999982	−	0.00594852i	$-0.998107\pi$
$5$	− 37.1782i	− 0.0118970i	0.999982	−	0.00594852i	$-0.00189348\pi$
$6$	2670.32i	0.343405i
$7$	0	0
$7$	0	0
$8$	−11585.2	−0.353553
$9$	45122.0	0.764146
$10$	841.247i	0.00841247i
$11$	−134080.	−0.832531	−0.416266	−	0.909243i	$-0.636661\pi$
$11$	−134080.	−0.832531	−0.416266	+	0.909243i	$0.636661\pi$
$12$	− 60422.4i	− 0.242824i
$13$	182276.i	0.490923i	0.969406	+	0.245462i	$0.0789396\pi$
$13$	182276.i	0.490923i	−0.969406	+	0.245462i	$0.921060\pi$
$14$	0	0
$15$	−4387.50	−0.00577777
$16$	262144.	0.250000
$17$	− 1.61330e6i	− 1.13624i	−0.822946	−	0.568119i	$-0.807671\pi$
$17$	− 1.61330e6i	− 1.13624i	0.822946	−	0.568119i	$-0.192329\pi$
$18$	−1.02100e6	−0.540333
$19$	1.62752e6i	0.657290i	0.944453	+	0.328645i	$0.106592\pi$
$19$	1.62752e6i	0.657290i	−0.944453	+	0.328645i	$0.893408\pi$
$20$	− 19035.3i	− 0.00594852i
$21$	0	0
$22$	3.03388e6	0.588688
$23$	−5.87288e6	−0.912457	−0.456228	−	0.889863i	$-0.650800\pi$
$23$	−5.87288e6	−0.912457	−0.456228	+	0.889863i	$0.650800\pi$
$24$	1.36720e6i	0.171703i
$25$	9.76424e6	0.999858
$26$	− 4.12444e6i	− 0.347135i
$27$	− 1.22935e7i	− 0.856754i
$28$	0	0
$29$	4.34134e6	0.211657	0.105829	−	0.994384i	$-0.466250\pi$
$29$	4.34134e6	0.211657	0.105829	+	0.994384i	$0.466250\pi$
$30$	99277.7	0.00408550
$31$	− 2.71871e7i	− 0.949629i	−0.880086	−	0.474815i	$-0.842515\pi$
$31$	− 2.71871e7i	− 0.949629i	0.880086	−	0.474815i	$-0.157485\pi$
$32$	−5.93164e6	−0.176777
$33$	1.58231e7i	0.404317i
$34$	3.65047e7i	0.803442i
$35$	0	0
$36$	2.31025e7	0.382073
$37$	3.97532e7	0.573276	0.286638	−	0.958039i	$-0.407462\pi$
$37$	3.97532e7	0.573276	0.286638	+	0.958039i	$0.407462\pi$
$38$	− 3.68265e7i	− 0.464775i
$39$	2.15109e7	0.238416
$40$	430719.i	0.00420624i
$41$	1.69868e8i	1.46619i	0.680124	+	0.733097i	$0.261926\pi$
$41$	1.69868e8i	1.46619i	−0.680124	+	0.733097i	$0.738074\pi$
$42$	0	0
$43$	1.87794e8	1.27744	0.638719	−	0.769440i	$-0.279465\pi$
$43$	1.87794e8	1.27744	0.638719	+	0.769440i	$0.279465\pi$
$44$	−6.86490e7	−0.416266
$45$	− 1.67756e6i	− 0.00909107i
$46$	1.32888e8	0.645204
$47$	− 2.00807e7i	− 0.0875568i	−0.999041	−	0.0437784i	$-0.986060\pi$
$47$	− 2.00807e7i	− 0.0875568i	0.999041	−	0.0437784i	$-0.0139396\pi$
$48$	− 3.09363e7i	− 0.121412i
$49$	0	0
$50$	−2.20940e8	−0.707007
$51$	−1.90389e8	−0.551812
$52$	9.33255e7i	0.245462i
$53$	−1.79045e8	−0.428137	−0.214069	−	0.976819i	$-0.568672\pi$
$53$	−1.79045e8	−0.428137	−0.214069	+	0.976819i	$0.568672\pi$
$54$	2.78170e8i	0.605817i
$55$	4.98486e6i	0.00990465i
$56$	0	0
$57$	1.92067e8	0.319212
$58$	−9.82332e7	−0.149664
$59$	− 4.79819e8i	− 0.671147i	−0.942014	−	0.335574i	$-0.891070\pi$
$59$	− 4.79819e8i	− 0.671147i	0.942014	−	0.335574i	$-0.108930\pi$
$60$	−2.24640e6	−0.00288889
$61$	− 6.31025e8i	− 0.747132i	−0.927604	−	0.373566i	$-0.878135\pi$
$61$	− 6.31025e8i	− 0.747132i	0.927604	−	0.373566i	$-0.121865\pi$
$62$	6.15173e8i	0.671489i
$63$	0	0
$64$	1.34218e8	0.125000
$65$	6.77671e6	0.00584053
$66$	− 3.58036e8i	− 0.285895i
$67$	−1.02259e9	−0.757403	−0.378701	−	0.925519i	$-0.623629\pi$
$67$	−1.02259e9	−0.757403	−0.378701	+	0.925519i	$0.623629\pi$
$68$	− 8.26007e8i	− 0.568119i
$69$	6.93074e8i	0.443133i
$70$	0	0
$71$	−1.95589e9	−1.08406	−0.542028	−	0.840360i	$-0.682343\pi$
$71$	−1.95589e9	−1.08406	−0.542028	+	0.840360i	$0.682343\pi$
$72$	−5.22750e8	−0.270166
$73$	− 2.35872e9i	− 1.13779i	−0.822410	−	0.568895i	$-0.807371\pi$
$73$	− 2.35872e9i	− 1.13779i	0.822410	−	0.568895i	$-0.192629\pi$
$74$	−8.99513e8	−0.405367
$75$	− 1.15230e9i	− 0.485579i
$76$	8.33288e8i	0.328645i
$77$	0	0
$78$	−4.86736e8	−0.168586
$79$	−5.73586e9	−1.86407	−0.932036	−	0.362365i	$-0.881969\pi$
$79$	−5.73586e9	−1.86407	−0.932036	+	0.362365i	$0.881969\pi$
$80$	− 9.74605e6i	− 0.00297426i
$81$	1.21363e9	0.348065
$82$	− 3.84367e9i	− 1.03676i
$83$	− 5.54809e9i	− 1.40849i	−0.709958	−	0.704244i	$-0.751286\pi$
$83$	− 5.54809e9i	− 1.40849i	0.709958	−	0.704244i	$-0.248714\pi$
$84$	0	0
$85$	−5.99795e7	−0.0135179
$86$	−4.24929e9	−0.903284
$87$	− 5.12332e8i	− 0.102791i
$88$	1.55335e9	0.294344
$89$	− 7.86098e9i	− 1.40775i	−0.710322	−	0.703877i	$-0.751451\pi$
$89$	− 7.86098e9i	− 1.40775i	0.710322	−	0.703877i	$-0.248549\pi$
$90$	3.79588e7i	0.00642836i
$91$	0	0
$92$	−3.00692e9	−0.456228
$93$	−3.20842e9	−0.461186
$94$	4.54375e8i	0.0619120i
$95$	6.05082e7	0.00781981
$96$	7.00008e8i	0.0858513i
$97$	1.40393e10i	1.63488i	0.576014	+	0.817440i	$0.304607\pi$
$97$	1.40393e10i	1.63488i	−0.576014	+	0.817440i	$0.695393\pi$
$98$	0	0
$99$	−6.04996e9	−0.636175
$100$	4.99929e9	0.499929
$101$	− 1.62209e10i	− 1.54337i	−0.636008	−	0.771683i	$-0.719415\pi$
$101$	− 1.62209e10i	− 1.54337i	0.636008	−	0.771683i	$-0.280585\pi$
$102$	4.30801e9	0.390190
$103$	− 1.88735e10i	− 1.62805i	−0.580832	−	0.814023i	$-0.697273\pi$
$103$	− 1.88735e10i	− 1.62805i	0.580832	−	0.814023i	$-0.302727\pi$
$104$	− 2.11172e9i	− 0.173568i
$105$	0	0
$106$	4.05133e9	0.302739
$107$	−1.81113e10	−1.29131	−0.645654	−	0.763630i	$-0.723415\pi$
$107$	−1.81113e10	−1.29131	−0.645654	+	0.763630i	$0.723415\pi$
$108$	− 6.29426e9i	− 0.428377i
$109$	−2.95887e10	−1.92306	−0.961532	−	0.274693i	$-0.911424\pi$
$109$	−2.95887e10	−1.92306	−0.961532	+	0.274693i	$0.911424\pi$
$110$	− 1.12794e8i	− 0.00700365i
$111$	− 4.69138e9i	− 0.278411i
$112$	0	0
$113$	−1.26465e10	−0.686403	−0.343201	−	0.939262i	$-0.611511\pi$
$113$	−1.26465e10	−0.686403	−0.343201	+	0.939262i	$0.611511\pi$
$114$	−4.34599e9	−0.225717
$115$	2.18343e8i	0.0108555i
$116$	2.22276e9	0.105829
$117$	8.22469e9i	0.375137i
$118$	1.08571e10i	0.474573i
$119$	0	0
$120$	5.08302e7	0.00204275
$121$	−7.95998e9	−0.306892
$122$	1.42785e10i	0.528302i
$123$	2.00465e10	0.712055
$124$	− 1.39198e10i	− 0.474815i
$125$	− 7.26086e8i	− 0.0237924i
$126$	0	0
$127$	2.05694e10	0.622592	0.311296	−	0.950313i	$-0.399237\pi$
$127$	2.05694e10	0.622592	0.311296	+	0.950313i	$0.399237\pi$
$128$	−3.03700e9	−0.0883883
$129$	− 2.21620e10i	− 0.620385i
$130$	−1.53340e8	−0.00412988
$131$	6.06986e10i	1.57334i	0.617375	+	0.786669i	$0.288196\pi$
$131$	6.06986e10i	1.57334i	−0.617375	+	0.786669i	$0.711804\pi$
$132$	8.10143e9i	0.202159i
$133$	0	0
$134$	2.31385e10	0.535564
$135$	−4.57050e8	−0.0101928
$136$	1.86904e10i	0.401721i
$137$	−3.45463e7	−0.000715811 0	−0.000357906	−	1.00000i	$-0.500114\pi$
$137$	−3.45463e7	−0.000715811 0	−0.000357906		1.00000i	$0.500114\pi$
$138$	− 1.56825e10i	− 0.313342i
$139$	2.00016e10i	0.385470i	0.981251	+	0.192735i	$0.0617358\pi$
$139$	2.00016e10i	0.385470i	−0.981251	+	0.192735i	$0.938264\pi$
$140$	0	0
$141$	−2.36978e9	−0.0425218
$142$	4.42566e10	0.766543
$143$	− 2.44396e10i	− 0.408709i
$144$	1.18285e10	0.191036
$145$	− 1.61403e8i	− 0.00251810i
$146$	5.33718e10i	0.804539i
$147$	0	0
$148$	2.03537e10	0.286638
$149$	5.86513e10	0.798631	0.399315	−	0.916814i	$-0.369248\pi$
$149$	5.86513e10	0.798631	0.399315	+	0.916814i	$0.369248\pi$
$150$	2.60736e10i	0.343356i
$151$	−4.29912e10	−0.547639	−0.273820	−	0.961781i	$-0.588287\pi$
$151$	−4.29912e10	−0.547639	−0.273820	+	0.961781i	$0.588287\pi$
$152$	− 1.88552e10i	− 0.232387i
$153$	− 7.27952e10i	− 0.868252i
$154$	0	0
$155$	−1.01077e9	−0.0112978
$156$	1.10136e10	0.119208
$157$	− 2.56719e9i	− 0.0269128i	−0.999909	−	0.0134564i	$-0.995717\pi$
$157$	− 2.56719e9i	− 0.0269128i	0.999909	−	0.0134564i	$-0.00428343\pi$
$158$	1.29788e11	1.31810
$159$	2.11296e10i	0.207924i
$160$	2.20528e8i	0.00210312i
$161$	0	0
$162$	−2.74612e10	−0.246119
$163$	5.26228e10	0.457337	0.228668	−	0.973504i	$-0.426563\pi$
$163$	5.26228e10	0.457337	0.228668	+	0.973504i	$0.426563\pi$
$164$	8.69723e10i	0.733097i
$165$	5.88275e8	0.00481018
$166$	1.25539e11i	0.995951i
$167$	− 1.38652e11i	− 1.06744i	−0.845661	−	0.533720i	$-0.820794\pi$
$167$	− 1.38652e11i	− 1.06744i	0.845661	−	0.533720i	$-0.179206\pi$
$168$	0	0
$169$	1.04634e11	0.758994
$170$	1.35718e9	0.00955857
$171$	7.34369e10i	0.502266i
$172$	9.61506e10	0.638719
$173$	1.04828e11i	0.676465i	0.941063	+	0.338232i	$0.109829\pi$
$173$	1.04828e11i	0.676465i	−0.941063	+	0.338232i	$0.890171\pi$
$174$	1.15928e10i	0.0726842i
$175$	0	0
$176$	−3.51483e10	−0.208133
$177$	−5.66247e10	−0.325941
$178$	1.77874e11i	0.995432i
$179$	−2.97241e11	−1.61750	−0.808749	−	0.588155i	$-0.799855\pi$
$179$	−2.97241e11	−1.61750	−0.808749	+	0.588155i	$0.799855\pi$
$180$	− 8.58910e8i	− 0.00454553i
$181$	− 2.97932e11i	− 1.53364i	−0.641860	−	0.766822i	$-0.721837\pi$
$181$	− 2.97932e11i	− 1.53364i	0.641860	−	0.766822i	$-0.278163\pi$
$182$	0	0
$183$	−7.44689e10	−0.362843
$184$	6.80388e10	0.322602
$185$	− 1.47796e9i	− 0.00682029i
$186$	7.25982e10	0.326108
$187$	2.16311e11i	0.945954i
$188$	− 1.02813e10i	− 0.0437784i
$189$	0	0
$190$	−1.36914e9	−0.00552944
$191$	3.94414e11	1.55162	0.775811	−	0.630965i	$-0.217341\pi$
$191$	3.94414e11	1.55162	0.775811	+	0.630965i	$0.217341\pi$
$192$	− 1.58394e10i	− 0.0607060i
$193$	3.84540e10	0.143600	0.0718001	−	0.997419i	$-0.477126\pi$
$193$	3.84540e10	0.143600	0.0718001	+	0.997419i	$0.477126\pi$
$194$	− 3.17672e11i	− 1.15603i
$195$	− 7.99737e8i	− 0.00283644i
$196$	0	0
$197$	−1.91495e11	−0.645396	−0.322698	−	0.946502i	$-0.604590\pi$
$197$	−1.91495e11	−0.645396	−0.322698	+	0.946502i	$0.604590\pi$
$198$	1.36895e11	0.449844
$199$	− 1.61000e11i	− 0.515893i	−0.966159	−	0.257946i	$-0.916954\pi$
$199$	− 1.61000e11i	− 0.515893i	0.966159	−	0.257946i	$-0.0830458\pi$
$200$	−1.13121e11	−0.353503
$201$	1.20678e11i	0.367831i
$202$	3.67038e11i	1.09132i
$203$	0	0
$204$	−9.74792e10	−0.275906
$205$	6.31538e9	0.0174434
$206$	4.27059e11i	1.15120i
$207$	−2.64997e11	−0.697250
$208$	4.77827e10i	0.122731i
$209$	− 2.18217e11i	− 0.547215i
$210$	0	0
$211$	−1.08000e11	−0.258232	−0.129116	−	0.991629i	$-0.541214\pi$
$211$	−1.08000e11	−0.258232	−0.129116	+	0.991629i	$0.541214\pi$
$212$	−9.16711e10	−0.214069
$213$	2.30819e11i	0.526470i
$214$	4.09811e11	0.913093
$215$	− 6.98185e9i	− 0.0151977i
$216$	1.42423e11i	0.302908i
$217$	0	0
$218$	6.69516e11	1.35981
$219$	−2.78359e11	−0.552566
$220$	2.55225e9i	0.00495233i
$221$	2.94066e11	0.557806
$222$	1.06154e11i	0.196866i
$223$	− 1.70102e10i	− 0.0308449i	−0.999881	−	0.0154225i	$-0.995091\pi$
$223$	− 1.70102e10i	− 0.0308449i	0.999881	−	0.0154225i	$-0.00490932\pi$
$224$	0	0
$225$	4.40583e11	0.764038
$226$	2.86158e11	0.485360
$227$	− 5.82369e11i	− 0.966204i	−0.875564	−	0.483102i	$-0.839510\pi$
$227$	− 5.82369e11i	− 0.966204i	0.875564	−	0.483102i	$-0.160490\pi$
$228$	9.83384e10	0.159606
$229$	4.69321e11i	0.745233i	0.927985	+	0.372617i	$0.121539\pi$
$229$	4.69321e11i	0.745233i	−0.927985	+	0.372617i	$0.878461\pi$
$230$	− 4.94055e9i	− 0.00767602i
$231$	0	0
$232$	−5.02954e10	−0.0748322
$233$	−9.41350e11	−1.37079	−0.685396	−	0.728171i	$-0.740371\pi$
$233$	−9.41350e11	−1.37079	−0.685396	+	0.728171i	$0.740371\pi$
$234$	− 1.86103e11i	− 0.265262i
$235$	−7.46565e8	−0.00104167
$236$	− 2.45668e11i	− 0.335574i
$237$	6.76903e11i	0.905283i
$238$	0	0
$239$	−2.93858e11	−0.376832	−0.188416	−	0.982089i	$-0.560335\pi$
$239$	−2.93858e11	−0.376832	−0.188416	+	0.982089i	$0.560335\pi$
$240$	−1.15016e9	−0.00144444
$241$	− 1.06234e12i	− 1.30670i	−0.757054	−	0.653352i	$-0.773362\pi$
$241$	− 1.06234e12i	− 1.30670i	0.757054	−	0.653352i	$-0.226638\pi$
$242$	1.80114e11	0.217005
$243$	− 8.69141e11i	− 1.02579i
$244$	− 3.23085e11i	− 0.373566i
$245$	0	0
$246$	−4.53601e11	−0.503499
$247$	−2.96658e11	−0.322679
$248$	3.14969e11i	0.335745i
$249$	−6.54744e11	−0.684029
$250$	1.64294e10i	0.0168238i
$251$	9.83808e11i	0.987511i	0.869601	+	0.493755i	$0.164376\pi$
$251$	9.83808e11i	0.987511i	−0.869601	+	0.493755i	$0.835624\pi$
$252$	0	0
$253$	7.87436e11	0.759649
$254$	−4.65433e11	−0.440239
$255$	7.07833e9i	0.00656492i
$256$	6.87195e10	0.0625000
$257$	− 1.38156e12i	− 1.23226i	−0.787643	−	0.616132i	$-0.788699\pi$
$257$	− 1.38156e12i	− 1.23226i	0.787643	−	0.616132i	$-0.211301\pi$
$258$	5.01470e11i	0.438678i
$259$	0	0
$260$	3.46968e9	0.00292027
$261$	1.95890e11	0.161737
$262$	− 1.37345e12i	− 1.11252i
$263$	−7.95564e11	−0.632261	−0.316130	−	0.948716i	$-0.602384\pi$
$263$	−7.95564e11	−0.632261	−0.316130	+	0.948716i	$0.602384\pi$
$264$	− 1.83315e11i	− 0.142948i
$265$	6.65658e9i	0.00509356i
$266$	0	0
$267$	−9.27694e11	−0.683673
$268$	−5.23565e11	−0.378701
$269$	− 2.37649e12i	− 1.68723i	−0.536946	−	0.843616i	$-0.680422\pi$
$269$	− 2.37649e12i	− 1.68723i	0.536946	−	0.843616i	$-0.319578\pi$
$270$	1.03419e10	0.00720742
$271$	6.57825e10i	0.0450053i	0.999747	+	0.0225026i	$0.00716342\pi$
$271$	6.57825e10i	0.0450053i	−0.999747	+	0.0225026i	$0.992837\pi$
$272$	− 4.22916e11i	− 0.284060i
$273$	0	0
$274$	7.81693e8	0.000506155 0
$275$	−1.30919e12	−0.832413
$276$	3.54854e11i	0.221566i
$277$	3.88658e11	0.238324	0.119162	−	0.992875i	$-0.461979\pi$
$277$	3.88658e11	0.238324	0.119162	+	0.992875i	$0.461979\pi$
$278$	− 4.52584e11i	− 0.272568i
$279$	− 1.22674e12i	− 0.725655i
$280$	0	0
$281$	−1.52718e12	−0.871682	−0.435841	−	0.900024i	$-0.643549\pi$
$281$	−1.52718e12	−0.871682	−0.435841	+	0.900024i	$0.643549\pi$
$282$	5.36219e10	0.0300675
$283$	3.25792e12i	1.79477i	0.441250	+	0.897384i	$0.354535\pi$
$283$	3.25792e12i	1.79477i	−0.441250	+	0.897384i	$0.645465\pi$
$284$	−1.00141e12	−0.542028
$285$	− 7.14072e9i	− 0.00379767i
$286$	5.53005e11i	0.289001i
$287$	0	0
$288$	−2.67648e11	−0.135083
$289$	−5.86729e11	−0.291037
$290$	3.65214e9i	0.00178056i
$291$	1.65681e12	0.793976
$292$	− 1.20766e12i	− 0.568895i
$293$	− 2.64317e11i	− 0.122402i	−0.998125	−	0.0612008i	$-0.980507\pi$
$293$	− 2.64317e11i	− 0.122402i	0.998125	−	0.0612008i	$-0.0194930\pi$
$294$	0	0
$295$	−1.78388e10	−0.00798466
$296$	−4.60551e11	−0.202684
$297$	1.64831e12i	0.713275i
$298$	−1.32713e12	−0.564717
$299$	− 1.07049e12i	− 0.447946i
$300$	− 5.89979e11i	− 0.242790i
$301$	0	0
$302$	9.72780e11	0.387240
$303$	−1.91427e12	−0.749533
$304$	4.26644e11i	0.164323i
$305$	−2.34604e10	−0.00888866
$306$	1.64717e12i	0.613947i
$307$	4.69415e10i	0.0172133i	0.999963	+	0.00860667i	$0.00273962\pi$
$307$	4.69415e10i	0.0172133i	−0.999963	+	0.00860667i	$0.997260\pi$
$308$	0	0
$309$	−2.22731e12	−0.790658
$310$	2.28711e10	0.00798873
$311$	− 2.08547e12i	− 0.716807i	−0.933567	−	0.358404i	$-0.883321\pi$
$311$	− 2.08547e12i	− 0.716807i	0.933567	−	0.358404i	$-0.116679\pi$
$312$	−2.49209e11	−0.0842928
$313$	− 3.58415e12i	− 1.19307i	−0.802588	−	0.596533i	$-0.796544\pi$
$313$	− 3.58415e12i	− 1.19307i	0.802588	−	0.596533i	$-0.203456\pi$
$314$	5.80888e10i	0.0190302i
$315$	0	0
$316$	−2.93676e12	−0.932036
$317$	4.61305e12	1.44109	0.720546	−	0.693407i	$-0.243891\pi$
$317$	4.61305e12	1.44109	0.720546	+	0.693407i	$0.243891\pi$
$318$	− 4.78107e11i	− 0.147025i
$319$	−5.82086e11	−0.176211
$320$	− 4.98998e9i	− 0.00148713i
$321$	2.13736e12i	0.627121i
$322$	0	0
$323$	2.62566e12	0.746838
$324$	6.21377e11	0.174032
$325$	1.77979e12i	0.490854i
$326$	−1.19072e12	−0.323386
$327$	3.49184e12i	0.933933i
$328$	− 1.96796e12i	− 0.518378i
$329$	0	0
$330$	−1.33112e10	−0.00340131
$331$	5.16746e12	1.30058	0.650290	−	0.759686i	$-0.274648\pi$
$331$	5.16746e12	1.30058	0.650290	+	0.759686i	$0.274648\pi$
$332$	− 2.84062e12i	− 0.704244i
$333$	1.79375e12	0.438067
$334$	3.13734e12i	0.754794i
$335$	3.80180e10i	0.00901084i
$336$	0	0
$337$	6.46509e12	1.48739	0.743695	−	0.668519i	$-0.233072\pi$
$337$	6.46509e12	1.48739	0.743695	+	0.668519i	$0.233072\pi$
$338$	−2.36759e12	−0.536690
$339$	1.49245e12i	0.333350i
$340$	−3.07095e10	−0.00675893
$341$	3.64524e12i	0.790596i
$342$	− 1.66169e12i	− 0.355156i
$343$	0	0
$344$	−2.17564e12	−0.451642
$345$	2.57673e10	0.00527197
$346$	− 2.37198e12i	− 0.478333i
$347$	4.50340e12	0.895144	0.447572	−	0.894248i	$-0.352289\pi$
$347$	4.50340e12	0.895144	0.447572	+	0.894248i	$0.352289\pi$
$348$	− 2.62314e11i	− 0.0513955i
$349$	− 3.43325e11i	− 0.0663099i	−0.999450	−	0.0331549i	$-0.989445\pi$
$349$	− 3.43325e11i	− 0.0663099i	0.999450	−	0.0331549i	$-0.0105555\pi$
$350$	0	0
$351$	2.24081e12	0.420601
$352$	7.95314e11	0.147172
$353$	8.71820e12i	1.59057i	0.606234	+	0.795286i	$0.292679\pi$
$353$	8.71820e12i	1.59057i	−0.606234	+	0.795286i	$0.707321\pi$
$354$	1.28127e12	0.230475
$355$	7.27164e10i	0.0128971i
$356$	− 4.02482e12i	− 0.703877i
$357$	0	0
$358$	6.72580e12	1.14374
$359$	−1.97254e12	−0.330791	−0.165395	−	0.986227i	$-0.552890\pi$
$359$	−1.97254e12	−0.330791	−0.165395	+	0.986227i	$0.552890\pi$
$360$	1.94349e10i	0.00321418i
$361$	3.48226e12	0.567969
$362$	6.74143e12i	1.08445i
$363$	9.39378e11i	0.149041i
$364$	0	0
$365$	−8.76931e10	−0.0135363
$366$	1.68504e12	0.256569
$367$	3.62145e12i	0.543941i	0.962306	+	0.271971i	$0.0876753\pi$
$367$	3.62145e12i	0.543941i	−0.962306	+	0.271971i	$0.912325\pi$
$368$	−1.53954e12	−0.228114
$369$	7.66478e12i	1.12039i
$370$	3.34423e10i	0.00482267i
$371$	0	0
$372$	−1.64271e12	−0.230593
$373$	9.25272e12	1.28152	0.640760	−	0.767741i	$-0.278619\pi$
$373$	9.25272e12	1.28152	0.640760	+	0.767741i	$0.278619\pi$
$374$	− 4.89455e12i	− 0.668890i
$375$	−8.56872e10	−0.0115547
$376$	2.32640e11i	0.0309560i
$377$	7.91323e11i	0.103908i
$378$	0	0
$379$	−2.53428e12	−0.324084	−0.162042	−	0.986784i	$-0.551808\pi$
$379$	−2.53428e12	−0.324084	−0.162042	+	0.986784i	$0.551808\pi$
$380$	3.09802e10	0.00390990
$381$	− 2.42745e12i	− 0.302361i
$382$	−8.92458e12	−1.09716
$383$	− 3.77595e12i	− 0.458176i	−0.973406	−	0.229088i	$-0.926426\pi$
$383$	− 3.77595e12i	− 0.458176i	0.973406	−	0.229088i	$-0.0735744\pi$
$384$	3.58404e11i	0.0429256i
$385$	0	0
$386$	−8.70114e11	−0.101541
$387$	8.47365e12	0.976148
$388$	7.18810e12i	0.817440i
$389$	4.26523e12	0.478844	0.239422	−	0.970916i	$-0.423042\pi$
$389$	4.26523e12	0.478844	0.239422	+	0.970916i	$0.423042\pi$
$390$	1.80960e10i	0.00200567i
$391$	9.47470e12i	1.03677i
$392$	0	0
$393$	7.16319e12	0.764088
$394$	4.33303e12	0.456364
$395$	2.13249e11i	0.0221769i
$396$	−3.09758e12	−0.318088
$397$	9.65829e12i	0.979372i	0.871899	+	0.489686i	$0.162889\pi$
$397$	9.65829e12i	0.979372i	−0.871899	+	0.489686i	$0.837111\pi$
$398$	3.64301e12i	0.364791i
$399$	0	0
$400$	2.55964e12	0.249965
$401$	−7.84612e12	−0.756717	−0.378358	−	0.925659i	$-0.623511\pi$
$401$	−7.84612e12	−0.756717	−0.378358	+	0.925659i	$0.623511\pi$
$402$	− 2.73064e12i	− 0.260096i
$403$	4.95556e12	0.466195
$404$	− 8.30511e12i	− 0.771683i
$405$	− 4.51205e10i	− 0.00414094i
$406$	0	0
$407$	−5.33011e12	−0.477270
$408$	2.20570e12	0.195095
$409$	1.57822e13i	1.37896i	0.724306	+	0.689479i	$0.242160\pi$
$409$	1.57822e13i	1.37896i	−0.724306	+	0.689479i	$0.757840\pi$
$410$	−1.42901e11	−0.0123343
$411$	4.07689e9i	0 0.000347632i
$412$	− 9.66324e12i	− 0.814023i
$413$	0	0
$414$	5.99619e12	0.493030
$415$	−2.06268e11	−0.0167568
$416$	− 1.08120e12i	− 0.0867838i
$417$	2.36044e12	0.187203
$418$	4.93769e12i	0.386939i
$419$	2.41325e12i	0.186867i	0.995626	+	0.0934336i	$0.0297843\pi$
$419$	2.41325e12i	0.186867i	−0.995626	+	0.0934336i	$0.970216\pi$
$420$	0	0
$421$	−2.06355e13	−1.56029	−0.780145	−	0.625599i	$-0.784855\pi$
$421$	−2.06355e13	−1.56029	−0.780145	+	0.625599i	$0.784855\pi$
$422$	2.44375e12	0.182598
$423$	− 9.06083e11i	− 0.0669062i
$424$	2.07428e12	0.151369
$425$	− 1.57526e13i	− 1.13608i
$426$	− 5.22284e12i	− 0.372270i
$427$	0	0
$428$	−9.27297e12	−0.645654
$429$	−2.88418e12	−0.198489
$430$	1.57981e11i	0.0107464i
$431$	−1.27992e13	−0.860591	−0.430296	−	0.902688i	$-0.641591\pi$
$431$	−1.27992e13	−0.860591	−0.430296	+	0.902688i	$0.641591\pi$
$432$	− 3.22266e12i	− 0.214189i
$433$	− 2.23235e13i	− 1.46664i	−0.679884	−	0.733320i	$-0.737970\pi$
$433$	− 2.23235e13i	− 1.46664i	0.679884	−	0.733320i	$-0.262030\pi$
$434$	0	0
$435$	−1.90476e10	−0.00122291
$436$	−1.51494e13	−0.961532
$437$	− 9.55821e12i	− 0.599749i
$438$	6.29853e12	0.390723
$439$	− 1.67269e13i	− 1.02587i	−0.858427	−	0.512936i	$-0.828558\pi$
$439$	− 1.67269e13i	− 1.02587i	0.858427	−	0.512936i	$-0.171442\pi$
$440$	− 5.77507e10i	− 0.00350182i
$441$	0	0
$442$	−6.65395e12	−0.394428
$443$	−2.40656e13	−1.41052	−0.705258	−	0.708951i	$-0.749169\pi$
$443$	−2.40656e13	−1.41052	−0.705258	+	0.708951i	$0.749169\pi$
$444$	− 2.40199e12i	− 0.139205i
$445$	−2.92257e11	−0.0167481
$446$	3.84896e11i	0.0218107i
$447$	− 6.92158e12i	− 0.387854i
$448$	0	0
$449$	1.66231e13	0.910919	0.455460	−	0.890256i	$-0.349475\pi$
$449$	1.66231e13	0.910919	0.455460	+	0.890256i	$0.349475\pi$
$450$	−9.96925e12	−0.540256
$451$	− 2.27759e13i	− 1.22065i
$452$	−6.47502e12	−0.343201
$453$	5.07350e12i	0.265960i
$454$	1.31775e13i	0.683210i
$455$	0	0
$456$	−2.22514e12	−0.112858
$457$	−3.74000e12	−0.187625	−0.0938124	−	0.995590i	$-0.529905\pi$
$457$	−3.74000e12	−0.187625	−0.0938124	+	0.995590i	$0.529905\pi$
$458$	− 1.06195e13i	− 0.526960i
$459$	−1.98330e13	−0.973477
$460$	1.11792e11i	0.00542776i
$461$	1.65515e13i	0.794936i	0.917616	+	0.397468i	$0.130111\pi$
$461$	1.65515e13i	0.794936i	−0.917616	+	0.397468i	$0.869889\pi$
$462$	0	0
$463$	−5.00015e12	−0.235006	−0.117503	−	0.993073i	$-0.537489\pi$
$463$	−5.00015e12	−0.235006	−0.117503	+	0.993073i	$0.537489\pi$
$464$	1.13806e12	0.0529144
$465$	1.19283e11i	0.00548674i
$466$	2.13003e13	0.969296
$467$	− 3.28542e13i	− 1.47913i	−0.673085	−	0.739565i	$-0.735031\pi$
$467$	− 3.28542e13i	− 1.47913i	0.673085	−	0.739565i	$-0.264969\pi$
$468$	4.21104e12i	0.187569i
$469$	0	0
$470$	1.68928e10	0.000736569 0
$471$	−3.02960e11	−0.0130702
$472$	5.55882e12i	0.237286i
$473$	−2.51794e13	−1.06351
$474$	− 1.53166e13i	− 0.640132i
$475$	1.58915e13i	0.657197i
$476$	0	0
$477$	−8.07888e12	−0.327159
$478$	6.64924e12	0.266460
$479$	− 4.04089e13i	− 1.60250i	−0.598327	−	0.801252i	$-0.704168\pi$
$479$	− 4.04089e13i	− 1.60250i	0.598327	−	0.801252i	$-0.295832\pi$
$480$	2.60251e10	0.00102138
$481$	7.24608e12i	0.281435i
$482$	2.40380e13i	0.923980i
$483$	0	0
$484$	−4.07551e12	−0.153446
$485$	5.21955e11	0.0194502
$486$	1.96664e13i	0.725344i
$487$	3.81237e13	1.39172	0.695858	−	0.718180i	$-0.255024\pi$
$487$	3.81237e13	1.39172	0.695858	+	0.718180i	$0.255024\pi$
$488$	7.31058e12i	0.264151i
$489$	− 6.21015e12i	− 0.222105i
$490$	0	0
$491$	3.95192e12	0.138484	0.0692422	−	0.997600i	$-0.477942\pi$
$491$	3.95192e12	0.138484	0.0692422	+	0.997600i	$0.477942\pi$
$492$	1.02638e13	0.356027
$493$	− 7.00386e12i	− 0.240493i
$494$	6.71260e12	0.228169
$495$	2.24927e11i	0.00756860i
$496$	− 7.12693e12i	− 0.237407i
$497$	0	0
$498$	1.48152e13	0.483682
$499$	−4.43425e13	−1.43324	−0.716618	−	0.697466i	$-0.754311\pi$
$499$	−4.43425e13	−1.43324	−0.716618	+	0.697466i	$0.754311\pi$
$500$	− 3.71756e11i	− 0.0118962i
$501$	−1.63627e13	−0.518400
$502$	− 2.22610e13i	− 0.698276i
$503$	− 1.60566e13i	− 0.498670i	−0.968417	−	0.249335i	$-0.919788\pi$
$503$	− 1.60566e13i	− 0.498670i	0.968417	−	0.249335i	$-0.0802121\pi$
$504$	0	0
$505$	−6.03065e11	−0.0183615
$506$	−1.78176e13	−0.537153
$507$	− 1.23481e13i	− 0.368604i
$508$	1.05315e13	0.311296
$509$	6.75801e12i	0.197802i	0.995097	+	0.0989009i	$0.0315327\pi$
$509$	6.75801e12i	0.197802i	−0.995097	+	0.0989009i	$0.968467\pi$
$510$	− 1.60164e11i	− 0.00464210i
$511$	0	0
$512$	−1.55494e12	−0.0441942
$513$	2.00078e13	0.563136
$514$	3.12611e13i	0.871342i
$515$	−7.01684e11	−0.0193689
$516$	− 1.13470e13i	− 0.310193i
$517$	2.69242e12i	0.0728938i
$518$	0	0
$519$	1.23710e13	0.328524
$520$	−7.85098e10	−0.00206494
$521$	1.13000e13i	0.294367i	0.989109	+	0.147183i	$0.0470208\pi$
$521$	1.13000e13i	0.294367i	−0.989109	+	0.147183i	$0.952979\pi$
$522$	−4.43249e12	−0.114365
$523$	3.27863e13i	0.837885i	0.908013	+	0.418943i	$0.137599\pi$
$523$	3.27863e13i	0.837885i	−0.908013	+	0.418943i	$0.862401\pi$
$524$	3.10777e13i	0.786669i
$525$	0	0
$526$	1.80016e13	0.447076
$527$	−4.38608e13	−1.07901
$528$	4.14793e12i	0.101079i
$529$	−6.93574e12	−0.167423
$530$	− 1.50621e11i	− 0.00360169i
$531$	− 2.16504e13i	− 0.512854i
$532$	0	0
$533$	−3.09629e13	−0.719789
$534$	2.09913e13	0.483430
$535$	6.73345e11i	0.0153627i
$536$	1.18469e13	0.267782
$537$	3.50781e13i	0.785534i
$538$	5.37739e13i	1.19305i
$539$	0	0
$540$	−2.34010e11	−0.00509642
$541$	8.62251e13	1.86058	0.930288	−	0.366831i	$-0.119557\pi$
$541$	8.62251e13	1.86058	0.930288	+	0.366831i	$0.119557\pi$
$542$	− 1.48849e12i	− 0.0318236i
$543$	−3.51597e13	−0.744811
$544$	9.56949e12i	0.200860i
$545$	1.10006e12i	0.0228788i
$546$	0	0
$547$	2.71151e13	0.553701	0.276850	−	0.960913i	$-0.410709\pi$
$547$	2.71151e13	0.553701	0.276850	+	0.960913i	$0.410709\pi$
$548$	−1.76877e10	−0.000357906 0
$549$	− 2.84731e13i	− 0.570918i
$550$	2.96236e13	0.588605
$551$	7.06560e12i	0.139120i
$552$	− 8.02942e12i	− 0.156671i
$553$	0	0
$554$	−8.79432e12	−0.168521
$555$	−1.74417e11	−0.00331226
$556$	1.02408e13i	0.192735i
$557$	−2.59296e13	−0.483637	−0.241818	−	0.970322i	$-0.577744\pi$
$557$	−2.59296e13	−0.483637	−0.241818	+	0.970322i	$0.577744\pi$
$558$	2.77579e13i	0.513116i
$559$	3.42304e13i	0.627124i
$560$	0	0
$561$	2.55274e13	0.459401
$562$	3.45561e13	0.616372
$563$	− 3.06641e13i	− 0.542111i	−0.962564	−	0.271055i	$-0.912627\pi$
$563$	− 3.06641e13i	− 0.542111i	0.962564	−	0.271055i	$-0.0873726\pi$
$564$	−1.21332e12	−0.0212609
$565$	4.70175e11i	0.00816615i
$566$	− 7.37183e13i	− 1.26909i
$567$	0	0
$568$	2.26594e13	0.383272
$569$	1.14119e13	0.191335	0.0956676	−	0.995413i	$-0.469501\pi$
$569$	1.14119e13	0.191335	0.0956676	+	0.995413i	$0.469501\pi$
$570$	1.61576e11i	0.00268536i
$571$	−3.27745e13	−0.539953	−0.269976	−	0.962867i	$-0.587016\pi$
$571$	−3.27745e13	−0.539953	−0.269976	+	0.962867i	$0.587016\pi$
$572$	− 1.25131e13i	− 0.204355i
$573$	− 4.65458e13i	− 0.753542i
$574$	0	0
$575$	−5.73443e13	−0.912328
$576$	6.05618e12	0.0955182
$577$	9.91918e13i	1.55095i	0.631381	+	0.775473i	$0.282488\pi$
$577$	9.91918e13i	1.55095i	−0.631381	+	0.775473i	$0.717512\pi$
$578$	1.32762e13	0.205794
$579$	− 4.53805e12i	− 0.0697391i
$580$	− 8.26385e10i	− 0.00125905i
$581$	0	0
$582$	−3.74893e13	−0.561426
$583$	2.40064e13	0.356438
$584$	2.73263e13i	0.402270i
$585$	3.05779e11	0.00446302
$586$	5.98081e12i	0.0865510i
$587$	− 9.19804e13i	− 1.31979i	−0.751358	−	0.659895i	$-0.770601\pi$
$587$	− 9.19804e13i	− 1.31979i	0.751358	−	0.659895i	$-0.229399\pi$
$588$	0	0
$589$	4.42474e13	0.624182
$590$	4.03647e11	0.00564601
$591$	2.25988e13i	0.313435i
$592$	1.04211e13	0.143319
$593$	8.86289e13i	1.20865i	0.796737	+	0.604327i	$0.206558\pi$
$593$	8.86289e13i	1.20865i	−0.796737	+	0.604327i	$0.793442\pi$
$594$	− 3.72970e13i	− 0.504361i
$595$	0	0
$596$	3.00294e13	0.399315
$597$	−1.90000e13	−0.250542
$598$	2.42224e13i	0.316746i
$599$	4.74444e13	0.615248	0.307624	−	0.951508i	$-0.400466\pi$
$599$	4.74444e13	0.615248	0.307624	+	0.951508i	$0.400466\pi$
$600$	1.33497e13i	0.171678i
$601$	2.46584e12i	0.0314479i	0.999876	+	0.0157240i	$0.00500530\pi$
$601$	2.46584e12i	0.0314479i	−0.999876	+	0.0157240i	$0.994995\pi$
$602$	0	0
$603$	−4.61413e13	−0.578766
$604$	−2.20115e13	−0.273820
$605$	2.95938e11i	0.00365110i
$606$	4.33150e13	0.530000
$607$	− 9.25130e13i	− 1.12269i	−0.827582	−	0.561344i	$-0.810284\pi$
$607$	− 9.25130e13i	− 1.12269i	0.827582	−	0.561344i	$-0.189716\pi$
$608$	− 9.65384e12i	− 0.116194i
$609$	0	0
$610$	5.30848e11	0.00628523
$611$	3.66024e12	0.0429837
$612$	− 3.72711e13i	− 0.434126i
$613$	1.31424e14	1.51835	0.759174	−	0.650888i	$-0.225603\pi$
$613$	1.31424e14	1.51835	0.759174	+	0.650888i	$0.225603\pi$
$614$	− 1.06217e12i	− 0.0121717i
$615$	− 7.45294e11i	− 0.00847134i
$616$	0	0
$617$	6.18670e12	0.0691884	0.0345942	−	0.999401i	$-0.488986\pi$
$617$	6.18670e12	0.0691884	0.0345942	+	0.999401i	$0.488986\pi$
$618$	5.03983e13	0.559080
$619$	4.59321e13i	0.505432i	0.967540	+	0.252716i	$0.0813238\pi$
$619$	4.59321e13i	0.505432i	−0.967540	+	0.252716i	$0.918676\pi$
$620$	−5.17513e11	−0.00564889
$621$	7.21982e13i	0.781751i
$622$	4.71888e13i	0.506859i
$623$	0	0
$624$	5.63895e12	0.0596040
$625$	9.53269e13	0.999575
$626$	8.11001e13i	0.843626i
$627$	−2.57524e13	−0.265754
$628$	− 1.31440e12i	− 0.0134564i
$629$	− 6.41337e13i	− 0.651378i
$630$	0	0
$631$	4.32442e13	0.432296	0.216148	−	0.976361i	$-0.430651\pi$
$631$	4.32442e13	0.432296	0.216148	+	0.976361i	$0.430651\pi$
$632$	6.64513e13	0.659049
$633$	1.27453e13i	0.125410i
$634$	−1.04381e14	−1.01901
$635$	− 7.64735e11i	− 0.00740700i
$636$	1.08183e13i	0.103962i
$637$	0	0
$638$	1.31711e13	0.124600
$639$	−8.82536e13	−0.828377
$640$	1.12910e11i	0.00105156i
$641$	−6.14651e13	−0.567987	−0.283993	−	0.958826i	$-0.591659\pi$
$641$	−6.14651e13	−0.567987	−0.283993	+	0.958826i	$0.591659\pi$
$642$	− 4.83628e13i	− 0.443442i
$643$	1.70194e14i	1.54842i	0.632930	+	0.774209i	$0.281852\pi$
$643$	1.70194e14i	1.54842i	−0.632930	+	0.774209i	$0.718148\pi$
$644$	0	0
$645$	−8.23946e11	−0.00738074
$646$	−5.94120e13	−0.528095
$647$	− 4.88517e13i	− 0.430882i	−0.976517	−	0.215441i	$-0.930881\pi$
$647$	− 4.88517e13i	− 0.430882i	0.976517	−	0.215441i	$-0.0691189\pi$
$648$	−1.40602e13	−0.123059
$649$	6.43342e13i	0.558751i
$650$	− 4.02721e13i	− 0.347086i
$651$	0	0
$652$	2.69429e13	0.228668
$653$	1.58495e14	1.33490	0.667450	−	0.744655i	$-0.267386\pi$
$653$	1.58495e14	1.33490	0.667450	+	0.744655i	$0.267386\pi$
$654$	− 7.90113e13i	− 0.660390i
$655$	2.25666e12	0.0187180
$656$	4.45298e13i	0.366549i
$657$	− 1.06430e14i	− 0.869438i
$658$	0	0
$659$	−1.22774e14	−0.987823	−0.493911	−	0.869512i	$-0.664433\pi$
$659$	−1.22774e14	−0.987823	−0.493911	+	0.869512i	$0.664433\pi$
$660$	3.01197e11	0.00240509
$661$	1.59591e14i	1.26474i	0.774667	+	0.632370i	$0.217918\pi$
$661$	1.59591e14i	1.26474i	−0.774667	+	0.632370i	$0.782082\pi$
$662$	−1.16926e14	−0.919648
$663$	− 3.47034e13i	− 0.270897i
$664$	6.42759e13i	0.497975i
$665$	0	0
$666$	−4.05879e13	−0.309760
$667$	−2.54962e13	−0.193128
$668$	− 7.09898e13i	− 0.533720i
$669$	−2.00741e12	−0.0149798
$670$	− 8.60250e11i	− 0.00637163i
$671$	8.46078e13i	0.622011i
$672$	0	0
$673$	2.65164e13	0.192061	0.0960307	−	0.995378i	$-0.469385\pi$
$673$	2.65164e13	0.192061	0.0960307	+	0.995378i	$0.469385\pi$
$674$	−1.46288e14	−1.05174
$675$	− 1.20037e14i	− 0.856633i
$676$	5.35725e13	0.379497
$677$	6.77696e13i	0.476531i	0.971200	+	0.238266i	$0.0765789\pi$
$677$	6.77696e13i	0.476531i	−0.971200	+	0.238266i	$0.923421\pi$
$678$	− 3.37702e13i	− 0.235714i
$679$	0	0
$680$	6.94876e11	0.00477929
$681$	−6.87268e13	−0.469235
$682$	− 8.24824e13i	− 0.559036i
$683$	−2.58372e12	−0.0173837	−0.00869184	−	0.999962i	$-0.502767\pi$
$683$	−2.58372e12	−0.0173837	−0.00869184	+	0.999962i	$0.502767\pi$
$684$	3.75997e13i	0.251133i
$685$	1.28437e9i	0 8.51603e-6i
$686$	0	0
$687$	5.53857e13	0.361921
$688$	4.92291e13	0.319359
$689$	− 3.26357e13i	− 0.210183i
$690$	−5.83046e11	−0.00372784
$691$	− 2.58029e14i	− 1.63786i	−0.573892	−	0.818931i	$-0.694567\pi$
$691$	− 2.58029e14i	− 1.63786i	0.573892	−	0.818931i	$-0.305433\pi$
$692$	5.36718e13i	0.338232i
$693$	0	0
$694$	−1.01900e14	−0.632962
$695$	7.43624e11	0.00458595
$696$	5.93549e12i	0.0363421i
$697$	2.74047e14	1.66595
$698$	7.76856e12i	0.0468882i
$699$	1.11091e14i	0.665722i
$700$	0	0
$701$	2.95013e14	1.74281	0.871407	−	0.490561i	$-0.163208\pi$
$701$	2.95013e14	1.74281	0.871407	+	0.490561i	$0.163208\pi$
$702$	−5.07038e13	−0.297410
$703$	6.46990e13i	0.376809i
$704$	−1.79959e13	−0.104066
$705$	8.81040e10i	0 0.000505883i
$706$	− 1.97270e14i	− 1.12470i
$707$	0	0
$708$	−2.89918e13	−0.162971
$709$	−1.65634e14	−0.924525	−0.462263	−	0.886743i	$-0.652962\pi$
$709$	−1.65634e14	−0.924525	−0.462263	+	0.886743i	$0.652962\pi$
$710$	− 1.64538e12i	− 0.00911959i
$711$	−2.58814e14	−1.42442
$712$	9.10713e13i	0.497716i
$713$	1.59667e14i	0.866496i
$714$	0	0
$715$	−9.08622e11	−0.00486242
$716$	−1.52187e14	−0.808749
$717$	3.46789e13i	0.183008i
$718$	4.46335e13	0.233904
$719$	− 7.58362e13i	− 0.394668i	−0.980336	−	0.197334i	$-0.936772\pi$
$719$	− 7.58362e13i	− 0.394668i	0.980336	−	0.197334i	$-0.0632284\pi$
$720$	− 4.39762e11i	− 0.00227277i
$721$	0	0
$722$	−7.87945e13	−0.401615
$723$	−1.25369e14	−0.634599
$724$	− 1.52541e14i	− 0.766822i
$725$	4.23899e13	0.211627
$726$	− 2.12557e13i	− 0.105388i
$727$	2.07361e14i	1.02107i	0.859858	+	0.510534i	$0.170552\pi$
$727$	2.07361e14i	1.02107i	−0.859858	+	0.510534i	$0.829448\pi$
$728$	0	0
$729$	−3.09061e13	−0.150109
$730$	1.98427e12	0.00957163
$731$	− 3.02967e14i	− 1.45147i
$732$	−3.81281e13	−0.181422
$733$	− 2.12068e14i	− 1.00220i	−0.865389	−	0.501100i	$-0.832929\pi$
$733$	− 2.12068e14i	− 1.00220i	0.865389	−	0.501100i	$-0.167071\pi$
$734$	− 8.19440e13i	− 0.384624i
$735$	0	0
$736$	3.48358e13	0.161301
$737$	1.37109e14	0.630561
$738$	− 1.73434e14i	− 0.792233i
$739$	8.64190e13	0.392091	0.196046	−	0.980595i	$-0.437190\pi$
$739$	8.64190e13	0.392091	0.196046	+	0.980595i	$0.437190\pi$
$740$	− 7.56713e11i	− 0.00341014i
$741$	3.50093e13i	0.156709i
$742$	0	0
$743$	−1.26430e14	−0.558350	−0.279175	−	0.960240i	$-0.590061\pi$
$743$	−1.26430e14	−0.558350	−0.279175	+	0.960240i	$0.590061\pi$
$744$	3.71703e13	0.163054
$745$	− 2.18055e12i	− 0.00950134i
$746$	−2.09365e14	−0.906172
$747$	− 2.50341e14i	− 1.07629i
$748$	1.10751e14i	0.472977i
$749$	0	0
$750$	1.93888e12	0.00817043
$751$	−1.22488e14	−0.512737	−0.256368	−	0.966579i	$-0.582526\pi$
$751$	−1.22488e14	−0.512737	−0.256368	+	0.966579i	$0.582526\pi$
$752$	− 5.26404e12i	− 0.0218892i
$753$	1.16102e14	0.479583
$754$	− 1.79056e13i	− 0.0734738i
$755$	1.59834e12i	0.00651528i
$756$	0	0
$757$	−1.47452e14	−0.593160	−0.296580	−	0.955008i	$-0.595846\pi$
$757$	−1.47452e14	−0.593160	−0.296580	+	0.955008i	$0.595846\pi$
$758$	5.73442e13	0.229162
$759$	− 9.29273e13i	− 0.368922i
$760$	−7.01002e11	−0.00276472
$761$	1.06668e14i	0.417938i	0.977922	+	0.208969i	$0.0670107\pi$
$761$	1.06668e14i	0.417938i	−0.977922	+	0.208969i	$0.932989\pi$
$762$	5.49269e13i	0.213801i
$763$	0	0
$764$	2.01940e14	0.775811
$765$	−2.70640e12	−0.0103296
$766$	8.54400e13i	0.323979i
$767$	8.74598e13	0.329482
$768$	− 8.10976e12i	− 0.0303530i
$769$	6.05828e12i	0.0225278i	0.999937	+	0.0112639i	$0.00358548\pi$
$769$	6.05828e12i	0.0225278i	−0.999937	+	0.0112639i	$0.996415\pi$
$770$	0	0
$771$	−1.63041e14	−0.598446
$772$	1.96884e13	0.0718001
$773$	4.83615e14i	1.75227i	0.482063	+	0.876137i	$0.339888\pi$
$773$	4.83615e14i	1.75227i	−0.482063	+	0.876137i	$0.660112\pi$
$774$	−1.91737e14	−0.690241
$775$	− 2.65461e14i	− 0.949495i
$776$	− 1.62648e14i	− 0.578017i
$777$	0	0
$778$	−9.65111e13	−0.338594
$779$	−2.76462e14	−0.963715
$780$	− 4.09465e11i	− 0.00141822i
$781$	2.62245e14	0.902510
$782$	− 2.14388e14i	− 0.733106i
$783$	− 5.33702e13i	− 0.181338i
$784$	0	0
$785$	−9.54434e10	−0.000320183 0
$786$	−1.62084e14	−0.540292
$787$	1.68737e14i	0.558903i	0.960160	+	0.279452i	$0.0901527\pi$
$787$	1.68737e14i	0.558903i	−0.960160	+	0.279452i	$0.909847\pi$
$788$	−9.80454e13	−0.322698
$789$	9.38865e13i	0.307056i
$790$	− 4.82527e12i	− 0.0156815i
$791$	0	0
$792$	7.00903e13	0.224922
$793$	1.15021e14	0.366785
$794$	− 2.18542e14i	− 0.692521i
$795$	7.85560e11	0.00247368
$796$	− 8.24318e13i	− 0.257946i
$797$	− 4.34432e14i	− 1.35092i	−0.737396	−	0.675461i	$-0.763945\pi$
$797$	− 4.34432e14i	− 1.35092i	0.737396	−	0.675461i	$-0.236055\pi$
$798$	0	0
$799$	−3.23961e13	−0.0994854
$800$	−5.79180e13	−0.176752
$801$	− 3.54704e14i	− 1.07573i
$802$	1.77538e14	0.535080
$803$	3.16257e14i	0.947246i
$804$	6.17872e13i	0.183916i
$805$	0	0
$806$	−1.12132e14	−0.329650
$807$	−2.80456e14	−0.819402
$808$	1.87923e14i	0.545662i
$809$	−4.35464e14	−1.25664	−0.628318	−	0.777956i	$-0.716256\pi$
$809$	−4.35464e14	−1.25664	−0.628318	+	0.777956i	$0.716256\pi$
$810$	1.02096e12i	0.00292809i
$811$	− 3.27146e13i	− 0.0932475i	−0.998913	−	0.0466238i	$-0.985154\pi$
$811$	− 3.27146e13i	− 0.0932475i	0.998913	−	0.0466238i	$-0.0148462\pi$
$812$	0	0
$813$	7.76315e12	0.0218567
$814$	1.20607e14	0.337481
$815$	− 1.95642e12i	− 0.00544095i
$816$	−4.99093e13	−0.137953
$817$	3.05638e14i	0.839647i
$818$	− 3.57110e14i	− 0.975070i
$819$	0	0
$820$	3.23347e12	0.00872168
$821$	6.95251e14	1.86391	0.931957	−	0.362569i	$-0.118100\pi$
$821$	6.95251e14	1.86391	0.931957	+	0.362569i	$0.118100\pi$
$822$	− 9.22496e10i	0 0.000245813i
$823$	3.07187e14	0.813588	0.406794	−	0.913520i	$-0.366647\pi$
$823$	3.07187e14	0.813588	0.406794	+	0.913520i	$0.366647\pi$
$824$	2.18654e14i	0.575601i
$825$	1.54501e14i	0.404260i
$826$	0	0
$827$	3.98069e13	0.102904	0.0514518	−	0.998675i	$-0.483615\pi$
$827$	3.98069e13	0.102904	0.0514518	+	0.998675i	$0.483615\pi$
$828$	−1.35678e14	−0.348625
$829$	5.48560e14i	1.40104i	0.713632	+	0.700521i	$0.247049\pi$
$829$	5.48560e14i	1.40104i	−0.713632	+	0.700521i	$0.752951\pi$
$830$	4.66731e12	0.0118489
$831$	− 4.58665e13i	− 0.115742i
$832$	2.44647e13i	0.0613654i
$833$	0	0
$834$	−5.34106e13	−0.132372
$835$	−5.15483e12	−0.0126994
$836$	− 1.11727e14i	− 0.273607i
$837$	−3.34224e14	−0.813599
$838$	− 5.46057e13i	− 0.132135i
$839$	− 1.31654e14i	− 0.316683i	−0.987384	−	0.158342i	$-0.949385\pi$
$839$	− 1.31654e14i	− 0.316683i	0.987384	−	0.158342i	$-0.0506148\pi$
$840$	0	0
$841$	−4.01860e14	−0.955201
$842$	4.66929e14	1.10329
$843$	1.80226e14i	0.423331i
$844$	−5.52958e13	−0.129116
$845$	− 3.89010e12i	− 0.00902978i
$846$	2.05023e13i	0.0473098i
$847$	0	0
$848$	−4.69356e13	−0.107034
$849$	3.84475e14	0.871626
$850$	3.56441e14i	0.803328i
$851$	−2.33466e14	−0.523090
$852$	1.18179e14i	0.263235i
$853$	3.44248e14i	0.762300i	0.924513	+	0.381150i	$0.124472\pi$
$853$	3.44248e14i	0.762300i	−0.924513	+	0.381150i	$0.875528\pi$
$854$	0	0
$855$	2.73025e12	0.00597547
$856$	2.09823e14	0.456546
$857$	− 2.26569e14i	− 0.490114i	−0.969509	−	0.245057i	$-0.921193\pi$
$857$	− 2.26569e14i	− 0.490114i	0.969509	−	0.245057i	$-0.0788066\pi$
$858$	6.52616e13	0.140353
$859$	− 2.68929e14i	− 0.575005i	−0.957780	−	0.287503i	$-0.907175\pi$
$859$	− 2.68929e14i	− 0.575005i	0.957780	−	0.287503i	$-0.0928250\pi$
$860$	− 3.57471e12i	− 0.00759886i
$861$	0	0
$862$	2.89613e14	0.608530
$863$	−2.31201e14	−0.482987	−0.241493	−	0.970402i	$-0.577637\pi$
$863$	−2.31201e14	−0.482987	−0.241493	+	0.970402i	$0.577637\pi$
$864$	7.29206e13i	0.151454i
$865$	3.89731e12	0.00804793
$866$	5.05124e14i	1.03707i
$867$	6.92413e13i	0.141342i
$868$	0	0
$869$	7.69063e14	1.55190
$870$	4.30998e11	0.000864727 0
$871$	− 1.86394e14i	− 0.371827i
$872$	3.42792e14	0.679906
$873$	6.33480e14i	1.24929i
$874$	2.16278e14i	0.424087i
$875$	0	0
$876$	−1.42520e14	−0.276283
$877$	6.82411e14	1.31537	0.657685	−	0.753293i	$-0.271536\pi$
$877$	6.82411e14	1.31537	0.657685	+	0.753293i	$0.271536\pi$
$878$	3.78487e14i	0.725401i
$879$	−3.11927e13	−0.0594441
$880$	1.30675e12i	0.00247616i
$881$	− 2.22417e14i	− 0.419071i	−0.977801	−	0.209536i	$-0.932805\pi$
$881$	− 2.22417e14i	− 0.419071i	0.977801	−	0.209536i	$-0.0671952\pi$
$882$	0	0
$883$	8.58401e14	1.59914	0.799570	−	0.600573i	$-0.205061\pi$
$883$	8.58401e14	1.59914	0.799570	+	0.600573i	$0.205061\pi$
$884$	1.50562e14	0.278903
$885$	2.10521e12i	0.00387774i
$886$	5.44542e14	0.997386
$887$	5.09928e14i	0.928732i	0.885643	+	0.464366i	$0.153718\pi$
$887$	5.09928e14i	0.928732i	−0.885643	+	0.464366i	$0.846282\pi$
$888$	5.43507e13i	0.0984330i
$889$	0	0
$890$	6.61303e12	0.0118427
$891$	−1.62723e14	−0.289775
$892$	− 8.70920e12i	− 0.0154225i
$893$	3.26817e13	0.0575502
$894$	1.56618e14i	0.274254i
$895$	1.10509e13i	0.0192434i
$896$	0	0
$897$	−1.26331e14	−0.217544
$898$	−3.76137e14	−0.644117
$899$	− 1.18028e14i	− 0.200996i
$900$	2.25578e14	0.382019
$901$	2.88853e14i	0.486466i
$902$	5.15359e14i	0.863132i
$903$	0	0
$904$	1.46513e14	0.242680
$905$	−1.10766e13	−0.0182458
$906$	− 1.14800e14i	− 0.188062i
$907$	3.25989e14	0.531088	0.265544	−	0.964099i	$-0.414448\pi$
$907$	3.25989e14	0.531088	0.265544	+	0.964099i	$0.414448\pi$
$908$	− 2.98173e14i	− 0.483102i
$909$	− 7.31921e14i	− 1.17936i
$910$	0	0
$911$	−4.29059e14	−0.683795	−0.341897	−	0.939737i	$-0.611069\pi$
$911$	−4.29059e14	−0.683795	−0.341897	+	0.939737i	$0.611069\pi$
$912$	5.03493e13	0.0798030
$913$	7.43888e14i	1.17261i
$914$	8.46265e13	0.132671
$915$	2.76862e12i	0.00431676i
$916$	2.40292e14i	0.372617i
$917$	0	0
$918$	4.48770e14	0.688352
$919$	2.43333e14	0.371214	0.185607	−	0.982624i	$-0.440575\pi$
$919$	2.43333e14	0.371214	0.185607	+	0.982624i	$0.440575\pi$
$920$	− 2.52956e12i	− 0.00383801i
$921$	5.53969e12	0.00835963
$922$	− 3.74517e14i	− 0.562105i
$923$	− 3.56512e14i	− 0.532188i
$924$	0	0
$925$	3.88160e14	0.573195
$926$	1.13140e14	0.166174
$927$	− 8.51612e14i	− 1.24407i
$928$	−2.57513e13	−0.0374161
$929$	1.09869e15i	1.58780i	0.608050	+	0.793898i	$0.291952\pi$
$929$	1.09869e15i	1.58780i	−0.608050	+	0.793898i	$0.708048\pi$
$930$	− 2.69907e12i	− 0.00387971i
$931$	0	0
$932$	−4.81971e14	−0.685396
$933$	−2.46112e14	−0.348116
$934$	7.43406e14i	1.04590i
$935$	8.04205e12	0.0112540
$936$	− 9.52849e13i	− 0.132631i
$937$	5.86960e12i	0.00812664i	0.999992	+	0.00406332i	$0.00129340\pi$
$937$	5.86960e12i	0.00812664i	−0.999992	+	0.00406332i	$0.998707\pi$
$938$	0	0
$939$	−4.22975e14	−0.579411
$940$	−3.82241e11	−0.000520833 0
$941$	− 5.10658e14i	− 0.692120i	−0.938212	−	0.346060i	$-0.887519\pi$
$941$	− 5.10658e14i	− 0.692120i	0.938212	−	0.346060i	$-0.112481\pi$
$942$	6.85520e12	0.00924199
$943$	− 9.97613e14i	− 1.33784i
$944$	− 1.25782e14i	− 0.167787i
$945$	0	0
$946$	5.69745e14	0.752013
$947$	4.85980e13	0.0638070	0.0319035	−	0.999491i	$-0.489843\pi$
$947$	4.85980e13	0.0638070	0.0319035	+	0.999491i	$0.489843\pi$
$948$	3.46574e14i	0.452642i
$949$	4.29939e14	0.558568
$950$	− 3.59583e14i	− 0.464709i
$951$	− 5.44397e14i	− 0.699863i
$952$	0	0
$953$	6.08156e14	0.773660	0.386830	−	0.922151i	$-0.373570\pi$
$953$	6.08156e14	0.773660	0.386830	+	0.922151i	$0.373570\pi$
$954$	1.82804e14	0.231337
$955$	− 1.46636e13i	− 0.0184597i
$956$	−1.50455e14	−0.188416
$957$	6.86935e13i	0.0855767i
$958$	9.14348e14i	1.13314i
$959$	0	0
$960$	−5.88880e11	−0.000722222 0
$961$	8.04908e13	0.0982040
$962$	− 1.63960e14i	− 0.199004i
$963$	−8.17217e14	−0.986748
$964$	− 5.43917e14i	− 0.653352i
$965$	− 1.42965e12i	− 0.00170842i
$966$	0	0
$967$	−6.41646e14	−0.758863	−0.379431	−	0.925220i	$-0.623880\pi$
$967$	−6.41646e14	−0.758863	−0.379431	+	0.925220i	$0.623880\pi$
$968$	9.22183e13	0.108503
$969$	− 3.09861e14i	− 0.362701i
$970$	−1.18105e13	−0.0137534
$971$	1.22898e14i	0.142380i	0.997463	+	0.0711901i	$0.0226797\pi$
$971$	1.22898e14i	0.142380i	−0.997463	+	0.0711901i	$0.977320\pi$
$972$	− 4.45000e14i	− 0.512896i
$973$	0	0
$974$	−8.62641e14	−0.984091
$975$	2.10038e14	0.238382
$976$	− 1.65419e14i	− 0.186783i
$977$	−1.01836e15	−1.14401	−0.572006	−	0.820250i	$-0.693835\pi$
$977$	−1.01836e15	−1.14401	−0.572006	+	0.820250i	$0.693835\pi$
$978$	1.40520e14i	0.157052i
$979$	1.05400e15i	1.17200i
$980$	0	0
$981$	−1.33510e15	−1.46950
$982$	−8.94218e13	−0.0979232
$983$	− 9.54958e14i	− 1.04044i	−0.854033	−	0.520219i	$-0.825850\pi$
$983$	− 9.54958e14i	− 1.04044i	0.854033	−	0.520219i	$-0.174150\pi$
$984$	−2.32244e14	−0.251749
$985$	7.11944e12i	0.00767829i
$986$	1.58479e14i	0.170054i
$987$	0	0
$988$	−1.51889e14	−0.161340
$989$	−1.10289e15	−1.16561
$990$	− 5.08952e12i	− 0.00535181i
$991$	−1.54962e15	−1.62128	−0.810638	−	0.585547i	$-0.800880\pi$
$991$	−1.54962e15	−1.62128	−0.810638	+	0.585547i	$0.800880\pi$
$992$	1.61264e14i	0.167872i
$993$	− 6.09824e14i	− 0.631624i
$994$	0	0
$995$	−5.98568e12	−0.00613759
$996$	−3.35229e14	−0.342015
$997$	− 6.82768e13i	− 0.0693103i	−0.999399	−	0.0346551i	$-0.988967\pi$
$997$	− 6.82768e13i	− 0.0693103i	0.999399	−	0.0346551i	$-0.0110333\pi$
$998$	1.00336e15	1.01345
$999$	− 4.88706e14i	− 0.491157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.11.b.c.97.3		12
7.2	even	3		98.11.d.a.31.6		12
7.3	odd	6		98.11.d.a.19.6		12
7.4	even	3		14.11.d.a.5.4	yes	12
7.5	odd	6		14.11.d.a.3.4	✓	12
7.6	odd	2	inner	98.11.b.c.97.4		12
21.5	even	6		126.11.n.b.73.2		12
21.11	odd	6		126.11.n.b.19.2		12
28.11	odd	6		112.11.s.a.33.5		12
28.19	even	6		112.11.s.a.17.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.11.d.a.3.4	✓	12	7.5	odd	6
14.11.d.a.5.4	yes	12	7.4	even	3
98.11.b.c.97.3		12	1.1	even	1	trivial
98.11.b.c.97.4		12	7.6	odd	2	inner
98.11.d.a.19.6		12	7.3	odd	6
98.11.d.a.31.6		12	7.2	even	3
112.11.s.a.17.5		12	28.19	even	6
112.11.s.a.33.5		12	28.11	odd	6
126.11.n.b.19.2		12	21.11	odd	6
126.11.n.b.73.2		12	21.5	even	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	98.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-22.6274 q^{2} -118.013i q^{3} +512.000 q^{4} -37.1782i q^{5} +2670.32i q^{6} -11585.2 q^{8} +45122.0 q^{9} +O(q^{10})\)	\(q-22.6274 q^{2} -118.013i q^{3} +512.000 q^{4} -37.1782i q^{5} +2670.32i q^{6} -11585.2 q^{8} +45122.0 q^{9} +841.247i q^{10} -134080. q^{11} -60422.4i q^{12} +182276. i q^{13} -4387.50 q^{15} +262144. q^{16} -1.61330e6i q^{17} -1.02100e6 q^{18} +1.62752e6i q^{19} -19035.3i q^{20} +3.03388e6 q^{22} -5.87288e6 q^{23} +1.36720e6i q^{24} +9.76424e6 q^{25} -4.12444e6i q^{26} -1.22935e7i q^{27} +4.34134e6 q^{29} +99277.7 q^{30} -2.71871e7i q^{31} -5.93164e6 q^{32} +1.58231e7i q^{33} +3.65047e7i q^{34} +2.31025e7 q^{36} +3.97532e7 q^{37} -3.68265e7i q^{38} +2.15109e7 q^{39} +430719. i q^{40} +1.69868e8i q^{41} +1.87794e8 q^{43} -6.86490e7 q^{44} -1.67756e6i q^{45} +1.32888e8 q^{46} -2.00807e7i q^{47} -3.09363e7i q^{48} -2.20940e8 q^{50} -1.90389e8 q^{51} +9.33255e7i q^{52} -1.79045e8 q^{53} +2.78170e8i q^{54} +4.98486e6i q^{55} +1.92067e8 q^{57} -9.82332e7 q^{58} -4.79819e8i q^{59} -2.24640e6 q^{60} -6.31025e8i q^{61} +6.15173e8i q^{62} +1.34218e8 q^{64} +6.77671e6 q^{65} -3.58036e8i q^{66} -1.02259e9 q^{67} -8.26007e8i q^{68} +6.93074e8i q^{69} -1.95589e9 q^{71} -5.22750e8 q^{72} -2.35872e9i q^{73} -8.99513e8 q^{74} -1.15230e9i q^{75} +8.33288e8i q^{76} -4.86736e8 q^{78} -5.73586e9 q^{79} -9.74605e6i q^{80} +1.21363e9 q^{81} -3.84367e9i q^{82} -5.54809e9i q^{83} -5.99795e7 q^{85} -4.24929e9 q^{86} -5.12332e8i q^{87} +1.55335e9 q^{88} -7.86098e9i q^{89} +3.79588e7i q^{90} -3.00692e9 q^{92} -3.20842e9 q^{93} +4.54375e8i q^{94} +6.05082e7 q^{95} +7.00008e8i q^{96} +1.40393e10i q^{97} -6.04996e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6144 q^{4} + 91056 q^{9}+O(q^{10}) \) 12 * q + 6144 * q^4 + 91056 * q^9	\( 12 q + 6144 q^{4} + 91056 q^{9} + 222420 q^{11} + 1065684 q^{15} + 3145728 q^{16} - 1430784 q^{18} - 1922688 q^{22} - 1706148 q^{23} - 33811608 q^{25} + 60157248 q^{29} + 74818944 q^{30} + 46620672 q^{36} + 15333012 q^{37} + 143256168 q^{39} + 1066803336 q^{43} + 113879040 q^{44} + 336490368 q^{46} + 1764094464 q^{50} + 638862780 q^{51} + 1200045108 q^{53} + 3357095652 q^{57} + 589196544 q^{58} + 545630208 q^{60} + 1610612736 q^{64} - 3072256152 q^{65} + 3180116652 q^{67} - 7739561160 q^{71} - 732561408 q^{72} - 2084616192 q^{74} - 8450806272 q^{78} - 4621124484 q^{79} - 15124682844 q^{81} - 39581743596 q^{85} + 9848173824 q^{86} - 984416256 q^{88} - 873547776 q^{92} + 15672528540 q^{93} - 58048533180 q^{95} - 13213951200 q^{99}+O(q^{100}) \) 12 * q + 6144 * q^4 + 91056 * q^9 + 222420 * q^11 + 1065684 * q^15 + 3145728 * q^16 - 1430784 * q^18 - 1922688 * q^22 - 1706148 * q^23 - 33811608 * q^25 + 60157248 * q^29 + 74818944 * q^30 + 46620672 * q^36 + 15333012 * q^37 + 143256168 * q^39 + 1066803336 * q^43 + 113879040 * q^44 + 336490368 * q^46 + 1764094464 * q^50 + 638862780 * q^51 + 1200045108 * q^53 + 3357095652 * q^57 + 589196544 * q^58 + 545630208 * q^60 + 1610612736 * q^64 - 3072256152 * q^65 + 3180116652 * q^67 - 7739561160 * q^71 - 732561408 * q^72 - 2084616192 * q^74 - 8450806272 * q^78 - 4621124484 * q^79 - 15124682844 * q^81 - 39581743596 * q^85 + 9848173824 * q^86 - 984416256 * q^88 - 873547776 * q^92 + 15672528540 * q^93 - 58048533180 * q^95 - 13213951200 * q^99

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