LMFDB - Embedded newform 98.13.b.c.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,13,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, 13, names="a")

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

chi := DirichletCharacter("98.97");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 13 $
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:	$89.5713940931$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 6613776 x^{14} + 17532494948988 x^{12} + \cdots + 16\!\cdots\!41 $ x^16 + 6613776x^14 + 17532494948988x^12 + 23874431083308410544x^10 + 17814546644991454004799078x^8 + 7194684838492777650788022411888x^6 + 1439579890626389563511626657632573372x^4 + 111400901558110496276819595183126508110288*x^2 + 166146008225686888975158615912586831592255841
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{56}\cdot 3^{8}\cdot 7^{24} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.8
Root			$1340.81i$ of defining polynomial
Character	$\chi$	$=$	98.97
Dual form			98.13.b.c.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-45.2548 q^{2} +1340.81i q^{3} +2048.00 q^{4} +16424.1i q^{5} -60678.2i q^{6} -92681.9 q^{8} -1.26633e6 q^{9} +O(q^{10})$	\(q-45.2548 q^{2} +1340.81i q^{3} +2048.00 q^{4} +16424.1i q^{5} -60678.2i q^{6} -92681.9 q^{8} -1.26633e6 q^{9} -743268. i q^{10} +928268. q^{11} +2.74598e6i q^{12} +8.24891e6i q^{13} -2.20216e7 q^{15} +4.19430e6 q^{16} -1.35429e7i q^{17} +5.73077e7 q^{18} +4.48980e7i q^{19} +3.36365e7i q^{20} -4.20086e7 q^{22} -7.07825e7 q^{23} -1.24269e8i q^{24} -2.56092e7 q^{25} -3.73303e8i q^{26} -9.85352e8i q^{27} -5.34101e8 q^{29} +9.96582e8 q^{30} -1.32412e9i q^{31} -1.89813e8 q^{32} +1.24463e9i q^{33} +6.12884e8i q^{34} -2.59345e9 q^{36} -1.05096e9 q^{37} -2.03185e9i q^{38} -1.10602e10 q^{39} -1.52221e9i q^{40} +1.78011e9i q^{41} -4.20662e9 q^{43} +1.90109e9 q^{44} -2.07983e10i q^{45} +3.20325e9 q^{46} -1.73741e10i q^{47} +5.62377e9i q^{48} +1.15894e9 q^{50} +1.81585e10 q^{51} +1.68938e10i q^{52} -4.93785e9 q^{53} +4.45919e10i q^{54} +1.52459e10i q^{55} -6.01997e10 q^{57} +2.41706e10 q^{58} -9.13053e9i q^{59} -4.51002e10 q^{60} +2.14226e10i q^{61} +5.99229e10i q^{62} +8.58993e9 q^{64} -1.35481e11 q^{65} -5.63256e10i q^{66} +6.42605e10 q^{67} -2.77360e10i q^{68} -9.49060e10i q^{69} -9.11975e10 q^{71} +1.17366e11 q^{72} +2.08093e11i q^{73} +4.75611e10 q^{74} -3.43371e10i q^{75} +9.19511e10i q^{76} +5.00529e11 q^{78} -3.05874e11 q^{79} +6.88875e10i q^{80} +6.48189e11 q^{81} -8.05584e10i q^{82} +2.37417e11i q^{83} +2.22430e11 q^{85} +1.90370e11 q^{86} -7.16128e11i q^{87} -8.60336e10 q^{88} +1.12155e11i q^{89} +9.41225e11i q^{90} -1.44963e11 q^{92} +1.77540e12 q^{93} +7.86263e11i q^{94} -7.37408e11 q^{95} -2.54503e11i q^{96} -9.61170e11i q^{97} -1.17550e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32768 q^{4} - 4724496 q^{9}+O(q^{10}) $ 16 * q + 32768 * q^4 - 4724496 * q^9	$ 16 q + 32768 q^{4} - 4724496 q^{9} - 4144176 q^{11} - 27163728 q^{15} + 67108864 q^{16} + 9185280 q^{18} + 62776320 q^{22} - 51261120 q^{23} - 1042411616 q^{25} + 532360944 q^{29} + 4303835136 q^{30} - 9675767808 q^{36} - 11529048080 q^{37} - 21052166544 q^{39} - 66929432000 q^{43} - 8487272448 q^{44} - 14406426624 q^{46} - 99248080896 q^{50} + 46598512752 q^{51} - 78268323600 q^{53} - 328243960080 q^{57} - 59274792960 q^{58} - 55631314944 q^{60} + 137438953472 q^{64} - 316645407792 q^{65} - 215534239840 q^{67} - 1150259029344 q^{71} + 18811453440 q^{72} - 9805556736 q^{74} - 786088888320 q^{78} - 455264129536 q^{79} + 783968356800 q^{81} + 710209696080 q^{85} + 76210384896 q^{86} + 128565903360 q^{88} - 104982773760 q^{92} + 917337537360 q^{93} + 373007725920 q^{95} + 3921180354576 q^{99}+O(q^{100}) $ 16 * q + 32768 * q^4 - 4724496 * q^9 - 4144176 * q^11 - 27163728 * q^15 + 67108864 * q^16 + 9185280 * q^18 + 62776320 * q^22 - 51261120 * q^23 - 1042411616 * q^25 + 532360944 * q^29 + 4303835136 * q^30 - 9675767808 * q^36 - 11529048080 * q^37 - 21052166544 * q^39 - 66929432000 * q^43 - 8487272448 * q^44 - 14406426624 * q^46 - 99248080896 * q^50 + 46598512752 * q^51 - 78268323600 * q^53 - 328243960080 * q^57 - 59274792960 * q^58 - 55631314944 * q^60 + 137438953472 * q^64 - 316645407792 * q^65 - 215534239840 * q^67 - 1150259029344 * q^71 + 18811453440 * q^72 - 9805556736 * q^74 - 786088888320 * q^78 - 455264129536 * q^79 + 783968356800 * q^81 + 710209696080 * q^85 + 76210384896 * q^86 + 128565903360 * q^88 - 104982773760 * q^92 + 917337537360 * q^93 + 373007725920 * q^95 + 3921180354576 * 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 $

$2$	−45.2548	−0.707107
$2$	−45.2548	−0.707107
$3$	1340.81i	1.83925i	0.392801	+	0.919623i	$0.371506\pi$
$3$	1340.81i	1.83925i	−0.392801	+	0.919623i	$0.628494\pi$
$4$	2048.00	0.500000
$5$	16424.1i	1.05114i	0.850750	+	0.525570i	$0.176148\pi$
$5$	16424.1i	1.05114i	−0.850750	+	0.525570i	$0.823852\pi$
$6$	− 60678.2i	− 1.30054i
$7$	0	0
$7$	0	0
$8$	−92681.9	−0.353553
$9$	−1.26633e6	−2.38283
$10$	− 743268.i	− 0.743268i
$11$	928268.	0.523983	0.261992	−	0.965070i	$-0.415621\pi$
$11$	928268.	0.523983	0.261992	+	0.965070i	$0.415621\pi$
$12$	2.74598e6i	0.919623i
$13$	8.24891e6i	1.70898i	0.519470	+	0.854489i	$0.326130\pi$
$13$	8.24891e6i	1.70898i	−0.519470	+	0.854489i	$0.673870\pi$
$14$	0	0
$15$	−2.20216e7	−1.93331
$16$	4.19430e6	0.250000
$17$	− 1.35429e7i	− 0.561073i	−0.959843	−	0.280537i	$-0.909488\pi$
$17$	− 1.35429e7i	− 0.561073i	0.959843	−	0.280537i	$-0.0905124\pi$
$18$	5.73077e7	1.68491
$19$	4.48980e7i	0.954345i	0.878810	+	0.477173i	$0.158338\pi$
$19$	4.48980e7i	0.954345i	−0.878810	+	0.477173i	$0.841662\pi$
$20$	3.36365e7i	0.525570i
$21$	0	0
$22$	−4.20086e7	−0.370512
$23$	−7.07825e7	−0.478144	−0.239072	−	0.971002i	$-0.576843\pi$
$23$	−7.07825e7	−0.478144	−0.239072	+	0.971002i	$0.576843\pi$
$24$	− 1.24269e8i	− 0.650272i
$25$	−2.56092e7	−0.104895
$26$	− 3.73303e8i	− 1.20843i
$27$	− 9.85352e8i	− 2.54336i
$28$	0	0
$29$	−5.34101e8	−0.897915	−0.448957	−	0.893553i	$-0.648205\pi$
$29$	−5.34101e8	−0.897915	−0.448957	+	0.893553i	$0.648205\pi$
$30$	9.96582e8	1.36705
$31$	− 1.32412e9i	− 1.49196i	−0.665968	−	0.745980i	$-0.731981\pi$
$31$	− 1.32412e9i	− 1.49196i	0.665968	−	0.745980i	$-0.268019\pi$
$32$	−1.89813e8	−0.176777
$33$	1.24463e9i	0.963734i
$34$	6.12884e8i	0.396739i
$35$	0	0
$36$	−2.59345e9	−1.19141
$37$	−1.05096e9	−0.409615	−0.204808	−	0.978802i	$-0.565657\pi$
$37$	−1.05096e9	−0.409615	−0.204808	+	0.978802i	$0.565657\pi$
$38$	− 2.03185e9i	− 0.674824i
$39$	−1.10602e10	−3.14323
$40$	− 1.52221e9i	− 0.371634i
$41$	1.78011e9i	0.374751i	0.982288	+	0.187375i	$0.0599981\pi$
$41$	1.78011e9i	0.374751i	−0.982288	+	0.187375i	$0.940002\pi$
$42$	0	0
$43$	−4.20662e9	−0.665461	−0.332730	−	0.943022i	$-0.607970\pi$
$43$	−4.20662e9	−0.665461	−0.332730	+	0.943022i	$0.607970\pi$
$44$	1.90109e9	0.261992
$45$	− 2.07983e10i	− 2.50469i
$46$	3.20325e9	0.338099
$47$	− 1.73741e10i	− 1.61182i	−0.592041	−	0.805908i	$-0.701678\pi$
$47$	− 1.73741e10i	− 1.61182i	0.592041	−	0.805908i	$-0.298322\pi$
$48$	5.62377e9i	0.459812i
$49$	0	0
$50$	1.15894e9	0.0741722
$51$	1.81585e10	1.03195
$52$	1.68938e10i	0.854489i
$53$	−4.93785e9	−0.222783	−0.111392	−	0.993777i	$-0.535531\pi$
$53$	−4.93785e9	−0.222783	−0.111392	+	0.993777i	$0.535531\pi$
$54$	4.45919e10i	1.79843i
$55$	1.52459e10i	0.550780i
$56$	0	0
$57$	−6.01997e10	−1.75528
$58$	2.41706e10	0.634922
$59$	− 9.13053e9i	− 0.216463i	−0.994126	−	0.108232i	$-0.965481\pi$
$59$	− 9.13053e9i	− 0.216463i	0.994126	−	0.108232i	$-0.0345188\pi$
$60$	−4.51002e10	−0.966653
$61$	2.14226e10i	0.415809i	0.978149	+	0.207905i	$0.0666644\pi$
$61$	2.14226e10i	0.415809i	−0.978149	+	0.207905i	$0.933336\pi$
$62$	5.99229e10i	1.05498i
$63$	0	0
$64$	8.58993e9	0.125000
$65$	−1.35481e11	−1.79638
$66$	− 5.63256e10i	− 0.681463i
$67$	6.42605e10	0.710388	0.355194	−	0.934793i	$-0.384415\pi$
$67$	6.42605e10	0.710388	0.355194	+	0.934793i	$0.384415\pi$
$68$	− 2.77360e10i	− 0.280537i
$69$	− 9.49060e10i	− 0.879425i
$70$	0	0
$71$	−9.11975e10	−0.711922	−0.355961	−	0.934501i	$-0.615846\pi$
$71$	−9.11975e10	−0.711922	−0.355961	+	0.934501i	$0.615846\pi$
$72$	1.17366e11	0.842457
$73$	2.08093e11i	1.37506i	0.726158	+	0.687528i	$0.241304\pi$
$73$	2.08093e11i	1.37506i	−0.726158	+	0.687528i	$0.758696\pi$
$74$	4.75611e10	0.289642
$75$	− 3.43371e10i	− 0.192928i
$76$	9.19511e10i	0.477173i
$77$	0	0
$78$	5.00529e11	2.22260
$79$	−3.05874e11	−1.25829	−0.629145	−	0.777288i	$-0.716595\pi$
$79$	−3.05874e11	−1.25829	−0.629145	+	0.777288i	$0.716595\pi$
$80$	6.88875e10i	0.262785i
$81$	6.48189e11	2.29505
$82$	− 8.05584e10i	− 0.264989i
$83$	2.37417e11i	0.726178i	0.931755	+	0.363089i	$0.118278\pi$
$83$	2.37417e11i	0.726178i	−0.931755	+	0.363089i	$0.881722\pi$
$84$	0	0
$85$	2.22430e11	0.589767
$86$	1.90370e11	0.470552
$87$	− 7.16128e11i	− 1.65149i
$88$	−8.60336e10	−0.185256
$89$	1.12155e11i	0.225672i	0.993614	+	0.112836i	$0.0359935\pi$
$89$	1.12155e11i	0.225672i	−0.993614	+	0.112836i	$0.964007\pi$
$90$	9.41225e11i	1.77108i
$91$	0	0
$92$	−1.44963e11	−0.239072
$93$	1.77540e12	2.74408
$94$	7.86263e11i	1.13973i
$95$	−7.37408e11	−1.00315
$96$	− 2.54503e11i	− 0.325136i
$97$	− 9.61170e11i	− 1.15390i	−0.816778	−	0.576952i	$-0.804242\pi$
$97$	− 9.61170e11i	− 1.15390i	0.816778	−	0.576952i	$-0.195758\pi$
$98$	0	0
$99$	−1.17550e12	−1.24856
$100$	−5.24477e10	−0.0524477
$101$	− 1.46554e12i	− 1.38060i	−0.723522	−	0.690302i	$-0.757478\pi$
$101$	− 1.46554e12i	− 1.38060i	0.723522	−	0.690302i	$-0.242522\pi$
$102$	−8.21761e11	−0.729701
$103$	− 1.05733e12i	− 0.885497i	−0.896646	−	0.442748i	$-0.854004\pi$
$103$	− 1.05733e12i	− 0.885497i	0.896646	−	0.442748i	$-0.145996\pi$
$104$	− 7.64525e11i	− 0.604215i
$105$	0	0
$106$	2.23462e11	0.157532
$107$	7.79883e11	0.519669	0.259834	−	0.965653i	$-0.416332\pi$
$107$	7.79883e11	0.519669	0.259834	+	0.965653i	$0.416332\pi$
$108$	− 2.01800e12i	− 1.27168i
$109$	6.14784e11	0.366576	0.183288	−	0.983059i	$-0.441326\pi$
$109$	6.14784e11	0.366576	0.183288	+	0.983059i	$0.441326\pi$
$110$	− 6.89952e11i	− 0.389460i
$111$	− 1.40914e12i	− 0.753384i
$112$	0	0
$113$	2.34507e12	1.12638	0.563190	−	0.826328i	$-0.309574\pi$
$113$	2.34507e12	1.12638	0.563190	+	0.826328i	$0.309574\pi$
$114$	2.72433e12	1.24117
$115$	− 1.16254e12i	− 0.502597i
$116$	−1.09384e12	−0.448957
$117$	− 1.04459e13i	− 4.07220i
$118$	4.13201e11i	0.153063i
$119$	0	0
$120$	2.04100e12	0.683527
$121$	−2.27675e12	−0.725442
$122$	− 9.69478e11i	− 0.294022i
$123$	−2.38678e12	−0.689259
$124$	− 2.71180e12i	− 0.745980i
$125$	3.58917e12i	0.940880i
$126$	0	0
$127$	−4.49588e12	−1.07150	−0.535750	−	0.844377i	$-0.679971\pi$
$127$	−4.49588e12	−1.07150	−0.535750	+	0.844377i	$0.679971\pi$
$128$	−3.88736e11	−0.0883883
$129$	− 5.64028e12i	− 1.22395i
$130$	6.13115e12	1.27023
$131$	8.95137e12i	1.77118i	0.464472	+	0.885588i	$0.346244\pi$
$131$	8.95137e12i	1.77118i	−0.464472	+	0.885588i	$0.653756\pi$
$132$	2.54901e12i	0.481867i
$133$	0	0
$134$	−2.90810e12	−0.502320
$135$	1.61835e13	2.67343
$136$	1.25519e12i	0.198369i
$137$	8.46615e12	1.28045	0.640225	−	0.768188i	$-0.278841\pi$
$137$	8.46615e12	1.28045	0.640225	+	0.768188i	$0.278841\pi$
$138$	4.29495e12i	0.621848i
$139$	5.06800e12i	0.702664i	0.936251	+	0.351332i	$0.114271\pi$
$139$	5.06800e12i	0.702664i	−0.936251	+	0.351332i	$0.885729\pi$
$140$	0	0
$141$	2.32954e13	2.96453
$142$	4.12713e12	0.503405
$143$	7.65720e12i	0.895475i
$144$	−5.31139e12	−0.595707
$145$	− 8.77210e12i	− 0.943834i
$146$	− 9.41722e12i	− 0.972312i
$147$	0	0
$148$	−2.15237e12	−0.204808
$149$	1.14847e13	1.04955	0.524775	−	0.851241i	$-0.324149\pi$
$149$	1.14847e13	1.04955	0.524775	+	0.851241i	$0.324149\pi$
$150$	1.55392e12i	0.136421i
$151$	1.22784e13	1.03581	0.517904	−	0.855439i	$-0.326712\pi$
$151$	1.22784e13	1.03581	0.517904	+	0.855439i	$0.326712\pi$
$152$	− 4.16123e12i	− 0.337412i
$153$	1.71499e13i	1.33694i
$154$	0	0
$155$	2.17474e13	1.56826
$156$	−2.26513e13	−1.57162
$157$	9.37833e11i	0.0626221i	0.999510	+	0.0313111i	$0.00996825\pi$
$157$	9.37833e11i	0.0626221i	−0.999510	+	0.0313111i	$0.990032\pi$
$158$	1.38423e13	0.889745
$159$	− 6.62072e12i	− 0.409753i
$160$	− 3.11749e12i	− 0.185817i
$161$	0	0
$162$	−2.93337e13	−1.62284
$163$	−8.43100e12	−0.449525	−0.224762	−	0.974414i	$-0.572161\pi$
$163$	−8.43100e12	−0.449525	−0.224762	+	0.974414i	$0.572161\pi$
$164$	3.64566e12i	0.187375i
$165$	−2.04419e13	−1.01302
$166$	− 1.07443e13i	− 0.513485i
$167$	− 1.23904e12i	− 0.0571199i	−0.999592	−	0.0285599i	$-0.990908\pi$
$167$	− 1.23904e12i	− 0.0571199i	0.999592	−	0.0285599i	$-0.00909215\pi$
$168$	0	0
$169$	−4.47464e13	−1.92061
$170$	−1.00660e13	−0.417028
$171$	− 5.68558e13i	− 2.27404i
$172$	−8.61515e12	−0.332730
$173$	3.94232e13i	1.47053i	0.677778	+	0.735267i	$0.262943\pi$
$173$	3.94232e13i	1.47053i	−0.677778	+	0.735267i	$0.737057\pi$
$174$	3.24083e13i	1.16778i
$175$	0	0
$176$	3.89344e12	0.130996
$177$	1.22423e13	0.398129
$178$	− 5.07555e12i	− 0.159574i
$179$	−2.79561e12	−0.0849882	−0.0424941	−	0.999097i	$-0.513530\pi$
$179$	−2.79561e12	−0.0849882	−0.0424941	+	0.999097i	$0.513530\pi$
$180$	− 4.25950e13i	− 1.25234i
$181$	3.44578e13i	0.979976i	0.871729	+	0.489988i	$0.162999\pi$
$181$	3.44578e13i	0.979976i	−0.871729	+	0.489988i	$0.837001\pi$
$182$	0	0
$183$	−2.87237e13	−0.764776
$184$	6.56026e12	0.169050
$185$	− 1.72610e13i	− 0.430563i
$186$	−8.03452e13	−1.94036
$187$	− 1.25715e13i	− 0.293993i
$188$	− 3.55822e13i	− 0.805908i
$189$	0	0
$190$	3.33713e13	0.709334
$191$	2.43323e13	0.501168	0.250584	−	0.968095i	$-0.419377\pi$
$191$	2.43323e13	0.501168	0.250584	+	0.968095i	$0.419377\pi$
$192$	1.15175e13i	0.229906i
$193$	−9.56839e12	−0.185138	−0.0925689	−	0.995706i	$-0.529508\pi$
$193$	−9.56839e12	−0.185138	−0.0925689	+	0.995706i	$0.529508\pi$
$194$	4.34976e13i	0.815933i
$195$	− 1.81654e14i	− 3.30398i
$196$	0	0
$197$	−3.14741e13	−0.538462	−0.269231	−	0.963076i	$-0.586770\pi$
$197$	−3.14741e13	−0.538462	−0.269231	+	0.963076i	$0.586770\pi$
$198$	5.31969e13	0.882867
$199$	1.07268e14i	1.72723i	0.504152	+	0.863615i	$0.331805\pi$
$199$	1.07268e14i	1.72723i	−0.504152	+	0.863615i	$0.668195\pi$
$200$	2.37351e12	0.0370861
$201$	8.61612e13i	1.30658i
$202$	6.63227e13i	0.976234i
$203$	0	0
$204$	3.71887e13	0.515976
$205$	−2.92366e13	−0.393915
$206$	4.78493e13i	0.626141i
$207$	8.96342e13	1.13934
$208$	3.45984e13i	0.427244i
$209$	4.16774e13i	0.500061i
$210$	0	0
$211$	3.92422e13	0.444691	0.222346	−	0.974968i	$-0.428629\pi$
$211$	3.92422e13	0.444691	0.222346	+	0.974968i	$0.428629\pi$
$212$	−1.01127e13	−0.111392
$213$	− 1.22279e14i	− 1.30940i
$214$	−3.52935e13	−0.367461
$215$	− 6.90898e13i	− 0.699492i
$216$	9.13243e13i	0.899215i
$217$	0	0
$218$	−2.78220e13	−0.259208
$219$	−2.79014e14	−2.52907
$220$	3.12237e13i	0.275390i
$221$	1.11715e14	0.958862
$222$	6.37704e13i	0.532723i
$223$	− 1.59588e14i	− 1.29769i	−0.760920	−	0.648845i	$-0.775252\pi$
$223$	− 1.59588e14i	− 1.29769i	0.760920	−	0.648845i	$-0.224748\pi$
$224$	0	0
$225$	3.24298e13	0.249948
$226$	−1.06126e14	−0.796470
$227$	4.66730e13i	0.341123i	0.985347	+	0.170561i	$0.0545581\pi$
$227$	4.66730e13i	0.341123i	−0.985347	+	0.170561i	$0.945442\pi$
$228$	−1.23289e14	−0.877638
$229$	− 2.62559e13i	− 0.182059i	−0.995848	−	0.0910297i	$-0.970984\pi$
$229$	− 2.62559e13i	− 0.182059i	0.995848	−	0.0910297i	$-0.0290158\pi$
$230$	5.26104e13i	0.355389i
$231$	0	0
$232$	4.95015e13	0.317461
$233$	−4.66359e13	−0.291464	−0.145732	−	0.989324i	$-0.546554\pi$
$233$	−4.66359e13	−0.291464	−0.145732	+	0.989324i	$0.546554\pi$
$234$	4.72726e14i	2.87948i
$235$	2.85354e14	1.69424
$236$	− 1.86993e13i	− 0.108232i
$237$	− 4.10120e14i	− 2.31431i
$238$	0	0
$239$	9.36225e13	0.502334	0.251167	−	0.967944i	$-0.419186\pi$
$239$	9.36225e13	0.502334	0.251167	+	0.967944i	$0.419186\pi$
$240$	−9.23651e13	−0.483327
$241$	7.79124e13i	0.397653i	0.980035	+	0.198826i	$0.0637130\pi$
$241$	7.79124e13i	0.397653i	−0.980035	+	0.198826i	$0.936287\pi$
$242$	1.03034e14	0.512965
$243$	3.45443e14i	1.67779i
$244$	4.38736e13i	0.207905i
$245$	0	0
$246$	1.08014e14	0.487380
$247$	−3.70360e14	−1.63095
$248$	1.22722e14i	0.527488i
$249$	−3.18331e14	−1.33562
$250$	− 1.62427e14i	− 0.665303i
$251$	− 1.06944e13i	− 0.0427675i	−0.999771	−	0.0213837i	$-0.993193\pi$
$251$	− 1.06944e13i	− 0.0427675i	0.999771	−	0.0213837i	$-0.00680717\pi$
$252$	0	0
$253$	−6.57051e13	−0.250539
$254$	2.03460e14	0.757665
$255$	2.98237e14i	1.08473i
$256$	1.75922e13	0.0625000
$257$	3.93414e14i	1.36537i	0.730712	+	0.682686i	$0.239188\pi$
$257$	3.93414e14i	1.36537i	−0.730712	+	0.682686i	$0.760812\pi$
$258$	2.55250e14i	0.865461i
$259$	0	0
$260$	−2.77464e14	−0.898188
$261$	6.76350e14	2.13958
$262$	− 4.05093e14i	− 1.25241i
$263$	3.14447e14	0.950195	0.475098	−	0.879933i	$-0.342413\pi$
$263$	3.14447e14	0.950195	0.475098	+	0.879933i	$0.342413\pi$
$264$	− 1.15355e14i	− 0.340731i
$265$	− 8.10995e13i	− 0.234176i
$266$	0	0
$267$	−1.50378e14	−0.415067
$268$	1.31606e14	0.355194
$269$	− 4.41360e14i	− 1.16487i	−0.812876	−	0.582437i	$-0.802099\pi$
$269$	− 4.41360e14i	− 1.16487i	0.812876	−	0.582437i	$-0.197901\pi$
$270$	−7.32381e14	−1.89040
$271$	4.93373e14i	1.24554i	0.782403	+	0.622772i	$0.213994\pi$
$271$	4.93373e14i	1.24554i	−0.782403	+	0.622772i	$0.786006\pi$
$272$	− 5.68032e13i	− 0.140268i
$273$	0	0
$274$	−3.83134e14	−0.905414
$275$	−2.37722e13	−0.0549634
$276$	− 1.94367e14i	− 0.439713i
$277$	−6.89606e14	−1.52659	−0.763295	−	0.646050i	$-0.776420\pi$
$277$	−6.89606e14	−1.52659	−0.763295	+	0.646050i	$0.776420\pi$
$278$	− 2.29351e14i	− 0.496859i
$279$	1.67678e15i	3.55509i
$280$	0	0
$281$	−4.08440e14	−0.829641	−0.414820	−	0.909903i	$-0.636156\pi$
$281$	−4.08440e14	−0.829641	−0.414820	+	0.909903i	$0.636156\pi$
$282$	−1.05423e15	−2.09624
$283$	− 9.59636e14i	− 1.86805i	−0.357212	−	0.934023i	$-0.616273\pi$
$283$	− 9.59636e14i	− 1.86805i	0.357212	−	0.934023i	$-0.383727\pi$
$284$	−1.86772e14	−0.355961
$285$	− 9.88724e14i	− 1.84504i
$286$	− 3.46525e14i	− 0.633197i
$287$	0	0
$288$	2.40366e14	0.421229
$289$	3.99211e14	0.685197
$290$	3.96980e14i	0.667392i
$291$	1.28875e15	2.12231
$292$	4.26175e14i	0.687528i
$293$	− 9.48005e14i	− 1.49832i	−0.662388	−	0.749161i	$-0.730457\pi$
$293$	− 9.48005e14i	− 1.49832i	0.662388	−	0.749161i	$-0.269543\pi$
$294$	0	0
$295$	1.49960e14	0.227533
$296$	9.74050e13	0.144821
$297$	− 9.14670e14i	− 1.33268i
$298$	−5.19740e14	−0.742145
$299$	− 5.83879e14i	− 0.817138i
$300$	− 7.03224e13i	− 0.0964642i
$301$	0	0
$302$	−5.55656e14	−0.732427
$303$	1.96501e15	2.53927
$304$	1.88316e14i	0.238586i
$305$	−3.51847e14	−0.437074
$306$	− 7.76115e14i	− 0.945361i
$307$	− 8.39849e14i	− 1.00316i	−0.865111	−	0.501581i	$-0.832752\pi$
$307$	− 8.39849e14i	− 1.00316i	0.865111	−	0.501581i	$-0.167248\pi$
$308$	0	0
$309$	1.41768e15	1.62865
$310$	−9.84177e14	−1.10893
$311$	3.81059e13i	0.0421143i	0.999778	+	0.0210572i	$0.00670320\pi$
$311$	3.81059e13i	0.0421143i	−0.999778	+	0.0210572i	$0.993297\pi$
$312$	1.02508e15	1.11130
$313$	2.99457e13i	0.0318470i	0.999873	+	0.0159235i	$0.00506882\pi$
$313$	2.99457e13i	0.0318470i	−0.999873	+	0.0159235i	$0.994931\pi$
$314$	− 4.24415e13i	− 0.0442805i
$315$	0	0
$316$	−6.26431e14	−0.629145
$317$	−3.63437e14	−0.358158	−0.179079	−	0.983835i	$-0.557312\pi$
$317$	−3.63437e14	−0.358158	−0.179079	+	0.983835i	$0.557312\pi$
$318$	2.99620e14i	0.289739i
$319$	−4.95789e14	−0.470492
$320$	1.41082e14i	0.131393i
$321$	1.04568e15i	0.955799i
$322$	0	0
$323$	6.08051e14	0.535458
$324$	1.32749e15	1.14752
$325$	− 2.11248e14i	− 0.179264i
$326$	3.81543e14	0.317862
$327$	8.24310e14i	0.674223i
$328$	− 1.64984e14i	− 0.132494i
$329$	0	0
$330$	9.25095e14	0.716313
$331$	−6.85508e14	−0.521248	−0.260624	−	0.965440i	$-0.583928\pi$
$331$	−6.85508e14	−0.521248	−0.260624	+	0.965440i	$0.583928\pi$
$332$	4.86230e14i	0.363089i
$333$	1.33087e15	0.976043
$334$	5.60727e13i	0.0403899i
$335$	1.05542e15i	0.746717i
$336$	0	0
$337$	−2.02273e15	−1.38089	−0.690445	−	0.723385i	$-0.742585\pi$
$337$	−2.02273e15	−1.38089	−0.690445	+	0.723385i	$0.742585\pi$
$338$	2.02499e15	1.35807
$339$	3.14429e15i	2.07169i
$340$	4.55537e14	0.294883
$341$	− 1.22914e15i	− 0.781762i
$342$	2.57300e15i	1.60799i
$343$	0	0
$344$	3.89877e14	0.235276
$345$	1.55874e15	0.924399
$346$	− 1.78409e15i	− 1.03982i
$347$	2.61602e15	1.49853	0.749263	−	0.662272i	$-0.230408\pi$
$347$	2.61602e15	1.49853	0.749263	+	0.662272i	$0.230408\pi$
$348$	− 1.46663e15i	− 0.825744i
$349$	− 2.07896e14i	− 0.115052i	−0.998344	−	0.0575260i	$-0.981679\pi$
$349$	− 2.07896e14i	− 0.115052i	0.998344	−	0.0575260i	$-0.0183212\pi$
$350$	0	0
$351$	8.12808e15	4.34655
$352$	−1.76197e14	−0.0926280
$353$	− 3.62630e15i	− 1.87420i	−0.349062	−	0.937100i	$-0.613500\pi$
$353$	− 3.62630e15i	− 1.87420i	0.349062	−	0.937100i	$-0.386500\pi$
$354$	−5.54024e14	−0.281520
$355$	− 1.49783e15i	− 0.748330i
$356$	2.29693e14i	0.112836i
$357$	0	0
$358$	1.26515e14	0.0600957
$359$	−3.24701e15	−1.51676	−0.758381	−	0.651811i	$-0.774009\pi$
$359$	−3.24701e15	−1.51676	−0.758381	+	0.651811i	$0.774009\pi$
$360$	1.92763e15i	0.885541i
$361$	1.97484e14	0.0892256
$362$	− 1.55938e15i	− 0.692948i
$363$	− 3.05269e15i	− 1.33427i
$364$	0	0
$365$	−3.41773e15	−1.44538
$366$	1.29989e15	0.540778
$367$	3.46220e15i	1.41696i	0.705733	+	0.708478i	$0.250618\pi$
$367$	3.46220e15i	1.41696i	−0.705733	+	0.708478i	$0.749382\pi$
$368$	−2.96883e14	−0.119536
$369$	− 2.25421e15i	− 0.892967i
$370$	7.81146e14i	0.304454i
$371$	0	0
$372$	3.63601e15	1.37204
$373$	−4.70849e13	−0.0174835	−0.00874176	−	0.999962i	$-0.502783\pi$
$373$	−4.70849e13	−0.0174835	−0.00874176	+	0.999962i	$0.502783\pi$
$374$	5.68920e14i	0.207884i
$375$	−4.81240e15	−1.73051
$376$	1.61027e15i	0.569863i
$377$	− 4.40575e15i	− 1.53452i
$378$	0	0
$379$	−4.47743e15	−1.51075	−0.755376	−	0.655292i	$-0.772546\pi$
$379$	−4.47743e15	−1.51075	−0.755376	+	0.655292i	$0.772546\pi$
$380$	−1.51021e15	−0.501575
$381$	− 6.02812e15i	− 1.97075i
$382$	−1.10115e15	−0.354379
$383$	− 2.68732e15i	− 0.851386i	−0.904868	−	0.425693i	$-0.860030\pi$
$383$	− 2.68732e15i	− 0.851386i	0.904868	−	0.425693i	$-0.139970\pi$
$384$	− 5.21222e14i	− 0.162568i
$385$	0	0
$386$	4.33016e14	0.130912
$387$	5.32698e15	1.58568
$388$	− 1.96848e15i	− 0.576952i
$389$	−4.94660e15	−1.42761	−0.713804	−	0.700345i	$-0.753029\pi$
$389$	−4.94660e15	−1.42761	−0.713804	+	0.700345i	$0.753029\pi$
$390$	8.22072e15i	2.33626i
$391$	9.58604e14i	0.268274i
$392$	0	0
$393$	−1.20021e16	−3.25763
$394$	1.42435e15	0.380750
$395$	− 5.02370e15i	− 1.32264i
$396$	−2.40742e15	−0.624281
$397$	1.37868e15i	0.352143i	0.984377	+	0.176072i	$0.0563390\pi$
$397$	1.37868e15i	0.352143i	−0.984377	+	0.176072i	$0.943661\pi$
$398$	− 4.85438e15i	− 1.22134i
$399$	0	0
$400$	−1.07413e14	−0.0262238
$401$	−1.96685e15	−0.473049	−0.236524	−	0.971626i	$-0.576008\pi$
$401$	−1.96685e15	−0.473049	−0.236524	+	0.971626i	$0.576008\pi$
$402$	− 3.89921e15i	− 0.923890i
$403$	1.09226e16	2.54973
$404$	− 3.00142e15i	− 0.690302i
$405$	1.06459e16i	2.41241i
$406$	0	0
$407$	−9.75573e14	−0.214631
$408$	−1.68297e15	−0.364850
$409$	3.31631e15i	0.708460i	0.935158	+	0.354230i	$0.115257\pi$
$409$	3.31631e15i	0.708460i	−0.935158	+	0.354230i	$0.884743\pi$
$410$	1.32310e15	0.278540
$411$	1.13515e16i	2.35506i
$412$	− 2.16541e15i	− 0.442748i
$413$	0	0
$414$	−4.05638e15	−0.805632
$415$	−3.89935e15	−0.763314
$416$	− 1.56575e15i	− 0.302107i
$417$	−6.79523e15	−1.29237
$418$	− 1.88610e15i	− 0.353596i
$419$	− 3.45895e15i	− 0.639235i	−0.947547	−	0.319618i	$-0.896446\pi$
$419$	− 3.45895e15i	− 0.639235i	0.947547	−	0.319618i	$-0.103554\pi$
$420$	0	0
$421$	2.52314e15	0.453156	0.226578	−	0.973993i	$-0.427246\pi$
$421$	2.52314e15	0.453156	0.226578	+	0.973993i	$0.427246\pi$
$422$	−1.77590e15	−0.314444
$423$	2.20014e16i	3.84068i
$424$	4.57649e14	0.0787658
$425$	3.46824e14i	0.0588540i
$426$	5.53370e15i	0.925886i
$427$	0	0
$428$	1.59720e15	0.259834
$429$	−1.02669e16	−1.64700
$430$	3.12665e15i	0.494616i
$431$	−5.72020e15	−0.892376	−0.446188	−	0.894939i	$-0.647219\pi$
$431$	−5.72020e15	−0.892376	−0.446188	+	0.894939i	$0.647219\pi$
$432$	− 4.13286e15i	− 0.635841i
$433$	− 5.07252e15i	− 0.769656i	−0.922988	−	0.384828i	$-0.874261\pi$
$433$	− 5.07252e15i	− 0.769656i	0.922988	−	0.384828i	$-0.125739\pi$
$434$	0	0
$435$	1.17617e16	1.73594
$436$	1.25908e15	0.183288
$437$	− 3.17799e15i	− 0.456315i
$438$	1.26267e16	1.78832
$439$	− 1.63005e14i	− 0.0227727i	−0.999935	−	0.0113864i	$-0.996376\pi$
$439$	− 1.63005e14i	− 0.0227727i	0.999935	−	0.0113864i	$-0.00362447\pi$
$440$	− 1.41302e15i	− 0.194730i
$441$	0	0
$442$	−5.05562e15	−0.678018
$443$	−2.07783e15	−0.274908	−0.137454	−	0.990508i	$-0.543892\pi$
$443$	−2.07783e15	−0.274908	−0.137454	+	0.990508i	$0.543892\pi$
$444$	− 2.88592e15i	− 0.376692i
$445$	−1.84204e15	−0.237213
$446$	7.22213e15i	0.917606i
$447$	1.53989e16i	1.93038i
$448$	0	0
$449$	8.24719e15	1.00653	0.503267	−	0.864131i	$-0.332131\pi$
$449$	8.24719e15	1.00653	0.503267	+	0.864131i	$0.332131\pi$
$450$	−1.46760e15	−0.176740
$451$	1.65241e15i	0.196363i
$452$	4.80270e15	0.563190
$453$	1.64630e16i	1.90511i
$454$	− 2.11218e15i	− 0.241210i
$455$	0	0
$456$	5.57943e15	0.620584
$457$	−9.74652e15	−1.06992	−0.534962	−	0.844876i	$-0.679674\pi$
$457$	−9.74652e15	−1.06992	−0.534962	+	0.844876i	$0.679674\pi$
$458$	1.18820e15i	0.128735i
$459$	−1.33446e16	−1.42701
$460$	− 2.38087e15i	− 0.251298i
$461$	5.11431e15i	0.532821i	0.963860	+	0.266410i	$0.0858377\pi$
$461$	5.11431e15i	0.532821i	−0.963860	+	0.266410i	$0.914162\pi$
$462$	0	0
$463$	−1.08295e16	−1.09931	−0.549656	−	0.835391i	$-0.685241\pi$
$463$	−1.08295e16	−1.09931	−0.549656	+	0.835391i	$0.685241\pi$
$464$	−2.24018e15	−0.224479
$465$	2.91592e16i	2.88442i
$466$	2.11050e15	0.206096
$467$	− 3.37089e15i	− 0.324970i	−0.986711	−	0.162485i	$-0.948049\pi$
$467$	− 3.37089e15i	− 0.324970i	0.986711	−	0.162485i	$-0.0519509\pi$
$468$	− 2.13931e16i	− 2.03610i
$469$	0	0
$470$	−1.29136e16	−1.19801
$471$	−1.25746e15	−0.115178
$472$	8.46235e14i	0.0765313i
$473$	−3.90487e15	−0.348690
$474$	1.85599e16i	1.63646i
$475$	− 1.14980e15i	− 0.100106i
$476$	0	0
$477$	6.25296e15	0.530854
$478$	−4.23687e15	−0.355204
$479$	− 1.16984e15i	− 0.0968532i	−0.998827	−	0.0484266i	$-0.984579\pi$
$479$	− 1.16984e15i	− 0.0968532i	0.998827	−	0.0484266i	$-0.0154207\pi$
$480$	4.17997e15	0.341763
$481$	− 8.66928e15i	− 0.700023i
$482$	− 3.52591e15i	− 0.281183i
$483$	0	0
$484$	−4.66278e15	−0.362721
$485$	1.57863e16	1.21291
$486$	− 1.56329e16i	− 1.18638i
$487$	8.42449e15	0.631495	0.315747	−	0.948843i	$-0.397745\pi$
$487$	8.42449e15	0.631495	0.315747	+	0.948843i	$0.397745\pi$
$488$	− 1.98549e15i	− 0.147011i
$489$	− 1.13044e16i	− 0.826787i
$490$	0	0
$491$	4.07478e15	0.290814	0.145407	−	0.989372i	$-0.453551\pi$
$491$	4.07478e15	0.290814	0.145407	+	0.989372i	$0.453551\pi$
$492$	−4.88813e15	−0.344630
$493$	7.23330e15i	0.503796i
$494$	1.67606e16	1.15326
$495$	− 1.93064e16i	− 1.31241i
$496$	− 5.55376e15i	− 0.372990i
$497$	0	0
$498$	1.44060e16	0.944426
$499$	−8.28300e15	−0.536518	−0.268259	−	0.963347i	$-0.586448\pi$
$499$	−8.28300e15	−0.536518	−0.268259	+	0.963347i	$0.586448\pi$
$500$	7.35063e15i	0.470440i
$501$	1.66132e15	0.105058
$502$	4.83972e14i	0.0302412i
$503$	1.35321e16i	0.835519i	0.908558	+	0.417759i	$0.137185\pi$
$503$	1.35321e16i	0.835519i	−0.908558	+	0.417759i	$0.862815\pi$
$504$	0	0
$505$	2.40701e16	1.45121
$506$	2.97347e15	0.177158
$507$	− 5.99965e16i	− 3.53247i
$508$	−9.20755e15	−0.535750
$509$	− 2.00720e16i	− 1.15420i	−0.816672	−	0.577102i	$-0.804183\pi$
$509$	− 2.00720e16i	− 1.15420i	0.816672	−	0.577102i	$-0.195817\pi$
$510$	− 1.34967e16i	− 0.767017i
$511$	0	0
$512$	−7.96131e14	−0.0441942
$513$	4.42403e16	2.42725
$514$	− 1.78039e16i	− 0.965464i
$515$	1.73656e16	0.930781
$516$	− 1.15513e16i	− 0.611973i
$517$	− 1.61278e16i	− 0.844564i
$518$	0	0
$519$	−5.28590e16	−2.70467
$520$	1.25566e16	0.635114
$521$	1.67626e16i	0.838135i	0.907955	+	0.419067i	$0.137643\pi$
$521$	1.67626e16i	0.838135i	−0.907955	+	0.419067i	$0.862357\pi$
$522$	−3.06081e16	−1.51291
$523$	9.73057e15i	0.475476i	0.971329	+	0.237738i	$0.0764059\pi$
$523$	9.73057e15i	0.475476i	−0.971329	+	0.237738i	$0.923594\pi$
$524$	1.83324e16i	0.885588i
$525$	0	0
$526$	−1.42302e16	−0.671890
$527$	−1.79325e16	−0.837099
$528$	5.22036e15i	0.240934i
$529$	−1.69045e16	−0.771378
$530$	3.67015e15i	0.165588i
$531$	1.15623e16i	0.515795i
$532$	0	0
$533$	−1.46839e16	−0.640441
$534$	6.80535e15	0.293496
$535$	1.28088e16i	0.546245i
$536$	−5.95579e15	−0.251160
$537$	− 3.74839e15i	− 0.156314i
$538$	1.99737e16i	0.823691i
$539$	0	0
$540$	3.31438e16	1.33672
$541$	−2.47683e16	−0.987898	−0.493949	−	0.869491i	$-0.664447\pi$
$541$	−2.47683e16	−0.987898	−0.493949	+	0.869491i	$0.664447\pi$
$542$	− 2.23275e16i	− 0.880733i
$543$	−4.62013e16	−1.80242
$544$	2.57062e15i	0.0991847i
$545$	1.00973e16i	0.385322i
$546$	0	0
$547$	1.37294e16	0.512540	0.256270	−	0.966605i	$-0.417506\pi$
$547$	1.37294e16	0.512540	0.256270	+	0.966605i	$0.417506\pi$
$548$	1.73387e16	0.640225
$549$	− 2.71282e16i	− 0.990802i
$550$	1.07581e15	0.0388650
$551$	− 2.39801e16i	− 0.856921i
$552$	8.79607e15i	0.310924i
$553$	0	0
$554$	3.12080e16	1.07946
$555$	2.31438e16	0.791912
$556$	1.03793e16i	0.351332i
$557$	1.70325e15	0.0570358	0.0285179	−	0.999593i	$-0.490921\pi$
$557$	1.70325e15	0.0570358	0.0285179	+	0.999593i	$0.490921\pi$
$558$	− 7.58823e16i	− 2.51383i
$559$	− 3.47000e16i	− 1.13726i
$560$	0	0
$561$	1.68560e16	0.540726
$562$	1.84839e16	0.586644
$563$	− 1.58125e16i	− 0.496535i	−0.968692	−	0.248267i	$-0.920139\pi$
$563$	− 1.58125e16i	− 0.496535i	0.968692	−	0.248267i	$-0.0798612\pi$
$564$	4.77090e16	1.48226
$565$	3.85155e16i	1.18398i
$566$	4.34282e16i	1.32091i
$567$	0	0
$568$	8.45235e15	0.251703
$569$	5.58942e16	1.64700	0.823499	−	0.567318i	$-0.192019\pi$
$569$	5.58942e16	1.64700	0.823499	+	0.567318i	$0.192019\pi$
$570$	4.47446e16i	1.30464i
$571$	−1.19221e16	−0.343983	−0.171991	−	0.985098i	$-0.555020\pi$
$571$	−1.19221e16	−0.343983	−0.171991	+	0.985098i	$0.555020\pi$
$572$	1.56819e16i	0.447738i
$573$	3.26250e16i	0.921771i
$574$	0	0
$575$	1.81268e15	0.0501551
$576$	−1.08777e16	−0.297854
$577$	3.71382e16i	1.00639i	0.864173	+	0.503194i	$0.167842\pi$
$577$	3.71382e16i	1.00639i	−0.864173	+	0.503194i	$0.832158\pi$
$578$	−1.80662e16	−0.484507
$579$	− 1.28294e16i	− 0.340514i
$580$	− 1.79653e16i	− 0.471917i
$581$	0	0
$582$	−5.83220e16	−1.50070
$583$	−4.58365e15	−0.116735
$584$	− 1.92865e16i	− 0.486156i
$585$	1.71564e17	4.28046
$586$	4.29018e16i	1.05947i
$587$	− 5.00677e16i	− 1.22385i	−0.790915	−	0.611926i	$-0.790395\pi$
$587$	− 5.00677e16i	− 1.22385i	0.790915	−	0.611926i	$-0.209605\pi$
$588$	0	0
$589$	5.94504e16	1.42385
$590$	−6.78643e15	−0.160890
$591$	− 4.22008e16i	− 0.990365i
$592$	−4.40805e15	−0.102404
$593$	4.39226e15i	0.101009i	0.998724	+	0.0505045i	$0.0160829\pi$
$593$	4.39226e15i	0.101009i	−0.998724	+	0.0505045i	$0.983917\pi$
$594$	4.13932e16i	0.942347i
$595$	0	0
$596$	2.35207e16	0.524775
$597$	−1.43826e17	−3.17680
$598$	2.64233e16i	0.577804i
$599$	7.91281e16	1.71305	0.856524	−	0.516107i	$-0.172619\pi$
$599$	7.91281e16	1.71305	0.856524	+	0.516107i	$0.172619\pi$
$600$	3.18243e15i	0.0682105i
$601$	7.67076e16i	1.62776i	0.581030	+	0.813882i	$0.302650\pi$
$601$	7.67076e16i	1.62776i	−0.581030	+	0.813882i	$0.697350\pi$
$602$	0	0
$603$	−8.13752e16	−1.69273
$604$	2.51461e16	0.517904
$605$	− 3.73934e16i	− 0.762541i
$606$	−8.89262e16	−1.79553
$607$	− 5.52617e16i	− 1.10482i	−0.833572	−	0.552411i	$-0.813708\pi$
$607$	− 5.52617e16i	− 1.10482i	0.833572	−	0.552411i	$-0.186292\pi$
$608$	− 8.52220e15i	− 0.168706i
$609$	0	0
$610$	1.59228e16	0.309058
$611$	1.43317e17	2.75456
$612$	3.51230e16i	0.668471i
$613$	−4.16351e16	−0.784688	−0.392344	−	0.919819i	$-0.628336\pi$
$613$	−4.16351e16	−0.784688	−0.392344	+	0.919819i	$0.628336\pi$
$614$	3.80072e16i	0.709342i
$615$	− 3.92007e16i	− 0.724508i
$616$	0	0
$617$	−8.46408e16	−1.53415	−0.767077	−	0.641556i	$-0.778289\pi$
$617$	−8.46408e16	−1.53415	−0.767077	+	0.641556i	$0.778289\pi$
$618$	−6.41568e16	−1.15163
$619$	− 7.25126e16i	− 1.28905i	−0.764584	−	0.644525i	$-0.777055\pi$
$619$	− 7.25126e16i	− 1.28905i	0.764584	−	0.644525i	$-0.222945\pi$
$620$	4.45388e16	0.784130
$621$	6.97457e16i	1.21610i
$622$	− 1.72448e15i	− 0.0297793i
$623$	0	0
$624$	−4.63900e16	−0.785808
$625$	−6.52011e16	−1.09389
$626$	− 1.35519e15i	− 0.0225192i
$627$	−5.58815e16	−0.919735
$628$	1.92068e15i	0.0313111i
$629$	1.42331e16i	0.229824i
$630$	0	0
$631$	9.77355e16	1.54838	0.774188	−	0.632956i	$-0.218159\pi$
$631$	9.77355e16	1.54838	0.774188	+	0.632956i	$0.218159\pi$
$632$	2.83490e16	0.444873
$633$	5.26164e16i	0.817897i
$634$	1.64473e16	0.253256
$635$	− 7.38405e16i	− 1.12630i
$636$	− 1.35592e16i	− 0.204877i
$637$	0	0
$638$	2.24368e16	0.332688
$639$	1.15486e17	1.69639
$640$	− 6.38463e15i	− 0.0929085i
$641$	−8.97546e16	−1.29392	−0.646962	−	0.762523i	$-0.723961\pi$
$641$	−8.97546e16	−1.29392	−0.646962	+	0.762523i	$0.723961\pi$
$642$	− 4.73219e16i	− 0.675852i
$643$	5.41761e16i	0.766553i	0.923634	+	0.383276i	$0.125204\pi$
$643$	5.41761e16i	0.766553i	−0.923634	+	0.383276i	$0.874796\pi$
$644$	0	0
$645$	9.26363e16	1.28654
$646$	−2.75173e16	−0.378626
$647$	− 3.29674e16i	− 0.449427i	−0.974425	−	0.224713i	$-0.927855\pi$
$647$	− 3.29674e16i	− 0.449427i	0.974425	−	0.224713i	$-0.0721446\pi$
$648$	−6.00754e16	−0.811421
$649$	− 8.47558e15i	− 0.113423i
$650$	9.56000e15i	0.126759i
$651$	0	0
$652$	−1.72667e16	−0.224762
$653$	−4.67044e16	−0.602391	−0.301196	−	0.953562i	$-0.597386\pi$
$653$	−4.67044e16	−0.602391	−0.301196	+	0.953562i	$0.597386\pi$
$654$	− 3.73040e16i	− 0.476748i
$655$	−1.47018e17	−1.86175
$656$	7.46630e15i	0.0936877i
$657$	− 2.63515e17i	− 3.27653i
$658$	0	0
$659$	5.21979e16	0.637295	0.318648	−	0.947873i	$-0.396771\pi$
$659$	5.21979e16	0.637295	0.318648	+	0.947873i	$0.396771\pi$
$660$	−4.18650e16	−0.506510
$661$	7.22442e16i	0.866152i	0.901357	+	0.433076i	$0.142572\pi$
$661$	7.22442e16i	0.866152i	−0.901357	+	0.433076i	$0.857428\pi$
$662$	3.10225e16	0.368578
$663$	1.49788e17i	1.76358i
$664$	− 2.20042e16i	− 0.256743i
$665$	0	0
$666$	−6.02281e16	−0.690167
$667$	3.78050e16	0.429333
$668$	− 2.53756e15i	− 0.0285599i
$669$	2.13977e17	2.38677
$670$	− 4.77628e16i	− 0.528009i
$671$	1.98860e16i	0.217877i
$672$	0	0
$673$	−1.64285e17	−1.76810	−0.884051	−	0.467391i	$-0.845194\pi$
$673$	−1.64285e17	−1.76810	−0.884051	+	0.467391i	$0.845194\pi$
$674$	9.15384e16	0.976437
$675$	2.52341e16i	0.266787i
$676$	−9.16407e16	−0.960303
$677$	− 4.43938e16i	− 0.461095i	−0.973061	−	0.230547i	$-0.925948\pi$
$677$	− 4.43938e16i	− 0.461095i	0.973061	−	0.230547i	$-0.0740517\pi$
$678$	− 1.42294e17i	− 1.46491i
$679$	0	0
$680$	−2.06153e16	−0.208514
$681$	−6.25797e16	−0.627409
$682$	5.56245e16i	0.552789i
$683$	−1.38409e17	−1.36345	−0.681725	−	0.731609i	$-0.738770\pi$
$683$	−1.38409e17	−1.36345	−0.681725	+	0.731609i	$0.738770\pi$
$684$	− 1.16441e17i	− 1.13702i
$685$	1.39049e17i	1.34593i
$686$	0	0
$687$	3.52041e16	0.334852
$688$	−1.76438e16	−0.166365
$689$	− 4.07319e16i	− 0.380732i
$690$	−7.05406e16	−0.653649
$691$	− 3.23178e16i	− 0.296875i	−0.988922	−	0.148437i	$-0.952576\pi$
$691$	− 3.23178e16i	− 0.296875i	0.988922	−	0.148437i	$-0.0474243\pi$
$692$	8.07387e16i	0.735267i
$693$	0	0
$694$	−1.18388e17	−1.05962
$695$	−8.32371e16	−0.738598
$696$	6.63721e16i	0.583889i
$697$	2.41079e16	0.210263
$698$	9.40832e15i	0.0813541i
$699$	− 6.25299e16i	− 0.536074i
$700$	0	0
$701$	1.88144e17	1.58556	0.792780	−	0.609508i	$-0.208633\pi$
$701$	1.88144e17	1.58556	0.792780	+	0.609508i	$0.208633\pi$
$702$	−3.67835e17	−3.07348
$703$	− 4.71860e16i	− 0.390914i
$704$	7.97376e15	0.0654979
$705$	3.82605e17i	3.11613i
$706$	1.64108e17i	1.32526i
$707$	0	0
$708$	2.50723e16	0.199065
$709$	7.74738e16	0.609927	0.304963	−	0.952364i	$-0.401356\pi$
$709$	7.74738e16	0.609927	0.304963	+	0.952364i	$0.401356\pi$
$710$	6.77842e16i	0.529149i
$711$	3.87339e17	2.99829
$712$	− 1.03947e16i	− 0.0797871i
$713$	9.37246e16i	0.713372i
$714$	0	0
$715$	−1.25762e17	−0.941270
$716$	−5.72541e15	−0.0424941
$717$	1.25530e17i	0.923916i
$718$	1.46943e17	1.07251
$719$	2.13379e17i	1.54447i	0.635340	+	0.772233i	$0.280860\pi$
$719$	2.13379e17i	1.54447i	−0.635340	+	0.772233i	$0.719140\pi$
$720$	− 8.72345e16i	− 0.626172i
$721$	0	0
$722$	−8.93712e15	−0.0630920
$723$	−1.04466e17	−0.731382
$724$	7.05695e16i	0.489988i
$725$	1.36779e16	0.0941871
$726$	1.38149e17i	0.943469i
$727$	− 9.14145e16i	− 0.619168i	−0.950872	−	0.309584i	$-0.899810\pi$
$727$	− 9.14145e16i	− 0.619168i	0.950872	−	0.309584i	$-0.100190\pi$
$728$	0	0
$729$	−1.18699e17	−0.790828
$730$	1.54669e17	1.02204
$731$	5.69700e16i	0.373372i
$732$	−5.88262e16	−0.382388
$733$	− 7.31906e16i	− 0.471880i	−0.971768	−	0.235940i	$-0.924183\pi$
$733$	− 7.31906e16i	− 0.471880i	0.971768	−	0.235940i	$-0.0758169\pi$
$734$	− 1.56681e17i	− 1.00194i
$735$	0	0
$736$	1.34354e16	0.0845248
$737$	5.96510e16	0.372231
$738$	1.02014e17i	0.631423i
$739$	−1.85991e17	−1.14189	−0.570945	−	0.820988i	$-0.693423\pi$
$739$	−1.85991e17	−1.14189	−0.570945	+	0.820988i	$0.693423\pi$
$740$	− 3.53506e16i	− 0.215282i
$741$	− 4.96582e17i	− 2.99973i
$742$	0	0
$743$	3.21389e17	1.91028	0.955141	−	0.296150i	$-0.0957029\pi$
$743$	3.21389e17	1.91028	0.955141	+	0.296150i	$0.0957029\pi$
$744$	−1.64547e17	−0.970180
$745$	1.88626e17i	1.10323i
$746$	2.13082e15	0.0123627
$747$	− 3.00649e17i	− 1.73036i
$748$	− 2.57464e16i	− 0.146996i
$749$	0	0
$750$	2.17785e17	1.22366
$751$	−4.83549e16	−0.269526	−0.134763	−	0.990878i	$-0.543027\pi$
$751$	−4.83549e16	−0.269526	−0.134763	+	0.990878i	$0.543027\pi$
$752$	− 7.28723e16i	− 0.402954i
$753$	1.43391e16	0.0786599
$754$	1.99381e17i	1.08507i
$755$	2.01661e17i	1.08878i
$756$	0	0
$757$	1.00275e17	0.532867	0.266433	−	0.963853i	$-0.414155\pi$
$757$	1.00275e17	0.532867	0.266433	+	0.963853i	$0.414155\pi$
$758$	2.02625e17	1.06826
$759$	− 8.80982e16i	− 0.460804i
$760$	6.83443e16	0.354667
$761$	− 2.99839e17i	− 1.54376i	−0.635767	−	0.771881i	$-0.719316\pi$
$761$	− 2.99839e17i	− 1.54376i	0.635767	−	0.771881i	$-0.280684\pi$
$762$	2.72802e17i	1.39353i
$763$	0	0
$764$	4.98325e16	0.250584
$765$	−2.81671e17	−1.40531
$766$	1.21614e17i	0.602021i
$767$	7.53169e16	0.369931
$768$	2.35878e16i	0.114953i
$769$	1.29642e17i	0.626886i	0.949607	+	0.313443i	$0.101483\pi$
$769$	1.29642e17i	0.626886i	−0.949607	+	0.313443i	$0.898517\pi$
$770$	0	0
$771$	−5.27494e17	−2.51126
$772$	−1.95961e16	−0.0925689
$773$	− 1.36884e17i	− 0.641618i	−0.947144	−	0.320809i	$-0.896045\pi$
$773$	− 1.36884e17i	− 0.641618i	0.947144	−	0.320809i	$-0.103955\pi$
$774$	−2.41072e17	−1.12124
$775$	3.39097e16i	0.156500i
$776$	8.90830e16i	0.407967i
$777$	0	0
$778$	2.23857e17	1.00947
$779$	−7.99232e16	−0.357641
$780$	− 3.72027e17i	− 1.65199i
$781$	−8.46557e16	−0.373035
$782$	− 4.33815e16i	− 0.189698i
$783$	5.26277e17i	2.28373i
$784$	0	0
$785$	−1.54030e16	−0.0658246
$786$	5.43153e17	2.30349
$787$	− 1.86036e16i	− 0.0782976i	−0.999233	−	0.0391488i	$-0.987535\pi$
$787$	− 1.86036e16i	− 0.0782976i	0.999233	−	0.0391488i	$-0.0124646\pi$
$788$	−6.44589e16	−0.269231
$789$	4.21614e17i	1.74764i
$790$	2.27347e17i	0.935247i
$791$	0	0
$792$	1.08947e17	0.441433
$793$	−1.76713e17	−0.710609
$794$	− 6.23918e16i	− 0.249003i
$795$	1.08739e17	0.430708
$796$	2.19684e17i	0.863615i
$797$	− 3.64359e17i	− 1.42161i	−0.703390	−	0.710804i	$-0.748331\pi$
$797$	− 3.64359e17i	− 1.42161i	0.703390	−	0.710804i	$-0.251669\pi$
$798$	0	0
$799$	−2.35297e17	−0.904347
$800$	4.86095e15	0.0185430
$801$	− 1.42025e17i	− 0.537738i
$802$	8.90097e16	0.334496
$803$	1.93166e17i	0.720506i
$804$	1.76458e17i	0.653289i
$805$	0	0
$806$	−4.94298e17	−1.80293
$807$	5.91780e17	2.14249
$808$	1.35829e17i	0.488117i
$809$	−1.59300e17	−0.568231	−0.284116	−	0.958790i	$-0.591700\pi$
$809$	−1.59300e17	−0.568231	−0.284116	+	0.958790i	$0.591700\pi$
$810$	− 4.81778e17i	− 1.70583i
$811$	1.20080e17i	0.422031i	0.977483	+	0.211015i	$0.0676770\pi$
$811$	1.20080e17i	0.422031i	−0.977483	+	0.211015i	$0.932323\pi$
$812$	0	0
$813$	−6.61519e17	−2.29086
$814$	4.41494e16	0.151767
$815$	− 1.38471e17i	− 0.472513i
$816$	7.61624e16	0.257988
$817$	− 1.88869e17i	− 0.635079i
$818$	− 1.50079e17i	− 0.500957i
$819$	0	0
$820$	−5.98765e16	−0.196958
$821$	−3.12221e17	−1.01954	−0.509768	−	0.860312i	$-0.670269\pi$
$821$	−3.12221e17	−1.01954	−0.509768	+	0.860312i	$0.670269\pi$
$822$	− 5.13710e17i	− 1.66528i
$823$	2.83295e17	0.911675	0.455838	−	0.890063i	$-0.349340\pi$
$823$	2.83295e17	0.911675	0.455838	+	0.890063i	$0.349340\pi$
$824$	9.79953e16i	0.313070i
$825$	− 3.18740e16i	− 0.101091i
$826$	0	0
$827$	4.70648e17	1.47117	0.735585	−	0.677433i	$-0.236907\pi$
$827$	4.70648e17	1.47117	0.735585	+	0.677433i	$0.236907\pi$
$828$	1.83571e17	0.569668
$829$	− 3.45452e16i	− 0.106429i	−0.998583	−	0.0532145i	$-0.983053\pi$
$829$	− 3.45452e16i	− 0.106429i	0.998583	−	0.0532145i	$-0.0169467\pi$
$830$	1.76464e17	0.539745
$831$	− 9.24631e17i	− 2.80778i
$832$	7.08576e16i	0.213622i
$833$	0	0
$834$	3.07517e17	0.913846
$835$	2.03501e16	0.0600410
$836$	8.53553e16i	0.250030i
$837$	−1.30472e18	−3.79460
$838$	1.56534e17i	0.452008i
$839$	− 1.99771e17i	− 0.572745i	−0.958118	−	0.286373i	$-0.907551\pi$
$839$	− 1.99771e17i	− 0.572745i	0.958118	−	0.286373i	$-0.0924495\pi$
$840$	0	0
$841$	−6.85511e16	−0.193749
$842$	−1.14184e17	−0.320430
$843$	− 5.47640e17i	− 1.52591i
$844$	8.03680e16	0.222346
$845$	− 7.34918e17i	− 2.01883i
$846$	− 9.95670e17i	− 2.71577i
$847$	0	0
$848$	−2.07108e16	−0.0556958
$849$	1.28669e18	3.43580
$850$	− 1.56955e16i	− 0.0416160i
$851$	7.43896e16	0.195855
$852$	− 2.50426e17i	− 0.654701i
$853$	− 9.66293e16i	− 0.250850i	−0.992103	−	0.125425i	$-0.959971\pi$
$853$	− 9.66293e16i	− 0.250850i	0.992103	−	0.125425i	$-0.0400295\pi$
$854$	0	0
$855$	9.33804e17	2.39034
$856$	−7.22810e16	−0.183731
$857$	− 6.10450e16i	− 0.154087i	−0.997028	−	0.0770434i	$-0.975452\pi$
$857$	− 6.10450e16i	− 0.154087i	0.997028	−	0.0770434i	$-0.0245480\pi$
$858$	4.64625e17	1.16461
$859$	− 5.20624e17i	− 1.29588i	−0.761691	−	0.647941i	$-0.775630\pi$
$859$	− 5.20624e17i	− 1.29588i	0.761691	−	0.647941i	$-0.224370\pi$
$860$	− 1.41496e17i	− 0.349746i
$861$	0	0
$862$	2.58867e17	0.631005
$863$	−1.68774e17	−0.408547	−0.204273	−	0.978914i	$-0.565483\pi$
$863$	−1.68774e17	−0.408547	−0.204273	+	0.978914i	$0.565483\pi$
$864$	1.87032e17i	0.449608i
$865$	−6.47489e17	−1.54574
$866$	2.29556e17i	0.544229i
$867$	5.35266e17i	1.26025i
$868$	0	0
$869$	−2.83933e17	−0.659322
$870$	−5.32275e17	−1.22750
$871$	5.30079e17i	1.21404i
$872$	−5.69794e16	−0.129604
$873$	1.21716e18i	2.74956i
$874$	1.43820e17i	0.322663i
$875$	0	0
$876$	−5.71420e17	−1.26453
$877$	−2.13870e17	−0.470060	−0.235030	−	0.971988i	$-0.575519\pi$
$877$	−2.13870e17	−0.470060	−0.235030	+	0.971988i	$0.575519\pi$
$878$	7.37678e15i	0.0161027i
$879$	1.27110e18	2.75578
$880$	6.39461e16i	0.137695i
$881$	2.38082e17i	0.509180i	0.967049	+	0.254590i	$0.0819406\pi$
$881$	2.38082e17i	0.509180i	−0.967049	+	0.254590i	$0.918059\pi$
$882$	0	0
$883$	5.50929e17	1.16233	0.581167	−	0.813784i	$-0.302596\pi$
$883$	5.50929e17	1.16233	0.581167	+	0.813784i	$0.302596\pi$
$884$	2.28791e17	0.479431
$885$	2.01069e17i	0.418489i
$886$	9.40319e16	0.194389
$887$	2.20028e16i	0.0451790i	0.999745	+	0.0225895i	$0.00719107\pi$
$887$	2.20028e16i	0.0451790i	−0.999745	+	0.0225895i	$0.992809\pi$
$888$	1.30602e17i	0.266361i
$889$	0	0
$890$	8.33611e16	0.167735
$891$	6.01693e17	1.20257
$892$	− 3.26836e17i	− 0.648845i
$893$	7.80063e17	1.53823
$894$	− 6.96873e17i	− 1.36499i
$895$	− 4.59153e16i	− 0.0893345i
$896$	0	0
$897$	7.82871e17	1.50292
$898$	−3.73225e17	−0.711727
$899$	7.07214e17i	1.33965i
$900$	6.64162e16	0.124974
$901$	6.68730e16i	0.124998i
$902$	− 7.47797e16i	− 0.138850i
$903$	0	0
$904$	−2.17345e17	−0.398235
$905$	−5.65936e17	−1.03009
$906$	− 7.45029e17i	− 1.34711i
$907$	−8.02112e17	−1.44076	−0.720379	−	0.693580i	$-0.756032\pi$
$907$	−8.02112e17	−1.44076	−0.720379	+	0.693580i	$0.756032\pi$
$908$	9.55863e16i	0.170561i
$909$	1.85586e18i	3.28974i
$910$	0	0
$911$	2.18794e17	0.382759	0.191379	−	0.981516i	$-0.438704\pi$
$911$	2.18794e17	0.382759	0.191379	+	0.981516i	$0.438704\pi$
$912$	−2.52496e17	−0.438819
$913$	2.20386e17i	0.380505i
$914$	4.41077e17	0.756550
$915$	− 4.71760e17i	− 0.803886i
$916$	− 5.37720e16i	− 0.0910297i
$917$	0	0
$918$	6.03906e17	1.00905
$919$	3.36243e17	0.558162	0.279081	−	0.960268i	$-0.409970\pi$
$919$	3.36243e17	0.558162	0.279081	+	0.960268i	$0.409970\pi$
$920$	1.07746e17i	0.177695i
$921$	1.12608e18	1.84506
$922$	− 2.31447e17i	− 0.376761i
$923$	− 7.52280e17i	− 1.21666i
$924$	0	0
$925$	2.69143e16	0.0429667
$926$	4.90086e17	0.777331
$927$	1.33893e18i	2.10999i
$928$	1.01379e17	0.158730
$929$	8.64672e17i	1.34511i	0.740048	+	0.672554i	$0.234803\pi$
$929$	8.64672e17i	1.34511i	−0.740048	+	0.672554i	$0.765197\pi$
$930$	− 1.31960e18i	− 2.03959i
$931$	0	0
$932$	−9.55103e16	−0.145732
$933$	−5.10928e16	−0.0774586
$934$	1.52549e17i	0.229788i
$935$	2.06475e17	0.309028
$936$	9.68143e17i	1.43974i
$937$	1.98208e17i	0.292876i	0.989220	+	0.146438i	$0.0467808\pi$
$937$	1.98208e17i	0.292876i	−0.989220	+	0.146438i	$0.953219\pi$
$938$	0	0
$939$	−4.01515e16	−0.0585745
$940$	5.84404e17	0.847122
$941$	− 4.24934e17i	− 0.612046i	−0.952024	−	0.306023i	$-0.901002\pi$
$941$	− 4.24934e17i	− 0.612046i	0.952024	−	0.306023i	$-0.0989984\pi$
$942$	5.69060e16	0.0814428
$943$	− 1.26000e17i	− 0.179185i
$944$	− 3.82962e16i	− 0.0541158i
$945$	0	0
$946$	1.76714e17	0.246561
$947$	−7.86733e17	−1.09076	−0.545378	−	0.838190i	$-0.683614\pi$
$947$	−7.86733e17	−1.09076	−0.545378	+	0.838190i	$0.683614\pi$
$948$	− 8.39925e17i	− 1.15715i
$949$	−1.71654e18	−2.34994
$950$	5.20341e16i	0.0707859i
$951$	− 4.87301e17i	− 0.658740i
$952$	0	0
$953$	−1.19506e18	−1.59526	−0.797631	−	0.603146i	$-0.793914\pi$
$953$	−1.19506e18	−1.59526	−0.797631	+	0.603146i	$0.793914\pi$
$954$	−2.82977e17	−0.375371
$955$	3.99635e17i	0.526797i
$956$	1.91739e17	0.251167
$957$	− 6.64759e17i	− 0.865351i
$958$	5.29410e16i	0.0684855i
$959$	0	0
$960$	−1.89164e17	−0.241663
$961$	−9.65633e17	−1.22595
$962$	3.92327e17i	0.494991i
$963$	−9.87591e17	−1.23828
$964$	1.59565e17i	0.198826i
$965$	− 1.57152e17i	− 0.194606i
$966$	0	0
$967$	−4.45589e17	−0.544974	−0.272487	−	0.962159i	$-0.587846\pi$
$967$	−4.45589e17	−0.544974	−0.272487	+	0.962159i	$0.587846\pi$
$968$	2.11013e17	0.256482
$969$	8.15282e17i	0.984839i
$970$	−7.14407e17	−0.857660
$971$	9.85135e17i	1.17539i	0.809084	+	0.587693i	$0.199964\pi$
$971$	9.85135e17i	1.17539i	−0.809084	+	0.587693i	$0.800036\pi$
$972$	7.07466e17i	0.838896i
$973$	0	0
$974$	−3.81249e17	−0.446534
$975$	2.83244e17	0.329710
$976$	8.98531e16i	0.103952i
$977$	−6.60508e17	−0.759470	−0.379735	−	0.925095i	$-0.623985\pi$
$977$	−6.60508e17	−0.759470	−0.379735	+	0.925095i	$0.623985\pi$
$978$	5.11578e17i	0.584626i
$979$	1.04110e17i	0.118248i
$980$	0	0
$981$	−7.78522e17	−0.873488
$982$	−1.84403e17	−0.205636
$983$	− 1.65650e18i	− 1.83599i	−0.396590	−	0.917996i	$-0.629806\pi$
$983$	− 1.65650e18i	− 1.83599i	0.396590	−	0.917996i	$-0.370194\pi$
$984$	2.21212e17	0.243690
$985$	− 5.16932e17i	− 0.565999i
$986$	− 3.27342e17i	− 0.356238i
$987$	0	0
$988$	−7.58496e17	−0.815477
$989$	2.97755e17	0.318186
$990$	8.73709e17i	0.928017i
$991$	−4.34173e17	−0.458375	−0.229187	−	0.973382i	$-0.573607\pi$
$991$	−4.34173e17	−0.458375	−0.229187	+	0.973382i	$0.573607\pi$
$992$	2.51335e17i	0.263744i
$993$	− 9.19136e17i	− 0.958704i
$994$	0	0
$995$	−1.76177e18	−1.81556
$996$	−6.51942e17	−0.667810
$997$	− 9.84535e17i	− 1.00244i	−0.865319	−	0.501222i	$-0.832884\pi$
$997$	− 9.84535e17i	− 1.00244i	0.865319	−	0.501222i	$-0.167116\pi$
$998$	3.74846e17	0.379376
$999$	1.03557e18i	1.04180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.b.c.97.8		16
7.2	even	3		14.13.d.a.3.5	✓	16
7.3	odd	6		14.13.d.a.5.5	yes	16
7.4	even	3		98.13.d.a.19.8		16
7.5	odd	6		98.13.d.a.31.8		16
7.6	odd	2	inner	98.13.b.c.97.1		16
21.2	odd	6		126.13.n.a.73.1		16
21.17	even	6		126.13.n.a.19.1		16
28.3	even	6		112.13.s.c.33.8		16
28.23	odd	6		112.13.s.c.17.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.5	✓	16	7.2	even	3
14.13.d.a.5.5	yes	16	7.3	odd	6
98.13.b.c.97.1		16	7.6	odd	2	inner
98.13.b.c.97.8		16	1.1	even	1	trivial
98.13.d.a.19.8		16	7.4	even	3
98.13.d.a.31.8		16	7.5	odd	6
112.13.s.c.17.8		16	28.23	odd	6
112.13.s.c.33.8		16	28.3	even	6
126.13.n.a.19.1		16	21.17	even	6
126.13.n.a.73.1		16	21.2	odd	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:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	98.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-45.2548 q^{2} +1340.81i q^{3} +2048.00 q^{4} +16424.1i q^{5} -60678.2i q^{6} -92681.9 q^{8} -1.26633e6 q^{9} +O(q^{10})\)	\(q-45.2548 q^{2} +1340.81i q^{3} +2048.00 q^{4} +16424.1i q^{5} -60678.2i q^{6} -92681.9 q^{8} -1.26633e6 q^{9} -743268. i q^{10} +928268. q^{11} +2.74598e6i q^{12} +8.24891e6i q^{13} -2.20216e7 q^{15} +4.19430e6 q^{16} -1.35429e7i q^{17} +5.73077e7 q^{18} +4.48980e7i q^{19} +3.36365e7i q^{20} -4.20086e7 q^{22} -7.07825e7 q^{23} -1.24269e8i q^{24} -2.56092e7 q^{25} -3.73303e8i q^{26} -9.85352e8i q^{27} -5.34101e8 q^{29} +9.96582e8 q^{30} -1.32412e9i q^{31} -1.89813e8 q^{32} +1.24463e9i q^{33} +6.12884e8i q^{34} -2.59345e9 q^{36} -1.05096e9 q^{37} -2.03185e9i q^{38} -1.10602e10 q^{39} -1.52221e9i q^{40} +1.78011e9i q^{41} -4.20662e9 q^{43} +1.90109e9 q^{44} -2.07983e10i q^{45} +3.20325e9 q^{46} -1.73741e10i q^{47} +5.62377e9i q^{48} +1.15894e9 q^{50} +1.81585e10 q^{51} +1.68938e10i q^{52} -4.93785e9 q^{53} +4.45919e10i q^{54} +1.52459e10i q^{55} -6.01997e10 q^{57} +2.41706e10 q^{58} -9.13053e9i q^{59} -4.51002e10 q^{60} +2.14226e10i q^{61} +5.99229e10i q^{62} +8.58993e9 q^{64} -1.35481e11 q^{65} -5.63256e10i q^{66} +6.42605e10 q^{67} -2.77360e10i q^{68} -9.49060e10i q^{69} -9.11975e10 q^{71} +1.17366e11 q^{72} +2.08093e11i q^{73} +4.75611e10 q^{74} -3.43371e10i q^{75} +9.19511e10i q^{76} +5.00529e11 q^{78} -3.05874e11 q^{79} +6.88875e10i q^{80} +6.48189e11 q^{81} -8.05584e10i q^{82} +2.37417e11i q^{83} +2.22430e11 q^{85} +1.90370e11 q^{86} -7.16128e11i q^{87} -8.60336e10 q^{88} +1.12155e11i q^{89} +9.41225e11i q^{90} -1.44963e11 q^{92} +1.77540e12 q^{93} +7.86263e11i q^{94} -7.37408e11 q^{95} -2.54503e11i q^{96} -9.61170e11i q^{97} -1.17550e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32768 q^{4} - 4724496 q^{9}+O(q^{10}) \) 16 * q + 32768 * q^4 - 4724496 * q^9	\( 16 q + 32768 q^{4} - 4724496 q^{9} - 4144176 q^{11} - 27163728 q^{15} + 67108864 q^{16} + 9185280 q^{18} + 62776320 q^{22} - 51261120 q^{23} - 1042411616 q^{25} + 532360944 q^{29} + 4303835136 q^{30} - 9675767808 q^{36} - 11529048080 q^{37} - 21052166544 q^{39} - 66929432000 q^{43} - 8487272448 q^{44} - 14406426624 q^{46} - 99248080896 q^{50} + 46598512752 q^{51} - 78268323600 q^{53} - 328243960080 q^{57} - 59274792960 q^{58} - 55631314944 q^{60} + 137438953472 q^{64} - 316645407792 q^{65} - 215534239840 q^{67} - 1150259029344 q^{71} + 18811453440 q^{72} - 9805556736 q^{74} - 786088888320 q^{78} - 455264129536 q^{79} + 783968356800 q^{81} + 710209696080 q^{85} + 76210384896 q^{86} + 128565903360 q^{88} - 104982773760 q^{92} + 917337537360 q^{93} + 373007725920 q^{95} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q + 32768 * q^4 - 4724496 * q^9 - 4144176 * q^11 - 27163728 * q^15 + 67108864 * q^16 + 9185280 * q^18 + 62776320 * q^22 - 51261120 * q^23 - 1042411616 * q^25 + 532360944 * q^29 + 4303835136 * q^30 - 9675767808 * q^36 - 11529048080 * q^37 - 21052166544 * q^39 - 66929432000 * q^43 - 8487272448 * q^44 - 14406426624 * q^46 - 99248080896 * q^50 + 46598512752 * q^51 - 78268323600 * q^53 - 328243960080 * q^57 - 59274792960 * q^58 - 55631314944 * q^60 + 137438953472 * q^64 - 316645407792 * q^65 - 215534239840 * q^67 - 1150259029344 * q^71 + 18811453440 * q^72 - 9805556736 * q^74 - 786088888320 * q^78 - 455264129536 * q^79 + 783968356800 * q^81 + 710209696080 * q^85 + 76210384896 * q^86 + 128565903360 * q^88 - 104982773760 * q^92 + 917337537360 * q^93 + 373007725920 * q^95 + 3921180354576 * q^99

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