LMFDB - Embedded newform 98.13.b.c.97.10

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			97.10
Root			$-861.382i$ of defining polynomial
Character	$\chi$	$=$	98.97
Dual form			98.13.b.c.97.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+45.2548 q^{2} -861.382i q^{3} +2048.00 q^{4} +8697.53i q^{5} -38981.7i q^{6} +92681.9 q^{8} -210538. q^{9} +O(q^{10})$	\(q+45.2548 q^{2} -861.382i q^{3} +2048.00 q^{4} +8697.53i q^{5} -38981.7i q^{6} +92681.9 q^{8} -210538. q^{9} +393605. i q^{10} -515845. q^{11} -1.76411e6i q^{12} +2.74786e6i q^{13} +7.49190e6 q^{15} +4.19430e6 q^{16} +6.35754e6i q^{17} -9.52787e6 q^{18} -7.75654e7i q^{19} +1.78125e7i q^{20} -2.33445e7 q^{22} -1.04058e8 q^{23} -7.98345e7i q^{24} +1.68494e8 q^{25} +1.24354e8i q^{26} -2.76420e8i q^{27} -1.41564e8 q^{29} +3.39045e8 q^{30} -8.07917e8i q^{31} +1.89813e8 q^{32} +4.44339e8i q^{33} +2.87709e8i q^{34} -4.31182e8 q^{36} -3.73517e9 q^{37} -3.51021e9i q^{38} +2.36696e9 q^{39} +8.06104e8i q^{40} -4.75235e9i q^{41} +8.94118e9 q^{43} -1.05645e9 q^{44} -1.83116e9i q^{45} -4.70912e9 q^{46} -2.06879e10i q^{47} -3.61290e9i q^{48} +7.62515e9 q^{50} +5.47627e9 q^{51} +5.62762e9i q^{52} +2.34542e10 q^{53} -1.25093e10i q^{54} -4.48657e9i q^{55} -6.68134e10 q^{57} -6.40647e9 q^{58} -2.11859e9i q^{59} +1.53434e10 q^{60} +8.41056e9i q^{61} -3.65622e10i q^{62} +8.58993e9 q^{64} -2.38996e10 q^{65} +2.01085e10i q^{66} -6.54478e10 q^{67} +1.30202e10i q^{68} +8.96336e10i q^{69} -2.46780e11 q^{71} -1.95131e10 q^{72} +1.02446e11i q^{73} -1.69035e11 q^{74} -1.45137e11i q^{75} -1.58854e11i q^{76} +1.07116e11 q^{78} -2.77097e11 q^{79} +3.64801e10i q^{80} -3.49992e11 q^{81} -2.15067e11i q^{82} +8.18271e10i q^{83} -5.52949e10 q^{85} +4.04632e11 q^{86} +1.21941e11i q^{87} -4.78095e10 q^{88} +5.42127e10i q^{89} -8.28689e10i q^{90} -2.13111e11 q^{92} -6.95926e11 q^{93} -9.36228e11i q^{94} +6.74627e11 q^{95} -1.63501e11i q^{96} +3.42738e11i q^{97} +1.08605e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	− 861.382i	− 1.18159i	−0.806820	−	0.590797i	$-0.798813\pi$
$3$	− 861.382i	− 1.18159i	0.806820	−	0.590797i	$-0.201187\pi$
$4$	2048.00	0.500000
$5$	8697.53i	0.556642i	0.960488	+	0.278321i	$0.0897779\pi$
$5$	8697.53i	0.556642i	−0.960488	+	0.278321i	$0.910222\pi$
$6$	− 38981.7i	− 0.835513i
$7$	0	0
$7$	0	0
$8$	92681.9	0.353553
$9$	−210538.	−0.396165
$10$	393605.i	0.393605i
$11$	−515845.	−0.291181	−0.145590	−	0.989345i	$-0.546508\pi$
$11$	−515845.	−0.291181	−0.145590	+	0.989345i	$0.546508\pi$
$12$	− 1.76411e6i	− 0.590797i
$13$	2.74786e6i	0.569292i	0.958633	+	0.284646i	$0.0918760\pi$
$13$	2.74786e6i	0.569292i	−0.958633	+	0.284646i	$0.908124\pi$
$14$	0	0
$15$	7.49190e6	0.657725
$16$	4.19430e6	0.250000
$17$	6.35754e6i	0.263388i	0.991290	+	0.131694i	$0.0420416\pi$
$17$	6.35754e6i	0.263388i	−0.991290	+	0.131694i	$0.957958\pi$
$18$	−9.52787e6	−0.280131
$19$	− 7.75654e7i	− 1.64872i	−0.566068	−	0.824359i	$-0.691536\pi$
$19$	− 7.75654e7i	− 1.64872i	0.566068	−	0.824359i	$-0.308464\pi$
$20$	1.78125e7i	0.278321i
$21$	0	0
$22$	−2.33445e7	−0.205896
$23$	−1.04058e8	−0.702923	−0.351462	−	0.936202i	$-0.614315\pi$
$23$	−1.04058e8	−0.702923	−0.351462	+	0.936202i	$0.614315\pi$
$24$	− 7.98345e7i	− 0.417757i
$25$	1.68494e8	0.690150
$26$	1.24354e8i	0.402550i
$27$	− 2.76420e8i	− 0.713488i
$28$	0	0
$29$	−1.41564e8	−0.237994	−0.118997	−	0.992895i	$-0.537968\pi$
$29$	−1.41564e8	−0.237994	−0.118997	+	0.992895i	$0.537968\pi$
$30$	3.39045e8	0.465082
$31$	− 8.07917e8i	− 0.910326i	−0.890408	−	0.455163i	$-0.849581\pi$
$31$	− 8.07917e8i	− 0.910326i	0.890408	−	0.455163i	$-0.150419\pi$
$32$	1.89813e8	0.176777
$33$	4.44339e8i	0.344058i
$34$	2.87709e8i	0.186243i
$35$	0	0
$36$	−4.31182e8	−0.198082
$37$	−3.73517e9	−1.45580	−0.727898	−	0.685686i	$-0.759502\pi$
$37$	−3.73517e9	−1.45580	−0.727898	+	0.685686i	$0.759502\pi$
$38$	− 3.51021e9i	− 1.16582i
$39$	2.36696e9	0.672672
$40$	8.06104e8i	0.196803i
$41$	− 4.75235e9i	− 1.00047i	−0.865889	−	0.500236i	$-0.833246\pi$
$41$	− 4.75235e9i	− 1.00047i	0.865889	−	0.500236i	$-0.166754\pi$
$42$	0	0
$43$	8.94118e9	1.41444	0.707219	−	0.706994i	$-0.249949\pi$
$43$	8.94118e9	1.41444	0.707219	+	0.706994i	$0.249949\pi$
$44$	−1.05645e9	−0.145590
$45$	− 1.83116e9i	− 0.220522i
$46$	−4.70912e9	−0.497042
$47$	− 2.06879e10i	− 1.91924i	−0.281298	−	0.959621i	$-0.590765\pi$
$47$	− 2.06879e10i	− 1.91924i	0.281298	−	0.959621i	$-0.409235\pi$
$48$	− 3.61290e9i	− 0.295399i
$49$	0	0
$50$	7.62515e9	0.488010
$51$	5.47627e9	0.311217
$52$	5.62762e9i	0.284646i
$53$	2.34542e10	1.05819	0.529097	−	0.848561i	$-0.322531\pi$
$53$	2.34542e10	1.05819	0.529097	+	0.848561i	$0.322531\pi$
$54$	− 1.25093e10i	− 0.504512i
$55$	− 4.48657e9i	− 0.162083i
$56$	0	0
$57$	−6.68134e10	−1.94811
$58$	−6.40647e9	−0.168287
$59$	− 2.11859e9i	− 0.0502266i	−0.999685	−	0.0251133i	$-0.992005\pi$
$59$	− 2.11859e9i	− 0.0502266i	0.999685	−	0.0251133i	$-0.00799466\pi$
$60$	1.53434e10	0.328862
$61$	8.41056e9i	0.163247i	0.996663	+	0.0816237i	$0.0260106\pi$
$61$	8.41056e9i	0.163247i	−0.996663	+	0.0816237i	$0.973989\pi$
$62$	− 3.65622e10i	− 0.643697i
$63$	0	0
$64$	8.58993e9	0.125000
$65$	−2.38996e10	−0.316892
$66$	2.01085e10i	0.243286i
$67$	−6.54478e10	−0.723512	−0.361756	−	0.932273i	$-0.617823\pi$
$67$	−6.54478e10	−0.723512	−0.361756	+	0.932273i	$0.617823\pi$
$68$	1.30202e10i	0.131694i
$69$	8.96336e10i	0.830570i
$70$	0	0
$71$	−2.46780e11	−1.92646	−0.963229	−	0.268683i	$-0.913411\pi$
$71$	−2.46780e11	−1.92646	−0.963229	+	0.268683i	$0.913411\pi$
$72$	−1.95131e10	−0.140065
$73$	1.02446e11i	0.676953i	0.940975	+	0.338477i	$0.109912\pi$
$73$	1.02446e11i	0.676953i	−0.940975	+	0.338477i	$0.890088\pi$
$74$	−1.69035e11	−1.02940
$75$	− 1.45137e11i	− 0.815477i
$76$	− 1.58854e11i	− 0.824359i
$77$	0	0
$78$	1.07116e11	0.475651
$79$	−2.77097e11	−1.13990	−0.569952	−	0.821678i	$-0.693038\pi$
$79$	−2.77097e11	−1.13990	−0.569952	+	0.821678i	$0.693038\pi$
$80$	3.64801e10i	0.139160i
$81$	−3.49992e11	−1.23922
$82$	− 2.15067e11i	− 0.707441i
$83$	8.18271e10i	0.250281i	0.992139	+	0.125141i	$0.0399382\pi$
$83$	8.18271e10i	0.250281i	−0.992139	+	0.125141i	$0.960062\pi$
$84$	0	0
$85$	−5.52949e10	−0.146613
$86$	4.04632e11	1.00016
$87$	1.21941e11i	0.281212i
$88$	−4.78095e10	−0.102948
$89$	5.42127e10i	0.109084i	0.998511	+	0.0545420i	$0.0173699\pi$
$89$	5.42127e10i	0.109084i	−0.998511	+	0.0545420i	$0.982630\pi$
$90$	− 8.28689e10i	− 0.155932i
$91$	0	0
$92$	−2.13111e11	−0.351462
$93$	−6.95926e11	−1.07564
$94$	− 9.36228e11i	− 1.35711i
$95$	6.74627e11	0.917745
$96$	− 1.63501e11i	− 0.208878i
$97$	3.42738e11i	0.411465i	0.978608	+	0.205732i	$0.0659576\pi$
$97$	3.42738e11i	0.411465i	−0.978608	+	0.205732i	$0.934042\pi$
$98$	0	0
$99$	1.08605e11	0.115356
$100$	3.45075e11	0.345075
$101$	− 1.70422e12i	− 1.60546i	−0.596345	−	0.802728i	$-0.703381\pi$
$101$	− 1.70422e12i	− 1.60546i	0.596345	−	0.802728i	$-0.296619\pi$
$102$	2.47828e11	0.220064
$103$	− 1.31093e12i	− 1.09788i	−0.835861	−	0.548941i	$-0.815031\pi$
$103$	− 1.31093e12i	− 1.09788i	0.835861	−	0.548941i	$-0.184969\pi$
$104$	2.54677e11i	0.201275i
$105$	0	0
$106$	1.06142e12	0.748256
$107$	−2.03417e12	−1.35545	−0.677727	−	0.735314i	$-0.737035\pi$
$107$	−2.03417e12	−1.35545	−0.677727	+	0.735314i	$0.737035\pi$
$108$	− 5.66108e11i	− 0.356744i
$109$	2.19462e12	1.30858	0.654290	−	0.756243i	$-0.272967\pi$
$109$	2.19462e12	1.30858	0.654290	+	0.756243i	$0.272967\pi$
$110$	− 2.03039e11i	− 0.114610i
$111$	3.21741e12i	1.72016i
$112$	0	0
$113$	−2.33384e11	−0.112098	−0.0560492	−	0.998428i	$-0.517850\pi$
$113$	−2.33384e11	−0.112098	−0.0560492	+	0.998428i	$0.517850\pi$
$114$	−3.02363e12	−1.37753
$115$	− 9.05047e11i	− 0.391277i
$116$	−2.89924e11	−0.118997
$117$	− 5.78530e11i	− 0.225533i
$118$	− 9.58763e10i	− 0.0355156i
$119$	0	0
$120$	6.94363e11	0.232541
$121$	−2.87233e12	−0.915214
$122$	3.80619e11i	0.115433i
$123$	−4.09359e12	−1.18215
$124$	− 1.65461e12i	− 0.455163i
$125$	3.58890e12i	0.940808i
$126$	0	0
$127$	5.43716e12	1.29583	0.647917	−	0.761711i	$-0.275640\pi$
$127$	5.43716e12	1.29583	0.647917	+	0.761711i	$0.275640\pi$
$128$	3.88736e11	0.0883883
$129$	− 7.70177e12i	− 1.67129i
$130$	−1.08157e12	−0.224076
$131$	− 8.29476e12i	− 1.64125i	−0.571463	−	0.820627i	$-0.693624\pi$
$131$	− 8.29476e12i	− 1.64125i	0.571463	−	0.820627i	$-0.306376\pi$
$132$	9.10007e11i	0.172029i
$133$	0	0
$134$	−2.96183e12	−0.511601
$135$	2.40417e12	0.397157
$136$	5.89229e11i	0.0931216i
$137$	2.87821e12	0.435311	0.217655	−	0.976026i	$-0.430159\pi$
$137$	2.87821e12	0.435311	0.217655	+	0.976026i	$0.430159\pi$
$138$	4.05635e12i	0.587302i
$139$	− 7.39529e12i	− 1.02534i	−0.858587	−	0.512669i	$-0.828657\pi$
$139$	− 7.39529e12i	− 1.02534i	0.858587	−	0.512669i	$-0.171343\pi$
$140$	0	0
$141$	−1.78202e13	−2.26776
$142$	−1.11680e13	−1.36221
$143$	− 1.41747e12i	− 0.165767i
$144$	−8.83061e11	−0.0990412
$145$	− 1.23126e12i	− 0.132477i
$146$	4.63619e12i	0.478678i
$147$	0	0
$148$	−7.64963e12	−0.727898
$149$	1.95625e12	0.178775	0.0893876	−	0.995997i	$-0.471509\pi$
$149$	1.95625e12	0.178775	0.0893876	+	0.995997i	$0.471509\pi$
$150$	− 6.56817e12i	− 0.576629i
$151$	−1.44087e13	−1.21553	−0.607763	−	0.794119i	$-0.707933\pi$
$151$	−1.44087e13	−1.21553	−0.607763	+	0.794119i	$0.707933\pi$
$152$	− 7.18891e12i	− 0.582910i
$153$	− 1.33850e12i	− 0.104345i
$154$	0	0
$155$	7.02689e12	0.506725
$156$	4.84753e12	0.336336
$157$	1.84380e13i	1.23116i	0.788073	+	0.615582i	$0.211079\pi$
$157$	1.84380e13i	1.23116i	−0.788073	+	0.615582i	$0.788921\pi$
$158$	−1.25400e13	−0.806034
$159$	− 2.02030e13i	− 1.25036i
$160$	1.65090e12i	0.0984013i
$161$	0	0
$162$	−1.58388e13	−0.876260
$163$	−2.77173e13	−1.47783	−0.738916	−	0.673798i	$-0.764662\pi$
$163$	−2.77173e13	−1.47783	−0.738916	+	0.673798i	$0.764662\pi$
$164$	− 9.73281e12i	− 0.500236i
$165$	−3.86466e12	−0.191517
$166$	3.70307e12i	0.176976i
$167$	1.19940e12i	0.0552923i	0.999618	+	0.0276461i	$0.00880116\pi$
$167$	1.19940e12i	0.0552923i	−0.999618	+	0.0276461i	$0.991199\pi$
$168$	0	0
$169$	1.57473e13	0.675907
$170$	−2.50236e12	−0.103671
$171$	1.63305e13i	0.653164i
$172$	1.83115e13	0.707219
$173$	− 4.43439e12i	− 0.165408i	−0.996574	−	0.0827041i	$-0.973644\pi$
$173$	− 4.43439e12i	− 0.165408i	0.996574	−	0.0827041i	$-0.0263556\pi$
$174$	5.51842e12i	0.198847i
$175$	0	0
$176$	−2.16361e12	−0.0727952
$177$	−1.82491e12	−0.0593475
$178$	2.45339e12i	0.0771341i
$179$	4.42032e13	1.34380	0.671902	−	0.740640i	$-0.265478\pi$
$179$	4.42032e13	1.34380	0.671902	+	0.740640i	$0.265478\pi$
$180$	− 3.75022e12i	− 0.110261i
$181$	1.41993e12i	0.0403828i	0.999796	+	0.0201914i	$0.00642756\pi$
$181$	1.41993e12i	0.0403828i	−0.999796	+	0.0201914i	$0.993572\pi$
$182$	0	0
$183$	7.24471e12	0.192892
$184$	−9.64428e12	−0.248521
$185$	− 3.24868e13i	− 0.810356i
$186$	−3.14940e13	−0.760589
$187$	− 3.27950e12i	− 0.0766935i
$188$	− 4.23688e13i	− 0.959621i
$189$	0	0
$190$	3.05301e13	0.648944
$191$	5.88857e13	1.21286	0.606428	−	0.795138i	$-0.292602\pi$
$191$	5.88857e13	1.21286	0.606428	+	0.795138i	$0.292602\pi$
$192$	− 7.39922e12i	− 0.147699i
$193$	5.68439e13	1.09987	0.549933	−	0.835209i	$-0.314653\pi$
$193$	5.68439e13	1.09987	0.549933	+	0.835209i	$0.314653\pi$
$194$	1.55106e13i	0.290949i
$195$	2.05867e13i	0.374437i
$196$	0	0
$197$	−5.01766e13	−0.858428	−0.429214	−	0.903203i	$-0.641209\pi$
$197$	−5.01766e13	−0.858428	−0.429214	+	0.903203i	$0.641209\pi$
$198$	4.91490e12	0.0815687
$199$	− 3.13220e13i	− 0.504348i	−0.967682	−	0.252174i	$-0.918854\pi$
$199$	− 3.13220e13i	− 0.504348i	0.967682	−	0.252174i	$-0.0811456\pi$
$200$	1.56163e13	0.244005
$201$	5.63755e13i	0.854898i
$202$	− 7.71244e13i	− 1.13523i
$203$	0	0
$204$	1.12154e13	0.155609
$205$	4.13337e13	0.556905
$206$	− 5.93258e13i	− 0.776319i
$207$	2.19082e13	0.278473
$208$	1.15254e13i	0.142323i
$209$	4.00117e13i	0.480075i
$210$	0	0
$211$	1.26653e14	1.43523	0.717616	−	0.696438i	$-0.245233\pi$
$211$	1.26653e14	1.43523	0.717616	+	0.696438i	$0.245233\pi$
$212$	4.80342e13	0.529097
$213$	2.12572e14i	2.27629i
$214$	−9.20560e13	−0.958450
$215$	7.77662e13i	0.787336i
$216$	− 2.56191e13i	− 0.252256i
$217$	0	0
$218$	9.93172e13	0.925306
$219$	8.82453e13	0.799884
$220$	− 9.18851e12i	− 0.0810417i
$221$	−1.74696e13	−0.149945
$222$	1.45603e14i	1.21634i
$223$	8.65375e13i	0.703680i	0.936060	+	0.351840i	$0.114444\pi$
$223$	8.65375e13i	0.703680i	−0.936060	+	0.351840i	$0.885556\pi$
$224$	0	0
$225$	−3.54743e13	−0.273413
$226$	−1.05617e13	−0.0792656
$227$	1.65067e14i	1.20644i	0.797575	+	0.603220i	$0.206116\pi$
$227$	1.65067e14i	1.20644i	−0.797575	+	0.603220i	$0.793884\pi$
$228$	−1.36834e14	−0.974057
$229$	9.71623e13i	0.673728i	0.941553	+	0.336864i	$0.109366\pi$
$229$	9.71623e13i	0.673728i	−0.941553	+	0.336864i	$0.890634\pi$
$230$	− 4.09577e13i	− 0.276674i
$231$	0	0
$232$	−1.31205e13	−0.0841436
$233$	4.24219e13	0.265127	0.132564	−	0.991174i	$-0.457679\pi$
$233$	4.24219e13	0.265127	0.132564	+	0.991174i	$0.457679\pi$
$234$	− 2.61813e13i	− 0.159476i
$235$	1.79934e14	1.06833
$236$	− 4.33887e12i	− 0.0251133i
$237$	2.38686e14i	1.34690i
$238$	0	0
$239$	−5.49165e13	−0.294656	−0.147328	−	0.989088i	$-0.547067\pi$
$239$	−5.49165e13	−0.294656	−0.147328	+	0.989088i	$0.547067\pi$
$240$	3.14233e13	0.164431
$241$	3.04529e14i	1.55427i	0.629335	+	0.777134i	$0.283327\pi$
$241$	3.04529e14i	1.55427i	−0.629335	+	0.777134i	$0.716673\pi$
$242$	−1.29987e14	−0.647154
$243$	1.54576e14i	0.750765i
$244$	1.72248e13i	0.0816237i
$245$	0	0
$246$	−1.85255e14	−0.835908
$247$	2.13139e14	0.938601
$248$	− 7.48793e13i	− 0.321849i
$249$	7.04844e13	0.295731
$250$	1.62415e14i	0.665252i
$251$	− 3.75080e14i	− 1.49996i	−0.661458	−	0.749982i	$-0.730062\pi$
$251$	− 3.75080e14i	− 1.49996i	0.661458	−	0.749982i	$-0.269938\pi$
$252$	0	0
$253$	5.36777e13	0.204678
$254$	2.46058e14	0.916294
$255$	4.76300e13i	0.173237i
$256$	1.75922e13	0.0625000
$257$	− 2.49327e14i	− 0.865307i	−0.901560	−	0.432653i	$-0.857577\pi$
$257$	− 2.49327e14i	− 0.865307i	0.901560	−	0.432653i	$-0.142423\pi$
$258$	− 3.48542e14i	− 1.18178i
$259$	0	0
$260$	−4.89464e13	−0.158446
$261$	2.98047e13	0.0942848
$262$	− 3.75378e14i	− 1.16054i
$263$	5.89147e14	1.78028	0.890141	−	0.455685i	$-0.150606\pi$
$263$	5.89147e14	1.78028	0.890141	+	0.455685i	$0.150606\pi$
$264$	4.11822e13i	0.121643i
$265$	2.03994e14i	0.589035i
$266$	0	0
$267$	4.66979e13	0.128893
$268$	−1.34037e14	−0.361756
$269$	3.20902e14i	0.846952i	0.905907	+	0.423476i	$0.139190\pi$
$269$	3.20902e14i	0.846952i	−0.905907	+	0.423476i	$0.860810\pi$
$270$	1.08800e14	0.280833
$271$	− 9.69326e13i	− 0.244711i	−0.992486	−	0.122356i	$-0.960955\pi$
$271$	− 9.69326e13i	− 0.244711i	0.992486	−	0.122356i	$-0.0390449\pi$
$272$	2.66655e13i	0.0658469i
$273$	0	0
$274$	1.30253e14	0.307811
$275$	−8.69165e13	−0.200958
$276$	1.83570e14i	0.415285i
$277$	−5.77406e14	−1.27821	−0.639106	−	0.769119i	$-0.720695\pi$
$277$	−5.77406e14	−1.27821	−0.639106	+	0.769119i	$0.720695\pi$
$278$	− 3.34673e14i	− 0.725023i
$279$	1.70097e14i	0.360639i
$280$	0	0
$281$	5.01179e14	1.01802	0.509009	−	0.860761i	$-0.330012\pi$
$281$	5.01179e14	1.01802	0.509009	+	0.860761i	$0.330012\pi$
$282$	−8.06450e14	−1.60355
$283$	− 8.41516e14i	− 1.63811i	−0.573712	−	0.819057i	$-0.694497\pi$
$283$	− 8.41516e14i	− 1.63811i	0.573712	−	0.819057i	$-0.305503\pi$
$284$	−5.05405e14	−0.963229
$285$	− 5.81112e14i	− 1.08440i
$286$	− 6.41474e13i	− 0.117215i
$287$	0	0
$288$	−3.99628e13	−0.0700327
$289$	5.42204e14	0.930627
$290$	− 5.57205e13i	− 0.0936757i
$291$	2.95229e14	0.486184
$292$	2.09810e14i	0.338477i
$293$	− 9.39106e14i	− 1.48426i	−0.670258	−	0.742128i	$-0.733817\pi$
$293$	− 9.39106e14i	− 1.48426i	0.670258	−	0.742128i	$-0.266183\pi$
$294$	0	0
$295$	1.84265e13	0.0279583
$296$	−3.46183e14	−0.514701
$297$	1.42590e14i	0.207754i
$298$	8.85299e13	0.126413
$299$	− 2.85937e14i	− 0.400169i
$300$	− 2.97241e14i	− 0.407738i
$301$	0	0
$302$	−6.52065e14	−0.859506
$303$	−1.46799e15	−1.89700
$304$	− 3.25333e14i	− 0.412179i
$305$	−7.31511e13	−0.0908703
$306$	− 6.05738e13i	− 0.0737830i
$307$	6.66830e14i	0.796498i	0.917277	+	0.398249i	$0.130382\pi$
$307$	6.66830e14i	0.796498i	−0.917277	+	0.398249i	$0.869618\pi$
$308$	0	0
$309$	−1.12921e15	−1.29725
$310$	3.18001e14	0.358309
$311$	− 3.12709e14i	− 0.345604i	−0.984957	−	0.172802i	$-0.944718\pi$
$311$	− 3.12709e14i	− 0.345604i	0.984957	−	0.172802i	$-0.0552820\pi$
$312$	2.19374e14	0.237825
$313$	2.41841e14i	0.257196i	0.991697	+	0.128598i	$0.0410477\pi$
$313$	2.41841e14i	0.257196i	−0.991697	+	0.128598i	$0.958952\pi$
$314$	8.34408e14i	0.870564i
$315$	0	0
$316$	−5.67494e14	−0.569952
$317$	−1.32420e14	−0.130496	−0.0652480	−	0.997869i	$-0.520784\pi$
$317$	−1.32420e14	−0.130496	−0.0652480	+	0.997869i	$0.520784\pi$
$318$	− 9.14285e14i	− 0.884135i
$319$	7.30252e13	0.0692993
$320$	7.47112e13i	0.0695802i
$321$	1.75220e15i	1.60160i
$322$	0	0
$323$	4.93125e14	0.434252
$324$	−7.16783e14	−0.619609
$325$	4.62997e14i	0.392897i
$326$	−1.25434e15	−1.04498
$327$	− 1.89041e15i	− 1.54621i
$328$	− 4.40457e14i	− 0.353720i
$329$	0	0
$330$	−1.74894e14	−0.135423
$331$	8.29704e14	0.630892	0.315446	−	0.948944i	$-0.397846\pi$
$331$	8.29704e14	0.630892	0.315446	+	0.948944i	$0.397846\pi$
$332$	1.67582e14i	0.125141i
$333$	7.86396e14	0.576734
$334$	5.42785e13i	0.0390975i
$335$	− 5.69234e14i	− 0.402737i
$336$	0	0
$337$	−2.75664e14	−0.188192	−0.0940958	−	0.995563i	$-0.529996\pi$
$337$	−2.75664e14	−0.188192	−0.0940958	+	0.995563i	$0.529996\pi$
$338$	7.12643e14	0.477938
$339$	2.01032e14i	0.132455i
$340$	−1.13244e14	−0.0733063
$341$	4.16760e14i	0.265069i
$342$	7.39033e14i	0.461856i
$343$	0	0
$344$	8.28685e14	0.500080
$345$	−7.79591e14	−0.462330
$346$	− 2.00677e14i	− 0.116961i
$347$	1.29078e13	0.00739395	0.00369698	−	0.999993i	$-0.498823\pi$
$347$	1.29078e13	0.00739395	0.00369698	+	0.999993i	$0.498823\pi$
$348$	2.49735e14i	0.140606i
$349$	7.51191e14i	0.415717i	0.978159	+	0.207858i	$0.0666493\pi$
$349$	7.51191e14i	0.415717i	−0.978159	+	0.207858i	$0.933351\pi$
$350$	0	0
$351$	7.59564e14	0.406183
$352$	−9.79138e13	−0.0514740
$353$	1.07184e15i	0.553965i	0.960875	+	0.276983i	$0.0893345\pi$
$353$	1.07184e15i	0.553965i	−0.960875	+	0.276983i	$0.910666\pi$
$354$	−8.25861e13	−0.0419650
$355$	− 2.14637e15i	− 1.07235i
$356$	1.11028e14i	0.0545420i
$357$	0	0
$358$	2.00041e15	0.950213
$359$	−1.83058e15	−0.855110	−0.427555	−	0.903989i	$-0.640625\pi$
$359$	−1.83058e15	−0.855110	−0.427555	+	0.903989i	$0.640625\pi$
$360$	− 1.69716e14i	− 0.0779662i
$361$	−3.80307e15	−1.71827
$362$	6.42589e13i	0.0285550i
$363$	2.47418e15i	1.08141i
$364$	0	0
$365$	−8.91029e14	−0.376821
$366$	3.27858e14	0.136395
$367$	− 2.01425e15i	− 0.824361i	−0.911102	−	0.412180i	$-0.864767\pi$
$367$	− 2.01425e15i	− 0.824361i	0.911102	−	0.412180i	$-0.135233\pi$
$368$	−4.36450e14	−0.175731
$369$	1.00055e15i	0.396352i
$370$	− 1.47018e15i	− 0.573009i
$371$	0	0
$372$	−1.42526e15	−0.537818
$373$	−1.93484e15	−0.718442	−0.359221	−	0.933252i	$-0.616958\pi$
$373$	−1.93484e15	−0.718442	−0.359221	+	0.933252i	$0.616958\pi$
$374$	− 1.48413e14i	− 0.0542305i
$375$	3.09141e15	1.11165
$376$	− 1.91740e15i	− 0.678554i
$377$	− 3.89000e14i	− 0.135488i
$378$	0	0
$379$	2.16588e15	0.730802	0.365401	−	0.930850i	$-0.380932\pi$
$379$	2.16588e15	0.730802	0.365401	+	0.930850i	$0.380932\pi$
$380$	1.38164e15	0.458873
$381$	− 4.68347e15i	− 1.53115i
$382$	2.66486e15	0.857619
$383$	5.32937e15i	1.68843i	0.536004	+	0.844215i	$0.319933\pi$
$383$	5.32937e15i	1.68843i	−0.536004	+	0.844215i	$0.680067\pi$
$384$	− 3.34850e14i	− 0.104439i
$385$	0	0
$386$	2.57246e15	0.777723
$387$	−1.88246e15	−0.560350
$388$	7.01928e14i	0.205732i
$389$	2.16521e15	0.624887	0.312444	−	0.949936i	$-0.398852\pi$
$389$	2.16521e15	0.624887	0.312444	+	0.949936i	$0.398852\pi$
$390$	9.31648e14i	0.264767i
$391$	− 6.61552e14i	− 0.185141i
$392$	0	0
$393$	−7.14496e15	−1.93930
$394$	−2.27073e15	−0.607000
$395$	− 2.41006e15i	− 0.634519i
$396$	2.22423e14	0.0576778
$397$	8.94976e14i	0.228596i	0.993447	+	0.114298i	$0.0364618\pi$
$397$	8.94976e14i	0.228596i	−0.993447	+	0.114298i	$0.963538\pi$
$398$	− 1.41747e15i	− 0.356628i
$399$	0	0
$400$	7.06713e14	0.172537
$401$	7.65583e15	1.84131	0.920653	−	0.390383i	$-0.127657\pi$
$401$	7.65583e15	1.84131	0.920653	+	0.390383i	$0.127657\pi$
$402$	2.55127e15i	0.604504i
$403$	2.22005e15	0.518241
$404$	− 3.49025e15i	− 0.802728i
$405$	− 3.04406e15i	− 0.689801i
$406$	0	0
$407$	1.92677e15	0.423900
$408$	5.07551e14	0.110032
$409$	3.61692e15i	0.772680i	0.922357	+	0.386340i	$0.126261\pi$
$409$	3.61692e15i	0.772680i	−0.922357	+	0.386340i	$0.873739\pi$
$410$	1.87055e15	0.393791
$411$	− 2.47924e15i	− 0.514361i
$412$	− 2.68478e15i	− 0.548941i
$413$	0	0
$414$	9.91450e14	0.196910
$415$	−7.11694e14	−0.139317
$416$	5.21579e14i	0.100638i
$417$	−6.37017e15	−1.21153
$418$	1.81072e15i	0.339464i
$419$	− 3.64888e15i	− 0.674335i	−0.941445	−	0.337168i	$-0.890531\pi$
$419$	− 3.64888e15i	− 0.674335i	0.941445	−	0.337168i	$-0.109469\pi$
$420$	0	0
$421$	3.29475e15	0.591739	0.295870	−	0.955228i	$-0.404391\pi$
$421$	3.29475e15	0.591739	0.295870	+	0.955228i	$0.404391\pi$
$422$	5.73168e15	1.01486
$423$	4.35559e15i	0.760335i
$424$	2.17378e15	0.374128
$425$	1.07120e15i	0.181777i
$426$	9.61989e15i	1.60958i
$427$	0	0
$428$	−4.16598e15	−0.677727
$429$	−1.22098e15	−0.195869
$430$	3.51929e15i	0.556730i
$431$	−9.45814e15	−1.47551	−0.737755	−	0.675068i	$-0.764114\pi$
$431$	−9.45814e15	−1.47551	−0.737755	+	0.675068i	$0.764114\pi$
$432$	− 1.15939e15i	− 0.178372i
$433$	− 9.38135e15i	− 1.42344i	−0.702465	−	0.711718i	$-0.747917\pi$
$433$	− 9.38135e15i	− 1.42344i	0.702465	−	0.711718i	$-0.252083\pi$
$434$	0	0
$435$	−1.06059e15	−0.156535
$436$	4.49458e15	0.654290
$437$	8.07129e15i	1.15892i
$438$	3.99353e15	0.565604
$439$	3.58177e14i	0.0500393i	0.999687	+	0.0250196i	$0.00796483\pi$
$439$	3.58177e14i	0.0500393i	−0.999687	+	0.0250196i	$0.992035\pi$
$440$	− 4.15824e14i	− 0.0573052i
$441$	0	0
$442$	−7.90586e14	−0.106027
$443$	2.89652e15	0.383225	0.191613	−	0.981471i	$-0.438628\pi$
$443$	2.89652e15	0.383225	0.191613	+	0.981471i	$0.438628\pi$
$444$	6.58926e15i	0.860079i
$445$	−4.71517e14	−0.0607207
$446$	3.91624e15i	0.497577i
$447$	− 1.68508e15i	− 0.211240i
$448$	0	0
$449$	5.51822e15	0.673474	0.336737	−	0.941599i	$-0.390677\pi$
$449$	5.51822e15	0.673474	0.336737	+	0.941599i	$0.390677\pi$
$450$	−1.60538e15	−0.193332
$451$	2.45147e15i	0.291319i
$452$	−4.77970e14	−0.0560492
$453$	1.24114e16i	1.43626i
$454$	7.47008e15i	0.853081i
$455$	0	0
$456$	−6.19239e15	−0.688763
$457$	7.16023e15	0.786013	0.393006	−	0.919536i	$-0.371435\pi$
$457$	7.16023e15	0.786013	0.393006	+	0.919536i	$0.371435\pi$
$458$	4.39706e15i	0.476398i
$459$	1.75735e15	0.187924
$460$	− 1.85354e15i	− 0.195638i
$461$	− 7.56470e15i	− 0.788108i	−0.919087	−	0.394054i	$-0.871072\pi$
$461$	− 7.56470e15i	− 0.788108i	0.919087	−	0.394054i	$-0.128928\pi$
$462$	0	0
$463$	−4.69921e15	−0.477022	−0.238511	−	0.971140i	$-0.576659\pi$
$463$	−4.69921e15	−0.477022	−0.238511	+	0.971140i	$0.576659\pi$
$464$	−5.93764e14	−0.0594985
$465$	− 6.05283e15i	− 0.598744i
$466$	1.91980e15	0.187473
$467$	1.44205e16i	1.39021i	0.718910	+	0.695103i	$0.244641\pi$
$467$	1.44205e16i	1.39021i	−0.718910	+	0.695103i	$0.755359\pi$
$468$	− 1.18483e15i	− 0.112767i
$469$	0	0
$470$	8.14287e15	0.755423
$471$	1.58822e16	1.45474
$472$	− 1.96355e14i	− 0.0177578i
$473$	−4.61226e15	−0.411858
$474$	1.08017e16i	0.952406i
$475$	− 1.30693e16i	− 1.13786i
$476$	0	0
$477$	−4.93800e15	−0.419219
$478$	−2.48524e15	−0.208353
$479$	− 1.01095e16i	− 0.836986i	−0.908220	−	0.418493i	$-0.862558\pi$
$479$	− 1.01095e16i	− 0.836986i	0.908220	−	0.418493i	$-0.137442\pi$
$480$	1.42206e15	0.116270
$481$	− 1.02637e16i	− 0.828772i
$482$	1.37814e16i	1.09903i
$483$	0	0
$484$	−5.88254e15	−0.457607
$485$	−2.98098e15	−0.229038
$486$	6.99530e15i	0.530871i
$487$	−6.42692e15	−0.481758	−0.240879	−	0.970555i	$-0.577436\pi$
$487$	−6.42692e15	−0.481758	−0.240879	+	0.970555i	$0.577436\pi$
$488$	7.79507e14i	0.0577166i
$489$	2.38752e16i	1.74620i
$490$	0	0
$491$	1.05122e16	0.750244	0.375122	−	0.926975i	$-0.377601\pi$
$491$	1.05122e16	0.750244	0.375122	+	0.926975i	$0.377601\pi$
$492$	−8.38367e15	−0.591076
$493$	− 9.00001e14i	− 0.0626847i
$494$	9.64557e15	0.663691
$495$	9.44595e14i	0.0642117i
$496$	− 3.38865e15i	− 0.227581i
$497$	0	0
$498$	3.18976e15	0.209113
$499$	−3.90136e14	−0.0252705	−0.0126352	−	0.999920i	$-0.504022\pi$
$499$	−3.90136e14	−0.0252705	−0.0126352	+	0.999920i	$0.504022\pi$
$500$	7.35006e15i	0.470404i
$501$	1.03314e15	0.0653330
$502$	− 1.69742e16i	− 1.06064i
$503$	− 1.10468e16i	− 0.682070i	−0.940051	−	0.341035i	$-0.889223\pi$
$503$	− 1.10468e16i	− 0.682070i	0.940051	−	0.341035i	$-0.110777\pi$
$504$	0	0
$505$	1.48225e16	0.893664
$506$	2.42918e15	0.144729
$507$	− 1.35645e16i	− 0.798647i
$508$	1.11353e16	0.647917
$509$	− 2.28169e15i	− 0.131205i	−0.997846	−	0.0656024i	$-0.979103\pi$
$509$	− 2.28169e15i	− 0.131205i	0.997846	−	0.0656024i	$-0.0208969\pi$
$510$	2.15549e15i	0.122497i
$511$	0	0
$512$	7.96131e14	0.0441942
$513$	−2.14406e16	−1.17634
$514$	− 1.12832e16i	− 0.611864i
$515$	1.14018e16	0.611127
$516$	− 1.57732e16i	− 0.835646i
$517$	1.06718e16i	0.558846i
$518$	0	0
$519$	−3.81970e15	−0.195445
$520$	−2.21506e15	−0.112038
$521$	− 2.72675e16i	− 1.36339i	−0.731638	−	0.681693i	$-0.761244\pi$
$521$	− 2.72675e16i	− 1.36339i	0.731638	−	0.681693i	$-0.238756\pi$
$522$	1.34881e15	0.0666694
$523$	1.00146e16i	0.489355i	0.969604	+	0.244678i	$0.0786821\pi$
$523$	1.00146e16i	0.489355i	−0.969604	+	0.244678i	$0.921318\pi$
$524$	− 1.69877e16i	− 0.820627i
$525$	0	0
$526$	2.66617e16	1.25885
$527$	5.13637e15	0.239769
$528$	1.86369e15i	0.0860144i
$529$	−1.10866e16	−0.505899
$530$	9.23169e15i	0.416511i
$531$	4.46043e14i	0.0198980i
$532$	0	0
$533$	1.30588e16	0.569561
$534$	2.11330e15	0.0911412
$535$	− 1.76922e16i	− 0.754502i
$536$	−6.06582e15	−0.255800
$537$	− 3.80759e16i	− 1.58783i
$538$	1.45224e16i	0.598885i
$539$	0	0
$540$	4.92374e15	0.198579
$541$	−4.06101e16	−1.61976	−0.809880	−	0.586596i	$-0.800468\pi$
$541$	−4.06101e16	−1.61976	−0.809880	+	0.586596i	$0.800468\pi$
$542$	− 4.38667e15i	− 0.173037i
$543$	1.22311e15	0.0477161
$544$	1.20674e15i	0.0465608i
$545$	1.90878e16i	0.728411i
$546$	0	0
$547$	−3.98211e16	−1.48658	−0.743291	−	0.668968i	$-0.766736\pi$
$547$	−3.98211e16	−1.48658	−0.743291	+	0.668968i	$0.766736\pi$
$548$	5.89458e15	0.217655
$549$	− 1.77074e15i	− 0.0646728i
$550$	−3.93339e15	−0.142099
$551$	1.09805e16i	0.392385i
$552$	8.30741e15i	0.293651i
$553$	0	0
$554$	−2.61304e16	−0.903832
$555$	−2.79835e16	−0.957512
$556$	− 1.51456e16i	− 0.512669i
$557$	2.75981e16	0.924163	0.462081	−	0.886838i	$-0.347103\pi$
$557$	2.75981e16	0.924163	0.462081	+	0.886838i	$0.347103\pi$
$558$	7.69773e15i	0.255010i
$559$	2.45691e16i	0.805228i
$560$	0	0
$561$	−2.82491e15	−0.0906206
$562$	2.26808e16	0.719847
$563$	5.78879e16i	1.81776i	0.417054	+	0.908882i	$0.363063\pi$
$563$	5.78879e16i	1.81776i	−0.417054	+	0.908882i	$0.636937\pi$
$564$	−3.64958e16	−1.13388
$565$	− 2.02986e15i	− 0.0623987i
$566$	− 3.80827e16i	− 1.15832i
$567$	0	0
$568$	−2.28720e16	−0.681105
$569$	−5.55973e15	−0.163825	−0.0819125	−	0.996640i	$-0.526103\pi$
$569$	−5.55973e15	−0.163825	−0.0819125	+	0.996640i	$0.526103\pi$
$570$	− 2.62981e16i	− 0.766788i
$571$	−2.04342e16	−0.589576	−0.294788	−	0.955563i	$-0.595249\pi$
$571$	−2.04342e16	−0.589576	−0.294788	+	0.955563i	$0.595249\pi$
$572$	− 2.90298e15i	− 0.0828835i
$573$	− 5.07231e16i	− 1.43310i
$574$	0	0
$575$	−1.75331e16	−0.485122
$576$	−1.80851e15	−0.0495206
$577$	4.11606e14i	0.0111539i	0.999984	+	0.00557695i	$0.00177521\pi$
$577$	4.11606e14i	0.0111539i	−0.999984	+	0.00557695i	$0.998225\pi$
$578$	2.45373e16	0.658053
$579$	− 4.89643e16i	− 1.29960i
$580$	− 2.52162e15i	− 0.0662387i
$581$	0	0
$582$	1.33605e16	0.343784
$583$	−1.20987e16	−0.308126
$584$	9.49491e15i	0.239339i
$585$	5.03178e15	0.125541
$586$	− 4.24991e16i	− 1.04953i
$587$	4.40809e16i	1.07751i	0.842462	+	0.538756i	$0.181106\pi$
$587$	4.40809e16i	1.07751i	−0.842462	+	0.538756i	$0.818894\pi$
$588$	0	0
$589$	−6.26664e16	−1.50087
$590$	8.33887e14	0.0197695
$591$	4.32212e16i	1.01431i
$592$	−1.56664e16	−0.363949
$593$	− 4.44121e16i	− 1.02135i	−0.859775	−	0.510674i	$-0.829396\pi$
$593$	− 4.44121e16i	− 1.02135i	0.859775	−	0.510674i	$-0.170604\pi$
$594$	6.45288e15i	0.146904i
$595$	0	0
$596$	4.00640e15	0.0893876
$597$	−2.69802e16	−0.595935
$598$	− 1.29400e16i	− 0.282962i
$599$	−8.06571e16	−1.74615	−0.873075	−	0.487585i	$-0.837878\pi$
$599$	−8.06571e16	−1.74615	−0.873075	+	0.487585i	$0.837878\pi$
$600$	− 1.34516e16i	− 0.288315i
$601$	5.23496e16i	1.11088i	0.831557	+	0.555439i	$0.187450\pi$
$601$	5.23496e16i	1.11088i	−0.831557	+	0.555439i	$0.812550\pi$
$602$	0	0
$603$	1.37792e16	0.286630
$604$	−2.95091e16	−0.607763
$605$	− 2.49822e16i	− 0.509446i
$606$	−6.64336e16	−1.34138
$607$	− 2.23720e16i	− 0.447273i	−0.974673	−	0.223636i	$-0.928207\pi$
$607$	− 2.23720e16i	− 0.447273i	0.974673	−	0.223636i	$-0.0717928\pi$
$608$	− 1.47229e16i	− 0.291455i
$609$	0	0
$610$	−3.31044e15	−0.0642550
$611$	5.68476e16	1.09261
$612$	− 2.74126e15i	− 0.0521724i
$613$	5.83701e16	1.10009	0.550045	−	0.835135i	$-0.314611\pi$
$613$	5.83701e16	1.10009	0.550045	+	0.835135i	$0.314611\pi$
$614$	3.01773e16i	0.563209i
$615$	− 3.56041e16i	− 0.658036i
$616$	0	0
$617$	−1.98026e16	−0.358931	−0.179466	−	0.983764i	$-0.557437\pi$
$617$	−1.98026e16	−0.358931	−0.179466	+	0.983764i	$0.557437\pi$
$618$	−5.11022e16	−0.917294
$619$	1.85439e16i	0.329653i	0.986323	+	0.164827i	$0.0527065\pi$
$619$	1.85439e16i	0.329653i	−0.986323	+	0.164827i	$0.947294\pi$
$620$	1.43911e16	0.253363
$621$	2.87637e16i	0.501528i
$622$	− 1.41516e16i	− 0.244379i
$623$	0	0
$624$	9.92775e15	0.168168
$625$	9.92159e15	0.166457
$626$	1.09445e16i	0.181865i
$627$	3.44654e16	0.567254
$628$	3.77610e16i	0.615582i
$629$	− 2.37465e16i	− 0.383439i
$630$	0	0
$631$	1.12464e16	0.178171	0.0890855	−	0.996024i	$-0.471606\pi$
$631$	1.12464e16	0.178171	0.0890855	+	0.996024i	$0.471606\pi$
$632$	−2.56818e16	−0.403017
$633$	− 1.09097e17i	− 1.69586i
$634$	−5.99264e15	−0.0922747
$635$	4.72898e16i	0.721316i
$636$	− 4.13758e16i	− 0.625178i
$637$	0	0
$638$	3.30474e15	0.0490020
$639$	5.19565e16	0.763194
$640$	3.38104e15i	0.0492007i
$641$	4.34695e16	0.626666	0.313333	−	0.949643i	$-0.398554\pi$
$641$	4.34695e16	0.626666	0.313333	+	0.949643i	$0.398554\pi$
$642$	7.92954e16i	1.13250i
$643$	3.56902e16i	0.504990i	0.967598	+	0.252495i	$0.0812512\pi$
$643$	3.56902e16i	0.504990i	−0.967598	+	0.252495i	$0.918749\pi$
$644$	0	0
$645$	6.69864e16	0.930311
$646$	2.23163e16	0.307062
$647$	1.01997e17i	1.39048i	0.718779	+	0.695238i	$0.244701\pi$
$647$	1.01997e17i	1.39048i	−0.718779	+	0.695238i	$0.755299\pi$
$648$	−3.24379e16	−0.438130
$649$	1.09286e15i	0.0146250i
$650$	2.09529e16i	0.277820i
$651$	0	0
$652$	−5.67650e16	−0.738916
$653$	2.75890e16	0.355841	0.177921	−	0.984045i	$-0.443063\pi$
$653$	2.75890e16	0.355841	0.177921	+	0.984045i	$0.443063\pi$
$654$	− 8.55501e16i	− 1.09334i
$655$	7.21439e16	0.913591
$656$	− 1.99328e16i	− 0.250118i
$657$	− 2.15688e16i	− 0.268185i
$658$	0	0
$659$	8.60974e16	1.05118	0.525590	−	0.850738i	$-0.323844\pi$
$659$	8.60974e16	1.05118	0.525590	+	0.850738i	$0.323844\pi$
$660$	−7.91481e15	−0.0957584
$661$	1.27438e16i	0.152788i	0.997078	+	0.0763939i	$0.0243407\pi$
$661$	1.27438e16i	0.152788i	−0.997078	+	0.0763939i	$0.975659\pi$
$662$	3.75481e16	0.446108
$663$	1.50480e16i	0.177174i
$664$	7.58389e15i	0.0884879i
$665$	0	0
$666$	3.55882e16	0.407813
$667$	1.47309e16	0.167292
$668$	2.45637e15i	0.0276461i
$669$	7.45418e16	0.831464
$670$	− 2.57606e16i	− 0.284778i
$671$	− 4.33854e15i	− 0.0475345i
$672$	0	0
$673$	1.37493e17	1.47976	0.739879	−	0.672740i	$-0.234883\pi$
$673$	1.37493e17	1.47976	0.739879	+	0.672740i	$0.234883\pi$
$674$	−1.24751e16	−0.133072
$675$	− 4.65750e16i	− 0.492414i
$676$	3.22505e16	0.337953
$677$	3.30511e16i	0.343285i	0.985159	+	0.171642i	$0.0549073\pi$
$677$	3.30511e16i	0.343285i	−0.985159	+	0.171642i	$0.945093\pi$
$678$	9.09769e15i	0.0936597i
$679$	0	0
$680$	−5.12483e15	−0.0518354
$681$	1.42186e17	1.42552
$682$	1.88604e16i	0.187432i
$683$	−3.96082e16	−0.390176	−0.195088	−	0.980786i	$-0.562499\pi$
$683$	−3.96082e16	−0.390176	−0.195088	+	0.980786i	$0.562499\pi$
$684$	3.34448e16i	0.326582i
$685$	2.50333e16i	0.242312i
$686$	0	0
$687$	8.36938e16	0.796073
$688$	3.75020e16	0.353610
$689$	6.44489e16i	0.602421i
$690$	−3.52803e16	−0.326917
$691$	7.32731e16i	0.673095i	0.941666	+	0.336548i	$0.109259\pi$
$691$	7.32731e16i	0.673095i	−0.941666	+	0.336548i	$0.890741\pi$
$692$	− 9.08162e15i	− 0.0827041i
$693$	0	0
$694$	5.84142e14	0.00522831
$695$	6.43208e16	0.570746
$696$	1.13017e16i	0.0994235i
$697$	3.02132e16	0.263512
$698$	3.39950e16i	0.293956i
$699$	− 3.65415e16i	− 0.313273i
$700$	0	0
$701$	−2.17411e16	−0.183220	−0.0916101	−	0.995795i	$-0.529201\pi$
$701$	−2.17411e16	−0.183220	−0.0916101	+	0.995795i	$0.529201\pi$
$702$	3.43740e16	0.287215
$703$	2.89720e17i	2.40019i
$704$	−4.43107e15	−0.0363976
$705$	− 1.54992e17i	− 1.26233i
$706$	4.85060e16i	0.391713i
$707$	0	0
$708$	−3.73742e15	−0.0296738
$709$	−2.07468e17	−1.63333	−0.816665	−	0.577113i	$-0.804179\pi$
$709$	−2.07468e17	−1.63333	−0.816665	+	0.577113i	$0.804179\pi$
$710$	− 9.71338e16i	− 0.758264i
$711$	5.83394e16	0.451590
$712$	5.02454e15i	0.0385670i
$713$	8.40702e16i	0.639889i
$714$	0	0
$715$	1.23285e16	0.0922728
$716$	9.05282e16	0.671902
$717$	4.73041e16i	0.348164i
$718$	−8.28426e16	−0.604654
$719$	2.39551e17i	1.73390i	0.498396	+	0.866950i	$0.333923\pi$
$719$	2.39551e17i	1.73390i	−0.498396	+	0.866950i	$0.666077\pi$
$720$	− 7.68045e15i	− 0.0551305i
$721$	0	0
$722$	−1.72107e17	−1.21500
$723$	2.62316e17	1.83651
$724$	2.90802e15i	0.0201914i
$725$	−2.38527e16	−0.164251
$726$	1.11968e17i	0.764673i
$727$	5.15434e16i	0.349113i	0.984647	+	0.174557i	$0.0558492\pi$
$727$	5.15434e16i	0.349113i	−0.984647	+	0.174557i	$0.944151\pi$
$728$	0	0
$729$	−5.28512e16	−0.352119
$730$	−4.03234e16	−0.266452
$731$	5.68439e16i	0.372546i
$732$	1.48372e16	0.0964460
$733$	1.17335e17i	0.756491i	0.925705	+	0.378245i	$0.123472\pi$
$733$	1.17335e17i	0.756491i	−0.925705	+	0.378245i	$0.876528\pi$
$734$	− 9.11546e16i	− 0.582911i
$735$	0	0
$736$	−1.97515e16	−0.124260
$737$	3.37609e16	0.210673
$738$	4.52797e16i	0.280263i
$739$	1.03573e16	0.0635886	0.0317943	−	0.999494i	$-0.489878\pi$
$739$	1.03573e16	0.0635886	0.0317943	+	0.999494i	$0.489878\pi$
$740$	− 6.65329e16i	− 0.405178i
$741$	− 1.83594e17i	− 1.10905i
$742$	0	0
$743$	−2.76902e17	−1.64586	−0.822929	−	0.568144i	$-0.807662\pi$
$743$	−2.76902e17	−1.64586	−0.822929	+	0.568144i	$0.807662\pi$
$744$	−6.44997e16	−0.380295
$745$	1.70146e16i	0.0995137i
$746$	−8.75609e16	−0.508016
$747$	− 1.72277e16i	− 0.0991527i
$748$	− 6.71642e15i	− 0.0383467i
$749$	0	0
$750$	1.39901e17	0.786058
$751$	5.67702e15	0.0316432	0.0158216	−	0.999875i	$-0.494964\pi$
$751$	5.67702e15	0.0316432	0.0158216	+	0.999875i	$0.494964\pi$
$752$	− 8.67714e16i	− 0.479810i
$753$	−3.23087e17	−1.77235
$754$	− 1.76041e16i	− 0.0958045i
$755$	− 1.25320e17i	− 0.676612i
$756$	0	0
$757$	5.87044e16	0.311957	0.155979	−	0.987760i	$-0.450147\pi$
$757$	5.87044e16	0.311957	0.155979	+	0.987760i	$0.450147\pi$
$758$	9.80167e16	0.516755
$759$	− 4.62370e16i	− 0.241846i
$760$	6.25257e16	0.324472
$761$	1.69906e17i	0.874783i	0.899271	+	0.437392i	$0.144098\pi$
$761$	1.69906e17i	0.874783i	−0.899271	+	0.437392i	$0.855902\pi$
$762$	− 2.11950e17i	− 1.08269i
$763$	0	0
$764$	1.20598e17	0.606428
$765$	1.16417e16	0.0580827
$766$	2.41180e17i	1.19390i
$767$	5.82159e15	0.0285936
$768$	− 1.51536e16i	− 0.0738496i
$769$	1.95491e17i	0.945298i	0.881251	+	0.472649i	$0.156702\pi$
$769$	1.95491e17i	0.945298i	−0.881251	+	0.472649i	$0.843298\pi$
$770$	0	0
$771$	−2.14766e17	−1.02244
$772$	1.16416e17	0.549933
$773$	− 1.30278e17i	− 0.610652i	−0.952248	−	0.305326i	$-0.901235\pi$
$773$	− 1.30278e17i	− 0.610652i	0.952248	−	0.305326i	$-0.0987654\pi$
$774$	−8.51904e16	−0.396228
$775$	− 1.36129e17i	− 0.628261i
$776$	3.17657e16i	0.145475i
$777$	0	0
$778$	9.79860e16	0.441862
$779$	−3.68618e17	−1.64950
$780$	4.21616e16i	0.187219i
$781$	1.27300e17	0.560948
$782$	− 2.99384e16i	− 0.130915i
$783$	3.91312e16i	0.169806i
$784$	0	0
$785$	−1.60365e17	−0.685317
$786$	−3.23344e17	−1.37129
$787$	− 1.35978e17i	− 0.572296i	−0.958186	−	0.286148i	$-0.907625\pi$
$787$	− 1.35978e17i	− 0.572296i	0.958186	−	0.286148i	$-0.0923748\pi$
$788$	−1.02762e17	−0.429214
$789$	− 5.07480e17i	− 2.10357i
$790$	− 1.09067e17i	− 0.448673i
$791$	0	0
$792$	1.00657e16	0.0407844
$793$	−2.31111e16	−0.0929354
$794$	4.05020e16i	0.161642i
$795$	1.75716e17	0.696000
$796$	− 6.41474e16i	− 0.252174i
$797$	7.42818e16i	0.289823i	0.989445	+	0.144911i	$0.0462897\pi$
$797$	7.42818e16i	0.289823i	−0.989445	+	0.144911i	$0.953710\pi$
$798$	0	0
$799$	1.31524e17	0.505505
$800$	3.19822e16	0.122002
$801$	− 1.14138e16i	− 0.0432152i
$802$	3.46463e17	1.30200
$803$	− 5.28464e16i	− 0.197116i
$804$	1.15457e17i	0.427449i
$805$	0	0
$806$	1.00468e17	0.366452
$807$	2.76419e17	1.00075
$808$	− 1.57951e17i	− 0.567614i
$809$	−1.72447e17	−0.615127	−0.307563	−	0.951528i	$-0.599514\pi$
$809$	−1.72447e17	−0.615127	−0.307563	+	0.951528i	$0.599514\pi$
$810$	− 1.37759e17i	− 0.487763i
$811$	− 9.05781e16i	− 0.318345i	−0.987251	−	0.159172i	$-0.949117\pi$
$811$	− 9.05781e16i	− 0.318345i	0.987251	−	0.159172i	$-0.0508826\pi$
$812$	0	0
$813$	−8.34960e16	−0.289150
$814$	8.71956e16	0.299742
$815$	− 2.41072e17i	− 0.822623i
$816$	2.29691e16	0.0778043
$817$	− 6.93526e17i	− 2.33201i
$818$	1.63683e17i	0.546367i
$819$	0	0
$820$	8.46514e16	0.278452
$821$	−5.80746e17	−1.89639	−0.948195	−	0.317689i	$-0.897093\pi$
$821$	−5.80746e17	−1.89639	−0.948195	+	0.317689i	$0.897093\pi$
$822$	− 1.12198e17i	− 0.363708i
$823$	1.80190e17	0.579872	0.289936	−	0.957046i	$-0.406366\pi$
$823$	1.80190e17	0.579872	0.289936	+	0.957046i	$0.406366\pi$
$824$	− 1.21499e17i	− 0.388160i
$825$	7.48684e16i	0.237451i
$826$	0	0
$827$	3.77617e17	1.18037	0.590185	−	0.807268i	$-0.299055\pi$
$827$	3.77617e17	1.18037	0.590185	+	0.807268i	$0.299055\pi$
$828$	4.48679e16	0.139237
$829$	− 6.00974e16i	− 0.185152i	−0.995706	−	0.0925760i	$-0.970490\pi$
$829$	− 6.00974e16i	− 0.185152i	0.995706	−	0.0925760i	$-0.0295101\pi$
$830$	−3.22076e16	−0.0985121
$831$	4.97367e17i	1.51033i
$832$	2.36040e16i	0.0711615i
$833$	0	0
$834$	−2.88281e17	−0.856683
$835$	−1.04318e16	−0.0307780
$836$	8.19439e16i	0.240038i
$837$	−2.23325e17	−0.649507
$838$	− 1.65130e17i	− 0.476827i
$839$	− 2.04585e17i	− 0.586546i	−0.956029	−	0.293273i	$-0.905256\pi$
$839$	− 2.04585e17i	− 0.586546i	0.956029	−	0.293273i	$-0.0947444\pi$
$840$	0	0
$841$	−3.33774e17	−0.943359
$842$	1.49104e17	0.418423
$843$	− 4.31707e17i	− 1.20288i
$844$	2.59386e17	0.717616
$845$	1.36963e17i	0.376238i
$846$	1.97112e17i	0.537638i
$847$	0	0
$848$	9.83740e16	0.264549
$849$	−7.24867e17	−1.93559
$850$	4.84772e16i	0.128536i
$851$	3.88674e17	1.02331
$852$	4.35347e17i	1.13815i
$853$	5.22323e17i	1.35595i	0.735083	+	0.677977i	$0.237143\pi$
$853$	5.22323e17i	1.35595i	−0.735083	+	0.677977i	$0.762857\pi$
$854$	0	0
$855$	−1.42035e17	−0.363578
$856$	−1.88531e17	−0.479225
$857$	− 3.15468e17i	− 0.796287i	−0.917323	−	0.398144i	$-0.869655\pi$
$857$	− 3.15468e17i	− 0.796287i	0.917323	−	0.398144i	$-0.130345\pi$
$858$	−5.52554e16	−0.138500
$859$	4.95669e17i	1.23377i	0.787055	+	0.616883i	$0.211605\pi$
$859$	4.95669e17i	1.23377i	−0.787055	+	0.616883i	$0.788395\pi$
$860$	1.59265e17i	0.393668i
$861$	0	0
$862$	−4.28027e17	−1.04334
$863$	−2.87048e17	−0.694847	−0.347424	−	0.937708i	$-0.612943\pi$
$863$	−2.87048e17	−0.694847	−0.347424	+	0.937708i	$0.612943\pi$
$864$	− 5.24680e16i	− 0.126128i
$865$	3.85682e16	0.0920731
$866$	− 4.24552e17i	− 1.00652i
$867$	− 4.67045e17i	− 1.09962i
$868$	0	0
$869$	1.42939e17	0.331919
$870$	−4.79966e16	−0.110687
$871$	− 1.79842e17i	− 0.411890i
$872$	2.03402e17	0.462653
$873$	− 7.21595e16i	− 0.163008i
$874$	3.65265e17i	0.819482i
$875$	0	0
$876$	1.80726e17	0.399942
$877$	3.80931e17	0.837237	0.418619	−	0.908162i	$-0.362514\pi$
$877$	3.80931e17	0.837237	0.418619	+	0.908162i	$0.362514\pi$
$878$	1.62093e16i	0.0353831i
$879$	−8.08929e17	−1.75379
$880$	− 1.88181e16i	− 0.0405209i
$881$	− 4.35093e17i	− 0.930522i	−0.885174	−	0.465261i	$-0.845961\pi$
$881$	− 4.35093e17i	− 0.930522i	0.885174	−	0.465261i	$-0.154039\pi$
$882$	0	0
$883$	7.33662e17	1.54786	0.773931	−	0.633270i	$-0.218288\pi$
$883$	7.33662e17	1.54786	0.773931	+	0.633270i	$0.218288\pi$
$884$	−3.57778e16	−0.0749723
$885$	− 1.58722e16i	− 0.0330353i
$886$	1.31082e17	0.270981
$887$	− 5.92170e17i	− 1.21592i	−0.793968	−	0.607959i	$-0.791988\pi$
$887$	− 5.92170e17i	− 1.21592i	0.793968	−	0.607959i	$-0.208012\pi$
$888$	2.98196e17i	0.608168i
$889$	0	0
$890$	−2.13384e16	−0.0429360
$891$	1.80541e17	0.360837
$892$	1.77229e17i	0.351840i
$893$	−1.60467e18	−3.16429
$894$	− 7.62580e16i	− 0.149369i
$895$	3.84459e17i	0.748018i
$896$	0	0
$897$	−2.46301e17	−0.472837
$898$	2.49726e17	0.476218
$899$	1.14372e17i	0.216652i
$900$	−7.26514e16	−0.136706
$901$	1.49111e17i	0.278715i
$902$	1.10941e17i	0.205993i
$903$	0	0
$904$	−2.16304e16	−0.0396328
$905$	−1.23499e16	−0.0224788
$906$	5.61677e17i	1.01559i
$907$	−2.60988e16	−0.0468788	−0.0234394	−	0.999725i	$-0.507462\pi$
$907$	−2.60988e16	−0.0468788	−0.0234394	+	0.999725i	$0.507462\pi$
$908$	3.38057e17i	0.603220i
$909$	3.58804e17i	0.636025i
$910$	0	0
$911$	3.22736e17	0.564595	0.282297	−	0.959327i	$-0.408904\pi$
$911$	3.22736e17	0.564595	0.282297	+	0.959327i	$0.408904\pi$
$912$	−2.80236e17	−0.487029
$913$	− 4.22101e16i	− 0.0728772i
$914$	3.24035e17	0.555795
$915$	6.30111e16i	0.107372i
$916$	1.98988e17i	0.336864i
$917$	0	0
$918$	7.95286e16	0.132882
$919$	6.95094e17	1.15385	0.576926	−	0.816796i	$-0.304252\pi$
$919$	6.95094e17	1.15385	0.576926	+	0.816796i	$0.304252\pi$
$920$	− 8.38814e16i	− 0.138337i
$921$	5.74395e17	0.941138
$922$	− 3.42339e17i	− 0.557277i
$923$	− 6.78117e17i	− 1.09672i
$924$	0	0
$925$	−6.29353e17	−1.00472
$926$	−2.12662e17	−0.337306
$927$	2.76000e17i	0.434942i
$928$	−2.68707e16	−0.0420718
$929$	2.95114e17i	0.459088i	0.973298	+	0.229544i	$0.0737234\pi$
$929$	2.95114e17i	0.459088i	−0.973298	+	0.229544i	$0.926277\pi$
$930$	− 2.73920e17i	− 0.423376i
$931$	0	0
$932$	8.68801e16	0.132564
$933$	−2.69362e17	−0.408363
$934$	6.52598e17i	0.983025i
$935$	2.85236e16	0.0426908
$936$	− 5.36193e16i	− 0.0797381i
$937$	− 6.78231e17i	− 1.00217i	−0.865399	−	0.501083i	$-0.832935\pi$
$937$	− 6.78231e17i	− 1.00217i	0.865399	−	0.501083i	$-0.167065\pi$
$938$	0	0
$939$	2.08317e17	0.303901
$940$	3.68504e17	0.534165
$941$	− 9.38744e17i	− 1.35210i	−0.736855	−	0.676051i	$-0.763690\pi$
$941$	− 9.38744e17i	− 1.35210i	0.736855	−	0.676051i	$-0.236310\pi$
$942$	7.18744e17	1.02865
$943$	4.94519e17i	0.703256i
$944$	− 8.88600e15i	− 0.0125567i
$945$	0	0
$946$	−2.08727e17	−0.291227
$947$	8.57346e17	1.18866	0.594328	−	0.804223i	$-0.297418\pi$
$947$	8.57346e17	1.18866	0.594328	+	0.804223i	$0.297418\pi$
$948$	4.88829e17i	0.673452i
$949$	−2.81508e17	−0.385384
$950$	− 5.91448e17i	− 0.804590i
$951$	1.14064e17i	0.154193i
$952$	0	0
$953$	−8.08071e17	−1.07868	−0.539339	−	0.842088i	$-0.681326\pi$
$953$	−8.08071e17	−1.07868	−0.539339	+	0.842088i	$0.681326\pi$
$954$	−2.23468e17	−0.296433
$955$	5.12160e17i	0.675127i
$956$	−1.12469e17	−0.147328
$957$	− 6.29026e16i	− 0.0818836i
$958$	− 4.57505e17i	− 0.591838i
$959$	0	0
$960$	6.43549e16	0.0822156
$961$	1.34932e17	0.171307
$962$	− 4.64484e17i	− 0.586031i
$963$	4.28270e17	0.536983
$964$	6.23675e17i	0.777134i
$965$	4.94401e17i	0.612232i
$966$	0	0
$967$	4.31160e17	0.527326	0.263663	−	0.964615i	$-0.415069\pi$
$967$	4.31160e17	0.527326	0.263663	+	0.964615i	$0.415069\pi$
$968$	−2.66213e17	−0.323577
$969$	− 4.24769e17i	− 0.513110i
$970$	−1.34904e17	−0.161955
$971$	2.59745e17i	0.309907i	0.987922	+	0.154953i	$0.0495227\pi$
$971$	2.59745e17i	0.309907i	−0.987922	+	0.154953i	$0.950477\pi$
$972$	3.16571e17i	0.375382i
$973$	0	0
$974$	−2.90849e17	−0.340654
$975$	3.98818e17	0.464244
$976$	3.52765e16i	0.0408118i
$977$	1.34288e18	1.54408	0.772042	−	0.635571i	$-0.219235\pi$
$977$	1.34288e18	1.54408	0.772042	+	0.635571i	$0.219235\pi$
$978$	1.08047e18i	1.23475i
$979$	− 2.79654e16i	− 0.0317632i
$980$	0	0
$981$	−4.62051e17	−0.518413
$982$	4.75726e17	0.530503
$983$	7.03157e17i	0.779348i	0.920953	+	0.389674i	$0.127412\pi$
$983$	7.03157e17i	0.779348i	−0.920953	+	0.389674i	$0.872588\pi$
$984$	−3.79402e17	−0.417954
$985$	− 4.36413e17i	− 0.477837i
$986$	− 4.07294e16i	− 0.0443248i
$987$	0	0
$988$	4.36509e17	0.469301
$989$	−9.30400e17	−0.994242
$990$	4.27475e16i	0.0454046i
$991$	8.45062e17	0.892168	0.446084	−	0.894991i	$-0.352818\pi$
$991$	8.45062e17	0.892168	0.446084	+	0.894991i	$0.352818\pi$
$992$	− 1.53353e17i	− 0.160924i
$993$	− 7.14692e17i	− 0.745458i
$994$	0	0
$995$	2.72424e17	0.280741
$996$	1.44352e17	0.147866
$997$	1.50724e18i	1.53466i	0.641252	+	0.767330i	$0.278415\pi$
$997$	1.50724e18i	1.53466i	−0.641252	+	0.767330i	$0.721585\pi$
$998$	−1.76556e16	−0.0178689
$999$	1.03248e18i	1.03869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.b.c.97.10		16
7.2	even	3		98.13.d.a.31.4		16
7.3	odd	6		98.13.d.a.19.4		16
7.4	even	3		14.13.d.a.5.1	yes	16
7.5	odd	6		14.13.d.a.3.1	✓	16
7.6	odd	2	inner	98.13.b.c.97.15		16
21.5	even	6		126.13.n.a.73.7		16
21.11	odd	6		126.13.n.a.19.7		16
28.11	odd	6		112.13.s.c.33.7		16
28.19	even	6		112.13.s.c.17.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.1	✓	16	7.5	odd	6
14.13.d.a.5.1	yes	16	7.4	even	3
98.13.b.c.97.10		16	1.1	even	1	trivial
98.13.b.c.97.15		16	7.6	odd	2	inner
98.13.d.a.19.4		16	7.3	odd	6
98.13.d.a.31.4		16	7.2	even	3
112.13.s.c.17.7		16	28.19	even	6
112.13.s.c.33.7		16	28.11	odd	6
126.13.n.a.19.7		16	21.11	odd	6
126.13.n.a.73.7		16	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:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	98.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+45.2548 q^{2} -861.382i q^{3} +2048.00 q^{4} +8697.53i q^{5} -38981.7i q^{6} +92681.9 q^{8} -210538. q^{9} +O(q^{10})\)	\(q+45.2548 q^{2} -861.382i q^{3} +2048.00 q^{4} +8697.53i q^{5} -38981.7i q^{6} +92681.9 q^{8} -210538. q^{9} +393605. i q^{10} -515845. q^{11} -1.76411e6i q^{12} +2.74786e6i q^{13} +7.49190e6 q^{15} +4.19430e6 q^{16} +6.35754e6i q^{17} -9.52787e6 q^{18} -7.75654e7i q^{19} +1.78125e7i q^{20} -2.33445e7 q^{22} -1.04058e8 q^{23} -7.98345e7i q^{24} +1.68494e8 q^{25} +1.24354e8i q^{26} -2.76420e8i q^{27} -1.41564e8 q^{29} +3.39045e8 q^{30} -8.07917e8i q^{31} +1.89813e8 q^{32} +4.44339e8i q^{33} +2.87709e8i q^{34} -4.31182e8 q^{36} -3.73517e9 q^{37} -3.51021e9i q^{38} +2.36696e9 q^{39} +8.06104e8i q^{40} -4.75235e9i q^{41} +8.94118e9 q^{43} -1.05645e9 q^{44} -1.83116e9i q^{45} -4.70912e9 q^{46} -2.06879e10i q^{47} -3.61290e9i q^{48} +7.62515e9 q^{50} +5.47627e9 q^{51} +5.62762e9i q^{52} +2.34542e10 q^{53} -1.25093e10i q^{54} -4.48657e9i q^{55} -6.68134e10 q^{57} -6.40647e9 q^{58} -2.11859e9i q^{59} +1.53434e10 q^{60} +8.41056e9i q^{61} -3.65622e10i q^{62} +8.58993e9 q^{64} -2.38996e10 q^{65} +2.01085e10i q^{66} -6.54478e10 q^{67} +1.30202e10i q^{68} +8.96336e10i q^{69} -2.46780e11 q^{71} -1.95131e10 q^{72} +1.02446e11i q^{73} -1.69035e11 q^{74} -1.45137e11i q^{75} -1.58854e11i q^{76} +1.07116e11 q^{78} -2.77097e11 q^{79} +3.64801e10i q^{80} -3.49992e11 q^{81} -2.15067e11i q^{82} +8.18271e10i q^{83} -5.52949e10 q^{85} +4.04632e11 q^{86} +1.21941e11i q^{87} -4.78095e10 q^{88} +5.42127e10i q^{89} -8.28689e10i q^{90} -2.13111e11 q^{92} -6.95926e11 q^{93} -9.36228e11i q^{94} +6.74627e11 q^{95} -1.63501e11i q^{96} +3.42738e11i q^{97} +1.08605e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32768 q^{4} - 4724496 q^{9}+O(q^{10}) \) 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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