LMFDB - Embedded newform 289.10.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$28.6400$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-28.6400 q^{2} -243.971 q^{3} +308.250 q^{4} -1776.79 q^{5} +6987.32 q^{6} +9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} +O(q^{10})$	\(q-28.6400 q^{2} -243.971 q^{3} +308.250 q^{4} -1776.79 q^{5} +6987.32 q^{6} +9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} +50887.2 q^{10} -18658.0 q^{11} -75204.0 q^{12} +118081. q^{13} -274904. q^{14} +433484. q^{15} -324950. q^{16} -1.14098e6 q^{18} +365652. q^{19} -547695. q^{20} -2.34178e6 q^{21} +534365. q^{22} -1.22678e6 q^{23} -1.42367e6 q^{24} +1.20385e6 q^{25} -3.38183e6 q^{26} -4.91741e6 q^{27} +2.95877e6 q^{28} +2.55483e6 q^{29} -1.24150e7 q^{30} -8.56431e6 q^{31} +6.31884e6 q^{32} +4.55201e6 q^{33} -1.70547e7 q^{35} +1.22803e7 q^{36} +7.97315e6 q^{37} -1.04723e7 q^{38} -2.88083e7 q^{39} -1.03683e7 q^{40} +3.21617e7 q^{41} +6.70686e7 q^{42} -2.38617e7 q^{43} -5.75133e6 q^{44} -7.07850e7 q^{45} +3.51351e7 q^{46} -1.94506e7 q^{47} +7.92783e7 q^{48} +5.17797e7 q^{49} -3.44784e7 q^{50} +3.63984e7 q^{52} -1.96101e7 q^{53} +1.40835e8 q^{54} +3.31513e7 q^{55} +5.60118e7 q^{56} -8.92083e7 q^{57} -7.31702e7 q^{58} +1.58423e7 q^{59} +1.33622e8 q^{60} +1.09913e8 q^{61} +2.45282e8 q^{62} +3.82396e8 q^{63} -1.45973e7 q^{64} -2.09805e8 q^{65} -1.30370e8 q^{66} -8.19198e7 q^{67} +2.99299e8 q^{69} +4.88447e8 q^{70} -1.93682e8 q^{71} +2.32475e8 q^{72} +1.53405e7 q^{73} -2.28351e8 q^{74} -2.93705e8 q^{75} +1.12712e8 q^{76} -1.79091e8 q^{77} +8.25069e8 q^{78} -1.36544e8 q^{79} +5.77367e8 q^{80} +4.15558e8 q^{81} -9.21111e8 q^{82} -6.51497e8 q^{83} -7.21854e8 q^{84} +6.83399e8 q^{86} -6.23303e8 q^{87} -1.08877e8 q^{88} -6.97006e8 q^{89} +2.02728e9 q^{90} +1.13341e9 q^{91} -3.78156e8 q^{92} +2.08944e9 q^{93} +5.57064e8 q^{94} -6.49686e8 q^{95} -1.54161e9 q^{96} +4.50260e8 q^{97} -1.48297e9 q^{98} -7.43311e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - 88 q^{3} + 2389 q^{4} - 1362 q^{5} + 11720 q^{6} - 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) $ 7 * q - q^2 - 88 * q^3 + 2389 * q^4 - 1362 * q^5 + 11720 * q^6 - 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} - 88 q^{3} + 2389 q^{4} - 1362 q^{5} + 11720 q^{6} - 9388 q^{7} + 16821 q^{8} + 81419 q^{9} - 154226 q^{10} - 135536 q^{11} - 198160 q^{12} + 166122 q^{13} - 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 149027 q^{18} + 777172 q^{19} + 917162 q^{20} - 3412104 q^{21} + 1222520 q^{22} - 1357764 q^{23} + 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} + 4519064 q^{27} + 3328892 q^{28} - 967002 q^{29} - 12558992 q^{30} - 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 530736 q^{35} + 4535009 q^{36} - 18296498 q^{37} - 49363020 q^{38} - 86306872 q^{39} - 127155062 q^{40} - 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} - 96696624 q^{44} - 108916410 q^{45} + 151509484 q^{46} + 56639800 q^{47} + 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} - 156226378 q^{52} + 121813562 q^{53} + 93375344 q^{54} + 40793128 q^{55} + 196175436 q^{56} - 153612960 q^{57} + 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} + 49915846 q^{61} + 73506556 q^{62} + 2185356 q^{63} + 317922057 q^{64} + 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 379683432 q^{69} + 966315960 q^{70} - 652473940 q^{71} + 655760385 q^{72} - 306656342 q^{73} - 249173874 q^{74} - 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} - 323434416 q^{78} - 959147884 q^{79} + 692173602 q^{80} - 374486977 q^{81} - 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} - 164953236 q^{86} - 1612550856 q^{87} - 1132038848 q^{88} - 1971327114 q^{89} + 2284664662 q^{90} + 1061062864 q^{91} - 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} + 3249631512 q^{95} + 4442036640 q^{96} - 2006526254 q^{97} - 2170640009 q^{98} + 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 - 88 * q^3 + 2389 * q^4 - 1362 * q^5 + 11720 * q^6 - 9388 * q^7 + 16821 * q^8 + 81419 * q^9 - 154226 * q^10 - 135536 * q^11 - 198160 * q^12 + 166122 * q^13 - 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 149027 * q^18 + 777172 * q^19 + 917162 * q^20 - 3412104 * q^21 + 1222520 * q^22 - 1357764 * q^23 + 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 + 4519064 * q^27 + 3328892 * q^28 - 967002 * q^29 - 12558992 * q^30 - 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 530736 * q^35 + 4535009 * q^36 - 18296498 * q^37 - 49363020 * q^38 - 86306872 * q^39 - 127155062 * q^40 - 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 - 96696624 * q^44 - 108916410 * q^45 + 151509484 * q^46 + 56639800 * q^47 + 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 - 156226378 * q^52 + 121813562 * q^53 + 93375344 * q^54 + 40793128 * q^55 + 196175436 * q^56 - 153612960 * q^57 + 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 + 49915846 * q^61 + 73506556 * q^62 + 2185356 * q^63 + 317922057 * q^64 + 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 379683432 * q^69 + 966315960 * q^70 - 652473940 * q^71 + 655760385 * q^72 - 306656342 * q^73 - 249173874 * q^74 - 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 - 323434416 * q^78 - 959147884 * q^79 + 692173602 * q^80 - 374486977 * q^81 - 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 - 164953236 * q^86 - 1612550856 * q^87 - 1132038848 * q^88 - 1971327114 * q^89 + 2284664662 * q^90 + 1061062864 * q^91 - 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 + 3249631512 * q^95 + 4442036640 * q^96 - 2006526254 * q^97 - 2170640009 * q^98 + 2579159272 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−28.6400	−1.26572	−0.632861	−	0.774266i	$-0.718119\pi$
$2$	−28.6400	−1.26572	−0.632861	+	0.774266i	$0.718119\pi$
$3$	−243.971	−1.73897	−0.869485	−	0.493959i	$-0.835549\pi$
$3$	−243.971	−1.73897	−0.869485	+	0.493959i	$0.835549\pi$
$4$	308.250	0.602051
$5$	−1776.79	−1.27137	−0.635683	−	0.771950i	$-0.719282\pi$
$5$	−1776.79	−1.27137	−0.635683	+	0.771950i	$0.719282\pi$
$6$	6987.32	2.20105
$7$	9598.61	1.51101	0.755505	−	0.655143i	$-0.227392\pi$
$7$	9598.61	1.51101	0.755505	+	0.655143i	$0.227392\pi$
$8$	5835.40	0.503693
$9$	39838.7	2.02402
$10$	50887.2	1.60920
$11$	−18658.0	−0.384236	−0.192118	−	0.981372i	$-0.561536\pi$
$11$	−18658.0	−0.384236	−0.192118	+	0.981372i	$0.561536\pi$
$12$	−75204.0	−1.04695
$13$	118081.	1.14666	0.573329	−	0.819325i	$-0.305652\pi$
$13$	118081.	1.14666	0.573329	+	0.819325i	$0.305652\pi$
$14$	−274904.	−1.91252
$15$	433484.	2.21087
$16$	−324950.	−1.23959
$17$	0	0
$17$	0	0
$18$	−1.14098e6	−2.56184
$19$	365652.	0.643690	0.321845	−	0.946792i	$-0.395697\pi$
$19$	365652.	0.643690	0.321845	+	0.946792i	$0.395697\pi$
$20$	−547695.	−0.765427
$21$	−2.34178e6	−2.62760
$22$	534365.	0.486336
$23$	−1.22678e6	−0.914098	−0.457049	−	0.889441i	$-0.651094\pi$
$23$	−1.22678e6	−0.914098	−0.457049	+	0.889441i	$0.651094\pi$
$24$	−1.42367e6	−0.875907
$25$	1.20385e6	0.616373
$26$	−3.38183e6	−1.45135
$27$	−4.91741e6	−1.78073
$28$	2.95877e6	0.909704
$29$	2.55483e6	0.670765	0.335382	−	0.942082i	$-0.391134\pi$
$29$	2.55483e6	0.670765	0.335382	+	0.942082i	$0.391134\pi$
$30$	−1.24150e7	−2.79834
$31$	−8.56431e6	−1.66558	−0.832789	−	0.553591i	$-0.813257\pi$
$31$	−8.56431e6	−1.66558	−0.832789	+	0.553591i	$0.813257\pi$
$32$	6.31884e6	1.06528
$33$	4.55201e6	0.668175
$34$	0	0
$35$	−1.70547e7	−1.92105
$36$	1.22803e7	1.21856
$37$	7.97315e6	0.699394	0.349697	−	0.936863i	$-0.386285\pi$
$37$	7.97315e6	0.699394	0.349697	+	0.936863i	$0.386285\pi$
$38$	−1.04723e7	−0.814732
$39$	−2.88083e7	−1.99400
$40$	−1.03683e7	−0.640378
$41$	3.21617e7	1.77751	0.888754	−	0.458384i	$-0.151572\pi$
$41$	3.21617e7	1.77751	0.888754	+	0.458384i	$0.151572\pi$
$42$	6.70686e7	3.32581
$43$	−2.38617e7	−1.06437	−0.532186	−	0.846628i	$-0.678629\pi$
$43$	−2.38617e7	−1.06437	−0.532186	+	0.846628i	$0.678629\pi$
$44$	−5.75133e6	−0.231330
$45$	−7.07850e7	−2.57327
$46$	3.51351e7	1.15699
$47$	−1.94506e7	−0.581423	−0.290711	−	0.956811i	$-0.593892\pi$
$47$	−1.94506e7	−0.581423	−0.290711	+	0.956811i	$0.593892\pi$
$48$	7.92783e7	2.15560
$49$	5.17797e7	1.28315
$50$	−3.44784e7	−0.780156
$51$	0	0
$52$	3.63984e7	0.690347
$53$	−1.96101e7	−0.341380	−0.170690	−	0.985325i	$-0.554600\pi$
$53$	−1.96101e7	−0.341380	−0.170690	+	0.985325i	$0.554600\pi$
$54$	1.40835e8	2.25391
$55$	3.31513e7	0.488505
$56$	5.60118e7	0.761085
$57$	−8.92083e7	−1.11936
$58$	−7.31702e7	−0.849002
$59$	1.58423e7	0.170210	0.0851051	−	0.996372i	$-0.472877\pi$
$59$	1.58423e7	0.170210	0.0851051	+	0.996372i	$0.472877\pi$
$60$	1.33622e8	1.33105
$61$	1.09913e8	1.01640	0.508201	−	0.861238i	$-0.330311\pi$
$61$	1.09913e8	1.01640	0.508201	+	0.861238i	$0.330311\pi$
$62$	2.45282e8	2.10816
$63$	3.82396e8	3.05831
$64$	−1.45973e7	−0.108759
$65$	−2.09805e8	−1.45782
$66$	−1.30370e8	−0.845723
$67$	−8.19198e7	−0.496652	−0.248326	−	0.968677i	$-0.579880\pi$
$67$	−8.19198e7	−0.496652	−0.248326	+	0.968677i	$0.579880\pi$
$68$	0	0
$69$	2.99299e8	1.58959
$70$	4.88447e8	2.43151
$71$	−1.93682e8	−0.904537	−0.452268	−	0.891882i	$-0.649385\pi$
$71$	−1.93682e8	−0.904537	−0.452268	+	0.891882i	$0.649385\pi$
$72$	2.32475e8	1.01948
$73$	1.53405e7	0.0632245	0.0316123	−	0.999500i	$-0.489936\pi$
$73$	1.53405e7	0.0632245	0.0316123	+	0.999500i	$0.489936\pi$
$74$	−2.28351e8	−0.885238
$75$	−2.93705e8	−1.07185
$76$	1.12712e8	0.387534
$77$	−1.79091e8	−0.580584
$78$	8.25069e8	2.52385
$79$	−1.36544e8	−0.394413	−0.197206	−	0.980362i	$-0.563187\pi$
$79$	−1.36544e8	−0.394413	−0.197206	+	0.980362i	$0.563187\pi$
$80$	5.77367e8	1.57597
$81$	4.15558e8	1.07263
$82$	−9.21111e8	−2.24983
$83$	−6.51497e8	−1.50682	−0.753409	−	0.657552i	$-0.771592\pi$
$83$	−6.51497e8	−1.50682	−0.753409	+	0.657552i	$0.771592\pi$
$84$	−7.21854e8	−1.58195
$85$	0	0
$86$	6.83399e8	1.34720
$87$	−6.23303e8	−1.16644
$88$	−1.08877e8	−0.193537
$89$	−6.97006e8	−1.17756	−0.588778	−	0.808295i	$-0.700391\pi$
$89$	−6.97006e8	−1.17756	−0.588778	+	0.808295i	$0.700391\pi$
$90$	2.02728e9	3.25704
$91$	1.13341e9	1.73261
$92$	−3.78156e8	−0.550334
$93$	2.08944e9	2.89639
$94$	5.57064e8	0.735919
$95$	−6.49686e8	−0.818365
$96$	−1.54161e9	−1.85249
$97$	4.50260e8	0.516405	0.258203	−	0.966091i	$-0.416870\pi$
$97$	4.50260e8	0.516405	0.258203	+	0.966091i	$0.416870\pi$
$98$	−1.48297e9	−1.62411
$99$	−7.43311e8	−0.777700
$100$	3.71088e8	0.371088
$101$	5.43766e8	0.519955	0.259978	−	0.965615i	$-0.416285\pi$
$101$	5.43766e8	0.519955	0.259978	+	0.965615i	$0.416285\pi$
$102$	0	0
$103$	9.99479e8	0.874996	0.437498	−	0.899219i	$-0.355865\pi$
$103$	9.99479e8	0.874996	0.437498	+	0.899219i	$0.355865\pi$
$104$	6.89049e8	0.577564
$105$	4.16085e9	3.34064
$106$	5.61633e8	0.432092
$107$	−2.11598e7	−0.0156058	−0.00780289	−	0.999970i	$-0.502484\pi$
$107$	−2.11598e7	−0.0156058	−0.00780289	+	0.999970i	$0.502484\pi$
$108$	−1.51579e9	−1.07209
$109$	2.38161e9	1.61604	0.808019	−	0.589156i	$-0.200540\pi$
$109$	2.38161e9	1.61604	0.808019	+	0.589156i	$0.200540\pi$
$110$	−9.49454e8	−0.618311
$111$	−1.94521e9	−1.21623
$112$	−3.11907e9	−1.87303
$113$	−1.14225e9	−0.659035	−0.329517	−	0.944150i	$-0.606886\pi$
$113$	−1.14225e9	−0.659035	−0.329517	+	0.944150i	$0.606886\pi$
$114$	2.55493e9	1.41679
$115$	2.17974e9	1.16215
$116$	7.87525e8	0.403835
$117$	4.70419e9	2.32086
$118$	−4.53725e8	−0.215439
$119$	0	0
$120$	2.52956e9	1.11360
$121$	−2.00983e9	−0.852363
$122$	−3.14792e9	−1.28648
$123$	−7.84651e9	−3.09103
$124$	−2.63995e9	−1.00276
$125$	1.33130e9	0.487731
$126$	−1.09518e10	−3.87097
$127$	5.42933e9	1.85195	0.925975	−	0.377584i	$-0.123245\pi$
$127$	5.42933e9	1.85195	0.925975	+	0.377584i	$0.123245\pi$
$128$	−2.81718e9	−0.927619
$129$	5.82156e9	1.85091
$130$	6.00881e9	1.84520
$131$	−2.35819e9	−0.699613	−0.349806	−	0.936822i	$-0.613753\pi$
$131$	−2.35819e9	−0.699613	−0.349806	+	0.936822i	$0.613753\pi$
$132$	1.40316e9	0.402275
$133$	3.50975e9	0.972621
$134$	2.34618e9	0.628623
$135$	8.73719e9	2.26397
$136$	0	0
$137$	−9.19603e8	−0.223027	−0.111514	−	0.993763i	$-0.535570\pi$
$137$	−9.19603e8	−0.223027	−0.111514	+	0.993763i	$0.535570\pi$
$138$	−8.57194e9	−2.01198
$139$	−1.27752e9	−0.290269	−0.145135	−	0.989412i	$-0.546362\pi$
$139$	−1.27752e9	−0.290269	−0.145135	+	0.989412i	$0.546362\pi$
$140$	−5.25711e9	−1.15657
$141$	4.74537e9	1.01108
$142$	5.54705e9	1.14489
$143$	−2.20315e9	−0.440588
$144$	−1.29456e10	−2.50894
$145$	−4.53939e9	−0.852788
$146$	−4.39351e8	−0.0800246
$147$	−1.26327e10	−2.23136
$148$	2.45772e9	0.421071
$149$	−1.13853e9	−0.189237	−0.0946183	−	0.995514i	$-0.530163\pi$
$149$	−1.13853e9	−0.189237	−0.0946183	+	0.995514i	$0.530163\pi$
$150$	8.41171e9	1.35667
$151$	1.89477e9	0.296593	0.148296	−	0.988943i	$-0.452621\pi$
$151$	1.89477e9	0.296593	0.148296	+	0.988943i	$0.452621\pi$
$152$	2.13373e9	0.324222
$153$	0	0
$154$	5.12917e9	0.734858
$155$	1.52170e10	2.11756
$156$	−8.88014e9	−1.20049
$157$	6.87991e9	0.903721	0.451860	−	0.892089i	$-0.350760\pi$
$157$	6.87991e9	0.903721	0.451860	+	0.892089i	$0.350760\pi$
$158$	3.91062e9	0.499217
$159$	4.78429e9	0.593650
$160$	−1.12272e10	−1.35436
$161$	−1.17754e10	−1.38121
$162$	−1.19016e10	−1.35765
$163$	−1.18995e10	−1.32034	−0.660171	−	0.751116i	$-0.729516\pi$
$163$	−1.18995e10	−1.32034	−0.660171	+	0.751116i	$0.729516\pi$
$164$	9.91384e9	1.07015
$165$	−8.08795e9	−0.849495
$166$	1.86589e10	1.90721
$167$	1.62243e10	1.61415	0.807073	−	0.590451i	$-0.201050\pi$
$167$	1.62243e10	1.61415	0.807073	+	0.590451i	$0.201050\pi$
$168$	−1.36652e10	−1.32350
$169$	3.33857e9	0.314826
$170$	0	0
$171$	1.45671e10	1.30284
$172$	−7.35537e9	−0.640806
$173$	−9.77316e9	−0.829521	−0.414761	−	0.909931i	$-0.636135\pi$
$173$	−9.77316e9	−0.829521	−0.414761	+	0.909931i	$0.636135\pi$
$174$	1.78514e10	1.47639
$175$	1.15553e10	0.931345
$176$	6.06292e9	0.476293
$177$	−3.86507e9	−0.295990
$178$	1.99623e10	1.49046
$179$	−1.22507e10	−0.891915	−0.445958	−	0.895054i	$-0.647137\pi$
$179$	−1.22507e10	−0.891915	−0.445958	+	0.895054i	$0.647137\pi$
$180$	−2.18195e10	−1.54924
$181$	−1.21812e10	−0.843597	−0.421798	−	0.906690i	$-0.638601\pi$
$181$	−1.21812e10	−0.843597	−0.421798	+	0.906690i	$0.638601\pi$
$182$	−3.24609e10	−2.19300
$183$	−2.68156e10	−1.76749
$184$	−7.15878e9	−0.460425
$185$	−1.41666e10	−0.889186
$186$	−5.98416e10	−3.66602
$187$	0	0
$188$	−5.99564e9	−0.350046
$189$	−4.72003e10	−2.69071
$190$	1.86070e10	1.03582
$191$	−1.62713e10	−0.884651	−0.442325	−	0.896855i	$-0.645846\pi$
$191$	−1.62713e10	−0.884651	−0.442325	+	0.896855i	$0.645846\pi$
$192$	3.56132e9	0.189128
$193$	−1.78626e10	−0.926696	−0.463348	−	0.886176i	$-0.653352\pi$
$193$	−1.78626e10	−0.926696	−0.463348	+	0.886176i	$0.653352\pi$
$194$	−1.28954e10	−0.653625
$195$	5.11862e10	2.53511
$196$	1.59611e10	0.772522
$197$	−1.24709e10	−0.589927	−0.294963	−	0.955509i	$-0.595307\pi$
$197$	−1.24709e10	−0.589927	−0.294963	+	0.955509i	$0.595307\pi$
$198$	2.12884e10	0.984352
$199$	1.76972e10	0.799957	0.399978	−	0.916525i	$-0.369018\pi$
$199$	1.76972e10	0.799957	0.399978	+	0.916525i	$0.369018\pi$
$200$	7.02497e9	0.310463
$201$	1.99860e10	0.863663
$202$	−1.55735e10	−0.658119
$203$	2.45228e10	1.01353
$204$	0	0
$205$	−5.71445e10	−2.25986
$206$	−2.86251e10	−1.10750
$207$	−4.88735e10	−1.85015
$208$	−3.83703e10	−1.42138
$209$	−6.82233e9	−0.247329
$210$	−1.19167e11	−4.22832
$211$	3.49985e10	1.21556	0.607782	−	0.794104i	$-0.292059\pi$
$211$	3.49985e10	1.21556	0.607782	+	0.794104i	$0.292059\pi$
$212$	−6.04481e9	−0.205528
$213$	4.72527e10	1.57296
$214$	6.06018e8	0.0197526
$215$	4.23972e10	1.35321
$216$	−2.86950e10	−0.896943
$217$	−8.22055e10	−2.51670
$218$	−6.82094e10	−2.04545
$219$	−3.74262e9	−0.109946
$220$	1.02189e10	0.294105
$221$	0	0
$222$	5.57110e10	1.53940
$223$	4.75965e10	1.28885	0.644426	−	0.764667i	$-0.277096\pi$
$223$	4.75965e10	1.28885	0.644426	+	0.764667i	$0.277096\pi$
$224$	6.06521e10	1.60964
$225$	4.79600e10	1.24755
$226$	3.27141e10	0.834154
$227$	−1.17164e10	−0.292873	−0.146436	−	0.989220i	$-0.546780\pi$
$227$	−1.17164e10	−0.292873	−0.146436	+	0.989220i	$0.546780\pi$
$228$	−2.74985e10	−0.673910
$229$	2.48997e10	0.598321	0.299161	−	0.954203i	$-0.403293\pi$
$229$	2.48997e10	0.598321	0.299161	+	0.954203i	$0.403293\pi$
$230$	−6.24277e10	−1.47096
$231$	4.36929e10	1.00962
$232$	1.49084e10	0.337860
$233$	−6.50866e10	−1.44674	−0.723369	−	0.690462i	$-0.757407\pi$
$233$	−6.50866e10	−1.44674	−0.723369	+	0.690462i	$0.757407\pi$
$234$	−1.34728e11	−2.93756
$235$	3.45596e10	0.739201
$236$	4.88340e9	0.102475
$237$	3.33128e10	0.685872
$238$	0	0
$239$	4.29823e10	0.852117	0.426058	−	0.904696i	$-0.359902\pi$
$239$	4.29823e10	0.852117	0.426058	+	0.904696i	$0.359902\pi$
$240$	−1.40861e11	−2.74056
$241$	7.83992e10	1.49705	0.748523	−	0.663109i	$-0.230764\pi$
$241$	7.83992e10	1.49705	0.748523	+	0.663109i	$0.230764\pi$
$242$	5.75614e10	1.07885
$243$	−4.59462e9	−0.0845320
$244$	3.38807e10	0.611926
$245$	−9.20017e10	−1.63135
$246$	2.24724e11	3.91239
$247$	4.31764e10	0.738092
$248$	−4.99762e10	−0.838940
$249$	1.58946e11	2.62031
$250$	−3.81284e10	−0.617331
$251$	2.92884e10	0.465762	0.232881	−	0.972505i	$-0.425185\pi$
$251$	2.92884e10	0.465762	0.232881	+	0.972505i	$0.425185\pi$
$252$	1.17874e11	1.84126
$253$	2.28893e10	0.351230
$254$	−1.55496e11	−2.34405
$255$	0	0
$256$	8.81579e10	1.28287
$257$	3.01696e10	0.431390	0.215695	−	0.976461i	$-0.430798\pi$
$257$	3.01696e10	0.431390	0.215695	+	0.976461i	$0.430798\pi$
$258$	−1.66729e11	−2.34274
$259$	7.65311e10	1.05679
$260$	−6.46723e10	−0.877684
$261$	1.01781e11	1.35764
$262$	6.75385e10	0.885515
$263$	−9.10348e10	−1.17329	−0.586647	−	0.809843i	$-0.699552\pi$
$263$	−9.10348e10	−1.17329	−0.586647	+	0.809843i	$0.699552\pi$
$264$	2.65628e10	0.336555
$265$	3.48430e10	0.434019
$266$	−1.00519e11	−1.23107
$267$	1.70049e11	2.04774
$268$	−2.52518e10	−0.299010
$269$	6.95622e10	0.810005	0.405003	−	0.914316i	$-0.367271\pi$
$269$	6.95622e10	0.810005	0.405003	+	0.914316i	$0.367271\pi$
$270$	−2.50233e11	−2.86555
$271$	−9.57591e10	−1.07849	−0.539247	−	0.842147i	$-0.681291\pi$
$271$	−9.57591e10	−1.07849	−0.539247	+	0.842147i	$0.681291\pi$
$272$	0	0
$273$	−2.76519e11	−3.01296
$274$	2.63374e10	0.282290
$275$	−2.24615e10	−0.236833
$276$	9.22591e10	0.957014
$277$	8.55452e10	0.873045	0.436523	−	0.899693i	$-0.356210\pi$
$277$	8.55452e10	0.873045	0.436523	+	0.899693i	$0.356210\pi$
$278$	3.65882e10	0.367400
$279$	−3.41191e11	−3.37116
$280$	−9.95211e10	−0.967618
$281$	−4.39159e10	−0.420188	−0.210094	−	0.977681i	$-0.567377\pi$
$281$	−4.39159e10	−0.420188	−0.210094	+	0.977681i	$0.567377\pi$
$282$	−1.35907e11	−1.27974
$283$	−8.04249e10	−0.745335	−0.372668	−	0.927965i	$-0.621557\pi$
$283$	−8.04249e10	−0.745335	−0.372668	+	0.927965i	$0.621557\pi$
$284$	−5.97024e10	−0.544577
$285$	1.58504e11	1.42311
$286$	6.30983e10	0.557661
$287$	3.08708e11	2.68583
$288$	2.51735e11	2.15614
$289$	0	0
$290$	1.30008e11	1.07939
$291$	−1.09850e11	−0.898013
$292$	4.72870e9	0.0380644
$293$	−2.21747e10	−0.175774	−0.0878869	−	0.996130i	$-0.528011\pi$
$293$	−2.21747e10	−0.175774	−0.0878869	+	0.996130i	$0.528011\pi$
$294$	3.61802e11	2.82428
$295$	−2.81485e10	−0.216399
$296$	4.65265e10	0.352280
$297$	9.17490e10	0.684222
$298$	3.26074e10	0.239521
$299$	−1.44860e11	−1.04816
$300$	−9.05345e10	−0.645310
$301$	−2.29039e11	−1.60828
$302$	−5.42663e10	−0.375404
$303$	−1.32663e11	−0.904187
$304$	−1.18819e11	−0.797908
$305$	−1.95293e11	−1.29222
$306$	0	0
$307$	1.36198e11	0.875081	0.437540	−	0.899199i	$-0.355850\pi$
$307$	1.36198e11	0.875081	0.437540	+	0.899199i	$0.355850\pi$
$308$	−5.52048e10	−0.349541
$309$	−2.43844e11	−1.52159
$310$	−4.35814e11	−2.68024
$311$	−2.63133e11	−1.59497	−0.797486	−	0.603337i	$-0.793837\pi$
$311$	−2.63133e11	−1.59497	−0.797486	+	0.603337i	$0.793837\pi$
$312$	−1.68108e11	−1.00437
$313$	−1.85944e11	−1.09504	−0.547522	−	0.836791i	$-0.684429\pi$
$313$	−1.85944e11	−1.09504	−0.547522	+	0.836791i	$0.684429\pi$
$314$	−1.97041e11	−1.14386
$315$	−6.79438e11	−3.88823
$316$	−4.20897e10	−0.237456
$317$	3.15409e11	1.75431	0.877157	−	0.480203i	$-0.159437\pi$
$317$	3.15409e11	1.75431	0.877157	+	0.480203i	$0.159437\pi$
$318$	−1.37022e11	−0.751395
$319$	−4.76680e10	−0.257732
$320$	2.59364e10	0.138272
$321$	5.16238e9	0.0271380
$322$	3.37248e11	1.74823
$323$	0	0
$324$	1.28096e11	0.645776
$325$	1.42152e11	0.706769
$326$	3.40803e11	1.67118
$327$	−5.81043e11	−2.81024
$328$	1.87676e11	0.895318
$329$	−1.86698e11	−0.878535
$330$	2.31639e11	1.07522
$331$	−1.33188e10	−0.0609871	−0.0304936	−	0.999535i	$-0.509708\pi$
$331$	−1.33188e10	−0.0609871	−0.0304936	+	0.999535i	$0.509708\pi$
$332$	−2.00824e11	−0.907181
$333$	3.17640e11	1.41559
$334$	−4.64665e11	−2.04306
$335$	1.45554e11	0.631426
$336$	7.60961e11	3.25714
$337$	8.96864e10	0.378785	0.189392	−	0.981902i	$-0.439348\pi$
$337$	8.96864e10	0.378785	0.189392	+	0.981902i	$0.439348\pi$
$338$	−9.56167e10	−0.398482
$339$	2.78676e11	1.14604
$340$	0	0
$341$	1.59793e11	0.639975
$342$	−4.17202e11	−1.64903
$343$	1.09675e11	0.427843
$344$	−1.39243e11	−0.536117
$345$	−5.31792e11	−2.02095
$346$	2.79903e11	1.04994
$347$	3.71901e11	1.37703	0.688516	−	0.725221i	$-0.258262\pi$
$347$	3.71901e11	1.37703	0.688516	+	0.725221i	$0.258262\pi$
$348$	−1.92133e11	−0.702256
$349$	2.40556e11	0.867963	0.433982	−	0.900922i	$-0.357108\pi$
$349$	2.40556e11	0.867963	0.433982	+	0.900922i	$0.357108\pi$
$350$	−3.30944e11	−1.17882
$351$	−5.80651e11	−2.04189
$352$	−1.17897e11	−0.409318
$353$	−2.31047e11	−0.791980	−0.395990	−	0.918255i	$-0.629599\pi$
$353$	−2.31047e11	−0.791980	−0.395990	+	0.918255i	$0.629599\pi$
$354$	1.10696e11	0.374641
$355$	3.44132e11	1.15000
$356$	−2.14852e11	−0.708949
$357$	0	0
$358$	3.50861e11	1.12892
$359$	2.17507e11	0.691110	0.345555	−	0.938398i	$-0.387691\pi$
$359$	2.17507e11	0.691110	0.345555	+	0.938398i	$0.387691\pi$
$360$	−4.13059e11	−1.29614
$361$	−1.88986e11	−0.585664
$362$	3.48868e11	1.06776
$363$	4.90339e11	1.48223
$364$	3.49374e11	1.04312
$365$	−2.72568e10	−0.0803815
$366$	7.67999e11	2.23715
$367$	−1.24703e11	−0.358823	−0.179412	−	0.983774i	$-0.557419\pi$
$367$	−1.24703e11	−0.358823	−0.179412	+	0.983774i	$0.557419\pi$
$368$	3.98644e11	1.13310
$369$	1.28128e12	3.59771
$370$	4.05731e11	1.12546
$371$	−1.88230e11	−0.515829
$372$	6.44070e11	1.74377
$373$	6.71444e11	1.79606	0.898028	−	0.439938i	$-0.144999\pi$
$373$	6.71444e11	1.79606	0.898028	+	0.439938i	$0.144999\pi$
$374$	0	0
$375$	−3.24798e11	−0.848149
$376$	−1.13502e11	−0.292858
$377$	3.01676e11	0.769138
$378$	1.35182e12	3.40569
$379$	2.57132e11	0.640147	0.320073	−	0.947393i	$-0.396292\pi$
$379$	2.57132e11	0.640147	0.320073	+	0.947393i	$0.396292\pi$
$380$	−2.00266e11	−0.492697
$381$	−1.32460e12	−3.22049
$382$	4.66010e11	1.11972
$383$	−1.54303e11	−0.366420	−0.183210	−	0.983074i	$-0.558649\pi$
$383$	−1.54303e11	−0.366420	−0.183210	+	0.983074i	$0.558649\pi$
$384$	6.87309e11	1.61310
$385$	3.18207e11	0.738135
$386$	5.11586e11	1.17294
$387$	−9.50620e11	−2.15431
$388$	1.38793e11	0.310902
$389$	1.53781e11	0.340510	0.170255	−	0.985400i	$-0.445541\pi$
$389$	1.53781e11	0.340510	0.170255	+	0.985400i	$0.445541\pi$
$390$	−1.46597e12	−3.20874
$391$	0	0
$392$	3.02156e11	0.646314
$393$	5.75329e11	1.21661
$394$	3.57165e11	0.746683
$395$	2.42610e11	0.501443
$396$	−2.29126e11	−0.468215
$397$	5.53284e10	0.111787	0.0558934	−	0.998437i	$-0.482199\pi$
$397$	5.53284e10	0.111787	0.0558934	+	0.998437i	$0.482199\pi$
$398$	−5.06849e11	−1.01252
$399$	−8.56276e11	−1.69136
$400$	−3.91192e11	−0.764047
$401$	5.98775e11	1.15642	0.578208	−	0.815890i	$-0.303752\pi$
$401$	5.98775e11	1.15642	0.578208	+	0.815890i	$0.303752\pi$
$402$	−5.72400e11	−1.09316
$403$	−1.01128e12	−1.90985
$404$	1.67616e11	0.313039
$405$	−7.38358e11	−1.36370
$406$	−7.02333e11	−1.28285
$407$	−1.48763e11	−0.268732
$408$	0	0
$409$	−8.67423e11	−1.53277	−0.766384	−	0.642383i	$-0.777946\pi$
$409$	−8.67423e11	−1.53277	−0.766384	+	0.642383i	$0.777946\pi$
$410$	1.63662e12	2.86036
$411$	2.24356e11	0.387838
$412$	3.08089e11	0.526792
$413$	1.52065e11	0.257189
$414$	1.39974e12	2.34178
$415$	1.15757e12	1.91572
$416$	7.46134e11	1.22151
$417$	3.11678e11	0.504770
$418$	1.95392e11	0.313049
$419$	6.41732e11	1.01716	0.508581	−	0.861014i	$-0.330170\pi$
$419$	6.41732e11	1.01716	0.508581	+	0.861014i	$0.330170\pi$
$420$	1.28258e12	2.01124
$421$	4.57623e11	0.709967	0.354983	−	0.934873i	$-0.384487\pi$
$421$	4.57623e11	0.709967	0.354983	+	0.934873i	$0.384487\pi$
$422$	−1.00236e12	−1.53857
$423$	−7.74886e11	−1.17681
$424$	−1.14433e11	−0.171951
$425$	0	0
$426$	−1.35332e12	−1.99093
$427$	1.05501e12	1.53579
$428$	−6.52252e9	−0.00939547
$429$	5.37505e11	0.766169
$430$	−1.21426e12	−1.71278
$431$	−7.38734e10	−0.103119	−0.0515597	−	0.998670i	$-0.516419\pi$
$431$	−7.38734e10	−0.103119	−0.0515597	+	0.998670i	$0.516419\pi$
$432$	1.59791e12	2.20737
$433$	1.03868e12	1.41999	0.709995	−	0.704206i	$-0.248697\pi$
$433$	1.03868e12	1.41999	0.709995	+	0.704206i	$0.248697\pi$
$434$	2.35437e12	3.18545
$435$	1.10748e12	1.48297
$436$	7.34132e11	0.972937
$437$	−4.48576e11	−0.588396
$438$	1.07189e11	0.139160
$439$	−9.61297e11	−1.23529	−0.617643	−	0.786459i	$-0.711912\pi$
$439$	−9.61297e11	−1.23529	−0.617643	+	0.786459i	$0.711912\pi$
$440$	1.93451e11	0.246056
$441$	2.06284e12	2.59712
$442$	0	0
$443$	2.39240e11	0.295132	0.147566	−	0.989052i	$-0.452856\pi$
$443$	2.39240e11	0.295132	0.147566	+	0.989052i	$0.452856\pi$
$444$	−5.99612e11	−0.732229
$445$	1.23843e12	1.49711
$446$	−1.36316e12	−1.63133
$447$	2.77767e11	0.329077
$448$	−1.40114e11	−0.164335
$449$	5.56831e11	0.646569	0.323285	−	0.946302i	$-0.395213\pi$
$449$	5.56831e11	0.646569	0.323285	+	0.946302i	$0.395213\pi$
$450$	−1.37357e12	−1.57905
$451$	−6.00073e11	−0.682983
$452$	−3.52099e11	−0.396772
$453$	−4.62269e11	−0.515766
$454$	3.35558e11	0.370695
$455$	−2.01383e12	−2.20279
$456$	−5.20566e11	−0.563812
$457$	6.83226e11	0.732726	0.366363	−	0.930472i	$-0.380603\pi$
$457$	6.83226e11	0.732726	0.366363	+	0.930472i	$0.380603\pi$
$458$	−7.13128e11	−0.757308
$459$	0	0
$460$	6.71904e11	0.699676
$461$	−9.09123e11	−0.937494	−0.468747	−	0.883333i	$-0.655294\pi$
$461$	−9.09123e11	−0.937494	−0.468747	+	0.883333i	$0.655294\pi$
$462$	−1.25137e12	−1.27790
$463$	3.46507e11	0.350427	0.175213	−	0.984530i	$-0.443938\pi$
$463$	3.46507e11	0.350427	0.175213	+	0.984530i	$0.443938\pi$
$464$	−8.30191e11	−0.831471
$465$	−3.71250e12	−3.68237
$466$	1.86408e12	1.83117
$467$	3.54586e11	0.344982	0.172491	−	0.985011i	$-0.444818\pi$
$467$	3.54586e11	0.344982	0.172491	+	0.985011i	$0.444818\pi$
$468$	1.45007e12	1.39727
$469$	−7.86316e11	−0.750446
$470$	−9.89786e11	−0.935623
$471$	−1.67850e12	−1.57154
$472$	9.24465e10	0.0857336
$473$	4.45212e11	0.408970
$474$	−9.54078e11	−0.868123
$475$	4.40191e11	0.396753
$476$	0	0
$477$	−7.81241e11	−0.690959
$478$	−1.23101e12	−1.07854
$479$	−1.13858e12	−0.988222	−0.494111	−	0.869399i	$-0.664506\pi$
$479$	−1.13858e12	−0.988222	−0.494111	+	0.869399i	$0.664506\pi$
$480$	2.73912e12	2.35519
$481$	9.41475e11	0.801966
$482$	−2.24535e12	−1.89484
$483$	2.87286e12	2.40189
$484$	−6.19529e11	−0.513166
$485$	−8.00017e11	−0.656540
$486$	1.31590e11	0.106994
$487$	−1.19842e10	−0.00965450	−0.00482725	−	0.999988i	$-0.501537\pi$
$487$	−1.19842e10	−0.00965450	−0.00482725	+	0.999988i	$0.501537\pi$
$488$	6.41388e11	0.511955
$489$	2.90314e12	2.29603
$490$	2.63493e12	2.06484
$491$	−1.60620e11	−0.124719	−0.0623597	−	0.998054i	$-0.519863\pi$
$491$	−1.60620e11	−0.124719	−0.0623597	+	0.998054i	$0.519863\pi$
$492$	−2.41869e12	−1.86096
$493$	0	0
$494$	−1.23657e12	−0.934219
$495$	1.32071e12	0.988742
$496$	2.78297e12	2.06463
$497$	−1.85908e12	−1.36676
$498$	−4.55222e12	−3.31658
$499$	1.44413e12	1.04269	0.521345	−	0.853346i	$-0.325431\pi$
$499$	1.44413e12	1.04269	0.521345	+	0.853346i	$0.325431\pi$
$500$	4.10373e11	0.293639
$501$	−3.95826e12	−2.80695
$502$	−8.38820e11	−0.589525
$503$	−1.19095e12	−0.829539	−0.414769	−	0.909927i	$-0.636138\pi$
$503$	−1.19095e12	−0.829539	−0.414769	+	0.909927i	$0.636138\pi$
$504$	2.23144e12	1.54045
$505$	−9.66158e11	−0.661054
$506$	−6.55551e11	−0.444559
$507$	−8.14514e11	−0.547473
$508$	1.67359e12	1.11497
$509$	−2.34412e12	−1.54793	−0.773963	−	0.633231i	$-0.781728\pi$
$509$	−2.34412e12	−1.54793	−0.773963	+	0.633231i	$0.781728\pi$
$510$	0	0
$511$	1.47247e11	0.0955328
$512$	−1.08245e12	−0.696132
$513$	−1.79806e12	−1.14624
$514$	−8.64056e11	−0.546019
$515$	−1.77586e12	−1.11244
$516$	1.79449e12	1.11434
$517$	3.62909e11	0.223404
$518$	−2.19185e12	−1.33760
$519$	2.38437e12	1.44251
$520$	−1.22429e12	−0.734295
$521$	−1.55789e12	−0.926333	−0.463166	−	0.886271i	$-0.653287\pi$
$521$	−1.55789e12	−0.926333	−0.463166	+	0.886271i	$0.653287\pi$
$522$	−2.91501e12	−1.71839
$523$	5.98253e10	0.0349645	0.0174823	−	0.999847i	$-0.494435\pi$
$523$	5.98253e10	0.0349645	0.0174823	+	0.999847i	$0.494435\pi$
$524$	−7.26912e11	−0.421202
$525$	−2.81916e12	−1.61958
$526$	2.60724e12	1.48506
$527$	0	0
$528$	−1.47917e12	−0.828260
$529$	−2.96153e11	−0.164424
$530$	−9.97904e11	−0.549348
$531$	6.31139e11	0.344508
$532$	1.08188e12	0.585567
$533$	3.79768e12	2.03820
$534$	−4.87021e12	−2.59186
$535$	3.75966e10	0.0198407
$536$	−4.78035e11	−0.250160
$537$	2.98882e12	1.55101
$538$	−1.99226e12	−1.02524
$539$	−9.66107e11	−0.493033
$540$	2.69324e12	1.36302
$541$	−2.35116e12	−1.18004	−0.590018	−	0.807390i	$-0.700879\pi$
$541$	−2.35116e12	−1.18004	−0.590018	+	0.807390i	$0.700879\pi$
$542$	2.74254e12	1.36507
$543$	2.97185e12	1.46699
$544$	0	0
$545$	−4.23162e12	−2.05458
$546$	7.91951e12	3.81357
$547$	−3.16333e12	−1.51078	−0.755391	−	0.655274i	$-0.772553\pi$
$547$	−3.16333e12	−1.51078	−0.755391	+	0.655274i	$0.772553\pi$
$548$	−2.83468e11	−0.134274
$549$	4.37880e12	2.05722
$550$	6.43297e11	0.299764
$551$	9.34177e11	0.431764
$552$	1.74653e12	0.800665
$553$	−1.31063e12	−0.595961
$554$	−2.45002e12	−1.10503
$555$	3.45624e12	1.54627
$556$	−3.93796e11	−0.174757
$557$	3.53542e12	1.55630	0.778148	−	0.628081i	$-0.216159\pi$
$557$	3.53542e12	1.55630	0.778148	+	0.628081i	$0.216159\pi$
$558$	9.77172e12	4.26695
$559$	−2.81761e12	−1.22047
$560$	5.54193e12	2.38130
$561$	0	0
$562$	1.25775e12	0.531841
$563$	−1.75567e12	−0.736472	−0.368236	−	0.929732i	$-0.620038\pi$
$563$	−1.75567e12	−0.736472	−0.368236	+	0.929732i	$0.620038\pi$
$564$	1.46276e12	0.608719
$565$	2.02954e12	0.837875
$566$	2.30337e12	0.943387
$567$	3.98878e12	1.62075
$568$	−1.13021e12	−0.455609
$569$	−2.32211e9	−0.000928706 0	−0.000464353	−	1.00000i	$-0.500148\pi$
$569$	−2.32211e9	−0.000928706 0	−0.000464353		1.00000i	$0.500148\pi$
$570$	−4.53957e12	−1.80126
$571$	2.57323e12	1.01302	0.506509	−	0.862235i	$-0.330936\pi$
$571$	2.57323e12	1.01302	0.506509	+	0.862235i	$0.330936\pi$
$572$	−6.79121e11	−0.265256
$573$	3.96972e12	1.53838
$574$	−8.84139e12	−3.39952
$575$	−1.47687e12	−0.563425
$576$	−5.81539e11	−0.220129
$577$	−1.59532e12	−0.599178	−0.299589	−	0.954068i	$-0.596850\pi$
$577$	−1.59532e12	−0.599178	−0.299589	+	0.954068i	$0.596850\pi$
$578$	0	0
$579$	4.35796e12	1.61150
$580$	−1.39927e12	−0.513422
$581$	−6.25346e12	−2.27682
$582$	3.14611e12	1.13663
$583$	3.65885e11	0.131171
$584$	8.95177e10	0.0318457
$585$	−8.35835e12	−2.95066
$586$	6.35085e11	0.222481
$587$	−2.68434e12	−0.933182	−0.466591	−	0.884473i	$-0.654518\pi$
$587$	−2.68434e12	−0.933182	−0.466591	+	0.884473i	$0.654518\pi$
$588$	−3.89404e12	−1.34339
$589$	−3.13156e12	−1.07212
$590$	8.06173e11	0.273901
$591$	3.04252e12	1.02586
$592$	−2.59087e12	−0.866959
$593$	4.50719e12	1.49679	0.748393	−	0.663256i	$-0.230826\pi$
$593$	4.50719e12	1.49679	0.748393	+	0.663256i	$0.230826\pi$
$594$	−2.62769e12	−0.866035
$595$	0	0
$596$	−3.50951e11	−0.113930
$597$	−4.31761e12	−1.39110
$598$	4.14878e12	1.32668
$599$	−4.19976e12	−1.33292	−0.666459	−	0.745542i	$-0.732191\pi$
$599$	−4.19976e12	−1.33292	−0.666459	+	0.745542i	$0.732191\pi$
$600$	−1.71389e12	−0.539885
$601$	−4.96222e12	−1.55146	−0.775730	−	0.631065i	$-0.782618\pi$
$601$	−4.96222e12	−1.55146	−0.775730	+	0.631065i	$0.782618\pi$
$602$	6.55968e12	2.03563
$603$	−3.26358e12	−1.00523
$604$	5.84063e11	0.178564
$605$	3.57104e12	1.08367
$606$	3.79947e12	1.14445
$607$	−4.06493e12	−1.21536	−0.607679	−	0.794183i	$-0.707899\pi$
$607$	−4.06493e12	−1.21536	−0.607679	+	0.794183i	$0.707899\pi$
$608$	2.31050e12	0.685708
$609$	−5.98284e12	−1.76250
$610$	5.59318e12	1.63559
$611$	−2.29674e12	−0.666693
$612$	0	0
$613$	−3.12747e12	−0.894583	−0.447291	−	0.894388i	$-0.647611\pi$
$613$	−3.12747e12	−0.894583	−0.447291	+	0.894388i	$0.647611\pi$
$614$	−3.90071e12	−1.10761
$615$	1.39416e13	3.92984
$616$	−1.04507e12	−0.292436
$617$	−1.99199e12	−0.553354	−0.276677	−	0.960963i	$-0.589233\pi$
$617$	−1.99199e12	−0.553354	−0.276677	+	0.960963i	$0.589233\pi$
$618$	6.98368e12	1.92591
$619$	−5.76812e12	−1.57916	−0.789581	−	0.613647i	$-0.789702\pi$
$619$	−5.76812e12	−1.57916	−0.789581	+	0.613647i	$0.789702\pi$
$620$	4.69063e12	1.27488
$621$	6.03260e12	1.62777
$622$	7.53613e12	2.01879
$623$	−6.69029e12	−1.77930
$624$	9.36124e12	2.47174
$625$	−4.71671e12	−1.23646
$626$	5.32543e12	1.38602
$627$	1.66445e12	0.430097
$628$	2.12073e12	0.544086
$629$	0	0
$630$	1.94591e13	4.92142
$631$	−2.73184e12	−0.685999	−0.342999	−	0.939336i	$-0.611443\pi$
$631$	−2.73184e12	−0.685999	−0.342999	+	0.939336i	$0.611443\pi$
$632$	−7.96789e11	−0.198663
$633$	−8.53860e12	−2.11383
$634$	−9.03332e12	−2.22047
$635$	−9.64677e12	−2.35451
$636$	1.47476e12	0.357407
$637$	6.11419e12	1.47134
$638$	1.36521e12	0.326217
$639$	−7.71604e12	−1.83080
$640$	5.00553e12	1.17934
$641$	3.77475e12	0.883135	0.441567	−	0.897228i	$-0.354423\pi$
$641$	3.77475e12	0.883135	0.441567	+	0.897228i	$0.354423\pi$
$642$	−1.47851e11	−0.0343491
$643$	−1.26222e12	−0.291197	−0.145598	−	0.989344i	$-0.546511\pi$
$643$	−1.26222e12	−0.291197	−0.145598	+	0.989344i	$0.546511\pi$
$644$	−3.62978e12	−0.831559
$645$	−1.03437e13	−2.35319
$646$	0	0
$647$	5.94830e12	1.33451	0.667257	−	0.744827i	$-0.267468\pi$
$647$	5.94830e12	1.33451	0.667257	+	0.744827i	$0.267468\pi$
$648$	2.42495e12	0.540275
$649$	−2.95587e11	−0.0654009
$650$	−4.07123e12	−0.894573
$651$	2.00557e13	4.37647
$652$	−3.66804e12	−0.794913
$653$	1.12364e12	0.241835	0.120918	−	0.992663i	$-0.461416\pi$
$653$	1.12364e12	0.241835	0.120918	+	0.992663i	$0.461416\pi$
$654$	1.66411e13	3.55698
$655$	4.19000e12	0.889464
$656$	−1.04509e13	−2.20337
$657$	6.11144e11	0.127967
$658$	5.34705e12	1.11198
$659$	−8.58385e11	−0.177296	−0.0886478	−	0.996063i	$-0.528255\pi$
$659$	−8.58385e11	−0.177296	−0.0886478	+	0.996063i	$0.528255\pi$
$660$	−2.49311e12	−0.511439
$661$	−2.45857e12	−0.500929	−0.250465	−	0.968126i	$-0.580583\pi$
$661$	−2.45857e12	−0.500929	−0.250465	+	0.968126i	$0.580583\pi$
$662$	3.81450e11	0.0771927
$663$	0	0
$664$	−3.80174e12	−0.758973
$665$	−6.23608e12	−1.23656
$666$	−9.09721e12	−1.79174
$667$	−3.13422e12	−0.613145
$668$	5.00115e12	0.971798
$669$	−1.16121e13	−2.24127
$670$	−4.16867e12	−0.799210
$671$	−2.05076e12	−0.390538
$672$	−1.47973e13	−2.79912
$673$	−2.80053e12	−0.526225	−0.263113	−	0.964765i	$-0.584749\pi$
$673$	−2.80053e12	−0.526225	−0.263113	+	0.964765i	$0.584749\pi$
$674$	−2.56862e12	−0.479436
$675$	−5.91984e12	−1.09760
$676$	1.02911e12	0.189541
$677$	3.74996e12	0.686085	0.343042	−	0.939320i	$-0.388543\pi$
$677$	3.74996e12	0.686085	0.343042	+	0.939320i	$0.388543\pi$
$678$	−7.98127e12	−1.45057
$679$	4.32187e12	0.780293
$680$	0	0
$681$	2.85846e12	0.509297
$682$	−4.57647e12	−0.810030
$683$	4.38021e12	0.770197	0.385099	−	0.922875i	$-0.374167\pi$
$683$	4.38021e12	0.770197	0.385099	+	0.922875i	$0.374167\pi$
$684$	4.49031e12	0.784375
$685$	1.63394e12	0.283549
$686$	−3.14109e12	−0.541530
$687$	−6.07480e12	−1.04046
$688$	7.75386e12	1.31938
$689$	−2.31558e12	−0.391447
$690$	1.52305e13	2.55796
$691$	−1.91905e11	−0.0320211	−0.0160105	−	0.999872i	$-0.505097\pi$
$691$	−1.91905e11	−0.0320211	−0.0160105	+	0.999872i	$0.505097\pi$
$692$	−3.01258e12	−0.499414
$693$	−7.13475e12	−1.17511
$694$	−1.06512e13	−1.74294
$695$	2.26988e12	0.369039
$696$	−3.63722e12	−0.587528
$697$	0	0
$698$	−6.88952e12	−1.09860
$699$	1.58792e13	2.51583
$700$	3.56193e12	0.560717
$701$	4.79909e12	0.750633	0.375316	−	0.926897i	$-0.377534\pi$
$701$	4.79909e12	0.750633	0.375316	+	0.926897i	$0.377534\pi$
$702$	1.66299e13	2.58447
$703$	2.91540e12	0.450193
$704$	2.72357e11	0.0417890
$705$	−8.43152e12	−1.28545
$706$	6.61719e12	1.00243
$707$	5.21940e12	0.785658
$708$	−1.19141e12	−0.178201
$709$	7.09288e12	1.05418	0.527090	−	0.849810i	$-0.323283\pi$
$709$	7.09288e12	1.05418	0.527090	+	0.849810i	$0.323283\pi$
$710$	−9.85593e12	−1.45558
$711$	−5.43974e12	−0.798298
$712$	−4.06731e12	−0.593127
$713$	1.05066e13	1.52250
$714$	0	0
$715$	3.91454e12	0.560148
$716$	−3.77629e12	−0.536978
$717$	−1.04864e13	−1.48181
$718$	−6.22939e12	−0.874753
$719$	−8.16373e12	−1.13922	−0.569611	−	0.821914i	$-0.692906\pi$
$719$	−8.16373e12	−1.13922	−0.569611	+	0.821914i	$0.692906\pi$
$720$	2.30016e13	3.18979
$721$	9.59361e12	1.32213
$722$	5.41257e12	0.741287
$723$	−1.91271e13	−2.60332
$724$	−3.75484e12	−0.507888
$725$	3.07564e12	0.413441
$726$	−1.40433e13	−1.87609
$727$	1.27003e13	1.68619	0.843097	−	0.537762i	$-0.180730\pi$
$727$	1.27003e13	1.68619	0.843097	+	0.537762i	$0.180730\pi$
$728$	6.61391e12	0.872705
$729$	−7.05847e12	−0.925629
$730$	7.80634e11	0.101741
$731$	0	0
$732$	−8.26591e12	−1.06412
$733$	−9.65924e12	−1.23588	−0.617938	−	0.786227i	$-0.712032\pi$
$733$	−9.65924e12	−1.23588	−0.617938	+	0.786227i	$0.712032\pi$
$734$	3.57150e12	0.454170
$735$	2.24457e13	2.83688
$736$	−7.75186e12	−0.973768
$737$	1.52846e12	0.190832
$738$	−3.66959e13	−4.55369
$739$	5.87320e11	0.0724394	0.0362197	−	0.999344i	$-0.488468\pi$
$739$	5.87320e11	0.0724394	0.0362197	+	0.999344i	$0.488468\pi$
$740$	−4.36685e12	−0.535335
$741$	−1.05338e13	−1.28352
$742$	5.39090e12	0.652895
$743$	6.32905e12	0.761884	0.380942	−	0.924599i	$-0.375600\pi$
$743$	6.32905e12	0.761884	0.380942	+	0.924599i	$0.375600\pi$
$744$	1.21927e13	1.45889
$745$	2.02292e12	0.240589
$746$	−1.92302e13	−2.27331
$747$	−2.59548e13	−3.04982
$748$	0	0
$749$	−2.03105e11	−0.0235805
$750$	9.30221e12	1.07352
$751$	5.48219e12	0.628889	0.314445	−	0.949276i	$-0.398182\pi$
$751$	5.48219e12	0.628889	0.314445	+	0.949276i	$0.398182\pi$
$752$	6.32046e12	0.720723
$753$	−7.14551e12	−0.809946
$754$	−8.64000e12	−0.973515
$755$	−3.36661e12	−0.377078
$756$	−1.45495e13	−1.61994
$757$	6.94071e12	0.768197	0.384099	−	0.923292i	$-0.374512\pi$
$757$	6.94071e12	0.768197	0.384099	+	0.923292i	$0.374512\pi$
$758$	−7.36426e12	−0.810247
$759$	−5.58433e12	−0.610778
$760$	−3.79118e12	−0.412205
$761$	−1.18446e13	−1.28023	−0.640117	−	0.768277i	$-0.721114\pi$
$761$	−1.18446e13	−1.28023	−0.640117	+	0.768277i	$0.721114\pi$
$762$	3.79365e13	4.07624
$763$	2.28602e13	2.44185
$764$	−5.01562e12	−0.532605
$765$	0	0
$766$	4.41923e12	0.463786
$767$	1.87068e12	0.195173
$768$	−2.15079e13	−2.23087
$769$	−1.22311e12	−0.126123	−0.0630617	−	0.998010i	$-0.520086\pi$
$769$	−1.22311e12	−0.126123	−0.0630617	+	0.998010i	$0.520086\pi$
$770$	−9.11344e12	−0.934274
$771$	−7.36049e12	−0.750174
$772$	−5.50615e12	−0.557918
$773$	2.56478e12	0.258370	0.129185	−	0.991621i	$-0.458764\pi$
$773$	2.56478e12	0.258370	0.129185	+	0.991621i	$0.458764\pi$
$774$	2.72258e13	2.72675
$775$	−1.03102e13	−1.02662
$776$	2.62745e12	0.260110
$777$	−1.86714e13	−1.83773
$778$	−4.40429e12	−0.430991
$779$	1.17600e13	1.14416
$780$	1.57781e13	1.52627
$781$	3.61372e12	0.347556
$782$	0	0
$783$	−1.25631e13	−1.19445
$784$	−1.68258e13	−1.59057
$785$	−1.22241e13	−1.14896
$786$	−1.64774e13	−1.53988
$787$	7.44338e12	0.691646	0.345823	−	0.938300i	$-0.387600\pi$
$787$	7.44338e12	0.691646	0.345823	+	0.938300i	$0.387600\pi$
$788$	−3.84414e12	−0.355166
$789$	2.22098e13	2.04032
$790$	−6.94835e12	−0.634687
$791$	−1.09640e13	−0.995808
$792$	−4.33752e12	−0.391722
$793$	1.29786e13	1.16547
$794$	−1.58460e12	−0.141491
$795$	−8.50067e12	−0.754747
$796$	5.45517e12	0.481615
$797$	1.00963e13	0.886337	0.443168	−	0.896438i	$-0.353854\pi$
$797$	1.00963e13	0.886337	0.443168	+	0.896438i	$0.353854\pi$
$798$	2.45238e13	2.14079
$799$	0	0
$800$	7.60696e12	0.656608
$801$	−2.77678e13	−2.38339
$802$	−1.71489e13	−1.46370
$803$	−2.86222e11	−0.0242931
$804$	6.16069e12	0.519969
$805$	2.09224e13	1.75603
$806$	2.89631e13	2.41734
$807$	−1.69711e13	−1.40857
$808$	3.17309e12	0.261898
$809$	8.02349e12	0.658560	0.329280	−	0.944232i	$-0.393194\pi$
$809$	8.02349e12	0.658560	0.329280	+	0.944232i	$0.393194\pi$
$810$	2.11466e13	1.72607
$811$	−2.03065e13	−1.64832	−0.824160	−	0.566357i	$-0.808352\pi$
$811$	−2.03065e13	−1.64832	−0.824160	+	0.566357i	$0.808352\pi$
$812$	7.55915e12	0.610198
$813$	2.33624e13	1.87547
$814$	4.26057e12	0.340140
$815$	2.11430e13	1.67864
$816$	0	0
$817$	−8.72507e12	−0.685125
$818$	2.48430e13	1.94006
$819$	4.51537e13	3.50684
$820$	−1.76148e13	−1.36055
$821$	−2.20512e13	−1.69390	−0.846951	−	0.531671i	$-0.821564\pi$
$821$	−2.20512e13	−1.69390	−0.846951	+	0.531671i	$0.821564\pi$
$822$	−6.42557e12	−0.490894
$823$	−8.31984e12	−0.632143	−0.316072	−	0.948735i	$-0.602364\pi$
$823$	−8.31984e12	−0.632143	−0.316072	+	0.948735i	$0.602364\pi$
$824$	5.83236e12	0.440729
$825$	5.47995e12	0.411845
$826$	−4.35513e12	−0.325530
$827$	−6.70382e12	−0.498365	−0.249182	−	0.968457i	$-0.580162\pi$
$827$	−6.70382e12	−0.498365	−0.249182	+	0.968457i	$0.580162\pi$
$828$	−1.50653e13	−1.11388
$829$	−1.86852e13	−1.37405	−0.687025	−	0.726634i	$-0.741084\pi$
$829$	−1.86852e13	−1.37405	−0.687025	+	0.726634i	$0.741084\pi$
$830$	−3.31529e13	−2.42476
$831$	−2.08705e13	−1.51820
$832$	−1.72366e12	−0.124709
$833$	0	0
$834$	−8.92645e12	−0.638898
$835$	−2.88272e13	−2.05217
$836$	−2.10298e12	−0.148904
$837$	4.21142e13	2.96595
$838$	−1.83792e13	−1.28744
$839$	−2.31979e13	−1.61629	−0.808147	−	0.588980i	$-0.799530\pi$
$839$	−2.31979e13	−1.61629	−0.808147	+	0.588980i	$0.799530\pi$
$840$	2.42802e13	1.68266
$841$	−7.98001e12	−0.550074
$842$	−1.31063e13	−0.898620
$843$	1.07142e13	0.730694
$844$	1.07883e13	0.731831
$845$	−5.93194e12	−0.400259
$846$	2.21927e13	1.48951
$847$	−1.92915e13	−1.28793
$848$	6.37230e12	0.423170
$849$	1.96213e13	1.29612
$850$	0	0
$851$	−9.78133e12	−0.639315
$852$	1.45656e13	0.947003
$853$	6.15810e12	0.398269	0.199134	−	0.979972i	$-0.436187\pi$
$853$	6.15810e12	0.398269	0.199134	+	0.979972i	$0.436187\pi$
$854$	−3.02156e13	−1.94389
$855$	−2.58827e13	−1.65639
$856$	−1.23476e11	−0.00786052
$857$	−8.90805e12	−0.564117	−0.282058	−	0.959397i	$-0.591017\pi$
$857$	−8.90805e12	−0.564117	−0.282058	+	0.959397i	$0.591017\pi$
$858$	−1.53941e13	−0.969756
$859$	−1.06938e13	−0.670135	−0.335068	−	0.942194i	$-0.608759\pi$
$859$	−1.06938e13	−0.670135	−0.335068	+	0.942194i	$0.608759\pi$
$860$	1.30689e13	0.814699
$861$	−7.53156e13	−4.67058
$862$	2.11574e12	0.130520
$863$	−6.21448e12	−0.381379	−0.190689	−	0.981650i	$-0.561072\pi$
$863$	−6.21448e12	−0.381379	−0.190689	+	0.981650i	$0.561072\pi$
$864$	−3.10723e13	−1.89698
$865$	1.73648e13	1.05463
$866$	−2.97478e13	−1.79731
$867$	0	0
$868$	−2.53399e13	−1.51518
$869$	2.54764e12	0.151548
$870$	−3.17182e13	−1.87703
$871$	−9.67315e12	−0.569490
$872$	1.38977e13	0.813987
$873$	1.79378e13	1.04521
$874$	1.28472e13	0.744745
$875$	1.27786e13	0.736966
$876$	−1.15366e12	−0.0661928
$877$	−1.74120e13	−0.993916	−0.496958	−	0.867775i	$-0.665550\pi$
$877$	−1.74120e13	−0.993916	−0.496958	+	0.867775i	$0.665550\pi$
$878$	2.75316e13	1.56353
$879$	5.40999e12	0.305665
$880$	−1.07725e13	−0.605544
$881$	−1.85361e13	−1.03664	−0.518318	−	0.855188i	$-0.673442\pi$
$881$	−1.85361e13	−1.03664	−0.518318	+	0.855188i	$0.673442\pi$
$882$	−5.90797e13	−3.28723
$883$	−5.46626e12	−0.302599	−0.151299	−	0.988488i	$-0.548346\pi$
$883$	−5.46626e12	−0.302599	−0.151299	+	0.988488i	$0.548346\pi$
$884$	0	0
$885$	6.86741e12	0.376312
$886$	−6.85183e12	−0.373555
$887$	3.61417e13	1.96043	0.980216	−	0.197930i	$-0.0634219\pi$
$887$	3.61417e13	1.96043	0.980216	+	0.197930i	$0.0634219\pi$
$888$	−1.13511e13	−0.612604
$889$	5.21140e13	2.79832
$890$	−3.54687e13	−1.89492
$891$	−7.75348e12	−0.412142
$892$	1.46716e13	0.775954
$893$	−7.11214e12	−0.374256
$894$	−7.95525e12	−0.416519
$895$	2.17670e13	1.13395
$896$	−2.70410e13	−1.40164
$897$	3.53415e13	1.82272
$898$	−1.59476e13	−0.818376
$899$	−2.18803e13	−1.11721
$900$	1.47837e13	0.751088
$901$	0	0
$902$	1.71861e13	0.864466
$903$	5.58789e13	2.79674
$904$	−6.66549e12	−0.331951
$905$	2.16433e13	1.07252
$906$	1.32394e13	0.652816
$907$	3.39738e13	1.66691	0.833454	−	0.552589i	$-0.186360\pi$
$907$	3.39738e13	1.66691	0.833454	+	0.552589i	$0.186360\pi$
$908$	−3.61159e12	−0.176324
$909$	2.16630e13	1.05240
$910$	5.76762e13	2.78811
$911$	−2.01195e12	−0.0967797	−0.0483898	−	0.998829i	$-0.515409\pi$
$911$	−2.01195e12	−0.0967797	−0.0483898	+	0.998829i	$0.515409\pi$
$912$	2.89882e13	1.38754
$913$	1.21556e13	0.578974
$914$	−1.95676e13	−0.927427
$915$	4.76457e13	2.24713
$916$	7.67533e12	0.360220
$917$	−2.26353e13	−1.05712
$918$	0	0
$919$	1.59408e11	0.00737207	0.00368604	−	0.999993i	$-0.498827\pi$
$919$	1.59408e11	0.00737207	0.00368604	+	0.999993i	$0.498827\pi$
$920$	1.27196e13	0.585369
$921$	−3.32283e13	−1.52174
$922$	2.60373e13	1.18661
$923$	−2.28701e13	−1.03720
$924$	1.34683e13	0.607842
$925$	9.59850e12	0.431088
$926$	−9.92396e12	−0.443543
$927$	3.98180e13	1.77101
$928$	1.61435e13	0.714551
$929$	−4.18504e13	−1.84344	−0.921721	−	0.387854i	$-0.873216\pi$
$929$	−4.18504e13	−1.84344	−0.921721	+	0.387854i	$0.873216\pi$
$930$	1.06326e14	4.66086
$931$	1.89334e13	0.825950
$932$	−2.00629e13	−0.871009
$933$	6.41967e13	2.77361
$934$	−1.01554e13	−0.436651
$935$	0	0
$936$	2.74508e13	1.16900
$937$	1.52091e13	0.644576	0.322288	−	0.946642i	$-0.395548\pi$
$937$	1.52091e13	0.644576	0.322288	+	0.946642i	$0.395548\pi$
$938$	2.25201e13	0.949855
$939$	4.53648e13	1.90425
$940$	1.06530e13	0.445037
$941$	1.93636e13	0.805067	0.402534	−	0.915405i	$-0.368130\pi$
$941$	1.93636e13	0.805067	0.402534	+	0.915405i	$0.368130\pi$
$942$	4.80722e13	1.98914
$943$	−3.94555e13	−1.62482
$944$	−5.14797e12	−0.210990
$945$	8.38649e13	3.42087
$946$	−1.27509e13	−0.517642
$947$	3.99237e13	1.61308	0.806540	−	0.591179i	$-0.201337\pi$
$947$	3.99237e13	1.61308	0.806540	+	0.591179i	$0.201337\pi$
$948$	1.02687e13	0.412930
$949$	1.81141e12	0.0724969
$950$	−1.26071e13	−0.502178
$951$	−7.69506e13	−3.05070
$952$	0	0
$953$	−3.60339e13	−1.41512	−0.707559	−	0.706654i	$-0.750204\pi$
$953$	−3.60339e13	−1.41512	−0.707559	+	0.706654i	$0.750204\pi$
$954$	2.23748e13	0.874562
$955$	2.89106e13	1.12472
$956$	1.32493e13	0.513018
$957$	1.16296e13	0.448188
$958$	3.26090e13	1.25081
$959$	−8.82691e12	−0.336996
$960$	−6.32771e12	−0.240451
$961$	4.69079e13	1.77415
$962$	−2.69639e13	−1.01507
$963$	−8.42981e11	−0.0315864
$964$	2.41666e13	0.901297
$965$	3.17381e13	1.17817
$966$	−8.22787e13	−3.04012
$967$	2.93298e13	1.07867	0.539337	−	0.842090i	$-0.318675\pi$
$967$	2.93298e13	1.07867	0.539337	+	0.842090i	$0.318675\pi$
$968$	−1.17281e13	−0.429329
$969$	0	0
$970$	2.29125e13	0.830997
$971$	4.26932e13	1.54125	0.770623	−	0.637291i	$-0.219945\pi$
$971$	4.26932e13	1.54125	0.770623	+	0.637291i	$0.219945\pi$
$972$	−1.41629e12	−0.0508925
$973$	−1.22624e13	−0.438600
$974$	3.43228e11	0.0122199
$975$	−3.46809e13	−1.22905
$976$	−3.57163e13	−1.25992
$977$	−3.65451e12	−0.128323	−0.0641613	−	0.997940i	$-0.520437\pi$
$977$	−3.65451e12	−0.128323	−0.0641613	+	0.997940i	$0.520437\pi$
$978$	−8.31460e13	−2.90614
$979$	1.30047e13	0.452460
$980$	−2.83595e13	−0.982158
$981$	9.48803e13	3.27089
$982$	4.60017e12	0.157860
$983$	5.51397e13	1.88353	0.941767	−	0.336265i	$-0.109164\pi$
$983$	5.51397e13	1.88353	0.941767	+	0.336265i	$0.109164\pi$
$984$	−4.57876e13	−1.55693
$985$	2.21581e13	0.750013
$986$	0	0
$987$	4.55490e13	1.52775
$988$	1.33091e13	0.444369
$989$	2.92732e13	0.972941
$990$	−3.78250e13	−1.25147
$991$	−4.65397e13	−1.53282	−0.766412	−	0.642350i	$-0.777960\pi$
$991$	−4.65397e13	−1.53282	−0.766412	+	0.642350i	$0.777960\pi$
$992$	−5.41166e13	−1.77430
$993$	3.24939e12	0.106055
$994$	5.32440e13	1.72994
$995$	−3.14442e13	−1.01704
$996$	4.89951e13	1.57756
$997$	−4.29398e13	−1.37636	−0.688179	−	0.725541i	$-0.741590\pi$
$997$	−4.29398e13	−1.37636	−0.688179	+	0.725541i	$0.741590\pi$
$998$	−4.13600e13	−1.31975
$999$	−3.92072e13	−1.24544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.b.1.2		7
17.16	even	2		17.10.a.b.1.2	✓	7
51.50	odd	2		153.10.a.f.1.6		7
68.67	odd	2		272.10.a.g.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.2	✓	7	17.16	even	2
153.10.a.f.1.6		7	51.50	odd	2
272.10.a.g.1.1		7	68.67	odd	2
289.10.a.b.1.2		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-28.6400 q^{2} -243.971 q^{3} +308.250 q^{4} -1776.79 q^{5} +6987.32 q^{6} +9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} +O(q^{10})\)	\(q-28.6400 q^{2} -243.971 q^{3} +308.250 q^{4} -1776.79 q^{5} +6987.32 q^{6} +9598.61 q^{7} +5835.40 q^{8} +39838.7 q^{9} +50887.2 q^{10} -18658.0 q^{11} -75204.0 q^{12} +118081. q^{13} -274904. q^{14} +433484. q^{15} -324950. q^{16} -1.14098e6 q^{18} +365652. q^{19} -547695. q^{20} -2.34178e6 q^{21} +534365. q^{22} -1.22678e6 q^{23} -1.42367e6 q^{24} +1.20385e6 q^{25} -3.38183e6 q^{26} -4.91741e6 q^{27} +2.95877e6 q^{28} +2.55483e6 q^{29} -1.24150e7 q^{30} -8.56431e6 q^{31} +6.31884e6 q^{32} +4.55201e6 q^{33} -1.70547e7 q^{35} +1.22803e7 q^{36} +7.97315e6 q^{37} -1.04723e7 q^{38} -2.88083e7 q^{39} -1.03683e7 q^{40} +3.21617e7 q^{41} +6.70686e7 q^{42} -2.38617e7 q^{43} -5.75133e6 q^{44} -7.07850e7 q^{45} +3.51351e7 q^{46} -1.94506e7 q^{47} +7.92783e7 q^{48} +5.17797e7 q^{49} -3.44784e7 q^{50} +3.63984e7 q^{52} -1.96101e7 q^{53} +1.40835e8 q^{54} +3.31513e7 q^{55} +5.60118e7 q^{56} -8.92083e7 q^{57} -7.31702e7 q^{58} +1.58423e7 q^{59} +1.33622e8 q^{60} +1.09913e8 q^{61} +2.45282e8 q^{62} +3.82396e8 q^{63} -1.45973e7 q^{64} -2.09805e8 q^{65} -1.30370e8 q^{66} -8.19198e7 q^{67} +2.99299e8 q^{69} +4.88447e8 q^{70} -1.93682e8 q^{71} +2.32475e8 q^{72} +1.53405e7 q^{73} -2.28351e8 q^{74} -2.93705e8 q^{75} +1.12712e8 q^{76} -1.79091e8 q^{77} +8.25069e8 q^{78} -1.36544e8 q^{79} +5.77367e8 q^{80} +4.15558e8 q^{81} -9.21111e8 q^{82} -6.51497e8 q^{83} -7.21854e8 q^{84} +6.83399e8 q^{86} -6.23303e8 q^{87} -1.08877e8 q^{88} -6.97006e8 q^{89} +2.02728e9 q^{90} +1.13341e9 q^{91} -3.78156e8 q^{92} +2.08944e9 q^{93} +5.57064e8 q^{94} -6.49686e8 q^{95} -1.54161e9 q^{96} +4.50260e8 q^{97} -1.48297e9 q^{98} -7.43311e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - 88 q^{3} + 2389 q^{4} - 1362 q^{5} + 11720 q^{6} - 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) \) 7 * q - q^2 - 88 * q^3 + 2389 * q^4 - 1362 * q^5 + 11720 * q^6 - 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} - 88 q^{3} + 2389 q^{4} - 1362 q^{5} + 11720 q^{6} - 9388 q^{7} + 16821 q^{8} + 81419 q^{9} - 154226 q^{10} - 135536 q^{11} - 198160 q^{12} + 166122 q^{13} - 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 149027 q^{18} + 777172 q^{19} + 917162 q^{20} - 3412104 q^{21} + 1222520 q^{22} - 1357764 q^{23} + 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} + 4519064 q^{27} + 3328892 q^{28} - 967002 q^{29} - 12558992 q^{30} - 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 530736 q^{35} + 4535009 q^{36} - 18296498 q^{37} - 49363020 q^{38} - 86306872 q^{39} - 127155062 q^{40} - 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} - 96696624 q^{44} - 108916410 q^{45} + 151509484 q^{46} + 56639800 q^{47} + 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} - 156226378 q^{52} + 121813562 q^{53} + 93375344 q^{54} + 40793128 q^{55} + 196175436 q^{56} - 153612960 q^{57} + 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} + 49915846 q^{61} + 73506556 q^{62} + 2185356 q^{63} + 317922057 q^{64} + 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 379683432 q^{69} + 966315960 q^{70} - 652473940 q^{71} + 655760385 q^{72} - 306656342 q^{73} - 249173874 q^{74} - 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} - 323434416 q^{78} - 959147884 q^{79} + 692173602 q^{80} - 374486977 q^{81} - 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} - 164953236 q^{86} - 1612550856 q^{87} - 1132038848 q^{88} - 1971327114 q^{89} + 2284664662 q^{90} + 1061062864 q^{91} - 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} + 3249631512 q^{95} + 4442036640 q^{96} - 2006526254 q^{97} - 2170640009 q^{98} + 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 - 88 * q^3 + 2389 * q^4 - 1362 * q^5 + 11720 * q^6 - 9388 * q^7 + 16821 * q^8 + 81419 * q^9 - 154226 * q^10 - 135536 * q^11 - 198160 * q^12 + 166122 * q^13 - 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 149027 * q^18 + 777172 * q^19 + 917162 * q^20 - 3412104 * q^21 + 1222520 * q^22 - 1357764 * q^23 + 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 + 4519064 * q^27 + 3328892 * q^28 - 967002 * q^29 - 12558992 * q^30 - 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 530736 * q^35 + 4535009 * q^36 - 18296498 * q^37 - 49363020 * q^38 - 86306872 * q^39 - 127155062 * q^40 - 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 - 96696624 * q^44 - 108916410 * q^45 + 151509484 * q^46 + 56639800 * q^47 + 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 - 156226378 * q^52 + 121813562 * q^53 + 93375344 * q^54 + 40793128 * q^55 + 196175436 * q^56 - 153612960 * q^57 + 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 + 49915846 * q^61 + 73506556 * q^62 + 2185356 * q^63 + 317922057 * q^64 + 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 379683432 * q^69 + 966315960 * q^70 - 652473940 * q^71 + 655760385 * q^72 - 306656342 * q^73 - 249173874 * q^74 - 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 - 323434416 * q^78 - 959147884 * q^79 + 692173602 * q^80 - 374486977 * q^81 - 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 - 164953236 * q^86 - 1612550856 * q^87 - 1132038848 * q^88 - 1971327114 * q^89 + 2284664662 * q^90 + 1061062864 * q^91 - 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 + 3249631512 * q^95 + 4442036640 * q^96 - 2006526254 * q^97 - 2170640009 * q^98 + 2579159272 * q^99

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