LMFDB - Embedded newform 169.10.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,10,Mod(1,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, 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("169.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	169.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:	$87.0410563117$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1602x^{2} + 1544x + 342272 $ x^4 - x^3 - 1602x^2 + 1544x + 342272
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$16.5360$ of defining polynomial
Character	$\chi$	$=$	169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+24.5360 q^{2} +49.9972 q^{3} +90.0171 q^{4} -1814.98 q^{5} +1226.73 q^{6} +8707.31 q^{7} -10353.8 q^{8} -17183.3 q^{9} +O(q^{10})$	\(q+24.5360 q^{2} +49.9972 q^{3} +90.0171 q^{4} -1814.98 q^{5} +1226.73 q^{6} +8707.31 q^{7} -10353.8 q^{8} -17183.3 q^{9} -44532.3 q^{10} +82919.7 q^{11} +4500.61 q^{12} +213643. q^{14} -90743.8 q^{15} -300130. q^{16} +374907. q^{17} -421610. q^{18} +361501. q^{19} -163379. q^{20} +435341. q^{21} +2.03452e6 q^{22} -2.31340e6 q^{23} -517661. q^{24} +1.34101e6 q^{25} -1.84321e6 q^{27} +783807. q^{28} -649654. q^{29} -2.22649e6 q^{30} -4.32521e6 q^{31} -2.06285e6 q^{32} +4.14575e6 q^{33} +9.19873e6 q^{34} -1.58036e7 q^{35} -1.54679e6 q^{36} -1.21021e7 q^{37} +8.86981e6 q^{38} +1.87919e7 q^{40} -2.59960e6 q^{41} +1.06816e7 q^{42} +3.08318e6 q^{43} +7.46419e6 q^{44} +3.11872e7 q^{45} -5.67617e7 q^{46} -2.60298e7 q^{47} -1.50057e7 q^{48} +3.54636e7 q^{49} +3.29032e7 q^{50} +1.87443e7 q^{51} -1.01982e8 q^{53} -4.52251e7 q^{54} -1.50497e8 q^{55} -9.01536e7 q^{56} +1.80741e7 q^{57} -1.59399e7 q^{58} -1.37562e8 q^{59} -8.16850e6 q^{60} -4.29579e7 q^{61} -1.06124e8 q^{62} -1.49620e8 q^{63} +1.03052e8 q^{64} +1.01720e8 q^{66} -5.54479e7 q^{67} +3.37480e7 q^{68} -1.15664e8 q^{69} -3.87757e8 q^{70} +1.43613e8 q^{71} +1.77912e8 q^{72} -3.37147e7 q^{73} -2.96937e8 q^{74} +6.70469e7 q^{75} +3.25413e7 q^{76} +7.22007e8 q^{77} -2.66652e8 q^{79} +5.44728e8 q^{80} +2.46063e8 q^{81} -6.37839e7 q^{82} +9.89542e7 q^{83} +3.91882e7 q^{84} -6.80447e8 q^{85} +7.56490e7 q^{86} -3.24809e7 q^{87} -8.58533e8 q^{88} +5.08803e8 q^{89} +7.65211e8 q^{90} -2.08246e8 q^{92} -2.16249e8 q^{93} -6.38667e8 q^{94} -6.56116e8 q^{95} -1.03137e8 q^{96} +4.53920e8 q^{97} +8.70137e8 q^{98} -1.42483e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9}+O(q^{10}) $ 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9	\( 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 67831 q^{10} + 40140 q^{11} - 155479 q^{12} - 277653 q^{14} - 83307 q^{15} + 726609 q^{16} + 78717 q^{17} - 1691026 q^{18} - 209664 q^{19} - 870843 q^{20} - 1138431 q^{21} + 1364090 q^{22} - 4257444 q^{23} - 3561573 q^{24} - 2900157 q^{25} - 2077801 q^{27} - 4035181 q^{28} - 1647936 q^{29} - 744143 q^{30} + 11366002 q^{31} + 29458959 q^{32} + 14413222 q^{33} - 26257659 q^{34} - 13789797 q^{35} - 11587714 q^{36} - 4636891 q^{37} + 25172466 q^{38} + 22536791 q^{40} - 13859538 q^{41} + 75564923 q^{42} - 33368081 q^{43} - 66489222 q^{44} + 17423928 q^{45} - 71369332 q^{46} + 3943005 q^{47} - 620787 q^{48} + 23294923 q^{49} + 4217748 q^{50} - 19664471 q^{51} - 171019326 q^{53} + 64946915 q^{54} - 121160538 q^{55} - 281552967 q^{56} + 47829030 q^{57} - 79964734 q^{58} + 63389388 q^{59} - 37708135 q^{60} + 77050190 q^{61} - 95878740 q^{62} + 155695476 q^{63} + 768962465 q^{64} - 42396374 q^{66} + 41174072 q^{67} - 717615423 q^{68} + 546642556 q^{69} - 409056389 q^{70} - 252460989 q^{71} - 562579254 q^{72} - 594415068 q^{73} - 957058539 q^{74} + 533318748 q^{75} + 326897170 q^{76} + 561950454 q^{77} + 115998984 q^{79} + 509107233 q^{80} + 437803700 q^{81} - 875148240 q^{82} + 79577862 q^{83} - 108899441 q^{84} - 549463469 q^{85} + 589924887 q^{86} - 1087526510 q^{87} - 2327564370 q^{88} + 1152240276 q^{89} + 877550038 q^{90} - 4213481460 q^{92} - 1618266556 q^{93} + 1859909503 q^{94} - 1273705170 q^{95} - 3171454029 q^{96} - 1049098084 q^{97} - 420532254 q^{98} - 2132181050 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 67831 * q^10 + 40140 * q^11 - 155479 * q^12 - 277653 * q^14 - 83307 * q^15 + 726609 * q^16 + 78717 * q^17 - 1691026 * q^18 - 209664 * q^19 - 870843 * q^20 - 1138431 * q^21 + 1364090 * q^22 - 4257444 * q^23 - 3561573 * q^24 - 2900157 * q^25 - 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 744143 * q^30 + 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 - 26257659 * q^34 - 13789797 * q^35 - 11587714 * q^36 - 4636891 * q^37 + 25172466 * q^38 + 22536791 * q^40 - 13859538 * q^41 + 75564923 * q^42 - 33368081 * q^43 - 66489222 * q^44 + 17423928 * q^45 - 71369332 * q^46 + 3943005 * q^47 - 620787 * q^48 + 23294923 * q^49 + 4217748 * q^50 - 19664471 * q^51 - 171019326 * q^53 + 64946915 * q^54 - 121160538 * q^55 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 + 63389388 * q^59 - 37708135 * q^60 + 77050190 * q^61 - 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 - 717615423 * q^68 + 546642556 * q^69 - 409056389 * q^70 - 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 + 533318748 * q^75 + 326897170 * q^76 + 561950454 * q^77 + 115998984 * q^79 + 509107233 * q^80 + 437803700 * q^81 - 875148240 * q^82 + 79577862 * q^83 - 108899441 * q^84 - 549463469 * q^85 + 589924887 * q^86 - 1087526510 * q^87 - 2327564370 * q^88 + 1152240276 * q^89 + 877550038 * q^90 - 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 - 1273705170 * q^95 - 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 - 2132181050 * 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 $

$2$	24.5360	1.08435	0.542175	−	0.840266i	$-0.317601\pi$
$2$	24.5360	1.08435	0.542175	+	0.840266i	$0.317601\pi$
$3$	49.9972	0.356369	0.178185	−	0.983997i	$-0.442978\pi$
$3$	49.9972	0.356369	0.178185	+	0.983997i	$0.442978\pi$
$4$	90.0171	0.175815
$5$	−1814.98	−1.29869	−0.649346	−	0.760493i	$-0.724957\pi$
$5$	−1814.98	−1.29869	−0.649346	+	0.760493i	$0.724957\pi$
$6$	1226.73	0.386429
$7$	8707.31	1.37070	0.685351	−	0.728213i	$-0.259649\pi$
$7$	8707.31	1.37070	0.685351	+	0.728213i	$0.259649\pi$
$8$	−10353.8	−0.893705
$9$	−17183.3	−0.873001
$10$	−44532.3	−1.40824
$11$	82919.7	1.70762	0.853809	−	0.520587i	$-0.174287\pi$
$11$	82919.7	1.70762	0.853809	+	0.520587i	$0.174287\pi$
$12$	4500.61	0.0626550
$13$	0	0
$13$	0	0
$14$	213643.	1.48632
$15$	−90743.8	−0.462814
$16$	−300130.	−1.14490
$17$	374907.	1.08869	0.544344	−	0.838862i	$-0.316779\pi$
$17$	374907.	1.08869	0.544344	+	0.838862i	$0.316779\pi$
$18$	−421610.	−0.946638
$19$	361501.	0.636383	0.318191	−	0.948026i	$-0.396925\pi$
$19$	361501.	0.636383	0.318191	+	0.948026i	$0.396925\pi$
$20$	−163379.	−0.228329
$21$	435341.	0.488476
$22$	2.03452e6	1.85165
$23$	−2.31340e6	−1.72376	−0.861878	−	0.507116i	$-0.830712\pi$
$23$	−2.31340e6	−1.72376	−0.861878	+	0.507116i	$0.830712\pi$
$24$	−517661.	−0.318489
$25$	1.34101e6	0.686599
$26$	0	0
$27$	−1.84321e6	−0.667480
$28$	783807.	0.240989
$29$	−649654.	−0.170565	−0.0852827	−	0.996357i	$-0.527179\pi$
$29$	−649654.	−0.170565	−0.0852827	+	0.996357i	$0.527179\pi$
$30$	−2.22649e6	−0.501852
$31$	−4.32521e6	−0.841162	−0.420581	−	0.907255i	$-0.638174\pi$
$31$	−4.32521e6	−0.841162	−0.420581	+	0.907255i	$0.638174\pi$
$32$	−2.06285e6	−0.347771
$33$	4.14575e6	0.608542
$34$	9.19873e6	1.18052
$35$	−1.58036e7	−1.78012
$36$	−1.54679e6	−0.153486
$37$	−1.21021e7	−1.06158	−0.530790	−	0.847503i	$-0.678105\pi$
$37$	−1.21021e7	−1.06158	−0.530790	+	0.847503i	$0.678105\pi$
$38$	8.86981e6	0.690062
$39$	0	0
$40$	1.87919e7	1.16065
$41$	−2.59960e6	−0.143674	−0.0718372	−	0.997416i	$-0.522886\pi$
$41$	−2.59960e6	−0.143674	−0.0718372	+	0.997416i	$0.522886\pi$
$42$	1.06816e7	0.529679
$43$	3.08318e6	0.137528	0.0687640	−	0.997633i	$-0.478094\pi$
$43$	3.08318e6	0.137528	0.0687640	+	0.997633i	$0.478094\pi$
$44$	7.46419e6	0.300224
$45$	3.11872e7	1.13376
$46$	−5.67617e7	−1.86915
$47$	−2.60298e7	−0.778090	−0.389045	−	0.921219i	$-0.627195\pi$
$47$	−2.60298e7	−0.778090	−0.389045	+	0.921219i	$0.627195\pi$
$48$	−1.50057e7	−0.408009
$49$	3.54636e7	0.878822
$50$	3.29032e7	0.744513
$51$	1.87443e7	0.387975
$52$	0	0
$53$	−1.01982e8	−1.77535	−0.887673	−	0.460475i	$-0.847679\pi$
$53$	−1.01982e8	−1.77535	−0.887673	+	0.460475i	$0.847679\pi$
$54$	−4.52251e7	−0.723782
$55$	−1.50497e8	−2.21767
$56$	−9.01536e7	−1.22500
$57$	1.80741e7	0.226787
$58$	−1.59399e7	−0.184953
$59$	−1.37562e8	−1.47797	−0.738985	−	0.673722i	$-0.764695\pi$
$59$	−1.37562e8	−1.47797	−0.738985	+	0.673722i	$0.764695\pi$
$60$	−8.16850e6	−0.0813695
$61$	−4.29579e7	−0.397245	−0.198623	−	0.980076i	$-0.563647\pi$
$61$	−4.29579e7	−0.397245	−0.198623	+	0.980076i	$0.563647\pi$
$62$	−1.06124e8	−0.912114
$63$	−1.49620e8	−1.19662
$64$	1.03052e8	0.767798
$65$	0	0
$66$	1.01720e8	0.659873
$67$	−5.54479e7	−0.336162	−0.168081	−	0.985773i	$-0.553757\pi$
$67$	−5.54479e7	−0.336162	−0.168081	+	0.985773i	$0.553757\pi$
$68$	3.37480e7	0.191407
$69$	−1.15664e8	−0.614294
$70$	−3.87757e8	−1.93027
$71$	1.43613e8	0.670706	0.335353	−	0.942093i	$-0.391144\pi$
$71$	1.43613e8	0.670706	0.335353	+	0.942093i	$0.391144\pi$
$72$	1.77912e8	0.780205
$73$	−3.37147e7	−0.138952	−0.0694762	−	0.997584i	$-0.522133\pi$
$73$	−3.37147e7	−0.138952	−0.0694762	+	0.997584i	$0.522133\pi$
$74$	−2.96937e8	−1.15112
$75$	6.70469e7	0.244683
$76$	3.25413e7	0.111886
$77$	7.22007e8	2.34063
$78$	0	0
$79$	−2.66652e8	−0.770236	−0.385118	−	0.922867i	$-0.625839\pi$
$79$	−2.66652e8	−0.770236	−0.385118	+	0.922867i	$0.625839\pi$
$80$	5.44728e8	1.48688
$81$	2.46063e8	0.635132
$82$	−6.37839e7	−0.155793
$83$	9.89542e7	0.228867	0.114433	−	0.993431i	$-0.463495\pi$
$83$	9.89542e7	0.228867	0.114433	+	0.993431i	$0.463495\pi$
$84$	3.91882e7	0.0858812
$85$	−6.80447e8	−1.41387
$86$	7.56490e7	0.149128
$87$	−3.24809e7	−0.0607843
$88$	−8.58533e8	−1.52611
$89$	5.08803e8	0.859597	0.429798	−	0.902925i	$-0.358585\pi$
$89$	5.08803e8	0.859597	0.429798	+	0.902925i	$0.358585\pi$
$90$	7.65211e8	1.22939
$91$	0	0
$92$	−2.08246e8	−0.303062
$93$	−2.16249e8	−0.299764
$94$	−6.38667e8	−0.843722
$95$	−6.56116e8	−0.826465
$96$	−1.03137e8	−0.123935
$97$	4.53920e8	0.520603	0.260301	−	0.965527i	$-0.416178\pi$
$97$	4.53920e8	0.520603	0.260301	+	0.965527i	$0.416178\pi$
$98$	8.70137e8	0.952950
$99$	−1.42483e9	−1.49075
$100$	1.20714e8	0.120714
$101$	6.44663e8	0.616434	0.308217	−	0.951316i	$-0.400268\pi$
$101$	6.44663e8	0.616434	0.308217	+	0.951316i	$0.400268\pi$
$102$	4.59911e8	0.420700
$103$	−1.14825e9	−1.00524	−0.502620	−	0.864507i	$-0.667631\pi$
$103$	−1.14825e9	−1.00524	−0.502620	+	0.864507i	$0.667631\pi$
$104$	0	0
$105$	−7.90134e8	−0.634379
$106$	−2.50224e9	−1.92510
$107$	5.95299e8	0.439044	0.219522	−	0.975607i	$-0.429550\pi$
$107$	5.95299e8	0.439044	0.219522	+	0.975607i	$0.429550\pi$
$108$	−1.65921e8	−0.117353
$109$	−1.00898e9	−0.684645	−0.342322	−	0.939583i	$-0.611213\pi$
$109$	−1.00898e9	−0.684645	−0.342322	+	0.939583i	$0.611213\pi$
$110$	−3.69261e9	−2.40473
$111$	−6.05071e8	−0.378315
$112$	−2.61332e9	−1.56932
$113$	−1.59931e9	−0.922739	−0.461370	−	0.887208i	$-0.652642\pi$
$113$	−1.59931e9	−0.922739	−0.461370	+	0.887208i	$0.652642\pi$
$114$	4.43466e8	0.245917
$115$	4.19877e9	2.23863
$116$	−5.84800e7	−0.0299879
$117$	0	0
$118$	−3.37524e9	−1.60264
$119$	3.26443e9	1.49226
$120$	9.39542e8	0.413619
$121$	4.51772e9	1.91596
$122$	−1.05402e9	−0.430753
$123$	−1.29973e8	−0.0512011
$124$	−3.89343e8	−0.147889
$125$	1.11097e9	0.407011
$126$	−3.67108e9	−1.29756
$127$	−1.58816e9	−0.541723	−0.270861	−	0.962618i	$-0.587308\pi$
$127$	−1.58816e9	−0.541723	−0.270861	+	0.962618i	$0.587308\pi$
$128$	3.58467e9	1.18033
$129$	1.54151e8	0.0490107
$130$	0	0
$131$	−3.54703e9	−1.05231	−0.526156	−	0.850388i	$-0.676367\pi$
$131$	−3.54703e9	−1.05231	−0.526156	+	0.850388i	$0.676367\pi$
$132$	3.73189e8	0.106991
$133$	3.14770e9	0.872291
$134$	−1.36047e9	−0.364517
$135$	3.34539e9	0.866850
$136$	−3.88170e9	−0.972965
$137$	3.79917e9	0.921395	0.460697	−	0.887557i	$-0.347599\pi$
$137$	3.79917e9	0.921395	0.460697	+	0.887557i	$0.347599\pi$
$138$	−2.83793e9	−0.666109
$139$	3.81526e9	0.866878	0.433439	−	0.901183i	$-0.357300\pi$
$139$	3.81526e9	0.866878	0.433439	+	0.901183i	$0.357300\pi$
$140$	−1.42259e9	−0.312971
$141$	−1.30142e9	−0.277287
$142$	3.52370e9	0.727280
$143$	0	0
$144$	5.15721e9	0.999502
$145$	1.17911e9	0.221512
$146$	−8.27225e8	−0.150673
$147$	1.77308e9	0.313185
$148$	−1.08940e9	−0.186641
$149$	−1.16149e10	−1.93054	−0.965269	−	0.261258i	$-0.915863\pi$
$149$	−1.16149e10	−1.93054	−0.965269	+	0.261258i	$0.915863\pi$
$150$	1.64507e9	0.265322
$151$	−3.19196e9	−0.499645	−0.249822	−	0.968292i	$-0.580372\pi$
$151$	−3.19196e9	−0.499645	−0.249822	+	0.968292i	$0.580372\pi$
$152$	−3.74291e9	−0.568739
$153$	−6.44213e9	−0.950425
$154$	1.77152e10	2.53806
$155$	7.85016e9	1.09241
$156$	0	0
$157$	−5.05861e9	−0.664481	−0.332240	−	0.943195i	$-0.607805\pi$
$157$	−5.05861e9	−0.664481	−0.332240	+	0.943195i	$0.607805\pi$
$158$	−6.54260e9	−0.835205
$159$	−5.09883e9	−0.632679
$160$	3.74403e9	0.451647
$161$	−2.01435e10	−2.36275
$162$	6.03741e9	0.688705
$163$	7.83438e9	0.869282	0.434641	−	0.900604i	$-0.356875\pi$
$163$	7.83438e9	0.869282	0.434641	+	0.900604i	$0.356875\pi$
$164$	−2.34009e8	−0.0252601
$165$	−7.52444e9	−0.790308
$166$	2.42794e9	0.248172
$167$	1.44048e8	0.0143312	0.00716559	−	0.999974i	$-0.497719\pi$
$167$	1.44048e8	0.0143312	0.00716559	+	0.999974i	$0.497719\pi$
$168$	−4.50743e9	−0.436553
$169$	0	0
$170$	−1.66955e10	−1.53313
$171$	−6.21178e9	−0.555563
$172$	2.77539e8	0.0241794
$173$	−1.36123e10	−1.15538	−0.577689	−	0.816257i	$-0.696045\pi$
$173$	−1.36123e10	−1.15538	−0.577689	+	0.816257i	$0.696045\pi$
$174$	−7.96952e8	−0.0659114
$175$	1.16766e10	0.941122
$176$	−2.48867e10	−1.95506
$177$	−6.87774e9	−0.526703
$178$	1.24840e10	0.932104
$179$	4.98195e8	0.0362711	0.0181355	−	0.999836i	$-0.494227\pi$
$179$	4.98195e8	0.0362711	0.0181355	+	0.999836i	$0.494227\pi$
$180$	2.80739e9	0.199331
$181$	2.86758e9	0.198592	0.0992961	−	0.995058i	$-0.468341\pi$
$181$	2.86758e9	0.198592	0.0992961	+	0.995058i	$0.468341\pi$
$182$	0	0
$183$	−2.14777e9	−0.141566
$184$	2.39525e10	1.54053
$185$	2.19650e10	1.37866
$186$	−5.30588e9	−0.325049
$187$	3.10871e10	1.85906
$188$	−2.34312e9	−0.136800
$189$	−1.60494e10	−0.914916
$190$	−1.60985e10	−0.896177
$191$	−2.83331e10	−1.54044	−0.770218	−	0.637781i	$-0.779852\pi$
$191$	−2.83331e10	−1.54044	−0.770218	+	0.637781i	$0.779852\pi$
$192$	5.15232e9	0.273620
$193$	−2.44273e10	−1.26726	−0.633632	−	0.773634i	$-0.718437\pi$
$193$	−2.44273e10	−1.26726	−0.633632	+	0.773634i	$0.718437\pi$
$194$	1.11374e10	0.564516
$195$	0	0
$196$	3.19233e9	0.154510
$197$	−1.37323e10	−0.649601	−0.324800	−	0.945783i	$-0.605297\pi$
$197$	−1.37323e10	−0.649601	−0.324800	+	0.945783i	$0.605297\pi$
$198$	−3.49597e10	−1.61650
$199$	−8.56614e9	−0.387210	−0.193605	−	0.981080i	$-0.562018\pi$
$199$	−8.56614e9	−0.387210	−0.193605	+	0.981080i	$0.562018\pi$
$200$	−1.38846e10	−0.613617
$201$	−2.77224e9	−0.119798
$202$	1.58175e10	0.668430
$203$	−5.65673e9	−0.233794
$204$	1.68731e9	0.0682117
$205$	4.71821e9	0.186589
$206$	−2.81736e10	−1.09003
$207$	3.97518e10	1.50484
$208$	0	0
$209$	2.99756e10	1.08670
$210$	−1.93868e10	−0.687889
$211$	2.70272e9	0.0938706	0.0469353	−	0.998898i	$-0.485055\pi$
$211$	2.70272e9	0.0938706	0.0469353	+	0.998898i	$0.485055\pi$
$212$	−9.18015e9	−0.312132
$213$	7.18027e9	0.239019
$214$	1.46063e10	0.476078
$215$	−5.59590e9	−0.178606
$216$	1.90842e10	0.596530
$217$	−3.76610e10	−1.15298
$218$	−2.47565e10	−0.742394
$219$	−1.68564e9	−0.0495184
$220$	−1.35473e10	−0.389899
$221$	0	0
$222$	−1.48460e10	−0.410225
$223$	3.57969e10	0.969333	0.484667	−	0.874699i	$-0.338941\pi$
$223$	3.57969e10	0.969333	0.484667	+	0.874699i	$0.338941\pi$
$224$	−1.79619e10	−0.476690
$225$	−2.30430e10	−0.599401
$226$	−3.92407e10	−1.00057
$227$	7.55373e10	1.88819	0.944094	−	0.329675i	$-0.106939\pi$
$227$	7.55373e10	1.88819	0.944094	+	0.329675i	$0.106939\pi$
$228$	1.62698e9	0.0398726
$229$	5.69066e10	1.36742	0.683711	−	0.729753i	$-0.260365\pi$
$229$	5.69066e10	1.36742	0.683711	+	0.729753i	$0.260365\pi$
$230$	1.03021e11	2.42745
$231$	3.60984e10	0.834130
$232$	6.72637e9	0.152435
$233$	−4.68000e10	−1.04026	−0.520132	−	0.854086i	$-0.674117\pi$
$233$	−4.68000e10	−1.04026	−0.520132	+	0.854086i	$0.674117\pi$
$234$	0	0
$235$	4.72434e10	1.01050
$236$	−1.23830e10	−0.259849
$237$	−1.33319e10	−0.274488
$238$	8.00961e10	1.61814
$239$	8.79993e9	0.174457	0.0872285	−	0.996188i	$-0.472199\pi$
$239$	8.79993e9	0.174457	0.0872285	+	0.996188i	$0.472199\pi$
$240$	2.72349e10	0.529877
$241$	1.76057e10	0.336183	0.168092	−	0.985771i	$-0.446240\pi$
$241$	1.76057e10	0.336183	0.168092	+	0.985771i	$0.446240\pi$
$242$	1.10847e11	2.07757
$243$	4.85824e10	0.893821
$244$	−3.86695e9	−0.0698415
$245$	−6.43656e10	−1.14132
$246$	−3.18902e9	−0.0555200
$247$	0	0
$248$	4.47823e10	0.751751
$249$	4.94743e9	0.0815611
$250$	2.72588e10	0.441343
$251$	−1.77113e10	−0.281655	−0.140828	−	0.990034i	$-0.544976\pi$
$251$	−1.77113e10	−0.281655	−0.140828	+	0.990034i	$0.544976\pi$
$252$	−1.34684e10	−0.210384
$253$	−1.91826e11	−2.94351
$254$	−3.89671e10	−0.587417
$255$	−3.40204e10	−0.503859
$256$	3.51910e10	0.512096
$257$	−6.26733e10	−0.896156	−0.448078	−	0.893994i	$-0.647891\pi$
$257$	−6.26733e10	−0.896156	−0.448078	+	0.893994i	$0.647891\pi$
$258$	3.78224e9	0.0531448
$259$	−1.05377e11	−1.45511
$260$	0	0
$261$	1.11632e10	0.148904
$262$	−8.70301e10	−1.14107
$263$	4.49501e10	0.579335	0.289667	−	0.957127i	$-0.406455\pi$
$263$	4.49501e10	0.579335	0.289667	+	0.957127i	$0.406455\pi$
$264$	−4.29243e10	−0.543857
$265$	1.85095e11	2.30563
$266$	7.72322e10	0.945869
$267$	2.54388e10	0.306334
$268$	−4.99126e9	−0.0591023
$269$	−8.65536e10	−1.00786	−0.503930	−	0.863745i	$-0.668113\pi$
$269$	−8.65536e10	−1.00786	−0.503930	+	0.863745i	$0.668113\pi$
$270$	8.20825e10	0.939969
$271$	−8.36056e10	−0.941615	−0.470808	−	0.882236i	$-0.656037\pi$
$271$	−8.36056e10	−0.941615	−0.470808	+	0.882236i	$0.656037\pi$
$272$	−1.12521e11	−1.24644
$273$	0	0
$274$	9.32165e10	0.999114
$275$	1.11196e11	1.17245
$276$	−1.04117e10	−0.108002
$277$	1.73137e11	1.76698	0.883489	−	0.468452i	$-0.155188\pi$
$277$	1.73137e11	1.76698	0.883489	+	0.468452i	$0.155188\pi$
$278$	9.36114e10	0.939999
$279$	7.43213e10	0.734335
$280$	1.63627e11	1.59090
$281$	−7.57598e10	−0.724871	−0.362435	−	0.932009i	$-0.618055\pi$
$281$	−7.57598e10	−0.724871	−0.362435	+	0.932009i	$0.618055\pi$
$282$	−3.19316e10	−0.300676
$283$	1.68901e11	1.56528	0.782642	−	0.622472i	$-0.213872\pi$
$283$	1.68901e11	1.56528	0.782642	+	0.622472i	$0.213872\pi$
$284$	1.29277e10	0.117920
$285$	−3.28040e10	−0.294527
$286$	0	0
$287$	−2.26355e10	−0.196935
$288$	3.54466e10	0.303605
$289$	2.19672e10	0.185240
$290$	2.89306e10	0.240196
$291$	2.26947e10	0.185527
$292$	−3.03490e9	−0.0244299
$293$	1.18842e11	0.942030	0.471015	−	0.882125i	$-0.343888\pi$
$293$	1.18842e11	0.942030	0.471015	+	0.882125i	$0.343888\pi$
$294$	4.35044e10	0.339602
$295$	2.49672e11	1.91943
$296$	1.25302e11	0.948740
$297$	−1.52839e11	−1.13980
$298$	−2.84984e11	−2.09338
$299$	0	0
$300$	6.03537e9	0.0430188
$301$	2.68462e10	0.188510
$302$	−7.83181e10	−0.541790
$303$	3.22313e10	0.219678
$304$	−1.08497e11	−0.728597
$305$	7.79675e10	0.515899
$306$	−1.58064e11	−1.03059
$307$	1.99530e11	1.28199	0.640997	−	0.767543i	$-0.278521\pi$
$307$	1.99530e11	1.28199	0.640997	+	0.767543i	$0.278521\pi$
$308$	6.49930e10	0.411518
$309$	−5.74095e10	−0.358237
$310$	1.92612e11	1.18455
$311$	1.90145e11	1.15256	0.576281	−	0.817252i	$-0.304503\pi$
$311$	1.90145e11	1.15256	0.576281	+	0.817252i	$0.304503\pi$
$312$	0	0
$313$	−3.39674e10	−0.200038	−0.100019	−	0.994986i	$-0.531890\pi$
$313$	−3.39674e10	−0.200038	−0.100019	+	0.994986i	$0.531890\pi$
$314$	−1.24118e11	−0.720530
$315$	2.71557e11	1.55404
$316$	−2.40033e10	−0.135419
$317$	8.53565e9	0.0474756	0.0237378	−	0.999718i	$-0.492443\pi$
$317$	8.53565e9	0.0474756	0.0237378	+	0.999718i	$0.492443\pi$
$318$	−1.25105e11	−0.686045
$319$	−5.38691e10	−0.291260
$320$	−1.87037e11	−0.997133
$321$	2.97633e10	0.156462
$322$	−4.94242e11	−2.56205
$323$	1.35529e11	0.692822
$324$	2.21499e10	0.111665
$325$	0	0
$326$	1.92225e11	0.942606
$327$	−5.04464e10	−0.243986
$328$	2.69157e10	0.128403
$329$	−2.26649e11	−1.06653
$330$	−1.84620e11	−0.856971
$331$	−5.09528e10	−0.233315	−0.116657	−	0.993172i	$-0.537218\pi$
$331$	−5.09528e10	−0.233315	−0.116657	+	0.993172i	$0.537218\pi$
$332$	8.90757e9	0.0402381
$333$	2.07954e11	0.926760
$334$	3.53436e9	0.0155400
$335$	1.00637e11	0.436571
$336$	−1.30659e11	−0.559258
$337$	2.31891e11	0.979375	0.489688	−	0.871898i	$-0.337111\pi$
$337$	2.31891e11	0.979375	0.489688	+	0.871898i	$0.337111\pi$
$338$	0	0
$339$	−7.99609e10	−0.328836
$340$	−6.12519e10	−0.248579
$341$	−3.58645e11	−1.43638
$342$	−1.52412e11	−0.602425
$343$	−4.25786e10	−0.166099
$344$	−3.19226e10	−0.122909
$345$	2.09927e11	0.797778
$346$	−3.33992e11	−1.25283
$347$	−3.64138e10	−0.134829	−0.0674146	−	0.997725i	$-0.521475\pi$
$347$	−3.64138e10	−0.134829	−0.0674146	+	0.997725i	$0.521475\pi$
$348$	−2.92384e9	−0.0106868
$349$	−9.86839e10	−0.356067	−0.178034	−	0.984024i	$-0.556974\pi$
$349$	−9.86839e10	−0.356067	−0.178034	+	0.984024i	$0.556974\pi$
$350$	2.86498e11	1.02051
$351$	0	0
$352$	−1.71051e11	−0.593860
$353$	3.90458e11	1.33841	0.669204	−	0.743078i	$-0.266635\pi$
$353$	3.90458e11	1.33841	0.669204	+	0.743078i	$0.266635\pi$
$354$	−1.68752e11	−0.571131
$355$	−2.60655e11	−0.871040
$356$	4.58010e10	0.151130
$357$	1.63212e11	0.531797
$358$	1.22237e10	0.0393305
$359$	3.86316e11	1.22749	0.613744	−	0.789505i	$-0.289663\pi$
$359$	3.86316e11	1.22749	0.613744	+	0.789505i	$0.289663\pi$
$360$	−3.22906e11	−1.01325
$361$	−1.92005e11	−0.595017
$362$	7.03591e10	0.215343
$363$	2.25874e11	0.682788
$364$	0	0
$365$	6.11914e10	0.180456
$366$	−5.26979e10	−0.153507
$367$	1.48155e11	0.426305	0.213152	−	0.977019i	$-0.431627\pi$
$367$	1.48155e11	0.426305	0.213152	+	0.977019i	$0.431627\pi$
$368$	6.94320e11	1.97353
$369$	4.46697e10	0.125428
$370$	5.38934e11	1.49495
$371$	−8.87991e11	−2.43347
$372$	−1.94661e10	−0.0527030
$373$	−6.15338e11	−1.64598	−0.822989	−	0.568057i	$-0.807695\pi$
$373$	−6.15338e11	−1.64598	−0.822989	+	0.568057i	$0.807695\pi$
$374$	7.62755e11	2.01587
$375$	5.55453e10	0.145046
$376$	2.69507e11	0.695383
$377$	0	0
$378$	−3.93789e11	−0.992089
$379$	−2.48822e10	−0.0619459	−0.0309729	−	0.999520i	$-0.509861\pi$
$379$	−2.48822e10	−0.0619459	−0.0309729	+	0.999520i	$0.509861\pi$
$380$	−5.90617e10	−0.145305
$381$	−7.94035e10	−0.193053
$382$	−6.95181e11	−1.67037
$383$	−4.82478e11	−1.14573	−0.572866	−	0.819649i	$-0.694168\pi$
$383$	−4.82478e11	−1.14573	−0.572866	+	0.819649i	$0.694168\pi$
$384$	1.79224e11	0.420634
$385$	−1.31043e12	−3.03976
$386$	−5.99349e11	−1.37416
$387$	−5.29792e10	−0.120062
$388$	4.08606e10	0.0915297
$389$	3.80215e11	0.841890	0.420945	−	0.907086i	$-0.361698\pi$
$389$	3.80215e11	0.841890	0.420945	+	0.907086i	$0.361698\pi$
$390$	0	0
$391$	−8.67310e11	−1.87663
$392$	−3.67183e11	−0.785408
$393$	−1.77342e11	−0.375012
$394$	−3.36937e11	−0.704394
$395$	4.83968e11	1.00030
$396$	−1.28259e11	−0.262096
$397$	−7.91759e11	−1.59969	−0.799845	−	0.600207i	$-0.795085\pi$
$397$	−7.91759e11	−1.59969	−0.799845	+	0.600207i	$0.795085\pi$
$398$	−2.10179e11	−0.419871
$399$	1.57376e11	0.310858
$400$	−4.02478e11	−0.786090
$401$	3.06132e11	0.591234	0.295617	−	0.955307i	$-0.404475\pi$
$401$	3.06132e11	0.591234	0.295617	+	0.955307i	$0.404475\pi$
$402$	−6.80199e10	−0.129903
$403$	0	0
$404$	5.80307e10	0.108378
$405$	−4.46598e11	−0.824840
$406$	−1.38794e11	−0.253515
$407$	−1.00350e12	−1.81277
$408$	−1.94074e11	−0.346735
$409$	−9.04916e11	−1.59902	−0.799509	−	0.600654i	$-0.794907\pi$
$409$	−9.04916e11	−1.59902	−0.799509	+	0.600654i	$0.794907\pi$
$410$	1.15766e11	0.202327
$411$	1.89948e11	0.328357
$412$	−1.03362e11	−0.176736
$413$	−1.19780e12	−2.02586
$414$	9.75352e11	1.63177
$415$	−1.79599e11	−0.297227
$416$	0	0
$417$	1.90753e11	0.308929
$418$	7.35482e11	1.17836
$419$	3.36210e11	0.532903	0.266451	−	0.963848i	$-0.414149\pi$
$419$	3.36210e11	0.532903	0.266451	+	0.963848i	$0.414149\pi$
$420$	−7.11256e10	−0.111533
$421$	1.87100e11	0.290271	0.145135	−	0.989412i	$-0.453638\pi$
$421$	1.87100e11	0.290271	0.145135	+	0.989412i	$0.453638\pi$
$422$	6.63140e10	0.101789
$423$	4.47276e11	0.679273
$424$	1.05590e12	1.58664
$425$	5.02755e11	0.747491
$426$	1.76175e11	0.259180
$427$	−3.74048e11	−0.544504
$428$	5.35872e10	0.0771905
$429$	0	0
$430$	−1.37301e11	−0.193672
$431$	−9.60500e11	−1.34076	−0.670378	−	0.742020i	$-0.733868\pi$
$431$	−9.60500e11	−1.34076	−0.670378	+	0.742020i	$0.733868\pi$
$432$	5.53203e11	0.764200
$433$	1.14812e12	1.56961	0.784806	−	0.619741i	$-0.212762\pi$
$433$	1.14812e12	1.56961	0.784806	+	0.619741i	$0.212762\pi$
$434$	−9.24051e11	−1.25024
$435$	5.89520e10	0.0789400
$436$	−9.08259e10	−0.120371
$437$	−8.36297e11	−1.09697
$438$	−4.13590e10	−0.0536953
$439$	5.44277e11	0.699407	0.349703	−	0.936860i	$-0.386282\pi$
$439$	5.44277e11	0.699407	0.349703	+	0.936860i	$0.386282\pi$
$440$	1.55822e12	1.98194
$441$	−6.09381e11	−0.767212
$442$	0	0
$443$	−1.12065e11	−0.138247	−0.0691233	−	0.997608i	$-0.522020\pi$
$443$	−1.12065e11	−0.138247	−0.0691233	+	0.997608i	$0.522020\pi$
$444$	−5.44668e10	−0.0665133
$445$	−9.23466e11	−1.11635
$446$	8.78313e11	1.05110
$447$	−5.80714e11	−0.687984
$448$	8.97307e11	1.05242
$449$	1.11883e12	1.29913	0.649567	−	0.760304i	$-0.274950\pi$
$449$	1.11883e12	1.29913	0.649567	+	0.760304i	$0.274950\pi$
$450$	−5.65384e11	−0.649961
$451$	−2.15558e11	−0.245341
$452$	−1.43965e11	−0.162231
$453$	−1.59589e11	−0.178058
$454$	1.85339e12	2.04746
$455$	0	0
$456$	−1.87135e11	−0.202681
$457$	1.38914e12	1.48978	0.744890	−	0.667188i	$-0.232502\pi$
$457$	1.38914e12	1.48978	0.744890	+	0.667188i	$0.232502\pi$
$458$	1.39626e12	1.48276
$459$	−6.91032e11	−0.726677
$460$	3.77961e11	0.393583
$461$	−1.06041e12	−1.09350	−0.546752	−	0.837294i	$-0.684136\pi$
$461$	−1.06041e12	−1.09350	−0.546752	+	0.837294i	$0.684136\pi$
$462$	8.85711e11	0.904488
$463$	−2.81576e11	−0.284762	−0.142381	−	0.989812i	$-0.545476\pi$
$463$	−2.81576e11	−0.284762	−0.142381	+	0.989812i	$0.545476\pi$
$464$	1.94980e11	0.195281
$465$	3.92486e11	0.389301
$466$	−1.14829e12	−1.12801
$467$	−9.91125e11	−0.964278	−0.482139	−	0.876095i	$-0.660140\pi$
$467$	−9.91125e11	−0.964278	−0.482139	+	0.876095i	$0.660140\pi$
$468$	0	0
$469$	−4.82802e11	−0.460778
$470$	1.15917e12	1.09573
$471$	−2.52916e11	−0.236801
$472$	1.42429e12	1.32087
$473$	2.55656e11	0.234845
$474$	−3.27112e11	−0.297641
$475$	4.84778e11	0.436940
$476$	2.93855e11	0.262362
$477$	1.75239e12	1.54988
$478$	2.15915e11	0.189173
$479$	1.38074e12	1.19841	0.599203	−	0.800597i	$-0.295484\pi$
$479$	1.38074e12	1.19841	0.599203	+	0.800597i	$0.295484\pi$
$480$	1.87191e11	0.160953
$481$	0	0
$482$	4.31974e11	0.364541
$483$	−1.00712e12	−0.842013
$484$	4.06673e11	0.336853
$485$	−8.23854e11	−0.676102
$486$	1.19202e12	0.969215
$487$	−9.65212e11	−0.777575	−0.388788	−	0.921327i	$-0.627106\pi$
$487$	−9.65212e11	−0.777575	−0.388788	+	0.921327i	$0.627106\pi$
$488$	4.44777e11	0.355020
$489$	3.91697e11	0.309785
$490$	−1.57928e12	−1.23759
$491$	−1.10735e12	−0.859841	−0.429920	−	0.902867i	$-0.641458\pi$
$491$	−1.10735e12	−0.859841	−0.429920	+	0.902867i	$0.641458\pi$
$492$	−1.16998e10	−0.00900191
$493$	−2.43559e11	−0.185692
$494$	0	0
$495$	2.58604e12	1.93603
$496$	1.29812e12	0.963050
$497$	1.25049e12	0.919338
$498$	1.21390e11	0.0884407
$499$	2.24583e12	1.62153	0.810763	−	0.585374i	$-0.199052\pi$
$499$	2.24583e12	1.62153	0.810763	+	0.585374i	$0.199052\pi$
$500$	1.00006e11	0.0715586
$501$	7.20198e9	0.00510719
$502$	−4.34564e11	−0.305413
$503$	3.98259e11	0.277402	0.138701	−	0.990334i	$-0.455707\pi$
$503$	3.98259e11	0.277402	0.138701	+	0.990334i	$0.455707\pi$
$504$	1.54913e12	1.06943
$505$	−1.17005e12	−0.800557
$506$	−4.70666e12	−3.19180
$507$	0	0
$508$	−1.42961e11	−0.0952428
$509$	−2.66411e12	−1.75923	−0.879615	−	0.475687i	$-0.842200\pi$
$509$	−2.66411e12	−1.75923	−0.879615	+	0.475687i	$0.842200\pi$
$510$	−8.34727e11	−0.546360
$511$	−2.93564e11	−0.190462
$512$	−9.71905e11	−0.625042
$513$	−6.66323e11	−0.424773
$514$	−1.53775e12	−0.971747
$515$	2.08405e12	1.30550
$516$	1.38762e10	0.00861681
$517$	−2.15838e12	−1.32868
$518$	−2.58553e12	−1.57785
$519$	−6.80577e11	−0.411741
$520$	0	0
$521$	−3.11961e12	−1.85494	−0.927472	−	0.373894i	$-0.878022\pi$
$521$	−3.11961e12	−1.85494	−0.927472	+	0.373894i	$0.878022\pi$
$522$	2.73900e11	0.161464
$523$	−2.05566e12	−1.20142	−0.600709	−	0.799468i	$-0.705115\pi$
$523$	−2.05566e12	−1.20142	−0.600709	+	0.799468i	$0.705115\pi$
$524$	−3.19294e11	−0.185012
$525$	5.83798e11	0.335387
$526$	1.10290e12	0.628202
$527$	−1.62155e12	−0.915762
$528$	−1.24426e12	−0.696722
$529$	3.55067e12	1.97133
$530$	4.54150e12	2.50011
$531$	2.36377e12	1.29027
$532$	2.83347e11	0.153362
$533$	0	0
$534$	6.24166e11	0.332173
$535$	−1.08045e12	−0.570183
$536$	5.74096e11	0.300430
$537$	2.49083e10	0.0129259
$538$	−2.12368e12	−1.09287
$539$	2.94063e12	1.50069
$540$	3.01142e11	0.152405
$541$	−8.06876e11	−0.404966	−0.202483	−	0.979286i	$-0.564901\pi$
$541$	−8.06876e11	−0.404966	−0.202483	+	0.979286i	$0.564901\pi$
$542$	−2.05135e12	−1.02104
$543$	1.43371e11	0.0707721
$544$	−7.73378e11	−0.378614
$545$	1.83128e12	0.889142
$546$	0	0
$547$	1.93370e12	0.923521	0.461760	−	0.887005i	$-0.347218\pi$
$547$	1.93370e12	0.923521	0.461760	+	0.887005i	$0.347218\pi$
$548$	3.41990e11	0.161995
$549$	7.38157e11	0.346795
$550$	2.72832e12	1.27134
$551$	−2.34851e11	−0.108545
$552$	1.19756e12	0.548997
$553$	−2.32183e12	−1.05576
$554$	4.24810e12	1.91602
$555$	1.09819e12	0.491314
$556$	3.43439e11	0.152410
$557$	−3.06623e12	−1.34976	−0.674879	−	0.737928i	$-0.735804\pi$
$557$	−3.06623e12	−1.34976	−0.674879	+	0.737928i	$0.735804\pi$
$558$	1.82355e12	0.796276
$559$	0	0
$560$	4.74312e12	2.03806
$561$	1.55427e12	0.662512
$562$	−1.85885e12	−0.786013
$563$	−2.59944e12	−1.09042	−0.545208	−	0.838301i	$-0.683549\pi$
$563$	−2.59944e12	−1.09042	−0.545208	+	0.838301i	$0.683549\pi$
$564$	−1.17150e11	−0.0487512
$565$	2.90270e12	1.19835
$566$	4.14416e12	1.69732
$567$	2.14255e12	0.870576
$568$	−1.48694e12	−0.599413
$569$	−1.63182e12	−0.652632	−0.326316	−	0.945261i	$-0.605807\pi$
$569$	−1.63182e12	−0.652632	−0.326316	+	0.945261i	$0.605807\pi$
$570$	−8.04880e11	−0.319370
$571$	−1.05673e12	−0.416010	−0.208005	−	0.978128i	$-0.566697\pi$
$571$	−1.05673e12	−0.416010	−0.208005	+	0.978128i	$0.566697\pi$
$572$	0	0
$573$	−1.41658e12	−0.548964
$574$	−5.55386e11	−0.213546
$575$	−3.10230e12	−1.18353
$576$	−1.77077e12	−0.670289
$577$	8.51110e11	0.319665	0.159832	−	0.987144i	$-0.448905\pi$
$577$	8.51110e11	0.319665	0.159832	+	0.987144i	$0.448905\pi$
$578$	5.38987e11	0.200865
$579$	−1.22130e12	−0.451614
$580$	1.06140e11	0.0389450
$581$	8.61624e11	0.313708
$582$	5.56839e11	0.201176
$583$	−8.45633e12	−3.03161
$584$	3.49075e11	0.124183
$585$	0	0
$586$	2.91591e12	1.02149
$587$	−6.19927e11	−0.215511	−0.107755	−	0.994177i	$-0.534366\pi$
$587$	−6.19927e11	−0.215511	−0.107755	+	0.994177i	$0.534366\pi$
$588$	1.59608e11	0.0550626
$589$	−1.56357e12	−0.535301
$590$	6.12597e12	2.08133
$591$	−6.86579e11	−0.231498
$592$	3.63220e12	1.21541
$593$	3.79034e12	1.25873	0.629364	−	0.777110i	$-0.283315\pi$
$593$	3.79034e12	1.25873	0.629364	+	0.777110i	$0.283315\pi$
$594$	−3.75005e12	−1.23594
$595$	−5.92486e12	−1.93799
$596$	−1.04554e12	−0.339417
$597$	−4.28283e11	−0.137990
$598$	0	0
$599$	2.62045e12	0.831679	0.415839	−	0.909438i	$-0.363488\pi$
$599$	2.62045e12	0.831679	0.415839	+	0.909438i	$0.363488\pi$
$600$	−6.94190e11	−0.218674
$601$	1.11042e12	0.347178	0.173589	−	0.984818i	$-0.444464\pi$
$601$	1.11042e12	0.347178	0.173589	+	0.984818i	$0.444464\pi$
$602$	6.58700e11	0.204411
$603$	9.52777e11	0.293470
$604$	−2.87331e11	−0.0878449
$605$	−8.19956e12	−2.48824
$606$	7.90829e11	0.238208
$607$	4.57077e12	1.36660	0.683298	−	0.730140i	$-0.260545\pi$
$607$	4.57077e12	1.36660	0.683298	+	0.730140i	$0.260545\pi$
$608$	−7.45724e11	−0.221316
$609$	−2.82821e11	−0.0833171
$610$	1.91301e12	0.559415
$611$	0	0
$612$	−5.79902e11	−0.167099
$613$	5.61998e12	1.60754	0.803772	−	0.594938i	$-0.202823\pi$
$613$	5.61998e12	1.60754	0.803772	+	0.594938i	$0.202823\pi$
$614$	4.89568e12	1.39013
$615$	2.35898e11	0.0664945
$616$	−7.47551e12	−2.09184
$617$	−2.17420e12	−0.603970	−0.301985	−	0.953313i	$-0.597649\pi$
$617$	−2.17420e12	−0.603970	−0.301985	+	0.953313i	$0.597649\pi$
$618$	−1.40860e12	−0.388454
$619$	−5.91455e12	−1.61925	−0.809625	−	0.586947i	$-0.800330\pi$
$619$	−5.91455e12	−1.61925	−0.809625	+	0.586947i	$0.800330\pi$
$620$	7.06649e11	0.192062
$621$	4.26409e12	1.15057
$622$	4.66542e12	1.24978
$623$	4.43031e12	1.17825
$624$	0	0
$625$	−4.63555e12	−1.21518
$626$	−8.33426e11	−0.216912
$627$	1.49869e12	0.387266
$628$	−4.55361e11	−0.116826
$629$	−4.53716e12	−1.15573
$630$	6.66293e12	1.68513
$631$	5.05658e12	1.26977	0.634884	−	0.772607i	$-0.281048\pi$
$631$	5.05658e12	1.26977	0.634884	+	0.772607i	$0.281048\pi$
$632$	2.76086e12	0.688364
$633$	1.35128e11	0.0334526
$634$	2.09431e11	0.0514801
$635$	2.88247e12	0.703530
$636$	−4.58982e11	−0.111234
$637$	0	0
$638$	−1.32173e12	−0.315828
$639$	−2.46775e12	−0.585527
$640$	−6.50609e12	−1.53289
$641$	1.51370e12	0.354142	0.177071	−	0.984198i	$-0.443338\pi$
$641$	1.51370e12	0.354142	0.177071	+	0.984198i	$0.443338\pi$
$642$	7.30274e11	0.169660
$643$	−3.90178e12	−0.900146	−0.450073	−	0.892992i	$-0.648602\pi$
$643$	−3.90178e12	−0.900146	−0.450073	+	0.892992i	$0.648602\pi$
$644$	−1.81326e12	−0.415407
$645$	−2.79779e11	−0.0636498
$646$	3.32535e12	0.751261
$647$	7.88115e12	1.76815	0.884077	−	0.467341i	$-0.154788\pi$
$647$	7.88115e12	1.76815	0.884077	+	0.467341i	$0.154788\pi$
$648$	−2.54768e12	−0.567620
$649$	−1.14066e13	−2.52381
$650$	0	0
$651$	−1.88294e12	−0.410887
$652$	7.05229e11	0.152833
$653$	−5.10697e12	−1.09914	−0.549571	−	0.835447i	$-0.685209\pi$
$653$	−5.10697e12	−1.09914	−0.549571	+	0.835447i	$0.685209\pi$
$654$	−1.23776e12	−0.264567
$655$	6.43778e12	1.36663
$656$	7.80217e11	0.164493
$657$	5.79329e11	0.121306
$658$	−5.56107e12	−1.15649
$659$	−5.45308e11	−0.112631	−0.0563154	−	0.998413i	$-0.517935\pi$
$659$	−5.45308e11	−0.112631	−0.0563154	+	0.998413i	$0.517935\pi$
$660$	−6.77329e11	−0.138948
$661$	3.05503e12	0.622456	0.311228	−	0.950335i	$-0.399260\pi$
$661$	3.05503e12	0.622456	0.311228	+	0.950335i	$0.399260\pi$
$662$	−1.25018e12	−0.252995
$663$	0	0
$664$	−1.02455e12	−0.204539
$665$	−5.71301e12	−1.13284
$666$	5.10236e12	1.00493
$667$	1.50291e12	0.294013
$668$	1.29668e10	0.00251963
$669$	1.78974e12	0.345441
$670$	2.46923e12	0.473395
$671$	−3.56205e12	−0.678343
$672$	−8.98046e11	−0.169878
$673$	−1.57419e12	−0.295795	−0.147897	−	0.989003i	$-0.547251\pi$
$673$	−1.57419e12	−0.295795	−0.147897	+	0.989003i	$0.547251\pi$
$674$	5.68968e12	1.06199
$675$	−2.47177e12	−0.458291
$676$	0	0
$677$	−2.62249e11	−0.0479805	−0.0239903	−	0.999712i	$-0.507637\pi$
$677$	−2.62249e11	−0.0479805	−0.0239903	+	0.999712i	$0.507637\pi$
$678$	−1.96192e12	−0.356573
$679$	3.95242e12	0.713591
$680$	7.04520e12	1.26358
$681$	3.77666e12	0.672892
$682$	−8.79973e12	−1.55754
$683$	3.64995e12	0.641791	0.320896	−	0.947115i	$-0.396016\pi$
$683$	3.64995e12	0.641791	0.320896	+	0.947115i	$0.396016\pi$
$684$	−5.59166e11	−0.0976762
$685$	−6.89539e12	−1.19661
$686$	−1.04471e12	−0.180110
$687$	2.84517e12	0.487307
$688$	−9.25354e11	−0.157456
$689$	0	0
$690$	5.15077e12	0.865070
$691$	1.69603e12	0.282998	0.141499	−	0.989938i	$-0.454808\pi$
$691$	1.69603e12	0.282998	0.141499	+	0.989938i	$0.454808\pi$
$692$	−1.22534e12	−0.203132
$693$	−1.24065e13	−2.04337
$694$	−8.93451e11	−0.146202
$695$	−6.92461e12	−1.12581
$696$	3.36300e11	0.0543232
$697$	−9.74608e11	−0.156416
$698$	−2.42131e12	−0.386101
$699$	−2.33987e12	−0.370718
$700$	1.05110e12	0.165463
$701$	1.15906e13	1.81291	0.906454	−	0.422304i	$-0.138778\pi$
$701$	1.15906e13	1.81291	0.906454	+	0.422304i	$0.138778\pi$
$702$	0	0
$703$	−4.37492e12	−0.675571
$704$	8.54505e12	1.31111
$705$	2.36204e12	0.360111
$706$	9.58030e12	1.45130
$707$	5.61328e12	0.844946
$708$	−6.19114e11	−0.0926022
$709$	6.98541e12	1.03821	0.519104	−	0.854711i	$-0.326266\pi$
$709$	6.98541e12	1.03821	0.519104	+	0.854711i	$0.326266\pi$
$710$	−6.39544e12	−0.944512
$711$	4.58196e12	0.672417
$712$	−5.26804e12	−0.768226
$713$	1.00059e13	1.44996
$714$	4.00459e12	0.576654
$715$	0	0
$716$	4.48461e10	0.00637699
$717$	4.39972e11	0.0621711
$718$	9.47866e12	1.33103
$719$	−3.43730e12	−0.479665	−0.239832	−	0.970814i	$-0.577092\pi$
$719$	−3.43730e12	−0.479665	−0.239832	+	0.970814i	$0.577092\pi$
$720$	−9.36022e12	−1.29804
$721$	−9.99820e12	−1.37788
$722$	−4.71103e12	−0.645206
$723$	8.80236e11	0.119805
$724$	2.58131e11	0.0349154
$725$	−8.71194e11	−0.117110
$726$	5.54205e12	0.740381
$727$	1.25723e12	0.166920	0.0834601	−	0.996511i	$-0.473403\pi$
$727$	1.25723e12	0.166920	0.0834601	+	0.996511i	$0.473403\pi$
$728$	0	0
$729$	−2.41427e12	−0.316601
$730$	1.50139e12	0.195678
$731$	1.15591e12	0.149725
$732$	−1.93337e11	−0.0248894
$733$	1.51950e12	0.194416	0.0972079	−	0.995264i	$-0.469009\pi$
$733$	1.51950e12	0.194416	0.0972079	+	0.995264i	$0.469009\pi$
$734$	3.63515e12	0.462264
$735$	−3.21810e12	−0.406731
$736$	4.77221e12	0.599473
$737$	−4.59772e12	−0.574036
$738$	1.09602e12	0.136008
$739$	−1.19661e13	−1.47589	−0.737944	−	0.674862i	$-0.764203\pi$
$739$	−1.19661e13	−1.47589	−0.737944	+	0.674862i	$0.764203\pi$
$740$	1.97723e12	0.242390
$741$	0	0
$742$	−2.17878e13	−2.63873
$743$	−1.52097e12	−0.183093	−0.0915465	−	0.995801i	$-0.529181\pi$
$743$	−1.52097e12	−0.183093	−0.0915465	+	0.995801i	$0.529181\pi$
$744$	2.23899e12	0.267901
$745$	2.10808e13	2.50717
$746$	−1.50980e13	−1.78482
$747$	−1.70036e12	−0.199801
$748$	2.79838e12	0.326850
$749$	5.18346e12	0.601799
$750$	1.36286e12	0.157281
$751$	−8.06595e12	−0.925286	−0.462643	−	0.886545i	$-0.653099\pi$
$751$	−8.06595e12	−0.925286	−0.462643	+	0.886545i	$0.653099\pi$
$752$	7.81230e12	0.890838
$753$	−8.85513e11	−0.100373
$754$	0	0
$755$	5.79333e12	0.648884
$756$	−1.44472e12	−0.160856
$757$	8.72882e12	0.966104	0.483052	−	0.875592i	$-0.339528\pi$
$757$	8.72882e12	0.966104	0.483052	+	0.875592i	$0.339528\pi$
$758$	−6.10511e11	−0.0671710
$759$	−9.59079e12	−1.04898
$760$	6.79329e12	0.738616
$761$	−7.63407e11	−0.0825135	−0.0412568	−	0.999149i	$-0.513136\pi$
$761$	−7.63407e11	−0.0825135	−0.0412568	+	0.999149i	$0.513136\pi$
$762$	−1.94825e12	−0.209337
$763$	−8.78554e12	−0.938443
$764$	−2.55046e12	−0.270831
$765$	1.16923e13	1.23431
$766$	−1.18381e13	−1.24237
$767$	0	0
$768$	1.75945e12	0.182495
$769$	5.30538e12	0.547076	0.273538	−	0.961861i	$-0.411806\pi$
$769$	5.30538e12	0.547076	0.273538	+	0.961861i	$0.411806\pi$
$770$	−3.21527e13	−3.29616
$771$	−3.13349e12	−0.319363
$772$	−2.19887e12	−0.222804
$773$	1.53974e12	0.155110	0.0775550	−	0.996988i	$-0.475289\pi$
$773$	1.53974e12	0.155110	0.0775550	+	0.996988i	$0.475289\pi$
$774$	−1.29990e12	−0.130189
$775$	−5.80017e12	−0.577541
$776$	−4.69979e12	−0.465266
$777$	−5.26854e12	−0.518556
$778$	9.32896e12	0.912904
$779$	−9.39759e11	−0.0914319
$780$	0	0
$781$	1.19084e13	1.14531
$782$	−2.12803e13	−2.03492
$783$	1.19745e12	0.113849
$784$	−1.06437e13	−1.00617
$785$	9.18125e12	0.862955
$786$	−4.35127e12	−0.406644
$787$	2.94759e12	0.273893	0.136946	−	0.990578i	$-0.456271\pi$
$787$	2.94759e12	0.273893	0.136946	+	0.990578i	$0.456271\pi$
$788$	−1.23615e12	−0.114209
$789$	2.24738e12	0.206457
$790$	1.18747e13	1.08467
$791$	−1.39257e13	−1.26480
$792$	1.47524e13	1.33229
$793$	0	0
$794$	−1.94266e13	−1.73462
$795$	9.25425e12	0.821654
$796$	−7.71099e11	−0.0680772
$797$	−1.83481e13	−1.61075	−0.805376	−	0.592764i	$-0.798037\pi$
$797$	−1.83481e13	−1.61075	−0.805376	+	0.592764i	$0.798037\pi$
$798$	3.86139e12	0.337079
$799$	−9.75873e12	−0.847096
$800$	−2.76632e12	−0.238779
$801$	−8.74291e12	−0.750429
$802$	7.51127e12	0.641104
$803$	−2.79561e12	−0.237278
$804$	−2.49549e11	−0.0210622
$805$	3.65600e13	3.06849
$806$	0	0
$807$	−4.32744e12	−0.359170
$808$	−6.67470e12	−0.550910
$809$	−9.70701e12	−0.796741	−0.398371	−	0.917225i	$-0.630424\pi$
$809$	−9.70701e12	−0.796741	−0.398371	+	0.917225i	$0.630424\pi$
$810$	−1.09578e13	−0.894415
$811$	−6.14421e12	−0.498738	−0.249369	−	0.968409i	$-0.580223\pi$
$811$	−6.14421e12	−0.498738	−0.249369	+	0.968409i	$0.580223\pi$
$812$	−5.09203e11	−0.0411045
$813$	−4.18005e12	−0.335563
$814$	−2.46220e13	−1.96568
$815$	−1.42192e13	−1.12893
$816$	−5.62572e12	−0.444194
$817$	1.11457e12	0.0875205
$818$	−2.22030e13	−1.73389
$819$	0	0
$820$	4.24720e11	0.0328050
$821$	−1.41092e13	−1.08383	−0.541913	−	0.840434i	$-0.682300\pi$
$821$	−1.41092e13	−1.08383	−0.541913	+	0.840434i	$0.682300\pi$
$822$	4.66057e12	0.356054
$823$	7.99374e12	0.607366	0.303683	−	0.952773i	$-0.401784\pi$
$823$	7.99374e12	0.607366	0.303683	+	0.952773i	$0.401784\pi$
$824$	1.18888e13	0.898389
$825$	5.55951e12	0.417824
$826$	−2.93892e13	−2.19674
$827$	4.82994e12	0.359060	0.179530	−	0.983752i	$-0.442542\pi$
$827$	4.82994e12	0.359060	0.179530	+	0.983752i	$0.442542\pi$
$828$	3.57834e12	0.264573
$829$	1.41648e13	1.04163	0.520816	−	0.853669i	$-0.325628\pi$
$829$	1.41648e13	1.04163	0.520816	+	0.853669i	$0.325628\pi$
$830$	−4.40666e12	−0.322298
$831$	8.65637e12	0.629697
$832$	0	0
$833$	1.32956e13	0.956762
$834$	4.68031e12	0.334987
$835$	−2.61443e11	−0.0186118
$836$	2.69831e12	0.191058
$837$	7.97228e12	0.561459
$838$	8.24927e12	0.577853
$839$	−1.79477e13	−1.25049	−0.625246	−	0.780428i	$-0.715001\pi$
$839$	−1.79477e13	−1.25049	−0.625246	+	0.780428i	$0.715001\pi$
$840$	8.18088e12	0.566948
$841$	−1.40851e13	−0.970907
$842$	4.59068e12	0.314755
$843$	−3.78778e12	−0.258322
$844$	2.43291e11	0.0165038
$845$	0	0
$846$	1.09744e13	0.736570
$847$	3.93372e13	2.62620
$848$	3.06079e13	2.03260
$849$	8.44458e12	0.557819
$850$	1.23356e13	0.810542
$851$	2.79970e13	1.82990
$852$	6.46347e11	0.0420231
$853$	8.65463e12	0.559729	0.279865	−	0.960039i	$-0.409710\pi$
$853$	8.65463e12	0.559729	0.279865	+	0.960039i	$0.409710\pi$
$854$	−9.17764e12	−0.590433
$855$	1.12742e13	0.721505
$856$	−6.16360e12	−0.392376
$857$	−1.17199e13	−0.742185	−0.371092	−	0.928596i	$-0.621017\pi$
$857$	−1.17199e13	−0.742185	−0.371092	+	0.928596i	$0.621017\pi$
$858$	0	0
$859$	−2.70022e13	−1.69211	−0.846057	−	0.533092i	$-0.821030\pi$
$859$	−2.70022e13	−1.69211	−0.846057	+	0.533092i	$0.821030\pi$
$860$	−5.03727e11	−0.0314016
$861$	−1.13171e12	−0.0701815
$862$	−2.35669e13	−1.45385
$863$	−2.11111e13	−1.29557	−0.647786	−	0.761823i	$-0.724305\pi$
$863$	−2.11111e13	−1.29557	−0.647786	+	0.761823i	$0.724305\pi$
$864$	3.80228e12	0.232130
$865$	2.47060e13	1.50048
$866$	2.81704e13	1.70201
$867$	1.09830e12	0.0660137
$868$	−3.39013e12	−0.202711
$869$	−2.21107e13	−1.31527
$870$	1.44645e12	0.0855986
$871$	0	0
$872$	1.04468e13	0.611870
$873$	−7.79984e12	−0.454487
$874$	−2.05194e13	−1.18950
$875$	9.67354e12	0.557891
$876$	−1.51737e11	−0.00870606
$877$	1.48840e13	0.849614	0.424807	−	0.905284i	$-0.360342\pi$
$877$	1.48840e13	0.849614	0.424807	+	0.905284i	$0.360342\pi$
$878$	1.33544e13	0.758402
$879$	5.94176e12	0.335711
$880$	4.51687e13	2.53902
$881$	8.21496e11	0.0459424	0.0229712	−	0.999736i	$-0.492687\pi$
$881$	8.21496e11	0.0459424	0.0229712	+	0.999736i	$0.492687\pi$
$882$	−1.49518e13	−0.831926
$883$	−5.06069e12	−0.280147	−0.140074	−	0.990141i	$-0.544734\pi$
$883$	−5.06069e12	−0.280147	−0.140074	+	0.990141i	$0.544734\pi$
$884$	0	0
$885$	1.24829e13	0.684025
$886$	−2.74964e12	−0.149908
$887$	−4.00796e12	−0.217404	−0.108702	−	0.994074i	$-0.534669\pi$
$887$	−4.00796e12	−0.217404	−0.108702	+	0.994074i	$0.534669\pi$
$888$	6.26478e12	0.338102
$889$	−1.38286e13	−0.742540
$890$	−2.26582e13	−1.21051
$891$	2.04035e13	1.08456
$892$	3.22233e12	0.170423
$893$	−9.40979e12	−0.495163
$894$	−1.42484e13	−0.746016
$895$	−9.04211e11	−0.0471049
$896$	3.12129e13	1.61788
$897$	0	0
$898$	2.74516e13	1.40872
$899$	2.80989e12	0.143473
$900$	−2.07427e12	−0.105384
$901$	−3.82338e13	−1.93280
$902$	−5.28894e12	−0.266035
$903$	1.34224e12	0.0671791
$904$	1.65589e13	0.824657
$905$	−5.20459e12	−0.257910
$906$	−3.91569e12	−0.193077
$907$	4.52189e12	0.221864	0.110932	−	0.993828i	$-0.464616\pi$
$907$	4.52189e12	0.221864	0.110932	+	0.993828i	$0.464616\pi$
$908$	6.79966e12	0.331971
$909$	−1.10774e13	−0.538147
$910$	0	0
$911$	−5.68437e12	−0.273432	−0.136716	−	0.990610i	$-0.543655\pi$
$911$	−5.68437e12	−0.273432	−0.136716	+	0.990610i	$0.543655\pi$
$912$	−5.42456e12	−0.259650
$913$	8.20525e12	0.390817
$914$	3.40839e13	1.61544
$915$	3.89816e12	0.183850
$916$	5.12257e12	0.240413
$917$	−3.08851e13	−1.44241
$918$	−1.69552e13	−0.787972
$919$	3.28047e13	1.51711	0.758555	−	0.651609i	$-0.225906\pi$
$919$	3.28047e13	1.51711	0.758555	+	0.651609i	$0.225906\pi$
$920$	−4.34731e13	−2.00067
$921$	9.97597e12	0.456864
$922$	−2.60183e13	−1.18574
$923$	0	0
$924$	3.24947e12	0.146652
$925$	−1.62291e13	−0.728880
$926$	−6.90877e12	−0.308782
$927$	1.97308e13	0.877576
$928$	1.34014e12	0.0593177
$929$	−1.82868e13	−0.805504	−0.402752	−	0.915309i	$-0.631946\pi$
$929$	−1.82868e13	−0.805504	−0.402752	+	0.915309i	$0.631946\pi$
$930$	9.63005e12	0.422139
$931$	1.28201e13	0.559267
$932$	−4.21280e12	−0.182894
$933$	9.50675e12	0.410738
$934$	−2.43183e13	−1.04562
$935$	−5.64224e13	−2.41435
$936$	0	0
$937$	2.71335e13	1.14995	0.574974	−	0.818171i	$-0.305012\pi$
$937$	2.71335e13	1.14995	0.574974	+	0.818171i	$0.305012\pi$
$938$	−1.18461e13	−0.499644
$939$	−1.69828e12	−0.0712875
$940$	4.25271e12	0.177660
$941$	9.48833e12	0.394490	0.197245	−	0.980354i	$-0.436800\pi$
$941$	9.48833e12	0.394490	0.197245	+	0.980354i	$0.436800\pi$
$942$	−6.20556e12	−0.256775
$943$	6.01392e12	0.247660
$944$	4.12866e13	1.69213
$945$	2.91293e13	1.18819
$946$	6.27279e12	0.254654
$947$	−1.99262e13	−0.805100	−0.402550	−	0.915398i	$-0.631876\pi$
$947$	−1.99262e13	−0.805100	−0.402550	+	0.915398i	$0.631876\pi$
$948$	−1.20010e12	−0.0482591
$949$	0	0
$950$	1.18945e13	0.473796
$951$	4.26759e11	0.0169188
$952$	−3.37992e13	−1.33364
$953$	2.48922e13	0.977565	0.488782	−	0.872406i	$-0.337441\pi$
$953$	2.48922e13	0.977565	0.488782	+	0.872406i	$0.337441\pi$
$954$	4.29967e13	1.68061
$955$	5.14238e13	2.00055
$956$	7.92144e11	0.0306721
$957$	−2.69330e12	−0.103796
$958$	3.38780e13	1.29949
$959$	3.30805e13	1.26296
$960$	−9.35134e12	−0.355347
$961$	−7.73217e12	−0.292446
$962$	0	0
$963$	−1.02292e13	−0.383286
$964$	1.58481e12	0.0591060
$965$	4.43349e13	1.64579
$966$	−2.47107e13	−0.913037
$967$	4.20642e13	1.54701	0.773505	−	0.633790i	$-0.218501\pi$
$967$	4.20642e13	1.54701	0.773505	+	0.633790i	$0.218501\pi$
$968$	−4.67756e13	−1.71230
$969$	6.77609e12	0.246900
$970$	−2.02141e13	−0.733132
$971$	−1.34740e12	−0.0486418	−0.0243209	−	0.999704i	$-0.507742\pi$
$971$	−1.34740e12	−0.0486418	−0.0243209	+	0.999704i	$0.507742\pi$
$972$	4.37325e12	0.157147
$973$	3.32207e13	1.18823
$974$	−2.36825e13	−0.843164
$975$	0	0
$976$	1.28929e13	0.454807
$977$	2.05822e13	0.722714	0.361357	−	0.932428i	$-0.382314\pi$
$977$	2.05822e13	0.722714	0.361357	+	0.932428i	$0.382314\pi$
$978$	9.61070e12	0.335916
$979$	4.21898e13	1.46786
$980$	−5.79401e12	−0.200661
$981$	1.73377e13	0.597695
$982$	−2.71700e13	−0.932368
$983$	5.72322e13	1.95501	0.977506	−	0.210906i	$-0.0676413\pi$
$983$	5.72322e13	1.95501	0.977506	+	0.210906i	$0.0676413\pi$
$984$	1.34571e12	0.0457587
$985$	2.49239e13	0.843631
$986$	−5.97598e12	−0.201355
$987$	−1.13318e13	−0.380078
$988$	0	0
$989$	−7.13263e12	−0.237065
$990$	6.34511e13	2.09933
$991$	1.46766e13	0.483386	0.241693	−	0.970353i	$-0.422297\pi$
$991$	1.46766e13	0.483386	0.241693	+	0.970353i	$0.422297\pi$
$992$	8.92228e12	0.292532
$993$	−2.54750e12	−0.0831462
$994$	3.06820e13	0.996884
$995$	1.55473e13	0.502866
$996$	4.45354e11	0.0143396
$997$	−5.31286e13	−1.70294	−0.851471	−	0.524402i	$-0.824289\pi$
$997$	−5.31286e13	−1.70294	−0.851471	+	0.524402i	$0.824289\pi$
$998$	5.51037e13	1.75830
$999$	2.23067e13	0.708583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.10.a.a.1.3		4
13.12	even	2		13.10.a.a.1.2	✓	4
39.38	odd	2		117.10.a.c.1.3		4
52.51	odd	2		208.10.a.g.1.1		4
65.64	even	2		325.10.a.a.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.a.1.2	✓	4	13.12	even	2
117.10.a.c.1.3		4	39.38	odd	2
169.10.a.a.1.3		4	1.1	even	1	trivial
208.10.a.g.1.1		4	52.51	odd	2
325.10.a.a.1.3		4	65.64	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

\(f(q)\)	\(=\)	\(q+24.5360 q^{2} +49.9972 q^{3} +90.0171 q^{4} -1814.98 q^{5} +1226.73 q^{6} +8707.31 q^{7} -10353.8 q^{8} -17183.3 q^{9} +O(q^{10})\)	\(q+24.5360 q^{2} +49.9972 q^{3} +90.0171 q^{4} -1814.98 q^{5} +1226.73 q^{6} +8707.31 q^{7} -10353.8 q^{8} -17183.3 q^{9} -44532.3 q^{10} +82919.7 q^{11} +4500.61 q^{12} +213643. q^{14} -90743.8 q^{15} -300130. q^{16} +374907. q^{17} -421610. q^{18} +361501. q^{19} -163379. q^{20} +435341. q^{21} +2.03452e6 q^{22} -2.31340e6 q^{23} -517661. q^{24} +1.34101e6 q^{25} -1.84321e6 q^{27} +783807. q^{28} -649654. q^{29} -2.22649e6 q^{30} -4.32521e6 q^{31} -2.06285e6 q^{32} +4.14575e6 q^{33} +9.19873e6 q^{34} -1.58036e7 q^{35} -1.54679e6 q^{36} -1.21021e7 q^{37} +8.86981e6 q^{38} +1.87919e7 q^{40} -2.59960e6 q^{41} +1.06816e7 q^{42} +3.08318e6 q^{43} +7.46419e6 q^{44} +3.11872e7 q^{45} -5.67617e7 q^{46} -2.60298e7 q^{47} -1.50057e7 q^{48} +3.54636e7 q^{49} +3.29032e7 q^{50} +1.87443e7 q^{51} -1.01982e8 q^{53} -4.52251e7 q^{54} -1.50497e8 q^{55} -9.01536e7 q^{56} +1.80741e7 q^{57} -1.59399e7 q^{58} -1.37562e8 q^{59} -8.16850e6 q^{60} -4.29579e7 q^{61} -1.06124e8 q^{62} -1.49620e8 q^{63} +1.03052e8 q^{64} +1.01720e8 q^{66} -5.54479e7 q^{67} +3.37480e7 q^{68} -1.15664e8 q^{69} -3.87757e8 q^{70} +1.43613e8 q^{71} +1.77912e8 q^{72} -3.37147e7 q^{73} -2.96937e8 q^{74} +6.70469e7 q^{75} +3.25413e7 q^{76} +7.22007e8 q^{77} -2.66652e8 q^{79} +5.44728e8 q^{80} +2.46063e8 q^{81} -6.37839e7 q^{82} +9.89542e7 q^{83} +3.91882e7 q^{84} -6.80447e8 q^{85} +7.56490e7 q^{86} -3.24809e7 q^{87} -8.58533e8 q^{88} +5.08803e8 q^{89} +7.65211e8 q^{90} -2.08246e8 q^{92} -2.16249e8 q^{93} -6.38667e8 q^{94} -6.56116e8 q^{95} -1.03137e8 q^{96} +4.53920e8 q^{97} +8.70137e8 q^{98} -1.42483e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9}+O(q^{10}) \) 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9	\( 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 67831 q^{10} + 40140 q^{11} - 155479 q^{12} - 277653 q^{14} - 83307 q^{15} + 726609 q^{16} + 78717 q^{17} - 1691026 q^{18} - 209664 q^{19} - 870843 q^{20} - 1138431 q^{21} + 1364090 q^{22} - 4257444 q^{23} - 3561573 q^{24} - 2900157 q^{25} - 2077801 q^{27} - 4035181 q^{28} - 1647936 q^{29} - 744143 q^{30} + 11366002 q^{31} + 29458959 q^{32} + 14413222 q^{33} - 26257659 q^{34} - 13789797 q^{35} - 11587714 q^{36} - 4636891 q^{37} + 25172466 q^{38} + 22536791 q^{40} - 13859538 q^{41} + 75564923 q^{42} - 33368081 q^{43} - 66489222 q^{44} + 17423928 q^{45} - 71369332 q^{46} + 3943005 q^{47} - 620787 q^{48} + 23294923 q^{49} + 4217748 q^{50} - 19664471 q^{51} - 171019326 q^{53} + 64946915 q^{54} - 121160538 q^{55} - 281552967 q^{56} + 47829030 q^{57} - 79964734 q^{58} + 63389388 q^{59} - 37708135 q^{60} + 77050190 q^{61} - 95878740 q^{62} + 155695476 q^{63} + 768962465 q^{64} - 42396374 q^{66} + 41174072 q^{67} - 717615423 q^{68} + 546642556 q^{69} - 409056389 q^{70} - 252460989 q^{71} - 562579254 q^{72} - 594415068 q^{73} - 957058539 q^{74} + 533318748 q^{75} + 326897170 q^{76} + 561950454 q^{77} + 115998984 q^{79} + 509107233 q^{80} + 437803700 q^{81} - 875148240 q^{82} + 79577862 q^{83} - 108899441 q^{84} - 549463469 q^{85} + 589924887 q^{86} - 1087526510 q^{87} - 2327564370 q^{88} + 1152240276 q^{89} + 877550038 q^{90} - 4213481460 q^{92} - 1618266556 q^{93} + 1859909503 q^{94} - 1273705170 q^{95} - 3171454029 q^{96} - 1049098084 q^{97} - 420532254 q^{98} - 2132181050 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 67831 * q^10 + 40140 * q^11 - 155479 * q^12 - 277653 * q^14 - 83307 * q^15 + 726609 * q^16 + 78717 * q^17 - 1691026 * q^18 - 209664 * q^19 - 870843 * q^20 - 1138431 * q^21 + 1364090 * q^22 - 4257444 * q^23 - 3561573 * q^24 - 2900157 * q^25 - 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 744143 * q^30 + 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 - 26257659 * q^34 - 13789797 * q^35 - 11587714 * q^36 - 4636891 * q^37 + 25172466 * q^38 + 22536791 * q^40 - 13859538 * q^41 + 75564923 * q^42 - 33368081 * q^43 - 66489222 * q^44 + 17423928 * q^45 - 71369332 * q^46 + 3943005 * q^47 - 620787 * q^48 + 23294923 * q^49 + 4217748 * q^50 - 19664471 * q^51 - 171019326 * q^53 + 64946915 * q^54 - 121160538 * q^55 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 + 63389388 * q^59 - 37708135 * q^60 + 77050190 * q^61 - 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 - 717615423 * q^68 + 546642556 * q^69 - 409056389 * q^70 - 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 + 533318748 * q^75 + 326897170 * q^76 + 561950454 * q^77 + 115998984 * q^79 + 509107233 * q^80 + 437803700 * q^81 - 875148240 * q^82 + 79577862 * q^83 - 108899441 * q^84 - 549463469 * q^85 + 589924887 * q^86 - 1087526510 * q^87 - 2327564370 * q^88 + 1152240276 * q^89 + 877550038 * q^90 - 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 - 1273705170 * q^95 - 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 - 2132181050 * q^99

Introduction

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