LMFDB - Embedded newform 289.10.a.g.1.26

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:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
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)

$f(q)$	$=$	$q+19.5847 q^{2} -220.079 q^{3} -128.440 q^{4} +130.049 q^{5} -4310.17 q^{6} -9771.35 q^{7} -12542.8 q^{8} +28751.6 q^{9} +O(q^{10})$	\(q+19.5847 q^{2} -220.079 q^{3} -128.440 q^{4} +130.049 q^{5} -4310.17 q^{6} -9771.35 q^{7} -12542.8 q^{8} +28751.6 q^{9} +2546.96 q^{10} -71260.2 q^{11} +28266.9 q^{12} +126726. q^{13} -191369. q^{14} -28621.0 q^{15} -179886. q^{16} +563092. q^{18} +604683. q^{19} -16703.5 q^{20} +2.15047e6 q^{21} -1.39561e6 q^{22} +1.07633e6 q^{23} +2.76041e6 q^{24} -1.93621e6 q^{25} +2.48189e6 q^{26} -1.99582e6 q^{27} +1.25503e6 q^{28} +1.91386e6 q^{29} -560533. q^{30} -7.71934e6 q^{31} +2.89892e6 q^{32} +1.56829e7 q^{33} -1.27075e6 q^{35} -3.69287e6 q^{36} +1.53482e7 q^{37} +1.18425e7 q^{38} -2.78897e7 q^{39} -1.63118e6 q^{40} +1.94717e7 q^{41} +4.21162e7 q^{42} -1.95272e7 q^{43} +9.15267e6 q^{44} +3.73912e6 q^{45} +2.10796e7 q^{46} +4.08642e7 q^{47} +3.95890e7 q^{48} +5.51256e7 q^{49} -3.79201e7 q^{50} -1.62767e7 q^{52} -489443. q^{53} -3.90874e7 q^{54} -9.26730e6 q^{55} +1.22560e8 q^{56} -1.33078e8 q^{57} +3.74824e7 q^{58} +1.93634e7 q^{59} +3.67608e6 q^{60} -9.43914e7 q^{61} -1.51181e8 q^{62} -2.80942e8 q^{63} +1.48876e8 q^{64} +1.64806e7 q^{65} +3.07144e8 q^{66} -1.30119e8 q^{67} -2.36878e8 q^{69} -2.48873e7 q^{70} +1.90225e8 q^{71} -3.60627e8 q^{72} -8.01389e7 q^{73} +3.00589e8 q^{74} +4.26119e8 q^{75} -7.76656e7 q^{76} +6.96308e8 q^{77} -5.46211e8 q^{78} -4.53181e8 q^{79} -2.33939e7 q^{80} -1.26682e8 q^{81} +3.81348e8 q^{82} +2.97054e8 q^{83} -2.76206e8 q^{84} -3.82434e8 q^{86} -4.21200e8 q^{87} +8.93804e8 q^{88} +7.19298e8 q^{89} +7.32294e7 q^{90} -1.23828e9 q^{91} -1.38244e8 q^{92} +1.69886e9 q^{93} +8.00312e8 q^{94} +7.86383e7 q^{95} -6.37990e8 q^{96} -2.68261e8 q^{97} +1.07962e9 q^{98} -2.04885e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) $ 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9} - 60000 q^{10} - 76902 q^{11} - 373248 q^{12} + 54216 q^{13} - 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} - 6439479 q^{20} - 138102 q^{21} - 267324 q^{22} - 4041462 q^{23} - 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} - 13281612 q^{27} - 18614784 q^{28} - 4005936 q^{29} + 22471686 q^{30} - 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} - 22076682 q^{37} - 27401376 q^{38} - 62736162 q^{39} + 12231630 q^{40} - 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} + 49578936 q^{44} - 129308238 q^{45} - 140524827 q^{46} - 118557912 q^{47} - 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} - 209848575 q^{54} - 365439924 q^{55} - 203095059 q^{56} + 4614108 q^{57} + 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} - 175597116 q^{61} - 720602571 q^{62} - 587415936 q^{63} + 853082511 q^{64} - 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} - 1308709542 q^{71} - 275337849 q^{72} - 494841342 q^{73} - 1545361890 q^{74} - 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} - 2270624538 q^{78} - 1980107868 q^{79} - 2897000199 q^{80} + 1598298840 q^{81} - 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} + 2705904618 q^{88} + 148394658 q^{89} - 117916215 q^{90} - 636340896 q^{91} + 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} - 4878626298 q^{95} + 8390096634 q^{96} + 891786822 q^{97} + 4285627647 q^{98} + 1476187998 q^{99}+O(q^{100}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9 - 60000 * q^10 - 76902 * q^11 - 373248 * q^12 + 54216 * q^13 - 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 - 6439479 * q^20 - 138102 * q^21 - 267324 * q^22 - 4041462 * q^23 - 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 - 13281612 * q^27 - 18614784 * q^28 - 4005936 * q^29 + 22471686 * q^30 - 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 - 22076682 * q^37 - 27401376 * q^38 - 62736162 * q^39 + 12231630 * q^40 - 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 + 49578936 * q^44 - 129308238 * q^45 - 140524827 * q^46 - 118557912 * q^47 - 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 - 209848575 * q^54 - 365439924 * q^55 - 203095059 * q^56 + 4614108 * q^57 + 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 - 175597116 * q^61 - 720602571 * q^62 - 587415936 * q^63 + 853082511 * q^64 - 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 - 1308709542 * q^71 - 275337849 * q^72 - 494841342 * q^73 - 1545361890 * q^74 - 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 - 2270624538 * q^78 - 1980107868 * q^79 - 2897000199 * q^80 + 1598298840 * q^81 - 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 + 2705904618 * q^88 + 148394658 * q^89 - 117916215 * q^90 - 636340896 * q^91 + 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 - 4878626298 * q^95 + 8390096634 * q^96 + 891786822 * q^97 + 4285627647 * q^98 + 1476187998 * 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 $

$2$	19.5847	0.865529	0.432764	−	0.901507i	$-0.357538\pi$
$2$	19.5847	0.865529	0.432764	+	0.901507i	$0.357538\pi$
$3$	−220.079	−1.56867	−0.784337	−	0.620336i	$-0.786996\pi$
$3$	−220.079	−1.56867	−0.784337	+	0.620336i	$0.786996\pi$
$4$	−128.440	−0.250860
$5$	130.049	0.0930553	0.0465277	−	0.998917i	$-0.485184\pi$
$5$	130.049	0.0930553	0.0465277	+	0.998917i	$0.485184\pi$
$6$	−4310.17	−1.35773
$7$	−9771.35	−1.53820	−0.769101	−	0.639127i	$-0.779296\pi$
$7$	−9771.35	−1.53820	−0.769101	+	0.639127i	$0.779296\pi$
$8$	−12542.8	−1.08266
$9$	28751.6	1.46074
$10$	2546.96	0.0805421
$11$	−71260.2	−1.46751	−0.733753	−	0.679416i	$-0.762233\pi$
$11$	−71260.2	−1.46751	−0.733753	+	0.679416i	$0.762233\pi$
$12$	28266.9	0.393517
$13$	126726.	1.23061	0.615306	−	0.788289i	$-0.289033\pi$
$13$	126726.	1.23061	0.615306	+	0.788289i	$0.289033\pi$
$14$	−191369.	−1.33136
$15$	−28621.0	−0.145973
$16$	−179886.	−0.686210
$17$	0	0
$17$	0	0
$18$	563092.	1.26431
$19$	604683.	1.06448	0.532239	−	0.846594i	$-0.321351\pi$
$19$	604683.	1.06448	0.532239	+	0.846594i	$0.321351\pi$
$20$	−16703.5	−0.0233438
$21$	2.15047e6	2.41294
$22$	−1.39561e6	−1.27017
$23$	1.07633e6	0.801994	0.400997	−	0.916079i	$-0.368664\pi$
$23$	1.07633e6	0.801994	0.400997	+	0.916079i	$0.368664\pi$
$24$	2.76041e6	1.69833
$25$	−1.93621e6	−0.991341
$26$	2.48189e6	1.06513
$27$	−1.99582e6	−0.722743
$28$	1.25503e6	0.385873
$29$	1.91386e6	0.502481	0.251240	−	0.967925i	$-0.419162\pi$
$29$	1.91386e6	0.502481	0.251240	+	0.967925i	$0.419162\pi$
$30$	−560533.	−0.126344
$31$	−7.71934e6	−1.50125	−0.750624	−	0.660729i	$-0.770247\pi$
$31$	−7.71934e6	−1.50125	−0.750624	+	0.660729i	$0.770247\pi$
$32$	2.89892e6	0.488721
$33$	1.56829e7	2.30204
$34$	0	0
$35$	−1.27075e6	−0.143138
$36$	−3.69287e6	−0.366439
$37$	1.53482e7	1.34632	0.673161	−	0.739496i	$-0.264936\pi$
$37$	1.53482e7	1.34632	0.673161	+	0.739496i	$0.264936\pi$
$38$	1.18425e7	0.921337
$39$	−2.78897e7	−1.93043
$40$	−1.63118e6	−0.100747
$41$	1.94717e7	1.07616	0.538081	−	0.842893i	$-0.319150\pi$
$41$	1.94717e7	1.07616	0.538081	+	0.842893i	$0.319150\pi$
$42$	4.21162e7	2.08847
$43$	−1.95272e7	−0.871027	−0.435513	−	0.900182i	$-0.643433\pi$
$43$	−1.95272e7	−0.871027	−0.435513	+	0.900182i	$0.643433\pi$
$44$	9.15267e6	0.368138
$45$	3.73912e6	0.135929
$46$	2.10796e7	0.694149
$47$	4.08642e7	1.22152	0.610762	−	0.791814i	$-0.290863\pi$
$47$	4.08642e7	1.22152	0.610762	+	0.791814i	$0.290863\pi$
$48$	3.95890e7	1.07644
$49$	5.51256e7	1.36606
$50$	−3.79201e7	−0.858034
$51$	0	0
$52$	−1.62767e7	−0.308711
$53$	−489443.	−0.00852041	−0.00426021	−	0.999991i	$-0.501356\pi$
$53$	−489443.	−0.00852041	−0.00426021	+	0.999991i	$0.501356\pi$
$54$	−3.90874e7	−0.625555
$55$	−9.26730e6	−0.136559
$56$	1.22560e8	1.66534
$57$	−1.33078e8	−1.66982
$58$	3.74824e7	0.434912
$59$	1.93634e7	0.208040	0.104020	−	0.994575i	$-0.466829\pi$
$59$	1.93634e7	0.208040	0.104020	+	0.994575i	$0.466829\pi$
$60$	3.67608e6	0.0366188
$61$	−9.43914e7	−0.872867	−0.436433	−	0.899737i	$-0.643759\pi$
$61$	−9.43914e7	−0.872867	−0.436433	+	0.899737i	$0.643759\pi$
$62$	−1.51181e8	−1.29937
$63$	−2.80942e8	−2.24691
$64$	1.48876e8	1.10921
$65$	1.64806e7	0.114515
$66$	3.07144e8	1.99248
$67$	−1.30119e8	−0.788870	−0.394435	−	0.918924i	$-0.629060\pi$
$67$	−1.30119e8	−0.788870	−0.394435	+	0.918924i	$0.629060\pi$
$68$	0	0
$69$	−2.36878e8	−1.25807
$70$	−2.48873e7	−0.123890
$71$	1.90225e8	0.888395	0.444197	−	0.895929i	$-0.353489\pi$
$71$	1.90225e8	0.888395	0.444197	+	0.895929i	$0.353489\pi$
$72$	−3.60627e8	−1.58147
$73$	−8.01389e7	−0.330286	−0.165143	−	0.986270i	$-0.552809\pi$
$73$	−8.01389e7	−0.330286	−0.165143	+	0.986270i	$0.552809\pi$
$74$	3.00589e8	1.16528
$75$	4.26119e8	1.55509
$76$	−7.76656e7	−0.267035
$77$	6.96308e8	2.25732
$78$	−5.46211e8	−1.67084
$79$	−4.53181e8	−1.30903	−0.654516	−	0.756049i	$-0.727127\pi$
$79$	−4.53181e8	−1.30903	−0.654516	+	0.756049i	$0.727127\pi$
$80$	−2.33939e7	−0.0638555
$81$	−1.26682e8	−0.326988
$82$	3.81348e8	0.931449
$83$	2.97054e8	0.687042	0.343521	−	0.939145i	$-0.388380\pi$
$83$	2.97054e8	0.687042	0.343521	+	0.939145i	$0.388380\pi$
$84$	−2.76206e8	−0.605308
$85$	0	0
$86$	−3.82434e8	−0.753899
$87$	−4.21200e8	−0.788228
$88$	8.93804e8	1.58880
$89$	7.19298e8	1.21522	0.607608	−	0.794237i	$-0.292129\pi$
$89$	7.19298e8	1.21522	0.607608	+	0.794237i	$0.292129\pi$
$90$	7.32294e7	0.117651
$91$	−1.23828e9	−1.89293
$92$	−1.38244e8	−0.201188
$93$	1.69886e9	2.35497
$94$	8.00312e8	1.05727
$95$	7.86383e7	0.0990554
$96$	−6.37990e8	−0.766643
$97$	−2.68261e8	−0.307670	−0.153835	−	0.988097i	$-0.549162\pi$
$97$	−2.68261e8	−0.307670	−0.153835	+	0.988097i	$0.549162\pi$
$98$	1.07962e9	1.18237
$99$	−2.04885e9	−2.14364
$100$	2.48687e8	0.248687
$101$	1.18587e9	1.13394	0.566972	−	0.823737i	$-0.308115\pi$
$101$	1.18587e9	1.13394	0.566972	+	0.823737i	$0.308115\pi$
$102$	0	0
$103$	1.67664e9	1.46782	0.733908	−	0.679249i	$-0.237694\pi$
$103$	1.67664e9	1.46782	0.733908	+	0.679249i	$0.237694\pi$
$104$	−1.58950e9	−1.33233
$105$	2.79665e8	0.224537
$106$	−9.58558e6	−0.00737466
$107$	−2.00739e9	−1.48049	−0.740245	−	0.672337i	$-0.765290\pi$
$107$	−2.00739e9	−1.48049	−0.740245	+	0.672337i	$0.765290\pi$
$108$	2.56343e8	0.181307
$109$	1.92164e9	1.30393	0.651963	−	0.758251i	$-0.273946\pi$
$109$	1.92164e9	1.30393	0.651963	+	0.758251i	$0.273946\pi$
$110$	−1.81497e8	−0.118196
$111$	−3.37780e9	−2.11194
$112$	1.75773e9	1.05553
$113$	−1.42093e9	−0.819820	−0.409910	−	0.912126i	$-0.634440\pi$
$113$	−1.42093e9	−0.819820	−0.409910	+	0.912126i	$0.634440\pi$
$114$	−2.60629e9	−1.44528
$115$	1.39976e8	0.0746298
$116$	−2.45817e8	−0.126052
$117$	3.64358e9	1.79760
$118$	3.79225e8	0.180065
$119$	0	0
$120$	3.58988e8	0.158039
$121$	2.72007e9	1.15357
$122$	−1.84863e9	−0.755492
$123$	−4.28531e9	−1.68814
$124$	9.91473e8	0.376603
$125$	−5.05804e8	−0.185305
$126$	−5.50217e9	−1.94476
$127$	−2.22693e9	−0.759609	−0.379805	−	0.925067i	$-0.624009\pi$
$127$	−2.22693e9	−0.759609	−0.379805	+	0.925067i	$0.624009\pi$
$128$	1.43144e9	0.471334
$129$	4.29752e9	1.36636
$130$	3.22767e8	0.0991160
$131$	3.56937e9	1.05894	0.529469	−	0.848329i	$-0.322391\pi$
$131$	3.56937e9	1.05894	0.529469	+	0.848329i	$0.322391\pi$
$132$	−2.01431e9	−0.577488
$133$	−5.90857e9	−1.63738
$134$	−2.54835e9	−0.682790
$135$	−2.59553e8	−0.0672551
$136$	0	0
$137$	−1.99937e9	−0.484899	−0.242449	−	0.970164i	$-0.577951\pi$
$137$	−1.99937e9	−0.484899	−0.242449	+	0.970164i	$0.577951\pi$
$138$	−4.63918e9	−1.08889
$139$	−2.89838e9	−0.658549	−0.329275	−	0.944234i	$-0.606804\pi$
$139$	−2.89838e9	−0.658549	−0.329275	+	0.944234i	$0.606804\pi$
$140$	1.63216e8	0.0359075
$141$	−8.99333e9	−1.91617
$142$	3.72550e9	0.768931
$143$	−9.03053e9	−1.80593
$144$	−5.17201e9	−1.00237
$145$	2.48895e8	0.0467585
$146$	−1.56949e9	−0.285872
$147$	−1.21320e10	−2.14291
$148$	−1.97132e9	−0.337738
$149$	−1.02281e10	−1.70003	−0.850014	−	0.526760i	$-0.823407\pi$
$149$	−1.02281e10	−1.70003	−0.850014	+	0.526760i	$0.823407\pi$
$150$	8.34541e9	1.34597
$151$	−3.39052e9	−0.530726	−0.265363	−	0.964149i	$-0.585492\pi$
$151$	−3.39052e9	−0.530726	−0.265363	+	0.964149i	$0.585492\pi$
$152$	−7.58443e9	−1.15246
$153$	0	0
$154$	1.36370e10	1.95378
$155$	−1.00389e9	−0.139699
$156$	3.58216e9	0.484266
$157$	−1.49487e10	−1.96360	−0.981802	−	0.189909i	$-0.939181\pi$
$157$	−1.49487e10	−1.96360	−0.981802	+	0.189909i	$0.939181\pi$
$158$	−8.87541e9	−1.13300
$159$	1.07716e8	0.0133657
$160$	3.77001e8	0.0454781
$161$	−1.05172e10	−1.23363
$162$	−2.48103e9	−0.283018
$163$	2.58066e9	0.286343	0.143171	−	0.989698i	$-0.454270\pi$
$163$	2.58066e9	0.286343	0.143171	+	0.989698i	$0.454270\pi$
$164$	−2.50095e9	−0.269965
$165$	2.03954e9	0.214217
$166$	5.81770e9	0.594655
$167$	−5.21438e9	−0.518774	−0.259387	−	0.965773i	$-0.583521\pi$
$167$	−5.21438e9	−0.518774	−0.259387	+	0.965773i	$0.583521\pi$
$168$	−2.69729e10	−2.61238
$169$	5.45500e9	0.514404
$170$	0	0
$171$	1.73856e10	1.55492
$172$	2.50807e9	0.218506
$173$	2.07537e10	1.76152	0.880760	−	0.473562i	$-0.157032\pi$
$173$	2.07537e10	1.76152	0.880760	+	0.473562i	$0.157032\pi$
$174$	−8.24907e9	−0.682234
$175$	1.89194e10	1.52488
$176$	1.28187e10	1.00702
$177$	−4.26147e9	−0.326347
$178$	1.40872e10	1.05181
$179$	−1.53399e10	−1.11682	−0.558411	−	0.829564i	$-0.688589\pi$
$179$	−1.53399e10	−1.11682	−0.558411	+	0.829564i	$0.688589\pi$
$180$	−4.80253e8	−0.0340991
$181$	2.17045e10	1.50313	0.751564	−	0.659660i	$-0.229300\pi$
$181$	2.17045e10	1.50313	0.751564	+	0.659660i	$0.229300\pi$
$182$	−2.42514e10	−1.63838
$183$	2.07735e10	1.36924
$184$	−1.35002e10	−0.868283
$185$	1.99601e9	0.125282
$186$	3.32717e10	2.03829
$187$	0	0
$188$	−5.24860e9	−0.306431
$189$	1.95018e10	1.11172
$190$	1.54011e9	0.0857353
$191$	1.93832e10	1.05384	0.526921	−	0.849914i	$-0.323346\pi$
$191$	1.93832e10	1.05384	0.526921	+	0.849914i	$0.323346\pi$
$192$	−3.27644e10	−1.73999
$193$	−1.51098e10	−0.783884	−0.391942	−	0.919990i	$-0.628197\pi$
$193$	−1.51098e10	−0.783884	−0.391942	+	0.919990i	$0.628197\pi$
$194$	−5.25381e9	−0.266297
$195$	−3.62702e9	−0.179637
$196$	−7.08034e9	−0.342691
$197$	−1.89475e10	−0.896303	−0.448152	−	0.893958i	$-0.647917\pi$
$197$	−1.89475e10	−0.896303	−0.448152	+	0.893958i	$0.647917\pi$
$198$	−4.01260e10	−1.85538
$199$	1.87541e10	0.847730	0.423865	−	0.905725i	$-0.360673\pi$
$199$	1.87541e10	0.847730	0.423865	+	0.905725i	$0.360673\pi$
$200$	2.42856e10	1.07328
$201$	2.86365e10	1.23748
$202$	2.32249e10	0.981461
$203$	−1.87010e10	−0.772917
$204$	0	0
$205$	2.53228e9	0.100143
$206$	3.28364e10	1.27044
$207$	3.09463e10	1.17150
$208$	−2.27962e10	−0.844458
$209$	−4.30898e10	−1.56213
$210$	5.47716e9	0.194343
$211$	−2.18570e10	−0.759137	−0.379568	−	0.925164i	$-0.623927\pi$
$211$	−2.18570e10	−0.759137	−0.379568	+	0.925164i	$0.623927\pi$
$212$	6.28641e7	0.00213743
$213$	−4.18646e10	−1.39360
$214$	−3.93142e10	−1.28141
$215$	−2.53949e9	−0.0810537
$216$	2.50332e10	0.782481
$217$	7.54284e10	2.30922
$218$	3.76347e10	1.12859
$219$	1.76369e10	0.518111
$220$	1.19029e9	0.0342572
$221$	0	0
$222$	−6.61532e10	−1.82794
$223$	3.02105e9	0.0818061	0.0409030	−	0.999163i	$-0.486977\pi$
$223$	3.02105e9	0.0818061	0.0409030	+	0.999163i	$0.486977\pi$
$224$	−2.83263e10	−0.751751
$225$	−5.56693e10	−1.44809
$226$	−2.78284e10	−0.709578
$227$	−4.81313e10	−1.20313	−0.601563	−	0.798825i	$-0.705455\pi$
$227$	−4.81313e10	−1.20313	−0.601563	+	0.798825i	$0.705455\pi$
$228$	1.70925e10	0.418890
$229$	−4.00686e10	−0.962817	−0.481409	−	0.876496i	$-0.659875\pi$
$229$	−4.00686e10	−0.962817	−0.481409	+	0.876496i	$0.659875\pi$
$230$	2.74138e9	0.0645943
$231$	−1.53243e11	−3.54100
$232$	−2.40052e10	−0.544014
$233$	8.39788e9	0.186667	0.0933336	−	0.995635i	$-0.470248\pi$
$233$	8.39788e9	0.186667	0.0933336	+	0.995635i	$0.470248\pi$
$234$	7.13584e10	1.55587
$235$	5.31434e9	0.113669
$236$	−2.48703e9	−0.0521888
$237$	9.97355e10	2.05344
$238$	0	0
$239$	6.01533e9	0.119253	0.0596264	−	0.998221i	$-0.481009\pi$
$239$	6.01533e9	0.119253	0.0596264	+	0.998221i	$0.481009\pi$
$240$	5.14851e9	0.100168
$241$	7.51031e10	1.43411	0.717053	−	0.697018i	$-0.245490\pi$
$241$	7.51031e10	1.43411	0.717053	+	0.697018i	$0.245490\pi$
$242$	5.32717e10	0.998452
$243$	6.71637e10	1.23568
$244$	1.21236e10	0.218967
$245$	7.16902e9	0.127120
$246$	−8.39265e10	−1.46114
$247$	7.66291e10	1.30996
$248$	9.68223e10	1.62533
$249$	−6.53752e10	−1.07774
$250$	−9.90600e9	−0.160387
$251$	6.51989e10	1.03683	0.518416	−	0.855129i	$-0.326522\pi$
$251$	6.51989e10	1.03683	0.518416	+	0.855129i	$0.326522\pi$
$252$	3.60843e10	0.563658
$253$	−7.66997e10	−1.17693
$254$	−4.36138e10	−0.657464
$255$	0	0
$256$	−4.81901e10	−0.701258
$257$	7.68717e10	1.09918	0.549589	−	0.835435i	$-0.314785\pi$
$257$	7.68717e10	1.09918	0.549589	+	0.835435i	$0.314785\pi$
$258$	8.41655e10	1.18262
$259$	−1.49972e11	−2.07091
$260$	−2.11677e9	−0.0287272
$261$	5.50267e10	0.733992
$262$	6.99050e10	0.916542
$263$	8.56612e10	1.10404	0.552018	−	0.833832i	$-0.313858\pi$
$263$	8.56612e10	1.10404	0.552018	+	0.833832i	$0.313858\pi$
$264$	−1.96707e11	−2.49231
$265$	−6.36514e7	−0.000792870 0
$266$	−1.15717e11	−1.41720
$267$	−1.58302e11	−1.90628
$268$	1.67126e10	0.197896
$269$	1.22894e11	1.43102	0.715510	−	0.698602i	$-0.246194\pi$
$269$	1.22894e11	1.43102	0.715510	+	0.698602i	$0.246194\pi$
$270$	−5.08327e9	−0.0582112
$271$	−2.64893e10	−0.298338	−0.149169	−	0.988812i	$-0.547660\pi$
$271$	−2.64893e10	−0.298338	−0.149169	+	0.988812i	$0.547660\pi$
$272$	0	0
$273$	2.72520e11	2.96939
$274$	−3.91571e10	−0.419694
$275$	1.37975e11	1.45480
$276$	3.04246e10	0.315598
$277$	−3.08003e10	−0.314337	−0.157169	−	0.987572i	$-0.550237\pi$
$277$	−3.08003e10	−0.314337	−0.157169	+	0.987572i	$0.550237\pi$
$278$	−5.67638e10	−0.569993
$279$	−2.21944e11	−2.19293
$280$	1.59388e10	0.154969
$281$	1.69421e11	1.62102	0.810512	−	0.585722i	$-0.199189\pi$
$281$	1.69421e11	1.62102	0.810512	+	0.585722i	$0.199189\pi$
$282$	−1.76132e11	−1.65850
$283$	1.15304e11	1.06857	0.534286	−	0.845304i	$-0.320581\pi$
$283$	1.15304e11	1.06857	0.534286	+	0.845304i	$0.320581\pi$
$284$	−2.44326e10	−0.222862
$285$	−1.73066e10	−0.155385
$286$	−1.76860e11	−1.56308
$287$	−1.90265e11	−1.65535
$288$	8.33486e10	0.713892
$289$	0	0
$290$	4.87454e9	0.0404709
$291$	5.90386e10	0.482634
$292$	1.02931e10	0.0828555
$293$	−1.05539e10	−0.0836581	−0.0418290	−	0.999125i	$-0.513318\pi$
$293$	−1.05539e10	−0.0836581	−0.0418290	+	0.999125i	$0.513318\pi$
$294$	−2.37601e11	−1.85475
$295$	2.51818e9	0.0193592
$296$	−1.92509e11	−1.45760
$297$	1.42222e11	1.06063
$298$	−2.00314e11	−1.47142
$299$	1.36399e11	0.986943
$300$	−5.47308e10	−0.390109
$301$	1.90807e11	1.33982
$302$	−6.64023e10	−0.459358
$303$	−2.60985e11	−1.77879
$304$	−1.08774e11	−0.730455
$305$	−1.22755e10	−0.0812249
$306$	0	0
$307$	−7.23530e10	−0.464872	−0.232436	−	0.972612i	$-0.574670\pi$
$307$	−7.23530e10	−0.464872	−0.232436	+	0.972612i	$0.574670\pi$
$308$	−8.94339e10	−0.566271
$309$	−3.68992e11	−2.30252
$310$	−1.96609e10	−0.120914
$311$	−8.82988e10	−0.535221	−0.267610	−	0.963527i	$-0.586234\pi$
$311$	−8.82988e10	−0.535221	−0.267610	+	0.963527i	$0.586234\pi$
$312$	3.49816e11	2.08999
$313$	8.39412e10	0.494340	0.247170	−	0.968972i	$-0.420499\pi$
$313$	8.39412e10	0.494340	0.247170	+	0.968972i	$0.420499\pi$
$314$	−2.92765e11	−1.69956
$315$	−3.65362e10	−0.209087
$316$	5.82067e10	0.328383
$317$	8.95945e10	0.498327	0.249164	−	0.968461i	$-0.419844\pi$
$317$	8.95945e10	0.498327	0.249164	+	0.968461i	$0.419844\pi$
$318$	2.10958e9	0.0115684
$319$	−1.36382e11	−0.737394
$320$	1.93611e10	0.103218
$321$	4.41785e11	2.32240
$322$	−2.05976e11	−1.06774
$323$	0	0
$324$	1.62710e10	0.0820281
$325$	−2.45369e11	−1.21996
$326$	5.05414e10	0.247838
$327$	−4.22912e11	−2.04543
$328$	−2.44230e11	−1.16511
$329$	−3.99298e11	−1.87895
$330$	3.99437e10	0.185411
$331$	−2.83756e11	−1.29933	−0.649664	−	0.760222i	$-0.725090\pi$
$331$	−2.83756e11	−1.29933	−0.649664	+	0.760222i	$0.725090\pi$
$332$	−3.81536e10	−0.172351
$333$	4.41285e11	1.96662
$334$	−1.02122e11	−0.449014
$335$	−1.69219e10	−0.0734086
$336$	−3.86838e11	−1.65578
$337$	3.79770e10	0.160393	0.0801965	−	0.996779i	$-0.474445\pi$
$337$	3.79770e10	0.160393	0.0801965	+	0.996779i	$0.474445\pi$
$338$	1.06834e11	0.445232
$339$	3.12716e11	1.28603
$340$	0	0
$341$	5.50082e11	2.20309
$342$	3.40492e11	1.34583
$343$	−1.44343e11	−0.563081
$344$	2.44926e11	0.943022
$345$	−3.08057e10	−0.117070
$346$	4.06454e11	1.52465
$347$	−2.53157e11	−0.937364	−0.468682	−	0.883367i	$-0.655271\pi$
$347$	−2.53157e11	−0.937364	−0.468682	+	0.883367i	$0.655271\pi$
$348$	5.40990e10	0.197735
$349$	1.41590e10	0.0510880	0.0255440	−	0.999674i	$-0.491868\pi$
$349$	1.41590e10	0.0510880	0.0255440	+	0.999674i	$0.491868\pi$
$350$	3.70531e11	1.31983
$351$	−2.52922e11	−0.889415
$352$	−2.06577e11	−0.717201
$353$	2.27285e11	0.779085	0.389542	−	0.921009i	$-0.372633\pi$
$353$	2.27285e11	0.779085	0.389542	+	0.921009i	$0.372633\pi$
$354$	−8.34595e10	−0.282463
$355$	2.47386e10	0.0826699
$356$	−9.23867e10	−0.304849
$357$	0	0
$358$	−3.00427e11	−0.966642
$359$	−2.15607e10	−0.0685076	−0.0342538	−	0.999413i	$-0.510905\pi$
$359$	−2.15607e10	−0.0685076	−0.0342538	+	0.999413i	$0.510905\pi$
$360$	−4.68991e10	−0.147164
$361$	4.29542e10	0.133114
$362$	4.25076e11	1.30100
$363$	−5.98629e11	−1.80958
$364$	1.59045e11	0.474859
$365$	−1.04220e10	−0.0307349
$366$	4.06843e11	1.18512
$367$	1.34746e11	0.387720	0.193860	−	0.981029i	$-0.437899\pi$
$367$	1.34746e11	0.387720	0.193860	+	0.981029i	$0.437899\pi$
$368$	−1.93617e11	−0.550336
$369$	5.59844e11	1.57199
$370$	3.90912e10	0.108436
$371$	4.78252e9	0.0131061
$372$	−2.18202e11	−0.590766
$373$	−6.32594e10	−0.169214	−0.0846068	−	0.996414i	$-0.526963\pi$
$373$	−6.32594e10	−0.169214	−0.0846068	+	0.996414i	$0.526963\pi$
$374$	0	0
$375$	1.11317e11	0.290683
$376$	−5.12552e11	−1.32249
$377$	2.42536e11	0.618359
$378$	3.81937e11	0.962229
$379$	5.65418e11	1.40764	0.703822	−	0.710376i	$-0.251475\pi$
$379$	5.65418e11	1.40764	0.703822	+	0.710376i	$0.251475\pi$
$380$	−1.01003e10	−0.0248490
$381$	4.90100e11	1.19158
$382$	3.79614e11	0.912130
$383$	−1.03757e11	−0.246391	−0.123196	−	0.992382i	$-0.539314\pi$
$383$	−1.03757e11	−0.246391	−0.123196	+	0.992382i	$0.539314\pi$
$384$	−3.15030e11	−0.739369
$385$	9.05540e10	0.210056
$386$	−2.95921e11	−0.678474
$387$	−5.61439e11	−1.27234
$388$	3.44555e10	0.0771820
$389$	2.18349e11	0.483479	0.241739	−	0.970341i	$-0.422282\pi$
$389$	2.18349e11	0.483479	0.241739	+	0.970341i	$0.422282\pi$
$390$	−7.10341e10	−0.155481
$391$	0	0
$392$	−6.91431e11	−1.47898
$393$	−7.85542e11	−1.66113
$394$	−3.71082e11	−0.775776
$395$	−5.89357e10	−0.121812
$396$	2.63154e11	0.537752
$397$	2.66965e9	0.00539383	0.00269691	−	0.999996i	$-0.499142\pi$
$397$	2.66965e9	0.00539383	0.00269691	+	0.999996i	$0.499142\pi$
$398$	3.67293e11	0.733734
$399$	1.30035e12	2.56852
$400$	3.48297e11	0.680268
$401$	−6.04105e11	−1.16671	−0.583355	−	0.812217i	$-0.698260\pi$
$401$	−6.04105e11	−1.16671	−0.583355	+	0.812217i	$0.698260\pi$
$402$	5.60837e11	1.07107
$403$	−9.78242e11	−1.84745
$404$	−1.52314e11	−0.284461
$405$	−1.64748e10	−0.0304280
$406$	−3.66253e11	−0.668982
$407$	−1.09371e12	−1.97573
$408$	0	0
$409$	−1.23512e11	−0.218250	−0.109125	−	0.994028i	$-0.534805\pi$
$409$	−1.23512e11	−0.218250	−0.109125	+	0.994028i	$0.534805\pi$
$410$	4.95938e10	0.0866763
$411$	4.40019e11	0.760648
$412$	−2.15348e11	−0.368216
$413$	−1.89206e11	−0.320008
$414$	6.06074e11	1.01397
$415$	3.86315e10	0.0639329
$416$	3.67368e11	0.601425
$417$	6.37871e11	1.03305
$418$	−8.43901e11	−1.35207
$419$	1.05297e12	1.66899	0.834496	−	0.551014i	$-0.185759\pi$
$419$	1.05297e12	1.66899	0.834496	+	0.551014i	$0.185759\pi$
$420$	−3.59203e10	−0.0563272
$421$	5.01032e11	0.777313	0.388656	−	0.921383i	$-0.372939\pi$
$421$	5.01032e11	0.777313	0.388656	+	0.921383i	$0.372939\pi$
$422$	−4.28063e11	−0.657055
$423$	1.17491e12	1.78432
$424$	6.13899e9	0.00922467
$425$	0	0
$426$	−8.19904e11	−1.20620
$427$	9.22331e11	1.34265
$428$	2.57830e11	0.371395
$429$	1.98743e12	2.83291
$430$	−4.97350e10	−0.0701543
$431$	1.29815e10	0.0181208	0.00906041	−	0.999959i	$-0.497116\pi$
$431$	1.29815e10	0.0181208	0.00906041	+	0.999959i	$0.497116\pi$
$432$	3.59019e11	0.495953
$433$	−4.46092e11	−0.609859	−0.304929	−	0.952375i	$-0.598633\pi$
$433$	−4.46092e11	−0.609859	−0.304929	+	0.952375i	$0.598633\pi$
$434$	1.47724e12	1.99870
$435$	−5.47766e10	−0.0733488
$436$	−2.46816e11	−0.327102
$437$	6.50840e11	0.853705
$438$	3.45412e11	0.448440
$439$	−1.26258e11	−0.162244	−0.0811218	−	0.996704i	$-0.525850\pi$
$439$	−1.26258e11	−0.162244	−0.0811218	+	0.996704i	$0.525850\pi$
$440$	1.16238e11	0.147847
$441$	1.58495e12	1.99546
$442$	0	0
$443$	−1.10374e12	−1.36160	−0.680801	−	0.732468i	$-0.738368\pi$
$443$	−1.10374e12	−1.36160	−0.680801	+	0.732468i	$0.738368\pi$
$444$	4.33846e11	0.529800
$445$	9.35438e10	0.113082
$446$	5.91662e10	0.0708055
$447$	2.25098e12	2.66679
$448$	−1.45472e12	−1.70619
$449$	7.22088e11	0.838459	0.419229	−	0.907880i	$-0.362300\pi$
$449$	7.22088e11	0.838459	0.419229	+	0.907880i	$0.362300\pi$
$450$	−1.09027e12	−1.25336
$451$	−1.38756e12	−1.57927
$452$	1.82504e11	0.205660
$453$	7.46181e11	0.832535
$454$	−9.42636e11	−1.04134
$455$	−1.61037e11	−0.176147
$456$	1.66917e12	1.80784
$457$	−2.66380e11	−0.285679	−0.142840	−	0.989746i	$-0.545623\pi$
$457$	−2.66380e11	−0.285679	−0.142840	+	0.989746i	$0.545623\pi$
$458$	−7.84730e11	−0.833346
$459$	0	0
$460$	−1.79785e10	−0.0187216
$461$	1.13987e11	0.117544	0.0587718	−	0.998271i	$-0.481282\pi$
$461$	1.13987e11	0.117544	0.0587718	+	0.998271i	$0.481282\pi$
$462$	−3.00121e12	−3.06484
$463$	1.41507e12	1.43108	0.715538	−	0.698574i	$-0.246182\pi$
$463$	1.41507e12	1.43108	0.715538	+	0.698574i	$0.246182\pi$
$464$	−3.44277e11	−0.344807
$465$	2.20935e11	0.219142
$466$	1.64470e11	0.161566
$467$	7.79171e11	0.758066	0.379033	−	0.925383i	$-0.376257\pi$
$467$	7.79171e11	0.758066	0.379033	+	0.925383i	$0.376257\pi$
$468$	−4.67982e11	−0.450945
$469$	1.27144e12	1.21344
$470$	1.04080e11	0.0983842
$471$	3.28988e12	3.08025
$472$	−2.42871e11	−0.225236
$473$	1.39151e12	1.27824
$474$	1.95329e12	1.77731
$475$	−1.17080e12	−1.05526
$476$	0	0
$477$	−1.40723e10	−0.0124461
$478$	1.17808e11	0.103217
$479$	−6.94378e11	−0.602679	−0.301339	−	0.953517i	$-0.597434\pi$
$479$	−6.94378e11	−0.602679	−0.301339	+	0.953517i	$0.597434\pi$
$480$	−8.29698e10	−0.0713402
$481$	1.94501e12	1.65680
$482$	1.47087e12	1.24126
$483$	2.31462e12	1.93516
$484$	−3.49366e11	−0.289385
$485$	−3.48870e10	−0.0286303
$486$	1.31538e12	1.06952
$487$	4.59496e11	0.370171	0.185085	−	0.982722i	$-0.440744\pi$
$487$	4.59496e11	0.370171	0.185085	+	0.982722i	$0.440744\pi$
$488$	1.18393e12	0.945014
$489$	−5.67948e11	−0.449178
$490$	1.40403e11	0.110026
$491$	−2.13503e12	−1.65782	−0.828911	−	0.559381i	$-0.811039\pi$
$491$	−2.13503e12	−1.65782	−0.828911	+	0.559381i	$0.811039\pi$
$492$	5.50406e11	0.423487
$493$	0	0
$494$	1.50076e12	1.13381
$495$	−2.66450e11	−0.199477
$496$	1.38860e12	1.03017
$497$	−1.85876e12	−1.36653
$498$	−1.28035e12	−0.932819
$499$	−1.50477e12	−1.08647	−0.543234	−	0.839581i	$-0.682801\pi$
$499$	−1.50477e12	−1.08647	−0.543234	+	0.839581i	$0.682801\pi$
$500$	6.49655e10	0.0464855
$501$	1.14757e12	0.813787
$502$	1.27690e12	0.897408
$503$	−1.44460e12	−1.00622	−0.503109	−	0.864223i	$-0.667811\pi$
$503$	−1.44460e12	−1.00622	−0.503109	+	0.864223i	$0.667811\pi$
$504$	3.52381e12	2.43262
$505$	1.54221e11	0.105519
$506$	−1.50214e12	−1.01867
$507$	−1.20053e12	−0.806932
$508$	2.86027e11	0.190555
$509$	1.23179e12	0.813404	0.406702	−	0.913561i	$-0.366679\pi$
$509$	1.23179e12	0.813404	0.406702	+	0.913561i	$0.366679\pi$
$510$	0	0
$511$	7.83065e11	0.508047
$512$	−1.67669e12	−1.07829
$513$	−1.20684e12	−0.769344
$514$	1.50551e12	0.951370
$515$	2.18045e11	0.136588
$516$	−5.51974e11	−0.342764
$517$	−2.91199e12	−1.79260
$518$	−2.93716e12	−1.79244
$519$	−4.56745e12	−2.76325
$520$	−2.06713e11	−0.123980
$521$	−1.08435e12	−0.644761	−0.322380	−	0.946610i	$-0.604483\pi$
$521$	−1.08435e12	−0.644761	−0.322380	+	0.946610i	$0.604483\pi$
$522$	1.07768e12	0.635291
$523$	−1.91259e12	−1.11780	−0.558899	−	0.829236i	$-0.688776\pi$
$523$	−1.91259e12	−1.11780	−0.558899	+	0.829236i	$0.688776\pi$
$524$	−4.58450e11	−0.265645
$525$	−4.16376e12	−2.39204
$526$	1.67765e12	0.955576
$527$	0	0
$528$	−2.82112e12	−1.57968
$529$	−6.42661e11	−0.356806
$530$	−1.24659e9	−0.000686252 0
$531$	5.56729e11	0.303891
$532$	7.58898e11	0.410753
$533$	2.46758e12	1.32434
$534$	−3.10030e12	−1.64994
$535$	−2.61059e11	−0.137767
$536$	1.63206e12	0.854074
$537$	3.37599e12	1.75193
$538$	2.40684e12	1.23859
$539$	−3.92826e12	−2.00471
$540$	3.33371e10	0.0168716
$541$	2.15523e12	1.08170	0.540850	−	0.841119i	$-0.318103\pi$
$541$	2.15523e12	1.08170	0.540850	+	0.841119i	$0.318103\pi$
$542$	−5.18784e11	−0.258220
$543$	−4.77670e12	−2.35792
$544$	0	0
$545$	2.49907e11	0.121337
$546$	5.33722e12	2.57009
$547$	−7.09837e10	−0.0339013	−0.0169506	−	0.999856i	$-0.505396\pi$
$547$	−7.09837e10	−0.0339013	−0.0169506	+	0.999856i	$0.505396\pi$
$548$	2.56800e11	0.121642
$549$	−2.71391e12	−1.27503
$550$	2.70219e12	1.25917
$551$	1.15728e12	0.534880
$552$	2.97112e12	1.36205
$553$	4.42819e12	2.01355
$554$	−6.03214e11	−0.272068
$555$	−4.39279e11	−0.196527
$556$	3.72268e11	0.165203
$557$	−6.52747e11	−0.287340	−0.143670	−	0.989626i	$-0.545890\pi$
$557$	−6.52747e11	−0.287340	−0.143670	+	0.989626i	$0.545890\pi$
$558$	−4.34670e12	−1.89804
$559$	−2.47460e12	−1.07190
$560$	2.28590e11	0.0982226
$561$	0	0
$562$	3.31806e12	1.40304
$563$	−1.22765e12	−0.514977	−0.257488	−	0.966281i	$-0.582895\pi$
$563$	−1.22765e12	−0.514977	−0.257488	+	0.966281i	$0.582895\pi$
$564$	1.15511e12	0.480691
$565$	−1.84790e11	−0.0762886
$566$	2.25818e12	0.924880
$567$	1.23785e12	0.502974
$568$	−2.38596e12	−0.961825
$569$	−6.00953e11	−0.240345	−0.120173	−	0.992753i	$-0.538345\pi$
$569$	−6.00953e11	−0.240345	−0.120173	+	0.992753i	$0.538345\pi$
$570$	−3.38945e11	−0.134491
$571$	−2.49531e12	−0.982339	−0.491170	−	0.871064i	$-0.663430\pi$
$571$	−2.49531e12	−0.982339	−0.491170	+	0.871064i	$0.663430\pi$
$572$	1.15988e12	0.453035
$573$	−4.26583e12	−1.65313
$574$	−3.72628e12	−1.43276
$575$	−2.08401e12	−0.795049
$576$	4.28043e12	1.62026
$577$	−2.87670e12	−1.08045	−0.540223	−	0.841522i	$-0.681660\pi$
$577$	−2.87670e12	−1.08045	−0.540223	+	0.841522i	$0.681660\pi$
$578$	0	0
$579$	3.32535e12	1.22966
$580$	−3.19682e10	−0.0117298
$581$	−2.90261e12	−1.05681
$582$	1.15625e12	0.417733
$583$	3.48778e10	0.0125038
$584$	1.00517e12	0.357586
$585$	4.73844e11	0.167276
$586$	−2.06694e11	−0.0724085
$587$	−2.45305e12	−0.852777	−0.426388	−	0.904540i	$-0.640214\pi$
$587$	−2.45305e12	−0.852777	−0.426388	+	0.904540i	$0.640214\pi$
$588$	1.55823e12	0.537569
$589$	−4.66776e12	−1.59805
$590$	4.93178e10	0.0167560
$591$	4.16995e12	1.40601
$592$	−2.76092e12	−0.923859
$593$	−2.15859e12	−0.716841	−0.358421	−	0.933560i	$-0.616685\pi$
$593$	−2.15859e12	−0.716841	−0.358421	+	0.933560i	$0.616685\pi$
$594$	2.78538e12	0.918005
$595$	0	0
$596$	1.31370e12	0.426469
$597$	−4.12738e12	−1.32981
$598$	2.67134e12	0.854228
$599$	−3.31263e12	−1.05136	−0.525680	−	0.850682i	$-0.676189\pi$
$599$	−3.31263e12	−1.05136	−0.525680	+	0.850682i	$0.676189\pi$
$600$	−5.34473e12	−1.68363
$601$	−4.10617e12	−1.28381	−0.641906	−	0.766783i	$-0.721856\pi$
$601$	−4.10617e12	−1.28381	−0.641906	+	0.766783i	$0.721856\pi$
$602$	3.73689e12	1.15965
$603$	−3.74115e12	−1.15233
$604$	4.35479e11	0.133138
$605$	3.53742e11	0.107346
$606$	−5.11131e12	−1.53959
$607$	3.99884e12	1.19560	0.597799	−	0.801646i	$-0.296042\pi$
$607$	3.99884e12	1.19560	0.597799	+	0.801646i	$0.296042\pi$
$608$	1.75293e12	0.520233
$609$	4.11569e12	1.21245
$610$	−2.40411e11	−0.0703025
$611$	5.17856e12	1.50322
$612$	0	0
$613$	−5.51148e12	−1.57651	−0.788254	−	0.615350i	$-0.789015\pi$
$613$	−5.51148e12	−1.57651	−0.788254	+	0.615350i	$0.789015\pi$
$614$	−1.41701e12	−0.402360
$615$	−5.57300e11	−0.157091
$616$	−8.73367e12	−2.44390
$617$	4.10732e12	1.14097	0.570486	−	0.821307i	$-0.306755\pi$
$617$	4.10732e12	1.14097	0.570486	+	0.821307i	$0.306755\pi$
$618$	−7.22660e12	−1.99290
$619$	−2.66297e12	−0.729052	−0.364526	−	0.931193i	$-0.618769\pi$
$619$	−2.66297e12	−0.729052	−0.364526	+	0.931193i	$0.618769\pi$
$620$	1.28940e11	0.0350449
$621$	−2.14816e12	−0.579635
$622$	−1.72930e12	−0.463249
$623$	−7.02851e12	−1.86925
$624$	5.01696e12	1.32468
$625$	3.71589e12	0.974097
$626$	1.64396e12	0.427866
$627$	9.48316e12	2.45047
$628$	1.92001e12	0.492589
$629$	0	0
$630$	−7.15550e11	−0.180970
$631$	−2.98865e12	−0.750486	−0.375243	−	0.926927i	$-0.622441\pi$
$631$	−2.98865e12	−0.750486	−0.375243	+	0.926927i	$0.622441\pi$
$632$	5.68417e12	1.41723
$633$	4.81027e12	1.19084
$634$	1.75468e12	0.431317
$635$	−2.89610e11	−0.0706857
$636$	−1.38351e10	−0.00335292
$637$	6.98586e12	1.68109
$638$	−2.67100e12	−0.638236
$639$	5.46929e12	1.29771
$640$	1.86157e11	0.0438601
$641$	−4.15467e12	−0.972020	−0.486010	−	0.873953i	$-0.661548\pi$
$641$	−4.15467e12	−0.972020	−0.486010	+	0.873953i	$0.661548\pi$
$642$	8.65221e12	2.01011
$643$	4.20371e12	0.969802	0.484901	−	0.874569i	$-0.338856\pi$
$643$	4.20371e12	0.969802	0.484901	+	0.874569i	$0.338856\pi$
$644$	1.35083e12	0.309468
$645$	5.58887e11	0.127147
$646$	0	0
$647$	−1.62658e12	−0.364927	−0.182463	−	0.983213i	$-0.558407\pi$
$647$	−1.62658e12	−0.364927	−0.182463	+	0.983213i	$0.558407\pi$
$648$	1.58895e12	0.354015
$649$	−1.37984e12	−0.305300
$650$	−4.80547e12	−1.05591
$651$	−1.66002e13	−3.62242
$652$	−3.31460e11	−0.0718318
$653$	3.12868e12	0.673366	0.336683	−	0.941618i	$-0.390695\pi$
$653$	3.12868e12	0.673366	0.336683	+	0.941618i	$0.390695\pi$
$654$	−8.28260e12	−1.77038
$655$	4.64192e11	0.0985398
$656$	−3.50269e12	−0.738472
$657$	−2.30413e12	−0.482461
$658$	−7.82013e12	−1.62629
$659$	−6.29602e12	−1.30041	−0.650207	−	0.759757i	$-0.725318\pi$
$659$	−6.29602e12	−1.30041	−0.650207	+	0.759757i	$0.725318\pi$
$660$	−2.61958e11	−0.0537384
$661$	5.35726e12	1.09153	0.545766	−	0.837938i	$-0.316239\pi$
$661$	5.35726e12	1.09153	0.545766	+	0.837938i	$0.316239\pi$
$662$	−5.55727e12	−1.12461
$663$	0	0
$664$	−3.72589e12	−0.743830
$665$	−7.68402e11	−0.152367
$666$	8.64243e12	1.70217
$667$	2.05995e12	0.402987
$668$	6.69736e11	0.130140
$669$	−6.64868e11	−0.128327
$670$	−3.31410e11	−0.0635372
$671$	6.72635e12	1.28094
$672$	6.23402e12	1.17925
$673$	−4.82131e12	−0.905935	−0.452968	−	0.891527i	$-0.649635\pi$
$673$	−4.82131e12	−0.905935	−0.452968	+	0.891527i	$0.649635\pi$
$674$	7.43767e11	0.138825
$675$	3.86432e12	0.716484
$676$	−7.00641e11	−0.129043
$677$	−3.90335e12	−0.714149	−0.357074	−	0.934076i	$-0.616226\pi$
$677$	−3.90335e12	−0.714149	−0.357074	+	0.934076i	$0.616226\pi$
$678$	6.12444e12	1.11310
$679$	2.62127e12	0.473258
$680$	0	0
$681$	1.05927e13	1.88731
$682$	1.07732e13	1.90684
$683$	4.33110e12	0.761561	0.380781	−	0.924665i	$-0.375655\pi$
$683$	4.33110e12	0.761561	0.380781	+	0.924665i	$0.375655\pi$
$684$	−2.23301e12	−0.390067
$685$	−2.60016e11	−0.0451224
$686$	−2.82691e12	−0.487363
$687$	8.81824e12	1.51035
$688$	3.51266e12	0.597707
$689$	−6.20252e10	−0.0104853
$690$	−6.03319e11	−0.101327
$691$	−1.03878e13	−1.73329	−0.866646	−	0.498923i	$-0.833729\pi$
$691$	−1.03878e13	−1.73329	−0.866646	+	0.498923i	$0.833729\pi$
$692$	−2.66561e12	−0.441895
$693$	2.00200e13	3.29735
$694$	−4.95801e12	−0.811315
$695$	−3.76930e11	−0.0612815
$696$	5.28304e12	0.853379
$697$	0	0
$698$	2.77300e11	0.0442181
$699$	−1.84819e12	−0.292820
$700$	−2.43001e12	−0.382531
$701$	−2.88822e12	−0.451752	−0.225876	−	0.974156i	$-0.572524\pi$
$701$	−2.88822e12	−0.451752	−0.225876	+	0.974156i	$0.572524\pi$
$702$	−4.95340e12	−0.769815
$703$	9.28078e12	1.43313
$704$	−1.06089e13	−1.62778
$705$	−1.16957e12	−0.178310
$706$	4.45131e12	0.674320
$707$	−1.15876e13	−1.74423
$708$	5.47343e11	0.0818672
$709$	−6.02354e12	−0.895249	−0.447624	−	0.894222i	$-0.647730\pi$
$709$	−6.02354e12	−0.895249	−0.447624	+	0.894222i	$0.647730\pi$
$710$	4.84497e11	0.0715532
$711$	−1.30297e13	−1.91215
$712$	−9.02202e12	−1.31566
$713$	−8.30857e12	−1.20399
$714$	0	0
$715$	−1.17441e12	−0.168051
$716$	1.97026e12	0.280166
$717$	−1.32385e12	−0.187069
$718$	−4.22260e11	−0.0592953
$719$	3.75893e12	0.524547	0.262274	−	0.964994i	$-0.415528\pi$
$719$	3.75893e12	0.524547	0.262274	+	0.964994i	$0.415528\pi$
$720$	−6.72614e11	−0.0932759
$721$	−1.63830e13	−2.25780
$722$	8.41244e11	0.115214
$723$	−1.65286e13	−2.24964
$724$	−2.78773e12	−0.377074
$725$	−3.70564e12	−0.498130
$726$	−1.17240e13	−1.56624
$727$	9.68647e12	1.28606	0.643029	−	0.765841i	$-0.277677\pi$
$727$	9.68647e12	1.28606	0.643029	+	0.765841i	$0.277677\pi$
$728$	1.55316e13	2.04939
$729$	−1.22878e13	−1.61139
$730$	−2.04111e11	−0.0266019
$731$	0	0
$732$	−2.66816e12	−0.343488
$733$	−2.52987e12	−0.323691	−0.161845	−	0.986816i	$-0.551745\pi$
$733$	−2.52987e12	−0.323691	−0.161845	+	0.986816i	$0.551745\pi$
$734$	2.63896e12	0.335583
$735$	−1.57775e12	−0.199409
$736$	3.12020e12	0.391951
$737$	9.27234e12	1.15767
$738$	1.09644e13	1.36060
$739$	−1.04522e13	−1.28916	−0.644579	−	0.764538i	$-0.722967\pi$
$739$	−1.04522e13	−1.28916	−0.644579	+	0.764538i	$0.722967\pi$
$740$	−2.56368e11	−0.0314283
$741$	−1.68644e13	−2.05490
$742$	9.36641e10	0.0113437
$743$	2.07330e12	0.249582	0.124791	−	0.992183i	$-0.460174\pi$
$743$	2.07330e12	0.249582	0.124791	+	0.992183i	$0.460174\pi$
$744$	−2.13085e13	−2.54962
$745$	−1.33015e12	−0.158197
$746$	−1.23892e12	−0.146459
$747$	8.54078e12	1.00359
$748$	0	0
$749$	1.96149e13	2.27729
$750$	2.18010e12	0.251594
$751$	7.54749e12	0.865811	0.432905	−	0.901439i	$-0.357488\pi$
$751$	7.54749e12	0.865811	0.432905	+	0.901439i	$0.357488\pi$
$752$	−7.35088e12	−0.838222
$753$	−1.43489e13	−1.62645
$754$	4.75000e12	0.535207
$755$	−4.40933e11	−0.0493869
$756$	−2.50482e12	−0.278887
$757$	3.67976e12	0.407276	0.203638	−	0.979046i	$-0.434723\pi$
$757$	3.67976e12	0.407276	0.203638	+	0.979046i	$0.434723\pi$
$758$	1.10735e13	1.21836
$759$	1.68800e13	1.84622
$760$	−9.86346e11	−0.107243
$761$	−5.86789e12	−0.634236	−0.317118	−	0.948386i	$-0.602715\pi$
$761$	−5.86789e12	−0.634236	−0.317118	+	0.948386i	$0.602715\pi$
$762$	9.59846e12	1.03135
$763$	−1.87770e13	−2.00570
$764$	−2.48958e12	−0.264366
$765$	0	0
$766$	−2.03206e12	−0.213259
$767$	2.45384e12	0.256016
$768$	1.06056e13	1.10005
$769$	3.89763e12	0.401913	0.200956	−	0.979600i	$-0.435595\pi$
$769$	3.89763e12	0.401913	0.200956	+	0.979600i	$0.435595\pi$
$770$	1.77347e12	0.181809
$771$	−1.69178e13	−1.72425
$772$	1.94071e12	0.196645
$773$	7.44642e12	0.750135	0.375068	−	0.926997i	$-0.377619\pi$
$773$	7.44642e12	0.750135	0.375068	+	0.926997i	$0.377619\pi$
$774$	−1.09956e13	−1.10125
$775$	1.49463e13	1.48825
$776$	3.36475e12	0.333100
$777$	3.30057e13	3.24859
$778$	4.27629e12	0.418465
$779$	1.17742e13	1.14555
$780$	4.65855e11	0.0450636
$781$	−1.35555e13	−1.30372
$782$	0	0
$783$	−3.81972e12	−0.363164
$784$	−9.91632e12	−0.937407
$785$	−1.94405e12	−0.182724
$786$	−1.53846e13	−1.43775
$787$	1.57052e13	1.45935	0.729673	−	0.683796i	$-0.239672\pi$
$787$	1.57052e13	1.45935	0.729673	+	0.683796i	$0.239672\pi$
$788$	2.43363e12	0.224846
$789$	−1.88522e13	−1.73187
$790$	−1.15424e12	−0.105432
$791$	1.38844e13	1.26105
$792$	2.56983e13	2.32082
$793$	−1.19618e13	−1.07416
$794$	5.22843e10	0.00466851
$795$	1.40083e10	0.00124375
$796$	−2.40878e12	−0.212661
$797$	7.79223e12	0.684068	0.342034	−	0.939688i	$-0.388884\pi$
$797$	7.79223e12	0.684068	0.342034	+	0.939688i	$0.388884\pi$
$798$	2.54670e13	2.22313
$799$	0	0
$800$	−5.61292e12	−0.484489
$801$	2.06810e13	1.77511
$802$	−1.18312e13	−1.00982
$803$	5.71071e12	0.484697
$804$	−3.67808e12	−0.310434
$805$	−1.36775e12	−0.114796
$806$	−1.91586e13	−1.59902
$807$	−2.70464e13	−2.24480
$808$	−1.48742e13	−1.22767
$809$	6.21234e12	0.509902	0.254951	−	0.966954i	$-0.417941\pi$
$809$	6.21234e12	0.509902	0.254951	+	0.966954i	$0.417941\pi$
$810$	−3.22654e11	−0.0263363
$811$	1.28983e13	1.04698	0.523488	−	0.852033i	$-0.324630\pi$
$811$	1.28983e13	1.04698	0.523488	+	0.852033i	$0.324630\pi$
$812$	2.40196e12	0.193894
$813$	5.82972e12	0.467994
$814$	−2.14200e13	−1.71006
$815$	3.35611e11	0.0266457
$816$	0	0
$817$	−1.18078e13	−0.927189
$818$	−2.41894e12	−0.188901
$819$	−3.56027e13	−2.76507
$820$	−3.25246e11	−0.0251217
$821$	−1.48692e13	−1.14221	−0.571103	−	0.820878i	$-0.693484\pi$
$821$	−1.48692e13	−1.14221	−0.571103	+	0.820878i	$0.693484\pi$
$822$	8.61764e12	0.658363
$823$	1.65419e13	1.25686	0.628429	−	0.777867i	$-0.283698\pi$
$823$	1.65419e13	1.25686	0.628429	+	0.777867i	$0.283698\pi$
$824$	−2.10298e13	−1.58914
$825$	−3.03653e13	−2.28210
$826$	−3.70554e12	−0.276976
$827$	6.35336e12	0.472312	0.236156	−	0.971715i	$-0.424112\pi$
$827$	6.35336e12	0.472312	0.236156	+	0.971715i	$0.424112\pi$
$828$	−3.97475e12	−0.293882
$829$	−9.20903e12	−0.677203	−0.338601	−	0.940930i	$-0.609954\pi$
$829$	−9.20903e12	−0.677203	−0.338601	+	0.940930i	$0.609954\pi$
$830$	7.56585e11	0.0553358
$831$	6.77849e12	0.493093
$832$	1.88665e13	1.36501
$833$	0	0
$834$	1.24925e13	0.894133
$835$	−6.78124e11	−0.0482747
$836$	5.53447e12	0.391875
$837$	1.54064e13	1.08502
$838$	2.06222e13	1.44456
$839$	−4.07347e12	−0.283815	−0.141907	−	0.989880i	$-0.545324\pi$
$839$	−4.07347e12	−0.283815	−0.141907	+	0.989880i	$0.545324\pi$
$840$	−3.50779e12	−0.243096
$841$	−1.08443e13	−0.747513
$842$	9.81255e12	0.672787
$843$	−3.72860e13	−2.54286
$844$	2.80732e12	0.190437
$845$	7.09416e11	0.0478681
$846$	2.30103e13	1.54438
$847$	−2.65787e13	−1.77443
$848$	8.80438e10	0.00584679
$849$	−2.53759e13	−1.67624
$850$	0	0
$851$	1.65197e13	1.07974
$852$	5.37709e12	0.349598
$853$	−9.92297e12	−0.641758	−0.320879	−	0.947120i	$-0.603978\pi$
$853$	−9.92297e12	−0.641758	−0.320879	+	0.947120i	$0.603978\pi$
$854$	1.80636e13	1.16210
$855$	2.26098e12	0.144694
$856$	2.51784e13	1.60286
$857$	7.30125e12	0.462363	0.231182	−	0.972911i	$-0.425741\pi$
$857$	7.30125e12	0.462363	0.231182	+	0.972911i	$0.425741\pi$
$858$	3.89231e13	2.45197
$859$	1.34564e13	0.843254	0.421627	−	0.906769i	$-0.361459\pi$
$859$	1.34564e13	0.843254	0.421627	+	0.906769i	$0.361459\pi$
$860$	3.26172e11	0.0203331
$861$	4.18733e13	2.59671
$862$	2.54239e11	0.0156841
$863$	−2.00180e13	−1.22849	−0.614247	−	0.789114i	$-0.710540\pi$
$863$	−2.00180e13	−1.22849	−0.614247	+	0.789114i	$0.710540\pi$
$864$	−5.78571e12	−0.353219
$865$	2.69899e12	0.163919
$866$	−8.73658e12	−0.527850
$867$	0	0
$868$	−9.68803e12	−0.579291
$869$	3.22938e13	1.92101
$870$	−1.07278e12	−0.0634855
$871$	−1.64895e13	−0.970793
$872$	−2.41028e13	−1.41170
$873$	−7.71295e12	−0.449424
$874$	1.27465e13	0.738906
$875$	4.94238e12	0.285036
$876$	−2.26528e12	−0.129973
$877$	−5.42206e12	−0.309504	−0.154752	−	0.987953i	$-0.549458\pi$
$877$	−5.42206e12	−0.309504	−0.154752	+	0.987953i	$0.549458\pi$
$878$	−2.47272e12	−0.140426
$879$	2.32269e12	0.131232
$880$	1.66706e12	0.0937083
$881$	−5.00837e12	−0.280095	−0.140047	−	0.990145i	$-0.544725\pi$
$881$	−5.00837e12	−0.280095	−0.140047	+	0.990145i	$0.544725\pi$
$882$	3.10408e13	1.72713
$883$	9.14629e12	0.506316	0.253158	−	0.967425i	$-0.418531\pi$
$883$	9.14629e12	0.506316	0.253158	+	0.967425i	$0.418531\pi$
$884$	0	0
$885$	−5.54198e11	−0.0303683
$886$	−2.16164e13	−1.17851
$887$	−6.90655e12	−0.374632	−0.187316	−	0.982300i	$-0.559979\pi$
$887$	−6.90655e12	−0.374632	−0.187316	+	0.982300i	$0.559979\pi$
$888$	4.23672e13	2.28650
$889$	2.17601e13	1.16843
$890$	1.83203e12	0.0978761
$891$	9.02738e12	0.479857
$892$	−3.88024e11	−0.0205218
$893$	2.47099e13	1.30029
$894$	4.40848e13	2.30818
$895$	−1.99494e12	−0.103926
$896$	−1.39871e13	−0.725007
$897$	−3.00186e13	−1.54819
$898$	1.41419e13	0.725710
$899$	−1.47737e13	−0.754349
$900$	7.15017e12	0.363266
$901$	0	0
$902$	−2.71749e13	−1.36691
$903$	−4.19925e13	−2.10173
$904$	1.78224e13	0.887583
$905$	2.82264e12	0.139874
$906$	1.46137e13	0.720583
$907$	−3.23902e13	−1.58921	−0.794604	−	0.607128i	$-0.792321\pi$
$907$	−3.23902e13	−1.58921	−0.794604	+	0.607128i	$0.792321\pi$
$908$	6.18199e12	0.301816
$909$	3.40958e13	1.65639
$910$	−3.15387e12	−0.152460
$911$	−3.75724e13	−1.80732	−0.903662	−	0.428246i	$-0.859132\pi$
$911$	−3.75724e13	−1.80732	−0.903662	+	0.428246i	$0.859132\pi$
$912$	2.39388e13	1.14585
$913$	−2.11681e13	−1.00824
$914$	−5.21697e12	−0.247264
$915$	2.70157e12	0.127415
$916$	5.14641e12	0.241532
$917$	−3.48775e13	−1.62886
$918$	0	0
$919$	1.23759e12	0.0572343	0.0286172	−	0.999590i	$-0.490890\pi$
$919$	1.23759e12	0.0572343	0.0286172	+	0.999590i	$0.490890\pi$
$920$	−1.75569e12	−0.0807984
$921$	1.59233e13	0.729232
$922$	2.23239e12	0.101737
$923$	2.41065e13	1.09327
$924$	1.96825e13	0.888294
$925$	−2.97173e13	−1.33466
$926$	2.77136e13	1.23864
$927$	4.82061e13	2.14409
$928$	5.54813e12	0.245573
$929$	−3.05199e13	−1.34435	−0.672175	−	0.740393i	$-0.734640\pi$
$929$	−3.05199e13	−1.34435	−0.672175	+	0.740393i	$0.734640\pi$
$930$	4.32694e12	0.189674
$931$	3.33336e13	1.45415
$932$	−1.07862e12	−0.0468273
$933$	1.94327e13	0.839586
$934$	1.52598e13	0.656128
$935$	0	0
$936$	−4.57008e13	−1.94618
$937$	3.94116e12	0.167030	0.0835152	−	0.996507i	$-0.473385\pi$
$937$	3.94116e12	0.167030	0.0835152	+	0.996507i	$0.473385\pi$
$938$	2.49008e13	1.05027
$939$	−1.84737e13	−0.775458
$940$	−6.82574e11	−0.0285151
$941$	−3.24583e13	−1.34950	−0.674750	−	0.738046i	$-0.735749\pi$
$941$	−3.24583e13	−1.34950	−0.674750	+	0.738046i	$0.735749\pi$
$942$	6.44313e13	2.66605
$943$	2.09581e13	0.863075
$944$	−3.48319e12	−0.142759
$945$	2.53619e12	0.103452
$946$	2.72523e13	1.10635
$947$	−1.58799e13	−0.641611	−0.320806	−	0.947145i	$-0.603954\pi$
$947$	−1.58799e13	−0.641611	−0.320806	+	0.947145i	$0.603954\pi$
$948$	−1.28100e13	−0.515126
$949$	−1.01557e13	−0.406454
$950$	−2.29297e13	−0.913359
$951$	−1.97178e13	−0.781713
$952$	0	0
$953$	−1.20490e13	−0.473188	−0.236594	−	0.971609i	$-0.576031\pi$
$953$	−1.20490e13	−0.473188	−0.236594	+	0.971609i	$0.576031\pi$
$954$	−2.75601e11	−0.0107724
$955$	2.52076e12	0.0980656
$956$	−7.72609e11	−0.0299157
$957$	3.00148e13	1.15673
$958$	−1.35992e13	−0.521636
$959$	1.95366e13	0.745872
$960$	−4.26097e12	−0.161915
$961$	3.31486e13	1.25375
$962$	3.80925e13	1.43401
$963$	−5.77159e13	−2.16260
$964$	−9.64626e12	−0.359759
$965$	−1.96502e12	−0.0729446
$966$	4.53310e13	1.67494
$967$	−2.33579e12	−0.0859044	−0.0429522	−	0.999077i	$-0.513676\pi$
$967$	−2.33579e12	−0.0859044	−0.0429522	+	0.999077i	$0.513676\pi$
$968$	−3.41173e13	−1.24892
$969$	0	0
$970$	−6.83252e11	−0.0247804
$971$	−4.77817e13	−1.72494	−0.862471	−	0.506106i	$-0.831085\pi$
$971$	−4.77817e13	−1.72494	−0.862471	+	0.506106i	$0.831085\pi$
$972$	−8.62651e12	−0.309982
$973$	2.83210e13	1.01298
$974$	8.99909e12	0.320393
$975$	5.40004e13	1.91371
$976$	1.69797e13	0.598970
$977$	1.26420e13	0.443905	0.221952	−	0.975057i	$-0.428757\pi$
$977$	1.26420e13	0.443905	0.221952	+	0.975057i	$0.428757\pi$
$978$	−1.11231e13	−0.388777
$979$	−5.12573e13	−1.78334
$980$	−9.20790e11	−0.0318892
$981$	5.52503e13	1.90469
$982$	−4.18139e13	−1.43489
$983$	1.21089e13	0.413633	0.206817	−	0.978380i	$-0.433690\pi$
$983$	1.21089e13	0.413633	0.206817	+	0.978380i	$0.433690\pi$
$984$	5.37499e13	1.82768
$985$	−2.46410e12	−0.0834058
$986$	0	0
$987$	8.78770e13	2.94746
$988$	−9.84226e12	−0.328616
$989$	−2.10177e13	−0.698558
$990$	−5.21834e12	−0.172653
$991$	1.14838e13	0.378228	0.189114	−	0.981955i	$-0.439438\pi$
$991$	1.14838e13	0.378228	0.189114	+	0.981955i	$0.439438\pi$
$992$	−2.23777e13	−0.733691
$993$	6.24486e13	2.03822
$994$	−3.64032e13	−1.18277
$995$	2.43895e12	0.0788858
$996$	8.39680e12	0.270363
$997$	1.48822e13	0.477021	0.238511	−	0.971140i	$-0.423341\pi$
$997$	1.48822e13	0.477021	0.238511	+	0.971140i	$0.423341\pi$
$998$	−2.94704e13	−0.940370
$999$	−3.06321e13	−0.973044

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.26	✓	36
17.16	even	2		289.10.a.h.1.26	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.26	✓	36	1.1	even	1	trivial
289.10.a.h.1.26	yes	36	17.16	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+19.5847 q^{2} -220.079 q^{3} -128.440 q^{4} +130.049 q^{5} -4310.17 q^{6} -9771.35 q^{7} -12542.8 q^{8} +28751.6 q^{9} +O(q^{10})\)	\(q+19.5847 q^{2} -220.079 q^{3} -128.440 q^{4} +130.049 q^{5} -4310.17 q^{6} -9771.35 q^{7} -12542.8 q^{8} +28751.6 q^{9} +2546.96 q^{10} -71260.2 q^{11} +28266.9 q^{12} +126726. q^{13} -191369. q^{14} -28621.0 q^{15} -179886. q^{16} +563092. q^{18} +604683. q^{19} -16703.5 q^{20} +2.15047e6 q^{21} -1.39561e6 q^{22} +1.07633e6 q^{23} +2.76041e6 q^{24} -1.93621e6 q^{25} +2.48189e6 q^{26} -1.99582e6 q^{27} +1.25503e6 q^{28} +1.91386e6 q^{29} -560533. q^{30} -7.71934e6 q^{31} +2.89892e6 q^{32} +1.56829e7 q^{33} -1.27075e6 q^{35} -3.69287e6 q^{36} +1.53482e7 q^{37} +1.18425e7 q^{38} -2.78897e7 q^{39} -1.63118e6 q^{40} +1.94717e7 q^{41} +4.21162e7 q^{42} -1.95272e7 q^{43} +9.15267e6 q^{44} +3.73912e6 q^{45} +2.10796e7 q^{46} +4.08642e7 q^{47} +3.95890e7 q^{48} +5.51256e7 q^{49} -3.79201e7 q^{50} -1.62767e7 q^{52} -489443. q^{53} -3.90874e7 q^{54} -9.26730e6 q^{55} +1.22560e8 q^{56} -1.33078e8 q^{57} +3.74824e7 q^{58} +1.93634e7 q^{59} +3.67608e6 q^{60} -9.43914e7 q^{61} -1.51181e8 q^{62} -2.80942e8 q^{63} +1.48876e8 q^{64} +1.64806e7 q^{65} +3.07144e8 q^{66} -1.30119e8 q^{67} -2.36878e8 q^{69} -2.48873e7 q^{70} +1.90225e8 q^{71} -3.60627e8 q^{72} -8.01389e7 q^{73} +3.00589e8 q^{74} +4.26119e8 q^{75} -7.76656e7 q^{76} +6.96308e8 q^{77} -5.46211e8 q^{78} -4.53181e8 q^{79} -2.33939e7 q^{80} -1.26682e8 q^{81} +3.81348e8 q^{82} +2.97054e8 q^{83} -2.76206e8 q^{84} -3.82434e8 q^{86} -4.21200e8 q^{87} +8.93804e8 q^{88} +7.19298e8 q^{89} +7.32294e7 q^{90} -1.23828e9 q^{91} -1.38244e8 q^{92} +1.69886e9 q^{93} +8.00312e8 q^{94} +7.86383e7 q^{95} -6.37990e8 q^{96} -2.68261e8 q^{97} +1.07962e9 q^{98} -2.04885e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9} - 60000 q^{10} - 76902 q^{11} - 373248 q^{12} + 54216 q^{13} - 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} - 6439479 q^{20} - 138102 q^{21} - 267324 q^{22} - 4041462 q^{23} - 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} - 13281612 q^{27} - 18614784 q^{28} - 4005936 q^{29} + 22471686 q^{30} - 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} - 22076682 q^{37} - 27401376 q^{38} - 62736162 q^{39} + 12231630 q^{40} - 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} + 49578936 q^{44} - 129308238 q^{45} - 140524827 q^{46} - 118557912 q^{47} - 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} - 209848575 q^{54} - 365439924 q^{55} - 203095059 q^{56} + 4614108 q^{57} + 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} - 175597116 q^{61} - 720602571 q^{62} - 587415936 q^{63} + 853082511 q^{64} - 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} - 1308709542 q^{71} - 275337849 q^{72} - 494841342 q^{73} - 1545361890 q^{74} - 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} - 2270624538 q^{78} - 1980107868 q^{79} - 2897000199 q^{80} + 1598298840 q^{81} - 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} + 2705904618 q^{88} + 148394658 q^{89} - 117916215 q^{90} - 636340896 q^{91} + 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} - 4878626298 q^{95} + 8390096634 q^{96} + 891786822 q^{97} + 4285627647 q^{98} + 1476187998 q^{99}+O(q^{100}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9 - 60000 * q^10 - 76902 * q^11 - 373248 * q^12 + 54216 * q^13 - 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 - 6439479 * q^20 - 138102 * q^21 - 267324 * q^22 - 4041462 * q^23 - 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 - 13281612 * q^27 - 18614784 * q^28 - 4005936 * q^29 + 22471686 * q^30 - 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 - 22076682 * q^37 - 27401376 * q^38 - 62736162 * q^39 + 12231630 * q^40 - 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 + 49578936 * q^44 - 129308238 * q^45 - 140524827 * q^46 - 118557912 * q^47 - 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 - 209848575 * q^54 - 365439924 * q^55 - 203095059 * q^56 + 4614108 * q^57 + 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 - 175597116 * q^61 - 720602571 * q^62 - 587415936 * q^63 + 853082511 * q^64 - 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 - 1308709542 * q^71 - 275337849 * q^72 - 494841342 * q^73 - 1545361890 * q^74 - 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 - 2270624538 * q^78 - 1980107868 * q^79 - 2897000199 * q^80 + 1598298840 * q^81 - 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 + 2705904618 * q^88 + 148394658 * q^89 - 117916215 * q^90 - 636340896 * q^91 + 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 - 4878626298 * q^95 + 8390096634 * q^96 + 891786822 * q^97 + 4285627647 * q^98 + 1476187998 * q^99

Introduction

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