LMFDB - Embedded newform 289.10.a.g.1.24

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			1.24
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)

$f(q)$	$=$	$q+18.5911 q^{2} +248.196 q^{3} -166.372 q^{4} +410.150 q^{5} +4614.23 q^{6} -5156.66 q^{7} -12611.7 q^{8} +41918.2 q^{9} +O(q^{10})$	\(q+18.5911 q^{2} +248.196 q^{3} -166.372 q^{4} +410.150 q^{5} +4614.23 q^{6} -5156.66 q^{7} -12611.7 q^{8} +41918.2 q^{9} +7625.14 q^{10} -36057.7 q^{11} -41292.7 q^{12} +126104. q^{13} -95867.9 q^{14} +101798. q^{15} -149282. q^{16} +779306. q^{18} -412482. q^{19} -68237.4 q^{20} -1.27986e6 q^{21} -670352. q^{22} -2.06485e6 q^{23} -3.13016e6 q^{24} -1.78490e6 q^{25} +2.34442e6 q^{26} +5.51870e6 q^{27} +857921. q^{28} +6.64485e6 q^{29} +1.89253e6 q^{30} -3.55201e6 q^{31} +3.68185e6 q^{32} -8.94938e6 q^{33} -2.11501e6 q^{35} -6.97400e6 q^{36} -1.09942e7 q^{37} -7.66848e6 q^{38} +3.12986e7 q^{39} -5.17268e6 q^{40} +2.24799e6 q^{41} -2.37940e7 q^{42} -3.86934e7 q^{43} +5.99898e6 q^{44} +1.71928e7 q^{45} -3.83877e7 q^{46} -3.45143e7 q^{47} -3.70513e7 q^{48} -1.37625e7 q^{49} -3.31833e7 q^{50} -2.09802e7 q^{52} +9.58655e7 q^{53} +1.02599e8 q^{54} -1.47891e7 q^{55} +6.50341e7 q^{56} -1.02376e8 q^{57} +1.23535e8 q^{58} +7.76635e7 q^{59} -1.69362e7 q^{60} -1.94932e7 q^{61} -6.60357e7 q^{62} -2.16158e8 q^{63} +1.44882e8 q^{64} +5.17217e7 q^{65} -1.66379e8 q^{66} -2.59672e8 q^{67} -5.12486e8 q^{69} -3.93203e7 q^{70} +1.12899e8 q^{71} -5.28659e8 q^{72} -1.57320e8 q^{73} -2.04394e8 q^{74} -4.43005e8 q^{75} +6.86252e7 q^{76} +1.85937e8 q^{77} +5.81875e8 q^{78} -5.78943e8 q^{79} -6.12282e7 q^{80} +5.44642e8 q^{81} +4.17926e7 q^{82} +1.91315e8 q^{83} +2.12933e8 q^{84} -7.19353e8 q^{86} +1.64923e9 q^{87} +4.54748e8 q^{88} -8.16637e8 q^{89} +3.19633e8 q^{90} -6.50277e8 q^{91} +3.43531e8 q^{92} -8.81594e8 q^{93} -6.41657e8 q^{94} -1.69180e8 q^{95} +9.13821e8 q^{96} -1.16982e9 q^{97} -2.55859e8 q^{98} -1.51148e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	18.5911	0.821618	0.410809	−	0.911721i	$-0.365246\pi$
$2$	18.5911	0.821618	0.410809	+	0.911721i	$0.365246\pi$
$3$	248.196	1.76909	0.884543	−	0.466458i	$-0.154470\pi$
$3$	248.196	1.76909	0.884543	+	0.466458i	$0.154470\pi$
$4$	−166.372	−0.324944
$5$	410.150	0.293480	0.146740	−	0.989175i	$-0.453122\pi$
$5$	410.150	0.293480	0.146740	+	0.989175i	$0.453122\pi$
$6$	4614.23	1.45351
$7$	−5156.66	−0.811760	−0.405880	−	0.913926i	$-0.633035\pi$
$7$	−5156.66	−0.811760	−0.405880	+	0.913926i	$0.633035\pi$
$8$	−12611.7	−1.08860
$9$	41918.2	2.12967
$10$	7625.14	0.241128
$11$	−36057.7	−0.742560	−0.371280	−	0.928521i	$-0.621081\pi$
$11$	−36057.7	−0.742560	−0.371280	+	0.928521i	$0.621081\pi$
$12$	−41292.7	−0.574855
$13$	126104.	1.22457	0.612287	−	0.790636i	$-0.290250\pi$
$13$	126104.	1.22457	0.612287	+	0.790636i	$0.290250\pi$
$14$	−95867.9	−0.666956
$15$	101798.	0.519191
$16$	−149282.	−0.569467
$17$	0	0
$17$	0	0
$18$	779306.	1.74977
$19$	−412482.	−0.726128	−0.363064	−	0.931764i	$-0.618269\pi$
$19$	−412482.	−0.726128	−0.363064	+	0.931764i	$0.618269\pi$
$20$	−68237.4	−0.0953646
$21$	−1.27986e6	−1.43607
$22$	−670352.	−0.610100
$23$	−2.06485e6	−1.53855	−0.769276	−	0.638917i	$-0.779383\pi$
$23$	−2.06485e6	−1.53855	−0.769276	+	0.638917i	$0.779383\pi$
$24$	−3.13016e6	−1.92582
$25$	−1.78490e6	−0.913870
$26$	2.34442e6	1.00613
$27$	5.51870e6	1.99848
$28$	857921.	0.263777
$29$	6.64485e6	1.74459	0.872297	−	0.488976i	$-0.162629\pi$
$29$	6.64485e6	1.74459	0.872297	+	0.488976i	$0.162629\pi$
$30$	1.89253e6	0.426577
$31$	−3.55201e6	−0.690790	−0.345395	−	0.938457i	$-0.612255\pi$
$31$	−3.55201e6	−0.690790	−0.345395	+	0.938457i	$0.612255\pi$
$32$	3.68185e6	0.620714
$33$	−8.94938e6	−1.31365
$34$	0	0
$35$	−2.11501e6	−0.238235
$36$	−6.97400e6	−0.692023
$37$	−1.09942e7	−0.964397	−0.482199	−	0.876062i	$-0.660162\pi$
$37$	−1.09942e7	−0.964397	−0.482199	+	0.876062i	$0.660162\pi$
$38$	−7.66848e6	−0.596600
$39$	3.12986e7	2.16638
$40$	−5.17268e6	−0.319481
$41$	2.24799e6	0.124242	0.0621209	−	0.998069i	$-0.480214\pi$
$41$	2.24799e6	0.124242	0.0621209	+	0.998069i	$0.480214\pi$
$42$	−2.37940e7	−1.17990
$43$	−3.86934e7	−1.72595	−0.862977	−	0.505244i	$-0.831403\pi$
$43$	−3.86934e7	−1.72595	−0.862977	+	0.505244i	$0.831403\pi$
$44$	5.99898e6	0.241291
$45$	1.71928e7	0.625014
$46$	−3.83877e7	−1.26410
$47$	−3.45143e7	−1.03171	−0.515856	−	0.856676i	$-0.672526\pi$
$47$	−3.45143e7	−1.03171	−0.515856	+	0.856676i	$0.672526\pi$
$48$	−3.70513e7	−1.00744
$49$	−1.37625e7	−0.341046
$50$	−3.31833e7	−0.750851
$51$	0	0
$52$	−2.09802e7	−0.397918
$53$	9.58655e7	1.66886	0.834432	−	0.551111i	$-0.185796\pi$
$53$	9.58655e7	1.66886	0.834432	+	0.551111i	$0.185796\pi$
$54$	1.02599e8	1.64199
$55$	−1.47891e7	−0.217926
$56$	6.50341e7	0.883680
$57$	−1.02376e8	−1.28458
$58$	1.23535e8	1.43339
$59$	7.76635e7	0.834416	0.417208	−	0.908811i	$-0.363009\pi$
$59$	7.76635e7	0.834416	0.417208	+	0.908811i	$0.363009\pi$
$60$	−1.69362e7	−0.168708
$61$	−1.94932e7	−0.180260	−0.0901301	−	0.995930i	$-0.528728\pi$
$61$	−1.94932e7	−0.180260	−0.0901301	+	0.995930i	$0.528728\pi$
$62$	−6.60357e7	−0.567566
$63$	−2.16158e8	−1.72878
$64$	1.44882e8	1.07946
$65$	5.17217e7	0.359388
$66$	−1.66379e8	−1.07932
$67$	−2.59672e8	−1.57430	−0.787151	−	0.616760i	$-0.788445\pi$
$67$	−2.59672e8	−1.57430	−0.787151	+	0.616760i	$0.788445\pi$
$68$	0	0
$69$	−5.12486e8	−2.72183
$70$	−3.93203e7	−0.195738
$71$	1.12899e8	0.527262	0.263631	−	0.964624i	$-0.415080\pi$
$71$	1.12899e8	0.527262	0.263631	+	0.964624i	$0.415080\pi$
$72$	−5.28659e8	−2.31835
$73$	−1.57320e8	−0.648383	−0.324191	−	0.945992i	$-0.605092\pi$
$73$	−1.57320e8	−0.648383	−0.324191	+	0.945992i	$0.605092\pi$
$74$	−2.04394e8	−0.792366
$75$	−4.43005e8	−1.61671
$76$	6.86252e7	0.235951
$77$	1.85937e8	0.602780
$78$	5.81875e8	1.77993
$79$	−5.78943e8	−1.67230	−0.836149	−	0.548502i	$-0.815198\pi$
$79$	−5.78943e8	−1.67230	−0.836149	+	0.548502i	$0.815198\pi$
$80$	−6.12282e7	−0.167127
$81$	5.44642e8	1.40582
$82$	4.17926e7	0.102079
$83$	1.91315e8	0.442483	0.221242	−	0.975219i	$-0.428989\pi$
$83$	1.91315e8	0.442483	0.221242	+	0.975219i	$0.428989\pi$
$84$	2.12933e8	0.466644
$85$	0	0
$86$	−7.19353e8	−1.41807
$87$	1.64923e9	3.08634
$88$	4.54748e8	0.808349
$89$	−8.16637e8	−1.37967	−0.689833	−	0.723969i	$-0.742316\pi$
$89$	−8.16637e8	−1.37967	−0.689833	+	0.723969i	$0.742316\pi$
$90$	3.19633e8	0.513523
$91$	−6.50277e8	−0.994059
$92$	3.43531e8	0.499944
$93$	−8.81594e8	−1.22207
$94$	−6.41657e8	−0.847672
$95$	−1.69180e8	−0.213104
$96$	9.13821e8	1.09810
$97$	−1.16982e9	−1.34167	−0.670837	−	0.741605i	$-0.734065\pi$
$97$	−1.16982e9	−1.34167	−0.670837	+	0.741605i	$0.734065\pi$
$98$	−2.55859e8	−0.280210
$99$	−1.51148e9	−1.58141
$100$	2.96957e8	0.296957
$101$	−4.80145e8	−0.459120	−0.229560	−	0.973294i	$-0.573729\pi$
$101$	−4.80145e8	−0.459120	−0.229560	+	0.973294i	$0.573729\pi$
$102$	0	0
$103$	−4.10770e8	−0.359609	−0.179805	−	0.983702i	$-0.557547\pi$
$103$	−4.10770e8	−0.359609	−0.179805	+	0.983702i	$0.557547\pi$
$104$	−1.59039e9	−1.33307
$105$	−5.24936e8	−0.421458
$106$	1.78224e9	1.37117
$107$	9.94330e8	0.733337	0.366668	−	0.930352i	$-0.380498\pi$
$107$	9.94330e8	0.733337	0.366668	+	0.930352i	$0.380498\pi$
$108$	−9.18154e8	−0.649395
$109$	−8.53840e7	−0.0579372	−0.0289686	−	0.999580i	$-0.509222\pi$
$109$	−8.53840e7	−0.0579372	−0.0289686	+	0.999580i	$0.509222\pi$
$110$	−2.74945e8	−0.179052
$111$	−2.72872e9	−1.70610
$112$	7.69798e8	0.462270
$113$	−3.43737e8	−0.198323	−0.0991616	−	0.995071i	$-0.531616\pi$
$113$	−3.43737e8	−0.198323	−0.0991616	+	0.995071i	$0.531616\pi$
$114$	−1.90329e9	−1.05544
$115$	−8.46897e8	−0.451534
$116$	−1.10551e9	−0.566896
$117$	5.28607e9	2.60793
$118$	1.44385e9	0.685571
$119$	0	0
$120$	−1.28384e9	−0.565190
$121$	−1.05779e9	−0.448605
$122$	−3.62400e8	−0.148105
$123$	5.57943e8	0.219794
$124$	5.90953e8	0.224468
$125$	−1.53315e9	−0.561682
$126$	−4.01862e9	−1.42039
$127$	1.89030e9	0.644784	0.322392	−	0.946606i	$-0.395513\pi$
$127$	1.89030e9	0.644784	0.322392	+	0.946606i	$0.395513\pi$
$128$	8.08409e8	0.266187
$129$	−9.60355e9	−3.05336
$130$	9.61563e8	0.295279
$131$	5.39985e9	1.60200	0.800998	−	0.598668i	$-0.204303\pi$
$131$	5.39985e9	1.60200	0.800998	+	0.598668i	$0.204303\pi$
$132$	1.48892e9	0.426864
$133$	2.12703e9	0.589442
$134$	−4.82758e9	−1.29347
$135$	2.26350e9	0.586514
$136$	0	0
$137$	1.08711e9	0.263652	0.131826	−	0.991273i	$-0.457916\pi$
$137$	1.08711e9	0.263652	0.131826	+	0.991273i	$0.457916\pi$
$138$	−9.52768e9	−2.23631
$139$	−1.08365e8	−0.0246220	−0.0123110	−	0.999924i	$-0.503919\pi$
$139$	−1.08365e8	−0.0246220	−0.0123110	+	0.999924i	$0.503919\pi$
$140$	3.51877e8	0.0774131
$141$	−8.56630e9	−1.82519
$142$	2.09891e9	0.433208
$143$	−4.54703e9	−0.909319
$144$	−6.25765e9	−1.21278
$145$	2.72539e9	0.512003
$146$	−2.92475e9	−0.532723
$147$	−3.41579e9	−0.603341
$148$	1.82912e9	0.313375
$149$	1.08943e10	1.81076	0.905379	−	0.424605i	$-0.139587\pi$
$149$	1.08943e10	1.81076	0.905379	+	0.424605i	$0.139587\pi$
$150$	−8.23595e9	−1.32832
$151$	1.09719e10	1.71745	0.858727	−	0.512434i	$-0.171256\pi$
$151$	1.09719e10	1.71745	0.858727	+	0.512434i	$0.171256\pi$
$152$	5.20208e9	0.790462
$153$	0	0
$154$	3.45678e9	0.495255
$155$	−1.45686e9	−0.202733
$156$	−5.20719e9	−0.703952
$157$	2.07360e9	0.272381	0.136191	−	0.990683i	$-0.456514\pi$
$157$	2.07360e9	0.272381	0.136191	+	0.990683i	$0.456514\pi$
$158$	−1.07632e10	−1.37399
$159$	2.37934e10	2.95236
$160$	1.51011e9	0.182167
$161$	1.06477e10	1.24893
$162$	1.01255e10	1.15504
$163$	−7.73957e9	−0.858761	−0.429381	−	0.903124i	$-0.641268\pi$
$163$	−7.73957e9	−0.858761	−0.429381	+	0.903124i	$0.641268\pi$
$164$	−3.74002e8	−0.0403717
$165$	−3.67059e9	−0.385530
$166$	3.55675e9	0.363552
$167$	−9.28912e9	−0.924167	−0.462084	−	0.886836i	$-0.652898\pi$
$167$	−9.28912e9	−0.924167	−0.462084	+	0.886836i	$0.652898\pi$
$168$	1.61412e10	1.56331
$169$	5.29780e9	0.499580
$170$	0	0
$171$	−1.72905e10	−1.54641
$172$	6.43748e9	0.560839
$173$	8.35804e8	0.0709409	0.0354705	−	0.999371i	$-0.488707\pi$
$173$	8.35804e8	0.0709409	0.0354705	+	0.999371i	$0.488707\pi$
$174$	3.06609e10	2.53579
$175$	9.20413e9	0.741842
$176$	5.38278e9	0.422863
$177$	1.92758e10	1.47615
$178$	−1.51822e10	−1.13356
$179$	−2.35485e9	−0.171445	−0.0857224	−	0.996319i	$-0.527320\pi$
$179$	−2.35485e9	−0.171445	−0.0857224	+	0.996319i	$0.527320\pi$
$180$	−2.86039e9	−0.203095
$181$	8.33018e9	0.576900	0.288450	−	0.957495i	$-0.406860\pi$
$181$	8.33018e9	0.576900	0.288450	+	0.957495i	$0.406860\pi$
$182$	−1.20894e10	−0.816737
$183$	−4.83814e9	−0.318896
$184$	2.60411e10	1.67486
$185$	−4.50928e9	−0.283031
$186$	−1.63898e10	−1.00407
$187$	0	0
$188$	5.74219e9	0.335249
$189$	−2.84581e10	−1.62229
$190$	−3.14523e9	−0.175090
$191$	−3.99840e9	−0.217388	−0.108694	−	0.994075i	$-0.534667\pi$
$191$	−3.99840e9	−0.217388	−0.108694	+	0.994075i	$0.534667\pi$
$192$	3.59592e10	1.90965
$193$	4.86796e9	0.252545	0.126273	−	0.991996i	$-0.459699\pi$
$193$	4.86796e9	0.252545	0.126273	+	0.991996i	$0.459699\pi$
$194$	−2.17483e10	−1.10234
$195$	1.28371e10	0.635788
$196$	2.28968e9	0.110821
$197$	1.77304e10	0.838726	0.419363	−	0.907819i	$-0.362253\pi$
$197$	1.77304e10	0.838726	0.419363	+	0.907819i	$0.362253\pi$
$198$	−2.81000e10	−1.29931
$199$	−2.27010e10	−1.02614	−0.513069	−	0.858347i	$-0.671492\pi$
$199$	−2.27010e10	−1.02614	−0.513069	+	0.858347i	$0.671492\pi$
$200$	2.25106e10	0.994836
$201$	−6.44495e10	−2.78508
$202$	−8.92642e9	−0.377221
$203$	−3.42653e10	−1.41619
$204$	0	0
$205$	9.22015e8	0.0364624
$206$	−7.63665e9	−0.295461
$207$	−8.65547e10	−3.27660
$208$	−1.88251e10	−0.697354
$209$	1.48731e10	0.539193
$210$	−9.75914e9	−0.346278
$211$	3.06097e10	1.06314	0.531568	−	0.847016i	$-0.321603\pi$
$211$	3.06097e10	1.06314	0.531568	+	0.847016i	$0.321603\pi$
$212$	−1.59493e10	−0.542288
$213$	2.80210e10	0.932772
$214$	1.84857e10	0.602522
$215$	−1.58701e10	−0.506532
$216$	−6.96000e10	−2.17554
$217$	1.83165e10	0.560756
$218$	−1.58738e9	−0.0476022
$219$	−3.90462e10	−1.14704
$220$	2.46048e9	0.0708139
$221$	0	0
$222$	−5.07298e10	−1.40176
$223$	−6.82357e10	−1.84774	−0.923868	−	0.382711i	$-0.874990\pi$
$223$	−6.82357e10	−1.84774	−0.923868	+	0.382711i	$0.874990\pi$
$224$	−1.89861e10	−0.503870
$225$	−7.48199e10	−1.94624
$226$	−6.39044e9	−0.162946
$227$	3.46724e9	0.0866698	0.0433349	−	0.999061i	$-0.486202\pi$
$227$	3.46724e9	0.0866698	0.0433349	+	0.999061i	$0.486202\pi$
$228$	1.70325e10	0.417418
$229$	−2.52553e9	−0.0606867	−0.0303433	−	0.999540i	$-0.509660\pi$
$229$	−2.52553e9	−0.0606867	−0.0303433	+	0.999540i	$0.509660\pi$
$230$	−1.57447e10	−0.370988
$231$	4.61489e10	1.06637
$232$	−8.38027e10	−1.89916
$233$	−2.89136e10	−0.642689	−0.321344	−	0.946962i	$-0.604135\pi$
$233$	−2.89136e10	−0.642689	−0.321344	+	0.946962i	$0.604135\pi$
$234$	9.82738e10	2.14273
$235$	−1.41560e10	−0.302786
$236$	−1.29210e10	−0.271139
$237$	−1.43691e11	−2.95844
$238$	0	0
$239$	1.56543e10	0.310344	0.155172	−	0.987887i	$-0.450407\pi$
$239$	1.56543e10	0.310344	0.155172	+	0.987887i	$0.450407\pi$
$240$	−1.51966e10	−0.295662
$241$	6.78562e10	1.29572	0.647862	−	0.761758i	$-0.275663\pi$
$241$	6.78562e10	1.29572	0.647862	+	0.761758i	$0.275663\pi$
$242$	−1.96654e10	−0.368582
$243$	2.65535e10	0.488532
$244$	3.24312e9	0.0585745
$245$	−5.64468e9	−0.100090
$246$	1.03728e10	0.180587
$247$	−5.20157e10	−0.889197
$248$	4.47967e10	0.751993
$249$	4.74835e10	0.782791
$250$	−2.85030e10	−0.461488
$251$	−2.13184e10	−0.339017	−0.169509	−	0.985529i	$-0.554218\pi$
$251$	−2.13184e10	−0.339017	−0.169509	+	0.985529i	$0.554218\pi$
$252$	3.59626e10	0.561757
$253$	7.44536e10	1.14247
$254$	3.51427e10	0.529766
$255$	0	0
$256$	−5.91505e10	−0.860753
$257$	1.08936e11	1.55765	0.778826	−	0.627240i	$-0.215815\pi$
$257$	1.08936e11	1.55765	0.778826	+	0.627240i	$0.215815\pi$
$258$	−1.78540e11	−2.50870
$259$	5.66934e10	0.782859
$260$	−8.60502e9	−0.116781
$261$	2.78541e11	3.71541
$262$	1.00389e11	1.31623
$263$	7.04152e10	0.907539	0.453770	−	0.891119i	$-0.350079\pi$
$263$	7.04152e10	0.907539	0.453770	+	0.891119i	$0.350079\pi$
$264$	1.12867e11	1.43004
$265$	3.93193e10	0.489778
$266$	3.95438e10	0.484296
$267$	−2.02686e11	−2.44075
$268$	4.32020e10	0.511561
$269$	−8.78447e10	−1.02289	−0.511447	−	0.859315i	$-0.670890\pi$
$269$	−8.78447e10	−1.02289	−0.511447	+	0.859315i	$0.670890\pi$
$270$	4.20809e10	0.481890
$271$	−1.28943e10	−0.145223	−0.0726116	−	0.997360i	$-0.523133\pi$
$271$	−1.28943e10	−0.145223	−0.0726116	+	0.997360i	$0.523133\pi$
$272$	0	0
$273$	−1.61396e11	−1.75858
$274$	2.02106e10	0.216621
$275$	6.43595e10	0.678603
$276$	8.52631e10	0.884444
$277$	1.18389e10	0.120824	0.0604119	−	0.998174i	$-0.480759\pi$
$277$	1.18389e10	0.120824	0.0604119	+	0.998174i	$0.480759\pi$
$278$	−2.01463e9	−0.0202299
$279$	−1.48894e11	−1.47115
$280$	2.66738e10	0.259342
$281$	−2.58693e10	−0.247517	−0.123759	−	0.992312i	$-0.539495\pi$
$281$	−2.58693e10	−0.247517	−0.123759	+	0.992312i	$0.539495\pi$
$282$	−1.59257e11	−1.49961
$283$	−1.78798e11	−1.65701	−0.828504	−	0.559983i	$-0.810808\pi$
$283$	−1.78798e11	−1.65701	−0.828504	+	0.559983i	$0.810808\pi$
$284$	−1.87831e10	−0.171331
$285$	−4.19897e10	−0.376999
$286$	−8.45343e10	−0.747112
$287$	−1.15921e10	−0.100854
$288$	1.54337e11	1.32191
$289$	0	0
$290$	5.06680e10	0.420671
$291$	−2.90345e11	−2.37354
$292$	2.61736e10	0.210688
$293$	1.20299e11	0.953583	0.476791	−	0.879016i	$-0.341800\pi$
$293$	1.20299e11	0.953583	0.476791	+	0.879016i	$0.341800\pi$
$294$	−6.35032e10	−0.495715
$295$	3.18537e10	0.244884
$296$	1.38655e11	1.04984
$297$	−1.98992e11	−1.48399
$298$	2.02536e11	1.48775
$299$	−2.60386e11	−1.88407
$300$	7.37035e10	0.525342
$301$	1.99529e11	1.40106
$302$	2.03979e11	1.41109
$303$	−1.19170e11	−0.812224
$304$	6.15762e10	0.413506
$305$	−7.99516e9	−0.0529027
$306$	0	0
$307$	2.59830e11	1.66942	0.834712	−	0.550686i	$-0.185634\pi$
$307$	2.59830e11	1.66942	0.834712	+	0.550686i	$0.185634\pi$
$308$	−3.09347e10	−0.195870
$309$	−1.01951e11	−0.636180
$310$	−2.70846e10	−0.166569
$311$	3.68315e9	0.0223253	0.0111627	−	0.999938i	$-0.496447\pi$
$311$	3.68315e9	0.0223253	0.0111627	+	0.999938i	$0.496447\pi$
$312$	−3.94727e11	−2.35831
$313$	−2.75095e11	−1.62007	−0.810033	−	0.586384i	$-0.800551\pi$
$313$	−2.75095e11	−1.62007	−0.810033	+	0.586384i	$0.800551\pi$
$314$	3.85505e10	0.223793
$315$	−8.86574e10	−0.507361
$316$	9.63196e10	0.543404
$317$	1.47009e10	0.0817671	0.0408835	−	0.999164i	$-0.486983\pi$
$317$	1.47009e10	0.0817671	0.0408835	+	0.999164i	$0.486983\pi$
$318$	4.42346e11	2.42572
$319$	−2.39598e11	−1.29547
$320$	5.94235e10	0.316799
$321$	2.46789e11	1.29734
$322$	1.97952e11	1.02615
$323$	0	0
$324$	−9.06129e10	−0.456812
$325$	−2.25084e11	−1.11910
$326$	−1.43887e11	−0.705574
$327$	−2.11920e10	−0.102496
$328$	−2.83509e10	−0.135249
$329$	1.77978e11	0.837501
$330$	−6.82403e10	−0.316759
$331$	5.56360e10	0.254759	0.127380	−	0.991854i	$-0.459343\pi$
$331$	5.56360e10	0.254759	0.127380	+	0.991854i	$0.459343\pi$
$332$	−3.18293e10	−0.143782
$333$	−4.60858e11	−2.05385
$334$	−1.72695e11	−0.759312
$335$	−1.06505e11	−0.462026
$336$	1.91061e11	0.817796
$337$	5.27885e10	0.222949	0.111474	−	0.993767i	$-0.464443\pi$
$337$	5.27885e10	0.222949	0.111474	+	0.993767i	$0.464443\pi$
$338$	9.84918e10	0.410464
$339$	−8.53141e10	−0.350851
$340$	0	0
$341$	1.28077e11	0.512953
$342$	−3.21449e11	−1.27056
$343$	2.79058e11	1.08861
$344$	4.87988e11	1.87887
$345$	−2.10196e11	−0.798803
$346$	1.55385e10	0.0582863
$347$	−1.59268e11	−0.589720	−0.294860	−	0.955540i	$-0.595273\pi$
$347$	−1.59268e11	−0.589720	−0.294860	+	0.955540i	$0.595273\pi$
$348$	−2.74384e11	−1.00289
$349$	−4.30824e11	−1.55448	−0.777241	−	0.629203i	$-0.783381\pi$
$349$	−4.30824e11	−1.55448	−0.777241	+	0.629203i	$0.783381\pi$
$350$	1.71115e11	0.609511
$351$	6.95932e11	2.44729
$352$	−1.32759e11	−0.460917
$353$	3.70012e11	1.26832	0.634161	−	0.773201i	$-0.281346\pi$
$353$	3.70012e11	1.26832	0.634161	+	0.773201i	$0.281346\pi$
$354$	3.58357e11	1.21283
$355$	4.63055e10	0.154741
$356$	1.35865e11	0.448314
$357$	0	0
$358$	−4.37792e10	−0.140862
$359$	3.85262e11	1.22414	0.612071	−	0.790803i	$-0.290337\pi$
$359$	3.85262e11	1.22414	0.612071	+	0.790803i	$0.290337\pi$
$360$	−2.16830e11	−0.680389
$361$	−1.52547e11	−0.472738
$362$	1.54867e11	0.473992
$363$	−2.62539e11	−0.793622
$364$	1.08188e11	0.323014
$365$	−6.45249e10	−0.190287
$366$	−8.99463e10	−0.262010
$367$	−2.64210e11	−0.760243	−0.380122	−	0.924936i	$-0.624118\pi$
$367$	−2.64210e11	−0.760243	−0.380122	+	0.924936i	$0.624118\pi$
$368$	3.08245e11	0.876154
$369$	9.42319e10	0.264594
$370$	−8.38324e10	−0.232543
$371$	−4.94346e11	−1.35472
$372$	1.46672e11	0.397104
$373$	1.02550e10	0.0274314	0.0137157	−	0.999906i	$-0.495634\pi$
$373$	1.02550e10	0.0274314	0.0137157	+	0.999906i	$0.495634\pi$
$374$	0	0
$375$	−3.80523e11	−0.993664
$376$	4.35282e11	1.12312
$377$	8.37945e11	2.13638
$378$	−5.29066e11	−1.33290
$379$	−2.28558e11	−0.569011	−0.284505	−	0.958674i	$-0.591829\pi$
$379$	−2.28558e11	−0.569011	−0.284505	+	0.958674i	$0.591829\pi$
$380$	2.81466e10	0.0692469
$381$	4.69165e11	1.14068
$382$	−7.43346e10	−0.178610
$383$	−7.29682e10	−0.173276	−0.0866382	−	0.996240i	$-0.527612\pi$
$383$	−7.29682e10	−0.173276	−0.0866382	+	0.996240i	$0.527612\pi$
$384$	2.00644e11	0.470907
$385$	7.62623e10	0.176904
$386$	9.05006e10	0.207495
$387$	−1.62196e12	−3.67571
$388$	1.94625e11	0.435969
$389$	−1.64952e11	−0.365246	−0.182623	−	0.983183i	$-0.558459\pi$
$389$	−1.64952e11	−0.365246	−0.182623	+	0.983183i	$0.558459\pi$
$390$	2.38656e11	0.522374
$391$	0	0
$392$	1.73567e11	0.371262
$393$	1.34022e12	2.83407
$394$	3.29627e11	0.689112
$395$	−2.37454e11	−0.490786
$396$	2.51467e11	0.513869
$397$	4.25456e11	0.859602	0.429801	−	0.902924i	$-0.358584\pi$
$397$	4.25456e11	0.859602	0.429801	+	0.902924i	$0.358584\pi$
$398$	−4.22036e11	−0.843094
$399$	5.27920e11	1.04277
$400$	2.66454e11	0.520418
$401$	9.58914e11	1.85195	0.925977	−	0.377580i	$-0.123244\pi$
$401$	9.58914e11	1.85195	0.925977	+	0.377580i	$0.123244\pi$
$402$	−1.19819e12	−2.28827
$403$	−4.47924e11	−0.845924
$404$	7.98825e10	0.149189
$405$	2.23385e11	0.412579
$406$	−6.37028e11	−1.16357
$407$	3.96426e11	0.716122
$408$	0	0
$409$	−5.90759e11	−1.04389	−0.521946	−	0.852979i	$-0.674794\pi$
$409$	−5.90759e11	−1.04389	−0.521946	+	0.852979i	$0.674794\pi$
$410$	1.71413e10	0.0299582
$411$	2.69817e11	0.466424
$412$	6.83404e10	0.116853
$413$	−4.00484e11	−0.677345
$414$	−1.60915e12	−2.69212
$415$	7.84678e10	0.129860
$416$	4.64297e11	0.760110
$417$	−2.68959e10	−0.0435585
$418$	2.76508e11	0.443011
$419$	−8.05292e11	−1.27641	−0.638205	−	0.769866i	$-0.720323\pi$
$419$	−8.05292e11	−1.27641	−0.638205	+	0.769866i	$0.720323\pi$
$420$	8.73344e10	0.136951
$421$	8.35895e11	1.29683	0.648414	−	0.761288i	$-0.275433\pi$
$421$	8.35895e11	1.29683	0.648414	+	0.761288i	$0.275433\pi$
$422$	5.69068e11	0.873491
$423$	−1.44678e12	−2.19720
$424$	−1.20902e12	−1.81672
$425$	0	0
$426$	5.20941e11	0.766382
$427$	1.00520e11	0.146328
$428$	−1.65428e11	−0.238294
$429$	−1.12856e12	−1.60866
$430$	−2.95043e11	−0.416176
$431$	−3.25104e11	−0.453811	−0.226906	−	0.973917i	$-0.572861\pi$
$431$	−3.25104e11	−0.453811	−0.226906	+	0.973917i	$0.572861\pi$
$432$	−8.23844e11	−1.13807
$433$	1.08918e12	1.48904	0.744519	−	0.667601i	$-0.232679\pi$
$433$	1.08918e12	1.48904	0.744519	+	0.667601i	$0.232679\pi$
$434$	3.40524e11	0.460727
$435$	6.76431e11	0.905778
$436$	1.42055e10	0.0188264
$437$	8.51711e11	1.11719
$438$	−7.25912e11	−0.942432
$439$	−3.88652e11	−0.499425	−0.249713	−	0.968320i	$-0.580336\pi$
$439$	−3.88652e11	−0.499425	−0.249713	+	0.968320i	$0.580336\pi$
$440$	1.86515e11	0.237234
$441$	−5.76898e11	−0.726316
$442$	0	0
$443$	3.67284e9	0.00453091	0.00226546	−	0.999997i	$-0.499279\pi$
$443$	3.67284e9	0.00453091	0.00226546	+	0.999997i	$0.499279\pi$
$444$	4.53981e11	0.554388
$445$	−3.34944e11	−0.404904
$446$	−1.26858e12	−1.51813
$447$	2.70392e12	3.20339
$448$	−7.47108e11	−0.876259
$449$	1.28583e12	1.49306	0.746528	−	0.665354i	$-0.231719\pi$
$449$	1.28583e12	1.49306	0.746528	+	0.665354i	$0.231719\pi$
$450$	−1.39098e12	−1.59906
$451$	−8.10575e10	−0.0922569
$452$	5.71880e10	0.0644440
$453$	2.72318e12	3.03832
$454$	6.44598e10	0.0712095
$455$	−2.66712e11	−0.291736
$456$	1.29114e12	1.39840
$457$	4.73539e11	0.507847	0.253923	−	0.967224i	$-0.418279\pi$
$457$	4.73539e11	0.507847	0.253923	+	0.967224i	$0.418279\pi$
$458$	−4.69524e10	−0.0498612
$459$	0	0
$460$	1.40900e11	0.146723
$461$	5.52192e11	0.569425	0.284712	−	0.958613i	$-0.408102\pi$
$461$	5.52192e11	0.569425	0.284712	+	0.958613i	$0.408102\pi$
$462$	8.57959e11	0.876148
$463$	1.27197e12	1.28635	0.643177	−	0.765717i	$-0.277616\pi$
$463$	1.27197e12	1.28635	0.643177	+	0.765717i	$0.277616\pi$
$464$	−9.91959e11	−0.993489
$465$	−3.61586e11	−0.358652
$466$	−5.37535e11	−0.528044
$467$	−3.10177e11	−0.301775	−0.150888	−	0.988551i	$-0.548213\pi$
$467$	−3.10177e11	−0.301775	−0.150888	+	0.988551i	$0.548213\pi$
$468$	−8.79452e11	−0.847434
$469$	1.33904e12	1.27796
$470$	−2.63176e11	−0.248775
$471$	5.14660e11	0.481866
$472$	−9.79465e11	−0.908343
$473$	1.39520e12	1.28162
$474$	−2.67138e12	−2.43071
$475$	7.36239e11	0.663587
$476$	0	0
$477$	4.01851e12	3.55413
$478$	2.91031e11	0.254984
$479$	1.96932e11	0.170925	0.0854626	−	0.996341i	$-0.472763\pi$
$479$	1.96932e11	0.170925	0.0854626	+	0.996341i	$0.472763\pi$
$480$	3.74804e11	0.322269
$481$	−1.38642e12	−1.18098
$482$	1.26152e12	1.06459
$483$	2.64272e12	2.20947
$484$	1.75986e11	0.145772
$485$	−4.79803e11	−0.393754
$486$	4.93658e11	0.401386
$487$	3.27253e11	0.263635	0.131818	−	0.991274i	$-0.457919\pi$
$487$	3.27253e11	0.263635	0.131818	+	0.991274i	$0.457919\pi$
$488$	2.45842e11	0.196231
$489$	−1.92093e12	−1.51922
$490$	−1.04941e11	−0.0822359
$491$	5.70388e11	0.442898	0.221449	−	0.975172i	$-0.428921\pi$
$491$	5.70388e11	0.442898	0.221449	+	0.975172i	$0.428921\pi$
$492$	−9.28258e10	−0.0714210
$493$	0	0
$494$	−9.67028e11	−0.730580
$495$	−6.19933e11	−0.464110
$496$	5.30252e11	0.393382
$497$	−5.82180e11	−0.428010
$498$	8.82770e11	0.643155
$499$	2.94493e11	0.212629	0.106314	−	0.994333i	$-0.466095\pi$
$499$	2.94493e11	0.212629	0.106314	+	0.994333i	$0.466095\pi$
$500$	2.55073e11	0.182515
$501$	−2.30552e12	−1.63493
$502$	−3.96331e11	−0.278543
$503$	−2.27158e12	−1.58224	−0.791118	−	0.611664i	$-0.790501\pi$
$503$	−2.27158e12	−1.58224	−0.791118	+	0.611664i	$0.790501\pi$
$504$	2.72611e12	1.88194
$505$	−1.96932e11	−0.134743
$506$	1.38417e12	0.938671
$507$	1.31489e12	0.883801
$508$	−3.14492e11	−0.209519
$509$	−2.98841e11	−0.197338	−0.0986690	−	0.995120i	$-0.531458\pi$
$509$	−2.98841e11	−0.197338	−0.0986690	+	0.995120i	$0.531458\pi$
$510$	0	0
$511$	8.11246e11	0.526331
$512$	−1.51358e12	−0.973396
$513$	−2.27636e12	−1.45115
$514$	2.02523e12	1.27979
$515$	−1.68477e11	−0.105538
$516$	1.59776e12	0.992172
$517$	1.24451e12	0.766107
$518$	1.05399e12	0.643211
$519$	2.07443e11	0.125501
$520$	−6.52297e11	−0.391229
$521$	−2.12328e12	−1.26252	−0.631260	−	0.775571i	$-0.717462\pi$
$521$	−2.12328e12	−1.26252	−0.631260	+	0.775571i	$0.717462\pi$
$522$	5.17837e12	3.05264
$523$	−1.28511e11	−0.0751076	−0.0375538	−	0.999295i	$-0.511957\pi$
$523$	−1.28511e11	−0.0751076	−0.0375538	+	0.999295i	$0.511957\pi$
$524$	−8.98382e11	−0.520559
$525$	2.28443e12	1.31238
$526$	1.30909e12	0.745650
$527$	0	0
$528$	1.33598e12	0.748081
$529$	2.46243e12	1.36714
$530$	7.30988e11	0.402410
$531$	3.25552e12	1.77703
$532$	−3.53877e11	−0.191536
$533$	2.83482e11	0.152143
$534$	−3.76815e12	−2.00536
$535$	4.07825e11	0.215220
$536$	3.27489e12	1.71378
$537$	−5.84464e11	−0.303301
$538$	−1.63313e12	−0.840428
$539$	4.96243e11	0.253247
$540$	−3.76581e11	−0.190584
$541$	2.15503e11	0.108160	0.0540798	−	0.998537i	$-0.482777\pi$
$541$	2.15503e11	0.108160	0.0540798	+	0.998537i	$0.482777\pi$
$542$	−2.39719e11	−0.119318
$543$	2.06752e12	1.02059
$544$	0	0
$545$	−3.50203e10	−0.0170034
$546$	−3.00053e12	−1.44488
$547$	1.35709e12	0.648136	0.324068	−	0.946034i	$-0.394949\pi$
$547$	1.35709e12	0.648136	0.324068	+	0.946034i	$0.394949\pi$
$548$	−1.80864e11	−0.0856723
$549$	−8.17122e11	−0.383894
$550$	1.19651e12	0.557552
$551$	−2.74088e12	−1.26680
$552$	6.46330e12	2.96298
$553$	2.98541e12	1.35750
$554$	2.20098e11	0.0992710
$555$	−1.11918e12	−0.500707
$556$	1.80289e10	0.00800080
$557$	−1.95126e12	−0.858947	−0.429473	−	0.903079i	$-0.641301\pi$
$557$	−1.95126e12	−0.858947	−0.429473	+	0.903079i	$0.641301\pi$
$558$	−2.76810e12	−1.20873
$559$	−4.87941e12	−2.11356
$560$	3.15733e11	0.135667
$561$	0	0
$562$	−4.80938e11	−0.203365
$563$	2.03431e12	0.853356	0.426678	−	0.904404i	$-0.359684\pi$
$563$	2.03431e12	0.853356	0.426678	+	0.904404i	$0.359684\pi$
$564$	1.42519e12	0.593084
$565$	−1.40984e11	−0.0582038
$566$	−3.32406e12	−1.36143
$567$	−2.80854e12	−1.14119
$568$	−1.42384e12	−0.573976
$569$	−1.10219e12	−0.440812	−0.220406	−	0.975408i	$-0.570738\pi$
$569$	−1.10219e12	−0.440812	−0.220406	+	0.975408i	$0.570738\pi$
$570$	−7.80634e11	−0.309749
$571$	−3.68331e12	−1.45003	−0.725013	−	0.688735i	$-0.758166\pi$
$571$	−3.68331e12	−1.45003	−0.725013	+	0.688735i	$0.758166\pi$
$572$	7.56497e11	0.295478
$573$	−9.92387e11	−0.384579
$574$	−2.15510e11	−0.0828638
$575$	3.68555e12	1.40604
$576$	6.07321e12	2.29888
$577$	4.96716e12	1.86559	0.932797	−	0.360402i	$-0.117361\pi$
$577$	4.96716e12	1.86559	0.932797	+	0.360402i	$0.117361\pi$
$578$	0	0
$579$	1.20821e12	0.446774
$580$	−4.53427e11	−0.166373
$581$	−9.86545e11	−0.359190
$582$	−5.39783e12	−1.95014
$583$	−3.45669e12	−1.23923
$584$	1.98407e12	0.705828
$585$	2.16808e12	0.765376
$586$	2.23649e12	0.783480
$587$	1.41626e12	0.492346	0.246173	−	0.969226i	$-0.420827\pi$
$587$	1.41626e12	0.492346	0.246173	+	0.969226i	$0.420827\pi$
$588$	5.68289e11	0.196052
$589$	1.46514e12	0.501602
$590$	5.92195e11	0.201201
$591$	4.40061e12	1.48378
$592$	1.64124e12	0.549192
$593$	2.84071e12	0.943368	0.471684	−	0.881768i	$-0.343646\pi$
$593$	2.84071e12	0.943368	0.471684	+	0.881768i	$0.343646\pi$
$594$	−3.69947e12	−1.21927
$595$	0	0
$596$	−1.81250e12	−0.588395
$597$	−5.63430e12	−1.81533
$598$	−4.84086e12	−1.54799
$599$	2.86774e12	0.910162	0.455081	−	0.890450i	$-0.349610\pi$
$599$	2.86774e12	0.910162	0.455081	+	0.890450i	$0.349610\pi$
$600$	5.58704e12	1.75995
$601$	7.96547e11	0.249044	0.124522	−	0.992217i	$-0.460260\pi$
$601$	7.96547e11	0.249044	0.124522	+	0.992217i	$0.460260\pi$
$602$	3.70946e12	1.15113
$603$	−1.08850e13	−3.35274
$604$	−1.82541e12	−0.558077
$605$	−4.33852e11	−0.131657
$606$	−2.21550e12	−0.667337
$607$	−6.24458e12	−1.86704	−0.933521	−	0.358522i	$-0.883281\pi$
$607$	−6.24458e12	−1.86704	−0.933521	+	0.358522i	$0.883281\pi$
$608$	−1.51870e12	−0.450718
$609$	−8.50450e12	−2.50536
$610$	−1.48639e11	−0.0434658
$611$	−4.35240e12	−1.26341
$612$	0	0
$613$	−5.86242e12	−1.67689	−0.838446	−	0.544985i	$-0.816536\pi$
$613$	−5.86242e12	−1.67689	−0.838446	+	0.544985i	$0.816536\pi$
$614$	4.83053e12	1.37163
$615$	2.28841e11	0.0645052
$616$	−2.34498e12	−0.656185
$617$	1.22260e12	0.339627	0.169813	−	0.985476i	$-0.445683\pi$
$617$	1.22260e12	0.339627	0.169813	+	0.985476i	$0.445683\pi$
$618$	−1.89539e12	−0.522697
$619$	−1.93897e12	−0.530839	−0.265419	−	0.964133i	$-0.585510\pi$
$619$	−1.93897e12	−0.530839	−0.265419	+	0.964133i	$0.585510\pi$
$620$	2.42380e11	0.0658769
$621$	−1.13953e13	−3.07477
$622$	6.84738e10	0.0183429
$623$	4.21112e12	1.11996
$624$	−4.67233e12	−1.23368
$625$	2.85731e12	0.749027
$626$	−5.11431e12	−1.33108
$627$	3.69146e12	0.953880
$628$	−3.44988e11	−0.0885087
$629$	0	0
$630$	−1.64824e12	−0.416857
$631$	1.81093e12	0.454745	0.227373	−	0.973808i	$-0.426986\pi$
$631$	1.81093e12	0.454745	0.227373	+	0.973808i	$0.426986\pi$
$632$	7.30143e12	1.82046
$633$	7.59721e12	1.88078
$634$	2.73307e11	0.0671813
$635$	7.75308e11	0.189231
$636$	−3.95855e12	−0.959354
$637$	−1.73550e12	−0.417636
$638$	−4.45439e12	−1.06438
$639$	4.73252e12	1.12289
$640$	3.31569e11	0.0781204
$641$	−4.97742e12	−1.16451	−0.582255	−	0.813006i	$-0.697829\pi$
$641$	−4.97742e12	−1.16451	−0.582255	+	0.813006i	$0.697829\pi$
$642$	4.58807e12	1.06591
$643$	2.90941e12	0.671205	0.335603	−	0.942004i	$-0.391060\pi$
$643$	2.90941e12	0.671205	0.335603	+	0.942004i	$0.391060\pi$
$644$	−1.77147e12	−0.405834
$645$	−3.93890e12	−0.896100
$646$	0	0
$647$	−7.03168e12	−1.57757	−0.788787	−	0.614667i	$-0.789291\pi$
$647$	−7.03168e12	−1.57757	−0.788787	+	0.614667i	$0.789291\pi$
$648$	−6.86884e12	−1.53037
$649$	−2.80037e12	−0.619604
$650$	−4.18455e12	−0.919473
$651$	4.54608e12	0.992025
$652$	1.28764e12	0.279050
$653$	4.91143e12	1.05706	0.528529	−	0.848915i	$-0.322744\pi$
$653$	4.91143e12	1.05706	0.528529	+	0.848915i	$0.322744\pi$
$654$	−3.93982e11	−0.0842125
$655$	2.21475e12	0.470153
$656$	−3.35586e11	−0.0707516
$657$	−6.59458e12	−1.38084
$658$	3.30881e12	0.688106
$659$	5.22854e12	1.07993	0.539965	−	0.841687i	$-0.318437\pi$
$659$	5.22854e12	1.07993	0.539965	+	0.841687i	$0.318437\pi$
$660$	6.10682e11	0.125276
$661$	6.13405e11	0.124980	0.0624900	−	0.998046i	$-0.480096\pi$
$661$	6.13405e11	0.124980	0.0624900	+	0.998046i	$0.480096\pi$
$662$	1.03433e12	0.209315
$663$	0	0
$664$	−2.41280e12	−0.481686
$665$	8.72401e11	0.172989
$666$	−8.56785e12	−1.68748
$667$	−1.37206e13	−2.68415
$668$	1.54545e12	0.300303
$669$	−1.69358e13	−3.26881
$670$	−1.98003e12	−0.379609
$671$	7.02882e11	0.133854
$672$	−4.71226e12	−0.891390
$673$	3.53388e12	0.664024	0.332012	−	0.943275i	$-0.392273\pi$
$673$	3.53388e12	0.664024	0.332012	+	0.943275i	$0.392273\pi$
$674$	9.81395e11	0.183178
$675$	−9.85034e12	−1.82635
$676$	−8.81403e11	−0.162336
$677$	6.61674e11	0.121058	0.0605292	−	0.998166i	$-0.480721\pi$
$677$	6.61674e11	0.121058	0.0605292	+	0.998166i	$0.480721\pi$
$678$	−1.58608e12	−0.288265
$679$	6.03237e12	1.08912
$680$	0	0
$681$	8.60556e11	0.153326
$682$	2.38110e12	0.421451
$683$	1.11478e12	0.196018	0.0980092	−	0.995186i	$-0.468753\pi$
$683$	1.11478e12	0.196018	0.0980092	+	0.995186i	$0.468753\pi$
$684$	2.87665e12	0.502498
$685$	4.45879e11	0.0773766
$686$	5.18799e12	0.894419
$687$	−6.26827e11	−0.107360
$688$	5.77624e12	0.982873
$689$	1.20891e13	2.04365
$690$	−3.90778e12	−0.656310
$691$	−4.47728e12	−0.747073	−0.373537	−	0.927615i	$-0.621855\pi$
$691$	−4.47728e12	−0.747073	−0.373537	+	0.927615i	$0.621855\pi$
$692$	−1.39054e11	−0.0230519
$693$	7.79417e12	1.28372
$694$	−2.96097e12	−0.484525
$695$	−4.44461e10	−0.00722607
$696$	−2.07995e13	−3.35978
$697$	0	0
$698$	−8.00949e12	−1.27719
$699$	−7.17624e12	−1.13697
$700$	−1.53131e12	−0.241057
$701$	−8.30446e11	−0.129891	−0.0649457	−	0.997889i	$-0.520687\pi$
$701$	−8.30446e11	−0.129891	−0.0649457	+	0.997889i	$0.520687\pi$
$702$	1.29381e13	2.01073
$703$	4.53491e12	0.700276
$704$	−5.22412e12	−0.801560
$705$	−3.51347e12	−0.535655
$706$	6.87892e12	1.04208
$707$	2.47595e12	0.372695
$708$	−3.20694e12	−0.479668
$709$	−4.64109e12	−0.689783	−0.344891	−	0.938643i	$-0.612084\pi$
$709$	−4.64109e12	−0.689783	−0.344891	+	0.938643i	$0.612084\pi$
$710$	8.60869e11	0.127138
$711$	−2.42683e13	−3.56144
$712$	1.02991e13	1.50190
$713$	7.33435e12	1.06282
$714$	0	0
$715$	−1.86497e12	−0.266867
$716$	3.91779e11	0.0557100
$717$	3.88534e12	0.549025
$718$	7.16245e12	1.00578
$719$	−1.16114e13	−1.62033	−0.810167	−	0.586200i	$-0.800623\pi$
$719$	−1.16114e13	−1.62033	−0.810167	+	0.586200i	$0.800623\pi$
$720$	−2.56658e12	−0.355925
$721$	2.11820e12	0.291916
$722$	−2.83601e12	−0.388410
$723$	1.68416e13	2.29225
$724$	−1.38590e12	−0.187461
$725$	−1.18604e13	−1.59433
$726$	−4.88088e12	−0.652054
$727$	−4.87352e12	−0.647051	−0.323525	−	0.946220i	$-0.604868\pi$
$727$	−4.87352e12	−0.647051	−0.323525	+	0.946220i	$0.604868\pi$
$728$	8.20108e12	1.08213
$729$	−4.12973e12	−0.541562
$730$	−1.19959e12	−0.156343
$731$	0	0
$732$	8.04929e11	0.103623
$733$	8.99318e11	0.115066	0.0575328	−	0.998344i	$-0.481677\pi$
$733$	8.99318e11	0.115066	0.0575328	+	0.998344i	$0.481677\pi$
$734$	−4.91196e12	−0.624630
$735$	−1.40099e12	−0.177068
$736$	−7.60245e12	−0.955000
$737$	9.36318e12	1.16901
$738$	1.75187e12	0.217395
$739$	7.06000e12	0.870772	0.435386	−	0.900244i	$-0.356612\pi$
$739$	7.06000e12	0.870772	0.435386	+	0.900244i	$0.356612\pi$
$740$	7.50215e11	0.0919694
$741$	−1.29101e13	−1.57307
$742$	−9.19043e12	−1.11306
$743$	2.21446e9	0.000266575 0	0.000133287	−	1.00000i	$-0.499958\pi$
$743$	2.21446e9	0.000266575 0	0.000133287		1.00000i	$0.499958\pi$
$744$	1.11184e13	1.33034
$745$	4.46829e12	0.531421
$746$	1.90652e11	0.0225381
$747$	8.01957e12	0.942342
$748$	0	0
$749$	−5.12742e12	−0.595293
$750$	−7.07433e12	−0.816412
$751$	1.08932e12	0.124961	0.0624806	−	0.998046i	$-0.480099\pi$
$751$	1.08932e12	0.124961	0.0624806	+	0.998046i	$0.480099\pi$
$752$	5.15237e12	0.587525
$753$	−5.29113e12	−0.599751
$754$	1.55783e13	1.75529
$755$	4.50012e12	0.504038
$756$	4.73461e12	0.527152
$757$	−1.96439e12	−0.217418	−0.108709	−	0.994074i	$-0.534672\pi$
$757$	−1.96439e12	−0.217418	−0.108709	+	0.994074i	$0.534672\pi$
$758$	−4.24915e12	−0.467509
$759$	1.84791e13	2.02112
$760$	2.13364e12	0.231985
$761$	−8.98233e12	−0.970863	−0.485431	−	0.874275i	$-0.661337\pi$
$761$	−8.98233e12	−0.970863	−0.485431	+	0.874275i	$0.661337\pi$
$762$	8.72229e12	0.937202
$763$	4.40297e11	0.0470311
$764$	6.65220e11	0.0706391
$765$	0	0
$766$	−1.35656e12	−0.142367
$767$	9.79370e12	1.02180
$768$	−1.46809e13	−1.52275
$769$	1.08966e12	0.112363	0.0561814	−	0.998421i	$-0.482107\pi$
$769$	1.08966e12	0.112363	0.0561814	+	0.998421i	$0.482107\pi$
$770$	1.41780e12	0.145347
$771$	2.70374e13	2.75562
$772$	−8.09889e11	−0.0820631
$773$	2.16020e12	0.217614	0.108807	−	0.994063i	$-0.465297\pi$
$773$	2.16020e12	0.217614	0.108807	+	0.994063i	$0.465297\pi$
$774$	−3.01540e13	−3.02003
$775$	6.33998e12	0.631292
$776$	1.47534e13	1.46054
$777$	1.40711e13	1.38495
$778$	−3.06665e12	−0.300093
$779$	−9.27256e11	−0.0902154
$780$	−2.13573e12	−0.206596
$781$	−4.07087e12	−0.391523
$782$	0	0
$783$	3.66710e13	3.48654
$784$	2.05449e12	0.194215
$785$	8.50489e11	0.0799384
$786$	2.49162e13	2.32852
$787$	8.31458e11	0.0772599	0.0386300	−	0.999254i	$-0.487701\pi$
$787$	8.31458e11	0.0772599	0.0386300	+	0.999254i	$0.487701\pi$
$788$	−2.94983e12	−0.272539
$789$	1.74768e13	1.60552
$790$	−4.41452e12	−0.403238
$791$	1.77254e12	0.160991
$792$	1.90622e13	1.72151
$793$	−2.45818e12	−0.220742
$794$	7.90969e12	0.706264
$795$	9.75889e12	0.866459
$796$	3.77680e12	0.333438
$797$	−1.51673e12	−0.133152	−0.0665759	−	0.997781i	$-0.521207\pi$
$797$	−1.51673e12	−0.133152	−0.0665759	+	0.997781i	$0.521207\pi$
$798$	9.81460e12	0.856761
$799$	0	0
$800$	−6.57174e12	−0.567251
$801$	−3.42320e13	−2.93823
$802$	1.78273e13	1.52160
$803$	5.67261e12	0.481463
$804$	1.07226e13	0.904995
$805$	4.36716e12	0.366537
$806$	−8.32738e12	−0.695026
$807$	−2.18027e13	−1.80959
$808$	6.05543e12	0.499797
$809$	−1.90042e13	−1.55985	−0.779923	−	0.625876i	$-0.784742\pi$
$809$	−1.90042e13	−1.55985	−0.779923	+	0.625876i	$0.784742\pi$
$810$	4.15298e12	0.338982
$811$	−1.01063e13	−0.820346	−0.410173	−	0.912008i	$-0.634532\pi$
$811$	−1.01063e13	−0.820346	−0.410173	+	0.912008i	$0.634532\pi$
$812$	5.70076e12	0.460183
$813$	−3.20031e12	−0.256912
$814$	7.36999e12	0.588379
$815$	−3.17439e12	−0.252029
$816$	0	0
$817$	1.59603e13	1.25326
$818$	−1.09828e13	−0.857680
$819$	−2.72585e13	−2.11702
$820$	−1.53397e11	−0.0118483
$821$	−1.37434e12	−0.105573	−0.0527863	−	0.998606i	$-0.516810\pi$
$821$	−1.37434e12	−0.105573	−0.0527863	+	0.998606i	$0.516810\pi$
$822$	5.01618e12	0.383222
$823$	−7.63090e12	−0.579798	−0.289899	−	0.957057i	$-0.593622\pi$
$823$	−7.63090e12	−0.579798	−0.289899	+	0.957057i	$0.593622\pi$
$824$	5.18049e12	0.391470
$825$	1.59738e13	1.20051
$826$	−7.44543e12	−0.556519
$827$	3.04066e12	0.226044	0.113022	−	0.993592i	$-0.463947\pi$
$827$	3.04066e12	0.226044	0.113022	+	0.993592i	$0.463947\pi$
$828$	1.44002e13	1.06471
$829$	−1.93690e13	−1.42434	−0.712169	−	0.702009i	$-0.752287\pi$
$829$	−1.93690e13	−1.42434	−0.712169	+	0.702009i	$0.752287\pi$
$830$	1.45880e12	0.106695
$831$	2.93837e12	0.213748
$832$	1.82703e13	1.32187
$833$	0	0
$834$	−5.00023e11	−0.0357885
$835$	−3.80994e12	−0.271224
$836$	−2.47447e12	−0.175208
$837$	−1.96025e13	−1.38053
$838$	−1.49713e13	−1.04872
$839$	−1.02488e13	−0.714075	−0.357038	−	0.934090i	$-0.616213\pi$
$839$	−1.02488e13	−0.714075	−0.357038	+	0.934090i	$0.616213\pi$
$840$	6.62032e12	0.458799
$841$	2.96469e13	2.04361
$842$	1.55402e13	1.06550
$843$	−6.42065e12	−0.437879
$844$	−5.09259e12	−0.345460
$845$	2.17289e12	0.146617
$846$	−2.68972e13	−1.80526
$847$	5.45465e12	0.364160
$848$	−1.43110e13	−0.950363
$849$	−4.43770e13	−2.93139
$850$	0	0
$851$	2.27013e13	1.48378
$852$	−4.66190e12	−0.303099
$853$	−2.38203e13	−1.54055	−0.770277	−	0.637709i	$-0.779882\pi$
$853$	−2.38203e13	−1.54055	−0.770277	+	0.637709i	$0.779882\pi$
$854$	1.86878e12	0.120226
$855$	−7.09171e12	−0.453841
$856$	−1.25402e13	−0.798309
$857$	−1.39643e13	−0.884313	−0.442156	−	0.896938i	$-0.645786\pi$
$857$	−1.39643e13	−0.884313	−0.442156	+	0.896938i	$0.645786\pi$
$858$	−2.09811e13	−1.32171
$859$	−2.35562e13	−1.47617	−0.738085	−	0.674708i	$-0.764270\pi$
$859$	−2.35562e13	−1.47617	−0.738085	+	0.674708i	$0.764270\pi$
$860$	2.64034e12	0.164595
$861$	−2.87712e12	−0.178420
$862$	−6.04404e12	−0.372859
$863$	3.14620e13	1.93080	0.965402	−	0.260768i	$-0.0839756\pi$
$863$	3.14620e13	1.93080	0.965402	+	0.260768i	$0.0839756\pi$
$864$	2.03190e13	1.24048
$865$	3.42805e11	0.0208197
$866$	2.02491e13	1.22342
$867$	0	0
$868$	−3.04734e12	−0.182214
$869$	2.08754e13	1.24178
$870$	1.25756e13	0.744203
$871$	−3.27457e13	−1.92785
$872$	1.07683e12	0.0630703
$873$	−4.90369e13	−2.85732
$874$	1.58342e13	0.917900
$875$	7.90595e12	0.455951
$876$	6.49618e12	0.372726
$877$	2.33297e12	0.133171	0.0665856	−	0.997781i	$-0.478789\pi$
$877$	2.33297e12	0.133171	0.0665856	+	0.997781i	$0.478789\pi$
$878$	−7.22546e12	−0.410337
$879$	2.98578e13	1.68697
$880$	2.20775e12	0.124102
$881$	−2.27950e13	−1.27482	−0.637410	−	0.770525i	$-0.719994\pi$
$881$	−2.27950e13	−1.27482	−0.637410	+	0.770525i	$0.719994\pi$
$882$	−1.07252e13	−0.596754
$883$	2.09851e13	1.16168	0.580842	−	0.814016i	$-0.302723\pi$
$883$	2.09851e13	1.16168	0.580842	+	0.814016i	$0.302723\pi$
$884$	0	0
$885$	7.90596e12	0.433221
$886$	6.82822e10	0.00372268
$887$	1.35033e13	0.732461	0.366231	−	0.930524i	$-0.380648\pi$
$887$	1.35033e13	0.732461	0.366231	+	0.930524i	$0.380648\pi$
$888$	3.44137e13	1.85726
$889$	−9.74764e12	−0.523409
$890$	−6.22697e12	−0.332676
$891$	−1.96386e13	−1.04390
$892$	1.13525e13	0.600411
$893$	1.42365e13	0.749155
$894$	5.02687e13	2.63196
$895$	−9.65842e11	−0.0503156
$896$	−4.16869e12	−0.216080
$897$	−6.46267e13	−3.33308
$898$	2.39050e13	1.22672
$899$	−2.36026e13	−1.20515
$900$	1.24479e13	0.632419
$901$	0	0
$902$	−1.50695e12	−0.0757999
$903$	4.95223e13	2.47859
$904$	4.33510e12	0.215894
$905$	3.41663e12	0.169309
$906$	5.06268e13	2.49634
$907$	1.89466e13	0.929604	0.464802	−	0.885415i	$-0.346125\pi$
$907$	1.89466e13	0.929604	0.464802	+	0.885415i	$0.346125\pi$
$908$	−5.76850e11	−0.0281629
$909$	−2.01269e13	−0.977774
$910$	−4.95846e12	−0.239696
$911$	−8.16279e12	−0.392650	−0.196325	−	0.980539i	$-0.562901\pi$
$911$	−8.16279e12	−0.392650	−0.196325	+	0.980539i	$0.562901\pi$
$912$	1.52830e13	0.731528
$913$	−6.89837e12	−0.328570
$914$	8.80360e12	0.417256
$915$	−1.98437e12	−0.0935895
$916$	4.20177e11	0.0197198
$917$	−2.78452e13	−1.30043
$918$	0	0
$919$	−1.43127e13	−0.661915	−0.330958	−	0.943646i	$-0.607372\pi$
$919$	−1.43127e13	−0.661915	−0.330958	+	0.943646i	$0.607372\pi$
$920$	1.06808e13	0.491539
$921$	6.44888e13	2.95336
$922$	1.02659e13	0.467849
$923$	1.42370e13	0.645671
$924$	−7.67787e12	−0.346511
$925$	1.96236e13	0.881333
$926$	2.36472e13	1.05689
$927$	−1.72187e13	−0.765848
$928$	2.44654e13	1.08289
$929$	−3.72716e13	−1.64175	−0.820876	−	0.571107i	$-0.806514\pi$
$929$	−3.72716e13	−1.64175	−0.820876	+	0.571107i	$0.806514\pi$
$930$	−6.72228e12	−0.294675
$931$	5.67676e12	0.247643
$932$	4.81040e12	0.208838
$933$	9.14144e11	0.0394955
$934$	−5.76653e12	−0.247944
$935$	0	0
$936$	−6.66662e13	−2.83899
$937$	2.60937e13	1.10588	0.552938	−	0.833222i	$-0.313507\pi$
$937$	2.60937e13	1.10588	0.552938	+	0.833222i	$0.313507\pi$
$938$	2.48942e13	1.04999
$939$	−6.82774e13	−2.86604
$940$	2.35516e12	0.0983887
$941$	1.50867e13	0.627249	0.313624	−	0.949547i	$-0.398457\pi$
$941$	1.50867e13	0.627249	0.313624	+	0.949547i	$0.398457\pi$
$942$	9.56809e12	0.395910
$943$	−4.64176e12	−0.191152
$944$	−1.15938e13	−0.475172
$945$	−1.16721e13	−0.476108
$946$	2.59382e13	1.05300
$947$	−2.11071e12	−0.0852812	−0.0426406	−	0.999090i	$-0.513577\pi$
$947$	−2.11071e12	−0.0852812	−0.0426406	+	0.999090i	$0.513577\pi$
$948$	2.39061e13	0.961329
$949$	−1.98387e13	−0.793992
$950$	1.36875e13	0.545214
$951$	3.64872e12	0.144653
$952$	0	0
$953$	−1.48999e13	−0.585149	−0.292574	−	0.956243i	$-0.594512\pi$
$953$	−1.48999e13	−0.585149	−0.292574	+	0.956243i	$0.594512\pi$
$954$	7.47085e13	2.92013
$955$	−1.63995e12	−0.0637990
$956$	−2.60443e12	−0.100844
$957$	−5.94673e13	−2.29179
$958$	3.66118e12	0.140435
$959$	−5.60586e12	−0.214022
$960$	1.47487e13	0.560444
$961$	−1.38229e13	−0.522809
$962$	−2.57750e13	−0.970310
$963$	4.16806e13	1.56176
$964$	−1.12893e13	−0.421038
$965$	1.99659e12	0.0741169
$966$	4.91310e13	1.81534
$967$	−1.89322e13	−0.696276	−0.348138	−	0.937443i	$-0.613186\pi$
$967$	−1.89322e13	−0.696276	−0.348138	+	0.937443i	$0.613186\pi$
$968$	1.33405e13	0.488351
$969$	0	0
$970$	−8.92006e12	−0.323515
$971$	−2.02308e12	−0.0730344	−0.0365172	−	0.999333i	$-0.511626\pi$
$971$	−2.02308e12	−0.0730344	−0.0365172	+	0.999333i	$0.511626\pi$
$972$	−4.41774e12	−0.158746
$973$	5.58804e11	0.0199872
$974$	6.08399e12	0.216607
$975$	−5.58649e13	−1.97979
$976$	2.91000e12	0.102652
$977$	−4.24880e13	−1.49190	−0.745952	−	0.666000i	$-0.768005\pi$
$977$	−4.24880e13	−1.49190	−0.745952	+	0.666000i	$0.768005\pi$
$978$	−3.57122e13	−1.24822
$979$	2.94461e13	1.02448
$980$	9.39113e11	0.0325238
$981$	−3.57915e12	−0.123387
$982$	1.06041e13	0.363893
$983$	−1.09738e13	−0.374859	−0.187429	−	0.982278i	$-0.560016\pi$
$983$	−1.09738e13	−0.374859	−0.187429	+	0.982278i	$0.560016\pi$
$984$	−7.03659e12	−0.239268
$985$	7.27212e12	0.246149
$986$	0	0
$987$	4.41735e13	1.48161
$988$	8.65393e12	0.288940
$989$	7.98959e13	2.65547
$990$	−1.15252e13	−0.381321
$991$	−2.60563e13	−0.858186	−0.429093	−	0.903260i	$-0.641167\pi$
$991$	−2.60563e13	−0.858186	−0.429093	+	0.903260i	$0.641167\pi$
$992$	−1.30780e13	−0.428783
$993$	1.38086e13	0.450691
$994$	−1.08234e13	−0.351660
$995$	−9.31083e12	−0.301151
$996$	−7.89991e12	−0.254364
$997$	−1.56129e13	−0.500445	−0.250223	−	0.968188i	$-0.580504\pi$
$997$	−1.56129e13	−0.500445	−0.250223	+	0.968188i	$0.580504\pi$
$998$	5.47494e12	0.174700
$999$	−6.06737e13	−1.92733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.24	✓	36
17.16	even	2		289.10.a.h.1.24	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.24	✓	36	1.1	even	1	trivial
289.10.a.h.1.24	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)

\(f(q)\)	\(=\)	\(q+18.5911 q^{2} +248.196 q^{3} -166.372 q^{4} +410.150 q^{5} +4614.23 q^{6} -5156.66 q^{7} -12611.7 q^{8} +41918.2 q^{9} +O(q^{10})\)	\(q+18.5911 q^{2} +248.196 q^{3} -166.372 q^{4} +410.150 q^{5} +4614.23 q^{6} -5156.66 q^{7} -12611.7 q^{8} +41918.2 q^{9} +7625.14 q^{10} -36057.7 q^{11} -41292.7 q^{12} +126104. q^{13} -95867.9 q^{14} +101798. q^{15} -149282. q^{16} +779306. q^{18} -412482. q^{19} -68237.4 q^{20} -1.27986e6 q^{21} -670352. q^{22} -2.06485e6 q^{23} -3.13016e6 q^{24} -1.78490e6 q^{25} +2.34442e6 q^{26} +5.51870e6 q^{27} +857921. q^{28} +6.64485e6 q^{29} +1.89253e6 q^{30} -3.55201e6 q^{31} +3.68185e6 q^{32} -8.94938e6 q^{33} -2.11501e6 q^{35} -6.97400e6 q^{36} -1.09942e7 q^{37} -7.66848e6 q^{38} +3.12986e7 q^{39} -5.17268e6 q^{40} +2.24799e6 q^{41} -2.37940e7 q^{42} -3.86934e7 q^{43} +5.99898e6 q^{44} +1.71928e7 q^{45} -3.83877e7 q^{46} -3.45143e7 q^{47} -3.70513e7 q^{48} -1.37625e7 q^{49} -3.31833e7 q^{50} -2.09802e7 q^{52} +9.58655e7 q^{53} +1.02599e8 q^{54} -1.47891e7 q^{55} +6.50341e7 q^{56} -1.02376e8 q^{57} +1.23535e8 q^{58} +7.76635e7 q^{59} -1.69362e7 q^{60} -1.94932e7 q^{61} -6.60357e7 q^{62} -2.16158e8 q^{63} +1.44882e8 q^{64} +5.17217e7 q^{65} -1.66379e8 q^{66} -2.59672e8 q^{67} -5.12486e8 q^{69} -3.93203e7 q^{70} +1.12899e8 q^{71} -5.28659e8 q^{72} -1.57320e8 q^{73} -2.04394e8 q^{74} -4.43005e8 q^{75} +6.86252e7 q^{76} +1.85937e8 q^{77} +5.81875e8 q^{78} -5.78943e8 q^{79} -6.12282e7 q^{80} +5.44642e8 q^{81} +4.17926e7 q^{82} +1.91315e8 q^{83} +2.12933e8 q^{84} -7.19353e8 q^{86} +1.64923e9 q^{87} +4.54748e8 q^{88} -8.16637e8 q^{89} +3.19633e8 q^{90} -6.50277e8 q^{91} +3.43531e8 q^{92} -8.81594e8 q^{93} -6.41657e8 q^{94} -1.69180e8 q^{95} +9.13821e8 q^{96} -1.16982e9 q^{97} -2.55859e8 q^{98} -1.51148e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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