LMFDB - Embedded newform 289.10.a.h.1.9

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:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-22.6693 q^{2} +265.602 q^{3} +1.89626 q^{4} +368.101 q^{5} -6021.01 q^{6} -2877.49 q^{7} +11563.7 q^{8} +50861.5 q^{9} +O(q^{10})$	\(q-22.6693 q^{2} +265.602 q^{3} +1.89626 q^{4} +368.101 q^{5} -6021.01 q^{6} -2877.49 q^{7} +11563.7 q^{8} +50861.5 q^{9} -8344.59 q^{10} -63835.2 q^{11} +503.651 q^{12} -149124. q^{13} +65230.7 q^{14} +97768.4 q^{15} -263111. q^{16} -1.15299e6 q^{18} +444434. q^{19} +698.016 q^{20} -764268. q^{21} +1.44710e6 q^{22} -1.56940e6 q^{23} +3.07134e6 q^{24} -1.81763e6 q^{25} +3.38054e6 q^{26} +8.28107e6 q^{27} -5456.48 q^{28} +5.40558e6 q^{29} -2.21634e6 q^{30} +759714. q^{31} +43937.0 q^{32} -1.69548e7 q^{33} -1.05921e6 q^{35} +96446.6 q^{36} +3.93163e6 q^{37} -1.00750e7 q^{38} -3.96077e7 q^{39} +4.25661e6 q^{40} -9.97180e6 q^{41} +1.73254e7 q^{42} +2.04493e7 q^{43} -121048. q^{44} +1.87222e7 q^{45} +3.55771e7 q^{46} +4.76880e7 q^{47} -6.98829e7 q^{48} -3.20736e7 q^{49} +4.12043e7 q^{50} -282778. q^{52} -5.80242e6 q^{53} -1.87726e8 q^{54} -2.34978e7 q^{55} -3.32744e7 q^{56} +1.18043e8 q^{57} -1.22540e8 q^{58} +9.50173e7 q^{59} +185394. q^{60} +1.59704e8 q^{61} -1.72222e7 q^{62} -1.46353e8 q^{63} +1.33717e8 q^{64} -5.48928e7 q^{65} +3.84352e8 q^{66} +8.38127e7 q^{67} -4.16835e8 q^{69} +2.40115e7 q^{70} +3.10856e8 q^{71} +5.88146e8 q^{72} +3.37571e8 q^{73} -8.91273e7 q^{74} -4.82765e8 q^{75} +842764. q^{76} +1.83685e8 q^{77} +8.97878e8 q^{78} -5.51861e7 q^{79} -9.68516e7 q^{80} +1.19836e9 q^{81} +2.26053e8 q^{82} +3.47302e8 q^{83} -1.44925e6 q^{84} -4.63570e8 q^{86} +1.43573e9 q^{87} -7.38171e8 q^{88} -3.74829e8 q^{89} -4.24418e8 q^{90} +4.29104e8 q^{91} -2.97598e6 q^{92} +2.01782e8 q^{93} -1.08105e9 q^{94} +1.63597e8 q^{95} +1.16698e7 q^{96} +1.18045e9 q^{97} +7.27087e8 q^{98} -3.24675e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−22.6693	−1.00185	−0.500925	−	0.865491i	$-0.667007\pi$
$2$	−22.6693	−1.00185	−0.500925	+	0.865491i	$0.667007\pi$
$3$	265.602	1.89315	0.946577	−	0.322479i	$-0.104516\pi$
$3$	265.602	1.89315	0.946577	+	0.322479i	$0.104516\pi$
$4$	1.89626	0.00370363
$5$	368.101	0.263392	0.131696	−	0.991290i	$-0.457958\pi$
$5$	368.101	0.263392	0.131696	+	0.991290i	$0.457958\pi$
$6$	−6021.01	−1.89666
$7$	−2877.49	−0.452974	−0.226487	−	0.974014i	$-0.572724\pi$
$7$	−2877.49	−0.452974	−0.226487	+	0.974014i	$0.572724\pi$
$8$	11563.7	0.998140
$9$	50861.5	2.58403
$10$	−8344.59	−0.263879
$11$	−63835.2	−1.31460	−0.657300	−	0.753629i	$-0.728301\pi$
$11$	−63835.2	−1.31460	−0.657300	+	0.753629i	$0.728301\pi$
$12$	503.651	0.00701155
$13$	−149124.	−1.44812	−0.724058	−	0.689740i	$-0.757725\pi$
$13$	−149124.	−1.44812	−0.724058	+	0.689740i	$0.757725\pi$
$14$	65230.7	0.453812
$15$	97768.4	0.498641
$16$	−263111.	−1.00369
$17$	0	0
$17$	0	0
$18$	−1.15299e6	−2.58881
$19$	444434.	0.782378	0.391189	−	0.920310i	$-0.372064\pi$
$19$	444434.	0.782378	0.391189	+	0.920310i	$0.372064\pi$
$20$	698.016	0.000975507 0
$21$	−764268.	−0.857549
$22$	1.44710e6	1.31703
$23$	−1.56940e6	−1.16938	−0.584692	−	0.811255i	$-0.698785\pi$
$23$	−1.56940e6	−1.16938	−0.584692	+	0.811255i	$0.698785\pi$
$24$	3.07134e6	1.88963
$25$	−1.81763e6	−0.930625
$26$	3.38054e6	1.45079
$27$	8.28107e6	2.99881
$28$	−5456.48	−0.00167765
$29$	5.40558e6	1.41922	0.709612	−	0.704593i	$-0.248870\pi$
$29$	5.40558e6	1.41922	0.709612	+	0.704593i	$0.248870\pi$
$30$	−2.21634e6	−0.499564
$31$	759714.	0.147748	0.0738742	−	0.997268i	$-0.476464\pi$
$31$	759714.	0.147748	0.0738742	+	0.997268i	$0.476464\pi$
$32$	43937.0	0.00740723
$33$	−1.69548e7	−2.48874
$34$	0	0
$35$	−1.05921e6	−0.119310
$36$	96446.6	0.00957031
$37$	3.93163e6	0.344878	0.172439	−	0.985020i	$-0.444835\pi$
$37$	3.93163e6	0.344878	0.172439	+	0.985020i	$0.444835\pi$
$38$	−1.00750e7	−0.783825
$39$	−3.96077e7	−2.74150
$40$	4.25661e6	0.262902
$41$	−9.97180e6	−0.551120	−0.275560	−	0.961284i	$-0.588863\pi$
$41$	−9.97180e6	−0.551120	−0.275560	+	0.961284i	$0.588863\pi$
$42$	1.73254e7	0.859135
$43$	2.04493e7	0.912157	0.456079	−	0.889939i	$-0.349254\pi$
$43$	2.04493e7	0.912157	0.456079	+	0.889939i	$0.349254\pi$
$44$	−121048.	−0.00486880
$45$	1.87222e7	0.680612
$46$	3.55771e7	1.17155
$47$	4.76880e7	1.42551	0.712753	−	0.701416i	$-0.247448\pi$
$47$	4.76880e7	1.42551	0.712753	+	0.701416i	$0.247448\pi$
$48$	−6.98829e7	−1.90014
$49$	−3.20736e7	−0.794815
$50$	4.12043e7	0.932347
$51$	0	0
$52$	−282778.	−0.00536329
$53$	−5.80242e6	−0.101011	−0.0505054	−	0.998724i	$-0.516083\pi$
$53$	−5.80242e6	−0.101011	−0.0505054	+	0.998724i	$0.516083\pi$
$54$	−1.87726e8	−3.00436
$55$	−2.34978e7	−0.346255
$56$	−3.32744e7	−0.452131
$57$	1.18043e8	1.48116
$58$	−1.22540e8	−1.42185
$59$	9.50173e7	1.02087	0.510433	−	0.859918i	$-0.329485\pi$
$59$	9.50173e7	1.02087	0.510433	+	0.859918i	$0.329485\pi$
$60$	185394.	0.00184678
$61$	1.59704e8	1.47683	0.738417	−	0.674344i	$-0.235574\pi$
$61$	1.59704e8	1.47683	0.738417	+	0.674344i	$0.235574\pi$
$62$	−1.72222e7	−0.148022
$63$	−1.46353e8	−1.17050
$64$	1.33717e8	0.996269
$65$	−5.48928e7	−0.381422
$66$	3.84352e8	2.49334
$67$	8.38127e7	0.508128	0.254064	−	0.967187i	$-0.418233\pi$
$67$	8.38127e7	0.508128	0.254064	+	0.967187i	$0.418233\pi$
$68$	0	0
$69$	−4.16835e8	−2.21382
$70$	2.40115e7	0.119530
$71$	3.10856e8	1.45177	0.725883	−	0.687818i	$-0.241431\pi$
$71$	3.10856e8	1.45177	0.725883	+	0.687818i	$0.241431\pi$
$72$	5.88146e8	2.57922
$73$	3.37571e8	1.39127	0.695636	−	0.718394i	$-0.255123\pi$
$73$	3.37571e8	1.39127	0.695636	+	0.718394i	$0.255123\pi$
$74$	−8.91273e7	−0.345516
$75$	−4.82765e8	−1.76182
$76$	842764.	0.00289764
$77$	1.83685e8	0.595479
$78$	8.97878e8	2.74658
$79$	−5.51861e7	−0.159407	−0.0797035	−	0.996819i	$-0.525397\pi$
$79$	−5.51861e7	−0.159407	−0.0797035	+	0.996819i	$0.525397\pi$
$80$	−9.68516e7	−0.264364
$81$	1.19836e9	3.09318
$82$	2.26053e8	0.552139
$83$	3.47302e8	0.803259	0.401630	−	0.915802i	$-0.368444\pi$
$83$	3.47302e8	0.803259	0.401630	+	0.915802i	$0.368444\pi$
$84$	−1.44925e6	−0.00317605
$85$	0	0
$86$	−4.63570e8	−0.913845
$87$	1.43573e9	2.68681
$88$	−7.38171e8	−1.31215
$89$	−3.74829e8	−0.633254	−0.316627	−	0.948550i	$-0.602550\pi$
$89$	−3.74829e8	−0.633254	−0.316627	+	0.948550i	$0.602550\pi$
$90$	−4.24418e8	−0.681872
$91$	4.29104e8	0.655958
$92$	−2.97598e6	−0.00433097
$93$	2.01782e8	0.279710
$94$	−1.08105e9	−1.42814
$95$	1.63597e8	0.206072
$96$	1.16698e7	0.0140230
$97$	1.18045e9	1.35386	0.676930	−	0.736048i	$-0.263310\pi$
$97$	1.18045e9	1.35386	0.676930	+	0.736048i	$0.263310\pi$
$98$	7.27087e8	0.796285
$99$	−3.24675e9	−3.39696
$100$	−3.44669e6	−0.00344669
$101$	8.07593e8	0.772229	0.386115	−	0.922451i	$-0.373817\pi$
$101$	8.07593e8	0.772229	0.386115	+	0.922451i	$0.373817\pi$
$102$	0	0
$103$	−6.25799e8	−0.547857	−0.273929	−	0.961750i	$-0.588323\pi$
$103$	−6.25799e8	−0.547857	−0.273929	+	0.961750i	$0.588323\pi$
$104$	−1.72443e9	−1.44542
$105$	−2.81328e8	−0.225871
$106$	1.31537e8	0.101198
$107$	−2.57640e9	−1.90015	−0.950073	−	0.312027i	$-0.898992\pi$
$107$	−2.57640e9	−1.90015	−0.950073	+	0.312027i	$0.898992\pi$
$108$	1.57031e7	0.0111065
$109$	−4.19046e8	−0.284343	−0.142171	−	0.989842i	$-0.545408\pi$
$109$	−4.19046e8	−0.284343	−0.142171	+	0.989842i	$0.545408\pi$
$110$	5.32679e8	0.346895
$111$	1.04425e9	0.652907
$112$	7.57101e8	0.454645
$113$	−1.22248e9	−0.705326	−0.352663	−	0.935750i	$-0.614724\pi$
$113$	−1.22248e9	−0.705326	−0.352663	+	0.935750i	$0.614724\pi$
$114$	−2.67594e9	−1.48390
$115$	−5.77696e8	−0.308006
$116$	1.02504e7	0.00525629
$117$	−7.58468e9	−3.74197
$118$	−2.15397e9	−1.02275
$119$	0	0
$120$	1.13056e9	0.497713
$121$	1.71699e9	0.728171
$122$	−3.62038e9	−1.47957
$123$	−2.64853e9	−1.04335
$124$	1.44062e6	0.000547206 0
$125$	−1.38802e9	−0.508511
$126$	3.31773e9	1.17266
$127$	−3.50661e9	−1.19611	−0.598055	−	0.801455i	$-0.704059\pi$
$127$	−3.50661e9	−1.19611	−0.598055	+	0.801455i	$0.704059\pi$
$128$	−3.05376e9	−1.00552
$129$	5.43137e9	1.72685
$130$	1.24438e9	0.382127
$131$	−1.25792e9	−0.373193	−0.186597	−	0.982437i	$-0.559746\pi$
$131$	−1.25792e9	−0.373193	−0.186597	+	0.982437i	$0.559746\pi$
$132$	−3.21507e7	−0.00921738
$133$	−1.27886e9	−0.354396
$134$	−1.89997e9	−0.509068
$135$	3.04827e9	0.789863
$136$	0	0
$137$	6.74406e9	1.63561	0.817804	−	0.575497i	$-0.195191\pi$
$137$	6.74406e9	1.63561	0.817804	+	0.575497i	$0.195191\pi$
$138$	9.44934e9	2.21792
$139$	8.02375e9	1.82310	0.911551	−	0.411188i	$-0.134886\pi$
$139$	8.02375e9	1.82310	0.911551	+	0.411188i	$0.134886\pi$
$140$	−2.00854e6	−0.000441879 0
$141$	1.26660e10	2.69870
$142$	−7.04689e9	−1.45445
$143$	9.51938e9	1.90369
$144$	−1.33822e10	−2.59357
$145$	1.98980e9	0.373812
$146$	−7.65249e9	−1.39385
$147$	−8.51883e9	−1.50471
$148$	7.45540e6	0.00127730
$149$	9.84116e8	0.163572	0.0817859	−	0.996650i	$-0.473938\pi$
$149$	9.84116e8	0.163572	0.0817859	+	0.996650i	$0.473938\pi$
$150$	1.09439e10	1.76508
$151$	5.81240e8	0.0909827	0.0454914	−	0.998965i	$-0.485515\pi$
$151$	5.81240e8	0.0909827	0.0454914	+	0.998965i	$0.485515\pi$
$152$	5.13930e9	0.780922
$153$	0	0
$154$	−4.16401e9	−0.596580
$155$	2.79652e8	0.0389157
$156$	−7.51065e7	−0.0101535
$157$	7.86711e9	1.03340	0.516698	−	0.856168i	$-0.327161\pi$
$157$	7.86711e9	1.03340	0.516698	+	0.856168i	$0.327161\pi$
$158$	1.25103e9	0.159702
$159$	−1.54114e9	−0.191229
$160$	1.61733e7	0.00195100
$161$	4.51592e9	0.529700
$162$	−2.71660e10	−3.09891
$163$	−1.00543e10	−1.11560	−0.557798	−	0.829976i	$-0.688354\pi$
$163$	−1.00543e10	−1.11560	−0.557798	+	0.829976i	$0.688354\pi$
$164$	−1.89091e7	−0.00204115
$165$	−6.24107e9	−0.655513
$166$	−7.87308e9	−0.804745
$167$	−3.17548e9	−0.315926	−0.157963	−	0.987445i	$-0.550493\pi$
$167$	−3.17548e9	−0.315926	−0.157963	+	0.987445i	$0.550493\pi$
$168$	−8.83775e9	−0.855953
$169$	1.16335e10	1.09704
$170$	0	0
$171$	2.26046e10	2.02169
$172$	3.87772e7	0.00337830
$173$	−5.55102e9	−0.471157	−0.235579	−	0.971855i	$-0.575698\pi$
$173$	−5.55102e9	−0.471157	−0.235579	+	0.971855i	$0.575698\pi$
$174$	−3.25470e10	−2.69178
$175$	5.23020e9	0.421548
$176$	1.67958e10	1.31945
$177$	2.52368e10	1.93266
$178$	8.49710e9	0.634426
$179$	−6.84671e9	−0.498475	−0.249237	−	0.968442i	$-0.580180\pi$
$179$	−6.84671e9	−0.498475	−0.249237	+	0.968442i	$0.580180\pi$
$180$	3.55021e7	0.00252074
$181$	1.81450e10	1.25662	0.628310	−	0.777963i	$-0.283747\pi$
$181$	1.81450e10	1.25662	0.628310	+	0.777963i	$0.283747\pi$
$182$	−9.72747e9	−0.657171
$183$	4.24177e10	2.79587
$184$	−1.81480e10	−1.16721
$185$	1.44724e9	0.0908380
$186$	−4.57425e9	−0.280228
$187$	0	0
$188$	9.04289e7	0.00527955
$189$	−2.38287e10	−1.35838
$190$	−3.70862e9	−0.206453
$191$	−2.55856e10	−1.39106	−0.695530	−	0.718497i	$-0.744830\pi$
$191$	−2.55856e10	−1.39106	−0.695530	+	0.718497i	$0.744830\pi$
$192$	3.55155e10	1.88609
$193$	−6.73140e9	−0.349219	−0.174609	−	0.984638i	$-0.555866\pi$
$193$	−6.73140e9	−0.349219	−0.174609	+	0.984638i	$0.555866\pi$
$194$	−2.67599e10	−1.35636
$195$	−1.45796e10	−0.722090
$196$	−6.08200e7	−0.00294370
$197$	8.13977e9	0.385047	0.192524	−	0.981292i	$-0.438333\pi$
$197$	8.13977e9	0.385047	0.192524	+	0.981292i	$0.438333\pi$
$198$	7.36016e10	3.40325
$199$	2.96922e10	1.34216	0.671079	−	0.741386i	$-0.265831\pi$
$199$	2.96922e10	1.34216	0.671079	+	0.741386i	$0.265831\pi$
$200$	−2.10185e10	−0.928893
$201$	2.22608e10	0.961965
$202$	−1.83075e10	−0.773658
$203$	−1.55545e10	−0.642871
$204$	0	0
$205$	−3.67063e9	−0.145160
$206$	1.41864e10	0.548871
$207$	−7.98218e10	−3.02172
$208$	3.92363e10	1.45346
$209$	−2.83706e10	−1.02851
$210$	6.37750e9	0.226289
$211$	1.10644e10	0.384288	0.192144	−	0.981367i	$-0.438456\pi$
$211$	1.10644e10	0.384288	0.192144	+	0.981367i	$0.438456\pi$
$212$	−1.10029e7	−0.000374107 0
$213$	8.25640e10	2.74842
$214$	5.84052e10	1.90366
$215$	7.52740e9	0.240255
$216$	9.57596e10	2.99323
$217$	−2.18607e9	−0.0669261
$218$	9.49947e9	0.284869
$219$	8.96595e10	2.63389
$220$	−4.45580e7	−0.00128240
$221$	0	0
$222$	−2.36724e10	−0.654115
$223$	1.25174e10	0.338956	0.169478	−	0.985534i	$-0.445792\pi$
$223$	1.25174e10	0.338956	0.169478	+	0.985534i	$0.445792\pi$
$224$	−1.26428e8	−0.00335528
$225$	−9.24472e10	−2.40476
$226$	2.77128e10	0.706631
$227$	−2.61220e10	−0.652966	−0.326483	−	0.945203i	$-0.605864\pi$
$227$	−2.61220e10	−0.652966	−0.326483	+	0.945203i	$0.605864\pi$
$228$	2.23840e8	0.00548568
$229$	−7.37974e9	−0.177330	−0.0886649	−	0.996062i	$-0.528260\pi$
$229$	−7.37974e9	−0.177330	−0.0886649	+	0.996062i	$0.528260\pi$
$230$	1.30960e10	0.308576
$231$	4.87872e10	1.12733
$232$	6.25084e10	1.41658
$233$	−1.54320e10	−0.343021	−0.171510	−	0.985182i	$-0.554865\pi$
$233$	−1.54320e10	−0.343021	−0.171510	+	0.985182i	$0.554865\pi$
$234$	1.71939e11	3.74890
$235$	1.75540e10	0.375466
$236$	1.80178e8	0.00378091
$237$	−1.46575e10	−0.301782
$238$	0	0
$239$	2.77534e10	0.550205	0.275103	−	0.961415i	$-0.411288\pi$
$239$	2.77534e10	0.550205	0.275103	+	0.961415i	$0.411288\pi$
$240$	−2.57240e10	−0.500481
$241$	−2.70806e10	−0.517109	−0.258554	−	0.965997i	$-0.583246\pi$
$241$	−2.70806e10	−0.517109	−0.258554	+	0.965997i	$0.583246\pi$
$242$	−3.89229e10	−0.729518
$243$	1.55291e11	2.85706
$244$	3.02841e8	0.00546966
$245$	−1.18063e10	−0.209348
$246$	6.00403e10	1.04528
$247$	−6.62759e10	−1.13297
$248$	8.78510e9	0.147474
$249$	9.22441e10	1.52069
$250$	3.14654e10	0.509451
$251$	2.29993e10	0.365748	0.182874	−	0.983136i	$-0.441460\pi$
$251$	2.29993e10	0.365748	0.182874	+	0.983136i	$0.441460\pi$
$252$	−2.77524e8	−0.00433510
$253$	1.00183e11	1.53727
$254$	7.94924e10	1.19832
$255$	0	0
$256$	7.63525e8	0.0111108
$257$	1.95178e10	0.279082	0.139541	−	0.990216i	$-0.455437\pi$
$257$	1.95178e10	0.279082	0.139541	+	0.990216i	$0.455437\pi$
$258$	−1.23125e11	−1.73005
$259$	−1.13132e10	−0.156221
$260$	−1.04091e8	−0.00141265
$261$	2.74935e11	3.66732
$262$	2.85162e10	0.373884
$263$	1.09688e11	1.41370	0.706849	−	0.707365i	$-0.250116\pi$
$263$	1.09688e11	1.41370	0.706849	+	0.707365i	$0.250116\pi$
$264$	−1.96060e11	−2.48411
$265$	−2.13588e9	−0.0266054
$266$	2.89907e10	0.355052
$267$	−9.95553e10	−1.19885
$268$	1.58931e8	0.00188192
$269$	5.43556e10	0.632935	0.316468	−	0.948603i	$-0.397503\pi$
$269$	5.43556e10	0.632935	0.316468	+	0.948603i	$0.397503\pi$
$270$	−6.91021e10	−0.791324
$271$	8.19304e10	0.922748	0.461374	−	0.887206i	$-0.347357\pi$
$271$	8.19304e10	0.922748	0.461374	+	0.887206i	$0.347357\pi$
$272$	0	0
$273$	1.13971e11	1.24183
$274$	−1.52883e11	−1.63863
$275$	1.16029e11	1.22340
$276$	−7.90428e8	−0.00819919
$277$	−7.10833e10	−0.725452	−0.362726	−	0.931896i	$-0.618154\pi$
$277$	−7.10833e10	−0.725452	−0.362726	+	0.931896i	$0.618154\pi$
$278$	−1.81893e11	−1.82647
$279$	3.86402e10	0.381786
$280$	−1.22483e10	−0.119088
$281$	6.64689e10	0.635975	0.317988	−	0.948095i	$-0.396993\pi$
$281$	6.64689e10	0.635975	0.317988	+	0.948095i	$0.396993\pi$
$282$	−2.87130e11	−2.70369
$283$	−6.72043e10	−0.622813	−0.311407	−	0.950277i	$-0.600800\pi$
$283$	−6.72043e10	−0.622813	−0.311407	+	0.950277i	$0.600800\pi$
$284$	5.89464e8	0.00537681
$285$	4.34517e10	0.390126
$286$	−2.15797e11	−1.90721
$287$	2.86938e10	0.249643
$288$	2.23470e9	0.0191405
$289$	0	0
$290$	−4.51073e10	−0.374503
$291$	3.13529e11	2.56306
$292$	6.40123e8	0.00515276
$293$	−9.43640e10	−0.748001	−0.374000	−	0.927429i	$-0.622014\pi$
$293$	−9.43640e10	−0.748001	−0.374000	+	0.927429i	$0.622014\pi$
$294$	1.93116e11	1.50749
$295$	3.49760e10	0.268888
$296$	4.54642e10	0.344236
$297$	−5.28624e11	−3.94224
$298$	−2.23092e10	−0.163874
$299$	2.34035e11	1.69340
$300$	−9.15449e8	−0.00652512
$301$	−5.88426e10	−0.413183
$302$	−1.31763e10	−0.0911511
$303$	2.14498e11	1.46195
$304$	−1.16936e11	−0.785265
$305$	5.87873e10	0.388986
$306$	0	0
$307$	1.72103e11	1.10577	0.552886	−	0.833257i	$-0.313526\pi$
$307$	1.72103e11	1.10577	0.552886	+	0.833257i	$0.313526\pi$
$308$	3.48315e8	0.00220544
$309$	−1.66214e11	−1.03718
$310$	−6.33951e9	−0.0389877
$311$	9.33037e10	0.565558	0.282779	−	0.959185i	$-0.408744\pi$
$311$	9.33037e10	0.565558	0.282779	+	0.959185i	$0.408744\pi$
$312$	−4.58011e11	−2.73640
$313$	2.05133e11	1.20805	0.604027	−	0.796964i	$-0.293562\pi$
$313$	2.05133e11	1.20805	0.604027	+	0.796964i	$0.293562\pi$
$314$	−1.78342e11	−1.03531
$315$	−5.38729e10	−0.308299
$316$	−1.04647e8	−0.000590386 0
$317$	7.07072e10	0.393276	0.196638	−	0.980476i	$-0.436998\pi$
$317$	7.07072e10	0.393276	0.196638	+	0.980476i	$0.436998\pi$
$318$	3.49364e10	0.191583
$319$	−3.45066e11	−1.86571
$320$	4.92214e10	0.262409
$321$	−6.84298e11	−3.59727
$322$	−1.02373e11	−0.530680
$323$	0	0
$324$	2.27241e9	0.0114560
$325$	2.71052e11	1.34765
$326$	2.27924e11	1.11766
$327$	−1.11300e11	−0.538305
$328$	−1.15311e11	−0.550095
$329$	−1.37222e11	−0.645716
$330$	1.41481e11	0.656726
$331$	2.55639e11	1.17058	0.585289	−	0.810825i	$-0.300981\pi$
$331$	2.55639e11	1.17058	0.585289	+	0.810825i	$0.300981\pi$
$332$	6.58575e8	0.00297498
$333$	1.99969e11	0.891175
$334$	7.19858e10	0.316510
$335$	3.08516e10	0.133837
$336$	2.01087e11	0.860713
$337$	−6.33659e10	−0.267622	−0.133811	−	0.991007i	$-0.542721\pi$
$337$	−6.33659e10	−0.267622	−0.133811	+	0.991007i	$0.542721\pi$
$338$	−2.63724e11	−1.09907
$339$	−3.24694e11	−1.33529
$340$	0	0
$341$	−4.84966e10	−0.194230
$342$	−5.12430e11	−2.02543
$343$	2.08409e11	0.813004
$344$	2.36469e11	0.910460
$345$	−1.53437e11	−0.583103
$346$	1.25838e11	0.472029
$347$	3.16301e11	1.17116	0.585582	−	0.810613i	$-0.300866\pi$
$347$	3.16301e11	1.17116	0.585582	+	0.810613i	$0.300866\pi$
$348$	2.72252e9	0.00995096
$349$	3.49570e11	1.26131	0.630653	−	0.776065i	$-0.282787\pi$
$349$	3.49570e11	1.26131	0.630653	+	0.776065i	$0.282787\pi$
$350$	−1.18565e11	−0.422328
$351$	−1.23491e12	−4.34263
$352$	−2.80473e9	−0.00973754
$353$	−4.06731e11	−1.39419	−0.697093	−	0.716980i	$-0.745524\pi$
$353$	−4.06731e11	−1.39419	−0.697093	+	0.716980i	$0.745524\pi$
$354$	−5.72100e11	−1.93623
$355$	1.14427e11	0.382383
$356$	−7.10773e8	−0.00234534
$357$	0	0
$358$	1.55210e11	0.499397
$359$	1.97113e11	0.626311	0.313156	−	0.949702i	$-0.398614\pi$
$359$	1.97113e11	0.626311	0.313156	+	0.949702i	$0.398614\pi$
$360$	2.16497e11	0.679346
$361$	−1.25166e11	−0.387885
$362$	−4.11335e11	−1.25894
$363$	4.56036e11	1.37854
$364$	8.13693e8	0.00242943
$365$	1.24260e11	0.366450
$366$	−9.61580e11	−2.80105
$367$	5.26961e10	0.151629	0.0758143	−	0.997122i	$-0.475844\pi$
$367$	5.26961e10	0.151629	0.0758143	+	0.997122i	$0.475844\pi$
$368$	4.12926e11	1.17370
$369$	−5.07180e11	−1.42411
$370$	−3.28079e10	−0.0910060
$371$	1.66964e10	0.0457553
$372$	3.82631e8	0.00103595
$373$	5.23122e11	1.39931	0.699655	−	0.714481i	$-0.253337\pi$
$373$	5.23122e11	1.39931	0.699655	+	0.714481i	$0.253337\pi$
$374$	0	0
$375$	−3.68661e11	−0.962689
$376$	5.51449e11	1.42285
$377$	−8.06102e11	−2.05520
$378$	5.40179e11	1.36090
$379$	−1.64935e11	−0.410616	−0.205308	−	0.978697i	$-0.565820\pi$
$379$	−1.64935e11	−0.410616	−0.205308	+	0.978697i	$0.565820\pi$
$380$	3.10222e8	0.000763215 0
$381$	−9.31363e11	−2.26442
$382$	5.80008e11	1.39363
$383$	−2.35006e11	−0.558064	−0.279032	−	0.960282i	$-0.590013\pi$
$383$	−2.35006e11	−0.558064	−0.279032	+	0.960282i	$0.590013\pi$
$384$	−8.11086e11	−1.90360
$385$	6.76148e10	0.156844
$386$	1.52596e11	0.349865
$387$	1.04008e12	2.35704
$388$	2.23843e9	0.00501420
$389$	6.18805e11	1.37019	0.685095	−	0.728454i	$-0.259761\pi$
$389$	6.18805e11	1.37019	0.685095	+	0.728454i	$0.259761\pi$
$390$	3.30510e11	0.723426
$391$	0	0
$392$	−3.70890e11	−0.793336
$393$	−3.34107e11	−0.706512
$394$	−1.84523e11	−0.385760
$395$	−2.03141e10	−0.0419865
$396$	−6.15669e9	−0.0125811
$397$	−6.88154e11	−1.39036	−0.695182	−	0.718834i	$-0.744676\pi$
$397$	−6.88154e11	−1.39036	−0.695182	+	0.718834i	$0.744676\pi$
$398$	−6.73101e11	−1.34464
$399$	−3.39667e11	−0.670927
$400$	4.78238e11	0.934059
$401$	5.46201e11	1.05488	0.527439	−	0.849593i	$-0.323152\pi$
$401$	5.46201e11	1.05488	0.527439	+	0.849593i	$0.323152\pi$
$402$	−5.04637e11	−0.963744
$403$	−1.13292e11	−0.213957
$404$	1.53141e9	0.00286006
$405$	4.41119e11	0.814719
$406$	3.52609e11	0.644060
$407$	−2.50977e11	−0.453376
$408$	0	0
$409$	3.45616e11	0.610715	0.305358	−	0.952238i	$-0.401224\pi$
$409$	3.45616e11	0.610715	0.305358	+	0.952238i	$0.401224\pi$
$410$	8.32105e10	0.145429
$411$	1.79124e12	3.09646
$412$	−1.18668e9	−0.00202906
$413$	−2.73411e11	−0.462425
$414$	1.80950e12	3.02731
$415$	1.27842e11	0.211572
$416$	−6.55208e9	−0.0107265
$417$	2.13112e12	3.45141
$418$	6.43140e11	1.03042
$419$	2.32307e11	0.368212	0.184106	−	0.982906i	$-0.441061\pi$
$419$	2.32307e11	0.368212	0.184106	+	0.982906i	$0.441061\pi$
$420$	−5.33471e8	−0.000836545 0
$421$	2.50534e10	0.0388684	0.0194342	−	0.999811i	$-0.493814\pi$
$421$	2.50534e10	0.0388684	0.0194342	+	0.999811i	$0.493814\pi$
$422$	−2.50822e11	−0.384999
$423$	2.42548e12	3.68355
$424$	−6.70974e10	−0.100823
$425$	0	0
$426$	−1.87167e12	−2.75350
$427$	−4.59547e11	−0.668967
$428$	−4.88554e9	−0.00703745
$429$	2.52837e12	3.60398
$430$	−1.70641e11	−0.240699
$431$	−6.39146e11	−0.892180	−0.446090	−	0.894988i	$-0.647184\pi$
$431$	−6.39146e11	−0.892180	−0.446090	+	0.894988i	$0.647184\pi$
$432$	−2.17884e12	−3.00988
$433$	−5.80057e11	−0.793003	−0.396502	−	0.918034i	$-0.629776\pi$
$433$	−5.80057e11	−0.793003	−0.396502	+	0.918034i	$0.629776\pi$
$434$	4.95567e10	0.0670499
$435$	5.28495e11	0.707683
$436$	−7.94621e8	−0.00105310
$437$	−6.97493e11	−0.914900
$438$	−2.03252e12	−2.63877
$439$	−3.04632e11	−0.391458	−0.195729	−	0.980658i	$-0.562707\pi$
$439$	−3.04632e11	−0.391458	−0.195729	+	0.980658i	$0.562707\pi$
$440$	−2.71721e11	−0.345610
$441$	−1.63131e12	−2.05383
$442$	0	0
$443$	3.18193e10	0.0392530	0.0196265	−	0.999807i	$-0.493752\pi$
$443$	3.18193e10	0.0392530	0.0196265	+	0.999807i	$0.493752\pi$
$444$	1.98017e9	0.00241813
$445$	−1.37975e11	−0.166794
$446$	−2.83761e11	−0.339583
$447$	2.61383e11	0.309666
$448$	−3.84769e11	−0.451284
$449$	5.35918e11	0.622286	0.311143	−	0.950363i	$-0.399288\pi$
$449$	5.35918e11	0.622286	0.311143	+	0.950363i	$0.399288\pi$
$450$	2.09571e12	2.40921
$451$	6.36552e11	0.724502
$452$	−2.31815e9	−0.00261227
$453$	1.54378e11	0.172244
$454$	5.92168e11	0.654174
$455$	1.57954e11	0.172774
$456$	1.36501e12	1.47841
$457$	−9.04468e11	−0.969997	−0.484998	−	0.874515i	$-0.661180\pi$
$457$	−9.04468e11	−0.969997	−0.484998	+	0.874515i	$0.661180\pi$
$458$	1.67293e11	0.177658
$459$	0	0
$460$	−1.09546e9	−0.00114074
$461$	−1.82659e12	−1.88359	−0.941795	−	0.336187i	$-0.890863\pi$
$461$	−1.82659e12	−1.88359	−0.941795	+	0.336187i	$0.890863\pi$
$462$	−1.10597e12	−1.12942
$463$	−1.31941e12	−1.33434	−0.667170	−	0.744906i	$-0.732494\pi$
$463$	−1.31941e12	−1.33434	−0.667170	+	0.744906i	$0.732494\pi$
$464$	−1.42227e12	−1.42446
$465$	7.42761e10	0.0736734
$466$	3.49832e11	0.343656
$467$	1.68454e12	1.63891	0.819456	−	0.573142i	$-0.194276\pi$
$467$	1.68454e12	1.63891	0.819456	+	0.573142i	$0.194276\pi$
$468$	−1.43825e10	−0.0138589
$469$	−2.41170e11	−0.230169
$470$	−3.97937e11	−0.376161
$471$	2.08952e12	1.95638
$472$	1.09875e12	1.01897
$473$	−1.30538e12	−1.19912
$474$	3.32276e11	0.302340
$475$	−8.07816e11	−0.728100
$476$	0	0
$477$	−2.95120e11	−0.261015
$478$	−6.29148e11	−0.551223
$479$	2.54147e11	0.220585	0.110292	−	0.993899i	$-0.464821\pi$
$479$	2.54147e11	0.220585	0.110292	+	0.993899i	$0.464821\pi$
$480$	4.29566e9	0.00369355
$481$	−5.86302e11	−0.499423
$482$	6.13898e11	0.518065
$483$	1.19944e12	1.00280
$484$	3.25586e9	0.00269688
$485$	4.34524e11	0.356595
$486$	−3.52034e12	−2.86234
$487$	7.07971e11	0.570342	0.285171	−	0.958477i	$-0.407950\pi$
$487$	7.07971e11	0.570342	0.285171	+	0.958477i	$0.407950\pi$
$488$	1.84677e12	1.47409
$489$	−2.67044e12	−2.11200
$490$	2.67641e11	0.209735
$491$	−8.71726e11	−0.676882	−0.338441	−	0.940988i	$-0.609900\pi$
$491$	−8.71726e11	−0.676882	−0.338441	+	0.940988i	$0.609900\pi$
$492$	−5.02230e9	−0.00386420
$493$	0	0
$494$	1.50243e12	1.13507
$495$	−1.19513e12	−0.894732
$496$	−1.99889e11	−0.148294
$497$	−8.94486e11	−0.657612
$498$	−2.09111e12	−1.52351
$499$	−9.44233e11	−0.681752	−0.340876	−	0.940108i	$-0.610724\pi$
$499$	−9.44233e11	−0.681752	−0.340876	+	0.940108i	$0.610724\pi$
$500$	−2.63204e9	−0.00188334
$501$	−8.43414e11	−0.598096
$502$	−5.21377e11	−0.366425
$503$	−1.32525e12	−0.923082	−0.461541	−	0.887119i	$-0.652703\pi$
$503$	−1.32525e12	−0.923082	−0.461541	+	0.887119i	$0.652703\pi$
$504$	−1.69239e12	−1.16832
$505$	2.97276e11	0.203399
$506$	−2.27107e12	−1.54012
$507$	3.08989e12	2.07686
$508$	−6.64945e9	−0.00442995
$509$	1.27464e11	0.0841703	0.0420851	−	0.999114i	$-0.486600\pi$
$509$	1.27464e11	0.0841703	0.0420851	+	0.999114i	$0.486600\pi$
$510$	0	0
$511$	−9.71357e11	−0.630210
$512$	1.54622e12	0.994388
$513$	3.68039e12	2.34620
$514$	−4.42455e11	−0.279599
$515$	−2.30357e11	−0.144301
$516$	1.02993e10	0.00639564
$517$	−3.04417e12	−1.87397
$518$	2.56463e11	0.156510
$519$	−1.47436e12	−0.891973
$520$	−6.34763e11	−0.380712
$521$	3.80565e11	0.226287	0.113143	−	0.993579i	$-0.463908\pi$
$521$	3.80565e11	0.226287	0.113143	+	0.993579i	$0.463908\pi$
$522$	−6.23259e12	−3.67410
$523$	−2.07388e12	−1.21207	−0.606033	−	0.795439i	$-0.707240\pi$
$523$	−2.07388e12	−1.21207	−0.606033	+	0.795439i	$0.707240\pi$
$524$	−2.38535e9	−0.00138217
$525$	1.38915e12	0.798056
$526$	−2.48654e12	−1.41631
$527$	0	0
$528$	4.46099e12	2.49792
$529$	6.61850e11	0.367459
$530$	4.84189e10	0.0266547
$531$	4.83272e12	2.63795
$532$	−2.42505e9	−0.00131256
$533$	1.48704e12	0.798085
$534$	2.25685e12	1.20107
$535$	−9.48378e11	−0.500483
$536$	9.69184e11	0.507183
$537$	−1.81850e12	−0.943689
$538$	−1.23220e12	−0.634106
$539$	2.04743e12	1.04486
$540$	5.78032e9	0.00292536
$541$	1.51143e11	0.0758580	0.0379290	−	0.999280i	$-0.487924\pi$
$541$	1.51143e11	0.0758580	0.0379290	+	0.999280i	$0.487924\pi$
$542$	−1.85730e12	−0.924455
$543$	4.81935e12	2.37897
$544$	0	0
$545$	−1.54251e11	−0.0748936
$546$	−2.58364e12	−1.24413
$547$	3.07902e12	1.47051	0.735257	−	0.677788i	$-0.237061\pi$
$547$	3.07902e12	1.47051	0.735257	+	0.677788i	$0.237061\pi$
$548$	1.27885e10	0.00605769
$549$	8.12279e12	3.81619
$550$	−2.63029e12	−1.22566
$551$	2.40242e12	1.11037
$552$	−4.82015e12	−2.20970
$553$	1.58797e11	0.0722072
$554$	1.61141e12	0.726795
$555$	3.84390e11	0.171970
$556$	1.52151e10	0.00675210
$557$	1.33787e12	0.588933	0.294467	−	0.955662i	$-0.404858\pi$
$557$	1.33787e12	0.588933	0.294467	+	0.955662i	$0.404858\pi$
$558$	−8.75945e11	−0.382493
$559$	−3.04948e12	−1.32091
$560$	2.78690e11	0.119750
$561$	0	0
$562$	−1.50680e12	−0.637152
$563$	1.95942e12	0.821940	0.410970	−	0.911649i	$-0.365190\pi$
$563$	1.95942e12	0.821940	0.410970	+	0.911649i	$0.365190\pi$
$564$	2.40181e10	0.00999500
$565$	−4.49997e11	−0.185777
$566$	1.52347e12	0.623966
$567$	−3.44828e12	−1.40113
$568$	3.59464e12	1.44907
$569$	−3.13617e12	−1.25428	−0.627139	−	0.778907i	$-0.715774\pi$
$569$	−3.13617e12	−1.25428	−0.627139	+	0.778907i	$0.715774\pi$
$570$	−9.85018e11	−0.390847
$571$	8.05728e11	0.317195	0.158597	−	0.987343i	$-0.449303\pi$
$571$	8.05728e11	0.317195	0.158597	+	0.987343i	$0.449303\pi$
$572$	1.80512e10	0.00705058
$573$	−6.79560e12	−2.63349
$574$	−6.50467e11	−0.250105
$575$	2.85257e12	1.08826
$576$	6.80104e12	2.57439
$577$	−5.19088e12	−1.94962	−0.974810	−	0.223039i	$-0.928402\pi$
$577$	−5.19088e12	−1.94962	−0.974810	+	0.223039i	$0.928402\pi$
$578$	0	0
$579$	−1.78787e12	−0.661124
$580$	3.77318e9	0.00138446
$581$	−9.99358e11	−0.363855
$582$	−7.10748e12	−2.56781
$583$	3.70399e11	0.132789
$584$	3.90356e12	1.38868
$585$	−2.79193e12	−0.985605
$586$	2.13916e12	0.749384
$587$	9.87567e11	0.343317	0.171659	−	0.985157i	$-0.445087\pi$
$587$	9.87567e11	0.343317	0.171659	+	0.985157i	$0.445087\pi$
$588$	−1.61539e10	−0.00557288
$589$	3.37643e11	0.115595
$590$	−7.92880e11	−0.269385
$591$	2.16194e12	0.728954
$592$	−1.03446e12	−0.346150
$593$	−3.64711e12	−1.21116	−0.605582	−	0.795783i	$-0.707060\pi$
$593$	−3.64711e12	−1.21116	−0.605582	+	0.795783i	$0.707060\pi$
$594$	1.19835e13	3.94953
$595$	0	0
$596$	1.86614e9	0.000605810 0
$597$	7.88632e12	2.54091
$598$	−5.30540e12	−1.69654
$599$	1.88140e12	0.597117	0.298559	−	0.954391i	$-0.403494\pi$
$599$	1.88140e12	0.597117	0.298559	+	0.954391i	$0.403494\pi$
$600$	−5.58255e12	−1.75854
$601$	−1.11397e12	−0.348287	−0.174144	−	0.984720i	$-0.555716\pi$
$601$	−1.11397e12	−0.348287	−0.174144	+	0.984720i	$0.555716\pi$
$602$	1.33392e12	0.413948
$603$	4.26284e12	1.31302
$604$	1.10218e9	0.000336967 0
$605$	6.32026e11	0.191794
$606$	−4.86252e12	−1.46465
$607$	2.22636e12	0.665652	0.332826	−	0.942988i	$-0.391998\pi$
$607$	2.22636e12	0.665652	0.332826	+	0.942988i	$0.391998\pi$
$608$	1.95271e10	0.00579525
$609$	−4.13131e12	−1.21705
$610$	−1.33267e12	−0.389706
$611$	−7.11144e12	−2.06430
$612$	0	0
$613$	1.60812e12	0.459989	0.229995	−	0.973192i	$-0.426129\pi$
$613$	1.60812e12	0.459989	0.229995	+	0.973192i	$0.426129\pi$
$614$	−3.90145e12	−1.10782
$615$	−9.74927e11	−0.274811
$616$	2.12408e12	0.594371
$617$	−3.71835e12	−1.03292	−0.516461	−	0.856311i	$-0.672751\pi$
$617$	−3.71835e12	−1.03292	−0.516461	+	0.856311i	$0.672751\pi$
$618$	3.76794e12	1.03910
$619$	−5.70656e12	−1.56231	−0.781154	−	0.624338i	$-0.785369\pi$
$619$	−5.70656e12	−1.56231	−0.781154	+	0.624338i	$0.785369\pi$
$620$	5.30293e8	0.000144130 0
$621$	−1.29963e13	−3.50676
$622$	−2.11513e12	−0.566604
$623$	1.07857e12	0.286847
$624$	1.04212e13	2.75162
$625$	3.03912e12	0.796687
$626$	−4.65022e12	−1.21029
$627$	−7.53528e12	−1.94713
$628$	1.49181e10	0.00382732
$629$	0	0
$630$	1.22126e12	0.308870
$631$	−6.04936e12	−1.51907	−0.759534	−	0.650467i	$-0.774573\pi$
$631$	−6.04936e12	−1.51907	−0.759534	+	0.650467i	$0.774573\pi$
$632$	−6.38154e11	−0.159110
$633$	2.93873e12	0.727516
$634$	−1.60288e12	−0.394003
$635$	−1.29079e12	−0.315045
$636$	−2.92240e9	−0.000708243 0
$637$	4.78296e12	1.15098
$638$	7.82240e12	1.86916
$639$	1.58106e13	3.75141
$640$	−1.12409e12	−0.264846
$641$	4.07126e12	0.952506	0.476253	−	0.879308i	$-0.341995\pi$
$641$	4.07126e12	0.952506	0.476253	+	0.879308i	$0.341995\pi$
$642$	1.55126e13	3.60392
$643$	−6.67925e12	−1.54091	−0.770457	−	0.637492i	$-0.779972\pi$
$643$	−6.67925e12	−1.54091	−0.770457	+	0.637492i	$0.779972\pi$
$644$	8.56337e9	0.00196182
$645$	1.99929e12	0.454839
$646$	0	0
$647$	−3.54638e12	−0.795640	−0.397820	−	0.917463i	$-0.630233\pi$
$647$	−3.54638e12	−0.795640	−0.397820	+	0.917463i	$0.630233\pi$
$648$	1.38575e13	3.08743
$649$	−6.06545e12	−1.34203
$650$	−6.14456e12	−1.35015
$651$	−5.80625e11	−0.126701
$652$	−1.90656e10	−0.00413176
$653$	6.92871e12	1.49123	0.745613	−	0.666379i	$-0.232157\pi$
$653$	6.92871e12	1.49123	0.745613	+	0.666379i	$0.232157\pi$
$654$	2.52308e12	0.539301
$655$	−4.63043e11	−0.0982960
$656$	2.62369e12	0.553153
$657$	1.71694e13	3.59509
$658$	3.11072e12	0.646911
$659$	2.61478e12	0.540071	0.270035	−	0.962850i	$-0.412965\pi$
$659$	2.61478e12	0.540071	0.270035	+	0.962850i	$0.412965\pi$
$660$	−1.18347e10	−0.00242778
$661$	−1.25747e12	−0.256207	−0.128104	−	0.991761i	$-0.540889\pi$
$661$	−1.25747e12	−0.256207	−0.128104	+	0.991761i	$0.540889\pi$
$662$	−5.79514e12	−1.17274
$663$	0	0
$664$	4.01609e12	0.801765
$665$	−4.70748e11	−0.0933451
$666$	−4.53315e12	−0.892824
$667$	−8.48349e12	−1.65962
$668$	−6.02153e9	−0.00117007
$669$	3.32465e12	0.641695
$670$	−6.99383e11	−0.134084
$671$	−1.01947e13	−1.94145
$672$	−3.35797e10	−0.00635206
$673$	8.91607e12	1.67535	0.837676	−	0.546168i	$-0.183914\pi$
$673$	8.91607e12	1.67535	0.837676	+	0.546168i	$0.183914\pi$
$674$	1.43646e12	0.268117
$675$	−1.50519e13	−2.79077
$676$	2.20602e10	0.00406303
$677$	7.73461e12	1.41511	0.707554	−	0.706660i	$-0.249799\pi$
$677$	7.73461e12	1.41511	0.707554	+	0.706660i	$0.249799\pi$
$678$	7.36058e12	1.33776
$679$	−3.39672e12	−0.613262
$680$	0	0
$681$	−6.93807e12	−1.23617
$682$	1.09938e12	0.194589
$683$	−6.47827e12	−1.13911	−0.569555	−	0.821953i	$-0.692885\pi$
$683$	−6.47827e12	−1.13911	−0.569555	+	0.821953i	$0.692885\pi$
$684$	4.28642e10	0.00748759
$685$	2.48250e12	0.430806
$686$	−4.72448e12	−0.814508
$687$	−1.96008e12	−0.335712
$688$	−5.38043e12	−0.915523
$689$	8.65282e11	0.146275
$690$	3.47831e12	0.584182
$691$	9.23897e11	0.154160	0.0770801	−	0.997025i	$-0.475440\pi$
$691$	9.23897e11	0.154160	0.0770801	+	0.997025i	$0.475440\pi$
$692$	−1.05262e10	−0.00174499
$693$	9.34251e12	1.53874
$694$	−7.17031e12	−1.17333
$695$	2.95355e12	0.480190
$696$	1.66024e13	2.68181
$697$	0	0
$698$	−7.92451e12	−1.26364
$699$	−4.09877e12	−0.649391
$700$	9.91783e9	0.00156126
$701$	1.13633e13	1.77735	0.888673	−	0.458542i	$-0.151628\pi$
$701$	1.13633e13	1.77735	0.888673	+	0.458542i	$0.151628\pi$
$702$	2.79945e13	4.35066
$703$	1.74735e12	0.269825
$704$	−8.53585e12	−1.30969
$705$	4.66238e12	0.710815
$706$	9.22029e12	1.39677
$707$	−2.32384e12	−0.349799
$708$	4.78556e10	0.00715785
$709$	9.41131e12	1.39876	0.699378	−	0.714752i	$-0.253460\pi$
$709$	9.41131e12	1.39876	0.699378	+	0.714752i	$0.253460\pi$
$710$	−2.59397e12	−0.383091
$711$	−2.80684e12	−0.411913
$712$	−4.33440e12	−0.632076
$713$	−1.19229e12	−0.172775
$714$	0	0
$715$	3.50409e12	0.501417
$716$	−1.29831e10	−0.00184617
$717$	7.37135e12	1.04162
$718$	−4.46841e12	−0.627470
$719$	−4.24063e12	−0.591767	−0.295883	−	0.955224i	$-0.595614\pi$
$719$	−4.24063e12	−0.591767	−0.295883	+	0.955224i	$0.595614\pi$
$720$	−4.92601e12	−0.683124
$721$	1.80073e12	0.248165
$722$	2.83742e12	0.388603
$723$	−7.19267e12	−0.978966
$724$	3.44077e10	0.00465406
$725$	−9.82532e12	−1.32076
$726$	−1.03380e13	−1.38109
$727$	−4.23459e12	−0.562221	−0.281110	−	0.959675i	$-0.590703\pi$
$727$	−4.23459e12	−0.562221	−0.281110	+	0.959675i	$0.590703\pi$
$728$	4.96202e12	0.654738
$729$	1.76583e13	2.31566
$730$	−2.81689e12	−0.367128
$731$	0	0
$732$	8.04351e10	0.0103549
$733$	3.24959e12	0.415778	0.207889	−	0.978152i	$-0.433341\pi$
$733$	3.24959e12	0.415778	0.207889	+	0.978152i	$0.433341\pi$
$734$	−1.19458e12	−0.151909
$735$	−3.13579e12	−0.396327
$736$	−6.89546e10	−0.00866190
$737$	−5.35020e12	−0.667985
$738$	1.14974e13	1.42675
$739$	−1.56819e13	−1.93419	−0.967094	−	0.254421i	$-0.918115\pi$
$739$	−1.56819e13	−1.93419	−0.967094	+	0.254421i	$0.918115\pi$
$740$	2.74434e9	0.000336431 0
$741$	−1.76030e13	−2.14489
$742$	−3.78496e11	−0.0458399
$743$	8.43750e11	0.101570	0.0507848	−	0.998710i	$-0.483828\pi$
$743$	8.43750e11	0.101570	0.0507848	+	0.998710i	$0.483828\pi$
$744$	2.33334e12	0.279190
$745$	3.62254e11	0.0430835
$746$	−1.18588e13	−1.40190
$747$	1.76643e13	2.07565
$748$	0	0
$749$	7.41358e12	0.860716
$750$	8.35727e12	0.964470
$751$	3.24193e11	0.0371898	0.0185949	−	0.999827i	$-0.494081\pi$
$751$	3.24193e11	0.0371898	0.0185949	+	0.999827i	$0.494081\pi$
$752$	−1.25473e13	−1.43077
$753$	6.10866e12	0.692418
$754$	1.82738e13	2.05900
$755$	2.13955e11	0.0239641
$756$	−4.51854e10	−0.00503095
$757$	−1.54452e13	−1.70947	−0.854734	−	0.519066i	$-0.826280\pi$
$757$	−1.54452e13	−1.70947	−0.854734	+	0.519066i	$0.826280\pi$
$758$	3.73896e12	0.411376
$759$	2.66087e13	2.91029
$760$	1.89178e12	0.205688
$761$	5.33814e12	0.576978	0.288489	−	0.957483i	$-0.406847\pi$
$761$	5.33814e12	0.576978	0.288489	+	0.957483i	$0.406847\pi$
$762$	2.11133e13	2.26861
$763$	1.20580e12	0.128800
$764$	−4.85170e10	−0.00515198
$765$	0	0
$766$	5.32741e12	0.559096
$767$	−1.41694e13	−1.47833
$768$	2.02794e11	0.0210344
$769$	−2.39607e12	−0.247076	−0.123538	−	0.992340i	$-0.539424\pi$
$769$	−2.39607e12	−0.247076	−0.123538	+	0.992340i	$0.539424\pi$
$770$	−1.53278e12	−0.157134
$771$	5.18398e12	0.528346
$772$	−1.27645e10	−0.00129338
$773$	9.42867e12	0.949823	0.474911	−	0.880034i	$-0.342480\pi$
$773$	9.42867e12	0.949823	0.474911	+	0.880034i	$0.342480\pi$
$774$	−2.35779e13	−2.36140
$775$	−1.38088e12	−0.137498
$776$	1.36503e13	1.35134
$777$	−3.00482e12	−0.295749
$778$	−1.40279e13	−1.37272
$779$	−4.43181e12	−0.431184
$780$	−2.76468e10	−0.00267436
$781$	−1.98436e13	−1.90849
$782$	0	0
$783$	4.47639e13	4.25599
$784$	8.43894e12	0.797748
$785$	2.89589e12	0.272188
$786$	7.57397e12	0.707819
$787$	−2.88613e12	−0.268182	−0.134091	−	0.990969i	$-0.542811\pi$
$787$	−2.88613e12	−0.268182	−0.134091	+	0.990969i	$0.542811\pi$
$788$	1.54351e10	0.00142607
$789$	2.91333e13	2.67635
$790$	4.60505e11	0.0420642
$791$	3.51768e12	0.319494
$792$	−3.75444e13	−3.39064
$793$	−2.38157e13	−2.13863
$794$	1.56000e13	1.39294
$795$	−5.67294e11	−0.0503682
$796$	5.63042e10	0.00497087
$797$	−1.80483e13	−1.58443	−0.792215	−	0.610242i	$-0.791072\pi$
$797$	−1.80483e13	−1.58443	−0.792215	+	0.610242i	$0.791072\pi$
$798$	7.70000e12	0.672168
$799$	0	0
$800$	−7.98611e10	−0.00689335
$801$	−1.90643e13	−1.63635
$802$	−1.23820e13	−1.05683
$803$	−2.15489e13	−1.82897
$804$	4.22123e10	0.00356277
$805$	1.66232e12	0.139519
$806$	2.56824e12	0.214353
$807$	1.44370e13	1.19824
$808$	9.33875e12	0.770793
$809$	−6.07623e12	−0.498731	−0.249365	−	0.968410i	$-0.580222\pi$
$809$	−6.07623e12	−0.498731	−0.249365	+	0.968410i	$0.580222\pi$
$810$	−9.99984e12	−0.816226
$811$	1.74997e12	0.142048	0.0710242	−	0.997475i	$-0.477373\pi$
$811$	1.74997e12	0.142048	0.0710242	+	0.997475i	$0.477373\pi$
$812$	−2.94954e10	−0.00238096
$813$	2.17609e13	1.74690
$814$	5.68946e12	0.454215
$815$	−3.70100e12	−0.293839
$816$	0	0
$817$	9.08836e12	0.713652
$818$	−7.83486e12	−0.611845
$819$	2.18248e13	1.69502
$820$	−6.96047e9	−0.000537621 0
$821$	−1.32681e12	−0.101921	−0.0509605	−	0.998701i	$-0.516228\pi$
$821$	−1.32681e12	−0.101921	−0.0509605	+	0.998701i	$0.516228\pi$
$822$	−4.06061e13	−3.10218
$823$	−1.26504e13	−0.961179	−0.480589	−	0.876946i	$-0.659577\pi$
$823$	−1.26504e13	−0.961179	−0.480589	+	0.876946i	$0.659577\pi$
$824$	−7.23654e12	−0.546838
$825$	3.08174e13	2.31608
$826$	6.19804e12	0.463281
$827$	4.79691e12	0.356604	0.178302	−	0.983976i	$-0.442940\pi$
$827$	4.79691e12	0.356604	0.178302	+	0.983976i	$0.442940\pi$
$828$	−1.51363e11	−0.0111914
$829$	−1.79243e13	−1.31810	−0.659048	−	0.752101i	$-0.729041\pi$
$829$	−1.79243e13	−1.31810	−0.659048	+	0.752101i	$0.729041\pi$
$830$	−2.89809e12	−0.211963
$831$	−1.88799e13	−1.37339
$832$	−1.99404e13	−1.44271
$833$	0	0
$834$	−4.83111e13	−3.45780
$835$	−1.16890e12	−0.0832122
$836$	−5.37980e10	−0.00380924
$837$	6.29125e12	0.443070
$838$	−5.26622e12	−0.368894
$839$	2.74032e12	0.190929	0.0954645	−	0.995433i	$-0.469566\pi$
$839$	2.74032e12	0.190929	0.0954645	+	0.995433i	$0.469566\pi$
$840$	−3.25319e12	−0.225451
$841$	1.47131e13	1.01420
$842$	−5.67942e11	−0.0389403
$843$	1.76543e13	1.20400
$844$	2.09810e10	0.00142326
$845$	4.28232e12	0.288951
$846$	−5.49839e13	−3.69036
$847$	−4.94062e12	−0.329842
$848$	1.52668e12	0.101384
$849$	−1.78496e13	−1.17908
$850$	0	0
$851$	−6.17029e12	−0.403295
$852$	1.56563e11	0.0101791
$853$	4.45814e12	0.288325	0.144163	−	0.989554i	$-0.453951\pi$
$853$	4.45814e12	0.288325	0.144163	+	0.989554i	$0.453951\pi$
$854$	1.04176e13	0.670205
$855$	8.32078e12	0.532496
$856$	−2.97927e13	−1.89661
$857$	2.22703e13	1.41030	0.705151	−	0.709057i	$-0.250879\pi$
$857$	2.22703e13	1.41030	0.705151	+	0.709057i	$0.250879\pi$
$858$	−5.73163e13	−3.61065
$859$	1.75068e13	1.09708	0.548539	−	0.836125i	$-0.315184\pi$
$859$	1.75068e13	1.09708	0.548539	+	0.836125i	$0.315184\pi$
$860$	1.42739e10	0.000889816 0
$861$	7.62112e12	0.472612
$862$	1.44890e13	0.893831
$863$	−1.01521e13	−0.623028	−0.311514	−	0.950242i	$-0.600836\pi$
$863$	−1.01521e13	−0.623028	−0.311514	+	0.950242i	$0.600836\pi$
$864$	3.63846e11	0.0222129
$865$	−2.04334e12	−0.124099
$866$	1.31495e13	0.794471
$867$	0	0
$868$	−4.14536e9	−0.000247870 0
$869$	3.52282e12	0.209556
$870$	−1.19806e13	−0.708993
$871$	−1.24985e13	−0.735828
$872$	−4.84572e12	−0.283814
$873$	6.00392e13	3.49841
$874$	1.58117e13	0.916593
$875$	3.99401e12	0.230342
$876$	1.70018e11	0.00975498
$877$	9.33904e12	0.533094	0.266547	−	0.963822i	$-0.414117\pi$
$877$	9.33904e12	0.533094	0.266547	+	0.963822i	$0.414117\pi$
$878$	6.90579e12	0.392182
$879$	−2.50633e13	−1.41608
$880$	6.18254e12	0.347532
$881$	−4.63896e12	−0.259435	−0.129718	−	0.991551i	$-0.541407\pi$
$881$	−4.63896e12	−0.259435	−0.129718	+	0.991551i	$0.541407\pi$
$882$	3.69807e13	2.05763
$883$	1.70186e13	0.942108	0.471054	−	0.882104i	$-0.343874\pi$
$883$	1.70186e13	0.942108	0.471054	+	0.882104i	$0.343874\pi$
$884$	0	0
$885$	9.28969e12	0.509046
$886$	−7.21320e11	−0.0393257
$887$	9.95483e12	0.539980	0.269990	−	0.962863i	$-0.412980\pi$
$887$	9.95483e12	0.539980	0.269990	+	0.962863i	$0.412980\pi$
$888$	1.20754e13	0.651692
$889$	1.00902e13	0.541806
$890$	3.12779e12	0.167103
$891$	−7.64977e13	−4.06630
$892$	2.37363e10	0.00125537
$893$	2.11942e13	1.11528
$894$	−5.92537e12	−0.310239
$895$	−2.52028e12	−0.131294
$896$	8.78718e12	0.455474
$897$	6.21602e13	3.20587
$898$	−1.21489e13	−0.623437
$899$	4.10669e12	0.209688
$900$	−1.75304e11	−0.00890636
$901$	0	0
$902$	−1.44302e13	−0.725842
$903$	−1.56287e13	−0.782219
$904$	−1.41364e13	−0.704014
$905$	6.67920e12	0.330983
$906$	−3.49965e12	−0.172563
$907$	−2.53299e13	−1.24280	−0.621400	−	0.783494i	$-0.713436\pi$
$907$	−2.53299e13	−1.24280	−0.621400	+	0.783494i	$0.713436\pi$
$908$	−4.95342e10	−0.00241835
$909$	4.10754e13	1.99546
$910$	−3.58069e12	−0.173094
$911$	−8.70542e12	−0.418752	−0.209376	−	0.977835i	$-0.567143\pi$
$911$	−8.70542e12	−0.418752	−0.209376	+	0.977835i	$0.567143\pi$
$912$	−3.10584e13	−1.48663
$913$	−2.21701e13	−1.05596
$914$	2.05036e13	0.971792
$915$	1.56140e13	0.736410
$916$	−1.39939e10	−0.000656765 0
$917$	3.61967e12	0.169047
$918$	0	0
$919$	4.10103e13	1.89659	0.948295	−	0.317391i	$-0.102807\pi$
$919$	4.10103e13	1.89659	0.948295	+	0.317391i	$0.102807\pi$
$920$	−6.68030e12	−0.307433
$921$	4.57109e13	2.09340
$922$	4.14074e13	1.88708
$923$	−4.63562e13	−2.10233
$924$	9.25133e10	0.00417523
$925$	−7.14624e12	−0.320952
$926$	2.99102e13	1.33681
$927$	−3.18291e13	−1.41568
$928$	2.37505e11	0.0105125
$929$	9.53729e12	0.420102	0.210051	−	0.977690i	$-0.432637\pi$
$929$	9.53729e12	0.420102	0.210051	+	0.977690i	$0.432637\pi$
$930$	−1.68379e12	−0.0738097
$931$	−1.42546e13	−0.621845
$932$	−2.92631e10	−0.00127042
$933$	2.47816e13	1.07069
$934$	−3.81873e13	−1.64194
$935$	0	0
$936$	−8.77068e13	−3.73501
$937$	4.18393e13	1.77320	0.886598	−	0.462542i	$-0.153062\pi$
$937$	4.18393e13	1.77320	0.886598	+	0.462542i	$0.153062\pi$
$938$	5.46716e12	0.230594
$939$	5.44838e13	2.28703
$940$	3.32870e10	0.00139059
$941$	3.73218e13	1.55171	0.775854	−	0.630913i	$-0.217320\pi$
$941$	3.73218e13	1.55171	0.775854	+	0.630913i	$0.217320\pi$
$942$	−4.73679e13	−1.96000
$943$	1.56497e13	0.644471
$944$	−2.50001e13	−1.02463
$945$	−8.77137e12	−0.357787
$946$	2.95921e13	1.20134
$947$	−1.29470e13	−0.523111	−0.261555	−	0.965188i	$-0.584235\pi$
$947$	−1.29470e13	−0.523111	−0.261555	+	0.965188i	$0.584235\pi$
$948$	−2.77945e10	−0.00111769
$949$	−5.03400e13	−2.01472
$950$	1.83126e13	0.729447
$951$	1.87800e13	0.744531
$952$	0	0
$953$	2.82478e12	0.110935	0.0554673	−	0.998461i	$-0.482335\pi$
$953$	2.82478e12	0.110935	0.0554673	+	0.998461i	$0.482335\pi$
$954$	6.69015e12	0.261498
$955$	−9.41810e12	−0.366394
$956$	5.26276e10	0.00203776
$957$	−9.16503e13	−3.53208
$958$	−5.76133e12	−0.220993
$959$	−1.94060e13	−0.740887
$960$	1.30733e13	0.496781
$961$	−2.58625e13	−0.978170
$962$	1.32910e13	0.500347
$963$	−1.31040e14	−4.91004
$964$	−5.13519e10	−0.00191518
$965$	−2.47784e12	−0.0919813
$966$	−2.71904e13	−1.00466
$967$	4.09001e13	1.50420	0.752100	−	0.659049i	$-0.229041\pi$
$967$	4.09001e13	1.50420	0.752100	+	0.659049i	$0.229041\pi$
$968$	1.98547e13	0.726817
$969$	0	0
$970$	−9.85034e12	−0.357255
$971$	−2.01184e13	−0.726286	−0.363143	−	0.931733i	$-0.618296\pi$
$971$	−2.01184e13	−0.726286	−0.363143	+	0.931733i	$0.618296\pi$
$972$	2.94473e11	0.0105815
$973$	−2.30883e13	−0.825817
$974$	−1.60492e13	−0.571397
$975$	7.19920e13	2.55131
$976$	−4.20200e13	−1.48228
$977$	−6.28033e11	−0.0220524	−0.0110262	−	0.999939i	$-0.503510\pi$
$977$	−6.28033e11	−0.0220524	−0.0110262	+	0.999939i	$0.503510\pi$
$978$	6.05370e13	2.11590
$979$	2.39273e13	0.832475
$980$	−2.23879e10	−0.000775348 0
$981$	−2.13133e13	−0.734751
$982$	1.97614e13	0.678135
$983$	3.88302e13	1.32641	0.663206	−	0.748437i	$-0.269195\pi$
$983$	3.88302e13	1.32641	0.663206	+	0.748437i	$0.269195\pi$
$984$	−3.06268e13	−1.04141
$985$	2.99626e12	0.101418
$986$	0	0
$987$	−3.64464e13	−1.22244
$988$	−1.25676e11	−0.00419612
$989$	−3.20930e13	−1.06666
$990$	2.70928e13	0.896388
$991$	3.63709e13	1.19791	0.598953	−	0.800784i	$-0.295584\pi$
$991$	3.63709e13	1.19791	0.598953	+	0.800784i	$0.295584\pi$
$992$	3.33796e10	0.00109441
$993$	6.78981e13	2.21608
$994$	2.02774e13	0.658829
$995$	1.09297e13	0.353514
$996$	1.74919e11	0.00563209
$997$	1.69767e13	0.544158	0.272079	−	0.962275i	$-0.412289\pi$
$997$	1.69767e13	0.544158	0.272079	+	0.962275i	$0.412289\pi$
$998$	2.14051e13	0.683014
$999$	3.25581e13	1.03422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.9	yes	36
17.16	even	2		289.10.a.g.1.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.9	✓	36	17.16	even	2
289.10.a.h.1.9	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-22.6693 q^{2} +265.602 q^{3} +1.89626 q^{4} +368.101 q^{5} -6021.01 q^{6} -2877.49 q^{7} +11563.7 q^{8} +50861.5 q^{9} +O(q^{10})\)	\(q-22.6693 q^{2} +265.602 q^{3} +1.89626 q^{4} +368.101 q^{5} -6021.01 q^{6} -2877.49 q^{7} +11563.7 q^{8} +50861.5 q^{9} -8344.59 q^{10} -63835.2 q^{11} +503.651 q^{12} -149124. q^{13} +65230.7 q^{14} +97768.4 q^{15} -263111. q^{16} -1.15299e6 q^{18} +444434. q^{19} +698.016 q^{20} -764268. q^{21} +1.44710e6 q^{22} -1.56940e6 q^{23} +3.07134e6 q^{24} -1.81763e6 q^{25} +3.38054e6 q^{26} +8.28107e6 q^{27} -5456.48 q^{28} +5.40558e6 q^{29} -2.21634e6 q^{30} +759714. q^{31} +43937.0 q^{32} -1.69548e7 q^{33} -1.05921e6 q^{35} +96446.6 q^{36} +3.93163e6 q^{37} -1.00750e7 q^{38} -3.96077e7 q^{39} +4.25661e6 q^{40} -9.97180e6 q^{41} +1.73254e7 q^{42} +2.04493e7 q^{43} -121048. q^{44} +1.87222e7 q^{45} +3.55771e7 q^{46} +4.76880e7 q^{47} -6.98829e7 q^{48} -3.20736e7 q^{49} +4.12043e7 q^{50} -282778. q^{52} -5.80242e6 q^{53} -1.87726e8 q^{54} -2.34978e7 q^{55} -3.32744e7 q^{56} +1.18043e8 q^{57} -1.22540e8 q^{58} +9.50173e7 q^{59} +185394. q^{60} +1.59704e8 q^{61} -1.72222e7 q^{62} -1.46353e8 q^{63} +1.33717e8 q^{64} -5.48928e7 q^{65} +3.84352e8 q^{66} +8.38127e7 q^{67} -4.16835e8 q^{69} +2.40115e7 q^{70} +3.10856e8 q^{71} +5.88146e8 q^{72} +3.37571e8 q^{73} -8.91273e7 q^{74} -4.82765e8 q^{75} +842764. q^{76} +1.83685e8 q^{77} +8.97878e8 q^{78} -5.51861e7 q^{79} -9.68516e7 q^{80} +1.19836e9 q^{81} +2.26053e8 q^{82} +3.47302e8 q^{83} -1.44925e6 q^{84} -4.63570e8 q^{86} +1.43573e9 q^{87} -7.38171e8 q^{88} -3.74829e8 q^{89} -4.24418e8 q^{90} +4.29104e8 q^{91} -2.97598e6 q^{92} +2.01782e8 q^{93} -1.08105e9 q^{94} +1.63597e8 q^{95} +1.16698e7 q^{96} +1.18045e9 q^{97} +7.27087e8 q^{98} -3.24675e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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

L-functions

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