LMFDB - Embedded newform 289.10.a.h.1.33

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			1.33
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)

$f(q)$	$=$	$q+38.8851 q^{2} -39.5980 q^{3} +1000.05 q^{4} -1326.61 q^{5} -1539.77 q^{6} +2031.17 q^{7} +18977.8 q^{8} -18115.0 q^{9} +O(q^{10})$	\(q+38.8851 q^{2} -39.5980 q^{3} +1000.05 q^{4} -1326.61 q^{5} -1539.77 q^{6} +2031.17 q^{7} +18977.8 q^{8} -18115.0 q^{9} -51585.4 q^{10} +79765.4 q^{11} -39600.0 q^{12} +19866.3 q^{13} +78982.0 q^{14} +52531.2 q^{15} +225928. q^{16} -704403. q^{18} -430239. q^{19} -1.32668e6 q^{20} -80430.2 q^{21} +3.10168e6 q^{22} +1.47745e6 q^{23} -751484. q^{24} -193226. q^{25} +772501. q^{26} +1.49673e6 q^{27} +2.03126e6 q^{28} -5.01398e6 q^{29} +2.04268e6 q^{30} +8.00000e6 q^{31} -931397. q^{32} -3.15856e6 q^{33} -2.69457e6 q^{35} -1.81159e7 q^{36} +688170. q^{37} -1.67299e7 q^{38} -786665. q^{39} -2.51762e7 q^{40} +8.23001e6 q^{41} -3.12753e6 q^{42} +4.37889e7 q^{43} +7.97693e7 q^{44} +2.40316e7 q^{45} +5.74509e7 q^{46} -3.64741e7 q^{47} -8.94632e6 q^{48} -3.62280e7 q^{49} -7.51362e6 q^{50} +1.98672e7 q^{52} +5.12196e7 q^{53} +5.82003e7 q^{54} -1.05818e8 q^{55} +3.85471e7 q^{56} +1.70366e7 q^{57} -1.94969e8 q^{58} +1.34598e8 q^{59} +5.25338e7 q^{60} +9.39211e7 q^{61} +3.11081e8 q^{62} -3.67946e7 q^{63} -1.51893e8 q^{64} -2.63548e7 q^{65} -1.22821e8 q^{66} +1.29800e8 q^{67} -5.85043e7 q^{69} -1.04778e8 q^{70} +2.39269e7 q^{71} -3.43783e8 q^{72} +4.14566e8 q^{73} +2.67595e7 q^{74} +7.65139e6 q^{75} -4.30260e8 q^{76} +1.62017e8 q^{77} -3.05895e7 q^{78} +3.87393e8 q^{79} -2.99719e8 q^{80} +2.97290e8 q^{81} +3.20024e8 q^{82} +2.80744e8 q^{83} -8.04341e7 q^{84} +1.70274e9 q^{86} +1.98544e8 q^{87} +1.51377e9 q^{88} +9.07508e8 q^{89} +9.34469e8 q^{90} +4.03516e7 q^{91} +1.47753e9 q^{92} -3.16784e8 q^{93} -1.41830e9 q^{94} +5.70760e8 q^{95} +3.68815e7 q^{96} -1.62096e9 q^{97} -1.40873e9 q^{98} -1.44495e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	38.8851	1.71849	0.859247	−	0.511561i	$-0.170933\pi$
$2$	38.8851	1.71849	0.859247	+	0.511561i	$0.170933\pi$
$3$	−39.5980	−0.282246	−0.141123	−	0.989992i	$-0.545071\pi$
$3$	−39.5980	−0.282246	−0.141123	+	0.989992i	$0.545071\pi$
$4$	1000.05	1.95322
$5$	−1326.61	−0.949246	−0.474623	−	0.880189i	$-0.657416\pi$
$5$	−1326.61	−0.949246	−0.474623	+	0.880189i	$0.657416\pi$
$6$	−1539.77	−0.485038
$7$	2031.17	0.319745	0.159873	−	0.987138i	$-0.448892\pi$
$7$	2031.17	0.319745	0.159873	+	0.987138i	$0.448892\pi$
$8$	18977.8	1.63810
$9$	−18115.0	−0.920337
$10$	−51585.4	−1.63127
$11$	79765.4	1.64266	0.821330	−	0.570453i	$-0.193233\pi$
$11$	79765.4	1.64266	0.821330	+	0.570453i	$0.193233\pi$
$12$	−39600.0	−0.551289
$13$	19866.3	0.192917	0.0964586	−	0.995337i	$-0.469248\pi$
$13$	19866.3	0.192917	0.0964586	+	0.995337i	$0.469248\pi$
$14$	78982.0	0.549480
$15$	52531.2	0.267921
$16$	225928.	0.861848
$17$	0	0
$17$	0	0
$18$	−704403.	−1.58159
$19$	−430239.	−0.757388	−0.378694	−	0.925522i	$-0.623627\pi$
$19$	−430239.	−0.757388	−0.378694	+	0.925522i	$0.623627\pi$
$20$	−1.32668e6	−1.85409
$21$	−80430.2	−0.0902469
$22$	3.10168e6	2.82290
$23$	1.47745e6	1.10088	0.550438	−	0.834876i	$-0.314461\pi$
$23$	1.47745e6	1.10088	0.550438	+	0.834876i	$0.314461\pi$
$24$	−751484.	−0.462348
$25$	−193226.	−0.0989319
$26$	772501.	0.331527
$27$	1.49673e6	0.542008
$28$	2.03126e6	0.624533
$29$	−5.01398e6	−1.31641	−0.658206	−	0.752838i	$-0.728684\pi$
$29$	−5.01398e6	−1.31641	−0.658206	+	0.752838i	$0.728684\pi$
$30$	2.04268e6	0.460421
$31$	8.00000e6	1.55583	0.777915	−	0.628369i	$-0.216277\pi$
$31$	8.00000e6	1.55583	0.777915	+	0.628369i	$0.216277\pi$
$32$	−931397.	−0.157022
$33$	−3.15856e6	−0.463635
$34$	0	0
$35$	−2.69457e6	−0.303517
$36$	−1.81159e7	−1.79762
$37$	688170.	0.0603653	0.0301827	−	0.999544i	$-0.490391\pi$
$37$	688170.	0.0603653	0.0301827	+	0.999544i	$0.490391\pi$
$38$	−1.67299e7	−1.30157
$39$	−786665.	−0.0544501
$40$	−2.51762e7	−1.55496
$41$	8.23001e6	0.454855	0.227427	−	0.973795i	$-0.426969\pi$
$41$	8.23001e6	0.454855	0.227427	+	0.973795i	$0.426969\pi$
$42$	−3.12753e6	−0.155089
$43$	4.37889e7	1.95324	0.976621	−	0.214967i	$-0.0689644\pi$
$43$	4.37889e7	1.95324	0.976621	+	0.214967i	$0.0689644\pi$
$44$	7.97693e7	3.20848
$45$	2.40316e7	0.873626
$46$	5.74509e7	1.89185
$47$	−3.64741e7	−1.09030	−0.545148	−	0.838340i	$-0.683526\pi$
$47$	−3.64741e7	−1.09030	−0.545148	+	0.838340i	$0.683526\pi$
$48$	−8.94632e6	−0.243253
$49$	−3.62280e7	−0.897763
$50$	−7.51362e6	−0.170014
$51$	0	0
$52$	1.98672e7	0.376810
$53$	5.12196e7	0.891651	0.445826	−	0.895120i	$-0.352910\pi$
$53$	5.12196e7	0.891651	0.445826	+	0.895120i	$0.352910\pi$
$54$	5.82003e7	0.931437
$55$	−1.05818e8	−1.55929
$56$	3.85471e7	0.523775
$57$	1.70366e7	0.213770
$58$	−1.94969e8	−2.26225
$59$	1.34598e8	1.44612	0.723060	−	0.690785i	$-0.242735\pi$
$59$	1.34598e8	1.44612	0.723060	+	0.690785i	$0.242735\pi$
$60$	5.25338e7	0.523309
$61$	9.39211e7	0.868518	0.434259	−	0.900788i	$-0.357010\pi$
$61$	9.39211e7	0.868518	0.434259	+	0.900788i	$0.357010\pi$
$62$	3.11081e8	2.67369
$63$	−3.67946e7	−0.294273
$64$	−1.51893e8	−1.13169
$65$	−2.63548e7	−0.183126
$66$	−1.22821e8	−0.796753
$67$	1.29800e8	0.786934	0.393467	−	0.919339i	$-0.371276\pi$
$67$	1.29800e8	0.786934	0.393467	+	0.919339i	$0.371276\pi$
$68$	0	0
$69$	−5.85043e7	−0.310718
$70$	−1.04778e8	−0.521592
$71$	2.39269e7	0.111744	0.0558720	−	0.998438i	$-0.482206\pi$
$71$	2.39269e7	0.111744	0.0558720	+	0.998438i	$0.482206\pi$
$72$	−3.43783e8	−1.50761
$73$	4.14566e8	1.70860	0.854301	−	0.519779i	$-0.173986\pi$
$73$	4.14566e8	1.70860	0.854301	+	0.519779i	$0.173986\pi$
$74$	2.67595e7	0.103737
$75$	7.65139e6	0.0279232
$76$	−4.30260e8	−1.47935
$77$	1.62017e8	0.525233
$78$	−3.05895e7	−0.0935722
$79$	3.87393e8	1.11900	0.559500	−	0.828830i	$-0.310993\pi$
$79$	3.87393e8	1.11900	0.559500	+	0.828830i	$0.310993\pi$
$80$	−2.99719e8	−0.818106
$81$	2.97290e8	0.767357
$82$	3.20024e8	0.781665
$83$	2.80744e8	0.649319	0.324660	−	0.945831i	$-0.394750\pi$
$83$	2.80744e8	0.649319	0.324660	+	0.945831i	$0.394750\pi$
$84$	−8.04341e7	−0.176272
$85$	0	0
$86$	1.70274e9	3.35663
$87$	1.98544e8	0.371552
$88$	1.51377e9	2.69084
$89$	9.07508e8	1.53319	0.766594	−	0.642132i	$-0.221950\pi$
$89$	9.07508e8	1.53319	0.766594	+	0.642132i	$0.221950\pi$
$90$	9.34469e8	1.50132
$91$	4.03516e7	0.0616843
$92$	1.47753e9	2.15025
$93$	−3.16784e8	−0.439127
$94$	−1.41830e9	−1.87367
$95$	5.70760e8	0.718948
$96$	3.68815e7	0.0443188
$97$	−1.62096e9	−1.85908	−0.929542	−	0.368716i	$-0.879798\pi$
$97$	−1.62096e9	−1.85908	−0.929542	+	0.368716i	$0.879798\pi$
$98$	−1.40873e9	−1.54280
$99$	−1.44495e9	−1.51180
$100$	−1.93236e8	−0.193236
$101$	1.25201e9	1.19719	0.598593	−	0.801053i	$-0.295727\pi$
$101$	1.25201e9	1.19719	0.598593	+	0.801053i	$0.295727\pi$
$102$	0	0
$103$	−1.74839e8	−0.153063	−0.0765315	−	0.997067i	$-0.524385\pi$
$103$	−1.74839e8	−0.153063	−0.0765315	+	0.997067i	$0.524385\pi$
$104$	3.77018e8	0.316018
$105$	1.06700e8	0.0856665
$106$	1.99168e9	1.53230
$107$	−1.01435e9	−0.748105	−0.374053	−	0.927407i	$-0.622032\pi$
$107$	−1.01435e9	−0.748105	−0.374053	+	0.927407i	$0.622032\pi$
$108$	1.49680e9	1.05866
$109$	6.13770e8	0.416472	0.208236	−	0.978079i	$-0.433228\pi$
$109$	6.13770e8	0.416472	0.208236	+	0.978079i	$0.433228\pi$
$110$	−4.11473e9	−2.67963
$111$	−2.72502e7	−0.0170379
$112$	4.58898e8	0.275572
$113$	−5.73250e7	−0.0330743	−0.0165372	−	0.999863i	$-0.505264\pi$
$113$	−5.73250e7	−0.0330743	−0.0165372	+	0.999863i	$0.505264\pi$
$114$	6.62470e8	0.367362
$115$	−1.96001e9	−1.04500
$116$	−5.01423e9	−2.57124
$117$	−3.59877e8	−0.177549
$118$	5.23385e9	2.48515
$119$	0	0
$120$	9.96927e8	0.438882
$121$	4.00458e9	1.69833
$122$	3.65213e9	1.49254
$123$	−3.25892e8	−0.128381
$124$	8.00039e9	3.03888
$125$	2.84737e9	1.04316
$126$	−1.43076e9	−0.505707
$127$	−5.54930e9	−1.89287	−0.946436	−	0.322892i	$-0.895345\pi$
$127$	−5.54930e9	−1.89287	−0.946436	+	0.322892i	$0.895345\pi$
$128$	−5.42948e9	−1.78778
$129$	−1.73396e9	−0.551295
$130$	−1.02481e9	−0.314701
$131$	−1.26351e9	−0.374851	−0.187425	−	0.982279i	$-0.560014\pi$
$131$	−1.26351e9	−0.374851	−0.187425	+	0.982279i	$0.560014\pi$
$132$	−3.15871e9	−0.905580
$133$	−8.73886e8	−0.242171
$134$	5.04728e9	1.35234
$135$	−1.98558e9	−0.514499
$136$	0	0
$137$	3.64045e9	0.882903	0.441452	−	0.897285i	$-0.354464\pi$
$137$	3.64045e9	0.882903	0.441452	+	0.897285i	$0.354464\pi$
$138$	−2.27494e9	−0.533967
$139$	2.14697e9	0.487820	0.243910	−	0.969798i	$-0.421570\pi$
$139$	2.14697e9	0.487820	0.243910	+	0.969798i	$0.421570\pi$
$140$	−2.69470e9	−0.592835
$141$	1.44430e9	0.307732
$142$	9.30400e8	0.192031
$143$	1.58464e9	0.316897
$144$	−4.09269e9	−0.793191
$145$	6.65161e9	1.24960
$146$	1.61204e10	2.93622
$147$	1.43456e9	0.253390
$148$	6.88203e8	0.117907
$149$	−2.29251e9	−0.381041	−0.190521	−	0.981683i	$-0.561018\pi$
$149$	−2.29251e9	−0.381041	−0.190521	+	0.981683i	$0.561018\pi$
$150$	2.97525e8	0.0479858
$151$	−2.31951e9	−0.363079	−0.181539	−	0.983384i	$-0.558108\pi$
$151$	−2.31951e9	−0.363079	−0.181539	+	0.983384i	$0.558108\pi$
$152$	−8.16499e9	−1.24068
$153$	0	0
$154$	6.30003e9	0.902609
$155$	−1.06129e10	−1.47687
$156$	−7.86703e8	−0.106353
$157$	−2.99512e9	−0.393429	−0.196714	−	0.980461i	$-0.563027\pi$
$157$	−2.99512e9	−0.393429	−0.196714	+	0.980461i	$0.563027\pi$
$158$	1.50638e10	1.92299
$159$	−2.02820e9	−0.251665
$160$	1.23560e9	0.149052
$161$	3.00095e9	0.352000
$162$	1.15601e10	1.31870
$163$	2.18156e9	0.242060	0.121030	−	0.992649i	$-0.461380\pi$
$163$	2.18156e9	0.242060	0.121030	+	0.992649i	$0.461380\pi$
$164$	8.23041e9	0.888432
$165$	4.19018e9	0.440103
$166$	1.09167e10	1.11585
$167$	1.30714e10	1.30046	0.650232	−	0.759736i	$-0.274672\pi$
$167$	1.30714e10	1.30046	0.650232	+	0.759736i	$0.274672\pi$
$168$	−1.52639e9	−0.147834
$169$	−1.02098e10	−0.962783
$170$	0	0
$171$	7.79378e9	0.697052
$172$	4.37911e10	3.81511
$173$	2.58955e9	0.219794	0.109897	−	0.993943i	$-0.464948\pi$
$173$	2.58955e9	0.219794	0.109897	+	0.993943i	$0.464948\pi$
$174$	7.72039e9	0.638510
$175$	−3.92475e8	−0.0316330
$176$	1.80213e10	1.41572
$177$	−5.32982e9	−0.408162
$178$	3.52885e10	2.63477
$179$	−6.20782e9	−0.451960	−0.225980	−	0.974132i	$-0.572558\pi$
$179$	−6.20782e9	−0.451960	−0.225980	+	0.974132i	$0.572558\pi$
$180$	2.40327e10	1.70638
$181$	1.12580e10	0.779664	0.389832	−	0.920886i	$-0.372533\pi$
$181$	1.12580e10	0.779664	0.389832	+	0.920886i	$0.372533\pi$
$182$	1.56908e9	0.106004
$183$	−3.71909e9	−0.245136
$184$	2.80388e10	1.80335
$185$	−9.12934e8	−0.0573016
$186$	−1.23182e10	−0.754638
$187$	0	0
$188$	−3.64759e10	−2.12959
$189$	3.04010e9	0.173304
$190$	2.21940e10	1.23551
$191$	−2.49016e10	−1.35387	−0.676936	−	0.736042i	$-0.736693\pi$
$191$	−2.49016e10	−1.35387	−0.676936	+	0.736042i	$0.736693\pi$
$192$	6.01466e9	0.319415
$193$	−2.70015e9	−0.140081	−0.0700407	−	0.997544i	$-0.522313\pi$
$193$	−2.70015e9	−0.140081	−0.0700407	+	0.997544i	$0.522313\pi$
$194$	−6.30311e10	−3.19482
$195$	1.04360e9	0.0516866
$196$	−3.62297e10	−1.75353
$197$	6.99326e8	0.0330813	0.0165406	−	0.999863i	$-0.494735\pi$
$197$	6.99326e8	0.0330813	0.0165406	+	0.999863i	$0.494735\pi$
$198$	−5.61870e10	−2.59802
$199$	1.79474e10	0.811267	0.405634	−	0.914036i	$-0.367051\pi$
$199$	1.79474e10	0.811267	0.405634	+	0.914036i	$0.367051\pi$
$200$	−3.66701e9	−0.162061
$201$	−5.13983e9	−0.222109
$202$	4.86845e10	2.05736
$203$	−1.01842e10	−0.420916
$204$	0	0
$205$	−1.09180e10	−0.431769
$206$	−6.79861e9	−0.263038
$207$	−2.67641e10	−1.01318
$208$	4.48835e9	0.166265
$209$	−3.43182e10	−1.24413
$210$	4.14902e9	0.147217
$211$	1.27607e10	0.443202	0.221601	−	0.975137i	$-0.428872\pi$
$211$	1.27607e10	0.443202	0.221601	+	0.975137i	$0.428872\pi$
$212$	5.12221e10	1.74159
$213$	−9.47459e8	−0.0315393
$214$	−3.94432e10	−1.28561
$215$	−5.80909e10	−1.85411
$216$	2.84046e10	0.887864
$217$	1.62493e10	0.497470
$218$	2.38665e10	0.715705
$219$	−1.64160e10	−0.482246
$220$	−1.05823e11	−3.04563
$221$	0	0
$222$	−1.05962e9	−0.0292795
$223$	4.40038e10	1.19157	0.595783	−	0.803145i	$-0.296842\pi$
$223$	4.40038e10	1.19157	0.595783	+	0.803145i	$0.296842\pi$
$224$	−1.89182e9	−0.0502070
$225$	3.50030e9	0.0910507
$226$	−2.22909e9	−0.0568381
$227$	5.01424e9	0.125340	0.0626698	−	0.998034i	$-0.480038\pi$
$227$	5.01424e9	0.125340	0.0626698	+	0.998034i	$0.480038\pi$
$228$	1.70374e10	0.417540
$229$	−4.24718e10	−1.02057	−0.510283	−	0.860007i	$-0.670459\pi$
$229$	−4.24718e10	−1.02057	−0.510283	+	0.860007i	$0.670459\pi$
$230$	−7.62150e10	−1.79583
$231$	−6.41555e9	−0.148245
$232$	−9.51544e10	−2.15642
$233$	−7.54306e10	−1.67666	−0.838332	−	0.545160i	$-0.816469\pi$
$233$	−7.54306e10	−1.67666	−0.838332	+	0.545160i	$0.816469\pi$
$234$	−1.39938e10	−0.305116
$235$	4.83870e10	1.03496
$236$	1.34605e11	2.82459
$237$	−1.53400e10	−0.315834
$238$	0	0
$239$	−4.07962e10	−0.808778	−0.404389	−	0.914587i	$-0.632516\pi$
$239$	−4.07962e10	−0.808778	−0.404389	+	0.914587i	$0.632516\pi$
$240$	1.18683e10	0.230907
$241$	−5.72156e10	−1.09254	−0.546271	−	0.837609i	$-0.683953\pi$
$241$	−5.72156e10	−1.09254	−0.546271	+	0.837609i	$0.683953\pi$
$242$	1.55718e11	2.91857
$243$	−4.12322e10	−0.758592
$244$	9.39257e10	1.69641
$245$	4.80605e10	0.852198
$246$	−1.26723e10	−0.220622
$247$	−8.54723e9	−0.146113
$248$	1.51822e11	2.54861
$249$	−1.11169e10	−0.183268
$250$	1.10720e11	1.79266
$251$	−2.21629e10	−0.352448	−0.176224	−	0.984350i	$-0.556388\pi$
$251$	−2.21629e10	−0.352448	−0.176224	+	0.984350i	$0.556388\pi$
$252$	−3.67963e10	−0.574781
$253$	1.17850e11	1.80837
$254$	−2.15785e11	−3.25289
$255$	0	0
$256$	−1.33357e11	−1.94060
$257$	−8.84957e10	−1.26539	−0.632693	−	0.774402i	$-0.718051\pi$
$257$	−8.84957e10	−1.26539	−0.632693	+	0.774402i	$0.718051\pi$
$258$	−6.74250e10	−0.947398
$259$	1.39779e9	0.0193015
$260$	−2.63561e10	−0.357685
$261$	9.08283e10	1.21154
$262$	−4.91317e10	−0.644179
$263$	6.15949e10	0.793860	0.396930	−	0.917849i	$-0.370076\pi$
$263$	6.15949e10	0.793860	0.396930	+	0.917849i	$0.370076\pi$
$264$	−5.99424e10	−0.759481
$265$	−6.79485e10	−0.846396
$266$	−3.39811e10	−0.416170
$267$	−3.59355e10	−0.432736
$268$	1.29806e11	1.53705
$269$	−4.19152e10	−0.488075	−0.244037	−	0.969766i	$-0.578472\pi$
$269$	−4.19152e10	−0.488075	−0.244037	+	0.969766i	$0.578472\pi$
$270$	−7.72092e10	−0.884163
$271$	1.56140e11	1.75854	0.879272	−	0.476319i	$-0.158029\pi$
$271$	1.56140e11	1.75854	0.879272	+	0.476319i	$0.158029\pi$
$272$	0	0
$273$	−1.59785e9	−0.0174102
$274$	1.41559e11	1.51726
$275$	−1.54128e10	−0.162511
$276$	−5.85071e10	−0.606901
$277$	1.43796e11	1.46753	0.733765	−	0.679404i	$-0.237762\pi$
$277$	1.43796e11	1.46753	0.733765	+	0.679404i	$0.237762\pi$
$278$	8.34851e10	0.838316
$279$	−1.44920e11	−1.43189
$280$	−5.11370e10	−0.497192
$281$	8.85329e10	0.847083	0.423542	−	0.905877i	$-0.360787\pi$
$281$	8.85329e10	0.847083	0.423542	+	0.905877i	$0.360787\pi$
$282$	5.61618e10	0.528835
$283$	−1.83307e10	−0.169879	−0.0849394	−	0.996386i	$-0.527070\pi$
$283$	−1.83307e10	−0.169879	−0.0849394	+	0.996386i	$0.527070\pi$
$284$	2.39281e10	0.218261
$285$	−2.26010e10	−0.202920
$286$	6.16188e10	0.544586
$287$	1.67165e10	0.145438
$288$	1.68722e10	0.144513
$289$	0	0
$290$	2.58648e11	2.14743
$291$	6.41868e10	0.524720
$292$	4.14586e11	3.33727
$293$	−8.61025e10	−0.682514	−0.341257	−	0.939970i	$-0.610853\pi$
$293$	−8.61025e10	−0.682514	−0.341257	+	0.939970i	$0.610853\pi$
$294$	5.57829e10	0.435449
$295$	−1.78559e11	−1.37272
$296$	1.30599e10	0.0988846
$297$	1.19387e11	0.890335
$298$	−8.91442e10	−0.654817
$299$	2.93515e10	0.212378
$300$	7.65176e9	0.0545401
$301$	8.89426e10	0.624540
$302$	−9.01945e10	−0.623949
$303$	−4.95772e10	−0.337901
$304$	−9.72032e10	−0.652754
$305$	−1.24597e11	−0.824438
$306$	0	0
$307$	−1.18874e11	−0.763775	−0.381887	−	0.924209i	$-0.624726\pi$
$307$	−1.18874e11	−0.763775	−0.381887	+	0.924209i	$0.624726\pi$
$308$	1.62025e11	1.02590
$309$	6.92327e9	0.0432014
$310$	−4.12683e11	−2.53798
$311$	2.72867e11	1.65397	0.826987	−	0.562220i	$-0.190053\pi$
$311$	2.72867e11	1.65397	0.826987	+	0.562220i	$0.190053\pi$
$312$	−1.49292e10	−0.0891949
$313$	−1.05123e11	−0.619080	−0.309540	−	0.950886i	$-0.600175\pi$
$313$	−1.05123e11	−0.619080	−0.309540	+	0.950886i	$0.600175\pi$
$314$	−1.16466e11	−0.676105
$315$	4.88121e10	0.279338
$316$	3.87412e11	2.18565
$317$	1.75077e11	0.973781	0.486891	−	0.873463i	$-0.338131\pi$
$317$	1.75077e11	0.973781	0.486891	+	0.873463i	$0.338131\pi$
$318$	−7.88666e10	−0.432485
$319$	−3.99942e11	−2.16242
$320$	2.01503e11	1.07425
$321$	4.01664e10	0.211150
$322$	1.16692e11	0.604910
$323$	0	0
$324$	2.97304e11	1.49882
$325$	−3.83868e9	−0.0190857
$326$	8.48300e10	0.415978
$327$	−2.43041e10	−0.117548
$328$	1.56187e11	0.745099
$329$	−7.40849e10	−0.348617
$330$	1.62935e11	0.756315
$331$	−1.62608e11	−0.744588	−0.372294	−	0.928115i	$-0.621429\pi$
$331$	−1.62608e11	−0.744588	−0.372294	+	0.928115i	$0.621429\pi$
$332$	2.80757e11	1.26826
$333$	−1.24662e10	−0.0555565
$334$	5.08282e11	2.23484
$335$	−1.72194e11	−0.746994
$336$	−1.81715e10	−0.0777791
$337$	5.36814e10	0.226720	0.113360	−	0.993554i	$-0.463839\pi$
$337$	5.36814e10	0.226720	0.113360	+	0.993554i	$0.463839\pi$
$338$	−3.97010e11	−1.65454
$339$	2.26996e9	0.00933511
$340$	0	0
$341$	6.38123e11	2.55570
$342$	3.03061e11	1.19788
$343$	−1.55550e11	−0.606801
$344$	8.31018e11	3.19961
$345$	7.76124e10	0.294948
$346$	1.00695e11	0.377715
$347$	1.15461e11	0.427517	0.213758	−	0.976887i	$-0.431430\pi$
$347$	1.15461e11	0.427517	0.213758	+	0.976887i	$0.431430\pi$
$348$	1.98554e11	0.725723
$349$	1.42013e11	0.512404	0.256202	−	0.966623i	$-0.417529\pi$
$349$	1.42013e11	0.512404	0.256202	+	0.966623i	$0.417529\pi$
$350$	−1.52614e10	−0.0543611
$351$	2.97344e10	0.104563
$352$	−7.42933e10	−0.257933
$353$	3.90958e11	1.34012	0.670060	−	0.742307i	$-0.266268\pi$
$353$	3.90958e11	1.34012	0.670060	+	0.742307i	$0.266268\pi$
$354$	−2.07250e11	−0.701424
$355$	−3.17417e10	−0.106073
$356$	9.07552e11	2.99465
$357$	0	0
$358$	−2.41391e11	−0.776691
$359$	−4.03346e11	−1.28160	−0.640800	−	0.767708i	$-0.721397\pi$
$359$	−4.03346e11	−1.28160	−0.640800	+	0.767708i	$0.721397\pi$
$360$	4.56066e11	1.43109
$361$	−1.37582e11	−0.426363
$362$	4.37768e11	1.33985
$363$	−1.58573e11	−0.479348
$364$	4.03536e10	0.120483
$365$	−5.49968e11	−1.62188
$366$	−1.44617e11	−0.421265
$367$	−1.76479e11	−0.507803	−0.253901	−	0.967230i	$-0.581714\pi$
$367$	−1.76479e11	−0.507803	−0.253901	+	0.967230i	$0.581714\pi$
$368$	3.33799e11	0.948788
$369$	−1.49087e11	−0.418620
$370$	−3.54995e10	−0.0984724
$371$	1.04036e11	0.285101
$372$	−3.16800e11	−0.857712
$373$	−1.09830e11	−0.293786	−0.146893	−	0.989152i	$-0.546927\pi$
$373$	−1.09830e11	−0.293786	−0.146893	+	0.989152i	$0.546927\pi$
$374$	0	0
$375$	−1.12750e11	−0.294427
$376$	−6.92198e11	−1.78601
$377$	−9.96090e10	−0.253958
$378$	1.18215e11	0.297823
$379$	2.01826e11	0.502459	0.251230	−	0.967928i	$-0.419165\pi$
$379$	2.01826e11	0.502459	0.251230	+	0.967928i	$0.419165\pi$
$380$	5.70788e11	1.40426
$381$	2.19741e11	0.534256
$382$	−9.68302e11	−2.32662
$383$	−4.10697e11	−0.975275	−0.487638	−	0.873046i	$-0.662141\pi$
$383$	−4.10697e11	−0.975275	−0.487638	+	0.873046i	$0.662141\pi$
$384$	2.14997e11	0.504594
$385$	−2.14933e11	−0.498575
$386$	−1.04996e11	−0.240729
$387$	−7.93236e11	−1.79764
$388$	−1.62104e12	−3.63120
$389$	8.47825e11	1.87730	0.938649	−	0.344875i	$-0.112079\pi$
$389$	8.47825e11	1.87730	0.938649	+	0.344875i	$0.112079\pi$
$390$	4.05804e10	0.0888230
$391$	0	0
$392$	−6.87527e11	−1.47063
$393$	5.00326e10	0.105800
$394$	2.71934e10	0.0568499
$395$	−5.13921e11	−1.06221
$396$	−1.44502e12	−2.95288
$397$	1.38204e11	0.279231	0.139615	−	0.990206i	$-0.455413\pi$
$397$	1.38204e11	0.279231	0.139615	+	0.990206i	$0.455413\pi$
$398$	6.97888e11	1.39416
$399$	3.46042e10	0.0683519
$400$	−4.36553e10	−0.0852643
$401$	−8.10829e11	−1.56596	−0.782978	−	0.622050i	$-0.786300\pi$
$401$	−8.10829e11	−1.56596	−0.782978	+	0.622050i	$0.786300\pi$
$402$	−1.99863e11	−0.381693
$403$	1.58930e11	0.300146
$404$	1.25207e12	2.33837
$405$	−3.94388e11	−0.728411
$406$	−3.96014e11	−0.723342
$407$	5.48921e10	0.0991597
$408$	0	0
$409$	5.60175e11	0.989849	0.494924	−	0.868936i	$-0.335196\pi$
$409$	5.60175e11	0.989849	0.494924	+	0.868936i	$0.335196\pi$
$410$	−4.24548e11	−0.741993
$411$	−1.44155e11	−0.249196
$412$	−1.74847e11	−0.298966
$413$	2.73391e11	0.462390
$414$	−1.04072e12	−1.74114
$415$	−3.72438e11	−0.616364
$416$	−1.85034e10	−0.0302922
$417$	−8.50159e10	−0.137685
$418$	−1.33447e12	−2.13803
$419$	−9.94635e11	−1.57652	−0.788262	−	0.615340i	$-0.789019\pi$
$419$	−9.94635e11	−1.57652	−0.788262	+	0.615340i	$0.789019\pi$
$420$	1.06705e11	0.167326
$421$	−4.43656e11	−0.688299	−0.344149	−	0.938915i	$-0.611833\pi$
$421$	−4.43656e11	−0.688299	−0.344149	+	0.938915i	$0.611833\pi$
$422$	4.96199e11	0.761640
$423$	6.60728e11	1.00344
$424$	9.72036e11	1.46062
$425$	0	0
$426$	−3.68420e10	−0.0542001
$427$	1.90769e11	0.277705
$428$	−1.01440e12	−1.46121
$429$	−6.27487e10	−0.0894430
$430$	−2.25887e12	−3.18627
$431$	−7.58706e11	−1.05907	−0.529536	−	0.848287i	$-0.677634\pi$
$431$	−7.58706e11	−1.05907	−0.529536	+	0.848287i	$0.677634\pi$
$432$	3.38153e11	0.467129
$433$	1.31991e12	1.80447	0.902234	−	0.431246i	$-0.141926\pi$
$433$	1.31991e12	1.80447	0.902234	+	0.431246i	$0.141926\pi$
$434$	6.31856e11	0.854898
$435$	−2.63391e11	−0.352695
$436$	6.13800e11	0.813462
$437$	−6.35658e11	−0.833790
$438$	−6.38337e11	−0.828737
$439$	−3.84672e11	−0.494312	−0.247156	−	0.968976i	$-0.579496\pi$
$439$	−3.84672e11	−0.494312	−0.247156	+	0.968976i	$0.579496\pi$
$440$	−2.00819e12	−2.55427
$441$	6.56270e11	0.826245
$442$	0	0
$443$	3.34971e11	0.413228	0.206614	−	0.978423i	$-0.433756\pi$
$443$	3.34971e11	0.413228	0.206614	+	0.978423i	$0.433756\pi$
$444$	−2.72515e10	−0.0332788
$445$	−1.20391e12	−1.45537
$446$	1.71109e12	2.04770
$447$	9.07787e10	0.107547
$448$	−3.08519e11	−0.361852
$449$	1.09901e12	1.27612	0.638060	−	0.769986i	$-0.279737\pi$
$449$	1.09901e12	1.27612	0.638060	+	0.769986i	$0.279737\pi$
$450$	1.36109e11	0.156470
$451$	6.56470e11	0.747172
$452$	−5.73278e10	−0.0646015
$453$	9.18483e10	0.102478
$454$	1.94979e11	0.215395
$455$	−5.35310e10	−0.0585536
$456$	3.23318e11	0.350177
$457$	1.31545e12	1.41075	0.705376	−	0.708833i	$-0.250778\pi$
$457$	1.31545e12	1.41075	0.705376	+	0.708833i	$0.250778\pi$
$458$	−1.65152e12	−1.75384
$459$	0	0
$460$	−1.96010e12	−2.04112
$461$	−1.21831e12	−1.25633	−0.628163	−	0.778082i	$-0.716193\pi$
$461$	−1.21831e12	−1.25633	−0.628163	+	0.778082i	$0.716193\pi$
$462$	−2.49469e11	−0.254758
$463$	−1.04671e12	−1.05856	−0.529278	−	0.848449i	$-0.677537\pi$
$463$	−1.04671e12	−1.05856	−0.529278	+	0.848449i	$0.677537\pi$
$464$	−1.13280e12	−1.13455
$465$	4.20250e11	0.416840
$466$	−2.93312e12	−2.88134
$467$	5.48990e11	0.534119	0.267060	−	0.963680i	$-0.413948\pi$
$467$	5.48990e11	0.534119	0.267060	+	0.963680i	$0.413948\pi$
$468$	−3.59895e11	−0.346792
$469$	2.63645e11	0.251618
$470$	1.88153e12	1.77857
$471$	1.18601e11	0.111044
$472$	2.55437e12	2.36889
$473$	3.49284e12	3.20851
$474$	−5.96498e11	−0.542758
$475$	8.31335e10	0.0749299
$476$	0	0
$477$	−9.27843e11	−0.820619
$478$	−1.58636e12	−1.38988
$479$	−8.94844e11	−0.776672	−0.388336	−	0.921518i	$-0.626950\pi$
$479$	−8.94844e11	−0.776672	−0.388336	+	0.921518i	$0.626950\pi$
$480$	−4.89274e10	−0.0420694
$481$	1.36713e10	0.0116455
$482$	−2.22483e12	−1.87753
$483$	−1.18832e11	−0.0993507
$484$	4.00477e12	3.31721
$485$	2.15038e12	1.76473
$486$	−1.60332e12	−1.30363
$487$	−4.43593e11	−0.357359	−0.178679	−	0.983907i	$-0.557182\pi$
$487$	−4.43593e11	−0.357359	−0.178679	+	0.983907i	$0.557182\pi$
$488$	1.78242e12	1.42272
$489$	−8.63854e10	−0.0683204
$490$	1.86883e12	1.46450
$491$	−7.29563e11	−0.566495	−0.283247	−	0.959047i	$-0.591412\pi$
$491$	−7.29563e11	−0.566495	−0.283247	+	0.959047i	$0.591412\pi$
$492$	−3.25908e11	−0.250757
$493$	0	0
$494$	−3.32360e11	−0.251094
$495$	1.91689e12	1.43507
$496$	1.80743e12	1.34089
$497$	4.85995e10	0.0357296
$498$	−4.32281e11	−0.314945
$499$	3.28866e11	0.237447	0.118723	−	0.992927i	$-0.462120\pi$
$499$	3.28866e11	0.237447	0.118723	+	0.992927i	$0.462120\pi$
$500$	2.84751e12	2.03751
$501$	−5.17602e11	−0.367051
$502$	−8.61808e11	−0.605680
$503$	−1.15730e12	−0.806099	−0.403049	−	0.915178i	$-0.632050\pi$
$503$	−1.15730e12	−0.806099	−0.403049	+	0.915178i	$0.632050\pi$
$504$	−6.98280e11	−0.482050
$505$	−1.66093e12	−1.13642
$506$	4.58259e12	3.10766
$507$	4.04289e11	0.271742
$508$	−5.54957e12	−3.69719
$509$	−1.53067e12	−1.01077	−0.505384	−	0.862895i	$-0.668649\pi$
$509$	−1.53067e12	−1.01077	−0.505384	+	0.862895i	$0.668649\pi$
$510$	0	0
$511$	8.42052e11	0.546317
$512$	−2.40569e12	−1.54712
$513$	−6.43950e11	−0.410510
$514$	−3.44116e12	−2.17456
$515$	2.31943e11	0.145294
$516$	−1.73404e12	−1.07680
$517$	−2.90937e12	−1.79098
$518$	5.43530e10	0.0331696
$519$	−1.02541e11	−0.0620361
$520$	−5.00156e11	−0.299979
$521$	8.28369e11	0.492554	0.246277	−	0.969199i	$-0.420793\pi$
$521$	8.28369e11	0.492554	0.246277	+	0.969199i	$0.420793\pi$
$522$	3.53186e12	2.08203
$523$	−1.93852e12	−1.13295	−0.566476	−	0.824078i	$-0.691694\pi$
$523$	−1.93852e12	−1.13295	−0.566476	+	0.824078i	$0.691694\pi$
$524$	−1.26357e12	−0.732166
$525$	1.55412e10	0.00892830
$526$	2.39512e12	1.36424
$527$	0	0
$528$	−7.13607e11	−0.399583
$529$	3.81715e11	0.211928
$530$	−2.64218e12	−1.45453
$531$	−2.43824e12	−1.33092
$532$	−8.73929e11	−0.473014
$533$	1.63499e11	0.0877493
$534$	−1.39736e12	−0.743655
$535$	1.34565e12	0.710136
$536$	2.46332e12	1.28908
$537$	2.45818e11	0.127564
$538$	−1.62988e12	−0.838753
$539$	−2.88974e12	−1.47472
$540$	−1.98567e12	−1.00493
$541$	−8.12932e11	−0.408006	−0.204003	−	0.978970i	$-0.565395\pi$
$541$	−8.12932e11	−0.408006	−0.204003	+	0.978970i	$0.565395\pi$
$542$	6.07153e12	3.02205
$543$	−4.45795e11	−0.220057
$544$	0	0
$545$	−8.14234e11	−0.395335
$546$	−6.21324e10	−0.0299193
$547$	−1.04434e12	−0.498768	−0.249384	−	0.968405i	$-0.580228\pi$
$547$	−1.04434e12	−0.498768	−0.249384	+	0.968405i	$0.580228\pi$
$548$	3.64063e12	1.72450
$549$	−1.70138e12	−0.799330
$550$	−5.99327e11	−0.279275
$551$	2.15721e12	0.997035
$552$	−1.11028e12	−0.508988
$553$	7.86860e11	0.357795
$554$	5.59150e12	2.52194
$555$	3.61504e10	0.0161732
$556$	2.14708e12	0.952820
$557$	−3.24890e12	−1.43017	−0.715086	−	0.699036i	$-0.753613\pi$
$557$	−3.24890e12	−1.43017	−0.715086	+	0.699036i	$0.753613\pi$
$558$	−5.63522e12	−2.46069
$559$	8.69922e11	0.376814
$560$	−6.08779e11	−0.261586
$561$	0	0
$562$	3.44261e12	1.45571
$563$	4.37456e11	0.183504	0.0917522	−	0.995782i	$-0.470753\pi$
$563$	4.37456e11	0.183504	0.0917522	+	0.995782i	$0.470753\pi$
$564$	1.44437e12	0.601068
$565$	7.60481e10	0.0313957
$566$	−7.12789e11	−0.291936
$567$	6.03845e11	0.245359
$568$	4.54080e11	0.183048
$569$	−2.44467e12	−0.977720	−0.488860	−	0.872362i	$-0.662587\pi$
$569$	−2.44467e12	−0.977720	−0.488860	+	0.872362i	$0.662587\pi$
$570$	−8.78841e11	−0.348717
$571$	−4.30219e12	−1.69366	−0.846832	−	0.531860i	$-0.821493\pi$
$571$	−4.30219e12	−1.69366	−0.846832	+	0.531860i	$0.821493\pi$
$572$	1.58472e12	0.618970
$573$	9.86056e11	0.382125
$574$	6.50023e11	0.249934
$575$	−2.85483e11	−0.108912
$576$	2.75154e12	1.04154
$577$	1.04390e12	0.392075	0.196037	−	0.980596i	$-0.437193\pi$
$577$	1.04390e12	0.392075	0.196037	+	0.980596i	$0.437193\pi$
$578$	0	0
$579$	1.06921e11	0.0395374
$580$	6.65193e12	2.44074
$581$	5.70237e11	0.207617
$582$	2.49591e12	0.901727
$583$	4.08555e12	1.46468
$584$	7.86755e12	2.79886
$585$	4.77417e11	0.168537
$586$	−3.34810e12	−1.17290
$587$	−2.53007e12	−0.879552	−0.439776	−	0.898107i	$-0.644942\pi$
$587$	−2.53007e12	−0.879552	−0.439776	+	0.898107i	$0.644942\pi$
$588$	1.43463e12	0.494927
$589$	−3.44191e12	−1.17837
$590$	−6.94329e12	−2.35902
$591$	−2.76920e10	−0.00933706
$592$	1.55477e11	0.0520258
$593$	2.29492e11	0.0762117	0.0381058	−	0.999274i	$-0.487868\pi$
$593$	2.29492e11	0.0762117	0.0381058	+	0.999274i	$0.487868\pi$
$594$	4.64237e12	1.53003
$595$	0	0
$596$	−2.29262e12	−0.744258
$597$	−7.10684e11	−0.228977
$598$	1.14133e12	0.364970
$599$	2.96044e12	0.939583	0.469792	−	0.882777i	$-0.344329\pi$
$599$	2.96044e12	0.939583	0.469792	+	0.882777i	$0.344329\pi$
$600$	1.45207e11	0.0457410
$601$	−2.71047e12	−0.847443	−0.423721	−	0.905793i	$-0.639276\pi$
$601$	−2.71047e12	−0.847443	−0.423721	+	0.905793i	$0.639276\pi$
$602$	3.45854e12	1.07327
$603$	−2.35133e12	−0.724244
$604$	−2.31963e12	−0.709173
$605$	−5.31252e12	−1.61213
$606$	−1.92781e12	−0.580681
$607$	2.72636e12	0.815142	0.407571	−	0.913173i	$-0.366376\pi$
$607$	2.72636e12	0.815142	0.407571	+	0.913173i	$0.366376\pi$
$608$	4.00723e11	0.118926
$609$	4.03276e11	0.118802
$610$	−4.84496e12	−1.41679
$611$	−7.24603e11	−0.210337
$612$	0	0
$613$	3.18239e12	0.910294	0.455147	−	0.890416i	$-0.349587\pi$
$613$	3.18239e12	0.910294	0.455147	+	0.890416i	$0.349587\pi$
$614$	−4.62243e12	−1.31254
$615$	4.32332e11	0.121865
$616$	3.07472e12	0.860385
$617$	5.80402e12	1.61230	0.806150	−	0.591712i	$-0.201548\pi$
$617$	5.80402e12	1.61230	0.806150	+	0.591712i	$0.201548\pi$
$618$	2.69212e11	0.0742414
$619$	2.54189e12	0.695903	0.347952	−	0.937512i	$-0.386877\pi$
$619$	2.54189e12	0.695903	0.347952	+	0.937512i	$0.386877\pi$
$620$	−1.06134e13	−2.88464
$621$	2.21134e12	0.596684
$622$	1.06104e13	2.84234
$623$	1.84330e12	0.490230
$624$	−1.77730e11	−0.0469278
$625$	−3.39997e12	−0.891281
$626$	−4.08770e12	−1.06388
$627$	1.35893e12	0.351151
$628$	−2.99527e12	−0.768453
$629$	0	0
$630$	1.89806e12	0.480040
$631$	−6.29472e12	−1.58068	−0.790340	−	0.612668i	$-0.790096\pi$
$631$	−6.29472e12	−1.58068	−0.790340	+	0.612668i	$0.790096\pi$
$632$	7.35187e12	1.83304
$633$	−5.05297e11	−0.125092
$634$	6.80787e12	1.67344
$635$	7.36176e12	1.79680
$636$	−2.02830e12	−0.491557
$637$	−7.19714e11	−0.173194
$638$	−1.55518e13	−3.71610
$639$	−4.33436e11	−0.102842
$640$	7.20282e12	1.69704
$641$	−4.27476e12	−1.00012	−0.500058	−	0.865992i	$-0.666688\pi$
$641$	−4.27476e12	−1.00012	−0.500058	+	0.865992i	$0.666688\pi$
$642$	1.56188e12	0.362860
$643$	−3.30486e12	−0.762437	−0.381218	−	0.924485i	$-0.624495\pi$
$643$	−3.30486e12	−0.762437	−0.381218	+	0.924485i	$0.624495\pi$
$644$	3.00110e12	0.687533
$645$	2.30029e12	0.523315
$646$	0	0
$647$	1.81390e12	0.406952	0.203476	−	0.979080i	$-0.434776\pi$
$647$	1.81390e12	0.406952	0.203476	+	0.979080i	$0.434776\pi$
$648$	5.64191e12	1.25701
$649$	1.07363e13	2.37548
$650$	−1.49268e11	−0.0327986
$651$	−6.43442e11	−0.140409
$652$	2.18166e12	0.472796
$653$	1.96397e12	0.422694	0.211347	−	0.977411i	$-0.432215\pi$
$653$	1.96397e12	0.422694	0.211347	+	0.977411i	$0.432215\pi$
$654$	−9.45066e11	−0.202005
$655$	1.67619e12	0.355826
$656$	1.85939e12	0.392016
$657$	−7.50986e12	−1.57249
$658$	−2.88080e12	−0.599096
$659$	1.93103e11	0.0398845	0.0199422	−	0.999801i	$-0.493652\pi$
$659$	1.93103e11	0.0398845	0.0199422	+	0.999801i	$0.493652\pi$
$660$	4.19038e12	0.859618
$661$	1.01510e10	0.00206825	0.00103413	−	0.999999i	$-0.499671\pi$
$661$	1.01510e10	0.00206825	0.00103413	+	0.999999i	$0.499671\pi$
$662$	−6.32302e12	−1.27957
$663$	0	0
$664$	5.32790e12	1.06365
$665$	1.15931e12	0.229880
$666$	−4.84749e11	−0.0954734
$667$	−7.40792e12	−1.44921
$668$	1.30720e13	2.54009
$669$	−1.74246e12	−0.336315
$670$	−6.69578e12	−1.28370
$671$	7.49166e12	1.42668
$672$	7.49124e10	0.0141707
$673$	6.50508e12	1.22232	0.611160	−	0.791507i	$-0.290703\pi$
$673$	6.50508e12	1.22232	0.611160	+	0.791507i	$0.290703\pi$
$674$	2.08741e12	0.389617
$675$	−2.89207e11	−0.0536219
$676$	−1.02103e13	−1.88053
$677$	9.60958e12	1.75815	0.879074	−	0.476685i	$-0.158162\pi$
$677$	9.60958e12	1.75815	0.879074	+	0.476685i	$0.158162\pi$
$678$	8.82675e10	0.0160423
$679$	−3.29244e12	−0.594433
$680$	0	0
$681$	−1.98554e11	−0.0353766
$682$	2.48135e13	4.39196
$683$	5.49684e11	0.0966541	0.0483271	−	0.998832i	$-0.484611\pi$
$683$	5.49684e11	0.0966541	0.0483271	+	0.998832i	$0.484611\pi$
$684$	7.79415e12	1.36150
$685$	−4.82947e12	−0.838092
$686$	−6.04857e12	−1.04278
$687$	1.68180e12	0.288051
$688$	9.89316e12	1.68340
$689$	1.01754e12	0.172015
$690$	3.01797e12	0.506866
$691$	1.00783e13	1.68166	0.840828	−	0.541302i	$-0.182068\pi$
$691$	1.00783e13	1.68166	0.840828	+	0.541302i	$0.182068\pi$
$692$	2.58967e12	0.429306
$693$	−2.93493e12	−0.483391
$694$	4.48971e12	0.734684
$695$	−2.84820e12	−0.463061
$696$	3.76793e12	0.608641
$697$	0	0
$698$	5.52217e12	0.880562
$699$	2.98691e12	0.473232
$700$	−3.92494e11	−0.0617862
$701$	−9.77792e11	−0.152938	−0.0764690	−	0.997072i	$-0.524365\pi$
$701$	−9.77792e11	−0.152938	−0.0764690	+	0.997072i	$0.524365\pi$
$702$	1.15622e12	0.179690
$703$	−2.96077e11	−0.0457200
$704$	−1.21158e13	−1.85898
$705$	−1.91603e12	−0.292113
$706$	1.52024e13	2.30299
$707$	2.54304e12	0.382795
$708$	−5.33008e12	−0.797230
$709$	1.08153e13	1.60743	0.803714	−	0.595016i	$-0.202854\pi$
$709$	1.08153e13	1.60743	0.803714	+	0.595016i	$0.202854\pi$
$710$	−1.23428e12	−0.182285
$711$	−7.01763e12	−1.02986
$712$	1.72225e13	2.51152
$713$	1.18196e13	1.71278
$714$	0	0
$715$	−2.10220e12	−0.300813
$716$	−6.20812e12	−0.882778
$717$	1.61545e12	0.228274
$718$	−1.56841e13	−2.20242
$719$	−1.62784e12	−0.227161	−0.113580	−	0.993529i	$-0.536232\pi$
$719$	−1.62784e12	−0.227161	−0.113580	+	0.993529i	$0.536232\pi$
$720$	5.42941e12	0.752933
$721$	−3.55126e11	−0.0489411
$722$	−5.34989e12	−0.732703
$723$	2.26563e12	0.308366
$724$	1.12585e13	1.52286
$725$	9.68834e11	0.130235
$726$	−6.16614e12	−0.823756
$727$	2.04920e12	0.272069	0.136035	−	0.990704i	$-0.456564\pi$
$727$	2.04920e12	0.272069	0.136035	+	0.990704i	$0.456564\pi$
$728$	7.65786e11	0.101045
$729$	−4.21884e12	−0.553248
$730$	−2.13855e13	−2.78720
$731$	0	0
$732$	−3.71927e12	−0.478805
$733$	−2.62355e12	−0.335677	−0.167839	−	0.985814i	$-0.553679\pi$
$733$	−2.62355e12	−0.335677	−0.167839	+	0.985814i	$0.553679\pi$
$734$	−6.86239e12	−0.872656
$735$	−1.90310e12	−0.240530
$736$	−1.37610e12	−0.172862
$737$	1.03536e13	1.29266
$738$	−5.79724e12	−0.719396
$739$	1.33151e13	1.64227	0.821133	−	0.570737i	$-0.193342\pi$
$739$	1.33151e13	1.64227	0.821133	+	0.570737i	$0.193342\pi$
$740$	−9.12978e11	−0.111923
$741$	3.38454e11	0.0412399
$742$	4.04543e12	0.489945
$743$	6.67750e11	0.0803830	0.0401915	−	0.999192i	$-0.487203\pi$
$743$	6.67750e11	0.0803830	0.0401915	+	0.999192i	$0.487203\pi$
$744$	−6.01187e12	−0.719336
$745$	3.04126e12	0.361702
$746$	−4.27074e12	−0.504869
$747$	−5.08567e12	−0.597593
$748$	0	0
$749$	−2.06032e12	−0.239203
$750$	−4.38431e12	−0.505971
$751$	−4.40301e12	−0.505092	−0.252546	−	0.967585i	$-0.581268\pi$
$751$	−4.40301e12	−0.505092	−0.252546	+	0.967585i	$0.581268\pi$
$752$	−8.24053e12	−0.939669
$753$	8.77609e11	0.0994773
$754$	−3.87330e12	−0.436426
$755$	3.07710e12	0.344651
$756$	3.04025e12	0.338502
$757$	1.43998e12	0.159376	0.0796882	−	0.996820i	$-0.474608\pi$
$757$	1.43998e12	0.159376	0.0796882	+	0.996820i	$0.474608\pi$
$758$	7.84802e12	0.863473
$759$	−4.66662e12	−0.510404
$760$	1.08318e13	1.17771
$761$	1.23305e13	1.33276	0.666379	−	0.745613i	$-0.267843\pi$
$761$	1.23305e13	1.33276	0.666379	+	0.745613i	$0.267843\pi$
$762$	8.54465e12	0.918115
$763$	1.24667e12	0.133165
$764$	−2.49028e13	−2.64441
$765$	0	0
$766$	−1.59700e13	−1.67600
$767$	2.67396e12	0.278982
$768$	5.28067e12	0.547726
$769$	7.33617e12	0.756486	0.378243	−	0.925706i	$-0.376528\pi$
$769$	7.33617e12	0.756486	0.378243	+	0.925706i	$0.376528\pi$
$770$	−8.35770e12	−0.856798
$771$	3.50426e12	0.357151
$772$	−2.70028e12	−0.273610
$773$	1.30977e13	1.31944	0.659718	−	0.751513i	$-0.270676\pi$
$773$	1.30977e13	1.31944	0.659718	+	0.751513i	$0.270676\pi$
$774$	−3.08450e13	−3.08924
$775$	−1.54581e12	−0.153921
$776$	−3.07622e13	−3.04537
$777$	−5.53496e10	−0.00544779
$778$	3.29677e13	3.22612
$779$	−3.54087e12	−0.344502
$780$	1.04365e12	0.100955
$781$	1.90854e12	0.183557
$782$	0	0
$783$	−7.50456e12	−0.713506
$784$	−8.18493e12	−0.773735
$785$	3.97337e12	0.373461
$786$	1.94552e12	0.181817
$787$	1.90562e13	1.77072	0.885358	−	0.464910i	$-0.153913\pi$
$787$	1.90562e13	1.77072	0.885358	+	0.464910i	$0.153913\pi$
$788$	6.99360e11	0.0646150
$789$	−2.43904e12	−0.224064
$790$	−1.99838e13	−1.82540
$791$	−1.16437e11	−0.0105754
$792$	−2.74220e13	−2.47648
$793$	1.86586e12	0.167552
$794$	5.37407e12	0.479856
$795$	2.69063e12	0.238892
$796$	1.79483e13	1.58458
$797$	1.05555e13	0.926652	0.463326	−	0.886188i	$-0.346656\pi$
$797$	1.05555e13	0.926652	0.463326	+	0.886188i	$0.346656\pi$
$798$	1.34559e12	0.117462
$799$	0	0
$800$	1.79970e11	0.0155345
$801$	−1.64395e13	−1.41105
$802$	−3.15291e13	−2.69108
$803$	3.30680e13	2.80665
$804$	−5.14008e12	−0.433828
$805$	−3.98110e12	−0.334135
$806$	6.18000e12	0.515800
$807$	1.65976e12	0.137757
$808$	2.37604e13	1.96111
$809$	−7.11754e12	−0.584200	−0.292100	−	0.956388i	$-0.594354\pi$
$809$	−7.11754e12	−0.584200	−0.292100	+	0.956388i	$0.594354\pi$
$810$	−1.53358e13	−1.25177
$811$	1.96032e13	1.59123	0.795616	−	0.605802i	$-0.207148\pi$
$811$	1.96032e13	1.59123	0.795616	+	0.605802i	$0.207148\pi$
$812$	−1.01847e13	−0.822142
$813$	−6.18285e12	−0.496343
$814$	2.13448e12	0.170405
$815$	−2.89408e12	−0.229774
$816$	0	0
$817$	−1.88397e13	−1.47936
$818$	2.17824e13	1.70105
$819$	−7.30970e11	−0.0567704
$820$	−1.09186e13	−0.843340
$821$	−2.57782e13	−1.98020	−0.990099	−	0.140370i	$-0.955171\pi$
$821$	−2.57782e13	−1.98020	−0.990099	+	0.140370i	$0.955171\pi$
$822$	−5.60547e12	−0.428242
$823$	1.81960e13	1.38254	0.691270	−	0.722597i	$-0.257052\pi$
$823$	1.81960e13	1.38254	0.691270	+	0.722597i	$0.257052\pi$
$824$	−3.31805e12	−0.250733
$825$	6.10316e11	0.0458683
$826$	1.06308e13	0.794615
$827$	−1.68619e13	−1.25352	−0.626760	−	0.779213i	$-0.715619\pi$
$827$	−1.68619e13	−1.25352	−0.626760	+	0.779213i	$0.715619\pi$
$828$	−2.67654e13	−1.97896
$829$	−2.04363e13	−1.50282	−0.751411	−	0.659834i	$-0.770626\pi$
$829$	−2.04363e13	−1.50282	−0.751411	+	0.659834i	$0.770626\pi$
$830$	−1.44823e13	−1.05922
$831$	−5.69403e12	−0.414205
$832$	−3.01754e12	−0.218322
$833$	0	0
$834$	−3.30585e12	−0.236611
$835$	−1.73407e13	−1.23446
$836$	−3.43199e13	−2.43006
$837$	1.19738e13	0.843273
$838$	−3.86765e13	−2.70925
$839$	1.01784e13	0.709167	0.354584	−	0.935024i	$-0.384623\pi$
$839$	1.01784e13	0.709167	0.354584	+	0.935024i	$0.384623\pi$
$840$	2.02492e12	0.140331
$841$	1.06329e13	0.732940
$842$	−1.72516e13	−1.18284
$843$	−3.50573e12	−0.239086
$844$	1.27613e13	0.865671
$845$	1.35445e13	0.913918
$846$	2.56924e13	1.72440
$847$	8.13396e12	0.543033
$848$	1.15720e13	0.768468
$849$	7.25859e11	0.0479477
$850$	0	0
$851$	1.01674e12	0.0664548
$852$	−9.47505e11	−0.0616032
$853$	1.86820e13	1.20824	0.604119	−	0.796894i	$-0.293525\pi$
$853$	1.86820e13	1.20824	0.604119	+	0.796894i	$0.293525\pi$
$854$	7.41808e12	0.477234
$855$	−1.03393e13	−0.661674
$856$	−1.92502e13	−1.22547
$857$	−7.29110e12	−0.461721	−0.230860	−	0.972987i	$-0.574154\pi$
$857$	−7.29110e12	−0.461721	−0.230860	+	0.972987i	$0.574154\pi$
$858$	−2.43999e12	−0.153707
$859$	4.02170e12	0.252023	0.126011	−	0.992029i	$-0.459782\pi$
$859$	4.02170e12	0.252023	0.126011	+	0.992029i	$0.459782\pi$
$860$	−5.80937e13	−3.62148
$861$	−6.61941e11	−0.0410492
$862$	−2.95023e13	−1.82001
$863$	−1.68689e13	−1.03523	−0.517617	−	0.855613i	$-0.673181\pi$
$863$	−1.68689e13	−1.03523	−0.517617	+	0.855613i	$0.673181\pi$
$864$	−1.39405e12	−0.0851070
$865$	−3.43532e12	−0.208639
$866$	5.13249e13	3.10097
$867$	0	0
$868$	1.62501e13	0.971667
$869$	3.09006e13	1.83814
$870$	−1.02420e13	−0.606103
$871$	2.57864e12	0.151813
$872$	1.16480e13	0.682224
$873$	2.93637e13	1.71098
$874$	−2.47176e13	−1.43286
$875$	5.78349e12	0.333544
$876$	−1.64168e13	−0.941933
$877$	9.39568e12	0.536328	0.268164	−	0.963373i	$-0.413583\pi$
$877$	9.39568e12	0.536328	0.268164	+	0.963373i	$0.413583\pi$
$878$	−1.49580e13	−0.849471
$879$	3.40949e12	0.192637
$880$	−2.39072e13	−1.34387
$881$	−2.49688e13	−1.39639	−0.698194	−	0.715909i	$-0.746013\pi$
$881$	−2.49688e13	−1.39639	−0.698194	+	0.715909i	$0.746013\pi$
$882$	2.55191e13	1.41990
$883$	−1.24749e13	−0.690578	−0.345289	−	0.938496i	$-0.612219\pi$
$883$	−1.24749e13	−0.690578	−0.345289	+	0.938496i	$0.612219\pi$
$884$	0	0
$885$	7.07060e12	0.387446
$886$	1.30254e13	0.710130
$887$	2.86371e13	1.55336	0.776682	−	0.629893i	$-0.216901\pi$
$887$	2.86371e13	1.55336	0.776682	+	0.629893i	$0.216901\pi$
$888$	−5.17148e11	−0.0279098
$889$	−1.12715e13	−0.605237
$890$	−4.68141e13	−2.50105
$891$	2.37135e13	1.26051
$892$	4.40059e13	2.32739
$893$	1.56926e13	0.825777
$894$	3.52994e12	0.184820
$895$	8.23537e12	0.429022
$896$	−1.10282e13	−0.571634
$897$	−1.16226e12	−0.0599429
$898$	4.27349e13	2.19301
$899$	−4.01119e13	−2.04811
$900$	3.50047e12	0.177842
$901$	0	0
$902$	2.55269e13	1.28401
$903$	−3.52195e12	−0.176274
$904$	−1.08790e12	−0.0541792
$905$	−1.49350e13	−0.740093
$906$	3.57153e12	0.176107
$907$	−1.51352e13	−0.742599	−0.371300	−	0.928513i	$-0.621088\pi$
$907$	−1.51352e13	−0.742599	−0.371300	+	0.928513i	$0.621088\pi$
$908$	5.01448e12	0.244816
$909$	−2.26802e13	−1.10182
$910$	−2.08156e12	−0.100624
$911$	−7.50977e12	−0.361238	−0.180619	−	0.983553i	$-0.557810\pi$
$911$	−7.50977e12	−0.361238	−0.180619	+	0.983553i	$0.557810\pi$
$912$	3.84906e12	0.184237
$913$	2.23936e13	1.06661
$914$	5.11513e13	2.42437
$915$	4.93379e12	0.232694
$916$	−4.24739e13	−1.99339
$917$	−2.56640e12	−0.119857
$918$	0	0
$919$	−2.29909e13	−1.06325	−0.531626	−	0.846979i	$-0.678419\pi$
$919$	−2.29909e13	−1.06325	−0.531626	+	0.846979i	$0.678419\pi$
$920$	−3.71966e13	−1.71182
$921$	4.70719e12	0.215572
$922$	−4.73739e13	−2.15899
$923$	4.75338e11	0.0215573
$924$	−6.41586e12	−0.289555
$925$	−1.32973e11	−0.00597206
$926$	−4.07016e13	−1.81912
$927$	3.16720e12	0.140869
$928$	4.67001e12	0.206705
$929$	4.46802e12	0.196809	0.0984044	−	0.995147i	$-0.468626\pi$
$929$	4.46802e12	0.196809	0.0984044	+	0.995147i	$0.468626\pi$
$930$	1.63414e13	0.716337
$931$	1.55867e13	0.679955
$932$	−7.54343e13	−3.27489
$933$	−1.08050e13	−0.466828
$934$	2.13475e13	0.917881
$935$	0	0
$936$	−6.82968e12	−0.290843
$937$	−3.69266e13	−1.56499	−0.782494	−	0.622658i	$-0.786053\pi$
$937$	−3.69266e13	−1.56499	−0.782494	+	0.622658i	$0.786053\pi$
$938$	1.02519e13	0.432404
$939$	4.16265e12	0.174733
$940$	4.83893e13	2.02150
$941$	2.73922e13	1.13887	0.569434	−	0.822037i	$-0.307162\pi$
$941$	2.73922e13	1.13887	0.569434	+	0.822037i	$0.307162\pi$
$942$	4.61181e12	0.190828
$943$	1.21595e13	0.500739
$944$	3.04095e13	1.24634
$945$	−4.03303e12	−0.164509
$946$	1.35819e14	5.51381
$947$	−4.08999e12	−0.165252	−0.0826261	−	0.996581i	$-0.526331\pi$
$947$	−4.08999e12	−0.165252	−0.0826261	+	0.996581i	$0.526331\pi$
$948$	−1.53408e13	−0.616893
$949$	8.23587e12	0.329618
$950$	3.23265e12	0.128766
$951$	−6.93269e12	−0.274846
$952$	0	0
$953$	−1.68559e13	−0.661964	−0.330982	−	0.943637i	$-0.607380\pi$
$953$	−1.68559e13	−0.661964	−0.330982	+	0.943637i	$0.607380\pi$
$954$	−3.60792e13	−1.41023
$955$	3.30348e13	1.28516
$956$	−4.07982e13	−1.57972
$957$	1.58369e13	0.610334
$958$	−3.47961e13	−1.33471
$959$	7.39437e12	0.282304
$960$	−7.97911e12	−0.303203
$961$	3.75604e13	1.42061
$962$	5.31611e11	0.0200127
$963$	1.83750e13	0.688509
$964$	−5.72184e13	−2.13397
$965$	3.58205e12	0.132972
$966$	−4.62078e12	−0.170733
$967$	−3.07043e13	−1.12922	−0.564611	−	0.825357i	$-0.690974\pi$
$967$	−3.07043e13	−1.12922	−0.564611	+	0.825357i	$0.690974\pi$
$968$	7.59981e13	2.78204
$969$	0	0
$970$	8.36178e13	3.03267
$971$	−6.39625e12	−0.230908	−0.115454	−	0.993313i	$-0.536832\pi$
$971$	−6.39625e12	−0.230908	−0.115454	+	0.993313i	$0.536832\pi$
$972$	−4.12342e13	−1.48170
$973$	4.36086e12	0.155978
$974$	−1.72492e13	−0.614119
$975$	1.52004e11	0.00538686
$976$	2.12194e13	0.748531
$977$	−1.10943e13	−0.389559	−0.194780	−	0.980847i	$-0.562399\pi$
$977$	−1.10943e13	−0.389559	−0.194780	+	0.980847i	$0.562399\pi$
$978$	−3.35910e12	−0.117408
$979$	7.23877e13	2.51851
$980$	4.80628e13	1.66453
$981$	−1.11184e13	−0.383295
$982$	−2.83691e13	−0.973518
$983$	1.58231e13	0.540506	0.270253	−	0.962789i	$-0.412893\pi$
$983$	1.58231e13	0.540506	0.270253	+	0.962789i	$0.412893\pi$
$984$	−6.18472e12	−0.210301
$985$	−9.27735e11	−0.0314022
$986$	0	0
$987$	2.93362e12	0.0983958
$988$	−8.54765e12	−0.285391
$989$	6.46961e13	2.15028
$990$	7.45383e13	2.46616
$991$	2.00594e13	0.660672	0.330336	−	0.943863i	$-0.392838\pi$
$991$	2.00594e13	0.660672	0.330336	+	0.943863i	$0.392838\pi$
$992$	−7.45117e12	−0.244299
$993$	6.43896e12	0.210157
$994$	1.88980e12	0.0614011
$995$	−2.38093e13	−0.770092
$996$	−1.11174e13	−0.357963
$997$	−2.94028e12	−0.0942455	−0.0471228	−	0.998889i	$-0.515005\pi$
$997$	−2.94028e12	−0.0942455	−0.0471228	+	0.998889i	$0.515005\pi$
$998$	1.27880e13	0.408051
$999$	1.03000e12	0.0327185

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.33	yes	36
17.16	even	2		289.10.a.g.1.33	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.33	✓	36	17.16	even	2
289.10.a.h.1.33	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)

\(f(q)\)	\(=\)	\(q+38.8851 q^{2} -39.5980 q^{3} +1000.05 q^{4} -1326.61 q^{5} -1539.77 q^{6} +2031.17 q^{7} +18977.8 q^{8} -18115.0 q^{9} +O(q^{10})\)	\(q+38.8851 q^{2} -39.5980 q^{3} +1000.05 q^{4} -1326.61 q^{5} -1539.77 q^{6} +2031.17 q^{7} +18977.8 q^{8} -18115.0 q^{9} -51585.4 q^{10} +79765.4 q^{11} -39600.0 q^{12} +19866.3 q^{13} +78982.0 q^{14} +52531.2 q^{15} +225928. q^{16} -704403. q^{18} -430239. q^{19} -1.32668e6 q^{20} -80430.2 q^{21} +3.10168e6 q^{22} +1.47745e6 q^{23} -751484. q^{24} -193226. q^{25} +772501. q^{26} +1.49673e6 q^{27} +2.03126e6 q^{28} -5.01398e6 q^{29} +2.04268e6 q^{30} +8.00000e6 q^{31} -931397. q^{32} -3.15856e6 q^{33} -2.69457e6 q^{35} -1.81159e7 q^{36} +688170. q^{37} -1.67299e7 q^{38} -786665. q^{39} -2.51762e7 q^{40} +8.23001e6 q^{41} -3.12753e6 q^{42} +4.37889e7 q^{43} +7.97693e7 q^{44} +2.40316e7 q^{45} +5.74509e7 q^{46} -3.64741e7 q^{47} -8.94632e6 q^{48} -3.62280e7 q^{49} -7.51362e6 q^{50} +1.98672e7 q^{52} +5.12196e7 q^{53} +5.82003e7 q^{54} -1.05818e8 q^{55} +3.85471e7 q^{56} +1.70366e7 q^{57} -1.94969e8 q^{58} +1.34598e8 q^{59} +5.25338e7 q^{60} +9.39211e7 q^{61} +3.11081e8 q^{62} -3.67946e7 q^{63} -1.51893e8 q^{64} -2.63548e7 q^{65} -1.22821e8 q^{66} +1.29800e8 q^{67} -5.85043e7 q^{69} -1.04778e8 q^{70} +2.39269e7 q^{71} -3.43783e8 q^{72} +4.14566e8 q^{73} +2.67595e7 q^{74} +7.65139e6 q^{75} -4.30260e8 q^{76} +1.62017e8 q^{77} -3.05895e7 q^{78} +3.87393e8 q^{79} -2.99719e8 q^{80} +2.97290e8 q^{81} +3.20024e8 q^{82} +2.80744e8 q^{83} -8.04341e7 q^{84} +1.70274e9 q^{86} +1.98544e8 q^{87} +1.51377e9 q^{88} +9.07508e8 q^{89} +9.34469e8 q^{90} +4.03516e7 q^{91} +1.47753e9 q^{92} -3.16784e8 q^{93} -1.41830e9 q^{94} +5.70760e8 q^{95} +3.68815e7 q^{96} -1.62096e9 q^{97} -1.40873e9 q^{98} -1.44495e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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