LMFDB - Embedded newform 289.10.a.h.1.29

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			1.29
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)

$f(q)$	$=$	$q+29.4104 q^{2} -172.236 q^{3} +352.969 q^{4} +865.601 q^{5} -5065.51 q^{6} +362.239 q^{7} -4677.16 q^{8} +9982.09 q^{9} +O(q^{10})$	\(q+29.4104 q^{2} -172.236 q^{3} +352.969 q^{4} +865.601 q^{5} -5065.51 q^{6} +362.239 q^{7} -4677.16 q^{8} +9982.09 q^{9} +25457.6 q^{10} -2584.84 q^{11} -60793.8 q^{12} +151968. q^{13} +10653.6 q^{14} -149087. q^{15} -318277. q^{16} +293577. q^{18} -614691. q^{19} +305530. q^{20} -62390.5 q^{21} -76021.2 q^{22} -92548.4 q^{23} +805573. q^{24} -1.20386e6 q^{25} +4.46944e6 q^{26} +1.67084e6 q^{27} +127859. q^{28} +4.01277e6 q^{29} -4.38471e6 q^{30} -1.53654e6 q^{31} -6.96593e6 q^{32} +445202. q^{33} +313555. q^{35} +3.52337e6 q^{36} -1.19661e7 q^{37} -1.80783e7 q^{38} -2.61744e7 q^{39} -4.04855e6 q^{40} +2.69074e7 q^{41} -1.83493e6 q^{42} +1.73165e7 q^{43} -912370. q^{44} +8.64050e6 q^{45} -2.72188e6 q^{46} -2.76619e7 q^{47} +5.48186e7 q^{48} -4.02224e7 q^{49} -3.54060e7 q^{50} +5.36401e7 q^{52} -5.68418e7 q^{53} +4.91401e7 q^{54} -2.23744e6 q^{55} -1.69425e6 q^{56} +1.05872e8 q^{57} +1.18017e8 q^{58} -4.42113e7 q^{59} -5.26231e7 q^{60} -1.39616e8 q^{61} -4.51901e7 q^{62} +3.61590e6 q^{63} -4.19127e7 q^{64} +1.31544e8 q^{65} +1.30936e7 q^{66} +2.98597e8 q^{67} +1.59401e7 q^{69} +9.22175e6 q^{70} +2.46574e8 q^{71} -4.66878e7 q^{72} +4.68407e8 q^{73} -3.51926e8 q^{74} +2.07348e8 q^{75} -2.16967e8 q^{76} -936333. q^{77} -7.69797e8 q^{78} +3.27161e8 q^{79} -2.75501e8 q^{80} -4.84256e8 q^{81} +7.91357e8 q^{82} +2.96019e8 q^{83} -2.20219e7 q^{84} +5.09286e8 q^{86} -6.91142e8 q^{87} +1.20897e7 q^{88} +5.63269e7 q^{89} +2.54120e8 q^{90} +5.50489e7 q^{91} -3.26667e7 q^{92} +2.64646e8 q^{93} -8.13547e8 q^{94} -5.32077e8 q^{95} +1.19978e9 q^{96} +9.04409e8 q^{97} -1.18295e9 q^{98} -2.58021e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	29.4104	1.29977	0.649883	−	0.760034i	$-0.274818\pi$
$2$	29.4104	1.29977	0.649883	+	0.760034i	$0.274818\pi$
$3$	−172.236	−1.22766	−0.613829	−	0.789439i	$-0.710371\pi$
$3$	−172.236	−1.22766	−0.613829	+	0.789439i	$0.710371\pi$
$4$	352.969	0.689392
$5$	865.601	0.619373	0.309687	−	0.950839i	$-0.399776\pi$
$5$	865.601	0.619373	0.309687	+	0.950839i	$0.399776\pi$
$6$	−5065.51	−1.59567
$7$	362.239	0.0570236	0.0285118	−	0.999593i	$-0.490923\pi$
$7$	362.239	0.0570236	0.0285118	+	0.999593i	$0.490923\pi$
$8$	−4677.16	−0.403717
$9$	9982.09	0.507142
$10$	25457.6	0.805041
$11$	−2584.84	−0.0532313	−0.0266157	−	0.999646i	$-0.508473\pi$
$11$	−2584.84	−0.0532313	−0.0266157	+	0.999646i	$0.508473\pi$
$12$	−60793.8	−0.846338
$13$	151968.	1.47573	0.737867	−	0.674946i	$-0.235833\pi$
$13$	151968.	1.47573	0.737867	+	0.674946i	$0.235833\pi$
$14$	10653.6	0.0741173
$15$	−149087.	−0.760378
$16$	−318277.	−1.21413
$17$	0	0
$17$	0	0
$18$	293577.	0.659167
$19$	−614691.	−1.08210	−0.541048	−	0.840992i	$-0.681972\pi$
$19$	−614691.	−1.08210	−0.541048	+	0.840992i	$0.681972\pi$
$20$	305530.	0.426991
$21$	−62390.5	−0.0700054
$22$	−76021.2	−0.0691883
$23$	−92548.4	−0.0689594	−0.0344797	−	0.999405i	$-0.510977\pi$
$23$	−92548.4	−0.0689594	−0.0344797	+	0.999405i	$0.510977\pi$
$24$	805573.	0.495626
$25$	−1.20386e6	−0.616377
$26$	4.46944e6	1.91811
$27$	1.67084e6	0.605060
$28$	127859.	0.0393116
$29$	4.01277e6	1.05355	0.526773	−	0.850006i	$-0.323402\pi$
$29$	4.01277e6	1.05355	0.526773	+	0.850006i	$0.323402\pi$
$30$	−4.38471e6	−0.988314
$31$	−1.53654e6	−0.298824	−0.149412	−	0.988775i	$-0.547738\pi$
$31$	−1.53654e6	−0.298824	−0.149412	+	0.988775i	$0.547738\pi$
$32$	−6.96593e6	−1.17437
$33$	445202.	0.0653498
$34$	0	0
$35$	313555.	0.0353189
$36$	3.52337e6	0.349620
$37$	−1.19661e7	−1.04965	−0.524824	−	0.851211i	$-0.675869\pi$
$37$	−1.19661e7	−1.04965	−0.524824	+	0.851211i	$0.675869\pi$
$38$	−1.80783e7	−1.40647
$39$	−2.61744e7	−1.81170
$40$	−4.04855e6	−0.250052
$41$	2.69074e7	1.48712	0.743558	−	0.668671i	$-0.233137\pi$
$41$	2.69074e7	1.48712	0.743558	+	0.668671i	$0.233137\pi$
$42$	−1.83493e6	−0.0909907
$43$	1.73165e7	0.772419	0.386210	−	0.922411i	$-0.373784\pi$
$43$	1.73165e7	0.772419	0.386210	+	0.922411i	$0.373784\pi$
$44$	−912370.	−0.0366973
$45$	8.64050e6	0.314111
$46$	−2.72188e6	−0.0896311
$47$	−2.76619e7	−0.826879	−0.413439	−	0.910532i	$-0.635673\pi$
$47$	−2.76619e7	−0.826879	−0.413439	+	0.910532i	$0.635673\pi$
$48$	5.48186e7	1.49054
$49$	−4.02224e7	−0.996748
$50$	−3.54060e7	−0.801146
$51$	0	0
$52$	5.36401e7	1.01736
$53$	−5.68418e7	−0.989524	−0.494762	−	0.869029i	$-0.664745\pi$
$53$	−5.68418e7	−0.989524	−0.494762	+	0.869029i	$0.664745\pi$
$54$	4.91401e7	0.786437
$55$	−2.23744e6	−0.0329701
$56$	−1.69425e6	−0.0230214
$57$	1.05872e8	1.32844
$58$	1.18017e8	1.36936
$59$	−4.42113e7	−0.475007	−0.237503	−	0.971387i	$-0.576329\pi$
$59$	−4.42113e7	−0.475007	−0.237503	+	0.971387i	$0.576329\pi$
$60$	−5.26231e7	−0.524199
$61$	−1.39616e8	−1.29107	−0.645536	−	0.763730i	$-0.723366\pi$
$61$	−1.39616e8	−1.29107	−0.645536	+	0.763730i	$0.723366\pi$
$62$	−4.51901e7	−0.388401
$63$	3.61590e6	0.0289191
$64$	−4.19127e7	−0.312274
$65$	1.31544e8	0.914030
$66$	1.30936e7	0.0849395
$67$	2.98597e8	1.81029	0.905145	−	0.425103i	$-0.139762\pi$
$67$	2.98597e8	1.81029	0.905145	+	0.425103i	$0.139762\pi$
$68$	0	0
$69$	1.59401e7	0.0846585
$70$	9.22175e6	0.0459063
$71$	2.46574e8	1.15155	0.575777	−	0.817607i	$-0.304700\pi$
$71$	2.46574e8	1.15155	0.575777	+	0.817607i	$0.304700\pi$
$72$	−4.66878e7	−0.204742
$73$	4.68407e8	1.93051	0.965253	−	0.261319i	$-0.0841574\pi$
$73$	4.68407e8	1.93051	0.965253	+	0.261319i	$0.0841574\pi$
$74$	−3.51926e8	−1.36430
$75$	2.07348e8	0.756699
$76$	−2.16967e8	−0.745989
$77$	−936333.	−0.00303544
$78$	−7.69797e8	−2.35478
$79$	3.27161e8	0.945016	0.472508	−	0.881326i	$-0.343349\pi$
$79$	3.27161e8	0.945016	0.472508	+	0.881326i	$0.343349\pi$
$80$	−2.75501e8	−0.752000
$81$	−4.84256e8	−1.24995
$82$	7.91357e8	1.93290
$83$	2.96019e8	0.684649	0.342324	−	0.939582i	$-0.388786\pi$
$83$	2.96019e8	0.684649	0.342324	+	0.939582i	$0.388786\pi$
$84$	−2.20219e7	−0.0482612
$85$	0	0
$86$	5.09286e8	1.00396
$87$	−6.91142e8	−1.29339
$88$	1.20897e7	0.0214904
$89$	5.63269e7	0.0951614	0.0475807	−	0.998867i	$-0.484849\pi$
$89$	5.63269e7	0.0951614	0.0475807	+	0.998867i	$0.484849\pi$
$90$	2.54120e8	0.408270
$91$	5.50489e7	0.0841516
$92$	−3.26667e7	−0.0475401
$93$	2.64646e8	0.366853
$94$	−8.13547e8	−1.07475
$95$	−5.32077e8	−0.670222
$96$	1.19978e9	1.44172
$97$	9.04409e8	1.03727	0.518635	−	0.854996i	$-0.326440\pi$
$97$	9.04409e8	1.03727	0.518635	+	0.854996i	$0.326440\pi$
$98$	−1.18295e9	−1.29554
$99$	−2.58021e7	−0.0269959
$100$	−4.24925e8	−0.424925
$101$	−1.66520e9	−1.59229	−0.796143	−	0.605109i	$-0.793130\pi$
$101$	−1.66520e9	−1.59229	−0.796143	+	0.605109i	$0.793130\pi$
$102$	0	0
$103$	1.20886e9	1.05830	0.529149	−	0.848529i	$-0.322511\pi$
$103$	1.20886e9	1.05830	0.529149	+	0.848529i	$0.322511\pi$
$104$	−7.10780e8	−0.595779
$105$	−5.40053e7	−0.0433595
$106$	−1.67174e9	−1.28615
$107$	1.40740e9	1.03799	0.518993	−	0.854779i	$-0.326307\pi$
$107$	1.40740e9	1.03799	0.518993	+	0.854779i	$0.326307\pi$
$108$	5.89755e8	0.417124
$109$	1.86311e8	0.126421	0.0632105	−	0.998000i	$-0.479866\pi$
$109$	1.86311e8	0.126421	0.0632105	+	0.998000i	$0.479866\pi$
$110$	−6.58040e7	−0.0428534
$111$	2.06098e9	1.28861
$112$	−1.15292e8	−0.0692341
$113$	1.37430e9	0.792918	0.396459	−	0.918052i	$-0.370239\pi$
$113$	1.37430e9	0.792918	0.396459	+	0.918052i	$0.370239\pi$
$114$	3.11372e9	1.72667
$115$	−8.01100e7	−0.0427116
$116$	1.41638e9	0.726307
$117$	1.51696e9	0.748407
$118$	−1.30027e9	−0.617398
$119$	0	0
$120$	6.97305e8	0.306978
$121$	−2.35127e9	−0.997166
$122$	−4.10615e9	−1.67809
$123$	−4.63442e9	−1.82567
$124$	−5.42350e8	−0.206007
$125$	−2.73269e9	−1.00114
$126$	1.06345e8	0.0375880
$127$	4.80802e9	1.64002	0.820011	−	0.572348i	$-0.193967\pi$
$127$	4.80802e9	1.64002	0.820011	+	0.572348i	$0.193967\pi$
$128$	2.33389e9	0.768485
$129$	−2.98252e9	−0.948266
$130$	3.86875e9	1.18803
$131$	3.17929e9	0.943213	0.471607	−	0.881809i	$-0.343674\pi$
$131$	3.17929e9	0.943213	0.471607	+	0.881809i	$0.343674\pi$
$132$	1.57143e8	0.0450517
$133$	−2.22665e8	−0.0617050
$134$	8.78183e9	2.35295
$135$	1.44628e9	0.374758
$136$	0	0
$137$	1.09263e9	0.264990	0.132495	−	0.991184i	$-0.457701\pi$
$137$	1.09263e9	0.264990	0.132495	+	0.991184i	$0.457701\pi$
$138$	4.68805e8	0.110036
$139$	2.07229e9	0.470852	0.235426	−	0.971892i	$-0.424352\pi$
$139$	2.07229e9	0.470852	0.235426	+	0.971892i	$0.424352\pi$
$140$	1.10675e8	0.0243486
$141$	4.76436e9	1.01512
$142$	7.25182e9	1.49675
$143$	−3.92815e8	−0.0785553
$144$	−3.17707e9	−0.615737
$145$	3.47346e9	0.652538
$146$	1.37760e10	2.50921
$147$	6.92773e9	1.22367
$148$	−4.22365e9	−0.723619
$149$	1.07229e10	1.78227	0.891137	−	0.453735i	$-0.149909\pi$
$149$	1.07229e10	1.78227	0.891137	+	0.453735i	$0.149909\pi$
$150$	6.09817e9	0.983532
$151$	3.54049e9	0.554200	0.277100	−	0.960841i	$-0.410627\pi$
$151$	3.54049e9	0.554200	0.277100	+	0.960841i	$0.410627\pi$
$152$	2.87501e9	0.436861
$153$	0	0
$154$	−2.75379e7	−0.00394536
$155$	−1.33003e9	−0.185084
$156$	−9.23873e9	−1.24897
$157$	5.54284e9	0.728089	0.364044	−	0.931382i	$-0.381396\pi$
$157$	5.54284e9	0.728089	0.364044	+	0.931382i	$0.381396\pi$
$158$	9.62191e9	1.22830
$159$	9.79018e9	1.21480
$160$	−6.02972e9	−0.727373
$161$	−3.35247e7	−0.00393231
$162$	−1.42421e10	−1.62464
$163$	−8.84185e9	−0.981068	−0.490534	−	0.871422i	$-0.663198\pi$
$163$	−8.84185e9	−0.981068	−0.490534	+	0.871422i	$0.663198\pi$
$164$	9.49749e9	1.02521
$165$	3.85367e8	0.0404760
$166$	8.70602e9	0.889883
$167$	1.65631e9	0.164785	0.0823926	−	0.996600i	$-0.473744\pi$
$167$	1.65631e9	0.164785	0.0823926	+	0.996600i	$0.473744\pi$
$168$	2.91810e8	0.0282624
$169$	1.24899e10	1.17779
$170$	0	0
$171$	−6.13590e9	−0.548777
$172$	6.11220e9	0.532500
$173$	−3.74439e9	−0.317815	−0.158907	−	0.987294i	$-0.550797\pi$
$173$	−3.74439e9	−0.317815	−0.158907	+	0.987294i	$0.550797\pi$
$174$	−2.03267e10	−1.68111
$175$	−4.36086e8	−0.0351480
$176$	8.22697e8	0.0646298
$177$	7.61477e9	0.583145
$178$	1.65659e9	0.123688
$179$	5.59185e8	0.0407114	0.0203557	−	0.999793i	$-0.493520\pi$
$179$	5.59185e8	0.0407114	0.0203557	+	0.999793i	$0.493520\pi$
$180$	3.04983e9	0.216545
$181$	4.60265e9	0.318753	0.159377	−	0.987218i	$-0.449052\pi$
$181$	4.60265e9	0.318753	0.159377	+	0.987218i	$0.449052\pi$
$182$	1.61901e9	0.109377
$183$	2.40468e10	1.58499
$184$	4.32864e8	0.0278401
$185$	−1.03578e10	−0.650124
$186$	7.78334e9	0.476823
$187$	0	0
$188$	−9.76379e9	−0.570044
$189$	6.05245e8	0.0345027
$190$	−1.56486e10	−0.871131
$191$	1.62447e10	0.883204	0.441602	−	0.897211i	$-0.354410\pi$
$191$	1.62447e10	0.883204	0.441602	+	0.897211i	$0.354410\pi$
$192$	7.21886e9	0.383366
$193$	−3.52328e10	−1.82784	−0.913922	−	0.405890i	$-0.866962\pi$
$193$	−3.52328e10	−1.82784	−0.913922	+	0.405890i	$0.866962\pi$
$194$	2.65990e10	1.34821
$195$	−2.26565e10	−1.12212
$196$	−1.41973e10	−0.687151
$197$	2.56964e10	1.21556	0.607778	−	0.794107i	$-0.292061\pi$
$197$	2.56964e10	1.21556	0.607778	+	0.794107i	$0.292061\pi$
$198$	−7.58850e8	−0.0350883
$199$	1.49975e10	0.677922	0.338961	−	0.940800i	$-0.389924\pi$
$199$	1.49975e10	0.677922	0.338961	+	0.940800i	$0.389924\pi$
$200$	5.63065e9	0.248842
$201$	−5.14289e10	−2.22242
$202$	−4.89742e10	−2.06960
$203$	1.45358e9	0.0600770
$204$	0	0
$205$	2.32911e10	0.921080
$206$	3.55529e10	1.37554
$207$	−9.23826e8	−0.0349723
$208$	−4.83680e10	−1.79173
$209$	1.58888e9	0.0576014
$210$	−1.58831e9	−0.0563572
$211$	3.69719e10	1.28411	0.642053	−	0.766660i	$-0.278083\pi$
$211$	3.69719e10	1.28411	0.642053	+	0.766660i	$0.278083\pi$
$212$	−2.00634e10	−0.682170
$213$	−4.24688e10	−1.41371
$214$	4.13922e10	1.34914
$215$	1.49892e10	0.478416
$216$	−7.81480e9	−0.244273
$217$	−5.56594e8	−0.0170400
$218$	5.47947e9	0.164318
$219$	−8.06764e10	−2.37000
$220$	−7.89748e8	−0.0227293
$221$	0	0
$222$	6.06142e10	1.67489
$223$	2.79578e10	0.757062	0.378531	−	0.925589i	$-0.376429\pi$
$223$	2.79578e10	0.757062	0.378531	+	0.925589i	$0.376429\pi$
$224$	−2.52334e9	−0.0669667
$225$	−1.20170e10	−0.312591
$226$	4.04186e10	1.03061
$227$	−6.15026e9	−0.153737	−0.0768683	−	0.997041i	$-0.524492\pi$
$227$	−6.15026e9	−0.153737	−0.0768683	+	0.997041i	$0.524492\pi$
$228$	3.73694e10	0.915819
$229$	−2.07284e10	−0.498088	−0.249044	−	0.968492i	$-0.580116\pi$
$229$	−2.07284e10	−0.498088	−0.249044	+	0.968492i	$0.580116\pi$
$230$	−2.35606e9	−0.0555151
$231$	1.61270e8	0.00372648
$232$	−1.87684e10	−0.425335
$233$	−2.66795e10	−0.593030	−0.296515	−	0.955028i	$-0.595824\pi$
$233$	−2.66795e10	−0.593030	−0.296515	+	0.955028i	$0.595824\pi$
$234$	4.46144e10	0.972755
$235$	−2.39442e10	−0.512147
$236$	−1.56052e10	−0.327466
$237$	−5.63487e10	−1.16016
$238$	0	0
$239$	−1.83182e10	−0.363155	−0.181578	−	0.983377i	$-0.558120\pi$
$239$	−1.83182e10	−0.363155	−0.181578	+	0.983377i	$0.558120\pi$
$240$	4.74510e10	0.923198
$241$	−4.31652e10	−0.824247	−0.412124	−	0.911128i	$-0.635213\pi$
$241$	−4.31652e10	−0.824247	−0.412124	+	0.911128i	$0.635213\pi$
$242$	−6.91516e10	−1.29608
$243$	5.05189e10	0.929449
$244$	−4.92801e10	−0.890055
$245$	−3.48165e10	−0.617359
$246$	−1.36300e11	−2.37294
$247$	−9.34136e10	−1.59689
$248$	7.18663e9	0.120640
$249$	−5.09850e10	−0.840514
$250$	−8.03693e10	−1.30125
$251$	−1.60962e9	−0.0255972	−0.0127986	−	0.999918i	$-0.504074\pi$
$251$	−1.60962e9	−0.0255972	−0.0127986	+	0.999918i	$0.504074\pi$
$252$	1.27630e9	0.0199366
$253$	2.39223e8	0.00367080
$254$	1.41406e11	2.13165
$255$	0	0
$256$	9.00998e10	1.31113
$257$	7.98170e10	1.14129	0.570646	−	0.821196i	$-0.306693\pi$
$257$	7.98170e10	1.14129	0.570646	+	0.821196i	$0.306693\pi$
$258$	−8.77171e10	−1.23252
$259$	−4.33458e9	−0.0598547
$260$	4.64309e10	0.630126
$261$	4.00558e10	0.534298
$262$	9.35042e10	1.22596
$263$	9.23455e10	1.19019	0.595093	−	0.803657i	$-0.297115\pi$
$263$	9.23455e10	1.19019	0.595093	+	0.803657i	$0.297115\pi$
$264$	−2.08228e9	−0.0263829
$265$	−4.92023e10	−0.612885
$266$	−6.54867e9	−0.0802021
$267$	−9.70150e9	−0.116826
$268$	1.05395e11	1.24800
$269$	−6.88265e10	−0.801439	−0.400720	−	0.916201i	$-0.631240\pi$
$269$	−6.88265e10	−0.801439	−0.400720	+	0.916201i	$0.631240\pi$
$270$	4.25357e10	0.487098
$271$	1.41235e11	1.59067	0.795337	−	0.606167i	$-0.207294\pi$
$271$	1.41235e11	1.59067	0.795337	+	0.606167i	$0.207294\pi$
$272$	0	0
$273$	−9.48138e9	−0.103309
$274$	3.21345e10	0.344425
$275$	3.11179e9	0.0328106
$276$	5.62637e9	0.0583630
$277$	3.95651e10	0.403788	0.201894	−	0.979407i	$-0.435290\pi$
$277$	3.95651e10	0.403788	0.201894	+	0.979407i	$0.435290\pi$
$278$	6.09468e10	0.611997
$279$	−1.53378e10	−0.151546
$280$	−1.46655e9	−0.0142588
$281$	−1.91177e11	−1.82919	−0.914593	−	0.404376i	$-0.867489\pi$
$281$	−1.91177e11	−1.82919	−0.914593	+	0.404376i	$0.867489\pi$
$282$	1.40122e11	1.31942
$283$	1.97146e11	1.82705	0.913523	−	0.406786i	$-0.133351\pi$
$283$	1.97146e11	1.82705	0.913523	+	0.406786i	$0.133351\pi$
$284$	8.70329e10	0.793873
$285$	9.16426e10	0.822802
$286$	−1.15528e10	−0.102104
$287$	9.74693e9	0.0848007
$288$	−6.95345e10	−0.595572
$289$	0	0
$290$	1.02156e11	0.848148
$291$	−1.55771e11	−1.27341
$292$	1.65333e11	1.33088
$293$	−4.99505e10	−0.395945	−0.197973	−	0.980208i	$-0.563436\pi$
$293$	−4.99505e10	−0.395945	−0.197973	+	0.980208i	$0.563436\pi$
$294$	2.03747e11	1.59048
$295$	−3.82694e10	−0.294206
$296$	5.59672e10	0.423761
$297$	−4.31887e9	−0.0322082
$298$	3.15364e11	2.31654
$299$	−1.40644e10	−0.101766
$300$	7.31873e10	0.521663
$301$	6.27273e9	0.0440461
$302$	1.04127e11	0.720331
$303$	2.86807e11	1.95478
$304$	1.95642e11	1.31381
$305$	−1.20852e11	−0.799656
$306$	0	0
$307$	−2.61083e11	−1.67748	−0.838738	−	0.544535i	$-0.816706\pi$
$307$	−2.61083e11	−1.67748	−0.838738	+	0.544535i	$0.816706\pi$
$308$	−3.30496e8	−0.00209261
$309$	−2.08208e11	−1.29923
$310$	−3.91166e10	−0.240565
$311$	−2.06391e11	−1.25103	−0.625516	−	0.780212i	$-0.715111\pi$
$311$	−2.06391e11	−1.25103	−0.625516	+	0.780212i	$0.715111\pi$
$312$	1.22422e11	0.731413
$313$	−1.65607e11	−0.975278	−0.487639	−	0.873045i	$-0.662142\pi$
$313$	−1.65607e11	−0.975278	−0.487639	+	0.873045i	$0.662142\pi$
$314$	1.63017e11	0.946345
$315$	3.12993e9	0.0179117
$316$	1.15478e11	0.651487
$317$	3.17222e11	1.76440	0.882200	−	0.470874i	$-0.156061\pi$
$317$	3.17222e11	1.76440	0.882200	+	0.470874i	$0.156061\pi$
$318$	2.87933e11	1.57895
$319$	−1.03724e10	−0.0560817
$320$	−3.62797e10	−0.193414
$321$	−2.42405e11	−1.27429
$322$	−9.85973e8	−0.00511109
$323$	0	0
$324$	−1.70927e11	−0.861705
$325$	−1.82949e11	−0.909608
$326$	−2.60042e11	−1.27516
$327$	−3.20894e10	−0.155202
$328$	−1.25850e11	−0.600375
$329$	−1.00202e10	−0.0471516
$330$	1.13338e10	0.0526093
$331$	6.00903e10	0.275156	0.137578	−	0.990491i	$-0.456068\pi$
$331$	6.00903e10	0.275156	0.137578	+	0.990491i	$0.456068\pi$
$332$	1.04485e11	0.471992
$333$	−1.19446e11	−0.532321
$334$	4.87127e10	0.214182
$335$	2.58465e11	1.12125
$336$	1.98575e10	0.0849957
$337$	−1.05908e10	−0.0447295	−0.0223648	−	0.999750i	$-0.507120\pi$
$337$	−1.05908e10	−0.0447295	−0.0223648	+	0.999750i	$0.507120\pi$
$338$	3.67332e11	1.53085
$339$	−2.36703e11	−0.973431
$340$	0	0
$341$	3.97171e9	0.0159068
$342$	−1.80459e11	−0.713282
$343$	−2.91878e10	−0.113862
$344$	−8.09923e10	−0.311839
$345$	1.37978e10	0.0524353
$346$	−1.10124e11	−0.413085
$347$	5.50040e10	0.203663	0.101831	−	0.994802i	$-0.467530\pi$
$347$	5.50040e10	0.203663	0.101831	+	0.994802i	$0.467530\pi$
$348$	−2.43952e11	−0.891656
$349$	3.79900e10	0.137074	0.0685370	−	0.997649i	$-0.478167\pi$
$349$	3.79900e10	0.137074	0.0685370	+	0.997649i	$0.478167\pi$
$350$	−1.28254e10	−0.0456842
$351$	2.53915e11	0.892908
$352$	1.80059e10	0.0625132
$353$	−4.34413e11	−1.48908	−0.744538	−	0.667581i	$-0.767330\pi$
$353$	−4.34413e11	−1.48908	−0.744538	+	0.667581i	$0.767330\pi$
$354$	2.23953e11	0.757953
$355$	2.13434e11	0.713242
$356$	1.98817e10	0.0656036
$357$	0	0
$358$	1.64458e10	0.0529154
$359$	−2.12485e11	−0.675155	−0.337577	−	0.941298i	$-0.609607\pi$
$359$	−2.12485e11	−0.675155	−0.337577	+	0.941298i	$0.609607\pi$
$360$	−4.04130e10	−0.126812
$361$	5.51578e10	0.170932
$362$	1.35366e11	0.414305
$363$	4.04972e11	1.22418
$364$	1.94306e10	0.0580135
$365$	4.05454e11	1.19570
$366$	7.07225e11	2.06012
$367$	−2.58548e11	−0.743951	−0.371976	−	0.928242i	$-0.621320\pi$
$367$	−2.58548e11	−0.743951	−0.371976	+	0.928242i	$0.621320\pi$
$368$	2.94560e10	0.0837257
$369$	2.68592e11	0.754180
$370$	−3.04628e11	−0.845009
$371$	−2.05903e10	−0.0564262
$372$	9.34119e10	0.252906
$373$	4.24117e11	1.13448	0.567239	−	0.823553i	$-0.308012\pi$
$373$	4.24117e11	1.13448	0.567239	+	0.823553i	$0.308012\pi$
$374$	0	0
$375$	4.70666e11	1.22906
$376$	1.29379e11	0.333825
$377$	6.09815e11	1.55475
$378$	1.78005e10	0.0448454
$379$	−5.56067e10	−0.138437	−0.0692183	−	0.997602i	$-0.522050\pi$
$379$	−5.56067e10	−0.138437	−0.0692183	+	0.997602i	$0.522050\pi$
$380$	−1.87807e11	−0.462046
$381$	−8.28112e11	−2.01339
$382$	4.77762e11	1.14796
$383$	−7.66095e11	−1.81923	−0.909616	−	0.415449i	$-0.863624\pi$
$383$	−7.66095e11	−1.81923	−0.909616	+	0.415449i	$0.863624\pi$
$384$	−4.01979e11	−0.943436
$385$	−8.10490e8	−0.00188007
$386$	−1.03621e12	−2.37577
$387$	1.72855e11	0.391727
$388$	3.19228e11	0.715086
$389$	3.34598e11	0.740884	0.370442	−	0.928856i	$-0.379206\pi$
$389$	3.34598e11	0.740884	0.370442	+	0.928856i	$0.379206\pi$
$390$	−6.66337e11	−1.45849
$391$	0	0
$392$	1.88127e11	0.402405
$393$	−5.47588e11	−1.15794
$394$	7.55741e11	1.57994
$395$	2.83191e11	0.585318
$396$	−9.10735e9	−0.0186108
$397$	−4.28574e10	−0.0865901	−0.0432951	−	0.999062i	$-0.513786\pi$
$397$	−4.28574e10	−0.0865901	−0.0432951	+	0.999062i	$0.513786\pi$
$398$	4.41082e11	0.881141
$399$	3.83509e10	0.0757526
$400$	3.83161e11	0.748362
$401$	−5.43233e11	−1.04915	−0.524573	−	0.851365i	$-0.675775\pi$
$401$	−5.43233e11	−1.04915	−0.524573	+	0.851365i	$0.675775\pi$
$402$	−1.51254e12	−2.88862
$403$	−2.33505e11	−0.440984
$404$	−5.87765e11	−1.09771
$405$	−4.19172e11	−0.774185
$406$	4.27504e10	0.0780860
$407$	3.09304e10	0.0558742
$408$	0	0
$409$	6.04096e11	1.06746	0.533729	−	0.845656i	$-0.320790\pi$
$409$	6.04096e11	1.06746	0.533729	+	0.845656i	$0.320790\pi$
$410$	6.84999e11	1.19719
$411$	−1.88189e11	−0.325317
$412$	4.26689e11	0.729582
$413$	−1.60151e10	−0.0270866
$414$	−2.71701e10	−0.0454558
$415$	2.56234e11	0.424053
$416$	−1.05860e12	−1.73306
$417$	−3.56922e11	−0.578045
$418$	4.67296e10	0.0748684
$419$	−1.10575e12	−1.75264	−0.876320	−	0.481729i	$-0.840009\pi$
$419$	−1.10575e12	−1.75264	−0.876320	+	0.481729i	$0.840009\pi$
$420$	−1.90622e10	−0.0298917
$421$	1.25890e11	0.195309	0.0976544	−	0.995220i	$-0.468866\pi$
$421$	1.25890e11	0.195309	0.0976544	+	0.995220i	$0.468866\pi$
$422$	1.08736e12	1.66904
$423$	−2.76124e11	−0.419345
$424$	2.65858e11	0.399488
$425$	0	0
$426$	−1.24902e12	−1.83750
$427$	−5.05744e10	−0.0736216
$428$	4.96769e11	0.715579
$429$	6.76566e10	0.0964390
$430$	4.40838e11	0.621829
$431$	−6.32839e11	−0.883376	−0.441688	−	0.897169i	$-0.645620\pi$
$431$	−6.32839e11	−0.883376	−0.441688	+	0.897169i	$0.645620\pi$
$432$	−5.31791e11	−0.734622
$433$	−8.56444e10	−0.117086	−0.0585428	−	0.998285i	$-0.518645\pi$
$433$	−8.56444e10	−0.117086	−0.0585428	+	0.998285i	$0.518645\pi$
$434$	−1.63696e10	−0.0221480
$435$	−5.98253e11	−0.801094
$436$	6.57620e10	0.0871537
$437$	5.68887e10	0.0746207
$438$	−2.37272e12	−3.08044
$439$	−1.27699e12	−1.64095	−0.820477	−	0.571680i	$-0.806292\pi$
$439$	−1.27699e12	−1.64095	−0.820477	+	0.571680i	$0.806292\pi$
$440$	1.04649e10	0.0133106
$441$	−4.01503e11	−0.505493
$442$	0	0
$443$	−4.07896e10	−0.0503191	−0.0251595	−	0.999683i	$-0.508009\pi$
$443$	−4.07896e10	−0.0503191	−0.0251595	+	0.999683i	$0.508009\pi$
$444$	7.27463e11	0.888357
$445$	4.87566e10	0.0589405
$446$	8.22249e11	0.984003
$447$	−1.84687e12	−2.18802
$448$	−1.51824e10	−0.0178070
$449$	5.70860e11	0.662859	0.331430	−	0.943480i	$-0.392469\pi$
$449$	5.70860e11	0.662859	0.331430	+	0.943480i	$0.392469\pi$
$450$	−3.53425e11	−0.406295
$451$	−6.95516e10	−0.0791612
$452$	4.85085e11	0.546632
$453$	−6.09798e11	−0.680368
$454$	−1.80881e11	−0.199822
$455$	4.76504e10	0.0521213
$456$	−4.95179e11	−0.536316
$457$	−1.52638e12	−1.63697	−0.818484	−	0.574529i	$-0.805185\pi$
$457$	−1.52638e12	−1.63697	−0.818484	+	0.574529i	$0.805185\pi$
$458$	−6.09630e11	−0.647398
$459$	0	0
$460$	−2.82763e10	−0.0294451
$461$	−1.75102e11	−0.180566	−0.0902831	−	0.995916i	$-0.528777\pi$
$461$	−1.75102e11	−0.180566	−0.0902831	+	0.995916i	$0.528777\pi$
$462$	4.74300e9	0.00484356
$463$	3.51744e11	0.355723	0.177862	−	0.984056i	$-0.443082\pi$
$463$	3.51744e11	0.355723	0.177862	+	0.984056i	$0.443082\pi$
$464$	−1.27717e12	−1.27914
$465$	2.29078e11	0.227219
$466$	−7.84655e11	−0.770800
$467$	1.86694e12	1.81637	0.908185	−	0.418569i	$-0.137468\pi$
$467$	1.86694e12	1.81637	0.908185	+	0.418569i	$0.137468\pi$
$468$	5.35440e11	0.515946
$469$	1.08163e11	0.103229
$470$	−7.04206e11	−0.665671
$471$	−9.54675e11	−0.893843
$472$	2.06784e11	0.191768
$473$	−4.47606e10	−0.0411169
$474$	−1.65724e12	−1.50793
$475$	7.40003e11	0.666979
$476$	0	0
$477$	−5.67399e11	−0.501830
$478$	−5.38745e11	−0.472017
$479$	1.68856e12	1.46557	0.732787	−	0.680458i	$-0.238219\pi$
$479$	1.68856e12	1.46557	0.732787	+	0.680458i	$0.238219\pi$
$480$	1.03853e12	0.892964
$481$	−1.81846e12	−1.54900
$482$	−1.26951e12	−1.07133
$483$	5.77414e9	0.00482753
$484$	−8.29924e11	−0.687439
$485$	7.82857e11	0.642458
$486$	1.48578e12	1.20807
$487$	−4.73964e11	−0.381826	−0.190913	−	0.981607i	$-0.561145\pi$
$487$	−4.73964e11	−0.381826	−0.190913	+	0.981607i	$0.561145\pi$
$488$	6.53006e11	0.521228
$489$	1.52288e12	1.20441
$490$	−1.02397e12	−0.802423
$491$	−1.41352e12	−1.09758	−0.548788	−	0.835961i	$-0.684911\pi$
$491$	−1.41352e12	−1.09758	−0.548788	+	0.835961i	$0.684911\pi$
$492$	−1.63581e12	−1.25860
$493$	0	0
$494$	−2.74733e12	−2.07558
$495$	−2.23344e10	−0.0167205
$496$	4.89044e11	0.362811
$497$	8.93187e10	0.0656657
$498$	−1.49949e12	−1.09247
$499$	7.60295e11	0.548946	0.274473	−	0.961595i	$-0.411497\pi$
$499$	7.60295e11	0.548946	0.274473	+	0.961595i	$0.411497\pi$
$500$	−9.64554e11	−0.690179
$501$	−2.85276e11	−0.202300
$502$	−4.73395e10	−0.0332703
$503$	8.43196e11	0.587317	0.293659	−	0.955910i	$-0.405127\pi$
$503$	8.43196e11	0.587317	0.293659	+	0.955910i	$0.405127\pi$
$504$	−1.69122e10	−0.0116751
$505$	−1.44140e12	−0.986219
$506$	7.03564e9	0.00477119
$507$	−2.15120e12	−1.44592
$508$	1.69708e12	1.13062
$509$	6.73047e11	0.444443	0.222221	−	0.974996i	$-0.428669\pi$
$509$	6.73047e11	0.444443	0.222221	+	0.974996i	$0.428669\pi$
$510$	0	0
$511$	1.69676e11	0.110084
$512$	1.45492e12	0.935671
$513$	−1.02705e12	−0.654733
$514$	2.34745e12	1.48341
$515$	1.04639e12	0.655481
$516$	−1.05274e12	−0.653728
$517$	7.15018e10	0.0440159
$518$	−1.27482e11	−0.0777971
$519$	6.44917e11	0.390167
$520$	−6.15252e11	−0.369010
$521$	−9.61216e11	−0.571546	−0.285773	−	0.958297i	$-0.592250\pi$
$521$	−9.61216e11	−0.571546	−0.285773	+	0.958297i	$0.592250\pi$
$522$	1.17806e12	0.694463
$523$	1.14346e12	0.668288	0.334144	−	0.942522i	$-0.391553\pi$
$523$	1.14346e12	0.668288	0.334144	+	0.942522i	$0.391553\pi$
$524$	1.12219e12	0.650244
$525$	7.51095e10	0.0431497
$526$	2.71591e12	1.54696
$527$	0	0
$528$	−1.41698e11	−0.0793432
$529$	−1.79259e12	−0.995245
$530$	−1.44706e12	−0.796607
$531$	−4.41321e11	−0.240896
$532$	−7.85940e10	−0.0425390
$533$	4.08908e12	2.19459
$534$	−2.85325e11	−0.151846
$535$	1.21825e12	0.642901
$536$	−1.39658e12	−0.730845
$537$	−9.63115e10	−0.0499797
$538$	−2.02421e12	−1.04168
$539$	1.03969e11	0.0530582
$540$	5.10493e11	0.258355
$541$	1.56626e12	0.786095	0.393047	−	0.919518i	$-0.371421\pi$
$541$	1.56626e12	0.786095	0.393047	+	0.919518i	$0.371421\pi$
$542$	4.15378e12	2.06751
$543$	−7.92740e11	−0.391320
$544$	0	0
$545$	1.61271e11	0.0783018
$546$	−2.78851e11	−0.134278
$547$	−3.84144e11	−0.183464	−0.0917320	−	0.995784i	$-0.529240\pi$
$547$	−3.84144e11	−0.183464	−0.0917320	+	0.995784i	$0.529240\pi$
$548$	3.85663e11	0.182682
$549$	−1.39366e12	−0.654758
$550$	9.15189e10	0.0426461
$551$	−2.46662e12	−1.14004
$552$	−7.45545e10	−0.0341781
$553$	1.18510e11	0.0538882
$554$	1.16362e12	0.524830
$555$	1.78399e12	0.798130
$556$	7.31454e11	0.324602
$557$	8.53269e11	0.375610	0.187805	−	0.982206i	$-0.439863\pi$
$557$	8.53269e11	0.375610	0.187805	+	0.982206i	$0.439863\pi$
$558$	−4.51091e11	−0.196975
$559$	2.63157e12	1.13989
$560$	−9.97972e10	−0.0428817
$561$	0	0
$562$	−5.62259e12	−2.37751
$563$	4.28303e12	1.79665	0.898325	−	0.439332i	$-0.144785\pi$
$563$	4.28303e12	1.79665	0.898325	+	0.439332i	$0.144785\pi$
$564$	1.68167e12	0.699819
$565$	1.18959e12	0.491112
$566$	5.79814e12	2.37473
$567$	−1.75417e11	−0.0712766
$568$	−1.15327e12	−0.464902
$569$	2.07615e12	0.830335	0.415168	−	0.909745i	$-0.363723\pi$
$569$	2.07615e12	0.830335	0.415168	+	0.909745i	$0.363723\pi$
$570$	2.69524e12	1.06945
$571$	−6.01981e11	−0.236985	−0.118492	−	0.992955i	$-0.537806\pi$
$571$	−6.01981e11	−0.236985	−0.118492	+	0.992955i	$0.537806\pi$
$572$	−1.38651e11	−0.0541554
$573$	−2.79791e12	−1.08427
$574$	2.86661e11	0.110221
$575$	1.11415e11	0.0425050
$576$	−4.18377e11	−0.158368
$577$	4.45469e10	0.0167312	0.00836559	−	0.999965i	$-0.497337\pi$
$577$	4.45469e10	0.0167312	0.00836559	+	0.999965i	$0.497337\pi$
$578$	0	0
$579$	6.06834e12	2.24397
$580$	1.22602e12	0.449855
$581$	1.07230e11	0.0390411
$582$	−4.58129e12	−1.65514
$583$	1.46927e11	0.0526737
$584$	−2.19082e12	−0.779378
$585$	1.31308e12	0.463544
$586$	−1.46906e12	−0.514636
$587$	−3.22710e12	−1.12187	−0.560934	−	0.827861i	$-0.689558\pi$
$587$	−3.22710e12	−1.12187	−0.560934	+	0.827861i	$0.689558\pi$
$588$	2.44527e12	0.843586
$589$	9.44496e11	0.323356
$590$	−1.12552e12	−0.382400
$591$	−4.42584e12	−1.49229
$592$	3.80852e12	1.27441
$593$	2.87664e12	0.955298	0.477649	−	0.878551i	$-0.341489\pi$
$593$	2.87664e12	0.955298	0.477649	+	0.878551i	$0.341489\pi$
$594$	−1.27019e11	−0.0418631
$595$	0	0
$596$	3.78485e12	1.22869
$597$	−2.58310e12	−0.832256
$598$	−4.13640e11	−0.132272
$599$	−1.78665e12	−0.567046	−0.283523	−	0.958966i	$-0.591503\pi$
$599$	−1.78665e12	−0.567046	−0.283523	+	0.958966i	$0.591503\pi$
$600$	−9.69798e11	−0.305493
$601$	4.00758e12	1.25299	0.626495	−	0.779426i	$-0.284489\pi$
$601$	4.00758e12	1.25299	0.626495	+	0.779426i	$0.284489\pi$
$602$	1.84483e11	0.0572497
$603$	2.98062e12	0.918075
$604$	1.24968e12	0.382061
$605$	−2.03526e12	−0.617618
$606$	8.43510e12	2.54076
$607$	−1.47529e11	−0.0441092	−0.0220546	−	0.999757i	$-0.507021\pi$
$607$	−1.47529e11	−0.0441092	−0.0220546	+	0.999757i	$0.507021\pi$
$608$	4.28190e12	1.27078
$609$	−2.50359e11	−0.0737539
$610$	−3.55429e12	−1.03937
$611$	−4.20374e12	−1.22025
$612$	0	0
$613$	5.51858e12	1.57854	0.789269	−	0.614047i	$-0.210460\pi$
$613$	5.51858e12	1.57854	0.789269	+	0.614047i	$0.210460\pi$
$614$	−7.67855e12	−2.18033
$615$	−4.01155e12	−1.13077
$616$	4.37938e9	0.00122546
$617$	2.78831e11	0.0774565	0.0387282	−	0.999250i	$-0.487669\pi$
$617$	2.78831e11	0.0774565	0.0387282	+	0.999250i	$0.487669\pi$
$618$	−6.12348e12	−1.68869
$619$	3.23444e12	0.885506	0.442753	−	0.896644i	$-0.354002\pi$
$619$	3.23444e12	0.885506	0.442753	+	0.896644i	$0.354002\pi$
$620$	−4.69458e11	−0.127595
$621$	−1.54634e11	−0.0417246
$622$	−6.07002e12	−1.62605
$623$	2.04038e10	0.00542645
$624$	8.33070e12	2.19963
$625$	−1.41268e10	−0.00370324
$626$	−4.87055e12	−1.26763
$627$	−2.73662e11	−0.0707148
$628$	1.95645e12	0.501939
$629$	0	0
$630$	9.20523e10	0.0232810
$631$	−2.17235e12	−0.545504	−0.272752	−	0.962084i	$-0.587934\pi$
$631$	−2.17235e12	−0.545504	−0.272752	+	0.962084i	$0.587934\pi$
$632$	−1.53018e12	−0.381519
$633$	−6.36788e12	−1.57644
$634$	9.32963e12	2.29331
$635$	4.16183e12	1.01579
$636$	3.45563e12	0.837471
$637$	−6.11253e12	−1.47094
$638$	−3.05056e11	−0.0728931
$639$	2.46132e12	0.584002
$640$	2.02022e12	0.475979
$641$	8.30112e12	1.94212	0.971059	−	0.238839i	$-0.0767669\pi$
$641$	8.30112e12	1.94212	0.971059	+	0.238839i	$0.0767669\pi$
$642$	−7.12921e12	−1.65628
$643$	5.34854e12	1.23392	0.616958	−	0.786996i	$-0.288365\pi$
$643$	5.34854e12	1.23392	0.616958	+	0.786996i	$0.288365\pi$
$644$	−1.18332e10	−0.00271091
$645$	−2.58168e12	−0.587331
$646$	0	0
$647$	1.48400e12	0.332940	0.166470	−	0.986047i	$-0.446763\pi$
$647$	1.48400e12	0.332940	0.166470	+	0.986047i	$0.446763\pi$
$648$	2.26494e12	0.504626
$649$	1.14279e11	0.0252852
$650$	−5.38059e12	−1.18228
$651$	9.58653e10	0.0209193
$652$	−3.12090e12	−0.676341
$653$	1.40443e10	0.00302267	0.00151133	−	0.999999i	$-0.499519\pi$
$653$	1.40443e10	0.00302267	0.00151133	+	0.999999i	$0.499519\pi$
$654$	−9.43760e11	−0.201726
$655$	2.75200e12	0.584201
$656$	−8.56402e12	−1.80555
$657$	4.67568e12	0.979041
$658$	−2.94699e11	−0.0612860
$659$	−2.06468e12	−0.426450	−0.213225	−	0.977003i	$-0.568397\pi$
$659$	−2.06468e12	−0.426450	−0.213225	+	0.977003i	$0.568397\pi$
$660$	1.36023e11	0.0279038
$661$	−4.29740e12	−0.875587	−0.437793	−	0.899076i	$-0.644240\pi$
$661$	−4.29740e12	−0.875587	−0.437793	+	0.899076i	$0.644240\pi$
$662$	1.76728e12	0.357638
$663$	0	0
$664$	−1.38453e12	−0.276405
$665$	−1.92739e11	−0.0382184
$666$	−3.51296e12	−0.691893
$667$	−3.71376e11	−0.0726519
$668$	5.84627e11	0.113602
$669$	−4.81533e12	−0.929412
$670$	7.60156e12	1.45736
$671$	3.60885e11	0.0687255
$672$	4.34608e11	0.0822122
$673$	3.57666e12	0.672064	0.336032	−	0.941851i	$-0.390915\pi$
$673$	3.57666e12	0.672064	0.336032	+	0.941851i	$0.390915\pi$
$674$	−3.11479e11	−0.0581380
$675$	−2.01146e12	−0.372945
$676$	4.40854e12	0.811960
$677$	6.68212e12	1.22255	0.611273	−	0.791420i	$-0.290658\pi$
$677$	6.68212e12	1.22255	0.611273	+	0.791420i	$0.290658\pi$
$678$	−6.96152e12	−1.26523
$679$	3.27612e11	0.0591489
$680$	0	0
$681$	1.05929e12	0.188736
$682$	1.16809e11	0.0206751
$683$	2.16417e12	0.380537	0.190269	−	0.981732i	$-0.439064\pi$
$683$	2.16417e12	0.380537	0.190269	+	0.981732i	$0.439064\pi$
$684$	−2.16578e12	−0.378323
$685$	9.45778e11	0.164128
$686$	−8.58424e11	−0.147994
$687$	3.57017e12	0.611482
$688$	−5.51146e12	−0.937818
$689$	−8.63815e12	−1.46027
$690$	4.05798e11	0.0681536
$691$	1.18113e13	1.97082	0.985410	−	0.170195i	$-0.0544396\pi$
$691$	1.18113e13	1.97082	0.985410	+	0.170195i	$0.0544396\pi$
$692$	−1.32165e12	−0.219099
$693$	−9.34655e9	−0.00153940
$694$	1.61769e12	0.264714
$695$	1.79378e12	0.291633
$696$	3.23258e12	0.522165
$697$	0	0
$698$	1.11730e12	0.178164
$699$	4.59517e12	0.728038
$700$	−1.53925e11	−0.0242308
$701$	5.01825e11	0.0784912	0.0392456	−	0.999230i	$-0.487505\pi$
$701$	5.01825e11	0.0784912	0.0392456	+	0.999230i	$0.487505\pi$
$702$	7.46774e12	1.16057
$703$	7.35544e12	1.13582
$704$	1.08338e11	0.0166228
$705$	4.12404e12	0.628741
$706$	−1.27762e13	−1.93545
$707$	−6.03202e11	−0.0907978
$708$	2.68778e12	0.402016
$709$	−1.05914e13	−1.57414	−0.787070	−	0.616864i	$-0.788403\pi$
$709$	−1.05914e13	−1.57414	−0.787070	+	0.616864i	$0.788403\pi$
$710$	6.27718e12	0.927048
$711$	3.26575e12	0.479258
$712$	−2.63450e11	−0.0384183
$713$	1.42204e11	0.0206067
$714$	0	0
$715$	−3.40021e11	−0.0486551
$716$	1.97375e11	0.0280662
$717$	3.15505e12	0.445830
$718$	−6.24926e12	−0.877543
$719$	5.41829e12	0.756105	0.378053	−	0.925784i	$-0.376594\pi$
$719$	5.41829e12	0.756105	0.378053	+	0.925784i	$0.376594\pi$
$720$	−2.75007e12	−0.381371
$721$	4.37896e11	0.0603479
$722$	1.62221e12	0.222172
$723$	7.43459e12	1.01189
$724$	1.62459e12	0.219746
$725$	−4.83082e12	−0.649381
$726$	1.19104e13	1.59115
$727$	9.64854e12	1.28102	0.640511	−	0.767949i	$-0.278722\pi$
$727$	9.64854e12	1.28102	0.640511	+	0.767949i	$0.278722\pi$
$728$	−2.57473e11	−0.0339735
$729$	8.30460e11	0.108904
$730$	1.19245e13	1.55414
$731$	0	0
$732$	8.48778e12	1.09268
$733$	−2.72496e12	−0.348653	−0.174326	−	0.984688i	$-0.555775\pi$
$733$	−2.72496e12	−0.348653	−0.174326	+	0.984688i	$0.555775\pi$
$734$	−7.60400e12	−0.966963
$735$	5.99664e12	0.757906
$736$	6.44686e11	0.0809838
$737$	−7.71826e11	−0.0963642
$738$	7.89940e12	0.980258
$739$	−7.51446e12	−0.926825	−0.463412	−	0.886143i	$-0.653375\pi$
$739$	−7.51446e12	−0.926825	−0.463412	+	0.886143i	$0.653375\pi$
$740$	−3.65599e12	−0.448191
$741$	1.60891e13	1.96043
$742$	−6.05569e11	−0.0733409
$743$	−1.52473e13	−1.83545	−0.917726	−	0.397215i	$-0.869977\pi$
$743$	−1.52473e13	−1.83545	−0.917726	+	0.397215i	$0.869977\pi$
$744$	−1.23779e12	−0.148105
$745$	9.28175e12	1.10389
$746$	1.24734e13	1.47456
$747$	2.95488e12	0.347214
$748$	0	0
$749$	5.09817e11	0.0591897
$750$	1.38425e13	1.59749
$751$	5.81211e12	0.666736	0.333368	−	0.942797i	$-0.391815\pi$
$751$	5.81211e12	0.666736	0.333368	+	0.942797i	$0.391815\pi$
$752$	8.80415e12	1.00394
$753$	2.77234e11	0.0314245
$754$	1.79349e13	2.02082
$755$	3.06465e12	0.343257
$756$	2.13633e11	0.0237859
$757$	−3.75393e12	−0.415485	−0.207742	−	0.978184i	$-0.566612\pi$
$757$	−3.75393e12	−0.415485	−0.207742	+	0.978184i	$0.566612\pi$
$758$	−1.63541e12	−0.179935
$759$	−4.12028e10	−0.00450649
$760$	2.48861e12	0.270580
$761$	1.37447e13	1.48561	0.742806	−	0.669507i	$-0.233495\pi$
$761$	1.37447e13	1.48561	0.742806	+	0.669507i	$0.233495\pi$
$762$	−2.43551e13	−2.61693
$763$	6.74892e10	0.00720898
$764$	5.73386e12	0.608874
$765$	0	0
$766$	−2.25311e13	−2.36458
$767$	−6.71873e12	−0.700983
$768$	−1.55184e13	−1.60961
$769$	8.66013e11	0.0893009	0.0446505	−	0.999003i	$-0.485783\pi$
$769$	8.66013e11	0.0893009	0.0446505	+	0.999003i	$0.485783\pi$
$770$	−2.38368e10	−0.00244365
$771$	−1.37473e13	−1.40111
$772$	−1.24361e13	−1.26010
$773$	−9.63400e12	−0.970507	−0.485254	−	0.874373i	$-0.661273\pi$
$773$	−9.63400e12	−0.970507	−0.485254	+	0.874373i	$0.661273\pi$
$774$	5.08373e12	0.509153
$775$	1.84978e12	0.184188
$776$	−4.23006e12	−0.418764
$777$	7.46569e11	0.0734810
$778$	9.84065e12	0.962976
$779$	−1.65398e13	−1.60920
$780$	−7.99705e12	−0.773578
$781$	−6.37355e11	−0.0612988
$782$	0	0
$783$	6.70471e12	0.637459
$784$	1.28019e13	1.21018
$785$	4.79789e12	0.450959
$786$	−1.61047e13	−1.50506
$787$	−9.49385e12	−0.882177	−0.441089	−	0.897464i	$-0.645408\pi$
$787$	−9.49385e12	−0.882177	−0.441089	+	0.897464i	$0.645408\pi$
$788$	9.07004e12	0.837995
$789$	−1.59052e13	−1.46114
$790$	8.32873e12	0.760776
$791$	4.97825e11	0.0452150
$792$	1.20681e11	0.0108987
$793$	−2.12172e13	−1.90528
$794$	−1.26045e12	−0.112547
$795$	8.47438e12	0.752412
$796$	5.29365e12	0.467355
$797$	−1.56397e13	−1.37299	−0.686493	−	0.727137i	$-0.740851\pi$
$797$	−1.56397e13	−1.37299	−0.686493	+	0.727137i	$0.740851\pi$
$798$	1.12791e12	0.0984607
$799$	0	0
$800$	8.38601e12	0.723853
$801$	5.62260e11	0.0482604
$802$	−1.59767e13	−1.36365
$803$	−1.21076e12	−0.102763
$804$	−1.81528e13	−1.53212
$805$	−2.90190e10	−0.00243557
$806$	−6.86746e12	−0.573177
$807$	1.18544e13	0.983893
$808$	7.78842e12	0.642833
$809$	1.86284e13	1.52900	0.764498	−	0.644626i	$-0.222987\pi$
$809$	1.86284e13	1.52900	0.764498	+	0.644626i	$0.222987\pi$
$810$	−1.23280e13	−1.00626
$811$	4.91802e11	0.0399206	0.0199603	−	0.999801i	$-0.493646\pi$
$811$	4.91802e11	0.0399206	0.0199603	+	0.999801i	$0.493646\pi$
$812$	5.13070e11	0.0414166
$813$	−2.43257e13	−1.95280
$814$	9.09675e11	0.0726234
$815$	−7.65351e12	−0.607647
$816$	0	0
$817$	−1.06443e13	−0.835832
$818$	1.77667e13	1.38745
$819$	5.49503e11	0.0426769
$820$	8.22103e12	0.634986
$821$	2.48956e13	1.91240	0.956200	−	0.292715i	$-0.0945587\pi$
$821$	2.48956e13	1.91240	0.956200	+	0.292715i	$0.0945587\pi$
$822$	−5.53471e12	−0.422836
$823$	1.47999e13	1.12450	0.562248	−	0.826968i	$-0.309936\pi$
$823$	1.47999e13	1.12450	0.562248	+	0.826968i	$0.309936\pi$
$824$	−5.65402e12	−0.427253
$825$	−5.35961e11	−0.0402801
$826$	−4.71009e11	−0.0352062
$827$	2.08121e13	1.54718	0.773591	−	0.633685i	$-0.218459\pi$
$827$	2.08121e13	1.54718	0.773591	+	0.633685i	$0.218459\pi$
$828$	−3.26082e11	−0.0241096
$829$	−3.28044e12	−0.241233	−0.120616	−	0.992699i	$-0.538487\pi$
$829$	−3.28044e12	−0.241233	−0.120616	+	0.992699i	$0.538487\pi$
$830$	7.53593e12	0.551170
$831$	−6.81451e12	−0.495713
$832$	−6.36941e12	−0.460834
$833$	0	0
$834$	−1.04972e13	−0.751323
$835$	1.43370e12	0.102064
$836$	5.60826e11	0.0397100
$837$	−2.56731e12	−0.180806
$838$	−3.25204e13	−2.27802
$839$	−1.67696e13	−1.16841	−0.584204	−	0.811607i	$-0.698593\pi$
$839$	−1.67696e13	−1.16841	−0.584204	+	0.811607i	$0.698593\pi$
$840$	2.52591e11	0.0175050
$841$	1.59520e12	0.109960
$842$	3.70247e12	0.253856
$843$	3.29275e13	2.24561
$844$	1.30499e13	0.885254
$845$	1.08112e13	0.729492
$846$	−8.12089e12	−0.545051
$847$	−8.51721e11	−0.0568620
$848$	1.80914e13	1.20141
$849$	−3.39556e13	−2.24299
$850$	0	0
$851$	1.10744e12	0.0723831
$852$	−1.49902e13	−0.974604
$853$	1.89821e13	1.22765	0.613825	−	0.789442i	$-0.289630\pi$
$853$	1.89821e13	1.22765	0.613825	+	0.789442i	$0.289630\pi$
$854$	−1.48741e12	−0.0956908
$855$	−5.31124e12	−0.339898
$856$	−6.58265e12	−0.419053
$857$	−2.03889e13	−1.29116	−0.645581	−	0.763692i	$-0.723385\pi$
$857$	−2.03889e13	−1.29116	−0.645581	+	0.763692i	$0.723385\pi$
$858$	1.98981e12	0.125348
$859$	−2.74900e11	−0.0172269	−0.00861343	−	0.999963i	$-0.502742\pi$
$859$	−2.74900e11	−0.0172269	−0.00861343	+	0.999963i	$0.502742\pi$
$860$	5.29073e12	0.329816
$861$	−1.67877e12	−0.104106
$862$	−1.86120e13	−1.14818
$863$	−2.21627e13	−1.36011	−0.680054	−	0.733162i	$-0.738044\pi$
$863$	−2.21627e13	−1.36011	−0.680054	+	0.733162i	$0.738044\pi$
$864$	−1.16390e13	−0.710564
$865$	−3.24115e12	−0.196846
$866$	−2.51883e12	−0.152184
$867$	0	0
$868$	−1.96460e11	−0.0117472
$869$	−8.45660e11	−0.0503045
$870$	−1.75948e13	−1.04123
$871$	4.53772e13	2.67151
$872$	−8.71406e11	−0.0510383
$873$	9.02788e12	0.526044
$874$	1.67312e12	0.0969895
$875$	−9.89887e11	−0.0570886
$876$	−2.84763e13	−1.63386
$877$	3.80527e12	0.217214	0.108607	−	0.994085i	$-0.465361\pi$
$877$	3.80527e12	0.217214	0.108607	+	0.994085i	$0.465361\pi$
$878$	−3.75567e13	−2.13286
$879$	8.60324e12	0.486085
$880$	7.12127e11	0.0400300
$881$	−7.43319e12	−0.415703	−0.207852	−	0.978160i	$-0.566647\pi$
$881$	−7.43319e12	−0.415703	−0.207852	+	0.978160i	$0.566647\pi$
$882$	−1.18084e13	−0.657023
$883$	1.98184e13	1.09710	0.548549	−	0.836118i	$-0.315180\pi$
$883$	1.98184e13	1.09710	0.548549	+	0.836118i	$0.315180\pi$
$884$	0	0
$885$	6.59135e12	0.361185
$886$	−1.19964e12	−0.0654030
$887$	2.80972e13	1.52407	0.762037	−	0.647533i	$-0.224199\pi$
$887$	2.80972e13	1.52407	0.762037	+	0.647533i	$0.224199\pi$
$888$	−9.63954e12	−0.520233
$889$	1.74166e12	0.0935199
$890$	1.43395e12	0.0766088
$891$	1.25173e12	0.0665365
$892$	9.86824e12	0.521913
$893$	1.70035e13	0.894762
$894$	−5.43170e13	−2.84392
$895$	4.84030e11	0.0252156
$896$	8.45427e11	0.0438218
$897$	2.42239e12	0.124933
$898$	1.67892e13	0.861562
$899$	−6.16577e12	−0.314825
$900$	−4.24164e12	−0.215498
$901$	0	0
$902$	−2.04554e12	−0.102891
$903$	−1.08039e12	−0.0540735
$904$	−6.42782e12	−0.320115
$905$	3.98406e12	0.197427
$906$	−1.79344e13	−0.884319
$907$	3.18897e12	0.156465	0.0782326	−	0.996935i	$-0.475072\pi$
$907$	3.18897e12	0.156465	0.0782326	+	0.996935i	$0.475072\pi$
$908$	−2.17085e12	−0.105985
$909$	−1.66222e13	−0.807516
$910$	1.40141e12	0.0677455
$911$	−3.36785e13	−1.62002	−0.810010	−	0.586416i	$-0.800538\pi$
$911$	−3.36785e13	−1.62002	−0.810010	+	0.586416i	$0.800538\pi$
$912$	−3.36965e13	−1.61290
$913$	−7.65163e11	−0.0364448
$914$	−4.48914e13	−2.12768
$915$	2.08149e13	0.981703
$916$	−7.31648e12	−0.343378
$917$	1.15167e12	0.0537854
$918$	0	0
$919$	−3.43740e13	−1.58968	−0.794841	−	0.606817i	$-0.792446\pi$
$919$	−3.43740e13	−1.58968	−0.794841	+	0.606817i	$0.792446\pi$
$920$	3.74687e11	0.0172434
$921$	4.49678e13	2.05937
$922$	−5.14981e12	−0.234694
$923$	3.74714e13	1.69939
$924$	5.69232e10	0.00256901
$925$	1.44055e13	0.646978
$926$	1.03449e13	0.462357
$927$	1.20669e13	0.536707
$928$	−2.79527e13	−1.23725
$929$	1.24776e13	0.549617	0.274808	−	0.961499i	$-0.411386\pi$
$929$	1.24776e13	0.549617	0.274808	+	0.961499i	$0.411386\pi$
$930$	6.73726e12	0.295332
$931$	2.47244e13	1.07858
$932$	−9.41705e12	−0.408830
$933$	3.55478e13	1.53584
$934$	5.49074e13	2.36086
$935$	0	0
$936$	−7.09507e12	−0.302145
$937$	−3.15615e13	−1.33761	−0.668806	−	0.743437i	$-0.733194\pi$
$937$	−3.15615e13	−1.33761	−0.668806	+	0.743437i	$0.733194\pi$
$938$	3.18112e12	0.134174
$939$	2.85234e13	1.19731
$940$	−8.45155e12	−0.353070
$941$	−4.53194e13	−1.88422	−0.942109	−	0.335308i	$-0.891160\pi$
$941$	−4.53194e13	−1.88422	−0.942109	+	0.335308i	$0.891160\pi$
$942$	−2.80773e13	−1.16179
$943$	−2.49024e12	−0.102551
$944$	1.40715e13	0.576720
$945$	5.23900e11	0.0213701
$946$	−1.31642e12	−0.0534424
$947$	−3.17154e13	−1.28143	−0.640715	−	0.767779i	$-0.721362\pi$
$947$	−3.17154e13	−1.28143	−0.640715	+	0.767779i	$0.721362\pi$
$948$	−1.98893e13	−0.799803
$949$	7.11831e13	2.84891
$950$	2.17637e13	0.866917
$951$	−5.46370e13	−2.16608
$952$	0	0
$953$	4.41151e13	1.73248	0.866242	−	0.499624i	$-0.166529\pi$
$953$	4.41151e13	1.73248	0.866242	+	0.499624i	$0.166529\pi$
$954$	−1.66874e13	−0.652261
$955$	1.40614e13	0.547033
$956$	−6.46575e12	−0.250356
$957$	1.78650e12	0.0688491
$958$	4.96613e13	1.90490
$959$	3.95792e11	0.0151107
$960$	6.24865e12	0.237447
$961$	−2.40787e13	−0.910704
$962$	−5.34817e13	−2.01334
$963$	1.40488e13	0.526407
$964$	−1.52360e13	−0.568230
$965$	−3.04975e13	−1.13212
$966$	1.69820e11	0.00627467
$967$	−1.54834e13	−0.569439	−0.284720	−	0.958611i	$-0.591900\pi$
$967$	−1.54834e13	−0.569439	−0.284720	+	0.958611i	$0.591900\pi$
$968$	1.09973e13	0.402573
$969$	0	0
$970$	2.30241e13	0.835045
$971$	−1.13279e12	−0.0408943	−0.0204471	−	0.999791i	$-0.506509\pi$
$971$	−1.13279e12	−0.0408943	−0.0204471	+	0.999791i	$0.506509\pi$
$972$	1.78316e13	0.640755
$973$	7.50666e11	0.0268497
$974$	−1.39395e13	−0.496284
$975$	3.15103e13	1.11669
$976$	4.44365e13	1.56753
$977$	7.12721e12	0.250262	0.125131	−	0.992140i	$-0.460065\pi$
$977$	7.12721e12	0.250262	0.125131	+	0.992140i	$0.460065\pi$
$978$	4.47885e13	1.56546
$979$	−1.45596e11	−0.00506557
$980$	−1.22892e13	−0.425603
$981$	1.85977e12	0.0641134
$982$	−4.15721e13	−1.42659
$983$	9.27672e12	0.316886	0.158443	−	0.987368i	$-0.449353\pi$
$983$	9.27672e12	0.316886	0.158443	+	0.987368i	$0.449353\pi$
$984$	2.16759e13	0.737054
$985$	2.22428e13	0.752883
$986$	0	0
$987$	1.72584e12	0.0578860
$988$	−3.29721e13	−1.10088
$989$	−1.60262e12	−0.0532656
$990$	−6.56861e11	−0.0217328
$991$	−3.76758e13	−1.24088	−0.620442	−	0.784252i	$-0.713047\pi$
$991$	−3.76758e13	−1.24088	−0.620442	+	0.784252i	$0.713047\pi$
$992$	1.07034e13	0.350929
$993$	−1.03497e13	−0.337797
$994$	2.62690e12	0.0853501
$995$	1.29818e13	0.419887
$996$	−1.79961e13	−0.579444
$997$	4.77781e13	1.53144	0.765721	−	0.643173i	$-0.222383\pi$
$997$	4.77781e13	1.53144	0.765721	+	0.643173i	$0.222383\pi$
$998$	2.23605e13	0.713502
$999$	−1.99934e13	−0.635100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.29	yes	36
17.16	even	2		289.10.a.g.1.29	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.29	✓	36	17.16	even	2
289.10.a.h.1.29	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)

\(f(q)\)	\(=\)	\(q+29.4104 q^{2} -172.236 q^{3} +352.969 q^{4} +865.601 q^{5} -5065.51 q^{6} +362.239 q^{7} -4677.16 q^{8} +9982.09 q^{9} +O(q^{10})\)	\(q+29.4104 q^{2} -172.236 q^{3} +352.969 q^{4} +865.601 q^{5} -5065.51 q^{6} +362.239 q^{7} -4677.16 q^{8} +9982.09 q^{9} +25457.6 q^{10} -2584.84 q^{11} -60793.8 q^{12} +151968. q^{13} +10653.6 q^{14} -149087. q^{15} -318277. q^{16} +293577. q^{18} -614691. q^{19} +305530. q^{20} -62390.5 q^{21} -76021.2 q^{22} -92548.4 q^{23} +805573. q^{24} -1.20386e6 q^{25} +4.46944e6 q^{26} +1.67084e6 q^{27} +127859. q^{28} +4.01277e6 q^{29} -4.38471e6 q^{30} -1.53654e6 q^{31} -6.96593e6 q^{32} +445202. q^{33} +313555. q^{35} +3.52337e6 q^{36} -1.19661e7 q^{37} -1.80783e7 q^{38} -2.61744e7 q^{39} -4.04855e6 q^{40} +2.69074e7 q^{41} -1.83493e6 q^{42} +1.73165e7 q^{43} -912370. q^{44} +8.64050e6 q^{45} -2.72188e6 q^{46} -2.76619e7 q^{47} +5.48186e7 q^{48} -4.02224e7 q^{49} -3.54060e7 q^{50} +5.36401e7 q^{52} -5.68418e7 q^{53} +4.91401e7 q^{54} -2.23744e6 q^{55} -1.69425e6 q^{56} +1.05872e8 q^{57} +1.18017e8 q^{58} -4.42113e7 q^{59} -5.26231e7 q^{60} -1.39616e8 q^{61} -4.51901e7 q^{62} +3.61590e6 q^{63} -4.19127e7 q^{64} +1.31544e8 q^{65} +1.30936e7 q^{66} +2.98597e8 q^{67} +1.59401e7 q^{69} +9.22175e6 q^{70} +2.46574e8 q^{71} -4.66878e7 q^{72} +4.68407e8 q^{73} -3.51926e8 q^{74} +2.07348e8 q^{75} -2.16967e8 q^{76} -936333. q^{77} -7.69797e8 q^{78} +3.27161e8 q^{79} -2.75501e8 q^{80} -4.84256e8 q^{81} +7.91357e8 q^{82} +2.96019e8 q^{83} -2.20219e7 q^{84} +5.09286e8 q^{86} -6.91142e8 q^{87} +1.20897e7 q^{88} +5.63269e7 q^{89} +2.54120e8 q^{90} +5.50489e7 q^{91} -3.26667e7 q^{92} +2.64646e8 q^{93} -8.13547e8 q^{94} -5.32077e8 q^{95} +1.19978e9 q^{96} +9.04409e8 q^{97} -1.18295e9 q^{98} -2.58021e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more