LMFDB - Embedded newform 289.10.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 122690 x^{10} + 5157152560 x^{8} - 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 $ x^12 - 122690x^10 + 5157152560x^8 - 87983684680032x^6 + 612743619071665152x^4 - 1335826553351738886144*x^2 + 203949399568932198678528
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-206.667$ of defining polynomial
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)

$f(q)$	$=$	$q+16.7531 q^{2} +206.667 q^{3} -231.335 q^{4} +1946.29 q^{5} +3462.30 q^{6} -1633.30 q^{7} -12453.1 q^{8} +23028.2 q^{9} +O(q^{10})$	\(q+16.7531 q^{2} +206.667 q^{3} -231.335 q^{4} +1946.29 q^{5} +3462.30 q^{6} -1633.30 q^{7} -12453.1 q^{8} +23028.2 q^{9} +32606.3 q^{10} +11623.3 q^{11} -47809.2 q^{12} -163541. q^{13} -27362.8 q^{14} +402234. q^{15} -90185.0 q^{16} +385793. q^{18} -673499. q^{19} -450244. q^{20} -337549. q^{21} +194725. q^{22} -1.37499e6 q^{23} -2.57365e6 q^{24} +1.83492e6 q^{25} -2.73981e6 q^{26} +691336. q^{27} +377839. q^{28} -4.32926e6 q^{29} +6.73865e6 q^{30} +3.45219e6 q^{31} +4.86513e6 q^{32} +2.40214e6 q^{33} -3.17888e6 q^{35} -5.32721e6 q^{36} -5.81427e6 q^{37} -1.12832e7 q^{38} -3.37985e7 q^{39} -2.42374e7 q^{40} -2.37653e7 q^{41} -5.65499e6 q^{42} +2.46177e7 q^{43} -2.68886e6 q^{44} +4.48195e7 q^{45} -2.30353e7 q^{46} -3.94057e7 q^{47} -1.86382e7 q^{48} -3.76859e7 q^{49} +3.07406e7 q^{50} +3.78327e7 q^{52} +9.66929e7 q^{53} +1.15820e7 q^{54} +2.26222e7 q^{55} +2.03397e7 q^{56} -1.39190e8 q^{57} -7.25285e7 q^{58} -2.37253e7 q^{59} -9.30506e7 q^{60} -4.31637e7 q^{61} +5.78348e7 q^{62} -3.76120e7 q^{63} +1.27681e8 q^{64} -3.18298e8 q^{65} +4.02432e7 q^{66} +3.50040e7 q^{67} -2.84165e8 q^{69} -5.32560e7 q^{70} -2.90407e8 q^{71} -2.86773e8 q^{72} +4.29259e8 q^{73} -9.74069e7 q^{74} +3.79217e8 q^{75} +1.55804e8 q^{76} -1.89843e7 q^{77} -5.66229e8 q^{78} +3.78639e8 q^{79} -1.75526e8 q^{80} -3.10387e8 q^{81} -3.98142e8 q^{82} -9.91655e7 q^{83} +7.80868e7 q^{84} +4.12423e8 q^{86} -8.94715e8 q^{87} -1.44746e8 q^{88} -5.39631e8 q^{89} +7.50864e8 q^{90} +2.67112e8 q^{91} +3.18083e8 q^{92} +7.13453e8 q^{93} -6.60166e8 q^{94} -1.31082e9 q^{95} +1.00546e9 q^{96} +1.21632e9 q^{97} -6.31355e8 q^{98} +2.67662e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9}+O(q^{10}) $ 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9	$ 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9} - 63204 q^{13} + 243480 q^{15} + 38978 q^{16} + 547706 q^{18} - 1110672 q^{19} - 172580 q^{21} + 4441796 q^{25} - 1336332 q^{26} - 500496 q^{30} + 1934850 q^{32} - 6557404 q^{33} + 3519864 q^{35} - 30244102 q^{36} + 28748136 q^{38} + 11901296 q^{42} - 10004616 q^{43} - 112552440 q^{47} - 121354720 q^{49} - 164889018 q^{50} - 59093180 q^{52} - 76804272 q^{53} + 300732568 q^{55} - 11618904 q^{59} - 101609232 q^{60} - 260062974 q^{64} - 18429632 q^{66} - 304208752 q^{67} - 211308236 q^{69} - 460311456 q^{70} + 493218954 q^{72} - 416024248 q^{76} - 138357828 q^{77} - 363335792 q^{81} + 845042136 q^{83} + 958037984 q^{84} + 127952904 q^{86} - 610860648 q^{87} - 938223804 q^{89} - 1635779524 q^{93} + 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) $ 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9 - 63204 * q^13 + 243480 * q^15 + 38978 * q^16 + 547706 * q^18 - 1110672 * q^19 - 172580 * q^21 + 4441796 * q^25 - 1336332 * q^26 - 500496 * q^30 + 1934850 * q^32 - 6557404 * q^33 + 3519864 * q^35 - 30244102 * q^36 + 28748136 * q^38 + 11901296 * q^42 - 10004616 * q^43 - 112552440 * q^47 - 121354720 * q^49 - 164889018 * q^50 - 59093180 * q^52 - 76804272 * q^53 + 300732568 * q^55 - 11618904 * q^59 - 101609232 * q^60 - 260062974 * q^64 - 18429632 * q^66 - 304208752 * q^67 - 211308236 * q^69 - 460311456 * q^70 + 493218954 * q^72 - 416024248 * q^76 - 138357828 * q^77 - 363335792 * q^81 + 845042136 * q^83 + 958037984 * q^84 + 127952904 * q^86 - 610860648 * q^87 - 938223804 * q^89 - 1635779524 * q^93 + 238629952 * q^94 - 152046078 * q^98

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 $

$2$	16.7531	0.740388	0.370194	−	0.928954i	$-0.379291\pi$
$2$	16.7531	0.740388	0.370194	+	0.928954i	$0.379291\pi$
$3$	206.667	1.47308	0.736538	−	0.676396i	$-0.236459\pi$
$3$	206.667	1.47308	0.736538	+	0.676396i	$0.236459\pi$
$4$	−231.335	−0.451825
$5$	1946.29	1.39265	0.696326	−	0.717726i	$-0.254817\pi$
$5$	1946.29	1.39265	0.696326	+	0.717726i	$0.254817\pi$
$6$	3462.30	1.09065
$7$	−1633.30	−0.257114	−0.128557	−	0.991702i	$-0.541034\pi$
$7$	−1633.30	−0.257114	−0.128557	+	0.991702i	$0.541034\pi$
$8$	−12453.1	−1.07491
$9$	23028.2	1.16995
$10$	32606.3	1.03110
$11$	11623.3	0.239365	0.119683	−	0.992812i	$-0.461812\pi$
$11$	11623.3	0.239365	0.119683	+	0.992812i	$0.461812\pi$
$12$	−47809.2	−0.665573
$13$	−163541.	−1.58811	−0.794057	−	0.607844i	$-0.792035\pi$
$13$	−163541.	−1.58811	−0.794057	+	0.607844i	$0.792035\pi$
$14$	−27362.8	−0.190364
$15$	402234.	2.05148
$16$	−90185.0	−0.344028
$17$	0	0
$17$	0	0
$18$	385793.	0.866219
$19$	−673499.	−1.18562	−0.592810	−	0.805342i	$-0.701981\pi$
$19$	−673499.	−1.18562	−0.592810	+	0.805342i	$0.701981\pi$
$20$	−450244.	−0.629236
$21$	−337549.	−0.378748
$22$	194725.	0.177223
$23$	−1.37499e6	−1.02453	−0.512264	−	0.858828i	$-0.671193\pi$
$23$	−1.37499e6	−1.02453	−0.512264	+	0.858828i	$0.671193\pi$
$24$	−2.57365e6	−1.58343
$25$	1.83492e6	0.939480
$26$	−2.73981e6	−1.17582
$27$	691336.	0.250353
$28$	377839.	0.116171
$29$	−4.32926e6	−1.13664	−0.568320	−	0.822808i	$-0.692406\pi$
$29$	−4.32926e6	−1.13664	−0.568320	+	0.822808i	$0.692406\pi$
$30$	6.73865e6	1.51889
$31$	3.45219e6	0.671378	0.335689	−	0.941973i	$-0.391031\pi$
$31$	3.45219e6	0.671378	0.335689	+	0.941973i	$0.391031\pi$
$32$	4.86513e6	0.820200
$33$	2.40214e6	0.352603
$34$	0	0
$35$	−3.17888e6	−0.358070
$36$	−5.32721e6	−0.528614
$37$	−5.81427e6	−0.510020	−0.255010	−	0.966938i	$-0.582079\pi$
$37$	−5.81427e6	−0.510020	−0.255010	+	0.966938i	$0.582079\pi$
$38$	−1.12832e7	−0.877819
$39$	−3.37985e7	−2.33941
$40$	−2.42374e7	−1.49698
$41$	−2.37653e7	−1.31346	−0.656729	−	0.754127i	$-0.728060\pi$
$41$	−2.37653e7	−1.31346	−0.656729	+	0.754127i	$0.728060\pi$
$42$	−5.65499e6	−0.280421
$43$	2.46177e7	1.09810	0.549048	−	0.835791i	$-0.314990\pi$
$43$	2.46177e7	1.09810	0.549048	+	0.835791i	$0.314990\pi$
$44$	−2.68886e6	−0.108151
$45$	4.48195e7	1.62934
$46$	−2.30353e7	−0.758549
$47$	−3.94057e7	−1.17793	−0.588963	−	0.808160i	$-0.700464\pi$
$47$	−3.94057e7	−1.17793	−0.588963	+	0.808160i	$0.700464\pi$
$48$	−1.86382e7	−0.506780
$49$	−3.76859e7	−0.933893
$50$	3.07406e7	0.695580
$51$	0	0
$52$	3.78327e7	0.717550
$53$	9.66929e7	1.68327	0.841634	−	0.540048i	$-0.181594\pi$
$53$	9.66929e7	1.68327	0.841634	+	0.540048i	$0.181594\pi$
$54$	1.15820e7	0.185358
$55$	2.26222e7	0.333352
$56$	2.03397e7	0.276375
$57$	−1.39190e8	−1.74651
$58$	−7.25285e7	−0.841555
$59$	−2.37253e7	−0.254905	−0.127453	−	0.991845i	$-0.540680\pi$
$59$	−2.37253e7	−0.254905	−0.127453	+	0.991845i	$0.540680\pi$
$60$	−9.30506e7	−0.926912
$61$	−4.31637e7	−0.399149	−0.199574	−	0.979883i	$-0.563956\pi$
$61$	−4.31637e7	−0.399149	−0.199574	+	0.979883i	$0.563956\pi$
$62$	5.78348e7	0.497080
$63$	−3.76120e7	−0.300811
$64$	1.27681e8	0.951295
$65$	−3.18298e8	−2.21169
$66$	4.02432e7	0.261063
$67$	3.50040e7	0.212217	0.106109	−	0.994355i	$-0.466161\pi$
$67$	3.50040e7	0.212217	0.106109	+	0.994355i	$0.466161\pi$
$68$	0	0
$69$	−2.84165e8	−1.50921
$70$	−5.32560e7	−0.265111
$71$	−2.90407e8	−1.35626	−0.678132	−	0.734940i	$-0.737210\pi$
$71$	−2.90407e8	−1.35626	−0.678132	+	0.734940i	$0.737210\pi$
$72$	−2.86773e8	−1.25760
$73$	4.29259e8	1.76916	0.884578	−	0.466392i	$-0.154446\pi$
$73$	4.29259e8	1.76916	0.884578	+	0.466392i	$0.154446\pi$
$74$	−9.74069e7	−0.377613
$75$	3.79217e8	1.38392
$76$	1.55804e8	0.535693
$77$	−1.89843e7	−0.0615440
$78$	−5.66229e8	−1.73207
$79$	3.78639e8	1.09371	0.546856	−	0.837226i	$-0.315824\pi$
$79$	3.78639e8	1.09371	0.546856	+	0.837226i	$0.315824\pi$
$80$	−1.75526e8	−0.479112
$81$	−3.10387e8	−0.801164
$82$	−3.98142e8	−0.972468
$83$	−9.91655e7	−0.229355	−0.114678	−	0.993403i	$-0.536584\pi$
$83$	−9.91655e7	−0.229355	−0.114678	+	0.993403i	$0.536584\pi$
$84$	7.80868e7	0.171128
$85$	0	0
$86$	4.12423e8	0.813017
$87$	−8.94715e8	−1.67436
$88$	−1.44746e8	−0.257297
$89$	−5.39631e8	−0.911679	−0.455840	−	0.890062i	$-0.650661\pi$
$89$	−5.39631e8	−0.911679	−0.455840	+	0.890062i	$0.650661\pi$
$90$	7.50864e8	1.20634
$91$	2.67112e8	0.408326
$92$	3.18083e8	0.462908
$93$	7.13453e8	0.988991
$94$	−6.60166e8	−0.872123
$95$	−1.31082e9	−1.65116
$96$	1.00546e9	1.20822
$97$	1.21632e9	1.39500	0.697502	−	0.716582i	$-0.254295\pi$
$97$	1.21632e9	1.39500	0.697502	+	0.716582i	$0.254295\pi$
$98$	−6.31355e8	−0.691443
$99$	2.67662e8	0.280046
$100$	−4.24481e8	−0.424481
$101$	1.24853e9	1.19386	0.596928	−	0.802295i	$-0.296388\pi$
$101$	1.24853e9	1.19386	0.596928	+	0.802295i	$0.296388\pi$
$102$	0	0
$103$	5.96498e7	0.0522206	0.0261103	−	0.999659i	$-0.491688\pi$
$103$	5.96498e7	0.0522206	0.0261103	+	0.999659i	$0.491688\pi$
$104$	2.03660e9	1.70709
$105$	−6.56969e8	−0.527464
$106$	1.61990e9	1.24627
$107$	−1.08084e9	−0.797143	−0.398572	−	0.917137i	$-0.630494\pi$
$107$	−1.08084e9	−0.797143	−0.398572	+	0.917137i	$0.630494\pi$
$108$	−1.59930e8	−0.113116
$109$	−1.42610e9	−0.967678	−0.483839	−	0.875157i	$-0.660758\pi$
$109$	−1.42610e9	−0.967678	−0.483839	+	0.875157i	$0.660758\pi$
$110$	3.78992e8	0.246810
$111$	−1.20162e9	−0.751299
$112$	1.47299e8	0.0884544
$113$	4.16774e8	0.240463	0.120231	−	0.992746i	$-0.461636\pi$
$113$	4.16774e8	0.240463	0.120231	+	0.992746i	$0.461636\pi$
$114$	−2.33186e9	−1.29309
$115$	−2.67613e9	−1.42681
$116$	1.00151e9	0.513563
$117$	−3.76605e9	−1.85802
$118$	−3.97472e8	−0.188729
$119$	0	0
$120$	−5.00907e9	−2.20517
$121$	−2.22285e9	−0.942704
$122$	−7.23125e8	−0.295525
$123$	−4.91150e9	−1.93482
$124$	−7.98611e8	−0.303346
$125$	−2.30059e8	−0.0842839
$126$	−6.30116e8	−0.222717
$127$	−3.27631e8	−0.111755	−0.0558777	−	0.998438i	$-0.517796\pi$
$127$	−3.27631e8	−0.111755	−0.0558777	+	0.998438i	$0.517796\pi$
$128$	−3.51905e8	−0.115873
$129$	5.08767e9	1.61758
$130$	−5.33247e9	−1.63751
$131$	3.69810e8	0.109713	0.0548565	−	0.998494i	$-0.482530\pi$
$131$	3.69810e8	0.109713	0.0548565	+	0.998494i	$0.482530\pi$
$132$	−5.55698e8	−0.159315
$133$	1.10003e9	0.304839
$134$	5.86424e8	0.157123
$135$	1.34554e9	0.348654
$136$	0	0
$137$	1.59553e9	0.386957	0.193478	−	0.981105i	$-0.438023\pi$
$137$	1.59553e9	0.386957	0.193478	+	0.981105i	$0.438023\pi$
$138$	−4.76063e9	−1.11740
$139$	6.26171e9	1.42274	0.711371	−	0.702817i	$-0.248075\pi$
$139$	6.26171e9	1.42274	0.711371	+	0.702817i	$0.248075\pi$
$140$	7.35385e8	0.161785
$141$	−8.14384e9	−1.73518
$142$	−4.86521e9	−1.00416
$143$	−1.90088e9	−0.380139
$144$	−2.07679e9	−0.402497
$145$	−8.42600e9	−1.58294
$146$	7.19140e9	1.30986
$147$	−7.78843e9	−1.37569
$148$	1.34504e9	0.230440
$149$	−6.90664e9	−1.14796	−0.573982	−	0.818868i	$-0.694602\pi$
$149$	−6.90664e9	−1.14796	−0.573982	+	0.818868i	$0.694602\pi$
$150$	6.35305e9	1.02464
$151$	8.82900e9	1.38202	0.691012	−	0.722843i	$-0.257165\pi$
$151$	8.82900e9	1.38202	0.691012	+	0.722843i	$0.257165\pi$
$152$	8.38717e9	1.27444
$153$	0	0
$154$	−3.18045e8	−0.0455665
$155$	6.71897e9	0.934996
$156$	7.81876e9	1.05701
$157$	6.94492e8	0.0912261	0.0456130	−	0.998959i	$-0.485476\pi$
$157$	6.94492e8	0.0912261	0.0456130	+	0.998959i	$0.485476\pi$
$158$	6.34336e9	0.809772
$159$	1.99832e10	2.47958
$160$	9.46896e9	1.14225
$161$	2.24577e9	0.263420
$162$	−5.19994e9	−0.593172
$163$	1.05314e10	1.16854	0.584270	−	0.811559i	$-0.301381\pi$
$163$	1.05314e10	1.16854	0.584270	+	0.811559i	$0.301381\pi$
$164$	5.49774e9	0.593454
$165$	4.67526e9	0.491053
$166$	−1.66133e9	−0.169812
$167$	−1.06743e10	−1.06198	−0.530990	−	0.847378i	$-0.678180\pi$
$167$	−1.06743e10	−1.06198	−0.530990	+	0.847378i	$0.678180\pi$
$168$	4.20355e9	0.407122
$169$	1.61412e10	1.52210
$170$	0	0
$171$	−1.55094e10	−1.38712
$172$	−5.69494e9	−0.496148
$173$	5.38138e9	0.456758	0.228379	−	0.973572i	$-0.426657\pi$
$173$	5.38138e9	0.456758	0.228379	+	0.973572i	$0.426657\pi$
$174$	−1.49892e10	−1.23967
$175$	−2.99698e9	−0.241553
$176$	−1.04824e9	−0.0823484
$177$	−4.90324e9	−0.375494
$178$	−9.04048e9	−0.674996
$179$	1.10785e10	0.806573	0.403286	−	0.915074i	$-0.367868\pi$
$179$	1.10785e10	0.806573	0.403286	+	0.915074i	$0.367868\pi$
$180$	−1.03683e10	−0.736176
$181$	−1.10717e10	−0.766761	−0.383380	−	0.923591i	$-0.625240\pi$
$181$	−1.10717e10	−0.766761	−0.383380	+	0.923591i	$0.625240\pi$
$182$	4.47494e9	0.302320
$183$	−8.92051e9	−0.587976
$184$	1.71229e10	1.10128
$185$	−1.13163e10	−0.710281
$186$	1.19525e10	0.732237
$187$	0	0
$188$	9.11589e9	0.532217
$189$	−1.12916e9	−0.0643691
$190$	−2.19603e10	−1.22250
$191$	1.39536e10	0.758642	0.379321	−	0.925265i	$-0.376158\pi$
$191$	1.39536e10	0.758642	0.379321	+	0.925265i	$0.376158\pi$
$192$	2.63873e10	1.40133
$193$	4.25693e9	0.220845	0.110423	−	0.993885i	$-0.464780\pi$
$193$	4.25693e9	0.220845	0.110423	+	0.993885i	$0.464780\pi$
$194$	2.03771e10	1.03285
$195$	−6.57817e10	−3.25799
$196$	8.71806e9	0.421956
$197$	−3.75774e10	−1.77758	−0.888789	−	0.458317i	$-0.848452\pi$
$197$	−3.75774e10	−1.77758	−0.888789	+	0.458317i	$0.848452\pi$
$198$	4.48417e9	0.207342
$199$	−8.68102e9	−0.392403	−0.196201	−	0.980564i	$-0.562861\pi$
$199$	−8.68102e9	−0.392403	−0.196201	+	0.980564i	$0.562861\pi$
$200$	−2.28505e10	−1.00986
$201$	7.23416e9	0.312612
$202$	2.09167e10	0.883916
$203$	7.07099e9	0.292246
$204$	0	0
$205$	−4.62542e10	−1.82919
$206$	9.99318e8	0.0386635
$207$	−3.16635e10	−1.19865
$208$	1.47489e10	0.546356
$209$	−7.82825e9	−0.283796
$210$	−1.10062e10	−0.390528
$211$	−3.93859e10	−1.36795	−0.683974	−	0.729507i	$-0.739750\pi$
$211$	−3.93859e10	−1.36795	−0.683974	+	0.729507i	$0.739750\pi$
$212$	−2.23684e10	−0.760543
$213$	−6.00175e10	−1.99788
$214$	−1.81075e10	−0.590195
$215$	4.79133e10	1.52927
$216$	−8.60930e9	−0.269108
$217$	−5.63847e9	−0.172621
$218$	−2.38916e10	−0.716457
$219$	8.87135e10	2.60610
$220$	−5.23330e9	−0.150617
$221$	0	0
$222$	−2.01308e10	−0.556253
$223$	−2.60341e9	−0.0704971	−0.0352486	−	0.999379i	$-0.511222\pi$
$223$	−2.60341e9	−0.0704971	−0.0352486	+	0.999379i	$0.511222\pi$
$224$	−7.94623e9	−0.210885
$225$	4.22549e10	1.09915
$226$	6.98225e9	0.178036
$227$	−6.62728e10	−1.65660	−0.828302	−	0.560282i	$-0.810693\pi$
$227$	−6.62728e10	−1.65660	−0.828302	+	0.560282i	$0.810693\pi$
$228$	3.21994e10	0.789117
$229$	1.37362e10	0.330071	0.165036	−	0.986288i	$-0.447226\pi$
$229$	1.37362e10	0.330071	0.165036	+	0.986288i	$0.447226\pi$
$230$	−4.48334e10	−1.05639
$231$	−3.92342e9	−0.0906590
$232$	5.39129e10	1.22179
$233$	8.93389e9	0.198582	0.0992908	−	0.995058i	$-0.468343\pi$
$233$	8.93389e9	0.198582	0.0992908	+	0.995058i	$0.468343\pi$
$234$	−6.30929e10	−1.37565
$235$	−7.66948e10	−1.64044
$236$	5.48849e9	0.115173
$237$	7.82521e10	1.61112
$238$	0	0
$239$	1.31552e10	0.260800	0.130400	−	0.991461i	$-0.458374\pi$
$239$	1.31552e10	0.260800	0.130400	+	0.991461i	$0.458374\pi$
$240$	−3.62754e10	−0.705768
$241$	−3.35182e9	−0.0640036	−0.0320018	−	0.999488i	$-0.510188\pi$
$241$	−3.35182e9	−0.0640036	−0.0320018	+	0.999488i	$0.510188\pi$
$242$	−3.72395e10	−0.697967
$243$	−7.77543e10	−1.43053
$244$	9.98526e9	0.180346
$245$	−7.33478e10	−1.30059
$246$	−8.22827e10	−1.43252
$247$	1.10145e11	1.88290
$248$	−4.29906e10	−0.721674
$249$	−2.04942e10	−0.337858
$250$	−3.85420e9	−0.0624028
$251$	−1.16052e9	−0.0184553	−0.00922766	−	0.999957i	$-0.502937\pi$
$251$	−1.16052e9	−0.0184553	−0.00922766	+	0.999957i	$0.502937\pi$
$252$	8.70095e9	0.135914
$253$	−1.59819e10	−0.245236
$254$	−5.48883e9	−0.0827424
$255$	0	0
$256$	−7.12680e10	−1.03709
$257$	−1.16697e11	−1.66864	−0.834319	−	0.551282i	$-0.814139\pi$
$257$	−1.16697e11	−1.66864	−0.834319	+	0.551282i	$0.814139\pi$
$258$	8.52341e10	1.19764
$259$	9.49646e9	0.131133
$260$	7.36334e10	0.999298
$261$	−9.96950e10	−1.32981
$262$	6.19546e9	0.0812302
$263$	−1.29675e11	−1.67130	−0.835652	−	0.549259i	$-0.814910\pi$
$263$	−1.29675e11	−1.67130	−0.835652	+	0.549259i	$0.814910\pi$
$264$	−2.99142e10	−0.379018
$265$	1.88193e11	2.34421
$266$	1.84288e10	0.225699
$267$	−1.11524e11	−1.34297
$268$	−8.09763e9	−0.0958852
$269$	−4.33626e10	−0.504928	−0.252464	−	0.967606i	$-0.581241\pi$
$269$	−4.33626e10	−0.504928	−0.252464	+	0.967606i	$0.581241\pi$
$270$	2.25419e10	0.258139
$271$	1.14864e11	1.29367	0.646834	−	0.762631i	$-0.276093\pi$
$271$	1.14864e11	1.29367	0.646834	+	0.762631i	$0.276093\pi$
$272$	0	0
$273$	5.52032e10	0.601495
$274$	2.67300e10	0.286498
$275$	2.13278e10	0.224879
$276$	6.57371e10	0.681899
$277$	9.76316e10	0.996395	0.498197	−	0.867064i	$-0.333996\pi$
$277$	9.76316e10	0.996395	0.498197	+	0.867064i	$0.333996\pi$
$278$	1.04903e11	1.05338
$279$	7.94977e10	0.785481
$280$	3.95870e10	0.384895
$281$	−1.09933e11	−1.05184	−0.525921	−	0.850534i	$-0.676279\pi$
$281$	−1.09933e11	−1.05184	−0.525921	+	0.850534i	$0.676279\pi$
$282$	−1.36434e11	−1.28470
$283$	−1.55506e11	−1.44115	−0.720574	−	0.693378i	$-0.756122\pi$
$283$	−1.55506e11	−1.44115	−0.720574	+	0.693378i	$0.756122\pi$
$284$	6.71812e10	0.612795
$285$	−2.70904e11	−2.43228
$286$	−3.18456e10	−0.281450
$287$	3.88159e10	0.337708
$288$	1.12035e11	0.959595
$289$	0	0
$290$	−1.41161e11	−1.17199
$291$	2.51373e11	2.05495
$292$	−9.93024e10	−0.799350
$293$	−1.34231e11	−1.06402	−0.532010	−	0.846738i	$-0.678563\pi$
$293$	−1.34231e11	−1.06402	−0.532010	+	0.846738i	$0.678563\pi$
$294$	−1.30480e11	−1.01855
$295$	−4.61764e10	−0.354994
$296$	7.24059e10	0.548228
$297$	8.03557e9	0.0599257
$298$	−1.15707e11	−0.849939
$299$	2.24867e11	1.62707
$300$	−8.77261e10	−0.625292
$301$	−4.02082e10	−0.282336
$302$	1.47913e11	1.02323
$303$	2.58029e11	1.75864
$304$	6.07394e10	0.407887
$305$	−8.40091e10	−0.555875
$306$	0	0
$307$	−1.61753e11	−1.03927	−0.519637	−	0.854387i	$-0.673933\pi$
$307$	−1.61753e11	−1.03927	−0.519637	+	0.854387i	$0.673933\pi$
$308$	4.39172e9	0.0278072
$309$	1.23276e10	0.0769249
$310$	1.12563e11	0.692260
$311$	−8.13115e10	−0.492867	−0.246434	−	0.969160i	$-0.579259\pi$
$311$	−8.13115e10	−0.492867	−0.246434	+	0.969160i	$0.579259\pi$
$312$	4.20897e11	2.51467
$313$	−1.35663e11	−0.798935	−0.399467	−	0.916747i	$-0.630805\pi$
$313$	−1.35663e11	−0.798935	−0.399467	+	0.916747i	$0.630805\pi$
$314$	1.16349e10	0.0675427
$315$	−7.32038e10	−0.418925
$316$	−8.75923e10	−0.494167
$317$	1.13377e11	0.630604	0.315302	−	0.948991i	$-0.397894\pi$
$317$	1.13377e11	0.630604	0.315302	+	0.948991i	$0.397894\pi$
$318$	3.34780e11	1.83585
$319$	−5.03201e10	−0.272072
$320$	2.48504e11	1.32482
$321$	−2.23375e11	−1.17425
$322$	3.76236e10	0.195033
$323$	0	0
$324$	7.18033e10	0.361986
$325$	−3.00085e11	−1.49200
$326$	1.76434e11	0.865173
$327$	−2.94728e11	−1.42546
$328$	2.95953e11	1.41185
$329$	6.43613e10	0.302861
$330$	7.83250e10	0.363570
$331$	−1.63912e11	−0.750557	−0.375279	−	0.926912i	$-0.622453\pi$
$331$	−1.63912e11	−0.750557	−0.375279	+	0.926912i	$0.622453\pi$
$332$	2.29404e10	0.103629
$333$	−1.33892e11	−0.596699
$334$	−1.78828e11	−0.786277
$335$	6.81279e10	0.295545
$336$	3.04419e10	0.130300
$337$	1.21263e11	0.512146	0.256073	−	0.966657i	$-0.417571\pi$
$337$	1.21263e11	0.512146	0.256073	+	0.966657i	$0.417571\pi$
$338$	2.70414e11	1.12695
$339$	8.61334e10	0.354220
$340$	0	0
$341$	4.01257e10	0.160704
$342$	−2.59831e11	−1.02701
$343$	1.27462e11	0.497230
$344$	−3.06568e11	−1.18036
$345$	−5.53067e11	−2.10180
$346$	9.01547e10	0.338178
$347$	9.25071e10	0.342525	0.171263	−	0.985225i	$-0.445215\pi$
$347$	9.25071e10	0.342525	0.171263	+	0.985225i	$0.445215\pi$
$348$	2.06979e11	0.756517
$349$	1.54729e11	0.558285	0.279143	−	0.960250i	$-0.409950\pi$
$349$	1.54729e11	0.558285	0.279143	+	0.960250i	$0.409950\pi$
$350$	−5.02086e10	−0.178843
$351$	−1.13062e11	−0.397588
$352$	5.65487e10	0.196327
$353$	−7.41434e9	−0.0254148	−0.0127074	−	0.999919i	$-0.504045\pi$
$353$	−7.41434e9	−0.0254148	−0.0127074	+	0.999919i	$0.504045\pi$
$354$	−8.21443e10	−0.278012
$355$	−5.65216e11	−1.88881
$356$	1.24835e11	0.411920
$357$	0	0
$358$	1.85599e11	0.597177
$359$	3.11894e11	0.991019	0.495509	−	0.868603i	$-0.334981\pi$
$359$	3.11894e11	0.991019	0.495509	+	0.868603i	$0.334981\pi$
$360$	−5.58143e11	−1.75140
$361$	1.30913e11	0.405694
$362$	−1.85485e11	−0.567701
$363$	−4.59389e11	−1.38868
$364$	−6.17922e10	−0.184492
$365$	8.35462e11	2.46382
$366$	−1.49446e11	−0.435331
$367$	3.42287e11	0.984902	0.492451	−	0.870340i	$-0.336101\pi$
$367$	3.42287e11	0.984902	0.492451	+	0.870340i	$0.336101\pi$
$368$	1.24003e11	0.352467
$369$	−5.47272e11	−1.53668
$370$	−1.89582e11	−0.525883
$371$	−1.57929e11	−0.432791
$372$	−1.65046e11	−0.446851
$373$	2.39957e11	0.641866	0.320933	−	0.947102i	$-0.396004\pi$
$373$	2.39957e11	0.641866	0.320933	+	0.947102i	$0.396004\pi$
$374$	0	0
$375$	−4.75456e10	−0.124157
$376$	4.90724e11	1.26617
$377$	7.08012e11	1.80511
$378$	−1.89169e10	−0.0476581
$379$	7.31981e11	1.82231	0.911157	−	0.412060i	$-0.135191\pi$
$379$	7.31981e11	1.82231	0.911157	+	0.412060i	$0.135191\pi$
$380$	3.03239e11	0.746034
$381$	−6.77105e10	−0.164624
$382$	2.33766e11	0.561689
$383$	3.51103e10	0.0833758	0.0416879	−	0.999131i	$-0.486726\pi$
$383$	3.51103e10	0.0833758	0.0416879	+	0.999131i	$0.486726\pi$
$384$	−7.27271e10	−0.170689
$385$	−3.69489e10	−0.0857094
$386$	7.13166e10	0.163511
$387$	5.66902e11	1.28472
$388$	−2.81377e11	−0.630299
$389$	4.06726e10	0.0900593	0.0450297	−	0.998986i	$-0.485662\pi$
$389$	4.06726e10	0.0900593	0.0450297	+	0.998986i	$0.485662\pi$
$390$	−1.10205e12	−2.41217
$391$	0	0
$392$	4.69308e11	1.00385
$393$	7.64275e10	0.161616
$394$	−6.29537e11	−1.31610
$395$	7.36941e11	1.52316
$396$	−6.19196e10	−0.126532
$397$	−8.82945e11	−1.78392	−0.891962	−	0.452110i	$-0.850672\pi$
$397$	−8.82945e11	−1.78392	−0.891962	+	0.452110i	$0.850672\pi$
$398$	−1.45434e11	−0.290530
$399$	2.27339e11	0.449051
$400$	−1.65482e11	−0.323208
$401$	5.06461e11	0.978130	0.489065	−	0.872247i	$-0.337338\pi$
$401$	5.06461e11	0.978130	0.489065	+	0.872247i	$0.337338\pi$
$402$	1.21194e11	0.231454
$403$	−5.64575e11	−1.06622
$404$	−2.88827e11	−0.539414
$405$	−6.04104e11	−1.11574
$406$	1.18461e11	0.216375
$407$	−6.75807e10	−0.122081
$408$	0	0
$409$	5.97268e11	1.05539	0.527697	−	0.849433i	$-0.323056\pi$
$409$	5.97268e11	1.05539	0.527697	+	0.849433i	$0.323056\pi$
$410$	−7.74900e11	−1.35431
$411$	3.29743e11	0.570016
$412$	−1.37991e10	−0.0235946
$413$	3.87506e10	0.0655396
$414$	−5.30461e11	−0.887466
$415$	−1.93005e11	−0.319412
$416$	−7.95648e11	−1.30257
$417$	1.29409e12	2.09581
$418$	−1.31147e11	−0.210119
$419$	6.76816e11	1.07277	0.536386	−	0.843972i	$-0.319789\pi$
$419$	6.76816e11	1.07277	0.536386	+	0.843972i	$0.319789\pi$
$420$	1.51980e11	0.238322
$421$	4.95533e11	0.768782	0.384391	−	0.923170i	$-0.374411\pi$
$421$	4.95533e11	0.768782	0.384391	+	0.923170i	$0.374411\pi$
$422$	−6.59834e11	−1.01281
$423$	−9.07440e11	−1.37812
$424$	−1.20413e12	−1.80937
$425$	0	0
$426$	−1.00548e12	−1.47921
$427$	7.04994e10	0.102627
$428$	2.50037e11	0.360169
$429$	−3.92849e11	−0.559973
$430$	8.02695e11	1.13225
$431$	1.02852e11	0.143571	0.0717854	−	0.997420i	$-0.477130\pi$
$431$	1.02852e11	0.143571	0.0717854	+	0.997420i	$0.477130\pi$
$432$	−6.23481e10	−0.0861284
$433$	2.70612e10	0.0369957	0.0184978	−	0.999829i	$-0.494112\pi$
$433$	2.70612e10	0.0369957	0.0184978	+	0.999829i	$0.494112\pi$
$434$	−9.44617e10	−0.127806
$435$	−1.74138e12	−2.33180
$436$	3.29906e11	0.437222
$437$	9.26053e11	1.21470
$438$	1.48622e12	1.92953
$439$	−5.59050e11	−0.718390	−0.359195	−	0.933263i	$-0.616949\pi$
$439$	−5.59050e11	−0.718390	−0.359195	+	0.933263i	$0.616949\pi$
$440$	−2.81718e11	−0.358325
$441$	−8.67838e11	−1.09261
$442$	0	0
$443$	4.39616e11	0.542321	0.271161	−	0.962534i	$-0.412593\pi$
$443$	4.39616e11	0.542321	0.271161	+	0.962534i	$0.412593\pi$
$444$	2.77976e11	0.339456
$445$	−1.05028e12	−1.26965
$446$	−4.36152e10	−0.0521952
$447$	−1.42737e12	−1.69104
$448$	−2.08541e11	−0.244591
$449$	3.20262e11	0.371874	0.185937	−	0.982562i	$-0.440468\pi$
$449$	3.20262e11	0.371874	0.185937	+	0.982562i	$0.440468\pi$
$450$	7.07899e11	0.813795
$451$	−2.76230e11	−0.314396
$452$	−9.64143e10	−0.108647
$453$	1.82466e12	2.03583
$454$	−1.11027e12	−1.22653
$455$	5.19877e11	0.568656
$456$	1.73335e12	1.87735
$457$	1.12742e12	1.20910	0.604550	−	0.796567i	$-0.293353\pi$
$457$	1.12742e12	1.20910	0.604550	+	0.796567i	$0.293353\pi$
$458$	2.30124e11	0.244381
$459$	0	0
$460$	6.19081e11	0.644670
$461$	1.06579e12	1.09905	0.549523	−	0.835478i	$-0.314809\pi$
$461$	1.06579e12	1.09905	0.549523	+	0.835478i	$0.314809\pi$
$462$	−6.57294e10	−0.0671229
$463$	2.47213e11	0.250010	0.125005	−	0.992156i	$-0.460105\pi$
$463$	2.47213e11	0.250010	0.125005	+	0.992156i	$0.460105\pi$
$464$	3.90434e11	0.391036
$465$	1.38859e12	1.37732
$466$	1.49670e11	0.147027
$467$	1.64486e12	1.60030	0.800151	−	0.599799i	$-0.204753\pi$
$467$	1.64486e12	1.60030	0.800151	+	0.599799i	$0.204753\pi$
$468$	8.71218e11	0.839499
$469$	−5.71721e10	−0.0545640
$470$	−1.28487e12	−1.21456
$471$	1.43528e11	0.134383
$472$	2.95455e11	0.274001
$473$	2.86138e11	0.262846
$474$	1.31096e12	1.19286
$475$	−1.23582e12	−1.11387
$476$	0	0
$477$	2.22666e12	1.96934
$478$	2.20390e11	0.193093
$479$	−5.67060e11	−0.492175	−0.246087	−	0.969248i	$-0.579145\pi$
$479$	−5.67060e11	−0.492175	−0.246087	+	0.969248i	$0.579145\pi$
$480$	1.95692e12	1.68263
$481$	9.50872e11	0.809970
$482$	−5.61533e10	−0.0473875
$483$	4.64127e11	0.388038
$484$	5.14222e11	0.425938
$485$	2.36732e12	1.94276
$486$	−1.30262e12	−1.05915
$487$	−2.01812e12	−1.62580	−0.812901	−	0.582402i	$-0.802113\pi$
$487$	−2.01812e12	−1.62580	−0.812901	+	0.582402i	$0.802113\pi$
$488$	5.37524e11	0.429051
$489$	2.17650e12	1.72135
$490$	−1.22880e12	−0.962939
$491$	−1.15865e12	−0.899672	−0.449836	−	0.893111i	$-0.648518\pi$
$491$	−1.15865e12	−0.899672	−0.449836	+	0.893111i	$0.648518\pi$
$492$	1.13620e12	0.874202
$493$	0	0
$494$	1.84526e12	1.39408
$495$	5.20949e11	0.390006
$496$	−3.11336e11	−0.230973
$497$	4.74322e11	0.348714
$498$	−3.43341e11	−0.250146
$499$	2.89972e11	0.209365	0.104682	−	0.994506i	$-0.466617\pi$
$499$	2.89972e11	0.209365	0.104682	+	0.994506i	$0.466617\pi$
$500$	5.32206e10	0.0380816
$501$	−2.20603e12	−1.56438
$502$	−1.94423e10	−0.0136641
$503$	−3.27029e11	−0.227788	−0.113894	−	0.993493i	$-0.536332\pi$
$503$	−3.27029e11	−0.227788	−0.113894	+	0.993493i	$0.536332\pi$
$504$	4.68387e11	0.323346
$505$	2.43000e12	1.66262
$506$	−2.67745e11	−0.181570
$507$	3.33584e12	2.24218
$508$	7.57924e10	0.0504939
$509$	5.42106e11	0.357976	0.178988	−	0.983851i	$-0.442718\pi$
$509$	5.42106e11	0.357976	0.178988	+	0.983851i	$0.442718\pi$
$510$	0	0
$511$	−7.01109e11	−0.454875
$512$	−1.01378e12	−0.651973
$513$	−4.65614e11	−0.296823
$514$	−1.95504e12	−1.23544
$515$	1.16096e11	0.0727251
$516$	−1.17695e12	−0.730863
$517$	−4.58022e11	−0.281954
$518$	1.59095e11	0.0970895
$519$	1.11215e12	0.672839
$520$	3.96381e12	2.37738
$521$	−7.31594e11	−0.435011	−0.217506	−	0.976059i	$-0.569792\pi$
$521$	−7.31594e11	−0.435011	−0.217506	+	0.976059i	$0.569792\pi$
$522$	−1.67020e12	−0.984579
$523$	−6.27765e11	−0.366893	−0.183447	−	0.983030i	$-0.558725\pi$
$523$	−6.27765e11	−0.366893	−0.183447	+	0.983030i	$0.558725\pi$
$524$	−8.55499e10	−0.0495711
$525$	−6.19376e11	−0.355826
$526$	−2.17245e12	−1.23741
$527$	0	0
$528$	−2.16637e11	−0.121305
$529$	8.94434e10	0.0496590
$530$	3.15280e12	1.73562
$531$	−5.46351e11	−0.298227
$532$	−2.54474e11	−0.137734
$533$	3.88660e12	2.08592
$534$	−1.86837e12	−0.994321
$535$	−2.10364e12	−1.11014
$536$	−4.35909e11	−0.228115
$537$	2.28957e12	1.18814
$538$	−7.26456e11	−0.373843
$539$	−4.38033e11	−0.223541
$540$	−3.11270e11	−0.157531
$541$	−9.88955e11	−0.496351	−0.248176	−	0.968715i	$-0.579831\pi$
$541$	−9.88955e11	−0.496351	−0.248176	+	0.968715i	$0.579831\pi$
$542$	1.92433e12	0.957816
$543$	−2.28815e12	−1.12950
$544$	0	0
$545$	−2.77561e12	−1.34764
$546$	9.24822e11	0.445340
$547$	1.80571e12	0.862394	0.431197	−	0.902258i	$-0.358091\pi$
$547$	1.80571e12	0.862394	0.431197	+	0.902258i	$0.358091\pi$
$548$	−3.69101e11	−0.174837
$549$	−9.93982e11	−0.466985
$550$	3.57305e11	0.166497
$551$	2.91575e12	1.34762
$552$	3.53874e12	1.62227
$553$	−6.18432e11	−0.281209
$554$	1.63563e12	0.737719
$555$	−2.33869e12	−1.04630
$556$	−1.44855e12	−0.642831
$557$	3.45273e12	1.51990	0.759949	−	0.649982i	$-0.225224\pi$
$557$	3.45273e12	1.51990	0.759949	+	0.649982i	$0.225224\pi$
$558$	1.33183e12	0.581560
$559$	−4.02601e12	−1.74390
$560$	2.86687e11	0.123186
$561$	0	0
$562$	−1.84172e12	−0.778771
$563$	−6.22962e11	−0.261321	−0.130660	−	0.991427i	$-0.541710\pi$
$563$	−6.22962e11	−0.261321	−0.130660	+	0.991427i	$0.541710\pi$
$564$	1.88395e12	0.783996
$565$	8.11163e11	0.334881
$566$	−2.60521e12	−1.06701
$567$	5.06956e11	0.205990
$568$	3.61648e12	1.45787
$569$	6.19292e11	0.247680	0.123840	−	0.992302i	$-0.460479\pi$
$569$	6.19292e11	0.247680	0.123840	+	0.992302i	$0.460479\pi$
$570$	−4.53847e12	−1.80083
$571$	7.93244e11	0.312280	0.156140	−	0.987735i	$-0.450095\pi$
$571$	7.93244e11	0.312280	0.156140	+	0.987735i	$0.450095\pi$
$572$	4.39739e11	0.171756
$573$	2.88375e12	1.11754
$574$	6.50286e11	0.250035
$575$	−2.52300e12	−0.962524
$576$	2.94025e12	1.11297
$577$	1.65552e12	0.621790	0.310895	−	0.950444i	$-0.399371\pi$
$577$	1.65552e12	0.621790	0.310895	+	0.950444i	$0.399371\pi$
$578$	0	0
$579$	8.79765e11	0.325322
$580$	1.94923e12	0.715214
$581$	1.61967e11	0.0589704
$582$	4.21128e12	1.52146
$583$	1.12389e12	0.402916
$584$	−5.34562e12	−1.90169
$585$	−7.32983e12	−2.58757
$586$	−2.24879e12	−0.787788
$587$	1.55182e12	0.539473	0.269736	−	0.962934i	$-0.413063\pi$
$587$	1.55182e12	0.539473	0.269736	+	0.962934i	$0.413063\pi$
$588$	1.80173e12	0.621574
$589$	−2.32505e12	−0.795999
$590$	−7.73596e11	−0.262833
$591$	−7.76600e12	−2.61851
$592$	5.24360e11	0.175461
$593$	6.74726e10	0.0224069	0.0112034	−	0.999937i	$-0.496434\pi$
$593$	6.74726e10	0.0224069	0.0112034	+	0.999937i	$0.496434\pi$
$594$	1.34621e11	0.0443682
$595$	0	0
$596$	1.59774e12	0.518680
$597$	−1.79408e12	−0.578039
$598$	3.76722e12	1.20466
$599$	−2.69514e12	−0.855384	−0.427692	−	0.903925i	$-0.640673\pi$
$599$	−2.69514e12	−0.855384	−0.427692	+	0.903925i	$0.640673\pi$
$600$	−4.72245e12	−1.48760
$601$	2.33770e11	0.0730893	0.0365447	−	0.999332i	$-0.488365\pi$
$601$	2.33770e11	0.0730893	0.0365447	+	0.999332i	$0.488365\pi$
$602$	−6.73611e11	−0.209038
$603$	8.06078e11	0.248284
$604$	−2.04245e12	−0.624433
$605$	−4.32631e12	−1.31286
$606$	4.32278e12	1.30208
$607$	−4.93542e12	−1.47562	−0.737811	−	0.675008i	$-0.764140\pi$
$607$	−4.93542e12	−1.47562	−0.737811	+	0.675008i	$0.764140\pi$
$608$	−3.27666e12	−0.972445
$609$	1.46134e12	0.430500
$610$	−1.40741e12	−0.411563
$611$	6.44444e12	1.87068
$612$	0	0
$613$	9.23540e11	0.264170	0.132085	−	0.991238i	$-0.457833\pi$
$613$	9.23540e11	0.264170	0.132085	+	0.991238i	$0.457833\pi$
$614$	−2.70986e12	−0.769467
$615$	−9.55921e12	−2.69453
$616$	2.36414e11	0.0661546
$617$	6.93577e12	1.92669	0.963344	−	0.268268i	$-0.0864513\pi$
$617$	6.93577e12	1.92669	0.963344	+	0.268268i	$0.0864513\pi$
$618$	2.06526e11	0.0569543
$619$	4.16055e12	1.13905	0.569525	−	0.821974i	$-0.307127\pi$
$619$	4.16055e12	1.13905	0.569525	+	0.821974i	$0.307127\pi$
$620$	−1.55433e12	−0.422455
$621$	−9.50579e11	−0.256493
$622$	−1.36222e12	−0.364913
$623$	8.81381e11	0.234405
$624$	3.04812e12	0.804824
$625$	−4.03159e12	−1.05686
$626$	−2.27277e12	−0.591522
$627$	−1.61784e12	−0.418053
$628$	−1.60660e11	−0.0412183
$629$	0	0
$630$	−1.22639e12	−0.310167
$631$	−6.87945e12	−1.72751	−0.863757	−	0.503909i	$-0.831895\pi$
$631$	−6.87945e12	−1.72751	−0.863757	+	0.503909i	$0.831895\pi$
$632$	−4.71524e12	−1.17565
$633$	−8.13975e12	−2.01509
$634$	1.89941e12	0.466892
$635$	−6.37665e11	−0.155636
$636$	−4.62281e12	−1.12034
$637$	6.16319e12	1.48313
$638$	−8.43017e11	−0.201439
$639$	−6.68754e12	−1.58677
$640$	−6.84909e11	−0.161370
$641$	3.56709e11	0.0834550	0.0417275	−	0.999129i	$-0.486714\pi$
$641$	3.56709e11	0.0834550	0.0417275	+	0.999129i	$0.486714\pi$
$642$	−3.74221e12	−0.869402
$643$	6.44704e11	0.148734	0.0743672	−	0.997231i	$-0.476306\pi$
$643$	6.44704e11	0.148734	0.0743672	+	0.997231i	$0.476306\pi$
$644$	−5.19525e11	−0.119020
$645$	9.90208e12	2.25272
$646$	0	0
$647$	−6.40320e12	−1.43657	−0.718287	−	0.695747i	$-0.755073\pi$
$647$	−6.40320e12	−1.43657	−0.718287	+	0.695747i	$0.755073\pi$
$648$	3.86530e12	0.861183
$649$	−2.75766e11	−0.0610153
$650$	−5.02734e12	−1.10466
$651$	−1.16528e12	−0.254283
$652$	−2.43629e12	−0.527976
$653$	2.26464e12	0.487404	0.243702	−	0.969850i	$-0.421638\pi$
$653$	2.26464e12	0.487404	0.243702	+	0.969850i	$0.421638\pi$
$654$	−4.93759e12	−1.05540
$655$	7.19758e11	0.152792
$656$	2.14327e12	0.451867
$657$	9.88504e12	2.06983
$658$	1.07825e12	0.224235
$659$	5.66256e12	1.16958	0.584788	−	0.811186i	$-0.301178\pi$
$659$	5.66256e12	1.16958	0.584788	+	0.811186i	$0.301178\pi$
$660$	−1.08155e12	−0.221870
$661$	−3.57090e12	−0.727563	−0.363782	−	0.931484i	$-0.618515\pi$
$661$	−3.57090e12	−0.727563	−0.363782	+	0.931484i	$0.618515\pi$
$662$	−2.74602e12	−0.555704
$663$	0	0
$664$	1.23492e12	0.246537
$665$	2.14097e12	0.424535
$666$	−2.24310e12	−0.441789
$667$	5.95269e12	1.16452
$668$	2.46934e12	0.479829
$669$	−5.38039e11	−0.103848
$670$	1.14135e12	0.218818
$671$	−5.01703e11	−0.0955422
$672$	−1.64222e12	−0.310649
$673$	−7.77167e12	−1.46031	−0.730157	−	0.683279i	$-0.760553\pi$
$673$	−7.77167e12	−1.46031	−0.730157	+	0.683279i	$0.760553\pi$
$674$	2.03153e12	0.379187
$675$	1.26855e12	0.235201
$676$	−3.73401e12	−0.687726
$677$	−7.80583e12	−1.42814	−0.714069	−	0.700076i	$-0.753150\pi$
$677$	−7.80583e12	−1.42814	−0.714069	+	0.700076i	$0.753150\pi$
$678$	1.44300e12	0.262260
$679$	−1.98662e12	−0.358675
$680$	0	0
$681$	−1.36964e13	−2.44030
$682$	6.72229e11	0.118984
$683$	−1.18413e12	−0.208212	−0.104106	−	0.994566i	$-0.533198\pi$
$683$	−1.18413e12	−0.208212	−0.104106	+	0.994566i	$0.533198\pi$
$684$	3.58787e12	0.626735
$685$	3.10536e12	0.538896
$686$	2.13538e12	0.368143
$687$	2.83882e12	0.486220
$688$	−2.22015e12	−0.377776
$689$	−1.58133e13	−2.67322
$690$	−9.26557e12	−1.55615
$691$	1.71186e12	0.285639	0.142820	−	0.989749i	$-0.454383\pi$
$691$	1.71186e12	0.285639	0.142820	+	0.989749i	$0.454383\pi$
$692$	−1.24490e12	−0.206375
$693$	−4.37173e11	−0.0720036
$694$	1.54978e12	0.253601
$695$	1.21871e13	1.98138
$696$	1.11420e13	1.79979
$697$	0	0
$698$	2.59218e12	0.413348
$699$	1.84634e12	0.292526
$700$	6.93305e11	0.109140
$701$	−3.61533e12	−0.565480	−0.282740	−	0.959197i	$-0.591243\pi$
$701$	−3.61533e12	−0.565480	−0.282740	+	0.959197i	$0.591243\pi$
$702$	−1.89413e12	−0.294370
$703$	3.91590e12	0.604690
$704$	1.48406e12	0.227707
$705$	−1.58503e13	−2.41650
$706$	−1.24213e11	−0.0188168
$707$	−2.03922e12	−0.306957
$708$	1.13429e12	0.169658
$709$	4.40149e12	0.654172	0.327086	−	0.944995i	$-0.393933\pi$
$709$	4.40149e12	0.654172	0.327086	+	0.944995i	$0.393933\pi$
$710$	−9.46911e12	−1.39845
$711$	8.71936e12	1.27959
$712$	6.72010e12	0.979977
$713$	−4.74673e12	−0.687846
$714$	0	0
$715$	−3.69966e12	−0.529401
$716$	−2.56285e12	−0.364430
$717$	2.71875e12	0.384178
$718$	5.22518e12	0.733739
$719$	6.79671e12	0.948459	0.474230	−	0.880401i	$-0.342727\pi$
$719$	6.79671e12	0.948459	0.474230	+	0.880401i	$0.342727\pi$
$720$	−4.04205e12	−0.560538
$721$	−9.74262e10	−0.0134266
$722$	2.19319e12	0.300371
$723$	−6.92710e11	−0.0942821
$724$	2.56126e12	0.346442
$725$	−7.94386e12	−1.06785
$726$	−7.69617e12	−1.02816
$727$	−2.72583e10	−0.00361904	−0.00180952	−	0.999998i	$-0.500576\pi$
$727$	−2.72583e10	−0.00361904	−0.00180952	+	0.999998i	$0.500576\pi$
$728$	−3.32638e12	−0.438915
$729$	−9.95988e12	−1.30611
$730$	1.39966e13	1.82418
$731$	0	0
$732$	2.06362e12	0.265663
$733$	−3.31700e12	−0.424403	−0.212201	−	0.977226i	$-0.568063\pi$
$733$	−3.31700e12	−0.424403	−0.212201	+	0.977226i	$0.568063\pi$
$734$	5.73436e12	0.729210
$735$	−1.51585e13	−1.91586
$736$	−6.68950e12	−0.840318
$737$	4.06860e11	0.0507974
$738$	−9.16848e12	−1.13774
$739$	−7.15630e12	−0.882650	−0.441325	−	0.897347i	$-0.645491\pi$
$739$	−7.15630e12	−0.882650	−0.441325	+	0.897347i	$0.645491\pi$
$740$	2.61784e12	0.320923
$741$	2.27632e13	2.77365
$742$	−2.64579e12	−0.320434
$743$	−9.58156e12	−1.15342	−0.576709	−	0.816950i	$-0.695663\pi$
$743$	−9.58156e12	−1.15342	−0.576709	+	0.816950i	$0.695663\pi$
$744$	−8.88473e12	−1.06308
$745$	−1.34423e13	−1.59872
$746$	4.02002e12	0.475230
$747$	−2.28360e12	−0.268335
$748$	0	0
$749$	1.76535e12	0.204956
$750$	−7.96535e11	−0.0919240
$751$	1.53884e13	1.76528	0.882641	−	0.470047i	$-0.155763\pi$
$751$	1.53884e13	1.76528	0.882641	+	0.470047i	$0.155763\pi$
$752$	3.55380e12	0.405240
$753$	−2.39841e11	−0.0271861
$754$	1.18614e13	1.33648
$755$	1.71838e13	1.92468
$756$	2.61214e11	0.0290836
$757$	1.07153e13	1.18597	0.592983	−	0.805215i	$-0.297950\pi$
$757$	1.07153e13	1.18597	0.592983	+	0.805215i	$0.297950\pi$
$758$	1.22629e13	1.34922
$759$	−3.30292e12	−0.361252
$760$	1.63239e13	1.77485
$761$	−2.41871e12	−0.261428	−0.130714	−	0.991420i	$-0.541727\pi$
$761$	−2.41871e12	−0.261428	−0.130714	+	0.991420i	$0.541727\pi$
$762$	−1.13436e12	−0.121886
$763$	2.32925e12	0.248803
$764$	−3.22795e12	−0.342774
$765$	0	0
$766$	5.88206e11	0.0617305
$767$	3.88007e12	0.404818
$768$	−1.47287e13	−1.52771
$769$	1.04607e13	1.07868	0.539339	−	0.842089i	$-0.318674\pi$
$769$	1.04607e13	1.07868	0.539339	+	0.842089i	$0.318674\pi$
$770$	−6.19008e11	−0.0634582
$771$	−2.41175e13	−2.45803
$772$	−9.84774e11	−0.0997835
$773$	−6.75781e12	−0.680767	−0.340383	−	0.940287i	$-0.610557\pi$
$773$	−6.75781e12	−0.680767	−0.340383	+	0.940287i	$0.610557\pi$
$774$	9.49734e12	0.951191
$775$	6.33450e12	0.630746
$776$	−1.51470e13	−1.49951
$777$	1.96260e12	0.193169
$778$	6.81391e11	0.0666789
$779$	1.60059e13	1.55726
$780$	1.52176e13	1.47204
$781$	−3.37547e12	−0.324642
$782$	0	0
$783$	−2.99297e12	−0.284561
$784$	3.39870e12	0.321286
$785$	1.35168e12	0.127046
$786$	1.28040e12	0.119658
$787$	−1.52232e13	−1.41456	−0.707279	−	0.706935i	$-0.750078\pi$
$787$	−1.52232e13	−1.41456	−0.707279	+	0.706935i	$0.750078\pi$
$788$	8.69295e12	0.803155
$789$	−2.67995e13	−2.46196
$790$	1.23460e13	1.12773
$791$	−6.80718e11	−0.0618263
$792$	−3.33324e12	−0.301025
$793$	7.05904e12	0.633893
$794$	−1.47920e13	−1.32080
$795$	3.88932e13	3.45319
$796$	2.00822e12	0.177298
$797$	−1.41512e13	−1.24231	−0.621155	−	0.783688i	$-0.713336\pi$
$797$	−1.41512e13	−1.24231	−0.621155	+	0.783688i	$0.713336\pi$
$798$	3.80863e12	0.332472
$799$	0	0
$800$	8.92713e12	0.770561
$801$	−1.24267e13	−1.06662
$802$	8.48478e12	0.724196
$803$	4.98938e12	0.423474
$804$	−1.67351e12	−0.141246
$805$	4.37093e12	0.366853
$806$	−9.45836e12	−0.789420
$807$	−8.96161e12	−0.743798
$808$	−1.55481e13	−1.28329
$809$	1.28851e13	1.05760	0.528798	−	0.848748i	$-0.322643\pi$
$809$	1.28851e13	1.05760	0.528798	+	0.848748i	$0.322643\pi$
$810$	−1.01206e13	−0.826083
$811$	−4.50010e12	−0.365282	−0.182641	−	0.983180i	$-0.558465\pi$
$811$	−4.50010e12	−0.365282	−0.182641	+	0.983180i	$0.558465\pi$
$812$	−1.63577e12	−0.132044
$813$	2.37386e13	1.90567
$814$	−1.13218e12	−0.0903873
$815$	2.04972e13	1.62737
$816$	0	0
$817$	−1.65800e13	−1.30192
$818$	1.00061e13	0.781401
$819$	6.15110e12	0.477722
$820$	1.07002e13	0.826474
$821$	−7.07667e12	−0.543606	−0.271803	−	0.962353i	$-0.587620\pi$
$821$	−7.07667e12	−0.543606	−0.271803	+	0.962353i	$0.587620\pi$
$822$	5.52421e12	0.422033
$823$	2.16722e13	1.64666	0.823330	−	0.567563i	$-0.192114\pi$
$823$	2.16722e13	1.64666	0.823330	+	0.567563i	$0.192114\pi$
$824$	−7.42827e11	−0.0561326
$825$	4.40774e12	0.331263
$826$	6.49192e11	0.0485247
$827$	−9.53709e12	−0.708992	−0.354496	−	0.935058i	$-0.615347\pi$
$827$	−9.53709e12	−0.708992	−0.354496	+	0.935058i	$0.615347\pi$
$828$	7.32486e12	0.541580
$829$	−1.85810e13	−1.36639	−0.683194	−	0.730237i	$-0.739410\pi$
$829$	−1.85810e13	−1.36639	−0.683194	+	0.730237i	$0.739410\pi$
$830$	−3.23342e12	−0.236489
$831$	2.01772e13	1.46776
$832$	−2.08810e13	−1.51076
$833$	0	0
$834$	2.16799e13	1.55171
$835$	−2.07753e13	−1.47897
$836$	1.81094e12	0.128226
$837$	2.38662e12	0.168081
$838$	1.13388e13	0.794268
$839$	−1.59920e12	−0.111422	−0.0557112	−	0.998447i	$-0.517743\pi$
$839$	−1.59920e12	−0.111422	−0.0557112	+	0.998447i	$0.517743\pi$
$840$	8.18133e12	0.566979
$841$	4.23537e12	0.291951
$842$	8.30170e12	0.569197
$843$	−2.27195e13	−1.54944
$844$	9.11132e12	0.618073
$845$	3.14154e13	2.11976
$846$	−1.52024e13	−1.02034
$847$	3.63058e12	0.242382
$848$	−8.72025e12	−0.579092
$849$	−3.21380e13	−2.12292
$850$	0	0
$851$	7.99456e12	0.522530
$852$	1.38841e13	0.902693
$853$	3.66406e10	0.00236969	0.00118485	−	0.999999i	$-0.499623\pi$
$853$	3.66406e10	0.00236969	0.00118485	+	0.999999i	$0.499623\pi$
$854$	1.18108e12	0.0759835
$855$	−3.01859e13	−1.93177
$856$	1.34599e13	0.856860
$857$	−1.12995e13	−0.715559	−0.357779	−	0.933806i	$-0.616466\pi$
$857$	−1.12995e13	−0.715559	−0.357779	+	0.933806i	$0.616466\pi$
$858$	−6.58142e12	−0.414598
$859$	1.13307e13	0.710049	0.355025	−	0.934857i	$-0.384472\pi$
$859$	1.13307e13	0.710049	0.355025	+	0.934857i	$0.384472\pi$
$860$	−1.10840e13	−0.690961
$861$	8.02196e12	0.497470
$862$	1.72309e12	0.106298
$863$	5.46870e12	0.335610	0.167805	−	0.985820i	$-0.446332\pi$
$863$	5.46870e12	0.335610	0.167805	+	0.985820i	$0.446332\pi$
$864$	3.36344e12	0.205339
$865$	1.04737e13	0.636105
$866$	4.53358e11	0.0273912
$867$	0	0
$868$	1.30437e12	0.0779944
$869$	4.40102e12	0.261797
$870$	−2.91734e13	−1.72643
$871$	−5.72459e12	−0.337025
$872$	1.77594e13	1.04017
$873$	2.80097e13	1.63209
$874$	1.55142e13	0.899351
$875$	3.75756e11	0.0216705
$876$	−2.05225e13	−1.17750
$877$	2.29940e12	0.131255	0.0656275	−	0.997844i	$-0.479095\pi$
$877$	2.29940e12	0.131255	0.0656275	+	0.997844i	$0.479095\pi$
$878$	−9.36580e12	−0.531887
$879$	−2.77412e13	−1.56738
$880$	−2.04019e12	−0.114683
$881$	−1.11997e13	−0.626348	−0.313174	−	0.949696i	$-0.601392\pi$
$881$	−1.11997e13	−0.626348	−0.313174	+	0.949696i	$0.601392\pi$
$882$	−1.45390e13	−0.808955
$883$	−3.12943e13	−1.73238	−0.866188	−	0.499718i	$-0.833437\pi$
$883$	−3.12943e13	−1.73238	−0.866188	+	0.499718i	$0.833437\pi$
$884$	0	0
$885$	−9.54313e12	−0.522933
$886$	7.36491e12	0.401528
$887$	1.69578e13	0.919840	0.459920	−	0.887960i	$-0.347878\pi$
$887$	1.69578e13	0.919840	0.459920	+	0.887960i	$0.347878\pi$
$888$	1.49639e13	0.807582
$889$	5.35121e11	0.0287338
$890$	−1.75954e13	−0.940035
$891$	−3.60771e12	−0.191771
$892$	6.02260e11	0.0318524
$893$	2.65397e13	1.39657
$894$	−2.39129e13	−1.25203
$895$	2.15620e13	1.12328
$896$	5.74767e11	0.0297924
$897$	4.64726e13	2.39679
$898$	5.36536e12	0.275331
$899$	−1.49454e13	−0.763115
$900$	−9.77502e12	−0.496622
$901$	0	0
$902$	−4.62770e12	−0.232775
$903$	−8.30970e12	−0.415902
$904$	−5.19014e12	−0.258477
$905$	−2.15487e13	−1.06783
$906$	3.05687e13	1.50730
$907$	−1.21182e13	−0.594575	−0.297288	−	0.954788i	$-0.596082\pi$
$907$	−1.21182e13	−0.594575	−0.297288	+	0.954788i	$0.596082\pi$
$908$	1.53312e13	0.748496
$909$	2.87513e13	1.39675
$910$	8.70954e12	0.421026
$911$	1.52506e13	0.733594	0.366797	−	0.930301i	$-0.380454\pi$
$911$	1.52506e13	0.733594	0.366797	+	0.930301i	$0.380454\pi$
$912$	1.25528e13	0.600848
$913$	−1.15263e12	−0.0548997
$914$	1.88877e13	0.895203
$915$	−1.73619e13	−0.818846
$916$	−3.17767e12	−0.149135
$917$	−6.04012e11	−0.0282087
$918$	0	0
$919$	−3.47751e12	−0.160823	−0.0804116	−	0.996762i	$-0.525623\pi$
$919$	−3.47751e12	−0.160823	−0.0804116	+	0.996762i	$0.525623\pi$
$920$	3.33262e13	1.53370
$921$	−3.34290e13	−1.53093
$922$	1.78552e13	0.813721
$923$	4.74935e13	2.15390
$924$	9.07623e11	0.0409621
$925$	−1.06687e13	−0.479154
$926$	4.14158e12	0.185104
$927$	1.37363e12	0.0610956
$928$	−2.10624e13	−0.932272
$929$	1.36859e13	0.602841	0.301421	−	0.953491i	$-0.402539\pi$
$929$	1.36859e13	0.602841	0.301421	+	0.953491i	$0.402539\pi$
$930$	2.32631e13	1.01975
$931$	2.53814e13	1.10724
$932$	−2.06672e12	−0.0897242
$933$	−1.68044e13	−0.726031
$934$	2.75564e13	1.18484
$935$	0	0
$936$	4.68991e13	1.99721
$937$	−2.71915e13	−1.15241	−0.576203	−	0.817307i	$-0.695466\pi$
$937$	−2.71915e13	−1.15241	−0.576203	+	0.817307i	$0.695466\pi$
$938$	−9.57808e11	−0.0403985
$939$	−2.80370e13	−1.17689
$940$	1.77422e13	0.741193
$941$	−1.67036e13	−0.694476	−0.347238	−	0.937777i	$-0.612880\pi$
$941$	−1.67036e13	−0.694476	−0.347238	+	0.937777i	$0.612880\pi$
$942$	2.40454e12	0.0994955
$943$	3.26770e13	1.34568
$944$	2.13967e12	0.0876946
$945$	−2.19767e12	−0.0896438
$946$	4.79370e12	0.194608
$947$	−2.14351e13	−0.866067	−0.433033	−	0.901378i	$-0.642557\pi$
$947$	−2.14351e13	−0.866067	−0.433033	+	0.901378i	$0.642557\pi$
$948$	−1.81024e13	−0.727946
$949$	−7.02014e13	−2.80962
$950$	−2.07037e13	−0.824693
$951$	2.34312e13	0.928927
$952$	0	0
$953$	−9.22579e12	−0.362314	−0.181157	−	0.983454i	$-0.557984\pi$
$953$	−9.22579e12	−0.362314	−0.181157	+	0.983454i	$0.557984\pi$
$954$	3.73034e13	1.45808
$955$	2.71578e13	1.05652
$956$	−3.04326e12	−0.117836
$957$	−1.03995e13	−0.400782
$958$	−9.50000e12	−0.364400
$959$	−2.60598e12	−0.0994919
$960$	5.13574e13	1.95156
$961$	−1.45220e13	−0.549251
$962$	1.59300e13	0.599692
$963$	−2.48899e13	−0.932619
$964$	7.75392e11	0.0289184
$965$	8.28521e12	0.307561
$966$	7.77555e12	0.287299
$967$	−5.20219e13	−1.91323	−0.956614	−	0.291359i	$-0.905893\pi$
$967$	−5.20219e13	−1.91323	−0.956614	+	0.291359i	$0.905893\pi$
$968$	2.76814e13	1.01333
$969$	0	0
$970$	3.96598e13	1.43839
$971$	−8.53408e12	−0.308085	−0.154042	−	0.988064i	$-0.549229\pi$
$971$	−8.53408e12	−0.308085	−0.154042	+	0.988064i	$0.549229\pi$
$972$	1.79873e13	0.646349
$973$	−1.02273e13	−0.365807
$974$	−3.38098e13	−1.20372
$975$	−6.20176e13	−2.19783
$976$	3.89272e12	0.137318
$977$	−1.09077e13	−0.383008	−0.191504	−	0.981492i	$-0.561337\pi$
$977$	−1.09077e13	−0.383008	−0.191504	+	0.981492i	$0.561337\pi$
$978$	3.64630e13	1.27447
$979$	−6.27227e12	−0.218224
$980$	1.69679e13	0.587638
$981$	−3.28405e13	−1.13214
$982$	−1.94109e13	−0.666106
$983$	−3.83440e12	−0.130981	−0.0654903	−	0.997853i	$-0.520861\pi$
$983$	−3.83440e12	−0.130981	−0.0654903	+	0.997853i	$0.520861\pi$
$984$	6.11636e13	2.07977
$985$	−7.31365e13	−2.47555
$986$	0	0
$987$	1.33014e13	0.446137
$988$	−2.54803e13	−0.850742
$989$	−3.38491e13	−1.12503
$990$	8.72749e12	0.288756
$991$	−3.67907e13	−1.21173	−0.605867	−	0.795566i	$-0.707173\pi$
$991$	−3.67907e13	−1.21173	−0.605867	+	0.795566i	$0.707173\pi$
$992$	1.67954e13	0.550664
$993$	−3.38751e13	−1.10563
$994$	7.94636e12	0.258184
$995$	−1.68958e13	−0.546480
$996$	4.74102e12	0.152653
$997$	−2.49866e13	−0.800901	−0.400451	−	0.916318i	$-0.631146\pi$
$997$	−2.49866e13	−0.800901	−0.400451	+	0.916318i	$0.631146\pi$
$998$	4.85792e12	0.155011
$999$	−4.01961e12	−0.127685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.c.1.10		12
17.4	even	4		17.10.b.a.16.3	✓	12
17.13	even	4		17.10.b.a.16.4	yes	12
17.16	even	2	inner	289.10.a.c.1.9		12
51.38	odd	4		153.10.d.b.118.10		12
51.47	odd	4		153.10.d.b.118.9		12
68.47	odd	4		272.10.b.c.33.2		12
68.55	odd	4		272.10.b.c.33.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.3	✓	12	17.4	even	4
17.10.b.a.16.4	yes	12	17.13	even	4
153.10.d.b.118.9		12	51.47	odd	4
153.10.d.b.118.10		12	51.38	odd	4
272.10.b.c.33.2		12	68.47	odd	4
272.10.b.c.33.11		12	68.55	odd	4
289.10.a.c.1.9		12	17.16	even	2	inner
289.10.a.c.1.10		12	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)

\(f(q)\)	\(=\)	\(q+16.7531 q^{2} +206.667 q^{3} -231.335 q^{4} +1946.29 q^{5} +3462.30 q^{6} -1633.30 q^{7} -12453.1 q^{8} +23028.2 q^{9} +O(q^{10})\)	\(q+16.7531 q^{2} +206.667 q^{3} -231.335 q^{4} +1946.29 q^{5} +3462.30 q^{6} -1633.30 q^{7} -12453.1 q^{8} +23028.2 q^{9} +32606.3 q^{10} +11623.3 q^{11} -47809.2 q^{12} -163541. q^{13} -27362.8 q^{14} +402234. q^{15} -90185.0 q^{16} +385793. q^{18} -673499. q^{19} -450244. q^{20} -337549. q^{21} +194725. q^{22} -1.37499e6 q^{23} -2.57365e6 q^{24} +1.83492e6 q^{25} -2.73981e6 q^{26} +691336. q^{27} +377839. q^{28} -4.32926e6 q^{29} +6.73865e6 q^{30} +3.45219e6 q^{31} +4.86513e6 q^{32} +2.40214e6 q^{33} -3.17888e6 q^{35} -5.32721e6 q^{36} -5.81427e6 q^{37} -1.12832e7 q^{38} -3.37985e7 q^{39} -2.42374e7 q^{40} -2.37653e7 q^{41} -5.65499e6 q^{42} +2.46177e7 q^{43} -2.68886e6 q^{44} +4.48195e7 q^{45} -2.30353e7 q^{46} -3.94057e7 q^{47} -1.86382e7 q^{48} -3.76859e7 q^{49} +3.07406e7 q^{50} +3.78327e7 q^{52} +9.66929e7 q^{53} +1.15820e7 q^{54} +2.26222e7 q^{55} +2.03397e7 q^{56} -1.39190e8 q^{57} -7.25285e7 q^{58} -2.37253e7 q^{59} -9.30506e7 q^{60} -4.31637e7 q^{61} +5.78348e7 q^{62} -3.76120e7 q^{63} +1.27681e8 q^{64} -3.18298e8 q^{65} +4.02432e7 q^{66} +3.50040e7 q^{67} -2.84165e8 q^{69} -5.32560e7 q^{70} -2.90407e8 q^{71} -2.86773e8 q^{72} +4.29259e8 q^{73} -9.74069e7 q^{74} +3.79217e8 q^{75} +1.55804e8 q^{76} -1.89843e7 q^{77} -5.66229e8 q^{78} +3.78639e8 q^{79} -1.75526e8 q^{80} -3.10387e8 q^{81} -3.98142e8 q^{82} -9.91655e7 q^{83} +7.80868e7 q^{84} +4.12423e8 q^{86} -8.94715e8 q^{87} -1.44746e8 q^{88} -5.39631e8 q^{89} +7.50864e8 q^{90} +2.67112e8 q^{91} +3.18083e8 q^{92} +7.13453e8 q^{93} -6.60166e8 q^{94} -1.31082e9 q^{95} +1.00546e9 q^{96} +1.21632e9 q^{97} -6.31355e8 q^{98} +2.67662e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9}+O(q^{10}) \) 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9	\( 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9} - 63204 q^{13} + 243480 q^{15} + 38978 q^{16} + 547706 q^{18} - 1110672 q^{19} - 172580 q^{21} + 4441796 q^{25} - 1336332 q^{26} - 500496 q^{30} + 1934850 q^{32} - 6557404 q^{33} + 3519864 q^{35} - 30244102 q^{36} + 28748136 q^{38} + 11901296 q^{42} - 10004616 q^{43} - 112552440 q^{47} - 121354720 q^{49} - 164889018 q^{50} - 59093180 q^{52} - 76804272 q^{53} + 300732568 q^{55} - 11618904 q^{59} - 101609232 q^{60} - 260062974 q^{64} - 18429632 q^{66} - 304208752 q^{67} - 211308236 q^{69} - 460311456 q^{70} + 493218954 q^{72} - 416024248 q^{76} - 138357828 q^{77} - 363335792 q^{81} + 845042136 q^{83} + 958037984 q^{84} + 127952904 q^{86} - 610860648 q^{87} - 938223804 q^{89} - 1635779524 q^{93} + 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) \) 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9 - 63204 * q^13 + 243480 * q^15 + 38978 * q^16 + 547706 * q^18 - 1110672 * q^19 - 172580 * q^21 + 4441796 * q^25 - 1336332 * q^26 - 500496 * q^30 + 1934850 * q^32 - 6557404 * q^33 + 3519864 * q^35 - 30244102 * q^36 + 28748136 * q^38 + 11901296 * q^42 - 10004616 * q^43 - 112552440 * q^47 - 121354720 * q^49 - 164889018 * q^50 - 59093180 * q^52 - 76804272 * q^53 + 300732568 * q^55 - 11618904 * q^59 - 101609232 * q^60 - 260062974 * q^64 - 18429632 * q^66 - 304208752 * q^67 - 211308236 * q^69 - 460311456 * q^70 + 493218954 * q^72 - 416024248 * q^76 - 138357828 * q^77 - 363335792 * q^81 + 845042136 * q^83 + 958037984 * q^84 + 127952904 * q^86 - 610860648 * q^87 - 938223804 * q^89 - 1635779524 * q^93 + 238629952 * q^94 - 152046078 * q^98

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