LMFDB - Embedded newform 289.10.a.b.1.7

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-43.1213$ 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)

$f(q)$	$=$	$q+43.1213 q^{2} +171.025 q^{3} +1347.45 q^{4} -1536.21 q^{5} +7374.84 q^{6} -3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} +O(q^{10})$	\(q+43.1213 q^{2} +171.025 q^{3} +1347.45 q^{4} -1536.21 q^{5} +7374.84 q^{6} -3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} -66243.5 q^{10} -51964.2 q^{11} +230448. q^{12} -166337. q^{13} -130558. q^{14} -262732. q^{15} +863574. q^{16} +412529. q^{18} -1.03482e6 q^{19} -2.06997e6 q^{20} -517811. q^{21} -2.24076e6 q^{22} +647595. q^{23} +6.16128e6 q^{24} +406829. q^{25} -7.17269e6 q^{26} -1.73014e6 q^{27} -4.07964e6 q^{28} -101038. q^{29} -1.13293e7 q^{30} -1.03448e6 q^{31} +1.87934e7 q^{32} -8.88720e6 q^{33} +4.65118e6 q^{35} +1.28906e7 q^{36} +5.58601e6 q^{37} -4.46226e7 q^{38} -2.84479e7 q^{39} -5.53429e7 q^{40} +4.18736e6 q^{41} -2.23287e7 q^{42} -9.60190e6 q^{43} -7.00190e7 q^{44} -1.46965e7 q^{45} +2.79251e7 q^{46} +3.98318e7 q^{47} +1.47693e8 q^{48} -3.11867e7 q^{49} +1.75430e7 q^{50} -2.24131e8 q^{52} +6.22183e7 q^{53} -7.46060e7 q^{54} +7.98282e7 q^{55} -1.09074e8 q^{56} -1.76980e8 q^{57} -4.35690e6 q^{58} +9.60858e7 q^{59} -3.54017e8 q^{60} +1.86877e8 q^{61} -4.46079e7 q^{62} -2.89650e7 q^{63} +3.68245e8 q^{64} +2.55530e8 q^{65} -3.83228e8 q^{66} +3.73689e7 q^{67} +1.10755e8 q^{69} +2.00565e8 q^{70} -2.04593e8 q^{71} +3.44645e8 q^{72} +1.95705e8 q^{73} +2.40876e8 q^{74} +6.95782e7 q^{75} -1.39436e9 q^{76} +1.57331e8 q^{77} -1.22671e9 q^{78} -2.72638e8 q^{79} -1.32663e9 q^{80} -4.84200e8 q^{81} +1.80564e8 q^{82} -1.96272e8 q^{83} -6.97723e8 q^{84} -4.14046e8 q^{86} -1.72801e7 q^{87} -1.87204e9 q^{88} -3.93217e8 q^{89} -6.33732e8 q^{90} +5.03618e8 q^{91} +8.72600e8 q^{92} -1.76922e8 q^{93} +1.71760e9 q^{94} +1.58970e9 q^{95} +3.21414e9 q^{96} -8.75485e8 q^{97} -1.34481e9 q^{98} -4.97126e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - 88 q^{3} + 2389 q^{4} - 1362 q^{5} + 11720 q^{6} - 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) $ 7 * q - q^2 - 88 * q^3 + 2389 * q^4 - 1362 * q^5 + 11720 * q^6 - 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} - 88 q^{3} + 2389 q^{4} - 1362 q^{5} + 11720 q^{6} - 9388 q^{7} + 16821 q^{8} + 81419 q^{9} - 154226 q^{10} - 135536 q^{11} - 198160 q^{12} + 166122 q^{13} - 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 149027 q^{18} + 777172 q^{19} + 917162 q^{20} - 3412104 q^{21} + 1222520 q^{22} - 1357764 q^{23} + 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} + 4519064 q^{27} + 3328892 q^{28} - 967002 q^{29} - 12558992 q^{30} - 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 530736 q^{35} + 4535009 q^{36} - 18296498 q^{37} - 49363020 q^{38} - 86306872 q^{39} - 127155062 q^{40} - 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} - 96696624 q^{44} - 108916410 q^{45} + 151509484 q^{46} + 56639800 q^{47} + 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} - 156226378 q^{52} + 121813562 q^{53} + 93375344 q^{54} + 40793128 q^{55} + 196175436 q^{56} - 153612960 q^{57} + 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} + 49915846 q^{61} + 73506556 q^{62} + 2185356 q^{63} + 317922057 q^{64} + 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 379683432 q^{69} + 966315960 q^{70} - 652473940 q^{71} + 655760385 q^{72} - 306656342 q^{73} - 249173874 q^{74} - 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} - 323434416 q^{78} - 959147884 q^{79} + 692173602 q^{80} - 374486977 q^{81} - 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} - 164953236 q^{86} - 1612550856 q^{87} - 1132038848 q^{88} - 1971327114 q^{89} + 2284664662 q^{90} + 1061062864 q^{91} - 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} + 3249631512 q^{95} + 4442036640 q^{96} - 2006526254 q^{97} - 2170640009 q^{98} + 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 - 88 * q^3 + 2389 * q^4 - 1362 * q^5 + 11720 * q^6 - 9388 * q^7 + 16821 * q^8 + 81419 * q^9 - 154226 * q^10 - 135536 * q^11 - 198160 * q^12 + 166122 * q^13 - 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 149027 * q^18 + 777172 * q^19 + 917162 * q^20 - 3412104 * q^21 + 1222520 * q^22 - 1357764 * q^23 + 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 + 4519064 * q^27 + 3328892 * q^28 - 967002 * q^29 - 12558992 * q^30 - 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 530736 * q^35 + 4535009 * q^36 - 18296498 * q^37 - 49363020 * q^38 - 86306872 * q^39 - 127155062 * q^40 - 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 - 96696624 * q^44 - 108916410 * q^45 + 151509484 * q^46 + 56639800 * q^47 + 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 - 156226378 * q^52 + 121813562 * q^53 + 93375344 * q^54 + 40793128 * q^55 + 196175436 * q^56 - 153612960 * q^57 + 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 + 49915846 * q^61 + 73506556 * q^62 + 2185356 * q^63 + 317922057 * q^64 + 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 379683432 * q^69 + 966315960 * q^70 - 652473940 * q^71 + 655760385 * q^72 - 306656342 * q^73 - 249173874 * q^74 - 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 - 323434416 * q^78 - 959147884 * q^79 + 692173602 * q^80 - 374486977 * q^81 - 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 - 164953236 * q^86 - 1612550856 * q^87 - 1132038848 * q^88 - 1971327114 * q^89 + 2284664662 * q^90 + 1061062864 * q^91 - 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 + 3249631512 * q^95 + 4442036640 * q^96 - 2006526254 * q^97 - 2170640009 * q^98 + 2579159272 * 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 $

$2$	43.1213	1.90571	0.952855	−	0.303426i	$-0.0981306\pi$
$2$	43.1213	1.90571	0.952855	+	0.303426i	$0.0981306\pi$
$3$	171.025	1.21903	0.609516	−	0.792774i	$-0.291364\pi$
$3$	171.025	1.21903	0.609516	+	0.792774i	$0.291364\pi$
$4$	1347.45	2.63173
$5$	−1536.21	−1.09923	−0.549613	−	0.835420i	$-0.685225\pi$
$5$	−1536.21	−1.09923	−0.549613	+	0.835420i	$0.685225\pi$
$6$	7374.84	2.32312
$7$	−3027.69	−0.476617	−0.238309	−	0.971189i	$-0.576593\pi$
$7$	−3027.69	−0.476617	−0.238309	+	0.971189i	$0.576593\pi$
$8$	36025.5	3.10960
$9$	9566.70	0.486039
$10$	−66243.5	−2.09480
$11$	−51964.2	−1.07013	−0.535066	−	0.844810i	$-0.679713\pi$
$11$	−51964.2	−1.07013	−0.535066	+	0.844810i	$0.679713\pi$
$12$	230448.	3.20816
$13$	−166337.	−1.61527	−0.807635	−	0.589683i	$-0.799253\pi$
$13$	−166337.	−1.61527	−0.807635	+	0.589683i	$0.799253\pi$
$14$	−130558.	−0.908294
$15$	−262732.	−1.33999
$16$	863574.	3.29427
$17$	0	0
$17$	0	0
$18$	412529.	0.926249
$19$	−1.03482e6	−1.82168	−0.910840	−	0.412759i	$-0.864565\pi$
$19$	−1.03482e6	−1.82168	−0.910840	+	0.412759i	$0.864565\pi$
$20$	−2.06997e6	−2.89286
$21$	−517811.	−0.581012
$22$	−2.24076e6	−2.03936
$23$	647595.	0.482535	0.241267	−	0.970459i	$-0.422437\pi$
$23$	647595.	0.482535	0.241267	+	0.970459i	$0.422437\pi$
$24$	6.16128e6	3.79071
$25$	406829.	0.208297
$26$	−7.17269e6	−3.07824
$27$	−1.73014e6	−0.626535
$28$	−4.07964e6	−1.25433
$29$	−101038.	−0.0265274	−0.0132637	−	0.999912i	$-0.504222\pi$
$29$	−101038.	−0.0265274	−0.0132637	+	0.999912i	$0.504222\pi$
$30$	−1.13293e7	−2.55363
$31$	−1.03448e6	−0.201184	−0.100592	−	0.994928i	$-0.532074\pi$
$31$	−1.03448e6	−0.201184	−0.100592	+	0.994928i	$0.532074\pi$
$32$	1.87934e7	3.16833
$33$	−8.88720e6	−1.30452
$34$	0	0
$35$	4.65118e6	0.523910
$36$	1.28906e7	1.27912
$37$	5.58601e6	0.489998	0.244999	−	0.969523i	$-0.421212\pi$
$37$	5.58601e6	0.489998	0.244999	+	0.969523i	$0.421212\pi$
$38$	−4.46226e7	−3.47159
$39$	−2.84479e7	−1.96907
$40$	−5.53429e7	−3.41816
$41$	4.18736e6	0.231426	0.115713	−	0.993283i	$-0.463085\pi$
$41$	4.18736e6	0.231426	0.115713	+	0.993283i	$0.463085\pi$
$42$	−2.23287e7	−1.10724
$43$	−9.60190e6	−0.428301	−0.214151	−	0.976801i	$-0.568698\pi$
$43$	−9.60190e6	−0.428301	−0.214151	+	0.976801i	$0.568698\pi$
$44$	−7.00190e7	−2.81630
$45$	−1.46965e7	−0.534266
$46$	2.79251e7	0.919571
$47$	3.98318e7	1.19067	0.595333	−	0.803479i	$-0.297020\pi$
$47$	3.98318e7	1.19067	0.595333	+	0.803479i	$0.297020\pi$
$48$	1.47693e8	4.01582
$49$	−3.11867e7	−0.772836
$50$	1.75430e7	0.396953
$51$	0	0
$52$	−2.24131e8	−4.25095
$53$	6.22183e7	1.08312	0.541560	−	0.840662i	$-0.317834\pi$
$53$	6.22183e7	1.08312	0.541560	+	0.840662i	$0.317834\pi$
$54$	−7.46060e7	−1.19399
$55$	7.98282e7	1.17632
$56$	−1.09074e8	−1.48209
$57$	−1.76980e8	−2.22069
$58$	−4.35690e6	−0.0505536
$59$	9.60858e7	1.03235	0.516173	−	0.856484i	$-0.327356\pi$
$59$	9.60858e7	1.03235	0.516173	+	0.856484i	$0.327356\pi$
$60$	−3.54017e8	−3.52649
$61$	1.86877e8	1.72811	0.864055	−	0.503398i	$-0.167917\pi$
$61$	1.86877e8	1.72811	0.864055	+	0.503398i	$0.167917\pi$
$62$	−4.46079e7	−0.383398
$63$	−2.89650e7	−0.231655
$64$	3.68245e8	2.74364
$65$	2.55530e8	1.77555
$66$	−3.83228e8	−2.48605
$67$	3.73689e7	0.226555	0.113278	−	0.993563i	$-0.463865\pi$
$67$	3.73689e7	0.226555	0.113278	+	0.993563i	$0.463865\pi$
$68$	0	0
$69$	1.10755e8	0.588225
$70$	2.00565e8	0.998420
$71$	−2.04593e8	−0.955495	−0.477748	−	0.878497i	$-0.658547\pi$
$71$	−2.04593e8	−0.955495	−0.477748	+	0.878497i	$0.658547\pi$
$72$	3.44645e8	1.51139
$73$	1.95705e8	0.806581	0.403291	−	0.915072i	$-0.367866\pi$
$73$	1.95705e8	0.806581	0.403291	+	0.915072i	$0.367866\pi$
$74$	2.40876e8	0.933793
$75$	6.95782e7	0.253920
$76$	−1.39436e9	−4.79417
$77$	1.57331e8	0.510043
$78$	−1.22671e9	−3.75247
$79$	−2.72638e8	−0.787524	−0.393762	−	0.919212i	$-0.628827\pi$
$79$	−2.72638e8	−0.787524	−0.393762	+	0.919212i	$0.628827\pi$
$80$	−1.32663e9	−3.62115
$81$	−4.84200e8	−1.24981
$82$	1.80564e8	0.441032
$83$	−1.96272e8	−0.453950	−0.226975	−	0.973901i	$-0.572884\pi$
$83$	−1.96272e8	−0.453950	−0.226975	+	0.973901i	$0.572884\pi$
$84$	−6.97723e8	−1.52907
$85$	0	0
$86$	−4.14046e8	−0.816218
$87$	−1.72801e7	−0.0323378
$88$	−1.87204e9	−3.32769
$89$	−3.93217e8	−0.664319	−0.332160	−	0.943223i	$-0.607777\pi$
$89$	−3.93217e8	−0.664319	−0.332160	+	0.943223i	$0.607777\pi$
$90$	−6.33732e8	−1.01816
$91$	5.03618e8	0.769865
$92$	8.72600e8	1.26990
$93$	−1.76922e8	−0.245249
$94$	1.71760e9	2.26906
$95$	1.58970e9	2.00244
$96$	3.21414e9	3.86229
$97$	−8.75485e8	−1.00410	−0.502049	−	0.864839i	$-0.667420\pi$
$97$	−8.75485e8	−1.00410	−0.502049	+	0.864839i	$0.667420\pi$
$98$	−1.34481e9	−1.47280
$99$	−4.97126e8	−0.520126
$100$	5.48180e8	0.548180
$101$	2.76987e8	0.264858	0.132429	−	0.991192i	$-0.457722\pi$
$101$	2.76987e8	0.264858	0.132429	+	0.991192i	$0.457722\pi$
$102$	0	0
$103$	−5.47928e7	−0.0479685	−0.0239842	−	0.999712i	$-0.507635\pi$
$103$	−5.47928e7	−0.0479685	−0.0239842	+	0.999712i	$0.507635\pi$
$104$	−5.99239e9	−5.02285
$105$	7.95469e8	0.638663
$106$	2.68293e9	2.06411
$107$	−1.33346e9	−0.983449	−0.491724	−	0.870751i	$-0.663633\pi$
$107$	−1.33346e9	−0.983449	−0.491724	+	0.870751i	$0.663633\pi$
$108$	−2.33128e9	−1.64887
$109$	7.04251e8	0.477868	0.238934	−	0.971036i	$-0.423202\pi$
$109$	7.04251e8	0.477868	0.238934	+	0.971036i	$0.423202\pi$
$110$	3.44229e9	2.24172
$111$	9.55350e8	0.597323
$112$	−2.61463e9	−1.57011
$113$	−1.40406e9	−0.810091	−0.405045	−	0.914297i	$-0.632744\pi$
$113$	−1.40406e9	−0.810091	−0.405045	+	0.914297i	$0.632744\pi$
$114$	−7.63160e9	−4.23198
$115$	−9.94845e8	−0.530414
$116$	−1.36144e8	−0.0698130
$117$	−1.59130e9	−0.785084
$118$	4.14335e9	1.96735
$119$	0	0
$120$	−9.46504e9	−4.16684
$121$	3.42331e8	0.145182
$122$	8.05837e9	3.29328
$123$	7.16145e8	0.282116
$124$	−1.39390e9	−0.529461
$125$	2.37544e9	0.870261
$126$	−1.24901e9	−0.441466
$127$	4.64719e8	0.158516	0.0792581	−	0.996854i	$-0.474745\pi$
$127$	4.64719e8	0.158516	0.0792581	+	0.996854i	$0.474745\pi$
$128$	6.25697e9	2.06025
$129$	−1.64217e9	−0.522113
$130$	1.10188e10	3.38367
$131$	−4.70705e9	−1.39646	−0.698229	−	0.715874i	$-0.746028\pi$
$131$	−4.70705e9	−1.39646	−0.698229	+	0.715874i	$0.746028\pi$
$132$	−1.19750e10	−3.43316
$133$	3.13310e9	0.868244
$134$	1.61140e9	0.431748
$135$	2.65787e9	0.688703
$136$	0	0
$137$	4.09197e9	0.992407	0.496203	−	0.868206i	$-0.334727\pi$
$137$	4.09197e9	0.992407	0.496203	+	0.868206i	$0.334727\pi$
$138$	4.77591e9	1.12099
$139$	4.61710e8	0.104907	0.0524533	−	0.998623i	$-0.483296\pi$
$139$	4.61710e8	0.104907	0.0524533	+	0.998623i	$0.483296\pi$
$140$	6.26721e9	1.37879
$141$	6.81226e9	1.45146
$142$	−8.82232e9	−1.82090
$143$	8.64359e9	1.72855
$144$	8.26156e9	1.60115
$145$	1.55216e8	0.0291596
$146$	8.43904e9	1.53711
$147$	−5.33372e9	−0.942112
$148$	7.52685e9	1.28954
$149$	1.87018e9	0.310847	0.155423	−	0.987848i	$-0.450326\pi$
$149$	1.87018e9	0.310847	0.155423	+	0.987848i	$0.450326\pi$
$150$	3.00030e9	0.483898
$151$	−6.04895e9	−0.946856	−0.473428	−	0.880833i	$-0.656984\pi$
$151$	−6.04895e9	−0.946856	−0.473428	+	0.880833i	$0.656984\pi$
$152$	−3.72798e10	−5.66470
$153$	0	0
$154$	6.78433e9	0.971994
$155$	1.58918e9	0.221146
$156$	−3.83321e10	−5.18205
$157$	5.87552e9	0.771788	0.385894	−	0.922543i	$-0.373893\pi$
$157$	5.87552e9	0.771788	0.385894	+	0.922543i	$0.373893\pi$
$158$	−1.17565e10	−1.50079
$159$	1.06409e10	1.32036
$160$	−2.88706e10	−3.48270
$161$	−1.96072e9	−0.229984
$162$	−2.08793e10	−2.38177
$163$	−1.19332e10	−1.32408	−0.662039	−	0.749470i	$-0.730309\pi$
$163$	−1.19332e10	−1.32408	−0.662039	+	0.749470i	$0.730309\pi$
$164$	5.64224e9	0.609052
$165$	1.36526e10	1.43397
$166$	−8.46352e9	−0.865096
$167$	−2.11741e9	−0.210659	−0.105330	−	0.994437i	$-0.533590\pi$
$167$	−2.11741e9	−0.210659	−0.105330	+	0.994437i	$0.533590\pi$
$168$	−1.86544e10	−1.80672
$169$	1.70637e10	1.60910
$170$	0	0
$171$	−9.89978e9	−0.885407
$172$	−1.29380e10	−1.12717
$173$	−4.37524e9	−0.371359	−0.185680	−	0.982610i	$-0.559449\pi$
$173$	−4.37524e9	−0.371359	−0.185680	+	0.982610i	$0.559449\pi$
$174$	−7.45141e8	−0.0616264
$175$	−1.23175e9	−0.0992777
$176$	−4.48749e10	−3.52531
$177$	1.64331e10	1.25846
$178$	−1.69560e10	−1.26600
$179$	2.12791e9	0.154922	0.0774612	−	0.996995i	$-0.475319\pi$
$179$	2.12791e9	0.154922	0.0774612	+	0.996995i	$0.475319\pi$
$180$	−1.98027e10	−1.40604
$181$	−1.80496e10	−1.25001	−0.625007	−	0.780619i	$-0.714904\pi$
$181$	−1.80496e10	−1.25001	−0.625007	+	0.780619i	$0.714904\pi$
$182$	2.17166e10	1.46714
$183$	3.19607e10	2.10662
$184$	2.33299e10	1.50049
$185$	−8.58131e9	−0.538618
$186$	−7.62909e9	−0.467374
$187$	0	0
$188$	5.36713e10	3.13351
$189$	5.23833e9	0.298617
$190$	6.85499e10	3.81606
$191$	−6.31774e8	−0.0343488	−0.0171744	−	0.999853i	$-0.505467\pi$
$191$	−6.31774e8	−0.0343488	−0.0171744	+	0.999853i	$0.505467\pi$
$192$	6.29792e10	3.34458
$193$	−1.51993e10	−0.788524	−0.394262	−	0.918998i	$-0.629000\pi$
$193$	−1.51993e10	−0.788524	−0.394262	+	0.918998i	$0.629000\pi$
$194$	−3.77520e10	−1.91352
$195$	4.37021e10	2.16445
$196$	−4.20224e10	−2.03390
$197$	2.63264e10	1.24535	0.622677	−	0.782479i	$-0.286045\pi$
$197$	2.63264e10	1.24535	0.622677	+	0.782479i	$0.286045\pi$
$198$	−2.14367e10	−0.991209
$199$	−3.40221e10	−1.53788	−0.768940	−	0.639321i	$-0.779216\pi$
$199$	−3.40221e10	−1.53788	−0.768940	+	0.639321i	$0.779216\pi$
$200$	1.46562e10	0.647720
$201$	6.39104e9	0.276178
$202$	1.19440e10	0.504743
$203$	3.05912e8	0.0126434
$204$	0	0
$205$	−6.43268e9	−0.254390
$206$	−2.36273e9	−0.0914140
$207$	6.19535e9	0.234531
$208$	−1.43645e11	−5.32114
$209$	5.37734e10	1.94944
$210$	3.43017e10	1.21711
$211$	2.29918e10	0.798550	0.399275	−	0.916831i	$-0.369262\pi$
$211$	2.29918e10	0.798550	0.399275	+	0.916831i	$0.369262\pi$
$212$	8.38358e10	2.85048
$213$	−3.49906e10	−1.16478
$214$	−5.75003e10	−1.87417
$215$	1.47506e10	0.470800
$216$	−6.23293e10	−1.94828
$217$	3.13207e9	0.0958876
$218$	3.03682e10	0.910678
$219$	3.34705e10	0.983248
$220$	1.07564e11	3.09575
$221$	0	0
$222$	4.11959e10	1.13832
$223$	−5.81614e10	−1.57494	−0.787468	−	0.616355i	$-0.788609\pi$
$223$	−5.81614e10	−1.57494	−0.787468	+	0.616355i	$0.788609\pi$
$224$	−5.69004e10	−1.51008
$225$	3.89201e9	0.101240
$226$	−6.05450e10	−1.54380
$227$	6.36497e9	0.159104	0.0795518	−	0.996831i	$-0.474651\pi$
$227$	6.36497e9	0.159104	0.0795518	+	0.996831i	$0.474651\pi$
$228$	−2.38471e11	−5.84425
$229$	−7.25334e10	−1.74292	−0.871461	−	0.490464i	$-0.836827\pi$
$229$	−7.25334e10	−1.74292	−0.871461	+	0.490464i	$0.836827\pi$
$230$	−4.28990e10	−1.01082
$231$	2.69077e10	0.621759
$232$	−3.63996e9	−0.0824898
$233$	8.13370e10	1.80795	0.903975	−	0.427585i	$-0.140635\pi$
$233$	8.13370e10	1.80795	0.903975	+	0.427585i	$0.140635\pi$
$234$	−6.86190e10	−1.49614
$235$	−6.11902e10	−1.30881
$236$	1.29470e11	2.71686
$237$	−4.66280e10	−0.960018
$238$	0	0
$239$	7.48651e10	1.48419	0.742094	−	0.670296i	$-0.233833\pi$
$239$	7.48651e10	1.48419	0.742094	+	0.670296i	$0.233833\pi$
$240$	−2.26888e11	−4.41430
$241$	1.06255e10	0.202896	0.101448	−	0.994841i	$-0.467652\pi$
$241$	1.06255e10	0.202896	0.101448	+	0.994841i	$0.467652\pi$
$242$	1.47618e10	0.276674
$243$	−4.87561e10	−0.897017
$244$	2.51806e11	4.54792
$245$	4.79095e10	0.849521
$246$	3.08811e10	0.537632
$247$	1.72129e11	2.94250
$248$	−3.72675e10	−0.625602
$249$	−3.35676e10	−0.553379
$250$	1.02432e11	1.65846
$251$	−9.55285e10	−1.51915	−0.759576	−	0.650418i	$-0.774594\pi$
$251$	−9.55285e10	−1.51915	−0.759576	+	0.650418i	$0.774594\pi$
$252$	−3.90287e10	−0.609652
$253$	−3.36518e10	−0.516376
$254$	2.00393e10	0.302086
$255$	0	0
$256$	8.12676e10	1.18260
$257$	6.50855e10	0.930647	0.465324	−	0.885141i	$-0.345938\pi$
$257$	6.50855e10	0.930647	0.465324	+	0.885141i	$0.345938\pi$
$258$	−7.08125e10	−0.994996
$259$	−1.69127e10	−0.233541
$260$	3.44313e11	4.67276
$261$	−9.66604e8	−0.0128934
$262$	−2.02974e11	−2.66124
$263$	−6.33984e10	−0.817104	−0.408552	−	0.912735i	$-0.633966\pi$
$263$	−6.33984e10	−0.817104	−0.408552	+	0.912735i	$0.633966\pi$
$264$	−3.20166e11	−4.05656
$265$	−9.55806e10	−1.19059
$266$	1.35103e11	1.65462
$267$	−6.72501e10	−0.809826
$268$	5.03526e10	0.596232
$269$	7.50317e10	0.873695	0.436847	−	0.899536i	$-0.356095\pi$
$269$	7.50317e10	0.873695	0.436847	+	0.899536i	$0.356095\pi$
$270$	1.14611e11	1.31247
$271$	−9.55753e10	−1.07643	−0.538213	−	0.842809i	$-0.680900\pi$
$271$	−9.55753e10	−1.07643	−0.538213	+	0.842809i	$0.680900\pi$
$272$	0	0
$273$	8.61314e10	0.938490
$274$	1.76451e11	1.89124
$275$	−2.11406e10	−0.222905
$276$	1.49237e11	1.54805
$277$	1.40532e10	0.143422	0.0717110	−	0.997425i	$-0.477154\pi$
$277$	1.40532e10	0.143422	0.0717110	+	0.997425i	$0.477154\pi$
$278$	1.99095e10	0.199922
$279$	−9.89653e9	−0.0977831
$280$	1.67561e11	1.62915
$281$	1.00661e11	0.963124	0.481562	−	0.876412i	$-0.340070\pi$
$281$	1.00661e11	0.963124	0.481562	+	0.876412i	$0.340070\pi$
$282$	2.93753e11	2.76606
$283$	−7.78714e10	−0.721670	−0.360835	−	0.932630i	$-0.617508\pi$
$283$	−7.78714e10	−0.721670	−0.360835	+	0.932630i	$0.617508\pi$
$284$	−2.75678e11	−2.51461
$285$	2.71879e11	2.44103
$286$	3.72723e11	3.29412
$287$	−1.26780e10	−0.110302
$288$	1.79791e11	1.53993
$289$	0	0
$290$	6.69314e9	0.0555698
$291$	−1.49730e11	−1.22403
$292$	2.63701e11	2.12270
$293$	−8.86150e10	−0.702429	−0.351215	−	0.936295i	$-0.614231\pi$
$293$	−8.86150e10	−0.702429	−0.351215	+	0.936295i	$0.614231\pi$
$294$	−2.29997e11	−1.79539
$295$	−1.47608e11	−1.13478
$296$	2.01239e11	1.52370
$297$	8.99056e10	0.670475
$298$	8.06447e10	0.592383
$299$	−1.07719e11	−0.779423
$300$	9.37528e10	0.668249
$301$	2.90716e10	0.204136
$302$	−2.60839e11	−1.80443
$303$	4.73718e10	0.322871
$304$	−8.93641e11	−6.00111
$305$	−2.87083e11	−1.89958
$306$	0	0
$307$	−1.69929e11	−1.09180	−0.545902	−	0.837849i	$-0.683813\pi$
$307$	−1.69929e11	−1.09180	−0.545902	+	0.837849i	$0.683813\pi$
$308$	2.11995e11	1.34230
$309$	−9.37096e9	−0.0584751
$310$	6.85274e10	0.421441
$311$	−1.18662e11	−0.719265	−0.359633	−	0.933094i	$-0.617098\pi$
$311$	−1.18662e11	−0.719265	−0.359633	+	0.933094i	$0.617098\pi$
$312$	−1.02485e12	−6.12301
$313$	−2.52103e11	−1.48467	−0.742333	−	0.670032i	$-0.766281\pi$
$313$	−2.52103e11	−1.48467	−0.742333	+	0.670032i	$0.766281\pi$
$314$	2.53360e11	1.47080
$315$	4.44964e10	0.254641
$316$	−3.67365e11	−2.07255
$317$	−7.54487e10	−0.419648	−0.209824	−	0.977739i	$-0.567289\pi$
$317$	−7.54487e10	−0.419648	−0.209824	+	0.977739i	$0.567289\pi$
$318$	4.58850e11	2.51622
$319$	5.25038e9	0.0283878
$320$	−5.65702e11	−3.01587
$321$	−2.28055e11	−1.19886
$322$	−8.45486e10	−0.438283
$323$	0	0
$324$	−6.52433e11	−3.28915
$325$	−6.76709e10	−0.336455
$326$	−5.14576e11	−2.52331
$327$	1.20445e11	0.582537
$328$	1.50852e11	0.719645
$329$	−1.20598e11	−0.567492
$330$	5.88720e11	2.73272
$331$	−2.39508e11	−1.09672	−0.548358	−	0.836244i	$-0.684747\pi$
$331$	−2.39508e11	−1.09672	−0.548358	+	0.836244i	$0.684747\pi$
$332$	−2.64466e11	−1.19467
$333$	5.34397e10	0.238158
$334$	−9.13054e10	−0.401455
$335$	−5.74067e10	−0.249035
$336$	−4.47169e11	−1.91401
$337$	−8.05715e10	−0.340288	−0.170144	−	0.985419i	$-0.554423\pi$
$337$	−8.05715e10	−0.340288	−0.170144	+	0.985419i	$0.554423\pi$
$338$	7.35807e11	3.06647
$339$	−2.40131e11	−0.987526
$340$	0	0
$341$	5.37557e10	0.215293
$342$	−4.26891e11	−1.68733
$343$	2.16602e11	0.844964
$344$	−3.45913e11	−1.33185
$345$	−1.70144e11	−0.646592
$346$	−1.88666e11	−0.707703
$347$	3.81897e11	1.41405	0.707024	−	0.707190i	$-0.250037\pi$
$347$	3.81897e11	1.41405	0.707024	+	0.707190i	$0.250037\pi$
$348$	−2.32840e10	−0.0851043
$349$	−2.86306e11	−1.03304	−0.516518	−	0.856276i	$-0.672772\pi$
$349$	−2.86306e11	−1.03304	−0.516518	+	0.856276i	$0.672772\pi$
$350$	−5.31147e10	−0.189195
$351$	2.87788e11	1.01202
$352$	−9.76583e11	−3.39053
$353$	3.83234e10	0.131364	0.0656822	−	0.997841i	$-0.479078\pi$
$353$	3.83234e10	0.131364	0.0656822	+	0.997841i	$0.479078\pi$
$354$	7.08618e11	2.39827
$355$	3.14299e11	1.05030
$356$	−5.29838e11	−1.74831
$357$	0	0
$358$	9.17581e10	0.295237
$359$	−8.46163e10	−0.268862	−0.134431	−	0.990923i	$-0.542921\pi$
$359$	−8.46163e10	−0.268862	−0.134431	+	0.990923i	$0.542921\pi$
$360$	−5.29449e11	−1.66136
$361$	7.48157e11	2.31852
$362$	−7.78323e11	−2.38216
$363$	5.85473e10	0.176981
$364$	6.78598e11	2.02608
$365$	−3.00644e11	−0.886615
$366$	1.37819e12	4.01461
$367$	−6.52825e11	−1.87845	−0.939225	−	0.343301i	$-0.888455\pi$
$367$	−6.52825e11	−1.87845	−0.939225	+	0.343301i	$0.888455\pi$
$368$	5.59246e11	1.58960
$369$	4.00592e10	0.112482
$370$	−3.70037e11	−1.02645
$371$	−1.88377e11	−0.516234
$372$	−2.38392e11	−0.645430
$373$	−9.69405e10	−0.259308	−0.129654	−	0.991559i	$-0.541387\pi$
$373$	−9.69405e10	−0.259308	−0.129654	+	0.991559i	$0.541387\pi$
$374$	0	0
$375$	4.06261e11	1.06088
$376$	1.43496e12	3.70250
$377$	1.68065e10	0.0428489
$378$	2.25884e11	0.569078
$379$	6.80659e11	1.69454	0.847272	−	0.531159i	$-0.178243\pi$
$379$	6.80659e11	1.69454	0.847272	+	0.531159i	$0.178243\pi$
$380$	2.14203e12	5.26987
$381$	7.94788e10	0.193236
$382$	−2.72429e10	−0.0654589
$383$	1.56533e11	0.371717	0.185858	−	0.982577i	$-0.440493\pi$
$383$	1.56533e11	0.371717	0.185858	+	0.982577i	$0.440493\pi$
$384$	1.07010e12	2.51151
$385$	−2.41695e11	−0.560652
$386$	−6.55412e11	−1.50270
$387$	−9.18586e10	−0.208171
$388$	−1.17967e12	−2.64251
$389$	−5.55777e11	−1.23063	−0.615315	−	0.788282i	$-0.710971\pi$
$389$	−5.55777e11	−1.23063	−0.615315	+	0.788282i	$0.710971\pi$
$390$	1.88449e12	4.12481
$391$	0	0
$392$	−1.12352e12	−2.40321
$393$	−8.05025e11	−1.70233
$394$	1.13523e12	2.37328
$395$	4.18830e11	0.865667
$396$	−6.69851e11	−1.36883
$397$	2.61410e11	0.528159	0.264079	−	0.964501i	$-0.414932\pi$
$397$	2.61410e11	0.528159	0.264079	+	0.964501i	$0.414932\pi$
$398$	−1.46708e12	−2.93075
$399$	5.35840e11	1.05842
$400$	3.51327e11	0.686186
$401$	−8.04746e10	−0.155421	−0.0777104	−	0.996976i	$-0.524761\pi$
$401$	−8.04746e10	−0.155421	−0.0777104	+	0.996976i	$0.524761\pi$
$402$	2.75590e11	0.526315
$403$	1.72072e11	0.324966
$404$	3.73225e11	0.697035
$405$	7.43835e11	1.37382
$406$	1.31913e10	0.0240947
$407$	−2.90273e11	−0.524362
$408$	0	0
$409$	4.96676e11	0.877643	0.438822	−	0.898574i	$-0.355396\pi$
$409$	4.96676e11	0.877643	0.438822	+	0.898574i	$0.355396\pi$
$410$	−2.77386e11	−0.484793
$411$	6.99831e11	1.20978
$412$	−7.38303e10	−0.126240
$413$	−2.90918e11	−0.492034
$414$	2.67152e11	0.446947
$415$	3.01516e11	0.498993
$416$	−3.12604e12	−5.11770
$417$	7.89642e10	0.127885
$418$	2.31878e12	3.71506
$419$	−5.00093e11	−0.792661	−0.396331	−	0.918108i	$-0.629717\pi$
$419$	−5.00093e11	−0.792661	−0.396331	+	0.918108i	$0.629717\pi$
$420$	1.07185e12	1.68079
$421$	9.47398e11	1.46982	0.734908	−	0.678167i	$-0.237225\pi$
$421$	9.47398e11	1.46982	0.734908	+	0.678167i	$0.237225\pi$
$422$	9.91436e11	1.52180
$423$	3.81059e11	0.578710
$424$	2.24145e12	3.36808
$425$	0	0
$426$	−1.50884e12	−2.21973
$427$	−5.65805e11	−0.823647
$428$	−1.79676e12	−2.58817
$429$	1.47827e12	2.10716
$430$	6.36064e11	0.897207
$431$	5.09374e11	0.711032	0.355516	−	0.934670i	$-0.384305\pi$
$431$	5.09374e11	0.711032	0.355516	+	0.934670i	$0.384305\pi$
$432$	−1.49411e12	−2.06398
$433$	1.25104e12	1.71032	0.855160	−	0.518365i	$-0.173459\pi$
$433$	1.25104e12	1.71032	0.855160	+	0.518365i	$0.173459\pi$
$434$	1.35059e11	0.182734
$435$	2.65460e10	0.0355465
$436$	9.48940e11	1.25762
$437$	−6.70142e11	−0.879024
$438$	1.44329e12	1.87379
$439$	1.15261e12	1.48112	0.740561	−	0.671989i	$-0.234560\pi$
$439$	1.15261e12	1.48112	0.740561	+	0.671989i	$0.234560\pi$
$440$	2.87585e12	3.65788
$441$	−2.98354e11	−0.375628
$442$	0	0
$443$	1.57617e12	1.94440	0.972199	−	0.234155i	$-0.0752322\pi$
$443$	1.57617e12	1.94440	0.972199	+	0.234155i	$0.0752322\pi$
$444$	1.28728e12	1.57199
$445$	6.04065e11	0.730237
$446$	−2.50800e12	−3.00137
$447$	3.19849e11	0.378932
$448$	−1.11493e12	−1.30766
$449$	1.39885e12	1.62428	0.812141	−	0.583461i	$-0.198302\pi$
$449$	1.39885e12	1.62428	0.812141	+	0.583461i	$0.198302\pi$
$450$	1.67829e11	0.192935
$451$	−2.17593e11	−0.247657
$452$	−1.89190e12	−2.13194
$453$	−1.03452e12	−1.15425
$454$	2.74466e11	0.303205
$455$	−7.73665e11	−0.846255
$456$	−6.37579e12	−6.90546
$457$	3.76472e11	0.403747	0.201874	−	0.979412i	$-0.435297\pi$
$457$	3.76472e11	0.403747	0.201874	+	0.979412i	$0.435297\pi$
$458$	−3.12773e12	−3.32151
$459$	0	0
$460$	−1.34050e12	−1.39591
$461$	2.03996e11	0.210362	0.105181	−	0.994453i	$-0.466458\pi$
$461$	2.03996e11	0.210362	0.105181	+	0.994453i	$0.466458\pi$
$462$	1.16029e12	1.18489
$463$	−1.19166e12	−1.20514	−0.602571	−	0.798065i	$-0.705857\pi$
$463$	−1.19166e12	−1.20514	−0.602571	+	0.798065i	$0.705857\pi$
$464$	−8.72541e10	−0.0873886
$465$	2.71790e11	0.269584
$466$	3.50736e12	3.44543
$467$	−1.20046e12	−1.16795	−0.583973	−	0.811773i	$-0.698503\pi$
$467$	−1.20046e12	−1.16795	−0.583973	+	0.811773i	$0.698503\pi$
$468$	−2.14419e12	−2.06613
$469$	−1.13141e11	−0.107980
$470$	−2.63860e12	−2.49421
$471$	1.00486e12	0.940834
$472$	3.46154e12	3.21019
$473$	4.98955e11	0.458339
$474$	−2.01066e12	−1.82951
$475$	−4.20994e11	−0.379450
$476$	0	0
$477$	5.95224e11	0.526439
$478$	3.22828e12	2.82843
$479$	3.78765e10	0.0328746	0.0164373	−	0.999865i	$-0.494768\pi$
$479$	3.78765e10	0.0328746	0.0164373	+	0.999865i	$0.494768\pi$
$480$	−4.93761e12	−4.24553
$481$	−9.29163e11	−0.791478
$482$	4.58187e11	0.386662
$483$	−3.35332e11	−0.280358
$484$	4.61273e11	0.382079
$485$	1.34493e12	1.10373
$486$	−2.10243e12	−1.70945
$487$	−1.88071e12	−1.51510	−0.757550	−	0.652778i	$-0.773604\pi$
$487$	−1.88071e12	−1.51510	−0.757550	+	0.652778i	$0.773604\pi$
$488$	6.73233e12	5.37374
$489$	−2.04088e12	−1.61409
$490$	2.06592e12	1.61894
$491$	−2.42874e11	−0.188588	−0.0942942	−	0.995544i	$-0.530059\pi$
$491$	−2.42874e11	−0.188588	−0.0942942	+	0.995544i	$0.530059\pi$
$492$	9.64967e11	0.742454
$493$	0	0
$494$	7.42241e12	5.60756
$495$	7.63692e11	0.571735
$496$	−8.93347e11	−0.662754
$497$	6.19444e11	0.455405
$498$	−1.44748e12	−1.05458
$499$	−7.88648e11	−0.569417	−0.284709	−	0.958614i	$-0.591897\pi$
$499$	−7.88648e11	−0.569417	−0.284709	+	0.958614i	$0.591897\pi$
$500$	3.20078e12	2.29029
$501$	−3.62131e11	−0.256800
$502$	−4.11931e12	−2.89506
$503$	−1.92372e12	−1.33994	−0.669972	−	0.742386i	$-0.733694\pi$
$503$	−1.92372e12	−1.33994	−0.669972	+	0.742386i	$0.733694\pi$
$504$	−1.04348e12	−0.720354
$505$	−4.25512e11	−0.291139
$506$	−1.45111e12	−0.984062
$507$	2.91832e12	1.96154
$508$	6.26184e11	0.417172
$509$	2.87805e12	1.90050	0.950250	−	0.311487i	$-0.100827\pi$
$509$	2.87805e12	1.90050	0.950250	+	0.311487i	$0.100827\pi$
$510$	0	0
$511$	−5.92532e11	−0.384431
$512$	3.00794e11	0.193443
$513$	1.79038e12	1.14135
$514$	2.80657e12	1.77354
$515$	8.41734e10	0.0527281
$516$	−2.21273e12	−1.37406
$517$	−2.06983e12	−1.27417
$518$	−7.29297e11	−0.445062
$519$	−7.48277e11	−0.452699
$520$	9.20560e12	5.52124
$521$	−2.41942e12	−1.43861	−0.719303	−	0.694697i	$-0.755539\pi$
$521$	−2.41942e12	−1.43861	−0.719303	+	0.694697i	$0.755539\pi$
$522$	−4.16812e10	−0.0245710
$523$	2.25636e12	1.31872	0.659358	−	0.751829i	$-0.270828\pi$
$523$	2.25636e12	1.31872	0.659358	+	0.751829i	$0.270828\pi$
$524$	−6.34249e12	−3.67510
$525$	−2.10661e11	−0.121023
$526$	−2.73382e12	−1.55716
$527$	0	0
$528$	−7.67476e12	−4.29746
$529$	−1.38177e12	−0.767160
$530$	−4.12156e12	−2.26893
$531$	9.19225e11	0.501760
$532$	4.22168e12	2.28498
$533$	−6.96515e11	−0.373816
$534$	−2.89991e12	−1.54329
$535$	2.04847e12	1.08103
$536$	1.34623e12	0.704497
$537$	3.63926e11	0.188855
$538$	3.23547e12	1.66501
$539$	1.62059e12	0.827036
$540$	3.58134e12	1.81248
$541$	2.18649e12	1.09739	0.548694	−	0.836023i	$-0.315125\pi$
$541$	2.18649e12	1.09739	0.548694	+	0.836023i	$0.315125\pi$
$542$	−4.12133e12	−2.05135
$543$	−3.08695e12	−1.52381
$544$	0	0
$545$	−1.08188e12	−0.525285
$546$	3.71410e12	1.78849
$547$	7.53862e11	0.360039	0.180019	−	0.983663i	$-0.442384\pi$
$547$	7.53862e11	0.360039	0.180019	+	0.983663i	$0.442384\pi$
$548$	5.51371e12	2.61175
$549$	1.78780e12	0.839929
$550$	−9.11608e11	−0.424792
$551$	1.04556e11	0.0483245
$552$	3.99001e12	1.82915
$553$	8.25462e11	0.375348
$554$	6.05991e11	0.273321
$555$	−1.46762e12	−0.656592
$556$	6.22130e11	0.276086
$557$	−2.08949e12	−0.919797	−0.459898	−	0.887972i	$-0.652114\pi$
$557$	−2.08949e12	−0.919797	−0.459898	+	0.887972i	$0.652114\pi$
$558$	−4.26751e11	−0.186346
$559$	1.59716e12	0.691822
$560$	4.01663e12	1.72590
$561$	0	0
$562$	4.34063e12	1.83544
$563$	−6.61278e11	−0.277393	−0.138697	−	0.990335i	$-0.544291\pi$
$563$	−6.61278e11	−0.277393	−0.138697	+	0.990335i	$0.544291\pi$
$564$	9.17915e12	3.81985
$565$	2.15694e12	0.890472
$566$	−3.35791e12	−1.37529
$567$	1.46601e12	0.595679
$568$	−7.37057e12	−2.97121
$569$	−1.47797e12	−0.591100	−0.295550	−	0.955327i	$-0.595503\pi$
$569$	−1.47797e12	−0.591100	−0.295550	+	0.955327i	$0.595503\pi$
$570$	1.17238e13	4.65190
$571$	2.27003e12	0.893652	0.446826	−	0.894621i	$-0.352554\pi$
$571$	2.27003e12	0.893652	0.446826	+	0.894621i	$0.352554\pi$
$572$	1.16468e13	4.54908
$573$	−1.08049e11	−0.0418723
$574$	−5.46692e11	−0.210203
$575$	2.63461e11	0.100510
$576$	3.52289e12	1.33351
$577$	−1.93038e12	−0.725021	−0.362511	−	0.931980i	$-0.618080\pi$
$577$	−1.93038e12	−0.725021	−0.362511	+	0.931980i	$0.618080\pi$
$578$	0	0
$579$	−2.59946e12	−0.961235
$580$	2.09146e11	0.0767402
$581$	5.94251e11	0.216360
$582$	−6.45656e12	−2.33264
$583$	−3.23312e12	−1.15908
$584$	7.05036e12	2.50815
$585$	2.44458e12	0.862984
$586$	−3.82119e12	−1.33863
$587$	2.62778e12	0.913518	0.456759	−	0.889590i	$-0.349010\pi$
$587$	2.62778e12	0.913518	0.456759	+	0.889590i	$0.349010\pi$
$588$	−7.18690e12	−2.47938
$589$	1.07049e12	0.366492
$590$	−6.36507e12	−2.16256
$591$	4.50248e12	1.51813
$592$	4.82393e12	1.61419
$593$	5.85157e12	1.94324	0.971620	−	0.236548i	$-0.0760162\pi$
$593$	5.85157e12	1.94324	0.971620	+	0.236548i	$0.0760162\pi$
$594$	3.87684e12	1.27773
$595$	0	0
$596$	2.51997e12	0.818064
$597$	−5.81865e12	−1.87472
$598$	−4.64500e12	−1.48535
$599$	4.56968e11	0.145033	0.0725163	−	0.997367i	$-0.476897\pi$
$599$	4.56968e11	0.145033	0.0725163	+	0.997367i	$0.476897\pi$
$600$	2.50659e12	0.789591
$601$	4.72333e12	1.47677	0.738385	−	0.674379i	$-0.235589\pi$
$601$	4.72333e12	1.47677	0.738385	+	0.674379i	$0.235589\pi$
$602$	1.25360e12	0.389023
$603$	3.57497e11	0.110115
$604$	−8.15063e12	−2.49187
$605$	−5.25894e11	−0.159588
$606$	2.04274e12	0.615298
$607$	−1.89920e12	−0.567836	−0.283918	−	0.958849i	$-0.591634\pi$
$607$	−1.89920e12	−0.567836	−0.283918	+	0.958849i	$0.591634\pi$
$608$	−1.94477e13	−5.77168
$609$	5.23188e10	0.0154127
$610$	−1.23794e13	−3.62005
$611$	−6.62553e12	−1.92325
$612$	0	0
$613$	−5.38704e12	−1.54091	−0.770456	−	0.637493i	$-0.779971\pi$
$613$	−5.38704e12	−1.54091	−0.770456	+	0.637493i	$0.779971\pi$
$614$	−7.32756e12	−2.08066
$615$	−1.10015e12	−0.310109
$616$	5.66794e12	1.58603
$617$	5.80011e11	0.161121	0.0805607	−	0.996750i	$-0.474329\pi$
$617$	5.80011e11	0.161121	0.0805607	+	0.996750i	$0.474329\pi$
$618$	−4.04088e11	−0.111437
$619$	1.58371e12	0.433579	0.216790	−	0.976218i	$-0.430441\pi$
$619$	1.58371e12	0.433579	0.216790	+	0.976218i	$0.430441\pi$
$620$	2.14133e12	0.581997
$621$	−1.12043e12	−0.302325
$622$	−5.11685e12	−1.37071
$623$	1.19054e12	0.316626
$624$	−2.45669e13	−6.48664
$625$	−4.44378e12	−1.16491
$626$	−1.08710e13	−2.82934
$627$	9.19662e12	2.37643
$628$	7.91695e12	2.03114
$629$	0	0
$630$	1.91874e12	0.485271
$631$	3.36740e12	0.845595	0.422797	−	0.906224i	$-0.361048\pi$
$631$	3.36740e12	0.845595	0.422797	+	0.906224i	$0.361048\pi$
$632$	−9.82191e12	−2.44889
$633$	3.93218e12	0.973458
$634$	−3.25344e12	−0.799727
$635$	−7.13908e11	−0.174245
$636$	1.43381e13	3.47483
$637$	5.18752e12	1.24834
$638$	2.26403e11	0.0540990
$639$	−1.95728e12	−0.464408
$640$	−9.61205e12	−2.26468
$641$	7.80868e12	1.82691	0.913454	−	0.406943i	$-0.133405\pi$
$641$	7.80868e12	1.82691	0.913454	+	0.406943i	$0.133405\pi$
$642$	−9.83402e12	−2.28467
$643$	2.11639e12	0.488255	0.244128	−	0.969743i	$-0.421498\pi$
$643$	2.11639e12	0.488255	0.244128	+	0.969743i	$0.421498\pi$
$644$	−2.64196e12	−0.605257
$645$	2.52272e12	0.573920
$646$	0	0
$647$	3.18454e12	0.714460	0.357230	−	0.934016i	$-0.383721\pi$
$647$	3.18454e12	0.714460	0.357230	+	0.934016i	$0.383721\pi$
$648$	−1.74436e13	−3.88640
$649$	−4.99302e12	−1.10475
$650$	−2.91806e12	−0.641186
$651$	5.35664e11	0.116890
$652$	−1.60794e13	−3.48462
$653$	−1.82854e12	−0.393545	−0.196772	−	0.980449i	$-0.563046\pi$
$653$	−1.82854e12	−0.393545	−0.196772	+	0.980449i	$0.563046\pi$
$654$	5.19374e12	1.11015
$655$	7.23104e12	1.53502
$656$	3.61609e12	0.762382
$657$	1.87225e12	0.392030
$658$	−5.20036e12	−1.08148
$659$	7.92252e11	0.163636	0.0818181	−	0.996647i	$-0.473927\pi$
$659$	7.92252e11	0.163636	0.0818181	+	0.996647i	$0.473927\pi$
$660$	1.83962e13	3.77381
$661$	−7.49133e11	−0.152634	−0.0763172	−	0.997084i	$-0.524316\pi$
$661$	−7.49133e11	−0.152634	−0.0763172	+	0.997084i	$0.524316\pi$
$662$	−1.03279e13	−2.09002
$663$	0	0
$664$	−7.07081e12	−1.41160
$665$	−4.81311e12	−0.954396
$666$	2.30439e12	0.453860
$667$	−6.54319e10	−0.0128004
$668$	−2.85309e12	−0.554398
$669$	−9.94708e12	−1.91990
$670$	−2.47545e12	−0.474589
$671$	−9.71091e12	−1.84931
$672$	−9.73142e12	−1.84083
$673$	−7.01486e12	−1.31811	−0.659055	−	0.752095i	$-0.729043\pi$
$673$	−7.01486e12	−1.31811	−0.659055	+	0.752095i	$0.729043\pi$
$674$	−3.47435e12	−0.648490
$675$	−7.03873e11	−0.130505
$676$	2.29923e13	4.23471
$677$	−7.71992e12	−1.41242	−0.706210	−	0.708002i	$-0.749597\pi$
$677$	−7.71992e12	−1.41242	−0.706210	+	0.708002i	$0.749597\pi$
$678$	−1.03547e13	−1.88194
$679$	2.65069e12	0.478570
$680$	0	0
$681$	1.08857e12	0.193952
$682$	2.31802e12	0.410286
$683$	4.25216e12	0.747680	0.373840	−	0.927493i	$-0.378041\pi$
$683$	4.25216e12	0.747680	0.373840	+	0.927493i	$0.378041\pi$
$684$	−1.33394e13	−2.33015
$685$	−6.28614e12	−1.09088
$686$	9.34014e12	1.61026
$687$	−1.24051e13	−2.12468
$688$	−8.29195e12	−1.41094
$689$	−1.03492e13	−1.74953
$690$	−7.33682e12	−1.23222
$691$	2.49111e12	0.415664	0.207832	−	0.978165i	$-0.433359\pi$
$691$	2.49111e12	0.415664	0.207832	+	0.978165i	$0.433359\pi$
$692$	−5.89539e12	−0.977317
$693$	1.50514e12	0.247901
$694$	1.64679e13	2.69476
$695$	−7.09286e11	−0.115316
$696$	−6.22525e11	−0.100558
$697$	0	0
$698$	−1.23459e13	−1.96867
$699$	1.39107e13	2.20395
$700$	−1.65972e12	−0.261272
$701$	−3.08136e11	−0.0481961	−0.0240980	−	0.999710i	$-0.507671\pi$
$701$	−3.08136e11	−0.0481961	−0.0240980	+	0.999710i	$0.507671\pi$
$702$	1.24098e13	1.92862
$703$	−5.78049e12	−0.892619
$704$	−1.91355e13	−2.93605
$705$	−1.04651e13	−1.59548
$706$	1.65255e12	0.250342
$707$	−8.38630e11	−0.126236
$708$	2.21427e13	3.31194
$709$	6.98388e12	1.03798	0.518990	−	0.854780i	$-0.326308\pi$
$709$	6.98388e12	1.03798	0.518990	+	0.854780i	$0.326308\pi$
$710$	1.35530e13	2.00158
$711$	−2.60824e12	−0.382768
$712$	−1.41658e13	−2.06577
$713$	−6.69922e11	−0.0970781
$714$	0	0
$715$	−1.32784e13	−1.90007
$716$	2.86724e12	0.407714
$717$	1.28038e13	1.80927
$718$	−3.64876e12	−0.512373
$719$	1.30686e13	1.82368	0.911842	−	0.410540i	$-0.134660\pi$
$719$	1.30686e13	1.82368	0.911842	+	0.410540i	$0.134660\pi$
$720$	−1.26915e13	−1.76002
$721$	1.65895e11	0.0228626
$722$	3.22615e13	4.41842
$723$	1.81724e12	0.247337
$724$	−2.43209e13	−3.28970
$725$	−4.11053e10	−0.00552557
$726$	2.52464e12	0.337275
$727$	−1.13650e12	−0.150891	−0.0754456	−	0.997150i	$-0.524038\pi$
$727$	−1.13650e12	−0.150891	−0.0754456	+	0.997150i	$0.524038\pi$
$728$	1.81431e13	2.39398
$729$	1.19197e12	0.156312
$730$	−1.29642e13	−1.68963
$731$	0	0
$732$	4.30653e13	5.54406
$733$	5.78287e12	0.739904	0.369952	−	0.929051i	$-0.379374\pi$
$733$	5.78287e12	0.739904	0.369952	+	0.929051i	$0.379374\pi$
$734$	−2.81507e13	−3.57978
$735$	8.19374e12	1.03559
$736$	1.21705e13	1.52883
$737$	−1.94185e12	−0.242444
$738$	1.72741e12	0.214359
$739$	−1.05562e13	−1.30199	−0.650996	−	0.759081i	$-0.725649\pi$
$739$	−1.05562e13	−1.30199	−0.650996	+	0.759081i	$0.725649\pi$
$740$	−1.15628e13	−1.41750
$741$	2.94384e13	3.58701
$742$	−8.12308e12	−0.983792
$743$	−1.33049e13	−1.60163	−0.800815	−	0.598912i	$-0.795600\pi$
$743$	−1.33049e13	−1.60163	−0.800815	+	0.598912i	$0.795600\pi$
$744$	−6.37370e12	−0.762629
$745$	−2.87300e12	−0.341690
$746$	−4.18020e12	−0.494165
$747$	−1.87768e12	−0.220637
$748$	0	0
$749$	4.03729e12	0.468729
$750$	1.75185e13	2.02172
$751$	2.33606e12	0.267982	0.133991	−	0.990983i	$-0.457221\pi$
$751$	2.33606e12	0.267982	0.133991	+	0.990983i	$0.457221\pi$
$752$	3.43977e13	3.92238
$753$	−1.63378e13	−1.85190
$754$	7.24716e11	0.0816576
$755$	9.29248e12	1.04081
$756$	7.05837e12	0.785880
$757$	−1.17644e13	−1.30208	−0.651039	−	0.759045i	$-0.725666\pi$
$757$	−1.17644e13	−1.30208	−0.651039	+	0.759045i	$0.725666\pi$
$758$	2.93509e13	3.22931
$759$	−5.75531e12	−0.629478
$760$	5.72697e13	6.22679
$761$	3.21795e12	0.347815	0.173907	−	0.984762i	$-0.444361\pi$
$761$	3.21795e12	0.347815	0.173907	+	0.984762i	$0.444361\pi$
$762$	3.42723e12	0.368252
$763$	−2.13225e12	−0.227760
$764$	−8.51281e11	−0.0903968
$765$	0	0
$766$	6.74991e12	0.708384
$767$	−1.59827e13	−1.66752
$768$	1.38988e13	1.44163
$769$	−9.65995e12	−0.996108	−0.498054	−	0.867146i	$-0.665952\pi$
$769$	−9.65995e12	−0.996108	−0.498054	+	0.867146i	$0.665952\pi$
$770$	−1.04222e13	−1.06844
$771$	1.11313e13	1.13449
$772$	−2.04802e13	−2.07518
$773$	−3.02219e12	−0.304449	−0.152224	−	0.988346i	$-0.548644\pi$
$773$	−3.02219e12	−0.304449	−0.152224	+	0.988346i	$0.548644\pi$
$774$	−3.96106e12	−0.396714
$775$	−4.20855e11	−0.0419059
$776$	−3.15398e13	−3.12235
$777$	−2.89250e12	−0.284694
$778$	−2.39658e13	−2.34522
$779$	−4.33315e12	−0.421585
$780$	5.88863e13	5.69624
$781$	1.06315e13	1.02251
$782$	0	0
$783$	1.74811e11	0.0166204
$784$	−2.69320e13	−2.54593
$785$	−9.02606e12	−0.848369
$786$	−3.47137e13	−3.24414
$787$	1.47037e13	1.36628	0.683141	−	0.730286i	$-0.260613\pi$
$787$	1.47037e13	1.36628	0.683141	+	0.730286i	$0.260613\pi$
$788$	3.54734e13	3.27744
$789$	−1.08427e13	−0.996076
$790$	1.80605e13	1.64971
$791$	4.25106e12	0.386103
$792$	−1.79092e13	−1.61739
$793$	−3.10846e13	−2.79136
$794$	1.12723e13	1.00652
$795$	−1.63467e13	−1.45137
$796$	−4.58430e13	−4.04729
$797$	−1.44405e13	−1.26771	−0.633856	−	0.773451i	$-0.718529\pi$
$797$	−1.44405e13	−1.26771	−0.633856	+	0.773451i	$0.718529\pi$
$798$	2.31061e13	2.01704
$799$	0	0
$800$	7.64569e12	0.659951
$801$	−3.76179e12	−0.322885
$802$	−3.47017e12	−0.296187
$803$	−1.01696e13	−0.863148
$804$	8.61158e12	0.726826
$805$	3.01208e12	0.252805
$806$	7.41997e12	0.619291
$807$	1.28323e13	1.06506
$808$	9.97860e12	0.823604
$809$	−1.10265e13	−0.905041	−0.452521	−	0.891754i	$-0.649475\pi$
$809$	−1.10265e13	−0.905041	−0.452521	+	0.891754i	$0.649475\pi$
$810$	3.20751e13	2.61810
$811$	−1.97221e12	−0.160088	−0.0800440	−	0.996791i	$-0.525506\pi$
$811$	−1.97221e12	−0.160088	−0.0800440	+	0.996791i	$0.525506\pi$
$812$	4.12200e11	0.0332741
$813$	−1.63458e13	−1.31220
$814$	−1.25169e13	−0.999282
$815$	1.83320e13	1.45546
$816$	0	0
$817$	9.93621e12	0.780228
$818$	2.14173e13	1.67253
$819$	4.81796e12	0.374184
$820$	−8.66769e12	−0.669485
$821$	1.24725e13	0.958093	0.479047	−	0.877789i	$-0.340982\pi$
$821$	1.24725e13	0.958093	0.479047	+	0.877789i	$0.340982\pi$
$822$	3.01776e13	2.30548
$823$	−5.63904e12	−0.428455	−0.214228	−	0.976784i	$-0.568723\pi$
$823$	−5.63904e12	−0.428455	−0.214228	+	0.976784i	$0.568723\pi$
$824$	−1.97394e12	−0.149163
$825$	−3.61557e12	−0.271728
$826$	−1.25448e13	−0.937674
$827$	6.43118e12	0.478097	0.239048	−	0.971008i	$-0.423165\pi$
$827$	6.43118e12	0.478097	0.239048	+	0.971008i	$0.423165\pi$
$828$	8.34790e12	0.617221
$829$	−4.51844e12	−0.332272	−0.166136	−	0.986103i	$-0.553129\pi$
$829$	−4.51844e12	−0.332272	−0.166136	+	0.986103i	$0.553129\pi$
$830$	1.30018e13	0.950936
$831$	2.40345e12	0.174836
$832$	−6.12529e13	−4.43171
$833$	0	0
$834$	3.40504e12	0.243711
$835$	3.25279e12	0.231562
$836$	7.24568e13	5.13039
$837$	1.78979e12	0.126049
$838$	−2.15647e13	−1.51058
$839$	−1.73764e13	−1.21068	−0.605342	−	0.795965i	$-0.706964\pi$
$839$	−1.73764e13	−1.21068	−0.605342	+	0.795965i	$0.706964\pi$
$840$	2.86572e13	1.98599
$841$	−1.44969e13	−0.999296
$842$	4.08530e13	2.80104
$843$	1.72156e13	1.17408
$844$	3.09802e13	2.10157
$845$	−2.62134e13	−1.76876
$846$	1.64318e13	1.10285
$847$	−1.03647e12	−0.0691962
$848$	5.37301e13	3.56809
$849$	−1.33180e13	−0.879739
$850$	0	0
$851$	3.61747e12	0.236441
$852$	−4.71480e13	−3.06538
$853$	3.23489e12	0.209213	0.104607	−	0.994514i	$-0.466642\pi$
$853$	3.23489e12	0.209213	0.104607	+	0.994514i	$0.466642\pi$
$854$	−2.43982e13	−1.56963
$855$	1.52082e13	0.973262
$856$	−4.80384e13	−3.05814
$857$	−6.56773e12	−0.415912	−0.207956	−	0.978138i	$-0.566681\pi$
$857$	−6.56773e12	−0.415912	−0.207956	+	0.978138i	$0.566681\pi$
$858$	6.37451e13	4.01563
$859$	−1.06597e13	−0.668001	−0.334000	−	0.942573i	$-0.608399\pi$
$859$	−1.06597e13	−0.668001	−0.334000	+	0.942573i	$0.608399\pi$
$860$	1.98756e13	1.23902
$861$	−2.16826e12	−0.134461
$862$	2.19649e13	1.35502
$863$	−2.96333e12	−0.181857	−0.0909287	−	0.995857i	$-0.528984\pi$
$863$	−2.96333e12	−0.181857	−0.0909287	+	0.995857i	$0.528984\pi$
$864$	−3.25152e13	−1.98507
$865$	6.72130e12	0.408207
$866$	5.39466e13	3.25937
$867$	0	0
$868$	4.22029e12	0.252350
$869$	1.41674e13	0.842755
$870$	1.14470e12	0.0677413
$871$	−6.21585e12	−0.365948
$872$	2.53710e13	1.48598
$873$	−8.37551e12	−0.488030
$874$	−2.88974e13	−1.67516
$875$	−7.19209e12	−0.414781
$876$	4.50996e13	2.58764
$877$	1.22652e13	0.700128	0.350064	−	0.936726i	$-0.386160\pi$
$877$	1.22652e13	0.700128	0.350064	+	0.936726i	$0.386160\pi$
$878$	4.97019e13	2.82259
$879$	−1.51554e13	−0.856284
$880$	6.89375e13	3.87511
$881$	−2.36185e13	−1.32087	−0.660435	−	0.750883i	$-0.729628\pi$
$881$	−2.36185e13	−1.32087	−0.660435	+	0.750883i	$0.729628\pi$
$882$	−1.28654e13	−0.715839
$883$	2.46792e13	1.36618	0.683089	−	0.730335i	$-0.260636\pi$
$883$	2.46792e13	1.36618	0.683089	+	0.730335i	$0.260636\pi$
$884$	0	0
$885$	−2.52448e13	−1.38333
$886$	6.79663e13	3.70546
$887$	8.49974e12	0.461051	0.230526	−	0.973066i	$-0.425955\pi$
$887$	8.49974e12	0.461051	0.230526	+	0.973066i	$0.425955\pi$
$888$	3.44170e13	1.85744
$889$	−1.40702e12	−0.0755516
$890$	2.60481e13	1.39162
$891$	2.51611e13	1.33746
$892$	−7.83694e13	−4.14481
$893$	−4.12186e13	−2.16901
$894$	1.37923e13	0.722134
$895$	−3.26892e12	−0.170295
$896$	−1.89442e13	−0.981950
$897$	−1.84228e13	−0.950142
$898$	6.03201e13	3.09541
$899$	1.04522e11	0.00533689
$900$	5.24428e12	0.266437
$901$	0	0
$902$	−9.38288e12	−0.471962
$903$	4.97197e12	0.248848
$904$	−5.05821e13	−2.51906
$905$	2.77281e13	1.37405
$906$	−4.46100e13	−2.19966
$907$	1.51717e13	0.744390	0.372195	−	0.928155i	$-0.378605\pi$
$907$	1.51717e13	0.744390	0.372195	+	0.928155i	$0.378605\pi$
$908$	8.57645e12	0.418718
$909$	2.64985e12	0.128731
$910$	−3.33614e13	−1.61272
$911$	2.65044e12	0.127493	0.0637464	−	0.997966i	$-0.479695\pi$
$911$	2.65044e12	0.127493	0.0637464	+	0.997966i	$0.479695\pi$
$912$	−1.52835e14	−7.31555
$913$	1.01991e13	0.485786
$914$	1.62340e13	0.769425
$915$	−4.90985e13	−2.31565
$916$	−9.77348e13	−4.58690
$917$	1.42515e13	0.665576
$918$	0	0
$919$	−1.10783e13	−0.512336	−0.256168	−	0.966632i	$-0.582460\pi$
$919$	−1.10783e13	−0.512336	−0.256168	+	0.966632i	$0.582460\pi$
$920$	−3.58398e13	−1.64938
$921$	−2.90622e13	−1.33094
$922$	8.79656e12	0.400889
$923$	3.40315e13	1.54338
$924$	3.62566e13	1.63630
$925$	2.27255e12	0.102065
$926$	−5.13860e13	−2.29665
$927$	−5.24186e11	−0.0233145
$928$	−1.89885e12	−0.0840475
$929$	1.10570e13	0.487044	0.243522	−	0.969895i	$-0.421697\pi$
$929$	1.10570e13	0.487044	0.243522	+	0.969895i	$0.421697\pi$
$930$	1.17199e13	0.513750
$931$	3.22725e13	1.40786
$932$	1.09597e14	4.75804
$933$	−2.02942e13	−0.876808
$934$	−5.17655e13	−2.22577
$935$	0	0
$936$	−5.73274e13	−2.44130
$937$	−3.12152e13	−1.32293	−0.661466	−	0.749975i	$-0.730065\pi$
$937$	−3.12152e13	−1.32293	−0.661466	+	0.749975i	$0.730065\pi$
$938$	−4.87880e12	−0.205779
$939$	−4.31160e13	−1.80985
$940$	−8.24505e13	−3.44444
$941$	−3.48495e13	−1.44891	−0.724457	−	0.689320i	$-0.757910\pi$
$941$	−3.48495e13	−1.44891	−0.724457	+	0.689320i	$0.757910\pi$
$942$	4.33310e13	1.79296
$943$	2.71171e12	0.111671
$944$	8.29772e13	3.40083
$945$	−8.04720e12	−0.328248
$946$	2.15156e13	0.873460
$947$	−2.89060e13	−1.16792	−0.583960	−	0.811783i	$-0.698497\pi$
$947$	−2.89060e13	−1.16792	−0.583960	+	0.811783i	$0.698497\pi$
$948$	−6.28287e13	−2.52651
$949$	−3.25530e13	−1.30285
$950$	−1.81538e13	−0.723121
$951$	−1.29036e13	−0.511564
$952$	0	0
$953$	1.17377e13	0.460963	0.230482	−	0.973077i	$-0.425970\pi$
$953$	1.17377e13	0.460963	0.230482	+	0.973077i	$0.425970\pi$
$954$	2.56668e13	1.00324
$955$	9.70540e11	0.0377571
$956$	1.00877e14	3.90598
$957$	8.97948e11	0.0346057
$958$	1.63328e12	0.0626494
$959$	−1.23892e13	−0.472998
$960$	−9.67495e13	−3.67645
$961$	−2.53695e13	−0.959525
$962$	−4.00667e13	−1.50833
$963$	−1.27568e13	−0.477994
$964$	1.43173e13	0.533969
$965$	2.33493e13	0.866765
$966$	−1.44600e13	−0.534281
$967$	4.64159e13	1.70705	0.853527	−	0.521048i	$-0.174459\pi$
$967$	4.64159e13	1.70705	0.853527	+	0.521048i	$0.174459\pi$
$968$	1.23327e13	0.451458
$969$	0	0
$970$	5.79952e13	2.10339
$971$	−3.56315e12	−0.128632	−0.0643158	−	0.997930i	$-0.520486\pi$
$971$	−3.56315e12	−0.128632	−0.0643158	+	0.997930i	$0.520486\pi$
$972$	−6.56962e13	−2.36071
$973$	−1.39791e12	−0.0500003
$974$	−8.10986e13	−2.88734
$975$	−1.15735e13	−0.410150
$976$	1.61382e14	5.69287
$977$	−1.39593e13	−0.490160	−0.245080	−	0.969503i	$-0.578814\pi$
$977$	−1.39593e13	−0.490160	−0.245080	+	0.969503i	$0.578814\pi$
$978$	−8.80056e13	−3.07599
$979$	2.04332e13	0.710909
$980$	6.45554e13	2.23571
$981$	6.73736e12	0.232263
$982$	−1.04731e13	−0.359395
$983$	6.28271e12	0.214613	0.107306	−	0.994226i	$-0.465777\pi$
$983$	6.28271e12	0.214613	0.107306	+	0.994226i	$0.465777\pi$
$984$	2.57995e13	0.877270
$985$	−4.04429e13	−1.36893
$986$	0	0
$987$	−2.06254e13	−0.691791
$988$	2.31934e14	7.74388
$989$	−6.21815e12	−0.206670
$990$	3.29314e13	1.08956
$991$	4.49640e13	1.48093	0.740463	−	0.672097i	$-0.234606\pi$
$991$	4.49640e13	1.48093	0.740463	+	0.672097i	$0.234606\pi$
$992$	−1.94413e13	−0.637416
$993$	−4.09619e13	−1.33693
$994$	2.67112e13	0.867871
$995$	5.22653e13	1.69048
$996$	−4.52305e13	−1.45634
$997$	1.21770e13	0.390311	0.195156	−	0.980772i	$-0.437479\pi$
$997$	1.21770e13	0.390311	0.195156	+	0.980772i	$0.437479\pi$
$998$	−3.40075e13	−1.08514
$999$	−9.66460e12	−0.307001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.b.1.7		7
17.16	even	2		17.10.a.b.1.7	✓	7
51.50	odd	2		153.10.a.f.1.1		7
68.67	odd	2		272.10.a.g.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.7	✓	7	17.16	even	2
153.10.a.f.1.1		7	51.50	odd	2
272.10.a.g.1.6		7	68.67	odd	2
289.10.a.b.1.7		7	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)

\(f(q)\)	\(=\)	\(q+43.1213 q^{2} +171.025 q^{3} +1347.45 q^{4} -1536.21 q^{5} +7374.84 q^{6} -3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} +O(q^{10})\)	\(q+43.1213 q^{2} +171.025 q^{3} +1347.45 q^{4} -1536.21 q^{5} +7374.84 q^{6} -3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} -66243.5 q^{10} -51964.2 q^{11} +230448. q^{12} -166337. q^{13} -130558. q^{14} -262732. q^{15} +863574. q^{16} +412529. q^{18} -1.03482e6 q^{19} -2.06997e6 q^{20} -517811. q^{21} -2.24076e6 q^{22} +647595. q^{23} +6.16128e6 q^{24} +406829. q^{25} -7.17269e6 q^{26} -1.73014e6 q^{27} -4.07964e6 q^{28} -101038. q^{29} -1.13293e7 q^{30} -1.03448e6 q^{31} +1.87934e7 q^{32} -8.88720e6 q^{33} +4.65118e6 q^{35} +1.28906e7 q^{36} +5.58601e6 q^{37} -4.46226e7 q^{38} -2.84479e7 q^{39} -5.53429e7 q^{40} +4.18736e6 q^{41} -2.23287e7 q^{42} -9.60190e6 q^{43} -7.00190e7 q^{44} -1.46965e7 q^{45} +2.79251e7 q^{46} +3.98318e7 q^{47} +1.47693e8 q^{48} -3.11867e7 q^{49} +1.75430e7 q^{50} -2.24131e8 q^{52} +6.22183e7 q^{53} -7.46060e7 q^{54} +7.98282e7 q^{55} -1.09074e8 q^{56} -1.76980e8 q^{57} -4.35690e6 q^{58} +9.60858e7 q^{59} -3.54017e8 q^{60} +1.86877e8 q^{61} -4.46079e7 q^{62} -2.89650e7 q^{63} +3.68245e8 q^{64} +2.55530e8 q^{65} -3.83228e8 q^{66} +3.73689e7 q^{67} +1.10755e8 q^{69} +2.00565e8 q^{70} -2.04593e8 q^{71} +3.44645e8 q^{72} +1.95705e8 q^{73} +2.40876e8 q^{74} +6.95782e7 q^{75} -1.39436e9 q^{76} +1.57331e8 q^{77} -1.22671e9 q^{78} -2.72638e8 q^{79} -1.32663e9 q^{80} -4.84200e8 q^{81} +1.80564e8 q^{82} -1.96272e8 q^{83} -6.97723e8 q^{84} -4.14046e8 q^{86} -1.72801e7 q^{87} -1.87204e9 q^{88} -3.93217e8 q^{89} -6.33732e8 q^{90} +5.03618e8 q^{91} +8.72600e8 q^{92} -1.76922e8 q^{93} +1.71760e9 q^{94} +1.58970e9 q^{95} +3.21414e9 q^{96} -8.75485e8 q^{97} -1.34481e9 q^{98} -4.97126e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - 88 q^{3} + 2389 q^{4} - 1362 q^{5} + 11720 q^{6} - 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) \) 7 * q - q^2 - 88 * q^3 + 2389 * q^4 - 1362 * q^5 + 11720 * q^6 - 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} - 88 q^{3} + 2389 q^{4} - 1362 q^{5} + 11720 q^{6} - 9388 q^{7} + 16821 q^{8} + 81419 q^{9} - 154226 q^{10} - 135536 q^{11} - 198160 q^{12} + 166122 q^{13} - 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 149027 q^{18} + 777172 q^{19} + 917162 q^{20} - 3412104 q^{21} + 1222520 q^{22} - 1357764 q^{23} + 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} + 4519064 q^{27} + 3328892 q^{28} - 967002 q^{29} - 12558992 q^{30} - 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 530736 q^{35} + 4535009 q^{36} - 18296498 q^{37} - 49363020 q^{38} - 86306872 q^{39} - 127155062 q^{40} - 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} - 96696624 q^{44} - 108916410 q^{45} + 151509484 q^{46} + 56639800 q^{47} + 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} - 156226378 q^{52} + 121813562 q^{53} + 93375344 q^{54} + 40793128 q^{55} + 196175436 q^{56} - 153612960 q^{57} + 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} + 49915846 q^{61} + 73506556 q^{62} + 2185356 q^{63} + 317922057 q^{64} + 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 379683432 q^{69} + 966315960 q^{70} - 652473940 q^{71} + 655760385 q^{72} - 306656342 q^{73} - 249173874 q^{74} - 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} - 323434416 q^{78} - 959147884 q^{79} + 692173602 q^{80} - 374486977 q^{81} - 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} - 164953236 q^{86} - 1612550856 q^{87} - 1132038848 q^{88} - 1971327114 q^{89} + 2284664662 q^{90} + 1061062864 q^{91} - 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} + 3249631512 q^{95} + 4442036640 q^{96} - 2006526254 q^{97} - 2170640009 q^{98} + 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 - 88 * q^3 + 2389 * q^4 - 1362 * q^5 + 11720 * q^6 - 9388 * q^7 + 16821 * q^8 + 81419 * q^9 - 154226 * q^10 - 135536 * q^11 - 198160 * q^12 + 166122 * q^13 - 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 149027 * q^18 + 777172 * q^19 + 917162 * q^20 - 3412104 * q^21 + 1222520 * q^22 - 1357764 * q^23 + 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 + 4519064 * q^27 + 3328892 * q^28 - 967002 * q^29 - 12558992 * q^30 - 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 530736 * q^35 + 4535009 * q^36 - 18296498 * q^37 - 49363020 * q^38 - 86306872 * q^39 - 127155062 * q^40 - 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 - 96696624 * q^44 - 108916410 * q^45 + 151509484 * q^46 + 56639800 * q^47 + 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 - 156226378 * q^52 + 121813562 * q^53 + 93375344 * q^54 + 40793128 * q^55 + 196175436 * q^56 - 153612960 * q^57 + 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 + 49915846 * q^61 + 73506556 * q^62 + 2185356 * q^63 + 317922057 * q^64 + 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 379683432 * q^69 + 966315960 * q^70 - 652473940 * q^71 + 655760385 * q^72 - 306656342 * q^73 - 249173874 * q^74 - 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 - 323434416 * q^78 - 959147884 * q^79 + 692173602 * q^80 - 374486977 * q^81 - 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 - 164953236 * q^86 - 1612550856 * q^87 - 1132038848 * q^88 - 1971327114 * q^89 + 2284664662 * q^90 + 1061062864 * q^91 - 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 + 3249631512 * q^95 + 4442036640 * q^96 - 2006526254 * q^97 - 2170640009 * q^98 + 2579159272 * q^99

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