LMFDB - Embedded newform 17.10.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, 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("17.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.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:	$8.75560921479$
Analytic rank:	$0$
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:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-43.1213$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+43.1213 q^{2} -171.025 q^{3} +1347.45 q^{4} +1536.21 q^{5} -7374.84 q^{6} +3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} +O(q^{10})$	\(q+43.1213 q^{2} -171.025 q^{3} +1347.45 q^{4} +1536.21 q^{5} -7374.84 q^{6} +3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} +66243.5 q^{10} +51964.2 q^{11} -230448. q^{12} -166337. q^{13} +130558. q^{14} -262732. q^{15} +863574. q^{16} +83521.0 q^{17} +412529. q^{18} -1.03482e6 q^{19} +2.06997e6 q^{20} -517811. q^{21} +2.24076e6 q^{22} -647595. q^{23} -6.16128e6 q^{24} +406829. q^{25} -7.17269e6 q^{26} +1.73014e6 q^{27} +4.07964e6 q^{28} +101038. q^{29} -1.13293e7 q^{30} +1.03448e6 q^{31} +1.87934e7 q^{32} -8.88720e6 q^{33} +3.60153e6 q^{34} +4.65118e6 q^{35} +1.28906e7 q^{36} -5.58601e6 q^{37} -4.46226e7 q^{38} +2.84479e7 q^{39} +5.53429e7 q^{40} -4.18736e6 q^{41} -2.23287e7 q^{42} -9.60190e6 q^{43} +7.00190e7 q^{44} +1.46965e7 q^{45} -2.79251e7 q^{46} +3.98318e7 q^{47} -1.47693e8 q^{48} -3.11867e7 q^{49} +1.75430e7 q^{50} -1.42842e7 q^{51} -2.24131e8 q^{52} +6.22183e7 q^{53} +7.46060e7 q^{54} +7.98282e7 q^{55} +1.09074e8 q^{56} +1.76980e8 q^{57} +4.35690e6 q^{58} +9.60858e7 q^{59} -3.54017e8 q^{60} -1.86877e8 q^{61} +4.46079e7 q^{62} +2.89650e7 q^{63} +3.68245e8 q^{64} -2.55530e8 q^{65} -3.83228e8 q^{66} +3.73689e7 q^{67} +1.12540e8 q^{68} +1.10755e8 q^{69} +2.00565e8 q^{70} +2.04593e8 q^{71} +3.44645e8 q^{72} -1.95705e8 q^{73} -2.40876e8 q^{74} -6.95782e7 q^{75} -1.39436e9 q^{76} +1.57331e8 q^{77} +1.22671e9 q^{78} +2.72638e8 q^{79} +1.32663e9 q^{80} -4.84200e8 q^{81} -1.80564e8 q^{82} -1.96272e8 q^{83} -6.97723e8 q^{84} +1.28306e8 q^{85} -4.14046e8 q^{86} -1.72801e7 q^{87} +1.87204e9 q^{88} -3.93217e8 q^{89} +6.33732e8 q^{90} -5.03618e8 q^{91} -8.72600e8 q^{92} -1.76922e8 q^{93} +1.71760e9 q^{94} -1.58970e9 q^{95} -3.21414e9 q^{96} +8.75485e8 q^{97} -1.34481e9 q^{98} +4.97126e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 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 + 584647 * q^17 + 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 - 83521 * q^34 - 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 + 7349848 * q^51 - 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 + 199531669 * q^68 + 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 + 113755602 * q^85 - 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	$-0.708636\pi$
$3$	−171.025	−1.21903	−0.609516	+	0.792774i	$0.708636\pi$
$4$	1347.45	2.63173
$5$	1536.21	1.09923	0.549613	−	0.835420i	$-0.314775\pi$
$5$	1536.21	1.09923	0.549613	+	0.835420i	$0.314775\pi$
$6$	−7374.84	−2.32312
$7$	3027.69	0.476617	0.238309	−	0.971189i	$-0.423407\pi$
$7$	3027.69	0.476617	0.238309	+	0.971189i	$0.423407\pi$
$8$	36025.5	3.10960
$9$	9566.70	0.486039
$10$	66243.5	2.09480
$11$	51964.2	1.07013	0.535066	−	0.844810i	$-0.320287\pi$
$11$	51964.2	1.07013	0.535066	+	0.844810i	$0.320287\pi$
$12$	−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
$17$	83521.0	0.242536
$17$	83521.0	0.242536
$18$	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	$-0.577563\pi$
$23$	−647595.	−0.482535	−0.241267	+	0.970459i	$0.577563\pi$
$24$	−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	$-0.495778\pi$
$29$	101038.	0.0265274	0.0132637	+	0.999912i	$0.495778\pi$
$30$	−1.13293e7	−2.55363
$31$	1.03448e6	0.201184	0.100592	−	0.994928i	$-0.467926\pi$
$31$	1.03448e6	0.201184	0.100592	+	0.994928i	$0.467926\pi$
$32$	1.87934e7	3.16833
$33$	−8.88720e6	−1.30452
$34$	3.60153e6	0.462203
$35$	4.65118e6	0.523910
$36$	1.28906e7	1.27912
$37$	−5.58601e6	−0.489998	−0.244999	−	0.969523i	$-0.578788\pi$
$37$	−5.58601e6	−0.489998	−0.244999	+	0.969523i	$0.578788\pi$
$38$	−4.46226e7	−3.47159
$39$	2.84479e7	1.96907
$40$	5.53429e7	3.41816
$41$	−4.18736e6	−0.231426	−0.115713	−	0.993283i	$-0.536915\pi$
$41$	−4.18736e6	−0.231426	−0.115713	+	0.993283i	$0.536915\pi$
$42$	−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
$51$	−1.42842e7	−0.295659
$52$	−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	$-0.832083\pi$
$61$	−1.86877e8	−1.72811	−0.864055	+	0.503398i	$0.832083\pi$
$62$	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	$0.463865\pi$
$68$	1.12540e8	0.638288
$69$	1.10755e8	0.588225
$70$	2.00565e8	0.998420
$71$	2.04593e8	0.955495	0.477748	−	0.878497i	$-0.341453\pi$
$71$	2.04593e8	0.955495	0.477748	+	0.878497i	$0.341453\pi$
$72$	3.44645e8	1.51139
$73$	−1.95705e8	−0.806581	−0.403291	−	0.915072i	$-0.632134\pi$
$73$	−1.95705e8	−0.806581	−0.403291	+	0.915072i	$0.632134\pi$
$74$	−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	$-0.371173\pi$
$79$	2.72638e8	0.787524	0.393762	+	0.919212i	$0.371173\pi$
$80$	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
$85$	1.28306e8	0.266601
$86$	−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	$-0.332580\pi$
$97$	8.75485e8	1.00410	0.502049	+	0.864839i	$0.332580\pi$
$98$	−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	$0.457722\pi$
$102$	−6.15954e8	−0.563440
$103$	−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	$-0.336367\pi$
$107$	1.33346e9	0.983449	0.491724	+	0.870751i	$0.336367\pi$
$108$	2.33128e9	1.64887
$109$	−7.04251e8	−0.477868	−0.238934	−	0.971036i	$-0.576798\pi$
$109$	−7.04251e8	−0.477868	−0.238934	+	0.971036i	$0.576798\pi$
$110$	3.44229e9	2.24172
$111$	9.55350e8	0.597323
$112$	2.61463e9	1.57011
$113$	1.40406e9	0.810091	0.405045	−	0.914297i	$-0.367256\pi$
$113$	1.40406e9	0.810091	0.405045	+	0.914297i	$0.367256\pi$
$114$	7.63160e9	4.23198
$115$	−9.94845e8	−0.530414
$116$	1.36144e8	0.0698130
$117$	−1.59130e9	−0.785084
$118$	4.14335e9	1.96735
$119$	2.52875e8	0.115597
$120$	−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	$-0.253972\pi$
$131$	4.70705e9	1.39646	0.698229	+	0.715874i	$0.253972\pi$
$132$	−1.19750e10	−3.43316
$133$	−3.13310e9	−0.868244
$134$	1.61140e9	0.431748
$135$	2.65787e9	0.688703
$136$	3.00889e9	0.754190
$137$	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	$-0.516704\pi$
$139$	−4.61710e8	−0.104907	−0.0524533	+	0.998623i	$0.516704\pi$
$140$	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
$153$	7.99021e8	0.117882
$154$	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	$-0.269691\pi$
$163$	1.19332e10	1.32408	0.662039	+	0.749470i	$0.269691\pi$
$164$	−5.64224e9	−0.609052
$165$	−1.36526e10	−1.43397
$166$	−8.46352e9	−0.865096
$167$	2.11741e9	0.210659	0.105330	−	0.994437i	$-0.466410\pi$
$167$	2.11741e9	0.210659	0.105330	+	0.994437i	$0.466410\pi$
$168$	−1.86544e10	−1.80672
$169$	1.70637e10	1.60910
$170$	5.53273e9	0.508065
$171$	−9.89978e9	−0.885407
$172$	−1.29380e10	−1.12717
$173$	4.37524e9	0.371359	0.185680	−	0.982610i	$-0.440551\pi$
$173$	4.37524e9	0.371359	0.185680	+	0.982610i	$0.440551\pi$
$174$	−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	$-0.285096\pi$
$181$	1.80496e10	1.25001	0.625007	+	0.780619i	$0.285096\pi$
$182$	−2.17166e10	−1.46714
$183$	3.19607e10	2.10662
$184$	−2.33299e10	−1.50049
$185$	−8.58131e9	−0.538618
$186$	−7.62909e9	−0.467374
$187$	4.34010e9	0.259545
$188$	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	$-0.371000\pi$
$193$	1.51993e10	0.788524	0.394262	+	0.918998i	$0.371000\pi$
$194$	3.77520e10	1.91352
$195$	4.37021e10	2.16445
$196$	−4.20224e10	−2.03390
$197$	−2.63264e10	−1.24535	−0.622677	−	0.782479i	$-0.713955\pi$
$197$	−2.63264e10	−1.24535	−0.622677	+	0.782479i	$0.713955\pi$
$198$	2.14367e10	0.991209
$199$	3.40221e10	1.53788	0.768940	−	0.639321i	$-0.220784\pi$
$199$	3.40221e10	1.53788	0.768940	+	0.639321i	$0.220784\pi$
$200$	1.46562e10	0.647720
$201$	−6.39104e9	−0.276178
$202$	1.19440e10	0.504743
$203$	3.05912e8	0.0126434
$204$	−1.92472e10	−0.778094
$205$	−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	$-0.630738\pi$
$211$	−2.29918e10	−0.798550	−0.399275	+	0.916831i	$0.630738\pi$
$212$	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
$221$	−1.38927e10	−0.391760
$222$	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	$-0.525349\pi$
$227$	−6.36497e9	−0.159104	−0.0795518	+	0.996831i	$0.525349\pi$
$228$	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	$-0.859365\pi$
$233$	−8.13370e10	−1.80795	−0.903975	+	0.427585i	$0.859365\pi$
$234$	−6.86190e10	−1.49614
$235$	6.11902e10	1.30881
$236$	1.29470e11	2.71686
$237$	−4.66280e10	−0.960018
$238$	1.09043e10	0.220294
$239$	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	$-0.532348\pi$
$241$	−1.06255e10	−0.202896	−0.101448	+	0.994841i	$0.532348\pi$
$242$	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
$255$	−2.19436e10	−0.324996
$256$	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	$-0.643905\pi$
$269$	−7.50317e10	−0.873695	−0.436847	+	0.899536i	$0.643905\pi$
$270$	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	$0.680900\pi$
$272$	7.21266e10	0.798979
$273$	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	$-0.522846\pi$
$277$	−1.40532e10	−0.143422	−0.0717110	+	0.997425i	$0.522846\pi$
$278$	−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	$-0.382492\pi$
$283$	7.78714e10	0.721670	0.360835	+	0.932630i	$0.382492\pi$
$284$	2.75678e11	2.51461
$285$	2.71879e11	2.44103
$286$	−3.72723e11	−3.29412
$287$	−1.26780e10	−0.110302
$288$	1.79791e11	1.53993
$289$	6.97576e9	0.0588235
$290$	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
$306$	3.44548e10	0.224648
$307$	−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	$-0.382902\pi$
$311$	1.18662e11	0.719265	0.359633	+	0.933094i	$0.382902\pi$
$312$	1.02485e12	6.12301
$313$	2.52103e11	1.48467	0.742333	−	0.670032i	$-0.233719\pi$
$313$	2.52103e11	1.48467	0.742333	+	0.670032i	$0.233719\pi$
$314$	2.53360e11	1.47080
$315$	4.44964e10	0.254641
$316$	3.67365e11	2.07255
$317$	7.54487e10	0.419648	0.209824	−	0.977739i	$-0.432711\pi$
$317$	7.54487e10	0.419648	0.209824	+	0.977739i	$0.432711\pi$
$318$	−4.58850e11	−2.51622
$319$	5.25038e9	0.0283878
$320$	5.65702e11	3.01587
$321$	−2.28055e11	−1.19886
$322$	−8.45486e10	−0.438283
$323$	−8.64289e10	−0.441822
$324$	−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	$-0.445577\pi$
$337$	8.05715e10	0.340288	0.170144	+	0.985419i	$0.445577\pi$
$338$	7.35807e11	3.06647
$339$	−2.40131e11	−0.987526
$340$	1.72886e11	0.701623
$341$	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	$-0.749963\pi$
$347$	−3.81897e11	−1.41405	−0.707024	+	0.707190i	$0.749963\pi$
$348$	−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
$357$	−4.32481e10	−0.140916
$358$	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	$-0.111545\pi$
$367$	6.52825e11	1.87845	0.939225	+	0.343301i	$0.111545\pi$
$368$	−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	$0.541387\pi$
$374$	1.87151e11	0.494618
$375$	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	$-0.821757\pi$
$379$	−6.80659e11	−1.69454	−0.847272	+	0.531159i	$0.821757\pi$
$380$	−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
$391$	−5.40878e10	−0.117032
$392$	−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	$-0.585068\pi$
$397$	−2.61410e11	−0.528159	−0.264079	+	0.964501i	$0.585068\pi$
$398$	1.46708e12	2.93075
$399$	5.35840e11	1.05842
$400$	3.51327e11	0.686186
$401$	8.04746e10	0.155421	0.0777104	−	0.996976i	$-0.475239\pi$
$401$	8.04746e10	0.155421	0.0777104	+	0.996976i	$0.475239\pi$
$402$	−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
$408$	−5.14596e11	−0.919382
$409$	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	$-0.370283\pi$
$419$	5.00093e11	0.792661	0.396331	+	0.918108i	$0.370283\pi$
$420$	−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
$425$	3.39788e10	0.0505193
$426$	−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	$-0.615695\pi$
$431$	−5.09374e11	−0.711032	−0.355516	+	0.934670i	$0.615695\pi$
$432$	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	$-0.765440\pi$
$439$	−1.15261e12	−1.48112	−0.740561	+	0.671989i	$0.765440\pi$
$440$	2.87585e12	3.65788
$441$	−2.98354e11	−0.375628
$442$	−5.99070e11	−0.746582
$443$	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	$-0.801698\pi$
$449$	−1.39885e12	−1.62428	−0.812141	+	0.583461i	$0.801698\pi$
$450$	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
$459$	1.44503e11	0.151957
$460$	−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
$476$	3.40736e11	0.304219
$477$	5.95224e11	0.526439
$478$	3.22828e12	2.82843
$479$	−3.78765e10	−0.0328746	−0.0164373	−	0.999865i	$-0.505232\pi$
$479$	−3.78765e10	−0.0328746	−0.0164373	+	0.999865i	$0.505232\pi$
$480$	−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	$-0.226396\pi$
$487$	1.88071e12	1.51510	0.757550	+	0.652778i	$0.226396\pi$
$488$	−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
$493$	8.43882e9	0.00643384
$494$	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	$-0.408103\pi$
$499$	7.88648e11	0.569417	0.284709	+	0.958614i	$0.408103\pi$
$500$	−3.20078e12	−2.29029
$501$	−3.62131e11	−0.256800
$502$	−4.11931e12	−2.89506
$503$	1.92372e12	1.33994	0.669972	−	0.742386i	$-0.266306\pi$
$503$	1.92372e12	1.33994	0.669972	+	0.742386i	$0.266306\pi$
$504$	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	$0.100827\pi$
$510$	−9.46237e11	−0.619347
$511$	−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	$-0.244461\pi$
$521$	2.41942e12	1.43861	0.719303	+	0.694697i	$0.244461\pi$
$522$	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
$527$	8.64005e10	0.0487942
$528$	−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	$-0.684875\pi$
$541$	−2.18649e12	−1.09739	−0.548694	+	0.836023i	$0.684875\pi$
$542$	−4.12133e12	−2.05135
$543$	−3.08695e12	−1.52381
$544$	1.56964e12	0.768432
$545$	−1.08188e12	−0.525285
$546$	3.71410e12	1.78849
$547$	−7.53862e11	−0.360039	−0.180019	−	0.983663i	$-0.557616\pi$
$547$	−7.53862e11	−0.360039	−0.180019	+	0.983663i	$0.557616\pi$
$548$	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
$561$	−7.42268e11	−0.316394
$562$	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	$-0.647446\pi$
$571$	−2.27003e12	−0.893652	−0.446826	+	0.894621i	$0.647446\pi$
$572$	−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	$0.618080\pi$
$578$	3.00804e11	0.112101
$579$	−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
$595$	3.88471e11	0.127067
$596$	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	$-0.764411\pi$
$601$	−4.72333e12	−1.47677	−0.738385	+	0.674379i	$0.764411\pi$
$602$	−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	$-0.408366\pi$
$607$	1.89920e12	0.567836	0.283918	+	0.958849i	$0.408366\pi$
$608$	−1.94477e13	−5.77168
$609$	−5.23188e10	−0.0154127
$610$	−1.23794e13	−3.62005
$611$	−6.62553e12	−1.92325
$612$	1.07664e12	0.310233
$613$	−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	$-0.525671\pi$
$617$	−5.80011e11	−0.161121	−0.0805607	+	0.996750i	$0.525671\pi$
$618$	4.04088e11	0.111437
$619$	−1.58371e12	−0.433579	−0.216790	−	0.976218i	$-0.569559\pi$
$619$	−1.58371e12	−0.433579	−0.216790	+	0.976218i	$0.569559\pi$
$620$	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
$629$	−4.66549e11	−0.118842
$630$	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	$-0.866595\pi$
$641$	−7.80868e12	−1.82691	−0.913454	+	0.406943i	$0.866595\pi$
$642$	−9.83402e12	−2.28467
$643$	−2.11639e12	−0.488255	−0.244128	−	0.969743i	$-0.578502\pi$
$643$	−2.11639e12	−0.488255	−0.244128	+	0.969743i	$0.578502\pi$
$644$	−2.64196e12	−0.605257
$645$	2.52272e12	0.573920
$646$	−3.72693e12	−0.841985
$647$	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	$-0.436954\pi$
$653$	1.82854e12	0.393545	0.196772	+	0.980449i	$0.436954\pi$
$654$	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
$663$	2.37600e12	0.477568
$664$	−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	$-0.270957\pi$
$673$	7.01486e12	1.31811	0.659055	+	0.752095i	$0.270957\pi$
$674$	3.47435e12	0.648490
$675$	7.03873e11	0.130505
$676$	2.29923e13	4.23471
$677$	7.71992e12	1.41242	0.706210	−	0.708002i	$-0.250403\pi$
$677$	7.71992e12	1.41242	0.706210	+	0.708002i	$0.250403\pi$
$678$	−1.03547e13	−1.88194
$679$	2.65069e12	0.478570
$680$	4.62229e12	0.829025
$681$	1.08857e12	0.193952
$682$	2.31802e12	0.410286
$683$	−4.25216e12	−0.747680	−0.373840	−	0.927493i	$-0.621959\pi$
$683$	−4.25216e12	−0.747680	−0.373840	+	0.927493i	$0.621959\pi$
$684$	−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	$-0.566641\pi$
$691$	−2.49111e12	−0.415664	−0.207832	+	0.978165i	$0.566641\pi$
$692$	5.89539e12	0.977317
$693$	1.50514e12	0.247901
$694$	−1.64679e13	−2.69476
$695$	−7.09286e11	−0.115316
$696$	−6.22525e11	−0.100558
$697$	−3.49732e11	−0.0561291
$698$	−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	$-0.673692\pi$
$709$	−6.98388e12	−1.03798	−0.518990	+	0.854780i	$0.673692\pi$
$710$	1.35530e13	2.00158
$711$	2.60824e12	0.382768
$712$	−1.41658e13	−2.06577
$713$	−6.69922e11	−0.0970781
$714$	−1.86492e12	−0.268545
$715$	−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	$-0.865340\pi$
$719$	−1.30686e13	−1.82368	−0.911842	+	0.410540i	$0.865340\pi$
$720$	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
$731$	−8.01960e11	−0.103878
$732$	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	$-0.204400\pi$
$743$	1.33049e13	1.60163	0.800815	+	0.598912i	$0.204400\pi$
$744$	−6.37370e12	−0.762629
$745$	2.87300e12	0.341690
$746$	−4.18020e12	−0.494165
$747$	−1.87768e12	−0.220637
$748$	5.84805e12	0.683053
$749$	4.03729e12	0.468729
$750$	1.75185e13	2.02172
$751$	−2.33606e12	−0.267982	−0.133991	−	0.990983i	$-0.542779\pi$
$751$	−2.33606e12	−0.267982	−0.133991	+	0.990983i	$0.542779\pi$
$752$	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
$765$	1.22747e12	0.129579
$766$	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
$782$	−2.33234e12	−0.223029
$783$	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	$-0.739387\pi$
$787$	−1.47037e13	−1.36628	−0.683141	+	0.730286i	$0.739387\pi$
$788$	−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
$799$	3.32680e12	0.288779
$800$	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	$-0.350525\pi$
$809$	1.10265e13	0.905041	0.452521	+	0.891754i	$0.350525\pi$
$810$	−3.20751e13	−2.61810
$811$	1.97221e12	0.160088	0.0800440	−	0.996791i	$-0.474494\pi$
$811$	1.97221e12	0.160088	0.0800440	+	0.996791i	$0.474494\pi$
$812$	4.12200e11	0.0332741
$813$	1.63458e13	1.31220
$814$	−1.25169e13	−0.999282
$815$	1.83320e13	1.45546
$816$	−1.23355e13	−0.973981
$817$	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	$-0.659018\pi$
$821$	−1.24725e13	−0.958093	−0.479047	+	0.877789i	$0.659018\pi$
$822$	−3.01776e13	−2.30548
$823$	5.63904e12	0.428455	0.214228	−	0.976784i	$-0.431277\pi$
$823$	5.63904e12	0.428455	0.214228	+	0.976784i	$0.431277\pi$
$824$	−1.97394e12	−0.149163
$825$	−3.61557e12	−0.271728
$826$	1.25448e13	0.937674
$827$	−6.43118e12	−0.478097	−0.239048	−	0.971008i	$-0.576835\pi$
$827$	−6.43118e12	−0.478097	−0.239048	+	0.971008i	$0.576835\pi$
$828$	−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
$833$	−2.60475e12	−0.187440
$834$	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	$-0.293036\pi$
$839$	1.73764e13	1.21068	0.605342	+	0.795965i	$0.293036\pi$
$840$	−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
$850$	1.46521e12	0.0962752
$851$	3.61747e12	0.236441
$852$	−4.71480e13	−3.06538
$853$	−3.23489e12	−0.209213	−0.104607	−	0.994514i	$-0.533358\pi$
$853$	−3.23489e12	−0.209213	−0.104607	+	0.994514i	$0.533358\pi$
$854$	−2.43982e13	−1.56963
$855$	−1.52082e13	−0.973262
$856$	4.80384e13	3.05814
$857$	6.56773e12	0.415912	0.207956	−	0.978138i	$-0.433319\pi$
$857$	6.56773e12	0.415912	0.207956	+	0.978138i	$0.433319\pi$
$858$	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
$867$	−1.19303e12	−0.0717078
$868$	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	$-0.613840\pi$
$877$	−1.22652e13	−0.700128	−0.350064	+	0.936726i	$0.613840\pi$
$878$	−4.97019e13	−2.82259
$879$	1.51554e13	0.856284
$880$	6.89375e13	3.87511
$881$	2.36185e13	1.32087	0.660435	−	0.750883i	$-0.270372\pi$
$881$	2.36185e13	1.32087	0.660435	+	0.750883i	$0.270372\pi$
$882$	−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	$0.260636\pi$
$884$	−1.87196e13	−1.03101
$885$	−2.52448e13	−1.38333
$886$	6.79663e13	3.70546
$887$	−8.49974e12	−0.461051	−0.230526	−	0.973066i	$-0.574045\pi$
$887$	−8.49974e12	−0.461051	−0.230526	+	0.973066i	$0.574045\pi$
$888$	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
$901$	5.19653e12	0.262695
$902$	−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	$-0.621395\pi$
$907$	−1.51717e13	−0.744390	−0.372195	+	0.928155i	$0.621395\pi$
$908$	−8.57645e12	−0.418718
$909$	2.64985e12	0.128731
$910$	−3.33614e13	−1.61272
$911$	−2.65044e12	−0.127493	−0.0637464	−	0.997966i	$-0.520305\pi$
$911$	−2.65044e12	−0.127493	−0.0637464	+	0.997966i	$0.520305\pi$
$912$	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
$918$	6.23117e12	0.289586
$919$	−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	$-0.578303\pi$
$929$	−1.10570e13	−0.487044	−0.243522	+	0.969895i	$0.578303\pi$
$930$	−1.17199e13	−0.513750
$931$	3.22725e13	1.40786
$932$	−1.09597e14	−4.75804
$933$	−2.02942e13	−0.876808
$934$	−5.17655e13	−2.22577
$935$	6.66733e12	0.285299
$936$	−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	$-0.242090\pi$
$941$	3.48495e13	1.44891	0.724457	+	0.689320i	$0.242090\pi$
$942$	−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	$-0.301503\pi$
$947$	2.89060e13	1.16792	0.583960	+	0.811783i	$0.301503\pi$
$948$	−6.28287e13	−2.52651
$949$	3.25530e13	1.30285
$950$	−1.81538e13	−0.723121
$951$	−1.29036e13	−0.511564
$952$	9.10996e12	0.359460
$953$	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
$969$	1.47815e13	0.538596
$970$	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	$-0.534223\pi$
$983$	−6.28271e12	−0.214613	−0.107306	+	0.994226i	$0.534223\pi$
$984$	2.57995e13	0.877270
$985$	−4.04429e13	−1.36893
$986$	3.63893e11	0.0122610
$987$	−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	$-0.765394\pi$
$991$	−4.49640e13	−1.48093	−0.740463	+	0.672097i	$0.765394\pi$
$992$	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	$-0.562521\pi$
$997$	−1.21770e13	−0.390311	−0.195156	+	0.980772i	$0.562521\pi$
$998$	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	17.10.a.b.1.7	✓	7
3.2	odd	2		153.10.a.f.1.1		7
4.3	odd	2		272.10.a.g.1.6		7
17.16	even	2		289.10.a.b.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.7	✓	7	1.1	even	1	trivial
153.10.a.f.1.1		7	3.2	odd	2
272.10.a.g.1.6		7	4.3	odd	2
289.10.a.b.1.7		7	17.16	even	2

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q+43.1213 q^{2} -171.025 q^{3} +1347.45 q^{4} +1536.21 q^{5} -7374.84 q^{6} +3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} +O(q^{10})\)	\(q+43.1213 q^{2} -171.025 q^{3} +1347.45 q^{4} +1536.21 q^{5} -7374.84 q^{6} +3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} +66243.5 q^{10} +51964.2 q^{11} -230448. q^{12} -166337. q^{13} +130558. q^{14} -262732. q^{15} +863574. q^{16} +83521.0 q^{17} +412529. q^{18} -1.03482e6 q^{19} +2.06997e6 q^{20} -517811. q^{21} +2.24076e6 q^{22} -647595. q^{23} -6.16128e6 q^{24} +406829. q^{25} -7.17269e6 q^{26} +1.73014e6 q^{27} +4.07964e6 q^{28} +101038. q^{29} -1.13293e7 q^{30} +1.03448e6 q^{31} +1.87934e7 q^{32} -8.88720e6 q^{33} +3.60153e6 q^{34} +4.65118e6 q^{35} +1.28906e7 q^{36} -5.58601e6 q^{37} -4.46226e7 q^{38} +2.84479e7 q^{39} +5.53429e7 q^{40} -4.18736e6 q^{41} -2.23287e7 q^{42} -9.60190e6 q^{43} +7.00190e7 q^{44} +1.46965e7 q^{45} -2.79251e7 q^{46} +3.98318e7 q^{47} -1.47693e8 q^{48} -3.11867e7 q^{49} +1.75430e7 q^{50} -1.42842e7 q^{51} -2.24131e8 q^{52} +6.22183e7 q^{53} +7.46060e7 q^{54} +7.98282e7 q^{55} +1.09074e8 q^{56} +1.76980e8 q^{57} +4.35690e6 q^{58} +9.60858e7 q^{59} -3.54017e8 q^{60} -1.86877e8 q^{61} +4.46079e7 q^{62} +2.89650e7 q^{63} +3.68245e8 q^{64} -2.55530e8 q^{65} -3.83228e8 q^{66} +3.73689e7 q^{67} +1.12540e8 q^{68} +1.10755e8 q^{69} +2.00565e8 q^{70} +2.04593e8 q^{71} +3.44645e8 q^{72} -1.95705e8 q^{73} -2.40876e8 q^{74} -6.95782e7 q^{75} -1.39436e9 q^{76} +1.57331e8 q^{77} +1.22671e9 q^{78} +2.72638e8 q^{79} +1.32663e9 q^{80} -4.84200e8 q^{81} -1.80564e8 q^{82} -1.96272e8 q^{83} -6.97723e8 q^{84} +1.28306e8 q^{85} -4.14046e8 q^{86} -1.72801e7 q^{87} +1.87204e9 q^{88} -3.93217e8 q^{89} +6.33732e8 q^{90} -5.03618e8 q^{91} -8.72600e8 q^{92} -1.76922e8 q^{93} +1.71760e9 q^{94} -1.58970e9 q^{95} -3.21414e9 q^{96} +8.75485e8 q^{97} -1.34481e9 q^{98} +4.97126e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) \) 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	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 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 + 584647 * q^17 + 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 - 83521 * q^34 - 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 + 7349848 * q^51 - 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 + 199531669 * q^68 + 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 + 113755602 * q^85 - 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more