LMFDB - Embedded newform 38.10.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(1,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, 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("38.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 34433x^{2} - 2723303x - 48270488 $ x^4 - x^3 - 34433x^2 - 2723303x - 48270488
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-26.2676$ of defining polynomial
Character	$\chi$	$=$	38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} +25.2570 q^{3} +256.000 q^{4} +2126.71 q^{5} -404.112 q^{6} +11469.0 q^{7} -4096.00 q^{8} -19045.1 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} +25.2570 q^{3} +256.000 q^{4} +2126.71 q^{5} -404.112 q^{6} +11469.0 q^{7} -4096.00 q^{8} -19045.1 q^{9} -34027.4 q^{10} -10430.4 q^{11} +6465.79 q^{12} +144659. q^{13} -183503. q^{14} +53714.4 q^{15} +65536.0 q^{16} -654214. q^{17} +304721. q^{18} +130321. q^{19} +544439. q^{20} +289672. q^{21} +166886. q^{22} +1.63517e6 q^{23} -103453. q^{24} +2.56979e6 q^{25} -2.31454e6 q^{26} -978155. q^{27} +2.93605e6 q^{28} +3.60690e6 q^{29} -859431. q^{30} +3.62937e6 q^{31} -1.04858e6 q^{32} -263440. q^{33} +1.04674e7 q^{34} +2.43912e7 q^{35} -4.87554e6 q^{36} -1.06553e7 q^{37} -2.08514e6 q^{38} +3.65364e6 q^{39} -8.71102e6 q^{40} +1.31851e7 q^{41} -4.63474e6 q^{42} -2.73590e6 q^{43} -2.67018e6 q^{44} -4.05035e7 q^{45} -2.61627e7 q^{46} -5.26213e7 q^{47} +1.65524e6 q^{48} +9.11835e7 q^{49} -4.11167e7 q^{50} -1.65235e7 q^{51} +3.70326e7 q^{52} +5.87078e7 q^{53} +1.56505e7 q^{54} -2.21825e7 q^{55} -4.69769e7 q^{56} +3.29152e6 q^{57} -5.77104e7 q^{58} -7.23340e7 q^{59} +1.37509e7 q^{60} -7.46069e7 q^{61} -5.80700e7 q^{62} -2.18427e8 q^{63} +1.67772e7 q^{64} +3.07647e8 q^{65} +4.21504e6 q^{66} +1.12380e8 q^{67} -1.67479e8 q^{68} +4.12994e7 q^{69} -3.90259e8 q^{70} +3.11980e8 q^{71} +7.80087e7 q^{72} +3.47317e6 q^{73} +1.70485e8 q^{74} +6.49052e7 q^{75} +3.33622e7 q^{76} -1.19626e8 q^{77} -5.84582e7 q^{78} +1.96071e8 q^{79} +1.39376e8 q^{80} +3.50159e8 q^{81} -2.10961e8 q^{82} -3.30282e8 q^{83} +7.41559e7 q^{84} -1.39133e9 q^{85} +4.37745e7 q^{86} +9.10995e7 q^{87} +4.27229e7 q^{88} -6.40446e8 q^{89} +6.48055e8 q^{90} +1.65908e9 q^{91} +4.18603e8 q^{92} +9.16671e7 q^{93} +8.41940e8 q^{94} +2.77156e8 q^{95} -2.64839e7 q^{96} +1.56258e9 q^{97} -1.45894e9 q^{98} +1.98648e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9}+O(q^{10}) $ 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9} + 22320 q^{10} - 104249 q^{11} + 21504 q^{12} + 120486 q^{13} - 196912 q^{14} - 591090 q^{15} + 262144 q^{16} - 412139 q^{17} - 264608 q^{18} + 521284 q^{19} - 357120 q^{20} + 2437006 q^{21} + 1667984 q^{22} + 3010300 q^{23} - 344064 q^{24} + 9760585 q^{25} - 1927776 q^{26} + 12387978 q^{27} + 3150592 q^{28} + 6153240 q^{29} + 9457440 q^{30} + 12774024 q^{31} - 4194304 q^{32} - 3258022 q^{33} + 6594224 q^{34} + 9823425 q^{35} + 4233728 q^{36} + 20506048 q^{37} - 8340544 q^{38} + 69881444 q^{39} + 5713920 q^{40} + 11620300 q^{41} - 38992096 q^{42} + 7698327 q^{43} - 26687744 q^{44} - 124015815 q^{45} - 48164800 q^{46} - 31581083 q^{47} + 5505024 q^{48} + 18970383 q^{49} - 156169360 q^{50} - 8594812 q^{51} + 30844416 q^{52} + 72549422 q^{53} - 198207648 q^{54} + 21332505 q^{55} - 50409472 q^{56} + 10946964 q^{57} - 98451840 q^{58} - 149234120 q^{59} - 151319040 q^{60} + 129004373 q^{61} - 204384384 q^{62} + 102967551 q^{63} + 67108864 q^{64} + 124691700 q^{65} + 52128352 q^{66} + 132595266 q^{67} - 105507584 q^{68} - 45529972 q^{69} - 157174800 q^{70} - 47138482 q^{71} - 67739648 q^{72} - 39332795 q^{73} - 328096768 q^{74} + 824627010 q^{75} + 133448704 q^{76} - 165933719 q^{77} - 1118103104 q^{78} - 307010840 q^{79} - 91422720 q^{80} + 1305551744 q^{81} - 185924800 q^{82} - 746568232 q^{83} + 623873536 q^{84} - 105005985 q^{85} - 123173232 q^{86} - 82148208 q^{87} + 427003904 q^{88} + 286943482 q^{89} + 1984253040 q^{90} + 3155781114 q^{91} + 770636800 q^{92} + 1151901596 q^{93} + 505297328 q^{94} - 181797795 q^{95} - 88080384 q^{96} + 793519958 q^{97} - 303526128 q^{98} - 1681833809 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9 + 22320 * q^10 - 104249 * q^11 + 21504 * q^12 + 120486 * q^13 - 196912 * q^14 - 591090 * q^15 + 262144 * q^16 - 412139 * q^17 - 264608 * q^18 + 521284 * q^19 - 357120 * q^20 + 2437006 * q^21 + 1667984 * q^22 + 3010300 * q^23 - 344064 * q^24 + 9760585 * q^25 - 1927776 * q^26 + 12387978 * q^27 + 3150592 * q^28 + 6153240 * q^29 + 9457440 * q^30 + 12774024 * q^31 - 4194304 * q^32 - 3258022 * q^33 + 6594224 * q^34 + 9823425 * q^35 + 4233728 * q^36 + 20506048 * q^37 - 8340544 * q^38 + 69881444 * q^39 + 5713920 * q^40 + 11620300 * q^41 - 38992096 * q^42 + 7698327 * q^43 - 26687744 * q^44 - 124015815 * q^45 - 48164800 * q^46 - 31581083 * q^47 + 5505024 * q^48 + 18970383 * q^49 - 156169360 * q^50 - 8594812 * q^51 + 30844416 * q^52 + 72549422 * q^53 - 198207648 * q^54 + 21332505 * q^55 - 50409472 * q^56 + 10946964 * q^57 - 98451840 * q^58 - 149234120 * q^59 - 151319040 * q^60 + 129004373 * q^61 - 204384384 * q^62 + 102967551 * q^63 + 67108864 * q^64 + 124691700 * q^65 + 52128352 * q^66 + 132595266 * q^67 - 105507584 * q^68 - 45529972 * q^69 - 157174800 * q^70 - 47138482 * q^71 - 67739648 * q^72 - 39332795 * q^73 - 328096768 * q^74 + 824627010 * q^75 + 133448704 * q^76 - 165933719 * q^77 - 1118103104 * q^78 - 307010840 * q^79 - 91422720 * q^80 + 1305551744 * q^81 - 185924800 * q^82 - 746568232 * q^83 + 623873536 * q^84 - 105005985 * q^85 - 123173232 * q^86 - 82148208 * q^87 + 427003904 * q^88 + 286943482 * q^89 + 1984253040 * q^90 + 3155781114 * q^91 + 770636800 * q^92 + 1151901596 * q^93 + 505297328 * q^94 - 181797795 * q^95 - 88080384 * q^96 + 793519958 * q^97 - 303526128 * q^98 - 1681833809 * 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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	25.2570	0.180026	0.0900132	−	0.995941i	$-0.471309\pi$
$3$	25.2570	0.180026	0.0900132	+	0.995941i	$0.471309\pi$
$4$	256.000	0.500000
$5$	2126.71	1.52175	0.760877	−	0.648897i	$-0.224769\pi$
$5$	2126.71	1.52175	0.760877	+	0.648897i	$0.224769\pi$
$6$	−404.112	−0.127298
$7$	11469.0	1.80544	0.902720	−	0.430229i	$-0.141567\pi$
$7$	11469.0	1.80544	0.902720	+	0.430229i	$0.141567\pi$
$8$	−4096.00	−0.353553
$9$	−19045.1	−0.967591
$10$	−34027.4	−1.07604
$11$	−10430.4	−0.214800	−0.107400	−	0.994216i	$-0.534252\pi$
$11$	−10430.4	−0.214800	−0.107400	+	0.994216i	$0.534252\pi$
$12$	6465.79	0.0900132
$13$	144659.	1.40475	0.702375	−	0.711807i	$-0.252123\pi$
$13$	144659.	1.40475	0.702375	+	0.711807i	$0.252123\pi$
$14$	−183503.	−1.27664
$15$	53714.4	0.273956
$16$	65536.0	0.250000
$17$	−654214.	−1.89976	−0.949882	−	0.312608i	$-0.898797\pi$
$17$	−654214.	−1.89976	−0.949882	+	0.312608i	$0.898797\pi$
$18$	304721.	0.684190
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	544439.	0.760877
$21$	289672.	0.325027
$22$	166886.	0.151886
$23$	1.63517e6	1.21839	0.609196	−	0.793020i	$-0.291492\pi$
$23$	1.63517e6	1.21839	0.609196	+	0.793020i	$0.291492\pi$
$24$	−103453.	−0.0636489
$25$	2.56979e6	1.31573
$26$	−2.31454e6	−0.993308
$27$	−978155.	−0.354218
$28$	2.93605e6	0.902720
$29$	3.60690e6	0.946985	0.473493	−	0.880798i	$-0.342993\pi$
$29$	3.60690e6	0.946985	0.473493	+	0.880798i	$0.342993\pi$
$30$	−859431.	−0.193716
$31$	3.62937e6	0.705836	0.352918	−	0.935654i	$-0.385189\pi$
$31$	3.62937e6	0.705836	0.352918	+	0.935654i	$0.385189\pi$
$32$	−1.04858e6	−0.176777
$33$	−263440.	−0.0386696
$34$	1.04674e7	1.34334
$35$	2.43912e7	2.74743
$36$	−4.87554e6	−0.483795
$37$	−1.06553e7	−0.934668	−0.467334	−	0.884081i	$-0.654785\pi$
$37$	−1.06553e7	−0.934668	−0.467334	+	0.884081i	$0.654785\pi$
$38$	−2.08514e6	−0.162221
$39$	3.65364e6	0.252892
$40$	−8.71102e6	−0.538021
$41$	1.31851e7	0.728710	0.364355	−	0.931260i	$-0.381289\pi$
$41$	1.31851e7	0.728710	0.364355	+	0.931260i	$0.381289\pi$
$42$	−4.63474e6	−0.229829
$43$	−2.73590e6	−0.122037	−0.0610187	−	0.998137i	$-0.519435\pi$
$43$	−2.73590e6	−0.122037	−0.0610187	+	0.998137i	$0.519435\pi$
$44$	−2.67018e6	−0.107400
$45$	−4.05035e7	−1.47243
$46$	−2.61627e7	−0.861533
$47$	−5.26213e7	−1.57297	−0.786486	−	0.617608i	$-0.788102\pi$
$47$	−5.26213e7	−1.57297	−0.786486	+	0.617608i	$0.788102\pi$
$48$	1.65524e6	0.0450066
$49$	9.11835e7	2.25961
$50$	−4.11167e7	−0.930364
$51$	−1.65235e7	−0.342008
$52$	3.70326e7	0.702375
$53$	5.87078e7	1.02201	0.511004	−	0.859578i	$-0.329274\pi$
$53$	5.87078e7	1.02201	0.511004	+	0.859578i	$0.329274\pi$
$54$	1.56505e7	0.250470
$55$	−2.21825e7	−0.326872
$56$	−4.69769e7	−0.638319
$57$	3.29152e6	0.0413009
$58$	−5.77104e7	−0.669620
$59$	−7.23340e7	−0.777157	−0.388578	−	0.921416i	$-0.627034\pi$
$59$	−7.23340e7	−0.777157	−0.388578	+	0.921416i	$0.627034\pi$
$60$	1.37509e7	0.136978
$61$	−7.46069e7	−0.689914	−0.344957	−	0.938619i	$-0.612106\pi$
$61$	−7.46069e7	−0.689914	−0.344957	+	0.938619i	$0.612106\pi$
$62$	−5.80700e7	−0.499102
$63$	−2.18427e8	−1.74693
$64$	1.67772e7	0.125000
$65$	3.07647e8	2.13768
$66$	4.21504e6	0.0273435
$67$	1.12380e8	0.681322	0.340661	−	0.940186i	$-0.389349\pi$
$67$	1.12380e8	0.681322	0.340661	+	0.940186i	$0.389349\pi$
$68$	−1.67479e8	−0.949882
$69$	4.12994e7	0.219343
$70$	−3.90259e8	−1.94273
$71$	3.11980e8	1.45701	0.728507	−	0.685038i	$-0.240214\pi$
$71$	3.11980e8	1.45701	0.728507	+	0.685038i	$0.240214\pi$
$72$	7.80087e7	0.342095
$73$	3.47317e6	0.0143144	0.00715720	−	0.999974i	$-0.497722\pi$
$73$	3.47317e6	0.0143144	0.00715720	+	0.999974i	$0.497722\pi$
$74$	1.70485e8	0.660910
$75$	6.49052e7	0.236867
$76$	3.33622e7	0.114708
$77$	−1.19626e8	−0.387808
$78$	−5.84582e7	−0.178822
$79$	1.96071e8	0.566359	0.283179	−	0.959067i	$-0.408611\pi$
$79$	1.96071e8	0.566359	0.283179	+	0.959067i	$0.408611\pi$
$80$	1.39376e8	0.380438
$81$	3.50159e8	0.903822
$82$	−2.10961e8	−0.515276
$83$	−3.30282e8	−0.763895	−0.381948	−	0.924184i	$-0.624747\pi$
$83$	−3.30282e8	−0.763895	−0.381948	+	0.924184i	$0.624747\pi$
$84$	7.41559e7	0.162513
$85$	−1.39133e9	−2.89097
$86$	4.37745e7	0.0862934
$87$	9.10995e7	0.170482
$88$	4.27229e7	0.0759431
$89$	−6.40446e8	−1.08200	−0.541000	−	0.841023i	$-0.681954\pi$
$89$	−6.40446e8	−1.08200	−0.541000	+	0.841023i	$0.681954\pi$
$90$	6.48055e8	1.04117
$91$	1.65908e9	2.53619
$92$	4.18603e8	0.609196
$93$	9.16671e7	0.127069
$94$	8.41940e8	1.11226
$95$	2.77156e8	0.349114
$96$	−2.64839e7	−0.0318245
$97$	1.56258e9	1.79213	0.896064	−	0.443925i	$-0.146414\pi$
$97$	1.56258e9	1.79213	0.896064	+	0.443925i	$0.146414\pi$
$98$	−1.45894e9	−1.59779
$99$	1.98648e8	0.207838
$100$	6.57866e8	0.657866
$101$	2.55498e8	0.244310	0.122155	−	0.992511i	$-0.461019\pi$
$101$	2.55498e8	0.244310	0.122155	+	0.992511i	$0.461019\pi$
$102$	2.64376e8	0.241836
$103$	−9.05731e8	−0.792925	−0.396462	−	0.918051i	$-0.629762\pi$
$103$	−9.05731e8	−0.792925	−0.396462	+	0.918051i	$0.629762\pi$
$104$	−5.92521e8	−0.496654
$105$	6.16049e8	0.494610
$106$	−9.39325e8	−0.722669
$107$	−3.97489e8	−0.293155	−0.146578	−	0.989199i	$-0.546826\pi$
$107$	−3.97489e8	−0.293155	−0.146578	+	0.989199i	$0.546826\pi$
$108$	−2.50408e8	−0.177109
$109$	5.91761e8	0.401538	0.200769	−	0.979639i	$-0.435656\pi$
$109$	5.91761e8	0.401538	0.200769	+	0.979639i	$0.435656\pi$
$110$	3.54919e8	0.231133
$111$	−2.69120e8	−0.168265
$112$	7.51630e8	0.451360
$113$	−2.57125e9	−1.48351	−0.741757	−	0.670668i	$-0.766007\pi$
$113$	−2.57125e9	−1.48351	−0.741757	+	0.670668i	$0.766007\pi$
$114$	−5.26643e7	−0.0292041
$115$	3.47753e9	1.85409
$116$	9.23367e8	0.473493
$117$	−2.75503e9	−1.35922
$118$	1.15734e9	0.549533
$119$	−7.50316e9	−3.42991
$120$	−2.20014e8	−0.0968579
$121$	−2.24915e9	−0.953861
$122$	1.19371e9	0.487843
$123$	3.33015e8	0.131187
$124$	9.29120e8	0.352918
$125$	1.31147e9	0.480468
$126$	3.49484e9	1.23526
$127$	1.47739e9	0.503938	0.251969	−	0.967735i	$-0.418922\pi$
$127$	1.47739e9	0.503938	0.251969	+	0.967735i	$0.418922\pi$
$128$	−2.68435e8	−0.0883883
$129$	−6.91007e7	−0.0219699
$130$	−4.92236e9	−1.51157
$131$	−5.81972e9	−1.72656	−0.863279	−	0.504726i	$-0.831593\pi$
$131$	−5.81972e9	−1.72656	−0.863279	+	0.504726i	$0.831593\pi$
$132$	−6.74407e7	−0.0193348
$133$	1.49465e9	0.414196
$134$	−1.79808e9	−0.481768
$135$	−2.08026e9	−0.539033
$136$	2.67966e9	0.671668
$137$	−2.81502e8	−0.0682715	−0.0341358	−	0.999417i	$-0.510868\pi$
$137$	−2.81502e8	−0.0682715	−0.0341358	+	0.999417i	$0.510868\pi$
$138$	−6.60791e8	−0.155099
$139$	−3.71990e9	−0.845210	−0.422605	−	0.906314i	$-0.638884\pi$
$139$	−3.71990e9	−0.845210	−0.422605	+	0.906314i	$0.638884\pi$
$140$	6.24415e9	1.37372
$141$	−1.32905e9	−0.283176
$142$	−4.99168e9	−1.03027
$143$	−1.50884e9	−0.301740
$144$	−1.24814e9	−0.241898
$145$	7.67085e9	1.44108
$146$	−5.55707e7	−0.0101218
$147$	2.30302e9	0.406790
$148$	−2.72775e9	−0.467334
$149$	2.98264e9	0.495750	0.247875	−	0.968792i	$-0.420268\pi$
$149$	2.98264e9	0.495750	0.247875	+	0.968792i	$0.420268\pi$
$150$	−1.03848e9	−0.167490
$151$	−1.07704e10	−1.68592	−0.842960	−	0.537977i	$-0.819189\pi$
$151$	−1.07704e10	−1.68592	−0.842960	+	0.537977i	$0.819189\pi$
$152$	−5.33795e8	−0.0811107
$153$	1.24596e10	1.83819
$154$	1.91401e9	0.274221
$155$	7.71864e9	1.07411
$156$	9.35332e8	0.126446
$157$	4.65738e8	0.0611777	0.0305889	−	0.999532i	$-0.490262\pi$
$157$	4.65738e8	0.0611777	0.0305889	+	0.999532i	$0.490262\pi$
$158$	−3.13714e9	−0.400476
$159$	1.48278e9	0.183988
$160$	−2.23002e9	−0.269011
$161$	1.87537e10	2.19973
$162$	−5.60255e9	−0.639099
$163$	−3.04519e9	−0.337885	−0.168943	−	0.985626i	$-0.554035\pi$
$163$	−3.04519e9	−0.337885	−0.168943	+	0.985626i	$0.554035\pi$
$164$	3.37538e9	0.364355
$165$	−5.60262e8	−0.0588455
$166$	5.28452e9	0.540155
$167$	−5.43187e9	−0.540413	−0.270206	−	0.962802i	$-0.587092\pi$
$167$	−5.43187e9	−0.540413	−0.270206	+	0.962802i	$0.587092\pi$
$168$	−1.18649e9	−0.114914
$169$	1.03216e10	0.973322
$170$	2.22612e10	2.04423
$171$	−2.48197e9	−0.221980
$172$	−7.00391e8	−0.0610187
$173$	−5.67736e8	−0.0481880	−0.0240940	−	0.999710i	$-0.507670\pi$
$173$	−5.67736e8	−0.0481880	−0.0240940	+	0.999710i	$0.507670\pi$
$174$	−1.45759e9	−0.120549
$175$	2.94728e10	2.37548
$176$	−6.83566e8	−0.0536999
$177$	−1.82694e9	−0.139909
$178$	1.02471e10	0.765089
$179$	−1.14816e9	−0.0835920	−0.0417960	−	0.999126i	$-0.513308\pi$
$179$	−1.14816e9	−0.0835920	−0.0417960	+	0.999126i	$0.513308\pi$
$180$	−1.03689e10	−0.736217
$181$	−1.40584e10	−0.973606	−0.486803	−	0.873512i	$-0.661837\pi$
$181$	−1.40584e10	−0.973606	−0.486803	+	0.873512i	$0.661837\pi$
$182$	−2.65453e10	−1.79336
$183$	−1.88435e9	−0.124203
$184$	−6.69765e9	−0.430767
$185$	−2.26608e10	−1.42233
$186$	−1.46667e9	−0.0898514
$187$	6.82370e9	0.408068
$188$	−1.34710e10	−0.786486
$189$	−1.12184e10	−0.639519
$190$	−4.43449e9	−0.246861
$191$	−1.97985e10	−1.07642	−0.538209	−	0.842811i	$-0.680899\pi$
$191$	−1.97985e10	−1.07642	−0.538209	+	0.842811i	$0.680899\pi$
$192$	4.23742e8	0.0225033
$193$	2.34501e10	1.21657	0.608284	−	0.793719i	$-0.291858\pi$
$193$	2.34501e10	1.21657	0.608284	+	0.793719i	$0.291858\pi$
$194$	−2.50013e10	−1.26723
$195$	7.77025e9	0.384839
$196$	2.33430e10	1.12981
$197$	6.29979e8	0.0298008	0.0149004	−	0.999889i	$-0.495257\pi$
$197$	6.29979e8	0.0298008	0.0149004	+	0.999889i	$0.495257\pi$
$198$	−3.17836e9	−0.146964
$199$	−6.30124e9	−0.284831	−0.142416	−	0.989807i	$-0.545487\pi$
$199$	−6.30124e9	−0.284831	−0.142416	+	0.989807i	$0.545487\pi$
$200$	−1.05259e10	−0.465182
$201$	2.83838e9	0.122656
$202$	−4.08797e9	−0.172753
$203$	4.13674e10	1.70973
$204$	−4.23001e9	−0.171004
$205$	2.80409e10	1.10892
$206$	1.44917e10	0.560682
$207$	−3.11419e10	−1.17890
$208$	9.48034e9	0.351187
$209$	−1.35930e9	−0.0492784
$210$	−9.85678e9	−0.349742
$211$	−4.85098e10	−1.68484	−0.842419	−	0.538823i	$-0.818869\pi$
$211$	−4.85098e10	−1.68484	−0.842419	+	0.538823i	$0.818869\pi$
$212$	1.50292e10	0.511004
$213$	7.87967e9	0.262301
$214$	6.35982e9	0.207292
$215$	−5.81849e9	−0.185711
$216$	4.00652e9	0.125235
$217$	4.16252e10	1.27435
$218$	−9.46818e9	−0.283931
$219$	8.77219e7	0.00257697
$220$	−5.67871e9	−0.163436
$221$	−9.46377e10	−2.66869
$222$	4.30593e9	0.118981
$223$	2.29208e10	0.620666	0.310333	−	0.950628i	$-0.399560\pi$
$223$	2.29208e10	0.620666	0.310333	+	0.950628i	$0.399560\pi$
$224$	−1.20261e10	−0.319160
$225$	−4.89419e10	−1.27309
$226$	4.11401e10	1.04900
$227$	−2.40728e10	−0.601742	−0.300871	−	0.953665i	$-0.597277\pi$
$227$	−2.40728e10	−0.601742	−0.300871	+	0.953665i	$0.597277\pi$
$228$	8.42628e8	0.0206504
$229$	1.31840e10	0.316801	0.158400	−	0.987375i	$-0.449366\pi$
$229$	1.31840e10	0.316801	0.158400	+	0.987375i	$0.449366\pi$
$230$	−5.56406e10	−1.31104
$231$	−3.02139e9	−0.0698156
$232$	−1.47739e10	−0.334810
$233$	1.64719e10	0.366135	0.183068	−	0.983100i	$-0.441397\pi$
$233$	1.64719e10	0.366135	0.183068	+	0.983100i	$0.441397\pi$
$234$	4.40805e10	0.961116
$235$	−1.11910e11	−2.39367
$236$	−1.85175e10	−0.388578
$237$	4.95217e9	0.101959
$238$	1.20051e11	2.42531
$239$	6.84337e9	0.135669	0.0678343	−	0.997697i	$-0.478391\pi$
$239$	6.84337e9	0.135669	0.0678343	+	0.997697i	$0.478391\pi$
$240$	3.52023e9	0.0684889
$241$	6.99690e10	1.33607	0.668034	−	0.744130i	$-0.267136\pi$
$241$	6.99690e10	1.33607	0.668034	+	0.744130i	$0.267136\pi$
$242$	3.59865e10	0.674482
$243$	2.80970e10	0.516930
$244$	−1.90994e10	−0.344957
$245$	1.93921e11	3.43857
$246$	−5.32824e9	−0.0927633
$247$	1.88520e10	0.322272
$248$	−1.48659e10	−0.249551
$249$	−8.34194e9	−0.137521
$250$	−2.09836e10	−0.339742
$251$	−6.10283e10	−0.970509	−0.485254	−	0.874373i	$-0.661273\pi$
$251$	−6.10283e10	−0.970509	−0.485254	+	0.874373i	$0.661273\pi$
$252$	−5.59174e10	−0.873463
$253$	−1.70554e10	−0.261710
$254$	−2.36382e10	−0.356338
$255$	−3.51407e10	−0.520451
$256$	4.29497e9	0.0625000
$257$	−5.46978e10	−0.782115	−0.391058	−	0.920366i	$-0.627891\pi$
$257$	−5.46978e10	−0.782115	−0.391058	+	0.920366i	$0.627891\pi$
$258$	1.10561e9	0.0155351
$259$	−1.22205e11	−1.68749
$260$	7.87578e10	1.06884
$261$	−6.86937e10	−0.916294
$262$	9.31155e10	1.22086
$263$	6.53058e9	0.0841688	0.0420844	−	0.999114i	$-0.486600\pi$
$263$	6.53058e9	0.0841688	0.0420844	+	0.999114i	$0.486600\pi$
$264$	1.07905e9	0.0136718
$265$	1.24855e11	1.55524
$266$	−2.39143e10	−0.292881
$267$	−1.61757e10	−0.194788
$268$	2.87693e10	0.340661
$269$	1.22877e11	1.43082	0.715409	−	0.698706i	$-0.246241\pi$
$269$	1.22877e11	1.43082	0.715409	+	0.698706i	$0.246241\pi$
$270$	3.32841e10	0.381154
$271$	3.90560e10	0.439872	0.219936	−	0.975514i	$-0.429415\pi$
$271$	3.90560e10	0.439872	0.219936	+	0.975514i	$0.429415\pi$
$272$	−4.28746e10	−0.474941
$273$	4.19035e10	0.456581
$274$	4.50404e9	0.0482752
$275$	−2.68039e10	−0.282619
$276$	1.05726e10	0.109671
$277$	−2.55807e10	−0.261068	−0.130534	−	0.991444i	$-0.541669\pi$
$277$	−2.55807e10	−0.261068	−0.130534	+	0.991444i	$0.541669\pi$
$278$	5.95184e10	0.597654
$279$	−6.91217e10	−0.682961
$280$	−9.99064e10	−0.971365
$281$	−1.33338e10	−0.127578	−0.0637888	−	0.997963i	$-0.520318\pi$
$281$	−1.33338e10	−0.127578	−0.0637888	+	0.997963i	$0.520318\pi$
$282$	2.12649e10	0.200236
$283$	−1.04221e11	−0.965862	−0.482931	−	0.875658i	$-0.660428\pi$
$283$	−1.04221e11	−0.965862	−0.482931	+	0.875658i	$0.660428\pi$
$284$	7.98668e10	0.728507
$285$	7.00012e9	0.0628497
$286$	2.41415e10	0.213362
$287$	1.51219e11	1.31564
$288$	1.99702e10	0.171047
$289$	3.09408e11	2.60910
$290$	−1.22734e11	−1.01900
$291$	3.94660e10	0.322630
$292$	8.89132e8	0.00715720
$293$	−2.48589e11	−1.97050	−0.985251	−	0.171114i	$-0.945263\pi$
$293$	−2.48589e11	−1.97050	−0.985251	+	0.171114i	$0.945263\pi$
$294$	−3.68483e10	−0.287644
$295$	−1.53834e11	−1.18264
$296$	4.36440e10	0.330455
$297$	1.02025e10	0.0760859
$298$	−4.77222e10	−0.350548
$299$	2.36541e11	1.71154
$300$	1.66157e10	0.118433
$301$	−3.13780e10	−0.220331
$302$	1.72327e11	1.19213
$303$	6.45312e9	0.0439823
$304$	8.54072e9	0.0573539
$305$	−1.58668e11	−1.04988
$306$	−1.99353e11	−1.29980
$307$	3.35661e10	0.215664	0.107832	−	0.994169i	$-0.465609\pi$
$307$	3.35661e10	0.215664	0.107832	+	0.994169i	$0.465609\pi$
$308$	−3.06242e10	−0.193904
$309$	−2.28761e10	−0.142747
$310$	−1.23498e11	−0.759510
$311$	6.13779e10	0.372041	0.186020	−	0.982546i	$-0.440441\pi$
$311$	6.13779e10	0.372041	0.186020	+	0.982546i	$0.440441\pi$
$312$	−1.49653e10	−0.0894108
$313$	−1.45987e11	−0.859738	−0.429869	−	0.902891i	$-0.641440\pi$
$313$	−1.45987e11	−0.859738	−0.429869	+	0.902891i	$0.641440\pi$
$314$	−7.45181e9	−0.0432592
$315$	−4.64533e11	−2.65839
$316$	5.01942e10	0.283179
$317$	2.34017e10	0.130161	0.0650806	−	0.997880i	$-0.479270\pi$
$317$	2.34017e10	0.130161	0.0650806	+	0.997880i	$0.479270\pi$
$318$	−2.37245e10	−0.130099
$319$	−3.76214e10	−0.203412
$320$	3.56804e10	0.190219
$321$	−1.00394e10	−0.0527757
$322$	−3.00059e11	−1.55545
$323$	−8.52578e10	−0.435836
$324$	8.96407e10	0.451911
$325$	3.71742e11	1.84828
$326$	4.87230e10	0.238921
$327$	1.49461e10	0.0722875
$328$	−5.40060e10	−0.257638
$329$	−6.03511e11	−2.83991
$330$	8.96419e9	0.0416101
$331$	1.52176e11	0.696818	0.348409	−	0.937343i	$-0.386722\pi$
$331$	1.52176e11	0.696818	0.348409	+	0.937343i	$0.386722\pi$
$332$	−8.45522e10	−0.381948
$333$	2.02931e11	0.904376
$334$	8.69100e10	0.382129
$335$	2.39000e11	1.03680
$336$	1.89839e10	0.0812567
$337$	1.05261e11	0.444565	0.222282	−	0.974982i	$-0.428649\pi$
$337$	1.05261e11	0.444565	0.222282	+	0.974982i	$0.428649\pi$
$338$	−1.65146e11	−0.688243
$339$	−6.49421e10	−0.267072
$340$	−3.56180e11	−1.44549
$341$	−3.78558e10	−0.151613
$342$	3.97116e10	0.156964
$343$	5.82967e11	2.27416
$344$	1.12063e10	0.0431467
$345$	8.78321e10	0.333785
$346$	9.08377e9	0.0340740
$347$	−2.81412e11	−1.04198	−0.520992	−	0.853562i	$-0.674438\pi$
$347$	−2.81412e11	−1.04198	−0.520992	+	0.853562i	$0.674438\pi$
$348$	2.33215e10	0.0852412
$349$	3.55958e11	1.28435	0.642176	−	0.766557i	$-0.278032\pi$
$349$	3.55958e11	1.28435	0.642176	+	0.766557i	$0.278032\pi$
$350$	−4.71565e11	−1.67972
$351$	−1.41498e11	−0.497588
$352$	1.09371e10	0.0379715
$353$	1.35601e11	0.464813	0.232406	−	0.972619i	$-0.425340\pi$
$353$	1.35601e11	0.464813	0.232406	+	0.972619i	$0.425340\pi$
$354$	2.92310e10	0.0989303
$355$	6.63492e11	2.21722
$356$	−1.63954e11	−0.541000
$357$	−1.89507e11	−0.617474
$358$	1.83706e10	0.0591085
$359$	−2.12047e11	−0.673764	−0.336882	−	0.941547i	$-0.609372\pi$
$359$	−2.12047e11	−0.673764	−0.336882	+	0.941547i	$0.609372\pi$
$360$	1.65902e11	0.520584
$361$	1.69836e10	0.0526316
$362$	2.24935e11	0.688443
$363$	−5.68069e10	−0.171720
$364$	4.24725e11	1.26810
$365$	7.38644e9	0.0217830
$366$	3.01495e10	0.0878245
$367$	−4.48163e11	−1.28955	−0.644775	−	0.764372i	$-0.723049\pi$
$367$	−4.48163e11	−1.28955	−0.644775	+	0.764372i	$0.723049\pi$
$368$	1.07162e11	0.304598
$369$	−2.51111e11	−0.705093
$370$	3.62572e11	1.00574
$371$	6.73318e11	1.84517
$372$	2.34668e10	0.0635346
$373$	1.86916e11	0.499985	0.249993	−	0.968248i	$-0.419572\pi$
$373$	1.86916e11	0.499985	0.249993	+	0.968248i	$0.419572\pi$
$374$	−1.09179e11	−0.288548
$375$	3.31239e10	0.0864968
$376$	2.15537e11	0.556129
$377$	5.21769e11	1.33028
$378$	1.79495e11	0.452209
$379$	−3.54895e11	−0.883535	−0.441768	−	0.897130i	$-0.645648\pi$
$379$	−3.54895e11	−0.883535	−0.441768	+	0.897130i	$0.645648\pi$
$380$	7.09518e10	0.174557
$381$	3.73143e10	0.0907221
$382$	3.16775e11	0.761143
$383$	6.87668e10	0.163299	0.0816497	−	0.996661i	$-0.473981\pi$
$383$	6.87668e10	0.163299	0.0816497	+	0.996661i	$0.473981\pi$
$384$	−6.77987e9	−0.0159122
$385$	−2.54410e11	−0.590147
$386$	−3.75201e11	−0.860244
$387$	5.21055e10	0.118082
$388$	4.00020e11	0.896064
$389$	7.25930e10	0.160739	0.0803696	−	0.996765i	$-0.474390\pi$
$389$	7.25930e10	0.160739	0.0803696	+	0.996765i	$0.474390\pi$
$390$	−1.24324e11	−0.272122
$391$	−1.06975e12	−2.31466
$392$	−3.73488e11	−0.798894
$393$	−1.46989e11	−0.310826
$394$	−1.00797e10	−0.0210724
$395$	4.16987e11	0.861858
$396$	5.08538e10	0.103919
$397$	2.87651e11	0.581178	0.290589	−	0.956848i	$-0.406149\pi$
$397$	2.87651e11	0.581178	0.290589	+	0.956848i	$0.406149\pi$
$398$	1.00820e11	0.201406
$399$	3.77503e10	0.0745662
$400$	1.68414e11	0.328933
$401$	−4.88308e11	−0.943071	−0.471535	−	0.881847i	$-0.656300\pi$
$401$	−4.88308e11	−0.943071	−0.471535	+	0.881847i	$0.656300\pi$
$402$	−4.54141e10	−0.0867308
$403$	5.25020e11	0.991524
$404$	6.54076e10	0.122155
$405$	7.44689e11	1.37539
$406$	−6.61879e11	−1.20896
$407$	1.11139e11	0.200766
$408$	6.76802e10	0.120918
$409$	5.83827e11	1.03164	0.515821	−	0.856696i	$-0.327487\pi$
$409$	5.83827e11	1.03164	0.515821	+	0.856696i	$0.327487\pi$
$410$	−4.48654e11	−0.784123
$411$	−7.10990e9	−0.0122907
$412$	−2.31867e11	−0.396462
$413$	−8.29596e11	−1.40311
$414$	4.98270e11	0.833611
$415$	−7.02416e11	−1.16246
$416$	−1.51685e11	−0.248327
$417$	−9.39535e10	−0.152160
$418$	2.17488e10	0.0348451
$419$	−2.09427e11	−0.331947	−0.165974	−	0.986130i	$-0.553077\pi$
$419$	−2.09427e11	−0.331947	−0.165974	+	0.986130i	$0.553077\pi$
$420$	1.57708e11	0.247305
$421$	−4.21346e11	−0.653687	−0.326844	−	0.945078i	$-0.605985\pi$
$421$	−4.21346e11	−0.653687	−0.326844	+	0.945078i	$0.605985\pi$
$422$	7.76157e11	1.19136
$423$	1.00218e12	1.52199
$424$	−2.40467e11	−0.361335
$425$	−1.68119e12	−2.49958
$426$	−1.26075e11	−0.185475
$427$	−8.55664e11	−1.24560
$428$	−1.01757e11	−0.146578
$429$	−3.81089e10	−0.0543211
$430$	9.30958e10	0.131317
$431$	−3.62152e11	−0.505525	−0.252763	−	0.967528i	$-0.581339\pi$
$431$	−3.62152e11	−0.505525	−0.252763	+	0.967528i	$0.581339\pi$
$432$	−6.41044e10	−0.0885545
$433$	−8.27434e10	−0.113120	−0.0565598	−	0.998399i	$-0.518013\pi$
$433$	−8.27434e10	−0.113120	−0.0565598	+	0.998399i	$0.518013\pi$
$434$	−6.66002e11	−0.901098
$435$	1.93743e11	0.259432
$436$	1.51491e11	0.200769
$437$	2.13097e11	0.279518
$438$	−1.40355e9	−0.00182219
$439$	−6.69663e11	−0.860530	−0.430265	−	0.902703i	$-0.641580\pi$
$439$	−6.69663e11	−0.860530	−0.430265	+	0.902703i	$0.641580\pi$
$440$	9.08593e10	0.115567
$441$	−1.73660e12	−2.18638
$442$	1.51420e12	1.88705
$443$	5.66791e11	0.699208	0.349604	−	0.936898i	$-0.386316\pi$
$443$	5.66791e11	0.699208	0.349604	+	0.936898i	$0.386316\pi$
$444$	−6.88948e10	−0.0841324
$445$	−1.36205e12	−1.64654
$446$	−3.66733e11	−0.438877
$447$	7.53325e10	0.0892480
$448$	1.92417e11	0.225680
$449$	3.81051e11	0.442461	0.221230	−	0.975222i	$-0.428993\pi$
$449$	3.81051e11	0.442461	0.221230	+	0.975222i	$0.428993\pi$
$450$	7.83070e11	0.900211
$451$	−1.37525e11	−0.156527
$452$	−6.58241e11	−0.741757
$453$	−2.72029e11	−0.303510
$454$	3.85165e11	0.425496
$455$	3.52840e12	3.85946
$456$	−1.34821e10	−0.0146021
$457$	−1.09800e12	−1.17755	−0.588775	−	0.808297i	$-0.700390\pi$
$457$	−1.09800e12	−1.17755	−0.588775	+	0.808297i	$0.700390\pi$
$458$	−2.10943e11	−0.224012
$459$	6.39923e11	0.672931
$460$	8.90249e11	0.927046
$461$	6.53157e11	0.673540	0.336770	−	0.941587i	$-0.390665\pi$
$461$	6.53157e11	0.673540	0.336770	+	0.941587i	$0.390665\pi$
$462$	4.83422e10	0.0493671
$463$	−9.03119e11	−0.913336	−0.456668	−	0.889637i	$-0.650957\pi$
$463$	−9.03119e11	−0.913336	−0.456668	+	0.889637i	$0.650957\pi$
$464$	2.36382e11	0.236746
$465$	1.94950e11	0.193368
$466$	−2.63550e11	−0.258897
$467$	−1.07789e12	−1.04869	−0.524345	−	0.851506i	$-0.675690\pi$
$467$	−1.07789e12	−1.04869	−0.524345	+	0.851506i	$0.675690\pi$
$468$	−7.05289e11	−0.679611
$469$	1.28888e12	1.23009
$470$	1.79057e12	1.69258
$471$	1.17631e10	0.0110136
$472$	2.96280e11	0.274766
$473$	2.85365e10	0.0262136
$474$	−7.92347e10	−0.0720962
$475$	3.34898e11	0.301850
$476$	−1.92081e12	−1.71495
$477$	−1.11810e12	−0.988886
$478$	−1.09494e11	−0.0959322
$479$	−1.13640e12	−0.986329	−0.493165	−	0.869936i	$-0.664160\pi$
$479$	−1.13640e12	−0.986329	−0.493165	+	0.869936i	$0.664160\pi$
$480$	−5.63237e10	−0.0484290
$481$	−1.54138e12	−1.31297
$482$	−1.11950e12	−0.944743
$483$	4.73661e11	0.396010
$484$	−5.75784e11	−0.476931
$485$	3.32316e12	2.72718
$486$	−4.49552e11	−0.365525
$487$	2.14926e11	0.173144	0.0865721	−	0.996246i	$-0.472409\pi$
$487$	2.14926e11	0.173144	0.0865721	+	0.996246i	$0.472409\pi$
$488$	3.05590e11	0.243921
$489$	−7.69122e10	−0.0608283
$490$	−3.10274e12	−2.43144
$491$	1.98317e12	1.53991	0.769953	−	0.638100i	$-0.220280\pi$
$491$	1.98317e12	1.53991	0.769953	+	0.638100i	$0.220280\pi$
$492$	8.52519e10	0.0655935
$493$	−2.35969e12	−1.79905
$494$	−3.01633e11	−0.227881
$495$	4.22467e11	0.316278
$496$	2.37855e11	0.176459
$497$	3.57809e12	2.63055
$498$	1.33471e11	0.0972422
$499$	1.66297e12	1.20070	0.600348	−	0.799739i	$-0.295029\pi$
$499$	1.66297e12	1.20070	0.600348	+	0.799739i	$0.295029\pi$
$500$	3.35737e11	0.240234
$501$	−1.37193e11	−0.0972885
$502$	9.76453e11	0.686253
$503$	2.73936e12	1.90806	0.954031	−	0.299707i	$-0.0968891\pi$
$503$	2.73936e12	1.90806	0.954031	+	0.299707i	$0.0968891\pi$
$504$	8.94679e11	0.617632
$505$	5.43372e11	0.371780
$506$	2.72887e11	0.185057
$507$	2.60693e11	0.175224
$508$	3.78211e11	0.251969
$509$	−1.41595e12	−0.935016	−0.467508	−	0.883989i	$-0.654848\pi$
$509$	−1.41595e12	−0.935016	−0.467508	+	0.883989i	$0.654848\pi$
$510$	5.62252e11	0.368015
$511$	3.98337e10	0.0258438
$512$	−6.87195e10	−0.0441942
$513$	−1.27474e11	−0.0812632
$514$	8.75165e11	0.553039
$515$	−1.92623e12	−1.20664
$516$	−1.76898e10	−0.0109850
$517$	5.48860e11	0.337874
$518$	1.95528e12	1.19323
$519$	−1.43393e10	−0.00867510
$520$	−1.26012e12	−0.755785
$521$	−2.76092e12	−1.64166	−0.820832	−	0.571170i	$-0.806490\pi$
$521$	−2.76092e12	−1.64166	−0.820832	+	0.571170i	$0.806490\pi$
$522$	1.09910e12	0.647918
$523$	5.34558e11	0.312419	0.156209	−	0.987724i	$-0.450073\pi$
$523$	5.34558e11	0.312419	0.156209	+	0.987724i	$0.450073\pi$
$524$	−1.48985e12	−0.863279
$525$	7.44395e11	0.427648
$526$	−1.04489e11	−0.0595163
$527$	−2.37439e12	−1.34092
$528$	−1.72648e10	−0.00966739
$529$	8.72619e11	0.484478
$530$	−1.99768e12	−1.09972
$531$	1.37761e12	0.751969
$532$	3.82630e11	0.207098
$533$	1.90733e12	1.02366
$534$	2.58812e11	0.137736
$535$	−8.45346e11	−0.446110
$536$	−4.60309e11	−0.240884
$537$	−2.89991e10	−0.0150488
$538$	−1.96603e12	−1.01174
$539$	−9.51079e11	−0.485364
$540$	−5.32546e11	−0.269516
$541$	−3.40287e12	−1.70788	−0.853941	−	0.520369i	$-0.825794\pi$
$541$	−3.40287e12	−1.70788	−0.853941	+	0.520369i	$0.825794\pi$
$542$	−6.24896e11	−0.311036
$543$	−3.55074e11	−0.175275
$544$	6.85993e11	0.335834
$545$	1.25851e12	0.611042
$546$	−6.70455e11	−0.322852
$547$	−1.07691e12	−0.514321	−0.257161	−	0.966369i	$-0.582787\pi$
$547$	−1.07691e12	−0.514321	−0.257161	+	0.966369i	$0.582787\pi$
$548$	−7.20646e10	−0.0341358
$549$	1.42090e12	0.667554
$550$	4.28863e11	0.199842
$551$	4.70055e11	0.217253
$552$	−1.69162e11	−0.0775493
$553$	2.24873e12	1.02253
$554$	4.09292e11	0.184603
$555$	−5.72342e11	−0.256058
$556$	−9.52295e11	−0.422605
$557$	3.44597e12	1.51692	0.758460	−	0.651720i	$-0.225952\pi$
$557$	3.44597e12	1.51692	0.758460	+	0.651720i	$0.225952\pi$
$558$	1.10595e12	0.482926
$559$	−3.95772e11	−0.171432
$560$	1.59850e12	0.686858
$561$	1.72346e11	0.0734631
$562$	2.13340e11	0.0902110
$563$	3.12894e12	1.31253	0.656266	−	0.754530i	$-0.272135\pi$
$563$	3.12894e12	1.31253	0.656266	+	0.754530i	$0.272135\pi$
$564$	−3.40238e11	−0.141588
$565$	−5.46832e12	−2.25754
$566$	1.66753e12	0.682968
$567$	4.01596e12	1.63180
$568$	−1.27787e12	−0.515133
$569$	−3.86048e12	−1.54396	−0.771980	−	0.635647i	$-0.780734\pi$
$569$	−3.86048e12	−1.54396	−0.771980	+	0.635647i	$0.780734\pi$
$570$	−1.12002e11	−0.0444415
$571$	4.04984e12	1.59432	0.797160	−	0.603768i	$-0.206335\pi$
$571$	4.04984e12	1.59432	0.797160	+	0.603768i	$0.206335\pi$
$572$	−3.86264e11	−0.150870
$573$	−5.00050e11	−0.193784
$574$	−2.41951e12	−0.930300
$575$	4.20204e12	1.60308
$576$	−3.19523e11	−0.120949
$577$	1.81317e11	0.0681001	0.0340500	−	0.999420i	$-0.489159\pi$
$577$	1.81317e11	0.0681001	0.0340500	+	0.999420i	$0.489159\pi$
$578$	−4.95053e12	−1.84492
$579$	5.92279e11	0.219014
$580$	1.96374e12	0.720539
$581$	−3.78799e12	−1.37917
$582$	−6.31456e11	−0.228134
$583$	−6.12345e11	−0.219527
$584$	−1.42261e10	−0.00506091
$585$	−5.85917e12	−2.06840
$586$	3.97742e12	1.39336
$587$	4.63066e11	0.160980	0.0804900	−	0.996755i	$-0.474351\pi$
$587$	4.63066e11	0.160980	0.0804900	+	0.996755i	$0.474351\pi$
$588$	5.89574e11	0.203395
$589$	4.72984e11	0.161930
$590$	2.46134e12	0.836253
$591$	1.59114e10	0.00536493
$592$	−6.98305e11	−0.233667
$593$	3.90685e12	1.29742	0.648711	−	0.761035i	$-0.275308\pi$
$593$	3.90685e12	1.29742	0.648711	+	0.761035i	$0.275308\pi$
$594$	−1.63241e11	−0.0538008
$595$	−1.59571e13	−5.21948
$596$	7.63555e11	0.247875
$597$	−1.59150e11	−0.0512771
$598$	−3.78465e12	−1.21024
$599$	−4.47991e11	−0.142183	−0.0710916	−	0.997470i	$-0.522648\pi$
$599$	−4.47991e11	−0.142183	−0.0710916	+	0.997470i	$0.522648\pi$
$600$	−2.65852e11	−0.0837450
$601$	2.01818e12	0.630994	0.315497	−	0.948927i	$-0.397829\pi$
$601$	2.01818e12	0.630994	0.315497	+	0.948927i	$0.397829\pi$
$602$	5.02048e11	0.155798
$603$	−2.14029e12	−0.659241
$604$	−2.75723e12	−0.842960
$605$	−4.78331e12	−1.45154
$606$	−1.03250e11	−0.0311002
$607$	6.23030e12	1.86277	0.931387	−	0.364032i	$-0.118600\pi$
$607$	6.23030e12	1.86277	0.931387	+	0.364032i	$0.118600\pi$
$608$	−1.36651e11	−0.0405554
$609$	1.04482e12	0.307796
$610$	2.53868e12	0.742376
$611$	−7.61212e12	−2.20963
$612$	3.18965e12	0.919097
$613$	3.59461e11	0.102820	0.0514102	−	0.998678i	$-0.483628\pi$
$613$	3.59461e11	0.102820	0.0514102	+	0.998678i	$0.483628\pi$
$614$	−5.37058e11	−0.152498
$615$	7.08228e11	0.199634
$616$	4.89987e11	0.137111
$617$	4.00051e12	1.11130	0.555650	−	0.831416i	$-0.312469\pi$
$617$	4.00051e12	1.11130	0.555650	+	0.831416i	$0.312469\pi$
$618$	3.66017e11	0.100938
$619$	−3.72631e12	−1.02017	−0.510084	−	0.860125i	$-0.670386\pi$
$619$	−3.72631e12	−1.02017	−0.510084	+	0.860125i	$0.670386\pi$
$620$	1.97597e12	0.537054
$621$	−1.59945e12	−0.431576
$622$	−9.82046e11	−0.263072
$623$	−7.34525e12	−1.95349
$624$	2.39445e11	0.0632230
$625$	−2.22999e12	−0.584580
$626$	2.33580e12	0.607926
$627$	−3.43318e10	−0.00887141
$628$	1.19229e11	0.0305889
$629$	6.97084e12	1.77565
$630$	7.43252e12	1.87977
$631$	5.38677e11	0.135268	0.0676342	−	0.997710i	$-0.478455\pi$
$631$	5.38677e11	0.135268	0.0676342	+	0.997710i	$0.478455\pi$
$632$	−8.03107e11	−0.200238
$633$	−1.22521e12	−0.303315
$634$	−3.74428e11	−0.0920378
$635$	3.14198e12	0.766869
$636$	3.79592e11	0.0919942
$637$	1.31905e13	3.17419
$638$	6.01942e11	0.143834
$639$	−5.94168e12	−1.40979
$640$	−5.70886e11	−0.134505
$641$	5.87686e12	1.37494	0.687471	−	0.726212i	$-0.258721\pi$
$641$	5.87686e12	1.37494	0.687471	+	0.726212i	$0.258721\pi$
$642$	1.60630e11	0.0373181
$643$	3.03822e12	0.700923	0.350462	−	0.936577i	$-0.386025\pi$
$643$	3.03822e12	0.700923	0.350462	+	0.936577i	$0.386025\pi$
$644$	4.80094e12	1.09987
$645$	−1.46957e11	−0.0334328
$646$	1.36413e12	0.308182
$647$	1.92485e12	0.431844	0.215922	−	0.976411i	$-0.430724\pi$
$647$	1.92485e12	0.431844	0.215922	+	0.976411i	$0.430724\pi$
$648$	−1.43425e12	−0.319549
$649$	7.54472e11	0.166933
$650$	−5.94788e12	−1.30693
$651$	1.05133e12	0.229416
$652$	−7.79567e11	−0.168943
$653$	−4.80531e12	−1.03422	−0.517109	−	0.855920i	$-0.672992\pi$
$653$	−4.80531e12	−1.03422	−0.517109	+	0.855920i	$0.672992\pi$
$654$	−2.39138e11	−0.0511150
$655$	−1.23769e13	−2.62740
$656$	8.64097e11	0.182178
$657$	−6.61468e10	−0.0138505
$658$	9.65618e12	2.00812
$659$	7.75087e12	1.60091	0.800454	−	0.599394i	$-0.204592\pi$
$659$	7.75087e12	1.60091	0.800454	+	0.599394i	$0.204592\pi$
$660$	−1.43427e11	−0.0294228
$661$	4.58458e12	0.934100	0.467050	−	0.884231i	$-0.345317\pi$
$661$	4.58458e12	0.934100	0.467050	+	0.884231i	$0.345317\pi$
$662$	−2.43481e12	−0.492725
$663$	−2.39026e12	−0.480435
$664$	1.35284e12	0.270078
$665$	3.17869e12	0.630305
$666$	−3.24689e12	−0.639490
$667$	5.89789e12	1.15380
$668$	−1.39056e12	−0.270206
$669$	5.78910e11	0.111736
$670$	−3.82400e12	−0.733131
$671$	7.78179e11	0.148193
$672$	−3.03743e11	−0.0574571
$673$	−7.38830e12	−1.38828	−0.694139	−	0.719841i	$-0.744215\pi$
$673$	−7.38830e12	−1.38828	−0.694139	+	0.719841i	$0.744215\pi$
$674$	−1.68418e12	−0.314355
$675$	−2.51365e12	−0.466056
$676$	2.64233e12	0.486661
$677$	−3.48101e12	−0.636878	−0.318439	−	0.947943i	$-0.603159\pi$
$677$	−3.48101e12	−0.636878	−0.318439	+	0.947943i	$0.603159\pi$
$678$	1.03907e12	0.188848
$679$	1.79212e13	3.23558
$680$	5.69887e12	1.02211
$681$	−6.08006e11	−0.108329
$682$	6.05692e11	0.107207
$683$	6.60095e12	1.16068	0.580341	−	0.814373i	$-0.302919\pi$
$683$	6.60095e12	1.16068	0.580341	+	0.814373i	$0.302919\pi$
$684$	−6.35385e11	−0.110990
$685$	−5.98675e11	−0.103892
$686$	−9.32746e12	−1.60807
$687$	3.32987e11	0.0570325
$688$	−1.79300e11	−0.0305093
$689$	8.49259e12	1.43567
$690$	−1.40531e12	−0.236022
$691$	−8.94184e12	−1.49202	−0.746012	−	0.665933i	$-0.768034\pi$
$691$	−8.94184e12	−1.49202	−0.746012	+	0.665933i	$0.768034\pi$
$692$	−1.45340e11	−0.0240940
$693$	2.27828e12	0.375239
$694$	4.50260e12	0.736793
$695$	−7.91117e12	−1.28620
$696$	−3.73144e11	−0.0602746
$697$	−8.62586e12	−1.38438
$698$	−5.69532e12	−0.908174
$699$	4.16030e11	0.0659140
$700$	7.54505e12	1.18774
$701$	−9.13468e11	−0.142877	−0.0714385	−	0.997445i	$-0.522759\pi$
$701$	−9.13468e11	−0.142877	−0.0714385	+	0.997445i	$0.522759\pi$
$702$	2.26398e12	0.351848
$703$	−1.38861e12	−0.214428
$704$	−1.74993e11	−0.0268499
$705$	−2.82652e12	−0.430924
$706$	−2.16962e12	−0.328672
$707$	2.93030e12	0.441088
$708$	−4.67697e11	−0.0699543
$709$	2.22286e12	0.330372	0.165186	−	0.986262i	$-0.447178\pi$
$709$	2.22286e12	0.330372	0.165186	+	0.986262i	$0.447178\pi$
$710$	−1.06159e13	−1.56781
$711$	−3.73419e12	−0.548003
$712$	2.62327e12	0.382545
$713$	5.93463e12	0.859985
$714$	3.03212e12	0.436620
$715$	−3.20888e12	−0.459173
$716$	−2.93930e11	−0.0417960
$717$	1.72843e11	0.0244239
$718$	3.39276e12	0.476423
$719$	−1.38107e12	−0.192724	−0.0963622	−	0.995346i	$-0.530721\pi$
$719$	−1.38107e12	−0.192724	−0.0963622	+	0.995346i	$0.530721\pi$
$720$	−2.65443e12	−0.368109
$721$	−1.03878e13	−1.43158
$722$	−2.71737e11	−0.0372161
$723$	1.76721e12	0.240528
$724$	−3.59896e12	−0.486803
$725$	9.26898e12	1.24598
$726$	9.08910e11	0.121424
$727$	−1.01054e13	−1.34168	−0.670838	−	0.741604i	$-0.734065\pi$
$727$	−1.01054e13	−1.34168	−0.670838	+	0.741604i	$0.734065\pi$
$728$	−6.79561e12	−0.896679
$729$	−6.18254e12	−0.810761
$730$	−1.18183e11	−0.0154029
$731$	1.78987e12	0.231842
$732$	−4.82393e11	−0.0621013
$733$	−2.46166e12	−0.314964	−0.157482	−	0.987522i	$-0.550338\pi$
$733$	−2.46166e12	−0.314964	−0.157482	+	0.987522i	$0.550338\pi$
$734$	7.17060e12	0.911850
$735$	4.89787e12	0.619034
$736$	−1.71460e12	−0.215383
$737$	−1.17217e12	−0.146348
$738$	4.01777e12	0.498576
$739$	8.80833e12	1.08641	0.543205	−	0.839600i	$-0.317211\pi$
$739$	8.80833e12	1.08641	0.543205	+	0.839600i	$0.317211\pi$
$740$	−5.80115e12	−0.711167
$741$	4.76146e11	0.0580174
$742$	−1.07731e13	−1.30474
$743$	−2.35539e11	−0.0283539	−0.0141770	−	0.999900i	$-0.504513\pi$
$743$	−2.35539e11	−0.0283539	−0.0141770	+	0.999900i	$0.504513\pi$
$744$	−3.75468e11	−0.0449257
$745$	6.34322e12	0.754409
$746$	−2.99066e12	−0.353543
$747$	6.29025e12	0.739138
$748$	1.74687e12	0.204034
$749$	−4.55879e12	−0.529275
$750$	−5.29982e11	−0.0611625
$751$	−6.15738e12	−0.706344	−0.353172	−	0.935558i	$-0.614897\pi$
$751$	−6.15738e12	−0.706344	−0.353172	+	0.935558i	$0.614897\pi$
$752$	−3.44859e12	−0.393243
$753$	−1.54139e12	−0.174717
$754$	−8.34831e12	−0.940648
$755$	−2.29056e13	−2.56555
$756$	−2.87192e12	−0.319760
$757$	1.74954e12	0.193639	0.0968195	−	0.995302i	$-0.469133\pi$
$757$	1.74954e12	0.193639	0.0968195	+	0.995302i	$0.469133\pi$
$758$	5.67833e12	0.624754
$759$	−4.30769e11	−0.0471147
$760$	−1.13523e12	−0.123430
$761$	−1.52097e13	−1.64395	−0.821976	−	0.569522i	$-0.807128\pi$
$761$	−1.52097e13	−1.64395	−0.821976	+	0.569522i	$0.807128\pi$
$762$	−5.97029e11	−0.0641502
$763$	6.78688e12	0.724953
$764$	−5.06840e12	−0.538209
$765$	2.64979e13	2.79728
$766$	−1.10027e12	−0.115470
$767$	−1.04637e13	−1.09171
$768$	1.08478e11	0.0112516
$769$	−9.63035e12	−0.993055	−0.496528	−	0.868021i	$-0.665392\pi$
$769$	−9.63035e12	−0.993055	−0.496528	+	0.868021i	$0.665392\pi$
$770$	4.07056e12	0.417297
$771$	−1.38150e12	−0.140801
$772$	6.00322e12	0.608284
$773$	1.49129e13	1.50230	0.751148	−	0.660134i	$-0.229501\pi$
$773$	1.49129e13	1.50230	0.751148	+	0.660134i	$0.229501\pi$
$774$	−8.33688e11	−0.0834967
$775$	9.32673e12	0.928692
$776$	−6.40032e12	−0.633613
$777$	−3.08653e12	−0.303792
$778$	−1.16149e12	−0.113660
$779$	1.71829e12	0.167178
$780$	1.98918e12	0.192420
$781$	−3.25407e12	−0.312966
$782$	1.71160e13	1.63671
$783$	−3.52811e12	−0.335439
$784$	5.97580e12	0.564903
$785$	9.90492e11	0.0930974
$786$	2.35182e12	0.219787
$787$	1.51917e13	1.41163	0.705816	−	0.708396i	$-0.250581\pi$
$787$	1.51917e13	1.41163	0.705816	+	0.708396i	$0.250581\pi$
$788$	1.61275e11	0.0149004
$789$	1.64943e11	0.0151526
$790$	−6.67180e12	−0.609426
$791$	−2.94896e13	−2.67840
$792$	−8.13660e11	−0.0734818
$793$	−1.07925e13	−0.969157
$794$	−4.60242e12	−0.410955
$795$	3.15346e12	0.279985
$796$	−1.61312e12	−0.142416
$797$	1.37336e13	1.20565	0.602827	−	0.797872i	$-0.294041\pi$
$797$	1.37336e13	1.20565	0.602827	+	0.797872i	$0.294041\pi$
$798$	−6.04005e11	−0.0527263
$799$	3.44256e13	2.98828
$800$	−2.69462e12	−0.232591
$801$	1.21973e13	1.04693
$802$	7.81293e12	0.666852
$803$	−3.62265e10	−0.00307473
$804$	7.26626e11	0.0613280
$805$	3.98837e13	3.34745
$806$	−8.40032e12	−0.701113
$807$	3.10349e12	0.257585
$808$	−1.04652e12	−0.0863767
$809$	−1.54605e12	−0.126898	−0.0634491	−	0.997985i	$-0.520210\pi$
$809$	−1.54605e12	−0.126898	−0.0634491	+	0.997985i	$0.520210\pi$
$810$	−1.19150e13	−0.972550
$811$	1.50745e13	1.22363	0.611814	−	0.791002i	$-0.290440\pi$
$811$	1.50745e13	1.22363	0.611814	+	0.791002i	$0.290440\pi$
$812$	1.05901e13	0.854863
$813$	9.86438e11	0.0791885
$814$	−1.77822e12	−0.141963
$815$	−6.47624e12	−0.514178
$816$	−1.08288e12	−0.0855019
$817$	−3.56546e11	−0.0279973
$818$	−9.34123e12	−0.729482
$819$	−3.15974e13	−2.45399
$820$	7.17846e12	0.554459
$821$	7.55550e12	0.580389	0.290194	−	0.956968i	$-0.406280\pi$
$821$	7.55550e12	0.580389	0.290194	+	0.956968i	$0.406280\pi$
$822$	1.13758e11	0.00869081
$823$	3.21334e12	0.244150	0.122075	−	0.992521i	$-0.461045\pi$
$823$	3.21334e12	0.244150	0.122075	+	0.992521i	$0.461045\pi$
$824$	3.70988e12	0.280341
$825$	−6.76986e11	−0.0508788
$826$	1.32735e13	0.992148
$827$	8.79853e12	0.654087	0.327043	−	0.945009i	$-0.393948\pi$
$827$	8.79853e12	0.654087	0.327043	+	0.945009i	$0.393948\pi$
$828$	−7.97233e12	−0.589452
$829$	2.39558e13	1.76163	0.880816	−	0.473459i	$-0.156995\pi$
$829$	2.39558e13	1.76163	0.880816	+	0.473459i	$0.156995\pi$
$830$	1.12387e13	0.821983
$831$	−6.46092e11	−0.0469991
$832$	2.42697e12	0.175594
$833$	−5.96535e13	−4.29273
$834$	1.50326e12	0.107593
$835$	−1.15520e13	−0.822375
$836$	−3.47980e11	−0.0246392
$837$	−3.55009e12	−0.250020
$838$	3.35083e12	0.234722
$839$	−2.38372e13	−1.66083	−0.830417	−	0.557143i	$-0.811897\pi$
$839$	−2.38372e13	−1.66083	−0.830417	+	0.557143i	$0.811897\pi$
$840$	−2.52334e12	−0.174871
$841$	−1.49741e12	−0.103219
$842$	6.74154e12	0.462227
$843$	−3.36771e11	−0.0229673
$844$	−1.24185e13	−0.842419
$845$	2.19511e13	1.48116
$846$	−1.60348e13	−1.07621
$847$	−2.57955e13	−1.72214
$848$	3.84747e12	0.255502
$849$	−2.63230e12	−0.173881
$850$	2.68991e13	1.76747
$851$	−1.74232e13	−1.13879
$852$	2.01720e12	0.131151
$853$	1.15908e13	0.749621	0.374811	−	0.927101i	$-0.377708\pi$
$853$	1.15908e13	0.749621	0.374811	+	0.927101i	$0.377708\pi$
$854$	1.36906e13	0.880771
$855$	−5.27845e12	−0.337800
$856$	1.62811e12	0.103646
$857$	2.40055e13	1.52019	0.760093	−	0.649815i	$-0.225154\pi$
$857$	2.40055e13	1.52019	0.760093	+	0.649815i	$0.225154\pi$
$858$	6.09742e11	0.0384108
$859$	−1.28254e13	−0.803712	−0.401856	−	0.915703i	$-0.631635\pi$
$859$	−1.28254e13	−0.803712	−0.401856	+	0.915703i	$0.631635\pi$
$860$	−1.48953e12	−0.0928553
$861$	3.81934e12	0.236850
$862$	5.79443e12	0.357460
$863$	1.10966e13	0.680994	0.340497	−	0.940246i	$-0.389405\pi$
$863$	1.10966e13	0.680994	0.340497	+	0.940246i	$0.389405\pi$
$864$	1.02567e12	0.0626175
$865$	−1.20741e12	−0.0733302
$866$	1.32390e12	0.0799877
$867$	7.81472e12	0.469707
$868$	1.06560e13	0.637173
$869$	−2.04510e12	−0.121654
$870$	−3.09988e12	−0.183446
$871$	1.62567e13	0.957087
$872$	−2.42385e12	−0.141965
$873$	−2.97594e13	−1.73405
$874$	−3.40955e12	−0.197649
$875$	1.50412e13	0.867455
$876$	2.24568e10	0.00128848
$877$	2.34043e12	0.133597	0.0667986	−	0.997766i	$-0.478721\pi$
$877$	2.34043e12	0.133597	0.0667986	+	0.997766i	$0.478721\pi$
$878$	1.07146e13	0.608486
$879$	−6.27860e12	−0.354742
$880$	−1.45375e12	−0.0817180
$881$	−1.38455e12	−0.0774315	−0.0387158	−	0.999250i	$-0.512327\pi$
$881$	−1.38455e12	−0.0774315	−0.0387158	+	0.999250i	$0.512327\pi$
$882$	2.77856e13	1.54600
$883$	−6.13771e12	−0.339769	−0.169884	−	0.985464i	$-0.554339\pi$
$883$	−6.13771e12	−0.339769	−0.169884	+	0.985464i	$0.554339\pi$
$884$	−2.42272e13	−1.33435
$885$	−3.88538e12	−0.212906
$886$	−9.06866e12	−0.494415
$887$	8.64012e12	0.468666	0.234333	−	0.972156i	$-0.424709\pi$
$887$	8.64012e12	0.468666	0.234333	+	0.972156i	$0.424709\pi$
$888$	1.10232e12	0.0594906
$889$	1.69441e13	0.909830
$890$	2.17927e13	1.16428
$891$	−3.65229e12	−0.194141
$892$	5.86772e12	0.310333
$893$	−6.85766e12	−0.360864
$894$	−1.20532e12	−0.0631079
$895$	−2.44181e12	−0.127206
$896$	−3.07868e12	−0.159580
$897$	5.97431e12	0.308121
$898$	−6.09682e12	−0.312867
$899$	1.30908e13	0.668417
$900$	−1.25291e13	−0.636545
$901$	−3.84075e13	−1.94157
$902$	2.20041e12	0.110681
$903$	−7.92513e11	−0.0396654
$904$	1.05319e13	0.524502
$905$	−2.98983e13	−1.48159
$906$	4.35246e12	0.214614
$907$	−3.36715e13	−1.65207	−0.826037	−	0.563616i	$-0.809410\pi$
$907$	−3.36715e13	−1.65207	−0.826037	+	0.563616i	$0.809410\pi$
$908$	−6.16263e12	−0.300871
$909$	−4.86599e12	−0.236392
$910$	−5.64544e13	−2.72905
$911$	2.03568e13	0.979211	0.489606	−	0.871944i	$-0.337141\pi$
$911$	2.03568e13	0.979211	0.489606	+	0.871944i	$0.337141\pi$
$912$	2.15713e11	0.0103252
$913$	3.44497e12	0.164084
$914$	1.75680e13	0.832654
$915$	−4.00747e12	−0.189006
$916$	3.37509e12	0.158400
$917$	−6.67462e13	−3.11720
$918$	−1.02388e13	−0.475834
$919$	2.44953e13	1.13282	0.566412	−	0.824122i	$-0.308331\pi$
$919$	2.44953e13	1.13282	0.566412	+	0.824122i	$0.308331\pi$
$920$	−1.42440e13	−0.655520
$921$	8.47779e11	0.0388252
$922$	−1.04505e13	−0.476265
$923$	4.51306e13	2.04674
$924$	−7.73475e11	−0.0349078
$925$	−2.73819e13	−1.22977
$926$	1.44499e13	0.645826
$927$	1.72497e13	0.767226
$928$	−3.78211e12	−0.167405
$929$	2.79588e13	1.23154	0.615768	−	0.787928i	$-0.288846\pi$
$929$	2.79588e13	1.23154	0.615768	+	0.787928i	$0.288846\pi$
$930$	−3.11920e12	−0.136732
$931$	1.18831e13	0.518391
$932$	4.21680e12	0.183068
$933$	1.55022e12	0.0669771
$934$	1.72462e13	0.741536
$935$	1.45121e13	0.620979
$936$	1.12846e13	0.480558
$937$	−8.07789e12	−0.342349	−0.171175	−	0.985241i	$-0.554756\pi$
$937$	−8.07789e12	−0.342349	−0.171175	+	0.985241i	$0.554756\pi$
$938$	−2.06221e13	−0.869802
$939$	−3.68720e12	−0.154775
$940$	−2.86491e13	−1.19684
$941$	1.80335e12	0.0749768	0.0374884	−	0.999297i	$-0.488064\pi$
$941$	1.80335e12	0.0749768	0.0374884	+	0.999297i	$0.488064\pi$
$942$	−1.88210e11	−0.00778779
$943$	2.15598e13	0.887855
$944$	−4.74048e12	−0.194289
$945$	−2.38584e13	−0.973191
$946$	−4.56584e11	−0.0185358
$947$	1.33152e13	0.537989	0.268995	−	0.963142i	$-0.413309\pi$
$947$	1.33152e13	0.537989	0.268995	+	0.963142i	$0.413309\pi$
$948$	1.26775e12	0.0509797
$949$	5.02424e11	0.0201082
$950$	−5.35836e12	−0.213440
$951$	5.91057e11	0.0234324
$952$	3.07329e13	1.21266
$953$	−3.50858e13	−1.37789	−0.688943	−	0.724815i	$-0.741925\pi$
$953$	−3.50858e13	−1.37789	−0.688943	+	0.724815i	$0.741925\pi$
$954$	1.78895e13	0.699248
$955$	−4.21057e13	−1.63804
$956$	1.75190e12	0.0678343
$957$	−9.50203e11	−0.0366195
$958$	1.81824e13	0.697440
$959$	−3.22854e12	−0.123260
$960$	9.01179e11	0.0342445
$961$	−1.32673e13	−0.501795
$962$	2.46620e13	0.928413
$963$	7.57021e12	0.283654
$964$	1.79121e13	0.668034
$965$	4.98716e13	1.85132
$966$	−7.57858e12	−0.280021
$967$	3.33371e13	1.22605	0.613026	−	0.790063i	$-0.289952\pi$
$967$	3.33371e13	1.22605	0.613026	+	0.790063i	$0.289952\pi$
$968$	9.21254e12	0.337241
$969$	−2.15336e12	−0.0784619
$970$	−5.31705e13	−1.92840
$971$	−3.31130e13	−1.19540	−0.597698	−	0.801722i	$-0.703918\pi$
$971$	−3.31130e13	−1.19540	−0.597698	+	0.801722i	$0.703918\pi$
$972$	7.19283e12	0.258465
$973$	−4.26634e13	−1.52598
$974$	−3.43881e12	−0.122431
$975$	9.38909e12	0.332738
$976$	−4.88944e12	−0.172478
$977$	−1.28147e12	−0.0449969	−0.0224984	−	0.999747i	$-0.507162\pi$
$977$	−1.28147e12	−0.0449969	−0.0224984	+	0.999747i	$0.507162\pi$
$978$	1.23060e12	0.0430121
$979$	6.68009e12	0.232413
$980$	4.96439e13	1.71929
$981$	−1.12701e13	−0.388525
$982$	−3.17308e13	−1.08888
$983$	3.93077e13	1.34272	0.671362	−	0.741130i	$-0.265710\pi$
$983$	3.93077e13	1.34272	0.671362	+	0.741130i	$0.265710\pi$
$984$	−1.36403e12	−0.0463816
$985$	1.33979e12	0.0453495
$986$	3.77550e13	1.27212
$987$	−1.52429e13	−0.511258
$988$	4.82612e12	0.161136
$989$	−4.47366e12	−0.148689
$990$	−6.75947e12	−0.223642
$991$	−3.13171e13	−1.03145	−0.515727	−	0.856753i	$-0.672478\pi$
$991$	−3.13171e13	−1.03145	−0.515727	+	0.856753i	$0.672478\pi$
$992$	−3.80567e12	−0.124775
$993$	3.84350e12	0.125446
$994$	−5.72494e13	−1.86008
$995$	−1.34010e13	−0.433443
$996$	−2.13554e12	−0.0687606
$997$	−8.04007e12	−0.257710	−0.128855	−	0.991663i	$-0.541130\pi$
$997$	−8.04007e12	−0.257710	−0.128855	+	0.991663i	$0.541130\pi$
$998$	−2.66076e13	−0.849021
$999$	1.04225e13	0.331076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.a.d.1.3	✓	4
3.2	odd	2		342.10.a.l.1.1		4
4.3	odd	2		304.10.a.e.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.d.1.3	✓	4	1.1	even	1	trivial
304.10.a.e.1.2		4	4.3	odd	2
342.10.a.l.1.1		4	3.2	odd	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +25.2570 q^{3} +256.000 q^{4} +2126.71 q^{5} -404.112 q^{6} +11469.0 q^{7} -4096.00 q^{8} -19045.1 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} +25.2570 q^{3} +256.000 q^{4} +2126.71 q^{5} -404.112 q^{6} +11469.0 q^{7} -4096.00 q^{8} -19045.1 q^{9} -34027.4 q^{10} -10430.4 q^{11} +6465.79 q^{12} +144659. q^{13} -183503. q^{14} +53714.4 q^{15} +65536.0 q^{16} -654214. q^{17} +304721. q^{18} +130321. q^{19} +544439. q^{20} +289672. q^{21} +166886. q^{22} +1.63517e6 q^{23} -103453. q^{24} +2.56979e6 q^{25} -2.31454e6 q^{26} -978155. q^{27} +2.93605e6 q^{28} +3.60690e6 q^{29} -859431. q^{30} +3.62937e6 q^{31} -1.04858e6 q^{32} -263440. q^{33} +1.04674e7 q^{34} +2.43912e7 q^{35} -4.87554e6 q^{36} -1.06553e7 q^{37} -2.08514e6 q^{38} +3.65364e6 q^{39} -8.71102e6 q^{40} +1.31851e7 q^{41} -4.63474e6 q^{42} -2.73590e6 q^{43} -2.67018e6 q^{44} -4.05035e7 q^{45} -2.61627e7 q^{46} -5.26213e7 q^{47} +1.65524e6 q^{48} +9.11835e7 q^{49} -4.11167e7 q^{50} -1.65235e7 q^{51} +3.70326e7 q^{52} +5.87078e7 q^{53} +1.56505e7 q^{54} -2.21825e7 q^{55} -4.69769e7 q^{56} +3.29152e6 q^{57} -5.77104e7 q^{58} -7.23340e7 q^{59} +1.37509e7 q^{60} -7.46069e7 q^{61} -5.80700e7 q^{62} -2.18427e8 q^{63} +1.67772e7 q^{64} +3.07647e8 q^{65} +4.21504e6 q^{66} +1.12380e8 q^{67} -1.67479e8 q^{68} +4.12994e7 q^{69} -3.90259e8 q^{70} +3.11980e8 q^{71} +7.80087e7 q^{72} +3.47317e6 q^{73} +1.70485e8 q^{74} +6.49052e7 q^{75} +3.33622e7 q^{76} -1.19626e8 q^{77} -5.84582e7 q^{78} +1.96071e8 q^{79} +1.39376e8 q^{80} +3.50159e8 q^{81} -2.10961e8 q^{82} -3.30282e8 q^{83} +7.41559e7 q^{84} -1.39133e9 q^{85} +4.37745e7 q^{86} +9.10995e7 q^{87} +4.27229e7 q^{88} -6.40446e8 q^{89} +6.48055e8 q^{90} +1.65908e9 q^{91} +4.18603e8 q^{92} +9.16671e7 q^{93} +8.41940e8 q^{94} +2.77156e8 q^{95} -2.64839e7 q^{96} +1.56258e9 q^{97} -1.45894e9 q^{98} +1.98648e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9}+O(q^{10}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9} + 22320 q^{10} - 104249 q^{11} + 21504 q^{12} + 120486 q^{13} - 196912 q^{14} - 591090 q^{15} + 262144 q^{16} - 412139 q^{17} - 264608 q^{18} + 521284 q^{19} - 357120 q^{20} + 2437006 q^{21} + 1667984 q^{22} + 3010300 q^{23} - 344064 q^{24} + 9760585 q^{25} - 1927776 q^{26} + 12387978 q^{27} + 3150592 q^{28} + 6153240 q^{29} + 9457440 q^{30} + 12774024 q^{31} - 4194304 q^{32} - 3258022 q^{33} + 6594224 q^{34} + 9823425 q^{35} + 4233728 q^{36} + 20506048 q^{37} - 8340544 q^{38} + 69881444 q^{39} + 5713920 q^{40} + 11620300 q^{41} - 38992096 q^{42} + 7698327 q^{43} - 26687744 q^{44} - 124015815 q^{45} - 48164800 q^{46} - 31581083 q^{47} + 5505024 q^{48} + 18970383 q^{49} - 156169360 q^{50} - 8594812 q^{51} + 30844416 q^{52} + 72549422 q^{53} - 198207648 q^{54} + 21332505 q^{55} - 50409472 q^{56} + 10946964 q^{57} - 98451840 q^{58} - 149234120 q^{59} - 151319040 q^{60} + 129004373 q^{61} - 204384384 q^{62} + 102967551 q^{63} + 67108864 q^{64} + 124691700 q^{65} + 52128352 q^{66} + 132595266 q^{67} - 105507584 q^{68} - 45529972 q^{69} - 157174800 q^{70} - 47138482 q^{71} - 67739648 q^{72} - 39332795 q^{73} - 328096768 q^{74} + 824627010 q^{75} + 133448704 q^{76} - 165933719 q^{77} - 1118103104 q^{78} - 307010840 q^{79} - 91422720 q^{80} + 1305551744 q^{81} - 185924800 q^{82} - 746568232 q^{83} + 623873536 q^{84} - 105005985 q^{85} - 123173232 q^{86} - 82148208 q^{87} + 427003904 q^{88} + 286943482 q^{89} + 1984253040 q^{90} + 3155781114 q^{91} + 770636800 q^{92} + 1151901596 q^{93} + 505297328 q^{94} - 181797795 q^{95} - 88080384 q^{96} + 793519958 q^{97} - 303526128 q^{98} - 1681833809 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9 + 22320 * q^10 - 104249 * q^11 + 21504 * q^12 + 120486 * q^13 - 196912 * q^14 - 591090 * q^15 + 262144 * q^16 - 412139 * q^17 - 264608 * q^18 + 521284 * q^19 - 357120 * q^20 + 2437006 * q^21 + 1667984 * q^22 + 3010300 * q^23 - 344064 * q^24 + 9760585 * q^25 - 1927776 * q^26 + 12387978 * q^27 + 3150592 * q^28 + 6153240 * q^29 + 9457440 * q^30 + 12774024 * q^31 - 4194304 * q^32 - 3258022 * q^33 + 6594224 * q^34 + 9823425 * q^35 + 4233728 * q^36 + 20506048 * q^37 - 8340544 * q^38 + 69881444 * q^39 + 5713920 * q^40 + 11620300 * q^41 - 38992096 * q^42 + 7698327 * q^43 - 26687744 * q^44 - 124015815 * q^45 - 48164800 * q^46 - 31581083 * q^47 + 5505024 * q^48 + 18970383 * q^49 - 156169360 * q^50 - 8594812 * q^51 + 30844416 * q^52 + 72549422 * q^53 - 198207648 * q^54 + 21332505 * q^55 - 50409472 * q^56 + 10946964 * q^57 - 98451840 * q^58 - 149234120 * q^59 - 151319040 * q^60 + 129004373 * q^61 - 204384384 * q^62 + 102967551 * q^63 + 67108864 * q^64 + 124691700 * q^65 + 52128352 * q^66 + 132595266 * q^67 - 105507584 * q^68 - 45529972 * q^69 - 157174800 * q^70 - 47138482 * q^71 - 67739648 * q^72 - 39332795 * q^73 - 328096768 * q^74 + 824627010 * q^75 + 133448704 * q^76 - 165933719 * q^77 - 1118103104 * q^78 - 307010840 * q^79 - 91422720 * q^80 + 1305551744 * q^81 - 185924800 * q^82 - 746568232 * q^83 + 623873536 * q^84 - 105005985 * q^85 - 123173232 * q^86 - 82148208 * q^87 + 427003904 * q^88 + 286943482 * q^89 + 1984253040 * q^90 + 3155781114 * q^91 + 770636800 * q^92 + 1151901596 * q^93 + 505297328 * q^94 - 181797795 * q^95 - 88080384 * q^96 + 793519958 * q^97 - 303526128 * q^98 - 1681833809 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more