LMFDB - Embedded newform 23.10.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,10,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, 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("23.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	23.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:	$11.8458242318$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 640x^{5} - 1455x^{4} + 114552x^{3} + 321544x^{2} - 5741296x - 13379024 $ x^7 - 640x^5 - 1455x^4 + 114552x^3 + 321544x^2 - 5741296*x - 13379024
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-15.0730$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-30.1460 q^{2} -193.374 q^{3} +396.783 q^{4} +568.966 q^{5} +5829.45 q^{6} +3614.33 q^{7} +3473.33 q^{8} +17710.4 q^{9} +O(q^{10})$	\(q-30.1460 q^{2} -193.374 q^{3} +396.783 q^{4} +568.966 q^{5} +5829.45 q^{6} +3614.33 q^{7} +3473.33 q^{8} +17710.4 q^{9} -17152.1 q^{10} -2709.83 q^{11} -76727.4 q^{12} +22818.6 q^{13} -108958. q^{14} -110023. q^{15} -307860. q^{16} -93871.0 q^{17} -533898. q^{18} +269048. q^{19} +225756. q^{20} -698916. q^{21} +81690.5 q^{22} -279841. q^{23} -671651. q^{24} -1.62940e6 q^{25} -687889. q^{26} +381449. q^{27} +1.43411e6 q^{28} +3.04153e6 q^{29} +3.31676e6 q^{30} +3.69093e6 q^{31} +7.50242e6 q^{32} +524009. q^{33} +2.82984e6 q^{34} +2.05643e6 q^{35} +7.02719e6 q^{36} -1.81385e7 q^{37} -8.11073e6 q^{38} -4.41251e6 q^{39} +1.97621e6 q^{40} -947287. q^{41} +2.10696e7 q^{42} -3.70325e7 q^{43} -1.07521e6 q^{44} +1.00766e7 q^{45} +8.43610e6 q^{46} -2.51305e7 q^{47} +5.95321e7 q^{48} -2.72902e7 q^{49} +4.91200e7 q^{50} +1.81522e7 q^{51} +9.05403e6 q^{52} -5.27006e7 q^{53} -1.14992e7 q^{54} -1.54180e6 q^{55} +1.25538e7 q^{56} -5.20268e7 q^{57} -9.16899e7 q^{58} +5.16175e7 q^{59} -4.36553e7 q^{60} -7.29696e7 q^{61} -1.11267e8 q^{62} +6.40112e7 q^{63} -6.85437e7 q^{64} +1.29830e7 q^{65} -1.57968e7 q^{66} -2.75931e8 q^{67} -3.72464e7 q^{68} +5.41139e7 q^{69} -6.19932e7 q^{70} +3.95007e8 q^{71} +6.15141e7 q^{72} +1.76598e8 q^{73} +5.46803e8 q^{74} +3.15084e8 q^{75} +1.06754e8 q^{76} -9.79421e6 q^{77} +1.33020e8 q^{78} +1.92073e8 q^{79} -1.75162e8 q^{80} -4.22356e8 q^{81} +2.85569e7 q^{82} +2.66138e8 q^{83} -2.77318e8 q^{84} -5.34094e7 q^{85} +1.11638e9 q^{86} -5.88151e8 q^{87} -9.41212e6 q^{88} -8.53374e8 q^{89} -3.03770e8 q^{90} +8.24738e7 q^{91} -1.11036e8 q^{92} -7.13729e8 q^{93} +7.57584e8 q^{94} +1.53079e8 q^{95} -1.45077e9 q^{96} -9.67673e8 q^{97} +8.22692e8 q^{98} -4.79921e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9}+O(q^{10}) $ 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9} - 60820 q^{10} - 78484 q^{11} - 343492 q^{12} - 296769 q^{13} - 711120 q^{14} - 237870 q^{15} - 253440 q^{16} - 1128820 q^{17} - 499874 q^{18} - 1301252 q^{19} - 3482704 q^{20} - 108908 q^{21} - 1562088 q^{22} - 1958887 q^{23} - 4606464 q^{24} - 1320899 q^{25} + 692230 q^{26} + 2977921 q^{27} - 8371144 q^{28} + 2813849 q^{29} + 25535196 q^{30} + 7334751 q^{31} + 26028800 q^{32} + 646330 q^{33} + 14981564 q^{34} + 23410104 q^{35} + 40211900 q^{36} - 13324320 q^{37} + 37578632 q^{38} + 6304533 q^{39} - 45307920 q^{40} - 15691573 q^{41} + 124523248 q^{42} - 46474818 q^{43} + 43428040 q^{44} - 72736710 q^{45} + 8232227 q^{47} - 163054384 q^{48} + 29219031 q^{49} + 50366304 q^{50} - 136344764 q^{51} - 100922292 q^{52} - 53545400 q^{53} - 26171642 q^{54} - 181608484 q^{55} - 420111696 q^{56} - 218913370 q^{57} - 39304854 q^{58} - 341275144 q^{59} + 420822384 q^{60} - 277157656 q^{61} + 464777594 q^{62} - 574619276 q^{63} + 340566208 q^{64} + 106659278 q^{65} + 258025876 q^{66} + 89654580 q^{67} + 62700400 q^{68} + 24905849 q^{69} + 1187910040 q^{70} - 286098961 q^{71} + 1446323640 q^{72} - 637495039 q^{73} + 189880036 q^{74} - 160733159 q^{75} + 228563936 q^{76} + 511682536 q^{77} + 1199383686 q^{78} + 274469546 q^{79} - 345318560 q^{80} - 237775217 q^{81} - 570256066 q^{82} + 1164579762 q^{83} + 3447171416 q^{84} - 18639492 q^{85} + 415245796 q^{86} - 595368433 q^{87} + 103329440 q^{88} - 504153000 q^{89} - 1414126968 q^{90} - 1692320156 q^{91} - 429835776 q^{92} - 2753858687 q^{93} - 2214048622 q^{94} + 162962164 q^{95} - 3332565856 q^{96} - 3519929016 q^{97} + 2474592568 q^{98} - 1883749262 q^{99}+O(q^{100}) \) 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9 - 60820 * q^10 - 78484 * q^11 - 343492 * q^12 - 296769 * q^13 - 711120 * q^14 - 237870 * q^15 - 253440 * q^16 - 1128820 * q^17 - 499874 * q^18 - 1301252 * q^19 - 3482704 * q^20 - 108908 * q^21 - 1562088 * q^22 - 1958887 * q^23 - 4606464 * q^24 - 1320899 * q^25 + 692230 * q^26 + 2977921 * q^27 - 8371144 * q^28 + 2813849 * q^29 + 25535196 * q^30 + 7334751 * q^31 + 26028800 * q^32 + 646330 * q^33 + 14981564 * q^34 + 23410104 * q^35 + 40211900 * q^36 - 13324320 * q^37 + 37578632 * q^38 + 6304533 * q^39 - 45307920 * q^40 - 15691573 * q^41 + 124523248 * q^42 - 46474818 * q^43 + 43428040 * q^44 - 72736710 * q^45 + 8232227 * q^47 - 163054384 * q^48 + 29219031 * q^49 + 50366304 * q^50 - 136344764 * q^51 - 100922292 * q^52 - 53545400 * q^53 - 26171642 * q^54 - 181608484 * q^55 - 420111696 * q^56 - 218913370 * q^57 - 39304854 * q^58 - 341275144 * q^59 + 420822384 * q^60 - 277157656 * q^61 + 464777594 * q^62 - 574619276 * q^63 + 340566208 * q^64 + 106659278 * q^65 + 258025876 * q^66 + 89654580 * q^67 + 62700400 * q^68 + 24905849 * q^69 + 1187910040 * q^70 - 286098961 * q^71 + 1446323640 * q^72 - 637495039 * q^73 + 189880036 * q^74 - 160733159 * q^75 + 228563936 * q^76 + 511682536 * q^77 + 1199383686 * q^78 + 274469546 * q^79 - 345318560 * q^80 - 237775217 * q^81 - 570256066 * q^82 + 1164579762 * q^83 + 3447171416 * q^84 - 18639492 * q^85 + 415245796 * q^86 - 595368433 * q^87 + 103329440 * q^88 - 504153000 * q^89 - 1414126968 * q^90 - 1692320156 * q^91 - 429835776 * q^92 - 2753858687 * q^93 - 2214048622 * q^94 + 162962164 * q^95 - 3332565856 * q^96 - 3519929016 * q^97 + 2474592568 * q^98 - 1883749262 * 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 $

$2$	−30.1460	−1.33228	−0.666139	−	0.745827i	$-0.732054\pi$
$2$	−30.1460	−1.33228	−0.666139	+	0.745827i	$0.732054\pi$
$3$	−193.374	−1.37833	−0.689163	−	0.724607i	$-0.742022\pi$
$3$	−193.374	−1.37833	−0.689163	+	0.724607i	$0.742022\pi$
$4$	396.783	0.774967
$5$	568.966	0.407119	0.203560	−	0.979063i	$-0.434749\pi$
$5$	568.966	0.407119	0.203560	+	0.979063i	$0.434749\pi$
$6$	5829.45	1.83631
$7$	3614.33	0.568966	0.284483	−	0.958681i	$-0.408178\pi$
$7$	3614.33	0.568966	0.284483	+	0.958681i	$0.408178\pi$
$8$	3473.33	0.299806
$9$	17710.4	0.899782
$10$	−17152.1	−0.542396
$11$	−2709.83	−0.0558052	−0.0279026	−	0.999611i	$-0.508883\pi$
$11$	−2709.83	−0.0558052	−0.0279026	+	0.999611i	$0.508883\pi$
$12$	−76727.4	−1.06816
$13$	22818.6	0.221587	0.110793	−	0.993843i	$-0.464661\pi$
$13$	22818.6	0.221587	0.110793	+	0.993843i	$0.464661\pi$
$14$	−108958.	−0.758022
$15$	−110023.	−0.561143
$16$	−307860.	−1.17439
$17$	−93871.0	−0.272591	−0.136295	−	0.990668i	$-0.543520\pi$
$17$	−93871.0	−0.272591	−0.136295	+	0.990668i	$0.543520\pi$
$18$	−533898.	−1.19876
$19$	269048.	0.473629	0.236815	−	0.971555i	$-0.423897\pi$
$19$	269048.	0.473629	0.236815	+	0.971555i	$0.423897\pi$
$20$	225756.	0.315504
$21$	−698916.	−0.784221
$22$	81690.5	0.0743480
$23$	−279841.	−0.208514
$23$	−279841.	−0.208514
$24$	−671651.	−0.413231
$25$	−1.62940e6	−0.834254
$26$	−687889.	−0.295215
$27$	381449.	0.138134
$28$	1.43411e6	0.440930
$29$	3.04153e6	0.798547	0.399274	−	0.916832i	$-0.369262\pi$
$29$	3.04153e6	0.798547	0.399274	+	0.916832i	$0.369262\pi$
$30$	3.31676e6	0.747599
$31$	3.69093e6	0.717808	0.358904	−	0.933374i	$-0.383150\pi$
$31$	3.69093e6	0.717808	0.358904	+	0.933374i	$0.383150\pi$
$32$	7.50242e6	1.26481
$33$	524009.	0.0769177
$34$	2.82984e6	0.363167
$35$	2.05643e6	0.231637
$36$	7.02719e6	0.697301
$37$	−1.81385e7	−1.59108	−0.795541	−	0.605900i	$-0.792813\pi$
$37$	−1.81385e7	−1.59108	−0.795541	+	0.605900i	$0.792813\pi$
$38$	−8.11073e6	−0.631006
$39$	−4.41251e6	−0.305418
$40$	1.97621e6	0.122057
$41$	−947287.	−0.0523545	−0.0261773	−	0.999657i	$-0.508333\pi$
$41$	−947287.	−0.0523545	−0.0261773	+	0.999657i	$0.508333\pi$
$42$	2.10696e7	1.04480
$43$	−3.70325e7	−1.65187	−0.825934	−	0.563766i	$-0.809352\pi$
$43$	−3.70325e7	−1.65187	−0.825934	+	0.563766i	$0.809352\pi$
$44$	−1.07521e6	−0.0432472
$45$	1.00766e7	0.366318
$46$	8.43610e6	0.277799
$47$	−2.51305e7	−0.751208	−0.375604	−	0.926780i	$-0.622565\pi$
$47$	−2.51305e7	−0.751208	−0.375604	+	0.926780i	$0.622565\pi$
$48$	5.95321e7	1.61870
$49$	−2.72902e7	−0.676277
$50$	4.91200e7	1.11146
$51$	1.81522e7	0.375719
$52$	9.05403e6	0.171722
$53$	−5.27006e7	−0.917432	−0.458716	−	0.888583i	$-0.651690\pi$
$53$	−5.27006e7	−0.917432	−0.458716	+	0.888583i	$0.651690\pi$
$54$	−1.14992e7	−0.184032
$55$	−1.54180e6	−0.0227193
$56$	1.25538e7	0.170580
$57$	−5.20268e7	−0.652815
$58$	−9.16899e7	−1.06389
$59$	5.16175e7	0.554579	0.277289	−	0.960786i	$-0.410564\pi$
$59$	5.16175e7	0.554579	0.277289	+	0.960786i	$0.410564\pi$
$60$	−4.36553e7	−0.434867
$61$	−7.29696e7	−0.674773	−0.337386	−	0.941366i	$-0.609543\pi$
$61$	−7.29696e7	−0.674773	−0.337386	+	0.941366i	$0.609543\pi$
$62$	−1.11267e8	−0.956321
$63$	6.40112e7	0.511945
$64$	−6.85437e7	−0.510690
$65$	1.29830e7	0.0902121
$66$	−1.57968e7	−0.102476
$67$	−2.75931e8	−1.67288	−0.836440	−	0.548059i	$-0.815367\pi$
$67$	−2.75931e8	−1.67288	−0.836440	+	0.548059i	$0.815367\pi$
$68$	−3.72464e7	−0.211249
$69$	5.41139e7	0.287401
$70$	−6.19932e7	−0.308605
$71$	3.95007e8	1.84477	0.922386	−	0.386271i	$-0.126237\pi$
$71$	3.95007e8	1.84477	0.922386	+	0.386271i	$0.126237\pi$
$72$	6.15141e7	0.269760
$73$	1.76598e8	0.727834	0.363917	−	0.931431i	$-0.381439\pi$
$73$	1.76598e8	0.727834	0.363917	+	0.931431i	$0.381439\pi$
$74$	5.46803e8	2.11977
$75$	3.15084e8	1.14987
$76$	1.06754e8	0.367047
$77$	−9.79421e6	−0.0317513
$78$	1.33020e8	0.406903
$79$	1.92073e8	0.554810	0.277405	−	0.960753i	$-0.410526\pi$
$79$	1.92073e8	0.554810	0.277405	+	0.960753i	$0.410526\pi$
$80$	−1.75162e8	−0.478118
$81$	−4.22356e8	−1.09017
$82$	2.85569e7	0.0697508
$83$	2.66138e8	0.615539	0.307770	−	0.951461i	$-0.400417\pi$
$83$	2.66138e8	0.615539	0.307770	+	0.951461i	$0.400417\pi$
$84$	−2.77318e8	−0.607745
$85$	−5.34094e7	−0.110977
$86$	1.11638e9	2.20075
$87$	−5.88151e8	−1.10066
$88$	−9.41212e6	−0.0167308
$89$	−8.53374e8	−1.44173	−0.720866	−	0.693075i	$-0.756255\pi$
$89$	−8.53374e8	−1.44173	−0.720866	+	0.693075i	$0.756255\pi$
$90$	−3.03770e8	−0.488038
$91$	8.24738e7	0.126075
$92$	−1.11036e8	−0.161592
$93$	−7.13729e8	−0.989374
$94$	7.57584e8	1.00082
$95$	1.53079e8	0.192823
$96$	−1.45077e9	−1.74332
$97$	−9.67673e8	−1.10983	−0.554914	−	0.831908i	$-0.687249\pi$
$97$	−9.67673e8	−1.10983	−0.554914	+	0.831908i	$0.687249\pi$
$98$	8.22692e8	0.900990
$99$	−4.79921e7	−0.0502125
$100$	−6.46520e8	−0.646520
$101$	1.01248e8	0.0968142	0.0484071	−	0.998828i	$-0.484586\pi$
$101$	1.01248e8	0.0968142	0.0484071	+	0.998828i	$0.484586\pi$
$102$	−5.47216e8	−0.500563
$103$	−1.66229e9	−1.45526	−0.727630	−	0.685970i	$-0.759378\pi$
$103$	−1.66229e9	−1.45526	−0.727630	+	0.685970i	$0.759378\pi$
$104$	7.92564e7	0.0664331
$105$	−3.97660e8	−0.319271
$106$	1.58871e9	1.22228
$107$	1.04996e9	0.774367	0.387184	−	0.922003i	$-0.373448\pi$
$107$	1.04996e9	0.774367	0.387184	+	0.922003i	$0.373448\pi$
$108$	1.51352e8	0.107049
$109$	−6.47595e8	−0.439424	−0.219712	−	0.975565i	$-0.570512\pi$
$109$	−6.47595e8	−0.439424	−0.219712	+	0.975565i	$0.570512\pi$
$110$	4.64791e7	0.0302685
$111$	3.50750e9	2.19303
$112$	−1.11271e9	−0.668190
$113$	2.75623e8	0.159024	0.0795121	−	0.996834i	$-0.474664\pi$
$113$	2.75623e8	0.159024	0.0795121	+	0.996834i	$0.474664\pi$
$114$	1.56840e9	0.869732
$115$	−1.59220e8	−0.0848902
$116$	1.20683e9	0.618848
$117$	4.04126e8	0.199380
$118$	−1.55606e9	−0.738854
$119$	−3.39281e8	−0.155095
$120$	−3.82147e8	−0.168234
$121$	−2.35060e9	−0.996886
$122$	2.19974e9	0.898986
$123$	1.83180e8	0.0721616
$124$	1.46450e9	0.556278
$125$	−2.03834e9	−0.746760
$126$	−1.92968e9	−0.682054
$127$	−2.49121e9	−0.849754	−0.424877	−	0.905251i	$-0.639683\pi$
$127$	−2.49121e9	−0.849754	−0.424877	+	0.905251i	$0.639683\pi$
$128$	−1.77492e9	−0.584431
$129$	7.16112e9	2.27681
$130$	−3.91386e8	−0.120188
$131$	−1.21572e9	−0.360673	−0.180336	−	0.983605i	$-0.557719\pi$
$131$	−1.21572e9	−0.360673	−0.180336	+	0.983605i	$0.557719\pi$
$132$	2.07918e8	0.0596087
$133$	9.72428e8	0.269479
$134$	8.31824e9	2.22874
$135$	2.17031e8	0.0562368
$136$	−3.26045e8	−0.0817245
$137$	−8.72201e8	−0.211531	−0.105766	−	0.994391i	$-0.533729\pi$
$137$	−8.72201e8	−0.211531	−0.105766	+	0.994391i	$0.533729\pi$
$138$	−1.63132e9	−0.382898
$139$	7.33639e9	1.66692	0.833462	−	0.552577i	$-0.186355\pi$
$139$	7.33639e9	1.66692	0.833462	+	0.552577i	$0.186355\pi$
$140$	8.15957e8	0.179511
$141$	4.85957e9	1.03541
$142$	−1.19079e10	−2.45775
$143$	−6.18344e7	−0.0123657
$144$	−5.45233e9	−1.05670
$145$	1.73053e9	0.325104
$146$	−5.32372e9	−0.969678
$147$	5.27721e9	0.932130
$148$	−7.19704e9	−1.23304
$149$	2.48159e8	0.0412469	0.0206235	−	0.999787i	$-0.493435\pi$
$149$	2.48159e8	0.0412469	0.0206235	+	0.999787i	$0.493435\pi$
$150$	−9.49852e9	−1.53195
$151$	−2.50463e9	−0.392055	−0.196028	−	0.980598i	$-0.562804\pi$
$151$	−2.50463e9	−0.392055	−0.196028	+	0.980598i	$0.562804\pi$
$152$	9.34492e8	0.141997
$153$	−1.66249e9	−0.245272
$154$	2.95256e8	0.0423015
$155$	2.10002e9	0.292233
$156$	−1.75081e9	−0.236689
$157$	8.06482e9	1.05937	0.529683	−	0.848195i	$-0.322311\pi$
$157$	8.06482e9	1.05937	0.529683	+	0.848195i	$0.322311\pi$
$158$	−5.79024e9	−0.739162
$159$	1.01909e10	1.26452
$160$	4.26862e9	0.514929
$161$	−1.01144e9	−0.118638
$162$	1.27324e10	1.45242
$163$	3.90876e9	0.433705	0.216853	−	0.976204i	$-0.430421\pi$
$163$	3.90876e9	0.433705	0.216853	+	0.976204i	$0.430421\pi$
$164$	−3.75867e8	−0.0405730
$165$	2.98144e8	0.0313147
$166$	−8.02301e9	−0.820070
$167$	−1.34486e10	−1.33799	−0.668997	−	0.743265i	$-0.733276\pi$
$167$	−1.34486e10	−1.33799	−0.668997	+	0.743265i	$0.733276\pi$
$168$	−2.42757e9	−0.235115
$169$	−1.00838e10	−0.950899
$170$	1.61008e9	0.147852
$171$	4.76495e9	0.426163
$172$	−1.46939e10	−1.28014
$173$	−1.05933e10	−0.899129	−0.449565	−	0.893248i	$-0.648421\pi$
$173$	−1.05933e10	−0.899129	−0.449565	+	0.893248i	$0.648421\pi$
$174$	1.77304e10	1.46638
$175$	−5.88920e9	−0.474662
$176$	8.34247e8	0.0655372
$177$	−9.98148e9	−0.764390
$178$	2.57258e10	1.92079
$179$	−1.95434e10	−1.42286	−0.711428	−	0.702759i	$-0.751951\pi$
$179$	−1.95434e10	−1.42286	−0.711428	+	0.702759i	$0.751951\pi$
$180$	3.99823e9	0.283885
$181$	−2.34645e9	−0.162502	−0.0812509	−	0.996694i	$-0.525892\pi$
$181$	−2.34645e9	−0.162502	−0.0812509	+	0.996694i	$0.525892\pi$
$182$	−2.48626e9	−0.167967
$183$	1.41104e10	0.930057
$184$	−9.71980e8	−0.0625140
$185$	−1.03202e10	−0.647760
$186$	2.15161e10	1.31812
$187$	2.54374e8	0.0152120
$188$	−9.97135e9	−0.582162
$189$	1.37868e9	0.0785933
$190$	−4.61473e9	−0.256895
$191$	1.01038e10	0.549329	0.274665	−	0.961540i	$-0.411433\pi$
$191$	1.01038e10	0.549329	0.274665	+	0.961540i	$0.411433\pi$
$192$	1.32545e10	0.703897
$193$	−1.53008e10	−0.793792	−0.396896	−	0.917864i	$-0.629913\pi$
$193$	−1.53008e10	−0.793792	−0.396896	+	0.917864i	$0.629913\pi$
$194$	2.91715e10	1.47860
$195$	−2.51057e9	−0.124342
$196$	−1.08283e10	−0.524093
$197$	3.02620e10	1.43153	0.715763	−	0.698343i	$-0.246079\pi$
$197$	3.02620e10	1.43153	0.715763	+	0.698343i	$0.246079\pi$
$198$	1.44677e9	0.0668970
$199$	−2.03377e10	−0.919312	−0.459656	−	0.888097i	$-0.652027\pi$
$199$	−2.03377e10	−0.919312	−0.459656	+	0.888097i	$0.652027\pi$
$200$	−5.65945e9	−0.250115
$201$	5.33579e10	2.30577
$202$	−3.05222e9	−0.128984
$203$	1.09931e10	0.454346
$204$	7.20248e9	0.291170
$205$	−5.38974e8	−0.0213145
$206$	5.01116e10	1.93881
$207$	−4.95610e9	−0.187617
$208$	−7.02493e9	−0.260230
$209$	−7.29073e8	−0.0264310
$210$	1.19879e10	0.425358
$211$	5.48455e10	1.90489	0.952445	−	0.304712i	$-0.0985602\pi$
$211$	5.48455e10	1.90489	0.952445	+	0.304712i	$0.0985602\pi$
$212$	−2.09107e10	−0.710980
$213$	−7.63840e10	−2.54270
$214$	−3.16522e10	−1.03167
$215$	−2.10703e10	−0.672507
$216$	1.32490e9	0.0414133
$217$	1.33402e10	0.408409
$218$	1.95224e10	0.585436
$219$	−3.41494e10	−1.00319
$220$	−6.11760e8	−0.0176067
$221$	−2.14200e9	−0.0604025
$222$	−1.05737e11	−2.92173
$223$	−6.64889e10	−1.80043	−0.900217	−	0.435441i	$-0.856592\pi$
$223$	−6.64889e10	−1.80043	−0.900217	+	0.435441i	$0.856592\pi$
$224$	2.71162e10	0.719636
$225$	−2.88574e10	−0.750646
$226$	−8.30895e9	−0.211864
$227$	−2.56089e10	−0.640139	−0.320070	−	0.947394i	$-0.603706\pi$
$227$	−2.56089e10	−0.640139	−0.320070	+	0.947394i	$0.603706\pi$
$228$	−2.06434e10	−0.505910
$229$	−4.89725e10	−1.17677	−0.588386	−	0.808580i	$-0.700236\pi$
$229$	−4.89725e10	−1.17677	−0.588386	+	0.808580i	$0.700236\pi$
$230$	4.79985e9	0.113097
$231$	1.89394e9	0.0437636
$232$	1.05642e10	0.239410
$233$	3.07350e10	0.683174	0.341587	−	0.939850i	$-0.389036\pi$
$233$	3.07350e10	0.683174	0.341587	+	0.939850i	$0.389036\pi$
$234$	−1.21828e10	−0.265629
$235$	−1.42984e10	−0.305831
$236$	2.04810e10	0.429780
$237$	−3.71419e10	−0.764709
$238$	1.02280e10	0.206630
$239$	4.30745e10	0.853944	0.426972	−	0.904265i	$-0.359580\pi$
$239$	4.30745e10	0.853944	0.426972	+	0.904265i	$0.359580\pi$
$240$	3.38717e10	0.659002
$241$	6.47036e10	1.23553	0.617763	−	0.786364i	$-0.288039\pi$
$241$	6.47036e10	1.23553	0.617763	+	0.786364i	$0.288039\pi$
$242$	7.08614e10	1.32813
$243$	7.41645e10	1.36448
$244$	−2.89531e10	−0.522927
$245$	−1.55272e10	−0.275325
$246$	−5.52216e9	−0.0961393
$247$	6.13929e9	0.104950
$248$	1.28198e10	0.215204
$249$	−5.14641e10	−0.848414
$250$	6.14478e10	0.994892
$251$	4.36672e10	0.694422	0.347211	−	0.937787i	$-0.387129\pi$
$251$	4.36672e10	0.694422	0.347211	+	0.937787i	$0.387129\pi$
$252$	2.53986e10	0.396741
$253$	7.58321e8	0.0116362
$254$	7.51000e10	1.13211
$255$	1.03280e10	0.152962
$256$	8.86011e10	1.28932
$257$	2.53955e10	0.363126	0.181563	−	0.983379i	$-0.441884\pi$
$257$	2.53955e10	0.363126	0.181563	+	0.983379i	$0.441884\pi$
$258$	−2.15879e11	−3.03335
$259$	−6.55584e10	−0.905272
$260$	5.15144e9	0.0699114
$261$	5.38666e10	0.718518
$262$	3.66492e10	0.480517
$263$	4.76037e10	0.613536	0.306768	−	0.951784i	$-0.400752\pi$
$263$	4.76037e10	0.613536	0.306768	+	0.951784i	$0.400752\pi$
$264$	1.82006e9	0.0230604
$265$	−2.99848e10	−0.373504
$266$	−2.93148e10	−0.359021
$267$	1.65020e11	1.98717
$268$	−1.09485e11	−1.29643
$269$	−1.39851e11	−1.62847	−0.814235	−	0.580536i	$-0.802843\pi$
$269$	−1.39851e11	−1.62847	−0.814235	+	0.580536i	$0.802843\pi$
$270$	−6.54263e9	−0.0749231
$271$	7.17786e10	0.808412	0.404206	−	0.914668i	$-0.367548\pi$
$271$	7.17786e10	0.808412	0.404206	+	0.914668i	$0.367548\pi$
$272$	2.88991e10	0.320129
$273$	−1.59483e10	−0.173773
$274$	2.62934e10	0.281818
$275$	4.41540e9	0.0465557
$276$	2.14715e10	0.222726
$277$	5.44172e10	0.555363	0.277682	−	0.960673i	$-0.410434\pi$
$277$	5.44172e10	0.555363	0.277682	+	0.960673i	$0.410434\pi$
$278$	−2.21163e11	−2.22081
$279$	6.53679e10	0.645871
$280$	7.14266e9	0.0694463
$281$	−1.28351e11	−1.22806	−0.614032	−	0.789281i	$-0.710453\pi$
$281$	−1.28351e11	−1.22806	−0.614032	+	0.789281i	$0.710453\pi$
$282$	−1.46497e11	−1.37945
$283$	1.16139e11	1.07631	0.538157	−	0.842845i	$-0.319121\pi$
$283$	1.16139e11	1.07631	0.538157	+	0.842845i	$0.319121\pi$
$284$	1.56732e11	1.42964
$285$	−2.96015e10	−0.265774
$286$	1.86406e9	0.0164745
$287$	−3.42381e9	−0.0297880
$288$	1.32871e11	1.13806
$289$	−1.09776e11	−0.925694
$290$	−5.21685e10	−0.433129
$291$	1.87123e11	1.52971
$292$	7.00711e10	0.564048
$293$	−1.92776e11	−1.52809	−0.764043	−	0.645165i	$-0.776789\pi$
$293$	−1.92776e11	−1.52809	−0.764043	+	0.645165i	$0.776789\pi$
$294$	−1.59087e11	−1.24186
$295$	2.93686e10	0.225780
$296$	−6.30008e10	−0.477017
$297$	−1.03366e9	−0.00770856
$298$	−7.48100e9	−0.0549524
$299$	−6.38557e9	−0.0462040
$300$	1.25020e11	0.891114
$301$	−1.33848e11	−0.939858
$302$	7.55046e10	0.522327
$303$	−1.95787e10	−0.133442
$304$	−8.28291e10	−0.556227
$305$	−4.15172e10	−0.274713
$306$	5.01176e10	0.326771
$307$	1.13343e11	0.728238	0.364119	−	0.931352i	$-0.381370\pi$
$307$	1.13343e11	0.728238	0.364119	+	0.931352i	$0.381370\pi$
$308$	−3.88618e9	−0.0246062
$309$	3.21444e11	2.00582
$310$	−6.33072e10	−0.389337
$311$	6.31825e10	0.382979	0.191490	−	0.981495i	$-0.438668\pi$
$311$	6.31825e10	0.382979	0.191490	+	0.981495i	$0.438668\pi$
$312$	−1.53261e10	−0.0915664
$313$	1.10450e11	0.650453	0.325226	−	0.945636i	$-0.394559\pi$
$313$	1.10450e11	0.650453	0.325226	+	0.945636i	$0.394559\pi$
$314$	−2.43122e11	−1.41137
$315$	3.64202e10	0.208423
$316$	7.62114e10	0.429960
$317$	−1.22792e11	−0.682971	−0.341485	−	0.939887i	$-0.610930\pi$
$317$	−1.22792e11	−0.682971	−0.341485	+	0.939887i	$0.610930\pi$
$318$	−3.07215e11	−1.68469
$319$	−8.24201e9	−0.0445631
$320$	−3.89990e10	−0.207912
$321$	−2.03035e11	−1.06733
$322$	3.04908e10	0.158058
$323$	−2.52558e10	−0.129107
$324$	−1.67584e11	−0.844850
$325$	−3.71806e10	−0.184859
$326$	−1.17834e11	−0.577817
$327$	1.25228e11	0.605670
$328$	−3.29024e9	−0.0156962
$329$	−9.08298e10	−0.427412
$330$	−8.98785e9	−0.0417199
$331$	2.90213e11	1.32889	0.664447	−	0.747335i	$-0.268667\pi$
$331$	2.90213e11	1.32889	0.664447	+	0.747335i	$0.268667\pi$
$332$	1.05599e11	0.477023
$333$	−3.21239e11	−1.43163
$334$	4.05423e11	1.78258
$335$	−1.56996e11	−0.681061
$336$	2.15168e11	0.920984
$337$	1.21543e11	0.513327	0.256664	−	0.966501i	$-0.417377\pi$
$337$	1.21543e11	0.513327	0.256664	+	0.966501i	$0.417377\pi$
$338$	3.03987e11	1.26686
$339$	−5.32983e10	−0.219187
$340$	−2.11920e10	−0.0860035
$341$	−1.00018e10	−0.0400574
$342$	−1.43644e11	−0.567768
$343$	−2.44487e11	−0.953745
$344$	−1.28626e11	−0.495241
$345$	3.07890e10	0.117006
$346$	3.19345e11	1.19789
$347$	1.74778e11	0.647149	0.323575	−	0.946203i	$-0.395115\pi$
$347$	1.74778e11	0.647149	0.323575	+	0.946203i	$0.395115\pi$
$348$	−2.33369e11	−0.852974
$349$	6.87558e10	0.248082	0.124041	−	0.992277i	$-0.460415\pi$
$349$	6.87558e10	0.248082	0.124041	+	0.992277i	$0.460415\pi$
$350$	1.77536e11	0.632383
$351$	8.70411e9	0.0306085
$352$	−2.03302e10	−0.0705831
$353$	−1.18593e11	−0.406511	−0.203256	−	0.979126i	$-0.565152\pi$
$353$	−1.18593e11	−0.406511	−0.203256	+	0.979126i	$0.565152\pi$
$354$	3.00902e11	1.01838
$355$	2.24746e11	0.751042
$356$	−3.38604e11	−1.11729
$357$	6.56080e10	0.213771
$358$	5.89155e11	1.89564
$359$	−1.90427e11	−0.605068	−0.302534	−	0.953139i	$-0.597833\pi$
$359$	−1.90427e11	−0.605068	−0.302534	+	0.953139i	$0.597833\pi$
$360$	3.49994e10	0.109825
$361$	−2.50301e11	−0.775675
$362$	7.07363e10	0.216498
$363$	4.54545e11	1.37403
$364$	3.27242e10	0.0977042
$365$	1.00478e11	0.296315
$366$	−4.25373e11	−1.23910
$367$	−3.16797e11	−0.911556	−0.455778	−	0.890094i	$-0.650639\pi$
$367$	−3.16797e11	−0.911556	−0.455778	+	0.890094i	$0.650639\pi$
$368$	8.61519e10	0.244878
$369$	−1.67768e10	−0.0471076
$370$	3.11112e11	0.862997
$371$	−1.90477e11	−0.521988
$372$	−2.83196e11	−0.766732
$373$	5.15367e11	1.37856	0.689281	−	0.724494i	$-0.257926\pi$
$373$	5.15367e11	1.37856	0.689281	+	0.724494i	$0.257926\pi$
$374$	−7.66837e9	−0.0202666
$375$	3.94161e11	1.02928
$376$	−8.72864e10	−0.225217
$377$	6.94033e10	0.176947
$378$	−4.15618e10	−0.104708
$379$	−2.55579e11	−0.636280	−0.318140	−	0.948044i	$-0.603058\pi$
$379$	−2.55579e11	−0.636280	−0.318140	+	0.948044i	$0.603058\pi$
$380$	6.07392e10	0.149432
$381$	4.81734e11	1.17124
$382$	−3.04588e11	−0.731860
$383$	−3.74466e11	−0.889238	−0.444619	−	0.895720i	$-0.646661\pi$
$383$	−3.74466e11	−0.889238	−0.444619	+	0.895720i	$0.646661\pi$
$384$	3.43222e11	0.805536
$385$	−5.57257e9	−0.0129265
$386$	4.61259e11	1.05755
$387$	−6.55861e11	−1.48632
$388$	−3.83956e11	−0.860081
$389$	−8.66427e11	−1.91849	−0.959243	−	0.282581i	$-0.908809\pi$
$389$	−8.66427e11	−1.91849	−0.959243	+	0.282581i	$0.908809\pi$
$390$	7.56837e10	0.165658
$391$	2.62690e10	0.0568391
$392$	−9.47880e10	−0.202752
$393$	2.35089e11	0.497125
$394$	−9.12279e11	−1.90719
$395$	1.09283e11	0.225874
$396$	−1.90425e10	−0.0389130
$397$	1.66641e11	0.336685	0.168342	−	0.985729i	$-0.446159\pi$
$397$	1.66641e11	0.336685	0.168342	+	0.985729i	$0.446159\pi$
$398$	6.13101e11	1.22478
$399$	−1.88042e11	−0.371430
$400$	5.01628e11	0.979742
$401$	2.04574e11	0.395093	0.197547	−	0.980293i	$-0.436703\pi$
$401$	2.04574e11	0.395093	0.197547	+	0.980293i	$0.436703\pi$
$402$	−1.60853e12	−3.07193
$403$	8.42218e10	0.159057
$404$	4.01734e10	0.0750279
$405$	−2.40306e11	−0.443831
$406$	−3.31398e11	−0.605316
$407$	4.91521e10	0.0887906
$408$	6.30485e10	0.112643
$409$	1.18833e11	0.209983	0.104991	−	0.994473i	$-0.466518\pi$
$409$	1.18833e11	0.209983	0.104991	+	0.994473i	$0.466518\pi$
$410$	1.62479e10	0.0283969
$411$	1.68661e11	0.291559
$412$	−6.59571e11	−1.12778
$413$	1.86563e11	0.315537
$414$	1.49407e11	0.249959
$415$	1.51424e11	0.250598
$416$	1.71194e11	0.280265
$417$	−1.41867e12	−2.29756
$418$	2.19787e10	0.0352134
$419$	1.16969e12	1.85399	0.926995	−	0.375073i	$-0.122382\pi$
$419$	1.16969e12	1.85399	0.926995	+	0.375073i	$0.122382\pi$
$420$	−1.57785e11	−0.247425
$421$	8.73343e11	1.35493	0.677463	−	0.735557i	$-0.263079\pi$
$421$	8.73343e11	1.35493	0.677463	+	0.735557i	$0.263079\pi$
$422$	−1.65337e12	−2.53784
$423$	−4.45071e11	−0.675923
$424$	−1.83046e11	−0.275052
$425$	1.52954e11	0.227410
$426$	2.30268e12	3.38758
$427$	−2.63736e11	−0.383923
$428$	4.16608e11	0.600109
$429$	1.19571e10	0.0170439
$430$	6.35185e11	0.895967
$431$	−6.45950e11	−0.901677	−0.450838	−	0.892606i	$-0.648875\pi$
$431$	−6.45950e11	−0.901677	−0.450838	+	0.892606i	$0.648875\pi$
$432$	−1.17433e11	−0.162223
$433$	1.99523e11	0.272771	0.136385	−	0.990656i	$-0.456452\pi$
$433$	1.99523e11	0.272771	0.136385	+	0.990656i	$0.456452\pi$
$434$	−4.02156e11	−0.544114
$435$	−3.34638e11	−0.448099
$436$	−2.56955e11	−0.340539
$437$	−7.52906e10	−0.0987585
$438$	1.02947e12	1.33653
$439$	−5.91885e11	−0.760584	−0.380292	−	0.924867i	$-0.624176\pi$
$439$	−5.91885e11	−0.760584	−0.380292	+	0.924867i	$0.624176\pi$
$440$	−5.35518e9	−0.00681141
$441$	−4.83321e11	−0.608502
$442$	6.45729e10	0.0804729
$443$	−2.88585e10	−0.0356005	−0.0178003	−	0.999842i	$-0.505666\pi$
$443$	−2.88585e10	−0.0356005	−0.0178003	+	0.999842i	$0.505666\pi$
$444$	1.39172e12	1.69953
$445$	−4.85541e11	−0.586956
$446$	2.00438e12	2.39868
$447$	−4.79874e10	−0.0568517
$448$	−2.47739e11	−0.290566
$449$	5.37175e11	0.623745	0.311873	−	0.950124i	$-0.399044\pi$
$449$	5.37175e11	0.623745	0.311873	+	0.950124i	$0.399044\pi$
$450$	8.69935e11	1.00007
$451$	2.56698e9	0.00292165
$452$	1.09363e11	0.123238
$453$	4.84330e11	0.540380
$454$	7.72007e11	0.852844
$455$	4.69248e10	0.0513277
$456$	−1.80706e11	−0.195718
$457$	5.37887e11	0.576857	0.288428	−	0.957502i	$-0.406867\pi$
$457$	5.37887e11	0.576857	0.288428	+	0.957502i	$0.406867\pi$
$458$	1.47633e12	1.56779
$459$	−3.58070e10	−0.0376539
$460$	−6.31759e10	−0.0657871
$461$	1.62437e12	1.67507	0.837533	−	0.546386i	$-0.183997\pi$
$461$	1.62437e12	1.67507	0.837533	+	0.546386i	$0.183997\pi$
$462$	−5.70948e10	−0.0583053
$463$	−4.89352e11	−0.494888	−0.247444	−	0.968902i	$-0.579591\pi$
$463$	−4.89352e11	−0.494888	−0.247444	+	0.968902i	$0.579591\pi$
$464$	−9.36364e11	−0.937808
$465$	−4.06088e11	−0.402793
$466$	−9.26538e11	−0.910179
$467$	6.75876e11	0.657569	0.328784	−	0.944405i	$-0.393361\pi$
$467$	6.75876e11	0.657569	0.328784	+	0.944405i	$0.393361\pi$
$468$	1.60350e11	0.154513
$469$	−9.97307e11	−0.951812
$470$	4.31040e11	0.407452
$471$	−1.55952e12	−1.46015
$472$	1.79285e11	0.166266
$473$	1.00352e11	0.0921828
$474$	1.11968e12	1.01881
$475$	−4.38387e11	−0.395127
$476$	−1.34621e11	−0.120194
$477$	−9.33348e11	−0.825489
$478$	−1.29852e12	−1.13769
$479$	−1.45296e12	−1.26108	−0.630540	−	0.776157i	$-0.717166\pi$
$479$	−1.45296e12	−1.26108	−0.630540	+	0.776157i	$0.717166\pi$
$480$	−8.25439e11	−0.709740
$481$	−4.13894e11	−0.352562
$482$	−1.95056e12	−1.64607
$483$	1.95585e11	0.163521
$484$	−9.32680e11	−0.772554
$485$	−5.50573e11	−0.451832
$486$	−2.23577e12	−1.81787
$487$	−1.70287e12	−1.37184	−0.685918	−	0.727679i	$-0.740599\pi$
$487$	−1.70287e12	−1.37184	−0.685918	+	0.727679i	$0.740599\pi$
$488$	−2.53447e11	−0.202301
$489$	−7.55852e11	−0.597787
$490$	4.68084e11	0.366810
$491$	1.97768e12	1.53564	0.767821	−	0.640665i	$-0.221341\pi$
$491$	1.97768e12	1.53564	0.767821	+	0.640665i	$0.221341\pi$
$492$	7.26829e10	0.0559228
$493$	−2.85511e11	−0.217677
$494$	−1.85075e11	−0.139822
$495$	−2.73059e10	−0.0204425
$496$	−1.13629e12	−0.842989
$497$	1.42769e12	1.04961
$498$	1.55144e12	1.13032
$499$	5.66669e11	0.409145	0.204572	−	0.978851i	$-0.434420\pi$
$499$	5.66669e11	0.409145	0.204572	+	0.978851i	$0.434420\pi$
$500$	−8.08778e11	−0.578714
$501$	2.60061e12	1.84419
$502$	−1.31639e12	−0.925163
$503$	2.66009e12	1.85285	0.926425	−	0.376478i	$-0.122865\pi$
$503$	2.66009e12	1.85285	0.926425	+	0.376478i	$0.122865\pi$
$504$	2.22332e11	0.153485
$505$	5.76065e10	0.0394149
$506$	−2.28604e10	−0.0155026
$507$	1.94994e12	1.31065
$508$	−9.88469e11	−0.658531
$509$	2.08975e12	1.37995	0.689975	−	0.723833i	$-0.257621\pi$
$509$	2.08975e12	1.37995	0.689975	+	0.723833i	$0.257621\pi$
$510$	−3.11348e11	−0.203789
$511$	6.38283e11	0.414113
$512$	−1.76221e12	−1.13330
$513$	1.02628e11	0.0654241
$514$	−7.65573e11	−0.483785
$515$	−9.45790e11	−0.592464
$516$	2.84141e12	1.76446
$517$	6.80992e10	0.0419213
$518$	1.97632e12	1.20608
$519$	2.04846e12	1.23929
$520$	4.50942e10	0.0270462
$521$	−2.43690e12	−1.44900	−0.724499	−	0.689276i	$-0.757929\pi$
$521$	−2.43690e12	−1.44900	−0.724499	+	0.689276i	$0.757929\pi$
$522$	−1.62387e12	−0.957266
$523$	−1.63387e12	−0.954905	−0.477452	−	0.878658i	$-0.658440\pi$
$523$	−1.63387e12	−0.954905	−0.477452	+	0.878658i	$0.658440\pi$
$524$	−4.82378e11	−0.279510
$525$	1.13882e12	0.654239
$526$	−1.43506e12	−0.817401
$527$	−3.46472e11	−0.195668
$528$	−1.61322e11	−0.0903316
$529$	7.83110e10	0.0434783
$530$	9.03924e11	0.497612
$531$	9.14167e11	0.499000
$532$	3.85843e11	0.208837
$533$	−2.16157e10	−0.0116011
$534$	−4.97470e12	−2.64747
$535$	5.97393e11	0.315260
$536$	−9.58401e11	−0.501540
$537$	3.77918e12	1.96116
$538$	4.21595e12	2.16958
$539$	7.39518e10	0.0377398
$540$	8.61144e10	0.0435817
$541$	−2.28401e12	−1.14633	−0.573167	−	0.819439i	$-0.694285\pi$
$541$	−2.28401e12	−1.14633	−0.573167	+	0.819439i	$0.694285\pi$
$542$	−2.16384e12	−1.07703
$543$	4.53743e11	0.223981
$544$	−7.04259e11	−0.344776
$545$	−3.68460e11	−0.178898
$546$	4.80777e11	0.231514
$547$	−2.43100e12	−1.16103	−0.580514	−	0.814251i	$-0.697148\pi$
$547$	−2.43100e12	−1.16103	−0.580514	+	0.814251i	$0.697148\pi$
$548$	−3.46075e11	−0.163930
$549$	−1.29232e12	−0.607148
$550$	−1.33107e11	−0.0620252
$551$	8.18316e11	0.378215
$552$	1.87955e11	0.0861646
$553$	6.94215e11	0.315668
$554$	−1.64046e12	−0.739899
$555$	1.99565e12	0.892824
$556$	2.91096e12	1.29181
$557$	2.78842e11	0.122747	0.0613733	−	0.998115i	$-0.480452\pi$
$557$	2.78842e11	0.122747	0.0613733	+	0.998115i	$0.480452\pi$
$558$	−1.97058e12	−0.860480
$559$	−8.45030e11	−0.366032
$560$	−6.33093e11	−0.272033
$561$	−4.91893e10	−0.0209671
$562$	3.86927e12	1.63612
$563$	−8.46953e11	−0.355281	−0.177640	−	0.984095i	$-0.556846\pi$
$563$	−8.46953e11	−0.355281	−0.177640	+	0.984095i	$0.556846\pi$
$564$	1.92820e12	0.802408
$565$	1.56820e11	0.0647417
$566$	−3.50113e12	−1.43395
$567$	−1.52653e12	−0.620273
$568$	1.37199e12	0.553074
$569$	3.39186e12	1.35654	0.678269	−	0.734813i	$-0.262730\pi$
$569$	3.39186e12	1.35654	0.678269	+	0.734813i	$0.262730\pi$
$570$	8.92368e11	0.354085
$571$	2.05010e12	0.807071	0.403535	−	0.914964i	$-0.367781\pi$
$571$	2.05010e12	0.807071	0.403535	+	0.914964i	$0.367781\pi$
$572$	−2.45348e10	−0.00958299
$573$	−1.95380e12	−0.757154
$574$	1.03214e11	0.0396859
$575$	4.55974e11	0.173954
$576$	−1.21394e12	−0.459510
$577$	−1.39631e12	−0.524435	−0.262217	−	0.965009i	$-0.584454\pi$
$577$	−1.39631e12	−0.524435	−0.262217	+	0.965009i	$0.584454\pi$
$578$	3.30931e12	1.23328
$579$	2.95878e12	1.09410
$580$	6.86643e11	0.251945
$581$	9.61911e11	0.350221
$582$	−5.64100e12	−2.03799
$583$	1.42809e11	0.0511974
$584$	6.13382e11	0.218209
$585$	2.29934e11	0.0811712
$586$	5.81142e12	2.03584
$587$	−6.11717e11	−0.212657	−0.106328	−	0.994331i	$-0.533909\pi$
$587$	−6.11717e11	−0.212657	−0.106328	+	0.994331i	$0.533909\pi$
$588$	2.09391e12	0.722370
$589$	9.93038e11	0.339975
$590$	−8.85348e11	−0.300801
$591$	−5.85187e12	−1.97311
$592$	5.58411e12	1.86856
$593$	−3.82353e12	−1.26975	−0.634876	−	0.772614i	$-0.718949\pi$
$593$	−3.82353e12	−1.26975	−0.634876	+	0.772614i	$0.718949\pi$
$594$	3.11607e10	0.0102700
$595$	−1.93039e11	−0.0631422
$596$	9.84652e10	0.0319650
$597$	3.93278e12	1.26711
$598$	1.92500e11	0.0615566
$599$	−3.74495e12	−1.18857	−0.594285	−	0.804254i	$-0.702565\pi$
$599$	−3.74495e12	−1.18857	−0.594285	+	0.804254i	$0.702565\pi$
$600$	1.09439e12	0.344740
$601$	4.58135e12	1.43238	0.716190	−	0.697905i	$-0.245884\pi$
$601$	4.58135e12	1.43238	0.716190	+	0.697905i	$0.245884\pi$
$602$	4.03498e12	1.25215
$603$	−4.88686e12	−1.50523
$604$	−9.93795e11	−0.303830
$605$	−1.33741e12	−0.405851
$606$	5.90219e11	0.177781
$607$	−1.40057e12	−0.418750	−0.209375	−	0.977835i	$-0.567143\pi$
$607$	−1.40057e12	−0.418750	−0.209375	+	0.977835i	$0.567143\pi$
$608$	2.01851e12	0.599052
$609$	−2.12577e12	−0.626237
$610$	1.25158e12	0.365994
$611$	−5.73441e11	−0.166458
$612$	−6.59649e11	−0.190078
$613$	−5.55287e12	−1.58835	−0.794173	−	0.607691i	$-0.792096\pi$
$613$	−5.55287e12	−1.58835	−0.794173	+	0.607691i	$0.792096\pi$
$614$	−3.41685e12	−0.970216
$615$	1.04223e11	0.0293784
$616$	−3.40185e10	−0.00951923
$617$	−1.18836e12	−0.330115	−0.165057	−	0.986284i	$-0.552781\pi$
$617$	−1.18836e12	−0.330115	−0.165057	+	0.986284i	$0.552781\pi$
$618$	−9.69027e12	−2.67231
$619$	−6.72810e12	−1.84198	−0.920990	−	0.389587i	$-0.872618\pi$
$619$	−6.72810e12	−1.84198	−0.920990	+	0.389587i	$0.872618\pi$
$620$	8.33251e11	0.226471
$621$	−1.06745e11	−0.0288028
$622$	−1.90470e12	−0.510235
$623$	−3.08437e12	−0.820296
$624$	1.35844e12	0.358681
$625$	2.02268e12	0.530234
$626$	−3.32963e12	−0.866585
$627$	1.40984e11	0.0364305
$628$	3.19999e12	0.820974
$629$	1.70268e12	0.433715
$630$	−1.09793e12	−0.277677
$631$	−4.65419e11	−0.116872	−0.0584362	−	0.998291i	$-0.518611\pi$
$631$	−4.65419e11	−0.116872	−0.0584362	+	0.998291i	$0.518611\pi$
$632$	6.67133e11	0.166336
$633$	−1.06057e13	−2.62556
$634$	3.70168e12	0.909908
$635$	−1.41741e12	−0.345951
$636$	4.04358e12	0.979962
$637$	−6.22724e11	−0.149854
$638$	2.48464e11	0.0593704
$639$	6.99574e12	1.65989
$640$	−1.00987e12	−0.237933
$641$	8.50007e12	1.98866	0.994332	−	0.106318i	$-0.0339060\pi$
$641$	8.50007e12	1.98866	0.994332	+	0.106318i	$0.0339060\pi$
$642$	6.12071e12	1.42198
$643$	−6.23593e12	−1.43864	−0.719319	−	0.694680i	$-0.755546\pi$
$643$	−6.23593e12	−1.43864	−0.719319	+	0.694680i	$0.755546\pi$
$644$	−4.01321e11	−0.0919403
$645$	4.07444e12	0.926934
$646$	7.61362e11	0.172007
$647$	3.74595e12	0.840413	0.420206	−	0.907429i	$-0.361958\pi$
$647$	3.74595e12	0.840413	0.420206	+	0.907429i	$0.361958\pi$
$648$	−1.46698e12	−0.326841
$649$	−1.39875e11	−0.0309484
$650$	1.12085e12	0.246284
$651$	−2.57965e12	−0.562920
$652$	1.55093e12	0.336107
$653$	−7.97117e11	−0.171559	−0.0857794	−	0.996314i	$-0.527338\pi$
$653$	−7.97117e11	−0.171559	−0.0857794	+	0.996314i	$0.527338\pi$
$654$	−3.77512e12	−0.806921
$655$	−6.91705e11	−0.146837
$656$	2.91632e11	0.0614848
$657$	3.12762e12	0.654892
$658$	2.73816e12	0.569432
$659$	−3.62920e12	−0.749594	−0.374797	−	0.927107i	$-0.622288\pi$
$659$	−3.62920e12	−0.749594	−0.374797	+	0.927107i	$0.622288\pi$
$660$	1.18298e11	0.0242678
$661$	2.03009e12	0.413627	0.206814	−	0.978380i	$-0.433691\pi$
$661$	2.03009e12	0.413627	0.206814	+	0.978380i	$0.433691\pi$
$662$	−8.74876e12	−1.77046
$663$	4.14207e11	0.0832543
$664$	9.24386e11	0.184543
$665$	5.53279e11	0.109710
$666$	9.68409e12	1.90733
$667$	−8.51144e11	−0.166509
$668$	−5.33619e12	−1.03690
$669$	1.28572e13	2.48159
$670$	4.73280e12	0.907363
$671$	1.97735e11	0.0376558
$672$	−5.24356e12	−0.991893
$673$	−5.44486e12	−1.02310	−0.511551	−	0.859253i	$-0.670929\pi$
$673$	−5.44486e12	−1.02310	−0.511551	+	0.859253i	$0.670929\pi$
$674$	−3.66403e12	−0.683895
$675$	−6.21533e11	−0.115238
$676$	−4.00109e12	−0.736916
$677$	4.32541e12	0.791367	0.395684	−	0.918387i	$-0.370508\pi$
$677$	4.32541e12	0.791367	0.395684	+	0.918387i	$0.370508\pi$
$678$	1.60673e12	0.292018
$679$	−3.49749e12	−0.631455
$680$	−1.85509e11	−0.0332716
$681$	4.95209e12	0.882321
$682$	3.01514e11	0.0533677
$683$	2.62976e12	0.462406	0.231203	−	0.972906i	$-0.425734\pi$
$683$	2.62976e12	0.462406	0.231203	+	0.972906i	$0.425734\pi$
$684$	1.89065e12	0.330262
$685$	−4.96253e11	−0.0861183
$686$	7.37032e12	1.27065
$687$	9.46999e12	1.62198
$688$	1.14008e13	1.93994
$689$	−1.20255e12	−0.203291
$690$	−9.28166e11	−0.155885
$691$	4.80473e12	0.801711	0.400855	−	0.916141i	$-0.368713\pi$
$691$	4.80473e12	0.801711	0.400855	+	0.916141i	$0.368713\pi$
$692$	−4.20323e12	−0.696795
$693$	−1.73459e11	−0.0285692
$694$	−5.26887e12	−0.862183
$695$	4.17416e12	0.678637
$696$	−2.04284e12	−0.329984
$697$	8.89228e10	0.0142714
$698$	−2.07272e12	−0.330514
$699$	−5.94334e12	−0.941637
$700$	−2.33673e12	−0.367848
$701$	1.06390e13	1.66406	0.832032	−	0.554728i	$-0.187178\pi$
$701$	1.06390e13	1.66406	0.832032	+	0.554728i	$0.187178\pi$
$702$	−2.62394e11	−0.0407791
$703$	−4.88012e12	−0.753583
$704$	1.85741e11	0.0284992
$705$	2.76493e12	0.421535
$706$	3.57510e12	0.541586
$707$	3.65943e11	0.0550840
$708$	−3.96048e12	−0.592377
$709$	2.27178e12	0.337643	0.168822	−	0.985647i	$-0.446004\pi$
$709$	2.27178e12	0.337643	0.168822	+	0.985647i	$0.446004\pi$
$710$	−6.77519e12	−1.00060
$711$	3.40169e12	0.499208
$712$	−2.96405e12	−0.432240
$713$	−1.03287e12	−0.149673
$714$	−1.97782e12	−0.284803
$715$	−3.51817e10	−0.00503430
$716$	−7.75448e12	−1.10267
$717$	−8.32947e12	−1.17701
$718$	5.74063e12	0.806120
$719$	−1.36943e12	−0.191100	−0.0955500	−	0.995425i	$-0.530461\pi$
$719$	−1.36943e12	−0.191100	−0.0955500	+	0.995425i	$0.530461\pi$
$720$	−3.10219e12	−0.430202
$721$	−6.00808e12	−0.827994
$722$	7.54558e12	1.03342
$723$	−1.25120e13	−1.70296
$724$	−9.31033e11	−0.125934
$725$	−4.95587e12	−0.666191
$726$	−1.37027e13	−1.83060
$727$	3.26652e12	0.433691	0.216846	−	0.976206i	$-0.430423\pi$
$727$	3.26652e12	0.433691	0.216846	+	0.976206i	$0.430423\pi$
$728$	2.86459e11	0.0377982
$729$	−6.02823e12	−0.790526
$730$	−3.02902e12	−0.394775
$731$	3.47628e12	0.450284
$732$	5.59877e12	0.720764
$733$	2.93741e12	0.375834	0.187917	−	0.982185i	$-0.439826\pi$
$733$	2.93741e12	0.375834	0.187917	+	0.982185i	$0.439826\pi$
$734$	9.55016e12	1.21445
$735$	3.00256e12	0.379488
$736$	−2.09948e12	−0.263732
$737$	7.47726e11	0.0933553
$738$	5.05755e11	0.0627605
$739$	−1.01275e13	−1.24912	−0.624559	−	0.780978i	$-0.714721\pi$
$739$	−1.01275e13	−1.24912	−0.624559	+	0.780978i	$0.714721\pi$
$740$	−4.09487e12	−0.501993
$741$	−1.18718e12	−0.144655
$742$	5.74213e12	0.695434
$743$	8.66249e12	1.04278	0.521390	−	0.853318i	$-0.325414\pi$
$743$	8.66249e12	1.04278	0.521390	+	0.853318i	$0.325414\pi$
$744$	−2.47902e12	−0.296621
$745$	1.41194e11	0.0167924
$746$	−1.55363e13	−1.83663
$747$	4.71342e12	0.553851
$748$	1.00931e11	0.0117888
$749$	3.79491e12	0.440589
$750$	−1.18824e13	−1.37129
$751$	7.79287e12	0.893960	0.446980	−	0.894544i	$-0.352500\pi$
$751$	7.79287e12	0.893960	0.446980	+	0.894544i	$0.352500\pi$
$752$	7.73667e12	0.882213
$753$	−8.44408e12	−0.957139
$754$	−2.09223e12	−0.235743
$755$	−1.42505e12	−0.159613
$756$	5.47037e11	0.0609072
$757$	4.88900e12	0.541114	0.270557	−	0.962704i	$-0.412792\pi$
$757$	4.88900e12	0.541114	0.270557	+	0.962704i	$0.412792\pi$
$758$	7.70469e12	0.847703
$759$	−1.46639e11	−0.0160384
$760$	5.31694e11	0.0578097
$761$	−1.05629e13	−1.14170	−0.570850	−	0.821054i	$-0.693386\pi$
$761$	−1.05629e13	−1.14170	−0.570850	+	0.821054i	$0.693386\pi$
$762$	−1.45224e13	−1.56042
$763$	−2.34062e12	−0.250018
$764$	4.00900e12	0.425712
$765$	−9.45903e11	−0.0998550
$766$	1.12887e13	1.18471
$767$	1.17784e12	0.122887
$768$	−1.71331e13	−1.77710
$769$	−3.75882e12	−0.387600	−0.193800	−	0.981041i	$-0.562081\pi$
$769$	−3.75882e12	−0.387600	−0.193800	+	0.981041i	$0.562081\pi$
$770$	1.67991e11	0.0172218
$771$	−4.91082e12	−0.500506
$772$	−6.07111e12	−0.615163
$773$	5.80047e12	0.584326	0.292163	−	0.956369i	$-0.405625\pi$
$773$	5.80047e12	0.584326	0.292163	+	0.956369i	$0.405625\pi$
$774$	1.97716e13	1.98019
$775$	−6.01401e12	−0.598835
$776$	−3.36105e12	−0.332734
$777$	1.26773e13	1.24776
$778$	2.61193e13	2.55596
$779$	−2.54866e11	−0.0247966
$780$	−9.96152e11	−0.0963607
$781$	−1.07040e12	−0.102948
$782$	−7.91905e11	−0.0757256
$783$	1.16019e12	0.110306
$784$	8.40157e12	0.794215
$785$	4.58861e12	0.431288
$786$	−7.08699e12	−0.662309
$787$	2.01602e13	1.87331	0.936655	−	0.350254i	$-0.113905\pi$
$787$	2.01602e13	1.87331	0.936655	+	0.350254i	$0.113905\pi$
$788$	1.20074e13	1.10939
$789$	−9.20531e12	−0.845653
$790$	−3.29445e12	−0.300927
$791$	9.96193e11	0.0904794
$792$	−1.66692e11	−0.0150540
$793$	−1.66506e12	−0.149521
$794$	−5.02355e12	−0.448558
$795$	5.79828e12	0.514810
$796$	−8.06966e12	−0.712437
$797$	4.25914e12	0.373903	0.186952	−	0.982369i	$-0.440139\pi$
$797$	4.25914e12	0.373903	0.186952	+	0.982369i	$0.440139\pi$
$798$	5.66872e12	0.494848
$799$	2.35902e12	0.204772
$800$	−1.22245e13	−1.05518
$801$	−1.51136e13	−1.29724
$802$	−6.16708e12	−0.526375
$803$	−4.78549e11	−0.0406169
$804$	2.11715e13	1.78690
$805$	−5.75474e11	−0.0482997
$806$	−2.53895e12	−0.211908
$807$	2.70435e13	2.24456
$808$	3.51667e11	0.0290255
$809$	1.61570e13	1.32615	0.663073	−	0.748555i	$-0.269252\pi$
$809$	1.61570e13	1.32615	0.663073	+	0.748555i	$0.269252\pi$
$810$	7.24428e12	0.591307
$811$	5.21546e12	0.423349	0.211675	−	0.977340i	$-0.432108\pi$
$811$	5.21546e12	0.423349	0.211675	+	0.977340i	$0.432108\pi$
$812$	4.36187e12	0.352104
$813$	−1.38801e13	−1.11426
$814$	−1.48174e12	−0.118294
$815$	2.22395e12	0.176570
$816$	−5.58833e12	−0.441242
$817$	−9.96353e12	−0.782373
$818$	−3.58236e12	−0.279756
$819$	1.46065e12	0.113440
$820$	−2.13856e11	−0.0165181
$821$	−6.04798e12	−0.464586	−0.232293	−	0.972646i	$-0.574623\pi$
$821$	−6.04798e12	−0.464586	−0.232293	+	0.972646i	$0.574623\pi$
$822$	−5.08445e12	−0.388437
$823$	1.96456e13	1.49268	0.746339	−	0.665566i	$-0.231810\pi$
$823$	1.96456e13	1.49268	0.746339	+	0.665566i	$0.231810\pi$
$824$	−5.77370e12	−0.436296
$825$	−8.53822e11	−0.0641689
$826$	−5.62413e12	−0.420383
$827$	−2.31432e13	−1.72047	−0.860236	−	0.509896i	$-0.829684\pi$
$827$	−2.31432e13	−1.72047	−0.860236	+	0.509896i	$0.829684\pi$
$828$	−1.96650e12	−0.145397
$829$	−1.58598e13	−1.16628	−0.583138	−	0.812373i	$-0.698175\pi$
$829$	−1.58598e13	−1.16628	−0.583138	+	0.812373i	$0.698175\pi$
$830$	−4.56482e12	−0.333866
$831$	−1.05229e13	−0.765472
$832$	−1.56407e12	−0.113162
$833$	2.56176e12	0.184347
$834$	4.27671e13	3.06100
$835$	−7.65182e12	−0.544723
$836$	−2.89284e11	−0.0204831
$837$	1.40790e12	0.0991534
$838$	−3.52615e13	−2.47003
$839$	−1.63271e11	−0.0113757	−0.00568787	−	0.999984i	$-0.501811\pi$
$839$	−1.63271e11	−0.0113757	−0.00568787	+	0.999984i	$0.501811\pi$
$840$	−1.38120e12	−0.0957196
$841$	−5.25627e12	−0.362323
$842$	−2.63278e13	−1.80514
$843$	2.48197e13	1.69267
$844$	2.17618e13	1.47623
$845$	−5.73735e12	−0.387129
$846$	1.34171e13	0.900518
$847$	−8.49586e12	−0.567194
$848$	1.62244e13	1.07743
$849$	−2.24582e13	−1.48351
$850$	−4.61095e12	−0.302974
$851$	5.07588e12	0.331764
$852$	−3.03079e13	−1.97051
$853$	1.57883e13	1.02109	0.510547	−	0.859850i	$-0.329443\pi$
$853$	1.57883e13	1.02109	0.510547	+	0.859850i	$0.329443\pi$
$854$	7.95060e12	0.511493
$855$	2.71109e12	0.173499
$856$	3.64687e12	0.232160
$857$	8.81358e12	0.558134	0.279067	−	0.960272i	$-0.409975\pi$
$857$	8.81358e12	0.558134	0.279067	+	0.960272i	$0.409975\pi$
$858$	−3.60460e11	−0.0227073
$859$	−1.43423e13	−0.898772	−0.449386	−	0.893338i	$-0.648357\pi$
$859$	−1.43423e13	−0.898772	−0.449386	+	0.893338i	$0.648357\pi$
$860$	−8.36033e12	−0.521171
$861$	6.62074e11	0.0410575
$862$	1.94728e13	1.20129
$863$	4.54572e12	0.278968	0.139484	−	0.990224i	$-0.455456\pi$
$863$	4.54572e12	0.278968	0.139484	+	0.990224i	$0.455456\pi$
$864$	2.86179e12	0.174713
$865$	−6.02720e12	−0.366053
$866$	−6.01483e12	−0.363406
$867$	2.12278e13	1.27591
$868$	5.29319e12	0.316503
$869$	−5.20485e11	−0.0309613
$870$	1.00880e13	0.596993
$871$	−6.29636e12	−0.370688
$872$	−2.24931e12	−0.131742
$873$	−1.71379e13	−0.998603
$874$	2.26971e12	0.131574
$875$	−7.36722e12	−0.424881
$876$	−1.35499e13	−0.777441
$877$	1.56417e13	0.892864	0.446432	−	0.894817i	$-0.352694\pi$
$877$	1.56417e13	0.892864	0.446432	+	0.894817i	$0.352694\pi$
$878$	1.78430e13	1.01331
$879$	3.72777e13	2.10620
$880$	4.74659e11	0.0266814
$881$	−2.98507e13	−1.66941	−0.834704	−	0.550699i	$-0.814361\pi$
$881$	−2.98507e13	−1.66941	−0.834704	+	0.550699i	$0.814361\pi$
$882$	1.45702e13	0.810694
$883$	−1.82981e12	−0.101294	−0.0506469	−	0.998717i	$-0.516128\pi$
$883$	−1.82981e12	−0.101294	−0.0506469	+	0.998717i	$0.516128\pi$
$884$	−8.49911e11	−0.0468099
$885$	−5.67912e12	−0.311198
$886$	8.69968e11	0.0474298
$887$	−1.68965e13	−0.916514	−0.458257	−	0.888820i	$-0.651526\pi$
$887$	−1.68965e13	−0.916514	−0.458257	+	0.888820i	$0.651526\pi$
$888$	1.21827e13	0.657484
$889$	−9.00404e12	−0.483481
$890$	1.46371e13	0.781989
$891$	1.14451e12	0.0608374
$892$	−2.63817e13	−1.39528
$893$	−6.76130e12	−0.355794
$894$	1.44663e12	0.0757423
$895$	−1.11195e13	−0.579272
$896$	−6.41513e12	−0.332521
$897$	1.23480e12	0.0636841
$898$	−1.61937e13	−0.831003
$899$	1.12261e13	0.573204
$900$	−1.14501e13	−0.581726
$901$	4.94706e12	0.250084
$902$	−7.73843e10	−0.00389246
$903$	2.58827e13	1.29543
$904$	9.57331e11	0.0476765
$905$	−1.33505e12	−0.0661576
$906$	−1.46006e13	−0.719937
$907$	−7.05348e11	−0.0346075	−0.0173038	−	0.999850i	$-0.505508\pi$
$907$	−7.05348e11	−0.0346075	−0.0173038	+	0.999850i	$0.505508\pi$
$908$	−1.01612e13	−0.496087
$909$	1.79314e12	0.0871117
$910$	−1.41460e12	−0.0683828
$911$	7.81769e12	0.376050	0.188025	−	0.982164i	$-0.439791\pi$
$911$	7.81769e12	0.376050	0.188025	+	0.982164i	$0.439791\pi$
$912$	1.60170e13	0.766662
$913$	−7.21189e11	−0.0343503
$914$	−1.62151e13	−0.768534
$915$	8.02834e12	0.378644
$916$	−1.94315e13	−0.911960
$917$	−4.39402e12	−0.205211
$918$	1.07944e12	0.0501655
$919$	−2.54885e13	−1.17876	−0.589379	−	0.807857i	$-0.700627\pi$
$919$	−2.54885e13	−1.17876	−0.589379	+	0.807857i	$0.700627\pi$
$920$	−5.53024e11	−0.0254506
$921$	−2.19176e13	−1.00375
$922$	−4.89685e13	−2.23166
$923$	9.01350e12	0.408776
$924$	7.51484e11	0.0339153
$925$	2.95549e13	1.32737
$926$	1.47520e13	0.659328
$927$	−2.94399e13	−1.30942
$928$	2.28188e13	1.01001
$929$	−8.40089e12	−0.370045	−0.185022	−	0.982734i	$-0.559236\pi$
$929$	−8.40089e12	−0.370045	−0.185022	+	0.982734i	$0.559236\pi$
$930$	1.22419e13	0.536633
$931$	−7.34238e12	−0.320305
$932$	1.21951e13	0.529438
$933$	−1.22178e13	−0.527870
$934$	−2.03750e13	−0.876065
$935$	1.44730e11	0.00619309
$936$	1.40366e12	0.0597753
$937$	−2.21409e13	−0.938356	−0.469178	−	0.883104i	$-0.655450\pi$
$937$	−2.21409e13	−0.938356	−0.469178	+	0.883104i	$0.655450\pi$
$938$	3.00649e13	1.26808
$939$	−2.13581e13	−0.896536
$940$	−5.67336e12	−0.237009
$941$	3.54870e12	0.147542	0.0737710	−	0.997275i	$-0.476497\pi$
$941$	3.54870e12	0.147542	0.0737710	+	0.997275i	$0.476497\pi$
$942$	4.70135e13	1.94533
$943$	2.65090e11	0.0109167
$944$	−1.58910e13	−0.651293
$945$	7.84423e11	0.0319968
$946$	−3.02521e12	−0.122813
$947$	3.65819e13	1.47806	0.739029	−	0.673674i	$-0.235285\pi$
$947$	3.65819e13	1.47806	0.739029	+	0.673674i	$0.235285\pi$
$948$	−1.47373e13	−0.592625
$949$	4.02971e12	0.161278
$950$	1.32156e13	0.526419
$951$	2.37447e13	0.941356
$952$	−1.17843e12	−0.0464985
$953$	−5.57643e12	−0.218997	−0.109498	−	0.993987i	$-0.534924\pi$
$953$	−5.57643e12	−0.218997	−0.109498	+	0.993987i	$0.534924\pi$
$954$	2.81367e13	1.09978
$955$	5.74869e12	0.223642
$956$	1.70912e13	0.661779
$957$	1.59379e12	0.0614224
$958$	4.38008e13	1.68011
$959$	−3.15242e12	−0.120354
$960$	7.54139e12	0.286570
$961$	−1.28166e13	−0.484751
$962$	1.24773e13	0.469712
$963$	1.85953e13	0.696761
$964$	2.56733e13	0.957492
$965$	−8.70565e12	−0.323168
$966$	−5.89613e12	−0.217856
$967$	2.24925e13	0.827217	0.413609	−	0.910455i	$-0.364268\pi$
$967$	2.24925e13	0.827217	0.413609	+	0.910455i	$0.364268\pi$
$968$	−8.16442e12	−0.298873
$969$	4.88381e12	0.177951
$970$	1.65976e13	0.601967
$971$	−4.76433e13	−1.71995	−0.859973	−	0.510339i	$-0.829520\pi$
$971$	−4.76433e13	−1.71995	−0.859973	+	0.510339i	$0.829520\pi$
$972$	2.94272e13	1.05743
$973$	2.65161e13	0.948424
$974$	5.13349e13	1.82767
$975$	7.18976e12	0.254797
$976$	2.24644e13	0.792449
$977$	5.67970e13	1.99434	0.997172	−	0.0751496i	$-0.0239434\pi$
$977$	5.67970e13	1.99434	0.997172	+	0.0751496i	$0.0239434\pi$
$978$	2.27859e13	0.796419
$979$	2.31249e12	0.0804560
$980$	−6.16094e12	−0.213368
$981$	−1.14692e13	−0.395386
$982$	−5.96193e13	−2.04590
$983$	−3.87160e13	−1.32251	−0.661256	−	0.750160i	$-0.729976\pi$
$983$	−3.87160e13	−1.32251	−0.661256	+	0.750160i	$0.729976\pi$
$984$	6.36246e11	0.0216345
$985$	1.72180e13	0.582802
$986$	8.60703e12	0.290006
$987$	1.75641e13	0.589113
$988$	2.43597e12	0.0813327
$989$	1.03632e13	0.344438
$990$	8.23164e11	0.0272350
$991$	7.44092e12	0.245073	0.122536	−	0.992464i	$-0.460897\pi$
$991$	7.44092e12	0.245073	0.122536	+	0.992464i	$0.460897\pi$
$992$	2.76909e13	0.907893
$993$	−5.61195e13	−1.83165
$994$	−4.30391e13	−1.39838
$995$	−1.15715e13	−0.374269
$996$	−2.04201e13	−0.657493
$997$	−3.21649e13	−1.03099	−0.515495	−	0.856893i	$-0.672392\pi$
$997$	−3.21649e13	−1.03099	−0.515495	+	0.856893i	$0.672392\pi$
$998$	−1.70828e13	−0.545095
$999$	−6.91889e12	−0.219782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.10.a.a.1.2	✓	7
3.2	odd	2		207.10.a.b.1.6		7
4.3	odd	2		368.10.a.f.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.10.a.a.1.2	✓	7	1.1	even	1	trivial
207.10.a.b.1.6		7	3.2	odd	2
368.10.a.f.1.6		7	4.3	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q-30.1460 q^{2} -193.374 q^{3} +396.783 q^{4} +568.966 q^{5} +5829.45 q^{6} +3614.33 q^{7} +3473.33 q^{8} +17710.4 q^{9} +O(q^{10})\)	\(q-30.1460 q^{2} -193.374 q^{3} +396.783 q^{4} +568.966 q^{5} +5829.45 q^{6} +3614.33 q^{7} +3473.33 q^{8} +17710.4 q^{9} -17152.1 q^{10} -2709.83 q^{11} -76727.4 q^{12} +22818.6 q^{13} -108958. q^{14} -110023. q^{15} -307860. q^{16} -93871.0 q^{17} -533898. q^{18} +269048. q^{19} +225756. q^{20} -698916. q^{21} +81690.5 q^{22} -279841. q^{23} -671651. q^{24} -1.62940e6 q^{25} -687889. q^{26} +381449. q^{27} +1.43411e6 q^{28} +3.04153e6 q^{29} +3.31676e6 q^{30} +3.69093e6 q^{31} +7.50242e6 q^{32} +524009. q^{33} +2.82984e6 q^{34} +2.05643e6 q^{35} +7.02719e6 q^{36} -1.81385e7 q^{37} -8.11073e6 q^{38} -4.41251e6 q^{39} +1.97621e6 q^{40} -947287. q^{41} +2.10696e7 q^{42} -3.70325e7 q^{43} -1.07521e6 q^{44} +1.00766e7 q^{45} +8.43610e6 q^{46} -2.51305e7 q^{47} +5.95321e7 q^{48} -2.72902e7 q^{49} +4.91200e7 q^{50} +1.81522e7 q^{51} +9.05403e6 q^{52} -5.27006e7 q^{53} -1.14992e7 q^{54} -1.54180e6 q^{55} +1.25538e7 q^{56} -5.20268e7 q^{57} -9.16899e7 q^{58} +5.16175e7 q^{59} -4.36553e7 q^{60} -7.29696e7 q^{61} -1.11267e8 q^{62} +6.40112e7 q^{63} -6.85437e7 q^{64} +1.29830e7 q^{65} -1.57968e7 q^{66} -2.75931e8 q^{67} -3.72464e7 q^{68} +5.41139e7 q^{69} -6.19932e7 q^{70} +3.95007e8 q^{71} +6.15141e7 q^{72} +1.76598e8 q^{73} +5.46803e8 q^{74} +3.15084e8 q^{75} +1.06754e8 q^{76} -9.79421e6 q^{77} +1.33020e8 q^{78} +1.92073e8 q^{79} -1.75162e8 q^{80} -4.22356e8 q^{81} +2.85569e7 q^{82} +2.66138e8 q^{83} -2.77318e8 q^{84} -5.34094e7 q^{85} +1.11638e9 q^{86} -5.88151e8 q^{87} -9.41212e6 q^{88} -8.53374e8 q^{89} -3.03770e8 q^{90} +8.24738e7 q^{91} -1.11036e8 q^{92} -7.13729e8 q^{93} +7.57584e8 q^{94} +1.53079e8 q^{95} -1.45077e9 q^{96} -9.67673e8 q^{97} +8.22692e8 q^{98} -4.79921e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9}+O(q^{10}) \) 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9} - 60820 q^{10} - 78484 q^{11} - 343492 q^{12} - 296769 q^{13} - 711120 q^{14} - 237870 q^{15} - 253440 q^{16} - 1128820 q^{17} - 499874 q^{18} - 1301252 q^{19} - 3482704 q^{20} - 108908 q^{21} - 1562088 q^{22} - 1958887 q^{23} - 4606464 q^{24} - 1320899 q^{25} + 692230 q^{26} + 2977921 q^{27} - 8371144 q^{28} + 2813849 q^{29} + 25535196 q^{30} + 7334751 q^{31} + 26028800 q^{32} + 646330 q^{33} + 14981564 q^{34} + 23410104 q^{35} + 40211900 q^{36} - 13324320 q^{37} + 37578632 q^{38} + 6304533 q^{39} - 45307920 q^{40} - 15691573 q^{41} + 124523248 q^{42} - 46474818 q^{43} + 43428040 q^{44} - 72736710 q^{45} + 8232227 q^{47} - 163054384 q^{48} + 29219031 q^{49} + 50366304 q^{50} - 136344764 q^{51} - 100922292 q^{52} - 53545400 q^{53} - 26171642 q^{54} - 181608484 q^{55} - 420111696 q^{56} - 218913370 q^{57} - 39304854 q^{58} - 341275144 q^{59} + 420822384 q^{60} - 277157656 q^{61} + 464777594 q^{62} - 574619276 q^{63} + 340566208 q^{64} + 106659278 q^{65} + 258025876 q^{66} + 89654580 q^{67} + 62700400 q^{68} + 24905849 q^{69} + 1187910040 q^{70} - 286098961 q^{71} + 1446323640 q^{72} - 637495039 q^{73} + 189880036 q^{74} - 160733159 q^{75} + 228563936 q^{76} + 511682536 q^{77} + 1199383686 q^{78} + 274469546 q^{79} - 345318560 q^{80} - 237775217 q^{81} - 570256066 q^{82} + 1164579762 q^{83} + 3447171416 q^{84} - 18639492 q^{85} + 415245796 q^{86} - 595368433 q^{87} + 103329440 q^{88} - 504153000 q^{89} - 1414126968 q^{90} - 1692320156 q^{91} - 429835776 q^{92} - 2753858687 q^{93} - 2214048622 q^{94} + 162962164 q^{95} - 3332565856 q^{96} - 3519929016 q^{97} + 2474592568 q^{98} - 1883749262 q^{99}+O(q^{100}) \) 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9 - 60820 * q^10 - 78484 * q^11 - 343492 * q^12 - 296769 * q^13 - 711120 * q^14 - 237870 * q^15 - 253440 * q^16 - 1128820 * q^17 - 499874 * q^18 - 1301252 * q^19 - 3482704 * q^20 - 108908 * q^21 - 1562088 * q^22 - 1958887 * q^23 - 4606464 * q^24 - 1320899 * q^25 + 692230 * q^26 + 2977921 * q^27 - 8371144 * q^28 + 2813849 * q^29 + 25535196 * q^30 + 7334751 * q^31 + 26028800 * q^32 + 646330 * q^33 + 14981564 * q^34 + 23410104 * q^35 + 40211900 * q^36 - 13324320 * q^37 + 37578632 * q^38 + 6304533 * q^39 - 45307920 * q^40 - 15691573 * q^41 + 124523248 * q^42 - 46474818 * q^43 + 43428040 * q^44 - 72736710 * q^45 + 8232227 * q^47 - 163054384 * q^48 + 29219031 * q^49 + 50366304 * q^50 - 136344764 * q^51 - 100922292 * q^52 - 53545400 * q^53 - 26171642 * q^54 - 181608484 * q^55 - 420111696 * q^56 - 218913370 * q^57 - 39304854 * q^58 - 341275144 * q^59 + 420822384 * q^60 - 277157656 * q^61 + 464777594 * q^62 - 574619276 * q^63 + 340566208 * q^64 + 106659278 * q^65 + 258025876 * q^66 + 89654580 * q^67 + 62700400 * q^68 + 24905849 * q^69 + 1187910040 * q^70 - 286098961 * q^71 + 1446323640 * q^72 - 637495039 * q^73 + 189880036 * q^74 - 160733159 * q^75 + 228563936 * q^76 + 511682536 * q^77 + 1199383686 * q^78 + 274469546 * q^79 - 345318560 * q^80 - 237775217 * q^81 - 570256066 * q^82 + 1164579762 * q^83 + 3447171416 * q^84 - 18639492 * q^85 + 415245796 * q^86 - 595368433 * q^87 + 103329440 * q^88 - 504153000 * q^89 - 1414126968 * q^90 - 1692320156 * q^91 - 429835776 * q^92 - 2753858687 * q^93 - 2214048622 * q^94 + 162962164 * q^95 - 3332565856 * q^96 - 3519929016 * q^97 + 2474592568 * q^98 - 1883749262 * q^99

Introduction

L-functions

Modular forms

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