LMFDB - Embedded newform 43.10.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,10,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	43.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:	$22.1465409550$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 6541 x^{15} + 10299 x^{14} + 17445509 x^{13} - 2347983 x^{12} + \cdots - 37\!\cdots\!40 $ x^17 - 3x^16 - 6541x^15 + 10299x^14 + 17445509x^13 - 2347983x^12 - 24275147889x^11 - 32817396993x^10 + 18668870018715x^9 + 54284997199479x^8 - 7688031373215127x^7 - 34414384567646799x^6 + 1472871456600457271x^5 + 8285298256630038219x^4 - 82173286944147552299x^3 - 301942019130667260459x^2 + 866271940633182378600x - 378136193010971707440
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-22.6959$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+25.6959 q^{2} -189.280 q^{3} +148.278 q^{4} -1738.18 q^{5} -4863.71 q^{6} +2771.25 q^{7} -9346.16 q^{8} +16143.9 q^{9} +O(q^{10})$	\(q+25.6959 q^{2} -189.280 q^{3} +148.278 q^{4} -1738.18 q^{5} -4863.71 q^{6} +2771.25 q^{7} -9346.16 q^{8} +16143.9 q^{9} -44664.0 q^{10} +77651.4 q^{11} -28066.0 q^{12} +26123.0 q^{13} +71209.7 q^{14} +329002. q^{15} -316076. q^{16} -208881. q^{17} +414831. q^{18} +802369. q^{19} -257733. q^{20} -524542. q^{21} +1.99532e6 q^{22} +965148. q^{23} +1.76904e6 q^{24} +1.06814e6 q^{25} +671253. q^{26} +669881. q^{27} +410914. q^{28} -4.78140e6 q^{29} +8.45399e6 q^{30} +2.47275e6 q^{31} -3.33661e6 q^{32} -1.46978e7 q^{33} -5.36739e6 q^{34} -4.81692e6 q^{35} +2.39378e6 q^{36} -9.14801e6 q^{37} +2.06176e7 q^{38} -4.94456e6 q^{39} +1.62453e7 q^{40} +3.01845e7 q^{41} -1.34786e7 q^{42} +3.41880e6 q^{43} +1.15140e7 q^{44} -2.80610e7 q^{45} +2.48003e7 q^{46} +4.43702e7 q^{47} +5.98268e7 q^{48} -3.26738e7 q^{49} +2.74467e7 q^{50} +3.95371e7 q^{51} +3.87345e6 q^{52} +7.35515e7 q^{53} +1.72132e7 q^{54} -1.34972e8 q^{55} -2.59006e7 q^{56} -1.51872e8 q^{57} -1.22862e8 q^{58} -4.64198e7 q^{59} +4.87836e7 q^{60} +3.71027e7 q^{61} +6.35394e7 q^{62} +4.47388e7 q^{63} +7.60938e7 q^{64} -4.54064e7 q^{65} -3.77674e8 q^{66} -5.65567e7 q^{67} -3.09724e7 q^{68} -1.82683e8 q^{69} -1.23775e8 q^{70} -1.28067e8 q^{71} -1.50883e8 q^{72} +2.92572e8 q^{73} -2.35066e8 q^{74} -2.02177e8 q^{75} +1.18973e8 q^{76} +2.15191e8 q^{77} -1.27055e8 q^{78} -1.58719e8 q^{79} +5.49396e8 q^{80} -4.44555e8 q^{81} +7.75618e8 q^{82} +4.23013e8 q^{83} -7.77778e7 q^{84} +3.63073e8 q^{85} +8.78491e7 q^{86} +9.05023e8 q^{87} -7.25742e8 q^{88} -7.51308e7 q^{89} -7.21051e8 q^{90} +7.23934e7 q^{91} +1.43110e8 q^{92} -4.68041e8 q^{93} +1.14013e9 q^{94} -1.39466e9 q^{95} +6.31553e8 q^{96} -8.11068e8 q^{97} -8.39581e8 q^{98} +1.25360e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) $ 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9} + 23763 q^{10} + 78370 q^{11} + 271339 q^{12} + 114452 q^{13} - 376208 q^{14} - 255820 q^{15} + 412586 q^{16} + 726937 q^{17} + 577055 q^{18} + 544263 q^{19} + 3642183 q^{20} + 3137394 q^{21} + 5269148 q^{22} + 5575241 q^{23} + 16215113 q^{24} + 10874708 q^{25} + 8009180 q^{26} + 8350126 q^{27} + 12534764 q^{28} + 8223345 q^{29} + 30612012 q^{30} + 13054147 q^{31} + 37111710 q^{32} + 36024808 q^{33} + 27991291 q^{34} + 17826330 q^{35} + 84105953 q^{36} + 46733879 q^{37} + 15733789 q^{38} + 8689898 q^{39} + 52241669 q^{40} + 53667013 q^{41} + 7708286 q^{42} + 58119617 q^{43} + 81727236 q^{44} + 124361968 q^{45} + 146859355 q^{46} + 122945511 q^{47} + 86356095 q^{48} + 111396073 q^{49} - 96642133 q^{50} - 187132423 q^{51} - 54447944 q^{52} - 993146 q^{53} - 219468490 q^{54} - 248155792 q^{55} - 141048116 q^{56} - 402917960 q^{57} - 466599837 q^{58} - 95519644 q^{59} - 621611940 q^{60} - 311752038 q^{61} - 212471691 q^{62} - 928966350 q^{63} - 829842590 q^{64} - 107969830 q^{65} - 978530932 q^{66} - 292438130 q^{67} - 88281129 q^{68} + 78577726 q^{69} - 1650972530 q^{70} - 13576908 q^{71} - 706943493 q^{72} - 501490738 q^{73} - 494831691 q^{74} - 641914030 q^{75} - 1248630771 q^{76} + 787365348 q^{77} - 946670550 q^{78} + 740350275 q^{79} - 27802861 q^{80} + 1582210525 q^{81} - 1600400057 q^{82} + 754109940 q^{83} - 1955423842 q^{84} + 1071609956 q^{85} + 164102448 q^{86} + 186301257 q^{87} + 1863375104 q^{88} + 1470581868 q^{89} - 698098630 q^{90} + 2895349644 q^{91} + 1041082071 q^{92} + 4540331515 q^{93} - 706582361 q^{94} + 3297255729 q^{95} + 2087289393 q^{96} + 1949310583 q^{97} + 6695989160 q^{98} + 1234191326 q^{99}+O(q^{100}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9 + 23763 * q^10 + 78370 * q^11 + 271339 * q^12 + 114452 * q^13 - 376208 * q^14 - 255820 * q^15 + 412586 * q^16 + 726937 * q^17 + 577055 * q^18 + 544263 * q^19 + 3642183 * q^20 + 3137394 * q^21 + 5269148 * q^22 + 5575241 * q^23 + 16215113 * q^24 + 10874708 * q^25 + 8009180 * q^26 + 8350126 * q^27 + 12534764 * q^28 + 8223345 * q^29 + 30612012 * q^30 + 13054147 * q^31 + 37111710 * q^32 + 36024808 * q^33 + 27991291 * q^34 + 17826330 * q^35 + 84105953 * q^36 + 46733879 * q^37 + 15733789 * q^38 + 8689898 * q^39 + 52241669 * q^40 + 53667013 * q^41 + 7708286 * q^42 + 58119617 * q^43 + 81727236 * q^44 + 124361968 * q^45 + 146859355 * q^46 + 122945511 * q^47 + 86356095 * q^48 + 111396073 * q^49 - 96642133 * q^50 - 187132423 * q^51 - 54447944 * q^52 - 993146 * q^53 - 219468490 * q^54 - 248155792 * q^55 - 141048116 * q^56 - 402917960 * q^57 - 466599837 * q^58 - 95519644 * q^59 - 621611940 * q^60 - 311752038 * q^61 - 212471691 * q^62 - 928966350 * q^63 - 829842590 * q^64 - 107969830 * q^65 - 978530932 * q^66 - 292438130 * q^67 - 88281129 * q^68 + 78577726 * q^69 - 1650972530 * q^70 - 13576908 * q^71 - 706943493 * q^72 - 501490738 * q^73 - 494831691 * q^74 - 641914030 * q^75 - 1248630771 * q^76 + 787365348 * q^77 - 946670550 * q^78 + 740350275 * q^79 - 27802861 * q^80 + 1582210525 * q^81 - 1600400057 * q^82 + 754109940 * q^83 - 1955423842 * q^84 + 1071609956 * q^85 + 164102448 * q^86 + 186301257 * q^87 + 1863375104 * q^88 + 1470581868 * q^89 - 698098630 * q^90 + 2895349644 * q^91 + 1041082071 * q^92 + 4540331515 * q^93 - 706582361 * q^94 + 3297255729 * q^95 + 2087289393 * q^96 + 1949310583 * q^97 + 6695989160 * q^98 + 1234191326 * 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 $

$2$	25.6959	1.13561	0.567804	−	0.823164i	$-0.307793\pi$
$2$	25.6959	1.13561	0.567804	+	0.823164i	$0.307793\pi$
$3$	−189.280	−1.34915	−0.674573	−	0.738208i	$-0.735672\pi$
$3$	−189.280	−1.34915	−0.674573	+	0.738208i	$0.735672\pi$
$4$	148.278	0.289605
$5$	−1738.18	−1.24374	−0.621869	−	0.783121i	$-0.713626\pi$
$5$	−1738.18	−1.24374	−0.621869	+	0.783121i	$0.713626\pi$
$6$	−4863.71	−1.53210
$7$	2771.25	0.436249	0.218125	−	0.975921i	$-0.430006\pi$
$7$	2771.25	0.436249	0.218125	+	0.975921i	$0.430006\pi$
$8$	−9346.16	−0.806730
$9$	16143.9	0.820195
$10$	−44664.0	−1.41240
$11$	77651.4	1.59912	0.799562	−	0.600584i	$-0.205065\pi$
$11$	77651.4	1.59912	0.799562	+	0.600584i	$0.205065\pi$
$12$	−28066.0	−0.390719
$13$	26123.0	0.253675	0.126838	−	0.991924i	$-0.459517\pi$
$13$	26123.0	0.253675	0.126838	+	0.991924i	$0.459517\pi$
$14$	71209.7	0.495408
$15$	329002.	1.67798
$16$	−316076.	−1.20573
$17$	−208881.	−0.606568	−0.303284	−	0.952900i	$-0.598083\pi$
$17$	−208881.	−0.606568	−0.303284	+	0.952900i	$0.598083\pi$
$18$	414831.	0.931420
$19$	802369.	1.41248	0.706241	−	0.707972i	$-0.250390\pi$
$19$	802369.	1.41248	0.706241	+	0.707972i	$0.250390\pi$
$20$	−257733.	−0.360192
$21$	−524542.	−0.588564
$22$	1.99532e6	1.81598
$23$	965148.	0.719148	0.359574	−	0.933116i	$-0.382922\pi$
$23$	965148.	0.719148	0.359574	+	0.933116i	$0.382922\pi$
$24$	1.76904e6	1.08840
$25$	1.06814e6	0.546885
$26$	671253.	0.288075
$27$	669881.	0.242583
$28$	410914.	0.126340
$29$	−4.78140e6	−1.25535	−0.627674	−	0.778476i	$-0.715993\pi$
$29$	−4.78140e6	−1.25535	−0.627674	+	0.778476i	$0.715993\pi$
$30$	8.45399e6	1.90553
$31$	2.47275e6	0.480897	0.240448	−	0.970662i	$-0.422706\pi$
$31$	2.47275e6	0.480897	0.240448	+	0.970662i	$0.422706\pi$
$32$	−3.33661e6	−0.562510
$33$	−1.46978e7	−2.15745
$34$	−5.36739e6	−0.688824
$35$	−4.81692e6	−0.542580
$36$	2.39378e6	0.237532
$37$	−9.14801e6	−0.802452	−0.401226	−	0.915979i	$-0.631416\pi$
$37$	−9.14801e6	−0.802452	−0.401226	+	0.915979i	$0.631416\pi$
$38$	2.06176e7	1.60403
$39$	−4.94456e6	−0.342245
$40$	1.62453e7	1.00336
$41$	3.01845e7	1.66823	0.834117	−	0.551587i	$-0.185978\pi$
$41$	3.01845e7	1.66823	0.834117	+	0.551587i	$0.185978\pi$
$42$	−1.34786e7	−0.668377
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	1.15140e7	0.463114
$45$	−2.80610e7	−1.02011
$46$	2.48003e7	0.816670
$47$	4.43702e7	1.32633	0.663164	−	0.748474i	$-0.269213\pi$
$47$	4.43702e7	1.32633	0.663164	+	0.748474i	$0.269213\pi$
$48$	5.98268e7	1.62671
$49$	−3.26738e7	−0.809687
$50$	2.74467e7	0.621047
$51$	3.95371e7	0.818349
$52$	3.87345e6	0.0734655
$53$	7.35515e7	1.28041	0.640207	−	0.768203i	$-0.278849\pi$
$53$	7.35515e7	1.28041	0.640207	+	0.768203i	$0.278849\pi$
$54$	1.72132e7	0.275479
$55$	−1.34972e8	−1.98889
$56$	−2.59006e7	−0.351935
$57$	−1.51872e8	−1.90564
$58$	−1.22862e8	−1.42558
$59$	−4.64198e7	−0.498734	−0.249367	−	0.968409i	$-0.580223\pi$
$59$	−4.64198e7	−0.498734	−0.249367	+	0.968409i	$0.580223\pi$
$60$	4.87836e7	0.485952
$61$	3.71027e7	0.343101	0.171550	−	0.985175i	$-0.445122\pi$
$61$	3.71027e7	0.343101	0.171550	+	0.985175i	$0.445122\pi$
$62$	6.35394e7	0.546110
$63$	4.47388e7	0.357809
$64$	7.60938e7	0.566943
$65$	−4.54064e7	−0.315506
$66$	−3.77674e8	−2.45002
$67$	−5.65567e7	−0.342884	−0.171442	−	0.985194i	$-0.554843\pi$
$67$	−5.65567e7	−0.342884	−0.171442	+	0.985194i	$0.554843\pi$
$68$	−3.09724e7	−0.175665
$69$	−1.82683e8	−0.970236
$70$	−1.23775e8	−0.616158
$71$	−1.28067e8	−0.598101	−0.299051	−	0.954237i	$-0.596670\pi$
$71$	−1.28067e8	−0.598101	−0.299051	+	0.954237i	$0.596670\pi$
$72$	−1.50883e8	−0.661676
$73$	2.92572e8	1.20581	0.602905	−	0.797813i	$-0.294010\pi$
$73$	2.92572e8	1.20581	0.602905	+	0.797813i	$0.294010\pi$
$74$	−2.35066e8	−0.911271
$75$	−2.02177e8	−0.737828
$76$	1.18973e8	0.409061
$77$	2.15191e8	0.697616
$78$	−1.27055e8	−0.388656
$79$	−1.58719e8	−0.458467	−0.229234	−	0.973371i	$-0.573622\pi$
$79$	−1.58719e8	−0.458467	−0.229234	+	0.973371i	$0.573622\pi$
$80$	5.49396e8	1.49962
$81$	−4.44555e8	−1.14748
$82$	7.75618e8	1.89446
$83$	4.23013e8	0.978368	0.489184	−	0.872181i	$-0.337295\pi$
$83$	4.23013e8	0.978368	0.489184	+	0.872181i	$0.337295\pi$
$84$	−7.77778e7	−0.170451
$85$	3.63073e8	0.754412
$86$	8.78491e7	0.173179
$87$	9.05023e8	1.69365
$88$	−7.25742e8	−1.29006
$89$	−7.51308e7	−0.126930	−0.0634648	−	0.997984i	$-0.520215\pi$
$89$	−7.51308e7	−0.126930	−0.0634648	+	0.997984i	$0.520215\pi$
$90$	−7.21051e8	−1.15844
$91$	7.23934e7	0.110666
$92$	1.43110e8	0.208269
$93$	−4.68041e8	−0.648800
$94$	1.14013e9	1.50619
$95$	−1.39466e9	−1.75676
$96$	6.31553e8	0.758908
$97$	−8.11068e8	−0.930217	−0.465109	−	0.885254i	$-0.653985\pi$
$97$	−8.11068e8	−0.930217	−0.465109	+	0.885254i	$0.653985\pi$
$98$	−8.39581e8	−0.919486
$99$	1.25360e9	1.31159
$100$	1.58381e8	0.158381
$101$	3.45362e8	0.330239	0.165120	−	0.986274i	$-0.447199\pi$
$101$	3.45362e8	0.330239	0.165120	+	0.986274i	$0.447199\pi$
$102$	1.01594e9	0.929324
$103$	2.15934e9	1.89040	0.945198	−	0.326499i	$-0.105869\pi$
$103$	2.15934e9	1.89040	0.945198	+	0.326499i	$0.105869\pi$
$104$	−2.44150e8	−0.204647
$105$	9.11747e8	0.732019
$106$	1.88997e9	1.45405
$107$	1.89360e9	1.39656	0.698282	−	0.715822i	$-0.253948\pi$
$107$	1.89360e9	1.39656	0.698282	+	0.715822i	$0.253948\pi$
$108$	9.93284e7	0.0702533
$109$	−3.55609e8	−0.241298	−0.120649	−	0.992695i	$-0.538498\pi$
$109$	−3.55609e8	−0.241298	−0.120649	+	0.992695i	$0.538498\pi$
$110$	−3.46822e9	−2.25860
$111$	1.73154e9	1.08263
$112$	−8.75925e8	−0.526000
$113$	2.22027e9	1.28101	0.640506	−	0.767953i	$-0.278725\pi$
$113$	2.22027e9	1.28101	0.640506	+	0.767953i	$0.278725\pi$
$114$	−3.90249e9	−2.16406
$115$	−1.67760e9	−0.894433
$116$	−7.08974e8	−0.363555
$117$	4.21727e8	0.208063
$118$	−1.19280e9	−0.566366
$119$	−5.78863e8	−0.264615
$120$	−3.07491e9	−1.35368
$121$	3.67179e9	1.55720
$122$	9.53387e8	0.389628
$123$	−5.71333e9	−2.25069
$124$	3.66653e8	0.139270
$125$	1.53827e9	0.563556
$126$	1.14960e9	0.406331
$127$	1.24541e9	0.424812	0.212406	−	0.977181i	$-0.431870\pi$
$127$	1.24541e9	0.424812	0.212406	+	0.977181i	$0.431870\pi$
$128$	3.66364e9	1.20633
$129$	−6.47110e8	−0.205743
$130$	−1.16676e9	−0.358290
$131$	4.57189e9	1.35636	0.678181	−	0.734895i	$-0.262769\pi$
$131$	4.57189e9	1.35636	0.678181	+	0.734895i	$0.262769\pi$
$132$	−2.17936e9	−0.624808
$133$	2.22356e9	0.616194
$134$	−1.45327e9	−0.389382
$135$	−1.16437e9	−0.301710
$136$	1.95224e9	0.489337
$137$	−7.76229e9	−1.88255	−0.941276	−	0.337637i	$-0.890372\pi$
$137$	−7.76229e9	−1.88255	−0.941276	+	0.337637i	$0.890372\pi$
$138$	−4.69420e9	−1.10181
$139$	−1.62840e9	−0.369995	−0.184997	−	0.982739i	$-0.559228\pi$
$139$	−1.62840e9	−0.369995	−0.184997	+	0.982739i	$0.559228\pi$
$140$	−7.14242e8	−0.157134
$141$	−8.39838e9	−1.78941
$142$	−3.29079e9	−0.679208
$143$	2.02849e9	0.405658
$144$	−5.10270e9	−0.988937
$145$	8.31092e9	1.56132
$146$	7.51788e9	1.36933
$147$	6.18449e9	1.09239
$148$	−1.35645e9	−0.232394
$149$	−2.33921e9	−0.388804	−0.194402	−	0.980922i	$-0.562277\pi$
$149$	−2.33921e9	−0.388804	−0.194402	+	0.980922i	$0.562277\pi$
$150$	−5.19510e9	−0.837883
$151$	8.37593e9	1.31110	0.655552	−	0.755150i	$-0.272436\pi$
$151$	8.37593e9	1.31110	0.655552	+	0.755150i	$0.272436\pi$
$152$	−7.49907e9	−1.13949
$153$	−3.37216e9	−0.497504
$154$	5.52953e9	0.792218
$155$	−4.29807e9	−0.598110
$156$	−7.33167e8	−0.0991157
$157$	1.05403e10	1.38453	0.692267	−	0.721642i	$-0.256612\pi$
$157$	1.05403e10	1.38453	0.692267	+	0.721642i	$0.256612\pi$
$158$	−4.07843e9	−0.520639
$159$	−1.39218e10	−1.72747
$160$	5.79962e9	0.699615
$161$	2.67467e9	0.313728
$162$	−1.14232e10	−1.30308
$163$	−8.65700e9	−0.960557	−0.480278	−	0.877116i	$-0.659464\pi$
$163$	−8.65700e9	−0.960557	−0.480278	+	0.877116i	$0.659464\pi$
$164$	4.47569e9	0.483128
$165$	2.55475e10	2.68331
$166$	1.08697e10	1.11104
$167$	−1.14466e10	−1.13881	−0.569405	−	0.822057i	$-0.692826\pi$
$167$	−1.14466e10	−1.13881	−0.569405	+	0.822057i	$0.692826\pi$
$168$	4.90246e9	0.474812
$169$	−9.92209e9	−0.935649
$170$	9.32948e9	0.856716
$171$	1.29534e10	1.15851
$172$	5.06932e8	0.0441643
$173$	−1.14167e9	−0.0969022	−0.0484511	−	0.998826i	$-0.515429\pi$
$173$	−1.14167e9	−0.0969022	−0.0484511	+	0.998826i	$0.515429\pi$
$174$	2.32554e10	1.92332
$175$	2.96007e9	0.238578
$176$	−2.45437e10	−1.92812
$177$	8.78633e9	0.672865
$178$	−1.93055e9	−0.144142
$179$	−9.08525e9	−0.661452	−0.330726	−	0.943727i	$-0.607294\pi$
$179$	−9.08525e9	−0.661452	−0.330726	+	0.943727i	$0.607294\pi$
$180$	−4.16081e9	−0.295428
$181$	8.05647e9	0.557945	0.278972	−	0.960299i	$-0.410006\pi$
$181$	8.05647e9	0.557945	0.278972	+	0.960299i	$0.410006\pi$
$182$	1.86021e9	0.125673
$183$	−7.02281e9	−0.462893
$184$	−9.02043e9	−0.580159
$185$	1.59009e10	0.998040
$186$	−1.20267e10	−0.736782
$187$	−1.62199e10	−0.969978
$188$	6.57910e9	0.384111
$189$	1.85641e9	0.105827
$190$	−3.58370e10	−1.99499
$191$	−2.96934e9	−0.161439	−0.0807197	−	0.996737i	$-0.525722\pi$
$191$	−2.96934e9	−0.161439	−0.0807197	+	0.996737i	$0.525722\pi$
$192$	−1.44030e10	−0.764889
$193$	7.57490e9	0.392979	0.196489	−	0.980506i	$-0.437046\pi$
$193$	7.57490e9	0.392979	0.196489	+	0.980506i	$0.437046\pi$
$194$	−2.08411e10	−1.05636
$195$	8.59452e9	0.425663
$196$	−4.84479e9	−0.234489
$197$	3.96594e10	1.87607	0.938033	−	0.346547i	$-0.112646\pi$
$197$	3.96594e10	1.87607	0.938033	+	0.346547i	$0.112646\pi$
$198$	3.22122e10	1.48946
$199$	1.10670e10	0.500256	0.250128	−	0.968213i	$-0.419527\pi$
$199$	1.10670e10	0.500256	0.250128	+	0.968213i	$0.419527\pi$
$200$	−9.98297e9	−0.441189
$201$	1.07050e10	0.462601
$202$	8.87438e9	0.375022
$203$	−1.32505e10	−0.547644
$204$	5.86246e9	0.236998
$205$	−5.24661e10	−2.07485
$206$	5.54860e10	2.14675
$207$	1.55812e10	0.589842
$208$	−8.25685e9	−0.305865
$209$	6.23050e10	2.25873
$210$	2.34281e10	0.831287
$211$	−1.06716e10	−0.370645	−0.185322	−	0.982678i	$-0.559333\pi$
$211$	−1.06716e10	−0.370645	−0.185322	+	0.982678i	$0.559333\pi$
$212$	1.09060e10	0.370814
$213$	2.42405e10	0.806926
$214$	4.86577e10	1.58595
$215$	−5.94248e9	−0.189668
$216$	−6.26082e9	−0.195699
$217$	6.85260e9	0.209791
$218$	−9.13769e9	−0.274020
$219$	−5.53779e10	−1.62681
$220$	−2.00133e10	−0.575992
$221$	−5.45661e9	−0.153871
$222$	4.44933e10	1.22944
$223$	−5.80302e10	−1.57138	−0.785692	−	0.618618i	$-0.787693\pi$
$223$	−5.80302e10	−1.57138	−0.785692	+	0.618618i	$0.787693\pi$
$224$	−9.24658e9	−0.245395
$225$	1.72439e10	0.448552
$226$	5.70518e10	1.45473
$227$	1.25218e10	0.313004	0.156502	−	0.987678i	$-0.449978\pi$
$227$	1.25218e10	0.313004	0.156502	+	0.987678i	$0.449978\pi$
$228$	−2.25193e10	−0.551883
$229$	−7.43531e10	−1.78665	−0.893325	−	0.449410i	$-0.851634\pi$
$229$	−7.43531e10	−1.78665	−0.893325	+	0.449410i	$0.851634\pi$
$230$	−4.31073e10	−1.01572
$231$	−4.07314e10	−0.941186
$232$	4.46877e10	1.01273
$233$	−3.54712e10	−0.788450	−0.394225	−	0.919014i	$-0.628987\pi$
$233$	−3.54712e10	−0.788450	−0.394225	+	0.919014i	$0.628987\pi$
$234$	1.08366e10	0.236278
$235$	−7.71232e10	−1.64960
$236$	−6.88301e9	−0.144436
$237$	3.00424e10	0.618539
$238$	−1.48744e10	−0.300499
$239$	−3.63782e10	−0.721191	−0.360596	−	0.932722i	$-0.617427\pi$
$239$	−3.63782e10	−0.721191	−0.360596	+	0.932722i	$0.617427\pi$
$240$	−1.03990e11	−2.02320
$241$	−6.05039e10	−1.15533	−0.577666	−	0.816273i	$-0.696036\pi$
$241$	−6.05039e10	−1.15533	−0.577666	+	0.816273i	$0.696036\pi$
$242$	9.43498e10	1.76836
$243$	7.09601e10	1.30553
$244$	5.50151e9	0.0993636
$245$	5.67928e10	1.00704
$246$	−1.46809e11	−2.55590
$247$	2.09603e10	0.358312
$248$	−2.31107e10	−0.387954
$249$	−8.00679e10	−1.31996
$250$	3.95272e10	0.639979
$251$	−1.04152e11	−1.65629	−0.828146	−	0.560513i	$-0.810604\pi$
$251$	−1.04152e11	−1.65629	−0.828146	+	0.560513i	$0.810604\pi$
$252$	6.63376e9	0.103623
$253$	7.49451e10	1.15001
$254$	3.20020e10	0.482420
$255$	−6.87224e10	−1.01781
$256$	5.51804e10	0.802980
$257$	−1.12732e11	−1.61194	−0.805970	−	0.591957i	$-0.798356\pi$
$257$	−1.12732e11	−1.61194	−0.805970	+	0.591957i	$0.798356\pi$
$258$	−1.66281e10	−0.233643
$259$	−2.53514e10	−0.350069
$260$	−6.73275e9	−0.0913719
$261$	−7.71904e10	−1.02963
$262$	1.17479e11	1.54029
$263$	8.63446e10	1.11284	0.556422	−	0.830900i	$-0.312174\pi$
$263$	8.63446e10	1.11284	0.556422	+	0.830900i	$0.312174\pi$
$264$	1.37368e11	1.74048
$265$	−1.27846e11	−1.59250
$266$	5.71364e10	0.699754
$267$	1.42207e10	0.171247
$268$	−8.38609e9	−0.0993008
$269$	9.44052e10	1.09929	0.549643	−	0.835400i	$-0.314764\pi$
$269$	9.44052e10	1.09929	0.549643	+	0.835400i	$0.314764\pi$
$270$	−2.99196e10	−0.342624
$271$	3.50789e10	0.395080	0.197540	−	0.980295i	$-0.436705\pi$
$271$	3.50789e10	0.395080	0.197540	+	0.980295i	$0.436705\pi$
$272$	6.60224e10	0.731360
$273$	−1.37026e10	−0.149304
$274$	−1.99459e11	−2.13784
$275$	8.29422e10	0.874537
$276$	−2.70878e10	−0.280985
$277$	1.16933e11	1.19338	0.596690	−	0.802472i	$-0.296482\pi$
$277$	1.16933e11	1.19338	0.596690	+	0.802472i	$0.296482\pi$
$278$	−4.18433e10	−0.420169
$279$	3.99198e10	0.394429
$280$	4.50198e10	0.437716
$281$	5.11213e10	0.489129	0.244564	−	0.969633i	$-0.421355\pi$
$281$	5.11213e10	0.489129	0.244564	+	0.969633i	$0.421355\pi$
$282$	−2.15804e11	−2.03207
$283$	−3.57708e10	−0.331505	−0.165752	−	0.986167i	$-0.553005\pi$
$283$	−3.57708e10	−0.331505	−0.165752	+	0.986167i	$0.553005\pi$
$284$	−1.89895e10	−0.173213
$285$	2.63981e11	2.37012
$286$	5.21237e10	0.460668
$287$	8.36489e10	0.727766
$288$	−5.38659e10	−0.461368
$289$	−7.49564e10	−0.632075
$290$	2.13556e11	1.77305
$291$	1.53519e11	1.25500
$292$	4.33818e10	0.349208
$293$	1.28386e11	1.01768	0.508841	−	0.860861i	$-0.330074\pi$
$293$	1.28386e11	1.01768	0.508841	+	0.860861i	$0.330074\pi$
$294$	1.58916e11	1.24052
$295$	8.06858e10	0.620295
$296$	8.54988e10	0.647362
$297$	5.20172e10	0.387921
$298$	−6.01081e10	−0.441529
$299$	2.52126e10	0.182430
$300$	−2.99783e10	−0.213678
$301$	9.47435e9	0.0665274
$302$	2.15227e11	1.48890
$303$	−6.53701e10	−0.445541
$304$	−2.53609e11	−1.70308
$305$	−6.44912e10	−0.426728
$306$	−8.66506e10	−0.564970
$307$	2.08362e11	1.33874	0.669369	−	0.742930i	$-0.266564\pi$
$307$	2.08362e11	1.33874	0.669369	+	0.742930i	$0.266564\pi$
$308$	3.19081e10	0.202033
$309$	−4.08719e11	−2.55042
$310$	−1.10443e11	−0.679218
$311$	2.14311e11	1.29904	0.649521	−	0.760343i	$-0.274969\pi$
$311$	2.14311e11	1.29904	0.649521	+	0.760343i	$0.274969\pi$
$312$	4.62127e10	0.276099
$313$	−9.08128e10	−0.534807	−0.267404	−	0.963585i	$-0.586166\pi$
$313$	−9.08128e10	−0.534807	−0.267404	+	0.963585i	$0.586166\pi$
$314$	2.70842e11	1.57229
$315$	−7.77639e10	−0.445021
$316$	−2.35345e10	−0.132774
$317$	1.03674e11	0.576637	0.288318	−	0.957535i	$-0.406904\pi$
$317$	1.03674e11	0.576637	0.288318	+	0.957535i	$0.406904\pi$
$318$	−3.57734e11	−1.96172
$319$	−3.71282e11	−2.00746
$320$	−1.32265e11	−0.705129
$321$	−3.58420e11	−1.88417
$322$	6.87279e10	0.356272
$323$	−1.67600e11	−0.856767
$324$	−6.59176e10	−0.332314
$325$	2.79029e10	0.138731
$326$	−2.22449e11	−1.09082
$327$	6.73097e10	0.325546
$328$	−2.82110e11	−1.34582
$329$	1.22961e11	0.578609
$330$	6.56464e11	3.04718
$331$	2.79557e11	1.28010	0.640050	−	0.768333i	$-0.278914\pi$
$331$	2.79557e11	1.28010	0.640050	+	0.768333i	$0.278914\pi$
$332$	6.27233e10	0.283340
$333$	−1.47685e11	−0.658167
$334$	−2.94129e11	−1.29324
$335$	9.83055e10	0.426458
$336$	1.65795e11	0.709651
$337$	−2.02653e11	−0.855892	−0.427946	−	0.903804i	$-0.640763\pi$
$337$	−2.02653e11	−0.855892	−0.427946	+	0.903804i	$0.640763\pi$
$338$	−2.54957e11	−1.06253
$339$	−4.20253e11	−1.72827
$340$	5.38356e10	0.218481
$341$	1.92012e11	0.769013
$342$	3.32848e11	1.31561
$343$	−2.02377e11	−0.789474
$344$	−3.19527e10	−0.123025
$345$	3.17536e11	1.20672
$346$	−2.93362e10	−0.110043
$347$	−5.18650e9	−0.0192040	−0.00960200	−	0.999954i	$-0.503056\pi$
$347$	−5.18650e9	−0.0192040	−0.00960200	+	0.999954i	$0.503056\pi$
$348$	1.34195e11	0.490488
$349$	−1.72003e11	−0.620615	−0.310307	−	0.950636i	$-0.600432\pi$
$349$	−1.72003e11	−0.620615	−0.310307	+	0.950636i	$0.600432\pi$
$350$	7.60616e10	0.270931
$351$	1.74993e10	0.0615374
$352$	−2.59092e11	−0.899523
$353$	3.42391e11	1.17364	0.586822	−	0.809716i	$-0.300379\pi$
$353$	3.42391e11	1.17364	0.586822	+	0.809716i	$0.300379\pi$
$354$	2.25772e11	0.764111
$355$	2.22603e11	0.743881
$356$	−1.11402e10	−0.0367594
$357$	1.09567e11	0.357004
$358$	−2.33453e11	−0.751150
$359$	3.08749e11	0.981027	0.490514	−	0.871433i	$-0.336809\pi$
$359$	3.08749e11	0.981027	0.490514	+	0.871433i	$0.336809\pi$
$360$	2.62262e11	0.822952
$361$	3.21108e11	0.995105
$362$	2.07018e11	0.633606
$363$	−6.94996e11	−2.10089
$364$	1.07343e10	0.0320493
$365$	−5.08541e11	−1.49971
$366$	−1.80457e11	−0.525665
$367$	−4.64428e11	−1.33635	−0.668176	−	0.744003i	$-0.732925\pi$
$367$	−4.64428e11	−1.33635	−0.668176	+	0.744003i	$0.732925\pi$
$368$	−3.05060e11	−0.867102
$369$	4.87296e11	1.36828
$370$	4.08587e11	1.13338
$371$	2.03830e11	0.558579
$372$	−6.94000e10	−0.187896
$373$	−2.79603e11	−0.747914	−0.373957	−	0.927446i	$-0.621999\pi$
$373$	−2.79603e11	−0.747914	−0.373957	+	0.927446i	$0.621999\pi$
$374$	−4.16785e11	−1.10151
$375$	−2.91163e11	−0.760320
$376$	−4.14691e11	−1.06999
$377$	−1.24904e11	−0.318451
$378$	4.77020e10	0.120178
$379$	5.72097e11	1.42427	0.712137	−	0.702041i	$-0.247728\pi$
$379$	5.72097e11	1.42427	0.712137	+	0.702041i	$0.247728\pi$
$380$	−2.06797e11	−0.508765
$381$	−2.35732e11	−0.573134
$382$	−7.62997e10	−0.183332
$383$	3.19812e11	0.759452	0.379726	−	0.925099i	$-0.376018\pi$
$383$	3.19812e11	0.759452	0.379726	+	0.925099i	$0.376018\pi$
$384$	−6.93454e11	−1.62752
$385$	−3.74041e11	−0.867652
$386$	1.94644e11	0.446270
$387$	5.51928e10	0.125079
$388$	−1.20263e11	−0.269395
$389$	5.05595e11	1.11951	0.559757	−	0.828656i	$-0.310894\pi$
$389$	5.05595e11	1.11951	0.559757	+	0.828656i	$0.310894\pi$
$390$	2.20844e11	0.483386
$391$	−2.01601e11	−0.436213
$392$	3.05374e11	0.653199
$393$	−8.65368e11	−1.82993
$394$	1.01908e12	2.13047
$395$	2.75883e11	0.570213
$396$	1.85880e11	0.379843
$397$	6.51686e11	1.31668	0.658341	−	0.752720i	$-0.271258\pi$
$397$	6.51686e11	1.31668	0.658341	+	0.752720i	$0.271258\pi$
$398$	2.84377e11	0.568094
$399$	−4.20876e11	−0.831335
$400$	−3.37612e11	−0.659398
$401$	−3.10631e10	−0.0599923	−0.0299962	−	0.999550i	$-0.509550\pi$
$401$	−3.10631e10	−0.0599923	−0.0299962	+	0.999550i	$0.509550\pi$
$402$	2.75075e11	0.525333
$403$	6.45955e10	0.121992
$404$	5.12095e10	0.0956388
$405$	7.72716e11	1.42716
$406$	−3.40482e11	−0.621909
$407$	−7.10356e11	−1.28322
$408$	−3.69520e11	−0.660187
$409$	−3.91510e11	−0.691812	−0.345906	−	0.938269i	$-0.612428\pi$
$409$	−3.91510e11	−0.691812	−0.345906	+	0.938269i	$0.612428\pi$
$410$	−1.34816e12	−2.35621
$411$	1.46925e12	2.53984
$412$	3.20181e11	0.547467
$413$	−1.28641e11	−0.217572
$414$	4.00374e11	0.669829
$415$	−7.35271e11	−1.21683
$416$	−8.71622e10	−0.142695
$417$	3.08224e11	0.499177
$418$	1.60098e12	2.56503
$419$	1.19235e12	1.88991	0.944956	−	0.327199i	$-0.106105\pi$
$419$	1.19235e12	1.88991	0.944956	+	0.327199i	$0.106105\pi$
$420$	1.35192e11	0.211996
$421$	6.60303e11	1.02441	0.512205	−	0.858863i	$-0.328829\pi$
$421$	6.60303e11	1.02441	0.512205	+	0.858863i	$0.328829\pi$
$422$	−2.74215e11	−0.420907
$423$	7.16307e11	1.08785
$424$	−6.87425e11	−1.03295
$425$	−2.23114e11	−0.331723
$426$	6.22881e11	0.916351
$427$	1.02821e11	0.149677
$428$	2.80778e11	0.404452
$429$	−3.83952e11	−0.547292
$430$	−1.52697e11	−0.215389
$431$	−1.03568e12	−1.44570	−0.722851	−	0.691004i	$-0.757169\pi$
$431$	−1.03568e12	−1.44570	−0.722851	+	0.691004i	$0.757169\pi$
$432$	−2.11733e11	−0.292491
$433$	2.88377e11	0.394245	0.197122	−	0.980379i	$-0.436840\pi$
$433$	2.88377e11	0.394245	0.197122	+	0.980379i	$0.436840\pi$
$434$	1.76083e11	0.238240
$435$	−1.57309e12	−2.10645
$436$	−5.27289e10	−0.0698810
$437$	7.74405e11	1.01578
$438$	−1.42298e12	−1.84742
$439$	−5.71595e11	−0.734511	−0.367255	−	0.930120i	$-0.619703\pi$
$439$	−5.71595e11	−0.734511	−0.367255	+	0.930120i	$0.619703\pi$
$440$	1.26147e12	1.60450
$441$	−5.27482e11	−0.664101
$442$	−1.40212e11	−0.174737
$443$	3.73820e11	0.461154	0.230577	−	0.973054i	$-0.425939\pi$
$443$	3.73820e11	0.461154	0.230577	+	0.973054i	$0.425939\pi$
$444$	2.56748e11	0.313533
$445$	1.30591e11	0.157867
$446$	−1.49114e12	−1.78448
$447$	4.42766e11	0.524554
$448$	2.10875e11	0.247328
$449$	1.29706e11	0.150609	0.0753046	−	0.997161i	$-0.476007\pi$
$449$	1.29706e11	0.150609	0.0753046	+	0.997161i	$0.476007\pi$
$450$	4.43096e11	0.509380
$451$	2.34387e12	2.66771
$452$	3.29216e11	0.370987
$453$	−1.58540e12	−1.76887
$454$	3.21758e11	0.355449
$455$	−1.25832e11	−0.137639
$456$	1.41942e12	1.53734
$457$	5.96816e11	0.640055	0.320028	−	0.947408i	$-0.396308\pi$
$457$	5.96816e11	0.640055	0.320028	+	0.947408i	$0.396308\pi$
$458$	−1.91057e12	−2.02893
$459$	−1.39926e11	−0.147143
$460$	−2.48750e11	−0.259032
$461$	1.57475e12	1.62389	0.811946	−	0.583732i	$-0.198408\pi$
$461$	1.57475e12	1.62389	0.811946	+	0.583732i	$0.198408\pi$
$462$	−1.04663e12	−1.06882
$463$	7.73255e11	0.782003	0.391001	−	0.920390i	$-0.372129\pi$
$463$	7.73255e11	0.782003	0.391001	+	0.920390i	$0.372129\pi$
$464$	1.51129e12	1.51362
$465$	8.13539e11	0.806937
$466$	−9.11463e11	−0.895370
$467$	−1.87433e12	−1.82356	−0.911781	−	0.410678i	$-0.865292\pi$
$467$	−1.87433e12	−1.82356	−0.911781	+	0.410678i	$0.865292\pi$
$468$	6.25327e10	0.0602560
$469$	−1.56733e11	−0.149583
$470$	−1.98175e12	−1.87330
$471$	−1.99506e12	−1.86794
$472$	4.33847e11	0.402344
$473$	2.65475e11	0.243864
$474$	7.71966e11	0.702418
$475$	8.57038e11	0.772465
$476$	−8.58324e10	−0.0766337
$477$	1.18741e12	1.05019
$478$	−9.34769e11	−0.818990
$479$	8.62964e11	0.749002	0.374501	−	0.927227i	$-0.377814\pi$
$479$	8.62964e11	0.749002	0.374501	+	0.927227i	$0.377814\pi$
$480$	−1.09775e12	−0.943883
$481$	−2.38974e11	−0.203562
$482$	−1.55470e12	−1.31200
$483$	−5.06261e11	−0.423265
$484$	5.44444e11	0.450971
$485$	1.40978e12	1.15695
$486$	1.82338e12	1.48257
$487$	−7.18536e11	−0.578853	−0.289426	−	0.957200i	$-0.593465\pi$
$487$	−7.18536e11	−0.578853	−0.289426	+	0.957200i	$0.593465\pi$
$488$	−3.46768e11	−0.276790
$489$	1.63860e12	1.29593
$490$	1.45934e12	1.14360
$491$	−1.22719e12	−0.952895	−0.476448	−	0.879203i	$-0.658076\pi$
$491$	−1.22719e12	−0.952895	−0.476448	+	0.879203i	$0.658076\pi$
$492$	−8.47158e11	−0.651811
$493$	9.98746e11	0.761454
$494$	5.38593e11	0.406901
$495$	−2.17897e12	−1.63128
$496$	−7.81575e11	−0.579834
$497$	−3.54906e11	−0.260921
$498$	−2.05741e12	−1.49896
$499$	3.33708e11	0.240943	0.120471	−	0.992717i	$-0.461559\pi$
$499$	3.33708e11	0.240943	0.120471	+	0.992717i	$0.461559\pi$
$500$	2.28091e11	0.163209
$501$	2.16661e12	1.53642
$502$	−2.67628e12	−1.88090
$503$	−1.24671e12	−0.868383	−0.434191	−	0.900821i	$-0.642966\pi$
$503$	−1.24671e12	−0.868383	−0.434191	+	0.900821i	$0.642966\pi$
$504$	−4.18136e11	−0.288656
$505$	−6.00301e11	−0.410731
$506$	1.92578e12	1.30596
$507$	1.87805e12	1.26233
$508$	1.84667e11	0.123028
$509$	−3.88143e11	−0.256308	−0.128154	−	0.991754i	$-0.540905\pi$
$509$	−3.88143e11	−0.256308	−0.128154	+	0.991754i	$0.540905\pi$
$510$	−1.76588e12	−1.15584
$511$	8.10789e11	0.526034
$512$	−4.57876e11	−0.294465
$513$	5.37492e11	0.342645
$514$	−2.89675e12	−1.83053
$515$	−3.75331e12	−2.35116
$516$	−9.59520e10	−0.0595841
$517$	3.44540e12	2.12096
$518$	−6.51427e11	−0.397541
$519$	2.16096e11	0.130735
$520$	4.24376e11	0.254528
$521$	1.21529e12	0.722623	0.361311	−	0.932445i	$-0.382329\pi$
$521$	1.21529e12	0.722623	0.361311	+	0.932445i	$0.382329\pi$
$522$	−1.98347e12	−1.16926
$523$	−1.44238e12	−0.842989	−0.421494	−	0.906831i	$-0.638494\pi$
$523$	−1.44238e12	−0.842989	−0.421494	+	0.906831i	$0.638494\pi$
$524$	6.77909e11	0.392808
$525$	−5.60282e11	−0.321877
$526$	2.21870e12	1.26375
$527$	−5.16511e11	−0.291697
$528$	4.64564e12	2.60131
$529$	−8.69642e11	−0.482825
$530$	−3.28510e12	−1.80845
$531$	−7.49396e11	−0.409059
$532$	3.29705e11	0.178453
$533$	7.88510e11	0.423190
$534$	3.65414e11	0.194469
$535$	−3.29141e12	−1.73696
$536$	5.28588e11	0.276615
$537$	1.71966e12	0.892395
$538$	2.42582e12	1.24836
$539$	−2.53716e12	−1.29479
$540$	−1.72650e11	−0.0873767
$541$	−3.07893e12	−1.54530	−0.772649	−	0.634833i	$-0.781069\pi$
$541$	−3.07893e12	−1.54530	−0.772649	+	0.634833i	$0.781069\pi$
$542$	9.01384e11	0.448656
$543$	−1.52493e12	−0.752749
$544$	6.96956e11	0.341201
$545$	6.18112e11	0.300112
$546$	−3.52100e11	−0.169551
$547$	1.19163e12	0.569112	0.284556	−	0.958659i	$-0.408154\pi$
$547$	1.19163e12	0.569112	0.284556	+	0.958659i	$0.408154\pi$
$548$	−1.15097e12	−0.545196
$549$	5.98983e11	0.281410
$550$	2.13127e12	0.993131
$551$	−3.83645e12	−1.77316
$552$	1.70739e12	0.782719
$553$	−4.39851e11	−0.200006
$554$	3.00470e12	1.35521
$555$	−3.00972e12	−1.34650
$556$	−2.41456e11	−0.107152
$557$	7.92912e11	0.349041	0.174521	−	0.984654i	$-0.444162\pi$
$557$	7.92912e11	0.349041	0.174521	+	0.984654i	$0.444162\pi$
$558$	1.02577e12	0.447917
$559$	8.93093e10	0.0386851
$560$	1.52251e12	0.654207
$561$	3.07011e12	1.30864
$562$	1.31361e12	0.555458
$563$	3.80163e12	1.59471	0.797355	−	0.603510i	$-0.206232\pi$
$563$	3.80163e12	1.59471	0.797355	+	0.603510i	$0.206232\pi$
$564$	−1.24529e12	−0.518221
$565$	−3.85922e12	−1.59324
$566$	−9.19162e11	−0.376460
$567$	−1.23197e12	−0.500585
$568$	1.19693e12	0.482506
$569$	3.02146e12	1.20840	0.604202	−	0.796831i	$-0.293492\pi$
$569$	3.02146e12	1.20840	0.604202	+	0.796831i	$0.293492\pi$
$570$	6.78322e12	2.69153
$571$	−3.94388e12	−1.55261	−0.776304	−	0.630359i	$-0.782908\pi$
$571$	−3.94388e12	−1.55261	−0.776304	+	0.630359i	$0.782908\pi$
$572$	3.00779e11	0.117480
$573$	5.62036e11	0.217805
$574$	2.14943e12	0.826456
$575$	1.03091e12	0.393292
$576$	1.22845e12	0.465004
$577$	−2.21871e12	−0.833316	−0.416658	−	0.909063i	$-0.636799\pi$
$577$	−2.21871e12	−0.833316	−0.416658	+	0.909063i	$0.636799\pi$
$578$	−1.92607e12	−0.717789
$579$	−1.43378e12	−0.530186
$580$	1.23232e12	0.452167
$581$	1.17227e12	0.426812
$582$	3.94480e12	1.42519
$583$	5.71138e12	2.04754
$584$	−2.73442e12	−0.972764
$585$	−7.33036e11	−0.258776
$586$	3.29898e12	1.15569
$587$	4.56967e12	1.58860	0.794299	−	0.607528i	$-0.207839\pi$
$587$	4.56967e12	1.58860	0.794299	+	0.607528i	$0.207839\pi$
$588$	9.17021e11	0.316360
$589$	1.98405e12	0.679258
$590$	2.07329e12	0.704411
$591$	−7.50673e12	−2.53109
$592$	2.89147e12	0.967544
$593$	1.71858e12	0.570721	0.285360	−	0.958420i	$-0.407887\pi$
$593$	1.71858e12	0.570721	0.285360	+	0.958420i	$0.407887\pi$
$594$	1.33663e12	0.440526
$595$	1.00617e12	0.329112
$596$	−3.46853e11	−0.112600
$597$	−2.09477e12	−0.674918
$598$	6.47858e11	0.207169
$599$	−2.39719e12	−0.760821	−0.380411	−	0.924818i	$-0.624217\pi$
$599$	−2.39719e12	−0.760821	−0.380411	+	0.924818i	$0.624217\pi$
$600$	1.88958e12	0.595228
$601$	−6.27025e12	−1.96042	−0.980212	−	0.197952i	$-0.936571\pi$
$601$	−6.27025e12	−1.96042	−0.980212	+	0.197952i	$0.936571\pi$
$602$	2.43452e11	0.0755490
$603$	−9.13045e11	−0.281232
$604$	1.24196e12	0.379702
$605$	−6.38222e12	−1.93675
$606$	−1.67974e12	−0.505960
$607$	−8.69259e11	−0.259896	−0.129948	−	0.991521i	$-0.541481\pi$
$607$	−8.69259e11	−0.259896	−0.129948	+	0.991521i	$0.541481\pi$
$608$	−2.67719e12	−0.794535
$609$	2.50804e12	0.738852
$610$	−1.65716e12	−0.484595
$611$	1.15908e12	0.336456
$612$	−5.00016e11	−0.144080
$613$	5.54919e12	1.58730	0.793648	−	0.608378i	$-0.208179\pi$
$613$	5.54919e12	1.58730	0.793648	+	0.608378i	$0.208179\pi$
$614$	5.35404e12	1.52028
$615$	9.93077e12	2.79927
$616$	−2.01121e12	−0.562788
$617$	−6.24966e12	−1.73609	−0.868047	−	0.496483i	$-0.834625\pi$
$617$	−6.24966e12	−1.73609	−0.868047	+	0.496483i	$0.834625\pi$
$618$	−1.05024e13	−2.89628
$619$	3.88295e11	0.106305	0.0531525	−	0.998586i	$-0.483073\pi$
$619$	3.88295e11	0.106305	0.0531525	+	0.998586i	$0.483073\pi$
$620$	−6.37308e11	−0.173215
$621$	6.46535e11	0.174453
$622$	5.50692e12	1.47520
$623$	−2.08206e11	−0.0553729
$624$	1.56286e12	0.412656
$625$	−4.75999e12	−1.24780
$626$	−2.33351e12	−0.607331
$627$	−1.17931e13	−3.04736
$628$	1.56289e12	0.400967
$629$	1.91085e12	0.486742
$630$	−1.99821e12	−0.505369
$631$	5.87460e12	1.47519	0.737593	−	0.675246i	$-0.235963\pi$
$631$	5.87460e12	1.47519	0.737593	+	0.675246i	$0.235963\pi$
$632$	1.48342e12	0.369859
$633$	2.01992e12	0.500054
$634$	2.66399e12	0.654833
$635$	−2.16475e12	−0.528355
$636$	−2.06430e12	−0.500282
$637$	−8.53537e11	−0.205397
$638$	−9.54042e12	−2.27968
$639$	−2.06750e12	−0.490559
$640$	−6.36806e12	−1.50037
$641$	2.43946e12	0.570732	0.285366	−	0.958419i	$-0.407885\pi$
$641$	2.43946e12	0.570732	0.285366	+	0.958419i	$0.407885\pi$
$642$	−9.20992e12	−2.13968
$643$	2.94870e12	0.680270	0.340135	−	0.940377i	$-0.389527\pi$
$643$	2.94870e12	0.680270	0.340135	+	0.940377i	$0.389527\pi$
$644$	3.96593e11	0.0908570
$645$	1.12479e12	0.255890
$646$	−4.30663e12	−0.972951
$647$	7.10561e12	1.59416	0.797080	−	0.603873i	$-0.206377\pi$
$647$	7.10561e12	1.59416	0.797080	+	0.603873i	$0.206377\pi$
$648$	4.15489e12	0.925703
$649$	−3.60456e12	−0.797537
$650$	7.16989e11	0.157544
$651$	−1.29706e12	−0.283038
$652$	−1.28364e12	−0.278182
$653$	−8.69658e12	−1.87171	−0.935856	−	0.352383i	$-0.885371\pi$
$653$	−8.69658e12	−1.87171	−0.935856	+	0.352383i	$0.885371\pi$
$654$	1.72958e12	0.369693
$655$	−7.94676e12	−1.68696
$656$	−9.54060e12	−2.01145
$657$	4.72324e12	0.989000
$658$	3.15959e12	0.657073
$659$	2.93734e12	0.606694	0.303347	−	0.952880i	$-0.401896\pi$
$659$	2.93734e12	0.606694	0.303347	+	0.952880i	$0.401896\pi$
$660$	3.78812e12	0.777098
$661$	−2.95321e12	−0.601711	−0.300855	−	0.953670i	$-0.597272\pi$
$661$	−2.95321e12	−0.601711	−0.300855	+	0.953670i	$0.597272\pi$
$662$	7.18345e12	1.45369
$663$	1.03283e12	0.207595
$664$	−3.95355e12	−0.789279
$665$	−3.86495e12	−0.766384
$666$	−3.79488e12	−0.747420
$667$	−4.61476e12	−0.902781
$668$	−1.69727e12	−0.329805
$669$	1.09840e13	2.12003
$670$	2.52605e12	0.484289
$671$	2.88108e12	0.548661
$672$	1.75019e12	0.331073
$673$	−2.62535e11	−0.0493309	−0.0246654	−	0.999696i	$-0.507852\pi$
$673$	−2.62535e11	−0.0493309	−0.0246654	+	0.999696i	$0.507852\pi$
$674$	−5.20735e12	−0.971958
$675$	7.15524e11	0.132665
$676$	−1.47122e12	−0.270968
$677$	2.73192e12	0.499826	0.249913	−	0.968268i	$-0.419598\pi$
$677$	2.73192e12	0.499826	0.249913	+	0.968268i	$0.419598\pi$
$678$	−1.07988e13	−1.96264
$679$	−2.24767e12	−0.405806
$680$	−3.39334e12	−0.608607
$681$	−2.37012e12	−0.422288
$682$	4.93392e12	0.873298
$683$	3.38636e12	0.595443	0.297722	−	0.954653i	$-0.403773\pi$
$683$	3.38636e12	0.595443	0.297722	+	0.954653i	$0.403773\pi$
$684$	1.92069e12	0.335510
$685$	1.34922e13	2.34140
$686$	−5.20026e12	−0.896533
$687$	1.40736e13	2.41045
$688$	−1.08060e12	−0.183873
$689$	1.92139e12	0.324809
$690$	8.15935e12	1.37036
$691$	−2.19263e12	−0.365860	−0.182930	−	0.983126i	$-0.558558\pi$
$691$	−2.19263e12	−0.365860	−0.182930	+	0.983126i	$0.558558\pi$
$692$	−1.69284e11	−0.0280633
$693$	3.47403e12	0.572181
$694$	−1.33272e11	−0.0218082
$695$	2.83046e12	0.460177
$696$	−8.45849e12	−1.36632
$697$	−6.30499e12	−1.01190
$698$	−4.41977e12	−0.704775
$699$	6.71398e12	1.06373
$700$	4.38912e11	0.0690934
$701$	1.05644e13	1.65239	0.826194	−	0.563385i	$-0.190501\pi$
$701$	1.05644e13	1.65239	0.826194	+	0.563385i	$0.190501\pi$
$702$	4.49660e11	0.0698823
$703$	−7.34008e12	−1.13345
$704$	5.90879e12	0.906612
$705$	1.45979e13	2.22556
$706$	8.79804e12	1.33280
$707$	9.57085e11	0.144067
$708$	1.30282e12	0.194865
$709$	−7.92555e12	−1.17793	−0.588967	−	0.808157i	$-0.700465\pi$
$709$	−7.92555e12	−1.17793	−0.588967	+	0.808157i	$0.700465\pi$
$710$	5.71998e12	0.844757
$711$	−2.56235e12	−0.376032
$712$	7.02185e11	0.102398
$713$	2.38657e12	0.345836
$714$	2.81542e12	0.405417
$715$	−3.52587e12	−0.504532
$716$	−1.34714e12	−0.191560
$717$	6.88566e12	0.972992
$718$	7.93358e12	1.11406
$719$	−1.29198e13	−1.80291	−0.901457	−	0.432868i	$-0.857502\pi$
$719$	−1.29198e13	−1.80291	−0.901457	+	0.432868i	$0.857502\pi$
$720$	8.86939e12	1.22998
$721$	5.98406e12	0.824683
$722$	8.25115e12	1.13005
$723$	1.14522e13	1.55871
$724$	1.19459e12	0.161583
$725$	−5.10718e12	−0.686531
$726$	−1.78585e13	−2.38578
$727$	−1.07672e12	−0.142954	−0.0714771	−	0.997442i	$-0.522771\pi$
$727$	−1.07672e12	−0.142954	−0.0714771	+	0.997442i	$0.522771\pi$
$728$	−6.76600e11	−0.0892773
$729$	−4.68115e12	−0.613873
$730$	−1.30674e13	−1.70309
$731$	−7.14124e11	−0.0925008
$732$	−1.04132e12	−0.134056
$733$	−9.75259e12	−1.24782	−0.623910	−	0.781496i	$-0.714457\pi$
$733$	−9.75259e12	−1.24782	−0.623910	+	0.781496i	$0.714457\pi$
$734$	−1.19339e13	−1.51757
$735$	−1.07497e13	−1.35864
$736$	−3.22032e12	−0.404528
$737$	−4.39170e12	−0.548314
$738$	1.25215e13	1.55383
$739$	−5.04349e12	−0.622058	−0.311029	−	0.950400i	$-0.600674\pi$
$739$	−5.04349e12	−0.622058	−0.311029	+	0.950400i	$0.600674\pi$
$740$	2.35774e12	0.289037
$741$	−3.96736e12	−0.483415
$742$	5.23758e12	0.634327
$743$	−1.18496e12	−0.142644	−0.0713220	−	0.997453i	$-0.522722\pi$
$743$	−1.18496e12	−0.142644	−0.0713220	+	0.997453i	$0.522722\pi$
$744$	4.37439e12	0.523407
$745$	4.06596e12	0.483571
$746$	−7.18464e12	−0.849337
$747$	6.82908e12	0.802452
$748$	−2.40505e12	−0.280910
$749$	5.24764e12	0.609250
$750$	−7.48170e12	−0.863425
$751$	−9.91772e12	−1.13771	−0.568856	−	0.822437i	$-0.692614\pi$
$751$	−9.91772e12	−1.13771	−0.568856	+	0.822437i	$0.692614\pi$
$752$	−1.40243e13	−1.59920
$753$	1.97139e13	2.23458
$754$	−3.20953e12	−0.361635
$755$	−1.45589e13	−1.63067
$756$	2.75264e11	0.0306479
$757$	−7.35165e12	−0.813679	−0.406840	−	0.913500i	$-0.633369\pi$
$757$	−7.35165e12	−0.813679	−0.406840	+	0.913500i	$0.633369\pi$
$758$	1.47005e13	1.61742
$759$	−1.41856e13	−1.55153
$760$	1.30347e13	1.41723
$761$	8.68715e12	0.938958	0.469479	−	0.882944i	$-0.344442\pi$
$761$	8.68715e12	0.938958	0.469479	+	0.882944i	$0.344442\pi$
$762$	−6.05734e12	−0.650855
$763$	−9.85482e11	−0.105266
$764$	−4.40286e11	−0.0467536
$765$	5.86141e12	0.618765
$766$	8.21785e12	0.862440
$767$	−1.21262e12	−0.126516
$768$	−1.04445e13	−1.08334
$769$	3.42654e12	0.353336	0.176668	−	0.984271i	$-0.443468\pi$
$769$	3.42654e12	0.353336	0.176668	+	0.984271i	$0.443468\pi$
$770$	−9.61130e12	−0.985312
$771$	2.13379e13	2.17474
$772$	1.12319e12	0.113808
$773$	1.70767e13	1.72026	0.860132	−	0.510072i	$-0.170381\pi$
$773$	1.70767e13	1.72026	0.860132	+	0.510072i	$0.170381\pi$
$774$	1.41823e12	0.142040
$775$	2.64123e12	0.262995
$776$	7.58037e12	0.750434
$777$	4.79852e12	0.472294
$778$	1.29917e13	1.27133
$779$	2.42191e13	2.35635
$780$	1.27437e12	0.123274
$781$	−9.94458e12	−0.956438
$782$	−5.18033e12	−0.495366
$783$	−3.20297e12	−0.304526
$784$	1.03274e13	0.976267
$785$	−1.83209e13	−1.72200
$786$	−2.22364e13	−2.07808
$787$	1.46085e13	1.35743	0.678717	−	0.734400i	$-0.262536\pi$
$787$	1.46085e13	1.35743	0.678717	+	0.734400i	$0.262536\pi$
$788$	5.88060e12	0.543317
$789$	−1.63433e13	−1.50139
$790$	7.08904e12	0.647539
$791$	6.15292e12	0.558840
$792$	−1.17163e13	−1.05810
$793$	9.69235e11	0.0870362
$794$	1.67456e13	1.49523
$795$	2.41986e13	2.14851
$796$	1.64099e12	0.144876
$797$	−1.27435e13	−1.11873	−0.559367	−	0.828920i	$-0.688956\pi$
$797$	−1.27435e13	−1.11873	−0.559367	+	0.828920i	$0.688956\pi$
$798$	−1.08148e13	−0.944071
$799$	−9.26811e12	−0.804508
$800$	−3.56395e12	−0.307628
$801$	−1.21290e12	−0.104107
$802$	−7.98194e11	−0.0681277
$803$	2.27186e13	1.92824
$804$	1.58732e12	0.133971
$805$	−4.64904e12	−0.390195
$806$	1.65984e12	0.138535
$807$	−1.78690e13	−1.48310
$808$	−3.22781e12	−0.266414
$809$	−1.04070e13	−0.854192	−0.427096	−	0.904206i	$-0.640463\pi$
$809$	−1.04070e13	−0.854192	−0.427096	+	0.904206i	$0.640463\pi$
$810$	1.98556e13	1.62069
$811$	−6.35388e12	−0.515757	−0.257878	−	0.966177i	$-0.583023\pi$
$811$	−6.35388e12	−0.515757	−0.257878	+	0.966177i	$0.583023\pi$
$812$	−1.96475e12	−0.158600
$813$	−6.63974e12	−0.533020
$814$	−1.82532e13	−1.45723
$815$	1.50474e13	1.19468
$816$	−1.24967e13	−0.986711
$817$	2.74314e12	0.215401
$818$	−1.00602e13	−0.785627
$819$	1.16871e12	0.0907673
$820$	−7.77954e12	−0.600885
$821$	−1.92268e13	−1.47694	−0.738472	−	0.674285i	$-0.764452\pi$
$821$	−1.92268e13	−1.47694	−0.738472	+	0.674285i	$0.764452\pi$
$822$	3.77535e13	2.88426
$823$	−2.10610e13	−1.60022	−0.800110	−	0.599854i	$-0.795226\pi$
$823$	−2.10610e13	−1.60022	−0.800110	+	0.599854i	$0.795226\pi$
$824$	−2.01815e13	−1.52504
$825$	−1.56993e13	−1.17988
$826$	−3.30554e12	−0.247077
$827$	1.34209e13	0.997713	0.498856	−	0.866685i	$-0.333754\pi$
$827$	1.34209e13	0.997713	0.498856	+	0.866685i	$0.333754\pi$
$828$	2.31035e12	0.170821
$829$	2.63393e12	0.193691	0.0968454	−	0.995299i	$-0.469125\pi$
$829$	2.63393e12	0.193691	0.0968454	+	0.995299i	$0.469125\pi$
$830$	−1.88934e13	−1.38185
$831$	−2.21331e13	−1.61004
$832$	1.98780e12	0.143819
$833$	6.82495e12	0.491130
$834$	7.92009e12	0.566869
$835$	1.98962e13	1.41638
$836$	9.23844e12	0.654140
$837$	1.65645e12	0.116658
$838$	3.06385e13	2.14620
$839$	−6.94390e11	−0.0483810	−0.0241905	−	0.999707i	$-0.507701\pi$
$839$	−6.94390e11	−0.0483810	−0.0241905	+	0.999707i	$0.507701\pi$
$840$	−8.52134e12	−0.590542
$841$	8.35464e12	0.575898
$842$	1.69671e13	1.16333
$843$	−9.67623e12	−0.659906
$844$	−1.58236e12	−0.107340
$845$	1.72463e13	1.16370
$846$	1.84061e13	1.23537
$847$	1.01754e13	0.679326
$848$	−2.32479e13	−1.54384
$849$	6.77070e12	0.447249
$850$	−5.73310e12	−0.376708
$851$	−8.82919e12	−0.577082
$852$	3.59432e12	0.233689
$853$	1.50289e13	0.971980	0.485990	−	0.873964i	$-0.338459\pi$
$853$	1.50289e13	0.971980	0.485990	+	0.873964i	$0.338459\pi$
$854$	2.64207e12	0.169975
$855$	−2.25152e13	−1.44088
$856$	−1.76979e13	−1.12665
$857$	−1.16945e13	−0.740572	−0.370286	−	0.928918i	$-0.620740\pi$
$857$	−1.16945e13	−0.740572	−0.370286	+	0.928918i	$0.620740\pi$
$858$	−9.86597e12	−0.621509
$859$	8.40566e12	0.526747	0.263374	−	0.964694i	$-0.415165\pi$
$859$	8.40566e12	0.526747	0.263374	+	0.964694i	$0.415165\pi$
$860$	−8.81137e11	−0.0549288
$861$	−1.58331e13	−0.981862
$862$	−2.66127e13	−1.64175
$863$	−9.68446e12	−0.594329	−0.297164	−	0.954826i	$-0.596041\pi$
$863$	−9.68446e12	−0.594329	−0.297164	+	0.954826i	$0.596041\pi$
$864$	−2.23513e12	−0.136456
$865$	1.98443e12	0.120521
$866$	7.41011e12	0.447707
$867$	1.41877e13	0.852761
$868$	1.01609e12	0.0607564
$869$	−1.23248e13	−0.733146
$870$	−4.04219e13	−2.39211
$871$	−1.47743e12	−0.0869812
$872$	3.32358e12	0.194662
$873$	−1.30938e13	−0.762959
$874$	1.98990e13	1.15353
$875$	4.26293e12	0.245851
$876$	−8.21130e12	−0.471133
$877$	−1.65366e13	−0.943950	−0.471975	−	0.881612i	$-0.656459\pi$
$877$	−1.65366e13	−0.943950	−0.471975	+	0.881612i	$0.656459\pi$
$878$	−1.46876e13	−0.834116
$879$	−2.43008e13	−1.37300
$880$	4.26613e13	2.39807
$881$	1.96602e13	1.09950	0.549752	−	0.835328i	$-0.314722\pi$
$881$	1.96602e13	1.09950	0.549752	+	0.835328i	$0.314722\pi$
$882$	−1.35541e13	−0.754158
$883$	8.24046e12	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$883$	8.24046e12	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$884$	−8.09093e11	−0.0445619
$885$	−1.52722e13	−0.836868
$886$	9.60563e12	0.523690
$887$	−8.83176e11	−0.0479061	−0.0239531	−	0.999713i	$-0.507625\pi$
$887$	−8.83176e11	−0.0479061	−0.0239531	+	0.999713i	$0.507625\pi$
$888$	−1.61832e13	−0.873386
$889$	3.45135e12	0.185324
$890$	3.35564e12	0.179275
$891$	−3.45203e13	−1.83495
$892$	−8.60458e12	−0.455080
$893$	3.56012e13	1.87341
$894$	1.13772e13	0.595687
$895$	1.57918e13	0.822673
$896$	1.01529e13	0.526262
$897$	−4.77223e12	−0.246125
$898$	3.33291e12	0.171033
$899$	−1.18232e13	−0.603693
$900$	2.55688e12	0.129903
$901$	−1.53636e13	−0.776659
$902$	6.02278e13	3.02948
$903$	−1.79330e12	−0.0897551
$904$	−2.07510e13	−1.03343
$905$	−1.40036e13	−0.693937
$906$	−4.07381e13	−2.00874
$907$	1.59751e13	0.783808	0.391904	−	0.920006i	$-0.371817\pi$
$907$	1.59751e13	0.783808	0.391904	+	0.920006i	$0.371817\pi$
$908$	1.85670e12	0.0906473
$909$	5.57549e12	0.270860
$910$	−3.23337e12	−0.156304
$911$	1.11506e13	0.536372	0.268186	−	0.963367i	$-0.413576\pi$
$911$	1.11506e13	0.536372	0.268186	+	0.963367i	$0.413576\pi$
$912$	4.80032e13	2.29770
$913$	3.28475e13	1.56453
$914$	1.53357e13	0.726852
$915$	1.22069e13	0.575718
$916$	−1.10249e13	−0.517422
$917$	1.26699e13	0.591711
$918$	−3.59551e12	−0.167097
$919$	1.33755e13	0.618571	0.309286	−	0.950969i	$-0.399910\pi$
$919$	1.33755e13	0.618571	0.309286	+	0.950969i	$0.399910\pi$
$920$	1.56791e13	0.721566
$921$	−3.94388e13	−1.80615
$922$	4.04646e13	1.84410
$923$	−3.34549e12	−0.151723
$924$	−6.03955e12	−0.272572
$925$	−9.77132e12	−0.438849
$926$	1.98695e13	0.888048
$927$	3.48601e13	1.55049
$928$	1.59537e13	0.706146
$929$	−1.32303e13	−0.582771	−0.291385	−	0.956606i	$-0.594116\pi$
$929$	−1.32303e13	−0.582771	−0.291385	+	0.956606i	$0.594116\pi$
$930$	2.09046e13	0.916364
$931$	−2.62164e13	−1.14367
$932$	−5.25958e12	−0.228339
$933$	−4.05648e13	−1.75260
$934$	−4.81626e13	−2.07085
$935$	2.81931e13	1.20640
$936$	−3.94153e12	−0.167851
$937$	5.43508e12	0.230344	0.115172	−	0.993346i	$-0.463258\pi$
$937$	5.43508e12	0.230344	0.115172	+	0.993346i	$0.463258\pi$
$938$	−4.02738e12	−0.169867
$939$	1.71890e13	0.721533
$940$	−1.14356e13	−0.477733
$941$	−2.47101e13	−1.02736	−0.513678	−	0.857983i	$-0.671717\pi$
$941$	−2.47101e13	−1.02736	−0.513678	+	0.857983i	$0.671717\pi$
$942$	−5.12649e13	−2.12124
$943$	2.91325e13	1.19971
$944$	1.46722e13	0.601340
$945$	−3.22677e12	−0.131621
$946$	6.82160e12	0.276934
$947$	9.17244e12	0.370604	0.185302	−	0.982682i	$-0.440674\pi$
$947$	9.17244e12	0.370604	0.185302	+	0.982682i	$0.440674\pi$
$948$	4.45462e12	0.179132
$949$	7.64284e12	0.305884
$950$	2.20223e13	0.877218
$951$	−1.96234e13	−0.777967
$952$	5.41015e12	0.213473
$953$	4.71406e13	1.85130	0.925651	−	0.378378i	$-0.123518\pi$
$953$	4.71406e13	1.85130	0.925651	+	0.378378i	$0.123518\pi$
$954$	3.05115e13	1.19260
$955$	5.16124e12	0.200788
$956$	−5.39407e12	−0.208860
$957$	7.02763e13	2.70835
$958$	2.21746e13	0.850572
$959$	−2.15112e13	−0.821262
$960$	2.50350e13	0.951322
$961$	−2.03251e13	−0.768738
$962$	−6.14063e12	−0.231167
$963$	3.05701e13	1.14546
$964$	−8.97138e12	−0.334590
$965$	−1.31665e13	−0.488763
$966$	−1.30088e13	−0.480663
$967$	1.15967e13	0.426497	0.213248	−	0.976998i	$-0.431596\pi$
$967$	1.15967e13	0.426497	0.213248	+	0.976998i	$0.431596\pi$
$968$	−3.43171e13	−1.25624
$969$	3.17233e13	1.15590
$970$	3.62255e13	1.31384
$971$	−4.97926e13	−1.79754	−0.898769	−	0.438422i	$-0.855538\pi$
$971$	−4.97926e13	−1.79754	−0.898769	+	0.438422i	$0.855538\pi$
$972$	1.05218e13	0.378087
$973$	−4.51272e12	−0.161410
$974$	−1.84634e13	−0.657350
$975$	−5.28146e12	−0.187169
$976$	−1.17273e13	−0.413688
$977$	−9.83922e12	−0.345490	−0.172745	−	0.984967i	$-0.555264\pi$
$977$	−9.83922e12	−0.345490	−0.172745	+	0.984967i	$0.555264\pi$
$978$	4.21052e13	1.47167
$979$	−5.83401e12	−0.202976
$980$	8.42110e12	0.291643
$981$	−5.74092e12	−0.197911
$982$	−3.15337e13	−1.08211
$983$	−1.58311e13	−0.540780	−0.270390	−	0.962751i	$-0.587153\pi$
$983$	−1.58311e13	−0.540780	−0.270390	+	0.962751i	$0.587153\pi$
$984$	5.33977e13	1.81570
$985$	−6.89350e13	−2.33333
$986$	2.56636e13	0.864713
$987$	−2.32740e13	−0.780628
$988$	3.10794e12	0.103769
$989$	3.29965e12	0.109669
$990$	−5.59906e13	−1.85249
$991$	−5.54691e13	−1.82692	−0.913460	−	0.406928i	$-0.866600\pi$
$991$	−5.54691e13	−1.82692	−0.913460	+	0.406928i	$0.866600\pi$
$992$	−8.25059e12	−0.270509
$993$	−5.29145e13	−1.72704
$994$	−9.11961e12	−0.296304
$995$	−1.92365e13	−0.622187
$996$	−1.18723e13	−0.382267
$997$	−2.73823e13	−0.877691	−0.438846	−	0.898562i	$-0.644613\pi$
$997$	−2.73823e13	−0.877691	−0.438846	+	0.898562i	$0.644613\pi$
$998$	8.57491e12	0.273617
$999$	−6.12808e12	−0.194661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.b.1.13	✓	17
3.2	odd	2		387.10.a.e.1.5		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.13	✓	17	1.1	even	1	trivial
387.10.a.e.1.5		17	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q+25.6959 q^{2} -189.280 q^{3} +148.278 q^{4} -1738.18 q^{5} -4863.71 q^{6} +2771.25 q^{7} -9346.16 q^{8} +16143.9 q^{9} +O(q^{10})\)	\(q+25.6959 q^{2} -189.280 q^{3} +148.278 q^{4} -1738.18 q^{5} -4863.71 q^{6} +2771.25 q^{7} -9346.16 q^{8} +16143.9 q^{9} -44664.0 q^{10} +77651.4 q^{11} -28066.0 q^{12} +26123.0 q^{13} +71209.7 q^{14} +329002. q^{15} -316076. q^{16} -208881. q^{17} +414831. q^{18} +802369. q^{19} -257733. q^{20} -524542. q^{21} +1.99532e6 q^{22} +965148. q^{23} +1.76904e6 q^{24} +1.06814e6 q^{25} +671253. q^{26} +669881. q^{27} +410914. q^{28} -4.78140e6 q^{29} +8.45399e6 q^{30} +2.47275e6 q^{31} -3.33661e6 q^{32} -1.46978e7 q^{33} -5.36739e6 q^{34} -4.81692e6 q^{35} +2.39378e6 q^{36} -9.14801e6 q^{37} +2.06176e7 q^{38} -4.94456e6 q^{39} +1.62453e7 q^{40} +3.01845e7 q^{41} -1.34786e7 q^{42} +3.41880e6 q^{43} +1.15140e7 q^{44} -2.80610e7 q^{45} +2.48003e7 q^{46} +4.43702e7 q^{47} +5.98268e7 q^{48} -3.26738e7 q^{49} +2.74467e7 q^{50} +3.95371e7 q^{51} +3.87345e6 q^{52} +7.35515e7 q^{53} +1.72132e7 q^{54} -1.34972e8 q^{55} -2.59006e7 q^{56} -1.51872e8 q^{57} -1.22862e8 q^{58} -4.64198e7 q^{59} +4.87836e7 q^{60} +3.71027e7 q^{61} +6.35394e7 q^{62} +4.47388e7 q^{63} +7.60938e7 q^{64} -4.54064e7 q^{65} -3.77674e8 q^{66} -5.65567e7 q^{67} -3.09724e7 q^{68} -1.82683e8 q^{69} -1.23775e8 q^{70} -1.28067e8 q^{71} -1.50883e8 q^{72} +2.92572e8 q^{73} -2.35066e8 q^{74} -2.02177e8 q^{75} +1.18973e8 q^{76} +2.15191e8 q^{77} -1.27055e8 q^{78} -1.58719e8 q^{79} +5.49396e8 q^{80} -4.44555e8 q^{81} +7.75618e8 q^{82} +4.23013e8 q^{83} -7.77778e7 q^{84} +3.63073e8 q^{85} +8.78491e7 q^{86} +9.05023e8 q^{87} -7.25742e8 q^{88} -7.51308e7 q^{89} -7.21051e8 q^{90} +7.23934e7 q^{91} +1.43110e8 q^{92} -4.68041e8 q^{93} +1.14013e9 q^{94} -1.39466e9 q^{95} +6.31553e8 q^{96} -8.11068e8 q^{97} -8.39581e8 q^{98} +1.25360e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9} + 23763 q^{10} + 78370 q^{11} + 271339 q^{12} + 114452 q^{13} - 376208 q^{14} - 255820 q^{15} + 412586 q^{16} + 726937 q^{17} + 577055 q^{18} + 544263 q^{19} + 3642183 q^{20} + 3137394 q^{21} + 5269148 q^{22} + 5575241 q^{23} + 16215113 q^{24} + 10874708 q^{25} + 8009180 q^{26} + 8350126 q^{27} + 12534764 q^{28} + 8223345 q^{29} + 30612012 q^{30} + 13054147 q^{31} + 37111710 q^{32} + 36024808 q^{33} + 27991291 q^{34} + 17826330 q^{35} + 84105953 q^{36} + 46733879 q^{37} + 15733789 q^{38} + 8689898 q^{39} + 52241669 q^{40} + 53667013 q^{41} + 7708286 q^{42} + 58119617 q^{43} + 81727236 q^{44} + 124361968 q^{45} + 146859355 q^{46} + 122945511 q^{47} + 86356095 q^{48} + 111396073 q^{49} - 96642133 q^{50} - 187132423 q^{51} - 54447944 q^{52} - 993146 q^{53} - 219468490 q^{54} - 248155792 q^{55} - 141048116 q^{56} - 402917960 q^{57} - 466599837 q^{58} - 95519644 q^{59} - 621611940 q^{60} - 311752038 q^{61} - 212471691 q^{62} - 928966350 q^{63} - 829842590 q^{64} - 107969830 q^{65} - 978530932 q^{66} - 292438130 q^{67} - 88281129 q^{68} + 78577726 q^{69} - 1650972530 q^{70} - 13576908 q^{71} - 706943493 q^{72} - 501490738 q^{73} - 494831691 q^{74} - 641914030 q^{75} - 1248630771 q^{76} + 787365348 q^{77} - 946670550 q^{78} + 740350275 q^{79} - 27802861 q^{80} + 1582210525 q^{81} - 1600400057 q^{82} + 754109940 q^{83} - 1955423842 q^{84} + 1071609956 q^{85} + 164102448 q^{86} + 186301257 q^{87} + 1863375104 q^{88} + 1470581868 q^{89} - 698098630 q^{90} + 2895349644 q^{91} + 1041082071 q^{92} + 4540331515 q^{93} - 706582361 q^{94} + 3297255729 q^{95} + 2087289393 q^{96} + 1949310583 q^{97} + 6695989160 q^{98} + 1234191326 q^{99}+O(q^{100}) \) 17 * q + 48 * q^2 + 169 * q^3 + 4522 * q^4 + 4033 * q^5 + 5871 * q^6 - 76 * q^7 + 41046 * q^8 + 135126 * q^9 + 23763 * q^10 + 78370 * q^11 + 271339 * q^12 + 114452 * q^13 - 376208 * q^14 - 255820 * q^15 + 412586 * q^16 + 726937 * q^17 + 577055 * q^18 + 544263 * q^19 + 3642183 * q^20 + 3137394 * q^21 + 5269148 * q^22 + 5575241 * q^23 + 16215113 * q^24 + 10874708 * q^25 + 8009180 * q^26 + 8350126 * q^27 + 12534764 * q^28 + 8223345 * q^29 + 30612012 * q^30 + 13054147 * q^31 + 37111710 * q^32 + 36024808 * q^33 + 27991291 * q^34 + 17826330 * q^35 + 84105953 * q^36 + 46733879 * q^37 + 15733789 * q^38 + 8689898 * q^39 + 52241669 * q^40 + 53667013 * q^41 + 7708286 * q^42 + 58119617 * q^43 + 81727236 * q^44 + 124361968 * q^45 + 146859355 * q^46 + 122945511 * q^47 + 86356095 * q^48 + 111396073 * q^49 - 96642133 * q^50 - 187132423 * q^51 - 54447944 * q^52 - 993146 * q^53 - 219468490 * q^54 - 248155792 * q^55 - 141048116 * q^56 - 402917960 * q^57 - 466599837 * q^58 - 95519644 * q^59 - 621611940 * q^60 - 311752038 * q^61 - 212471691 * q^62 - 928966350 * q^63 - 829842590 * q^64 - 107969830 * q^65 - 978530932 * q^66 - 292438130 * q^67 - 88281129 * q^68 + 78577726 * q^69 - 1650972530 * q^70 - 13576908 * q^71 - 706943493 * q^72 - 501490738 * q^73 - 494831691 * q^74 - 641914030 * q^75 - 1248630771 * q^76 + 787365348 * q^77 - 946670550 * q^78 + 740350275 * q^79 - 27802861 * q^80 + 1582210525 * q^81 - 1600400057 * q^82 + 754109940 * q^83 - 1955423842 * q^84 + 1071609956 * q^85 + 164102448 * q^86 + 186301257 * q^87 + 1863375104 * q^88 + 1470581868 * q^89 - 698098630 * q^90 + 2895349644 * q^91 + 1041082071 * q^92 + 4540331515 * q^93 - 706582361 * q^94 + 3297255729 * q^95 + 2087289393 * q^96 + 1949310583 * q^97 + 6695989160 * q^98 + 1234191326 * q^99

Introduction

L-functions

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