LMFDB - Embedded newform 43.10.a.b.1.1

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			1.1
Root			$40.5953$ 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)

$f(q)$	$=$	$q-37.5953 q^{2} -105.944 q^{3} +901.404 q^{4} -205.302 q^{5} +3983.01 q^{6} +7435.13 q^{7} -14639.7 q^{8} -8458.78 q^{9} +O(q^{10})$	\(q-37.5953 q^{2} -105.944 q^{3} +901.404 q^{4} -205.302 q^{5} +3983.01 q^{6} +7435.13 q^{7} -14639.7 q^{8} -8458.78 q^{9} +7718.39 q^{10} +30246.9 q^{11} -95498.7 q^{12} -147839. q^{13} -279526. q^{14} +21750.6 q^{15} +88865.7 q^{16} -141391. q^{17} +318010. q^{18} -297987. q^{19} -185060. q^{20} -787711. q^{21} -1.13714e6 q^{22} +1.01694e6 q^{23} +1.55100e6 q^{24} -1.91098e6 q^{25} +5.55805e6 q^{26} +2.98146e6 q^{27} +6.70205e6 q^{28} +3.61847e6 q^{29} -817721. q^{30} +287505. q^{31} +4.15461e6 q^{32} -3.20449e6 q^{33} +5.31565e6 q^{34} -1.52645e6 q^{35} -7.62477e6 q^{36} -7.45525e6 q^{37} +1.12029e7 q^{38} +1.56627e7 q^{39} +3.00557e6 q^{40} -1.37565e7 q^{41} +2.96142e7 q^{42} +3.41880e6 q^{43} +2.72646e7 q^{44} +1.73661e6 q^{45} -3.82323e7 q^{46} +2.60924e7 q^{47} -9.41483e6 q^{48} +1.49275e7 q^{49} +7.18436e7 q^{50} +1.49796e7 q^{51} -1.33263e8 q^{52} -4.82445e6 q^{53} -1.12089e8 q^{54} -6.20975e6 q^{55} -1.08848e8 q^{56} +3.15701e7 q^{57} -1.36037e8 q^{58} +1.03849e8 q^{59} +1.96061e7 q^{60} -1.20615e8 q^{61} -1.08088e7 q^{62} -6.28921e7 q^{63} -2.01693e8 q^{64} +3.03517e7 q^{65} +1.20473e8 q^{66} +2.55811e8 q^{67} -1.27451e8 q^{68} -1.07740e8 q^{69} +5.73873e7 q^{70} +3.21080e7 q^{71} +1.23834e8 q^{72} +2.71959e8 q^{73} +2.80282e8 q^{74} +2.02457e8 q^{75} -2.68607e8 q^{76} +2.24889e8 q^{77} -5.88844e8 q^{78} +4.52387e8 q^{79} -1.82443e7 q^{80} -1.49376e8 q^{81} +5.17179e8 q^{82} +2.25247e8 q^{83} -7.10045e8 q^{84} +2.90280e7 q^{85} -1.28531e8 q^{86} -3.83357e8 q^{87} -4.42806e8 q^{88} -7.81736e7 q^{89} -6.52882e7 q^{90} -1.09920e9 q^{91} +9.16677e8 q^{92} -3.04595e7 q^{93} -9.80951e8 q^{94} +6.11775e7 q^{95} -4.40158e8 q^{96} +1.42865e9 q^{97} -5.61205e8 q^{98} -2.55851e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−37.5953	−1.66149	−0.830746	−	0.556652i	$-0.812086\pi$
$2$	−37.5953	−1.66149	−0.830746	+	0.556652i	$0.812086\pi$
$3$	−105.944	−0.755149	−0.377574	−	0.925979i	$-0.623242\pi$
$3$	−105.944	−0.755149	−0.377574	+	0.925979i	$0.623242\pi$
$4$	901.404	1.76055
$5$	−205.302	−0.146902	−0.0734512	−	0.997299i	$-0.523401\pi$
$5$	−205.302	−0.146902	−0.0734512	+	0.997299i	$0.523401\pi$
$6$	3983.01	1.25467
$7$	7435.13	1.17044	0.585218	−	0.810876i	$-0.301009\pi$
$7$	7435.13	1.17044	0.585218	+	0.810876i	$0.301009\pi$
$8$	−14639.7	−1.26365
$9$	−8458.78	−0.429750
$10$	7718.39	0.244077
$11$	30246.9	0.622893	0.311446	−	0.950264i	$-0.399187\pi$
$11$	30246.9	0.622893	0.311446	+	0.950264i	$0.399187\pi$
$12$	−95498.7	−1.32948
$13$	−147839.	−1.43564	−0.717818	−	0.696231i	$-0.754859\pi$
$13$	−147839.	−1.43564	−0.717818	+	0.696231i	$0.754859\pi$
$14$	−279526.	−1.94467
$15$	21750.6	0.110933
$16$	88865.7	0.338996
$17$	−141391.	−0.410585	−0.205292	−	0.978701i	$-0.565815\pi$
$17$	−141391.	−0.410585	−0.205292	+	0.978701i	$0.565815\pi$
$18$	318010.	0.714026
$19$	−297987.	−0.524574	−0.262287	−	0.964990i	$-0.584477\pi$
$19$	−297987.	−0.524574	−0.262287	+	0.964990i	$0.584477\pi$
$20$	−185060.	−0.258630
$21$	−787711.	−0.883853
$22$	−1.13714e6	−1.03493
$23$	1.01694e6	0.757743	0.378872	−	0.925449i	$-0.376312\pi$
$23$	1.01694e6	0.757743	0.378872	+	0.925449i	$0.376312\pi$
$24$	1.55100e6	0.954246
$25$	−1.91098e6	−0.978420
$26$	5.55805e6	2.38530
$27$	2.98146e6	1.07967
$28$	6.70205e6	2.06061
$29$	3.61847e6	0.950023	0.475011	−	0.879980i	$-0.342444\pi$
$29$	3.61847e6	0.950023	0.475011	+	0.879980i	$0.342444\pi$
$30$	−817721.	−0.184315
$31$	287505.	0.0559136	0.0279568	−	0.999609i	$-0.491100\pi$
$31$	287505.	0.0559136	0.0279568	+	0.999609i	$0.491100\pi$
$32$	4.15461e6	0.700415
$33$	−3.20449e6	−0.470377
$34$	5.31565e6	0.682183
$35$	−1.52645e6	−0.171940
$36$	−7.62477e6	−0.756599
$37$	−7.45525e6	−0.653965	−0.326982	−	0.945030i	$-0.606032\pi$
$37$	−7.45525e6	−0.653965	−0.326982	+	0.945030i	$0.606032\pi$
$38$	1.12029e7	0.871575
$39$	1.56627e7	1.08412
$40$	3.00557e6	0.185634
$41$	−1.37565e7	−0.760292	−0.380146	−	0.924927i	$-0.624126\pi$
$41$	−1.37565e7	−0.760292	−0.380146	+	0.924927i	$0.624126\pi$
$42$	2.96142e7	1.46851
$43$	3.41880e6	0.152499
$43$	3.41880e6	0.152499
$44$	2.72646e7	1.09664
$45$	1.73661e6	0.0631314
$46$	−3.82323e7	−1.25898
$47$	2.60924e7	0.779963	0.389981	−	0.920823i	$-0.372481\pi$
$47$	2.60924e7	0.779963	0.389981	+	0.920823i	$0.372481\pi$
$48$	−9.41483e6	−0.255992
$49$	1.49275e7	0.369918
$50$	7.18436e7	1.62564
$51$	1.49796e7	0.310053
$52$	−1.33263e8	−2.52751
$53$	−4.82445e6	−0.0839859	−0.0419930	−	0.999118i	$-0.513371\pi$
$53$	−4.82445e6	−0.0839859	−0.0419930	+	0.999118i	$0.513371\pi$
$54$	−1.12089e8	−1.79387
$55$	−6.20975e6	−0.0915044
$56$	−1.08848e8	−1.47902
$57$	3.15701e7	0.396131
$58$	−1.36037e8	−1.57845
$59$	1.03849e8	1.11576	0.557878	−	0.829923i	$-0.311616\pi$
$59$	1.03849e8	1.11576	0.557878	+	0.829923i	$0.311616\pi$
$60$	1.96061e7	0.195304
$61$	−1.20615e8	−1.11536	−0.557681	−	0.830055i	$-0.688309\pi$
$61$	−1.20615e8	−1.11536	−0.557681	+	0.830055i	$0.688309\pi$
$62$	−1.08088e7	−0.0928999
$63$	−6.28921e7	−0.502995
$64$	−2.01693e8	−1.50273
$65$	3.03517e7	0.210898
$66$	1.20473e8	0.781527
$67$	2.55811e8	1.55090	0.775449	−	0.631410i	$-0.217523\pi$
$67$	2.55811e8	1.55090	0.775449	+	0.631410i	$0.217523\pi$
$68$	−1.27451e8	−0.722857
$69$	−1.07740e8	−0.572209
$70$	5.73873e7	0.285676
$71$	3.21080e7	0.149951	0.0749757	−	0.997185i	$-0.476112\pi$
$71$	3.21080e7	0.149951	0.0749757	+	0.997185i	$0.476112\pi$
$72$	1.23834e8	0.543056
$73$	2.71959e8	1.12086	0.560430	−	0.828202i	$-0.310636\pi$
$73$	2.71959e8	1.12086	0.560430	+	0.828202i	$0.310636\pi$
$74$	2.80282e8	1.08656
$75$	2.02457e8	0.738852
$76$	−2.68607e8	−0.923540
$77$	2.24889e8	0.729055
$78$	−5.88844e8	−1.80125
$79$	4.52387e8	1.30674	0.653368	−	0.757041i	$-0.273356\pi$
$79$	4.52387e8	1.30674	0.653368	+	0.757041i	$0.273356\pi$
$80$	−1.82443e7	−0.0497993
$81$	−1.49376e8	−0.385564
$82$	5.17179e8	1.26322
$83$	2.25247e8	0.520963	0.260482	−	0.965479i	$-0.416119\pi$
$83$	2.25247e8	0.520963	0.260482	+	0.965479i	$0.416119\pi$
$84$	−7.10045e8	−1.55607
$85$	2.90280e7	0.0603159
$86$	−1.28531e8	−0.253375
$87$	−3.83357e8	−0.717409
$88$	−4.42806e8	−0.787120
$89$	−7.81736e7	−0.132070	−0.0660351	−	0.997817i	$-0.521035\pi$
$89$	−7.81736e7	−0.132070	−0.0660351	+	0.997817i	$0.521035\pi$
$90$	−6.52882e7	−0.104892
$91$	−1.09920e9	−1.68032
$92$	9.16677e8	1.33405
$93$	−3.04595e7	−0.0422231
$94$	−9.80951e8	−1.29590
$95$	6.11775e7	0.0770611
$96$	−4.40158e8	−0.528917
$97$	1.42865e9	1.63853	0.819264	−	0.573416i	$-0.194382\pi$
$97$	1.42865e9	1.63853	0.819264	+	0.573416i	$0.194382\pi$
$98$	−5.61205e8	−0.614616
$99$	−2.55851e8	−0.267688
$100$	−1.72256e9	−1.72256
$101$	1.49225e9	1.42690	0.713452	−	0.700704i	$-0.247131\pi$
$101$	1.49225e9	1.42690	0.713452	+	0.700704i	$0.247131\pi$
$102$	−5.63163e8	−0.515150
$103$	1.55520e9	1.36151	0.680754	−	0.732513i	$-0.261652\pi$
$103$	1.55520e9	1.36151	0.680754	+	0.732513i	$0.261652\pi$
$104$	2.16432e9	1.81415
$105$	1.61719e8	0.129840
$106$	1.81377e8	0.139542
$107$	1.02284e9	0.754361	0.377181	−	0.926140i	$-0.376894\pi$
$107$	1.02284e9	0.754361	0.377181	+	0.926140i	$0.376894\pi$
$108$	2.68750e9	1.90082
$109$	−2.01983e8	−0.137055	−0.0685275	−	0.997649i	$-0.521830\pi$
$109$	−2.01983e8	−0.137055	−0.0685275	+	0.997649i	$0.521830\pi$
$110$	2.33457e8	0.152034
$111$	7.89842e8	0.493841
$112$	6.60728e8	0.396773
$113$	−2.14053e9	−1.23501	−0.617503	−	0.786569i	$-0.711856\pi$
$113$	−2.14053e9	−1.23501	−0.617503	+	0.786569i	$0.711856\pi$
$114$	−1.18689e9	−0.658169
$115$	−2.08781e8	−0.111314
$116$	3.26170e9	1.67257
$117$	1.25054e9	0.616965
$118$	−3.90424e9	−1.85382
$119$	−1.05126e9	−0.480563
$120$	−3.18423e8	−0.140181
$121$	−1.44308e9	−0.612005
$122$	4.53454e9	1.85316
$123$	1.45742e9	0.574133
$124$	2.59158e8	0.0984388
$125$	7.93309e8	0.290635
$126$	2.36444e9	0.835722
$127$	−3.05275e9	−1.04130	−0.520649	−	0.853771i	$-0.674310\pi$
$127$	−3.05275e9	−1.04130	−0.520649	+	0.853771i	$0.674310\pi$
$128$	5.45554e9	1.79636
$129$	−3.62203e8	−0.115159
$130$	−1.14108e9	−0.350406
$131$	−3.33156e8	−0.0988386	−0.0494193	−	0.998778i	$-0.515737\pi$
$131$	−3.33156e8	−0.0988386	−0.0494193	+	0.998778i	$0.515737\pi$
$132$	−2.88854e9	−0.828123
$133$	−2.21557e9	−0.613980
$134$	−9.61730e9	−2.57680
$135$	−6.12102e8	−0.158607
$136$	2.06993e9	0.518837
$137$	−1.70389e9	−0.413238	−0.206619	−	0.978422i	$-0.566246\pi$
$137$	−1.70389e9	−0.413238	−0.206619	+	0.978422i	$0.566246\pi$
$138$	4.05050e9	0.950720
$139$	−2.83716e8	−0.0644641	−0.0322320	−	0.999480i	$-0.510262\pi$
$139$	−2.83716e8	−0.0644641	−0.0322320	+	0.999480i	$0.510262\pi$
$140$	−1.37595e9	−0.302709
$141$	−2.76435e9	−0.588988
$142$	−1.20711e9	−0.249143
$143$	−4.47167e9	−0.894247
$144$	−7.51695e8	−0.145684
$145$	−7.42881e8	−0.139561
$146$	−1.02244e10	−1.86230
$147$	−1.58149e9	−0.279343
$148$	−6.72019e9	−1.15134
$149$	9.39868e9	1.56217	0.781086	−	0.624424i	$-0.214666\pi$
$149$	9.39868e9	1.56217	0.781086	+	0.624424i	$0.214666\pi$
$150$	−7.61143e9	−1.22760
$151$	−4.46677e9	−0.699193	−0.349597	−	0.936900i	$-0.613681\pi$
$151$	−4.46677e9	−0.699193	−0.349597	+	0.936900i	$0.613681\pi$
$152$	4.36245e9	0.662880
$153$	1.19600e9	0.176449
$154$	−8.45477e9	−1.21132
$155$	−5.90254e7	−0.00821384
$156$	1.41184e10	1.90865
$157$	9.18696e9	1.20677	0.603383	−	0.797451i	$-0.293819\pi$
$157$	9.18696e9	1.20677	0.603383	+	0.797451i	$0.293819\pi$
$158$	−1.70076e10	−2.17113
$159$	5.11124e8	0.0634219
$160$	−8.52951e8	−0.102893
$161$	7.56111e9	0.886889
$162$	5.61581e9	0.640612
$163$	1.88421e8	0.0209067	0.0104533	−	0.999945i	$-0.496673\pi$
$163$	1.88421e8	0.0209067	0.0104533	+	0.999945i	$0.496673\pi$
$164$	−1.24001e10	−1.33853
$165$	6.57889e8	0.0690994
$166$	−8.46821e9	−0.865576
$167$	3.71215e9	0.369319	0.184659	−	0.982803i	$-0.440882\pi$
$167$	3.71215e9	0.369319	0.184659	+	0.982803i	$0.440882\pi$
$168$	1.15319e10	1.11688
$169$	1.12519e10	1.06105
$170$	−1.09131e9	−0.100214
$171$	2.52061e9	0.225436
$172$	3.08172e9	0.268482
$173$	1.36778e10	1.16094	0.580468	−	0.814283i	$-0.302870\pi$
$173$	1.36778e10	1.16094	0.580468	+	0.814283i	$0.302870\pi$
$174$	1.44124e10	1.19197
$175$	−1.42084e10	−1.14518
$176$	2.68791e9	0.211158
$177$	−1.10023e10	−0.842563
$178$	2.93896e9	0.219434
$179$	−747875.	−5.44490e−5 0	−2.72245e−5	−	1.00000i	$-0.500009\pi$
$179$	−747875.	−5.44490e−5 0	−2.72245e−5		1.00000i	$0.500009\pi$
$180$	1.56538e9	0.111146
$181$	−8.19784e9	−0.567736	−0.283868	−	0.958863i	$-0.591618\pi$
$181$	−8.19784e9	−0.567736	−0.283868	+	0.958863i	$0.591618\pi$
$182$	4.13248e10	2.79183
$183$	1.27784e10	0.842264
$184$	−1.48878e10	−0.957525
$185$	1.53058e9	0.0960690
$186$	1.14513e9	0.0701532
$187$	−4.27665e9	−0.255750
$188$	2.35198e10	1.37317
$189$	2.21676e10	1.26369
$190$	−2.29998e9	−0.128036
$191$	2.11368e10	1.14918	0.574592	−	0.818440i	$-0.305161\pi$
$191$	2.11368e10	1.14918	0.574592	+	0.818440i	$0.305161\pi$
$192$	2.13682e10	1.13478
$193$	2.16539e10	1.12339	0.561693	−	0.827346i	$-0.310150\pi$
$193$	2.16539e10	1.12339	0.561693	+	0.827346i	$0.310150\pi$
$194$	−5.37106e10	−2.72240
$195$	−3.21560e9	−0.159260
$196$	1.34557e10	0.651261
$197$	1.03360e10	0.488937	0.244469	−	0.969657i	$-0.421386\pi$
$197$	1.03360e10	0.488937	0.244469	+	0.969657i	$0.421386\pi$
$198$	9.61880e9	0.444762
$199$	−1.13167e10	−0.511541	−0.255770	−	0.966738i	$-0.582329\pi$
$199$	−1.13167e10	−0.511541	−0.255770	+	0.966738i	$0.582329\pi$
$200$	2.79762e10	1.23638
$201$	−2.71018e10	−1.17116
$202$	−5.61014e10	−2.37079
$203$	2.69038e10	1.11194
$204$	1.35027e10	0.545864
$205$	2.82424e9	0.111689
$206$	−5.84683e10	−2.26213
$207$	−8.60211e9	−0.325640
$208$	−1.31378e10	−0.486675
$209$	−9.01318e9	−0.326753
$210$	−6.07986e9	−0.215728
$211$	−5.27721e10	−1.83288	−0.916438	−	0.400177i	$-0.868949\pi$
$211$	−5.27721e10	−1.83288	−0.916438	+	0.400177i	$0.868949\pi$
$212$	−4.34878e9	−0.147862
$213$	−3.40166e9	−0.113236
$214$	−3.84538e10	−1.25336
$215$	−7.01888e8	−0.0224024
$216$	−4.36478e10	−1.36433
$217$	2.13763e9	0.0654432
$218$	7.59360e9	0.227716
$219$	−2.88126e10	−0.846415
$220$	−5.59749e9	−0.161098
$221$	2.09032e10	0.589450
$222$	−2.96943e10	−0.820512
$223$	6.42441e10	1.73965	0.869824	−	0.493362i	$-0.164232\pi$
$223$	6.42441e10	1.73965	0.869824	+	0.493362i	$0.164232\pi$
$224$	3.08901e10	0.819790
$225$	1.61645e10	0.420476
$226$	8.04739e10	2.05195
$227$	5.86771e10	1.46674	0.733369	−	0.679831i	$-0.237947\pi$
$227$	5.86771e10	1.46674	0.733369	+	0.679831i	$0.237947\pi$
$228$	2.84574e10	0.697410
$229$	−7.08361e10	−1.70214	−0.851070	−	0.525053i	$-0.824046\pi$
$229$	−7.08361e10	−1.70214	−0.851070	+	0.525053i	$0.824046\pi$
$230$	7.84918e9	0.184948
$231$	−2.38258e10	−0.550545
$232$	−5.29734e10	−1.20050
$233$	5.80001e10	1.28922	0.644610	−	0.764512i	$-0.277020\pi$
$233$	5.80001e10	1.28922	0.644610	+	0.764512i	$0.277020\pi$
$234$	−4.70143e10	−1.02508
$235$	−5.35683e9	−0.114578
$236$	9.36101e10	1.96435
$237$	−4.79278e10	−0.986780
$238$	3.95225e10	0.798451
$239$	−6.10507e10	−1.21032	−0.605159	−	0.796104i	$-0.706891\pi$
$239$	−6.10507e10	−1.21032	−0.605159	+	0.796104i	$0.706891\pi$
$240$	1.93289e9	0.0376059
$241$	6.36098e10	1.21464	0.607320	−	0.794458i	$-0.292245\pi$
$241$	6.36098e10	1.21464	0.607320	+	0.794458i	$0.292245\pi$
$242$	5.42528e10	1.01684
$243$	−4.28587e10	−0.788516
$244$	−1.08722e11	−1.96365
$245$	−3.06466e9	−0.0543419
$246$	−5.47922e10	−0.953918
$247$	4.40542e10	0.753097
$248$	−4.20899e9	−0.0706554
$249$	−2.38636e10	−0.393405
$250$	−2.98247e10	−0.482887
$251$	6.19985e10	0.985938	0.492969	−	0.870047i	$-0.335912\pi$
$251$	6.19985e10	0.985938	0.492969	+	0.870047i	$0.335912\pi$
$252$	−5.66912e10	−0.885550
$253$	3.07594e10	0.471993
$254$	1.14769e11	1.73011
$255$	−3.07535e9	−0.0455475
$256$	−1.01836e11	−1.48190
$257$	−1.30416e11	−1.86480	−0.932402	−	0.361423i	$-0.882291\pi$
$257$	−1.30416e11	−1.86480	−0.932402	+	0.361423i	$0.882291\pi$
$258$	1.36171e10	0.191336
$259$	−5.54308e10	−0.765424
$260$	2.73591e10	0.371298
$261$	−3.06078e10	−0.408273
$262$	1.25251e10	0.164219
$263$	−9.79046e10	−1.26183	−0.630917	−	0.775850i	$-0.717321\pi$
$263$	−9.79046e10	−1.26183	−0.630917	+	0.775850i	$0.717321\pi$
$264$	4.69128e10	0.594393
$265$	9.90471e8	0.0123377
$266$	8.32951e10	1.02012
$267$	8.28205e9	0.0997327
$268$	2.30589e11	2.73044
$269$	5.69781e9	0.0663472	0.0331736	−	0.999450i	$-0.489439\pi$
$269$	5.69781e9	0.0663472	0.0331736	+	0.999450i	$0.489439\pi$
$270$	2.30121e10	0.263524
$271$	−8.31043e10	−0.935970	−0.467985	−	0.883736i	$-0.655020\pi$
$271$	−8.31043e10	−0.935970	−0.467985	+	0.883736i	$0.655020\pi$
$272$	−1.25649e10	−0.139187
$273$	1.16454e11	1.26889
$274$	6.40583e10	0.686591
$275$	−5.78010e10	−0.609450
$276$	−9.71169e10	−1.00740
$277$	−1.00062e11	−1.02120	−0.510599	−	0.859819i	$-0.670577\pi$
$277$	−1.00062e11	−1.02120	−0.510599	+	0.859819i	$0.670577\pi$
$278$	1.06664e10	0.107106
$279$	−2.43194e9	−0.0240289
$280$	2.23468e10	0.217272
$281$	−1.58185e11	−1.51351	−0.756757	−	0.653696i	$-0.773218\pi$
$281$	−1.58185e11	−1.51351	−0.756757	+	0.653696i	$0.773218\pi$
$282$	1.03926e11	0.978598
$283$	1.60571e11	1.48809	0.744044	−	0.668131i	$-0.232905\pi$
$283$	1.60571e11	1.48809	0.744044	+	0.668131i	$0.232905\pi$
$284$	2.89423e10	0.263998
$285$	−6.48142e9	−0.0581926
$286$	1.68114e11	1.48578
$287$	−1.02281e11	−0.889872
$288$	−3.51429e10	−0.301004
$289$	−9.85963e10	−0.831420
$290$	2.79288e10	0.231879
$291$	−1.51358e11	−1.23733
$292$	2.45145e11	1.97333
$293$	4.09516e10	0.324613	0.162307	−	0.986740i	$-0.448107\pi$
$293$	4.09516e10	0.324613	0.162307	+	0.986740i	$0.448107\pi$
$294$	5.94565e10	0.464127
$295$	−2.13205e10	−0.163907
$296$	1.09143e11	0.826385
$297$	9.01799e10	0.672521
$298$	−3.53346e11	−2.59553
$299$	−1.50344e11	−1.08784
$300$	1.82496e11	1.30079
$301$	2.54192e10	0.178490
$302$	1.67929e11	1.16170
$303$	−1.58095e11	−1.07752
$304$	−2.64809e10	−0.177828
$305$	2.47625e10	0.163849
$306$	−4.49639e10	−0.293168
$307$	1.75403e11	1.12697	0.563487	−	0.826125i	$-0.309460\pi$
$307$	1.75403e11	1.12697	0.563487	+	0.826125i	$0.309460\pi$
$308$	2.02716e11	1.28354
$309$	−1.64765e11	−1.02814
$310$	2.21907e9	0.0136472
$311$	−1.24919e11	−0.757196	−0.378598	−	0.925561i	$-0.623594\pi$
$311$	−1.24919e11	−0.757196	−0.378598	+	0.925561i	$0.623594\pi$
$312$	−2.29298e11	−1.36995
$313$	8.33656e10	0.490950	0.245475	−	0.969403i	$-0.421056\pi$
$313$	8.33656e10	0.490950	0.245475	+	0.969403i	$0.421056\pi$
$314$	−3.45386e11	−2.00503
$315$	1.29119e10	0.0738912
$316$	4.07783e11	2.30058
$317$	2.99907e10	0.166809	0.0834047	−	0.996516i	$-0.473421\pi$
$317$	2.99907e10	0.166809	0.0834047	+	0.996516i	$0.473421\pi$
$318$	−1.92158e10	−0.105375
$319$	1.09447e11	0.591762
$320$	4.14080e10	0.220755
$321$	−1.08364e11	−0.569655
$322$	−2.84262e11	−1.47356
$323$	4.21328e10	0.215382
$324$	−1.34648e11	−0.678807
$325$	2.82517e11	1.40465
$326$	−7.08373e9	−0.0347362
$327$	2.13990e10	0.103497
$328$	2.01391e11	0.960745
$329$	1.94000e11	0.912896
$330$	−2.47335e10	−0.114808
$331$	4.17144e11	1.91012	0.955059	−	0.296417i	$-0.0957919\pi$
$331$	4.17144e11	1.91012	0.955059	+	0.296417i	$0.0957919\pi$
$332$	2.03038e11	0.917184
$333$	6.30623e10	0.281042
$334$	−1.39559e11	−0.613620
$335$	−5.25187e10	−0.227831
$336$	−7.00005e10	−0.299622
$337$	3.40845e11	1.43954	0.719768	−	0.694215i	$-0.244248\pi$
$337$	3.40845e11	1.43954	0.719768	+	0.694215i	$0.244248\pi$
$338$	−4.23018e11	−1.76292
$339$	2.26778e11	0.932613
$340$	2.61659e10	0.106189
$341$	8.69611e9	0.0348281
$342$	−9.47629e10	−0.374560
$343$	−1.89046e11	−0.737470
$344$	−5.00503e10	−0.192705
$345$	2.21192e10	0.0840588
$346$	−5.14220e11	−1.92889
$347$	−8.95748e10	−0.331668	−0.165834	−	0.986154i	$-0.553032\pi$
$347$	−8.95748e10	−0.331668	−0.165834	+	0.986154i	$0.553032\pi$
$348$	−3.45559e11	−1.26304
$349$	−8.79678e10	−0.317402	−0.158701	−	0.987327i	$-0.550731\pi$
$349$	−8.79678e10	−0.317402	−0.158701	+	0.987327i	$0.550731\pi$
$350$	5.34167e11	1.90270
$351$	−4.40777e11	−1.55002
$352$	1.25664e11	0.436283
$353$	−2.35915e10	−0.0808665	−0.0404333	−	0.999182i	$-0.512874\pi$
$353$	−2.35915e10	−0.0808665	−0.0404333	+	0.999182i	$0.512874\pi$
$354$	4.13633e11	1.39991
$355$	−6.59185e9	−0.0220282
$356$	−7.04659e10	−0.232517
$357$	1.11376e11	0.362897
$358$	2.81165e7	9.04666e−5 0
$359$	4.74628e11	1.50809	0.754046	−	0.656821i	$-0.228099\pi$
$359$	4.74628e11	1.50809	0.754046	+	0.656821i	$0.228099\pi$
$360$	−2.54234e10	−0.0797762
$361$	−2.33891e11	−0.724822
$362$	3.08200e11	0.943288
$363$	1.52886e11	0.462155
$364$	−9.90825e11	−2.95829
$365$	−5.58339e10	−0.164657
$366$	−4.80409e11	−1.39941
$367$	−5.48861e11	−1.57930	−0.789651	−	0.613556i	$-0.789739\pi$
$367$	−5.48861e11	−1.57930	−0.789651	+	0.613556i	$0.789739\pi$
$368$	9.03715e10	0.256872
$369$	1.16363e11	0.326736
$370$	−5.75426e10	−0.159618
$371$	−3.58704e10	−0.0983001
$372$	−2.74563e10	−0.0743360
$373$	−1.12720e11	−0.301517	−0.150759	−	0.988571i	$-0.548172\pi$
$373$	−1.12720e11	−0.301517	−0.150759	+	0.988571i	$0.548172\pi$
$374$	1.60782e11	0.424927
$375$	−8.40467e10	−0.219472
$376$	−3.81986e11	−0.985603
$377$	−5.34951e11	−1.36389
$378$	−8.33396e11	−2.09961
$379$	5.00203e11	1.24529	0.622644	−	0.782505i	$-0.286059\pi$
$379$	5.00203e11	1.24529	0.622644	+	0.782505i	$0.286059\pi$
$380$	5.51456e10	0.135670
$381$	3.23422e11	0.786335
$382$	−7.94644e11	−1.90936
$383$	4.50346e11	1.06943	0.534715	−	0.845033i	$-0.320419\pi$
$383$	4.50346e11	1.06943	0.534715	+	0.845033i	$0.320419\pi$
$384$	−5.77984e11	−1.35652
$385$	−4.61703e10	−0.107100
$386$	−8.14086e11	−1.86650
$387$	−2.89189e10	−0.0655363
$388$	1.28779e12	2.88472
$389$	−5.17694e11	−1.14630	−0.573152	−	0.819449i	$-0.694279\pi$
$389$	−5.17694e11	−1.14630	−0.573152	+	0.819449i	$0.694279\pi$
$390$	1.20891e11	0.264608
$391$	−1.43787e11	−0.311118
$392$	−2.18535e11	−0.467449
$393$	3.52960e10	0.0746378
$394$	−3.88583e11	−0.812365
$395$	−9.28760e10	−0.191963
$396$	−2.30625e11	−0.471280
$397$	4.30362e11	0.869513	0.434757	−	0.900548i	$-0.356834\pi$
$397$	4.30362e11	0.869513	0.434757	+	0.900548i	$0.356834\pi$
$398$	4.25453e11	0.849920
$399$	2.34728e11	0.463646
$400$	−1.69820e11	−0.331680
$401$	7.47987e11	1.44459	0.722294	−	0.691586i	$-0.243088\pi$
$401$	7.47987e11	1.44459	0.722294	+	0.691586i	$0.243088\pi$
$402$	1.01890e12	1.94587
$403$	−4.25044e10	−0.0802715
$404$	1.34512e12	2.51214
$405$	3.06671e10	0.0566403
$406$	−1.01146e12	−1.84748
$407$	−2.25498e11	−0.407350
$408$	−2.19298e11	−0.391799
$409$	1.06852e12	1.88812	0.944058	−	0.329780i	$-0.106975\pi$
$409$	1.06852e12	1.88812	0.944058	+	0.329780i	$0.106975\pi$
$410$	−1.06178e11	−0.185570
$411$	1.80518e11	0.312056
$412$	1.40187e12	2.39701
$413$	7.72133e11	1.30592
$414$	3.23398e11	0.541049
$415$	−4.62437e10	−0.0765308
$416$	−6.14214e11	−1.00554
$417$	3.00582e10	0.0486800
$418$	3.38853e11	0.542897
$419$	8.06512e11	1.27834	0.639172	−	0.769064i	$-0.279277\pi$
$419$	8.06512e11	1.27834	0.639172	+	0.769064i	$0.279277\pi$
$420$	1.45774e11	0.228590
$421$	−8.57772e11	−1.33077	−0.665384	−	0.746501i	$-0.731732\pi$
$421$	−8.57772e11	−1.33077	−0.665384	+	0.746501i	$0.731732\pi$
$422$	1.98398e12	3.04531
$423$	−2.20710e11	−0.335189
$424$	7.06287e10	0.106129
$425$	2.70196e11	0.401724
$426$	1.27886e11	0.188140
$427$	−8.96785e11	−1.30546
$428$	9.21989e11	1.32809
$429$	4.73748e11	0.675289
$430$	2.63877e10	0.0372214
$431$	6.67092e11	0.931189	0.465594	−	0.884998i	$-0.345841\pi$
$431$	6.67092e11	0.931189	0.465594	+	0.884998i	$0.345841\pi$
$432$	2.64950e11	0.366005
$433$	1.60041e11	0.218795	0.109397	−	0.993998i	$-0.465108\pi$
$433$	1.60041e11	0.218795	0.109397	+	0.993998i	$0.465108\pi$
$434$	−8.03649e10	−0.108733
$435$	7.87041e10	0.105389
$436$	−1.82068e11	−0.241293
$437$	−3.03037e11	−0.397492
$438$	1.08322e12	1.40631
$439$	8.08663e11	1.03915	0.519574	−	0.854426i	$-0.326091\pi$
$439$	8.08663e11	1.03915	0.519574	+	0.854426i	$0.326091\pi$
$440$	9.09091e10	0.115630
$441$	−1.26269e11	−0.158973
$442$	−7.85860e11	−0.979366
$443$	−4.30605e11	−0.531205	−0.265602	−	0.964083i	$-0.585571\pi$
$443$	−4.30605e11	−0.531205	−0.265602	+	0.964083i	$0.585571\pi$
$444$	7.11967e11	0.869433
$445$	1.60492e10	0.0194014
$446$	−2.41527e12	−2.89041
$447$	−9.95738e11	−1.17967
$448$	−1.49961e12	−1.75885
$449$	−8.16570e11	−0.948167	−0.474083	−	0.880480i	$-0.657221\pi$
$449$	−8.16570e11	−0.948167	−0.474083	+	0.880480i	$0.657221\pi$
$450$	−6.07709e11	−0.698618
$451$	−4.16091e11	−0.473580
$452$	−1.92948e12	−2.17429
$453$	4.73229e11	0.527995
$454$	−2.20598e12	−2.43697
$455$	2.25669e11	0.246843
$456$	−4.62178e11	−0.500573
$457$	−3.51130e11	−0.376569	−0.188285	−	0.982115i	$-0.560293\pi$
$457$	−3.51130e11	−0.376569	−0.188285	+	0.982115i	$0.560293\pi$
$458$	2.66310e12	2.82809
$459$	−4.21554e11	−0.443298
$460$	−1.88196e11	−0.195975
$461$	−5.39021e11	−0.555842	−0.277921	−	0.960604i	$-0.589645\pi$
$461$	−5.39021e11	−0.555842	−0.277921	+	0.960604i	$0.589645\pi$
$462$	8.95736e11	0.914726
$463$	−8.43400e11	−0.852941	−0.426470	−	0.904501i	$-0.640243\pi$
$463$	−8.43400e11	−0.852941	−0.426470	+	0.904501i	$0.640243\pi$
$464$	3.21558e11	0.322054
$465$	6.25341e9	0.00620267
$466$	−2.18053e12	−2.14203
$467$	7.46110e11	0.725900	0.362950	−	0.931809i	$-0.381769\pi$
$467$	7.46110e11	0.725900	0.362950	+	0.931809i	$0.381769\pi$
$468$	1.12724e12	1.08620
$469$	1.90199e12	1.81523
$470$	2.01391e11	0.190371
$471$	−9.73307e11	−0.911288
$472$	−1.52033e12	−1.40993
$473$	1.03408e11	0.0949902
$474$	1.80186e12	1.63953
$475$	5.69447e11	0.513253
$476$	−9.47613e11	−0.846057
$477$	4.08090e10	0.0360930
$478$	2.29522e12	2.01093
$479$	4.41994e11	0.383625	0.191812	−	0.981432i	$-0.438563\pi$
$479$	4.41994e11	0.383625	0.191812	+	0.981432i	$0.438563\pi$
$480$	9.03654e10	0.0776992
$481$	1.10218e12	0.938855
$482$	−2.39143e12	−2.01811
$483$	−8.01058e11	−0.669733
$484$	−1.30079e12	−1.07747
$485$	−2.93306e11	−0.240704
$486$	1.61128e12	1.31011
$487$	−2.17097e12	−1.74893	−0.874465	−	0.485088i	$-0.838788\pi$
$487$	−2.17097e12	−1.74893	−0.874465	+	0.485088i	$0.838788\pi$
$488$	1.76577e12	1.40943
$489$	−1.99621e10	−0.0157876
$490$	1.15217e11	0.0902886
$491$	−1.29154e12	−1.00286	−0.501430	−	0.865198i	$-0.667193\pi$
$491$	−1.29154e12	−1.00286	−0.501430	+	0.865198i	$0.667193\pi$
$492$	1.31373e12	1.01079
$493$	−5.11621e11	−0.390065
$494$	−1.65623e12	−1.25126
$495$	5.25269e10	0.0393241
$496$	2.55493e10	0.0189545
$497$	2.38727e11	0.175508
$498$	8.97160e11	0.653639
$499$	−4.40903e11	−0.318340	−0.159170	−	0.987251i	$-0.550882\pi$
$499$	−4.40903e11	−0.318340	−0.159170	+	0.987251i	$0.550882\pi$
$500$	7.15092e11	0.511678
$501$	−3.93282e11	−0.278891
$502$	−2.33085e12	−1.63813
$503$	−2.51027e12	−1.74849	−0.874246	−	0.485483i	$-0.838644\pi$
$503$	−2.51027e12	−1.74849	−0.874246	+	0.485483i	$0.838644\pi$
$504$	9.20723e11	0.635611
$505$	−3.06362e11	−0.209616
$506$	−1.15641e12	−0.784212
$507$	−1.19208e12	−0.801250
$508$	−2.75176e12	−1.83326
$509$	2.25234e12	1.48732	0.743658	−	0.668560i	$-0.233089\pi$
$509$	2.25234e12	1.48732	0.743658	+	0.668560i	$0.233089\pi$
$510$	1.15619e11	0.0756767
$511$	2.02205e12	1.31189
$512$	1.03530e12	0.665811
$513$	−8.88439e11	−0.566369
$514$	4.90304e12	3.09836
$515$	−3.19287e11	−0.200009
$516$	−3.26491e11	−0.202744
$517$	7.89213e11	0.485833
$518$	2.08393e12	1.27174
$519$	−1.44909e12	−0.876680
$520$	−4.44341e11	−0.266502
$521$	−1.96536e12	−1.16862	−0.584310	−	0.811531i	$-0.698635\pi$
$521$	−1.96536e12	−1.16862	−0.584310	+	0.811531i	$0.698635\pi$
$522$	1.15071e12	0.678342
$523$	−1.94685e11	−0.113782	−0.0568912	−	0.998380i	$-0.518119\pi$
$523$	−1.94685e11	−0.113782	−0.0568912	+	0.998380i	$0.518119\pi$
$524$	−3.00308e11	−0.174011
$525$	1.50530e12	0.864779
$526$	3.68075e12	2.09653
$527$	−4.06507e10	−0.0229573
$528$	−2.84769e11	−0.159456
$529$	−7.66977e11	−0.425825
$530$	−3.72370e10	−0.0204990
$531$	−8.78438e11	−0.479497
$532$	−1.99713e12	−1.08094
$533$	2.03375e12	1.09150
$534$	−3.11366e11	−0.165705
$535$	−2.09991e11	−0.110817
$536$	−3.74501e12	−1.95980
$537$	7.92332e7	4.11171e−5 0
$538$	−2.14211e11	−0.110235
$539$	4.51511e11	0.230419
$540$	−5.51751e11	−0.279236
$541$	3.96660e12	1.99081	0.995406	−	0.0957430i	$-0.0305227\pi$
$541$	3.96660e12	1.99081	0.995406	+	0.0957430i	$0.0305227\pi$
$542$	3.12433e12	1.55511
$543$	8.68516e11	0.428725
$544$	−5.87426e11	−0.287580
$545$	4.14675e10	0.0201337
$546$	−4.37813e12	−2.10825
$547$	6.79936e11	0.324732	0.162366	−	0.986731i	$-0.448088\pi$
$547$	6.79936e11	0.324732	0.162366	+	0.986731i	$0.448088\pi$
$548$	−1.53590e12	−0.727527
$549$	1.02025e12	0.479327
$550$	2.17304e12	1.01260
$551$	−1.07826e12	−0.498357
$552$	1.57728e12	0.723074
$553$	3.36355e12	1.52945
$554$	3.76186e12	1.69671
$555$	−1.62156e11	−0.0725464
$556$	−2.55743e11	−0.113492
$557$	−2.27773e12	−1.00266	−0.501329	−	0.865256i	$-0.667156\pi$
$557$	−2.27773e12	−1.00266	−0.501329	+	0.865256i	$0.667156\pi$
$558$	9.14293e10	0.0399238
$559$	−5.05432e11	−0.218932
$560$	−1.35649e11	−0.0582869
$561$	4.53087e11	0.193129
$562$	5.94700e12	2.51469
$563$	3.02050e11	0.126704	0.0633520	−	0.997991i	$-0.479821\pi$
$563$	3.02050e11	0.126704	0.0633520	+	0.997991i	$0.479821\pi$
$564$	−2.49179e12	−1.03694
$565$	4.39457e11	0.181425
$566$	−6.03671e12	−2.47244
$567$	−1.11063e12	−0.451278
$568$	−4.70052e11	−0.189487
$569$	−4.19779e12	−1.67887	−0.839433	−	0.543464i	$-0.817113\pi$
$569$	−4.19779e12	−1.67887	−0.839433	+	0.543464i	$0.817113\pi$
$570$	2.43670e11	0.0966866
$571$	−5.90682e11	−0.232536	−0.116268	−	0.993218i	$-0.537093\pi$
$571$	−5.90682e11	−0.232536	−0.116268	+	0.993218i	$0.537093\pi$
$572$	−4.03078e12	−1.57437
$573$	−2.23933e12	−0.867805
$574$	3.84529e12	1.47851
$575$	−1.94336e12	−0.741391
$576$	1.70607e12	0.645798
$577$	1.62218e12	0.609267	0.304634	−	0.952470i	$-0.401466\pi$
$577$	1.62218e12	0.609267	0.304634	+	0.952470i	$0.401466\pi$
$578$	3.70676e12	1.38140
$579$	−2.29412e12	−0.848324
$580$	−6.69635e11	−0.245704
$581$	1.67474e12	0.609754
$582$	5.69034e12	2.05582
$583$	−1.45924e11	−0.0523142
$584$	−3.98141e12	−1.41638
$585$	−2.56738e11	−0.0906336
$586$	−1.53959e12	−0.539342
$587$	−8.50011e11	−0.295497	−0.147749	−	0.989025i	$-0.547203\pi$
$587$	−8.50011e11	−0.295497	−0.147749	+	0.989025i	$0.547203\pi$
$588$	−1.42556e12	−0.491799
$589$	−8.56727e10	−0.0293308
$590$	8.01550e11	0.272331
$591$	−1.09504e12	−0.369220
$592$	−6.62516e11	−0.221691
$593$	1.57424e12	0.522787	0.261394	−	0.965232i	$-0.415818\pi$
$593$	1.57424e12	0.522787	0.261394	+	0.965232i	$0.415818\pi$
$594$	−3.39034e12	−1.11739
$595$	2.15827e11	0.0705958
$596$	8.47201e12	2.75029
$597$	1.19894e12	0.386289
$598$	5.65223e12	1.80744
$599$	3.95743e12	1.25601	0.628004	−	0.778210i	$-0.283872\pi$
$599$	3.95743e12	1.25601	0.628004	+	0.778210i	$0.283872\pi$
$600$	−2.96392e12	−0.933654
$601$	1.35180e12	0.422646	0.211323	−	0.977416i	$-0.432223\pi$
$601$	1.35180e12	0.422646	0.211323	+	0.977416i	$0.432223\pi$
$602$	−9.55642e11	−0.296559
$603$	−2.16385e12	−0.666499
$604$	−4.02636e12	−1.23097
$605$	2.96267e11	0.0899050
$606$	5.94363e12	1.79030
$607$	−2.55817e12	−0.764856	−0.382428	−	0.923985i	$-0.624912\pi$
$607$	−2.55817e12	−0.764856	−0.382428	+	0.923985i	$0.624912\pi$
$608$	−1.23802e12	−0.367419
$609$	−2.85031e12	−0.839680
$610$	−9.30951e11	−0.272234
$611$	−3.85748e12	−1.11974
$612$	1.07808e12	0.310648
$613$	1.25908e12	0.360148	0.180074	−	0.983653i	$-0.442366\pi$
$613$	1.25908e12	0.360148	0.180074	+	0.983653i	$0.442366\pi$
$614$	−6.59431e12	−1.87246
$615$	−2.99212e11	−0.0843416
$616$	−3.29232e12	−0.921273
$617$	1.16942e12	0.324853	0.162427	−	0.986721i	$-0.448068\pi$
$617$	1.16942e12	0.324853	0.162427	+	0.986721i	$0.448068\pi$
$618$	6.19439e12	1.70825
$619$	−5.33978e12	−1.46189	−0.730946	−	0.682435i	$-0.760921\pi$
$619$	−5.33978e12	−1.46189	−0.730946	+	0.682435i	$0.760921\pi$
$620$	−5.32057e10	−0.0144609
$621$	3.03198e12	0.818116
$622$	4.69638e12	1.25807
$623$	−5.81231e11	−0.154580
$624$	1.39188e12	0.367512
$625$	3.56951e12	0.935725
$626$	−3.13415e12	−0.815710
$627$	9.54896e11	0.246747
$628$	8.28115e12	2.12458
$629$	1.05411e12	0.268508
$630$	−4.85426e11	−0.122770
$631$	−3.83054e11	−0.0961896	−0.0480948	−	0.998843i	$-0.515315\pi$
$631$	−3.83054e11	−0.0961896	−0.0480948	+	0.998843i	$0.515315\pi$
$632$	−6.62282e12	−1.65126
$633$	5.59091e12	1.38409
$634$	−1.12751e12	−0.277152
$635$	6.26737e11	0.152969
$636$	4.60729e11	0.111658
$637$	−2.20687e12	−0.531068
$638$	−4.11470e12	−0.983208
$639$	−2.71594e11	−0.0644417
$640$	−1.12003e12	−0.263889
$641$	3.52121e12	0.823816	0.411908	−	0.911225i	$-0.364862\pi$
$641$	3.52121e12	0.823816	0.411908	+	0.911225i	$0.364862\pi$
$642$	4.07397e12	0.946477
$643$	6.26646e12	1.44568	0.722841	−	0.691015i	$-0.242836\pi$
$643$	6.26646e12	1.44568	0.722841	+	0.691015i	$0.242836\pi$
$644$	6.81562e12	1.56142
$645$	7.43611e10	0.0169171
$646$	−1.58400e12	−0.357855
$647$	−2.33520e12	−0.523907	−0.261954	−	0.965080i	$-0.584367\pi$
$647$	−2.33520e12	−0.523907	−0.261954	+	0.965080i	$0.584367\pi$
$648$	2.18682e12	0.487220
$649$	3.14112e12	0.694997
$650$	−1.06213e13	−2.33382
$651$	−2.26470e11	−0.0494193
$652$	1.69843e11	0.0368073
$653$	7.16958e12	1.54307	0.771533	−	0.636189i	$-0.219490\pi$
$653$	7.16958e12	1.54307	0.771533	+	0.636189i	$0.219490\pi$
$654$	−8.04499e11	−0.171959
$655$	6.83977e10	0.0145196
$656$	−1.22248e12	−0.257736
$657$	−2.30044e12	−0.481690
$658$	−7.29350e12	−1.51677
$659$	4.49352e12	0.928115	0.464058	−	0.885805i	$-0.346393\pi$
$659$	4.49352e12	0.928115	0.464058	+	0.885805i	$0.346393\pi$
$660$	5.93023e11	0.121653
$661$	−4.35714e12	−0.887759	−0.443879	−	0.896087i	$-0.646398\pi$
$661$	−4.35714e12	−0.887759	−0.443879	+	0.896087i	$0.646398\pi$
$662$	−1.56826e13	−3.17364
$663$	−2.21458e12	−0.445123
$664$	−3.29755e12	−0.658317
$665$	4.54863e11	0.0901951
$666$	−2.37084e12	−0.466948
$667$	3.67978e12	0.719873
$668$	3.34614e12	0.650205
$669$	−6.80630e12	−1.31369
$670$	1.97445e12	0.378539
$671$	−3.64821e12	−0.694751
$672$	−3.27263e12	−0.619064
$673$	−3.51923e12	−0.661272	−0.330636	−	0.943758i	$-0.607263\pi$
$673$	−3.51923e12	−0.661272	−0.330636	+	0.943758i	$0.607263\pi$
$674$	−1.28142e13	−2.39178
$675$	−5.69751e12	−1.05637
$676$	1.01425e13	1.86803
$677$	−6.52874e12	−1.19448	−0.597242	−	0.802061i	$-0.703737\pi$
$677$	−6.52874e12	−1.19448	−0.597242	+	0.802061i	$0.703737\pi$
$678$	−8.52576e12	−1.54953
$679$	1.06222e13	1.91779
$680$	−4.24962e11	−0.0762184
$681$	−6.21651e12	−1.10760
$682$	−3.26932e11	−0.0578667
$683$	−5.20881e12	−0.915894	−0.457947	−	0.888979i	$-0.651415\pi$
$683$	−5.20881e12	−0.915894	−0.457947	+	0.888979i	$0.651415\pi$
$684$	2.27208e12	0.396892
$685$	3.49813e11	0.0607056
$686$	7.10724e12	1.22530
$687$	7.50469e12	1.28537
$688$	3.03814e11	0.0516964
$689$	7.13243e11	0.120573
$690$	−8.31577e11	−0.139663
$691$	−1.52736e12	−0.254853	−0.127426	−	0.991848i	$-0.540672\pi$
$691$	−1.52736e12	−0.254853	−0.127426	+	0.991848i	$0.540672\pi$
$692$	1.23292e13	2.04389
$693$	−1.90229e12	−0.313312
$694$	3.36759e12	0.551063
$695$	5.82476e10	0.00946992
$696$	5.61224e12	0.906556
$697$	1.94505e12	0.312164
$698$	3.30717e12	0.527360
$699$	−6.14479e12	−0.973553
$700$	−1.28075e13	−2.01615
$701$	−9.66521e12	−1.51175	−0.755876	−	0.654715i	$-0.772789\pi$
$701$	−9.66521e12	−1.51175	−0.755876	+	0.654715i	$0.772789\pi$
$702$	1.65711e13	2.57534
$703$	2.22157e12	0.343053
$704$	−6.10058e12	−0.936039
$705$	5.67527e11	0.0865237
$706$	8.86928e11	0.134359
$707$	1.10951e13	1.67010
$708$	−9.91747e12	−1.48338
$709$	−2.96426e12	−0.440563	−0.220281	−	0.975436i	$-0.570698\pi$
$709$	−2.96426e12	−0.440563	−0.220281	+	0.975436i	$0.570698\pi$
$710$	2.47822e11	0.0365997
$711$	−3.82664e12	−0.561570
$712$	1.14444e12	0.166891
$713$	2.92376e11	0.0423681
$714$	−4.18719e12	−0.602949
$715$	9.18044e11	0.131367
$716$	−6.74137e8	−9.58605e−5 0
$717$	6.46798e12	0.913971
$718$	−1.78437e13	−2.50568
$719$	9.52433e12	1.32909	0.664545	−	0.747248i	$-0.268625\pi$
$719$	9.52433e12	1.32909	0.664545	+	0.747248i	$0.268625\pi$
$720$	1.54325e11	0.0214013
$721$	1.15631e13	1.59356
$722$	8.79320e12	1.20429
$723$	−6.73910e12	−0.917233
$724$	−7.38957e12	−0.999529
$725$	−6.91481e12	−0.929521
$726$	−5.74778e12	−0.767866
$727$	−8.82435e12	−1.17160	−0.585798	−	0.810457i	$-0.699219\pi$
$727$	−8.82435e12	−1.17160	−0.585798	+	0.810457i	$0.699219\pi$
$728$	1.60920e13	2.12334
$729$	7.48080e12	0.981011
$730$	2.09909e12	0.273576
$731$	−4.83389e11	−0.0626136
$732$	1.15185e13	1.48285
$733$	−3.54439e12	−0.453497	−0.226748	−	0.973953i	$-0.572810\pi$
$733$	−3.54439e12	−0.453497	−0.226748	+	0.973953i	$0.572810\pi$
$734$	2.06346e13	2.62400
$735$	3.24684e11	0.0410362
$736$	4.22501e12	0.530735
$737$	7.73749e12	0.966043
$738$	−4.37470e12	−0.542868
$739$	1.30193e13	1.60578	0.802890	−	0.596127i	$-0.203295\pi$
$739$	1.30193e13	1.60578	0.802890	+	0.596127i	$0.203295\pi$
$740$	1.37967e12	0.169135
$741$	−4.66729e12	−0.568700
$742$	1.34856e12	0.163325
$743$	−1.15519e13	−1.39061	−0.695303	−	0.718717i	$-0.744730\pi$
$743$	−1.15519e13	−1.39061	−0.695303	+	0.718717i	$0.744730\pi$
$744$	4.45919e11	0.0533553
$745$	−1.92957e12	−0.229487
$746$	4.23775e12	0.500969
$747$	−1.90531e12	−0.223884
$748$	−3.85498e12	−0.450262
$749$	7.60492e12	0.882931
$750$	3.15976e12	0.364651
$751$	3.12550e12	0.358542	0.179271	−	0.983800i	$-0.442626\pi$
$751$	3.12550e12	0.358542	0.179271	+	0.983800i	$0.442626\pi$
$752$	2.31872e12	0.264404
$753$	−6.56840e12	−0.744530
$754$	2.01116e13	2.26609
$755$	9.17038e11	0.102713
$756$	1.99819e13	2.22479
$757$	1.11743e13	1.23677	0.618387	−	0.785874i	$-0.287786\pi$
$757$	1.11743e13	1.23677	0.618387	+	0.785874i	$0.287786\pi$
$758$	−1.88053e13	−2.06904
$759$	−3.25878e12	−0.356425
$760$	−8.95622e11	−0.0973786
$761$	−9.37537e12	−1.01335	−0.506673	−	0.862139i	$-0.669125\pi$
$761$	−9.37537e12	−1.01335	−0.506673	+	0.862139i	$0.669125\pi$
$762$	−1.21591e13	−1.30649
$763$	−1.50177e12	−0.160414
$764$	1.90528e13	2.02320
$765$	−2.45541e11	−0.0259208
$766$	−1.69309e13	−1.77685
$767$	−1.53530e13	−1.60182
$768$	1.07889e13	1.11906
$769$	−1.27720e13	−1.31701	−0.658506	−	0.752575i	$-0.728811\pi$
$769$	−1.27720e13	−1.31701	−0.658506	+	0.752575i	$0.728811\pi$
$770$	1.73578e12	0.177946
$771$	1.38169e13	1.40820
$772$	1.95189e13	1.97778
$773$	−1.71214e13	−1.72477	−0.862385	−	0.506253i	$-0.831030\pi$
$773$	−1.71214e13	−1.72477	−0.862385	+	0.506253i	$0.831030\pi$
$774$	1.08721e12	0.108888
$775$	−5.49414e11	−0.0547069
$776$	−2.09151e13	−2.07053
$777$	5.87258e12	0.578009
$778$	1.94628e13	1.90457
$779$	4.09926e12	0.398829
$780$	−2.89855e12	−0.280385
$781$	9.71166e11	0.0934036
$782$	5.40572e12	0.516920
$783$	1.07883e13	1.02572
$784$	1.32655e12	0.125401
$785$	−1.88610e12	−0.177277
$786$	−1.32696e12	−0.124010
$787$	−9.90899e12	−0.920753	−0.460376	−	0.887724i	$-0.652286\pi$
$787$	−9.90899e12	−0.920753	−0.460376	+	0.887724i	$0.652286\pi$
$788$	9.31688e12	0.860801
$789$	1.03724e13	0.952872
$790$	3.49170e12	0.318944
$791$	−1.59151e13	−1.44549
$792$	3.74559e12	0.338265
$793$	1.78316e13	1.60125
$794$	−1.61796e13	−1.44469
$795$	−1.04935e11	−0.00931682
$796$	−1.02009e13	−0.900595
$797$	1.22447e13	1.07494	0.537470	−	0.843283i	$-0.319380\pi$
$797$	1.22447e13	1.07494	0.537470	+	0.843283i	$0.319380\pi$
$798$	−8.82465e12	−0.770344
$799$	−3.68924e12	−0.320241
$800$	−7.93936e12	−0.685300
$801$	6.61253e11	0.0567572
$802$	−2.81207e13	−2.40017
$803$	8.22591e12	0.698175
$804$	−2.44297e13	−2.06189
$805$	−1.55231e12	−0.130286
$806$	1.59796e12	0.133370
$807$	−6.03651e11	−0.0501020
$808$	−2.18461e13	−1.80311
$809$	1.75854e13	1.44339	0.721695	−	0.692211i	$-0.243363\pi$
$809$	1.75854e13	1.44339	0.721695	+	0.692211i	$0.243363\pi$
$810$	−1.15294e12	−0.0941074
$811$	4.40402e12	0.357483	0.178742	−	0.983896i	$-0.442797\pi$
$811$	4.40402e12	0.357483	0.178742	+	0.983896i	$0.442797\pi$
$812$	2.42512e13	1.95763
$813$	8.80444e12	0.706796
$814$	8.47765e12	0.676808
$815$	−3.86832e10	−0.00307124
$816$	1.33118e12	0.105107
$817$	−1.01876e12	−0.0799968
$818$	−4.01714e13	−3.13709
$819$	9.29791e12	0.722117
$820$	2.54578e12	0.196634
$821$	3.71434e12	0.285323	0.142662	−	0.989772i	$-0.454434\pi$
$821$	3.71434e12	0.285323	0.142662	+	0.989772i	$0.454434\pi$
$822$	−6.78662e12	−0.518478
$823$	1.59197e12	0.120958	0.0604790	−	0.998169i	$-0.480737\pi$
$823$	1.59197e12	0.120958	0.0604790	+	0.998169i	$0.480737\pi$
$824$	−2.27678e13	−1.72047
$825$	6.12370e12	0.460226
$826$	−2.90285e13	−2.16978
$827$	6.05682e11	0.0450267	0.0225133	−	0.999747i	$-0.492833\pi$
$827$	6.05682e11	0.0450267	0.0225133	+	0.999747i	$0.492833\pi$
$828$	−7.75397e12	−0.573307
$829$	−4.55788e12	−0.335172	−0.167586	−	0.985857i	$-0.553597\pi$
$829$	−4.55788e12	−0.335172	−0.167586	+	0.985857i	$0.553597\pi$
$830$	1.73854e12	0.127155
$831$	1.06010e13	0.771157
$832$	2.98181e13	2.15737
$833$	−2.11063e12	−0.151883
$834$	−1.13004e12	−0.0808813
$835$	−7.62113e11	−0.0542538
$836$	−8.12451e12	−0.575266
$837$	8.57185e11	0.0603684
$838$	−3.03210e13	−2.12396
$839$	1.13152e13	0.788376	0.394188	−	0.919030i	$-0.371026\pi$
$839$	1.13152e13	0.788376	0.394188	+	0.919030i	$0.371026\pi$
$840$	−2.36752e12	−0.164073
$841$	−1.41381e12	−0.0974564
$842$	3.22482e13	2.21106
$843$	1.67588e13	1.14293
$844$	−4.75689e13	−3.22688
$845$	−2.31004e12	−0.155871
$846$	8.29764e12	0.556914
$847$	−1.07295e13	−0.716312
$848$	−4.28728e11	−0.0284709
$849$	−1.70116e13	−1.12373
$850$	−1.01581e13	−0.667461
$851$	−7.58158e12	−0.495537
$852$	−3.06627e12	−0.199357
$853$	−4.71326e12	−0.304825	−0.152413	−	0.988317i	$-0.548704\pi$
$853$	−4.71326e12	−0.304825	−0.152413	+	0.988317i	$0.548704\pi$
$854$	3.37149e13	2.16901
$855$	−5.17487e11	−0.0331171
$856$	−1.49740e13	−0.953251
$857$	−2.17755e13	−1.37897	−0.689486	−	0.724299i	$-0.742163\pi$
$857$	−2.17755e13	−1.37897	−0.689486	+	0.724299i	$0.742163\pi$
$858$	−1.78107e13	−1.12199
$859$	9.89222e12	0.619904	0.309952	−	0.950752i	$-0.399687\pi$
$859$	9.89222e12	0.619904	0.309952	+	0.950752i	$0.399687\pi$
$860$	−6.32684e11	−0.0394406
$861$	1.08361e13	0.671986
$862$	−2.50795e13	−1.54716
$863$	−6.68756e12	−0.410411	−0.205206	−	0.978719i	$-0.565786\pi$
$863$	−6.68756e12	−0.410411	−0.205206	+	0.978719i	$0.565786\pi$
$864$	1.23868e13	0.756220
$865$	−2.80808e12	−0.170544
$866$	−6.01679e12	−0.363525
$867$	1.04457e13	0.627846
$868$	1.92687e12	0.115216
$869$	1.36833e13	0.813956
$870$	−2.95890e12	−0.175103
$871$	−3.78189e13	−2.22653
$872$	2.95697e12	0.173190
$873$	−1.20847e13	−0.704158
$874$	1.13927e13	0.660430
$875$	5.89836e12	0.340169
$876$	−2.59718e13	−1.49016
$877$	−5.11595e12	−0.292030	−0.146015	−	0.989282i	$-0.546645\pi$
$877$	−5.11595e12	−0.292030	−0.146015	+	0.989282i	$0.546645\pi$
$878$	−3.04019e13	−1.72654
$879$	−4.33859e12	−0.245131
$880$	−5.51834e11	−0.0310196
$881$	1.95601e13	1.09391	0.546953	−	0.837163i	$-0.315788\pi$
$881$	1.95601e13	1.09391	0.546953	+	0.837163i	$0.315788\pi$
$882$	4.74711e12	0.264132
$883$	2.19947e13	1.21757	0.608786	−	0.793335i	$-0.291657\pi$
$883$	2.19947e13	1.21757	0.608786	+	0.793335i	$0.291657\pi$
$884$	1.88422e13	1.03776
$885$	2.25879e12	0.123774
$886$	1.61887e13	0.882592
$887$	3.41991e13	1.85506	0.927530	−	0.373749i	$-0.121928\pi$
$887$	3.41991e13	1.85506	0.927530	+	0.373749i	$0.121928\pi$
$888$	−1.15631e13	−0.624044
$889$	−2.26976e13	−1.21877
$890$	−6.03374e11	−0.0322353
$891$	−4.51814e12	−0.240165
$892$	5.79099e13	3.06274
$893$	−7.77521e12	−0.409148
$894$	3.74350e13	1.96002
$895$	1.53540e8	7.99870e−6 0
$896$	4.05626e13	2.10252
$897$	1.59281e13	0.821483
$898$	3.06992e13	1.57537
$899$	1.04033e12	0.0531192
$900$	1.45708e13	0.740271
$901$	6.82136e11	0.0344833
$902$	1.56430e13	0.786849
$903$	−2.69303e12	−0.134786
$904$	3.13368e13	1.56062
$905$	1.68304e12	0.0834017
$906$	−1.77912e13	−0.877259
$907$	1.61616e13	0.792963	0.396481	−	0.918043i	$-0.370231\pi$
$907$	1.61616e13	0.792963	0.396481	+	0.918043i	$0.370231\pi$
$908$	5.28918e13	2.58227
$909$	−1.26226e13	−0.613212
$910$	−8.48408e12	−0.410127
$911$	1.85018e13	0.889984	0.444992	−	0.895534i	$-0.353206\pi$
$911$	1.85018e13	0.889984	0.444992	+	0.895534i	$0.353206\pi$
$912$	2.80550e12	0.134287
$913$	6.81301e12	0.324504
$914$	1.32008e13	0.625667
$915$	−2.62345e12	−0.123731
$916$	−6.38519e13	−2.99671
$917$	−2.47706e12	−0.115684
$918$	1.58484e13	0.736536
$919$	−1.57446e13	−0.728134	−0.364067	−	0.931373i	$-0.618612\pi$
$919$	−1.57446e13	−0.728134	−0.364067	+	0.931373i	$0.618612\pi$
$920$	3.05650e12	0.140663
$921$	−1.85830e13	−0.851033
$922$	2.02646e13	0.923527
$923$	−4.74682e12	−0.215276
$924$	−2.14766e13	−0.969265
$925$	1.42468e13	0.639852
$926$	3.17078e13	1.41715
$927$	−1.31551e13	−0.585108
$928$	1.50333e13	0.665410
$929$	1.87066e12	0.0823992	0.0411996	−	0.999151i	$-0.486882\pi$
$929$	1.87066e12	0.0823992	0.0411996	+	0.999151i	$0.486882\pi$
$930$	−2.35099e11	−0.0103057
$931$	−4.44822e12	−0.194050
$932$	5.22815e13	2.26974
$933$	1.32345e13	0.571795
$934$	−2.80502e13	−1.20608
$935$	8.78005e11	0.0375703
$936$	−1.83075e13	−0.779630
$937$	−2.58528e13	−1.09567	−0.547834	−	0.836587i	$-0.684548\pi$
$937$	−2.58528e13	−1.09567	−0.547834	+	0.836587i	$0.684548\pi$
$938$	−7.15059e13	−3.01598
$939$	−8.83212e12	−0.370740
$940$	−4.82867e12	−0.201721
$941$	2.80468e13	1.16608	0.583042	−	0.812442i	$-0.301862\pi$
$941$	2.80468e13	1.16608	0.583042	+	0.812442i	$0.301862\pi$
$942$	3.65917e13	1.51410
$943$	−1.39896e13	−0.576106
$944$	9.22865e12	0.378237
$945$	−4.55106e12	−0.185639
$946$	−3.88765e12	−0.157825
$947$	2.67293e13	1.07997	0.539987	−	0.841673i	$-0.318429\pi$
$947$	2.67293e13	1.07997	0.539987	+	0.841673i	$0.318429\pi$
$948$	−4.32023e13	−1.73728
$949$	−4.02062e13	−1.60915
$950$	−2.14085e13	−0.852766
$951$	−3.17735e12	−0.125966
$952$	1.53902e13	0.607265
$953$	−3.84609e13	−1.51043	−0.755217	−	0.655475i	$-0.772468\pi$
$953$	−3.84609e13	−1.51043	−0.755217	+	0.655475i	$0.772468\pi$
$954$	−1.53422e12	−0.0599682
$955$	−4.33944e12	−0.168818
$956$	−5.50313e13	−2.13083
$957$	−1.15953e13	−0.446869
$958$	−1.66169e13	−0.637389
$959$	−1.26687e13	−0.483668
$960$	−4.38695e12	−0.166703
$961$	−2.63570e13	−0.996874
$962$	−4.14366e13	−1.55990
$963$	−8.65195e12	−0.324187
$964$	5.73381e13	2.13844
$965$	−4.44561e12	−0.165028
$966$	3.01160e13	1.11276
$967$	−2.53959e13	−0.933994	−0.466997	−	0.884259i	$-0.654664\pi$
$967$	−2.53959e13	−0.933994	−0.466997	+	0.884259i	$0.654664\pi$
$968$	2.11262e13	0.773362
$969$	−4.46374e12	−0.162645
$970$	1.10269e13	0.399927
$971$	4.57054e13	1.64999	0.824994	−	0.565142i	$-0.191178\pi$
$971$	4.57054e13	1.64999	0.824994	+	0.565142i	$0.191178\pi$
$972$	−3.86330e13	−1.38822
$973$	−2.10947e12	−0.0754510
$974$	8.16180e13	2.90583
$975$	−2.99311e13	−1.06072
$976$	−1.07185e13	−0.378103
$977$	−2.08990e13	−0.733839	−0.366919	−	0.930253i	$-0.619588\pi$
$977$	−2.08990e13	−0.733839	−0.366919	+	0.930253i	$0.619588\pi$
$978$	7.50482e11	0.0262310
$979$	−2.36450e12	−0.0822656
$980$	−2.76250e12	−0.0956719
$981$	1.70853e12	0.0588995
$982$	4.85557e13	1.66624
$983$	−3.50805e12	−0.119832	−0.0599162	−	0.998203i	$-0.519083\pi$
$983$	−3.50805e12	−0.119832	−0.0599162	+	0.998203i	$0.519083\pi$
$984$	−2.13363e13	−0.725506
$985$	−2.12200e12	−0.0718261
$986$	1.92345e13	0.648090
$987$	−2.05533e13	−0.689372
$988$	3.97106e13	1.32587
$989$	3.47673e12	0.115555
$990$	−1.97476e12	−0.0653366
$991$	5.36093e13	1.76567	0.882833	−	0.469687i	$-0.155633\pi$
$991$	5.36093e13	1.76567	0.882833	+	0.469687i	$0.155633\pi$
$992$	1.19447e12	0.0391627
$993$	−4.41941e13	−1.44242
$994$	−8.97501e12	−0.291606
$995$	2.32334e12	0.0751465
$996$	−2.15108e13	−0.692610
$997$	−1.81254e11	−0.00580976	−0.00290488	−	0.999996i	$-0.500925\pi$
$997$	−1.81254e11	−0.00580976	−0.00290488	+	0.999996i	$0.500925\pi$
$998$	1.65759e13	0.528919
$999$	−2.22276e13	−0.706069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.b.1.1	✓	17
3.2	odd	2		387.10.a.e.1.17		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.b.1.1	✓	17	1.1	even	1	trivial
387.10.a.e.1.17		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)

\(f(q)\)	\(=\)	\(q-37.5953 q^{2} -105.944 q^{3} +901.404 q^{4} -205.302 q^{5} +3983.01 q^{6} +7435.13 q^{7} -14639.7 q^{8} -8458.78 q^{9} +O(q^{10})\)	\(q-37.5953 q^{2} -105.944 q^{3} +901.404 q^{4} -205.302 q^{5} +3983.01 q^{6} +7435.13 q^{7} -14639.7 q^{8} -8458.78 q^{9} +7718.39 q^{10} +30246.9 q^{11} -95498.7 q^{12} -147839. q^{13} -279526. q^{14} +21750.6 q^{15} +88865.7 q^{16} -141391. q^{17} +318010. q^{18} -297987. q^{19} -185060. q^{20} -787711. q^{21} -1.13714e6 q^{22} +1.01694e6 q^{23} +1.55100e6 q^{24} -1.91098e6 q^{25} +5.55805e6 q^{26} +2.98146e6 q^{27} +6.70205e6 q^{28} +3.61847e6 q^{29} -817721. q^{30} +287505. q^{31} +4.15461e6 q^{32} -3.20449e6 q^{33} +5.31565e6 q^{34} -1.52645e6 q^{35} -7.62477e6 q^{36} -7.45525e6 q^{37} +1.12029e7 q^{38} +1.56627e7 q^{39} +3.00557e6 q^{40} -1.37565e7 q^{41} +2.96142e7 q^{42} +3.41880e6 q^{43} +2.72646e7 q^{44} +1.73661e6 q^{45} -3.82323e7 q^{46} +2.60924e7 q^{47} -9.41483e6 q^{48} +1.49275e7 q^{49} +7.18436e7 q^{50} +1.49796e7 q^{51} -1.33263e8 q^{52} -4.82445e6 q^{53} -1.12089e8 q^{54} -6.20975e6 q^{55} -1.08848e8 q^{56} +3.15701e7 q^{57} -1.36037e8 q^{58} +1.03849e8 q^{59} +1.96061e7 q^{60} -1.20615e8 q^{61} -1.08088e7 q^{62} -6.28921e7 q^{63} -2.01693e8 q^{64} +3.03517e7 q^{65} +1.20473e8 q^{66} +2.55811e8 q^{67} -1.27451e8 q^{68} -1.07740e8 q^{69} +5.73873e7 q^{70} +3.21080e7 q^{71} +1.23834e8 q^{72} +2.71959e8 q^{73} +2.80282e8 q^{74} +2.02457e8 q^{75} -2.68607e8 q^{76} +2.24889e8 q^{77} -5.88844e8 q^{78} +4.52387e8 q^{79} -1.82443e7 q^{80} -1.49376e8 q^{81} +5.17179e8 q^{82} +2.25247e8 q^{83} -7.10045e8 q^{84} +2.90280e7 q^{85} -1.28531e8 q^{86} -3.83357e8 q^{87} -4.42806e8 q^{88} -7.81736e7 q^{89} -6.52882e7 q^{90} -1.09920e9 q^{91} +9.16677e8 q^{92} -3.04595e7 q^{93} -9.80951e8 q^{94} +6.11775e7 q^{95} -4.40158e8 q^{96} +1.42865e9 q^{97} -5.61205e8 q^{98} -2.55851e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 48 q^{2} + 169 q^{3} + 4522 q^{4} + 4033 q^{5} + 5871 q^{6} - 76 q^{7} + 41046 q^{8} + 135126 q^{9}+O(q^{10}) \) 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

Modular forms

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