LMFDB - Embedded newform 17.10.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-34.1532$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+34.1532 q^{2} +169.801 q^{3} +654.438 q^{4} +195.287 q^{5} +5799.26 q^{6} -356.628 q^{7} +4864.71 q^{8} +9149.54 q^{9} +O(q^{10})$	\(q+34.1532 q^{2} +169.801 q^{3} +654.438 q^{4} +195.287 q^{5} +5799.26 q^{6} -356.628 q^{7} +4864.71 q^{8} +9149.54 q^{9} +6669.66 q^{10} -21467.8 q^{11} +111125. q^{12} -6206.76 q^{13} -12180.0 q^{14} +33160.0 q^{15} -168927. q^{16} +83521.0 q^{17} +312486. q^{18} +907187. q^{19} +127803. q^{20} -60556.0 q^{21} -733194. q^{22} -1.23486e6 q^{23} +826035. q^{24} -1.91499e6 q^{25} -211980. q^{26} -1.78860e6 q^{27} -233391. q^{28} -3.01596e6 q^{29} +1.13252e6 q^{30} -334277. q^{31} -8.26012e6 q^{32} -3.64527e6 q^{33} +2.85251e6 q^{34} -69644.7 q^{35} +5.98781e6 q^{36} +2.06102e7 q^{37} +3.09833e7 q^{38} -1.05392e6 q^{39} +950014. q^{40} +1.47571e7 q^{41} -2.06818e6 q^{42} -7.75953e6 q^{43} -1.40494e7 q^{44} +1.78679e6 q^{45} -4.21744e7 q^{46} +3.19993e7 q^{47} -2.86841e7 q^{48} -4.02264e7 q^{49} -6.54029e7 q^{50} +1.41820e7 q^{51} -4.06194e6 q^{52} +9.46750e7 q^{53} -6.10862e7 q^{54} -4.19238e6 q^{55} -1.73489e6 q^{56} +1.54042e8 q^{57} -1.03005e8 q^{58} +6.01771e7 q^{59} +2.17012e7 q^{60} +6.05254e7 q^{61} -1.14166e7 q^{62} -3.26298e6 q^{63} -1.95619e8 q^{64} -1.21210e6 q^{65} -1.24497e8 q^{66} -1.26316e8 q^{67} +5.46593e7 q^{68} -2.09681e8 q^{69} -2.37859e6 q^{70} +3.33917e7 q^{71} +4.45099e7 q^{72} +2.85706e8 q^{73} +7.03903e8 q^{74} -3.25168e8 q^{75} +5.93698e8 q^{76} +7.65603e6 q^{77} -3.59946e7 q^{78} -7.60575e7 q^{79} -3.29892e7 q^{80} -4.83797e8 q^{81} +5.04001e8 q^{82} -1.73620e7 q^{83} -3.96301e7 q^{84} +1.63105e7 q^{85} -2.65012e8 q^{86} -5.12115e8 q^{87} -1.04435e8 q^{88} +3.96876e8 q^{89} +6.10244e7 q^{90} +2.21350e6 q^{91} -8.08139e8 q^{92} -5.67608e7 q^{93} +1.09288e9 q^{94} +1.77162e8 q^{95} -1.40258e9 q^{96} +1.13120e9 q^{97} -1.37386e9 q^{98} -1.96421e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) $ 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	34.1532	1.50937	0.754685	−	0.656087i	$-0.227790\pi$
$2$	34.1532	1.50937	0.754685	+	0.656087i	$0.227790\pi$
$3$	169.801	1.21031	0.605154	−	0.796109i	$-0.293112\pi$
$3$	169.801	1.21031	0.605154	+	0.796109i	$0.293112\pi$
$4$	654.438	1.27820
$5$	195.287	0.139736	0.0698679	−	0.997556i	$-0.477742\pi$
$5$	195.287	0.139736	0.0698679	+	0.997556i	$0.477742\pi$
$6$	5799.26	1.82680
$7$	−356.628	−0.0561402	−0.0280701	−	0.999606i	$-0.508936\pi$
$7$	−356.628	−0.0561402	−0.0280701	+	0.999606i	$0.508936\pi$
$8$	4864.71	0.419906
$9$	9149.54	0.464845
$10$	6669.66	0.210913
$11$	−21467.8	−0.442101	−0.221050	−	0.975262i	$-0.570949\pi$
$11$	−21467.8	−0.442101	−0.221050	+	0.975262i	$0.570949\pi$
$12$	111125.	1.54701
$13$	−6206.76	−0.0602726	−0.0301363	−	0.999546i	$-0.509594\pi$
$13$	−6206.76	−0.0602726	−0.0301363	+	0.999546i	$0.509594\pi$
$14$	−12180.0	−0.0847364
$15$	33160.0	0.169123
$16$	−168927.	−0.644406
$17$	83521.0	0.242536
$17$	83521.0	0.242536
$18$	312486.	0.701623
$19$	907187.	1.59700	0.798501	−	0.601993i	$-0.205627\pi$
$19$	907187.	1.59700	0.798501	+	0.601993i	$0.205627\pi$
$20$	127803.	0.178610
$21$	−60556.0	−0.0679470
$22$	−733194.	−0.667294
$23$	−1.23486e6	−0.920115	−0.460058	−	0.887889i	$-0.652171\pi$
$23$	−1.23486e6	−0.920115	−0.460058	+	0.887889i	$0.652171\pi$
$24$	826035.	0.508216
$25$	−1.91499e6	−0.980474
$26$	−211980.	−0.0909737
$27$	−1.78860e6	−0.647702
$28$	−233391.	−0.0717584
$29$	−3.01596e6	−0.791835	−0.395917	−	0.918286i	$-0.629573\pi$
$29$	−3.01596e6	−0.791835	−0.395917	+	0.918286i	$0.629573\pi$
$30$	1.13252e6	0.255270
$31$	−334277.	−0.0650099	−0.0325049	−	0.999472i	$-0.510348\pi$
$31$	−334277.	−0.0650099	−0.0325049	+	0.999472i	$0.510348\pi$
$32$	−8.26012e6	−1.39255
$33$	−3.64527e6	−0.535078
$34$	2.85251e6	0.366076
$35$	−69644.7	−0.00784481
$36$	5.98781e6	0.594165
$37$	2.06102e7	1.80790	0.903949	−	0.427640i	$-0.140655\pi$
$37$	2.06102e7	1.80790	0.903949	+	0.427640i	$0.140655\pi$
$38$	3.09833e7	2.41047
$39$	−1.05392e6	−0.0729484
$40$	950014.	0.0586759
$41$	1.47571e7	0.815593	0.407796	−	0.913073i	$-0.366297\pi$
$41$	1.47571e7	0.815593	0.407796	+	0.913073i	$0.366297\pi$
$42$	−2.06818e6	−0.102557
$43$	−7.75953e6	−0.346120	−0.173060	−	0.984911i	$-0.555366\pi$
$43$	−7.75953e6	−0.346120	−0.173060	+	0.984911i	$0.555366\pi$
$44$	−1.40494e7	−0.565093
$45$	1.78679e6	0.0649555
$46$	−4.21744e7	−1.38880
$47$	3.19993e7	0.956534	0.478267	−	0.878214i	$-0.341265\pi$
$47$	3.19993e7	0.956534	0.478267	+	0.878214i	$0.341265\pi$
$48$	−2.86841e7	−0.779929
$49$	−4.02264e7	−0.996848
$50$	−6.54029e7	−1.47990
$51$	1.41820e7	0.293543
$52$	−4.06194e6	−0.0770404
$53$	9.46750e7	1.64814	0.824070	−	0.566488i	$-0.191698\pi$
$53$	9.46750e7	1.64814	0.824070	+	0.566488i	$0.191698\pi$
$54$	−6.10862e7	−0.977623
$55$	−4.19238e6	−0.0617773
$56$	−1.73489e6	−0.0235736
$57$	1.54042e8	1.93286
$58$	−1.03005e8	−1.19517
$59$	6.01771e7	0.646542	0.323271	−	0.946306i	$-0.395217\pi$
$59$	6.01771e7	0.646542	0.323271	+	0.946306i	$0.395217\pi$
$60$	2.17012e7	0.216173
$61$	6.05254e7	0.559698	0.279849	−	0.960044i	$-0.409716\pi$
$61$	6.05254e7	0.559698	0.279849	+	0.960044i	$0.409716\pi$
$62$	−1.14166e7	−0.0981240
$63$	−3.26298e6	−0.0260965
$64$	−1.95619e8	−1.45747
$65$	−1.21210e6	−0.00842224
$66$	−1.24497e8	−0.807631
$67$	−1.26316e8	−0.765813	−0.382907	−	0.923787i	$-0.625077\pi$
$67$	−1.26316e8	−0.765813	−0.382907	+	0.923787i	$0.625077\pi$
$68$	5.46593e7	0.310009
$69$	−2.09681e8	−1.11362
$70$	−2.37859e6	−0.0118407
$71$	3.33917e7	0.155947	0.0779734	−	0.996955i	$-0.475155\pi$
$71$	3.33917e7	0.155947	0.0779734	+	0.996955i	$0.475155\pi$
$72$	4.45099e7	0.195191
$73$	2.85706e8	1.17752	0.588758	−	0.808309i	$-0.299617\pi$
$73$	2.85706e8	1.17752	0.588758	+	0.808309i	$0.299617\pi$
$74$	7.03903e8	2.72879
$75$	−3.25168e8	−1.18668
$76$	5.93698e8	2.04129
$77$	7.65603e6	0.0248196
$78$	−3.59946e7	−0.110106
$79$	−7.60575e7	−0.219695	−0.109848	−	0.993948i	$-0.535036\pi$
$79$	−7.60575e7	−0.219695	−0.109848	+	0.993948i	$0.535036\pi$
$80$	−3.29892e7	−0.0900466
$81$	−4.83797e8	−1.24876
$82$	5.04001e8	1.23103
$83$	−1.73620e7	−0.0401558	−0.0200779	−	0.999798i	$-0.506391\pi$
$83$	−1.73620e7	−0.0401558	−0.0200779	+	0.999798i	$0.506391\pi$
$84$	−3.96301e7	−0.0868498
$85$	1.63105e7	0.0338909
$86$	−2.65012e8	−0.522424
$87$	−5.12115e8	−0.958364
$88$	−1.04435e8	−0.185641
$89$	3.96876e8	0.670501	0.335251	−	0.942129i	$-0.391179\pi$
$89$	3.96876e8	0.670501	0.335251	+	0.942129i	$0.391179\pi$
$90$	6.10244e7	0.0980419
$91$	2.21350e6	0.00338372
$92$	−8.08139e8	−1.17609
$93$	−5.67608e7	−0.0786819
$94$	1.09288e9	1.44376
$95$	1.77162e8	0.223159
$96$	−1.40258e9	−1.68542
$97$	1.13120e9	1.29737	0.648687	−	0.761055i	$-0.275318\pi$
$97$	1.13120e9	1.29737	0.648687	+	0.761055i	$0.275318\pi$
$98$	−1.37386e9	−1.50461
$99$	−1.96421e8	−0.205508
$100$	−1.25324e9	−1.25324
$101$	−1.58638e9	−1.51692	−0.758458	−	0.651722i	$-0.774047\pi$
$101$	−1.58638e9	−1.51692	−0.758458	+	0.651722i	$0.774047\pi$
$102$	4.84360e8	0.443065
$103$	−9.77937e8	−0.856137	−0.428068	−	0.903746i	$-0.640806\pi$
$103$	−9.77937e8	−0.856137	−0.428068	+	0.903746i	$0.640806\pi$
$104$	−3.01941e7	−0.0253088
$105$	−1.18258e7	−0.00949463
$106$	3.23345e9	2.48765
$107$	−1.71253e8	−0.126302	−0.0631511	−	0.998004i	$-0.520115\pi$
$107$	−1.71253e8	−0.126302	−0.0631511	+	0.998004i	$0.520115\pi$
$108$	−1.17053e9	−0.827893
$109$	1.66962e9	1.13292	0.566461	−	0.824089i	$-0.308312\pi$
$109$	1.66962e9	1.13292	0.566461	+	0.824089i	$0.308312\pi$
$110$	−1.43183e8	−0.0932449
$111$	3.49964e9	2.18811
$112$	6.02441e7	0.0361771
$113$	−2.55660e9	−1.47506	−0.737531	−	0.675313i	$-0.764008\pi$
$113$	−2.55660e9	−1.47506	−0.737531	+	0.675313i	$0.764008\pi$
$114$	5.26101e9	2.91741
$115$	−2.41152e8	−0.128573
$116$	−1.97376e9	−1.01212
$117$	−5.67890e7	−0.0280174
$118$	2.05524e9	0.975872
$119$	−2.97859e7	−0.0136160
$120$	1.61314e8	0.0710159
$121$	−1.89708e9	−0.804547
$122$	2.06713e9	0.844792
$123$	2.50578e9	0.987118
$124$	−2.18764e8	−0.0830956
$125$	−7.55391e8	−0.276743
$126$	−1.11441e8	−0.0393893
$127$	−1.57297e9	−0.536542	−0.268271	−	0.963344i	$-0.586452\pi$
$127$	−1.57297e9	−0.536542	−0.268271	+	0.963344i	$0.586452\pi$
$128$	−2.45181e9	−0.807313
$129$	−1.31758e9	−0.418912
$130$	−4.13970e7	−0.0127123
$131$	1.54185e9	0.457426	0.228713	−	0.973494i	$-0.426548\pi$
$131$	1.54185e9	0.457426	0.228713	+	0.973494i	$0.426548\pi$
$132$	−2.38560e9	−0.683936
$133$	−3.23528e8	−0.0896561
$134$	−4.31410e9	−1.15590
$135$	−3.49289e8	−0.0905072
$136$	4.06306e8	0.101842
$137$	−7.48495e9	−1.81529	−0.907646	−	0.419736i	$-0.862123\pi$
$137$	−7.48495e9	−1.81529	−0.907646	+	0.419736i	$0.862123\pi$
$138$	−7.16127e9	−1.68087
$139$	4.97076e9	1.12942	0.564711	−	0.825289i	$-0.308988\pi$
$139$	4.97076e9	1.12942	0.564711	+	0.825289i	$0.308988\pi$
$140$	−4.55782e7	−0.0100272
$141$	5.43353e9	1.15770
$142$	1.14043e9	0.235382
$143$	1.33246e8	0.0266465
$144$	−1.54561e9	−0.299549
$145$	−5.88977e8	−0.110648
$146$	9.75777e9	1.77731
$147$	−6.83051e9	−1.20649
$148$	1.34881e10	2.31085
$149$	−2.17167e9	−0.360957	−0.180479	−	0.983579i	$-0.557765\pi$
$149$	−2.17167e9	−0.360957	−0.180479	+	0.983579i	$0.557765\pi$
$150$	−1.11055e10	−1.79113
$151$	5.05353e9	0.791040	0.395520	−	0.918457i	$-0.370564\pi$
$151$	5.05353e9	0.791040	0.395520	+	0.918457i	$0.370564\pi$
$152$	4.41320e9	0.670591
$153$	7.64179e8	0.112741
$154$	2.61478e8	0.0374620
$155$	−6.52799e7	−0.00908421
$156$	−6.89723e8	−0.0932426
$157$	−1.14585e10	−1.50515	−0.752577	−	0.658504i	$-0.771190\pi$
$157$	−1.14585e10	−1.50515	−0.752577	+	0.658504i	$0.771190\pi$
$158$	−2.59760e9	−0.331601
$159$	1.60760e10	1.99476
$160$	−1.61309e9	−0.194590
$161$	4.40386e8	0.0516555
$162$	−1.65232e10	−1.88485
$163$	1.58612e10	1.75992	0.879960	−	0.475048i	$-0.157569\pi$
$163$	1.58612e10	1.75992	0.879960	+	0.475048i	$0.157569\pi$
$164$	9.65760e9	1.04249
$165$	−7.11873e8	−0.0747696
$166$	−5.92966e8	−0.0606099
$167$	−7.94993e9	−0.790932	−0.395466	−	0.918481i	$-0.629417\pi$
$167$	−7.94993e9	−0.790932	−0.395466	+	0.918481i	$0.629417\pi$
$168$	−2.94587e8	−0.0285313
$169$	−1.05660e10	−0.996367
$170$	5.57057e8	0.0511540
$171$	8.30035e9	0.742359
$172$	−5.07813e9	−0.442411
$173$	4.82389e9	0.409440	0.204720	−	0.978821i	$-0.434372\pi$
$173$	4.82389e9	0.409440	0.204720	+	0.978821i	$0.434372\pi$
$174$	−1.74903e10	−1.44653
$175$	6.82938e8	0.0550440
$176$	3.62650e9	0.284892
$177$	1.02182e10	0.782515
$178$	1.35546e10	1.01203
$179$	−6.50866e9	−0.473863	−0.236932	−	0.971526i	$-0.576142\pi$
$179$	−6.50866e9	−0.473863	−0.236932	+	0.971526i	$0.576142\pi$
$180$	1.16934e9	0.0830261
$181$	9.87513e9	0.683895	0.341947	−	0.939719i	$-0.388914\pi$
$181$	9.87513e9	0.683895	0.341947	+	0.939719i	$0.388914\pi$
$182$	7.55982e7	0.00510728
$183$	1.02773e10	0.677407
$184$	−6.00724e9	−0.386362
$185$	4.02490e9	0.252628
$186$	−1.93856e9	−0.118760
$187$	−1.79301e9	−0.107225
$188$	2.09416e10	1.22264
$189$	6.37864e8	0.0363622
$190$	6.05063e9	0.336829
$191$	1.73272e10	0.942060	0.471030	−	0.882117i	$-0.343882\pi$
$191$	1.73272e10	0.942060	0.471030	+	0.882117i	$0.343882\pi$
$192$	−3.32163e10	−1.76399
$193$	−5.92773e9	−0.307525	−0.153763	−	0.988108i	$-0.549139\pi$
$193$	−5.92773e9	−0.307525	−0.153763	+	0.988108i	$0.549139\pi$
$194$	3.86339e10	1.95822
$195$	−2.05816e8	−0.0101935
$196$	−2.63257e10	−1.27417
$197$	−1.61285e10	−0.762948	−0.381474	−	0.924380i	$-0.624583\pi$
$197$	−1.61285e10	−0.762948	−0.381474	+	0.924380i	$0.624583\pi$
$198$	−6.70839e9	−0.310188
$199$	−4.38224e10	−1.98088	−0.990438	−	0.137958i	$-0.955946\pi$
$199$	−4.38224e10	−1.98088	−0.990438	+	0.137958i	$0.955946\pi$
$200$	−9.31586e9	−0.411707
$201$	−2.14487e10	−0.926870
$202$	−5.41800e10	−2.28959
$203$	1.07558e9	0.0444538
$204$	9.28123e9	0.375206
$205$	2.88186e9	0.113968
$206$	−3.33996e10	−1.29223
$207$	−1.12984e10	−0.427711
$208$	1.04849e9	0.0388400
$209$	−1.94753e10	−0.706036
$210$	−4.03888e8	−0.0143309
$211$	4.85013e10	1.68454	0.842272	−	0.539053i	$-0.181218\pi$
$211$	4.85013e10	1.68454	0.842272	+	0.539053i	$0.181218\pi$
$212$	6.19589e10	2.10665
$213$	5.66997e9	0.188744
$214$	−5.84883e9	−0.190637
$215$	−1.51533e9	−0.0483654
$216$	−8.70100e9	−0.271974
$217$	1.19213e8	0.00364967
$218$	5.70230e10	1.71000
$219$	4.85133e10	1.42516
$220$	−2.74366e9	−0.0789637
$221$	−5.18395e8	−0.0146182
$222$	1.19524e11	3.30267
$223$	−1.32607e9	−0.0359082	−0.0179541	−	0.999839i	$-0.505715\pi$
$223$	−1.32607e9	−0.0359082	−0.0179541	+	0.999839i	$0.505715\pi$
$224$	2.94579e9	0.0781783
$225$	−1.75213e10	−0.455768
$226$	−8.73161e10	−2.22642
$227$	−6.30032e10	−1.57487	−0.787437	−	0.616395i	$-0.788593\pi$
$227$	−6.30032e10	−1.57487	−0.787437	+	0.616395i	$0.788593\pi$
$228$	1.00811e11	2.47059
$229$	3.36520e10	0.808632	0.404316	−	0.914619i	$-0.367510\pi$
$229$	3.36520e10	0.808632	0.404316	+	0.914619i	$0.367510\pi$
$230$	−8.23610e9	−0.194064
$231$	1.30001e9	0.0300394
$232$	−1.46718e10	−0.332496
$233$	−3.25593e10	−0.723724	−0.361862	−	0.932232i	$-0.617859\pi$
$233$	−3.25593e10	−0.723724	−0.361862	+	0.932232i	$0.617859\pi$
$234$	−1.93952e9	−0.0422887
$235$	6.24905e9	0.133662
$236$	3.93822e10	0.826410
$237$	−1.29147e10	−0.265899
$238$	−1.01728e9	−0.0205516
$239$	4.25086e10	0.842725	0.421363	−	0.906892i	$-0.361552\pi$
$239$	4.25086e10	0.842725	0.421363	+	0.906892i	$0.361552\pi$
$240$	−5.60162e9	−0.108984
$241$	−6.46314e10	−1.23415	−0.617074	−	0.786905i	$-0.711682\pi$
$241$	−6.46314e10	−1.23415	−0.617074	+	0.786905i	$0.711682\pi$
$242$	−6.47913e10	−1.21436
$243$	−4.69445e10	−0.863687
$244$	3.96102e10	0.715406
$245$	−7.85569e9	−0.139295
$246$	8.55801e10	1.48993
$247$	−5.63069e9	−0.0962555
$248$	−1.62616e9	−0.0272980
$249$	−2.94809e9	−0.0486008
$250$	−2.57990e10	−0.417708
$251$	−1.00795e11	−1.60290	−0.801452	−	0.598060i	$-0.795939\pi$
$251$	−1.00795e11	−1.60290	−0.801452	+	0.598060i	$0.795939\pi$
$252$	−2.13542e9	−0.0333565
$253$	2.65098e10	0.406784
$254$	−5.37219e10	−0.809840
$255$	2.76956e9	0.0410185
$256$	1.64197e10	0.238938
$257$	−7.98430e10	−1.14166	−0.570831	−	0.821067i	$-0.693379\pi$
$257$	−7.98430e10	−1.14166	−0.570831	+	0.821067i	$0.693379\pi$
$258$	−4.49995e10	−0.632294
$259$	−7.35017e9	−0.101496
$260$	−7.93243e8	−0.0107653
$261$	−2.75947e10	−0.368080
$262$	5.26590e10	0.690425
$263$	9.26392e10	1.19397	0.596986	−	0.802252i	$-0.296365\pi$
$263$	9.26392e10	1.19397	0.596986	+	0.802252i	$0.296365\pi$
$264$	−1.77332e10	−0.224682
$265$	1.84888e10	0.230304
$266$	−1.10495e10	−0.135324
$267$	6.73901e10	0.811513
$268$	−8.26662e10	−0.978862
$269$	−6.38400e10	−0.743375	−0.371687	−	0.928358i	$-0.621221\pi$
$269$	−6.38400e10	−0.743375	−0.371687	+	0.928358i	$0.621221\pi$
$270$	−1.19293e10	−0.136609
$271$	1.39281e11	1.56866	0.784331	−	0.620343i	$-0.213007\pi$
$271$	1.39281e11	1.56866	0.784331	+	0.620343i	$0.213007\pi$
$272$	−1.41090e10	−0.156291
$273$	3.75856e8	0.00409534
$274$	−2.55635e11	−2.73995
$275$	4.11106e10	0.433468
$276$	−1.37223e11	−1.42343
$277$	1.33421e11	1.36165	0.680826	−	0.732445i	$-0.261621\pi$
$277$	1.33421e11	1.36165	0.680826	+	0.732445i	$0.261621\pi$
$278$	1.69767e11	1.70472
$279$	−3.05848e9	−0.0302195
$280$	−3.38802e8	−0.00329408
$281$	−1.22205e11	−1.16926	−0.584629	−	0.811301i	$-0.698760\pi$
$281$	−1.22205e11	−1.16926	−0.584629	+	0.811301i	$0.698760\pi$
$282$	1.85572e11	1.74740
$283$	1.48138e11	1.37286	0.686430	−	0.727196i	$-0.259177\pi$
$283$	1.48138e11	1.37286	0.686430	+	0.727196i	$0.259177\pi$
$284$	2.18528e10	0.199331
$285$	3.00823e10	0.270090
$286$	4.55076e9	0.0402195
$287$	−5.26279e9	−0.0457876
$288$	−7.55764e10	−0.647321
$289$	6.97576e9	0.0588235
$290$	−2.01154e10	−0.167008
$291$	1.92079e11	1.57022
$292$	1.86977e11	1.50510
$293$	1.17196e11	0.928986	0.464493	−	0.885577i	$-0.346237\pi$
$293$	1.17196e11	0.928986	0.464493	+	0.885577i	$0.346237\pi$
$294$	−2.33283e11	−1.82105
$295$	1.17518e10	0.0903452
$296$	1.00263e11	0.759147
$297$	3.83973e10	0.286350
$298$	−7.41694e10	−0.544818
$299$	7.66448e9	0.0554577
$300$	−2.12802e11	−1.51681
$301$	2.76726e9	0.0194313
$302$	1.72594e11	1.19397
$303$	−2.69370e11	−1.83594
$304$	−1.53248e11	−1.02912
$305$	1.18198e10	0.0782099
$306$	2.60991e10	0.170169
$307$	−4.33130e10	−0.278288	−0.139144	−	0.990272i	$-0.544435\pi$
$307$	−4.33130e10	−0.278288	−0.139144	+	0.990272i	$0.544435\pi$
$308$	5.01040e9	0.0317244
$309$	−1.66055e11	−1.03619
$310$	−2.22952e9	−0.0137114
$311$	1.79166e11	1.08601	0.543006	−	0.839729i	$-0.317286\pi$
$311$	1.79166e11	1.08601	0.543006	+	0.839729i	$0.317286\pi$
$312$	−5.12700e9	−0.0306315
$313$	−6.30182e10	−0.371122	−0.185561	−	0.982633i	$-0.559410\pi$
$313$	−6.30182e10	−0.371122	−0.185561	+	0.982633i	$0.559410\pi$
$314$	−3.91346e11	−2.27184
$315$	−6.37218e8	−0.00364662
$316$	−4.97749e10	−0.280814
$317$	4.25331e10	0.236570	0.118285	−	0.992980i	$-0.462260\pi$
$317$	4.25331e10	0.236570	0.118285	+	0.992980i	$0.462260\pi$
$318$	5.49045e11	3.01083
$319$	6.47461e10	0.350071
$320$	−3.82017e10	−0.203661
$321$	−2.90790e10	−0.152865
$322$	1.50406e10	0.0779673
$323$	7.57692e10	0.387330
$324$	−3.16615e11	−1.59617
$325$	1.18859e10	0.0590957
$326$	5.41711e11	2.65637
$327$	2.83505e11	1.37118
$328$	7.17890e10	0.342472
$329$	−1.14119e10	−0.0537001
$330$	−2.43127e10	−0.112855
$331$	−1.36038e11	−0.622921	−0.311461	−	0.950259i	$-0.600818\pi$
$331$	−1.36038e11	−0.622921	−0.311461	+	0.950259i	$0.600818\pi$
$332$	−1.13623e10	−0.0513271
$333$	1.88574e11	0.840393
$334$	−2.71515e11	−1.19381
$335$	−2.46679e10	−0.107012
$336$	1.02295e10	0.0437854
$337$	−4.52614e11	−1.91158	−0.955792	−	0.294042i	$-0.904999\pi$
$337$	−4.52614e11	−1.91158	−0.955792	+	0.294042i	$0.904999\pi$
$338$	−3.60861e11	−1.50389
$339$	−4.34115e11	−1.78528
$340$	1.06742e10	0.0433194
$341$	7.17621e9	0.0287409
$342$	2.83483e11	1.12049
$343$	2.87371e10	0.112104
$344$	−3.77479e10	−0.145338
$345$	−4.09479e10	−0.155613
$346$	1.64751e11	0.617996
$347$	−2.00653e11	−0.742955	−0.371478	−	0.928442i	$-0.621149\pi$
$347$	−2.00653e11	−0.742955	−0.371478	+	0.928442i	$0.621149\pi$
$348$	−3.35147e11	−1.22498
$349$	1.48945e11	0.537416	0.268708	−	0.963222i	$-0.413403\pi$
$349$	1.48945e11	0.537416	0.268708	+	0.963222i	$0.413403\pi$
$350$	2.33245e10	0.0830819
$351$	1.11014e10	0.0390387
$352$	1.77327e11	0.615649
$353$	−3.46998e11	−1.18944	−0.594718	−	0.803934i	$-0.702736\pi$
$353$	−3.46998e11	−1.18944	−0.594718	+	0.803934i	$0.702736\pi$
$354$	3.48982e11	1.18111
$355$	6.52097e9	0.0217914
$356$	2.59731e11	0.857034
$357$	−5.05769e9	−0.0164796
$358$	−2.22291e11	−0.715235
$359$	−5.87619e11	−1.86711	−0.933556	−	0.358431i	$-0.883312\pi$
$359$	−5.87619e11	−1.86711	−0.933556	+	0.358431i	$0.883312\pi$
$360$	8.69219e9	0.0272752
$361$	5.00300e11	1.55042
$362$	3.37267e11	1.03225
$363$	−3.22127e11	−0.973750
$364$	1.44860e9	0.00432507
$365$	5.57947e10	0.164541
$366$	3.51003e11	1.02246
$367$	−8.17833e10	−0.235325	−0.117662	−	0.993054i	$-0.537540\pi$
$367$	−8.17833e10	−0.235325	−0.117662	+	0.993054i	$0.537540\pi$
$368$	2.08601e11	0.592928
$369$	1.35021e11	0.379124
$370$	1.37463e11	0.381310
$371$	−3.37638e10	−0.0925269
$372$	−3.71464e10	−0.100571
$373$	3.70187e11	0.990218	0.495109	−	0.868831i	$-0.335128\pi$
$373$	3.70187e11	0.990218	0.495109	+	0.868831i	$0.335128\pi$
$374$	−6.12371e10	−0.161842
$375$	−1.28267e11	−0.334945
$376$	1.55668e11	0.401655
$377$	1.87193e10	0.0477259
$378$	2.17851e10	0.0548840
$379$	5.17440e11	1.28820	0.644100	−	0.764941i	$-0.277232\pi$
$379$	5.17440e11	1.28820	0.644100	+	0.764941i	$0.277232\pi$
$380$	1.15941e11	0.285241
$381$	−2.67092e11	−0.649380
$382$	5.91779e11	1.42192
$383$	2.03437e11	0.483099	0.241549	−	0.970389i	$-0.422344\pi$
$383$	2.03437e11	0.483099	0.241549	+	0.970389i	$0.422344\pi$
$384$	−4.16321e11	−0.977098
$385$	1.49512e9	0.00346819
$386$	−2.02451e11	−0.464170
$387$	−7.09961e10	−0.160892
$388$	7.40298e11	1.65830
$389$	7.76405e11	1.71916	0.859578	−	0.511005i	$-0.170727\pi$
$389$	7.76405e11	1.71916	0.859578	+	0.511005i	$0.170727\pi$
$390$	−7.02927e9	−0.0153858
$391$	−1.03137e11	−0.223161
$392$	−1.95690e11	−0.418583
$393$	2.61808e11	0.553626
$394$	−5.50838e11	−1.15157
$395$	−1.48530e10	−0.0306993
$396$	−1.28545e11	−0.262681
$397$	4.33956e11	0.876776	0.438388	−	0.898786i	$-0.355550\pi$
$397$	4.33956e11	0.876776	0.438388	+	0.898786i	$0.355550\pi$
$398$	−1.49667e12	−2.98988
$399$	−5.49356e10	−0.108511
$400$	3.23493e11	0.631823
$401$	3.07899e11	0.594645	0.297323	−	0.954777i	$-0.403906\pi$
$401$	3.07899e11	0.594645	0.297323	+	0.954777i	$0.403906\pi$
$402$	−7.32541e11	−1.39899
$403$	2.07478e9	0.00391831
$404$	−1.03819e12	−1.93892
$405$	−9.44791e10	−0.174497
$406$	3.67343e10	0.0670973
$407$	−4.42456e11	−0.799273
$408$	6.89913e10	0.123260
$409$	−5.32344e11	−0.940671	−0.470335	−	0.882488i	$-0.655867\pi$
$409$	−5.32344e11	−0.940671	−0.470335	+	0.882488i	$0.655867\pi$
$410$	9.84248e10	0.172019
$411$	−1.27096e12	−2.19706
$412$	−6.39999e11	−1.09431
$413$	−2.14608e10	−0.0362970
$414$	−3.85876e11	−0.645574
$415$	−3.39057e9	−0.00561120
$416$	5.12686e10	0.0839328
$417$	8.44042e11	1.36695
$418$	−6.65144e11	−1.06567
$419$	−1.78965e11	−0.283665	−0.141833	−	0.989891i	$-0.545299\pi$
$419$	−1.78965e11	−0.283665	−0.141833	+	0.989891i	$0.545299\pi$
$420$	−7.73924e9	−0.0121360
$421$	1.88185e11	0.291954	0.145977	−	0.989288i	$-0.453367\pi$
$421$	1.88185e11	0.291954	0.145977	+	0.989288i	$0.453367\pi$
$422$	1.65647e12	2.54260
$423$	2.92779e11	0.444640
$424$	4.60567e11	0.692064
$425$	−1.59942e11	−0.237800
$426$	1.93647e11	0.284884
$427$	−2.15851e10	−0.0314216
$428$	−1.12074e11	−0.161439
$429$	2.26253e10	0.0322505
$430$	−5.17534e10	−0.0730014
$431$	−6.39015e11	−0.891997	−0.445998	−	0.895034i	$-0.647151\pi$
$431$	−6.39015e11	−0.891997	−0.445998	+	0.895034i	$0.647151\pi$
$432$	3.02142e11	0.417383
$433$	3.97400e11	0.543291	0.271645	−	0.962397i	$-0.412432\pi$
$433$	3.97400e11	0.543291	0.271645	+	0.962397i	$0.412432\pi$
$434$	4.07149e9	0.00550870
$435$	−1.00009e11	−0.133918
$436$	1.09267e12	1.44810
$437$	−1.12025e12	−1.46943
$438$	1.65688e12	2.15109
$439$	−1.41931e11	−0.182384	−0.0911918	−	0.995833i	$-0.529068\pi$
$439$	−1.41931e11	−0.182384	−0.0911918	+	0.995833i	$0.529068\pi$
$440$	−2.03947e10	−0.0259407
$441$	−3.68053e11	−0.463380
$442$	−1.77048e10	−0.0220644
$443$	1.16614e12	1.43858	0.719289	−	0.694711i	$-0.244468\pi$
$443$	1.16614e12	1.43858	0.719289	+	0.694711i	$0.244468\pi$
$444$	2.29030e12	2.79685
$445$	7.75046e10	0.0936931
$446$	−4.52893e10	−0.0541987
$447$	−3.68753e11	−0.436870
$448$	6.97631e10	0.0818229
$449$	9.04654e11	1.05045	0.525223	−	0.850964i	$-0.323982\pi$
$449$	9.04654e11	1.05045	0.525223	+	0.850964i	$0.323982\pi$
$450$	−5.98407e11	−0.687923
$451$	−3.16803e11	−0.360574
$452$	−1.67314e12	−1.88542
$453$	8.58097e11	0.957402
$454$	−2.15176e12	−2.37707
$455$	4.32268e8	0.000472827 0
$456$	7.49368e11	0.811621
$457$	−2.89019e10	−0.0309959	−0.0154979	−	0.999880i	$-0.504933\pi$
$457$	−2.89019e10	−0.0309959	−0.0154979	+	0.999880i	$0.504933\pi$
$458$	1.14932e12	1.22052
$459$	−1.49385e11	−0.157091
$460$	−1.57819e11	−0.164342
$461$	−3.33362e11	−0.343765	−0.171883	−	0.985117i	$-0.554985\pi$
$461$	−3.33362e11	−0.343765	−0.171883	+	0.985117i	$0.554985\pi$
$462$	4.43993e10	0.0453406
$463$	9.65145e11	0.976064	0.488032	−	0.872826i	$-0.337715\pi$
$463$	9.65145e11	0.976064	0.488032	+	0.872826i	$0.337715\pi$
$464$	5.09477e11	0.510263
$465$	−1.10846e10	−0.0109947
$466$	−1.11200e12	−1.09237
$467$	−7.21341e11	−0.701802	−0.350901	−	0.936413i	$-0.614125\pi$
$467$	−7.21341e11	−0.701802	−0.350901	+	0.936413i	$0.614125\pi$
$468$	−3.71649e10	−0.0358118
$469$	4.50479e10	0.0429929
$470$	2.13425e11	0.201746
$471$	−1.94568e12	−1.82170
$472$	2.92744e11	0.271487
$473$	1.66580e11	0.153020
$474$	−4.41077e11	−0.401340
$475$	−1.73725e12	−1.56582
$476$	−1.94930e10	−0.0174040
$477$	8.66233e11	0.766129
$478$	1.45180e12	1.27198
$479$	1.57016e12	1.36281	0.681403	−	0.731909i	$-0.261370\pi$
$479$	1.57016e12	1.36281	0.681403	+	0.731909i	$0.261370\pi$
$480$	−2.73906e11	−0.235513
$481$	−1.27922e11	−0.108967
$482$	−2.20737e12	−1.86279
$483$	7.47781e10	0.0625191
$484$	−1.24152e12	−1.02837
$485$	2.20908e11	0.181290
$486$	−1.60330e12	−1.30362
$487$	1.48730e12	1.19817	0.599084	−	0.800686i	$-0.295532\pi$
$487$	1.48730e12	1.19817	0.599084	+	0.800686i	$0.295532\pi$
$488$	2.94439e11	0.235021
$489$	2.69326e12	2.13004
$490$	−2.68297e11	−0.210248
$491$	9.71236e11	0.754150	0.377075	−	0.926183i	$-0.376930\pi$
$491$	9.71236e11	0.754150	0.377075	+	0.926183i	$0.376930\pi$
$492$	1.63987e12	1.26173
$493$	−2.51896e11	−0.192048
$494$	−1.92306e11	−0.145285
$495$	−3.83584e10	−0.0287169
$496$	5.64685e10	0.0418927
$497$	−1.19084e10	−0.00875489
$498$	−1.00687e11	−0.0733567
$499$	1.21621e12	0.878127	0.439064	−	0.898456i	$-0.355310\pi$
$499$	1.21621e12	0.878127	0.439064	+	0.898456i	$0.355310\pi$
$500$	−4.94357e11	−0.353733
$501$	−1.34991e12	−0.957272
$502$	−3.44247e12	−2.41938
$503$	2.43415e12	1.69548	0.847739	−	0.530414i	$-0.177964\pi$
$503$	2.43415e12	1.69548	0.847739	+	0.530414i	$0.177964\pi$
$504$	−1.58735e10	−0.0109581
$505$	−3.09799e11	−0.211968
$506$	9.05392e11	0.613987
$507$	−1.79412e12	−1.20591
$508$	−1.02941e12	−0.685807
$509$	−2.50151e12	−1.65186	−0.825930	−	0.563773i	$-0.809349\pi$
$509$	−2.50151e12	−1.65186	−0.825930	+	0.563773i	$0.809349\pi$
$510$	9.45891e10	0.0619120
$511$	−1.01891e11	−0.0661060
$512$	1.81611e12	1.16796
$513$	−1.62259e12	−1.03438
$514$	−2.72689e12	−1.72319
$515$	−1.90978e11	−0.119633
$516$	−8.62274e11	−0.535453
$517$	−6.86956e11	−0.422884
$518$	−2.51031e11	−0.153195
$519$	8.19103e11	0.495548
$520$	−5.89651e9	−0.00353655
$521$	2.28180e12	1.35678	0.678388	−	0.734704i	$-0.262679\pi$
$521$	2.28180e12	1.35678	0.678388	+	0.734704i	$0.262679\pi$
$522$	−9.42445e11	−0.555570
$523$	1.67259e12	0.977537	0.488768	−	0.872414i	$-0.337446\pi$
$523$	1.67259e12	0.977537	0.488768	+	0.872414i	$0.337446\pi$
$524$	1.00904e12	0.584682
$525$	1.15964e11	0.0666202
$526$	3.16392e12	1.80215
$527$	−2.79192e10	−0.0157672
$528$	6.15785e11	0.344807
$529$	−2.76274e11	−0.153388
$530$	6.31450e11	0.347614
$531$	5.50593e11	0.300542
$532$	−2.11729e11	−0.114598
$533$	−9.15937e10	−0.0491579
$534$	2.30158e12	1.22487
$535$	−3.34434e10	−0.0176489
$536$	−6.14492e11	−0.321570
$537$	−1.10518e12	−0.573520
$538$	−2.18034e12	−1.12203
$539$	8.63574e11	0.440707
$540$	−2.28588e11	−0.115686
$541$	−8.84734e11	−0.444043	−0.222021	−	0.975042i	$-0.571265\pi$
$541$	−8.84734e11	−0.444043	−0.222021	+	0.975042i	$0.571265\pi$
$542$	4.75688e12	2.36769
$543$	1.67681e12	0.827723
$544$	−6.89894e11	−0.337744
$545$	3.26056e11	0.158310
$546$	1.28367e10	0.00618138
$547$	−2.72146e12	−1.29975	−0.649874	−	0.760042i	$-0.725178\pi$
$547$	−2.72146e12	−1.29975	−0.649874	+	0.760042i	$0.725178\pi$
$548$	−4.89844e12	−2.32031
$549$	5.53780e11	0.260173
$550$	1.40406e12	0.654264
$551$	−2.73604e12	−1.26456
$552$	−1.02004e12	−0.467617
$553$	2.71242e10	0.0123337
$554$	4.55676e12	2.05524
$555$	6.83433e11	0.305758
$556$	3.25305e12	1.44363
$557$	−2.68557e12	−1.18219	−0.591096	−	0.806601i	$-0.701305\pi$
$557$	−2.68557e12	−1.18219	−0.591096	+	0.806601i	$0.701305\pi$
$558$	−1.04457e11	−0.0456124
$559$	4.81615e10	0.0208616
$560$	1.17649e10	0.00505524
$561$	−3.04457e11	−0.129775
$562$	−4.17369e12	−1.76484
$563$	−2.81923e12	−1.18261	−0.591307	−	0.806446i	$-0.701388\pi$
$563$	−2.81923e12	−1.18261	−0.591307	+	0.806446i	$0.701388\pi$
$564$	3.55591e12	1.47977
$565$	−4.99271e11	−0.206119
$566$	5.05936e12	2.07215
$567$	1.72535e11	0.0701059
$568$	1.62441e11	0.0654830
$569$	3.57453e11	0.142960	0.0714799	−	0.997442i	$-0.477228\pi$
$569$	3.57453e11	0.142960	0.0714799	+	0.997442i	$0.477228\pi$
$570$	1.02741e12	0.407667
$571$	−3.25953e11	−0.128319	−0.0641596	−	0.997940i	$-0.520437\pi$
$571$	−3.25953e11	−0.128319	−0.0641596	+	0.997940i	$0.520437\pi$
$572$	8.72010e10	0.0340596
$573$	2.94219e12	1.14018
$574$	−1.79741e11	−0.0691104
$575$	2.36474e12	0.902149
$576$	−1.78982e12	−0.677499
$577$	−2.50107e11	−0.0939365	−0.0469683	−	0.998896i	$-0.514956\pi$
$577$	−2.50107e11	−0.0939365	−0.0469683	+	0.998896i	$0.514956\pi$
$578$	2.38244e11	0.0887865
$579$	−1.00654e12	−0.372200
$580$	−3.85449e11	−0.141430
$581$	6.19177e9	0.00225435
$582$	6.56010e12	2.37005
$583$	−2.03247e12	−0.728643
$584$	1.38988e12	0.494446
$585$	−1.10901e10	−0.00391504
$586$	4.00262e12	1.40218
$587$	9.14514e10	0.0317921	0.0158960	−	0.999874i	$-0.494940\pi$
$587$	9.14514e10	0.0317921	0.0158960	+	0.999874i	$0.494940\pi$
$588$	−4.47014e12	−1.54214
$589$	−3.03252e11	−0.103821
$590$	4.01361e11	0.136364
$591$	−2.73864e12	−0.923402
$592$	−3.48162e12	−1.16502
$593$	−2.60815e12	−0.866138	−0.433069	−	0.901361i	$-0.642569\pi$
$593$	−2.60815e12	−0.866138	−0.433069	+	0.901361i	$0.642569\pi$
$594$	1.31139e12	0.432208
$595$	−5.81680e9	−0.00190264
$596$	−1.42122e12	−0.461376
$597$	−7.44111e12	−2.39747
$598$	2.61766e11	0.0837063
$599$	1.25671e12	0.398853	0.199427	−	0.979913i	$-0.436092\pi$
$599$	1.25671e12	0.398853	0.199427	+	0.979913i	$0.436092\pi$
$600$	−1.58185e12	−0.498292
$601$	−9.01991e11	−0.282012	−0.141006	−	0.990009i	$-0.545034\pi$
$601$	−9.01991e11	−0.282012	−0.141006	+	0.990009i	$0.545034\pi$
$602$	9.45108e10	0.0293290
$603$	−1.15574e12	−0.355984
$604$	3.30722e12	1.01111
$605$	−3.70475e11	−0.112424
$606$	−9.19984e12	−2.77111
$607$	4.29234e12	1.28335	0.641675	−	0.766977i	$-0.278240\pi$
$607$	4.29234e12	1.28335	0.641675	+	0.766977i	$0.278240\pi$
$608$	−7.49348e12	−2.22391
$609$	1.82634e11	0.0538028
$610$	4.03684e11	0.118048
$611$	−1.98612e11	−0.0576528
$612$	5.00108e11	0.144106
$613$	3.09808e12	0.886178	0.443089	−	0.896478i	$-0.353883\pi$
$613$	3.09808e12	0.886178	0.443089	+	0.896478i	$0.353883\pi$
$614$	−1.47927e12	−0.420040
$615$	4.89345e11	0.137936
$616$	3.72444e10	0.0104219
$617$	−2.97483e12	−0.826378	−0.413189	−	0.910645i	$-0.635585\pi$
$617$	−2.97483e12	−0.826378	−0.413189	+	0.910645i	$0.635585\pi$
$618$	−5.67131e12	−1.56399
$619$	−3.10484e10	−0.00850025	−0.00425012	−	0.999991i	$-0.501353\pi$
$619$	−3.10484e10	−0.00850025	−0.00425012	+	0.999991i	$0.501353\pi$
$620$	−4.27217e10	−0.0116114
$621$	2.20867e12	0.595961
$622$	6.11910e12	1.63920
$623$	−1.41537e11	−0.0376421
$624$	1.78035e11	0.0470083
$625$	3.59269e12	0.941803
$626$	−2.15227e12	−0.560160
$627$	−3.30694e12	−0.854521
$628$	−7.49891e12	−1.92389
$629$	1.72138e12	0.438480
$630$	−2.17630e10	−0.00550410
$631$	5.20764e12	1.30770	0.653851	−	0.756623i	$-0.273152\pi$
$631$	5.20764e12	1.30770	0.653851	+	0.756623i	$0.273152\pi$
$632$	−3.69998e11	−0.0922513
$633$	8.23559e12	2.03882
$634$	1.45264e12	0.357072
$635$	−3.07180e11	−0.0749741
$636$	1.05207e13	2.54970
$637$	2.49676e11	0.0600826
$638$	2.21128e12	0.528386
$639$	3.05519e11	0.0724911
$640$	−4.78806e11	−0.112811
$641$	2.80533e12	0.656330	0.328165	−	0.944620i	$-0.393570\pi$
$641$	2.80533e12	0.656330	0.328165	+	0.944620i	$0.393570\pi$
$642$	−9.93139e11	−0.230729
$643$	2.80520e12	0.647164	0.323582	−	0.946200i	$-0.395113\pi$
$643$	2.80520e12	0.647164	0.323582	+	0.946200i	$0.395113\pi$
$644$	2.88205e11	0.0660260
$645$	−2.57306e11	−0.0585371
$646$	2.58776e12	0.584624
$647$	4.72530e12	1.06013	0.530066	−	0.847956i	$-0.322167\pi$
$647$	4.72530e12	1.06013	0.530066	+	0.847956i	$0.322167\pi$
$648$	−2.35353e12	−0.524364
$649$	−1.29187e12	−0.285837
$650$	4.05940e11	0.0891973
$651$	2.02425e10	0.00441722
$652$	1.03802e13	2.24953
$653$	−7.04467e12	−1.51618	−0.758091	−	0.652149i	$-0.773868\pi$
$653$	−7.04467e12	−1.51618	−0.758091	+	0.652149i	$0.773868\pi$
$654$	9.68258e12	2.06962
$655$	3.01103e11	0.0639188
$656$	−2.49287e12	−0.525572
$657$	2.61408e12	0.547362
$658$	−3.89751e11	−0.0810533
$659$	−2.93823e12	−0.606879	−0.303439	−	0.952851i	$-0.598135\pi$
$659$	−2.93823e12	−0.606879	−0.303439	+	0.952851i	$0.598135\pi$
$660$	−4.65877e11	−0.0955704
$661$	−7.72453e11	−0.157386	−0.0786929	−	0.996899i	$-0.525075\pi$
$661$	−7.72453e11	−0.157386	−0.0786929	+	0.996899i	$0.525075\pi$
$662$	−4.64611e12	−0.940219
$663$	−8.80242e10	−0.0176926
$664$	−8.44610e10	−0.0168616
$665$	−6.31808e10	−0.0125282
$666$	6.44039e12	1.26846
$667$	3.72429e12	0.728580
$668$	−5.20274e12	−1.01097
$669$	−2.25168e11	−0.0434599
$670$	−8.42487e11	−0.161520
$671$	−1.29935e12	−0.247443
$672$	5.00200e11	0.0946198
$673$	2.83634e12	0.532954	0.266477	−	0.963841i	$-0.414140\pi$
$673$	2.83634e12	0.532954	0.266477	+	0.963841i	$0.414140\pi$
$674$	−1.54582e13	−2.88529
$675$	3.42514e12	0.635055
$676$	−6.91478e12	−1.27356
$677$	−2.65986e12	−0.486642	−0.243321	−	0.969946i	$-0.578237\pi$
$677$	−2.65986e12	−0.486642	−0.243321	+	0.969946i	$0.578237\pi$
$678$	−1.48264e13	−2.69465
$679$	−4.03416e11	−0.0728349
$680$	7.93461e10	0.0142310
$681$	−1.06980e13	−1.90608
$682$	2.45090e11	0.0433807
$683$	−2.44022e12	−0.429078	−0.214539	−	0.976715i	$-0.568825\pi$
$683$	−2.44022e12	−0.429078	−0.214539	+	0.976715i	$0.568825\pi$
$684$	5.43206e12	0.948882
$685$	−1.46171e12	−0.253661
$686$	9.81463e11	0.169206
$687$	5.71415e12	0.978693
$688$	1.31079e12	0.223042
$689$	−5.87625e11	−0.0993376
$690$	−1.39850e12	−0.234878
$691$	5.13446e12	0.856730	0.428365	−	0.903606i	$-0.359090\pi$
$691$	5.13446e12	0.856730	0.428365	+	0.903606i	$0.359090\pi$
$692$	3.15694e12	0.523345
$693$	7.00492e10	0.0115373
$694$	−6.85293e12	−1.12139
$695$	9.70724e11	0.157821
$696$	−2.49129e12	−0.402423
$697$	1.23253e12	0.197810
$698$	5.08693e12	0.811159
$699$	−5.52861e12	−0.875929
$700$	4.46941e11	0.0703573
$701$	−4.00510e12	−0.626444	−0.313222	−	0.949680i	$-0.601408\pi$
$701$	−4.00510e12	−0.626444	−0.313222	+	0.949680i	$0.601408\pi$
$702$	3.79147e11	0.0589238
$703$	1.86973e13	2.88722
$704$	4.19951e12	0.644350
$705$	1.06110e12	0.161772
$706$	−1.18511e13	−1.79530
$707$	5.65748e11	0.0851600
$708$	6.68715e12	1.00021
$709$	−7.18171e12	−1.06738	−0.533691	−	0.845680i	$-0.679195\pi$
$709$	−7.18171e12	−1.06738	−0.533691	+	0.845680i	$0.679195\pi$
$710$	2.22712e11	0.0328912
$711$	−6.95892e11	−0.102124
$712$	1.93069e12	0.281548
$713$	4.12785e11	0.0598166
$714$	−1.72736e11	−0.0248738
$715$	2.60211e10	0.00372348
$716$	−4.25951e12	−0.605691
$717$	7.21802e12	1.01996
$718$	−2.00690e13	−2.81816
$719$	2.19372e10	0.00306127	0.00153063	−	0.999999i	$-0.499513\pi$
$719$	2.19372e10	0.00306127	0.00153063	+	0.999999i	$0.499513\pi$
$720$	−3.01836e11	−0.0418577
$721$	3.48760e11	0.0480637
$722$	1.70868e13	2.34015
$723$	−1.09745e13	−1.49370
$724$	6.46266e12	0.874154
$725$	5.77553e12	0.776373
$726$	−1.10017e13	−1.46975
$727$	3.47360e11	0.0461185	0.0230593	−	0.999734i	$-0.492659\pi$
$727$	3.47360e11	0.0461185	0.0230593	+	0.999734i	$0.492659\pi$
$728$	1.07681e10	0.00142084
$729$	1.55133e12	0.203437
$730$	1.90556e12	0.248354
$731$	−6.48083e11	−0.0839465
$732$	6.72586e12	0.865861
$733$	3.58285e11	0.0458417	0.0229208	−	0.999737i	$-0.492703\pi$
$733$	3.58285e11	0.0458417	0.0229208	+	0.999737i	$0.492703\pi$
$734$	−2.79316e12	−0.355192
$735$	−1.33391e12	−0.168590
$736$	1.02001e13	1.28131
$737$	2.71174e12	0.338566
$738$	4.61138e12	0.572239
$739$	−2.16274e12	−0.266750	−0.133375	−	0.991066i	$-0.542581\pi$
$739$	−2.16274e12	−0.266750	−0.133375	+	0.991066i	$0.542581\pi$
$740$	2.63405e12	0.322909
$741$	−9.56100e11	−0.116499
$742$	−1.15314e12	−0.139657
$743$	6.42105e12	0.772959	0.386479	−	0.922298i	$-0.373691\pi$
$743$	6.42105e12	0.772959	0.386479	+	0.922298i	$0.373691\pi$
$744$	−2.76125e11	−0.0330390
$745$	−4.24099e11	−0.0504387
$746$	1.26430e13	1.49461
$747$	−1.58854e11	−0.0186662
$748$	−1.17342e12	−0.137055
$749$	6.10736e10	0.00709064
$750$	−4.38071e12	−0.505555
$751$	−1.15069e13	−1.32002	−0.660010	−	0.751257i	$-0.729448\pi$
$751$	−1.15069e13	−1.32002	−0.660010	+	0.751257i	$0.729448\pi$
$752$	−5.40555e12	−0.616396
$753$	−1.71151e13	−1.94001
$754$	6.39325e11	0.0720361
$755$	9.86888e11	0.110537
$756$	4.17442e11	0.0464781
$757$	−7.80850e12	−0.864243	−0.432122	−	0.901815i	$-0.642235\pi$
$757$	−7.80850e12	−0.864243	−0.432122	+	0.901815i	$0.642235\pi$
$758$	1.76722e13	1.94437
$759$	4.50140e12	0.492333
$760$	8.61840e11	0.0937056
$761$	−6.58284e12	−0.711512	−0.355756	−	0.934579i	$-0.615777\pi$
$761$	−6.58284e12	−0.711512	−0.355756	+	0.934579i	$0.615777\pi$
$762$	−9.12205e12	−0.980156
$763$	−5.95435e11	−0.0636025
$764$	1.13396e13	1.20414
$765$	1.49234e11	0.0157540
$766$	6.94803e12	0.729175
$767$	−3.73505e11	−0.0389688
$768$	2.78808e12	0.289188
$769$	−1.27459e13	−1.31433	−0.657163	−	0.753748i	$-0.728244\pi$
$769$	−1.27459e13	−1.31433	−0.657163	+	0.753748i	$0.728244\pi$
$770$	5.10631e10	0.00523479
$771$	−1.35575e13	−1.38176
$772$	−3.87933e12	−0.393079
$773$	−1.07389e13	−1.08181	−0.540907	−	0.841083i	$-0.681919\pi$
$773$	−1.07389e13	−1.08181	−0.540907	+	0.841083i	$0.681919\pi$
$774$	−2.42474e12	−0.242846
$775$	6.40137e11	0.0637405
$776$	5.50294e12	0.544775
$777$	−1.24807e12	−0.122841
$778$	2.65167e13	2.59484
$779$	1.33874e13	1.30250
$780$	−1.34694e11	−0.0130293
$781$	−7.16848e11	−0.0689442
$782$	−3.52244e12	−0.336832
$783$	5.39434e12	0.512873
$784$	6.79533e12	0.642375
$785$	−2.23770e12	−0.210324
$786$	8.94158e12	0.835627
$787$	3.76105e12	0.349481	0.174740	−	0.984615i	$-0.444091\pi$
$787$	3.76105e12	0.349481	0.174740	+	0.984615i	$0.444091\pi$
$788$	−1.05551e13	−0.975200
$789$	1.57303e13	1.44507
$790$	−5.07278e11	−0.0463366
$791$	9.11756e11	0.0828103
$792$	−9.55531e11	−0.0862942
$793$	−3.75667e11	−0.0337344
$794$	1.48210e13	1.32338
$795$	3.13942e12	0.278739
$796$	−2.86790e13	−2.53195
$797$	2.18200e13	1.91555	0.957773	−	0.287524i	$-0.0928322\pi$
$797$	2.18200e13	1.91555	0.957773	+	0.287524i	$0.0928322\pi$
$798$	−1.87622e12	−0.163784
$799$	2.67262e12	0.231994
$800$	1.58180e13	1.36536
$801$	3.63123e12	0.311679
$802$	1.05157e13	0.897540
$803$	−6.13349e12	−0.520581
$804$	−1.40368e13	−1.18472
$805$	8.60015e10	0.00721813
$806$	7.08602e10	0.00591418
$807$	−1.08401e13	−0.899712
$808$	−7.71729e12	−0.636962
$809$	−1.90714e13	−1.56536	−0.782681	−	0.622423i	$-0.786148\pi$
$809$	−1.90714e13	−1.56536	−0.782681	+	0.622423i	$0.786148\pi$
$810$	−3.22676e12	−0.263381
$811$	−1.86624e13	−1.51486	−0.757430	−	0.652916i	$-0.773546\pi$
$811$	−1.86624e13	−1.51486	−0.757430	+	0.652916i	$0.773546\pi$
$812$	7.03898e11	0.0568208
$813$	2.36501e13	1.89856
$814$	−1.51113e13	−1.20640
$815$	3.09749e12	0.245924
$816$	−2.39572e12	−0.189161
$817$	−7.03934e12	−0.552755
$818$	−1.81812e13	−1.41982
$819$	2.02526e10	0.00157290
$820$	1.88600e12	0.145673
$821$	−4.79906e12	−0.368648	−0.184324	−	0.982866i	$-0.559010\pi$
$821$	−4.79906e12	−0.368648	−0.184324	+	0.982866i	$0.559010\pi$
$822$	−4.34072e13	−3.31618
$823$	2.14502e13	1.62979	0.814895	−	0.579609i	$-0.196795\pi$
$823$	2.14502e13	1.62979	0.814895	+	0.579609i	$0.196795\pi$
$824$	−4.75738e12	−0.359497
$825$	6.98065e12	0.524630
$826$	−7.32955e11	−0.0547857
$827$	−1.32157e13	−0.982463	−0.491231	−	0.871029i	$-0.663453\pi$
$827$	−1.32157e13	−0.982463	−0.491231	+	0.871029i	$0.663453\pi$
$828$	−7.39411e12	−0.546700
$829$	−7.78893e12	−0.572773	−0.286386	−	0.958114i	$-0.592454\pi$
$829$	−7.78893e12	−0.572773	−0.286386	+	0.958114i	$0.592454\pi$
$830$	−1.15799e11	−0.00846938
$831$	2.26551e13	1.64802
$832$	1.21416e12	0.0878456
$833$	−3.35975e12	−0.241771
$834$	2.88267e13	2.06323
$835$	−1.55252e12	−0.110522
$836$	−1.27454e13	−0.902454
$837$	5.97887e11	0.0421070
$838$	−6.11223e12	−0.428156
$839$	−9.65976e12	−0.673035	−0.336517	−	0.941677i	$-0.609249\pi$
$839$	−9.65976e12	−0.673035	−0.336517	+	0.941677i	$0.609249\pi$
$840$	−5.75290e10	−0.00398685
$841$	−5.41113e12	−0.372997
$842$	6.42710e12	0.440667
$843$	−2.07506e13	−1.41516
$844$	3.17411e13	2.15318
$845$	−2.06340e12	−0.139228
$846$	9.99934e12	0.671127
$847$	6.76552e11	0.0451675
$848$	−1.59932e13	−1.06207
$849$	2.51540e13	1.66158
$850$	−5.46251e12	−0.358928
$851$	−2.54507e13	−1.66348
$852$	3.71064e12	0.241252
$853$	2.43508e13	1.57486	0.787430	−	0.616404i	$-0.211411\pi$
$853$	2.43508e13	1.57486	0.787430	+	0.616404i	$0.211411\pi$
$854$	−7.37198e11	−0.0474268
$855$	1.62095e12	0.103734
$856$	−8.33096e11	−0.0530351
$857$	2.45424e13	1.55419	0.777095	−	0.629383i	$-0.216692\pi$
$857$	2.45424e13	1.55419	0.777095	+	0.629383i	$0.216692\pi$
$858$	7.72726e11	0.0486780
$859$	−2.12084e13	−1.32904	−0.664521	−	0.747270i	$-0.731364\pi$
$859$	−2.12084e13	−1.32904	−0.664521	+	0.747270i	$0.731364\pi$
$860$	−9.91692e11	−0.0618207
$861$	−8.93630e11	−0.0554170
$862$	−2.18244e13	−1.34635
$863$	1.64190e13	1.00762	0.503811	−	0.863814i	$-0.331931\pi$
$863$	1.64190e13	1.00762	0.503811	+	0.863814i	$0.331931\pi$
$864$	1.47740e13	0.901960
$865$	9.42042e11	0.0572134
$866$	1.35725e13	0.820027
$867$	1.18449e12	0.0711946
$868$	7.80173e10	0.00466500
$869$	1.63279e12	0.0971273
$870$	−3.41563e12	−0.202132
$871$	7.84015e11	0.0461575
$872$	8.12224e12	0.475720
$873$	1.03499e13	0.603078
$874$	−3.82600e13	−2.21791
$875$	2.69394e11	0.0155364
$876$	3.17490e13	1.82163
$877$	7.74986e12	0.442380	0.221190	−	0.975231i	$-0.429006\pi$
$877$	7.74986e12	0.442380	0.221190	+	0.975231i	$0.429006\pi$
$878$	−4.84738e12	−0.275285
$879$	1.99001e13	1.12436
$880$	7.08207e11	0.0398096
$881$	1.47006e12	0.0822135	0.0411068	−	0.999155i	$-0.486912\pi$
$881$	1.47006e12	0.0822135	0.0411068	+	0.999155i	$0.486912\pi$
$882$	−1.25702e13	−0.699412
$883$	−2.27229e13	−1.25788	−0.628941	−	0.777453i	$-0.716511\pi$
$883$	−2.27229e13	−1.25788	−0.628941	+	0.777453i	$0.716511\pi$
$884$	−3.39257e11	−0.0186850
$885$	1.99547e12	0.109345
$886$	3.98273e13	2.17135
$887$	−2.54193e13	−1.37882	−0.689411	−	0.724371i	$-0.742130\pi$
$887$	−2.54193e13	−1.37882	−0.689411	+	0.724371i	$0.742130\pi$
$888$	1.70247e13	0.918802
$889$	5.60965e11	0.0301216
$890$	2.64703e12	0.141418
$891$	1.03861e13	0.552079
$892$	−8.67828e11	−0.0458978
$893$	2.90294e13	1.52759
$894$	−1.25941e13	−0.659398
$895$	−1.27106e12	−0.0662157
$896$	8.74385e11	0.0453228
$897$	1.30144e12	0.0671209
$898$	3.08968e13	1.58551
$899$	1.00817e12	0.0514771
$900$	−1.14666e13	−0.582563
$901$	7.90735e12	0.399733
$902$	−1.08198e13	−0.544240
$903$	4.69886e11	0.0235178
$904$	−1.24371e13	−0.619387
$905$	1.92848e12	0.0955646
$906$	2.93067e13	1.44508
$907$	2.33059e13	1.14349	0.571745	−	0.820431i	$-0.306267\pi$
$907$	2.33059e13	1.14349	0.571745	+	0.820431i	$0.306267\pi$
$908$	−4.12317e13	−2.01300
$909$	−1.45147e13	−0.705131
$910$	1.47633e10	0.000713671 0
$911$	−6.19635e12	−0.298060	−0.149030	−	0.988833i	$-0.547615\pi$
$911$	−6.19635e12	−0.298060	−0.149030	+	0.988833i	$0.547615\pi$
$912$	−2.60218e13	−1.24555
$913$	3.72724e11	0.0177529
$914$	−9.87092e11	−0.0467842
$915$	2.00702e12	0.0946580
$916$	2.20231e13	1.03359
$917$	−5.49866e11	−0.0256800
$918$	−5.10198e12	−0.237108
$919$	−2.57602e13	−1.19132	−0.595661	−	0.803236i	$-0.703110\pi$
$919$	−2.57602e13	−1.19132	−0.595661	+	0.803236i	$0.703110\pi$
$920$	−1.17313e12	−0.0539886
$921$	−7.35460e12	−0.336815
$922$	−1.13854e13	−0.518869
$923$	−2.07255e11	−0.00939932
$924$	8.50773e11	0.0383963
$925$	−3.94682e13	−1.77260
$926$	3.29628e13	1.47324
$927$	−8.94768e12	−0.397971
$928$	2.49122e13	1.10267
$929$	1.87578e13	0.826251	0.413126	−	0.910674i	$-0.364437\pi$
$929$	1.87578e13	0.826251	0.413126	+	0.910674i	$0.364437\pi$
$930$	−3.78575e11	−0.0165951
$931$	−3.64929e13	−1.59197
$932$	−2.13080e13	−0.925064
$933$	3.04227e13	1.31441
$934$	−2.46361e13	−1.05928
$935$	−3.50152e11	−0.0149832
$936$	−2.76262e11	−0.0117647
$937$	5.64054e12	0.239052	0.119526	−	0.992831i	$-0.461863\pi$
$937$	5.64054e12	0.239052	0.119526	+	0.992831i	$0.461863\pi$
$938$	1.53853e12	0.0648923
$939$	−1.07006e13	−0.449172
$940$	4.08962e12	0.170847
$941$	2.26889e13	0.943321	0.471660	−	0.881780i	$-0.343655\pi$
$941$	2.26889e13	0.943321	0.471660	+	0.881780i	$0.343655\pi$
$942$	−6.64511e13	−2.74962
$943$	−1.82229e13	−0.750439
$944$	−1.01655e13	−0.416636
$945$	1.24566e11	0.00508110
$946$	5.68924e12	0.230964
$947$	−1.49881e13	−0.605582	−0.302791	−	0.953057i	$-0.597918\pi$
$947$	−1.49881e13	−0.605582	−0.302791	+	0.953057i	$0.597918\pi$
$948$	−8.45186e12	−0.339871
$949$	−1.77331e12	−0.0709719
$950$	−5.93326e13	−2.36340
$951$	7.22218e12	0.286323
$952$	−1.44900e11	−0.00571744
$953$	−4.04272e13	−1.58765	−0.793827	−	0.608143i	$-0.791915\pi$
$953$	−4.04272e13	−1.58765	−0.793827	+	0.608143i	$0.791915\pi$
$954$	2.95846e13	1.15637
$955$	3.38377e12	0.131640
$956$	2.78192e13	1.07717
$957$	1.09940e13	0.423693
$958$	5.36259e13	2.05698
$959$	2.66934e12	0.101911
$960$	−6.48671e12	−0.246493
$961$	−2.63279e13	−0.995774
$962$	−4.36895e12	−0.164471
$963$	−1.56689e12	−0.0587109
$964$	−4.22973e13	−1.57749
$965$	−1.15761e12	−0.0429723
$966$	2.55391e12	0.0943644
$967$	−7.15269e12	−0.263057	−0.131529	−	0.991312i	$-0.541989\pi$
$967$	−7.15269e12	−0.263057	−0.131529	+	0.991312i	$0.541989\pi$
$968$	−9.22875e12	−0.337834
$969$	1.28657e13	0.468788
$970$	7.54470e12	0.273633
$971$	2.34500e13	0.846556	0.423278	−	0.906000i	$-0.360879\pi$
$971$	2.34500e13	0.846556	0.423278	+	0.906000i	$0.360879\pi$
$972$	−3.07223e13	−1.10396
$973$	−1.77271e12	−0.0634060
$974$	5.07959e13	1.80848
$975$	2.01824e12	0.0715240
$976$	−1.02244e13	−0.360673
$977$	3.75171e13	1.31736	0.658678	−	0.752425i	$-0.271116\pi$
$977$	3.75171e13	1.31736	0.658678	+	0.752425i	$0.271116\pi$
$978$	9.19834e13	3.21503
$979$	−8.52006e12	−0.296429
$980$	−5.14106e12	−0.178047
$981$	1.52763e13	0.526633
$982$	3.31708e13	1.13829
$983$	5.31777e13	1.81651	0.908256	−	0.418414i	$-0.137414\pi$
$983$	5.31777e13	1.81651	0.908256	+	0.418414i	$0.137414\pi$
$984$	1.21899e13	0.414497
$985$	−3.14968e12	−0.106611
$986$	−8.60304e12	−0.289872
$987$	−1.93775e12	−0.0649936
$988$	−3.68494e12	−0.123034
$989$	9.58193e12	0.318471
$990$	−1.31006e12	−0.0433444
$991$	3.41823e13	1.12582	0.562912	−	0.826517i	$-0.309681\pi$
$991$	3.41823e13	1.12582	0.562912	+	0.826517i	$0.309681\pi$
$992$	2.76117e12	0.0905297
$993$	−2.30994e13	−0.753926
$994$	−4.06711e11	−0.0132144
$995$	−8.55794e12	−0.276799
$996$	−1.92934e12	−0.0621216
$997$	4.83269e13	1.54903	0.774517	−	0.632553i	$-0.217993\pi$
$997$	4.83269e13	1.54903	0.774517	+	0.632553i	$0.217993\pi$
$998$	4.15375e13	1.32542
$999$	−3.68633e13	−1.17098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.a.b.1.6	✓	7
3.2	odd	2		153.10.a.f.1.2		7
4.3	odd	2		272.10.a.g.1.2		7
17.16	even	2		289.10.a.b.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.6	✓	7	1.1	even	1	trivial
153.10.a.f.1.2		7	3.2	odd	2
272.10.a.g.1.2		7	4.3	odd	2
289.10.a.b.1.6		7	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+34.1532 q^{2} +169.801 q^{3} +654.438 q^{4} +195.287 q^{5} +5799.26 q^{6} -356.628 q^{7} +4864.71 q^{8} +9149.54 q^{9} +O(q^{10})\)	\(q+34.1532 q^{2} +169.801 q^{3} +654.438 q^{4} +195.287 q^{5} +5799.26 q^{6} -356.628 q^{7} +4864.71 q^{8} +9149.54 q^{9} +6669.66 q^{10} -21467.8 q^{11} +111125. q^{12} -6206.76 q^{13} -12180.0 q^{14} +33160.0 q^{15} -168927. q^{16} +83521.0 q^{17} +312486. q^{18} +907187. q^{19} +127803. q^{20} -60556.0 q^{21} -733194. q^{22} -1.23486e6 q^{23} +826035. q^{24} -1.91499e6 q^{25} -211980. q^{26} -1.78860e6 q^{27} -233391. q^{28} -3.01596e6 q^{29} +1.13252e6 q^{30} -334277. q^{31} -8.26012e6 q^{32} -3.64527e6 q^{33} +2.85251e6 q^{34} -69644.7 q^{35} +5.98781e6 q^{36} +2.06102e7 q^{37} +3.09833e7 q^{38} -1.05392e6 q^{39} +950014. q^{40} +1.47571e7 q^{41} -2.06818e6 q^{42} -7.75953e6 q^{43} -1.40494e7 q^{44} +1.78679e6 q^{45} -4.21744e7 q^{46} +3.19993e7 q^{47} -2.86841e7 q^{48} -4.02264e7 q^{49} -6.54029e7 q^{50} +1.41820e7 q^{51} -4.06194e6 q^{52} +9.46750e7 q^{53} -6.10862e7 q^{54} -4.19238e6 q^{55} -1.73489e6 q^{56} +1.54042e8 q^{57} -1.03005e8 q^{58} +6.01771e7 q^{59} +2.17012e7 q^{60} +6.05254e7 q^{61} -1.14166e7 q^{62} -3.26298e6 q^{63} -1.95619e8 q^{64} -1.21210e6 q^{65} -1.24497e8 q^{66} -1.26316e8 q^{67} +5.46593e7 q^{68} -2.09681e8 q^{69} -2.37859e6 q^{70} +3.33917e7 q^{71} +4.45099e7 q^{72} +2.85706e8 q^{73} +7.03903e8 q^{74} -3.25168e8 q^{75} +5.93698e8 q^{76} +7.65603e6 q^{77} -3.59946e7 q^{78} -7.60575e7 q^{79} -3.29892e7 q^{80} -4.83797e8 q^{81} +5.04001e8 q^{82} -1.73620e7 q^{83} -3.96301e7 q^{84} +1.63105e7 q^{85} -2.65012e8 q^{86} -5.12115e8 q^{87} -1.04435e8 q^{88} +3.96876e8 q^{89} +6.10244e7 q^{90} +2.21350e6 q^{91} -8.08139e8 q^{92} -5.67608e7 q^{93} +1.09288e9 q^{94} +1.77162e8 q^{95} -1.40258e9 q^{96} +1.13120e9 q^{97} -1.37386e9 q^{98} -1.96421e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * q^99

Introduction

L-functions

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