LMFDB - Embedded newform 289.10.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 4542 x^{10} + 30079 x^{9} + 7481825 x^{8} - 58373994 x^{7} - 5553197164 x^{6} + \cdots + 245077910606835 $ x^12 - 5x^11 - 4542x^10 + 30079x^9 + 7481825x^8 - 58373994x^7 - 5553197164x^6 + 45662797046x^5 + 1825619566875x^4 - 13493392282513x^3 - 214257360688838x^2 + 1064197876989579*x + 245077910606835
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$30.1791$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+31.1791 q^{2} +218.085 q^{3} +460.136 q^{4} +1545.34 q^{5} +6799.71 q^{6} -9980.37 q^{7} -1617.07 q^{8} +27878.3 q^{9} +O(q^{10})$	\(q+31.1791 q^{2} +218.085 q^{3} +460.136 q^{4} +1545.34 q^{5} +6799.71 q^{6} -9980.37 q^{7} -1617.07 q^{8} +27878.3 q^{9} +48182.2 q^{10} -83798.0 q^{11} +100349. q^{12} -139458. q^{13} -311179. q^{14} +337016. q^{15} -286008. q^{16} +869219. q^{18} +296948. q^{19} +711065. q^{20} -2.17657e6 q^{21} -2.61275e6 q^{22} +1.40001e6 q^{23} -352660. q^{24} +434942. q^{25} -4.34819e6 q^{26} +1.78727e6 q^{27} -4.59233e6 q^{28} +2.36124e6 q^{29} +1.05078e7 q^{30} -248397. q^{31} -8.08955e6 q^{32} -1.82751e7 q^{33} -1.54230e7 q^{35} +1.28278e7 q^{36} +866212. q^{37} +9.25856e6 q^{38} -3.04139e7 q^{39} -2.49892e6 q^{40} -1.21048e7 q^{41} -6.78636e7 q^{42} -2.04730e7 q^{43} -3.85585e7 q^{44} +4.30813e7 q^{45} +4.36509e7 q^{46} +3.26948e7 q^{47} -6.23743e7 q^{48} +5.92541e7 q^{49} +1.35611e7 q^{50} -6.41699e7 q^{52} -9.81801e7 q^{53} +5.57254e7 q^{54} -1.29496e8 q^{55} +1.61390e7 q^{56} +6.47600e7 q^{57} +7.36213e7 q^{58} -6.91312e7 q^{59} +1.55073e8 q^{60} -7.72797e6 q^{61} -7.74479e6 q^{62} -2.78235e8 q^{63} -1.05788e8 q^{64} -2.15510e8 q^{65} -5.69802e8 q^{66} +5.63107e6 q^{67} +3.05321e8 q^{69} -4.80876e8 q^{70} -3.00691e8 q^{71} -4.50811e7 q^{72} -2.29683e8 q^{73} +2.70077e7 q^{74} +9.48544e7 q^{75} +1.36636e8 q^{76} +8.36334e8 q^{77} -9.48277e8 q^{78} +6.25980e7 q^{79} -4.41980e8 q^{80} -1.58951e8 q^{81} -3.77416e8 q^{82} +4.72628e8 q^{83} -1.00152e9 q^{84} -6.38329e8 q^{86} +5.14952e8 q^{87} +1.35507e8 q^{88} +1.11220e9 q^{89} +1.34324e9 q^{90} +1.39185e9 q^{91} +6.44194e8 q^{92} -5.41717e7 q^{93} +1.01940e9 q^{94} +4.58884e8 q^{95} -1.76421e9 q^{96} -2.54924e8 q^{97} +1.84749e9 q^{98} -2.33614e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) $ 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9} + 2449 q^{10} - 152886 q^{11} - 41717 q^{12} + 23478 q^{13} - 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} + 2477218 q^{20} - 1395256 q^{21} - 2391095 q^{22} - 2012428 q^{23} - 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} - 3231638 q^{27} + 5978216 q^{28} - 12772842 q^{29} + 181633 q^{30} - 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} - 1352872 q^{37} + 3704404 q^{38} + 1380780 q^{39} - 44739331 q^{40} - 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} - 148233417 q^{44} + 79449336 q^{45} - 31855859 q^{46} + 133558002 q^{47} + 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} + 50215469 q^{54} - 91197532 q^{55} - 267350757 q^{56} - 49507694 q^{57} - 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} - 262041240 q^{61} + 314328847 q^{62} - 218532626 q^{63} + 595820098 q^{64} - 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} - 204290852 q^{71} - 208030791 q^{72} - 673538852 q^{73} - 1274510282 q^{74} - 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} - 165043245 q^{78} - 434002980 q^{79} - 599590757 q^{80} - 389011392 q^{81} + 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} + 262108460 q^{88} + 911678128 q^{89} + 2734590475 q^{90} + 560105446 q^{91} + 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} + 1116511966 q^{95} - 2204198979 q^{96} + 3589270998 q^{97} - 2677144485 q^{98} - 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9 + 2449 * q^10 - 152886 * q^11 - 41717 * q^12 + 23478 * q^13 - 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 + 2477218 * q^20 - 1395256 * q^21 - 2391095 * q^22 - 2012428 * q^23 - 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 - 3231638 * q^27 + 5978216 * q^28 - 12772842 * q^29 + 181633 * q^30 - 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 - 1352872 * q^37 + 3704404 * q^38 + 1380780 * q^39 - 44739331 * q^40 - 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 - 148233417 * q^44 + 79449336 * q^45 - 31855859 * q^46 + 133558002 * q^47 + 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 + 50215469 * q^54 - 91197532 * q^55 - 267350757 * q^56 - 49507694 * q^57 - 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 - 262041240 * q^61 + 314328847 * q^62 - 218532626 * q^63 + 595820098 * q^64 - 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 - 204290852 * q^71 - 208030791 * q^72 - 673538852 * q^73 - 1274510282 * q^74 - 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 - 165043245 * q^78 - 434002980 * q^79 - 599590757 * q^80 - 389011392 * q^81 + 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 + 262108460 * q^88 + 911678128 * q^89 + 2734590475 * q^90 + 560105446 * q^91 + 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 + 1116511966 * q^95 - 2204198979 * q^96 + 3589270998 * q^97 - 2677144485 * q^98 - 2056683494 * 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 $

$2$	31.1791	1.37793	0.688967	−	0.724793i	$-0.258064\pi$
$2$	31.1791	1.37793	0.688967	+	0.724793i	$0.258064\pi$
$3$	218.085	1.55447	0.777233	−	0.629213i	$-0.216623\pi$
$3$	218.085	1.55447	0.777233	+	0.629213i	$0.216623\pi$
$4$	460.136	0.898703
$5$	1545.34	1.10575	0.552877	−	0.833263i	$-0.313530\pi$
$5$	1545.34	1.10575	0.552877	+	0.833263i	$0.313530\pi$
$6$	6799.71	2.14195
$7$	−9980.37	−1.57111	−0.785553	−	0.618795i	$-0.787621\pi$
$7$	−9980.37	−1.57111	−0.785553	+	0.618795i	$0.787621\pi$
$8$	−1617.07	−0.139580
$9$	27878.3	1.41636
$10$	48182.2	1.52366
$11$	−83798.0	−1.72570	−0.862852	−	0.505456i	$-0.831324\pi$
$11$	−83798.0	−1.72570	−0.862852	+	0.505456i	$0.831324\pi$
$12$	100349.	1.39700
$13$	−139458.	−1.35425	−0.677127	−	0.735867i	$-0.736775\pi$
$13$	−139458.	−1.35425	−0.677127	+	0.735867i	$0.736775\pi$
$14$	−311179.	−2.16488
$15$	337016.	1.71885
$16$	−286008.	−1.09104
$17$	0	0
$17$	0	0
$18$	869219.	1.95165
$19$	296948.	0.522744	0.261372	−	0.965238i	$-0.415825\pi$
$19$	296948.	0.522744	0.261372	+	0.965238i	$0.415825\pi$
$20$	711065.	0.993744
$21$	−2.17657e6	−2.44223
$22$	−2.61275e6	−2.37791
$23$	1.40001e6	1.04317	0.521585	−	0.853199i	$-0.325341\pi$
$23$	1.40001e6	1.04317	0.521585	+	0.853199i	$0.325341\pi$
$24$	−352660.	−0.216973
$25$	434942.	0.222690
$26$	−4.34819e6	−1.86607
$27$	1.78727e6	0.647221
$28$	−4.59233e6	−1.41196
$29$	2.36124e6	0.619939	0.309970	−	0.950746i	$-0.399681\pi$
$29$	2.36124e6	0.619939	0.309970	+	0.950746i	$0.399681\pi$
$30$	1.05078e7	2.36847
$31$	−248397.	−0.0483079	−0.0241540	−	0.999708i	$-0.507689\pi$
$31$	−248397.	−0.0483079	−0.0241540	+	0.999708i	$0.507689\pi$
$32$	−8.08955e6	−1.36380
$33$	−1.82751e7	−2.68255
$34$	0	0
$35$	−1.54230e7	−1.73725
$36$	1.28278e7	1.27289
$37$	866212.	0.0759830	0.0379915	−	0.999278i	$-0.487904\pi$
$37$	866212.	0.0759830	0.0379915	+	0.999278i	$0.487904\pi$
$38$	9.25856e6	0.720306
$39$	−3.04139e7	−2.10514
$40$	−2.49892e6	−0.154341
$41$	−1.21048e7	−0.669004	−0.334502	−	0.942395i	$-0.608568\pi$
$41$	−1.21048e7	−0.669004	−0.334502	+	0.942395i	$0.608568\pi$
$42$	−6.78636e7	−3.36523
$43$	−2.04730e7	−0.913216	−0.456608	−	0.889668i	$-0.650936\pi$
$43$	−2.04730e7	−0.913216	−0.456608	+	0.889668i	$0.650936\pi$
$44$	−3.85585e7	−1.55090
$45$	4.30813e7	1.56615
$46$	4.36509e7	1.43742
$47$	3.26948e7	0.977325	0.488662	−	0.872473i	$-0.337485\pi$
$47$	3.26948e7	0.977325	0.488662	+	0.872473i	$0.337485\pi$
$48$	−6.23743e7	−1.69598
$49$	5.92541e7	1.46837
$50$	1.35611e7	0.306852
$51$	0	0
$52$	−6.41699e7	−1.21707
$53$	−9.81801e7	−1.70916	−0.854579	−	0.519322i	$-0.826184\pi$
$53$	−9.81801e7	−1.70916	−0.854579	+	0.519322i	$0.826184\pi$
$54$	5.57254e7	0.891828
$55$	−1.29496e8	−1.90820
$56$	1.61390e7	0.219295
$57$	6.47600e7	0.812587
$58$	7.36213e7	0.854235
$59$	−6.91312e7	−0.742745	−0.371373	−	0.928484i	$-0.621113\pi$
$59$	−6.91312e7	−0.742745	−0.371373	+	0.928484i	$0.621113\pi$
$60$	1.55073e8	1.54474
$61$	−7.72797e6	−0.0714630	−0.0357315	−	0.999361i	$-0.511376\pi$
$61$	−7.72797e6	−0.0714630	−0.0357315	+	0.999361i	$0.511376\pi$
$62$	−7.74479e6	−0.0665652
$63$	−2.78235e8	−2.22525
$64$	−1.05788e8	−0.788185
$65$	−2.15510e8	−1.49747
$66$	−5.69802e8	−3.69637
$67$	5.63107e6	0.0341393	0.0170696	−	0.999854i	$-0.494566\pi$
$67$	5.63107e6	0.0341393	0.0170696	+	0.999854i	$0.494566\pi$
$68$	0	0
$69$	3.05321e8	1.62157
$70$	−4.80876e8	−2.39382
$71$	−3.00691e8	−1.40429	−0.702146	−	0.712033i	$-0.747775\pi$
$71$	−3.00691e8	−1.40429	−0.702146	+	0.712033i	$0.747775\pi$
$72$	−4.50811e7	−0.197696
$73$	−2.29683e8	−0.946620	−0.473310	−	0.880896i	$-0.656941\pi$
$73$	−2.29683e8	−0.946620	−0.473310	+	0.880896i	$0.656941\pi$
$74$	2.70077e7	0.104700
$75$	9.48544e7	0.346164
$76$	1.36636e8	0.469791
$77$	8.36334e8	2.71126
$78$	−9.48277e8	−2.90074
$79$	6.25980e7	0.180817	0.0904084	−	0.995905i	$-0.471183\pi$
$79$	6.25980e7	0.180817	0.0904084	+	0.995905i	$0.471183\pi$
$80$	−4.41980e8	−1.20642
$81$	−1.58951e8	−0.410280
$82$	−3.77416e8	−0.921844
$83$	4.72628e8	1.09312	0.546560	−	0.837420i	$-0.315937\pi$
$83$	4.72628e8	1.09312	0.546560	+	0.837420i	$0.315937\pi$
$84$	−1.00152e9	−2.19484
$85$	0	0
$86$	−6.38329e8	−1.25835
$87$	5.14952e8	0.963674
$88$	1.35507e8	0.240874
$89$	1.11220e9	1.87901	0.939503	−	0.342540i	$-0.111287\pi$
$89$	1.11220e9	1.87901	0.939503	+	0.342540i	$0.111287\pi$
$90$	1.34324e9	2.15805
$91$	1.39185e9	2.12767
$92$	6.44194e8	0.937500
$93$	−5.41717e7	−0.0750930
$94$	1.01940e9	1.34669
$95$	4.58884e8	0.578025
$96$	−1.76421e9	−2.11997
$97$	−2.54924e8	−0.292373	−0.146187	−	0.989257i	$-0.546700\pi$
$97$	−2.54924e8	−0.292373	−0.146187	+	0.989257i	$0.546700\pi$
$98$	1.84749e9	2.02332
$99$	−2.33614e9	−2.44422
$100$	2.00132e8	0.200132
$101$	−1.56102e8	−0.149267	−0.0746334	−	0.997211i	$-0.523779\pi$
$101$	−1.56102e8	−0.149267	−0.0746334	+	0.997211i	$0.523779\pi$
$102$	0	0
$103$	−1.09329e9	−0.957126	−0.478563	−	0.878053i	$-0.658842\pi$
$103$	−1.09329e9	−0.957126	−0.478563	+	0.878053i	$0.658842\pi$
$104$	2.25514e8	0.189027
$105$	−3.36354e9	−2.70050
$106$	−3.06117e9	−2.35511
$107$	5.99576e8	0.442199	0.221099	−	0.975251i	$-0.429036\pi$
$107$	5.99576e8	0.442199	0.221099	+	0.975251i	$0.429036\pi$
$108$	8.22386e8	0.581659
$109$	−2.30079e9	−1.56120	−0.780599	−	0.625032i	$-0.785086\pi$
$109$	−2.30079e9	−1.56120	−0.780599	+	0.625032i	$0.785086\pi$
$110$	−4.03757e9	−2.62938
$111$	1.88908e8	0.118113
$112$	2.85447e9	1.71413
$113$	1.56970e9	0.905655	0.452828	−	0.891598i	$-0.350415\pi$
$113$	1.56970e9	0.905655	0.452828	+	0.891598i	$0.350415\pi$
$114$	2.01916e9	1.11969
$115$	2.16348e9	1.15349
$116$	1.08649e9	0.557141
$117$	−3.88786e9	−1.91811
$118$	−2.15545e9	−1.02345
$119$	0	0
$120$	−5.44978e8	−0.239918
$121$	4.66415e9	1.97806
$122$	−2.40951e8	−0.0984713
$123$	−2.63987e9	−1.03994
$124$	−1.14296e8	−0.0434145
$125$	−2.34610e9	−0.859513
$126$	−8.67512e9	−3.06625
$127$	5.24469e9	1.78897	0.894486	−	0.447096i	$-0.147542\pi$
$127$	5.24469e9	1.78897	0.894486	+	0.447096i	$0.147542\pi$
$128$	8.43462e8	0.277728
$129$	−4.46486e9	−1.41956
$130$	−6.71942e9	−2.06342
$131$	−3.07931e8	−0.0913551	−0.0456776	−	0.998956i	$-0.514545\pi$
$131$	−3.07931e8	−0.0913551	−0.0456776	+	0.998956i	$0.514545\pi$
$132$	−8.40904e9	−2.41081
$133$	−2.96365e9	−0.821285
$134$	1.75572e8	0.0470417
$135$	2.76193e9	0.715666
$136$	0	0
$137$	−9.97197e8	−0.241846	−0.120923	−	0.992662i	$-0.538585\pi$
$137$	−9.97197e8	−0.241846	−0.120923	+	0.992662i	$0.538585\pi$
$138$	9.51964e9	2.23442
$139$	−5.18117e9	−1.17723	−0.588615	−	0.808413i	$-0.700327\pi$
$139$	−5.18117e9	−1.17723	−0.588615	+	0.808413i	$0.700327\pi$
$140$	−7.09669e9	−1.56128
$141$	7.13027e9	1.51922
$142$	−9.37527e9	−1.93502
$143$	1.16863e10	2.33704
$144$	−7.97342e9	−1.54530
$145$	3.64891e9	0.685500
$146$	−7.16130e9	−1.30438
$147$	1.29225e10	2.28253
$148$	3.98575e8	0.0682862
$149$	−8.19371e8	−0.136189	−0.0680945	−	0.997679i	$-0.521692\pi$
$149$	−8.19371e8	−0.136189	−0.0680945	+	0.997679i	$0.521692\pi$
$150$	2.95748e9	0.476991
$151$	4.49983e9	0.704368	0.352184	−	0.935931i	$-0.385439\pi$
$151$	4.49983e9	0.704368	0.352184	+	0.935931i	$0.385439\pi$
$152$	−4.80186e8	−0.0729647
$153$	0	0
$154$	2.60762e10	3.73594
$155$	−3.83857e8	−0.0534167
$156$	−1.39945e10	−1.89190
$157$	9.27242e9	1.21799	0.608997	−	0.793173i	$-0.291572\pi$
$157$	9.27242e9	1.21799	0.608997	+	0.793173i	$0.291572\pi$
$158$	1.95175e9	0.249154
$159$	−2.14116e10	−2.65683
$160$	−1.25011e10	−1.50802
$161$	−1.39726e10	−1.63893
$162$	−4.95595e9	−0.565339
$163$	1.26067e10	1.39881	0.699404	−	0.714727i	$-0.253449\pi$
$163$	1.26067e10	1.39881	0.699404	+	0.714727i	$0.253449\pi$
$164$	−5.56984e9	−0.601236
$165$	−2.82412e10	−2.96624
$166$	1.47361e10	1.50625
$167$	4.82015e9	0.479553	0.239776	−	0.970828i	$-0.422926\pi$
$167$	4.82015e9	0.479553	0.239776	+	0.970828i	$0.422926\pi$
$168$	3.51967e9	0.340887
$169$	8.84417e9	0.834002
$170$	0	0
$171$	8.27838e9	0.740394
$172$	−9.42036e9	−0.820710
$173$	−1.50038e10	−1.27348	−0.636742	−	0.771077i	$-0.719718\pi$
$173$	−1.50038e10	−1.27348	−0.636742	+	0.771077i	$0.719718\pi$
$174$	1.60557e10	1.32788
$175$	−4.34088e9	−0.349870
$176$	2.39669e10	1.88281
$177$	−1.50765e10	−1.15457
$178$	3.46774e10	2.58915
$179$	1.73939e9	0.126637	0.0633183	−	0.997993i	$-0.479832\pi$
$179$	1.73939e9	0.126637	0.0633183	+	0.997993i	$0.479832\pi$
$180$	1.98233e10	1.40750
$181$	1.21588e10	0.842050	0.421025	−	0.907049i	$-0.361670\pi$
$181$	1.21588e10	0.842050	0.421025	+	0.907049i	$0.361670\pi$
$182$	4.33965e10	2.93180
$183$	−1.68536e9	−0.111087
$184$	−2.26391e9	−0.145606
$185$	1.33859e9	0.0840185
$186$	−1.68903e9	−0.103473
$187$	0	0
$188$	1.50441e10	0.878325
$189$	−1.78376e10	−1.01685
$190$	1.43076e10	0.796481
$191$	2.02435e10	1.10062	0.550308	−	0.834962i	$-0.314510\pi$
$191$	2.02435e10	1.10062	0.550308	+	0.834962i	$0.314510\pi$
$192$	−2.30709e10	−1.22521
$193$	−7.65687e8	−0.0397231	−0.0198616	−	0.999803i	$-0.506323\pi$
$193$	−7.65687e8	−0.0397231	−0.0198616	+	0.999803i	$0.506323\pi$
$194$	−7.94830e9	−0.402871
$195$	−4.69997e10	−2.32776
$196$	2.72649e10	1.31963
$197$	−1.12327e10	−0.531355	−0.265677	−	0.964062i	$-0.585596\pi$
$197$	−1.12327e10	−0.531355	−0.265677	+	0.964062i	$0.585596\pi$
$198$	−7.28388e10	−3.36798
$199$	2.72056e10	1.22976	0.614880	−	0.788621i	$-0.289205\pi$
$199$	2.72056e10	1.22976	0.614880	+	0.788621i	$0.289205\pi$
$200$	−7.03332e8	−0.0310832
$201$	1.22805e9	0.0530683
$202$	−4.86713e9	−0.205680
$203$	−2.35660e10	−0.973990
$204$	0	0
$205$	−1.87059e10	−0.739754
$206$	−3.40879e10	−1.31886
$207$	3.90298e10	1.47751
$208$	3.98863e10	1.47754
$209$	−2.48836e10	−0.902101
$210$	−1.04872e11	−3.72111
$211$	1.85194e9	0.0643215	0.0321608	−	0.999483i	$-0.489761\pi$
$211$	1.85194e9	0.0643215	0.0321608	+	0.999483i	$0.489761\pi$
$212$	−4.51762e10	−1.53602
$213$	−6.55763e10	−2.18292
$214$	1.86942e10	0.609321
$215$	−3.16377e10	−1.00979
$216$	−2.89014e9	−0.0903393
$217$	2.47909e9	0.0758969
$218$	−7.17366e10	−2.15123
$219$	−5.00905e10	−1.47149
$220$	−5.95858e10	−1.71491
$221$	0	0
$222$	5.88999e9	0.162752
$223$	−1.35663e10	−0.367358	−0.183679	−	0.982986i	$-0.558801\pi$
$223$	−1.35663e10	−0.367358	−0.183679	+	0.982986i	$0.558801\pi$
$224$	8.07366e10	2.14267
$225$	1.21254e10	0.315410
$226$	4.89417e10	1.24793
$227$	2.99028e9	0.0747474	0.0373737	−	0.999301i	$-0.488101\pi$
$227$	2.99028e9	0.0747474	0.0373737	+	0.999301i	$0.488101\pi$
$228$	2.97984e10	0.730274
$229$	−6.13858e9	−0.147505	−0.0737527	−	0.997277i	$-0.523498\pi$
$229$	−6.13858e9	−0.147505	−0.0737527	+	0.997277i	$0.523498\pi$
$230$	6.74554e10	1.58943
$231$	1.82392e11	4.21457
$232$	−3.81829e9	−0.0865313
$233$	2.64325e10	0.587539	0.293769	−	0.955876i	$-0.405090\pi$
$233$	2.64325e10	0.587539	0.293769	+	0.955876i	$0.405090\pi$
$234$	−1.21220e11	−2.64303
$235$	5.05245e10	1.08068
$236$	−3.18097e10	−0.667508
$237$	1.36517e10	0.281074
$238$	0	0
$239$	−7.83694e10	−1.55366	−0.776830	−	0.629711i	$-0.783173\pi$
$239$	−7.83694e10	−1.55366	−0.776830	+	0.629711i	$0.783173\pi$
$240$	−9.63893e10	−1.87533
$241$	−4.11727e10	−0.786200	−0.393100	−	0.919496i	$-0.628597\pi$
$241$	−4.11727e10	−0.786200	−0.393100	+	0.919496i	$0.628597\pi$
$242$	1.45424e11	2.72563
$243$	−6.98437e10	−1.28499
$244$	−3.55592e9	−0.0642240
$245$	9.15676e10	1.62366
$246$	−8.23088e10	−1.43297
$247$	−4.14119e10	−0.707927
$248$	4.01676e8	0.00674284
$249$	1.03073e11	1.69922
$250$	−7.31494e10	−1.18435
$251$	−4.70854e10	−0.748781	−0.374390	−	0.927271i	$-0.622148\pi$
$251$	−4.70854e10	−0.748781	−0.374390	+	0.927271i	$0.622148\pi$
$252$	−1.28026e11	−1.99984
$253$	−1.17318e11	−1.80020
$254$	1.63525e11	2.46509
$255$	0	0
$256$	8.04620e10	1.17088
$257$	5.61063e10	0.802255	0.401127	−	0.916022i	$-0.368618\pi$
$257$	5.61063e10	0.802255	0.401127	+	0.916022i	$0.368618\pi$
$258$	−1.39210e11	−1.95606
$259$	−8.64512e9	−0.119377
$260$	−9.91641e10	−1.34578
$261$	6.58272e10	0.878058
$262$	−9.60102e9	−0.125881
$263$	−3.77706e10	−0.486803	−0.243401	−	0.969926i	$-0.578263\pi$
$263$	−3.77706e10	−0.486803	−0.243401	+	0.969926i	$0.578263\pi$
$264$	2.95522e10	0.374431
$265$	−1.51721e11	−1.88991
$266$	−9.24038e10	−1.13168
$267$	2.42555e11	2.92085
$268$	2.59106e9	0.0306811
$269$	−7.83779e10	−0.912659	−0.456329	−	0.889811i	$-0.650836\pi$
$269$	−7.83779e10	−0.912659	−0.456329	+	0.889811i	$0.650836\pi$
$270$	8.61145e10	0.986141
$271$	4.77464e10	0.537749	0.268874	−	0.963175i	$-0.413348\pi$
$271$	4.77464e10	0.537749	0.268874	+	0.963175i	$0.413348\pi$
$272$	0	0
$273$	3.03542e11	3.30740
$274$	−3.10917e10	−0.333247
$275$	−3.64472e10	−0.384297
$276$	1.40489e11	1.45731
$277$	−7.84504e10	−0.800638	−0.400319	−	0.916376i	$-0.631101\pi$
$277$	−7.84504e10	−0.800638	−0.400319	+	0.916376i	$0.631101\pi$
$278$	−1.61544e11	−1.62215
$279$	−6.92487e9	−0.0684215
$280$	2.49401e10	0.242487
$281$	1.84770e11	1.76789	0.883943	−	0.467595i	$-0.154880\pi$
$281$	1.84770e11	1.76789	0.883943	+	0.467595i	$0.154880\pi$
$282$	2.22315e11	2.09338
$283$	−1.77650e11	−1.64637	−0.823183	−	0.567776i	$-0.807804\pi$
$283$	−1.77650e11	−1.64637	−0.823183	+	0.567776i	$0.807804\pi$
$284$	−1.38359e11	−1.26204
$285$	1.00076e11	0.898520
$286$	3.64369e11	3.22029
$287$	1.20810e11	1.05108
$288$	−2.25522e11	−1.93163
$289$	0	0
$290$	1.13770e11	0.944574
$291$	−5.55952e10	−0.454484
$292$	−1.05685e11	−0.850731
$293$	−1.13551e11	−0.900094	−0.450047	−	0.893005i	$-0.648593\pi$
$293$	−1.13551e11	−0.900094	−0.450047	+	0.893005i	$0.648593\pi$
$294$	4.02911e11	3.14518
$295$	−1.06831e11	−0.821293
$296$	−1.40073e9	−0.0106057
$297$	−1.49769e11	−1.11691
$298$	−2.55472e10	−0.187660
$299$	−1.95243e11	−1.41272
$300$	4.36459e10	0.311099
$301$	2.04328e11	1.43476
$302$	1.40301e11	0.970573
$303$	−3.40437e10	−0.232030
$304$	−8.49296e10	−0.570332
$305$	−1.19423e10	−0.0790204
$306$	0	0
$307$	−1.81924e11	−1.16887	−0.584436	−	0.811440i	$-0.698684\pi$
$307$	−1.81924e11	−1.16887	−0.584436	+	0.811440i	$0.698684\pi$
$308$	3.84828e11	2.43662
$309$	−2.38431e11	−1.48782
$310$	−1.19683e10	−0.0736047
$311$	−1.52392e11	−0.923723	−0.461861	−	0.886952i	$-0.652818\pi$
$311$	−1.52392e11	−0.923723	−0.461861	+	0.886952i	$0.652818\pi$
$312$	4.91814e10	0.293836
$313$	−2.50524e11	−1.47537	−0.737683	−	0.675147i	$-0.764080\pi$
$313$	−2.50524e11	−1.47537	−0.737683	+	0.675147i	$0.764080\pi$
$314$	2.89106e11	1.67831
$315$	−4.29967e11	−2.46058
$316$	2.88036e10	0.162501
$317$	1.28442e11	0.714397	0.357198	−	0.934029i	$-0.383732\pi$
$317$	1.28442e11	0.714397	0.357198	+	0.934029i	$0.383732\pi$
$318$	−6.67596e11	−3.66093
$319$	−1.97867e11	−1.06983
$320$	−1.63479e11	−0.871538
$321$	1.30759e11	0.687382
$322$	−4.35652e11	−2.25834
$323$	0	0
$324$	−7.31391e10	−0.368720
$325$	−6.06563e10	−0.301579
$326$	3.93066e11	1.92746
$327$	−5.01769e11	−2.42683
$328$	1.95743e10	0.0933799
$329$	−3.26306e11	−1.53548
$330$	−8.80536e11	−4.08728
$331$	−2.48010e11	−1.13565	−0.567823	−	0.823151i	$-0.692214\pi$
$331$	−2.48010e11	−1.13565	−0.567823	+	0.823151i	$0.692214\pi$
$332$	2.17473e11	0.982391
$333$	2.41485e10	0.107619
$334$	1.50288e11	0.660792
$335$	8.70190e9	0.0377496
$336$	6.22518e11	2.66456
$337$	−1.87991e11	−0.793967	−0.396983	−	0.917826i	$-0.629943\pi$
$337$	−1.87991e11	−0.793967	−0.396983	+	0.917826i	$0.629943\pi$
$338$	2.75753e11	1.14920
$339$	3.42328e11	1.40781
$340$	0	0
$341$	2.08152e10	0.0833652
$342$	2.58113e11	1.02021
$343$	−1.88634e11	−0.735862
$344$	3.31063e10	0.127467
$345$	4.71824e11	1.79306
$346$	−4.67804e11	−1.75478
$347$	−4.73717e11	−1.75403	−0.877014	−	0.480464i	$-0.840468\pi$
$347$	−4.73717e11	−1.75403	−0.877014	+	0.480464i	$0.840468\pi$
$348$	2.36948e11	0.866057
$349$	3.53609e11	1.27588	0.637939	−	0.770087i	$-0.279787\pi$
$349$	3.53609e11	1.27588	0.637939	+	0.770087i	$0.279787\pi$
$350$	−1.35345e11	−0.482097
$351$	−2.49250e11	−0.876501
$352$	6.77887e11	2.35351
$353$	−1.34391e11	−0.460665	−0.230332	−	0.973112i	$-0.573981\pi$
$353$	−1.34391e11	−0.460665	−0.230332	+	0.973112i	$0.573981\pi$
$354$	−4.70072e11	−1.59092
$355$	−4.64669e11	−1.55280
$356$	5.11764e11	1.68867
$357$	0	0
$358$	5.42327e10	0.174497
$359$	2.93783e11	0.933474	0.466737	−	0.884396i	$-0.345430\pi$
$359$	2.93783e11	0.933474	0.466737	+	0.884396i	$0.345430\pi$
$360$	−6.96656e10	−0.218603
$361$	−2.34510e11	−0.726739
$362$	3.79101e11	1.16029
$363$	1.01718e12	3.07482
$364$	6.40439e11	1.91215
$365$	−3.54937e11	−1.04673
$366$	−5.25479e10	−0.153070
$367$	−5.26010e11	−1.51355	−0.756774	−	0.653676i	$-0.773226\pi$
$367$	−5.26010e11	−1.51355	−0.756774	+	0.653676i	$0.773226\pi$
$368$	−4.00414e11	−1.13814
$369$	−3.37460e11	−0.947553
$370$	4.17360e10	0.115772
$371$	9.79873e11	2.68527
$372$	−2.49264e10	−0.0674863
$373$	4.00028e11	1.07004	0.535021	−	0.844839i	$-0.320304\pi$
$373$	4.00028e11	1.07004	0.535021	+	0.844839i	$0.320304\pi$
$374$	0	0
$375$	−5.11651e11	−1.33608
$376$	−5.28699e10	−0.136415
$377$	−3.29295e11	−0.839554
$378$	−5.56159e11	−1.40116
$379$	−1.20998e11	−0.301233	−0.150616	−	0.988592i	$-0.548126\pi$
$379$	−1.20998e11	−0.301233	−0.150616	+	0.988592i	$0.548126\pi$
$380$	2.11149e11	0.519473
$381$	1.14379e12	2.78089
$382$	6.31175e11	1.51658
$383$	6.24558e11	1.48313	0.741563	−	0.670883i	$-0.234085\pi$
$383$	6.24558e11	1.48313	0.741563	+	0.670883i	$0.234085\pi$
$384$	1.83947e11	0.431719
$385$	1.29242e12	2.99799
$386$	−2.38734e10	−0.0547358
$387$	−5.70751e11	−1.29344
$388$	−1.17300e11	−0.262757
$389$	1.90862e11	0.422617	0.211308	−	0.977419i	$-0.432228\pi$
$389$	1.90862e11	0.422617	0.211308	+	0.977419i	$0.432228\pi$
$390$	−1.46541e12	−3.20751
$391$	0	0
$392$	−9.58181e10	−0.204956
$393$	−6.71553e10	−0.142008
$394$	−3.50224e11	−0.732172
$395$	9.67351e10	0.199939
$396$	−1.07494e12	−2.19663
$397$	8.15682e11	1.64802	0.824012	−	0.566572i	$-0.191731\pi$
$397$	8.15682e11	1.64802	0.824012	+	0.566572i	$0.191731\pi$
$398$	8.48247e11	1.69453
$399$	−6.46328e11	−1.27666
$400$	−1.24397e11	−0.242963
$401$	−3.42201e11	−0.660894	−0.330447	−	0.943825i	$-0.607199\pi$
$401$	−3.42201e11	−0.660894	−0.330447	+	0.943825i	$0.607199\pi$
$402$	3.82896e10	0.0731246
$403$	3.46411e10	0.0654212
$404$	−7.18283e10	−0.134147
$405$	−2.45633e11	−0.453669
$406$	−7.34768e11	−1.34209
$407$	−7.25868e10	−0.131124
$408$	0	0
$409$	7.22967e11	1.27751	0.638754	−	0.769411i	$-0.279450\pi$
$409$	7.22967e11	1.27751	0.638754	+	0.769411i	$0.279450\pi$
$410$	−5.83234e11	−1.01933
$411$	−2.17474e11	−0.375941
$412$	−5.03064e11	−0.860172
$413$	6.89955e11	1.16693
$414$	1.21691e12	2.03591
$415$	7.30369e11	1.20872
$416$	1.12816e12	1.84692
$417$	−1.12994e12	−1.82996
$418$	−7.75849e11	−1.24304
$419$	−2.95392e11	−0.468204	−0.234102	−	0.972212i	$-0.575215\pi$
$419$	−2.95392e11	−0.468204	−0.234102	+	0.972212i	$0.575215\pi$
$420$	−1.54769e12	−2.42695
$421$	1.95142e11	0.302748	0.151374	−	0.988477i	$-0.451630\pi$
$421$	1.95142e11	0.302748	0.151374	+	0.988477i	$0.451630\pi$
$422$	5.77419e10	0.0886309
$423$	9.11475e11	1.38425
$424$	1.58764e11	0.238565
$425$	0	0
$426$	−2.04461e12	−3.00793
$427$	7.71279e10	0.112276
$428$	2.75887e11	0.397405
$429$	2.54862e12	3.63285
$430$	−9.86434e11	−1.39143
$431$	−4.13520e11	−0.577230	−0.288615	−	0.957445i	$-0.593195\pi$
$431$	−4.13520e11	−0.577230	−0.288615	+	0.957445i	$0.593195\pi$
$432$	−5.11173e11	−0.706141
$433$	3.61061e11	0.493611	0.246806	−	0.969065i	$-0.420619\pi$
$433$	3.61061e11	0.493611	0.246806	+	0.969065i	$0.420619\pi$
$434$	7.72958e10	0.104581
$435$	7.95774e11	1.06559
$436$	−1.05868e12	−1.40305
$437$	4.15729e11	0.545310
$438$	−1.56178e12	−2.02761
$439$	−1.06195e12	−1.36463	−0.682313	−	0.731060i	$-0.739026\pi$
$439$	−1.06195e12	−1.36463	−0.682313	+	0.731060i	$0.739026\pi$
$440$	2.09405e11	0.266348
$441$	1.65190e12	2.07975
$442$	0	0
$443$	−5.48588e11	−0.676751	−0.338376	−	0.941011i	$-0.609877\pi$
$443$	−5.48588e11	−0.676751	−0.338376	+	0.941011i	$0.609877\pi$
$444$	8.69235e10	0.106148
$445$	1.71873e12	2.07772
$446$	−4.22985e11	−0.506196
$447$	−1.78693e11	−0.211701
$448$	1.05581e12	1.23832
$449$	1.06957e12	1.24194	0.620970	−	0.783834i	$-0.286739\pi$
$449$	1.06957e12	1.24194	0.620970	+	0.783834i	$0.286739\pi$
$450$	3.78060e11	0.434614
$451$	1.01435e12	1.15450
$452$	7.22274e11	0.813915
$453$	9.81347e11	1.09492
$454$	9.32344e10	0.102997
$455$	2.15087e12	2.35268
$456$	−1.04722e11	−0.113421
$457$	−8.66940e11	−0.929750	−0.464875	−	0.885376i	$-0.653901\pi$
$457$	−8.66940e11	−0.929750	−0.464875	+	0.885376i	$0.653901\pi$
$458$	−1.91395e11	−0.203253
$459$	0	0
$460$	9.95496e11	1.03664
$461$	1.91135e11	0.197100	0.0985498	−	0.995132i	$-0.468580\pi$
$461$	1.91135e11	0.197100	0.0985498	+	0.995132i	$0.468580\pi$
$462$	5.68683e12	5.80739
$463$	−1.42973e12	−1.44590	−0.722952	−	0.690898i	$-0.757215\pi$
$463$	−1.42973e12	−1.44590	−0.722952	+	0.690898i	$0.757215\pi$
$464$	−6.75334e11	−0.676376
$465$	−8.37136e10	−0.0830343
$466$	8.24141e11	0.809590
$467$	−5.06094e11	−0.492386	−0.246193	−	0.969221i	$-0.579180\pi$
$467$	−5.06094e11	−0.492386	−0.246193	+	0.969221i	$0.579180\pi$
$468$	−1.78894e12	−1.72381
$469$	−5.62001e10	−0.0536364
$470$	1.57531e12	1.48911
$471$	2.02218e12	1.89333
$472$	1.11790e11	0.103673
$473$	1.71560e12	1.57594
$474$	4.25648e11	0.387301
$475$	1.29155e11	0.116410
$476$	0	0
$477$	−2.73709e12	−2.42079
$478$	−2.44349e12	−2.14084
$479$	−8.87448e11	−0.770253	−0.385126	−	0.922864i	$-0.625842\pi$
$479$	−8.87448e11	−0.770253	−0.385126	+	0.922864i	$0.625842\pi$
$480$	−2.72630e12	−2.34417
$481$	−1.20801e11	−0.102900
$482$	−1.28373e12	−1.08333
$483$	−3.04722e12	−2.54766
$484$	2.14614e12	1.77769
$485$	−3.93943e11	−0.323293
$486$	−2.17766e12	−1.77063
$487$	−2.43406e11	−0.196088	−0.0980441	−	0.995182i	$-0.531259\pi$
$487$	−2.43406e11	−0.196088	−0.0980441	+	0.995182i	$0.531259\pi$
$488$	1.24967e10	0.00997483
$489$	2.74934e12	2.17440
$490$	2.85499e12	2.23729
$491$	1.10541e12	0.858331	0.429166	−	0.903226i	$-0.358808\pi$
$491$	1.10541e12	0.858331	0.429166	+	0.903226i	$0.358808\pi$
$492$	−1.21470e12	−0.934601
$493$	0	0
$494$	−1.29118e12	−0.975477
$495$	−3.61013e12	−2.70271
$496$	7.10436e10	0.0527057
$497$	3.00100e12	2.20629
$498$	3.21373e12	2.34141
$499$	7.42812e11	0.536323	0.268162	−	0.963374i	$-0.413584\pi$
$499$	7.42812e11	0.536323	0.268162	+	0.963374i	$0.413584\pi$
$500$	−1.07953e12	−0.772447
$501$	1.05120e12	0.745448
$502$	−1.46808e12	−1.03177
$503$	1.35404e12	0.943141	0.471571	−	0.881828i	$-0.343687\pi$
$503$	1.35404e12	0.943141	0.471571	+	0.881828i	$0.343687\pi$
$504$	4.49926e11	0.310602
$505$	−2.41231e11	−0.165052
$506$	−3.65786e12	−2.48056
$507$	1.92878e12	1.29643
$508$	2.41327e12	1.60775
$509$	1.57444e12	1.03967	0.519837	−	0.854266i	$-0.325993\pi$
$509$	1.57444e12	1.03967	0.519837	+	0.854266i	$0.325993\pi$
$510$	0	0
$511$	2.29232e12	1.48724
$512$	2.07688e12	1.33566
$513$	5.30725e11	0.338330
$514$	1.74934e12	1.10545
$515$	−1.68951e12	−1.05835
$516$	−2.05444e12	−1.27576
$517$	−2.73976e12	−1.68657
$518$	−2.69547e11	−0.164494
$519$	−3.27211e12	−1.97959
$520$	3.48496e11	0.209017
$521$	1.14272e12	0.679467	0.339733	−	0.940522i	$-0.389663\pi$
$521$	1.14272e12	0.679467	0.339733	+	0.940522i	$0.389663\pi$
$522$	2.05243e12	1.20991
$523$	−1.83723e12	−1.07376	−0.536878	−	0.843660i	$-0.680396\pi$
$523$	−1.83723e12	−1.07376	−0.536878	+	0.843660i	$0.680396\pi$
$524$	−1.41690e11	−0.0821011
$525$	−9.46682e11	−0.543860
$526$	−1.17765e12	−0.670782
$527$	0	0
$528$	5.22684e12	2.92676
$529$	1.58866e11	0.0882026
$530$	−4.73053e12	−2.60417
$531$	−1.92726e12	−1.05200
$532$	−1.36368e12	−0.738092
$533$	1.68811e12	0.906001
$534$	7.56264e12	4.02474
$535$	9.26547e11	0.488962
$536$	−9.10584e9	−0.00476517
$537$	3.79336e11	0.196852
$538$	−2.44375e12	−1.25758
$539$	−4.96537e12	−2.53398
$540$	1.27086e12	0.643172
$541$	3.32268e10	0.0166763	0.00833817	−	0.999965i	$-0.497346\pi$
$541$	3.32268e10	0.0166763	0.00833817	+	0.999965i	$0.497346\pi$
$542$	1.48869e12	0.740982
$543$	2.65166e12	1.30894
$544$	0	0
$545$	−3.55550e12	−1.72630
$546$	9.46415e12	4.55737
$547$	3.00591e11	0.143560	0.0717800	−	0.997420i	$-0.477132\pi$
$547$	3.00591e11	0.143560	0.0717800	+	0.997420i	$0.477132\pi$
$548$	−4.58846e11	−0.217347
$549$	−2.15442e11	−0.101217
$550$	−1.13639e12	−0.529537
$551$	7.01165e11	0.324069
$552$	−4.93726e11	−0.226339
$553$	−6.24751e11	−0.284082
$554$	−2.44601e12	−1.10323
$555$	2.91927e11	0.130604
$556$	−2.38404e12	−1.05798
$557$	2.43845e11	0.107341	0.0536704	−	0.998559i	$-0.482908\pi$
$557$	2.43845e11	0.107341	0.0536704	+	0.998559i	$0.482908\pi$
$558$	−2.15911e11	−0.0942804
$559$	2.85513e12	1.23673
$560$	4.41112e12	1.89541
$561$	0	0
$562$	5.76098e12	2.43603
$563$	−2.53898e12	−1.06505	−0.532527	−	0.846413i	$-0.678758\pi$
$563$	−2.53898e12	−1.06505	−0.532527	+	0.846413i	$0.678758\pi$
$564$	3.28089e12	1.36533
$565$	2.42571e12	1.00143
$566$	−5.53897e12	−2.26858
$567$	1.58639e12	0.644593
$568$	4.86239e11	0.196012
$569$	2.31952e12	0.927670	0.463835	−	0.885922i	$-0.346473\pi$
$569$	2.31952e12	0.927670	0.463835	+	0.885922i	$0.346473\pi$
$570$	3.12028e12	1.23810
$571$	−3.14584e12	−1.23844	−0.619218	−	0.785219i	$-0.712550\pi$
$571$	−3.14584e12	−1.23844	−0.619218	+	0.785219i	$0.712550\pi$
$572$	5.37731e12	2.10031
$573$	4.41482e12	1.71087
$574$	3.76675e12	1.44831
$575$	6.08921e11	0.232304
$576$	−2.94920e12	−1.11636
$577$	−8.37162e11	−0.314426	−0.157213	−	0.987565i	$-0.550251\pi$
$577$	−8.37162e11	−0.314426	−0.157213	+	0.987565i	$0.550251\pi$
$578$	0	0
$579$	−1.66985e11	−0.0617482
$580$	1.67900e12	0.616061
$581$	−4.71700e12	−1.71741
$582$	−1.73341e12	−0.626249
$583$	8.22729e12	2.94950
$584$	3.71414e11	0.132130
$585$	−6.00805e12	−2.12096
$586$	−3.54043e12	−1.24027
$587$	4.67576e12	1.62548	0.812738	−	0.582629i	$-0.197976\pi$
$587$	4.67576e12	1.62548	0.812738	+	0.582629i	$0.197976\pi$
$588$	5.94609e12	2.05132
$589$	−7.37609e10	−0.0252527
$590$	−3.33089e12	−1.13169
$591$	−2.44968e12	−0.825972
$592$	−2.47744e11	−0.0829002
$593$	−3.60760e12	−1.19804	−0.599021	−	0.800733i	$-0.704444\pi$
$593$	−3.60760e12	−1.19804	−0.599021	+	0.800733i	$0.704444\pi$
$594$	−4.66967e12	−1.53903
$595$	0	0
$596$	−3.77022e11	−0.122394
$597$	5.93315e12	1.91162
$598$	−6.08749e12	−1.94663
$599$	−3.60685e12	−1.14474	−0.572370	−	0.819996i	$-0.693976\pi$
$599$	−3.60685e12	−1.14474	−0.572370	+	0.819996i	$0.693976\pi$
$600$	−1.53386e11	−0.0483177
$601$	−2.96141e12	−0.925898	−0.462949	−	0.886385i	$-0.653209\pi$
$601$	−2.96141e12	−0.925898	−0.462949	+	0.886385i	$0.653209\pi$
$602$	6.37076e12	1.97700
$603$	1.56984e11	0.0483536
$604$	2.07053e12	0.633018
$605$	7.20769e12	2.18724
$606$	−1.06145e12	−0.319722
$607$	2.50640e12	0.749378	0.374689	−	0.927151i	$-0.377750\pi$
$607$	2.50640e12	0.749378	0.374689	+	0.927151i	$0.377750\pi$
$608$	−2.40217e12	−0.712915
$609$	−5.13941e12	−1.51403
$610$	−3.72351e11	−0.108885
$611$	−4.55957e12	−1.32354
$612$	0	0
$613$	−3.04574e12	−0.871206	−0.435603	−	0.900139i	$-0.643465\pi$
$613$	−3.04574e12	−0.871206	−0.435603	+	0.900139i	$0.643465\pi$
$614$	−5.67222e12	−1.61063
$615$	−4.07949e12	−1.14992
$616$	−1.35241e12	−0.378439
$617$	3.14735e12	0.874301	0.437151	−	0.899388i	$-0.355988\pi$
$617$	3.14735e12	0.874301	0.437151	+	0.899388i	$0.355988\pi$
$618$	−7.43407e12	−2.05012
$619$	−2.96677e12	−0.812223	−0.406112	−	0.913823i	$-0.633116\pi$
$619$	−2.96677e12	−0.812223	−0.406112	+	0.913823i	$0.633116\pi$
$620$	−1.76626e11	−0.0480057
$621$	2.50219e12	0.675161
$622$	−4.75146e12	−1.27283
$623$	−1.11002e13	−2.95212
$624$	8.69862e12	2.29678
$625$	−4.47502e12	−1.17310
$626$	−7.81111e12	−2.03296
$627$	−5.42675e12	−1.40228
$628$	4.26658e12	1.09461
$629$	0	0
$630$	−1.34060e13	−3.39052
$631$	−6.07921e12	−1.52656	−0.763282	−	0.646066i	$-0.776413\pi$
$631$	−6.07921e12	−1.52656	−0.763282	+	0.646066i	$0.776413\pi$
$632$	−1.01226e11	−0.0252385
$633$	4.03882e11	0.0999856
$634$	4.00470e12	0.984392
$635$	8.10482e12	1.97816
$636$	−9.85227e12	−2.38770
$637$	−8.26349e12	−1.98855
$638$	−6.16932e12	−1.47416
$639$	−8.38273e12	−1.98899
$640$	1.30343e12	0.307099
$641$	−6.53069e10	−0.0152791	−0.00763956	−	0.999971i	$-0.502432\pi$
$641$	−6.53069e10	−0.0152791	−0.00763956	+	0.999971i	$0.502432\pi$
$642$	4.07694e12	0.947168
$643$	3.79510e12	0.875536	0.437768	−	0.899088i	$-0.355769\pi$
$643$	3.79510e12	0.875536	0.437768	+	0.899088i	$0.355769\pi$
$644$	−6.42929e12	−1.47291
$645$	−6.89972e12	−1.56969
$646$	0	0
$647$	5.68198e12	1.27477	0.637383	−	0.770547i	$-0.280017\pi$
$647$	5.68198e12	1.27477	0.637383	+	0.770547i	$0.280017\pi$
$648$	2.57035e11	0.0572671
$649$	5.79305e12	1.28176
$650$	−1.89121e12	−0.415556
$651$	5.40654e11	0.117979
$652$	5.80081e12	1.25711
$653$	−6.04404e12	−1.30082	−0.650411	−	0.759582i	$-0.725403\pi$
$653$	−6.04404e12	−1.30082	−0.650411	+	0.759582i	$0.725403\pi$
$654$	−1.56447e13	−3.34401
$655$	−4.75858e11	−0.101016
$656$	3.46207e12	0.729908
$657$	−6.40316e12	−1.34076
$658$	−1.01739e13	−2.11579
$659$	−6.09570e11	−0.125904	−0.0629519	−	0.998017i	$-0.520051\pi$
$659$	−6.09570e11	−0.125904	−0.0629519	+	0.998017i	$0.520051\pi$
$660$	−1.29948e13	−2.66577
$661$	1.69850e12	0.346065	0.173033	−	0.984916i	$-0.444643\pi$
$661$	1.69850e12	0.346065	0.173033	+	0.984916i	$0.444643\pi$
$662$	−7.73272e12	−1.56485
$663$	0	0
$664$	−7.64273e11	−0.152578
$665$	−4.57983e12	−0.908139
$666$	7.52928e11	0.148293
$667$	3.30575e12	0.646702
$668$	2.21792e12	0.430976
$669$	−2.95861e12	−0.571046
$670$	2.71317e11	0.0520165
$671$	6.47588e11	0.123324
$672$	1.76075e13	3.33070
$673$	−6.96256e12	−1.30828	−0.654141	−	0.756373i	$-0.726970\pi$
$673$	−6.96256e12	−1.30828	−0.654141	+	0.756373i	$0.726970\pi$
$674$	−5.86139e12	−1.09403
$675$	7.77357e11	0.144130
$676$	4.06952e12	0.749520
$677$	5.93983e12	1.08674	0.543369	−	0.839494i	$-0.317148\pi$
$677$	5.93983e12	1.08674	0.543369	+	0.839494i	$0.317148\pi$
$678$	1.06735e13	1.93987
$679$	2.54423e12	0.459349
$680$	0	0
$681$	6.52137e11	0.116192
$682$	6.48998e11	0.114872
$683$	4.21795e12	0.741665	0.370833	−	0.928700i	$-0.379072\pi$
$683$	4.21795e12	0.741665	0.370833	+	0.928700i	$0.379072\pi$
$684$	3.80918e12	0.665395
$685$	−1.54100e12	−0.267422
$686$	−5.88143e12	−1.01397
$687$	−1.33873e12	−0.229292
$688$	5.85545e12	0.996351
$689$	1.36920e13	2.31463
$690$	1.47110e13	2.47072
$691$	7.83018e12	1.30653	0.653266	−	0.757128i	$-0.273398\pi$
$691$	7.83018e12	1.30653	0.653266	+	0.757128i	$0.273398\pi$
$692$	−6.90378e12	−1.14448
$693$	2.33155e13	3.84013
$694$	−1.47701e13	−2.41694
$695$	−8.00666e12	−1.30173
$696$	−8.32714e11	−0.134510
$697$	0	0
$698$	1.10252e13	1.75808
$699$	5.76454e12	0.913308
$700$	−1.99739e12	−0.314429
$701$	1.75615e12	0.274683	0.137341	−	0.990524i	$-0.456144\pi$
$701$	1.75615e12	0.274683	0.137341	+	0.990524i	$0.456144\pi$
$702$	−7.77137e12	−1.20776
$703$	2.57220e11	0.0397196
$704$	8.86485e12	1.36017
$705$	1.10187e13	1.67988
$706$	−4.19020e12	−0.634766
$707$	1.55796e12	0.234514
$708$	−6.93724e12	−1.03762
$709$	−1.13656e13	−1.68922	−0.844609	−	0.535384i	$-0.820167\pi$
$709$	−1.13656e13	−1.68922	−0.844609	+	0.535384i	$0.820167\pi$
$710$	−1.44879e13	−2.13966
$711$	1.74512e12	0.256102
$712$	−1.79851e12	−0.262272
$713$	−3.47757e11	−0.0503934
$714$	0	0
$715$	1.80593e13	2.58419
$716$	8.00357e11	0.113809
$717$	−1.70912e13	−2.41511
$718$	9.15990e12	1.28627
$719$	−7.38890e12	−1.03110	−0.515549	−	0.856860i	$-0.672412\pi$
$719$	−7.38890e12	−1.03110	−0.515549	+	0.856860i	$0.672412\pi$
$720$	−1.23216e13	−1.70872
$721$	1.09115e13	1.50375
$722$	−7.31180e12	−1.00140
$723$	−8.97917e12	−1.22212
$724$	5.59471e12	0.756753
$725$	1.02700e12	0.138054
$726$	3.17149e13	4.23690
$727$	−1.08332e13	−1.43831	−0.719154	−	0.694851i	$-0.755470\pi$
$727$	−1.08332e13	−1.43831	−0.719154	+	0.694851i	$0.755470\pi$
$728$	−2.25072e12	−0.296982
$729$	−1.21033e13	−1.58719
$730$	−1.10666e13	−1.44232
$731$	0	0
$732$	−7.75494e11	−0.0998340
$733$	−7.77407e12	−0.994673	−0.497337	−	0.867558i	$-0.665689\pi$
$733$	−7.77407e12	−0.994673	−0.497337	+	0.867558i	$0.665689\pi$
$734$	−1.64005e13	−2.08557
$735$	1.99696e13	2.52392
$736$	−1.13254e13	−1.42267
$737$	−4.71872e11	−0.0589143
$738$	−1.05217e13	−1.30567
$739$	−9.28948e12	−1.14575	−0.572877	−	0.819641i	$-0.694173\pi$
$739$	−9.28948e12	−1.14575	−0.572877	+	0.819641i	$0.694173\pi$
$740$	6.15933e11	0.0755077
$741$	−9.03133e12	−1.10045
$742$	3.05516e13	3.70012
$743$	−1.33207e13	−1.60353	−0.801764	−	0.597641i	$-0.796105\pi$
$743$	−1.33207e13	−1.60353	−0.801764	+	0.597641i	$0.796105\pi$
$744$	8.75996e10	0.0104815
$745$	−1.26620e12	−0.150592
$746$	1.24725e13	1.47445
$747$	1.31760e13	1.54825
$748$	0	0
$749$	−5.98399e12	−0.694741
$750$	−1.59528e13	−1.84103
$751$	−1.44267e12	−0.165496	−0.0827478	−	0.996571i	$-0.526370\pi$
$751$	−1.44267e12	−0.165496	−0.0827478	+	0.996571i	$0.526370\pi$
$752$	−9.35100e12	−1.06630
$753$	−1.02686e13	−1.16395
$754$	−1.02671e13	−1.15685
$755$	6.95375e12	0.778857
$756$	−8.20771e12	−0.913848
$757$	−4.15075e12	−0.459404	−0.229702	−	0.973261i	$-0.573775\pi$
$757$	−4.15075e12	−0.459404	−0.229702	+	0.973261i	$0.573775\pi$
$758$	−3.77261e12	−0.415079
$759$	−2.55853e13	−2.79835
$760$	−7.42049e11	−0.0806810
$761$	−3.92144e12	−0.423853	−0.211926	−	0.977286i	$-0.567974\pi$
$761$	−3.92144e12	−0.423853	−0.211926	+	0.977286i	$0.567974\pi$
$762$	3.56624e13	3.83189
$763$	2.29627e13	2.45281
$764$	9.31478e12	0.989127
$765$	0	0
$766$	1.94731e13	2.04365
$767$	9.64093e12	1.00587
$768$	1.75476e13	1.82009
$769$	−1.09821e13	−1.13244	−0.566220	−	0.824254i	$-0.691595\pi$
$769$	−1.09821e13	−1.13244	−0.566220	+	0.824254i	$0.691595\pi$
$770$	4.02964e13	4.13103
$771$	1.22360e13	1.24708
$772$	−3.52320e11	−0.0356993
$773$	1.04201e13	1.04970	0.524850	−	0.851195i	$-0.324121\pi$
$773$	1.04201e13	1.04970	0.524850	+	0.851195i	$0.324121\pi$
$774$	−1.77955e13	−1.78228
$775$	−1.08038e11	−0.0107577
$776$	4.12230e11	0.0408096
$777$	−1.88537e12	−0.185568
$778$	5.95091e12	0.582338
$779$	−3.59448e12	−0.349718
$780$	−2.16262e13	−2.09197
$781$	2.51973e13	2.42339
$782$	0	0
$783$	4.22016e12	0.401237
$784$	−1.69472e13	−1.60205
$785$	1.43290e13	1.34680
$786$	−2.09384e12	−0.195678
$787$	−1.01301e13	−0.941295	−0.470647	−	0.882321i	$-0.655980\pi$
$787$	−1.01301e13	−0.941295	−0.470647	+	0.882321i	$0.655980\pi$
$788$	−5.16855e12	−0.477530
$789$	−8.23722e12	−0.756718
$790$	3.01611e12	0.275503
$791$	−1.56662e13	−1.42288
$792$	3.77771e12	0.341166
$793$	1.07773e12	0.0967789
$794$	2.54322e13	2.27087
$795$	−3.30882e13	−2.93779
$796$	1.25183e13	1.10519
$797$	7.66073e12	0.672524	0.336262	−	0.941769i	$-0.390837\pi$
$797$	7.66073e12	0.672524	0.336262	+	0.941769i	$0.390837\pi$
$798$	−2.01519e13	−1.75915
$799$	0	0
$800$	−3.51848e12	−0.303704
$801$	3.10062e13	2.66135
$802$	−1.06695e13	−0.910668
$803$	1.92470e13	1.63359
$804$	5.65072e11	0.0476926
$805$	−2.15923e13	−1.81225
$806$	1.08008e12	0.0901461
$807$	−1.70931e13	−1.41870
$808$	2.52429e11	0.0208347
$809$	1.49302e13	1.22545	0.612726	−	0.790295i	$-0.290073\pi$
$809$	1.49302e13	1.22545	0.612726	+	0.790295i	$0.290073\pi$
$810$	−7.65861e12	−0.625126
$811$	−7.52041e11	−0.0610447	−0.0305223	−	0.999534i	$-0.509717\pi$
$811$	−7.52041e11	−0.0610447	−0.0305223	+	0.999534i	$0.509717\pi$
$812$	−1.08436e13	−0.875328
$813$	1.04128e13	0.835911
$814$	−2.26319e12	−0.180681
$815$	1.94816e13	1.54674
$816$	0	0
$817$	−6.07941e12	−0.477378
$818$	2.25414e13	1.76032
$819$	3.88023e13	3.01356
$820$	−8.60728e12	−0.664819
$821$	−8.12012e12	−0.623761	−0.311880	−	0.950121i	$-0.600959\pi$
$821$	−8.12012e12	−0.623761	−0.311880	+	0.950121i	$0.600959\pi$
$822$	−6.78065e12	−0.518022
$823$	−1.76087e13	−1.33791	−0.668956	−	0.743302i	$-0.733258\pi$
$823$	−1.76087e13	−1.33791	−0.668956	+	0.743302i	$0.733258\pi$
$824$	1.76793e12	0.133596
$825$	−7.94861e12	−0.597377
$826$	2.15122e13	1.60795
$827$	9.47991e12	0.704741	0.352370	−	0.935861i	$-0.385376\pi$
$827$	9.47991e12	0.704741	0.352370	+	0.935861i	$0.385376\pi$
$828$	1.79590e13	1.32784
$829$	5.86857e12	0.431556	0.215778	−	0.976442i	$-0.430771\pi$
$829$	5.86857e12	0.431556	0.215778	+	0.976442i	$0.430771\pi$
$830$	2.27723e13	1.66554
$831$	−1.71089e13	−1.24456
$832$	1.47531e13	1.06740
$833$	0	0
$834$	−3.52304e13	−2.52157
$835$	7.44876e12	0.530267
$836$	−1.14498e13	−0.810721
$837$	−4.43951e11	−0.0312659
$838$	−9.21005e12	−0.645155
$839$	−6.89015e12	−0.480065	−0.240033	−	0.970765i	$-0.577158\pi$
$839$	−6.89015e12	−0.480065	−0.240033	+	0.970765i	$0.577158\pi$
$840$	5.43908e12	0.376937
$841$	−8.93169e12	−0.615676
$842$	6.08434e12	0.417166
$843$	4.02957e13	2.74812
$844$	8.52146e11	0.0578060
$845$	1.36672e13	0.922200
$846$	2.84190e13	1.90740
$847$	−4.65500e13	−3.10773
$848$	2.80803e13	1.86475
$849$	−3.87429e13	−2.55922
$850$	0	0
$851$	1.21270e12	0.0792632
$852$	−3.01740e13	−1.96180
$853$	8.54909e12	0.552903	0.276452	−	0.961028i	$-0.410841\pi$
$853$	8.54909e12	0.552903	0.276452	+	0.961028i	$0.410841\pi$
$854$	2.40478e12	0.154709
$855$	1.27929e13	0.818693
$856$	−9.69558e11	−0.0617222
$857$	−3.13914e12	−0.198791	−0.0993954	−	0.995048i	$-0.531691\pi$
$857$	−3.13914e12	−0.198791	−0.0993954	+	0.995048i	$0.531691\pi$
$858$	7.94637e13	5.00583
$859$	−1.08402e13	−0.679307	−0.339654	−	0.940551i	$-0.610310\pi$
$859$	−1.08402e13	−0.679307	−0.339654	+	0.940551i	$0.610310\pi$
$860$	−1.45576e13	−0.907502
$861$	2.63469e13	1.63386
$862$	−1.28932e13	−0.795385
$863$	1.62380e13	0.996512	0.498256	−	0.867030i	$-0.333974\pi$
$863$	1.62380e13	0.996512	0.498256	+	0.867030i	$0.333974\pi$
$864$	−1.44582e13	−0.882677
$865$	−2.31859e13	−1.40816
$866$	1.12576e13	0.680164
$867$	0	0
$868$	1.14072e12	0.0682088
$869$	−5.24559e12	−0.312036
$870$	2.48115e13	1.46831
$871$	−7.85300e11	−0.0462332
$872$	3.72054e12	0.217913
$873$	−7.10684e12	−0.414107
$874$	1.29620e13	0.751402
$875$	2.34150e13	1.35039
$876$	−2.30484e13	−1.32243
$877$	−2.72299e13	−1.55435	−0.777173	−	0.629288i	$-0.783347\pi$
$877$	−2.72299e13	−1.55435	−0.777173	+	0.629288i	$0.783347\pi$
$878$	−3.31106e13	−1.88036
$879$	−2.47639e13	−1.39917
$880$	3.70370e13	2.08192
$881$	1.02004e13	0.570462	0.285231	−	0.958459i	$-0.407930\pi$
$881$	1.02004e13	0.570462	0.285231	+	0.958459i	$0.407930\pi$
$882$	5.15048e13	2.86575
$883$	−1.89592e13	−1.04954	−0.524768	−	0.851245i	$-0.675848\pi$
$883$	−1.89592e13	−1.04954	−0.524768	+	0.851245i	$0.675848\pi$
$884$	0	0
$885$	−2.32983e13	−1.27667
$886$	−1.71045e13	−0.932519
$887$	−3.32227e12	−0.180210	−0.0901050	−	0.995932i	$-0.528720\pi$
$887$	−3.32227e12	−0.180210	−0.0901050	+	0.995932i	$0.528720\pi$
$888$	−3.05478e11	−0.0164863
$889$	−5.23440e13	−2.81066
$890$	5.35883e13	2.86296
$891$	1.33198e13	0.708022
$892$	−6.24235e12	−0.330146
$893$	9.70866e12	0.510890
$894$	−5.57148e12	−0.291710
$895$	2.68795e12	0.140029
$896$	−8.41806e12	−0.436341
$897$	−4.25796e13	−2.19602
$898$	3.33482e13	1.71131
$899$	−5.86525e11	−0.0299480
$900$	5.57934e12	0.283460
$901$	0	0
$902$	3.16267e13	1.59083
$903$	4.45610e13	2.23028
$904$	−2.53831e12	−0.126412
$905$	1.87895e13	0.931099
$906$	3.05975e13	1.50872
$907$	2.50137e13	1.22729	0.613643	−	0.789583i	$-0.289703\pi$
$907$	2.50137e13	1.22729	0.613643	+	0.789583i	$0.289703\pi$
$908$	1.37594e12	0.0671757
$909$	−4.35186e12	−0.211416
$910$	6.70623e13	3.24184
$911$	−3.86671e13	−1.85998	−0.929992	−	0.367580i	$-0.880186\pi$
$911$	−3.86671e13	−1.85998	−0.929992	+	0.367580i	$0.880186\pi$
$912$	−1.85219e13	−0.886561
$913$	−3.96053e13	−1.88640
$914$	−2.70304e13	−1.28114
$915$	−2.60444e12	−0.122834
$916$	−2.82458e12	−0.132564
$917$	3.07327e12	0.143529
$918$	0	0
$919$	−1.76405e13	−0.815814	−0.407907	−	0.913024i	$-0.633741\pi$
$919$	−1.76405e13	−0.815814	−0.407907	+	0.913024i	$0.633741\pi$
$920$	−3.49851e12	−0.161004
$921$	−3.96750e13	−1.81697
$922$	5.95941e12	0.271590
$923$	4.19339e13	1.90177
$924$	8.39253e13	3.78764
$925$	3.76752e11	0.0169207
$926$	−4.45777e13	−1.99236
$927$	−3.04791e13	−1.35564
$928$	−1.91014e13	−0.845470
$929$	−1.34112e13	−0.590741	−0.295370	−	0.955383i	$-0.595443\pi$
$929$	−1.34112e13	−0.590741	−0.295370	+	0.955383i	$0.595443\pi$
$930$	−2.61011e12	−0.114416
$931$	1.75954e13	0.767582
$932$	1.21625e13	0.528023
$933$	−3.32346e13	−1.43589
$934$	−1.57796e13	−0.678475
$935$	0	0
$936$	6.28695e12	0.267731
$937$	−3.19535e13	−1.35422	−0.677112	−	0.735880i	$-0.736769\pi$
$937$	−3.19535e13	−1.35422	−0.677112	+	0.735880i	$0.736769\pi$
$938$	−1.75227e12	−0.0739074
$939$	−5.46356e13	−2.29341
$940$	2.32482e13	0.971210
$941$	1.88935e13	0.785523	0.392762	−	0.919640i	$-0.371520\pi$
$941$	1.88935e13	0.785523	0.392762	+	0.919640i	$0.371520\pi$
$942$	6.30498e13	2.60888
$943$	−1.69468e13	−0.697885
$944$	1.97721e13	0.810362
$945$	−2.75651e13	−1.12439
$946$	5.34907e13	2.17154
$947$	3.95731e13	1.59891	0.799457	−	0.600723i	$-0.205121\pi$
$947$	3.95731e13	1.59891	0.799457	+	0.600723i	$0.205121\pi$
$948$	6.28165e12	0.252602
$949$	3.20312e13	1.28196
$950$	4.02693e12	0.160405
$951$	2.80113e13	1.11051
$952$	0	0
$953$	1.42691e13	0.560375	0.280188	−	0.959945i	$-0.409603\pi$
$953$	1.42691e13	0.560375	0.280188	+	0.959945i	$0.409603\pi$
$954$	−8.53400e13	−3.33568
$955$	3.12831e13	1.21701
$956$	−3.60606e13	−1.39628
$957$	−4.31519e13	−1.66302
$958$	−2.76698e13	−1.06136
$959$	9.95239e12	0.379965
$960$	−3.56523e13	−1.35478
$961$	−2.63779e13	−0.997666
$962$	−3.76645e12	−0.141790
$963$	1.67151e13	0.626313
$964$	−1.89451e13	−0.706560
$965$	−1.18324e12	−0.0439239
$966$	−9.50095e13	−3.51051
$967$	1.75539e13	0.645585	0.322793	−	0.946470i	$-0.395378\pi$
$967$	1.75539e13	0.645585	0.322793	+	0.946470i	$0.395378\pi$
$968$	−7.54227e12	−0.276098
$969$	0	0
$970$	−1.22828e13	−0.445476
$971$	4.77868e13	1.72513	0.862563	−	0.505949i	$-0.168858\pi$
$971$	4.77868e13	1.72513	0.862563	+	0.505949i	$0.168858\pi$
$972$	−3.21376e13	−1.15482
$973$	5.17100e13	1.84955
$974$	−7.58919e12	−0.270197
$975$	−1.32283e13	−0.468794
$976$	2.21026e12	0.0779686
$977$	5.62999e13	1.97689	0.988445	−	0.151581i	$-0.0484365\pi$
$977$	5.62999e13	1.97689	0.988445	+	0.151581i	$0.0484365\pi$
$978$	8.57220e13	2.99618
$979$	−9.32002e13	−3.24261
$980$	4.21335e13	1.45919
$981$	−6.41421e13	−2.21122
$982$	3.44656e13	1.18272
$983$	−5.05922e13	−1.72819	−0.864097	−	0.503325i	$-0.832110\pi$
$983$	−5.05922e13	−1.72819	−0.864097	+	0.503325i	$0.832110\pi$
$984$	4.26886e12	0.145156
$985$	−1.73582e13	−0.587547
$986$	0	0
$987$	−7.11627e13	−2.38685
$988$	−1.90551e13	−0.636216
$989$	−2.86623e13	−0.952639
$990$	−1.12560e14	−3.72415
$991$	−5.82546e13	−1.91866	−0.959331	−	0.282283i	$-0.908908\pi$
$991$	−5.82546e13	−1.91866	−0.959331	+	0.282283i	$0.908908\pi$
$992$	2.00942e12	0.0658821
$993$	−5.40873e13	−1.76532
$994$	9.35686e13	3.04012
$995$	4.20419e13	1.35981
$996$	4.74277e13	1.52709
$997$	1.64840e13	0.528365	0.264183	−	0.964473i	$-0.414898\pi$
$997$	1.64840e13	0.528365	0.264183	+	0.964473i	$0.414898\pi$
$998$	2.31602e13	0.739018
$999$	1.54815e12	0.0491778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.d.1.11	✓	12
17.16	even	2		289.10.a.e.1.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.11	✓	12	1.1	even	1	trivial
289.10.a.e.1.11	yes	12	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+31.1791 q^{2} +218.085 q^{3} +460.136 q^{4} +1545.34 q^{5} +6799.71 q^{6} -9980.37 q^{7} -1617.07 q^{8} +27878.3 q^{9} +O(q^{10})\)	\(q+31.1791 q^{2} +218.085 q^{3} +460.136 q^{4} +1545.34 q^{5} +6799.71 q^{6} -9980.37 q^{7} -1617.07 q^{8} +27878.3 q^{9} +48182.2 q^{10} -83798.0 q^{11} +100349. q^{12} -139458. q^{13} -311179. q^{14} +337016. q^{15} -286008. q^{16} +869219. q^{18} +296948. q^{19} +711065. q^{20} -2.17657e6 q^{21} -2.61275e6 q^{22} +1.40001e6 q^{23} -352660. q^{24} +434942. q^{25} -4.34819e6 q^{26} +1.78727e6 q^{27} -4.59233e6 q^{28} +2.36124e6 q^{29} +1.05078e7 q^{30} -248397. q^{31} -8.08955e6 q^{32} -1.82751e7 q^{33} -1.54230e7 q^{35} +1.28278e7 q^{36} +866212. q^{37} +9.25856e6 q^{38} -3.04139e7 q^{39} -2.49892e6 q^{40} -1.21048e7 q^{41} -6.78636e7 q^{42} -2.04730e7 q^{43} -3.85585e7 q^{44} +4.30813e7 q^{45} +4.36509e7 q^{46} +3.26948e7 q^{47} -6.23743e7 q^{48} +5.92541e7 q^{49} +1.35611e7 q^{50} -6.41699e7 q^{52} -9.81801e7 q^{53} +5.57254e7 q^{54} -1.29496e8 q^{55} +1.61390e7 q^{56} +6.47600e7 q^{57} +7.36213e7 q^{58} -6.91312e7 q^{59} +1.55073e8 q^{60} -7.72797e6 q^{61} -7.74479e6 q^{62} -2.78235e8 q^{63} -1.05788e8 q^{64} -2.15510e8 q^{65} -5.69802e8 q^{66} +5.63107e6 q^{67} +3.05321e8 q^{69} -4.80876e8 q^{70} -3.00691e8 q^{71} -4.50811e7 q^{72} -2.29683e8 q^{73} +2.70077e7 q^{74} +9.48544e7 q^{75} +1.36636e8 q^{76} +8.36334e8 q^{77} -9.48277e8 q^{78} +6.25980e7 q^{79} -4.41980e8 q^{80} -1.58951e8 q^{81} -3.77416e8 q^{82} +4.72628e8 q^{83} -1.00152e9 q^{84} -6.38329e8 q^{86} +5.14952e8 q^{87} +1.35507e8 q^{88} +1.11220e9 q^{89} +1.34324e9 q^{90} +1.39185e9 q^{91} +6.44194e8 q^{92} -5.41717e7 q^{93} +1.01940e9 q^{94} +4.58884e8 q^{95} -1.76421e9 q^{96} -2.54924e8 q^{97} +1.84749e9 q^{98} -2.33614e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9} + 2449 q^{10} - 152886 q^{11} - 41717 q^{12} + 23478 q^{13} - 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} + 2477218 q^{20} - 1395256 q^{21} - 2391095 q^{22} - 2012428 q^{23} - 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} - 3231638 q^{27} + 5978216 q^{28} - 12772842 q^{29} + 181633 q^{30} - 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} - 1352872 q^{37} + 3704404 q^{38} + 1380780 q^{39} - 44739331 q^{40} - 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} - 148233417 q^{44} + 79449336 q^{45} - 31855859 q^{46} + 133558002 q^{47} + 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} + 50215469 q^{54} - 91197532 q^{55} - 267350757 q^{56} - 49507694 q^{57} - 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} - 262041240 q^{61} + 314328847 q^{62} - 218532626 q^{63} + 595820098 q^{64} - 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} - 204290852 q^{71} - 208030791 q^{72} - 673538852 q^{73} - 1274510282 q^{74} - 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} - 165043245 q^{78} - 434002980 q^{79} - 599590757 q^{80} - 389011392 q^{81} + 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} + 262108460 q^{88} + 911678128 q^{89} + 2734590475 q^{90} + 560105446 q^{91} + 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} + 1116511966 q^{95} - 2204198979 q^{96} + 3589270998 q^{97} - 2677144485 q^{98} - 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9 + 2449 * q^10 - 152886 * q^11 - 41717 * q^12 + 23478 * q^13 - 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 + 2477218 * q^20 - 1395256 * q^21 - 2391095 * q^22 - 2012428 * q^23 - 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 - 3231638 * q^27 + 5978216 * q^28 - 12772842 * q^29 + 181633 * q^30 - 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 - 1352872 * q^37 + 3704404 * q^38 + 1380780 * q^39 - 44739331 * q^40 - 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 - 148233417 * q^44 + 79449336 * q^45 - 31855859 * q^46 + 133558002 * q^47 + 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 + 50215469 * q^54 - 91197532 * q^55 - 267350757 * q^56 - 49507694 * q^57 - 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 - 262041240 * q^61 + 314328847 * q^62 - 218532626 * q^63 + 595820098 * q^64 - 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 - 204290852 * q^71 - 208030791 * q^72 - 673538852 * q^73 - 1274510282 * q^74 - 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 - 165043245 * q^78 - 434002980 * q^79 - 599590757 * q^80 - 389011392 * q^81 + 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 + 262108460 * q^88 + 911678128 * q^89 + 2734590475 * q^90 + 560105446 * q^91 + 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 + 1116511966 * q^95 - 2204198979 * q^96 + 3589270998 * q^97 - 2677144485 * q^98 - 2056683494 * q^99

Introduction

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