LMFDB - Embedded newform 273.8.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,8,Mod(1,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("273.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	273.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:	$85.2811119572$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4 x^{8} - 747 x^{7} + 3070 x^{6} + 180816 x^{5} - 678576 x^{4} - 15901072 x^{3} + \cdots + 220377344 $ x^9 - 4x^8 - 747x^7 + 3070x^6 + 180816x^5 - 678576x^4 - 15901072x^3 + 39784096x^2 + 394981632x + 220377344
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$8.66493$ of defining polynomial
Character	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.66493 q^{2} -27.0000 q^{3} -52.9191 q^{4} +59.9733 q^{5} -233.953 q^{6} -343.000 q^{7} -1567.65 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.66493 q^{2} -27.0000 q^{3} -52.9191 q^{4} +59.9733 q^{5} -233.953 q^{6} -343.000 q^{7} -1567.65 q^{8} +729.000 q^{9} +519.664 q^{10} -7541.69 q^{11} +1428.81 q^{12} -2197.00 q^{13} -2972.07 q^{14} -1619.28 q^{15} -6809.93 q^{16} -23600.0 q^{17} +6316.73 q^{18} +20553.3 q^{19} -3173.73 q^{20} +9261.00 q^{21} -65348.2 q^{22} +44075.2 q^{23} +42326.6 q^{24} -74528.2 q^{25} -19036.8 q^{26} -19683.0 q^{27} +18151.2 q^{28} +66133.1 q^{29} -14030.9 q^{30} -155994. q^{31} +141652. q^{32} +203626. q^{33} -204492. q^{34} -20570.8 q^{35} -38578.0 q^{36} -148245. q^{37} +178093. q^{38} +59319.0 q^{39} -94017.2 q^{40} -233779. q^{41} +80245.9 q^{42} -134679. q^{43} +399099. q^{44} +43720.5 q^{45} +381908. q^{46} -120800. q^{47} +183868. q^{48} +117649. q^{49} -645781. q^{50} +637199. q^{51} +116263. q^{52} +763830. q^{53} -170552. q^{54} -452300. q^{55} +537704. q^{56} -554939. q^{57} +573038. q^{58} -228326. q^{59} +85690.7 q^{60} -552697. q^{61} -1.35168e6 q^{62} -250047. q^{63} +2.09907e6 q^{64} -131761. q^{65} +1.76440e6 q^{66} -44779.4 q^{67} +1.24889e6 q^{68} -1.19003e6 q^{69} -178245. q^{70} +1.20517e6 q^{71} -1.14282e6 q^{72} +2.55380e6 q^{73} -1.28453e6 q^{74} +2.01226e6 q^{75} -1.08766e6 q^{76} +2.58680e6 q^{77} +513995. q^{78} +8.29123e6 q^{79} -408414. q^{80} +531441. q^{81} -2.02568e6 q^{82} +703310. q^{83} -490083. q^{84} -1.41537e6 q^{85} -1.16699e6 q^{86} -1.78559e6 q^{87} +1.18227e7 q^{88} +3.90565e6 q^{89} +378835. q^{90} +753571. q^{91} -2.33242e6 q^{92} +4.21183e6 q^{93} -1.04672e6 q^{94} +1.23265e6 q^{95} -3.82460e6 q^{96} +9.52017e6 q^{97} +1.01942e6 q^{98} -5.49789e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 4 q^{2} - 243 q^{3} + 358 q^{4} + 330 q^{5} - 108 q^{6} - 3087 q^{7} - 1206 q^{8} + 6561 q^{9}+O(q^{10}) $ 9 * q + 4 * q^2 - 243 * q^3 + 358 * q^4 + 330 * q^5 - 108 * q^6 - 3087 * q^7 - 1206 * q^8 + 6561 * q^9	\( 9 q + 4 q^{2} - 243 q^{3} + 358 q^{4} + 330 q^{5} - 108 q^{6} - 3087 q^{7} - 1206 q^{8} + 6561 q^{9} + 6335 q^{10} + 2176 q^{11} - 9666 q^{12} - 19773 q^{13} - 1372 q^{14} - 8910 q^{15} - 40686 q^{16} - 1022 q^{17} + 2916 q^{18} + 63240 q^{19} + 29105 q^{20} + 83349 q^{21} + 24635 q^{22} + 16212 q^{23} + 32562 q^{24} + 238075 q^{25} - 8788 q^{26} - 177147 q^{27} - 122794 q^{28} - 328180 q^{29} - 171045 q^{30} - 242182 q^{31} - 245454 q^{32} - 58752 q^{33} - 115535 q^{34} - 113190 q^{35} + 260982 q^{36} - 550054 q^{37} - 1199959 q^{38} + 533871 q^{39} + 1402045 q^{40} + 641846 q^{41} + 37044 q^{42} + 905942 q^{43} + 522021 q^{44} + 240570 q^{45} - 1903907 q^{46} + 466642 q^{47} + 1098522 q^{48} + 1058841 q^{49} + 1300175 q^{50} + 27594 q^{51} - 786526 q^{52} - 979208 q^{53} - 78732 q^{54} - 1101220 q^{55} + 413658 q^{56} - 1707480 q^{57} + 6478077 q^{58} - 335664 q^{59} - 785835 q^{60} - 2848696 q^{61} - 2122244 q^{62} - 2250423 q^{63} - 5017310 q^{64} - 725010 q^{65} - 665145 q^{66} - 3036728 q^{67} + 5605051 q^{68} - 437724 q^{69} - 2172905 q^{70} - 2190772 q^{71} - 879174 q^{72} + 1337916 q^{73} + 1481537 q^{74} - 6428025 q^{75} + 8974475 q^{76} - 746368 q^{77} + 237276 q^{78} + 137070 q^{79} - 367955 q^{80} + 4782969 q^{81} + 2947202 q^{82} + 13013474 q^{83} + 3315438 q^{84} + 9096820 q^{85} + 1222661 q^{86} + 8860860 q^{87} + 8139465 q^{88} + 9126740 q^{89} + 4618215 q^{90} + 6782139 q^{91} + 34403367 q^{92} + 6538914 q^{93} + 32954276 q^{94} + 34578180 q^{95} + 6627258 q^{96} + 18345820 q^{97} + 470596 q^{98} + 1586304 q^{99}+O(q^{100}) \) 9 * q + 4 * q^2 - 243 * q^3 + 358 * q^4 + 330 * q^5 - 108 * q^6 - 3087 * q^7 - 1206 * q^8 + 6561 * q^9 + 6335 * q^10 + 2176 * q^11 - 9666 * q^12 - 19773 * q^13 - 1372 * q^14 - 8910 * q^15 - 40686 * q^16 - 1022 * q^17 + 2916 * q^18 + 63240 * q^19 + 29105 * q^20 + 83349 * q^21 + 24635 * q^22 + 16212 * q^23 + 32562 * q^24 + 238075 * q^25 - 8788 * q^26 - 177147 * q^27 - 122794 * q^28 - 328180 * q^29 - 171045 * q^30 - 242182 * q^31 - 245454 * q^32 - 58752 * q^33 - 115535 * q^34 - 113190 * q^35 + 260982 * q^36 - 550054 * q^37 - 1199959 * q^38 + 533871 * q^39 + 1402045 * q^40 + 641846 * q^41 + 37044 * q^42 + 905942 * q^43 + 522021 * q^44 + 240570 * q^45 - 1903907 * q^46 + 466642 * q^47 + 1098522 * q^48 + 1058841 * q^49 + 1300175 * q^50 + 27594 * q^51 - 786526 * q^52 - 979208 * q^53 - 78732 * q^54 - 1101220 * q^55 + 413658 * q^56 - 1707480 * q^57 + 6478077 * q^58 - 335664 * q^59 - 785835 * q^60 - 2848696 * q^61 - 2122244 * q^62 - 2250423 * q^63 - 5017310 * q^64 - 725010 * q^65 - 665145 * q^66 - 3036728 * q^67 + 5605051 * q^68 - 437724 * q^69 - 2172905 * q^70 - 2190772 * q^71 - 879174 * q^72 + 1337916 * q^73 + 1481537 * q^74 - 6428025 * q^75 + 8974475 * q^76 - 746368 * q^77 + 237276 * q^78 + 137070 * q^79 - 367955 * q^80 + 4782969 * q^81 + 2947202 * q^82 + 13013474 * q^83 + 3315438 * q^84 + 9096820 * q^85 + 1222661 * q^86 + 8860860 * q^87 + 8139465 * q^88 + 9126740 * q^89 + 4618215 * q^90 + 6782139 * q^91 + 34403367 * q^92 + 6538914 * q^93 + 32954276 * q^94 + 34578180 * q^95 + 6627258 * q^96 + 18345820 * q^97 + 470596 * q^98 + 1586304 * 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 $

$2$	8.66493	0.765878	0.382939	−	0.923774i	$-0.374912\pi$
$2$	8.66493	0.765878	0.382939	+	0.923774i	$0.374912\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−52.9191	−0.413430
$5$	59.9733	0.214567	0.107284	−	0.994228i	$-0.465785\pi$
$5$	59.9733	0.214567	0.107284	+	0.994228i	$0.465785\pi$
$6$	−233.953	−0.442180
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−1567.65	−1.08252
$9$	729.000	0.333333
$10$	519.664	0.164332
$11$	−7541.69	−1.70842	−0.854209	−	0.519929i	$-0.825958\pi$
$11$	−7541.69	−1.70842	−0.854209	+	0.519929i	$0.825958\pi$
$12$	1428.81	0.238694
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2972.07	−0.289475
$15$	−1619.28	−0.123880
$16$	−6809.93	−0.415645
$17$	−23600.0	−1.16504	−0.582519	−	0.812817i	$-0.697933\pi$
$17$	−23600.0	−1.16504	−0.582519	+	0.812817i	$0.697933\pi$
$18$	6316.73	0.255293
$19$	20553.3	0.687454	0.343727	−	0.939070i	$-0.388311\pi$
$19$	20553.3	0.687454	0.343727	+	0.939070i	$0.388311\pi$
$20$	−3173.73	−0.0887085
$21$	9261.00	0.218218
$22$	−65348.2	−1.30844
$23$	44075.2	0.755347	0.377674	−	0.925939i	$-0.376724\pi$
$23$	44075.2	0.755347	0.377674	+	0.925939i	$0.376724\pi$
$24$	42326.6	0.624991
$25$	−74528.2	−0.953961
$26$	−19036.8	−0.212416
$27$	−19683.0	−0.192450
$28$	18151.2	0.156262
$29$	66133.1	0.503530	0.251765	−	0.967788i	$-0.418989\pi$
$29$	66133.1	0.503530	0.251765	+	0.967788i	$0.418989\pi$
$30$	−14030.9	−0.0948773
$31$	−155994.	−0.940463	−0.470231	−	0.882543i	$-0.655830\pi$
$31$	−155994.	−0.940463	−0.470231	+	0.882543i	$0.655830\pi$
$32$	141652.	0.764182
$33$	203626.	0.986356
$34$	−204492.	−0.892278
$35$	−20570.8	−0.0810987
$36$	−38578.0	−0.137810
$37$	−148245.	−0.481142	−0.240571	−	0.970632i	$-0.577335\pi$
$37$	−148245.	−0.481142	−0.240571	+	0.970632i	$0.577335\pi$
$38$	178093.	0.526506
$39$	59319.0	0.160128
$40$	−94017.2	−0.232272
$41$	−233779.	−0.529739	−0.264870	−	0.964284i	$-0.585329\pi$
$41$	−233779.	−0.529739	−0.264870	+	0.964284i	$0.585329\pi$
$42$	80245.9	0.167128
$43$	−134679.	−0.258322	−0.129161	−	0.991624i	$-0.541228\pi$
$43$	−134679.	−0.258322	−0.129161	+	0.991624i	$0.541228\pi$
$44$	399099.	0.706312
$45$	43720.5	0.0715223
$46$	381908.	0.578504
$47$	−120800.	−0.169717	−0.0848585	−	0.996393i	$-0.527044\pi$
$47$	−120800.	−0.169717	−0.0848585	+	0.996393i	$0.527044\pi$
$48$	183868.	0.239973
$49$	117649.	0.142857
$50$	−645781.	−0.730618
$51$	637199.	0.672635
$52$	116263.	0.114665
$53$	763830.	0.704743	0.352372	−	0.935860i	$-0.385375\pi$
$53$	763830.	0.704743	0.352372	+	0.935860i	$0.385375\pi$
$54$	−170552.	−0.147393
$55$	−452300.	−0.366570
$56$	537704.	0.409152
$57$	−554939.	−0.396902
$58$	573038.	0.385643
$59$	−228326.	−0.144735	−0.0723676	−	0.997378i	$-0.523055\pi$
$59$	−228326.	−0.144735	−0.0723676	+	0.997378i	$0.523055\pi$
$60$	85690.7	0.0512159
$61$	−552697.	−0.311769	−0.155884	−	0.987775i	$-0.549823\pi$
$61$	−552697.	−0.311769	−0.155884	+	0.987775i	$0.549823\pi$
$62$	−1.35168e6	−0.720280
$63$	−250047.	−0.125988
$64$	2.09907e6	1.00092
$65$	−131761.	−0.0595102
$66$	1.76440e6	0.755429
$67$	−44779.4	−0.0181893	−0.00909465	−	0.999959i	$-0.502895\pi$
$67$	−44779.4	−0.0181893	−0.00909465	+	0.999959i	$0.502895\pi$
$68$	1.24889e6	0.481662
$69$	−1.19003e6	−0.436100
$70$	−178245.	−0.0621118
$71$	1.20517e6	0.399616	0.199808	−	0.979835i	$-0.435968\pi$
$71$	1.20517e6	0.399616	0.199808	+	0.979835i	$0.435968\pi$
$72$	−1.14282e6	−0.360839
$73$	2.55380e6	0.768347	0.384173	−	0.923261i	$-0.374486\pi$
$73$	2.55380e6	0.768347	0.384173	+	0.923261i	$0.374486\pi$
$74$	−1.28453e6	−0.368496
$75$	2.01226e6	0.550770
$76$	−1.08766e6	−0.284214
$77$	2.58680e6	0.645721
$78$	513995.	0.122639
$79$	8.29123e6	1.89201	0.946007	−	0.324147i	$-0.105077\pi$
$79$	8.29123e6	1.89201	0.946007	+	0.324147i	$0.105077\pi$
$80$	−408414.	−0.0891838
$81$	531441.	0.111111
$82$	−2.02568e6	−0.405716
$83$	703310.	0.135012	0.0675062	−	0.997719i	$-0.478496\pi$
$83$	703310.	0.135012	0.0675062	+	0.997719i	$0.478496\pi$
$84$	−490083.	−0.0902179
$85$	−1.41537e6	−0.249979
$86$	−1.16699e6	−0.197843
$87$	−1.78559e6	−0.290713
$88$	1.18227e7	1.84939
$89$	3.90565e6	0.587256	0.293628	−	0.955920i	$-0.405137\pi$
$89$	3.90565e6	0.587256	0.293628	+	0.955920i	$0.405137\pi$
$90$	378835.	0.0547774
$91$	753571.	0.104828
$92$	−2.33242e6	−0.312283
$93$	4.21183e6	0.542976
$94$	−1.04672e6	−0.129983
$95$	1.23265e6	0.147505
$96$	−3.82460e6	−0.441201
$97$	9.52017e6	1.05912	0.529558	−	0.848274i	$-0.322358\pi$
$97$	9.52017e6	1.05912	0.529558	+	0.848274i	$0.322358\pi$
$98$	1.01942e6	0.109411
$99$	−5.49789e6	−0.569473
$100$	3.94396e6	0.394396
$101$	7.68639e6	0.742331	0.371166	−	0.928567i	$-0.378958\pi$
$101$	7.68639e6	0.742331	0.371166	+	0.928567i	$0.378958\pi$
$102$	5.52128e6	0.515157
$103$	2.58703e6	0.233276	0.116638	−	0.993174i	$-0.462788\pi$
$103$	2.58703e6	0.233276	0.116638	+	0.993174i	$0.462788\pi$
$104$	3.44413e6	0.300236
$105$	555413.	0.0468224
$106$	6.61853e6	0.539748
$107$	6.45413e6	0.509325	0.254662	−	0.967030i	$-0.418036\pi$
$107$	6.45413e6	0.509325	0.254662	+	0.967030i	$0.418036\pi$
$108$	1.04161e6	0.0795647
$109$	7.71122e6	0.570335	0.285168	−	0.958478i	$-0.407951\pi$
$109$	7.71122e6	0.570335	0.285168	+	0.958478i	$0.407951\pi$
$110$	−3.91915e6	−0.280748
$111$	4.00261e6	0.277788
$112$	2.33581e6	0.157099
$113$	2.50396e6	0.163250	0.0816249	−	0.996663i	$-0.473989\pi$
$113$	2.50396e6	0.163250	0.0816249	+	0.996663i	$0.473989\pi$
$114$	−4.80850e6	−0.303979
$115$	2.64333e6	0.162073
$116$	−3.49970e6	−0.208175
$117$	−1.60161e6	−0.0924500
$118$	−1.97843e6	−0.110850
$119$	8.09479e6	0.440343
$120$	2.53846e6	0.134102
$121$	3.73899e7	1.91869
$122$	−4.78908e6	−0.238777
$123$	6.31204e6	0.305845
$124$	8.25505e6	0.388816
$125$	−9.15512e6	−0.419256
$126$	−2.16664e6	−0.0964916
$127$	−1.47329e7	−0.638228	−0.319114	−	0.947716i	$-0.603385\pi$
$127$	−1.47329e7	−0.638228	−0.319114	+	0.947716i	$0.603385\pi$
$128$	56893.8	0.00239789
$129$	3.63634e6	0.149142
$130$	−1.14170e6	−0.0455776
$131$	2.46085e6	0.0956391	0.0478195	−	0.998856i	$-0.484773\pi$
$131$	2.46085e6	0.0956391	0.0478195	+	0.998856i	$0.484773\pi$
$132$	−1.07757e7	−0.407789
$133$	−7.04978e6	−0.259833
$134$	−388010.	−0.0139308
$135$	−1.18045e6	−0.0412934
$136$	3.69965e7	1.26117
$137$	−5.48919e7	−1.82384	−0.911919	−	0.410369i	$-0.865400\pi$
$137$	−5.48919e7	−1.82384	−0.911919	+	0.410369i	$0.865400\pi$
$138$	−1.03115e7	−0.334000
$139$	−5.88697e7	−1.85926	−0.929630	−	0.368495i	$-0.879873\pi$
$139$	−5.88697e7	−1.85926	−0.929630	+	0.368495i	$0.879873\pi$
$140$	1.08859e6	0.0335287
$141$	3.26161e6	0.0979861
$142$	1.04427e7	0.306057
$143$	1.65691e7	0.473830
$144$	−4.96444e6	−0.138548
$145$	3.96622e6	0.108041
$146$	2.21285e7	0.588460
$147$	−3.17652e6	−0.0824786
$148$	7.84497e6	0.198919
$149$	3.98247e7	0.986280	0.493140	−	0.869950i	$-0.335849\pi$
$149$	3.98247e7	0.986280	0.493140	+	0.869950i	$0.335849\pi$
$150$	1.74361e7	0.421823
$151$	−4.41640e7	−1.04388	−0.521939	−	0.852983i	$-0.674791\pi$
$151$	−4.41640e7	−1.04388	−0.521939	+	0.852983i	$0.674791\pi$
$152$	−3.22204e7	−0.744180
$153$	−1.72044e7	−0.388346
$154$	2.24144e7	0.494544
$155$	−9.35547e6	−0.201792
$156$	−3.13911e6	−0.0662018
$157$	−9.28451e7	−1.91474	−0.957371	−	0.288863i	$-0.906723\pi$
$157$	−9.28451e7	−1.91474	−0.957371	+	0.288863i	$0.906723\pi$
$158$	7.18429e7	1.44905
$159$	−2.06234e7	−0.406884
$160$	8.49532e6	0.163968
$161$	−1.51178e7	−0.285494
$162$	4.60490e6	0.0850976
$163$	9.87941e7	1.78679	0.893397	−	0.449269i	$-0.148315\pi$
$163$	9.87941e7	1.78679	0.893397	+	0.449269i	$0.148315\pi$
$164$	1.23714e7	0.219010
$165$	1.22121e7	0.211639
$166$	6.09413e6	0.103403
$167$	4.07731e7	0.677433	0.338716	−	0.940889i	$-0.390007\pi$
$167$	4.07731e7	0.677433	0.338716	+	0.940889i	$0.390007\pi$
$168$	−1.45180e7	−0.236224
$169$	4.82681e6	0.0769231
$170$	−1.22641e7	−0.191453
$171$	1.49833e7	0.229151
$172$	7.12711e6	0.106798
$173$	1.28250e8	1.88320	0.941601	−	0.336729i	$-0.109321\pi$
$173$	1.28250e8	1.88320	0.941601	+	0.336729i	$0.109321\pi$
$174$	−1.54720e7	−0.222651
$175$	2.55632e7	0.360563
$176$	5.13584e7	0.710096
$177$	6.16481e6	0.0835629
$178$	3.38421e7	0.449767
$179$	−6.52591e7	−0.850463	−0.425231	−	0.905085i	$-0.639807\pi$
$179$	−6.52591e7	−0.850463	−0.425231	+	0.905085i	$0.639807\pi$
$180$	−2.31365e6	−0.0295695
$181$	−4.36057e7	−0.546599	−0.273299	−	0.961929i	$-0.588115\pi$
$181$	−4.36057e7	−0.546599	−0.273299	+	0.961929i	$0.588115\pi$
$182$	6.52964e6	0.0802859
$183$	1.49228e7	0.180000
$184$	−6.90945e7	−0.817675
$185$	−8.89073e6	−0.103237
$186$	3.64952e7	0.415854
$187$	1.77984e8	1.99037
$188$	6.39263e6	0.0701661
$189$	6.75127e6	0.0727393
$190$	1.06808e7	0.112971
$191$	−1.76296e8	−1.83074	−0.915368	−	0.402618i	$-0.868100\pi$
$191$	−1.76296e8	−1.83074	−0.915368	+	0.402618i	$0.868100\pi$
$192$	−5.66750e7	−0.577879
$193$	−5.82452e7	−0.583190	−0.291595	−	0.956542i	$-0.594186\pi$
$193$	−5.82452e7	−0.583190	−0.291595	+	0.956542i	$0.594186\pi$
$194$	8.24916e7	0.811155
$195$	3.55756e6	0.0343582
$196$	−6.22587e6	−0.0590615
$197$	−9.82784e7	−0.915855	−0.457927	−	0.888990i	$-0.651408\pi$
$197$	−9.82784e7	−0.915855	−0.457927	+	0.888990i	$0.651408\pi$
$198$	−4.76388e7	−0.436147
$199$	−5.51560e6	−0.0496143	−0.0248072	−	0.999692i	$-0.507897\pi$
$199$	−5.51560e6	−0.0496143	−0.0248072	+	0.999692i	$0.507897\pi$
$200$	1.16834e8	1.03268
$201$	1.20904e6	0.0105016
$202$	6.66020e7	0.568535
$203$	−2.26836e7	−0.190317
$204$	−3.37200e7	−0.278088
$205$	−1.40205e7	−0.113665
$206$	2.24164e7	0.178661
$207$	3.21308e7	0.251782
$208$	1.49614e7	0.115279
$209$	−1.55007e8	−1.17446
$210$	4.81261e6	0.0358602
$211$	−6.31824e6	−0.0463028	−0.0231514	−	0.999732i	$-0.507370\pi$
$211$	−6.31824e6	−0.0463028	−0.0231514	+	0.999732i	$0.507370\pi$
$212$	−4.04211e7	−0.291362
$213$	−3.25395e7	−0.230718
$214$	5.59246e7	0.390081
$215$	−8.07717e6	−0.0554274
$216$	3.08561e7	0.208330
$217$	5.35059e7	0.355462
$218$	6.68171e7	0.436807
$219$	−6.89527e7	−0.443605
$220$	2.39353e7	0.151551
$221$	5.18491e7	0.323123
$222$	3.46823e7	0.212751
$223$	2.92880e8	1.76857	0.884287	−	0.466943i	$-0.154645\pi$
$223$	2.92880e8	1.76857	0.884287	+	0.466943i	$0.154645\pi$
$224$	−4.85865e7	−0.288834
$225$	−5.43311e7	−0.317987
$226$	2.16966e7	0.125029
$227$	1.26067e8	0.715336	0.357668	−	0.933849i	$-0.383572\pi$
$227$	1.26067e8	0.715336	0.357668	+	0.933849i	$0.383572\pi$
$228$	2.93668e7	0.164091
$229$	1.62557e8	0.894501	0.447251	−	0.894409i	$-0.352403\pi$
$229$	1.62557e8	0.894501	0.447251	+	0.894409i	$0.352403\pi$
$230$	2.29043e7	0.124128
$231$	−6.98436e7	−0.372807
$232$	−1.03674e8	−0.545079
$233$	−2.47835e8	−1.28356	−0.641780	−	0.766889i	$-0.721804\pi$
$233$	−2.47835e8	−1.28356	−0.641780	+	0.766889i	$0.721804\pi$
$234$	−1.38779e7	−0.0708055
$235$	−7.24479e6	−0.0364157
$236$	1.20828e7	0.0598379
$237$	−2.23863e8	−1.09235
$238$	7.01407e7	0.337249
$239$	1.50011e8	0.710771	0.355385	−	0.934720i	$-0.384350\pi$
$239$	1.50011e8	0.710771	0.355385	+	0.934720i	$0.384350\pi$
$240$	1.10272e7	0.0514903
$241$	4.28918e7	0.197385	0.0986927	−	0.995118i	$-0.468534\pi$
$241$	4.28918e7	0.197385	0.0986927	+	0.995118i	$0.468534\pi$
$242$	3.23981e8	1.46949
$243$	−1.43489e7	−0.0641500
$244$	2.92482e7	0.128895
$245$	7.05580e6	0.0306524
$246$	5.46933e7	0.234240
$247$	−4.51556e7	−0.190665
$248$	2.44544e8	1.01807
$249$	−1.89894e7	−0.0779494
$250$	−7.93284e7	−0.321099
$251$	3.76308e8	1.50205	0.751026	−	0.660272i	$-0.229559\pi$
$251$	3.76308e8	1.50205	0.751026	+	0.660272i	$0.229559\pi$
$252$	1.32323e7	0.0520873
$253$	−3.32401e8	−1.29045
$254$	−1.27660e8	−0.488805
$255$	3.82149e7	0.144325
$256$	−2.68188e8	−0.999079
$257$	−3.02101e8	−1.11016	−0.555081	−	0.831796i	$-0.687313\pi$
$257$	−3.02101e8	−1.11016	−0.555081	+	0.831796i	$0.687313\pi$
$258$	3.15086e7	0.114225
$259$	5.08480e7	0.181855
$260$	6.97269e6	0.0246033
$261$	4.82110e7	0.167843
$262$	2.13231e7	0.0732479
$263$	3.13349e8	1.06214	0.531071	−	0.847327i	$-0.321790\pi$
$263$	3.13349e8	1.06214	0.531071	+	0.847327i	$0.321790\pi$
$264$	−3.19214e8	−1.06775
$265$	4.58094e7	0.151215
$266$	−6.10858e7	−0.199001
$267$	−1.05452e8	−0.339053
$268$	2.36968e6	0.00752001
$269$	−2.25596e7	−0.0706640	−0.0353320	−	0.999376i	$-0.511249\pi$
$269$	−2.25596e7	−0.0706640	−0.0353320	+	0.999376i	$0.511249\pi$
$270$	−1.02286e7	−0.0316258
$271$	−6.33579e6	−0.0193378	−0.00966892	−	0.999953i	$-0.503078\pi$
$271$	−6.33579e6	−0.0193378	−0.00966892	+	0.999953i	$0.503078\pi$
$272$	1.60714e8	0.484243
$273$	−2.03464e7	−0.0605228
$274$	−4.75634e8	−1.39684
$275$	5.62069e8	1.62976
$276$	6.29753e7	0.180297
$277$	−2.70931e8	−0.765912	−0.382956	−	0.923767i	$-0.625094\pi$
$277$	−2.70931e8	−0.765912	−0.382956	+	0.923767i	$0.625094\pi$
$278$	−5.10101e8	−1.42397
$279$	−1.13720e8	−0.313488
$280$	3.22479e7	0.0877906
$281$	−5.59959e7	−0.150551	−0.0752756	−	0.997163i	$-0.523984\pi$
$281$	−5.59959e7	−0.150551	−0.0752756	+	0.997163i	$0.523984\pi$
$282$	2.82616e7	0.0750455
$283$	2.90300e8	0.761368	0.380684	−	0.924705i	$-0.375689\pi$
$283$	2.90300e8	0.761368	0.380684	+	0.924705i	$0.375689\pi$
$284$	−6.37762e7	−0.165213
$285$	−3.32815e7	−0.0851620
$286$	1.43570e8	0.362896
$287$	8.01863e7	0.200223
$288$	1.03264e8	0.254727
$289$	1.46620e8	0.357314
$290$	3.43670e7	0.0827463
$291$	−2.57045e8	−0.611481
$292$	−1.35145e8	−0.317658
$293$	−8.52785e8	−1.98063	−0.990314	−	0.138844i	$-0.955661\pi$
$293$	−8.52785e8	−1.98063	−0.990314	+	0.138844i	$0.955661\pi$
$294$	−2.75243e7	−0.0631686
$295$	−1.36935e7	−0.0310554
$296$	2.32396e8	0.520844
$297$	1.48443e8	0.328785
$298$	3.45078e8	0.755371
$299$	−9.68332e7	−0.209496
$300$	−1.06487e8	−0.227705
$301$	4.61950e7	0.0976366
$302$	−3.82678e8	−0.799483
$303$	−2.07533e8	−0.428585
$304$	−1.39967e8	−0.285737
$305$	−3.31471e7	−0.0668953
$306$	−1.49075e8	−0.297426
$307$	−9.72253e7	−0.191776	−0.0958881	−	0.995392i	$-0.530569\pi$
$307$	−9.72253e7	−0.191776	−0.0958881	+	0.995392i	$0.530569\pi$
$308$	−1.36891e8	−0.266961
$309$	−6.98497e7	−0.134682
$310$	−8.10644e7	−0.154548
$311$	−1.56283e8	−0.294611	−0.147306	−	0.989091i	$-0.547060\pi$
$311$	−1.56283e8	−0.294611	−0.147306	+	0.989091i	$0.547060\pi$
$312$	−9.29914e7	−0.173341
$313$	−8.50152e8	−1.56708	−0.783540	−	0.621341i	$-0.786588\pi$
$313$	−8.50152e8	−1.56708	−0.783540	+	0.621341i	$0.786588\pi$
$314$	−8.04496e8	−1.46646
$315$	−1.49961e7	−0.0270329
$316$	−4.38764e8	−0.782215
$317$	2.46258e8	0.434193	0.217096	−	0.976150i	$-0.430341\pi$
$317$	2.46258e8	0.434193	0.217096	+	0.976150i	$0.430341\pi$
$318$	−1.78700e8	−0.311623
$319$	−4.98755e8	−0.860240
$320$	1.25888e8	0.214764
$321$	−1.74262e8	−0.294059
$322$	−1.30994e8	−0.218654
$323$	−4.85057e8	−0.800910
$324$	−2.81234e7	−0.0459367
$325$	1.63738e8	0.264581
$326$	8.56043e8	1.36847
$327$	−2.08203e8	−0.329283
$328$	3.66484e8	0.573451
$329$	4.14345e7	0.0641470
$330$	1.05817e8	0.162090
$331$	−2.29500e7	−0.0347844	−0.0173922	−	0.999849i	$-0.505536\pi$
$331$	−2.29500e7	−0.0347844	−0.0173922	+	0.999849i	$0.505536\pi$
$332$	−3.72185e7	−0.0558182
$333$	−1.08070e8	−0.160381
$334$	3.53296e8	0.518831
$335$	−2.68557e6	−0.00390282
$336$	−6.30668e7	−0.0907012
$337$	1.73868e8	0.247465	0.123733	−	0.992316i	$-0.460513\pi$
$337$	1.73868e8	0.247465	0.123733	+	0.992316i	$0.460513\pi$
$338$	4.18239e7	0.0589137
$339$	−6.76069e7	−0.0942523
$340$	7.48999e7	0.103349
$341$	1.17646e9	1.60670
$342$	1.29830e8	0.175502
$343$	−4.03536e7	−0.0539949
$344$	2.11130e8	0.279638
$345$	−7.13700e7	−0.0935727
$346$	1.11128e9	1.44230
$347$	7.27275e8	0.934428	0.467214	−	0.884144i	$-0.345258\pi$
$347$	7.27275e8	0.934428	0.467214	+	0.884144i	$0.345258\pi$
$348$	9.44919e7	0.120190
$349$	−2.60535e8	−0.328078	−0.164039	−	0.986454i	$-0.552452\pi$
$349$	−2.60535e8	−0.328078	−0.164039	+	0.986454i	$0.552452\pi$
$350$	2.21503e8	0.276148
$351$	4.32436e7	0.0533761
$352$	−1.06829e9	−1.30554
$353$	2.41488e7	0.0292202	0.0146101	−	0.999893i	$-0.495349\pi$
$353$	2.41488e7	0.0292202	0.0146101	+	0.999893i	$0.495349\pi$
$354$	5.34177e7	0.0639990
$355$	7.22778e7	0.0857443
$356$	−2.06683e8	−0.242790
$357$	−2.18559e8	−0.254232
$358$	−5.65465e8	−0.651351
$359$	−8.32980e8	−0.950175	−0.475088	−	0.879938i	$-0.657584\pi$
$359$	−8.32980e8	−0.950175	−0.475088	+	0.879938i	$0.657584\pi$
$360$	−6.85385e7	−0.0774241
$361$	−4.71434e8	−0.527407
$362$	−3.77840e8	−0.418628
$363$	−1.00953e9	−1.10776
$364$	−3.98783e7	−0.0433393
$365$	1.53160e8	0.164862
$366$	1.29305e8	0.137858
$367$	3.35448e8	0.354237	0.177119	−	0.984189i	$-0.443322\pi$
$367$	3.35448e8	0.354237	0.177119	+	0.984189i	$0.443322\pi$
$368$	−3.00149e8	−0.313957
$369$	−1.70425e8	−0.176580
$370$	−7.70375e7	−0.0790672
$371$	−2.61994e8	−0.266368
$372$	−2.22886e8	−0.224483
$373$	−1.52373e9	−1.52029	−0.760145	−	0.649753i	$-0.774872\pi$
$373$	−1.52373e9	−1.52029	−0.760145	+	0.649753i	$0.774872\pi$
$374$	1.54221e9	1.52438
$375$	2.47188e8	0.242057
$376$	1.89372e8	0.183721
$377$	−1.45294e8	−0.139654
$378$	5.84992e7	0.0557095
$379$	−1.90954e9	−1.80173	−0.900867	−	0.434094i	$-0.857068\pi$
$379$	−1.90954e9	−1.80173	−0.900867	+	0.434094i	$0.857068\pi$
$380$	−6.52306e7	−0.0609830
$381$	3.97789e8	0.368481
$382$	−1.52759e9	−1.40212
$383$	−5.94639e8	−0.540826	−0.270413	−	0.962744i	$-0.587160\pi$
$383$	−5.94639e8	−0.540826	−0.270413	+	0.962744i	$0.587160\pi$
$384$	−1.53613e6	−0.00138442
$385$	1.55139e8	0.138551
$386$	−5.04691e8	−0.446652
$387$	−9.81813e7	−0.0861074
$388$	−5.03799e8	−0.437871
$389$	−6.39110e8	−0.550493	−0.275246	−	0.961374i	$-0.588759\pi$
$389$	−6.39110e8	−0.550493	−0.275246	+	0.961374i	$0.588759\pi$
$390$	3.08260e7	0.0263142
$391$	−1.04017e9	−0.880008
$392$	−1.84432e8	−0.154645
$393$	−6.64429e7	−0.0552172
$394$	−8.51575e8	−0.701433
$395$	4.97252e8	0.405964
$396$	2.90943e8	0.235437
$397$	−2.24016e8	−0.179685	−0.0898425	−	0.995956i	$-0.528636\pi$
$397$	−2.24016e8	−0.179685	−0.0898425	+	0.995956i	$0.528636\pi$
$398$	−4.77923e7	−0.0379986
$399$	1.90344e8	0.150015
$400$	5.07532e8	0.396509
$401$	1.29199e9	1.00059	0.500294	−	0.865856i	$-0.333225\pi$
$401$	1.29199e9	1.00059	0.500294	+	0.865856i	$0.333225\pi$
$402$	1.04763e7	0.00804295
$403$	3.42719e8	0.260837
$404$	−4.06757e8	−0.306902
$405$	3.18723e7	0.0238408
$406$	−1.96552e8	−0.145759
$407$	1.11802e9	0.821992
$408$	−9.98905e8	−0.728138
$409$	7.68554e8	0.555447	0.277724	−	0.960661i	$-0.410420\pi$
$409$	7.68554e8	0.555447	0.277724	+	0.960661i	$0.410420\pi$
$410$	−1.21487e8	−0.0870533
$411$	1.48208e9	1.05299
$412$	−1.36903e8	−0.0964435
$413$	7.83160e7	0.0547048
$414$	2.78411e8	0.192835
$415$	4.21798e7	0.0289692
$416$	−3.11209e8	−0.211946
$417$	1.58948e9	1.07344
$418$	−1.34312e9	−0.899493
$419$	2.12460e9	1.41100	0.705501	−	0.708709i	$-0.250722\pi$
$419$	2.12460e9	1.41100	0.705501	+	0.708709i	$0.250722\pi$
$420$	−2.93919e7	−0.0193578
$421$	1.86032e9	1.21506	0.607532	−	0.794295i	$-0.292160\pi$
$421$	1.86032e9	1.21506	0.607532	+	0.794295i	$0.292160\pi$
$422$	−5.47471e7	−0.0354623
$423$	−8.80634e7	−0.0565723
$424$	−1.19742e9	−0.762896
$425$	1.75886e9	1.11140
$426$	−2.81952e8	−0.176702
$427$	1.89575e8	0.117838
$428$	−3.41547e8	−0.210570
$429$	−4.47365e8	−0.273566
$430$	−6.99881e7	−0.0424507
$431$	−9.56246e8	−0.575306	−0.287653	−	0.957735i	$-0.592875\pi$
$431$	−9.56246e8	−0.575306	−0.287653	+	0.957735i	$0.592875\pi$
$432$	1.34040e8	0.0799910
$433$	1.35133e9	0.799931	0.399965	−	0.916530i	$-0.369022\pi$
$433$	1.35133e9	0.799931	0.399965	+	0.916530i	$0.369022\pi$
$434$	4.63625e8	0.272240
$435$	−1.07088e8	−0.0623775
$436$	−4.08070e8	−0.235794
$437$	9.05890e8	0.519267
$438$	−5.97470e8	−0.339748
$439$	9.50496e7	0.0536197	0.0268098	−	0.999641i	$-0.491465\pi$
$439$	9.50496e7	0.0536197	0.0268098	+	0.999641i	$0.491465\pi$
$440$	7.09048e8	0.396818
$441$	8.57661e7	0.0476190
$442$	4.49269e8	0.247473
$443$	2.58945e9	1.41512	0.707561	−	0.706652i	$-0.249795\pi$
$443$	2.58945e9	1.41512	0.707561	+	0.706652i	$0.249795\pi$
$444$	−2.11814e8	−0.114846
$445$	2.34234e8	0.126006
$446$	2.53779e9	1.35451
$447$	−1.07527e9	−0.569429
$448$	−7.19982e8	−0.378311
$449$	9.96863e8	0.519725	0.259862	−	0.965646i	$-0.416323\pi$
$449$	9.96863e8	0.519725	0.259862	+	0.965646i	$0.416323\pi$
$450$	−4.70775e8	−0.243539
$451$	1.76309e9	0.905017
$452$	−1.32507e8	−0.0674924
$453$	1.19243e9	0.602683
$454$	1.09236e9	0.547860
$455$	4.51941e7	0.0224927
$456$	8.69950e8	0.429652
$457$	2.40035e9	1.17643	0.588217	−	0.808703i	$-0.299830\pi$
$457$	2.40035e9	1.17643	0.588217	+	0.808703i	$0.299830\pi$
$458$	1.40854e9	0.685079
$459$	4.64518e8	0.224212
$460$	−1.39883e8	−0.0670057
$461$	7.16087e8	0.340418	0.170209	−	0.985408i	$-0.445556\pi$
$461$	7.16087e8	0.340418	0.170209	+	0.985408i	$0.445556\pi$
$462$	−6.05189e8	−0.285525
$463$	9.70846e8	0.454587	0.227293	−	0.973826i	$-0.427012\pi$
$463$	9.70846e8	0.454587	0.227293	+	0.973826i	$0.427012\pi$
$464$	−4.50362e8	−0.209290
$465$	2.52598e8	0.116505
$466$	−2.14747e9	−0.983051
$467$	2.66085e9	1.20896	0.604480	−	0.796620i	$-0.293381\pi$
$467$	2.66085e9	1.20896	0.604480	+	0.796620i	$0.293381\pi$
$468$	8.47559e7	0.0382216
$469$	1.53593e7	0.00687491
$470$	−6.27755e7	−0.0278900
$471$	2.50682e9	1.10548
$472$	3.57936e8	0.156678
$473$	1.01571e9	0.441322
$474$	−1.93976e9	−0.836611
$475$	−1.53180e9	−0.655804
$476$	−4.28369e8	−0.182051
$477$	5.56832e8	0.234914
$478$	1.29983e9	0.544364
$479$	4.58747e9	1.90721	0.953606	−	0.301058i	$-0.0973398\pi$
$479$	4.58747e9	1.90721	0.953606	+	0.301058i	$0.0973398\pi$
$480$	−2.29374e8	−0.0946671
$481$	3.25694e8	0.133445
$482$	3.71655e8	0.151173
$483$	4.08180e8	0.164830
$484$	−1.97864e9	−0.793246
$485$	5.70956e8	0.227251
$486$	−1.24332e8	−0.0491311
$487$	−2.20328e9	−0.864406	−0.432203	−	0.901776i	$-0.642264\pi$
$487$	−2.20328e9	−0.864406	−0.432203	+	0.901776i	$0.642264\pi$
$488$	8.66436e8	0.337495
$489$	−2.66744e9	−1.03161
$490$	6.11380e7	0.0234760
$491$	−1.46283e8	−0.0557712	−0.0278856	−	0.999611i	$-0.508877\pi$
$491$	−1.46283e8	−0.0557712	−0.0278856	+	0.999611i	$0.508877\pi$
$492$	−3.34027e8	−0.126446
$493$	−1.56074e9	−0.586632
$494$	−3.91270e8	−0.146027
$495$	−3.29727e8	−0.122190
$496$	1.06231e9	0.390899
$497$	−4.13372e8	−0.151041
$498$	−1.64541e8	−0.0596998
$499$	1.49570e8	0.0538882	0.0269441	−	0.999637i	$-0.491422\pi$
$499$	1.49570e8	0.0538882	0.0269441	+	0.999637i	$0.491422\pi$
$500$	4.84480e8	0.173333
$501$	−1.10087e9	−0.391116
$502$	3.26068e9	1.15039
$503$	2.12433e9	0.744275	0.372138	−	0.928178i	$-0.378625\pi$
$503$	2.12433e9	0.744275	0.372138	+	0.928178i	$0.378625\pi$
$504$	3.91986e8	0.136384
$505$	4.60978e8	0.159280
$506$	−2.88023e9	−0.988327
$507$	−1.30324e8	−0.0444116
$508$	7.79653e8	0.263863
$509$	3.84864e9	1.29359	0.646793	−	0.762666i	$-0.276110\pi$
$509$	3.84864e9	1.29359	0.646793	+	0.762666i	$0.276110\pi$
$510$	3.31130e8	0.110536
$511$	−8.75954e8	−0.290408
$512$	−2.33111e9	−0.767571
$513$	−4.04550e8	−0.132301
$514$	−2.61769e9	−0.850250
$515$	1.55153e8	0.0500534
$516$	−1.92432e8	−0.0616599
$517$	9.11038e8	0.289948
$518$	4.40594e8	0.139279
$519$	−3.46276e9	−1.08727
$520$	2.06556e8	0.0644207
$521$	2.48370e9	0.769427	0.384714	−	0.923036i	$-0.374300\pi$
$521$	2.48370e9	0.769427	0.384714	+	0.923036i	$0.374300\pi$
$522$	4.17745e8	0.128548
$523$	2.09789e9	0.641249	0.320624	−	0.947206i	$-0.396107\pi$
$523$	2.09789e9	0.641249	0.320624	+	0.947206i	$0.396107\pi$
$524$	−1.30226e8	−0.0395401
$525$	−6.90206e8	−0.208171
$526$	2.71514e9	0.813472
$527$	3.68145e9	1.09568
$528$	−1.38668e9	−0.409974
$529$	−1.46220e9	−0.429450
$530$	3.96935e8	0.115812
$531$	−1.66450e8	−0.0482451
$532$	3.73068e8	0.107423
$533$	5.13613e8	0.146923
$534$	−9.13737e8	−0.259673
$535$	3.87076e8	0.109284
$536$	7.01984e7	0.0196902
$537$	1.76199e9	0.491015
$538$	−1.95477e8	−0.0541201
$539$	−8.87272e8	−0.244060
$540$	6.24685e7	0.0170720
$541$	−4.37771e9	−1.18866	−0.594329	−	0.804222i	$-0.702582\pi$
$541$	−4.37771e9	−1.18866	−0.594329	+	0.804222i	$0.702582\pi$
$542$	−5.48991e7	−0.0148104
$543$	1.17735e9	0.315579
$544$	−3.34297e9	−0.890301
$545$	4.62467e8	0.122375
$546$	−1.76300e8	−0.0463531
$547$	3.36024e9	0.877839	0.438919	−	0.898526i	$-0.355361\pi$
$547$	3.36024e9	0.877839	0.438919	+	0.898526i	$0.355361\pi$
$548$	2.90483e9	0.754030
$549$	−4.02916e8	−0.103923
$550$	4.87028e9	1.24820
$551$	1.35925e9	0.346154
$552$	1.86555e9	0.472085
$553$	−2.84389e9	−0.715114
$554$	−2.34759e9	−0.586596
$555$	2.40050e8	0.0596040
$556$	3.11533e9	0.768674
$557$	−8.73496e8	−0.214174	−0.107087	−	0.994250i	$-0.534152\pi$
$557$	−8.73496e8	−0.214174	−0.107087	+	0.994250i	$0.534152\pi$
$558$	−9.85371e8	−0.240093
$559$	2.95891e8	0.0716457
$560$	1.40086e8	0.0337083
$561$	−4.80556e9	−1.14914
$562$	−4.85200e8	−0.115304
$563$	−1.18720e8	−0.0280378	−0.0140189	−	0.999902i	$-0.504463\pi$
$563$	−1.18720e8	−0.0280378	−0.0140189	+	0.999902i	$0.504463\pi$
$564$	−1.72601e8	−0.0405104
$565$	1.50171e8	0.0350280
$566$	2.51543e9	0.583115
$567$	−1.82284e8	−0.0419961
$568$	−1.88928e9	−0.432590
$569$	2.27455e7	0.00517610	0.00258805	−	0.999997i	$-0.499176\pi$
$569$	2.27455e7	0.00517610	0.00258805	+	0.999997i	$0.499176\pi$
$570$	−2.88382e8	−0.0652238
$571$	−4.17610e9	−0.938737	−0.469369	−	0.883002i	$-0.655518\pi$
$571$	−4.17610e9	−0.938737	−0.469369	+	0.883002i	$0.655518\pi$
$572$	−8.76821e8	−0.195896
$573$	4.75999e9	1.05698
$574$	6.94808e8	0.153346
$575$	−3.28484e9	−0.720572
$576$	1.53022e9	0.333639
$577$	4.58747e9	0.994164	0.497082	−	0.867704i	$-0.334405\pi$
$577$	4.58747e9	0.994164	0.497082	+	0.867704i	$0.334405\pi$
$578$	1.27045e9	0.273659
$579$	1.57262e9	0.336705
$580$	−2.09889e8	−0.0446674
$581$	−2.41235e8	−0.0510299
$582$	−2.22727e9	−0.468320
$583$	−5.76057e9	−1.20400
$584$	−4.00347e9	−0.831748
$585$	−9.60540e7	−0.0198367
$586$	−7.38932e9	−1.51692
$587$	5.98181e9	1.22067	0.610337	−	0.792142i	$-0.291034\pi$
$587$	5.98181e9	1.22067	0.610337	+	0.792142i	$0.291034\pi$
$588$	1.68099e8	0.0340991
$589$	−3.20619e9	−0.646525
$590$	−1.18653e8	−0.0237847
$591$	2.65352e9	0.528769
$592$	1.00954e9	0.199984
$593$	−3.04580e9	−0.599804	−0.299902	−	0.953970i	$-0.596954\pi$
$593$	−3.04580e9	−0.599804	−0.299902	+	0.953970i	$0.596954\pi$
$594$	1.28625e9	0.251810
$595$	4.85471e8	0.0944831
$596$	−2.10748e9	−0.407758
$597$	1.48921e8	0.0286449
$598$	−8.39052e8	−0.160448
$599$	6.15131e9	1.16943	0.584714	−	0.811239i	$-0.301207\pi$
$599$	6.15131e9	1.16943	0.584714	+	0.811239i	$0.301207\pi$
$600$	−3.15452e9	−0.596217
$601$	−3.70393e9	−0.695989	−0.347995	−	0.937497i	$-0.613137\pi$
$601$	−3.70393e9	−0.695989	−0.347995	+	0.937497i	$0.613137\pi$
$602$	4.00277e8	0.0747778
$603$	−3.26441e7	−0.00606310
$604$	2.33712e9	0.431570
$605$	2.24240e9	0.411688
$606$	−1.79825e9	−0.328244
$607$	−1.08114e10	−1.96209	−0.981047	−	0.193771i	$-0.937928\pi$
$607$	−1.08114e10	−1.96209	−0.981047	+	0.193771i	$0.937928\pi$
$608$	2.91141e9	0.525340
$609$	6.12458e8	0.109879
$610$	−2.87217e8	−0.0512337
$611$	2.65398e8	0.0470710
$612$	9.10439e8	0.160554
$613$	1.97582e9	0.346446	0.173223	−	0.984883i	$-0.444582\pi$
$613$	1.97582e9	0.346446	0.173223	+	0.984883i	$0.444582\pi$
$614$	−8.42450e8	−0.146877
$615$	3.78554e8	0.0656243
$616$	−4.05520e9	−0.699004
$617$	−2.64003e8	−0.0452492	−0.0226246	−	0.999744i	$-0.507202\pi$
$617$	−2.64003e8	−0.0452492	−0.0226246	+	0.999744i	$0.507202\pi$
$618$	−6.05243e8	−0.103150
$619$	4.45769e9	0.755427	0.377713	−	0.925923i	$-0.376711\pi$
$619$	4.45769e9	0.755427	0.377713	+	0.925923i	$0.376711\pi$
$620$	4.95083e8	0.0834270
$621$	−8.67532e8	−0.145367
$622$	−1.35418e9	−0.225637
$623$	−1.33964e9	−0.221962
$624$	−4.03958e8	−0.0665565
$625$	5.27345e9	0.864003
$626$	−7.36650e9	−1.20019
$627$	4.18518e9	0.678074
$628$	4.91327e9	0.791612
$629$	3.49857e9	0.560549
$630$	−1.29940e8	−0.0207039
$631$	−4.09991e9	−0.649639	−0.324819	−	0.945776i	$-0.605304\pi$
$631$	−4.09991e9	−0.649639	−0.324819	+	0.945776i	$0.605304\pi$
$632$	−1.29977e10	−2.04813
$633$	1.70592e8	0.0267329
$634$	2.13381e9	0.332539
$635$	−8.83582e8	−0.136943
$636$	1.09137e9	0.168218
$637$	−2.58475e8	−0.0396214
$638$	−4.32167e9	−0.658840
$639$	8.78566e8	0.133205
$640$	3.41211e6	0.000514509 0
$641$	5.18290e9	0.777266	0.388633	−	0.921393i	$-0.372947\pi$
$641$	5.18290e9	0.777266	0.388633	+	0.921393i	$0.372947\pi$
$642$	−1.50996e9	−0.225213
$643$	4.04948e9	0.600704	0.300352	−	0.953828i	$-0.402896\pi$
$643$	4.04948e9	0.600704	0.300352	+	0.953828i	$0.402896\pi$
$644$	8.00019e8	0.118032
$645$	2.18084e8	0.0320010
$646$	−4.20298e9	−0.613400
$647$	4.64696e9	0.674534	0.337267	−	0.941409i	$-0.390498\pi$
$647$	4.64696e9	0.674534	0.337267	+	0.941409i	$0.390498\pi$
$648$	−8.33114e8	−0.120280
$649$	1.72197e9	0.247268
$650$	1.41878e9	0.202637
$651$	−1.44466e9	−0.205226
$652$	−5.22809e9	−0.738714
$653$	8.80121e9	1.23693	0.618467	−	0.785811i	$-0.287754\pi$
$653$	8.80121e9	1.23693	0.618467	+	0.785811i	$0.287754\pi$
$654$	−1.80406e9	−0.252191
$655$	1.47585e8	0.0205210
$656$	1.59202e9	0.220184
$657$	1.86172e9	0.256116
$658$	3.59027e8	0.0491288
$659$	−1.01344e10	−1.37943	−0.689715	−	0.724081i	$-0.742264\pi$
$659$	−1.01344e10	−1.37943	−0.689715	+	0.724081i	$0.742264\pi$
$660$	−6.46253e8	−0.0874981
$661$	−2.34871e9	−0.316318	−0.158159	−	0.987414i	$-0.550556\pi$
$661$	−2.34871e9	−0.316318	−0.158159	+	0.987414i	$0.550556\pi$
$662$	−1.98860e8	−0.0266406
$663$	−1.39993e9	−0.186555
$664$	−1.10254e9	−0.146153
$665$	−4.22798e8	−0.0557516
$666$	−9.36422e8	−0.122832
$667$	2.91483e9	0.380340
$668$	−2.15768e9	−0.280071
$669$	−7.90777e9	−1.02109
$670$	−2.32702e7	−0.00298909
$671$	4.16827e9	0.532632
$672$	1.31184e9	0.166758
$673$	5.20707e9	0.658477	0.329238	−	0.944247i	$-0.393208\pi$
$673$	5.20707e9	0.658477	0.329238	+	0.944247i	$0.393208\pi$
$674$	1.50655e9	0.189528
$675$	1.46694e9	0.183590
$676$	−2.55430e8	−0.0318023
$677$	−1.06712e10	−1.32176	−0.660882	−	0.750490i	$-0.729818\pi$
$677$	−1.06712e10	−1.32176	−0.660882	+	0.750490i	$0.729818\pi$
$678$	−5.85808e8	−0.0721858
$679$	−3.26542e9	−0.400308
$680$	2.21880e9	0.270606
$681$	−3.40380e9	−0.412999
$682$	1.01939e10	1.23054
$683$	4.72212e9	0.567106	0.283553	−	0.958957i	$-0.408487\pi$
$683$	4.72212e9	0.567106	0.283553	+	0.958957i	$0.408487\pi$
$684$	−7.92905e8	−0.0947381
$685$	−3.29205e9	−0.391336
$686$	−3.49661e8	−0.0413535
$687$	−4.38903e9	−0.516441
$688$	9.17158e8	0.107370
$689$	−1.67813e9	−0.195461
$690$	−6.18416e8	−0.0716653
$691$	−3.97972e9	−0.458859	−0.229429	−	0.973325i	$-0.573686\pi$
$691$	−3.97972e9	−0.458859	−0.229429	+	0.973325i	$0.573686\pi$
$692$	−6.78689e9	−0.778573
$693$	1.88578e9	0.215240
$694$	6.30179e9	0.715658
$695$	−3.53061e9	−0.398936
$696$	2.79918e9	0.314702
$697$	5.51718e9	0.617167
$698$	−2.25752e9	−0.251268
$699$	6.69153e9	0.741064
$700$	−1.35278e9	−0.149068
$701$	−1.24839e10	−1.36880	−0.684398	−	0.729109i	$-0.739935\pi$
$701$	−1.24839e10	−1.36880	−0.684398	+	0.729109i	$0.739935\pi$
$702$	3.74702e8	0.0408796
$703$	−3.04692e9	−0.330763
$704$	−1.58306e10	−1.70998
$705$	1.95609e8	0.0210246
$706$	2.09247e8	0.0223791
$707$	−2.63643e9	−0.280575
$708$	−3.26236e8	−0.0345474
$709$	−8.91742e9	−0.939674	−0.469837	−	0.882753i	$-0.655687\pi$
$709$	−8.91742e9	−0.939674	−0.469837	+	0.882753i	$0.655687\pi$
$710$	6.26281e8	0.0656697
$711$	6.04431e9	0.630671
$712$	−6.12269e9	−0.635714
$713$	−6.87546e9	−0.710376
$714$	−1.89380e9	−0.194711
$715$	9.93703e8	0.101668
$716$	3.45345e9	0.351607
$717$	−4.05029e9	−0.410364
$718$	−7.21771e9	−0.727719
$719$	1.31965e10	1.32406	0.662029	−	0.749478i	$-0.269695\pi$
$719$	1.31965e10	1.32406	0.662029	+	0.749478i	$0.269695\pi$
$720$	−2.97734e8	−0.0297279
$721$	−8.87350e8	−0.0881702
$722$	−4.08494e9	−0.403930
$723$	−1.15808e9	−0.113960
$724$	2.30757e9	0.225980
$725$	−4.92878e9	−0.480348
$726$	−8.74748e9	−0.848408
$727$	1.32385e10	1.27782	0.638908	−	0.769283i	$-0.279386\pi$
$727$	1.32385e10	1.27782	0.638908	+	0.769283i	$0.279386\pi$
$728$	−1.18134e9	−0.113478
$729$	3.87420e8	0.0370370
$730$	1.32712e9	0.126264
$731$	3.17843e9	0.300955
$732$	−7.89702e8	−0.0744174
$733$	7.50792e9	0.704135	0.352068	−	0.935975i	$-0.385479\pi$
$733$	7.50792e9	0.704135	0.352068	+	0.935975i	$0.385479\pi$
$734$	2.90664e9	0.271303
$735$	−1.90507e8	−0.0176972
$736$	6.24332e9	0.577223
$737$	3.37712e8	0.0310749
$738$	−1.47672e9	−0.135239
$739$	1.49451e10	1.36221	0.681103	−	0.732187i	$-0.261501\pi$
$739$	1.49451e10	1.36221	0.681103	+	0.732187i	$0.261501\pi$
$740$	4.70489e8	0.0426814
$741$	1.21920e9	0.110081
$742$	−2.27015e9	−0.204005
$743$	−1.08367e10	−0.969252	−0.484626	−	0.874721i	$-0.661044\pi$
$743$	−1.08367e10	−0.969252	−0.484626	+	0.874721i	$0.661044\pi$
$744$	−6.60268e9	−0.587781
$745$	2.38842e9	0.211623
$746$	−1.32030e10	−1.16436
$747$	5.12713e8	0.0450041
$748$	−9.41873e9	−0.822880
$749$	−2.21377e9	−0.192507
$750$	2.14187e9	0.185386
$751$	1.57167e10	1.35401	0.677003	−	0.735980i	$-0.263278\pi$
$751$	1.57167e10	1.35401	0.677003	+	0.735980i	$0.263278\pi$
$752$	8.22641e8	0.0705420
$753$	−1.01603e10	−0.867211
$754$	−1.25896e9	−0.106958
$755$	−2.64866e9	−0.223982
$756$	−3.57271e8	−0.0300726
$757$	3.29282e9	0.275887	0.137944	−	0.990440i	$-0.455951\pi$
$757$	3.29282e9	0.275887	0.137944	+	0.990440i	$0.455951\pi$
$758$	−1.65460e10	−1.37991
$759$	8.97484e9	0.745041
$760$	−1.93236e9	−0.159676
$761$	−1.03433e10	−0.850775	−0.425387	−	0.905011i	$-0.639862\pi$
$761$	−1.03433e10	−0.850775	−0.425387	+	0.905011i	$0.639862\pi$
$762$	3.44681e9	0.282212
$763$	−2.64495e9	−0.215566
$764$	9.32942e9	0.756882
$765$	−1.03180e9	−0.0833263
$766$	−5.15251e9	−0.414207
$767$	5.01633e8	0.0401423
$768$	7.24108e9	0.576819
$769$	2.34400e10	1.85873	0.929363	−	0.369167i	$-0.120357\pi$
$769$	2.34400e10	1.85873	0.929363	+	0.369167i	$0.120357\pi$
$770$	1.34427e9	0.106113
$771$	8.15674e9	0.640953
$772$	3.08228e9	0.241108
$773$	−1.27278e10	−0.991121	−0.495560	−	0.868574i	$-0.665037\pi$
$773$	−1.27278e10	−0.991121	−0.495560	+	0.868574i	$0.665037\pi$
$774$	−8.50733e8	−0.0659478
$775$	1.16259e10	0.897165
$776$	−1.49243e10	−1.14651
$777$	−1.37289e9	−0.104994
$778$	−5.53784e9	−0.421611
$779$	−4.80493e9	−0.364172
$780$	−1.88263e8	−0.0142047
$781$	−9.08898e9	−0.682711
$782$	−9.01302e9	−0.673979
$783$	−1.30170e9	−0.0969045
$784$	−8.01182e8	−0.0593779
$785$	−5.56823e9	−0.410840
$786$	−5.75723e8	−0.0422897
$787$	−2.29949e10	−1.68159	−0.840793	−	0.541356i	$-0.817911\pi$
$787$	−2.29949e10	−1.68159	−0.840793	+	0.541356i	$0.817911\pi$
$788$	5.20080e9	0.378642
$789$	−8.46041e9	−0.613228
$790$	4.30866e9	0.310919
$791$	−8.58858e8	−0.0617026
$792$	8.61877e9	0.616463
$793$	1.21428e9	0.0864692
$794$	−1.94108e9	−0.137617
$795$	−1.23685e9	−0.0873038
$796$	2.91881e8	0.0205121
$797$	1.55696e10	1.08936	0.544682	−	0.838643i	$-0.316650\pi$
$797$	1.55696e10	1.08936	0.544682	+	0.838643i	$0.316650\pi$
$798$	1.64932e9	0.114893
$799$	2.85088e9	0.197727
$800$	−1.05570e10	−0.729000
$801$	2.84722e9	0.195752
$802$	1.11950e10	0.766328
$803$	−1.92600e10	−1.31266
$804$	−6.39814e7	−0.00434168
$805$	−9.06664e8	−0.0612577
$806$	2.96963e9	0.199770
$807$	6.09109e8	0.0407979
$808$	−1.20496e10	−0.803585
$809$	1.42486e10	0.946135	0.473067	−	0.881026i	$-0.343147\pi$
$809$	1.42486e10	0.946135	0.473067	+	0.881026i	$0.343147\pi$
$810$	2.76171e8	0.0182591
$811$	1.29982e10	0.855677	0.427838	−	0.903855i	$-0.359275\pi$
$811$	1.29982e10	0.855677	0.427838	+	0.903855i	$0.359275\pi$
$812$	1.20040e9	0.0786826
$813$	1.71066e8	0.0111647
$814$	9.68753e9	0.629546
$815$	5.92501e9	0.383387
$816$	−4.33928e9	−0.279578
$817$	−2.76810e9	−0.177585
$818$	6.65946e9	0.425405
$819$	5.49353e8	0.0349428
$820$	7.41952e8	0.0469924
$821$	5.67880e9	0.358142	0.179071	−	0.983836i	$-0.442691\pi$
$821$	5.67880e9	0.358142	0.179071	+	0.983836i	$0.442691\pi$
$822$	1.28421e10	0.806465
$823$	2.26799e9	0.141821	0.0709106	−	0.997483i	$-0.477409\pi$
$823$	2.26799e9	0.141821	0.0709106	+	0.997483i	$0.477409\pi$
$824$	−4.05555e9	−0.252525
$825$	−1.51759e10	−0.940945
$826$	6.78602e8	0.0418972
$827$	2.41782e10	1.48646	0.743232	−	0.669033i	$-0.233292\pi$
$827$	2.41782e10	1.48646	0.743232	+	0.669033i	$0.233292\pi$
$828$	−1.70033e9	−0.104094
$829$	−1.63789e9	−0.0998489	−0.0499245	−	0.998753i	$-0.515898\pi$
$829$	−1.63789e9	−0.0998489	−0.0499245	+	0.998753i	$0.515898\pi$
$830$	3.65485e8	0.0221869
$831$	7.31513e9	0.442200
$832$	−4.61166e9	−0.277604
$833$	−2.77651e9	−0.166434
$834$	1.37727e10	0.822127
$835$	2.44530e9	0.145355
$836$	8.20280e9	0.485557
$837$	3.07043e9	0.180992
$838$	1.84095e10	1.08066
$839$	1.36405e10	0.797378	0.398689	−	0.917086i	$-0.369465\pi$
$839$	1.36405e10	0.797378	0.398689	+	0.917086i	$0.369465\pi$
$840$	−8.70693e8	−0.0506859
$841$	−1.28763e10	−0.746457
$842$	1.61195e10	0.930592
$843$	1.51189e9	0.0869207
$844$	3.34355e8	0.0191430
$845$	2.89480e8	0.0165052
$846$	−7.63062e8	−0.0433275
$847$	−1.28247e10	−0.725198
$848$	−5.20163e9	−0.292923
$849$	−7.83810e9	−0.439576
$850$	1.52404e10	0.851198
$851$	−6.53392e9	−0.363429
$852$	1.72196e9	0.0953859
$853$	1.70241e10	0.939168	0.469584	−	0.882888i	$-0.344404\pi$
$853$	1.70241e10	0.939168	0.469584	+	0.882888i	$0.344404\pi$
$854$	1.64265e9	0.0902493
$855$	8.98601e8	0.0491683
$856$	−1.01178e10	−0.551352
$857$	−1.26444e10	−0.686221	−0.343110	−	0.939295i	$-0.611480\pi$
$857$	−1.26444e10	−0.686221	−0.343110	+	0.939295i	$0.611480\pi$
$858$	−3.87639e9	−0.209518
$859$	−2.03247e10	−1.09408	−0.547038	−	0.837108i	$-0.684245\pi$
$859$	−2.03247e10	−1.09408	−0.547038	+	0.837108i	$0.684245\pi$
$860$	4.27436e8	0.0229154
$861$	−2.16503e9	−0.115599
$862$	−8.28580e9	−0.440615
$863$	−3.84186e9	−0.203472	−0.101736	−	0.994811i	$-0.532440\pi$
$863$	−3.84186e9	−0.203472	−0.101736	+	0.994811i	$0.532440\pi$
$864$	−2.78813e9	−0.147067
$865$	7.69160e9	0.404073
$866$	1.17091e10	0.612650
$867$	−3.95873e9	−0.206295
$868$	−2.83148e9	−0.146959
$869$	−6.25299e10	−3.23235
$870$	−9.27909e8	−0.0477736
$871$	9.83802e7	0.00504480
$872$	−1.20885e10	−0.617397
$873$	6.94021e9	0.353039
$874$	7.84947e9	0.397695
$875$	3.14021e9	0.158464
$876$	3.64891e9	0.183400
$877$	−1.63932e10	−0.820666	−0.410333	−	0.911936i	$-0.634588\pi$
$877$	−1.63932e10	−0.820666	−0.410333	+	0.911936i	$0.634588\pi$
$878$	8.23597e8	0.0410662
$879$	2.30252e10	1.14352
$880$	3.08013e9	0.152363
$881$	2.27101e10	1.11893	0.559466	−	0.828853i	$-0.311006\pi$
$881$	2.27101e10	1.11893	0.559466	+	0.828853i	$0.311006\pi$
$882$	7.43157e8	0.0364704
$883$	−2.40758e10	−1.17684	−0.588420	−	0.808555i	$-0.700250\pi$
$883$	−2.40758e10	−1.17684	−0.588420	+	0.808555i	$0.700250\pi$
$884$	−2.74381e9	−0.133589
$885$	3.69724e8	0.0179298
$886$	2.24374e10	1.08381
$887$	5.74425e9	0.276376	0.138188	−	0.990406i	$-0.455872\pi$
$887$	5.74425e9	0.276376	0.138188	+	0.990406i	$0.455872\pi$
$888$	−6.27469e9	−0.300709
$889$	5.05339e9	0.241228
$890$	2.02962e9	0.0965052
$891$	−4.00796e9	−0.189824
$892$	−1.54990e10	−0.731182
$893$	−2.48284e9	−0.116673
$894$	−9.31710e9	−0.436113
$895$	−3.91380e9	−0.182481
$896$	−1.95146e7	−0.000906318 0
$897$	2.61450e9	0.120952
$898$	8.63775e9	0.398046
$899$	−1.03164e10	−0.473552
$900$	2.87515e9	0.131465
$901$	−1.80264e10	−0.821053
$902$	1.52770e10	0.693133
$903$	−1.24727e9	−0.0563705
$904$	−3.92533e9	−0.176720
$905$	−2.61518e9	−0.117282
$906$	1.03323e10	0.461582
$907$	2.81321e10	1.25192	0.625960	−	0.779855i	$-0.284707\pi$
$907$	2.81321e10	1.25192	0.625960	+	0.779855i	$0.284707\pi$
$908$	−6.67133e9	−0.295741
$909$	5.60338e9	0.247444
$910$	3.91604e8	0.0172267
$911$	2.88323e10	1.26347	0.631735	−	0.775184i	$-0.282343\pi$
$911$	2.88323e10	1.26347	0.631735	+	0.775184i	$0.282343\pi$
$912$	3.77910e9	0.164970
$913$	−5.30414e9	−0.230658
$914$	2.07988e10	0.901005
$915$	8.94971e8	0.0386220
$916$	−8.60235e9	−0.369814
$917$	−8.44071e8	−0.0361482
$918$	4.02502e9	0.171719
$919$	1.10981e10	0.471676	0.235838	−	0.971792i	$-0.424216\pi$
$919$	1.10981e10	0.471676	0.235838	+	0.971792i	$0.424216\pi$
$920$	−4.14382e9	−0.175446
$921$	2.62508e9	0.110722
$922$	6.20484e9	0.260719
$923$	−2.64775e9	−0.110833
$924$	3.69606e9	0.154130
$925$	1.10484e10	0.458991
$926$	8.41230e9	0.348158
$927$	1.88594e9	0.0777588
$928$	9.36786e9	0.384789
$929$	8.95279e9	0.366356	0.183178	−	0.983080i	$-0.441362\pi$
$929$	8.95279e9	0.366356	0.183178	+	0.983080i	$0.441362\pi$
$930$	2.18874e9	0.0892285
$931$	2.41807e9	0.0982077
$932$	1.31152e10	0.530662
$933$	4.21963e9	0.170094
$934$	2.30561e10	0.925916
$935$	1.06743e10	0.427068
$936$	2.51077e9	0.100079
$937$	4.19212e10	1.66473	0.832367	−	0.554225i	$-0.186985\pi$
$937$	4.19212e10	1.66473	0.832367	+	0.554225i	$0.186985\pi$
$938$	1.33087e8	0.00526534
$939$	2.29541e10	0.904754
$940$	3.83387e8	0.0150553
$941$	3.10588e10	1.21513	0.607563	−	0.794271i	$-0.292147\pi$
$941$	3.10588e10	1.21513	0.607563	+	0.794271i	$0.292147\pi$
$942$	2.17214e10	0.846660
$943$	−1.03039e10	−0.400137
$944$	1.55489e9	0.0601585
$945$	4.04896e8	0.0156075
$946$	8.80105e9	0.337999
$947$	−4.55493e10	−1.74284	−0.871418	−	0.490542i	$-0.836799\pi$
$947$	−4.55493e10	−1.74284	−0.871418	+	0.490542i	$0.836799\pi$
$948$	1.18466e10	0.451612
$949$	−5.61071e9	−0.213101
$950$	−1.32729e10	−0.502266
$951$	−6.64896e9	−0.250681
$952$	−1.26898e10	−0.476678
$953$	5.39343e9	0.201855	0.100928	−	0.994894i	$-0.467819\pi$
$953$	5.39343e9	0.201855	0.100928	+	0.994894i	$0.467819\pi$
$954$	4.82491e9	0.179916
$955$	−1.05731e10	−0.392816
$956$	−7.93842e9	−0.293854
$957$	1.34664e10	0.496660
$958$	3.97501e10	1.46069
$959$	1.88279e10	0.689346
$960$	−3.39898e9	−0.123994
$961$	−3.17852e9	−0.115530
$962$	2.82211e9	0.102203
$963$	4.70506e9	0.169775
$964$	−2.26980e9	−0.0816051
$965$	−3.49316e9	−0.125133
$966$	3.53685e9	0.126240
$967$	−2.10199e10	−0.747547	−0.373773	−	0.927520i	$-0.621936\pi$
$967$	−2.10199e10	−0.747547	−0.373773	+	0.927520i	$0.621936\pi$
$968$	−5.86143e10	−2.07702
$969$	1.30965e10	0.462406
$970$	4.94729e9	0.174047
$971$	−3.06378e10	−1.07397	−0.536983	−	0.843593i	$-0.680436\pi$
$971$	−3.06378e10	−1.07397	−0.536983	+	0.843593i	$0.680436\pi$
$972$	7.59331e8	0.0265216
$973$	2.01923e10	0.702734
$974$	−1.90912e10	−0.662030
$975$	−4.42094e9	−0.152756
$976$	3.76383e9	0.129585
$977$	3.04169e10	1.04348	0.521739	−	0.853105i	$-0.325283\pi$
$977$	3.04169e10	1.04348	0.521739	+	0.853105i	$0.325283\pi$
$978$	−2.31132e10	−0.790084
$979$	−2.94552e10	−1.00328
$980$	−3.73386e8	−0.0126726
$981$	5.62148e9	0.190112
$982$	−1.26753e9	−0.0427139
$983$	3.76552e9	0.126441	0.0632204	−	0.998000i	$-0.479863\pi$
$983$	3.76552e9	0.126441	0.0632204	+	0.998000i	$0.479863\pi$
$984$	−9.89507e9	−0.331082
$985$	−5.89408e9	−0.196512
$986$	−1.35237e10	−0.449289
$987$	−1.11873e9	−0.0370353
$988$	2.38959e9	0.0788269
$989$	−5.93602e9	−0.195123
$990$	−2.85706e9	−0.0935827
$991$	−5.01776e9	−0.163777	−0.0818884	−	0.996642i	$-0.526095\pi$
$991$	−5.01776e9	−0.163777	−0.0818884	+	0.996642i	$0.526095\pi$
$992$	−2.20968e10	−0.718685
$993$	6.19649e8	0.0200828
$994$	−3.58184e9	−0.115679
$995$	−3.30789e8	−0.0106456
$996$	1.00490e9	0.0322266
$997$	−1.20499e8	−0.00385080	−0.00192540	−	0.999998i	$-0.500613\pi$
$997$	−1.20499e8	−0.00385080	−0.00192540	+	0.999998i	$0.500613\pi$
$998$	1.29602e9	0.0412718
$999$	2.91790e9	0.0925958

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.8.a.b.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.8.a.b.1.6	✓	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

\(f(q)\)	\(=\)	\(q+8.66493 q^{2} -27.0000 q^{3} -52.9191 q^{4} +59.9733 q^{5} -233.953 q^{6} -343.000 q^{7} -1567.65 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.66493 q^{2} -27.0000 q^{3} -52.9191 q^{4} +59.9733 q^{5} -233.953 q^{6} -343.000 q^{7} -1567.65 q^{8} +729.000 q^{9} +519.664 q^{10} -7541.69 q^{11} +1428.81 q^{12} -2197.00 q^{13} -2972.07 q^{14} -1619.28 q^{15} -6809.93 q^{16} -23600.0 q^{17} +6316.73 q^{18} +20553.3 q^{19} -3173.73 q^{20} +9261.00 q^{21} -65348.2 q^{22} +44075.2 q^{23} +42326.6 q^{24} -74528.2 q^{25} -19036.8 q^{26} -19683.0 q^{27} +18151.2 q^{28} +66133.1 q^{29} -14030.9 q^{30} -155994. q^{31} +141652. q^{32} +203626. q^{33} -204492. q^{34} -20570.8 q^{35} -38578.0 q^{36} -148245. q^{37} +178093. q^{38} +59319.0 q^{39} -94017.2 q^{40} -233779. q^{41} +80245.9 q^{42} -134679. q^{43} +399099. q^{44} +43720.5 q^{45} +381908. q^{46} -120800. q^{47} +183868. q^{48} +117649. q^{49} -645781. q^{50} +637199. q^{51} +116263. q^{52} +763830. q^{53} -170552. q^{54} -452300. q^{55} +537704. q^{56} -554939. q^{57} +573038. q^{58} -228326. q^{59} +85690.7 q^{60} -552697. q^{61} -1.35168e6 q^{62} -250047. q^{63} +2.09907e6 q^{64} -131761. q^{65} +1.76440e6 q^{66} -44779.4 q^{67} +1.24889e6 q^{68} -1.19003e6 q^{69} -178245. q^{70} +1.20517e6 q^{71} -1.14282e6 q^{72} +2.55380e6 q^{73} -1.28453e6 q^{74} +2.01226e6 q^{75} -1.08766e6 q^{76} +2.58680e6 q^{77} +513995. q^{78} +8.29123e6 q^{79} -408414. q^{80} +531441. q^{81} -2.02568e6 q^{82} +703310. q^{83} -490083. q^{84} -1.41537e6 q^{85} -1.16699e6 q^{86} -1.78559e6 q^{87} +1.18227e7 q^{88} +3.90565e6 q^{89} +378835. q^{90} +753571. q^{91} -2.33242e6 q^{92} +4.21183e6 q^{93} -1.04672e6 q^{94} +1.23265e6 q^{95} -3.82460e6 q^{96} +9.52017e6 q^{97} +1.01942e6 q^{98} -5.49789e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 4 q^{2} - 243 q^{3} + 358 q^{4} + 330 q^{5} - 108 q^{6} - 3087 q^{7} - 1206 q^{8} + 6561 q^{9}+O(q^{10}) \) 9 * q + 4 * q^2 - 243 * q^3 + 358 * q^4 + 330 * q^5 - 108 * q^6 - 3087 * q^7 - 1206 * q^8 + 6561 * q^9	\( 9 q + 4 q^{2} - 243 q^{3} + 358 q^{4} + 330 q^{5} - 108 q^{6} - 3087 q^{7} - 1206 q^{8} + 6561 q^{9} + 6335 q^{10} + 2176 q^{11} - 9666 q^{12} - 19773 q^{13} - 1372 q^{14} - 8910 q^{15} - 40686 q^{16} - 1022 q^{17} + 2916 q^{18} + 63240 q^{19} + 29105 q^{20} + 83349 q^{21} + 24635 q^{22} + 16212 q^{23} + 32562 q^{24} + 238075 q^{25} - 8788 q^{26} - 177147 q^{27} - 122794 q^{28} - 328180 q^{29} - 171045 q^{30} - 242182 q^{31} - 245454 q^{32} - 58752 q^{33} - 115535 q^{34} - 113190 q^{35} + 260982 q^{36} - 550054 q^{37} - 1199959 q^{38} + 533871 q^{39} + 1402045 q^{40} + 641846 q^{41} + 37044 q^{42} + 905942 q^{43} + 522021 q^{44} + 240570 q^{45} - 1903907 q^{46} + 466642 q^{47} + 1098522 q^{48} + 1058841 q^{49} + 1300175 q^{50} + 27594 q^{51} - 786526 q^{52} - 979208 q^{53} - 78732 q^{54} - 1101220 q^{55} + 413658 q^{56} - 1707480 q^{57} + 6478077 q^{58} - 335664 q^{59} - 785835 q^{60} - 2848696 q^{61} - 2122244 q^{62} - 2250423 q^{63} - 5017310 q^{64} - 725010 q^{65} - 665145 q^{66} - 3036728 q^{67} + 5605051 q^{68} - 437724 q^{69} - 2172905 q^{70} - 2190772 q^{71} - 879174 q^{72} + 1337916 q^{73} + 1481537 q^{74} - 6428025 q^{75} + 8974475 q^{76} - 746368 q^{77} + 237276 q^{78} + 137070 q^{79} - 367955 q^{80} + 4782969 q^{81} + 2947202 q^{82} + 13013474 q^{83} + 3315438 q^{84} + 9096820 q^{85} + 1222661 q^{86} + 8860860 q^{87} + 8139465 q^{88} + 9126740 q^{89} + 4618215 q^{90} + 6782139 q^{91} + 34403367 q^{92} + 6538914 q^{93} + 32954276 q^{94} + 34578180 q^{95} + 6627258 q^{96} + 18345820 q^{97} + 470596 q^{98} + 1586304 q^{99}+O(q^{100}) \) 9 * q + 4 * q^2 - 243 * q^3 + 358 * q^4 + 330 * q^5 - 108 * q^6 - 3087 * q^7 - 1206 * q^8 + 6561 * q^9 + 6335 * q^10 + 2176 * q^11 - 9666 * q^12 - 19773 * q^13 - 1372 * q^14 - 8910 * q^15 - 40686 * q^16 - 1022 * q^17 + 2916 * q^18 + 63240 * q^19 + 29105 * q^20 + 83349 * q^21 + 24635 * q^22 + 16212 * q^23 + 32562 * q^24 + 238075 * q^25 - 8788 * q^26 - 177147 * q^27 - 122794 * q^28 - 328180 * q^29 - 171045 * q^30 - 242182 * q^31 - 245454 * q^32 - 58752 * q^33 - 115535 * q^34 - 113190 * q^35 + 260982 * q^36 - 550054 * q^37 - 1199959 * q^38 + 533871 * q^39 + 1402045 * q^40 + 641846 * q^41 + 37044 * q^42 + 905942 * q^43 + 522021 * q^44 + 240570 * q^45 - 1903907 * q^46 + 466642 * q^47 + 1098522 * q^48 + 1058841 * q^49 + 1300175 * q^50 + 27594 * q^51 - 786526 * q^52 - 979208 * q^53 - 78732 * q^54 - 1101220 * q^55 + 413658 * q^56 - 1707480 * q^57 + 6478077 * q^58 - 335664 * q^59 - 785835 * q^60 - 2848696 * q^61 - 2122244 * q^62 - 2250423 * q^63 - 5017310 * q^64 - 725010 * q^65 - 665145 * q^66 - 3036728 * q^67 + 5605051 * q^68 - 437724 * q^69 - 2172905 * q^70 - 2190772 * q^71 - 879174 * q^72 + 1337916 * q^73 + 1481537 * q^74 - 6428025 * q^75 + 8974475 * q^76 - 746368 * q^77 + 237276 * q^78 + 137070 * q^79 - 367955 * q^80 + 4782969 * q^81 + 2947202 * q^82 + 13013474 * q^83 + 3315438 * q^84 + 9096820 * q^85 + 1222661 * q^86 + 8860860 * q^87 + 8139465 * q^88 + 9126740 * q^89 + 4618215 * q^90 + 6782139 * q^91 + 34403367 * q^92 + 6538914 * q^93 + 32954276 * q^94 + 34578180 * q^95 + 6627258 * q^96 + 18345820 * q^97 + 470596 * q^98 + 1586304 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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