LMFDB - Embedded newform 289.10.a.d.1.4

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			1.4
Root			$-20.4468$ 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)

$f(q)$	$=$	$q-19.4468 q^{2} +193.562 q^{3} -133.821 q^{4} +1266.43 q^{5} -3764.16 q^{6} +1846.43 q^{7} +12559.2 q^{8} +17783.1 q^{9} +O(q^{10})$	\(q-19.4468 q^{2} +193.562 q^{3} -133.821 q^{4} +1266.43 q^{5} -3764.16 q^{6} +1846.43 q^{7} +12559.2 q^{8} +17783.1 q^{9} -24628.1 q^{10} +40331.9 q^{11} -25902.6 q^{12} -88051.4 q^{13} -35907.1 q^{14} +245133. q^{15} -175720. q^{16} -345824. q^{18} +288509. q^{19} -169475. q^{20} +357397. q^{21} -784328. q^{22} -1.90139e6 q^{23} +2.43097e6 q^{24} -349267. q^{25} +1.71232e6 q^{26} -367752. q^{27} -247090. q^{28} -7.53535e6 q^{29} -4.76706e6 q^{30} +1.53583e6 q^{31} -3.01310e6 q^{32} +7.80671e6 q^{33} +2.33838e6 q^{35} -2.37975e6 q^{36} -9.87058e6 q^{37} -5.61059e6 q^{38} -1.70434e7 q^{39} +1.59054e7 q^{40} +2.47113e7 q^{41} -6.95024e6 q^{42} +1.11639e7 q^{43} -5.39725e6 q^{44} +2.25211e7 q^{45} +3.69760e7 q^{46} -4.55933e7 q^{47} -3.40126e7 q^{48} -3.69443e7 q^{49} +6.79214e6 q^{50} +1.17831e7 q^{52} -6.10614e7 q^{53} +7.15162e6 q^{54} +5.10778e7 q^{55} +2.31896e7 q^{56} +5.58443e7 q^{57} +1.46539e8 q^{58} -1.08012e8 q^{59} -3.28039e7 q^{60} -818353. q^{61} -2.98670e7 q^{62} +3.28351e7 q^{63} +1.48564e8 q^{64} -1.11511e8 q^{65} -1.51816e8 q^{66} -2.28794e8 q^{67} -3.68036e8 q^{69} -4.54740e7 q^{70} +3.98617e8 q^{71} +2.23341e8 q^{72} -3.46257e8 q^{73} +1.91951e8 q^{74} -6.76047e7 q^{75} -3.86086e7 q^{76} +7.44699e7 q^{77} +3.31440e8 q^{78} -4.18246e8 q^{79} -2.22538e8 q^{80} -4.21207e8 q^{81} -4.80557e8 q^{82} +6.69380e7 q^{83} -4.78272e7 q^{84} -2.17102e8 q^{86} -1.45855e9 q^{87} +5.06535e8 q^{88} +4.19362e8 q^{89} -4.37964e8 q^{90} -1.62580e8 q^{91} +2.54445e8 q^{92} +2.97277e8 q^{93} +8.86645e8 q^{94} +3.65378e8 q^{95} -5.83221e8 q^{96} +9.50267e8 q^{97} +7.18450e8 q^{98} +7.17226e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−19.4468	−0.859437	−0.429718	−	0.902963i	$-0.641387\pi$
$2$	−19.4468	−0.859437	−0.429718	+	0.902963i	$0.641387\pi$
$3$	193.562	1.37966	0.689832	−	0.723969i	$-0.257684\pi$
$3$	193.562	1.37966	0.689832	+	0.723969i	$0.257684\pi$
$4$	−133.821	−0.261369
$5$	1266.43	0.906187	0.453094	−	0.891463i	$-0.350320\pi$
$5$	1266.43	0.906187	0.453094	+	0.891463i	$0.350320\pi$
$6$	−3764.16	−1.18573
$7$	1846.43	0.290664	0.145332	−	0.989383i	$-0.453575\pi$
$7$	1846.43	0.290664	0.145332	+	0.989383i	$0.453575\pi$
$8$	12559.2	1.08407
$9$	17783.1	0.903474
$10$	−24628.1	−0.778810
$11$	40331.9	0.830581	0.415290	−	0.909689i	$-0.363680\pi$
$11$	40331.9	0.830581	0.415290	+	0.909689i	$0.363680\pi$
$12$	−25902.6	−0.360601
$13$	−88051.4	−0.855050	−0.427525	−	0.904004i	$-0.640614\pi$
$13$	−88051.4	−0.855050	−0.427525	+	0.904004i	$0.640614\pi$
$14$	−35907.1	−0.249807
$15$	245133.	1.25023
$16$	−175720.	−0.670317
$17$	0	0
$17$	0	0
$18$	−345824.	−0.776478
$19$	288509.	0.507889	0.253944	−	0.967219i	$-0.418272\pi$
$19$	288509.	0.507889	0.253944	+	0.967219i	$0.418272\pi$
$20$	−169475.	−0.236849
$21$	357397.	0.401018
$22$	−784328.	−0.713831
$23$	−1.90139e6	−1.41676	−0.708379	−	0.705833i	$-0.750573\pi$
$23$	−1.90139e6	−1.41676	−0.708379	+	0.705833i	$0.750573\pi$
$24$	2.43097e6	1.49565
$25$	−349267.	−0.178825
$26$	1.71232e6	0.734861
$27$	−367752.	−0.133174
$28$	−247090.	−0.0759704
$29$	−7.53535e6	−1.97839	−0.989197	−	0.146593i	$-0.953169\pi$
$29$	−7.53535e6	−1.97839	−0.989197	+	0.146593i	$0.953169\pi$
$30$	−4.76706e6	−1.07450
$31$	1.53583e6	0.298686	0.149343	−	0.988785i	$-0.452284\pi$
$31$	1.53583e6	0.298686	0.149343	+	0.988785i	$0.452284\pi$
$32$	−3.01310e6	−0.507971
$33$	7.80671e6	1.14592
$34$	0	0
$35$	2.33838e6	0.263396
$36$	−2.37975e6	−0.236140
$37$	−9.87058e6	−0.865834	−0.432917	−	0.901434i	$-0.642516\pi$
$37$	−9.87058e6	−0.865834	−0.432917	+	0.901434i	$0.642516\pi$
$38$	−5.61059e6	−0.436498
$39$	−1.70434e7	−1.17968
$40$	1.59054e7	0.982367
$41$	2.47113e7	1.36574	0.682871	−	0.730539i	$-0.260731\pi$
$41$	2.47113e7	1.36574	0.682871	+	0.730539i	$0.260731\pi$
$42$	−6.95024e6	−0.344650
$43$	1.11639e7	0.497974	0.248987	−	0.968507i	$-0.419902\pi$
$43$	1.11639e7	0.497974	0.248987	+	0.968507i	$0.419902\pi$
$44$	−5.39725e6	−0.217088
$45$	2.25211e7	0.818716
$46$	3.69760e7	1.21761
$47$	−4.55933e7	−1.36289	−0.681445	−	0.731869i	$-0.738648\pi$
$47$	−4.55933e7	−1.36289	−0.681445	+	0.731869i	$0.738648\pi$
$48$	−3.40126e7	−0.924813
$49$	−3.69443e7	−0.915515
$50$	6.79214e6	0.153689
$51$	0	0
$52$	1.17831e7	0.223483
$53$	−6.10614e7	−1.06298	−0.531490	−	0.847064i	$-0.678368\pi$
$53$	−6.10614e7	−1.06298	−0.531490	+	0.847064i	$0.678368\pi$
$54$	7.15162e6	0.114454
$55$	5.10778e7	0.752662
$56$	2.31896e7	0.315099
$57$	5.58443e7	0.700716
$58$	1.46539e8	1.70030
$59$	−1.08012e8	−1.16048	−0.580240	−	0.814446i	$-0.697041\pi$
$59$	−1.08012e8	−1.16048	−0.580240	+	0.814446i	$0.697041\pi$
$60$	−3.28039e7	−0.326772
$61$	−818353.	−0.00756757	−0.00378379	−	0.999993i	$-0.501204\pi$
$61$	−818353.	−0.00756757	−0.00378379	+	0.999993i	$0.501204\pi$
$62$	−2.98670e7	−0.256701
$63$	3.28351e7	0.262607
$64$	1.48564e8	1.10689
$65$	−1.11511e8	−0.774835
$66$	−1.51816e8	−0.984848
$67$	−2.28794e8	−1.38710	−0.693552	−	0.720407i	$-0.743955\pi$
$67$	−2.28794e8	−1.38710	−0.693552	+	0.720407i	$0.743955\pi$
$68$	0	0
$69$	−3.68036e8	−1.95465
$70$	−4.54740e7	−0.226372
$71$	3.98617e8	1.86163	0.930815	−	0.365490i	$-0.119098\pi$
$71$	3.98617e8	1.86163	0.930815	+	0.365490i	$0.119098\pi$
$72$	2.23341e8	0.979426
$73$	−3.46257e8	−1.42707	−0.713535	−	0.700620i	$-0.752907\pi$
$73$	−3.46257e8	−1.42707	−0.713535	+	0.700620i	$0.752907\pi$
$74$	1.91951e8	0.744130
$75$	−6.76047e7	−0.246718
$76$	−3.86086e7	−0.132746
$77$	7.44699e7	0.241420
$78$	3.31440e8	1.01386
$79$	−4.18246e8	−1.20812	−0.604060	−	0.796939i	$-0.706451\pi$
$79$	−4.18246e8	−1.20812	−0.604060	+	0.796939i	$0.706451\pi$
$80$	−2.22538e8	−0.607433
$81$	−4.21207e8	−1.08721
$82$	−4.80557e8	−1.17377
$83$	6.69380e7	0.154818	0.0774089	−	0.996999i	$-0.475335\pi$
$83$	6.69380e7	0.154818	0.0774089	+	0.996999i	$0.475335\pi$
$84$	−4.78272e7	−0.104814
$85$	0	0
$86$	−2.17102e8	−0.427977
$87$	−1.45855e9	−2.72952
$88$	5.06535e8	0.900405
$89$	4.19362e8	0.708491	0.354246	−	0.935152i	$-0.384738\pi$
$89$	4.19362e8	0.708491	0.354246	+	0.935152i	$0.384738\pi$
$90$	−4.37964e8	−0.703635
$91$	−1.62580e8	−0.248532
$92$	2.54445e8	0.370296
$93$	2.97277e8	0.412086
$94$	8.86645e8	1.17132
$95$	3.65378e8	0.460242
$96$	−5.83221e8	−0.700830
$97$	9.50267e8	1.08987	0.544933	−	0.838480i	$-0.316555\pi$
$97$	9.50267e8	1.08987	0.544933	+	0.838480i	$0.316555\pi$
$98$	7.18450e8	0.786827
$99$	7.17226e8	0.750408
$100$	4.67393e7	0.0467393
$101$	8.62891e7	0.0825106	0.0412553	−	0.999149i	$-0.486864\pi$
$101$	8.62891e7	0.0825106	0.0412553	+	0.999149i	$0.486864\pi$
$102$	0	0
$103$	6.45223e8	0.564862	0.282431	−	0.959288i	$-0.408859\pi$
$103$	6.45223e8	0.564862	0.282431	+	0.959288i	$0.408859\pi$
$104$	−1.10585e9	−0.926931
$105$	4.52620e8	0.363397
$106$	1.18745e9	0.913565
$107$	4.80129e8	0.354104	0.177052	−	0.984202i	$-0.443344\pi$
$107$	4.80129e8	0.354104	0.177052	+	0.984202i	$0.443344\pi$
$108$	4.92129e7	0.0348075
$109$	1.54281e9	1.04687	0.523435	−	0.852065i	$-0.324650\pi$
$109$	1.54281e9	1.04687	0.523435	+	0.852065i	$0.324650\pi$
$110$	−9.93301e8	−0.646865
$111$	−1.91056e9	−1.19456
$112$	−3.24453e8	−0.194837
$113$	1.65344e9	0.953972	0.476986	−	0.878911i	$-0.341729\pi$
$113$	1.65344e9	0.953972	0.476986	+	0.878911i	$0.341729\pi$
$114$	−1.08599e9	−0.602221
$115$	−2.40798e9	−1.28385
$116$	1.00839e9	0.517091
$117$	−1.56583e9	−0.772515
$118$	2.10049e9	0.997359
$119$	0	0
$120$	3.07867e9	1.35534
$121$	−7.31283e8	−0.310135
$122$	1.59144e7	0.00650385
$123$	4.78316e9	1.88427
$124$	−2.05526e8	−0.0780672
$125$	−2.91583e9	−1.06824
$126$	−6.38539e8	−0.225694
$127$	7.63519e8	0.260437	0.130219	−	0.991485i	$-0.458432\pi$
$127$	7.63519e8	0.260437	0.130219	+	0.991485i	$0.458432\pi$
$128$	−1.34639e9	−0.443327
$129$	2.16089e9	0.687036
$130$	2.16854e9	0.665922
$131$	3.54265e9	1.05101	0.525506	−	0.850790i	$-0.323876\pi$
$131$	3.54265e9	1.05101	0.525506	+	0.850790i	$0.323876\pi$
$132$	−1.04470e9	−0.299509
$133$	5.32711e8	0.147625
$134$	4.44933e9	1.19213
$135$	−4.65734e8	−0.120680
$136$	0	0
$137$	5.30702e9	1.28709	0.643544	−	0.765410i	$-0.277464\pi$
$137$	5.30702e9	1.28709	0.643544	+	0.765410i	$0.277464\pi$
$138$	7.15713e9	1.67990
$139$	−2.25290e9	−0.511887	−0.255944	−	0.966692i	$-0.582386\pi$
$139$	−2.25290e9	−0.511887	−0.255944	+	0.966692i	$0.582386\pi$
$140$	−3.12924e8	−0.0688434
$141$	−8.82511e9	−1.88033
$142$	−7.75184e9	−1.59995
$143$	−3.55128e9	−0.710188
$144$	−3.12484e9	−0.605614
$145$	−9.54304e9	−1.79279
$146$	6.73359e9	1.22648
$147$	−7.15100e9	−1.26310
$148$	1.32089e9	0.226302
$149$	1.22355e9	0.203369	0.101685	−	0.994817i	$-0.467577\pi$
$149$	1.22355e9	0.203369	0.101685	+	0.994817i	$0.467577\pi$
$150$	1.31470e9	0.212039
$151$	−2.49476e9	−0.390511	−0.195255	−	0.980752i	$-0.562554\pi$
$151$	−2.49476e9	−0.390511	−0.195255	+	0.980752i	$0.562554\pi$
$152$	3.62344e9	0.550585
$153$	0	0
$154$	−1.44820e9	−0.207485
$155$	1.94502e9	0.270665
$156$	2.28076e9	0.308332
$157$	−1.33013e10	−1.74721	−0.873604	−	0.486638i	$-0.838223\pi$
$157$	−1.33013e10	−1.74721	−0.873604	+	0.486638i	$0.838223\pi$
$158$	8.13356e9	1.03830
$159$	−1.18191e10	−1.46656
$160$	−3.81590e9	−0.460317
$161$	−3.51077e9	−0.411800
$162$	8.19114e9	0.934387
$163$	9.57910e9	1.06287	0.531436	−	0.847099i	$-0.321653\pi$
$163$	9.57910e9	1.06287	0.531436	+	0.847099i	$0.321653\pi$
$164$	−3.30689e9	−0.356963
$165$	9.88669e9	1.03842
$166$	−1.30173e9	−0.133056
$167$	1.75335e10	1.74439	0.872197	−	0.489155i	$-0.162695\pi$
$167$	1.75335e10	1.74439	0.872197	+	0.489155i	$0.162695\pi$
$168$	4.48861e9	0.434730
$169$	−2.85144e9	−0.268890
$170$	0	0
$171$	5.13058e9	0.458864
$172$	−1.49396e9	−0.130155
$173$	−1.61340e10	−1.36941	−0.684706	−	0.728819i	$-0.740069\pi$
$173$	−1.61340e10	−1.36941	−0.684706	+	0.728819i	$0.740069\pi$
$174$	2.83643e10	2.34585
$175$	−6.44896e8	−0.0519779
$176$	−7.08711e9	−0.556753
$177$	−2.09070e10	−1.60107
$178$	−8.15527e9	−0.608903
$179$	5.26701e9	0.383465	0.191732	−	0.981447i	$-0.438589\pi$
$179$	5.26701e9	0.383465	0.191732	+	0.981447i	$0.438589\pi$
$180$	−3.01379e9	−0.213987
$181$	−9.57706e9	−0.663252	−0.331626	−	0.943411i	$-0.607597\pi$
$181$	−9.57706e9	−0.663252	−0.331626	+	0.943411i	$0.607597\pi$
$182$	3.16167e9	0.213597
$183$	−1.58402e8	−0.0104407
$184$	−2.38798e10	−1.53586
$185$	−1.25004e10	−0.784608
$186$	−5.78109e9	−0.354162
$187$	0	0
$188$	6.10134e9	0.356217
$189$	−6.79027e8	−0.0387087
$190$	−7.10545e9	−0.395549
$191$	8.18604e9	0.445065	0.222533	−	0.974925i	$-0.428568\pi$
$191$	8.18604e9	0.445065	0.222533	+	0.974925i	$0.428568\pi$
$192$	2.87562e10	1.52713
$193$	−1.11731e9	−0.0579651	−0.0289825	−	0.999580i	$-0.509227\pi$
$193$	−1.11731e9	−0.0579651	−0.0289825	+	0.999580i	$0.509227\pi$
$194$	−1.84797e10	−0.936670
$195$	−2.15843e10	−1.06901
$196$	4.94392e9	0.239287
$197$	1.07763e10	0.509769	0.254884	−	0.966972i	$-0.417963\pi$
$197$	1.07763e10	0.509769	0.254884	+	0.966972i	$0.417963\pi$
$198$	−1.39478e10	−0.644928
$199$	−2.07750e10	−0.939081	−0.469540	−	0.882911i	$-0.655580\pi$
$199$	−2.07750e10	−0.939081	−0.469540	+	0.882911i	$0.655580\pi$
$200$	−4.38651e9	−0.193858
$201$	−4.42858e10	−1.91374
$202$	−1.67805e9	−0.0709127
$203$	−1.39135e10	−0.575047
$204$	0	0
$205$	3.12953e10	1.23762
$206$	−1.25476e10	−0.485463
$207$	−3.38125e10	−1.28000
$208$	1.54724e10	0.573155
$209$	1.16361e10	0.421843
$210$	−8.80202e9	−0.312317
$211$	4.91063e10	1.70556	0.852778	−	0.522274i	$-0.174916\pi$
$211$	4.91063e10	1.70556	0.852778	+	0.522274i	$0.174916\pi$
$212$	8.17129e9	0.277830
$213$	7.71570e10	2.56843
$214$	−9.33698e9	−0.304330
$215$	1.41383e10	0.451257
$216$	−4.61866e9	−0.144369
$217$	2.83579e9	0.0868171
$218$	−3.00027e10	−0.899719
$219$	−6.70220e10	−1.96888
$220$	−6.83527e9	−0.196722
$221$	0	0
$222$	3.71544e10	1.02665
$223$	−1.31700e10	−0.356628	−0.178314	−	0.983974i	$-0.557064\pi$
$223$	−1.31700e10	−0.356628	−0.178314	+	0.983974i	$0.557064\pi$
$224$	−5.56347e9	−0.147649
$225$	−6.21105e9	−0.161564
$226$	−3.21542e10	−0.819878
$227$	−1.05898e10	−0.264710	−0.132355	−	0.991202i	$-0.542254\pi$
$227$	−1.05898e10	−0.264710	−0.132355	+	0.991202i	$0.542254\pi$
$228$	−7.47314e9	−0.183145
$229$	−8.02568e10	−1.92851	−0.964256	−	0.264972i	$-0.914637\pi$
$229$	−8.02568e10	−1.92851	−0.964256	+	0.264972i	$0.914637\pi$
$230$	4.68277e10	1.10339
$231$	1.44145e10	0.333078
$232$	−9.46378e10	−2.14471
$233$	−2.70362e10	−0.600958	−0.300479	−	0.953788i	$-0.597146\pi$
$233$	−2.70362e10	−0.600958	−0.300479	+	0.953788i	$0.597146\pi$
$234$	3.04503e10	0.663928
$235$	−5.77410e10	−1.23503
$236$	1.44542e10	0.303313
$237$	−8.09564e10	−1.66680
$238$	0	0
$239$	−1.32760e10	−0.263194	−0.131597	−	0.991303i	$-0.542011\pi$
$239$	−1.32760e10	−0.263194	−0.131597	+	0.991303i	$0.542011\pi$
$240$	−4.30747e10	−0.838054
$241$	−8.16114e10	−1.55838	−0.779191	−	0.626786i	$-0.784370\pi$
$241$	−8.16114e10	−1.55838	−0.779191	+	0.626786i	$0.784370\pi$
$242$	1.42211e10	0.266542
$243$	−7.42910e10	−1.36681
$244$	1.09513e8	0.00197793
$245$	−4.67876e10	−0.829628
$246$	−9.30174e10	−1.61941
$247$	−2.54037e10	−0.434270
$248$	1.92887e10	0.323795
$249$	1.29566e10	0.213597
$250$	5.67037e10	0.918081
$251$	−8.08502e10	−1.28573	−0.642864	−	0.765980i	$-0.722254\pi$
$251$	−8.08502e10	−1.28573	−0.642864	+	0.765980i	$0.722254\pi$
$252$	−4.39402e9	−0.0686373
$253$	−7.66866e10	−1.17673
$254$	−1.48480e10	−0.223829
$255$	0	0
$256$	−4.98817e10	−0.725875
$257$	6.72954e10	0.962246	0.481123	−	0.876653i	$-0.340229\pi$
$257$	6.72954e10	0.962246	0.481123	+	0.876653i	$0.340229\pi$
$258$	−4.20225e10	−0.590464
$259$	−1.82253e10	−0.251667
$260$	1.49226e10	0.202518
$261$	−1.34002e11	−1.78743
$262$	−6.88934e10	−0.903279
$263$	−1.38868e11	−1.78978	−0.894892	−	0.446284i	$-0.852747\pi$
$263$	−1.38868e11	−1.78978	−0.894892	+	0.446284i	$0.852747\pi$
$264$	9.80458e10	1.24226
$265$	−7.73303e10	−0.963260
$266$	−1.03595e10	−0.126874
$267$	8.11724e10	0.977480
$268$	3.06175e10	0.362546
$269$	−9.67484e10	−1.12657	−0.563286	−	0.826262i	$-0.690463\pi$
$269$	−9.67484e10	−1.12657	−0.563286	+	0.826262i	$0.690463\pi$
$270$	9.05706e9	0.103717
$271$	8.71228e10	0.981229	0.490614	−	0.871377i	$-0.336772\pi$
$271$	8.71228e10	0.981229	0.490614	+	0.871377i	$0.336772\pi$
$272$	0	0
$273$	−3.14693e10	−0.342890
$274$	−1.03205e11	−1.10617
$275$	−1.40866e10	−0.148529
$276$	4.92508e10	0.510885
$277$	4.93260e10	0.503404	0.251702	−	0.967805i	$-0.419010\pi$
$277$	4.93260e10	0.503404	0.251702	+	0.967805i	$0.419010\pi$
$278$	4.38117e10	0.439935
$279$	2.73117e10	0.269855
$280$	2.93681e10	0.285538
$281$	−1.59453e11	−1.52565	−0.762824	−	0.646607i	$-0.776188\pi$
$281$	−1.59453e11	−1.52565	−0.762824	+	0.646607i	$0.776188\pi$
$282$	1.71620e11	1.61602
$283$	−4.85133e10	−0.449596	−0.224798	−	0.974405i	$-0.572172\pi$
$283$	−4.85133e10	−0.449596	−0.224798	+	0.974405i	$0.572172\pi$
$284$	−5.33433e10	−0.486572
$285$	7.07232e10	0.634980
$286$	6.90612e10	0.610361
$287$	4.56276e10	0.396972
$288$	−5.35822e10	−0.458939
$289$	0	0
$290$	1.85582e11	1.54079
$291$	1.83935e11	1.50365
$292$	4.63364e10	0.372992
$293$	9.16323e10	0.726347	0.363174	−	0.931721i	$-0.381693\pi$
$293$	9.16323e10	0.726347	0.363174	+	0.931721i	$0.381693\pi$
$294$	1.39064e11	1.08556
$295$	−1.36790e11	−1.05161
$296$	−1.23966e11	−0.938622
$297$	−1.48322e10	−0.110612
$298$	−2.37943e10	−0.174783
$299$	1.67420e11	1.21140
$300$	9.04693e9	0.0644845
$301$	2.06132e10	0.144743
$302$	4.85152e10	0.335619
$303$	1.67023e10	0.113837
$304$	−5.06968e10	−0.340447
$305$	−1.03639e9	−0.00685764
$306$	0	0
$307$	2.63442e11	1.69263	0.846316	−	0.532682i	$-0.178816\pi$
$307$	2.63442e11	1.69263	0.846316	+	0.532682i	$0.178816\pi$
$308$	−9.96563e9	−0.0630996
$309$	1.24890e11	0.779321
$310$	−3.78246e10	−0.232620
$311$	−1.49371e11	−0.905407	−0.452703	−	0.891661i	$-0.649540\pi$
$311$	−1.49371e11	−0.905407	−0.452703	+	0.891661i	$0.649540\pi$
$312$	−2.14051e11	−1.27885
$313$	3.66121e10	0.215613	0.107807	−	0.994172i	$-0.465617\pi$
$313$	3.66121e10	0.215613	0.107807	+	0.994172i	$0.465617\pi$
$314$	2.58667e11	1.50161
$315$	4.15835e10	0.237971
$316$	5.59701e10	0.315765
$317$	1.35093e11	0.751391	0.375695	−	0.926743i	$-0.377404\pi$
$317$	1.35093e11	0.751391	0.375695	+	0.926743i	$0.377404\pi$
$318$	2.29845e11	1.26041
$319$	−3.03915e11	−1.64322
$320$	1.88146e11	1.00305
$321$	9.29344e10	0.488544
$322$	6.82734e10	0.353916
$323$	0	0
$324$	5.63663e10	0.284163
$325$	3.07535e10	0.152904
$326$	−1.86283e11	−0.913470
$327$	2.98629e11	1.44433
$328$	3.10354e11	1.48056
$329$	−8.41846e10	−0.396142
$330$	−1.92265e11	−0.892456
$331$	2.50025e11	1.14487	0.572437	−	0.819949i	$-0.305998\pi$
$331$	2.50025e11	1.14487	0.572437	+	0.819949i	$0.305998\pi$
$332$	−8.95770e9	−0.0404646
$333$	−1.75529e11	−0.782259
$334$	−3.40971e11	−1.49920
$335$	−2.89753e11	−1.25698
$336$	−6.28017e10	−0.268809
$337$	2.48239e11	1.04842	0.524211	−	0.851589i	$-0.324360\pi$
$337$	2.48239e11	1.04842	0.524211	+	0.851589i	$0.324360\pi$
$338$	5.54515e10	0.231094
$339$	3.20043e11	1.31616
$340$	0	0
$341$	6.19428e10	0.248083
$342$	−9.97736e10	−0.394365
$343$	−1.42725e11	−0.556770
$344$	1.40209e11	0.539837
$345$	−4.66093e11	−1.77128
$346$	3.13755e11	1.17692
$347$	3.38605e11	1.25375	0.626874	−	0.779121i	$-0.284334\pi$
$347$	3.38605e11	1.25375	0.626874	+	0.779121i	$0.284334\pi$
$348$	1.95185e11	0.713411
$349$	−3.75034e11	−1.35318	−0.676592	−	0.736358i	$-0.736544\pi$
$349$	−3.75034e11	−1.35318	−0.676592	+	0.736358i	$0.736544\pi$
$350$	1.25412e10	0.0446717
$351$	3.23811e10	0.113870
$352$	−1.21524e11	−0.421911
$353$	−1.77859e10	−0.0609663	−0.0304831	−	0.999535i	$-0.509705\pi$
$353$	−1.77859e10	−0.0609663	−0.0304831	+	0.999535i	$0.509705\pi$
$354$	4.06574e11	1.37602
$355$	5.04823e11	1.68699
$356$	−5.61195e10	−0.185178
$357$	0	0
$358$	−1.02427e11	−0.329563
$359$	2.17639e10	0.0691531	0.0345766	−	0.999402i	$-0.488992\pi$
$359$	2.17639e10	0.0691531	0.0345766	+	0.999402i	$0.488992\pi$
$360$	2.82846e11	0.887543
$361$	−2.39450e11	−0.742049
$362$	1.86243e11	0.570023
$363$	−1.41548e11	−0.427883
$364$	2.17567e10	0.0649585
$365$	−4.38511e11	−1.29319
$366$	3.08041e9	0.00897313
$367$	3.32752e11	0.957466	0.478733	−	0.877961i	$-0.341096\pi$
$367$	3.32752e11	0.957466	0.478733	+	0.877961i	$0.341096\pi$
$368$	3.34111e11	0.949677
$369$	4.39443e11	1.23391
$370$	2.43094e11	0.674321
$371$	−1.12745e11	−0.308970
$372$	−3.97819e10	−0.107706
$373$	−5.53653e10	−0.148098	−0.0740488	−	0.997255i	$-0.523592\pi$
$373$	−5.53653e10	−0.148098	−0.0740488	+	0.997255i	$0.523592\pi$
$374$	0	0
$375$	−5.64393e11	−1.47381
$376$	−5.72614e11	−1.47746
$377$	6.63499e11	1.69163
$378$	1.32049e10	0.0332677
$379$	−3.51291e11	−0.874561	−0.437281	−	0.899325i	$-0.644058\pi$
$379$	−3.51291e11	−0.874561	−0.437281	+	0.899325i	$0.644058\pi$
$380$	−4.88952e10	−0.120293
$381$	1.47788e11	0.359316
$382$	−1.59193e11	−0.382505
$383$	−9.08329e10	−0.215699	−0.107850	−	0.994167i	$-0.534397\pi$
$383$	−9.08329e10	−0.215699	−0.107850	+	0.994167i	$0.534397\pi$
$384$	−2.60608e11	−0.611643
$385$	9.43113e10	0.218771
$386$	2.17282e10	0.0498173
$387$	1.98528e11	0.449906
$388$	−1.27166e11	−0.284857
$389$	−6.16131e11	−1.36427	−0.682135	−	0.731227i	$-0.738948\pi$
$389$	−6.16131e11	−1.36427	−0.682135	+	0.731227i	$0.738948\pi$
$390$	4.19747e11	0.918748
$391$	0	0
$392$	−4.63990e11	−0.992479
$393$	6.85722e11	1.45004
$394$	−2.09566e11	−0.438114
$395$	−5.29682e11	−1.09478
$396$	−9.59798e10	−0.196133
$397$	6.58425e11	1.33030	0.665149	−	0.746711i	$-0.268368\pi$
$397$	6.58425e11	1.33030	0.665149	+	0.746711i	$0.268368\pi$
$398$	4.04009e11	0.807080
$399$	1.03112e11	0.203673
$400$	6.13732e10	0.119869
$401$	−1.60050e11	−0.309105	−0.154553	−	0.987985i	$-0.549394\pi$
$401$	−1.60050e11	−0.309105	−0.154553	+	0.987985i	$0.549394\pi$
$402$	8.61219e11	1.64474
$403$	−1.35232e11	−0.255391
$404$	−1.15473e10	−0.0215657
$405$	−5.33431e11	−0.985215
$406$	2.70573e11	0.494216
$407$	−3.98099e11	−0.719145
$408$	0	0
$409$	3.77306e11	0.666713	0.333357	−	0.942801i	$-0.391819\pi$
$409$	3.77306e11	0.666713	0.333357	+	0.942801i	$0.391819\pi$
$410$	−6.08594e11	−1.06365
$411$	1.02723e12	1.77575
$412$	−8.63444e10	−0.147637
$413$	−1.99436e11	−0.337309
$414$	6.57546e11	1.10008
$415$	8.47726e10	0.140294
$416$	2.65308e11	0.434341
$417$	−4.36074e11	−0.706233
$418$	−2.26286e11	−0.362547
$419$	−2.04247e11	−0.323737	−0.161868	−	0.986812i	$-0.551752\pi$
$419$	−2.04247e11	−0.323737	−0.161868	+	0.986812i	$0.551752\pi$
$420$	−6.05700e10	−0.0949808
$421$	−6.31659e11	−0.979972	−0.489986	−	0.871730i	$-0.662998\pi$
$421$	−6.31659e11	−0.979972	−0.489986	+	0.871730i	$0.662998\pi$
$422$	−9.54961e11	−1.46582
$423$	−8.10789e11	−1.23134
$424$	−7.66881e11	−1.15234
$425$	0	0
$426$	−1.50046e12	−2.20740
$427$	−1.51103e9	−0.00219962
$428$	−6.42512e10	−0.0925517
$429$	−6.87392e11	−0.979821
$430$	−2.74945e11	−0.387827
$431$	1.18297e12	1.65130	0.825650	−	0.564183i	$-0.190809\pi$
$431$	1.18297e12	1.65130	0.825650	+	0.564183i	$0.190809\pi$
$432$	6.46213e10	0.0892687
$433$	9.78872e11	1.33823	0.669114	−	0.743159i	$-0.266674\pi$
$433$	9.78872e11	1.33823	0.669114	+	0.743159i	$0.266674\pi$
$434$	−5.51471e10	−0.0746138
$435$	−1.84717e12	−2.47346
$436$	−2.06460e11	−0.273619
$437$	−5.48568e11	−0.719555
$438$	1.30336e12	1.69212
$439$	4.58326e11	0.588958	0.294479	−	0.955658i	$-0.404854\pi$
$439$	4.58326e11	0.588958	0.294479	+	0.955658i	$0.404854\pi$
$440$	6.41494e11	0.815935
$441$	−6.56984e11	−0.827144
$442$	0	0
$443$	−1.94207e11	−0.239579	−0.119789	−	0.992799i	$-0.538222\pi$
$443$	−1.94207e11	−0.239579	−0.119789	+	0.992799i	$0.538222\pi$
$444$	2.55673e11	0.312221
$445$	5.31095e11	0.642026
$446$	2.56116e11	0.306499
$447$	2.36833e11	0.280581
$448$	2.74312e11	0.321732
$449$	8.57057e11	0.995179	0.497589	−	0.867413i	$-0.334219\pi$
$449$	8.57057e11	0.995179	0.497589	+	0.867413i	$0.334219\pi$
$450$	1.20785e11	0.138854
$451$	9.96656e11	1.13436
$452$	−2.21265e11	−0.249339
$453$	−4.82890e11	−0.538774
$454$	2.05938e11	0.227502
$455$	−2.05898e11	−0.225216
$456$	7.01358e11	0.759623
$457$	−9.01803e11	−0.967138	−0.483569	−	0.875306i	$-0.660660\pi$
$457$	−9.01803e11	−0.967138	−0.483569	+	0.875306i	$0.660660\pi$
$458$	1.56074e12	1.65743
$459$	0	0
$460$	3.22239e11	0.335558
$461$	−5.68276e11	−0.586010	−0.293005	−	0.956111i	$-0.594655\pi$
$461$	−5.68276e11	−0.586010	−0.293005	+	0.956111i	$0.594655\pi$
$462$	−2.80316e11	−0.286259
$463$	−1.23086e12	−1.24478	−0.622392	−	0.782705i	$-0.713839\pi$
$463$	−1.23086e12	−1.24478	−0.622392	+	0.782705i	$0.713839\pi$
$464$	1.32411e12	1.32615
$465$	3.76482e11	0.373427
$466$	5.25768e11	0.516485
$467$	1.95074e10	0.0189790	0.00948948	−	0.999955i	$-0.496979\pi$
$467$	1.95074e10	0.0189790	0.00948948	+	0.999955i	$0.496979\pi$
$468$	2.09540e11	0.201911
$469$	−4.22452e11	−0.403180
$470$	1.12288e12	1.06143
$471$	−2.57461e12	−2.41056
$472$	−1.35654e12	−1.25804
$473$	4.50260e11	0.413607
$474$	1.57434e12	1.43251
$475$	−1.00767e11	−0.0908232
$476$	0	0
$477$	−1.08586e12	−0.960375
$478$	2.58176e11	0.226199
$479$	−1.96561e12	−1.70603	−0.853015	−	0.521887i	$-0.825228\pi$
$479$	−1.96561e12	−1.70603	−0.853015	+	0.521887i	$0.825228\pi$
$480$	−7.38611e11	−0.635083
$481$	8.69119e11	0.740332
$482$	1.58708e12	1.33933
$483$	−6.79550e11	−0.568145
$484$	9.78610e10	0.0810598
$485$	1.20345e12	0.987622
$486$	1.44472e12	1.17469
$487$	1.34673e11	0.108493	0.0542463	−	0.998528i	$-0.482724\pi$
$487$	1.34673e11	0.108493	0.0542463	+	0.998528i	$0.482724\pi$
$488$	−1.02778e10	−0.00820375
$489$	1.85415e12	1.46641
$490$	9.09870e11	0.713012
$491$	2.09979e12	1.63046	0.815230	−	0.579138i	$-0.196611\pi$
$491$	2.09979e12	1.63046	0.815230	+	0.579138i	$0.196611\pi$
$492$	−6.40087e11	−0.492489
$493$	0	0
$494$	4.94021e11	0.373228
$495$	9.08320e11	0.680010
$496$	−2.69875e11	−0.200214
$497$	7.36017e11	0.541108
$498$	−2.51965e11	−0.183573
$499$	1.65833e11	0.119734	0.0598672	−	0.998206i	$-0.480932\pi$
$499$	1.65833e11	0.119734	0.0598672	+	0.998206i	$0.480932\pi$
$500$	3.90199e11	0.279204
$501$	3.39381e12	2.40668
$502$	1.57228e12	1.10500
$503$	−1.17402e12	−0.817750	−0.408875	−	0.912590i	$-0.634079\pi$
$503$	−1.17402e12	−0.817750	−0.408875	+	0.912590i	$0.634079\pi$
$504$	4.12382e11	0.284683
$505$	1.09280e11	0.0747701
$506$	1.49131e12	1.01133
$507$	−5.51930e11	−0.370978
$508$	−1.02175e11	−0.0680702
$509$	9.33643e11	0.616525	0.308263	−	0.951301i	$-0.400252\pi$
$509$	9.33643e11	0.616525	0.308263	+	0.951301i	$0.400252\pi$
$510$	0	0
$511$	−6.39337e11	−0.414797
$512$	1.65939e12	1.06717
$513$	−1.06100e11	−0.0676374
$514$	−1.30868e12	−0.826989
$515$	8.17134e11	0.511871
$516$	−2.89173e11	−0.179570
$517$	−1.83887e12	−1.13199
$518$	3.54424e11	0.216291
$519$	−3.12292e12	−1.88933
$520$	−1.40049e12	−0.839973
$521$	2.54572e11	0.151371	0.0756853	−	0.997132i	$-0.475886\pi$
$521$	2.54572e11	0.151371	0.0756853	+	0.997132i	$0.475886\pi$
$522$	2.60591e12	1.53618
$523$	−1.23043e12	−0.719115	−0.359558	−	0.933123i	$-0.617072\pi$
$523$	−1.23043e12	−0.719115	−0.359558	+	0.933123i	$0.617072\pi$
$524$	−4.74081e11	−0.274702
$525$	−1.24827e11	−0.0717120
$526$	2.70054e12	1.53820
$527$	0	0
$528$	−1.37179e12	−0.768132
$529$	1.81412e12	1.00720
$530$	1.50383e12	0.827861
$531$	−1.92078e12	−1.04846
$532$	−7.12879e10	−0.0385845
$533$	−2.17587e12	−1.16778
$534$	−1.57855e12	−0.840082
$535$	6.08052e11	0.320884
$536$	−2.87347e12	−1.50371
$537$	1.01949e12	0.529052
$538$	1.88145e12	0.968216
$539$	−1.49004e12	−0.760409
$540$	6.23250e10	0.0315421
$541$	2.63964e12	1.32482	0.662410	−	0.749141i	$-0.269534\pi$
$541$	2.63964e12	1.32482	0.662410	+	0.749141i	$0.269534\pi$
$542$	−1.69426e12	−0.843304
$543$	−1.85375e12	−0.915065
$544$	0	0
$545$	1.95387e12	0.948660
$546$	6.11978e11	0.294693
$547$	−5.94564e10	−0.0283959	−0.0141979	−	0.999899i	$-0.504519\pi$
$547$	−5.94564e10	−0.0283959	−0.0141979	+	0.999899i	$0.504519\pi$
$548$	−7.10190e11	−0.336405
$549$	−1.45528e10	−0.00683710
$550$	2.73940e11	0.127651
$551$	−2.17402e12	−1.00480
$552$	−4.62222e12	−2.11897
$553$	−7.72260e11	−0.351156
$554$	−9.59233e11	−0.432644
$555$	−2.41961e12	−1.08250
$556$	3.01484e11	0.133791
$557$	−9.95121e11	−0.438054	−0.219027	−	0.975719i	$-0.570288\pi$
$557$	−9.95121e11	−0.438054	−0.219027	+	0.975719i	$0.570288\pi$
$558$	−5.31126e11	−0.231923
$559$	−9.82994e11	−0.425792
$560$	−4.10899e11	−0.176559
$561$	0	0
$562$	3.10085e12	1.31120
$563$	1.63209e12	0.684631	0.342315	−	0.939585i	$-0.388789\pi$
$563$	1.63209e12	0.684631	0.342315	+	0.939585i	$0.388789\pi$
$564$	1.18098e12	0.491460
$565$	2.09398e12	0.864477
$566$	9.43431e11	0.386399
$567$	−7.77727e11	−0.316012
$568$	5.00630e12	2.01813
$569$	2.67510e12	1.06988	0.534940	−	0.844890i	$-0.320334\pi$
$569$	2.67510e12	1.06988	0.534940	+	0.844890i	$0.320334\pi$
$570$	−1.37534e12	−0.545725
$571$	2.03536e12	0.801269	0.400635	−	0.916238i	$-0.368790\pi$
$571$	2.03536e12	0.801269	0.400635	+	0.916238i	$0.368790\pi$
$572$	4.75236e11	0.185621
$573$	1.58450e12	0.614041
$574$	−8.87313e11	−0.341172
$575$	6.64093e11	0.253352
$576$	2.64192e12	1.00004
$577$	−3.12551e12	−1.17390	−0.586948	−	0.809625i	$-0.699671\pi$
$577$	−3.12551e12	−1.17390	−0.586948	+	0.809625i	$0.699671\pi$
$578$	0	0
$579$	−2.16269e11	−0.0799723
$580$	1.27706e12	0.468581
$581$	1.23596e11	0.0449999
$582$	−3.57695e12	−1.29229
$583$	−2.46272e12	−0.882892
$584$	−4.34869e12	−1.54704
$585$	−1.98302e12	−0.700043
$586$	−1.78196e12	−0.624250
$587$	2.87539e11	0.0999599	0.0499799	−	0.998750i	$-0.484084\pi$
$587$	2.87539e11	0.0999599	0.0499799	+	0.998750i	$0.484084\pi$
$588$	9.56953e11	0.330136
$589$	4.43100e11	0.151699
$590$	2.66013e12	0.903794
$591$	2.08588e12	0.703309
$592$	1.73445e12	0.580384
$593$	−1.51880e12	−0.504376	−0.252188	−	0.967678i	$-0.581150\pi$
$593$	−1.51880e12	−0.504376	−0.252188	+	0.967678i	$0.581150\pi$
$594$	2.88438e11	0.0950636
$595$	0	0
$596$	−1.63737e11	−0.0531544
$597$	−4.02125e12	−1.29562
$598$	−3.25579e12	−1.04112
$599$	5.23028e12	1.65999	0.829993	−	0.557774i	$-0.188344\pi$
$599$	5.23028e12	1.65999	0.829993	+	0.557774i	$0.188344\pi$
$600$	−8.49059e11	−0.267459
$601$	2.43216e12	0.760426	0.380213	−	0.924899i	$-0.375851\pi$
$601$	2.43216e12	0.760426	0.380213	+	0.924899i	$0.375851\pi$
$602$	−4.00862e11	−0.124397
$603$	−4.06867e12	−1.25321
$604$	3.33851e11	0.102067
$605$	−9.26123e11	−0.281041
$606$	−3.24806e11	−0.0978357
$607$	−2.32326e12	−0.694621	−0.347311	−	0.937750i	$-0.612905\pi$
$607$	−2.32326e12	−0.694621	−0.347311	+	0.937750i	$0.612905\pi$
$608$	−8.69308e11	−0.257993
$609$	−2.69311e12	−0.793372
$610$	2.01545e10	0.00589370
$611$	4.01456e12	1.16534
$612$	0	0
$613$	−2.20219e12	−0.629916	−0.314958	−	0.949106i	$-0.601990\pi$
$613$	−2.20219e12	−0.629916	−0.314958	+	0.949106i	$0.601990\pi$
$614$	−5.12311e12	−1.45471
$615$	6.05757e12	1.70750
$616$	9.35280e11	0.261715
$617$	−3.32024e12	−0.922331	−0.461165	−	0.887314i	$-0.652569\pi$
$617$	−3.32024e12	−0.922331	−0.461165	+	0.887314i	$0.652569\pi$
$618$	−2.42872e12	−0.669776
$619$	1.17816e12	0.322549	0.161275	−	0.986910i	$-0.448439\pi$
$619$	1.17816e12	0.322549	0.161275	+	0.986910i	$0.448439\pi$
$620$	−2.60285e11	−0.0707435
$621$	6.99240e11	0.188675
$622$	2.90479e12	0.778139
$623$	7.74321e11	0.205933
$624$	2.99486e12	0.790761
$625$	−3.01055e12	−0.789197
$626$	−7.11990e11	−0.185306
$627$	2.25231e12	0.582001
$628$	1.77999e12	0.456666
$629$	0	0
$630$	−8.08668e11	−0.204521
$631$	−4.59073e12	−1.15279	−0.576395	−	0.817171i	$-0.695541\pi$
$631$	−4.59073e12	−1.15279	−0.576395	+	0.817171i	$0.695541\pi$
$632$	−5.25282e12	−1.30968
$633$	9.50508e12	2.35309
$634$	−2.62713e12	−0.645773
$635$	9.66947e11	0.236005
$636$	1.58165e12	0.383312
$637$	3.25300e12	0.782811
$638$	5.91019e12	1.41224
$639$	7.08864e12	1.68193
$640$	−1.70511e12	−0.401738
$641$	−5.12557e12	−1.19917	−0.599586	−	0.800311i	$-0.704668\pi$
$641$	−5.12557e12	−1.19917	−0.599586	+	0.800311i	$0.704668\pi$
$642$	−1.80728e12	−0.419873
$643$	−4.65773e12	−1.07455	−0.537273	−	0.843408i	$-0.680546\pi$
$643$	−4.65773e12	−1.07455	−0.537273	+	0.843408i	$0.680546\pi$
$644$	4.69814e11	0.107632
$645$	2.73663e12	0.622584
$646$	0	0
$647$	8.79031e12	1.97213	0.986064	−	0.166369i	$-0.0532041\pi$
$647$	8.79031e12	1.97213	0.986064	+	0.166369i	$0.0532041\pi$
$648$	−5.29001e12	−1.17861
$649$	−4.35633e12	−0.963872
$650$	−5.98058e11	−0.131411
$651$	5.48900e11	0.119778
$652$	−1.28188e12	−0.277801
$653$	3.45550e12	0.743707	0.371853	−	0.928292i	$-0.378722\pi$
$653$	3.45550e12	0.743707	0.371853	+	0.928292i	$0.378722\pi$
$654$	−5.80738e12	−1.24131
$655$	4.48654e12	0.952414
$656$	−4.34227e12	−0.915481
$657$	−6.15751e12	−1.28932
$658$	1.63712e12	0.340459
$659$	2.15788e12	0.445701	0.222850	−	0.974853i	$-0.428464\pi$
$659$	2.15788e12	0.445701	0.222850	+	0.974853i	$0.428464\pi$
$660$	−1.32305e12	−0.271411
$661$	−7.13948e12	−1.45466	−0.727328	−	0.686290i	$-0.759238\pi$
$661$	−7.13948e12	−1.45466	−0.727328	+	0.686290i	$0.759238\pi$
$662$	−4.86220e12	−0.983947
$663$	0	0
$664$	8.40685e11	0.167833
$665$	6.74644e11	0.133776
$666$	3.41349e12	0.672302
$667$	1.43276e13	2.80290
$668$	−2.34635e12	−0.455930
$669$	−2.54921e12	−0.492027
$670$	5.63478e12	1.08029
$671$	−3.30058e10	−0.00628548
$672$	−1.07687e12	−0.203706
$673$	8.54036e10	0.0160475	0.00802377	−	0.999968i	$-0.497446\pi$
$673$	8.54036e10	0.0160475	0.00802377	+	0.999968i	$0.497446\pi$
$674$	−4.82746e12	−0.901051
$675$	1.28444e11	0.0238148
$676$	3.81582e11	0.0702794
$677$	4.00036e12	0.731897	0.365949	−	0.930635i	$-0.380745\pi$
$677$	4.00036e12	0.731897	0.365949	+	0.930635i	$0.380745\pi$
$678$	−6.22381e12	−1.13116
$679$	1.75460e12	0.316784
$680$	0	0
$681$	−2.04977e12	−0.365211
$682$	−1.20459e12	−0.213211
$683$	7.69619e12	1.35326	0.676632	−	0.736321i	$-0.263439\pi$
$683$	7.69619e12	1.35326	0.676632	+	0.736321i	$0.263439\pi$
$684$	−6.86579e11	−0.119933
$685$	6.72099e12	1.16634
$686$	2.77555e12	0.478509
$687$	−1.55346e13	−2.66070
$688$	−1.96171e12	−0.333800
$689$	5.37655e12	0.908902
$690$	9.06403e12	1.52230
$691$	−5.94387e12	−0.991786	−0.495893	−	0.868384i	$-0.665159\pi$
$691$	−5.94387e12	−0.991786	−0.495893	+	0.868384i	$0.665159\pi$
$692$	2.15906e12	0.357922
$693$	1.32430e12	0.218116
$694$	−6.58479e12	−1.07752
$695$	−2.85315e12	−0.463866
$696$	−1.83182e13	−2.95898
$697$	0	0
$698$	7.29323e12	1.16298
$699$	−5.23317e12	−0.829120
$700$	8.63006e10	0.0135854
$701$	−3.29849e12	−0.515922	−0.257961	−	0.966155i	$-0.583051\pi$
$701$	−3.29849e12	−0.515922	−0.257961	+	0.966155i	$0.583051\pi$
$702$	−6.29710e11	−0.0978642
$703$	−2.84775e12	−0.439748
$704$	5.99186e12	0.919359
$705$	−1.11764e13	−1.70393
$706$	3.45879e11	0.0523967
$707$	1.59326e11	0.0239828
$708$	2.79779e12	0.418471
$709$	1.99124e12	0.295948	0.147974	−	0.988991i	$-0.452725\pi$
$709$	1.99124e12	0.295948	0.147974	+	0.988991i	$0.452725\pi$
$710$	−9.81720e12	−1.44986
$711$	−7.43770e12	−1.09150
$712$	5.26684e12	0.768052
$713$	−2.92020e12	−0.423165
$714$	0	0
$715$	−4.49747e12	−0.643563
$716$	−7.04835e11	−0.100226
$717$	−2.56972e12	−0.363120
$718$	−4.23239e11	−0.0594327
$719$	2.97108e12	0.414605	0.207303	−	0.978277i	$-0.433532\pi$
$719$	2.97108e12	0.414605	0.207303	+	0.978277i	$0.433532\pi$
$720$	−3.95740e12	−0.548800
$721$	1.19136e12	0.164185
$722$	4.65654e12	0.637744
$723$	−1.57968e13	−2.15004
$724$	1.28161e12	0.173353
$725$	2.63185e12	0.353786
$726$	2.75267e12	0.367738
$727$	−2.82074e12	−0.374506	−0.187253	−	0.982312i	$-0.559958\pi$
$727$	−2.82074e12	−0.374506	−0.187253	+	0.982312i	$0.559958\pi$
$728$	−2.04187e12	−0.269425
$729$	−6.08927e12	−0.798530
$730$	8.52766e12	1.11142
$731$	0	0
$732$	2.11975e10	0.00272888
$733$	6.07992e12	0.777911	0.388956	−	0.921257i	$-0.372836\pi$
$733$	6.07992e12	0.777911	0.388956	+	0.921257i	$0.372836\pi$
$734$	−6.47097e12	−0.822881
$735$	−9.05628e12	−1.14461
$736$	5.72908e12	0.719672
$737$	−9.22772e12	−1.15210
$738$	−8.54578e12	−1.06047
$739$	−2.91421e12	−0.359436	−0.179718	−	0.983718i	$-0.557518\pi$
$739$	−2.91421e12	−0.359436	−0.179718	+	0.983718i	$0.557518\pi$
$740$	1.67282e12	0.205072
$741$	−4.91717e12	−0.599147
$742$	2.19254e12	0.265540
$743$	6.47698e12	0.779691	0.389846	−	0.920880i	$-0.372528\pi$
$743$	6.47698e12	0.779691	0.389846	+	0.920880i	$0.372528\pi$
$744$	3.73355e12	0.446729
$745$	1.54955e12	0.184291
$746$	1.07668e12	0.127280
$747$	1.19036e12	0.139874
$748$	0	0
$749$	8.86521e11	0.102925
$750$	1.09756e13	1.26664
$751$	−4.98040e12	−0.571327	−0.285663	−	0.958330i	$-0.592214\pi$
$751$	−4.98040e12	−0.571327	−0.285663	+	0.958330i	$0.592214\pi$
$752$	8.01164e12	0.913569
$753$	−1.56495e13	−1.77387
$754$	−1.29029e13	−1.45384
$755$	−3.15945e12	−0.353876
$756$	9.08680e10	0.0101173
$757$	1.28715e13	1.42461	0.712306	−	0.701869i	$-0.247651\pi$
$757$	1.28715e13	1.42461	0.712306	+	0.701869i	$0.247651\pi$
$758$	6.83149e12	0.751630
$759$	−1.48436e13	−1.62349
$760$	4.58885e12	0.498933
$761$	1.04253e13	1.12683	0.563414	−	0.826175i	$-0.309488\pi$
$761$	1.04253e13	1.12683	0.563414	+	0.826175i	$0.309488\pi$
$762$	−2.87400e12	−0.308809
$763$	2.84868e12	0.304287
$764$	−1.09546e12	−0.116326
$765$	0	0
$766$	1.76641e12	0.185380
$767$	9.51060e12	0.992268
$768$	−9.65519e12	−1.00146
$769$	2.45318e12	0.252965	0.126482	−	0.991969i	$-0.459631\pi$
$769$	2.45318e12	0.252965	0.126482	+	0.991969i	$0.459631\pi$
$770$	−1.83406e12	−0.188020
$771$	1.30258e13	1.32758
$772$	1.49520e11	0.0151503
$773$	−1.79815e13	−1.81141	−0.905707	−	0.423904i	$-0.860659\pi$
$773$	−1.79815e13	−1.81141	−0.905707	+	0.423904i	$0.860659\pi$
$774$	−3.86074e12	−0.386666
$775$	−5.36414e11	−0.0534125
$776$	1.19346e13	1.18149
$777$	−3.52771e12	−0.347215
$778$	1.19818e13	1.17250
$779$	7.12945e12	0.693645
$780$	2.88843e12	0.279407
$781$	1.60770e13	1.54623
$782$	0	0
$783$	2.77114e12	0.263470
$784$	6.49184e12	0.613685
$785$	−1.68452e13	−1.58330
$786$	−1.33351e13	−1.24622
$787$	1.26574e13	1.17614	0.588070	−	0.808810i	$-0.299888\pi$
$787$	1.26574e13	1.17614	0.588070	+	0.808810i	$0.299888\pi$
$788$	−1.44210e12	−0.133238
$789$	−2.68794e13	−2.46930
$790$	1.03006e13	0.940896
$791$	3.05296e12	0.277285
$792$	9.00776e12	0.813492
$793$	7.20572e10	0.00647065
$794$	−1.28043e13	−1.14331
$795$	−1.49682e13	−1.32898
$796$	2.78013e12	0.245446
$797$	−2.82215e12	−0.247752	−0.123876	−	0.992298i	$-0.539533\pi$
$797$	−2.82215e12	−0.247752	−0.123876	+	0.992298i	$0.539533\pi$
$798$	−2.00521e12	−0.175044
$799$	0	0
$800$	1.05238e12	0.0908379
$801$	7.45755e12	0.640103
$802$	3.11247e12	0.265656
$803$	−1.39652e13	−1.18530
$804$	5.92637e12	0.500191
$805$	−4.44616e12	−0.373168
$806$	2.62983e12	0.219493
$807$	−1.87268e13	−1.55429
$808$	1.08372e12	0.0894470
$809$	−1.80905e13	−1.48485	−0.742426	−	0.669928i	$-0.766325\pi$
$809$	−1.80905e13	−1.48485	−0.742426	+	0.669928i	$0.766325\pi$
$810$	1.03735e13	0.846729
$811$	−5.90333e12	−0.479185	−0.239593	−	0.970874i	$-0.577014\pi$
$811$	−5.90333e12	−0.479185	−0.239593	+	0.970874i	$0.577014\pi$
$812$	1.86191e12	0.150299
$813$	1.68636e13	1.35377
$814$	7.74177e12	0.618060
$815$	1.21313e13	0.963160
$816$	0	0
$817$	3.22088e12	0.252915
$818$	−7.33741e12	−0.572998
$819$	−2.89118e12	−0.224542
$820$	−4.18796e12	−0.323475
$821$	−4.68167e12	−0.359630	−0.179815	−	0.983700i	$-0.557550\pi$
$821$	−4.68167e12	−0.359630	−0.179815	+	0.983700i	$0.557550\pi$
$822$	−1.99765e13	−1.52614
$823$	2.10506e13	1.59943	0.799716	−	0.600379i	$-0.204984\pi$
$823$	2.10506e13	1.59943	0.799716	+	0.600379i	$0.204984\pi$
$824$	8.10347e12	0.612348
$825$	−2.72663e12	−0.204920
$826$	3.87840e12	0.289896
$827$	2.70402e12	0.201018	0.100509	−	0.994936i	$-0.467953\pi$
$827$	2.70402e12	0.201018	0.100509	+	0.994936i	$0.467953\pi$
$828$	4.52482e12	0.334553
$829$	−3.70419e12	−0.272394	−0.136197	−	0.990682i	$-0.543488\pi$
$829$	−3.70419e12	−0.272394	−0.136197	+	0.990682i	$0.543488\pi$
$830$	−1.64856e12	−0.120574
$831$	9.54761e12	0.694528
$832$	−1.30813e13	−0.946443
$833$	0	0
$834$	8.48026e12	0.606962
$835$	2.22050e13	1.58075
$836$	−1.55716e12	−0.110257
$837$	−5.64804e11	−0.0397771
$838$	3.97195e12	0.278231
$839$	2.09474e13	1.45949	0.729745	−	0.683719i	$-0.239639\pi$
$839$	2.09474e13	1.45949	0.729745	+	0.683719i	$0.239639\pi$
$840$	5.68453e12	0.393947
$841$	4.22744e13	2.91404
$842$	1.22838e13	0.842223
$843$	−3.08640e13	−2.10488
$844$	−6.57144e12	−0.445779
$845$	−3.61117e12	−0.243664
$846$	1.57673e13	1.05825
$847$	−1.35026e12	−0.0901451
$848$	1.07297e13	0.712535
$849$	−9.39032e12	−0.620291
$850$	0	0
$851$	1.87678e13	1.22668
$852$	−1.03252e13	−0.671307
$853$	−2.65921e13	−1.71982	−0.859909	−	0.510448i	$-0.829480\pi$
$853$	−2.65921e13	−1.71982	−0.859909	+	0.510448i	$0.829480\pi$
$854$	2.93847e10	0.00189043
$855$	6.49755e12	0.415817
$856$	6.03001e12	0.383872
$857$	−1.14217e13	−0.723298	−0.361649	−	0.932314i	$-0.617786\pi$
$857$	−1.14217e13	−0.723298	−0.361649	+	0.932314i	$0.617786\pi$
$858$	1.33676e13	0.842094
$859$	−2.00231e13	−1.25477	−0.627384	−	0.778710i	$-0.715874\pi$
$859$	−2.00231e13	−1.25477	−0.627384	+	0.778710i	$0.715874\pi$
$860$	−1.89200e12	−0.117945
$861$	8.83176e12	0.547688
$862$	−2.30050e13	−1.41919
$863$	−2.23182e13	−1.36965	−0.684826	−	0.728707i	$-0.740122\pi$
$863$	−2.23182e13	−1.36965	−0.684826	+	0.728707i	$0.740122\pi$
$864$	1.10808e12	0.0676484
$865$	−2.04326e13	−1.24094
$866$	−1.90360e13	−1.15012
$867$	0	0
$868$	−3.79488e11	−0.0226913
$869$	−1.68687e13	−1.00344
$870$	3.59215e13	2.12578
$871$	2.01457e13	1.18604
$872$	1.93764e13	1.13488
$873$	1.68987e13	0.984665
$874$	1.06679e13	0.618412
$875$	−5.38386e12	−0.310497
$876$	8.96894e12	0.514603
$877$	1.34536e13	0.767961	0.383980	−	0.923341i	$-0.374553\pi$
$877$	1.34536e13	0.767961	0.383980	+	0.923341i	$0.374553\pi$
$878$	−8.91299e12	−0.506172
$879$	1.77365e13	1.00212
$880$	−8.97537e12	−0.504522
$881$	−7.53546e12	−0.421423	−0.210711	−	0.977548i	$-0.567578\pi$
$881$	−7.53546e12	−0.421423	−0.210711	+	0.977548i	$0.567578\pi$
$882$	1.27762e13	0.710877
$883$	1.42293e13	0.787701	0.393851	−	0.919174i	$-0.371143\pi$
$883$	1.42293e13	0.787701	0.393851	+	0.919174i	$0.371143\pi$
$884$	0	0
$885$	−2.64773e13	−1.45087
$886$	3.77671e12	0.205903
$887$	1.65685e12	0.0898724	0.0449362	−	0.998990i	$-0.485692\pi$
$887$	1.65685e12	0.0898724	0.0449362	+	0.998990i	$0.485692\pi$
$888$	−2.39951e13	−1.29498
$889$	1.40978e12	0.0756996
$890$	−1.03281e13	−0.551780
$891$	−1.69881e13	−0.903015
$892$	1.76243e12	0.0932115
$893$	−1.31541e13	−0.692196
$894$	−4.60565e12	−0.241142
$895$	6.67032e12	0.347491
$896$	−2.48600e12	−0.128859
$897$	3.24061e13	1.67132
$898$	−1.66670e13	−0.855293
$899$	−1.15730e13	−0.590918
$900$	8.31168e11	0.0422277
$901$	0	0
$902$	−1.93818e13	−0.974910
$903$	3.98993e12	0.199696
$904$	2.07658e13	1.03417
$905$	−1.21287e13	−0.601030
$906$	9.39068e12	0.463042
$907$	3.50188e13	1.71818	0.859088	−	0.511827i	$-0.171031\pi$
$907$	3.50188e13	1.71818	0.859088	+	0.511827i	$0.171031\pi$
$908$	1.41713e12	0.0691870
$909$	1.53449e12	0.0745462
$910$	4.00405e12	0.193559
$911$	−1.95125e13	−0.938602	−0.469301	−	0.883038i	$-0.655494\pi$
$911$	−1.95125e13	−0.938602	−0.469301	+	0.883038i	$0.655494\pi$
$912$	−9.81295e12	−0.469702
$913$	2.69974e12	0.128589
$914$	1.75372e13	0.831194
$915$	−2.00605e11	−0.00946124
$916$	1.07400e13	0.504053
$917$	6.54125e12	0.305491
$918$	0	0
$919$	−2.07388e13	−0.959101	−0.479551	−	0.877514i	$-0.659200\pi$
$919$	−2.07388e13	−0.959101	−0.479551	+	0.877514i	$0.659200\pi$
$920$	−3.02423e13	−1.39178
$921$	5.09922e13	2.33526
$922$	1.10512e13	0.503638
$923$	−3.50988e13	−1.59179
$924$	−1.92896e12	−0.0870562
$925$	3.44747e12	0.154833
$926$	2.39363e13	1.06981
$927$	1.14741e13	0.510338
$928$	2.27048e13	1.00497
$929$	3.07061e13	1.35255	0.676275	−	0.736649i	$-0.263593\pi$
$929$	3.07061e13	1.35255	0.676275	+	0.736649i	$0.263593\pi$
$930$	−7.32138e12	−0.320937
$931$	−1.06588e13	−0.464980
$932$	3.61801e12	0.157072
$933$	−2.89124e13	−1.24916
$934$	−3.79356e11	−0.0163112
$935$	0	0
$936$	−1.96655e13	−0.837458
$937$	−7.44549e12	−0.315548	−0.157774	−	0.987475i	$-0.550432\pi$
$937$	−7.44549e12	−0.315548	−0.157774	+	0.987475i	$0.550432\pi$
$938$	8.21535e12	0.346508
$939$	7.08670e12	0.297474
$940$	7.72695e12	0.322799
$941$	3.25874e13	1.35487	0.677433	−	0.735584i	$-0.263092\pi$
$941$	3.25874e13	1.35487	0.677433	+	0.735584i	$0.263092\pi$
$942$	5.00681e13	2.07172
$943$	−4.69858e13	−1.93493
$944$	1.89798e13	0.777890
$945$	−8.59944e11	−0.0350774
$946$	−8.75613e12	−0.355469
$947$	−6.68319e12	−0.270028	−0.135014	−	0.990844i	$-0.543108\pi$
$947$	−6.68319e12	−0.270028	−0.135014	+	0.990844i	$0.543108\pi$
$948$	1.08337e13	0.435650
$949$	3.04884e13	1.22022
$950$	1.95960e12	0.0780568
$951$	2.61488e13	1.03667
$952$	0	0
$953$	−3.86643e13	−1.51842	−0.759211	−	0.650845i	$-0.774415\pi$
$953$	−3.86643e13	−1.51842	−0.759211	+	0.650845i	$0.774415\pi$
$954$	2.11165e13	0.825382
$955$	1.03671e13	0.403312
$956$	1.77660e12	0.0687908
$957$	−5.88263e13	−2.26709
$958$	3.82248e13	1.46622
$959$	9.79901e12	0.374109
$960$	3.64179e13	1.38387
$961$	−2.40809e13	−0.910787
$962$	−1.69016e13	−0.636268
$963$	8.53816e12	0.319923
$964$	1.09213e13	0.407313
$965$	−1.41500e12	−0.0525272
$966$	1.32151e13	0.488285
$967$	1.10388e13	0.405977	0.202989	−	0.979181i	$-0.434935\pi$
$967$	1.10388e13	0.405977	0.202989	+	0.979181i	$0.434935\pi$
$968$	−9.18431e12	−0.336207
$969$	0	0
$970$	−2.34033e13	−0.848798
$971$	−3.44849e13	−1.24492	−0.622461	−	0.782651i	$-0.713867\pi$
$971$	−3.44849e13	−1.24492	−0.622461	+	0.782651i	$0.713867\pi$
$972$	9.94169e12	0.357242
$973$	−4.15980e12	−0.148787
$974$	−2.61896e12	−0.0932424
$975$	5.95270e12	0.210956
$976$	1.43801e11	0.00507268
$977$	6.46911e11	0.0227153	0.0113577	−	0.999935i	$-0.496385\pi$
$977$	6.46911e11	0.0227153	0.0113577	+	0.999935i	$0.496385\pi$
$978$	−3.60573e13	−1.26028
$979$	1.69137e13	0.588459
$980$	6.26116e12	0.216839
$981$	2.74359e13	0.945820
$982$	−4.08343e13	−1.40128
$983$	−1.22767e13	−0.419362	−0.209681	−	0.977770i	$-0.567243\pi$
$983$	−1.22767e13	−0.419362	−0.209681	+	0.977770i	$0.567243\pi$
$984$	6.00726e13	2.04267
$985$	1.36475e13	0.461946
$986$	0	0
$987$	−1.62949e13	−0.546544
$988$	3.39954e12	0.113505
$989$	−2.12268e13	−0.705508
$990$	−1.76639e13	−0.584426
$991$	4.66226e12	0.153555	0.0767776	−	0.997048i	$-0.475537\pi$
$991$	4.66226e12	0.153555	0.0767776	+	0.997048i	$0.475537\pi$
$992$	−4.62760e12	−0.151724
$993$	4.83953e13	1.57954
$994$	−1.43132e13	−0.465048
$995$	−2.63102e13	−0.850983
$996$	−1.73387e12	−0.0558275
$997$	−3.32746e12	−0.106656	−0.0533279	−	0.998577i	$-0.516983\pi$
$997$	−3.32746e12	−0.106656	−0.0533279	+	0.998577i	$0.516983\pi$
$998$	−3.22493e12	−0.102904
$999$	3.62993e12	0.115306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.d.1.4	✓	12
17.16	even	2		289.10.a.e.1.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.4	✓	12	1.1	even	1	trivial
289.10.a.e.1.4	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)

\(f(q)\)	\(=\)	\(q-19.4468 q^{2} +193.562 q^{3} -133.821 q^{4} +1266.43 q^{5} -3764.16 q^{6} +1846.43 q^{7} +12559.2 q^{8} +17783.1 q^{9} +O(q^{10})\)	\(q-19.4468 q^{2} +193.562 q^{3} -133.821 q^{4} +1266.43 q^{5} -3764.16 q^{6} +1846.43 q^{7} +12559.2 q^{8} +17783.1 q^{9} -24628.1 q^{10} +40331.9 q^{11} -25902.6 q^{12} -88051.4 q^{13} -35907.1 q^{14} +245133. q^{15} -175720. q^{16} -345824. q^{18} +288509. q^{19} -169475. q^{20} +357397. q^{21} -784328. q^{22} -1.90139e6 q^{23} +2.43097e6 q^{24} -349267. q^{25} +1.71232e6 q^{26} -367752. q^{27} -247090. q^{28} -7.53535e6 q^{29} -4.76706e6 q^{30} +1.53583e6 q^{31} -3.01310e6 q^{32} +7.80671e6 q^{33} +2.33838e6 q^{35} -2.37975e6 q^{36} -9.87058e6 q^{37} -5.61059e6 q^{38} -1.70434e7 q^{39} +1.59054e7 q^{40} +2.47113e7 q^{41} -6.95024e6 q^{42} +1.11639e7 q^{43} -5.39725e6 q^{44} +2.25211e7 q^{45} +3.69760e7 q^{46} -4.55933e7 q^{47} -3.40126e7 q^{48} -3.69443e7 q^{49} +6.79214e6 q^{50} +1.17831e7 q^{52} -6.10614e7 q^{53} +7.15162e6 q^{54} +5.10778e7 q^{55} +2.31896e7 q^{56} +5.58443e7 q^{57} +1.46539e8 q^{58} -1.08012e8 q^{59} -3.28039e7 q^{60} -818353. q^{61} -2.98670e7 q^{62} +3.28351e7 q^{63} +1.48564e8 q^{64} -1.11511e8 q^{65} -1.51816e8 q^{66} -2.28794e8 q^{67} -3.68036e8 q^{69} -4.54740e7 q^{70} +3.98617e8 q^{71} +2.23341e8 q^{72} -3.46257e8 q^{73} +1.91951e8 q^{74} -6.76047e7 q^{75} -3.86086e7 q^{76} +7.44699e7 q^{77} +3.31440e8 q^{78} -4.18246e8 q^{79} -2.22538e8 q^{80} -4.21207e8 q^{81} -4.80557e8 q^{82} +6.69380e7 q^{83} -4.78272e7 q^{84} -2.17102e8 q^{86} -1.45855e9 q^{87} +5.06535e8 q^{88} +4.19362e8 q^{89} -4.37964e8 q^{90} -1.62580e8 q^{91} +2.54445e8 q^{92} +2.97277e8 q^{93} +8.86645e8 q^{94} +3.65378e8 q^{95} -5.83221e8 q^{96} +9.50267e8 q^{97} +7.18450e8 q^{98} +7.17226e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 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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