LMFDB - Embedded newform 289.10.a.i.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-26.9890 q^{2} -111.659 q^{3} +216.409 q^{4} -2126.40 q^{5} +3013.56 q^{6} -8475.21 q^{7} +7977.73 q^{8} -7215.34 q^{9} +O(q^{10})$	\(q-26.9890 q^{2} -111.659 q^{3} +216.409 q^{4} -2126.40 q^{5} +3013.56 q^{6} -8475.21 q^{7} +7977.73 q^{8} -7215.34 q^{9} +57389.5 q^{10} -7768.93 q^{11} -24163.9 q^{12} +188698. q^{13} +228738. q^{14} +237431. q^{15} -326113. q^{16} +194735. q^{18} +117938. q^{19} -460172. q^{20} +946331. q^{21} +209676. q^{22} +1.84165e6 q^{23} -890782. q^{24} +2.56845e6 q^{25} -5.09279e6 q^{26} +3.00343e6 q^{27} -1.83411e6 q^{28} -5.18387e6 q^{29} -6.40804e6 q^{30} -4.70232e6 q^{31} +4.71687e6 q^{32} +867468. q^{33} +1.80217e7 q^{35} -1.56146e6 q^{36} +337590. q^{37} -3.18303e6 q^{38} -2.10698e7 q^{39} -1.69638e7 q^{40} -1.68128e7 q^{41} -2.55406e7 q^{42} -1.06248e7 q^{43} -1.68126e6 q^{44} +1.53427e7 q^{45} -4.97043e7 q^{46} +9.90984e6 q^{47} +3.64133e7 q^{48} +3.14756e7 q^{49} -6.93202e7 q^{50} +4.08360e7 q^{52} +8.09197e7 q^{53} -8.10598e7 q^{54} +1.65199e7 q^{55} -6.76129e7 q^{56} -1.31688e7 q^{57} +1.39908e8 q^{58} +3.54248e7 q^{59} +5.13822e7 q^{60} +1.51754e7 q^{61} +1.26911e8 q^{62} +6.11516e7 q^{63} +3.96658e7 q^{64} -4.01248e8 q^{65} -2.34121e7 q^{66} -1.17520e8 q^{67} -2.05636e8 q^{69} -4.86388e8 q^{70} -3.17626e8 q^{71} -5.75620e7 q^{72} +1.04290e8 q^{73} -9.11124e6 q^{74} -2.86790e8 q^{75} +2.55228e7 q^{76} +6.58433e7 q^{77} +5.68654e8 q^{78} -1.97824e8 q^{79} +6.93446e8 q^{80} -1.93340e8 q^{81} +4.53760e8 q^{82} +1.02741e7 q^{83} +2.04794e8 q^{84} +2.86754e8 q^{86} +5.78823e8 q^{87} -6.19784e7 q^{88} -9.95387e8 q^{89} -4.14085e8 q^{90} -1.59926e9 q^{91} +3.98549e8 q^{92} +5.25054e8 q^{93} -2.67457e8 q^{94} -2.50783e8 q^{95} -5.26679e8 q^{96} +2.90283e8 q^{97} -8.49497e8 q^{98} +5.60555e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

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 $

$2$	−26.9890	−1.19276	−0.596379	−	0.802703i	$-0.703395\pi$
$2$	−26.9890	−1.19276	−0.596379	+	0.802703i	$0.703395\pi$
$3$	−111.659	−0.795878	−0.397939	−	0.917412i	$-0.630275\pi$
$3$	−111.659	−0.795878	−0.397939	+	0.917412i	$0.630275\pi$
$4$	216.409	0.422673
$5$	−2126.40	−1.52153	−0.760764	−	0.649028i	$-0.775176\pi$
$5$	−2126.40	−1.52153	−0.760764	+	0.649028i	$0.775176\pi$
$6$	3013.56	0.949291
$7$	−8475.21	−1.33416	−0.667082	−	0.744984i	$-0.732457\pi$
$7$	−8475.21	−1.33416	−0.667082	+	0.744984i	$0.732457\pi$
$8$	7977.73	0.688611
$9$	−7215.34	−0.366577
$10$	57389.5	1.81482
$11$	−7768.93	−0.159990	−0.0799952	−	0.996795i	$-0.525491\pi$
$11$	−7768.93	−0.159990	−0.0799952	+	0.996795i	$0.525491\pi$
$12$	−24163.9	−0.336397
$13$	188698.	1.83241	0.916205	−	0.400709i	$-0.131236\pi$
$13$	188698.	1.83241	0.916205	+	0.400709i	$0.131236\pi$
$14$	228738.	1.59134
$15$	237431.	1.21095
$16$	−326113.	−1.24402
$17$	0	0
$17$	0	0
$18$	194735.	0.437238
$19$	117938.	0.207616	0.103808	−	0.994597i	$-0.466897\pi$
$19$	117938.	0.207616	0.103808	+	0.994597i	$0.466897\pi$
$20$	−460172.	−0.643109
$21$	946331.	1.06183
$22$	209676.	0.190830
$23$	1.84165e6	1.37224	0.686122	−	0.727486i	$-0.259311\pi$
$23$	1.84165e6	1.37224	0.686122	+	0.727486i	$0.259311\pi$
$24$	−890782.	−0.548051
$25$	2.56845e6	1.31505
$26$	−5.09279e6	−2.18562
$27$	3.00343e6	1.08763
$28$	−1.83411e6	−0.563916
$29$	−5.18387e6	−1.36101	−0.680507	−	0.732741i	$-0.738240\pi$
$29$	−5.18387e6	−1.36101	−0.680507	+	0.732741i	$0.738240\pi$
$30$	−6.40804e6	−1.44437
$31$	−4.70232e6	−0.914501	−0.457250	−	0.889338i	$-0.651166\pi$
$31$	−4.70232e6	−0.914501	−0.457250	+	0.889338i	$0.651166\pi$
$32$	4.71687e6	0.795205
$33$	867468.	0.127333
$34$	0	0
$35$	1.80217e7	2.02997
$36$	−1.56146e6	−0.154942
$37$	337590.	0.0296130	0.0148065	−	0.999890i	$-0.495287\pi$
$37$	337590.	0.0296130	0.0148065	+	0.999890i	$0.495287\pi$
$38$	−3.18303e6	−0.247636
$39$	−2.10698e7	−1.45838
$40$	−1.69638e7	−1.04774
$41$	−1.68128e7	−0.929205	−0.464603	−	0.885519i	$-0.653803\pi$
$41$	−1.68128e7	−0.929205	−0.464603	+	0.885519i	$0.653803\pi$
$42$	−2.55406e7	−1.26651
$43$	−1.06248e7	−0.473929	−0.236965	−	0.971518i	$-0.576153\pi$
$43$	−1.06248e7	−0.473929	−0.236965	+	0.971518i	$0.576153\pi$
$44$	−1.68126e6	−0.0676237
$45$	1.53427e7	0.557758
$46$	−4.97043e7	−1.63676
$47$	9.90984e6	0.296228	0.148114	−	0.988970i	$-0.452680\pi$
$47$	9.90984e6	0.296228	0.148114	+	0.988970i	$0.452680\pi$
$48$	3.64133e7	0.990089
$49$	3.14756e7	0.779995
$50$	−6.93202e7	−1.56854
$51$	0	0
$52$	4.08360e7	0.774511
$53$	8.09197e7	1.40868	0.704341	−	0.709862i	$-0.251243\pi$
$53$	8.09197e7	1.40868	0.704341	+	0.709862i	$0.251243\pi$
$54$	−8.10598e7	−1.29728
$55$	1.65199e7	0.243430
$56$	−6.76129e7	−0.918721
$57$	−1.31688e7	−0.165237
$58$	1.39908e8	1.62336
$59$	3.54248e7	0.380604	0.190302	−	0.981726i	$-0.439053\pi$
$59$	3.54248e7	0.380604	0.190302	+	0.981726i	$0.439053\pi$
$60$	5.13822e7	0.511837
$61$	1.51754e7	0.140331	0.0701657	−	0.997535i	$-0.477647\pi$
$61$	1.51754e7	0.140331	0.0701657	+	0.997535i	$0.477647\pi$
$62$	1.26911e8	1.09078
$63$	6.11516e7	0.489075
$64$	3.96658e7	0.295533
$65$	−4.01248e8	−2.78806
$66$	−2.34121e7	−0.151878
$67$	−1.17520e8	−0.712486	−0.356243	−	0.934393i	$-0.615943\pi$
$67$	−1.17520e8	−0.712486	−0.356243	+	0.934393i	$0.615943\pi$
$68$	0	0
$69$	−2.05636e8	−1.09214
$70$	−4.86388e8	−2.42126
$71$	−3.17626e8	−1.48338	−0.741692	−	0.670740i	$-0.765976\pi$
$71$	−3.17626e8	−1.48338	−0.741692	+	0.670740i	$0.765976\pi$
$72$	−5.75620e7	−0.252429
$73$	1.04290e8	0.429824	0.214912	−	0.976633i	$-0.431053\pi$
$73$	1.04290e8	0.429824	0.214912	+	0.976633i	$0.431053\pi$
$74$	−9.11124e6	−0.0353211
$75$	−2.86790e8	−1.04662
$76$	2.55228e7	0.0877539
$77$	6.58433e7	0.213454
$78$	5.68654e8	1.73949
$79$	−1.97824e8	−0.571423	−0.285712	−	0.958316i	$-0.592230\pi$
$79$	−1.97824e8	−0.571423	−0.285712	+	0.958316i	$0.592230\pi$
$80$	6.93446e8	1.89281
$81$	−1.93340e8	−0.499044
$82$	4.53760e8	1.10832
$83$	1.02741e7	0.0237626	0.0118813	−	0.999929i	$-0.496218\pi$
$83$	1.02741e7	0.0237626	0.0118813	+	0.999929i	$0.496218\pi$
$84$	2.04794e8	0.448808
$85$	0	0
$86$	2.86754e8	0.565283
$87$	5.78823e8	1.08320
$88$	−6.19784e7	−0.110171
$89$	−9.95387e8	−1.68166	−0.840828	−	0.541303i	$-0.817931\pi$
$89$	−9.95387e8	−1.68166	−0.840828	+	0.541303i	$0.817931\pi$
$90$	−4.14085e8	−0.665271
$91$	−1.59926e9	−2.44474
$92$	3.98549e8	0.580011
$93$	5.25054e8	0.727832
$94$	−2.67457e8	−0.353329
$95$	−2.50783e8	−0.315894
$96$	−5.26679e8	−0.632887
$97$	2.90283e8	0.332926	0.166463	−	0.986048i	$-0.446765\pi$
$97$	2.90283e8	0.332926	0.166463	+	0.986048i	$0.446765\pi$
$98$	−8.49497e8	−0.930346
$99$	5.60555e7	0.0586489
$100$	5.55836e8	0.555836
$101$	−1.04616e8	−0.100035	−0.0500176	−	0.998748i	$-0.515928\pi$
$101$	−1.04616e8	−0.100035	−0.0500176	+	0.998748i	$0.515928\pi$
$102$	0	0
$103$	−2.89721e8	−0.253637	−0.126818	−	0.991926i	$-0.540477\pi$
$103$	−2.89721e8	−0.253637	−0.126818	+	0.991926i	$0.540477\pi$
$104$	1.50538e9	1.26182
$105$	−2.01228e9	−1.61561
$106$	−2.18395e9	−1.68022
$107$	2.59660e8	0.191504	0.0957520	−	0.995405i	$-0.469474\pi$
$107$	2.59660e8	0.191504	0.0957520	+	0.995405i	$0.469474\pi$
$108$	6.49969e8	0.459712
$109$	−8.72678e8	−0.592154	−0.296077	−	0.955164i	$-0.595679\pi$
$109$	−8.72678e8	−0.592154	−0.296077	+	0.955164i	$0.595679\pi$
$110$	−4.45855e8	−0.290353
$111$	−3.76949e7	−0.0235683
$112$	2.76387e9	1.65973
$113$	1.61677e9	0.932815	0.466408	−	0.884570i	$-0.345548\pi$
$113$	1.61677e9	0.932815	0.466408	+	0.884570i	$0.345548\pi$
$114$	3.55413e8	0.197088
$115$	−3.91608e9	−2.08791
$116$	−1.12183e9	−0.575264
$117$	−1.36152e9	−0.671720
$118$	−9.56082e8	−0.453969
$119$	0	0
$120$	1.89416e9	0.833875
$121$	−2.29759e9	−0.974403
$122$	−4.09569e8	−0.167382
$123$	1.87729e9	0.739535
$124$	−1.01762e9	−0.386535
$125$	−1.30844e9	−0.479356
$126$	−1.65042e9	−0.583348
$127$	−4.64829e9	−1.58554	−0.792769	−	0.609522i	$-0.791361\pi$
$127$	−4.64829e9	−1.58554	−0.792769	+	0.609522i	$0.791361\pi$
$128$	−3.48558e9	−1.14770
$129$	1.18635e9	0.377190
$130$	1.08293e10	3.32549
$131$	3.87389e9	1.14928	0.574641	−	0.818405i	$-0.305142\pi$
$131$	3.87389e9	1.14928	0.574641	+	0.818405i	$0.305142\pi$
$132$	1.87728e8	0.0538203
$133$	−9.99547e8	−0.276994
$134$	3.17176e9	0.849824
$135$	−6.38650e9	−1.65486
$136$	0	0
$137$	−2.81827e9	−0.683502	−0.341751	−	0.939790i	$-0.611020\pi$
$137$	−2.81827e9	−0.683502	−0.341751	+	0.939790i	$0.611020\pi$
$138$	5.54992e9	1.30266
$139$	−6.78367e9	−1.54134	−0.770670	−	0.637235i	$-0.780078\pi$
$139$	−6.78367e9	−1.54134	−0.770670	+	0.637235i	$0.780078\pi$
$140$	3.90005e9	0.858014
$141$	−1.10652e9	−0.235762
$142$	8.57243e9	1.76932
$143$	−1.46598e9	−0.293168
$144$	2.35301e9	0.456030
$145$	1.10230e10	2.07082
$146$	−2.81469e9	−0.512677
$147$	−3.51453e9	−0.620781
$148$	7.30575e7	0.0125166
$149$	−8.91855e9	−1.48237	−0.741184	−	0.671302i	$-0.765736\pi$
$149$	−8.91855e9	−1.48237	−0.741184	+	0.671302i	$0.765736\pi$
$150$	7.74020e9	1.24836
$151$	9.82516e9	1.53795	0.768977	−	0.639276i	$-0.220766\pi$
$151$	9.82516e9	1.53795	0.768977	+	0.639276i	$0.220766\pi$
$152$	9.40875e8	0.142967
$153$	0	0
$154$	−1.77705e9	−0.254599
$155$	9.99901e9	1.39144
$156$	−4.55969e9	−0.616417
$157$	−3.59938e8	−0.0472802	−0.0236401	−	0.999721i	$-0.507526\pi$
$157$	−3.59938e8	−0.0472802	−0.0236401	+	0.999721i	$0.507526\pi$
$158$	5.33909e9	0.681570
$159$	−9.03539e9	−1.12114
$160$	−1.00300e10	−1.20993
$161$	−1.56084e10	−1.83080
$162$	5.21805e9	0.595239
$163$	−2.33468e9	−0.259050	−0.129525	−	0.991576i	$-0.541345\pi$
$163$	−2.33468e9	−0.259050	−0.129525	+	0.991576i	$0.541345\pi$
$164$	−3.63843e9	−0.392750
$165$	−1.84459e9	−0.193741
$166$	−2.77289e8	−0.0283431
$167$	−1.41903e10	−1.41178	−0.705891	−	0.708321i	$-0.749453\pi$
$167$	−1.41903e10	−1.41178	−0.705891	+	0.708321i	$0.749453\pi$
$168$	7.54957e9	0.731190
$169$	2.50025e10	2.35773
$170$	0	0
$171$	−8.50961e8	−0.0761075
$172$	−2.29930e9	−0.200317
$173$	1.14445e10	0.971380	0.485690	−	0.874131i	$-0.338568\pi$
$173$	1.14445e10	0.971380	0.485690	+	0.874131i	$0.338568\pi$
$174$	−1.56219e10	−1.29200
$175$	−2.17682e10	−1.75449
$176$	2.53355e9	0.199031
$177$	−3.95549e9	−0.302915
$178$	2.68645e10	2.00581
$179$	1.03273e10	0.751883	0.375941	−	0.926643i	$-0.377319\pi$
$179$	1.03273e10	0.751883	0.375941	+	0.926643i	$0.377319\pi$
$180$	3.32030e9	0.235749
$181$	−7.53319e9	−0.521706	−0.260853	−	0.965379i	$-0.584004\pi$
$181$	−7.53319e9	−0.521706	−0.260853	+	0.965379i	$0.584004\pi$
$182$	4.31624e10	2.91598
$183$	−1.69446e9	−0.111687
$184$	1.46922e10	0.944943
$185$	−7.17852e8	−0.0450570
$186$	−1.41707e10	−0.868127
$187$	0	0
$188$	2.14458e9	0.125208
$189$	−2.54547e10	−1.45108
$190$	6.76839e9	0.376786
$191$	1.86443e10	1.01367	0.506834	−	0.862044i	$-0.330816\pi$
$191$	1.86443e10	1.01367	0.506834	+	0.862044i	$0.330816\pi$
$192$	−4.42903e9	−0.235208
$193$	2.71011e10	1.40598	0.702989	−	0.711200i	$-0.251848\pi$
$193$	2.71011e10	1.40598	0.702989	+	0.711200i	$0.251848\pi$
$194$	−7.83445e9	−0.397101
$195$	4.48028e10	2.21896
$196$	6.81160e9	0.329683
$197$	−1.57089e9	−0.0743101	−0.0371551	−	0.999310i	$-0.511830\pi$
$197$	−1.57089e9	−0.0743101	−0.0371551	+	0.999310i	$0.511830\pi$
$198$	−1.51288e9	−0.0699540
$199$	−1.15986e10	−0.524285	−0.262143	−	0.965029i	$-0.584429\pi$
$199$	−1.15986e10	−0.524285	−0.262143	+	0.965029i	$0.584429\pi$
$200$	2.04904e10	0.905558
$201$	1.31222e10	0.567052
$202$	2.82349e9	0.119318
$203$	4.39344e10	1.81582
$204$	0	0
$205$	3.57507e10	1.41381
$206$	7.81928e9	0.302527
$207$	−1.32881e10	−0.503034
$208$	−6.15369e10	−2.27956
$209$	−9.16250e8	−0.0332166
$210$	5.43095e10	1.92703
$211$	3.17418e10	1.10246	0.551228	−	0.834355i	$-0.314160\pi$
$211$	3.17418e10	1.10246	0.551228	+	0.834355i	$0.314160\pi$
$212$	1.75117e10	0.595412
$213$	3.54657e10	1.18059
$214$	−7.00797e9	−0.228418
$215$	2.25926e10	0.721097
$216$	2.39606e10	0.748954
$217$	3.98531e10	1.22009
$218$	2.35527e10	0.706297
$219$	−1.16449e10	−0.342088
$220$	3.57504e9	0.102891
$221$	0	0
$222$	1.01735e9	0.0281113
$223$	4.39482e10	1.19006	0.595030	−	0.803704i	$-0.297140\pi$
$223$	4.39482e10	1.19006	0.595030	+	0.803704i	$0.297140\pi$
$224$	−3.99765e10	−1.06093
$225$	−1.85323e10	−0.482067
$226$	−4.36351e10	−1.11262
$227$	3.84258e10	0.960520	0.480260	−	0.877126i	$-0.340542\pi$
$227$	3.84258e10	0.960520	0.480260	+	0.877126i	$0.340542\pi$
$228$	−2.84984e9	−0.0698414
$229$	−1.92884e10	−0.463487	−0.231744	−	0.972777i	$-0.574443\pi$
$229$	−1.92884e10	−0.463487	−0.231744	+	0.972777i	$0.574443\pi$
$230$	1.05691e11	2.49037
$231$	−7.35198e9	−0.169883
$232$	−4.13555e10	−0.937210
$233$	−7.60123e10	−1.68959	−0.844797	−	0.535087i	$-0.820279\pi$
$233$	−7.60123e10	−1.68959	−0.844797	+	0.535087i	$0.820279\pi$
$234$	3.67462e10	0.801200
$235$	−2.10723e10	−0.450720
$236$	7.66624e9	0.160871
$237$	2.20888e10	0.454784
$238$	0	0
$239$	2.69458e10	0.534196	0.267098	−	0.963669i	$-0.413935\pi$
$239$	2.69458e10	0.534196	0.267098	+	0.963669i	$0.413935\pi$
$240$	−7.74292e10	−1.50645
$241$	−7.71206e10	−1.47263	−0.736315	−	0.676639i	$-0.763436\pi$
$241$	−7.71206e10	−1.47263	−0.736315	+	0.676639i	$0.763436\pi$
$242$	6.20098e10	1.16223
$243$	−3.75285e10	−0.690452
$244$	3.28408e9	0.0593144
$245$	−6.69298e10	−1.18678
$246$	−5.06663e10	−0.882086
$247$	2.22546e10	0.380438
$248$	−3.75138e10	−0.629736
$249$	−1.14720e9	−0.0189122
$250$	3.53135e10	0.571756
$251$	−2.37776e10	−0.378125	−0.189063	−	0.981965i	$-0.560545\pi$
$251$	−2.37776e10	−0.378125	−0.189063	+	0.981965i	$0.560545\pi$
$252$	1.32337e10	0.206719
$253$	−1.43076e10	−0.219546
$254$	1.25453e11	1.89116
$255$	0	0
$256$	7.37636e10	1.07340
$257$	−4.21200e10	−0.602267	−0.301134	−	0.953582i	$-0.597365\pi$
$257$	−4.21200e10	−0.602267	−0.301134	+	0.953582i	$0.597365\pi$
$258$	−3.20185e10	−0.449897
$259$	−2.86115e9	−0.0395086
$260$	−8.68336e10	−1.17844
$261$	3.74034e10	0.498917
$262$	−1.04553e11	−1.37082
$263$	4.71166e10	0.607257	0.303629	−	0.952790i	$-0.401802\pi$
$263$	4.71166e10	0.607257	0.303629	+	0.952790i	$0.401802\pi$
$264$	6.92043e9	0.0876829
$265$	−1.72068e11	−2.14335
$266$	2.69768e10	0.330388
$267$	1.11144e11	1.33839
$268$	−2.54324e10	−0.301149
$269$	−5.69389e9	−0.0663015	−0.0331508	−	0.999450i	$-0.510554\pi$
$269$	−5.69389e9	−0.0663015	−0.0331508	+	0.999450i	$0.510554\pi$
$270$	1.72366e11	1.97385
$271$	−1.51533e11	−1.70666	−0.853328	−	0.521375i	$-0.825419\pi$
$271$	−1.51533e11	−1.70666	−0.853328	+	0.521375i	$0.825419\pi$
$272$	0	0
$273$	1.78571e11	1.94571
$274$	7.60624e10	0.815253
$275$	−1.99541e10	−0.210395
$276$	−4.45014e10	−0.461618
$277$	5.65276e10	0.576901	0.288451	−	0.957495i	$-0.406860\pi$
$277$	5.65276e10	0.576901	0.288451	+	0.957495i	$0.406860\pi$
$278$	1.83085e11	1.83845
$279$	3.39288e10	0.335235
$280$	1.43772e11	1.39786
$281$	−3.63183e10	−0.347493	−0.173747	−	0.984790i	$-0.555587\pi$
$281$	−3.63183e10	−0.347493	−0.173747	+	0.984790i	$0.555587\pi$
$282$	2.98639e10	0.281207
$283$	2.29141e10	0.212355	0.106178	−	0.994347i	$-0.466139\pi$
$283$	2.29141e10	0.212355	0.106178	+	0.994347i	$0.466139\pi$
$284$	−6.87371e10	−0.626987
$285$	2.80021e10	0.251413
$286$	3.95655e10	0.349679
$287$	1.42492e11	1.23971
$288$	−3.40338e10	−0.291504
$289$	0	0
$290$	−2.97500e11	−2.46999
$291$	−3.24126e10	−0.264969
$292$	2.25693e10	0.181675
$293$	7.83040e10	0.620697	0.310348	−	0.950623i	$-0.399554\pi$
$293$	7.83040e10	0.620697	0.310348	+	0.950623i	$0.399554\pi$
$294$	9.48537e10	0.740442
$295$	−7.53273e10	−0.579100
$296$	2.69320e9	0.0203918
$297$	−2.33335e10	−0.174010
$298$	2.40703e11	1.76811
$299$	3.47516e11	2.51452
$300$	−6.20639e10	−0.442378
$301$	9.00476e10	0.632300
$302$	−2.65172e11	−1.83441
$303$	1.16813e10	0.0796158
$304$	−3.84610e10	−0.258279
$305$	−3.22689e10	−0.213518
$306$	0	0
$307$	−9.62528e10	−0.618430	−0.309215	−	0.950992i	$-0.600066\pi$
$307$	−9.62528e10	−0.618430	−0.309215	+	0.950992i	$0.600066\pi$
$308$	1.42491e10	0.0902212
$309$	3.23498e10	0.201864
$310$	−2.69864e11	−1.65965
$311$	−2.06836e11	−1.25373	−0.626865	−	0.779128i	$-0.715662\pi$
$311$	−2.06836e11	−1.25373	−0.626865	+	0.779128i	$0.715662\pi$
$312$	−1.68089e11	−1.00425
$313$	−4.43872e10	−0.261402	−0.130701	−	0.991422i	$-0.541723\pi$
$313$	−4.43872e10	−0.261402	−0.130701	+	0.991422i	$0.541723\pi$
$314$	9.71439e9	0.0563939
$315$	−1.30033e11	−0.744141
$316$	−4.28109e10	−0.241525
$317$	1.67214e10	0.0930052	0.0465026	−	0.998918i	$-0.485192\pi$
$317$	1.67214e10	0.0930052	0.0465026	+	0.998918i	$0.485192\pi$
$318$	2.43857e11	1.33725
$319$	4.02731e10	0.217749
$320$	−8.43453e10	−0.449662
$321$	−2.89933e10	−0.152414
$322$	4.21255e11	2.18370
$323$	0	0
$324$	−4.18404e10	−0.210932
$325$	4.84663e11	2.40971
$326$	6.30107e10	0.308984
$327$	9.74420e10	0.471283
$328$	−1.34128e11	−0.639861
$329$	−8.39880e10	−0.395217
$330$	4.97836e10	0.231086
$331$	−2.85648e11	−1.30799	−0.653995	−	0.756499i	$-0.726908\pi$
$331$	−2.85648e11	−1.30799	−0.653995	+	0.756499i	$0.726908\pi$
$332$	2.22341e9	0.0100438
$333$	−2.43583e9	−0.0108554
$334$	3.82983e11	1.68391
$335$	2.49895e11	1.08407
$336$	−3.08610e11	−1.32094
$337$	1.51192e11	0.638549	0.319274	−	0.947662i	$-0.396561\pi$
$337$	1.51192e11	0.638549	0.319274	+	0.947662i	$0.396561\pi$
$338$	−6.74795e11	−2.81220
$339$	−1.80526e11	−0.742407
$340$	0	0
$341$	3.65320e10	0.146311
$342$	2.29666e10	0.0907779
$343$	7.52429e10	0.293523
$344$	−8.47619e10	−0.326353
$345$	4.37265e11	1.66172
$346$	−3.08876e11	−1.15862
$347$	3.16975e9	0.0117366	0.00586830	−	0.999983i	$-0.498132\pi$
$347$	3.16975e9	0.0117366	0.00586830	+	0.999983i	$0.498132\pi$
$348$	1.25262e11	0.457841
$349$	−1.16871e11	−0.421689	−0.210844	−	0.977520i	$-0.567621\pi$
$349$	−1.16871e11	−0.421689	−0.210844	+	0.977520i	$0.567621\pi$
$350$	5.87503e11	2.09269
$351$	5.66743e11	1.99298
$352$	−3.66450e10	−0.127225
$353$	6.42891e9	0.0220369	0.0110185	−	0.999939i	$-0.496493\pi$
$353$	6.42891e9	0.0220369	0.0110185	+	0.999939i	$0.496493\pi$
$354$	1.06755e11	0.361304
$355$	6.75401e11	2.25701
$356$	−2.15410e11	−0.710791
$357$	0	0
$358$	−2.78725e11	−0.896815
$359$	−4.93384e10	−0.156769	−0.0783846	−	0.996923i	$-0.524976\pi$
$359$	−4.93384e10	−0.156769	−0.0783846	+	0.996923i	$0.524976\pi$
$360$	1.22400e11	0.384079
$361$	−3.08778e11	−0.956895
$362$	2.03314e11	0.622269
$363$	2.56546e11	0.775506
$364$	−3.46093e11	−1.03333
$365$	−2.21763e11	−0.653990
$366$	4.57319e10	0.133215
$367$	−4.03374e11	−1.16068	−0.580338	−	0.814376i	$-0.697079\pi$
$367$	−4.03374e11	−1.16068	−0.580338	+	0.814376i	$0.697079\pi$
$368$	−6.00585e11	−1.70710
$369$	1.21310e11	0.340626
$370$	1.93741e10	0.0537421
$371$	−6.85812e11	−1.87941
$372$	1.13626e11	0.307635
$373$	−4.66959e10	−0.124908	−0.0624538	−	0.998048i	$-0.519893\pi$
$373$	−4.66959e10	−0.124908	−0.0624538	+	0.998048i	$0.519893\pi$
$374$	0	0
$375$	1.46098e11	0.381509
$376$	7.90580e10	0.203986
$377$	−9.78186e11	−2.49394
$378$	6.86999e11	1.73078
$379$	4.32289e10	0.107621	0.0538106	−	0.998551i	$-0.482863\pi$
$379$	4.32289e10	0.107621	0.0538106	+	0.998551i	$0.482863\pi$
$380$	−5.42716e10	−0.133520
$381$	5.19022e11	1.26190
$382$	−5.03192e11	−1.20906
$383$	−6.63545e11	−1.57571	−0.787854	−	0.615862i	$-0.788808\pi$
$383$	−6.63545e11	−1.57571	−0.787854	+	0.615862i	$0.788808\pi$
$384$	3.89195e11	0.913433
$385$	−1.40009e11	−0.324776
$386$	−7.31432e11	−1.67699
$387$	7.66617e10	0.173732
$388$	6.28197e10	0.140719
$389$	3.77536e11	0.835959	0.417979	−	0.908456i	$-0.362738\pi$
$389$	3.77536e11	0.835959	0.417979	+	0.908456i	$0.362738\pi$
$390$	−1.20919e12	−2.64668
$391$	0	0
$392$	2.51104e11	0.537114
$393$	−4.32554e11	−0.914690
$394$	4.23969e10	0.0886341
$395$	4.20654e11	0.869437
$396$	1.21309e10	0.0247893
$397$	−8.10743e11	−1.63805	−0.819023	−	0.573760i	$-0.805484\pi$
$397$	−8.10743e11	−1.63805	−0.819023	+	0.573760i	$0.805484\pi$
$398$	3.13036e11	0.625346
$399$	1.11608e11	0.220454
$400$	−8.37605e11	−1.63595
$401$	−7.54539e11	−1.45724	−0.728622	−	0.684916i	$-0.759839\pi$
$401$	−7.54539e11	−1.45724	−0.728622	+	0.684916i	$0.759839\pi$
$402$	−3.54155e11	−0.676357
$403$	−8.87319e11	−1.67574
$404$	−2.26398e10	−0.0422822
$405$	4.11118e11	0.759309
$406$	−1.18575e12	−2.16583
$407$	−2.62271e9	−0.00473779
$408$	0	0
$409$	4.84207e11	0.855611	0.427805	−	0.903871i	$-0.359287\pi$
$409$	4.84207e11	0.855611	0.427805	+	0.903871i	$0.359287\pi$
$410$	−9.64877e11	−1.68634
$411$	3.14684e11	0.543985
$412$	−6.26981e10	−0.107205
$413$	−3.00233e11	−0.507788
$414$	3.58634e11	0.599998
$415$	−2.18469e10	−0.0361555
$416$	8.90065e11	1.45714
$417$	7.57456e11	1.22672
$418$	2.47287e10	0.0396194
$419$	7.47691e10	0.118511	0.0592555	−	0.998243i	$-0.481127\pi$
$419$	7.47691e10	0.118511	0.0592555	+	0.998243i	$0.481127\pi$
$420$	−4.35475e11	−0.682875
$421$	−5.91134e11	−0.917100	−0.458550	−	0.888669i	$-0.651631\pi$
$421$	−5.91134e11	−0.917100	−0.458550	+	0.888669i	$0.651631\pi$
$422$	−8.56682e11	−1.31496
$423$	−7.15029e10	−0.108591
$424$	6.45556e11	0.970035
$425$	0	0
$426$	−9.57186e11	−1.40816
$427$	−1.28614e11	−0.187225
$428$	5.61927e10	0.0809436
$429$	1.63690e11	0.233326
$430$	−6.09753e11	−0.860094
$431$	−4.74524e11	−0.662386	−0.331193	−	0.943563i	$-0.607451\pi$
$431$	−4.74524e11	−0.662386	−0.331193	+	0.943563i	$0.607451\pi$
$432$	−9.79457e11	−1.35303
$433$	−1.35727e12	−1.85554	−0.927770	−	0.373153i	$-0.878277\pi$
$433$	−1.35727e12	−1.85554	−0.927770	+	0.373153i	$0.878277\pi$
$434$	−1.07560e12	−1.45528
$435$	−1.23081e12	−1.64812
$436$	−1.88855e11	−0.250288
$437$	2.17200e11	0.284900
$438$	3.14285e11	0.408028
$439$	5.54359e11	0.712362	0.356181	−	0.934417i	$-0.384079\pi$
$439$	5.54359e11	0.712362	0.356181	+	0.934417i	$0.384079\pi$
$440$	1.31791e11	0.167629
$441$	−2.27107e11	−0.285929
$442$	0	0
$443$	1.17232e12	1.44621	0.723103	−	0.690740i	$-0.242715\pi$
$443$	1.17232e12	1.44621	0.723103	+	0.690740i	$0.242715\pi$
$444$	−8.15750e9	−0.00996170
$445$	2.11659e12	2.55869
$446$	−1.18612e12	−1.41945
$447$	9.95834e11	1.17979
$448$	−3.36176e11	−0.394290
$449$	9.38348e11	1.08957	0.544786	−	0.838575i	$-0.316611\pi$
$449$	9.38348e11	1.08957	0.544786	+	0.838575i	$0.316611\pi$
$450$	5.00169e11	0.574990
$451$	1.30617e11	0.148664
$452$	3.49883e11	0.394276
$453$	−1.09706e12	−1.22402
$454$	−1.03708e12	−1.14567
$455$	3.40066e12	3.71974
$456$	−1.05057e11	−0.113784
$457$	−1.33793e12	−1.43487	−0.717433	−	0.696628i	$-0.754683\pi$
$457$	−1.33793e12	−1.43487	−0.717433	+	0.696628i	$0.754683\pi$
$458$	5.20577e11	0.552828
$459$	0	0
$460$	−8.47475e11	−0.882504
$461$	8.45027e11	0.871398	0.435699	−	0.900092i	$-0.356501\pi$
$461$	8.45027e11	0.871398	0.435699	+	0.900092i	$0.356501\pi$
$462$	1.98423e11	0.202630
$463$	−3.24656e11	−0.328328	−0.164164	−	0.986433i	$-0.552493\pi$
$463$	−3.24656e11	−0.328328	−0.164164	+	0.986433i	$0.552493\pi$
$464$	1.69052e12	1.69313
$465$	−1.11648e12	−1.10742
$466$	2.05150e12	2.01528
$467$	7.41373e11	0.721292	0.360646	−	0.932703i	$-0.382556\pi$
$467$	7.41373e11	0.721292	0.360646	+	0.932703i	$0.382556\pi$
$468$	−2.94645e11	−0.283918
$469$	9.96010e11	0.950574
$470$	5.68721e11	0.537600
$471$	4.01902e10	0.0376293
$472$	2.82609e11	0.262088
$473$	8.25435e10	0.0758242
$474$	−5.96156e11	−0.542447
$475$	3.02918e11	0.273026
$476$	0	0
$477$	−5.83864e11	−0.516391
$478$	−7.27242e11	−0.637167
$479$	3.31368e11	0.287608	0.143804	−	0.989606i	$-0.454067\pi$
$479$	3.31368e11	0.287608	0.143804	+	0.989606i	$0.454067\pi$
$480$	1.11993e12	0.962955
$481$	6.37027e10	0.0542631
$482$	2.08141e12	1.75649
$483$	1.74281e12	1.45709
$484$	−4.97219e11	−0.411854
$485$	−6.17257e11	−0.506557
$486$	1.01286e12	0.823542
$487$	−1.84180e12	−1.48375	−0.741877	−	0.670536i	$-0.766064\pi$
$487$	−1.84180e12	−1.48375	−0.741877	+	0.670536i	$0.766064\pi$
$488$	1.21065e11	0.0966338
$489$	2.60687e11	0.206172
$490$	1.80637e12	1.41555
$491$	−1.63755e12	−1.27153	−0.635767	−	0.771881i	$-0.719316\pi$
$491$	−1.63755e12	−1.27153	−0.635767	+	0.771881i	$0.719316\pi$
$492$	4.06262e11	0.312582
$493$	0	0
$494$	−6.00632e11	−0.453771
$495$	−1.19196e11	−0.0892360
$496$	1.53348e12	1.13766
$497$	2.69195e12	1.97908
$498$	3.09618e10	0.0225576
$499$	8.40100e11	0.606567	0.303283	−	0.952900i	$-0.401917\pi$
$499$	8.40100e11	0.606567	0.303283	+	0.952900i	$0.401917\pi$
$500$	−2.83157e11	−0.202611
$501$	1.58447e12	1.12361
$502$	6.41734e11	0.451012
$503$	8.41199e11	0.585926	0.292963	−	0.956124i	$-0.405359\pi$
$503$	8.41199e11	0.585926	0.292963	+	0.956124i	$0.405359\pi$
$504$	4.87850e11	0.336782
$505$	2.22456e11	0.152206
$506$	3.86150e11	0.261865
$507$	−2.79175e12	−1.87647
$508$	−1.00593e12	−0.670165
$509$	1.64594e12	1.08688	0.543442	−	0.839447i	$-0.317121\pi$
$509$	1.64594e12	1.08688	0.543442	+	0.839447i	$0.317121\pi$
$510$	0	0
$511$	−8.83882e11	−0.573456
$512$	−2.06193e11	−0.132605
$513$	3.54218e11	0.225810
$514$	1.13678e12	0.718359
$515$	6.16062e11	0.385915
$516$	2.56737e11	0.159428
$517$	−7.69889e10	−0.0473937
$518$	7.72197e10	0.0471242
$519$	−1.27788e12	−0.773101
$520$	−3.20105e12	−1.91989
$521$	3.51701e11	0.209124	0.104562	−	0.994518i	$-0.466656\pi$
$521$	3.51701e11	0.209124	0.104562	+	0.994518i	$0.466656\pi$
$522$	−1.00948e12	−0.595088
$523$	5.05119e11	0.295213	0.147607	−	0.989046i	$-0.452843\pi$
$523$	5.05119e11	0.295213	0.147607	+	0.989046i	$0.452843\pi$
$524$	8.38345e11	0.485771
$525$	2.43061e12	1.39636
$526$	−1.27163e12	−0.724311
$527$	0	0
$528$	−2.82892e11	−0.158405
$529$	1.59052e12	0.883055
$530$	4.64395e12	2.55650
$531$	−2.55602e11	−0.139521
$532$	−2.16311e11	−0.117078
$533$	−3.17254e12	−1.70269
$534$	−2.99966e12	−1.59638
$535$	−5.52141e11	−0.291379
$536$	−9.37545e11	−0.490626
$537$	−1.15314e12	−0.598407
$538$	1.53673e11	0.0790817
$539$	−2.44532e11	−0.124792
$540$	−1.38209e12	−0.699465
$541$	−2.41525e11	−0.121220	−0.0606099	−	0.998162i	$-0.519305\pi$
$541$	−2.41525e11	−0.121220	−0.0606099	+	0.998162i	$0.519305\pi$
$542$	4.08974e12	2.03563
$543$	8.41146e11	0.415214
$544$	0	0
$545$	1.85566e12	0.900979
$546$	−4.81946e12	−2.32077
$547$	−2.61893e12	−1.25078	−0.625389	−	0.780313i	$-0.715060\pi$
$547$	−2.61893e12	−1.25078	−0.625389	+	0.780313i	$0.715060\pi$
$548$	−6.09898e11	−0.288898
$549$	−1.09495e11	−0.0514423
$550$	5.38543e11	0.250951
$551$	−6.11373e11	−0.282569
$552$	−1.64051e12	−0.752060
$553$	1.67660e12	0.762373
$554$	−1.52563e12	−0.688104
$555$	8.01544e10	0.0358599
$556$	−1.46805e12	−0.651483
$557$	−1.90268e12	−0.837565	−0.418782	−	0.908087i	$-0.637543\pi$
$557$	−1.90268e12	−0.837565	−0.418782	+	0.908087i	$0.637543\pi$
$558$	−9.15707e11	−0.399855
$559$	−2.00488e12	−0.868433
$560$	−5.87710e12	−2.52532
$561$	0	0
$562$	9.80195e11	0.414476
$563$	2.77945e12	1.16593	0.582964	−	0.812498i	$-0.301893\pi$
$563$	2.77945e12	1.16593	0.582964	+	0.812498i	$0.301893\pi$
$564$	−2.39460e11	−0.0996501
$565$	−3.43790e12	−1.41930
$566$	−6.18429e11	−0.253289
$567$	1.63860e12	0.665806
$568$	−2.53394e12	−1.02148
$569$	−2.91719e12	−1.16670	−0.583350	−	0.812221i	$-0.698258\pi$
$569$	−2.91719e12	−1.16670	−0.583350	+	0.812221i	$0.698258\pi$
$570$	−7.55750e11	−0.299876
$571$	−1.08718e12	−0.427994	−0.213997	−	0.976834i	$-0.568648\pi$
$571$	−1.08718e12	−0.427994	−0.213997	+	0.976834i	$0.568648\pi$
$572$	−3.17252e11	−0.123914
$573$	−2.08180e12	−0.806756
$574$	−3.84572e12	−1.47868
$575$	4.73019e12	1.80457
$576$	−2.86202e11	−0.108336
$577$	7.13293e11	0.267902	0.133951	−	0.990988i	$-0.457233\pi$
$577$	7.13293e11	0.267902	0.133951	+	0.990988i	$0.457233\pi$
$578$	0	0
$579$	−3.02607e12	−1.11899
$580$	2.38547e12	0.875281
$581$	−8.70755e10	−0.0317032
$582$	8.74784e11	0.316044
$583$	−6.28660e11	−0.225376
$584$	8.31999e11	0.295982
$585$	2.89514e12	1.02204
$586$	−2.11335e12	−0.740341
$587$	−6.12219e11	−0.212831	−0.106416	−	0.994322i	$-0.533937\pi$
$587$	−6.12219e11	−0.212831	−0.106416	+	0.994322i	$0.533937\pi$
$588$	−7.60574e11	−0.262388
$589$	−5.54580e11	−0.189865
$590$	2.03301e12	0.690726
$591$	1.75404e11	0.0591418
$592$	−1.10092e11	−0.0368391
$593$	1.86289e12	0.618643	0.309322	−	0.950957i	$-0.399898\pi$
$593$	1.86289e12	0.618643	0.309322	+	0.950957i	$0.399898\pi$
$594$	6.29748e11	0.207552
$595$	0	0
$596$	−1.93005e12	−0.626558
$597$	1.29509e12	0.417267
$598$	−9.37912e12	−2.99921
$599$	5.47380e12	1.73727	0.868637	−	0.495449i	$-0.164996\pi$
$599$	5.47380e12	1.73727	0.868637	+	0.495449i	$0.164996\pi$
$600$	−2.28793e12	−0.720714
$601$	−4.44329e12	−1.38921	−0.694607	−	0.719389i	$-0.744422\pi$
$601$	−4.44329e12	−1.38921	−0.694607	+	0.719389i	$0.744422\pi$
$602$	−2.43030e12	−0.754181
$603$	8.47950e11	0.261181
$604$	2.12625e12	0.650052
$605$	4.88560e12	1.48258
$606$	−3.15267e11	−0.0949624
$607$	1.25061e12	0.373916	0.186958	−	0.982368i	$-0.440137\pi$
$607$	1.25061e12	0.373916	0.186958	+	0.982368i	$0.440137\pi$
$608$	5.56297e11	0.165098
$609$	−4.90565e12	−1.44517
$610$	8.70907e11	0.254676
$611$	1.86997e12	0.542812
$612$	0	0
$613$	6.34599e12	1.81521	0.907606	−	0.419823i	$-0.137908\pi$
$613$	6.34599e12	1.81521	0.907606	+	0.419823i	$0.137908\pi$
$614$	2.59777e12	0.737638
$615$	−3.99187e12	−1.12522
$616$	5.25280e11	0.146987
$617$	3.48028e12	0.966786	0.483393	−	0.875403i	$-0.339404\pi$
$617$	3.48028e12	0.966786	0.483393	+	0.875403i	$0.339404\pi$
$618$	−8.73091e11	−0.240775
$619$	2.75090e12	0.753125	0.376563	−	0.926391i	$-0.377106\pi$
$619$	2.75090e12	0.753125	0.376563	+	0.926391i	$0.377106\pi$
$620$	2.16387e12	0.588124
$621$	5.53127e12	1.49249
$622$	5.58230e12	1.49540
$623$	8.43612e12	2.24360
$624$	6.87112e12	1.81425
$625$	−2.23425e12	−0.585695
$626$	1.19797e12	0.311789
$627$	1.02307e11	0.0264364
$628$	−7.78938e10	−0.0199841
$629$	0	0
$630$	3.50946e12	0.887581
$631$	−3.13630e12	−0.787563	−0.393782	−	0.919204i	$-0.628833\pi$
$631$	−3.13630e12	−0.787563	−0.393782	+	0.919204i	$0.628833\pi$
$632$	−1.57819e12	−0.393489
$633$	−3.54425e12	−0.877421
$634$	−4.51296e11	−0.110933
$635$	9.88413e12	2.41244
$636$	−1.95534e12	−0.473876
$637$	5.93939e12	1.42927
$638$	−1.08693e12	−0.259722
$639$	2.29178e12	0.543775
$640$	7.41174e12	1.74627
$641$	3.99573e12	0.934836	0.467418	−	0.884036i	$-0.345184\pi$
$641$	3.99573e12	0.934836	0.467418	+	0.884036i	$0.345184\pi$
$642$	7.82501e11	0.181793
$643$	−4.46811e12	−1.03080	−0.515400	−	0.856950i	$-0.672357\pi$
$643$	−4.46811e12	−1.03080	−0.515400	+	0.856950i	$0.672357\pi$
$644$	−3.37779e12	−0.773830
$645$	−2.52266e12	−0.573905
$646$	0	0
$647$	−2.65786e12	−0.596297	−0.298148	−	0.954520i	$-0.596369\pi$
$647$	−2.65786e12	−0.596297	−0.298148	+	0.954520i	$0.596369\pi$
$648$	−1.54241e12	−0.343647
$649$	−2.75213e11	−0.0608930
$650$	−1.30806e13	−2.87420
$651$	−4.44995e12	−0.971047
$652$	−5.05245e11	−0.109493
$653$	1.39817e12	0.300919	0.150459	−	0.988616i	$-0.451925\pi$
$653$	1.39817e12	0.300919	0.150459	+	0.988616i	$0.451925\pi$
$654$	−2.62987e12	−0.562126
$655$	−8.23745e12	−1.74867
$656$	5.48285e12	1.15595
$657$	−7.52490e11	−0.157564
$658$	2.26676e12	0.471399
$659$	−3.25916e12	−0.673165	−0.336582	−	0.941654i	$-0.609271\pi$
$659$	−3.25916e12	−0.673165	−0.336582	+	0.941654i	$0.609271\pi$
$660$	−3.99184e11	−0.0818890
$661$	−3.38834e12	−0.690368	−0.345184	−	0.938535i	$-0.612183\pi$
$661$	−3.38834e12	−0.690368	−0.345184	+	0.938535i	$0.612183\pi$
$662$	7.70936e12	1.56012
$663$	0	0
$664$	8.19643e10	0.0163632
$665$	2.12544e12	0.421455
$666$	6.57407e10	0.0129479
$667$	−9.54686e12	−1.86764
$668$	−3.07090e12	−0.596722
$669$	−4.90719e12	−0.947143
$670$	−6.74444e12	−1.29303
$671$	−1.17896e11	−0.0224517
$672$	4.46372e12	0.844375
$673$	3.81702e12	0.717228	0.358614	−	0.933486i	$-0.383250\pi$
$673$	3.81702e12	0.717228	0.358614	+	0.933486i	$0.383250\pi$
$674$	−4.08052e12	−0.761634
$675$	7.71418e12	1.43029
$676$	5.41077e12	0.996549
$677$	9.52051e12	1.74185	0.870926	−	0.491414i	$-0.163520\pi$
$677$	9.52051e12	1.74185	0.870926	+	0.491414i	$0.163520\pi$
$678$	4.87224e12	0.885513
$679$	−2.46021e12	−0.444178
$680$	0	0
$681$	−4.29057e12	−0.764457
$682$	−9.85963e11	−0.174514
$683$	−3.65262e12	−0.642260	−0.321130	−	0.947035i	$-0.604063\pi$
$683$	−3.65262e12	−0.642260	−0.321130	+	0.947035i	$0.604063\pi$
$684$	−1.84155e11	−0.0321686
$685$	5.99277e12	1.03997
$686$	−2.03073e12	−0.350102
$687$	2.15372e12	0.368879
$688$	3.46489e12	0.589578
$689$	1.52694e13	2.58128
$690$	−1.18014e13	−1.98203
$691$	−7.17157e12	−1.19664	−0.598320	−	0.801258i	$-0.704165\pi$
$691$	−7.17157e12	−1.19664	−0.598320	+	0.801258i	$0.704165\pi$
$692$	2.47669e12	0.410577
$693$	−4.75082e11	−0.0782473
$694$	−8.55485e10	−0.0139989
$695$	1.44248e13	2.34519
$696$	4.61770e12	0.745905
$697$	0	0
$698$	3.15424e12	0.502973
$699$	8.48743e12	1.34471
$700$	−4.71083e12	−0.741577
$701$	2.77953e12	0.434750	0.217375	−	0.976088i	$-0.430251\pi$
$701$	2.77953e12	0.434750	0.217375	+	0.976088i	$0.430251\pi$
$702$	−1.52958e13	−2.37715
$703$	3.98146e10	0.00614814
$704$	−3.08161e11	−0.0472825
$705$	2.35290e12	0.358718
$706$	−1.73510e11	−0.0262847
$707$	8.86644e11	0.133463
$708$	−8.56002e11	−0.128034
$709$	2.42496e12	0.360410	0.180205	−	0.983629i	$-0.442324\pi$
$709$	2.42496e12	0.360410	0.180205	+	0.983629i	$0.442324\pi$
$710$	−1.82284e13	−2.69207
$711$	1.42737e12	0.209471
$712$	−7.94093e12	−1.15801
$713$	−8.66001e12	−1.25492
$714$	0	0
$715$	3.11727e12	0.446064
$716$	2.23493e12	0.317801
$717$	−3.00874e12	−0.425155
$718$	1.33160e12	0.186988
$719$	−1.26802e13	−1.76948	−0.884742	−	0.466081i	$-0.845666\pi$
$719$	−1.26802e13	−1.76948	−0.884742	+	0.466081i	$0.845666\pi$
$720$	−5.00345e12	−0.693862
$721$	2.45544e12	0.338393
$722$	8.33363e12	1.14135
$723$	8.61118e12	1.17203
$724$	−1.63025e12	−0.220511
$725$	−1.33145e13	−1.78980
$726$	−6.92393e12	−0.924992
$727$	3.80482e12	0.505160	0.252580	−	0.967576i	$-0.418721\pi$
$727$	3.80482e12	0.505160	0.252580	+	0.967576i	$0.418721\pi$
$728$	−1.27584e13	−1.68347
$729$	7.99589e12	1.04856
$730$	5.98517e12	0.780052
$731$	0	0
$732$	−3.66696e11	−0.0472070
$733$	−1.10980e13	−1.41996	−0.709979	−	0.704223i	$-0.751296\pi$
$733$	−1.10980e13	−1.41996	−0.709979	+	0.704223i	$0.751296\pi$
$734$	1.08867e13	1.38441
$735$	7.47329e12	0.944537
$736$	8.68682e12	1.09122
$737$	9.13007e11	0.113991
$738$	−3.27404e12	−0.406284
$739$	2.33123e12	0.287531	0.143765	−	0.989612i	$-0.454079\pi$
$739$	2.33123e12	0.287531	0.143765	+	0.989612i	$0.454079\pi$
$740$	−1.55349e11	−0.0190444
$741$	−2.48492e12	−0.302783
$742$	1.85094e13	2.24169
$743$	−1.09510e13	−1.31827	−0.659136	−	0.752024i	$-0.729078\pi$
$743$	−1.09510e13	−1.31827	−0.659136	+	0.752024i	$0.729078\pi$
$744$	4.18874e12	0.501193
$745$	1.89644e13	2.25547
$746$	1.26028e12	0.148985
$747$	−7.41315e10	−0.00871084
$748$	0	0
$749$	−2.20067e12	−0.255498
$750$	−3.94306e12	−0.455048
$751$	−4.36338e12	−0.500545	−0.250272	−	0.968175i	$-0.580520\pi$
$751$	−4.36338e12	−0.500545	−0.250272	+	0.968175i	$0.580520\pi$
$752$	−3.23172e12	−0.368514
$753$	2.65497e12	0.300942
$754$	2.64003e13	2.97467
$755$	−2.08922e13	−2.34004
$756$	−5.50863e12	−0.613331
$757$	5.31168e12	0.587896	0.293948	−	0.955821i	$-0.405031\pi$
$757$	5.31168e12	0.587896	0.293948	+	0.955821i	$0.405031\pi$
$758$	−1.16671e12	−0.128366
$759$	1.59757e12	0.174732
$760$	−2.00068e12	−0.217528
$761$	1.63902e13	1.77155	0.885777	−	0.464111i	$-0.153626\pi$
$761$	1.63902e13	1.77155	0.885777	+	0.464111i	$0.153626\pi$
$762$	−1.40079e13	−1.50514
$763$	7.39613e12	0.790031
$764$	4.03479e12	0.428450
$765$	0	0
$766$	1.79084e13	1.87944
$767$	6.68460e12	0.697423
$768$	−8.23634e12	−0.854297
$769$	1.34189e13	1.38372	0.691859	−	0.722033i	$-0.256792\pi$
$769$	1.34189e13	1.38372	0.691859	+	0.722033i	$0.256792\pi$
$770$	3.77872e12	0.387379
$771$	4.70306e12	0.479331
$772$	5.86491e12	0.594270
$773$	−5.22917e12	−0.526775	−0.263387	−	0.964690i	$-0.584840\pi$
$773$	−5.22917e12	−0.526775	−0.263387	+	0.964690i	$0.584840\pi$
$774$	−2.06903e12	−0.207220
$775$	−1.20777e13	−1.20261
$776$	2.31579e12	0.229257
$777$	3.19472e11	0.0314440
$778$	−1.01893e13	−0.997097
$779$	−1.98286e12	−0.192918
$780$	9.69572e12	0.937896
$781$	2.46762e12	0.237327
$782$	0	0
$783$	−1.55694e13	−1.48028
$784$	−1.02646e13	−0.970330
$785$	7.65373e11	0.0719382
$786$	1.16742e13	1.09100
$787$	6.84661e12	0.636194	0.318097	−	0.948058i	$-0.396956\pi$
$787$	6.84661e12	0.636194	0.318097	+	0.948058i	$0.396956\pi$
$788$	−3.39955e11	−0.0314089
$789$	−5.26097e12	−0.483303
$790$	−1.13531e13	−1.03703
$791$	−1.37025e13	−1.24453
$792$	4.47195e11	0.0403863
$793$	2.86357e12	0.257145
$794$	2.18812e13	1.95379
$795$	1.92129e13	1.70585
$796$	−2.51004e12	−0.221601
$797$	−1.71243e13	−1.50332	−0.751658	−	0.659553i	$-0.770745\pi$
$797$	−1.71243e13	−1.50332	−0.751658	+	0.659553i	$0.770745\pi$
$798$	−3.01220e12	−0.262948
$799$	0	0
$800$	1.21151e13	1.04573
$801$	7.18206e12	0.616457
$802$	2.03643e13	1.73814
$803$	−8.10224e11	−0.0687678
$804$	2.83975e12	0.239678
$805$	3.31896e13	2.78561
$806$	2.39479e13	1.99875
$807$	6.35772e11	0.0527680
$808$	−8.34599e11	−0.0688853
$809$	−1.37472e13	−1.12836	−0.564178	−	0.825653i	$-0.690807\pi$
$809$	−1.37472e13	−1.12836	−0.564178	+	0.825653i	$0.690807\pi$
$810$	−1.10957e13	−0.905672
$811$	−4.44088e12	−0.360475	−0.180237	−	0.983623i	$-0.557687\pi$
$811$	−4.44088e12	−0.360475	−0.180237	+	0.983623i	$0.557687\pi$
$812$	9.50778e12	0.767497
$813$	1.69200e13	1.35829
$814$	7.07846e10	0.00565104
$815$	4.96446e12	0.394151
$816$	0	0
$817$	−1.25307e12	−0.0983955
$818$	−1.30683e13	−1.02054
$819$	1.15392e13	0.896185
$820$	7.73676e12	0.597581
$821$	−3.20955e12	−0.246547	−0.123274	−	0.992373i	$-0.539339\pi$
$821$	−3.20955e12	−0.246547	−0.123274	+	0.992373i	$0.539339\pi$
$822$	−8.49303e12	−0.648843
$823$	1.82964e12	0.139016	0.0695081	−	0.997581i	$-0.477857\pi$
$823$	1.82964e12	0.139016	0.0695081	+	0.997581i	$0.477857\pi$
$824$	−2.31131e12	−0.174657
$825$	2.22805e12	0.167449
$826$	8.10299e12	0.605669
$827$	4.67524e12	0.347560	0.173780	−	0.984785i	$-0.444402\pi$
$827$	4.67524e12	0.347560	0.173780	+	0.984785i	$0.444402\pi$
$828$	−2.87567e12	−0.212619
$829$	−2.09218e13	−1.53852	−0.769260	−	0.638936i	$-0.779375\pi$
$829$	−2.09218e13	−1.53852	−0.769260	+	0.638936i	$0.779375\pi$
$830$	5.89628e11	0.0431248
$831$	−6.31179e12	−0.459143
$832$	7.48486e12	0.541538
$833$	0	0
$834$	−2.04430e13	−1.46318
$835$	3.01743e13	2.14807
$836$	−1.98285e11	−0.0140398
$837$	−1.41231e13	−0.994638
$838$	−2.01795e12	−0.141355
$839$	−2.22899e13	−1.55303	−0.776515	−	0.630098i	$-0.783015\pi$
$839$	−2.22899e13	−1.55303	−0.776515	+	0.630098i	$0.783015\pi$
$840$	−1.60534e13	−1.11253
$841$	1.23653e13	0.852360
$842$	1.59541e13	1.09388
$843$	4.05525e12	0.276563
$844$	6.86921e12	0.465979
$845$	−5.31654e13	−3.58735
$846$	1.92980e12	0.129522
$847$	1.94726e13	1.30001
$848$	−2.63889e13	−1.75243
$849$	−2.55855e12	−0.169009
$850$	0	0
$851$	6.21722e11	0.0406362
$852$	7.67509e12	0.499006
$853$	−1.82969e13	−1.18333	−0.591666	−	0.806183i	$-0.701530\pi$
$853$	−1.82969e13	−1.18333	−0.591666	+	0.806183i	$0.701530\pi$
$854$	3.47118e12	0.223315
$855$	1.80948e12	0.115800
$856$	2.07150e12	0.131872
$857$	2.46088e13	1.55839	0.779197	−	0.626780i	$-0.215627\pi$
$857$	2.46088e13	1.55839	0.779197	+	0.626780i	$0.215627\pi$
$858$	−4.41783e12	−0.278302
$859$	9.01006e12	0.564623	0.282311	−	0.959323i	$-0.408899\pi$
$859$	9.01006e12	0.564623	0.282311	+	0.959323i	$0.408899\pi$
$860$	4.88924e12	0.304788
$861$	−1.59104e13	−0.986661
$862$	1.28070e13	0.790066
$863$	2.76290e13	1.69557	0.847785	−	0.530339i	$-0.177935\pi$
$863$	2.76290e13	1.69557	0.847785	+	0.530339i	$0.177935\pi$
$864$	1.41668e13	0.864888
$865$	−2.43356e13	−1.47798
$866$	3.66314e13	2.21321
$867$	0	0
$868$	8.62456e12	0.515701
$869$	1.53688e12	0.0914223
$870$	3.32184e13	1.96581
$871$	−2.21759e13	−1.30557
$872$	−6.96198e12	−0.407764
$873$	−2.09449e12	−0.122043
$874$	−5.86202e12	−0.339817
$875$	1.10893e13	0.639540
$876$	−2.52006e12	−0.144591
$877$	1.67098e12	0.0953833	0.0476916	−	0.998862i	$-0.484814\pi$
$877$	1.67098e12	0.0953833	0.0476916	+	0.998862i	$0.484814\pi$
$878$	−1.49616e13	−0.849677
$879$	−8.74332e12	−0.493999
$880$	−5.38733e12	−0.302832
$881$	−2.17946e13	−1.21887	−0.609434	−	0.792837i	$-0.708603\pi$
$881$	−2.17946e13	−1.21887	−0.609434	+	0.792837i	$0.708603\pi$
$882$	6.12941e12	0.341044
$883$	−2.01668e13	−1.11639	−0.558193	−	0.829711i	$-0.688505\pi$
$883$	−2.01668e13	−1.11639	−0.558193	+	0.829711i	$0.688505\pi$
$884$	0	0
$885$	8.41095e12	0.460893
$886$	−3.16399e13	−1.72497
$887$	1.66457e13	0.902914	0.451457	−	0.892293i	$-0.350904\pi$
$887$	1.66457e13	0.902914	0.451457	+	0.892293i	$0.350904\pi$
$888$	−3.00719e11	−0.0162294
$889$	3.93953e13	2.11537
$890$	−5.71248e13	−3.05190
$891$	1.50204e12	0.0798422
$892$	9.51077e12	0.503007
$893$	1.16874e12	0.0615018
$894$	−2.68766e13	−1.40720
$895$	−2.19601e13	−1.14401
$896$	2.95410e13	1.53123
$897$	−3.88032e13	−2.00125
$898$	−2.53251e13	−1.29960
$899$	2.43762e13	1.24465
$900$	−4.01055e12	−0.203757
$901$	0	0
$902$	−3.52523e12	−0.177320
$903$	−1.00546e13	−0.503234
$904$	1.28982e13	0.642347
$905$	1.60186e13	0.793790
$906$	2.96087e13	1.45997
$907$	2.83791e13	1.39241	0.696204	−	0.717844i	$-0.254871\pi$
$907$	2.83791e13	1.39241	0.696204	+	0.717844i	$0.254871\pi$
$908$	8.31568e12	0.405986
$909$	7.54841e11	0.0366706
$910$	−9.17807e13	−4.43675
$911$	2.64888e13	1.27418	0.637088	−	0.770791i	$-0.280139\pi$
$911$	2.64888e13	1.27418	0.637088	+	0.770791i	$0.280139\pi$
$912$	4.29450e12	0.205559
$913$	−7.98191e10	−0.00380179
$914$	3.61095e13	1.71145
$915$	3.60310e12	0.169935
$916$	−4.17419e12	−0.195904
$917$	−3.28321e13	−1.53333
$918$	0	0
$919$	−3.71751e13	−1.71922	−0.859612	−	0.510947i	$-0.829295\pi$
$919$	−3.71751e13	−1.71922	−0.859612	+	0.510947i	$0.829295\pi$
$920$	−3.12414e13	−1.43776
$921$	1.07475e13	0.492195
$922$	−2.28065e13	−1.03937
$923$	−5.99355e13	−2.71817
$924$	−1.59103e12	−0.0718051
$925$	8.67085e11	0.0389425
$926$	8.76214e12	0.391616
$927$	2.09043e12	0.0929774
$928$	−2.44516e13	−1.08229
$929$	1.56182e13	0.687953	0.343977	−	0.938978i	$-0.388226\pi$
$929$	1.56182e13	0.687953	0.343977	+	0.938978i	$0.388226\pi$
$930$	3.01326e13	1.32088
$931$	3.71216e12	0.161940
$932$	−1.64497e13	−0.714146
$933$	2.30950e13	0.997816
$934$	−2.00090e13	−0.860327
$935$	0	0
$936$	−1.08619e13	−0.462554
$937$	−1.17488e13	−0.497927	−0.248964	−	0.968513i	$-0.580090\pi$
$937$	−1.17488e13	−0.497927	−0.248964	+	0.968513i	$0.580090\pi$
$938$	−2.68814e13	−1.13381
$939$	4.95621e12	0.208044
$940$	−4.56023e12	−0.190507
$941$	−6.72829e12	−0.279738	−0.139869	−	0.990170i	$-0.544668\pi$
$941$	−6.72829e12	−0.279738	−0.139869	+	0.990170i	$0.544668\pi$
$942$	−1.08470e12	−0.0448827
$943$	−3.09632e13	−1.27510
$944$	−1.15525e13	−0.473479
$945$	5.41270e13	2.20785
$946$	−2.22777e12	−0.0904399
$947$	−3.08477e13	−1.24637	−0.623186	−	0.782074i	$-0.714162\pi$
$947$	−3.08477e13	−1.24637	−0.623186	+	0.782074i	$0.714162\pi$
$948$	4.78021e12	0.192225
$949$	1.96794e13	0.787614
$950$	−8.17546e12	−0.325654
$951$	−1.86709e12	−0.0740208
$952$	0	0
$953$	1.93554e13	0.760123	0.380062	−	0.924961i	$-0.375903\pi$
$953$	1.93554e13	0.760123	0.380062	+	0.924961i	$0.375903\pi$
$954$	1.57579e13	0.615930
$955$	−3.96452e13	−1.54232
$956$	5.83131e12	0.225791
$957$	−4.49684e12	−0.173302
$958$	−8.94330e12	−0.343047
$959$	2.38854e13	0.911905
$960$	9.41788e12	0.357876
$961$	−4.32785e12	−0.163688
$962$	−1.71927e12	−0.0647228
$963$	−1.87354e12	−0.0702010
$964$	−1.66896e13	−0.622441
$965$	−5.76278e13	−2.13924
$966$	−4.70368e13	−1.73796
$967$	−3.72066e13	−1.36836	−0.684181	−	0.729312i	$-0.739840\pi$
$967$	−3.72066e13	−1.36836	−0.684181	+	0.729312i	$0.739840\pi$
$968$	−1.83296e13	−0.670985
$969$	0	0
$970$	1.66592e13	0.604200
$971$	4.17404e13	1.50685	0.753426	−	0.657533i	$-0.228400\pi$
$971$	4.17404e13	1.50685	0.753426	+	0.657533i	$0.228400\pi$
$972$	−8.12150e12	−0.291835
$973$	5.74931e13	2.05640
$974$	4.97084e13	1.76976
$975$	−5.41168e13	−1.91784
$976$	−4.94888e12	−0.174575
$977$	−3.20906e12	−0.112681	−0.0563407	−	0.998412i	$-0.517943\pi$
$977$	−3.20906e12	−0.112681	−0.0563407	+	0.998412i	$0.517943\pi$
$978$	−7.03569e12	−0.245913
$979$	7.73309e12	0.269049
$980$	−1.44842e13	−0.501622
$981$	6.29667e12	0.217070
$982$	4.41959e13	1.51663
$983$	−7.14967e12	−0.244228	−0.122114	−	0.992516i	$-0.538967\pi$
$983$	−7.14967e12	−0.244228	−0.122114	+	0.992516i	$0.538967\pi$
$984$	1.49765e13	0.509252
$985$	3.34034e12	0.113065
$986$	0	0
$987$	9.37799e12	0.314545
$988$	4.81610e12	0.160801
$989$	−1.95672e13	−0.650347
$990$	3.21700e12	0.106437
$991$	4.53035e13	1.49211	0.746053	−	0.665886i	$-0.231946\pi$
$991$	4.53035e13	1.49211	0.746053	+	0.665886i	$0.231946\pi$
$992$	−2.21802e13	−0.727216
$993$	3.18950e13	1.04100
$994$	−7.26532e13	−2.36056
$995$	2.46633e13	0.797715
$996$	−2.48263e11	−0.00799366
$997$	1.60620e13	0.514838	0.257419	−	0.966300i	$-0.417128\pi$
$997$	1.60620e13	0.514838	0.257419	+	0.966300i	$0.417128\pi$
$998$	−2.26735e13	−0.723488
$999$	1.01393e12	0.0322079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.11		52
17.3	odd	16		17.10.d.a.9.4	yes	52
17.6	odd	16		17.10.d.a.2.4	✓	52
17.16	even	2	inner	289.10.a.i.1.12		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.2.4	✓	52	17.6	odd	16
17.10.d.a.9.4	yes	52	17.3	odd	16
289.10.a.i.1.11		52	1.1	even	1	trivial
289.10.a.i.1.12		52	17.16	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-26.9890 q^{2} -111.659 q^{3} +216.409 q^{4} -2126.40 q^{5} +3013.56 q^{6} -8475.21 q^{7} +7977.73 q^{8} -7215.34 q^{9} +O(q^{10})\)	\(q-26.9890 q^{2} -111.659 q^{3} +216.409 q^{4} -2126.40 q^{5} +3013.56 q^{6} -8475.21 q^{7} +7977.73 q^{8} -7215.34 q^{9} +57389.5 q^{10} -7768.93 q^{11} -24163.9 q^{12} +188698. q^{13} +228738. q^{14} +237431. q^{15} -326113. q^{16} +194735. q^{18} +117938. q^{19} -460172. q^{20} +946331. q^{21} +209676. q^{22} +1.84165e6 q^{23} -890782. q^{24} +2.56845e6 q^{25} -5.09279e6 q^{26} +3.00343e6 q^{27} -1.83411e6 q^{28} -5.18387e6 q^{29} -6.40804e6 q^{30} -4.70232e6 q^{31} +4.71687e6 q^{32} +867468. q^{33} +1.80217e7 q^{35} -1.56146e6 q^{36} +337590. q^{37} -3.18303e6 q^{38} -2.10698e7 q^{39} -1.69638e7 q^{40} -1.68128e7 q^{41} -2.55406e7 q^{42} -1.06248e7 q^{43} -1.68126e6 q^{44} +1.53427e7 q^{45} -4.97043e7 q^{46} +9.90984e6 q^{47} +3.64133e7 q^{48} +3.14756e7 q^{49} -6.93202e7 q^{50} +4.08360e7 q^{52} +8.09197e7 q^{53} -8.10598e7 q^{54} +1.65199e7 q^{55} -6.76129e7 q^{56} -1.31688e7 q^{57} +1.39908e8 q^{58} +3.54248e7 q^{59} +5.13822e7 q^{60} +1.51754e7 q^{61} +1.26911e8 q^{62} +6.11516e7 q^{63} +3.96658e7 q^{64} -4.01248e8 q^{65} -2.34121e7 q^{66} -1.17520e8 q^{67} -2.05636e8 q^{69} -4.86388e8 q^{70} -3.17626e8 q^{71} -5.75620e7 q^{72} +1.04290e8 q^{73} -9.11124e6 q^{74} -2.86790e8 q^{75} +2.55228e7 q^{76} +6.58433e7 q^{77} +5.68654e8 q^{78} -1.97824e8 q^{79} +6.93446e8 q^{80} -1.93340e8 q^{81} +4.53760e8 q^{82} +1.02741e7 q^{83} +2.04794e8 q^{84} +2.86754e8 q^{86} +5.78823e8 q^{87} -6.19784e7 q^{88} -9.95387e8 q^{89} -4.14085e8 q^{90} -1.59926e9 q^{91} +3.98549e8 q^{92} +5.25054e8 q^{93} -2.67457e8 q^{94} -2.50783e8 q^{95} -5.26679e8 q^{96} +2.90283e8 q^{97} -8.49497e8 q^{98} +5.60555e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

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