LMFDB - Embedded newform 289.10.a.i.1.5

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			1.5
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)

$f(q)$	$=$	$q-37.3725 q^{2} -245.740 q^{3} +884.705 q^{4} -1549.27 q^{5} +9183.93 q^{6} -9379.03 q^{7} -13928.9 q^{8} +40705.3 q^{9} +O(q^{10})$	\(q-37.3725 q^{2} -245.740 q^{3} +884.705 q^{4} -1549.27 q^{5} +9183.93 q^{6} -9379.03 q^{7} -13928.9 q^{8} +40705.3 q^{9} +57900.2 q^{10} -31847.9 q^{11} -217408. q^{12} -3836.87 q^{13} +350518. q^{14} +380719. q^{15} +67590.2 q^{16} -1.52126e6 q^{18} +704878. q^{19} -1.37065e6 q^{20} +2.30481e6 q^{21} +1.19024e6 q^{22} -141435. q^{23} +3.42290e6 q^{24} +447119. q^{25} +143393. q^{26} -5.16603e6 q^{27} -8.29768e6 q^{28} +5.40375e6 q^{29} -1.42284e7 q^{30} +8.78788e6 q^{31} +4.60560e6 q^{32} +7.82631e6 q^{33} +1.45307e7 q^{35} +3.60122e7 q^{36} -294998. q^{37} -2.63431e7 q^{38} +942873. q^{39} +2.15797e7 q^{40} +1.41403e7 q^{41} -8.61364e7 q^{42} +1.87804e7 q^{43} -2.81760e7 q^{44} -6.30636e7 q^{45} +5.28577e6 q^{46} +2.19574e7 q^{47} -1.66096e7 q^{48} +4.76127e7 q^{49} -1.67099e7 q^{50} -3.39450e6 q^{52} +8.33595e7 q^{53} +1.93067e8 q^{54} +4.93411e7 q^{55} +1.30640e8 q^{56} -1.73217e8 q^{57} -2.01952e8 q^{58} +1.05044e8 q^{59} +3.36824e8 q^{60} +9.79774e6 q^{61} -3.28425e8 q^{62} -3.81776e8 q^{63} -2.06729e8 q^{64} +5.94435e6 q^{65} -2.92489e8 q^{66} +1.49532e8 q^{67} +3.47562e7 q^{69} -5.43048e8 q^{70} -7.01885e6 q^{71} -5.66981e8 q^{72} -9.11878e7 q^{73} +1.10248e7 q^{74} -1.09875e8 q^{75} +6.23609e8 q^{76} +2.98703e8 q^{77} -3.52375e7 q^{78} -8.25648e7 q^{79} -1.04716e8 q^{80} +4.68298e8 q^{81} -5.28458e8 q^{82} -5.73696e7 q^{83} +2.03907e9 q^{84} -7.01872e8 q^{86} -1.32792e9 q^{87} +4.43607e8 q^{88} -6.66119e7 q^{89} +2.35684e9 q^{90} +3.59861e7 q^{91} -1.25128e8 q^{92} -2.15954e9 q^{93} -8.20603e8 q^{94} -1.09205e9 q^{95} -1.13178e9 q^{96} -5.74571e8 q^{97} -1.77941e9 q^{98} -1.29638e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−37.3725	−1.65165	−0.825824	−	0.563928i	$-0.809289\pi$
$2$	−37.3725	−1.65165	−0.825824	+	0.563928i	$0.809289\pi$
$3$	−245.740	−1.75158	−0.875792	−	0.482690i	$-0.839660\pi$
$3$	−245.740	−1.75158	−0.875792	+	0.482690i	$0.839660\pi$
$4$	884.705	1.72794
$5$	−1549.27	−1.10857	−0.554284	−	0.832327i	$-0.687008\pi$
$5$	−1549.27	−1.10857	−0.554284	+	0.832327i	$0.687008\pi$
$6$	9183.93	2.89300
$7$	−9379.03	−1.47644	−0.738222	−	0.674558i	$-0.764334\pi$
$7$	−9379.03	−1.47644	−0.738222	+	0.674558i	$0.764334\pi$
$8$	−13928.9	−1.20230
$9$	40705.3	2.06804
$10$	57900.2	1.83096
$11$	−31847.9	−0.655864	−0.327932	−	0.944701i	$-0.606352\pi$
$11$	−31847.9	−0.655864	−0.327932	+	0.944701i	$0.606352\pi$
$12$	−217408.	−3.02663
$13$	−3836.87	−0.0372590	−0.0186295	−	0.999826i	$-0.505930\pi$
$13$	−3836.87	−0.0372590	−0.0186295	+	0.999826i	$0.505930\pi$
$14$	350518.	2.43856
$15$	380719.	1.94175
$16$	67590.2	0.257836
$17$	0	0
$17$	0	0
$18$	−1.52126e6	−3.41568
$19$	704878.	1.24086	0.620430	−	0.784262i	$-0.286958\pi$
$19$	704878.	1.24086	0.620430	+	0.784262i	$0.286958\pi$
$20$	−1.37065e6	−1.91554
$21$	2.30481e6	2.58611
$22$	1.19024e6	1.08326
$23$	−141435.	−0.105385	−0.0526927	−	0.998611i	$-0.516780\pi$
$23$	−141435.	−0.105385	−0.0526927	+	0.998611i	$0.516780\pi$
$24$	3.42290e6	2.10593
$25$	447119.	0.228925
$26$	143393.	0.0615388
$27$	−5.16603e6	−1.87077
$28$	−8.29768e6	−2.55121
$29$	5.40375e6	1.41874	0.709372	−	0.704834i	$-0.248978\pi$
$29$	5.40375e6	1.41874	0.709372	+	0.704834i	$0.248978\pi$
$30$	−1.42284e7	−3.20709
$31$	8.78788e6	1.70906	0.854528	−	0.519405i	$-0.173846\pi$
$31$	8.78788e6	1.70906	0.854528	+	0.519405i	$0.173846\pi$
$32$	4.60560e6	0.776445
$33$	7.82631e6	1.14880
$34$	0	0
$35$	1.45307e7	1.63674
$36$	3.60122e7	3.57345
$37$	−294998.	−0.0258768	−0.0129384	−	0.999916i	$-0.504119\pi$
$37$	−294998.	−0.0258768	−0.0129384	+	0.999916i	$0.504119\pi$
$38$	−2.63431e7	−2.04946
$39$	942873.	0.0652623
$40$	2.15797e7	1.33283
$41$	1.41403e7	0.781503	0.390752	−	0.920496i	$-0.372215\pi$
$41$	1.41403e7	0.781503	0.390752	+	0.920496i	$0.372215\pi$
$42$	−8.61364e7	−4.27135
$43$	1.87804e7	0.837717	0.418858	−	0.908052i	$-0.362430\pi$
$43$	1.87804e7	0.837717	0.418858	+	0.908052i	$0.362430\pi$
$44$	−2.81760e7	−1.13329
$45$	−6.30636e7	−2.29257
$46$	5.28577e6	0.174060
$47$	2.19574e7	0.656357	0.328179	−	0.944616i	$-0.393565\pi$
$47$	2.19574e7	0.656357	0.328179	+	0.944616i	$0.393565\pi$
$48$	−1.66096e7	−0.451622
$49$	4.76127e7	1.17989
$50$	−1.67099e7	−0.378103
$51$	0	0
$52$	−3.39450e6	−0.0643814
$53$	8.33595e7	1.45115	0.725577	−	0.688141i	$-0.241573\pi$
$53$	8.33595e7	1.45115	0.725577	+	0.688141i	$0.241573\pi$
$54$	1.93067e8	3.08985
$55$	4.93411e7	0.727070
$56$	1.30640e8	1.77513
$57$	−1.73217e8	−2.17347
$58$	−2.01952e8	−2.34327
$59$	1.05044e8	1.12860	0.564298	−	0.825571i	$-0.309147\pi$
$59$	1.05044e8	1.12860	0.564298	+	0.825571i	$0.309147\pi$
$60$	3.36824e8	3.35523
$61$	9.79774e6	0.0906028	0.0453014	−	0.998973i	$-0.485575\pi$
$61$	9.79774e6	0.0906028	0.0453014	+	0.998973i	$0.485575\pi$
$62$	−3.28425e8	−2.82276
$63$	−3.81776e8	−3.05335
$64$	−2.06729e8	−1.54025
$65$	5.94435e6	0.0413042
$66$	−2.92489e8	−1.89741
$67$	1.49532e8	0.906560	0.453280	−	0.891368i	$-0.350254\pi$
$67$	1.49532e8	0.906560	0.453280	+	0.891368i	$0.350254\pi$
$68$	0	0
$69$	3.47562e7	0.184591
$70$	−5.43048e8	−2.70332
$71$	−7.01885e6	−0.0327796	−0.0163898	−	0.999866i	$-0.505217\pi$
$71$	−7.01885e6	−0.0327796	−0.0163898	+	0.999866i	$0.505217\pi$
$72$	−5.66981e8	−2.48641
$73$	−9.11878e7	−0.375824	−0.187912	−	0.982186i	$-0.560172\pi$
$73$	−9.11878e7	−0.375824	−0.187912	+	0.982186i	$0.560172\pi$
$74$	1.10248e7	0.0427394
$75$	−1.09875e8	−0.400981
$76$	6.23609e8	2.14413
$77$	2.98703e8	0.968346
$78$	−3.52375e7	−0.107790
$79$	−8.25648e7	−0.238492	−0.119246	−	0.992865i	$-0.538048\pi$
$79$	−8.25648e7	−0.238492	−0.119246	+	0.992865i	$0.538048\pi$
$80$	−1.04716e8	−0.285829
$81$	4.68298e8	1.20876
$82$	−5.28458e8	−1.29077
$83$	−5.73696e7	−0.132688	−0.0663438	−	0.997797i	$-0.521133\pi$
$83$	−5.73696e7	−0.132688	−0.0663438	+	0.997797i	$0.521133\pi$
$84$	2.03907e9	4.46865
$85$	0	0
$86$	−7.01872e8	−1.38361
$87$	−1.32792e9	−2.48505
$88$	4.43607e8	0.788545
$89$	−6.66119e7	−0.112537	−0.0562687	−	0.998416i	$-0.517920\pi$
$89$	−6.66119e7	−0.112537	−0.0562687	+	0.998416i	$0.517920\pi$
$90$	2.35684e9	3.78651
$91$	3.59861e7	0.0550109
$92$	−1.25128e8	−0.182100
$93$	−2.15954e9	−2.99355
$94$	−8.20603e8	−1.08407
$95$	−1.09205e9	−1.37558
$96$	−1.13178e9	−1.36001
$97$	−5.74571e8	−0.658978	−0.329489	−	0.944159i	$-0.606876\pi$
$97$	−5.74571e8	−0.658978	−0.329489	+	0.944159i	$0.606876\pi$
$98$	−1.77941e9	−1.94876
$99$	−1.29638e9	−1.35636
$100$	3.95568e8	0.395568
$101$	−4.50136e8	−0.430425	−0.215213	−	0.976567i	$-0.569044\pi$
$101$	−4.50136e8	−0.430425	−0.215213	+	0.976567i	$0.569044\pi$
$102$	0	0
$103$	−7.34932e8	−0.643398	−0.321699	−	0.946842i	$-0.604254\pi$
$103$	−7.34932e8	−0.643398	−0.321699	+	0.946842i	$0.604254\pi$
$104$	5.34435e7	0.0447965
$105$	−3.57077e9	−2.86689
$106$	−3.11535e9	−2.39679
$107$	−1.23544e9	−0.911161	−0.455580	−	0.890195i	$-0.650568\pi$
$107$	−1.23544e9	−0.911161	−0.455580	+	0.890195i	$0.650568\pi$
$108$	−4.57041e9	−3.23257
$109$	3.55565e8	0.241268	0.120634	−	0.992697i	$-0.461507\pi$
$109$	3.55565e8	0.241268	0.120634	+	0.992697i	$0.461507\pi$
$110$	−1.84400e9	−1.20086
$111$	7.24929e7	0.0453254
$112$	−6.33931e8	−0.380681
$113$	7.14356e8	0.412156	0.206078	−	0.978536i	$-0.433930\pi$
$113$	7.14356e8	0.412156	0.206078	+	0.978536i	$0.433930\pi$
$114$	6.47355e9	3.58980
$115$	2.19121e8	0.116827
$116$	4.78073e9	2.45151
$117$	−1.56181e8	−0.0770533
$118$	−3.92577e9	−1.86404
$119$	0	0
$120$	−5.30300e9	−2.33457
$121$	−1.34366e9	−0.569842
$122$	−3.66166e8	−0.149644
$123$	−3.47484e9	−1.36887
$124$	7.77468e9	2.95315
$125$	2.33321e9	0.854790
$126$	1.42679e10	5.04306
$127$	1.03138e9	0.351806	0.175903	−	0.984407i	$-0.443715\pi$
$127$	1.03138e9	0.351806	0.175903	+	0.984407i	$0.443715\pi$
$128$	5.36792e9	1.76751
$129$	−4.61511e9	−1.46733
$130$	−2.22155e8	−0.0682200
$131$	5.41553e9	1.60665	0.803324	−	0.595543i	$-0.203063\pi$
$131$	5.41553e9	1.60665	0.803324	+	0.595543i	$0.203063\pi$
$132$	6.92398e9	1.98506
$133$	−6.61107e9	−1.83206
$134$	−5.58838e9	−1.49732
$135$	8.00358e9	2.07387
$136$	0	0
$137$	3.16964e9	0.768718	0.384359	−	0.923184i	$-0.374423\pi$
$137$	3.16964e9	0.768718	0.384359	+	0.923184i	$0.374423\pi$
$138$	−1.29893e9	−0.304880
$139$	7.17848e9	1.63104	0.815522	−	0.578726i	$-0.196450\pi$
$139$	7.17848e9	1.63104	0.815522	+	0.578726i	$0.196450\pi$
$140$	1.28554e10	2.82819
$141$	−5.39582e9	−1.14966
$142$	2.62312e8	0.0541403
$143$	1.22196e8	0.0244369
$144$	2.75128e9	0.533217
$145$	−8.37188e9	−1.57278
$146$	3.40792e9	0.620728
$147$	−1.17004e10	−2.06667
$148$	−2.60986e8	−0.0447136
$149$	9.84251e9	1.63594	0.817971	−	0.575260i	$-0.195099\pi$
$149$	9.84251e9	1.63594	0.817971	+	0.575260i	$0.195099\pi$
$150$	4.10631e9	0.662279
$151$	9.89807e9	1.54937	0.774683	−	0.632350i	$-0.217909\pi$
$151$	9.89807e9	1.54937	0.774683	+	0.632350i	$0.217909\pi$
$152$	−9.81819e9	−1.49189
$153$	0	0
$154$	−1.11633e10	−1.59937
$155$	−1.36148e10	−1.89461
$156$	8.34164e8	0.112769
$157$	−1.10838e9	−0.145593	−0.0727964	−	0.997347i	$-0.523192\pi$
$157$	−1.10838e9	−0.145593	−0.0727964	+	0.997347i	$0.523192\pi$
$158$	3.08565e9	0.393904
$159$	−2.04848e10	−2.54182
$160$	−7.13532e9	−0.860743
$161$	1.32652e9	0.155596
$162$	−1.75015e10	−1.99645
$163$	1.00573e10	1.11593	0.557967	−	0.829863i	$-0.311582\pi$
$163$	1.00573e10	1.11593	0.557967	+	0.829863i	$0.311582\pi$
$164$	1.25100e10	1.35039
$165$	−1.21251e10	−1.27352
$166$	2.14405e9	0.219153
$167$	−4.81504e6	−0.000479044 0	−0.000239522	−	1.00000i	$-0.500076\pi$
$167$	−4.81504e6	−0.000479044 0	−0.000239522		1.00000i	$0.500076\pi$
$168$	−3.21035e10	−3.10929
$169$	−1.05898e10	−0.998612
$170$	0	0
$171$	2.86923e10	2.56615
$172$	1.66151e10	1.44752
$173$	−7.29075e9	−0.618821	−0.309410	−	0.950929i	$-0.600132\pi$
$173$	−7.29075e9	−0.618821	−0.309410	+	0.950929i	$0.600132\pi$
$174$	4.96277e10	4.10443
$175$	−4.19354e9	−0.337994
$176$	−2.15261e9	−0.169106
$177$	−2.58136e10	−1.97683
$178$	2.48946e9	0.185872
$179$	−4.38658e9	−0.319365	−0.159682	−	0.987168i	$-0.551047\pi$
$179$	−4.38658e9	−0.319365	−0.159682	+	0.987168i	$0.551047\pi$
$180$	−5.57927e10	−3.96142
$181$	−9.95343e9	−0.689317	−0.344659	−	0.938728i	$-0.612005\pi$
$181$	−9.95343e9	−0.689317	−0.344659	+	0.938728i	$0.612005\pi$
$182$	−1.34489e9	−0.0908586
$183$	−2.40770e9	−0.158698
$184$	1.97003e9	0.126705
$185$	4.57032e8	0.0286863
$186$	8.07073e10	4.94430
$187$	0	0
$188$	1.94258e10	1.13415
$189$	4.84523e10	2.76208
$190$	4.08126e10	2.27197
$191$	−3.59313e9	−0.195354	−0.0976771	−	0.995218i	$-0.531141\pi$
$191$	−3.59313e9	−0.195354	−0.0976771	+	0.995218i	$0.531141\pi$
$192$	5.08016e10	2.69788
$193$	1.85484e10	0.962272	0.481136	−	0.876646i	$-0.340224\pi$
$193$	1.85484e10	0.962272	0.481136	+	0.876646i	$0.340224\pi$
$194$	2.14732e10	1.08840
$195$	−1.46077e9	−0.0723477
$196$	4.21232e10	2.03877
$197$	2.31892e10	1.09695	0.548477	−	0.836166i	$-0.315208\pi$
$197$	2.31892e10	1.09695	0.548477	+	0.836166i	$0.315208\pi$
$198$	4.84489e10	2.24022
$199$	2.35070e10	1.06257	0.531287	−	0.847192i	$-0.321709\pi$
$199$	2.35070e10	1.06257	0.531287	+	0.847192i	$0.321709\pi$
$200$	−6.22788e9	−0.275236
$201$	−3.67460e10	−1.58792
$202$	1.68227e10	0.710911
$203$	−5.06820e10	−2.09470
$204$	0	0
$205$	−2.19071e10	−0.866350
$206$	2.74663e10	1.06267
$207$	−5.75714e9	−0.217942
$208$	−2.59335e8	−0.00960673
$209$	−2.24489e10	−0.813835
$210$	1.33449e11	4.73508
$211$	2.50626e10	0.870474	0.435237	−	0.900316i	$-0.356665\pi$
$211$	2.50626e10	0.870474	0.435237	+	0.900316i	$0.356665\pi$
$212$	7.37485e10	2.50751
$213$	1.72481e9	0.0574162
$214$	4.61715e10	1.50492
$215$	−2.90960e10	−0.928667
$216$	7.19572e10	2.24922
$217$	−8.24218e10	−2.52333
$218$	−1.32884e10	−0.398489
$219$	2.24085e10	0.658286
$220$	4.36523e10	1.25633
$221$	0	0
$222$	−2.70924e9	−0.0748616
$223$	3.01971e10	0.817699	0.408850	−	0.912602i	$-0.365930\pi$
$223$	3.01971e10	0.817699	0.408850	+	0.912602i	$0.365930\pi$
$224$	−4.31960e10	−1.14638
$225$	1.82001e10	0.473426
$226$	−2.66973e10	−0.680737
$227$	−5.94304e10	−1.48557	−0.742783	−	0.669532i	$-0.766495\pi$
$227$	−5.94304e10	−1.48557	−0.742783	+	0.669532i	$0.766495\pi$
$228$	−1.53246e11	−3.75562
$229$	3.17019e10	0.761772	0.380886	−	0.924622i	$-0.375619\pi$
$229$	3.17019e10	0.761772	0.380886	+	0.924622i	$0.375619\pi$
$230$	−8.18909e9	−0.192957
$231$	−7.34033e10	−1.69614
$232$	−7.52685e10	−1.70576
$233$	7.42261e10	1.64989	0.824945	−	0.565212i	$-0.191206\pi$
$233$	7.42261e10	1.64989	0.824945	+	0.565212i	$0.191206\pi$
$234$	5.83687e9	0.127265
$235$	−3.40180e10	−0.727617
$236$	9.29333e10	1.95015
$237$	2.02895e10	0.417738
$238$	0	0
$239$	−5.76902e10	−1.14370	−0.571850	−	0.820358i	$-0.693774\pi$
$239$	−5.76902e10	−1.14370	−0.571850	+	0.820358i	$0.693774\pi$
$240$	2.57329e10	0.500654
$241$	−3.06790e10	−0.585820	−0.292910	−	0.956140i	$-0.594624\pi$
$241$	−3.06790e10	−0.585820	−0.292910	+	0.956140i	$0.594624\pi$
$242$	5.02159e10	0.941179
$243$	−1.33969e10	−0.246477
$244$	8.66811e9	0.156556
$245$	−7.37650e10	−1.30799
$246$	1.29863e11	2.26089
$247$	−2.70452e9	−0.0462332
$248$	−1.22406e11	−2.05480
$249$	1.40980e10	0.232413
$250$	−8.71981e10	−1.41181
$251$	6.41373e10	1.01995	0.509975	−	0.860189i	$-0.329655\pi$
$251$	6.41373e10	1.01995	0.509975	+	0.860189i	$0.329655\pi$
$252$	−3.37760e11	−5.27600
$253$	4.50440e9	0.0691185
$254$	−3.85454e10	−0.581060
$255$	0	0
$256$	−9.47673e10	−1.37905
$257$	9.19659e9	0.131501	0.0657503	−	0.997836i	$-0.479056\pi$
$257$	9.19659e9	0.131501	0.0657503	+	0.997836i	$0.479056\pi$
$258$	1.72478e11	2.42351
$259$	2.76680e9	0.0382057
$260$	5.25900e9	0.0713712
$261$	2.19961e11	2.93403
$262$	−2.02392e11	−2.65361
$263$	6.78885e10	0.874975	0.437487	−	0.899225i	$-0.355868\pi$
$263$	6.78885e10	0.874975	0.437487	+	0.899225i	$0.355868\pi$
$264$	−1.09012e11	−1.38120
$265$	−1.29146e11	−1.60870
$266$	2.47072e11	3.02592
$267$	1.63692e10	0.197119
$268$	1.32291e11	1.56648
$269$	1.36377e11	1.58802	0.794009	−	0.607906i	$-0.207990\pi$
$269$	1.36377e11	1.58802	0.794009	+	0.607906i	$0.207990\pi$
$270$	−2.99114e11	−3.42531
$271$	2.89117e10	0.325621	0.162810	−	0.986657i	$-0.447944\pi$
$271$	2.89117e10	0.325621	0.162810	+	0.986657i	$0.447944\pi$
$272$	0	0
$273$	−8.84324e9	−0.0963561
$274$	−1.18457e11	−1.26965
$275$	−1.42398e10	−0.150143
$276$	3.07490e10	0.318963
$277$	−1.70630e11	−1.74139	−0.870694	−	0.491825i	$-0.836330\pi$
$277$	−1.70630e11	−1.74139	−0.870694	+	0.491825i	$0.836330\pi$
$278$	−2.68278e11	−2.69391
$279$	3.57713e11	3.53440
$280$	−2.02397e11	−1.96785
$281$	7.62266e10	0.729336	0.364668	−	0.931138i	$-0.381182\pi$
$281$	7.62266e10	0.729336	0.364668	+	0.931138i	$0.381182\pi$
$282$	2.01655e11	1.89884
$283$	−7.83779e10	−0.726364	−0.363182	−	0.931718i	$-0.618310\pi$
$283$	−7.83779e10	−0.726364	−0.363182	+	0.931718i	$0.618310\pi$
$284$	−6.20961e9	−0.0566412
$285$	2.68360e11	2.40944
$286$	−4.56678e9	−0.0403611
$287$	−1.32622e11	−1.15385
$288$	1.87472e11	1.60572
$289$	0	0
$290$	3.12878e11	2.59767
$291$	1.41195e11	1.15426
$292$	−8.06744e10	−0.649401
$293$	4.34293e10	0.344253	0.172127	−	0.985075i	$-0.444936\pi$
$293$	4.34293e10	0.344253	0.172127	+	0.985075i	$0.444936\pi$
$294$	4.37272e11	3.41341
$295$	−1.62742e11	−1.25113
$296$	4.10901e9	0.0311117
$297$	1.64527e11	1.22697
$298$	−3.67840e11	−2.70200
$299$	5.42666e8	0.00392656
$300$	−9.72070e10	−0.692870
$301$	−1.76142e11	−1.23684
$302$	−3.69916e11	−2.55901
$303$	1.10617e11	0.753925
$304$	4.76429e10	0.319939
$305$	−1.51794e10	−0.100439
$306$	0	0
$307$	−2.26738e11	−1.45681	−0.728404	−	0.685148i	$-0.759738\pi$
$307$	−2.26738e11	−1.45681	−0.728404	+	0.685148i	$0.759738\pi$
$308$	2.64264e11	1.67324
$309$	1.80603e11	1.12697
$310$	5.08820e11	3.12922
$311$	2.50433e11	1.51799	0.758997	−	0.651094i	$-0.225690\pi$
$311$	2.50433e11	1.51799	0.758997	+	0.651094i	$0.225690\pi$
$312$	−1.31332e10	−0.0784649
$313$	1.81824e11	1.07078	0.535390	−	0.844605i	$-0.320165\pi$
$313$	1.81824e11	1.07078	0.535390	+	0.844605i	$0.320165\pi$
$314$	4.14229e10	0.240468
$315$	5.91475e11	3.38485
$316$	−7.30455e10	−0.412099
$317$	−3.08703e11	−1.71701	−0.858507	−	0.512802i	$-0.828607\pi$
$317$	−3.08703e11	−1.71701	−0.858507	+	0.512802i	$0.828607\pi$
$318$	7.65568e11	4.19819
$319$	−1.72098e11	−0.930504
$320$	3.20279e11	1.70747
$321$	3.03598e11	1.59597
$322$	−4.95754e10	−0.256989
$323$	0	0
$324$	4.14306e11	2.08866
$325$	−1.71553e9	−0.00852951
$326$	−3.75868e11	−1.84313
$327$	−8.73766e10	−0.422601
$328$	−1.96959e11	−0.939601
$329$	−2.05939e11	−0.969075
$330$	4.53145e11	2.10341
$331$	−2.42882e11	−1.11216	−0.556082	−	0.831127i	$-0.687696\pi$
$331$	−2.42882e11	−1.11216	−0.556082	+	0.831127i	$0.687696\pi$
$332$	−5.07552e10	−0.229276
$333$	−1.20080e10	−0.0535144
$334$	1.79950e8	0.000791213 0
$335$	−2.31665e11	−1.00498
$336$	1.55782e11	0.666794
$337$	1.17468e11	0.496117	0.248059	−	0.968745i	$-0.420207\pi$
$337$	1.17468e11	0.496117	0.248059	+	0.968745i	$0.420207\pi$
$338$	3.95767e11	1.64935
$339$	−1.75546e11	−0.721926
$340$	0	0
$341$	−2.79876e11	−1.12091
$342$	−1.07230e12	−4.23838
$343$	−6.80830e10	−0.265592
$344$	−2.61591e11	−1.00719
$345$	−5.38468e10	−0.204632
$346$	2.72474e11	1.02207
$347$	2.60408e11	0.964208	0.482104	−	0.876114i	$-0.339873\pi$
$347$	2.60408e11	0.964208	0.482104	+	0.876114i	$0.339873\pi$
$348$	−1.17482e12	−4.29402
$349$	−4.81285e11	−1.73655	−0.868276	−	0.496081i	$-0.834772\pi$
$349$	−4.81285e11	−1.73655	−0.868276	+	0.496081i	$0.834772\pi$
$350$	1.56723e11	0.558248
$351$	1.98213e10	0.0697030
$352$	−1.46679e11	−0.509243
$353$	1.13877e11	0.390347	0.195173	−	0.980769i	$-0.437473\pi$
$353$	1.13877e11	0.390347	0.195173	+	0.980769i	$0.437473\pi$
$354$	9.64721e11	3.26503
$355$	1.08741e10	0.0363384
$356$	−5.89319e10	−0.194458
$357$	0	0
$358$	1.63937e11	0.527478
$359$	4.78307e11	1.51978	0.759891	−	0.650050i	$-0.225252\pi$
$359$	4.78307e11	1.51978	0.759891	+	0.650050i	$0.225252\pi$
$360$	8.78408e11	2.75635
$361$	1.74165e11	0.539732
$362$	3.71985e11	1.13851
$363$	3.30191e11	0.998126
$364$	3.18371e10	0.0950555
$365$	1.41275e11	0.416626
$366$	8.99818e10	0.262114
$367$	3.77978e11	1.08760	0.543800	−	0.839215i	$-0.316985\pi$
$367$	3.77978e11	1.08760	0.543800	+	0.839215i	$0.316985\pi$
$368$	−9.55960e9	−0.0271722
$369$	5.75584e11	1.61618
$370$	−1.70804e10	−0.0473796
$371$	−7.81831e11	−2.14255
$372$	−1.91055e12	−5.17268
$373$	6.03744e10	0.161496	0.0807482	−	0.996735i	$-0.474269\pi$
$373$	6.03744e10	0.161496	0.0807482	+	0.996735i	$0.474269\pi$
$374$	0	0
$375$	−5.73365e11	−1.49724
$376$	−3.05843e11	−0.789139
$377$	−2.07335e10	−0.0528611
$378$	−1.81079e12	−4.56199
$379$	5.35886e11	1.33412	0.667062	−	0.745003i	$-0.267552\pi$
$379$	5.35886e11	1.33412	0.667062	+	0.745003i	$0.267552\pi$
$380$	−9.66140e11	−2.37692
$381$	−2.53453e11	−0.616218
$382$	1.34284e11	0.322656
$383$	6.19459e11	1.47102	0.735509	−	0.677514i	$-0.236943\pi$
$383$	6.19459e11	1.47102	0.735509	+	0.677514i	$0.236943\pi$
$384$	−1.31911e12	−3.09593
$385$	−4.62772e11	−1.07348
$386$	−6.93199e11	−1.58933
$387$	7.64462e11	1.73243
$388$	−5.08326e11	−1.13867
$389$	1.39515e10	0.0308921	0.0154460	−	0.999881i	$-0.495083\pi$
$389$	1.39515e10	0.0308921	0.0154460	+	0.999881i	$0.495083\pi$
$390$	5.45925e10	0.119493
$391$	0	0
$392$	−6.63194e11	−1.41858
$393$	−1.33082e12	−2.81418
$394$	−8.66640e11	−1.81178
$395$	1.27915e11	0.264384
$396$	−1.14691e12	−2.34370
$397$	−8.11705e11	−1.63999	−0.819995	−	0.572371i	$-0.806024\pi$
$397$	−8.11705e11	−1.63999	−0.819995	+	0.572371i	$0.806024\pi$
$398$	−8.78518e11	−1.75500
$399$	1.62461e12	3.20900
$400$	3.02208e10	0.0590251
$401$	6.78845e10	0.131106	0.0655528	−	0.997849i	$-0.479119\pi$
$401$	6.78845e10	0.131106	0.0655528	+	0.997849i	$0.479119\pi$
$402$	1.37329e12	2.62268
$403$	−3.37179e10	−0.0636778
$404$	−3.98238e11	−0.743749
$405$	−7.25521e11	−1.33999
$406$	1.89411e12	3.45970
$407$	9.39507e9	0.0169717
$408$	0	0
$409$	−3.62017e11	−0.639697	−0.319848	−	0.947469i	$-0.603632\pi$
$409$	−3.62017e11	−0.639697	−0.319848	+	0.947469i	$0.603632\pi$
$410$	8.18725e11	1.43090
$411$	−7.78908e11	−1.34647
$412$	−6.50198e11	−1.11175
$413$	−9.85215e11	−1.66631
$414$	2.15159e11	0.359963
$415$	8.88811e10	0.147093
$416$	−1.76711e10	−0.0289296
$417$	−1.76404e12	−2.85691
$418$	8.38971e11	1.34417
$419$	−5.23509e11	−0.829777	−0.414889	−	0.909872i	$-0.636179\pi$
$419$	−5.23509e11	−0.829777	−0.414889	+	0.909872i	$0.636179\pi$
$420$	−3.15908e12	−4.95381
$421$	−3.45685e11	−0.536303	−0.268152	−	0.963377i	$-0.586413\pi$
$421$	−3.45685e11	−0.536303	−0.268152	+	0.963377i	$0.586413\pi$
$422$	−9.36654e11	−1.43772
$423$	8.93782e11	1.35738
$424$	−1.16111e12	−1.74472
$425$	0	0
$426$	−6.44607e10	−0.0948313
$427$	−9.18933e10	−0.133770
$428$	−1.09300e12	−1.57443
$429$	−3.00285e10	−0.0428032
$430$	1.08739e12	1.53383
$431$	−3.61546e11	−0.504680	−0.252340	−	0.967639i	$-0.581200\pi$
$431$	−3.61546e11	−0.504680	−0.252340	+	0.967639i	$0.581200\pi$
$432$	−3.49173e11	−0.482351
$433$	−1.39065e12	−1.90118	−0.950588	−	0.310454i	$-0.899519\pi$
$433$	−1.39065e12	−1.90118	−0.950588	+	0.310454i	$0.899519\pi$
$434$	3.08031e12	4.16765
$435$	2.05731e12	2.75485
$436$	3.14570e11	0.416896
$437$	−9.96941e10	−0.130769
$438$	−8.37463e11	−1.08726
$439$	5.58212e11	0.717313	0.358656	−	0.933470i	$-0.383235\pi$
$439$	5.58212e11	0.717313	0.358656	+	0.933470i	$0.383235\pi$
$440$	−6.87268e11	−0.874157
$441$	1.93809e12	2.44006
$442$	0	0
$443$	1.13238e12	1.39693	0.698463	−	0.715646i	$-0.253868\pi$
$443$	1.13238e12	1.39693	0.698463	+	0.715646i	$0.253868\pi$
$444$	6.41348e10	0.0783196
$445$	1.03200e11	0.124755
$446$	−1.12854e12	−1.35055
$447$	−2.41870e12	−2.86549
$448$	1.93892e12	2.27409
$449$	8.27212e11	0.960524	0.480262	−	0.877125i	$-0.340542\pi$
$449$	8.27212e11	0.960524	0.480262	+	0.877125i	$0.340542\pi$
$450$	−6.80183e11	−0.781933
$451$	−4.50338e11	−0.512560
$452$	6.31995e11	0.712181
$453$	−2.43235e12	−2.71384
$454$	2.22106e12	2.45363
$455$	−5.57523e10	−0.0609833
$456$	2.41273e12	2.61316
$457$	1.17863e12	1.26402	0.632011	−	0.774960i	$-0.282230\pi$
$457$	1.17863e12	1.26402	0.632011	+	0.774960i	$0.282230\pi$
$458$	−1.18478e12	−1.25818
$459$	0	0
$460$	1.93857e11	0.201870
$461$	−2.50375e11	−0.258188	−0.129094	−	0.991632i	$-0.541207\pi$
$461$	−2.50375e11	−0.258188	−0.129094	+	0.991632i	$0.541207\pi$
$462$	2.74327e12	2.80142
$463$	8.92342e10	0.0902437	0.0451218	−	0.998981i	$-0.485632\pi$
$463$	8.92342e10	0.0902437	0.0451218	+	0.998981i	$0.485632\pi$
$464$	3.65241e11	0.365804
$465$	3.34571e12	3.31856
$466$	−2.77402e12	−2.72504
$467$	7.95224e11	0.773684	0.386842	−	0.922146i	$-0.373566\pi$
$467$	7.95224e11	0.773684	0.386842	+	0.922146i	$0.373566\pi$
$468$	−1.38174e11	−0.133143
$469$	−1.40246e12	−1.33849
$470$	1.27134e12	1.20177
$471$	2.72373e11	0.255018
$472$	−1.46316e12	−1.35691
$473$	−5.98117e11	−0.549428
$474$	−7.58270e11	−0.689956
$475$	3.15164e11	0.284063
$476$	0	0
$477$	3.39317e12	3.00105
$478$	2.15603e12	1.88899
$479$	6.73511e11	0.584568	0.292284	−	0.956332i	$-0.405585\pi$
$479$	6.73511e11	0.584568	0.292284	+	0.956332i	$0.405585\pi$
$480$	1.75344e12	1.50766
$481$	1.13187e9	0.000964146 0
$482$	1.14655e12	0.967568
$483$	−3.25980e11	−0.272539
$484$	−1.18874e12	−0.984653
$485$	8.90167e11	0.730523
$486$	5.00676e11	0.407093
$487$	1.30057e12	1.04774	0.523869	−	0.851799i	$-0.324488\pi$
$487$	1.30057e12	1.04774	0.523869	+	0.851799i	$0.324488\pi$
$488$	−1.36472e11	−0.108932
$489$	−2.47149e12	−1.95465
$490$	2.75678e12	2.16033
$491$	1.27535e11	0.0990288	0.0495144	−	0.998773i	$-0.484233\pi$
$491$	1.27535e11	0.0990288	0.0495144	+	0.998773i	$0.484233\pi$
$492$	−3.07421e12	−2.36532
$493$	0	0
$494$	1.01075e11	0.0763610
$495$	2.00844e12	1.50361
$496$	5.93975e11	0.440657
$497$	6.58300e10	0.0483972
$498$	−5.26879e11	−0.383865
$499$	−4.44774e11	−0.321134	−0.160567	−	0.987025i	$-0.551332\pi$
$499$	−4.44774e11	−0.321134	−0.160567	+	0.987025i	$0.551332\pi$
$500$	2.06421e12	1.47703
$501$	1.18325e9	0.000839086 0
$502$	−2.39697e12	−1.68460
$503$	1.27414e12	0.887482	0.443741	−	0.896155i	$-0.353651\pi$
$503$	1.27414e12	0.887482	0.443741	+	0.896155i	$0.353651\pi$
$504$	5.31774e12	3.67104
$505$	6.97383e11	0.477156
$506$	−1.68341e11	−0.114159
$507$	2.60234e12	1.74915
$508$	9.12471e11	0.607900
$509$	−1.02878e12	−0.679348	−0.339674	−	0.940543i	$-0.610317\pi$
$509$	−1.02878e12	−0.679348	−0.339674	+	0.940543i	$0.610317\pi$
$510$	0	0
$511$	8.55254e11	0.554882
$512$	7.93321e11	0.510192
$513$	−3.64142e12	−2.32136
$514$	−3.43700e11	−0.217193
$515$	1.13861e12	0.713251
$516$	−4.08301e12	−2.53546
$517$	−6.99297e11	−0.430481
$518$	−1.03402e11	−0.0631023
$519$	1.79163e12	1.08392
$520$	−8.27984e10	−0.0496600
$521$	−1.60781e11	−0.0956014	−0.0478007	−	0.998857i	$-0.515221\pi$
$521$	−1.60781e11	−0.0956014	−0.0478007	+	0.998857i	$0.515221\pi$
$522$	−8.22051e12	−4.84598
$523$	5.92253e11	0.346138	0.173069	−	0.984910i	$-0.444632\pi$
$523$	5.92253e11	0.346138	0.173069	+	0.984910i	$0.444632\pi$
$524$	4.79115e12	2.77619
$525$	1.03052e12	0.592025
$526$	−2.53717e12	−1.44515
$527$	0	0
$528$	5.28982e11	0.296202
$529$	−1.78115e12	−0.988894
$530$	4.82653e12	2.65701
$531$	4.27586e12	2.33399
$532$	−5.84885e12	−3.16569
$533$	−5.42544e10	−0.0291180
$534$	−6.11760e11	−0.325571
$535$	1.91403e12	1.01008
$536$	−2.08282e12	−1.08996
$537$	1.07796e12	0.559394
$538$	−5.09675e12	−2.62285
$539$	−1.51636e12	−0.773845
$540$	7.08081e12	3.58353
$541$	−3.17243e12	−1.59222	−0.796112	−	0.605149i	$-0.793113\pi$
$541$	−3.17243e12	−1.59222	−0.796112	+	0.605149i	$0.793113\pi$
$542$	−1.08050e12	−0.537810
$543$	2.44596e12	1.20740
$544$	0	0
$545$	−5.50867e11	−0.267462
$546$	3.30494e11	0.159146
$547$	−3.50051e12	−1.67182	−0.835908	−	0.548870i	$-0.815058\pi$
$547$	−3.50051e12	−1.67182	−0.835908	+	0.548870i	$0.815058\pi$
$548$	2.80419e12	1.32830
$549$	3.98820e11	0.187371
$550$	5.32177e11	0.247984
$551$	3.80898e12	1.76046
$552$	−4.84117e11	−0.221934
$553$	7.74378e11	0.352119
$554$	6.37686e12	2.87616
$555$	−1.12311e11	−0.0502464
$556$	6.35084e12	2.81835
$557$	1.35176e12	0.595045	0.297522	−	0.954715i	$-0.403840\pi$
$557$	1.35176e12	0.595045	0.297522	+	0.954715i	$0.403840\pi$
$558$	−1.33686e13	−5.83759
$559$	−7.20580e10	−0.0312125
$560$	9.82132e11	0.422011
$561$	0	0
$562$	−2.84878e12	−1.20461
$563$	1.35952e12	0.570292	0.285146	−	0.958484i	$-0.407958\pi$
$563$	1.35952e12	0.570292	0.285146	+	0.958484i	$0.407958\pi$
$564$	−4.77371e12	−1.98655
$565$	−1.10673e12	−0.456903
$566$	2.92918e12	1.19970
$567$	−4.39219e12	−1.78467
$568$	9.77651e10	0.0394109
$569$	1.47215e12	0.588774	0.294387	−	0.955686i	$-0.404885\pi$
$569$	1.47215e12	0.588774	0.294387	+	0.955686i	$0.404885\pi$
$570$	−1.00293e13	−3.97954
$571$	−2.07965e12	−0.818706	−0.409353	−	0.912376i	$-0.634246\pi$
$571$	−2.07965e12	−0.818706	−0.409353	+	0.912376i	$0.634246\pi$
$572$	1.08108e11	0.0422254
$573$	8.82977e11	0.342179
$574$	4.95642e12	1.90575
$575$	−6.32380e10	−0.0241253
$576$	−8.41496e12	−3.18530
$577$	4.38287e12	1.64614	0.823072	−	0.567938i	$-0.192259\pi$
$577$	4.38287e12	1.64614	0.823072	+	0.567938i	$0.192259\pi$
$578$	0	0
$579$	−4.55808e12	−1.68550
$580$	−7.40664e12	−2.71766
$581$	5.38072e11	0.195906
$582$	−5.27682e12	−1.90642
$583$	−2.65482e12	−0.951760
$584$	1.27015e12	0.451853
$585$	2.41967e11	0.0854189
$586$	−1.62306e12	−0.568585
$587$	1.49551e12	0.519897	0.259948	−	0.965623i	$-0.416294\pi$
$587$	1.49551e12	0.519897	0.259948	+	0.965623i	$0.416294\pi$
$588$	−1.03514e13	−3.57108
$589$	6.19438e12	2.12070
$590$	6.08209e12	2.06642
$591$	−5.69853e12	−1.92141
$592$	−1.99390e10	−0.00667199
$593$	3.53473e12	1.17384	0.586921	−	0.809644i	$-0.300340\pi$
$593$	3.53473e12	1.17384	0.586921	+	0.809644i	$0.300340\pi$
$594$	−6.14879e12	−2.02652
$595$	0	0
$596$	8.70772e12	2.82681
$597$	−5.77663e12	−1.86119
$598$	−2.02808e10	−0.00648529
$599$	−1.01514e12	−0.322186	−0.161093	−	0.986939i	$-0.551502\pi$
$599$	−1.01514e12	−0.322186	−0.161093	+	0.986939i	$0.551502\pi$
$600$	1.53044e12	0.482099
$601$	4.12211e12	1.28880	0.644399	−	0.764689i	$-0.277108\pi$
$601$	4.12211e12	1.28880	0.644399	+	0.764689i	$0.277108\pi$
$602$	6.58288e12	2.04283
$603$	6.08673e12	1.87481
$604$	8.75687e12	2.67721
$605$	2.08169e12	0.631709
$606$	−4.13402e12	−1.24522
$607$	−1.34313e12	−0.401577	−0.200789	−	0.979635i	$-0.564350\pi$
$607$	−1.34313e12	−0.401577	−0.200789	+	0.979635i	$0.564350\pi$
$608$	3.24638e12	0.963460
$609$	1.24546e13	3.66904
$610$	5.67291e11	0.165891
$611$	−8.42476e10	−0.0244552
$612$	0	0
$613$	−2.53955e11	−0.0726413	−0.0363207	−	0.999340i	$-0.511564\pi$
$613$	−2.53955e11	−0.0726413	−0.0363207	+	0.999340i	$0.511564\pi$
$614$	8.47379e12	2.40613
$615$	5.38347e12	1.51748
$616$	−4.16061e12	−1.16424
$617$	−8.49667e11	−0.236029	−0.118015	−	0.993012i	$-0.537653\pi$
$617$	−8.49667e11	−0.236029	−0.118015	+	0.993012i	$0.537653\pi$
$618$	−6.74957e12	−1.86135
$619$	2.81906e12	0.771784	0.385892	−	0.922544i	$-0.373894\pi$
$619$	2.81906e12	0.771784	0.385892	+	0.922544i	$0.373894\pi$
$620$	−1.20451e13	−3.27377
$621$	7.30655e11	0.197152
$622$	−9.35932e12	−2.50719
$623$	6.24756e11	0.166155
$624$	6.37290e10	0.0168270
$625$	−4.48806e12	−1.17652
$626$	−6.79520e12	−1.76855
$627$	5.51659e12	1.42550
$628$	−9.80589e11	−0.251576
$629$	0	0
$630$	−2.21049e13	−5.59058
$631$	−5.32991e12	−1.33841	−0.669203	−	0.743080i	$-0.733364\pi$
$631$	−5.32991e12	−1.33841	−0.669203	+	0.743080i	$0.733364\pi$
$632$	1.15004e12	0.286738
$633$	−6.15890e12	−1.52471
$634$	1.15370e13	2.83590
$635$	−1.59789e12	−0.390002
$636$	−1.81230e13	−4.39211
$637$	−1.82683e11	−0.0439614
$638$	6.43174e12	1.53686
$639$	−2.85704e11	−0.0677896
$640$	−8.31636e12	−1.95940
$641$	7.83977e12	1.83418	0.917090	−	0.398679i	$-0.130531\pi$
$641$	7.83977e12	1.83418	0.917090	+	0.398679i	$0.130531\pi$
$642$	−1.13462e13	−2.63599
$643$	7.96124e12	1.83667	0.918336	−	0.395802i	$-0.129533\pi$
$643$	7.96124e12	1.83667	0.918336	+	0.395802i	$0.129533\pi$
$644$	1.17358e12	0.268860
$645$	7.15005e12	1.62664
$646$	0	0
$647$	−6.01408e12	−1.34927	−0.674636	−	0.738150i	$-0.735700\pi$
$647$	−6.01408e12	−1.34927	−0.674636	+	0.738150i	$0.735700\pi$
$648$	−6.52290e12	−1.45329
$649$	−3.34544e12	−0.740206
$650$	6.41138e10	0.0140877
$651$	2.02544e13	4.41981
$652$	8.89777e12	1.92827
$653$	3.99158e12	0.859083	0.429542	−	0.903047i	$-0.358675\pi$
$653$	3.99158e12	0.859083	0.429542	+	0.903047i	$0.358675\pi$
$654$	3.26548e12	0.697987
$655$	−8.39014e12	−1.78108
$656$	9.55745e11	0.201500
$657$	−3.71183e12	−0.777219
$658$	7.69646e12	1.60057
$659$	5.58329e12	1.15320	0.576601	−	0.817026i	$-0.304379\pi$
$659$	5.58329e12	1.15320	0.576601	+	0.817026i	$0.304379\pi$
$660$	−1.07271e13	−2.20057
$661$	−7.26295e12	−1.47981	−0.739906	−	0.672711i	$-0.765130\pi$
$661$	−7.26295e12	−1.47981	−0.739906	+	0.672711i	$0.765130\pi$
$662$	9.07710e12	1.83690
$663$	0	0
$664$	7.99098e11	0.159530
$665$	1.02423e13	2.03096
$666$	4.48768e11	0.0883870
$667$	−7.64277e11	−0.149515
$668$	−4.25989e9	−0.000827760 0
$669$	−7.42065e12	−1.43227
$670$	8.65791e12	1.65988
$671$	−3.12038e11	−0.0594231
$672$	1.06150e13	2.00798
$673$	−2.22311e12	−0.417727	−0.208863	−	0.977945i	$-0.566976\pi$
$673$	−2.22311e12	−0.417727	−0.208863	+	0.977945i	$0.566976\pi$
$674$	−4.39007e12	−0.819410
$675$	−2.30983e12	−0.428265
$676$	−9.36883e12	−1.72554
$677$	−9.57742e11	−0.175226	−0.0876132	−	0.996155i	$-0.527924\pi$
$677$	−9.57742e11	−0.175226	−0.0876132	+	0.996155i	$0.527924\pi$
$678$	6.56060e12	1.19237
$679$	5.38892e12	0.972944
$680$	0	0
$681$	1.46044e13	2.60209
$682$	1.04597e13	1.85135
$683$	5.01362e12	0.881574	0.440787	−	0.897612i	$-0.354699\pi$
$683$	5.01362e12	0.881574	0.440787	+	0.897612i	$0.354699\pi$
$684$	2.53842e13	4.43415
$685$	−4.91063e12	−0.852177
$686$	2.54443e12	0.438665
$687$	−7.79043e12	−1.33431
$688$	1.26937e12	0.215994
$689$	−3.19839e11	−0.0540686
$690$	2.01239e12	0.337980
$691$	2.77965e12	0.463809	0.231905	−	0.972739i	$-0.425504\pi$
$691$	2.77965e12	0.463809	0.231905	+	0.972739i	$0.425504\pi$
$692$	−6.45017e12	−1.06929
$693$	1.21588e13	2.00258
$694$	−9.73209e12	−1.59253
$695$	−1.11214e13	−1.80812
$696$	1.84965e13	2.98777
$697$	0	0
$698$	1.79868e13	2.86817
$699$	−1.82404e13	−2.88992
$700$	−3.71005e12	−0.584034
$701$	−2.98928e12	−0.467558	−0.233779	−	0.972290i	$-0.575109\pi$
$701$	−2.98928e12	−0.467558	−0.233779	+	0.972290i	$0.575109\pi$
$702$	−7.40774e11	−0.115125
$703$	−2.07937e11	−0.0321095
$704$	6.58388e12	1.01019
$705$	8.35959e12	1.27448
$706$	−4.25588e12	−0.644715
$707$	4.22184e12	0.635498
$708$	−2.28375e13	−3.41585
$709$	−1.62623e12	−0.241699	−0.120850	−	0.992671i	$-0.538562\pi$
$709$	−1.62623e12	−0.241699	−0.120850	+	0.992671i	$0.538562\pi$
$710$	−4.06393e11	−0.0600183
$711$	−3.36082e12	−0.493211
$712$	9.27833e11	0.135304
$713$	−1.24291e12	−0.180110
$714$	0	0
$715$	−1.89315e11	−0.0270899
$716$	−3.88083e12	−0.551843
$717$	1.41768e13	2.00328
$718$	−1.78755e13	−2.51014
$719$	−3.20372e12	−0.447069	−0.223535	−	0.974696i	$-0.571760\pi$
$719$	−3.20372e12	−0.447069	−0.223535	+	0.974696i	$0.571760\pi$
$720$	−4.26248e12	−0.591107
$721$	6.89296e12	0.949941
$722$	−6.50898e12	−0.891448
$723$	7.53906e12	1.02611
$724$	−8.80585e12	−1.19110
$725$	2.41612e12	0.324786
$726$	−1.23401e13	−1.64855
$727$	−1.01002e13	−1.34099	−0.670495	−	0.741914i	$-0.733918\pi$
$727$	−1.01002e13	−1.34099	−0.670495	+	0.741914i	$0.733918\pi$
$728$	−5.01248e11	−0.0661396
$729$	−5.92536e12	−0.777035
$730$	−5.27979e12	−0.688120
$731$	0	0
$732$	−2.13010e12	−0.274221
$733$	1.50783e13	1.92923	0.964613	−	0.263669i	$-0.0849326\pi$
$733$	1.50783e13	1.92923	0.964613	+	0.263669i	$0.0849326\pi$
$734$	−1.41260e13	−1.79633
$735$	1.81270e13	2.29104
$736$	−6.51391e11	−0.0818260
$737$	−4.76227e12	−0.594580
$738$	−2.15110e13	−2.66936
$739$	−4.47241e12	−0.551622	−0.275811	−	0.961212i	$-0.588946\pi$
$739$	−4.47241e12	−0.551622	−0.275811	+	0.961212i	$0.588946\pi$
$740$	4.04339e11	0.0495681
$741$	6.64610e11	0.0809813
$742$	2.92190e13	3.53873
$743$	−1.32246e13	−1.59197	−0.795984	−	0.605318i	$-0.793046\pi$
$743$	−1.32246e13	−1.59197	−0.795984	+	0.605318i	$0.793046\pi$
$744$	3.00800e13	3.59915
$745$	−1.52487e13	−1.81355
$746$	−2.25634e12	−0.266735
$747$	−2.33525e12	−0.274404
$748$	0	0
$749$	1.15872e13	1.34528
$750$	2.14281e13	2.47291
$751$	4.66313e10	0.00534931	0.00267466	−	0.999996i	$-0.499149\pi$
$751$	4.66313e10	0.00534931	0.00267466	+	0.999996i	$0.499149\pi$
$752$	1.48411e12	0.169233
$753$	−1.57611e13	−1.78653
$754$	7.74862e11	0.0873078
$755$	−1.53348e13	−1.71758
$756$	4.28660e13	4.77271
$757$	−8.50250e12	−0.941056	−0.470528	−	0.882385i	$-0.655936\pi$
$757$	−8.50250e12	−0.941056	−0.470528	+	0.882385i	$0.655936\pi$
$758$	−2.00274e13	−2.20350
$759$	−1.10691e12	−0.121067
$760$	1.52111e13	1.65386
$761$	−1.78762e12	−0.193217	−0.0966083	−	0.995322i	$-0.530799\pi$
$761$	−1.78762e12	−0.193217	−0.0966083	+	0.995322i	$0.530799\pi$
$762$	9.47217e12	1.01778
$763$	−3.33485e12	−0.356218
$764$	−3.17886e12	−0.337560
$765$	0	0
$766$	−2.31508e13	−2.42960
$767$	−4.03041e11	−0.0420504
$768$	2.32882e13	2.41551
$769$	9.44034e12	0.973462	0.486731	−	0.873552i	$-0.338189\pi$
$769$	9.44034e12	0.973462	0.486731	+	0.873552i	$0.338189\pi$
$770$	1.72949e13	1.77301
$771$	−2.25997e12	−0.230334
$772$	1.64098e13	1.66275
$773$	1.07678e12	0.108472	0.0542362	−	0.998528i	$-0.482728\pi$
$773$	1.07678e12	0.108472	0.0542362	+	0.998528i	$0.482728\pi$
$774$	−2.85699e13	−2.86137
$775$	3.92922e12	0.391245
$776$	8.00316e12	0.792290
$777$	−6.79913e11	−0.0669205
$778$	−5.21402e11	−0.0510228
$779$	9.96717e12	0.969736
$780$	−1.29235e12	−0.125013
$781$	2.23536e11	0.0214990
$782$	0	0
$783$	−2.79159e13	−2.65414
$784$	3.21815e12	0.304218
$785$	1.71718e12	0.161400
$786$	4.97359e13	4.64803
$787$	6.72445e11	0.0624842	0.0312421	−	0.999512i	$-0.490054\pi$
$787$	6.72445e11	0.0624842	0.0312421	+	0.999512i	$0.490054\pi$
$788$	2.05156e13	1.89547
$789$	−1.66829e13	−1.53259
$790$	−4.78052e12	−0.436670
$791$	−6.69997e12	−0.608525
$792$	1.80572e13	1.63075
$793$	−3.75926e10	−0.00337577
$794$	3.03355e13	2.70868
$795$	3.17365e13	2.81778
$796$	2.07968e13	1.83606
$797$	7.96983e12	0.699659	0.349829	−	0.936813i	$-0.386240\pi$
$797$	7.96983e12	0.699659	0.349829	+	0.936813i	$0.386240\pi$
$798$	−6.07157e13	−5.30014
$799$	0	0
$800$	2.05925e12	0.177748
$801$	−2.71146e12	−0.232732
$802$	−2.53702e12	−0.216540
$803$	2.90414e12	0.246489
$804$	−3.25093e13	−2.74382
$805$	−2.05514e12	−0.172488
$806$	1.26012e12	0.105173
$807$	−3.35133e13	−2.78155
$808$	6.26991e12	0.517500
$809$	−1.71821e12	−0.141029	−0.0705146	−	0.997511i	$-0.522464\pi$
$809$	−1.71821e12	−0.141029	−0.0705146	+	0.997511i	$0.522464\pi$
$810$	2.71146e13	2.21320
$811$	1.78570e13	1.44949	0.724743	−	0.689019i	$-0.241959\pi$
$811$	1.78570e13	1.44949	0.724743	+	0.689019i	$0.241959\pi$
$812$	−4.48386e13	−3.61951
$813$	−7.10477e12	−0.570351
$814$	−3.51117e11	−0.0280312
$815$	−1.55815e13	−1.23709
$816$	0	0
$817$	1.32379e13	1.03949
$818$	1.35295e13	1.05655
$819$	1.46482e12	0.113765
$820$	−1.93814e13	−1.49700
$821$	−1.45867e13	−1.12051	−0.560253	−	0.828322i	$-0.689296\pi$
$821$	−1.45867e13	−1.12051	−0.560253	+	0.828322i	$0.689296\pi$
$822$	2.91097e13	2.22390
$823$	9.62246e12	0.731117	0.365559	−	0.930788i	$-0.380878\pi$
$823$	9.62246e12	0.731117	0.365559	+	0.930788i	$0.380878\pi$
$824$	1.02368e13	0.773558
$825$	3.49929e12	0.262989
$826$	3.68200e13	2.75216
$827$	−2.45399e13	−1.82430	−0.912152	−	0.409852i	$-0.865580\pi$
$827$	−2.45399e13	−1.82430	−0.912152	+	0.409852i	$0.865580\pi$
$828$	−5.09337e12	−0.376590
$829$	8.58781e12	0.631520	0.315760	−	0.948839i	$-0.397741\pi$
$829$	8.58781e12	0.631520	0.315760	+	0.948839i	$0.397741\pi$
$830$	−3.32171e12	−0.242946
$831$	4.19306e13	3.05019
$832$	7.93191e11	0.0573882
$833$	0	0
$834$	6.59267e13	4.71861
$835$	7.45981e9	0.000531054 0
$836$	−1.98606e13	−1.40626
$837$	−4.53984e13	−3.19725
$838$	1.95649e13	1.37050
$839$	1.66622e13	1.16092	0.580461	−	0.814288i	$-0.302872\pi$
$839$	1.66622e13	1.16092	0.580461	+	0.814288i	$0.302872\pi$
$840$	4.97370e13	3.44686
$841$	1.46934e13	1.01284
$842$	1.29191e13	0.885784
$843$	−1.87319e13	−1.27749
$844$	2.21730e13	1.50413
$845$	1.64064e13	1.10703
$846$	−3.34029e13	−2.24191
$847$	1.26022e13	0.841340
$848$	5.63428e12	0.374160
$849$	1.92606e13	1.27229
$850$	0	0
$851$	4.17229e10	0.00272704
$852$	1.52595e12	0.0992117
$853$	−1.23286e13	−0.797342	−0.398671	−	0.917094i	$-0.630528\pi$
$853$	−1.23286e13	−0.797342	−0.398671	+	0.917094i	$0.630528\pi$
$854$	3.43429e12	0.220941
$855$	−4.44521e13	−2.84476
$856$	1.72084e13	1.09549
$857$	−3.69217e12	−0.233813	−0.116906	−	0.993143i	$-0.537298\pi$
$857$	−3.69217e12	−0.233813	−0.116906	+	0.993143i	$0.537298\pi$
$858$	1.12224e12	0.0706958
$859$	−3.06191e13	−1.91877	−0.959385	−	0.282101i	$-0.908969\pi$
$859$	−3.06191e13	−1.91877	−0.959385	+	0.282101i	$0.908969\pi$
$860$	−2.57414e13	−1.60468
$861$	3.25906e13	2.02106
$862$	1.35119e13	0.833554
$863$	1.76323e13	1.08208	0.541042	−	0.840996i	$-0.318030\pi$
$863$	1.76323e13	1.08208	0.541042	+	0.840996i	$0.318030\pi$
$864$	−2.37926e13	−1.45255
$865$	1.12954e13	0.686006
$866$	5.19721e13	3.14007
$867$	0	0
$868$	−7.29190e13	−4.36016
$869$	2.62952e12	0.156418
$870$	−7.68868e13	−4.55004
$871$	−5.73733e11	−0.0337776
$872$	−4.95264e12	−0.290076
$873$	−2.33881e13	−1.36280
$874$	3.72582e12	0.215983
$875$	−2.18833e13	−1.26205
$876$	1.98249e13	1.13748
$877$	−8.61760e12	−0.491913	−0.245956	−	0.969281i	$-0.579102\pi$
$877$	−8.61760e12	−0.491913	−0.245956	+	0.969281i	$0.579102\pi$
$878$	−2.08618e13	−1.18475
$879$	−1.06723e13	−0.602989
$880$	3.33497e12	0.187465
$881$	1.33579e13	0.747043	0.373521	−	0.927622i	$-0.378150\pi$
$881$	1.33579e13	0.747043	0.373521	+	0.927622i	$0.378150\pi$
$882$	−7.24312e13	−4.03011
$883$	−6.98562e12	−0.386707	−0.193354	−	0.981129i	$-0.561936\pi$
$883$	−6.98562e12	−0.386707	−0.193354	+	0.981129i	$0.561936\pi$
$884$	0	0
$885$	3.99924e13	2.19145
$886$	−4.23197e13	−2.30723
$887$	3.15821e13	1.71311	0.856555	−	0.516056i	$-0.172600\pi$
$887$	3.15821e13	1.71311	0.856555	+	0.516056i	$0.172600\pi$
$888$	−1.00975e12	−0.0544948
$889$	−9.67339e12	−0.519422
$890$	−3.85684e12	−0.206052
$891$	−1.49143e13	−0.792782
$892$	2.67155e13	1.41294
$893$	1.54773e13	0.814447
$894$	9.03930e13	4.73278
$895$	6.79600e12	0.354038
$896$	−5.03459e13	−2.60962
$897$	−1.33355e11	−0.00687769
$898$	−3.09150e13	−1.58645
$899$	4.74875e13	2.42471
$900$	1.61017e13	0.818052
$901$	0	0
$902$	1.68303e13	0.846568
$903$	4.32852e13	2.16643
$904$	−9.95022e12	−0.495535
$905$	1.54206e13	0.764156
$906$	9.09032e13	4.48231
$907$	−3.17616e12	−0.155837	−0.0779183	−	0.996960i	$-0.524827\pi$
$907$	−3.17616e12	−0.155837	−0.0779183	+	0.996960i	$0.524827\pi$
$908$	−5.25784e13	−2.56697
$909$	−1.83229e13	−0.890138
$910$	2.08360e12	0.100723
$911$	−7.76844e12	−0.373681	−0.186840	−	0.982390i	$-0.559825\pi$
$911$	−7.76844e12	−0.373681	−0.186840	+	0.982390i	$0.559825\pi$
$912$	−1.17078e13	−0.560399
$913$	1.82710e12	0.0870251
$914$	−4.40484e13	−2.08772
$915$	3.73018e12	0.175928
$916$	2.80468e13	1.31630
$917$	−5.07925e13	−2.37212
$918$	0	0
$919$	−2.31177e13	−1.06912	−0.534559	−	0.845131i	$-0.679522\pi$
$919$	−2.31177e13	−1.06912	−0.534559	+	0.845131i	$0.679522\pi$
$920$	−3.05212e12	−0.140461
$921$	5.57188e13	2.55172
$922$	9.35713e12	0.426436
$923$	2.69304e10	0.00122134
$924$	−6.49403e13	−2.93083
$925$	−1.31899e11	−0.00592385
$926$	−3.33491e12	−0.149051
$927$	−2.99156e13	−1.33058
$928$	2.48875e13	1.10158
$929$	−3.14470e13	−1.38519	−0.692593	−	0.721329i	$-0.743532\pi$
$929$	−3.14470e13	−1.38519	−0.692593	+	0.721329i	$0.743532\pi$
$930$	−1.25038e14	−5.48109
$931$	3.35611e13	1.46407
$932$	6.56682e13	2.85091
$933$	−6.15415e13	−2.65889
$934$	−2.97195e13	−1.27785
$935$	0	0
$936$	2.17543e12	0.0926412
$937$	−3.04920e13	−1.29228	−0.646142	−	0.763217i	$-0.723619\pi$
$937$	−3.04920e13	−1.29228	−0.646142	+	0.763217i	$0.723619\pi$
$938$	5.24136e13	2.21071
$939$	−4.46814e13	−1.87556
$940$	−3.00959e13	−1.25728
$941$	−2.55953e13	−1.06416	−0.532081	−	0.846694i	$-0.678590\pi$
$941$	−2.55953e13	−1.06416	−0.532081	+	0.846694i	$0.678590\pi$
$942$	−1.01793e13	−0.421200
$943$	−1.99993e12	−0.0823590
$944$	7.09998e12	0.290993
$945$	−7.50658e13	−3.06196
$946$	2.23531e13	0.907462
$947$	−1.98034e13	−0.800137	−0.400069	−	0.916485i	$-0.631014\pi$
$947$	−1.98034e13	−0.800137	−0.400069	+	0.916485i	$0.631014\pi$
$948$	1.79502e13	0.721826
$949$	3.49876e11	0.0140028
$950$	−1.17785e13	−0.469173
$951$	7.58607e13	3.00749
$952$	0	0
$953$	−3.81669e13	−1.49889	−0.749444	−	0.662068i	$-0.769679\pi$
$953$	−3.81669e13	−1.49889	−0.749444	+	0.662068i	$0.769679\pi$
$954$	−1.26811e14	−4.95668
$955$	5.56673e12	0.216564
$956$	−5.10389e13	−1.97624
$957$	4.22914e13	1.62985
$958$	−2.51708e13	−0.965500
$959$	−2.97281e13	−1.13497
$960$	−7.87055e13	−2.99078
$961$	5.07872e13	1.92087
$962$	−4.23007e10	−0.00159243
$963$	−5.02890e13	−1.88432
$964$	−2.71418e13	−1.01226
$965$	−2.87365e13	−1.06674
$966$	1.21827e13	0.450138
$967$	−4.29739e13	−1.58047	−0.790234	−	0.612805i	$-0.790041\pi$
$967$	−4.29739e13	−1.58047	−0.790234	+	0.612805i	$0.790041\pi$
$968$	1.87157e13	0.685122
$969$	0	0
$970$	−3.32678e13	−1.20657
$971$	1.07872e13	0.389425	0.194712	−	0.980860i	$-0.437623\pi$
$971$	1.07872e13	0.389425	0.194712	+	0.980860i	$0.437623\pi$
$972$	−1.18523e13	−0.425897
$973$	−6.73272e13	−2.40815
$974$	−4.86055e13	−1.73049
$975$	4.21576e11	0.0149401
$976$	6.62232e11	0.0233607
$977$	1.08674e13	0.381594	0.190797	−	0.981629i	$-0.438893\pi$
$977$	1.08674e13	0.381594	0.190797	+	0.981629i	$0.438893\pi$
$978$	9.23658e13	3.22839
$979$	2.12145e12	0.0738093
$980$	−6.52603e13	−2.26012
$981$	1.44734e13	0.498952
$982$	−4.76629e12	−0.163561
$983$	−1.21504e13	−0.415050	−0.207525	−	0.978230i	$-0.566541\pi$
$983$	−1.21504e13	−0.415050	−0.207525	+	0.978230i	$0.566541\pi$
$984$	4.84008e13	1.64579
$985$	−3.59264e13	−1.21605
$986$	0	0
$987$	5.06075e13	1.69742
$988$	−2.39270e12	−0.0798882
$989$	−2.65620e12	−0.0882831
$990$	−7.50606e13	−2.48344
$991$	1.69943e13	0.559723	0.279861	−	0.960040i	$-0.409712\pi$
$991$	1.69943e13	0.559723	0.279861	+	0.960040i	$0.409712\pi$
$992$	4.04734e13	1.32699
$993$	5.96858e13	1.94805
$994$	−2.46023e12	−0.0799352
$995$	−3.64188e13	−1.17794
$996$	1.24726e13	0.401597
$997$	4.80699e13	1.54079	0.770397	−	0.637564i	$-0.220058\pi$
$997$	4.80699e13	1.54079	0.770397	+	0.637564i	$0.220058\pi$
$998$	1.66223e13	0.530401
$999$	1.52397e12	0.0484095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.5		52
17.10	odd	16		17.10.d.a.15.12	yes	52
17.12	odd	16		17.10.d.a.8.12	✓	52
17.16	even	2	inner	289.10.a.i.1.6		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.8.12	✓	52	17.12	odd	16
17.10.d.a.15.12	yes	52	17.10	odd	16
289.10.a.i.1.5		52	1.1	even	1	trivial
289.10.a.i.1.6		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)

\(f(q)\)	\(=\)	\(q-37.3725 q^{2} -245.740 q^{3} +884.705 q^{4} -1549.27 q^{5} +9183.93 q^{6} -9379.03 q^{7} -13928.9 q^{8} +40705.3 q^{9} +O(q^{10})\)	\(q-37.3725 q^{2} -245.740 q^{3} +884.705 q^{4} -1549.27 q^{5} +9183.93 q^{6} -9379.03 q^{7} -13928.9 q^{8} +40705.3 q^{9} +57900.2 q^{10} -31847.9 q^{11} -217408. q^{12} -3836.87 q^{13} +350518. q^{14} +380719. q^{15} +67590.2 q^{16} -1.52126e6 q^{18} +704878. q^{19} -1.37065e6 q^{20} +2.30481e6 q^{21} +1.19024e6 q^{22} -141435. q^{23} +3.42290e6 q^{24} +447119. q^{25} +143393. q^{26} -5.16603e6 q^{27} -8.29768e6 q^{28} +5.40375e6 q^{29} -1.42284e7 q^{30} +8.78788e6 q^{31} +4.60560e6 q^{32} +7.82631e6 q^{33} +1.45307e7 q^{35} +3.60122e7 q^{36} -294998. q^{37} -2.63431e7 q^{38} +942873. q^{39} +2.15797e7 q^{40} +1.41403e7 q^{41} -8.61364e7 q^{42} +1.87804e7 q^{43} -2.81760e7 q^{44} -6.30636e7 q^{45} +5.28577e6 q^{46} +2.19574e7 q^{47} -1.66096e7 q^{48} +4.76127e7 q^{49} -1.67099e7 q^{50} -3.39450e6 q^{52} +8.33595e7 q^{53} +1.93067e8 q^{54} +4.93411e7 q^{55} +1.30640e8 q^{56} -1.73217e8 q^{57} -2.01952e8 q^{58} +1.05044e8 q^{59} +3.36824e8 q^{60} +9.79774e6 q^{61} -3.28425e8 q^{62} -3.81776e8 q^{63} -2.06729e8 q^{64} +5.94435e6 q^{65} -2.92489e8 q^{66} +1.49532e8 q^{67} +3.47562e7 q^{69} -5.43048e8 q^{70} -7.01885e6 q^{71} -5.66981e8 q^{72} -9.11878e7 q^{73} +1.10248e7 q^{74} -1.09875e8 q^{75} +6.23609e8 q^{76} +2.98703e8 q^{77} -3.52375e7 q^{78} -8.25648e7 q^{79} -1.04716e8 q^{80} +4.68298e8 q^{81} -5.28458e8 q^{82} -5.73696e7 q^{83} +2.03907e9 q^{84} -7.01872e8 q^{86} -1.32792e9 q^{87} +4.43607e8 q^{88} -6.66119e7 q^{89} +2.35684e9 q^{90} +3.59861e7 q^{91} -1.25128e8 q^{92} -2.15954e9 q^{93} -8.20603e8 q^{94} -1.09205e9 q^{95} -1.13178e9 q^{96} -5.74571e8 q^{97} -1.77941e9 q^{98} -1.29638e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 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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