LMFDB - Embedded newform 289.10.a.i.1.24

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			1.24
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)

$f(q)$	$=$	$q-3.95683 q^{2} +182.625 q^{3} -496.344 q^{4} +659.768 q^{5} -722.614 q^{6} +1391.19 q^{7} +3989.84 q^{8} +13668.8 q^{9} +O(q^{10})$	\(q-3.95683 q^{2} +182.625 q^{3} -496.344 q^{4} +659.768 q^{5} -722.614 q^{6} +1391.19 q^{7} +3989.84 q^{8} +13668.8 q^{9} -2610.59 q^{10} +19867.6 q^{11} -90644.6 q^{12} +137813. q^{13} -5504.71 q^{14} +120490. q^{15} +238341. q^{16} -54085.2 q^{18} +546542. q^{19} -327472. q^{20} +254066. q^{21} -78612.5 q^{22} +106894. q^{23} +728644. q^{24} -1.51783e6 q^{25} -545303. q^{26} -1.09834e6 q^{27} -690510. q^{28} +4.27320e6 q^{29} -476758. q^{30} -117869. q^{31} -2.98587e6 q^{32} +3.62831e6 q^{33} +917865. q^{35} -6.78443e6 q^{36} +3.86458e6 q^{37} -2.16257e6 q^{38} +2.51681e7 q^{39} +2.63237e6 q^{40} -1.38784e7 q^{41} -1.00530e6 q^{42} +1.16571e7 q^{43} -9.86113e6 q^{44} +9.01826e6 q^{45} -422963. q^{46} -2.85629e7 q^{47} +4.35269e7 q^{48} -3.84182e7 q^{49} +6.00579e6 q^{50} -6.84028e7 q^{52} +5.76966e7 q^{53} +4.34593e6 q^{54} +1.31080e7 q^{55} +5.55064e6 q^{56} +9.98121e7 q^{57} -1.69083e7 q^{58} -1.01064e8 q^{59} -5.98045e7 q^{60} -9.08550e7 q^{61} +466388. q^{62} +1.90160e7 q^{63} -1.10216e8 q^{64} +9.09249e7 q^{65} -1.43566e7 q^{66} +1.28322e8 q^{67} +1.95216e7 q^{69} -3.63183e6 q^{70} +2.69254e8 q^{71} +5.45364e7 q^{72} +4.17080e8 q^{73} -1.52915e7 q^{74} -2.77194e8 q^{75} -2.71273e8 q^{76} +2.76396e7 q^{77} -9.95859e7 q^{78} +5.30648e8 q^{79} +1.57250e8 q^{80} -4.69627e8 q^{81} +5.49143e7 q^{82} +2.09652e8 q^{83} -1.26104e8 q^{84} -4.61249e7 q^{86} +7.80392e8 q^{87} +7.92684e7 q^{88} +9.09011e8 q^{89} -3.56837e7 q^{90} +1.91725e8 q^{91} -5.30564e7 q^{92} -2.15258e7 q^{93} +1.13018e8 q^{94} +3.60591e8 q^{95} -5.45294e8 q^{96} +1.28450e8 q^{97} +1.52014e8 q^{98} +2.71566e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.95683	−0.174869	−0.0874343	−	0.996170i	$-0.527867\pi$
$2$	−3.95683	−0.174869	−0.0874343	+	0.996170i	$0.527867\pi$
$3$	182.625	1.30171	0.650855	−	0.759202i	$-0.274411\pi$
$3$	182.625	1.30171	0.650855	+	0.759202i	$0.274411\pi$
$4$	−496.344	−0.969421
$5$	659.768	0.472092	0.236046	−	0.971742i	$-0.424148\pi$
$5$	659.768	0.472092	0.236046	+	0.971742i	$0.424148\pi$
$6$	−722.614	−0.227628
$7$	1391.19	0.219001	0.109501	−	0.993987i	$-0.465075\pi$
$7$	1391.19	0.219001	0.109501	+	0.993987i	$0.465075\pi$
$8$	3989.84	0.344390
$9$	13668.8	0.694448
$10$	−2610.59	−0.0825540
$11$	19867.6	0.409145	0.204573	−	0.978851i	$-0.434420\pi$
$11$	19867.6	0.409145	0.204573	+	0.978851i	$0.434420\pi$
$12$	−90644.6	−1.26190
$13$	137813.	1.33828	0.669139	−	0.743138i	$-0.266663\pi$
$13$	137813.	1.33828	0.669139	+	0.743138i	$0.266663\pi$
$14$	−5504.71	−0.0382964
$15$	120490.	0.614526
$16$	238341.	0.909198
$17$	0	0
$17$	0	0
$18$	−54085.2	−0.121437
$19$	546542.	0.962127	0.481063	−	0.876686i	$-0.340251\pi$
$19$	546542.	0.962127	0.481063	+	0.876686i	$0.340251\pi$
$20$	−327472.	−0.457656
$21$	254066.	0.285076
$22$	−78612.5	−0.0715466
$23$	106894.	0.0796489	0.0398245	−	0.999207i	$-0.487320\pi$
$23$	106894.	0.0796489	0.0398245	+	0.999207i	$0.487320\pi$
$24$	728644.	0.448296
$25$	−1.51783e6	−0.777129
$26$	−545303.	−0.234023
$27$	−1.09834e6	−0.397740
$28$	−690510.	−0.212304
$29$	4.27320e6	1.12192	0.560960	−	0.827843i	$-0.310432\pi$
$29$	4.27320e6	1.12192	0.560960	+	0.827843i	$0.310432\pi$
$30$	−476758.	−0.107461
$31$	−117869.	−0.0229231	−0.0114615	−	0.999934i	$-0.503648\pi$
$31$	−117869.	−0.0229231	−0.0114615	+	0.999934i	$0.503648\pi$
$32$	−2.98587e6	−0.503380
$33$	3.62831e6	0.532588
$34$	0	0
$35$	917865.	0.103389
$36$	−6.78443e6	−0.673213
$37$	3.86458e6	0.338996	0.169498	−	0.985531i	$-0.445785\pi$
$37$	3.86458e6	0.338996	0.169498	+	0.985531i	$0.445785\pi$
$38$	−2.16257e6	−0.168246
$39$	2.51681e7	1.74205
$40$	2.63237e6	0.162584
$41$	−1.38784e7	−0.767028	−0.383514	−	0.923535i	$-0.625286\pi$
$41$	−1.38784e7	−0.767028	−0.383514	+	0.923535i	$0.625286\pi$
$42$	−1.00530e6	−0.0498508
$43$	1.16571e7	0.519973	0.259986	−	0.965612i	$-0.416282\pi$
$43$	1.16571e7	0.519973	0.259986	+	0.965612i	$0.416282\pi$
$44$	−9.86113e6	−0.396634
$45$	9.01826e6	0.327843
$46$	−422963.	−0.0139281
$47$	−2.85629e7	−0.853812	−0.426906	−	0.904296i	$-0.640396\pi$
$47$	−2.85629e7	−0.853812	−0.426906	+	0.904296i	$0.640396\pi$
$48$	4.35269e7	1.18351
$49$	−3.84182e7	−0.952038
$50$	6.00579e6	0.135896
$51$	0	0
$52$	−6.84028e7	−1.29735
$53$	5.76966e7	1.00440	0.502202	−	0.864750i	$-0.332523\pi$
$53$	5.76966e7	1.00440	0.502202	+	0.864750i	$0.332523\pi$
$54$	4.34593e6	0.0695522
$55$	1.31080e7	0.193154
$56$	5.55064e6	0.0754218
$57$	9.98121e7	1.25241
$58$	−1.69083e7	−0.196189
$59$	−1.01064e8	−1.08584	−0.542918	−	0.839786i	$-0.682680\pi$
$59$	−1.01064e8	−1.08584	−0.542918	+	0.839786i	$0.682680\pi$
$60$	−5.98045e7	−0.595735
$61$	−9.08550e7	−0.840165	−0.420083	−	0.907486i	$-0.637999\pi$
$61$	−9.08550e7	−0.840165	−0.420083	+	0.907486i	$0.637999\pi$
$62$	466388.	0.00400852
$63$	1.90160e7	0.152085
$64$	−1.10216e8	−0.821173
$65$	9.09249e7	0.631790
$66$	−1.43566e7	−0.0931330
$67$	1.28322e8	0.777975	0.388987	−	0.921243i	$-0.372825\pi$
$67$	1.28322e8	0.777975	0.388987	+	0.921243i	$0.372825\pi$
$68$	0	0
$69$	1.95216e7	0.103680
$70$	−3.63183e6	−0.0180794
$71$	2.69254e8	1.25748	0.628739	−	0.777617i	$-0.283572\pi$
$71$	2.69254e8	1.25748	0.628739	+	0.777617i	$0.283572\pi$
$72$	5.45364e7	0.239161
$73$	4.17080e8	1.71896	0.859481	−	0.511167i	$-0.170787\pi$
$73$	4.17080e8	1.71896	0.859481	+	0.511167i	$0.170787\pi$
$74$	−1.52915e7	−0.0592798
$75$	−2.77194e8	−1.01160
$76$	−2.71273e8	−0.932706
$77$	2.76396e7	0.0896033
$78$	−9.95859e7	−0.304630
$79$	5.30648e8	1.53280	0.766398	−	0.642366i	$-0.222047\pi$
$79$	5.30648e8	1.53280	0.766398	+	0.642366i	$0.222047\pi$
$80$	1.57250e8	0.429225
$81$	−4.69627e8	−1.21219
$82$	5.49143e7	0.134129
$83$	2.09652e8	0.484896	0.242448	−	0.970164i	$-0.422050\pi$
$83$	2.09652e8	0.484896	0.242448	+	0.970164i	$0.422050\pi$
$84$	−1.26104e8	−0.276359
$85$	0	0
$86$	−4.61249e7	−0.0909269
$87$	7.80392e8	1.46042
$88$	7.92684e7	0.140905
$89$	9.09011e8	1.53573	0.767864	−	0.640613i	$-0.221320\pi$
$89$	9.09011e8	1.53573	0.767864	+	0.640613i	$0.221320\pi$
$90$	−3.56837e7	−0.0573295
$91$	1.91725e8	0.293084
$92$	−5.30564e7	−0.0772134
$93$	−2.15258e7	−0.0298392
$94$	1.13018e8	0.149305
$95$	3.60591e8	0.454212
$96$	−5.45294e8	−0.655255
$97$	1.28450e8	0.147320	0.0736601	−	0.997283i	$-0.476532\pi$
$97$	1.28450e8	0.147320	0.0736601	+	0.997283i	$0.476532\pi$
$98$	1.52014e8	0.166482
$99$	2.71566e8	0.284130
$100$	7.53365e8	0.753365
$101$	−2.26820e8	−0.216887	−0.108444	−	0.994103i	$-0.534587\pi$
$101$	−2.26820e8	−0.216887	−0.108444	+	0.994103i	$0.534587\pi$
$102$	0	0
$103$	−1.59588e9	−1.39712	−0.698559	−	0.715552i	$-0.746175\pi$
$103$	−1.59588e9	−1.39712	−0.698559	+	0.715552i	$0.746175\pi$
$104$	5.49853e8	0.460889
$105$	1.67625e8	0.134582
$106$	−2.28295e8	−0.175639
$107$	−1.69705e9	−1.25161	−0.625803	−	0.779981i	$-0.715229\pi$
$107$	−1.69705e9	−1.25161	−0.625803	+	0.779981i	$0.715229\pi$
$108$	5.45153e8	0.385577
$109$	−3.85965e8	−0.261896	−0.130948	−	0.991389i	$-0.541802\pi$
$109$	−3.85965e8	−0.261896	−0.130948	+	0.991389i	$0.541802\pi$
$110$	−5.18660e7	−0.0337766
$111$	7.05768e8	0.441274
$112$	3.31578e8	0.199115
$113$	1.57141e9	0.906643	0.453322	−	0.891347i	$-0.350239\pi$
$113$	1.57141e9	0.906643	0.453322	+	0.891347i	$0.350239\pi$
$114$	−3.94939e8	−0.219007
$115$	7.05256e7	0.0376016
$116$	−2.12098e9	−1.08761
$117$	1.88375e9	0.929364
$118$	3.99894e8	0.189879
$119$	0	0
$120$	4.80736e8	0.211637
$121$	−1.96323e9	−0.832600
$122$	3.59497e8	0.146919
$123$	−2.53454e9	−0.998448
$124$	5.85036e7	0.0222221
$125$	−2.29003e9	−0.838968
$126$	−7.52429e7	−0.0265949
$127$	3.39852e9	1.15924	0.579619	−	0.814888i	$-0.303201\pi$
$127$	3.39852e9	1.15924	0.579619	+	0.814888i	$0.303201\pi$
$128$	1.96487e9	0.646977
$129$	2.12887e9	0.676854
$130$	−3.59774e8	−0.110480
$131$	5.93370e9	1.76037	0.880186	−	0.474629i	$-0.157418\pi$
$131$	5.93370e9	1.76037	0.880186	+	0.474629i	$0.157418\pi$
$132$	−1.80089e9	−0.516302
$133$	7.60346e8	0.210707
$134$	−5.07749e8	−0.136043
$135$	−7.24648e8	−0.187770
$136$	0	0
$137$	7.26132e9	1.76106	0.880528	−	0.473994i	$-0.157188\pi$
$137$	7.26132e9	1.76106	0.880528	+	0.473994i	$0.157188\pi$
$138$	−7.72435e7	−0.0181303
$139$	−6.70642e9	−1.52379	−0.761893	−	0.647703i	$-0.775730\pi$
$139$	−6.70642e9	−1.52379	−0.761893	+	0.647703i	$0.775730\pi$
$140$	−4.55577e8	−0.100227
$141$	−5.21630e9	−1.11142
$142$	−1.06539e9	−0.219893
$143$	2.73801e9	0.547550
$144$	3.25784e9	0.631391
$145$	2.81932e9	0.529650
$146$	−1.65031e9	−0.300593
$147$	−7.01611e9	−1.23928
$148$	−1.91816e9	−0.328630
$149$	7.55693e9	1.25605	0.628026	−	0.778193i	$-0.283863\pi$
$149$	7.55693e9	1.25605	0.628026	+	0.778193i	$0.283863\pi$
$150$	1.09681e9	0.176897
$151$	−1.76066e9	−0.275600	−0.137800	−	0.990460i	$-0.544003\pi$
$151$	−1.76066e9	−0.275600	−0.137800	+	0.990460i	$0.544003\pi$
$152$	2.18061e9	0.331347
$153$	0	0
$154$	−1.09365e8	−0.0156688
$155$	−7.77663e7	−0.0108218
$156$	−1.24920e10	−1.68878
$157$	−1.39309e10	−1.82991	−0.914956	−	0.403553i	$-0.867775\pi$
$157$	−1.39309e10	−1.82991	−0.914956	+	0.403553i	$0.867775\pi$
$158$	−2.09968e9	−0.268038
$159$	1.05368e10	1.30744
$160$	−1.96998e9	−0.237642
$161$	1.48711e8	0.0174432
$162$	1.85823e9	0.211974
$163$	3.43406e9	0.381034	0.190517	−	0.981684i	$-0.438984\pi$
$163$	3.43406e9	0.381034	0.190517	+	0.981684i	$0.438984\pi$
$164$	6.88844e9	0.743573
$165$	2.39384e9	0.251431
$166$	−8.29558e8	−0.0847930
$167$	1.47734e9	0.146980	0.0734899	−	0.997296i	$-0.476586\pi$
$167$	1.47734e9	0.146980	0.0734899	+	0.997296i	$0.476586\pi$
$168$	1.01368e9	0.0981773
$169$	8.38802e9	0.790987
$170$	0	0
$171$	7.47059e9	0.668147
$172$	−5.78590e9	−0.504073
$173$	−1.54415e10	−1.31064	−0.655318	−	0.755353i	$-0.727465\pi$
$173$	−1.54415e10	−1.31064	−0.655318	+	0.755353i	$0.727465\pi$
$174$	−3.08788e9	−0.255381
$175$	−2.11160e9	−0.170192
$176$	4.73525e9	0.371994
$177$	−1.84569e10	−1.41344
$178$	−3.59680e9	−0.268551
$179$	1.22379e10	0.890978	0.445489	−	0.895287i	$-0.353030\pi$
$179$	1.22379e10	0.890978	0.445489	+	0.895287i	$0.353030\pi$
$180$	−4.47615e9	−0.317818
$181$	9.38301e9	0.649813	0.324907	−	0.945746i	$-0.394667\pi$
$181$	9.38301e9	0.649813	0.324907	+	0.945746i	$0.394667\pi$
$182$	−7.58622e8	−0.0512512
$183$	−1.65924e10	−1.09365
$184$	4.26492e8	0.0274303
$185$	2.54973e9	0.160037
$186$	8.51739e7	0.00521793
$187$	0	0
$188$	1.41770e10	0.827703
$189$	−1.52800e9	−0.0871054
$190$	−1.42680e9	−0.0794275
$191$	−7.56585e9	−0.411346	−0.205673	−	0.978621i	$-0.565938\pi$
$191$	−7.56585e9	−0.411346	−0.205673	+	0.978621i	$0.565938\pi$
$192$	−2.01282e10	−1.06893
$193$	2.92026e10	1.51500	0.757502	−	0.652833i	$-0.226420\pi$
$193$	2.92026e10	1.51500	0.757502	+	0.652833i	$0.226420\pi$
$194$	−5.08255e8	−0.0257617
$195$	1.66051e10	0.822407
$196$	1.90686e10	0.922926
$197$	−1.95972e10	−0.927035	−0.463517	−	0.886088i	$-0.653413\pi$
$197$	−1.95972e10	−0.927035	−0.463517	+	0.886088i	$0.653413\pi$
$198$	−1.07454e9	−0.0496854
$199$	3.50959e10	1.58642	0.793209	−	0.608949i	$-0.208409\pi$
$199$	3.50959e10	1.58642	0.793209	+	0.608949i	$0.208409\pi$
$200$	−6.05590e9	−0.267636
$201$	2.34348e10	1.01270
$202$	8.97486e8	0.0379268
$203$	5.94485e9	0.245702
$204$	0	0
$205$	−9.15652e9	−0.362108
$206$	6.31463e9	0.244312
$207$	1.46112e9	0.0553121
$208$	3.28465e10	1.21676
$209$	1.08585e10	0.393650
$210$	−6.63263e8	−0.0235342
$211$	−6.15055e9	−0.213621	−0.106810	−	0.994279i	$-0.534064\pi$
$211$	−6.15055e9	−0.213621	−0.106810	+	0.994279i	$0.534064\pi$
$212$	−2.86373e10	−0.973690
$213$	4.91725e10	1.63687
$214$	6.71493e9	0.218867
$215$	7.69095e9	0.245475
$216$	−4.38219e9	−0.136978
$217$	−1.63979e8	−0.00502017
$218$	1.52720e9	0.0457974
$219$	7.61692e10	2.23759
$220$	−6.50606e9	−0.187248
$221$	0	0
$222$	−2.79260e9	−0.0771650
$223$	6.54916e10	1.77343	0.886715	−	0.462317i	$-0.152982\pi$
$223$	6.54916e10	1.77343	0.886715	+	0.462317i	$0.152982\pi$
$224$	−4.15392e9	−0.110241
$225$	−2.07470e10	−0.539676
$226$	−6.21780e9	−0.158543
$227$	2.44562e10	0.611326	0.305663	−	0.952140i	$-0.401122\pi$
$227$	2.44562e10	0.611326	0.305663	+	0.952140i	$0.401122\pi$
$228$	−4.95411e10	−1.21411
$229$	4.48555e10	1.07784	0.538922	−	0.842355i	$-0.318832\pi$
$229$	4.48555e10	1.07784	0.538922	+	0.842355i	$0.318832\pi$
$230$	−2.79057e8	−0.00657534
$231$	5.04768e9	0.116637
$232$	1.70494e10	0.386378
$233$	6.47327e10	1.43887	0.719436	−	0.694559i	$-0.244401\pi$
$233$	6.47327e10	1.43887	0.719436	+	0.694559i	$0.244401\pi$
$234$	−7.45366e9	−0.162517
$235$	−1.88449e10	−0.403078
$236$	5.01627e10	1.05263
$237$	9.69094e10	1.99526
$238$	0	0
$239$	−6.08077e10	−1.20550	−0.602752	−	0.797929i	$-0.705929\pi$
$239$	−6.08077e10	−1.20550	−0.602752	+	0.797929i	$0.705929\pi$
$240$	2.87177e10	0.558726
$241$	5.03583e10	0.961600	0.480800	−	0.876830i	$-0.340346\pi$
$241$	5.03583e10	0.961600	0.480800	+	0.876830i	$0.340346\pi$
$242$	7.76815e9	0.145596
$243$	−6.41470e10	−1.18018
$244$	4.50953e10	0.814474
$245$	−2.53471e10	−0.449450
$246$	1.00287e10	0.174597
$247$	7.53208e10	1.28759
$248$	−4.70279e8	−0.00789447
$249$	3.82877e10	0.631194
$250$	9.06124e9	0.146709
$251$	−2.14989e10	−0.341888	−0.170944	−	0.985281i	$-0.554682\pi$
$251$	−2.14989e10	−0.341888	−0.170944	+	0.985281i	$0.554682\pi$
$252$	−9.43846e9	−0.147434
$253$	2.12373e9	0.0325880
$254$	−1.34473e10	−0.202714
$255$	0	0
$256$	4.86559e10	0.708037
$257$	−1.92356e10	−0.275046	−0.137523	−	0.990499i	$-0.543914\pi$
$257$	−1.92356e10	−0.275046	−0.137523	+	0.990499i	$0.543914\pi$
$258$	−8.42355e9	−0.118360
$259$	5.37638e9	0.0742405
$260$	−4.51300e10	−0.612470
$261$	5.84096e10	0.779116
$262$	−2.34786e10	−0.307834
$263$	4.81245e10	0.620248	0.310124	−	0.950696i	$-0.399629\pi$
$263$	4.81245e10	0.620248	0.310124	+	0.950696i	$0.399629\pi$
$264$	1.44764e10	0.183418
$265$	3.80664e10	0.474171
$266$	−3.00856e9	−0.0368460
$267$	1.66008e11	1.99907
$268$	−6.36919e10	−0.754185
$269$	1.06346e11	1.23833	0.619166	−	0.785260i	$-0.287471\pi$
$269$	1.06346e11	1.23833	0.619166	+	0.785260i	$0.287471\pi$
$270$	2.86731e9	0.0328350
$271$	4.23092e10	0.476511	0.238255	−	0.971203i	$-0.423424\pi$
$271$	4.23092e10	0.476511	0.238255	+	0.971203i	$0.423424\pi$
$272$	0	0
$273$	3.50138e10	0.381511
$274$	−2.87318e10	−0.307953
$275$	−3.01556e10	−0.317959
$276$	−9.68941e9	−0.100509
$277$	1.52647e10	0.155786	0.0778930	−	0.996962i	$-0.475181\pi$
$277$	1.52647e10	0.155786	0.0778930	+	0.996962i	$0.475181\pi$
$278$	2.65361e10	0.266462
$279$	−1.61113e9	−0.0159189
$280$	3.66214e9	0.0356060
$281$	1.53313e11	1.46690	0.733451	−	0.679743i	$-0.237909\pi$
$281$	1.53313e11	1.46690	0.733451	+	0.679743i	$0.237909\pi$
$282$	2.06400e10	0.194352
$283$	−7.55627e10	−0.700275	−0.350137	−	0.936698i	$-0.613865\pi$
$283$	−7.55627e10	−0.700275	−0.350137	+	0.936698i	$0.613865\pi$
$284$	−1.33643e11	−1.21902
$285$	6.58529e10	0.591252
$286$	−1.08338e10	−0.0957493
$287$	−1.93075e10	−0.167980
$288$	−4.08133e10	−0.349571
$289$	0	0
$290$	−1.11556e10	−0.0926191
$291$	2.34582e10	0.191768
$292$	−2.07015e11	−1.66640
$293$	−2.31333e11	−1.83372	−0.916860	−	0.399208i	$-0.869285\pi$
$293$	−2.31333e11	−1.83372	−0.916860	+	0.399208i	$0.869285\pi$
$294$	2.77615e10	0.216711
$295$	−6.66791e10	−0.512614
$296$	1.54191e10	0.116747
$297$	−2.18213e10	−0.162733
$298$	−2.99015e10	−0.219644
$299$	1.47315e10	0.106592
$300$	1.37583e11	0.980663
$301$	1.62172e10	0.113875
$302$	6.96662e9	0.0481938
$303$	−4.14229e10	−0.282325
$304$	1.30263e11	0.874764
$305$	−5.99433e10	−0.396635
$306$	0	0
$307$	1.65847e11	1.06557	0.532787	−	0.846249i	$-0.321145\pi$
$307$	1.65847e11	1.06557	0.532787	+	0.846249i	$0.321145\pi$
$308$	−1.37187e10	−0.0868633
$309$	−2.91448e11	−1.81864
$310$	3.07708e8	0.00189239
$311$	−1.66218e11	−1.00753	−0.503764	−	0.863841i	$-0.668052\pi$
$311$	−1.66218e11	−1.00753	−0.503764	+	0.863841i	$0.668052\pi$
$312$	1.00417e11	0.599944
$313$	7.92579e9	0.0466759	0.0233380	−	0.999728i	$-0.492571\pi$
$313$	7.92579e9	0.0466759	0.0233380	+	0.999728i	$0.492571\pi$
$314$	5.51221e10	0.319994
$315$	1.25461e10	0.0717981
$316$	−2.63384e11	−1.48592
$317$	−8.14922e10	−0.453262	−0.226631	−	0.973981i	$-0.572771\pi$
$317$	−8.14922e10	−0.453262	−0.226631	+	0.973981i	$0.572771\pi$
$318$	−4.16924e10	−0.228631
$319$	8.48981e10	0.459029
$320$	−7.27170e10	−0.387669
$321$	−3.09923e11	−1.62923
$322$	−5.88423e8	−0.00305027
$323$	0	0
$324$	2.33096e11	1.17512
$325$	−2.09177e11	−1.04001
$326$	−1.35880e10	−0.0666309
$327$	−7.04868e10	−0.340913
$328$	−5.53725e10	−0.264157
$329$	−3.97365e10	−0.186986
$330$	−9.47202e9	−0.0439673
$331$	9.08127e10	0.415834	0.207917	−	0.978146i	$-0.433332\pi$
$331$	9.08127e10	0.415834	0.207917	+	0.978146i	$0.433332\pi$
$332$	−1.04060e11	−0.470068
$333$	5.28243e10	0.235415
$334$	−5.84559e9	−0.0257022
$335$	8.46630e10	0.367276
$336$	6.05544e10	0.259190
$337$	−4.49506e10	−0.189846	−0.0949228	−	0.995485i	$-0.530260\pi$
$337$	−4.49506e10	−0.189846	−0.0949228	+	0.995485i	$0.530260\pi$
$338$	−3.31899e10	−0.138319
$339$	2.86978e11	1.18019
$340$	0	0
$341$	−2.34177e9	−0.00937886
$342$	−2.95598e10	−0.116838
$343$	−1.09587e11	−0.427499
$344$	4.65098e10	0.179073
$345$	1.28797e10	0.0489464
$346$	6.10993e10	0.229189
$347$	−3.04913e10	−0.112900	−0.0564500	−	0.998405i	$-0.517978\pi$
$347$	−3.04913e10	−0.112900	−0.0564500	+	0.998405i	$0.517978\pi$
$348$	−3.87343e11	−1.41576
$349$	−2.13456e11	−0.770182	−0.385091	−	0.922879i	$-0.625830\pi$
$349$	−2.13456e11	−0.770182	−0.385091	+	0.922879i	$0.625830\pi$
$350$	8.35522e9	0.0297613
$351$	−1.51366e11	−0.532286
$352$	−5.93220e10	−0.205956
$353$	−2.39863e11	−0.822199	−0.411100	−	0.911590i	$-0.634855\pi$
$353$	−2.39863e11	−0.822199	−0.411100	+	0.911590i	$0.634855\pi$
$354$	7.30306e10	0.247167
$355$	1.77646e11	0.593645
$356$	−4.51182e11	−1.48877
$357$	0	0
$358$	−4.84231e10	−0.155804
$359$	−1.53027e11	−0.486232	−0.243116	−	0.969997i	$-0.578170\pi$
$359$	−1.53027e11	−0.486232	−0.243116	+	0.969997i	$0.578170\pi$
$360$	3.59814e10	0.112906
$361$	−2.39795e10	−0.0743119
$362$	−3.71269e10	−0.113632
$363$	−3.58534e11	−1.08380
$364$	−9.51615e10	−0.284122
$365$	2.75176e11	0.811508
$366$	6.56532e10	0.191245
$367$	4.44977e11	1.28038	0.640192	−	0.768215i	$-0.278855\pi$
$367$	4.44977e11	1.28038	0.640192	+	0.768215i	$0.278855\pi$
$368$	2.54773e10	0.0724167
$369$	−1.89701e11	−0.532662
$370$	−1.00888e10	−0.0279855
$371$	8.02671e10	0.219966
$372$	1.06842e10	0.0289267
$373$	−5.36112e10	−0.143406	−0.0717028	−	0.997426i	$-0.522843\pi$
$373$	−5.36112e10	−0.143406	−0.0717028	+	0.997426i	$0.522843\pi$
$374$	0	0
$375$	−4.18216e11	−1.09209
$376$	−1.13961e11	−0.294044
$377$	5.88904e11	1.50144
$378$	6.04603e9	0.0152320
$379$	7.58881e11	1.88928	0.944642	−	0.328103i	$-0.106409\pi$
$379$	7.58881e11	1.88928	0.944642	+	0.328103i	$0.106409\pi$
$380$	−1.78977e11	−0.440323
$381$	6.20654e11	1.50899
$382$	2.99367e10	0.0719316
$383$	2.01994e11	0.479672	0.239836	−	0.970813i	$-0.422906\pi$
$383$	2.01994e11	0.479672	0.239836	+	0.970813i	$0.422906\pi$
$384$	3.58834e11	0.842177
$385$	1.82357e10	0.0423010
$386$	−1.15550e11	−0.264927
$387$	1.59338e11	0.361094
$388$	−6.37555e10	−0.142815
$389$	−8.87156e10	−0.196439	−0.0982193	−	0.995165i	$-0.531315\pi$
$389$	−8.87156e10	−0.196439	−0.0982193	+	0.995165i	$0.531315\pi$
$390$	−6.57036e10	−0.143813
$391$	0	0
$392$	−1.53282e11	−0.327872
$393$	1.08364e12	2.29149
$394$	7.75427e10	0.162109
$395$	3.50105e11	0.723620
$396$	−1.34790e11	−0.275442
$397$	−2.73560e10	−0.0552708	−0.0276354	−	0.999618i	$-0.508798\pi$
$397$	−2.73560e10	−0.0552708	−0.0276354	+	0.999618i	$0.508798\pi$
$398$	−1.38868e11	−0.277415
$399$	1.38858e11	0.274279
$400$	−3.61761e11	−0.706564
$401$	−7.16674e11	−1.38411	−0.692057	−	0.721843i	$-0.743295\pi$
$401$	−7.16674e11	−1.38411	−0.692057	+	0.721843i	$0.743295\pi$
$402$	−9.27276e10	−0.177089
$403$	−1.62439e10	−0.0306774
$404$	1.12580e11	0.210255
$405$	−3.09845e11	−0.572265
$406$	−2.35227e10	−0.0429656
$407$	7.67798e10	0.138699
$408$	0	0
$409$	−7.13651e11	−1.26105	−0.630523	−	0.776170i	$-0.717160\pi$
$409$	−7.13651e11	−1.26105	−0.630523	+	0.776170i	$0.717160\pi$
$410$	3.62307e10	0.0633213
$411$	1.32610e12	2.29238
$412$	7.92106e11	1.35440
$413$	−1.40600e11	−0.237799
$414$	−5.78140e9	−0.00967235
$415$	1.38322e11	0.228915
$416$	−4.11493e11	−0.673662
$417$	−1.22476e12	−1.98353
$418$	−4.29650e10	−0.0688370
$419$	3.65834e11	0.579857	0.289929	−	0.957048i	$-0.406368\pi$
$419$	3.65834e11	0.579857	0.289929	+	0.957048i	$0.406368\pi$
$420$	−8.31996e10	−0.130467
$421$	1.11491e11	0.172971	0.0864853	−	0.996253i	$-0.472436\pi$
$421$	1.11491e11	0.172971	0.0864853	+	0.996253i	$0.472436\pi$
$422$	2.43367e10	0.0373555
$423$	−3.90422e11	−0.592928
$424$	2.30200e11	0.345907
$425$	0	0
$426$	−1.94567e11	−0.286237
$427$	−1.26397e11	−0.183997
$428$	8.42320e11	1.21333
$429$	5.00029e11	0.712751
$430$	−3.04318e10	−0.0429259
$431$	−7.96580e11	−1.11194	−0.555970	−	0.831202i	$-0.687653\pi$
$431$	−7.96580e11	−1.11194	−0.555970	+	0.831202i	$0.687653\pi$
$432$	−2.61779e11	−0.361624
$433$	−8.15766e11	−1.11524	−0.557622	−	0.830095i	$-0.688286\pi$
$433$	−8.15766e11	−1.11524	−0.557622	+	0.830095i	$0.688286\pi$
$434$	6.48835e8	0.000877871 0
$435$	5.14878e11	0.689450
$436$	1.91571e11	0.253887
$437$	5.84223e10	0.0766324
$438$	−3.01388e11	−0.391284
$439$	−3.43284e11	−0.441126	−0.220563	−	0.975373i	$-0.570790\pi$
$439$	−3.43284e11	−0.441126	−0.220563	+	0.975373i	$0.570790\pi$
$440$	5.22988e10	0.0665203
$441$	−5.25131e11	−0.661141
$442$	0	0
$443$	−3.16747e11	−0.390748	−0.195374	−	0.980729i	$-0.562592\pi$
$443$	−3.16747e11	−0.390748	−0.195374	+	0.980729i	$0.562592\pi$
$444$	−3.50304e11	−0.427781
$445$	5.99737e11	0.725005
$446$	−2.59139e11	−0.310117
$447$	1.38008e12	1.63501
$448$	−1.53332e11	−0.179838
$449$	9.33133e11	1.08351	0.541757	−	0.840535i	$-0.317759\pi$
$449$	9.33133e11	1.08351	0.541757	+	0.840535i	$0.317759\pi$
$450$	8.20921e10	0.0943724
$451$	−2.75730e11	−0.313826
$452$	−7.79959e11	−0.878919
$453$	−3.21540e11	−0.358751
$454$	−9.67690e10	−0.106902
$455$	1.26494e11	0.138363
$456$	3.98234e11	0.431317
$457$	4.53643e10	0.0486510	0.0243255	−	0.999704i	$-0.492256\pi$
$457$	4.53643e10	0.0486510	0.0243255	+	0.999704i	$0.492256\pi$
$458$	−1.77485e11	−0.188481
$459$	0	0
$460$	−3.50049e10	−0.0364518
$461$	−6.13653e11	−0.632803	−0.316402	−	0.948625i	$-0.602475\pi$
$461$	−6.13653e11	−0.632803	−0.316402	+	0.948625i	$0.602475\pi$
$462$	−1.99728e10	−0.0203962
$463$	8.36356e11	0.845817	0.422909	−	0.906172i	$-0.361009\pi$
$463$	8.36356e11	0.845817	0.422909	+	0.906172i	$0.361009\pi$
$464$	1.01848e12	1.02005
$465$	−1.42021e10	−0.0140868
$466$	−2.56136e11	−0.251613
$467$	−1.27053e12	−1.23612	−0.618058	−	0.786132i	$-0.712080\pi$
$467$	−1.27053e12	−1.23612	−0.618058	+	0.786132i	$0.712080\pi$
$468$	−9.34985e11	−0.900945
$469$	1.78521e11	0.170377
$470$	7.45660e10	0.0704856
$471$	−2.54413e12	−2.38202
$472$	−4.03231e11	−0.373951
$473$	2.31597e11	0.212744
$474$	−3.83454e11	−0.348908
$475$	−8.29558e11	−0.747697
$476$	0	0
$477$	7.88644e11	0.697507
$478$	2.40606e11	0.210805
$479$	−9.42115e11	−0.817700	−0.408850	−	0.912602i	$-0.634070\pi$
$479$	−9.42115e11	−0.817700	−0.408850	+	0.912602i	$0.634070\pi$
$480$	−3.59768e11	−0.309340
$481$	5.32591e11	0.453671
$482$	−1.99259e11	−0.168154
$483$	2.71583e10	0.0227060
$484$	9.74435e11	0.807140
$485$	8.47474e10	0.0695487
$486$	2.53818e11	0.206376
$487$	−2.27491e12	−1.83267	−0.916334	−	0.400416i	$-0.868866\pi$
$487$	−2.27491e12	−1.83267	−0.916334	+	0.400416i	$0.868866\pi$
$488$	−3.62497e11	−0.289344
$489$	6.27145e11	0.495996
$490$	1.00294e11	0.0785946
$491$	−1.37358e12	−1.06657	−0.533283	−	0.845937i	$-0.679042\pi$
$491$	−1.37358e12	−1.06657	−0.533283	+	0.845937i	$0.679042\pi$
$492$	1.25800e12	0.967917
$493$	0	0
$494$	−2.98031e11	−0.225160
$495$	1.79171e11	0.134136
$496$	−2.80930e10	−0.0208416
$497$	3.74585e11	0.275389
$498$	−1.51498e11	−0.110376
$499$	1.15079e12	0.830888	0.415444	−	0.909619i	$-0.363626\pi$
$499$	1.15079e12	0.830888	0.415444	+	0.909619i	$0.363626\pi$
$500$	1.13664e12	0.813313
$501$	2.69800e11	0.191325
$502$	8.50673e10	0.0597855
$503$	−2.14538e12	−1.49434	−0.747169	−	0.664634i	$-0.768587\pi$
$503$	−2.14538e12	−1.49434	−0.747169	+	0.664634i	$0.768587\pi$
$504$	7.58707e10	0.0523765
$505$	−1.49648e11	−0.102391
$506$	−8.40324e9	−0.00569862
$507$	1.53186e12	1.02963
$508$	−1.68683e12	−1.12379
$509$	−1.84538e12	−1.21858	−0.609292	−	0.792946i	$-0.708546\pi$
$509$	−1.84538e12	−1.21858	−0.609292	+	0.792946i	$0.708546\pi$
$510$	0	0
$511$	5.80239e11	0.376455
$512$	−1.19854e12	−0.770791
$513$	−6.00288e11	−0.382676
$514$	7.61118e10	0.0480970
$515$	−1.05291e12	−0.659568
$516$	−1.05665e12	−0.656156
$517$	−5.67475e11	−0.349333
$518$	−2.12734e10	−0.0129823
$519$	−2.82000e12	−1.70607
$520$	3.62776e11	0.217582
$521$	1.19539e12	0.710789	0.355394	−	0.934716i	$-0.384347\pi$
$521$	1.19539e12	0.710789	0.355394	+	0.934716i	$0.384347\pi$
$522$	−2.31117e11	−0.136243
$523$	1.69163e12	0.988664	0.494332	−	0.869273i	$-0.335413\pi$
$523$	1.69163e12	0.988664	0.494332	+	0.869273i	$0.335413\pi$
$524$	−2.94515e12	−1.70654
$525$	−3.85630e11	−0.221541
$526$	−1.90420e11	−0.108462
$527$	0	0
$528$	8.64774e11	0.484228
$529$	−1.78973e12	−0.993656
$530$	−1.50622e11	−0.0829176
$531$	−1.38143e12	−0.754057
$532$	−3.77393e11	−0.204264
$533$	−1.91263e12	−1.02650
$534$	−6.56865e11	−0.349575
$535$	−1.11966e12	−0.590873
$536$	5.11985e11	0.267927
$537$	2.23494e12	1.15979
$538$	−4.20793e11	−0.216545
$539$	−7.63276e11	−0.389522
$540$	3.59675e11	0.182028
$541$	−6.33349e11	−0.317874	−0.158937	−	0.987289i	$-0.550807\pi$
$541$	−6.33349e11	−0.317874	−0.158937	+	0.987289i	$0.550807\pi$
$542$	−1.67410e11	−0.0833268
$543$	1.71357e12	0.845868
$544$	0	0
$545$	−2.54648e11	−0.123639
$546$	−1.38543e11	−0.0667142
$547$	−2.98980e12	−1.42790	−0.713951	−	0.700195i	$-0.753096\pi$
$547$	−2.98980e12	−1.42790	−0.713951	+	0.700195i	$0.753096\pi$
$548$	−3.60411e12	−1.70720
$549$	−1.24188e12	−0.583451
$550$	1.19320e11	0.0556010
$551$	2.33548e12	1.07943
$552$	7.78880e10	0.0357063
$553$	7.38234e11	0.335684
$554$	−6.03996e10	−0.0272421
$555$	4.65644e11	0.208322
$556$	3.32869e12	1.47719
$557$	1.91155e12	0.841467	0.420734	−	0.907184i	$-0.361773\pi$
$557$	1.91155e12	0.841467	0.420734	+	0.907184i	$0.361773\pi$
$558$	6.37497e9	0.00278371
$559$	1.60650e12	0.695868
$560$	2.18765e11	0.0940007
$561$	0	0
$562$	−6.06633e11	−0.256515
$563$	−1.60070e11	−0.0671464	−0.0335732	−	0.999436i	$-0.510689\pi$
$563$	−1.60070e11	−0.0671464	−0.0335732	+	0.999436i	$0.510689\pi$
$564$	2.58908e12	1.07743
$565$	1.03677e12	0.428019
$566$	2.98988e11	0.122456
$567$	−6.53342e11	−0.265471
$568$	1.07428e12	0.433063
$569$	3.51734e12	1.40673	0.703363	−	0.710831i	$-0.251681\pi$
$569$	3.51734e12	1.40673	0.703363	+	0.710831i	$0.251681\pi$
$570$	−2.60568e11	−0.103391
$571$	−9.48264e11	−0.373307	−0.186654	−	0.982426i	$-0.559764\pi$
$571$	−9.48264e11	−0.373307	−0.186654	+	0.982426i	$0.559764\pi$
$572$	−1.35900e12	−0.530806
$573$	−1.38171e12	−0.535453
$574$	7.63965e10	0.0293744
$575$	−1.62248e11	−0.0618975
$576$	−1.50652e12	−0.570262
$577$	−9.37507e11	−0.352114	−0.176057	−	0.984380i	$-0.556334\pi$
$577$	−9.37507e11	−0.352114	−0.176057	+	0.984380i	$0.556334\pi$
$578$	0	0
$579$	5.33312e12	1.97210
$580$	−1.39935e12	−0.513454
$581$	2.91667e11	0.106193
$582$	−9.28201e10	−0.0335342
$583$	1.14629e12	0.410947
$584$	1.66408e12	0.591993
$585$	1.24284e12	0.438745
$586$	9.15344e11	0.320660
$587$	4.85666e12	1.68837	0.844183	−	0.536056i	$-0.180086\pi$
$587$	4.85666e12	1.68837	0.844183	+	0.536056i	$0.180086\pi$
$588$	3.48240e12	1.20138
$589$	−6.44204e10	−0.0220549
$590$	2.63837e11	0.0896401
$591$	−3.57894e12	−1.20673
$592$	9.21087e11	0.308214
$593$	5.42334e12	1.80103	0.900514	−	0.434827i	$-0.143191\pi$
$593$	5.42334e12	1.80103	0.900514	+	0.434827i	$0.143191\pi$
$594$	8.63430e10	0.0284569
$595$	0	0
$596$	−3.75083e12	−1.21764
$597$	6.40939e12	2.06506
$598$	−5.82899e10	−0.0186397
$599$	3.12151e12	0.990705	0.495353	−	0.868692i	$-0.335039\pi$
$599$	3.12151e12	0.990705	0.495353	+	0.868692i	$0.335039\pi$
$600$	−1.10596e12	−0.348384
$601$	−7.75927e11	−0.242597	−0.121299	−	0.992616i	$-0.538706\pi$
$601$	−7.75927e11	−0.242597	−0.121299	+	0.992616i	$0.538706\pi$
$602$	−6.41687e10	−0.0199131
$603$	1.75402e12	0.540263
$604$	8.73892e11	0.267172
$605$	−1.29528e12	−0.393064
$606$	1.63903e11	0.0493697
$607$	1.25360e12	0.374809	0.187405	−	0.982283i	$-0.439992\pi$
$607$	1.25360e12	0.374809	0.187405	+	0.982283i	$0.439992\pi$
$608$	−1.63190e12	−0.484316
$609$	1.08568e12	0.319833
$610$	2.37185e11	0.0693590
$611$	−3.93635e12	−1.14264
$612$	0	0
$613$	−3.33713e12	−0.954554	−0.477277	−	0.878753i	$-0.658376\pi$
$613$	−3.33713e12	−0.954554	−0.477277	+	0.878753i	$0.658376\pi$
$614$	−6.56226e11	−0.186335
$615$	−1.67221e12	−0.471359
$616$	1.10278e11	0.0308585
$617$	−4.96319e12	−1.37873	−0.689363	−	0.724416i	$-0.742109\pi$
$617$	−4.96319e12	−1.37873	−0.689363	+	0.724416i	$0.742109\pi$
$618$	1.15321e12	0.318024
$619$	−3.95959e12	−1.08403	−0.542016	−	0.840368i	$-0.682339\pi$
$619$	−3.95959e12	−1.08403	−0.542016	+	0.840368i	$0.682339\pi$
$620$	3.85988e10	0.0104909
$621$	−1.17406e11	−0.0316795
$622$	6.57697e11	0.176185
$623$	1.26461e12	0.336326
$624$	5.99859e12	1.58387
$625$	1.45363e12	0.381059
$626$	−3.13610e10	−0.00816215
$627$	1.98302e12	0.512417
$628$	6.91451e12	1.77396
$629$	0	0
$630$	−4.96429e10	−0.0125552
$631$	3.13859e12	0.788138	0.394069	−	0.919081i	$-0.371067\pi$
$631$	3.13859e12	0.788138	0.394069	+	0.919081i	$0.371067\pi$
$632$	2.11720e12	0.527879
$633$	−1.12324e12	−0.278072
$634$	3.22451e11	0.0792613
$635$	2.24223e12	0.547267
$636$	−5.22988e12	−1.26746
$637$	−5.29454e12	−1.27409
$638$	−3.35927e11	−0.0802697
$639$	3.68039e12	0.873253
$640$	1.29636e12	0.305433
$641$	−1.76581e12	−0.413127	−0.206563	−	0.978433i	$-0.566228\pi$
$641$	−1.76581e12	−0.413127	−0.206563	+	0.978433i	$0.566228\pi$
$642$	1.22631e12	0.284901
$643$	−6.17913e11	−0.142554	−0.0712768	−	0.997457i	$-0.522707\pi$
$643$	−6.17913e11	−0.142554	−0.0712768	+	0.997457i	$0.522707\pi$
$644$	−7.38117e10	−0.0169098
$645$	1.40456e12	0.319537
$646$	0	0
$647$	−2.60438e12	−0.584299	−0.292150	−	0.956373i	$-0.594371\pi$
$647$	−2.60438e12	−0.584299	−0.292150	+	0.956373i	$0.594371\pi$
$648$	−1.87374e12	−0.417466
$649$	−2.00790e12	−0.444264
$650$	8.27678e11	0.181866
$651$	−2.99466e10	−0.00653481
$652$	−1.70447e12	−0.369383
$653$	−8.76865e12	−1.88722	−0.943612	−	0.331053i	$-0.892596\pi$
$653$	−8.76865e12	−1.88722	−0.943612	+	0.331053i	$0.892596\pi$
$654$	2.78904e11	0.0596149
$655$	3.91486e12	0.831057
$656$	−3.30778e12	−0.697381
$657$	5.70099e12	1.19373
$658$	1.57231e11	0.0326979
$659$	−7.61129e12	−1.57208	−0.786039	−	0.618177i	$-0.787871\pi$
$659$	−7.61129e12	−1.57208	−0.786039	+	0.618177i	$0.787871\pi$
$660$	−1.18817e12	−0.243742
$661$	8.20966e12	1.67270	0.836351	−	0.548194i	$-0.184684\pi$
$661$	8.20966e12	1.67270	0.836351	+	0.548194i	$0.184684\pi$
$662$	−3.59330e11	−0.0727164
$663$	0	0
$664$	8.36479e11	0.166993
$665$	5.01652e11	0.0994730
$666$	−2.09016e11	−0.0411667
$667$	4.56782e11	0.0893598
$668$	−7.33270e11	−0.142485
$669$	1.19604e13	2.30849
$670$	−3.34997e11	−0.0642250
$671$	−1.80507e12	−0.343750
$672$	−7.58610e11	−0.143502
$673$	−8.10528e12	−1.52300	−0.761500	−	0.648165i	$-0.775537\pi$
$673$	−8.10528e12	−1.52300	−0.761500	+	0.648165i	$0.775537\pi$
$674$	1.77861e11	0.0331980
$675$	1.66709e12	0.309095
$676$	−4.16334e12	−0.766799
$677$	4.13004e12	0.755622	0.377811	−	0.925883i	$-0.376677\pi$
$677$	4.13004e12	0.755622	0.377811	+	0.925883i	$0.376677\pi$
$678$	−1.13552e12	−0.206378
$679$	1.78699e11	0.0322633
$680$	0	0
$681$	4.46631e12	0.795769
$682$	9.26598e9	0.00164007
$683$	−6.98832e11	−0.122880	−0.0614398	−	0.998111i	$-0.519569\pi$
$683$	−6.98832e11	−0.122880	−0.0614398	+	0.998111i	$0.519569\pi$
$684$	−3.70798e12	−0.647716
$685$	4.79079e12	0.831380
$686$	4.33616e11	0.0747561
$687$	8.19173e12	1.40304
$688$	2.77835e12	0.472758
$689$	7.95135e12	1.34417
$690$	−5.09628e10	−0.00855919
$691$	−1.71972e12	−0.286951	−0.143475	−	0.989654i	$-0.545828\pi$
$691$	−1.71972e12	−0.286951	−0.143475	+	0.989654i	$0.545828\pi$
$692$	7.66429e12	1.27056
$693$	3.77801e11	0.0622248
$694$	1.20649e11	0.0197427
$695$	−4.42468e12	−0.719367
$696$	3.11364e12	0.502952
$697$	0	0
$698$	8.44606e11	0.134681
$699$	1.18218e13	1.87299
$700$	1.04808e12	0.164988
$701$	3.68982e12	0.577130	0.288565	−	0.957460i	$-0.406822\pi$
$701$	3.68982e12	0.577130	0.288565	+	0.957460i	$0.406822\pi$
$702$	5.98927e11	0.0930801
$703$	2.11216e12	0.326157
$704$	−2.18972e12	−0.335979
$705$	−3.44155e12	−0.524690
$706$	9.49096e11	0.143777
$707$	−3.15550e11	−0.0474986
$708$	9.16095e12	1.37022
$709$	−2.52294e11	−0.0374973	−0.0187486	−	0.999824i	$-0.505968\pi$
$709$	−2.52294e11	−0.0374973	−0.0187486	+	0.999824i	$0.505968\pi$
$710$	−7.02912e11	−0.103810
$711$	7.25333e12	1.06445
$712$	3.62681e12	0.528889
$713$	−1.25996e10	−0.00182580
$714$	0	0
$715$	1.80646e12	0.258494
$716$	−6.07418e12	−0.863733
$717$	−1.11050e13	−1.56922
$718$	6.05501e11	0.0850267
$719$	−3.80356e12	−0.530775	−0.265387	−	0.964142i	$-0.585500\pi$
$719$	−3.80356e12	−0.530775	−0.265387	+	0.964142i	$0.585500\pi$
$720$	2.14942e12	0.298074
$721$	−2.22018e12	−0.305971
$722$	9.48828e10	0.0129948
$723$	9.19668e12	1.25172
$724$	−4.65720e12	−0.629943
$725$	−6.48599e12	−0.871878
$726$	1.41866e12	0.189523
$727$	−4.08142e12	−0.541885	−0.270942	−	0.962596i	$-0.587335\pi$
$727$	−4.08142e12	−0.541885	−0.270942	+	0.962596i	$0.587335\pi$
$728$	7.64952e11	0.100935
$729$	−2.47116e12	−0.324062
$730$	−1.08882e12	−0.141907
$731$	0	0
$732$	8.23552e12	1.06021
$733$	−5.65477e11	−0.0723514	−0.0361757	−	0.999345i	$-0.511518\pi$
$733$	−5.65477e11	−0.0723514	−0.0361757	+	0.999345i	$0.511518\pi$
$734$	−1.76069e12	−0.223899
$735$	−4.62901e12	−0.585053
$736$	−3.19173e11	−0.0400937
$737$	2.54945e12	0.318305
$738$	7.50614e11	0.0931458
$739$	3.23806e12	0.399378	0.199689	−	0.979859i	$-0.436007\pi$
$739$	3.23806e12	0.399378	0.199689	+	0.979859i	$0.436007\pi$
$740$	−1.26554e12	−0.155143
$741$	1.37554e13	1.67607
$742$	−3.17603e11	−0.0384651
$743$	1.12331e11	0.0135223	0.00676116	−	0.999977i	$-0.497848\pi$
$743$	1.12331e11	0.0135223	0.00676116	+	0.999977i	$0.497848\pi$
$744$	−8.58846e10	−0.0102763
$745$	4.98582e12	0.592971
$746$	2.12130e11	0.0250771
$747$	2.86570e12	0.336735
$748$	0	0
$749$	−2.36092e12	−0.274103
$750$	1.65481e12	0.190973
$751$	−1.11898e13	−1.28364	−0.641818	−	0.766857i	$-0.721819\pi$
$751$	−1.11898e13	−1.28364	−0.641818	+	0.766857i	$0.721819\pi$
$752$	−6.80771e12	−0.776284
$753$	−3.92623e12	−0.445039
$754$	−2.33019e12	−0.262555
$755$	−1.16163e12	−0.130108
$756$	7.58413e11	0.0844418
$757$	−1.09891e12	−0.121627	−0.0608136	−	0.998149i	$-0.519370\pi$
$757$	−1.09891e12	−0.121627	−0.0608136	+	0.998149i	$0.519370\pi$
$758$	−3.00276e12	−0.330376
$759$	3.87846e11	0.0424201
$760$	1.43870e12	0.156426
$761$	1.52331e13	1.64649	0.823243	−	0.567688i	$-0.192162\pi$
$761$	1.52331e13	1.64649	0.823243	+	0.567688i	$0.192162\pi$
$762$	−2.45582e12	−0.263875
$763$	−5.36952e11	−0.0573555
$764$	3.75526e12	0.398768
$765$	0	0
$766$	−7.99256e11	−0.0838796
$767$	−1.39280e13	−1.45315
$768$	8.88578e12	0.921658
$769$	−1.36591e13	−1.40849	−0.704245	−	0.709957i	$-0.748714\pi$
$769$	−1.36591e13	−1.40849	−0.704245	+	0.709957i	$0.748714\pi$
$770$	−7.21557e10	−0.00739711
$771$	−3.51289e12	−0.358030
$772$	−1.44945e13	−1.46868
$773$	1.00570e13	1.01312	0.506559	−	0.862206i	$-0.330917\pi$
$773$	1.00570e13	1.01312	0.506559	+	0.862206i	$0.330917\pi$
$774$	−6.30473e11	−0.0631441
$775$	1.78905e11	0.0178142
$776$	5.12496e11	0.0507356
$777$	9.81860e11	0.0966396
$778$	3.51032e11	0.0343509
$779$	−7.58512e12	−0.737979
$780$	−8.24185e12	−0.797259
$781$	5.34943e12	0.514491
$782$	0	0
$783$	−4.69342e12	−0.446232
$784$	−9.15662e12	−0.865591
$785$	−9.19116e12	−0.863887
$786$	−4.28777e12	−0.400710
$787$	−1.41556e13	−1.31536	−0.657678	−	0.753300i	$-0.728461\pi$
$787$	−1.41556e13	−1.31536	−0.657678	+	0.753300i	$0.728461\pi$
$788$	9.72695e12	0.898687
$789$	8.78873e12	0.807383
$790$	−1.38530e12	−0.126538
$791$	2.18614e12	0.198556
$792$	1.08351e12	0.0978516
$793$	−1.25210e13	−1.12437
$794$	1.08243e11	0.00966513
$795$	6.95186e12	0.617233
$796$	−1.74196e13	−1.53791
$797$	9.87015e12	0.866486	0.433243	−	0.901277i	$-0.357369\pi$
$797$	9.87015e12	0.866486	0.433243	+	0.901277i	$0.357369\pi$
$798$	−5.49437e11	−0.0479628
$799$	0	0
$800$	4.53205e12	0.391191
$801$	1.24251e13	1.06648
$802$	2.83575e12	0.242038
$803$	8.28636e12	0.703305
$804$	−1.16317e13	−0.981730
$805$	9.81148e10	0.00823480
$806$	6.42744e10	0.00536452
$807$	1.94215e13	1.61195
$808$	−9.04974e11	−0.0746939
$809$	−5.78041e12	−0.474450	−0.237225	−	0.971455i	$-0.576238\pi$
$809$	−5.78041e12	−0.474450	−0.237225	+	0.971455i	$0.576238\pi$
$810$	1.22600e12	0.100071
$811$	−5.52768e12	−0.448693	−0.224346	−	0.974509i	$-0.572025\pi$
$811$	−5.52768e12	−0.448693	−0.224346	+	0.974509i	$0.572025\pi$
$812$	−2.95069e12	−0.238189
$813$	7.72671e12	0.620279
$814$	−3.03804e11	−0.0242540
$815$	2.26569e12	0.179883
$816$	0	0
$817$	6.37107e12	0.500280
$818$	2.82379e12	0.220517
$819$	2.62066e12	0.203532
$820$	4.54478e12	0.351035
$821$	1.18850e13	0.912966	0.456483	−	0.889732i	$-0.349109\pi$
$821$	1.18850e13	0.912966	0.456483	+	0.889732i	$0.349109\pi$
$822$	−5.24714e12	−0.400866
$823$	1.77543e13	1.34897	0.674486	−	0.738287i	$-0.264365\pi$
$823$	1.77543e13	1.34897	0.674486	+	0.738287i	$0.264365\pi$
$824$	−6.36731e12	−0.481154
$825$	−5.50716e12	−0.413890
$826$	5.56330e11	0.0415836
$827$	−8.74312e12	−0.649968	−0.324984	−	0.945720i	$-0.605359\pi$
$827$	−8.74312e12	−0.649968	−0.324984	+	0.945720i	$0.605359\pi$
$828$	−7.25219e11	−0.0536207
$829$	−1.48141e12	−0.108938	−0.0544691	−	0.998515i	$-0.517347\pi$
$829$	−1.48141e12	−0.108938	−0.0544691	+	0.998515i	$0.517347\pi$
$830$	−5.47316e11	−0.0400301
$831$	2.78771e12	0.202788
$832$	−1.51892e13	−1.09896
$833$	0	0
$834$	4.84615e12	0.346857
$835$	9.74705e11	0.0693880
$836$	−5.38952e12	−0.381612
$837$	1.29460e11	0.00911741
$838$	−1.44754e12	−0.101399
$839$	−2.38370e13	−1.66082	−0.830412	−	0.557150i	$-0.811895\pi$
$839$	−2.38370e13	−1.66082	−0.830412	+	0.557150i	$0.811895\pi$
$840$	6.68797e11	0.0463487
$841$	3.75310e12	0.258707
$842$	−4.41152e11	−0.0302471
$843$	2.79988e13	1.90948
$844$	3.05279e12	0.207088
$845$	5.53415e12	0.373418
$846$	1.54483e12	0.103685
$847$	−2.73123e12	−0.182340
$848$	1.37514e13	0.913202
$849$	−1.37996e13	−0.911555
$850$	0	0
$851$	4.13102e11	0.0270007
$852$	−2.44065e13	−1.58682
$853$	6.02491e12	0.389655	0.194827	−	0.980838i	$-0.437585\pi$
$853$	6.02491e12	0.389655	0.194827	+	0.980838i	$0.437585\pi$
$854$	5.00130e11	0.0321753
$855$	4.92886e12	0.315427
$856$	−6.77095e12	−0.431040
$857$	1.89231e13	1.19834	0.599169	−	0.800622i	$-0.295498\pi$
$857$	1.89231e13	1.19834	0.599169	+	0.800622i	$0.295498\pi$
$858$	−1.97853e12	−0.124638
$859$	2.99413e13	1.87630	0.938149	−	0.346231i	$-0.112539\pi$
$859$	2.99413e13	1.87630	0.938149	+	0.346231i	$0.112539\pi$
$860$	−3.81736e12	−0.237969
$861$	−3.52603e12	−0.218661
$862$	3.15193e12	0.194443
$863$	1.33807e13	0.821163	0.410581	−	0.911824i	$-0.365326\pi$
$863$	1.33807e13	0.821163	0.410581	+	0.911824i	$0.365326\pi$
$864$	3.27949e12	0.200214
$865$	−1.01878e13	−0.618740
$866$	3.22784e12	0.195021
$867$	0	0
$868$	8.13898e10	0.00486666
$869$	1.05427e13	0.627136
$870$	−2.03728e12	−0.120563
$871$	1.76845e13	1.04115
$872$	−1.53994e12	−0.0901943
$873$	1.75576e12	0.102306
$874$	−2.31167e11	−0.0134006
$875$	−3.18587e12	−0.183735
$876$	−3.78061e13	−2.16917
$877$	−1.95864e13	−1.11804	−0.559019	−	0.829155i	$-0.688822\pi$
$877$	−1.95864e13	−1.11804	−0.559019	+	0.829155i	$0.688822\pi$
$878$	1.35831e12	0.0771392
$879$	−4.22471e13	−2.38697
$880$	3.12417e12	0.175615
$881$	4.31229e12	0.241166	0.120583	−	0.992703i	$-0.461524\pi$
$881$	4.31229e12	0.241166	0.120583	+	0.992703i	$0.461524\pi$
$882$	2.07785e12	0.115613
$883$	−1.27070e13	−0.703427	−0.351714	−	0.936108i	$-0.614401\pi$
$883$	−1.27070e13	−0.703427	−0.351714	+	0.936108i	$0.614401\pi$
$884$	0	0
$885$	−1.21773e13	−0.667275
$886$	1.25331e12	0.0683295
$887$	2.57301e13	1.39568	0.697838	−	0.716255i	$-0.254145\pi$
$887$	2.57301e13	1.39568	0.697838	+	0.716255i	$0.254145\pi$
$888$	2.81590e12	0.151970
$889$	4.72799e12	0.253874
$890$	−2.37305e12	−0.126781
$891$	−9.33035e12	−0.495962
$892$	−3.25064e13	−1.71920
$893$	−1.56108e13	−0.821475
$894$	−5.46075e12	−0.285913
$895$	8.07416e12	0.420623
$896$	2.73352e12	0.141689
$897$	2.69034e12	0.138752
$898$	−3.69224e12	−0.189473
$899$	−5.03678e11	−0.0257179
$900$	1.02976e13	0.523173
$901$	0	0
$902$	1.09101e12	0.0548783
$903$	2.96167e12	0.148232
$904$	6.26967e12	0.312239
$905$	6.19061e12	0.306772
$906$	1.27228e12	0.0627343
$907$	2.36399e12	0.115988	0.0579940	−	0.998317i	$-0.481530\pi$
$907$	2.36399e12	0.115988	0.0579940	+	0.998317i	$0.481530\pi$
$908$	−1.21387e13	−0.592632
$909$	−3.10036e12	−0.150617
$910$	−5.00515e11	−0.0241953
$911$	2.71074e12	0.130393	0.0651967	−	0.997872i	$-0.479233\pi$
$911$	2.71074e12	0.130393	0.0651967	+	0.997872i	$0.479233\pi$
$912$	2.37893e13	1.13869
$913$	4.16528e12	0.198393
$914$	−1.79499e11	−0.00850753
$915$	−1.09471e13	−0.516304
$916$	−2.22637e13	−1.04489
$917$	8.25492e12	0.385523
$918$	0	0
$919$	−3.88596e13	−1.79713	−0.898563	−	0.438845i	$-0.855388\pi$
$919$	−3.88596e13	−1.79713	−0.898563	+	0.438845i	$0.855388\pi$
$920$	2.81386e11	0.0129496
$921$	3.02877e13	1.38707
$922$	2.42812e12	0.110657
$923$	3.71068e13	1.68285
$924$	−2.50538e12	−0.113071
$925$	−5.86578e12	−0.263444
$926$	−3.30931e12	−0.147907
$927$	−2.18138e13	−0.970227
$928$	−1.27592e13	−0.564753
$929$	−1.25508e13	−0.552842	−0.276421	−	0.961037i	$-0.589148\pi$
$929$	−1.25508e13	−0.552842	−0.276421	+	0.961037i	$0.589148\pi$
$930$	5.61951e10	0.00246334
$931$	−2.09972e13	−0.915982
$932$	−3.21296e13	−1.39487
$933$	−3.03556e13	−1.31151
$934$	5.02727e12	0.216158
$935$	0	0
$936$	7.51585e12	0.320064
$937$	2.53353e13	1.07374	0.536869	−	0.843666i	$-0.319607\pi$
$937$	2.53353e13	1.07374	0.536869	+	0.843666i	$0.319607\pi$
$938$	−7.06377e11	−0.0297937
$939$	1.44745e12	0.0607585
$940$	9.35355e12	0.390752
$941$	2.00799e13	0.834848	0.417424	−	0.908712i	$-0.362933\pi$
$941$	2.00799e13	0.834848	0.417424	+	0.908712i	$0.362933\pi$
$942$	1.00667e13	0.416540
$943$	−1.48352e12	−0.0610930
$944$	−2.40878e13	−0.987240
$945$	−1.00813e12	−0.0411218
$946$	−9.16389e11	−0.0372023
$947$	−3.95500e12	−0.159798	−0.0798990	−	0.996803i	$-0.525460\pi$
$947$	−3.95500e12	−0.159798	−0.0798990	+	0.996803i	$0.525460\pi$
$948$	−4.81004e13	−1.93424
$949$	5.74792e13	2.30045
$950$	3.28242e12	0.130749
$951$	−1.48825e13	−0.590016
$952$	0	0
$953$	−1.66236e13	−0.652839	−0.326420	−	0.945225i	$-0.605842\pi$
$953$	−1.66236e13	−0.652839	−0.326420	+	0.945225i	$0.605842\pi$
$954$	−3.12053e12	−0.121972
$955$	−4.99171e12	−0.194193
$956$	3.01815e13	1.16864
$957$	1.55045e13	0.597522
$958$	3.72778e12	0.142990
$959$	1.01019e13	0.385673
$960$	−1.32799e13	−0.504632
$961$	−2.64257e13	−0.999475
$962$	−2.10737e12	−0.0793328
$963$	−2.31967e13	−0.869175
$964$	−2.49950e13	−0.932195
$965$	1.92670e13	0.715221
$966$	−1.07461e11	−0.00397057
$967$	−1.78634e13	−0.656971	−0.328485	−	0.944509i	$-0.606538\pi$
$967$	−1.78634e13	−0.656971	−0.328485	+	0.944509i	$0.606538\pi$
$968$	−7.83296e12	−0.286739
$969$	0	0
$970$	−3.35331e11	−0.0121619
$971$	1.38434e13	0.499753	0.249876	−	0.968278i	$-0.419610\pi$
$971$	1.38434e13	0.499753	0.249876	+	0.968278i	$0.419610\pi$
$972$	3.18390e13	1.14409
$973$	−9.32993e12	−0.333711
$974$	9.00142e12	0.320476
$975$	−3.82010e13	−1.35380
$976$	−2.16545e13	−0.763876
$977$	−2.71440e13	−0.953120	−0.476560	−	0.879142i	$-0.658117\pi$
$977$	−2.71440e13	−0.953120	−0.476560	+	0.879142i	$0.658117\pi$
$978$	−2.48150e12	−0.0867341
$979$	1.80598e13	0.628336
$980$	1.25809e13	0.435706
$981$	−5.27569e12	−0.181873
$982$	5.43502e12	0.186509
$983$	2.30552e13	0.787549	0.393774	−	0.919207i	$-0.371169\pi$
$983$	2.30552e13	0.787549	0.393774	+	0.919207i	$0.371169\pi$
$984$	−1.01124e13	−0.343856
$985$	−1.29296e13	−0.437646
$986$	0	0
$987$	−7.25688e12	−0.243401
$988$	−3.73850e13	−1.24822
$989$	1.24607e12	0.0414153
$990$	−7.08947e11	−0.0234561
$991$	4.38273e13	1.44349	0.721744	−	0.692160i	$-0.243341\pi$
$991$	4.38273e13	1.44349	0.721744	+	0.692160i	$0.243341\pi$
$992$	3.51942e11	0.0115390
$993$	1.65846e13	0.541296
$994$	−1.48217e12	−0.0481569
$995$	2.31552e13	0.748935
$996$	−1.90039e13	−0.611892
$997$	1.29940e13	0.416499	0.208250	−	0.978076i	$-0.433223\pi$
$997$	1.29940e13	0.416499	0.208250	+	0.978076i	$0.433223\pi$
$998$	−4.55346e12	−0.145296
$999$	−4.24461e12	−0.134832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.24		52
17.3	odd	16		17.10.d.a.9.6	yes	52
17.6	odd	16		17.10.d.a.2.6	✓	52
17.16	even	2	inner	289.10.a.i.1.23		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.2.6	✓	52	17.6	odd	16
17.10.d.a.9.6	yes	52	17.3	odd	16
289.10.a.i.1.23		52	17.16	even	2	inner
289.10.a.i.1.24		52	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-3.95683 q^{2} +182.625 q^{3} -496.344 q^{4} +659.768 q^{5} -722.614 q^{6} +1391.19 q^{7} +3989.84 q^{8} +13668.8 q^{9} +O(q^{10})\)	\(q-3.95683 q^{2} +182.625 q^{3} -496.344 q^{4} +659.768 q^{5} -722.614 q^{6} +1391.19 q^{7} +3989.84 q^{8} +13668.8 q^{9} -2610.59 q^{10} +19867.6 q^{11} -90644.6 q^{12} +137813. q^{13} -5504.71 q^{14} +120490. q^{15} +238341. q^{16} -54085.2 q^{18} +546542. q^{19} -327472. q^{20} +254066. q^{21} -78612.5 q^{22} +106894. q^{23} +728644. q^{24} -1.51783e6 q^{25} -545303. q^{26} -1.09834e6 q^{27} -690510. q^{28} +4.27320e6 q^{29} -476758. q^{30} -117869. q^{31} -2.98587e6 q^{32} +3.62831e6 q^{33} +917865. q^{35} -6.78443e6 q^{36} +3.86458e6 q^{37} -2.16257e6 q^{38} +2.51681e7 q^{39} +2.63237e6 q^{40} -1.38784e7 q^{41} -1.00530e6 q^{42} +1.16571e7 q^{43} -9.86113e6 q^{44} +9.01826e6 q^{45} -422963. q^{46} -2.85629e7 q^{47} +4.35269e7 q^{48} -3.84182e7 q^{49} +6.00579e6 q^{50} -6.84028e7 q^{52} +5.76966e7 q^{53} +4.34593e6 q^{54} +1.31080e7 q^{55} +5.55064e6 q^{56} +9.98121e7 q^{57} -1.69083e7 q^{58} -1.01064e8 q^{59} -5.98045e7 q^{60} -9.08550e7 q^{61} +466388. q^{62} +1.90160e7 q^{63} -1.10216e8 q^{64} +9.09249e7 q^{65} -1.43566e7 q^{66} +1.28322e8 q^{67} +1.95216e7 q^{69} -3.63183e6 q^{70} +2.69254e8 q^{71} +5.45364e7 q^{72} +4.17080e8 q^{73} -1.52915e7 q^{74} -2.77194e8 q^{75} -2.71273e8 q^{76} +2.76396e7 q^{77} -9.95859e7 q^{78} +5.30648e8 q^{79} +1.57250e8 q^{80} -4.69627e8 q^{81} +5.49143e7 q^{82} +2.09652e8 q^{83} -1.26104e8 q^{84} -4.61249e7 q^{86} +7.80392e8 q^{87} +7.92684e7 q^{88} +9.09011e8 q^{89} -3.56837e7 q^{90} +1.91725e8 q^{91} -5.30564e7 q^{92} -2.15258e7 q^{93} +1.13018e8 q^{94} +3.60591e8 q^{95} -5.45294e8 q^{96} +1.28450e8 q^{97} +1.52014e8 q^{98} +2.71566e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 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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