LMFDB - Embedded newform 49.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,10,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, 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("49.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	49.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:	$25.2367559720$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{193}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 48 $ x^2 - x - 48
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$7.44622$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.8924 q^{2} -109.817 q^{3} -226.645 q^{4} +2438.78 q^{5} +1855.08 q^{6} +12477.5 q^{8} -7623.25 q^{9} +O(q^{10})$	\(q-16.8924 q^{2} -109.817 q^{3} -226.645 q^{4} +2438.78 q^{5} +1855.08 q^{6} +12477.5 q^{8} -7623.25 q^{9} -41197.0 q^{10} -28548.3 q^{11} +24889.5 q^{12} -138149. q^{13} -267819. q^{15} -94733.5 q^{16} +101010. q^{17} +128775. q^{18} +488928. q^{19} -552739. q^{20} +482250. q^{22} -140071. q^{23} -1.37024e6 q^{24} +3.99453e6 q^{25} +2.33367e6 q^{26} +2.99869e6 q^{27} -6.31716e6 q^{29} +4.52413e6 q^{30} +1.00903e6 q^{31} -4.78821e6 q^{32} +3.13508e6 q^{33} -1.70630e6 q^{34} +1.72777e6 q^{36} +1.19206e7 q^{37} -8.25919e6 q^{38} +1.51711e7 q^{39} +3.04300e7 q^{40} +2.15106e7 q^{41} +1.65957e7 q^{43} +6.47033e6 q^{44} -1.85915e7 q^{45} +2.36615e6 q^{46} +2.67441e7 q^{47} +1.04033e7 q^{48} -6.74774e7 q^{50} -1.10926e7 q^{51} +3.13108e7 q^{52} +3.74991e7 q^{53} -5.06552e7 q^{54} -6.96230e7 q^{55} -5.36926e7 q^{57} +1.06712e8 q^{58} -1.81907e7 q^{59} +6.07000e7 q^{60} +2.50111e7 q^{61} -1.70449e7 q^{62} +1.29388e8 q^{64} -3.36915e8 q^{65} -5.29592e7 q^{66} -2.18572e8 q^{67} -2.28934e7 q^{68} +1.53822e7 q^{69} +3.12688e8 q^{71} -9.51193e7 q^{72} +2.89038e8 q^{73} -2.01369e8 q^{74} -4.38667e8 q^{75} -1.10813e8 q^{76} -2.56276e8 q^{78} +4.68685e8 q^{79} -2.31034e8 q^{80} -1.79258e8 q^{81} -3.63366e8 q^{82} +7.75407e7 q^{83} +2.46341e8 q^{85} -2.80342e8 q^{86} +6.93730e8 q^{87} -3.56212e8 q^{88} -3.37680e8 q^{89} +3.14055e8 q^{90} +3.17465e7 q^{92} -1.10808e8 q^{93} -4.51773e8 q^{94} +1.19239e9 q^{95} +5.25827e8 q^{96} +7.36733e8 q^{97} +2.17631e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{2} + 86 q^{3} - 620 q^{4} + 2238 q^{5} + 3988 q^{6} + 2616 q^{8} + 11038 q^{9}+O(q^{10}) $ 2 * q - 6 * q^2 + 86 * q^3 - 620 * q^4 + 2238 * q^5 + 3988 * q^6 + 2616 * q^8 + 11038 * q^9	\( 2 q - 6 q^{2} + 86 q^{3} - 620 q^{4} + 2238 q^{5} + 3988 q^{6} + 2616 q^{8} + 11038 q^{9} - 43384 q^{10} + 35316 q^{11} - 52136 q^{12} + 26530 q^{13} - 307136 q^{15} - 752 q^{16} + 463920 q^{17} + 332042 q^{18} + 925426 q^{19} - 473760 q^{20} + 1177888 q^{22} + 778128 q^{23} - 3301296 q^{24} + 2081722 q^{25} + 4127424 q^{26} + 2798612 q^{27} - 10003584 q^{29} + 4095872 q^{30} - 2467260 q^{31} + 1284576 q^{32} + 15640784 q^{33} + 2246676 q^{34} - 5612716 q^{36} + 30735552 q^{37} - 3504660 q^{38} + 47417944 q^{39} + 32409984 q^{40} + 19103448 q^{41} + 4065100 q^{43} - 18650976 q^{44} - 22338298 q^{45} + 12367584 q^{46} + 82195020 q^{47} + 28806496 q^{48} - 88312626 q^{50} + 59971356 q^{51} - 33466384 q^{52} - 55189812 q^{53} - 52834472 q^{54} - 82445816 q^{55} + 31781116 q^{57} + 66558004 q^{58} + 7069218 q^{59} + 76165376 q^{60} - 44316386 q^{61} - 54910200 q^{62} + 147417152 q^{64} - 369979260 q^{65} + 83258464 q^{66} - 241921336 q^{67} - 165645816 q^{68} + 195181152 q^{69} + 206493816 q^{71} - 279147720 q^{72} + 499153188 q^{73} + 3571524 q^{74} - 813228014 q^{75} - 282511768 q^{76} + 94970960 q^{78} + 468535096 q^{79} - 249904128 q^{80} - 585745634 q^{81} - 389586092 q^{82} - 444023958 q^{83} + 173475060 q^{85} - 416830608 q^{86} - 28134340 q^{87} - 986010816 q^{88} - 636267396 q^{89} + 273242728 q^{90} - 329431488 q^{92} - 791523960 q^{93} + 152223192 q^{94} + 1104747984 q^{95} + 1714981184 q^{96} + 1632716064 q^{97} + 1409417860 q^{99}+O(q^{100}) \) 2 * q - 6 * q^2 + 86 * q^3 - 620 * q^4 + 2238 * q^5 + 3988 * q^6 + 2616 * q^8 + 11038 * q^9 - 43384 * q^10 + 35316 * q^11 - 52136 * q^12 + 26530 * q^13 - 307136 * q^15 - 752 * q^16 + 463920 * q^17 + 332042 * q^18 + 925426 * q^19 - 473760 * q^20 + 1177888 * q^22 + 778128 * q^23 - 3301296 * q^24 + 2081722 * q^25 + 4127424 * q^26 + 2798612 * q^27 - 10003584 * q^29 + 4095872 * q^30 - 2467260 * q^31 + 1284576 * q^32 + 15640784 * q^33 + 2246676 * q^34 - 5612716 * q^36 + 30735552 * q^37 - 3504660 * q^38 + 47417944 * q^39 + 32409984 * q^40 + 19103448 * q^41 + 4065100 * q^43 - 18650976 * q^44 - 22338298 * q^45 + 12367584 * q^46 + 82195020 * q^47 + 28806496 * q^48 - 88312626 * q^50 + 59971356 * q^51 - 33466384 * q^52 - 55189812 * q^53 - 52834472 * q^54 - 82445816 * q^55 + 31781116 * q^57 + 66558004 * q^58 + 7069218 * q^59 + 76165376 * q^60 - 44316386 * q^61 - 54910200 * q^62 + 147417152 * q^64 - 369979260 * q^65 + 83258464 * q^66 - 241921336 * q^67 - 165645816 * q^68 + 195181152 * q^69 + 206493816 * q^71 - 279147720 * q^72 + 499153188 * q^73 + 3571524 * q^74 - 813228014 * q^75 - 282511768 * q^76 + 94970960 * q^78 + 468535096 * q^79 - 249904128 * q^80 - 585745634 * q^81 - 389586092 * q^82 - 444023958 * q^83 + 173475060 * q^85 - 416830608 * q^86 - 28134340 * q^87 - 986010816 * q^88 - 636267396 * q^89 + 273242728 * q^90 - 329431488 * q^92 - 791523960 * q^93 + 152223192 * q^94 + 1104747984 * q^95 + 1714981184 * q^96 + 1632716064 * q^97 + 1409417860 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−16.8924	−0.746548	−0.373274	−	0.927721i	$-0.621765\pi$
$2$	−16.8924	−0.746548	−0.373274	+	0.927721i	$0.621765\pi$
$3$	−109.817	−0.782751	−0.391375	−	0.920231i	$-0.628001\pi$
$3$	−109.817	−0.782751	−0.391375	+	0.920231i	$0.628001\pi$
$4$	−226.645	−0.442667
$5$	2438.78	1.74505	0.872525	−	0.488569i	$-0.162481\pi$
$5$	2438.78	1.74505	0.872525	+	0.488569i	$0.162481\pi$
$6$	1855.08	0.584361
$7$	0	0
$7$	0	0
$8$	12477.5	1.07702
$9$	−7623.25	−0.387301
$10$	−41197.0	−1.30276
$11$	−28548.3	−0.587912	−0.293956	−	0.955819i	$-0.594972\pi$
$11$	−28548.3	−0.587912	−0.293956	+	0.955819i	$0.594972\pi$
$12$	24889.5	0.346498
$13$	−138149.	−1.34153	−0.670767	−	0.741668i	$-0.734035\pi$
$13$	−138149.	−1.34153	−0.670767	+	0.741668i	$0.734035\pi$
$14$	0	0
$15$	−267819.	−1.36594
$16$	−94733.5	−0.361380
$17$	101010.	0.293321	0.146661	−	0.989187i	$-0.453147\pi$
$17$	101010.	0.293321	0.146661	+	0.989187i	$0.453147\pi$
$18$	128775.	0.289139
$19$	488928.	0.860704	0.430352	−	0.902661i	$-0.358389\pi$
$19$	488928.	0.860704	0.430352	+	0.902661i	$0.358389\pi$
$20$	−552739.	−0.772476
$21$	0	0
$22$	482250.	0.438905
$23$	−140071.	−0.104370	−0.0521848	−	0.998637i	$-0.516618\pi$
$23$	−140071.	−0.104370	−0.0521848	+	0.998637i	$0.516618\pi$
$24$	−1.37024e6	−0.843038
$25$	3.99453e6	2.04520
$26$	2.33367e6	1.00152
$27$	2.99869e6	1.08591
$28$	0	0
$29$	−6.31716e6	−1.65856	−0.829279	−	0.558835i	$-0.811249\pi$
$29$	−6.31716e6	−1.65856	−0.829279	+	0.558835i	$0.811249\pi$
$30$	4.52413e6	1.01974
$31$	1.00903e6	0.196234	0.0981172	−	0.995175i	$-0.468718\pi$
$31$	1.00903e6	0.196234	0.0981172	+	0.995175i	$0.468718\pi$
$32$	−4.78821e6	−0.807232
$33$	3.13508e6	0.460189
$34$	−1.70630e6	−0.218978
$35$	0	0
$36$	1.72777e6	0.171445
$37$	1.19206e7	1.04566	0.522832	−	0.852436i	$-0.324876\pi$
$37$	1.19206e7	1.04566	0.522832	+	0.852436i	$0.324876\pi$
$38$	−8.25919e6	−0.642556
$39$	1.51711e7	1.05009
$40$	3.04300e7	1.87945
$41$	2.15106e7	1.18884	0.594422	−	0.804153i	$-0.297381\pi$
$41$	2.15106e7	1.18884	0.594422	+	0.804153i	$0.297381\pi$
$42$	0	0
$43$	1.65957e7	0.740265	0.370133	−	0.928979i	$-0.379312\pi$
$43$	1.65957e7	0.740265	0.370133	+	0.928979i	$0.379312\pi$
$44$	6.47033e6	0.260249
$45$	−1.85915e7	−0.675860
$46$	2.36615e6	0.0779169
$47$	2.67441e7	0.799443	0.399721	−	0.916637i	$-0.369107\pi$
$47$	2.67441e7	0.799443	0.399721	+	0.916637i	$0.369107\pi$
$48$	1.04033e7	0.282870
$49$	0	0
$50$	−6.74774e7	−1.52684
$51$	−1.10926e7	−0.229597
$52$	3.13108e7	0.593853
$53$	3.74991e7	0.652799	0.326399	−	0.945232i	$-0.394165\pi$
$53$	3.74991e7	0.652799	0.326399	+	0.945232i	$0.394165\pi$
$54$	−5.06552e7	−0.810684
$55$	−6.96230e7	−1.02594
$56$	0	0
$57$	−5.36926e7	−0.673717
$58$	1.06712e8	1.23819
$59$	−1.81907e7	−0.195441	−0.0977207	−	0.995214i	$-0.531155\pi$
$59$	−1.81907e7	−0.195441	−0.0977207	+	0.995214i	$0.531155\pi$
$60$	6.07000e7	0.604656
$61$	2.50111e7	0.231285	0.115643	−	0.993291i	$-0.463107\pi$
$61$	2.50111e7	0.231285	0.115643	+	0.993291i	$0.463107\pi$
$62$	−1.70449e7	−0.146498
$63$	0	0
$64$	1.29388e8	0.964017
$65$	−3.36915e8	−2.34105
$66$	−5.29592e7	−0.343553
$67$	−2.18572e8	−1.32513	−0.662564	−	0.749005i	$-0.730532\pi$
$67$	−2.18572e8	−1.32513	−0.662564	+	0.749005i	$0.730532\pi$
$68$	−2.28934e7	−0.129844
$69$	1.53822e7	0.0816954
$70$	0	0
$71$	3.12688e8	1.46032	0.730161	−	0.683275i	$-0.239445\pi$
$71$	3.12688e8	1.46032	0.730161	+	0.683275i	$0.239445\pi$
$72$	−9.51193e7	−0.417131
$73$	2.89038e8	1.19125	0.595624	−	0.803264i	$-0.296905\pi$
$73$	2.89038e8	1.19125	0.595624	+	0.803264i	$0.296905\pi$
$74$	−2.01369e8	−0.780638
$75$	−4.38667e8	−1.60088
$76$	−1.10813e8	−0.381005
$77$	0	0
$78$	−2.56276e8	−0.783940
$79$	4.68685e8	1.35381	0.676907	−	0.736069i	$-0.263320\pi$
$79$	4.68685e8	1.35381	0.676907	+	0.736069i	$0.263320\pi$
$80$	−2.31034e8	−0.630626
$81$	−1.79258e8	−0.462696
$82$	−3.63366e8	−0.887529
$83$	7.75407e7	0.179341	0.0896703	−	0.995972i	$-0.471419\pi$
$83$	7.75407e7	0.179341	0.0896703	+	0.995972i	$0.471419\pi$
$84$	0	0
$85$	2.46341e8	0.511860
$86$	−2.80342e8	−0.552643
$87$	6.93730e8	1.29824
$88$	−3.56212e8	−0.633193
$89$	−3.37680e8	−0.570493	−0.285246	−	0.958454i	$-0.592075\pi$
$89$	−3.37680e8	−0.570493	−0.285246	+	0.958454i	$0.592075\pi$
$90$	3.14055e8	0.504562
$91$	0	0
$92$	3.17465e7	0.0462010
$93$	−1.10808e8	−0.153603
$94$	−4.51773e8	−0.596822
$95$	1.19239e9	1.50197
$96$	5.25827e8	0.631862
$97$	7.36733e8	0.844962	0.422481	−	0.906372i	$-0.361159\pi$
$97$	7.36733e8	0.844962	0.422481	+	0.906372i	$0.361159\pi$
$98$	0	0
$99$	2.17631e8	0.227699
$100$	−9.05342e8	−0.905342
$101$	−1.97428e8	−0.188783	−0.0943914	−	0.995535i	$-0.530091\pi$
$101$	−1.97428e8	−0.188783	−0.0943914	+	0.995535i	$0.530091\pi$
$102$	1.87381e8	0.171405
$103$	1.27449e9	1.11576	0.557879	−	0.829922i	$-0.311615\pi$
$103$	1.27449e9	1.11576	0.557879	+	0.829922i	$0.311615\pi$
$104$	−1.72375e9	−1.44486
$105$	0	0
$106$	−6.33451e8	−0.487345
$107$	1.81937e9	1.34182	0.670908	−	0.741541i	$-0.265905\pi$
$107$	1.81937e9	1.34182	0.670908	+	0.741541i	$0.265905\pi$
$108$	−6.79639e8	−0.480697
$109$	−2.31425e8	−0.157033	−0.0785167	−	0.996913i	$-0.525018\pi$
$109$	−2.31425e8	−0.157033	−0.0785167	+	0.996913i	$0.525018\pi$
$110$	1.17610e9	0.765911
$111$	−1.30909e9	−0.818494
$112$	0	0
$113$	−1.51983e9	−0.876885	−0.438443	−	0.898759i	$-0.644470\pi$
$113$	−1.51983e9	−0.876885	−0.438443	+	0.898759i	$0.644470\pi$
$114$	9.06998e8	0.502961
$115$	−3.41604e8	−0.182130
$116$	1.43175e9	0.734188
$117$	1.05314e9	0.519578
$118$	3.07286e8	0.145906
$119$	0	0
$120$	−3.34172e9	−1.47114
$121$	−1.54294e9	−0.654359
$122$	−4.22498e8	−0.172666
$123$	−2.36223e9	−0.930569
$124$	−2.28691e8	−0.0868665
$125$	4.97855e9	1.82393
$126$	0	0
$127$	4.20951e9	1.43587	0.717934	−	0.696111i	$-0.245088\pi$
$127$	4.20951e9	1.43587	0.717934	+	0.696111i	$0.245088\pi$
$128$	2.65883e8	0.0875478
$129$	−1.82249e9	−0.579443
$130$	5.69131e9	1.74770
$131$	4.12131e9	1.22268	0.611342	−	0.791367i	$-0.290630\pi$
$131$	4.12131e9	1.22268	0.611342	+	0.791367i	$0.290630\pi$
$132$	−7.10552e8	−0.203710
$133$	0	0
$134$	3.69221e9	0.989271
$135$	7.31315e9	1.89497
$136$	1.26035e9	0.315913
$137$	−1.27942e9	−0.310292	−0.155146	−	0.987892i	$-0.549585\pi$
$137$	−1.27942e9	−0.310292	−0.155146	+	0.987892i	$0.549585\pi$
$138$	−2.59843e8	−0.0609895
$139$	4.02340e9	0.914170	0.457085	−	0.889423i	$-0.348893\pi$
$139$	4.02340e9	0.914170	0.457085	+	0.889423i	$0.348893\pi$
$140$	0	0
$141$	−2.93695e9	−0.625764
$142$	−5.28206e9	−1.09020
$143$	3.94391e9	0.788705
$144$	7.22177e8	0.139963
$145$	−1.54062e10	−2.89427
$146$	−4.88256e9	−0.889323
$147$	0	0
$148$	−2.70176e9	−0.462880
$149$	−7.67785e8	−0.127615	−0.0638075	−	0.997962i	$-0.520324\pi$
$149$	−7.67785e8	−0.127615	−0.0638075	+	0.997962i	$0.520324\pi$
$150$	7.41016e9	1.19514
$151$	−9.84752e9	−1.54145	−0.770727	−	0.637165i	$-0.780107\pi$
$151$	−9.84752e9	−1.54145	−0.770727	+	0.637165i	$0.780107\pi$
$152$	6.10061e9	0.926995
$153$	−7.70023e8	−0.113604
$154$	0	0
$155$	2.46080e9	0.342439
$156$	−3.43845e9	−0.464839
$157$	−8.04096e9	−1.05623	−0.528116	−	0.849172i	$-0.677102\pi$
$157$	−8.04096e9	−1.05623	−0.528116	+	0.849172i	$0.677102\pi$
$158$	−7.91723e9	−1.01069
$159$	−4.11803e9	−0.510979
$160$	−1.16774e10	−1.40866
$161$	0	0
$162$	3.02811e9	0.345425
$163$	−9.07348e9	−1.00677	−0.503384	−	0.864063i	$-0.667912\pi$
$163$	−9.07348e9	−1.00677	−0.503384	+	0.864063i	$0.667912\pi$
$164$	−4.87527e9	−0.526262
$165$	7.64578e9	0.803053
$166$	−1.30985e9	−0.133886
$167$	8.83471e9	0.878958	0.439479	−	0.898253i	$-0.355163\pi$
$167$	8.83471e9	0.878958	0.439479	+	0.898253i	$0.355163\pi$
$168$	0	0
$169$	8.48058e9	0.799715
$170$	−4.16130e9	−0.382128
$171$	−3.72722e9	−0.333352
$172$	−3.76134e9	−0.327691
$173$	−7.89871e9	−0.670423	−0.335211	−	0.942143i	$-0.608808\pi$
$173$	−7.89871e9	−0.670423	−0.335211	+	0.942143i	$0.608808\pi$
$174$	−1.17188e10	−0.969196
$175$	0	0
$176$	2.70448e9	0.212460
$177$	1.99765e9	0.152982
$178$	5.70424e9	0.425900
$179$	4.59871e9	0.334810	0.167405	−	0.985888i	$-0.446461\pi$
$179$	4.59871e9	0.334810	0.167405	+	0.985888i	$0.446461\pi$
$180$	4.21367e9	0.299181
$181$	6.70993e8	0.0464691	0.0232346	−	0.999730i	$-0.492604\pi$
$181$	6.70993e8	0.0464691	0.0232346	+	0.999730i	$0.492604\pi$
$182$	0	0
$183$	−2.74664e9	−0.181039
$184$	−1.74774e9	−0.112408
$185$	2.90719e10	1.82474
$186$	1.87182e9	0.114672
$187$	−2.88366e9	−0.172447
$188$	−6.06142e9	−0.353887
$189$	0	0
$190$	−2.01424e10	−1.12129
$191$	1.00686e10	0.547416	0.273708	−	0.961813i	$-0.411750\pi$
$191$	1.00686e10	0.547416	0.273708	+	0.961813i	$0.411750\pi$
$192$	−1.42090e10	−0.754585
$193$	−1.97876e10	−1.02656	−0.513281	−	0.858221i	$-0.671570\pi$
$193$	−1.97876e10	−1.02656	−0.513281	+	0.858221i	$0.671570\pi$
$194$	−1.24452e10	−0.630805
$195$	3.69989e10	1.83246
$196$	0	0
$197$	−1.07508e10	−0.508560	−0.254280	−	0.967131i	$-0.581839\pi$
$197$	−1.07508e10	−0.508560	−0.254280	+	0.967131i	$0.581839\pi$
$198$	−3.67631e9	−0.169988
$199$	1.58060e9	0.0714468	0.0357234	−	0.999362i	$-0.488626\pi$
$199$	1.58060e9	0.0714468	0.0357234	+	0.999362i	$0.488626\pi$
$200$	4.98419e10	2.20272
$201$	2.40029e10	1.03724
$202$	3.33504e9	0.140935
$203$	0	0
$204$	2.51408e9	0.101635
$205$	5.24596e10	2.07459
$206$	−2.15293e10	−0.832967
$207$	1.06780e9	0.0404225
$208$	1.30873e10	0.484803
$209$	−1.39580e10	−0.506019
$210$	0	0
$211$	4.44247e10	1.54295	0.771477	−	0.636257i	$-0.219518\pi$
$211$	4.44247e10	1.54295	0.771477	+	0.636257i	$0.219518\pi$
$212$	−8.49899e9	−0.288972
$213$	−3.43384e10	−1.14307
$214$	−3.07335e10	−1.00173
$215$	4.04733e10	1.29180
$216$	3.74162e10	1.16955
$217$	0	0
$218$	3.90934e9	0.117233
$219$	−3.17412e10	−0.932450
$220$	1.57797e10	0.454148
$221$	−1.39544e10	−0.393501
$222$	2.21137e10	0.611045
$223$	−2.40745e10	−0.651907	−0.325954	−	0.945386i	$-0.605685\pi$
$223$	−2.40745e10	−0.651907	−0.325954	+	0.945386i	$0.605685\pi$
$224$	0	0
$225$	−3.04513e10	−0.792109
$226$	2.56737e10	0.654636
$227$	1.71588e8	0.00428915	0.00214458	−	0.999998i	$-0.499317\pi$
$227$	1.71588e8	0.00428915	0.00214458	+	0.999998i	$0.499317\pi$
$228$	1.21692e10	0.298232
$229$	1.11777e10	0.268592	0.134296	−	0.990941i	$-0.457123\pi$
$229$	1.11777e10	0.268592	0.134296	+	0.990941i	$0.457123\pi$
$230$	5.77052e9	0.135969
$231$	0	0
$232$	−7.88225e10	−1.78630
$233$	6.54487e9	0.145479	0.0727393	−	0.997351i	$-0.476826\pi$
$233$	6.54487e9	0.145479	0.0727393	+	0.997351i	$0.476826\pi$
$234$	−1.77902e10	−0.387890
$235$	6.52230e10	1.39507
$236$	4.12285e9	0.0865154
$237$	−5.14695e10	−1.05970
$238$	0	0
$239$	−9.08610e9	−0.180130	−0.0900651	−	0.995936i	$-0.528708\pi$
$239$	−9.08610e9	−0.180130	−0.0900651	+	0.995936i	$0.528708\pi$
$240$	2.53715e10	0.493623
$241$	5.36400e10	1.02426	0.512132	−	0.858906i	$-0.328856\pi$
$241$	5.36400e10	1.02426	0.512132	+	0.858906i	$0.328856\pi$
$242$	2.60641e10	0.488510
$243$	−3.93376e10	−0.723735
$244$	−5.66865e9	−0.102382
$245$	0	0
$246$	3.99038e10	0.694714
$247$	−6.75448e10	−1.15466
$248$	1.25902e10	0.211348
$249$	−8.51528e9	−0.140379
$250$	−8.40999e10	−1.36165
$251$	−3.92651e10	−0.624418	−0.312209	−	0.950013i	$-0.601069\pi$
$251$	−3.92651e10	−0.624418	−0.312209	+	0.950013i	$0.601069\pi$
$252$	0	0
$253$	3.99880e9	0.0613602
$254$	−7.11089e10	−1.07194
$255$	−2.70524e10	−0.400659
$256$	−7.07381e10	−1.02938
$257$	7.70786e9	0.110213	0.0551067	−	0.998480i	$-0.482450\pi$
$257$	7.70786e9	0.110213	0.0551067	+	0.998480i	$0.482450\pi$
$258$	3.07863e10	0.432582
$259$	0	0
$260$	7.63601e10	1.03630
$261$	4.81573e10	0.642362
$262$	−6.96189e10	−0.912791
$263$	3.65878e10	0.471559	0.235779	−	0.971807i	$-0.424236\pi$
$263$	3.65878e10	0.471559	0.235779	+	0.971807i	$0.424236\pi$
$264$	3.91181e10	0.495632
$265$	9.14521e10	1.13917
$266$	0	0
$267$	3.70830e10	0.446554
$268$	4.95383e10	0.586590
$269$	1.65478e11	1.92688	0.963442	−	0.267916i	$-0.0863349\pi$
$269$	1.65478e11	1.92688	0.963442	+	0.267916i	$0.0863349\pi$
$270$	−1.23537e11	−1.41469
$271$	−5.47248e10	−0.616343	−0.308171	−	0.951331i	$-0.599717\pi$
$271$	−5.47248e10	−0.616343	−0.308171	+	0.951331i	$0.599717\pi$
$272$	−9.56901e9	−0.106000
$273$	0	0
$274$	2.16125e10	0.231648
$275$	−1.14037e11	−1.20240
$276$	−3.48631e9	−0.0361638
$277$	−2.55019e10	−0.260264	−0.130132	−	0.991497i	$-0.541540\pi$
$277$	−2.55019e10	−0.260264	−0.130132	+	0.991497i	$0.541540\pi$
$278$	−6.79651e10	−0.682472
$279$	−7.69207e9	−0.0760019
$280$	0	0
$281$	−2.44664e10	−0.234095	−0.117047	−	0.993126i	$-0.537343\pi$
$281$	−2.44664e10	−0.234095	−0.117047	+	0.993126i	$0.537343\pi$
$282$	4.96123e10	0.467163
$283$	−1.83938e11	−1.70464	−0.852318	−	0.523024i	$-0.824804\pi$
$283$	−1.83938e11	−1.70464	−0.852318	+	0.523024i	$0.824804\pi$
$284$	−7.08693e10	−0.646436
$285$	−1.30944e11	−1.17567
$286$	−6.66222e10	−0.588806
$287$	0	0
$288$	3.65018e10	0.312642
$289$	−1.08385e11	−0.913963
$290$	2.60248e11	2.16071
$291$	−8.09057e10	−0.661395
$292$	−6.55091e10	−0.527325
$293$	−1.39840e11	−1.10848	−0.554241	−	0.832356i	$-0.686991\pi$
$293$	−1.39840e11	−1.10848	−0.554241	+	0.832356i	$0.686991\pi$
$294$	0	0
$295$	−4.43633e10	−0.341055
$296$	1.48740e11	1.12620
$297$	−8.56073e10	−0.638421
$298$	1.29698e10	0.0952706
$299$	1.93507e10	0.140015
$300$	9.94219e10	0.708657
$301$	0	0
$302$	1.66349e11	1.15077
$303$	2.16809e10	0.147770
$304$	−4.63179e10	−0.311041
$305$	6.09966e10	0.403605
$306$	1.30076e10	0.0848106
$307$	1.22633e11	0.787922	0.393961	−	0.919127i	$-0.371105\pi$
$307$	1.22633e11	0.787922	0.393961	+	0.919127i	$0.371105\pi$
$308$	0	0
$309$	−1.39961e11	−0.873361
$310$	−4.15689e10	−0.255647
$311$	1.44117e11	0.873564	0.436782	−	0.899567i	$-0.356118\pi$
$311$	1.44117e11	0.873564	0.436782	+	0.899567i	$0.356118\pi$
$312$	1.89297e11	1.13096
$313$	2.74753e11	1.61805	0.809027	−	0.587771i	$-0.199994\pi$
$313$	2.74753e11	1.61805	0.809027	+	0.587771i	$0.199994\pi$
$314$	1.35832e11	0.788528
$315$	0	0
$316$	−1.06225e11	−0.599288
$317$	−1.23139e11	−0.684904	−0.342452	−	0.939535i	$-0.611257\pi$
$317$	−1.23139e11	−0.684904	−0.342452	+	0.939535i	$0.611257\pi$
$318$	6.95636e10	0.381470
$319$	1.80344e11	0.975087
$320$	3.15550e11	1.68226
$321$	−1.99797e11	−1.05031
$322$	0	0
$323$	4.93865e10	0.252463
$324$	4.06280e10	0.204820
$325$	−5.51840e11	−2.74371
$326$	1.53273e11	0.751601
$327$	2.54144e10	0.122918
$328$	2.68399e11	1.28041
$329$	0	0
$330$	−1.29156e11	−0.599517
$331$	3.37245e11	1.54426	0.772129	−	0.635466i	$-0.219192\pi$
$331$	3.37245e11	1.54426	0.772129	+	0.635466i	$0.219192\pi$
$332$	−1.75742e10	−0.0793881
$333$	−9.08741e10	−0.404987
$334$	−1.49240e11	−0.656184
$335$	−5.33049e11	−2.31242
$336$	0	0
$337$	−2.84144e11	−1.20006	−0.600032	−	0.799976i	$-0.704846\pi$
$337$	−2.84144e11	−1.20006	−0.600032	+	0.799976i	$0.704846\pi$
$338$	−1.43258e11	−0.597025
$339$	1.66903e11	0.686382
$340$	−5.58320e10	−0.226584
$341$	−2.88060e10	−0.115369
$342$	6.29619e10	0.248863
$343$	0	0
$344$	2.07073e11	0.797280
$345$	3.75138e10	0.142563
$346$	1.33429e11	0.500503
$347$	1.38776e11	0.513846	0.256923	−	0.966432i	$-0.417291\pi$
$347$	1.38776e11	0.513846	0.256923	+	0.966432i	$0.417291\pi$
$348$	−1.57231e11	−0.574686
$349$	1.52561e11	0.550463	0.275231	−	0.961378i	$-0.411246\pi$
$349$	1.52561e11	0.550463	0.275231	+	0.961378i	$0.411246\pi$
$350$	0	0
$351$	−4.14265e11	−1.45679
$352$	1.36695e11	0.474582
$353$	−1.24628e11	−0.427199	−0.213599	−	0.976921i	$-0.568519\pi$
$353$	−1.24628e11	−0.427199	−0.213599	+	0.976921i	$0.568519\pi$
$354$	−3.37452e10	−0.114208
$355$	7.62578e11	2.54834
$356$	7.65336e10	0.252538
$357$	0	0
$358$	−7.76835e10	−0.249951
$359$	−7.69379e10	−0.244464	−0.122232	−	0.992502i	$-0.539005\pi$
$359$	−7.69379e10	−0.244464	−0.122232	+	0.992502i	$0.539005\pi$
$360$	−2.31975e11	−0.727915
$361$	−8.36371e10	−0.259189
$362$	−1.13347e10	−0.0346914
$363$	1.69441e11	0.512200
$364$	0	0
$365$	7.04900e11	2.07879
$366$	4.63975e10	0.135154
$367$	4.36607e11	1.25630	0.628150	−	0.778092i	$-0.283813\pi$
$367$	4.36607e11	1.25630	0.628150	+	0.778092i	$0.283813\pi$
$368$	1.32695e10	0.0377171
$369$	−1.63981e11	−0.460441
$370$	−4.91095e11	−1.36225
$371$	0	0
$372$	2.51142e10	0.0679948
$373$	1.66545e11	0.445495	0.222747	−	0.974876i	$-0.428497\pi$
$373$	1.66545e11	0.445495	0.222747	+	0.974876i	$0.428497\pi$
$374$	4.87120e10	0.128740
$375$	−5.46729e11	−1.42768
$376$	3.33700e11	0.861015
$377$	8.72707e11	2.22501
$378$	0	0
$379$	4.10213e11	1.02125	0.510627	−	0.859803i	$-0.329413\pi$
$379$	4.10213e11	1.02125	0.510627	+	0.859803i	$0.329413\pi$
$380$	−2.70249e11	−0.664873
$381$	−4.62275e11	−1.12393
$382$	−1.70083e11	−0.408672
$383$	−7.01166e11	−1.66505	−0.832523	−	0.553990i	$-0.813105\pi$
$383$	−7.01166e11	−1.66505	−0.832523	+	0.553990i	$0.813105\pi$
$384$	−2.91984e10	−0.0685281
$385$	0	0
$386$	3.34261e11	0.766377
$387$	−1.26513e11	−0.286706
$388$	−1.66977e11	−0.374037
$389$	8.46752e11	1.87492	0.937461	−	0.348090i	$-0.113170\pi$
$389$	8.46752e11	1.87492	0.937461	+	0.348090i	$0.113170\pi$
$390$	−6.25002e11	−1.36801
$391$	−1.41486e10	−0.0306138
$392$	0	0
$393$	−4.52589e11	−0.957056
$394$	1.81607e11	0.379665
$395$	1.14302e12	2.36247
$396$	−4.93250e10	−0.100795
$397$	−8.75287e11	−1.76845	−0.884226	−	0.467059i	$-0.845313\pi$
$397$	−8.75287e11	−1.76845	−0.884226	+	0.467059i	$0.845313\pi$
$398$	−2.67002e10	−0.0533385
$399$	0	0
$400$	−3.78416e11	−0.739094
$401$	−2.47491e11	−0.477980	−0.238990	−	0.971022i	$-0.576816\pi$
$401$	−2.47491e11	−0.477980	−0.238990	+	0.971022i	$0.576816\pi$
$402$	−4.05468e11	−0.774353
$403$	−1.39396e11	−0.263255
$404$	4.47461e10	0.0835679
$405$	−4.37171e11	−0.807428
$406$	0	0
$407$	−3.40314e11	−0.614759
$408$	−1.38408e11	−0.247281
$409$	9.48426e10	0.167590	0.0837951	−	0.996483i	$-0.473296\pi$
$409$	9.48426e10	0.167590	0.0837951	+	0.996483i	$0.473296\pi$
$410$	−8.86172e11	−1.54878
$411$	1.40502e11	0.242881
$412$	−2.88858e11	−0.493909
$413$	0	0
$414$	−1.80377e10	−0.0301773
$415$	1.89105e11	0.312958
$416$	6.61486e11	1.08293
$417$	−4.41838e11	−0.715567
$418$	2.35786e11	0.377767
$419$	−9.93237e11	−1.57431	−0.787154	−	0.616756i	$-0.788446\pi$
$419$	−9.93237e11	−1.57431	−0.787154	+	0.616756i	$0.788446\pi$
$420$	0	0
$421$	3.88328e11	0.602461	0.301230	−	0.953551i	$-0.402603\pi$
$421$	3.88328e11	0.602461	0.301230	+	0.953551i	$0.402603\pi$
$422$	−7.50441e11	−1.15189
$423$	−2.03877e11	−0.309625
$424$	4.67896e11	0.703077
$425$	4.03487e11	0.599901
$426$	5.80060e11	0.853355
$427$	0	0
$428$	−4.12351e11	−0.593977
$429$	−4.33108e11	−0.617359
$430$	−6.83693e11	−0.964390
$431$	2.08495e11	0.291036	0.145518	−	0.989356i	$-0.453515\pi$
$431$	2.08495e11	0.291036	0.145518	+	0.989356i	$0.453515\pi$
$432$	−2.84076e11	−0.392426
$433$	3.43270e11	0.469289	0.234645	−	0.972081i	$-0.424607\pi$
$433$	3.43270e11	0.469289	0.234645	+	0.972081i	$0.424607\pi$
$434$	0	0
$435$	1.69186e12	2.26549
$436$	5.24515e10	0.0695134
$437$	−6.84848e10	−0.0898314
$438$	5.36187e11	0.696118
$439$	−5.98857e11	−0.769543	−0.384771	−	0.923012i	$-0.625720\pi$
$439$	−5.98857e11	−0.769543	−0.384771	+	0.923012i	$0.625720\pi$
$440$	−8.68723e11	−1.10495
$441$	0	0
$442$	2.35724e11	0.293767
$443$	−3.05169e11	−0.376464	−0.188232	−	0.982125i	$-0.560276\pi$
$443$	−3.05169e11	−0.376464	−0.188232	+	0.982125i	$0.560276\pi$
$444$	2.96699e11	0.362320
$445$	−8.23528e11	−0.995539
$446$	4.06678e11	0.486680
$447$	8.43158e10	0.0998907
$448$	0	0
$449$	2.40802e11	0.279610	0.139805	−	0.990179i	$-0.455352\pi$
$449$	2.40802e11	0.279610	0.139805	+	0.990179i	$0.455352\pi$
$450$	5.14397e11	0.591347
$451$	−6.14090e11	−0.698936
$452$	3.44463e11	0.388168
$453$	1.08142e12	1.20657
$454$	−2.89855e9	−0.00320206
$455$	0	0
$456$	−6.69950e11	−0.725606
$457$	2.36226e11	0.253341	0.126671	−	0.991945i	$-0.459571\pi$
$457$	2.36226e11	0.253341	0.126671	+	0.991945i	$0.459571\pi$
$458$	−1.88819e11	−0.200517
$459$	3.02897e11	0.318521
$460$	7.74229e10	0.0806230
$461$	1.17120e12	1.20775	0.603873	−	0.797081i	$-0.293624\pi$
$461$	1.17120e12	1.20775	0.603873	+	0.797081i	$0.293624\pi$
$462$	0	0
$463$	−1.78934e12	−1.80958	−0.904791	−	0.425856i	$-0.859973\pi$
$463$	−1.78934e12	−1.80958	−0.904791	+	0.425856i	$0.859973\pi$
$464$	5.98446e11	0.599369
$465$	−2.70237e11	−0.268044
$466$	−1.10559e11	−0.108607
$467$	3.81202e11	0.370877	0.185438	−	0.982656i	$-0.440630\pi$
$467$	3.81202e11	0.370877	0.185438	+	0.982656i	$0.440630\pi$
$468$	−2.38690e11	−0.230000
$469$	0	0
$470$	−1.10178e12	−1.04148
$471$	8.83034e11	0.826767
$472$	−2.26975e11	−0.210494
$473$	−4.73778e11	−0.435211
$474$	8.69446e11	0.791115
$475$	1.95304e12	1.76031
$476$	0	0
$477$	−2.85865e11	−0.252830
$478$	1.53486e11	0.134476
$479$	1.71146e12	1.48545	0.742725	−	0.669597i	$-0.233533\pi$
$479$	1.71146e12	1.48545	0.742725	+	0.669597i	$0.233533\pi$
$480$	1.28238e12	1.10263
$481$	−1.64682e12	−1.40279
$482$	−9.06111e11	−0.764663
$483$	0	0
$484$	3.49701e11	0.289663
$485$	1.79673e12	1.47450
$486$	6.64508e11	0.540303
$487$	7.38713e11	0.595108	0.297554	−	0.954705i	$-0.403829\pi$
$487$	7.38713e11	0.595108	0.297554	+	0.954705i	$0.403829\pi$
$488$	3.12076e11	0.249099
$489$	9.96422e11	0.788049
$490$	0	0
$491$	1.52117e12	1.18116	0.590582	−	0.806978i	$-0.298898\pi$
$491$	1.52117e12	1.18116	0.590582	+	0.806978i	$0.298898\pi$
$492$	5.35387e11	0.411932
$493$	−6.38095e11	−0.486490
$494$	1.14100e12	0.862012
$495$	5.30754e11	0.397347
$496$	−9.55887e10	−0.0709151
$497$	0	0
$498$	1.43844e11	0.104800
$499$	−1.67720e12	−1.21097	−0.605484	−	0.795857i	$-0.707021\pi$
$499$	−1.67720e12	−1.21097	−0.605484	+	0.795857i	$0.707021\pi$
$500$	−1.12837e12	−0.807392
$501$	−9.70200e11	−0.688005
$502$	6.63284e11	0.466158
$503$	−2.93328e11	−0.204314	−0.102157	−	0.994768i	$-0.532574\pi$
$503$	−2.93328e11	−0.204314	−0.102157	+	0.994768i	$0.532574\pi$
$504$	0	0
$505$	−4.81484e11	−0.329436
$506$	−6.75494e10	−0.0458083
$507$	−9.31311e11	−0.625977
$508$	−9.54065e11	−0.635611
$509$	2.87498e12	1.89848	0.949238	−	0.314559i	$-0.101857\pi$
$509$	2.87498e12	1.89848	0.949238	+	0.314559i	$0.101857\pi$
$510$	4.56981e11	0.299111
$511$	0	0
$512$	1.05881e12	0.680930
$513$	1.46614e12	0.934648
$514$	−1.30205e11	−0.0822796
$515$	3.10821e12	1.94706
$516$	4.13058e11	0.256500
$517$	−7.63497e11	−0.470002
$518$	0	0
$519$	8.67412e11	0.524774
$520$	−4.20386e12	−2.52135
$521$	−1.69333e12	−1.00687	−0.503434	−	0.864034i	$-0.667930\pi$
$521$	−1.69333e12	−1.00687	−0.503434	+	0.864034i	$0.667930\pi$
$522$	−8.13494e11	−0.479554
$523$	−9.48465e11	−0.554324	−0.277162	−	0.960823i	$-0.589394\pi$
$523$	−9.48465e11	−0.554324	−0.277162	+	0.960823i	$0.589394\pi$
$524$	−9.34075e11	−0.541241
$525$	0	0
$526$	−6.18058e11	−0.352041
$527$	1.01922e11	0.0575597
$528$	−2.96997e11	−0.166303
$529$	−1.78153e12	−0.989107
$530$	−1.54485e12	−0.850442
$531$	1.38673e11	0.0756947
$532$	0	0
$533$	−2.97166e12	−1.59488
$534$	−6.26422e11	−0.333374
$535$	4.43704e12	2.34154
$536$	−2.72724e12	−1.42719
$537$	−5.05017e11	−0.262072
$538$	−2.79533e12	−1.43851
$539$	0	0
$540$	−1.65749e12	−0.838840
$541$	2.60488e12	1.30738	0.653688	−	0.756764i	$-0.273221\pi$
$541$	2.60488e12	1.30738	0.653688	+	0.756764i	$0.273221\pi$
$542$	9.24436e11	0.460129
$543$	−7.36864e10	−0.0363738
$544$	−4.83657e11	−0.236778
$545$	−5.64396e11	−0.274031
$546$	0	0
$547$	2.01576e12	0.962711	0.481356	−	0.876525i	$-0.340145\pi$
$547$	2.01576e12	0.962711	0.481356	+	0.876525i	$0.340145\pi$
$548$	2.89974e11	0.137356
$549$	−1.90666e11	−0.0895772
$550$	1.92636e12	0.897648
$551$	−3.08863e12	−1.42753
$552$	1.91932e11	0.0879875
$553$	0	0
$554$	4.30790e11	0.194300
$555$	−3.19258e12	−1.42831
$556$	−9.11886e11	−0.404673
$557$	−3.04194e12	−1.33907	−0.669534	−	0.742782i	$-0.733506\pi$
$557$	−3.04194e12	−1.33907	−0.669534	+	0.742782i	$0.733506\pi$
$558$	1.29938e11	0.0567390
$559$	−2.29267e12	−0.993091
$560$	0	0
$561$	3.16674e11	0.134983
$562$	4.13297e11	0.174763
$563$	−4.23912e12	−1.77823	−0.889115	−	0.457684i	$-0.848679\pi$
$563$	−4.23912e12	−1.77823	−0.889115	+	0.457684i	$0.848679\pi$
$564$	6.65647e11	0.277005
$565$	−3.70654e12	−1.53021
$566$	3.10716e12	1.27259
$567$	0	0
$568$	3.90157e12	1.57280
$569$	1.34119e11	0.0536397	0.0268199	−	0.999640i	$-0.491462\pi$
$569$	1.34119e11	0.0536397	0.0268199	+	0.999640i	$0.491462\pi$
$570$	2.21197e12	0.877693
$571$	−1.51210e11	−0.0595277	−0.0297638	−	0.999557i	$-0.509476\pi$
$571$	−1.51210e11	−0.0595277	−0.0297638	+	0.999557i	$0.509476\pi$
$572$	−8.93868e11	−0.349133
$573$	−1.10570e12	−0.428491
$574$	0	0
$575$	−5.59520e11	−0.213457
$576$	−9.86359e11	−0.373365
$577$	1.84681e12	0.693633	0.346817	−	0.937933i	$-0.387263\pi$
$577$	1.84681e12	0.693633	0.346817	+	0.937933i	$0.387263\pi$
$578$	1.83089e12	0.682317
$579$	2.17301e12	0.803541
$580$	3.49174e12	1.28120
$581$	0	0
$582$	1.36670e12	0.493763
$583$	−1.07053e12	−0.383788
$584$	3.60648e12	1.28300
$585$	2.56839e12	0.906690
$586$	2.36225e12	0.827535
$587$	2.97730e12	1.03503	0.517513	−	0.855675i	$-0.326858\pi$
$587$	2.97730e12	1.03503	0.517513	+	0.855675i	$0.326858\pi$
$588$	0	0
$589$	4.93342e11	0.168900
$590$	7.49404e11	0.254614
$591$	1.18062e12	0.398076
$592$	−1.12928e12	−0.377881
$593$	−1.06093e12	−0.352322	−0.176161	−	0.984361i	$-0.556368\pi$
$593$	−1.06093e12	−0.352322	−0.176161	+	0.984361i	$0.556368\pi$
$594$	1.44612e12	0.476611
$595$	0	0
$596$	1.74015e11	0.0564909
$597$	−1.73576e11	−0.0559250
$598$	−3.26880e11	−0.104528
$599$	−4.53108e12	−1.43807	−0.719037	−	0.694972i	$-0.755417\pi$
$599$	−4.53108e12	−1.43807	−0.719037	+	0.694972i	$0.755417\pi$
$600$	−5.47348e12	−1.72418
$601$	1.05588e12	0.330127	0.165063	−	0.986283i	$-0.447217\pi$
$601$	1.05588e12	0.330127	0.165063	+	0.986283i	$0.447217\pi$
$602$	0	0
$603$	1.66623e12	0.513224
$604$	2.23190e12	0.682351
$605$	−3.76290e12	−1.14189
$606$	−3.66244e11	−0.110317
$607$	3.25042e12	0.971831	0.485916	−	0.874006i	$-0.338486\pi$
$607$	3.25042e12	0.971831	0.485916	+	0.874006i	$0.338486\pi$
$608$	−2.34109e12	−0.694788
$609$	0	0
$610$	−1.03038e12	−0.301310
$611$	−3.69466e12	−1.07248
$612$	1.74522e11	0.0502886
$613$	−2.48670e12	−0.711299	−0.355649	−	0.934619i	$-0.615740\pi$
$613$	−2.48670e12	−0.711299	−0.355649	+	0.934619i	$0.615740\pi$
$614$	−2.07156e12	−0.588221
$615$	−5.76095e12	−1.62389
$616$	0	0
$617$	−4.06622e12	−1.12956	−0.564778	−	0.825243i	$-0.691038\pi$
$617$	−4.06622e12	−1.12956	−0.564778	+	0.825243i	$0.691038\pi$
$618$	2.36428e12	0.652006
$619$	4.24730e12	1.16280	0.581400	−	0.813618i	$-0.302505\pi$
$619$	4.24730e12	1.16280	0.581400	+	0.813618i	$0.302505\pi$
$620$	−5.57728e11	−0.151586
$621$	−4.20030e11	−0.113336
$622$	−2.43450e12	−0.652157
$623$	0	0
$624$	−1.43721e12	−0.379480
$625$	4.33978e12	1.13765
$626$	−4.64125e12	−1.20796
$627$	1.53283e12	0.396086
$628$	1.82245e12	0.467559
$629$	1.20410e12	0.306715
$630$	0	0
$631$	1.44130e12	0.361929	0.180965	−	0.983490i	$-0.442078\pi$
$631$	1.44130e12	0.361929	0.180965	+	0.983490i	$0.442078\pi$
$632$	5.84803e12	1.45808
$633$	−4.87858e12	−1.20775
$634$	2.08012e12	0.511314
$635$	1.02661e13	2.50566
$636$	9.33333e11	0.226193
$637$	0	0
$638$	−3.04645e12	−0.727949
$639$	−2.38370e12	−0.565585
$640$	6.48430e11	0.152775
$641$	6.00980e12	1.40604	0.703022	−	0.711168i	$-0.251833\pi$
$641$	6.00980e12	1.40604	0.703022	+	0.711168i	$0.251833\pi$
$642$	3.37506e12	0.784105
$643$	−2.09069e12	−0.482327	−0.241163	−	0.970485i	$-0.577529\pi$
$643$	−2.09069e12	−0.482327	−0.241163	+	0.970485i	$0.577529\pi$
$644$	0	0
$645$	−4.44465e12	−1.01116
$646$	−8.34259e11	−0.188475
$647$	1.34894e12	0.302638	0.151319	−	0.988485i	$-0.451648\pi$
$647$	1.34894e12	0.302638	0.151319	+	0.988485i	$0.451648\pi$
$648$	−2.23670e12	−0.498333
$649$	5.19314e11	0.114902
$650$	9.32192e12	2.04831
$651$	0	0
$652$	2.05646e12	0.445663
$653$	−7.38295e12	−1.58899	−0.794494	−	0.607272i	$-0.792264\pi$
$653$	−7.38295e12	−1.58899	−0.794494	+	0.607272i	$0.792264\pi$
$654$	−4.29312e11	−0.0917641
$655$	1.00510e13	2.13364
$656$	−2.03777e12	−0.429624
$657$	−2.20341e12	−0.461372
$658$	0	0
$659$	3.34345e12	0.690574	0.345287	−	0.938497i	$-0.387782\pi$
$659$	3.34345e12	0.690574	0.345287	+	0.938497i	$0.387782\pi$
$660$	−1.73288e12	−0.355485
$661$	−8.14808e12	−1.66016	−0.830078	−	0.557648i	$-0.811704\pi$
$661$	−8.14808e12	−1.66016	−0.830078	+	0.557648i	$0.811704\pi$
$662$	−5.69690e12	−1.15286
$663$	1.53243e12	0.308013
$664$	9.67516e11	0.193153
$665$	0	0
$666$	1.53509e12	0.302342
$667$	8.84853e11	0.173103
$668$	−2.00235e12	−0.389085
$669$	2.64379e12	0.510281
$670$	9.00451e12	1.72633
$671$	−7.14023e11	−0.135976
$672$	0	0
$673$	−6.60403e12	−1.24091	−0.620457	−	0.784241i	$-0.713053\pi$
$673$	−6.60403e12	−1.24091	−0.620457	+	0.784241i	$0.713053\pi$
$674$	4.79989e12	0.895905
$675$	1.19784e13	2.22091
$676$	−1.92208e12	−0.354007
$677$	−3.16321e12	−0.578735	−0.289367	−	0.957218i	$-0.593445\pi$
$677$	−3.16321e12	−0.578735	−0.289367	+	0.957218i	$0.593445\pi$
$678$	−2.81940e12	−0.512417
$679$	0	0
$680$	3.07373e12	0.551283
$681$	−1.88433e10	−0.00335734
$682$	4.86603e11	0.0861282
$683$	7.85876e12	1.38185	0.690925	−	0.722927i	$-0.257204\pi$
$683$	7.85876e12	1.38185	0.690925	+	0.722927i	$0.257204\pi$
$684$	8.44757e11	0.147564
$685$	−3.12022e12	−0.541475
$686$	0	0
$687$	−1.22750e12	−0.210241
$688$	−1.57217e12	−0.267517
$689$	−5.18045e12	−0.875752
$690$	−6.33701e11	−0.106430
$691$	−3.21525e12	−0.536492	−0.268246	−	0.963350i	$-0.586444\pi$
$691$	−3.21525e12	−0.536492	−0.268246	+	0.963350i	$0.586444\pi$
$692$	1.79021e12	0.296774
$693$	0	0
$694$	−2.34427e12	−0.383611
$695$	9.81221e12	1.59527
$696$	8.65604e12	1.39823
$697$	2.17278e12	0.348713
$698$	−2.57712e12	−0.410947
$699$	−7.18737e11	−0.113874
$700$	0	0
$701$	−6.07789e12	−0.950652	−0.475326	−	0.879810i	$-0.657670\pi$
$701$	−6.07789e12	−0.950652	−0.475326	+	0.879810i	$0.657670\pi$
$702$	6.99795e12	1.08756
$703$	5.82834e12	0.900007
$704$	−3.69381e12	−0.566758
$705$	−7.16259e12	−1.09199
$706$	2.10528e12	0.318924
$707$	0	0
$708$	−4.52758e11	−0.0677200
$709$	−6.79921e12	−1.01053	−0.505266	−	0.862963i	$-0.668606\pi$
$709$	−6.79921e12	−1.01053	−0.505266	+	0.862963i	$0.668606\pi$
$710$	−1.28818e13	−1.90245
$711$	−3.57290e12	−0.524334
$712$	−4.21341e12	−0.614432
$713$	−1.41336e11	−0.0204809
$714$	0	0
$715$	9.61833e12	1.37633
$716$	−1.04228e12	−0.148209
$717$	9.97807e11	0.140997
$718$	1.29967e12	0.182504
$719$	−8.63238e11	−0.120462	−0.0602311	−	0.998184i	$-0.519184\pi$
$719$	−8.63238e11	−0.120462	−0.0602311	+	0.998184i	$0.519184\pi$
$720$	1.76123e12	0.244242
$721$	0	0
$722$	1.41283e12	0.193497
$723$	−5.89058e12	−0.801744
$724$	−1.52078e11	−0.0205703
$725$	−2.52341e13	−3.39208
$726$	−2.86228e12	−0.382382
$727$	9.34730e12	1.24103	0.620514	−	0.784195i	$-0.286924\pi$
$727$	9.34730e12	1.24103	0.620514	+	0.784195i	$0.286924\pi$
$728$	0	0
$729$	7.84827e12	1.02920
$730$	−1.19075e13	−1.55191
$731$	1.67633e12	0.217135
$732$	6.22513e11	0.0801399
$733$	1.12045e13	1.43359	0.716793	−	0.697286i	$-0.245609\pi$
$733$	1.12045e13	1.43359	0.716793	+	0.697286i	$0.245609\pi$
$734$	−7.37536e12	−0.937887
$735$	0	0
$736$	6.70692e11	0.0842506
$737$	6.23985e12	0.779059
$738$	2.77003e12	0.343741
$739$	−4.55769e12	−0.562140	−0.281070	−	0.959687i	$-0.590689\pi$
$739$	−4.55769e12	−0.562140	−0.281070	+	0.959687i	$0.590689\pi$
$740$	−6.58900e12	−0.807750
$741$	7.41756e12	0.903814
$742$	0	0
$743$	3.57016e12	0.429772	0.214886	−	0.976639i	$-0.431062\pi$
$743$	3.57016e12	0.429772	0.214886	+	0.976639i	$0.431062\pi$
$744$	−1.38261e12	−0.165433
$745$	−1.87246e12	−0.222695
$746$	−2.81336e12	−0.332583
$747$	−5.91112e11	−0.0694588
$748$	6.53567e11	0.0763366
$749$	0	0
$750$	9.23559e12	1.06583
$751$	−2.38313e12	−0.273380	−0.136690	−	0.990614i	$-0.543646\pi$
$751$	−2.38313e12	−0.273380	−0.136690	+	0.990614i	$0.543646\pi$
$752$	−2.53356e12	−0.288902
$753$	4.31198e12	0.488764
$754$	−1.47422e13	−1.66108
$755$	−2.40160e13	−2.68992
$756$	0	0
$757$	4.96674e12	0.549718	0.274859	−	0.961484i	$-0.411369\pi$
$757$	4.96674e12	0.549718	0.274859	+	0.961484i	$0.411369\pi$
$758$	−6.92951e12	−0.762414
$759$	−4.39135e11	−0.0480298
$760$	1.48781e13	1.61765
$761$	−1.01660e13	−1.09880	−0.549401	−	0.835559i	$-0.685144\pi$
$761$	−1.01660e13	−1.09880	−0.549401	+	0.835559i	$0.685144\pi$
$762$	7.80896e12	0.839065
$763$	0	0
$764$	−2.28200e12	−0.242323
$765$	−1.87792e12	−0.198244
$766$	1.18444e13	1.24304
$767$	2.51303e12	0.262191
$768$	7.76824e12	0.805744
$769$	4.53519e12	0.467656	0.233828	−	0.972278i	$-0.424875\pi$
$769$	4.53519e12	0.467656	0.233828	+	0.972278i	$0.424875\pi$
$770$	0	0
$771$	−8.46453e11	−0.0862697
$772$	4.48476e12	0.454424
$773$	3.64760e12	0.367451	0.183725	−	0.982978i	$-0.441184\pi$
$773$	3.64760e12	0.367451	0.183725	+	0.982978i	$0.441184\pi$
$774$	2.13712e12	0.214039
$775$	4.03059e12	0.401339
$776$	9.19261e12	0.910041
$777$	0	0
$778$	−1.43037e13	−1.39972
$779$	1.05171e13	1.02324
$780$	−8.38563e12	−0.811167
$781$	−8.92670e12	−0.858542
$782$	2.39004e11	0.0228547
$783$	−1.89432e13	−1.80105
$784$	0	0
$785$	−1.96102e13	−1.84318
$786$	7.64533e12	0.714488
$787$	2.68084e12	0.249106	0.124553	−	0.992213i	$-0.460250\pi$
$787$	2.68084e12	0.249106	0.124553	+	0.992213i	$0.460250\pi$
$788$	2.43662e12	0.225123
$789$	−4.01796e12	−0.369113
$790$	−1.93084e13	−1.76370
$791$	0	0
$792$	2.71549e12	0.245237
$793$	−3.45525e12	−0.310277
$794$	1.47857e13	1.32023
$795$	−1.00430e13	−0.891683
$796$	−3.58235e11	−0.0316271
$797$	9.88359e12	0.867665	0.433833	−	0.900994i	$-0.357161\pi$
$797$	9.88359e12	0.867665	0.433833	+	0.900994i	$0.357161\pi$
$798$	0	0
$799$	2.70142e12	0.234494
$800$	−1.91267e13	−1.65095
$801$	2.57422e12	0.220953
$802$	4.18073e12	0.356835
$803$	−8.25153e12	−0.700349
$804$	−5.44014e12	−0.459154
$805$	0	0
$806$	2.35474e12	0.196533
$807$	−1.81723e13	−1.50827
$808$	−2.46341e12	−0.203323
$809$	1.62405e13	1.33300	0.666502	−	0.745503i	$-0.267791\pi$
$809$	1.62405e13	1.33300	0.666502	+	0.745503i	$0.267791\pi$
$810$	7.38489e12	0.602784
$811$	2.28548e13	1.85517	0.927584	−	0.373614i	$-0.121882\pi$
$811$	2.28548e13	1.85517	0.927584	+	0.373614i	$0.121882\pi$
$812$	0	0
$813$	6.00971e12	0.482443
$814$	5.74873e12	0.458947
$815$	−2.21282e13	−1.75686
$816$	1.05084e12	0.0829718
$817$	8.11410e12	0.637149
$818$	−1.60212e12	−0.125114
$819$	0	0
$820$	−1.18897e13	−0.918353
$821$	1.65900e13	1.27439	0.637193	−	0.770704i	$-0.280095\pi$
$821$	1.65900e13	1.27439	0.637193	+	0.770704i	$0.280095\pi$
$822$	−2.37342e12	−0.181322
$823$	9.87616e12	0.750393	0.375197	−	0.926945i	$-0.377575\pi$
$823$	9.87616e12	0.750393	0.375197	+	0.926945i	$0.377575\pi$
$824$	1.59025e13	1.20169
$825$	1.25232e13	0.941179
$826$	0	0
$827$	−3.15367e12	−0.234445	−0.117223	−	0.993106i	$-0.537399\pi$
$827$	−3.15367e12	−0.234445	−0.117223	+	0.993106i	$0.537399\pi$
$828$	−2.42012e11	−0.0178937
$829$	−2.02328e13	−1.48785	−0.743927	−	0.668261i	$-0.767039\pi$
$829$	−2.02328e13	−1.48785	−0.743927	+	0.668261i	$0.767039\pi$
$830$	−3.19444e12	−0.233638
$831$	2.80054e12	0.203722
$832$	−1.78748e13	−1.29326
$833$	0	0
$834$	7.46372e12	0.534205
$835$	2.15459e13	1.53383
$836$	3.16353e12	0.223998
$837$	3.02576e12	0.213093
$838$	1.67782e13	1.17530
$839$	2.38915e13	1.66462	0.832310	−	0.554311i	$-0.187018\pi$
$839$	2.38915e13	1.66462	0.832310	+	0.554311i	$0.187018\pi$
$840$	0	0
$841$	2.53993e13	1.75081
$842$	−6.55980e12	−0.449766
$843$	2.68682e12	0.183238
$844$	−1.00686e13	−0.683015
$845$	2.06823e13	1.39554
$846$	3.44398e12	0.231150
$847$	0	0
$848$	−3.55242e12	−0.235908
$849$	2.01995e13	1.33431
$850$	−6.81588e12	−0.447855
$851$	−1.66974e12	−0.109136
$852$	7.78264e12	0.505998
$853$	−1.68078e13	−1.08703	−0.543514	−	0.839400i	$-0.682906\pi$
$853$	−1.68078e13	−1.08703	−0.543514	+	0.839400i	$0.682906\pi$
$854$	0	0
$855$	−9.08988e12	−0.581716
$856$	2.27012e13	1.44516
$857$	6.68278e12	0.423198	0.211599	−	0.977357i	$-0.432133\pi$
$857$	6.68278e12	0.423198	0.211599	+	0.977357i	$0.432133\pi$
$858$	7.31625e12	0.460888
$859$	−2.04541e13	−1.28177	−0.640887	−	0.767635i	$-0.721433\pi$
$859$	−2.04541e13	−1.28177	−0.640887	+	0.767635i	$0.721433\pi$
$860$	−9.17308e12	−0.571837
$861$	0	0
$862$	−3.52198e12	−0.217272
$863$	−1.87505e13	−1.15071	−0.575353	−	0.817905i	$-0.695135\pi$
$863$	−1.87505e13	−1.15071	−0.575353	+	0.817905i	$0.695135\pi$
$864$	−1.43584e13	−0.876583
$865$	−1.92632e13	−1.16992
$866$	−5.79867e12	−0.350347
$867$	1.19025e13	0.715405
$868$	0	0
$869$	−1.33801e13	−0.795924
$870$	−2.85796e13	−1.69130
$871$	3.01954e13	1.77771
$872$	−2.88762e12	−0.169128
$873$	−5.61630e12	−0.327255
$874$	1.15688e12	0.0670634
$875$	0	0
$876$	7.19400e12	0.412764
$877$	2.02759e13	1.15740	0.578699	−	0.815542i	$-0.303561\pi$
$877$	2.02759e13	1.15740	0.578699	+	0.815542i	$0.303561\pi$
$878$	1.01162e13	0.574500
$879$	1.53568e13	0.867665
$880$	6.59563e12	0.370753
$881$	2.17613e13	1.21701	0.608505	−	0.793550i	$-0.291770\pi$
$881$	2.17613e13	1.21701	0.608505	+	0.793550i	$0.291770\pi$
$882$	0	0
$883$	−3.44540e13	−1.90729	−0.953645	−	0.300933i	$-0.902702\pi$
$883$	−3.44540e13	−1.90729	−0.953645	+	0.300933i	$0.902702\pi$
$884$	3.16270e12	0.174190
$885$	4.87183e12	0.266961
$886$	5.15505e12	0.281048
$887$	−5.98069e12	−0.324410	−0.162205	−	0.986757i	$-0.551861\pi$
$887$	−5.98069e12	−0.324410	−0.162205	+	0.986757i	$0.551861\pi$
$888$	−1.63342e13	−0.881534
$889$	0	0
$890$	1.39114e13	0.743217
$891$	5.11751e12	0.272025
$892$	5.45638e12	0.288578
$893$	1.30759e13	0.688084
$894$	−1.42430e12	−0.0745732
$895$	1.12153e13	0.584260
$896$	0	0
$897$	−2.12503e12	−0.109597
$898$	−4.06774e12	−0.208742
$899$	−6.37418e12	−0.325466
$900$	6.90165e12	0.350640
$901$	3.78778e12	0.191480
$902$	1.03735e13	0.521789
$903$	0	0
$904$	−1.89637e13	−0.944422
$905$	1.63641e12	0.0810910
$906$	−1.82679e13	−0.900766
$907$	−2.51683e12	−0.123487	−0.0617434	−	0.998092i	$-0.519666\pi$
$907$	−2.51683e12	−0.123487	−0.0617434	+	0.998092i	$0.519666\pi$
$908$	−3.88897e10	−0.00189867
$909$	1.50504e12	0.0731158
$910$	0	0
$911$	3.96021e13	1.90496	0.952478	−	0.304607i	$-0.0985252\pi$
$911$	3.96021e13	1.90496	0.952478	+	0.304607i	$0.0985252\pi$
$912$	5.08648e12	0.243467
$913$	−2.21365e12	−0.105437
$914$	−3.99044e12	−0.189131
$915$	−6.69846e12	−0.315922
$916$	−2.53338e12	−0.118897
$917$	0	0
$918$	−5.11667e12	−0.237791
$919$	−4.00850e13	−1.85380	−0.926899	−	0.375310i	$-0.877536\pi$
$919$	−4.00850e13	−1.85380	−0.926899	+	0.375310i	$0.877536\pi$
$920$	−4.26237e12	−0.196158
$921$	−1.34671e13	−0.616746
$922$	−1.97844e13	−0.901640
$923$	−4.31975e13	−1.95907
$924$	0	0
$925$	4.76174e13	2.13859
$926$	3.02263e13	1.35094
$927$	−9.71579e12	−0.432135
$928$	3.02479e13	1.33884
$929$	8.38470e12	0.369332	0.184666	−	0.982801i	$-0.440880\pi$
$929$	8.38470e12	0.369332	0.184666	+	0.982801i	$0.440880\pi$
$930$	4.56497e12	0.200108
$931$	0	0
$932$	−1.48336e12	−0.0643986
$933$	−1.58265e13	−0.683783
$934$	−6.43944e12	−0.276877
$935$	−7.03261e12	−0.300929
$936$	1.31406e13	0.559596
$937$	−2.33983e12	−0.0991645	−0.0495822	−	0.998770i	$-0.515789\pi$
$937$	−2.33983e12	−0.0991645	−0.0495822	+	0.998770i	$0.515789\pi$
$938$	0	0
$939$	−3.01725e13	−1.26653
$940$	−1.47825e13	−0.617550
$941$	6.45893e12	0.268539	0.134270	−	0.990945i	$-0.457131\pi$
$941$	6.45893e12	0.268539	0.134270	+	0.990945i	$0.457131\pi$
$942$	−1.49166e13	−0.617221
$943$	−3.01302e12	−0.124079
$944$	1.72327e12	0.0706285
$945$	0	0
$946$	8.00327e12	0.324906
$947$	−2.43323e13	−0.983123	−0.491561	−	0.870843i	$-0.663574\pi$
$947$	−2.43323e13	−0.983123	−0.491561	+	0.870843i	$0.663574\pi$
$948$	1.16653e13	0.469093
$949$	−3.99302e13	−1.59810
$950$	−3.29916e13	−1.31416
$951$	1.35228e13	0.536109
$952$	0	0
$953$	2.50351e12	0.0983177	0.0491589	−	0.998791i	$-0.484346\pi$
$953$	2.50351e12	0.0983177	0.0491589	+	0.998791i	$0.484346\pi$
$954$	4.82896e12	0.188749
$955$	2.45551e13	0.955269
$956$	2.05932e12	0.0797377
$957$	−1.98048e13	−0.763250
$958$	−2.89108e13	−1.10896
$959$	0	0
$960$	−3.46527e13	−1.31679
$961$	−2.54215e13	−0.961492
$962$	2.78188e13	1.04725
$963$	−1.38695e13	−0.519687
$964$	−1.21573e13	−0.453408
$965$	−4.82576e13	−1.79140
$966$	0	0
$967$	2.19887e13	0.808686	0.404343	−	0.914607i	$-0.367500\pi$
$967$	2.19887e13	0.808686	0.404343	+	0.914607i	$0.367500\pi$
$968$	−1.92521e13	−0.704757
$969$	−5.42348e12	−0.197615
$970$	−3.03512e13	−1.10079
$971$	9.07743e12	0.327700	0.163850	−	0.986485i	$-0.447609\pi$
$971$	9.07743e12	0.327700	0.163850	+	0.986485i	$0.447609\pi$
$972$	8.91568e12	0.320373
$973$	0	0
$974$	−1.24787e13	−0.444276
$975$	6.06013e13	2.14764
$976$	−2.36939e12	−0.0835818
$977$	2.73152e13	0.959134	0.479567	−	0.877505i	$-0.340794\pi$
$977$	2.73152e13	0.959134	0.479567	+	0.877505i	$0.340794\pi$
$978$	−1.68320e13	−0.588316
$979$	9.64018e12	0.335400
$980$	0	0
$981$	1.76421e12	0.0608192
$982$	−2.56962e13	−0.881795
$983$	−1.07541e13	−0.367351	−0.183676	−	0.982987i	$-0.558800\pi$
$983$	−1.07541e13	−0.367351	−0.183676	+	0.982987i	$0.558800\pi$
$984$	−2.94747e13	−1.00224
$985$	−2.62188e13	−0.887464
$986$	1.07790e13	0.363188
$987$	0	0
$988$	1.53087e13	0.511131
$989$	−2.32458e12	−0.0772612
$990$	−8.96573e12	−0.296638
$991$	−2.06047e13	−0.678633	−0.339317	−	0.940672i	$-0.610196\pi$
$991$	−2.06047e13	−0.678633	−0.339317	+	0.940672i	$0.610196\pi$
$992$	−4.83144e12	−0.158407
$993$	−3.70352e13	−1.20877
$994$	0	0
$995$	3.85474e12	0.124678
$996$	1.92995e12	0.0621411
$997$	−2.30380e13	−0.738444	−0.369222	−	0.929341i	$-0.620376\pi$
$997$	−2.30380e13	−0.738444	−0.369222	+	0.929341i	$0.620376\pi$
$998$	2.83320e13	0.904046
$999$	3.57463e13	1.13550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.a.b.1.1		2
7.2	even	3		49.10.c.b.18.2		4
7.3	odd	6		49.10.c.c.30.2		4
7.4	even	3		49.10.c.b.30.2		4
7.5	odd	6		49.10.c.c.18.2		4
7.6	odd	2		7.10.a.a.1.1	✓	2
21.20	even	2		63.10.a.d.1.2		2
28.27	even	2		112.10.a.e.1.1		2
35.13	even	4		175.10.b.b.99.4		4
35.27	even	4		175.10.b.b.99.1		4
35.34	odd	2		175.10.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.a.1.1	✓	2	7.6	odd	2
49.10.a.b.1.1		2	1.1	even	1	trivial
49.10.c.b.18.2		4	7.2	even	3
49.10.c.b.30.2		4	7.4	even	3
49.10.c.c.18.2		4	7.5	odd	6
49.10.c.c.30.2		4	7.3	odd	6
63.10.a.d.1.2		2	21.20	even	2
112.10.a.e.1.1		2	28.27	even	2
175.10.a.b.1.2		2	35.34	odd	2
175.10.b.b.99.1		4	35.27	even	4
175.10.b.b.99.4		4	35.13	even	4

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q-16.8924 q^{2} -109.817 q^{3} -226.645 q^{4} +2438.78 q^{5} +1855.08 q^{6} +12477.5 q^{8} -7623.25 q^{9} +O(q^{10})\)	\(q-16.8924 q^{2} -109.817 q^{3} -226.645 q^{4} +2438.78 q^{5} +1855.08 q^{6} +12477.5 q^{8} -7623.25 q^{9} -41197.0 q^{10} -28548.3 q^{11} +24889.5 q^{12} -138149. q^{13} -267819. q^{15} -94733.5 q^{16} +101010. q^{17} +128775. q^{18} +488928. q^{19} -552739. q^{20} +482250. q^{22} -140071. q^{23} -1.37024e6 q^{24} +3.99453e6 q^{25} +2.33367e6 q^{26} +2.99869e6 q^{27} -6.31716e6 q^{29} +4.52413e6 q^{30} +1.00903e6 q^{31} -4.78821e6 q^{32} +3.13508e6 q^{33} -1.70630e6 q^{34} +1.72777e6 q^{36} +1.19206e7 q^{37} -8.25919e6 q^{38} +1.51711e7 q^{39} +3.04300e7 q^{40} +2.15106e7 q^{41} +1.65957e7 q^{43} +6.47033e6 q^{44} -1.85915e7 q^{45} +2.36615e6 q^{46} +2.67441e7 q^{47} +1.04033e7 q^{48} -6.74774e7 q^{50} -1.10926e7 q^{51} +3.13108e7 q^{52} +3.74991e7 q^{53} -5.06552e7 q^{54} -6.96230e7 q^{55} -5.36926e7 q^{57} +1.06712e8 q^{58} -1.81907e7 q^{59} +6.07000e7 q^{60} +2.50111e7 q^{61} -1.70449e7 q^{62} +1.29388e8 q^{64} -3.36915e8 q^{65} -5.29592e7 q^{66} -2.18572e8 q^{67} -2.28934e7 q^{68} +1.53822e7 q^{69} +3.12688e8 q^{71} -9.51193e7 q^{72} +2.89038e8 q^{73} -2.01369e8 q^{74} -4.38667e8 q^{75} -1.10813e8 q^{76} -2.56276e8 q^{78} +4.68685e8 q^{79} -2.31034e8 q^{80} -1.79258e8 q^{81} -3.63366e8 q^{82} +7.75407e7 q^{83} +2.46341e8 q^{85} -2.80342e8 q^{86} +6.93730e8 q^{87} -3.56212e8 q^{88} -3.37680e8 q^{89} +3.14055e8 q^{90} +3.17465e7 q^{92} -1.10808e8 q^{93} -4.51773e8 q^{94} +1.19239e9 q^{95} +5.25827e8 q^{96} +7.36733e8 q^{97} +2.17631e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{2} + 86 q^{3} - 620 q^{4} + 2238 q^{5} + 3988 q^{6} + 2616 q^{8} + 11038 q^{9}+O(q^{10}) \) 2 * q - 6 * q^2 + 86 * q^3 - 620 * q^4 + 2238 * q^5 + 3988 * q^6 + 2616 * q^8 + 11038 * q^9	\( 2 q - 6 q^{2} + 86 q^{3} - 620 q^{4} + 2238 q^{5} + 3988 q^{6} + 2616 q^{8} + 11038 q^{9} - 43384 q^{10} + 35316 q^{11} - 52136 q^{12} + 26530 q^{13} - 307136 q^{15} - 752 q^{16} + 463920 q^{17} + 332042 q^{18} + 925426 q^{19} - 473760 q^{20} + 1177888 q^{22} + 778128 q^{23} - 3301296 q^{24} + 2081722 q^{25} + 4127424 q^{26} + 2798612 q^{27} - 10003584 q^{29} + 4095872 q^{30} - 2467260 q^{31} + 1284576 q^{32} + 15640784 q^{33} + 2246676 q^{34} - 5612716 q^{36} + 30735552 q^{37} - 3504660 q^{38} + 47417944 q^{39} + 32409984 q^{40} + 19103448 q^{41} + 4065100 q^{43} - 18650976 q^{44} - 22338298 q^{45} + 12367584 q^{46} + 82195020 q^{47} + 28806496 q^{48} - 88312626 q^{50} + 59971356 q^{51} - 33466384 q^{52} - 55189812 q^{53} - 52834472 q^{54} - 82445816 q^{55} + 31781116 q^{57} + 66558004 q^{58} + 7069218 q^{59} + 76165376 q^{60} - 44316386 q^{61} - 54910200 q^{62} + 147417152 q^{64} - 369979260 q^{65} + 83258464 q^{66} - 241921336 q^{67} - 165645816 q^{68} + 195181152 q^{69} + 206493816 q^{71} - 279147720 q^{72} + 499153188 q^{73} + 3571524 q^{74} - 813228014 q^{75} - 282511768 q^{76} + 94970960 q^{78} + 468535096 q^{79} - 249904128 q^{80} - 585745634 q^{81} - 389586092 q^{82} - 444023958 q^{83} + 173475060 q^{85} - 416830608 q^{86} - 28134340 q^{87} - 986010816 q^{88} - 636267396 q^{89} + 273242728 q^{90} - 329431488 q^{92} - 791523960 q^{93} + 152223192 q^{94} + 1104747984 q^{95} + 1714981184 q^{96} + 1632716064 q^{97} + 1409417860 q^{99}+O(q^{100}) \) 2 * q - 6 * q^2 + 86 * q^3 - 620 * q^4 + 2238 * q^5 + 3988 * q^6 + 2616 * q^8 + 11038 * q^9 - 43384 * q^10 + 35316 * q^11 - 52136 * q^12 + 26530 * q^13 - 307136 * q^15 - 752 * q^16 + 463920 * q^17 + 332042 * q^18 + 925426 * q^19 - 473760 * q^20 + 1177888 * q^22 + 778128 * q^23 - 3301296 * q^24 + 2081722 * q^25 + 4127424 * q^26 + 2798612 * q^27 - 10003584 * q^29 + 4095872 * q^30 - 2467260 * q^31 + 1284576 * q^32 + 15640784 * q^33 + 2246676 * q^34 - 5612716 * q^36 + 30735552 * q^37 - 3504660 * q^38 + 47417944 * q^39 + 32409984 * q^40 + 19103448 * q^41 + 4065100 * q^43 - 18650976 * q^44 - 22338298 * q^45 + 12367584 * q^46 + 82195020 * q^47 + 28806496 * q^48 - 88312626 * q^50 + 59971356 * q^51 - 33466384 * q^52 - 55189812 * q^53 - 52834472 * q^54 - 82445816 * q^55 + 31781116 * q^57 + 66558004 * q^58 + 7069218 * q^59 + 76165376 * q^60 - 44316386 * q^61 - 54910200 * q^62 + 147417152 * q^64 - 369979260 * q^65 + 83258464 * q^66 - 241921336 * q^67 - 165645816 * q^68 + 195181152 * q^69 + 206493816 * q^71 - 279147720 * q^72 + 499153188 * q^73 + 3571524 * q^74 - 813228014 * q^75 - 282511768 * q^76 + 94970960 * q^78 + 468535096 * q^79 - 249904128 * q^80 - 585745634 * q^81 - 389586092 * q^82 - 444023958 * q^83 + 173475060 * q^85 - 416830608 * q^86 - 28134340 * q^87 - 986010816 * q^88 - 636267396 * q^89 + 273242728 * q^90 - 329431488 * q^92 - 791523960 * q^93 + 152223192 * q^94 + 1104747984 * q^95 + 1714981184 * q^96 + 1632716064 * q^97 + 1409417860 * q^99

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