LMFDB - Embedded newform 29.8.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,8,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	29.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:	$9.05916573904$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 616x^{5} + 1864x^{4} + 96785x^{3} - 257817x^{2} - 3929114x + 2682946 $ x^7 - x^6 - 616x^5 + 1864x^4 + 96785x^3 - 257817x^2 - 3929114*x + 2682946
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$16.4977$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.4977 q^{2} -74.2053 q^{3} +178.170 q^{4} +273.079 q^{5} +1298.42 q^{6} +59.8847 q^{7} -877.860 q^{8} +3319.43 q^{9} +O(q^{10})$	\(q-17.4977 q^{2} -74.2053 q^{3} +178.170 q^{4} +273.079 q^{5} +1298.42 q^{6} +59.8847 q^{7} -877.860 q^{8} +3319.43 q^{9} -4778.26 q^{10} -4664.59 q^{11} -13221.2 q^{12} +7969.82 q^{13} -1047.84 q^{14} -20263.9 q^{15} -7445.22 q^{16} +28307.2 q^{17} -58082.4 q^{18} -36301.7 q^{19} +48654.5 q^{20} -4443.76 q^{21} +81619.7 q^{22} -30001.6 q^{23} +65141.8 q^{24} -3552.92 q^{25} -139454. q^{26} -84032.1 q^{27} +10669.6 q^{28} +24389.0 q^{29} +354572. q^{30} +95324.5 q^{31} +242640. q^{32} +346137. q^{33} -495312. q^{34} +16353.2 q^{35} +591422. q^{36} -547194. q^{37} +635197. q^{38} -591403. q^{39} -239725. q^{40} -826205. q^{41} +77755.6 q^{42} -894021. q^{43} -831090. q^{44} +906466. q^{45} +524960. q^{46} +956351. q^{47} +552475. q^{48} -819957. q^{49} +62168.0 q^{50} -2.10055e6 q^{51} +1.41998e6 q^{52} +622780. q^{53} +1.47037e6 q^{54} -1.27380e6 q^{55} -52570.3 q^{56} +2.69378e6 q^{57} -426752. q^{58} +1.71181e6 q^{59} -3.61042e6 q^{60} -1.49703e6 q^{61} -1.66796e6 q^{62} +198783. q^{63} -3.29266e6 q^{64} +2.17639e6 q^{65} -6.05661e6 q^{66} +498627. q^{67} +5.04350e6 q^{68} +2.22628e6 q^{69} -286144. q^{70} -2.96410e6 q^{71} -2.91399e6 q^{72} +1.26270e6 q^{73} +9.57465e6 q^{74} +263645. q^{75} -6.46788e6 q^{76} -279337. q^{77} +1.03482e7 q^{78} -499373. q^{79} -2.03313e6 q^{80} -1.02396e6 q^{81} +1.44567e7 q^{82} -4.90677e6 q^{83} -791745. q^{84} +7.73010e6 q^{85} +1.56433e7 q^{86} -1.80979e6 q^{87} +4.09486e6 q^{88} +3.18423e6 q^{89} -1.58611e7 q^{90} +477270. q^{91} -5.34539e6 q^{92} -7.07358e6 q^{93} -1.67340e7 q^{94} -9.91324e6 q^{95} -1.80052e7 q^{96} -2.31165e6 q^{97} +1.43474e7 q^{98} -1.54838e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 8 q^{2} - 82 q^{3} + 346 q^{4} - 320 q^{5} - 938 q^{6} - 1704 q^{7} + 2082 q^{8} + 4061 q^{9}+O(q^{10}) $ 7 * q - 8 * q^2 - 82 * q^3 + 346 * q^4 - 320 * q^5 - 938 * q^6 - 1704 * q^7 + 2082 * q^8 + 4061 * q^9	\( 7 q - 8 q^{2} - 82 q^{3} + 346 q^{4} - 320 q^{5} - 938 q^{6} - 1704 q^{7} + 2082 q^{8} + 4061 q^{9} - 14114 q^{10} - 14498 q^{11} - 42334 q^{12} - 9024 q^{13} - 45880 q^{14} - 24238 q^{15} - 3022 q^{16} - 54882 q^{17} + 17218 q^{18} - 100572 q^{19} - 86022 q^{20} + 34304 q^{21} + 9086 q^{22} + 55340 q^{23} - 138966 q^{24} + 125759 q^{25} + 257206 q^{26} - 176146 q^{27} - 41760 q^{28} + 170723 q^{29} + 1132178 q^{30} - 153330 q^{31} + 825478 q^{32} + 555898 q^{33} - 194256 q^{34} + 561160 q^{35} + 1939652 q^{36} - 457050 q^{37} + 617164 q^{38} - 1173662 q^{39} - 1151986 q^{40} - 864230 q^{41} + 2046224 q^{42} - 1590058 q^{43} - 1399966 q^{44} - 2268610 q^{45} + 1557900 q^{46} - 204750 q^{47} - 2501730 q^{48} - 1892625 q^{49} + 2115526 q^{50} - 2481996 q^{51} + 1469690 q^{52} - 2696092 q^{53} - 2918978 q^{54} - 2596662 q^{55} - 2818440 q^{56} - 96196 q^{57} - 195112 q^{58} + 1434256 q^{59} + 7687830 q^{60} - 5622798 q^{61} - 4660550 q^{62} - 5632816 q^{63} - 944442 q^{64} - 353086 q^{65} + 8421370 q^{66} - 5380324 q^{67} + 6393964 q^{68} - 2248580 q^{69} + 10805432 q^{70} + 4605140 q^{71} + 17475264 q^{72} + 3979266 q^{73} + 15124836 q^{74} - 2365120 q^{75} - 3893220 q^{76} + 8666288 q^{77} + 7790850 q^{78} - 6355522 q^{79} - 4424794 q^{80} + 6442139 q^{81} + 6831364 q^{82} + 3077704 q^{83} + 29008056 q^{84} + 5117008 q^{85} + 11620998 q^{86} - 1999898 q^{87} - 24708046 q^{88} + 743498 q^{89} - 38296444 q^{90} - 24167656 q^{91} + 11053132 q^{92} + 25723782 q^{93} - 29029210 q^{94} + 1137892 q^{95} - 34019010 q^{96} - 7924270 q^{97} + 19298152 q^{98} - 43451600 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 82 * q^3 + 346 * q^4 - 320 * q^5 - 938 * q^6 - 1704 * q^7 + 2082 * q^8 + 4061 * q^9 - 14114 * q^10 - 14498 * q^11 - 42334 * q^12 - 9024 * q^13 - 45880 * q^14 - 24238 * q^15 - 3022 * q^16 - 54882 * q^17 + 17218 * q^18 - 100572 * q^19 - 86022 * q^20 + 34304 * q^21 + 9086 * q^22 + 55340 * q^23 - 138966 * q^24 + 125759 * q^25 + 257206 * q^26 - 176146 * q^27 - 41760 * q^28 + 170723 * q^29 + 1132178 * q^30 - 153330 * q^31 + 825478 * q^32 + 555898 * q^33 - 194256 * q^34 + 561160 * q^35 + 1939652 * q^36 - 457050 * q^37 + 617164 * q^38 - 1173662 * q^39 - 1151986 * q^40 - 864230 * q^41 + 2046224 * q^42 - 1590058 * q^43 - 1399966 * q^44 - 2268610 * q^45 + 1557900 * q^46 - 204750 * q^47 - 2501730 * q^48 - 1892625 * q^49 + 2115526 * q^50 - 2481996 * q^51 + 1469690 * q^52 - 2696092 * q^53 - 2918978 * q^54 - 2596662 * q^55 - 2818440 * q^56 - 96196 * q^57 - 195112 * q^58 + 1434256 * q^59 + 7687830 * q^60 - 5622798 * q^61 - 4660550 * q^62 - 5632816 * q^63 - 944442 * q^64 - 353086 * q^65 + 8421370 * q^66 - 5380324 * q^67 + 6393964 * q^68 - 2248580 * q^69 + 10805432 * q^70 + 4605140 * q^71 + 17475264 * q^72 + 3979266 * q^73 + 15124836 * q^74 - 2365120 * q^75 - 3893220 * q^76 + 8666288 * q^77 + 7790850 * q^78 - 6355522 * q^79 - 4424794 * q^80 + 6442139 * q^81 + 6831364 * q^82 + 3077704 * q^83 + 29008056 * q^84 + 5117008 * q^85 + 11620998 * q^86 - 1999898 * q^87 - 24708046 * q^88 + 743498 * q^89 - 38296444 * q^90 - 24167656 * q^91 + 11053132 * q^92 + 25723782 * q^93 - 29029210 * q^94 + 1137892 * q^95 - 34019010 * q^96 - 7924270 * q^97 + 19298152 * q^98 - 43451600 * 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 $

$2$	−17.4977	−1.54659	−0.773297	−	0.634044i	$-0.781394\pi$
$2$	−17.4977	−1.54659	−0.773297	+	0.634044i	$0.781394\pi$
$3$	−74.2053	−1.58676	−0.793379	−	0.608728i	$-0.791680\pi$
$3$	−74.2053	−1.58676	−0.793379	+	0.608728i	$0.791680\pi$
$4$	178.170	1.39195
$5$	273.079	0.976997	0.488498	−	0.872565i	$-0.337545\pi$
$5$	273.079	0.976997	0.488498	+	0.872565i	$0.337545\pi$
$6$	1298.42	2.45407
$7$	59.8847	0.0659891	0.0329946	−	0.999456i	$-0.489496\pi$
$7$	59.8847	0.0659891	0.0329946	+	0.999456i	$0.489496\pi$
$8$	−877.860	−0.606192
$9$	3319.43	1.51780
$10$	−4778.26	−1.51102
$11$	−4664.59	−1.05667	−0.528335	−	0.849036i	$-0.677183\pi$
$11$	−4664.59	−1.05667	−0.528335	+	0.849036i	$0.677183\pi$
$12$	−13221.2	−2.20869
$13$	7969.82	1.00611	0.503057	−	0.864253i	$-0.332209\pi$
$13$	7969.82	1.00611	0.503057	+	0.864253i	$0.332209\pi$
$14$	−1047.84	−0.102058
$15$	−20263.9	−1.55026
$16$	−7445.22	−0.454420
$17$	28307.2	1.39742	0.698708	−	0.715407i	$-0.253758\pi$
$17$	28307.2	1.39742	0.698708	+	0.715407i	$0.253758\pi$
$18$	−58082.4	−2.34742
$19$	−36301.7	−1.21420	−0.607099	−	0.794626i	$-0.707667\pi$
$19$	−36301.7	−1.21420	−0.607099	+	0.794626i	$0.707667\pi$
$20$	48654.5	1.35993
$21$	−4443.76	−0.104709
$22$	81619.7	1.63424
$23$	−30001.6	−0.514159	−0.257080	−	0.966390i	$-0.582760\pi$
$23$	−30001.6	−0.514159	−0.257080	+	0.966390i	$0.582760\pi$
$24$	65141.8	0.961880
$25$	−3552.92	−0.0454774
$26$	−139454.	−1.55605
$27$	−84032.1	−0.821622
$28$	10669.6	0.0918538
$29$	24389.0	0.185695
$29$	24389.0	0.185695
$30$	354572.	2.39762
$31$	95324.5	0.574697	0.287348	−	0.957826i	$-0.407226\pi$
$31$	95324.5	0.574697	0.287348	+	0.957826i	$0.407226\pi$
$32$	242640.	1.30900
$33$	346137.	1.67668
$34$	−495312.	−2.16124
$35$	16353.2	0.0644712
$36$	591422.	2.11271
$37$	−547194.	−1.77597	−0.887985	−	0.459873i	$-0.847895\pi$
$37$	−547194.	−1.77597	−0.887985	+	0.459873i	$0.847895\pi$
$38$	635197.	1.87787
$39$	−591403.	−1.59646
$40$	−239725.	−0.592248
$41$	−826205.	−1.87217	−0.936083	−	0.351780i	$-0.885577\pi$
$41$	−826205.	−1.87217	−0.936083	+	0.351780i	$0.885577\pi$
$42$	77755.6	0.161942
$43$	−894021.	−1.71478	−0.857389	−	0.514669i	$-0.827915\pi$
$43$	−894021.	−1.71478	−0.857389	+	0.514669i	$0.827915\pi$
$44$	−831090.	−1.47083
$45$	906466.	1.48289
$46$	524960.	0.795195
$47$	956351.	1.34361	0.671807	−	0.740726i	$-0.265518\pi$
$47$	956351.	1.34361	0.671807	+	0.740726i	$0.265518\pi$
$48$	552475.	0.721055
$49$	−819957.	−0.995645
$50$	62168.0	0.0703350
$51$	−2.10055e6	−2.21736
$52$	1.41998e6	1.40046
$53$	622780.	0.574605	0.287302	−	0.957840i	$-0.407242\pi$
$53$	622780.	0.574605	0.287302	+	0.957840i	$0.407242\pi$
$54$	1.47037e6	1.27072
$55$	−1.27380e6	−1.03236
$56$	−52570.3	−0.0400021
$57$	2.69378e6	1.92664
$58$	−426752.	−0.287195
$59$	1.71181e6	1.08511	0.542553	−	0.840021i	$-0.317458\pi$
$59$	1.71181e6	1.08511	0.542553	+	0.840021i	$0.317458\pi$
$60$	−3.61042e6	−2.15788
$61$	−1.49703e6	−0.844454	−0.422227	−	0.906490i	$-0.638751\pi$
$61$	−1.49703e6	−0.844454	−0.422227	+	0.906490i	$0.638751\pi$
$62$	−1.66796e6	−0.888822
$63$	198783.	0.100158
$64$	−3.29266e6	−1.57006
$65$	2.17639e6	0.982970
$66$	−6.05661e6	−2.59314
$67$	498627.	0.202542	0.101271	−	0.994859i	$-0.467709\pi$
$67$	498627.	0.202542	0.101271	+	0.994859i	$0.467709\pi$
$68$	5.04350e6	1.94514
$69$	2.22628e6	0.815846
$70$	−286144.	−0.0997107
$71$	−2.96410e6	−0.982854	−0.491427	−	0.870919i	$-0.663525\pi$
$71$	−2.96410e6	−0.982854	−0.491427	+	0.870919i	$0.663525\pi$
$72$	−2.91399e6	−0.920078
$73$	1.26270e6	0.379901	0.189951	−	0.981794i	$-0.439167\pi$
$73$	1.26270e6	0.379901	0.189951	+	0.981794i	$0.439167\pi$
$74$	9.57465e6	2.74670
$75$	263645.	0.0721616
$76$	−6.46788e6	−1.69011
$77$	−279337.	−0.0697287
$78$	1.03482e7	2.46907
$79$	−499373.	−0.113954	−0.0569771	−	0.998375i	$-0.518146\pi$
$79$	−499373.	−0.113954	−0.0569771	+	0.998375i	$0.518146\pi$
$80$	−2.03313e6	−0.443967
$81$	−1.02396e6	−0.214084
$82$	1.44567e7	2.89548
$83$	−4.90677e6	−0.941938	−0.470969	−	0.882150i	$-0.656096\pi$
$83$	−4.90677e6	−0.941938	−0.470969	+	0.882150i	$0.656096\pi$
$84$	−791745.	−0.145750
$85$	7.73010e6	1.36527
$86$	1.56433e7	2.65207
$87$	−1.80979e6	−0.294653
$88$	4.09486e6	0.640544
$89$	3.18423e6	0.478783	0.239392	−	0.970923i	$-0.423052\pi$
$89$	3.18423e6	0.478783	0.239392	+	0.970923i	$0.423052\pi$
$90$	−1.58611e7	−2.29342
$91$	477270.	0.0663926
$92$	−5.34539e6	−0.715685
$93$	−7.07358e6	−0.911904
$94$	−1.67340e7	−2.07803
$95$	−9.91324e6	−1.18627
$96$	−1.80052e7	−2.07706
$97$	−2.31165e6	−0.257170	−0.128585	−	0.991698i	$-0.541044\pi$
$97$	−2.31165e6	−0.257170	−0.128585	+	0.991698i	$0.541044\pi$
$98$	1.43474e7	1.53986
$99$	−1.54838e7	−1.60381
$100$	−633023.	−0.0633023
$101$	4.54726e6	0.439163	0.219581	−	0.975594i	$-0.429531\pi$
$101$	4.54726e6	0.439163	0.219581	+	0.975594i	$0.429531\pi$
$102$	3.67547e7	3.42936
$103$	−2.68759e6	−0.242345	−0.121172	−	0.992631i	$-0.538665\pi$
$103$	−2.68759e6	−0.242345	−0.121172	+	0.992631i	$0.538665\pi$
$104$	−6.99639e6	−0.609898
$105$	−1.21350e6	−0.102300
$106$	−1.08972e7	−0.888680
$107$	−2.32486e7	−1.83465	−0.917325	−	0.398139i	$-0.869656\pi$
$107$	−2.32486e7	−1.83465	−0.917325	+	0.398139i	$0.869656\pi$
$108$	−1.49720e7	−1.14366
$109$	−1.35121e7	−0.999382	−0.499691	−	0.866204i	$-0.666553\pi$
$109$	−1.35121e7	−0.999382	−0.499691	+	0.866204i	$0.666553\pi$
$110$	2.22886e7	1.59665
$111$	4.06047e7	2.81803
$112$	−445855.	−0.0299868
$113$	−2.14958e6	−0.140146	−0.0700728	−	0.997542i	$-0.522323\pi$
$113$	−2.14958e6	−0.140146	−0.0700728	+	0.997542i	$0.522323\pi$
$114$	−4.71350e7	−2.97973
$115$	−8.19281e6	−0.502332
$116$	4.34539e6	0.258479
$117$	2.64553e7	1.52708
$118$	−2.99527e7	−1.67822
$119$	1.69517e6	0.0922143
$120$	1.77889e7	0.939753
$121$	2.27124e6	0.116550
$122$	2.61946e7	1.30603
$123$	6.13088e7	2.97067
$124$	1.69840e7	0.799951
$125$	−2.23045e7	−1.02143
$126$	−3.47825e6	−0.154904
$127$	−2.08962e7	−0.905220	−0.452610	−	0.891709i	$-0.649507\pi$
$127$	−2.08962e7	−0.905220	−0.452610	+	0.891709i	$0.649507\pi$
$128$	2.65561e7	1.11926
$129$	6.63411e7	2.72094
$130$	−3.80819e7	−1.52025
$131$	2.38707e6	0.0927717	0.0463859	−	0.998924i	$-0.485230\pi$
$131$	2.38707e6	0.0927717	0.0463859	+	0.998924i	$0.485230\pi$
$132$	6.16713e7	2.33386
$133$	−2.17392e6	−0.0801239
$134$	−8.72484e6	−0.313250
$135$	−2.29474e7	−0.802722
$136$	−2.48498e7	−0.847103
$137$	−1.14356e7	−0.379959	−0.189980	−	0.981788i	$-0.560842\pi$
$137$	−1.14356e7	−0.379959	−0.189980	+	0.981788i	$0.560842\pi$
$138$	−3.89548e7	−1.26178
$139$	4.24162e6	0.133961	0.0669807	−	0.997754i	$-0.478663\pi$
$139$	4.24162e6	0.133961	0.0669807	+	0.997754i	$0.478663\pi$
$140$	2.91366e6	0.0897408
$141$	−7.09663e7	−2.13199
$142$	5.18650e7	1.52008
$143$	−3.71760e7	−1.06313
$144$	−2.47139e7	−0.689719
$145$	6.66012e6	0.181424
$146$	−2.20944e7	−0.587553
$147$	6.08451e7	1.57985
$148$	−9.74936e7	−2.47207
$149$	−9.47077e6	−0.234549	−0.117274	−	0.993100i	$-0.537416\pi$
$149$	−9.47077e6	−0.234549	−0.117274	+	0.993100i	$0.537416\pi$
$150$	−4.61319e6	−0.111605
$151$	7.59829e7	1.79596	0.897980	−	0.440036i	$-0.145034\pi$
$151$	7.59829e7	1.79596	0.897980	+	0.440036i	$0.145034\pi$
$152$	3.18678e7	0.736037
$153$	9.39638e7	2.12100
$154$	4.88777e6	0.107842
$155$	2.60311e7	0.561477
$156$	−1.05370e8	−2.22219
$157$	4.39352e7	0.906073	0.453037	−	0.891492i	$-0.350341\pi$
$157$	4.39352e7	0.906073	0.453037	+	0.891492i	$0.350341\pi$
$158$	8.73789e6	0.176241
$159$	−4.62136e7	−0.911758
$160$	6.62600e7	1.27888
$161$	−1.79664e6	−0.0339289
$162$	1.79169e7	0.331101
$163$	−3.02176e7	−0.546516	−0.273258	−	0.961941i	$-0.588101\pi$
$163$	−3.02176e7	−0.546516	−0.273258	+	0.961941i	$0.588101\pi$
$164$	−1.47205e8	−2.60597
$165$	9.45228e7	1.63811
$166$	8.58573e7	1.45680
$167$	−1.15318e7	−0.191597	−0.0957986	−	0.995401i	$-0.530540\pi$
$167$	−1.15318e7	−0.191597	−0.0957986	+	0.995401i	$0.530540\pi$
$168$	3.90100e6	0.0634736
$169$	769568.	0.0122643
$170$	−1.35259e8	−2.11152
$171$	−1.20501e8	−1.84291
$172$	−1.59288e8	−2.38689
$173$	7.59049e7	1.11457	0.557286	−	0.830320i	$-0.311843\pi$
$173$	7.59049e7	1.11457	0.557286	+	0.830320i	$0.311843\pi$
$174$	3.16672e7	0.455709
$175$	−212765.	−0.00300101
$176$	3.47289e7	0.480172
$177$	−1.27025e8	−1.72180
$178$	−5.57167e7	−0.740483
$179$	4.96965e7	0.647649	0.323825	−	0.946117i	$-0.395031\pi$
$179$	4.96965e7	0.647649	0.323825	+	0.946117i	$0.395031\pi$
$180$	1.61505e8	2.06411
$181$	−6.56927e7	−0.823459	−0.411729	−	0.911306i	$-0.635075\pi$
$181$	−6.56927e7	−0.823459	−0.411729	+	0.911306i	$0.635075\pi$
$182$	−8.35114e6	−0.102682
$183$	1.11087e8	1.33994
$184$	2.63372e7	0.311679
$185$	−1.49427e8	−1.73512
$186$	1.23772e8	1.41035
$187$	−1.32042e8	−1.47661
$188$	1.70393e8	1.87025
$189$	−5.03224e6	−0.0542182
$190$	1.73459e8	1.83468
$191$	−3.00426e7	−0.311975	−0.155988	−	0.987759i	$-0.549856\pi$
$191$	−3.00426e7	−0.311975	−0.155988	+	0.987759i	$0.549856\pi$
$192$	2.44333e8	2.49131
$193$	1.76781e8	1.77004	0.885022	−	0.465550i	$-0.154143\pi$
$193$	1.76781e8	1.77004	0.885022	+	0.465550i	$0.154143\pi$
$194$	4.04486e7	0.397738
$195$	−1.61500e8	−1.55973
$196$	−1.46092e8	−1.38589
$197$	−1.75943e8	−1.63961	−0.819803	−	0.572645i	$-0.805917\pi$
$197$	−1.75943e8	−1.63961	−0.819803	+	0.572645i	$0.805917\pi$
$198$	2.70931e8	2.48045
$199$	−1.24440e8	−1.11937	−0.559684	−	0.828706i	$-0.689077\pi$
$199$	−1.24440e8	−1.11937	−0.559684	+	0.828706i	$0.689077\pi$
$200$	3.11896e6	0.0275680
$201$	−3.70008e7	−0.321385
$202$	−7.95667e7	−0.679206
$203$	1.46053e6	0.0122539
$204$	−3.74254e8	−3.08646
$205$	−2.25619e8	−1.82910
$206$	4.70267e7	0.374809
$207$	−9.95883e7	−0.780390
$208$	−5.93371e7	−0.457198
$209$	1.69333e8	1.28301
$210$	2.12334e7	0.158217
$211$	2.36656e8	1.73432	0.867161	−	0.498028i	$-0.165942\pi$
$211$	2.36656e8	1.73432	0.867161	+	0.498028i	$0.165942\pi$
$212$	1.10961e8	0.799823
$213$	2.19952e8	1.55955
$214$	4.06797e8	2.83746
$215$	−2.44138e8	−1.67533
$216$	7.37684e7	0.498061
$217$	5.70848e6	0.0379237
$218$	2.36432e8	1.54564
$219$	−9.36991e7	−0.602811
$220$	−2.26953e8	−1.43700
$221$	2.25604e8	1.40596
$222$	−7.10490e8	−4.35835
$223$	1.32525e8	0.800262	0.400131	−	0.916458i	$-0.368965\pi$
$223$	1.32525e8	0.800262	0.400131	+	0.916458i	$0.368965\pi$
$224$	1.45304e7	0.0863795
$225$	−1.17937e7	−0.0690255
$226$	3.76128e7	0.216748
$227$	1.93235e8	1.09646	0.548232	−	0.836326i	$-0.315301\pi$
$227$	1.93235e8	1.09646	0.548232	+	0.836326i	$0.315301\pi$
$228$	4.79951e8	2.68179
$229$	−2.40981e8	−1.32605	−0.663024	−	0.748599i	$-0.730727\pi$
$229$	−2.40981e8	−1.32605	−0.663024	+	0.748599i	$0.730727\pi$
$230$	1.43355e8	0.776903
$231$	2.07283e7	0.110643
$232$	−2.14101e7	−0.112567
$233$	2.32366e8	1.20345	0.601724	−	0.798704i	$-0.294481\pi$
$233$	2.32366e8	1.20345	0.601724	+	0.798704i	$0.294481\pi$
$234$	−4.62906e8	−2.36177
$235$	2.61159e8	1.31271
$236$	3.04992e8	1.51042
$237$	3.70562e7	0.180818
$238$	−2.96616e7	−0.142618
$239$	−2.48266e8	−1.17632	−0.588158	−	0.808746i	$-0.700147\pi$
$239$	−2.48266e8	−1.17632	−0.588158	+	0.808746i	$0.700147\pi$
$240$	1.50869e8	0.704468
$241$	−1.78925e8	−0.823402	−0.411701	−	0.911319i	$-0.635065\pi$
$241$	−1.78925e8	−0.823402	−0.411701	+	0.911319i	$0.635065\pi$
$242$	−3.97414e7	−0.180256
$243$	2.59761e8	1.16132
$244$	−2.66726e8	−1.17544
$245$	−2.23913e8	−0.972742
$246$	−1.07276e9	−4.59442
$247$	−2.89318e8	−1.22162
$248$	−8.36815e7	−0.348376
$249$	3.64108e8	1.49463
$250$	3.90278e8	1.57973
$251$	2.66064e7	0.106201	0.0531005	−	0.998589i	$-0.483090\pi$
$251$	2.66064e7	0.106201	0.0531005	+	0.998589i	$0.483090\pi$
$252$	3.54171e7	0.139416
$253$	1.39945e8	0.543296
$254$	3.65636e8	1.40001
$255$	−5.73615e8	−2.16636
$256$	−4.32103e7	−0.160971
$257$	−4.35738e7	−0.160125	−0.0800625	−	0.996790i	$-0.525512\pi$
$257$	−4.35738e7	−0.160125	−0.0800625	+	0.996790i	$0.525512\pi$
$258$	−1.16082e9	−4.20818
$259$	−3.27686e7	−0.117195
$260$	3.87767e8	1.36825
$261$	8.09575e7	0.281848
$262$	−4.17683e7	−0.143480
$263$	−3.32474e8	−1.12697	−0.563485	−	0.826126i	$-0.690540\pi$
$263$	−3.32474e8	−1.12697	−0.563485	+	0.826126i	$0.690540\pi$
$264$	−3.03860e8	−1.01639
$265$	1.70068e8	0.561387
$266$	3.80386e7	0.123919
$267$	−2.36286e8	−0.759713
$268$	8.88404e7	0.281928
$269$	−3.96906e7	−0.124324	−0.0621620	−	0.998066i	$-0.519800\pi$
$269$	−3.96906e7	−0.124324	−0.0621620	+	0.998066i	$0.519800\pi$
$270$	4.01527e8	1.24149
$271$	−2.68219e7	−0.0818647	−0.0409323	−	0.999162i	$-0.513033\pi$
$271$	−2.68219e7	−0.0818647	−0.0409323	+	0.999162i	$0.513033\pi$
$272$	−2.10753e8	−0.635014
$273$	−3.54160e7	−0.105349
$274$	2.00097e8	0.587643
$275$	1.65729e7	0.0480545
$276$	3.96656e8	1.13562
$277$	4.18264e6	0.0118242	0.00591209	−	0.999983i	$-0.498118\pi$
$277$	4.18264e6	0.0118242	0.00591209	+	0.999983i	$0.498118\pi$
$278$	−7.42186e7	−0.207184
$279$	3.16423e8	0.872274
$280$	−1.43558e7	−0.0390819
$281$	5.59009e8	1.50296	0.751479	−	0.659757i	$-0.229341\pi$
$281$	5.59009e8	1.50296	0.751479	+	0.659757i	$0.229341\pi$
$282$	1.24175e9	3.29732
$283$	−3.44359e8	−0.903149	−0.451574	−	0.892234i	$-0.649137\pi$
$283$	−3.44359e8	−0.903149	−0.451574	+	0.892234i	$0.649137\pi$
$284$	−5.28114e8	−1.36809
$285$	7.35615e8	1.88232
$286$	6.50494e8	1.64423
$287$	−4.94770e7	−0.123543
$288$	8.05427e8	1.98679
$289$	3.90960e8	0.952774
$290$	−1.16537e8	−0.280589
$291$	1.71537e8	0.408067
$292$	2.24975e8	0.528804
$293$	3.02885e8	0.703463	0.351731	−	0.936101i	$-0.385593\pi$
$293$	3.02885e8	0.703463	0.351731	+	0.936101i	$0.385593\pi$
$294$	−1.06465e9	−2.44338
$295$	4.67458e8	1.06015
$296$	4.80360e8	1.07658
$297$	3.91976e8	0.868183
$298$	1.65717e8	0.362752
$299$	−2.39108e8	−0.517302
$300$	4.69737e7	0.100445
$301$	−5.35381e7	−0.113157
$302$	−1.32953e9	−2.77762
$303$	−3.37431e8	−0.696845
$304$	2.70274e8	0.551756
$305$	−4.08807e8	−0.825028
$306$	−1.64415e9	−3.28032
$307$	−2.11108e8	−0.416408	−0.208204	−	0.978085i	$-0.566762\pi$
$307$	−2.11108e8	−0.416408	−0.208204	+	0.978085i	$0.566762\pi$
$308$	−4.97695e7	−0.0970591
$309$	1.99434e8	0.384542
$310$	−4.55485e8	−0.868376
$311$	−6.08545e8	−1.14718	−0.573589	−	0.819143i	$-0.694449\pi$
$311$	−6.08545e8	−1.14718	−0.573589	+	0.819143i	$0.694449\pi$
$312$	5.19169e8	0.967760
$313$	8.84261e8	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$313$	8.84261e8	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$314$	−7.68765e8	−1.40133
$315$	5.42834e7	0.0978543
$316$	−8.89734e7	−0.158619
$317$	−9.10327e8	−1.60505	−0.802527	−	0.596615i	$-0.796512\pi$
$317$	−9.10327e8	−1.60505	−0.802527	+	0.596615i	$0.796512\pi$
$318$	8.08632e8	1.41012
$319$	−1.13765e8	−0.196219
$320$	−8.99157e8	−1.53395
$321$	1.72517e9	2.91115
$322$	3.14371e7	0.0524743
$323$	−1.02760e9	−1.69674
$324$	−1.82438e8	−0.297995
$325$	−2.83161e7	−0.0457554
$326$	5.28738e8	0.845238
$327$	1.00267e9	1.58578
$328$	7.25292e8	1.13489
$329$	5.72708e7	0.0886640
$330$	−1.65393e9	−2.53349
$331$	−1.21371e8	−0.183958	−0.0919789	−	0.995761i	$-0.529319\pi$
$331$	−1.21371e8	−0.183958	−0.0919789	+	0.995761i	$0.529319\pi$
$332$	−8.74239e8	−1.31113
$333$	−1.81637e9	−2.69557
$334$	2.01780e8	0.296323
$335$	1.36165e8	0.197883
$336$	3.30848e7	0.0475818
$337$	8.82499e8	1.25606	0.628029	−	0.778190i	$-0.283862\pi$
$337$	8.82499e8	1.25606	0.628029	+	0.778190i	$0.283862\pi$
$338$	−1.34657e7	−0.0189679
$339$	1.59510e8	0.222377
$340$	1.37727e9	1.90039
$341$	−4.44650e8	−0.607264
$342$	2.10849e9	2.85023
$343$	−9.84204e7	−0.131691
$344$	7.84825e8	1.03948
$345$	6.07950e8	0.797079
$346$	−1.32816e9	−1.72379
$347$	−7.96824e8	−1.02379	−0.511893	−	0.859049i	$-0.671056\pi$
$347$	−7.96824e8	−1.02379	−0.511893	+	0.859049i	$0.671056\pi$
$348$	−3.22451e8	−0.410144
$349$	−1.52524e9	−1.92065	−0.960325	−	0.278884i	$-0.910036\pi$
$349$	−1.52524e9	−1.92065	−0.960325	+	0.278884i	$0.910036\pi$
$350$	3.72291e6	0.00464135
$351$	−6.69721e8	−0.826645
$352$	−1.13182e9	−1.38318
$353$	9.72813e8	1.17711	0.588556	−	0.808457i	$-0.299697\pi$
$353$	9.72813e8	1.17711	0.588556	+	0.808457i	$0.299697\pi$
$354$	2.22265e9	2.66293
$355$	−8.09434e8	−0.960246
$356$	5.67333e8	0.666443
$357$	−1.25790e8	−0.146322
$358$	−8.69574e8	−1.00165
$359$	8.95733e8	1.02176	0.510879	−	0.859653i	$-0.329320\pi$
$359$	8.95733e8	1.02176	0.510879	+	0.859653i	$0.329320\pi$
$360$	−7.95750e8	−0.898913
$361$	4.23944e8	0.474279
$362$	1.14947e9	1.27356
$363$	−1.68538e8	−0.184937
$364$	8.50352e7	0.0924153
$365$	3.44817e8	0.371162
$366$	−1.94378e9	−2.07235
$367$	9.88938e8	1.04433	0.522165	−	0.852844i	$-0.325124\pi$
$367$	9.88938e8	1.04433	0.522165	+	0.852844i	$0.325124\pi$
$368$	2.23369e8	0.233644
$369$	−2.74253e9	−2.84157
$370$	2.61463e9	2.68352
$371$	3.72950e7	0.0379177
$372$	−1.26030e9	−1.26933
$373$	−7.86596e8	−0.784821	−0.392410	−	0.919790i	$-0.628359\pi$
$373$	−7.86596e8	−0.784821	−0.392410	+	0.919790i	$0.628359\pi$
$374$	2.31043e9	2.28371
$375$	1.65511e9	1.62076
$376$	−8.39542e8	−0.814489
$377$	1.94376e8	0.186831
$378$	8.80526e7	0.0838535
$379$	1.77587e9	1.67561	0.837807	−	0.545967i	$-0.183838\pi$
$379$	1.77587e9	1.67561	0.837807	+	0.545967i	$0.183838\pi$
$380$	−1.76624e9	−1.65123
$381$	1.55061e9	1.43636
$382$	5.25676e8	0.482499
$383$	1.31337e9	1.19451	0.597256	−	0.802051i	$-0.296258\pi$
$383$	1.31337e9	1.19451	0.597256	+	0.802051i	$0.296258\pi$
$384$	−1.97060e9	−1.77599
$385$	−7.62812e7	−0.0681247
$386$	−3.09326e9	−2.73754
$387$	−2.96764e9	−2.60269
$388$	−4.11867e8	−0.357969
$389$	−6.16398e8	−0.530930	−0.265465	−	0.964120i	$-0.585526\pi$
$389$	−6.16398e8	−0.530930	−0.265465	+	0.964120i	$0.585526\pi$
$390$	2.82588e9	2.41228
$391$	−8.49263e8	−0.718494
$392$	7.19807e8	0.603552
$393$	−1.77133e8	−0.147206
$394$	3.07860e9	2.53581
$395$	−1.36368e8	−0.111333
$396$	−2.75874e9	−2.23243
$397$	−1.89324e9	−1.51858	−0.759292	−	0.650750i	$-0.774455\pi$
$397$	−1.89324e9	−1.51858	−0.759292	+	0.650750i	$0.774455\pi$
$398$	2.17741e9	1.73121
$399$	1.61316e8	0.127137
$400$	2.64523e7	0.0206658
$401$	−1.42869e9	−1.10645	−0.553226	−	0.833031i	$-0.686604\pi$
$401$	−1.42869e9	−1.10645	−0.553226	+	0.833031i	$0.686604\pi$
$402$	6.47429e8	0.497051
$403$	7.59719e8	0.578210
$404$	8.10186e8	0.611294
$405$	−2.79621e8	−0.209159
$406$	−2.55559e7	−0.0189518
$407$	2.55244e9	1.87661
$408$	1.84398e9	1.34415
$409$	−4.88837e8	−0.353291	−0.176646	−	0.984275i	$-0.556525\pi$
$409$	−4.88837e8	−0.353291	−0.176646	+	0.984275i	$0.556525\pi$
$410$	3.94782e9	2.82887
$411$	8.48582e8	0.602903
$412$	−4.78848e8	−0.337332
$413$	1.02511e8	0.0716052
$414$	1.74257e9	1.20695
$415$	−1.33994e9	−0.920270
$416$	1.93380e9	1.31700
$417$	−3.14751e8	−0.212564
$418$	−2.96294e9	−1.98429
$419$	−1.59035e9	−1.05619	−0.528095	−	0.849185i	$-0.677094\pi$
$419$	−1.59035e9	−1.05619	−0.528095	+	0.849185i	$0.677094\pi$
$420$	−2.16209e8	−0.142397
$421$	−1.22191e9	−0.798089	−0.399044	−	0.916932i	$-0.630658\pi$
$421$	−1.22191e9	−0.798089	−0.399044	+	0.916932i	$0.630658\pi$
$422$	−4.14095e9	−2.68229
$423$	3.17454e9	2.03934
$424$	−5.46713e8	−0.348321
$425$	−1.00573e8	−0.0635508
$426$	−3.84866e9	−2.41199
$427$	−8.96491e7	−0.0557248
$428$	−4.14220e9	−2.55375
$429$	2.75865e9	1.68693
$430$	4.27186e9	2.59106
$431$	8.85739e8	0.532887	0.266443	−	0.963851i	$-0.414151\pi$
$431$	8.85739e8	0.532887	0.266443	+	0.963851i	$0.414151\pi$
$432$	6.25638e8	0.373362
$433$	8.99432e8	0.532428	0.266214	−	0.963914i	$-0.414227\pi$
$433$	8.99432e8	0.532428	0.266214	+	0.963914i	$0.414227\pi$
$434$	−9.98853e7	−0.0586526
$435$	−4.94216e8	−0.287875
$436$	−2.40746e9	−1.39109
$437$	1.08911e9	0.624291
$438$	1.63952e9	0.932304
$439$	4.16500e8	0.234957	0.117479	−	0.993075i	$-0.462519\pi$
$439$	4.16500e8	0.234957	0.117479	+	0.993075i	$0.462519\pi$
$440$	1.11822e9	0.625810
$441$	−2.72179e9	−1.51119
$442$	−3.94755e9	−2.17445
$443$	−1.07545e9	−0.587728	−0.293864	−	0.955847i	$-0.594941\pi$
$443$	−1.07545e9	−0.587728	−0.293864	+	0.955847i	$0.594941\pi$
$444$	7.23454e9	3.92257
$445$	8.69545e8	0.467769
$446$	−2.31889e9	−1.23768
$447$	7.02781e8	0.372172
$448$	−1.97180e8	−0.103607
$449$	−3.56153e8	−0.185684	−0.0928421	−	0.995681i	$-0.529595\pi$
$449$	−3.56153e8	−0.185684	−0.0928421	+	0.995681i	$0.529595\pi$
$450$	2.06362e8	0.106754
$451$	3.85391e9	1.97826
$452$	−3.82991e8	−0.195076
$453$	−5.63834e9	−2.84975
$454$	−3.38116e9	−1.69578
$455$	1.30332e8	0.0648653
$456$	−2.36476e9	−1.16791
$457$	−2.39550e9	−1.17406	−0.587028	−	0.809567i	$-0.699702\pi$
$457$	−2.39550e9	−1.17406	−0.587028	+	0.809567i	$0.699702\pi$
$458$	4.21662e9	2.05086
$459$	−2.37872e9	−1.14815
$460$	−1.45971e9	−0.699222
$461$	9.51832e8	0.452488	0.226244	−	0.974071i	$-0.427355\pi$
$461$	9.51832e8	0.452488	0.226244	+	0.974071i	$0.427355\pi$
$462$	−3.62698e8	−0.171119
$463$	2.52803e9	1.18372	0.591859	−	0.806041i	$-0.298394\pi$
$463$	2.52803e9	1.18372	0.591859	+	0.806041i	$0.298394\pi$
$464$	−1.81581e8	−0.0843837
$465$	−1.93165e9	−0.890927
$466$	−4.06588e9	−1.86124
$467$	8.92878e8	0.405679	0.202840	−	0.979212i	$-0.434983\pi$
$467$	8.92878e8	0.405679	0.202840	+	0.979212i	$0.434983\pi$
$468$	4.71353e9	2.12562
$469$	2.98601e7	0.0133656
$470$	−4.56969e9	−2.03023
$471$	−3.26022e9	−1.43772
$472$	−1.50272e9	−0.657783
$473$	4.17024e9	1.81195
$474$	−6.48398e8	−0.279652
$475$	1.28977e8	0.0552186
$476$	3.02028e8	0.128358
$477$	2.06727e9	0.872135
$478$	4.34408e9	1.81928
$479$	1.18426e9	0.492350	0.246175	−	0.969225i	$-0.420826\pi$
$479$	1.18426e9	0.492350	0.246175	+	0.969225i	$0.420826\pi$
$480$	−4.91684e9	−2.02928
$481$	−4.36104e9	−1.78683
$482$	3.13078e9	1.27347
$483$	1.33320e8	0.0538370
$484$	4.04666e8	0.162233
$485$	−6.31263e8	−0.251255
$486$	−4.54523e9	−1.79609
$487$	−2.35832e8	−0.0925234	−0.0462617	−	0.998929i	$-0.514731\pi$
$487$	−2.35832e8	−0.0925234	−0.0462617	+	0.998929i	$0.514731\pi$
$488$	1.31418e9	0.511901
$489$	2.24230e9	0.867188
$490$	3.91796e9	1.50444
$491$	2.04927e9	0.781293	0.390647	−	0.920541i	$-0.372251\pi$
$491$	2.04927e9	0.781293	0.390647	+	0.920541i	$0.372251\pi$
$492$	1.09234e10	4.13504
$493$	6.90385e8	0.259494
$494$	5.06241e9	1.88935
$495$	−4.22829e9	−1.56692
$496$	−7.09712e8	−0.261154
$497$	−1.77504e8	−0.0648577
$498$	−6.37106e9	−2.31158
$499$	−2.77727e9	−1.00061	−0.500306	−	0.865848i	$-0.666779\pi$
$499$	−2.77727e9	−1.00061	−0.500306	+	0.865848i	$0.666779\pi$
$500$	−3.97399e9	−1.42178
$501$	8.55720e8	0.304018
$502$	−4.65552e8	−0.164250
$503$	3.51725e9	1.23230	0.616149	−	0.787630i	$-0.288692\pi$
$503$	3.51725e9	1.23230	0.616149	+	0.787630i	$0.288692\pi$
$504$	−1.74503e8	−0.0607152
$505$	1.24176e9	0.429060
$506$	−2.44872e9	−0.840259
$507$	−5.71060e7	−0.0194605
$508$	−3.72307e9	−1.26002
$509$	5.43819e9	1.82786	0.913929	−	0.405874i	$-0.133033\pi$
$509$	5.43819e9	1.82786	0.913929	+	0.405874i	$0.133033\pi$
$510$	1.00369e10	3.35047
$511$	7.56164e7	0.0250694
$512$	−2.64310e9	−0.870300
$513$	3.05051e9	0.997613
$514$	7.62441e8	0.247648
$515$	−7.33925e8	−0.236770
$516$	1.18200e10	3.78742
$517$	−4.46099e9	−1.41976
$518$	5.73375e8	0.181253
$519$	−5.63254e9	−1.76856
$520$	−1.91057e9	−0.595868
$521$	−3.26215e6	−0.00101058	−0.000505291	−	1.00000i	$-0.500161\pi$
$521$	−3.26215e6	−0.00101058	−0.000505291		1.00000i	$0.500161\pi$
$522$	−1.41657e9	−0.435905
$523$	−1.42556e9	−0.435743	−0.217872	−	0.975977i	$-0.569911\pi$
$523$	−1.42556e9	−0.435743	−0.217872	+	0.975977i	$0.569911\pi$
$524$	4.25304e8	0.129134
$525$	1.57883e7	0.00476188
$526$	5.81754e9	1.74297
$527$	2.69837e9	0.803091
$528$	−2.57707e9	−0.761916
$529$	−2.50473e9	−0.735640
$530$	−2.97580e9	−0.868237
$531$	5.68221e9	1.64697
$532$	−3.87327e8	−0.111529
$533$	−6.58471e9	−1.88361
$534$	4.13447e9	1.17497
$535$	−6.34870e9	−1.79245
$536$	−4.37725e8	−0.122779
$537$	−3.68774e9	−1.02766
$538$	6.94495e8	0.192279
$539$	3.82476e9	1.05207
$540$	−4.08854e9	−1.11735
$541$	2.56661e9	0.696898	0.348449	−	0.937328i	$-0.386708\pi$
$541$	2.56661e9	0.696898	0.348449	+	0.937328i	$0.386708\pi$
$542$	4.69321e8	0.126611
$543$	4.87474e9	1.30663
$544$	6.86847e9	1.82921
$545$	−3.68988e9	−0.976393
$546$	6.19699e8	0.162932
$547$	5.82110e9	1.52072	0.760360	−	0.649502i	$-0.225023\pi$
$547$	5.82110e9	1.52072	0.760360	+	0.649502i	$0.225023\pi$
$548$	−2.03748e9	−0.528885
$549$	−4.96928e9	−1.28171
$550$	−2.89988e8	−0.0743209
$551$	−8.85363e8	−0.225471
$552$	−1.95436e9	−0.494559
$553$	−2.99048e7	−0.00751975
$554$	−7.31866e7	−0.0182872
$555$	1.10883e10	2.75321
$556$	7.55729e8	0.186468
$557$	3.64120e9	0.892794	0.446397	−	0.894835i	$-0.352707\pi$
$557$	3.64120e9	0.892794	0.446397	+	0.894835i	$0.352707\pi$
$558$	−5.53668e9	−1.34905
$559$	−7.12519e9	−1.72526
$560$	−1.21753e8	−0.0292970
$561$	9.79819e9	2.34302
$562$	−9.78139e9	−2.32447
$563$	−4.81121e9	−1.13625	−0.568126	−	0.822941i	$-0.692331\pi$
$563$	−4.81121e9	−1.13625	−0.568126	+	0.822941i	$0.692331\pi$
$564$	−1.26441e10	−2.96763
$565$	−5.87005e8	−0.136922
$566$	6.02550e9	1.39680
$567$	−6.13193e7	−0.0141272
$568$	2.60207e9	0.595798
$569$	6.93723e9	1.57868	0.789338	−	0.613959i	$-0.210424\pi$
$569$	6.93723e9	1.57868	0.789338	+	0.613959i	$0.210424\pi$
$570$	−1.28716e10	−2.91118
$571$	−3.77619e9	−0.848842	−0.424421	−	0.905465i	$-0.639522\pi$
$571$	−3.77619e9	−0.848842	−0.424421	+	0.905465i	$0.639522\pi$
$572$	−6.62364e9	−1.47983
$573$	2.22932e9	0.495029
$574$	8.65735e8	0.191070
$575$	1.06593e8	0.0233826
$576$	−1.09298e10	−2.38304
$577$	−1.46450e9	−0.317376	−0.158688	−	0.987329i	$-0.550726\pi$
$577$	−1.46450e9	−0.317376	−0.158688	+	0.987329i	$0.550726\pi$
$578$	−6.84090e9	−1.47355
$579$	−1.31181e10	−2.80863
$580$	1.18663e9	0.252533
$581$	−2.93840e8	−0.0621577
$582$	−3.00150e9	−0.631114
$583$	−2.90501e9	−0.607167
$584$	−1.10847e9	−0.230293
$585$	7.22437e9	1.49195
$586$	−5.29979e9	−1.08797
$587$	−2.16859e9	−0.442531	−0.221265	−	0.975214i	$-0.571019\pi$
$587$	−2.16859e9	−0.442531	−0.221265	+	0.975214i	$0.571019\pi$
$588$	1.08408e10	2.19907
$589$	−3.46044e9	−0.697796
$590$	−8.17944e9	−1.63961
$591$	1.30559e10	2.60166
$592$	4.07398e9	0.807036
$593$	4.85335e9	0.955764	0.477882	−	0.878424i	$-0.341405\pi$
$593$	4.85335e9	0.955764	0.477882	+	0.878424i	$0.341405\pi$
$594$	−6.85868e9	−1.34273
$595$	4.62915e8	0.0900931
$596$	−1.68741e9	−0.326481
$597$	9.23408e9	1.77616
$598$	4.18384e9	0.800057
$599$	3.56699e9	0.678122	0.339061	−	0.940764i	$-0.389891\pi$
$599$	3.56699e9	0.678122	0.339061	+	0.940764i	$0.389891\pi$
$600$	−2.31444e8	−0.0437438
$601$	1.82624e9	0.343160	0.171580	−	0.985170i	$-0.445113\pi$
$601$	1.82624e9	0.343160	0.171580	+	0.985170i	$0.445113\pi$
$602$	9.36795e8	0.175008
$603$	1.65516e9	0.307418
$604$	1.35379e10	2.49989
$605$	6.20227e8	0.113869
$606$	5.90427e9	1.07774
$607$	2.94903e9	0.535203	0.267601	−	0.963530i	$-0.413769\pi$
$607$	2.94903e9	0.535203	0.267601	+	0.963530i	$0.413769\pi$
$608$	−8.80827e9	−1.58938
$609$	−1.08379e8	−0.0194439
$610$	7.15319e9	1.27598
$611$	7.62195e9	1.35183
$612$	1.67415e10	2.95233
$613$	2.35401e9	0.412759	0.206380	−	0.978472i	$-0.433832\pi$
$613$	2.35401e9	0.412759	0.206380	+	0.978472i	$0.433832\pi$
$614$	3.69390e9	0.644015
$615$	1.67421e10	2.90234
$616$	2.45219e8	0.0422690
$617$	−3.06556e9	−0.525427	−0.262713	−	0.964874i	$-0.584617\pi$
$617$	−3.06556e9	−0.525427	−0.262713	+	0.964874i	$0.584617\pi$
$618$	−3.48963e9	−0.594730
$619$	−1.81945e9	−0.308335	−0.154167	−	0.988045i	$-0.549270\pi$
$619$	−1.81945e9	−0.308335	−0.154167	+	0.988045i	$0.549270\pi$
$620$	4.63796e9	0.781549
$621$	2.52110e9	0.422445
$622$	1.06481e10	1.77422
$623$	1.90686e8	0.0315945
$624$	4.40313e9	0.725463
$625$	−5.81332e9	−0.952454
$626$	−1.54725e10	−2.52088
$627$	−1.25654e10	−2.03582
$628$	7.82792e9	1.26121
$629$	−1.54895e10	−2.48177
$630$	−9.49835e8	−0.151341
$631$	−3.79039e9	−0.600594	−0.300297	−	0.953846i	$-0.597086\pi$
$631$	−3.79039e9	−0.600594	−0.300297	+	0.953846i	$0.597086\pi$
$632$	4.38380e8	0.0690782
$633$	−1.75612e10	−2.75195
$634$	1.59286e10	2.48237
$635$	−5.70631e9	−0.884397
$636$	−8.23387e9	−1.26912
$637$	−6.53491e9	−1.00173
$638$	1.99062e9	0.303470
$639$	−9.83913e9	−1.49178
$640$	7.25191e9	1.09351
$641$	−1.09897e10	−1.64810	−0.824051	−	0.566515i	$-0.808291\pi$
$641$	−1.09897e10	−1.64810	−0.824051	+	0.566515i	$0.808291\pi$
$642$	−3.01865e10	−4.50236
$643$	4.19417e9	0.622168	0.311084	−	0.950382i	$-0.399308\pi$
$643$	4.19417e9	0.622168	0.311084	+	0.950382i	$0.399308\pi$
$644$	−3.20107e8	−0.0472275
$645$	1.81163e10	2.65835
$646$	1.79807e10	2.62417
$647$	5.61134e9	0.814520	0.407260	−	0.913312i	$-0.366484\pi$
$647$	5.61134e9	0.814520	0.407260	+	0.913312i	$0.366484\pi$
$648$	8.98891e8	0.129776
$649$	−7.98487e9	−1.14660
$650$	4.95468e8	0.0707650
$651$	−4.23599e8	−0.0601758
$652$	−5.38386e9	−0.760724
$653$	5.83843e9	0.820541	0.410270	−	0.911964i	$-0.365434\pi$
$653$	5.83843e9	0.820541	0.410270	+	0.911964i	$0.365434\pi$
$654$	−1.75445e10	−2.45255
$655$	6.51858e8	0.0906377
$656$	6.15128e9	0.850750
$657$	4.19145e9	0.576614
$658$	−1.00211e9	−0.137127
$659$	−6.18969e9	−0.842500	−0.421250	−	0.906944i	$-0.638409\pi$
$659$	−6.18969e9	−0.842500	−0.421250	+	0.906944i	$0.638409\pi$
$660$	1.68411e10	2.28017
$661$	7.32815e8	0.0986936	0.0493468	−	0.998782i	$-0.484286\pi$
$661$	7.32815e8	0.0986936	0.0493468	+	0.998782i	$0.484286\pi$
$662$	2.12372e9	0.284508
$663$	−1.67410e10	−2.23092
$664$	4.30746e9	0.570995
$665$	−5.93651e8	−0.0782808
$666$	3.17824e10	4.16895
$667$	−7.31710e8	−0.0954769
$668$	−2.05462e9	−0.266694
$669$	−9.83409e9	−1.26982
$670$	−2.38257e9	−0.306044
$671$	6.98303e9	0.892308
$672$	−1.07824e9	−0.137063
$673$	1.14599e10	1.44920	0.724599	−	0.689171i	$-0.242025\pi$
$673$	1.14599e10	1.44920	0.724599	+	0.689171i	$0.242025\pi$
$674$	−1.54417e10	−1.94261
$675$	2.98559e8	0.0373652
$676$	1.37114e8	0.0170714
$677$	−9.16698e8	−0.113544	−0.0567722	−	0.998387i	$-0.518081\pi$
$677$	−9.16698e8	−0.113544	−0.0567722	+	0.998387i	$0.518081\pi$
$678$	−2.79107e9	−0.343927
$679$	−1.38432e8	−0.0169705
$680$	−6.78595e9	−0.827617
$681$	−1.43390e10	−1.73982
$682$	7.78035e9	0.939191
$683$	5.10989e9	0.613677	0.306838	−	0.951762i	$-0.400729\pi$
$683$	5.10989e9	0.613677	0.306838	+	0.951762i	$0.400729\pi$
$684$	−2.14697e10	−2.56524
$685$	−3.12282e9	−0.371219
$686$	1.72213e9	0.203672
$687$	1.78821e10	2.10412
$688$	6.65618e9	0.779230
$689$	4.96345e9	0.578117
$690$	−1.06377e10	−1.23276
$691$	1.14722e10	1.32274	0.661368	−	0.750062i	$-0.269976\pi$
$691$	1.14722e10	1.32274	0.661368	+	0.750062i	$0.269976\pi$
$692$	1.35240e10	1.55143
$693$	−9.27241e8	−0.105834
$694$	1.39426e10	1.58338
$695$	1.15830e9	0.130880
$696$	1.58874e9	0.178617
$697$	−2.33876e10	−2.61620
$698$	2.66881e10	2.97047
$699$	−1.72428e10	−1.90958
$700$	−3.79084e7	−0.00417727
$701$	3.14382e9	0.344702	0.172351	−	0.985036i	$-0.444864\pi$
$701$	3.14382e9	0.344702	0.172351	+	0.985036i	$0.444864\pi$
$702$	1.17186e10	1.27848
$703$	1.98641e10	2.15638
$704$	1.53589e10	1.65904
$705$	−1.93794e10	−2.08295
$706$	−1.70220e10	−1.82051
$707$	2.72311e8	0.0289800
$708$	−2.26320e10	−2.39667
$709$	−6.75325e9	−0.711624	−0.355812	−	0.934558i	$-0.615796\pi$
$709$	−6.75325e9	−0.711624	−0.355812	+	0.934558i	$0.615796\pi$
$710$	1.41632e10	1.48511
$711$	−1.65763e9	−0.172960
$712$	−2.79530e9	−0.290234
$713$	−2.85989e9	−0.295485
$714$	2.20105e9	0.226300
$715$	−1.01520e10	−1.03867
$716$	8.85442e9	0.901497
$717$	1.84226e10	1.86653
$718$	−1.56733e10	−1.58024
$719$	−1.47286e10	−1.47778	−0.738891	−	0.673825i	$-0.764650\pi$
$719$	−1.47286e10	−1.47778	−0.738891	+	0.673825i	$0.764650\pi$
$720$	−6.74884e9	−0.673853
$721$	−1.60946e8	−0.0159921
$722$	−7.41805e9	−0.733516
$723$	1.32772e10	1.30654
$724$	−1.17045e10	−1.14622
$725$	−8.66521e7	−0.00844493
$726$	2.94903e9	0.286023
$727$	−1.23285e10	−1.18998	−0.594989	−	0.803734i	$-0.702844\pi$
$727$	−1.23285e10	−1.18998	−0.594989	+	0.803734i	$0.702844\pi$
$728$	−4.18976e8	−0.0402466
$729$	−1.70363e10	−1.62865
$730$	−6.03351e9	−0.574037
$731$	−2.53072e10	−2.39626
$732$	1.97925e10	1.86514
$733$	5.89079e9	0.552471	0.276236	−	0.961090i	$-0.410913\pi$
$733$	5.89079e9	0.552471	0.276236	+	0.961090i	$0.410913\pi$
$734$	−1.73042e10	−1.61516
$735$	1.66155e10	1.54351
$736$	−7.27961e9	−0.673032
$737$	−2.32589e9	−0.214020
$738$	4.79880e10	4.39476
$739$	9.95910e9	0.907747	0.453873	−	0.891066i	$-0.350042\pi$
$739$	9.95910e9	0.907747	0.453873	+	0.891066i	$0.350042\pi$
$740$	−2.66234e10	−2.41520
$741$	2.14690e10	1.93842
$742$	−6.52577e8	−0.0586432
$743$	7.49880e9	0.670704	0.335352	−	0.942093i	$-0.391145\pi$
$743$	7.49880e9	0.670704	0.335352	+	0.942093i	$0.391145\pi$
$744$	6.20961e9	0.552789
$745$	−2.58627e9	−0.229153
$746$	1.37636e10	1.21380
$747$	−1.62877e10	−1.42967
$748$	−2.35258e10	−2.05537
$749$	−1.39223e9	−0.121067
$750$	−2.89607e10	−2.50666
$751$	−5.17686e9	−0.445991	−0.222996	−	0.974819i	$-0.571584\pi$
$751$	−5.17686e9	−0.445991	−0.222996	+	0.974819i	$0.571584\pi$
$752$	−7.12024e9	−0.610566
$753$	−1.97434e9	−0.168515
$754$	−3.40114e9	−0.288951
$755$	2.07493e10	1.75465
$756$	−8.96594e8	−0.0754691
$757$	2.62402e9	0.219852	0.109926	−	0.993940i	$-0.464939\pi$
$757$	2.62402e9	0.219852	0.109926	+	0.993940i	$0.464939\pi$
$758$	−3.10737e10	−2.59149
$759$	−1.03847e10	−0.862079
$760$	8.70243e9	0.719106
$761$	1.58485e10	1.30359	0.651794	−	0.758396i	$-0.274017\pi$
$761$	1.58485e10	1.30359	0.651794	+	0.758396i	$0.274017\pi$
$762$	−2.71321e10	−2.22147
$763$	−8.09171e8	−0.0659484
$764$	−5.35268e9	−0.434255
$765$	2.56595e10	2.07221
$766$	−2.29809e10	−1.84743
$767$	1.36428e10	1.09174
$768$	3.20644e9	0.255422
$769$	8.36433e9	0.663268	0.331634	−	0.943408i	$-0.392400\pi$
$769$	8.36433e9	0.663268	0.331634	+	0.943408i	$0.392400\pi$
$770$	1.33475e9	0.105361
$771$	3.23340e9	0.254079
$772$	3.14970e10	2.46382
$773$	−3.43168e9	−0.267226	−0.133613	−	0.991034i	$-0.542658\pi$
$773$	−3.43168e9	−0.267226	−0.133613	+	0.991034i	$0.542658\pi$
$774$	5.19269e10	4.02530
$775$	−3.38680e8	−0.0261357
$776$	2.02930e9	0.155895
$777$	2.43160e9	0.185960
$778$	1.07856e10	0.821134
$779$	2.99927e10	2.27318
$780$	−2.87744e10	−2.17108
$781$	1.38263e10	1.03855
$782$	1.48602e10	1.11122
$783$	−2.04946e9	−0.152571
$784$	6.10476e9	0.452441
$785$	1.19978e10	0.885231
$786$	3.09943e9	0.227668
$787$	−2.11626e10	−1.54759	−0.773796	−	0.633435i	$-0.781645\pi$
$787$	−2.11626e10	−1.54759	−0.773796	+	0.633435i	$0.781645\pi$
$788$	−3.13477e10	−2.28226
$789$	2.46713e10	1.78823
$790$	2.38613e9	0.172187
$791$	−1.28727e8	−0.00924809
$792$	1.35926e10	0.972218
$793$	−1.19311e10	−0.849616
$794$	3.31274e10	2.34863
$795$	−1.26200e10	−0.890785
$796$	−2.21714e10	−1.55811
$797$	−2.13797e10	−1.49588	−0.747942	−	0.663764i	$-0.768958\pi$
$797$	−2.13797e10	−1.49588	−0.747942	+	0.663764i	$0.768958\pi$
$798$	−2.82266e9	−0.196630
$799$	2.70716e10	1.87759
$800$	−8.62082e8	−0.0595297
$801$	1.05698e10	0.726697
$802$	2.49988e10	1.71123
$803$	−5.88998e9	−0.401430
$804$	−6.59243e9	−0.447352
$805$	−4.90624e8	−0.0331484
$806$	−1.32934e10	−0.894256
$807$	2.94526e9	0.197272
$808$	−3.99186e9	−0.266217
$809$	1.32189e10	0.877759	0.438879	−	0.898546i	$-0.355376\pi$
$809$	1.32189e10	0.877759	0.438879	+	0.898546i	$0.355376\pi$
$810$	4.89273e9	0.323485
$811$	−1.69189e10	−1.11378	−0.556891	−	0.830586i	$-0.688006\pi$
$811$	−1.69189e10	−1.11378	−0.556891	+	0.830586i	$0.688006\pi$
$812$	2.60222e8	0.0170568
$813$	1.99033e9	0.129899
$814$	−4.46618e10	−2.90236
$815$	−8.25178e9	−0.533944
$816$	1.56390e10	1.00761
$817$	3.24545e10	2.08208
$818$	8.55354e9	0.546398
$819$	1.58426e9	0.100771
$820$	−4.01985e10	−2.54602
$821$	7.52663e9	0.474678	0.237339	−	0.971427i	$-0.423725\pi$
$821$	7.52663e9	0.474678	0.237339	+	0.971427i	$0.423725\pi$
$822$	−1.48483e10	−0.932447
$823$	−1.08023e10	−0.675487	−0.337744	−	0.941238i	$-0.609664\pi$
$823$	−1.08023e10	−0.675487	−0.337744	+	0.941238i	$0.609664\pi$
$824$	2.35933e9	0.146907
$825$	−1.22980e9	−0.0762509
$826$	−1.79371e9	−0.110744
$827$	−1.99362e10	−1.22567	−0.612836	−	0.790210i	$-0.709971\pi$
$827$	−1.99362e10	−1.22567	−0.612836	+	0.790210i	$0.709971\pi$
$828$	−1.77436e10	−1.08627
$829$	1.63313e10	0.995589	0.497795	−	0.867295i	$-0.334143\pi$
$829$	1.63313e10	0.995589	0.497795	+	0.867295i	$0.334143\pi$
$830$	2.34458e10	1.42328
$831$	−3.10374e8	−0.0187621
$832$	−2.62419e10	−1.57966
$833$	−2.32107e10	−1.39133
$834$	5.50741e9	0.328751
$835$	−3.14909e9	−0.187190
$836$	3.01700e10	1.78588
$837$	−8.01032e9	−0.472184
$838$	2.78274e10	1.63350
$839$	6.14781e9	0.359380	0.179690	−	0.983723i	$-0.442491\pi$
$839$	6.14781e9	0.359380	0.179690	+	0.983723i	$0.442491\pi$
$840$	1.06528e9	0.0620135
$841$	5.94823e8	0.0344828
$842$	2.13806e10	1.23432
$843$	−4.14815e10	−2.38483
$844$	4.21651e10	2.41409
$845$	2.10153e8	0.0119822
$846$	−5.55472e10	−3.15403
$847$	1.36012e8	0.00769106
$848$	−4.63673e9	−0.261112
$849$	2.55533e10	1.43308
$850$	1.75980e9	0.0982873
$851$	1.64167e10	0.913131
$852$	3.91889e10	2.17082
$853$	−8.01494e7	−0.00442159	−0.00221080	−	0.999998i	$-0.500704\pi$
$853$	−8.01494e7	−0.00442159	−0.00221080	+	0.999998i	$0.500704\pi$
$854$	1.56865e9	0.0861836
$855$	−3.29063e10	−1.80052
$856$	2.04090e10	1.11215
$857$	7.85162e9	0.426115	0.213057	−	0.977040i	$-0.431658\pi$
$857$	7.85162e9	0.426115	0.213057	+	0.977040i	$0.431658\pi$
$858$	−4.82701e10	−2.60899
$859$	−1.40618e9	−0.0756944	−0.0378472	−	0.999284i	$-0.512050\pi$
$859$	−1.40618e9	−0.0756944	−0.0378472	+	0.999284i	$0.512050\pi$
$860$	−4.34981e10	−2.33198
$861$	3.67146e9	0.196032
$862$	−1.54984e10	−0.824160
$863$	−1.06192e10	−0.562412	−0.281206	−	0.959647i	$-0.590734\pi$
$863$	−1.06192e10	−0.562412	−0.281206	+	0.959647i	$0.590734\pi$
$864$	−2.03896e10	−1.07550
$865$	2.07280e10	1.08893
$866$	−1.57380e10	−0.823450
$867$	−2.90113e10	−1.51182
$868$	1.01708e9	0.0527881
$869$	2.32937e9	0.120412
$870$	8.64766e9	0.445226
$871$	3.97397e9	0.203780
$872$	1.18618e10	0.605817
$873$	−7.67336e9	−0.390333
$874$	−1.90570e10	−0.965525
$875$	−1.33570e9	−0.0674032
$876$	−1.66944e10	−0.839084
$877$	−2.37232e10	−1.18761	−0.593807	−	0.804608i	$-0.702376\pi$
$877$	−2.37232e10	−1.18761	−0.593807	+	0.804608i	$0.702376\pi$
$878$	−7.28779e9	−0.363384
$879$	−2.24757e10	−1.11622
$880$	9.48373e9	0.469126
$881$	1.26543e10	0.623478	0.311739	−	0.950168i	$-0.399089\pi$
$881$	1.26543e10	0.623478	0.311739	+	0.950168i	$0.399089\pi$
$882$	4.76251e10	2.33720
$883$	−2.80097e9	−0.136913	−0.0684566	−	0.997654i	$-0.521807\pi$
$883$	−2.80097e9	−0.136913	−0.0684566	+	0.997654i	$0.521807\pi$
$884$	4.01958e10	1.95703
$885$	−3.46879e10	−1.68219
$886$	1.88179e10	0.908976
$887$	3.09663e9	0.148990	0.0744948	−	0.997221i	$-0.476266\pi$
$887$	3.09663e9	0.148990	0.0744948	+	0.997221i	$0.476266\pi$
$888$	−3.56452e10	−1.70827
$889$	−1.25136e9	−0.0597347
$890$	−1.52150e10	−0.723449
$891$	4.77634e9	0.226216
$892$	2.36120e10	1.11393
$893$	−3.47172e10	−1.63142
$894$	−1.22971e10	−0.575599
$895$	1.35711e10	0.632751
$896$	1.59030e9	0.0738588
$897$	1.77431e10	0.820833
$898$	6.23187e9	0.287178
$899$	2.32487e9	0.106718
$900$	−2.10128e9	−0.0960803
$901$	1.76292e10	0.802962
$902$	−6.74346e10	−3.05957
$903$	3.97281e9	0.179552
$904$	1.88703e9	0.0849551
$905$	−1.79393e10	−0.804517
$906$	9.86580e10	4.40741
$907$	−2.22633e10	−0.990751	−0.495375	−	0.868679i	$-0.664969\pi$
$907$	−2.22633e10	−0.990751	−0.495375	+	0.868679i	$0.664969\pi$
$908$	3.44286e10	1.52623
$909$	1.50943e10	0.666561
$910$	−2.28052e9	−0.100320
$911$	2.66809e10	1.16919	0.584597	−	0.811324i	$-0.301253\pi$
$911$	2.66809e10	1.16919	0.584597	+	0.811324i	$0.301253\pi$
$912$	−2.00558e10	−0.875504
$913$	2.28881e10	0.995317
$914$	4.19157e10	1.81579
$915$	3.03356e10	1.30912
$916$	−4.29356e10	−1.84580
$917$	1.42949e8	0.00612193
$918$	4.16221e10	1.77572
$919$	2.81190e10	1.19508	0.597538	−	0.801841i	$-0.296146\pi$
$919$	2.81190e10	1.19508	0.597538	+	0.801841i	$0.296146\pi$
$920$	7.19214e9	0.304509
$921$	1.56653e10	0.660739
$922$	−1.66549e10	−0.699816
$923$	−2.36234e10	−0.988863
$924$	3.69316e9	0.154009
$925$	1.94414e9	0.0807664
$926$	−4.42347e10	−1.83073
$927$	−8.92127e9	−0.367830
$928$	5.91776e9	0.243074
$929$	−1.28293e10	−0.524988	−0.262494	−	0.964934i	$-0.584545\pi$
$929$	−1.28293e10	−0.524988	−0.262494	+	0.964934i	$0.584545\pi$
$930$	3.37994e10	1.37790
$931$	2.97659e10	1.20891
$932$	4.14007e10	1.67514
$933$	4.51572e10	1.82029
$934$	−1.56233e10	−0.627421
$935$	−3.60578e10	−1.44264
$936$	−2.32240e10	−0.925703
$937$	−3.81492e10	−1.51495	−0.757473	−	0.652866i	$-0.773566\pi$
$937$	−3.81492e10	−1.51495	−0.757473	+	0.652866i	$0.773566\pi$
$938$	−5.22484e8	−0.0206711
$939$	−6.56168e10	−2.58634
$940$	4.65307e10	1.82723
$941$	−3.61833e10	−1.41561	−0.707806	−	0.706407i	$-0.750315\pi$
$941$	−3.61833e10	−1.41561	−0.707806	+	0.706407i	$0.750315\pi$
$942$	5.70464e10	2.22357
$943$	2.47875e10	0.962591
$944$	−1.27448e10	−0.493094
$945$	−1.37420e9	−0.0529710
$946$	−7.29697e10	−2.80236
$947$	5.03040e10	1.92476	0.962382	−	0.271699i	$-0.0875855\pi$
$947$	5.03040e10	1.92476	0.962382	+	0.271699i	$0.0875855\pi$
$948$	6.60229e9	0.251690
$949$	1.00635e10	0.382224
$950$	−2.25680e9	−0.0854007
$951$	6.75511e10	2.54683
$952$	−1.48812e9	−0.0558996
$953$	−1.47909e10	−0.553566	−0.276783	−	0.960932i	$-0.589268\pi$
$953$	−1.47909e10	−0.553566	−0.276783	+	0.960932i	$0.589268\pi$
$954$	−3.61726e10	−1.34884
$955$	−8.20399e9	−0.304799
$956$	−4.42335e10	−1.63738
$957$	8.44194e9	0.311351
$958$	−2.07219e10	−0.761465
$959$	−6.84817e8	−0.0250732
$960$	6.67222e10	2.43400
$961$	−1.84259e10	−0.669724
$962$	7.63083e10	2.76350
$963$	−7.71720e10	−2.78463
$964$	−3.18791e10	−1.14614
$965$	4.82750e10	1.72933
$966$	−2.33280e9	−0.0832639
$967$	1.28089e10	0.455534	0.227767	−	0.973716i	$-0.426858\pi$
$967$	1.28089e10	0.455534	0.227767	+	0.973716i	$0.426858\pi$
$968$	−1.99383e9	−0.0706519
$969$	7.62535e10	2.69232
$970$	1.10457e10	0.388589
$971$	−2.87124e10	−1.00647	−0.503236	−	0.864149i	$-0.667858\pi$
$971$	−2.87124e10	−1.00647	−0.503236	+	0.864149i	$0.667858\pi$
$972$	4.62817e10	1.61651
$973$	2.54008e8	0.00884000
$974$	4.12652e9	0.143096
$975$	2.10121e9	0.0726027
$976$	1.11457e10	0.383737
$977$	−5.60335e9	−0.192228	−0.0961140	−	0.995370i	$-0.530641\pi$
$977$	−5.60335e9	−0.192228	−0.0961140	+	0.995370i	$0.530641\pi$
$978$	−3.92352e10	−1.34119
$979$	−1.48531e10	−0.505915
$980$	−3.98946e10	−1.35401
$981$	−4.48526e10	−1.51686
$982$	−3.58576e10	−1.20834
$983$	−1.32393e10	−0.444557	−0.222278	−	0.974983i	$-0.571349\pi$
$983$	−1.32393e10	−0.444557	−0.222278	+	0.974983i	$0.571349\pi$
$984$	−5.38205e10	−1.80080
$985$	−4.80463e10	−1.60189
$986$	−1.20802e10	−0.401332
$987$	−4.24979e9	−0.140688
$988$	−5.15479e10	−1.70044
$989$	2.68221e10	0.881669
$990$	7.39854e10	2.42339
$991$	−1.50500e10	−0.491223	−0.245611	−	0.969368i	$-0.578989\pi$
$991$	−1.50500e10	−0.491223	−0.245611	+	0.969368i	$0.578989\pi$
$992$	2.31296e10	0.752275
$993$	9.00640e9	0.291896
$994$	3.10592e9	0.100309
$995$	−3.39818e10	−1.09362
$996$	6.48732e10	2.08045
$997$	−2.68365e10	−0.857615	−0.428807	−	0.903396i	$-0.641066\pi$
$997$	−2.68365e10	−0.857615	−0.428807	+	0.903396i	$0.641066\pi$
$998$	4.85959e10	1.54754
$999$	4.59819e10	1.45918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.a.a.1.1	✓	7
3.2	odd	2		261.8.a.b.1.7		7
4.3	odd	2		464.8.a.f.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.a.a.1.1	✓	7	1.1	even	1	trivial
261.8.a.b.1.7		7	3.2	odd	2
464.8.a.f.1.6		7	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-17.4977 q^{2} -74.2053 q^{3} +178.170 q^{4} +273.079 q^{5} +1298.42 q^{6} +59.8847 q^{7} -877.860 q^{8} +3319.43 q^{9} +O(q^{10})\)	\(q-17.4977 q^{2} -74.2053 q^{3} +178.170 q^{4} +273.079 q^{5} +1298.42 q^{6} +59.8847 q^{7} -877.860 q^{8} +3319.43 q^{9} -4778.26 q^{10} -4664.59 q^{11} -13221.2 q^{12} +7969.82 q^{13} -1047.84 q^{14} -20263.9 q^{15} -7445.22 q^{16} +28307.2 q^{17} -58082.4 q^{18} -36301.7 q^{19} +48654.5 q^{20} -4443.76 q^{21} +81619.7 q^{22} -30001.6 q^{23} +65141.8 q^{24} -3552.92 q^{25} -139454. q^{26} -84032.1 q^{27} +10669.6 q^{28} +24389.0 q^{29} +354572. q^{30} +95324.5 q^{31} +242640. q^{32} +346137. q^{33} -495312. q^{34} +16353.2 q^{35} +591422. q^{36} -547194. q^{37} +635197. q^{38} -591403. q^{39} -239725. q^{40} -826205. q^{41} +77755.6 q^{42} -894021. q^{43} -831090. q^{44} +906466. q^{45} +524960. q^{46} +956351. q^{47} +552475. q^{48} -819957. q^{49} +62168.0 q^{50} -2.10055e6 q^{51} +1.41998e6 q^{52} +622780. q^{53} +1.47037e6 q^{54} -1.27380e6 q^{55} -52570.3 q^{56} +2.69378e6 q^{57} -426752. q^{58} +1.71181e6 q^{59} -3.61042e6 q^{60} -1.49703e6 q^{61} -1.66796e6 q^{62} +198783. q^{63} -3.29266e6 q^{64} +2.17639e6 q^{65} -6.05661e6 q^{66} +498627. q^{67} +5.04350e6 q^{68} +2.22628e6 q^{69} -286144. q^{70} -2.96410e6 q^{71} -2.91399e6 q^{72} +1.26270e6 q^{73} +9.57465e6 q^{74} +263645. q^{75} -6.46788e6 q^{76} -279337. q^{77} +1.03482e7 q^{78} -499373. q^{79} -2.03313e6 q^{80} -1.02396e6 q^{81} +1.44567e7 q^{82} -4.90677e6 q^{83} -791745. q^{84} +7.73010e6 q^{85} +1.56433e7 q^{86} -1.80979e6 q^{87} +4.09486e6 q^{88} +3.18423e6 q^{89} -1.58611e7 q^{90} +477270. q^{91} -5.34539e6 q^{92} -7.07358e6 q^{93} -1.67340e7 q^{94} -9.91324e6 q^{95} -1.80052e7 q^{96} -2.31165e6 q^{97} +1.43474e7 q^{98} -1.54838e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 8 q^{2} - 82 q^{3} + 346 q^{4} - 320 q^{5} - 938 q^{6} - 1704 q^{7} + 2082 q^{8} + 4061 q^{9}+O(q^{10}) \) 7 * q - 8 * q^2 - 82 * q^3 + 346 * q^4 - 320 * q^5 - 938 * q^6 - 1704 * q^7 + 2082 * q^8 + 4061 * q^9	\( 7 q - 8 q^{2} - 82 q^{3} + 346 q^{4} - 320 q^{5} - 938 q^{6} - 1704 q^{7} + 2082 q^{8} + 4061 q^{9} - 14114 q^{10} - 14498 q^{11} - 42334 q^{12} - 9024 q^{13} - 45880 q^{14} - 24238 q^{15} - 3022 q^{16} - 54882 q^{17} + 17218 q^{18} - 100572 q^{19} - 86022 q^{20} + 34304 q^{21} + 9086 q^{22} + 55340 q^{23} - 138966 q^{24} + 125759 q^{25} + 257206 q^{26} - 176146 q^{27} - 41760 q^{28} + 170723 q^{29} + 1132178 q^{30} - 153330 q^{31} + 825478 q^{32} + 555898 q^{33} - 194256 q^{34} + 561160 q^{35} + 1939652 q^{36} - 457050 q^{37} + 617164 q^{38} - 1173662 q^{39} - 1151986 q^{40} - 864230 q^{41} + 2046224 q^{42} - 1590058 q^{43} - 1399966 q^{44} - 2268610 q^{45} + 1557900 q^{46} - 204750 q^{47} - 2501730 q^{48} - 1892625 q^{49} + 2115526 q^{50} - 2481996 q^{51} + 1469690 q^{52} - 2696092 q^{53} - 2918978 q^{54} - 2596662 q^{55} - 2818440 q^{56} - 96196 q^{57} - 195112 q^{58} + 1434256 q^{59} + 7687830 q^{60} - 5622798 q^{61} - 4660550 q^{62} - 5632816 q^{63} - 944442 q^{64} - 353086 q^{65} + 8421370 q^{66} - 5380324 q^{67} + 6393964 q^{68} - 2248580 q^{69} + 10805432 q^{70} + 4605140 q^{71} + 17475264 q^{72} + 3979266 q^{73} + 15124836 q^{74} - 2365120 q^{75} - 3893220 q^{76} + 8666288 q^{77} + 7790850 q^{78} - 6355522 q^{79} - 4424794 q^{80} + 6442139 q^{81} + 6831364 q^{82} + 3077704 q^{83} + 29008056 q^{84} + 5117008 q^{85} + 11620998 q^{86} - 1999898 q^{87} - 24708046 q^{88} + 743498 q^{89} - 38296444 q^{90} - 24167656 q^{91} + 11053132 q^{92} + 25723782 q^{93} - 29029210 q^{94} + 1137892 q^{95} - 34019010 q^{96} - 7924270 q^{97} + 19298152 q^{98} - 43451600 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 82 * q^3 + 346 * q^4 - 320 * q^5 - 938 * q^6 - 1704 * q^7 + 2082 * q^8 + 4061 * q^9 - 14114 * q^10 - 14498 * q^11 - 42334 * q^12 - 9024 * q^13 - 45880 * q^14 - 24238 * q^15 - 3022 * q^16 - 54882 * q^17 + 17218 * q^18 - 100572 * q^19 - 86022 * q^20 + 34304 * q^21 + 9086 * q^22 + 55340 * q^23 - 138966 * q^24 + 125759 * q^25 + 257206 * q^26 - 176146 * q^27 - 41760 * q^28 + 170723 * q^29 + 1132178 * q^30 - 153330 * q^31 + 825478 * q^32 + 555898 * q^33 - 194256 * q^34 + 561160 * q^35 + 1939652 * q^36 - 457050 * q^37 + 617164 * q^38 - 1173662 * q^39 - 1151986 * q^40 - 864230 * q^41 + 2046224 * q^42 - 1590058 * q^43 - 1399966 * q^44 - 2268610 * q^45 + 1557900 * q^46 - 204750 * q^47 - 2501730 * q^48 - 1892625 * q^49 + 2115526 * q^50 - 2481996 * q^51 + 1469690 * q^52 - 2696092 * q^53 - 2918978 * q^54 - 2596662 * q^55 - 2818440 * q^56 - 96196 * q^57 - 195112 * q^58 + 1434256 * q^59 + 7687830 * q^60 - 5622798 * q^61 - 4660550 * q^62 - 5632816 * q^63 - 944442 * q^64 - 353086 * q^65 + 8421370 * q^66 - 5380324 * q^67 + 6393964 * q^68 - 2248580 * q^69 + 10805432 * q^70 + 4605140 * q^71 + 17475264 * q^72 + 3979266 * q^73 + 15124836 * q^74 - 2365120 * q^75 - 3893220 * q^76 + 8666288 * q^77 + 7790850 * q^78 - 6355522 * q^79 - 4424794 * q^80 + 6442139 * q^81 + 6831364 * q^82 + 3077704 * q^83 + 29008056 * q^84 + 5117008 * q^85 + 11620998 * q^86 - 1999898 * q^87 - 24708046 * q^88 + 743498 * q^89 - 38296444 * q^90 - 24167656 * q^91 + 11053132 * q^92 + 25723782 * q^93 - 29029210 * q^94 + 1137892 * q^95 - 34019010 * q^96 - 7924270 * q^97 + 19298152 * q^98 - 43451600 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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