LMFDB - Embedded newform 29.8.a.b.1.8

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 1101 x^{8} - 1540 x^{7} + 405148 x^{6} + 870160 x^{5} - 54569376 x^{4} - 87078400 x^{3} + \cdots - 9372051456 $ x^10 - 1101x^8 - 1540x^7 + 405148x^6 + 870160x^5 - 54569376x^4 - 87078400x^3 + 2140673280x^2 - 1918315520x - 9372051456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-14.7228$ 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)

$f(q)$	$=$	$q+14.7228 q^{2} +83.8824 q^{3} +88.7619 q^{4} +246.177 q^{5} +1234.99 q^{6} -1219.72 q^{7} -577.696 q^{8} +4849.26 q^{9} +O(q^{10})$	\(q+14.7228 q^{2} +83.8824 q^{3} +88.7619 q^{4} +246.177 q^{5} +1234.99 q^{6} -1219.72 q^{7} -577.696 q^{8} +4849.26 q^{9} +3624.43 q^{10} -7012.73 q^{11} +7445.56 q^{12} -1495.18 q^{13} -17957.7 q^{14} +20649.9 q^{15} -19866.8 q^{16} +11323.7 q^{17} +71394.9 q^{18} +36702.1 q^{19} +21851.2 q^{20} -102313. q^{21} -103247. q^{22} +97484.5 q^{23} -48458.6 q^{24} -17521.8 q^{25} -22013.3 q^{26} +223317. q^{27} -108265. q^{28} -24389.0 q^{29} +304026. q^{30} -129953. q^{31} -218551. q^{32} -588245. q^{33} +166716. q^{34} -300267. q^{35} +430430. q^{36} -233416. q^{37} +540359. q^{38} -125420. q^{39} -142216. q^{40} +53077.0 q^{41} -1.50634e6 q^{42} +219265. q^{43} -622463. q^{44} +1.19378e6 q^{45} +1.43525e6 q^{46} +188678. q^{47} -1.66648e6 q^{48} +664173. q^{49} -257970. q^{50} +949856. q^{51} -132715. q^{52} +519745. q^{53} +3.28786e6 q^{54} -1.72637e6 q^{55} +704628. q^{56} +3.07866e6 q^{57} -359075. q^{58} +2.82088e6 q^{59} +1.83293e6 q^{60} -1.46644e6 q^{61} -1.91328e6 q^{62} -5.91474e6 q^{63} -674737. q^{64} -368080. q^{65} -8.66063e6 q^{66} +472290. q^{67} +1.00511e6 q^{68} +8.17723e6 q^{69} -4.42079e6 q^{70} +1.12647e6 q^{71} -2.80140e6 q^{72} -5.69206e6 q^{73} -3.43655e6 q^{74} -1.46977e6 q^{75} +3.25775e6 q^{76} +8.55356e6 q^{77} -1.84653e6 q^{78} +2.06938e6 q^{79} -4.89077e6 q^{80} +8.12705e6 q^{81} +781444. q^{82} +2.92151e6 q^{83} -9.08150e6 q^{84} +2.78763e6 q^{85} +3.22820e6 q^{86} -2.04581e6 q^{87} +4.05123e6 q^{88} -1.13139e7 q^{89} +1.75758e7 q^{90} +1.82370e6 q^{91} +8.65290e6 q^{92} -1.09008e7 q^{93} +2.77788e6 q^{94} +9.03522e6 q^{95} -1.83326e7 q^{96} +1.16895e7 q^{97} +9.77852e6 q^{98} -3.40066e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) $ 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9} + 8496 q^{10} + 7384 q^{11} + 49720 q^{12} + 20820 q^{13} + 50976 q^{14} + 43516 q^{15} + 122082 q^{16} - 11620 q^{17} + 66060 q^{18} + 75068 q^{19} - 42914 q^{20} + 51480 q^{21} - 36950 q^{22} + 62040 q^{23} - 205942 q^{24} + 261022 q^{25} - 201528 q^{26} - 28060 q^{27} - 24980 q^{28} - 243890 q^{29} - 1284894 q^{30} + 200600 q^{31} - 1761460 q^{32} - 1068000 q^{33} - 503932 q^{34} + 107528 q^{35} - 26300 q^{36} - 367740 q^{37} + 766880 q^{38} + 392692 q^{39} - 865000 q^{40} + 932764 q^{41} - 2058060 q^{42} + 1443560 q^{43} - 1325912 q^{44} + 4245684 q^{45} + 1760460 q^{46} - 286960 q^{47} + 3187120 q^{48} + 4713194 q^{49} - 3682652 q^{50} + 1451016 q^{51} + 2560210 q^{52} + 3953220 q^{53} - 3147534 q^{54} + 3981316 q^{55} + 2082464 q^{56} + 2050640 q^{57} + 6712320 q^{59} + 7476756 q^{60} + 1905196 q^{61} - 8048490 q^{62} + 3643800 q^{63} + 8445458 q^{64} + 4667544 q^{65} - 12425580 q^{66} - 2718200 q^{67} - 17699740 q^{68} + 1109064 q^{69} - 30441624 q^{70} + 3447736 q^{71} - 22466840 q^{72} - 2554460 q^{73} - 4214584 q^{74} + 1088084 q^{75} - 8294848 q^{76} - 3967800 q^{77} - 24809970 q^{78} + 4187744 q^{79} - 17715290 q^{80} + 5161402 q^{81} + 7020500 q^{82} + 3498720 q^{83} + 22947224 q^{84} + 1817072 q^{85} - 361638 q^{86} - 1951120 q^{87} + 15118470 q^{88} - 303268 q^{89} - 28959160 q^{90} + 27215080 q^{91} - 10783380 q^{92} + 1097360 q^{93} + 55641726 q^{94} - 8810536 q^{95} - 53327238 q^{96} + 4908620 q^{97} + 40120080 q^{98} - 14408716 q^{99}+O(q^{100}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9 + 8496 * q^10 + 7384 * q^11 + 49720 * q^12 + 20820 * q^13 + 50976 * q^14 + 43516 * q^15 + 122082 * q^16 - 11620 * q^17 + 66060 * q^18 + 75068 * q^19 - 42914 * q^20 + 51480 * q^21 - 36950 * q^22 + 62040 * q^23 - 205942 * q^24 + 261022 * q^25 - 201528 * q^26 - 28060 * q^27 - 24980 * q^28 - 243890 * q^29 - 1284894 * q^30 + 200600 * q^31 - 1761460 * q^32 - 1068000 * q^33 - 503932 * q^34 + 107528 * q^35 - 26300 * q^36 - 367740 * q^37 + 766880 * q^38 + 392692 * q^39 - 865000 * q^40 + 932764 * q^41 - 2058060 * q^42 + 1443560 * q^43 - 1325912 * q^44 + 4245684 * q^45 + 1760460 * q^46 - 286960 * q^47 + 3187120 * q^48 + 4713194 * q^49 - 3682652 * q^50 + 1451016 * q^51 + 2560210 * q^52 + 3953220 * q^53 - 3147534 * q^54 + 3981316 * q^55 + 2082464 * q^56 + 2050640 * q^57 + 6712320 * q^59 + 7476756 * q^60 + 1905196 * q^61 - 8048490 * q^62 + 3643800 * q^63 + 8445458 * q^64 + 4667544 * q^65 - 12425580 * q^66 - 2718200 * q^67 - 17699740 * q^68 + 1109064 * q^69 - 30441624 * q^70 + 3447736 * q^71 - 22466840 * q^72 - 2554460 * q^73 - 4214584 * q^74 + 1088084 * q^75 - 8294848 * q^76 - 3967800 * q^77 - 24809970 * q^78 + 4187744 * q^79 - 17715290 * q^80 + 5161402 * q^81 + 7020500 * q^82 + 3498720 * q^83 + 22947224 * q^84 + 1817072 * q^85 - 361638 * q^86 - 1951120 * q^87 + 15118470 * q^88 - 303268 * q^89 - 28959160 * q^90 + 27215080 * q^91 - 10783380 * q^92 + 1097360 * q^93 + 55641726 * q^94 - 8810536 * q^95 - 53327238 * q^96 + 4908620 * q^97 + 40120080 * q^98 - 14408716 * 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 $

$2$	14.7228	1.30133	0.650664	−	0.759366i	$-0.274491\pi$
$2$	14.7228	1.30133	0.650664	+	0.759366i	$0.274491\pi$
$3$	83.8824	1.79369	0.896843	−	0.442348i	$-0.145854\pi$
$3$	83.8824	1.79369	0.896843	+	0.442348i	$0.145854\pi$
$4$	88.7619	0.693452
$5$	246.177	0.880750	0.440375	−	0.897814i	$-0.354845\pi$
$5$	246.177	0.880750	0.440375	+	0.897814i	$0.354845\pi$
$6$	1234.99	2.33417
$7$	−1219.72	−1.34405	−0.672027	−	0.740526i	$-0.734576\pi$
$7$	−1219.72	−1.34405	−0.672027	+	0.740526i	$0.734576\pi$
$8$	−577.696	−0.398919
$9$	4849.26	2.21731
$10$	3624.43	1.14614
$11$	−7012.73	−1.58859	−0.794296	−	0.607531i	$-0.792160\pi$
$11$	−7012.73	−1.58859	−0.794296	+	0.607531i	$0.792160\pi$
$12$	7445.56	1.24384
$13$	−1495.18	−0.188753	−0.0943763	−	0.995537i	$-0.530086\pi$
$13$	−1495.18	−0.188753	−0.0943763	+	0.995537i	$0.530086\pi$
$14$	−17957.7	−1.74905
$15$	20649.9	1.57979
$16$	−19866.8	−1.21258
$17$	11323.7	0.559005	0.279502	−	0.960145i	$-0.409831\pi$
$17$	11323.7	0.559005	0.279502	+	0.960145i	$0.409831\pi$
$18$	71394.9	2.88545
$19$	36702.1	1.22759	0.613795	−	0.789466i	$-0.289642\pi$
$19$	36702.1	1.22759	0.613795	+	0.789466i	$0.289642\pi$
$20$	21851.2	0.610758
$21$	−102313.	−2.41081
$22$	−103247.	−2.06728
$23$	97484.5	1.67066	0.835330	−	0.549749i	$-0.185277\pi$
$23$	97484.5	1.67066	0.835330	+	0.549749i	$0.185277\pi$
$24$	−48458.6	−0.715536
$25$	−17521.8	−0.224279
$26$	−22013.3	−0.245629
$27$	223317.	2.18348
$28$	−108265.	−0.932038
$29$	−24389.0	−0.185695
$29$	−24389.0	−0.185695
$30$	304026.	2.05582
$31$	−129953.	−0.783469	−0.391734	−	0.920078i	$-0.628125\pi$
$31$	−129953.	−0.783469	−0.391734	+	0.920078i	$0.628125\pi$
$32$	−218551.	−1.17904
$33$	−588245.	−2.84944
$34$	166716.	0.727448
$35$	−300267.	−1.18378
$36$	430430.	1.53760
$37$	−233416.	−0.757574	−0.378787	−	0.925484i	$-0.623659\pi$
$37$	−233416.	−0.757574	−0.378787	+	0.925484i	$0.623659\pi$
$38$	540359.	1.59750
$39$	−125420.	−0.338563
$40$	−142216.	−0.351348
$41$	53077.0	0.120272	0.0601358	−	0.998190i	$-0.480847\pi$
$41$	53077.0	0.120272	0.0601358	+	0.998190i	$0.480847\pi$
$42$	−1.50634e6	−3.13726
$43$	219265.	0.420561	0.210280	−	0.977641i	$-0.432562\pi$
$43$	219265.	0.420561	0.210280	+	0.977641i	$0.432562\pi$
$44$	−622463.	−1.10161
$45$	1.19378e6	1.95290
$46$	1.43525e6	2.17407
$47$	188678.	0.265081	0.132541	−	0.991178i	$-0.457686\pi$
$47$	188678.	0.265081	0.132541	+	0.991178i	$0.457686\pi$
$48$	−1.66648e6	−2.17498
$49$	664173.	0.806483
$50$	−257970.	−0.291860
$51$	949856.	1.00268
$52$	−132715.	−0.130891
$53$	519745.	0.479540	0.239770	−	0.970830i	$-0.422928\pi$
$53$	519745.	0.479540	0.239770	+	0.970830i	$0.422928\pi$
$54$	3.28786e6	2.84142
$55$	−1.72637e6	−1.39915
$56$	704628.	0.536169
$57$	3.07866e6	2.20191
$58$	−359075.	−0.241650
$59$	2.82088e6	1.78814	0.894071	−	0.447926i	$-0.147837\pi$
$59$	2.82088e6	1.78814	0.894071	+	0.447926i	$0.147837\pi$
$60$	1.83293e6	1.09551
$61$	−1.46644e6	−0.827196	−0.413598	−	0.910460i	$-0.635728\pi$
$61$	−1.46644e6	−0.827196	−0.413598	+	0.910460i	$0.635728\pi$
$62$	−1.91328e6	−1.01955
$63$	−5.91474e6	−2.98019
$64$	−674737.	−0.321740
$65$	−368080.	−0.166244
$66$	−8.66063e6	−3.70805
$67$	472290.	0.191843	0.0959217	−	0.995389i	$-0.469420\pi$
$67$	472290.	0.191843	0.0959217	+	0.995389i	$0.469420\pi$
$68$	1.00511e6	0.387643
$69$	8.17723e6	2.99664
$70$	−4.42079e6	−1.54048
$71$	1.12647e6	0.373521	0.186761	−	0.982405i	$-0.440201\pi$
$71$	1.12647e6	0.373521	0.186761	+	0.982405i	$0.440201\pi$
$72$	−2.80140e6	−0.884528
$73$	−5.69206e6	−1.71253	−0.856267	−	0.516534i	$-0.827222\pi$
$73$	−5.69206e6	−1.71253	−0.856267	+	0.516534i	$0.827222\pi$
$74$	−3.43655e6	−0.985851
$75$	−1.46977e6	−0.402286
$76$	3.25775e6	0.851275
$77$	8.55356e6	2.13516
$78$	−1.84653e6	−0.440581
$79$	2.06938e6	0.472222	0.236111	−	0.971726i	$-0.424127\pi$
$79$	2.06938e6	0.472222	0.236111	+	0.971726i	$0.424127\pi$
$80$	−4.89077e6	−1.06798
$81$	8.12705e6	1.69916
$82$	781444.	0.156513
$83$	2.92151e6	0.560833	0.280417	−	0.959878i	$-0.409527\pi$
$83$	2.92151e6	0.560833	0.280417	+	0.959878i	$0.409527\pi$
$84$	−9.08150e6	−1.67178
$85$	2.78763e6	0.492344
$86$	3.22820e6	0.547287
$87$	−2.04581e6	−0.333079
$88$	4.05123e6	0.633720
$89$	−1.13139e7	−1.70117	−0.850587	−	0.525835i	$-0.823753\pi$
$89$	−1.13139e7	−1.70117	−0.850587	+	0.525835i	$0.823753\pi$
$90$	1.75758e7	2.54136
$91$	1.82370e6	0.253694
$92$	8.65290e6	1.15852
$93$	−1.09008e7	−1.40530
$94$	2.77788e6	0.344958
$95$	9.03522e6	1.08120
$96$	−1.83326e7	−2.11483
$97$	1.16895e7	1.30046	0.650228	−	0.759739i	$-0.274673\pi$
$97$	1.16895e7	1.30046	0.650228	+	0.759739i	$0.274673\pi$
$98$	9.77852e6	1.04950
$99$	−3.40066e7	−3.52241
$100$	−1.55526e6	−0.155526
$101$	−7.61618e6	−0.735551	−0.367775	−	0.929915i	$-0.619880\pi$
$101$	−7.61618e6	−0.735551	−0.367775	+	0.929915i	$0.619880\pi$
$102$	1.39846e7	1.30481
$103$	−7.95776e6	−0.717564	−0.358782	−	0.933421i	$-0.616808\pi$
$103$	−7.95776e6	−0.717564	−0.358782	+	0.933421i	$0.616808\pi$
$104$	863762.	0.0752969
$105$	−2.51871e7	−2.12332
$106$	7.65212e6	0.624039
$107$	6.82294e6	0.538429	0.269214	−	0.963080i	$-0.413236\pi$
$107$	6.82294e6	0.538429	0.269214	+	0.963080i	$0.413236\pi$
$108$	1.98220e7	1.51414
$109$	3.94178e6	0.291541	0.145771	−	0.989318i	$-0.453434\pi$
$109$	3.94178e6	0.291541	0.145771	+	0.989318i	$0.453434\pi$
$110$	−2.54171e7	−1.82076
$111$	−1.95795e7	−1.35885
$112$	2.42320e7	1.62977
$113$	2.77809e7	1.81122	0.905611	−	0.424110i	$-0.139413\pi$
$113$	2.77809e7	1.81122	0.905611	+	0.424110i	$0.139413\pi$
$114$	4.53266e7	2.86541
$115$	2.39985e7	1.47143
$116$	−2.16481e6	−0.128771
$117$	−7.25054e6	−0.418523
$118$	4.15313e7	2.32696
$119$	−1.38117e7	−0.751333
$120$	−1.19294e7	−0.630208
$121$	2.96912e7	1.52363
$122$	−2.15901e7	−1.07645
$123$	4.45223e6	0.215730
$124$	−1.15349e7	−0.543298
$125$	−2.35461e7	−1.07828
$126$	−8.70818e7	−3.87820
$127$	−3.53141e7	−1.52980	−0.764901	−	0.644148i	$-0.777212\pi$
$127$	−3.53141e7	−1.52980	−0.764901	+	0.644148i	$0.777212\pi$
$128$	1.80405e7	0.760351
$129$	1.83924e7	0.754355
$130$	−5.41918e6	−0.216338
$131$	−2.19634e7	−0.853593	−0.426796	−	0.904348i	$-0.640358\pi$
$131$	−2.19634e7	−0.853593	−0.426796	+	0.904348i	$0.640358\pi$
$132$	−5.22137e7	−1.97595
$133$	−4.47663e7	−1.64995
$134$	6.95345e6	0.249651
$135$	5.49756e7	1.92310
$136$	−6.54163e6	−0.222997
$137$	−2.02896e7	−0.674142	−0.337071	−	0.941479i	$-0.609436\pi$
$137$	−2.02896e7	−0.674142	−0.337071	+	0.941479i	$0.609436\pi$
$138$	1.20392e8	3.89961
$139$	2.33979e7	0.738967	0.369483	−	0.929237i	$-0.379535\pi$
$139$	2.33979e7	0.738967	0.369483	+	0.929237i	$0.379535\pi$
$140$	−2.66523e7	−0.820893
$141$	1.58268e7	0.475473
$142$	1.65848e7	0.486073
$143$	1.04853e7	0.299851
$144$	−9.63396e7	−2.68866
$145$	−6.00402e6	−0.163551
$146$	−8.38032e7	−2.22857
$147$	5.57125e7	1.44658
$148$	−2.07185e7	−0.525341
$149$	−4.64103e7	−1.14938	−0.574689	−	0.818372i	$-0.694877\pi$
$149$	−4.64103e7	−1.14938	−0.574689	+	0.818372i	$0.694877\pi$
$150$	−2.16392e7	−0.523505
$151$	5.62491e7	1.32952	0.664762	−	0.747055i	$-0.268533\pi$
$151$	5.62491e7	1.32952	0.664762	+	0.747055i	$0.268533\pi$
$152$	−2.12027e7	−0.489709
$153$	5.49114e7	1.23949
$154$	1.25933e8	2.77854
$155$	−3.19916e7	−0.690040
$156$	−1.11325e7	−0.234777
$157$	7.09831e6	0.146388	0.0731941	−	0.997318i	$-0.476681\pi$
$157$	7.09831e6	0.146388	0.0731941	+	0.997318i	$0.476681\pi$
$158$	3.04672e7	0.614515
$159$	4.35975e7	0.860145
$160$	−5.38023e7	−1.03844
$161$	−1.18904e8	−2.24546
$162$	1.19653e8	2.21117
$163$	2.28201e7	0.412725	0.206363	−	0.978476i	$-0.433837\pi$
$163$	2.28201e7	0.412725	0.206363	+	0.978476i	$0.433837\pi$
$164$	4.71122e6	0.0834026
$165$	−1.44812e8	−2.50964
$166$	4.30129e7	0.729827
$167$	−2.62832e7	−0.436687	−0.218343	−	0.975872i	$-0.570065\pi$
$167$	−2.62832e7	−0.436687	−0.218343	+	0.975872i	$0.570065\pi$
$168$	5.91059e7	0.961719
$169$	−6.05129e7	−0.964372
$170$	4.10418e7	0.640700
$171$	1.77978e8	2.72195
$172$	1.94623e7	0.291639
$173$	−6.83572e7	−1.00374	−0.501872	−	0.864942i	$-0.667355\pi$
$173$	−6.83572e7	−1.00374	−0.501872	+	0.864942i	$0.667355\pi$
$174$	−3.01201e7	−0.433445
$175$	2.13716e7	0.301443
$176$	1.39321e8	1.92629
$177$	2.36622e8	3.20737
$178$	−1.66573e8	−2.21378
$179$	2.13091e7	0.277703	0.138851	−	0.990313i	$-0.455659\pi$
$179$	2.13091e7	0.277703	0.138851	+	0.990313i	$0.455659\pi$
$180$	1.05962e8	1.35424
$181$	3.08189e7	0.386316	0.193158	−	0.981168i	$-0.438127\pi$
$181$	3.08189e7	0.386316	0.193158	+	0.981168i	$0.438127\pi$
$182$	2.68501e7	0.330138
$183$	−1.23008e8	−1.48373
$184$	−5.63164e7	−0.666458
$185$	−5.74617e7	−0.667233
$186$	−1.60491e8	−1.82875
$187$	−7.94097e7	−0.888030
$188$	1.67474e7	0.183821
$189$	−2.72384e8	−2.93471
$190$	1.33024e8	1.40700
$191$	1.54246e8	1.60175	0.800877	−	0.598829i	$-0.204367\pi$
$191$	1.54246e8	1.60175	0.800877	+	0.598829i	$0.204367\pi$
$192$	−5.65986e7	−0.577100
$193$	1.32705e8	1.32873	0.664363	−	0.747410i	$-0.268703\pi$
$193$	1.32705e8	1.32873	0.664363	+	0.747410i	$0.268703\pi$
$194$	1.72103e8	1.69232
$195$	−3.08755e7	−0.298189
$196$	5.89533e7	0.559257
$197$	−7.75002e7	−0.722223	−0.361111	−	0.932523i	$-0.617603\pi$
$197$	−7.75002e7	−0.722223	−0.361111	+	0.932523i	$0.617603\pi$
$198$	−5.00673e8	−4.58380
$199$	−2.45946e7	−0.221235	−0.110617	−	0.993863i	$-0.535283\pi$
$199$	−2.45946e7	−0.221235	−0.110617	+	0.993863i	$0.535283\pi$
$200$	1.01223e7	0.0894690
$201$	3.96168e7	0.344107
$202$	−1.12132e8	−0.957192
$203$	2.97477e7	0.249585
$204$	8.43110e7	0.695310
$205$	1.30664e7	0.105929
$206$	−1.17161e8	−0.933786
$207$	4.72728e8	3.70438
$208$	2.97046e7	0.228877
$209$	−2.57382e8	−1.95014
$210$	−3.70826e8	−2.76314
$211$	−5.26041e7	−0.385506	−0.192753	−	0.981247i	$-0.561742\pi$
$211$	−5.26041e7	−0.385506	−0.192753	+	0.981247i	$0.561742\pi$
$212$	4.61336e7	0.332538
$213$	9.44910e7	0.669980
$214$	1.00453e8	0.700672
$215$	5.39779e7	0.370409
$216$	−1.29009e8	−0.871031
$217$	1.58507e8	1.05302
$218$	5.80342e7	0.379390
$219$	−4.77463e8	−3.07175
$220$	−1.53236e8	−0.970246
$221$	−1.69309e7	−0.105514
$222$	−2.88266e8	−1.76831
$223$	4.04759e7	0.244416	0.122208	−	0.992505i	$-0.461003\pi$
$223$	4.04759e7	0.244416	0.122208	+	0.992505i	$0.461003\pi$
$224$	2.66571e8	1.58469
$225$	−8.49676e7	−0.497296
$226$	4.09013e8	2.35699
$227$	7.87275e6	0.0446721	0.0223360	−	0.999751i	$-0.492890\pi$
$227$	7.87275e6	0.0446721	0.0223360	+	0.999751i	$0.492890\pi$
$228$	2.73268e8	1.52692
$229$	−3.06832e8	−1.68841	−0.844203	−	0.536024i	$-0.819926\pi$
$229$	−3.06832e8	−1.68841	−0.844203	+	0.536024i	$0.819926\pi$
$230$	3.53325e8	1.91482
$231$	7.17494e8	3.82980
$232$	1.40894e7	0.0740774
$233$	−3.78608e7	−0.196085	−0.0980424	−	0.995182i	$-0.531258\pi$
$233$	−3.78608e7	−0.196085	−0.0980424	+	0.995182i	$0.531258\pi$
$234$	−1.06748e8	−0.544636
$235$	4.64483e7	0.233471
$236$	2.50386e8	1.23999
$237$	1.73585e8	0.847018
$238$	−2.03347e8	−0.977730
$239$	−1.97888e8	−0.937621	−0.468811	−	0.883299i	$-0.655317\pi$
$239$	−1.97888e8	−0.937621	−0.468811	+	0.883299i	$0.655317\pi$
$240$	−4.10249e8	−1.91562
$241$	1.21436e8	0.558842	0.279421	−	0.960169i	$-0.409858\pi$
$241$	1.21436e8	0.558842	0.279421	+	0.960169i	$0.409858\pi$
$242$	4.37138e8	1.98274
$243$	1.93322e8	0.864289
$244$	−1.30164e8	−0.573621
$245$	1.63504e8	0.710310
$246$	6.55495e7	0.280735
$247$	−5.48764e7	−0.231711
$248$	7.50736e7	0.312540
$249$	2.45063e8	1.00596
$250$	−3.46665e8	−1.40320
$251$	−1.23152e8	−0.491569	−0.245785	−	0.969324i	$-0.579046\pi$
$251$	−1.23152e8	−0.491569	−0.245785	+	0.969324i	$0.579046\pi$
$252$	−5.25004e8	−2.06662
$253$	−6.83632e8	−2.65400
$254$	−5.19924e8	−1.99077
$255$	2.33833e8	0.883110
$256$	3.51974e8	1.31120
$257$	3.21340e8	1.18086	0.590431	−	0.807088i	$-0.298958\pi$
$257$	3.21340e8	1.18086	0.590431	+	0.807088i	$0.298958\pi$
$258$	2.70789e8	0.981662
$259$	2.84702e8	1.01822
$260$	−3.26715e7	−0.115282
$261$	−1.18269e8	−0.411745
$262$	−3.23364e8	−1.11080
$263$	−2.67482e8	−0.906669	−0.453335	−	0.891340i	$-0.649766\pi$
$263$	−2.67482e8	−0.906669	−0.453335	+	0.891340i	$0.649766\pi$
$264$	3.39827e8	1.13669
$265$	1.27949e8	0.422355
$266$	−6.59087e8	−2.14712
$267$	−9.49040e8	−3.05137
$268$	4.19213e7	0.133034
$269$	5.76155e8	1.80470	0.902352	−	0.430999i	$-0.141839\pi$
$269$	5.76155e8	1.80470	0.902352	+	0.430999i	$0.141839\pi$
$270$	8.09397e8	2.50258
$271$	−2.37714e8	−0.725541	−0.362771	−	0.931879i	$-0.618169\pi$
$271$	−2.37714e8	−0.725541	−0.362771	+	0.931879i	$0.618169\pi$
$272$	−2.24965e8	−0.677836
$273$	1.52977e8	0.455047
$274$	−2.98720e8	−0.877279
$275$	1.22875e8	0.356287
$276$	7.25827e8	2.07803
$277$	7.21214e7	0.203885	0.101942	−	0.994790i	$-0.467494\pi$
$277$	7.21214e7	0.203885	0.101942	+	0.994790i	$0.467494\pi$
$278$	3.44483e8	0.961637
$279$	−6.30178e8	−1.73720
$280$	1.73463e8	0.472231
$281$	−3.57808e8	−0.962007	−0.481004	−	0.876719i	$-0.659728\pi$
$281$	−3.57808e8	−0.962007	−0.481004	+	0.876719i	$0.659728\pi$
$282$	2.33015e8	0.618746
$283$	1.39748e8	0.366515	0.183258	−	0.983065i	$-0.441336\pi$
$283$	1.39748e8	0.366515	0.183258	+	0.983065i	$0.441336\pi$
$284$	9.99876e7	0.259019
$285$	7.57896e8	1.93934
$286$	1.54374e8	0.390204
$287$	−6.47391e7	−0.161652
$288$	−1.05981e9	−2.61430
$289$	−2.82114e8	−0.687514
$290$	−8.83962e7	−0.212834
$291$	9.80546e8	2.33261
$292$	−5.05238e8	−1.18756
$293$	7.23881e7	0.168124	0.0840621	−	0.996461i	$-0.473211\pi$
$293$	7.23881e7	0.168124	0.0840621	+	0.996461i	$0.473211\pi$
$294$	8.20246e8	1.88247
$295$	6.94435e8	1.57491
$296$	1.34844e8	0.302210
$297$	−1.56606e9	−3.46866
$298$	−6.83291e8	−1.49572
$299$	−1.45757e8	−0.315341
$300$	−1.30459e8	−0.278966
$301$	−2.67441e8	−0.565257
$302$	8.28146e8	1.73015
$303$	−6.38864e8	−1.31935
$304$	−7.29155e8	−1.48855
$305$	−3.61003e8	−0.728554
$306$	8.08451e8	1.61298
$307$	3.76442e8	0.742529	0.371264	−	0.928527i	$-0.378924\pi$
$307$	3.76442e8	0.742529	0.371264	+	0.928527i	$0.378924\pi$
$308$	7.59230e8	1.48063
$309$	−6.67517e8	−1.28709
$310$	−4.71007e8	−0.897968
$311$	−2.08445e8	−0.392944	−0.196472	−	0.980509i	$-0.562948\pi$
$311$	−2.08445e8	−0.392944	−0.196472	+	0.980509i	$0.562948\pi$
$312$	7.24545e7	0.135059
$313$	6.51662e8	1.20120	0.600602	−	0.799548i	$-0.294927\pi$
$313$	6.51662e8	1.20120	0.600602	+	0.799548i	$0.294927\pi$
$314$	1.04507e8	0.190499
$315$	−1.45607e9	−2.62480
$316$	1.83682e8	0.327463
$317$	−4.03239e8	−0.710977	−0.355488	−	0.934681i	$-0.615685\pi$
$317$	−4.03239e8	−0.710977	−0.355488	+	0.934681i	$0.615685\pi$
$318$	6.41879e8	1.11933
$319$	1.71033e8	0.294994
$320$	−1.66105e8	−0.283372
$321$	5.72325e8	0.965772
$322$	−1.75060e9	−2.92208
$323$	4.15602e8	0.686228
$324$	7.21372e8	1.17829
$325$	2.61982e7	0.0423331
$326$	3.35977e8	0.537091
$327$	3.30646e8	0.522933
$328$	−3.06624e7	−0.0479786
$329$	−2.30135e8	−0.356284
$330$	−2.13205e9	−3.26587
$331$	−7.58494e8	−1.14962	−0.574810	−	0.818287i	$-0.694924\pi$
$331$	−7.58494e8	−1.14962	−0.574810	+	0.818287i	$0.694924\pi$
$332$	2.59319e8	0.388911
$333$	−1.13190e9	−1.67978
$334$	−3.86963e8	−0.568272
$335$	1.16267e8	0.168966
$336$	2.03264e9	2.92329
$337$	4.64538e8	0.661175	0.330588	−	0.943775i	$-0.392753\pi$
$337$	4.64538e8	0.661175	0.330588	+	0.943775i	$0.392753\pi$
$338$	−8.90922e8	−1.25496
$339$	2.33033e9	3.24876
$340$	2.47435e8	0.341417
$341$	9.11328e8	1.24461
$342$	2.62034e9	3.54215
$343$	1.94386e8	0.260098
$344$	−1.26668e8	−0.167770
$345$	2.01305e9	2.63929
$346$	−1.00641e9	−1.30620
$347$	−6.25514e8	−0.803682	−0.401841	−	0.915710i	$-0.631630\pi$
$347$	−6.25514e8	−0.803682	−0.401841	+	0.915710i	$0.631630\pi$
$348$	−1.81590e8	−0.230975
$349$	1.55192e8	0.195425	0.0977123	−	0.995215i	$-0.468848\pi$
$349$	1.55192e8	0.195425	0.0977123	+	0.995215i	$0.468848\pi$
$350$	3.14651e8	0.392275
$351$	−3.33900e8	−0.412137
$352$	1.53264e9	1.87301
$353$	−5.74513e8	−0.695166	−0.347583	−	0.937649i	$-0.612998\pi$
$353$	−5.74513e8	−0.695166	−0.347583	+	0.937649i	$0.612998\pi$
$354$	3.48375e9	4.17383
$355$	2.77311e8	0.328979
$356$	−1.00425e9	−1.17968
$357$	−1.15856e9	−1.34766
$358$	3.13731e8	0.361382
$359$	−1.60089e9	−1.82613	−0.913063	−	0.407820i	$-0.866289\pi$
$359$	−1.60089e9	−1.82613	−0.913063	+	0.407820i	$0.866289\pi$
$360$	−6.89641e8	−0.779049
$361$	4.53172e8	0.506977
$362$	4.53742e8	0.502723
$363$	2.49057e9	2.73291
$364$	1.61875e8	0.175924
$365$	−1.40125e9	−1.50831
$366$	−1.81103e9	−1.93082
$367$	5.20955e8	0.550135	0.275067	−	0.961425i	$-0.411300\pi$
$367$	5.20955e8	0.550135	0.275067	+	0.961425i	$0.411300\pi$
$368$	−1.93671e9	−2.02580
$369$	2.57384e8	0.266680
$370$	−8.46000e8	−0.868289
$371$	−6.33943e8	−0.644528
$372$	−9.67576e8	−0.974507
$373$	−7.42205e8	−0.740531	−0.370265	−	0.928926i	$-0.620733\pi$
$373$	−7.42205e8	−0.740531	−0.370265	+	0.928926i	$0.620733\pi$
$374$	−1.16914e9	−1.15562
$375$	−1.97510e9	−1.93410
$376$	−1.08999e8	−0.105746
$377$	3.64660e7	0.0350505
$378$	−4.01027e9	−3.81902
$379$	1.22560e9	1.15641	0.578205	−	0.815892i	$-0.303753\pi$
$379$	1.22560e9	1.15641	0.578205	+	0.815892i	$0.303753\pi$
$380$	8.01983e8	0.749761
$381$	−2.96223e9	−2.74399
$382$	2.27093e9	2.08441
$383$	5.13012e8	0.466586	0.233293	−	0.972407i	$-0.425050\pi$
$383$	5.13012e8	0.466586	0.233293	+	0.972407i	$0.425050\pi$
$384$	1.51328e9	1.36383
$385$	2.10569e9	1.88054
$386$	1.95379e9	1.72911
$387$	1.06327e9	0.932515
$388$	1.03758e9	0.901804
$389$	1.12918e9	0.972610	0.486305	−	0.873789i	$-0.338344\pi$
$389$	1.12918e9	0.972610	0.486305	+	0.873789i	$0.338344\pi$
$390$	−4.54574e8	−0.388042
$391$	1.10388e9	0.933906
$392$	−3.83690e8	−0.321721
$393$	−1.84235e9	−1.53108
$394$	−1.14102e9	−0.939848
$395$	5.09435e8	0.415910
$396$	−3.01849e9	−2.44262
$397$	−2.10773e9	−1.69063	−0.845313	−	0.534271i	$-0.820586\pi$
$397$	−2.10773e9	−1.69063	−0.845313	+	0.534271i	$0.820586\pi$
$398$	−3.62102e8	−0.287899
$399$	−3.75510e9	−2.95949
$400$	3.48102e8	0.271955
$401$	1.40598e9	1.08887	0.544433	−	0.838804i	$-0.316745\pi$
$401$	1.40598e9	1.08887	0.544433	+	0.838804i	$0.316745\pi$
$402$	5.83272e8	0.447796
$403$	1.94304e8	0.147882
$404$	−6.76027e8	−0.510069
$405$	2.00069e9	1.49654
$406$	4.37971e8	0.324791
$407$	1.63688e9	1.20348
$408$	−5.48728e8	−0.399988
$409$	−6.84540e8	−0.494729	−0.247364	−	0.968923i	$-0.579564\pi$
$409$	−6.84540e8	−0.494729	−0.247364	+	0.968923i	$0.579564\pi$
$410$	1.92374e8	0.137849
$411$	−1.70194e9	−1.20920
$412$	−7.06346e8	−0.497597
$413$	−3.44068e9	−2.40336
$414$	6.95989e9	4.82060
$415$	7.19209e8	0.493954
$416$	3.26774e8	0.222547
$417$	1.96267e9	1.32547
$418$	−3.78939e9	−2.53777
$419$	1.43604e9	0.953713	0.476856	−	0.878981i	$-0.341776\pi$
$419$	1.43604e9	0.953713	0.476856	+	0.878981i	$0.341776\pi$
$420$	−2.23566e9	−1.47242
$421$	1.52880e9	0.998534	0.499267	−	0.866448i	$-0.333603\pi$
$421$	1.52880e9	0.998534	0.499267	+	0.866448i	$0.333603\pi$
$422$	−7.74481e8	−0.501669
$423$	9.14950e8	0.587768
$424$	−3.00255e8	−0.191298
$425$	−1.98410e8	−0.125373
$426$	1.39118e9	0.871863
$427$	1.78864e9	1.11180
$428$	6.05617e8	0.373375
$429$	8.79534e8	0.537839
$430$	7.94708e8	0.482023
$431$	2.16883e9	1.30483	0.652416	−	0.757861i	$-0.273755\pi$
$431$	2.16883e9	1.30483	0.652416	+	0.757861i	$0.273755\pi$
$432$	−4.43661e9	−2.64763
$433$	1.12085e9	0.663499	0.331750	−	0.943367i	$-0.392361\pi$
$433$	1.12085e9	0.663499	0.331750	+	0.943367i	$0.392361\pi$
$434$	2.33367e9	1.37033
$435$	−5.03632e8	−0.293360
$436$	3.49880e8	0.202170
$437$	3.57788e9	2.05088
$438$	−7.02962e9	−3.99735
$439$	−8.12625e7	−0.0458421	−0.0229210	−	0.999737i	$-0.507297\pi$
$439$	−8.12625e7	−0.0458421	−0.0229210	+	0.999737i	$0.507297\pi$
$440$	9.97320e8	0.558149
$441$	3.22075e9	1.78822
$442$	−2.49271e8	−0.137308
$443$	9.45741e8	0.516844	0.258422	−	0.966032i	$-0.416798\pi$
$443$	9.45741e8	0.516844	0.258422	+	0.966032i	$0.416798\pi$
$444$	−1.73791e9	−0.942298
$445$	−2.78523e9	−1.49831
$446$	5.95920e8	0.318065
$447$	−3.89301e9	−2.06162
$448$	8.22990e8	0.432436
$449$	−1.80771e9	−0.942465	−0.471233	−	0.882009i	$-0.656191\pi$
$449$	−1.80771e9	−0.942465	−0.471233	+	0.882009i	$0.656191\pi$
$450$	−1.25096e9	−0.647144
$451$	−3.72215e8	−0.191063
$452$	2.46588e9	1.25600
$453$	4.71831e9	2.38475
$454$	1.15909e8	0.0581330
$455$	4.48955e8	0.223441
$456$	−1.77853e9	−0.878384
$457$	9.58073e8	0.469561	0.234780	−	0.972048i	$-0.424563\pi$
$457$	9.58073e8	0.469561	0.234780	+	0.972048i	$0.424563\pi$
$458$	−4.51744e9	−2.19717
$459$	2.52877e9	1.22057
$460$	2.13015e9	1.02037
$461$	−3.10254e9	−1.47491	−0.737453	−	0.675398i	$-0.763972\pi$
$461$	−3.10254e9	−1.47491	−0.737453	+	0.675398i	$0.763972\pi$
$462$	1.05635e10	4.98382
$463$	8.50198e8	0.398095	0.199047	−	0.979990i	$-0.436215\pi$
$463$	8.50198e8	0.398095	0.199047	+	0.979990i	$0.436215\pi$
$464$	4.84533e8	0.225170
$465$	−2.68353e9	−1.23772
$466$	−5.57418e8	−0.255170
$467$	4.00190e9	1.81827	0.909133	−	0.416505i	$-0.136745\pi$
$467$	4.00190e9	1.81827	0.909133	+	0.416505i	$0.136745\pi$
$468$	−6.43571e8	−0.290226
$469$	−5.76061e8	−0.257848
$470$	6.83850e8	0.303822
$471$	5.95423e8	0.262575
$472$	−1.62961e9	−0.713324
$473$	−1.53764e9	−0.668100
$474$	2.55566e9	1.10225
$475$	−6.43085e8	−0.275322
$476$	−1.22595e9	−0.521013
$477$	2.52038e9	1.06329
$478$	−2.91348e9	−1.22015
$479$	−1.38073e9	−0.574031	−0.287016	−	0.957926i	$-0.592663\pi$
$479$	−1.38073e9	−0.574031	−0.287016	+	0.957926i	$0.592663\pi$
$480$	−4.51307e9	−1.86264
$481$	3.49000e8	0.142994
$482$	1.78789e9	0.727236
$483$	−9.97393e9	−4.02765
$484$	2.63544e9	1.05656
$485$	2.87769e9	1.14538
$486$	2.84625e9	1.12472
$487$	−2.11345e9	−0.829164	−0.414582	−	0.910012i	$-0.636072\pi$
$487$	−2.11345e9	−0.829164	−0.414582	+	0.910012i	$0.636072\pi$
$488$	8.47155e8	0.329984
$489$	1.91421e9	0.740300
$490$	2.40725e9	0.924346
$491$	−2.79901e9	−1.06713	−0.533567	−	0.845758i	$-0.679149\pi$
$491$	−2.79901e9	−1.06713	−0.533567	+	0.845758i	$0.679149\pi$
$492$	3.95188e8	0.149598
$493$	−2.76173e8	−0.103805
$494$	−8.07936e8	−0.301531
$495$	−8.37164e9	−3.10236
$496$	2.58176e9	0.950016
$497$	−1.37398e9	−0.502033
$498$	3.60802e9	1.30908
$499$	−3.95475e9	−1.42484	−0.712421	−	0.701752i	$-0.752401\pi$
$499$	−3.95475e9	−1.42484	−0.712421	+	0.701752i	$0.752401\pi$
$500$	−2.08999e9	−0.747738
$501$	−2.20469e9	−0.783279
$502$	−1.81315e9	−0.639692
$503$	3.90223e8	0.136718	0.0683589	−	0.997661i	$-0.478224\pi$
$503$	3.90223e8	0.136718	0.0683589	+	0.997661i	$0.478224\pi$
$504$	3.41692e9	1.18885
$505$	−1.87493e9	−0.647836
$506$	−1.00650e10	−3.45372
$507$	−5.07597e9	−1.72978
$508$	−3.13455e9	−1.06084
$509$	−8.22310e8	−0.276391	−0.138195	−	0.990405i	$-0.544130\pi$
$509$	−8.22310e8	−0.276391	−0.138195	+	0.990405i	$0.544130\pi$
$510$	3.44268e9	1.14922
$511$	6.94271e9	2.30174
$512$	2.87287e9	0.945956
$513$	8.19621e9	2.68042
$514$	4.73104e9	1.53669
$515$	−1.95902e9	−0.631995
$516$	1.63255e9	0.523109
$517$	−1.32315e9	−0.421106
$518$	4.19163e9	1.32504
$519$	−5.73397e9	−1.80040
$520$	2.12639e8	0.0663178
$521$	−1.51374e9	−0.468942	−0.234471	−	0.972123i	$-0.575336\pi$
$521$	−1.51374e9	−0.468942	−0.234471	+	0.972123i	$0.575336\pi$
$522$	−1.74125e9	−0.535814
$523$	6.35375e8	0.194211	0.0971056	−	0.995274i	$-0.469042\pi$
$523$	6.35375e8	0.194211	0.0971056	+	0.995274i	$0.469042\pi$
$524$	−1.94952e9	−0.591926
$525$	1.79271e9	0.540694
$526$	−3.93809e9	−1.17987
$527$	−1.47155e9	−0.437963
$528$	1.16866e10	3.45516
$529$	6.09839e9	1.79110
$530$	1.88378e9	0.549622
$531$	1.36792e10	3.96487
$532$	−3.97354e9	−1.14416
$533$	−7.93599e7	−0.0227016
$534$	−1.39726e10	−3.97083
$535$	1.67965e9	0.474221
$536$	−2.72840e8	−0.0765300
$537$	1.78746e9	0.498112
$538$	8.48263e9	2.34851
$539$	−4.65767e9	−1.28117
$540$	4.87974e9	1.33358
$541$	−3.09048e9	−0.839143	−0.419571	−	0.907722i	$-0.637820\pi$
$541$	−3.09048e9	−0.839143	−0.419571	+	0.907722i	$0.637820\pi$
$542$	−3.49982e9	−0.944166
$543$	2.58517e9	0.692929
$544$	−2.47480e9	−0.659088
$545$	9.70377e8	0.256775
$546$	2.25225e9	0.592165
$547$	−6.99677e8	−0.182786	−0.0913929	−	0.995815i	$-0.529132\pi$
$547$	−6.99677e8	−0.182786	−0.0913929	+	0.995815i	$0.529132\pi$
$548$	−1.80094e9	−0.467485
$549$	−7.11113e9	−1.83415
$550$	1.80907e9	0.463646
$551$	−8.95127e8	−0.227958
$552$	−4.72396e9	−1.19542
$553$	−2.52407e9	−0.634692
$554$	1.06183e9	0.265321
$555$	−4.82003e9	−1.19681
$556$	2.07684e9	0.512438
$557$	−1.87657e9	−0.460122	−0.230061	−	0.973176i	$-0.573893\pi$
$557$	−1.87657e9	−0.460122	−0.230061	+	0.973176i	$0.573893\pi$
$558$	−9.27801e9	−2.26066
$559$	−3.27841e8	−0.0793819
$560$	5.96536e9	1.43542
$561$	−6.66108e9	−1.59285
$562$	−5.26795e9	−1.25189
$563$	−1.67232e9	−0.394948	−0.197474	−	0.980308i	$-0.563274\pi$
$563$	−1.67232e9	−0.394948	−0.197474	+	0.980308i	$0.563274\pi$
$564$	1.40482e9	0.329718
$565$	6.83902e9	1.59523
$566$	2.05748e9	0.476956
$567$	−9.91272e9	−2.28377
$568$	−6.50757e8	−0.149005
$569$	2.84586e9	0.647620	0.323810	−	0.946122i	$-0.395036\pi$
$569$	2.84586e9	0.647620	0.323810	+	0.946122i	$0.395036\pi$
$570$	1.11584e10	2.52371
$571$	−1.33070e9	−0.299125	−0.149562	−	0.988752i	$-0.547786\pi$
$571$	−1.33070e9	−0.299125	−0.149562	+	0.988752i	$0.547786\pi$
$572$	9.30696e8	0.207932
$573$	1.29385e10	2.87304
$574$	−9.53143e8	−0.210362
$575$	−1.70810e9	−0.374693
$576$	−3.27198e9	−0.713398
$577$	8.96007e9	1.94176	0.970881	−	0.239563i	$-0.0770042\pi$
$577$	8.96007e9	1.94176	0.970881	+	0.239563i	$0.0770042\pi$
$578$	−4.15351e9	−0.894680
$579$	1.11316e10	2.38332
$580$	−5.32928e8	−0.113415
$581$	−3.56342e9	−0.753790
$582$	1.44364e10	3.03549
$583$	−3.64483e9	−0.761794
$584$	3.28828e9	0.683162
$585$	−1.78492e9	−0.368615
$586$	1.06576e9	0.218785
$587$	3.32613e9	0.678744	0.339372	−	0.940652i	$-0.389786\pi$
$587$	3.32613e9	0.678744	0.339372	+	0.940652i	$0.389786\pi$
$588$	4.94514e9	1.00313
$589$	−4.76956e9	−0.961778
$590$	1.02241e10	2.04947
$591$	−6.50091e9	−1.29544
$592$	4.63724e9	0.918616
$593$	−5.13399e9	−1.01103	−0.505514	−	0.862818i	$-0.668697\pi$
$593$	−5.13399e9	−1.01103	−0.505514	+	0.862818i	$0.668697\pi$
$594$	−2.30569e10	−4.51386
$595$	−3.40012e9	−0.661737
$596$	−4.11947e9	−0.797038
$597$	−2.06305e9	−0.396826
$598$	−2.14596e9	−0.410362
$599$	7.14346e9	1.35805	0.679023	−	0.734117i	$-0.262404\pi$
$599$	7.14346e9	1.35805	0.679023	+	0.734117i	$0.262404\pi$
$600$	8.49080e8	0.160479
$601$	8.45760e9	1.58923	0.794614	−	0.607115i	$-0.207673\pi$
$601$	8.45760e9	1.58923	0.794614	+	0.607115i	$0.207673\pi$
$602$	−3.93749e9	−0.735584
$603$	2.29026e9	0.425377
$604$	4.99278e9	0.921962
$605$	7.30929e9	1.34193
$606$	−9.40589e9	−1.71690
$607$	4.48826e9	0.814550	0.407275	−	0.913306i	$-0.366479\pi$
$607$	4.48826e9	0.814550	0.407275	+	0.913306i	$0.366479\pi$
$608$	−8.02129e9	−1.44738
$609$	2.49531e9	0.447677
$610$	−5.31499e9	−0.948087
$611$	−2.82109e8	−0.0500348
$612$	4.87404e9	0.859526
$613$	1.49137e9	0.261502	0.130751	−	0.991415i	$-0.458261\pi$
$613$	1.49137e9	0.261502	0.130751	+	0.991415i	$0.458261\pi$
$614$	5.54229e9	0.966273
$615$	1.09604e9	0.190004
$616$	−4.94136e9	−0.851754
$617$	6.09506e9	1.04467	0.522336	−	0.852740i	$-0.325061\pi$
$617$	6.09506e9	1.04467	0.522336	+	0.852740i	$0.325061\pi$
$618$	−9.82774e9	−1.67492
$619$	3.75791e9	0.636839	0.318419	−	0.947950i	$-0.396848\pi$
$619$	3.75791e9	0.636839	0.318419	+	0.947950i	$0.396848\pi$
$620$	−2.83963e9	−0.478510
$621$	2.17700e10	3.64785
$622$	−3.06890e9	−0.511348
$623$	1.37998e10	2.28647
$624$	2.49169e9	0.410533
$625$	−4.42762e9	−0.725421
$626$	9.59431e9	1.56316
$627$	−2.15898e10	−3.49794
$628$	6.30059e8	0.101513
$629$	−2.64312e9	−0.423487
$630$	−2.14376e10	−3.41573
$631$	9.72982e9	1.54171	0.770854	−	0.637012i	$-0.219830\pi$
$631$	9.72982e9	1.54171	0.770854	+	0.637012i	$0.219830\pi$
$632$	−1.19547e9	−0.188378
$633$	−4.41256e9	−0.691477
$634$	−5.93682e9	−0.925213
$635$	−8.69353e9	−1.34737
$636$	3.86980e9	0.596469
$637$	−9.93061e8	−0.152226
$638$	2.51810e9	0.383884
$639$	5.46255e9	0.828214
$640$	4.44116e9	0.669679
$641$	−1.09795e10	−1.64657	−0.823286	−	0.567626i	$-0.807862\pi$
$641$	−1.09795e10	−1.64657	−0.823286	+	0.567626i	$0.807862\pi$
$642$	8.42624e9	1.25679
$643$	−5.68737e9	−0.843672	−0.421836	−	0.906672i	$-0.638614\pi$
$643$	−5.68737e9	−0.843672	−0.421836	+	0.906672i	$0.638614\pi$
$644$	−1.05541e10	−1.55712
$645$	4.52780e9	0.664398
$646$	6.11884e9	0.893008
$647$	−5.88262e9	−0.853898	−0.426949	−	0.904276i	$-0.640412\pi$
$647$	−5.88262e9	−0.853898	−0.426949	+	0.904276i	$0.640412\pi$
$648$	−4.69496e9	−0.677828
$649$	−1.97820e10	−2.84063
$650$	3.85713e8	0.0550893
$651$	1.32959e10	1.88880
$652$	2.02556e9	0.286205
$653$	2.15643e9	0.303068	0.151534	−	0.988452i	$-0.451579\pi$
$653$	2.15643e9	0.303068	0.151534	+	0.988452i	$0.451579\pi$
$654$	4.86805e9	0.680507
$655$	−5.40690e9	−0.751802
$656$	−1.05447e9	−0.145838
$657$	−2.76023e10	−3.79722
$658$	−3.38823e9	−0.463642
$659$	9.02348e9	1.22822	0.614108	−	0.789222i	$-0.289516\pi$
$659$	9.02348e9	1.22822	0.614108	+	0.789222i	$0.289516\pi$
$660$	−1.28538e10	−1.74032
$661$	5.06123e9	0.681633	0.340816	−	0.940130i	$-0.389297\pi$
$661$	5.06123e9	0.681633	0.340816	+	0.940130i	$0.389297\pi$
$662$	−1.11672e10	−1.49603
$663$	−1.42021e9	−0.189258
$664$	−1.68774e9	−0.223727
$665$	−1.10204e10	−1.45319
$666$	−1.66647e10	−2.18594
$667$	−2.37755e9	−0.310234
$668$	−2.33294e9	−0.302821
$669$	3.39522e9	0.438405
$670$	1.71178e9	0.219880
$671$	1.02837e10	1.31408
$672$	2.23606e10	2.84244
$673$	4.42185e9	0.559180	0.279590	−	0.960120i	$-0.409802\pi$
$673$	4.42185e9	0.559180	0.279590	+	0.960120i	$0.409802\pi$
$674$	6.83932e9	0.860405
$675$	−3.91291e9	−0.489707
$676$	−5.37124e9	−0.668746
$677$	8.09269e8	0.100238	0.0501190	−	0.998743i	$-0.484040\pi$
$677$	8.09269e8	0.100238	0.0501190	+	0.998743i	$0.484040\pi$
$678$	3.43090e10	4.22770
$679$	−1.42579e10	−1.74788
$680$	−1.61040e9	−0.196405
$681$	6.60385e8	0.0801277
$682$	1.34173e10	1.61965
$683$	−5.46931e8	−0.0656841	−0.0328421	−	0.999461i	$-0.510456\pi$
$683$	−5.46931e8	−0.0656841	−0.0328421	+	0.999461i	$0.510456\pi$
$684$	1.57977e10	1.88754
$685$	−4.99484e9	−0.593751
$686$	2.86192e9	0.338472
$687$	−2.57378e10	−3.02847
$688$	−4.35610e9	−0.509962
$689$	−7.77114e8	−0.0905144
$690$	2.96378e10	3.43458
$691$	1.32395e10	1.52650	0.763250	−	0.646103i	$-0.223602\pi$
$691$	1.32395e10	1.52650	0.763250	+	0.646103i	$0.223602\pi$
$692$	−6.06752e9	−0.696049
$693$	4.14785e10	4.73431
$694$	−9.20934e9	−1.04585
$695$	5.76003e9	0.650845
$696$	1.18186e9	0.132872
$697$	6.01026e8	0.0672324
$698$	2.28486e9	0.254311
$699$	−3.17586e9	−0.351715
$700$	1.89699e9	0.209036
$701$	1.24027e10	1.35988	0.679942	−	0.733265i	$-0.262005\pi$
$701$	1.24027e10	1.35988	0.679942	+	0.733265i	$0.262005\pi$
$702$	−4.91596e9	−0.536325
$703$	−8.56686e9	−0.929990
$704$	4.73175e9	0.511113
$705$	3.89619e9	0.418773
$706$	−8.45847e9	−0.904639
$707$	9.28961e9	0.988620
$708$	2.10030e10	2.22416
$709$	−3.01212e9	−0.317403	−0.158701	−	0.987327i	$-0.550731\pi$
$709$	−3.01212e9	−0.317403	−0.158701	+	0.987327i	$0.550731\pi$
$710$	4.08281e9	0.428109
$711$	1.00350e10	1.04706
$712$	6.53602e9	0.678630
$713$	−1.26684e10	−1.30891
$714$	−1.70573e10	−1.75374
$715$	2.58125e9	0.264094
$716$	1.89144e9	0.192574
$717$	−1.65994e10	−1.68180
$718$	−2.35696e10	−2.37639
$719$	−8.79647e9	−0.882586	−0.441293	−	0.897363i	$-0.645480\pi$
$719$	−8.79647e9	−0.882586	−0.441293	+	0.897363i	$0.645480\pi$
$720$	−2.37166e10	−2.36804
$721$	9.70624e9	0.964446
$722$	6.67198e9	0.659743
$723$	1.01864e10	1.00239
$724$	2.73554e9	0.267891
$725$	4.27338e8	0.0416475
$726$	3.66682e10	3.55641
$727$	−3.18103e9	−0.307042	−0.153521	−	0.988145i	$-0.549061\pi$
$727$	−3.18103e9	−0.307042	−0.153521	+	0.988145i	$0.549061\pi$
$728$	−1.05355e9	−0.101203
$729$	−1.55754e9	−0.148899
$730$	−2.06304e10	−1.96281
$731$	2.48288e9	0.235095
$732$	−1.09184e10	−1.02890
$733$	−9.47751e9	−0.888854	−0.444427	−	0.895815i	$-0.646593\pi$
$733$	−9.47751e9	−0.888854	−0.444427	+	0.895815i	$0.646593\pi$
$734$	7.66993e9	0.715905
$735$	1.37151e10	1.27407
$736$	−2.13053e10	−1.96977
$737$	−3.31204e9	−0.304761
$738$	3.78943e9	0.347038
$739$	2.11846e10	1.93092	0.965461	−	0.260548i	$-0.0839032\pi$
$739$	2.11846e10	1.93092	0.965461	+	0.260548i	$0.0839032\pi$
$740$	−5.10041e9	−0.462695
$741$	−4.60316e9	−0.415616
$742$	−9.33345e9	−0.838742
$743$	1.87367e10	1.67584	0.837921	−	0.545791i	$-0.183771\pi$
$743$	1.87367e10	1.67584	0.837921	+	0.545791i	$0.183771\pi$
$744$	6.29736e9	0.560600
$745$	−1.14252e10	−1.01231
$746$	−1.09274e10	−0.963673
$747$	1.41672e10	1.24354
$748$	−7.04855e9	−0.615807
$749$	−8.32207e9	−0.723677
$750$	−2.90791e10	−2.51690
$751$	4.63651e9	0.399440	0.199720	−	0.979853i	$-0.435997\pi$
$751$	4.63651e9	0.399440	0.199720	+	0.979853i	$0.435997\pi$
$752$	−3.74844e9	−0.321431
$753$	−1.03303e10	−0.881721
$754$	5.36883e8	0.0456121
$755$	1.38473e10	1.17098
$756$	−2.41773e10	−2.03508
$757$	2.07851e10	1.74147	0.870736	−	0.491752i	$-0.163643\pi$
$757$	2.07851e10	1.74147	0.870736	+	0.491752i	$0.163643\pi$
$758$	1.80443e10	1.50487
$759$	−5.73447e10	−4.76044
$760$	−5.21961e9	−0.431311
$761$	−1.99241e10	−1.63882	−0.819411	−	0.573207i	$-0.805699\pi$
$761$	−1.99241e10	−1.63882	−0.819411	+	0.573207i	$0.805699\pi$
$762$	−4.36125e10	−3.57082
$763$	−4.80787e9	−0.391847
$764$	1.36911e10	1.11074
$765$	1.35179e10	1.09168
$766$	7.55299e9	0.607181
$767$	−4.21773e9	−0.337516
$768$	2.95244e10	2.35189
$769$	−1.38121e9	−0.109526	−0.0547632	−	0.998499i	$-0.517440\pi$
$769$	−1.38121e9	−0.109526	−0.0547632	+	0.998499i	$0.517440\pi$
$770$	3.10018e10	2.44720
$771$	2.69548e10	2.11810
$772$	1.17791e10	0.921408
$773$	−9.41220e9	−0.732931	−0.366465	−	0.930432i	$-0.619432\pi$
$773$	−9.41220e9	−0.732931	−0.366465	+	0.930432i	$0.619432\pi$
$774$	1.56544e10	1.21351
$775$	2.27701e9	0.175715
$776$	−6.75299e9	−0.518777
$777$	2.38815e10	1.82637
$778$	1.66247e10	1.26568
$779$	1.94804e9	0.147644
$780$	−2.74056e9	−0.206780
$781$	−7.89963e9	−0.593373
$782$	1.62522e10	1.21532
$783$	−5.44648e9	−0.405462
$784$	−1.31950e10	−0.977922
$785$	1.74744e9	0.128931
$786$	−2.71246e10	−1.99243
$787$	1.19074e10	0.870777	0.435389	−	0.900243i	$-0.356611\pi$
$787$	1.19074e10	0.870777	0.435389	+	0.900243i	$0.356611\pi$
$788$	−6.87906e9	−0.500827
$789$	−2.24370e10	−1.62628
$790$	7.50033e9	0.541234
$791$	−3.38849e10	−2.43438
$792$	1.96455e10	1.40515
$793$	2.19259e9	0.156135
$794$	−3.10317e10	−2.20006
$795$	1.07327e10	0.757573
$796$	−2.18306e9	−0.153416
$797$	1.26669e10	0.886267	0.443134	−	0.896456i	$-0.353867\pi$
$797$	1.26669e10	0.886267	0.443134	+	0.896456i	$0.353867\pi$
$798$	−5.52858e10	−3.85126
$799$	2.13653e9	0.148182
$800$	3.82940e9	0.264433
$801$	−5.48643e10	−3.77203
$802$	2.07000e10	1.41697
$803$	3.99168e10	2.72052
$804$	3.51646e9	0.238622
$805$	−2.92714e10	−1.97769
$806$	2.86071e9	0.192442
$807$	4.83293e10	3.23707
$808$	4.39984e9	0.293425
$809$	7.12830e9	0.473332	0.236666	−	0.971591i	$-0.423945\pi$
$809$	7.12830e9	0.473332	0.236666	+	0.971591i	$0.423945\pi$
$810$	2.94559e10	1.94749
$811$	1.11604e10	0.734695	0.367347	−	0.930084i	$-0.380266\pi$
$811$	1.11604e10	0.734695	0.367347	+	0.930084i	$0.380266\pi$
$812$	2.64047e9	0.173075
$813$	−1.99400e10	−1.30139
$814$	2.40996e10	1.56612
$815$	5.61779e9	0.363508
$816$	−1.88706e10	−1.21582
$817$	8.04747e9	0.516276
$818$	−1.00784e10	−0.643804
$819$	8.84362e9	0.562518
$820$	1.15979e9	0.0734569
$821$	−1.28292e9	−0.0809093	−0.0404547	−	0.999181i	$-0.512881\pi$
$821$	−1.28292e9	−0.0809093	−0.0404547	+	0.999181i	$0.512881\pi$
$822$	−2.50574e10	−1.57356
$823$	1.22536e10	0.766239	0.383120	−	0.923699i	$-0.374850\pi$
$823$	1.22536e10	0.766239	0.383120	+	0.923699i	$0.374850\pi$
$824$	4.59717e9	0.286250
$825$	1.03071e10	0.639068
$826$	−5.06565e10	−3.12756
$827$	−2.77712e10	−1.70736	−0.853682	−	0.520795i	$-0.825636\pi$
$827$	−2.77712e10	−1.70736	−0.853682	+	0.520795i	$0.825636\pi$
$828$	4.19602e10	2.56881
$829$	−5.29906e9	−0.323041	−0.161521	−	0.986869i	$-0.551640\pi$
$829$	−5.29906e9	−0.323041	−0.161521	+	0.986869i	$0.551640\pi$
$830$	1.05888e10	0.642796
$831$	6.04972e9	0.365706
$832$	1.00886e9	0.0607292
$833$	7.52087e9	0.450828
$834$	2.88961e10	1.72488
$835$	−6.47031e9	−0.384612
$836$	−2.28457e10	−1.35233
$837$	−2.90208e10	−1.71069
$838$	2.11426e10	1.24109
$839$	8.48591e9	0.496057	0.248029	−	0.968753i	$-0.420217\pi$
$839$	8.48591e9	0.496057	0.248029	+	0.968753i	$0.420217\pi$
$840$	1.45505e10	0.847035
$841$	5.94823e8	0.0344828
$842$	2.25082e10	1.29942
$843$	−3.00138e10	−1.72554
$844$	−4.66924e9	−0.267330
$845$	−1.48969e10	−0.849372
$846$	1.34707e10	0.764879
$847$	−3.62149e10	−2.04784
$848$	−1.03257e10	−0.581479
$849$	1.17224e10	0.657414
$850$	−2.92116e9	−0.163151
$851$	−2.27544e10	−1.26565
$852$	8.38720e9	0.464599
$853$	−1.34313e10	−0.740960	−0.370480	−	0.928840i	$-0.620807\pi$
$853$	−1.34313e10	−0.740960	−0.370480	+	0.928840i	$0.620807\pi$
$854$	2.63339e10	1.44681
$855$	4.38142e10	2.39736
$856$	−3.94159e9	−0.214789
$857$	−9.53625e9	−0.517541	−0.258771	−	0.965939i	$-0.583317\pi$
$857$	−9.53625e9	−0.517541	−0.258771	+	0.965939i	$0.583317\pi$
$858$	1.29492e10	0.699904
$859$	−5.40501e9	−0.290951	−0.145476	−	0.989362i	$-0.546471\pi$
$859$	−5.40501e9	−0.290951	−0.145476	+	0.989362i	$0.546471\pi$
$860$	4.79118e9	0.256861
$861$	−5.43047e9	−0.289952
$862$	3.19313e10	1.69801
$863$	−1.71726e10	−0.909489	−0.454745	−	0.890622i	$-0.650269\pi$
$863$	−1.71726e10	−0.909489	−0.454745	+	0.890622i	$0.650269\pi$
$864$	−4.88062e10	−2.57441
$865$	−1.68280e10	−0.884048
$866$	1.65021e10	0.863430
$867$	−2.36644e10	−1.23318
$868$	1.40694e10	0.730222
$869$	−1.45120e10	−0.750168
$870$	−7.41488e9	−0.381757
$871$	−7.06160e8	−0.0362109
$872$	−2.27715e9	−0.116301
$873$	5.66856e10	2.88352
$874$	5.26766e10	2.66887
$875$	2.87196e10	1.44927
$876$	−4.23806e10	−2.13011
$877$	2.69807e10	1.35069	0.675344	−	0.737503i	$-0.263995\pi$
$877$	2.69807e10	1.35069	0.675344	+	0.737503i	$0.263995\pi$
$878$	−1.19641e9	−0.0596555
$879$	6.07209e9	0.301562
$880$	3.42976e10	1.69658
$881$	4.04415e9	0.199256	0.0996280	−	0.995025i	$-0.468235\pi$
$881$	4.04415e9	0.199256	0.0996280	+	0.995025i	$0.468235\pi$
$882$	4.74186e10	2.32707
$883$	−5.10344e8	−0.0249460	−0.0124730	−	0.999922i	$-0.503970\pi$
$883$	−5.10344e8	−0.0249460	−0.0124730	+	0.999922i	$0.503970\pi$
$884$	−1.50282e9	−0.0731686
$885$	5.82509e10	2.82489
$886$	1.39240e10	0.672583
$887$	−3.13533e10	−1.50852	−0.754259	−	0.656577i	$-0.772004\pi$
$887$	−3.13533e10	−1.50852	−0.754259	+	0.656577i	$0.772004\pi$
$888$	1.13110e10	0.542071
$889$	4.30733e10	2.05614
$890$	−4.10065e10	−1.94979
$891$	−5.69928e10	−2.69928
$892$	3.59272e9	0.169491
$893$	6.92489e9	0.325411
$894$	−5.73161e10	−2.68285
$895$	5.24582e9	0.244587
$896$	−2.20044e10	−1.02195
$897$	−1.22265e10	−0.565623
$898$	−2.66145e10	−1.22646
$899$	3.16943e9	0.145486
$900$	−7.54189e9	−0.344851
$901$	5.88541e9	0.268065
$902$	−5.48006e9	−0.248635
$903$	−2.24336e10	−1.01389
$904$	−1.60489e10	−0.722530
$905$	7.58692e9	0.340248
$906$	6.94669e10	3.10334
$907$	−1.35006e10	−0.600798	−0.300399	−	0.953814i	$-0.597120\pi$
$907$	−1.35006e10	−0.600798	−0.300399	+	0.953814i	$0.597120\pi$
$908$	6.98800e8	0.0309779
$909$	−3.69329e10	−1.63095
$910$	6.60988e9	0.290770
$911$	−2.28467e10	−1.00117	−0.500586	−	0.865687i	$-0.666882\pi$
$911$	−2.28467e10	−1.00117	−0.500586	+	0.865687i	$0.666882\pi$
$912$	−6.11633e10	−2.66999
$913$	−2.04877e10	−0.890935
$914$	1.41055e10	0.611052
$915$	−3.02818e10	−1.30680
$916$	−2.72350e10	−1.17083
$917$	2.67892e10	1.14728
$918$	3.72306e10	1.58837
$919$	−1.30228e10	−0.553478	−0.276739	−	0.960945i	$-0.589254\pi$
$919$	−1.30228e10	−0.553478	−0.276739	+	0.960945i	$0.589254\pi$
$920$	−1.38638e10	−0.586983
$921$	3.15768e10	1.33186
$922$	−4.56782e10	−1.91934
$923$	−1.68428e9	−0.0705031
$924$	6.36861e10	2.65578
$925$	4.08986e9	0.169908
$926$	1.25173e10	0.518051
$927$	−3.85893e10	−1.59106
$928$	5.33025e9	0.218942
$929$	3.29603e10	1.34876	0.674382	−	0.738383i	$-0.264410\pi$
$929$	3.29603e10	1.34876	0.674382	+	0.738383i	$0.264410\pi$
$930$	−3.95092e10	−1.61067
$931$	2.43766e10	0.990030
$932$	−3.36060e9	−0.135975
$933$	−1.74849e10	−0.704818
$934$	5.89194e10	2.36616
$935$	−1.95489e10	−0.782133
$936$	4.18861e9	0.166957
$937$	3.23610e10	1.28509	0.642545	−	0.766248i	$-0.277879\pi$
$937$	3.23610e10	1.28509	0.642545	+	0.766248i	$0.277879\pi$
$938$	−8.48126e9	−0.335545
$939$	5.46630e10	2.15459
$940$	4.12284e9	0.161901
$941$	2.81702e10	1.10211	0.551056	−	0.834468i	$-0.314225\pi$
$941$	2.81702e10	1.10211	0.551056	+	0.834468i	$0.314225\pi$
$942$	8.76632e9	0.341695
$943$	5.17419e9	0.200933
$944$	−5.60419e10	−2.16826
$945$	−6.70548e10	−2.58475
$946$	−2.26385e10	−0.869416
$947$	−1.07072e10	−0.409687	−0.204844	−	0.978795i	$-0.565669\pi$
$947$	−1.07072e10	−0.409687	−0.204844	+	0.978795i	$0.565669\pi$
$948$	1.54077e10	0.587367
$949$	8.51067e9	0.323245
$950$	−9.46804e9	−0.358284
$951$	−3.38247e10	−1.27527
$952$	7.97896e9	0.299721
$953$	−2.64823e10	−0.991128	−0.495564	−	0.868571i	$-0.665039\pi$
$953$	−2.64823e10	−0.991128	−0.495564	+	0.868571i	$0.665039\pi$
$954$	3.71072e10	1.38369
$955$	3.79717e10	1.41075
$956$	−1.75649e10	−0.650196
$957$	1.43467e10	0.529127
$958$	−2.03283e10	−0.747002
$959$	2.47476e10	0.906083
$960$	−1.39333e10	−0.508281
$961$	−1.06247e10	−0.386177
$962$	5.13827e9	0.186082
$963$	3.30862e10	1.19386
$964$	1.07789e10	0.387530
$965$	3.26689e10	1.17028
$966$	−1.46845e11	−5.24129
$967$	2.46400e10	0.876291	0.438146	−	0.898904i	$-0.355635\pi$
$967$	2.46400e10	0.876291	0.438146	+	0.898904i	$0.355635\pi$
$968$	−1.71525e10	−0.607803
$969$	3.48617e10	1.23088
$970$	4.23678e10	1.49051
$971$	−2.22757e10	−0.780844	−0.390422	−	0.920636i	$-0.627671\pi$
$971$	−2.22757e10	−0.780844	−0.390422	+	0.920636i	$0.627671\pi$
$972$	1.71596e10	0.599343
$973$	−2.85389e10	−0.993212
$974$	−3.11160e10	−1.07901
$975$	2.19757e9	0.0759324
$976$	2.91335e10	1.00304
$977$	−1.31199e10	−0.450091	−0.225046	−	0.974348i	$-0.572253\pi$
$977$	−1.31199e10	−0.450091	−0.225046	+	0.974348i	$0.572253\pi$
$978$	2.81826e10	0.963373
$979$	7.93415e10	2.70247
$980$	1.45130e10	0.492566
$981$	1.91147e10	0.646438
$982$	−4.12094e10	−1.38869
$983$	−1.72080e10	−0.577821	−0.288910	−	0.957356i	$-0.593293\pi$
$983$	−1.72080e10	−0.577821	−0.288910	+	0.957356i	$0.593293\pi$
$984$	−2.57204e9	−0.0860586
$985$	−1.90788e10	−0.636098
$986$	−4.06604e9	−0.135084
$987$	−1.93042e10	−0.639062
$988$	−4.87093e9	−0.160680
$989$	2.13749e10	0.702614
$990$	−1.23254e11	−4.03719
$991$	4.31401e10	1.40807	0.704034	−	0.710167i	$-0.251380\pi$
$991$	4.31401e10	1.40807	0.704034	+	0.710167i	$0.251380\pi$
$992$	2.84015e10	0.923740
$993$	−6.36243e10	−2.06206
$994$	−2.02288e10	−0.653309
$995$	−6.05462e9	−0.194853
$996$	2.17523e10	0.697585
$997$	−1.86296e10	−0.595347	−0.297674	−	0.954668i	$-0.596211\pi$
$997$	−1.86296e10	−0.595347	−0.297674	+	0.954668i	$0.596211\pi$
$998$	−5.82251e10	−1.85419
$999$	−5.21258e10	−1.65415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.a.b.1.8	✓	10
3.2	odd	2		261.8.a.f.1.3		10
4.3	odd	2		464.8.a.g.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.a.b.1.8	✓	10	1.1	even	1	trivial
261.8.a.f.1.3		10	3.2	odd	2
464.8.a.g.1.1		10	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)

\(f(q)\)	\(=\)	\(q+14.7228 q^{2} +83.8824 q^{3} +88.7619 q^{4} +246.177 q^{5} +1234.99 q^{6} -1219.72 q^{7} -577.696 q^{8} +4849.26 q^{9} +O(q^{10})\)	\(q+14.7228 q^{2} +83.8824 q^{3} +88.7619 q^{4} +246.177 q^{5} +1234.99 q^{6} -1219.72 q^{7} -577.696 q^{8} +4849.26 q^{9} +3624.43 q^{10} -7012.73 q^{11} +7445.56 q^{12} -1495.18 q^{13} -17957.7 q^{14} +20649.9 q^{15} -19866.8 q^{16} +11323.7 q^{17} +71394.9 q^{18} +36702.1 q^{19} +21851.2 q^{20} -102313. q^{21} -103247. q^{22} +97484.5 q^{23} -48458.6 q^{24} -17521.8 q^{25} -22013.3 q^{26} +223317. q^{27} -108265. q^{28} -24389.0 q^{29} +304026. q^{30} -129953. q^{31} -218551. q^{32} -588245. q^{33} +166716. q^{34} -300267. q^{35} +430430. q^{36} -233416. q^{37} +540359. q^{38} -125420. q^{39} -142216. q^{40} +53077.0 q^{41} -1.50634e6 q^{42} +219265. q^{43} -622463. q^{44} +1.19378e6 q^{45} +1.43525e6 q^{46} +188678. q^{47} -1.66648e6 q^{48} +664173. q^{49} -257970. q^{50} +949856. q^{51} -132715. q^{52} +519745. q^{53} +3.28786e6 q^{54} -1.72637e6 q^{55} +704628. q^{56} +3.07866e6 q^{57} -359075. q^{58} +2.82088e6 q^{59} +1.83293e6 q^{60} -1.46644e6 q^{61} -1.91328e6 q^{62} -5.91474e6 q^{63} -674737. q^{64} -368080. q^{65} -8.66063e6 q^{66} +472290. q^{67} +1.00511e6 q^{68} +8.17723e6 q^{69} -4.42079e6 q^{70} +1.12647e6 q^{71} -2.80140e6 q^{72} -5.69206e6 q^{73} -3.43655e6 q^{74} -1.46977e6 q^{75} +3.25775e6 q^{76} +8.55356e6 q^{77} -1.84653e6 q^{78} +2.06938e6 q^{79} -4.89077e6 q^{80} +8.12705e6 q^{81} +781444. q^{82} +2.92151e6 q^{83} -9.08150e6 q^{84} +2.78763e6 q^{85} +3.22820e6 q^{86} -2.04581e6 q^{87} +4.05123e6 q^{88} -1.13139e7 q^{89} +1.75758e7 q^{90} +1.82370e6 q^{91} +8.65290e6 q^{92} -1.09008e7 q^{93} +2.77788e6 q^{94} +9.03522e6 q^{95} -1.83326e7 q^{96} +1.16895e7 q^{97} +9.77852e6 q^{98} -3.40066e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9} + 8496 q^{10} + 7384 q^{11} + 49720 q^{12} + 20820 q^{13} + 50976 q^{14} + 43516 q^{15} + 122082 q^{16} - 11620 q^{17} + 66060 q^{18} + 75068 q^{19} - 42914 q^{20} + 51480 q^{21} - 36950 q^{22} + 62040 q^{23} - 205942 q^{24} + 261022 q^{25} - 201528 q^{26} - 28060 q^{27} - 24980 q^{28} - 243890 q^{29} - 1284894 q^{30} + 200600 q^{31} - 1761460 q^{32} - 1068000 q^{33} - 503932 q^{34} + 107528 q^{35} - 26300 q^{36} - 367740 q^{37} + 766880 q^{38} + 392692 q^{39} - 865000 q^{40} + 932764 q^{41} - 2058060 q^{42} + 1443560 q^{43} - 1325912 q^{44} + 4245684 q^{45} + 1760460 q^{46} - 286960 q^{47} + 3187120 q^{48} + 4713194 q^{49} - 3682652 q^{50} + 1451016 q^{51} + 2560210 q^{52} + 3953220 q^{53} - 3147534 q^{54} + 3981316 q^{55} + 2082464 q^{56} + 2050640 q^{57} + 6712320 q^{59} + 7476756 q^{60} + 1905196 q^{61} - 8048490 q^{62} + 3643800 q^{63} + 8445458 q^{64} + 4667544 q^{65} - 12425580 q^{66} - 2718200 q^{67} - 17699740 q^{68} + 1109064 q^{69} - 30441624 q^{70} + 3447736 q^{71} - 22466840 q^{72} - 2554460 q^{73} - 4214584 q^{74} + 1088084 q^{75} - 8294848 q^{76} - 3967800 q^{77} - 24809970 q^{78} + 4187744 q^{79} - 17715290 q^{80} + 5161402 q^{81} + 7020500 q^{82} + 3498720 q^{83} + 22947224 q^{84} + 1817072 q^{85} - 361638 q^{86} - 1951120 q^{87} + 15118470 q^{88} - 303268 q^{89} - 28959160 q^{90} + 27215080 q^{91} - 10783380 q^{92} + 1097360 q^{93} + 55641726 q^{94} - 8810536 q^{95} - 53327238 q^{96} + 4908620 q^{97} + 40120080 q^{98} - 14408716 q^{99}+O(q^{100}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9 + 8496 * q^10 + 7384 * q^11 + 49720 * q^12 + 20820 * q^13 + 50976 * q^14 + 43516 * q^15 + 122082 * q^16 - 11620 * q^17 + 66060 * q^18 + 75068 * q^19 - 42914 * q^20 + 51480 * q^21 - 36950 * q^22 + 62040 * q^23 - 205942 * q^24 + 261022 * q^25 - 201528 * q^26 - 28060 * q^27 - 24980 * q^28 - 243890 * q^29 - 1284894 * q^30 + 200600 * q^31 - 1761460 * q^32 - 1068000 * q^33 - 503932 * q^34 + 107528 * q^35 - 26300 * q^36 - 367740 * q^37 + 766880 * q^38 + 392692 * q^39 - 865000 * q^40 + 932764 * q^41 - 2058060 * q^42 + 1443560 * q^43 - 1325912 * q^44 + 4245684 * q^45 + 1760460 * q^46 - 286960 * q^47 + 3187120 * q^48 + 4713194 * q^49 - 3682652 * q^50 + 1451016 * q^51 + 2560210 * q^52 + 3953220 * q^53 - 3147534 * q^54 + 3981316 * q^55 + 2082464 * q^56 + 2050640 * q^57 + 6712320 * q^59 + 7476756 * q^60 + 1905196 * q^61 - 8048490 * q^62 + 3643800 * q^63 + 8445458 * q^64 + 4667544 * q^65 - 12425580 * q^66 - 2718200 * q^67 - 17699740 * q^68 + 1109064 * q^69 - 30441624 * q^70 + 3447736 * q^71 - 22466840 * q^72 - 2554460 * q^73 - 4214584 * q^74 + 1088084 * q^75 - 8294848 * q^76 - 3967800 * q^77 - 24809970 * q^78 + 4187744 * q^79 - 17715290 * q^80 + 5161402 * q^81 + 7020500 * q^82 + 3498720 * q^83 + 22947224 * q^84 + 1817072 * q^85 - 361638 * q^86 - 1951120 * q^87 + 15118470 * q^88 - 303268 * q^89 - 28959160 * q^90 + 27215080 * q^91 - 10783380 * q^92 + 1097360 * q^93 + 55641726 * q^94 - 8810536 * q^95 - 53327238 * q^96 + 4908620 * q^97 + 40120080 * q^98 - 14408716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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