LMFDB - Embedded newform 29.6.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,6,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, 6, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 6 $
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:	$4.65113077458$
Analytic rank:	$0$
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} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 $ x^7 - 3x^6 - 184x^5 + 584x^4 + 10145x^3 - 34491x^2 - 149754x + 524902
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-8.92709$ 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)

$f(q)$	$=$	$q+9.92709 q^{2} +15.4219 q^{3} +66.5471 q^{4} -58.0818 q^{5} +153.094 q^{6} -210.388 q^{7} +342.952 q^{8} -5.16616 q^{9} +O(q^{10})$	\(q+9.92709 q^{2} +15.4219 q^{3} +66.5471 q^{4} -58.0818 q^{5} +153.094 q^{6} -210.388 q^{7} +342.952 q^{8} -5.16616 q^{9} -576.583 q^{10} +527.254 q^{11} +1026.28 q^{12} -92.3017 q^{13} -2088.54 q^{14} -895.729 q^{15} +1275.01 q^{16} +1791.54 q^{17} -51.2849 q^{18} +1639.87 q^{19} -3865.17 q^{20} -3244.57 q^{21} +5234.10 q^{22} -2765.87 q^{23} +5288.96 q^{24} +248.491 q^{25} -916.287 q^{26} -3827.18 q^{27} -14000.7 q^{28} +841.000 q^{29} -8891.98 q^{30} +689.400 q^{31} +1682.66 q^{32} +8131.24 q^{33} +17784.8 q^{34} +12219.7 q^{35} -343.793 q^{36} -1274.51 q^{37} +16279.2 q^{38} -1423.46 q^{39} -19919.3 q^{40} +18048.8 q^{41} -32209.1 q^{42} -6419.14 q^{43} +35087.2 q^{44} +300.060 q^{45} -27457.0 q^{46} +2066.40 q^{47} +19663.0 q^{48} +27456.0 q^{49} +2466.79 q^{50} +27628.8 q^{51} -6142.41 q^{52} -28738.1 q^{53} -37992.8 q^{54} -30623.8 q^{55} -72152.9 q^{56} +25289.9 q^{57} +8348.68 q^{58} -34729.5 q^{59} -59608.2 q^{60} +35599.4 q^{61} +6843.74 q^{62} +1086.90 q^{63} -24096.4 q^{64} +5361.05 q^{65} +80719.5 q^{66} -18011.5 q^{67} +119222. q^{68} -42654.9 q^{69} +121306. q^{70} +4174.40 q^{71} -1771.75 q^{72} -55919.3 q^{73} -12652.2 q^{74} +3832.19 q^{75} +109129. q^{76} -110928. q^{77} -14130.9 q^{78} +96202.6 q^{79} -74054.8 q^{80} -57766.9 q^{81} +179172. q^{82} +67821.3 q^{83} -215917. q^{84} -104056. q^{85} -63723.4 q^{86} +12969.8 q^{87} +180823. q^{88} -78390.8 q^{89} +2978.72 q^{90} +19419.1 q^{91} -184061. q^{92} +10631.8 q^{93} +20513.3 q^{94} -95246.6 q^{95} +25949.8 q^{96} -10374.5 q^{97} +272558. q^{98} -2723.88 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9	\( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9} + 922 q^{10} + 1106 q^{11} + 214 q^{12} + 408 q^{13} - 2008 q^{14} - 614 q^{15} + 242 q^{16} - 874 q^{17} - 5598 q^{18} + 4288 q^{19} - 6350 q^{20} - 4200 q^{21} - 6114 q^{22} - 4532 q^{23} - 4318 q^{24} + 5527 q^{25} - 19806 q^{26} + 5942 q^{27} - 496 q^{28} + 5887 q^{29} - 16734 q^{30} + 7794 q^{31} + 7898 q^{32} + 34410 q^{33} + 20840 q^{34} + 7088 q^{35} - 572 q^{36} + 5086 q^{37} + 23732 q^{38} + 33394 q^{39} + 22906 q^{40} + 19826 q^{41} - 55440 q^{42} + 19498 q^{43} - 6074 q^{44} + 7854 q^{45} - 12404 q^{46} + 14278 q^{47} - 16406 q^{48} + 38431 q^{49} - 41066 q^{50} + 23892 q^{51} - 34302 q^{52} - 58644 q^{53} - 31194 q^{54} - 25574 q^{55} - 79560 q^{56} - 88540 q^{57} + 3364 q^{58} + 12888 q^{59} - 180822 q^{60} + 102866 q^{61} - 42654 q^{62} - 88632 q^{63} - 10170 q^{64} - 149206 q^{65} + 7710 q^{66} + 102996 q^{67} + 85100 q^{68} - 107244 q^{69} + 349480 q^{70} - 51596 q^{71} + 135568 q^{72} - 17566 q^{73} + 12132 q^{74} + 39356 q^{75} + 360740 q^{76} - 94104 q^{77} + 46386 q^{78} + 212058 q^{79} + 142510 q^{80} - 128285 q^{81} + 201924 q^{82} - 122928 q^{83} - 12328 q^{84} - 109336 q^{85} - 63290 q^{86} + 21866 q^{87} + 136666 q^{88} - 66510 q^{89} + 56084 q^{90} + 194368 q^{91} - 110108 q^{92} - 474274 q^{93} + 438926 q^{94} - 131676 q^{95} - 117018 q^{96} - 118182 q^{97} - 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9 + 922 * q^10 + 1106 * q^11 + 214 * q^12 + 408 * q^13 - 2008 * q^14 - 614 * q^15 + 242 * q^16 - 874 * q^17 - 5598 * q^18 + 4288 * q^19 - 6350 * q^20 - 4200 * q^21 - 6114 * q^22 - 4532 * q^23 - 4318 * q^24 + 5527 * q^25 - 19806 * q^26 + 5942 * q^27 - 496 * q^28 + 5887 * q^29 - 16734 * q^30 + 7794 * q^31 + 7898 * q^32 + 34410 * q^33 + 20840 * q^34 + 7088 * q^35 - 572 * q^36 + 5086 * q^37 + 23732 * q^38 + 33394 * q^39 + 22906 * q^40 + 19826 * q^41 - 55440 * q^42 + 19498 * q^43 - 6074 * q^44 + 7854 * q^45 - 12404 * q^46 + 14278 * q^47 - 16406 * q^48 + 38431 * q^49 - 41066 * q^50 + 23892 * q^51 - 34302 * q^52 - 58644 * q^53 - 31194 * q^54 - 25574 * q^55 - 79560 * q^56 - 88540 * q^57 + 3364 * q^58 + 12888 * q^59 - 180822 * q^60 + 102866 * q^61 - 42654 * q^62 - 88632 * q^63 - 10170 * q^64 - 149206 * q^65 + 7710 * q^66 + 102996 * q^67 + 85100 * q^68 - 107244 * q^69 + 349480 * q^70 - 51596 * q^71 + 135568 * q^72 - 17566 * q^73 + 12132 * q^74 + 39356 * q^75 + 360740 * q^76 - 94104 * q^77 + 46386 * q^78 + 212058 * q^79 + 142510 * q^80 - 128285 * q^81 + 201924 * q^82 - 122928 * q^83 - 12328 * q^84 - 109336 * q^85 - 63290 * q^86 + 21866 * q^87 + 136666 * q^88 - 66510 * q^89 + 56084 * q^90 + 194368 * q^91 - 110108 * q^92 - 474274 * q^93 + 438926 * q^94 - 131676 * q^95 - 117018 * q^96 - 118182 * q^97 - 29132 * q^98 + 300668 * 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 $

$2$	9.92709	1.75488	0.877439	−	0.479688i	$-0.159250\pi$
$2$	9.92709	1.75488	0.877439	+	0.479688i	$0.159250\pi$
$3$	15.4219	0.989313	0.494656	−	0.869089i	$-0.335294\pi$
$3$	15.4219	0.989313	0.494656	+	0.869089i	$0.335294\pi$
$4$	66.5471	2.07960
$5$	−58.0818	−1.03900	−0.519499	−	0.854471i	$-0.673881\pi$
$5$	−58.0818	−1.03900	−0.519499	+	0.854471i	$0.673881\pi$
$6$	153.094	1.73612
$7$	−210.388	−1.62284	−0.811419	−	0.584464i	$-0.801305\pi$
$7$	−210.388	−1.62284	−0.811419	+	0.584464i	$0.801305\pi$
$8$	342.952	1.89456
$9$	−5.16616	−0.0212599
$10$	−576.583	−1.82331
$11$	527.254	1.31383	0.656914	−	0.753966i	$-0.271862\pi$
$11$	527.254	1.31383	0.656914	+	0.753966i	$0.271862\pi$
$12$	1026.28	2.05737
$13$	−92.3017	−0.151479	−0.0757393	−	0.997128i	$-0.524132\pi$
$13$	−92.3017	−0.151479	−0.0757393	+	0.997128i	$0.524132\pi$
$14$	−2088.54	−2.84788
$15$	−895.729	−1.02789
$16$	1275.01	1.24513
$17$	1791.54	1.50350	0.751750	−	0.659448i	$-0.229210\pi$
$17$	1791.54	1.50350	0.751750	+	0.659448i	$0.229210\pi$
$18$	−51.2849	−0.0373086
$19$	1639.87	1.04214	0.521070	−	0.853514i	$-0.325533\pi$
$19$	1639.87	1.04214	0.521070	+	0.853514i	$0.325533\pi$
$20$	−3865.17	−2.16070
$21$	−3244.57	−1.60550
$22$	5234.10	2.30561
$23$	−2765.87	−1.09021	−0.545107	−	0.838366i	$-0.683511\pi$
$23$	−2765.87	−1.09021	−0.545107	+	0.838366i	$0.683511\pi$
$24$	5288.96	1.87431
$25$	248.491	0.0795171
$26$	−916.287	−0.265827
$27$	−3827.18	−1.01035
$28$	−14000.7	−3.37485
$29$	841.000	0.185695
$29$	841.000	0.185695
$30$	−8891.98	−1.80383
$31$	689.400	0.128845	0.0644224	−	0.997923i	$-0.479479\pi$
$31$	689.400	0.128845	0.0644224	+	0.997923i	$0.479479\pi$
$32$	1682.66	0.290484
$33$	8131.24	1.29979
$34$	17784.8	2.63846
$35$	12219.7	1.68613
$36$	−343.793	−0.0442121
$37$	−1274.51	−0.153052	−0.0765260	−	0.997068i	$-0.524383\pi$
$37$	−1274.51	−0.153052	−0.0765260	+	0.997068i	$0.524383\pi$
$38$	16279.2	1.82883
$39$	−1423.46	−0.149860
$40$	−19919.3	−1.96845
$41$	18048.8	1.67683	0.838414	−	0.545034i	$-0.183483\pi$
$41$	18048.8	1.67683	0.838414	+	0.545034i	$0.183483\pi$
$42$	−32209.1	−2.81745
$43$	−6419.14	−0.529427	−0.264713	−	0.964327i	$-0.585277\pi$
$43$	−6419.14	−0.529427	−0.264713	+	0.964327i	$0.585277\pi$
$44$	35087.2	2.73223
$45$	300.060	0.0220890
$46$	−27457.0	−1.91319
$47$	2066.40	0.136449	0.0682244	−	0.997670i	$-0.478267\pi$
$47$	2066.40	0.136449	0.0682244	+	0.997670i	$0.478267\pi$
$48$	19663.0	1.23182
$49$	27456.0	1.63361
$50$	2466.79	0.139543
$51$	27628.8	1.48743
$52$	−6142.41	−0.315015
$53$	−28738.1	−1.40530	−0.702650	−	0.711536i	$-0.748000\pi$
$53$	−28738.1	−1.40530	−0.702650	+	0.711536i	$0.748000\pi$
$54$	−37992.8	−1.77303
$55$	−30623.8	−1.36506
$56$	−72152.9	−3.07457
$57$	25289.9	1.03100
$58$	8348.68	0.325873
$59$	−34729.5	−1.29888	−0.649439	−	0.760414i	$-0.724996\pi$
$59$	−34729.5	−1.29888	−0.649439	+	0.760414i	$0.724996\pi$
$60$	−59608.2	−2.13761
$61$	35599.4	1.22495	0.612475	−	0.790490i	$-0.290174\pi$
$61$	35599.4	1.22495	0.612475	+	0.790490i	$0.290174\pi$
$62$	6843.74	0.226107
$63$	1086.90	0.0345014
$64$	−24096.4	−0.735362
$65$	5361.05	0.157386
$66$	80719.5	2.28097
$67$	−18011.5	−0.490189	−0.245095	−	0.969499i	$-0.578819\pi$
$67$	−18011.5	−0.490189	−0.245095	+	0.969499i	$0.578819\pi$
$68$	119222.	3.12668
$69$	−42654.9	−1.07856
$70$	121306.	2.95895
$71$	4174.40	0.0982762	0.0491381	−	0.998792i	$-0.484353\pi$
$71$	4174.40	0.0982762	0.0491381	+	0.998792i	$0.484353\pi$
$72$	−1771.75	−0.0402782
$73$	−55919.3	−1.22816	−0.614080	−	0.789244i	$-0.710473\pi$
$73$	−55919.3	−1.22816	−0.614080	+	0.789244i	$0.710473\pi$
$74$	−12652.2	−0.268588
$75$	3832.19	0.0786673
$76$	109129.	2.16723
$77$	−110928.	−2.13213
$78$	−14130.9	−0.262986
$79$	96202.6	1.73428	0.867139	−	0.498066i	$-0.165956\pi$
$79$	96202.6	1.73428	0.867139	+	0.498066i	$0.165956\pi$
$80$	−74054.8	−1.29368
$81$	−57766.9	−0.978288
$82$	179172.	2.94263
$83$	67821.3	1.08061	0.540307	−	0.841468i	$-0.318308\pi$
$83$	67821.3	1.08061	0.540307	+	0.841468i	$0.318308\pi$
$84$	−215917.	−3.33878
$85$	−104056.	−1.56213
$86$	−63723.4	−0.929079
$87$	12969.8	0.183711
$88$	180823.	2.48913
$89$	−78390.8	−1.04904	−0.524518	−	0.851400i	$-0.675754\pi$
$89$	−78390.8	−1.04904	−0.524518	+	0.851400i	$0.675754\pi$
$90$	2978.72	0.0387635
$91$	19419.1	0.245825
$92$	−184061.	−2.26721
$93$	10631.8	0.127468
$94$	20513.3	0.239451
$95$	−95246.6	−1.08278
$96$	25949.8	0.287380
$97$	−10374.5	−0.111953	−0.0559765	−	0.998432i	$-0.517827\pi$
$97$	−10374.5	−0.111953	−0.0559765	+	0.998432i	$0.517827\pi$
$98$	272558.	2.86678
$99$	−2723.88	−0.0279319
$100$	16536.3	0.165363
$101$	−15354.8	−0.149776	−0.0748880	−	0.997192i	$-0.523860\pi$
$101$	−15354.8	−0.149776	−0.0748880	+	0.997192i	$0.523860\pi$
$102$	274274.	2.61026
$103$	136830.	1.27083	0.635415	−	0.772171i	$-0.280829\pi$
$103$	136830.	1.27083	0.635415	+	0.772171i	$0.280829\pi$
$104$	−31655.1	−0.286985
$105$	188450.	1.66811
$106$	−285286.	−2.46613
$107$	82551.8	0.697055	0.348527	−	0.937299i	$-0.386682\pi$
$107$	82551.8	0.697055	0.348527	+	0.937299i	$0.386682\pi$
$108$	−254688.	−2.10111
$109$	−31621.7	−0.254929	−0.127465	−	0.991843i	$-0.540684\pi$
$109$	−31621.7	−0.254929	−0.127465	+	0.991843i	$0.540684\pi$
$110$	−304006.	−2.39552
$111$	−19655.3	−0.151416
$112$	−268246.	−2.02064
$113$	26182.9	0.192895	0.0964476	−	0.995338i	$-0.469252\pi$
$113$	26182.9	0.192895	0.0964476	+	0.995338i	$0.469252\pi$
$114$	251055.	1.80928
$115$	160647.	1.13273
$116$	55966.1	0.386171
$117$	476.846	0.00322042
$118$	−344763.	−2.27937
$119$	−376918.	−2.43994
$120$	−307192.	−1.94741
$121$	116946.	0.726142
$122$	353399.	2.14964
$123$	278346.	1.65891
$124$	45877.6	0.267945
$125$	167073.	0.956380
$126$	10789.7	0.0605458
$127$	31565.7	0.173663	0.0868313	−	0.996223i	$-0.472326\pi$
$127$	31565.7	0.173663	0.0868313	+	0.996223i	$0.472326\pi$
$128$	−293052.	−1.58096
$129$	−98995.1	−0.523768
$130$	53219.6	0.276193
$131$	−143630.	−0.731250	−0.365625	−	0.930762i	$-0.619145\pi$
$131$	−143630.	−0.731250	−0.365625	+	0.930762i	$0.619145\pi$
$132$	541110.	2.70303
$133$	−345009.	−1.69122
$134$	−178802.	−0.860222
$135$	222290.	1.04975
$136$	614412.	2.84847
$137$	−120976.	−0.550677	−0.275338	−	0.961347i	$-0.588790\pi$
$137$	−120976.	−0.550677	−0.275338	+	0.961347i	$0.588790\pi$
$138$	−423439.	−1.89275
$139$	70220.3	0.308266	0.154133	−	0.988050i	$-0.450742\pi$
$139$	70220.3	0.308266	0.154133	+	0.988050i	$0.450742\pi$
$140$	813185.	3.50646
$141$	31867.7	0.134990
$142$	41439.7	0.172463
$143$	−48666.5	−0.199017
$144$	−6586.90	−0.0264713
$145$	−48846.8	−0.192937
$146$	−555116.	−2.15527
$147$	423423.	1.61615
$148$	−84815.0	−0.318286
$149$	−249053.	−0.919024	−0.459512	−	0.888172i	$-0.651976\pi$
$149$	−249053.	−0.919024	−0.459512	+	0.888172i	$0.651976\pi$
$150$	38042.5	0.138051
$151$	337447.	1.20438	0.602190	−	0.798353i	$-0.294295\pi$
$151$	337447.	1.20438	0.602190	+	0.798353i	$0.294295\pi$
$152$	562398.	1.97440
$153$	−9255.37	−0.0319643
$154$	−1.10119e6	−3.74163
$155$	−40041.6	−0.133870
$156$	−94727.4	−0.311648
$157$	−60595.1	−0.196195	−0.0980976	−	0.995177i	$-0.531276\pi$
$157$	−60595.1	−0.196195	−0.0980976	+	0.995177i	$0.531276\pi$
$158$	955011.	3.04345
$159$	−443195.	−1.39028
$160$	−97732.0	−0.301812
$161$	581905.	1.76924
$162$	−573458.	−1.71678
$163$	316079.	0.931808	0.465904	−	0.884835i	$-0.345729\pi$
$163$	316079.	0.931808	0.465904	+	0.884835i	$0.345729\pi$
$164$	1.20109e6	3.48712
$165$	−472277.	−1.35048
$166$	673268.	1.89635
$167$	−169743.	−0.470978	−0.235489	−	0.971877i	$-0.575669\pi$
$167$	−169743.	−0.470978	−0.235489	+	0.971877i	$0.575669\pi$
$168$	−1.11273e6	−3.04171
$169$	−362773.	−0.977054
$170$	−1.03297e6	−2.74136
$171$	−8471.84	−0.0221558
$172$	−427175.	−1.10099
$173$	−269463.	−0.684516	−0.342258	−	0.939606i	$-0.611192\pi$
$173$	−269463.	−0.684516	−0.342258	+	0.939606i	$0.611192\pi$
$174$	128752.	0.322390
$175$	−52279.4	−0.129043
$176$	672254.	1.63588
$177$	−535593.	−1.28500
$178$	−778193.	−1.84093
$179$	−637873.	−1.48799	−0.743997	−	0.668183i	$-0.767072\pi$
$179$	−637873.	−1.48799	−0.743997	+	0.668183i	$0.767072\pi$
$180$	19968.1	0.0459363
$181$	505742.	1.14745	0.573724	−	0.819049i	$-0.305498\pi$
$181$	505742.	1.14745	0.573724	+	0.819049i	$0.305498\pi$
$182$	192776.	0.431394
$183$	549009.	1.21186
$184$	−948561.	−2.06548
$185$	74025.8	0.159021
$186$	105543.	0.223691
$187$	944596.	1.97534
$188$	137513.	0.283758
$189$	805193.	1.63963
$190$	−945522.	−1.90015
$191$	310087.	0.615035	0.307517	−	0.951543i	$-0.400502\pi$
$191$	310087.	0.615035	0.307517	+	0.951543i	$0.400502\pi$
$192$	−371611.	−0.727504
$193$	−547378.	−1.05778	−0.528888	−	0.848692i	$-0.677391\pi$
$193$	−547378.	−1.05778	−0.528888	+	0.848692i	$0.677391\pi$
$194$	−102988.	−0.196464
$195$	82677.3	0.155704
$196$	1.82712e6	3.39724
$197$	56434.3	0.103604	0.0518021	−	0.998657i	$-0.483503\pi$
$197$	56434.3	0.103604	0.0518021	+	0.998657i	$0.483503\pi$
$198$	−27040.2	−0.0490170
$199$	411565.	0.736726	0.368363	−	0.929682i	$-0.379918\pi$
$199$	411565.	0.736726	0.368363	+	0.929682i	$0.379918\pi$
$200$	85220.5	0.150650
$201$	−277771.	−0.484951
$202$	−152429.	−0.262838
$203$	−176936.	−0.301354
$204$	1.83862e6	3.09326
$205$	−1.04831e6	−1.74222
$206$	1.35832e6	2.23015
$207$	14288.9	0.0231779
$208$	−117686.	−0.188610
$209$	864629.	1.36919
$210$	1.87076e6	2.92732
$211$	−213777.	−0.330563	−0.165281	−	0.986246i	$-0.552853\pi$
$211$	−213777.	−0.330563	−0.165281	+	0.986246i	$0.552853\pi$
$212$	−1.91244e6	−2.92246
$213$	64377.0	0.0972259
$214$	819499.	1.22325
$215$	372835.	0.550073
$216$	−1.31254e6	−1.91416
$217$	−145041.	−0.209094
$218$	−313912.	−0.447369
$219$	−862380.	−1.21503
$220$	−2.03793e6	−2.83878
$221$	−165362.	−0.227748
$222$	−195120.	−0.265717
$223$	704304.	0.948415	0.474207	−	0.880413i	$-0.342735\pi$
$223$	704304.	0.948415	0.474207	+	0.880413i	$0.342735\pi$
$224$	−354012.	−0.471409
$225$	−1283.74	−0.00169053
$226$	259920.	0.338507
$227$	−565745.	−0.728712	−0.364356	−	0.931260i	$-0.618711\pi$
$227$	−565745.	−0.728712	−0.364356	+	0.931260i	$0.618711\pi$
$228$	1.68297e6	2.14407
$229$	525166.	0.661771	0.330886	−	0.943671i	$-0.392653\pi$
$229$	525166.	0.661771	0.330886	+	0.943671i	$0.392653\pi$
$230$	1.59475e6	1.98780
$231$	−1.71071e6	−2.10934
$232$	288423.	0.351811
$233$	647478.	0.781332	0.390666	−	0.920533i	$-0.372245\pi$
$233$	647478.	0.781332	0.390666	+	0.920533i	$0.372245\pi$
$234$	4733.69	0.00565145
$235$	−120020.	−0.141770
$236$	−2.31115e6	−2.70114
$237$	1.48362e6	1.71574
$238$	−3.74169e6	−4.28180
$239$	−1.37154e6	−1.55315	−0.776577	−	0.630022i	$-0.783046\pi$
$239$	−1.37154e6	−1.55315	−0.776577	+	0.630022i	$0.783046\pi$
$240$	−1.14206e6	−1.27986
$241$	125435.	0.139116	0.0695580	−	0.997578i	$-0.477841\pi$
$241$	125435.	0.139116	0.0695580	+	0.997578i	$0.477841\pi$
$242$	1.16093e6	1.27429
$243$	39132.1	0.0425126
$244$	2.36904e6	2.54740
$245$	−1.59469e6	−1.69731
$246$	2.76316e6	2.91118
$247$	−151363.	−0.157862
$248$	236431.	0.244104
$249$	1.04593e6	1.06907
$250$	1.65855e6	1.67833
$251$	1.07758e6	1.07960	0.539802	−	0.841792i	$-0.318499\pi$
$251$	1.07758e6	1.07960	0.539802	+	0.841792i	$0.318499\pi$
$252$	72329.8	0.0717491
$253$	−1.45832e6	−1.43235
$254$	313356.	0.304757
$255$	−1.60473e6	−1.54544
$256$	−2.13807e6	−2.03902
$257$	−300653.	−0.283944	−0.141972	−	0.989871i	$-0.545344\pi$
$257$	−300653.	−0.283944	−0.141972	+	0.989871i	$0.545344\pi$
$258$	−982733.	−0.919150
$259$	268141.	0.248379
$260$	356762.	0.327299
$261$	−4344.74	−0.00394787
$262$	−1.42582e6	−1.28326
$263$	1.14659e6	1.02216	0.511080	−	0.859533i	$-0.329245\pi$
$263$	1.14659e6	1.02216	0.511080	+	0.859533i	$0.329245\pi$
$264$	2.78863e6	2.46252
$265$	1.66916e6	1.46010
$266$	−3.42493e6	−2.96789
$267$	−1.20893e6	−1.03782
$268$	−1.19862e6	−1.01940
$269$	−1.18627e6	−0.999547	−0.499774	−	0.866156i	$-0.666583\pi$
$269$	−1.18627e6	−0.999547	−0.499774	+	0.866156i	$0.666583\pi$
$270$	2.20669e6	1.84218
$271$	1.28048e6	1.05913	0.529567	−	0.848268i	$-0.322354\pi$
$271$	1.28048e6	1.05913	0.529567	+	0.848268i	$0.322354\pi$
$272$	2.28423e6	1.87205
$273$	299479.	0.243198
$274$	−1.20094e6	−0.966371
$275$	131018.	0.104472
$276$	−2.83856e6	−2.24298
$277$	1.77690e6	1.39144	0.695718	−	0.718315i	$-0.255086\pi$
$277$	1.77690e6	1.39144	0.695718	+	0.718315i	$0.255086\pi$
$278$	697084.	0.540970
$279$	−3561.55	−0.00273923
$280$	4.19077e6	3.19447
$281$	−649378.	−0.490605	−0.245302	−	0.969447i	$-0.578887\pi$
$281$	−649378.	−0.490605	−0.245302	+	0.969447i	$0.578887\pi$
$282$	316354.	0.236892
$283$	−152296.	−0.113038	−0.0565188	−	0.998402i	$-0.518000\pi$
$283$	−152296.	−0.113038	−0.0565188	+	0.998402i	$0.518000\pi$
$284$	277794.	0.204375
$285$	−1.46888e6	−1.07121
$286$	−483116.	−0.349250
$287$	−3.79724e6	−2.72122
$288$	−8692.91	−0.00617567
$289$	1.78975e6	1.26051
$290$	−484906.	−0.338581
$291$	−159993.	−0.110757
$292$	−3.72127e6	−2.55408
$293$	−799868.	−0.544314	−0.272157	−	0.962253i	$-0.587737\pi$
$293$	−799868.	−0.544314	−0.272157	+	0.962253i	$0.587737\pi$
$294$	4.20336e6	2.83614
$295$	2.01715e6	1.34953
$296$	−437096.	−0.289966
$297$	−2.01790e6	−1.32742
$298$	−2.47237e6	−1.61277
$299$	255294.	0.165144
$300$	255021.	0.163596
$301$	1.35051e6	0.859174
$302$	3.34987e6	2.11354
$303$	−236800.	−0.148175
$304$	2.09085e6	1.29760
$305$	−2.06768e6	−1.27272
$306$	−91878.9	−0.0560935
$307$	478184.	0.289567	0.144783	−	0.989463i	$-0.453751\pi$
$307$	478184.	0.289567	0.144783	+	0.989463i	$0.453751\pi$
$308$	−7.38192e6	−4.43397
$309$	2.11017e6	1.25725
$310$	−397496.	−0.234925
$311$	2.63423e6	1.54437	0.772187	−	0.635395i	$-0.219163\pi$
$311$	2.63423e6	1.54437	0.772187	+	0.635395i	$0.219163\pi$
$312$	−488180.	−0.283918
$313$	−1.38599e6	−0.799651	−0.399826	−	0.916591i	$-0.630929\pi$
$313$	−1.38599e6	−0.799651	−0.399826	+	0.916591i	$0.630929\pi$
$314$	−601533.	−0.344299
$315$	−63128.9	−0.0358469
$316$	6.40200e6	3.60660
$317$	2.58220e6	1.44325	0.721626	−	0.692283i	$-0.243395\pi$
$317$	2.58220e6	1.44325	0.721626	+	0.692283i	$0.243395\pi$
$318$	−4.39964e6	−2.43977
$319$	443421.	0.243972
$320$	1.39956e6	0.764040
$321$	1.27310e6	0.689605
$322$	5.77662e6	3.10480
$323$	2.93789e6	1.56686
$324$	−3.84422e6	−2.03444
$325$	−22936.1	−0.0120451
$326$	3.13774e6	1.63521
$327$	−487666.	−0.252205
$328$	6.18987e6	3.17685
$329$	−434745.	−0.221434
$330$	−4.68833e6	−2.36992
$331$	−1.13450e6	−0.569162	−0.284581	−	0.958652i	$-0.591855\pi$
$331$	−1.13450e6	−0.569162	−0.284581	+	0.958652i	$0.591855\pi$
$332$	4.51331e6	2.24724
$333$	6584.33	0.00325387
$334$	−1.68505e6	−0.826508
$335$	1.04614e6	0.509306
$336$	−4.13686e6	−1.99904
$337$	149357.	0.0716392	0.0358196	−	0.999358i	$-0.488596\pi$
$337$	149357.	0.0716392	0.0358196	+	0.999358i	$0.488596\pi$
$338$	−3.60128e6	−1.71461
$339$	403789.	0.190834
$340$	−6.92460e6	−3.24861
$341$	363489.	0.169280
$342$	−84100.7	−0.0388807
$343$	−2.24042e6	−1.02824
$344$	−2.20146e6	−1.00303
$345$	2.47747e6	1.12063
$346$	−2.67498e6	−1.20124
$347$	−2.53791e6	−1.13150	−0.565748	−	0.824578i	$-0.691413\pi$
$347$	−2.53791e6	−1.13150	−0.565748	+	0.824578i	$0.691413\pi$
$348$	863102.	0.382044
$349$	−1.77115e6	−0.778380	−0.389190	−	0.921157i	$-0.627245\pi$
$349$	−1.77115e6	−0.778380	−0.389190	+	0.921157i	$0.627245\pi$
$350$	−518983.	−0.226455
$351$	353256.	0.153046
$352$	887191.	0.381646
$353$	2.26199e6	0.966171	0.483085	−	0.875573i	$-0.339516\pi$
$353$	2.26199e6	0.966171	0.483085	+	0.875573i	$0.339516\pi$
$354$	−5.31688e6	−2.25501
$355$	−242457.	−0.102109
$356$	−5.21668e6	−2.18157
$357$	−5.81277e6	−2.41386
$358$	−6.33222e6	−2.61125
$359$	−1.72972e6	−0.708338	−0.354169	−	0.935181i	$-0.615236\pi$
$359$	−1.72972e6	−0.708338	−0.354169	+	0.935181i	$0.615236\pi$
$360$	102906.	0.0418490
$361$	213081.	0.0860550
$362$	5.02055e6	2.01363
$363$	1.80352e6	0.718381
$364$	1.29229e6	0.511218
$365$	3.24789e6	1.27606
$366$	5.45006e6	2.12666
$367$	1.57623e6	0.610877	0.305438	−	0.952212i	$-0.401197\pi$
$367$	1.57623e6	0.610877	0.305438	+	0.952212i	$0.401197\pi$
$368$	−3.52651e6	−1.35745
$369$	−93242.9	−0.0356492
$370$	734861.	0.279062
$371$	6.04615e6	2.28057
$372$	707518.	0.265082
$373$	−1.23586e6	−0.459935	−0.229968	−	0.973198i	$-0.573862\pi$
$373$	−1.23586e6	−0.459935	−0.229968	+	0.973198i	$0.573862\pi$
$374$	9.37708e6	3.46648
$375$	2.57657e6	0.946159
$376$	708676.	0.258510
$377$	−77625.7	−0.0281289
$378$	7.99322e6	2.87735
$379$	339945.	0.121566	0.0607829	−	0.998151i	$-0.480640\pi$
$379$	339945.	0.121566	0.0607829	+	0.998151i	$0.480640\pi$
$380$	−6.33839e6	−2.25175
$381$	486802.	0.171807
$382$	3.07826e6	1.07931
$383$	−3.13257e6	−1.09120	−0.545600	−	0.838046i	$-0.683698\pi$
$383$	−3.13257e6	−1.09120	−0.545600	+	0.838046i	$0.683698\pi$
$384$	−4.51941e6	−1.56406
$385$	6.44288e6	2.21528
$386$	−5.43387e6	−1.85627
$387$	33162.3	0.0112556
$388$	−690390.	−0.232817
$389$	3.26603e6	1.09433	0.547163	−	0.837026i	$-0.315708\pi$
$389$	3.26603e6	1.09433	0.547163	+	0.837026i	$0.315708\pi$
$390$	820745.	0.273242
$391$	−4.95516e6	−1.63914
$392$	9.41610e6	3.09496
$393$	−2.21504e6	−0.723435
$394$	560228.	0.181813
$395$	−5.58761e6	−1.80191
$396$	−181266.	−0.0580870
$397$	−1.47446e6	−0.469522	−0.234761	−	0.972053i	$-0.575431\pi$
$397$	−1.47446e6	−0.469522	−0.234761	+	0.972053i	$0.575431\pi$
$398$	4.08565e6	1.29286
$399$	−5.32068e6	−1.67315
$400$	316828.	0.0990088
$401$	2.37462e6	0.737450	0.368725	−	0.929539i	$-0.379794\pi$
$401$	2.37462e6	0.737450	0.368725	+	0.929539i	$0.379794\pi$
$402$	−2.75746e6	−0.851029
$403$	−63632.8	−0.0195172
$404$	−1.02182e6	−0.311474
$405$	3.35521e6	1.01644
$406$	−1.75646e6	−0.528839
$407$	−671991.	−0.201084
$408$	9.47537e6	2.81803
$409$	−3.82996e6	−1.13210	−0.566051	−	0.824370i	$-0.691530\pi$
$409$	−3.82996e6	−1.13210	−0.566051	+	0.824370i	$0.691530\pi$
$410$	−1.04066e7	−3.05738
$411$	−1.86567e6	−0.544792
$412$	9.10563e6	2.64282
$413$	7.30666e6	2.10787
$414$	141847.	0.0406744
$415$	−3.93918e6	−1.12276
$416$	−155313.	−0.0440021
$417$	1.08293e6	0.304972
$418$	8.58325e6	2.40276
$419$	621328.	0.172897	0.0864483	−	0.996256i	$-0.472448\pi$
$419$	621328.	0.172897	0.0864483	+	0.996256i	$0.472448\pi$
$420$	1.25408e7	3.46899
$421$	−4.99920e6	−1.37466	−0.687330	−	0.726345i	$-0.741217\pi$
$421$	−4.99920e6	−1.37466	−0.687330	+	0.726345i	$0.741217\pi$
$422$	−2.12218e6	−0.580097
$423$	−10675.3	−0.00290089
$424$	−9.85580e6	−2.66242
$425$	445181.	0.119554
$426$	639077.	0.170620
$427$	−7.48968e6	−1.98790
$428$	5.49358e6	1.44959
$429$	−750527.	−0.196890
$430$	3.70117e6	0.965311
$431$	−5.42664e6	−1.40714	−0.703570	−	0.710626i	$-0.748412\pi$
$431$	−5.42664e6	−1.40714	−0.703570	+	0.710626i	$0.748412\pi$
$432$	−4.87970e6	−1.25801
$433$	1.21607e6	0.311702	0.155851	−	0.987781i	$-0.450188\pi$
$433$	1.21607e6	0.311702	0.155851	+	0.987781i	$0.450188\pi$
$434$	−1.43984e6	−0.366935
$435$	−753308.	−0.190875
$436$	−2.10433e6	−0.530150
$437$	−4.53567e6	−1.13616
$438$	−8.56093e6	−2.13224
$439$	−2.34458e6	−0.580635	−0.290317	−	0.956930i	$-0.593761\pi$
$439$	−2.34458e6	−0.580635	−0.290317	+	0.956930i	$0.593761\pi$
$440$	−1.05025e7	−2.58620
$441$	−141842.	−0.0347303
$442$	−1.64156e6	−0.399670
$443$	4.17338e6	1.01036	0.505182	−	0.863013i	$-0.331425\pi$
$443$	4.17338e6	1.01036	0.505182	+	0.863013i	$0.331425\pi$
$444$	−1.30800e6	−0.314885
$445$	4.55308e6	1.08995
$446$	6.99169e6	1.66435
$447$	−3.84087e6	−0.909202
$448$	5.06958e6	1.19337
$449$	−7.89264e6	−1.84759	−0.923797	−	0.382883i	$-0.874931\pi$
$449$	−7.89264e6	−1.84759	−0.923797	+	0.382883i	$0.874931\pi$
$450$	−12743.8	−0.00296667
$451$	9.51630e6	2.20306
$452$	1.74239e6	0.401144
$453$	5.20406e6	1.19151
$454$	−5.61620e6	−1.27880
$455$	−1.12790e6	−0.255412
$456$	8.67322e6	1.95330
$457$	−3.36902e6	−0.754593	−0.377297	−	0.926092i	$-0.623146\pi$
$457$	−3.36902e6	−0.754593	−0.377297	+	0.926092i	$0.623146\pi$
$458$	5.21337e6	1.16133
$459$	−6.85655e6	−1.51906
$460$	1.06906e7	2.35562
$461$	−35186.9	−0.00771132	−0.00385566	−	0.999993i	$-0.501227\pi$
$461$	−35186.9	−0.00771132	−0.00385566	+	0.999993i	$0.501227\pi$
$462$	−1.69824e7	−3.70164
$463$	−1.98494e6	−0.430322	−0.215161	−	0.976579i	$-0.569028\pi$
$463$	−1.98494e6	−0.430322	−0.215161	+	0.976579i	$0.569028\pi$
$464$	1.07228e6	0.231214
$465$	−617516.	−0.132439
$466$	6.42758e6	1.37114
$467$	5.84649e6	1.24052	0.620259	−	0.784397i	$-0.287028\pi$
$467$	5.84649e6	1.24052	0.620259	+	0.784397i	$0.287028\pi$
$468$	31732.7	0.00669718
$469$	3.78941e6	0.795498
$470$	−1.19145e6	−0.248789
$471$	−934490.	−0.194099
$472$	−1.19105e7	−2.46080
$473$	−3.38452e6	−0.695575
$474$	1.47281e7	3.01092
$475$	407493.	0.0828679
$476$	−2.50828e7	−5.07409
$477$	148466.	0.0298766
$478$	−1.36154e7	−2.72560
$479$	3.76308e6	0.749385	0.374693	−	0.927149i	$-0.377748\pi$
$479$	3.76308e6	0.749385	0.374693	+	0.927149i	$0.377748\pi$
$480$	−1.50721e6	−0.298587
$481$	117639.	0.0231841
$482$	1.24521e6	0.244132
$483$	8.97406e6	1.75033
$484$	7.78241e6	1.51008
$485$	602567.	0.116319
$486$	388468.	0.0746044
$487$	−179343.	−0.0342658	−0.0171329	−	0.999853i	$-0.505454\pi$
$487$	−179343.	−0.0342658	−0.0171329	+	0.999853i	$0.505454\pi$
$488$	1.22089e7	2.32074
$489$	4.87452e6	0.921850
$490$	−1.58307e7	−2.97858
$491$	1.00202e7	1.87574	0.937869	−	0.346990i	$-0.112796\pi$
$491$	1.00202e7	1.87574	0.937869	+	0.346990i	$0.112796\pi$
$492$	1.85231e7	3.44986
$493$	1.50668e6	0.279193
$494$	−1.50259e6	−0.277028
$495$	158208.	0.0290212
$496$	878991.	0.160428
$497$	−878243.	−0.159486
$498$	1.03830e7	1.87608
$499$	8.59738e6	1.54566	0.772831	−	0.634612i	$-0.218840\pi$
$499$	8.59738e6	1.54566	0.772831	+	0.634612i	$0.218840\pi$
$500$	1.11182e7	1.98888
$501$	−2.61775e6	−0.465944
$502$	1.06972e7	1.89457
$503$	−9.46324e6	−1.66771	−0.833854	−	0.551985i	$-0.813870\pi$
$503$	−9.46324e6	−1.66771	−0.833854	+	0.551985i	$0.813870\pi$
$504$	372754.	0.0653650
$505$	891837.	0.155617
$506$	−1.44768e7	−2.51361
$507$	−5.59464e6	−0.966612
$508$	2.10061e6	0.361148
$509$	−742258.	−0.126987	−0.0634937	−	0.997982i	$-0.520224\pi$
$509$	−742258.	−0.126987	−0.0634937	+	0.997982i	$0.520224\pi$
$510$	−1.59303e7	−2.71206
$511$	1.17647e7	1.99310
$512$	−1.18471e7	−1.99728
$513$	−6.27609e6	−1.05292
$514$	−2.98461e6	−0.498287
$515$	−7.94732e6	−1.32039
$516$	−6.58784e6	−1.08923
$517$	1.08952e6	0.179270
$518$	2.66186e6	0.435874
$519$	−4.15562e6	−0.677200
$520$	1.83858e6	0.298177
$521$	−3.00978e6	−0.485781	−0.242890	−	0.970054i	$-0.578096\pi$
$521$	−3.00978e6	−0.485781	−0.242890	+	0.970054i	$0.578096\pi$
$522$	−43130.6	−0.00692803
$523$	8.78961e6	1.40513	0.702563	−	0.711621i	$-0.252039\pi$
$523$	8.78961e6	1.40513	0.702563	+	0.711621i	$0.252039\pi$
$524$	−9.55814e6	−1.52071
$525$	−806246.	−0.127664
$526$	1.13823e7	1.79377
$527$	1.23509e6	0.193718
$528$	1.03674e7	1.61840
$529$	1.21369e6	0.188568
$530$	1.65699e7	2.56230
$531$	179418.	0.0276140
$532$	−2.29593e7	−3.51707
$533$	−1.66593e6	−0.254004
$534$	−1.20012e7	−1.82126
$535$	−4.79475e6	−0.724239
$536$	−6.17710e6	−0.928693
$537$	−9.83718e6	−1.47209
$538$	−1.17762e7	−1.75408
$539$	1.44763e7	2.14627
$540$	1.47927e7	2.18305
$541$	8.42234e6	1.23720	0.618599	−	0.785707i	$-0.287700\pi$
$541$	8.42234e6	1.23720	0.618599	+	0.785707i	$0.287700\pi$
$542$	1.27115e7	1.85865
$543$	7.79949e6	1.13518
$544$	3.01455e6	0.436743
$545$	1.83665e6	0.264871
$546$	2.97296e6	0.426783
$547$	−2.55152e6	−0.364612	−0.182306	−	0.983242i	$-0.558356\pi$
$547$	−2.55152e6	−0.364612	−0.182306	+	0.983242i	$0.558356\pi$
$548$	−8.05058e6	−1.14519
$549$	−183912.	−0.0260423
$550$	1.30063e6	0.183335
$551$	1.37913e6	0.193520
$552$	−1.46286e7	−2.04340
$553$	−2.02398e7	−2.81445
$554$	1.76394e7	2.44180
$555$	1.14162e6	0.157321
$556$	4.67296e6	0.641069
$557$	4.38436e6	0.598782	0.299391	−	0.954131i	$-0.403217\pi$
$557$	4.38436e6	0.598782	0.299391	+	0.954131i	$0.403217\pi$
$558$	−35355.8	−0.00480702
$559$	592498.	0.0801968
$560$	1.55802e7	2.09944
$561$	1.45674e7	1.95423
$562$	−6.44643e6	−0.860951
$563$	9.56112e6	1.27127	0.635635	−	0.771990i	$-0.280738\pi$
$563$	9.56112e6	1.27127	0.635635	+	0.771990i	$0.280738\pi$
$564$	2.12070e6	0.280726
$565$	−1.52075e6	−0.200418
$566$	−1.51186e6	−0.198367
$567$	1.21535e7	1.58760
$568$	1.43162e6	0.186190
$569$	4.02277e6	0.520889	0.260444	−	0.965489i	$-0.416131\pi$
$569$	4.02277e6	0.520889	0.260444	+	0.965489i	$0.416131\pi$
$570$	−1.45817e7	−1.87984
$571$	8.31378e6	1.06711	0.533554	−	0.845766i	$-0.320856\pi$
$571$	8.31378e6	1.06711	0.533554	+	0.845766i	$0.320856\pi$
$572$	−3.23861e6	−0.413875
$573$	4.78211e6	0.608462
$574$	−3.76956e7	−4.77541
$575$	−687293.	−0.0866907
$576$	124486.	0.0156337
$577$	−1.03727e7	−1.29703	−0.648517	−	0.761200i	$-0.724611\pi$
$577$	−1.03727e7	−1.29703	−0.648517	+	0.761200i	$0.724611\pi$
$578$	1.77670e7	2.21205
$579$	−8.44158e6	−1.04647
$580$	−3.25061e6	−0.401231
$581$	−1.42688e7	−1.75366
$582$	−1.58827e6	−0.194364
$583$	−1.51523e7	−1.84632
$584$	−1.91777e7	−2.32682
$585$	−27696.0	−0.00334601
$586$	−7.94036e6	−0.955204
$587$	−9.76113e6	−1.16924	−0.584622	−	0.811306i	$-0.698757\pi$
$587$	−9.76113e6	−1.16924	−0.584622	+	0.811306i	$0.698757\pi$
$588$	2.81776e7	3.36093
$589$	1.13053e6	0.134274
$590$	2.00244e7	2.36826
$591$	870322.	0.102497
$592$	−1.62501e6	−0.190569
$593$	−6.43984e6	−0.752036	−0.376018	−	0.926612i	$-0.622707\pi$
$593$	−6.43984e6	−0.752036	−0.376018	+	0.926612i	$0.622707\pi$
$594$	−2.00319e7	−2.32946
$595$	2.18920e7	2.53509
$596$	−1.65738e7	−1.91120
$597$	6.34710e6	0.728853
$598$	2.53433e6	0.289808
$599$	−1.74577e7	−1.98802	−0.994009	−	0.109301i	$-0.965139\pi$
$599$	−1.74577e7	−1.98802	−0.994009	+	0.109301i	$0.965139\pi$
$600$	1.31426e6	0.149040
$601$	1.70010e7	1.91994	0.959969	−	0.280106i	$-0.0903695\pi$
$601$	1.70010e7	1.91994	0.959969	+	0.280106i	$0.0903695\pi$
$602$	1.34066e7	1.50775
$603$	93050.5	0.0104214
$604$	2.24561e7	2.50462
$605$	−6.79242e6	−0.754460
$606$	−2.35074e6	−0.260030
$607$	−9.77787e6	−1.07714	−0.538570	−	0.842581i	$-0.681035\pi$
$607$	−9.77787e6	−1.07714	−0.538570	+	0.842581i	$0.681035\pi$
$608$	2.75935e6	0.302725
$609$	−2.72868e6	−0.298133
$610$	−2.05260e7	−2.23347
$611$	−190732.	−0.0206691
$612$	−615918.	−0.0664729
$613$	−1.43306e7	−1.54033	−0.770165	−	0.637844i	$-0.779826\pi$
$613$	−1.43306e7	−1.54033	−0.770165	+	0.637844i	$0.779826\pi$
$614$	4.74697e6	0.508155
$615$	−1.61668e7	−1.72360
$616$	−3.80429e7	−4.03945
$617$	−1.05568e6	−0.111640	−0.0558202	−	0.998441i	$-0.517777\pi$
$617$	−1.05568e6	−0.111640	−0.0558202	+	0.998441i	$0.517777\pi$
$618$	2.09479e7	2.20632
$619$	−3.57533e6	−0.375051	−0.187525	−	0.982260i	$-0.560047\pi$
$619$	−3.57533e6	−0.375051	−0.187525	+	0.982260i	$0.560047\pi$
$620$	−2.66465e6	−0.278395
$621$	1.05855e7	1.10149
$622$	2.61502e7	2.71019
$623$	1.64925e7	1.70242
$624$	−1.81493e6	−0.186594
$625$	−1.04804e7	−1.07319
$626$	−1.37589e7	−1.40329
$627$	1.33342e7	1.35456
$628$	−4.03243e6	−0.408007
$629$	−2.28333e6	−0.230114
$630$	−626686.	−0.0629070
$631$	1.66113e7	1.66085	0.830423	−	0.557134i	$-0.188099\pi$
$631$	1.66113e7	1.66085	0.830423	+	0.557134i	$0.188099\pi$
$632$	3.29929e7	3.28570
$633$	−3.29683e6	−0.327030
$634$	2.56338e7	2.53273
$635$	−1.83339e6	−0.180435
$636$	−2.94934e7	−2.89122
$637$	−2.53424e6	−0.247456
$638$	4.40188e6	0.428140
$639$	−21565.6	−0.00208934
$640$	1.70210e7	1.64261
$641$	−1.77657e7	−1.70780	−0.853902	−	0.520434i	$-0.825770\pi$
$641$	−1.77657e7	−1.70780	−0.853902	+	0.520434i	$0.825770\pi$
$642$	1.26382e7	1.21017
$643$	−5.29461e6	−0.505018	−0.252509	−	0.967595i	$-0.581256\pi$
$643$	−5.29461e6	−0.505018	−0.252509	+	0.967595i	$0.581256\pi$
$644$	3.87241e7	3.67931
$645$	5.74981e6	0.544194
$646$	2.91647e7	2.74964
$647$	−1.47774e7	−1.38783	−0.693916	−	0.720056i	$-0.744116\pi$
$647$	−1.47774e7	−1.38783	−0.693916	+	0.720056i	$0.744116\pi$
$648$	−1.98113e7	−1.85343
$649$	−1.83113e7	−1.70650
$650$	−227689.	−0.0211378
$651$	−2.23681e6	−0.206860
$652$	2.10341e7	1.93778
$653$	−1.36335e7	−1.25119	−0.625595	−	0.780148i	$-0.715144\pi$
$653$	−1.36335e7	−1.25119	−0.625595	+	0.780148i	$0.715144\pi$
$654$	−4.84110e6	−0.442588
$655$	8.34227e6	0.759768
$656$	2.30124e7	2.08786
$657$	288888.	0.0261106
$658$	−4.31575e6	−0.388590
$659$	1.60545e7	1.44007	0.720033	−	0.693940i	$-0.244127\pi$
$659$	1.60545e7	1.44007	0.720033	+	0.693940i	$0.244127\pi$
$660$	−3.14286e7	−2.80844
$661$	−2.01227e7	−1.79136	−0.895678	−	0.444704i	$-0.853309\pi$
$661$	−2.01227e7	−1.79136	−0.895678	+	0.444704i	$0.853309\pi$
$662$	−1.12623e7	−0.998811
$663$	−2.55019e6	−0.225314
$664$	2.32595e7	2.04729
$665$	2.00387e7	1.75718
$666$	65363.2	0.00571015
$667$	−2.32610e6	−0.202448
$668$	−1.12959e7	−0.979444
$669$	1.08617e7	0.938279
$670$	1.03851e7	0.893770
$671$	1.87699e7	1.60937
$672$	−5.45952e6	−0.466371
$673$	2.01674e7	1.71637	0.858187	−	0.513338i	$-0.171591\pi$
$673$	2.01674e7	1.71637	0.858187	+	0.513338i	$0.171591\pi$
$674$	1.48268e6	0.125718
$675$	−951020.	−0.0803397
$676$	−2.41415e7	−2.03188
$677$	3.35832e6	0.281612	0.140806	−	0.990037i	$-0.455031\pi$
$677$	3.35832e6	0.281612	0.140806	+	0.990037i	$0.455031\pi$
$678$	4.00845e6	0.334890
$679$	2.18266e6	0.181682
$680$	−3.56861e7	−2.95956
$681$	−8.72484e6	−0.720924
$682$	3.60839e6	0.297065
$683$	6.40198e6	0.525125	0.262563	−	0.964915i	$-0.415432\pi$
$683$	6.40198e6	0.525125	0.262563	+	0.964915i	$0.415432\pi$
$684$	−563777.	−0.0460752
$685$	7.02648e6	0.572152
$686$	−2.22409e7	−1.80443
$687$	8.09904e6	0.654699
$688$	−8.18446e6	−0.659203
$689$	2.65258e6	0.212873
$690$	2.45941e7	1.96656
$691$	−2.19756e7	−1.75084	−0.875418	−	0.483367i	$-0.839414\pi$
$691$	−2.19756e7	−1.75084	−0.875418	+	0.483367i	$0.839414\pi$
$692$	−1.79320e7	−1.42352
$693$	573071.	0.0453289
$694$	−2.51941e7	−1.98564
$695$	−4.07852e6	−0.320288
$696$	4.44802e6	0.348051
$697$	3.23351e7	2.52111
$698$	−1.75824e7	−1.36596
$699$	9.98532e6	0.772982
$700$	−3.47905e6	−0.268358
$701$	7.90411e6	0.607516	0.303758	−	0.952749i	$-0.401759\pi$
$701$	7.90411e6	0.607516	0.303758	+	0.952749i	$0.401759\pi$
$702$	3.50680e6	0.268577
$703$	−2.09003e6	−0.159502
$704$	−1.27049e7	−0.966139
$705$	−1.85093e6	−0.140255
$706$	2.24550e7	1.69551
$707$	3.23047e6	0.243062
$708$	−3.56422e7	−2.67227
$709$	1.88248e7	1.40642	0.703211	−	0.710981i	$-0.251749\pi$
$709$	1.88248e7	1.40642	0.703211	+	0.710981i	$0.251749\pi$
$710$	−2.40689e6	−0.179188
$711$	−496998.	−0.0368706
$712$	−2.68843e7	−1.98746
$713$	−1.90679e6	−0.140469
$714$	−5.77039e7	−4.23604
$715$	2.82663e6	0.206778
$716$	−4.24486e7	−3.09443
$717$	−2.11517e7	−1.53656
$718$	−1.71711e7	−1.24305
$719$	9.95692e6	0.718295	0.359148	−	0.933281i	$-0.383067\pi$
$719$	9.95692e6	0.718295	0.359148	+	0.933281i	$0.383067\pi$
$720$	382579.	0.0275036
$721$	−2.87873e7	−2.06235
$722$	2.11527e6	0.151016
$723$	1.93445e6	0.137629
$724$	3.36557e7	2.38623
$725$	208981.	0.0147660
$726$	1.79037e7	1.26067
$727$	7.47960e6	0.524859	0.262429	−	0.964951i	$-0.415476\pi$
$727$	7.47960e6	0.524859	0.262429	+	0.964951i	$0.415476\pi$
$728$	6.65984e6	0.465731
$729$	1.46409e7	1.02035
$730$	3.22421e7	2.23932
$731$	−1.15001e7	−0.795993
$732$	3.65350e7	2.52018
$733$	−1.87960e7	−1.29213	−0.646065	−	0.763282i	$-0.723587\pi$
$733$	−1.87960e7	−1.29213	−0.646065	+	0.763282i	$0.723587\pi$
$734$	1.56473e7	1.07201
$735$	−2.45931e7	−1.67917
$736$	−4.65402e6	−0.316690
$737$	−9.49666e6	−0.644024
$738$	−925631.	−0.0625600
$739$	−1.54929e7	−1.04357	−0.521784	−	0.853078i	$-0.674733\pi$
$739$	−1.54929e7	−1.04357	−0.521784	+	0.853078i	$0.674733\pi$
$740$	4.92620e6	0.330699
$741$	−2.33430e6	−0.156175
$742$	6.00207e7	4.00213
$743$	−1.97660e7	−1.31355	−0.656776	−	0.754086i	$-0.728080\pi$
$743$	−1.97660e7	−1.31355	−0.656776	+	0.754086i	$0.728080\pi$
$744$	3.64621e6	0.241496
$745$	1.44655e7	0.954864
$746$	−1.22685e7	−0.807130
$747$	−350376.	−0.0229738
$748$	6.28601e7	4.10791
$749$	−1.73679e7	−1.13121
$750$	2.55779e7	1.66039
$751$	−1.72461e6	−0.111581	−0.0557905	−	0.998442i	$-0.517768\pi$
$751$	−1.72461e6	−0.111581	−0.0557905	+	0.998442i	$0.517768\pi$
$752$	2.63468e6	0.169896
$753$	1.66183e7	1.06807
$754$	−770598.	−0.0493627
$755$	−1.95995e7	−1.25135
$756$	5.35832e7	3.40977
$757$	−2.52697e7	−1.60273	−0.801364	−	0.598177i	$-0.795892\pi$
$757$	−2.52697e7	−1.60273	−0.801364	+	0.598177i	$0.795892\pi$
$758$	3.37467e6	0.213333
$759$	−2.24899e7	−1.41705
$760$	−3.26650e7	−2.05139
$761$	1.08483e7	0.679050	0.339525	−	0.940597i	$-0.389734\pi$
$761$	1.08483e7	0.679050	0.339525	+	0.940597i	$0.389734\pi$
$762$	4.83253e6	0.301500
$763$	6.65282e6	0.413709
$764$	2.06354e7	1.27902
$765$	537568.	0.0332109
$766$	−3.10973e7	−1.91492
$767$	3.20559e6	0.196752
$768$	−3.29730e7	−2.01723
$769$	3.05501e7	1.86293	0.931465	−	0.363830i	$-0.118531\pi$
$769$	3.05501e7	1.86293	0.931465	+	0.363830i	$0.118531\pi$
$770$	6.39591e7	3.88754
$771$	−4.63663e6	−0.280910
$772$	−3.64264e7	−2.19975
$773$	2.59485e6	0.156194	0.0780968	−	0.996946i	$-0.475116\pi$
$773$	2.59485e6	0.156194	0.0780968	+	0.996946i	$0.475116\pi$
$774$	329205.	0.0197521
$775$	171310.	0.0102454
$776$	−3.55794e6	−0.212102
$777$	4.13524e6	0.245724
$778$	3.24222e7	1.92041
$779$	2.95977e7	1.74749
$780$	5.50194e6	0.323802
$781$	2.20097e6	0.129118
$782$	−4.91903e7	−2.87649
$783$	−3.21866e6	−0.187616
$784$	3.50067e7	2.03404
$785$	3.51947e6	0.203847
$786$	−2.19889e7	−1.26954
$787$	−5.86903e6	−0.337776	−0.168888	−	0.985635i	$-0.554018\pi$
$787$	−5.86903e6	−0.337776	−0.168888	+	0.985635i	$0.554018\pi$
$788$	3.75554e6	0.215455
$789$	1.76826e7	1.01124
$790$	−5.54687e7	−3.16214
$791$	−5.50856e6	−0.313038
$792$	−934160.	−0.0529186
$793$	−3.28589e6	−0.185554
$794$	−1.46371e7	−0.823954
$795$	2.57416e7	1.44450
$796$	2.73885e7	1.53209
$797$	−5.23510e6	−0.291930	−0.145965	−	0.989290i	$-0.546629\pi$
$797$	−5.23510e6	−0.291930	−0.145965	+	0.989290i	$0.546629\pi$
$798$	−5.28189e7	−2.93617
$799$	3.70203e6	0.205151
$800$	418126.	0.0230984
$801$	404980.	0.0223024
$802$	2.35730e7	1.29413
$803$	−2.94837e7	−1.61359
$804$	−1.84849e7	−1.00850
$805$	−3.37981e7	−1.83824
$806$	−631688.	−0.0342504
$807$	−1.82945e7	−0.988865
$808$	−5.26598e6	−0.283760
$809$	1.68943e7	0.907548	0.453774	−	0.891117i	$-0.350077\pi$
$809$	1.68943e7	0.907548	0.453774	+	0.891117i	$0.350077\pi$
$810$	3.33074e7	1.78373
$811$	332001.	0.0177251	0.00886253	−	0.999961i	$-0.497179\pi$
$811$	332001.	0.0177251	0.00886253	+	0.999961i	$0.497179\pi$
$812$	−1.17746e7	−0.626694
$813$	1.97474e7	1.04782
$814$	−6.67091e6	−0.352878
$815$	−1.83584e7	−0.968147
$816$	3.52270e7	1.85204
$817$	−1.05266e7	−0.551736
$818$	−3.80203e7	−1.98670
$819$	−100322.	−0.00522623
$820$	−6.97617e7	−3.62312
$821$	−1.19256e6	−0.0617479	−0.0308739	−	0.999523i	$-0.509829\pi$
$821$	−1.19256e6	−0.0617479	−0.0308739	+	0.999523i	$0.509829\pi$
$822$	−1.85207e7	−0.956043
$823$	1.34488e7	0.692123	0.346061	−	0.938212i	$-0.387519\pi$
$823$	1.34488e7	0.692123	0.346061	+	0.938212i	$0.387519\pi$
$824$	4.69261e7	2.40767
$825$	2.02054e6	0.103355
$826$	7.25338e7	3.69905
$827$	−1.99983e6	−0.101678	−0.0508392	−	0.998707i	$-0.516190\pi$
$827$	−1.99983e6	−0.101678	−0.0508392	+	0.998707i	$0.516190\pi$
$828$	950887.	0.0482006
$829$	−1.19093e7	−0.601866	−0.300933	−	0.953645i	$-0.597298\pi$
$829$	−1.19093e7	−0.601866	−0.300933	+	0.953645i	$0.597298\pi$
$830$	−3.91046e7	−1.97030
$831$	2.74031e7	1.37657
$832$	2.22413e6	0.111392
$833$	4.91885e7	2.45613
$834$	1.07503e7	0.535188
$835$	9.85896e6	0.489345
$836$	5.75386e7	2.84737
$837$	−2.63846e6	−0.130178
$838$	6.16798e6	0.303412
$839$	1.45360e7	0.712919	0.356459	−	0.934311i	$-0.383984\pi$
$839$	1.45360e7	0.712919	0.356459	+	0.934311i	$0.383984\pi$
$840$	6.46295e7	3.16033
$841$	707281.	0.0344828
$842$	−4.96275e7	−2.41236
$843$	−1.00146e7	−0.485362
$844$	−1.42262e7	−0.687437
$845$	2.10705e7	1.01516
$846$	−105975.	−0.00509071
$847$	−2.46040e7	−1.17841
$848$	−3.66414e7	−1.74977
$849$	−2.34869e6	−0.111830
$850$	4.41935e6	0.209803
$851$	3.52513e6	0.166860
$852$	4.28411e6	0.202191
$853$	−6.18563e6	−0.291079	−0.145540	−	0.989352i	$-0.546492\pi$
$853$	−6.18563e6	−0.291079	−0.145540	+	0.989352i	$0.546492\pi$
$854$	−7.43507e7	−3.48851
$855$	492060.	0.0230198
$856$	2.83113e7	1.32061
$857$	−2.85410e7	−1.32745	−0.663724	−	0.747978i	$-0.731025\pi$
$857$	−2.85410e7	−1.32745	−0.663724	+	0.747978i	$0.731025\pi$
$858$	−7.45055e6	−0.345518
$859$	3.50491e7	1.62067	0.810333	−	0.585970i	$-0.199286\pi$
$859$	3.50491e7	1.62067	0.810333	+	0.585970i	$0.199286\pi$
$860$	2.48111e7	1.14393
$861$	−5.85606e7	−2.69214
$862$	−5.38707e7	−2.46936
$863$	1.75590e7	0.802550	0.401275	−	0.915958i	$-0.368567\pi$
$863$	1.75590e7	0.802550	0.401275	+	0.915958i	$0.368567\pi$
$864$	−6.43986e6	−0.293489
$865$	1.56509e7	0.711210
$866$	1.20721e7	0.546999
$867$	2.76013e7	1.24704
$868$	−9.65208e6	−0.434832
$869$	5.07232e7	2.27854
$870$	−7.47816e6	−0.334963
$871$	1.66250e6	0.0742532
$872$	−1.08447e7	−0.482979
$873$	53596.1	0.00238011
$874$	−4.50260e7	−1.99382
$875$	−3.51501e7	−1.55205
$876$	−5.73889e7	−2.52678
$877$	−9.57523e6	−0.420388	−0.210194	−	0.977660i	$-0.567410\pi$
$877$	−9.57523e6	−0.420388	−0.210194	+	0.977660i	$0.567410\pi$
$878$	−2.32748e7	−1.01894
$879$	−1.23355e7	−0.538497
$880$	−3.90457e7	−1.69968
$881$	−2.60927e6	−0.113261	−0.0566303	−	0.998395i	$-0.518036\pi$
$881$	−2.60927e6	−0.113261	−0.0566303	+	0.998395i	$0.518036\pi$
$882$	−1.40808e6	−0.0609475
$883$	2.20388e7	0.951231	0.475616	−	0.879653i	$-0.342225\pi$
$883$	2.20388e7	0.951231	0.475616	+	0.879653i	$0.342225\pi$
$884$	−1.10044e7	−0.473625
$885$	3.11082e7	1.33511
$886$	4.14295e7	1.77307
$887$	1.32296e7	0.564596	0.282298	−	0.959327i	$-0.408903\pi$
$887$	1.32296e7	0.564596	0.282298	+	0.959327i	$0.408903\pi$
$888$	−6.74084e6	−0.286867
$889$	−6.64104e6	−0.281826
$890$	4.51988e7	1.91272
$891$	−3.04579e7	−1.28530
$892$	4.68694e7	1.97232
$893$	3.38863e6	0.142199
$894$	−3.81286e7	−1.59554
$895$	3.70488e7	1.54602
$896$	6.16545e7	2.56564
$897$	3.93712e6	0.163379
$898$	−7.83509e7	−3.24230
$899$	579785.	0.0239259
$900$	−85429.4	−0.00351562
$901$	−5.14854e7	−2.11287
$902$	9.44691e7	3.86610
$903$	2.08274e7	0.849992
$904$	8.97947e6	0.365452
$905$	−2.93744e7	−1.19220
$906$	5.16612e7	2.09095
$907$	2.28630e7	0.922814	0.461407	−	0.887189i	$-0.347345\pi$
$907$	2.28630e7	0.922814	0.461407	+	0.887189i	$0.347345\pi$
$908$	−3.76487e7	−1.51543
$909$	79325.6	0.00318422
$910$	−1.11967e7	−0.448217
$911$	−1.86891e7	−0.746091	−0.373046	−	0.927813i	$-0.621687\pi$
$911$	−1.86891e7	−0.746091	−0.373046	+	0.927813i	$0.621687\pi$
$912$	3.22448e7	1.28373
$913$	3.57590e7	1.41974
$914$	−3.34446e7	−1.32422
$915$	−3.18874e7	−1.25912
$916$	3.49483e7	1.37622
$917$	3.02179e7	1.18670
$918$	−6.80655e7	−2.66576
$919$	−6.34791e6	−0.247937	−0.123969	−	0.992286i	$-0.539562\pi$
$919$	−6.34791e6	−0.247937	−0.123969	+	0.992286i	$0.539562\pi$
$920$	5.50941e7	2.14603
$921$	7.37448e6	0.286472
$922$	−349303.	−0.0135324
$923$	−385304.	−0.0148867
$924$	−1.13843e8	−4.38658
$925$	−316704.	−0.0121703
$926$	−1.97046e7	−0.755163
$927$	−706885.	−0.0270178
$928$	1.41512e6	0.0539415
$929$	2.80133e7	1.06494	0.532469	−	0.846449i	$-0.321264\pi$
$929$	2.80133e7	1.06494	0.532469	+	0.846449i	$0.321264\pi$
$930$	−6.13013e6	−0.232414
$931$	4.50243e7	1.70244
$932$	4.30878e7	1.62486
$933$	4.06247e7	1.52787
$934$	5.80386e7	2.17696
$935$	−5.48638e7	−2.05237
$936$	163535.	0.00610129
$937$	8.32451e6	0.309749	0.154874	−	0.987934i	$-0.450503\pi$
$937$	8.32451e6	0.309749	0.154874	+	0.987934i	$0.450503\pi$
$938$	3.76178e7	1.39600
$939$	−2.13746e7	−0.791105
$940$	−7.98699e6	−0.294824
$941$	5.98374e6	0.220292	0.110146	−	0.993915i	$-0.464868\pi$
$941$	5.98374e6	0.220292	0.110146	+	0.993915i	$0.464868\pi$
$942$	−9.27676e6	−0.340619
$943$	−4.99206e7	−1.82810
$944$	−4.42804e7	−1.61727
$945$	−4.67670e7	−1.70357
$946$	−3.35984e7	−1.22065
$947$	1.30352e7	0.472326	0.236163	−	0.971713i	$-0.424110\pi$
$947$	1.30352e7	0.472326	0.236163	+	0.971713i	$0.424110\pi$
$948$	9.87308e7	3.56806
$949$	5.16145e6	0.186040
$950$	4.04522e6	0.145423
$951$	3.98224e7	1.42783
$952$	−1.29265e8	−4.62261
$953$	−3.21255e7	−1.14582	−0.572911	−	0.819617i	$-0.694186\pi$
$953$	−3.21255e7	−1.14582	−0.572911	+	0.819617i	$0.694186\pi$
$954$	1.47383e6	0.0524297
$955$	−1.80104e7	−0.639020
$956$	−9.12722e7	−3.22994
$957$	6.83837e6	0.241364
$958$	3.73565e7	1.31508
$959$	2.54518e7	0.893660
$960$	2.15838e7	0.755875
$961$	−2.81539e7	−0.983399
$962$	1.16782e6	0.0406853
$963$	−426476.	−0.0148193
$964$	8.34736e6	0.289305
$965$	3.17927e7	1.09903
$966$	8.90863e7	3.07162
$967$	−4.86640e7	−1.67356	−0.836781	−	0.547538i	$-0.815565\pi$
$967$	−4.86640e7	−1.67356	−0.836781	+	0.547538i	$0.815565\pi$
$968$	4.01068e7	1.37572
$969$	4.53078e7	1.55011
$970$	5.98173e6	0.204126
$971$	448444.	0.0152637	0.00763185	−	0.999971i	$-0.497571\pi$
$971$	448444.	0.0152637	0.00763185	+	0.999971i	$0.497571\pi$
$972$	2.60413e6	0.0884090
$973$	−1.47735e7	−0.500266
$974$	−1.78035e6	−0.0601323
$975$	−353718.	−0.0119164
$976$	4.53896e7	1.52522
$977$	2.42795e7	0.813773	0.406887	−	0.913479i	$-0.366614\pi$
$977$	2.42795e7	0.813773	0.406887	+	0.913479i	$0.366614\pi$
$978$	4.83898e7	1.61773
$979$	−4.13319e7	−1.37825
$980$	−1.06122e8	−3.52973
$981$	163363.	0.00541977
$982$	9.94713e7	3.29169
$983$	−1.75735e7	−0.580062	−0.290031	−	0.957017i	$-0.593666\pi$
$983$	−1.75735e7	−0.580062	−0.290031	+	0.957017i	$0.593666\pi$
$984$	9.54593e7	3.14290
$985$	−3.27780e6	−0.107645
$986$	1.49570e7	0.489950
$987$	−6.70458e6	−0.219068
$988$	−1.00728e7	−0.328289
$989$	1.77545e7	0.577189
$990$	1.57054e6	0.0509286
$991$	2.20320e7	0.712640	0.356320	−	0.934364i	$-0.384031\pi$
$991$	2.20320e7	0.712640	0.356320	+	0.934364i	$0.384031\pi$
$992$	1.16003e6	0.0374274
$993$	−1.74962e7	−0.563080
$994$	−8.71840e6	−0.279879
$995$	−2.39044e7	−0.765457
$996$	6.96036e7	2.22323
$997$	1.20049e7	0.382490	0.191245	−	0.981542i	$-0.438748\pi$
$997$	1.20049e7	0.382490	0.191245	+	0.981542i	$0.438748\pi$
$998$	8.53469e7	2.71245
$999$	4.87779e6	0.154635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.a.b.1.6	✓	7
3.2	odd	2		261.6.a.e.1.2		7
4.3	odd	2		464.6.a.k.1.4		7
5.4	even	2		725.6.a.b.1.2		7
29.28	even	2		841.6.a.b.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.a.b.1.6	✓	7	1.1	even	1	trivial
261.6.a.e.1.2		7	3.2	odd	2
464.6.a.k.1.4		7	4.3	odd	2
725.6.a.b.1.2		7	5.4	even	2
841.6.a.b.1.2		7	29.28	even	2

Overview	Random
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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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+9.92709 q^{2} +15.4219 q^{3} +66.5471 q^{4} -58.0818 q^{5} +153.094 q^{6} -210.388 q^{7} +342.952 q^{8} -5.16616 q^{9} +O(q^{10})\)	\(q+9.92709 q^{2} +15.4219 q^{3} +66.5471 q^{4} -58.0818 q^{5} +153.094 q^{6} -210.388 q^{7} +342.952 q^{8} -5.16616 q^{9} -576.583 q^{10} +527.254 q^{11} +1026.28 q^{12} -92.3017 q^{13} -2088.54 q^{14} -895.729 q^{15} +1275.01 q^{16} +1791.54 q^{17} -51.2849 q^{18} +1639.87 q^{19} -3865.17 q^{20} -3244.57 q^{21} +5234.10 q^{22} -2765.87 q^{23} +5288.96 q^{24} +248.491 q^{25} -916.287 q^{26} -3827.18 q^{27} -14000.7 q^{28} +841.000 q^{29} -8891.98 q^{30} +689.400 q^{31} +1682.66 q^{32} +8131.24 q^{33} +17784.8 q^{34} +12219.7 q^{35} -343.793 q^{36} -1274.51 q^{37} +16279.2 q^{38} -1423.46 q^{39} -19919.3 q^{40} +18048.8 q^{41} -32209.1 q^{42} -6419.14 q^{43} +35087.2 q^{44} +300.060 q^{45} -27457.0 q^{46} +2066.40 q^{47} +19663.0 q^{48} +27456.0 q^{49} +2466.79 q^{50} +27628.8 q^{51} -6142.41 q^{52} -28738.1 q^{53} -37992.8 q^{54} -30623.8 q^{55} -72152.9 q^{56} +25289.9 q^{57} +8348.68 q^{58} -34729.5 q^{59} -59608.2 q^{60} +35599.4 q^{61} +6843.74 q^{62} +1086.90 q^{63} -24096.4 q^{64} +5361.05 q^{65} +80719.5 q^{66} -18011.5 q^{67} +119222. q^{68} -42654.9 q^{69} +121306. q^{70} +4174.40 q^{71} -1771.75 q^{72} -55919.3 q^{73} -12652.2 q^{74} +3832.19 q^{75} +109129. q^{76} -110928. q^{77} -14130.9 q^{78} +96202.6 q^{79} -74054.8 q^{80} -57766.9 q^{81} +179172. q^{82} +67821.3 q^{83} -215917. q^{84} -104056. q^{85} -63723.4 q^{86} +12969.8 q^{87} +180823. q^{88} -78390.8 q^{89} +2978.72 q^{90} +19419.1 q^{91} -184061. q^{92} +10631.8 q^{93} +20513.3 q^{94} -95246.6 q^{95} +25949.8 q^{96} -10374.5 q^{97} +272558. q^{98} -2723.88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9	\( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9} + 922 q^{10} + 1106 q^{11} + 214 q^{12} + 408 q^{13} - 2008 q^{14} - 614 q^{15} + 242 q^{16} - 874 q^{17} - 5598 q^{18} + 4288 q^{19} - 6350 q^{20} - 4200 q^{21} - 6114 q^{22} - 4532 q^{23} - 4318 q^{24} + 5527 q^{25} - 19806 q^{26} + 5942 q^{27} - 496 q^{28} + 5887 q^{29} - 16734 q^{30} + 7794 q^{31} + 7898 q^{32} + 34410 q^{33} + 20840 q^{34} + 7088 q^{35} - 572 q^{36} + 5086 q^{37} + 23732 q^{38} + 33394 q^{39} + 22906 q^{40} + 19826 q^{41} - 55440 q^{42} + 19498 q^{43} - 6074 q^{44} + 7854 q^{45} - 12404 q^{46} + 14278 q^{47} - 16406 q^{48} + 38431 q^{49} - 41066 q^{50} + 23892 q^{51} - 34302 q^{52} - 58644 q^{53} - 31194 q^{54} - 25574 q^{55} - 79560 q^{56} - 88540 q^{57} + 3364 q^{58} + 12888 q^{59} - 180822 q^{60} + 102866 q^{61} - 42654 q^{62} - 88632 q^{63} - 10170 q^{64} - 149206 q^{65} + 7710 q^{66} + 102996 q^{67} + 85100 q^{68} - 107244 q^{69} + 349480 q^{70} - 51596 q^{71} + 135568 q^{72} - 17566 q^{73} + 12132 q^{74} + 39356 q^{75} + 360740 q^{76} - 94104 q^{77} + 46386 q^{78} + 212058 q^{79} + 142510 q^{80} - 128285 q^{81} + 201924 q^{82} - 122928 q^{83} - 12328 q^{84} - 109336 q^{85} - 63290 q^{86} + 21866 q^{87} + 136666 q^{88} - 66510 q^{89} + 56084 q^{90} + 194368 q^{91} - 110108 q^{92} - 474274 q^{93} + 438926 q^{94} - 131676 q^{95} - 117018 q^{96} - 118182 q^{97} - 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9 + 922 * q^10 + 1106 * q^11 + 214 * q^12 + 408 * q^13 - 2008 * q^14 - 614 * q^15 + 242 * q^16 - 874 * q^17 - 5598 * q^18 + 4288 * q^19 - 6350 * q^20 - 4200 * q^21 - 6114 * q^22 - 4532 * q^23 - 4318 * q^24 + 5527 * q^25 - 19806 * q^26 + 5942 * q^27 - 496 * q^28 + 5887 * q^29 - 16734 * q^30 + 7794 * q^31 + 7898 * q^32 + 34410 * q^33 + 20840 * q^34 + 7088 * q^35 - 572 * q^36 + 5086 * q^37 + 23732 * q^38 + 33394 * q^39 + 22906 * q^40 + 19826 * q^41 - 55440 * q^42 + 19498 * q^43 - 6074 * q^44 + 7854 * q^45 - 12404 * q^46 + 14278 * q^47 - 16406 * q^48 + 38431 * q^49 - 41066 * q^50 + 23892 * q^51 - 34302 * q^52 - 58644 * q^53 - 31194 * q^54 - 25574 * q^55 - 79560 * q^56 - 88540 * q^57 + 3364 * q^58 + 12888 * q^59 - 180822 * q^60 + 102866 * q^61 - 42654 * q^62 - 88632 * q^63 - 10170 * q^64 - 149206 * q^65 + 7710 * q^66 + 102996 * q^67 + 85100 * q^68 - 107244 * q^69 + 349480 * q^70 - 51596 * q^71 + 135568 * q^72 - 17566 * q^73 + 12132 * q^74 + 39356 * q^75 + 360740 * q^76 - 94104 * q^77 + 46386 * q^78 + 212058 * q^79 + 142510 * q^80 - 128285 * q^81 + 201924 * q^82 - 122928 * q^83 - 12328 * q^84 - 109336 * q^85 - 63290 * q^86 + 21866 * q^87 + 136666 * q^88 - 66510 * q^89 + 56084 * q^90 + 194368 * q^91 - 110108 * q^92 - 474274 * q^93 + 438926 * q^94 - 131676 * q^95 - 117018 * q^96 - 118182 * q^97 - 29132 * q^98 + 300668 * q^99

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