LMFDB - Embedded newform 177.6.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.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:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + \cdots - 6400833792 $ x^13 - 331x^11 - 41x^10 + 41990x^9 + 7229x^8 - 2592364x^7 - 312100x^6 + 81977088x^5 - 3773728x^4 - 1245415104x^3 + 453320896x^2 + 6872784896*x - 6400833792
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$9.82137$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.82137 q^{2} -9.00000 q^{3} +64.4594 q^{4} +77.2018 q^{5} -88.3924 q^{6} -23.9833 q^{7} +318.795 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+9.82137 q^{2} -9.00000 q^{3} +64.4594 q^{4} +77.2018 q^{5} -88.3924 q^{6} -23.9833 q^{7} +318.795 q^{8} +81.0000 q^{9} +758.228 q^{10} +145.850 q^{11} -580.134 q^{12} +635.574 q^{13} -235.549 q^{14} -694.816 q^{15} +1068.31 q^{16} -1157.66 q^{17} +795.531 q^{18} +90.4356 q^{19} +4976.38 q^{20} +215.850 q^{21} +1432.44 q^{22} +1481.39 q^{23} -2869.16 q^{24} +2835.12 q^{25} +6242.21 q^{26} -729.000 q^{27} -1545.95 q^{28} +6899.00 q^{29} -6824.05 q^{30} +4590.44 q^{31} +290.810 q^{32} -1312.65 q^{33} -11369.8 q^{34} -1851.55 q^{35} +5221.21 q^{36} -9380.53 q^{37} +888.202 q^{38} -5720.17 q^{39} +24611.6 q^{40} -10612.2 q^{41} +2119.94 q^{42} +10318.3 q^{43} +9401.37 q^{44} +6253.35 q^{45} +14549.3 q^{46} +17173.7 q^{47} -9614.78 q^{48} -16231.8 q^{49} +27844.8 q^{50} +10418.9 q^{51} +40968.7 q^{52} -17429.0 q^{53} -7159.78 q^{54} +11259.8 q^{55} -7645.77 q^{56} -813.921 q^{57} +67757.6 q^{58} +3481.00 q^{59} -44787.4 q^{60} +6696.62 q^{61} +45084.4 q^{62} -1942.65 q^{63} -31329.7 q^{64} +49067.5 q^{65} -12892.0 q^{66} -13365.2 q^{67} -74622.0 q^{68} -13332.5 q^{69} -18184.8 q^{70} -5189.82 q^{71} +25822.4 q^{72} -47216.7 q^{73} -92129.7 q^{74} -25516.1 q^{75} +5829.42 q^{76} -3497.95 q^{77} -56179.9 q^{78} -98735.9 q^{79} +82475.4 q^{80} +6561.00 q^{81} -104227. q^{82} +21535.3 q^{83} +13913.5 q^{84} -89373.4 q^{85} +101340. q^{86} -62091.0 q^{87} +46496.2 q^{88} -41556.2 q^{89} +61416.4 q^{90} -15243.2 q^{91} +95489.5 q^{92} -41313.9 q^{93} +168669. q^{94} +6981.79 q^{95} -2617.29 q^{96} -37931.4 q^{97} -159419. q^{98} +11813.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) $ 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9} + 137 q^{10} + 250 q^{11} - 2214 q^{12} + 1054 q^{13} - 575 q^{14} + 126 q^{15} + 922 q^{16} + 271 q^{17} + 671 q^{19} - 5491 q^{20} - 3357 q^{21} + 1094 q^{22} + 3975 q^{23} - 1107 q^{24} + 15569 q^{25} + 4622 q^{26} - 9477 q^{27} + 21214 q^{28} - 10613 q^{29} - 1233 q^{30} + 25597 q^{31} + 15966 q^{32} - 2250 q^{33} + 31796 q^{34} + 6729 q^{35} + 19926 q^{36} + 17585 q^{37} + 34903 q^{38} - 9486 q^{39} + 31382 q^{40} + 12537 q^{41} + 5175 q^{42} + 26644 q^{43} + 6654 q^{44} - 1134 q^{45} + 149005 q^{46} + 52087 q^{47} - 8298 q^{48} + 95384 q^{49} + 121821 q^{50} - 2439 q^{51} + 263630 q^{52} + 20014 q^{53} + 120932 q^{55} + 126688 q^{56} - 6039 q^{57} + 86066 q^{58} + 45253 q^{59} + 49419 q^{60} - 11667 q^{61} + 164794 q^{62} + 30213 q^{63} + 151893 q^{64} - 28674 q^{65} - 9846 q^{66} + 1106 q^{67} - 4043 q^{68} - 35775 q^{69} + 56066 q^{70} + 21230 q^{71} + 9963 q^{72} + 81131 q^{73} + 102042 q^{74} - 140121 q^{75} + 73900 q^{76} - 104655 q^{77} - 41598 q^{78} - 13470 q^{79} - 191969 q^{80} + 85293 q^{81} + 79909 q^{82} - 76149 q^{83} - 190926 q^{84} + 10035 q^{85} - 321496 q^{86} + 95517 q^{87} - 276779 q^{88} - 190205 q^{89} + 11097 q^{90} + 80601 q^{91} + 45672 q^{92} - 230373 q^{93} + 36768 q^{94} + 9875 q^{95} - 143694 q^{96} + 160850 q^{97} - 116644 q^{98} + 20250 q^{99}+O(q^{100}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9 + 137 * q^10 + 250 * q^11 - 2214 * q^12 + 1054 * q^13 - 575 * q^14 + 126 * q^15 + 922 * q^16 + 271 * q^17 + 671 * q^19 - 5491 * q^20 - 3357 * q^21 + 1094 * q^22 + 3975 * q^23 - 1107 * q^24 + 15569 * q^25 + 4622 * q^26 - 9477 * q^27 + 21214 * q^28 - 10613 * q^29 - 1233 * q^30 + 25597 * q^31 + 15966 * q^32 - 2250 * q^33 + 31796 * q^34 + 6729 * q^35 + 19926 * q^36 + 17585 * q^37 + 34903 * q^38 - 9486 * q^39 + 31382 * q^40 + 12537 * q^41 + 5175 * q^42 + 26644 * q^43 + 6654 * q^44 - 1134 * q^45 + 149005 * q^46 + 52087 * q^47 - 8298 * q^48 + 95384 * q^49 + 121821 * q^50 - 2439 * q^51 + 263630 * q^52 + 20014 * q^53 + 120932 * q^55 + 126688 * q^56 - 6039 * q^57 + 86066 * q^58 + 45253 * q^59 + 49419 * q^60 - 11667 * q^61 + 164794 * q^62 + 30213 * q^63 + 151893 * q^64 - 28674 * q^65 - 9846 * q^66 + 1106 * q^67 - 4043 * q^68 - 35775 * q^69 + 56066 * q^70 + 21230 * q^71 + 9963 * q^72 + 81131 * q^73 + 102042 * q^74 - 140121 * q^75 + 73900 * q^76 - 104655 * q^77 - 41598 * q^78 - 13470 * q^79 - 191969 * q^80 + 85293 * q^81 + 79909 * q^82 - 76149 * q^83 - 190926 * q^84 + 10035 * q^85 - 321496 * q^86 + 95517 * q^87 - 276779 * q^88 - 190205 * q^89 + 11097 * q^90 + 80601 * q^91 + 45672 * q^92 - 230373 * q^93 + 36768 * q^94 + 9875 * q^95 - 143694 * q^96 + 160850 * q^97 - 116644 * q^98 + 20250 * 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 $

$2$	9.82137	1.73619	0.868095	−	0.496398i	$-0.165344\pi$
$2$	9.82137	1.73619	0.868095	+	0.496398i	$0.165344\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	64.4594	2.01435
$5$	77.2018	1.38103	0.690514	−	0.723319i	$-0.257384\pi$
$5$	77.2018	1.38103	0.690514	+	0.723319i	$0.257384\pi$
$6$	−88.3924	−1.00239
$7$	−23.9833	−0.184997	−0.0924983	−	0.995713i	$-0.529485\pi$
$7$	−23.9833	−0.184997	−0.0924983	+	0.995713i	$0.529485\pi$
$8$	318.795	1.76111
$9$	81.0000	0.333333
$10$	758.228	2.39773
$11$	145.850	0.363432	0.181716	−	0.983351i	$-0.441835\pi$
$11$	145.850	0.363432	0.181716	+	0.983351i	$0.441835\pi$
$12$	−580.134	−1.16299
$13$	635.574	1.04306	0.521528	−	0.853234i	$-0.325362\pi$
$13$	635.574	1.04306	0.521528	+	0.853234i	$0.325362\pi$
$14$	−235.549	−0.321189
$15$	−694.816	−0.797337
$16$	1068.31	1.04327
$17$	−1157.66	−0.971535	−0.485768	−	0.874088i	$-0.661460\pi$
$17$	−1157.66	−0.971535	−0.485768	+	0.874088i	$0.661460\pi$
$18$	795.531	0.578730
$19$	90.4356	0.0574719	0.0287359	−	0.999587i	$-0.490852\pi$
$19$	90.4356	0.0574719	0.0287359	+	0.999587i	$0.490852\pi$
$20$	4976.38	2.78188
$21$	215.850	0.106808
$22$	1432.44	0.630987
$23$	1481.39	0.583916	0.291958	−	0.956431i	$-0.405693\pi$
$23$	1481.39	0.583916	0.291958	+	0.956431i	$0.405693\pi$
$24$	−2869.16	−1.01678
$25$	2835.12	0.907238
$26$	6242.21	1.81094
$27$	−729.000	−0.192450
$28$	−1545.95	−0.372649
$29$	6899.00	1.52332	0.761660	−	0.647977i	$-0.224385\pi$
$29$	6899.00	1.52332	0.761660	+	0.647977i	$0.224385\pi$
$30$	−6824.05	−1.38433
$31$	4590.44	0.857926	0.428963	−	0.903322i	$-0.358879\pi$
$31$	4590.44	0.857926	0.428963	+	0.903322i	$0.358879\pi$
$32$	290.810	0.0502035
$33$	−1312.65	−0.209828
$34$	−11369.8	−1.68677
$35$	−1851.55	−0.255486
$36$	5221.21	0.671452
$37$	−9380.53	−1.12648	−0.563240	−	0.826294i	$-0.690445\pi$
$37$	−9380.53	−1.12648	−0.563240	+	0.826294i	$0.690445\pi$
$38$	888.202	0.0997821
$39$	−5720.17	−0.602209
$40$	24611.6	2.43215
$41$	−10612.2	−0.985934	−0.492967	−	0.870048i	$-0.664088\pi$
$41$	−10612.2	−0.985934	−0.492967	+	0.870048i	$0.664088\pi$
$42$	2119.94	0.185439
$43$	10318.3	0.851015	0.425507	−	0.904955i	$-0.360096\pi$
$43$	10318.3	0.851015	0.425507	+	0.904955i	$0.360096\pi$
$44$	9401.37	0.732081
$45$	6253.35	0.460343
$46$	14549.3	1.01379
$47$	17173.7	1.13402	0.567008	−	0.823712i	$-0.308101\pi$
$47$	17173.7	1.13402	0.567008	+	0.823712i	$0.308101\pi$
$48$	−9614.78	−0.602333
$49$	−16231.8	−0.965776
$50$	27844.8	1.57514
$51$	10418.9	0.560916
$52$	40968.7	2.10109
$53$	−17429.0	−0.852279	−0.426139	−	0.904658i	$-0.640127\pi$
$53$	−17429.0	−0.852279	−0.426139	+	0.904658i	$0.640127\pi$
$54$	−7159.78	−0.334130
$55$	11259.8	0.501910
$56$	−7645.77	−0.325800
$57$	−813.921	−0.0331814
$58$	67757.6	2.64477
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−44787.4	−1.60612
$61$	6696.62	0.230426	0.115213	−	0.993341i	$-0.463245\pi$
$61$	6696.62	0.230426	0.115213	+	0.993341i	$0.463245\pi$
$62$	45084.4	1.48952
$63$	−1942.65	−0.0616655
$64$	−31329.7	−0.956108
$65$	49067.5	1.44049
$66$	−12892.0	−0.364301
$67$	−13365.2	−0.363738	−0.181869	−	0.983323i	$-0.558215\pi$
$67$	−13365.2	−0.363738	−0.181869	+	0.983323i	$0.558215\pi$
$68$	−74622.0	−1.95702
$69$	−13332.5	−0.337124
$70$	−18184.8	−0.443571
$71$	−5189.82	−0.122182	−0.0610909	−	0.998132i	$-0.519458\pi$
$71$	−5189.82	−0.122182	−0.0610909	+	0.998132i	$0.519458\pi$
$72$	25822.4	0.587038
$73$	−47216.7	−1.03702	−0.518512	−	0.855071i	$-0.673514\pi$
$73$	−47216.7	−1.03702	−0.518512	+	0.855071i	$0.673514\pi$
$74$	−92129.7	−1.95578
$75$	−25516.1	−0.523794
$76$	5829.42	0.115769
$77$	−3497.95	−0.0672337
$78$	−56179.9	−1.04555
$79$	−98735.9	−1.77995	−0.889974	−	0.456012i	$-0.849278\pi$
$79$	−98735.9	−1.77995	−0.889974	+	0.456012i	$0.849278\pi$
$80$	82475.4	1.44079
$81$	6561.00	0.111111
$82$	−104227.	−1.71177
$83$	21535.3	0.343127	0.171563	−	0.985173i	$-0.445118\pi$
$83$	21535.3	0.343127	0.171563	+	0.985173i	$0.445118\pi$
$84$	13913.5	0.215149
$85$	−89373.4	−1.34172
$86$	101340.	1.47752
$87$	−62091.0	−0.879489
$88$	46496.2	0.640045
$89$	−41556.2	−0.556110	−0.278055	−	0.960565i	$-0.589690\pi$
$89$	−41556.2	−0.556110	−0.278055	+	0.960565i	$0.589690\pi$
$90$	61416.4	0.799242
$91$	−15243.2	−0.192962
$92$	95489.5	1.17621
$93$	−41313.9	−0.495324
$94$	168669.	1.96887
$95$	6981.79	0.0793703
$96$	−2617.29	−0.0289850
$97$	−37931.4	−0.409326	−0.204663	−	0.978832i	$-0.565610\pi$
$97$	−37931.4	−0.409326	−0.204663	+	0.978832i	$0.565610\pi$
$98$	−159419.	−1.67677
$99$	11813.8	0.121144
$100$	182750.	1.82750
$101$	−59808.0	−0.583386	−0.291693	−	0.956512i	$-0.594219\pi$
$101$	−59808.0	−0.583386	−0.291693	+	0.956512i	$0.594219\pi$
$102$	102328.	0.973857
$103$	−110782.	−1.02891	−0.514453	−	0.857519i	$-0.672005\pi$
$103$	−110782.	−1.02891	−0.514453	+	0.857519i	$0.672005\pi$
$104$	202618.	1.83694
$105$	16664.0	0.147505
$106$	−171176.	−1.47972
$107$	142915.	1.20675	0.603376	−	0.797457i	$-0.293822\pi$
$107$	142915.	1.20675	0.603376	+	0.797457i	$0.293822\pi$
$108$	−46990.9	−0.387663
$109$	−134106.	−1.08114	−0.540569	−	0.841299i	$-0.681791\pi$
$109$	−134106.	−1.08114	−0.540569	+	0.841299i	$0.681791\pi$
$110$	110587.	0.871411
$111$	84424.8	0.650373
$112$	−25621.6	−0.193002
$113$	−5645.33	−0.0415904	−0.0207952	−	0.999784i	$-0.506620\pi$
$113$	−5645.33	−0.0415904	−0.0207952	+	0.999784i	$0.506620\pi$
$114$	−7993.82	−0.0576092
$115$	114366.	0.806404
$116$	444705.	3.06851
$117$	51481.5	0.347685
$118$	34188.2	0.226033
$119$	27764.5	0.179731
$120$	−221504.	−1.40420
$121$	−139779.	−0.867917
$122$	65770.0	0.400063
$123$	95510.2	0.569229
$124$	295897.	1.72817
$125$	−22379.3	−0.128107
$126$	−19079.5	−0.107063
$127$	143473.	0.789336	0.394668	−	0.918824i	$-0.370860\pi$
$127$	143473.	0.789336	0.394668	+	0.918824i	$0.370860\pi$
$128$	−317007.	−1.71019
$129$	−92864.7	−0.491334
$130$	481910.	2.50096
$131$	16953.1	0.0863117	0.0431559	−	0.999068i	$-0.486259\pi$
$131$	16953.1	0.0863117	0.0431559	+	0.999068i	$0.486259\pi$
$132$	−84612.3	−0.422667
$133$	−2168.94	−0.0106321
$134$	−131265.	−0.631518
$135$	−56280.1	−0.265779
$136$	−369057.	−1.71098
$137$	−212200.	−0.965928	−0.482964	−	0.875640i	$-0.660440\pi$
$137$	−212200.	−0.965928	−0.482964	+	0.875640i	$0.660440\pi$
$138$	−130944.	−0.585311
$139$	−237803.	−1.04395	−0.521975	−	0.852961i	$-0.674805\pi$
$139$	−237803.	−1.04395	−0.521975	+	0.852961i	$0.674805\pi$
$140$	−119350.	−0.514638
$141$	−154563.	−0.654724
$142$	−50971.2	−0.212131
$143$	92698.2	0.379080
$144$	86533.1	0.347757
$145$	532615.	2.10375
$146$	−463733.	−1.80047
$147$	146086.	0.557591
$148$	−604663.	−2.26913
$149$	−153478.	−0.566344	−0.283172	−	0.959069i	$-0.591387\pi$
$149$	−153478.	−0.566344	−0.283172	+	0.959069i	$0.591387\pi$
$150$	−250603.	−0.909406
$151$	220634.	0.787463	0.393732	−	0.919225i	$-0.371184\pi$
$151$	220634.	0.787463	0.393732	+	0.919225i	$0.371184\pi$
$152$	28830.5	0.101214
$153$	−93770.4	−0.323845
$154$	−34354.7	−0.116730
$155$	354390.	1.18482
$156$	−368718.	−1.21306
$157$	426394.	1.38058	0.690291	−	0.723532i	$-0.257482\pi$
$157$	426394.	1.38058	0.690291	+	0.723532i	$0.257482\pi$
$158$	−969722.	−3.09033
$159$	156861.	0.492063
$160$	22451.0	0.0693324
$161$	−35528.6	−0.108022
$162$	64438.0	0.192910
$163$	285746.	0.842387	0.421194	−	0.906971i	$-0.361611\pi$
$163$	285746.	0.842387	0.421194	+	0.906971i	$0.361611\pi$
$164$	−684059.	−1.98602
$165$	−101339.	−0.289778
$166$	211506.	0.595734
$167$	−598834.	−1.66156	−0.830779	−	0.556602i	$-0.812105\pi$
$167$	−598834.	−1.66156	−0.830779	+	0.556602i	$0.812105\pi$
$168$	68811.9	0.188101
$169$	32661.4	0.0879668
$170$	−877770.	−2.32948
$171$	7325.29	0.0191573
$172$	665111.	1.71425
$173$	79733.5	0.202547	0.101273	−	0.994859i	$-0.467708\pi$
$173$	79733.5	0.202547	0.101273	+	0.994859i	$0.467708\pi$
$174$	−609819.	−1.52696
$175$	−67995.5	−0.167836
$176$	155812.	0.379158
$177$	−31329.0	−0.0751646
$178$	−408139.	−0.965512
$179$	598259.	1.39559	0.697794	−	0.716299i	$-0.254165\pi$
$179$	598259.	1.39559	0.697794	+	0.716299i	$0.254165\pi$
$180$	403087.	0.927294
$181$	750480.	1.70272	0.851358	−	0.524584i	$-0.175779\pi$
$181$	750480.	1.70272	0.851358	+	0.524584i	$0.175779\pi$
$182$	−149709.	−0.335019
$183$	−60269.5	−0.133036
$184$	472261.	1.02834
$185$	−724194.	−1.55570
$186$	−405759.	−0.859976
$187$	−168844.	−0.353087
$188$	1.10701e6	2.28431
$189$	17483.8	0.0356026
$190$	68570.8	0.137802
$191$	−252954.	−0.501716	−0.250858	−	0.968024i	$-0.580713\pi$
$191$	−252954.	−0.501716	−0.250858	+	0.968024i	$0.580713\pi$
$192$	281968.	0.552009
$193$	−93061.2	−0.179836	−0.0899178	−	0.995949i	$-0.528660\pi$
$193$	−93061.2	−0.179836	−0.0899178	+	0.995949i	$0.528660\pi$
$194$	−372538.	−0.710668
$195$	−441607.	−0.831667
$196$	−1.04629e6	−1.94542
$197$	147289.	0.270399	0.135200	−	0.990818i	$-0.456832\pi$
$197$	147289.	0.270399	0.135200	+	0.990818i	$0.456832\pi$
$198$	116028.	0.210329
$199$	715021.	1.27993	0.639965	−	0.768404i	$-0.278949\pi$
$199$	715021.	1.27993	0.639965	+	0.768404i	$0.278949\pi$
$200$	903823.	1.59775
$201$	120287.	0.210004
$202$	−587397.	−1.01287
$203$	−165461.	−0.281809
$204$	671598.	1.12988
$205$	−819285.	−1.36160
$206$	−1.08803e6	−1.78638
$207$	119993.	0.194639
$208$	678990.	1.08819
$209$	13190.0	0.0208871
$210$	163663.	0.256096
$211$	320613.	0.495764	0.247882	−	0.968790i	$-0.420265\pi$
$211$	320613.	0.495764	0.247882	+	0.968790i	$0.420265\pi$
$212$	−1.12346e6	−1.71679
$213$	46708.4	0.0705417
$214$	1.40362e6	2.09515
$215$	796592.	1.17528
$216$	−232402.	−0.338926
$217$	−110094.	−0.158713
$218$	−1.31710e6	−1.87706
$219$	424950.	0.598726
$220$	725803.	1.01102
$221$	−735778.	−1.01337
$222$	829167.	1.12917
$223$	95065.5	0.128015	0.0640075	−	0.997949i	$-0.479612\pi$
$223$	95065.5	0.128015	0.0640075	+	0.997949i	$0.479612\pi$
$224$	−6974.58	−0.00928748
$225$	229645.	0.302413
$226$	−55444.9	−0.0722088
$227$	725771.	0.934835	0.467418	−	0.884037i	$-0.345184\pi$
$227$	725771.	0.934835	0.467418	+	0.884037i	$0.345184\pi$
$228$	−52464.8	−0.0668391
$229$	1.35458e6	1.70693	0.853467	−	0.521146i	$-0.174495\pi$
$229$	1.35458e6	1.70693	0.853467	+	0.521146i	$0.174495\pi$
$230$	1.12323e6	1.40007
$231$	31481.6	0.0388174
$232$	2.19937e6	2.68274
$233$	796439.	0.961087	0.480543	−	0.876971i	$-0.340439\pi$
$233$	796439.	0.961087	0.480543	+	0.876971i	$0.340439\pi$
$234$	505619.	0.603648
$235$	1.32584e6	1.56611
$236$	224383.	0.262247
$237$	888623.	1.02765
$238$	272685.	0.312047
$239$	−84637.6	−0.0958449	−0.0479224	−	0.998851i	$-0.515260\pi$
$239$	−84637.6	−0.0958449	−0.0479224	+	0.998851i	$0.515260\pi$
$240$	−742279.	−0.831838
$241$	1.36923e6	1.51857	0.759283	−	0.650761i	$-0.225550\pi$
$241$	1.36923e6	1.51857	0.759283	+	0.650761i	$0.225550\pi$
$242$	−1.37282e6	−1.50687
$243$	−59049.0	−0.0641500
$244$	431660.	0.464159
$245$	−1.25312e6	−1.33376
$246$	938041.	0.988290
$247$	57478.5	0.0599464
$248$	1.46341e6	1.51090
$249$	−193817.	−0.198104
$250$	−219795.	−0.222417
$251$	−267021.	−0.267523	−0.133761	−	0.991014i	$-0.542706\pi$
$251$	−267021.	−0.267523	−0.133761	+	0.991014i	$0.542706\pi$
$252$	−125222.	−0.124216
$253$	216060.	0.212214
$254$	1.40910e6	1.37044
$255$	804361.	0.774641
$256$	−2.11089e6	−2.01310
$257$	−1.07867e6	−1.01872	−0.509359	−	0.860554i	$-0.670118\pi$
$257$	−1.07867e6	−1.01872	−0.509359	+	0.860554i	$0.670118\pi$
$258$	−912059.	−0.853048
$259$	224976.	0.208395
$260$	3.16286e6	2.90166
$261$	558819.	0.507773
$262$	166502.	0.149854
$263$	840608.	0.749383	0.374692	−	0.927149i	$-0.377749\pi$
$263$	840608.	0.749383	0.374692	+	0.927149i	$0.377749\pi$
$264$	−418466.	−0.369530
$265$	−1.34555e6	−1.17702
$266$	−21302.0	−0.0184594
$267$	374006.	0.321070
$268$	−861512.	−0.732697
$269$	−812528.	−0.684633	−0.342316	−	0.939585i	$-0.611211\pi$
$269$	−812528.	−0.684633	−0.342316	+	0.939585i	$0.611211\pi$
$270$	−552748.	−0.461443
$271$	−1.90571e6	−1.57628	−0.788139	−	0.615497i	$-0.788955\pi$
$271$	−1.90571e6	−1.57628	−0.788139	+	0.615497i	$0.788955\pi$
$272$	−1.23674e6	−1.01357
$273$	137188.	0.111407
$274$	−2.08410e6	−1.67703
$275$	413501.	0.329720
$276$	−859406.	−0.679087
$277$	−1.23583e6	−0.967743	−0.483872	−	0.875139i	$-0.660770\pi$
$277$	−1.23583e6	−0.967743	−0.483872	+	0.875139i	$0.660770\pi$
$278$	−2.33555e6	−1.81250
$279$	371825.	0.285975
$280$	−590267.	−0.449939
$281$	143251.	0.108226	0.0541132	−	0.998535i	$-0.482767\pi$
$281$	143251.	0.108226	0.0541132	+	0.998535i	$0.482767\pi$
$282$	−1.51802e6	−1.13673
$283$	1.76710e6	1.31158	0.655791	−	0.754943i	$-0.272335\pi$
$283$	1.76710e6	1.31158	0.655791	+	0.754943i	$0.272335\pi$
$284$	−334533.	−0.246118
$285$	−62836.1	−0.0458245
$286$	910423.	0.658155
$287$	254517.	0.182394
$288$	23555.6	0.0167345
$289$	−79681.2	−0.0561191
$290$	5.23101e6	3.65251
$291$	341383.	0.236325
$292$	−3.04356e6	−2.08893
$293$	2.55216e6	1.73676	0.868379	−	0.495902i	$-0.165162\pi$
$293$	2.55216e6	1.73676	0.868379	+	0.495902i	$0.165162\pi$
$294$	1.43477e6	0.968084
$295$	268740.	0.179795
$296$	−2.99047e6	−1.98386
$297$	−106324.	−0.0699426
$298$	−1.50736e6	−0.983281
$299$	941534.	0.609057
$300$	−1.64475e6	−1.05511
$301$	−247467.	−0.157435
$302$	2.16693e6	1.36719
$303$	538272.	0.336818
$304$	96613.2	0.0599588
$305$	516991.	0.318224
$306$	−920954.	−0.562257
$307$	1.81361e6	1.09824	0.549121	−	0.835743i	$-0.314963\pi$
$307$	1.81361e6	1.09824	0.549121	+	0.835743i	$0.314963\pi$
$308$	−225476.	−0.135433
$309$	997037.	0.594039
$310$	3.48060e6	2.05707
$311$	−2.65916e6	−1.55899	−0.779494	−	0.626409i	$-0.784524\pi$
$311$	−2.65916e6	−1.55899	−0.779494	+	0.626409i	$0.784524\pi$
$312$	−1.82356e6	−1.06056
$313$	−3.38531e6	−1.95316	−0.976581	−	0.215152i	$-0.930975\pi$
$313$	−3.38531e6	−1.95316	−0.976581	+	0.215152i	$0.930975\pi$
$314$	4.18778e6	2.39695
$315$	−149976.	−0.0851618
$316$	−6.36445e6	−3.58545
$317$	−1.58937e6	−0.888336	−0.444168	−	0.895943i	$-0.646501\pi$
$317$	−1.58937e6	−0.888336	−0.444168	+	0.895943i	$0.646501\pi$
$318$	1.54059e6	0.854315
$319$	1.00622e6	0.553623
$320$	−2.41871e6	−1.32041
$321$	−1.28623e6	−0.696719
$322$	−348940.	−0.187547
$323$	−104694.	−0.0558360
$324$	422918.	0.223817
$325$	1.80193e6	0.946301
$326$	2.80642e6	1.46254
$327$	1.20695e6	0.624196
$328$	−3.38314e6	−1.73634
$329$	−411882.	−0.209789
$330$	−995285.	−0.503109
$331$	341793.	0.171472	0.0857359	−	0.996318i	$-0.472676\pi$
$331$	341793.	0.171472	0.0857359	+	0.996318i	$0.472676\pi$
$332$	1.38815e6	0.691180
$333$	−759823.	−0.375493
$334$	−5.88137e6	−2.88478
$335$	−1.03182e6	−0.502332
$336$	230594.	0.111430
$337$	−1.48322e6	−0.711429	−0.355714	−	0.934595i	$-0.615762\pi$
$337$	−1.48322e6	−0.711429	−0.355714	+	0.934595i	$0.615762\pi$
$338$	320780.	0.152727
$339$	50808.0	0.0240122
$340$	−5.76095e6	−2.70270
$341$	669513.	0.311798
$342$	71944.4	0.0332607
$343$	792379.	0.363662
$344$	3.28943e6	1.49873
$345$	−1.02929e6	−0.465578
$346$	783092.	0.351660
$347$	−2.17696e6	−0.970568	−0.485284	−	0.874357i	$-0.661284\pi$
$347$	−2.17696e6	−0.970568	−0.485284	+	0.874357i	$0.661284\pi$
$348$	−4.00235e6	−1.77160
$349$	3.75756e6	1.65136	0.825681	−	0.564137i	$-0.190791\pi$
$349$	3.75756e6	1.65136	0.825681	+	0.564137i	$0.190791\pi$
$350$	−667809.	−0.291395
$351$	−463334.	−0.200736
$352$	42414.5	0.0182456
$353$	2.46041e6	1.05092	0.525462	−	0.850817i	$-0.323893\pi$
$353$	2.46041e6	1.05092	0.525462	+	0.850817i	$0.323893\pi$
$354$	−307694.	−0.130500
$355$	−400664.	−0.168737
$356$	−2.67868e6	−1.12020
$357$	−249880.	−0.103768
$358$	5.87573e6	2.42300
$359$	−4.25780e6	−1.74361	−0.871805	−	0.489853i	$-0.837050\pi$
$359$	−4.25780e6	−1.74361	−0.871805	+	0.489853i	$0.837050\pi$
$360$	1.99354e6	0.810715
$361$	−2.46792e6	−0.996697
$362$	7.37074e6	2.95624
$363$	1.25801e6	0.501092
$364$	−982564.	−0.388694
$365$	−3.64522e6	−1.43216
$366$	−591930.	−0.230976
$367$	3.82672e6	1.48307	0.741535	−	0.670914i	$-0.234098\pi$
$367$	3.82672e6	1.48307	0.741535	+	0.670914i	$0.234098\pi$
$368$	1.58258e6	0.609182
$369$	−859592.	−0.328645
$370$	−7.11258e6	−2.70099
$371$	418004.	0.157669
$372$	−2.66307e6	−0.997757
$373$	2.43707e6	0.906976	0.453488	−	0.891262i	$-0.350179\pi$
$373$	2.43707e6	0.906976	0.453488	+	0.891262i	$0.350179\pi$
$374$	−1.65828e6	−0.613026
$375$	201414.	0.0739623
$376$	5.47490e6	1.99713
$377$	4.38483e6	1.58891
$378$	171715.	0.0618129
$379$	667622.	0.238744	0.119372	−	0.992850i	$-0.461912\pi$
$379$	667622.	0.238744	0.119372	+	0.992850i	$0.461912\pi$
$380$	450042.	0.159880
$381$	−1.29126e6	−0.455723
$382$	−2.48435e6	−0.871074
$383$	−2.48371e6	−0.865176	−0.432588	−	0.901592i	$-0.642400\pi$
$383$	−2.48371e6	−0.865176	−0.432588	+	0.901592i	$0.642400\pi$
$384$	2.85306e6	0.987378
$385$	−270048.	−0.0928517
$386$	−913989.	−0.312229
$387$	835783.	0.283672
$388$	−2.44503e6	−0.824528
$389$	−206595.	−0.0692222	−0.0346111	−	0.999401i	$-0.511019\pi$
$389$	−206595.	−0.0692222	−0.0346111	+	0.999401i	$0.511019\pi$
$390$	−4.33719e6	−1.44393
$391$	−1.71495e6	−0.567295
$392$	−5.17462e6	−1.70084
$393$	−152578.	−0.0498321
$394$	1.44658e6	0.469464
$395$	−7.62259e6	−2.45816
$396$	761511.	0.244027
$397$	2.77270e6	0.882931	0.441466	−	0.897278i	$-0.354459\pi$
$397$	2.77270e6	0.882931	0.441466	+	0.897278i	$0.354459\pi$
$398$	7.02249e6	2.22220
$399$	19520.5	0.00613845
$400$	3.02878e6	0.946495
$401$	944549.	0.293335	0.146667	−	0.989186i	$-0.453145\pi$
$401$	944549.	0.293335	0.146667	+	0.989186i	$0.453145\pi$
$402$	1.18138e6	0.364607
$403$	2.91756e6	0.894865
$404$	−3.85519e6	−1.17515
$405$	506521.	0.153448
$406$	−1.62505e6	−0.489274
$407$	−1.36815e6	−0.409399
$408$	3.32151e6	0.987837
$409$	3.83304e6	1.13301	0.566507	−	0.824057i	$-0.308294\pi$
$409$	3.83304e6	1.13301	0.566507	+	0.824057i	$0.308294\pi$
$410$	−8.04650e6	−2.36400
$411$	1.90980e6	0.557679
$412$	−7.14093e6	−2.07258
$413$	−83485.9	−0.0240845
$414$	1.17849e6	0.337930
$415$	1.66256e6	0.473868
$416$	184831.	0.0523651
$417$	2.14023e6	0.602725
$418$	129544.	0.0362640
$419$	1.17123e6	0.325916	0.162958	−	0.986633i	$-0.447896\pi$
$419$	1.17123e6	0.325916	0.162958	+	0.986633i	$0.447896\pi$
$420$	1.07415e6	0.297127
$421$	2.54999e6	0.701186	0.350593	−	0.936528i	$-0.385980\pi$
$421$	2.54999e6	0.701186	0.350593	+	0.936528i	$0.385980\pi$
$422$	3.14886e6	0.860741
$423$	1.39107e6	0.378005
$424$	−5.55627e6	−1.50096
$425$	−3.28210e6	−0.881414
$426$	458741.	0.122474
$427$	−160607.	−0.0426280
$428$	9.21221e6	2.43083
$429$	−834284.	−0.218862
$430$	7.82362e6	2.04050
$431$	−6.14769e6	−1.59411	−0.797056	−	0.603905i	$-0.793611\pi$
$431$	−6.14769e6	−1.59411	−0.797056	+	0.603905i	$0.793611\pi$
$432$	−778798.	−0.200778
$433$	4.20211e6	1.07708	0.538540	−	0.842600i	$-0.318976\pi$
$433$	4.20211e6	1.07708	0.538540	+	0.842600i	$0.318976\pi$
$434$	−1.08127e6	−0.275556
$435$	−4.79354e6	−1.21460
$436$	−8.64438e6	−2.17780
$437$	133971.	0.0335587
$438$	4.17360e6	1.03950
$439$	27657.9	0.00684948	0.00342474	−	0.999994i	$-0.498910\pi$
$439$	27657.9	0.00684948	0.00342474	+	0.999994i	$0.498910\pi$
$440$	3.58959e6	0.883920
$441$	−1.31478e6	−0.321925
$442$	−7.22635e6	−1.75940
$443$	4.50548e6	1.09077	0.545383	−	0.838187i	$-0.316384\pi$
$443$	4.50548e6	1.09077	0.545383	+	0.838187i	$0.316384\pi$
$444$	5.44197e6	1.31008
$445$	−3.20821e6	−0.768003
$446$	933674.	0.222258
$447$	1.38130e6	0.326979
$448$	751391.	0.176877
$449$	188862.	0.0442109	0.0221054	−	0.999756i	$-0.492963\pi$
$449$	188862.	0.0442109	0.0221054	+	0.999756i	$0.492963\pi$
$450$	2.25543e6	0.525046
$451$	−1.54779e6	−0.358320
$452$	−363894.	−0.0837778
$453$	−1.98571e6	−0.454642
$454$	7.12807e6	1.62305
$455$	−1.17680e6	−0.266486
$456$	−259474.	−0.0584362
$457$	−2.89584e6	−0.648610	−0.324305	−	0.945953i	$-0.605130\pi$
$457$	−2.89584e6	−0.648610	−0.324305	+	0.945953i	$0.605130\pi$
$458$	1.33039e7	2.96356
$459$	843934.	0.186972
$460$	7.37197e6	1.62438
$461$	−2.84845e6	−0.624246	−0.312123	−	0.950042i	$-0.601040\pi$
$461$	−2.84845e6	−0.624246	−0.312123	+	0.950042i	$0.601040\pi$
$462$	309192.	0.0673944
$463$	−757707.	−0.164267	−0.0821333	−	0.996621i	$-0.526173\pi$
$463$	−757707.	−0.164267	−0.0821333	+	0.996621i	$0.526173\pi$
$464$	7.37027e6	1.58924
$465$	−3.18951e6	−0.684056
$466$	7.82212e6	1.66863
$467$	5.82938e6	1.23689	0.618443	−	0.785829i	$-0.287764\pi$
$467$	5.82938e6	1.23689	0.618443	+	0.785829i	$0.287764\pi$
$468$	3.31846e6	0.700362
$469$	320542.	0.0672903
$470$	1.30216e7	2.71906
$471$	−3.83755e6	−0.797080
$472$	1.10973e6	0.229277
$473$	1.50492e6	0.309286
$474$	8.72750e6	1.78420
$475$	256396.	0.0521407
$476$	1.78968e6	0.362042
$477$	−1.41175e6	−0.284093
$478$	−831258.	−0.166405
$479$	727597.	0.144895	0.0724473	−	0.997372i	$-0.476919\pi$
$479$	727597.	0.144895	0.0724473	+	0.997372i	$0.476919\pi$
$480$	−202059.	−0.0400291
$481$	−5.96202e6	−1.17498
$482$	1.34477e7	2.63652
$483$	319758.	0.0623668
$484$	−9.01006e6	−1.74829
$485$	−2.92837e6	−0.565291
$486$	−579942.	−0.111377
$487$	−9.50076e6	−1.81525	−0.907624	−	0.419785i	$-0.862106\pi$
$487$	−9.50076e6	−1.81525	−0.907624	+	0.419785i	$0.862106\pi$
$488$	2.13485e6	0.405805
$489$	−2.57172e6	−0.486353
$490$	−1.23074e7	−2.31567
$491$	−9.63743e6	−1.80409	−0.902043	−	0.431645i	$-0.857933\pi$
$491$	−9.63743e6	−1.80409	−0.902043	+	0.431645i	$0.857933\pi$
$492$	6.15653e6	1.14663
$493$	−7.98669e6	−1.47996
$494$	564518.	0.104078
$495$	912048.	0.167303
$496$	4.90400e6	0.895049
$497$	124469.	0.0226032
$498$	−1.90355e6	−0.343947
$499$	7.42979e6	1.33575	0.667875	−	0.744274i	$-0.267204\pi$
$499$	7.42979e6	1.33575	0.667875	+	0.744274i	$0.267204\pi$
$500$	−1.44255e6	−0.258052
$501$	5.38951e6	0.959301
$502$	−2.62251e6	−0.464470
$503$	1.06712e7	1.88058	0.940292	−	0.340370i	$-0.110552\pi$
$503$	1.06712e7	1.88058	0.940292	+	0.340370i	$0.110552\pi$
$504$	−619307.	−0.108600
$505$	−4.61729e6	−0.805673
$506$	2.12201e6	0.368443
$507$	−293953.	−0.0507876
$508$	9.24819e6	1.59000
$509$	−5.26228e6	−0.900283	−0.450142	−	0.892957i	$-0.648627\pi$
$509$	−5.26228e6	−0.900283	−0.450142	+	0.892957i	$0.648627\pi$
$510$	7.89993e6	1.34492
$511$	1.13241e6	0.191846
$512$	−1.05876e7	−1.78494
$513$	−65927.6	−0.0110605
$514$	−1.05940e7	−1.76869
$515$	−8.55256e6	−1.42095
$516$	−5.98600e6	−0.989720
$517$	2.50478e6	0.412138
$518$	2.20957e6	0.361813
$519$	−717601.	−0.116940
$520$	1.56425e7	2.53687
$521$	7.19552e6	1.16136	0.580682	−	0.814131i	$-0.302786\pi$
$521$	7.19552e6	1.16136	0.580682	+	0.814131i	$0.302786\pi$
$522$	5.48837e6	0.881591
$523$	−1.24540e7	−1.99092	−0.995458	−	0.0951974i	$-0.969652\pi$
$523$	−1.24540e7	−1.99092	−0.995458	+	0.0951974i	$0.969652\pi$
$524$	1.09278e6	0.173862
$525$	611960.	0.0969002
$526$	8.25592e6	1.30107
$527$	−5.31416e6	−0.833505
$528$	−1.40231e6	−0.218907
$529$	−4.24182e6	−0.659042
$530$	−1.32151e7	−2.04353
$531$	281961.	0.0433963
$532$	−139809.	−0.0214168
$533$	−6.74487e6	−1.02838
$534$	3.67325e6	0.557439
$535$	1.10333e7	1.66656
$536$	−4.26076e6	−0.640583
$537$	−5.38433e6	−0.805743
$538$	−7.98014e6	−1.18865
$539$	−2.36740e6	−0.350994
$540$	−3.62778e6	−0.535373
$541$	−8.48547e6	−1.24647	−0.623236	−	0.782034i	$-0.714182\pi$
$541$	−8.48547e6	−1.24647	−0.623236	+	0.782034i	$0.714182\pi$
$542$	−1.87167e7	−2.73672
$543$	−6.75432e6	−0.983064
$544$	−336659.	−0.0487745
$545$	−1.03532e7	−1.49308
$546$	1.34738e6	0.193423
$547$	−928302.	−0.132654	−0.0663271	−	0.997798i	$-0.521128\pi$
$547$	−928302.	−0.132654	−0.0663271	+	0.997798i	$0.521128\pi$
$548$	−1.36783e7	−1.94572
$549$	542426.	0.0768085
$550$	4.06115e6	0.572456
$551$	623915.	0.0875481
$552$	−4.25035e6	−0.593713
$553$	2.36801e6	0.329284
$554$	−1.21376e7	−1.68019
$555$	6.51775e6	0.898183
$556$	−1.53286e7	−2.10289
$557$	−1.03984e7	−1.42013	−0.710063	−	0.704139i	$-0.751333\pi$
$557$	−1.03984e7	−1.42013	−0.710063	+	0.704139i	$0.751333\pi$
$558$	3.65183e6	0.496507
$559$	6.55805e6	0.887657
$560$	−1.97803e6	−0.266541
$561$	1.51960e6	0.203855
$562$	1.40692e6	0.187901
$563$	−5.47533e6	−0.728013	−0.364006	−	0.931396i	$-0.618591\pi$
$563$	−5.47533e6	−0.728013	−0.364006	+	0.931396i	$0.618591\pi$
$564$	−9.96305e6	−1.31885
$565$	−435830.	−0.0574375
$566$	1.73554e7	2.27715
$567$	−157354.	−0.0205552
$568$	−1.65449e6	−0.215176
$569$	1.13304e7	1.46711	0.733557	−	0.679628i	$-0.237859\pi$
$569$	1.13304e7	1.46711	0.733557	+	0.679628i	$0.237859\pi$
$570$	−617137.	−0.0795600
$571$	1.87564e6	0.240746	0.120373	−	0.992729i	$-0.461591\pi$
$571$	1.87564e6	0.240746	0.120373	+	0.992729i	$0.461591\pi$
$572$	5.97527e6	0.763602
$573$	2.27659e6	0.289666
$574$	2.49970e6	0.316671
$575$	4.19992e6	0.529751
$576$	−2.53771e6	−0.318703
$577$	5.38208e6	0.672993	0.336496	−	0.941685i	$-0.390758\pi$
$577$	5.38208e6	0.672993	0.336496	+	0.941685i	$0.390758\pi$
$578$	−782578.	−0.0974335
$579$	837551.	0.103828
$580$	3.43320e7	4.23769
$581$	−516487.	−0.0634773
$582$	3.35285e6	0.410304
$583$	−2.54200e6	−0.309745
$584$	−1.50525e7	−1.82632
$585$	3.97447e6	0.480163
$586$	2.50657e7	3.01534
$587$	2.31403e6	0.277187	0.138594	−	0.990349i	$-0.455742\pi$
$587$	2.31403e6	0.277187	0.138594	+	0.990349i	$0.455742\pi$
$588$	9.41662e6	1.12319
$589$	415139.	0.0493066
$590$	2.63939e6	0.312157
$591$	−1.32560e6	−0.156115
$592$	−1.00213e7	−1.17522
$593$	1.02708e7	1.19941	0.599704	−	0.800222i	$-0.295285\pi$
$593$	1.02708e7	1.19941	0.599704	+	0.800222i	$0.295285\pi$
$594$	−1.04425e6	−0.121434
$595$	2.14347e6	0.248213
$596$	−9.89310e6	−1.14082
$597$	−6.43519e6	−0.738968
$598$	9.24716e6	1.05744
$599$	485116.	0.0552432	0.0276216	−	0.999618i	$-0.491207\pi$
$599$	485116.	0.0552432	0.0276216	+	0.999618i	$0.491207\pi$
$600$	−8.13441e6	−0.922461
$601$	1.45413e7	1.64217	0.821086	−	0.570805i	$-0.193369\pi$
$601$	1.45413e7	1.64217	0.821086	+	0.570805i	$0.193369\pi$
$602$	−2.43046e6	−0.273337
$603$	−1.08258e6	−0.121246
$604$	1.42219e7	1.58623
$605$	−1.07912e7	−1.19862
$606$	5.28657e6	0.584780
$607$	3.14771e6	0.346755	0.173378	−	0.984855i	$-0.444532\pi$
$607$	3.14771e6	0.346755	0.173378	+	0.984855i	$0.444532\pi$
$608$	26299.6	0.00288529
$609$	1.48915e6	0.162703
$610$	5.07756e6	0.552498
$611$	1.09152e7	1.18284
$612$	−6.04438e6	−0.652339
$613$	−5.50087e6	−0.591262	−0.295631	−	0.955302i	$-0.595530\pi$
$613$	−5.50087e6	−0.591262	−0.295631	+	0.955302i	$0.595530\pi$
$614$	1.78121e7	1.90676
$615$	7.37356e6	0.786121
$616$	−1.11513e6	−0.118406
$617$	−2.89935e6	−0.306611	−0.153305	−	0.988179i	$-0.548992\pi$
$617$	−2.89935e6	−0.306611	−0.153305	+	0.988179i	$0.548992\pi$
$618$	9.79227e6	1.03136
$619$	1.70775e7	1.79142	0.895711	−	0.444636i	$-0.146667\pi$
$619$	1.70775e7	1.79142	0.895711	+	0.444636i	$0.146667\pi$
$620$	2.28437e7	2.38665
$621$	−1.07993e6	−0.112375
$622$	−2.61166e7	−2.70670
$623$	996654.	0.102878
$624$	−6.11091e6	−0.628267
$625$	−1.05875e7	−1.08416
$626$	−3.32484e7	−3.39106
$627$	−118710.	−0.0120592
$628$	2.74851e7	2.78098
$629$	1.08595e7	1.09441
$630$	−1.47297e6	−0.147857
$631$	−1.02681e7	−1.02664	−0.513318	−	0.858198i	$-0.671584\pi$
$631$	−1.02681e7	−1.02664	−0.513318	+	0.858198i	$0.671584\pi$
$632$	−3.14765e7	−3.13469
$633$	−2.88552e6	−0.286230
$634$	−1.56098e7	−1.54232
$635$	1.10764e7	1.09009
$636$	1.01111e7	0.991190
$637$	−1.03165e7	−1.00736
$638$	9.88242e6	0.961195
$639$	−420376.	−0.0407273
$640$	−2.44735e7	−2.36182
$641$	−8.24583e6	−0.792664	−0.396332	−	0.918107i	$-0.629717\pi$
$641$	−8.24583e6	−0.792664	−0.396332	+	0.918107i	$0.629717\pi$
$642$	−1.26326e7	−1.20964
$643$	3.04613e6	0.290550	0.145275	−	0.989391i	$-0.453593\pi$
$643$	3.04613e6	0.290550	0.145275	+	0.989391i	$0.453593\pi$
$644$	−2.29015e6	−0.217596
$645$	−7.16933e6	−0.678546
$646$	−1.02824e6	−0.0969418
$647$	4.38912e6	0.412208	0.206104	−	0.978530i	$-0.433921\pi$
$647$	4.38912e6	0.412208	0.206104	+	0.978530i	$0.433921\pi$
$648$	2.09162e6	0.195679
$649$	507702.	0.0473148
$650$	1.76974e7	1.64296
$651$	990844.	0.0916332
$652$	1.84190e7	1.69687
$653$	2.10963e7	1.93608	0.968038	−	0.250803i	$-0.0806945\pi$
$653$	2.10963e7	1.93608	0.968038	+	0.250803i	$0.0806945\pi$
$654$	1.18539e7	1.08372
$655$	1.30881e6	0.119199
$656$	−1.13372e7	−1.02860
$657$	−3.82455e6	−0.345675
$658$	−4.04525e6	−0.364234
$659$	−4.51249e6	−0.404765	−0.202383	−	0.979307i	$-0.564868\pi$
$659$	−4.51249e6	−0.404765	−0.202383	+	0.979307i	$0.564868\pi$
$660$	−6.53222e6	−0.583715
$661$	1.93822e7	1.72544	0.862720	−	0.505682i	$-0.168759\pi$
$661$	1.93822e7	1.72544	0.862720	+	0.505682i	$0.168759\pi$
$662$	3.35687e6	0.297708
$663$	6.62201e6	0.585067
$664$	6.86534e6	0.604285
$665$	−167446.	−0.0146832
$666$	−7.46251e6	−0.651927
$667$	1.02201e7	0.889491
$668$	−3.86005e7	−3.34697
$669$	−855590.	−0.0739095
$670$	−1.01339e7	−0.872144
$671$	976698.	0.0837441
$672$	62771.2	0.00536213
$673$	902112.	0.0767755	0.0383877	−	0.999263i	$-0.487778\pi$
$673$	902112.	0.0767755	0.0383877	+	0.999263i	$0.487778\pi$
$674$	−1.45673e7	−1.23518
$675$	−2.06680e6	−0.174598
$676$	2.10534e6	0.177196
$677$	−5.88950e6	−0.493864	−0.246932	−	0.969033i	$-0.579422\pi$
$677$	−5.88950e6	−0.493864	−0.246932	+	0.969033i	$0.579422\pi$
$678$	499004.	0.0416898
$679$	909720.	0.0757240
$680$	−2.84918e7	−2.36292
$681$	−6.53194e6	−0.539727
$682$	6.57554e6	0.541340
$683$	1.32934e7	1.09040	0.545200	−	0.838306i	$-0.316454\pi$
$683$	1.32934e7	1.09040	0.545200	+	0.838306i	$0.316454\pi$
$684$	472183.	0.0385896
$685$	−1.63823e7	−1.33397
$686$	7.78225e6	0.631386
$687$	−1.21912e7	−0.985499
$688$	1.10231e7	0.887839
$689$	−1.10774e7	−0.888975
$690$	−1.01091e7	−0.808331
$691$	4.60848e6	0.367166	0.183583	−	0.983004i	$-0.441230\pi$
$691$	4.60848e6	0.367166	0.183583	+	0.983004i	$0.441230\pi$
$692$	5.13957e6	0.408001
$693$	−283334.	−0.0224112
$694$	−2.13807e7	−1.68509
$695$	−1.83588e7	−1.44173
$696$	−1.97943e7	−1.54888
$697$	1.22854e7	0.957869
$698$	3.69044e7	2.86708
$699$	−7.16795e6	−0.554884
$700$	−4.38295e6	−0.338081
$701$	2.41007e7	1.85240	0.926199	−	0.377035i	$-0.123056\pi$
$701$	2.41007e7	1.85240	0.926199	+	0.377035i	$0.123056\pi$
$702$	−4.55057e6	−0.348516
$703$	−848334.	−0.0647409
$704$	−4.56943e6	−0.347480
$705$	−1.19326e7	−0.904193
$706$	2.41646e7	1.82460
$707$	1.43439e6	0.107924
$708$	−2.01945e6	−0.151408
$709$	−1.77088e7	−1.32304	−0.661522	−	0.749926i	$-0.730089\pi$
$709$	−1.77088e7	−1.32304	−0.661522	+	0.749926i	$0.730089\pi$
$710$	−3.93507e6	−0.292959
$711$	−7.99761e6	−0.593316
$712$	−1.32479e7	−0.979372
$713$	6.80023e6	0.500956
$714$	−2.45417e6	−0.180160
$715$	7.15647e6	0.523520
$716$	3.85634e7	2.81121
$717$	761739.	0.0553361
$718$	−4.18175e7	−3.02724
$719$	−1.07276e7	−0.773893	−0.386947	−	0.922102i	$-0.626470\pi$
$719$	−1.07276e7	−0.773893	−0.386947	+	0.922102i	$0.626470\pi$
$720$	6.68051e6	0.480262
$721$	2.65691e6	0.190344
$722$	−2.42384e7	−1.73046
$723$	−1.23231e7	−0.876744
$724$	4.83754e7	3.42988
$725$	1.95595e7	1.38201
$726$	1.23554e7	0.869991
$727$	1.56895e7	1.10096	0.550482	−	0.834847i	$-0.314444\pi$
$727$	1.56895e7	1.10096	0.550482	+	0.834847i	$0.314444\pi$
$728$	−4.85945e6	−0.339828
$729$	531441.	0.0370370
$730$	−3.58010e7	−2.48650
$731$	−1.19451e7	−0.826791
$732$	−3.88494e6	−0.267982
$733$	−2.14295e7	−1.47317	−0.736585	−	0.676345i	$-0.763563\pi$
$733$	−2.14295e7	−1.47317	−0.736585	+	0.676345i	$0.763563\pi$
$734$	3.75837e7	2.57489
$735$	1.12781e7	0.770049
$736$	430803.	0.0293146
$737$	−1.94931e6	−0.132194
$738$	−8.44237e6	−0.570589
$739$	−5.14780e6	−0.346745	−0.173373	−	0.984856i	$-0.555466\pi$
$739$	−5.14780e6	−0.346745	−0.173373	+	0.984856i	$0.555466\pi$
$740$	−4.66811e7	−3.13373
$741$	−517307.	−0.0346101
$742$	4.10537e6	0.273743
$743$	2.25185e7	1.49647	0.748235	−	0.663434i	$-0.230902\pi$
$743$	2.25185e7	1.49647	0.748235	+	0.663434i	$0.230902\pi$
$744$	−1.31707e7	−0.872321
$745$	−1.18488e7	−0.782137
$746$	2.39354e7	1.57468
$747$	1.74436e6	0.114376
$748$	−1.08836e7	−0.711243
$749$	−3.42757e6	−0.223245
$750$	1.97816e6	0.128413
$751$	−2.01952e6	−0.130662	−0.0653309	−	0.997864i	$-0.520810\pi$
$751$	−2.01952e6	−0.130662	−0.0653309	+	0.997864i	$0.520810\pi$
$752$	1.83468e7	1.18309
$753$	2.40319e6	0.154454
$754$	4.30650e7	2.75865
$755$	1.70334e7	1.08751
$756$	1.12700e6	0.0717163
$757$	3.18019e6	0.201703	0.100852	−	0.994901i	$-0.467843\pi$
$757$	3.18019e6	0.201703	0.100852	+	0.994901i	$0.467843\pi$
$758$	6.55696e6	0.414505
$759$	−1.94454e6	−0.122522
$760$	2.22576e6	0.139780
$761$	−2.42934e7	−1.52064	−0.760322	−	0.649547i	$-0.774959\pi$
$761$	−2.42934e7	−1.52064	−0.760322	+	0.649547i	$0.774959\pi$
$762$	−1.26819e7	−0.791222
$763$	3.21630e6	0.200007
$764$	−1.63052e7	−1.01063
$765$	−7.23925e6	−0.447239
$766$	−2.43935e7	−1.50211
$767$	2.21243e6	0.135794
$768$	1.89980e7	1.16227
$769$	1.88942e7	1.15216	0.576079	−	0.817394i	$-0.304582\pi$
$769$	1.88942e7	1.15216	0.576079	+	0.817394i	$0.304582\pi$
$770$	−2.65224e6	−0.161208
$771$	9.70800e6	0.588158
$772$	−5.99867e6	−0.362253
$773$	−2.30588e6	−0.138799	−0.0693997	−	0.997589i	$-0.522108\pi$
$773$	−2.30588e6	−0.138799	−0.0693997	+	0.997589i	$0.522108\pi$
$774$	8.20853e6	0.492508
$775$	1.30144e7	0.778343
$776$	−1.20924e7	−0.720870
$777$	−2.02479e6	−0.120317
$778$	−2.02904e6	−0.120183
$779$	−959725.	−0.0566635
$780$	−2.84657e7	−1.67527
$781$	−756933.	−0.0444048
$782$	−1.68431e7	−0.984931
$783$	−5.02937e6	−0.293163
$784$	−1.73406e7	−1.00757
$785$	3.29184e7	1.90662
$786$	−1.49852e6	−0.0865180
$787$	1.26430e7	0.727635	0.363818	−	0.931470i	$-0.381473\pi$
$787$	1.26430e7	0.727635	0.363818	+	0.931470i	$0.381473\pi$
$788$	9.49417e6	0.544680
$789$	−7.56547e6	−0.432657
$790$	−7.48643e7	−4.26783
$791$	135394.	0.00769408
$792$	3.76619e6	0.213348
$793$	4.25620e6	0.240347
$794$	2.72317e7	1.53294
$795$	1.21099e7	0.679553
$796$	4.60898e7	2.57823
$797$	−2.72228e7	−1.51805	−0.759026	−	0.651061i	$-0.774324\pi$
$797$	−2.72228e7	−1.51805	−0.759026	+	0.651061i	$0.774324\pi$
$798$	191718.	0.0106575
$799$	−1.98813e7	−1.10174
$800$	824480.	0.0455465
$801$	−3.36605e6	−0.185370
$802$	9.27677e6	0.509285
$803$	−6.88654e6	−0.376888
$804$	7.75361e6	0.423023
$805$	−2.74288e6	−0.149182
$806$	2.86545e7	1.55366
$807$	7.31275e6	0.395273
$808$	−1.90665e7	−1.02741
$809$	−8.23285e6	−0.442261	−0.221131	−	0.975244i	$-0.570975\pi$
$809$	−8.23285e6	−0.442261	−0.221131	+	0.975244i	$0.570975\pi$
$810$	4.97473e6	0.266414
$811$	3.11061e7	1.66071	0.830354	−	0.557236i	$-0.188138\pi$
$811$	3.11061e7	1.66071	0.830354	+	0.557236i	$0.188138\pi$
$812$	−1.06655e7	−0.567663
$813$	1.71514e7	0.910064
$814$	−1.34371e7	−0.710794
$815$	2.20601e7	1.16336
$816$	1.11306e7	0.585187
$817$	933142.	0.0489094
$818$	3.76457e7	1.96713
$819$	−1.23470e6	−0.0643206
$820$	−5.28106e7	−2.74275
$821$	1.24690e6	0.0645615	0.0322807	−	0.999479i	$-0.489723\pi$
$821$	1.24690e6	0.0645615	0.0322807	+	0.999479i	$0.489723\pi$
$822$	1.87569e7	0.968236
$823$	−1.26194e7	−0.649440	−0.324720	−	0.945810i	$-0.605270\pi$
$823$	−1.26194e7	−0.649440	−0.324720	+	0.945810i	$0.605270\pi$
$824$	−3.53167e7	−1.81202
$825$	−3.72151e6	−0.190364
$826$	−819946.	−0.0418153
$827$	2.70078e7	1.37317	0.686587	−	0.727048i	$-0.259108\pi$
$827$	2.70078e7	1.37317	0.686587	+	0.727048i	$0.259108\pi$
$828$	7.73465e6	0.392071
$829$	1.46007e7	0.737885	0.368942	−	0.929452i	$-0.379720\pi$
$829$	1.46007e7	0.737885	0.368942	+	0.929452i	$0.379720\pi$
$830$	1.63286e7	0.822725
$831$	1.11225e7	0.558727
$832$	−1.99124e7	−0.997275
$833$	1.87909e7	0.938286
$834$	2.10199e7	1.04645
$835$	−4.62311e7	−2.29466
$836$	850219.	0.0420741
$837$	−3.34643e6	−0.165108
$838$	1.15030e7	0.565852
$839$	3.66864e7	1.79929	0.899644	−	0.436624i	$-0.143826\pi$
$839$	3.66864e7	1.79929	0.899644	+	0.436624i	$0.143826\pi$
$840$	5.31240e6	0.259772
$841$	2.70851e7	1.32050
$842$	2.50444e7	1.21739
$843$	−1.28926e6	−0.0624845
$844$	2.06665e7	0.998645
$845$	2.52152e6	0.121485
$846$	1.36622e7	0.656289
$847$	3.35236e6	0.160562
$848$	−1.86195e7	−0.889157
$849$	−1.59039e7	−0.757242
$850$	−3.22348e7	−1.53030
$851$	−1.38962e7	−0.657769
$852$	3.01079e6	0.142096
$853$	2.51796e7	1.18489	0.592443	−	0.805612i	$-0.298164\pi$
$853$	2.51796e7	1.18489	0.592443	+	0.805612i	$0.298164\pi$
$854$	−1.57738e6	−0.0740102
$855$	565525.	0.0264568
$856$	4.55606e7	2.12523
$857$	−3.74346e7	−1.74109	−0.870544	−	0.492090i	$-0.836233\pi$
$857$	−3.74346e7	−1.74109	−0.870544	+	0.492090i	$0.836233\pi$
$858$	−8.19381e6	−0.379986
$859$	1.02558e7	0.474227	0.237113	−	0.971482i	$-0.423799\pi$
$859$	1.02558e7	0.474227	0.237113	+	0.971482i	$0.423799\pi$
$860$	5.13478e7	2.36742
$861$	−2.29065e6	−0.105305
$862$	−6.03788e7	−2.76768
$863$	−3.78798e7	−1.73133	−0.865667	−	0.500620i	$-0.833105\pi$
$863$	−3.78798e7	−1.73133	−0.865667	+	0.500620i	$0.833105\pi$
$864$	−212000.	−0.00966167
$865$	6.15557e6	0.279723
$866$	4.12705e7	1.87001
$867$	717131.	0.0324004
$868$	−7.09657e6	−0.319705
$869$	−1.44006e7	−0.646890
$870$	−4.70791e7	−2.10877
$871$	−8.49458e6	−0.379399
$872$	−4.27523e7	−1.90401
$873$	−3.07244e6	−0.136442
$874$	1.31577e6	0.0582644
$875$	536729.	0.0236993
$876$	2.73920e7	1.20605
$877$	−2.45816e7	−1.07922	−0.539612	−	0.841914i	$-0.681429\pi$
$877$	−2.45816e7	−1.07922	−0.539612	+	0.841914i	$0.681429\pi$
$878$	271638.	0.0118920
$879$	−2.29695e7	−1.00272
$880$	1.20290e7	0.523628
$881$	−2.23783e7	−0.971374	−0.485687	−	0.874133i	$-0.661431\pi$
$881$	−2.23783e7	−0.971374	−0.485687	+	0.874133i	$0.661431\pi$
$882$	−1.29129e7	−0.558924
$883$	4.77619e6	0.206148	0.103074	−	0.994674i	$-0.467132\pi$
$883$	4.77619e6	0.206148	0.103074	+	0.994674i	$0.467132\pi$
$884$	−4.74278e7	−2.04128
$885$	−2.41866e6	−0.103804
$886$	4.42500e7	1.89378
$887$	−3.04240e7	−1.29840	−0.649198	−	0.760619i	$-0.724895\pi$
$887$	−3.04240e7	−1.29840	−0.649198	+	0.760619i	$0.724895\pi$
$888$	2.69142e7	1.14538
$889$	−3.44096e6	−0.146024
$890$	−3.15090e7	−1.33340
$891$	956919.	0.0403814
$892$	6.12786e6	0.257868
$893$	1.55311e6	0.0651741
$894$	1.35663e7	0.567698
$895$	4.61867e7	1.92734
$896$	7.60287e6	0.316379
$897$	−8.47381e6	−0.351639
$898$	1.85488e6	0.0767584
$899$	3.16694e7	1.30690
$900$	1.48027e7	0.609167
$901$	2.01768e7	0.828019
$902$	−1.52014e7	−0.622111
$903$	2.22720e6	0.0908951
$904$	−1.79970e6	−0.0732454
$905$	5.79384e7	2.35150
$906$	−1.95024e7	−0.789345
$907$	4.34590e7	1.75413	0.877064	−	0.480374i	$-0.159499\pi$
$907$	4.34590e7	1.75413	0.877064	+	0.480374i	$0.159499\pi$
$908$	4.67828e7	1.88309
$909$	−4.84445e6	−0.194462
$910$	−1.15578e7	−0.462670
$911$	−81087.9	−0.00323713	−0.00161856	−	0.999999i	$-0.500515\pi$
$911$	−81087.9	−0.00323713	−0.00161856	+	0.999999i	$0.500515\pi$
$912$	−869519.	−0.0346172
$913$	3.14091e6	0.124703
$914$	−2.84411e7	−1.12611
$915$	−4.65292e6	−0.183727
$916$	8.73156e7	3.43837
$917$	−406590.	−0.0159674
$918$	8.28859e6	0.324619
$919$	1.61478e7	0.630703	0.315352	−	0.948975i	$-0.397878\pi$
$919$	1.61478e7	0.630703	0.315352	+	0.948975i	$0.397878\pi$
$920$	3.64594e7	1.42017
$921$	−1.63225e7	−0.634070
$922$	−2.79756e7	−1.08381
$923$	−3.29852e6	−0.127443
$924$	2.02928e6	0.0781920
$925$	−2.65949e7	−1.02199
$926$	−7.44173e6	−0.285198
$927$	−8.97333e6	−0.342969
$928$	2.00630e6	0.0764760
$929$	−2.62592e7	−0.998255	−0.499128	−	0.866528i	$-0.666346\pi$
$929$	−2.62592e7	−0.998255	−0.499128	+	0.866528i	$0.666346\pi$
$930$	−3.13254e7	−1.18765
$931$	−1.46793e6	−0.0555050
$932$	5.13379e7	1.93597
$933$	2.39324e7	0.900083
$934$	5.72525e7	2.14747
$935$	−1.30351e7	−0.487623
$936$	1.64121e7	0.612313
$937$	1.79989e7	0.669725	0.334863	−	0.942267i	$-0.391310\pi$
$937$	1.79989e7	0.669725	0.334863	+	0.942267i	$0.391310\pi$
$938$	3.14816e6	0.116829
$939$	3.04678e7	1.12766
$940$	8.54628e7	3.15470
$941$	1.71873e7	0.632753	0.316377	−	0.948634i	$-0.397534\pi$
$941$	1.71873e7	0.632753	0.316377	+	0.948634i	$0.397534\pi$
$942$	−3.76900e7	−1.38388
$943$	−1.57209e7	−0.575702
$944$	3.71878e6	0.135822
$945$	1.34978e6	0.0491682
$946$	1.47804e7	0.536979
$947$	2.93974e7	1.06521	0.532604	−	0.846364i	$-0.321213\pi$
$947$	2.93974e7	1.06521	0.532604	+	0.846364i	$0.321213\pi$
$948$	5.72801e7	2.07006
$949$	−3.00097e7	−1.08167
$950$	2.51816e6	0.0905262
$951$	1.43044e7	0.512881
$952$	8.85119e6	0.316526
$953$	−4.78458e7	−1.70652	−0.853260	−	0.521486i	$-0.825378\pi$
$953$	−4.78458e7	−1.70652	−0.853260	+	0.521486i	$0.825378\pi$
$954$	−1.38653e7	−0.493239
$955$	−1.95285e7	−0.692884
$956$	−5.45569e6	−0.193066
$957$	−9.05594e6	−0.319635
$958$	7.14601e6	0.251565
$959$	5.08927e6	0.178693
$960$	2.17684e7	0.762340
$961$	−7.55706e6	−0.263964
$962$	−5.85553e7	−2.03999
$963$	1.15761e7	0.402251
$964$	8.82596e7	3.05893
$965$	−7.18449e6	−0.248358
$966$	3.14046e6	0.108281
$967$	1.01041e7	0.347482	0.173741	−	0.984791i	$-0.444414\pi$
$967$	1.01041e7	0.347482	0.173741	+	0.984791i	$0.444414\pi$
$968$	−4.45609e7	−1.52850
$969$	942243.	0.0322369
$970$	−2.87606e7	−0.981453
$971$	−3.23719e7	−1.10184	−0.550922	−	0.834557i	$-0.685724\pi$
$971$	−3.23719e7	−1.10184	−0.550922	+	0.834557i	$0.685724\pi$
$972$	−3.80626e6	−0.129221
$973$	5.70330e6	0.193127
$974$	−9.33105e7	−3.15161
$975$	−1.62174e7	−0.546347
$976$	7.15406e6	0.240396
$977$	2.17318e7	0.728382	0.364191	−	0.931324i	$-0.381346\pi$
$977$	2.17318e7	0.728382	0.364191	+	0.931324i	$0.381346\pi$
$978$	−2.52578e7	−0.844400
$979$	−6.06095e6	−0.202108
$980$	−8.07756e7	−2.68667
$981$	−1.08626e7	−0.360380
$982$	−9.46528e7	−3.13224
$983$	3.61962e7	1.19476	0.597378	−	0.801960i	$-0.296209\pi$
$983$	3.61962e7	1.19476	0.597378	+	0.801960i	$0.296209\pi$
$984$	3.04482e7	1.00248
$985$	1.13710e7	0.373429
$986$	−7.84403e7	−2.56949
$987$	3.70694e6	0.121122
$988$	3.70503e6	0.120753
$989$	1.52854e7	0.496921
$990$	8.95756e6	0.290470
$991$	−4.13388e6	−0.133713	−0.0668566	−	0.997763i	$-0.521297\pi$
$991$	−4.13388e6	−0.133713	−0.0668566	+	0.997763i	$0.521297\pi$
$992$	1.33494e6	0.0430709
$993$	−3.07613e6	−0.0989993
$994$	1.22246e6	0.0392435
$995$	5.52009e7	1.76762
$996$	−1.24933e7	−0.399053
$997$	−4.91646e7	−1.56644	−0.783222	−	0.621742i	$-0.786425\pi$
$997$	−4.91646e7	−1.56644	−0.783222	+	0.621742i	$0.786425\pi$
$998$	7.29707e7	2.31911
$999$	6.83841e6	0.216791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.d.1.12	✓	13
3.2	odd	2		531.6.a.e.1.2		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.d.1.12	✓	13	1.1	even	1	trivial
531.6.a.e.1.2		13	3.2	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+9.82137 q^{2} -9.00000 q^{3} +64.4594 q^{4} +77.2018 q^{5} -88.3924 q^{6} -23.9833 q^{7} +318.795 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+9.82137 q^{2} -9.00000 q^{3} +64.4594 q^{4} +77.2018 q^{5} -88.3924 q^{6} -23.9833 q^{7} +318.795 q^{8} +81.0000 q^{9} +758.228 q^{10} +145.850 q^{11} -580.134 q^{12} +635.574 q^{13} -235.549 q^{14} -694.816 q^{15} +1068.31 q^{16} -1157.66 q^{17} +795.531 q^{18} +90.4356 q^{19} +4976.38 q^{20} +215.850 q^{21} +1432.44 q^{22} +1481.39 q^{23} -2869.16 q^{24} +2835.12 q^{25} +6242.21 q^{26} -729.000 q^{27} -1545.95 q^{28} +6899.00 q^{29} -6824.05 q^{30} +4590.44 q^{31} +290.810 q^{32} -1312.65 q^{33} -11369.8 q^{34} -1851.55 q^{35} +5221.21 q^{36} -9380.53 q^{37} +888.202 q^{38} -5720.17 q^{39} +24611.6 q^{40} -10612.2 q^{41} +2119.94 q^{42} +10318.3 q^{43} +9401.37 q^{44} +6253.35 q^{45} +14549.3 q^{46} +17173.7 q^{47} -9614.78 q^{48} -16231.8 q^{49} +27844.8 q^{50} +10418.9 q^{51} +40968.7 q^{52} -17429.0 q^{53} -7159.78 q^{54} +11259.8 q^{55} -7645.77 q^{56} -813.921 q^{57} +67757.6 q^{58} +3481.00 q^{59} -44787.4 q^{60} +6696.62 q^{61} +45084.4 q^{62} -1942.65 q^{63} -31329.7 q^{64} +49067.5 q^{65} -12892.0 q^{66} -13365.2 q^{67} -74622.0 q^{68} -13332.5 q^{69} -18184.8 q^{70} -5189.82 q^{71} +25822.4 q^{72} -47216.7 q^{73} -92129.7 q^{74} -25516.1 q^{75} +5829.42 q^{76} -3497.95 q^{77} -56179.9 q^{78} -98735.9 q^{79} +82475.4 q^{80} +6561.00 q^{81} -104227. q^{82} +21535.3 q^{83} +13913.5 q^{84} -89373.4 q^{85} +101340. q^{86} -62091.0 q^{87} +46496.2 q^{88} -41556.2 q^{89} +61416.4 q^{90} -15243.2 q^{91} +95489.5 q^{92} -41313.9 q^{93} +168669. q^{94} +6981.79 q^{95} -2617.29 q^{96} -37931.4 q^{97} -159419. q^{98} +11813.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9} + 137 q^{10} + 250 q^{11} - 2214 q^{12} + 1054 q^{13} - 575 q^{14} + 126 q^{15} + 922 q^{16} + 271 q^{17} + 671 q^{19} - 5491 q^{20} - 3357 q^{21} + 1094 q^{22} + 3975 q^{23} - 1107 q^{24} + 15569 q^{25} + 4622 q^{26} - 9477 q^{27} + 21214 q^{28} - 10613 q^{29} - 1233 q^{30} + 25597 q^{31} + 15966 q^{32} - 2250 q^{33} + 31796 q^{34} + 6729 q^{35} + 19926 q^{36} + 17585 q^{37} + 34903 q^{38} - 9486 q^{39} + 31382 q^{40} + 12537 q^{41} + 5175 q^{42} + 26644 q^{43} + 6654 q^{44} - 1134 q^{45} + 149005 q^{46} + 52087 q^{47} - 8298 q^{48} + 95384 q^{49} + 121821 q^{50} - 2439 q^{51} + 263630 q^{52} + 20014 q^{53} + 120932 q^{55} + 126688 q^{56} - 6039 q^{57} + 86066 q^{58} + 45253 q^{59} + 49419 q^{60} - 11667 q^{61} + 164794 q^{62} + 30213 q^{63} + 151893 q^{64} - 28674 q^{65} - 9846 q^{66} + 1106 q^{67} - 4043 q^{68} - 35775 q^{69} + 56066 q^{70} + 21230 q^{71} + 9963 q^{72} + 81131 q^{73} + 102042 q^{74} - 140121 q^{75} + 73900 q^{76} - 104655 q^{77} - 41598 q^{78} - 13470 q^{79} - 191969 q^{80} + 85293 q^{81} + 79909 q^{82} - 76149 q^{83} - 190926 q^{84} + 10035 q^{85} - 321496 q^{86} + 95517 q^{87} - 276779 q^{88} - 190205 q^{89} + 11097 q^{90} + 80601 q^{91} + 45672 q^{92} - 230373 q^{93} + 36768 q^{94} + 9875 q^{95} - 143694 q^{96} + 160850 q^{97} - 116644 q^{98} + 20250 q^{99}+O(q^{100}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9 + 137 * q^10 + 250 * q^11 - 2214 * q^12 + 1054 * q^13 - 575 * q^14 + 126 * q^15 + 922 * q^16 + 271 * q^17 + 671 * q^19 - 5491 * q^20 - 3357 * q^21 + 1094 * q^22 + 3975 * q^23 - 1107 * q^24 + 15569 * q^25 + 4622 * q^26 - 9477 * q^27 + 21214 * q^28 - 10613 * q^29 - 1233 * q^30 + 25597 * q^31 + 15966 * q^32 - 2250 * q^33 + 31796 * q^34 + 6729 * q^35 + 19926 * q^36 + 17585 * q^37 + 34903 * q^38 - 9486 * q^39 + 31382 * q^40 + 12537 * q^41 + 5175 * q^42 + 26644 * q^43 + 6654 * q^44 - 1134 * q^45 + 149005 * q^46 + 52087 * q^47 - 8298 * q^48 + 95384 * q^49 + 121821 * q^50 - 2439 * q^51 + 263630 * q^52 + 20014 * q^53 + 120932 * q^55 + 126688 * q^56 - 6039 * q^57 + 86066 * q^58 + 45253 * q^59 + 49419 * q^60 - 11667 * q^61 + 164794 * q^62 + 30213 * q^63 + 151893 * q^64 - 28674 * q^65 - 9846 * q^66 + 1106 * q^67 - 4043 * q^68 - 35775 * q^69 + 56066 * q^70 + 21230 * q^71 + 9963 * q^72 + 81131 * q^73 + 102042 * q^74 - 140121 * q^75 + 73900 * q^76 - 104655 * q^77 - 41598 * q^78 - 13470 * q^79 - 191969 * q^80 + 85293 * q^81 + 79909 * q^82 - 76149 * q^83 - 190926 * q^84 + 10035 * q^85 - 321496 * q^86 + 95517 * q^87 - 276779 * q^88 - 190205 * q^89 + 11097 * q^90 + 80601 * q^91 + 45672 * q^92 - 230373 * q^93 + 36768 * q^94 + 9875 * q^95 - 143694 * q^96 + 160850 * q^97 - 116644 * q^98 + 20250 * q^99

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