LMFDB - Embedded newform 165.6.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.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:	$26.4633302691$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.18257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 26x + 8 $ x^3 - x^2 - 26*x + 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.305203$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.694797 q^{2} -9.00000 q^{3} -31.5173 q^{4} +25.0000 q^{5} -6.25317 q^{6} +83.1683 q^{7} -44.1316 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+0.694797 q^{2} -9.00000 q^{3} -31.5173 q^{4} +25.0000 q^{5} -6.25317 q^{6} +83.1683 q^{7} -44.1316 q^{8} +81.0000 q^{9} +17.3699 q^{10} +121.000 q^{11} +283.655 q^{12} -674.655 q^{13} +57.7851 q^{14} -225.000 q^{15} +977.890 q^{16} +1927.66 q^{17} +56.2785 q^{18} -149.751 q^{19} -787.931 q^{20} -748.514 q^{21} +84.0704 q^{22} -1355.59 q^{23} +397.184 q^{24} +625.000 q^{25} -468.748 q^{26} -729.000 q^{27} -2621.24 q^{28} -7320.99 q^{29} -156.329 q^{30} -4215.76 q^{31} +2091.65 q^{32} -1089.00 q^{33} +1339.33 q^{34} +2079.21 q^{35} -2552.90 q^{36} -13420.1 q^{37} -104.046 q^{38} +6071.90 q^{39} -1103.29 q^{40} +2865.39 q^{41} -520.065 q^{42} -22078.1 q^{43} -3813.59 q^{44} +2025.00 q^{45} -941.861 q^{46} -14556.4 q^{47} -8801.01 q^{48} -9890.04 q^{49} +434.248 q^{50} -17348.9 q^{51} +21263.3 q^{52} +13349.7 q^{53} -506.507 q^{54} +3025.00 q^{55} -3670.35 q^{56} +1347.76 q^{57} -5086.60 q^{58} +45803.3 q^{59} +7091.38 q^{60} +18996.5 q^{61} -2929.10 q^{62} +6736.63 q^{63} -29839.2 q^{64} -16866.4 q^{65} -756.634 q^{66} +6651.05 q^{67} -60754.5 q^{68} +12200.3 q^{69} +1444.63 q^{70} -61028.7 q^{71} -3574.66 q^{72} -17353.4 q^{73} -9324.27 q^{74} -5625.00 q^{75} +4719.73 q^{76} +10063.4 q^{77} +4218.74 q^{78} +61676.5 q^{79} +24447.2 q^{80} +6561.00 q^{81} +1990.87 q^{82} -65230.8 q^{83} +23591.1 q^{84} +48191.4 q^{85} -15339.8 q^{86} +65888.9 q^{87} -5339.92 q^{88} -109563. q^{89} +1406.96 q^{90} -56109.9 q^{91} +42724.5 q^{92} +37941.8 q^{93} -10113.8 q^{94} -3743.76 q^{95} -18824.8 q^{96} +83736.1 q^{97} -6871.57 q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9	\( 3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 378 q^{12} + 290 q^{13} + 916 q^{14} - 675 q^{15} - 590 q^{16} + 434 q^{17} + 162 q^{18} - 2856 q^{19} - 1050 q^{20} + 612 q^{21} + 242 q^{22} - 640 q^{23} + 216 q^{24} + 1875 q^{25} + 2132 q^{26} - 2187 q^{27} - 580 q^{28} - 4538 q^{29} - 450 q^{30} - 14968 q^{31} - 2496 q^{32} - 3267 q^{33} - 13704 q^{34} - 1700 q^{35} - 3402 q^{36} - 6190 q^{37} - 11668 q^{38} - 2610 q^{39} - 600 q^{40} - 8926 q^{41} - 8244 q^{42} - 33592 q^{43} - 5082 q^{44} + 6075 q^{45} - 35680 q^{46} - 24640 q^{47} + 5310 q^{48} - 14693 q^{49} + 1250 q^{50} - 3906 q^{51} + 18780 q^{52} - 22934 q^{53} - 1458 q^{54} + 9075 q^{55} - 40012 q^{56} + 25704 q^{57} - 32304 q^{58} - 13756 q^{59} + 9450 q^{60} + 24602 q^{61} - 7704 q^{62} - 5508 q^{63} + 35474 q^{64} + 7250 q^{65} - 2178 q^{66} + 16868 q^{67} - 71288 q^{68} + 5760 q^{69} + 22900 q^{70} + 4856 q^{71} - 1944 q^{72} + 1910 q^{73} + 29404 q^{74} - 16875 q^{75} + 6116 q^{76} - 8228 q^{77} - 19188 q^{78} - 36844 q^{79} - 14750 q^{80} + 19683 q^{81} + 84000 q^{82} - 48796 q^{83} + 5220 q^{84} + 10850 q^{85} - 83492 q^{86} + 40842 q^{87} - 2904 q^{88} - 188978 q^{89} + 4050 q^{90} - 93208 q^{91} - 6976 q^{92} + 134712 q^{93} + 70472 q^{94} - 71400 q^{95} + 22464 q^{96} + 247526 q^{97} - 154654 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 378 * q^12 + 290 * q^13 + 916 * q^14 - 675 * q^15 - 590 * q^16 + 434 * q^17 + 162 * q^18 - 2856 * q^19 - 1050 * q^20 + 612 * q^21 + 242 * q^22 - 640 * q^23 + 216 * q^24 + 1875 * q^25 + 2132 * q^26 - 2187 * q^27 - 580 * q^28 - 4538 * q^29 - 450 * q^30 - 14968 * q^31 - 2496 * q^32 - 3267 * q^33 - 13704 * q^34 - 1700 * q^35 - 3402 * q^36 - 6190 * q^37 - 11668 * q^38 - 2610 * q^39 - 600 * q^40 - 8926 * q^41 - 8244 * q^42 - 33592 * q^43 - 5082 * q^44 + 6075 * q^45 - 35680 * q^46 - 24640 * q^47 + 5310 * q^48 - 14693 * q^49 + 1250 * q^50 - 3906 * q^51 + 18780 * q^52 - 22934 * q^53 - 1458 * q^54 + 9075 * q^55 - 40012 * q^56 + 25704 * q^57 - 32304 * q^58 - 13756 * q^59 + 9450 * q^60 + 24602 * q^61 - 7704 * q^62 - 5508 * q^63 + 35474 * q^64 + 7250 * q^65 - 2178 * q^66 + 16868 * q^67 - 71288 * q^68 + 5760 * q^69 + 22900 * q^70 + 4856 * q^71 - 1944 * q^72 + 1910 * q^73 + 29404 * q^74 - 16875 * q^75 + 6116 * q^76 - 8228 * q^77 - 19188 * q^78 - 36844 * q^79 - 14750 * q^80 + 19683 * q^81 + 84000 * q^82 - 48796 * q^83 + 5220 * q^84 + 10850 * q^85 - 83492 * q^86 + 40842 * q^87 - 2904 * q^88 - 188978 * q^89 + 4050 * q^90 - 93208 * q^91 - 6976 * q^92 + 134712 * q^93 + 70472 * q^94 - 71400 * q^95 + 22464 * q^96 + 247526 * q^97 - 154654 * q^98 + 29403 * 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 $

$2$	0.694797	0.122824	0.0614120	−	0.998113i	$-0.480440\pi$
$2$	0.694797	0.122824	0.0614120	+	0.998113i	$0.480440\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−31.5173	−0.984914
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−6.25317	−0.0709124
$7$	83.1683	0.641523	0.320762	−	0.947160i	$-0.396061\pi$
$7$	83.1683	0.641523	0.320762	+	0.947160i	$0.396061\pi$
$8$	−44.1316	−0.243795
$9$	81.0000	0.333333
$10$	17.3699	0.0549285
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	283.655	0.568641
$13$	−674.655	−1.10719	−0.553597	−	0.832785i	$-0.686745\pi$
$13$	−674.655	−1.10719	−0.553597	+	0.832785i	$0.686745\pi$
$14$	57.7851	0.0787944
$15$	−225.000	−0.258199
$16$	977.890	0.954970
$17$	1927.66	1.61774	0.808868	−	0.587991i	$-0.200081\pi$
$17$	1927.66	1.61774	0.808868	+	0.587991i	$0.200081\pi$
$18$	56.2785	0.0409413
$19$	−149.751	−0.0951666	−0.0475833	−	0.998867i	$-0.515152\pi$
$19$	−149.751	−0.0951666	−0.0475833	+	0.998867i	$0.515152\pi$
$20$	−787.931	−0.440467
$21$	−748.514	−0.370384
$22$	84.0704	0.0370328
$23$	−1355.59	−0.534330	−0.267165	−	0.963651i	$-0.586087\pi$
$23$	−1355.59	−0.534330	−0.267165	+	0.963651i	$0.586087\pi$
$24$	397.184	0.140755
$25$	625.000	0.200000
$26$	−468.748	−0.135990
$27$	−729.000	−0.192450
$28$	−2621.24	−0.631846
$29$	−7320.99	−1.61650	−0.808248	−	0.588842i	$-0.799584\pi$
$29$	−7320.99	−1.61650	−0.808248	+	0.588842i	$0.799584\pi$
$30$	−156.329	−0.0317130
$31$	−4215.76	−0.787901	−0.393951	−	0.919132i	$-0.628892\pi$
$31$	−4215.76	−0.787901	−0.393951	+	0.919132i	$0.628892\pi$
$32$	2091.65	0.361088
$33$	−1089.00	−0.174078
$34$	1339.33	0.198697
$35$	2079.21	0.286898
$36$	−2552.90	−0.328305
$37$	−13420.1	−1.61158	−0.805792	−	0.592199i	$-0.798260\pi$
$37$	−13420.1	−1.61158	−0.805792	+	0.592199i	$0.798260\pi$
$38$	−104.046	−0.0116887
$39$	6071.90	0.639238
$40$	−1103.29	−0.109028
$41$	2865.39	0.266210	0.133105	−	0.991102i	$-0.457505\pi$
$41$	2865.39	0.266210	0.133105	+	0.991102i	$0.457505\pi$
$42$	−520.065	−0.0454920
$43$	−22078.1	−1.82092	−0.910458	−	0.413601i	$-0.864271\pi$
$43$	−22078.1	−1.82092	−0.910458	+	0.413601i	$0.864271\pi$
$44$	−3813.59	−0.296963
$45$	2025.00	0.149071
$46$	−941.861	−0.0656285
$47$	−14556.4	−0.961192	−0.480596	−	0.876942i	$-0.659580\pi$
$47$	−14556.4	−0.961192	−0.480596	+	0.876942i	$0.659580\pi$
$48$	−8801.01	−0.551352
$49$	−9890.04	−0.588448
$50$	434.248	0.0245648
$51$	−17348.9	−0.934000
$52$	21263.3	1.09049
$53$	13349.7	0.652805	0.326402	−	0.945231i	$-0.394164\pi$
$53$	13349.7	0.652805	0.326402	+	0.945231i	$0.394164\pi$
$54$	−506.507	−0.0236375
$55$	3025.00	0.134840
$56$	−3670.35	−0.156400
$57$	1347.76	0.0549445
$58$	−5086.60	−0.198544
$59$	45803.3	1.71304	0.856518	−	0.516117i	$-0.172623\pi$
$59$	45803.3	1.71304	0.856518	+	0.516117i	$0.172623\pi$
$60$	7091.38	0.254304
$61$	18996.5	0.653655	0.326827	−	0.945084i	$-0.394020\pi$
$61$	18996.5	0.653655	0.326827	+	0.945084i	$0.394020\pi$
$62$	−2929.10	−0.0967731
$63$	6736.63	0.213841
$64$	−29839.2	−0.910620
$65$	−16866.4	−0.495152
$66$	−756.634	−0.0213809
$67$	6651.05	0.181010	0.0905052	−	0.995896i	$-0.471152\pi$
$67$	6651.05	0.181010	0.0905052	+	0.995896i	$0.471152\pi$
$68$	−60754.5	−1.59333
$69$	12200.3	0.308495
$70$	1444.63	0.0352379
$71$	−61028.7	−1.43677	−0.718386	−	0.695644i	$-0.755119\pi$
$71$	−61028.7	−1.43677	−0.718386	+	0.695644i	$0.755119\pi$
$72$	−3574.66	−0.0812650
$73$	−17353.4	−0.381134	−0.190567	−	0.981674i	$-0.561033\pi$
$73$	−17353.4	−0.381134	−0.190567	+	0.981674i	$0.561033\pi$
$74$	−9324.27	−0.197941
$75$	−5625.00	−0.115470
$76$	4719.73	0.0937309
$77$	10063.4	0.193427
$78$	4218.74	0.0785138
$79$	61676.5	1.11187	0.555933	−	0.831227i	$-0.312361\pi$
$79$	61676.5	1.11187	0.555933	+	0.831227i	$0.312361\pi$
$80$	24447.2	0.427076
$81$	6561.00	0.111111
$82$	1990.87	0.0326969
$83$	−65230.8	−1.03934	−0.519670	−	0.854367i	$-0.673945\pi$
$83$	−65230.8	−1.03934	−0.519670	+	0.854367i	$0.673945\pi$
$84$	23591.1	0.364796
$85$	48191.4	0.723473
$86$	−15339.8	−0.223652
$87$	65888.9	0.933284
$88$	−5339.92	−0.0735069
$89$	−109563.	−1.46618	−0.733091	−	0.680131i	$-0.761923\pi$
$89$	−109563.	−1.46618	−0.733091	+	0.680131i	$0.761923\pi$
$90$	1406.96	0.0183095
$91$	−56109.9	−0.710291
$92$	42724.5	0.526269
$93$	37941.8	0.454895
$94$	−10113.8	−0.118057
$95$	−3743.76	−0.0425598
$96$	−18824.8	−0.208474
$97$	83736.1	0.903615	0.451808	−	0.892115i	$-0.350779\pi$
$97$	83736.1	0.903615	0.451808	+	0.892115i	$0.350779\pi$
$98$	−6871.57	−0.0722754
$99$	9801.00	0.100504
$100$	−19698.3	−0.196983
$101$	−129877.	−1.26686	−0.633428	−	0.773801i	$-0.718353\pi$
$101$	−129877.	−1.26686	−0.633428	+	0.773801i	$0.718353\pi$
$102$	−12054.0	−0.114718
$103$	201851.	1.87472	0.937362	−	0.348358i	$-0.113261\pi$
$103$	201851.	1.87472	0.937362	+	0.348358i	$0.113261\pi$
$104$	29773.6	0.269928
$105$	−18712.9	−0.165641
$106$	9275.36	0.0801800
$107$	−132285.	−1.11699	−0.558496	−	0.829507i	$-0.688622\pi$
$107$	−132285.	−1.11699	−0.558496	+	0.829507i	$0.688622\pi$
$108$	22976.1	0.189547
$109$	−144044.	−1.16126	−0.580629	−	0.814168i	$-0.697193\pi$
$109$	−144044.	−1.16126	−0.580629	+	0.814168i	$0.697193\pi$
$110$	2101.76	0.0165616
$111$	120781.	0.930448
$112$	81329.4	0.612636
$113$	−1095.62	−0.00807165	−0.00403582	−	0.999992i	$-0.501285\pi$
$113$	−1095.62	−0.00807165	−0.00403582	+	0.999992i	$0.501285\pi$
$114$	936.416	0.00674849
$115$	−33889.8	−0.238960
$116$	230737.	1.59211
$117$	−54647.1	−0.369065
$118$	31824.0	0.210402
$119$	160320.	1.03782
$120$	9929.61	0.0629476
$121$	14641.0	0.0909091
$122$	13198.7	0.0802844
$123$	−25788.5	−0.153696
$124$	132869.	0.776015
$125$	15625.0	0.0894427
$126$	4680.59	0.0262648
$127$	315758.	1.73718	0.868591	−	0.495529i	$-0.165026\pi$
$127$	315758.	1.73718	0.868591	+	0.495529i	$0.165026\pi$
$128$	−87664.9	−0.472934
$129$	198703.	1.05131
$130$	−11718.7	−0.0608165
$131$	−187001.	−0.952064	−0.476032	−	0.879428i	$-0.657925\pi$
$131$	−187001.	−0.952064	−0.476032	+	0.879428i	$0.657925\pi$
$132$	34322.3	0.171452
$133$	−12454.5	−0.0610516
$134$	4621.13	0.0222324
$135$	−18225.0	−0.0860663
$136$	−85070.6	−0.394396
$137$	232301.	1.05743	0.528713	−	0.848801i	$-0.322675\pi$
$137$	232301.	1.05743	0.528713	+	0.848801i	$0.322675\pi$
$138$	8476.75	0.0378906
$139$	−311665.	−1.36820	−0.684102	−	0.729386i	$-0.739806\pi$
$139$	−311665.	−1.36820	−0.684102	+	0.729386i	$0.739806\pi$
$140$	−65530.9	−0.282570
$141$	131008.	0.554944
$142$	−42402.5	−0.176470
$143$	−81633.3	−0.333831
$144$	79209.1	0.318323
$145$	−183025.	−0.722919
$146$	−12057.1	−0.0468124
$147$	89010.4	0.339740
$148$	422966.	1.58727
$149$	30354.5	0.112010	0.0560050	−	0.998430i	$-0.482164\pi$
$149$	30354.5	0.112010	0.0560050	+	0.998430i	$0.482164\pi$
$150$	−3908.23	−0.0141825
$151$	131015.	0.467604	0.233802	−	0.972284i	$-0.424883\pi$
$151$	131015.	0.467604	0.233802	+	0.972284i	$0.424883\pi$
$152$	6608.73	0.0232011
$153$	156140.	0.539245
$154$	6991.99	0.0237574
$155$	−105394.	−0.352360
$156$	−191370.	−0.629595
$157$	326922.	1.05851	0.529255	−	0.848463i	$-0.322472\pi$
$157$	326922.	1.05851	0.529255	+	0.848463i	$0.322472\pi$
$158$	42852.7	0.136564
$159$	−120148.	−0.376897
$160$	52291.1	0.161484
$161$	−112742.	−0.342785
$162$	4558.56	0.0136471
$163$	−501854.	−1.47948	−0.739739	−	0.672894i	$-0.765051\pi$
$163$	−501854.	−1.47948	−0.739739	+	0.672894i	$0.765051\pi$
$164$	−90309.3	−0.262194
$165$	−27225.0	−0.0778499
$166$	−45322.2	−0.127656
$167$	−590462.	−1.63833	−0.819164	−	0.573559i	$-0.805562\pi$
$167$	−590462.	−1.63833	−0.819164	+	0.573559i	$0.805562\pi$
$168$	33033.1	0.0902977
$169$	83866.7	0.225877
$170$	33483.3	0.0888598
$171$	−12129.8	−0.0317222
$172$	695840.	1.79345
$173$	570934.	1.45034	0.725172	−	0.688568i	$-0.241760\pi$
$173$	570934.	1.45034	0.725172	+	0.688568i	$0.241760\pi$
$174$	45779.4	0.114630
$175$	51980.2	0.128305
$176$	118325.	0.287934
$177$	−412230.	−0.989022
$178$	−76123.9	−0.180082
$179$	−464402.	−1.08333	−0.541666	−	0.840594i	$-0.682206\pi$
$179$	−464402.	−1.08333	−0.541666	+	0.840594i	$0.682206\pi$
$180$	−63822.4	−0.146822
$181$	−409792.	−0.929751	−0.464876	−	0.885376i	$-0.653901\pi$
$181$	−409792.	−0.929751	−0.464876	+	0.885376i	$0.653901\pi$
$182$	−38985.0	−0.0872407
$183$	−170968.	−0.377388
$184$	59824.4	0.130267
$185$	−335504.	−0.720722
$186$	26361.9	0.0558720
$187$	233247.	0.487766
$188$	458778.	0.946691
$189$	−60629.7	−0.123461
$190$	−2601.16	−0.00522736
$191$	−591029.	−1.17226	−0.586132	−	0.810216i	$-0.699350\pi$
$191$	−591029.	−1.17226	−0.586132	+	0.810216i	$0.699350\pi$
$192$	268553.	0.525747
$193$	−310907.	−0.600811	−0.300405	−	0.953812i	$-0.597122\pi$
$193$	−310907.	−0.600811	−0.300405	+	0.953812i	$0.597122\pi$
$194$	58179.6	0.110986
$195$	151797.	0.285876
$196$	311707.	0.579571
$197$	161613.	0.296695	0.148348	−	0.988935i	$-0.452605\pi$
$197$	161613.	0.296695	0.148348	+	0.988935i	$0.452605\pi$
$198$	6809.70	0.0123443
$199$	435622.	0.779790	0.389895	−	0.920859i	$-0.372511\pi$
$199$	435622.	0.779790	0.389895	+	0.920859i	$0.372511\pi$
$200$	−27582.2	−0.0487590
$201$	−59859.5	−0.104506
$202$	−90237.8	−0.155600
$203$	−608874.	−1.03702
$204$	546790.	0.919910
$205$	71634.8	0.119053
$206$	140245.	0.230261
$207$	−109803.	−0.178110
$208$	−659738.	−1.05734
$209$	−18119.8	−0.0286938
$210$	−13001.6	−0.0203446
$211$	−539434.	−0.834127	−0.417063	−	0.908877i	$-0.636941\pi$
$211$	−539434.	−0.834127	−0.417063	+	0.908877i	$0.636941\pi$
$212$	−420747.	−0.642957
$213$	549258.	0.829521
$214$	−91911.1	−0.137193
$215$	−551952.	−0.814339
$216$	32171.9	0.0469184
$217$	−350618.	−0.505457
$218$	−100081.	−0.142630
$219$	156181.	0.220048
$220$	−95339.7	−0.132806
$221$	−1.30050e6	−1.79115
$222$	83918.5	0.114281
$223$	452834.	0.609786	0.304893	−	0.952387i	$-0.401379\pi$
$223$	452834.	0.609786	0.304893	+	0.952387i	$0.401379\pi$
$224$	173959.	0.231646
$225$	50625.0	0.0666667
$226$	−761.230	−0.000991391 0
$227$	−40608.6	−0.0523062	−0.0261531	−	0.999658i	$-0.508326\pi$
$227$	−40608.6	−0.0523062	−0.0261531	+	0.999658i	$0.508326\pi$
$228$	−42477.5	−0.0541156
$229$	988410.	1.24551	0.622757	−	0.782415i	$-0.286013\pi$
$229$	988410.	1.24551	0.622757	+	0.782415i	$0.286013\pi$
$230$	−23546.5	−0.0293499
$231$	−90570.2	−0.111675
$232$	323087.	0.394093
$233$	−47673.4	−0.0575289	−0.0287645	−	0.999586i	$-0.509157\pi$
$233$	−47673.4	−0.0575289	−0.0287645	+	0.999586i	$0.509157\pi$
$234$	−37968.6	−0.0453299
$235$	−363911.	−0.429858
$236$	−1.44359e6	−1.68719
$237$	−555089.	−0.641936
$238$	111390.	0.127469
$239$	−165174.	−0.187045	−0.0935224	−	0.995617i	$-0.529813\pi$
$239$	−165174.	−0.187045	−0.0935224	+	0.995617i	$0.529813\pi$
$240$	−220025.	−0.246572
$241$	−1.13302e6	−1.25659	−0.628294	−	0.777976i	$-0.716247\pi$
$241$	−1.13302e6	−1.25659	−0.628294	+	0.777976i	$0.716247\pi$
$242$	10172.5	0.0111658
$243$	−59049.0	−0.0641500
$244$	−598717.	−0.643794
$245$	−247251.	−0.263162
$246$	−17917.8	−0.0188776
$247$	101030.	0.105368
$248$	186048.	0.192086
$249$	587078.	0.600063
$250$	10856.2	0.0109857
$251$	−1.08030e6	−1.08233	−0.541165	−	0.840917i	$-0.682016\pi$
$251$	−1.08030e6	−1.08233	−0.541165	+	0.840917i	$0.682016\pi$
$252$	−212320.	−0.210615
$253$	−164027.	−0.161106
$254$	219388.	0.213368
$255$	−433723.	−0.417698
$256$	893945.	0.852533
$257$	301460.	0.284707	0.142353	−	0.989816i	$-0.454533\pi$
$257$	301460.	0.284707	0.142353	+	0.989816i	$0.454533\pi$
$258$	138058.	0.129126
$259$	−1.11613e6	−1.03387
$260$	531582.	0.487682
$261$	−593000.	−0.538832
$262$	−129928.	−0.116936
$263$	−347755.	−0.310016	−0.155008	−	0.987913i	$-0.549540\pi$
$263$	−347755.	−0.310016	−0.155008	+	0.987913i	$0.549540\pi$
$264$	48059.3	0.0424392
$265$	333744.	0.291943
$266$	−8653.34	−0.00749860
$267$	986065.	0.846501
$268$	−209623.	−0.178280
$269$	980953.	0.826547	0.413274	−	0.910607i	$-0.364385\pi$
$269$	980953.	0.826547	0.413274	+	0.910607i	$0.364385\pi$
$270$	−12662.7	−0.0105710
$271$	9630.73	0.00796592	0.00398296	−	0.999992i	$-0.498732\pi$
$271$	9630.73	0.00796592	0.00398296	+	0.999992i	$0.498732\pi$
$272$	1.88504e6	1.54489
$273$	504989.	0.410086
$274$	161402.	0.129877
$275$	75625.0	0.0603023
$276$	−384521.	−0.303842
$277$	324368.	0.254003	0.127001	−	0.991903i	$-0.459465\pi$
$277$	324368.	0.254003	0.127001	+	0.991903i	$0.459465\pi$
$278$	−216544.	−0.168048
$279$	−341477.	−0.262634
$280$	−91758.7	−0.0699443
$281$	866856.	0.654909	0.327455	−	0.944867i	$-0.393809\pi$
$281$	866856.	0.654909	0.327455	+	0.944867i	$0.393809\pi$
$282$	91023.8	0.0681604
$283$	−575157.	−0.426895	−0.213447	−	0.976955i	$-0.568469\pi$
$283$	−575157.	−0.426895	−0.213447	+	0.976955i	$0.568469\pi$
$284$	1.92346e6	1.41510
$285$	33693.9	0.0245719
$286$	−56718.6	−0.0410025
$287$	238310.	0.170780
$288$	169423.	0.120363
$289$	2.29601e6	1.61707
$290$	−127165.	−0.0887917
$291$	−753625.	−0.521702
$292$	546932.	0.375384
$293$	1.96073e6	1.33429	0.667144	−	0.744929i	$-0.267517\pi$
$293$	1.96073e6	1.33429	0.667144	+	0.744929i	$0.267517\pi$
$294$	61844.1	0.0417282
$295$	1.14508e6	0.766093
$296$	592252.	0.392896
$297$	−88209.0	−0.0580259
$298$	21090.2	0.0137575
$299$	914557.	0.591606
$300$	177285.	0.113728
$301$	−1.83620e6	−1.16816
$302$	91028.8	0.0574330
$303$	1.16889e6	0.731420
$304$	−146440.	−0.0908813
$305$	474912.	0.292323
$306$	108486.	0.0662322
$307$	1.60549e6	0.972215	0.486108	−	0.873899i	$-0.338416\pi$
$307$	1.60549e6	0.972215	0.486108	+	0.873899i	$0.338416\pi$
$308$	−317170.	−0.190509
$309$	−1.81666e6	−1.08237
$310$	−73227.4	−0.0432782
$311$	6622.52	0.00388260	0.00194130	−	0.999998i	$-0.499382\pi$
$311$	6622.52	0.00388260	0.00194130	+	0.999998i	$0.499382\pi$
$312$	−267963.	−0.155843
$313$	−1.08764e6	−0.627516	−0.313758	−	0.949503i	$-0.601588\pi$
$313$	−1.08764e6	−0.627516	−0.313758	+	0.949503i	$0.601588\pi$
$314$	227144.	0.130010
$315$	168416.	0.0956327
$316$	−1.94387e6	−1.09509
$317$	−456183.	−0.254971	−0.127486	−	0.991840i	$-0.540691\pi$
$317$	−456183.	−0.254971	−0.127486	+	0.991840i	$0.540691\pi$
$318$	−83478.2	−0.0462920
$319$	−885839.	−0.487392
$320$	−745980.	−0.407242
$321$	1.19056e6	0.644896
$322$	−78332.9	−0.0421022
$323$	−288668.	−0.153954
$324$	−206785.	−0.109435
$325$	−421660.	−0.221439
$326$	−348687.	−0.181715
$327$	1.29640e6	0.670452
$328$	−126454.	−0.0649006
$329$	−1.21063e6	−0.616627
$330$	−18915.8	−0.00956183
$331$	1.73077e6	0.868297	0.434149	−	0.900841i	$-0.357049\pi$
$331$	1.73077e6	0.868297	0.434149	+	0.900841i	$0.357049\pi$
$332$	2.05590e6	1.02366
$333$	−1.08703e6	−0.537194
$334$	−410251.	−0.201226
$335$	166276.	0.0809503
$336$	−731965.	−0.353706
$337$	3.01707e6	1.44714	0.723571	−	0.690250i	$-0.242499\pi$
$337$	3.01707e6	1.44714	0.723571	+	0.690250i	$0.242499\pi$
$338$	58270.3	0.0277431
$339$	9860.54	0.00466017
$340$	−1.51886e6	−0.712559
$341$	−510107.	−0.237561
$342$	−8427.75	−0.00389624
$343$	−2.22035e6	−1.01903
$344$	974341.	0.443930
$345$	305008.	0.137963
$346$	396683.	0.178137
$347$	1.26947e6	0.565978	0.282989	−	0.959123i	$-0.408674\pi$
$347$	1.26947e6	0.565978	0.282989	+	0.959123i	$0.408674\pi$
$348$	−2.07664e6	−0.919205
$349$	3.26420e6	1.43454	0.717270	−	0.696795i	$-0.245391\pi$
$349$	3.26420e6	1.43454	0.717270	+	0.696795i	$0.245391\pi$
$350$	36115.7	0.0157589
$351$	491824.	0.213079
$352$	253089.	0.108872
$353$	1.70741e6	0.729290	0.364645	−	0.931147i	$-0.381190\pi$
$353$	1.70741e6	0.729290	0.364645	+	0.931147i	$0.381190\pi$
$354$	−286416.	−0.121476
$355$	−1.52572e6	−0.642544
$356$	3.45312e6	1.44406
$357$	−1.44288e6	−0.599183
$358$	−322665.	−0.133059
$359$	257688.	0.105526	0.0527628	−	0.998607i	$-0.483197\pi$
$359$	257688.	0.105526	0.0527628	+	0.998607i	$0.483197\pi$
$360$	−89366.5	−0.0363428
$361$	−2.45367e6	−0.990943
$362$	−284722.	−0.114196
$363$	−131769.	−0.0524864
$364$	1.76843e6	0.699575
$365$	−433835.	−0.170448
$366$	−118788.	−0.0463522
$367$	−683489.	−0.264891	−0.132445	−	0.991190i	$-0.542283\pi$
$367$	−683489.	−0.264891	−0.132445	+	0.991190i	$0.542283\pi$
$368$	−1.32562e6	−0.510269
$369$	232097.	0.0887367
$370$	−233107.	−0.0885219
$371$	1.11027e6	0.418790
$372$	−1.19582e6	−0.448033
$373$	3.58176e6	1.33298	0.666492	−	0.745512i	$-0.267795\pi$
$373$	3.58176e6	1.33298	0.666492	+	0.745512i	$0.267795\pi$
$374$	162059.	0.0599093
$375$	−140625.	−0.0516398
$376$	642398.	0.234334
$377$	4.93914e6	1.78977
$378$	−42125.3	−0.0151640
$379$	−4.87955e6	−1.74494	−0.872472	−	0.488665i	$-0.837484\pi$
$379$	−4.87955e6	−1.74494	−0.872472	+	0.488665i	$0.837484\pi$
$380$	117993.	0.0419177
$381$	−2.84182e6	−1.00296
$382$	−410645.	−0.143982
$383$	4.97559e6	1.73319	0.866597	−	0.499008i	$-0.166302\pi$
$383$	4.97559e6	1.73319	0.866597	+	0.499008i	$0.166302\pi$
$384$	788984.	0.273049
$385$	251584.	0.0865030
$386$	−216017.	−0.0737939
$387$	−1.78832e6	−0.606972
$388$	−2.63913e6	−0.889983
$389$	−4.09866e6	−1.37331	−0.686654	−	0.726984i	$-0.740921\pi$
$389$	−4.09866e6	−1.37331	−0.686654	+	0.726984i	$0.740921\pi$
$390$	105468.	0.0351124
$391$	−2.61312e6	−0.864404
$392$	436463.	0.143461
$393$	1.68301e6	0.549674
$394$	112288.	0.0364413
$395$	1.54191e6	0.497241
$396$	−308901.	−0.0989876
$397$	1.61215e6	0.513369	0.256684	−	0.966495i	$-0.417370\pi$
$397$	1.61215e6	0.513369	0.256684	+	0.966495i	$0.417370\pi$
$398$	302669.	0.0957768
$399$	112090.	0.0352482
$400$	611181.	0.190994
$401$	−648362.	−0.201352	−0.100676	−	0.994919i	$-0.532101\pi$
$401$	−648362.	−0.201352	−0.100676	+	0.994919i	$0.532101\pi$
$402$	−41590.2	−0.0128359
$403$	2.84419e6	0.872359
$404$	4.09335e6	1.24775
$405$	164025.	0.0496904
$406$	−423044.	−0.127371
$407$	−1.62384e6	−0.485911
$408$	765635.	0.227704
$409$	1.88327e6	0.556677	0.278338	−	0.960483i	$-0.410216\pi$
$409$	1.88327e6	0.556677	0.278338	+	0.960483i	$0.410216\pi$
$410$	49771.6	0.0146225
$411$	−2.09071e6	−0.610505
$412$	−6.36178e6	−1.84644
$413$	3.80938e6	1.09895
$414$	−76290.7	−0.0218762
$415$	−1.63077e6	−0.464807
$416$	−1.41114e6	−0.399794
$417$	2.80499e6	0.789933
$418$	−12589.6	−0.00352429
$419$	−5.10510e6	−1.42059	−0.710296	−	0.703903i	$-0.751439\pi$
$419$	−5.10510e6	−1.42059	−0.710296	+	0.703903i	$0.751439\pi$
$420$	589778.	0.163142
$421$	5.48811e6	1.50910	0.754550	−	0.656243i	$-0.227855\pi$
$421$	5.48811e6	1.50910	0.754550	+	0.656243i	$0.227855\pi$
$422$	−374797.	−0.102451
$423$	−1.17907e6	−0.320397
$424$	−589145.	−0.159150
$425$	1.20479e6	0.323547
$426$	381623.	0.101885
$427$	1.57990e6	0.419335
$428$	4.16925e6	1.10014
$429$	734700.	0.192738
$430$	−383494.	−0.100020
$431$	−3.59589e6	−0.932424	−0.466212	−	0.884673i	$-0.654382\pi$
$431$	−3.59589e6	−0.932424	−0.466212	+	0.884673i	$0.654382\pi$
$432$	−712882.	−0.183784
$433$	−5.03603e6	−1.29083	−0.645414	−	0.763833i	$-0.723315\pi$
$433$	−5.03603e6	−1.29083	−0.645414	+	0.763833i	$0.723315\pi$
$434$	−243608.	−0.0620822
$435$	1.64722e6	0.417377
$436$	4.53987e6	1.14374
$437$	203001.	0.0508503
$438$	108514.	0.0270271
$439$	−3.25961e6	−0.807244	−0.403622	−	0.914926i	$-0.632249\pi$
$439$	−3.25961e6	−0.807244	−0.403622	+	0.914926i	$0.632249\pi$
$440$	−133498.	−0.0328733
$441$	−801093.	−0.196149
$442$	−903586.	−0.219996
$443$	−1.35658e6	−0.328424	−0.164212	−	0.986425i	$-0.552508\pi$
$443$	−1.35658e6	−0.328424	−0.164212	+	0.986425i	$0.552508\pi$
$444$	−3.80669e6	−0.916412
$445$	−2.73907e6	−0.655696
$446$	314628.	0.0748962
$447$	−273190.	−0.0646690
$448$	−2.48167e6	−0.584184
$449$	−6.80906e6	−1.59394	−0.796969	−	0.604020i	$-0.793565\pi$
$449$	−6.80906e6	−1.59394	−0.796969	+	0.604020i	$0.793565\pi$
$450$	35174.1	0.00818826
$451$	346712.	0.0802653
$452$	34530.8	0.00794988
$453$	−1.17913e6	−0.269972
$454$	−28214.7	−0.00642445
$455$	−1.40275e6	−0.317652
$456$	−59478.6	−0.0133952
$457$	−3.03977e6	−0.680848	−0.340424	−	0.940272i	$-0.610571\pi$
$457$	−3.03977e6	−0.680848	−0.340424	+	0.940272i	$0.610571\pi$
$458$	686744.	0.152979
$459$	−1.40526e6	−0.311333
$460$	1.06811e6	0.235355
$461$	3.27858e6	0.718511	0.359256	−	0.933239i	$-0.383031\pi$
$461$	3.27858e6	0.718511	0.359256	+	0.933239i	$0.383031\pi$
$462$	−62927.9	−0.0137163
$463$	5.51970e6	1.19664	0.598319	−	0.801258i	$-0.295836\pi$
$463$	5.51970e6	1.19664	0.598319	+	0.801258i	$0.295836\pi$
$464$	−7.15912e6	−1.54371
$465$	948546.	0.203435
$466$	−33123.3	−0.00706593
$467$	−4.07534e6	−0.864711	−0.432356	−	0.901703i	$-0.642317\pi$
$467$	−4.07534e6	−0.864711	−0.432356	+	0.901703i	$0.642317\pi$
$468$	1.72233e6	0.363497
$469$	553157.	0.116122
$470$	−252844.	−0.0527968
$471$	−2.94230e6	−0.611131
$472$	−2.02137e6	−0.417630
$473$	−2.67145e6	−0.549027
$474$	−385674.	−0.0788450
$475$	−93594.1	−0.0190333
$476$	−5.05284e6	−1.02216
$477$	1.08133e6	0.217602
$478$	−114762.	−0.0229736
$479$	4.77799e6	0.951495	0.475748	−	0.879582i	$-0.342178\pi$
$479$	4.77799e6	0.951495	0.475748	+	0.879582i	$0.342178\pi$
$480$	−470620.	−0.0932325
$481$	9.05397e6	1.78433
$482$	−787216.	−0.154339
$483$	1.01468e6	0.197907
$484$	−461444.	−0.0895377
$485$	2.09340e6	0.404109
$486$	−41027.1	−0.00787916
$487$	1.76923e6	0.338035	0.169017	−	0.985613i	$-0.445941\pi$
$487$	1.76923e6	0.338035	0.169017	+	0.985613i	$0.445941\pi$
$488$	−838345.	−0.159358
$489$	4.51669e6	0.854177
$490$	−171789.	−0.0323226
$491$	−1.04139e6	−0.194943	−0.0974716	−	0.995238i	$-0.531076\pi$
$491$	−1.04139e6	−0.194943	−0.0974716	+	0.995238i	$0.531076\pi$
$492$	812784.	0.151378
$493$	−1.41124e7	−2.61506
$494$	70195.3	0.0129417
$495$	245025.	0.0449467
$496$	−4.12255e6	−0.752422
$497$	−5.07565e6	−0.921723
$498$	407900.	0.0737021
$499$	2.03068e6	0.365082	0.182541	−	0.983198i	$-0.441568\pi$
$499$	2.03068e6	0.365082	0.182541	+	0.983198i	$0.441568\pi$
$500$	−492457.	−0.0880934
$501$	5.31416e6	0.945890
$502$	−750588.	−0.132936
$503$	−5.06008e6	−0.891739	−0.445869	−	0.895098i	$-0.647105\pi$
$503$	−5.06008e6	−0.891739	−0.445869	+	0.895098i	$0.647105\pi$
$504$	−297298.	−0.0521334
$505$	−3.24691e6	−0.566555
$506$	−113965.	−0.0197877
$507$	−754800.	−0.130410
$508$	−9.95183e6	−1.71098
$509$	5.64302e6	0.965421	0.482711	−	0.875780i	$-0.339652\pi$
$509$	5.64302e6	0.965421	0.482711	+	0.875780i	$0.339652\pi$
$510$	−301349.	−0.0513032
$511$	−1.44325e6	−0.244506
$512$	3.42639e6	0.577645
$513$	109168.	0.0183148
$514$	209454.	0.0349688
$515$	5.04627e6	0.838402
$516$	−6.26256e6	−1.03545
$517$	−1.76133e6	−0.289810
$518$	−775484.	−0.126984
$519$	−5.13841e6	−0.837356
$520$	744340.	0.120716
$521$	5.37673e6	0.867809	0.433905	−	0.900959i	$-0.357136\pi$
$521$	5.37673e6	0.867809	0.433905	+	0.900959i	$0.357136\pi$
$522$	−412014.	−0.0661814
$523$	8.42403e6	1.34668	0.673342	−	0.739331i	$-0.264858\pi$
$523$	8.42403e6	1.34668	0.673342	+	0.739331i	$0.264858\pi$
$524$	5.89376e6	0.937701
$525$	−467821.	−0.0740767
$526$	−241619.	−0.0380773
$527$	−8.12654e6	−1.27462
$528$	−1.06492e6	−0.166239
$529$	−4.59871e6	−0.714492
$530$	231884.	0.0358576
$531$	3.71007e6	0.571012
$532$	392532.	0.0601306
$533$	−1.93315e6	−0.294746
$534$	685115.	0.103970
$535$	−3.30712e6	−0.499534
$536$	−293522.	−0.0441294
$537$	4.17962e6	0.625462
$538$	681563.	0.101520
$539$	−1.19669e6	−0.177424
$540$	574402.	0.0847679
$541$	8.85130e6	1.30021	0.650106	−	0.759844i	$-0.274725\pi$
$541$	8.85130e6	1.30021	0.650106	+	0.759844i	$0.274725\pi$
$542$	6691.40	0.000978405 0
$543$	3.68813e6	0.536792
$544$	4.03198e6	0.584145
$545$	−3.60110e6	−0.519330
$546$	350865.	0.0503684
$547$	3.13327e6	0.447744	0.223872	−	0.974619i	$-0.428130\pi$
$547$	3.13327e6	0.447744	0.223872	+	0.974619i	$0.428130\pi$
$548$	−7.32150e6	−1.04147
$549$	1.53871e6	0.217885
$550$	52544.0	0.00740656
$551$	1.09632e6	0.153836
$552$	−538420.	−0.0752096
$553$	5.12953e6	0.713288
$554$	225370.	0.0311976
$555$	3.01953e6	0.416109
$556$	9.82283e6	1.34756
$557$	−5.46691e6	−0.746627	−0.373313	−	0.927705i	$-0.621778\pi$
$557$	−5.46691e6	−0.746627	−0.373313	+	0.927705i	$0.621778\pi$
$558$	−237257.	−0.0322577
$559$	1.48951e7	2.01611
$560$	2.03323e6	0.273979
$561$	−2.09922e6	−0.281612
$562$	602289.	0.0804385
$563$	5.19043e6	0.690132	0.345066	−	0.938578i	$-0.387857\pi$
$563$	5.19043e6	0.690132	0.345066	+	0.938578i	$0.387857\pi$
$564$	−4.12901e6	−0.546573
$565$	−27390.4	−0.00360975
$566$	−399618.	−0.0524329
$567$	545667.	0.0712804
$568$	2.69329e6	0.350278
$569$	1.24058e7	1.60636	0.803180	−	0.595737i	$-0.203140\pi$
$569$	1.24058e7	1.60636	0.803180	+	0.595737i	$0.203140\pi$
$570$	23410.4	0.00301802
$571$	8.79234e6	1.12853	0.564266	−	0.825593i	$-0.309159\pi$
$571$	8.79234e6	1.12853	0.564266	+	0.825593i	$0.309159\pi$
$572$	2.57286e6	0.328795
$573$	5.31926e6	0.676807
$574$	165577.	0.0209759
$575$	−847245.	−0.106866
$576$	−2.41698e6	−0.303540
$577$	−1.14336e7	−1.42969	−0.714845	−	0.699283i	$-0.753503\pi$
$577$	−1.14336e7	−1.42969	−0.714845	+	0.699283i	$0.753503\pi$
$578$	1.59526e6	0.198615
$579$	2.79817e6	0.346878
$580$	5.76843e6	0.712013
$581$	−5.42514e6	−0.666761
$582$	−523616.	−0.0640775
$583$	1.61532e6	0.196828
$584$	765834.	0.0929185
$585$	−1.36618e6	−0.165051
$586$	1.36231e6	0.163882
$587$	−2.32244e6	−0.278195	−0.139097	−	0.990279i	$-0.544420\pi$
$587$	−2.32244e6	−0.278195	−0.139097	+	0.990279i	$0.544420\pi$
$588$	−2.80536e6	−0.334615
$589$	631313.	0.0749819
$590$	795599.	0.0940945
$591$	−1.45452e6	−0.171297
$592$	−1.31234e7	−1.53901
$593$	7.98435e6	0.932401	0.466201	−	0.884679i	$-0.345623\pi$
$593$	7.98435e6	0.932401	0.466201	+	0.884679i	$0.345623\pi$
$594$	−61287.3	−0.00712697
$595$	4.00800e6	0.464125
$596$	−956690.	−0.110320
$597$	−3.92060e6	−0.450212
$598$	635431.	0.0726634
$599$	−139225.	−0.0158544	−0.00792721	−	0.999969i	$-0.502523\pi$
$599$	−139225.	−0.0158544	−0.00792721	+	0.999969i	$0.502523\pi$
$600$	248240.	0.0281510
$601$	1.55602e7	1.75723	0.878616	−	0.477529i	$-0.158467\pi$
$601$	1.55602e7	1.75723	0.878616	+	0.477529i	$0.158467\pi$
$602$	−1.27578e6	−0.143478
$603$	538735.	0.0603368
$604$	−4.12923e6	−0.460550
$605$	366025.	0.0406558
$606$	812141.	0.0898358
$607$	−6.00544e6	−0.661566	−0.330783	−	0.943707i	$-0.607313\pi$
$607$	−6.00544e6	−0.661566	−0.330783	+	0.943707i	$0.607313\pi$
$608$	−313225.	−0.0343635
$609$	5.47986e6	0.598724
$610$	329967.	0.0359043
$611$	9.82057e6	1.06423
$612$	−4.92111e6	−0.531110
$613$	−2.32775e6	−0.250199	−0.125099	−	0.992144i	$-0.539925\pi$
$613$	−2.32775e6	−0.250199	−0.125099	+	0.992144i	$0.539925\pi$
$614$	1.11549e6	0.119411
$615$	−644713.	−0.0687351
$616$	−444112.	−0.0471564
$617$	1.30284e7	1.37777	0.688886	−	0.724870i	$-0.258100\pi$
$617$	1.30284e7	1.37777	0.688886	+	0.724870i	$0.258100\pi$
$618$	−1.26221e6	−0.132941
$619$	−2.53159e6	−0.265562	−0.132781	−	0.991145i	$-0.542391\pi$
$619$	−2.53159e6	−0.265562	−0.132781	+	0.991145i	$0.542391\pi$
$620$	3.32173e6	0.347045
$621$	988226.	0.102832
$622$	4601.30	0.000476876 0
$623$	−9.11214e6	−0.940590
$624$	5.93765e6	0.610454
$625$	390625.	0.0400000
$626$	−755689.	−0.0770739
$627$	163078.	0.0165664
$628$	−1.03037e7	−1.04254
$629$	−2.58694e7	−2.60712
$630$	117015.	0.0117460
$631$	−2.17733e6	−0.217696	−0.108848	−	0.994058i	$-0.534716\pi$
$631$	−2.17733e6	−0.217696	−0.108848	+	0.994058i	$0.534716\pi$
$632$	−2.72188e6	−0.271067
$633$	4.85491e6	0.481583
$634$	−316955.	−0.0313166
$635$	7.89396e6	0.776892
$636$	3.78673e6	0.371211
$637$	6.67237e6	0.651525
$638$	−615478.	−0.0598634
$639$	−4.94332e6	−0.478924
$640$	−2.19162e6	−0.211503
$641$	−2.58180e6	−0.248187	−0.124093	−	0.992271i	$-0.539602\pi$
$641$	−2.58180e6	−0.248187	−0.124093	+	0.992271i	$0.539602\pi$
$642$	827200.	0.0792087
$643$	−1.67813e7	−1.60066	−0.800329	−	0.599561i	$-0.795342\pi$
$643$	−1.67813e7	−1.60066	−0.800329	+	0.599561i	$0.795342\pi$
$644$	3.55333e6	0.337614
$645$	4.96757e6	0.470159
$646$	−200566.	−0.0189093
$647$	−1.01691e7	−0.955037	−0.477518	−	0.878622i	$-0.658464\pi$
$647$	−1.01691e7	−0.955037	−0.477518	+	0.878622i	$0.658464\pi$
$648$	−289547.	−0.0270883
$649$	5.54220e6	0.516500
$650$	−292968.	−0.0271980
$651$	3.15556e6	0.291826
$652$	1.58171e7	1.45716
$653$	−8.99282e6	−0.825302	−0.412651	−	0.910889i	$-0.635397\pi$
$653$	−8.99282e6	−0.825302	−0.412651	+	0.910889i	$0.635397\pi$
$654$	900731.	0.0823476
$655$	−4.67503e6	−0.425776
$656$	2.80204e6	0.254223
$657$	−1.40563e6	−0.127045
$658$	−841144.	−0.0757365
$659$	−1.03480e7	−0.928203	−0.464102	−	0.885782i	$-0.653623\pi$
$659$	−1.03480e7	−0.928203	−0.464102	+	0.885782i	$0.653623\pi$
$660$	858057.	0.0766755
$661$	1.48595e7	1.32282	0.661409	−	0.750025i	$-0.269959\pi$
$661$	1.48595e7	1.32282	0.661409	+	0.750025i	$0.269959\pi$
$662$	1.20253e6	0.106648
$663$	1.17045e7	1.03412
$664$	2.87874e6	0.253386
$665$	−311362.	−0.0273031
$666$	−755266.	−0.0659803
$667$	9.92427e6	0.863742
$668$	1.86098e7	1.61361
$669$	−4.07551e6	−0.352060
$670$	115528.	0.00994263
$671$	2.29857e6	0.197084
$672$	−1.56563e6	−0.133741
$673$	217545.	0.0185145	0.00925725	−	0.999957i	$-0.497053\pi$
$673$	217545.	0.0185145	0.00925725	+	0.999957i	$0.497053\pi$
$674$	2.09625e6	0.177744
$675$	−455625.	−0.0384900
$676$	−2.64325e6	−0.222470
$677$	−2.64314e6	−0.221640	−0.110820	−	0.993840i	$-0.535348\pi$
$677$	−2.64314e6	−0.221640	−0.110820	+	0.993840i	$0.535348\pi$
$678$	6851.07	0.000572380 0
$679$	6.96419e6	0.579690
$680$	−2.12676e6	−0.176379
$681$	365477.	0.0301990
$682$	−354421.	−0.0291782
$683$	4.66785e6	0.382882	0.191441	−	0.981504i	$-0.438684\pi$
$683$	4.66785e6	0.382882	0.191441	+	0.981504i	$0.438684\pi$
$684$	382298.	0.0312436
$685$	5.80753e6	0.472895
$686$	−1.54269e6	−0.125161
$687$	−8.89569e6	−0.719098
$688$	−2.15899e7	−1.73892
$689$	−9.00647e6	−0.722781
$690$	211919.	0.0169452
$691$	3.11273e6	0.247997	0.123998	−	0.992282i	$-0.460428\pi$
$691$	3.11273e6	0.247997	0.123998	+	0.992282i	$0.460428\pi$
$692$	−1.79943e7	−1.42846
$693$	815132.	0.0644755
$694$	882026.	0.0695156
$695$	−7.79163e6	−0.611880
$696$	−2.90778e6	−0.227530
$697$	5.52349e6	0.430657
$698$	2.26795e6	0.176196
$699$	429061.	0.0332143
$700$	−1.63827e6	−0.126369
$701$	1.16786e7	0.897629	0.448815	−	0.893625i	$-0.351846\pi$
$701$	1.16786e7	0.897629	0.448815	+	0.893625i	$0.351846\pi$
$702$	341718.	0.0261713
$703$	2.00967e6	0.153369
$704$	−3.61054e6	−0.274562
$705$	3.27519e6	0.248179
$706$	1.18630e6	0.0895743
$707$	−1.08016e7	−0.812718
$708$	1.29923e7	0.974102
$709$	−1.96571e7	−1.46860	−0.734302	−	0.678823i	$-0.762490\pi$
$709$	−1.96571e7	−1.46860	−0.734302	+	0.678823i	$0.762490\pi$
$710$	−1.06006e6	−0.0789198
$711$	4.99580e6	0.370622
$712$	4.83518e6	0.357448
$713$	5.71485e6	0.420999
$714$	−1.00251e6	−0.0735940
$715$	−2.04083e6	−0.149294
$716$	1.46367e7	1.06699
$717$	1.48656e6	0.107990
$718$	179041.	0.0129611
$719$	−1.89013e7	−1.36354	−0.681772	−	0.731565i	$-0.738790\pi$
$719$	−1.89013e7	−1.36354	−0.681772	+	0.731565i	$0.738790\pi$
$720$	1.98023e6	0.142359
$721$	1.67876e7	1.20268
$722$	−1.70480e6	−0.121712
$723$	1.01971e7	0.725492
$724$	1.29155e7	0.915725
$725$	−4.57562e6	−0.323299
$726$	−91552.7	−0.00644658
$727$	6.78994e6	0.476463	0.238232	−	0.971208i	$-0.423432\pi$
$727$	6.78994e6	0.476463	0.238232	+	0.971208i	$0.423432\pi$
$728$	2.47622e6	0.173165
$729$	531441.	0.0370370
$730$	−301427.	−0.0209351
$731$	−4.25590e7	−2.94576
$732$	5.38845e6	0.371695
$733$	−3.60300e6	−0.247688	−0.123844	−	0.992302i	$-0.539522\pi$
$733$	−3.60300e6	−0.247688	−0.123844	+	0.992302i	$0.539522\pi$
$734$	−474886.	−0.0325349
$735$	2.22526e6	0.151937
$736$	−2.83542e6	−0.192940
$737$	804778.	0.0545767
$738$	161260.	0.0108990
$739$	−7.58466e6	−0.510887	−0.255443	−	0.966824i	$-0.582221\pi$
$739$	−7.58466e6	−0.510887	−0.255443	+	0.966824i	$0.582221\pi$
$740$	1.05742e7	0.709849
$741$	−909270.	−0.0608341
$742$	771416.	0.0514374
$743$	1.17473e7	0.780669	0.390335	−	0.920673i	$-0.372359\pi$
$743$	1.17473e7	0.780669	0.390335	+	0.920673i	$0.372359\pi$
$744$	−1.67443e6	−0.110901
$745$	758862.	0.0500924
$746$	2.48860e6	0.163722
$747$	−5.28370e6	−0.346447
$748$	−7.35129e6	−0.480407
$749$	−1.10019e7	−0.716577
$750$	−97705.8	−0.00634260
$751$	4.05057e6	0.262070	0.131035	−	0.991378i	$-0.458170\pi$
$751$	4.05057e6	0.262070	0.131035	+	0.991378i	$0.458170\pi$
$752$	−1.42346e7	−0.917910
$753$	9.72269e6	0.624883
$754$	3.43170e6	0.219827
$755$	3.27537e6	0.209119
$756$	1.91088e6	0.121599
$757$	2.12290e7	1.34645	0.673225	−	0.739438i	$-0.264909\pi$
$757$	2.12290e7	1.34645	0.673225	+	0.739438i	$0.264909\pi$
$758$	−3.39029e6	−0.214321
$759$	1.47624e6	0.0930149
$760$	165218.	0.0103759
$761$	−1.06438e7	−0.666247	−0.333123	−	0.942883i	$-0.608103\pi$
$761$	−1.06438e7	−0.666247	−0.333123	+	0.942883i	$0.608103\pi$
$762$	−1.97449e6	−0.123188
$763$	−1.19799e7	−0.744974
$764$	1.86276e7	1.15458
$765$	3.90351e6	0.241158
$766$	3.45702e6	0.212878
$767$	−3.09014e7	−1.89666
$768$	−8.04551e6	−0.492210
$769$	3.17109e6	0.193372	0.0966859	−	0.995315i	$-0.469176\pi$
$769$	3.17109e6	0.193372	0.0966859	+	0.995315i	$0.469176\pi$
$770$	174800.	0.0106246
$771$	−2.71314e6	−0.164375
$772$	9.79894e6	0.591747
$773$	1.80501e7	1.08650	0.543252	−	0.839570i	$-0.317193\pi$
$773$	1.80501e7	1.08650	0.543252	+	0.839570i	$0.317193\pi$
$774$	−1.24252e6	−0.0745507
$775$	−2.63485e6	−0.157580
$776$	−3.69541e6	−0.220297
$777$	1.00452e7	0.596904
$778$	−2.84774e6	−0.168675
$779$	−429094.	−0.0253343
$780$	−4.78424e6	−0.281563
$781$	−7.38447e6	−0.433203
$782$	−1.81559e6	−0.106169
$783$	5.33700e6	0.311095
$784$	−9.67137e6	−0.561950
$785$	8.17304e6	0.473380
$786$	1.16935e6	0.0675132
$787$	−2.58223e7	−1.48614	−0.743068	−	0.669216i	$-0.766630\pi$
$787$	−2.58223e7	−1.48614	−0.743068	+	0.669216i	$0.766630\pi$
$788$	−5.09360e6	−0.292219
$789$	3.12979e6	0.178988
$790$	1.07132e6	0.0610731
$791$	−91120.5	−0.00517815
$792$	−432534.	−0.0245023
$793$	−1.28161e7	−0.723722
$794$	1.12012e6	0.0630540
$795$	−3.00369e6	−0.168553
$796$	−1.37296e7	−0.768026
$797$	1.50658e7	0.840129	0.420065	−	0.907494i	$-0.362007\pi$
$797$	1.50658e7	0.840129	0.420065	+	0.907494i	$0.362007\pi$
$798$	77880.1	0.00432932
$799$	−2.80598e7	−1.55495
$800$	1.30728e6	0.0722176
$801$	−8.87458e6	−0.488727
$802$	−450480.	−0.0247309
$803$	−2.09976e6	−0.114916
$804$	1.88661e6	0.102930
$805$	−2.81856e6	−0.153298
$806$	1.97613e6	0.107147
$807$	−8.82858e6	−0.477207
$808$	5.73166e6	0.308853
$809$	−2.08560e7	−1.12037	−0.560183	−	0.828369i	$-0.689269\pi$
$809$	−2.08560e7	−1.12037	−0.560183	+	0.828369i	$0.689269\pi$
$810$	113964.	0.00610317
$811$	8.46233e6	0.451791	0.225896	−	0.974152i	$-0.427469\pi$
$811$	8.46233e6	0.451791	0.225896	+	0.974152i	$0.427469\pi$
$812$	1.91900e7	1.02138
$813$	−86676.5	−0.00459912
$814$	−1.12824e6	−0.0596814
$815$	−1.25464e7	−0.661643
$816$	−1.69653e7	−0.891943
$817$	3.30620e6	0.173290
$818$	1.30849e6	0.0683732
$819$	−4.54490e6	−0.236764
$820$	−2.25773e6	−0.117257
$821$	8.67359e6	0.449098	0.224549	−	0.974463i	$-0.427909\pi$
$821$	8.67359e6	0.449098	0.224549	+	0.974463i	$0.427909\pi$
$822$	−1.45262e6	−0.0749846
$823$	−1.24194e7	−0.639148	−0.319574	−	0.947561i	$-0.603540\pi$
$823$	−1.24194e7	−0.639148	−0.319574	+	0.947561i	$0.603540\pi$
$824$	−8.90799e6	−0.457048
$825$	−680625.	−0.0348155
$826$	2.64675e6	0.134978
$827$	−2.38473e7	−1.21248	−0.606242	−	0.795280i	$-0.707324\pi$
$827$	−2.38473e7	−1.21248	−0.606242	+	0.795280i	$0.707324\pi$
$828$	3.46069e6	0.175423
$829$	−3.26873e7	−1.65193	−0.825967	−	0.563719i	$-0.809370\pi$
$829$	−3.26873e7	−1.65193	−0.825967	+	0.563719i	$0.809370\pi$
$830$	−1.13305e6	−0.0570894
$831$	−2.91931e6	−0.146649
$832$	2.01312e7	1.00823
$833$	−1.90646e7	−0.951953
$834$	1.94890e6	0.0970227
$835$	−1.47616e7	−0.732683
$836$	571087.	0.0282609
$837$	3.07329e6	0.151632
$838$	−3.54701e6	−0.174483
$839$	8.09423e6	0.396982	0.198491	−	0.980103i	$-0.436396\pi$
$839$	8.09423e6	0.396982	0.198491	+	0.980103i	$0.436396\pi$
$840$	825828.	0.0403823
$841$	3.30857e7	1.61306
$842$	3.81313e6	0.185354
$843$	−7.80171e6	−0.378112
$844$	1.70015e7	0.821544
$845$	2.09667e6	0.101015
$846$	−819214.	−0.0393524
$847$	1.21767e6	0.0583203
$848$	1.30546e7	0.623409
$849$	5.17642e6	0.246468
$850$	837082.	0.0397393
$851$	1.81922e7	0.861117
$852$	−1.73111e7	−0.817007
$853$	3.67970e6	0.173157	0.0865785	−	0.996245i	$-0.472407\pi$
$853$	3.67970e6	0.173157	0.0865785	+	0.996245i	$0.472407\pi$
$854$	1.09771e6	0.0515043
$855$	−303245.	−0.0141866
$856$	5.83794e6	0.272317
$857$	2.17589e7	1.01201	0.506004	−	0.862531i	$-0.331122\pi$
$857$	2.17589e7	1.01201	0.506004	+	0.862531i	$0.331122\pi$
$858$	510467.	0.0236728
$859$	−3.76305e7	−1.74003	−0.870015	−	0.493025i	$-0.835891\pi$
$859$	−3.76305e7	−1.74003	−0.870015	+	0.493025i	$0.835891\pi$
$860$	1.73960e7	0.802054
$861$	−2.14479e6	−0.0985998
$862$	−2.49841e6	−0.114524
$863$	−2.50264e7	−1.14386	−0.571928	−	0.820304i	$-0.693804\pi$
$863$	−2.50264e7	−1.14386	−0.571928	+	0.820304i	$0.693804\pi$
$864$	−1.52481e6	−0.0694914
$865$	1.42734e7	0.648613
$866$	−3.49902e6	−0.158545
$867$	−2.06641e7	−0.933615
$868$	1.10505e7	0.497832
$869$	7.46286e6	0.335240
$870$	1.14448e6	0.0512639
$871$	−4.48717e6	−0.200414
$872$	6.35689e6	0.283109
$873$	6.78263e6	0.301205
$874$	141044.	0.00624564
$875$	1.29950e6	0.0573796
$876$	−4.92239e6	−0.216728
$877$	1.12677e7	0.494692	0.247346	−	0.968927i	$-0.420442\pi$
$877$	1.12677e7	0.494692	0.247346	+	0.968927i	$0.420442\pi$
$878$	−2.26477e6	−0.0991488
$879$	−1.76466e7	−0.770351
$880$	2.95812e6	0.128768
$881$	−4.36223e7	−1.89352	−0.946758	−	0.321947i	$-0.895663\pi$
$881$	−4.36223e7	−1.89352	−0.946758	+	0.321947i	$0.895663\pi$
$882$	−556597.	−0.0240918
$883$	−3.14744e7	−1.35849	−0.679244	−	0.733912i	$-0.737692\pi$
$883$	−3.14744e7	−1.35849	−0.679244	+	0.733912i	$0.737692\pi$
$884$	4.09883e7	1.76413
$885$	−1.03057e7	−0.442304
$886$	−942545.	−0.0403383
$887$	2.33777e7	0.997684	0.498842	−	0.866693i	$-0.333759\pi$
$887$	2.33777e7	0.997684	0.498842	+	0.866693i	$0.333759\pi$
$888$	−5.33027e6	−0.226839
$889$	2.62611e7	1.11444
$890$	−1.90310e6	−0.0805352
$891$	793881.	0.0335013
$892$	−1.42721e7	−0.600587
$893$	2.17983e6	0.0914733
$894$	−189812.	−0.00794290
$895$	−1.16101e7	−0.484481
$896$	−7.29093e6	−0.303398
$897$	−8.23101e6	−0.341564
$898$	−4.73091e6	−0.195774
$899$	3.08635e7	1.27364
$900$	−1.59556e6	−0.0656610
$901$	2.57337e7	1.05607
$902$	240895.	0.00985850
$903$	1.65258e7	0.674438
$904$	48351.3	0.00196783
$905$	−1.02448e7	−0.415797
$906$	−819259.	−0.0331590
$907$	2.58345e7	1.04275	0.521377	−	0.853326i	$-0.325418\pi$
$907$	2.58345e7	1.04275	0.521377	+	0.853326i	$0.325418\pi$
$908$	1.27987e6	0.0515171
$909$	−1.05200e7	−0.422285
$910$	−974625.	−0.0390152
$911$	1.24995e7	0.498996	0.249498	−	0.968375i	$-0.419734\pi$
$911$	1.24995e7	0.498996	0.249498	+	0.968375i	$0.419734\pi$
$912$	1.31796e6	0.0524703
$913$	−7.89293e6	−0.313373
$914$	−2.11202e6	−0.0836244
$915$	−4.27421e6	−0.168773
$916$	−3.11520e7	−1.22672
$917$	−1.55526e7	−0.610771
$918$	−976372.	−0.0382392
$919$	1.24766e7	0.487313	0.243657	−	0.969862i	$-0.421653\pi$
$919$	1.24766e7	0.487313	0.243657	+	0.969862i	$0.421653\pi$
$920$	1.49561e6	0.0582571
$921$	−1.44494e7	−0.561309
$922$	2.27795e6	0.0882503
$923$	4.11733e7	1.59079
$924$	2.85453e6	0.109990
$925$	−8.38759e6	−0.322317
$926$	3.83507e6	0.146976
$927$	1.63499e7	0.624908
$928$	−1.53129e7	−0.583697
$929$	−1.63852e6	−0.0622891	−0.0311445	−	0.999515i	$-0.509915\pi$
$929$	−1.63852e6	−0.0622891	−0.0311445	+	0.999515i	$0.509915\pi$
$930$	659047.	0.0249867
$931$	1.48104e6	0.0560006
$932$	1.50253e6	0.0566611
$933$	−59602.7	−0.00224162
$934$	−2.83153e6	−0.106207
$935$	5.83116e6	0.218135
$936$	2.41166e6	0.0899760
$937$	1.03137e7	0.383766	0.191883	−	0.981418i	$-0.438541\pi$
$937$	1.03137e7	0.383766	0.191883	+	0.981418i	$0.438541\pi$
$938$	384331.	0.0142626
$939$	9.78876e6	0.362296
$940$	1.14695e7	0.423373
$941$	−1.30200e7	−0.479332	−0.239666	−	0.970855i	$-0.577038\pi$
$941$	−1.30200e7	−0.479332	−0.239666	+	0.970855i	$0.577038\pi$
$942$	−2.04430e6	−0.0750615
$943$	−3.88430e6	−0.142244
$944$	4.47906e7	1.63590
$945$	−1.51574e6	−0.0552135
$946$	−1.85611e6	−0.0674336
$947$	4.07950e7	1.47820	0.739098	−	0.673598i	$-0.235252\pi$
$947$	4.07950e7	1.47820	0.739098	+	0.673598i	$0.235252\pi$
$948$	1.74949e7	0.632252
$949$	1.17076e7	0.421989
$950$	−65028.9	−0.00233775
$951$	4.10565e6	0.147208
$952$	−7.07517e6	−0.253014
$953$	4.68439e7	1.67078	0.835392	−	0.549654i	$-0.185240\pi$
$953$	4.68439e7	1.67078	0.835392	+	0.549654i	$0.185240\pi$
$954$	751304.	0.0267267
$955$	−1.47757e7	−0.524252
$956$	5.20582e6	0.184223
$957$	7.97255e6	0.281396
$958$	3.31973e6	0.116866
$959$	1.93201e7	0.678364
$960$	6.71382e6	0.235121
$961$	−1.08565e7	−0.379212
$962$	6.29067e6	0.219159
$963$	−1.07151e7	−0.372331
$964$	3.57095e7	1.23763
$965$	−7.77268e6	−0.268691
$966$	704996.	0.0243077
$967$	1.63484e7	0.562223	0.281111	−	0.959675i	$-0.409297\pi$
$967$	1.63484e7	0.562223	0.281111	+	0.959675i	$0.409297\pi$
$968$	−646131.	−0.0221632
$969$	2.59801e6	0.0888856
$970$	1.45449e6	0.0496342
$971$	−1.62139e6	−0.0551875	−0.0275937	−	0.999619i	$-0.508784\pi$
$971$	−1.62139e6	−0.0551875	−0.0275937	+	0.999619i	$0.508784\pi$
$972$	1.86106e6	0.0631823
$973$	−2.59206e7	−0.877735
$974$	1.22925e6	0.0415187
$975$	3.79494e6	0.127848
$976$	1.85765e7	0.624221
$977$	−2.33840e7	−0.783759	−0.391880	−	0.920017i	$-0.628175\pi$
$977$	−2.33840e7	−0.783759	−0.391880	+	0.920017i	$0.628175\pi$
$978$	3.13818e6	0.104913
$979$	−1.32571e7	−0.442070
$980$	7.79267e6	0.259192
$981$	−1.16676e7	−0.387086
$982$	−723552.	−0.0239437
$983$	1.96781e7	0.649529	0.324764	−	0.945795i	$-0.394715\pi$
$983$	1.96781e7	0.649529	0.324764	+	0.945795i	$0.394715\pi$
$984$	1.13809e6	0.0374704
$985$	4.04033e6	0.132686
$986$	−9.80522e6	−0.321192
$987$	1.08957e7	0.356010
$988$	−3.18419e6	−0.103778
$989$	2.99289e7	0.972970
$990$	170243.	0.00552052
$991$	1.56015e7	0.504642	0.252321	−	0.967644i	$-0.418806\pi$
$991$	1.56015e7	0.504642	0.252321	+	0.967644i	$0.418806\pi$
$992$	−8.81788e6	−0.284502
$993$	−1.55769e7	−0.501312
$994$	−3.52654e6	−0.113210
$995$	1.08906e7	0.348733
$996$	−1.85031e7	−0.591011
$997$	−5.71913e6	−0.182218	−0.0911091	−	0.995841i	$-0.529041\pi$
$997$	−5.71913e6	−0.182218	−0.0911091	+	0.995841i	$0.529041\pi$
$998$	1.41091e6	0.0448408
$999$	9.78328e6	0.310149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.c.1.2	✓	3
3.2	odd	2		495.6.a.b.1.2		3
5.4	even	2		825.6.a.g.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.c.1.2	✓	3	1.1	even	1	trivial
495.6.a.b.1.2		3	3.2	odd	2
825.6.a.g.1.2		3	5.4	even	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q+0.694797 q^{2} -9.00000 q^{3} -31.5173 q^{4} +25.0000 q^{5} -6.25317 q^{6} +83.1683 q^{7} -44.1316 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+0.694797 q^{2} -9.00000 q^{3} -31.5173 q^{4} +25.0000 q^{5} -6.25317 q^{6} +83.1683 q^{7} -44.1316 q^{8} +81.0000 q^{9} +17.3699 q^{10} +121.000 q^{11} +283.655 q^{12} -674.655 q^{13} +57.7851 q^{14} -225.000 q^{15} +977.890 q^{16} +1927.66 q^{17} +56.2785 q^{18} -149.751 q^{19} -787.931 q^{20} -748.514 q^{21} +84.0704 q^{22} -1355.59 q^{23} +397.184 q^{24} +625.000 q^{25} -468.748 q^{26} -729.000 q^{27} -2621.24 q^{28} -7320.99 q^{29} -156.329 q^{30} -4215.76 q^{31} +2091.65 q^{32} -1089.00 q^{33} +1339.33 q^{34} +2079.21 q^{35} -2552.90 q^{36} -13420.1 q^{37} -104.046 q^{38} +6071.90 q^{39} -1103.29 q^{40} +2865.39 q^{41} -520.065 q^{42} -22078.1 q^{43} -3813.59 q^{44} +2025.00 q^{45} -941.861 q^{46} -14556.4 q^{47} -8801.01 q^{48} -9890.04 q^{49} +434.248 q^{50} -17348.9 q^{51} +21263.3 q^{52} +13349.7 q^{53} -506.507 q^{54} +3025.00 q^{55} -3670.35 q^{56} +1347.76 q^{57} -5086.60 q^{58} +45803.3 q^{59} +7091.38 q^{60} +18996.5 q^{61} -2929.10 q^{62} +6736.63 q^{63} -29839.2 q^{64} -16866.4 q^{65} -756.634 q^{66} +6651.05 q^{67} -60754.5 q^{68} +12200.3 q^{69} +1444.63 q^{70} -61028.7 q^{71} -3574.66 q^{72} -17353.4 q^{73} -9324.27 q^{74} -5625.00 q^{75} +4719.73 q^{76} +10063.4 q^{77} +4218.74 q^{78} +61676.5 q^{79} +24447.2 q^{80} +6561.00 q^{81} +1990.87 q^{82} -65230.8 q^{83} +23591.1 q^{84} +48191.4 q^{85} -15339.8 q^{86} +65888.9 q^{87} -5339.92 q^{88} -109563. q^{89} +1406.96 q^{90} -56109.9 q^{91} +42724.5 q^{92} +37941.8 q^{93} -10113.8 q^{94} -3743.76 q^{95} -18824.8 q^{96} +83736.1 q^{97} -6871.57 q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9	\( 3 q + 2 q^{2} - 27 q^{3} - 42 q^{4} + 75 q^{5} - 18 q^{6} - 68 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 378 q^{12} + 290 q^{13} + 916 q^{14} - 675 q^{15} - 590 q^{16} + 434 q^{17} + 162 q^{18} - 2856 q^{19} - 1050 q^{20} + 612 q^{21} + 242 q^{22} - 640 q^{23} + 216 q^{24} + 1875 q^{25} + 2132 q^{26} - 2187 q^{27} - 580 q^{28} - 4538 q^{29} - 450 q^{30} - 14968 q^{31} - 2496 q^{32} - 3267 q^{33} - 13704 q^{34} - 1700 q^{35} - 3402 q^{36} - 6190 q^{37} - 11668 q^{38} - 2610 q^{39} - 600 q^{40} - 8926 q^{41} - 8244 q^{42} - 33592 q^{43} - 5082 q^{44} + 6075 q^{45} - 35680 q^{46} - 24640 q^{47} + 5310 q^{48} - 14693 q^{49} + 1250 q^{50} - 3906 q^{51} + 18780 q^{52} - 22934 q^{53} - 1458 q^{54} + 9075 q^{55} - 40012 q^{56} + 25704 q^{57} - 32304 q^{58} - 13756 q^{59} + 9450 q^{60} + 24602 q^{61} - 7704 q^{62} - 5508 q^{63} + 35474 q^{64} + 7250 q^{65} - 2178 q^{66} + 16868 q^{67} - 71288 q^{68} + 5760 q^{69} + 22900 q^{70} + 4856 q^{71} - 1944 q^{72} + 1910 q^{73} + 29404 q^{74} - 16875 q^{75} + 6116 q^{76} - 8228 q^{77} - 19188 q^{78} - 36844 q^{79} - 14750 q^{80} + 19683 q^{81} + 84000 q^{82} - 48796 q^{83} + 5220 q^{84} + 10850 q^{85} - 83492 q^{86} + 40842 q^{87} - 2904 q^{88} - 188978 q^{89} + 4050 q^{90} - 93208 q^{91} - 6976 q^{92} + 134712 q^{93} + 70472 q^{94} - 71400 q^{95} + 22464 q^{96} + 247526 q^{97} - 154654 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 27 * q^3 - 42 * q^4 + 75 * q^5 - 18 * q^6 - 68 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 378 * q^12 + 290 * q^13 + 916 * q^14 - 675 * q^15 - 590 * q^16 + 434 * q^17 + 162 * q^18 - 2856 * q^19 - 1050 * q^20 + 612 * q^21 + 242 * q^22 - 640 * q^23 + 216 * q^24 + 1875 * q^25 + 2132 * q^26 - 2187 * q^27 - 580 * q^28 - 4538 * q^29 - 450 * q^30 - 14968 * q^31 - 2496 * q^32 - 3267 * q^33 - 13704 * q^34 - 1700 * q^35 - 3402 * q^36 - 6190 * q^37 - 11668 * q^38 - 2610 * q^39 - 600 * q^40 - 8926 * q^41 - 8244 * q^42 - 33592 * q^43 - 5082 * q^44 + 6075 * q^45 - 35680 * q^46 - 24640 * q^47 + 5310 * q^48 - 14693 * q^49 + 1250 * q^50 - 3906 * q^51 + 18780 * q^52 - 22934 * q^53 - 1458 * q^54 + 9075 * q^55 - 40012 * q^56 + 25704 * q^57 - 32304 * q^58 - 13756 * q^59 + 9450 * q^60 + 24602 * q^61 - 7704 * q^62 - 5508 * q^63 + 35474 * q^64 + 7250 * q^65 - 2178 * q^66 + 16868 * q^67 - 71288 * q^68 + 5760 * q^69 + 22900 * q^70 + 4856 * q^71 - 1944 * q^72 + 1910 * q^73 + 29404 * q^74 - 16875 * q^75 + 6116 * q^76 - 8228 * q^77 - 19188 * q^78 - 36844 * q^79 - 14750 * q^80 + 19683 * q^81 + 84000 * q^82 - 48796 * q^83 + 5220 * q^84 + 10850 * q^85 - 83492 * q^86 + 40842 * q^87 - 2904 * q^88 - 188978 * q^89 + 4050 * q^90 - 93208 * q^91 - 6976 * q^92 + 134712 * q^93 + 70472 * q^94 - 71400 * q^95 + 22464 * q^96 + 247526 * q^97 - 154654 * q^98 + 29403 * q^99

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