LMFDB - Embedded newform 165.6.a.b.1.3

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:	3.3.3368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 15x + 11 $ x^3 - x^2 - 15*x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.76300$ 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)

$f(q)$	$=$	$q+7.52601 q^{2} +9.00000 q^{3} +24.6408 q^{4} -25.0000 q^{5} +67.7341 q^{6} -234.126 q^{7} -55.3856 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+7.52601 q^{2} +9.00000 q^{3} +24.6408 q^{4} -25.0000 q^{5} +67.7341 q^{6} -234.126 q^{7} -55.3856 q^{8} +81.0000 q^{9} -188.150 q^{10} +121.000 q^{11} +221.767 q^{12} +236.184 q^{13} -1762.04 q^{14} -225.000 q^{15} -1205.34 q^{16} -608.015 q^{17} +609.607 q^{18} -1799.81 q^{19} -616.019 q^{20} -2107.14 q^{21} +910.647 q^{22} -4773.40 q^{23} -498.470 q^{24} +625.000 q^{25} +1777.52 q^{26} +729.000 q^{27} -5769.05 q^{28} +2804.99 q^{29} -1693.35 q^{30} +10258.3 q^{31} -7299.04 q^{32} +1089.00 q^{33} -4575.93 q^{34} +5853.16 q^{35} +1995.90 q^{36} -7629.84 q^{37} -13545.4 q^{38} +2125.66 q^{39} +1384.64 q^{40} +8355.48 q^{41} -15858.3 q^{42} -11967.9 q^{43} +2981.53 q^{44} -2025.00 q^{45} -35924.7 q^{46} +8385.48 q^{47} -10848.0 q^{48} +38008.1 q^{49} +4703.75 q^{50} -5472.14 q^{51} +5819.76 q^{52} +3453.00 q^{53} +5486.46 q^{54} -3025.00 q^{55} +12967.2 q^{56} -16198.3 q^{57} +21110.4 q^{58} -51032.4 q^{59} -5544.17 q^{60} +9988.24 q^{61} +77204.1 q^{62} -18964.2 q^{63} -16361.8 q^{64} -5904.60 q^{65} +8195.82 q^{66} -36567.6 q^{67} -14982.0 q^{68} -42960.6 q^{69} +44050.9 q^{70} -30522.3 q^{71} -4486.23 q^{72} +83879.5 q^{73} -57422.2 q^{74} +5625.00 q^{75} -44348.7 q^{76} -28329.3 q^{77} +15997.7 q^{78} +103505. q^{79} +30133.4 q^{80} +6561.00 q^{81} +62883.4 q^{82} -4341.54 q^{83} -51921.5 q^{84} +15200.4 q^{85} -90070.3 q^{86} +25244.9 q^{87} -6701.65 q^{88} -45464.1 q^{89} -15240.2 q^{90} -55296.9 q^{91} -117620. q^{92} +92324.8 q^{93} +63109.2 q^{94} +44995.2 q^{95} -65691.3 q^{96} -183170. q^{97} +286049. q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9	\( 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 252 q^{12} + 450 q^{13} - 1504 q^{14} - 675 q^{15} - 1360 q^{16} - 334 q^{17} - 162 q^{18} - 4036 q^{19} - 700 q^{20} - 2088 q^{21} - 242 q^{22} - 7060 q^{23} + 216 q^{24} + 1875 q^{25} + 2932 q^{26} + 2187 q^{27} - 8320 q^{28} + 4042 q^{29} + 450 q^{30} - 608 q^{31} - 3104 q^{32} + 3267 q^{33} - 3644 q^{34} + 5800 q^{35} + 2268 q^{36} + 2250 q^{37} - 12632 q^{38} + 4050 q^{39} - 600 q^{40} + 10654 q^{41} - 13536 q^{42} - 35528 q^{43} + 3388 q^{44} - 6075 q^{45} - 41800 q^{46} - 2100 q^{47} - 12240 q^{48} + 7667 q^{49} - 1250 q^{50} - 3006 q^{51} - 14520 q^{52} - 12826 q^{53} - 1458 q^{54} - 9075 q^{55} + 17088 q^{56} - 36324 q^{57} - 17196 q^{58} - 81876 q^{59} - 6300 q^{60} - 62298 q^{61} + 109184 q^{62} - 18792 q^{63} - 72256 q^{64} - 11250 q^{65} - 2178 q^{66} - 46148 q^{67} - 35832 q^{68} - 63540 q^{69} + 37600 q^{70} - 64724 q^{71} + 1944 q^{72} + 810 q^{73} - 44796 q^{74} + 16875 q^{75} + 44656 q^{76} - 28072 q^{77} + 26388 q^{78} + 43876 q^{79} + 34000 q^{80} + 19683 q^{81} + 56060 q^{82} - 101024 q^{83} - 74880 q^{84} + 8350 q^{85} + 24128 q^{86} + 36378 q^{87} + 2904 q^{88} + 60022 q^{89} + 4050 q^{90} - 28568 q^{91} + 38256 q^{92} - 5472 q^{93} + 74552 q^{94} + 100900 q^{95} - 27936 q^{96} - 319746 q^{97} + 431134 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 252 * q^12 + 450 * q^13 - 1504 * q^14 - 675 * q^15 - 1360 * q^16 - 334 * q^17 - 162 * q^18 - 4036 * q^19 - 700 * q^20 - 2088 * q^21 - 242 * q^22 - 7060 * q^23 + 216 * q^24 + 1875 * q^25 + 2932 * q^26 + 2187 * q^27 - 8320 * q^28 + 4042 * q^29 + 450 * q^30 - 608 * q^31 - 3104 * q^32 + 3267 * q^33 - 3644 * q^34 + 5800 * q^35 + 2268 * q^36 + 2250 * q^37 - 12632 * q^38 + 4050 * q^39 - 600 * q^40 + 10654 * q^41 - 13536 * q^42 - 35528 * q^43 + 3388 * q^44 - 6075 * q^45 - 41800 * q^46 - 2100 * q^47 - 12240 * q^48 + 7667 * q^49 - 1250 * q^50 - 3006 * q^51 - 14520 * q^52 - 12826 * q^53 - 1458 * q^54 - 9075 * q^55 + 17088 * q^56 - 36324 * q^57 - 17196 * q^58 - 81876 * q^59 - 6300 * q^60 - 62298 * q^61 + 109184 * q^62 - 18792 * q^63 - 72256 * q^64 - 11250 * q^65 - 2178 * q^66 - 46148 * q^67 - 35832 * q^68 - 63540 * q^69 + 37600 * q^70 - 64724 * q^71 + 1944 * q^72 + 810 * q^73 - 44796 * q^74 + 16875 * q^75 + 44656 * q^76 - 28072 * q^77 + 26388 * q^78 + 43876 * q^79 + 34000 * q^80 + 19683 * q^81 + 56060 * q^82 - 101024 * q^83 - 74880 * q^84 + 8350 * q^85 + 24128 * q^86 + 36378 * q^87 + 2904 * q^88 + 60022 * q^89 + 4050 * q^90 - 28568 * q^91 + 38256 * q^92 - 5472 * q^93 + 74552 * q^94 + 100900 * q^95 - 27936 * q^96 - 319746 * q^97 + 431134 * 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 $

$2$	7.52601	1.33042	0.665211	−	0.746655i	$-0.268341\pi$
$2$	7.52601	1.33042	0.665211	+	0.746655i	$0.268341\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	24.6408	0.770024
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	67.7341	0.768120
$7$	−234.126	−1.80595	−0.902973	−	0.429696i	$-0.858621\pi$
$7$	−234.126	−1.80595	−0.902973	+	0.429696i	$0.858621\pi$
$8$	−55.3856	−0.305965
$9$	81.0000	0.333333
$10$	−188.150	−0.594983
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	221.767	0.444574
$13$	236.184	0.387608	0.193804	−	0.981040i	$-0.437917\pi$
$13$	236.184	0.387608	0.193804	+	0.981040i	$0.437917\pi$
$14$	−1762.04	−2.40267
$15$	−225.000	−0.258199
$16$	−1205.34	−1.17709
$17$	−608.015	−0.510261	−0.255130	−	0.966907i	$-0.582118\pi$
$17$	−608.015	−0.510261	−0.255130	+	0.966907i	$0.582118\pi$
$18$	609.607	0.443474
$19$	−1799.81	−1.14378	−0.571890	−	0.820331i	$-0.693789\pi$
$19$	−1799.81	−1.14378	−0.571890	+	0.820331i	$0.693789\pi$
$20$	−616.019	−0.344365
$21$	−2107.14	−1.04266
$22$	910.647	0.401137
$23$	−4773.40	−1.88152	−0.940759	−	0.339075i	$-0.889886\pi$
$23$	−4773.40	−1.88152	−0.940759	+	0.339075i	$0.889886\pi$
$24$	−498.470	−0.176649
$25$	625.000	0.200000
$26$	1777.52	0.515682
$27$	729.000	0.192450
$28$	−5769.05	−1.39062
$29$	2804.99	0.619351	0.309676	−	0.950842i	$-0.399780\pi$
$29$	2804.99	0.619351	0.309676	+	0.950842i	$0.399780\pi$
$30$	−1693.35	−0.343514
$31$	10258.3	1.91722	0.958610	−	0.284724i	$-0.0919019\pi$
$31$	10258.3	1.91722	0.958610	+	0.284724i	$0.0919019\pi$
$32$	−7299.04	−1.26006
$33$	1089.00	0.174078
$34$	−4575.93	−0.678862
$35$	5853.16	0.807644
$36$	1995.90	0.256675
$37$	−7629.84	−0.916244	−0.458122	−	0.888889i	$-0.651478\pi$
$37$	−7629.84	−0.916244	−0.458122	+	0.888889i	$0.651478\pi$
$38$	−13545.4	−1.52171
$39$	2125.66	0.223785
$40$	1384.64	0.136832
$41$	8355.48	0.776268	0.388134	−	0.921603i	$-0.373120\pi$
$41$	8355.48	0.776268	0.388134	+	0.921603i	$0.373120\pi$
$42$	−15858.3	−1.38718
$43$	−11967.9	−0.987065	−0.493533	−	0.869727i	$-0.664295\pi$
$43$	−11967.9	−0.987065	−0.493533	+	0.869727i	$0.664295\pi$
$44$	2981.53	0.232171
$45$	−2025.00	−0.149071
$46$	−35924.7	−2.50321
$47$	8385.48	0.553711	0.276856	−	0.960912i	$-0.410708\pi$
$47$	8385.48	0.553711	0.276856	+	0.960912i	$0.410708\pi$
$48$	−10848.0	−0.679591
$49$	38008.1	2.26144
$50$	4703.75	0.266085
$51$	−5472.14	−0.294599
$52$	5819.76	0.298467
$53$	3453.00	0.168852	0.0844261	−	0.996430i	$-0.473094\pi$
$53$	3453.00	0.168852	0.0844261	+	0.996430i	$0.473094\pi$
$54$	5486.46	0.256040
$55$	−3025.00	−0.134840
$56$	12967.2	0.552556
$57$	−16198.3	−0.660361
$58$	21110.4	0.823999
$59$	−51032.4	−1.90860	−0.954302	−	0.298842i	$-0.903400\pi$
$59$	−51032.4	−1.90860	−0.954302	+	0.298842i	$0.903400\pi$
$60$	−5544.17	−0.198819
$61$	9988.24	0.343688	0.171844	−	0.985124i	$-0.445028\pi$
$61$	9988.24	0.343688	0.171844	+	0.985124i	$0.445028\pi$
$62$	77204.1	2.55071
$63$	−18964.2	−0.601982
$64$	−16361.8	−0.499323
$65$	−5904.60	−0.173343
$66$	8195.82	0.231597
$67$	−36567.6	−0.995198	−0.497599	−	0.867407i	$-0.665785\pi$
$67$	−36567.6	−0.995198	−0.497599	+	0.867407i	$0.665785\pi$
$68$	−14982.0	−0.392913
$69$	−42960.6	−1.08630
$70$	44050.9	1.07451
$71$	−30522.3	−0.718573	−0.359286	−	0.933227i	$-0.616980\pi$
$71$	−30522.3	−0.718573	−0.359286	+	0.933227i	$0.616980\pi$
$72$	−4486.23	−0.101988
$73$	83879.5	1.84225	0.921125	−	0.389267i	$-0.127272\pi$
$73$	83879.5	1.84225	0.921125	+	0.389267i	$0.127272\pi$
$74$	−57422.2	−1.21899
$75$	5625.00	0.115470
$76$	−44348.7	−0.880738
$77$	−28329.3	−0.544513
$78$	15997.7	0.297729
$79$	103505.	1.86592	0.932961	−	0.359978i	$-0.117216\pi$
$79$	103505.	1.86592	0.932961	+	0.359978i	$0.117216\pi$
$80$	30133.4	0.526409
$81$	6561.00	0.111111
$82$	62883.4	1.03276
$83$	−4341.54	−0.0691749	−0.0345875	−	0.999402i	$-0.511012\pi$
$83$	−4341.54	−0.0691749	−0.0345875	+	0.999402i	$0.511012\pi$
$84$	−51921.5	−0.802876
$85$	15200.4	0.228196
$86$	−90070.3	−1.31321
$87$	25244.9	0.357583
$88$	−6701.65	−0.0922519
$89$	−45464.1	−0.608406	−0.304203	−	0.952607i	$-0.598390\pi$
$89$	−45464.1	−0.608406	−0.304203	+	0.952607i	$0.598390\pi$
$90$	−15240.2	−0.198328
$91$	−55296.9	−0.699999
$92$	−117620.	−1.44881
$93$	92324.8	1.10691
$94$	63109.2	0.736670
$95$	44995.2	0.511514
$96$	−65691.3	−0.727495
$97$	−183170.	−1.97663	−0.988314	−	0.152432i	$-0.951289\pi$
$97$	−183170.	−1.97663	−0.988314	+	0.152432i	$0.951289\pi$
$98$	286049.	3.00868
$99$	9801.00	0.100504
$100$	15400.5	0.154005
$101$	−28833.3	−0.281249	−0.140625	−	0.990063i	$-0.544911\pi$
$101$	−28833.3	−0.281249	−0.140625	+	0.990063i	$0.544911\pi$
$102$	−41183.3	−0.391941
$103$	−59444.6	−0.552102	−0.276051	−	0.961143i	$-0.589026\pi$
$103$	−59444.6	−0.552102	−0.276051	+	0.961143i	$0.589026\pi$
$104$	−13081.2	−0.118594
$105$	52678.4	0.466293
$106$	25987.3	0.224645
$107$	13840.6	0.116868	0.0584342	−	0.998291i	$-0.481389\pi$
$107$	13840.6	0.116868	0.0584342	+	0.998291i	$0.481389\pi$
$108$	17963.1	0.148191
$109$	−13278.1	−0.107046	−0.0535231	−	0.998567i	$-0.517045\pi$
$109$	−13278.1	−0.107046	−0.0535231	+	0.998567i	$0.517045\pi$
$110$	−22766.2	−0.179394
$111$	−68668.5	−0.528993
$112$	282201.	2.12576
$113$	130086.	0.958370	0.479185	−	0.877714i	$-0.340932\pi$
$113$	130086.	0.958370	0.479185	+	0.877714i	$0.340932\pi$
$114$	−121908.	−0.878560
$115$	119335.	0.841441
$116$	69117.2	0.476915
$117$	19130.9	0.129203
$118$	−384070.	−2.53925
$119$	142352.	0.921504
$120$	12461.8	0.0789998
$121$	14641.0	0.0909091
$122$	75171.5	0.457250
$123$	75199.3	0.448178
$124$	252773.	1.47631
$125$	−15625.0	−0.0894427
$126$	−142725.	−0.800891
$127$	−274904.	−1.51242	−0.756209	−	0.654330i	$-0.772951\pi$
$127$	−274904.	−1.51242	−0.756209	+	0.654330i	$0.772951\pi$
$128$	110430.	0.595748
$129$	−107711.	−0.569882
$130$	−44438.1	−0.230620
$131$	−119374.	−0.607761	−0.303881	−	0.952710i	$-0.598282\pi$
$131$	−119374.	−0.607761	−0.303881	+	0.952710i	$0.598282\pi$
$132$	26833.8	0.134044
$133$	421382.	2.06560
$134$	−275208.	−1.32403
$135$	−18225.0	−0.0860663
$136$	33675.3	0.156122
$137$	−132278.	−0.602123	−0.301061	−	0.953605i	$-0.597341\pi$
$137$	−132278.	−0.602123	−0.301061	+	0.953605i	$0.597341\pi$
$138$	−323322.	−1.44523
$139$	−102326.	−0.449209	−0.224604	−	0.974450i	$-0.572109\pi$
$139$	−102326.	−0.449209	−0.224604	+	0.974450i	$0.572109\pi$
$140$	144226.	0.621905
$141$	75469.3	0.319685
$142$	−229711.	−0.956005
$143$	28578.3	0.116868
$144$	−97632.3	−0.392362
$145$	−70124.8	−0.276982
$146$	631278.	2.45097
$147$	342073.	1.30565
$148$	−188005.	−0.705530
$149$	371696.	1.37158	0.685791	−	0.727798i	$-0.259456\pi$
$149$	371696.	1.37158	0.685791	+	0.727798i	$0.259456\pi$
$150$	42333.8	0.153624
$151$	−111725.	−0.398757	−0.199379	−	0.979923i	$-0.563892\pi$
$151$	−111725.	−0.398757	−0.199379	+	0.979923i	$0.563892\pi$
$152$	99683.4	0.349956
$153$	−49249.2	−0.170087
$154$	−213206.	−0.724433
$155$	−256458.	−0.857406
$156$	52377.8	0.172320
$157$	−244726.	−0.792375	−0.396187	−	0.918170i	$-0.629667\pi$
$157$	−244726.	−0.792375	−0.396187	+	0.918170i	$0.629667\pi$
$158$	778979.	2.48246
$159$	31077.0	0.0974869
$160$	182476.	0.563515
$161$	1.11758e6	3.39792
$162$	49378.1	0.147825
$163$	435623.	1.28423	0.642114	−	0.766610i	$-0.278058\pi$
$163$	435623.	1.28423	0.642114	+	0.766610i	$0.278058\pi$
$164$	205885.	0.597745
$165$	−27225.0	−0.0778499
$166$	−32674.5	−0.0920319
$167$	288486.	0.800450	0.400225	−	0.916417i	$-0.368932\pi$
$167$	288486.	0.800450	0.400225	+	0.916417i	$0.368932\pi$
$168$	116705.	0.319019
$169$	−315510.	−0.849760
$170$	114398.	0.303597
$171$	−145784.	−0.381260
$172$	−294898.	−0.760064
$173$	539633.	1.37083	0.685414	−	0.728154i	$-0.259621\pi$
$173$	539633.	1.37083	0.685414	+	0.728154i	$0.259621\pi$
$174$	189994.	0.475736
$175$	−146329.	−0.361189
$176$	−145846.	−0.354905
$177$	−459292.	−1.10193
$178$	−342163.	−0.809438
$179$	−378874.	−0.883816	−0.441908	−	0.897060i	$-0.645698\pi$
$179$	−378874.	−0.883816	−0.441908	+	0.897060i	$0.645698\pi$
$180$	−49897.6	−0.114788
$181$	−621633.	−1.41038	−0.705192	−	0.709016i	$-0.749139\pi$
$181$	−621633.	−1.41038	−0.705192	+	0.709016i	$0.749139\pi$
$182$	−416165.	−0.931294
$183$	89894.1	0.198428
$184$	264378.	0.575679
$185$	190746.	0.409757
$186$	694837.	1.47265
$187$	−73569.8	−0.153849
$188$	206625.	0.426371
$189$	−170678.	−0.347555
$190$	338634.	0.680529
$191$	8509.61	0.0168782	0.00843911	−	0.999964i	$-0.497314\pi$
$191$	8509.61	0.0168782	0.00843911	+	0.999964i	$0.497314\pi$
$192$	−147256.	−0.288284
$193$	−564588.	−1.09103	−0.545517	−	0.838100i	$-0.683667\pi$
$193$	−564588.	−1.09103	−0.545517	+	0.838100i	$0.683667\pi$
$194$	−1.37854e6	−2.62975
$195$	−53141.4	−0.100080
$196$	936549.	1.74137
$197$	−432994.	−0.794908	−0.397454	−	0.917622i	$-0.630106\pi$
$197$	−432994.	−0.794908	−0.397454	+	0.917622i	$0.630106\pi$
$198$	73762.4	0.133712
$199$	−614871.	−1.10066	−0.550328	−	0.834949i	$-0.685497\pi$
$199$	−614871.	−1.10066	−0.550328	+	0.834949i	$0.685497\pi$
$200$	−34616.0	−0.0611930
$201$	−329108.	−0.574578
$202$	−217000.	−0.374180
$203$	−656723.	−1.11852
$204$	−134838.	−0.226849
$205$	−208887.	−0.347158
$206$	−447380.	−0.734528
$207$	−386646.	−0.627173
$208$	−284682.	−0.456248
$209$	−217777.	−0.344862
$210$	396458.	0.620367
$211$	72348.2	0.111872	0.0559360	−	0.998434i	$-0.482186\pi$
$211$	72348.2	0.111872	0.0559360	+	0.998434i	$0.482186\pi$
$212$	85084.6	0.130020
$213$	−274700.	−0.414868
$214$	104165.	0.155484
$215$	299197.	0.441429
$216$	−40376.1	−0.0588830
$217$	−2.40174e6	−3.46240
$218$	−99931.4	−0.142417
$219$	754915.	1.06362
$220$	−74538.3	−0.103830
$221$	−143604.	−0.197781
$222$	−516800.	−0.703785
$223$	370371.	0.498740	0.249370	−	0.968408i	$-0.419776\pi$
$223$	370371.	0.498740	0.249370	+	0.968408i	$0.419776\pi$
$224$	1.70890e6	2.27560
$225$	50625.0	0.0666667
$226$	979025.	1.27504
$227$	325481.	0.419239	0.209619	−	0.977783i	$-0.432778\pi$
$227$	325481.	0.419239	0.209619	+	0.977783i	$0.432778\pi$
$228$	−399138.	−0.508494
$229$	−57345.0	−0.0722614	−0.0361307	−	0.999347i	$-0.511503\pi$
$229$	−57345.0	−0.0722614	−0.0361307	+	0.999347i	$0.511503\pi$
$230$	898116.	1.11947
$231$	−254963.	−0.314375
$232$	−155356.	−0.189500
$233$	−833891.	−1.00628	−0.503141	−	0.864205i	$-0.667822\pi$
$233$	−833891.	−1.00628	−0.503141	+	0.864205i	$0.667822\pi$
$234$	143979.	0.171894
$235$	−209637.	−0.247627
$236$	−1.25748e6	−1.46967
$237$	931545.	1.07729
$238$	1.07134e6	1.22599
$239$	−813986.	−0.921769	−0.460885	−	0.887460i	$-0.652468\pi$
$239$	−813986.	−0.921769	−0.460885	+	0.887460i	$0.652468\pi$
$240$	271201.	0.303923
$241$	−1.18456e6	−1.31376	−0.656878	−	0.753997i	$-0.728123\pi$
$241$	−1.18456e6	−1.31376	−0.656878	+	0.753997i	$0.728123\pi$
$242$	110188.	0.120948
$243$	59049.0	0.0641500
$244$	246118.	0.264648
$245$	−950202.	−1.01135
$246$	565950.	0.596267
$247$	−425086.	−0.443338
$248$	−568163.	−0.586602
$249$	−39073.9	−0.0399382
$250$	−117594.	−0.118997
$251$	−601749.	−0.602880	−0.301440	−	0.953485i	$-0.597467\pi$
$251$	−601749.	−0.602880	−0.301440	+	0.953485i	$0.597467\pi$
$252$	−467293.	−0.463541
$253$	−577582.	−0.567299
$254$	−2.06893e6	−2.01216
$255$	136803.	0.131749
$256$	1.35468e6	1.29192
$257$	904570.	0.854298	0.427149	−	0.904181i	$-0.359518\pi$
$257$	904570.	0.854298	0.427149	+	0.904181i	$0.359518\pi$
$258$	−810633.	−0.758184
$259$	1.78634e6	1.65469
$260$	−145494.	−0.133479
$261$	227204.	0.206450
$262$	−898413.	−0.808580
$263$	1.47174e6	1.31202	0.656011	−	0.754751i	$-0.272242\pi$
$263$	1.47174e6	1.31202	0.656011	+	0.754751i	$0.272242\pi$
$264$	−60314.9	−0.0532617
$265$	−86325.0	−0.0755130
$266$	3.17133e6	2.74813
$267$	−409177.	−0.351264
$268$	−901054.	−0.766327
$269$	897427.	0.756168	0.378084	−	0.925771i	$-0.376583\pi$
$269$	897427.	0.756168	0.378084	+	0.925771i	$0.376583\pi$
$270$	−137161.	−0.114505
$271$	134225.	0.111022	0.0555111	−	0.998458i	$-0.482321\pi$
$271$	134225.	0.111022	0.0555111	+	0.998458i	$0.482321\pi$
$272$	732863.	0.600621
$273$	−497672.	−0.404145
$274$	−995523.	−0.801078
$275$	75625.0	0.0603023
$276$	−1.05858e6	−0.836474
$277$	−2.01306e6	−1.57637	−0.788184	−	0.615439i	$-0.788979\pi$
$277$	−2.01306e6	−1.57637	−0.788184	+	0.615439i	$0.788979\pi$
$278$	−770105.	−0.597637
$279$	830923.	0.639073
$280$	−324180.	−0.247111
$281$	1.45204e6	1.09702	0.548509	−	0.836145i	$-0.315196\pi$
$281$	1.45204e6	1.09702	0.548509	+	0.836145i	$0.315196\pi$
$282$	567983.	0.425316
$283$	−2.24416e6	−1.66566	−0.832832	−	0.553525i	$-0.813282\pi$
$283$	−2.24416e6	−1.66566	−0.832832	+	0.553525i	$0.813282\pi$
$284$	−752092.	−0.553318
$285$	404957.	0.295323
$286$	215080.	0.155484
$287$	−1.95624e6	−1.40190
$288$	−591222.	−0.420019
$289$	−1.05017e6	−0.739634
$290$	−527760.	−0.368503
$291$	−1.64853e6	−1.14121
$292$	2.06686e6	1.41858
$293$	148693.	0.101187	0.0505933	−	0.998719i	$-0.483889\pi$
$293$	148693.	0.101187	0.0505933	+	0.998719i	$0.483889\pi$
$294$	2.57444e6	1.73706
$295$	1.27581e6	0.853554
$296$	422583.	0.280338
$297$	88209.0	0.0580259
$298$	2.79739e6	1.82478
$299$	−1.12740e6	−0.729291
$300$	138604.	0.0889147
$301$	2.80199e6	1.78259
$302$	−840845.	−0.530516
$303$	−259500.	−0.162379
$304$	2.16938e6	1.34633
$305$	−249706.	−0.153702
$306$	−370650.	−0.226287
$307$	2.02304e6	1.22507	0.612533	−	0.790445i	$-0.290151\pi$
$307$	2.02304e6	1.22507	0.612533	+	0.790445i	$0.290151\pi$
$308$	−698055.	−0.419289
$309$	−535001.	−0.318756
$310$	−1.93010e6	−1.14071
$311$	1.87652e6	1.10015	0.550074	−	0.835116i	$-0.314599\pi$
$311$	1.87652e6	1.10015	0.550074	+	0.835116i	$0.314599\pi$
$312$	−117731.	−0.0684705
$313$	−89494.6	−0.0516340	−0.0258170	−	0.999667i	$-0.508219\pi$
$313$	−89494.6	−0.0516340	−0.0258170	+	0.999667i	$0.508219\pi$
$314$	−1.84181e6	−1.05419
$315$	474106.	0.269215
$316$	2.55044e6	1.43680
$317$	260115.	0.145384	0.0726920	−	0.997354i	$-0.476841\pi$
$317$	260115.	0.145384	0.0726920	+	0.997354i	$0.476841\pi$
$318$	233886.	0.129699
$319$	339404.	0.186741
$320$	409045.	0.223304
$321$	124566.	0.0674740
$322$	8.41090e6	4.52067
$323$	1.09431e6	0.583626
$324$	161668.	0.0855582
$325$	147615.	0.0775215
$326$	3.27850e6	1.70856
$327$	−119503.	−0.0618031
$328$	−462773.	−0.237511
$329$	−1.96326e6	−0.999973
$330$	−204896.	−0.103573
$331$	2.19339e6	1.10039	0.550193	−	0.835037i	$-0.314554\pi$
$331$	2.19339e6	1.10039	0.550193	+	0.835037i	$0.314554\pi$
$332$	−106979.	−0.0532664
$333$	−618017.	−0.305415
$334$	2.17115e6	1.06494
$335$	914190.	0.445066
$336$	2.53981e6	1.22731
$337$	933037.	0.447532	0.223766	−	0.974643i	$-0.428165\pi$
$337$	933037.	0.447532	0.223766	+	0.974643i	$0.428165\pi$
$338$	−2.37453e6	−1.13054
$339$	1.17077e6	0.553315
$340$	374549.	0.175716
$341$	1.24126e6	0.578063
$342$	−1.09717e6	−0.507237
$343$	−4.96373e6	−2.27810
$344$	662848.	0.302007
$345$	1.07402e6	0.485806
$346$	4.06128e6	1.82378
$347$	−1.72984e6	−0.771229	−0.385615	−	0.922660i	$-0.626011\pi$
$347$	−1.72984e6	−0.771229	−0.385615	+	0.922660i	$0.626011\pi$
$348$	622055.	0.275347
$349$	1.01770e6	0.447258	0.223629	−	0.974674i	$-0.428210\pi$
$349$	1.01770e6	0.447258	0.223629	+	0.974674i	$0.428210\pi$
$350$	−1.10127e6	−0.480534
$351$	172178.	0.0745951
$352$	−883183.	−0.379922
$353$	−3.29128e6	−1.40581	−0.702907	−	0.711282i	$-0.748115\pi$
$353$	−3.29128e6	−1.40581	−0.702907	+	0.711282i	$0.748115\pi$
$354$	−3.45663e6	−1.46604
$355$	763056.	0.321355
$356$	−1.12027e6	−0.468488
$357$	1.28117e6	0.532030
$358$	−2.85140e6	−1.17585
$359$	2.32128e6	0.950584	0.475292	−	0.879828i	$-0.342342\pi$
$359$	2.32128e6	0.950584	0.475292	+	0.879828i	$0.342342\pi$
$360$	112156.	0.0456106
$361$	763211.	0.308231
$362$	−4.67841e6	−1.87641
$363$	131769.	0.0524864
$364$	−1.36256e6	−0.539016
$365$	−2.09699e6	−0.823879
$366$	676544.	0.263993
$367$	−1.81399e6	−0.703024	−0.351512	−	0.936183i	$-0.614332\pi$
$367$	−1.81399e6	−0.703024	−0.351512	+	0.936183i	$0.614332\pi$
$368$	5.75356e6	2.21471
$369$	676794.	0.258756
$370$	1.43556e6	0.545149
$371$	−808438.	−0.304938
$372$	2.27496e6	0.852345
$373$	−160496.	−0.0597298	−0.0298649	−	0.999554i	$-0.509508\pi$
$373$	−160496.	−0.0597298	−0.0298649	+	0.999554i	$0.509508\pi$
$374$	−553687.	−0.204685
$375$	−140625.	−0.0516398
$376$	−464435.	−0.169416
$377$	662495.	0.240065
$378$	−1.28452e6	−0.462395
$379$	−622442.	−0.222587	−0.111294	−	0.993788i	$-0.535499\pi$
$379$	−622442.	−0.222587	−0.111294	+	0.993788i	$0.535499\pi$
$380$	1.10872e6	0.393878
$381$	−2.47414e6	−0.873195
$382$	64043.4	0.0224552
$383$	1.49075e6	0.519289	0.259644	−	0.965704i	$-0.416395\pi$
$383$	1.49075e6	0.519289	0.259644	+	0.965704i	$0.416395\pi$
$384$	993871.	0.343955
$385$	708232.	0.243514
$386$	−4.24909e6	−1.45154
$387$	−969398.	−0.329022
$388$	−4.51345e6	−1.52205
$389$	−1.66085e6	−0.556490	−0.278245	−	0.960510i	$-0.589753\pi$
$389$	−1.66085e6	−0.556490	−0.278245	+	0.960510i	$0.589753\pi$
$390$	−399943.	−0.133149
$391$	2.90230e6	0.960065
$392$	−2.10510e6	−0.691923
$393$	−1.07437e6	−0.350891
$394$	−3.25872e6	−1.05756
$395$	−2.58762e6	−0.834465
$396$	241504.	0.0773903
$397$	2.46357e6	0.784493	0.392247	−	0.919860i	$-0.371698\pi$
$397$	2.46357e6	0.784493	0.392247	+	0.919860i	$0.371698\pi$
$398$	−4.62752e6	−1.46434
$399$	3.79244e6	1.19258
$400$	−753336.	−0.235417
$401$	−664739.	−0.206438	−0.103219	−	0.994659i	$-0.532914\pi$
$401$	−664739.	−0.206438	−0.103219	+	0.994659i	$0.532914\pi$
$402$	−2.47687e6	−0.764431
$403$	2.42285e6	0.743129
$404$	−710475.	−0.216569
$405$	−164025.	−0.0496904
$406$	−4.94250e6	−1.48810
$407$	−923210.	−0.276258
$408$	303077.	0.0901370
$409$	−111122.	−0.0328468	−0.0164234	−	0.999865i	$-0.505228\pi$
$409$	−111122.	−0.0328468	−0.0164234	+	0.999865i	$0.505228\pi$
$410$	−1.57208e6	−0.461866
$411$	−1.19050e6	−0.347636
$412$	−1.46476e6	−0.425132
$413$	1.19480e7	3.44684
$414$	−2.90990e6	−0.834405
$415$	108539.	0.0309360
$416$	−1.72392e6	−0.488408
$417$	−920932.	−0.259351
$418$	−1.63899e6	−0.458813
$419$	−5.34446e6	−1.48720	−0.743598	−	0.668627i	$-0.766882\pi$
$419$	−5.34446e6	−1.48720	−0.743598	+	0.668627i	$0.766882\pi$
$420$	1.29804e6	0.359057
$421$	−483590.	−0.132976	−0.0664878	−	0.997787i	$-0.521179\pi$
$421$	−483590.	−0.132976	−0.0664878	+	0.997787i	$0.521179\pi$
$422$	544493.	0.148837
$423$	679224.	0.184570
$424$	−191246.	−0.0516629
$425$	−380010.	−0.102052
$426$	−2.06740e6	−0.551950
$427$	−2.33851e6	−0.620682
$428$	341044.	0.0899915
$429$	257205.	0.0674738
$430$	2.25176e6	0.587287
$431$	−241542.	−0.0626325	−0.0313162	−	0.999510i	$-0.509970\pi$
$431$	−241542.	−0.0626325	−0.0313162	+	0.999510i	$0.509970\pi$
$432$	−878691.	−0.226530
$433$	−1.03998e6	−0.266567	−0.133284	−	0.991078i	$-0.542552\pi$
$433$	−1.03998e6	−0.266567	−0.133284	+	0.991078i	$0.542552\pi$
$434$	−1.80755e7	−4.60645
$435$	−631124.	−0.159916
$436$	−327184.	−0.0824281
$437$	8.59121e6	2.15204
$438$	5.68150e6	1.41507
$439$	−3.32986e6	−0.824642	−0.412321	−	0.911039i	$-0.635282\pi$
$439$	−3.32986e6	−0.824642	−0.412321	+	0.911039i	$0.635282\pi$
$440$	167541.	0.0412563
$441$	3.07866e6	0.753815
$442$	−1.08076e6	−0.263132
$443$	5.12280e6	1.24022	0.620109	−	0.784515i	$-0.287088\pi$
$443$	5.12280e6	1.24022	0.620109	+	0.784515i	$0.287088\pi$
$444$	−1.69205e6	−0.407338
$445$	1.13660e6	0.272088
$446$	2.78741e6	0.663535
$447$	3.34526e6	0.791884
$448$	3.83073e6	0.901750
$449$	5.82328e6	1.36318	0.681588	−	0.731736i	$-0.261290\pi$
$449$	5.82328e6	1.36318	0.681588	+	0.731736i	$0.261290\pi$
$450$	381004.	0.0886948
$451$	1.01101e6	0.234054
$452$	3.20541e6	0.737968
$453$	−1.00553e6	−0.230223
$454$	2.44957e6	0.557765
$455$	1.38242e6	0.313049
$456$	897151.	0.202047
$457$	−5.32427e6	−1.19253	−0.596266	−	0.802787i	$-0.703349\pi$
$457$	−5.32427e6	−1.19253	−0.596266	+	0.802787i	$0.703349\pi$
$458$	−431579.	−0.0961382
$459$	−443243.	−0.0981997
$460$	2.94051e6	0.647930
$461$	673694.	0.147642	0.0738211	−	0.997272i	$-0.476481\pi$
$461$	673694.	0.147642	0.0738211	+	0.997272i	$0.476481\pi$
$462$	−1.91886e6	−0.418252
$463$	−1.92230e6	−0.416742	−0.208371	−	0.978050i	$-0.566816\pi$
$463$	−1.92230e6	−0.416742	−0.208371	+	0.978050i	$0.566816\pi$
$464$	−3.38096e6	−0.729030
$465$	−2.30812e6	−0.495024
$466$	−6.27587e6	−1.33878
$467$	−7.94668e6	−1.68614	−0.843070	−	0.537804i	$-0.819254\pi$
$467$	−7.94668e6	−1.68614	−0.843070	+	0.537804i	$0.819254\pi$
$468$	471401.	0.0994891
$469$	8.56144e6	1.79727
$470$	−1.57773e6	−0.329449
$471$	−2.20253e6	−0.457478
$472$	2.82646e6	0.583966
$473$	−1.44811e6	−0.297611
$474$	7.01081e6	1.43325
$475$	−1.12488e6	−0.228756
$476$	3.50767e6	0.709580
$477$	279693.	0.0562841
$478$	−6.12606e6	−1.22634
$479$	−1.80345e6	−0.359141	−0.179570	−	0.983745i	$-0.557471\pi$
$479$	−1.80345e6	−0.359141	−0.179570	+	0.983745i	$0.557471\pi$
$480$	1.64228e6	0.325346
$481$	−1.80205e6	−0.355143
$482$	−8.91501e6	−1.74785
$483$	1.00582e7	1.96179
$484$	360766.	0.0700022
$485$	4.57925e6	0.883975
$486$	444403.	0.0853466
$487$	3.04965e6	0.582678	0.291339	−	0.956620i	$-0.405899\pi$
$487$	3.04965e6	0.582678	0.291339	+	0.956620i	$0.405899\pi$
$488$	−553204.	−0.105156
$489$	3.92061e6	0.741449
$490$	−7.15123e6	−1.34552
$491$	−7.53319e6	−1.41018	−0.705091	−	0.709117i	$-0.749094\pi$
$491$	−7.53319e6	−1.41018	−0.705091	+	0.709117i	$0.749094\pi$
$492$	1.85297e6	0.345108
$493$	−1.70548e6	−0.316031
$494$	−3.19920e6	−0.589826
$495$	−245025.	−0.0449467
$496$	−1.23647e7	−2.25673
$497$	7.14606e6	1.29770
$498$	−294070.	−0.0531346
$499$	6.01840e6	1.08201	0.541003	−	0.841021i	$-0.318045\pi$
$499$	6.01840e6	1.08201	0.541003	+	0.841021i	$0.318045\pi$
$500$	−385012.	−0.0688731
$501$	2.59638e6	0.462140
$502$	−4.52876e6	−0.802085
$503$	8.91752e6	1.57153	0.785767	−	0.618522i	$-0.212268\pi$
$503$	8.91752e6	1.57153	0.785767	+	0.618522i	$0.212268\pi$
$504$	1.05034e6	0.184185
$505$	720833.	0.125778
$506$	−4.34688e6	−0.754748
$507$	−2.83959e6	−0.490609
$508$	−6.77385e6	−1.16460
$509$	9.71294e6	1.66171	0.830857	−	0.556486i	$-0.187851\pi$
$509$	9.71294e6	1.66171	0.830857	+	0.556486i	$0.187851\pi$
$510$	1.02958e6	0.175282
$511$	−1.96384e7	−3.32701
$512$	6.66153e6	1.12305
$513$	−1.31206e6	−0.220120
$514$	6.80780e6	1.13658
$515$	1.48611e6	0.246907
$516$	−2.65408e6	−0.438823
$517$	1.01464e6	0.166950
$518$	1.34440e7	2.20143
$519$	4.85669e6	0.791448
$520$	327030.	0.0530370
$521$	−591081.	−0.0954009	−0.0477004	−	0.998862i	$-0.515189\pi$
$521$	−591081.	−0.0954009	−0.0477004	+	0.998862i	$0.515189\pi$
$522$	1.70994e6	0.274666
$523$	2.83152e6	0.452653	0.226327	−	0.974051i	$-0.427328\pi$
$523$	2.83152e6	0.452653	0.226327	+	0.974051i	$0.427328\pi$
$524$	−2.94148e6	−0.467991
$525$	−1.31696e6	−0.208533
$526$	1.10763e7	1.74554
$527$	−6.23721e6	−0.978282
$528$	−1.31261e6	−0.204905
$529$	1.63490e7	2.54011
$530$	−649682.	−0.100464
$531$	−4.13363e6	−0.636202
$532$	1.03832e7	1.59057
$533$	1.97343e6	0.300887
$534$	−3.07947e6	−0.467329
$535$	−346016.	−0.0522651
$536$	2.02532e6	0.304496
$537$	−3.40986e6	−0.510271
$538$	6.75404e6	1.00602
$539$	4.59898e6	0.681851
$540$	−449078.	−0.0662731
$541$	9.93914e6	1.46001	0.730004	−	0.683442i	$-0.239518\pi$
$541$	9.93914e6	1.46001	0.730004	+	0.683442i	$0.239518\pi$
$542$	1.01018e6	0.147706
$543$	−5.59469e6	−0.814286
$544$	4.43793e6	0.642958
$545$	331953.	0.0478725
$546$	−3.74548e6	−0.537683
$547$	−4.34846e6	−0.621394	−0.310697	−	0.950509i	$-0.600563\pi$
$547$	−4.34846e6	−0.621394	−0.310697	+	0.950509i	$0.600563\pi$
$548$	−3.25942e6	−0.463649
$549$	809047.	0.114563
$550$	569154.	0.0802275
$551$	−5.04845e6	−0.708401
$552$	2.37940e6	0.332368
$553$	−2.42332e7	−3.36976
$554$	−1.51503e7	−2.09724
$555$	1.71671e6	0.236573
$556$	−2.52139e6	−0.345902
$557$	1.07234e7	1.46452	0.732261	−	0.681024i	$-0.238465\pi$
$557$	1.07234e7	1.46452	0.732261	+	0.681024i	$0.238465\pi$
$558$	6.25354e6	0.850237
$559$	−2.82662e6	−0.382594
$560$	−7.05503e6	−0.950667
$561$	−662129.	−0.0888250
$562$	1.09281e7	1.45950
$563$	1.67966e6	0.223332	0.111666	−	0.993746i	$-0.464381\pi$
$563$	1.67966e6	0.223332	0.111666	+	0.993746i	$0.464381\pi$
$564$	1.85962e6	0.246165
$565$	−3.25214e6	−0.428596
$566$	−1.68896e7	−2.21604
$567$	−1.53610e6	−0.200661
$568$	1.69049e6	0.219858
$569$	1.04510e7	1.35325	0.676626	−	0.736327i	$-0.263441\pi$
$569$	1.04510e7	1.35325	0.676626	+	0.736327i	$0.263441\pi$
$570$	3.04771e6	0.392904
$571$	670155.	0.0860171	0.0430085	−	0.999075i	$-0.486306\pi$
$571$	670155.	0.0860171	0.0430085	+	0.999075i	$0.486306\pi$
$572$	704191.	0.0899913
$573$	76586.5	0.00974464
$574$	−1.47226e7	−1.86512
$575$	−2.98338e6	−0.376304
$576$	−1.32531e6	−0.166441
$577$	−7.87543e6	−0.984769	−0.492385	−	0.870378i	$-0.663875\pi$
$577$	−7.87543e6	−0.984769	−0.492385	+	0.870378i	$0.663875\pi$
$578$	−7.90362e6	−0.984026
$579$	−5.08129e6	−0.629909
$580$	−1.72793e6	−0.213283
$581$	1.01647e6	0.124926
$582$	−1.24068e7	−1.51829
$583$	417813.	0.0509109
$584$	−4.64571e6	−0.563664
$585$	−478273.	−0.0577811
$586$	1.11907e6	0.134621
$587$	−9.13414e6	−1.09414	−0.547069	−	0.837087i	$-0.684257\pi$
$587$	−9.13414e6	−1.09414	−0.547069	+	0.837087i	$0.684257\pi$
$588$	8.42894e6	1.00538
$589$	−1.84630e7	−2.19288
$590$	9.60176e6	1.13559
$591$	−3.89695e6	−0.458940
$592$	9.19652e6	1.07850
$593$	1.25096e7	1.46085	0.730425	−	0.682993i	$-0.239322\pi$
$593$	1.25096e7	1.46085	0.730425	+	0.682993i	$0.239322\pi$
$594$	663862.	0.0771989
$595$	−3.55881e6	−0.412109
$596$	9.15887e6	1.05615
$597$	−5.53384e6	−0.635464
$598$	−8.48484e6	−0.970265
$599$	1.59560e7	1.81700	0.908502	−	0.417881i	$-0.137227\pi$
$599$	1.59560e7	1.81700	0.908502	+	0.417881i	$0.137227\pi$
$600$	−311544.	−0.0353298
$601$	763693.	0.0862448	0.0431224	−	0.999070i	$-0.486269\pi$
$601$	763693.	0.0862448	0.0431224	+	0.999070i	$0.486269\pi$
$602$	2.10878e7	2.37159
$603$	−2.96198e6	−0.331733
$604$	−2.75300e6	−0.307053
$605$	−366025.	−0.0406558
$606$	−1.95300e6	−0.216033
$607$	−8.51753e6	−0.938301	−0.469150	−	0.883118i	$-0.655440\pi$
$607$	−8.51753e6	−0.938301	−0.469150	+	0.883118i	$0.655440\pi$
$608$	1.31369e7	1.44123
$609$	−5.91050e6	−0.645775
$610$	−1.87929e6	−0.204488
$611$	1.98052e6	0.214623
$612$	−1.21354e6	−0.130971
$613$	9.58182e6	1.02990	0.514952	−	0.857219i	$-0.327810\pi$
$613$	9.58182e6	1.02990	0.514952	+	0.857219i	$0.327810\pi$
$614$	1.52254e7	1.62985
$615$	−1.87998e6	−0.200431
$616$	1.56903e6	0.166602
$617$	−1.12974e7	−1.19472	−0.597362	−	0.801972i	$-0.703784\pi$
$617$	−1.12974e7	−1.19472	−0.597362	+	0.801972i	$0.703784\pi$
$618$	−4.02642e6	−0.424080
$619$	−4.12945e6	−0.433177	−0.216588	−	0.976263i	$-0.569493\pi$
$619$	−4.12945e6	−0.433177	−0.216588	+	0.976263i	$0.569493\pi$
$620$	−6.31932e6	−0.660224
$621$	−3.47981e6	−0.362098
$622$	1.41227e7	1.46366
$623$	1.06443e7	1.09875
$624$	−2.56213e6	−0.263415
$625$	390625.	0.0400000
$626$	−673537.	−0.0686951
$627$	−1.95999e6	−0.199106
$628$	−6.03023e6	−0.610148
$629$	4.63906e6	0.467523
$630$	3.56812e6	0.358169
$631$	1.29753e7	1.29731	0.648656	−	0.761082i	$-0.275332\pi$
$631$	1.29753e7	1.29731	0.648656	+	0.761082i	$0.275332\pi$
$632$	−5.73268e6	−0.570907
$633$	651133.	0.0645893
$634$	1.95762e6	0.193422
$635$	6.87260e6	0.676374
$636$	765761.	0.0750672
$637$	8.97691e6	0.876553
$638$	2.55436e6	0.248445
$639$	−2.47230e6	−0.239524
$640$	−2.76075e6	−0.266427
$641$	−130086.	−0.0125051	−0.00625255	−	0.999980i	$-0.501990\pi$
$641$	−130086.	−0.0125051	−0.00625255	+	0.999980i	$0.501990\pi$
$642$	937483.	0.0897689
$643$	−6.47507e6	−0.617614	−0.308807	−	0.951125i	$-0.599930\pi$
$643$	−6.47507e6	−0.617614	−0.308807	+	0.951125i	$0.599930\pi$
$644$	2.75380e7	2.61648
$645$	2.69277e6	0.254859
$646$	8.23579e6	0.776469
$647$	−5.42540e6	−0.509531	−0.254766	−	0.967003i	$-0.581998\pi$
$647$	−5.42540e6	−0.509531	−0.254766	+	0.967003i	$0.581998\pi$
$648$	−363385.	−0.0339961
$649$	−6.17492e6	−0.575466
$650$	1.11095e6	0.103136
$651$	−2.16157e7	−1.99902
$652$	1.07341e7	0.988886
$653$	9.15697e6	0.840367	0.420183	−	0.907439i	$-0.361966\pi$
$653$	9.15697e6	0.840367	0.420183	+	0.907439i	$0.361966\pi$
$654$	−899382.	−0.0822243
$655$	2.98436e6	0.271799
$656$	−1.00712e7	−0.913735
$657$	6.79424e6	0.614083
$658$	−1.47755e7	−1.33039
$659$	−4.88080e6	−0.437802	−0.218901	−	0.975747i	$-0.570247\pi$
$659$	−4.88080e6	−0.437802	−0.218901	+	0.975747i	$0.570247\pi$
$660$	−670845.	−0.0599463
$661$	1.75690e7	1.56402	0.782010	−	0.623266i	$-0.214194\pi$
$661$	1.75690e7	1.56402	0.782010	+	0.623266i	$0.214194\pi$
$662$	1.65074e7	1.46398
$663$	−1.29243e6	−0.114189
$664$	240459.	0.0211651
$665$	−1.05346e7	−0.923767
$666$	−4.65120e6	−0.406330
$667$	−1.33894e7	−1.16532
$668$	7.10853e6	0.616366
$669$	3.33333e6	0.287948
$670$	6.88020e6	0.592126
$671$	1.20858e6	0.103626
$672$	1.53801e7	1.31382
$673$	1.60675e7	1.36745	0.683725	−	0.729740i	$-0.260359\pi$
$673$	1.60675e7	1.36745	0.683725	+	0.729740i	$0.260359\pi$
$674$	7.02205e6	0.595407
$675$	455625.	0.0384900
$676$	−7.77441e6	−0.654336
$677$	−1.51931e7	−1.27401	−0.637007	−	0.770858i	$-0.719828\pi$
$677$	−1.51931e7	−1.27401	−0.637007	+	0.770858i	$0.719828\pi$
$678$	8.81123e6	0.736143
$679$	4.28849e7	3.56968
$680$	−841882.	−0.0698198
$681$	2.92933e6	0.242048
$682$	9.34170e6	0.769068
$683$	−9.75866e6	−0.800457	−0.400229	−	0.916415i	$-0.631069\pi$
$683$	−9.75866e6	−0.800457	−0.400229	+	0.916415i	$0.631069\pi$
$684$	−3.59224e6	−0.293579
$685$	3.30694e6	0.269278
$686$	−3.73571e7	−3.03084
$687$	−516105.	−0.0417202
$688$	1.44253e7	1.16186
$689$	815544.	0.0654484
$690$	8.08305e6	0.646327
$691$	−1.74840e7	−1.39298	−0.696490	−	0.717567i	$-0.745256\pi$
$691$	−1.74840e7	−1.39298	−0.696490	+	0.717567i	$0.745256\pi$
$692$	1.32970e7	1.05557
$693$	−2.29467e6	−0.181504
$694$	−1.30188e7	−1.02606
$695$	2.55815e6	0.200892
$696$	−1.39821e6	−0.109408
$697$	−5.08026e6	−0.396099
$698$	7.65925e6	0.595042
$699$	−7.50502e6	−0.580977
$700$	−3.60566e6	−0.278125
$701$	4.31053e6	0.331311	0.165656	−	0.986184i	$-0.447026\pi$
$701$	4.31053e6	0.331311	0.165656	+	0.986184i	$0.447026\pi$
$702$	1.29581e6	0.0992431
$703$	1.37322e7	1.04798
$704$	−1.97978e6	−0.150551
$705$	−1.88673e6	−0.142968
$706$	−2.47702e7	−1.87033
$707$	6.75064e6	0.507921
$708$	−1.13173e7	−0.848516
$709$	−1.44521e6	−0.107973	−0.0539866	−	0.998542i	$-0.517193\pi$
$709$	−1.44521e6	−0.107973	−0.0539866	+	0.998542i	$0.517193\pi$
$710$	5.74277e6	0.427539
$711$	8.38390e6	0.621974
$712$	2.51806e6	0.186151
$713$	−4.89671e7	−3.60728
$714$	9.64210e6	0.707825
$715$	−714457.	−0.0522650
$716$	−9.33574e6	−0.680559
$717$	−7.32587e6	−0.532184
$718$	1.74699e7	1.26468
$719$	−4.22567e6	−0.304841	−0.152420	−	0.988316i	$-0.548707\pi$
$719$	−4.22567e6	−0.304841	−0.152420	+	0.988316i	$0.548707\pi$
$720$	2.44081e6	0.175470
$721$	1.39175e7	0.997066
$722$	5.74393e6	0.410078
$723$	−1.06610e7	−0.758498
$724$	−1.53175e7	−1.08603
$725$	1.75312e6	0.123870
$726$	991694.	0.0698291
$727$	1.62930e7	1.14331	0.571657	−	0.820493i	$-0.306301\pi$
$727$	1.62930e7	1.14331	0.571657	+	0.820493i	$0.306301\pi$
$728$	3.06265e6	0.214175
$729$	531441.	0.0370370
$730$	−1.57819e7	−1.09611
$731$	7.27665e6	0.503661
$732$	2.21506e6	0.152795
$733$	−3.00376e6	−0.206493	−0.103247	−	0.994656i	$-0.532923\pi$
$733$	−3.00376e6	−0.206493	−0.103247	+	0.994656i	$0.532923\pi$
$734$	−1.36521e7	−0.935319
$735$	−8.55182e6	−0.583902
$736$	3.48412e7	2.37082
$737$	−4.42468e6	−0.300064
$738$	5.09355e6	0.344255
$739$	5.58694e6	0.376325	0.188163	−	0.982138i	$-0.439747\pi$
$739$	5.58694e6	0.376325	0.188163	+	0.982138i	$0.439747\pi$
$740$	4.70013e6	0.315522
$741$	−3.82578e6	−0.255961
$742$	−6.08431e6	−0.405697
$743$	−8.33428e6	−0.553855	−0.276927	−	0.960891i	$-0.589316\pi$
$743$	−8.33428e6	−0.553855	−0.276927	+	0.960891i	$0.589316\pi$
$744$	−5.11346e6	−0.338675
$745$	−9.29240e6	−0.613390
$746$	−1.20789e6	−0.0794659
$747$	−351665.	−0.0230583
$748$	−1.81282e6	−0.118468
$749$	−3.24046e6	−0.211058
$750$	−1.05834e6	−0.0687027
$751$	−1.55555e7	−1.00643	−0.503215	−	0.864162i	$-0.667849\pi$
$751$	−1.55555e7	−1.00643	−0.503215	+	0.864162i	$0.667849\pi$
$752$	−1.01073e7	−0.651766
$753$	−5.41574e6	−0.348073
$754$	4.98594e6	0.319388
$755$	2.79313e6	0.178330
$756$	−4.20564e6	−0.267625
$757$	2.42999e7	1.54122	0.770611	−	0.637306i	$-0.219951\pi$
$757$	2.42999e7	1.54122	0.770611	+	0.637306i	$0.219951\pi$
$758$	−4.68450e6	−0.296135
$759$	−5.19824e6	−0.327530
$760$	−2.49209e6	−0.156505
$761$	1.84687e7	1.15605	0.578023	−	0.816021i	$-0.303825\pi$
$761$	1.84687e7	1.15605	0.578023	+	0.816021i	$0.303825\pi$
$762$	−1.86204e7	−1.16172
$763$	3.10876e6	0.193320
$764$	209684.	0.0129966
$765$	1.23123e6	0.0760652
$766$	1.12194e7	0.690873
$767$	−1.20530e7	−0.739790
$768$	1.21921e7	0.745890
$769$	−1.51725e6	−0.0925210	−0.0462605	−	0.998929i	$-0.514730\pi$
$769$	−1.51725e6	−0.0925210	−0.0462605	+	0.998929i	$0.514730\pi$
$770$	5.33016e6	0.323976
$771$	8.14113e6	0.493229
$772$	−1.39119e7	−0.840122
$773$	3.28907e6	0.197981	0.0989907	−	0.995088i	$-0.468439\pi$
$773$	3.28907e6	0.197981	0.0989907	+	0.995088i	$0.468439\pi$
$774$	−7.29569e6	−0.437738
$775$	6.41145e6	0.383444
$776$	1.01450e7	0.604779
$777$	1.60771e7	0.955334
$778$	−1.24996e7	−0.740367
$779$	−1.50383e7	−0.887879
$780$	−1.30945e6	−0.0770639
$781$	−3.69319e6	−0.216658
$782$	2.18427e7	1.27729
$783$	2.04484e6	0.119194
$784$	−4.58126e7	−2.66192
$785$	6.11815e6	0.354361
$786$	−8.08572e6	−0.466834
$787$	−1.46769e7	−0.844692	−0.422346	−	0.906435i	$-0.638793\pi$
$787$	−1.46769e7	−0.844692	−0.422346	+	0.906435i	$0.638793\pi$
$788$	−1.06693e7	−0.612098
$789$	1.32457e7	0.757497
$790$	−1.94745e7	−1.11019
$791$	−3.04564e7	−1.73076
$792$	−542834.	−0.0307506
$793$	2.35906e6	0.133216
$794$	1.85409e7	1.04371
$795$	−776925.	−0.0435975
$796$	−1.51509e7	−0.847531
$797$	4.95422e6	0.276267	0.138134	−	0.990414i	$-0.455890\pi$
$797$	4.95422e6	0.276267	0.138134	+	0.990414i	$0.455890\pi$
$798$	2.85419e7	1.58663
$799$	−5.09850e6	−0.282537
$800$	−4.56190e6	−0.252012
$801$	−3.68259e6	−0.202802
$802$	−5.00283e6	−0.274650
$803$	1.01494e7	0.555459
$804$	−8.10949e6	−0.442439
$805$	−2.79395e7	−1.51960
$806$	1.82344e7	0.988675
$807$	8.07685e6	0.436574
$808$	1.59695e6	0.0860524
$809$	1.90776e7	1.02483	0.512414	−	0.858738i	$-0.328751\pi$
$809$	1.90776e7	1.02483	0.512414	+	0.858738i	$0.328751\pi$
$810$	−1.23445e6	−0.0661092
$811$	2.54611e7	1.35933	0.679665	−	0.733523i	$-0.262125\pi$
$811$	2.54611e7	1.35933	0.679665	+	0.733523i	$0.262125\pi$
$812$	−1.61822e7	−0.861284
$813$	1.20802e6	0.0640987
$814$	−6.94809e6	−0.367540
$815$	−1.08906e7	−0.574324
$816$	6.59577e6	0.346769
$817$	2.15399e7	1.12899
$818$	−836308.	−0.0437002
$819$	−4.47905e6	−0.233333
$820$	−5.14714e6	−0.267320
$821$	−3.75556e7	−1.94454	−0.972269	−	0.233867i	$-0.924862\pi$
$821$	−3.75556e7	−1.94454	−0.972269	+	0.233867i	$0.924862\pi$
$822$	−8.95970e6	−0.462502
$823$	−3.42815e7	−1.76425	−0.882126	−	0.471014i	$-0.843888\pi$
$823$	−3.42815e7	−1.76425	−0.882126	+	0.471014i	$0.843888\pi$
$824$	3.29237e6	0.168924
$825$	680625.	0.0348155
$826$	8.99209e7	4.58575
$827$	2.92800e7	1.48870	0.744351	−	0.667789i	$-0.232759\pi$
$827$	2.92800e7	1.48870	0.744351	+	0.667789i	$0.232759\pi$
$828$	−9.52725e6	−0.482938
$829$	−7.40301e6	−0.374130	−0.187065	−	0.982348i	$-0.559897\pi$
$829$	−7.40301e6	−0.374130	−0.187065	+	0.982348i	$0.559897\pi$
$830$	816862.	0.0411579
$831$	−1.81176e7	−0.910117
$832$	−3.86440e6	−0.193541
$833$	−2.31095e7	−1.15393
$834$	−6.93094e6	−0.345046
$835$	−7.21216e6	−0.357972
$836$	−5.36619e6	−0.265552
$837$	7.47831e6	0.368969
$838$	−4.02224e7	−1.97860
$839$	−3.44573e7	−1.68996	−0.844981	−	0.534797i	$-0.820388\pi$
$839$	−3.44573e7	−1.68996	−0.844981	+	0.534797i	$0.820388\pi$
$840$	−2.91762e6	−0.142669
$841$	−1.26432e7	−0.616404
$842$	−3.63950e6	−0.176914
$843$	1.30684e7	0.633364
$844$	1.78271e6	0.0861441
$845$	7.88775e6	0.380024
$846$	5.11184e6	0.245557
$847$	−3.42784e6	−0.164177
$848$	−4.16203e6	−0.198754
$849$	−2.01974e7	−0.961672
$850$	−2.85995e6	−0.135772
$851$	3.64203e7	1.72393
$852$	−6.76883e6	−0.319459
$853$	−1.70125e7	−0.800561	−0.400281	−	0.916393i	$-0.631087\pi$
$853$	−1.70125e7	−0.800561	−0.400281	+	0.916393i	$0.631087\pi$
$854$	−1.75996e7	−0.825769
$855$	3.64461e6	0.170505
$856$	−766572.	−0.0357576
$857$	2.11650e7	0.984387	0.492194	−	0.870486i	$-0.336195\pi$
$857$	2.11650e7	0.984387	0.492194	+	0.870486i	$0.336195\pi$
$858$	1.93572e6	0.0897687
$859$	−3.17802e7	−1.46952	−0.734758	−	0.678330i	$-0.762704\pi$
$859$	−3.17802e7	−1.46952	−0.734758	+	0.678330i	$0.762704\pi$
$860$	7.37244e6	0.339911
$861$	−1.76061e7	−0.809386
$862$	−1.81785e6	−0.0833277
$863$	−3.53199e7	−1.61433	−0.807166	−	0.590325i	$-0.799000\pi$
$863$	−3.53199e7	−1.61433	−0.807166	+	0.590325i	$0.799000\pi$
$864$	−5.32100e6	−0.242498
$865$	−1.34908e7	−0.613053
$866$	−7.82692e6	−0.354647
$867$	−9.45157e6	−0.427028
$868$	−5.91807e7	−2.66613
$869$	1.25241e7	0.562597
$870$	−4.74984e6	−0.212756
$871$	−8.63669e6	−0.385746
$872$	735417.	0.0327524
$873$	−1.48368e7	−0.658876
$874$	6.46575e7	2.86313
$875$	3.65822e6	0.161529
$876$	1.86017e7	0.819016
$877$	256700.	0.0112701	0.00563503	−	0.999984i	$-0.498206\pi$
$877$	256700.	0.0112701	0.00563503	+	0.999984i	$0.498206\pi$
$878$	−2.50606e7	−1.09712
$879$	1.33824e6	0.0584201
$880$	3.64614e6	0.158718
$881$	3.37169e7	1.46355	0.731776	−	0.681545i	$-0.238692\pi$
$881$	3.37169e7	1.46355	0.731776	+	0.681545i	$0.238692\pi$
$882$	2.31700e7	1.00289
$883$	−2.45722e7	−1.06058	−0.530289	−	0.847817i	$-0.677917\pi$
$883$	−2.45722e7	−1.06058	−0.530289	+	0.847817i	$0.677917\pi$
$884$	−3.53850e6	−0.152296
$885$	1.14823e7	0.492800
$886$	3.85542e7	1.65001
$887$	220190.	0.00939697	0.00469849	−	0.999989i	$-0.498504\pi$
$887$	220190.	0.00939697	0.00469849	+	0.999989i	$0.498504\pi$
$888$	3.80325e6	0.161853
$889$	6.43623e7	2.73135
$890$	8.55408e6	0.361991
$891$	793881.	0.0335013
$892$	9.12622e6	0.384042
$893$	−1.50923e7	−0.633323
$894$	2.51765e7	1.05354
$895$	9.47184e6	0.395254
$896$	−2.58546e7	−1.07589
$897$	−1.01466e7	−0.421056
$898$	4.38260e7	1.81360
$899$	2.87745e7	1.18743
$900$	1.24744e6	0.0513349
$901$	−2.09948e6	−0.0861587
$902$	7.60889e6	0.311390
$903$	2.52179e7	1.02918
$904$	−7.20487e6	−0.293228
$905$	1.55408e7	0.630743
$906$	−7.56760e6	−0.306293
$907$	−6.02862e6	−0.243332	−0.121666	−	0.992571i	$-0.538824\pi$
$907$	−6.02862e6	−0.243332	−0.121666	+	0.992571i	$0.538824\pi$
$908$	8.02011e6	0.322824
$909$	−2.33550e6	−0.0937497
$910$	1.04041e7	0.416487
$911$	1.68076e7	0.670979	0.335490	−	0.942044i	$-0.391098\pi$
$911$	1.68076e7	0.670979	0.335490	+	0.942044i	$0.391098\pi$
$912$	1.95244e7	0.777303
$913$	−525327.	−0.0208570
$914$	−4.00705e7	−1.58657
$915$	−2.24735e6	−0.0887398
$916$	−1.41302e6	−0.0556430
$917$	2.79487e7	1.09758
$918$	−3.33585e6	−0.130647
$919$	4.57189e7	1.78569	0.892846	−	0.450362i	$-0.148705\pi$
$919$	4.57189e7	1.78569	0.892846	+	0.450362i	$0.148705\pi$
$920$	−6.60944e6	−0.257451
$921$	1.82074e7	0.707292
$922$	5.07022e6	0.196426
$923$	−7.20887e6	−0.278524
$924$	−6.28250e6	−0.242076
$925$	−4.76865e6	−0.183249
$926$	−1.44672e7	−0.554443
$927$	−4.81501e6	−0.184034
$928$	−2.04737e7	−0.780418
$929$	−2.84053e7	−1.07984	−0.539921	−	0.841716i	$-0.681546\pi$
$929$	−2.84053e7	−1.07984	−0.539921	+	0.841716i	$0.681546\pi$
$930$	−1.73709e7	−0.658591
$931$	−6.84073e7	−2.58659
$932$	−2.05477e7	−0.774861
$933$	1.68886e7	0.635171
$934$	−5.98068e7	−2.24328
$935$	1.83925e6	0.0688035
$936$	−1.05958e6	−0.0395315
$937$	−8.99373e6	−0.334650	−0.167325	−	0.985902i	$-0.553513\pi$
$937$	−8.99373e6	−0.334650	−0.167325	+	0.985902i	$0.553513\pi$
$938$	6.44334e7	2.39113
$939$	−805452.	−0.0298109
$940$	−5.16562e6	−0.190679
$941$	−2.96562e7	−1.09180	−0.545898	−	0.837852i	$-0.683811\pi$
$941$	−2.96562e7	−1.09180	−0.545898	+	0.837852i	$0.683811\pi$
$942$	−1.65763e7	−0.608639
$943$	−3.98841e7	−1.46056
$944$	6.15113e7	2.24659
$945$	4.26695e6	0.155431
$946$	−1.08985e7	−0.395949
$947$	−1.62357e7	−0.588297	−0.294148	−	0.955760i	$-0.595036\pi$
$947$	−1.62357e7	−0.588297	−0.294148	+	0.955760i	$0.595036\pi$
$948$	2.29540e7	0.829540
$949$	1.98110e7	0.714070
$950$	−8.46586e6	−0.304342
$951$	2.34103e6	0.0839375
$952$	−7.88427e6	−0.281948
$953$	2.13990e7	0.763241	0.381621	−	0.924319i	$-0.375366\pi$
$953$	2.13990e7	0.763241	0.381621	+	0.924319i	$0.375366\pi$
$954$	2.10497e6	0.0748816
$955$	−212740.	−0.00754817
$956$	−2.00572e7	−0.709785
$957$	3.05464e6	0.107815
$958$	−1.35728e7	−0.477809
$959$	3.09697e7	1.08740
$960$	3.68141e6	0.128925
$961$	7.66039e7	2.67573
$962$	−1.35622e7	−0.472490
$963$	1.12109e6	0.0389561
$964$	−2.91885e7	−1.01162
$965$	1.41147e7	0.487925
$966$	7.56981e7	2.61001
$967$	−6.31736e6	−0.217255	−0.108627	−	0.994083i	$-0.534646\pi$
$967$	−6.31736e6	−0.217255	−0.108627	+	0.994083i	$0.534646\pi$
$968$	−810900.	−0.0278150
$969$	9.84880e6	0.336956
$970$	3.44635e7	1.17606
$971$	4.14293e7	1.41013	0.705065	−	0.709142i	$-0.250918\pi$
$971$	4.14293e7	1.41013	0.705065	+	0.709142i	$0.250918\pi$
$972$	1.45501e6	0.0493971
$973$	2.39572e7	0.811247
$974$	2.29517e7	0.775207
$975$	1.32854e6	0.0447571
$976$	−1.20392e7	−0.404550
$977$	−333761.	−0.0111866	−0.00559331	−	0.999984i	$-0.501780\pi$
$977$	−333761.	−0.0111866	−0.00559331	+	0.999984i	$0.501780\pi$
$978$	2.95065e7	0.986440
$979$	−5.50116e6	−0.183441
$980$	−2.34137e7	−0.778763
$981$	−1.07553e6	−0.0356820
$982$	−5.66948e7	−1.87614
$983$	−3.43832e7	−1.13491	−0.567457	−	0.823403i	$-0.692073\pi$
$983$	−3.43832e7	−1.13491	−0.567457	+	0.823403i	$0.692073\pi$
$984$	−4.16496e6	−0.137127
$985$	1.08249e7	0.355493
$986$	−1.28354e7	−0.420454
$987$	−1.76693e7	−0.577335
$988$	−1.04745e7	−0.341381
$989$	5.71275e7	1.85718
$990$	−1.84406e6	−0.0597980
$991$	4.26710e6	0.138022	0.0690111	−	0.997616i	$-0.478016\pi$
$991$	4.26710e6	0.138022	0.0690111	+	0.997616i	$0.478016\pi$
$992$	−7.48758e7	−2.41581
$993$	1.97405e7	0.635308
$994$	5.37813e7	1.72649
$995$	1.53718e7	0.492228
$996$	−962811.	−0.0307534
$997$	2.61381e7	0.832790	0.416395	−	0.909184i	$-0.363293\pi$
$997$	2.61381e7	0.832790	0.416395	+	0.909184i	$0.363293\pi$
$998$	4.52945e7	1.43953
$999$	−5.56215e6	−0.176331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.b.1.3	✓	3
3.2	odd	2		495.6.a.d.1.1		3
5.4	even	2		825.6.a.i.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.b.1.3	✓	3	1.1	even	1	trivial
495.6.a.d.1.1		3	3.2	odd	2
825.6.a.i.1.1		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)

\(f(q)\)	\(=\)	\(q+7.52601 q^{2} +9.00000 q^{3} +24.6408 q^{4} -25.0000 q^{5} +67.7341 q^{6} -234.126 q^{7} -55.3856 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+7.52601 q^{2} +9.00000 q^{3} +24.6408 q^{4} -25.0000 q^{5} +67.7341 q^{6} -234.126 q^{7} -55.3856 q^{8} +81.0000 q^{9} -188.150 q^{10} +121.000 q^{11} +221.767 q^{12} +236.184 q^{13} -1762.04 q^{14} -225.000 q^{15} -1205.34 q^{16} -608.015 q^{17} +609.607 q^{18} -1799.81 q^{19} -616.019 q^{20} -2107.14 q^{21} +910.647 q^{22} -4773.40 q^{23} -498.470 q^{24} +625.000 q^{25} +1777.52 q^{26} +729.000 q^{27} -5769.05 q^{28} +2804.99 q^{29} -1693.35 q^{30} +10258.3 q^{31} -7299.04 q^{32} +1089.00 q^{33} -4575.93 q^{34} +5853.16 q^{35} +1995.90 q^{36} -7629.84 q^{37} -13545.4 q^{38} +2125.66 q^{39} +1384.64 q^{40} +8355.48 q^{41} -15858.3 q^{42} -11967.9 q^{43} +2981.53 q^{44} -2025.00 q^{45} -35924.7 q^{46} +8385.48 q^{47} -10848.0 q^{48} +38008.1 q^{49} +4703.75 q^{50} -5472.14 q^{51} +5819.76 q^{52} +3453.00 q^{53} +5486.46 q^{54} -3025.00 q^{55} +12967.2 q^{56} -16198.3 q^{57} +21110.4 q^{58} -51032.4 q^{59} -5544.17 q^{60} +9988.24 q^{61} +77204.1 q^{62} -18964.2 q^{63} -16361.8 q^{64} -5904.60 q^{65} +8195.82 q^{66} -36567.6 q^{67} -14982.0 q^{68} -42960.6 q^{69} +44050.9 q^{70} -30522.3 q^{71} -4486.23 q^{72} +83879.5 q^{73} -57422.2 q^{74} +5625.00 q^{75} -44348.7 q^{76} -28329.3 q^{77} +15997.7 q^{78} +103505. q^{79} +30133.4 q^{80} +6561.00 q^{81} +62883.4 q^{82} -4341.54 q^{83} -51921.5 q^{84} +15200.4 q^{85} -90070.3 q^{86} +25244.9 q^{87} -6701.65 q^{88} -45464.1 q^{89} -15240.2 q^{90} -55296.9 q^{91} -117620. q^{92} +92324.8 q^{93} +63109.2 q^{94} +44995.2 q^{95} -65691.3 q^{96} -183170. q^{97} +286049. q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9	\( 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 252 q^{12} + 450 q^{13} - 1504 q^{14} - 675 q^{15} - 1360 q^{16} - 334 q^{17} - 162 q^{18} - 4036 q^{19} - 700 q^{20} - 2088 q^{21} - 242 q^{22} - 7060 q^{23} + 216 q^{24} + 1875 q^{25} + 2932 q^{26} + 2187 q^{27} - 8320 q^{28} + 4042 q^{29} + 450 q^{30} - 608 q^{31} - 3104 q^{32} + 3267 q^{33} - 3644 q^{34} + 5800 q^{35} + 2268 q^{36} + 2250 q^{37} - 12632 q^{38} + 4050 q^{39} - 600 q^{40} + 10654 q^{41} - 13536 q^{42} - 35528 q^{43} + 3388 q^{44} - 6075 q^{45} - 41800 q^{46} - 2100 q^{47} - 12240 q^{48} + 7667 q^{49} - 1250 q^{50} - 3006 q^{51} - 14520 q^{52} - 12826 q^{53} - 1458 q^{54} - 9075 q^{55} + 17088 q^{56} - 36324 q^{57} - 17196 q^{58} - 81876 q^{59} - 6300 q^{60} - 62298 q^{61} + 109184 q^{62} - 18792 q^{63} - 72256 q^{64} - 11250 q^{65} - 2178 q^{66} - 46148 q^{67} - 35832 q^{68} - 63540 q^{69} + 37600 q^{70} - 64724 q^{71} + 1944 q^{72} + 810 q^{73} - 44796 q^{74} + 16875 q^{75} + 44656 q^{76} - 28072 q^{77} + 26388 q^{78} + 43876 q^{79} + 34000 q^{80} + 19683 q^{81} + 56060 q^{82} - 101024 q^{83} - 74880 q^{84} + 8350 q^{85} + 24128 q^{86} + 36378 q^{87} + 2904 q^{88} + 60022 q^{89} + 4050 q^{90} - 28568 q^{91} + 38256 q^{92} - 5472 q^{93} + 74552 q^{94} + 100900 q^{95} - 27936 q^{96} - 319746 q^{97} + 431134 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 252 * q^12 + 450 * q^13 - 1504 * q^14 - 675 * q^15 - 1360 * q^16 - 334 * q^17 - 162 * q^18 - 4036 * q^19 - 700 * q^20 - 2088 * q^21 - 242 * q^22 - 7060 * q^23 + 216 * q^24 + 1875 * q^25 + 2932 * q^26 + 2187 * q^27 - 8320 * q^28 + 4042 * q^29 + 450 * q^30 - 608 * q^31 - 3104 * q^32 + 3267 * q^33 - 3644 * q^34 + 5800 * q^35 + 2268 * q^36 + 2250 * q^37 - 12632 * q^38 + 4050 * q^39 - 600 * q^40 + 10654 * q^41 - 13536 * q^42 - 35528 * q^43 + 3388 * q^44 - 6075 * q^45 - 41800 * q^46 - 2100 * q^47 - 12240 * q^48 + 7667 * q^49 - 1250 * q^50 - 3006 * q^51 - 14520 * q^52 - 12826 * q^53 - 1458 * q^54 - 9075 * q^55 + 17088 * q^56 - 36324 * q^57 - 17196 * q^58 - 81876 * q^59 - 6300 * q^60 - 62298 * q^61 + 109184 * q^62 - 18792 * q^63 - 72256 * q^64 - 11250 * q^65 - 2178 * q^66 - 46148 * q^67 - 35832 * q^68 - 63540 * q^69 + 37600 * q^70 - 64724 * q^71 + 1944 * q^72 + 810 * q^73 - 44796 * q^74 + 16875 * q^75 + 44656 * q^76 - 28072 * q^77 + 26388 * q^78 + 43876 * q^79 + 34000 * q^80 + 19683 * q^81 + 56060 * q^82 - 101024 * q^83 - 74880 * q^84 + 8350 * q^85 + 24128 * q^86 + 36378 * q^87 + 2904 * q^88 + 60022 * q^89 + 4050 * q^90 - 28568 * q^91 + 38256 * q^92 - 5472 * q^93 + 74552 * q^94 + 100900 * q^95 - 27936 * q^96 - 319746 * q^97 + 431134 * q^98 + 29403 * q^99

Introduction

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