LMFDB - Embedded newform 165.6.a.g.1.1

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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 143x^{3} + 71x^{2} + 4216x - 3740 $ x^5 - x^4 - 143x^3 + 71x^2 + 4216*x - 3740
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			1.1
Root			$10.6119$ 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)

$f(q)$	$=$	$q-10.6119 q^{2} -9.00000 q^{3} +80.6130 q^{4} -25.0000 q^{5} +95.5073 q^{6} +32.7446 q^{7} -515.877 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-10.6119 q^{2} -9.00000 q^{3} +80.6130 q^{4} -25.0000 q^{5} +95.5073 q^{6} +32.7446 q^{7} -515.877 q^{8} +81.0000 q^{9} +265.298 q^{10} -121.000 q^{11} -725.517 q^{12} -345.517 q^{13} -347.483 q^{14} +225.000 q^{15} +2894.84 q^{16} -1789.04 q^{17} -859.566 q^{18} +2400.01 q^{19} -2015.32 q^{20} -294.701 q^{21} +1284.04 q^{22} +4871.60 q^{23} +4642.90 q^{24} +625.000 q^{25} +3666.60 q^{26} -729.000 q^{27} +2639.64 q^{28} +3208.59 q^{29} -2387.68 q^{30} +1918.50 q^{31} -14211.7 q^{32} +1089.00 q^{33} +18985.1 q^{34} -818.615 q^{35} +6529.65 q^{36} +458.331 q^{37} -25468.7 q^{38} +3109.65 q^{39} +12896.9 q^{40} -10891.9 q^{41} +3127.35 q^{42} +9663.83 q^{43} -9754.17 q^{44} -2025.00 q^{45} -51697.0 q^{46} -16525.0 q^{47} -26053.5 q^{48} -15734.8 q^{49} -6632.45 q^{50} +16101.3 q^{51} -27853.1 q^{52} -11612.1 q^{53} +7736.09 q^{54} +3025.00 q^{55} -16892.2 q^{56} -21600.1 q^{57} -34049.3 q^{58} +28860.7 q^{59} +18137.9 q^{60} +33305.0 q^{61} -20359.0 q^{62} +2652.31 q^{63} +58179.0 q^{64} +8637.92 q^{65} -11556.4 q^{66} +3516.32 q^{67} -144220. q^{68} -43844.4 q^{69} +8687.08 q^{70} -9172.96 q^{71} -41786.1 q^{72} -83544.1 q^{73} -4863.78 q^{74} -5625.00 q^{75} +193472. q^{76} -3962.10 q^{77} -32999.4 q^{78} -71559.4 q^{79} -72370.9 q^{80} +6561.00 q^{81} +115584. q^{82} -33724.0 q^{83} -23756.8 q^{84} +44725.9 q^{85} -102552. q^{86} -28877.3 q^{87} +62421.2 q^{88} +107930. q^{89} +21489.2 q^{90} -11313.8 q^{91} +392714. q^{92} -17266.5 q^{93} +175362. q^{94} -60000.2 q^{95} +127906. q^{96} +103309. q^{97} +166976. q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9} + 25 q^{10} - 605 q^{11} - 1143 q^{12} - 926 q^{13} + 368 q^{14} + 1125 q^{15} + 1891 q^{16} - 246 q^{17} - 81 q^{18} + 3420 q^{19} - 3175 q^{20} - 1044 q^{21} + 121 q^{22} - 4244 q^{23} + 1377 q^{24} + 3125 q^{25} - 8862 q^{26} - 3645 q^{27} - 4904 q^{28} - 2922 q^{29} - 225 q^{30} - 6112 q^{31} - 24757 q^{32} + 5445 q^{33} + 10866 q^{34} - 2900 q^{35} + 10287 q^{36} + 6654 q^{37} - 45692 q^{38} + 8334 q^{39} + 3825 q^{40} - 14934 q^{41} - 3312 q^{42} + 10804 q^{43} - 15367 q^{44} - 10125 q^{45} - 101500 q^{46} - 41460 q^{47} - 17019 q^{48} - 12099 q^{49} - 625 q^{50} + 2214 q^{51} - 97742 q^{52} - 62398 q^{53} + 729 q^{54} + 15125 q^{55} - 74368 q^{56} - 30780 q^{57} - 27822 q^{58} + 8524 q^{59} + 28575 q^{60} + 59010 q^{61} - 142624 q^{62} + 9396 q^{63} + 13799 q^{64} + 23150 q^{65} - 1089 q^{66} - 15772 q^{67} - 83686 q^{68} + 38196 q^{69} - 9200 q^{70} + 88124 q^{71} - 12393 q^{72} - 118358 q^{73} + 67194 q^{74} - 28125 q^{75} + 100668 q^{76} - 14036 q^{77} + 79758 q^{78} + 57324 q^{79} - 47275 q^{80} + 32805 q^{81} + 29102 q^{82} - 7268 q^{83} + 44136 q^{84} + 6150 q^{85} - 35288 q^{86} + 26298 q^{87} + 18513 q^{88} + 72978 q^{89} + 2025 q^{90} - 1464 q^{91} + 62148 q^{92} + 55008 q^{93} + 344836 q^{94} - 85500 q^{95} + 222813 q^{96} - 59174 q^{97} + 272767 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9 + 25 * q^10 - 605 * q^11 - 1143 * q^12 - 926 * q^13 + 368 * q^14 + 1125 * q^15 + 1891 * q^16 - 246 * q^17 - 81 * q^18 + 3420 * q^19 - 3175 * q^20 - 1044 * q^21 + 121 * q^22 - 4244 * q^23 + 1377 * q^24 + 3125 * q^25 - 8862 * q^26 - 3645 * q^27 - 4904 * q^28 - 2922 * q^29 - 225 * q^30 - 6112 * q^31 - 24757 * q^32 + 5445 * q^33 + 10866 * q^34 - 2900 * q^35 + 10287 * q^36 + 6654 * q^37 - 45692 * q^38 + 8334 * q^39 + 3825 * q^40 - 14934 * q^41 - 3312 * q^42 + 10804 * q^43 - 15367 * q^44 - 10125 * q^45 - 101500 * q^46 - 41460 * q^47 - 17019 * q^48 - 12099 * q^49 - 625 * q^50 + 2214 * q^51 - 97742 * q^52 - 62398 * q^53 + 729 * q^54 + 15125 * q^55 - 74368 * q^56 - 30780 * q^57 - 27822 * q^58 + 8524 * q^59 + 28575 * q^60 + 59010 * q^61 - 142624 * q^62 + 9396 * q^63 + 13799 * q^64 + 23150 * q^65 - 1089 * q^66 - 15772 * q^67 - 83686 * q^68 + 38196 * q^69 - 9200 * q^70 + 88124 * q^71 - 12393 * q^72 - 118358 * q^73 + 67194 * q^74 - 28125 * q^75 + 100668 * q^76 - 14036 * q^77 + 79758 * q^78 + 57324 * q^79 - 47275 * q^80 + 32805 * q^81 + 29102 * q^82 - 7268 * q^83 + 44136 * q^84 + 6150 * q^85 - 35288 * q^86 + 26298 * q^87 + 18513 * q^88 + 72978 * q^89 + 2025 * q^90 - 1464 * q^91 + 62148 * q^92 + 55008 * q^93 + 344836 * q^94 - 85500 * q^95 + 222813 * q^96 - 59174 * q^97 + 272767 * q^98 - 49005 * 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 $

$2$	−10.6119	−1.87594	−0.937971	−	0.346715i	$-0.887297\pi$
$2$	−10.6119	−1.87594	−0.937971	+	0.346715i	$0.887297\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	80.6130	2.51916
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	95.5073	1.08308
$7$	32.7446	0.252577	0.126289	−	0.991994i	$-0.459693\pi$
$7$	32.7446	0.252577	0.126289	+	0.991994i	$0.459693\pi$
$8$	−515.877	−2.84985
$9$	81.0000	0.333333
$10$	265.298	0.838946
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−725.517	−1.45444
$13$	−345.517	−0.567036	−0.283518	−	0.958967i	$-0.591502\pi$
$13$	−345.517	−0.567036	−0.283518	+	0.958967i	$0.591502\pi$
$14$	−347.483	−0.473820
$15$	225.000	0.258199
$16$	2894.84	2.82699
$17$	−1789.04	−1.50140	−0.750701	−	0.660643i	$-0.770284\pi$
$17$	−1789.04	−1.50140	−0.750701	+	0.660643i	$0.770284\pi$
$18$	−859.566	−0.625314
$19$	2400.01	1.52521	0.762603	−	0.646867i	$-0.223921\pi$
$19$	2400.01	1.52521	0.762603	+	0.646867i	$0.223921\pi$
$20$	−2015.32	−1.12660
$21$	−294.701	−0.145826
$22$	1284.04	0.565618
$23$	4871.60	1.92022	0.960112	−	0.279617i	$-0.0902076\pi$
$23$	4871.60	1.92022	0.960112	+	0.279617i	$0.0902076\pi$
$24$	4642.90	1.64536
$25$	625.000	0.200000
$26$	3666.60	1.06373
$27$	−729.000	−0.192450
$28$	2639.64	0.636282
$29$	3208.59	0.708466	0.354233	−	0.935157i	$-0.384742\pi$
$29$	3208.59	0.708466	0.354233	+	0.935157i	$0.384742\pi$
$30$	−2387.68	−0.484366
$31$	1918.50	0.358557	0.179278	−	0.983798i	$-0.442624\pi$
$31$	1918.50	0.358557	0.179278	+	0.983798i	$0.442624\pi$
$32$	−14211.7	−2.45342
$33$	1089.00	0.174078
$34$	18985.1	2.81654
$35$	−818.615	−0.112956
$36$	6529.65	0.839719
$37$	458.331	0.0550396	0.0275198	−	0.999621i	$-0.491239\pi$
$37$	458.331	0.0550396	0.0275198	+	0.999621i	$0.491239\pi$
$38$	−25468.7	−2.86120
$39$	3109.65	0.327379
$40$	12896.9	1.27449
$41$	−10891.9	−1.01192	−0.505959	−	0.862558i	$-0.668861\pi$
$41$	−10891.9	−1.01192	−0.505959	+	0.862558i	$0.668861\pi$
$42$	3127.35	0.273560
$43$	9663.83	0.797036	0.398518	−	0.917160i	$-0.369525\pi$
$43$	9663.83	0.797036	0.398518	+	0.917160i	$0.369525\pi$
$44$	−9754.17	−0.759554
$45$	−2025.00	−0.149071
$46$	−51697.0	−3.60223
$47$	−16525.0	−1.09118	−0.545591	−	0.838051i	$-0.683695\pi$
$47$	−16525.0	−1.09118	−0.545591	+	0.838051i	$0.683695\pi$
$48$	−26053.5	−1.63216
$49$	−15734.8	−0.936205
$50$	−6632.45	−0.375188
$51$	16101.3	0.866834
$52$	−27853.1	−1.42845
$53$	−11612.1	−0.567833	−0.283917	−	0.958849i	$-0.591634\pi$
$53$	−11612.1	−0.567833	−0.283917	+	0.958849i	$0.591634\pi$
$54$	7736.09	0.361025
$55$	3025.00	0.134840
$56$	−16892.2	−0.719807
$57$	−21600.1	−0.880578
$58$	−34049.3	−1.32904
$59$	28860.7	1.07939	0.539694	−	0.841862i	$-0.318540\pi$
$59$	28860.7	1.07939	0.539694	+	0.841862i	$0.318540\pi$
$60$	18137.9	0.650443
$61$	33305.0	1.14600	0.573000	−	0.819555i	$-0.305780\pi$
$61$	33305.0	1.14600	0.573000	+	0.819555i	$0.305780\pi$
$62$	−20359.0	−0.672631
$63$	2652.31	0.0841925
$64$	58179.0	1.77548
$65$	8637.92	0.253586
$66$	−11556.4	−0.326559
$67$	3516.32	0.0956976	0.0478488	−	0.998855i	$-0.484763\pi$
$67$	3516.32	0.0956976	0.0478488	+	0.998855i	$0.484763\pi$
$68$	−144220.	−3.78226
$69$	−43844.4	−1.10864
$70$	8687.08	0.211899
$71$	−9172.96	−0.215955	−0.107978	−	0.994153i	$-0.534437\pi$
$71$	−9172.96	−0.215955	−0.107978	+	0.994153i	$0.534437\pi$
$72$	−41786.1	−0.949949
$73$	−83544.1	−1.83488	−0.917442	−	0.397870i	$-0.869749\pi$
$73$	−83544.1	−1.83488	−0.917442	+	0.397870i	$0.869749\pi$
$74$	−4863.78	−0.103251
$75$	−5625.00	−0.115470
$76$	193472.	3.84223
$77$	−3962.10	−0.0761550
$78$	−32999.4	−0.614143
$79$	−71559.4	−1.29003	−0.645014	−	0.764171i	$-0.723149\pi$
$79$	−71559.4	−1.29003	−0.645014	+	0.764171i	$0.723149\pi$
$80$	−72370.9	−1.26427
$81$	6561.00	0.111111
$82$	115584.	1.89830
$83$	−33724.0	−0.537333	−0.268667	−	0.963233i	$-0.586583\pi$
$83$	−33724.0	−0.537333	−0.268667	+	0.963233i	$0.586583\pi$
$84$	−23756.8	−0.367358
$85$	44725.9	0.671447
$86$	−102552.	−1.49519
$87$	−28877.3	−0.409033
$88$	62421.2	0.859261
$89$	107930.	1.44433	0.722165	−	0.691721i	$-0.243147\pi$
$89$	107930.	1.44433	0.722165	+	0.691721i	$0.243147\pi$
$90$	21489.2	0.279649
$91$	−11313.8	−0.143221
$92$	392714.	4.83734
$93$	−17266.5	−0.207013
$94$	175362.	2.04699
$95$	−60000.2	−0.682093
$96$	127906.	1.41648
$97$	103309.	1.11483	0.557415	−	0.830234i	$-0.311793\pi$
$97$	103309.	1.11483	0.557415	+	0.830234i	$0.311793\pi$
$98$	166976.	1.75626
$99$	−9801.00	−0.100504
$100$	50383.1	0.503831
$101$	−106397.	−1.03782	−0.518912	−	0.854827i	$-0.673663\pi$
$101$	−106397.	−1.03782	−0.518912	+	0.854827i	$0.673663\pi$
$102$	−170866.	−1.62613
$103$	−147060.	−1.36585	−0.682924	−	0.730489i	$-0.739292\pi$
$103$	−147060.	−1.36585	−0.682924	+	0.730489i	$0.739292\pi$
$104$	178244.	1.61597
$105$	7367.53	0.0652152
$106$	123227.	1.06522
$107$	−34128.5	−0.288176	−0.144088	−	0.989565i	$-0.546025\pi$
$107$	−34128.5	−0.288176	−0.144088	+	0.989565i	$0.546025\pi$
$108$	−58766.9	−0.484812
$109$	−131650.	−1.06134	−0.530672	−	0.847577i	$-0.678060\pi$
$109$	−131650.	−1.06134	−0.530672	+	0.847577i	$0.678060\pi$
$110$	−32101.1	−0.252952
$111$	−4124.98	−0.0317771
$112$	94790.3	0.714034
$113$	−56581.5	−0.416848	−0.208424	−	0.978039i	$-0.566833\pi$
$113$	−56581.5	−0.416848	−0.208424	+	0.978039i	$0.566833\pi$
$114$	229218.	1.65191
$115$	−121790.	−0.858750
$116$	258654.	1.78474
$117$	−27986.9	−0.189012
$118$	−306268.	−2.02487
$119$	−58581.3	−0.379220
$120$	−116072.	−0.735827
$121$	14641.0	0.0909091
$122$	−353430.	−2.14983
$123$	98027.3	0.584231
$124$	154656.	0.903260
$125$	−15625.0	−0.0894427
$126$	−28146.1	−0.157940
$127$	−77859.0	−0.428351	−0.214175	−	0.976795i	$-0.568706\pi$
$127$	−77859.0	−0.428351	−0.214175	+	0.976795i	$0.568706\pi$
$128$	−162616.	−0.877281
$129$	−86974.4	−0.460169
$130$	−91665.0	−0.475713
$131$	−312685.	−1.59195	−0.795973	−	0.605332i	$-0.793040\pi$
$131$	−312685.	−1.59195	−0.795973	+	0.605332i	$0.793040\pi$
$132$	87787.5	0.438529
$133$	78587.2	0.385233
$134$	−37314.9	−0.179523
$135$	18225.0	0.0860663
$136$	922923.	4.27876
$137$	172664.	0.785958	0.392979	−	0.919547i	$-0.371444\pi$
$137$	172664.	0.785958	0.392979	+	0.919547i	$0.371444\pi$
$138$	465273.	2.07975
$139$	−311563.	−1.36775	−0.683877	−	0.729597i	$-0.739708\pi$
$139$	−311563.	−1.36775	−0.683877	+	0.729597i	$0.739708\pi$
$140$	−65991.0	−0.284554
$141$	148725.	0.629994
$142$	97342.7	0.405119
$143$	41807.5	0.170968
$144$	234482.	0.942330
$145$	−80214.7	−0.316836
$146$	886564.	3.44213
$147$	141613.	0.540518
$148$	36947.4	0.138653
$149$	−384446.	−1.41863	−0.709317	−	0.704890i	$-0.750996\pi$
$149$	−384446.	−1.41863	−0.709317	+	0.704890i	$0.750996\pi$
$150$	59692.1	0.216615
$151$	221238.	0.789617	0.394809	−	0.918763i	$-0.370811\pi$
$151$	221238.	0.789617	0.394809	+	0.918763i	$0.370811\pi$
$152$	−1.23811e6	−4.34660
$153$	−144912.	−0.500467
$154$	42045.5	0.142862
$155$	−47962.5	−0.160351
$156$	250678.	0.824718
$157$	−23673.6	−0.0766507	−0.0383253	−	0.999265i	$-0.512202\pi$
$157$	−23673.6	−0.0766507	−0.0383253	+	0.999265i	$0.512202\pi$
$158$	759384.	2.42002
$159$	104509.	0.327839
$160$	355293.	1.09720
$161$	159518.	0.485005
$162$	−69624.9	−0.208438
$163$	61962.0	0.182666	0.0913328	−	0.995820i	$-0.470887\pi$
$163$	61962.0	0.182666	0.0913328	+	0.995820i	$0.470887\pi$
$164$	−878031.	−2.54918
$165$	−27225.0	−0.0778499
$166$	357877.	1.00801
$167$	35496.4	0.0984903	0.0492451	−	0.998787i	$-0.484318\pi$
$167$	35496.4	0.0984903	0.0492451	+	0.998787i	$0.484318\pi$
$168$	152030.	0.415581
$169$	−251911.	−0.678470
$170$	−474628.	−1.25960
$171$	194401.	0.508402
$172$	779030.	2.00786
$173$	−349784.	−0.888556	−0.444278	−	0.895889i	$-0.646540\pi$
$173$	−349784.	−0.888556	−0.444278	+	0.895889i	$0.646540\pi$
$174$	306444.	0.767322
$175$	20465.4	0.0505155
$176$	−350275.	−0.852370
$177$	−259747.	−0.623184
$178$	−1.14534e6	−2.70948
$179$	275517.	0.642711	0.321355	−	0.946959i	$-0.395862\pi$
$179$	275517.	0.642711	0.321355	+	0.946959i	$0.395862\pi$
$180$	−163241.	−0.375534
$181$	−742955.	−1.68565	−0.842823	−	0.538191i	$-0.819108\pi$
$181$	−742955.	−1.68565	−0.842823	+	0.538191i	$0.819108\pi$
$182$	120061.	0.268673
$183$	−299745.	−0.661643
$184$	−2.51315e6	−5.47234
$185$	−11458.3	−0.0246144
$186$	183231.	0.388344
$187$	216473.	0.452689
$188$	−1.33213e6	−2.74886
$189$	−23870.8	−0.0486086
$190$	636717.	1.27957
$191$	425896.	0.844734	0.422367	−	0.906425i	$-0.361199\pi$
$191$	425896.	0.844734	0.422367	+	0.906425i	$0.361199\pi$
$192$	−523611.	−1.02508
$193$	599319.	1.15815	0.579075	−	0.815274i	$-0.303414\pi$
$193$	599319.	1.15815	0.579075	+	0.815274i	$0.303414\pi$
$194$	−1.09631e6	−2.09136
$195$	−77741.3	−0.146408
$196$	−1.26843e6	−2.35845
$197$	179561.	0.329645	0.164823	−	0.986323i	$-0.447295\pi$
$197$	179561.	0.329645	0.164823	+	0.986323i	$0.447295\pi$
$198$	104007.	0.188539
$199$	−390430.	−0.698893	−0.349446	−	0.936956i	$-0.613630\pi$
$199$	−390430.	−0.698893	−0.349446	+	0.936956i	$0.613630\pi$
$200$	−322423.	−0.569969
$201$	−31646.9	−0.0552511
$202$	1.12907e6	1.94690
$203$	105064.	0.178942
$204$	1.29798e6	2.18369
$205$	272298.	0.452543
$206$	1.56059e6	2.56225
$207$	394599.	0.640074
$208$	−1.00022e6	−1.60301
$209$	−290401.	−0.459867
$210$	−78183.7	−0.122340
$211$	−609911.	−0.943105	−0.471553	−	0.881838i	$-0.656306\pi$
$211$	−609911.	−0.943105	−0.471553	+	0.881838i	$0.656306\pi$
$212$	−936085.	−1.43046
$213$	82556.6	0.124682
$214$	362169.	0.540600
$215$	−241596.	−0.356445
$216$	376075.	0.548453
$217$	62820.5	0.0905633
$218$	1.39706e6	1.99102
$219$	751897.	1.05937
$220$	243854.	0.339683
$221$	618142.	0.851349
$222$	43774.0	0.0596120
$223$	−622124.	−0.837751	−0.418876	−	0.908044i	$-0.637576\pi$
$223$	−622124.	−0.837751	−0.418876	+	0.908044i	$0.637576\pi$
$224$	−465357.	−0.619679
$225$	50625.0	0.0666667
$226$	600438.	0.781983
$227$	−653428.	−0.841653	−0.420827	−	0.907141i	$-0.638260\pi$
$227$	−653428.	−0.841653	−0.420827	+	0.907141i	$0.638260\pi$
$228$	−1.74125e6	−2.21831
$229$	−874801.	−1.10235	−0.551176	−	0.834389i	$-0.685821\pi$
$229$	−874801.	−1.10235	−0.551176	+	0.834389i	$0.685821\pi$
$230$	1.29243e6	1.61096
$231$	35658.9	0.0439681
$232$	−1.65524e6	−2.01902
$233$	847197.	1.02234	0.511169	−	0.859480i	$-0.329213\pi$
$233$	847197.	1.02234	0.511169	+	0.859480i	$0.329213\pi$
$234$	296995.	0.354576
$235$	413125.	0.487992
$236$	2.32655e6	2.71914
$237$	644035.	0.744798
$238$	621660.	0.711395
$239$	−495770.	−0.561417	−0.280709	−	0.959793i	$-0.590569\pi$
$239$	−495770.	−0.561417	−0.280709	+	0.959793i	$0.590569\pi$
$240$	651339.	0.729926
$241$	−1.69608e6	−1.88107	−0.940534	−	0.339699i	$-0.889675\pi$
$241$	−1.69608e6	−1.88107	−0.940534	+	0.339699i	$0.889675\pi$
$242$	−155369.	−0.170540
$243$	−59049.0	−0.0641500
$244$	2.68481e6	2.88695
$245$	393370.	0.418683
$246$	−1.04026e6	−1.09598
$247$	−829243.	−0.864847
$248$	−989711.	−1.02183
$249$	303516.	0.310230
$250$	165811.	0.167789
$251$	1.04073e6	1.04269	0.521344	−	0.853346i	$-0.325431\pi$
$251$	1.04073e6	1.04269	0.521344	+	0.853346i	$0.325431\pi$
$252$	213811.	0.212094
$253$	−589463.	−0.578969
$254$	826234.	0.803561
$255$	−402533.	−0.387660
$256$	−136058.	−0.129755
$257$	1.73758e6	1.64101	0.820506	−	0.571637i	$-0.193692\pi$
$257$	1.73758e6	1.64101	0.820506	+	0.571637i	$0.193692\pi$
$258$	922966.	0.863250
$259$	15007.9	0.0139018
$260$	696329.	0.638824
$261$	259896.	0.236155
$262$	3.31819e6	2.98640
$263$	1.01369e6	0.903686	0.451843	−	0.892097i	$-0.350767\pi$
$263$	1.01369e6	0.903686	0.451843	+	0.892097i	$0.350767\pi$
$264$	−561791.	−0.496095
$265$	290302.	0.253943
$266$	−833962.	−0.722674
$267$	−971368.	−0.833884
$268$	283461.	0.241077
$269$	2.30540e6	1.94252	0.971260	−	0.238019i	$-0.0764982\pi$
$269$	2.30540e6	1.94252	0.971260	+	0.238019i	$0.0764982\pi$
$270$	−193402.	−0.161455
$271$	1.51489e6	1.25302	0.626511	−	0.779412i	$-0.284482\pi$
$271$	1.51489e6	1.25302	0.626511	+	0.779412i	$0.284482\pi$
$272$	−5.17897e6	−4.24445
$273$	101824.	0.0826884
$274$	−1.83229e6	−1.47441
$275$	−75625.0	−0.0603023
$276$	−3.53443e6	−2.79284
$277$	677490.	0.530522	0.265261	−	0.964177i	$-0.414542\pi$
$277$	677490.	0.530522	0.265261	+	0.964177i	$0.414542\pi$
$278$	3.30628e6	2.56583
$279$	155399.	0.119519
$280$	422305.	0.321908
$281$	−2.26763e6	−1.71319	−0.856597	−	0.515986i	$-0.827426\pi$
$281$	−2.26763e6	−1.71319	−0.856597	+	0.515986i	$0.827426\pi$
$282$	−1.57826e6	−1.18183
$283$	−2.04884e6	−1.52069	−0.760346	−	0.649518i	$-0.774971\pi$
$283$	−2.04884e6	−1.52069	−0.760346	+	0.649518i	$0.774971\pi$
$284$	−739459.	−0.544024
$285$	540001.	0.393806
$286$	−443659.	−0.320726
$287$	−356652.	−0.255587
$288$	−1.15115e6	−0.817807
$289$	1.78079e6	1.25421
$290$	851232.	0.594365
$291$	−929781.	−0.643648
$292$	−6.73474e6	−4.62236
$293$	427355.	0.290817	0.145409	−	0.989372i	$-0.453550\pi$
$293$	427355.	0.290817	0.145409	+	0.989372i	$0.453550\pi$
$294$	−1.50279e6	−1.01398
$295$	−721518.	−0.482717
$296$	−236443.	−0.156854
$297$	88209.0	0.0580259
$298$	4.07972e6	2.66127
$299$	−1.68322e6	−1.08884
$300$	−453448.	−0.290887
$301$	316438.	0.201313
$302$	−2.34776e6	−1.48128
$303$	957569.	0.599188
$304$	6.94763e6	4.31174
$305$	−832624.	−0.512507
$306$	1.53779e6	0.938847
$307$	2.15140e6	1.30279	0.651397	−	0.758737i	$-0.274183\pi$
$307$	2.15140e6	1.30279	0.651397	+	0.758737i	$0.274183\pi$
$308$	−319396.	−0.191846
$309$	1.32354e6	0.788573
$310$	508975.	0.300810
$311$	−565482.	−0.331526	−0.165763	−	0.986166i	$-0.553009\pi$
$311$	−565482.	−0.331526	−0.165763	+	0.986166i	$0.553009\pi$
$312$	−1.60420e6	−0.932979
$313$	−1.11757e6	−0.644783	−0.322391	−	0.946606i	$-0.604487\pi$
$313$	−1.11757e6	−0.644783	−0.322391	+	0.946606i	$0.604487\pi$
$314$	251223.	0.143792
$315$	−66307.8	−0.0376520
$316$	−5.76862e6	−3.24978
$317$	151250.	0.0845368	0.0422684	−	0.999106i	$-0.486542\pi$
$317$	151250.	0.0845368	0.0422684	+	0.999106i	$0.486542\pi$
$318$	−1.10904e6	−0.615006
$319$	−388239.	−0.213610
$320$	−1.45448e6	−0.794020
$321$	307156.	0.166378
$322$	−1.69280e6	−0.909841
$323$	−4.29370e6	−2.28995
$324$	528902.	0.279906
$325$	−215948.	−0.113407
$326$	−657537.	−0.342670
$327$	1.18485e6	0.612767
$328$	5.61890e6	2.88381
$329$	−541105.	−0.275608
$330$	288910.	0.146042
$331$	1.46211e6	0.733515	0.366757	−	0.930317i	$-0.380468\pi$
$331$	1.46211e6	0.733515	0.366757	+	0.930317i	$0.380468\pi$
$332$	−2.71859e6	−1.35363
$333$	37124.8	0.0183465
$334$	−376685.	−0.184762
$335$	−87908.0	−0.0427973
$336$	−853113.	−0.412248
$337$	2.43548e6	1.16818	0.584091	−	0.811688i	$-0.301451\pi$
$337$	2.43548e6	1.16818	0.584091	+	0.811688i	$0.301451\pi$
$338$	2.67326e6	1.27277
$339$	509233.	0.240668
$340$	3.60549e6	1.69148
$341$	−232139.	−0.108109
$342$	−2.06296e6	−0.953732
$343$	−1.06557e6	−0.489042
$344$	−4.98535e6	−2.27143
$345$	1.09611e6	0.495799
$346$	3.71188e6	1.66688
$347$	1.27474e6	0.568324	0.284162	−	0.958776i	$-0.408285\pi$
$347$	1.27474e6	0.568324	0.284162	+	0.958776i	$0.408285\pi$
$348$	−2.32788e6	−1.03042
$349$	−463470.	−0.203685	−0.101842	−	0.994801i	$-0.532474\pi$
$349$	−463470.	−0.203685	−0.101842	+	0.994801i	$0.532474\pi$
$350$	−217177.	−0.0947641
$351$	251882.	0.109126
$352$	1.71962e6	0.739734
$353$	−849656.	−0.362916	−0.181458	−	0.983399i	$-0.558082\pi$
$353$	−849656.	−0.362916	−0.181458	+	0.983399i	$0.558082\pi$
$354$	2.75641e6	1.16906
$355$	229324.	0.0965780
$356$	8.70054e6	3.63849
$357$	527231.	0.218943
$358$	−2.92376e6	−1.20569
$359$	−105057.	−0.0430220	−0.0215110	−	0.999769i	$-0.506848\pi$
$359$	−105057.	−0.0430220	−0.0215110	+	0.999769i	$0.506848\pi$
$360$	1.04465e6	0.424830
$361$	3.28393e6	1.32625
$362$	7.88419e6	3.16217
$363$	−131769.	−0.0524864
$364$	−912040.	−0.360795
$365$	2.08860e6	0.820585
$366$	3.18087e6	1.24120
$367$	622989.	0.241443	0.120722	−	0.992686i	$-0.461479\pi$
$367$	622989.	0.241443	0.120722	+	0.992686i	$0.461479\pi$
$368$	1.41025e7	5.42845
$369$	−882246.	−0.337306
$370$	121594.	0.0461752
$371$	−380233.	−0.143422
$372$	−1.39190e6	−0.521497
$373$	−3.30681e6	−1.23066	−0.615329	−	0.788270i	$-0.710977\pi$
$373$	−3.30681e6	−1.23066	−0.615329	+	0.788270i	$0.710977\pi$
$374$	−2.29720e6	−0.849219
$375$	140625.	0.0516398
$376$	8.52488e6	3.10970
$377$	−1.10862e6	−0.401726
$378$	253315.	0.0911868
$379$	−4.46889e6	−1.59809	−0.799046	−	0.601269i	$-0.794662\pi$
$379$	−4.46889e6	−1.59809	−0.799046	+	0.601269i	$0.794662\pi$
$380$	−4.83679e6	−1.71830
$381$	700731.	0.247308
$382$	−4.51958e6	−1.58467
$383$	3.94653e6	1.37473	0.687366	−	0.726311i	$-0.258767\pi$
$383$	3.94653e6	1.37473	0.687366	+	0.726311i	$0.258767\pi$
$384$	1.46355e6	0.506498
$385$	99052.4	0.0340575
$386$	−6.35993e6	−2.17262
$387$	782770.	0.265679
$388$	8.32805e6	2.80843
$389$	−4.75854e6	−1.59441	−0.797204	−	0.603710i	$-0.793688\pi$
$389$	−4.75854e6	−1.59441	−0.797204	+	0.603710i	$0.793688\pi$
$390$	824985.	0.274653
$391$	−8.71546e6	−2.88303
$392$	8.11722e6	2.66804
$393$	2.81416e6	0.919110
$394$	−1.90549e6	−0.618395
$395$	1.78899e6	0.576918
$396$	−790088.	−0.253185
$397$	−5.64273e6	−1.79686	−0.898428	−	0.439121i	$-0.855290\pi$
$397$	−5.64273e6	−1.79686	−0.898428	+	0.439121i	$0.855290\pi$
$398$	4.14321e6	1.31108
$399$	−707285.	−0.222414
$400$	1.80927e6	0.565398
$401$	−226604.	−0.0703731	−0.0351866	−	0.999381i	$-0.511203\pi$
$401$	−226604.	−0.0703731	−0.0351866	+	0.999381i	$0.511203\pi$
$402$	335834.	0.103648
$403$	−662874.	−0.203315
$404$	−8.57694e6	−2.61444
$405$	−164025.	−0.0496904
$406$	−1.11493e6	−0.335686
$407$	−55458.1	−0.0165951
$408$	−8.30631e6	−2.47035
$409$	1.45335e6	0.429598	0.214799	−	0.976658i	$-0.431090\pi$
$409$	1.45335e6	0.429598	0.214799	+	0.976658i	$0.431090\pi$
$410$	−2.88961e6	−0.848944
$411$	−1.55397e6	−0.453773
$412$	−1.18550e7	−3.44079
$413$	945033.	0.272629
$414$	−4.18746e6	−1.20074
$415$	843100.	0.240303
$416$	4.91039e6	1.39118
$417$	2.80406e6	0.789674
$418$	3.08171e6	0.862683
$419$	−4.65297e6	−1.29478	−0.647389	−	0.762160i	$-0.724139\pi$
$419$	−4.65297e6	−1.29478	−0.647389	+	0.762160i	$0.724139\pi$
$420$	593919.	0.164287
$421$	3.20449e6	0.881158	0.440579	−	0.897714i	$-0.354773\pi$
$421$	3.20449e6	0.881158	0.440579	+	0.897714i	$0.354773\pi$
$422$	6.47233e6	1.76921
$423$	−1.33853e6	−0.363727
$424$	5.99041e6	1.61824
$425$	−1.11815e6	−0.300280
$426$	−876085.	−0.233896
$427$	1.09056e6	0.289454
$428$	−2.75120e6	−0.725959
$429$	−376268.	−0.0987084
$430$	2.56380e6	0.668671
$431$	1.47887e6	0.383474	0.191737	−	0.981446i	$-0.438588\pi$
$431$	1.47887e6	0.383474	0.191737	+	0.981446i	$0.438588\pi$
$432$	−2.11034e6	−0.544055
$433$	6.68401e6	1.71324	0.856618	−	0.515951i	$-0.172562\pi$
$433$	6.68401e6	1.71324	0.856618	+	0.515951i	$0.172562\pi$
$434$	−666647.	−0.169891
$435$	721932.	0.182925
$436$	−1.06127e7	−2.67369
$437$	1.16919e7	2.92874
$438$	−7.97907e6	−1.98732
$439$	−431193.	−0.106785	−0.0533925	−	0.998574i	$-0.517003\pi$
$439$	−431193.	−0.106785	−0.0533925	+	0.998574i	$0.517003\pi$
$440$	−1.56053e6	−0.384273
$441$	−1.27452e6	−0.312068
$442$	−6.55968e6	−1.59708
$443$	−6.34950e6	−1.53720	−0.768600	−	0.639729i	$-0.779046\pi$
$443$	−6.34950e6	−1.53720	−0.768600	+	0.639729i	$0.779046\pi$
$444$	−332527.	−0.0800515
$445$	−2.69825e6	−0.645924
$446$	6.60194e6	1.57157
$447$	3.46002e6	0.819048
$448$	1.90505e6	0.448447
$449$	−1.57313e6	−0.368255	−0.184127	−	0.982902i	$-0.558946\pi$
$449$	−1.57313e6	−0.368255	−0.184127	+	0.982902i	$0.558946\pi$
$450$	−537229.	−0.125063
$451$	1.31792e6	0.305105
$452$	−4.56120e6	−1.05011
$453$	−1.99114e6	−0.455886
$454$	6.93413e6	1.57889
$455$	282845.	0.0640502
$456$	1.11430e7	2.50951
$457$	−1.88353e6	−0.421873	−0.210936	−	0.977500i	$-0.567651\pi$
$457$	−1.88353e6	−0.421873	−0.210936	+	0.977500i	$0.567651\pi$
$458$	9.28333e6	2.06795
$459$	1.30421e6	0.288945
$460$	−9.81785e6	−2.16332
$461$	−4.98003e6	−1.09139	−0.545694	−	0.837984i	$-0.683734\pi$
$461$	−4.98003e6	−1.09139	−0.545694	+	0.837984i	$0.683734\pi$
$462$	−378409.	−0.0824816
$463$	−6.83548e6	−1.48189	−0.740946	−	0.671565i	$-0.765623\pi$
$463$	−6.83548e6	−1.48189	−0.740946	+	0.671565i	$0.765623\pi$
$464$	9.28834e6	2.00283
$465$	431663.	0.0925789
$466$	−8.99039e6	−1.91785
$467$	−7.63239e6	−1.61945	−0.809726	−	0.586808i	$-0.800384\pi$
$467$	−7.63239e6	−1.61945	−0.809726	+	0.586808i	$0.800384\pi$
$468$	−2.25611e6	−0.476151
$469$	115140.	0.0241711
$470$	−4.38406e6	−0.915444
$471$	213063.	0.0442543
$472$	−1.48886e7	−3.07609
$473$	−1.16932e6	−0.240315
$474$	−6.83445e6	−1.39720
$475$	1.50000e6	0.305041
$476$	−4.72241e6	−0.955314
$477$	−940579.	−0.189278
$478$	5.26108e6	1.05319
$479$	8.81029e6	1.75449	0.877247	−	0.480040i	$-0.159378\pi$
$479$	8.81029e6	1.75449	0.877247	+	0.480040i	$0.159378\pi$
$480$	−3.19764e6	−0.633470
$481$	−158361.	−0.0312094
$482$	1.79987e7	3.52877
$483$	−1.43567e6	−0.280018
$484$	1.18025e6	0.229014
$485$	−2.58273e6	−0.498568
$486$	626624.	0.120342
$487$	5.09425e6	0.973325	0.486663	−	0.873590i	$-0.338214\pi$
$487$	5.09425e6	0.973325	0.486663	+	0.873590i	$0.338214\pi$
$488$	−1.71813e7	−3.26592
$489$	−557658.	−0.105462
$490$	−4.17441e6	−0.785426
$491$	−3.28278e6	−0.614523	−0.307261	−	0.951625i	$-0.599413\pi$
$491$	−3.28278e6	−0.614523	−0.307261	+	0.951625i	$0.599413\pi$
$492$	7.90228e6	1.47177
$493$	−5.74028e6	−1.06369
$494$	8.79986e6	1.62240
$495$	245025.	0.0449467
$496$	5.55375e6	1.01364
$497$	−300365.	−0.0545454
$498$	−3.22089e6	−0.581973
$499$	3.21935e6	0.578785	0.289392	−	0.957211i	$-0.406547\pi$
$499$	3.21935e6	0.578785	0.289392	+	0.957211i	$0.406547\pi$
$500$	−1.25958e6	−0.225320
$501$	−319468.	−0.0568634
$502$	−1.10442e7	−1.95602
$503$	−1.26964e6	−0.223749	−0.111875	−	0.993722i	$-0.535685\pi$
$503$	−1.26964e6	−0.223749	−0.111875	+	0.993722i	$0.535685\pi$
$504$	−1.36827e6	−0.239936
$505$	2.65991e6	0.464129
$506$	6.25534e6	1.08611
$507$	2.26720e6	0.391715
$508$	−6.27645e6	−1.07908
$509$	−6.71608e6	−1.14900	−0.574502	−	0.818504i	$-0.694804\pi$
$509$	−6.71608e6	−1.14900	−0.574502	+	0.818504i	$0.694804\pi$
$510$	4.27165e6	0.727228
$511$	−2.73562e6	−0.463450
$512$	6.64756e6	1.12069
$513$	−1.74960e6	−0.293526
$514$	−1.84391e7	−3.07844
$515$	3.67651e6	0.610826
$516$	−7.01127e6	−1.15924
$517$	1.99953e6	0.329004
$518$	−159262.	−0.0260789
$519$	3.14806e6	0.513008
$520$	−4.45611e6	−0.722682
$521$	1.07268e7	1.73132	0.865659	−	0.500635i	$-0.166900\pi$
$521$	1.07268e7	1.73132	0.865659	+	0.500635i	$0.166900\pi$
$522$	−2.75799e6	−0.443013
$523$	−5.54058e6	−0.885730	−0.442865	−	0.896588i	$-0.646038\pi$
$523$	−5.54058e6	−0.885730	−0.442865	+	0.896588i	$0.646038\pi$
$524$	−2.52064e7	−4.01036
$525$	−184188.	−0.0291651
$526$	−1.07572e7	−1.69526
$527$	−3.43227e6	−0.538337
$528$	3.15248e6	0.492116
$529$	1.72961e7	2.68726
$530$	−3.08067e6	−0.476382
$531$	2.33772e6	0.359796
$532$	6.33515e6	0.970461
$533$	3.76334e6	0.573794
$534$	1.03081e7	1.56432
$535$	853211.	0.128876
$536$	−1.81399e6	−0.272724
$537$	−2.47965e6	−0.371069
$538$	−2.44647e7	−3.64405
$539$	1.90391e6	0.282276
$540$	1.46917e6	0.216814
$541$	9.75059e6	1.43231	0.716156	−	0.697940i	$-0.245900\pi$
$541$	9.75059e6	1.43231	0.716156	+	0.697940i	$0.245900\pi$
$542$	−1.60759e7	−2.35060
$543$	6.68660e6	0.973208
$544$	2.54253e7	3.68357
$545$	3.29126e6	0.474647
$546$	−1.08055e6	−0.155119
$547$	2.02886e6	0.289924	0.144962	−	0.989437i	$-0.453694\pi$
$547$	2.02886e6	0.289924	0.144962	+	0.989437i	$0.453694\pi$
$548$	1.39189e7	1.97995
$549$	2.69770e6	0.382000
$550$	802527.	0.113124
$551$	7.70063e6	1.08056
$552$	2.26183e7	3.15946
$553$	−2.34319e6	−0.325832
$554$	−7.18947e6	−0.995228
$555$	103124.	0.0142112
$556$	−2.51160e7	−3.44559
$557$	−3.66452e6	−0.500471	−0.250236	−	0.968185i	$-0.580508\pi$
$557$	−3.66452e6	−0.500471	−0.250236	+	0.968185i	$0.580508\pi$
$558$	−1.64908e6	−0.224210
$559$	−3.33902e6	−0.451948
$560$	−2.36976e6	−0.319326
$561$	−1.94826e6	−0.261360
$562$	2.40639e7	3.21385
$563$	−1.29167e7	−1.71744	−0.858718	−	0.512449i	$-0.828738\pi$
$563$	−1.29167e7	−1.71744	−0.858718	+	0.512449i	$0.828738\pi$
$564$	1.19892e7	1.58705
$565$	1.41454e6	0.186420
$566$	2.17421e7	2.85273
$567$	214837.	0.0280642
$568$	4.73212e6	0.615439
$569$	−9.41931e6	−1.21966	−0.609830	−	0.792533i	$-0.708762\pi$
$569$	−9.41931e6	−1.21966	−0.609830	+	0.792533i	$0.708762\pi$
$570$	−5.73046e6	−0.738758
$571$	3.34413e6	0.429232	0.214616	−	0.976698i	$-0.431150\pi$
$571$	3.34413e6	0.429232	0.214616	+	0.976698i	$0.431150\pi$
$572$	3.37023e6	0.430695
$573$	−3.83306e6	−0.487708
$574$	3.78476e6	0.479467
$575$	3.04475e6	0.384045
$576$	4.71250e6	0.591828
$577$	8.07144e6	1.00928	0.504640	−	0.863330i	$-0.331625\pi$
$577$	8.07144e6	1.00928	0.504640	+	0.863330i	$0.331625\pi$
$578$	−1.88976e7	−2.35282
$579$	−5.39387e6	−0.668658
$580$	−6.46635e6	−0.798158
$581$	−1.10428e6	−0.135718
$582$	9.86677e6	1.20745
$583$	1.40506e6	0.171208
$584$	4.30985e7	5.22914
$585$	699672.	0.0845288
$586$	−4.53506e6	−0.545556
$587$	1.29864e6	0.155558	0.0777790	−	0.996971i	$-0.475217\pi$
$587$	1.29864e6	0.155558	0.0777790	+	0.996971i	$0.475217\pi$
$588$	1.14159e7	1.36165
$589$	4.60441e6	0.546873
$590$	7.65670e6	0.905548
$591$	−1.61605e6	−0.190321
$592$	1.32679e6	0.155596
$593$	−437771.	−0.0511223	−0.0255612	−	0.999673i	$-0.508137\pi$
$593$	−437771.	−0.0511223	−0.0255612	+	0.999673i	$0.508137\pi$
$594$	−936067.	−0.108853
$595$	1.46453e6	0.169592
$596$	−3.09914e7	−3.57376
$597$	3.51387e6	0.403506
$598$	1.78622e7	2.04259
$599$	−9.72859e6	−1.10785	−0.553927	−	0.832565i	$-0.686871\pi$
$599$	−9.72859e6	−1.10785	−0.553927	+	0.832565i	$0.686871\pi$
$600$	2.90181e6	0.329072
$601$	−6.31361e6	−0.713004	−0.356502	−	0.934295i	$-0.616031\pi$
$601$	−6.31361e6	−0.713004	−0.356502	+	0.934295i	$0.616031\pi$
$602$	−3.35802e6	−0.377652
$603$	284822.	0.0318992
$604$	1.78346e7	1.98917
$605$	−366025.	−0.0406558
$606$	−1.01616e7	−1.12404
$607$	8.23150e6	0.906791	0.453396	−	0.891309i	$-0.350212\pi$
$607$	8.23150e6	0.906791	0.453396	+	0.891309i	$0.350212\pi$
$608$	−3.41082e7	−3.74197
$609$	−945575.	−0.103312
$610$	8.83575e6	0.961433
$611$	5.70967e6	0.618740
$612$	−1.16818e7	−1.26075
$613$	1.31533e7	1.41378	0.706892	−	0.707321i	$-0.250097\pi$
$613$	1.31533e7	1.41378	0.706892	+	0.707321i	$0.250097\pi$
$614$	−2.28305e7	−2.44396
$615$	−2.45068e6	−0.261276
$616$	2.04396e6	0.217030
$617$	1.21036e7	1.27997	0.639986	−	0.768386i	$-0.278940\pi$
$617$	1.21036e7	1.27997	0.639986	+	0.768386i	$0.278940\pi$
$618$	−1.40453e7	−1.47932
$619$	−8.34609e6	−0.875501	−0.437750	−	0.899097i	$-0.644225\pi$
$619$	−8.34609e6	−0.875501	−0.437750	+	0.899097i	$0.644225\pi$
$620$	−3.86640e6	−0.403950
$621$	−3.55139e6	−0.369547
$622$	6.00085e6	0.621923
$623$	3.53412e6	0.364805
$624$	9.00194e6	0.925496
$625$	390625.	0.0400000
$626$	1.18596e7	1.20957
$627$	2.61361e6	0.265504
$628$	−1.90840e6	−0.193095
$629$	−819971.	−0.0826365
$630$	703654.	0.0706330
$631$	−8.87072e6	−0.886922	−0.443461	−	0.896294i	$-0.646250\pi$
$631$	−8.87072e6	−0.886922	−0.443461	+	0.896294i	$0.646250\pi$
$632$	3.69159e7	3.67638
$633$	5.48920e6	0.544502
$634$	−1.60505e6	−0.158586
$635$	1.94648e6	0.191564
$636$	8.42477e6	0.825876
$637$	5.43664e6	0.530862
$638$	4.11996e6	0.400721
$639$	−743009.	−0.0719850
$640$	4.06540e6	0.392332
$641$	−6.81313e6	−0.654940	−0.327470	−	0.944862i	$-0.606196\pi$
$641$	−6.81313e6	−0.654940	−0.327470	+	0.944862i	$0.606196\pi$
$642$	−3.25952e6	−0.312116
$643$	1.25321e7	1.19536	0.597679	−	0.801736i	$-0.296090\pi$
$643$	1.25321e7	1.19536	0.597679	+	0.801736i	$0.296090\pi$
$644$	1.28593e7	1.22180
$645$	2.17436e6	0.205794
$646$	4.55644e7	4.29580
$647$	506623.	0.0475800	0.0237900	−	0.999717i	$-0.492427\pi$
$647$	506623.	0.0475800	0.0237900	+	0.999717i	$0.492427\pi$
$648$	−3.38467e6	−0.316650
$649$	−3.49215e6	−0.325447
$650$	2.29162e6	0.212745
$651$	−565385.	−0.0522868
$652$	4.99495e6	0.460163
$653$	−1.24678e7	−1.14421	−0.572104	−	0.820181i	$-0.693873\pi$
$653$	−1.24678e7	−1.14421	−0.572104	+	0.820181i	$0.693873\pi$
$654$	−1.25736e7	−1.14952
$655$	7.81711e6	0.711940
$656$	−3.15304e7	−2.86068
$657$	−6.76707e6	−0.611628
$658$	5.74217e6	0.517024
$659$	1.85231e7	1.66150	0.830749	−	0.556648i	$-0.187913\pi$
$659$	1.85231e7	1.66150	0.830749	+	0.556648i	$0.187913\pi$
$660$	−2.19469e6	−0.196116
$661$	7.95710e6	0.708355	0.354178	−	0.935178i	$-0.384761\pi$
$661$	7.95710e6	0.708355	0.354178	+	0.935178i	$0.384761\pi$
$662$	−1.55158e7	−1.37603
$663$	−5.56328e6	−0.491527
$664$	1.73975e7	1.53132
$665$	−1.96468e6	−0.172281
$666$	−393966.	−0.0344170
$667$	1.56309e7	1.36041
$668$	2.86147e6	0.248112
$669$	5.59912e6	0.483676
$670$	932873.	0.0802852
$671$	−4.02990e6	−0.345532
$672$	4.18822e6	0.357772
$673$	316146.	0.0269061	0.0134530	−	0.999910i	$-0.495718\pi$
$673$	316146.	0.0269061	0.0134530	+	0.999910i	$0.495718\pi$
$674$	−2.58452e7	−2.19144
$675$	−455625.	−0.0384900
$676$	−2.03073e7	−1.70917
$677$	−5.30126e6	−0.444536	−0.222268	−	0.974986i	$-0.571346\pi$
$677$	−5.30126e6	−0.444536	−0.222268	+	0.974986i	$0.571346\pi$
$678$	−5.40395e6	−0.451478
$679$	3.38281e6	0.281581
$680$	−2.30731e7	−1.91352
$681$	5.88086e6	0.485929
$682$	2.46344e6	0.202806
$683$	−1.33791e7	−1.09743	−0.548713	−	0.836011i	$-0.684882\pi$
$683$	−1.33791e7	−1.09743	−0.548713	+	0.836011i	$0.684882\pi$
$684$	1.56712e7	1.28074
$685$	−4.31659e6	−0.351491
$686$	1.13077e7	0.917413
$687$	7.87321e6	0.636444
$688$	2.79752e7	2.25321
$689$	4.01217e6	0.321982
$690$	−1.16318e7	−0.930091
$691$	−2.83200e6	−0.225630	−0.112815	−	0.993616i	$-0.535987\pi$
$691$	−2.83200e6	−0.225630	−0.112815	+	0.993616i	$0.535987\pi$
$692$	−2.81971e7	−2.23841
$693$	−320930.	−0.0253850
$694$	−1.35274e7	−1.06614
$695$	7.78906e6	0.611679
$696$	1.48971e7	1.16568
$697$	1.94860e7	1.51929
$698$	4.91831e6	0.382100
$699$	−7.62477e6	−0.590247
$700$	1.64977e6	0.127256
$701$	2.00684e7	1.54248	0.771238	−	0.636547i	$-0.219638\pi$
$701$	2.00684e7	1.54248	0.771238	+	0.636547i	$0.219638\pi$
$702$	−2.67295e6	−0.204714
$703$	1.10000e6	0.0839466
$704$	−7.03966e6	−0.535328
$705$	−3.71813e6	−0.281742
$706$	9.01648e6	0.680809
$707$	−3.48391e6	−0.262131
$708$	−2.09389e7	−1.56990
$709$	−1.16022e7	−0.866813	−0.433407	−	0.901198i	$-0.642689\pi$
$709$	−1.16022e7	−0.866813	−0.433407	+	0.901198i	$0.642689\pi$
$710$	−2.43357e6	−0.181175
$711$	−5.79632e6	−0.430009
$712$	−5.56786e7	−4.11612
$713$	9.34616e6	0.688509
$714$	−5.59494e6	−0.410724
$715$	−1.04519e6	−0.0764592
$716$	2.22102e7	1.61909
$717$	4.46193e6	0.324134
$718$	1.11486e6	0.0807067
$719$	1.02727e7	0.741078	0.370539	−	0.928817i	$-0.379173\pi$
$719$	1.02727e7	0.741078	0.370539	+	0.928817i	$0.379173\pi$
$720$	−5.86205e6	−0.421423
$721$	−4.81543e6	−0.344983
$722$	−3.48488e7	−2.48797
$723$	1.52648e7	1.08604
$724$	−5.98919e7	−4.24640
$725$	2.00537e6	0.141693
$726$	1.39832e6	0.0984614
$727$	−2.38172e7	−1.67130	−0.835651	−	0.549261i	$-0.814909\pi$
$727$	−2.38172e7	−1.67130	−0.835651	+	0.549261i	$0.814909\pi$
$728$	5.83654e6	0.408157
$729$	531441.	0.0370370
$730$	−2.21641e7	−1.53937
$731$	−1.72889e7	−1.19667
$732$	−2.41633e7	−1.66678
$733$	2.04894e6	0.140854	0.0704270	−	0.997517i	$-0.477564\pi$
$733$	2.04894e6	0.140854	0.0704270	+	0.997517i	$0.477564\pi$
$734$	−6.61111e6	−0.452934
$735$	−3.54033e6	−0.241727
$736$	−6.92338e7	−4.71111
$737$	−425475.	−0.0288539
$738$	9.36233e6	0.632766
$739$	−1.35761e7	−0.914459	−0.457229	−	0.889349i	$-0.651158\pi$
$739$	−1.35761e7	−0.914459	−0.457229	+	0.889349i	$0.651158\pi$
$740$	−923686.	−0.0620076
$741$	7.46319e6	0.499320
$742$	4.03501e6	0.269051
$743$	−2.83464e7	−1.88376	−0.941882	−	0.335944i	$-0.890945\pi$
$743$	−2.83464e7	−1.88376	−0.941882	+	0.335944i	$0.890945\pi$
$744$	8.90740e6	0.589955
$745$	9.61116e6	0.634432
$746$	3.50917e7	2.30864
$747$	−2.73164e6	−0.179111
$748$	1.74506e7	1.14040
$749$	−1.11752e6	−0.0727866
$750$	−1.49230e6	−0.0968732
$751$	2.70922e6	0.175285	0.0876425	−	0.996152i	$-0.472067\pi$
$751$	2.70922e6	0.175285	0.0876425	+	0.996152i	$0.472067\pi$
$752$	−4.78373e7	−3.08476
$753$	−9.36659e6	−0.601997
$754$	1.17646e7	0.753614
$755$	−5.53094e6	−0.353127
$756$	−1.92430e6	−0.122453
$757$	−6.54364e6	−0.415030	−0.207515	−	0.978232i	$-0.566538\pi$
$757$	−6.54364e6	−0.415030	−0.207515	+	0.978232i	$0.566538\pi$
$758$	4.74236e7	2.99793
$759$	5.30517e6	0.334268
$760$	3.09527e7	1.94386
$761$	−3.01101e7	−1.88474	−0.942368	−	0.334579i	$-0.891406\pi$
$761$	−3.01101e7	−1.88474	−0.942368	+	0.334579i	$0.891406\pi$
$762$	−7.43611e6	−0.463936
$763$	−4.31084e6	−0.268072
$764$	3.43328e7	2.12802
$765$	3.62280e6	0.223816
$766$	−4.18802e7	−2.57892
$767$	−9.97187e6	−0.612052
$768$	1.22452e6	0.0749143
$769$	1.51986e7	0.926802	0.463401	−	0.886149i	$-0.346629\pi$
$769$	1.51986e7	0.926802	0.463401	+	0.886149i	$0.346629\pi$
$770$	−1.05114e6	−0.0638899
$771$	−1.56382e7	−0.947439
$772$	4.83129e7	2.91756
$773$	1.02126e7	0.614735	0.307367	−	0.951591i	$-0.400552\pi$
$773$	1.02126e7	0.614735	0.307367	+	0.951591i	$0.400552\pi$
$774$	−8.30670e6	−0.498398
$775$	1.19906e6	0.0717113
$776$	−5.32948e7	−3.17710
$777$	−135071.	−0.00802618
$778$	5.04972e7	2.99102
$779$	−2.61407e7	−1.54338
$780$	−6.26696e6	−0.368825
$781$	1.10993e6	0.0651129
$782$	9.24878e7	5.40839
$783$	−2.33906e6	−0.136344
$784$	−4.55497e7	−2.64664
$785$	591841.	0.0342792
$786$	−2.98637e7	−1.72420
$787$	7.04071e6	0.405210	0.202605	−	0.979261i	$-0.435059\pi$
$787$	7.04071e6	0.405210	0.202605	+	0.979261i	$0.435059\pi$
$788$	1.44750e7	0.830428
$789$	−9.12325e6	−0.521743
$790$	−1.89846e7	−1.08226
$791$	−1.85274e6	−0.105286
$792$	5.05611e6	0.286420
$793$	−1.15074e7	−0.649824
$794$	5.98803e7	3.37080
$795$	−2.61272e6	−0.146614
$796$	−3.14737e7	−1.76062
$797$	−1.09198e7	−0.608931	−0.304466	−	0.952523i	$-0.598478\pi$
$797$	−1.09198e7	−0.608931	−0.304466	+	0.952523i	$0.598478\pi$
$798$	7.50566e6	0.417236
$799$	2.95639e7	1.63830
$800$	−8.88233e6	−0.490684
$801$	8.74231e6	0.481443
$802$	2.40471e6	0.132016
$803$	1.01088e7	0.553238
$804$	−2.55115e6	−0.139186
$805$	−3.98796e6	−0.216901
$806$	7.03437e6	0.381406
$807$	−2.07486e7	−1.12151
$808$	5.48876e7	2.95764
$809$	−2.93986e7	−1.57927	−0.789633	−	0.613579i	$-0.789729\pi$
$809$	−2.93986e7	−1.57927	−0.789633	+	0.613579i	$0.789729\pi$
$810$	1.74062e6	0.0932163
$811$	2.65223e7	1.41599	0.707993	−	0.706219i	$-0.249601\pi$
$811$	2.65223e7	1.41599	0.707993	+	0.706219i	$0.249601\pi$
$812$	8.46952e6	0.450784
$813$	−1.36340e7	−0.723433
$814$	588517.	0.0311313
$815$	−1.54905e6	−0.0816905
$816$	4.66107e7	2.45053
$817$	2.31932e7	1.21564
$818$	−1.54229e7	−0.805901
$819$	−916419.	−0.0477402
$820$	2.19508e7	1.14003
$821$	1.98787e7	1.02927	0.514637	−	0.857408i	$-0.327927\pi$
$821$	1.98787e7	1.02927	0.514637	+	0.857408i	$0.327927\pi$
$822$	1.64906e7	0.851252
$823$	2.60096e7	1.33855	0.669273	−	0.743016i	$-0.266606\pi$
$823$	2.60096e7	1.33855	0.669273	+	0.743016i	$0.266606\pi$
$824$	7.58651e7	3.89246
$825$	680625.	0.0348155
$826$	−1.00286e7	−0.511436
$827$	8.95145e6	0.455124	0.227562	−	0.973764i	$-0.426925\pi$
$827$	8.95145e6	0.455124	0.227562	+	0.973764i	$0.426925\pi$
$828$	3.18098e7	1.61245
$829$	1.51055e7	0.763396	0.381698	−	0.924287i	$-0.375340\pi$
$829$	1.51055e7	0.763396	0.381698	+	0.924287i	$0.375340\pi$
$830$	−8.94692e6	−0.450794
$831$	−6.09741e6	−0.306297
$832$	−2.01018e7	−1.00676
$833$	2.81501e7	1.40562
$834$	−2.97565e7	−1.48138
$835$	−887411.	−0.0440462
$836$	−2.34101e7	−1.15848
$837$	−1.39859e6	−0.0690043
$838$	4.93770e7	2.42893
$839$	−2.92902e7	−1.43654	−0.718269	−	0.695766i	$-0.755065\pi$
$839$	−2.92902e7	−1.43654	−0.718269	+	0.695766i	$0.755065\pi$
$840$	−3.80074e6	−0.185853
$841$	−1.02161e7	−0.498076
$842$	−3.40058e7	−1.65300
$843$	2.04087e7	0.989113
$844$	−4.91667e7	−2.37583
$845$	6.29778e6	0.303421
$846$	1.42043e7	0.682331
$847$	479414.	0.0229616
$848$	−3.36151e7	−1.60526
$849$	1.84395e7	0.877972
$850$	1.18657e7	0.563308
$851$	2.23280e6	0.105688
$852$	6.65513e6	0.314093
$853$	−1.37053e7	−0.644936	−0.322468	−	0.946580i	$-0.604513\pi$
$853$	−1.37053e7	−0.644936	−0.322468	+	0.946580i	$0.604513\pi$
$854$	−1.15729e7	−0.542998
$855$	−4.86001e6	−0.227364
$856$	1.76061e7	0.821256
$857$	−2.44782e7	−1.13848	−0.569242	−	0.822170i	$-0.692763\pi$
$857$	−2.44782e7	−1.13848	−0.569242	+	0.822170i	$0.692763\pi$
$858$	3.99293e6	0.185171
$859$	−3.36198e7	−1.55458	−0.777288	−	0.629145i	$-0.783405\pi$
$859$	−3.36198e7	−1.55458	−0.777288	+	0.629145i	$0.783405\pi$
$860$	−1.94757e7	−0.897942
$861$	3.20987e6	0.147563
$862$	−1.56936e7	−0.719376
$863$	−2.86332e6	−0.130871	−0.0654355	−	0.997857i	$-0.520844\pi$
$863$	−2.86332e6	−0.130871	−0.0654355	+	0.997857i	$0.520844\pi$
$864$	1.03604e7	0.472161
$865$	8.74460e6	0.397374
$866$	−7.09302e7	−3.21393
$867$	−1.60271e7	−0.724116
$868$	5.06415e6	0.228143
$869$	8.65869e6	0.388958
$870$	−7.66109e6	−0.343157
$871$	−1.21495e6	−0.0542640
$872$	6.79155e7	3.02467
$873$	8.36803e6	0.371610
$874$	−1.24073e8	−5.49414
$875$	−511634.	−0.0225912
$876$	6.06126e7	2.66872
$877$	−8.28629e6	−0.363799	−0.181899	−	0.983317i	$-0.558224\pi$
$877$	−8.28629e6	−0.363799	−0.181899	+	0.983317i	$0.558224\pi$
$878$	4.57579e6	0.200323
$879$	−3.84620e6	−0.167903
$880$	8.75688e6	0.381191
$881$	−3.94424e7	−1.71208	−0.856040	−	0.516909i	$-0.827082\pi$
$881$	−3.94424e7	−1.71208	−0.856040	+	0.516909i	$0.827082\pi$
$882$	1.35251e7	0.585422
$883$	−3.01012e7	−1.29922	−0.649608	−	0.760269i	$-0.725067\pi$
$883$	−3.01012e7	−1.29922	−0.649608	+	0.760269i	$0.725067\pi$
$884$	4.98303e7	2.14468
$885$	6.49366e6	0.278697
$886$	6.73805e7	2.88370
$887$	−1.06500e7	−0.454509	−0.227255	−	0.973835i	$-0.572975\pi$
$887$	−1.06500e7	−0.454509	−0.227255	+	0.973835i	$0.572975\pi$
$888$	2.12798e6	0.0905599
$889$	−2.54946e6	−0.108192
$890$	2.86336e7	1.21172
$891$	−793881.	−0.0335013
$892$	−5.01513e7	−2.11043
$893$	−3.96602e7	−1.66428
$894$	−3.67175e7	−1.53649
$895$	−6.88792e6	−0.287429
$896$	−5.32480e6	−0.221581
$897$	1.51490e7	0.628640
$898$	1.66939e7	0.690824
$899$	6.15568e6	0.254025
$900$	4.08103e6	0.167944
$901$	2.07744e7	0.852545
$902$	−1.39857e7	−0.572358
$903$	−2.84794e6	−0.116228
$904$	2.91891e7	1.18795
$905$	1.85739e7	0.753844
$906$	2.11298e7	0.855215
$907$	1.66521e7	0.672126	0.336063	−	0.941839i	$-0.390904\pi$
$907$	1.66521e7	0.672126	0.336063	+	0.941839i	$0.390904\pi$
$908$	−5.26748e7	−2.12026
$909$	−8.61812e6	−0.345942
$910$	−3.00153e6	−0.120154
$911$	−1.47408e7	−0.588472	−0.294236	−	0.955733i	$-0.595065\pi$
$911$	−1.47408e7	−0.588472	−0.294236	+	0.955733i	$0.595065\pi$
$912$	−6.25287e7	−2.48939
$913$	4.08060e6	0.162012
$914$	1.99879e7	0.791409
$915$	7.49362e6	0.295896
$916$	−7.05203e7	−2.77700
$917$	−1.02387e7	−0.402090
$918$	−1.38402e7	−0.542043
$919$	−1.39478e7	−0.544776	−0.272388	−	0.962188i	$-0.587813\pi$
$919$	−1.39478e7	−0.544776	−0.272388	+	0.962188i	$0.587813\pi$
$920$	6.28287e7	2.44731
$921$	−1.93626e7	−0.752168
$922$	5.28477e7	2.04738
$923$	3.16941e6	0.122454
$924$	2.87457e6	0.110762
$925$	286457.	0.0110079
$926$	7.25376e7	2.77994
$927$	−1.19119e7	−0.455283
$928$	−4.55996e7	−1.73816
$929$	2.62001e7	0.996008	0.498004	−	0.867175i	$-0.334066\pi$
$929$	2.62001e7	0.996008	0.498004	+	0.867175i	$0.334066\pi$
$930$	−4.58077e6	−0.173673
$931$	−3.77636e7	−1.42790
$932$	6.82951e7	2.57543
$933$	5.08934e6	0.191407
$934$	8.09943e7	3.03800
$935$	−5.41183e6	−0.202449
$936$	1.44378e7	0.538656
$937$	−3.44098e7	−1.28037	−0.640183	−	0.768223i	$-0.721141\pi$
$937$	−3.44098e7	−1.28037	−0.640183	+	0.768223i	$0.721141\pi$
$938$	−1.22186e6	−0.0453435
$939$	1.00581e7	0.372266
$940$	3.33033e7	1.22933
$941$	−1.78999e7	−0.658985	−0.329492	−	0.944158i	$-0.606878\pi$
$941$	−1.78999e7	−0.658985	−0.329492	+	0.944158i	$0.606878\pi$
$942$	−2.26101e6	−0.0830185
$943$	−5.30611e7	−1.94311
$944$	8.35471e7	3.05142
$945$	596770.	0.0217384
$946$	1.24088e7	0.450818
$947$	−9.39933e6	−0.340582	−0.170291	−	0.985394i	$-0.554471\pi$
$947$	−9.39933e6	−0.340582	−0.170291	+	0.985394i	$0.554471\pi$
$948$	5.19176e7	1.87626
$949$	2.88659e7	1.04045
$950$	−1.59179e7	−0.572239
$951$	−1.36125e6	−0.0488074
$952$	3.02208e7	1.08072
$953$	6.31241e6	0.225145	0.112573	−	0.993643i	$-0.464091\pi$
$953$	6.31241e6	0.225145	0.112573	+	0.993643i	$0.464091\pi$
$954$	9.98136e6	0.355074
$955$	−1.06474e7	−0.377777
$956$	−3.99655e7	−1.41430
$957$	3.49415e6	0.123328
$958$	−9.34942e7	−3.29133
$959$	5.65380e6	0.198515
$960$	1.30903e7	0.458428
$961$	−2.49485e7	−0.871437
$962$	1.68052e6	0.0585471
$963$	−2.76440e6	−0.0960585
$964$	−1.36726e8	−4.73871
$965$	−1.49830e7	−0.517940
$966$	1.52352e7	0.525297
$967$	−1.33151e7	−0.457909	−0.228954	−	0.973437i	$-0.573531\pi$
$967$	−1.33151e7	−0.457909	−0.228954	+	0.973437i	$0.573531\pi$
$968$	−7.55296e6	−0.259077
$969$	3.86433e7	1.32210
$970$	2.74077e7	0.935283
$971$	−4.55735e7	−1.55119	−0.775594	−	0.631232i	$-0.782549\pi$
$971$	−4.55735e7	−1.55119	−0.775594	+	0.631232i	$0.782549\pi$
$972$	−4.76012e6	−0.161604
$973$	−1.02020e7	−0.345464
$974$	−5.40598e7	−1.82590
$975$	1.94353e6	0.0654757
$976$	9.64125e7	3.23973
$977$	−3.11207e7	−1.04307	−0.521535	−	0.853230i	$-0.674640\pi$
$977$	−3.11207e7	−1.04307	−0.521535	+	0.853230i	$0.674640\pi$
$978$	5.91783e6	0.197841
$979$	−1.30595e7	−0.435482
$980$	3.17107e7	1.05473
$981$	−1.06637e7	−0.353781
$982$	3.48366e7	1.15281
$983$	2.79890e6	0.0923856	0.0461928	−	0.998933i	$-0.485291\pi$
$983$	2.79890e6	0.0923856	0.0461928	+	0.998933i	$0.485291\pi$
$984$	−5.05701e7	−1.66497
$985$	−4.48903e6	−0.147422
$986$	6.09154e7	1.99542
$987$	4.86995e6	0.159122
$988$	−6.68477e7	−2.17868
$989$	4.70783e7	1.53049
$990$	−2.60019e6	−0.0843173
$991$	−4.23867e6	−0.137103	−0.0685513	−	0.997648i	$-0.521838\pi$
$991$	−4.23867e6	−0.137103	−0.0685513	+	0.997648i	$0.521838\pi$
$992$	−2.72652e7	−0.879690
$993$	−1.31590e7	−0.423495
$994$	3.18745e6	0.102324
$995$	9.76075e6	0.312554
$996$	2.44673e7	0.781517
$997$	177060.	0.00564136	0.00282068	−	0.999996i	$-0.499102\pi$
$997$	177060.	0.00564136	0.00282068	+	0.999996i	$0.499102\pi$
$998$	−3.41635e7	−1.08577
$999$	−334123.	−0.0105924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.g.1.1	✓	5
3.2	odd	2		495.6.a.i.1.5		5
5.4	even	2		825.6.a.k.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.g.1.1	✓	5	1.1	even	1	trivial
495.6.a.i.1.5		5	3.2	odd	2
825.6.a.k.1.5		5	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)

\(f(q)\)	\(=\)	\(q-10.6119 q^{2} -9.00000 q^{3} +80.6130 q^{4} -25.0000 q^{5} +95.5073 q^{6} +32.7446 q^{7} -515.877 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-10.6119 q^{2} -9.00000 q^{3} +80.6130 q^{4} -25.0000 q^{5} +95.5073 q^{6} +32.7446 q^{7} -515.877 q^{8} +81.0000 q^{9} +265.298 q^{10} -121.000 q^{11} -725.517 q^{12} -345.517 q^{13} -347.483 q^{14} +225.000 q^{15} +2894.84 q^{16} -1789.04 q^{17} -859.566 q^{18} +2400.01 q^{19} -2015.32 q^{20} -294.701 q^{21} +1284.04 q^{22} +4871.60 q^{23} +4642.90 q^{24} +625.000 q^{25} +3666.60 q^{26} -729.000 q^{27} +2639.64 q^{28} +3208.59 q^{29} -2387.68 q^{30} +1918.50 q^{31} -14211.7 q^{32} +1089.00 q^{33} +18985.1 q^{34} -818.615 q^{35} +6529.65 q^{36} +458.331 q^{37} -25468.7 q^{38} +3109.65 q^{39} +12896.9 q^{40} -10891.9 q^{41} +3127.35 q^{42} +9663.83 q^{43} -9754.17 q^{44} -2025.00 q^{45} -51697.0 q^{46} -16525.0 q^{47} -26053.5 q^{48} -15734.8 q^{49} -6632.45 q^{50} +16101.3 q^{51} -27853.1 q^{52} -11612.1 q^{53} +7736.09 q^{54} +3025.00 q^{55} -16892.2 q^{56} -21600.1 q^{57} -34049.3 q^{58} +28860.7 q^{59} +18137.9 q^{60} +33305.0 q^{61} -20359.0 q^{62} +2652.31 q^{63} +58179.0 q^{64} +8637.92 q^{65} -11556.4 q^{66} +3516.32 q^{67} -144220. q^{68} -43844.4 q^{69} +8687.08 q^{70} -9172.96 q^{71} -41786.1 q^{72} -83544.1 q^{73} -4863.78 q^{74} -5625.00 q^{75} +193472. q^{76} -3962.10 q^{77} -32999.4 q^{78} -71559.4 q^{79} -72370.9 q^{80} +6561.00 q^{81} +115584. q^{82} -33724.0 q^{83} -23756.8 q^{84} +44725.9 q^{85} -102552. q^{86} -28877.3 q^{87} +62421.2 q^{88} +107930. q^{89} +21489.2 q^{90} -11313.8 q^{91} +392714. q^{92} -17266.5 q^{93} +175362. q^{94} -60000.2 q^{95} +127906. q^{96} +103309. q^{97} +166976. q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9} + 25 q^{10} - 605 q^{11} - 1143 q^{12} - 926 q^{13} + 368 q^{14} + 1125 q^{15} + 1891 q^{16} - 246 q^{17} - 81 q^{18} + 3420 q^{19} - 3175 q^{20} - 1044 q^{21} + 121 q^{22} - 4244 q^{23} + 1377 q^{24} + 3125 q^{25} - 8862 q^{26} - 3645 q^{27} - 4904 q^{28} - 2922 q^{29} - 225 q^{30} - 6112 q^{31} - 24757 q^{32} + 5445 q^{33} + 10866 q^{34} - 2900 q^{35} + 10287 q^{36} + 6654 q^{37} - 45692 q^{38} + 8334 q^{39} + 3825 q^{40} - 14934 q^{41} - 3312 q^{42} + 10804 q^{43} - 15367 q^{44} - 10125 q^{45} - 101500 q^{46} - 41460 q^{47} - 17019 q^{48} - 12099 q^{49} - 625 q^{50} + 2214 q^{51} - 97742 q^{52} - 62398 q^{53} + 729 q^{54} + 15125 q^{55} - 74368 q^{56} - 30780 q^{57} - 27822 q^{58} + 8524 q^{59} + 28575 q^{60} + 59010 q^{61} - 142624 q^{62} + 9396 q^{63} + 13799 q^{64} + 23150 q^{65} - 1089 q^{66} - 15772 q^{67} - 83686 q^{68} + 38196 q^{69} - 9200 q^{70} + 88124 q^{71} - 12393 q^{72} - 118358 q^{73} + 67194 q^{74} - 28125 q^{75} + 100668 q^{76} - 14036 q^{77} + 79758 q^{78} + 57324 q^{79} - 47275 q^{80} + 32805 q^{81} + 29102 q^{82} - 7268 q^{83} + 44136 q^{84} + 6150 q^{85} - 35288 q^{86} + 26298 q^{87} + 18513 q^{88} + 72978 q^{89} + 2025 q^{90} - 1464 q^{91} + 62148 q^{92} + 55008 q^{93} + 344836 q^{94} - 85500 q^{95} + 222813 q^{96} - 59174 q^{97} + 272767 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9 + 25 * q^10 - 605 * q^11 - 1143 * q^12 - 926 * q^13 + 368 * q^14 + 1125 * q^15 + 1891 * q^16 - 246 * q^17 - 81 * q^18 + 3420 * q^19 - 3175 * q^20 - 1044 * q^21 + 121 * q^22 - 4244 * q^23 + 1377 * q^24 + 3125 * q^25 - 8862 * q^26 - 3645 * q^27 - 4904 * q^28 - 2922 * q^29 - 225 * q^30 - 6112 * q^31 - 24757 * q^32 + 5445 * q^33 + 10866 * q^34 - 2900 * q^35 + 10287 * q^36 + 6654 * q^37 - 45692 * q^38 + 8334 * q^39 + 3825 * q^40 - 14934 * q^41 - 3312 * q^42 + 10804 * q^43 - 15367 * q^44 - 10125 * q^45 - 101500 * q^46 - 41460 * q^47 - 17019 * q^48 - 12099 * q^49 - 625 * q^50 + 2214 * q^51 - 97742 * q^52 - 62398 * q^53 + 729 * q^54 + 15125 * q^55 - 74368 * q^56 - 30780 * q^57 - 27822 * q^58 + 8524 * q^59 + 28575 * q^60 + 59010 * q^61 - 142624 * q^62 + 9396 * q^63 + 13799 * q^64 + 23150 * q^65 - 1089 * q^66 - 15772 * q^67 - 83686 * q^68 + 38196 * q^69 - 9200 * q^70 + 88124 * q^71 - 12393 * q^72 - 118358 * q^73 + 67194 * q^74 - 28125 * q^75 + 100668 * q^76 - 14036 * q^77 + 79758 * q^78 + 57324 * q^79 - 47275 * q^80 + 32805 * q^81 + 29102 * q^82 - 7268 * q^83 + 44136 * q^84 + 6150 * q^85 - 35288 * q^86 + 26298 * q^87 + 18513 * q^88 + 72978 * q^89 + 2025 * q^90 - 1464 * q^91 + 62148 * q^92 + 55008 * q^93 + 344836 * q^94 - 85500 * q^95 + 222813 * q^96 - 59174 * q^97 + 272767 * q^98 - 49005 * q^99

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