LMFDB - Embedded newform 165.6.a.d.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:	$0$
Dimension:	$3$
Coefficient field:	3.3.788.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 7x - 3 $ x^3 - x^2 - 7*x - 3
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			$-0.476452$ 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)

$f(q)$	$=$	$q-5.64018 q^{2} -9.00000 q^{3} -0.188384 q^{4} +25.0000 q^{5} +50.7616 q^{6} +145.021 q^{7} +181.548 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-5.64018 q^{2} -9.00000 q^{3} -0.188384 q^{4} +25.0000 q^{5} +50.7616 q^{6} +145.021 q^{7} +181.548 q^{8} +81.0000 q^{9} -141.004 q^{10} -121.000 q^{11} +1.69545 q^{12} -69.9067 q^{13} -817.946 q^{14} -225.000 q^{15} -1017.94 q^{16} -500.495 q^{17} -456.854 q^{18} -670.685 q^{19} -4.70959 q^{20} -1305.19 q^{21} +682.462 q^{22} +791.025 q^{23} -1633.93 q^{24} +625.000 q^{25} +394.287 q^{26} -729.000 q^{27} -27.3196 q^{28} +1545.91 q^{29} +1269.04 q^{30} +2703.09 q^{31} -68.2013 q^{32} +1089.00 q^{33} +2822.88 q^{34} +3625.53 q^{35} -15.2591 q^{36} -2667.13 q^{37} +3782.78 q^{38} +629.161 q^{39} +4538.71 q^{40} +9622.09 q^{41} +7361.51 q^{42} -6681.57 q^{43} +22.7944 q^{44} +2025.00 q^{45} -4461.52 q^{46} -1167.06 q^{47} +9161.43 q^{48} +4224.17 q^{49} -3525.11 q^{50} +4504.46 q^{51} +13.1693 q^{52} +28872.9 q^{53} +4111.69 q^{54} -3025.00 q^{55} +26328.4 q^{56} +6036.16 q^{57} -8719.22 q^{58} +23599.3 q^{59} +42.3863 q^{60} +17601.3 q^{61} -15245.9 q^{62} +11746.7 q^{63} +32958.6 q^{64} -1747.67 q^{65} -6142.15 q^{66} +16501.5 q^{67} +94.2851 q^{68} -7119.22 q^{69} -20448.6 q^{70} +72059.4 q^{71} +14705.4 q^{72} -45480.8 q^{73} +15043.1 q^{74} -5625.00 q^{75} +126.346 q^{76} -17547.6 q^{77} -3548.58 q^{78} -21688.7 q^{79} -25448.4 q^{80} +6561.00 q^{81} -54270.3 q^{82} +6934.34 q^{83} +245.877 q^{84} -12512.4 q^{85} +37685.2 q^{86} -13913.2 q^{87} -21967.3 q^{88} +42779.8 q^{89} -11421.4 q^{90} -10138.0 q^{91} -149.016 q^{92} -24327.8 q^{93} +6582.41 q^{94} -16767.1 q^{95} +613.812 q^{96} -20992.6 q^{97} -23825.1 q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9	\( 3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} - 363 q^{11} + 180 q^{12} - 546 q^{13} - 8 q^{14} - 675 q^{15} - 1360 q^{16} - 314 q^{17} + 162 q^{18} + 1808 q^{19} - 500 q^{20} - 1368 q^{21} - 242 q^{22} + 4288 q^{23} + 216 q^{24} + 1875 q^{25} + 812 q^{26} - 2187 q^{27} + 5888 q^{28} + 5582 q^{29} - 450 q^{30} + 6328 q^{31} - 736 q^{32} + 3267 q^{33} + 11596 q^{34} + 3800 q^{35} - 1620 q^{36} + 16866 q^{37} + 9584 q^{38} + 4914 q^{39} - 600 q^{40} + 23282 q^{41} + 72 q^{42} + 20572 q^{43} + 2420 q^{44} + 6075 q^{45} + 16592 q^{46} + 3432 q^{47} + 12240 q^{48} + 11531 q^{49} + 1250 q^{50} + 2826 q^{51} + 21816 q^{52} + 16138 q^{53} - 1458 q^{54} - 9075 q^{55} + 15648 q^{56} - 16272 q^{57} + 17460 q^{58} + 21972 q^{59} + 4500 q^{60} + 8322 q^{61} + 5056 q^{62} + 12312 q^{63} + 22208 q^{64} - 13650 q^{65} + 2178 q^{66} - 84332 q^{67} + 59832 q^{68} - 38592 q^{69} - 200 q^{70} + 50528 q^{71} - 1944 q^{72} - 53838 q^{73} + 79212 q^{74} - 16875 q^{75} - 52448 q^{76} - 18392 q^{77} - 7308 q^{78} + 6364 q^{79} - 34000 q^{80} + 19683 q^{81} - 68020 q^{82} + 96272 q^{83} - 52992 q^{84} - 7850 q^{85} + 143152 q^{86} - 50238 q^{87} + 2904 q^{88} - 38938 q^{89} + 4050 q^{90} + 104968 q^{91} + 24000 q^{92} - 56952 q^{93} + 49088 q^{94} + 45200 q^{95} + 6624 q^{96} - 103242 q^{97} + 9554 q^{98} - 29403 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 - 363 * q^11 + 180 * q^12 - 546 * q^13 - 8 * q^14 - 675 * q^15 - 1360 * q^16 - 314 * q^17 + 162 * q^18 + 1808 * q^19 - 500 * q^20 - 1368 * q^21 - 242 * q^22 + 4288 * q^23 + 216 * q^24 + 1875 * q^25 + 812 * q^26 - 2187 * q^27 + 5888 * q^28 + 5582 * q^29 - 450 * q^30 + 6328 * q^31 - 736 * q^32 + 3267 * q^33 + 11596 * q^34 + 3800 * q^35 - 1620 * q^36 + 16866 * q^37 + 9584 * q^38 + 4914 * q^39 - 600 * q^40 + 23282 * q^41 + 72 * q^42 + 20572 * q^43 + 2420 * q^44 + 6075 * q^45 + 16592 * q^46 + 3432 * q^47 + 12240 * q^48 + 11531 * q^49 + 1250 * q^50 + 2826 * q^51 + 21816 * q^52 + 16138 * q^53 - 1458 * q^54 - 9075 * q^55 + 15648 * q^56 - 16272 * q^57 + 17460 * q^58 + 21972 * q^59 + 4500 * q^60 + 8322 * q^61 + 5056 * q^62 + 12312 * q^63 + 22208 * q^64 - 13650 * q^65 + 2178 * q^66 - 84332 * q^67 + 59832 * q^68 - 38592 * q^69 - 200 * q^70 + 50528 * q^71 - 1944 * q^72 - 53838 * q^73 + 79212 * q^74 - 16875 * q^75 - 52448 * q^76 - 18392 * q^77 - 7308 * q^78 + 6364 * q^79 - 34000 * q^80 + 19683 * q^81 - 68020 * q^82 + 96272 * q^83 - 52992 * q^84 - 7850 * q^85 + 143152 * q^86 - 50238 * q^87 + 2904 * q^88 - 38938 * q^89 + 4050 * q^90 + 104968 * q^91 + 24000 * q^92 - 56952 * q^93 + 49088 * q^94 + 45200 * q^95 + 6624 * q^96 - 103242 * q^97 + 9554 * 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 $

$2$	−5.64018	−0.997052	−0.498526	−	0.866875i	$-0.666125\pi$
$2$	−5.64018	−0.997052	−0.498526	+	0.866875i	$0.666125\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−0.188384	−0.00588699
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	50.7616	0.575648
$7$	145.021	1.11863	0.559315	−	0.828955i	$-0.311064\pi$
$7$	145.021	1.11863	0.559315	+	0.828955i	$0.311064\pi$
$8$	181.548	1.00292
$9$	81.0000	0.333333
$10$	−141.004	−0.445895
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	1.69545	0.00339886
$13$	−69.9067	−0.114726	−0.0573628	−	0.998353i	$-0.518269\pi$
$13$	−69.9067	−0.114726	−0.0573628	+	0.998353i	$0.518269\pi$
$14$	−817.946	−1.11533
$15$	−225.000	−0.258199
$16$	−1017.94	−0.994078
$17$	−500.495	−0.420027	−0.210014	−	0.977698i	$-0.567351\pi$
$17$	−500.495	−0.420027	−0.210014	+	0.977698i	$0.567351\pi$
$18$	−456.854	−0.332351
$19$	−670.685	−0.426221	−0.213110	−	0.977028i	$-0.568359\pi$
$19$	−670.685	−0.426221	−0.213110	+	0.977028i	$0.568359\pi$
$20$	−4.70959	−0.00263274
$21$	−1305.19	−0.645842
$22$	682.462	0.300623
$23$	791.025	0.311796	0.155898	−	0.987773i	$-0.450173\pi$
$23$	791.025	0.311796	0.155898	+	0.987773i	$0.450173\pi$
$24$	−1633.93	−0.579037
$25$	625.000	0.200000
$26$	394.287	0.114388
$27$	−729.000	−0.192450
$28$	−27.3196	−0.00658537
$29$	1545.91	0.341342	0.170671	−	0.985328i	$-0.445406\pi$
$29$	1545.91	0.341342	0.170671	+	0.985328i	$0.445406\pi$
$30$	1269.04	0.257438
$31$	2703.09	0.505191	0.252596	−	0.967572i	$-0.418716\pi$
$31$	2703.09	0.505191	0.252596	+	0.967572i	$0.418716\pi$
$32$	−68.2013	−0.0117738
$33$	1089.00	0.174078
$34$	2822.88	0.418789
$35$	3625.53	0.500267
$36$	−15.2591	−0.00196233
$37$	−2667.13	−0.320287	−0.160144	−	0.987094i	$-0.551196\pi$
$37$	−2667.13	−0.320287	−0.160144	+	0.987094i	$0.551196\pi$
$38$	3782.78	0.424964
$39$	629.161	0.0662369
$40$	4538.71	0.448520
$41$	9622.09	0.893942	0.446971	−	0.894548i	$-0.352503\pi$
$41$	9622.09	0.893942	0.446971	+	0.894548i	$0.352503\pi$
$42$	7361.51	0.643938
$43$	−6681.57	−0.551070	−0.275535	−	0.961291i	$-0.588855\pi$
$43$	−6681.57	−0.551070	−0.275535	+	0.961291i	$0.588855\pi$
$44$	22.7944	0.00177499
$45$	2025.00	0.149071
$46$	−4461.52	−0.310877
$47$	−1167.06	−0.0770632	−0.0385316	−	0.999257i	$-0.512268\pi$
$47$	−1167.06	−0.0770632	−0.0385316	+	0.999257i	$0.512268\pi$
$48$	9161.43	0.573931
$49$	4224.17	0.251334
$50$	−3525.11	−0.199410
$51$	4504.46	0.242503
$52$	13.1693	0.000675389 0
$53$	28872.9	1.41189	0.705944	−	0.708268i	$-0.250523\pi$
$53$	28872.9	1.41189	0.705944	+	0.708268i	$0.250523\pi$
$54$	4111.69	0.191883
$55$	−3025.00	−0.134840
$56$	26328.4	1.12190
$57$	6036.16	0.246079
$58$	−8719.22	−0.340336
$59$	23599.3	0.882610	0.441305	−	0.897357i	$-0.354516\pi$
$59$	23599.3	0.882610	0.441305	+	0.897357i	$0.354516\pi$
$60$	42.3863	0.00152001
$61$	17601.3	0.605648	0.302824	−	0.953046i	$-0.402070\pi$
$61$	17601.3	0.605648	0.302824	+	0.953046i	$0.402070\pi$
$62$	−15245.9	−0.503702
$63$	11746.7	0.372877
$64$	32958.6	1.00582
$65$	−1747.67	−0.0513069
$66$	−6142.15	−0.173565
$67$	16501.5	0.449092	0.224546	−	0.974463i	$-0.427910\pi$
$67$	16501.5	0.449092	0.224546	+	0.974463i	$0.427910\pi$
$68$	94.2851	0.00247270
$69$	−7119.22	−0.180016
$70$	−20448.6	−0.498792
$71$	72059.4	1.69646	0.848232	−	0.529625i	$-0.177667\pi$
$71$	72059.4	1.69646	0.848232	+	0.529625i	$0.177667\pi$
$72$	14705.4	0.334307
$73$	−45480.8	−0.998898	−0.499449	−	0.866343i	$-0.666464\pi$
$73$	−45480.8	−0.998898	−0.499449	+	0.866343i	$0.666464\pi$
$74$	15043.1	0.319343
$75$	−5625.00	−0.115470
$76$	126.346	0.00250916
$77$	−17547.6	−0.337280
$78$	−3548.58	−0.0660417
$79$	−21688.7	−0.390990	−0.195495	−	0.980705i	$-0.562631\pi$
$79$	−21688.7	−0.390990	−0.195495	+	0.980705i	$0.562631\pi$
$80$	−25448.4	−0.444565
$81$	6561.00	0.111111
$82$	−54270.3	−0.891307
$83$	6934.34	0.110487	0.0552434	−	0.998473i	$-0.482407\pi$
$83$	6934.34	0.110487	0.0552434	+	0.998473i	$0.482407\pi$
$84$	245.877	0.00380206
$85$	−12512.4	−0.187842
$86$	37685.2	0.549446
$87$	−13913.2	−0.197074
$88$	−21967.3	−0.302392
$89$	42779.8	0.572484	0.286242	−	0.958157i	$-0.407594\pi$
$89$	42779.8	0.572484	0.286242	+	0.958157i	$0.407594\pi$
$90$	−11421.4	−0.148632
$91$	−10138.0	−0.128336
$92$	−149.016	−0.00183554
$93$	−24327.8	−0.291672
$94$	6582.41	0.0768361
$95$	−16767.1	−0.190612
$96$	613.812	0.00679762
$97$	−20992.6	−0.226535	−0.113268	−	0.993565i	$-0.536132\pi$
$97$	−20992.6	−0.226535	−0.113268	+	0.993565i	$0.536132\pi$
$98$	−23825.1	−0.250593
$99$	−9801.00	−0.100504
$100$	−117.740	−0.00117740
$101$	189654.	1.84995	0.924973	−	0.380033i	$-0.124087\pi$
$101$	189654.	1.84995	0.924973	+	0.380033i	$0.124087\pi$
$102$	−25405.9	−0.241788
$103$	−160899.	−1.49438	−0.747190	−	0.664611i	$-0.768597\pi$
$103$	−160899.	−1.49438	−0.747190	+	0.664611i	$0.768597\pi$
$104$	−12691.4	−0.115061
$105$	−32629.8	−0.288829
$106$	−162848.	−1.40773
$107$	113244.	0.956216	0.478108	−	0.878301i	$-0.341323\pi$
$107$	113244.	0.956216	0.478108	+	0.878301i	$0.341323\pi$
$108$	137.332	0.00113295
$109$	−1768.32	−0.0142559	−0.00712797	−	0.999975i	$-0.502269\pi$
$109$	−1768.32	−0.0142559	−0.00712797	+	0.999975i	$0.502269\pi$
$110$	17061.5	0.134442
$111$	24004.1	0.184918
$112$	−147622.	−1.11201
$113$	−77273.2	−0.569289	−0.284645	−	0.958633i	$-0.591876\pi$
$113$	−77273.2	−0.569289	−0.284645	+	0.958633i	$0.591876\pi$
$114$	−34045.0	−0.245353
$115$	19775.6	0.139439
$116$	−291.224	−0.00200948
$117$	−5662.45	−0.0382419
$118$	−133104.	−0.880008
$119$	−72582.5	−0.469855
$120$	−40848.4	−0.258953
$121$	14641.0	0.0909091
$122$	−99274.6	−0.603863
$123$	−86598.8	−0.516118
$124$	−509.218	−0.00297406
$125$	15625.0	0.0894427
$126$	−66253.6	−0.371778
$127$	104707.	0.576058	0.288029	−	0.957622i	$-0.407000\pi$
$127$	104707.	0.576058	0.288029	+	0.957622i	$0.407000\pi$
$128$	−183710.	−0.991079
$129$	60134.1	0.318161
$130$	9857.16	0.0511556
$131$	101248.	0.515476	0.257738	−	0.966215i	$-0.417023\pi$
$131$	101248.	0.515476	0.257738	+	0.966215i	$0.417023\pi$
$132$	−205.150	−0.00102479
$133$	−97263.6	−0.476783
$134$	−93071.2	−0.447768
$135$	−18225.0	−0.0860663
$136$	−90864.0	−0.421255
$137$	128311.	0.584068	0.292034	−	0.956408i	$-0.405668\pi$
$137$	128311.	0.584068	0.292034	+	0.956408i	$0.405668\pi$
$138$	40153.7	0.179485
$139$	161754.	0.710100	0.355050	−	0.934847i	$-0.384464\pi$
$139$	161754.	0.710100	0.355050	+	0.934847i	$0.384464\pi$
$140$	−682.991	−0.00294507
$141$	10503.5	0.0444925
$142$	−406428.	−1.69146
$143$	8458.72	0.0345911
$144$	−82452.8	−0.331359
$145$	38647.8	0.152653
$146$	256520.	0.995954
$147$	−38017.5	−0.145108
$148$	502.443	0.00188553
$149$	−404421.	−1.49234	−0.746170	−	0.665755i	$-0.768110\pi$
$149$	−404421.	−1.49234	−0.746170	+	0.665755i	$0.768110\pi$
$150$	31726.0	0.115130
$151$	416180.	1.48538	0.742692	−	0.669633i	$-0.233549\pi$
$151$	416180.	1.48538	0.742692	+	0.669633i	$0.233549\pi$
$152$	−121762.	−0.427466
$153$	−40540.1	−0.140009
$154$	98971.5	0.336286
$155$	67577.2	0.225929
$156$	−118.524	−0.000389936 0
$157$	332834.	1.07765	0.538827	−	0.842417i	$-0.318868\pi$
$157$	332834.	1.07765	0.538827	+	0.842417i	$0.318868\pi$
$158$	122328.	0.389837
$159$	−259856.	−0.815154
$160$	−1705.03	−0.00526542
$161$	114715.	0.348785
$162$	−37005.2	−0.110784
$163$	−14764.9	−0.0435272	−0.0217636	−	0.999763i	$-0.506928\pi$
$163$	−14764.9	−0.0435272	−0.0217636	+	0.999763i	$0.506928\pi$
$164$	−1812.64	−0.00526263
$165$	27225.0	0.0778499
$166$	−39110.9	−0.110161
$167$	169960.	0.471579	0.235790	−	0.971804i	$-0.424232\pi$
$167$	169960.	0.471579	0.235790	+	0.971804i	$0.424232\pi$
$168$	−236955.	−0.647729
$169$	−366406.	−0.986838
$170$	70572.1	0.187288
$171$	−54325.5	−0.142074
$172$	1258.70	0.00324415
$173$	725869.	1.84392	0.921962	−	0.387281i	$-0.126586\pi$
$173$	725869.	1.84392	0.921962	+	0.387281i	$0.126586\pi$
$174$	78472.9	0.196493
$175$	90638.3	0.223726
$176$	123170.	0.299726
$177$	−212394.	−0.509575
$178$	−241286.	−0.570797
$179$	69311.4	0.161686	0.0808429	−	0.996727i	$-0.474239\pi$
$179$	69311.4	0.161686	0.0808429	+	0.996727i	$0.474239\pi$
$180$	−381.477	−0.000877581 0
$181$	790396.	1.79328	0.896640	−	0.442761i	$-0.146001\pi$
$181$	790396.	1.79328	0.896640	+	0.442761i	$0.146001\pi$
$182$	57179.9	0.127957
$183$	−158412.	−0.349671
$184$	143609.	0.312707
$185$	−66678.2	−0.143237
$186$	137213.	0.290813
$187$	60559.9	0.126643
$188$	219.854	0.000453670 0
$189$	−105721.	−0.215281
$190$	94569.6	0.190050
$191$	418979.	0.831015	0.415507	−	0.909590i	$-0.363604\pi$
$191$	418979.	0.831015	0.415507	+	0.909590i	$0.363604\pi$
$192$	−296628.	−0.580709
$193$	265524.	0.513110	0.256555	−	0.966530i	$-0.417413\pi$
$193$	265524.	0.513110	0.256555	+	0.966530i	$0.417413\pi$
$194$	118402.	0.225868
$195$	15729.0	0.0296220
$196$	−795.765	−0.00147960
$197$	−87754.1	−0.161102	−0.0805512	−	0.996750i	$-0.525668\pi$
$197$	−87754.1	−0.161102	−0.0805512	+	0.996750i	$0.525668\pi$
$198$	55279.4	0.100208
$199$	380988.	0.681992	0.340996	−	0.940065i	$-0.389236\pi$
$199$	380988.	0.681992	0.340996	+	0.940065i	$0.389236\pi$
$200$	113468.	0.200584
$201$	−148513.	−0.259284
$202$	−1.06968e6	−1.84449
$203$	224190.	0.381835
$204$	−848.566	−0.00142761
$205$	240552.	0.399783
$206$	907501.	1.48997
$207$	64073.0	0.103932
$208$	71160.6	0.114046
$209$	81152.9	0.128510
$210$	184038.	0.287978
$211$	624404.	0.965516	0.482758	−	0.875754i	$-0.339635\pi$
$211$	624404.	0.965516	0.482758	+	0.875754i	$0.339635\pi$
$212$	−5439.18	−0.00831177
$213$	−648534.	−0.979454
$214$	−638717.	−0.953398
$215$	−167039.	−0.246446
$216$	−132349.	−0.193012
$217$	392005.	0.565123
$218$	9973.67	0.0142139
$219$	409328.	0.576714
$220$	569.861	0.000793802 0
$221$	34988.0	0.0481879
$222$	−135388.	−0.184373
$223$	−658298.	−0.886462	−0.443231	−	0.896407i	$-0.646168\pi$
$223$	−658298.	−0.886462	−0.443231	+	0.896407i	$0.646168\pi$
$224$	−9890.64	−0.0131706
$225$	50625.0	0.0666667
$226$	435835.	0.567611
$227$	219954.	0.283313	0.141657	−	0.989916i	$-0.454757\pi$
$227$	219954.	0.283313	0.141657	+	0.989916i	$0.454757\pi$
$228$	−1137.11	−0.00144866
$229$	−313324.	−0.394825	−0.197412	−	0.980321i	$-0.563254\pi$
$229$	−313324.	−0.394825	−0.197412	+	0.980321i	$0.563254\pi$
$230$	−111538.	−0.139028
$231$	157928.	0.194729
$232$	280657.	0.342339
$233$	−1.01608e6	−1.22614	−0.613069	−	0.790030i	$-0.710065\pi$
$233$	−1.01608e6	−1.22614	−0.613069	+	0.790030i	$0.710065\pi$
$234$	31937.2	0.0381292
$235$	−29176.4	−0.0344637
$236$	−4445.72	−0.00519592
$237$	195198.	0.225738
$238$	409378.	0.468470
$239$	762420.	0.863375	0.431688	−	0.902023i	$-0.357918\pi$
$239$	762420.	0.863375	0.431688	+	0.902023i	$0.357918\pi$
$240$	229036.	0.256670
$241$	−22909.2	−0.0254078	−0.0127039	−	0.999919i	$-0.504044\pi$
$241$	−22909.2	−0.0254078	−0.0127039	+	0.999919i	$0.504044\pi$
$242$	−82577.9	−0.0906411
$243$	−59049.0	−0.0641500
$244$	−3315.80	−0.00356545
$245$	105604.	0.112400
$246$	488433.	0.514596
$247$	46885.4	0.0488985
$248$	490741.	0.506668
$249$	−62409.1	−0.0637895
$250$	−88127.8	−0.0891791
$251$	−691159.	−0.692458	−0.346229	−	0.938150i	$-0.612538\pi$
$251$	−691159.	−0.692458	−0.346229	+	0.938150i	$0.612538\pi$
$252$	−2212.89	−0.00219512
$253$	−95714.0	−0.0940100
$254$	−590566.	−0.574360
$255$	112611.	0.108451
$256$	−18518.2	−0.0176604
$257$	−1.34845e6	−1.27351	−0.636753	−	0.771068i	$-0.719723\pi$
$257$	−1.34845e6	−1.27351	−0.636753	+	0.771068i	$0.719723\pi$
$258$	−339167.	−0.317223
$259$	−386790.	−0.358283
$260$	329.232	0.000302043 0
$261$	125219.	0.113781
$262$	−571057.	−0.513957
$263$	1.34541e6	1.19940	0.599700	−	0.800225i	$-0.295287\pi$
$263$	1.34541e6	1.19940	0.599700	+	0.800225i	$0.295287\pi$
$264$	197706.	0.174586
$265$	721821.	0.631415
$266$	548584.	0.475378
$267$	−385018.	−0.330524
$268$	−3108.61	−0.00264380
$269$	−2.03803e6	−1.71724	−0.858620	−	0.512613i	$-0.828678\pi$
$269$	−2.03803e6	−1.71724	−0.858620	+	0.512613i	$0.828678\pi$
$270$	102792.	0.0858126
$271$	−218053.	−0.180360	−0.0901799	−	0.995925i	$-0.528744\pi$
$271$	−218053.	−0.180360	−0.0901799	+	0.995925i	$0.528744\pi$
$272$	509472.	0.417540
$273$	91241.7	0.0740946
$274$	−723698.	−0.582346
$275$	−75625.0	−0.0603023
$276$	1341.15	0.00105975
$277$	−410179.	−0.321199	−0.160599	−	0.987020i	$-0.551343\pi$
$277$	−410179.	−0.321199	−0.160599	+	0.987020i	$0.551343\pi$
$278$	−912324.	−0.708006
$279$	218950.	0.168397
$280$	658209.	0.501728
$281$	−406589.	−0.307178	−0.153589	−	0.988135i	$-0.549083\pi$
$281$	−406589.	−0.307178	−0.153589	+	0.988135i	$0.549083\pi$
$282$	−59241.7	−0.0443613
$283$	1.26416e6	0.938291	0.469146	−	0.883121i	$-0.344562\pi$
$283$	1.26416e6	0.938291	0.469146	+	0.883121i	$0.344562\pi$
$284$	−13574.8	−0.00998707
$285$	150904.	0.110050
$286$	−47708.7	−0.0344891
$287$	1.39541e6	0.999991
$288$	−5524.30	−0.00392461
$289$	−1.16936e6	−0.823577
$290$	−217980.	−0.152203
$291$	188933.	0.130790
$292$	8567.85	0.00588050
$293$	351099.	0.238924	0.119462	−	0.992839i	$-0.461883\pi$
$293$	351099.	0.238924	0.119462	+	0.992839i	$0.461883\pi$
$294$	214426.	0.144680
$295$	589982.	0.394715
$296$	−484212.	−0.321223
$297$	88209.0	0.0580259
$298$	2.28101e6	1.48794
$299$	−55298.0	−0.0357710
$300$	1059.66	0.000679771 0
$301$	−968969.	−0.616444
$302$	−2.34733e6	−1.48101
$303$	−1.70689e6	−1.06807
$304$	682714.	0.423697
$305$	440033.	0.270854
$306$	228654.	0.139596
$307$	−1.46228e6	−0.885493	−0.442747	−	0.896647i	$-0.645996\pi$
$307$	−1.46228e6	−0.885493	−0.442747	+	0.896647i	$0.645996\pi$
$308$	3305.68	0.00198556
$309$	1.44809e6	0.862781
$310$	−381148.	−0.225263
$311$	2.20292e6	1.29151	0.645755	−	0.763545i	$-0.276543\pi$
$311$	2.20292e6	1.29151	0.645755	+	0.763545i	$0.276543\pi$
$312$	114223.	0.0664304
$313$	647848.	0.373777	0.186888	−	0.982381i	$-0.440160\pi$
$313$	647848.	0.373777	0.186888	+	0.982381i	$0.440160\pi$
$314$	−1.87725e6	−1.07448
$315$	293668.	0.166756
$316$	4085.80	0.00230175
$317$	−1.62933e6	−0.910670	−0.455335	−	0.890320i	$-0.650481\pi$
$317$	−1.62933e6	−0.910670	−0.455335	+	0.890320i	$0.650481\pi$
$318$	1.46563e6	0.812751
$319$	−187055.	−0.102918
$320$	823966.	0.449815
$321$	−1.01920e6	−0.552072
$322$	−647016.	−0.347756
$323$	335675.	0.179024
$324$	−1235.99	−0.000654110 0
$325$	−43691.7	−0.0229451
$326$	83276.6	0.0433989
$327$	15914.9	0.00823067
$328$	1.74687e6	0.896554
$329$	−169248.	−0.0862053
$330$	−153554.	−0.0776204
$331$	799339.	0.401016	0.200508	−	0.979692i	$-0.435741\pi$
$331$	799339.	0.401016	0.200508	+	0.979692i	$0.435741\pi$
$332$	−1306.32	−0.000650434 0
$333$	−216037.	−0.106762
$334$	−958603.	−0.470189
$335$	412537.	0.200840
$336$	1.32860e6	0.642017
$337$	−3.76736e6	−1.80702	−0.903508	−	0.428570i	$-0.859017\pi$
$337$	−3.76736e6	−1.80702	−0.903508	+	0.428570i	$0.859017\pi$
$338$	2.06660e6	0.983929
$339$	695459.	0.328679
$340$	2357.13	0.00110582
$341$	−327074.	−0.152321
$342$	306405.	0.141655
$343$	−1.82478e6	−0.837481
$344$	−1.21303e6	−0.552681
$345$	−177981.	−0.0805054
$346$	−4.09403e6	−1.83849
$347$	923519.	0.411739	0.205869	−	0.978579i	$-0.433998\pi$
$347$	923519.	0.411739	0.205869	+	0.978579i	$0.433998\pi$
$348$	2621.02	0.00116017
$349$	2.61022e6	1.14713	0.573567	−	0.819159i	$-0.305559\pi$
$349$	2.61022e6	1.14713	0.573567	+	0.819159i	$0.305559\pi$
$350$	−511216.	−0.223067
$351$	50962.0	0.0220790
$352$	8252.36	0.00354994
$353$	1.25644e6	0.536669	0.268335	−	0.963326i	$-0.413527\pi$
$353$	1.25644e6	0.536669	0.268335	+	0.963326i	$0.413527\pi$
$354$	1.19794e6	0.508073
$355$	1.80148e6	0.758682
$356$	−8059.01	−0.00337021
$357$	653242.	0.271271
$358$	−390928.	−0.161209
$359$	−2.38200e6	−0.975451	−0.487726	−	0.872997i	$-0.662173\pi$
$359$	−2.38200e6	−0.975451	−0.487726	+	0.872997i	$0.662173\pi$
$360$	367635.	0.149507
$361$	−2.02628e6	−0.818336
$362$	−4.45797e6	−1.78799
$363$	−131769.	−0.0524864
$364$	1909.83	0.000755511 0
$365$	−1.13702e6	−0.446721
$366$	893471.	0.348641
$367$	−3.46320e6	−1.34219	−0.671093	−	0.741373i	$-0.734175\pi$
$367$	−3.46320e6	−1.34219	−0.671093	+	0.741373i	$0.734175\pi$
$368$	−805213.	−0.309950
$369$	779389.	0.297981
$370$	376077.	0.142815
$371$	4.18718e6	1.57938
$372$	4582.96	0.00171707
$373$	811517.	0.302013	0.151006	−	0.988533i	$-0.451749\pi$
$373$	811517.	0.302013	0.151006	+	0.988533i	$0.451749\pi$
$374$	−341569.	−0.126270
$375$	−140625.	−0.0516398
$376$	−211877.	−0.0772884
$377$	−108070.	−0.0391607
$378$	596283.	0.214646
$379$	−522481.	−0.186841	−0.0934206	−	0.995627i	$-0.529780\pi$
$379$	−522481.	−0.186841	−0.0934206	+	0.995627i	$0.529780\pi$
$380$	3158.65	0.00112213
$381$	−942362.	−0.332587
$382$	−2.36312e6	−0.828565
$383$	−2.24960e6	−0.783625	−0.391813	−	0.920045i	$-0.628152\pi$
$383$	−2.24960e6	−0.783625	−0.391813	+	0.920045i	$0.628152\pi$
$384$	1.65339e6	0.572200
$385$	−438689.	−0.150836
$386$	−1.49760e6	−0.511598
$387$	−541207.	−0.183690
$388$	3954.65	0.00133361
$389$	−2.42055e6	−0.811035	−0.405518	−	0.914087i	$-0.632909\pi$
$389$	−2.42055e6	−0.811035	−0.405518	+	0.914087i	$0.632909\pi$
$390$	−88714.5	−0.0295347
$391$	−395904.	−0.130963
$392$	766891.	0.252068
$393$	−911233.	−0.297610
$394$	494949.	0.160627
$395$	−542217.	−0.174856
$396$	1846.35	0.000591665 0
$397$	1.96075e6	0.624375	0.312187	−	0.950021i	$-0.398938\pi$
$397$	1.96075e6	0.624375	0.312187	+	0.950021i	$0.398938\pi$
$398$	−2.14884e6	−0.679981
$399$	875372.	0.275271
$400$	−636210.	−0.198816
$401$	−3.86313e6	−1.19972	−0.599858	−	0.800107i	$-0.704776\pi$
$401$	−3.86313e6	−1.19972	−0.599858	+	0.800107i	$0.704776\pi$
$402$	837641.	0.258519
$403$	−188964.	−0.0579584
$404$	−35727.8	−0.0108906
$405$	164025.	0.0496904
$406$	−1.26447e6	−0.380710
$407$	322722.	0.0965702
$408$	817776.	0.243212
$409$	1.75292e6	0.518149	0.259075	−	0.965857i	$-0.416582\pi$
$409$	1.75292e6	0.518149	0.259075	+	0.965857i	$0.416582\pi$
$410$	−1.35676e6	−0.398605
$411$	−1.15480e6	−0.337212
$412$	30310.8	0.00879740
$413$	3.42240e6	0.987314
$414$	−361383.	−0.103626
$415$	173359.	0.0494112
$416$	4767.73	0.00135076
$417$	−1.45579e6	−0.409976
$418$	−457717.	−0.128132
$419$	−4.28414e6	−1.19214	−0.596071	−	0.802932i	$-0.703272\pi$
$419$	−4.28414e6	−1.19214	−0.596071	+	0.802932i	$0.703272\pi$
$420$	6146.92	0.00170033
$421$	5.74050e6	1.57850	0.789250	−	0.614072i	$-0.210470\pi$
$421$	5.74050e6	1.57850	0.789250	+	0.614072i	$0.210470\pi$
$422$	−3.52175e6	−0.962670
$423$	−94531.6	−0.0256877
$424$	5.24182e6	1.41601
$425$	−312810.	−0.0840055
$426$	3.65785e6	0.976567
$427$	2.55257e6	0.677497
$428$	−21333.3	−0.00562924
$429$	−76128.4	−0.0199712
$430$	942131.	0.245720
$431$	5.29228e6	1.37230	0.686150	−	0.727460i	$-0.259299\pi$
$431$	5.29228e6	1.37230	0.686150	+	0.727460i	$0.259299\pi$
$432$	742076.	0.191310
$433$	−2.37840e6	−0.609628	−0.304814	−	0.952412i	$-0.598594\pi$
$433$	−2.37840e6	−0.609628	−0.304814	+	0.952412i	$0.598594\pi$
$434$	−2.21098e6	−0.563457
$435$	−347830.	−0.0881341
$436$	333.123	8.39245e−5 0
$437$	−530528.	−0.132894
$438$	−2.30868e6	−0.575014
$439$	6.44393e6	1.59584	0.797921	−	0.602762i	$-0.205933\pi$
$439$	6.44393e6	1.59584	0.797921	+	0.602762i	$0.205933\pi$
$440$	−549183.	−0.135234
$441$	342158.	0.0837780
$442$	−197339.	−0.0480459
$443$	2501.14	0.000605520 0	0.000302760	−	1.00000i	$-0.499904\pi$
$443$	2501.14	0.000605520 0	0.000302760		1.00000i	$0.499904\pi$
$444$	−4521.99	−0.00108861
$445$	1.06949e6	0.256023
$446$	3.71292e6	0.883849
$447$	3.63979e6	0.861603
$448$	4.77970e6	1.12514
$449$	−5.04731e6	−1.18153	−0.590764	−	0.806844i	$-0.701174\pi$
$449$	−5.04731e6	−1.18153	−0.590764	+	0.806844i	$0.701174\pi$
$450$	−285534.	−0.0664701
$451$	−1.16427e6	−0.269534
$452$	14557.0	0.00335140
$453$	−3.74562e6	−0.857587
$454$	−1.24058e6	−0.282478
$455$	−253449.	−0.0573934
$456$	1.09585e6	0.246798
$457$	4.62692e6	1.03634	0.518169	−	0.855278i	$-0.326614\pi$
$457$	4.62692e6	1.03634	0.518169	+	0.855278i	$0.326614\pi$
$458$	1.76720e6	0.393661
$459$	364861.	0.0808343
$460$	−3725.40	−0.000820879 0
$461$	1.43209e6	0.313846	0.156923	−	0.987611i	$-0.449842\pi$
$461$	1.43209e6	0.313846	0.156923	+	0.987611i	$0.449842\pi$
$462$	−890743.	−0.194155
$463$	1.58115e6	0.342785	0.171393	−	0.985203i	$-0.445173\pi$
$463$	1.58115e6	0.342785	0.171393	+	0.985203i	$0.445173\pi$
$464$	−1.57364e6	−0.339321
$465$	−608195.	−0.130440
$466$	5.73089e6	1.22252
$467$	8724.92	0.00185127	0.000925634	−	1.00000i	$-0.499705\pi$
$467$	8724.92	0.00185127	0.000925634		1.00000i	$0.499705\pi$
$468$	1066.71	0.000225130 0
$469$	2.39306e6	0.502368
$470$	164560.	0.0343621
$471$	−2.99551e6	−0.622183
$472$	4.28441e6	0.885189
$473$	808470.	0.166154
$474$	−1.10095e6	−0.225073
$475$	−419178.	−0.0852441
$476$	13673.4	0.00276603
$477$	2.33870e6	0.470629
$478$	−4.30018e6	−0.860830
$479$	8.15482e6	1.62396	0.811981	−	0.583684i	$-0.198389\pi$
$479$	8.15482e6	1.62396	0.811981	+	0.583684i	$0.198389\pi$
$480$	15345.3	0.00303999
$481$	186450.	0.0367452
$482$	129212.	0.0253329
$483$	−1.03244e6	−0.201371
$484$	−2758.13	−0.000535181 0
$485$	−524814.	−0.101310
$486$	333047.	0.0639609
$487$	9.00123e6	1.71981	0.859903	−	0.510457i	$-0.170524\pi$
$487$	9.00123e6	1.71981	0.859903	+	0.510457i	$0.170524\pi$
$488$	3.19549e6	0.607418
$489$	132884.	0.0251305
$490$	−595627.	−0.112069
$491$	6.03644e6	1.13000	0.564999	−	0.825092i	$-0.308877\pi$
$491$	6.03644e6	1.13000	0.564999	+	0.825092i	$0.308877\pi$
$492$	16313.8	0.00303838
$493$	−773721.	−0.143373
$494$	−264442.	−0.0487543
$495$	−245025.	−0.0449467
$496$	−2.75157e6	−0.502200
$497$	1.04501e7	1.89772
$498$	351998.	0.0636015
$499$	233452.	0.0419707	0.0209853	−	0.999780i	$-0.493320\pi$
$499$	233452.	0.0419707	0.0209853	+	0.999780i	$0.493320\pi$
$500$	−2943.50	−0.000526548 0
$501$	−1.52964e6	−0.272267
$502$	3.89826e6	0.690417
$503$	−7.79728e6	−1.37412	−0.687058	−	0.726603i	$-0.741098\pi$
$503$	−7.79728e6	−1.37412	−0.687058	+	0.726603i	$0.741098\pi$
$504$	2.13260e6	0.373966
$505$	4.74135e6	0.827321
$506$	539844.	0.0937329
$507$	3.29765e6	0.569751
$508$	−19725.1	−0.00339125
$509$	5.32415e6	0.910869	0.455434	−	0.890269i	$-0.349484\pi$
$509$	5.32415e6	0.910869	0.455434	+	0.890269i	$0.349484\pi$
$510$	−635149.	−0.108131
$511$	−6.59569e6	−1.11740
$512$	5.98317e6	1.00869
$513$	488929.	0.0820262
$514$	7.60548e6	1.26975
$515$	−4.02248e6	−0.668307
$516$	−11328.3	−0.00187301
$517$	141214.	0.0232354
$518$	2.18157e6	0.357227
$519$	−6.53282e6	−1.06459
$520$	−317286.	−0.0514568
$521$	−8.42076e6	−1.35912	−0.679559	−	0.733621i	$-0.737829\pi$
$521$	−8.42076e6	−1.35912	−0.679559	+	0.733621i	$0.737829\pi$
$522$	−706257.	−0.113445
$523$	−6.81759e6	−1.08988	−0.544938	−	0.838476i	$-0.683447\pi$
$523$	−6.81759e6	−1.08988	−0.544938	+	0.838476i	$0.683447\pi$
$524$	−19073.5	−0.00303460
$525$	−815745.	−0.129168
$526$	−7.58833e6	−1.19586
$527$	−1.35288e6	−0.212194
$528$	−1.10853e6	−0.173047
$529$	−5.81062e6	−0.902783
$530$	−4.07120e6	−0.629554
$531$	1.91154e6	0.294203
$532$	18322.9	0.00280682
$533$	−672649.	−0.102558
$534$	2.17157e6	0.329550
$535$	2.83110e6	0.427633
$536$	2.99581e6	0.450404
$537$	−623802.	−0.0933493
$538$	1.14949e7	1.71218
$539$	−511125.	−0.0757801
$540$	3433.29	0.000506671 0
$541$	−1.00313e7	−1.47354	−0.736770	−	0.676143i	$-0.763650\pi$
$541$	−1.00313e7	−1.47354	−0.736770	+	0.676143i	$0.763650\pi$
$542$	1.22986e6	0.179828
$543$	−7.11356e6	−1.03535
$544$	34134.4	0.00494533
$545$	−44208.1	−0.00637545
$546$	−514619.	−0.0738762
$547$	341056.	0.0487368	0.0243684	−	0.999703i	$-0.492243\pi$
$547$	341056.	0.0487368	0.0243684	+	0.999703i	$0.492243\pi$
$548$	−24171.7	−0.00343840
$549$	1.42571e6	0.201883
$550$	426539.	0.0601245
$551$	−1.03682e6	−0.145487
$552$	−1.29248e6	−0.180541
$553$	−3.14532e6	−0.437373
$554$	2.31348e6	0.320252
$555$	600104.	0.0826978
$556$	−30471.9	−0.00418035
$557$	8.70989e6	1.18953	0.594764	−	0.803901i	$-0.297246\pi$
$557$	8.70989e6	1.18953	0.594764	+	0.803901i	$0.297246\pi$
$558$	−1.23492e6	−0.167901
$559$	467087.	0.0632219
$560$	−3.69056e6	−0.497304
$561$	−545039.	−0.0731174
$562$	2.29324e6	0.306272
$563$	−1.05570e7	−1.40369	−0.701845	−	0.712330i	$-0.747640\pi$
$563$	−1.05570e7	−1.40369	−0.701845	+	0.712330i	$0.747640\pi$
$564$	−1978.69	−0.000261927 0
$565$	−1.93183e6	−0.254594
$566$	−7.13011e6	−0.935525
$567$	951485.	0.124292
$568$	1.30823e7	1.70142
$569$	−2.88092e6	−0.373035	−0.186518	−	0.982452i	$-0.559720\pi$
$569$	−2.88092e6	−0.373035	−0.186518	+	0.982452i	$0.559720\pi$
$570$	−851126.	−0.109725
$571$	−8.00484e6	−1.02745	−0.513727	−	0.857954i	$-0.671735\pi$
$571$	−8.00484e6	−1.02745	−0.513727	+	0.857954i	$0.671735\pi$
$572$	−1593.48	−0.000203637 0
$573$	−3.77081e6	−0.479786
$574$	−7.87035e6	−0.997043
$575$	494391.	0.0623592
$576$	2.66965e6	0.335272
$577$	−1.42967e7	−1.78770	−0.893852	−	0.448361i	$-0.852008\pi$
$577$	−1.42967e7	−1.78770	−0.893852	+	0.448361i	$0.852008\pi$
$578$	6.59541e6	0.821149
$579$	−2.38972e6	−0.296244
$580$	−7280.61	−0.000898665 0
$581$	1.00563e6	0.123594
$582$	−1.06562e6	−0.130405
$583$	−3.49362e6	−0.425700
$584$	−8.25697e6	−1.00182
$585$	−141561.	−0.0171023
$586$	−1.98026e6	−0.238220
$587$	9.83619e6	1.17823	0.589117	−	0.808047i	$-0.299476\pi$
$587$	9.83619e6	1.17823	0.589117	+	0.808047i	$0.299476\pi$
$588$	7161.88	0.000854248 0
$589$	−1.81292e6	−0.215323
$590$	−3.32760e6	−0.393552
$591$	789787.	0.0930125
$592$	2.71497e6	0.318390
$593$	−9.84429e6	−1.14960	−0.574801	−	0.818293i	$-0.694921\pi$
$593$	−9.84429e6	−1.14960	−0.574801	+	0.818293i	$0.694921\pi$
$594$	−497515.	−0.0578548
$595$	−1.81456e6	−0.210126
$596$	76186.3	0.00878540
$597$	−3.42890e6	−0.393748
$598$	311890.	0.0356656
$599$	−3.94699e6	−0.449468	−0.224734	−	0.974420i	$-0.572151\pi$
$599$	−3.94699e6	−0.449468	−0.224734	+	0.974420i	$0.572151\pi$
$600$	−1.02121e6	−0.115807
$601$	−7.63150e6	−0.861834	−0.430917	−	0.902392i	$-0.641810\pi$
$601$	−7.63150e6	−0.861834	−0.430917	+	0.902392i	$0.641810\pi$
$602$	5.46516e6	0.614627
$603$	1.33662e6	0.149697
$604$	−78401.5	−0.00874444
$605$	366025.	0.0406558
$606$	9.62715e6	1.06492
$607$	−1.12292e7	−1.23703	−0.618513	−	0.785775i	$-0.712264\pi$
$607$	−1.12292e7	−1.23703	−0.618513	+	0.785775i	$0.712264\pi$
$608$	45741.6	0.00501825
$609$	−2.01771e6	−0.220453
$610$	−2.48186e6	−0.270056
$611$	81585.1	0.00884113
$612$	7637.10	0.000824232 0
$613$	2.62390e6	0.282031	0.141016	−	0.990007i	$-0.454963\pi$
$613$	2.62390e6	0.282031	0.141016	+	0.990007i	$0.454963\pi$
$614$	8.24753e6	0.882883
$615$	−2.16497e6	−0.230815
$616$	−3.18573e6	−0.338265
$617$	−3.59228e6	−0.379889	−0.189945	−	0.981795i	$-0.560831\pi$
$617$	−3.59228e6	−0.379889	−0.189945	+	0.981795i	$0.560831\pi$
$618$	−8.16750e6	−0.860237
$619$	−1.19777e7	−1.25646	−0.628228	−	0.778029i	$-0.716219\pi$
$619$	−1.19777e7	−1.25646	−0.628228	+	0.778029i	$0.716219\pi$
$620$	−12730.4	−0.00133004
$621$	−576657.	−0.0600052
$622$	−1.24249e7	−1.28770
$623$	6.20398e6	0.640398
$624$	−640445.	−0.0658447
$625$	390625.	0.0400000
$626$	−3.65398e6	−0.372675
$627$	−730376.	−0.0741955
$628$	−62700.6	−0.00634413
$629$	1.33488e6	0.134529
$630$	−1.65634e6	−0.166264
$631$	2.50844e6	0.250801	0.125401	−	0.992106i	$-0.459978\pi$
$631$	2.50844e6	0.250801	0.125401	+	0.992106i	$0.459978\pi$
$632$	−3.93754e6	−0.392132
$633$	−5.61963e6	−0.557441
$634$	9.18972e6	0.907986
$635$	2.61767e6	0.257621
$636$	48952.6	0.00479880
$637$	−295298.	−0.0288345
$638$	1.05503e6	0.102615
$639$	5.83681e6	0.565488
$640$	−4.59275e6	−0.443224
$641$	1.12431e7	1.08079	0.540395	−	0.841411i	$-0.318275\pi$
$641$	1.12431e7	1.08079	0.540395	+	0.841411i	$0.318275\pi$
$642$	5.74845e6	0.550444
$643$	5.61271e6	0.535360	0.267680	−	0.963508i	$-0.413743\pi$
$643$	5.61271e6	0.535360	0.267680	+	0.963508i	$0.413743\pi$
$644$	−21610.5	−0.00205329
$645$	1.50335e6	0.142286
$646$	−1.89326e6	−0.178497
$647$	1.10739e7	1.04002	0.520008	−	0.854162i	$-0.325929\pi$
$647$	1.10739e7	1.04002	0.520008	+	0.854162i	$0.325929\pi$
$648$	1.19114e6	0.111436
$649$	−2.85551e6	−0.266117
$650$	246429.	0.0228775
$651$	−3.52805e6	−0.326274
$652$	2781.46	0.000256244 0
$653$	−7.83486e6	−0.719032	−0.359516	−	0.933139i	$-0.617058\pi$
$653$	−7.83486e6	−0.719032	−0.359516	+	0.933139i	$0.617058\pi$
$654$	−89763.0	−0.00820640
$655$	2.53120e6	0.230528
$656$	−9.79467e6	−0.888649
$657$	−3.68395e6	−0.332966
$658$	954589.	0.0859511
$659$	1.02774e7	0.921868	0.460934	−	0.887434i	$-0.347514\pi$
$659$	1.02774e7	0.921868	0.460934	+	0.887434i	$0.347514\pi$
$660$	−5128.75	−0.000458302 0
$661$	−1.42467e7	−1.26827	−0.634134	−	0.773223i	$-0.718643\pi$
$661$	−1.42467e7	−1.26827	−0.634134	+	0.773223i	$0.718643\pi$
$662$	−4.50842e6	−0.399833
$663$	−314892.	−0.0278213
$664$	1.25892e6	0.110810
$665$	−2.43159e6	−0.213224
$666$	1.21849e6	0.106448
$667$	1.22285e6	0.106429
$668$	−32017.6	−0.00277618
$669$	5.92468e6	0.511799
$670$	−2.32678e6	−0.200248
$671$	−2.12976e6	−0.182610
$672$	89015.7	0.00760403
$673$	−3.85183e6	−0.327815	−0.163908	−	0.986476i	$-0.552410\pi$
$673$	−3.85183e6	−0.327815	−0.163908	+	0.986476i	$0.552410\pi$
$674$	2.12486e7	1.80169
$675$	−455625.	−0.0384900
$676$	69024.9	0.00580951
$677$	1.39430e7	1.16919	0.584594	−	0.811326i	$-0.301254\pi$
$677$	1.39430e7	1.16919	0.584594	+	0.811326i	$0.301254\pi$
$678$	−3.92251e6	−0.327710
$679$	−3.04437e6	−0.253409
$680$	−2.27160e6	−0.188391
$681$	−1.97959e6	−0.163571
$682$	1.84475e6	0.151872
$683$	−1.24329e7	−1.01981	−0.509905	−	0.860231i	$-0.670319\pi$
$683$	−1.24329e7	−1.01981	−0.509905	+	0.860231i	$0.670319\pi$
$684$	10234.0	0.000836386 0
$685$	3.20778e6	0.261203
$686$	1.02921e7	0.835012
$687$	2.81991e6	0.227952
$688$	6.80141e6	0.547807
$689$	−2.01841e6	−0.161980
$690$	1.00384e6	0.0802681
$691$	1.46905e7	1.17042	0.585208	−	0.810883i	$-0.301013\pi$
$691$	1.46905e7	1.17042	0.585208	+	0.810883i	$0.301013\pi$
$692$	−136742.	−0.0108552
$693$	−1.42135e6	−0.112427
$694$	−5.20881e6	−0.410525
$695$	4.04386e6	0.317566
$696$	−2.52592e6	−0.197650
$697$	−4.81581e6	−0.375480
$698$	−1.47221e7	−1.14375
$699$	9.14474e6	0.707911
$700$	−17074.8	−0.00131707
$701$	−3.55096e6	−0.272930	−0.136465	−	0.990645i	$-0.543574\pi$
$701$	−3.55096e6	−0.272930	−0.136465	+	0.990645i	$0.543574\pi$
$702$	−287435.	−0.0220139
$703$	1.78880e6	0.136513
$704$	−3.98799e6	−0.303265
$705$	262588.	0.0198976
$706$	−7.08657e6	−0.535087
$707$	2.75039e7	2.06941
$708$	40011.5	0.00299986
$709$	−8.56408e6	−0.639831	−0.319915	−	0.947446i	$-0.603654\pi$
$709$	−8.56408e6	−0.639831	−0.319915	+	0.947446i	$0.603654\pi$
$710$	−1.01607e7	−0.756445
$711$	−1.75678e6	−0.130330
$712$	7.76659e6	0.574157
$713$	2.13821e6	0.157517
$714$	−3.68440e6	−0.270472
$715$	211468.	0.0154696
$716$	−13057.1	−0.000951843 0
$717$	−6.86178e6	−0.498470
$718$	1.34349e7	0.972576
$719$	1.07318e7	0.774195	0.387097	−	0.922039i	$-0.373478\pi$
$719$	1.07318e7	0.774195	0.387097	+	0.922039i	$0.373478\pi$
$720$	−2.06132e6	−0.148188
$721$	−2.33338e7	−1.67166
$722$	1.14286e7	0.815924
$723$	206182.	0.0146692
$724$	−148898.	−0.0105570
$725$	966195.	0.0682684
$726$	743201.	0.0523317
$727$	1.49237e7	1.04722	0.523611	−	0.851957i	$-0.324584\pi$
$727$	1.49237e7	1.04722	0.523611	+	0.851957i	$0.324584\pi$
$728$	−1.84053e6	−0.128711
$729$	531441.	0.0370370
$730$	6.41300e6	0.445404
$731$	3.34409e6	0.231465
$732$	29842.2	0.00205851
$733$	1.21777e7	0.837155	0.418577	−	0.908181i	$-0.362529\pi$
$733$	1.21777e7	0.837155	0.418577	+	0.908181i	$0.362529\pi$
$734$	1.95331e7	1.33823
$735$	−950438.	−0.0648942
$736$	−53948.9	−0.00367103
$737$	−1.99668e6	−0.135406
$738$	−4.39589e6	−0.297102
$739$	4.10708e6	0.276644	0.138322	−	0.990387i	$-0.455829\pi$
$739$	4.10708e6	0.276644	0.138322	+	0.990387i	$0.455829\pi$
$740$	12561.1	0.000843233 0
$741$	−421969.	−0.0282315
$742$	−2.36164e7	−1.57472
$743$	2.73077e7	1.81474	0.907368	−	0.420337i	$-0.138088\pi$
$743$	2.73077e7	1.81474	0.907368	+	0.420337i	$0.138088\pi$
$744$	−4.41667e6	−0.292525
$745$	−1.01105e7	−0.667395
$746$	−4.57710e6	−0.301123
$747$	561682.	0.0368289
$748$	−11408.5	−0.000745546 0
$749$	1.64228e7	1.06965
$750$	793150.	0.0514876
$751$	−1.54004e7	−0.996398	−0.498199	−	0.867063i	$-0.666005\pi$
$751$	−1.54004e7	−0.996398	−0.498199	+	0.867063i	$0.666005\pi$
$752$	1.18799e6	0.0766069
$753$	6.22043e6	0.399791
$754$	609532.	0.0390452
$755$	1.04045e7	0.664284
$756$	19916.0	0.00126735
$757$	8.23327e6	0.522195	0.261097	−	0.965312i	$-0.415916\pi$
$757$	8.23327e6	0.522195	0.261097	+	0.965312i	$0.415916\pi$
$758$	2.94689e6	0.186290
$759$	861426.	0.0542767
$760$	−3.04404e6	−0.191169
$761$	1.69020e7	1.05798	0.528989	−	0.848629i	$-0.322571\pi$
$761$	1.69020e7	1.05798	0.528989	+	0.848629i	$0.322571\pi$
$762$	5.31509e6	0.331607
$763$	−256445.	−0.0159471
$764$	−78928.8	−0.00489217
$765$	−1.01350e6	−0.0626140
$766$	1.26881e7	0.781315
$767$	−1.64975e6	−0.101258
$768$	166664.	0.0101962
$769$	−1.72204e7	−1.05009	−0.525045	−	0.851075i	$-0.675951\pi$
$769$	−1.72204e7	−1.05009	−0.525045	+	0.851075i	$0.675951\pi$
$770$	2.47429e6	0.150391
$771$	1.21360e7	0.735259
$772$	−50020.4	−0.00302067
$773$	1.86902e7	1.12503	0.562517	−	0.826786i	$-0.309833\pi$
$773$	1.86902e7	1.12503	0.562517	+	0.826786i	$0.309833\pi$
$774$	3.05250e6	0.183149
$775$	1.68943e6	0.101038
$776$	−3.81116e6	−0.227197
$777$	3.48111e6	0.206855
$778$	1.36523e7	0.808644
$779$	−6.45339e6	−0.381017
$780$	−2963.09	−0.000174385 0
$781$	−8.71919e6	−0.511503
$782$	2.23297e6	0.130577
$783$	−1.12697e6	−0.0656913
$784$	−4.29994e6	−0.249846
$785$	8.32086e6	0.481941
$786$	5.13952e6	0.296733
$787$	−8.17563e6	−0.470527	−0.235264	−	0.971932i	$-0.575595\pi$
$787$	−8.17563e6	−0.470527	−0.235264	+	0.971932i	$0.575595\pi$
$788$	16531.4	0.000948408 0
$789$	−1.21087e7	−0.692474
$790$	3.05820e6	0.174341
$791$	−1.12063e7	−0.636824
$792$	−1.77935e6	−0.100797
$793$	−1.23045e6	−0.0694834
$794$	−1.10590e7	−0.622534
$795$	−6.49639e6	−0.364548
$796$	−71772.0	−0.00401488
$797$	−3.39844e7	−1.89511	−0.947554	−	0.319595i	$-0.896453\pi$
$797$	−3.39844e7	−1.89511	−0.947554	+	0.319595i	$0.896453\pi$
$798$	−4.93726e6	−0.274460
$799$	584106.	0.0323687
$800$	−42625.8	−0.00235477
$801$	3.46516e6	0.190828
$802$	2.17887e7	1.19618
$803$	5.50318e6	0.301179
$804$	27977.5	0.00152640
$805$	2.86789e6	0.155981
$806$	1.06579e6	0.0577876
$807$	1.83423e7	0.991449
$808$	3.44314e7	1.85535
$809$	2.50619e7	1.34630	0.673151	−	0.739505i	$-0.264940\pi$
$809$	2.50619e7	1.34630	0.673151	+	0.739505i	$0.264940\pi$
$810$	−925130.	−0.0495439
$811$	−1.73791e7	−0.927844	−0.463922	−	0.885876i	$-0.653558\pi$
$811$	−1.73791e7	−0.927844	−0.463922	+	0.885876i	$0.653558\pi$
$812$	−42233.7	−0.00224786
$813$	1.96248e6	0.104131
$814$	−1.82021e6	−0.0962855
$815$	−369122.	−0.0194660
$816$	−4.58525e6	−0.241067
$817$	4.48123e6	0.234878
$818$	−9.88681e6	−0.516622
$819$	−821175.	−0.0427786
$820$	−45316.1	−0.00235352
$821$	−1.21448e7	−0.628827	−0.314413	−	0.949286i	$-0.601808\pi$
$821$	−1.21448e7	−0.628827	−0.314413	+	0.949286i	$0.601808\pi$
$822$	6.51329e6	0.336218
$823$	9.33503e6	0.480415	0.240207	−	0.970722i	$-0.422785\pi$
$823$	9.33503e6	0.480415	0.240207	+	0.970722i	$0.422785\pi$
$824$	−2.92110e7	−1.49875
$825$	680625.	0.0348155
$826$	−1.93029e7	−0.984404
$827$	−1.15378e7	−0.586622	−0.293311	−	0.956017i	$-0.594757\pi$
$827$	−1.15378e7	−0.586622	−0.293311	+	0.956017i	$0.594757\pi$
$828$	−12070.3	−0.000611847 0
$829$	−1.25927e7	−0.636404	−0.318202	−	0.948023i	$-0.603079\pi$
$829$	−1.25927e7	−0.636404	−0.318202	+	0.948023i	$0.603079\pi$
$830$	−977773.	−0.0492655
$831$	3.69161e6	0.185444
$832$	−2.30403e6	−0.115393
$833$	−2.11418e6	−0.105567
$834$	8.21092e6	0.408768
$835$	4.24899e6	0.210897
$836$	−15287.9	−0.000756539 0
$837$	−1.97055e6	−0.0972241
$838$	2.41633e7	1.18863
$839$	3.69853e7	1.81395	0.906973	−	0.421189i	$-0.138387\pi$
$839$	3.69853e7	1.81395	0.906973	+	0.421189i	$0.138387\pi$
$840$	−5.92388e6	−0.289673
$841$	−1.81213e7	−0.883486
$842$	−3.23775e7	−1.57385
$843$	3.65930e6	0.177349
$844$	−117627.	−0.00568398
$845$	−9.16015e6	−0.441327
$846$	533175.	0.0256120
$847$	2.12326e6	0.101694
$848$	−2.93907e7	−1.40353
$849$	−1.13775e7	−0.541723
$850$	1.76430e6	0.0837579
$851$	−2.10976e6	−0.0998642
$852$	122173.	0.00576604
$853$	3.49513e7	1.64471	0.822357	−	0.568972i	$-0.192659\pi$
$853$	3.49513e7	1.64471	0.822357	+	0.568972i	$0.192659\pi$
$854$	−1.43969e7	−0.675500
$855$	−1.35814e6	−0.0635372
$856$	2.05593e7	0.959010
$857$	−2.24410e7	−1.04373	−0.521867	−	0.853027i	$-0.674764\pi$
$857$	−2.24410e7	−1.04373	−0.521867	+	0.853027i	$0.674764\pi$
$858$	429378.	0.0199123
$859$	3.30887e7	1.53002	0.765010	−	0.644019i	$-0.222734\pi$
$859$	3.30887e7	1.53002	0.765010	+	0.644019i	$0.222734\pi$
$860$	31467.5	0.00145083
$861$	−1.25587e7	−0.577345
$862$	−2.98494e7	−1.36826
$863$	1.58950e6	0.0726495	0.0363248	−	0.999340i	$-0.488435\pi$
$863$	1.58950e6	0.0726495	0.0363248	+	0.999340i	$0.488435\pi$
$864$	49718.7	0.00226587
$865$	1.81467e7	0.824628
$866$	1.34146e7	0.607830
$867$	1.05243e7	0.475492
$868$	−73847.4	−0.00332687
$869$	2.62433e6	0.117888
$870$	1.96182e6	0.0878743
$871$	−1.15356e6	−0.0515224
$872$	−321036.	−0.0142976
$873$	−1.70040e6	−0.0755118
$874$	2.99228e6	0.132502
$875$	2.26596e6	0.100053
$876$	−77110.6	−0.00339511
$877$	−1.78401e7	−0.783246	−0.391623	−	0.920126i	$-0.628086\pi$
$877$	−1.78401e7	−0.783246	−0.391623	+	0.920126i	$0.628086\pi$
$878$	−3.63449e7	−1.59114
$879$	−3.15989e6	−0.137943
$880$	3.07926e6	0.134041
$881$	−1.53213e7	−0.665054	−0.332527	−	0.943094i	$-0.607901\pi$
$881$	−1.53213e7	−0.665054	−0.332527	+	0.943094i	$0.607901\pi$
$882$	−1.92983e6	−0.0835310
$883$	1.92226e7	0.829680	0.414840	−	0.909894i	$-0.363838\pi$
$883$	1.92226e7	0.829680	0.414840	+	0.909894i	$0.363838\pi$
$884$	−6591.17	−0.000283682 0
$885$	−5.30984e6	−0.227889
$886$	−14106.9	−0.000603735 0
$887$	−1.78729e7	−0.762756	−0.381378	−	0.924419i	$-0.624550\pi$
$887$	−1.78729e7	−0.762756	−0.381378	+	0.924419i	$0.624550\pi$
$888$	4.35791e6	0.185458
$889$	1.51847e7	0.644396
$890$	−6.03214e6	−0.255268
$891$	−793881.	−0.0335013
$892$	124013.	0.00521860
$893$	782727.	0.0328459
$894$	−2.05291e7	−0.859063
$895$	1.73278e6	0.0723081
$896$	−2.66419e7	−1.10865
$897$	497682.	0.0206524
$898$	2.84677e7	1.17804
$899$	4.17874e6	0.172443
$900$	−9536.92	−0.000392466 0
$901$	−1.44507e7	−0.593032
$902$	6.56670e6	0.268739
$903$	8.72072e6	0.355904
$904$	−1.40288e7	−0.570953
$905$	1.97599e7	0.801979
$906$	2.11260e7	0.855059
$907$	2.36602e7	0.954993	0.477497	−	0.878634i	$-0.341544\pi$
$907$	2.36602e7	0.954993	0.477497	+	0.878634i	$0.341544\pi$
$908$	−41435.7	−0.00166786
$909$	1.53620e7	0.616649
$910$	1.42950e6	0.0572243
$911$	2.62399e7	1.04753	0.523766	−	0.851862i	$-0.324527\pi$
$911$	2.62399e7	1.04753	0.523766	+	0.851862i	$0.324527\pi$
$912$	−6.14443e6	−0.244621
$913$	−839056.	−0.0333130
$914$	−2.60966e7	−1.03328
$915$	−3.96030e6	−0.156378
$916$	59025.0	0.00232433
$917$	1.46831e7	0.576627
$918$	−2.05788e6	−0.0805960
$919$	1.05336e7	0.411422	0.205711	−	0.978613i	$-0.434049\pi$
$919$	1.05336e7	0.411422	0.205711	+	0.978613i	$0.434049\pi$
$920$	3.59023e6	0.139847
$921$	1.31605e7	0.511240
$922$	−8.07723e6	−0.312921
$923$	−5.03744e6	−0.194628
$924$	−29751.1	−0.00114637
$925$	−1.66695e6	−0.0640574
$926$	−8.91800e6	−0.341775
$927$	−1.30328e7	−0.498127
$928$	−105433.	−0.00401890
$929$	4.93218e7	1.87499	0.937497	−	0.347993i	$-0.113137\pi$
$929$	4.93218e7	1.87499	0.937497	+	0.347993i	$0.113137\pi$
$930$	3.43033e6	0.130055
$931$	−2.83309e6	−0.107124
$932$	191413.	0.00721826
$933$	−1.98263e7	−0.745653
$934$	−49210.1	−0.00184581
$935$	1.51400e6	0.0566365
$936$	−1.02801e6	−0.0383536
$937$	3.96100e6	0.147386	0.0736929	−	0.997281i	$-0.476522\pi$
$937$	3.96100e6	0.147386	0.0736929	+	0.997281i	$0.476522\pi$
$938$	−1.34973e7	−0.500887
$939$	−5.83063e6	−0.215800
$940$	5496.36	0.000202888 0
$941$	3.82868e7	1.40953	0.704766	−	0.709440i	$-0.251052\pi$
$941$	3.82868e7	1.40953	0.704766	+	0.709440i	$0.251052\pi$
$942$	1.68952e7	0.620349
$943$	7.61131e6	0.278728
$944$	−2.40226e7	−0.877383
$945$	−2.64301e6	−0.0962764
$946$	−4.55991e6	−0.165664
$947$	−1.34832e7	−0.488562	−0.244281	−	0.969705i	$-0.578552\pi$
$947$	−1.34832e7	−0.488562	−0.244281	+	0.969705i	$0.578552\pi$
$948$	−36772.2	−0.00132892
$949$	3.17942e6	0.114599
$950$	2.36424e6	0.0849928
$951$	1.46640e7	0.525776
$952$	−1.31772e7	−0.471228
$953$	−9.20696e6	−0.328385	−0.164193	−	0.986428i	$-0.552502\pi$
$953$	−9.20696e6	−0.328385	−0.164193	+	0.986428i	$0.552502\pi$
$954$	−1.31907e7	−0.469242
$955$	1.04745e7	0.371641
$956$	−143627.	−0.00508268
$957$	1.68350e6	0.0594200
$958$	−4.59947e7	−1.61917
$959$	1.86079e7	0.653356
$960$	−7.41569e6	−0.259701
$961$	−2.13225e7	−0.744782
$962$	−1.05161e6	−0.0366368
$963$	9.17277e6	0.318739
$964$	4315.71	0.000149575 0
$965$	6.63810e6	0.229470
$966$	5.82314e6	0.200777
$967$	2.95285e6	0.101549	0.0507745	−	0.998710i	$-0.483831\pi$
$967$	2.95285e6	0.101549	0.0507745	+	0.998710i	$0.483831\pi$
$968$	2.65805e6	0.0911747
$969$	−3.02107e6	−0.103360
$970$	2.96004e6	0.101011
$971$	−3.09624e7	−1.05387	−0.526935	−	0.849906i	$-0.676659\pi$
$971$	−3.09624e7	−1.05387	−0.526935	+	0.849906i	$0.676659\pi$
$972$	11123.9	0.000377651 0
$973$	2.34578e7	0.794339
$974$	−5.07686e7	−1.71474
$975$	393225.	0.0132474
$976$	−1.79170e7	−0.602062
$977$	−2.85400e7	−0.956573	−0.478287	−	0.878204i	$-0.658742\pi$
$977$	−2.85400e7	−0.956573	−0.478287	+	0.878204i	$0.658742\pi$
$978$	−749489.	−0.0250564
$979$	−5.17635e6	−0.172610
$980$	−19894.1	−0.000661698 0
$981$	−143234.	−0.00475198
$982$	−3.40466e7	−1.12667
$983$	−4.46869e7	−1.47501	−0.737507	−	0.675340i	$-0.763997\pi$
$983$	−4.46869e7	−1.47501	−0.737507	+	0.675340i	$0.763997\pi$
$984$	−1.57219e7	−0.517626
$985$	−2.19385e6	−0.0720472
$986$	4.36393e6	0.142950
$987$	1.52323e6	0.0497706
$988$	−8832.44	−0.000287865 0
$989$	−5.28529e6	−0.171822
$990$	1.38198e6	0.0448142
$991$	5.85115e7	1.89259	0.946296	−	0.323302i	$-0.104793\pi$
$991$	5.85115e7	1.89259	0.946296	+	0.323302i	$0.104793\pi$
$992$	−184354.	−0.00594804
$993$	−7.19405e6	−0.231526
$994$	−5.89407e7	−1.89212
$995$	9.52471e6	0.304996
$996$	11756.9	0.000375528 0
$997$	−4.32684e7	−1.37858	−0.689292	−	0.724483i	$-0.742078\pi$
$997$	−4.32684e7	−1.37858	−0.689292	+	0.724483i	$0.742078\pi$
$998$	−1.31671e6	−0.0418469
$999$	1.94434e6	0.0616393

Twists

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

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

\(f(q)\)	\(=\)	\(q-5.64018 q^{2} -9.00000 q^{3} -0.188384 q^{4} +25.0000 q^{5} +50.7616 q^{6} +145.021 q^{7} +181.548 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-5.64018 q^{2} -9.00000 q^{3} -0.188384 q^{4} +25.0000 q^{5} +50.7616 q^{6} +145.021 q^{7} +181.548 q^{8} +81.0000 q^{9} -141.004 q^{10} -121.000 q^{11} +1.69545 q^{12} -69.9067 q^{13} -817.946 q^{14} -225.000 q^{15} -1017.94 q^{16} -500.495 q^{17} -456.854 q^{18} -670.685 q^{19} -4.70959 q^{20} -1305.19 q^{21} +682.462 q^{22} +791.025 q^{23} -1633.93 q^{24} +625.000 q^{25} +394.287 q^{26} -729.000 q^{27} -27.3196 q^{28} +1545.91 q^{29} +1269.04 q^{30} +2703.09 q^{31} -68.2013 q^{32} +1089.00 q^{33} +2822.88 q^{34} +3625.53 q^{35} -15.2591 q^{36} -2667.13 q^{37} +3782.78 q^{38} +629.161 q^{39} +4538.71 q^{40} +9622.09 q^{41} +7361.51 q^{42} -6681.57 q^{43} +22.7944 q^{44} +2025.00 q^{45} -4461.52 q^{46} -1167.06 q^{47} +9161.43 q^{48} +4224.17 q^{49} -3525.11 q^{50} +4504.46 q^{51} +13.1693 q^{52} +28872.9 q^{53} +4111.69 q^{54} -3025.00 q^{55} +26328.4 q^{56} +6036.16 q^{57} -8719.22 q^{58} +23599.3 q^{59} +42.3863 q^{60} +17601.3 q^{61} -15245.9 q^{62} +11746.7 q^{63} +32958.6 q^{64} -1747.67 q^{65} -6142.15 q^{66} +16501.5 q^{67} +94.2851 q^{68} -7119.22 q^{69} -20448.6 q^{70} +72059.4 q^{71} +14705.4 q^{72} -45480.8 q^{73} +15043.1 q^{74} -5625.00 q^{75} +126.346 q^{76} -17547.6 q^{77} -3548.58 q^{78} -21688.7 q^{79} -25448.4 q^{80} +6561.00 q^{81} -54270.3 q^{82} +6934.34 q^{83} +245.877 q^{84} -12512.4 q^{85} +37685.2 q^{86} -13913.2 q^{87} -21967.3 q^{88} +42779.8 q^{89} -11421.4 q^{90} -10138.0 q^{91} -149.016 q^{92} -24327.8 q^{93} +6582.41 q^{94} -16767.1 q^{95} +613.812 q^{96} -20992.6 q^{97} -23825.1 q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9	\( 3 q + 2 q^{2} - 27 q^{3} - 20 q^{4} + 75 q^{5} - 18 q^{6} + 152 q^{7} - 24 q^{8} + 243 q^{9} + 50 q^{10} - 363 q^{11} + 180 q^{12} - 546 q^{13} - 8 q^{14} - 675 q^{15} - 1360 q^{16} - 314 q^{17} + 162 q^{18} + 1808 q^{19} - 500 q^{20} - 1368 q^{21} - 242 q^{22} + 4288 q^{23} + 216 q^{24} + 1875 q^{25} + 812 q^{26} - 2187 q^{27} + 5888 q^{28} + 5582 q^{29} - 450 q^{30} + 6328 q^{31} - 736 q^{32} + 3267 q^{33} + 11596 q^{34} + 3800 q^{35} - 1620 q^{36} + 16866 q^{37} + 9584 q^{38} + 4914 q^{39} - 600 q^{40} + 23282 q^{41} + 72 q^{42} + 20572 q^{43} + 2420 q^{44} + 6075 q^{45} + 16592 q^{46} + 3432 q^{47} + 12240 q^{48} + 11531 q^{49} + 1250 q^{50} + 2826 q^{51} + 21816 q^{52} + 16138 q^{53} - 1458 q^{54} - 9075 q^{55} + 15648 q^{56} - 16272 q^{57} + 17460 q^{58} + 21972 q^{59} + 4500 q^{60} + 8322 q^{61} + 5056 q^{62} + 12312 q^{63} + 22208 q^{64} - 13650 q^{65} + 2178 q^{66} - 84332 q^{67} + 59832 q^{68} - 38592 q^{69} - 200 q^{70} + 50528 q^{71} - 1944 q^{72} - 53838 q^{73} + 79212 q^{74} - 16875 q^{75} - 52448 q^{76} - 18392 q^{77} - 7308 q^{78} + 6364 q^{79} - 34000 q^{80} + 19683 q^{81} - 68020 q^{82} + 96272 q^{83} - 52992 q^{84} - 7850 q^{85} + 143152 q^{86} - 50238 q^{87} + 2904 q^{88} - 38938 q^{89} + 4050 q^{90} + 104968 q^{91} + 24000 q^{92} - 56952 q^{93} + 49088 q^{94} + 45200 q^{95} + 6624 q^{96} - 103242 q^{97} + 9554 q^{98} - 29403 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 27 * q^3 - 20 * q^4 + 75 * q^5 - 18 * q^6 + 152 * q^7 - 24 * q^8 + 243 * q^9 + 50 * q^10 - 363 * q^11 + 180 * q^12 - 546 * q^13 - 8 * q^14 - 675 * q^15 - 1360 * q^16 - 314 * q^17 + 162 * q^18 + 1808 * q^19 - 500 * q^20 - 1368 * q^21 - 242 * q^22 + 4288 * q^23 + 216 * q^24 + 1875 * q^25 + 812 * q^26 - 2187 * q^27 + 5888 * q^28 + 5582 * q^29 - 450 * q^30 + 6328 * q^31 - 736 * q^32 + 3267 * q^33 + 11596 * q^34 + 3800 * q^35 - 1620 * q^36 + 16866 * q^37 + 9584 * q^38 + 4914 * q^39 - 600 * q^40 + 23282 * q^41 + 72 * q^42 + 20572 * q^43 + 2420 * q^44 + 6075 * q^45 + 16592 * q^46 + 3432 * q^47 + 12240 * q^48 + 11531 * q^49 + 1250 * q^50 + 2826 * q^51 + 21816 * q^52 + 16138 * q^53 - 1458 * q^54 - 9075 * q^55 + 15648 * q^56 - 16272 * q^57 + 17460 * q^58 + 21972 * q^59 + 4500 * q^60 + 8322 * q^61 + 5056 * q^62 + 12312 * q^63 + 22208 * q^64 - 13650 * q^65 + 2178 * q^66 - 84332 * q^67 + 59832 * q^68 - 38592 * q^69 - 200 * q^70 + 50528 * q^71 - 1944 * q^72 - 53838 * q^73 + 79212 * q^74 - 16875 * q^75 - 52448 * q^76 - 18392 * q^77 - 7308 * q^78 + 6364 * q^79 - 34000 * q^80 + 19683 * q^81 - 68020 * q^82 + 96272 * q^83 - 52992 * q^84 - 7850 * q^85 + 143152 * q^86 - 50238 * q^87 + 2904 * q^88 - 38938 * q^89 + 4050 * q^90 + 104968 * q^91 + 24000 * q^92 - 56952 * q^93 + 49088 * q^94 + 45200 * q^95 + 6624 * q^96 - 103242 * q^97 + 9554 * q^98 - 29403 * q^99

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