LMFDB - Embedded newform 529.6.a.j.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,6,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("529.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	529.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:	$84.8430406811$
Analytic rank:	$1$
Dimension:	$45$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.11115 q^{2} +29.8757 q^{3} +18.5685 q^{4} -10.7320 q^{5} -212.451 q^{6} -93.0172 q^{7} +95.5134 q^{8} +649.559 q^{9} +O(q^{10})$	\(q-7.11115 q^{2} +29.8757 q^{3} +18.5685 q^{4} -10.7320 q^{5} -212.451 q^{6} -93.0172 q^{7} +95.5134 q^{8} +649.559 q^{9} +76.3166 q^{10} +466.180 q^{11} +554.748 q^{12} -208.435 q^{13} +661.459 q^{14} -320.625 q^{15} -1273.40 q^{16} -652.205 q^{17} -4619.11 q^{18} -2658.55 q^{19} -199.276 q^{20} -2778.96 q^{21} -3315.08 q^{22} +2853.53 q^{24} -3009.83 q^{25} +1482.21 q^{26} +12146.2 q^{27} -1727.19 q^{28} -1111.99 q^{29} +2280.01 q^{30} -3239.40 q^{31} +5998.93 q^{32} +13927.5 q^{33} +4637.93 q^{34} +998.256 q^{35} +12061.3 q^{36} -14348.5 q^{37} +18905.4 q^{38} -6227.14 q^{39} -1025.05 q^{40} +6869.58 q^{41} +19761.6 q^{42} +1659.37 q^{43} +8656.27 q^{44} -6971.03 q^{45} +12556.7 q^{47} -38043.8 q^{48} -8154.81 q^{49} +21403.3 q^{50} -19485.1 q^{51} -3870.32 q^{52} -14457.9 q^{53} -86373.8 q^{54} -5003.03 q^{55} -8884.39 q^{56} -79426.1 q^{57} +7907.53 q^{58} +24645.7 q^{59} -5953.52 q^{60} -22279.2 q^{61} +23035.8 q^{62} -60420.1 q^{63} -1910.45 q^{64} +2236.91 q^{65} -99040.4 q^{66} +2224.86 q^{67} -12110.5 q^{68} -7098.75 q^{70} +11527.6 q^{71} +62041.6 q^{72} -30494.5 q^{73} +102034. q^{74} -89920.7 q^{75} -49365.3 q^{76} -43362.8 q^{77} +44282.2 q^{78} +51041.6 q^{79} +13666.1 q^{80} +205035. q^{81} -48850.6 q^{82} -52094.6 q^{83} -51601.0 q^{84} +6999.44 q^{85} -11800.0 q^{86} -33221.5 q^{87} +44526.5 q^{88} +18873.5 q^{89} +49572.1 q^{90} +19388.0 q^{91} -96779.3 q^{93} -89292.4 q^{94} +28531.4 q^{95} +179222. q^{96} -119275. q^{97} +57990.1 q^{98} +302812. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q + 2 q^{3} + 640 q^{4} - 267 q^{5} - 382 q^{6} - 548 q^{7} + 1155 q^{8} + 2677 q^{9}+O(q^{10}) $ 45 * q + 2 * q^3 + 640 * q^4 - 267 * q^5 - 382 * q^6 - 548 * q^7 + 1155 * q^8 + 2677 * q^9	\( 45 q + 2 q^{3} + 640 q^{4} - 267 q^{5} - 382 q^{6} - 548 q^{7} + 1155 q^{8} + 2677 q^{9} - 1017 q^{10} - 2701 q^{11} + 2305 q^{12} + 162 q^{13} - 3828 q^{14} - 4745 q^{15} + 9336 q^{16} - 5710 q^{17} - 1954 q^{18} - 10138 q^{19} - 10390 q^{20} - 6443 q^{21} - 5025 q^{22} - 10021 q^{24} + 15878 q^{25} - 18418 q^{26} + 8315 q^{27} - 16901 q^{28} - 13505 q^{29} - 16663 q^{30} - 7619 q^{31} + 30860 q^{32} - 29493 q^{33} - 11713 q^{34} + 10137 q^{35} - 12276 q^{36} - 32241 q^{37} - 49002 q^{38} + 56679 q^{39} - 59635 q^{40} + 34925 q^{41} - 37304 q^{42} - 23272 q^{43} - 83463 q^{44} - 48953 q^{45} - 36261 q^{47} - 32516 q^{48} + 51857 q^{49} + 17956 q^{50} - 103797 q^{51} - 120873 q^{52} - 110012 q^{53} - 93972 q^{54} + 12048 q^{55} - 250769 q^{56} - 26318 q^{57} - 24792 q^{58} + 69296 q^{59} - 200115 q^{60} - 100662 q^{61} - 109136 q^{62} - 197501 q^{63} + 169417 q^{64} - 189877 q^{65} - 177787 q^{66} - 85847 q^{67} - 309649 q^{68} - 308157 q^{70} + 194121 q^{71} + 329967 q^{72} - 106792 q^{73} - 238219 q^{74} - 99472 q^{75} - 423596 q^{76} - 127932 q^{77} - 455516 q^{78} - 390789 q^{79} - 404751 q^{80} - 135339 q^{81} + 485075 q^{82} - 421445 q^{83} - 264219 q^{84} + 258029 q^{85} - 452061 q^{86} - 100797 q^{87} - 117190 q^{88} - 544607 q^{89} - 350405 q^{90} - 315066 q^{91} - 700704 q^{93} + 986987 q^{94} + 620544 q^{95} - 774244 q^{96} - 199878 q^{97} - 353401 q^{98} - 897462 q^{99}+O(q^{100}) \) 45 * q + 2 * q^3 + 640 * q^4 - 267 * q^5 - 382 * q^6 - 548 * q^7 + 1155 * q^8 + 2677 * q^9 - 1017 * q^10 - 2701 * q^11 + 2305 * q^12 + 162 * q^13 - 3828 * q^14 - 4745 * q^15 + 9336 * q^16 - 5710 * q^17 - 1954 * q^18 - 10138 * q^19 - 10390 * q^20 - 6443 * q^21 - 5025 * q^22 - 10021 * q^24 + 15878 * q^25 - 18418 * q^26 + 8315 * q^27 - 16901 * q^28 - 13505 * q^29 - 16663 * q^30 - 7619 * q^31 + 30860 * q^32 - 29493 * q^33 - 11713 * q^34 + 10137 * q^35 - 12276 * q^36 - 32241 * q^37 - 49002 * q^38 + 56679 * q^39 - 59635 * q^40 + 34925 * q^41 - 37304 * q^42 - 23272 * q^43 - 83463 * q^44 - 48953 * q^45 - 36261 * q^47 - 32516 * q^48 + 51857 * q^49 + 17956 * q^50 - 103797 * q^51 - 120873 * q^52 - 110012 * q^53 - 93972 * q^54 + 12048 * q^55 - 250769 * q^56 - 26318 * q^57 - 24792 * q^58 + 69296 * q^59 - 200115 * q^60 - 100662 * q^61 - 109136 * q^62 - 197501 * q^63 + 169417 * q^64 - 189877 * q^65 - 177787 * q^66 - 85847 * q^67 - 309649 * q^68 - 308157 * q^70 + 194121 * q^71 + 329967 * q^72 - 106792 * q^73 - 238219 * q^74 - 99472 * q^75 - 423596 * q^76 - 127932 * q^77 - 455516 * q^78 - 390789 * q^79 - 404751 * q^80 - 135339 * q^81 + 485075 * q^82 - 421445 * q^83 - 264219 * q^84 + 258029 * q^85 - 452061 * q^86 - 100797 * q^87 - 117190 * q^88 - 544607 * q^89 - 350405 * q^90 - 315066 * q^91 - 700704 * q^93 + 986987 * q^94 + 620544 * q^95 - 774244 * q^96 - 199878 * q^97 - 353401 * q^98 - 897462 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−7.11115	−1.25709	−0.628543	−	0.777775i	$-0.716348\pi$
$2$	−7.11115	−1.25709	−0.628543	+	0.777775i	$0.716348\pi$
$3$	29.8757	1.91653	0.958264	−	0.285884i	$-0.0922872\pi$
$3$	29.8757	1.91653	0.958264	+	0.285884i	$0.0922872\pi$
$4$	18.5685	0.580266
$5$	−10.7320	−0.191979	−0.0959895	−	0.995382i	$-0.530602\pi$
$5$	−10.7320	−0.191979	−0.0959895	+	0.995382i	$0.530602\pi$
$6$	−212.451	−2.40924
$7$	−93.0172	−0.717494	−0.358747	−	0.933435i	$-0.616796\pi$
$7$	−93.0172	−0.717494	−0.358747	+	0.933435i	$0.616796\pi$
$8$	95.5134	0.527642
$9$	649.559	2.67308
$10$	76.3166	0.241334
$11$	466.180	1.16164	0.580821	−	0.814031i	$-0.302732\pi$
$11$	466.180	1.16164	0.580821	+	0.814031i	$0.302732\pi$
$12$	554.748	1.11210
$13$	−208.435	−0.342068	−0.171034	−	0.985265i	$-0.554711\pi$
$13$	−208.435	−0.342068	−0.171034	+	0.985265i	$0.554711\pi$
$14$	661.459	0.901951
$15$	−320.625	−0.367933
$16$	−1273.40	−1.24356
$17$	−652.205	−0.547346	−0.273673	−	0.961823i	$-0.588239\pi$
$17$	−652.205	−0.547346	−0.273673	+	0.961823i	$0.588239\pi$
$18$	−4619.11	−3.36029
$19$	−2658.55	−1.68951	−0.844755	−	0.535153i	$-0.820254\pi$
$19$	−2658.55	−1.68951	−0.844755	+	0.535153i	$0.820254\pi$
$20$	−199.276	−0.111399
$21$	−2778.96	−1.37510
$22$	−3315.08	−1.46028
$23$	0	0
$23$	0	0
$24$	2853.53	1.01124
$25$	−3009.83	−0.963144
$26$	1482.21	0.430009
$27$	12146.2	3.20651
$28$	−1727.19	−0.416337
$29$	−1111.99	−0.245531	−0.122765	−	0.992436i	$-0.539176\pi$
$29$	−1111.99	−0.245531	−0.122765	+	0.992436i	$0.539176\pi$
$30$	2280.01	0.462524
$31$	−3239.40	−0.605424	−0.302712	−	0.953082i	$-0.597892\pi$
$31$	−3239.40	−0.605424	−0.302712	+	0.953082i	$0.597892\pi$
$32$	5998.93	1.03562
$33$	13927.5	2.22632
$34$	4637.93	0.688061
$35$	998.256	0.137744
$36$	12061.3	1.55110
$37$	−14348.5	−1.72307	−0.861533	−	0.507701i	$-0.830495\pi$
$37$	−14348.5	−1.72307	−0.861533	+	0.507701i	$0.830495\pi$
$38$	18905.4	2.12386
$39$	−6227.14	−0.655582
$40$	−1025.05	−0.101296
$41$	6869.58	0.638220	0.319110	−	0.947718i	$-0.396616\pi$
$41$	6869.58	0.638220	0.319110	+	0.947718i	$0.396616\pi$
$42$	19761.6	1.72862
$43$	1659.37	0.136859	0.0684293	−	0.997656i	$-0.478201\pi$
$43$	1659.37	0.136859	0.0684293	+	0.997656i	$0.478201\pi$
$44$	8656.27	0.674061
$45$	−6971.03	−0.513176
$46$	0	0
$47$	12556.7	0.829144	0.414572	−	0.910017i	$-0.363931\pi$
$47$	12556.7	0.829144	0.414572	+	0.910017i	$0.363931\pi$
$48$	−38043.8	−2.38331
$49$	−8154.81	−0.485203
$50$	21403.3	1.21076
$51$	−19485.1	−1.04900
$52$	−3870.32	−0.198490
$53$	−14457.9	−0.706995	−0.353498	−	0.935435i	$-0.615008\pi$
$53$	−14457.9	−0.706995	−0.353498	+	0.935435i	$0.615008\pi$
$54$	−86373.8	−4.03086
$55$	−5003.03	−0.223011
$56$	−8884.39	−0.378580
$57$	−79426.1	−3.23800
$58$	7907.53	0.308653
$59$	24645.7	0.921745	0.460872	−	0.887466i	$-0.347537\pi$
$59$	24645.7	0.921745	0.460872	+	0.887466i	$0.347537\pi$
$60$	−5953.52	−0.213499
$61$	−22279.2	−0.766611	−0.383306	−	0.923622i	$-0.625214\pi$
$61$	−22279.2	−0.766611	−0.383306	+	0.923622i	$0.625214\pi$
$62$	23035.8	0.761070
$63$	−60420.1	−1.91792
$64$	−1910.45	−0.0583022
$65$	2236.91	0.0656698
$66$	−99040.4	−2.79868
$67$	2224.86	0.0605503	0.0302751	−	0.999542i	$-0.490362\pi$
$67$	2224.86	0.0605503	0.0302751	+	0.999542i	$0.490362\pi$
$68$	−12110.5	−0.317606
$69$	0	0
$70$	−7098.75	−0.173156
$71$	11527.6	0.271389	0.135695	−	0.990751i	$-0.456673\pi$
$71$	11527.6	0.271389	0.135695	+	0.990751i	$0.456673\pi$
$72$	62041.6	1.41043
$73$	−30494.5	−0.669752	−0.334876	−	0.942262i	$-0.608694\pi$
$73$	−30494.5	−0.669752	−0.334876	+	0.942262i	$0.608694\pi$
$74$	102034.	2.16604
$75$	−89920.7	−1.84589
$76$	−49365.3	−0.980365
$77$	−43362.8	−0.833471
$78$	44282.2	0.824124
$79$	51041.6	0.920145	0.460073	−	0.887881i	$-0.347823\pi$
$79$	51041.6	0.920145	0.460073	+	0.887881i	$0.347823\pi$
$80$	13666.1	0.238737
$81$	205035.	3.47228
$82$	−48850.6	−0.802298
$83$	−52094.6	−0.830036	−0.415018	−	0.909813i	$-0.636225\pi$
$83$	−52094.6	−0.830036	−0.415018	+	0.909813i	$0.636225\pi$
$84$	−51601.0	−0.797922
$85$	6999.44	0.105079
$86$	−11800.0	−0.172043
$87$	−33221.5	−0.470566
$88$	44526.5	0.612931
$89$	18873.5	0.252567	0.126284	−	0.991994i	$-0.459695\pi$
$89$	18873.5	0.252567	0.126284	+	0.991994i	$0.459695\pi$
$90$	49572.1	0.645106
$91$	19388.0	0.245431
$92$	0	0
$93$	−96779.3	−1.16031
$94$	−89292.4	−1.04231
$95$	28531.4	0.324351
$96$	179222.	1.98479
$97$	−119275.	−1.28712	−0.643562	−	0.765394i	$-0.722544\pi$
$97$	−119275.	−1.28712	−0.643562	+	0.765394i	$0.722544\pi$
$98$	57990.1	0.609942
$99$	302812.	3.10516
$100$	−55888.0	−0.558880
$101$	−127505.	−1.24372	−0.621862	−	0.783127i	$-0.713623\pi$
$101$	−127505.	−1.24372	−0.621862	+	0.783127i	$0.713623\pi$
$102$	138562.	1.31869
$103$	62705.8	0.582391	0.291196	−	0.956664i	$-0.405947\pi$
$103$	62705.8	0.582391	0.291196	+	0.956664i	$0.405947\pi$
$104$	−19908.3	−0.180489
$105$	29823.6	0.263990
$106$	102813.	0.888754
$107$	125559.	1.06020	0.530102	−	0.847934i	$-0.322154\pi$
$107$	125559.	1.06020	0.530102	+	0.847934i	$0.322154\pi$
$108$	225538.	1.86063
$109$	−126195.	−1.01736	−0.508682	−	0.860955i	$-0.669867\pi$
$109$	−126195.	−1.01736	−0.508682	+	0.860955i	$0.669867\pi$
$110$	35577.3	0.280344
$111$	−428672.	−3.30231
$112$	118448.	0.892244
$113$	−66919.2	−0.493009	−0.246504	−	0.969142i	$-0.579282\pi$
$113$	−66919.2	−0.493009	−0.246504	+	0.969142i	$0.579282\pi$
$114$	564811.	4.07044
$115$	0	0
$116$	−20648.0	−0.142473
$117$	−135391.	−0.914375
$118$	−175259.	−1.15871
$119$	60666.3	0.392717
$120$	−30624.0	−0.194137
$121$	56273.2	0.349413
$122$	158431.	0.963696
$123$	205234.	1.22317
$124$	−60150.7	−0.351307
$125$	65838.6	0.376882
$126$	429657.	2.41099
$127$	−146937.	−0.808391	−0.404195	−	0.914673i	$-0.632448\pi$
$127$	−146937.	−0.808391	−0.404195	+	0.914673i	$0.632448\pi$
$128$	−178380.	−0.962326
$129$	49574.9	0.262294
$130$	−15907.0	−0.0825526
$131$	−1251.99	−0.00637417	−0.00318708	−	0.999995i	$-0.501014\pi$
$131$	−1251.99	−0.00637417	−0.00318708	+	0.999995i	$0.501014\pi$
$132$	258612.	1.29186
$133$	247291.	1.21221
$134$	−15821.3	−0.0761169
$135$	−130353.	−0.615582
$136$	−62294.4	−0.288803
$137$	213141.	0.970207	0.485104	−	0.874457i	$-0.338782\pi$
$137$	213141.	0.970207	0.485104	+	0.874457i	$0.338782\pi$
$138$	0	0
$139$	160419.	0.704239	0.352119	−	0.935955i	$-0.385461\pi$
$139$	160419.	0.704239	0.352119	+	0.935955i	$0.385461\pi$
$140$	18536.1	0.0799280
$141$	375140.	1.58908
$142$	−81974.4	−0.341159
$143$	−97168.3	−0.397360
$144$	−827150.	−3.32413
$145$	11933.8	0.0471367
$146$	216851.	0.841936
$147$	−243631.	−0.929905
$148$	−266430.	−0.999837
$149$	−187466.	−0.691761	−0.345881	−	0.938278i	$-0.612420\pi$
$149$	−187466.	−0.691761	−0.345881	+	0.938278i	$0.612420\pi$
$150$	639440.	2.32045
$151$	−370560.	−1.32256	−0.661282	−	0.750138i	$-0.729987\pi$
$151$	−370560.	−1.32256	−0.661282	+	0.750138i	$0.729987\pi$
$152$	−253927.	−0.891457
$153$	−423646.	−1.46310
$154$	308359.	1.04774
$155$	34765.0	0.116229
$156$	−115629.	−0.380412
$157$	−200828.	−0.650241	−0.325121	−	0.945673i	$-0.605405\pi$
$157$	−200828.	−0.650241	−0.325121	+	0.945673i	$0.605405\pi$
$158$	−362964.	−1.15670
$159$	−431941.	−1.35498
$160$	−64380.3	−0.198817
$161$	0	0
$162$	−1.45803e6	−4.36496
$163$	168131.	0.495654	0.247827	−	0.968804i	$-0.420283\pi$
$163$	168131.	0.495654	0.247827	+	0.968804i	$0.420283\pi$
$164$	127558.	0.370337
$165$	−149469.	−0.427407
$166$	370452.	1.04343
$167$	636912.	1.76721	0.883605	−	0.468233i	$-0.155109\pi$
$167$	636912.	1.76721	0.883605	+	0.468233i	$0.155109\pi$
$168$	−265428.	−0.725559
$169$	−327848.	−0.882990
$170$	−49774.1	−0.132093
$171$	−1.72688e6	−4.51620
$172$	30812.0	0.0794144
$173$	−315170.	−0.800626	−0.400313	−	0.916379i	$-0.631099\pi$
$173$	−315170.	−0.800626	−0.400313	+	0.916379i	$0.631099\pi$
$174$	236243.	0.591543
$175$	279965.	0.691050
$176$	−593636.	−1.44457
$177$	736307.	1.76655
$178$	−134212.	−0.317499
$179$	294116.	0.686099	0.343049	−	0.939317i	$-0.388540\pi$
$179$	294116.	0.686099	0.343049	+	0.939317i	$0.388540\pi$
$180$	−129442.	−0.297778
$181$	−676064.	−1.53388	−0.766940	−	0.641719i	$-0.778222\pi$
$181$	−676064.	−1.53388	−0.766940	+	0.641719i	$0.778222\pi$
$182$	−137871.	−0.308528
$183$	−665607.	−1.46923
$184$	0	0
$185$	153987.	0.330793
$186$	688212.	1.45861
$187$	−304045.	−0.635820
$188$	233159.	0.481124
$189$	−1.12981e6	−2.30065
$190$	−202891.	−0.407737
$191$	−704022.	−1.39638	−0.698189	−	0.715914i	$-0.746010\pi$
$191$	−704022.	−1.39638	−0.698189	+	0.715914i	$0.746010\pi$
$192$	−57076.0	−0.111738
$193$	−27707.0	−0.0535423	−0.0267711	−	0.999642i	$-0.508523\pi$
$193$	−27707.0	−0.0535423	−0.0267711	+	0.999642i	$0.508523\pi$
$194$	848183.	1.61802
$195$	66829.4	0.125858
$196$	−151423.	−0.281547
$197$	326518.	0.599435	0.299718	−	0.954028i	$-0.403108\pi$
$197$	326518.	0.599435	0.299718	+	0.954028i	$0.403108\pi$
$198$	−2.15334e6	−3.90346
$199$	18939.2	0.0339024	0.0169512	−	0.999856i	$-0.494604\pi$
$199$	18939.2	0.0339024	0.0169512	+	0.999856i	$0.494604\pi$
$200$	−287479.	−0.508195
$201$	66469.4	0.116046
$202$	906708.	1.56347
$203$	103434.	0.176167
$204$	−361809.	−0.608702
$205$	−73724.0	−0.122525
$206$	−445911.	−0.732116
$207$	0	0
$208$	265422.	0.425381
$209$	−1.23936e6	−1.96261
$210$	−212080.	−0.331858
$211$	120903.	0.186952	0.0934760	−	0.995622i	$-0.470202\pi$
$211$	120903.	0.186952	0.0934760	+	0.995622i	$0.470202\pi$
$212$	−268462.	−0.410245
$213$	344395.	0.520125
$214$	−892872.	−1.33277
$215$	−17808.3	−0.0262740
$216$	1.16013e6	1.69189
$217$	301319.	0.434388
$218$	897392.	1.27891
$219$	−911045.	−1.28360
$220$	−92898.7	−0.129406
$221$	135942.	0.187229
$222$	3.04835e6	4.15128
$223$	325035.	0.437691	0.218845	−	0.975760i	$-0.429771\pi$
$223$	325035.	0.437691	0.218845	+	0.975760i	$0.429771\pi$
$224$	−558004.	−0.743048
$225$	−1.95506e6	−2.57456
$226$	475873.	0.619755
$227$	−605627.	−0.780083	−0.390041	−	0.920797i	$-0.627539\pi$
$227$	−605627.	−0.780083	−0.390041	+	0.920797i	$0.627539\pi$
$228$	−1.47482e6	−1.87890
$229$	784862.	0.989019	0.494510	−	0.869172i	$-0.335348\pi$
$229$	784862.	0.989019	0.494510	+	0.869172i	$0.335348\pi$
$230$	0	0
$231$	−1.29549e6	−1.59737
$232$	−106210.	−0.129552
$233$	−983552.	−1.18688	−0.593441	−	0.804877i	$-0.702231\pi$
$233$	−983552.	−1.18688	−0.593441	+	0.804877i	$0.702231\pi$
$234$	962784.	1.14945
$235$	−134758.	−0.159178
$236$	457633.	0.534857
$237$	1.52490e6	1.76348
$238$	−431407.	−0.493680
$239$	151359.	0.171401	0.0857007	−	0.996321i	$-0.472687\pi$
$239$	151359.	0.171401	0.0857007	+	0.996321i	$0.472687\pi$
$240$	408285.	0.457546
$241$	141256.	0.156662	0.0783310	−	0.996927i	$-0.475041\pi$
$241$	141256.	0.156662	0.0783310	+	0.996927i	$0.475041\pi$
$242$	−400168.	−0.439242
$243$	3.17403e6	3.44822
$244$	−413692.	−0.444838
$245$	87517.0	0.0931488
$246$	−1.45945e6	−1.53763
$247$	554135.	0.577927
$248$	−309406.	−0.319447
$249$	−1.55636e6	−1.59079
$250$	−468189.	−0.473774
$251$	−633033.	−0.634223	−0.317111	−	0.948388i	$-0.602713\pi$
$251$	−633033.	−0.634223	−0.317111	+	0.948388i	$0.602713\pi$
$252$	−1.12191e6	−1.11290
$253$	0	0
$254$	1.04489e6	1.01622
$255$	209113.	0.201387
$256$	1.32962e6	1.26803
$257$	1.40399e6	1.32597	0.662983	−	0.748635i	$-0.269290\pi$
$257$	1.40399e6	1.32597	0.662983	+	0.748635i	$0.269290\pi$
$258$	−352535.	−0.329726
$259$	1.33466e6	1.23629
$260$	41536.1	0.0381059
$261$	−722303.	−0.656323
$262$	8903.11	0.00801288
$263$	−1.48499e6	−1.32384	−0.661919	−	0.749575i	$-0.730258\pi$
$263$	−1.48499e6	−1.32384	−0.661919	+	0.749575i	$0.730258\pi$
$264$	1.33026e6	1.17470
$265$	155162.	0.135728
$266$	−1.75852e6	−1.52386
$267$	563859.	0.484052
$268$	41312.4	0.0351353
$269$	−443302.	−0.373524	−0.186762	−	0.982405i	$-0.559799\pi$
$269$	−443302.	−0.373524	−0.186762	+	0.982405i	$0.559799\pi$
$270$	926959.	0.773840
$271$	−1.45991e6	−1.20755	−0.603774	−	0.797156i	$-0.706337\pi$
$271$	−1.45991e6	−1.20755	−0.603774	+	0.797156i	$0.706337\pi$
$272$	830520.	0.680656
$273$	579231.	0.470376
$274$	−1.51567e6	−1.21963
$275$	−1.40312e6	−1.11883
$276$	0	0
$277$	739810.	0.579323	0.289661	−	0.957129i	$-0.406457\pi$
$277$	739810.	0.579323	0.289661	+	0.957129i	$0.406457\pi$
$278$	−1.14077e6	−0.885289
$279$	−2.10418e6	−1.61835
$280$	95346.8	0.0726794
$281$	2.09694e6	1.58424	0.792118	−	0.610368i	$-0.208979\pi$
$281$	2.09694e6	1.58424	0.792118	+	0.610368i	$0.208979\pi$
$282$	−2.66768e6	−1.99761
$283$	−2.25052e6	−1.67038	−0.835192	−	0.549959i	$-0.814643\pi$
$283$	−2.25052e6	−1.67038	−0.835192	+	0.549959i	$0.814643\pi$
$284$	214050.	0.157478
$285$	852397.	0.621627
$286$	690978.	0.499516
$287$	−638989.	−0.457919
$288$	3.89666e6	2.76829
$289$	−994485.	−0.700412
$290$	−84863.2	−0.0592549
$291$	−3.56343e6	−2.46681
$292$	−566237.	−0.388634
$293$	−2.78135e6	−1.89272	−0.946362	−	0.323108i	$-0.895272\pi$
$293$	−2.78135e6	−1.89272	−0.946362	+	0.323108i	$0.895272\pi$
$294$	1.73250e6	1.16897
$295$	−264496.	−0.176956
$296$	−1.37047e6	−0.909162
$297$	5.66234e6	3.72482
$298$	1.33310e6	0.869604
$299$	0	0
$300$	−1.66969e6	−1.07111
$301$	−154350.	−0.0981952
$302$	2.63511e6	1.66258
$303$	−3.80930e6	−2.38363
$304$	3.38541e6	2.10100
$305$	239099.	0.147173
$306$	3.01261e6	1.83924
$307$	1.08405e6	0.656451	0.328226	−	0.944599i	$-0.393549\pi$
$307$	1.08405e6	0.656451	0.328226	+	0.944599i	$0.393549\pi$
$308$	−805182.	−0.483635
$309$	1.87338e6	1.11617
$310$	−247219.	−0.146110
$311$	284515.	0.166803	0.0834016	−	0.996516i	$-0.473422\pi$
$311$	284515.	0.166803	0.0834016	+	0.996516i	$0.473422\pi$
$312$	−594776.	−0.345913
$313$	1.64109e6	0.946829	0.473414	−	0.880840i	$-0.343021\pi$
$313$	1.64109e6	0.946829	0.473414	+	0.880840i	$0.343021\pi$
$314$	1.42812e6	0.817409
$315$	648426.	0.368200
$316$	947766.	0.533929
$317$	2.54980e6	1.42514	0.712570	−	0.701601i	$-0.247531\pi$
$317$	2.54980e6	1.42514	0.712570	+	0.701601i	$0.247531\pi$
$318$	3.07160e6	1.70332
$319$	−518388.	−0.285219
$320$	20502.8	0.0111928
$321$	3.75118e6	2.03191
$322$	0	0
$323$	1.73392e6	0.924747
$324$	3.80719e6	2.01485
$325$	627353.	0.329460
$326$	−1.19561e6	−0.623080
$327$	−3.77017e6	−1.94981
$328$	656137.	0.336752
$329$	−1.16799e6	−0.594905
$330$	1.06290e6	0.537287
$331$	−2.09104e6	−1.04904	−0.524520	−	0.851398i	$-0.675755\pi$
$331$	−2.09104e6	−1.04904	−0.524520	+	0.851398i	$0.675755\pi$
$332$	−967318.	−0.481642
$333$	−9.32019e6	−4.60590
$334$	−4.52918e6	−2.22154
$335$	−23877.1	−0.0116244
$336$	3.53873e6	1.71001
$337$	−3.44171e6	−1.65082	−0.825410	−	0.564533i	$-0.809056\pi$
$337$	−3.44171e6	−1.65082	−0.825410	+	0.564533i	$0.809056\pi$
$338$	2.33138e6	1.10999
$339$	−1.99926e6	−0.944866
$340$	129969.	0.0609737
$341$	−1.51014e6	−0.703286
$342$	1.22801e7	5.67725
$343$	2.32188e6	1.06562
$344$	158492.	0.0722124
$345$	0	0
$346$	2.24122e6	1.00646
$347$	329430.	0.146872	0.0734360	−	0.997300i	$-0.476604\pi$
$347$	329430.	0.146872	0.0734360	+	0.997300i	$0.476604\pi$
$348$	−616873.	−0.273054
$349$	−455642.	−0.200244	−0.100122	−	0.994975i	$-0.531923\pi$
$349$	−455642.	−0.200244	−0.100122	+	0.994975i	$0.531923\pi$
$350$	−1.99088e6	−0.868709
$351$	−2.53170e6	−1.09684
$352$	2.79659e6	1.20302
$353$	−3.53835e6	−1.51135	−0.755674	−	0.654948i	$-0.772691\pi$
$353$	−3.53835e6	−1.51135	−0.755674	+	0.654948i	$0.772691\pi$
$354$	−5.23599e6	−2.22071
$355$	−123713.	−0.0521010
$356$	350452.	0.146556
$357$	1.81245e6	0.752654
$358$	−2.09151e6	−0.862485
$359$	544134.	0.222828	0.111414	−	0.993774i	$-0.464462\pi$
$359$	544134.	0.222828	0.111414	+	0.993774i	$0.464462\pi$
$360$	−665827.	−0.270773
$361$	4.59179e6	1.85445
$362$	4.80760e6	1.92822
$363$	1.68120e6	0.669659
$364$	360007.	0.142415
$365$	327265.	0.128578
$366$	4.73324e6	1.84695
$367$	970259.	0.376030	0.188015	−	0.982166i	$-0.439795\pi$
$367$	970259.	0.376030	0.188015	+	0.982166i	$0.439795\pi$
$368$	0	0
$369$	4.46219e6	1.70601
$370$	−1.09503e6	−0.415835
$371$	1.34484e6	0.507265
$372$	−1.79705e6	−0.673290
$373$	1.68042e6	0.625382	0.312691	−	0.949855i	$-0.398770\pi$
$373$	1.68042e6	0.625382	0.312691	+	0.949855i	$0.398770\pi$
$374$	2.16211e6	0.799281
$375$	1.96698e6	0.722306
$376$	1.19933e6	0.437491
$377$	231777.	0.0839881
$378$	8.03424e6	2.89211
$379$	5.13203e6	1.83523	0.917616	−	0.397468i	$-0.130111\pi$
$379$	5.13203e6	1.83523	0.917616	+	0.397468i	$0.130111\pi$
$380$	529786.	0.188210
$381$	−4.38984e6	−1.54930
$382$	5.00641e6	1.75537
$383$	3.24730e6	1.13116	0.565582	−	0.824692i	$-0.308651\pi$
$383$	3.24730e6	1.13116	0.565582	+	0.824692i	$0.308651\pi$
$384$	−5.32924e6	−1.84433
$385$	465367.	0.160009
$386$	197029.	0.0673072
$387$	1.07786e6	0.365834
$388$	−2.21476e6	−0.746874
$389$	−2.42201e6	−0.811524	−0.405762	−	0.913979i	$-0.632994\pi$
$389$	−2.42201e6	−0.811524	−0.405762	+	0.913979i	$0.632994\pi$
$390$	−475234.	−0.158214
$391$	0	0
$392$	−778893.	−0.256014
$393$	−37404.2	−0.0122163
$394$	−2.32192e6	−0.753542
$395$	−547776.	−0.176649
$396$	5.62276e6	1.80182
$397$	−2.23897e6	−0.712970	−0.356485	−	0.934301i	$-0.616025\pi$
$397$	−2.23897e6	−0.712970	−0.356485	+	0.934301i	$0.616025\pi$
$398$	−134680.	−0.0426182
$399$	7.38799e6	2.32324
$400$	3.83272e6	1.19772
$401$	553540.	0.171905	0.0859525	−	0.996299i	$-0.472607\pi$
$401$	553540.	0.171905	0.0859525	+	0.996299i	$0.472607\pi$
$402$	−472674.	−0.145880
$403$	675203.	0.207096
$404$	−2.36758e6	−0.721690
$405$	−2.20042e6	−0.666606
$406$	−735536.	−0.221457
$407$	−6.68899e6	−2.00159
$408$	−1.86109e6	−0.553499
$409$	30750.1	0.00908948	0.00454474	−	0.999990i	$-0.498553\pi$
$409$	30750.1	0.00908948	0.00454474	+	0.999990i	$0.498553\pi$
$410$	524262.	0.154024
$411$	6.36773e6	1.85943
$412$	1.16435e6	0.337942
$413$	−2.29247e6	−0.661346
$414$	0	0
$415$	559076.	0.159350
$416$	−1.25039e6	−0.354251
$417$	4.79265e6	1.34969
$418$	8.81331e6	2.46717
$419$	−811218.	−0.225737	−0.112868	−	0.993610i	$-0.536004\pi$
$419$	−811218.	−0.225737	−0.112868	+	0.993610i	$0.536004\pi$
$420$	553780.	0.153184
$421$	1.82251e6	0.501146	0.250573	−	0.968098i	$-0.419381\pi$
$421$	1.82251e6	0.501146	0.250573	+	0.968098i	$0.419381\pi$
$422$	−859758.	−0.235015
$423$	8.15630e6	2.21637
$424$	−1.38093e6	−0.373040
$425$	1.96302e6	0.527173
$426$	−2.44904e6	−0.653842
$427$	2.07235e6	0.550039
$428$	2.33145e6	0.615200
$429$	−2.90297e6	−0.761552
$430$	126637.	0.0330287
$431$	2.20074e6	0.570658	0.285329	−	0.958430i	$-0.407897\pi$
$431$	2.20074e6	0.570658	0.285329	+	0.958430i	$0.407897\pi$
$432$	−1.54671e7	−3.98748
$433$	4.32339e6	1.10817	0.554083	−	0.832461i	$-0.313069\pi$
$433$	4.32339e6	1.10817	0.554083	+	0.832461i	$0.313069\pi$
$434$	−2.14273e6	−0.546063
$435$	356531.	0.0903389
$436$	−2.34325e6	−0.590341
$437$	0	0
$438$	6.47858e6	1.61360
$439$	−5.65342e6	−1.40007	−0.700036	−	0.714108i	$-0.746833\pi$
$439$	−5.65342e6	−1.40007	−0.700036	+	0.714108i	$0.746833\pi$
$440$	−477856.	−0.117670
$441$	−5.29703e6	−1.29699
$442$	−966707.	−0.235364
$443$	1.08709e6	0.263183	0.131591	−	0.991304i	$-0.457991\pi$
$443$	1.08709e6	0.263183	0.131591	+	0.991304i	$0.457991\pi$
$444$	−7.95979e6	−1.91622
$445$	−202549.	−0.0484876
$446$	−2.31137e6	−0.550215
$447$	−5.60068e6	−1.32578
$448$	177704.	0.0418315
$449$	−3.72019e6	−0.870861	−0.435430	−	0.900222i	$-0.643404\pi$
$449$	−3.72019e6	−0.870861	−0.435430	+	0.900222i	$0.643404\pi$
$450$	1.39027e7	3.23645
$451$	3.20246e6	0.741383
$452$	−1.24259e6	−0.286076
$453$	−1.10708e7	−2.53473
$454$	4.30671e6	0.980631
$455$	−208071.	−0.0471177
$456$	−7.58626e6	−1.70850
$457$	−3.27027e6	−0.732476	−0.366238	−	0.930521i	$-0.619354\pi$
$457$	−3.27027e6	−0.732476	−0.366238	+	0.930521i	$0.619354\pi$
$458$	−5.58128e6	−1.24328
$459$	−7.92184e6	−1.75507
$460$	0	0
$461$	652438.	0.142984	0.0714919	−	0.997441i	$-0.477224\pi$
$461$	652438.	0.142984	0.0714919	+	0.997441i	$0.477224\pi$
$462$	9.21246e6	2.00803
$463$	347737.	0.0753874	0.0376937	−	0.999289i	$-0.487999\pi$
$463$	347737.	0.0753874	0.0376937	+	0.999289i	$0.487999\pi$
$464$	1.41601e6	0.305331
$465$	1.03863e6	0.222756
$466$	6.99419e6	1.49201
$467$	7.49039e6	1.58932	0.794661	−	0.607053i	$-0.207648\pi$
$467$	7.49039e6	1.58932	0.794661	+	0.607053i	$0.207648\pi$
$468$	−2.51400e6	−0.530580
$469$	−206950.	−0.0434444
$470$	958282.	0.200101
$471$	−5.99987e6	−1.24621
$472$	2.35399e6	0.486351
$473$	773566.	0.158981
$474$	−1.08438e7	−2.21685
$475$	8.00177e6	1.62724
$476$	1.12648e6	0.227880
$477$	−9.39128e6	−1.88986
$478$	−1.07634e6	−0.215466
$479$	6.31081e6	1.25674	0.628372	−	0.777913i	$-0.283722\pi$
$479$	6.31081e6	1.25674	0.628372	+	0.777913i	$0.283722\pi$
$480$	−1.92341e6	−0.381038
$481$	2.99073e6	0.589405
$482$	−1.00449e6	−0.196938
$483$	0	0
$484$	1.04491e6	0.202752
$485$	1.28005e6	0.247101
$486$	−2.25710e7	−4.33471
$487$	−8.63002e6	−1.64888	−0.824441	−	0.565948i	$-0.808510\pi$
$487$	−8.63002e6	−1.64888	−0.824441	+	0.565948i	$0.808510\pi$
$488$	−2.12796e6	−0.404496
$489$	5.02304e6	0.949936
$490$	−622347.	−0.117096
$491$	−432784.	−0.0810154	−0.0405077	−	0.999179i	$-0.512898\pi$
$491$	−432784.	−0.0810154	−0.0405077	+	0.999179i	$0.512898\pi$
$492$	3.81088e6	0.709762
$493$	725246.	0.134390
$494$	−3.94054e6	−0.726504
$495$	−3.24976e6	−0.596126
$496$	4.12505e6	0.752880
$497$	−1.07226e6	−0.194720
$498$	1.10675e7	1.99976
$499$	1.64297e6	0.295377	0.147689	−	0.989034i	$-0.452817\pi$
$499$	1.64297e6	0.295377	0.147689	+	0.989034i	$0.452817\pi$
$500$	1.22253e6	0.218692
$501$	1.90282e7	3.38691
$502$	4.50159e6	0.797273
$503$	−5.21132e6	−0.918391	−0.459195	−	0.888335i	$-0.651862\pi$
$503$	−5.21132e6	−0.918391	−0.459195	+	0.888335i	$0.651862\pi$
$504$	−5.77093e6	−1.01197
$505$	1.36838e6	0.238769
$506$	0	0
$507$	−9.79469e6	−1.69228
$508$	−2.72840e6	−0.469082
$509$	5.00695e6	0.856601	0.428300	−	0.903636i	$-0.359113\pi$
$509$	5.00695e6	0.856601	0.428300	+	0.903636i	$0.359113\pi$
$510$	−1.48704e6	−0.253161
$511$	2.83651e6	0.480543
$512$	−3.74699e6	−0.631696
$513$	−3.22914e7	−5.41743
$514$	−9.98401e6	−1.66685
$515$	−672956.	−0.111807
$516$	920532.	0.152200
$517$	5.85367e6	0.963168
$518$	−9.49095e6	−1.55412
$519$	−9.41593e6	−1.53442
$520$	213655.	0.0346502
$521$	6.58520e6	1.06286	0.531428	−	0.847103i	$-0.321655\pi$
$521$	6.58520e6	1.06286	0.531428	+	0.847103i	$0.321655\pi$
$522$	5.13640e6	0.825055
$523$	3.46791e6	0.554388	0.277194	−	0.960814i	$-0.410595\pi$
$523$	3.46791e6	0.554388	0.277194	+	0.960814i	$0.410595\pi$
$524$	−23247.6	−0.00369871
$525$	8.36417e6	1.32442
$526$	1.05600e7	1.66418
$527$	2.11275e6	0.331377
$528$	−1.77353e7	−2.76856
$529$	0	0
$530$	−1.10338e6	−0.170622
$531$	1.60088e7	2.46390
$532$	4.59182e6	0.703406
$533$	−1.43186e6	−0.218314
$534$	−4.00969e6	−0.608495
$535$	−1.34750e6	−0.203537
$536$	212504.	0.0319489
$537$	8.78694e6	1.31493
$538$	3.15239e6	0.469552
$539$	−3.80161e6	−0.563632
$540$	−2.42046e6	−0.357201
$541$	−8.34065e6	−1.22520	−0.612600	−	0.790393i	$-0.709876\pi$
$541$	−8.34065e6	−1.22520	−0.612600	+	0.790393i	$0.709876\pi$
$542$	1.03817e7	1.51799
$543$	−2.01979e7	−2.93973
$544$	−3.91254e6	−0.566841
$545$	1.35432e6	0.195312
$546$	−4.11900e6	−0.591303
$547$	−530066.	−0.0757463	−0.0378732	−	0.999283i	$-0.512058\pi$
$547$	−530066.	−0.0757463	−0.0378732	+	0.999283i	$0.512058\pi$
$548$	3.95770e6	0.562978
$549$	−1.44717e7	−2.04921
$550$	9.97781e6	1.40646
$551$	2.95628e6	0.414827
$552$	0	0
$553$	−4.74774e6	−0.660198
$554$	−5.26090e6	−0.728259
$555$	4.60048e6	0.633973
$556$	2.97875e6	0.408646
$557$	−1.70318e6	−0.232606	−0.116303	−	0.993214i	$-0.537104\pi$
$557$	−1.70318e6	−0.232606	−0.116303	+	0.993214i	$0.537104\pi$
$558$	1.49631e7	2.03440
$559$	−345871.	−0.0468149
$560$	−1.27118e6	−0.171292
$561$	−9.08358e6	−1.21857
$562$	−1.49116e7	−1.99152
$563$	−4.66360e6	−0.620084	−0.310042	−	0.950723i	$-0.600343\pi$
$563$	−4.66360e6	−0.620084	−0.310042	+	0.950723i	$0.600343\pi$
$564$	6.96578e6	0.922087
$565$	718174.	0.0946474
$566$	1.60038e7	2.09982
$567$	−1.90718e7	−2.49134
$568$	1.10104e6	0.143196
$569$	−6.59677e6	−0.854182	−0.427091	−	0.904209i	$-0.640462\pi$
$569$	−6.59677e6	−0.854182	−0.427091	+	0.904209i	$0.640462\pi$
$570$	−6.06153e6	−0.781439
$571$	7.64813e6	0.981668	0.490834	−	0.871253i	$-0.336692\pi$
$571$	7.64813e6	0.981668	0.490834	+	0.871253i	$0.336692\pi$
$572$	−1.80427e6	−0.230575
$573$	−2.10332e7	−2.67620
$574$	4.54395e6	0.575643
$575$	0	0
$576$	−1.24095e6	−0.155847
$577$	−97391.8	−0.0121782	−0.00608909	−	0.999981i	$-0.501938\pi$
$577$	−97391.8	−0.0121782	−0.00608909	+	0.999981i	$0.501938\pi$
$578$	7.07194e6	0.880478
$579$	−827768.	−0.102615
$580$	221593.	0.0273518
$581$	4.84569e6	0.595546
$582$	2.53401e7	3.10099
$583$	−6.74001e6	−0.821275
$584$	−2.91263e6	−0.353389
$585$	1.45301e6	0.175541
$586$	1.97786e7	2.37932
$587$	1.25835e7	1.50732	0.753661	−	0.657264i	$-0.228286\pi$
$587$	1.25835e7	1.50732	0.753661	+	0.657264i	$0.228286\pi$
$588$	−4.52386e6	−0.539592
$589$	8.61210e6	1.02287
$590$	1.88087e6	0.222448
$591$	9.75497e6	1.14883
$592$	1.82714e7	2.14273
$593$	−1.02646e7	−1.19869	−0.599346	−	0.800490i	$-0.704572\pi$
$593$	−1.02646e7	−1.19869	−0.599346	+	0.800490i	$0.704572\pi$
$594$	−4.02658e7	−4.68241
$595$	−651068.	−0.0753935
$596$	−3.48096e6	−0.401405
$597$	565824.	0.0649749
$598$	0	0
$599$	−2.94878e6	−0.335796	−0.167898	−	0.985804i	$-0.553698\pi$
$599$	−2.94878e6	−0.335796	−0.167898	+	0.985804i	$0.553698\pi$
$600$	−8.58863e6	−0.973971
$601$	−1.12911e7	−1.27512	−0.637558	−	0.770402i	$-0.720055\pi$
$601$	−1.12911e7	−1.27512	−0.637558	+	0.770402i	$0.720055\pi$
$602$	1.09761e6	0.123440
$603$	1.44518e6	0.161856
$604$	−6.88075e6	−0.767438
$605$	−603922.	−0.0670799
$606$	2.70885e7	2.99643
$607$	1.33898e7	1.47504	0.737518	−	0.675328i	$-0.235998\pi$
$607$	1.33898e7	1.47504	0.737518	+	0.675328i	$0.235998\pi$
$608$	−1.59485e7	−1.74969
$609$	3.09017e6	0.337628
$610$	−1.70027e6	−0.185009
$611$	−2.61725e6	−0.283623
$612$	−7.86647e6	−0.848988
$613$	−5.47783e6	−0.588786	−0.294393	−	0.955684i	$-0.595117\pi$
$613$	−5.47783e6	−0.588786	−0.294393	+	0.955684i	$0.595117\pi$
$614$	−7.70883e6	−0.825216
$615$	−2.20256e6	−0.234822
$616$	−4.14173e6	−0.439774
$617$	−9.76821e6	−1.03300	−0.516502	−	0.856286i	$-0.672766\pi$
$617$	−9.76821e6	−1.03300	−0.516502	+	0.856286i	$0.672766\pi$
$618$	−1.33219e7	−1.40312
$619$	1.75560e7	1.84162	0.920810	−	0.390012i	$-0.127529\pi$
$619$	1.75560e7	1.84162	0.920810	+	0.390012i	$0.127529\pi$
$620$	645535.	0.0674435
$621$	0	0
$622$	−2.02323e6	−0.209686
$623$	−1.75556e6	−0.181215
$624$	7.92966e6	0.815254
$625$	8.69913e6	0.890791
$626$	−1.16700e7	−1.19025
$627$	−3.70269e7	−3.76139
$628$	−3.72907e6	−0.377313
$629$	9.35817e6	0.943114
$630$	−4.61106e6	−0.462859
$631$	9.20940e6	0.920784	0.460392	−	0.887716i	$-0.347709\pi$
$631$	9.20940e6	0.920784	0.460392	+	0.887716i	$0.347709\pi$
$632$	4.87516e6	0.485507
$633$	3.61206e6	0.358299
$634$	−1.81320e7	−1.79152
$635$	1.57692e6	0.155194
$636$	−8.02050e6	−0.786247
$637$	1.69975e6	0.165972
$638$	3.68634e6	0.358545
$639$	7.48784e6	0.725445
$640$	1.91437e6	0.184746
$641$	1.83849e7	1.76733	0.883664	−	0.468122i	$-0.155069\pi$
$641$	1.83849e7	1.76733	0.883664	+	0.468122i	$0.155069\pi$
$642$	−2.66752e7	−2.55429
$643$	4.93519e6	0.470735	0.235368	−	0.971906i	$-0.424371\pi$
$643$	4.93519e6	0.470735	0.235368	+	0.971906i	$0.424371\pi$
$644$	0	0
$645$	−532035.	−0.0503548
$646$	−1.23302e7	−1.16249
$647$	1.29614e7	1.21729	0.608643	−	0.793444i	$-0.291714\pi$
$647$	1.29614e7	1.21729	0.608643	+	0.793444i	$0.291714\pi$
$648$	1.95836e7	1.83212
$649$	1.14893e7	1.07074
$650$	−4.46120e6	−0.414160
$651$	9.00213e6	0.832517
$652$	3.12194e6	0.287611
$653$	4.27184e6	0.392042	0.196021	−	0.980600i	$-0.437198\pi$
$653$	4.27184e6	0.392042	0.196021	+	0.980600i	$0.437198\pi$
$654$	2.68102e7	2.45107
$655$	13436.3	0.00122371
$656$	−8.74774e6	−0.793663
$657$	−1.98080e7	−1.79030
$658$	8.30573e6	0.747847
$659$	6.39258e6	0.573407	0.286703	−	0.958019i	$-0.407441\pi$
$659$	6.39258e6	0.573407	0.286703	+	0.958019i	$0.407441\pi$
$660$	−2.77542e6	−0.248010
$661$	1.56915e7	1.39689	0.698443	−	0.715666i	$-0.253877\pi$
$661$	1.56915e7	1.39689	0.698443	+	0.715666i	$0.253877\pi$
$662$	1.48697e7	1.31873
$663$	4.06138e6	0.358831
$664$	−4.97573e6	−0.437962
$665$	−2.65391e6	−0.232719
$666$	6.62773e7	5.79001
$667$	0	0
$668$	1.18265e7	1.02545
$669$	9.71065e6	0.838847
$670$	169794.	0.0146129
$671$	−1.03861e7	−0.890528
$672$	−1.66708e7	−1.42407
$673$	7.75756e6	0.660218	0.330109	−	0.943943i	$-0.392914\pi$
$673$	7.75756e6	0.660218	0.330109	+	0.943943i	$0.392914\pi$
$674$	2.44746e7	2.07522
$675$	−3.65581e7	−3.08833
$676$	−6.08765e6	−0.512369
$677$	−5.01427e6	−0.420471	−0.210235	−	0.977651i	$-0.567423\pi$
$677$	−5.01427e6	−0.420471	−0.210235	+	0.977651i	$0.567423\pi$
$678$	1.42170e7	1.18778
$679$	1.10946e7	0.923503
$680$	668540.	0.0554441
$681$	−1.80936e7	−1.49505
$682$	1.07389e7	0.884091
$683$	9.73644e6	0.798635	0.399318	−	0.916813i	$-0.369247\pi$
$683$	9.73644e6	0.798635	0.399318	+	0.916813i	$0.369247\pi$
$684$	−3.20657e7	−2.62060
$685$	−2.28741e6	−0.186259
$686$	−1.65112e7	−1.33958
$687$	2.34483e7	1.89548
$688$	−2.11305e6	−0.170192
$689$	3.01354e6	0.241840
$690$	0	0
$691$	−1.99433e7	−1.58892	−0.794460	−	0.607316i	$-0.792246\pi$
$691$	−1.99433e7	−1.58892	−0.794460	+	0.607316i	$0.792246\pi$
$692$	−5.85224e6	−0.464576
$693$	−2.81667e7	−2.22794
$694$	−2.34262e6	−0.184631
$695$	−1.72161e6	−0.135199
$696$	−3.17310e6	−0.248291
$697$	−4.48038e6	−0.349327
$698$	3.24014e6	0.251724
$699$	−2.93843e7	−2.27469
$700$	5.19854e6	0.400992
$701$	−1.99671e6	−0.153469	−0.0767344	−	0.997052i	$-0.524449\pi$
$701$	−1.99671e6	−0.153469	−0.0767344	+	0.997052i	$0.524449\pi$
$702$	1.80033e7	1.37883
$703$	3.81462e7	2.91114
$704$	−890613.	−0.0677263
$705$	−4.02598e6	−0.305070
$706$	2.51618e7	1.89989
$707$	1.18602e7	0.892364
$708$	1.36721e7	1.02507
$709$	4.51238e6	0.337125	0.168562	−	0.985691i	$-0.446088\pi$
$709$	4.51238e6	0.337125	0.168562	+	0.985691i	$0.446088\pi$
$710$	879745.	0.0654955
$711$	3.31545e7	2.45962
$712$	1.80267e6	0.133265
$713$	0	0
$714$	−1.28886e7	−0.946151
$715$	1.04281e6	0.0762848
$716$	5.46130e6	0.398120
$717$	4.52197e6	0.328496
$718$	−3.86942e6	−0.280114
$719$	−649353.	−0.0468445	−0.0234223	−	0.999726i	$-0.507456\pi$
$719$	−649353.	−0.0468445	−0.0234223	+	0.999726i	$0.507456\pi$
$720$	8.87693e6	0.638163
$721$	−5.83272e6	−0.417862
$722$	−3.26529e7	−2.33120
$723$	4.22012e6	0.300247
$724$	−1.25535e7	−0.890058
$725$	3.34689e6	0.236481
$726$	−1.19553e7	−0.841819
$727$	2.04453e7	1.43469	0.717343	−	0.696720i	$-0.245358\pi$
$727$	2.04453e7	1.43469	0.717343	+	0.696720i	$0.245358\pi$
$728$	1.85182e6	0.129500
$729$	4.50030e7	3.13633
$730$	−2.32723e6	−0.161634
$731$	−1.08225e6	−0.0749091
$732$	−1.23593e7	−0.852545
$733$	−2.23891e7	−1.53913	−0.769567	−	0.638566i	$-0.779528\pi$
$733$	−2.23891e7	−1.53913	−0.769567	+	0.638566i	$0.779528\pi$
$734$	−6.89966e6	−0.472702
$735$	2.61463e6	0.178522
$736$	0	0
$737$	1.03719e6	0.0703378
$738$	−3.17314e7	−2.14461
$739$	1.45948e7	0.983075	0.491537	−	0.870856i	$-0.336435\pi$
$739$	1.45948e7	0.983075	0.491537	+	0.870856i	$0.336435\pi$
$740$	2.85931e6	0.191948
$741$	1.65552e7	1.10761
$742$	−9.56333e6	−0.637675
$743$	2.62661e7	1.74552	0.872758	−	0.488152i	$-0.162329\pi$
$743$	2.62661e7	1.74552	0.872758	+	0.488152i	$0.162329\pi$
$744$	−9.24372e6	−0.612230
$745$	2.01187e6	0.132804
$746$	−1.19497e7	−0.786159
$747$	−3.38385e7	−2.21876
$748$	−5.64567e6	−0.368945
$749$	−1.16792e7	−0.760690
$750$	−1.39875e7	−0.908001
$751$	−2.02939e7	−1.31300	−0.656502	−	0.754324i	$-0.727965\pi$
$751$	−2.02939e7	−1.31300	−0.656502	+	0.754324i	$0.727965\pi$
$752$	−1.59897e7	−1.03109
$753$	−1.89123e7	−1.21551
$754$	−1.64820e6	−0.105580
$755$	3.97683e6	0.253904
$756$	−2.09789e7	−1.33499
$757$	1.96302e7	1.24504	0.622521	−	0.782603i	$-0.286108\pi$
$757$	1.96302e7	1.24504	0.622521	+	0.782603i	$0.286108\pi$
$758$	−3.64946e7	−2.30705
$759$	0	0
$760$	2.72513e6	0.171141
$761$	1.35803e7	0.850058	0.425029	−	0.905180i	$-0.360264\pi$
$761$	1.35803e7	0.850058	0.425029	+	0.905180i	$0.360264\pi$
$762$	3.12169e7	1.94761
$763$	1.17383e7	0.729951
$764$	−1.30726e7	−0.810270
$765$	4.54655e6	0.280885
$766$	−2.30921e7	−1.42197
$767$	−5.13702e6	−0.315299
$768$	3.97235e7	2.43021
$769$	−1.38060e7	−0.841885	−0.420943	−	0.907087i	$-0.638301\pi$
$769$	−1.38060e7	−0.841885	−0.420943	+	0.907087i	$0.638301\pi$
$770$	−3.30930e6	−0.201145
$771$	4.19453e7	2.54125
$772$	−514478.	−0.0310687
$773$	−1.24327e7	−0.748371	−0.374186	−	0.927354i	$-0.622078\pi$
$773$	−1.24327e7	−0.748371	−0.374186	+	0.927354i	$0.622078\pi$
$774$	−7.66482e6	−0.459885
$775$	9.75001e6	0.583111
$776$	−1.13924e7	−0.679140
$777$	3.98738e7	2.36938
$778$	1.72233e7	1.02016
$779$	−1.82631e7	−1.07828
$780$	1.24092e6	0.0730311
$781$	5.37393e6	0.315257
$782$	0	0
$783$	−1.35065e7	−0.787296
$784$	1.03844e7	0.603378
$785$	2.15527e6	0.124833
$786$	265987.	0.0153569
$787$	2.51358e7	1.44663	0.723313	−	0.690520i	$-0.242618\pi$
$787$	2.51358e7	1.44663	0.723313	+	0.690520i	$0.242618\pi$
$788$	6.06296e6	0.347832
$789$	−4.43652e7	−2.53717
$790$	3.89532e6	0.222062
$791$	6.22464e6	0.353731
$792$	2.89226e7	1.63842
$793$	4.64376e6	0.262233
$794$	1.59216e7	0.896264
$795$	4.63557e6	0.260127
$796$	351673.	0.0196724
$797$	−9.05650e6	−0.505027	−0.252514	−	0.967593i	$-0.581257\pi$
$797$	−9.05650e6	−0.505027	−0.252514	+	0.967593i	$0.581257\pi$
$798$	−5.25371e7	−2.92051
$799$	−8.18953e6	−0.453829
$800$	−1.80557e7	−0.997448
$801$	1.22594e7	0.675133
$802$	−3.93631e6	−0.216099
$803$	−1.42159e7	−0.778013
$804$	1.23424e6	0.0673377
$805$	0	0
$806$	−4.80147e6	−0.260338
$807$	−1.32440e7	−0.715870
$808$	−1.21784e7	−0.656241
$809$	−1.43026e7	−0.768321	−0.384160	−	0.923266i	$-0.625509\pi$
$809$	−1.43026e7	−0.768321	−0.384160	+	0.923266i	$0.625509\pi$
$810$	1.56476e7	0.837981
$811$	−221525.	−0.0118269	−0.00591345	−	0.999983i	$-0.501882\pi$
$811$	−221525.	−0.0118269	−0.00591345	+	0.999983i	$0.501882\pi$
$812$	1.92062e6	0.102223
$813$	−4.36160e7	−2.31430
$814$	4.75664e7	2.51617
$815$	−1.80437e6	−0.0951552
$816$	2.48124e7	1.30450
$817$	−4.41152e6	−0.231224
$818$	−218669.	−0.0114263
$819$	1.25937e7	0.656058
$820$	−1.36894e6	−0.0710970
$821$	1.89749e7	0.982475	0.491237	−	0.871026i	$-0.336545\pi$
$821$	1.89749e7	0.982475	0.491237	+	0.871026i	$0.336545\pi$
$822$	−4.52819e7	−2.33746
$823$	−3.27103e7	−1.68339	−0.841697	−	0.539951i	$-0.818443\pi$
$823$	−3.27103e7	−1.68339	−0.841697	+	0.539951i	$0.818443\pi$
$824$	5.98925e6	0.307294
$825$	−4.19193e7	−2.14427
$826$	1.63021e7	0.831369
$827$	1.37227e7	0.697709	0.348855	−	0.937177i	$-0.386571\pi$
$827$	1.37227e7	0.697709	0.348855	+	0.937177i	$0.386571\pi$
$828$	0	0
$829$	1.36037e7	0.687499	0.343749	−	0.939061i	$-0.388303\pi$
$829$	1.36037e7	0.687499	0.343749	+	0.939061i	$0.388303\pi$
$830$	−3.97568e6	−0.200316
$831$	2.21023e7	1.11029
$832$	398204.	0.0199433
$833$	5.31861e6	0.265574
$834$	−3.40812e7	−1.69668
$835$	−6.83531e6	−0.339267
$836$	−2.30131e7	−1.13883
$837$	−3.93465e7	−1.94130
$838$	5.76870e6	0.283771
$839$	6.51594e6	0.319574	0.159787	−	0.987151i	$-0.448919\pi$
$839$	6.51594e6	0.319574	0.159787	+	0.987151i	$0.448919\pi$
$840$	2.84856e6	0.139292
$841$	−1.92746e7	−0.939715
$842$	−1.29601e7	−0.629983
$843$	6.26475e7	3.03623
$844$	2.24498e6	0.108482
$845$	3.51845e6	0.169515
$846$	−5.80007e7	−2.78617
$847$	−5.23438e6	−0.250701
$848$	1.84108e7	0.879189
$849$	−6.72358e7	−3.20134
$850$	−1.39594e7	−0.662702
$851$	0	0
$852$	6.39490e6	0.301811
$853$	−121911.	−0.00573679	−0.00286839	−	0.999996i	$-0.500913\pi$
$853$	−121911.	−0.00573679	−0.00286839	+	0.999996i	$0.500913\pi$
$854$	−1.47368e7	−0.691446
$855$	1.85328e7	0.867015
$856$	1.19926e7	0.559409
$857$	3.98944e7	1.85550	0.927749	−	0.373206i	$-0.121742\pi$
$857$	3.98944e7	1.85550	0.927749	+	0.373206i	$0.121742\pi$
$858$	2.06435e7	0.957337
$859$	−1.74657e7	−0.807611	−0.403806	−	0.914845i	$-0.632313\pi$
$859$	−1.74657e7	−0.807611	−0.403806	+	0.914845i	$0.632313\pi$
$860$	−330673.	−0.0152459
$861$	−1.90902e7	−0.877614
$862$	−1.56498e7	−0.717366
$863$	−7.84502e6	−0.358564	−0.179282	−	0.983798i	$-0.557377\pi$
$863$	−7.84502e6	−0.358564	−0.179282	+	0.983798i	$0.557377\pi$
$864$	7.28645e7	3.32071
$865$	3.38239e6	0.153703
$866$	−3.07443e7	−1.39306
$867$	−2.97110e7	−1.34236
$868$	5.59505e6	0.252060
$869$	2.37946e7	1.06888
$870$	−2.53535e6	−0.113564
$871$	−463739.	−0.0207123
$872$	−1.20533e7	−0.536804
$873$	−7.74761e7	−3.44059
$874$	0	0
$875$	−6.12412e6	−0.270411
$876$	−1.69167e7	−0.744829
$877$	−4.10211e7	−1.80098	−0.900488	−	0.434881i	$-0.856790\pi$
$877$	−4.10211e7	−1.80098	−0.900488	+	0.434881i	$0.856790\pi$
$878$	4.02024e7	1.76001
$879$	−8.30950e7	−3.62746
$880$	6.37087e6	0.277327
$881$	2.37485e6	0.103085	0.0515427	−	0.998671i	$-0.483586\pi$
$881$	2.37485e6	0.103085	0.0515427	+	0.998671i	$0.483586\pi$
$882$	3.76680e7	1.63042
$883$	−1.27925e7	−0.552147	−0.276073	−	0.961137i	$-0.589033\pi$
$883$	−1.27925e7	−0.552147	−0.276073	+	0.961137i	$0.589033\pi$
$884$	2.52425e6	0.108643
$885$	−7.90201e6	−0.339140
$886$	−7.73049e6	−0.330844
$887$	1.42765e7	0.609275	0.304637	−	0.952468i	$-0.401465\pi$
$887$	1.42765e7	0.609275	0.304637	+	0.952468i	$0.401465\pi$
$888$	−4.09439e7	−1.74244
$889$	1.36676e7	0.580015
$890$	1.44036e6	0.0609531
$891$	9.55833e7	4.03355
$892$	6.03541e6	0.253977
$893$	−3.33825e7	−1.40085
$894$	3.98273e7	1.66662
$895$	−3.15644e6	−0.131717
$896$	1.65924e7	0.690463
$897$	0	0
$898$	2.64548e7	1.09475
$899$	3.60217e6	0.148650
$900$	−3.63025e7	−1.49393
$901$	9.42954e6	0.386971
$902$	−2.27732e7	−0.931983
$903$	−4.61132e6	−0.188194
$904$	−6.39168e6	−0.260132
$905$	7.25549e6	0.294473
$906$	7.87258e7	3.18637
$907$	3.02955e7	1.22281	0.611406	−	0.791317i	$-0.290604\pi$
$907$	3.02955e7	1.22281	0.611406	+	0.791317i	$0.290604\pi$
$908$	−1.12456e7	−0.452655
$909$	−8.28220e7	−3.32457
$910$	1.47963e6	0.0592310
$911$	4.01857e7	1.60426	0.802131	−	0.597148i	$-0.203700\pi$
$911$	4.01857e7	1.60426	0.802131	+	0.597148i	$0.203700\pi$
$912$	1.01141e8	4.02663
$913$	−2.42855e7	−0.964205
$914$	2.32554e7	0.920786
$915$	7.14327e6	0.282062
$916$	1.45737e7	0.573894
$917$	116457.	0.00457342
$918$	5.63335e7	2.20628
$919$	−1.00275e6	−0.0391654	−0.0195827	−	0.999808i	$-0.506234\pi$
$919$	−1.00275e6	−0.0391654	−0.0195827	+	0.999808i	$0.506234\pi$
$920$	0	0
$921$	3.23867e7	1.25811
$922$	−4.63958e6	−0.179743
$923$	−2.40275e6	−0.0928334
$924$	−2.40554e7	−0.926900
$925$	4.31865e7	1.65956
$926$	−2.47281e6	−0.0947685
$927$	4.07311e7	1.55678
$928$	−6.67075e6	−0.254276
$929$	−4.99710e7	−1.89967	−0.949837	−	0.312747i	$-0.898751\pi$
$929$	−4.99710e7	−1.89967	−0.949837	+	0.312747i	$0.898751\pi$
$930$	−7.38586e6	−0.280023
$931$	2.16800e7	0.819756
$932$	−1.82631e7	−0.688707
$933$	8.50010e6	0.319683
$934$	−5.32653e7	−1.99792
$935$	3.26300e6	0.122064
$936$	−1.29316e7	−0.482463
$937$	−3.14548e7	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$937$	−3.14548e7	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$938$	1.47166e6	0.0546134
$939$	4.90287e7	1.81462
$940$	−2.50225e6	−0.0923656
$941$	5.57541e6	0.205259	0.102630	−	0.994720i	$-0.467274\pi$
$941$	5.57541e6	0.205259	0.102630	+	0.994720i	$0.467274\pi$
$942$	4.26660e7	1.56659
$943$	0	0
$944$	−3.13839e7	−1.14624
$945$	1.21251e7	0.441676
$946$	−5.50095e6	−0.199853
$947$	−5.18769e6	−0.187974	−0.0939872	−	0.995573i	$-0.529961\pi$
$947$	−5.18769e6	−0.187974	−0.0939872	+	0.995573i	$0.529961\pi$
$948$	2.83152e7	1.02329
$949$	6.35612e6	0.229101
$950$	−5.69018e7	−2.04558
$951$	7.61770e7	2.73132
$952$	5.79445e6	0.207214
$953$	2.95996e7	1.05573	0.527866	−	0.849327i	$-0.322992\pi$
$953$	2.95996e7	1.05573	0.527866	+	0.849327i	$0.322992\pi$
$954$	6.67828e7	2.37571
$955$	7.55553e6	0.268075
$956$	2.81052e6	0.0994584
$957$	−1.54872e7	−0.546630
$958$	−4.48772e7	−1.57983
$959$	−1.98257e7	−0.696118
$960$	612537.	0.0214513
$961$	−1.81355e7	−0.633462
$962$	−2.12675e7	−0.740933
$963$	8.15582e7	2.83401
$964$	2.62291e6	0.0909056
$965$	297351.	0.0102790
$966$	0	0
$967$	5.53584e6	0.190378	0.0951890	−	0.995459i	$-0.469654\pi$
$967$	5.53584e6	0.190378	0.0951890	+	0.995459i	$0.469654\pi$
$968$	5.37485e6	0.184365
$969$	5.18021e7	1.77230
$970$	−9.10266e6	−0.310627
$971$	−1.45910e7	−0.496636	−0.248318	−	0.968679i	$-0.579878\pi$
$971$	−1.45910e7	−0.496636	−0.248318	+	0.968679i	$0.579878\pi$
$972$	5.89370e7	2.00089
$973$	−1.49218e7	−0.505287
$974$	6.13694e7	2.07279
$975$	1.87426e7	0.631420
$976$	2.83704e7	0.953325
$977$	−3.31437e7	−1.11087	−0.555437	−	0.831558i	$-0.687449\pi$
$977$	−3.31437e7	−1.11087	−0.555437	+	0.831558i	$0.687449\pi$
$978$	−3.57196e7	−1.19415
$979$	8.79845e6	0.293393
$980$	1.62506e6	0.0540510
$981$	−8.19711e7	−2.71949
$982$	3.07759e6	0.101843
$983$	−4.52931e7	−1.49502	−0.747511	−	0.664249i	$-0.768751\pi$
$983$	−4.52931e7	−1.49502	−0.747511	+	0.664249i	$0.768751\pi$
$984$	1.96026e7	0.645394
$985$	−3.50418e6	−0.115079
$986$	−5.15733e6	−0.168940
$987$	−3.48944e7	−1.14015
$988$	1.02895e7	0.335351
$989$	0	0
$990$	2.31095e7	0.749382
$991$	1.81433e7	0.586857	0.293428	−	0.955981i	$-0.405204\pi$
$991$	1.81433e7	0.586857	0.293428	+	0.955981i	$0.405204\pi$
$992$	−1.94329e7	−0.626987
$993$	−6.24712e7	−2.01051
$994$	7.62503e6	0.244780
$995$	−203255.	−0.00650854
$996$	−2.88993e7	−0.923080
$997$	−6.91560e6	−0.220339	−0.110170	−	0.993913i	$-0.535139\pi$
$997$	−6.91560e6	−0.220339	−0.110170	+	0.993913i	$0.535139\pi$
$998$	−1.16834e7	−0.371315
$999$	−1.74280e8	−5.52503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.6.a.j.1.9		45
23.9	even	11		23.6.c.a.12.2	yes	90
23.18	even	11		23.6.c.a.2.2	✓	90
23.22	odd	2		529.6.a.k.1.9		45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.6.c.a.2.2	✓	90	23.18	even	11
23.6.c.a.12.2	yes	90	23.9	even	11
529.6.a.j.1.9		45	1.1	even	1	trivial
529.6.a.k.1.9		45	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-7.11115 q^{2} +29.8757 q^{3} +18.5685 q^{4} -10.7320 q^{5} -212.451 q^{6} -93.0172 q^{7} +95.5134 q^{8} +649.559 q^{9} +O(q^{10})\)	\(q-7.11115 q^{2} +29.8757 q^{3} +18.5685 q^{4} -10.7320 q^{5} -212.451 q^{6} -93.0172 q^{7} +95.5134 q^{8} +649.559 q^{9} +76.3166 q^{10} +466.180 q^{11} +554.748 q^{12} -208.435 q^{13} +661.459 q^{14} -320.625 q^{15} -1273.40 q^{16} -652.205 q^{17} -4619.11 q^{18} -2658.55 q^{19} -199.276 q^{20} -2778.96 q^{21} -3315.08 q^{22} +2853.53 q^{24} -3009.83 q^{25} +1482.21 q^{26} +12146.2 q^{27} -1727.19 q^{28} -1111.99 q^{29} +2280.01 q^{30} -3239.40 q^{31} +5998.93 q^{32} +13927.5 q^{33} +4637.93 q^{34} +998.256 q^{35} +12061.3 q^{36} -14348.5 q^{37} +18905.4 q^{38} -6227.14 q^{39} -1025.05 q^{40} +6869.58 q^{41} +19761.6 q^{42} +1659.37 q^{43} +8656.27 q^{44} -6971.03 q^{45} +12556.7 q^{47} -38043.8 q^{48} -8154.81 q^{49} +21403.3 q^{50} -19485.1 q^{51} -3870.32 q^{52} -14457.9 q^{53} -86373.8 q^{54} -5003.03 q^{55} -8884.39 q^{56} -79426.1 q^{57} +7907.53 q^{58} +24645.7 q^{59} -5953.52 q^{60} -22279.2 q^{61} +23035.8 q^{62} -60420.1 q^{63} -1910.45 q^{64} +2236.91 q^{65} -99040.4 q^{66} +2224.86 q^{67} -12110.5 q^{68} -7098.75 q^{70} +11527.6 q^{71} +62041.6 q^{72} -30494.5 q^{73} +102034. q^{74} -89920.7 q^{75} -49365.3 q^{76} -43362.8 q^{77} +44282.2 q^{78} +51041.6 q^{79} +13666.1 q^{80} +205035. q^{81} -48850.6 q^{82} -52094.6 q^{83} -51601.0 q^{84} +6999.44 q^{85} -11800.0 q^{86} -33221.5 q^{87} +44526.5 q^{88} +18873.5 q^{89} +49572.1 q^{90} +19388.0 q^{91} -96779.3 q^{93} -89292.4 q^{94} +28531.4 q^{95} +179222. q^{96} -119275. q^{97} +57990.1 q^{98} +302812. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q + 2 q^{3} + 640 q^{4} - 267 q^{5} - 382 q^{6} - 548 q^{7} + 1155 q^{8} + 2677 q^{9}+O(q^{10}) \) 45 * q + 2 * q^3 + 640 * q^4 - 267 * q^5 - 382 * q^6 - 548 * q^7 + 1155 * q^8 + 2677 * q^9	\( 45 q + 2 q^{3} + 640 q^{4} - 267 q^{5} - 382 q^{6} - 548 q^{7} + 1155 q^{8} + 2677 q^{9} - 1017 q^{10} - 2701 q^{11} + 2305 q^{12} + 162 q^{13} - 3828 q^{14} - 4745 q^{15} + 9336 q^{16} - 5710 q^{17} - 1954 q^{18} - 10138 q^{19} - 10390 q^{20} - 6443 q^{21} - 5025 q^{22} - 10021 q^{24} + 15878 q^{25} - 18418 q^{26} + 8315 q^{27} - 16901 q^{28} - 13505 q^{29} - 16663 q^{30} - 7619 q^{31} + 30860 q^{32} - 29493 q^{33} - 11713 q^{34} + 10137 q^{35} - 12276 q^{36} - 32241 q^{37} - 49002 q^{38} + 56679 q^{39} - 59635 q^{40} + 34925 q^{41} - 37304 q^{42} - 23272 q^{43} - 83463 q^{44} - 48953 q^{45} - 36261 q^{47} - 32516 q^{48} + 51857 q^{49} + 17956 q^{50} - 103797 q^{51} - 120873 q^{52} - 110012 q^{53} - 93972 q^{54} + 12048 q^{55} - 250769 q^{56} - 26318 q^{57} - 24792 q^{58} + 69296 q^{59} - 200115 q^{60} - 100662 q^{61} - 109136 q^{62} - 197501 q^{63} + 169417 q^{64} - 189877 q^{65} - 177787 q^{66} - 85847 q^{67} - 309649 q^{68} - 308157 q^{70} + 194121 q^{71} + 329967 q^{72} - 106792 q^{73} - 238219 q^{74} - 99472 q^{75} - 423596 q^{76} - 127932 q^{77} - 455516 q^{78} - 390789 q^{79} - 404751 q^{80} - 135339 q^{81} + 485075 q^{82} - 421445 q^{83} - 264219 q^{84} + 258029 q^{85} - 452061 q^{86} - 100797 q^{87} - 117190 q^{88} - 544607 q^{89} - 350405 q^{90} - 315066 q^{91} - 700704 q^{93} + 986987 q^{94} + 620544 q^{95} - 774244 q^{96} - 199878 q^{97} - 353401 q^{98} - 897462 q^{99}+O(q^{100}) \) 45 * q + 2 * q^3 + 640 * q^4 - 267 * q^5 - 382 * q^6 - 548 * q^7 + 1155 * q^8 + 2677 * q^9 - 1017 * q^10 - 2701 * q^11 + 2305 * q^12 + 162 * q^13 - 3828 * q^14 - 4745 * q^15 + 9336 * q^16 - 5710 * q^17 - 1954 * q^18 - 10138 * q^19 - 10390 * q^20 - 6443 * q^21 - 5025 * q^22 - 10021 * q^24 + 15878 * q^25 - 18418 * q^26 + 8315 * q^27 - 16901 * q^28 - 13505 * q^29 - 16663 * q^30 - 7619 * q^31 + 30860 * q^32 - 29493 * q^33 - 11713 * q^34 + 10137 * q^35 - 12276 * q^36 - 32241 * q^37 - 49002 * q^38 + 56679 * q^39 - 59635 * q^40 + 34925 * q^41 - 37304 * q^42 - 23272 * q^43 - 83463 * q^44 - 48953 * q^45 - 36261 * q^47 - 32516 * q^48 + 51857 * q^49 + 17956 * q^50 - 103797 * q^51 - 120873 * q^52 - 110012 * q^53 - 93972 * q^54 + 12048 * q^55 - 250769 * q^56 - 26318 * q^57 - 24792 * q^58 + 69296 * q^59 - 200115 * q^60 - 100662 * q^61 - 109136 * q^62 - 197501 * q^63 + 169417 * q^64 - 189877 * q^65 - 177787 * q^66 - 85847 * q^67 - 309649 * q^68 - 308157 * q^70 + 194121 * q^71 + 329967 * q^72 - 106792 * q^73 - 238219 * q^74 - 99472 * q^75 - 423596 * q^76 - 127932 * q^77 - 455516 * q^78 - 390789 * q^79 - 404751 * q^80 - 135339 * q^81 + 485075 * q^82 - 421445 * q^83 - 264219 * q^84 + 258029 * q^85 - 452061 * q^86 - 100797 * q^87 - 117190 * q^88 - 544607 * q^89 - 350405 * q^90 - 315066 * q^91 - 700704 * q^93 + 986987 * q^94 + 620544 * q^95 - 774244 * q^96 - 199878 * q^97 - 353401 * q^98 - 897462 * q^99

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