LMFDB - Embedded newform 22.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,6,Mod(1,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, 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("22.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	22.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:	$3.52844403589$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{793}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 198 $ x^2 - x - 198
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$14.5801$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +0.419872 q^{3} +16.0000 q^{4} +63.9006 q^{5} +1.67949 q^{6} +77.4808 q^{7} +64.0000 q^{8} -242.824 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +0.419872 q^{3} +16.0000 q^{4} +63.9006 q^{5} +1.67949 q^{6} +77.4808 q^{7} +64.0000 q^{8} -242.824 q^{9} +255.603 q^{10} -121.000 q^{11} +6.71795 q^{12} -182.199 q^{13} +309.923 q^{14} +26.8301 q^{15} +256.000 q^{16} -1849.94 q^{17} -971.295 q^{18} -454.474 q^{19} +1022.41 q^{20} +32.5320 q^{21} -484.000 q^{22} +273.061 q^{23} +26.8718 q^{24} +958.292 q^{25} -728.795 q^{26} -203.984 q^{27} +1239.69 q^{28} +7364.33 q^{29} +107.320 q^{30} +5937.37 q^{31} +1024.00 q^{32} -50.8045 q^{33} -7399.74 q^{34} +4951.07 q^{35} -3885.18 q^{36} -4231.44 q^{37} -1817.90 q^{38} -76.5002 q^{39} +4089.64 q^{40} -19332.2 q^{41} +130.128 q^{42} +1718.66 q^{43} -1936.00 q^{44} -15516.6 q^{45} +1092.24 q^{46} +14965.0 q^{47} +107.487 q^{48} -10803.7 q^{49} +3833.17 q^{50} -776.737 q^{51} -2915.18 q^{52} +14328.9 q^{53} -815.935 q^{54} -7731.98 q^{55} +4958.77 q^{56} -190.821 q^{57} +29457.3 q^{58} +50164.2 q^{59} +429.282 q^{60} -22181.1 q^{61} +23749.5 q^{62} -18814.2 q^{63} +4096.00 q^{64} -11642.6 q^{65} -203.218 q^{66} -53124.3 q^{67} -29599.0 q^{68} +114.651 q^{69} +19804.3 q^{70} +70547.9 q^{71} -15540.7 q^{72} +21669.5 q^{73} -16925.8 q^{74} +402.360 q^{75} -7271.59 q^{76} -9375.17 q^{77} -306.001 q^{78} -73360.1 q^{79} +16358.6 q^{80} +58920.5 q^{81} -77329.0 q^{82} +89307.9 q^{83} +520.512 q^{84} -118212. q^{85} +6874.64 q^{86} +3092.08 q^{87} -7744.00 q^{88} -23117.7 q^{89} -62066.4 q^{90} -14116.9 q^{91} +4368.97 q^{92} +2492.94 q^{93} +59860.0 q^{94} -29041.2 q^{95} +429.949 q^{96} +100486. q^{97} -43214.9 q^{98} +29381.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} + 29 q^{3} + 32 q^{4} - 13 q^{5} + 116 q^{6} - 14 q^{7} + 128 q^{8} + 331 q^{9}+O(q^{10}) $ 2 * q + 8 * q^2 + 29 * q^3 + 32 * q^4 - 13 * q^5 + 116 * q^6 - 14 * q^7 + 128 * q^8 + 331 * q^9	\( 2 q + 8 q^{2} + 29 q^{3} + 32 q^{4} - 13 q^{5} + 116 q^{6} - 14 q^{7} + 128 q^{8} + 331 q^{9} - 52 q^{10} - 242 q^{11} + 464 q^{12} - 646 q^{13} - 56 q^{14} - 2171 q^{15} + 512 q^{16} - 208 q^{17} + 1324 q^{18} - 2148 q^{19} - 208 q^{20} - 2582 q^{21} - 968 q^{22} + 349 q^{23} + 1856 q^{24} + 3747 q^{25} - 2584 q^{26} + 9251 q^{27} - 224 q^{28} + 4422 q^{29} - 8684 q^{30} + 14381 q^{31} + 2048 q^{32} - 3509 q^{33} - 832 q^{34} + 11986 q^{35} + 5296 q^{36} - 4267 q^{37} - 8592 q^{38} - 13332 q^{39} - 832 q^{40} - 10110 q^{41} - 10328 q^{42} - 9798 q^{43} - 3872 q^{44} - 59644 q^{45} + 1396 q^{46} + 21144 q^{47} + 7424 q^{48} - 19242 q^{49} + 14988 q^{50} + 46150 q^{51} - 10336 q^{52} + 39584 q^{53} + 37004 q^{54} + 1573 q^{55} - 896 q^{56} - 48592 q^{57} + 17688 q^{58} + 90951 q^{59} - 34736 q^{60} - 29550 q^{61} + 57524 q^{62} - 71308 q^{63} + 8192 q^{64} + 24024 q^{65} - 14036 q^{66} - 64149 q^{67} - 3328 q^{68} + 2285 q^{69} + 47944 q^{70} + 23583 q^{71} + 21184 q^{72} - 39058 q^{73} - 17068 q^{74} + 80104 q^{75} - 34368 q^{76} + 1694 q^{77} - 53328 q^{78} - 54974 q^{79} - 3328 q^{80} + 189706 q^{81} - 40440 q^{82} + 29986 q^{83} - 41312 q^{84} - 244478 q^{85} - 39192 q^{86} - 81000 q^{87} - 15488 q^{88} - 18047 q^{89} - 238576 q^{90} + 28312 q^{91} + 5584 q^{92} + 243813 q^{93} + 84576 q^{94} + 101192 q^{95} + 29696 q^{96} - 30309 q^{97} - 76968 q^{98} - 40051 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 29 * q^3 + 32 * q^4 - 13 * q^5 + 116 * q^6 - 14 * q^7 + 128 * q^8 + 331 * q^9 - 52 * q^10 - 242 * q^11 + 464 * q^12 - 646 * q^13 - 56 * q^14 - 2171 * q^15 + 512 * q^16 - 208 * q^17 + 1324 * q^18 - 2148 * q^19 - 208 * q^20 - 2582 * q^21 - 968 * q^22 + 349 * q^23 + 1856 * q^24 + 3747 * q^25 - 2584 * q^26 + 9251 * q^27 - 224 * q^28 + 4422 * q^29 - 8684 * q^30 + 14381 * q^31 + 2048 * q^32 - 3509 * q^33 - 832 * q^34 + 11986 * q^35 + 5296 * q^36 - 4267 * q^37 - 8592 * q^38 - 13332 * q^39 - 832 * q^40 - 10110 * q^41 - 10328 * q^42 - 9798 * q^43 - 3872 * q^44 - 59644 * q^45 + 1396 * q^46 + 21144 * q^47 + 7424 * q^48 - 19242 * q^49 + 14988 * q^50 + 46150 * q^51 - 10336 * q^52 + 39584 * q^53 + 37004 * q^54 + 1573 * q^55 - 896 * q^56 - 48592 * q^57 + 17688 * q^58 + 90951 * q^59 - 34736 * q^60 - 29550 * q^61 + 57524 * q^62 - 71308 * q^63 + 8192 * q^64 + 24024 * q^65 - 14036 * q^66 - 64149 * q^67 - 3328 * q^68 + 2285 * q^69 + 47944 * q^70 + 23583 * q^71 + 21184 * q^72 - 39058 * q^73 - 17068 * q^74 + 80104 * q^75 - 34368 * q^76 + 1694 * q^77 - 53328 * q^78 - 54974 * q^79 - 3328 * q^80 + 189706 * q^81 - 40440 * q^82 + 29986 * q^83 - 41312 * q^84 - 244478 * q^85 - 39192 * q^86 - 81000 * q^87 - 15488 * q^88 - 18047 * q^89 - 238576 * q^90 + 28312 * q^91 + 5584 * q^92 + 243813 * q^93 + 84576 * q^94 + 101192 * q^95 + 29696 * q^96 - 30309 * q^97 - 76968 * q^98 - 40051 * 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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	0.419872	0.0269348	0.0134674	−	0.999909i	$-0.495713\pi$
$3$	0.419872	0.0269348	0.0134674	+	0.999909i	$0.495713\pi$
$4$	16.0000	0.500000
$5$	63.9006	1.14309	0.571545	−	0.820571i	$-0.306344\pi$
$5$	63.9006	1.14309	0.571545	+	0.820571i	$0.306344\pi$
$6$	1.67949	0.0190458
$7$	77.4808	0.597653	0.298826	−	0.954308i	$-0.403405\pi$
$7$	77.4808	0.597653	0.298826	+	0.954308i	$0.403405\pi$
$8$	64.0000	0.353553
$9$	−242.824	−0.999275
$10$	255.603	0.808286
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	6.71795	0.0134674
$13$	−182.199	−0.299011	−0.149505	−	0.988761i	$-0.547768\pi$
$13$	−182.199	−0.299011	−0.149505	+	0.988761i	$0.547768\pi$
$14$	309.923	0.422604
$15$	26.8301	0.0307889
$16$	256.000	0.250000
$17$	−1849.94	−1.55251	−0.776255	−	0.630419i	$-0.782883\pi$
$17$	−1849.94	−1.55251	−0.776255	+	0.630419i	$0.782883\pi$
$18$	−971.295	−0.706594
$19$	−454.474	−0.288819	−0.144409	−	0.989518i	$-0.546128\pi$
$19$	−454.474	−0.288819	−0.144409	+	0.989518i	$0.546128\pi$
$20$	1022.41	0.571545
$21$	32.5320	0.0160977
$22$	−484.000	−0.213201
$23$	273.061	0.107632	0.0538158	−	0.998551i	$-0.482862\pi$
$23$	273.061	0.107632	0.0538158	+	0.998551i	$0.482862\pi$
$24$	26.8718	0.00952289
$25$	958.292	0.306653
$26$	−728.795	−0.211433
$27$	−203.984	−0.0538501
$28$	1239.69	0.298826
$29$	7364.33	1.62607	0.813033	−	0.582218i	$-0.197815\pi$
$29$	7364.33	1.62607	0.813033	+	0.582218i	$0.197815\pi$
$30$	107.320	0.0217710
$31$	5937.37	1.10966	0.554830	−	0.831964i	$-0.312783\pi$
$31$	5937.37	1.10966	0.554830	+	0.831964i	$0.312783\pi$
$32$	1024.00	0.176777
$33$	−50.8045	−0.00812115
$34$	−7399.74	−1.09779
$35$	4951.07	0.683170
$36$	−3885.18	−0.499637
$37$	−4231.44	−0.508140	−0.254070	−	0.967186i	$-0.581769\pi$
$37$	−4231.44	−0.508140	−0.254070	+	0.967186i	$0.581769\pi$
$38$	−1817.90	−0.204226
$39$	−76.5002	−0.00805380
$40$	4089.64	0.404143
$41$	−19332.2	−1.79607	−0.898034	−	0.439926i	$-0.855005\pi$
$41$	−19332.2	−1.79607	−0.898034	+	0.439926i	$0.855005\pi$
$42$	130.128	0.0113828
$43$	1718.66	0.141749	0.0708743	−	0.997485i	$-0.477421\pi$
$43$	1718.66	0.141749	0.0708743	+	0.997485i	$0.477421\pi$
$44$	−1936.00	−0.150756
$45$	−15516.6	−1.14226
$46$	1092.24	0.0761071
$47$	14965.0	0.988171	0.494085	−	0.869413i	$-0.335503\pi$
$47$	14965.0	0.988171	0.494085	+	0.869413i	$0.335503\pi$
$48$	107.487	0.00673370
$49$	−10803.7	−0.642811
$50$	3833.17	0.216837
$51$	−776.737	−0.0418166
$52$	−2915.18	−0.149505
$53$	14328.9	0.700686	0.350343	−	0.936621i	$-0.386065\pi$
$53$	14328.9	0.700686	0.350343	+	0.936621i	$0.386065\pi$
$54$	−815.935	−0.0380778
$55$	−7731.98	−0.344654
$56$	4958.77	0.211302
$57$	−190.821	−0.00777928
$58$	29457.3	1.14980
$59$	50164.2	1.87613	0.938067	−	0.346455i	$-0.112615\pi$
$59$	50164.2	1.87613	0.938067	+	0.346455i	$0.112615\pi$
$60$	429.282	0.0153944
$61$	−22181.1	−0.763237	−0.381619	−	0.924320i	$-0.624633\pi$
$61$	−22181.1	−0.763237	−0.381619	+	0.924320i	$0.624633\pi$
$62$	23749.5	0.784648
$63$	−18814.2	−0.597219
$64$	4096.00	0.125000
$65$	−11642.6	−0.341796
$66$	−203.218	−0.00574252
$67$	−53124.3	−1.44579	−0.722897	−	0.690956i	$-0.757190\pi$
$67$	−53124.3	−1.44579	−0.722897	+	0.690956i	$0.757190\pi$
$68$	−29599.0	−0.776255
$69$	114.651	0.00289904
$70$	19804.3	0.483074
$71$	70547.9	1.66088	0.830440	−	0.557109i	$-0.188089\pi$
$71$	70547.9	1.66088	0.830440	+	0.557109i	$0.188089\pi$
$72$	−15540.7	−0.353297
$73$	21669.5	0.475928	0.237964	−	0.971274i	$-0.423520\pi$
$73$	21669.5	0.475928	0.237964	+	0.971274i	$0.423520\pi$
$74$	−16925.8	−0.359310
$75$	402.360	0.00825965
$76$	−7271.59	−0.144409
$77$	−9375.17	−0.180199
$78$	−306.001	−0.00569490
$79$	−73360.1	−1.32249	−0.661244	−	0.750171i	$-0.729971\pi$
$79$	−73360.1	−1.32249	−0.661244	+	0.750171i	$0.729971\pi$
$80$	16358.6	0.285772
$81$	58920.5	0.997824
$82$	−77329.0	−1.27001
$83$	89307.9	1.42297	0.711483	−	0.702703i	$-0.248024\pi$
$83$	89307.9	1.42297	0.711483	+	0.702703i	$0.248024\pi$
$84$	520.512	0.00804883
$85$	−118212.	−1.77466
$86$	6874.64	0.100231
$87$	3092.08	0.0437978
$88$	−7744.00	−0.106600
$89$	−23117.7	−0.309364	−0.154682	−	0.987964i	$-0.549435\pi$
$89$	−23117.7	−0.309364	−0.154682	+	0.987964i	$0.549435\pi$
$90$	−62066.4	−0.807700
$91$	−14116.9	−0.178705
$92$	4368.97	0.0538158
$93$	2492.94	0.0298885
$94$	59860.0	0.698742
$95$	−29041.2	−0.330146
$96$	429.949	0.00476145
$97$	100486.	1.08436	0.542181	−	0.840262i	$-0.317599\pi$
$97$	100486.	1.08436	0.542181	+	0.840262i	$0.317599\pi$
$98$	−43214.9	−0.454536
$99$	29381.7	0.301293
$100$	15332.7	0.153327
$101$	68066.8	0.663945	0.331972	−	0.943289i	$-0.392286\pi$
$101$	68066.8	0.663945	0.331972	+	0.943289i	$0.392286\pi$
$102$	−3106.95	−0.0295688
$103$	166747.	1.54869	0.774345	−	0.632763i	$-0.218079\pi$
$103$	166747.	1.54869	0.774345	+	0.632763i	$0.218079\pi$
$104$	−11660.7	−0.105716
$105$	2078.82	0.0184011
$106$	57315.6	0.495460
$107$	−139883.	−1.18115	−0.590574	−	0.806984i	$-0.701098\pi$
$107$	−139883.	−1.18115	−0.590574	+	0.806984i	$0.701098\pi$
$108$	−3263.74	−0.0269250
$109$	541.857	0.00436836	0.00218418	−	0.999998i	$-0.499305\pi$
$109$	541.857	0.00436836	0.00218418	+	0.999998i	$0.499305\pi$
$110$	−30927.9	−0.243707
$111$	−1776.66	−0.0136867
$112$	19835.1	0.149413
$113$	28689.7	0.211363	0.105682	−	0.994400i	$-0.466298\pi$
$113$	28689.7	0.211363	0.105682	+	0.994400i	$0.466298\pi$
$114$	−763.285	−0.00550078
$115$	17448.8	0.123033
$116$	117829.	0.813033
$117$	44242.2	0.298794
$118$	200657.	1.32663
$119$	−143334.	−0.927862
$120$	1717.13	0.0108855
$121$	14641.0	0.0909091
$122$	−88724.6	−0.539690
$123$	−8117.07	−0.0483768
$124$	94997.9	0.554830
$125$	−138454.	−0.792557
$126$	−75256.7	−0.422298
$127$	−305780.	−1.68229	−0.841144	−	0.540812i	$-0.818117\pi$
$127$	−305780.	−1.68229	−0.841144	+	0.540812i	$0.818117\pi$
$128$	16384.0	0.0883883
$129$	721.618	0.00381797
$130$	−46570.5	−0.241686
$131$	−228353.	−1.16259	−0.581297	−	0.813692i	$-0.697454\pi$
$131$	−228353.	−1.16259	−0.581297	+	0.813692i	$0.697454\pi$
$132$	−812.873	−0.00406058
$133$	−35213.0	−0.172613
$134$	−212497.	−1.02233
$135$	−13034.7	−0.0615555
$136$	−118396.	−0.548895
$137$	251659.	1.14554	0.572771	−	0.819716i	$-0.305869\pi$
$137$	251659.	1.14554	0.572771	+	0.819716i	$0.305869\pi$
$138$	458.603	0.00204993
$139$	−248742.	−1.09197	−0.545986	−	0.837794i	$-0.683845\pi$
$139$	−248742.	−1.09197	−0.545986	+	0.837794i	$0.683845\pi$
$140$	79217.1	0.341585
$141$	6283.39	0.0266162
$142$	282191.	1.17442
$143$	22046.0	0.0901552
$144$	−62162.9	−0.249819
$145$	470585.	1.85874
$146$	86677.8	0.336532
$147$	−4536.19	−0.0173140
$148$	−67703.0	−0.254070
$149$	−219972.	−0.811710	−0.405855	−	0.913937i	$-0.633026\pi$
$149$	−219972.	−0.811710	−0.405855	+	0.913937i	$0.633026\pi$
$150$	1609.44	0.00584045
$151$	147226.	0.525464	0.262732	−	0.964869i	$-0.415377\pi$
$151$	147226.	0.525464	0.262732	+	0.964869i	$0.415377\pi$
$152$	−29086.4	−0.102113
$153$	449208.	1.55138
$154$	−37500.7	−0.127420
$155$	379402.	1.26844
$156$	−1224.00	−0.00402690
$157$	−303524.	−0.982751	−0.491375	−	0.870948i	$-0.663506\pi$
$157$	−303524.	−0.982751	−0.491375	+	0.870948i	$0.663506\pi$
$158$	−293440.	−0.935141
$159$	6016.31	0.0188728
$160$	65434.3	0.202072
$161$	21157.0	0.0643263
$162$	235682.	0.705568
$163$	216596.	0.638531	0.319266	−	0.947665i	$-0.396564\pi$
$163$	216596.	0.638531	0.319266	+	0.947665i	$0.396564\pi$
$164$	−309316.	−0.898034
$165$	−3246.44	−0.00928320
$166$	357232.	1.00619
$167$	379086.	1.05183	0.525916	−	0.850537i	$-0.323723\pi$
$167$	379086.	1.05183	0.525916	+	0.850537i	$0.323723\pi$
$168$	2082.05	0.00569138
$169$	−338097.	−0.910593
$170$	−472848.	−1.25487
$171$	110357.	0.288609
$172$	27498.6	0.0708743
$173$	154509.	0.392498	0.196249	−	0.980554i	$-0.437124\pi$
$173$	154509.	0.392498	0.196249	+	0.980554i	$0.437124\pi$
$174$	12368.3	0.0309697
$175$	74249.2	0.183272
$176$	−30976.0	−0.0753778
$177$	21062.5	0.0505333
$178$	−92470.8	−0.218753
$179$	−756412.	−1.76452	−0.882259	−	0.470765i	$-0.843978\pi$
$179$	−756412.	−1.76452	−0.882259	+	0.470765i	$0.843978\pi$
$180$	−248265.	−0.571130
$181$	247433.	0.561385	0.280693	−	0.959798i	$-0.409436\pi$
$181$	247433.	0.561385	0.280693	+	0.959798i	$0.409436\pi$
$182$	−56467.6	−0.126363
$183$	−9313.25	−0.0205576
$184$	17475.9	0.0380535
$185$	−270392.	−0.580850
$186$	9971.74	0.0211343
$187$	223842.	0.468099
$188$	239440.	0.494085
$189$	−15804.8	−0.0321836
$190$	−116165.	−0.233448
$191$	−719584.	−1.42724	−0.713622	−	0.700531i	$-0.752946\pi$
$191$	−719584.	−1.42724	−0.713622	+	0.700531i	$0.752946\pi$
$192$	1719.80	0.00336685
$193$	−83369.3	−0.161107	−0.0805533	−	0.996750i	$-0.525669\pi$
$193$	−83369.3	−0.161107	−0.0805533	+	0.996750i	$0.525669\pi$
$194$	401942.	0.766760
$195$	−4888.41	−0.00920621
$196$	−172860.	−0.321406
$197$	24689.0	0.0453251	0.0226625	−	0.999743i	$-0.492786\pi$
$197$	24689.0	0.0453251	0.0226625	+	0.999743i	$0.492786\pi$
$198$	117527.	0.213046
$199$	−136039.	−0.243517	−0.121759	−	0.992560i	$-0.538853\pi$
$199$	−136039.	−0.243517	−0.121759	+	0.992560i	$0.538853\pi$
$200$	61330.7	0.108418
$201$	−22305.4	−0.0389422
$202$	272267.	0.469480
$203$	570594.	0.971822
$204$	−12427.8	−0.0209083
$205$	−1.23534e6	−2.05307
$206$	666988.	1.09509
$207$	−66305.7	−0.107554
$208$	−46642.9	−0.0747527
$209$	54991.4	0.0870821
$210$	8315.27	0.0130115
$211$	−72377.6	−0.111918	−0.0559588	−	0.998433i	$-0.517822\pi$
$211$	−72377.6	−0.111918	−0.0559588	+	0.998433i	$0.517822\pi$
$212$	229263.	0.350343
$213$	29621.1	0.0447355
$214$	−559530.	−0.835197
$215$	109823.	0.162031
$216$	−13055.0	−0.0190389
$217$	460032.	0.663191
$218$	2167.43	0.00308890
$219$	9098.40	0.0128190
$220$	−123712.	−0.172327
$221$	337056.	0.464217
$222$	−7106.65	−0.00967794
$223$	755832.	1.01780	0.508901	−	0.860825i	$-0.330052\pi$
$223$	755832.	1.01780	0.508901	+	0.860825i	$0.330052\pi$
$224$	79340.3	0.105651
$225$	−232696.	−0.306431
$226$	114759.	0.149456
$227$	36346.3	0.0468161	0.0234080	−	0.999726i	$-0.492548\pi$
$227$	36346.3	0.0468161	0.0234080	+	0.999726i	$0.492548\pi$
$228$	−3053.14	−0.00388964
$229$	−868671.	−1.09463	−0.547314	−	0.836927i	$-0.684350\pi$
$229$	−868671.	−1.09463	−0.547314	+	0.836927i	$0.684350\pi$
$230$	69795.1	0.0869972
$231$	−3936.37	−0.00485363
$232$	471317.	0.574901
$233$	327735.	0.395488	0.197744	−	0.980254i	$-0.436639\pi$
$233$	327735.	0.395488	0.197744	+	0.980254i	$0.436639\pi$
$234$	176969.	0.211279
$235$	956273.	1.12957
$236$	802627.	0.938067
$237$	−30801.8	−0.0356210
$238$	−573338.	−0.656097
$239$	705004.	0.798356	0.399178	−	0.916873i	$-0.369295\pi$
$239$	705004.	0.798356	0.399178	+	0.916873i	$0.369295\pi$
$240$	6868.51	0.00769722
$241$	−693744.	−0.769408	−0.384704	−	0.923040i	$-0.625696\pi$
$241$	−693744.	−0.769408	−0.384704	+	0.923040i	$0.625696\pi$
$242$	58564.0	0.0642824
$243$	74307.2	0.0807263
$244$	−354898.	−0.381619
$245$	−690365.	−0.734791
$246$	−32468.3	−0.0342075
$247$	82804.7	0.0863599
$248$	379992.	0.392324
$249$	37497.9	0.0383273
$250$	−553816.	−0.560423
$251$	151448.	0.151732	0.0758662	−	0.997118i	$-0.475828\pi$
$251$	151448.	0.151732	0.0758662	+	0.997118i	$0.475828\pi$
$252$	−301027.	−0.298610
$253$	−33040.4	−0.0324522
$254$	−1.22312e6	−1.18956
$255$	−49634.0	−0.0478001
$256$	65536.0	0.0625000
$257$	1.78320e6	1.68410	0.842049	−	0.539401i	$-0.181349\pi$
$257$	1.78320e6	1.68410	0.842049	+	0.539401i	$0.181349\pi$
$258$	2886.47	0.00269971
$259$	−327855.	−0.303691
$260$	−186282.	−0.170898
$261$	−1.78823e6	−1.62489
$262$	−913411.	−0.822078
$263$	−119456.	−0.106493	−0.0532464	−	0.998581i	$-0.516957\pi$
$263$	−119456.	−0.106493	−0.0532464	+	0.998581i	$0.516957\pi$
$264$	−3251.49	−0.00287126
$265$	915627.	0.800947
$266$	−140852.	−0.122056
$267$	−9706.48	−0.00833266
$268$	−849989.	−0.722897
$269$	−1.16970e6	−0.985587	−0.492793	−	0.870146i	$-0.664024\pi$
$269$	−1.16970e6	−0.985587	−0.492793	+	0.870146i	$0.664024\pi$
$270$	−52138.8	−0.0435263
$271$	1.26986e6	1.05035	0.525174	−	0.850995i	$-0.324000\pi$
$271$	1.26986e6	1.05035	0.525174	+	0.850995i	$0.324000\pi$
$272$	−473584.	−0.388127
$273$	−5927.29	−0.00481338
$274$	1.00664e6	0.810020
$275$	−115953.	−0.0924595
$276$	1834.41	0.00144952
$277$	−2.08490e6	−1.63262	−0.816312	−	0.577611i	$-0.803985\pi$
$277$	−2.08490e6	−1.63262	−0.816312	+	0.577611i	$0.803985\pi$
$278$	−994966.	−0.772141
$279$	−1.44173e6	−1.10885
$280$	316869.	0.241537
$281$	1.39670e6	1.05521	0.527603	−	0.849491i	$-0.323091\pi$
$281$	1.39670e6	1.05521	0.527603	+	0.849491i	$0.323091\pi$
$282$	25133.5	0.0188205
$283$	−207611.	−0.154094	−0.0770469	−	0.997027i	$-0.524549\pi$
$283$	−207611.	−0.154094	−0.0770469	+	0.997027i	$0.524549\pi$
$284$	1.12877e6	0.830440
$285$	−12193.6	−0.00889241
$286$	88184.2	0.0637493
$287$	−1.49788e6	−1.07342
$288$	−248651.	−0.176648
$289$	2.00241e6	1.41029
$290$	1.88234e6	1.31433
$291$	42191.1	0.0292071
$292$	346711.	0.237964
$293$	2.30951e6	1.57163	0.785816	−	0.618460i	$-0.212243\pi$
$293$	2.30951e6	1.57163	0.785816	+	0.618460i	$0.212243\pi$
$294$	−18144.7	−0.0122428
$295$	3.20552e6	2.14459
$296$	−270812.	−0.179655
$297$	24682.0	0.0162364
$298$	−879886.	−0.573966
$299$	−49751.3	−0.0321830
$300$	6437.76	0.00412982
$301$	133163.	0.0847164
$302$	588905.	0.371559
$303$	28579.4	0.0178832
$304$	−116345.	−0.0722047
$305$	−1.41739e6	−0.872448
$306$	1.79683e6	1.09699
$307$	−307414.	−0.186156	−0.0930782	−	0.995659i	$-0.529671\pi$
$307$	−307414.	−0.186156	−0.0930782	+	0.995659i	$0.529671\pi$
$308$	−150003.	−0.0900995
$309$	70012.4	0.0417137
$310$	1.51761e6	0.896923
$311$	−379761.	−0.222643	−0.111322	−	0.993784i	$-0.535508\pi$
$311$	−379761.	−0.222643	−0.111322	+	0.993784i	$0.535508\pi$
$312$	−4896.01	−0.00284745
$313$	167942.	0.0968942	0.0484471	−	0.998826i	$-0.484573\pi$
$313$	167942.	0.0968942	0.0484471	+	0.998826i	$0.484573\pi$
$314$	−1.21409e6	−0.694910
$315$	−1.20224e6	−0.682675
$316$	−1.17376e6	−0.661244
$317$	−668834.	−0.373826	−0.186913	−	0.982376i	$-0.559848\pi$
$317$	−668834.	−0.373826	−0.186913	+	0.982376i	$0.559848\pi$
$318$	24065.2	0.0133451
$319$	−891084.	−0.490277
$320$	261737.	0.142886
$321$	−58732.8	−0.0318140
$322$	84627.9	0.0454856
$323$	840748.	0.448394
$324$	942728.	0.498912
$325$	−174600.	−0.0916927
$326$	866386.	0.451510
$327$	227.511	0.000117661 0
$328$	−1.23726e6	−0.635006
$329$	1.15950e6	0.590583
$330$	−12985.8	−0.00656421
$331$	−3.49335e6	−1.75256	−0.876278	−	0.481806i	$-0.839981\pi$
$331$	−3.49335e6	−1.75256	−0.876278	+	0.481806i	$0.839981\pi$
$332$	1.42893e6	0.711483
$333$	1.02749e6	0.507772
$334$	1.51634e6	0.743757
$335$	−3.39468e6	−1.65267
$336$	8328.20	0.00402442
$337$	744216.	0.356964	0.178482	−	0.983943i	$-0.442881\pi$
$337$	744216.	0.356964	0.178482	+	0.983943i	$0.442881\pi$
$338$	−1.35239e6	−0.643886
$339$	12046.0	0.00569303
$340$	−1.89139e6	−0.887329
$341$	−718422.	−0.334575
$342$	441429.	0.204078
$343$	−2.13930e6	−0.981830
$344$	109994.	0.0501157
$345$	7326.25	0.00331386
$346$	618035.	0.277538
$347$	−2.55399e6	−1.13866	−0.569332	−	0.822108i	$-0.692798\pi$
$347$	−2.55399e6	−1.13866	−0.569332	+	0.822108i	$0.692798\pi$
$348$	49473.2	0.0218989
$349$	739179.	0.324852	0.162426	−	0.986721i	$-0.448068\pi$
$349$	739179.	0.324852	0.162426	+	0.986721i	$0.448068\pi$
$350$	296997.	0.129593
$351$	37165.6	0.0161018
$352$	−123904.	−0.0533002
$353$	−1.56982e6	−0.670521	−0.335261	−	0.942125i	$-0.608824\pi$
$353$	−1.56982e6	−0.670521	−0.335261	+	0.942125i	$0.608824\pi$
$354$	84250.2	0.0357324
$355$	4.50805e6	1.89853
$356$	−369883.	−0.154682
$357$	−60182.1	−0.0249918
$358$	−3.02565e6	−1.24770
$359$	3.00654e6	1.23121	0.615603	−	0.788057i	$-0.288913\pi$
$359$	3.00654e6	1.23121	0.615603	+	0.788057i	$0.288913\pi$
$360$	−993062.	−0.403850
$361$	−2.26955e6	−0.916584
$362$	989731.	0.396959
$363$	6147.35	0.00244862
$364$	−225870.	−0.0893523
$365$	1.38469e6	0.544028
$366$	−37253.0	−0.0145365
$367$	−1.82204e6	−0.706144	−0.353072	−	0.935596i	$-0.614863\pi$
$367$	−1.82204e6	−0.706144	−0.353072	+	0.935596i	$0.614863\pi$
$368$	69903.6	0.0269079
$369$	4.69433e6	1.79476
$370$	−1.08157e6	−0.410723
$371$	1.11021e6	0.418767
$372$	39887.0	0.0149442
$373$	2.78168e6	1.03523	0.517613	−	0.855615i	$-0.326821\pi$
$373$	2.78168e6	1.03523	0.517613	+	0.855615i	$0.326821\pi$
$374$	895369.	0.330996
$375$	−58133.0	−0.0213474
$376$	957760.	0.349371
$377$	−1.34177e6	−0.486211
$378$	−63219.3	−0.0227573
$379$	4.25264e6	1.52076	0.760379	−	0.649479i	$-0.225013\pi$
$379$	4.25264e6	1.52076	0.760379	+	0.649479i	$0.225013\pi$
$380$	−464659.	−0.165073
$381$	−128389.	−0.0453121
$382$	−2.87834e6	−1.00921
$383$	1.12656e6	0.392427	0.196213	−	0.980561i	$-0.437135\pi$
$383$	1.12656e6	0.392427	0.196213	+	0.980561i	$0.437135\pi$
$384$	6879.19	0.00238072
$385$	−599080.	−0.205984
$386$	−333477.	−0.113920
$387$	−417331.	−0.141646
$388$	1.60777e6	0.542181
$389$	1.20762e6	0.404630	0.202315	−	0.979321i	$-0.435154\pi$
$389$	1.20762e6	0.404630	0.202315	+	0.979321i	$0.435154\pi$
$390$	−19553.6	−0.00650978
$391$	−505145.	−0.167099
$392$	−691439.	−0.227268
$393$	−95879.0	−0.0313142
$394$	98756.2	0.0320497
$395$	−4.68775e6	−1.51172
$396$	470107.	0.150646
$397$	2.08499e6	0.663938	0.331969	−	0.943290i	$-0.392287\pi$
$397$	2.08499e6	0.663938	0.331969	+	0.943290i	$0.392287\pi$
$398$	−544155.	−0.172193
$399$	−14785.0	−0.00464931
$400$	245323.	0.0766633
$401$	−4.94315e6	−1.53512	−0.767560	−	0.640977i	$-0.778529\pi$
$401$	−4.94315e6	−1.53512	−0.767560	+	0.640977i	$0.778529\pi$
$402$	−89221.6	−0.0275363
$403$	−1.08178e6	−0.331800
$404$	1.08907e6	0.331972
$405$	3.76506e6	1.14060
$406$	2.28237e6	0.687182
$407$	512004.	0.153210
$408$	−49711.1	−0.0147844
$409$	851481.	0.251691	0.125845	−	0.992050i	$-0.459836\pi$
$409$	851481.	0.251691	0.125845	+	0.992050i	$0.459836\pi$
$410$	−4.94137e6	−1.45174
$411$	105665.	0.0308549
$412$	2.66795e6	0.774345
$413$	3.88676e6	1.12128
$414$	−265223.	−0.0760518
$415$	5.70683e6	1.62658
$416$	−186571.	−0.0528581
$417$	−104440.	−0.0294121
$418$	219966.	0.0615764
$419$	2.70342e6	0.752278	0.376139	−	0.926563i	$-0.377251\pi$
$419$	2.70342e6	0.752278	0.376139	+	0.926563i	$0.377251\pi$
$420$	33261.1	0.00920053
$421$	−2.72723e6	−0.749923	−0.374962	−	0.927040i	$-0.622344\pi$
$421$	−2.72723e6	−0.749923	−0.374962	+	0.927040i	$0.622344\pi$
$422$	−289510.	−0.0791376
$423$	−3.63386e6	−0.987454
$424$	917050.	0.247730
$425$	−1.77278e6	−0.476082
$426$	118484.	0.0316328
$427$	−1.71861e6	−0.456151
$428$	−2.23812e6	−0.590574
$429$	9256.52	0.00242831
$430$	439294.	0.114573
$431$	−5.64590e6	−1.46400	−0.731998	−	0.681307i	$-0.761412\pi$
$431$	−5.64590e6	−1.46400	−0.731998	+	0.681307i	$0.761412\pi$
$432$	−52219.9	−0.0134625
$433$	−2.82741e6	−0.724717	−0.362358	−	0.932039i	$-0.618028\pi$
$433$	−2.82741e6	−0.724717	−0.362358	+	0.932039i	$0.618028\pi$
$434$	1.84013e6	0.468947
$435$	197586.	0.0500648
$436$	8669.72	0.00218418
$437$	−124099.	−0.0310860
$438$	36393.6	0.00906441
$439$	−1.44817e6	−0.358639	−0.179319	−	0.983791i	$-0.557390\pi$
$439$	−1.44817e6	−0.358639	−0.179319	+	0.983791i	$0.557390\pi$
$440$	−494847.	−0.121854
$441$	2.62340e6	0.642345
$442$	1.34822e6	0.328251
$443$	−5.58529e6	−1.35219	−0.676093	−	0.736816i	$-0.736328\pi$
$443$	−5.58529e6	−1.35219	−0.676093	+	0.736816i	$0.736328\pi$
$444$	−28426.6	−0.00684333
$445$	−1.47724e6	−0.353631
$446$	3.02333e6	0.719695
$447$	−92359.9	−0.0218633
$448$	317361.	0.0747066
$449$	−5.28597e6	−1.23740	−0.618698	−	0.785629i	$-0.712340\pi$
$449$	−5.28597e6	−1.23740	−0.618698	+	0.785629i	$0.712340\pi$
$450$	−930784.	−0.216679
$451$	2.33920e6	0.541535
$452$	459035.	0.105682
$453$	61816.2	0.0141533
$454$	145385.	0.0331040
$455$	−902079.	−0.204275
$456$	−12212.6	−0.00275039
$457$	−7.13412e6	−1.59790	−0.798950	−	0.601397i	$-0.794611\pi$
$457$	−7.13412e6	−1.59790	−0.798950	+	0.601397i	$0.794611\pi$
$458$	−3.47469e6	−0.774019
$459$	377357.	0.0836028
$460$	279180.	0.0615163
$461$	3.19749e6	0.700740	0.350370	−	0.936611i	$-0.386056\pi$
$461$	3.19749e6	0.700740	0.350370	+	0.936611i	$0.386056\pi$
$462$	−15745.5	−0.00343203
$463$	4.64377e6	1.00674	0.503371	−	0.864070i	$-0.332093\pi$
$463$	4.64377e6	1.00674	0.503371	+	0.864070i	$0.332093\pi$
$464$	1.88527e6	0.406516
$465$	159300.	0.0341652
$466$	1.31094e6	0.279652
$467$	4.84622e6	1.02828	0.514140	−	0.857707i	$-0.328111\pi$
$467$	4.84622e6	1.02828	0.514140	+	0.857707i	$0.328111\pi$
$468$	707875.	0.149397
$469$	−4.11611e6	−0.864082
$470$	3.82509e6	0.798725
$471$	−127441.	−0.0264702
$472$	3.21051e6	0.663313
$473$	−207958.	−0.0427388
$474$	−123207.	−0.0251878
$475$	−435519.	−0.0885672
$476$	−2.29335e6	−0.463931
$477$	−3.47940e6	−0.700178
$478$	2.82002e6	0.564523
$479$	3.80671e6	0.758072	0.379036	−	0.925382i	$-0.376256\pi$
$479$	3.80671e6	0.758072	0.379036	+	0.925382i	$0.376256\pi$
$480$	27474.0	0.00544276
$481$	770963.	0.151940
$482$	−2.77497e6	−0.544053
$483$	8883.22	0.00173262
$484$	234256.	0.0454545
$485$	6.42109e6	1.23952
$486$	297229.	0.0570821
$487$	9.22316e6	1.76221	0.881104	−	0.472923i	$-0.156801\pi$
$487$	9.22316e6	1.76221	0.881104	+	0.472923i	$0.156801\pi$
$488$	−1.41959e6	−0.269845
$489$	90942.8	0.0171987
$490$	−2.76146e6	−0.519576
$491$	616697.	0.115443	0.0577215	−	0.998333i	$-0.481616\pi$
$491$	616697.	0.115443	0.0577215	+	0.998333i	$0.481616\pi$
$492$	−129873.	−0.0241884
$493$	−1.36235e7	−2.52448
$494$	331219.	0.0610657
$495$	1.87751e6	0.344404
$496$	1.51997e6	0.277415
$497$	5.46610e6	0.992629
$498$	149992.	0.0271015
$499$	3.20659e6	0.576490	0.288245	−	0.957557i	$-0.406928\pi$
$499$	3.20659e6	0.576490	0.288245	+	0.957557i	$0.406928\pi$
$500$	−2.21526e6	−0.396279
$501$	159168.	0.0283309
$502$	605791.	0.107291
$503$	8.94986e6	1.57723	0.788617	−	0.614884i	$-0.210797\pi$
$503$	8.94986e6	1.57723	0.788617	+	0.614884i	$0.210797\pi$
$504$	−1.20411e6	−0.211149
$505$	4.34951e6	0.758948
$506$	−132161.	−0.0229471
$507$	−141957.	−0.0245266
$508$	−4.89249e6	−0.841144
$509$	1.17247e6	0.200588	0.100294	−	0.994958i	$-0.468022\pi$
$509$	1.17247e6	0.200588	0.100294	+	0.994958i	$0.468022\pi$
$510$	−198536.	−0.0337998
$511$	1.67897e6	0.284439
$512$	262144.	0.0441942
$513$	92705.4	0.0155529
$514$	7.13280e6	1.19084
$515$	1.06552e7	1.77029
$516$	11545.9	0.00190899
$517$	−1.81076e6	−0.297945
$518$	−1.31142e6	−0.214742
$519$	64873.9	0.0105719
$520$	−745127.	−0.120843
$521$	−6.06798e6	−0.979377	−0.489689	−	0.871897i	$-0.662889\pi$
$521$	−6.06798e6	−0.979377	−0.489689	+	0.871897i	$0.662889\pi$
$522$	−7.15293e6	−1.14897
$523$	−6.01472e6	−0.961527	−0.480764	−	0.876850i	$-0.659640\pi$
$523$	−6.01472e6	−0.961527	−0.480764	+	0.876850i	$0.659640\pi$
$524$	−3.65364e6	−0.581297
$525$	31175.2	0.00493640
$526$	−477826.	−0.0753017
$527$	−1.09838e7	−1.72276
$528$	−13006.0	−0.00203029
$529$	−6.36178e6	−0.988415
$530$	3.66251e6	0.566355
$531$	−1.21811e7	−1.87477
$532$	−563408.	−0.0863066
$533$	3.52231e6	0.537044
$534$	−38825.9	−0.00589208
$535$	−8.93858e6	−1.35016
$536$	−3.39995e6	−0.511165
$537$	−317596.	−0.0475270
$538$	−4.67881e6	−0.696915
$539$	1.30725e6	0.193815
$540$	−208555.	−0.0307777
$541$	8.50236e6	1.24895	0.624477	−	0.781043i	$-0.285312\pi$
$541$	8.50236e6	1.24895	0.624477	+	0.781043i	$0.285312\pi$
$542$	5.07944e6	0.742708
$543$	103890.	0.0151208
$544$	−1.89433e6	−0.274448
$545$	34625.0	0.00499343
$546$	−23709.2	−0.00340357
$547$	3.99730e6	0.571214	0.285607	−	0.958347i	$-0.407805\pi$
$547$	3.99730e6	0.571214	0.285607	+	0.958347i	$0.407805\pi$
$548$	4.02654e6	0.572771
$549$	5.38611e6	0.762683
$550$	−463813.	−0.0653787
$551$	−3.34690e6	−0.469638
$552$	7337.64	0.00102496
$553$	−5.68399e6	−0.790389
$554$	−8.33961e6	−1.15444
$555$	−113530.	−0.0156451
$556$	−3.97987e6	−0.545986
$557$	9.09530e6	1.24216	0.621082	−	0.783745i	$-0.286693\pi$
$557$	9.09530e6	1.24216	0.621082	+	0.783745i	$0.286693\pi$
$558$	−5.76694e6	−0.784079
$559$	−313138.	−0.0423844
$560$	1.26747e6	0.170793
$561$	93985.1	0.0126082
$562$	5.58680e6	0.746143
$563$	6.17614e6	0.821195	0.410597	−	0.911817i	$-0.365320\pi$
$563$	6.17614e6	0.821195	0.410597	+	0.911817i	$0.365320\pi$
$564$	100534.	0.0133081
$565$	1.83329e6	0.241607
$566$	−830445.	−0.108961
$567$	4.56521e6	0.596352
$568$	4.51506e6	0.587209
$569$	−1.32050e7	−1.70984	−0.854922	−	0.518757i	$-0.826395\pi$
$569$	−1.32050e7	−1.70984	−0.854922	+	0.518757i	$0.826395\pi$
$570$	−48774.4	−0.00628788
$571$	4.14020e6	0.531412	0.265706	−	0.964054i	$-0.414395\pi$
$571$	4.14020e6	0.531412	0.265706	+	0.964054i	$0.414395\pi$
$572$	352737.	0.0450776
$573$	−302133.	−0.0384425
$574$	−5.99151e6	−0.759026
$575$	261672.	0.0330056
$576$	−994606.	−0.124909
$577$	−1.57797e6	−0.197314	−0.0986570	−	0.995121i	$-0.531455\pi$
$577$	−1.57797e6	−0.197314	−0.0986570	+	0.995121i	$0.531455\pi$
$578$	8.00962e6	0.997223
$579$	−35004.5	−0.00433937
$580$	7.52936e6	0.929369
$581$	6.91965e6	0.850440
$582$	168764.	0.0206525
$583$	−1.73380e6	−0.211265
$584$	1.38685e6	0.168266
$585$	2.82710e6	0.341548
$586$	9.23804e6	1.11131
$587$	−7.04930e6	−0.844404	−0.422202	−	0.906502i	$-0.638743\pi$
$587$	−7.04930e6	−0.844404	−0.422202	+	0.906502i	$0.638743\pi$
$588$	−72579.0	−0.00865700
$589$	−2.69838e6	−0.320491
$590$	1.28221e7	1.51645
$591$	10366.2	0.00122082
$592$	−1.08325e6	−0.127035
$593$	5.13524e6	0.599686	0.299843	−	0.953989i	$-0.403066\pi$
$593$	5.13524e6	0.599686	0.299843	+	0.953989i	$0.403066\pi$
$594$	98728.2	0.0114809
$595$	−9.15916e6	−1.06063
$596$	−3.51955e6	−0.405855
$597$	−57118.9	−0.00655909
$598$	−199005.	−0.0227568
$599$	5.62683e6	0.640762	0.320381	−	0.947289i	$-0.396189\pi$
$599$	5.62683e6	0.640762	0.320381	+	0.947289i	$0.396189\pi$
$600$	25751.0	0.00292023
$601$	−2.76597e6	−0.312364	−0.156182	−	0.987728i	$-0.549919\pi$
$601$	−2.76597e6	−0.312364	−0.156182	+	0.987728i	$0.549919\pi$
$602$	532652.	0.0599036
$603$	1.28998e7	1.44474
$604$	2.35562e6	0.262732
$605$	935569.	0.103917
$606$	114317.	0.0126454
$607$	−1.16596e7	−1.28443	−0.642215	−	0.766524i	$-0.721985\pi$
$607$	−1.16596e7	−1.28443	−0.642215	+	0.766524i	$0.721985\pi$
$608$	−465382.	−0.0510564
$609$	239576.	0.0261759
$610$	−5.66956e6	−0.616914
$611$	−2.72660e6	−0.295474
$612$	7.18733e6	0.775692
$613$	−9.43965e6	−1.01462	−0.507311	−	0.861763i	$-0.669361\pi$
$613$	−9.43965e6	−1.01462	−0.507311	+	0.861763i	$0.669361\pi$
$614$	−1.22966e6	−0.131632
$615$	−518686.	−0.0552990
$616$	−600011.	−0.0637100
$617$	1.06816e7	1.12960	0.564801	−	0.825227i	$-0.308953\pi$
$617$	1.06816e7	1.12960	0.564801	+	0.825227i	$0.308953\pi$
$618$	280050.	0.0294960
$619$	1.72178e6	0.180614	0.0903071	−	0.995914i	$-0.471215\pi$
$619$	1.72178e6	0.180614	0.0903071	+	0.995914i	$0.471215\pi$
$620$	6.07043e6	0.634220
$621$	−55700.0	−0.00579597
$622$	−1.51904e6	−0.157432
$623$	−1.79118e6	−0.184892
$624$	−19584.0	−0.00201345
$625$	−1.18420e7	−1.21262
$626$	671767.	0.0685145
$627$	23089.4	0.00234554
$628$	−4.85638e6	−0.491375
$629$	7.82789e6	0.788893
$630$	−4.80895e6	−0.482724
$631$	1.30798e7	1.30776	0.653878	−	0.756600i	$-0.273141\pi$
$631$	1.30798e7	1.30776	0.653878	+	0.756600i	$0.273141\pi$
$632$	−4.69504e6	−0.467570
$633$	−30389.3	−0.00301448
$634$	−2.67534e6	−0.264335
$635$	−1.95396e7	−1.92301
$636$	96261.0	0.00943642
$637$	1.96843e6	0.192208
$638$	−3.56433e6	−0.346678
$639$	−1.71307e7	−1.65967
$640$	1.04695e6	0.101036
$641$	4.58213e6	0.440477	0.220238	−	0.975446i	$-0.429317\pi$
$641$	4.58213e6	0.440477	0.220238	+	0.975446i	$0.429317\pi$
$642$	−234931.	−0.0224959
$643$	1.47711e7	1.40892	0.704458	−	0.709746i	$-0.251190\pi$
$643$	1.47711e7	1.40892	0.704458	+	0.709746i	$0.251190\pi$
$644$	338511.	0.0321632
$645$	46111.8	0.00436428
$646$	3.36299e6	0.317062
$647$	6.63851e6	0.623462	0.311731	−	0.950170i	$-0.399091\pi$
$647$	6.63851e6	0.623462	0.311731	+	0.950170i	$0.399091\pi$
$648$	3.77091e6	0.352784
$649$	−6.06987e6	−0.565675
$650$	−698398.	−0.0648365
$651$	193155.	0.0178629
$652$	3.46554e6	0.319266
$653$	1.31245e7	1.20448	0.602240	−	0.798315i	$-0.294275\pi$
$653$	1.31245e7	1.20448	0.602240	+	0.798315i	$0.294275\pi$
$654$	910.043	8.31989e−5 0
$655$	−1.45919e7	−1.32895
$656$	−4.94906e6	−0.449017
$657$	−5.26186e6	−0.475582
$658$	4.63800e6	0.417605
$659$	−1.42580e7	−1.27893	−0.639465	−	0.768821i	$-0.720844\pi$
$659$	−1.42580e7	−1.27893	−0.639465	+	0.768821i	$0.720844\pi$
$660$	−51943.1	−0.00464160
$661$	5.52495e6	0.491841	0.245921	−	0.969290i	$-0.420910\pi$
$661$	5.52495e6	0.491841	0.245921	+	0.969290i	$0.420910\pi$
$662$	−1.39734e7	−1.23924
$663$	141520.	0.0125036
$664$	5.71571e6	0.503095
$665$	−2.25013e6	−0.197312
$666$	4.10997e6	0.359049
$667$	2.01091e6	0.175016
$668$	6.06537e6	0.525916
$669$	317353.	0.0274143
$670$	−1.35787e7	−1.16861
$671$	2.68392e6	0.230125
$672$	33312.8	0.00284569
$673$	−1.42637e6	−0.121394	−0.0606968	−	0.998156i	$-0.519332\pi$
$673$	−1.42637e6	−0.121394	−0.0606968	+	0.998156i	$0.519332\pi$
$674$	2.97687e6	0.252412
$675$	−195476.	−0.0165133
$676$	−5.40955e6	−0.455296
$677$	1.94547e6	0.163137	0.0815687	−	0.996668i	$-0.474007\pi$
$677$	1.94547e6	0.163137	0.0815687	+	0.996668i	$0.474007\pi$
$678$	48184.0	0.00402558
$679$	7.78570e6	0.648072
$680$	−7.56557e6	−0.627436
$681$	15260.8	0.00126098
$682$	−2.87369e6	−0.236580
$683$	−1.21006e7	−0.992556	−0.496278	−	0.868164i	$-0.665300\pi$
$683$	−1.21006e7	−0.992556	−0.496278	+	0.868164i	$0.665300\pi$
$684$	1.76571e6	0.144305
$685$	1.60812e7	1.30946
$686$	−8.55720e6	−0.694259
$687$	−364731.	−0.0294836
$688$	439977.	0.0354372
$689$	−2.61071e6	−0.209513
$690$	29305.0	0.00234325
$691$	2.45248e6	0.195394	0.0976968	−	0.995216i	$-0.468852\pi$
$691$	2.45248e6	0.195394	0.0976968	+	0.995216i	$0.468852\pi$
$692$	2.47214e6	0.196249
$693$	2.27651e6	0.180068
$694$	−1.02160e7	−0.805157
$695$	−1.58947e7	−1.24822
$696$	197893.	0.0154849
$697$	3.57634e7	2.78841
$698$	2.95672e6	0.229705
$699$	137607.	0.0106524
$700$	1.18799e6	0.0916361
$701$	−1.57028e7	−1.20693	−0.603465	−	0.797389i	$-0.706214\pi$
$701$	−1.57028e7	−1.20693	−0.603465	+	0.797389i	$0.706214\pi$
$702$	148662.	0.0113857
$703$	1.92308e6	0.146760
$704$	−495616.	−0.0376889
$705$	401512.	0.0304247
$706$	−6.27927e6	−0.474130
$707$	5.27387e6	0.396808
$708$	337001.	0.0252666
$709$	5.84114e6	0.436398	0.218199	−	0.975904i	$-0.429982\pi$
$709$	5.84114e6	0.436398	0.218199	+	0.975904i	$0.429982\pi$
$710$	1.80322e7	1.34247
$711$	1.78136e7	1.32153
$712$	−1.47953e6	−0.109377
$713$	1.62126e6	0.119434
$714$	−240729.	−0.0176719
$715$	1.40876e6	0.103055
$716$	−1.21026e7	−0.882259
$717$	296012.	0.0215036
$718$	1.20262e7	0.870594
$719$	−5.42837e6	−0.391604	−0.195802	−	0.980643i	$-0.562731\pi$
$719$	−5.42837e6	−0.391604	−0.195802	+	0.980643i	$0.562731\pi$
$720$	−3.97225e6	−0.285565
$721$	1.29197e7	0.925579
$722$	−9.07821e6	−0.648123
$723$	−291284.	−0.0207238
$724$	3.95892e6	0.280693
$725$	7.05717e6	0.498638
$726$	24589.4	0.00173144
$727$	9.35968e6	0.656788	0.328394	−	0.944541i	$-0.393493\pi$
$727$	9.35968e6	0.656788	0.328394	+	0.944541i	$0.393493\pi$
$728$	−903481.	−0.0631816
$729$	−1.42865e7	−0.995650
$730$	5.53877e6	0.384686
$731$	−3.17941e6	−0.220066
$732$	−149012.	−0.0102788
$733$	−1.56636e6	−0.107679	−0.0538394	−	0.998550i	$-0.517146\pi$
$733$	−1.56636e6	−0.107679	−0.0538394	+	0.998550i	$0.517146\pi$
$734$	−7.28816e6	−0.499319
$735$	−289865.	−0.0197915
$736$	279614.	0.0190268
$737$	6.42804e6	0.435923
$738$	1.87773e7	1.26909
$739$	1.73561e7	1.16907	0.584535	−	0.811368i	$-0.301277\pi$
$739$	1.73561e7	1.16907	0.584535	+	0.811368i	$0.301277\pi$
$740$	−4.32627e6	−0.290425
$741$	34767.4	0.00232609
$742$	4.44086e6	0.296113
$743$	−2.06751e6	−0.137397	−0.0686984	−	0.997637i	$-0.521885\pi$
$743$	−2.06751e6	−0.137397	−0.0686984	+	0.997637i	$0.521885\pi$
$744$	159548.	0.0105672
$745$	−1.40563e7	−0.927857
$746$	1.11267e7	0.732016
$747$	−2.16861e7	−1.42193
$748$	3.58148e6	0.234050
$749$	−1.08382e7	−0.705916
$750$	−232532.	−0.0150949
$751$	6.44737e6	0.417141	0.208571	−	0.978007i	$-0.433119\pi$
$751$	6.44737e6	0.417141	0.208571	+	0.978007i	$0.433119\pi$
$752$	3.83104e6	0.247043
$753$	63588.7	0.00408688
$754$	−5.36708e6	−0.343803
$755$	9.40785e6	0.600652
$756$	−252877.	−0.0160918
$757$	−2.07595e7	−1.31667	−0.658336	−	0.752725i	$-0.728739\pi$
$757$	−2.07595e7	−1.31667	−0.658336	+	0.752725i	$0.728739\pi$
$758$	1.70105e7	1.07534
$759$	−13872.7	−0.000874093 0
$760$	−1.85864e6	−0.116724
$761$	−1.23568e7	−0.773473	−0.386737	−	0.922190i	$-0.626398\pi$
$761$	−1.23568e7	−0.773473	−0.386737	+	0.922190i	$0.626398\pi$
$762$	−513555.	−0.0320405
$763$	41983.5	0.00261076
$764$	−1.15133e7	−0.713622
$765$	2.87047e7	1.77337
$766$	4.50625e6	0.277488
$767$	−9.13985e6	−0.560984
$768$	27516.7	0.00168343
$769$	−5.73035e6	−0.349434	−0.174717	−	0.984619i	$-0.555901\pi$
$769$	−5.73035e6	−0.349434	−0.174717	+	0.984619i	$0.555901\pi$
$770$	−2.39632e6	−0.145652
$771$	748716.	0.0453609
$772$	−1.33391e6	−0.0805533
$773$	−2.47328e7	−1.48876	−0.744379	−	0.667757i	$-0.767255\pi$
$773$	−2.47328e7	−1.48876	−0.744379	+	0.667757i	$0.767255\pi$
$774$	−1.66933e6	−0.100159
$775$	5.68973e6	0.340281
$776$	6.43108e6	0.383380
$777$	−137657.	−0.00817987
$778$	4.83050e6	0.286117
$779$	8.78601e6	0.518738
$780$	−78214.6	−0.00460311
$781$	−8.53629e6	−0.500774
$782$	−2.02058e6	−0.118157
$783$	−1.50220e6	−0.0875638
$784$	−2.76576e6	−0.160703
$785$	−1.93954e7	−1.12337
$786$	−383516.	−0.0221425
$787$	−2.90978e7	−1.67465	−0.837324	−	0.546707i	$-0.815881\pi$
$787$	−2.90978e7	−1.67465	−0.837324	+	0.546707i	$0.815881\pi$
$788$	395025.	0.0226625
$789$	−50156.4	−0.00286836
$790$	−1.87510e7	−1.06895
$791$	2.22290e6	0.126322
$792$	1.88043e6	0.106523
$793$	4.04138e6	0.228216
$794$	8.33996e6	0.469475
$795$	384446.	0.0215734
$796$	−2.17662e6	−0.121759
$797$	−3.23694e7	−1.80505	−0.902525	−	0.430637i	$-0.858289\pi$
$797$	−3.23694e7	−1.80505	−0.902525	+	0.430637i	$0.858289\pi$
$798$	−59139.9	−0.00328756
$799$	−2.76843e7	−1.53415
$800$	981291.	0.0542092
$801$	5.61353e6	0.309140
$802$	−1.97726e7	−1.08549
$803$	−2.62200e6	−0.143498
$804$	−356887.	−0.0194711
$805$	1.35194e6	0.0735307
$806$	−4.32712e6	−0.234618
$807$	−491126.	−0.0265466
$808$	4.35628e6	0.234740
$809$	9.52388e6	0.511614	0.255807	−	0.966728i	$-0.417659\pi$
$809$	9.52388e6	0.511614	0.255807	+	0.966728i	$0.417659\pi$
$810$	1.50602e7	0.806527
$811$	3.71374e7	1.98271	0.991356	−	0.131197i	$-0.0418821\pi$
$811$	3.71374e7	1.98271	0.991356	+	0.131197i	$0.0418821\pi$
$812$	9.12950e6	0.485911
$813$	533179.	0.0282909
$814$	2.04802e6	0.108336
$815$	1.38406e7	0.729898
$816$	−198845.	−0.0104541
$817$	−781087.	−0.0409397
$818$	3.40593e6	0.177972
$819$	3.42792e6	0.178575
$820$	−1.97655e7	−1.02653
$821$	−1.96824e7	−1.01911	−0.509554	−	0.860439i	$-0.670189\pi$
$821$	−1.96824e7	−1.01911	−0.509554	+	0.860439i	$0.670189\pi$
$822$	422658.	0.0218177
$823$	2.48467e7	1.27870	0.639352	−	0.768914i	$-0.279203\pi$
$823$	2.48467e7	1.27870	0.639352	+	0.768914i	$0.279203\pi$
$824$	1.06718e7	0.547545
$825$	−48685.6	−0.00249038
$826$	1.55470e7	0.792862
$827$	3.16505e6	0.160923	0.0804613	−	0.996758i	$-0.474361\pi$
$827$	3.16505e6	0.160923	0.0804613	+	0.996758i	$0.474361\pi$
$828$	−1.06089e6	−0.0537768
$829$	−7.93948e6	−0.401241	−0.200621	−	0.979669i	$-0.564296\pi$
$829$	−7.93948e6	−0.401241	−0.200621	+	0.979669i	$0.564296\pi$
$830$	2.28273e7	1.15016
$831$	−875393.	−0.0439744
$832$	−746286.	−0.0373764
$833$	1.99862e7	0.997971
$834$	−417759.	−0.0207975
$835$	2.42238e7	1.20234
$836$	879862.	0.0435411
$837$	−1.21113e6	−0.0597553
$838$	1.08137e7	0.531941
$839$	1.49285e7	0.732170	0.366085	−	0.930581i	$-0.380698\pi$
$839$	1.49285e7	0.732170	0.366085	+	0.930581i	$0.380698\pi$
$840$	133044.	0.00650576
$841$	3.37222e7	1.64409
$842$	−1.09089e7	−0.530276
$843$	586435.	0.0284218
$844$	−1.15804e6	−0.0559588
$845$	−2.16046e7	−1.04089
$846$	−1.45354e7	−0.698235
$847$	1.13440e6	0.0543321
$848$	3.66820e6	0.175172
$849$	−87170.2	−0.00415049
$850$	−7.09111e6	−0.336641
$851$	−1.15544e6	−0.0546920
$852$	473937.	0.0223677
$853$	−1.61978e7	−0.762225	−0.381113	−	0.924529i	$-0.624459\pi$
$853$	−1.61978e7	−0.762225	−0.381113	+	0.924529i	$0.624459\pi$
$854$	−6.87445e6	−0.322547
$855$	7.05189e6	0.329906
$856$	−8.95248e6	−0.417599
$857$	3.86682e7	1.79846	0.899232	−	0.437472i	$-0.144126\pi$
$857$	3.86682e7	1.79846	0.899232	+	0.437472i	$0.144126\pi$
$858$	37026.1	0.00171708
$859$	−1.39979e7	−0.647260	−0.323630	−	0.946184i	$-0.604903\pi$
$859$	−1.39979e7	−0.647260	−0.323630	+	0.946184i	$0.604903\pi$
$860$	1.75718e6	0.0810157
$861$	−628917.	−0.0289125
$862$	−2.25836e7	−1.03520
$863$	−7.28425e6	−0.332934	−0.166467	−	0.986047i	$-0.553236\pi$
$863$	−7.28425e6	−0.332934	−0.166467	+	0.986047i	$0.553236\pi$
$864$	−208879.	−0.00951944
$865$	9.87320e6	0.448660
$866$	−1.13096e7	−0.512452
$867$	840754.	0.0379858
$868$	7.36051e6	0.331595
$869$	8.87657e6	0.398745
$870$	790342.	0.0354011
$871$	9.67918e6	0.432308
$872$	34678.9	0.00154445
$873$	−2.44003e7	−1.08358
$874$	−496397.	−0.0219811
$875$	−1.07275e7	−0.473674
$876$	145574.	0.00640951
$877$	2.21230e7	0.971283	0.485642	−	0.874158i	$-0.338586\pi$
$877$	2.21230e7	0.971283	0.485642	+	0.874158i	$0.338586\pi$
$878$	−5.79267e6	−0.253596
$879$	969699.	0.0423316
$880$	−1.97939e6	−0.0861636
$881$	3.07411e7	1.33438	0.667190	−	0.744888i	$-0.267497\pi$
$881$	3.07411e7	1.33438	0.667190	+	0.744888i	$0.267497\pi$
$882$	1.04936e7	0.454207
$883$	5.27648e6	0.227742	0.113871	−	0.993496i	$-0.463675\pi$
$883$	5.27648e6	0.227742	0.113871	+	0.993496i	$0.463675\pi$
$884$	5.39290e6	0.232109
$885$	1.34591e6	0.0577641
$886$	−2.23412e7	−0.956140
$887$	2.00647e7	0.856295	0.428147	−	0.903709i	$-0.359166\pi$
$887$	2.00647e7	0.856295	0.428147	+	0.903709i	$0.359166\pi$
$888$	−113706.	−0.00483897
$889$	−2.36921e7	−1.00542
$890$	−5.90895e6	−0.250055
$891$	−7.12938e6	−0.300855
$892$	1.20933e7	0.508901
$893$	−6.80121e6	−0.285402
$894$	−369440.	−0.0154597
$895$	−4.83352e7	−2.01700
$896$	1.26944e6	0.0528255
$897$	−20889.2	−0.000866844 0
$898$	−2.11439e7	−0.874972
$899$	4.37247e7	1.80438
$900$	−3.72314e6	−0.153215
$901$	−2.65076e7	−1.08782
$902$	9.35681e6	0.382923
$903$	55911.5	0.00228182
$904$	1.83614e6	0.0747282
$905$	1.58111e7	0.641713
$906$	247265.	0.0100079
$907$	−1.95045e7	−0.787259	−0.393629	−	0.919269i	$-0.628781\pi$
$907$	−1.95045e7	−0.787259	−0.393629	+	0.919269i	$0.628781\pi$
$908$	581540.	0.0234080
$909$	−1.65282e7	−0.663463
$910$	−3.60831e6	−0.144444
$911$	2.22572e6	0.0888535	0.0444268	−	0.999013i	$-0.485854\pi$
$911$	2.22572e6	0.0888535	0.0444268	+	0.999013i	$0.485854\pi$
$912$	−48850.2	−0.00194482
$913$	−1.08063e7	−0.429041
$914$	−2.85365e7	−1.12989
$915$	−595122.	−0.0234992
$916$	−1.38987e7	−0.547314
$917$	−1.76929e7	−0.694827
$918$	1.50943e6	0.0591161
$919$	2.52463e7	0.986071	0.493036	−	0.870009i	$-0.335887\pi$
$919$	2.52463e7	0.986071	0.493036	+	0.870009i	$0.335887\pi$
$920$	1.11672e6	0.0434986
$921$	−129075.	−0.00501409
$922$	1.27900e7	0.495498
$923$	−1.28537e7	−0.496621
$924$	−62982.0	−0.00242681
$925$	−4.05495e6	−0.155823
$926$	1.85751e7	0.711874
$927$	−4.04901e7	−1.54757
$928$	7.54107e6	0.287450
$929$	−3.89545e7	−1.48088	−0.740438	−	0.672125i	$-0.765382\pi$
$929$	−3.89545e7	−1.48088	−0.740438	+	0.672125i	$0.765382\pi$
$930$	637201.	0.0241584
$931$	4.91002e6	0.185656
$932$	5.24376e6	0.197744
$933$	−159451.	−0.00599685
$934$	1.93849e7	0.727103
$935$	1.43037e7	0.535079
$936$	2.83150e6	0.105640
$937$	2.91474e7	1.08455	0.542276	−	0.840200i	$-0.317563\pi$
$937$	2.91474e7	1.08455	0.542276	+	0.840200i	$0.317563\pi$
$938$	−1.64644e7	−0.610998
$939$	70514.0	0.00260983
$940$	1.53004e7	0.564784
$941$	−1.10718e7	−0.407611	−0.203806	−	0.979011i	$-0.565331\pi$
$941$	−1.10718e7	−0.407611	−0.203806	+	0.979011i	$0.565331\pi$
$942$	−509764.	−0.0187173
$943$	−5.27888e6	−0.193314
$944$	1.28420e7	0.469033
$945$	−1.00994e6	−0.0367888
$946$	−831831.	−0.0302209
$947$	4.27501e7	1.54904	0.774520	−	0.632550i	$-0.217992\pi$
$947$	4.27501e7	1.54904	0.774520	+	0.632550i	$0.217992\pi$
$948$	−492830.	−0.0178105
$949$	−3.94815e6	−0.142307
$950$	−1.74208e6	−0.0626265
$951$	−280825.	−0.0100689
$952$	−9.17340e6	−0.328049
$953$	6.60347e6	0.235526	0.117763	−	0.993042i	$-0.462428\pi$
$953$	6.60347e6	0.235526	0.117763	+	0.993042i	$0.462428\pi$
$954$	−1.39176e7	−0.495100
$955$	−4.59819e7	−1.63147
$956$	1.12801e7	0.399178
$957$	−374141.	−0.0132055
$958$	1.52268e7	0.536038
$959$	1.94987e7	0.684636
$960$	109896.	0.00384861
$961$	6.62320e6	0.231344
$962$	3.08385e6	0.107437
$963$	3.39668e7	1.18029
$964$	−1.10999e7	−0.384704
$965$	−5.32735e6	−0.184159
$966$	35532.9	0.00122515
$967$	−7.21337e6	−0.248069	−0.124034	−	0.992278i	$-0.539583\pi$
$967$	−7.21337e6	−0.248069	−0.124034	+	0.992278i	$0.539583\pi$
$968$	937024.	0.0321412
$969$	353007.	0.0120774
$970$	2.56844e7	0.876475
$971$	−1.30299e7	−0.443500	−0.221750	−	0.975104i	$-0.571177\pi$
$971$	−1.30299e7	−0.443500	−0.221750	+	0.975104i	$0.571177\pi$
$972$	1.18891e6	0.0403631
$973$	−1.92727e7	−0.652620
$974$	3.68926e7	1.24607
$975$	−73309.5	−0.00246972
$976$	−5.67837e6	−0.190809
$977$	3.24964e7	1.08918	0.544589	−	0.838703i	$-0.316686\pi$
$977$	3.24964e7	1.08918	0.544589	+	0.838703i	$0.316686\pi$
$978$	363771.	0.0121613
$979$	2.79724e6	0.0932768
$980$	−1.10458e7	−0.367395
$981$	−131576.	−0.00436519
$982$	2.46679e6	0.0816306
$983$	−3.69322e6	−0.121905	−0.0609525	−	0.998141i	$-0.519414\pi$
$983$	−3.69322e6	−0.121905	−0.0609525	+	0.998141i	$0.519414\pi$
$984$	−519493.	−0.0171038
$985$	1.57765e6	0.0518106
$986$	−5.44941e7	−1.78508
$987$	486842.	0.0159072
$988$	1.32487e6	0.0431800
$989$	469299.	0.0152566
$990$	7.51003e6	0.243531
$991$	−2.32791e7	−0.752977	−0.376488	−	0.926421i	$-0.622869\pi$
$991$	−2.32791e7	−0.752977	−0.376488	+	0.926421i	$0.622869\pi$
$992$	6.07987e6	0.196162
$993$	−1.46676e6	−0.0472048
$994$	2.18644e7	0.701895
$995$	−8.69296e6	−0.278362
$996$	599967.	0.0191637
$997$	2.84648e7	0.906923	0.453461	−	0.891276i	$-0.350189\pi$
$997$	2.84648e7	0.906923	0.453461	+	0.891276i	$0.350189\pi$
$998$	1.28264e7	0.407640
$999$	863145.	0.0273634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.6.a.d.1.1	✓	2
3.2	odd	2		198.6.a.k.1.1		2
4.3	odd	2		176.6.a.f.1.2		2
5.2	odd	4		550.6.b.j.199.4		4
5.3	odd	4		550.6.b.j.199.1		4
5.4	even	2		550.6.a.h.1.2		2
7.6	odd	2		1078.6.a.h.1.2		2
8.3	odd	2		704.6.a.p.1.1		2
8.5	even	2		704.6.a.k.1.2		2
11.10	odd	2		242.6.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.6.a.d.1.1	✓	2	1.1	even	1	trivial
176.6.a.f.1.2		2	4.3	odd	2
198.6.a.k.1.1		2	3.2	odd	2
242.6.a.g.1.1		2	11.10	odd	2
550.6.a.h.1.2		2	5.4	even	2
550.6.b.j.199.1		4	5.3	odd	4
550.6.b.j.199.4		4	5.2	odd	4
704.6.a.k.1.2		2	8.5	even	2
704.6.a.p.1.1		2	8.3	odd	2
1078.6.a.h.1.2		2	7.6	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +0.419872 q^{3} +16.0000 q^{4} +63.9006 q^{5} +1.67949 q^{6} +77.4808 q^{7} +64.0000 q^{8} -242.824 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +0.419872 q^{3} +16.0000 q^{4} +63.9006 q^{5} +1.67949 q^{6} +77.4808 q^{7} +64.0000 q^{8} -242.824 q^{9} +255.603 q^{10} -121.000 q^{11} +6.71795 q^{12} -182.199 q^{13} +309.923 q^{14} +26.8301 q^{15} +256.000 q^{16} -1849.94 q^{17} -971.295 q^{18} -454.474 q^{19} +1022.41 q^{20} +32.5320 q^{21} -484.000 q^{22} +273.061 q^{23} +26.8718 q^{24} +958.292 q^{25} -728.795 q^{26} -203.984 q^{27} +1239.69 q^{28} +7364.33 q^{29} +107.320 q^{30} +5937.37 q^{31} +1024.00 q^{32} -50.8045 q^{33} -7399.74 q^{34} +4951.07 q^{35} -3885.18 q^{36} -4231.44 q^{37} -1817.90 q^{38} -76.5002 q^{39} +4089.64 q^{40} -19332.2 q^{41} +130.128 q^{42} +1718.66 q^{43} -1936.00 q^{44} -15516.6 q^{45} +1092.24 q^{46} +14965.0 q^{47} +107.487 q^{48} -10803.7 q^{49} +3833.17 q^{50} -776.737 q^{51} -2915.18 q^{52} +14328.9 q^{53} -815.935 q^{54} -7731.98 q^{55} +4958.77 q^{56} -190.821 q^{57} +29457.3 q^{58} +50164.2 q^{59} +429.282 q^{60} -22181.1 q^{61} +23749.5 q^{62} -18814.2 q^{63} +4096.00 q^{64} -11642.6 q^{65} -203.218 q^{66} -53124.3 q^{67} -29599.0 q^{68} +114.651 q^{69} +19804.3 q^{70} +70547.9 q^{71} -15540.7 q^{72} +21669.5 q^{73} -16925.8 q^{74} +402.360 q^{75} -7271.59 q^{76} -9375.17 q^{77} -306.001 q^{78} -73360.1 q^{79} +16358.6 q^{80} +58920.5 q^{81} -77329.0 q^{82} +89307.9 q^{83} +520.512 q^{84} -118212. q^{85} +6874.64 q^{86} +3092.08 q^{87} -7744.00 q^{88} -23117.7 q^{89} -62066.4 q^{90} -14116.9 q^{91} +4368.97 q^{92} +2492.94 q^{93} +59860.0 q^{94} -29041.2 q^{95} +429.949 q^{96} +100486. q^{97} -43214.9 q^{98} +29381.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 29 q^{3} + 32 q^{4} - 13 q^{5} + 116 q^{6} - 14 q^{7} + 128 q^{8} + 331 q^{9}+O(q^{10}) \) 2 * q + 8 * q^2 + 29 * q^3 + 32 * q^4 - 13 * q^5 + 116 * q^6 - 14 * q^7 + 128 * q^8 + 331 * q^9	\( 2 q + 8 q^{2} + 29 q^{3} + 32 q^{4} - 13 q^{5} + 116 q^{6} - 14 q^{7} + 128 q^{8} + 331 q^{9} - 52 q^{10} - 242 q^{11} + 464 q^{12} - 646 q^{13} - 56 q^{14} - 2171 q^{15} + 512 q^{16} - 208 q^{17} + 1324 q^{18} - 2148 q^{19} - 208 q^{20} - 2582 q^{21} - 968 q^{22} + 349 q^{23} + 1856 q^{24} + 3747 q^{25} - 2584 q^{26} + 9251 q^{27} - 224 q^{28} + 4422 q^{29} - 8684 q^{30} + 14381 q^{31} + 2048 q^{32} - 3509 q^{33} - 832 q^{34} + 11986 q^{35} + 5296 q^{36} - 4267 q^{37} - 8592 q^{38} - 13332 q^{39} - 832 q^{40} - 10110 q^{41} - 10328 q^{42} - 9798 q^{43} - 3872 q^{44} - 59644 q^{45} + 1396 q^{46} + 21144 q^{47} + 7424 q^{48} - 19242 q^{49} + 14988 q^{50} + 46150 q^{51} - 10336 q^{52} + 39584 q^{53} + 37004 q^{54} + 1573 q^{55} - 896 q^{56} - 48592 q^{57} + 17688 q^{58} + 90951 q^{59} - 34736 q^{60} - 29550 q^{61} + 57524 q^{62} - 71308 q^{63} + 8192 q^{64} + 24024 q^{65} - 14036 q^{66} - 64149 q^{67} - 3328 q^{68} + 2285 q^{69} + 47944 q^{70} + 23583 q^{71} + 21184 q^{72} - 39058 q^{73} - 17068 q^{74} + 80104 q^{75} - 34368 q^{76} + 1694 q^{77} - 53328 q^{78} - 54974 q^{79} - 3328 q^{80} + 189706 q^{81} - 40440 q^{82} + 29986 q^{83} - 41312 q^{84} - 244478 q^{85} - 39192 q^{86} - 81000 q^{87} - 15488 q^{88} - 18047 q^{89} - 238576 q^{90} + 28312 q^{91} + 5584 q^{92} + 243813 q^{93} + 84576 q^{94} + 101192 q^{95} + 29696 q^{96} - 30309 q^{97} - 76968 q^{98} - 40051 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 29 * q^3 + 32 * q^4 - 13 * q^5 + 116 * q^6 - 14 * q^7 + 128 * q^8 + 331 * q^9 - 52 * q^10 - 242 * q^11 + 464 * q^12 - 646 * q^13 - 56 * q^14 - 2171 * q^15 + 512 * q^16 - 208 * q^17 + 1324 * q^18 - 2148 * q^19 - 208 * q^20 - 2582 * q^21 - 968 * q^22 + 349 * q^23 + 1856 * q^24 + 3747 * q^25 - 2584 * q^26 + 9251 * q^27 - 224 * q^28 + 4422 * q^29 - 8684 * q^30 + 14381 * q^31 + 2048 * q^32 - 3509 * q^33 - 832 * q^34 + 11986 * q^35 + 5296 * q^36 - 4267 * q^37 - 8592 * q^38 - 13332 * q^39 - 832 * q^40 - 10110 * q^41 - 10328 * q^42 - 9798 * q^43 - 3872 * q^44 - 59644 * q^45 + 1396 * q^46 + 21144 * q^47 + 7424 * q^48 - 19242 * q^49 + 14988 * q^50 + 46150 * q^51 - 10336 * q^52 + 39584 * q^53 + 37004 * q^54 + 1573 * q^55 - 896 * q^56 - 48592 * q^57 + 17688 * q^58 + 90951 * q^59 - 34736 * q^60 - 29550 * q^61 + 57524 * q^62 - 71308 * q^63 + 8192 * q^64 + 24024 * q^65 - 14036 * q^66 - 64149 * q^67 - 3328 * q^68 + 2285 * q^69 + 47944 * q^70 + 23583 * q^71 + 21184 * q^72 - 39058 * q^73 - 17068 * q^74 + 80104 * q^75 - 34368 * q^76 + 1694 * q^77 - 53328 * q^78 - 54974 * q^79 - 3328 * q^80 + 189706 * q^81 - 40440 * q^82 + 29986 * q^83 - 41312 * q^84 - 244478 * q^85 - 39192 * q^86 - 81000 * q^87 - 15488 * q^88 - 18047 * q^89 - 238576 * q^90 + 28312 * q^91 + 5584 * q^92 + 243813 * q^93 + 84576 * q^94 + 101192 * q^95 + 29696 * q^96 - 30309 * q^97 - 76968 * q^98 - 40051 * q^99

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