LMFDB - Embedded newform 11.6.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,6,Mod(1,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, 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("11.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	11.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:	$1.76422201794$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.54492.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 52x - 38 $ x^3 - x^2 - 52*x - 38
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			1.2
Root			$8.04796$ of defining polynomial
Character	$\chi$	$=$	11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.20859 q^{2} +16.8394 q^{3} -27.1221 q^{4} +75.2230 q^{5} +37.1913 q^{6} -225.525 q^{7} -130.577 q^{8} +40.5643 q^{9} +O(q^{10})$	\(q+2.20859 q^{2} +16.8394 q^{3} -27.1221 q^{4} +75.2230 q^{5} +37.1913 q^{6} -225.525 q^{7} -130.577 q^{8} +40.5643 q^{9} +166.137 q^{10} +121.000 q^{11} -456.719 q^{12} +455.465 q^{13} -498.092 q^{14} +1266.71 q^{15} +579.518 q^{16} +190.657 q^{17} +89.5900 q^{18} -135.393 q^{19} -2040.21 q^{20} -3797.69 q^{21} +267.240 q^{22} +2796.65 q^{23} -2198.83 q^{24} +2533.51 q^{25} +1005.94 q^{26} -3408.89 q^{27} +6116.71 q^{28} -2608.58 q^{29} +2797.64 q^{30} -1056.76 q^{31} +5458.37 q^{32} +2037.56 q^{33} +421.082 q^{34} -16964.7 q^{35} -1100.19 q^{36} +12536.8 q^{37} -299.028 q^{38} +7669.74 q^{39} -9822.37 q^{40} +1130.09 q^{41} -8387.55 q^{42} -14671.0 q^{43} -3281.78 q^{44} +3051.37 q^{45} +6176.65 q^{46} -16882.2 q^{47} +9758.71 q^{48} +34054.4 q^{49} +5595.48 q^{50} +3210.54 q^{51} -12353.2 q^{52} +3313.02 q^{53} -7528.84 q^{54} +9101.99 q^{55} +29448.3 q^{56} -2279.93 q^{57} -5761.29 q^{58} +11454.0 q^{59} -34355.8 q^{60} -28227.5 q^{61} -2333.95 q^{62} -9148.26 q^{63} -6489.25 q^{64} +34261.4 q^{65} +4500.15 q^{66} -51431.0 q^{67} -5171.01 q^{68} +47093.8 q^{69} -37468.0 q^{70} -16218.0 q^{71} -5296.75 q^{72} -10168.8 q^{73} +27688.7 q^{74} +42662.6 q^{75} +3672.15 q^{76} -27288.5 q^{77} +16939.3 q^{78} +60841.2 q^{79} +43593.1 q^{80} -67260.7 q^{81} +2495.90 q^{82} +45770.6 q^{83} +103002. q^{84} +14341.8 q^{85} -32402.3 q^{86} -43926.9 q^{87} -15799.8 q^{88} -82267.9 q^{89} +6739.23 q^{90} -102719. q^{91} -75851.0 q^{92} -17795.1 q^{93} -37285.8 q^{94} -10184.7 q^{95} +91915.5 q^{96} +53097.0 q^{97} +75212.2 q^{98} +4908.28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9}+O(q^{10}) $ 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9	\( 3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9} - 414 q^{10} + 363 q^{11} + 992 q^{12} + 486 q^{13} - 1020 q^{14} + 1654 q^{15} + 1992 q^{16} + 1086 q^{17} - 3706 q^{18} + 1380 q^{19} - 3480 q^{20} - 908 q^{21} - 3066 q^{23} - 11748 q^{24} - 57 q^{25} + 12132 q^{26} - 2990 q^{27} + 23712 q^{28} - 3426 q^{29} + 2650 q^{30} - 4098 q^{31} - 12408 q^{32} + 4114 q^{33} + 25320 q^{34} - 24228 q^{35} + 4756 q^{36} + 17724 q^{37} - 9240 q^{38} - 6560 q^{39} - 15276 q^{40} + 5994 q^{41} - 47828 q^{42} - 26208 q^{43} + 10164 q^{44} + 18458 q^{45} - 16806 q^{46} - 17232 q^{47} + 61064 q^{48} + 48531 q^{49} + 41070 q^{50} - 22724 q^{51} - 35304 q^{52} + 50586 q^{53} + 18814 q^{54} + 2904 q^{55} - 42312 q^{56} + 20160 q^{57} - 29172 q^{58} - 3738 q^{59} - 13456 q^{60} + 18486 q^{61} - 19974 q^{62} - 12496 q^{63} - 20352 q^{64} - 7668 q^{65} - 24926 q^{66} - 47754 q^{67} - 12600 q^{68} + 35042 q^{69} - 123372 q^{70} + 39282 q^{71} - 95040 q^{72} + 15426 q^{73} + 153294 q^{74} - 21916 q^{75} + 103920 q^{76} + 10164 q^{77} + 124984 q^{78} + 125148 q^{79} + 118680 q^{80} - 86917 q^{81} - 255372 q^{82} - 143928 q^{83} + 343616 q^{84} - 104040 q^{85} + 243060 q^{86} - 19368 q^{87} - 68244 q^{88} - 106824 q^{89} + 103424 q^{90} - 109632 q^{91} - 336528 q^{92} - 16622 q^{93} - 74928 q^{94} - 22200 q^{95} - 76456 q^{96} + 9684 q^{97} + 3480 q^{98} - 847 q^{99}+O(q^{100}) \) 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9 - 414 * q^10 + 363 * q^11 + 992 * q^12 + 486 * q^13 - 1020 * q^14 + 1654 * q^15 + 1992 * q^16 + 1086 * q^17 - 3706 * q^18 + 1380 * q^19 - 3480 * q^20 - 908 * q^21 - 3066 * q^23 - 11748 * q^24 - 57 * q^25 + 12132 * q^26 - 2990 * q^27 + 23712 * q^28 - 3426 * q^29 + 2650 * q^30 - 4098 * q^31 - 12408 * q^32 + 4114 * q^33 + 25320 * q^34 - 24228 * q^35 + 4756 * q^36 + 17724 * q^37 - 9240 * q^38 - 6560 * q^39 - 15276 * q^40 + 5994 * q^41 - 47828 * q^42 - 26208 * q^43 + 10164 * q^44 + 18458 * q^45 - 16806 * q^46 - 17232 * q^47 + 61064 * q^48 + 48531 * q^49 + 41070 * q^50 - 22724 * q^51 - 35304 * q^52 + 50586 * q^53 + 18814 * q^54 + 2904 * q^55 - 42312 * q^56 + 20160 * q^57 - 29172 * q^58 - 3738 * q^59 - 13456 * q^60 + 18486 * q^61 - 19974 * q^62 - 12496 * q^63 - 20352 * q^64 - 7668 * q^65 - 24926 * q^66 - 47754 * q^67 - 12600 * q^68 + 35042 * q^69 - 123372 * q^70 + 39282 * q^71 - 95040 * q^72 + 15426 * q^73 + 153294 * q^74 - 21916 * q^75 + 103920 * q^76 + 10164 * q^77 + 124984 * q^78 + 125148 * q^79 + 118680 * q^80 - 86917 * q^81 - 255372 * q^82 - 143928 * q^83 + 343616 * q^84 - 104040 * q^85 + 243060 * q^86 - 19368 * q^87 - 68244 * q^88 - 106824 * q^89 + 103424 * q^90 - 109632 * q^91 - 336528 * q^92 - 16622 * q^93 - 74928 * q^94 - 22200 * q^95 - 76456 * q^96 + 9684 * q^97 + 3480 * q^98 - 847 * 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 $

$2$	2.20859	0.390428	0.195214	−	0.980761i	$-0.437460\pi$
$2$	2.20859	0.390428	0.195214	+	0.980761i	$0.437460\pi$
$3$	16.8394	1.08025	0.540123	−	0.841586i	$-0.318378\pi$
$3$	16.8394	1.08025	0.540123	+	0.841586i	$0.318378\pi$
$4$	−27.1221	−0.847566
$5$	75.2230	1.34563	0.672815	−	0.739810i	$-0.265085\pi$
$5$	75.2230	1.34563	0.672815	+	0.739810i	$0.265085\pi$
$6$	37.1913	0.421758
$7$	−225.525	−1.73960	−0.869799	−	0.493406i	$-0.835752\pi$
$7$	−225.525	−1.73960	−0.869799	+	0.493406i	$0.835752\pi$
$8$	−130.577	−0.721341
$9$	40.5643	0.166931
$10$	166.137	0.525371
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−456.719	−0.915580
$13$	455.465	0.747474	0.373737	−	0.927535i	$-0.378076\pi$
$13$	455.465	0.747474	0.373737	+	0.927535i	$0.378076\pi$
$14$	−498.092	−0.679187
$15$	1266.71	1.45361
$16$	579.518	0.565935
$17$	190.657	0.160003	0.0800017	−	0.996795i	$-0.474507\pi$
$17$	190.657	0.160003	0.0800017	+	0.996795i	$0.474507\pi$
$18$	89.5900	0.0651746
$19$	−135.393	−0.0860424	−0.0430212	−	0.999074i	$-0.513698\pi$
$19$	−135.393	−0.0860424	−0.0430212	+	0.999074i	$0.513698\pi$
$20$	−2040.21	−1.14051
$21$	−3797.69	−1.87919
$22$	267.240	0.117718
$23$	2796.65	1.10235	0.551173	−	0.834391i	$-0.314180\pi$
$23$	2796.65	1.10235	0.551173	+	0.834391i	$0.314180\pi$
$24$	−2198.83	−0.779225
$25$	2533.51	0.810722
$26$	1005.94	0.291835
$27$	−3408.89	−0.899919
$28$	6116.71	1.47443
$29$	−2608.58	−0.575983	−0.287991	−	0.957633i	$-0.592987\pi$
$29$	−2608.58	−0.575983	−0.287991	+	0.957633i	$0.592987\pi$
$30$	2797.64	0.567530
$31$	−1056.76	−0.197502	−0.0987510	−	0.995112i	$-0.531485\pi$
$31$	−1056.76	−0.197502	−0.0987510	+	0.995112i	$0.531485\pi$
$32$	5458.37	0.942297
$33$	2037.56	0.325706
$34$	421.082	0.0624697
$35$	−16964.7	−2.34086
$36$	−1100.19	−0.141485
$37$	12536.8	1.50550	0.752752	−	0.658304i	$-0.228726\pi$
$37$	12536.8	1.50550	0.752752	+	0.658304i	$0.228726\pi$
$38$	−299.028	−0.0335933
$39$	7669.74	0.807456
$40$	−9822.37	−0.970658
$41$	1130.09	0.104991	0.0524954	−	0.998621i	$-0.483282\pi$
$41$	1130.09	0.104991	0.0524954	+	0.998621i	$0.483282\pi$
$42$	−8387.55	−0.733689
$43$	−14671.0	−1.21001	−0.605005	−	0.796222i	$-0.706829\pi$
$43$	−14671.0	−1.21001	−0.605005	+	0.796222i	$0.706829\pi$
$44$	−3281.78	−0.255551
$45$	3051.37	0.224628
$46$	6176.65	0.430386
$47$	−16882.2	−1.11477	−0.557383	−	0.830256i	$-0.688194\pi$
$47$	−16882.2	−1.11477	−0.557383	+	0.830256i	$0.688194\pi$
$48$	9758.71	0.611349
$49$	34054.4	2.02620
$50$	5595.48	0.316528
$51$	3210.54	0.172843
$52$	−12353.2	−0.633534
$53$	3313.02	0.162007	0.0810035	−	0.996714i	$-0.474187\pi$
$53$	3313.02	0.162007	0.0810035	+	0.996714i	$0.474187\pi$
$54$	−7528.84	−0.351353
$55$	9101.99	0.405723
$56$	29448.3	1.25484
$57$	−2279.93	−0.0929469
$58$	−5761.29	−0.224880
$59$	11454.0	0.428378	0.214189	−	0.976792i	$-0.431289\pi$
$59$	11454.0	0.428378	0.214189	+	0.976792i	$0.431289\pi$
$60$	−34355.8	−1.23203
$61$	−28227.5	−0.971286	−0.485643	−	0.874157i	$-0.661415\pi$
$61$	−28227.5	−0.971286	−0.485643	+	0.874157i	$0.661415\pi$
$62$	−2333.95	−0.0771102
$63$	−9148.26	−0.290394
$64$	−6489.25	−0.198036
$65$	34261.4	1.00582
$66$	4500.15	0.127165
$67$	−51431.0	−1.39971	−0.699855	−	0.714285i	$-0.746752\pi$
$67$	−51431.0	−1.39971	−0.699855	+	0.714285i	$0.746752\pi$
$68$	−5171.01	−0.135614
$69$	47093.8	1.19081
$70$	−37468.0	−0.913935
$71$	−16218.0	−0.381814	−0.190907	−	0.981608i	$-0.561143\pi$
$71$	−16218.0	−0.381814	−0.190907	+	0.981608i	$0.561143\pi$
$72$	−5296.75	−0.120414
$73$	−10168.8	−0.223337	−0.111669	−	0.993745i	$-0.535620\pi$
$73$	−10168.8	−0.223337	−0.111669	+	0.993745i	$0.535620\pi$
$74$	27688.7	0.587791
$75$	42662.6	0.875779
$76$	3672.15	0.0729266
$77$	−27288.5	−0.524509
$78$	16939.3	0.315253
$79$	60841.2	1.09681	0.548404	−	0.836214i	$-0.315236\pi$
$79$	60841.2	1.09681	0.548404	+	0.836214i	$0.315236\pi$
$80$	43593.1	0.761540
$81$	−67260.7	−1.13907
$82$	2495.90	0.0409913
$83$	45770.6	0.729275	0.364638	−	0.931150i	$-0.381193\pi$
$83$	45770.6	0.729275	0.364638	+	0.931150i	$0.381193\pi$
$84$	103002.	1.59274
$85$	14341.8	0.215306
$86$	−32402.3	−0.472421
$87$	−43926.9	−0.622203
$88$	−15799.8	−0.217492
$89$	−82267.9	−1.10092	−0.550460	−	0.834862i	$-0.685548\pi$
$89$	−82267.9	−1.10092	−0.550460	+	0.834862i	$0.685548\pi$
$90$	6739.23	0.0877009
$91$	−102719.	−1.30031
$92$	−75851.0	−0.934312
$93$	−17795.1	−0.213351
$94$	−37285.8	−0.435235
$95$	−10184.7	−0.115781
$96$	91915.5	1.01791
$97$	53097.0	0.572981	0.286491	−	0.958083i	$-0.407511\pi$
$97$	53097.0	0.572981	0.286491	+	0.958083i	$0.407511\pi$
$98$	75212.2	0.791085
$99$	4908.28	0.0503317
$100$	−68714.1	−0.687141
$101$	186821.	1.82231	0.911153	−	0.412069i	$-0.135194\pi$
$101$	186821.	1.82231	0.911153	+	0.412069i	$0.135194\pi$
$102$	7090.76	0.0674827
$103$	34290.5	0.318479	0.159240	−	0.987240i	$-0.449096\pi$
$103$	34290.5	0.318479	0.159240	+	0.987240i	$0.449096\pi$
$104$	−59473.0	−0.539184
$105$	−285674.	−2.52870
$106$	7317.10	0.0632520
$107$	−224117.	−1.89241	−0.946206	−	0.323565i	$-0.895119\pi$
$107$	−224117.	−1.89241	−0.946206	+	0.323565i	$0.895119\pi$
$108$	92456.3	0.762741
$109$	162229.	1.30786	0.653931	−	0.756554i	$-0.273118\pi$
$109$	162229.	1.30786	0.653931	+	0.756554i	$0.273118\pi$
$110$	20102.6	0.158405
$111$	211112.	1.62632
$112$	−130696.	−0.984500
$113$	92225.0	0.679442	0.339721	−	0.940526i	$-0.389667\pi$
$113$	92225.0	0.679442	0.339721	+	0.940526i	$0.389667\pi$
$114$	−5035.44	−0.0362890
$115$	210372.	1.48335
$116$	70750.3	0.488184
$117$	18475.6	0.124777
$118$	25297.2	0.167251
$119$	−42997.8	−0.278342
$120$	−165403.	−1.04855
$121$	14641.0	0.0909091
$122$	−62342.9	−0.379217
$123$	19029.9	0.113416
$124$	28661.5	0.167396
$125$	−44493.9	−0.254698
$126$	−20204.8	−0.113378
$127$	138299.	0.760868	0.380434	−	0.924808i	$-0.375775\pi$
$127$	138299.	0.760868	0.380434	+	0.924808i	$0.375775\pi$
$128$	−189000.	−1.01962
$129$	−247051.	−1.30711
$130$	75669.5	0.392702
$131$	−54420.4	−0.277066	−0.138533	−	0.990358i	$-0.544239\pi$
$131$	−54420.4	−0.277066	−0.138533	+	0.990358i	$0.544239\pi$
$132$	−55263.0	−0.276058
$133$	30534.5	0.149679
$134$	−113590.	−0.546485
$135$	−256427.	−1.21096
$136$	−24895.3	−0.115417
$137$	40555.1	0.184605	0.0923025	−	0.995731i	$-0.470577\pi$
$137$	40555.1	0.184605	0.0923025	+	0.995731i	$0.470577\pi$
$138$	104011.	0.464923
$139$	140537.	0.616955	0.308477	−	0.951232i	$-0.400181\pi$
$139$	140537.	0.616955	0.308477	+	0.951232i	$0.400181\pi$
$140$	460117.	1.98403
$141$	−284285.	−1.20422
$142$	−35818.9	−0.149071
$143$	55111.2	0.225372
$144$	23507.7	0.0944723
$145$	−196225.	−0.775060
$146$	−22458.7	−0.0871971
$147$	573454.	2.18880
$148$	−340024.	−1.27602
$149$	176073.	0.649722	0.324861	−	0.945762i	$-0.394683\pi$
$149$	176073.	0.649722	0.324861	+	0.945762i	$0.394683\pi$
$150$	94224.4	0.341928
$151$	409241.	1.46062	0.730309	−	0.683117i	$-0.239376\pi$
$151$	409241.	1.46062	0.730309	+	0.683117i	$0.239376\pi$
$152$	17679.2	0.0620659
$153$	7733.85	0.0267096
$154$	−60269.1	−0.204783
$155$	−79492.6	−0.265765
$156$	−208020.	−0.684373
$157$	14294.5	0.0462829	0.0231414	−	0.999732i	$-0.492633\pi$
$157$	14294.5	0.0462829	0.0231414	+	0.999732i	$0.492633\pi$
$158$	134373.	0.428224
$159$	55789.1	0.175007
$160$	410595.	1.26798
$161$	−630713.	−1.91764
$162$	−148551.	−0.444722
$163$	−418474.	−1.23367	−0.616836	−	0.787091i	$-0.711586\pi$
$163$	−418474.	−1.23367	−0.616836	+	0.787091i	$0.711586\pi$
$164$	−30650.3	−0.0889868
$165$	153272.	0.438281
$166$	101089.	0.284729
$167$	−139747.	−0.387749	−0.193875	−	0.981026i	$-0.562106\pi$
$167$	−139747.	−0.387749	−0.193875	+	0.981026i	$0.562106\pi$
$168$	495890.	1.35554
$169$	−163845.	−0.441282
$170$	31675.1	0.0840612
$171$	−5492.13	−0.0143632
$172$	397909.	1.02556
$173$	−687104.	−1.74545	−0.872725	−	0.488213i	$-0.837649\pi$
$173$	−687104.	−1.74545	−0.872725	+	0.488213i	$0.837649\pi$
$174$	−97016.5	−0.242925
$175$	−571368.	−1.41033
$176$	70121.6	0.170636
$177$	192878.	0.462754
$178$	−181696.	−0.429829
$179$	35496.4	0.0828042	0.0414021	−	0.999143i	$-0.486818\pi$
$179$	35496.4	0.0828042	0.0414021	+	0.999143i	$0.486818\pi$
$180$	−82759.7	−0.190387
$181$	260469.	0.590963	0.295481	−	0.955349i	$-0.404520\pi$
$181$	260469.	0.590963	0.295481	+	0.955349i	$0.404520\pi$
$182$	−226863.	−0.507675
$183$	−475333.	−1.04923
$184$	−365177.	−0.795167
$185$	943056.	2.02585
$186$	−39302.2	−0.0832980
$187$	23069.4	0.0482429
$188$	457880.	0.944837
$189$	768789.	1.56550
$190$	−22493.8	−0.0452042
$191$	392051.	0.777605	0.388803	−	0.921321i	$-0.372889\pi$
$191$	392051.	0.777605	0.388803	+	0.921321i	$0.372889\pi$
$192$	−109275.	−0.213928
$193$	15776.8	0.0304878	0.0152439	−	0.999884i	$-0.495148\pi$
$193$	15776.8	0.0304878	0.0152439	+	0.999884i	$0.495148\pi$
$194$	117270.	0.223708
$195$	576941.	1.08654
$196$	−923627.	−1.71734
$197$	545551.	1.00154	0.500771	−	0.865580i	$-0.333050\pi$
$197$	545551.	1.00154	0.500771	+	0.865580i	$0.333050\pi$
$198$	10840.4	0.0196509
$199$	−546514.	−0.978293	−0.489146	−	0.872202i	$-0.662692\pi$
$199$	−546514.	−0.978293	−0.489146	+	0.872202i	$0.662692\pi$
$200$	−330817.	−0.584807
$201$	−866065.	−1.51203
$202$	412610.	0.711478
$203$	588300.	1.00198
$204$	−87076.5	−0.146496
$205$	85008.5	0.141279
$206$	75733.7	0.124343
$207$	113444.	0.184016
$208$	263950.	0.423022
$209$	−16382.6	−0.0259428
$210$	−630937.	−0.987275
$211$	537150.	0.830596	0.415298	−	0.909686i	$-0.363677\pi$
$211$	537150.	0.830596	0.415298	+	0.909686i	$0.363677\pi$
$212$	−89856.0	−0.137312
$213$	−273101.	−0.412453
$214$	−494983.	−0.738850
$215$	−1.10360e6	−1.62823
$216$	445121.	0.649148
$217$	238325.	0.343574
$218$	358298.	0.510626
$219$	−171236.	−0.241259
$220$	−246865.	−0.343877
$221$	86837.3	0.119598
$222$	466259.	0.634958
$223$	−189640.	−0.255368	−0.127684	−	0.991815i	$-0.540754\pi$
$223$	−189640.	−0.255368	−0.127684	+	0.991815i	$0.540754\pi$
$224$	−1.23100e6	−1.63922
$225$	102770.	0.135335
$226$	203687.	0.265273
$227$	363428.	0.468116	0.234058	−	0.972223i	$-0.424799\pi$
$227$	363428.	0.468116	0.234058	+	0.972223i	$0.424799\pi$
$228$	61836.6	0.0787787
$229$	504331.	0.635516	0.317758	−	0.948172i	$-0.397070\pi$
$229$	504331.	0.635516	0.317758	+	0.948172i	$0.397070\pi$
$230$	464627.	0.579141
$231$	−459521.	−0.566598
$232$	340620.	0.415480
$233$	−1.20159e6	−1.45000	−0.724999	−	0.688750i	$-0.758160\pi$
$233$	−1.20159e6	−1.45000	−0.724999	+	0.688750i	$0.758160\pi$
$234$	40805.1	0.0487163
$235$	−1.26993e6	−1.50006
$236$	−310657.	−0.363079
$237$	1.02453e6	1.18482
$238$	−94964.5	−0.108672
$239$	−185929.	−0.210549	−0.105275	−	0.994443i	$-0.533572\pi$
$239$	−185929.	−0.210549	−0.105275	+	0.994443i	$0.533572\pi$
$240$	734080.	0.822650
$241$	174842.	0.193911	0.0969556	−	0.995289i	$-0.469090\pi$
$241$	174842.	0.193911	0.0969556	+	0.995289i	$0.469090\pi$
$242$	32336.0	0.0354934
$243$	−304267.	−0.330552
$244$	765589.	0.823229
$245$	2.56168e6	2.72652
$246$	42029.3	0.0442807
$247$	−61666.8	−0.0643145
$248$	137988.	0.142466
$249$	770748.	0.787797
$250$	−98269.0	−0.0994412
$251$	447906.	0.448748	0.224374	−	0.974503i	$-0.427966\pi$
$251$	447906.	0.448748	0.224374	+	0.974503i	$0.427966\pi$
$252$	248120.	0.246128
$253$	338394.	0.332370
$254$	305446.	0.297064
$255$	241506.	0.232583
$256$	−209768.	−0.200050
$257$	−1.14572e6	−1.08204	−0.541022	−	0.841009i	$-0.681962\pi$
$257$	−1.14572e6	−1.08204	−0.541022	+	0.841009i	$0.681962\pi$
$258$	−545634.	−0.510331
$259$	−2.82736e6	−2.61897
$260$	−929243.	−0.852503
$261$	−105815.	−0.0961496
$262$	−120192.	−0.108174
$263$	443228.	0.395128	0.197564	−	0.980290i	$-0.436697\pi$
$263$	443228.	0.395128	0.197564	+	0.980290i	$0.436697\pi$
$264$	−266058.	−0.234945
$265$	249215.	0.218002
$266$	67438.2	0.0584389
$267$	−1.38534e6	−1.18926
$268$	1.39492e6	1.18635
$269$	−1.88722e6	−1.59016	−0.795082	−	0.606502i	$-0.792572\pi$
$269$	−1.88722e6	−1.59016	−0.795082	+	0.606502i	$0.792572\pi$
$270$	−566343.	−0.472792
$271$	2.24203e6	1.85446	0.927230	−	0.374491i	$-0.122183\pi$
$271$	2.24203e6	1.85446	0.927230	+	0.374491i	$0.122183\pi$
$272$	110489.	0.0905516
$273$	−1.72972e6	−1.40465
$274$	89569.6	0.0720749
$275$	306554.	0.244442
$276$	−1.27728e6	−1.00929
$277$	1.27824e6	1.00095	0.500474	−	0.865751i	$-0.333159\pi$
$277$	1.27824e6	1.00095	0.500474	+	0.865751i	$0.333159\pi$
$278$	310389.	0.240876
$279$	−42866.7	−0.0329693
$280$	2.21519e6	1.68856
$281$	549325.	0.415015	0.207508	−	0.978233i	$-0.433465\pi$
$281$	549325.	0.415015	0.207508	+	0.978233i	$0.433465\pi$
$282$	−627869.	−0.470161
$283$	−135813.	−0.100803	−0.0504016	−	0.998729i	$-0.516050\pi$
$283$	−135813.	−0.100803	−0.0504016	+	0.998729i	$0.516050\pi$
$284$	439867.	0.323612
$285$	−171504.	−0.125072
$286$	121718.	0.0879914
$287$	−254862.	−0.182642
$288$	221415.	0.157299
$289$	−1.38351e6	−0.974399
$290$	−433382.	−0.302605
$291$	894120.	0.618961
$292$	275799.	0.189293
$293$	−1.76403e6	−1.20043	−0.600215	−	0.799839i	$-0.704918\pi$
$293$	−1.76403e6	−1.20043	−0.600215	+	0.799839i	$0.704918\pi$
$294$	1.26653e6	0.854567
$295$	861606.	0.576439
$296$	−1.63701e6	−1.08598
$297$	−412476.	−0.271336
$298$	388874.	0.253669
$299$	1.27377e6	0.823976
$300$	−1.15710e6	−0.742281
$301$	3.30868e6	2.10493
$302$	903846.	0.570266
$303$	3.14594e6	1.96854
$304$	−78462.7	−0.0486944
$305$	−2.12336e6	−1.30699
$306$	17080.9	0.0104282
$307$	−1.93533e6	−1.17195	−0.585975	−	0.810329i	$-0.699288\pi$
$307$	−1.93533e6	−1.17195	−0.585975	+	0.810329i	$0.699288\pi$
$308$	740122.	0.444556
$309$	577431.	0.344036
$310$	−175567.	−0.103762
$311$	2.98327e6	1.74901	0.874504	−	0.485019i	$-0.161187\pi$
$311$	2.98327e6	1.74901	0.874504	+	0.485019i	$0.161187\pi$
$312$	−1.00149e6	−0.582451
$313$	−10701.5	−0.00617426	−0.00308713	−	0.999995i	$-0.500983\pi$
$313$	−10701.5	−0.00617426	−0.00308713	+	0.999995i	$0.500983\pi$
$314$	31570.8	0.0180701
$315$	−688160.	−0.390762
$316$	−1.65014e6	−0.929617
$317$	−2.43658e6	−1.36186	−0.680929	−	0.732349i	$-0.738424\pi$
$317$	−2.43658e6	−1.36186	−0.680929	+	0.732349i	$0.738424\pi$
$318$	123215.	0.0683277
$319$	−315638.	−0.173665
$320$	−488141.	−0.266484
$321$	−3.77399e6	−2.04427
$322$	−1.39299e6	−0.748699
$323$	−25813.6	−0.0137671
$324$	1.82425e6	0.965433
$325$	1.15392e6	0.605994
$326$	−924239.	−0.481660
$327$	2.73183e6	1.41281
$328$	−147563.	−0.0757342
$329$	3.80734e6	1.93924
$330$	338515.	0.171117
$331$	119576.	0.0599894	0.0299947	−	0.999550i	$-0.490451\pi$
$331$	119576.	0.0599894	0.0299947	+	0.999550i	$0.490451\pi$
$332$	−1.24140e6	−0.618109
$333$	508546.	0.251316
$334$	−308644.	−0.151388
$335$	−3.86880e6	−1.88349
$336$	−2.20083e6	−1.06350
$337$	−2.02195e6	−0.969830	−0.484915	−	0.874561i	$-0.661149\pi$
$337$	−2.02195e6	−0.969830	−0.484915	+	0.874561i	$0.661149\pi$
$338$	−361867.	−0.172289
$339$	1.55301e6	0.733965
$340$	−388979.	−0.182486
$341$	−127868.	−0.0595491
$342$	−12129.9	−0.00560778
$343$	−3.88971e6	−1.78518
$344$	1.91569e6	0.872829
$345$	3.54254e6	1.60238
$346$	−1.51753e6	−0.681471
$347$	3.01864e6	1.34582	0.672912	−	0.739723i	$-0.265043\pi$
$347$	3.01864e6	1.34582	0.672912	+	0.739723i	$0.265043\pi$
$348$	1.19139e6	0.527358
$349$	2.40399e6	1.05650	0.528250	−	0.849089i	$-0.322848\pi$
$349$	2.40399e6	1.05650	0.528250	+	0.849089i	$0.322848\pi$
$350$	−1.26192e6	−0.550632
$351$	−1.55263e6	−0.672666
$352$	660463.	0.284113
$353$	3.62981e6	1.55041	0.775206	−	0.631709i	$-0.217646\pi$
$353$	3.62981e6	1.55041	0.775206	+	0.631709i	$0.217646\pi$
$354$	425989.	0.180672
$355$	−1.21997e6	−0.513780
$356$	2.23128e6	0.933102
$357$	−724055.	−0.300678
$358$	78397.1	0.0323290
$359$	939181.	0.384603	0.192302	−	0.981336i	$-0.438405\pi$
$359$	939181.	0.384603	0.192302	+	0.981336i	$0.438405\pi$
$360$	−398438.	−0.162033
$361$	−2.45777e6	−0.992597
$362$	575270.	0.230728
$363$	246545.	0.0982042
$364$	2.78594e6	1.10210
$365$	−764926.	−0.300530
$366$	−1.04982e6	−0.409647
$367$	−2.26697e6	−0.878577	−0.439288	−	0.898346i	$-0.644769\pi$
$367$	−2.26697e6	−0.878577	−0.439288	+	0.898346i	$0.644769\pi$
$368$	1.62071e6	0.623857
$369$	45841.1	0.0175263
$370$	2.08283e6	0.790949
$371$	−747167.	−0.281827
$372$	482642.	0.180829
$373$	−4.55029e6	−1.69343	−0.846714	−	0.532048i	$-0.821423\pi$
$373$	−4.55029e6	−1.69343	−0.846714	+	0.532048i	$0.821423\pi$
$374$	50951.0	0.0188353
$375$	−749250.	−0.275137
$376$	2.20442e6	0.804125
$377$	−1.18812e6	−0.430532
$378$	1.69794e6	0.611213
$379$	618788.	0.221281	0.110641	−	0.993860i	$-0.464710\pi$
$379$	618788.	0.221281	0.110641	+	0.993860i	$0.464710\pi$
$380$	276230.	0.0981323
$381$	2.32886e6	0.821924
$382$	865881.	0.303599
$383$	2.23829e6	0.779686	0.389843	−	0.920881i	$-0.372529\pi$
$383$	2.23829e6	0.779686	0.389843	+	0.920881i	$0.372529\pi$
$384$	−3.18264e6	−1.10144
$385$	−2.05272e6	−0.705795
$386$	34844.5	0.0119033
$387$	−595120.	−0.201989
$388$	−1.44010e6	−0.485640
$389$	−4.60206e6	−1.54198	−0.770989	−	0.636848i	$-0.780238\pi$
$389$	−4.60206e6	−1.54198	−0.770989	+	0.636848i	$0.780238\pi$
$390$	1.27423e6	0.424214
$391$	533199.	0.176379
$392$	−4.44671e6	−1.46158
$393$	−916405.	−0.299299
$394$	1.20490e6	0.391030
$395$	4.57666e6	1.47590
$396$	−133123.	−0.0426595
$397$	−4.35532e6	−1.38690	−0.693448	−	0.720506i	$-0.743909\pi$
$397$	−4.35532e6	−1.38690	−0.693448	+	0.720506i	$0.743909\pi$
$398$	−1.20703e6	−0.381952
$399$	514181.	0.161690
$400$	1.46821e6	0.458816
$401$	3.62515e6	1.12581	0.562905	−	0.826522i	$-0.309684\pi$
$401$	3.62515e6	1.12581	0.562905	+	0.826522i	$0.309684\pi$
$402$	−1.91278e6	−0.590338
$403$	−481316.	−0.147628
$404$	−5.06697e6	−1.54453
$405$	−5.05955e6	−1.53276
$406$	1.29931e6	0.391200
$407$	1.51695e6	0.453927
$408$	−419221.	−0.124679
$409$	4.13585e6	1.22252	0.611260	−	0.791430i	$-0.290663\pi$
$409$	4.13585e6	1.22252	0.611260	+	0.791430i	$0.290663\pi$
$410$	187749.	0.0551592
$411$	682922.	0.199419
$412$	−930032.	−0.269932
$413$	−2.58316e6	−0.745206
$414$	250552.	0.0718450
$415$	3.44300e6	0.981335
$416$	2.48609e6	0.704343
$417$	2.36655e6	0.666463
$418$	−36182.4	−0.0101288
$419$	−2.46691e6	−0.686464	−0.343232	−	0.939251i	$-0.611522\pi$
$419$	−2.46691e6	−0.686464	−0.343232	+	0.939251i	$0.611522\pi$
$420$	7.74809e6	2.14324
$421$	3.45258e6	0.949376	0.474688	−	0.880154i	$-0.342561\pi$
$421$	3.45258e6	0.949376	0.474688	+	0.880154i	$0.342561\pi$
$422$	1.18635e6	0.324287
$423$	−684813.	−0.186089
$424$	−432602.	−0.116862
$425$	483029.	0.129718
$426$	−603168.	−0.161033
$427$	6.36599e6	1.68965
$428$	6.07853e6	1.60394
$429$	928038.	0.243457
$430$	−2.43740e6	−0.635704
$431$	−3.65893e6	−0.948770	−0.474385	−	0.880318i	$-0.657329\pi$
$431$	−3.65893e6	−0.948770	−0.474385	+	0.880318i	$0.657329\pi$
$432$	−1.97551e6	−0.509296
$433$	−1.59716e6	−0.409381	−0.204690	−	0.978827i	$-0.565619\pi$
$433$	−1.59716e6	−0.409381	−0.204690	+	0.978827i	$0.565619\pi$
$434$	526363.	0.134141
$435$	−3.30431e6	−0.837256
$436$	−4.39999e6	−1.10850
$437$	−378647.	−0.0948485
$438$	−378190.	−0.0941943
$439$	−1.58464e6	−0.392437	−0.196219	−	0.980560i	$-0.562866\pi$
$439$	−1.58464e6	−0.392437	−0.196219	+	0.980560i	$0.562866\pi$
$440$	−1.18851e6	−0.292664
$441$	1.38139e6	0.338237
$442$	191788.	0.0466945
$443$	2.29633e6	0.555936	0.277968	−	0.960590i	$-0.410339\pi$
$443$	2.29633e6	0.555936	0.277968	+	0.960590i	$0.410339\pi$
$444$	−5.72580e6	−1.37841
$445$	−6.18844e6	−1.48143
$446$	−418837.	−0.0997029
$447$	2.96496e6	0.701859
$448$	1.46349e6	0.344504
$449$	3.31569e6	0.776171	0.388086	−	0.921623i	$-0.373136\pi$
$449$	3.31569e6	0.776171	0.388086	+	0.921623i	$0.373136\pi$
$450$	226977.	0.0528385
$451$	136740.	0.0316559
$452$	−2.50134e6	−0.575872
$453$	6.89136e6	1.57783
$454$	802664.	0.182765
$455$	−7.72680e6	−1.74973
$456$	297706.	0.0670464
$457$	2.20892e6	0.494754	0.247377	−	0.968919i	$-0.420431\pi$
$457$	2.20892e6	0.494754	0.247377	+	0.968919i	$0.420431\pi$
$458$	1.11386e6	0.248123
$459$	−649927.	−0.143990
$460$	−5.70574e6	−1.25724
$461$	−1.86064e6	−0.407764	−0.203882	−	0.978995i	$-0.565356\pi$
$461$	−1.86064e6	−0.407764	−0.203882	+	0.978995i	$0.565356\pi$
$462$	−1.01489e6	−0.221216
$463$	1.20592e6	0.261437	0.130718	−	0.991420i	$-0.458272\pi$
$463$	1.20592e6	0.261437	0.130718	+	0.991420i	$0.458272\pi$
$464$	−1.51172e6	−0.325969
$465$	−1.33861e6	−0.287091
$466$	−2.65383e6	−0.566119
$467$	2.29388e6	0.486719	0.243360	−	0.969936i	$-0.421750\pi$
$467$	2.29388e6	0.486719	0.243360	+	0.969936i	$0.421750\pi$
$468$	−501098.	−0.105757
$469$	1.15990e7	2.43493
$470$	−2.80475e6	−0.585666
$471$	240711.	0.0499969
$472$	−1.49563e6	−0.309007
$473$	−1.77519e6	−0.364832
$474$	2.26276e6	0.462587
$475$	−343019.	−0.0697565
$476$	1.16619e6	0.235913
$477$	134390.	0.0270441
$478$	−410642.	−0.0822041
$479$	−7.90892e6	−1.57499	−0.787496	−	0.616320i	$-0.788623\pi$
$479$	−7.90892e6	−1.57499	−0.787496	+	0.616320i	$0.788623\pi$
$480$	6.91416e6	1.36973
$481$	5.71007e6	1.12533
$482$	386154.	0.0757083
$483$	−1.06208e7	−2.07152
$484$	−397095.	−0.0770515
$485$	3.99412e6	0.771021
$486$	−672002.	−0.129056
$487$	3.48410e6	0.665684	0.332842	−	0.942983i	$-0.391992\pi$
$487$	3.48410e6	0.665684	0.332842	+	0.942983i	$0.391992\pi$
$488$	3.68585e6	0.700628
$489$	−7.04684e6	−1.33267
$490$	5.65769e6	1.06451
$491$	−8.98096e6	−1.68120	−0.840599	−	0.541658i	$-0.817797\pi$
$491$	−8.98096e6	−1.68120	−0.840599	+	0.541658i	$0.817797\pi$
$492$	−516132.	−0.0961276
$493$	−497343.	−0.0921592
$494$	−136197.	−0.0251101
$495$	369216.	0.0677279
$496$	−612410.	−0.111773
$497$	3.65756e6	0.664203
$498$	1.70227e6	0.307577
$499$	6.67736e6	1.20048	0.600238	−	0.799821i	$-0.295072\pi$
$499$	6.67736e6	1.20048	0.600238	+	0.799821i	$0.295072\pi$
$500$	1.20677e6	0.215874
$501$	−2.35325e6	−0.418865
$502$	989242.	0.175204
$503$	7.58428e6	1.33658	0.668289	−	0.743902i	$-0.267027\pi$
$503$	7.58428e6	1.33658	0.668289	+	0.743902i	$0.267027\pi$
$504$	1.19455e6	0.209473
$505$	1.40532e7	2.45215
$506$	747375.	0.129766
$507$	−2.75905e6	−0.476693
$508$	−3.75096e6	−0.644886
$509$	−6.02580e6	−1.03091	−0.515454	−	0.856917i	$-0.672377\pi$
$509$	−6.02580e6	−1.03091	−0.515454	+	0.856917i	$0.672377\pi$
$510$	533389.	0.0908068
$511$	2.29331e6	0.388518
$512$	5.58471e6	0.941511
$513$	461540.	0.0774312
$514$	−2.53042e6	−0.422460
$515$	2.57944e6	0.428555
$516$	6.70054e6	1.10786
$517$	−2.04274e6	−0.336114
$518$	−6.24448e6	−1.02252
$519$	−1.15704e7	−1.88551
$520$	−4.47374e6	−0.725542
$521$	−4.58541e6	−0.740088	−0.370044	−	0.929014i	$-0.620657\pi$
$521$	−4.58541e6	−0.740088	−0.370044	+	0.929014i	$0.620657\pi$
$522$	−233703.	−0.0375394
$523$	−4.88145e6	−0.780359	−0.390179	−	0.920739i	$-0.627587\pi$
$523$	−4.88145e6	−0.780359	−0.390179	+	0.920739i	$0.627587\pi$
$524$	1.47600e6	0.234832
$525$	−9.62148e6	−1.52350
$526$	978910.	0.154269
$527$	−201478.	−0.0316010
$528$	1.18080e6	0.184329
$529$	1.38489e6	0.215168
$530$	550414.	0.0851138
$531$	464624.	0.0715098
$532$	−828160.	−0.126863
$533$	514714.	0.0784780
$534$	−3.05965e6	−0.464321
$535$	−1.68588e7	−2.54649
$536$	6.71568e6	1.00967
$537$	597738.	0.0894489
$538$	−4.16810e6	−0.620844
$539$	4.12058e6	0.610923
$540$	6.95484e6	1.02637
$541$	6.21940e6	0.913598	0.456799	−	0.889570i	$-0.348996\pi$
$541$	6.21940e6	0.913598	0.456799	+	0.889570i	$0.348996\pi$
$542$	4.95172e6	0.724033
$543$	4.38614e6	0.638385
$544$	1.04067e6	0.150771
$545$	1.22034e7	1.75990
$546$	−3.82023e6	−0.548414
$547$	−9.49047e6	−1.35619	−0.678093	−	0.734976i	$-0.737193\pi$
$547$	−9.49047e6	−1.35619	−0.678093	+	0.734976i	$0.737193\pi$
$548$	−1.09994e6	−0.156465
$549$	−1.14503e6	−0.162138
$550$	677053.	0.0954368
$551$	353184.	0.0495589
$552$	−6.14935e6	−0.858976
$553$	−1.37212e7	−1.90800
$554$	2.82310e6	0.390798
$555$	1.58805e7	2.18842
$556$	−3.81166e6	−0.522910
$557$	−2.92907e6	−0.400029	−0.200014	−	0.979793i	$-0.564099\pi$
$557$	−2.92907e6	−0.400029	−0.200014	+	0.979793i	$0.564099\pi$
$558$	−94675.0	−0.0128721
$559$	−6.68213e6	−0.904451
$560$	−9.83131e6	−1.32477
$561$	388475.	0.0521141
$562$	1.21324e6	0.162033
$563$	−455079.	−0.0605084	−0.0302542	−	0.999542i	$-0.509632\pi$
$563$	−455079.	−0.0605084	−0.0302542	+	0.999542i	$0.509632\pi$
$564$	7.71041e6	1.02066
$565$	6.93744e6	0.914278
$566$	−299955.	−0.0393563
$567$	1.51689e7	1.98152
$568$	2.11769e6	0.275418
$569$	−6.27664e6	−0.812730	−0.406365	−	0.913711i	$-0.633204\pi$
$569$	−6.27664e6	−0.812730	−0.406365	+	0.913711i	$0.633204\pi$
$570$	−378781.	−0.0488316
$571$	−621794.	−0.0798098	−0.0399049	−	0.999203i	$-0.512706\pi$
$571$	−621794.	−0.0798098	−0.0399049	+	0.999203i	$0.512706\pi$
$572$	−1.49473e6	−0.191018
$573$	6.60189e6	0.840005
$574$	−562886.	−0.0713085
$575$	7.08532e6	0.893697
$576$	−263232.	−0.0330585
$577$	1.28776e7	1.61026	0.805130	−	0.593098i	$-0.202095\pi$
$577$	1.28776e7	1.61026	0.805130	+	0.593098i	$0.202095\pi$
$578$	−3.05560e6	−0.380432
$579$	265671.	0.0329343
$580$	5.32205e6	0.656915
$581$	−1.03224e7	−1.26865
$582$	1.97475e6	0.241659
$583$	400875.	0.0488470
$584$	1.32780e6	0.161102
$585$	1.38979e6	0.167904
$586$	−3.89602e6	−0.468681
$587$	1.08775e7	1.30296	0.651482	−	0.758664i	$-0.274148\pi$
$587$	1.08775e7	1.30296	0.651482	+	0.758664i	$0.274148\pi$
$588$	−1.55533e7	−1.85515
$589$	143078.	0.0169935
$590$	1.90293e6	0.225058
$591$	9.18673e6	1.08191
$592$	7.26529e6	0.852018
$593$	−7.50449e6	−0.876364	−0.438182	−	0.898886i	$-0.644378\pi$
$593$	−7.50449e6	−0.876364	−0.438182	+	0.898886i	$0.644378\pi$
$594$	−910990.	−0.105937
$595$	−3.23442e6	−0.374545
$596$	−4.77548e6	−0.550682
$597$	−9.20295e6	−1.05680
$598$	2.81325e6	0.321703
$599$	−7.69438e6	−0.876207	−0.438104	−	0.898925i	$-0.644350\pi$
$599$	−7.69438e6	−0.876207	−0.438104	+	0.898925i	$0.644350\pi$
$600$	−5.57074e6	−0.631735
$601$	3.14770e6	0.355473	0.177737	−	0.984078i	$-0.443123\pi$
$601$	3.14770e6	0.355473	0.177737	+	0.984078i	$0.443123\pi$
$602$	7.30751e6	0.821823
$603$	−2.08626e6	−0.233655
$604$	−1.10995e7	−1.23797
$605$	1.10134e6	0.122330
$606$	6.94810e6	0.768572
$607$	−4.57397e6	−0.503874	−0.251937	−	0.967744i	$-0.581068\pi$
$607$	−4.57397e6	−0.503874	−0.251937	+	0.967744i	$0.581068\pi$
$608$	−739025.	−0.0810775
$609$	9.90660e6	1.08238
$610$	−4.68962e6	−0.510286
$611$	−7.68923e6	−0.833258
$612$	−209758.	−0.0226381
$613$	−1.56075e7	−1.67758	−0.838790	−	0.544455i	$-0.816736\pi$
$613$	−1.56075e7	−1.67758	−0.838790	+	0.544455i	$0.816736\pi$
$614$	−4.27436e6	−0.457562
$615$	1.43149e6	0.152616
$616$	3.56324e6	0.378349
$617$	−1.18602e7	−1.25424	−0.627119	−	0.778924i	$-0.715766\pi$
$617$	−1.18602e7	−1.25424	−0.627119	+	0.778924i	$0.715766\pi$
$618$	1.27531e6	0.134321
$619$	7.91821e6	0.830616	0.415308	−	0.909681i	$-0.363674\pi$
$619$	7.91821e6	0.830616	0.415308	+	0.909681i	$0.363674\pi$
$620$	2.15601e6	0.225253
$621$	−9.53346e6	−0.992023
$622$	6.58883e6	0.682861
$623$	1.85534e7	1.91516
$624$	4.44475e6	0.456968
$625$	−1.12642e7	−1.15345
$626$	−23635.3	−0.00241060
$627$	−275872.	−0.0280246
$628$	−387698.	−0.0392278
$629$	2.39022e6	0.240886
$630$	−1.51986e6	−0.152564
$631$	−1.11561e7	−1.11542	−0.557709	−	0.830037i	$-0.688319\pi$
$631$	−1.11561e7	−1.11542	−0.557709	+	0.830037i	$0.688319\pi$
$632$	−7.94444e6	−0.791172
$633$	9.04527e6	0.897248
$634$	−5.38140e6	−0.531707
$635$	1.04033e7	1.02385
$636$	−1.51312e6	−0.148330
$637$	1.55106e7	1.51453
$638$	−697116.	−0.0678037
$639$	−657872.	−0.0637367
$640$	−1.42172e7	−1.37203
$641$	7.17389e6	0.689620	0.344810	−	0.938672i	$-0.387943\pi$
$641$	7.17389e6	0.689620	0.344810	+	0.938672i	$0.387943\pi$
$642$	−8.33521e6	−0.798139
$643$	7.14025e6	0.681061	0.340531	−	0.940233i	$-0.389393\pi$
$643$	7.14025e6	0.681061	0.340531	+	0.940233i	$0.389393\pi$
$644$	1.71063e7	1.62533
$645$	−1.85839e7	−1.75889
$646$	−57011.6	−0.00537505
$647$	1.56897e7	1.47351	0.736756	−	0.676159i	$-0.236357\pi$
$647$	1.56897e7	1.47351	0.736756	+	0.676159i	$0.236357\pi$
$648$	8.78267e6	0.821654
$649$	1.38594e6	0.129161
$650$	2.54854e6	0.236597
$651$	4.01324e6	0.371145
$652$	1.13499e7	1.04562
$653$	−5.04236e6	−0.462755	−0.231378	−	0.972864i	$-0.574323\pi$
$653$	−5.04236e6	−0.462755	−0.231378	+	0.972864i	$0.574323\pi$
$654$	6.03350e6	0.551601
$655$	−4.09367e6	−0.372829
$656$	654904.	0.0594180
$657$	−412489.	−0.0372820
$658$	8.40887e6	0.757134
$659$	−9.10902e6	−0.817068	−0.408534	−	0.912743i	$-0.633960\pi$
$659$	−9.10902e6	−0.817068	−0.408534	+	0.912743i	$0.633960\pi$
$660$	−4.15705e6	−0.371472
$661$	1.31308e7	1.16893	0.584464	−	0.811420i	$-0.301305\pi$
$661$	1.31308e7	1.16893	0.584464	+	0.811420i	$0.301305\pi$
$662$	264095.	0.0234215
$663$	1.46229e6	0.129196
$664$	−5.97657e6	−0.526056
$665$	2.29690e6	0.201413
$666$	1.12317e6	0.0981207
$667$	−7.29528e6	−0.634933
$668$	3.79023e6	0.328643
$669$	−3.19341e6	−0.275861
$670$	−8.54459e6	−0.735367
$671$	−3.41552e6	−0.292854
$672$	−2.07292e7	−1.77076
$673$	1.55171e7	1.32061	0.660303	−	0.750999i	$-0.270428\pi$
$673$	1.55171e7	1.32061	0.660303	+	0.750999i	$0.270428\pi$
$674$	−4.46566e6	−0.378648
$675$	−8.63644e6	−0.729584
$676$	4.44382e6	0.374016
$677$	−1.40356e7	−1.17695	−0.588476	−	0.808515i	$-0.700272\pi$
$677$	−1.40356e7	−1.17695	−0.588476	+	0.808515i	$0.700272\pi$
$678$	3.42997e6	0.286560
$679$	−1.19747e7	−0.996758
$680$	−1.87270e6	−0.155309
$681$	6.11990e6	0.505681
$682$	−282408.	−0.0232496
$683$	5.34969e6	0.438810	0.219405	−	0.975634i	$-0.429588\pi$
$683$	5.34969e6	0.438810	0.219405	+	0.975634i	$0.429588\pi$
$684$	148958.	0.0121737
$685$	3.05068e6	0.248410
$686$	−8.59079e6	−0.696984
$687$	8.49261e6	0.686514
$688$	−8.50211e6	−0.684787
$689$	1.50896e6	0.121096
$690$	7.82402e6	0.625615
$691$	1.31390e7	1.04681	0.523404	−	0.852084i	$-0.324662\pi$
$691$	1.31390e7	1.04681	0.523404	+	0.852084i	$0.324662\pi$
$692$	1.86357e7	1.47938
$693$	−1.10694e6	−0.0875569
$694$	6.66695e6	0.525447
$695$	1.05716e7	0.830194
$696$	5.73582e6	0.448820
$697$	215458.	0.0167989
$698$	5.30944e6	0.412487
$699$	−2.02341e7	−1.56636
$700$	1.54967e7	1.19535
$701$	−2.49888e7	−1.92066	−0.960330	−	0.278865i	$-0.910042\pi$
$701$	−2.49888e7	−1.92066	−0.960330	+	0.278865i	$0.910042\pi$
$702$	−3.42912e6	−0.262627
$703$	−1.69740e6	−0.129537
$704$	−785200.	−0.0597102
$705$	−2.13848e7	−1.62044
$706$	8.01676e6	0.605323
$707$	−4.21327e7	−3.17008
$708$	−5.23127e6	−0.392215
$709$	−8.86200e6	−0.662089	−0.331044	−	0.943615i	$-0.607401\pi$
$709$	−8.86200e6	−0.662089	−0.331044	+	0.943615i	$0.607401\pi$
$710$	−2.69441e6	−0.200594
$711$	2.46798e6	0.183092
$712$	1.07423e7	0.794138
$713$	−2.95538e6	−0.217716
$714$	−1.59914e6	−0.117393
$715$	4.14563e6	0.303268
$716$	−962739.	−0.0701820
$717$	−3.13093e6	−0.227445
$718$	2.07427e6	0.150160
$719$	2.58635e7	1.86580	0.932901	−	0.360132i	$-0.117268\pi$
$719$	2.58635e7	1.86580	0.932901	+	0.360132i	$0.117268\pi$
$720$	1.76832e6	0.127125
$721$	−7.73336e6	−0.554026
$722$	−5.42820e6	−0.387537
$723$	2.94423e6	0.209472
$724$	−7.06448e6	−0.500880
$725$	−6.60886e6	−0.466962
$726$	544518.	0.0383416
$727$	−1.71871e7	−1.20605	−0.603026	−	0.797721i	$-0.706039\pi$
$727$	−1.71871e7	−1.20605	−0.603026	+	0.797721i	$0.706039\pi$
$728$	1.34126e7	0.937963
$729$	1.12207e7	0.781988
$730$	−1.68941e6	−0.117335
$731$	−2.79712e6	−0.193606
$732$	1.28920e7	0.889290
$733$	1.85650e7	1.27625	0.638125	−	0.769932i	$-0.279710\pi$
$733$	1.85650e7	1.27625	0.638125	+	0.769932i	$0.279710\pi$
$734$	−5.00680e6	−0.343021
$735$	4.31370e7	2.94531
$736$	1.52651e7	1.03874
$737$	−6.22315e6	−0.422028
$738$	101244.	0.00684274
$739$	5.94724e6	0.400594	0.200297	−	0.979735i	$-0.435809\pi$
$739$	5.94724e6	0.400594	0.200297	+	0.979735i	$0.435809\pi$
$740$	−2.55777e7	−1.71705
$741$	−1.03843e6	−0.0694755
$742$	−1.65019e6	−0.110033
$743$	−2.72654e7	−1.81193	−0.905963	−	0.423357i	$-0.860852\pi$
$743$	−2.72654e7	−1.81193	−0.905963	+	0.423357i	$0.860852\pi$
$744$	2.32363e6	0.153899
$745$	1.32448e7	0.874285
$746$	−1.00497e7	−0.661161
$747$	1.85665e6	0.121739
$748$	−625692.	−0.0408890
$749$	5.05440e7	3.29204
$750$	−1.65479e6	−0.107421
$751$	1.30069e7	0.841541	0.420770	−	0.907167i	$-0.361760\pi$
$751$	1.30069e7	0.841541	0.420770	+	0.907167i	$0.361760\pi$
$752$	−9.78351e6	−0.630885
$753$	7.54245e6	0.484758
$754$	−2.62407e6	−0.168092
$755$	3.07844e7	1.96545
$756$	−2.08512e7	−1.32686
$757$	−9.22009e6	−0.584784	−0.292392	−	0.956299i	$-0.594451\pi$
$757$	−9.22009e6	−0.584784	−0.292392	+	0.956299i	$0.594451\pi$
$758$	1.36665e6	0.0863942
$759$	5.69835e6	0.359041
$760$	1.32988e6	0.0835177
$761$	328083.	0.0205363	0.0102682	−	0.999947i	$-0.496731\pi$
$761$	328083.	0.0205363	0.0102682	+	0.999947i	$0.496731\pi$
$762$	5.14351e6	0.320902
$763$	−3.65866e7	−2.27516
$764$	−1.06333e7	−0.659072
$765$	581764.	0.0359412
$766$	4.94347e6	0.304411
$767$	5.21690e6	0.320202
$768$	−3.53235e6	−0.216103
$769$	2.19214e6	0.133676	0.0668380	−	0.997764i	$-0.478709\pi$
$769$	2.19214e6	0.133676	0.0668380	+	0.997764i	$0.478709\pi$
$770$	−4.53363e6	−0.275562
$771$	−1.92932e7	−1.16887
$772$	−427900.	−0.0258404
$773$	2.18539e7	1.31547	0.657735	−	0.753249i	$-0.271515\pi$
$773$	2.18539e7	1.31547	0.657735	+	0.753249i	$0.271515\pi$
$774$	−1.31438e6	−0.0788619
$775$	−2.67730e6	−0.160119
$776$	−6.93323e6	−0.413315
$777$	−4.76109e7	−2.82914
$778$	−1.01641e7	−0.602031
$779$	−153006.	−0.00903367
$780$	−1.56479e7	−0.920913
$781$	−1.96238e6	−0.115121
$782$	1.17762e6	0.0688633
$783$	8.89237e6	0.518338
$784$	1.97351e7	1.14670
$785$	1.07528e6	0.0622797
$786$	−2.02396e6	−0.116855
$787$	2.61010e7	1.50217	0.751087	−	0.660203i	$-0.229530\pi$
$787$	2.61010e7	1.50217	0.751087	+	0.660203i	$0.229530\pi$
$788$	−1.47965e7	−0.848874
$789$	7.46368e6	0.426835
$790$	1.01080e7	0.576231
$791$	−2.07990e7	−1.18196
$792$	−640907.	−0.0363063
$793$	−1.28566e7	−0.726011
$794$	−9.61913e6	−0.541483
$795$	4.19663e6	0.235495
$796$	1.48226e7	0.829168
$797$	1.39846e7	0.779840	0.389920	−	0.920849i	$-0.372503\pi$
$797$	1.39846e7	0.779840	0.389920	+	0.920849i	$0.372503\pi$
$798$	1.13562e6	0.0631284
$799$	−3.21869e6	−0.178366
$800$	1.38288e7	0.763941
$801$	−3.33714e6	−0.183778
$802$	8.00647e6	0.439547
$803$	−1.23042e6	−0.0673388
$804$	2.34895e7	1.28155
$805$	−4.74442e7	−2.58044
$806$	−1.06303e6	−0.0576379
$807$	−3.17796e7	−1.71777
$808$	−2.43944e7	−1.31450
$809$	2.70989e7	1.45573	0.727865	−	0.685721i	$-0.240513\pi$
$809$	2.70989e7	1.45573	0.727865	+	0.685721i	$0.240513\pi$
$810$	−1.11745e7	−0.598432
$811$	1.99644e7	1.06587	0.532936	−	0.846156i	$-0.321089\pi$
$811$	1.99644e7	1.06587	0.532936	+	0.846156i	$0.321089\pi$
$812$	−1.59559e7	−0.849244
$813$	3.77543e7	2.00327
$814$	3.35033e6	0.177226
$815$	−3.14789e7	−1.66007
$816$	1.86056e6	0.0978180
$817$	1.98635e6	0.104112
$818$	9.13439e6	0.477306
$819$	−4.16671e6	−0.217062
$820$	−2.30561e6	−0.119743
$821$	3.18829e7	1.65082	0.825410	−	0.564533i	$-0.190944\pi$
$821$	3.18829e7	1.65082	0.825410	+	0.564533i	$0.190944\pi$
$822$	1.50829e6	0.0778586
$823$	−1.34203e7	−0.690655	−0.345328	−	0.938482i	$-0.612232\pi$
$823$	−1.34203e7	−0.690655	−0.345328	+	0.938482i	$0.612232\pi$
$824$	−4.47754e6	−0.229732
$825$	5.16218e6	0.264057
$826$	−5.70515e6	−0.290949
$827$	1.19386e7	0.607002	0.303501	−	0.952831i	$-0.401844\pi$
$827$	1.19386e7	0.607002	0.303501	+	0.952831i	$0.401844\pi$
$828$	−3.07684e6	−0.155966
$829$	2.59274e7	1.31031	0.655153	−	0.755497i	$-0.272604\pi$
$829$	2.59274e7	1.31031	0.655153	+	0.755497i	$0.272604\pi$
$830$	7.60419e6	0.383140
$831$	2.15247e7	1.08127
$832$	−2.95563e6	−0.148027
$833$	6.49269e6	0.324199
$834$	5.22675e6	0.260206
$835$	−1.05122e7	−0.521768
$836$	444330.	0.0219882
$837$	3.60237e6	0.177736
$838$	−5.44839e6	−0.268015
$839$	−3.21482e7	−1.57671	−0.788354	−	0.615222i	$-0.789067\pi$
$839$	−3.21482e7	−1.57671	−0.788354	+	0.615222i	$0.789067\pi$
$840$	3.73024e7	1.82406
$841$	−1.37064e7	−0.668244
$842$	7.62533e6	0.370662
$843$	9.25029e6	0.448318
$844$	−1.45687e7	−0.703985
$845$	−1.23249e7	−0.593803
$846$	−1.51247e6	−0.0726544
$847$	−3.30191e6	−0.158145
$848$	1.91995e6	0.0916855
$849$	−2.28700e6	−0.108892
$850$	1.06681e6	0.0506456
$851$	3.50610e7	1.65959
$852$	7.40708e6	0.349581
$853$	−5.64308e6	−0.265548	−0.132774	−	0.991146i	$-0.542388\pi$
$853$	−5.64308e6	−0.265548	−0.132774	+	0.991146i	$0.542388\pi$
$854$	1.40599e7	0.659685
$855$	−413135.	−0.0193275
$856$	2.92645e7	1.36507
$857$	−1.77067e7	−0.823543	−0.411772	−	0.911287i	$-0.635090\pi$
$857$	−1.77067e7	−0.823543	−0.411772	+	0.911287i	$0.635090\pi$
$858$	2.04966e6	0.0950524
$859$	1.57119e7	0.726515	0.363258	−	0.931689i	$-0.381664\pi$
$859$	1.57119e7	0.726515	0.363258	+	0.931689i	$0.381664\pi$
$860$	2.99319e7	1.38003
$861$	−4.29172e6	−0.197298
$862$	−8.08108e6	−0.370426
$863$	245263.	0.0112100	0.00560500	−	0.999984i	$-0.498216\pi$
$863$	245263.	0.0112100	0.00560500	+	0.999984i	$0.498216\pi$
$864$	−1.86070e7	−0.847991
$865$	−5.16861e7	−2.34873
$866$	−3.52747e6	−0.159834
$867$	−2.32974e7	−1.05259
$868$	−6.46388e6	−0.291202
$869$	7.36179e6	0.330700
$870$	−7.29788e6	−0.326888
$871$	−2.34250e7	−1.04625
$872$	−2.11833e7	−0.943415
$873$	2.15384e6	0.0956486
$874$	−836276.	−0.0370315
$875$	1.00345e7	0.443073
$876$	4.64428e6	0.204483
$877$	1.04352e7	0.458142	0.229071	−	0.973410i	$-0.426431\pi$
$877$	1.04352e7	0.458142	0.229071	+	0.973410i	$0.426431\pi$
$878$	−3.49983e6	−0.153218
$879$	−2.97051e7	−1.29676
$880$	5.27476e6	0.229613
$881$	−1.10430e7	−0.479344	−0.239672	−	0.970854i	$-0.577040\pi$
$881$	−1.10430e7	−0.479344	−0.239672	+	0.970854i	$0.577040\pi$
$882$	3.05093e6	0.132057
$883$	5.41498e6	0.233720	0.116860	−	0.993148i	$-0.462717\pi$
$883$	5.41498e6	0.233720	0.116860	+	0.993148i	$0.462717\pi$
$884$	−2.35521e6	−0.101368
$885$	1.45089e7	0.622696
$886$	5.07166e6	0.217053
$887$	−1.52663e7	−0.651515	−0.325757	−	0.945453i	$-0.605619\pi$
$887$	−1.52663e7	−0.651515	−0.325757	+	0.945453i	$0.605619\pi$
$888$	−2.75663e7	−1.17313
$889$	−3.11898e7	−1.32360
$890$	−1.36677e7	−0.578391
$891$	−8.13854e6	−0.343441
$892$	5.14343e6	0.216442
$893$	2.28573e6	0.0959170
$894$	6.54838e6	0.274025
$895$	2.67015e6	0.111424
$896$	4.26242e7	1.77372
$897$	2.14496e7	0.890096
$898$	7.32300e6	0.303039
$899$	2.75664e6	0.113758
$900$	−2.78734e6	−0.114705
$901$	631648.	0.0259217
$902$	302004.	0.0123594
$903$	5.57160e7	2.27384
$904$	−1.20424e7	−0.490109
$905$	1.95933e7	0.795218
$906$	1.52202e7	0.616027
$907$	2.02437e7	0.817094	0.408547	−	0.912737i	$-0.366036\pi$
$907$	2.02437e7	0.817094	0.408547	+	0.912737i	$0.366036\pi$
$908$	−9.85694e6	−0.396759
$909$	7.57825e6	0.304200
$910$	−1.70653e7	−0.683143
$911$	−1.17158e7	−0.467708	−0.233854	−	0.972272i	$-0.575134\pi$
$911$	−1.17158e7	−0.467708	−0.233854	+	0.972272i	$0.575134\pi$
$912$	−1.32126e6	−0.0526019
$913$	5.53824e6	0.219885
$914$	4.87860e6	0.193166
$915$	−3.57560e7	−1.41187
$916$	−1.36785e7	−0.538642
$917$	1.22731e7	0.481984
$918$	−1.43542e6	−0.0562177
$919$	−1.95296e7	−0.762788	−0.381394	−	0.924413i	$-0.624556\pi$
$919$	−1.95296e7	−0.762788	−0.381394	+	0.924413i	$0.624556\pi$
$920$	−2.74697e7	−1.07000
$921$	−3.25898e7	−1.26599
$922$	−4.10939e6	−0.159202
$923$	−7.38673e6	−0.285396
$924$	1.24632e7	0.480230
$925$	3.17620e7	1.22055
$926$	2.66339e6	0.102072
$927$	1.39097e6	0.0531641
$928$	−1.42386e7	−0.542747
$929$	−4.29425e7	−1.63248	−0.816240	−	0.577713i	$-0.803945\pi$
$929$	−4.29425e7	−1.63248	−0.816240	+	0.577713i	$0.803945\pi$
$930$	−2.95643e6	−0.112088
$931$	−4.61073e6	−0.174339
$932$	3.25898e7	1.22897
$933$	5.02364e7	1.88936
$934$	5.06625e6	0.190029
$935$	1.73535e6	0.0649171
$936$	−2.41248e6	−0.0900067
$937$	2.27191e7	0.845361	0.422681	−	0.906279i	$-0.361089\pi$
$937$	2.27191e7	0.845361	0.422681	+	0.906279i	$0.361089\pi$
$938$	2.56174e7	0.950665
$939$	−180207.	−0.00666972
$940$	3.44431e7	1.27140
$941$	3.98095e6	0.146559	0.0732795	−	0.997311i	$-0.476653\pi$
$941$	3.98095e6	0.146559	0.0732795	+	0.997311i	$0.476653\pi$
$942$	531632.	0.0195202
$943$	3.16045e6	0.115736
$944$	6.63780e6	0.242434
$945$	5.78306e7	2.10658
$946$	−3.92067e6	−0.142440
$947$	−2.43639e7	−0.882818	−0.441409	−	0.897306i	$-0.645521\pi$
$947$	−2.43639e7	−0.882818	−0.441409	+	0.897306i	$0.645521\pi$
$948$	−2.77874e7	−1.00422
$949$	−4.63152e6	−0.166939
$950$	−757589.	−0.0272348
$951$	−4.10304e7	−1.47114
$952$	5.61450e6	0.200779
$953$	1.39017e7	0.495833	0.247916	−	0.968781i	$-0.420254\pi$
$953$	1.39017e7	0.495833	0.247916	+	0.968781i	$0.420254\pi$
$954$	296813.	0.0105587
$955$	2.94913e7	1.04637
$956$	5.04280e6	0.178454
$957$	−5.31515e6	−0.187601
$958$	−1.74676e7	−0.614920
$959$	−9.14617e6	−0.321139
$960$	−8.21999e6	−0.287868
$961$	−2.75124e7	−0.960993
$962$	1.26112e7	0.439358
$963$	−9.09116e6	−0.315903
$964$	−4.74208e6	−0.164353
$965$	1.18678e6	0.0410253
$966$	−2.34570e7	−0.808780
$967$	5.16682e7	1.77688	0.888438	−	0.458998i	$-0.151791\pi$
$967$	5.16682e7	1.77688	0.888438	+	0.458998i	$0.151791\pi$
$968$	−1.91177e6	−0.0655764
$969$	−434684.	−0.0148718
$970$	8.82137e6	0.301028
$971$	−1.45794e7	−0.496240	−0.248120	−	0.968729i	$-0.579813\pi$
$971$	−1.45794e7	−0.496240	−0.248120	+	0.968729i	$0.579813\pi$
$972$	8.25237e6	0.280164
$973$	−3.16945e7	−1.07325
$974$	7.69495e6	0.259901
$975$	1.94313e7	0.654623
$976$	−1.63583e7	−0.549685
$977$	−3.09921e6	−0.103876	−0.0519379	−	0.998650i	$-0.516540\pi$
$977$	−3.09921e6	−0.103876	−0.0519379	+	0.998650i	$0.516540\pi$
$978$	−1.55636e7	−0.520311
$979$	−9.95442e6	−0.331940
$980$	−6.94781e7	−2.31091
$981$	6.58071e6	0.218323
$982$	−1.98353e7	−0.656386
$983$	1.53445e7	0.506489	0.253245	−	0.967402i	$-0.418502\pi$
$983$	1.53445e7	0.506489	0.253245	+	0.967402i	$0.418502\pi$
$984$	−2.48486e6	−0.0818116
$985$	4.10380e7	1.34771
$986$	−1.09843e6	−0.0359815
$987$	6.41133e7	2.09486
$988$	1.67253e6	0.0545108
$989$	−4.10296e7	−1.33385
$990$	815447.	0.0264428
$991$	1.57747e7	0.510244	0.255122	−	0.966909i	$-0.417884\pi$
$991$	1.57747e7	0.510244	0.255122	+	0.966909i	$0.417884\pi$
$992$	−5.76818e6	−0.186106
$993$	2.01359e6	0.0648033
$994$	8.07806e6	0.259323
$995$	−4.11105e7	−1.31642
$996$	−2.09043e7	−0.667710
$997$	1.85577e6	0.0591270	0.0295635	−	0.999563i	$-0.490588\pi$
$997$	1.85577e6	0.0591270	0.0295635	+	0.999563i	$0.490588\pi$
$998$	1.47476e7	0.468699
$999$	−4.27365e7	−1.35483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.6.a.b.1.2	✓	3
3.2	odd	2		99.6.a.g.1.2		3
4.3	odd	2		176.6.a.i.1.2		3
5.2	odd	4		275.6.b.b.199.4		6
5.3	odd	4		275.6.b.b.199.3		6
5.4	even	2		275.6.a.b.1.2		3
7.6	odd	2		539.6.a.e.1.2		3
8.3	odd	2		704.6.a.t.1.2		3
8.5	even	2		704.6.a.q.1.2		3
11.10	odd	2		121.6.a.d.1.2		3
33.32	even	2		1089.6.a.r.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.6.a.b.1.2	✓	3	1.1	even	1	trivial
99.6.a.g.1.2		3	3.2	odd	2
121.6.a.d.1.2		3	11.10	odd	2
176.6.a.i.1.2		3	4.3	odd	2
275.6.a.b.1.2		3	5.4	even	2
275.6.b.b.199.3		6	5.3	odd	4
275.6.b.b.199.4		6	5.2	odd	4
539.6.a.e.1.2		3	7.6	odd	2
704.6.a.q.1.2		3	8.5	even	2
704.6.a.t.1.2		3	8.3	odd	2
1089.6.a.r.1.2		3	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)

\(f(q)\)	\(=\)	\(q+2.20859 q^{2} +16.8394 q^{3} -27.1221 q^{4} +75.2230 q^{5} +37.1913 q^{6} -225.525 q^{7} -130.577 q^{8} +40.5643 q^{9} +O(q^{10})\)	\(q+2.20859 q^{2} +16.8394 q^{3} -27.1221 q^{4} +75.2230 q^{5} +37.1913 q^{6} -225.525 q^{7} -130.577 q^{8} +40.5643 q^{9} +166.137 q^{10} +121.000 q^{11} -456.719 q^{12} +455.465 q^{13} -498.092 q^{14} +1266.71 q^{15} +579.518 q^{16} +190.657 q^{17} +89.5900 q^{18} -135.393 q^{19} -2040.21 q^{20} -3797.69 q^{21} +267.240 q^{22} +2796.65 q^{23} -2198.83 q^{24} +2533.51 q^{25} +1005.94 q^{26} -3408.89 q^{27} +6116.71 q^{28} -2608.58 q^{29} +2797.64 q^{30} -1056.76 q^{31} +5458.37 q^{32} +2037.56 q^{33} +421.082 q^{34} -16964.7 q^{35} -1100.19 q^{36} +12536.8 q^{37} -299.028 q^{38} +7669.74 q^{39} -9822.37 q^{40} +1130.09 q^{41} -8387.55 q^{42} -14671.0 q^{43} -3281.78 q^{44} +3051.37 q^{45} +6176.65 q^{46} -16882.2 q^{47} +9758.71 q^{48} +34054.4 q^{49} +5595.48 q^{50} +3210.54 q^{51} -12353.2 q^{52} +3313.02 q^{53} -7528.84 q^{54} +9101.99 q^{55} +29448.3 q^{56} -2279.93 q^{57} -5761.29 q^{58} +11454.0 q^{59} -34355.8 q^{60} -28227.5 q^{61} -2333.95 q^{62} -9148.26 q^{63} -6489.25 q^{64} +34261.4 q^{65} +4500.15 q^{66} -51431.0 q^{67} -5171.01 q^{68} +47093.8 q^{69} -37468.0 q^{70} -16218.0 q^{71} -5296.75 q^{72} -10168.8 q^{73} +27688.7 q^{74} +42662.6 q^{75} +3672.15 q^{76} -27288.5 q^{77} +16939.3 q^{78} +60841.2 q^{79} +43593.1 q^{80} -67260.7 q^{81} +2495.90 q^{82} +45770.6 q^{83} +103002. q^{84} +14341.8 q^{85} -32402.3 q^{86} -43926.9 q^{87} -15799.8 q^{88} -82267.9 q^{89} +6739.23 q^{90} -102719. q^{91} -75851.0 q^{92} -17795.1 q^{93} -37285.8 q^{94} -10184.7 q^{95} +91915.5 q^{96} +53097.0 q^{97} +75212.2 q^{98} +4908.28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9}+O(q^{10}) \) 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9	\( 3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9} - 414 q^{10} + 363 q^{11} + 992 q^{12} + 486 q^{13} - 1020 q^{14} + 1654 q^{15} + 1992 q^{16} + 1086 q^{17} - 3706 q^{18} + 1380 q^{19} - 3480 q^{20} - 908 q^{21} - 3066 q^{23} - 11748 q^{24} - 57 q^{25} + 12132 q^{26} - 2990 q^{27} + 23712 q^{28} - 3426 q^{29} + 2650 q^{30} - 4098 q^{31} - 12408 q^{32} + 4114 q^{33} + 25320 q^{34} - 24228 q^{35} + 4756 q^{36} + 17724 q^{37} - 9240 q^{38} - 6560 q^{39} - 15276 q^{40} + 5994 q^{41} - 47828 q^{42} - 26208 q^{43} + 10164 q^{44} + 18458 q^{45} - 16806 q^{46} - 17232 q^{47} + 61064 q^{48} + 48531 q^{49} + 41070 q^{50} - 22724 q^{51} - 35304 q^{52} + 50586 q^{53} + 18814 q^{54} + 2904 q^{55} - 42312 q^{56} + 20160 q^{57} - 29172 q^{58} - 3738 q^{59} - 13456 q^{60} + 18486 q^{61} - 19974 q^{62} - 12496 q^{63} - 20352 q^{64} - 7668 q^{65} - 24926 q^{66} - 47754 q^{67} - 12600 q^{68} + 35042 q^{69} - 123372 q^{70} + 39282 q^{71} - 95040 q^{72} + 15426 q^{73} + 153294 q^{74} - 21916 q^{75} + 103920 q^{76} + 10164 q^{77} + 124984 q^{78} + 125148 q^{79} + 118680 q^{80} - 86917 q^{81} - 255372 q^{82} - 143928 q^{83} + 343616 q^{84} - 104040 q^{85} + 243060 q^{86} - 19368 q^{87} - 68244 q^{88} - 106824 q^{89} + 103424 q^{90} - 109632 q^{91} - 336528 q^{92} - 16622 q^{93} - 74928 q^{94} - 22200 q^{95} - 76456 q^{96} + 9684 q^{97} + 3480 q^{98} - 847 q^{99}+O(q^{100}) \) 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9 - 414 * q^10 + 363 * q^11 + 992 * q^12 + 486 * q^13 - 1020 * q^14 + 1654 * q^15 + 1992 * q^16 + 1086 * q^17 - 3706 * q^18 + 1380 * q^19 - 3480 * q^20 - 908 * q^21 - 3066 * q^23 - 11748 * q^24 - 57 * q^25 + 12132 * q^26 - 2990 * q^27 + 23712 * q^28 - 3426 * q^29 + 2650 * q^30 - 4098 * q^31 - 12408 * q^32 + 4114 * q^33 + 25320 * q^34 - 24228 * q^35 + 4756 * q^36 + 17724 * q^37 - 9240 * q^38 - 6560 * q^39 - 15276 * q^40 + 5994 * q^41 - 47828 * q^42 - 26208 * q^43 + 10164 * q^44 + 18458 * q^45 - 16806 * q^46 - 17232 * q^47 + 61064 * q^48 + 48531 * q^49 + 41070 * q^50 - 22724 * q^51 - 35304 * q^52 + 50586 * q^53 + 18814 * q^54 + 2904 * q^55 - 42312 * q^56 + 20160 * q^57 - 29172 * q^58 - 3738 * q^59 - 13456 * q^60 + 18486 * q^61 - 19974 * q^62 - 12496 * q^63 - 20352 * q^64 - 7668 * q^65 - 24926 * q^66 - 47754 * q^67 - 12600 * q^68 + 35042 * q^69 - 123372 * q^70 + 39282 * q^71 - 95040 * q^72 + 15426 * q^73 + 153294 * q^74 - 21916 * q^75 + 103920 * q^76 + 10164 * q^77 + 124984 * q^78 + 125148 * q^79 + 118680 * q^80 - 86917 * q^81 - 255372 * q^82 - 143928 * q^83 + 343616 * q^84 - 104040 * q^85 + 243060 * q^86 - 19368 * q^87 - 68244 * q^88 - 106824 * q^89 + 103424 * q^90 - 109632 * q^91 - 336528 * q^92 - 16622 * q^93 - 74928 * q^94 - 22200 * q^95 - 76456 * q^96 + 9684 * q^97 + 3480 * q^98 - 847 * q^99

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