LMFDB - Embedded newform 309.6.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,6,Mod(1,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("309.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	309.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:	$49.5586003222$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.666354 q^{2} +9.00000 q^{3} -31.5560 q^{4} -57.3315 q^{5} -5.99719 q^{6} +172.727 q^{7} +42.3508 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-0.666354 q^{2} +9.00000 q^{3} -31.5560 q^{4} -57.3315 q^{5} -5.99719 q^{6} +172.727 q^{7} +42.3508 q^{8} +81.0000 q^{9} +38.2031 q^{10} -477.875 q^{11} -284.004 q^{12} +315.009 q^{13} -115.097 q^{14} -515.983 q^{15} +981.570 q^{16} -227.624 q^{17} -53.9747 q^{18} -1239.42 q^{19} +1809.15 q^{20} +1554.55 q^{21} +318.434 q^{22} -3748.88 q^{23} +381.157 q^{24} +161.898 q^{25} -209.907 q^{26} +729.000 q^{27} -5450.58 q^{28} -4620.71 q^{29} +343.828 q^{30} +7495.50 q^{31} -2009.30 q^{32} -4300.87 q^{33} +151.678 q^{34} -9902.71 q^{35} -2556.03 q^{36} +14707.3 q^{37} +825.894 q^{38} +2835.08 q^{39} -2428.03 q^{40} -2869.53 q^{41} -1035.88 q^{42} +7003.05 q^{43} +15079.8 q^{44} -4643.85 q^{45} +2498.08 q^{46} +26342.7 q^{47} +8834.13 q^{48} +13027.7 q^{49} -107.882 q^{50} -2048.62 q^{51} -9940.41 q^{52} +16735.3 q^{53} -485.772 q^{54} +27397.3 q^{55} +7315.13 q^{56} -11154.8 q^{57} +3079.03 q^{58} +34997.9 q^{59} +16282.4 q^{60} +21291.6 q^{61} -4994.66 q^{62} +13990.9 q^{63} -30071.4 q^{64} -18059.9 q^{65} +2865.90 q^{66} -20097.4 q^{67} +7182.91 q^{68} -33739.9 q^{69} +6598.71 q^{70} +76009.0 q^{71} +3430.41 q^{72} +19145.2 q^{73} -9800.27 q^{74} +1457.09 q^{75} +39111.2 q^{76} -82542.0 q^{77} -1889.17 q^{78} -46573.1 q^{79} -56274.9 q^{80} +6561.00 q^{81} +1912.12 q^{82} -17207.9 q^{83} -49055.2 q^{84} +13050.0 q^{85} -4666.51 q^{86} -41586.4 q^{87} -20238.4 q^{88} -42209.5 q^{89} +3094.45 q^{90} +54410.6 q^{91} +118299. q^{92} +67459.5 q^{93} -17553.6 q^{94} +71057.9 q^{95} -18083.7 q^{96} -68304.9 q^{97} -8681.06 q^{98} -38707.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9}+O(q^{10}) $ 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9} + 693 q^{10} + 1470 q^{11} + 4374 q^{12} + 2515 q^{13} + 254 q^{14} + 423 q^{15} + 11542 q^{16} + 880 q^{17} + 1134 q^{18} + 7412 q^{19} + 1927 q^{20} + 3618 q^{21} + 5461 q^{22} + 5567 q^{23} + 3078 q^{24} + 31584 q^{25} + 18502 q^{26} + 18225 q^{27} + 25011 q^{28} + 17230 q^{29} + 6237 q^{30} + 22821 q^{31} + 50233 q^{32} + 13230 q^{33} + 38342 q^{34} + 30664 q^{35} + 39366 q^{36} + 13342 q^{37} + 25860 q^{38} + 22635 q^{39} + 40701 q^{40} + 36374 q^{41} + 2286 q^{42} + 48371 q^{43} - 4133 q^{44} + 3807 q^{45} + 30489 q^{46} + 17740 q^{47} + 103878 q^{48} + 119201 q^{49} - 9505 q^{50} + 7920 q^{51} + 50699 q^{52} - 52204 q^{53} + 10206 q^{54} + 90638 q^{55} - 80285 q^{56} + 66708 q^{57} + 15313 q^{58} + 34099 q^{59} + 17343 q^{60} + 71175 q^{61} - 92130 q^{62} + 32562 q^{63} + 289374 q^{64} - 32899 q^{65} + 49149 q^{66} + 85201 q^{67} - 41169 q^{68} + 50103 q^{69} - 92312 q^{70} + 102652 q^{71} + 27702 q^{72} + 186396 q^{73} - 258113 q^{74} + 284256 q^{75} + 148369 q^{76} - 109016 q^{77} + 166518 q^{78} + 210994 q^{79} + 17955 q^{80} + 164025 q^{81} + 635103 q^{82} + 68429 q^{83} + 225099 q^{84} + 375692 q^{85} + 360833 q^{86} + 155070 q^{87} + 556985 q^{88} + 163508 q^{89} + 56133 q^{90} + 591882 q^{91} + 388500 q^{92} + 205389 q^{93} + 205288 q^{94} + 87988 q^{95} + 452097 q^{96} + 385683 q^{97} - 61147 q^{98} + 119070 q^{99}+O(q^{100}) \) 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9 + 693 * q^10 + 1470 * q^11 + 4374 * q^12 + 2515 * q^13 + 254 * q^14 + 423 * q^15 + 11542 * q^16 + 880 * q^17 + 1134 * q^18 + 7412 * q^19 + 1927 * q^20 + 3618 * q^21 + 5461 * q^22 + 5567 * q^23 + 3078 * q^24 + 31584 * q^25 + 18502 * q^26 + 18225 * q^27 + 25011 * q^28 + 17230 * q^29 + 6237 * q^30 + 22821 * q^31 + 50233 * q^32 + 13230 * q^33 + 38342 * q^34 + 30664 * q^35 + 39366 * q^36 + 13342 * q^37 + 25860 * q^38 + 22635 * q^39 + 40701 * q^40 + 36374 * q^41 + 2286 * q^42 + 48371 * q^43 - 4133 * q^44 + 3807 * q^45 + 30489 * q^46 + 17740 * q^47 + 103878 * q^48 + 119201 * q^49 - 9505 * q^50 + 7920 * q^51 + 50699 * q^52 - 52204 * q^53 + 10206 * q^54 + 90638 * q^55 - 80285 * q^56 + 66708 * q^57 + 15313 * q^58 + 34099 * q^59 + 17343 * q^60 + 71175 * q^61 - 92130 * q^62 + 32562 * q^63 + 289374 * q^64 - 32899 * q^65 + 49149 * q^66 + 85201 * q^67 - 41169 * q^68 + 50103 * q^69 - 92312 * q^70 + 102652 * q^71 + 27702 * q^72 + 186396 * q^73 - 258113 * q^74 + 284256 * q^75 + 148369 * q^76 - 109016 * q^77 + 166518 * q^78 + 210994 * q^79 + 17955 * q^80 + 164025 * q^81 + 635103 * q^82 + 68429 * q^83 + 225099 * q^84 + 375692 * q^85 + 360833 * q^86 + 155070 * q^87 + 556985 * q^88 + 163508 * q^89 + 56133 * q^90 + 591882 * q^91 + 388500 * q^92 + 205389 * q^93 + 205288 * q^94 + 87988 * q^95 + 452097 * q^96 + 385683 * q^97 - 61147 * q^98 + 119070 * 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 $

$2$	−0.666354	−0.117796	−0.0588979	−	0.998264i	$-0.518759\pi$
$2$	−0.666354	−0.117796	−0.0588979	+	0.998264i	$0.518759\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−31.5560	−0.986124
$5$	−57.3315	−1.02558	−0.512788	−	0.858515i	$-0.671387\pi$
$5$	−57.3315	−1.02558	−0.512788	+	0.858515i	$0.671387\pi$
$6$	−5.99719	−0.0680095
$7$	172.727	1.33234	0.666171	−	0.745799i	$-0.267932\pi$
$7$	172.727	1.33234	0.666171	+	0.745799i	$0.267932\pi$
$8$	42.3508	0.233957
$9$	81.0000	0.333333
$10$	38.2031	0.120809
$11$	−477.875	−1.19078	−0.595391	−	0.803436i	$-0.703003\pi$
$11$	−477.875	−1.19078	−0.595391	+	0.803436i	$0.703003\pi$
$12$	−284.004	−0.569339
$13$	315.009	0.516969	0.258484	−	0.966015i	$-0.416777\pi$
$13$	315.009	0.516969	0.258484	+	0.966015i	$0.416777\pi$
$14$	−115.097	−0.156944
$15$	−515.983	−0.592117
$16$	981.570	0.958565
$17$	−227.624	−0.191028	−0.0955139	−	0.995428i	$-0.530449\pi$
$17$	−227.624	−0.191028	−0.0955139	+	0.995428i	$0.530449\pi$
$18$	−53.9747	−0.0392653
$19$	−1239.42	−0.787654	−0.393827	−	0.919185i	$-0.628849\pi$
$19$	−1239.42	−0.787654	−0.393827	+	0.919185i	$0.628849\pi$
$20$	1809.15	1.01135
$21$	1554.55	0.769228
$22$	318.434	0.140269
$23$	−3748.88	−1.47768	−0.738842	−	0.673879i	$-0.764627\pi$
$23$	−3748.88	−1.47768	−0.738842	+	0.673879i	$0.764627\pi$
$24$	381.157	0.135075
$25$	161.898	0.0518075
$26$	−209.907	−0.0608968
$27$	729.000	0.192450
$28$	−5450.58	−1.31385
$29$	−4620.71	−1.02027	−0.510134	−	0.860095i	$-0.670404\pi$
$29$	−4620.71	−1.02027	−0.510134	+	0.860095i	$0.670404\pi$
$30$	343.828	0.0697489
$31$	7495.50	1.40086	0.700432	−	0.713719i	$-0.252990\pi$
$31$	7495.50	1.40086	0.700432	+	0.713719i	$0.252990\pi$
$32$	−2009.30	−0.346872
$33$	−4300.87	−0.687499
$34$	151.678	0.0225023
$35$	−9902.71	−1.36642
$36$	−2556.03	−0.328708
$37$	14707.3	1.76615	0.883077	−	0.469228i	$-0.155468\pi$
$37$	14707.3	1.76615	0.883077	+	0.469228i	$0.155468\pi$
$38$	825.894	0.0927823
$39$	2835.08	0.298472
$40$	−2428.03	−0.239941
$41$	−2869.53	−0.266594	−0.133297	−	0.991076i	$-0.542556\pi$
$41$	−2869.53	−0.266594	−0.133297	+	0.991076i	$0.542556\pi$
$42$	−1035.88	−0.0906119
$43$	7003.05	0.577586	0.288793	−	0.957392i	$-0.406746\pi$
$43$	7003.05	0.577586	0.288793	+	0.957392i	$0.406746\pi$
$44$	15079.8	1.17426
$45$	−4643.85	−0.341859
$46$	2498.08	0.174065
$47$	26342.7	1.73947	0.869733	−	0.493522i	$-0.164291\pi$
$47$	26342.7	1.73947	0.869733	+	0.493522i	$0.164291\pi$
$48$	8834.13	0.553428
$49$	13027.7	0.775135
$50$	−107.882	−0.00610271
$51$	−2048.62	−0.110290
$52$	−9940.41	−0.509795
$53$	16735.3	0.818358	0.409179	−	0.912454i	$-0.365815\pi$
$53$	16735.3	0.818358	0.409179	+	0.912454i	$0.365815\pi$
$54$	−485.772	−0.0226698
$55$	27397.3	1.22124
$56$	7315.13	0.311711
$57$	−11154.8	−0.454752
$58$	3079.03	0.120183
$59$	34997.9	1.30892	0.654458	−	0.756098i	$-0.272897\pi$
$59$	34997.9	1.30892	0.654458	+	0.756098i	$0.272897\pi$
$60$	16282.4	0.583901
$61$	21291.6	0.732628	0.366314	−	0.930491i	$-0.380620\pi$
$61$	21291.6	0.732628	0.366314	+	0.930491i	$0.380620\pi$
$62$	−4994.66	−0.165016
$63$	13990.9	0.444114
$64$	−30071.4	−0.917705
$65$	−18059.9	−0.530191
$66$	2865.90	0.0809845
$67$	−20097.4	−0.546956	−0.273478	−	0.961878i	$-0.588174\pi$
$67$	−20097.4	−0.546956	−0.273478	+	0.961878i	$0.588174\pi$
$68$	7182.91	0.188377
$69$	−33739.9	−0.853141
$70$	6598.71	0.160959
$71$	76009.0	1.78945	0.894725	−	0.446618i	$-0.147372\pi$
$71$	76009.0	1.78945	0.894725	+	0.446618i	$0.147372\pi$
$72$	3430.41	0.0779857
$73$	19145.2	0.420487	0.210244	−	0.977649i	$-0.432574\pi$
$73$	19145.2	0.420487	0.210244	+	0.977649i	$0.432574\pi$
$74$	−9800.27	−0.208046
$75$	1457.09	0.0299111
$76$	39111.2	0.776724
$77$	−82542.0	−1.58653
$78$	−1889.17	−0.0351588
$79$	−46573.1	−0.839590	−0.419795	−	0.907619i	$-0.637898\pi$
$79$	−46573.1	−0.839590	−0.419795	+	0.907619i	$0.637898\pi$
$80$	−56274.9	−0.983082
$81$	6561.00	0.111111
$82$	1912.12	0.0314037
$83$	−17207.9	−0.274178	−0.137089	−	0.990559i	$-0.543775\pi$
$83$	−17207.9	−0.274178	−0.137089	+	0.990559i	$0.543775\pi$
$84$	−49055.2	−0.758554
$85$	13050.0	0.195914
$86$	−4666.51	−0.0680372
$87$	−41586.4	−0.589052
$88$	−20238.4	−0.278592
$89$	−42209.5	−0.564853	−0.282426	−	0.959289i	$-0.591139\pi$
$89$	−42209.5	−0.564853	−0.282426	+	0.959289i	$0.591139\pi$
$90$	3094.45	0.0402696
$91$	54410.6	0.688779
$92$	118299.	1.45718
$93$	67459.5	0.808790
$94$	−17553.6	−0.204902
$95$	71057.9	0.807799
$96$	−18083.7	−0.200267
$97$	−68304.9	−0.737094	−0.368547	−	0.929609i	$-0.620145\pi$
$97$	−68304.9	−0.737094	−0.368547	+	0.929609i	$0.620145\pi$
$98$	−8681.06	−0.0913077
$99$	−38707.9	−0.396928
$100$	−5108.86	−0.0510886
$101$	111360.	1.08624	0.543122	−	0.839654i	$-0.317242\pi$
$101$	111360.	1.08624	0.543122	+	0.839654i	$0.317242\pi$
$102$	1365.11	0.0129917
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	13340.9	0.120949
$105$	−89124.4	−0.788902
$106$	−11151.6	−0.0963992
$107$	132821.	1.12152	0.560759	−	0.827979i	$-0.310509\pi$
$107$	132821.	1.12152	0.560759	+	0.827979i	$0.310509\pi$
$108$	−23004.3	−0.189780
$109$	168078.	1.35502	0.677508	−	0.735515i	$-0.263060\pi$
$109$	168078.	1.35502	0.677508	+	0.735515i	$0.263060\pi$
$110$	−18256.3	−0.143857
$111$	132366.	1.01969
$112$	169544.	1.27714
$113$	−129323.	−0.952748	−0.476374	−	0.879243i	$-0.658049\pi$
$113$	−129323.	−0.952748	−0.476374	+	0.879243i	$0.658049\pi$
$114$	7433.05	0.0535679
$115$	214929.	1.51548
$116$	145811.	1.00611
$117$	25515.7	0.172323
$118$	−23321.0	−0.154185
$119$	−39316.9	−0.254514
$120$	−21852.3	−0.138530
$121$	67313.4	0.417963
$122$	−14187.7	−0.0863005
$123$	−25825.7	−0.153918
$124$	−236528.	−1.38143
$125$	169879.	0.972444
$126$	−9322.90	−0.0523148
$127$	174149.	0.958099	0.479050	−	0.877788i	$-0.340981\pi$
$127$	174149.	0.958099	0.479050	+	0.877788i	$0.340981\pi$
$128$	84335.7	0.454974
$129$	63027.5	0.333469
$130$	12034.3	0.0624543
$131$	−262384.	−1.33585	−0.667927	−	0.744227i	$-0.732818\pi$
$131$	−262384.	−1.33585	−0.667927	+	0.744227i	$0.732818\pi$
$132$	135718.	0.677959
$133$	−214082.	−1.04942
$134$	13392.0	0.0644292
$135$	−41794.6	−0.197372
$136$	−9640.07	−0.0446923
$137$	88176.5	0.401376	0.200688	−	0.979655i	$-0.435682\pi$
$137$	88176.5	0.401376	0.200688	+	0.979655i	$0.435682\pi$
$138$	22482.7	0.100496
$139$	191709.	0.841598	0.420799	−	0.907154i	$-0.361750\pi$
$139$	191709.	0.841598	0.420799	+	0.907154i	$0.361750\pi$
$140$	312490.	1.34746
$141$	237085.	1.00428
$142$	−50648.9	−0.210790
$143$	−150535.	−0.615598
$144$	79507.2	0.319522
$145$	264912.	1.04636
$146$	−12757.5	−0.0495317
$147$	117249.	0.447524
$148$	−464103.	−1.74165
$149$	330040.	1.21787	0.608935	−	0.793220i	$-0.291597\pi$
$149$	330040.	1.21787	0.608935	+	0.793220i	$0.291597\pi$
$150$	−970.936	−0.00352340
$151$	140745.	0.502333	0.251167	−	0.967944i	$-0.419186\pi$
$151$	140745.	0.502333	0.251167	+	0.967944i	$0.419186\pi$
$152$	−52490.5	−0.184277
$153$	−18437.6	−0.0636759
$154$	55002.2	0.186887
$155$	−429728.	−1.43669
$156$	−89463.7	−0.294331
$157$	−294919.	−0.954890	−0.477445	−	0.878662i	$-0.658437\pi$
$157$	−294919.	−0.954890	−0.477445	+	0.878662i	$0.658437\pi$
$158$	31034.2	0.0989003
$159$	150618.	0.472479
$160$	115196.	0.355744
$161$	−647533.	−1.96878
$162$	−4371.95	−0.0130884
$163$	476363.	1.40433	0.702165	−	0.712014i	$-0.252217\pi$
$163$	476363.	1.40433	0.702165	+	0.712014i	$0.252217\pi$
$164$	90550.7	0.262895
$165$	246575.	0.705083
$166$	11466.6	0.0322970
$167$	45555.3	0.126400	0.0632001	−	0.998001i	$-0.479869\pi$
$167$	45555.3	0.126400	0.0632001	+	0.998001i	$0.479869\pi$
$168$	65836.2	0.179966
$169$	−272062.	−0.732743
$170$	−8695.95	−0.0230778
$171$	−100393.	−0.262551
$172$	−220988.	−0.569571
$173$	84545.4	0.214771	0.107385	−	0.994217i	$-0.465752\pi$
$173$	84545.4	0.214771	0.107385	+	0.994217i	$0.465752\pi$
$174$	27711.3	0.0693878
$175$	27964.3	0.0690253
$176$	−469068.	−1.14144
$177$	314981.	0.755703
$178$	28126.5	0.0665373
$179$	−580231.	−1.35353	−0.676766	−	0.736198i	$-0.736619\pi$
$179$	−580231.	−1.35353	−0.676766	+	0.736198i	$0.736619\pi$
$180$	146541.	0.337115
$181$	359552.	0.815765	0.407883	−	0.913034i	$-0.366267\pi$
$181$	359552.	0.815765	0.407883	+	0.913034i	$0.366267\pi$
$182$	−36256.7	−0.0811354
$183$	191624.	0.422983
$184$	−158768.	−0.345715
$185$	−843191.	−1.81133
$186$	−44951.9	−0.0952721
$187$	108776.	0.227473
$188$	−831270.	−1.71533
$189$	125918.	0.256409
$190$	−47349.7	−0.0951554
$191$	−379669.	−0.753045	−0.376523	−	0.926407i	$-0.622880\pi$
$191$	−379669.	−0.753045	−0.376523	+	0.926407i	$0.622880\pi$
$192$	−270642.	−0.529837
$193$	835839.	1.61521	0.807606	−	0.589723i	$-0.200763\pi$
$193$	835839.	1.61521	0.807606	+	0.589723i	$0.200763\pi$
$194$	45515.3	0.0868266
$195$	−162539.	−0.306106
$196$	−411102.	−0.764379
$197$	−105695.	−0.194039	−0.0970197	−	0.995282i	$-0.530931\pi$
$197$	−105695.	−0.194039	−0.0970197	+	0.995282i	$0.530931\pi$
$198$	25793.1	0.0467564
$199$	−380936.	−0.681899	−0.340949	−	0.940082i	$-0.610748\pi$
$199$	−380936.	−0.681899	−0.340949	+	0.940082i	$0.610748\pi$
$200$	6856.53	0.0121207
$201$	−180876.	−0.315785
$202$	−74205.4	−0.127955
$203$	−798123.	−1.35934
$204$	64646.2	0.108760
$205$	164514.	0.273413
$206$	7069.35	0.0116068
$207$	−303659.	−0.492561
$208$	309203.	0.495548
$209$	592289.	0.937924
$210$	59388.4	0.0929294
$211$	−1.00025e6	−1.54668	−0.773340	−	0.633992i	$-0.781415\pi$
$211$	−1.00025e6	−1.54668	−0.773340	+	0.633992i	$0.781415\pi$
$212$	−528098.	−0.807003
$213$	684081.	1.03314
$214$	−88505.6	−0.132110
$215$	−401495.	−0.592358
$216$	30873.7	0.0450251
$217$	1.29468e6	1.86643
$218$	−111999.	−0.159615
$219$	172307.	0.242768
$220$	−864548.	−1.20429
$221$	−71703.7	−0.0987554
$222$	−88202.4	−0.120115
$223$	1.40399e6	1.89061	0.945306	−	0.326184i	$-0.105763\pi$
$223$	1.40399e6	1.89061	0.945306	+	0.326184i	$0.105763\pi$
$224$	−347061.	−0.462152
$225$	13113.8	0.0172692
$226$	86174.6	0.112230
$227$	−176634.	−0.227514	−0.113757	−	0.993509i	$-0.536289\pi$
$227$	−176634.	−0.227514	−0.113757	+	0.993509i	$0.536289\pi$
$228$	352001.	0.448442
$229$	96496.9	0.121598	0.0607988	−	0.998150i	$-0.480635\pi$
$229$	96496.9	0.121598	0.0607988	+	0.998150i	$0.480635\pi$
$230$	−143219.	−0.178517
$231$	−742878.	−0.915983
$232$	−195691.	−0.238699
$233$	933125.	1.12603	0.563015	−	0.826447i	$-0.309641\pi$
$233$	933125.	1.12603	0.563015	+	0.826447i	$0.309641\pi$
$234$	−17002.5	−0.0202989
$235$	−1.51027e6	−1.78396
$236$	−1.10439e6	−1.29075
$237$	−419158.	−0.484738
$238$	26199.0	0.0299807
$239$	378408.	0.428514	0.214257	−	0.976777i	$-0.431267\pi$
$239$	378408.	0.428514	0.214257	+	0.976777i	$0.431267\pi$
$240$	−506474.	−0.567583
$241$	−960517.	−1.06528	−0.532638	−	0.846343i	$-0.678799\pi$
$241$	−960517.	−1.06528	−0.532638	+	0.846343i	$0.678799\pi$
$242$	−44854.5	−0.0492343
$243$	59049.0	0.0641500
$244$	−671877.	−0.722462
$245$	−746897.	−0.794961
$246$	17209.1	0.0181309
$247$	−390429.	−0.407192
$248$	317440.	0.327742
$249$	−154871.	−0.158297
$250$	−113200.	−0.114550
$251$	−341978.	−0.342621	−0.171310	−	0.985217i	$-0.554800\pi$
$251$	−341978.	−0.342621	−0.171310	+	0.985217i	$0.554800\pi$
$252$	−441497.	−0.437952
$253$	1.79149e6	1.75960
$254$	−116045.	−0.112860
$255$	117450.	0.113111
$256$	906086.	0.864111
$257$	1.56651e6	1.47945	0.739725	−	0.672910i	$-0.234956\pi$
$257$	1.56651e6	1.47945	0.739725	+	0.672910i	$0.234956\pi$
$258$	−41998.6	−0.0392813
$259$	2.54035e6	2.35312
$260$	569898.	0.522834
$261$	−374278.	−0.340089
$262$	174841.	0.157358
$263$	−601513.	−0.536235	−0.268118	−	0.963386i	$-0.586402\pi$
$263$	−601513.	−0.536235	−0.268118	+	0.963386i	$0.586402\pi$
$264$	−182145.	−0.160845
$265$	−959459.	−0.839289
$266$	142654.	0.123618
$267$	−379886.	−0.326118
$268$	634192.	0.539367
$269$	−1.70628e6	−1.43770	−0.718852	−	0.695163i	$-0.755332\pi$
$269$	−1.70628e6	−1.43770	−0.718852	+	0.695163i	$0.755332\pi$
$270$	27850.0	0.0232496
$271$	−728722.	−0.602752	−0.301376	−	0.953505i	$-0.597446\pi$
$271$	−728722.	−0.602752	−0.301376	+	0.953505i	$0.597446\pi$
$272$	−223429.	−0.183113
$273$	489695.	0.397667
$274$	−58756.8	−0.0472805
$275$	−77367.2	−0.0616915
$276$	1.06469e6	0.841303
$277$	2.00411e6	1.56936	0.784680	−	0.619901i	$-0.212827\pi$
$277$	2.00411e6	1.56936	0.784680	+	0.619901i	$0.212827\pi$
$278$	−127746.	−0.0991368
$279$	607135.	0.466955
$280$	−419387.	−0.319684
$281$	860626.	0.650202	0.325101	−	0.945679i	$-0.394602\pi$
$281$	860626.	0.650202	0.325101	+	0.945679i	$0.394602\pi$
$282$	−157982.	−0.118300
$283$	−1.89838e6	−1.40902	−0.704509	−	0.709695i	$-0.748833\pi$
$283$	−1.89838e6	−1.40902	−0.704509	+	0.709695i	$0.748833\pi$
$284$	−2.39854e6	−1.76462
$285$	639521.	0.466383
$286$	100309.	0.0725148
$287$	−495645.	−0.355195
$288$	−162753.	−0.115624
$289$	−1.36804e6	−0.963508
$290$	−176525.	−0.123257
$291$	−614744.	−0.425561
$292$	−604145.	−0.414653
$293$	−694440.	−0.472570	−0.236285	−	0.971684i	$-0.575930\pi$
$293$	−694440.	−0.472570	−0.236285	+	0.971684i	$0.575930\pi$
$294$	−78129.5	−0.0527165
$295$	−2.00648e6	−1.34239
$296$	622866.	0.413205
$297$	−348371.	−0.229166
$298$	−219923.	−0.143460
$299$	−1.18093e6	−0.763916
$300$	−45979.8	−0.0294960
$301$	1.20962e6	0.769542
$302$	−93786.3	−0.0591728
$303$	1.00224e6	0.627143
$304$	−1.21658e6	−0.755017
$305$	−1.22068e6	−0.751366
$306$	12286.0	0.00750076
$307$	1.80078e6	1.09047	0.545237	−	0.838282i	$-0.316440\pi$
$307$	1.80078e6	1.09047	0.545237	+	0.838282i	$0.316440\pi$
$308$	2.60469e6	1.56452
$309$	−95481.0	−0.0568880
$310$	286351.	0.169237
$311$	−1.50441e6	−0.881994	−0.440997	−	0.897509i	$-0.645375\pi$
$311$	−1.50441e6	−0.881994	−0.440997	+	0.897509i	$0.645375\pi$
$312$	120068.	0.0698297
$313$	571151.	0.329527	0.164763	−	0.986333i	$-0.447314\pi$
$313$	571151.	0.329527	0.164763	+	0.986333i	$0.447314\pi$
$314$	196520.	0.112482
$315$	−802119.	−0.455473
$316$	1.46966e6	0.827940
$317$	2.60738e6	1.45732	0.728661	−	0.684874i	$-0.240143\pi$
$317$	2.60738e6	1.45732	0.728661	+	0.684874i	$0.240143\pi$
$318$	−100365.	−0.0556561
$319$	2.20812e6	1.21492
$320$	1.72404e6	0.941177
$321$	1.19539e6	0.647509
$322$	431486.	0.231914
$323$	282123.	0.150464
$324$	−207039.	−0.109569
$325$	50999.5	0.0267829
$326$	−317427.	−0.165424
$327$	1.51270e6	0.782319
$328$	−121527.	−0.0623716
$329$	4.55011e6	2.31756
$330$	−164307.	−0.0830558
$331$	1.20506e6	0.604558	0.302279	−	0.953220i	$-0.402253\pi$
$331$	1.20506e6	0.604558	0.302279	+	0.953220i	$0.402253\pi$
$332$	543012.	0.270374
$333$	1.19129e6	0.588718
$334$	−30356.0	−0.0148894
$335$	1.15221e6	0.560945
$336$	1.52590e6	0.737355
$337$	−573716.	−0.275183	−0.137592	−	0.990489i	$-0.543936\pi$
$337$	−573716.	−0.275183	−0.137592	+	0.990489i	$0.543936\pi$
$338$	181290.	0.0863141
$339$	−1.16390e6	−0.550069
$340$	−411807.	−0.193195
$341$	−3.58191e6	−1.66813
$342$	66897.4	0.0309274
$343$	−652789.	−0.299597
$344$	296585.	0.135130
$345$	1.93436e6	0.874962
$346$	−56337.2	−0.0252991
$347$	−90196.3	−0.0402129	−0.0201064	−	0.999798i	$-0.506401\pi$
$347$	−90196.3	−0.0402129	−0.0201064	+	0.999798i	$0.506401\pi$
$348$	1.31230e6	0.580878
$349$	−2.91914e6	−1.28290	−0.641448	−	0.767166i	$-0.721666\pi$
$349$	−2.91914e6	−1.28290	−0.641448	+	0.767166i	$0.721666\pi$
$350$	−18634.1	−0.00813090
$351$	229641.	0.0994907
$352$	960193.	0.413049
$353$	−704890.	−0.301082	−0.150541	−	0.988604i	$-0.548101\pi$
$353$	−704890.	−0.301082	−0.150541	+	0.988604i	$0.548101\pi$
$354$	−209889.	−0.0890187
$355$	−4.35771e6	−1.83522
$356$	1.33196e6	0.557015
$357$	−353852.	−0.146944
$358$	386640.	0.159441
$359$	−1.74656e6	−0.715235	−0.357617	−	0.933868i	$-0.616411\pi$
$359$	−1.74656e6	−0.715235	−0.357617	+	0.933868i	$0.616411\pi$
$360$	−196671.	−0.0799804
$361$	−939932.	−0.379602
$362$	−239589.	−0.0960938
$363$	605820.	0.241311
$364$	−1.71698e6	−0.679222
$365$	−1.09762e6	−0.431242
$366$	−127690.	−0.0498256
$367$	−3.29950e6	−1.27874	−0.639372	−	0.768898i	$-0.720805\pi$
$367$	−3.29950e6	−1.27874	−0.639372	+	0.768898i	$0.720805\pi$
$368$	−3.67979e6	−1.41646
$369$	−232432.	−0.0888647
$370$	561864.	0.213367
$371$	2.89064e6	1.09033
$372$	−2.12875e6	−0.797567
$373$	−251205.	−0.0934880	−0.0467440	−	0.998907i	$-0.514884\pi$
$373$	−251205.	−0.0934880	−0.0467440	+	0.998907i	$0.514884\pi$
$374$	−72483.3	−0.0267953
$375$	1.52891e6	0.561441
$376$	1.11564e6	0.406961
$377$	−1.45557e6	−0.527446
$378$	−83906.1	−0.0302040
$379$	2.64163e6	0.944657	0.472328	−	0.881423i	$-0.343414\pi$
$379$	2.64163e6	0.944657	0.472328	+	0.881423i	$0.343414\pi$
$380$	−2.24230e6	−0.796590
$381$	1.56734e6	0.553159
$382$	252994.	0.0887056
$383$	−1.47775e6	−0.514760	−0.257380	−	0.966310i	$-0.582859\pi$
$383$	−1.47775e6	−0.514760	−0.257380	+	0.966310i	$0.582859\pi$
$384$	759022.	0.262679
$385$	4.73226e6	1.62711
$386$	−556965.	−0.190265
$387$	567247.	0.192529
$388$	2.15543e6	0.726866
$389$	−233784.	−0.0783324	−0.0391662	−	0.999233i	$-0.512470\pi$
$389$	−233784.	−0.0783324	−0.0391662	+	0.999233i	$0.512470\pi$
$390$	108309.	0.0360580
$391$	853336.	0.282279
$392$	551733.	0.181348
$393$	−2.36146e6	−0.771256
$394$	70430.5	0.0228570
$395$	2.67011e6	0.861064
$396$	1.22146e6	0.391420
$397$	1.59574e6	0.508144	0.254072	−	0.967185i	$-0.418230\pi$
$397$	1.59574e6	0.508144	0.254072	+	0.967185i	$0.418230\pi$
$398$	253839.	0.0803249
$399$	−1.92674e6	−0.605885
$400$	158915.	0.0496609
$401$	−4.08994e6	−1.27015	−0.635077	−	0.772449i	$-0.719032\pi$
$401$	−4.08994e6	−1.27015	−0.635077	+	0.772449i	$0.719032\pi$
$402$	120528.	0.0371982
$403$	2.36115e6	0.724204
$404$	−3.51408e6	−1.07117
$405$	−376152.	−0.113953
$406$	531832.	0.160125
$407$	−7.02825e6	−2.10311
$408$	−86760.7	−0.0258031
$409$	−2.04851e6	−0.605523	−0.302761	−	0.953066i	$-0.597909\pi$
$409$	−2.04851e6	−0.605523	−0.302761	+	0.953066i	$0.597909\pi$
$410$	−109625.	−0.0322069
$411$	793589.	0.231735
$412$	334777.	0.0971657
$413$	6.04509e6	1.74392
$414$	202344.	0.0580217
$415$	986554.	0.281191
$416$	−632947.	−0.179322
$417$	1.72538e6	0.485897
$418$	−394674.	−0.110484
$419$	2.05307e6	0.571305	0.285652	−	0.958333i	$-0.407790\pi$
$419$	2.05307e6	0.571305	0.285652	+	0.958333i	$0.407790\pi$
$420$	2.81241e6	0.777956
$421$	6.49567e6	1.78615	0.893077	−	0.449904i	$-0.148542\pi$
$421$	6.49567e6	1.78615	0.893077	+	0.449904i	$0.148542\pi$
$422$	666518.	0.182193
$423$	2.13376e6	0.579822
$424$	708752.	0.191461
$425$	−36852.1	−0.00989668
$426$	−455840.	−0.121700
$427$	3.67764e6	0.976111
$428$	−4.19129e6	−1.10596
$429$	−1.35481e6	−0.355415
$430$	267538.	0.0697774
$431$	−1.25805e6	−0.326217	−0.163108	−	0.986608i	$-0.552152\pi$
$431$	−1.25805e6	−0.326217	−0.163108	+	0.986608i	$0.552152\pi$
$432$	715565.	0.184476
$433$	7.10785e6	1.82188	0.910938	−	0.412544i	$-0.135360\pi$
$433$	7.10785e6	1.82188	0.910938	+	0.412544i	$0.135360\pi$
$434$	−862713.	−0.219858
$435$	2.38421e6	0.604118
$436$	−5.30387e6	−1.33621
$437$	4.64644e6	1.16390
$438$	−114817.	−0.0285971
$439$	754574.	0.186870	0.0934352	−	0.995625i	$-0.470215\pi$
$439$	754574.	0.186870	0.0934352	+	0.995625i	$0.470215\pi$
$440$	1.16030e6	0.285718
$441$	1.05524e6	0.258378
$442$	47780.1	0.0116330
$443$	−440514.	−0.106647	−0.0533237	−	0.998577i	$-0.516982\pi$
$443$	−440514.	−0.106647	−0.0533237	+	0.998577i	$0.516982\pi$
$444$	−4.17693e6	−1.00554
$445$	2.41993e6	0.579300
$446$	−935556.	−0.222706
$447$	2.97036e6	0.703137
$448$	−5.19414e6	−1.22270
$449$	2.92069e6	0.683706	0.341853	−	0.939754i	$-0.388946\pi$
$449$	2.92069e6	0.683706	0.341853	+	0.939754i	$0.388946\pi$
$450$	−8738.42	−0.00203424
$451$	1.37127e6	0.317456
$452$	4.08090e6	0.939528
$453$	1.26671e6	0.290022
$454$	117700.	0.0268002
$455$	−3.11944e6	−0.706396
$456$	−472414.	−0.106393
$457$	−1.77051e6	−0.396559	−0.198280	−	0.980146i	$-0.563535\pi$
$457$	−1.77051e6	−0.396559	−0.198280	+	0.980146i	$0.563535\pi$
$458$	−64301.1	−0.0143237
$459$	−165938.	−0.0367633
$460$	−6.78228e6	−1.49445
$461$	6.68250e6	1.46449	0.732246	−	0.681040i	$-0.238472\pi$
$461$	6.68250e6	1.46449	0.732246	+	0.681040i	$0.238472\pi$
$462$	495020.	0.107899
$463$	7.34274e6	1.59186	0.795931	−	0.605387i	$-0.206982\pi$
$463$	7.34274e6	1.59186	0.795931	+	0.605387i	$0.206982\pi$
$464$	−4.53555e6	−0.977992
$465$	−3.86755e6	−0.829476
$466$	−621792.	−0.132642
$467$	3.31400e6	0.703170	0.351585	−	0.936156i	$-0.385643\pi$
$467$	3.31400e6	0.703170	0.351585	+	0.936156i	$0.385643\pi$
$468$	−805173.	−0.169932
$469$	−3.47137e6	−0.728733
$470$	1.00637e6	0.210143
$471$	−2.65427e6	−0.551306
$472$	1.48219e6	0.306230
$473$	−3.34658e6	−0.687779
$474$	279308.	0.0571001
$475$	−200661.	−0.0408064
$476$	1.24068e6	0.250983
$477$	1.35556e6	0.272786
$478$	−252154.	−0.0504772
$479$	5.46814e6	1.08893	0.544466	−	0.838783i	$-0.316732\pi$
$479$	5.46814e6	1.08893	0.544466	+	0.838783i	$0.316732\pi$
$480$	1.03676e6	0.205389
$481$	4.63293e6	0.913047
$482$	640044.	0.125485
$483$	−5.82780e6	−1.13668
$484$	−2.12414e6	−0.412164
$485$	3.91602e6	0.755946
$486$	−39347.5	−0.00755661
$487$	−87832.7	−0.0167816	−0.00839081	−	0.999965i	$-0.502671\pi$
$487$	−87832.7	−0.0167816	−0.00839081	+	0.999965i	$0.502671\pi$
$488$	901715.	0.171404
$489$	4.28727e6	0.810790
$490$	497698.	0.0936431
$491$	−8.22196e6	−1.53912	−0.769558	−	0.638577i	$-0.779524\pi$
$491$	−8.22196e6	−1.53912	−0.769558	+	0.638577i	$0.779524\pi$
$492$	814956.	0.151782
$493$	1.05179e6	0.194899
$494$	260164.	0.0479656
$495$	2.21918e6	0.407080
$496$	7.35736e6	1.34282
$497$	1.31288e7	2.38416
$498$	103199.	0.0186467
$499$	−7.20328e6	−1.29503	−0.647514	−	0.762054i	$-0.724191\pi$
$499$	−7.20328e6	−1.29503	−0.647514	+	0.762054i	$0.724191\pi$
$500$	−5.36070e6	−0.958951
$501$	409998.	0.0729772
$502$	227879.	0.0403593
$503$	1.11878e7	1.97163	0.985815	−	0.167835i	$-0.0536775\pi$
$503$	1.11878e7	1.97163	0.985815	+	0.167835i	$0.0536775\pi$
$504$	592526.	0.103904
$505$	−6.38445e6	−1.11403
$506$	−1.19377e6	−0.207274
$507$	−2.44856e6	−0.423049
$508$	−5.49543e6	−0.944805
$509$	−5.56150e6	−0.951476	−0.475738	−	0.879587i	$-0.657819\pi$
$509$	−5.56150e6	−0.951476	−0.475738	+	0.879587i	$0.657819\pi$
$510$	−78263.6	−0.0133240
$511$	3.30690e6	0.560233
$512$	−3.30252e6	−0.556763
$513$	−903539.	−0.151584
$514$	−1.04385e6	−0.174273
$515$	608230.	0.101053
$516$	−1.98889e6	−0.328842
$517$	−1.25885e7	−2.07133
$518$	−1.69277e6	−0.277188
$519$	760908.	0.123998
$520$	−764852.	−0.124042
$521$	−739567.	−0.119367	−0.0596833	−	0.998217i	$-0.519009\pi$
$521$	−739567.	−0.119367	−0.0596833	+	0.998217i	$0.519009\pi$
$522$	249401.	0.0400611
$523$	513564.	0.0820995	0.0410497	−	0.999157i	$-0.486930\pi$
$523$	513564.	0.0820995	0.0410497	+	0.999157i	$0.486930\pi$
$524$	8.27978e6	1.31732
$525$	251679.	0.0398518
$526$	400820.	0.0631663
$527$	−1.70616e6	−0.267604
$528$	−4.22161e6	−0.659012
$529$	7.61773e6	1.18355
$530$	639339.	0.0988648
$531$	2.83483e6	0.436305
$532$	6.75556e6	1.03486
$533$	−903926.	−0.137821
$534$	253138.	0.0384153
$535$	−7.61481e6	−1.15020
$536$	−851140.	−0.127964
$537$	−5.22208e6	−0.781462
$538$	1.13699e6	0.169356
$539$	−6.22561e6	−0.923017
$540$	1.31887e6	0.194634
$541$	1.25807e7	1.84805	0.924023	−	0.382336i	$-0.124880\pi$
$541$	1.25807e7	1.84805	0.924023	+	0.382336i	$0.124880\pi$
$542$	485587.	0.0710017
$543$	3.23597e6	0.470982
$544$	457365.	0.0662622
$545$	−9.63616e6	−1.38967
$546$	−326311.	−0.0468435
$547$	1.02877e7	1.47011	0.735056	−	0.678007i	$-0.237156\pi$
$547$	1.02877e7	1.47011	0.735056	+	0.678007i	$0.237156\pi$
$548$	−2.78250e6	−0.395807
$549$	1.72462e6	0.244209
$550$	51554.0	0.00726700
$551$	5.72701e6	0.803617
$552$	−1.42891e6	−0.199599
$553$	−8.04444e6	−1.11862
$554$	−1.33545e6	−0.184864
$555$	−7.58872e6	−1.04577
$556$	−6.04955e6	−0.829920
$557$	1.59508e6	0.217844	0.108922	−	0.994050i	$-0.465260\pi$
$557$	1.59508e6	0.217844	0.108922	+	0.994050i	$0.465260\pi$
$558$	−404567.	−0.0550054
$559$	2.20602e6	0.298594
$560$	−9.72021e6	−1.30980
$561$	978984.	0.131331
$562$	−573481.	−0.0765911
$563$	−3.70830e6	−0.493064	−0.246532	−	0.969135i	$-0.579291\pi$
$563$	−3.70830e6	−0.493064	−0.246532	+	0.969135i	$0.579291\pi$
$564$	−7.48143e6	−0.990346
$565$	7.41425e6	0.977116
$566$	1.26499e6	0.165977
$567$	1.13326e6	0.148038
$568$	3.21904e6	0.418655
$569$	−1.03084e7	−1.33478	−0.667392	−	0.744707i	$-0.732589\pi$
$569$	−1.03084e7	−1.33478	−0.667392	+	0.744707i	$0.732589\pi$
$570$	−426147.	−0.0549380
$571$	−3.74217e6	−0.480323	−0.240161	−	0.970733i	$-0.577200\pi$
$571$	−3.74217e6	−0.480323	−0.240161	+	0.970733i	$0.577200\pi$
$572$	4.75027e6	0.607056
$573$	−3.41702e6	−0.434771
$574$	330275.	0.0418405
$575$	−606937.	−0.0765551
$576$	−2.43578e6	−0.305902
$577$	−7.59746e6	−0.950012	−0.475006	−	0.879983i	$-0.657554\pi$
$577$	−7.59746e6	−0.950012	−0.475006	+	0.879983i	$0.657554\pi$
$578$	911602.	0.113497
$579$	7.52255e6	0.932543
$580$	−8.35956e6	−1.03184
$581$	−2.97227e6	−0.365299
$582$	409637.	0.0501294
$583$	−7.99737e6	−0.974487
$584$	810814.	0.0983760
$585$	−1.46285e6	−0.176730
$586$	462743.	0.0556668
$587$	1.63146e7	1.95425	0.977125	−	0.212668i	$-0.0682152\pi$
$587$	1.63146e7	1.95425	0.977125	+	0.212668i	$0.0682152\pi$
$588$	−3.69991e6	−0.441315
$589$	−9.29009e6	−1.10340
$590$	1.33703e6	0.158128
$591$	−951258.	−0.112029
$592$	1.44363e7	1.69297
$593$	3.78889e6	0.442462	0.221231	−	0.975221i	$-0.428993\pi$
$593$	3.78889e6	0.442462	0.221231	+	0.975221i	$0.428993\pi$
$594$	232138.	0.0269948
$595$	2.25410e6	0.261024
$596$	−1.04147e7	−1.20097
$597$	−3.42843e6	−0.393694
$598$	786917.	0.0899862
$599$	−32296.0	−0.00367775	−0.00183887	−	0.999998i	$-0.500585\pi$
$599$	−32296.0	−0.00367775	−0.00183887	+	0.999998i	$0.500585\pi$
$600$	61708.8	0.00699791
$601$	−1.40952e7	−1.59179	−0.795896	−	0.605433i	$-0.793000\pi$
$601$	−1.40952e7	−1.59179	−0.795896	+	0.605433i	$0.793000\pi$
$602$	−806034.	−0.0906488
$603$	−1.62789e6	−0.182319
$604$	−4.44136e6	−0.495363
$605$	−3.85918e6	−0.428653
$606$	−667849.	−0.0738748
$607$	1.62701e7	1.79233	0.896165	−	0.443720i	$-0.146342\pi$
$607$	1.62701e7	1.79233	0.896165	+	0.443720i	$0.146342\pi$
$608$	2.49037e6	0.273215
$609$	−7.18311e6	−0.784818
$610$	813404.	0.0885078
$611$	8.29819e6	0.899250
$612$	581816.	0.0627924
$613$	−7.87438e6	−0.846380	−0.423190	−	0.906041i	$-0.639090\pi$
$613$	−7.87438e6	−0.846380	−0.423190	+	0.906041i	$0.639090\pi$
$614$	−1.19996e6	−0.128453
$615$	1.48063e6	0.157855
$616$	−3.49572e6	−0.371180
$617$	−3.12302e6	−0.330265	−0.165132	−	0.986271i	$-0.552805\pi$
$617$	−3.12302e6	−0.330265	−0.165132	+	0.986271i	$0.552805\pi$
$618$	63624.2	0.00670117
$619$	−1.05911e7	−1.11101	−0.555503	−	0.831515i	$-0.687474\pi$
$619$	−1.05911e7	−1.11101	−0.555503	+	0.831515i	$0.687474\pi$
$620$	1.35605e7	1.41676
$621$	−2.73293e6	−0.284380
$622$	1.00247e6	0.103895
$623$	−7.29073e6	−0.752577
$624$	2.78283e6	0.286105
$625$	−1.02453e7	−1.04912
$626$	−380589.	−0.0388169
$627$	5.33060e6	0.541511
$628$	9.30645e6	0.941640
$629$	−3.34774e6	−0.337385
$630$	534495.	0.0536528
$631$	−4.70582e6	−0.470503	−0.235251	−	0.971935i	$-0.575591\pi$
$631$	−4.70582e6	−0.470503	−0.235251	+	0.971935i	$0.575591\pi$
$632$	−1.97241e6	−0.196428
$633$	−9.00221e6	−0.892976
$634$	−1.73744e6	−0.171667
$635$	−9.98420e6	−0.982604
$636$	−4.75288e6	−0.465923
$637$	4.10384e6	0.400721
$638$	−1.47139e6	−0.143112
$639$	6.15673e6	0.596483
$640$	−4.83509e6	−0.466611
$641$	−4.46316e6	−0.429040	−0.214520	−	0.976720i	$-0.568819\pi$
$641$	−4.46316e6	−0.429040	−0.214520	+	0.976720i	$0.568819\pi$
$642$	−796551.	−0.0762739
$643$	−9.92147e6	−0.946343	−0.473171	−	0.880970i	$-0.656891\pi$
$643$	−9.92147e6	−0.946343	−0.473171	+	0.880970i	$0.656891\pi$
$644$	2.04335e7	1.94146
$645$	−3.61346e6	−0.341998
$646$	−187994.	−0.0177240
$647$	6.12646e6	0.575372	0.287686	−	0.957725i	$-0.407114\pi$
$647$	6.12646e6	0.575372	0.287686	+	0.957725i	$0.407114\pi$
$648$	277863.	0.0259952
$649$	−1.67246e7	−1.55863
$650$	−33983.7	−0.00315491
$651$	1.16521e7	1.07758
$652$	−1.50321e7	−1.38484
$653$	123465.	0.0113308	0.00566541	−	0.999984i	$-0.498197\pi$
$653$	123465.	0.0113308	0.00566541	+	0.999984i	$0.498197\pi$
$654$	−1.00800e6	−0.0921540
$655$	1.50429e7	1.37002
$656$	−2.81664e6	−0.255548
$657$	1.55076e6	0.140162
$658$	−3.03198e6	−0.273000
$659$	9.51112e6	0.853136	0.426568	−	0.904456i	$-0.359722\pi$
$659$	9.51112e6	0.853136	0.426568	+	0.904456i	$0.359722\pi$
$660$	−7.78093e6	−0.695299
$661$	−4.93824e6	−0.439611	−0.219806	−	0.975544i	$-0.570542\pi$
$661$	−4.93824e6	−0.439611	−0.219806	+	0.975544i	$0.570542\pi$
$662$	−802995.	−0.0712144
$663$	−645333.	−0.0570165
$664$	−728768.	−0.0641459
$665$	1.22736e7	1.07626
$666$	−793822.	−0.0693486
$667$	1.73225e7	1.50763
$668$	−1.43754e6	−0.124646
$669$	1.26359e7	1.09155
$670$	−767782.	−0.0660771
$671$	−1.01747e7	−0.872400
$672$	−3.12355e6	−0.266824
$673$	−1.95900e7	−1.66724	−0.833618	−	0.552341i	$-0.813735\pi$
$673$	−1.95900e7	−1.66724	−0.833618	+	0.552341i	$0.813735\pi$
$674$	382298.	0.0324155
$675$	118024.	0.00997036
$676$	8.58519e6	0.722576
$677$	−8.89408e6	−0.745812	−0.372906	−	0.927869i	$-0.621639\pi$
$677$	−8.89408e6	−0.745812	−0.372906	+	0.927869i	$0.621639\pi$
$678$	775571.	0.0647959
$679$	−1.17981e7	−0.982061
$680$	552680.	0.0458354
$681$	−1.58970e6	−0.131355
$682$	2.38682e6	0.196498
$683$	1.70001e7	1.39444	0.697219	−	0.716858i	$-0.254421\pi$
$683$	1.70001e7	1.39444	0.697219	+	0.716858i	$0.254421\pi$
$684$	3.16800e6	0.258908
$685$	−5.05529e6	−0.411642
$686$	434988.	0.0352913
$687$	868472.	0.0702044
$688$	6.87399e6	0.553653
$689$	5.27176e6	0.423066
$690$	−1.28897e6	−0.103067
$691$	−3.91514e6	−0.311926	−0.155963	−	0.987763i	$-0.549848\pi$
$691$	−3.91514e6	−0.311926	−0.155963	+	0.987763i	$0.549848\pi$
$692$	−2.66791e6	−0.211790
$693$	−6.68590e6	−0.528843
$694$	60102.7	0.00473691
$695$	−1.09909e7	−0.863124
$696$	−1.76122e6	−0.137813
$697$	653174.	0.0509269
$698$	1.94518e6	0.151120
$699$	8.39813e6	0.650114
$700$	−882440.	−0.0680675
$701$	1.05318e7	0.809479	0.404740	−	0.914432i	$-0.367362\pi$
$701$	1.05318e7	0.809479	0.404740	+	0.914432i	$0.367362\pi$
$702$	−153023.	−0.0117196
$703$	−1.82286e7	−1.39112
$704$	1.43703e7	1.09279
$705$	−1.35924e7	−1.02997
$706$	469706.	0.0354662
$707$	1.92350e7	1.44725
$708$	−9.93953e6	−0.745217
$709$	2.18709e7	1.63399	0.816996	−	0.576643i	$-0.195638\pi$
$709$	2.18709e7	1.63399	0.816996	+	0.576643i	$0.195638\pi$
$710$	2.90378e6	0.216181
$711$	−3.77242e6	−0.279863
$712$	−1.78761e6	−0.132151
$713$	−2.80997e7	−2.07004
$714$	235791.	0.0173094
$715$	8.63038e6	0.631342
$716$	1.83098e7	1.33475
$717$	3.40567e6	0.247403
$718$	1.16383e6	0.0842517
$719$	−1.49134e7	−1.07586	−0.537930	−	0.842989i	$-0.680794\pi$
$719$	−1.49134e7	−1.07586	−0.537930	+	0.842989i	$0.680794\pi$
$720$	−4.55827e6	−0.327694
$721$	−1.83246e6	−0.131280
$722$	626328.	0.0447155
$723$	−8.64465e6	−0.615038
$724$	−1.13460e7	−0.804446
$725$	−748086.	−0.0528575
$726$	−403691.	−0.0284255
$727$	3.59861e6	0.252522	0.126261	−	0.991997i	$-0.459702\pi$
$727$	3.59861e6	0.252522	0.126261	+	0.991997i	$0.459702\pi$
$728$	2.30433e6	0.161145
$729$	531441.	0.0370370
$730$	731405.	0.0507985
$731$	−1.59407e6	−0.110335
$732$	−6.04689e6	−0.417114
$733$	1.88514e7	1.29594	0.647969	−	0.761667i	$-0.275619\pi$
$733$	1.88514e7	1.29594	0.647969	+	0.761667i	$0.275619\pi$
$734$	2.19864e6	0.150631
$735$	−6.72207e6	−0.458971
$736$	7.53261e6	0.512567
$737$	9.60403e6	0.651306
$738$	154882.	0.0104679
$739$	−1.58127e7	−1.06511	−0.532554	−	0.846396i	$-0.678768\pi$
$739$	−1.58127e7	−1.06511	−0.532554	+	0.846396i	$0.678768\pi$
$740$	2.66077e7	1.78619
$741$	−3.51386e6	−0.235093
$742$	−1.92619e6	−0.128437
$743$	−1.78325e7	−1.18506	−0.592529	−	0.805549i	$-0.701870\pi$
$743$	−1.78325e7	−1.18506	−0.592529	+	0.805549i	$0.701870\pi$
$744$	2.85696e6	0.189222
$745$	−1.89217e7	−1.24902
$746$	167391.	0.0110125
$747$	−1.39384e6	−0.0913927
$748$	−3.43253e6	−0.224316
$749$	2.29418e7	1.49425
$750$	−1.01880e6	−0.0661354
$751$	1.40618e7	0.909790	0.454895	−	0.890545i	$-0.349677\pi$
$751$	1.40618e7	0.909790	0.454895	+	0.890545i	$0.349677\pi$
$752$	2.58572e7	1.66739
$753$	−3.07780e6	−0.197812
$754$	969922.	0.0621310
$755$	−8.06914e6	−0.515181
$756$	−3.97347e6	−0.252851
$757$	−6.32231e6	−0.400992	−0.200496	−	0.979695i	$-0.564255\pi$
$757$	−6.32231e6	−0.400992	−0.200496	+	0.979695i	$0.564255\pi$
$758$	−1.76026e6	−0.111277
$759$	1.61234e7	1.01591
$760$	3.00936e6	0.188990
$761$	2.17783e7	1.36321	0.681605	−	0.731720i	$-0.261282\pi$
$761$	2.17783e7	1.36321	0.681605	+	0.731720i	$0.261282\pi$
$762$	−1.04440e6	−0.0651598
$763$	2.90317e7	1.80535
$764$	1.19808e7	0.742596
$765$	1.05705e6	0.0653046
$766$	984706.	0.0606366
$767$	1.10246e7	0.676669
$768$	8.15477e6	0.498895
$769$	−2.37857e6	−0.145044	−0.0725221	−	0.997367i	$-0.523105\pi$
$769$	−2.37857e6	−0.145044	−0.0725221	+	0.997367i	$0.523105\pi$
$770$	−3.15336e6	−0.191667
$771$	1.40986e7	0.854160
$772$	−2.63757e7	−1.59280
$773$	−3.75967e6	−0.226309	−0.113154	−	0.993577i	$-0.536095\pi$
$773$	−3.75967e6	−0.226309	−0.113154	+	0.993577i	$0.536095\pi$
$774$	−377988.	−0.0226791
$775$	1.21351e6	0.0725753
$776$	−2.89277e6	−0.172448
$777$	2.28632e7	1.35858
$778$	155783.	0.00922723
$779$	3.55655e6	0.209984
$780$	5.12909e6	0.301859
$781$	−3.63228e7	−2.13085
$782$	−568624.	−0.0332513
$783$	−3.36850e6	−0.196351
$784$	1.27876e7	0.743017
$785$	1.69081e7	0.979313
$786$	1.57357e6	0.0908508
$787$	−1.03253e7	−0.594247	−0.297123	−	0.954839i	$-0.596027\pi$
$787$	−1.03253e7	−0.594247	−0.297123	+	0.954839i	$0.596027\pi$
$788$	3.33532e6	0.191347
$789$	−5.41361e6	−0.309596
$790$	−1.77924e6	−0.101430
$791$	−2.23375e7	−1.26939
$792$	−1.63931e6	−0.0928641
$793$	6.70704e6	0.378746
$794$	−1.06333e6	−0.0598573
$795$	−8.63513e6	−0.484564
$796$	1.20208e7	0.672437
$797$	2.04825e7	1.14219	0.571093	−	0.820885i	$-0.306520\pi$
$797$	2.04825e7	1.14219	0.571093	+	0.820885i	$0.306520\pi$
$798$	1.28389e6	0.0713708
$799$	−5.99625e6	−0.332287
$800$	−325302.	−0.0179706
$801$	−3.41897e6	−0.188284
$802$	2.72535e6	0.149619
$803$	−9.14901e6	−0.500709
$804$	5.70773e6	0.311403
$805$	3.71240e7	2.01913
$806$	−1.57336e6	−0.0853082
$807$	−1.53565e7	−0.830058
$808$	4.71620e6	0.254134
$809$	−2.99493e7	−1.60885	−0.804425	−	0.594054i	$-0.797526\pi$
$809$	−2.99493e7	−1.60885	−0.804425	+	0.594054i	$0.797526\pi$
$810$	250650.	0.0134232
$811$	−3.59767e7	−1.92074	−0.960371	−	0.278726i	$-0.910088\pi$
$811$	−3.59767e7	−1.92074	−0.960371	+	0.278726i	$0.910088\pi$
$812$	2.51855e7	1.34048
$813$	−6.55850e6	−0.347999
$814$	4.68330e6	0.247737
$815$	−2.73106e7	−1.44025
$816$	−2.01086e6	−0.105720
$817$	−8.67974e6	−0.454937
$818$	1.36504e6	0.0713281
$819$	4.40726e6	0.229593
$820$	−5.19141e6	−0.269619
$821$	2.43500e6	0.126078	0.0630392	−	0.998011i	$-0.479921\pi$
$821$	2.43500e6	0.126078	0.0630392	+	0.998011i	$0.479921\pi$
$822$	−528811.	−0.0272974
$823$	−1.82053e7	−0.936908	−0.468454	−	0.883488i	$-0.655189\pi$
$823$	−1.82053e7	−0.936908	−0.468454	+	0.883488i	$0.655189\pi$
$824$	−449299.	−0.0230525
$825$	−696305.	−0.0356176
$826$	−4.02817e6	−0.205427
$827$	1.97397e7	1.00364	0.501818	−	0.864973i	$-0.332665\pi$
$827$	1.97397e7	1.00364	0.501818	+	0.864973i	$0.332665\pi$
$828$	9.58225e6	0.485726
$829$	1.61334e7	0.815340	0.407670	−	0.913129i	$-0.366341\pi$
$829$	1.61334e7	0.815340	0.407670	+	0.913129i	$0.366341\pi$
$830$	−657395.	−0.0331231
$831$	1.80370e7	0.906070
$832$	−9.47274e6	−0.474425
$833$	−2.96542e6	−0.148072
$834$	−1.14971e6	−0.0572367
$835$	−2.61175e6	−0.129633
$836$	−1.86902e7	−0.924910
$837$	5.46422e6	0.269597
$838$	−1.36807e6	−0.0672974
$839$	−2.19023e7	−1.07420	−0.537100	−	0.843519i	$-0.680480\pi$
$839$	−2.19023e7	−1.07420	−0.537100	+	0.843519i	$0.680480\pi$
$840$	−3.77449e6	−0.184569
$841$	839834.	0.0409453
$842$	−4.32842e6	−0.210402
$843$	7.74563e6	0.375394
$844$	3.15637e7	1.52522
$845$	1.55977e7	0.751484
$846$	−1.42184e6	−0.0683007
$847$	1.16269e7	0.556870
$848$	1.64269e7	0.784449
$849$	−1.70854e7	−0.813497
$850$	24556.5	0.00116579
$851$	−5.51358e7	−2.60982
$852$	−2.15869e7	−1.01880
$853$	2.53408e7	1.19247	0.596236	−	0.802809i	$-0.296662\pi$
$853$	2.53408e7	1.19247	0.596236	+	0.802809i	$0.296662\pi$
$854$	−2.45061e6	−0.114982
$855$	5.75569e6	0.269266
$856$	5.62506e6	0.262387
$857$	7.39048e6	0.343732	0.171866	−	0.985120i	$-0.445020\pi$
$857$	7.39048e6	0.343732	0.171866	+	0.985120i	$0.445020\pi$
$858$	902785.	0.0418665
$859$	2.55693e7	1.18232	0.591161	−	0.806554i	$-0.298670\pi$
$859$	2.55693e7	1.18232	0.591161	+	0.806554i	$0.298670\pi$
$860$	1.26696e7	0.584139
$861$	−4.46081e6	−0.205072
$862$	838310.	0.0384270
$863$	6.09525e6	0.278590	0.139295	−	0.990251i	$-0.455516\pi$
$863$	6.09525e6	0.278590	0.139295	+	0.990251i	$0.455516\pi$
$864$	−1.46478e6	−0.0667556
$865$	−4.84711e6	−0.220264
$866$	−4.73635e6	−0.214609
$867$	−1.23124e7	−0.556282
$868$	−4.08548e7	−1.84053
$869$	2.22561e7	0.999770
$870$	−1.58873e6	−0.0711626
$871$	−6.33085e6	−0.282759
$872$	7.11824e6	0.317016
$873$	−5.53270e6	−0.245698
$874$	−3.09617e6	−0.137103
$875$	2.93427e7	1.29563
$876$	−5.43731e6	−0.239400
$877$	3.67312e7	1.61263	0.806317	−	0.591484i	$-0.201458\pi$
$877$	3.67312e7	1.61263	0.806317	+	0.591484i	$0.201458\pi$
$878$	−502814.	−0.0220126
$879$	−6.24996e6	−0.272838
$880$	2.68924e7	1.17064
$881$	4.31502e6	0.187302	0.0936510	−	0.995605i	$-0.470146\pi$
$881$	4.31502e6	0.187302	0.0936510	+	0.995605i	$0.470146\pi$
$882$	−703166.	−0.0304359
$883$	2.80880e7	1.21233	0.606163	−	0.795340i	$-0.292708\pi$
$883$	2.80880e7	1.21233	0.606163	+	0.795340i	$0.292708\pi$
$884$	2.26268e6	0.0973851
$885$	−1.80583e7	−0.775031
$886$	293538.	0.0125626
$887$	2.66395e7	1.13689	0.568443	−	0.822723i	$-0.307546\pi$
$887$	2.66395e7	1.13689	0.568443	+	0.822723i	$0.307546\pi$
$888$	5.60579e6	0.238564
$889$	3.00802e7	1.27652
$890$	−1.61253e6	−0.0682391
$891$	−3.13534e6	−0.132309
$892$	−4.43043e7	−1.86438
$893$	−3.26498e7	−1.37010
$894$	−1.97931e6	−0.0828267
$895$	3.32655e7	1.38815
$896$	1.45671e7	0.606181
$897$	−1.06284e7	−0.441047
$898$	−1.94621e6	−0.0805377
$899$	−3.46345e7	−1.42926
$900$	−413818.	−0.0170295
$901$	−3.80936e6	−0.156329
$902$	−913755.	−0.0373950
$903$	1.08866e7	0.444295
$904$	−5.47691e6	−0.222902
$905$	−2.06136e7	−0.836630
$906$	−844077.	−0.0341634
$907$	−1.62967e7	−0.657781	−0.328890	−	0.944368i	$-0.606675\pi$
$907$	−1.62967e7	−0.657781	−0.328890	+	0.944368i	$0.606675\pi$
$908$	5.57384e6	0.224357
$909$	9.02019e6	0.362081
$910$	2.07865e6	0.0832105
$911$	4.43543e7	1.77068	0.885340	−	0.464945i	$-0.153926\pi$
$911$	4.43543e7	1.77068	0.885340	+	0.464945i	$0.153926\pi$
$912$	−1.09492e7	−0.435909
$913$	8.22322e6	0.326486
$914$	1.17979e6	0.0467130
$915$	−1.09861e7	−0.433801
$916$	−3.04505e6	−0.119910
$917$	−4.53209e7	−1.77981
$918$	110574.	0.00433057
$919$	−1.75918e7	−0.687103	−0.343551	−	0.939134i	$-0.611630\pi$
$919$	−1.75918e7	−0.687103	−0.343551	+	0.939134i	$0.611630\pi$
$920$	9.10239e6	0.354557
$921$	1.62070e7	0.629585
$922$	−4.45291e6	−0.172511
$923$	2.39435e7	0.925090
$924$	2.34422e7	0.903273
$925$	2.38109e6	0.0915001
$926$	−4.89286e6	−0.187515
$927$	−859329.	−0.0328443
$928$	9.28439e6	0.353902
$929$	−2.32970e7	−0.885648	−0.442824	−	0.896609i	$-0.646023\pi$
$929$	−2.32970e7	−0.885648	−0.442824	+	0.896609i	$0.646023\pi$
$930$	2.57716e6	0.0977088
$931$	−1.61468e7	−0.610538
$932$	−2.94457e7	−1.11041
$933$	−1.35397e7	−0.509219
$934$	−2.20830e6	−0.0828305
$935$	−6.23629e6	−0.233291
$936$	1.08061e6	0.0403162
$937$	50838.9	0.00189168	0.000945839	−	1.00000i	$-0.499699\pi$
$937$	50838.9	0.00189168	0.000945839		1.00000i	$0.499699\pi$
$938$	2.31316e6	0.0858417
$939$	5.14036e6	0.190252
$940$	4.76580e7	1.75920
$941$	1.25435e7	0.461792	0.230896	−	0.972978i	$-0.425834\pi$
$941$	1.25435e7	0.461792	0.230896	+	0.972978i	$0.425834\pi$
$942$	1.76868e6	0.0649416
$943$	1.07575e7	0.393942
$944$	3.43529e7	1.25468
$945$	−7.21907e6	−0.262967
$946$	2.23001e6	0.0810175
$947$	4.66206e7	1.68929	0.844643	−	0.535331i	$-0.179813\pi$
$947$	4.66206e7	1.68929	0.844643	+	0.535331i	$0.179813\pi$
$948$	1.32269e7	0.478012
$949$	6.03091e6	0.217379
$950$	133711.	0.00480682
$951$	2.34664e7	0.841385
$952$	−1.66510e6	−0.0595455
$953$	−2.50447e7	−0.893270	−0.446635	−	0.894716i	$-0.647378\pi$
$953$	−2.50447e7	−0.893270	−0.446635	+	0.894716i	$0.647378\pi$
$954$	−903282.	−0.0321331
$955$	2.17670e7	0.772306
$956$	−1.19410e7	−0.422568
$957$	1.98731e7	0.701432
$958$	−3.64372e6	−0.128272
$959$	1.52305e7	0.534770
$960$	1.55163e7	0.543389
$961$	2.75533e7	0.962423
$962$	−3.08717e6	−0.107553
$963$	1.07585e7	0.373840
$964$	3.03101e7	1.05050
$965$	−4.79199e7	−1.65652
$966$	3.88338e6	0.133896
$967$	−4.56526e7	−1.57000	−0.785000	−	0.619496i	$-0.787337\pi$
$967$	−4.56526e7	−1.57000	−0.785000	+	0.619496i	$0.787337\pi$
$968$	2.85077e6	0.0977855
$969$	2.53910e6	0.0868703
$970$	−2.60946e6	−0.0890473
$971$	−4.83551e7	−1.64586	−0.822932	−	0.568140i	$-0.807663\pi$
$971$	−4.83551e7	−1.64586	−0.822932	+	0.568140i	$0.807663\pi$
$972$	−1.86335e6	−0.0632599
$973$	3.31133e7	1.12130
$974$	58527.7	0.00197681
$975$	458995.	0.0154631
$976$	2.08992e7	0.702271
$977$	2.90148e7	0.972487	0.486244	−	0.873823i	$-0.338367\pi$
$977$	2.90148e7	0.972487	0.486244	+	0.873823i	$0.338367\pi$
$978$	−2.85684e6	−0.0955078
$979$	2.01709e7	0.672617
$980$	2.35691e7	0.783930
$981$	1.36143e7	0.451672
$982$	5.47874e6	0.181302
$983$	−3.75809e7	−1.24046	−0.620231	−	0.784419i	$-0.712961\pi$
$983$	−3.75809e7	−1.24046	−0.620231	+	0.784419i	$0.712961\pi$
$984$	−1.09374e6	−0.0360103
$985$	6.05967e6	0.199002
$986$	−700863.	−0.0229583
$987$	4.09510e7	1.33805
$988$	1.23204e7	0.401542
$989$	−2.62536e7	−0.853489
$990$	−1.47876e6	−0.0479523
$991$	−1.74425e6	−0.0564187	−0.0282094	−	0.999602i	$-0.508981\pi$
$991$	−1.74425e6	−0.0564187	−0.0282094	+	0.999602i	$0.508981\pi$
$992$	−1.50607e7	−0.485921
$993$	1.08455e7	0.349041
$994$	−8.74845e6	−0.280844
$995$	2.18397e7	0.699339
$996$	4.88711e6	0.156100
$997$	1.17141e7	0.373224	0.186612	−	0.982434i	$-0.440249\pi$
$997$	1.17141e7	0.373224	0.186612	+	0.982434i	$0.440249\pi$
$998$	4.79994e6	0.152549
$999$	1.07216e7	0.339897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.d.1.11	✓	25
3.2	odd	2		927.6.a.f.1.15		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.d.1.11	✓	25	1.1	even	1	trivial
927.6.a.f.1.15		25	3.2	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:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	309.a (trivial)

\(f(q)\)	\(=\)	\(q-0.666354 q^{2} +9.00000 q^{3} -31.5560 q^{4} -57.3315 q^{5} -5.99719 q^{6} +172.727 q^{7} +42.3508 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-0.666354 q^{2} +9.00000 q^{3} -31.5560 q^{4} -57.3315 q^{5} -5.99719 q^{6} +172.727 q^{7} +42.3508 q^{8} +81.0000 q^{9} +38.2031 q^{10} -477.875 q^{11} -284.004 q^{12} +315.009 q^{13} -115.097 q^{14} -515.983 q^{15} +981.570 q^{16} -227.624 q^{17} -53.9747 q^{18} -1239.42 q^{19} +1809.15 q^{20} +1554.55 q^{21} +318.434 q^{22} -3748.88 q^{23} +381.157 q^{24} +161.898 q^{25} -209.907 q^{26} +729.000 q^{27} -5450.58 q^{28} -4620.71 q^{29} +343.828 q^{30} +7495.50 q^{31} -2009.30 q^{32} -4300.87 q^{33} +151.678 q^{34} -9902.71 q^{35} -2556.03 q^{36} +14707.3 q^{37} +825.894 q^{38} +2835.08 q^{39} -2428.03 q^{40} -2869.53 q^{41} -1035.88 q^{42} +7003.05 q^{43} +15079.8 q^{44} -4643.85 q^{45} +2498.08 q^{46} +26342.7 q^{47} +8834.13 q^{48} +13027.7 q^{49} -107.882 q^{50} -2048.62 q^{51} -9940.41 q^{52} +16735.3 q^{53} -485.772 q^{54} +27397.3 q^{55} +7315.13 q^{56} -11154.8 q^{57} +3079.03 q^{58} +34997.9 q^{59} +16282.4 q^{60} +21291.6 q^{61} -4994.66 q^{62} +13990.9 q^{63} -30071.4 q^{64} -18059.9 q^{65} +2865.90 q^{66} -20097.4 q^{67} +7182.91 q^{68} -33739.9 q^{69} +6598.71 q^{70} +76009.0 q^{71} +3430.41 q^{72} +19145.2 q^{73} -9800.27 q^{74} +1457.09 q^{75} +39111.2 q^{76} -82542.0 q^{77} -1889.17 q^{78} -46573.1 q^{79} -56274.9 q^{80} +6561.00 q^{81} +1912.12 q^{82} -17207.9 q^{83} -49055.2 q^{84} +13050.0 q^{85} -4666.51 q^{86} -41586.4 q^{87} -20238.4 q^{88} -42209.5 q^{89} +3094.45 q^{90} +54410.6 q^{91} +118299. q^{92} +67459.5 q^{93} -17553.6 q^{94} +71057.9 q^{95} -18083.7 q^{96} -68304.9 q^{97} -8681.06 q^{98} -38707.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9}+O(q^{10}) \) 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9} + 693 q^{10} + 1470 q^{11} + 4374 q^{12} + 2515 q^{13} + 254 q^{14} + 423 q^{15} + 11542 q^{16} + 880 q^{17} + 1134 q^{18} + 7412 q^{19} + 1927 q^{20} + 3618 q^{21} + 5461 q^{22} + 5567 q^{23} + 3078 q^{24} + 31584 q^{25} + 18502 q^{26} + 18225 q^{27} + 25011 q^{28} + 17230 q^{29} + 6237 q^{30} + 22821 q^{31} + 50233 q^{32} + 13230 q^{33} + 38342 q^{34} + 30664 q^{35} + 39366 q^{36} + 13342 q^{37} + 25860 q^{38} + 22635 q^{39} + 40701 q^{40} + 36374 q^{41} + 2286 q^{42} + 48371 q^{43} - 4133 q^{44} + 3807 q^{45} + 30489 q^{46} + 17740 q^{47} + 103878 q^{48} + 119201 q^{49} - 9505 q^{50} + 7920 q^{51} + 50699 q^{52} - 52204 q^{53} + 10206 q^{54} + 90638 q^{55} - 80285 q^{56} + 66708 q^{57} + 15313 q^{58} + 34099 q^{59} + 17343 q^{60} + 71175 q^{61} - 92130 q^{62} + 32562 q^{63} + 289374 q^{64} - 32899 q^{65} + 49149 q^{66} + 85201 q^{67} - 41169 q^{68} + 50103 q^{69} - 92312 q^{70} + 102652 q^{71} + 27702 q^{72} + 186396 q^{73} - 258113 q^{74} + 284256 q^{75} + 148369 q^{76} - 109016 q^{77} + 166518 q^{78} + 210994 q^{79} + 17955 q^{80} + 164025 q^{81} + 635103 q^{82} + 68429 q^{83} + 225099 q^{84} + 375692 q^{85} + 360833 q^{86} + 155070 q^{87} + 556985 q^{88} + 163508 q^{89} + 56133 q^{90} + 591882 q^{91} + 388500 q^{92} + 205389 q^{93} + 205288 q^{94} + 87988 q^{95} + 452097 q^{96} + 385683 q^{97} - 61147 q^{98} + 119070 q^{99}+O(q^{100}) \) 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9 + 693 * q^10 + 1470 * q^11 + 4374 * q^12 + 2515 * q^13 + 254 * q^14 + 423 * q^15 + 11542 * q^16 + 880 * q^17 + 1134 * q^18 + 7412 * q^19 + 1927 * q^20 + 3618 * q^21 + 5461 * q^22 + 5567 * q^23 + 3078 * q^24 + 31584 * q^25 + 18502 * q^26 + 18225 * q^27 + 25011 * q^28 + 17230 * q^29 + 6237 * q^30 + 22821 * q^31 + 50233 * q^32 + 13230 * q^33 + 38342 * q^34 + 30664 * q^35 + 39366 * q^36 + 13342 * q^37 + 25860 * q^38 + 22635 * q^39 + 40701 * q^40 + 36374 * q^41 + 2286 * q^42 + 48371 * q^43 - 4133 * q^44 + 3807 * q^45 + 30489 * q^46 + 17740 * q^47 + 103878 * q^48 + 119201 * q^49 - 9505 * q^50 + 7920 * q^51 + 50699 * q^52 - 52204 * q^53 + 10206 * q^54 + 90638 * q^55 - 80285 * q^56 + 66708 * q^57 + 15313 * q^58 + 34099 * q^59 + 17343 * q^60 + 71175 * q^61 - 92130 * q^62 + 32562 * q^63 + 289374 * q^64 - 32899 * q^65 + 49149 * q^66 + 85201 * q^67 - 41169 * q^68 + 50103 * q^69 - 92312 * q^70 + 102652 * q^71 + 27702 * q^72 + 186396 * q^73 - 258113 * q^74 + 284256 * q^75 + 148369 * q^76 - 109016 * q^77 + 166518 * q^78 + 210994 * q^79 + 17955 * q^80 + 164025 * q^81 + 635103 * q^82 + 68429 * q^83 + 225099 * q^84 + 375692 * q^85 + 360833 * q^86 + 155070 * q^87 + 556985 * q^88 + 163508 * q^89 + 56133 * q^90 + 591882 * q^91 + 388500 * q^92 + 205389 * q^93 + 205288 * q^94 + 87988 * q^95 + 452097 * q^96 + 385683 * q^97 - 61147 * q^98 + 119070 * q^99

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