LMFDB - Embedded newform 583.6.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [583,6,Mod(1,583)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(583, 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("583.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 583 = 11 \cdot 53 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	583.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:	$93.5037669510$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	583.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.9473 q^{2} +10.7847 q^{3} +87.8440 q^{4} +102.528 q^{5} -118.063 q^{6} +88.8850 q^{7} -611.342 q^{8} -126.691 q^{9} +O(q^{10})$	\(q-10.9473 q^{2} +10.7847 q^{3} +87.8440 q^{4} +102.528 q^{5} -118.063 q^{6} +88.8850 q^{7} -611.342 q^{8} -126.691 q^{9} -1122.41 q^{10} -121.000 q^{11} +947.368 q^{12} +38.6873 q^{13} -973.054 q^{14} +1105.73 q^{15} +3881.55 q^{16} -2069.44 q^{17} +1386.93 q^{18} -1560.19 q^{19} +9006.48 q^{20} +958.596 q^{21} +1324.63 q^{22} +2496.10 q^{23} -6593.12 q^{24} +7387.03 q^{25} -423.523 q^{26} -3986.99 q^{27} +7808.01 q^{28} +2001.41 q^{29} -12104.8 q^{30} -5230.84 q^{31} -22929.7 q^{32} -1304.95 q^{33} +22654.9 q^{34} +9113.23 q^{35} -11129.0 q^{36} +2996.46 q^{37} +17079.9 q^{38} +417.230 q^{39} -62679.8 q^{40} -17917.8 q^{41} -10494.1 q^{42} -10791.7 q^{43} -10629.1 q^{44} -12989.4 q^{45} -27325.6 q^{46} -11196.2 q^{47} +41861.3 q^{48} -8906.45 q^{49} -80868.3 q^{50} -22318.3 q^{51} +3398.45 q^{52} -2809.00 q^{53} +43646.9 q^{54} -12405.9 q^{55} -54339.2 q^{56} -16826.2 q^{57} -21910.1 q^{58} -10680.9 q^{59} +97132.0 q^{60} +44278.6 q^{61} +57263.8 q^{62} -11260.9 q^{63} +126809. q^{64} +3966.54 q^{65} +14285.7 q^{66} -2334.75 q^{67} -181788. q^{68} +26919.6 q^{69} -99765.5 q^{70} -42552.5 q^{71} +77451.5 q^{72} -72653.3 q^{73} -32803.2 q^{74} +79666.7 q^{75} -137053. q^{76} -10755.1 q^{77} -4567.55 q^{78} +97712.5 q^{79} +397969. q^{80} -12212.5 q^{81} +196152. q^{82} +31448.0 q^{83} +84206.9 q^{84} -212176. q^{85} +118140. q^{86} +21584.6 q^{87} +73972.4 q^{88} -69152.2 q^{89} +142199. q^{90} +3438.72 q^{91} +219267. q^{92} -56412.9 q^{93} +122569. q^{94} -159964. q^{95} -247289. q^{96} -72964.7 q^{97} +97501.8 q^{98} +15329.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9}+O(q^{10}) $ 54 * q - 16 * q^2 + 906 * q^4 - 225 * q^5 - 197 * q^6 - 341 * q^7 - 1152 * q^8 + 4240 * q^9	\( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9} - 233 q^{10} - 6534 q^{11} - 327 q^{12} - 1455 q^{13} + 2254 q^{14} - 694 q^{15} + 16610 q^{16} - 9275 q^{17} - 6797 q^{18} - 2515 q^{19} - 6840 q^{20} - 4744 q^{21} + 1936 q^{22} - 6307 q^{23} - 5681 q^{24} + 26923 q^{25} - 5196 q^{26} - 5190 q^{27} - 36405 q^{28} - 8356 q^{29} - 28719 q^{30} - 4357 q^{31} - 68580 q^{32} + 9406 q^{34} - 3747 q^{35} + 38059 q^{36} - 25798 q^{37} - 32169 q^{38} - 28347 q^{39} - 15014 q^{40} - 89685 q^{41} - 103207 q^{42} - 26640 q^{43} - 109626 q^{44} - 66786 q^{45} - 28271 q^{46} - 26237 q^{47} - 20371 q^{48} + 132327 q^{49} - 189646 q^{50} + 10856 q^{51} - 179789 q^{52} - 151686 q^{53} - 167182 q^{54} + 27225 q^{55} + 24845 q^{56} - 33857 q^{57} - 31384 q^{58} - 49035 q^{59} - 183481 q^{60} - 101718 q^{61} - 103315 q^{62} - 214794 q^{63} + 154912 q^{64} - 55703 q^{65} + 23837 q^{66} + 105905 q^{67} - 267681 q^{68} - 56033 q^{69} - 90034 q^{70} - 107016 q^{71} - 580829 q^{72} - 161641 q^{73} - 259552 q^{74} - 69519 q^{75} - 240846 q^{76} + 41261 q^{77} - 65716 q^{78} - 35649 q^{79} - 279887 q^{80} + 316682 q^{81} + 206196 q^{82} - 326347 q^{83} - 29955 q^{84} - 189486 q^{85} - 444656 q^{86} - 222331 q^{87} + 139392 q^{88} - 633400 q^{89} + 110940 q^{90} - 25954 q^{91} + 18304 q^{92} - 191747 q^{93} - 62405 q^{94} - 515756 q^{95} - 527591 q^{96} - 405641 q^{97} - 919621 q^{98} - 513040 q^{99}+O(q^{100}) \) 54 * q - 16 * q^2 + 906 * q^4 - 225 * q^5 - 197 * q^6 - 341 * q^7 - 1152 * q^8 + 4240 * q^9 - 233 * q^10 - 6534 * q^11 - 327 * q^12 - 1455 * q^13 + 2254 * q^14 - 694 * q^15 + 16610 * q^16 - 9275 * q^17 - 6797 * q^18 - 2515 * q^19 - 6840 * q^20 - 4744 * q^21 + 1936 * q^22 - 6307 * q^23 - 5681 * q^24 + 26923 * q^25 - 5196 * q^26 - 5190 * q^27 - 36405 * q^28 - 8356 * q^29 - 28719 * q^30 - 4357 * q^31 - 68580 * q^32 + 9406 * q^34 - 3747 * q^35 + 38059 * q^36 - 25798 * q^37 - 32169 * q^38 - 28347 * q^39 - 15014 * q^40 - 89685 * q^41 - 103207 * q^42 - 26640 * q^43 - 109626 * q^44 - 66786 * q^45 - 28271 * q^46 - 26237 * q^47 - 20371 * q^48 + 132327 * q^49 - 189646 * q^50 + 10856 * q^51 - 179789 * q^52 - 151686 * q^53 - 167182 * q^54 + 27225 * q^55 + 24845 * q^56 - 33857 * q^57 - 31384 * q^58 - 49035 * q^59 - 183481 * q^60 - 101718 * q^61 - 103315 * q^62 - 214794 * q^63 + 154912 * q^64 - 55703 * q^65 + 23837 * q^66 + 105905 * q^67 - 267681 * q^68 - 56033 * q^69 - 90034 * q^70 - 107016 * q^71 - 580829 * q^72 - 161641 * q^73 - 259552 * q^74 - 69519 * q^75 - 240846 * q^76 + 41261 * q^77 - 65716 * q^78 - 35649 * q^79 - 279887 * q^80 + 316682 * q^81 + 206196 * q^82 - 326347 * q^83 - 29955 * q^84 - 189486 * q^85 - 444656 * q^86 - 222331 * q^87 + 139392 * q^88 - 633400 * q^89 + 110940 * q^90 - 25954 * q^91 + 18304 * q^92 - 191747 * q^93 - 62405 * q^94 - 515756 * q^95 - 527591 * q^96 - 405641 * q^97 - 919621 * q^98 - 513040 * 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 $

$2$	−10.9473	−1.93523	−0.967616	−	0.252426i	$-0.918771\pi$
$2$	−10.9473	−1.93523	−0.967616	+	0.252426i	$0.918771\pi$
$3$	10.7847	0.691837	0.345918	−	0.938265i	$-0.387567\pi$
$3$	10.7847	0.691837	0.345918	+	0.938265i	$0.387567\pi$
$4$	87.8440	2.74512
$5$	102.528	1.83408	0.917040	−	0.398795i	$-0.130571\pi$
$5$	102.528	1.83408	0.917040	+	0.398795i	$0.130571\pi$
$6$	−118.063	−1.33887
$7$	88.8850	0.685620	0.342810	−	0.939405i	$-0.388621\pi$
$7$	88.8850	0.685620	0.342810	+	0.939405i	$0.388621\pi$
$8$	−611.342	−3.37722
$9$	−126.691	−0.521362
$10$	−1122.41	−3.54937
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	947.368	1.89918
$13$	38.6873	0.0634907	0.0317454	−	0.999496i	$-0.489893\pi$
$13$	38.6873	0.0634907	0.0317454	+	0.999496i	$0.489893\pi$
$14$	−973.054	−1.32683
$15$	1105.73	1.26888
$16$	3881.55	3.79058
$17$	−2069.44	−1.73673	−0.868363	−	0.495929i	$-0.834828\pi$
$17$	−2069.44	−1.73673	−0.868363	+	0.495929i	$0.834828\pi$
$18$	1386.93	1.00896
$19$	−1560.19	−0.991503	−0.495751	−	0.868464i	$-0.665107\pi$
$19$	−1560.19	−0.991503	−0.495751	+	0.868464i	$0.665107\pi$
$20$	9006.48	5.03478
$21$	958.596	0.474337
$22$	1324.63	0.583494
$23$	2496.10	0.983880	0.491940	−	0.870629i	$-0.336288\pi$
$23$	2496.10	0.983880	0.491940	+	0.870629i	$0.336288\pi$
$24$	−6593.12	−2.33649
$25$	7387.03	2.36385
$26$	−423.523	−0.122869
$27$	−3986.99	−1.05253
$28$	7808.01	1.88211
$29$	2001.41	0.441918	0.220959	−	0.975283i	$-0.429081\pi$
$29$	2001.41	0.441918	0.220959	+	0.975283i	$0.429081\pi$
$30$	−12104.8	−2.45559
$31$	−5230.84	−0.977614	−0.488807	−	0.872392i	$-0.662568\pi$
$31$	−5230.84	−0.977614	−0.488807	+	0.872392i	$0.662568\pi$
$32$	−22929.7	−3.95843
$33$	−1304.95	−0.208597
$34$	22654.9	3.36097
$35$	9113.23	1.25748
$36$	−11129.0	−1.43120
$37$	2996.46	0.359835	0.179918	−	0.983682i	$-0.442417\pi$
$37$	2996.46	0.359835	0.179918	+	0.983682i	$0.442417\pi$
$38$	17079.9	1.91879
$39$	417.230	0.0439252
$40$	−62679.8	−6.19409
$41$	−17917.8	−1.66466	−0.832329	−	0.554282i	$-0.812993\pi$
$41$	−17917.8	−1.66466	−0.832329	+	0.554282i	$0.812993\pi$
$42$	−10494.1	−0.917953
$43$	−10791.7	−0.890059	−0.445030	−	0.895516i	$-0.646807\pi$
$43$	−10791.7	−0.890059	−0.445030	+	0.895516i	$0.646807\pi$
$44$	−10629.1	−0.827686
$45$	−12989.4	−0.956219
$46$	−27325.6	−1.90404
$47$	−11196.2	−0.739310	−0.369655	−	0.929169i	$-0.620524\pi$
$47$	−11196.2	−0.739310	−0.369655	+	0.929169i	$0.620524\pi$
$48$	41861.3	2.62246
$49$	−8906.45	−0.529925
$50$	−80868.3	−4.57460
$51$	−22318.3	−1.20153
$52$	3398.45	0.174290
$53$	−2809.00	−0.137361
$53$	−2809.00	−0.137361
$54$	43646.9	2.03690
$55$	−12405.9	−0.552996
$56$	−54339.2	−2.31549
$57$	−16826.2	−0.685958
$58$	−21910.1	−0.855214
$59$	−10680.9	−0.399463	−0.199731	−	0.979851i	$-0.564007\pi$
$59$	−10680.9	−0.399463	−0.199731	+	0.979851i	$0.564007\pi$
$60$	97132.0	3.48324
$61$	44278.6	1.52359	0.761797	−	0.647816i	$-0.224317\pi$
$61$	44278.6	1.52359	0.761797	+	0.647816i	$0.224317\pi$
$62$	57263.8	1.89191
$63$	−11260.9	−0.357456
$64$	126809.	3.86991
$65$	3966.54	0.116447
$66$	14285.7	0.403683
$67$	−2334.75	−0.0635410	−0.0317705	−	0.999495i	$-0.510115\pi$
$67$	−2334.75	−0.0635410	−0.0317705	+	0.999495i	$0.510115\pi$
$68$	−181788.	−4.76753
$69$	26919.6	0.680684
$70$	−99765.5	−2.43352
$71$	−42552.5	−1.00179	−0.500897	−	0.865507i	$-0.666997\pi$
$71$	−42552.5	−1.00179	−0.500897	+	0.865507i	$0.666997\pi$
$72$	77451.5	1.76075
$73$	−72653.3	−1.59569	−0.797844	−	0.602864i	$-0.794026\pi$
$73$	−72653.3	−1.59569	−0.797844	+	0.602864i	$0.794026\pi$
$74$	−32803.2	−0.696365
$75$	79666.7	1.63540
$76$	−137053.	−2.72180
$77$	−10755.1	−0.206722
$78$	−4567.55	−0.0850055
$79$	97712.5	1.76150	0.880750	−	0.473582i	$-0.157039\pi$
$79$	97712.5	1.76150	0.880750	+	0.473582i	$0.157039\pi$
$80$	397969.	6.95223
$81$	−12212.5	−0.206820
$82$	196152.	3.22150
$83$	31448.0	0.501070	0.250535	−	0.968108i	$-0.419394\pi$
$83$	31448.0	0.501070	0.250535	+	0.968108i	$0.419394\pi$
$84$	84206.9	1.30211
$85$	−212176.	−3.18530
$86$	118140.	1.72247
$87$	21584.6	0.305735
$88$	73972.4	1.01827
$89$	−69152.2	−0.925404	−0.462702	−	0.886514i	$-0.653120\pi$
$89$	−69152.2	−0.925404	−0.462702	+	0.886514i	$0.653120\pi$
$90$	142199.	1.85051
$91$	3438.72	0.0435305
$92$	219267.	2.70087
$93$	−56412.9	−0.676350
$94$	122569.	1.43074
$95$	−159964.	−1.81850
$96$	−247289.	−2.73859
$97$	−72964.7	−0.787378	−0.393689	−	0.919244i	$-0.628801\pi$
$97$	−72964.7	−0.787378	−0.393689	+	0.919244i	$0.628801\pi$
$98$	97501.8	1.02553
$99$	15329.6	0.157196
$100$	648906.	6.48906
$101$	−38378.2	−0.374352	−0.187176	−	0.982326i	$-0.559934\pi$
$101$	−38378.2	−0.374352	−0.187176	+	0.982326i	$0.559934\pi$
$102$	244325.	2.32524
$103$	32521.2	0.302046	0.151023	−	0.988530i	$-0.451743\pi$
$103$	32521.2	0.302046	0.151023	+	0.988530i	$0.451743\pi$
$104$	−23651.2	−0.214422
$105$	98283.1	0.869973
$106$	30751.0	0.265825
$107$	−131007.	−1.10620	−0.553101	−	0.833114i	$-0.686556\pi$
$107$	−131007.	−1.10620	−0.553101	+	0.833114i	$0.686556\pi$
$108$	−350233.	−2.88934
$109$	−206661.	−1.66607	−0.833034	−	0.553221i	$-0.813398\pi$
$109$	−206661.	−1.66607	−0.833034	+	0.553221i	$0.813398\pi$
$110$	135812.	1.07018
$111$	32315.8	0.248947
$112$	345012.	2.59890
$113$	223054.	1.64329	0.821643	−	0.570003i	$-0.193058\pi$
$113$	223054.	1.64329	0.821643	+	0.570003i	$0.193058\pi$
$114$	184201.	1.32749
$115$	255920.	1.80451
$116$	175812.	1.21312
$117$	−4901.33	−0.0331016
$118$	116927.	0.773053
$119$	−183943.	−1.19073
$120$	−675981.	−4.28530
$121$	14641.0	0.0909091
$122$	−484732.	−2.94851
$123$	−193238.	−1.15167
$124$	−459498.	−2.68367
$125$	436979.	2.50141
$126$	123277.	0.691761
$127$	283527.	1.55986	0.779929	−	0.625867i	$-0.215255\pi$
$127$	283527.	1.55986	0.779929	+	0.625867i	$0.215255\pi$
$128$	−654471.	−3.53074
$129$	−116385.	−0.615776
$130$	−43423.0	−0.225352
$131$	−316458.	−1.61116	−0.805579	−	0.592488i	$-0.798146\pi$
$131$	−316458.	−1.61116	−0.805579	+	0.592488i	$0.798146\pi$
$132$	−114632.	−0.572624
$133$	−138678.	−0.679794
$134$	25559.3	0.122967
$135$	−408779.	−1.93043
$136$	1.26514e6	5.86531
$137$	−323789.	−1.47388	−0.736938	−	0.675960i	$-0.763729\pi$
$137$	−323789.	−1.47388	−0.736938	+	0.675960i	$0.763729\pi$
$138$	−294698.	−1.31728
$139$	−129289.	−0.567578	−0.283789	−	0.958887i	$-0.591591\pi$
$139$	−129289.	−0.567578	−0.283789	+	0.958887i	$0.591591\pi$
$140$	800542.	3.45195
$141$	−120747.	−0.511482
$142$	465836.	1.93871
$143$	−4681.17	−0.0191432
$144$	−491758.	−1.97626
$145$	205201.	0.810513
$146$	795359.	3.08803
$147$	−96053.1	−0.366622
$148$	263221.	0.987792
$149$	356272.	1.31467	0.657334	−	0.753599i	$-0.271684\pi$
$149$	356272.	1.31467	0.657334	+	0.753599i	$0.271684\pi$
$150$	−872138.	−3.16488
$151$	−200246.	−0.714698	−0.357349	−	0.933971i	$-0.616319\pi$
$151$	−200246.	−0.714698	−0.357349	+	0.933971i	$0.616319\pi$
$152$	953811.	3.34852
$153$	262180.	0.905463
$154$	117739.	0.400056
$155$	−536309.	−1.79302
$156$	36651.1	0.120580
$157$	−102021.	−0.330323	−0.165162	−	0.986267i	$-0.552815\pi$
$157$	−102021.	−0.330323	−0.165162	+	0.986267i	$0.552815\pi$
$158$	−1.06969e6	−3.40891
$159$	−30294.1	−0.0950311
$160$	−2.35094e6	−7.26009
$161$	221866.	0.674568
$162$	133695.	0.400245
$163$	−253656.	−0.747785	−0.373892	−	0.927472i	$-0.621977\pi$
$163$	−253656.	−0.747785	−0.373892	+	0.927472i	$0.621977\pi$
$164$	−1.57397e6	−4.56969
$165$	−133794.	−0.382583
$166$	−344272.	−0.969687
$167$	397524.	1.10299	0.551496	−	0.834178i	$-0.314057\pi$
$167$	397524.	1.10299	0.551496	+	0.834178i	$0.314057\pi$
$168$	−586030.	−1.60194
$169$	−369796.	−0.995969
$170$	2.32276e6	6.16429
$171$	197662.	0.516932
$172$	−947986.	−2.44332
$173$	−96673.0	−0.245578	−0.122789	−	0.992433i	$-0.539184\pi$
$173$	−96673.0	−0.245578	−0.122789	+	0.992433i	$0.539184\pi$
$174$	−236293.	−0.591669
$175$	656597.	1.62070
$176$	−469668.	−1.14290
$177$	−115190.	−0.276363
$178$	757032.	1.79087
$179$	416218.	0.970932	0.485466	−	0.874256i	$-0.338650\pi$
$179$	416218.	0.970932	0.485466	+	0.874256i	$0.338650\pi$
$180$	−1.14104e6	−2.62494
$181$	493480.	1.11963	0.559813	−	0.828619i	$-0.310873\pi$
$181$	493480.	1.11963	0.559813	+	0.828619i	$0.310873\pi$
$182$	−37644.8	−0.0842417
$183$	477530.	1.05408
$184$	−1.52597e6	−3.32278
$185$	307221.	0.659967
$186$	617571.	1.30889
$187$	250403.	0.523643
$188$	−983520.	−2.02950
$189$	−354384.	−0.721639
$190$	1.75117e6	3.51921
$191$	−173043.	−0.343219	−0.171609	−	0.985165i	$-0.554897\pi$
$191$	−173043.	−0.343219	−0.171609	+	0.985165i	$0.554897\pi$
$192$	1.36760e6	2.67735
$193$	639769.	1.23632	0.618159	−	0.786053i	$-0.287879\pi$
$193$	639769.	1.23632	0.618159	+	0.786053i	$0.287879\pi$
$194$	798768.	1.52376
$195$	42777.8	0.0805624
$196$	−782378.	−1.45471
$197$	−80768.4	−0.148278	−0.0741389	−	0.997248i	$-0.523621\pi$
$197$	−80768.4	−0.148278	−0.0741389	+	0.997248i	$0.523621\pi$
$198$	−167818.	−0.304212
$199$	270162.	0.483606	0.241803	−	0.970325i	$-0.422261\pi$
$199$	270162.	0.483606	0.241803	+	0.970325i	$0.422261\pi$
$200$	−4.51600e6	−7.98324
$201$	−25179.6	−0.0439600
$202$	420138.	0.724459
$203$	177896.	0.302988
$204$	−1.96053e6	−3.29835
$205$	−1.83708e6	−3.05312
$206$	−356020.	−0.584529
$207$	−316233.	−0.512957
$208$	150167.	0.240667
$209$	188783.	0.298949
$210$	−1.07594e6	−1.68360
$211$	91367.6	0.141282	0.0706409	−	0.997502i	$-0.477496\pi$
$211$	91367.6	0.141282	0.0706409	+	0.997502i	$0.477496\pi$
$212$	−246754.	−0.377072
$213$	−458914.	−0.693079
$214$	1.43418e6	2.14076
$215$	−1.10645e6	−1.63244
$216$	2.43742e6	3.55464
$217$	−464944.	−0.670272
$218$	2.26239e6	3.22423
$219$	−783542.	−1.10396
$220$	−1.08978e6	−1.51804
$221$	−80061.3	−0.110266
$222$	−353771.	−0.481771
$223$	316963.	0.426821	0.213411	−	0.976963i	$-0.431543\pi$
$223$	316963.	0.426821	0.213411	+	0.976963i	$0.431543\pi$
$224$	−2.03811e6	−2.71398
$225$	−935870.	−1.23242
$226$	−2.44184e6	−3.18014
$227$	−624931.	−0.804948	−0.402474	−	0.915431i	$-0.631850\pi$
$227$	−624931.	−0.804948	−0.402474	+	0.915431i	$0.631850\pi$
$228$	−1.47808e6	−1.88304
$229$	157035.	0.197883	0.0989415	−	0.995093i	$-0.468454\pi$
$229$	157035.	0.197883	0.0989415	+	0.995093i	$0.468454\pi$
$230$	−2.80164e6	−3.49215
$231$	−115990.	−0.143018
$232$	−1.22355e6	−1.49245
$233$	−95953.4	−0.115790	−0.0578949	−	0.998323i	$-0.518439\pi$
$233$	−95953.4	−0.115790	−0.0578949	+	0.998323i	$0.518439\pi$
$234$	53656.5	0.0640593
$235$	−1.14793e6	−1.35595
$236$	−938249.	−1.09657
$237$	1.05380e6	1.21867
$238$	2.01368e6	2.30435
$239$	−706798.	−0.800388	−0.400194	−	0.916431i	$-0.631057\pi$
$239$	−706798.	−0.800388	−0.400194	+	0.916431i	$0.631057\pi$
$240$	4.29196e6	4.80981
$241$	1.20654e6	1.33813	0.669067	−	0.743202i	$-0.266694\pi$
$241$	1.20654e6	1.33813	0.669067	+	0.743202i	$0.266694\pi$
$242$	−160280.	−0.175930
$243$	837132.	0.909448
$244$	3.88961e6	4.18245
$245$	−913162.	−0.971925
$246$	2.11543e6	2.22875
$247$	−60359.6	−0.0629512
$248$	3.19783e6	3.30162
$249$	339157.	0.346659
$250$	−4.78375e6	−4.84081
$251$	−335725.	−0.336356	−0.168178	−	0.985757i	$-0.553788\pi$
$251$	−335725.	−0.336356	−0.168178	+	0.985757i	$0.553788\pi$
$252$	−989204.	−0.981261
$253$	−302028.	−0.296651
$254$	−3.10386e6	−3.01869
$255$	−2.28825e6	−2.20371
$256$	3.10682e6	2.96289
$257$	−1.61174e6	−1.52216	−0.761082	−	0.648655i	$-0.775332\pi$
$257$	−1.61174e6	−1.52216	−0.761082	+	0.648655i	$0.775332\pi$
$258$	1.27410e6	1.19167
$259$	266340.	0.246710
$260$	348437.	0.319662
$261$	−253561.	−0.230399
$262$	3.46437e6	3.11797
$263$	−1.21427e6	−1.08250	−0.541250	−	0.840862i	$-0.682049\pi$
$263$	−1.21427e6	−1.08250	−0.541250	+	0.840862i	$0.682049\pi$
$264$	797768.	0.704477
$265$	−288002.	−0.251930
$266$	1.51815e6	1.31556
$267$	−745784.	−0.640228
$268$	−205094.	−0.174428
$269$	1.94066e6	1.63519	0.817595	−	0.575794i	$-0.195307\pi$
$269$	1.94066e6	1.63519	0.817595	+	0.575794i	$0.195307\pi$
$270$	4.47504e6	3.73583
$271$	702867.	0.581366	0.290683	−	0.956819i	$-0.406117\pi$
$271$	702867.	0.581366	0.290683	+	0.956819i	$0.406117\pi$
$272$	−8.03266e6	−6.58320
$273$	37085.5	0.0301160
$274$	3.54463e6	2.85229
$275$	−893831.	−0.712728
$276$	2.36472e6	1.86856
$277$	−1.62238e6	−1.27044	−0.635219	−	0.772332i	$-0.719090\pi$
$277$	−1.62238e6	−1.27044	−0.635219	+	0.772332i	$0.719090\pi$
$278$	1.41537e6	1.09839
$279$	662700.	0.509691
$280$	−5.57130e6	−4.24680
$281$	1.85351e6	1.40033	0.700165	−	0.713981i	$-0.253110\pi$
$281$	1.85351e6	1.40033	0.700165	+	0.713981i	$0.253110\pi$
$282$	1.32186e6	0.989836
$283$	1.65307e6	1.22694	0.613472	−	0.789716i	$-0.289772\pi$
$283$	1.65307e6	1.22694	0.613472	+	0.789716i	$0.289772\pi$
$284$	−3.73798e6	−2.75005
$285$	−1.72516e6	−1.25810
$286$	51246.2	0.0370465
$287$	−1.59262e6	−1.14132
$288$	2.90498e6	2.06378
$289$	2.86274e6	2.01622
$290$	−2.24641e6	−1.56853
$291$	−786900.	−0.544737
$292$	−6.38215e6	−4.38036
$293$	1.67016e6	1.13655	0.568274	−	0.822839i	$-0.307611\pi$
$293$	1.67016e6	1.13655	0.568274	+	0.822839i	$0.307611\pi$
$294$	1.05152e6	0.709498
$295$	−1.09509e6	−0.732647
$296$	−1.83186e6	−1.21524
$297$	482426.	0.317351
$298$	−3.90023e6	−2.54419
$299$	96567.3	0.0624672
$300$	6.99824e6	4.48937
$301$	−959221.	−0.610243
$302$	2.19216e6	1.38311
$303$	−413896.	−0.258991
$304$	−6.05597e6	−3.75837
$305$	4.53981e6	2.79439
$306$	−2.87017e6	−1.75228
$307$	99790.9	0.0604289	0.0302145	−	0.999543i	$-0.490381\pi$
$307$	99790.9	0.0604289	0.0302145	+	0.999543i	$0.490381\pi$
$308$	−944770.	−0.567478
$309$	350730.	0.208967
$310$	5.87115e6	3.46992
$311$	−415381.	−0.243526	−0.121763	−	0.992559i	$-0.538855\pi$
$311$	−415381.	−0.243526	−0.121763	+	0.992559i	$0.538855\pi$
$312$	−255070.	−0.148345
$313$	−2.14019e6	−1.23479	−0.617393	−	0.786655i	$-0.711811\pi$
$313$	−2.14019e6	−1.23479	−0.617393	+	0.786655i	$0.711811\pi$
$314$	1.11685e6	0.639252
$315$	−1.15456e6	−0.655603
$316$	8.58346e6	4.83553
$317$	1.24280e6	0.694632	0.347316	−	0.937748i	$-0.387093\pi$
$317$	1.24280e6	0.694632	0.347316	+	0.937748i	$0.387093\pi$
$318$	331640.	0.183907
$319$	−242171.	−0.133243
$320$	1.30015e7	7.09772
$321$	−1.41287e6	−0.765312
$322$	−2.42884e6	−1.30545
$323$	3.22873e6	1.72197
$324$	−1.07280e6	−0.567747
$325$	285785.	0.150083
$326$	2.77686e6	1.44714
$327$	−2.22877e6	−1.15265
$328$	1.09539e7	5.62192
$329$	−995176.	−0.506886
$330$	1.46468e6	0.740387
$331$	1.66980e6	0.837713	0.418857	−	0.908052i	$-0.362431\pi$
$331$	1.66980e6	0.837713	0.418857	+	0.908052i	$0.362431\pi$
$332$	2.76252e6	1.37550
$333$	−379624.	−0.187604
$334$	−4.35183e6	−2.13455
$335$	−239378.	−0.116539
$336$	3.72084e6	1.79801
$337$	884940.	0.424462	0.212231	−	0.977219i	$-0.431927\pi$
$337$	884940.	0.424462	0.212231	+	0.977219i	$0.431927\pi$
$338$	4.04828e6	1.92743
$339$	2.40556e6	1.13689
$340$	−1.86384e7	−8.74403
$341$	632932.	0.294762
$342$	−2.16387e6	−1.00038
$343$	−2.28554e6	−1.04895
$344$	6.59742e6	3.00593
$345$	2.76002e6	1.24843
$346$	1.05831e6	0.475251
$347$	−3.51480e6	−1.56703	−0.783514	−	0.621374i	$-0.786575\pi$
$347$	−3.51480e6	−1.56703	−0.783514	+	0.621374i	$0.786575\pi$
$348$	1.89608e6	0.839281
$349$	3.72683e6	1.63786	0.818928	−	0.573896i	$-0.194569\pi$
$349$	3.72683e6	1.63786	0.818928	+	0.573896i	$0.194569\pi$
$350$	−7.18798e6	−3.13644
$351$	−154246.	−0.0668261
$352$	2.77449e6	1.19351
$353$	−964679.	−0.412046	−0.206023	−	0.978547i	$-0.566052\pi$
$353$	−964679.	−0.412046	−0.206023	+	0.978547i	$0.566052\pi$
$354$	1.26102e6	0.534827
$355$	−4.36283e6	−1.83737
$356$	−6.07461e6	−2.54035
$357$	−1.98376e6	−0.823794
$358$	−4.55648e6	−1.87898
$359$	−1.62387e6	−0.664992	−0.332496	−	0.943105i	$-0.607891\pi$
$359$	−1.62387e6	−0.664992	−0.332496	+	0.943105i	$0.607891\pi$
$360$	7.94096e6	3.22936
$361$	−41900.3	−0.0169219
$362$	−5.40229e6	−2.16674
$363$	157898.	0.0628943
$364$	302071.	0.119497
$365$	−7.44901e6	−2.92662
$366$	−5.22768e6	−2.03989
$367$	4.55475e6	1.76522	0.882612	−	0.470103i	$-0.155783\pi$
$367$	4.55475e6	1.76522	0.882612	+	0.470103i	$0.155783\pi$
$368$	9.68874e6	3.72948
$369$	2.27002e6	0.867889
$370$	−3.36325e6	−1.27719
$371$	−249678.	−0.0941772
$372$	−4.95553e6	−1.85666
$373$	−428804.	−0.159583	−0.0797916	−	0.996812i	$-0.525425\pi$
$373$	−428804.	−0.159583	−0.0797916	+	0.996812i	$0.525425\pi$
$374$	−2.74124e6	−1.01337
$375$	4.71267e6	1.73057
$376$	6.84472e6	2.49681
$377$	77429.3	0.0280577
$378$	3.87956e6	1.39654
$379$	1.76417e6	0.630875	0.315437	−	0.948946i	$-0.397849\pi$
$379$	1.76417e6	0.630875	0.315437	+	0.948946i	$0.397849\pi$
$380$	−1.40518e7	−4.99200
$381$	3.05775e6	1.07917
$382$	1.89436e6	0.664208
$383$	−2.92211e6	−1.01789	−0.508944	−	0.860800i	$-0.669964\pi$
$383$	−2.92211e6	−1.01789	−0.508944	+	0.860800i	$0.669964\pi$
$384$	−7.05825e6	−2.44270
$385$	−1.10270e6	−0.379145
$386$	−7.00376e6	−2.39256
$387$	1.36721e6	0.464043
$388$	−6.40951e6	−2.16145
$389$	−2.73521e6	−0.916467	−0.458233	−	0.888832i	$-0.651518\pi$
$389$	−2.73521e6	−0.916467	−0.458233	+	0.888832i	$0.651518\pi$
$390$	−468303.	−0.155907
$391$	−5.16554e6	−1.70873
$392$	5.44489e6	1.78967
$393$	−3.41290e6	−1.11466
$394$	884198.	0.286952
$395$	1.00183e7	3.23073
$396$	1.34661e6	0.431524
$397$	1.62699e6	0.518096	0.259048	−	0.965865i	$-0.416591\pi$
$397$	1.62699e6	0.518096	0.259048	+	0.965865i	$0.416591\pi$
$398$	−2.95755e6	−0.935889
$399$	−1.49559e6	−0.470307
$400$	2.86732e7	8.96037
$401$	−1.92264e6	−0.597086	−0.298543	−	0.954396i	$-0.596501\pi$
$401$	−1.92264e6	−0.597086	−0.298543	+	0.954396i	$0.596501\pi$
$402$	275649.	0.0850728
$403$	−202367.	−0.0620694
$404$	−3.37129e6	−1.02764
$405$	−1.25213e6	−0.379325
$406$	−1.94748e6	−0.586352
$407$	−362571.	−0.108494
$408$	1.36441e7	4.05784
$409$	−4.88217e6	−1.44313	−0.721564	−	0.692348i	$-0.756576\pi$
$409$	−4.88217e6	−1.44313	−0.721564	+	0.692348i	$0.756576\pi$
$410$	2.01111e7	5.90849
$411$	−3.49196e6	−1.01968
$412$	2.85679e6	0.829154
$413$	−949369.	−0.273880
$414$	3.46190e6	0.992691
$415$	3.22431e6	0.919002
$416$	−887089.	−0.251324
$417$	−1.39434e6	−0.392671
$418$	−2.06667e6	−0.578536
$419$	−1.23381e6	−0.343331	−0.171665	−	0.985155i	$-0.554915\pi$
$419$	−1.23381e6	−0.343331	−0.171665	+	0.985155i	$0.554915\pi$
$420$	8.63358e6	2.38818
$421$	−540823.	−0.148713	−0.0743567	−	0.997232i	$-0.523690\pi$
$421$	−540823.	−0.148713	−0.0743567	+	0.997232i	$0.523690\pi$
$422$	−1.00023e6	−0.273413
$423$	1.41846e6	0.385448
$424$	1.71726e6	0.463897
$425$	−1.52871e7	−4.10536
$426$	5.02388e6	1.34127
$427$	3.93571e6	1.04461
$428$	−1.15082e7	−3.03666
$429$	−50484.8	−0.0132440
$430$	1.21127e7	3.15915
$431$	−858679.	−0.222658	−0.111329	−	0.993784i	$-0.535511\pi$
$431$	−858679.	−0.222658	−0.111329	+	0.993784i	$0.535511\pi$
$432$	−1.54757e7	−3.98972
$433$	3.79200e6	0.971960	0.485980	−	0.873970i	$-0.338463\pi$
$433$	3.79200e6	0.971960	0.485980	+	0.873970i	$0.338463\pi$
$434$	5.08989e6	1.29713
$435$	2.21303e6	0.560743
$436$	−1.81539e7	−4.57357
$437$	−3.89439e6	−0.975520
$438$	8.57769e6	2.13641
$439$	3.78427e6	0.937175	0.468587	−	0.883417i	$-0.344763\pi$
$439$	3.78427e6	0.937175	0.468587	+	0.883417i	$0.344763\pi$
$440$	7.58426e6	1.86759
$441$	1.12837e6	0.276283
$442$	876457.	0.213390
$443$	−3.21935e6	−0.779397	−0.389698	−	0.920943i	$-0.627421\pi$
$443$	−3.21935e6	−0.779397	−0.389698	+	0.920943i	$0.627421\pi$
$444$	2.83875e6	0.683391
$445$	−7.09005e6	−1.69726
$446$	−3.46989e6	−0.825998
$447$	3.84228e6	0.909536
$448$	1.12714e7	2.65329
$449$	−2.37378e6	−0.555680	−0.277840	−	0.960627i	$-0.589618\pi$
$449$	−2.37378e6	−0.555680	−0.277840	+	0.960627i	$0.589618\pi$
$450$	1.02453e7	2.38502
$451$	2.16805e6	0.501913
$452$	1.95939e7	4.51102
$453$	−2.15959e6	−0.494454
$454$	6.84133e6	1.55776
$455$	352566.	0.0798385
$456$	1.02865e7	2.31663
$457$	−1.77783e6	−0.398199	−0.199100	−	0.979979i	$-0.563802\pi$
$457$	−1.77783e6	−0.398199	−0.199100	+	0.979979i	$0.563802\pi$
$458$	−1.71912e6	−0.382949
$459$	8.25086e6	1.82796
$460$	2.24811e7	4.95362
$461$	−3.50662e6	−0.768486	−0.384243	−	0.923232i	$-0.625537\pi$
$461$	−3.50662e6	−0.768486	−0.384243	+	0.923232i	$0.625537\pi$
$462$	1.26978e6	0.276773
$463$	3.53814e6	0.767047	0.383523	−	0.923531i	$-0.374711\pi$
$463$	3.53814e6	0.767047	0.383523	+	0.923531i	$0.374711\pi$
$464$	7.76860e6	1.67513
$465$	−5.78392e6	−1.24048
$466$	1.05043e6	0.224080
$467$	−1.22698e6	−0.260342	−0.130171	−	0.991492i	$-0.541553\pi$
$467$	−1.22698e6	−0.260342	−0.130171	+	0.991492i	$0.541553\pi$
$468$	−430552.	−0.0908681
$469$	−207525.	−0.0435650
$470$	1.25667e7	2.62409
$471$	−1.10026e6	−0.228530
$472$	6.52966e6	1.34907
$473$	1.30580e6	0.268363
$474$	−1.15363e7	−2.35841
$475$	−1.15252e7	−2.34377
$476$	−1.61583e7	−3.26871
$477$	355875.	0.0716145
$478$	7.73755e6	1.54894
$479$	−9.35247e6	−1.86246	−0.931231	−	0.364429i	$-0.881264\pi$
$479$	−9.35247e6	−1.86246	−0.931231	+	0.364429i	$0.881264\pi$
$480$	−2.53541e7	−5.02280
$481$	115925.	0.0228462
$482$	−1.32084e7	−2.58960
$483$	2.39275e6	0.466691
$484$	1.28612e6	0.249557
$485$	−7.48094e6	−1.44412
$486$	−9.16435e6	−1.75999
$487$	−99341.2	−0.0189805	−0.00949024	−	0.999955i	$-0.503021\pi$
$487$	−99341.2	−0.0189805	−0.00949024	+	0.999955i	$0.503021\pi$
$488$	−2.70694e7	−5.14551
$489$	−2.73560e6	−0.517345
$490$	9.99668e6	1.88090
$491$	854955.	0.160044	0.0800220	−	0.996793i	$-0.474501\pi$
$491$	854955.	0.160044	0.0800220	+	0.996793i	$0.474501\pi$
$492$	−1.69747e7	−3.16148
$493$	−4.14181e6	−0.767491
$494$	660777.	0.121825
$495$	1.57172e6	0.288311
$496$	−2.03038e7	−3.70573
$497$	−3.78228e6	−0.686851
$498$	−3.71286e6	−0.670865
$499$	9.66253e6	1.73716	0.868580	−	0.495549i	$-0.165033\pi$
$499$	9.66253e6	1.73716	0.868580	+	0.495549i	$0.165033\pi$
$500$	3.83859e7	6.86669
$501$	4.28717e6	0.763090
$502$	3.67529e6	0.650927
$503$	−8.17357e6	−1.44043	−0.720214	−	0.693752i	$-0.755957\pi$
$503$	−8.17357e6	−1.44043	−0.720214	+	0.693752i	$0.755957\pi$
$504$	6.88428e6	1.20721
$505$	−3.93484e6	−0.686592
$506$	3.30640e6	0.574088
$507$	−3.98813e6	−0.689048
$508$	2.49061e7	4.28201
$509$	−4.49197e6	−0.768497	−0.384248	−	0.923230i	$-0.625539\pi$
$509$	−4.49197e6	−0.768497	−0.384248	+	0.923230i	$0.625539\pi$
$510$	2.50503e7	4.26468
$511$	−6.45779e6	−1.09404
$512$	−1.30682e7	−2.20314
$513$	6.22048e6	1.04359
$514$	1.76442e7	2.94574
$515$	3.33434e6	0.553977
$516$	−1.02237e7	−1.69038
$517$	1.35474e6	0.222910
$518$	−2.91571e6	−0.477442
$519$	−1.04259e6	−0.169900
$520$	−2.42491e6	−0.393267
$521$	−5.54760e6	−0.895387	−0.447693	−	0.894187i	$-0.647754\pi$
$521$	−5.54760e6	−0.895387	−0.447693	+	0.894187i	$0.647754\pi$
$522$	2.77581e6	0.445876
$523$	1.05242e6	0.168243	0.0841214	−	0.996456i	$-0.473192\pi$
$523$	1.05242e6	0.168243	0.0841214	+	0.996456i	$0.473192\pi$
$524$	−2.77989e7	−4.42283
$525$	7.08118e6	1.12126
$526$	1.32931e7	2.09489
$527$	1.08249e7	1.69785
$528$	−5.06522e6	−0.790703
$529$	−205840.	−0.0319808
$530$	3.15285e6	0.487544
$531$	1.35317e6	0.208265
$532$	−1.21820e7	−1.86612
$533$	−693191.	−0.105690
$534$	8.16434e6	1.23899
$535$	−1.34319e7	−2.02887
$536$	1.42733e6	0.214592
$537$	4.48878e6	0.671726
$538$	−2.12450e7	−3.16447
$539$	1.07768e6	0.159778
$540$	−3.59088e7	−5.29928
$541$	8.43654e6	1.23929	0.619643	−	0.784884i	$-0.287277\pi$
$541$	8.43654e6	1.23929	0.619643	+	0.784884i	$0.287277\pi$
$542$	−7.69451e6	−1.12508
$543$	5.32202e6	0.774599
$544$	4.74517e7	6.87472
$545$	−2.11886e7	−3.05570
$546$	−405987.	−0.0582815
$547$	−1.00323e7	−1.43361	−0.716805	−	0.697274i	$-0.754396\pi$
$547$	−1.00323e7	−1.43361	−0.716805	+	0.697274i	$0.754396\pi$
$548$	−2.84429e7	−4.04597
$549$	−5.60970e6	−0.794344
$550$	9.78506e6	1.37929
$551$	−3.12259e6	−0.438163
$552$	−1.64571e7	−2.29882
$553$	8.68518e6	1.20772
$554$	1.77607e7	2.45859
$555$	3.31328e6	0.456589
$556$	−1.13573e7	−1.55807
$557$	6.87031e6	0.938293	0.469147	−	0.883120i	$-0.344562\pi$
$557$	6.87031e6	0.938293	0.469147	+	0.883120i	$0.344562\pi$
$558$	−7.25480e6	−0.986370
$559$	−417502.	−0.0565105
$560$	3.53735e7	4.76659
$561$	2.70051e6	0.362275
$562$	−2.02910e7	−2.70996
$563$	7.17848e6	0.954469	0.477234	−	0.878776i	$-0.341639\pi$
$563$	7.17848e6	0.954469	0.477234	+	0.878776i	$0.341639\pi$
$564$	−1.06069e7	−1.40408
$565$	2.28693e7	3.01392
$566$	−1.80967e7	−2.37442
$567$	−1.08551e6	−0.141800
$568$	2.60141e7	3.38328
$569$	−828683.	−0.107302	−0.0536510	−	0.998560i	$-0.517086\pi$
$569$	−828683.	−0.107302	−0.0536510	+	0.998560i	$0.517086\pi$
$570$	1.88858e7	2.43472
$571$	−4.32290e6	−0.554863	−0.277431	−	0.960745i	$-0.589483\pi$
$571$	−4.32290e6	−0.554863	−0.277431	+	0.960745i	$0.589483\pi$
$572$	−411212.	−0.0525504
$573$	−1.86621e6	−0.237451
$574$	1.74350e7	2.20873
$575$	1.84388e7	2.32574
$576$	−1.60656e7	−2.01762
$577$	−8.21060e6	−1.02668	−0.513340	−	0.858185i	$-0.671592\pi$
$577$	−8.21060e6	−1.02668	−0.513340	+	0.858185i	$0.671592\pi$
$578$	−3.13394e7	−3.90185
$579$	6.89970e6	0.855330
$580$	1.80257e7	2.22496
$581$	2.79526e6	0.343544
$582$	8.61445e6	1.05419
$583$	339889.	0.0414158
$584$	4.44160e7	5.38899
$585$	−502525.	−0.0607111
$586$	−1.82837e7	−2.19948
$587$	−4.50266e6	−0.539354	−0.269677	−	0.962951i	$-0.586917\pi$
$587$	−4.50266e6	−0.539354	−0.269677	+	0.962951i	$0.586917\pi$
$588$	−8.43768e6	−1.00642
$589$	8.16112e6	0.969307
$590$	1.19883e7	1.41784
$591$	−871060.	−0.102584
$592$	1.16309e7	1.36398
$593$	−1.42486e7	−1.66394	−0.831968	−	0.554823i	$-0.812786\pi$
$593$	−1.42486e7	−1.66394	−0.831968	+	0.554823i	$0.812786\pi$
$594$	−5.28128e6	−0.614148
$595$	−1.88593e7	−2.18390
$596$	3.12964e7	3.60893
$597$	2.91361e6	0.334576
$598$	−1.05715e6	−0.120889
$599$	4.28566e6	0.488035	0.244018	−	0.969771i	$-0.421535\pi$
$599$	4.28566e6	0.488035	0.244018	+	0.969771i	$0.421535\pi$
$600$	−4.87036e7	−5.52310
$601$	8.04687e6	0.908742	0.454371	−	0.890812i	$-0.349864\pi$
$601$	8.04687e6	0.908742	0.454371	+	0.890812i	$0.349864\pi$
$602$	1.05009e7	1.18096
$603$	295792.	0.0331279
$604$	−1.75904e7	−1.96193
$605$	1.50112e6	0.166735
$606$	4.53105e6	0.501207
$607$	−2.10094e6	−0.231442	−0.115721	−	0.993282i	$-0.536918\pi$
$607$	−2.10094e6	−0.231442	−0.115721	+	0.993282i	$0.536918\pi$
$608$	3.57747e7	3.92480
$609$	1.91855e6	0.209618
$610$	−4.96987e7	−5.40780
$611$	−433151.	−0.0469393
$612$	2.30309e7	2.48561
$613$	−1.55063e7	−1.66669	−0.833347	−	0.552750i	$-0.813578\pi$
$613$	−1.55063e7	−1.66669	−0.833347	+	0.552750i	$0.813578\pi$
$614$	−1.09244e6	−0.116944
$615$	−1.98123e7	−2.11226
$616$	6.57504e6	0.698147
$617$	−8.86952e6	−0.937966	−0.468983	−	0.883207i	$-0.655379\pi$
$617$	−8.86952e6	−0.937966	−0.468983	+	0.883207i	$0.655379\pi$
$618$	−3.83956e6	−0.404399
$619$	7.06898e6	0.741533	0.370766	−	0.928726i	$-0.379095\pi$
$619$	7.06898e6	0.741533	0.370766	+	0.928726i	$0.379095\pi$
$620$	−4.71115e7	−4.92207
$621$	−9.95193e6	−1.03557
$622$	4.54731e6	0.471280
$623$	−6.14660e6	−0.634475
$624$	1.61950e6	0.166502
$625$	2.17182e7	2.22394
$626$	2.34294e7	2.38960
$627$	2.03596e6	0.206824
$628$	−8.96190e6	−0.906778
$629$	−6.20100e6	−0.624935
$630$	1.26394e7	1.26874
$631$	−9.94738e6	−0.994570	−0.497285	−	0.867587i	$-0.665670\pi$
$631$	−9.94738e6	−0.994570	−0.497285	+	0.867587i	$0.665670\pi$
$632$	−5.97358e7	−5.94897
$633$	985370.	0.0977440
$634$	−1.36054e7	−1.34427
$635$	2.90695e7	2.86091
$636$	−2.66116e6	−0.260872
$637$	−344567.	−0.0336453
$638$	2.65113e6	0.257857
$639$	5.39101e6	0.522298
$640$	−6.71018e7	−6.47566
$641$	3.46672e6	0.333252	0.166626	−	0.986020i	$-0.446713\pi$
$641$	3.46672e6	0.333252	0.166626	+	0.986020i	$0.446713\pi$
$642$	1.54671e7	1.48106
$643$	−2.15302e6	−0.205362	−0.102681	−	0.994714i	$-0.532742\pi$
$643$	−2.15302e6	−0.205362	−0.102681	+	0.994714i	$0.532742\pi$
$644$	1.94896e7	1.85177
$645$	−1.19327e7	−1.12938
$646$	−3.53460e7	−3.33241
$647$	6.83323e6	0.641749	0.320875	−	0.947122i	$-0.396023\pi$
$647$	6.83323e6	0.641749	0.320875	+	0.947122i	$0.396023\pi$
$648$	7.46603e6	0.698477
$649$	1.29238e6	0.120443
$650$	−3.12858e6	−0.290445
$651$	−5.01426e6	−0.463719
$652$	−2.22822e7	−2.05276
$653$	−6.24526e6	−0.573149	−0.286574	−	0.958058i	$-0.592517\pi$
$653$	−6.24526e6	−0.573149	−0.286574	+	0.958058i	$0.592517\pi$
$654$	2.43991e7	2.23064
$655$	−3.24459e7	−2.95499
$656$	−6.95489e7	−6.31002
$657$	9.20451e6	0.831931
$658$	1.08945e7	0.980942
$659$	1.48186e7	1.32921	0.664606	−	0.747194i	$-0.268599\pi$
$659$	1.48186e7	1.32921	0.664606	+	0.747194i	$0.268599\pi$
$660$	−1.17530e7	−1.05024
$661$	−1.22963e7	−1.09464	−0.547321	−	0.836923i	$-0.684352\pi$
$661$	−1.22963e7	−1.09464	−0.547321	+	0.836923i	$0.684352\pi$
$662$	−1.82799e7	−1.62117
$663$	−863434.	−0.0762861
$664$	−1.92255e7	−1.69222
$665$	−1.42184e7	−1.24680
$666$	4.15586e6	0.363058
$667$	4.99572e6	0.434794
$668$	3.49201e7	3.02785
$669$	3.41834e6	0.295291
$670$	2.62055e6	0.225531
$671$	−5.35771e6	−0.459381
$672$	−2.19803e7	−1.87763
$673$	1.68459e7	1.43370	0.716848	−	0.697229i	$-0.245584\pi$
$673$	1.68459e7	1.43370	0.716848	+	0.697229i	$0.245584\pi$
$674$	−9.68773e6	−0.821433
$675$	−2.94521e7	−2.48803
$676$	−3.24844e7	−2.73406
$677$	−6.00718e6	−0.503731	−0.251866	−	0.967762i	$-0.581044\pi$
$677$	−6.00718e6	−0.503731	−0.251866	+	0.967762i	$0.581044\pi$
$678$	−2.63344e7	−2.20014
$679$	−6.48547e6	−0.539842
$680$	1.29712e8	10.7574
$681$	−6.73968e6	−0.556892
$682$	−6.92891e6	−0.570432
$683$	7.64090e6	0.626747	0.313374	−	0.949630i	$-0.398541\pi$
$683$	7.64090e6	0.626747	0.313374	+	0.949630i	$0.398541\pi$
$684$	1.73634e7	1.41904
$685$	−3.31975e7	−2.70321
$686$	2.50206e7	2.02996
$687$	1.69357e6	0.136903
$688$	−4.18886e7	−3.37384
$689$	−108673.	−0.00872112
$690$	−3.02148e7	−2.41600
$691$	7.01172e6	0.558636	0.279318	−	0.960199i	$-0.409892\pi$
$691$	7.01172e6	0.558636	0.279318	+	0.960199i	$0.409892\pi$
$692$	−8.49214e6	−0.674143
$693$	1.36257e6	0.107777
$694$	3.84777e7	3.03256
$695$	−1.32558e7	−1.04098
$696$	−1.31956e7	−1.03254
$697$	3.70799e7	2.89106
$698$	−4.07988e7	−3.16963
$699$	−1.03483e6	−0.0801077
$700$	5.76781e7	4.44903
$701$	1.35313e7	1.04003	0.520014	−	0.854158i	$-0.325927\pi$
$701$	1.35313e7	1.04003	0.520014	+	0.854158i	$0.325927\pi$
$702$	1.68858e6	0.129324
$703$	−4.67505e6	−0.356778
$704$	−1.53439e7	−1.16682
$705$	−1.23800e7	−0.938099
$706$	1.05607e7	0.797406
$707$	−3.41124e6	−0.256664
$708$	−1.01187e7	−0.758651
$709$	−6.24867e6	−0.466844	−0.233422	−	0.972376i	$-0.574992\pi$
$709$	−6.24867e6	−0.466844	−0.233422	+	0.972376i	$0.574992\pi$
$710$	4.77613e7	3.55574
$711$	−1.23793e7	−0.918379
$712$	4.22757e7	3.12529
$713$	−1.30567e7	−0.961855
$714$	2.17169e7	1.59423
$715$	−479951.	−0.0351101
$716$	3.65623e7	2.66533
$717$	−7.62258e6	−0.553738
$718$	1.77771e7	1.28691
$719$	2.27263e7	1.63948	0.819741	−	0.572735i	$-0.194117\pi$
$719$	2.27263e7	1.63948	0.819741	+	0.572735i	$0.194117\pi$
$720$	−5.04190e7	−3.62463
$721$	2.89065e6	0.207089
$722$	458696.	0.0327478
$723$	1.30121e7	0.925770
$724$	4.33492e7	3.07351
$725$	1.47845e7	1.04463
$726$	−1.72856e6	−0.121715
$727$	2.13060e7	1.49508	0.747541	−	0.664215i	$-0.231234\pi$
$727$	2.13060e7	1.49508	0.747541	+	0.664215i	$0.231234\pi$
$728$	−2.10224e6	−0.147012
$729$	1.19958e7	0.836010
$730$	8.15468e7	5.66369
$731$	2.23328e7	1.54579
$732$	4.19481e7	2.89358
$733$	−1.85150e7	−1.27281	−0.636406	−	0.771354i	$-0.719580\pi$
$733$	−1.85150e7	−1.27281	−0.636406	+	0.771354i	$0.719580\pi$
$734$	−4.98624e7	−3.41612
$735$	−9.84815e6	−0.672413
$736$	−5.72348e7	−3.89462
$737$	282505.	0.0191583
$738$	−2.48507e7	−1.67957
$739$	2.15508e7	1.45162	0.725809	−	0.687896i	$-0.241465\pi$
$739$	2.15508e7	1.45162	0.725809	+	0.687896i	$0.241465\pi$
$740$	2.69875e7	1.81169
$741$	−650959.	−0.0435520
$742$	2.73331e6	0.182255
$743$	1.31092e7	0.871175	0.435588	−	0.900146i	$-0.356541\pi$
$743$	1.31092e7	0.871175	0.435588	+	0.900146i	$0.356541\pi$
$744$	3.44876e7	2.28418
$745$	3.65280e7	2.41121
$746$	4.69426e6	0.308830
$747$	−3.98418e6	−0.261239
$748$	2.19964e7	1.43746
$749$	−1.16446e7	−0.758435
$750$	−5.15911e7	−3.34905
$751$	−2.00007e7	−1.29403	−0.647016	−	0.762476i	$-0.723983\pi$
$751$	−2.00007e7	−1.29403	−0.647016	+	0.762476i	$0.723983\pi$
$752$	−4.34587e7	−2.80241
$753$	−3.62068e6	−0.232703
$754$	−847644.	−0.0542982
$755$	−2.05309e7	−1.31081
$756$	−3.11305e7	−1.98099
$757$	549507.	0.0348524	0.0174262	−	0.999848i	$-0.494453\pi$
$757$	549507.	0.0348524	0.0174262	+	0.999848i	$0.494453\pi$
$758$	−1.93130e7	−1.22089
$759$	−3.25727e6	−0.205234
$760$	9.77925e7	6.14146
$761$	1.74304e7	1.09105	0.545525	−	0.838094i	$-0.316330\pi$
$761$	1.74304e7	1.09105	0.545525	+	0.838094i	$0.316330\pi$
$762$	−3.34742e7	−2.08844
$763$	−1.83691e7	−1.14229
$764$	−1.52008e7	−0.942178
$765$	2.68808e7	1.66069
$766$	3.19893e7	1.96985
$767$	−413214.	−0.0253622
$768$	3.35060e7	2.04984
$769$	2.29910e7	1.40198	0.700991	−	0.713170i	$-0.252741\pi$
$769$	2.29910e7	1.40198	0.700991	+	0.713170i	$0.252741\pi$
$770$	1.20716e7	0.733734
$771$	−1.73821e7	−1.05309
$772$	5.61998e7	3.39384
$773$	−2.31665e6	−0.139448	−0.0697240	−	0.997566i	$-0.522212\pi$
$773$	−2.31665e6	−0.139448	−0.0697240	+	0.997566i	$0.522212\pi$
$774$	−1.49673e7	−0.898031
$775$	−3.86404e7	−2.31093
$776$	4.46064e7	2.65915
$777$	2.87239e6	0.170683
$778$	2.99432e7	1.77358
$779$	2.79552e7	1.65051
$780$	3.75777e6	0.221154
$781$	5.14885e6	0.302053
$782$	5.65488e7	3.30679
$783$	−7.97962e6	−0.465134
$784$	−3.45709e7	−2.00872
$785$	−1.04600e7	−0.605839
$786$	3.73621e7	2.15712
$787$	−1.43880e7	−0.828066	−0.414033	−	0.910262i	$-0.635880\pi$
$787$	−1.43880e7	−0.828066	−0.414033	+	0.910262i	$0.635880\pi$
$788$	−7.09502e6	−0.407041
$789$	−1.30956e7	−0.748913
$790$	−1.09674e8	−6.25222
$791$	1.98261e7	1.12667
$792$	−9.37163e6	−0.530887
$793$	1.71302e6	0.0967341
$794$	−1.78112e7	−1.00264
$795$	−3.10600e6	−0.174295
$796$	2.37321e7	1.32756
$797$	−2.31602e7	−1.29150	−0.645752	−	0.763547i	$-0.723456\pi$
$797$	−2.31602e7	−1.29150	−0.645752	+	0.763547i	$0.723456\pi$
$798$	1.63728e7	0.910153
$799$	2.31699e7	1.28398
$800$	−1.69382e8	−9.35715
$801$	8.76096e6	0.482470
$802$	2.10477e7	1.15550
$803$	8.79105e6	0.481118
$804$	−2.21187e6	−0.120676
$805$	2.27475e7	1.23721
$806$	2.21538e6	0.120119
$807$	2.09294e7	1.13128
$808$	2.34622e7	1.26427
$809$	−4.46736e6	−0.239983	−0.119991	−	0.992775i	$-0.538287\pi$
$809$	−4.46736e6	−0.239983	−0.119991	+	0.992775i	$0.538287\pi$
$810$	1.37075e7	0.734082
$811$	5.46597e6	0.291820	0.145910	−	0.989298i	$-0.453389\pi$
$811$	5.46597e6	0.291820	0.145910	+	0.989298i	$0.453389\pi$
$812$	1.56271e7	0.831740
$813$	7.58018e6	0.402211
$814$	3.96918e6	0.209962
$815$	−2.60069e7	−1.37150
$816$	−8.66296e7	−4.55450
$817$	1.68371e7	0.882496
$818$	5.34467e7	2.79279
$819$	−435655.	−0.0226951
$820$	−1.61376e8	−8.38118
$821$	5.38988e6	0.279075	0.139537	−	0.990217i	$-0.455438\pi$
$821$	5.38988e6	0.279075	0.139537	+	0.990217i	$0.455438\pi$
$822$	3.82276e7	1.97332
$823$	6.55837e6	0.337518	0.168759	−	0.985657i	$-0.446024\pi$
$823$	6.55837e6	0.337518	0.168759	+	0.985657i	$0.446024\pi$
$824$	−1.98816e7	−1.02008
$825$	−9.63967e6	−0.493091
$826$	1.03930e7	0.530021
$827$	−7.56945e6	−0.384858	−0.192429	−	0.981311i	$-0.561636\pi$
$827$	−7.56945e6	−0.384858	−0.192429	+	0.981311i	$0.561636\pi$
$828$	−2.77791e7	−1.40813
$829$	−1.69245e7	−0.855324	−0.427662	−	0.903939i	$-0.640663\pi$
$829$	−1.69245e7	−0.855324	−0.427662	+	0.903939i	$0.640663\pi$
$830$	−3.52976e7	−1.77848
$831$	−1.74969e7	−0.878936
$832$	4.90591e6	0.245703
$833$	1.84314e7	0.920335
$834$	1.52643e7	0.759910
$835$	4.07574e7	2.02298
$836$	1.65835e7	0.820653
$837$	2.08553e7	1.02897
$838$	1.35069e7	0.664425
$839$	−3.16918e7	−1.55433	−0.777164	−	0.629298i	$-0.783342\pi$
$839$	−3.16918e7	−1.55433	−0.777164	+	0.629298i	$0.783342\pi$
$840$	−6.00846e7	−2.93809
$841$	−1.65055e7	−0.804708
$842$	5.92057e6	0.287795
$843$	1.99895e7	0.968799
$844$	8.02609e6	0.387836
$845$	−3.79146e7	−1.82669
$846$	−1.55283e7	−0.745931
$847$	1.30137e6	0.0623291
$848$	−1.09033e7	−0.520676
$849$	1.78278e7	0.848846
$850$	1.67352e8	7.94483
$851$	7.47945e6	0.354034
$852$	−4.03128e7	−1.90259
$853$	2.56954e7	1.20916	0.604578	−	0.796546i	$-0.293342\pi$
$853$	2.56954e7	1.20916	0.604578	+	0.796546i	$0.293342\pi$
$854$	−4.30855e7	−2.02156
$855$	2.02659e7	0.948094
$856$	8.00900e7	3.73589
$857$	−3.60573e6	−0.167703	−0.0838516	−	0.996478i	$-0.526722\pi$
$857$	−3.60573e6	−0.167703	−0.0838516	+	0.996478i	$0.526722\pi$
$858$	552674.	0.0256301
$859$	−1.81175e7	−0.837752	−0.418876	−	0.908044i	$-0.637576\pi$
$859$	−1.81175e7	−0.837752	−0.418876	+	0.908044i	$0.637576\pi$
$860$	−9.71953e7	−4.48125
$861$	−1.71759e7	−0.789609
$862$	9.40023e6	0.430894
$863$	−8.55828e6	−0.391164	−0.195582	−	0.980687i	$-0.562660\pi$
$863$	−8.55828e6	−0.391164	−0.195582	+	0.980687i	$0.562660\pi$
$864$	9.14206e7	4.16639
$865$	−9.91171e6	−0.450410
$866$	−4.15123e7	−1.88097
$867$	3.08737e7	1.39489
$868$	−4.08425e7	−1.83998
$869$	−1.18232e7	−0.531112
$870$	−2.42267e7	−1.08517
$871$	−90325.4	−0.00403426
$872$	1.26341e8	5.62668
$873$	9.24396e6	0.410509
$874$	4.26332e7	1.88786
$875$	3.88409e7	1.71502
$876$	−6.88294e7	−3.03050
$877$	−2.07660e6	−0.0911703	−0.0455852	−	0.998960i	$-0.514515\pi$
$877$	−2.07660e6	−0.0911703	−0.0455852	+	0.998960i	$0.514515\pi$
$878$	−4.14276e7	−1.81365
$879$	1.80121e7	0.786306
$880$	−4.81542e7	−2.09618
$881$	6.66194e6	0.289175	0.144587	−	0.989492i	$-0.453814\pi$
$881$	6.66194e6	0.289175	0.144587	+	0.989492i	$0.453814\pi$
$882$	−1.23526e7	−0.534671
$883$	−5.84997e6	−0.252494	−0.126247	−	0.991999i	$-0.540293\pi$
$883$	−5.84997e6	−0.252494	−0.126247	+	0.991999i	$0.540293\pi$
$884$	−7.03290e6	−0.302694
$885$	−1.18102e7	−0.506872
$886$	3.52433e7	1.50831
$887$	−3.72606e7	−1.59016	−0.795080	−	0.606504i	$-0.792571\pi$
$887$	−3.72606e7	−1.59016	−0.795080	+	0.606504i	$0.792571\pi$
$888$	−1.97560e7	−0.840749
$889$	2.52013e7	1.06947
$890$	7.76171e7	3.28460
$891$	1.47772e6	0.0623586
$892$	2.78433e7	1.17168
$893$	1.74682e7	0.733028
$894$	−4.20627e7	−1.76016
$895$	4.26741e7	1.78077
$896$	−5.81727e7	−2.42075
$897$	1.04145e6	0.0432171
$898$	2.59865e7	1.07537
$899$	−1.04691e7	−0.432025
$900$	−8.22105e7	−3.38315
$901$	5.81307e6	0.238558
$902$	−2.37344e7	−0.971319
$903$	−1.03449e7	−0.422188
$904$	−1.36362e8	−5.54974
$905$	5.05956e7	2.05349
$906$	2.36418e7	0.956884
$907$	1.32037e7	0.532938	0.266469	−	0.963844i	$-0.414143\pi$
$907$	1.32037e7	0.532938	0.266469	+	0.963844i	$0.414143\pi$
$908$	−5.48964e7	−2.20968
$909$	4.86216e6	0.195173
$910$	−3.85966e6	−0.154506
$911$	3.86440e7	1.54272	0.771358	−	0.636401i	$-0.219578\pi$
$911$	3.86440e7	1.54272	0.771358	+	0.636401i	$0.219578\pi$
$912$	−6.53116e7	−2.60018
$913$	−3.80521e6	−0.151078
$914$	1.94625e7	0.770608
$915$	4.89603e7	1.93326
$916$	1.37946e7	0.543213
$917$	−2.81284e7	−1.10464
$918$	−9.03249e7	−3.53754
$919$	4.25393e7	1.66151	0.830753	−	0.556642i	$-0.187910\pi$
$919$	4.25393e7	1.66151	0.830753	+	0.556642i	$0.187910\pi$
$920$	−1.56455e8	−6.09424
$921$	1.07621e6	0.0418070
$922$	3.83881e7	1.48720
$923$	−1.64624e6	−0.0636047
$924$	−1.01890e7	−0.392602
$925$	2.21349e7	0.850597
$926$	−3.87331e7	−1.48441
$927$	−4.12014e6	−0.157475
$928$	−4.58918e7	−1.74930
$929$	5.17433e7	1.96705	0.983523	−	0.180781i	$-0.0578625\pi$
$929$	5.17433e7	1.96705	0.983523	+	0.180781i	$0.0578625\pi$
$930$	6.33184e7	2.40062
$931$	1.38958e7	0.525422
$932$	−8.42893e6	−0.317858
$933$	−4.47975e6	−0.168480
$934$	1.34321e7	0.503822
$935$	2.56733e7	0.960403
$936$	2.99639e6	0.111791
$937$	−3.82246e7	−1.42231	−0.711154	−	0.703036i	$-0.751827\pi$
$937$	−3.82246e7	−1.42231	−0.711154	+	0.703036i	$0.751827\pi$
$938$	2.27184e6	0.0843084
$939$	−2.30812e7	−0.854270
$940$	−1.00839e8	−3.72226
$941$	7.21013e6	0.265442	0.132721	−	0.991153i	$-0.457629\pi$
$941$	7.21013e6	0.265442	0.132721	+	0.991153i	$0.457629\pi$
$942$	1.20449e7	0.442258
$943$	−4.47246e7	−1.63782
$944$	−4.14583e7	−1.51420
$945$	−3.63344e7	−1.32354
$946$	−1.42950e7	−0.519345
$947$	−2.55825e7	−0.926973	−0.463487	−	0.886104i	$-0.653402\pi$
$947$	−2.55825e7	−0.926973	−0.463487	+	0.886104i	$0.653402\pi$
$948$	9.25697e7	3.34540
$949$	−2.81076e6	−0.101311
$950$	1.26170e8	4.53573
$951$	1.34032e7	0.480572
$952$	1.12452e8	4.02137
$953$	4.02409e7	1.43527	0.717637	−	0.696417i	$-0.245224\pi$
$953$	4.02409e7	1.43527	0.717637	+	0.696417i	$0.245224\pi$
$954$	−3.89588e6	−0.138591
$955$	−1.77418e7	−0.629491
$956$	−6.20879e7	−2.19716
$957$	−2.61173e6	−0.0921826
$958$	1.02385e8	3.60430
$959$	−2.87800e7	−1.01052
$960$	1.40217e8	4.91047
$961$	−1.26743e6	−0.0442705
$962$	−1.26907e6	−0.0442127
$963$	1.65974e7	0.576732
$964$	1.05987e8	3.67334
$965$	6.55944e7	2.26751
$966$	−2.61942e7	−0.903155
$967$	−2.18087e7	−0.750004	−0.375002	−	0.927024i	$-0.622358\pi$
$967$	−2.18087e7	−0.750004	−0.375002	+	0.927024i	$0.622358\pi$
$968$	−8.95066e6	−0.307020
$969$	3.48208e7	1.19132
$970$	8.18963e7	2.79470
$971$	1.44882e7	0.493136	0.246568	−	0.969125i	$-0.420697\pi$
$971$	1.44882e7	0.493136	0.246568	+	0.969125i	$0.420697\pi$
$972$	7.35370e7	2.49655
$973$	−1.14919e7	−0.389143
$974$	1.08752e6	0.0367316
$975$	3.08209e6	0.103833
$976$	1.71870e8	5.77531
$977$	−4.60845e7	−1.54461	−0.772304	−	0.635253i	$-0.780896\pi$
$977$	−4.60845e7	−1.54461	−0.772304	+	0.635253i	$0.780896\pi$
$978$	2.99475e7	1.00118
$979$	8.36742e6	0.279020
$980$	−8.02158e7	−2.66805
$981$	2.61821e7	0.868625
$982$	−9.35947e6	−0.309722
$983$	1.93618e7	0.639089	0.319545	−	0.947571i	$-0.396470\pi$
$983$	1.93618e7	0.639089	0.319545	+	0.947571i	$0.396470\pi$
$984$	1.18134e8	3.88945
$985$	−8.28104e6	−0.271953
$986$	4.53418e7	1.48527
$987$	−1.07326e7	−0.350682
$988$	−5.30223e6	−0.172809
$989$	−2.69372e7	−0.875711
$990$	−1.72061e7	−0.557949
$991$	−3.36919e7	−1.08978	−0.544892	−	0.838506i	$-0.683430\pi$
$991$	−3.36919e7	−1.08978	−0.544892	+	0.838506i	$0.683430\pi$
$992$	1.19942e8	3.86982
$993$	1.80083e7	0.579561
$994$	4.14058e7	1.32922
$995$	2.76992e7	0.886971
$996$	2.97929e7	0.951621
$997$	−5.04518e7	−1.60745	−0.803727	−	0.594998i	$-0.797153\pi$
$997$	−5.04518e7	−1.60745	−0.803727	+	0.594998i	$0.797153\pi$
$998$	−1.05779e8	−3.36181
$999$	−1.19469e7	−0.378739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	583.6.a.b.1.2	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
583.6.a.b.1.2	✓	54	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 583 = 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	583.a (trivial)

\(f(q)\)	\(=\)	\(q-10.9473 q^{2} +10.7847 q^{3} +87.8440 q^{4} +102.528 q^{5} -118.063 q^{6} +88.8850 q^{7} -611.342 q^{8} -126.691 q^{9} +O(q^{10})\)	\(q-10.9473 q^{2} +10.7847 q^{3} +87.8440 q^{4} +102.528 q^{5} -118.063 q^{6} +88.8850 q^{7} -611.342 q^{8} -126.691 q^{9} -1122.41 q^{10} -121.000 q^{11} +947.368 q^{12} +38.6873 q^{13} -973.054 q^{14} +1105.73 q^{15} +3881.55 q^{16} -2069.44 q^{17} +1386.93 q^{18} -1560.19 q^{19} +9006.48 q^{20} +958.596 q^{21} +1324.63 q^{22} +2496.10 q^{23} -6593.12 q^{24} +7387.03 q^{25} -423.523 q^{26} -3986.99 q^{27} +7808.01 q^{28} +2001.41 q^{29} -12104.8 q^{30} -5230.84 q^{31} -22929.7 q^{32} -1304.95 q^{33} +22654.9 q^{34} +9113.23 q^{35} -11129.0 q^{36} +2996.46 q^{37} +17079.9 q^{38} +417.230 q^{39} -62679.8 q^{40} -17917.8 q^{41} -10494.1 q^{42} -10791.7 q^{43} -10629.1 q^{44} -12989.4 q^{45} -27325.6 q^{46} -11196.2 q^{47} +41861.3 q^{48} -8906.45 q^{49} -80868.3 q^{50} -22318.3 q^{51} +3398.45 q^{52} -2809.00 q^{53} +43646.9 q^{54} -12405.9 q^{55} -54339.2 q^{56} -16826.2 q^{57} -21910.1 q^{58} -10680.9 q^{59} +97132.0 q^{60} +44278.6 q^{61} +57263.8 q^{62} -11260.9 q^{63} +126809. q^{64} +3966.54 q^{65} +14285.7 q^{66} -2334.75 q^{67} -181788. q^{68} +26919.6 q^{69} -99765.5 q^{70} -42552.5 q^{71} +77451.5 q^{72} -72653.3 q^{73} -32803.2 q^{74} +79666.7 q^{75} -137053. q^{76} -10755.1 q^{77} -4567.55 q^{78} +97712.5 q^{79} +397969. q^{80} -12212.5 q^{81} +196152. q^{82} +31448.0 q^{83} +84206.9 q^{84} -212176. q^{85} +118140. q^{86} +21584.6 q^{87} +73972.4 q^{88} -69152.2 q^{89} +142199. q^{90} +3438.72 q^{91} +219267. q^{92} -56412.9 q^{93} +122569. q^{94} -159964. q^{95} -247289. q^{96} -72964.7 q^{97} +97501.8 q^{98} +15329.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9}+O(q^{10}) \) 54 * q - 16 * q^2 + 906 * q^4 - 225 * q^5 - 197 * q^6 - 341 * q^7 - 1152 * q^8 + 4240 * q^9	\( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9} - 233 q^{10} - 6534 q^{11} - 327 q^{12} - 1455 q^{13} + 2254 q^{14} - 694 q^{15} + 16610 q^{16} - 9275 q^{17} - 6797 q^{18} - 2515 q^{19} - 6840 q^{20} - 4744 q^{21} + 1936 q^{22} - 6307 q^{23} - 5681 q^{24} + 26923 q^{25} - 5196 q^{26} - 5190 q^{27} - 36405 q^{28} - 8356 q^{29} - 28719 q^{30} - 4357 q^{31} - 68580 q^{32} + 9406 q^{34} - 3747 q^{35} + 38059 q^{36} - 25798 q^{37} - 32169 q^{38} - 28347 q^{39} - 15014 q^{40} - 89685 q^{41} - 103207 q^{42} - 26640 q^{43} - 109626 q^{44} - 66786 q^{45} - 28271 q^{46} - 26237 q^{47} - 20371 q^{48} + 132327 q^{49} - 189646 q^{50} + 10856 q^{51} - 179789 q^{52} - 151686 q^{53} - 167182 q^{54} + 27225 q^{55} + 24845 q^{56} - 33857 q^{57} - 31384 q^{58} - 49035 q^{59} - 183481 q^{60} - 101718 q^{61} - 103315 q^{62} - 214794 q^{63} + 154912 q^{64} - 55703 q^{65} + 23837 q^{66} + 105905 q^{67} - 267681 q^{68} - 56033 q^{69} - 90034 q^{70} - 107016 q^{71} - 580829 q^{72} - 161641 q^{73} - 259552 q^{74} - 69519 q^{75} - 240846 q^{76} + 41261 q^{77} - 65716 q^{78} - 35649 q^{79} - 279887 q^{80} + 316682 q^{81} + 206196 q^{82} - 326347 q^{83} - 29955 q^{84} - 189486 q^{85} - 444656 q^{86} - 222331 q^{87} + 139392 q^{88} - 633400 q^{89} + 110940 q^{90} - 25954 q^{91} + 18304 q^{92} - 191747 q^{93} - 62405 q^{94} - 515756 q^{95} - 527591 q^{96} - 405641 q^{97} - 919621 q^{98} - 513040 q^{99}+O(q^{100}) \) 54 * q - 16 * q^2 + 906 * q^4 - 225 * q^5 - 197 * q^6 - 341 * q^7 - 1152 * q^8 + 4240 * q^9 - 233 * q^10 - 6534 * q^11 - 327 * q^12 - 1455 * q^13 + 2254 * q^14 - 694 * q^15 + 16610 * q^16 - 9275 * q^17 - 6797 * q^18 - 2515 * q^19 - 6840 * q^20 - 4744 * q^21 + 1936 * q^22 - 6307 * q^23 - 5681 * q^24 + 26923 * q^25 - 5196 * q^26 - 5190 * q^27 - 36405 * q^28 - 8356 * q^29 - 28719 * q^30 - 4357 * q^31 - 68580 * q^32 + 9406 * q^34 - 3747 * q^35 + 38059 * q^36 - 25798 * q^37 - 32169 * q^38 - 28347 * q^39 - 15014 * q^40 - 89685 * q^41 - 103207 * q^42 - 26640 * q^43 - 109626 * q^44 - 66786 * q^45 - 28271 * q^46 - 26237 * q^47 - 20371 * q^48 + 132327 * q^49 - 189646 * q^50 + 10856 * q^51 - 179789 * q^52 - 151686 * q^53 - 167182 * q^54 + 27225 * q^55 + 24845 * q^56 - 33857 * q^57 - 31384 * q^58 - 49035 * q^59 - 183481 * q^60 - 101718 * q^61 - 103315 * q^62 - 214794 * q^63 + 154912 * q^64 - 55703 * q^65 + 23837 * q^66 + 105905 * q^67 - 267681 * q^68 - 56033 * q^69 - 90034 * q^70 - 107016 * q^71 - 580829 * q^72 - 161641 * q^73 - 259552 * q^74 - 69519 * q^75 - 240846 * q^76 + 41261 * q^77 - 65716 * q^78 - 35649 * q^79 - 279887 * q^80 + 316682 * q^81 + 206196 * q^82 - 326347 * q^83 - 29955 * q^84 - 189486 * q^85 - 444656 * q^86 - 222331 * q^87 + 139392 * q^88 - 633400 * q^89 + 110940 * q^90 - 25954 * q^91 + 18304 * q^92 - 191747 * q^93 - 62405 * q^94 - 515756 * q^95 - 527591 * q^96 - 405641 * q^97 - 919621 * q^98 - 513040 * q^99

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