LMFDB - Embedded newform 583.6.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q-6.05423 q^{2} +8.23240 q^{3} +4.65375 q^{4} +45.2787 q^{5} -49.8409 q^{6} +110.010 q^{7} +165.561 q^{8} -175.228 q^{9} +O(q^{10})$	\(q-6.05423 q^{2} +8.23240 q^{3} +4.65375 q^{4} +45.2787 q^{5} -49.8409 q^{6} +110.010 q^{7} +165.561 q^{8} -175.228 q^{9} -274.128 q^{10} -121.000 q^{11} +38.3115 q^{12} -406.349 q^{13} -666.027 q^{14} +372.752 q^{15} -1151.26 q^{16} +2030.99 q^{17} +1060.87 q^{18} +815.479 q^{19} +210.715 q^{20} +905.647 q^{21} +732.562 q^{22} -442.496 q^{23} +1362.96 q^{24} -1074.84 q^{25} +2460.13 q^{26} -3443.02 q^{27} +511.960 q^{28} -1886.40 q^{29} -2256.73 q^{30} -7435.37 q^{31} +1672.07 q^{32} -996.120 q^{33} -12296.1 q^{34} +4981.11 q^{35} -815.465 q^{36} -11951.9 q^{37} -4937.10 q^{38} -3345.23 q^{39} +7496.36 q^{40} +9537.60 q^{41} -5483.00 q^{42} -9196.52 q^{43} -563.103 q^{44} -7934.08 q^{45} +2678.98 q^{46} -1493.15 q^{47} -9477.65 q^{48} -4704.76 q^{49} +6507.34 q^{50} +16719.9 q^{51} -1891.05 q^{52} -2809.00 q^{53} +20844.8 q^{54} -5478.72 q^{55} +18213.4 q^{56} +6713.34 q^{57} +11420.7 q^{58} +4643.44 q^{59} +1734.69 q^{60} +19582.3 q^{61} +45015.5 q^{62} -19276.8 q^{63} +26717.3 q^{64} -18399.0 q^{65} +6030.74 q^{66} -9697.65 q^{67} +9451.71 q^{68} -3642.80 q^{69} -30156.8 q^{70} +14943.0 q^{71} -29010.8 q^{72} -25148.2 q^{73} +72359.4 q^{74} -8848.52 q^{75} +3795.03 q^{76} -13311.2 q^{77} +20252.8 q^{78} -4682.25 q^{79} -52127.6 q^{80} +14236.1 q^{81} -57742.9 q^{82} +81402.0 q^{83} +4214.65 q^{84} +91960.5 q^{85} +55677.9 q^{86} -15529.6 q^{87} -20032.8 q^{88} -136634. q^{89} +48034.7 q^{90} -44702.6 q^{91} -2059.27 q^{92} -61210.9 q^{93} +9039.88 q^{94} +36923.8 q^{95} +13765.2 q^{96} +48279.8 q^{97} +28483.7 q^{98} +21202.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.05423	−1.07025	−0.535124	−	0.844774i	$-0.679735\pi$
$2$	−6.05423	−1.07025	−0.535124	+	0.844774i	$0.679735\pi$
$3$	8.23240	0.528108	0.264054	−	0.964508i	$-0.414940\pi$
$3$	8.23240	0.528108	0.264054	+	0.964508i	$0.414940\pi$
$4$	4.65375	0.145430
$5$	45.2787	0.809969	0.404985	−	0.914323i	$-0.367277\pi$
$5$	45.2787	0.809969	0.404985	+	0.914323i	$0.367277\pi$
$6$	−49.8409	−0.565207
$7$	110.010	0.848570	0.424285	−	0.905529i	$-0.360525\pi$
$7$	110.010	0.848570	0.424285	+	0.905529i	$0.360525\pi$
$8$	165.561	0.914602
$9$	−175.228	−0.721101
$10$	−274.128	−0.866868
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	38.3115	0.0768026
$13$	−406.349	−0.666870	−0.333435	−	0.942773i	$-0.608208\pi$
$13$	−406.349	−0.666870	−0.333435	+	0.942773i	$0.608208\pi$
$14$	−666.027	−0.908180
$15$	372.752	0.427752
$16$	−1151.26	−1.12428
$17$	2030.99	1.70446	0.852228	−	0.523171i	$-0.175251\pi$
$17$	2030.99	1.70446	0.852228	+	0.523171i	$0.175251\pi$
$18$	1060.87	0.771757
$19$	815.479	0.518237	0.259119	−	0.965846i	$-0.416568\pi$
$19$	815.479	0.518237	0.259119	+	0.965846i	$0.416568\pi$
$20$	210.715	0.117794
$21$	905.647	0.448137
$22$	732.562	0.322692
$23$	−442.496	−0.174417	−0.0872087	−	0.996190i	$-0.527795\pi$
$23$	−442.496	−0.174417	−0.0872087	+	0.996190i	$0.527795\pi$
$24$	1362.96	0.483009
$25$	−1074.84	−0.343949
$26$	2460.13	0.713716
$27$	−3443.02	−0.908928
$28$	511.960	0.123407
$29$	−1886.40	−0.416524	−0.208262	−	0.978073i	$-0.566781\pi$
$29$	−1886.40	−0.416524	−0.208262	+	0.978073i	$0.566781\pi$
$30$	−2256.73	−0.457800
$31$	−7435.37	−1.38963	−0.694814	−	0.719190i	$-0.744513\pi$
$31$	−7435.37	−1.38963	−0.694814	+	0.719190i	$0.744513\pi$
$32$	1672.07	0.288656
$33$	−996.120	−0.159231
$34$	−12296.1	−1.82419
$35$	4981.11	0.687316
$36$	−815.465	−0.104869
$37$	−11951.9	−1.43526	−0.717631	−	0.696423i	$-0.754774\pi$
$37$	−11951.9	−1.43526	−0.717631	+	0.696423i	$0.754774\pi$
$38$	−4937.10	−0.554642
$39$	−3345.23	−0.352180
$40$	7496.36	0.740800
$41$	9537.60	0.886094	0.443047	−	0.896498i	$-0.353898\pi$
$41$	9537.60	0.886094	0.443047	+	0.896498i	$0.353898\pi$
$42$	−5483.00	−0.479618
$43$	−9196.52	−0.758494	−0.379247	−	0.925295i	$-0.623817\pi$
$43$	−9196.52	−0.758494	−0.379247	+	0.925295i	$0.623817\pi$
$44$	−563.103	−0.0438487
$45$	−7934.08	−0.584070
$46$	2678.98	0.186670
$47$	−1493.15	−0.0985959	−0.0492980	−	0.998784i	$-0.515698\pi$
$47$	−1493.15	−0.0985959	−0.0492980	+	0.998784i	$0.515698\pi$
$48$	−9477.65	−0.593742
$49$	−4704.76	−0.279929
$50$	6507.34	0.368111
$51$	16719.9	0.900137
$52$	−1891.05	−0.0969826
$53$	−2809.00	−0.137361
$53$	−2809.00	−0.137361
$54$	20844.8	0.972778
$55$	−5478.72	−0.244215
$56$	18213.4	0.776104
$57$	6713.34	0.273685
$58$	11420.7	0.445783
$59$	4643.44	0.173664	0.0868319	−	0.996223i	$-0.472326\pi$
$59$	4643.44	0.173664	0.0868319	+	0.996223i	$0.472326\pi$
$60$	1734.69	0.0622078
$61$	19582.3	0.673811	0.336906	−	0.941538i	$-0.390620\pi$
$61$	19582.3	0.673811	0.336906	+	0.941538i	$0.390620\pi$
$62$	45015.5	1.48725
$63$	−19276.8	−0.611905
$64$	26717.3	0.815347
$65$	−18399.0	−0.540144
$66$	6030.74	0.170416
$67$	−9697.65	−0.263924	−0.131962	−	0.991255i	$-0.542128\pi$
$67$	−9697.65	−0.263924	−0.131962	+	0.991255i	$0.542128\pi$
$68$	9451.71	0.247878
$69$	−3642.80	−0.0921113
$70$	−30156.8	−0.735598
$71$	14943.0	0.351798	0.175899	−	0.984408i	$-0.443717\pi$
$71$	14943.0	0.351798	0.175899	+	0.984408i	$0.443717\pi$
$72$	−29010.8	−0.659521
$73$	−25148.2	−0.552332	−0.276166	−	0.961110i	$-0.589064\pi$
$73$	−25148.2	−0.552332	−0.276166	+	0.961110i	$0.589064\pi$
$74$	72359.4	1.53609
$75$	−8848.52	−0.181643
$76$	3795.03	0.0753670
$77$	−13311.2	−0.255854
$78$	20252.8	0.376919
$79$	−4682.25	−0.0844086	−0.0422043	−	0.999109i	$-0.513438\pi$
$79$	−4682.25	−0.0844086	−0.0422043	+	0.999109i	$0.513438\pi$
$80$	−52127.6	−0.910632
$81$	14236.1	0.241089
$82$	−57742.9	−0.948340
$83$	81402.0	1.29700	0.648500	−	0.761215i	$-0.275397\pi$
$83$	81402.0	1.29700	0.648500	+	0.761215i	$0.275397\pi$
$84$	4214.65	0.0651724
$85$	91960.5	1.38056
$86$	55677.9	0.811777
$87$	−15529.6	−0.219970
$88$	−20032.8	−0.275763
$89$	−136634.	−1.82845	−0.914227	−	0.405202i	$-0.867201\pi$
$89$	−136634.	−1.82845	−0.914227	+	0.405202i	$0.867201\pi$
$90$	48034.7	0.625100
$91$	−44702.6	−0.565886
$92$	−2059.27	−0.0253655
$93$	−61210.9	−0.733874
$94$	9039.88	0.105522
$95$	36923.8	0.419756
$96$	13765.2	0.152442
$97$	48279.8	0.520998	0.260499	−	0.965474i	$-0.416113\pi$
$97$	48279.8	0.520998	0.260499	+	0.965474i	$0.416113\pi$
$98$	28483.7	0.299593
$99$	21202.5	0.217420
$100$	−5002.04	−0.0500204
$101$	−106462.	−1.03846	−0.519232	−	0.854633i	$-0.673782\pi$
$101$	−106462.	−1.03846	−0.519232	+	0.854633i	$0.673782\pi$
$102$	−101226.	−0.963369
$103$	13043.9	0.121147	0.0605737	−	0.998164i	$-0.480707\pi$
$103$	13043.9	0.121147	0.0605737	+	0.998164i	$0.480707\pi$
$104$	−67275.5	−0.609921
$105$	41006.5	0.362977
$106$	17006.3	0.147010
$107$	9295.63	0.0784909	0.0392455	−	0.999230i	$-0.487505\pi$
$107$	9295.63	0.0784909	0.0392455	+	0.999230i	$0.487505\pi$
$108$	−16022.9	−0.132185
$109$	−9486.82	−0.0764812	−0.0382406	−	0.999269i	$-0.512175\pi$
$109$	−9486.82	−0.0764812	−0.0382406	+	0.999269i	$0.512175\pi$
$110$	33169.4	0.261370
$111$	−98392.5	−0.757974
$112$	−126651.	−0.954030
$113$	261246.	1.92465	0.962327	−	0.271894i	$-0.0876500\pi$
$113$	261246.	1.92465	0.962327	+	0.271894i	$0.0876500\pi$
$114$	−40644.1	−0.292911
$115$	−20035.6	−0.141273
$116$	−8778.84	−0.0605748
$117$	71203.7	0.480881
$118$	−28112.5	−0.185863
$119$	223430.	1.44635
$120$	61713.0	0.391223
$121$	14641.0	0.0909091
$122$	−118556.	−0.721145
$123$	78517.3	0.467954
$124$	−34602.3	−0.202093
$125$	−190163.	−1.08856
$126$	116706.	0.654890
$127$	127839.	0.703321	0.351660	−	0.936128i	$-0.385617\pi$
$127$	127839.	0.703321	0.351660	+	0.936128i	$0.385617\pi$
$128$	−215259.	−1.16128
$129$	−75709.4	−0.400567
$130$	111392.	0.578088
$131$	54758.4	0.278787	0.139393	−	0.990237i	$-0.455485\pi$
$131$	54758.4	0.278787	0.139393	+	0.990237i	$0.455485\pi$
$132$	−4635.69	−0.0231569
$133$	89710.9	0.439761
$134$	58711.8	0.282464
$135$	−155895.	−0.736204
$136$	336252.	1.55890
$137$	−175742.	−0.799972	−0.399986	−	0.916521i	$-0.630985\pi$
$137$	−175742.	−0.799972	−0.399986	+	0.916521i	$0.630985\pi$
$138$	22054.4	0.0985819
$139$	−446346.	−1.95945	−0.979727	−	0.200338i	$-0.935796\pi$
$139$	−446346.	−1.95945	−0.979727	+	0.200338i	$0.935796\pi$
$140$	23180.8	0.0999561
$141$	−12292.2	−0.0520693
$142$	−90468.6	−0.376511
$143$	49168.3	0.201069
$144$	201733.	0.810720
$145$	−85413.8	−0.337371
$146$	152253.	0.591132
$147$	−38731.4	−0.147833
$148$	−55620.9	−0.208730
$149$	−63195.8	−0.233197	−0.116598	−	0.993179i	$-0.537199\pi$
$149$	−63195.8	−0.233197	−0.116598	+	0.993179i	$0.537199\pi$
$150$	53571.0	0.194403
$151$	−307989.	−1.09924	−0.549621	−	0.835414i	$-0.685228\pi$
$151$	−307989.	−1.09924	−0.549621	+	0.835414i	$0.685228\pi$
$152$	135011.	0.473981
$153$	−355886.	−1.22909
$154$	80589.3	0.273827
$155$	−336664.	−1.12556
$156$	−15567.9	−0.0512174
$157$	254280.	0.823308	0.411654	−	0.911340i	$-0.364951\pi$
$157$	254280.	0.823308	0.411654	+	0.911340i	$0.364951\pi$
$158$	28347.4	0.0903381
$159$	−23124.8	−0.0725413
$160$	75709.2	0.233802
$161$	−48679.1	−0.148005
$162$	−86188.4	−0.258025
$163$	−109038.	−0.321446	−0.160723	−	0.987000i	$-0.551383\pi$
$163$	−109038.	−0.321446	−0.160723	+	0.987000i	$0.551383\pi$
$164$	44385.6	0.128864
$165$	−45103.0	−0.128972
$166$	−492827.	−1.38811
$167$	317473.	0.880877	0.440438	−	0.897783i	$-0.354823\pi$
$167$	317473.	0.880877	0.440438	+	0.897783i	$0.354823\pi$
$168$	149940.	0.409867
$169$	−206173.	−0.555284
$170$	−556751.	−1.47754
$171$	−142894.	−0.373702
$172$	−42798.3	−0.110308
$173$	188224.	0.478144	0.239072	−	0.971002i	$-0.423157\pi$
$173$	188224.	0.478144	0.239072	+	0.971002i	$0.423157\pi$
$174$	94019.9	0.235422
$175$	−118244.	−0.291865
$176$	139303.	0.338983
$177$	38226.6	0.0917134
$178$	827215.	1.95690
$179$	−102293.	−0.238624	−0.119312	−	0.992857i	$-0.538069\pi$
$179$	−102293.	−0.238624	−0.119312	+	0.992857i	$0.538069\pi$
$180$	−36923.2	−0.0849411
$181$	−690793.	−1.56730	−0.783649	−	0.621204i	$-0.786644\pi$
$181$	−690793.	−1.56730	−0.783649	+	0.621204i	$0.786644\pi$
$182$	270640.	0.605638
$183$	161209.	0.355845
$184$	−73259.9	−0.159523
$185$	−541164.	−1.16252
$186$	370585.	0.785427
$187$	−245750.	−0.513913
$188$	−6948.74	−0.0143388
$189$	−378767.	−0.771289
$190$	−223545.	−0.449243
$191$	337673.	0.669751	0.334876	−	0.942262i	$-0.391306\pi$
$191$	337673.	0.669751	0.334876	+	0.942262i	$0.391306\pi$
$192$	219947.	0.430591
$193$	−664130.	−1.28339	−0.641696	−	0.766959i	$-0.721769\pi$
$193$	−664130.	−1.28339	−0.641696	+	0.766959i	$0.721769\pi$
$194$	−292297.	−0.557597
$195$	−151468.	−0.285255
$196$	−21894.8	−0.0407099
$197$	−109755.	−0.201493	−0.100746	−	0.994912i	$-0.532123\pi$
$197$	−109755.	−0.201493	−0.100746	+	0.994912i	$0.532123\pi$
$198$	−128365.	−0.232693
$199$	−1.10271e6	−1.97391	−0.986956	−	0.160991i	$-0.948531\pi$
$199$	−1.10271e6	−1.97391	−0.986956	+	0.160991i	$0.948531\pi$
$200$	−177951.	−0.314577
$201$	−79834.9	−0.139381
$202$	644546.	1.11141
$203$	−207524.	−0.353449
$204$	77810.3	0.130907
$205$	431850.	0.717709
$206$	−78970.8	−0.129658
$207$	77537.6	0.125773
$208$	467815.	0.749749
$209$	−98672.9	−0.156254
$210$	−248263.	−0.388476
$211$	−896366.	−1.38605	−0.693025	−	0.720913i	$-0.743723\pi$
$211$	−896366.	−1.38605	−0.693025	+	0.720913i	$0.743723\pi$
$212$	−13072.4	−0.0199763
$213$	123017.	0.185787
$214$	−56277.9	−0.0840047
$215$	−416406.	−0.614357
$216$	−570028.	−0.831307
$217$	−817966.	−1.17920
$218$	57435.4	0.0818538
$219$	−207030.	−0.291691
$220$	−25496.6	−0.0355161
$221$	−825292.	−1.13665
$222$	595691.	0.811220
$223$	−423919.	−0.570849	−0.285424	−	0.958401i	$-0.592135\pi$
$223$	−423919.	−0.570849	−0.285424	+	0.958401i	$0.592135\pi$
$224$	183945.	0.244945
$225$	188342.	0.248022
$226$	−1.58164e6	−2.05986
$227$	410606.	0.528884	0.264442	−	0.964402i	$-0.414812\pi$
$227$	410606.	0.528884	0.264442	+	0.964402i	$0.414812\pi$
$228$	31242.2	0.0398020
$229$	126105.	0.158907	0.0794537	−	0.996839i	$-0.474682\pi$
$229$	126105.	0.158907	0.0794537	+	0.996839i	$0.474682\pi$
$230$	121300.	0.151197
$231$	−109583.	−0.135118
$232$	−312314.	−0.380953
$233$	202168.	0.243962	0.121981	−	0.992532i	$-0.461075\pi$
$233$	202168.	0.243962	0.121981	+	0.992532i	$0.461075\pi$
$234$	−431084.	−0.514662
$235$	−67607.9	−0.0798597
$236$	21609.4	0.0252559
$237$	−38546.1	−0.0445769
$238$	−1.35270e6	−1.54795
$239$	−996967.	−1.12898	−0.564489	−	0.825440i	$-0.690927\pi$
$239$	−996967.	−1.12898	−0.564489	+	0.825440i	$0.690927\pi$
$240$	−429135.	−0.480913
$241$	75407.2	0.0836316	0.0418158	−	0.999125i	$-0.486686\pi$
$241$	75407.2	0.0836316	0.0418158	+	0.999125i	$0.486686\pi$
$242$	−88640.0	−0.0972952
$243$	953850.	1.03625
$244$	91130.9	0.0979921
$245$	−213025.	−0.226734
$246$	−475362.	−0.500826
$247$	−331369.	−0.345597
$248$	−1.23100e6	−1.27096
$249$	670134.	0.684957
$250$	1.15129e6	1.16503
$251$	−1.19976e6	−1.20202	−0.601009	−	0.799242i	$-0.705234\pi$
$251$	−1.19976e6	−1.20202	−0.601009	+	0.799242i	$0.705234\pi$
$252$	−89709.5	−0.0889891
$253$	53542.0	0.0525888
$254$	−773966.	−0.752727
$255$	757056.	0.729084
$256$	448275.	0.427509
$257$	513997.	0.485432	0.242716	−	0.970097i	$-0.421962\pi$
$257$	513997.	0.485432	0.242716	+	0.970097i	$0.421962\pi$
$258$	458362.	0.428706
$259$	−1.31483e6	−1.21792
$260$	−85624.1	−0.0785530
$261$	330550.	0.300356
$262$	−331520.	−0.298371
$263$	275445.	0.245553	0.122777	−	0.992434i	$-0.460820\pi$
$263$	275445.	0.245553	0.122777	+	0.992434i	$0.460820\pi$
$264$	−164918.	−0.145633
$265$	−127188.	−0.111258
$266$	−543131.	−0.470653
$267$	−1.12483e6	−0.965622
$268$	−45130.4	−0.0383824
$269$	97946.8	0.0825296	0.0412648	−	0.999148i	$-0.486861\pi$
$269$	97946.8	0.0825296	0.0412648	+	0.999148i	$0.486861\pi$
$270$	943826.	0.787921
$271$	1.58399e6	1.31017	0.655086	−	0.755554i	$-0.272632\pi$
$271$	1.58399e6	1.31017	0.655086	+	0.755554i	$0.272632\pi$
$272$	−2.33820e6	−1.91628
$273$	−368009.	−0.298849
$274$	1.06398e6	0.856168
$275$	130056.	0.103705
$276$	−16952.7	−0.0133957
$277$	2.18994e6	1.71488	0.857439	−	0.514586i	$-0.172054\pi$
$277$	2.18994e6	1.71488	0.857439	+	0.514586i	$0.172054\pi$
$278$	2.70229e6	2.09710
$279$	1.30288e6	1.00206
$280$	824676.	0.628620
$281$	−1.62364e6	−1.22666	−0.613329	−	0.789827i	$-0.710170\pi$
$281$	−1.62364e6	−1.22666	−0.613329	+	0.789827i	$0.710170\pi$
$282$	74419.9	0.0557271
$283$	20622.0	0.0153061	0.00765304	−	0.999971i	$-0.497564\pi$
$283$	20622.0	0.0153061	0.00765304	+	0.999971i	$0.497564\pi$
$284$	69541.1	0.0511618
$285$	303971.	0.221677
$286$	−297676.	−0.215193
$287$	1.04923e6	0.751913
$288$	−292993.	−0.208150
$289$	2.70506e6	1.90517
$290$	517115.	0.361071
$291$	397458.	0.275143
$292$	−117033.	−0.0803254
$293$	−377549.	−0.256924	−0.128462	−	0.991714i	$-0.541004\pi$
$293$	−377549.	−0.256924	−0.128462	+	0.991714i	$0.541004\pi$
$294$	234489.	0.158218
$295$	210249.	0.140662
$296$	−1.97876e6	−1.31269
$297$	416605.	0.274052
$298$	382602.	0.249578
$299$	179808.	0.116314
$300$	−41178.8	−0.0264162
$301$	−1.01171e6	−0.643636
$302$	1.86464e6	1.17646
$303$	−876438.	−0.548421
$304$	−938830.	−0.582644
$305$	886659.	0.545766
$306$	2.15462e6	1.31543
$307$	−3.09586e6	−1.87471	−0.937357	−	0.348371i	$-0.886735\pi$
$307$	−3.09586e6	−1.87471	−0.937357	+	0.348371i	$0.886735\pi$
$308$	−61947.1	−0.0372087
$309$	107383.	0.0639790
$310$	2.03824e6	1.20462
$311$	−1.69775e6	−0.995341	−0.497671	−	0.867366i	$-0.665811\pi$
$311$	−1.69775e6	−0.995341	−0.497671	+	0.867366i	$0.665811\pi$
$312$	−553838.	−0.322104
$313$	669052.	0.386010	0.193005	−	0.981198i	$-0.438177\pi$
$313$	669052.	0.386010	0.193005	+	0.981198i	$0.438177\pi$
$314$	−1.53947e6	−0.881144
$315$	−872829.	−0.495625
$316$	−21790.0	−0.0122755
$317$	−2.61124e6	−1.45948	−0.729740	−	0.683724i	$-0.760359\pi$
$317$	−2.61124e6	−1.45948	−0.729740	+	0.683724i	$0.760359\pi$
$318$	140003.	0.0776371
$319$	228255.	0.125587
$320$	1.20972e6	0.660406
$321$	76525.3	0.0414517
$322$	294715.	0.158402
$323$	1.65623e6	0.883312
$324$	66251.0	0.0350614
$325$	436761.	0.229370
$326$	660140.	0.344027
$327$	−78099.3	−0.0403903
$328$	1.57905e6	0.810423
$329$	−164262.	−0.0836656
$330$	273064.	0.138032
$331$	−1.42856e6	−0.716687	−0.358344	−	0.933590i	$-0.616658\pi$
$331$	−1.42856e6	−0.716687	−0.358344	+	0.933590i	$0.616658\pi$
$332$	378824.	0.188622
$333$	2.09430e6	1.03497
$334$	−1.92205e6	−0.942756
$335$	−439097.	−0.213771
$336$	−1.04264e6	−0.503832
$337$	−900961.	−0.432147	−0.216073	−	0.976377i	$-0.569325\pi$
$337$	−900961.	−0.432147	−0.216073	+	0.976377i	$0.569325\pi$
$338$	1.24822e6	0.594292
$339$	2.15068e6	1.01643
$340$	427961.	0.200774
$341$	899680.	0.418988
$342$	865116.	0.399953
$343$	−2.36651e6	−1.08611
$344$	−1.52258e6	−0.693720
$345$	−164941.	−0.0746074
$346$	−1.13955e6	−0.511733
$347$	218131.	0.0972508	0.0486254	−	0.998817i	$-0.484516\pi$
$347$	218131.	0.0972508	0.0486254	+	0.998817i	$0.484516\pi$
$348$	−72270.9	−0.0319901
$349$	2.37933e6	1.04566	0.522831	−	0.852437i	$-0.324876\pi$
$349$	2.37933e6	1.04566	0.522831	+	0.852437i	$0.324876\pi$
$350$	715874.	0.312368
$351$	1.39907e6	0.606137
$352$	−202321.	−0.0870330
$353$	−2.52861e6	−1.08005	−0.540027	−	0.841648i	$-0.681586\pi$
$353$	−2.52861e6	−1.08005	−0.540027	+	0.841648i	$0.681586\pi$
$354$	−231433.	−0.0981560
$355$	676601.	0.284945
$356$	−635861.	−0.265911
$357$	1.83936e6	0.763830
$358$	619307.	0.255387
$359$	−3.39778e6	−1.39142	−0.695712	−	0.718321i	$-0.744911\pi$
$359$	−3.39778e6	−1.39142	−0.695712	+	0.718321i	$0.744911\pi$
$360$	−1.31357e6	−0.534192
$361$	−1.81109e6	−0.731430
$362$	4.18222e6	1.67740
$363$	120531.	0.0480099
$364$	−208034.	−0.0822966
$365$	−1.13868e6	−0.447372
$366$	−975996.	−0.380843
$367$	−1.16856e6	−0.452882	−0.226441	−	0.974025i	$-0.572709\pi$
$367$	−1.16856e6	−0.452882	−0.226441	+	0.974025i	$0.572709\pi$
$368$	509429.	0.196094
$369$	−1.67125e6	−0.638963
$370$	3.27634e6	1.24418
$371$	−309019.	−0.116560
$372$	−284860.	−0.106727
$373$	1.84148e6	0.685324	0.342662	−	0.939459i	$-0.388671\pi$
$373$	1.84148e6	0.685324	0.342662	+	0.939459i	$0.388671\pi$
$374$	1.48783e6	0.550014
$375$	−1.56550e6	−0.574877
$376$	−247207.	−0.0901760
$377$	766539.	0.277767
$378$	2.29314e6	0.825471
$379$	1.47692e6	0.528153	0.264076	−	0.964502i	$-0.414933\pi$
$379$	1.47692e6	0.528153	0.264076	+	0.964502i	$0.414933\pi$
$380$	171834.	0.0610450
$381$	1.05242e6	0.371430
$382$	−2.04435e6	−0.716800
$383$	−3.86100e6	−1.34494	−0.672470	−	0.740125i	$-0.734766\pi$
$383$	−3.86100e6	−1.34494	−0.672470	+	0.740125i	$0.734766\pi$
$384$	−1.77210e6	−0.613281
$385$	−602715.	−0.207234
$386$	4.02080e6	1.37355
$387$	1.61148e6	0.546951
$388$	224682.	0.0757685
$389$	5.51954e6	1.84939	0.924695	−	0.380709i	$-0.124320\pi$
$389$	5.51954e6	1.84939	0.924695	+	0.380709i	$0.124320\pi$
$390$	917020.	0.305293
$391$	−898705.	−0.297287
$392$	−778923.	−0.256023
$393$	450793.	0.147230
$394$	664483.	0.215647
$395$	−212006.	−0.0683684
$396$	98671.3	0.0316193
$397$	2.73362e6	0.870486	0.435243	−	0.900313i	$-0.356663\pi$
$397$	2.73362e6	0.870486	0.435243	+	0.900313i	$0.356663\pi$
$398$	6.67605e6	2.11257
$399$	738536.	0.232241
$400$	1.23743e6	0.386695
$401$	−5.22912e6	−1.62393	−0.811966	−	0.583705i	$-0.801602\pi$
$401$	−5.22912e6	−1.62393	−0.811966	+	0.583705i	$0.801602\pi$
$402$	483339.	0.149172
$403$	3.02136e6	0.926701
$404$	−495447.	−0.151023
$405$	644589.	0.195275
$406$	1.25640e6	0.378278
$407$	1.44618e6	0.432748
$408$	2.76816e6	0.823267
$409$	−2.71552e6	−0.802683	−0.401342	−	0.915928i	$-0.631456\pi$
$409$	−2.71552e6	−0.802683	−0.401342	+	0.915928i	$0.631456\pi$
$410$	−2.61452e6	−0.768126
$411$	−1.44678e6	−0.422472
$412$	60703.0	0.0176184
$413$	510825.	0.147366
$414$	−469431.	−0.134608
$415$	3.68578e6	1.05053
$416$	−679446.	−0.192496
$417$	−3.67450e6	−1.03480
$418$	597389.	0.167231
$419$	−1.46019e6	−0.406325	−0.203163	−	0.979145i	$-0.565122\pi$
$419$	−1.46019e6	−0.406325	−0.203163	+	0.979145i	$0.565122\pi$
$420$	190834.	0.0527877
$421$	3.76663e6	1.03573	0.517867	−	0.855461i	$-0.326726\pi$
$421$	3.76663e6	1.03573	0.517867	+	0.855461i	$0.326726\pi$
$422$	5.42681e6	1.48342
$423$	261641.	0.0710977
$424$	−465060.	−0.125630
$425$	−2.18299e6	−0.586246
$426$	−744774.	−0.198838
$427$	2.15425e6	0.571776
$428$	43259.5	0.0114149
$429$	404773.	0.106186
$430$	2.52102e6	0.657514
$431$	7.34618e6	1.90488	0.952442	−	0.304720i	$-0.0985627\pi$
$431$	7.34618e6	1.90488	0.952442	+	0.304720i	$0.0985627\pi$
$432$	3.96382e6	1.02189
$433$	7.74511e6	1.98522	0.992609	−	0.121358i	$-0.0387250\pi$
$433$	7.74511e6	1.98522	0.992609	+	0.121358i	$0.0387250\pi$
$434$	4.95216e6	1.26203
$435$	−703160.	−0.178169
$436$	−44149.3	−0.0111226
$437$	−360846.	−0.0903896
$438$	1.25341e6	0.312182
$439$	3.29717e6	0.816545	0.408272	−	0.912860i	$-0.366131\pi$
$439$	3.29717e6	0.816545	0.408272	+	0.912860i	$0.366131\pi$
$440$	−907060.	−0.223359
$441$	824404.	0.201857
$442$	4.99651e6	1.21650
$443$	4.08677e6	0.989398	0.494699	−	0.869064i	$-0.335278\pi$
$443$	4.08677e6	0.989398	0.494699	+	0.869064i	$0.335278\pi$
$444$	−457894.	−0.110232
$445$	−6.18661e6	−1.48099
$446$	2.56651e6	0.610949
$447$	−520253.	−0.123153
$448$	2.93917e6	0.691879
$449$	2.48876e6	0.582595	0.291298	−	0.956632i	$-0.405913\pi$
$449$	2.48876e6	0.582595	0.291298	+	0.956632i	$0.405913\pi$
$450$	−1.14027e6	−0.265445
$451$	−1.15405e6	−0.267167
$452$	1.21577e6	0.279902
$453$	−2.53549e6	−0.580519
$454$	−2.48590e6	−0.566036
$455$	−2.02407e6	−0.458351
$456$	1.11147e6	0.250313
$457$	−2.16301e6	−0.484472	−0.242236	−	0.970217i	$-0.577881\pi$
$457$	−2.16301e6	−0.484472	−0.242236	+	0.970217i	$0.577881\pi$
$458$	−763470.	−0.170070
$459$	−6.99273e6	−1.54923
$460$	−93240.8	−0.0205452
$461$	1.37232e6	0.300747	0.150374	−	0.988629i	$-0.451952\pi$
$461$	1.37232e6	0.300747	0.150374	+	0.988629i	$0.451952\pi$
$462$	663443.	0.144610
$463$	−4.77621e6	−1.03545	−0.517727	−	0.855546i	$-0.673222\pi$
$463$	−4.77621e6	−1.03545	−0.517727	+	0.855546i	$0.673222\pi$
$464$	2.17175e6	0.468289
$465$	−2.77155e6	−0.594415
$466$	−1.22397e6	−0.261100
$467$	−209261.	−0.0444013	−0.0222006	−	0.999754i	$-0.507067\pi$
$467$	−209261.	−0.0444013	−0.0222006	+	0.999754i	$0.507067\pi$
$468$	331364.	0.0699343
$469$	−1.06684e6	−0.223958
$470$	409314.	0.0854696
$471$	2.09333e6	0.434796
$472$	768770.	0.158833
$473$	1.11278e6	0.228695
$474$	233367.	0.0477083
$475$	−876511.	−0.178247
$476$	1.03978e6	0.210342
$477$	492214.	0.0990509
$478$	6.03587e6	1.20829
$479$	5.07168e6	1.00998	0.504991	−	0.863125i	$-0.331496\pi$
$479$	5.07168e6	1.00998	0.504991	+	0.863125i	$0.331496\pi$
$480$	623269.	0.123473
$481$	4.85663e6	0.957134
$482$	−456533.	−0.0895065
$483$	−400745.	−0.0781629
$484$	68135.5	0.0132209
$485$	2.18604e6	0.421992
$486$	−5.77483e6	−1.10904
$487$	3.11084e6	0.594367	0.297184	−	0.954820i	$-0.403953\pi$
$487$	3.11084e6	0.594367	0.297184	+	0.954820i	$0.403953\pi$
$488$	3.24205e6	0.616269
$489$	−897642.	−0.169758
$490$	1.28970e6	0.242661
$491$	−5.52346e6	−1.03397	−0.516984	−	0.855995i	$-0.672945\pi$
$491$	−5.52346e6	−1.03397	−0.516984	+	0.855995i	$0.672945\pi$
$492$	365400.	0.0680543
$493$	−3.83127e6	−0.709946
$494$	2.00619e6	0.369874
$495$	960023.	0.176104
$496$	8.56006e6	1.56233
$497$	1.64389e6	0.298525
$498$	−4.05715e6	−0.733073
$499$	−6.36882e6	−1.14501	−0.572503	−	0.819903i	$-0.694027\pi$
$499$	−6.36882e6	−1.14501	−0.572503	+	0.819903i	$0.694027\pi$
$500$	−884972.	−0.158309
$501$	2.61356e6	0.465199
$502$	7.26364e6	1.28646
$503$	259451.	0.0457230	0.0228615	−	0.999739i	$-0.492722\pi$
$503$	259451.	0.0457230	0.0228615	+	0.999739i	$0.492722\pi$
$504$	−3.19148e6	−0.559650
$505$	−4.82046e6	−0.841124
$506$	−324156.	−0.0562831
$507$	−1.69730e6	−0.293250
$508$	594929.	0.102284
$509$	−2.21234e6	−0.378493	−0.189247	−	0.981930i	$-0.560605\pi$
$509$	−2.21234e6	−0.378493	−0.189247	+	0.981930i	$0.560605\pi$
$510$	−4.58339e6	−0.780300
$511$	−2.76656e6	−0.468692
$512$	4.17432e6	0.703738
$513$	−2.80771e6	−0.471040
$514$	−3.11186e6	−0.519532
$515$	590610.	0.0981257
$516$	−352332.	−0.0582543
$517$	180671.	0.0297278
$518$	7.96027e6	1.30348
$519$	1.54953e6	0.252512
$520$	−3.04614e6	−0.494017
$521$	3.88051e6	0.626317	0.313159	−	0.949701i	$-0.398613\pi$
$521$	3.88051e6	0.626317	0.313159	+	0.949701i	$0.398613\pi$
$522$	−2.00123e6	−0.321455
$523$	−582755.	−0.0931606	−0.0465803	−	0.998915i	$-0.514832\pi$
$523$	−582755.	−0.0931606	−0.0465803	+	0.998915i	$0.514832\pi$
$524$	254832.	0.0405439
$525$	−973428.	−0.154136
$526$	−1.66761e6	−0.262803
$527$	−1.51012e7	−2.36856
$528$	1.14680e6	0.179020
$529$	−6.24054e6	−0.969579
$530$	770025.	0.119073
$531$	−813659.	−0.125229
$532$	417492.	0.0639542
$533$	−3.87560e6	−0.590909
$534$	6.80996e6	1.03345
$535$	420894.	0.0635752
$536$	−1.60555e6	−0.241386
$537$	−842118.	−0.126019
$538$	−592993.	−0.0883271
$539$	569276.	0.0844016
$540$	−725497.	−0.107066
$541$	7.06518e6	1.03784	0.518919	−	0.854823i	$-0.326334\pi$
$541$	7.06518e6	1.03784	0.518919	+	0.854823i	$0.326334\pi$
$542$	−9.58983e6	−1.40221
$543$	−5.68688e6	−0.827703
$544$	3.39596e6	0.492001
$545$	−429551.	−0.0619474
$546$	2.22801e6	0.319843
$547$	1.31698e7	1.88196	0.940982	−	0.338455i	$-0.109904\pi$
$547$	1.31698e7	1.88196	0.940982	+	0.338455i	$0.109904\pi$
$548$	−817860.	−0.116340
$549$	−3.43135e6	−0.485886
$550$	−787389.	−0.110990
$551$	−1.53832e6	−0.215858
$552$	−603105.	−0.0842452
$553$	−515095.	−0.0716266
$554$	−1.32584e7	−1.83534
$555$	−4.45508e6	−0.613936
$556$	−2.07718e6	−0.284963
$557$	−1.03830e7	−1.41803	−0.709017	−	0.705191i	$-0.750861\pi$
$557$	−1.03830e7	−1.41803	−0.709017	+	0.705191i	$0.750861\pi$
$558$	−7.88795e6	−1.07245
$559$	3.73700e6	0.505817
$560$	−5.73457e6	−0.772735
$561$	−2.02311e6	−0.271402
$562$	9.82989e6	1.31283
$563$	−3.72010e6	−0.494634	−0.247317	−	0.968935i	$-0.579549\pi$
$563$	−3.72010e6	−0.494634	−0.247317	+	0.968935i	$0.579549\pi$
$564$	−57204.8	−0.00757242
$565$	1.18289e7	1.55891
$566$	−124850.	−0.0163813
$567$	1.56611e6	0.204581
$568$	2.47398e6	0.321755
$569$	−1.13775e7	−1.47321	−0.736606	−	0.676322i	$-0.763573\pi$
$569$	−1.13775e7	−1.47321	−0.736606	+	0.676322i	$0.763573\pi$
$570$	−1.84031e6	−0.237249
$571$	−5.89264e6	−0.756345	−0.378172	−	0.925735i	$-0.623447\pi$
$571$	−5.89264e6	−0.756345	−0.378172	+	0.925735i	$0.623447\pi$
$572$	228817.	0.0292414
$573$	2.77986e6	0.353701
$574$	−6.35231e6	−0.804733
$575$	475613.	0.0599908
$576$	−4.68161e6	−0.587948
$577$	−5.28933e6	−0.661396	−0.330698	−	0.943737i	$-0.607284\pi$
$577$	−5.28933e6	−0.661396	−0.330698	+	0.943737i	$0.607284\pi$
$578$	−1.63771e7	−2.03900
$579$	−5.46738e6	−0.677770
$580$	−397494.	−0.0490638
$581$	8.95505e6	1.10060
$582$	−2.40631e6	−0.294472
$583$	339889.	0.0414158
$584$	−4.16355e6	−0.505164
$585$	3.22401e6	0.389499
$586$	2.28577e6	0.274972
$587$	−3.20141e6	−0.383483	−0.191742	−	0.981445i	$-0.561414\pi$
$587$	−3.20141e6	−0.383483	−0.191742	+	0.981445i	$0.561414\pi$
$588$	−180246.	−0.0214992
$589$	−6.06338e6	−0.720157
$590$	−1.27289e6	−0.150544
$591$	−903548.	−0.106410
$592$	1.37597e7	1.61364
$593$	7.44350e6	0.869241	0.434621	−	0.900614i	$-0.356883\pi$
$593$	7.44350e6	0.869241	0.434621	+	0.900614i	$0.356883\pi$
$594$	−2.52222e6	−0.293304
$595$	1.01166e7	1.17150
$596$	−294097.	−0.0339137
$597$	−9.07793e6	−1.04244
$598$	−1.08860e6	−0.124485
$599$	−5.68284e6	−0.647141	−0.323570	−	0.946204i	$-0.604883\pi$
$599$	−5.68284e6	−0.647141	−0.323570	+	0.946204i	$0.604883\pi$
$600$	−1.46497e6	−0.166131
$601$	−1.40438e7	−1.58599	−0.792993	−	0.609230i	$-0.791479\pi$
$601$	−1.40438e7	−1.58599	−0.792993	+	0.609230i	$0.791479\pi$
$602$	6.12513e6	0.688849
$603$	1.69930e6	0.190316
$604$	−1.43330e6	−0.159862
$605$	662925.	0.0736336
$606$	5.30616e6	0.586947
$607$	3.87633e6	0.427021	0.213511	−	0.976941i	$-0.431510\pi$
$607$	3.87633e6	0.427021	0.213511	+	0.976941i	$0.431510\pi$
$608$	1.36354e6	0.149592
$609$	−1.70842e6	−0.186660
$610$	−5.36804e6	−0.584105
$611$	606741.	0.0657507
$612$	−1.65620e6	−0.178745
$613$	−2.54337e6	−0.273374	−0.136687	−	0.990614i	$-0.543646\pi$
$613$	−2.54337e6	−0.273374	−0.136687	+	0.990614i	$0.543646\pi$
$614$	1.87430e7	2.00641
$615$	3.55516e6	0.379028
$616$	−2.20382e6	−0.234004
$617$	6.74401e6	0.713190	0.356595	−	0.934259i	$-0.383938\pi$
$617$	6.74401e6	0.713190	0.356595	+	0.934259i	$0.383938\pi$
$618$	−650119.	−0.0684734
$619$	8.90635e6	0.934271	0.467136	−	0.884186i	$-0.345286\pi$
$619$	8.90635e6	0.934271	0.467136	+	0.884186i	$0.345286\pi$
$620$	−1.56675e6	−0.163689
$621$	1.52352e6	0.158533
$622$	1.02786e7	1.06526
$623$	−1.50311e7	−1.55157
$624$	3.85124e6	0.395949
$625$	−5.25146e6	−0.537749
$626$	−4.05060e6	−0.413127
$627$	−812314.	−0.0825193
$628$	1.18335e6	0.119733
$629$	−2.42741e7	−2.44634
$630$	5.28431e6	0.530441
$631$	−1.38174e7	−1.38150	−0.690752	−	0.723092i	$-0.742720\pi$
$631$	−1.38174e7	−1.38150	−0.690752	+	0.723092i	$0.742720\pi$
$632$	−775196.	−0.0772002
$633$	−7.37924e6	−0.731985
$634$	1.58090e7	1.56201
$635$	5.78837e6	0.569668
$636$	−107617.	−0.0105496
$637$	1.91178e6	0.186676
$638$	−1.38191e6	−0.134409
$639$	−2.61843e6	−0.253682
$640$	−9.74664e6	−0.940600
$641$	8.15626e6	0.784054	0.392027	−	0.919954i	$-0.371774\pi$
$641$	8.15626e6	0.784054	0.392027	+	0.919954i	$0.371774\pi$
$642$	−463302.	−0.0443636
$643$	1.87489e7	1.78833	0.894165	−	0.447737i	$-0.147770\pi$
$643$	1.87489e7	1.78833	0.894165	+	0.447737i	$0.147770\pi$
$644$	−226540.	−0.0215244
$645$	−3.42802e6	−0.324447
$646$	−1.00272e7	−0.945362
$647$	1.42928e7	1.34232	0.671159	−	0.741314i	$-0.265797\pi$
$647$	1.42928e7	1.34232	0.671159	+	0.741314i	$0.265797\pi$
$648$	2.35693e6	0.220500
$649$	−561856.	−0.0523616
$650$	−2.64426e6	−0.245482
$651$	−6.73382e6	−0.622744
$652$	−507434.	−0.0467477
$653$	−1.54230e7	−1.41542	−0.707712	−	0.706501i	$-0.750272\pi$
$653$	−1.54230e7	−1.41542	−0.707712	+	0.706501i	$0.750272\pi$
$654$	472831.	0.0432277
$655$	2.47939e6	0.225809
$656$	−1.09803e7	−0.996217
$657$	4.40666e6	0.398287
$658$	994479.	0.0895428
$659$	−2.26986e6	−0.203604	−0.101802	−	0.994805i	$-0.532461\pi$
$659$	−2.26986e6	−0.203604	−0.101802	+	0.994805i	$0.532461\pi$
$660$	−209898.	−0.0187563
$661$	−7.83129e6	−0.697155	−0.348578	−	0.937280i	$-0.613335\pi$
$661$	−7.83129e6	−0.697155	−0.348578	+	0.937280i	$0.613335\pi$
$662$	8.64886e6	0.767033
$663$	−6.79413e6	−0.600275
$664$	1.34770e7	1.18624
$665$	4.06199e6	0.356193
$666$	−1.26794e7	−1.10767
$667$	834726.	0.0726490
$668$	1.47744e6	0.128106
$669$	−3.48987e6	−0.301470
$670$	2.65839e6	0.228788
$671$	−2.36945e6	−0.203162
$672$	1.51431e6	0.129357
$673$	1.38262e7	1.17670	0.588348	−	0.808608i	$-0.299779\pi$
$673$	1.38262e7	1.17670	0.588348	+	0.808608i	$0.299779\pi$
$674$	5.45463e6	0.462504
$675$	3.70070e6	0.312625
$676$	−959478.	−0.0807548
$677$	−1.48767e6	−0.124748	−0.0623740	−	0.998053i	$-0.519867\pi$
$677$	−1.48767e6	−0.124748	−0.0623740	+	0.998053i	$0.519867\pi$
$678$	−1.30207e7	−1.08783
$679$	5.31127e6	0.442103
$680$	1.52250e7	1.26266
$681$	3.38027e6	0.279308
$682$	−5.44687e6	−0.448421
$683$	1.99317e7	1.63491	0.817454	−	0.575994i	$-0.195385\pi$
$683$	1.99317e7	1.63491	0.817454	+	0.575994i	$0.195385\pi$
$684$	−664994.	−0.0543473
$685$	−7.95738e6	−0.647953
$686$	1.43274e7	1.16241
$687$	1.03815e6	0.0839203
$688$	1.05876e7	0.852760
$689$	1.14144e6	0.0916017
$690$	998593.	0.0798483
$691$	6.21733e6	0.495346	0.247673	−	0.968844i	$-0.420334\pi$
$691$	6.21733e6	0.495346	0.247673	+	0.968844i	$0.420334\pi$
$692$	875946.	0.0695364
$693$	2.33250e6	0.184496
$694$	−1.32061e6	−0.104082
$695$	−2.02100e7	−1.58710
$696$	−2.57109e6	−0.201185
$697$	1.93708e7	1.51031
$698$	−1.44050e7	−1.11912
$699$	1.66432e6	0.128838
$700$	−550276.	−0.0424458
$701$	−1.27285e7	−0.978323	−0.489161	−	0.872193i	$-0.662697\pi$
$701$	−1.27285e7	−0.978323	−0.489161	+	0.872193i	$0.662697\pi$
$702$	−8.47028e6	−0.648717
$703$	−9.74649e6	−0.743806
$704$	−3.23279e6	−0.245836
$705$	−556575.	−0.0421746
$706$	1.53088e7	1.15592
$707$	−1.17119e7	−0.881209
$708$	177897.	0.0133378
$709$	1.31427e7	0.981904	0.490952	−	0.871187i	$-0.336649\pi$
$709$	1.31427e7	0.981904	0.490952	+	0.871187i	$0.336649\pi$
$710$	−4.09630e6	−0.304962
$711$	820459.	0.0608671
$712$	−2.26212e7	−1.67231
$713$	3.29012e6	0.242375
$714$	−1.11359e7	−0.817487
$715$	2.22627e6	0.162860
$716$	−476047.	−0.0347030
$717$	−8.20742e6	−0.596223
$718$	2.05710e7	1.48917
$719$	1.15046e7	0.829945	0.414972	−	0.909834i	$-0.363791\pi$
$719$	1.15046e7	0.829945	0.414972	+	0.909834i	$0.363791\pi$
$720$	9.13420e6	0.656658
$721$	1.43496e6	0.102802
$722$	1.09648e7	0.782811
$723$	620782.	0.0441665
$724$	−3.21478e6	−0.227931
$725$	2.02759e6	0.143263
$726$	−729720.	−0.0513824
$727$	−1.71361e6	−0.120247	−0.0601236	−	0.998191i	$-0.519149\pi$
$727$	−1.71361e6	−0.120247	−0.0601236	+	0.998191i	$0.519149\pi$
$728$	−7.40099e6	−0.517560
$729$	4.39311e6	0.306163
$730$	6.89382e6	0.478799
$731$	−1.86780e7	−1.29282
$732$	750225.	0.0517504
$733$	−5.30774e6	−0.364880	−0.182440	−	0.983217i	$-0.558399\pi$
$733$	−5.30774e6	−0.364880	−0.182440	+	0.983217i	$0.558399\pi$
$734$	7.07472e6	0.484695
$735$	−1.75371e6	−0.119740
$736$	−739886.	−0.0503466
$737$	1.17342e6	0.0795762
$738$	1.01182e7	0.683849
$739$	−1.78852e7	−1.20471	−0.602354	−	0.798229i	$-0.705770\pi$
$739$	−1.78852e7	−1.20471	−0.602354	+	0.798229i	$0.705770\pi$
$740$	−2.51844e6	−0.169065
$741$	−2.72796e6	−0.182513
$742$	1.87087e6	0.124748
$743$	−2.27344e6	−0.151082	−0.0755408	−	0.997143i	$-0.524068\pi$
$743$	−2.27344e6	−0.151082	−0.0755408	+	0.997143i	$0.524068\pi$
$744$	−1.01341e7	−0.671202
$745$	−2.86142e6	−0.188882
$746$	−1.11488e7	−0.733466
$747$	−1.42639e7	−0.935268
$748$	−1.14366e6	−0.0747381
$749$	1.02261e6	0.0666050
$750$	9.47790e6	0.615260
$751$	1.94683e7	1.25959	0.629793	−	0.776763i	$-0.283140\pi$
$751$	1.94683e7	1.25959	0.629793	+	0.776763i	$0.283140\pi$
$752$	1.71901e6	0.110849
$753$	−9.87692e6	−0.634796
$754$	−4.64081e6	−0.297280
$755$	−1.39453e7	−0.890352
$756$	−1.76268e6	−0.112168
$757$	6.02920e6	0.382402	0.191201	−	0.981551i	$-0.438762\pi$
$757$	6.02920e6	0.382402	0.191201	+	0.981551i	$0.438762\pi$
$758$	−8.94163e6	−0.565254
$759$	440779.	0.0277726
$760$	6.11312e6	0.383910
$761$	2.31720e7	1.45044	0.725222	−	0.688515i	$-0.241737\pi$
$761$	2.31720e7	1.45044	0.725222	+	0.688515i	$0.241737\pi$
$762$	−6.37159e6	−0.397522
$763$	−1.04365e6	−0.0648996
$764$	1.57145e6	0.0974016
$765$	−1.61140e7	−0.995521
$766$	2.33754e7	1.43942
$767$	−1.88686e6	−0.115811
$768$	3.69038e6	0.225771
$769$	−2.84579e7	−1.73535	−0.867674	−	0.497133i	$-0.834386\pi$
$769$	−2.84579e7	−1.73535	−0.867674	+	0.497133i	$0.834386\pi$
$770$	3.64898e6	0.221791
$771$	4.23143e6	0.256361
$772$	−3.09069e6	−0.186643
$773$	2.80898e7	1.69083	0.845415	−	0.534111i	$-0.179353\pi$
$773$	2.80898e7	1.69083	0.845415	+	0.534111i	$0.179353\pi$
$774$	−9.75630e6	−0.585373
$775$	7.99185e6	0.477961
$776$	7.99323e6	0.476506
$777$	−1.08242e7	−0.643194
$778$	−3.34166e7	−1.97931
$779$	7.77771e6	0.459207
$780$	−704892.	−0.0414845
$781$	−1.80811e6	−0.106071
$782$	5.44097e6	0.318170
$783$	6.49492e6	0.378590
$784$	5.41641e6	0.314718
$785$	1.15134e7	0.666855
$786$	−2.72920e6	−0.157572
$787$	5.23206e6	0.301118	0.150559	−	0.988601i	$-0.451893\pi$
$787$	5.23206e6	0.301118	0.150559	+	0.988601i	$0.451893\pi$
$788$	−510773.	−0.0293030
$789$	2.26757e6	0.129679
$790$	1.28353e6	0.0731711
$791$	2.87397e7	1.63320
$792$	3.51031e6	0.198853
$793$	−7.95724e6	−0.449345
$794$	−1.65500e7	−0.931635
$795$	−1.04706e6	−0.0587562
$796$	−5.13172e6	−0.287065
$797$	−2.13974e7	−1.19321	−0.596604	−	0.802536i	$-0.703484\pi$
$797$	−2.13974e7	−1.19321	−0.596604	+	0.802536i	$0.703484\pi$
$798$	−4.47127e6	−0.248556
$799$	−3.03257e6	−0.168052
$800$	−1.79721e6	−0.0992830
$801$	2.39421e7	1.31850
$802$	3.16583e7	1.73801
$803$	3.04293e6	0.166534
$804$	−371531.	−0.0202701
$805$	−2.20412e6	−0.119880
$806$	−1.82920e7	−0.991799
$807$	806337.	0.0435846
$808$	−1.76259e7	−0.949781
$809$	−1.38556e7	−0.744309	−0.372154	−	0.928171i	$-0.621381\pi$
$809$	−1.38556e7	−0.744309	−0.372154	+	0.928171i	$0.621381\pi$
$810$	−3.90250e6	−0.208992
$811$	3.49492e7	1.86589	0.932944	−	0.360022i	$-0.117231\pi$
$811$	3.49492e7	1.86589	0.932944	+	0.360022i	$0.117231\pi$
$812$	−965762.	−0.0514020
$813$	1.30400e7	0.691913
$814$	−8.75548e6	−0.463147
$815$	−4.93708e6	−0.260361
$816$	−1.92490e7	−1.01201
$817$	−7.49956e6	−0.393080
$818$	1.64404e7	0.859070
$819$	7.83313e6	0.408061
$820$	2.00972e6	0.104376
$821$	5.28311e6	0.273547	0.136773	−	0.990602i	$-0.456327\pi$
$821$	5.28311e6	0.273547	0.136773	+	0.990602i	$0.456327\pi$
$822$	8.75914e6	0.452150
$823$	−1.90127e7	−0.978460	−0.489230	−	0.872155i	$-0.662722\pi$
$823$	−1.90127e7	−0.978460	−0.489230	+	0.872155i	$0.662722\pi$
$824$	2.15956e6	0.110802
$825$	1.07067e6	0.0547673
$826$	−3.09266e6	−0.157718
$827$	7.81940e6	0.397567	0.198783	−	0.980043i	$-0.436301\pi$
$827$	7.81940e6	0.397567	0.198783	+	0.980043i	$0.436301\pi$
$828$	360840.	0.0182911
$829$	−3.17300e6	−0.160355	−0.0801777	−	0.996781i	$-0.525549\pi$
$829$	−3.17300e6	−0.160355	−0.0801777	+	0.996781i	$0.525549\pi$
$830$	−2.23145e7	−1.12433
$831$	1.80285e7	0.905642
$832$	−1.08566e7	−0.543730
$833$	−9.55532e6	−0.477126
$834$	2.22463e7	1.10750
$835$	1.43747e7	0.713483
$836$	−459199.	−0.0227240
$837$	2.56001e7	1.26307
$838$	8.84032e6	0.434868
$839$	4.68251e6	0.229654	0.114827	−	0.993386i	$-0.463369\pi$
$839$	4.68251e6	0.229654	0.114827	+	0.993386i	$0.463369\pi$
$840$	6.78906e6	0.331980
$841$	−1.69526e7	−0.826508
$842$	−2.28041e7	−1.10849
$843$	−1.33664e7	−0.647809
$844$	−4.17146e6	−0.201573
$845$	−9.33525e6	−0.449763
$846$	−1.58404e6	−0.0760921
$847$	1.61066e6	0.0771427
$848$	3.23390e6	0.154432
$849$	169768.	0.00808327
$850$	1.32164e7	0.627429
$851$	5.28865e6	0.250335
$852$	572490.	0.0270190
$853$	−7.48889e6	−0.352407	−0.176204	−	0.984354i	$-0.556382\pi$
$853$	−7.48889e6	−0.352407	−0.176204	+	0.984354i	$0.556382\pi$
$854$	−1.30423e7	−0.611942
$855$	−6.47007e6	−0.302687
$856$	1.53899e6	0.0717879
$857$	−1.32131e7	−0.614545	−0.307272	−	0.951622i	$-0.599416\pi$
$857$	−1.32131e7	−0.614545	−0.307272	+	0.951622i	$0.599416\pi$
$858$	−2.45059e6	−0.113646
$859$	1.83932e7	0.850498	0.425249	−	0.905076i	$-0.360187\pi$
$859$	1.83932e7	0.850498	0.425249	+	0.905076i	$0.360187\pi$
$860$	−1.93785e6	−0.0893457
$861$	8.63771e6	0.397091
$862$	−4.44755e7	−2.03870
$863$	−2.00562e7	−0.916687	−0.458344	−	0.888775i	$-0.651557\pi$
$863$	−2.00562e7	−0.916687	−0.458344	+	0.888775i	$0.651557\pi$
$864$	−5.75697e6	−0.262367
$865$	8.52252e6	0.387282
$866$	−4.68907e7	−2.12467
$867$	2.22692e7	1.00613
$868$	−3.80661e6	−0.171490
$869$	566552.	0.0254501
$870$	4.25710e6	0.190685
$871$	3.94063e6	0.176003
$872$	−1.57064e6	−0.0699498
$873$	−8.45995e6	−0.375692
$874$	2.18465e6	0.0967392
$875$	−2.09199e7	−0.923718
$876$	−963466.	−0.0424205
$877$	3.03899e7	1.33423	0.667115	−	0.744955i	$-0.267529\pi$
$877$	3.03899e7	1.33423	0.667115	+	0.744955i	$0.267529\pi$
$878$	−1.99618e7	−0.873905
$879$	−3.10813e6	−0.135684
$880$	6.30744e6	0.274566
$881$	−4.39979e6	−0.190982	−0.0954909	−	0.995430i	$-0.530442\pi$
$881$	−4.39979e6	−0.190982	−0.0954909	+	0.995430i	$0.530442\pi$
$882$	−4.99113e6	−0.216037
$883$	−3.17796e7	−1.37166	−0.685831	−	0.727761i	$-0.740561\pi$
$883$	−3.17796e7	−1.37166	−0.685831	+	0.727761i	$0.740561\pi$
$884$	−3.84070e6	−0.165303
$885$	1.73085e6	0.0742850
$886$	−2.47423e7	−1.05890
$887$	−8.38651e6	−0.357909	−0.178954	−	0.983857i	$-0.557271\pi$
$887$	−8.38651e6	−0.357909	−0.178954	+	0.983857i	$0.557271\pi$
$888$	−1.62899e7	−0.693245
$889$	1.40636e7	0.596817
$890$	3.74552e7	1.58503
$891$	−1.72256e6	−0.0726910
$892$	−1.97281e6	−0.0830183
$893$	−1.21763e6	−0.0510961
$894$	3.14973e6	0.131804
$895$	−4.63170e6	−0.193278
$896$	−2.36807e7	−0.985426
$897$	1.48025e6	0.0614263
$898$	−1.50675e7	−0.623521
$899$	1.40261e7	0.578812
$900$	876496.	0.0360698
$901$	−5.70505e6	−0.234125
$902$	6.98689e6	0.285935
$903$	−8.32880e6	−0.339909
$904$	4.32520e7	1.76029
$905$	−3.12782e7	−1.26946
$906$	1.53504e7	0.621299
$907$	2.15804e7	0.871047	0.435524	−	0.900177i	$-0.356563\pi$
$907$	2.15804e7	0.871047	0.435524	+	0.900177i	$0.356563\pi$
$908$	1.91085e6	0.0769153
$909$	1.86551e7	0.748838
$910$	1.22542e7	0.490548
$911$	−2.76400e7	−1.10343	−0.551713	−	0.834034i	$-0.686025\pi$
$911$	−2.76400e7	−1.10343	−0.551713	+	0.834034i	$0.686025\pi$
$912$	−7.72882e6	−0.307699
$913$	−9.84964e6	−0.391060
$914$	1.30954e7	0.518504
$915$	7.29932e6	0.288224
$916$	586861.	0.0231098
$917$	6.02398e6	0.236570
$918$	4.23356e7	1.65806
$919$	5.88963e6	0.230038	0.115019	−	0.993363i	$-0.463307\pi$
$919$	5.88963e6	0.230038	0.115019	+	0.993363i	$0.463307\pi$
$920$	−3.31711e6	−0.129208
$921$	−2.54863e7	−0.990052
$922$	−8.30832e6	−0.321874
$923$	−6.07209e6	−0.234603
$924$	−509973.	−0.0196502
$925$	1.28464e7	0.493658
$926$	2.89163e7	1.10819
$927$	−2.28565e6	−0.0873596
$928$	−3.15420e6	−0.120232
$929$	−2.81699e7	−1.07089	−0.535447	−	0.844569i	$-0.679857\pi$
$929$	−2.81699e7	−1.07089	−0.535447	+	0.844569i	$0.679857\pi$
$930$	1.67796e7	0.636172
$931$	−3.83663e6	−0.145069
$932$	940837.	0.0354793
$933$	−1.39765e7	−0.525648
$934$	1.26691e6	0.0475203
$935$	−1.11272e7	−0.416253
$936$	1.17885e7	0.439815
$937$	3.09291e7	1.15085	0.575424	−	0.817855i	$-0.304837\pi$
$937$	3.09291e7	1.15085	0.575424	+	0.817855i	$0.304837\pi$
$938$	6.45890e6	0.239691
$939$	5.50790e6	0.203855
$940$	−314630.	−0.0116140
$941$	−5.04152e6	−0.185604	−0.0928021	−	0.995685i	$-0.529582\pi$
$941$	−5.04152e6	−0.185604	−0.0928021	+	0.995685i	$0.529582\pi$
$942$	−1.26735e7	−0.465339
$943$	−4.22035e6	−0.154550
$944$	−5.34581e6	−0.195247
$945$	−1.71501e7	−0.624721
$946$	−6.73702e6	−0.244760
$947$	−2.73474e6	−0.0990926	−0.0495463	−	0.998772i	$-0.515778\pi$
$947$	−2.73474e6	−0.0990926	−0.0495463	+	0.998772i	$0.515778\pi$
$948$	−179384.	−0.00648280
$949$	1.02190e7	0.368334
$950$	5.30660e6	0.190769
$951$	−2.14968e7	−0.770764
$952$	3.69911e7	1.32283
$953$	3.60955e7	1.28742	0.643711	−	0.765268i	$-0.277394\pi$
$953$	3.60955e7	1.28742	0.643711	+	0.765268i	$0.277394\pi$
$954$	−2.97998e6	−0.106009
$955$	1.52894e7	0.542478
$956$	−4.63963e6	−0.164187
$957$	1.87908e6	0.0663233
$958$	−3.07052e7	−1.08093
$959$	−1.93334e7	−0.678832
$960$	9.95892e6	0.348766
$961$	2.66556e7	0.931064
$962$	−2.94032e7	−1.02437
$963$	−1.62885e6	−0.0565999
$964$	350926.	0.0121625
$965$	−3.00709e7	−1.03951
$966$	2.42621e6	0.0836537
$967$	3.55706e7	1.22328	0.611639	−	0.791137i	$-0.290510\pi$
$967$	3.55706e7	1.22328	0.611639	+	0.791137i	$0.290510\pi$
$968$	2.42397e6	0.0831456
$969$	1.36347e7	0.466485
$970$	−1.32348e7	−0.451636
$971$	1.52927e7	0.520520	0.260260	−	0.965539i	$-0.416192\pi$
$971$	1.52927e7	0.520520	0.260260	+	0.965539i	$0.416192\pi$
$972$	4.43897e6	0.150701
$973$	−4.91026e7	−1.66273
$974$	−1.88337e7	−0.636120
$975$	3.59559e6	0.121132
$976$	−2.25443e7	−0.757552
$977$	2.22523e6	0.0745828	0.0372914	−	0.999304i	$-0.488127\pi$
$977$	2.22523e6	0.0745828	0.0372914	+	0.999304i	$0.488127\pi$
$978$	5.43453e6	0.181683
$979$	1.65327e7	0.551300
$980$	−991366.	−0.0329738
$981$	1.66235e6	0.0551507
$982$	3.34403e7	1.10660
$983$	−1.08565e7	−0.358350	−0.179175	−	0.983817i	$-0.557343\pi$
$983$	−1.08565e7	−0.358350	−0.179175	+	0.983817i	$0.557343\pi$
$984$	1.29994e7	0.427991
$985$	−4.96957e6	−0.163203
$986$	2.31954e7	0.759817
$987$	−1.35227e6	−0.0441845
$988$	−1.54211e6	−0.0502600
$989$	4.06942e6	0.132295
$990$	−5.81220e6	−0.188475
$991$	2.24306e7	0.725533	0.362766	−	0.931880i	$-0.381832\pi$
$991$	2.24306e7	0.725533	0.362766	+	0.931880i	$0.381832\pi$
$992$	−1.24325e7	−0.401124
$993$	−1.17605e7	−0.378489
$994$	−9.95247e6	−0.319496
$995$	−4.99291e7	−1.59881
$996$	3.11863e6	0.0996130
$997$	1.93237e7	0.615676	0.307838	−	0.951439i	$-0.400395\pi$
$997$	1.93237e7	0.615676	0.307838	+	0.951439i	$0.400395\pi$
$998$	3.85583e7	1.22544
$999$	4.11504e7	1.30455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	583.6.a.b.1.16	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
583.6.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-6.05423 q^{2} +8.23240 q^{3} +4.65375 q^{4} +45.2787 q^{5} -49.8409 q^{6} +110.010 q^{7} +165.561 q^{8} -175.228 q^{9} +O(q^{10})\)	\(q-6.05423 q^{2} +8.23240 q^{3} +4.65375 q^{4} +45.2787 q^{5} -49.8409 q^{6} +110.010 q^{7} +165.561 q^{8} -175.228 q^{9} -274.128 q^{10} -121.000 q^{11} +38.3115 q^{12} -406.349 q^{13} -666.027 q^{14} +372.752 q^{15} -1151.26 q^{16} +2030.99 q^{17} +1060.87 q^{18} +815.479 q^{19} +210.715 q^{20} +905.647 q^{21} +732.562 q^{22} -442.496 q^{23} +1362.96 q^{24} -1074.84 q^{25} +2460.13 q^{26} -3443.02 q^{27} +511.960 q^{28} -1886.40 q^{29} -2256.73 q^{30} -7435.37 q^{31} +1672.07 q^{32} -996.120 q^{33} -12296.1 q^{34} +4981.11 q^{35} -815.465 q^{36} -11951.9 q^{37} -4937.10 q^{38} -3345.23 q^{39} +7496.36 q^{40} +9537.60 q^{41} -5483.00 q^{42} -9196.52 q^{43} -563.103 q^{44} -7934.08 q^{45} +2678.98 q^{46} -1493.15 q^{47} -9477.65 q^{48} -4704.76 q^{49} +6507.34 q^{50} +16719.9 q^{51} -1891.05 q^{52} -2809.00 q^{53} +20844.8 q^{54} -5478.72 q^{55} +18213.4 q^{56} +6713.34 q^{57} +11420.7 q^{58} +4643.44 q^{59} +1734.69 q^{60} +19582.3 q^{61} +45015.5 q^{62} -19276.8 q^{63} +26717.3 q^{64} -18399.0 q^{65} +6030.74 q^{66} -9697.65 q^{67} +9451.71 q^{68} -3642.80 q^{69} -30156.8 q^{70} +14943.0 q^{71} -29010.8 q^{72} -25148.2 q^{73} +72359.4 q^{74} -8848.52 q^{75} +3795.03 q^{76} -13311.2 q^{77} +20252.8 q^{78} -4682.25 q^{79} -52127.6 q^{80} +14236.1 q^{81} -57742.9 q^{82} +81402.0 q^{83} +4214.65 q^{84} +91960.5 q^{85} +55677.9 q^{86} -15529.6 q^{87} -20032.8 q^{88} -136634. q^{89} +48034.7 q^{90} -44702.6 q^{91} -2059.27 q^{92} -61210.9 q^{93} +9039.88 q^{94} +36923.8 q^{95} +13765.2 q^{96} +48279.8 q^{97} +28483.7 q^{98} +21202.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9}+O(q^{10}) \) 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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