LMFDB - Embedded newform 583.6.a.b.1.5

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			1.5
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)

$f(q)$	$=$	$q-10.0399 q^{2} -1.70053 q^{3} +68.8000 q^{4} +76.1717 q^{5} +17.0732 q^{6} -193.816 q^{7} -369.469 q^{8} -240.108 q^{9} +O(q^{10})$	\(q-10.0399 q^{2} -1.70053 q^{3} +68.8000 q^{4} +76.1717 q^{5} +17.0732 q^{6} -193.816 q^{7} -369.469 q^{8} -240.108 q^{9} -764.758 q^{10} -121.000 q^{11} -116.997 q^{12} -793.051 q^{13} +1945.89 q^{14} -129.532 q^{15} +1507.84 q^{16} +932.123 q^{17} +2410.67 q^{18} +899.043 q^{19} +5240.61 q^{20} +329.589 q^{21} +1214.83 q^{22} +2269.57 q^{23} +628.294 q^{24} +2677.13 q^{25} +7962.17 q^{26} +821.541 q^{27} -13334.5 q^{28} +985.267 q^{29} +1300.49 q^{30} +4808.15 q^{31} -3315.60 q^{32} +205.764 q^{33} -9358.44 q^{34} -14763.3 q^{35} -16519.4 q^{36} +1945.61 q^{37} -9026.32 q^{38} +1348.61 q^{39} -28143.1 q^{40} +17944.2 q^{41} -3309.05 q^{42} -12012.5 q^{43} -8324.80 q^{44} -18289.4 q^{45} -22786.3 q^{46} +10683.5 q^{47} -2564.13 q^{48} +20757.5 q^{49} -26878.1 q^{50} -1585.10 q^{51} -54561.9 q^{52} -2809.00 q^{53} -8248.20 q^{54} -9216.77 q^{55} +71608.9 q^{56} -1528.85 q^{57} -9892.01 q^{58} +23332.0 q^{59} -8911.83 q^{60} -22884.3 q^{61} -48273.5 q^{62} +46536.7 q^{63} -14962.6 q^{64} -60408.0 q^{65} -2065.86 q^{66} -36157.2 q^{67} +64130.1 q^{68} -3859.47 q^{69} +148222. q^{70} +71681.2 q^{71} +88712.6 q^{72} +8672.65 q^{73} -19533.7 q^{74} -4552.54 q^{75} +61854.1 q^{76} +23451.7 q^{77} -13539.9 q^{78} -54758.6 q^{79} +114855. q^{80} +56949.2 q^{81} -180159. q^{82} -8675.13 q^{83} +22675.8 q^{84} +71001.4 q^{85} +120605. q^{86} -1675.48 q^{87} +44705.8 q^{88} -4776.91 q^{89} +183625. q^{90} +153706. q^{91} +156146. q^{92} -8176.41 q^{93} -107262. q^{94} +68481.6 q^{95} +5638.28 q^{96} -93460.7 q^{97} -208403. q^{98} +29053.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.0399	−1.77482	−0.887412	−	0.460977i	$-0.847499\pi$
$2$	−10.0399	−1.77482	−0.887412	+	0.460977i	$0.847499\pi$
$3$	−1.70053	−0.109089	−0.0545446	−	0.998511i	$-0.517371\pi$
$3$	−1.70053	−0.109089	−0.0545446	+	0.998511i	$0.517371\pi$
$4$	68.8000	2.15000
$5$	76.1717	1.36260	0.681300	−	0.732004i	$-0.261415\pi$
$5$	76.1717	1.36260	0.681300	+	0.732004i	$0.261415\pi$
$6$	17.0732	0.193614
$7$	−193.816	−1.49501	−0.747504	−	0.664257i	$-0.768748\pi$
$7$	−193.816	−1.49501	−0.747504	+	0.664257i	$0.768748\pi$
$8$	−369.469	−2.04105
$9$	−240.108	−0.988100
$10$	−764.758	−2.41838
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−116.997	−0.234542
$13$	−793.051	−1.30150	−0.650748	−	0.759294i	$-0.725544\pi$
$13$	−793.051	−1.30150	−0.650748	+	0.759294i	$0.725544\pi$
$14$	1945.89	2.65338
$15$	−129.532	−0.148645
$16$	1507.84	1.47250
$17$	932.123	0.782260	0.391130	−	0.920336i	$-0.372084\pi$
$17$	932.123	0.782260	0.391130	+	0.920336i	$0.372084\pi$
$18$	2410.67	1.75370
$19$	899.043	0.571342	0.285671	−	0.958328i	$-0.407784\pi$
$19$	899.043	0.571342	0.285671	+	0.958328i	$0.407784\pi$
$20$	5240.61	2.92959
$21$	329.589	0.163089
$22$	1214.83	0.535130
$23$	2269.57	0.894588	0.447294	−	0.894387i	$-0.352388\pi$
$23$	2269.57	0.894588	0.447294	+	0.894387i	$0.352388\pi$
$24$	628.294	0.222656
$25$	2677.13	0.856680
$26$	7962.17	2.30992
$27$	821.541	0.216880
$28$	−13334.5	−3.21427
$29$	985.267	0.217550	0.108775	−	0.994066i	$-0.465307\pi$
$29$	985.267	0.217550	0.108775	+	0.994066i	$0.465307\pi$
$30$	1300.49	0.263819
$31$	4808.15	0.898615	0.449308	−	0.893377i	$-0.351671\pi$
$31$	4808.15	0.898615	0.449308	+	0.893377i	$0.351671\pi$
$32$	−3315.60	−0.572383
$33$	205.764	0.0328916
$34$	−9358.44	−1.38837
$35$	−14763.3	−2.03710
$36$	−16519.4	−2.12441
$37$	1945.61	0.233642	0.116821	−	0.993153i	$-0.462730\pi$
$37$	1945.61	0.233642	0.116821	+	0.993153i	$0.462730\pi$
$38$	−9026.32	−1.01403
$39$	1348.61	0.141979
$40$	−28143.1	−2.78113
$41$	17944.2	1.66711	0.833556	−	0.552434i	$-0.186301\pi$
$41$	17944.2	1.66711	0.833556	+	0.552434i	$0.186301\pi$
$42$	−3309.05	−0.289455
$43$	−12012.5	−0.990748	−0.495374	−	0.868680i	$-0.664969\pi$
$43$	−12012.5	−0.990748	−0.495374	+	0.868680i	$0.664969\pi$
$44$	−8324.80	−0.648250
$45$	−18289.4	−1.34639
$46$	−22786.3	−1.58774
$47$	10683.5	0.705455	0.352728	−	0.935726i	$-0.385254\pi$
$47$	10683.5	0.705455	0.352728	+	0.935726i	$0.385254\pi$
$48$	−2564.13	−0.160634
$49$	20757.5	1.23505
$50$	−26878.1	−1.52046
$51$	−1585.10	−0.0853360
$52$	−54561.9	−2.79822
$53$	−2809.00	−0.137361
$53$	−2809.00	−0.137361
$54$	−8248.20	−0.384924
$55$	−9216.77	−0.410840
$56$	71608.9	3.05138
$57$	−1528.85	−0.0623272
$58$	−9892.01	−0.386113
$59$	23332.0	0.872615	0.436307	−	0.899798i	$-0.356286\pi$
$59$	23332.0	0.872615	0.436307	+	0.899798i	$0.356286\pi$
$60$	−8911.83	−0.319587
$61$	−22884.3	−0.787433	−0.393716	−	0.919232i	$-0.628811\pi$
$61$	−22884.3	−0.787433	−0.393716	+	0.919232i	$0.628811\pi$
$62$	−48273.5	−1.59488
$63$	46536.7	1.47722
$64$	−14962.6	−0.456622
$65$	−60408.0	−1.77342
$66$	−2065.86	−0.0583768
$67$	−36157.2	−0.984028	−0.492014	−	0.870587i	$-0.663739\pi$
$67$	−36157.2	−0.984028	−0.492014	+	0.870587i	$0.663739\pi$
$68$	64130.1	1.68186
$69$	−3859.47	−0.0975899
$70$	148222.	3.61549
$71$	71681.2	1.68756	0.843780	−	0.536689i	$-0.180325\pi$
$71$	71681.2	1.68756	0.843780	+	0.536689i	$0.180325\pi$
$72$	88712.6	2.01676
$73$	8672.65	0.190478	0.0952390	−	0.995454i	$-0.469638\pi$
$73$	8672.65	0.190478	0.0952390	+	0.995454i	$0.469638\pi$
$74$	−19533.7	−0.414673
$75$	−4552.54	−0.0934545
$76$	61854.1	1.22839
$77$	23451.7	0.450762
$78$	−13539.9	−0.251988
$79$	−54758.6	−0.987153	−0.493576	−	0.869703i	$-0.664311\pi$
$79$	−54758.6	−0.987153	−0.493576	+	0.869703i	$0.664311\pi$
$80$	114855.	2.00643
$81$	56949.2	0.964440
$82$	−180159.	−2.95883
$83$	−8675.13	−0.138223	−0.0691115	−	0.997609i	$-0.522016\pi$
$83$	−8675.13	−0.138223	−0.0691115	+	0.997609i	$0.522016\pi$
$84$	22675.8	0.350642
$85$	71001.4	1.06591
$86$	120605.	1.75840
$87$	−1675.48	−0.0237323
$88$	44705.8	0.615399
$89$	−4776.91	−0.0639253	−0.0319626	−	0.999489i	$-0.510176\pi$
$89$	−4776.91	−0.0639253	−0.0319626	+	0.999489i	$0.510176\pi$
$90$	183625.	2.38960
$91$	153706.	1.94575
$92$	156146.	1.92336
$93$	−8176.41	−0.0980292
$94$	−107262.	−1.25206
$95$	68481.6	0.778511
$96$	5638.28	0.0624408
$97$	−93460.7	−1.00856	−0.504278	−	0.863541i	$-0.668241\pi$
$97$	−93460.7	−1.00856	−0.504278	+	0.863541i	$0.668241\pi$
$98$	−208403.	−2.19199
$99$	29053.1	0.297923
$100$	184186.	1.84186
$101$	−14454.9	−0.140998	−0.0704988	−	0.997512i	$-0.522459\pi$
$101$	−14454.9	−0.140998	−0.0704988	+	0.997512i	$0.522459\pi$
$102$	15914.3	0.151456
$103$	−44735.5	−0.415489	−0.207744	−	0.978183i	$-0.566612\pi$
$103$	−44735.5	−0.415489	−0.207744	+	0.978183i	$0.566612\pi$
$104$	293008.	2.65642
$105$	25105.4	0.222225
$106$	28202.1	0.243791
$107$	63932.1	0.539833	0.269917	−	0.962884i	$-0.413004\pi$
$107$	63932.1	0.539833	0.269917	+	0.962884i	$0.413004\pi$
$108$	56522.0	0.466292
$109$	−88319.8	−0.712019	−0.356010	−	0.934482i	$-0.615863\pi$
$109$	−88319.8	−0.712019	−0.356010	+	0.934482i	$0.615863\pi$
$110$	92535.7	0.729168
$111$	−3308.56	−0.0254878
$112$	−292243.	−2.20140
$113$	−188292.	−1.38719	−0.693595	−	0.720365i	$-0.743974\pi$
$113$	−188292.	−1.38719	−0.693595	+	0.720365i	$0.743974\pi$
$114$	15349.5	0.110620
$115$	172877.	1.21897
$116$	67786.4	0.467733
$117$	190418.	1.28601
$118$	−234252.	−1.54874
$119$	−180660.	−1.16948
$120$	47858.2	0.303392
$121$	14641.0	0.0909091
$122$	229757.	1.39755
$123$	−30514.7	−0.181864
$124$	330801.	1.93202
$125$	−34115.3	−0.195287
$126$	−467225.	−2.62180
$127$	−106109.	−0.583774	−0.291887	−	0.956453i	$-0.594283\pi$
$127$	−106109.	−0.583774	−0.291887	+	0.956453i	$0.594283\pi$
$128$	256322.	1.38281
$129$	20427.7	0.108080
$130$	606492.	3.14751
$131$	−271551.	−1.38253	−0.691263	−	0.722603i	$-0.742945\pi$
$131$	−271551.	−1.38253	−0.691263	+	0.722603i	$0.742945\pi$
$132$	14156.6	0.0707170
$133$	−174248.	−0.854161
$134$	363015.	1.74648
$135$	62578.1	0.295521
$136$	−344391.	−1.59663
$137$	157048.	0.714875	0.357438	−	0.933937i	$-0.383650\pi$
$137$	157048.	0.714875	0.357438	+	0.933937i	$0.383650\pi$
$138$	38748.7	0.173205
$139$	−227733.	−0.999744	−0.499872	−	0.866099i	$-0.666620\pi$
$139$	−227733.	−0.999744	−0.499872	+	0.866099i	$0.666620\pi$
$140$	−1.01571e6	−4.37976
$141$	−18167.6	−0.0769575
$142$	−719673.	−2.99512
$143$	95959.1	0.392416
$144$	−362045.	−1.45498
$145$	75049.5	0.296434
$146$	−87072.8	−0.338065
$147$	−35298.7	−0.134730
$148$	133858.	0.502330
$149$	159438.	0.588338	0.294169	−	0.955753i	$-0.404957\pi$
$149$	159438.	0.588338	0.294169	+	0.955753i	$0.404957\pi$
$150$	45707.1	0.165865
$151$	−503370.	−1.79657	−0.898287	−	0.439409i	$-0.855188\pi$
$151$	−503370.	−1.79657	−0.898287	+	0.439409i	$0.855188\pi$
$152$	−332169.	−1.16614
$153$	−223810.	−0.772950
$154$	−235453.	−0.800023
$155$	366245.	1.22445
$156$	92784.2	0.305255
$157$	234170.	0.758196	0.379098	−	0.925357i	$-0.376234\pi$
$157$	234170.	0.758196	0.379098	+	0.925357i	$0.376234\pi$
$158$	549772.	1.75202
$159$	4776.79	0.0149845
$160$	−252555.	−0.779930
$161$	−439877.	−1.33742
$162$	−571766.	−1.71171
$163$	349993.	1.03179	0.515894	−	0.856653i	$-0.327460\pi$
$163$	349993.	1.03179	0.515894	+	0.856653i	$0.327460\pi$
$164$	1.23456e6	3.58429
$165$	15673.4	0.0448181
$166$	87097.6	0.245322
$167$	265031.	0.735368	0.367684	−	0.929951i	$-0.380151\pi$
$167$	265031.	0.735368	0.367684	+	0.929951i	$0.380151\pi$
$168$	−121773.	−0.332873
$169$	257636.	0.693890
$170$	−712848.	−1.89180
$171$	−215867.	−0.564543
$172$	−826462.	−2.13011
$173$	−696801.	−1.77008	−0.885041	−	0.465513i	$-0.845870\pi$
$173$	−696801.	−1.77008	−0.885041	+	0.465513i	$0.845870\pi$
$174$	16821.7	0.0421207
$175$	−518869.	−1.28074
$176$	−182449.	−0.443976
$177$	−39676.9	−0.0951928
$178$	47959.8	0.113456
$179$	−357129.	−0.833090	−0.416545	−	0.909115i	$-0.636759\pi$
$179$	−357129.	−0.833090	−0.416545	+	0.909115i	$0.636759\pi$
$180$	−1.25831e6	−2.89473
$181$	666119.	1.51132	0.755659	−	0.654966i	$-0.227317\pi$
$181$	666119.	1.51132	0.755659	+	0.654966i	$0.227317\pi$
$182$	−1.54319e6	−3.45336
$183$	38915.5	0.0859004
$184$	−838535.	−1.82590
$185$	148200.	0.318361
$186$	82090.5	0.173985
$187$	−112787.	−0.235860
$188$	735026.	1.51673
$189$	−159227.	−0.324237
$190$	−687550.	−1.38172
$191$	−613143.	−1.21613	−0.608063	−	0.793889i	$-0.708053\pi$
$191$	−613143.	−1.21613	−0.608063	+	0.793889i	$0.708053\pi$
$192$	25444.4	0.0498126
$193$	550583.	1.06397	0.531985	−	0.846754i	$-0.321446\pi$
$193$	550583.	1.06397	0.531985	+	0.846754i	$0.321446\pi$
$194$	938339.	1.79001
$195$	102726.	0.193461
$196$	1.42811e6	2.65536
$197$	−869184.	−1.59568	−0.797841	−	0.602869i	$-0.794024\pi$
$197$	−869184.	−1.59568	−0.797841	+	0.602869i	$0.794024\pi$
$198$	−291691.	−0.528761
$199$	30375.2	0.0543734	0.0271867	−	0.999630i	$-0.491345\pi$
$199$	30375.2	0.0543734	0.0271867	+	0.999630i	$0.491345\pi$
$200$	−989116.	−1.74853
$201$	61486.4	0.107347
$202$	145126.	0.250246
$203$	−190960.	−0.325239
$204$	−109055.	−0.183473
$205$	1.36684e6	2.27161
$206$	449141.	0.737419
$207$	−544941.	−0.883942
$208$	−1.19580e6	−1.91645
$209$	−108784.	−0.172266
$210$	−252056.	−0.394411
$211$	706933.	1.09313	0.546566	−	0.837416i	$-0.315935\pi$
$211$	706933.	1.09313	0.546566	+	0.837416i	$0.315935\pi$
$212$	−193259.	−0.295325
$213$	−121896.	−0.184095
$214$	−641873.	−0.958109
$215$	−915015.	−1.34999
$216$	−303534.	−0.442663
$217$	−931894.	−1.34344
$218$	886724.	1.26371
$219$	−14748.1	−0.0207791
$220$	−634114.	−0.883305
$221$	−739221.	−1.01811
$222$	33217.7	0.0452363
$223$	−847335.	−1.14102	−0.570510	−	0.821291i	$-0.693254\pi$
$223$	−847335.	−1.14102	−0.570510	+	0.821291i	$0.693254\pi$
$224$	642614.	0.855717
$225$	−642800.	−0.846486
$226$	1.89044e6	2.46202
$227$	495917.	0.638770	0.319385	−	0.947625i	$-0.396524\pi$
$227$	495917.	0.638770	0.319385	+	0.947625i	$0.396524\pi$
$228$	−105185.	−0.134004
$229$	864581.	1.08947	0.544737	−	0.838607i	$-0.316629\pi$
$229$	864581.	1.08947	0.544737	+	0.838607i	$0.316629\pi$
$230$	−1.73567e6	−2.16345
$231$	−39880.3	−0.0491732
$232$	−364026.	−0.444030
$233$	−543472.	−0.655824	−0.327912	−	0.944708i	$-0.606345\pi$
$233$	−543472.	−0.655824	−0.327912	+	0.944708i	$0.606345\pi$
$234$	−1.91178e6	−2.28244
$235$	813781.	0.961254
$236$	1.60524e6	1.87612
$237$	93118.6	0.107688
$238$	1.81381e6	2.07563
$239$	494396.	0.559861	0.279930	−	0.960020i	$-0.409689\pi$
$239$	494396.	0.559861	0.279930	+	0.960020i	$0.409689\pi$
$240$	−195314.	−0.218880
$241$	−163943.	−0.181824	−0.0909118	−	0.995859i	$-0.528978\pi$
$241$	−163943.	−0.181824	−0.0909118	+	0.995859i	$0.528978\pi$
$242$	−146994.	−0.161348
$243$	−296478.	−0.322090
$244$	−1.57444e6	−1.69298
$245$	1.58113e6	1.68288
$246$	306365.	0.322776
$247$	−712986.	−0.743599
$248$	−1.77646e6	−1.83412
$249$	14752.3	0.0150786
$250$	342515.	0.346601
$251$	89.5763	8.97447e−5 0	4.48724e−5	−	1.00000i	$-0.499986\pi$
$251$	89.5763	8.97447e−5 0	4.48724e−5		1.00000i	$0.499986\pi$
$252$	3.20173e6	3.17602
$253$	−274617.	−0.269728
$254$	1.06533e6	1.03610
$255$	−120740.	−0.116279
$256$	−2.09465e6	−1.99762
$257$	−1.19265e6	−1.12637	−0.563185	−	0.826331i	$-0.690424\pi$
$257$	−1.19265e6	−1.12637	−0.563185	+	0.826331i	$0.690424\pi$
$258$	−205092.	−0.191823
$259$	−377089.	−0.349296
$260$	−4.15607e6	−3.81285
$261$	−236571.	−0.214961
$262$	2.72635e6	2.45374
$263$	−27711.0	−0.0247037	−0.0123519	−	0.999924i	$-0.503932\pi$
$263$	−27711.0	−0.0247037	−0.0123519	+	0.999924i	$0.503932\pi$
$264$	−76023.6	−0.0671334
$265$	−213966.	−0.187168
$266$	1.74944e6	1.51599
$267$	8123.29	0.00697355
$268$	−2.48762e6	−2.11566
$269$	1.76591e6	1.48795	0.743973	−	0.668210i	$-0.232939\pi$
$269$	1.76591e6	1.48795	0.743973	+	0.668210i	$0.232939\pi$
$270$	−628280.	−0.524498
$271$	459828.	0.380340	0.190170	−	0.981751i	$-0.439096\pi$
$271$	459828.	0.380340	0.190170	+	0.981751i	$0.439096\pi$
$272$	1.40549e6	1.15188
$273$	−261381.	−0.212260
$274$	−1.57675e6	−1.26878
$275$	−323932.	−0.258299
$276$	−265531.	−0.209818
$277$	−1.16111e6	−0.909229	−0.454615	−	0.890688i	$-0.650223\pi$
$277$	−1.16111e6	−0.909229	−0.454615	+	0.890688i	$0.650223\pi$
$278$	2.28642e6	1.77437
$279$	−1.15448e6	−0.887921
$280$	5.45457e6	4.15782
$281$	−2.07179e6	−1.56524	−0.782619	−	0.622501i	$-0.786117\pi$
$281$	−2.07179e6	−1.56524	−0.782619	+	0.622501i	$0.786117\pi$
$282$	182402.	0.136586
$283$	1.78446e6	1.32447	0.662233	−	0.749298i	$-0.269609\pi$
$283$	1.78446e6	1.32447	0.662233	+	0.749298i	$0.269609\pi$
$284$	4.93167e6	3.62826
$285$	−116455.	−0.0849271
$286$	−963422.	−0.696469
$287$	−3.47787e6	−2.49235
$288$	796102.	0.565572
$289$	−551004.	−0.388070
$290$	−753491.	−0.526118
$291$	158933.	0.110022
$292$	596679.	0.409528
$293$	−2.34489e6	−1.59571	−0.797855	−	0.602850i	$-0.794032\pi$
$293$	−2.34489e6	−1.59571	−0.797855	+	0.602850i	$0.794032\pi$
$294$	354396.	0.239123
$295$	1.77724e6	1.18903
$296$	−718842.	−0.476874
$297$	−99406.4	−0.0653918
$298$	−1.60075e6	−1.04420
$299$	−1.79988e6	−1.16430
$300$	−313215.	−0.200927
$301$	2.32821e6	1.48118
$302$	5.05380e6	3.18860
$303$	24581.0	0.0153813
$304$	1.35561e6	0.841302
$305$	−1.74314e6	−1.07296
$306$	2.24704e6	1.37185
$307$	−13602.6	−0.00823710	−0.00411855	−	0.999992i	$-0.501311\pi$
$307$	−13602.6	−0.00823710	−0.00411855	+	0.999992i	$0.501311\pi$
$308$	1.61348e6	0.969138
$309$	76074.1	0.0453253
$310$	−3.67707e6	−2.17319
$311$	2.08619e6	1.22308	0.611538	−	0.791215i	$-0.290551\pi$
$311$	2.08619e6	1.22308	0.611538	+	0.791215i	$0.290551\pi$
$312$	−498269.	−0.289786
$313$	−485083.	−0.279869	−0.139935	−	0.990161i	$-0.544689\pi$
$313$	−485083.	−0.279869	−0.139935	+	0.990161i	$0.544689\pi$
$314$	−2.35104e6	−1.34566
$315$	3.54478e6	2.01286
$316$	−3.76739e6	−2.12238
$317$	−2.23098e6	−1.24695	−0.623473	−	0.781845i	$-0.714279\pi$
$317$	−2.23098e6	−1.24695	−0.623473	+	0.781845i	$0.714279\pi$
$318$	−47958.6	−0.0265949
$319$	−119217.	−0.0655938
$320$	−1.13973e6	−0.622194
$321$	−108719.	−0.0588899
$322$	4.41633e6	2.37368
$323$	838018.	0.446938
$324$	3.91811e6	2.07355
$325$	−2.12310e6	−1.11497
$326$	−3.51390e6	−1.83124
$327$	150191.	0.0776736
$328$	−6.62984e6	−3.40266
$329$	−2.07063e6	−1.05466
$330$	−157360.	−0.0795443
$331$	1.19262e6	0.598319	0.299159	−	0.954203i	$-0.403294\pi$
$331$	1.19262e6	0.598319	0.299159	+	0.954203i	$0.403294\pi$
$332$	−596849.	−0.297180
$333$	−467156.	−0.230861
$334$	−2.66089e6	−1.30515
$335$	−2.75415e6	−1.34084
$336$	496969.	0.240149
$337$	−3.79173e6	−1.81871	−0.909353	−	0.416026i	$-0.863422\pi$
$337$	−3.79173e6	−1.81871	−0.909353	+	0.416026i	$0.863422\pi$
$338$	−2.58665e6	−1.23153
$339$	320197.	0.151327
$340$	4.88490e6	2.29170
$341$	−581786.	−0.270943
$342$	2.16729e6	1.00196
$343$	−765661.	−0.351400
$344$	4.43826e6	2.02217
$345$	−293982.	−0.132976
$346$	6.99583e6	3.14158
$347$	1.47994e6	0.659812	0.329906	−	0.944014i	$-0.392983\pi$
$347$	1.47994e6	0.659812	0.329906	+	0.944014i	$0.392983\pi$
$348$	−115273.	−0.0510246
$349$	3.68621e6	1.62001	0.810003	−	0.586426i	$-0.199466\pi$
$349$	3.68621e6	1.62001	0.810003	+	0.586426i	$0.199466\pi$
$350$	5.20940e6	2.27310
$351$	−651523.	−0.282268
$352$	401187.	0.172580
$353$	−640053.	−0.273388	−0.136694	−	0.990613i	$-0.543648\pi$
$353$	−640053.	−0.273388	−0.136694	+	0.990613i	$0.543648\pi$
$354$	398352.	0.168950
$355$	5.46008e6	2.29947
$356$	−328652.	−0.137439
$357$	307218.	0.127578
$358$	3.58554e6	1.47859
$359$	4.07301e6	1.66794	0.833968	−	0.551812i	$-0.186063\pi$
$359$	4.07301e6	1.66794	0.833968	+	0.551812i	$0.186063\pi$
$360$	6.75739e6	2.74804
$361$	−1.66782e6	−0.673568
$362$	−6.68779e6	−2.68232
$363$	−24897.5	−0.00991719
$364$	1.05749e7	4.18335
$365$	660611.	0.259545
$366$	−390709.	−0.152458
$367$	−487761.	−0.189035	−0.0945175	−	0.995523i	$-0.530131\pi$
$367$	−487761.	−0.189035	−0.0945175	+	0.995523i	$0.530131\pi$
$368$	3.42215e6	1.31728
$369$	−4.30855e6	−1.64727
$370$	−1.48792e6	−0.565034
$371$	544428.	0.205355
$372$	−562537.	−0.210763
$373$	−626238.	−0.233060	−0.116530	−	0.993187i	$-0.537177\pi$
$373$	−626238.	−0.233060	−0.116530	+	0.993187i	$0.537177\pi$
$374$	1.13237e6	0.418610
$375$	58014.1	0.0213037
$376$	−3.94723e6	−1.43987
$377$	−781367.	−0.283140
$378$	1.59863e6	0.575464
$379$	−4.53041e6	−1.62009	−0.810046	−	0.586366i	$-0.800558\pi$
$379$	−4.53041e6	−1.62009	−0.810046	+	0.586366i	$0.800558\pi$
$380$	4.71153e6	1.67380
$381$	180443.	0.0636834
$382$	6.15591e6	2.15841
$383$	−3.96973e6	−1.38282	−0.691408	−	0.722464i	$-0.743009\pi$
$383$	−3.96973e6	−1.38282	−0.691408	+	0.722464i	$0.743009\pi$
$384$	−435884.	−0.150849
$385$	1.78635e6	0.614208
$386$	−5.52781e6	−1.88836
$387$	2.88431e6	0.978958
$388$	−6.43010e6	−2.16840
$389$	−2.55596e6	−0.856408	−0.428204	−	0.903682i	$-0.640854\pi$
$389$	−2.55596e6	−0.856408	−0.428204	+	0.903682i	$0.640854\pi$
$390$	−1.03136e6	−0.343359
$391$	2.11551e6	0.699800
$392$	−7.66925e6	−2.52079
$393$	461781.	0.150819
$394$	8.72654e6	2.83205
$395$	−4.17105e6	−1.34509
$396$	1.99885e6	0.640535
$397$	1.56653e6	0.498843	0.249421	−	0.968395i	$-0.419760\pi$
$397$	1.56653e6	0.498843	0.249421	+	0.968395i	$0.419760\pi$
$398$	−304964.	−0.0965032
$399$	296315.	0.0931797
$400$	4.03668e6	1.26146
$401$	4.76447e6	1.47963	0.739815	−	0.672810i	$-0.234913\pi$
$401$	4.76447e6	1.47963	0.739815	+	0.672810i	$0.234913\pi$
$402$	−617319.	−0.190522
$403$	−3.81311e6	−1.16954
$404$	−994497.	−0.303145
$405$	4.33792e6	1.31415
$406$	1.91722e6	0.577242
$407$	−235418.	−0.0704457
$408$	585647.	0.174175
$409$	1.18429e6	0.350067	0.175034	−	0.984562i	$-0.443997\pi$
$409$	1.18429e6	0.350067	0.175034	+	0.984562i	$0.443997\pi$
$410$	−1.37230e7	−4.03171
$411$	−267065.	−0.0779851
$412$	−3.07780e6	−0.893301
$413$	−4.52211e6	−1.30457
$414$	5.47117e6	1.56884
$415$	−660799.	−0.188343
$416$	2.62944e6	0.744954
$417$	387267.	0.109061
$418$	1.09218e6	0.305742
$419$	−1.74323e6	−0.485087	−0.242544	−	0.970140i	$-0.577982\pi$
$419$	−1.74323e6	−0.485087	−0.242544	+	0.970140i	$0.577982\pi$
$420$	1.72725e6	0.477785
$421$	−5.30660e6	−1.45919	−0.729594	−	0.683880i	$-0.760291\pi$
$421$	−5.30660e6	−1.45919	−0.729594	+	0.683880i	$0.760291\pi$
$422$	−7.09755e6	−1.94012
$423$	−2.56520e6	−0.697060
$424$	1.03784e6	0.280360
$425$	2.49541e6	0.670146
$426$	1.22383e6	0.326735
$427$	4.43534e6	1.17722
$428$	4.39853e6	1.16064
$429$	−163182.	−0.0428083
$430$	9.18667e6	2.39600
$431$	−739270.	−0.191695	−0.0958473	−	0.995396i	$-0.530556\pi$
$431$	−739270.	−0.191695	−0.0958473	+	0.995396i	$0.530556\pi$
$432$	1.23875e6	0.319356
$433$	3.37122e6	0.864106	0.432053	−	0.901848i	$-0.357789\pi$
$433$	3.37122e6	0.864106	0.432053	+	0.901848i	$0.357789\pi$
$434$	9.35615e6	2.38436
$435$	−127624.	−0.0323377
$436$	−6.07640e6	−1.53084
$437$	2.04044e6	0.511116
$438$	148070.	0.0368792
$439$	−5.97372e6	−1.47939	−0.739696	−	0.672941i	$-0.765031\pi$
$439$	−5.97372e6	−1.47939	−0.739696	+	0.672941i	$0.765031\pi$
$440$	3.40532e6	0.838544
$441$	−4.98404e6	−1.22035
$442$	7.42172e6	1.80696
$443$	−3.85319e6	−0.932849	−0.466424	−	0.884561i	$-0.654458\pi$
$443$	−3.85319e6	−0.932849	−0.466424	+	0.884561i	$0.654458\pi$
$444$	−227629.	−0.0547988
$445$	−363866.	−0.0871046
$446$	8.50718e6	2.02511
$447$	−271130.	−0.0641813
$448$	2.89999e6	0.682654
$449$	6.32513e6	1.48065	0.740327	−	0.672247i	$-0.234671\pi$
$449$	6.32513e6	1.48065	0.740327	+	0.672247i	$0.234671\pi$
$450$	6.45366e6	1.50236
$451$	−2.17125e6	−0.502653
$452$	−1.29545e7	−2.98246
$453$	855997.	0.195987
$454$	−4.97897e6	−1.13370
$455$	1.17080e7	2.65127
$456$	564863.	0.127213
$457$	−4.86067e6	−1.08869	−0.544347	−	0.838860i	$-0.683222\pi$
$457$	−4.86067e6	−1.08869	−0.544347	+	0.838860i	$0.683222\pi$
$458$	−8.68033e6	−1.93363
$459$	765777.	0.169657
$460$	1.18939e7	2.62078
$461$	7.05354e6	1.54581	0.772903	−	0.634525i	$-0.218804\pi$
$461$	7.05354e6	1.54581	0.772903	+	0.634525i	$0.218804\pi$
$462$	400395.	0.0872738
$463$	−1.29928e6	−0.281676	−0.140838	−	0.990033i	$-0.544980\pi$
$463$	−1.29928e6	−0.281676	−0.140838	+	0.990033i	$0.544980\pi$
$464$	1.48563e6	0.320343
$465$	−622811.	−0.133575
$466$	5.45641e6	1.16397
$467$	3.68942e6	0.782827	0.391413	−	0.920215i	$-0.371986\pi$
$467$	3.68942e6	0.782827	0.391413	+	0.920215i	$0.371986\pi$
$468$	1.31008e7	2.76492
$469$	7.00783e6	1.47113
$470$	−8.17030e6	−1.70606
$471$	−398213.	−0.0827109
$472$	−8.62047e6	−1.78105
$473$	1.45352e6	0.298722
$474$	−934904.	−0.191127
$475$	2.40685e6	0.489458
$476$	−1.24294e7	−2.51439
$477$	674464.	0.135726
$478$	−4.96369e6	−0.993654
$479$	1.92620e6	0.383586	0.191793	−	0.981435i	$-0.438570\pi$
$479$	1.92620e6	0.383586	0.191793	+	0.981435i	$0.438570\pi$
$480$	429477.	0.0850819
$481$	−1.54296e6	−0.304084
$482$	1.64598e6	0.322705
$483$	748025.	0.145898
$484$	1.00730e6	0.195455
$485$	−7.11906e6	−1.37426
$486$	2.97662e6	0.571653
$487$	4.19600e6	0.801702	0.400851	−	0.916143i	$-0.368714\pi$
$487$	4.19600e6	0.801702	0.400851	+	0.916143i	$0.368714\pi$
$488$	8.45505e6	1.60719
$489$	−595174.	−0.112557
$490$	−1.58744e7	−2.98681
$491$	−1.79673e6	−0.336340	−0.168170	−	0.985758i	$-0.553786\pi$
$491$	−1.79673e6	−0.336340	−0.168170	+	0.985758i	$0.553786\pi$
$492$	−2.09941e6	−0.391008
$493$	918390.	0.170181
$494$	7.15833e6	1.31976
$495$	2.21302e6	0.405950
$496$	7.24993e6	1.32321
$497$	−1.38929e7	−2.52292
$498$	−148112.	−0.0267619
$499$	1.52491e6	0.274153	0.137076	−	0.990560i	$-0.456229\pi$
$499$	1.52491e6	0.274153	0.137076	+	0.990560i	$0.456229\pi$
$500$	−2.34713e6	−0.419868
$501$	−450693.	−0.0802207
$502$	−899.339	−0.000159281 0
$503$	6.59953e6	1.16304	0.581518	−	0.813533i	$-0.302459\pi$
$503$	6.59953e6	1.16304	0.581518	+	0.813533i	$0.302459\pi$
$504$	−1.71939e7	−3.01507
$505$	−1.10105e6	−0.192123
$506$	2.75714e6	0.478721
$507$	−438119.	−0.0756958
$508$	−7.30033e6	−1.25511
$509$	−1.06294e7	−1.81850	−0.909252	−	0.416246i	$-0.863345\pi$
$509$	−1.06294e7	−1.81850	−0.909252	+	0.416246i	$0.863345\pi$
$510$	1.21222e6	0.206375
$511$	−1.68090e6	−0.284766
$512$	1.28278e7	2.16261
$513$	738600.	0.123913
$514$	1.19741e7	1.99911
$515$	−3.40758e6	−0.566145
$516$	1.40542e6	0.232372
$517$	−1.29270e6	−0.212703
$518$	3.78594e6	0.619940
$519$	1.18493e6	0.193097
$520$	2.23189e7	3.61963
$521$	−3.26155e6	−0.526417	−0.263209	−	0.964739i	$-0.584781\pi$
$521$	−3.26155e6	−0.526417	−0.263209	+	0.964739i	$0.584781\pi$
$522$	2.37515e6	0.381518
$523$	−1.52676e6	−0.244072	−0.122036	−	0.992526i	$-0.538942\pi$
$523$	−1.52676e6	−0.244072	−0.122036	+	0.992526i	$0.538942\pi$
$524$	−1.86827e7	−2.97243
$525$	882352.	0.139715
$526$	278216.	0.0438447
$527$	4.48179e6	0.702951
$528$	310260.	0.0484330
$529$	−1.28542e6	−0.199712
$530$	2.14820e6	0.332190
$531$	−5.60221e6	−0.862230
$532$	−1.19883e7	−1.83645
$533$	−1.42307e7	−2.16974
$534$	−81557.2	−0.0123768
$535$	4.86982e6	0.735577
$536$	1.33590e7	2.00845
$537$	607309.	0.0908811
$538$	−1.77296e7	−2.64084
$539$	−2.51165e6	−0.372381
$540$	4.30538e6	0.635370
$541$	−8.68947e6	−1.27644	−0.638220	−	0.769854i	$-0.720329\pi$
$541$	−8.68947e6	−1.27644	−0.638220	+	0.769854i	$0.720329\pi$
$542$	−4.61664e6	−0.675037
$543$	−1.13276e6	−0.164868
$544$	−3.09054e6	−0.447752
$545$	−6.72747e6	−0.970198
$546$	2.62425e6	0.376724
$547$	566092.	0.0808944	0.0404472	−	0.999182i	$-0.487122\pi$
$547$	566092.	0.0808944	0.0404472	+	0.999182i	$0.487122\pi$
$548$	1.08049e7	1.53698
$549$	5.49471e6	0.778062
$550$	3.25225e6	0.458435
$551$	885797.	0.124295
$552$	1.42595e6	0.199186
$553$	1.06131e7	1.47580
$554$	1.16574e7	1.61372
$555$	−252019.	−0.0347297
$556$	−1.56680e7	−2.14945
$557$	−2.09212e6	−0.285725	−0.142863	−	0.989743i	$-0.545631\pi$
$557$	−2.09212e6	−0.285725	−0.142863	+	0.989743i	$0.545631\pi$
$558$	1.15909e7	1.57590
$559$	9.52654e6	1.28945
$560$	−2.22607e7	−2.99963
$561$	191798.	0.0257298
$562$	2.08006e7	2.77802
$563$	1.03540e7	1.37669	0.688346	−	0.725382i	$-0.258337\pi$
$563$	1.03540e7	1.37669	0.688346	+	0.725382i	$0.258337\pi$
$564$	−1.24993e6	−0.165459
$565$	−1.43425e7	−1.89019
$566$	−1.79158e7	−2.35069
$567$	−1.10376e7	−1.44185
$568$	−2.64840e7	−3.44439
$569$	2.29763e6	0.297508	0.148754	−	0.988874i	$-0.452474\pi$
$569$	2.29763e6	0.297508	0.148754	+	0.988874i	$0.452474\pi$
$570$	1.16920e6	0.150731
$571$	1.28733e7	1.65234	0.826168	−	0.563423i	$-0.190516\pi$
$571$	1.28733e7	1.65234	0.826168	+	0.563423i	$0.190516\pi$
$572$	6.60199e6	0.843694
$573$	1.04267e6	0.132666
$574$	3.49175e7	4.42348
$575$	6.07591e6	0.766376
$576$	3.59264e6	0.451188
$577$	−8.41817e6	−1.05264	−0.526318	−	0.850288i	$-0.676428\pi$
$577$	−8.41817e6	−1.05264	−0.526318	+	0.850288i	$0.676428\pi$
$578$	5.53203e6	0.688756
$579$	−936284.	−0.116068
$580$	5.16341e6	0.637333
$581$	1.68137e6	0.206645
$582$	−1.59567e6	−0.195271
$583$	339889.	0.0414158
$584$	−3.20428e6	−0.388775
$585$	1.45045e7	1.75231
$586$	2.35425e7	2.83210
$587$	−966776.	−0.115806	−0.0579030	−	0.998322i	$-0.518441\pi$
$587$	−966776.	−0.115806	−0.0579030	+	0.998322i	$0.518441\pi$
$588$	−2.42855e6	−0.289670
$589$	4.32273e6	0.513417
$590$	−1.78434e7	−2.11031
$591$	1.47807e6	0.174071
$592$	2.93367e6	0.344038
$593$	−1.13919e7	−1.33033	−0.665165	−	0.746696i	$-0.731639\pi$
$593$	−1.13919e7	−1.33033	−0.665165	+	0.746696i	$0.731639\pi$
$594$	998033.	0.116059
$595$	−1.37612e7	−1.59354
$596$	1.09694e7	1.26493
$597$	−51654.0	−0.00593154
$598$	1.80707e7	2.06643
$599$	4.06292e6	0.462670	0.231335	−	0.972874i	$-0.425691\pi$
$599$	4.06292e6	0.462670	0.231335	+	0.972874i	$0.425691\pi$
$600$	1.68202e6	0.190745
$601$	−1.15180e7	−1.30075	−0.650373	−	0.759615i	$-0.725387\pi$
$601$	−1.15180e7	−1.30075	−0.650373	+	0.759615i	$0.725387\pi$
$602$	−2.33751e7	−2.62883
$603$	8.68164e6	0.972318
$604$	−3.46319e7	−3.86264
$605$	1.11523e6	0.123873
$606$	−246791.	−0.0272991
$607$	−1.89792e6	−0.209076	−0.104538	−	0.994521i	$-0.533336\pi$
$607$	−1.89792e6	−0.209076	−0.104538	+	0.994521i	$0.533336\pi$
$608$	−2.98086e6	−0.327027
$609$	324734.	0.0354800
$610$	1.75010e7	1.90431
$611$	−8.47257e6	−0.918146
$612$	−1.53982e7	−1.66184
$613$	−1.42627e7	−1.53303	−0.766517	−	0.642224i	$-0.778012\pi$
$613$	−1.42627e7	−1.53303	−0.766517	+	0.642224i	$0.778012\pi$
$614$	136569.	0.0146194
$615$	−2.32436e6	−0.247808
$616$	−8.66468e6	−0.920027
$617$	−1.20693e7	−1.27635	−0.638176	−	0.769891i	$-0.720311\pi$
$617$	−1.20693e7	−1.27635	−0.638176	+	0.769891i	$0.720311\pi$
$618$	−763778.	−0.0804444
$619$	−7.73431e6	−0.811325	−0.405663	−	0.914023i	$-0.632959\pi$
$619$	−7.73431e6	−0.811325	−0.405663	+	0.914023i	$0.632959\pi$
$620$	2.51977e7	2.63258
$621$	1.86454e6	0.194018
$622$	−2.09452e7	−2.17075
$623$	925840.	0.0955688
$624$	2.03349e6	0.209064
$625$	−1.09646e7	−1.12278
$626$	4.87019e6	0.496718
$627$	184991.	0.0187924
$628$	1.61109e7	1.63012
$629$	1.81354e6	0.182769
$630$	−3.55893e7	−3.57247
$631$	−1.15333e7	−1.15313	−0.576567	−	0.817050i	$-0.695608\pi$
$631$	−1.15333e7	−1.15313	−0.576567	+	0.817050i	$0.695608\pi$
$632$	2.02316e7	2.01483
$633$	−1.20216e6	−0.119249
$634$	2.23989e7	2.21311
$635$	−8.08254e6	−0.795451
$636$	328643.	0.0322168
$637$	−1.64617e7	−1.60741
$638$	1.19693e6	0.116417
$639$	−1.72112e7	−1.66748
$640$	1.95245e7	1.88421
$641$	−2.69947e6	−0.259498	−0.129749	−	0.991547i	$-0.541417\pi$
$641$	−2.69947e6	−0.259498	−0.129749	+	0.991547i	$0.541417\pi$
$642$	1.09153e6	0.104519
$643$	−1.64697e7	−1.57093	−0.785466	−	0.618904i	$-0.787577\pi$
$643$	−1.64697e7	−1.57093	−0.785466	+	0.618904i	$0.787577\pi$
$644$	−3.02635e7	−2.87545
$645$	1.55601e6	0.147270
$646$	−8.41364e6	−0.793236
$647$	1.29099e7	1.21244	0.606221	−	0.795296i	$-0.292685\pi$
$647$	1.29099e7	1.21244	0.606221	+	0.795296i	$0.292685\pi$
$648$	−2.10410e7	−1.96847
$649$	−2.82318e6	−0.263103
$650$	2.13157e7	1.97887
$651$	1.58472e6	0.146554
$652$	2.40795e7	2.21834
$653$	−1.14342e7	−1.04936	−0.524679	−	0.851300i	$-0.675814\pi$
$653$	−1.14342e7	−1.04936	−0.524679	+	0.851300i	$0.675814\pi$
$654$	−1.50790e6	−0.137857
$655$	−2.06845e7	−1.88383
$656$	2.70571e7	2.45483
$657$	−2.08238e6	−0.188211
$658$	2.07890e7	1.87184
$659$	1.90457e7	1.70837	0.854186	−	0.519967i	$-0.174056\pi$
$659$	1.90457e7	1.70837	0.854186	+	0.519967i	$0.174056\pi$
$660$	1.07833e6	0.0963590
$661$	−2.72176e6	−0.242296	−0.121148	−	0.992634i	$-0.538658\pi$
$661$	−2.72176e6	−0.242296	−0.121148	+	0.992634i	$0.538658\pi$
$662$	−1.19738e7	−1.06191
$663$	1.25707e6	0.111064
$664$	3.20519e6	0.282120
$665$	−1.32728e7	−1.16388
$666$	4.69021e6	0.409738
$667$	2.23613e6	0.194618
$668$	1.82341e7	1.58104
$669$	1.44092e6	0.124473
$670$	2.76515e7	2.37975
$671$	2.76900e6	0.237420
$672$	−1.09279e6	−0.0933495
$673$	−1.11608e7	−0.949859	−0.474929	−	0.880024i	$-0.657526\pi$
$673$	−1.11608e7	−0.949859	−0.474929	+	0.880024i	$0.657526\pi$
$674$	3.80686e7	3.22788
$675$	2.19937e6	0.185797
$676$	1.77254e7	1.49186
$677$	−1.91080e7	−1.60230	−0.801150	−	0.598463i	$-0.795778\pi$
$677$	−1.91080e7	−1.60230	−0.801150	+	0.598463i	$0.795778\pi$
$678$	−3.21475e6	−0.268579
$679$	1.81141e7	1.50780
$680$	−2.62328e7	−2.17557
$681$	−843323.	−0.0696829
$682$	5.84109e6	0.480876
$683$	−1.12823e7	−0.925433	−0.462717	−	0.886506i	$-0.653125\pi$
$683$	−1.12823e7	−0.925433	−0.462717	+	0.886506i	$0.653125\pi$
$684$	−1.48517e7	−1.21377
$685$	1.19626e7	0.974089
$686$	7.68718e6	0.623672
$687$	−1.47025e6	−0.118850
$688$	−1.81130e7	−1.45888
$689$	2.22768e6	0.178774
$690$	2.95156e6	0.236009
$691$	2.53086e6	0.201639	0.100819	−	0.994905i	$-0.467854\pi$
$691$	2.53086e6	0.201639	0.100819	+	0.994905i	$0.467854\pi$
$692$	−4.79399e7	−3.80568
$693$	−5.63094e6	−0.445398
$694$	−1.48585e7	−1.17105
$695$	−1.73468e7	−1.36225
$696$	619038.	0.0484389
$697$	1.67262e7	1.30412
$698$	−3.70092e7	−2.87522
$699$	924191.	0.0715432
$700$	−3.56982e7	−2.75360
$701$	1.61652e7	1.24247	0.621236	−	0.783624i	$-0.286631\pi$
$701$	1.61652e7	1.24247	0.621236	+	0.783624i	$0.286631\pi$
$702$	6.54124e6	0.500977
$703$	1.74918e6	0.133489
$704$	1.81048e6	0.137677
$705$	−1.38386e6	−0.104862
$706$	6.42609e6	0.485216
$707$	2.80158e6	0.210792
$708$	−2.72977e6	−0.204665
$709$	−1.55662e7	−1.16296	−0.581482	−	0.813560i	$-0.697527\pi$
$709$	−1.55662e7	−1.16296	−0.581482	+	0.813560i	$0.697527\pi$
$710$	−5.48187e7	−4.08116
$711$	1.31480e7	0.975405
$712$	1.76492e6	0.130475
$713$	1.09124e7	0.803891
$714$	−3.08444e6	−0.226429
$715$	7.30937e6	0.534706
$716$	−2.45705e7	−1.79114
$717$	−840736.	−0.0610747
$718$	−4.08927e7	−2.96029
$719$	−2.29923e6	−0.165867	−0.0829335	−	0.996555i	$-0.526429\pi$
$719$	−2.29923e6	−0.165867	−0.0829335	+	0.996555i	$0.526429\pi$
$720$	−2.75776e7	−1.98255
$721$	8.67043e6	0.621159
$722$	1.67448e7	1.19547
$723$	278790.	0.0198350
$724$	4.58290e7	3.24933
$725$	2.63769e6	0.186371
$726$	249969.	0.0176013
$727$	−1.56253e7	−1.09646	−0.548230	−	0.836327i	$-0.684698\pi$
$727$	−1.56253e7	−1.09646	−0.548230	+	0.836327i	$0.684698\pi$
$728$	−5.67895e7	−3.97136
$729$	−1.33345e7	−0.929304
$730$	−6.63248e6	−0.460648
$731$	−1.11972e7	−0.775022
$732$	2.67739e6	0.184686
$733$	1.35752e7	0.933223	0.466611	−	0.884462i	$-0.345475\pi$
$733$	1.35752e7	0.933223	0.466611	+	0.884462i	$0.345475\pi$
$734$	4.89708e6	0.335504
$735$	−2.68876e6	−0.183584
$736$	−7.52497e6	−0.512047
$737$	4.37502e6	0.296696
$738$	4.32576e7	2.92362
$739$	2.22098e7	1.49601	0.748003	−	0.663696i	$-0.231013\pi$
$739$	2.22098e7	1.49601	0.748003	+	0.663696i	$0.231013\pi$
$740$	1.01962e7	0.684475
$741$	1.21246e6	0.0811186
$742$	−5.46601e6	−0.364469
$743$	739268.	0.0491281	0.0245640	−	0.999698i	$-0.492180\pi$
$743$	739268.	0.0491281	0.0245640	+	0.999698i	$0.492180\pi$
$744$	3.02093e6	0.200082
$745$	1.21447e7	0.801670
$746$	6.28738e6	0.413640
$747$	2.08297e6	0.136578
$748$	−7.75974e6	−0.507099
$749$	−1.23910e7	−0.807055
$750$	−582457.	−0.0378104
$751$	2.96012e7	1.91518	0.957589	−	0.288136i	$-0.0930355\pi$
$751$	2.96012e7	1.91518	0.957589	+	0.288136i	$0.0930355\pi$
$752$	1.61090e7	1.03878
$753$	−152.327	−9.79018e−6 0
$754$	7.84486e6	0.502524
$755$	−3.83426e7	−2.44801
$756$	−1.09548e7	−0.697111
$757$	4.71650e6	0.299144	0.149572	−	0.988751i	$-0.452210\pi$
$757$	4.71650e6	0.299144	0.149572	+	0.988751i	$0.452210\pi$
$758$	4.54850e7	2.87538
$759$	466996.	0.0294244
$760$	−2.53018e7	−1.58898
$761$	−2.90566e7	−1.81879	−0.909395	−	0.415934i	$-0.863455\pi$
$761$	−2.90566e7	−1.81879	−0.909395	+	0.415934i	$0.863455\pi$
$762$	−1.81163e6	−0.113027
$763$	1.71178e7	1.06447
$764$	−4.21843e7	−2.61467
$765$	−1.70480e7	−1.05322
$766$	3.98558e7	2.45426
$767$	−1.85035e7	−1.13570
$768$	3.56203e6	0.217918
$769$	2.45883e7	1.49938	0.749692	−	0.661786i	$-0.230201\pi$
$769$	2.45883e7	1.49938	0.749692	+	0.661786i	$0.230201\pi$
$770$	−1.79349e7	−1.09011
$771$	2.02814e6	0.122875
$772$	3.78801e7	2.28754
$773$	−1.29117e6	−0.0777202	−0.0388601	−	0.999245i	$-0.512373\pi$
$773$	−1.29117e6	−0.0777202	−0.0388601	+	0.999245i	$0.512373\pi$
$774$	−2.89582e7	−1.73748
$775$	1.28720e7	0.769826
$776$	3.45309e7	2.05851
$777$	641251.	0.0381044
$778$	2.56617e7	1.51997
$779$	1.61326e7	0.952492
$780$	7.06753e6	0.415941
$781$	−8.67342e6	−0.508819
$782$	−2.12396e7	−1.24202
$783$	809437.	0.0471823
$784$	3.12990e7	1.81861
$785$	1.78371e7	1.03312
$786$	−4.63625e6	−0.267676
$787$	1.92285e7	1.10665	0.553324	−	0.832966i	$-0.313359\pi$
$787$	1.92285e7	1.10665	0.553324	+	0.832966i	$0.313359\pi$
$788$	−5.97999e7	−3.43072
$789$	47123.3	0.00269491
$790$	4.18770e7	2.38731
$791$	3.64939e7	2.07386
$792$	−1.07342e7	−0.608076
$793$	1.81484e7	1.02484
$794$	−1.57279e7	−0.885358
$795$	363856.	0.0204180
$796$	2.08981e6	0.116903
$797$	1.15830e7	0.645916	0.322958	−	0.946413i	$-0.395323\pi$
$797$	1.15830e7	0.645916	0.322958	+	0.946413i	$0.395323\pi$
$798$	−2.97498e6	−0.165378
$799$	9.95835e6	0.551849
$800$	−8.87627e6	−0.490349
$801$	1.14698e6	0.0631645
$802$	−4.78349e7	−2.62608
$803$	−1.04939e6	−0.0574313
$804$	4.23027e6	0.230796
$805$	−3.35062e7	−1.82236
$806$	3.82833e7	2.07573
$807$	−3.00298e6	−0.162319
$808$	5.34064e6	0.287783
$809$	2.41005e7	1.29466	0.647328	−	0.762212i	$-0.275887\pi$
$809$	2.41005e7	1.29466	0.647328	+	0.762212i	$0.275887\pi$
$810$	−4.35524e7	−2.33238
$811$	−1.25492e7	−0.669983	−0.334991	−	0.942221i	$-0.608733\pi$
$811$	−1.25492e7	−0.669983	−0.334991	+	0.942221i	$0.608733\pi$
$812$	−1.31381e7	−0.699264
$813$	−781953.	−0.0414910
$814$	2.36358e6	0.125029
$815$	2.66595e7	1.40591
$816$	−2.39009e6	−0.125657
$817$	−1.07998e7	−0.566056
$818$	−1.18902e7	−0.621308
$819$	−3.69060e7	−1.92259
$820$	9.40387e7	4.88396
$821$	9.91177e6	0.513208	0.256604	−	0.966517i	$-0.417396\pi$
$821$	9.91177e6	0.513208	0.256604	+	0.966517i	$0.417396\pi$
$822$	2.68131e6	0.138410
$823$	1.36967e7	0.704880	0.352440	−	0.935834i	$-0.385352\pi$
$823$	1.36967e7	0.704880	0.352440	+	0.935834i	$0.385352\pi$
$824$	1.65284e7	0.848032
$825$	550857.	0.0281776
$826$	4.54016e7	2.31537
$827$	−571257.	−0.0290448	−0.0145224	−	0.999895i	$-0.504623\pi$
$827$	−571257.	−0.0290448	−0.0145224	+	0.999895i	$0.504623\pi$
$828$	−3.74920e7	−1.90048
$829$	2.22291e7	1.12340	0.561702	−	0.827339i	$-0.310147\pi$
$829$	2.22291e7	1.12340	0.561702	+	0.827339i	$0.310147\pi$
$830$	6.63437e6	0.334275
$831$	1.97450e6	0.0991871
$832$	1.18661e7	0.594292
$833$	1.93485e7	0.966129
$834$	−3.88813e6	−0.193564
$835$	2.01878e7	1.00201
$836$	−7.48435e6	−0.370372
$837$	3.95009e6	0.194892
$838$	1.75019e7	0.860945
$839$	1.48117e7	0.726440	0.363220	−	0.931703i	$-0.381677\pi$
$839$	1.48117e7	0.726440	0.363220	+	0.931703i	$0.381677\pi$
$840$	−9.27567e6	−0.453573
$841$	−1.95404e7	−0.952672
$842$	5.32779e7	2.58980
$843$	3.52315e6	0.170751
$844$	4.86370e7	2.35023
$845$	1.96246e7	0.945494
$846$	2.57544e7	1.23716
$847$	−2.83765e6	−0.135910
$848$	−4.23553e6	−0.202264
$849$	−3.03453e6	−0.144485
$850$	−2.50537e7	−1.18939
$851$	4.41568e6	0.209013
$852$	−8.38645e6	−0.395803
$853$	−1.13641e7	−0.534764	−0.267382	−	0.963591i	$-0.586159\pi$
$853$	−1.13641e7	−0.534764	−0.267382	+	0.963591i	$0.586159\pi$
$854$	−4.45304e7	−2.08936
$855$	−1.64430e7	−0.769247
$856$	−2.36210e7	−1.10183
$857$	−32279.1	−0.00150131	−0.000750653	−	1.00000i	$-0.500239\pi$
$857$	−32279.1	−0.00150131	−0.000750653		1.00000i	$0.500239\pi$
$858$	1.63833e6	0.0759772
$859$	1.63488e7	0.755967	0.377984	−	0.925812i	$-0.376618\pi$
$859$	1.63488e7	0.755967	0.377984	+	0.925812i	$0.376618\pi$
$860$	−6.29530e7	−2.90249
$861$	5.91423e6	0.271888
$862$	7.42221e6	0.340224
$863$	9.39443e6	0.429382	0.214691	−	0.976682i	$-0.431126\pi$
$863$	9.39443e6	0.429382	0.214691	+	0.976682i	$0.431126\pi$
$864$	−2.72390e6	−0.124139
$865$	−5.30765e7	−2.41192
$866$	−3.38467e7	−1.53364
$867$	936999.	0.0423342
$868$	−6.41144e7	−2.88839
$869$	6.62579e6	0.297638
$870$	1.28133e6	0.0573937
$871$	2.86745e7	1.28071
$872$	3.26315e7	1.45327
$873$	2.24407e7	0.996553
$874$	−2.04858e7	−0.907141
$875$	6.61207e6	0.291956
$876$	−1.01467e6	−0.0446750
$877$	2.58918e7	1.13675	0.568374	−	0.822771i	$-0.307573\pi$
$877$	2.58918e7	1.13675	0.568374	+	0.822771i	$0.307573\pi$
$878$	5.99757e7	2.62566
$879$	3.98756e6	0.174075
$880$	−1.38974e7	−0.604962
$881$	−4.42510e7	−1.92080	−0.960402	−	0.278619i	$-0.910123\pi$
$881$	−4.42510e7	−1.92080	−0.960402	+	0.278619i	$0.910123\pi$
$882$	5.00393e7	2.16591
$883$	2.45049e7	1.05767	0.528836	−	0.848724i	$-0.322629\pi$
$883$	2.45049e7	1.05767	0.528836	+	0.848724i	$0.322629\pi$
$884$	−5.08584e7	−2.18893
$885$	−3.02225e6	−0.129710
$886$	3.86857e7	1.65564
$887$	3.17827e7	1.35638	0.678190	−	0.734887i	$-0.262765\pi$
$887$	3.17827e7	1.35638	0.678190	+	0.734887i	$0.262765\pi$
$888$	1.22241e6	0.0520218
$889$	2.05657e7	0.872747
$890$	3.65318e6	0.154595
$891$	−6.89086e6	−0.290790
$892$	−5.82967e7	−2.45319
$893$	9.60493e6	0.403056
$894$	2.72212e6	0.113911
$895$	−2.72031e7	−1.13517
$896$	−4.96793e7	−2.06731
$897$	3.06075e6	0.127013
$898$	−6.35038e7	−2.62790
$899$	4.73731e6	0.195494
$900$	−4.42246e7	−1.81994
$901$	−2.61833e6	−0.107452
$902$	2.17992e7	0.892121
$903$	−3.95920e6	−0.161580
$904$	6.95681e7	2.83132
$905$	5.07394e7	2.05932
$906$	−8.59414e6	−0.347842
$907$	2.37972e7	0.960522	0.480261	−	0.877126i	$-0.340542\pi$
$907$	2.37972e7	0.960522	0.480261	+	0.877126i	$0.340542\pi$
$908$	3.41191e7	1.37336
$909$	3.47074e6	0.139320
$910$	−1.17548e8	−4.70554
$911$	3.10287e7	1.23870	0.619352	−	0.785113i	$-0.287395\pi$
$911$	3.10287e7	1.23870	0.619352	+	0.785113i	$0.287395\pi$
$912$	−2.30526e6	−0.0917770
$913$	1.04969e6	0.0416758
$914$	4.88007e7	1.93224
$915$	2.96426e6	0.117048
$916$	5.94832e7	2.34237
$917$	5.26308e7	2.06689
$918$	−7.68834e6	−0.301110
$919$	3.00818e7	1.17494	0.587469	−	0.809247i	$-0.300124\pi$
$919$	3.00818e7	1.17494	0.587469	+	0.809247i	$0.300124\pi$
$920$	−6.38726e7	−2.48797
$921$	23131.6	0.000898579 0
$922$	−7.08170e7	−2.74353
$923$	−5.68468e7	−2.19635
$924$	−2.74377e6	−0.105722
$925$	5.20863e6	0.200156
$926$	1.30447e7	0.499926
$927$	1.07414e7	0.410544
$928$	−3.26675e6	−0.124522
$929$	−5.85920e6	−0.222741	−0.111370	−	0.993779i	$-0.535524\pi$
$929$	−5.85920e6	−0.222741	−0.111370	+	0.993779i	$0.535524\pi$
$930$	6.25297e6	0.237071
$931$	1.86618e7	0.705635
$932$	−3.73909e7	−1.41002
$933$	−3.54764e6	−0.133424
$934$	−3.70415e7	−1.38938
$935$	−8.59117e6	−0.321383
$936$	−7.03536e7	−2.62480
$937$	−3.35477e7	−1.24828	−0.624142	−	0.781311i	$-0.714551\pi$
$937$	−3.35477e7	−1.24828	−0.624142	+	0.781311i	$0.714551\pi$
$938$	−7.03580e7	−2.61100
$939$	824898.	0.0305307
$940$	5.59882e7	2.06670
$941$	4.25210e7	1.56541	0.782707	−	0.622390i	$-0.213838\pi$
$941$	4.25210e7	1.56541	0.782707	+	0.622390i	$0.213838\pi$
$942$	3.99802e6	0.146797
$943$	4.07256e7	1.49138
$944$	3.51810e7	1.28493
$945$	−1.21286e7	−0.441806
$946$	−1.45932e7	−0.530179
$947$	−1.55130e7	−0.562109	−0.281055	−	0.959692i	$-0.590684\pi$
$947$	−1.55130e7	−0.562109	−0.281055	+	0.959692i	$0.590684\pi$
$948$	6.40656e6	0.231528
$949$	−6.87785e6	−0.247906
$950$	−2.41646e7	−0.868701
$951$	3.79385e6	0.136028
$952$	6.67483e7	2.38697
$953$	1.98572e7	0.708249	0.354125	−	0.935198i	$-0.384779\pi$
$953$	1.98572e7	0.708249	0.354125	+	0.935198i	$0.384779\pi$
$954$	−6.77156e6	−0.240890
$955$	−4.67041e7	−1.65709
$956$	3.40144e7	1.20370
$957$	202733.	0.00715557
$958$	−1.93389e7	−0.680798
$959$	−3.04383e7	−1.06874
$960$	1.93814e6	0.0678746
$961$	−5.51084e6	−0.192490
$962$	1.54912e7	0.539695
$963$	−1.53506e7	−0.533409
$964$	−1.12793e7	−0.390921
$965$	4.19388e7	1.44977
$966$	−7.51011e6	−0.258943
$967$	−2.48246e6	−0.0853721	−0.0426861	−	0.999089i	$-0.513592\pi$
$967$	−2.48246e6	−0.0853721	−0.0426861	+	0.999089i	$0.513592\pi$
$968$	−5.40940e6	−0.185550
$969$	−1.42508e6	−0.0487561
$970$	7.14748e7	2.43907
$971$	−3.39479e7	−1.15549	−0.577743	−	0.816218i	$-0.696067\pi$
$971$	−3.39479e7	−1.15549	−0.577743	+	0.816218i	$0.696067\pi$
$972$	−2.03977e7	−0.692494
$973$	4.41382e7	1.49463
$974$	−4.21275e7	−1.42288
$975$	3.61039e6	0.121631
$976$	−3.45059e7	−1.15950
$977$	4.00008e7	1.34070	0.670351	−	0.742044i	$-0.266143\pi$
$977$	4.00008e7	1.34070	0.670351	+	0.742044i	$0.266143\pi$
$978$	5.97550e6	0.199769
$979$	578007.	0.0192742
$980$	1.08782e8	3.61819
$981$	2.12063e7	0.703546
$982$	1.80390e7	0.596945
$983$	−4.90823e7	−1.62010	−0.810049	−	0.586362i	$-0.800560\pi$
$983$	−4.90823e7	−1.62010	−0.810049	+	0.586362i	$0.800560\pi$
$984$	1.12743e7	0.371193
$985$	−6.62072e7	−2.17428
$986$	−9.22057e6	−0.302041
$987$	3.52117e6	0.115052
$988$	−4.90535e7	−1.59874
$989$	−2.72632e7	−0.886312
$990$	−2.22186e7	−0.720490
$991$	−3.19263e7	−1.03268	−0.516338	−	0.856385i	$-0.672705\pi$
$991$	−3.19263e7	−1.03268	−0.516338	+	0.856385i	$0.672705\pi$
$992$	−1.59419e7	−0.514352
$993$	−2.02809e6	−0.0652701
$994$	1.39484e8	4.47773
$995$	2.31373e6	0.0740892
$996$	1.01496e6	0.0324191
$997$	4.76869e6	0.151936	0.0759681	−	0.997110i	$-0.475795\pi$
$997$	4.76869e6	0.151936	0.0759681	+	0.997110i	$0.475795\pi$
$998$	−1.53100e7	−0.486573
$999$	1.59839e6	0.0506723

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	583.6.a.b.1.5	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
583.6.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-10.0399 q^{2} -1.70053 q^{3} +68.8000 q^{4} +76.1717 q^{5} +17.0732 q^{6} -193.816 q^{7} -369.469 q^{8} -240.108 q^{9} +O(q^{10})\)	\(q-10.0399 q^{2} -1.70053 q^{3} +68.8000 q^{4} +76.1717 q^{5} +17.0732 q^{6} -193.816 q^{7} -369.469 q^{8} -240.108 q^{9} -764.758 q^{10} -121.000 q^{11} -116.997 q^{12} -793.051 q^{13} +1945.89 q^{14} -129.532 q^{15} +1507.84 q^{16} +932.123 q^{17} +2410.67 q^{18} +899.043 q^{19} +5240.61 q^{20} +329.589 q^{21} +1214.83 q^{22} +2269.57 q^{23} +628.294 q^{24} +2677.13 q^{25} +7962.17 q^{26} +821.541 q^{27} -13334.5 q^{28} +985.267 q^{29} +1300.49 q^{30} +4808.15 q^{31} -3315.60 q^{32} +205.764 q^{33} -9358.44 q^{34} -14763.3 q^{35} -16519.4 q^{36} +1945.61 q^{37} -9026.32 q^{38} +1348.61 q^{39} -28143.1 q^{40} +17944.2 q^{41} -3309.05 q^{42} -12012.5 q^{43} -8324.80 q^{44} -18289.4 q^{45} -22786.3 q^{46} +10683.5 q^{47} -2564.13 q^{48} +20757.5 q^{49} -26878.1 q^{50} -1585.10 q^{51} -54561.9 q^{52} -2809.00 q^{53} -8248.20 q^{54} -9216.77 q^{55} +71608.9 q^{56} -1528.85 q^{57} -9892.01 q^{58} +23332.0 q^{59} -8911.83 q^{60} -22884.3 q^{61} -48273.5 q^{62} +46536.7 q^{63} -14962.6 q^{64} -60408.0 q^{65} -2065.86 q^{66} -36157.2 q^{67} +64130.1 q^{68} -3859.47 q^{69} +148222. q^{70} +71681.2 q^{71} +88712.6 q^{72} +8672.65 q^{73} -19533.7 q^{74} -4552.54 q^{75} +61854.1 q^{76} +23451.7 q^{77} -13539.9 q^{78} -54758.6 q^{79} +114855. q^{80} +56949.2 q^{81} -180159. q^{82} -8675.13 q^{83} +22675.8 q^{84} +71001.4 q^{85} +120605. q^{86} -1675.48 q^{87} +44705.8 q^{88} -4776.91 q^{89} +183625. q^{90} +153706. q^{91} +156146. q^{92} -8176.41 q^{93} -107262. q^{94} +68481.6 q^{95} +5638.28 q^{96} -93460.7 q^{97} -208403. q^{98} +29053.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9}+O(q^{10}) \) 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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