LMFDB - Embedded newform 547.6.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,6,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	547.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:	$87.7299494377$
Analytic rank:	$1$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.7598 q^{2} -8.37500 q^{3} +83.7726 q^{4} +78.2630 q^{5} +90.1130 q^{6} -21.6310 q^{7} -557.061 q^{8} -172.859 q^{9} +O(q^{10})$	\(q-10.7598 q^{2} -8.37500 q^{3} +83.7726 q^{4} +78.2630 q^{5} +90.1130 q^{6} -21.6310 q^{7} -557.061 q^{8} -172.859 q^{9} -842.092 q^{10} +133.688 q^{11} -701.595 q^{12} +1056.68 q^{13} +232.745 q^{14} -655.452 q^{15} +3313.12 q^{16} -609.825 q^{17} +1859.93 q^{18} +194.599 q^{19} +6556.29 q^{20} +181.160 q^{21} -1438.46 q^{22} +308.413 q^{23} +4665.38 q^{24} +3000.10 q^{25} -11369.7 q^{26} +3482.82 q^{27} -1812.09 q^{28} -5346.67 q^{29} +7052.51 q^{30} -3753.75 q^{31} -17822.5 q^{32} -1119.64 q^{33} +6561.58 q^{34} -1692.91 q^{35} -14480.9 q^{36} +3812.21 q^{37} -2093.84 q^{38} -8849.71 q^{39} -43597.3 q^{40} -10069.0 q^{41} -1949.24 q^{42} -7669.49 q^{43} +11199.4 q^{44} -13528.5 q^{45} -3318.45 q^{46} +1397.26 q^{47} -27747.4 q^{48} -16339.1 q^{49} -32280.4 q^{50} +5107.28 q^{51} +88521.1 q^{52} -26884.2 q^{53} -37474.3 q^{54} +10462.9 q^{55} +12049.8 q^{56} -1629.77 q^{57} +57528.9 q^{58} +4522.19 q^{59} -54908.9 q^{60} +12346.8 q^{61} +40389.5 q^{62} +3739.13 q^{63} +85745.9 q^{64} +82699.2 q^{65} +12047.1 q^{66} -35521.1 q^{67} -51086.6 q^{68} -2582.95 q^{69} +18215.3 q^{70} +55629.3 q^{71} +96293.3 q^{72} +30278.9 q^{73} -41018.5 q^{74} -25125.8 q^{75} +16302.1 q^{76} -2891.82 q^{77} +95220.9 q^{78} -32783.4 q^{79} +259295. q^{80} +12836.2 q^{81} +108340. q^{82} -103387. q^{83} +15176.2 q^{84} -47726.8 q^{85} +82521.9 q^{86} +44778.3 q^{87} -74472.6 q^{88} +77761.7 q^{89} +145564. q^{90} -22857.2 q^{91} +25836.5 q^{92} +31437.6 q^{93} -15034.2 q^{94} +15229.9 q^{95} +149263. q^{96} -115894. q^{97} +175805. q^{98} -23109.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) $ 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9} - 950 q^{10} - 1832 q^{11} - 4143 q^{12} - 4369 q^{13} - 4777 q^{14} - 3487 q^{15} + 26274 q^{16} - 13648 q^{17} - 10269 q^{18} - 5446 q^{19} - 26032 q^{20} - 8428 q^{21} - 8248 q^{22} - 24142 q^{23} - 18577 q^{24} + 58062 q^{25} - 17656 q^{26} - 33269 q^{27} - 23512 q^{28} - 33752 q^{29} - 12418 q^{30} - 13781 q^{31} - 44076 q^{32} - 39186 q^{33} - 7207 q^{34} - 30833 q^{35} + 120044 q^{36} - 61582 q^{37} - 91259 q^{38} - 20077 q^{39} - 66032 q^{40} - 54181 q^{41} - 69252 q^{42} - 38600 q^{43} - 95712 q^{44} - 190880 q^{45} - 9354 q^{46} - 83886 q^{47} - 173886 q^{48} + 194148 q^{49} - 70896 q^{50} - 60673 q^{51} - 145186 q^{52} - 286874 q^{53} - 116519 q^{54} - 74821 q^{55} - 240407 q^{56} - 95180 q^{57} - 66900 q^{58} - 135740 q^{59} - 144550 q^{60} - 227450 q^{61} - 308766 q^{62} - 249721 q^{63} + 347514 q^{64} - 290374 q^{65} - 178980 q^{66} - 91006 q^{67} - 521943 q^{68} - 414510 q^{69} - 165057 q^{70} - 236165 q^{71} - 527945 q^{72} - 184618 q^{73} - 206443 q^{74} - 243897 q^{75} - 221676 q^{76} - 751131 q^{77} - 306839 q^{78} - 107446 q^{79} - 856691 q^{80} + 382187 q^{81} - 244614 q^{82} - 499547 q^{83} - 330289 q^{84} - 287103 q^{85} - 272441 q^{86} - 391281 q^{87} - 588937 q^{88} - 740774 q^{89} - 687179 q^{90} - 237213 q^{91} - 1367678 q^{92} - 754880 q^{93} - 32851 q^{94} - 295814 q^{95} - 816078 q^{96} - 320770 q^{97} - 661922 q^{98} - 547439 q^{99}+O(q^{100}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9 - 950 * q^10 - 1832 * q^11 - 4143 * q^12 - 4369 * q^13 - 4777 * q^14 - 3487 * q^15 + 26274 * q^16 - 13648 * q^17 - 10269 * q^18 - 5446 * q^19 - 26032 * q^20 - 8428 * q^21 - 8248 * q^22 - 24142 * q^23 - 18577 * q^24 + 58062 * q^25 - 17656 * q^26 - 33269 * q^27 - 23512 * q^28 - 33752 * q^29 - 12418 * q^30 - 13781 * q^31 - 44076 * q^32 - 39186 * q^33 - 7207 * q^34 - 30833 * q^35 + 120044 * q^36 - 61582 * q^37 - 91259 * q^38 - 20077 * q^39 - 66032 * q^40 - 54181 * q^41 - 69252 * q^42 - 38600 * q^43 - 95712 * q^44 - 190880 * q^45 - 9354 * q^46 - 83886 * q^47 - 173886 * q^48 + 194148 * q^49 - 70896 * q^50 - 60673 * q^51 - 145186 * q^52 - 286874 * q^53 - 116519 * q^54 - 74821 * q^55 - 240407 * q^56 - 95180 * q^57 - 66900 * q^58 - 135740 * q^59 - 144550 * q^60 - 227450 * q^61 - 308766 * q^62 - 249721 * q^63 + 347514 * q^64 - 290374 * q^65 - 178980 * q^66 - 91006 * q^67 - 521943 * q^68 - 414510 * q^69 - 165057 * q^70 - 236165 * q^71 - 527945 * q^72 - 184618 * q^73 - 206443 * q^74 - 243897 * q^75 - 221676 * q^76 - 751131 * q^77 - 306839 * q^78 - 107446 * q^79 - 856691 * q^80 + 382187 * q^81 - 244614 * q^82 - 499547 * q^83 - 330289 * q^84 - 287103 * q^85 - 272441 * q^86 - 391281 * q^87 - 588937 * q^88 - 740774 * q^89 - 687179 * q^90 - 237213 * q^91 - 1367678 * q^92 - 754880 * q^93 - 32851 * q^94 - 295814 * q^95 - 816078 * q^96 - 320770 * q^97 - 661922 * q^98 - 547439 * 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 $

$2$	−10.7598	−1.90208	−0.951038	−	0.309074i	$-0.899981\pi$
$2$	−10.7598	−1.90208	−0.951038	+	0.309074i	$0.899981\pi$
$3$	−8.37500	−0.537256	−0.268628	−	0.963244i	$-0.586570\pi$
$3$	−8.37500	−0.537256	−0.268628	+	0.963244i	$0.586570\pi$
$4$	83.7726	2.61789
$5$	78.2630	1.40001	0.700006	−	0.714137i	$-0.253181\pi$
$5$	78.2630	1.40001	0.700006	+	0.714137i	$0.253181\pi$
$6$	90.1130	1.02190
$7$	−21.6310	−0.166852	−0.0834262	−	0.996514i	$-0.526586\pi$
$7$	−21.6310	−0.166852	−0.0834262	+	0.996514i	$0.526586\pi$
$8$	−557.061	−3.07736
$9$	−172.859	−0.711356
$10$	−842.092	−2.66293
$11$	133.688	0.333129	0.166564	−	0.986031i	$-0.446733\pi$
$11$	133.688	0.333129	0.166564	+	0.986031i	$0.446733\pi$
$12$	−701.595	−1.40648
$13$	1056.68	1.73415	0.867074	−	0.498179i	$-0.165998\pi$
$13$	1056.68	1.73415	0.867074	+	0.498179i	$0.165998\pi$
$14$	232.745	0.317366
$15$	−655.452	−0.752165
$16$	3313.12	3.23547
$17$	−609.825	−0.511780	−0.255890	−	0.966706i	$-0.582368\pi$
$17$	−609.825	−0.511780	−0.255890	+	0.966706i	$0.582368\pi$
$18$	1859.93	1.35305
$19$	194.599	0.123668	0.0618339	−	0.998086i	$-0.480305\pi$
$19$	194.599	0.123668	0.0618339	+	0.998086i	$0.480305\pi$
$20$	6556.29	3.66508
$21$	181.160	0.0896425
$22$	−1438.46	−0.633636
$23$	308.413	0.121566	0.0607831	−	0.998151i	$-0.480640\pi$
$23$	308.413	0.121566	0.0607831	+	0.998151i	$0.480640\pi$
$24$	4665.38	1.65333
$25$	3000.10	0.960032
$26$	−11369.7	−3.29848
$27$	3482.82	0.919436
$28$	−1812.09	−0.436802
$29$	−5346.67	−1.18056	−0.590280	−	0.807198i	$-0.700983\pi$
$29$	−5346.67	−1.18056	−0.590280	+	0.807198i	$0.700983\pi$
$30$	7052.51	1.43067
$31$	−3753.75	−0.701554	−0.350777	−	0.936459i	$-0.614082\pi$
$31$	−3753.75	−0.701554	−0.350777	+	0.936459i	$0.614082\pi$
$32$	−17822.5	−3.07676
$33$	−1119.64	−0.178976
$34$	6561.58	0.973444
$35$	−1692.91	−0.233595
$36$	−14480.9	−1.86225
$37$	3812.21	0.457797	0.228898	−	0.973450i	$-0.426488\pi$
$37$	3812.21	0.457797	0.228898	+	0.973450i	$0.426488\pi$
$38$	−2093.84	−0.235226
$39$	−8849.71	−0.931682
$40$	−43597.3	−4.30833
$41$	−10069.0	−0.935465	−0.467733	−	0.883870i	$-0.654929\pi$
$41$	−10069.0	−0.935465	−0.467733	+	0.883870i	$0.654929\pi$
$42$	−1949.24	−0.170507
$43$	−7669.49	−0.632551	−0.316275	−	0.948667i	$-0.602432\pi$
$43$	−7669.49	−0.632551	−0.316275	+	0.948667i	$0.602432\pi$
$44$	11199.4	0.872096
$45$	−13528.5	−0.995906
$46$	−3318.45	−0.231228
$47$	1397.26	0.0922641	0.0461320	−	0.998935i	$-0.485311\pi$
$47$	1397.26	0.0922641	0.0461320	+	0.998935i	$0.485311\pi$
$48$	−27747.4	−1.73828
$49$	−16339.1	−0.972160
$50$	−32280.4	−1.82605
$51$	5107.28	0.274957
$52$	88521.1	4.53982
$53$	−26884.2	−1.31464	−0.657321	−	0.753611i	$-0.728310\pi$
$53$	−26884.2	−1.31464	−0.657321	+	0.753611i	$0.728310\pi$
$54$	−37474.3	−1.74884
$55$	10462.9	0.466384
$56$	12049.8	0.513464
$57$	−1629.77	−0.0664413
$58$	57528.9	2.24552
$59$	4522.19	0.169129	0.0845646	−	0.996418i	$-0.473050\pi$
$59$	4522.19	0.169129	0.0845646	+	0.996418i	$0.473050\pi$
$60$	−54908.9	−1.96909
$61$	12346.8	0.424843	0.212422	−	0.977178i	$-0.431865\pi$
$61$	12346.8	0.424843	0.212422	+	0.977178i	$0.431865\pi$
$62$	40389.5	1.33441
$63$	3739.13	0.118691
$64$	85745.9	2.61676
$65$	82699.2	2.42783
$66$	12047.1	0.340425
$67$	−35521.1	−0.966718	−0.483359	−	0.875422i	$-0.660583\pi$
$67$	−35521.1	−0.966718	−0.483359	+	0.875422i	$0.660583\pi$
$68$	−51086.6	−1.33978
$69$	−2582.95	−0.0653122
$70$	18215.3	0.444316
$71$	55629.3	1.30966	0.654829	−	0.755777i	$-0.272741\pi$
$71$	55629.3	1.30966	0.654829	+	0.755777i	$0.272741\pi$
$72$	96293.3	2.18910
$73$	30278.9	0.665018	0.332509	−	0.943100i	$-0.392105\pi$
$73$	30278.9	0.665018	0.332509	+	0.943100i	$0.392105\pi$
$74$	−41018.5	−0.870764
$75$	−25125.8	−0.515783
$76$	16302.1	0.323749
$77$	−2891.82	−0.0555834
$78$	95220.9	1.77213
$79$	−32783.4	−0.590999	−0.295499	−	0.955343i	$-0.595486\pi$
$79$	−32783.4	−0.590999	−0.295499	+	0.955343i	$0.595486\pi$
$80$	259295.	4.52970
$81$	12836.2	0.217383
$82$	108340.	1.77933
$83$	−103387.	−1.64730	−0.823648	−	0.567101i	$-0.808065\pi$
$83$	−103387.	−1.64730	−0.823648	+	0.567101i	$0.808065\pi$
$84$	15176.2	0.234674
$85$	−47726.8	−0.716497
$86$	82521.9	1.20316
$87$	44778.3	0.634264
$88$	−74472.6	−1.02516
$89$	77761.7	1.04062	0.520308	−	0.853978i	$-0.325817\pi$
$89$	77761.7	1.04062	0.520308	+	0.853978i	$0.325817\pi$
$90$	145564.	1.89429
$91$	−22857.2	−0.289347
$92$	25836.5	0.318247
$93$	31437.6	0.376914
$94$	−15034.2	−0.175493
$95$	15229.9	0.173136
$96$	149263.	1.65301
$97$	−115894.	−1.25064	−0.625318	−	0.780370i	$-0.715031\pi$
$97$	−115894.	−1.25064	−0.625318	+	0.780370i	$0.715031\pi$
$98$	175805.	1.84912
$99$	−23109.3	−0.236973
$100$	251326.	2.51326
$101$	86527.9	0.844020	0.422010	−	0.906591i	$-0.361325\pi$
$101$	86527.9	0.844020	0.422010	+	0.906591i	$0.361325\pi$
$102$	−54953.2	−0.522989
$103$	7391.19	0.0686470	0.0343235	−	0.999411i	$-0.489072\pi$
$103$	7391.19	0.0686470	0.0343235	+	0.999411i	$0.489072\pi$
$104$	−588637.	−5.33659
$105$	14178.1	0.125500
$106$	289268.	2.50055
$107$	−38530.1	−0.325342	−0.162671	−	0.986680i	$-0.552011\pi$
$107$	−38530.1	−0.325342	−0.162671	+	0.986680i	$0.552011\pi$
$108$	291765.	2.40699
$109$	120443.	0.970991	0.485495	−	0.874239i	$-0.338639\pi$
$109$	120443.	0.970991	0.485495	+	0.874239i	$0.338639\pi$
$110$	−112578.	−0.887098
$111$	−31927.3	−0.245954
$112$	−71666.3	−0.539846
$113$	−105449.	−0.776867	−0.388434	−	0.921477i	$-0.626984\pi$
$113$	−105449.	−0.776867	−0.388434	+	0.921477i	$0.626984\pi$
$114$	17535.9	0.126376
$115$	24137.3	0.170194
$116$	−447904.	−3.09058
$117$	−182658.	−1.23360
$118$	−48657.7	−0.321697
$119$	13191.2	0.0853917
$120$	365127.	2.31468
$121$	−143178.	−0.889025
$122$	−132848.	−0.808084
$123$	84328.0	0.502584
$124$	−314461.	−1.83659
$125$	−9775.15	−0.0559562
$126$	−40232.2	−0.225760
$127$	132876.	0.731033	0.365517	−	0.930805i	$-0.380892\pi$
$127$	132876.	0.731033	0.365517	+	0.930805i	$0.380892\pi$
$128$	−352286.	−1.90051
$129$	64231.9	0.339842
$130$	−889824.	−4.61791
$131$	76121.6	0.387552	0.193776	−	0.981046i	$-0.437927\pi$
$131$	76121.6	0.387552	0.193776	+	0.981046i	$0.437927\pi$
$132$	−93795.2	−0.468539
$133$	−4209.38	−0.0206343
$134$	382199.	1.83877
$135$	272576.	1.28722
$136$	339710.	1.57493
$137$	−268529.	−1.22233	−0.611167	−	0.791501i	$-0.709300\pi$
$137$	−268529.	−1.22233	−0.611167	+	0.791501i	$0.709300\pi$
$138$	27792.0	0.124229
$139$	244669.	1.07409	0.537046	−	0.843553i	$-0.319540\pi$
$139$	244669.	1.07409	0.537046	+	0.843553i	$0.319540\pi$
$140$	−141820.	−0.611527
$141$	−11702.0	−0.0495694
$142$	−598559.	−2.49107
$143$	141266.	0.577695
$144$	−572705.	−2.30157
$145$	−418447.	−1.65280
$146$	−325794.	−1.26491
$147$	136840.	0.522299
$148$	319359.	1.19846
$149$	599.437	0.00221196	0.00110598	−	0.999999i	$-0.499648\pi$
$149$	599.437	0.00221196	0.00110598	+	0.999999i	$0.499648\pi$
$150$	270348.	0.981058
$151$	39430.7	0.140732	0.0703658	−	0.997521i	$-0.477583\pi$
$151$	39430.7	0.140732	0.0703658	+	0.997521i	$0.477583\pi$
$152$	−108404.	−0.380570
$153$	105414.	0.364057
$154$	31115.3	0.105724
$155$	−293780.	−0.982183
$156$	−741363.	−2.43904
$157$	34287.5	0.111016	0.0555081	−	0.998458i	$-0.482322\pi$
$157$	34287.5	0.111016	0.0555081	+	0.998458i	$0.482322\pi$
$158$	352742.	1.12412
$159$	225155.	0.706299
$160$	−1.39484e6	−4.30750
$161$	−6671.29	−0.0202836
$162$	−138115.	−0.413479
$163$	−86092.0	−0.253801	−0.126901	−	0.991915i	$-0.540503\pi$
$163$	−86092.0	−0.253801	−0.126901	+	0.991915i	$0.540503\pi$
$164$	−843508.	−2.44895
$165$	−87626.4	−0.250568
$166$	1.11242e6	3.13328
$167$	−65152.6	−0.180776	−0.0903880	−	0.995907i	$-0.528811\pi$
$167$	−65152.6	−0.180776	−0.0903880	+	0.995907i	$0.528811\pi$
$168$	−100917.	−0.275862
$169$	745286.	2.00727
$170$	513529.	1.36283
$171$	−33638.3	−0.0879719
$172$	−642493.	−1.65595
$173$	39647.7	0.100717	0.0503585	−	0.998731i	$-0.483964\pi$
$173$	39647.7	0.100717	0.0503585	+	0.998731i	$0.483964\pi$
$174$	−481804.	−1.20642
$175$	−64895.3	−0.160184
$176$	442926.	1.07783
$177$	−37873.3	−0.0908657
$178$	−836698.	−1.97933
$179$	393609.	0.918189	0.459094	−	0.888387i	$-0.348174\pi$
$179$	393609.	0.918189	0.459094	+	0.888387i	$0.348174\pi$
$180$	−1.13332e6	−2.60718
$181$	−285157.	−0.646975	−0.323488	−	0.946232i	$-0.604855\pi$
$181$	−285157.	−0.646975	−0.323488	+	0.946232i	$0.604855\pi$
$182$	245938.	0.550360
$183$	−103404.	−0.228250
$184$	−171805.	−0.374102
$185$	298355.	0.640921
$186$	−338262.	−0.716919
$187$	−81526.6	−0.170489
$188$	117052.	0.241537
$189$	−75337.1	−0.153410
$190$	−163870.	−0.329319
$191$	−55944.0	−0.110961	−0.0554804	−	0.998460i	$-0.517669\pi$
$191$	−55944.0	−0.110961	−0.0554804	+	0.998460i	$0.517669\pi$
$192$	−718121.	−1.40587
$193$	1.01958e6	1.97029	0.985143	−	0.171737i	$-0.0549380\pi$
$193$	1.01958e6	1.97029	0.985143	+	0.171737i	$0.0549380\pi$
$194$	1.24699e6	2.37881
$195$	−692605.	−1.30437
$196$	−1.36877e6	−2.54501
$197$	−527841.	−0.969030	−0.484515	−	0.874783i	$-0.661004\pi$
$197$	−527841.	−0.969030	−0.484515	+	0.874783i	$0.661004\pi$
$198$	248651.	0.450741
$199$	874324.	1.56509	0.782545	−	0.622594i	$-0.213921\pi$
$199$	874324.	1.56509	0.782545	+	0.622594i	$0.213921\pi$
$200$	−1.67124e6	−2.95436
$201$	297489.	0.519375
$202$	−931020.	−1.60539
$203$	115654.	0.196979
$204$	427850.	0.719808
$205$	−788032.	−1.30966
$206$	−79527.5	−0.130572
$207$	−53312.0	−0.0864768
$208$	3.50092e6	5.61079
$209$	26015.7	0.0411973
$210$	−152553.	−0.238711
$211$	852645.	1.31845	0.659223	−	0.751948i	$-0.270885\pi$
$211$	852645.	1.31845	0.659223	+	0.751948i	$0.270885\pi$
$212$	−2.25216e6	−3.44159
$213$	−465896.	−0.703622
$214$	414574.	0.618825
$215$	−600237.	−0.885578
$216$	−1.94014e6	−2.82943
$217$	81197.5	0.117056
$218$	−1.29594e6	−1.84690
$219$	−253586.	−0.357285
$220$	876501.	1.22094
$221$	−644392.	−0.887502
$222$	343530.	0.467824
$223$	−1.35503e6	−1.82468	−0.912342	−	0.409430i	$-0.865728\pi$
$223$	−1.35503e6	−1.82468	−0.912342	+	0.409430i	$0.865728\pi$
$224$	385519.	0.513365
$225$	−518595.	−0.682924
$226$	1.13461e6	1.47766
$227$	−833412.	−1.07348	−0.536742	−	0.843747i	$-0.680345\pi$
$227$	−833412.	−1.07348	−0.536742	+	0.843747i	$0.680345\pi$
$228$	−136530.	−0.173936
$229$	−357364.	−0.450321	−0.225161	−	0.974322i	$-0.572291\pi$
$229$	−357364.	−0.450321	−0.225161	+	0.974322i	$0.572291\pi$
$230$	−259712.	−0.323722
$231$	24219.0	0.0298625
$232$	2.97842e6	3.63301
$233$	−1.47719e6	−1.78257	−0.891287	−	0.453440i	$-0.850197\pi$
$233$	−1.47719e6	−1.78257	−0.891287	+	0.453440i	$0.850197\pi$
$234$	1.96535e6	2.34639
$235$	109354.	0.129171
$236$	378836.	0.442762
$237$	274561.	0.317518
$238$	−141934.	−0.162421
$239$	−1.55960e6	−1.76612	−0.883059	−	0.469262i	$-0.844520\pi$
$239$	−1.55960e6	−1.76612	−0.883059	+	0.469262i	$0.844520\pi$
$240$	−2.17159e6	−2.43361
$241$	763200.	0.846440	0.423220	−	0.906027i	$-0.360900\pi$
$241$	763200.	0.846440	0.423220	+	0.906027i	$0.360900\pi$
$242$	1.54057e6	1.69099
$243$	−953829.	−1.03623
$244$	1.03432e6	1.11219
$245$	−1.27875e6	−1.36104
$246$	−907350.	−0.955954
$247$	205630.	0.214458
$248$	2.09107e6	2.15893
$249$	865868.	0.885020
$250$	105178.	0.106433
$251$	932649.	0.934403	0.467201	−	0.884151i	$-0.345262\pi$
$251$	932649.	0.934403	0.467201	+	0.884151i	$0.345262\pi$
$252$	313237.	0.310721
$253$	41231.2	0.0404972
$254$	−1.42971e6	−1.39048
$255$	399711.	0.384943
$256$	1.04665e6	0.998160
$257$	−1.76111e6	−1.66323	−0.831616	−	0.555350i	$-0.812584\pi$
$257$	−1.76111e6	−1.66323	−0.831616	+	0.555350i	$0.812584\pi$
$258$	−691121.	−0.646405
$259$	−82462.1	−0.0763845
$260$	6.92792e6	6.35579
$261$	924223.	0.839799
$262$	−819050.	−0.737153
$263$	−774612.	−0.690550	−0.345275	−	0.938502i	$-0.612214\pi$
$263$	−774612.	−0.690550	−0.345275	+	0.938502i	$0.612214\pi$
$264$	623708.	0.550772
$265$	−2.10404e6	−1.84051
$266$	45292.0	0.0392480
$267$	−651254.	−0.559078
$268$	−2.97570e6	−2.53077
$269$	−571048.	−0.481163	−0.240581	−	0.970629i	$-0.577338\pi$
$269$	−571048.	−0.481163	−0.240581	+	0.970629i	$0.577338\pi$
$270$	−2.93285e6	−2.44839
$271$	−360040.	−0.297802	−0.148901	−	0.988852i	$-0.547574\pi$
$271$	−360040.	−0.297802	−0.148901	+	0.988852i	$0.547574\pi$
$272$	−2.02043e6	−1.65585
$273$	191429.	0.155453
$274$	2.88931e6	2.32497
$275$	401079.	0.319814
$276$	−216381.	−0.170980
$277$	−2.07152e6	−1.62214	−0.811072	−	0.584946i	$-0.801116\pi$
$277$	−2.07152e6	−1.62214	−0.811072	+	0.584946i	$0.801116\pi$
$278$	−2.63258e6	−2.04301
$279$	648871.	0.499054
$280$	943055.	0.718856
$281$	367400.	0.277570	0.138785	−	0.990323i	$-0.455680\pi$
$281$	367400.	0.277570	0.138785	+	0.990323i	$0.455680\pi$
$282$	125911.	0.0942848
$283$	560330.	0.415889	0.207945	−	0.978141i	$-0.433323\pi$
$283$	560330.	0.415889	0.207945	+	0.978141i	$0.433323\pi$
$284$	4.66021e6	3.42855
$285$	−127550.	−0.0930186
$286$	−1.51999e6	−1.09882
$287$	217803.	0.156085
$288$	3.08079e6	2.18867
$289$	−1.04797e6	−0.738082
$290$	4.50239e6	3.14375
$291$	970610.	0.671912
$292$	2.53654e6	1.74095
$293$	−243804.	−0.165910	−0.0829549	−	0.996553i	$-0.526436\pi$
$293$	−243804.	−0.165910	−0.0829549	+	0.996553i	$0.526436\pi$
$294$	−1.47237e6	−0.993453
$295$	353920.	0.236783
$296$	−2.12363e6	−1.40880
$297$	465613.	0.306291
$298$	−6449.81	−0.00420733
$299$	325894.	0.210814
$300$	−2.10485e6	−1.35026
$301$	165899.	0.105543
$302$	−424265.	−0.267682
$303$	−724671.	−0.453455
$304$	644731.	0.400124
$305$	966296.	0.594786
$306$	−1.13423e6	−0.692465
$307$	549165.	0.332550	0.166275	−	0.986079i	$-0.446826\pi$
$307$	549165.	0.332550	0.166275	+	0.986079i	$0.446826\pi$
$308$	−242255.	−0.145511
$309$	−61901.2	−0.0368810
$310$	3.16100e6	1.86819
$311$	−186340.	−0.109246	−0.0546229	−	0.998507i	$-0.517396\pi$
$311$	−186340.	−0.109246	−0.0546229	+	0.998507i	$0.517396\pi$
$312$	4.92983e6	2.86712
$313$	1.50478e6	0.868186	0.434093	−	0.900868i	$-0.357069\pi$
$313$	1.50478e6	0.868186	0.434093	+	0.900868i	$0.357069\pi$
$314$	−368925.	−0.211161
$315$	292636.	0.166169
$316$	−2.74635e6	−1.54717
$317$	1.63311e6	0.912782	0.456391	−	0.889779i	$-0.349142\pi$
$317$	1.63311e6	0.912782	0.456391	+	0.889779i	$0.349142\pi$
$318$	−2.42261e6	−1.34343
$319$	−714788.	−0.393279
$320$	6.71073e6	3.66349
$321$	322689.	0.174792
$322$	71781.5	0.0385810
$323$	−118671.	−0.0632907
$324$	1.07533e6	0.569085
$325$	3.17015e6	1.66484
$326$	926330.	0.482749
$327$	−1.00871e6	−0.521671
$328$	5.60906e6	2.87876
$329$	−30224.2	−0.0153945
$330$	942840.	0.476599
$331$	−1.69585e6	−0.850778	−0.425389	−	0.905011i	$-0.639863\pi$
$331$	−1.69585e6	−0.850778	−0.425389	+	0.905011i	$0.639863\pi$
$332$	−8.66102e6	−4.31245
$333$	−658977.	−0.325656
$334$	701027.	0.343850
$335$	−2.77999e6	−1.35342
$336$	600205.	0.290036
$337$	−3.79005e6	−1.81790	−0.908952	−	0.416902i	$-0.863116\pi$
$337$	−3.79005e6	−1.81790	−0.908952	+	0.416902i	$0.863116\pi$
$338$	−8.01910e6	−3.81798
$339$	883136.	0.417377
$340$	−3.99819e6	−1.87571
$341$	−501833.	−0.233708
$342$	361940.	0.167329
$343$	716985.	0.329060
$344$	4.27237e6	1.94658
$345$	−202150.	−0.0914378
$346$	−426600.	−0.191571
$347$	2.92169e6	1.30260	0.651299	−	0.758821i	$-0.274224\pi$
$347$	2.92169e6	1.30260	0.651299	+	0.758821i	$0.274224\pi$
$348$	3.75120e6	1.66043
$349$	−334272.	−0.146905	−0.0734525	−	0.997299i	$-0.523402\pi$
$349$	−334272.	−0.146905	−0.0734525	+	0.997299i	$0.523402\pi$
$350$	698258.	0.304681
$351$	3.68024e6	1.59444
$352$	−2.38266e6	−1.02496
$353$	−1.99061e6	−0.850256	−0.425128	−	0.905133i	$-0.639771\pi$
$353$	−1.99061e6	−0.850256	−0.425128	+	0.905133i	$0.639771\pi$
$354$	407508.	0.172834
$355$	4.35372e6	1.83354
$356$	6.51430e6	2.72422
$357$	−110476.	−0.0458772
$358$	−4.23514e6	−1.74646
$359$	−279388.	−0.114412	−0.0572060	−	0.998362i	$-0.518219\pi$
$359$	−279388.	−0.114412	−0.0572060	+	0.998362i	$0.518219\pi$
$360$	7.53620e6	3.06476
$361$	−2.43823e6	−0.984706
$362$	3.06822e6	1.23060
$363$	1.19912e6	0.477634
$364$	−1.91480e6	−0.757479
$365$	2.36972e6	0.931032
$366$	1.11260e6	0.434148
$367$	2.90631e6	1.12636	0.563180	−	0.826334i	$-0.309578\pi$
$367$	2.90631e6	1.12636	0.563180	+	0.826334i	$0.309578\pi$
$368$	1.02181e6	0.393324
$369$	1.74053e6	0.665449
$370$	−3.21023e6	−1.21908
$371$	581533.	0.219351
$372$	2.63361e6	0.986721
$373$	385367.	0.143418	0.0717089	−	0.997426i	$-0.477155\pi$
$373$	385367.	0.143418	0.0717089	+	0.997426i	$0.477155\pi$
$374$	877207.	0.324282
$375$	81866.8	0.0300628
$376$	−778359.	−0.283929
$377$	−5.64973e6	−2.04727
$378$	810609.	0.291798
$379$	3.40369e6	1.21717	0.608586	−	0.793488i	$-0.291737\pi$
$379$	3.40369e6	1.21717	0.608586	+	0.793488i	$0.291737\pi$
$380$	1.27585e6	0.453253
$381$	−1.11284e6	−0.392752
$382$	601944.	0.211056
$383$	−4.39450e6	−1.53078	−0.765389	−	0.643568i	$-0.777454\pi$
$383$	−4.39450e6	−1.53078	−0.765389	+	0.643568i	$0.777454\pi$
$384$	2.95039e6	1.02106
$385$	−226323.	−0.0778173
$386$	−1.09705e7	−3.74763
$387$	1.32574e6	0.449968
$388$	−9.70873e6	−3.27403
$389$	−1.67727e6	−0.561991	−0.280995	−	0.959709i	$-0.590665\pi$
$389$	−1.67727e6	−0.561991	−0.280995	+	0.959709i	$0.590665\pi$
$390$	7.45227e6	2.48100
$391$	−188078.	−0.0622151
$392$	9.10187e6	2.99168
$393$	−637518.	−0.208215
$394$	5.67944e6	1.84317
$395$	−2.56573e6	−0.827405
$396$	−1.93593e6	−0.620370
$397$	597822.	0.190369	0.0951844	−	0.995460i	$-0.469656\pi$
$397$	597822.	0.190369	0.0951844	+	0.995460i	$0.469656\pi$
$398$	−9.40752e6	−2.97692
$399$	35253.6	0.0110859
$400$	9.93970e6	3.10616
$401$	−5.38486e6	−1.67230	−0.836149	−	0.548503i	$-0.815198\pi$
$401$	−5.38486e6	−1.67230	−0.836149	+	0.548503i	$0.815198\pi$
$402$	−3.20092e6	−0.987891
$403$	−3.96652e6	−1.21660
$404$	7.24867e6	2.20956
$405$	1.00460e6	0.304338
$406$	−1.24441e6	−0.374670
$407$	509649.	0.152505
$408$	−2.84507e6	−0.846140
$409$	−2.53642e6	−0.749744	−0.374872	−	0.927077i	$-0.622313\pi$
$409$	−2.53642e6	−0.749744	−0.374872	+	0.927077i	$0.622313\pi$
$410$	8.47904e6	2.49108
$411$	2.24893e6	0.656707
$412$	619179.	0.179711
$413$	−97819.7	−0.0282196
$414$	573625.	0.164485
$415$	−8.09140e6	−2.30623
$416$	−1.88327e7	−5.33556
$417$	−2.04910e6	−0.577063
$418$	−279922.	−0.0783605
$419$	−4.40958e6	−1.22705	−0.613525	−	0.789676i	$-0.710249\pi$
$419$	−4.40958e6	−1.22705	−0.613525	+	0.789676i	$0.710249\pi$
$420$	1.18774e6	0.328547
$421$	4.42458e6	1.21665	0.608326	−	0.793687i	$-0.291841\pi$
$421$	4.42458e6	1.21665	0.608326	+	0.793687i	$0.291841\pi$
$422$	−9.17426e6	−2.50778
$423$	−241530.	−0.0656326
$424$	1.49761e7	4.04562
$425$	−1.82954e6	−0.491325
$426$	5.01293e6	1.33834
$427$	−267074.	−0.0708861
$428$	−3.22776e6	−0.851711
$429$	−1.18310e6	−0.310370
$430$	6.45841e6	1.68444
$431$	−4.46304e6	−1.15728	−0.578638	−	0.815584i	$-0.696416\pi$
$431$	−4.46304e6	−1.15728	−0.578638	+	0.815584i	$0.696416\pi$
$432$	1.15390e7	2.97481
$433$	1.98234e6	0.508111	0.254056	−	0.967190i	$-0.418235\pi$
$433$	1.98234e6	0.508111	0.254056	+	0.967190i	$0.418235\pi$
$434$	−873666.	−0.222649
$435$	3.50449e6	0.887976
$436$	1.00898e7	2.54195
$437$	60016.8	0.0150338
$438$	2.72852e6	0.679583
$439$	−6.08667e6	−1.50737	−0.753683	−	0.657238i	$-0.771725\pi$
$439$	−6.08667e6	−1.50737	−0.753683	+	0.657238i	$0.771725\pi$
$440$	−5.82845e6	−1.43523
$441$	2.82437e6	0.691552
$442$	6.93351e6	1.68810
$443$	1.91789e6	0.464317	0.232159	−	0.972678i	$-0.425421\pi$
$443$	1.91789e6	0.464317	0.232159	+	0.972678i	$0.425421\pi$
$444$	−2.67463e6	−0.643882
$445$	6.08587e6	1.45688
$446$	1.45798e7	3.47069
$447$	−5020.29	−0.00118839
$448$	−1.85477e6	−0.436612
$449$	−3.33211e6	−0.780016	−0.390008	−	0.920811i	$-0.627528\pi$
$449$	−3.33211e6	−0.780016	−0.390008	+	0.920811i	$0.627528\pi$
$450$	5.57997e6	1.29897
$451$	−1.34611e6	−0.311630
$452$	−8.83374e6	−2.03376
$453$	−330232.	−0.0756090
$454$	8.96732e6	2.04185
$455$	−1.78887e6	−0.405089
$456$	907879.	0.204464
$457$	−1.80242e6	−0.403706	−0.201853	−	0.979416i	$-0.564696\pi$
$457$	−1.80242e6	−0.403706	−0.201853	+	0.979416i	$0.564696\pi$
$458$	3.84515e6	0.856545
$459$	−2.12391e6	−0.470549
$460$	2.02204e6	0.445550
$461$	−4.65236e6	−1.01958	−0.509790	−	0.860299i	$-0.670277\pi$
$461$	−4.65236e6	−1.01958	−0.509790	+	0.860299i	$0.670277\pi$
$462$	−260591.	−0.0568007
$463$	−4.86544e6	−1.05480	−0.527399	−	0.849618i	$-0.676833\pi$
$463$	−4.86544e6	−1.05480	−0.527399	+	0.849618i	$0.676833\pi$
$464$	−1.77142e7	−3.81967
$465$	2.46040e6	0.527684
$466$	1.58943e7	3.39059
$467$	−6.14116e6	−1.30304	−0.651521	−	0.758630i	$-0.725869\pi$
$467$	−6.14116e6	−1.30304	−0.651521	+	0.758630i	$0.725869\pi$
$468$	−1.53017e7	−3.22942
$469$	768359.	0.161299
$470$	−1.17662e6	−0.245693
$471$	−287158.	−0.0596442
$472$	−2.51914e6	−0.520471
$473$	−1.02532e6	−0.210721
$474$	−2.95421e6	−0.603943
$475$	583817.	0.118725
$476$	1.10506e6	0.223546
$477$	4.64719e6	0.935178
$478$	1.67810e7	3.35929
$479$	6.69878e6	1.33400	0.667002	−	0.745056i	$-0.267577\pi$
$479$	6.69878e6	1.33400	0.667002	+	0.745056i	$0.267577\pi$
$480$	1.16818e7	2.31423
$481$	4.02830e6	0.793888
$482$	−8.21186e6	−1.60999
$483$	55872.0	0.0108975
$484$	−1.19944e7	−2.32737
$485$	−9.07020e6	−1.75090
$486$	1.02630e7	1.97098
$487$	−1.81209e6	−0.346225	−0.173112	−	0.984902i	$-0.555382\pi$
$487$	−1.81209e6	−0.346225	−0.173112	+	0.984902i	$0.555382\pi$
$488$	−6.87791e6	−1.30739
$489$	721020.	0.136356
$490$	1.37590e7	2.58879
$491$	968254.	0.181253	0.0906266	−	0.995885i	$-0.471113\pi$
$491$	968254.	0.181253	0.0906266	+	0.995885i	$0.471113\pi$
$492$	7.06438e6	1.31571
$493$	3.26053e6	0.604187
$494$	−2.21253e6	−0.407916
$495$	−1.80860e6	−0.331765
$496$	−1.24366e7	−2.26986
$497$	−1.20332e6	−0.218520
$498$	−9.31653e6	−1.68338
$499$	6.30327e6	1.13322	0.566610	−	0.823986i	$-0.308254\pi$
$499$	6.30327e6	1.13322	0.566610	+	0.823986i	$0.308254\pi$
$500$	−818889.	−0.146487
$501$	545653.	0.0971230
$502$	−1.00351e7	−1.77730
$503$	8.71320e6	1.53553	0.767764	−	0.640733i	$-0.221369\pi$
$503$	8.71320e6	1.53553	0.767764	+	0.640733i	$0.221369\pi$
$504$	−2.08292e6	−0.365256
$505$	6.77194e6	1.18164
$506$	−443638.	−0.0770287
$507$	−6.24176e6	−1.07842
$508$	1.11314e7	1.91377
$509$	−7.72864e6	−1.32223	−0.661117	−	0.750283i	$-0.729917\pi$
$509$	−7.72864e6	−1.32223	−0.661117	+	0.750283i	$0.729917\pi$
$510$	−4.30080e6	−0.732190
$511$	−654965.	−0.110960
$512$	11475.2	0.00193458
$513$	677754.	0.113705
$514$	1.89491e7	3.16360
$515$	578457.	0.0961066
$516$	5.38087e6	0.889669
$517$	186798.	0.0307358
$518$	887274.	0.145289
$519$	−332049.	−0.0541108
$520$	−4.60685e7	−7.47129
$521$	6.00966e6	0.969964	0.484982	−	0.874524i	$-0.338826\pi$
$521$	6.00966e6	0.969964	0.484982	+	0.874524i	$0.338826\pi$
$522$	−9.94442e6	−1.59736
$523$	3.83896e6	0.613704	0.306852	−	0.951757i	$-0.400724\pi$
$523$	3.83896e6	0.613704	0.306852	+	0.951757i	$0.400724\pi$
$524$	6.37690e6	1.01457
$525$	543498.	0.0860596
$526$	8.33465e6	1.31348
$527$	2.28913e6	0.359041
$528$	−3.70951e6	−0.579070
$529$	−6.34122e6	−0.985222
$530$	2.26390e7	3.50080
$531$	−781703.	−0.120311
$532$	−352631.	−0.0540183
$533$	−1.06398e7	−1.62224
$534$	7.00734e6	1.06341
$535$	−3.01548e6	−0.455482
$536$	1.97874e7	2.97494
$537$	−3.29647e6	−0.493303
$538$	6.14434e6	0.915208
$539$	−2.18435e6	−0.323855
$540$	2.28344e7	3.36981
$541$	7.90954e6	1.16187	0.580936	−	0.813949i	$-0.302687\pi$
$541$	7.90954e6	1.16187	0.580936	+	0.813949i	$0.302687\pi$
$542$	3.87394e6	0.566442
$543$	2.38819e6	0.347591
$544$	1.08686e7	1.57462
$545$	9.42623e6	1.35940
$546$	−2.05973e6	−0.295684
$547$	−299209.	−0.0427569
$547$	−299209.	−0.0427569
$548$	−2.24954e7	−3.19994
$549$	−2.13426e6	−0.302215
$550$	−4.31551e6	−0.608311
$551$	−1.04046e6	−0.145997
$552$	1.43886e6	0.200989
$553$	709140.	0.0986096
$554$	2.22891e7	3.08544
$555$	−2.49872e6	−0.344339
$556$	2.04965e7	2.81186
$557$	−3.47837e6	−0.475048	−0.237524	−	0.971382i	$-0.576336\pi$
$557$	−3.47837e6	−0.475048	−0.237524	+	0.971382i	$0.576336\pi$
$558$	−6.98170e6	−0.949239
$559$	−8.10422e6	−1.09694
$560$	−5.60882e6	−0.755791
$561$	682785.	0.0915960
$562$	−3.95313e6	−0.527960
$563$	9.86215e6	1.31130	0.655648	−	0.755067i	$-0.272396\pi$
$563$	9.86215e6	1.31130	0.655648	+	0.755067i	$0.272396\pi$
$564$	−980311.	−0.129767
$565$	−8.25276e6	−1.08762
$566$	−6.02902e6	−0.791053
$567$	−277661.	−0.0362708
$568$	−3.09889e7	−4.03029
$569$	−4.54787e6	−0.588881	−0.294440	−	0.955670i	$-0.595133\pi$
$569$	−4.54787e6	−0.588881	−0.294440	+	0.955670i	$0.595133\pi$
$570$	1.37241e6	0.176928
$571$	−7.88376e6	−1.01191	−0.505957	−	0.862559i	$-0.668860\pi$
$571$	−7.88376e6	−1.01191	−0.505957	+	0.862559i	$0.668860\pi$
$572$	1.18342e7	1.51234
$573$	468531.	0.0596144
$574$	−2.34351e6	−0.296885
$575$	925269.	0.116707
$576$	−1.48220e7	−1.86144
$577$	−7.02481e6	−0.878406	−0.439203	−	0.898388i	$-0.644739\pi$
$577$	−7.02481e6	−0.878406	−0.439203	+	0.898388i	$0.644739\pi$
$578$	1.12759e7	1.40389
$579$	−8.53900e6	−1.05855
$580$	−3.50543e7	−4.32685
$581$	2.23637e6	0.274855
$582$	−1.04435e7	−1.27803
$583$	−3.59411e6	−0.437945
$584$	−1.68672e7	−2.04650
$585$	−1.42953e7	−1.72705
$586$	2.62328e6	0.315573
$587$	−1.86395e6	−0.223274	−0.111637	−	0.993749i	$-0.535609\pi$
$587$	−1.86395e6	−0.223274	−0.111637	+	0.993749i	$0.535609\pi$
$588$	1.14634e7	1.36732
$589$	−730476.	−0.0867597
$590$	−3.80810e6	−0.450379
$591$	4.42066e6	0.520618
$592$	1.26303e7	1.48119
$593$	−430038.	−0.0502192	−0.0251096	−	0.999685i	$-0.507993\pi$
$593$	−430038.	−0.0502192	−0.0251096	+	0.999685i	$0.507993\pi$
$594$	−5.00989e6	−0.582588
$595$	1.03238e6	0.119549
$596$	50216.4	0.00579069
$597$	−7.32246e6	−0.840855
$598$	−3.50655e6	−0.400984
$599$	−3.91644e6	−0.445989	−0.222995	−	0.974820i	$-0.571583\pi$
$599$	−3.91644e6	−0.445989	−0.222995	+	0.974820i	$0.571583\pi$
$600$	1.39966e7	1.58725
$601$	−1.07453e7	−1.21348	−0.606741	−	0.794899i	$-0.707524\pi$
$601$	−1.07453e7	−1.21348	−0.606741	+	0.794899i	$0.707524\pi$
$602$	−1.78504e6	−0.200750
$603$	6.14016e6	0.687681
$604$	3.30321e6	0.368421
$605$	−1.12056e7	−1.24465
$606$	7.79729e6	0.862506
$607$	1.60654e7	1.76978	0.884892	−	0.465796i	$-0.154232\pi$
$607$	1.60654e7	1.76978	0.884892	+	0.465796i	$0.154232\pi$
$608$	−3.46824e6	−0.380496
$609$	−968602.	−0.105828
$610$	−1.03971e7	−1.13133
$611$	1.47646e6	0.160000
$612$	8.83081e6	0.953064
$613$	−7.25670e6	−0.779988	−0.389994	−	0.920817i	$-0.627523\pi$
$613$	−7.25670e6	−0.779988	−0.389994	+	0.920817i	$0.627523\pi$
$614$	−5.90889e6	−0.632536
$615$	6.59976e6	0.703624
$616$	1.61092e6	0.171050
$617$	−5.99280e6	−0.633748	−0.316874	−	0.948468i	$-0.602633\pi$
$617$	−5.99280e6	−0.633748	−0.316874	+	0.948468i	$0.602633\pi$
$618$	666043.	0.0701505
$619$	−9.95727e6	−1.04451	−0.522256	−	0.852789i	$-0.674910\pi$
$619$	−9.95727e6	−1.04451	−0.522256	+	0.852789i	$0.674910\pi$
$620$	−2.46107e7	−2.57125
$621$	1.07415e6	0.111772
$622$	2.00497e6	0.207794
$623$	−1.68207e6	−0.173629
$624$	−2.93202e7	−3.01443
$625$	−1.01403e7	−1.03837
$626$	−1.61911e7	−1.65136
$627$	−217881.	−0.0221335
$628$	2.87235e6	0.290629
$629$	−2.32478e6	−0.234291
$630$	−3.14869e6	−0.316067
$631$	9.05066e6	0.904913	0.452457	−	0.891786i	$-0.350548\pi$
$631$	9.05066e6	0.904913	0.452457	+	0.891786i	$0.350548\pi$
$632$	1.82624e7	1.81871
$633$	−7.14090e6	−0.708343
$634$	−1.75719e7	−1.73618
$635$	1.03993e7	1.02345
$636$	1.88618e7	1.84902
$637$	−1.72652e7	−1.68587
$638$	7.69095e6	0.748046
$639$	−9.61606e6	−0.931633
$640$	−2.75710e7	−2.66074
$641$	−1.61498e7	−1.55247	−0.776234	−	0.630445i	$-0.782872\pi$
$641$	−1.61498e7	−1.55247	−0.776234	+	0.630445i	$0.782872\pi$
$642$	−3.47206e6	−0.332468
$643$	−1.16245e7	−1.10879	−0.554393	−	0.832255i	$-0.687049\pi$
$643$	−1.16245e7	−1.10879	−0.554393	+	0.832255i	$0.687049\pi$
$644$	−558871.	−0.0531003
$645$	5.02698e6	0.475782
$646$	1.27688e6	0.120384
$647$	−1.51688e7	−1.42459	−0.712295	−	0.701880i	$-0.752344\pi$
$647$	−1.51688e7	−1.42459	−0.712295	+	0.701880i	$0.752344\pi$
$648$	−7.15057e6	−0.668964
$649$	604565.	0.0563418
$650$	−3.41101e7	−3.16665
$651$	−680029.	−0.0628890
$652$	−7.21215e6	−0.664425
$653$	1.18851e7	1.09073	0.545366	−	0.838198i	$-0.316391\pi$
$653$	1.18851e7	1.09073	0.545366	+	0.838198i	$0.316391\pi$
$654$	1.08535e7	0.992258
$655$	5.95750e6	0.542577
$656$	−3.33599e7	−3.02667
$657$	−5.23400e6	−0.473064
$658$	325205.	0.0292815
$659$	−2.66850e6	−0.239361	−0.119680	−	0.992812i	$-0.538187\pi$
$659$	−2.66850e6	−0.239361	−0.119680	+	0.992812i	$0.538187\pi$
$660$	−7.34069e6	−0.655960
$661$	1.03749e7	0.923596	0.461798	−	0.886985i	$-0.347204\pi$
$661$	1.03749e7	0.923596	0.461798	+	0.886985i	$0.347204\pi$
$662$	1.82469e7	1.61824
$663$	5.39678e6	0.476816
$664$	5.75930e7	5.06932
$665$	−329439.	−0.0288882
$666$	7.09044e6	0.619423
$667$	−1.64898e6	−0.143516
$668$	−5.45800e6	−0.473252
$669$	1.13484e7	0.980322
$670$	2.99121e7	2.57430
$671$	1.65062e6	0.141528
$672$	−3.22872e6	−0.275808
$673$	1.78175e7	1.51638	0.758192	−	0.652031i	$-0.226083\pi$
$673$	1.78175e7	1.51638	0.758192	+	0.652031i	$0.226083\pi$
$674$	4.07801e7	3.45779
$675$	1.04488e7	0.882688
$676$	6.24345e7	5.25482
$677$	−387450.	−0.0324896	−0.0162448	−	0.999868i	$-0.505171\pi$
$677$	−387450.	−0.0324896	−0.0162448	+	0.999868i	$0.505171\pi$
$678$	−9.50233e6	−0.793882
$679$	2.50690e6	0.208672
$680$	2.65867e7	2.20492
$681$	6.97982e6	0.576735
$682$	5.39961e6	0.444530
$683$	1.27272e7	1.04396	0.521979	−	0.852959i	$-0.325194\pi$
$683$	1.27272e7	1.04396	0.521979	+	0.852959i	$0.325194\pi$
$684$	−2.81797e6	−0.230301
$685$	−2.10159e7	−1.71128
$686$	−7.71459e6	−0.625897
$687$	2.99292e6	0.241938
$688$	−2.54100e7	−2.04660
$689$	−2.84081e7	−2.27978
$690$	2.17508e6	0.173922
$691$	1.68943e7	1.34600	0.673000	−	0.739642i	$-0.265005\pi$
$691$	1.68943e7	1.34600	0.673000	+	0.739642i	$0.265005\pi$
$692$	3.32139e6	0.263666
$693$	499879.	0.0395395
$694$	−3.14367e7	−2.47764
$695$	1.91485e7	1.50374
$696$	−2.49443e7	−1.95186
$697$	6.14034e6	0.478752
$698$	3.59669e6	0.279425
$699$	1.23715e7	0.957699
$700$	−5.43645e6	−0.419344
$701$	2.63310e6	0.202382	0.101191	−	0.994867i	$-0.467735\pi$
$701$	2.63310e6	0.202382	0.101191	+	0.994867i	$0.467735\pi$
$702$	−3.95985e7	−3.03275
$703$	741853.	0.0566148
$704$	1.14632e7	0.871717
$705$	−915837.	−0.0693978
$706$	2.14185e7	1.61725
$707$	−1.87169e6	−0.140827
$708$	−3.17275e6	−0.237877
$709$	1.19354e7	0.891702	0.445851	−	0.895107i	$-0.352901\pi$
$709$	1.19354e7	0.891702	0.445851	+	0.895107i	$0.352901\pi$
$710$	−4.68450e7	−3.48753
$711$	5.66692e6	0.420410
$712$	−4.33180e7	−3.20235
$713$	−1.15770e6	−0.0852852
$714$	1.18869e6	0.0872619
$715$	1.10559e7	0.808779
$716$	3.29736e7	2.40372
$717$	1.30617e7	0.948858
$718$	3.00615e6	0.217620
$719$	−7.46191e6	−0.538304	−0.269152	−	0.963098i	$-0.586743\pi$
$719$	−7.46191e6	−0.538304	−0.269152	+	0.963098i	$0.586743\pi$
$720$	−4.48216e7	−3.22223
$721$	−159879.	−0.0114539
$722$	2.62348e7	1.87299
$723$	−6.39180e6	−0.454755
$724$	−2.38883e7	−1.69371
$725$	−1.60405e7	−1.13338
$726$	−1.29022e7	−0.908497
$727$	−7.02204e6	−0.492751	−0.246375	−	0.969175i	$-0.579240\pi$
$727$	−7.02204e6	−0.492751	−0.246375	+	0.969175i	$0.579240\pi$
$728$	1.27328e7	0.890423
$729$	4.86911e6	0.339336
$730$	−2.54976e7	−1.77089
$731$	4.67705e6	0.323726
$732$	−8.66243e6	−0.597533
$733$	1.09991e7	0.756130	0.378065	−	0.925779i	$-0.376590\pi$
$733$	1.09991e7	0.756130	0.378065	+	0.925779i	$0.376590\pi$
$734$	−3.12713e7	−2.14242
$735$	1.07095e7	0.731225
$736$	−5.49668e6	−0.374030
$737$	−4.74877e6	−0.322042
$738$	−1.87277e7	−1.26573
$739$	−2.57653e7	−1.73550	−0.867750	−	0.497002i	$-0.834434\pi$
$739$	−2.57653e7	−1.73550	−0.867750	+	0.497002i	$0.834434\pi$
$740$	2.49940e7	1.67786
$741$	−1.72215e6	−0.115219
$742$	−6.25716e6	−0.417222
$743$	1.16240e7	0.772475	0.386237	−	0.922399i	$-0.373775\pi$
$743$	1.16240e7	0.772475	0.386237	+	0.922399i	$0.373775\pi$
$744$	−1.75127e7	−1.15990
$745$	46913.8	0.00309678
$746$	−4.14646e6	−0.272792
$747$	1.78715e7	1.17181
$748$	−6.82969e6	−0.446321
$749$	833445.	0.0542841
$750$	−880868.	−0.0571818
$751$	2.60249e7	1.68380	0.841898	−	0.539637i	$-0.181439\pi$
$751$	2.60249e7	1.68380	0.841898	+	0.539637i	$0.181439\pi$
$752$	4.62929e6	0.298518
$753$	−7.81093e6	−0.502014
$754$	6.07898e7	3.89406
$755$	3.08596e6	0.197026
$756$	−6.31118e6	−0.401612
$757$	1.12448e7	0.713201	0.356601	−	0.934257i	$-0.383936\pi$
$757$	1.12448e7	0.713201	0.356601	+	0.934257i	$0.383936\pi$
$758$	−3.66229e7	−2.31516
$759$	−345311.	−0.0217574
$760$	−8.48399e6	−0.532802
$761$	−1.09493e7	−0.685371	−0.342685	−	0.939450i	$-0.611336\pi$
$761$	−1.09493e7	−0.685371	−0.342685	+	0.939450i	$0.611336\pi$
$762$	1.19738e7	0.747044
$763$	−2.60531e6	−0.162012
$764$	−4.68657e6	−0.290484
$765$	8.25002e6	0.509685
$766$	4.72838e7	2.91166
$767$	4.77852e6	0.293295
$768$	−8.76566e6	−0.536268
$769$	6.64259e6	0.405062	0.202531	−	0.979276i	$-0.435083\pi$
$769$	6.64259e6	0.405062	0.202531	+	0.979276i	$0.435083\pi$
$770$	2.43518e6	0.148014
$771$	1.47493e7	0.893582
$772$	8.54131e7	5.15800
$773$	−1.84743e7	−1.11203	−0.556017	−	0.831171i	$-0.687671\pi$
$773$	−1.84743e7	−1.11203	−0.556017	+	0.831171i	$0.687671\pi$
$774$	−1.42647e7	−0.855874
$775$	−1.12616e7	−0.673514
$776$	6.45599e7	3.84865
$777$	690620.	0.0410380
$778$	1.80470e7	1.06895
$779$	−1.95942e6	−0.115687
$780$	−5.80213e7	−3.41469
$781$	7.43700e6	0.436285
$782$	2.02367e6	0.118338
$783$	−1.86215e7	−1.08545
$784$	−5.41335e7	−3.14540
$785$	2.68344e6	0.155424
$786$	6.85954e6	0.396040
$787$	2.71884e7	1.56476	0.782378	−	0.622804i	$-0.214007\pi$
$787$	2.71884e7	1.56476	0.782378	+	0.622804i	$0.214007\pi$
$788$	−4.42186e7	−2.53682
$789$	6.48738e6	0.371002
$790$	2.76067e7	1.57379
$791$	2.28097e6	0.129622
$792$	1.28733e7	0.729251
$793$	1.30466e7	0.736742
$794$	−6.43243e6	−0.362096
$795$	1.76213e7	0.988827
$796$	7.32443e7	4.09724
$797$	2.09341e7	1.16737	0.583685	−	0.811980i	$-0.301610\pi$
$797$	2.09341e7	1.16737	0.583685	+	0.811980i	$0.301610\pi$
$798$	−379320.	−0.0210862
$799$	−852084.	−0.0472189
$800$	−5.34692e7	−2.95379
$801$	−1.34419e7	−0.740249
$802$	5.79398e7	3.18084
$803$	4.04794e6	0.221537
$804$	2.49215e7	1.35967
$805$	−522115.	−0.0283973
$806$	4.26789e7	2.31406
$807$	4.78252e6	0.258508
$808$	−4.82013e7	−2.59735
$809$	−3.43046e7	−1.84281	−0.921406	−	0.388602i	$-0.872958\pi$
$809$	−3.43046e7	−1.84281	−0.921406	+	0.388602i	$0.872958\pi$
$810$	−1.08093e7	−0.578875
$811$	−3.62677e7	−1.93628	−0.968140	−	0.250408i	$-0.919435\pi$
$811$	−3.62677e7	−1.93628	−0.968140	+	0.250408i	$0.919435\pi$
$812$	9.68864e6	0.515671
$813$	3.01533e6	0.159996
$814$	−5.48370e6	−0.290077
$815$	−6.73782e6	−0.355325
$816$	1.69211e7	0.889615
$817$	−1.49248e6	−0.0782262
$818$	2.72913e7	1.42607
$819$	3.95108e6	0.205829
$820$	−6.60155e7	−3.42856
$821$	8.38211e6	0.434006	0.217003	−	0.976171i	$-0.430372\pi$
$821$	8.38211e6	0.434006	0.217003	+	0.976171i	$0.430372\pi$
$822$	−2.41980e7	−1.24911
$823$	−2.49809e7	−1.28561	−0.642805	−	0.766030i	$-0.722229\pi$
$823$	−2.49809e7	−1.28561	−0.642805	+	0.766030i	$0.722229\pi$
$824$	−4.11735e6	−0.211251
$825$	−3.35903e6	−0.171822
$826$	1.05252e6	0.0536759
$827$	2.20447e7	1.12083	0.560415	−	0.828212i	$-0.310642\pi$
$827$	2.20447e7	1.12083	0.560415	+	0.828212i	$0.310642\pi$
$828$	−4.46609e6	−0.226387
$829$	8.85999e6	0.447762	0.223881	−	0.974617i	$-0.428127\pi$
$829$	8.85999e6	0.447762	0.223881	+	0.974617i	$0.428127\pi$
$830$	8.70615e7	4.38663
$831$	1.73490e7	0.871507
$832$	9.06062e7	4.53784
$833$	9.96399e6	0.497532
$834$	2.20478e7	1.09762
$835$	−5.09904e6	−0.253088
$836$	2.17940e6	0.107850
$837$	−1.30736e7	−0.645034
$838$	4.74460e7	2.33394
$839$	2.01631e7	0.988901	0.494451	−	0.869206i	$-0.335369\pi$
$839$	2.01631e7	0.988901	0.494451	+	0.869206i	$0.335369\pi$
$840$	−7.89808e6	−0.386210
$841$	8.07573e6	0.393724
$842$	−4.76074e7	−2.31417
$843$	−3.07697e6	−0.149126
$844$	7.14283e7	3.45155
$845$	5.83283e7	2.81020
$846$	2.59880e6	0.124838
$847$	3.09710e6	0.148336
$848$	−8.90706e7	−4.25349
$849$	−4.69276e6	−0.223439
$850$	1.96854e7	0.934537
$851$	1.17573e6	0.0556526
$852$	−3.90293e7	−1.84201
$853$	−1.20265e7	−0.565936	−0.282968	−	0.959129i	$-0.591319\pi$
$853$	−1.20265e7	−0.565936	−0.282968	+	0.959129i	$0.591319\pi$
$854$	2.87365e6	0.134831
$855$	−2.63263e6	−0.123162
$856$	2.14636e7	1.00119
$857$	−1.81157e7	−0.842566	−0.421283	−	0.906929i	$-0.638420\pi$
$857$	−1.81157e7	−0.842566	−0.421283	+	0.906929i	$0.638420\pi$
$858$	1.27299e7	0.590348
$859$	2.06821e7	0.956337	0.478169	−	0.878268i	$-0.341301\pi$
$859$	2.06821e7	0.956337	0.478169	+	0.878268i	$0.341301\pi$
$860$	−5.02834e7	−2.31835
$861$	−1.82410e6	−0.0838574
$862$	4.80212e7	2.20123
$863$	−2.28554e6	−0.104463	−0.0522315	−	0.998635i	$-0.516633\pi$
$863$	−2.28554e6	−0.104463	−0.0522315	+	0.998635i	$0.516633\pi$
$864$	−6.20725e7	−2.82888
$865$	3.10295e6	0.141005
$866$	−2.13295e7	−0.966466
$867$	8.77675e6	0.396539
$868$	6.80213e6	0.306440
$869$	−4.38277e6	−0.196879
$870$	−3.77075e7	−1.68900
$871$	−3.75346e7	−1.67643
$872$	−6.70941e7	−2.98808
$873$	2.00333e7	0.889647
$874$	−645767.	−0.0285955
$875$	211447.	0.00933643
$876$	−2.12435e7	−0.935334
$877$	−4.45924e7	−1.95777	−0.978885	−	0.204412i	$-0.934472\pi$
$877$	−4.45924e7	−1.95777	−0.978885	+	0.204412i	$0.934472\pi$
$878$	6.54912e7	2.86713
$879$	2.04186e6	0.0891360
$880$	3.46648e7	1.50897
$881$	2.74130e7	1.18992	0.594958	−	0.803757i	$-0.297169\pi$
$881$	2.74130e7	1.18992	0.594958	+	0.803757i	$0.297169\pi$
$882$	−3.03895e7	−1.31538
$883$	−3.00723e7	−1.29797	−0.648986	−	0.760801i	$-0.724806\pi$
$883$	−3.00723e7	−1.29797	−0.648986	+	0.760801i	$0.724806\pi$
$884$	−5.39824e7	−2.32339
$885$	−2.96408e6	−0.127213
$886$	−2.06361e7	−0.883167
$887$	8.88986e6	0.379390	0.189695	−	0.981843i	$-0.439250\pi$
$887$	8.88986e6	0.379390	0.189695	+	0.981843i	$0.439250\pi$
$888$	1.77854e7	0.756889
$889$	−2.87425e6	−0.121975
$890$	−6.54825e7	−2.77109
$891$	1.71606e6	0.0724165
$892$	−1.13515e8	−4.77683
$893$	271906.	0.0114101
$894$	54017.1	0.00226041
$895$	3.08050e7	1.28547
$896$	7.62031e6	0.317105
$897$	−2.72936e6	−0.113261
$898$	3.58527e7	1.48365
$899$	2.00701e7	0.828227
$900$	−4.34441e7	−1.78782
$901$	1.63947e7	0.672807
$902$	1.44839e7	0.592745
$903$	−1.38940e6	−0.0567034
$904$	5.87416e7	2.39070
$905$	−2.23172e7	−0.905773
$906$	3.55322e6	0.143814
$907$	−1.75687e7	−0.709122	−0.354561	−	0.935033i	$-0.615370\pi$
$907$	−1.75687e7	−0.709122	−0.354561	+	0.935033i	$0.615370\pi$
$908$	−6.98171e7	−2.81026
$909$	−1.49572e7	−0.600399
$910$	1.92478e7	0.770510
$911$	947941.	0.0378430	0.0189215	−	0.999821i	$-0.493977\pi$
$911$	947941.	0.0378430	0.0189215	+	0.999821i	$0.493977\pi$
$912$	−5.39962e6	−0.214969
$913$	−1.38217e7	−0.548762
$914$	1.93936e7	0.767880
$915$	−8.09272e6	−0.319552
$916$	−2.99373e7	−1.17889
$917$	−1.64659e6	−0.0646639
$918$	2.28528e7	0.895020
$919$	2.39881e7	0.936931	0.468465	−	0.883482i	$-0.344807\pi$
$919$	2.39881e7	0.936931	0.468465	+	0.883482i	$0.344807\pi$
$920$	−1.34460e7	−0.523748
$921$	−4.59926e6	−0.178665
$922$	5.00583e7	1.93932
$923$	5.87826e7	2.27114
$924$	2.02889e6	0.0781768
$925$	1.14370e7	0.439499
$926$	5.23510e7	2.00631
$927$	−1.27764e6	−0.0488324
$928$	9.52910e7	3.63230
$929$	−4.29627e7	−1.63325	−0.816624	−	0.577169i	$-0.804157\pi$
$929$	−4.29627e7	−1.63325	−0.816624	+	0.577169i	$0.804157\pi$
$930$	−2.64734e7	−1.00370
$931$	−3.17957e6	−0.120225
$932$	−1.23748e8	−4.66659
$933$	1.56060e6	0.0586930
$934$	6.60775e7	2.47849
$935$	−6.38052e6	−0.238686
$936$	1.01751e8	3.79622
$937$	−8.99711e6	−0.334776	−0.167388	−	0.985891i	$-0.553533\pi$
$937$	−8.99711e6	−0.334776	−0.167388	+	0.985891i	$0.553533\pi$
$938$	−8.26737e6	−0.306803
$939$	−1.26025e7	−0.466438
$940$	9.16085e6	0.338155
$941$	3.60748e7	1.32810	0.664049	−	0.747689i	$-0.268837\pi$
$941$	3.60748e7	1.32810	0.664049	+	0.747689i	$0.268837\pi$
$942$	3.08975e6	0.113448
$943$	−3.10541e6	−0.113721
$944$	1.49826e7	0.547213
$945$	−5.89611e6	−0.214776
$946$	1.10322e7	0.400807
$947$	5.05860e6	0.183297	0.0916485	−	0.995791i	$-0.470786\pi$
$947$	5.05860e6	0.183297	0.0916485	+	0.995791i	$0.470786\pi$
$948$	2.30007e7	0.831228
$949$	3.19952e7	1.15324
$950$	−6.28173e6	−0.225824
$951$	−1.36773e7	−0.490398
$952$	−7.34828e6	−0.262781
$953$	1.09715e7	0.391323	0.195662	−	0.980671i	$-0.437315\pi$
$953$	1.09715e7	0.391323	0.195662	+	0.980671i	$0.437315\pi$
$954$	−5.00026e7	−1.77878
$955$	−4.37834e6	−0.155347
$956$	−1.30652e8	−4.62351
$957$	5.98635e6	0.211292
$958$	−7.20773e7	−2.53738
$959$	5.80857e6	0.203950
$960$	−5.62023e7	−1.96823
$961$	−1.45385e7	−0.507822
$962$	−4.33436e7	−1.51003
$963$	6.66028e6	0.231434
$964$	6.39353e7	2.21589
$965$	7.97956e7	2.75842
$966$	−601170.	−0.0207279
$967$	3.26990e7	1.12452	0.562262	−	0.826959i	$-0.309931\pi$
$967$	3.26990e7	1.12452	0.562262	+	0.826959i	$0.309931\pi$
$968$	7.97591e7	2.73585
$969$	993873.	0.0340033
$970$	9.75932e7	3.33035
$971$	−2.24107e7	−0.762796	−0.381398	−	0.924411i	$-0.624557\pi$
$971$	−2.24107e7	−0.762796	−0.381398	+	0.924411i	$0.624557\pi$
$972$	−7.99047e7	−2.71273
$973$	−5.29244e6	−0.179215
$974$	1.94977e7	0.658546
$975$	−2.65500e7	−0.894444
$976$	4.09064e7	1.37457
$977$	−2.81695e7	−0.944155	−0.472078	−	0.881557i	$-0.656496\pi$
$977$	−2.81695e7	−0.944155	−0.472078	+	0.881557i	$0.656496\pi$
$978$	−7.75801e6	−0.259360
$979$	1.03958e7	0.346660
$980$	−1.07124e8	−3.56305
$981$	−2.08197e7	−0.690720
$982$	−1.04182e7	−0.344757
$983$	−1.85719e6	−0.0613018	−0.0306509	−	0.999530i	$-0.509758\pi$
$983$	−1.85719e6	−0.0613018	−0.0306509	+	0.999530i	$0.509758\pi$
$984$	−4.69758e7	−1.54663
$985$	−4.13104e7	−1.35665
$986$	−3.50826e7	−1.14921
$987$	253127.	0.00827078
$988$	1.72261e7	0.561429
$989$	−2.36537e6	−0.0768967
$990$	1.94602e7	0.631042
$991$	1.91436e7	0.619214	0.309607	−	0.950865i	$-0.399803\pi$
$991$	1.91436e7	0.619214	0.309607	+	0.950865i	$0.399803\pi$
$992$	6.69011e7	2.15851
$993$	1.42027e7	0.457086
$994$	1.29475e7	0.415641
$995$	6.84272e7	2.19114
$996$	7.25360e7	2.31689
$997$	−6.99436e6	−0.222849	−0.111424	−	0.993773i	$-0.535541\pi$
$997$	−6.99436e6	−0.222849	−0.111424	+	0.993773i	$0.535541\pi$
$998$	−6.78217e7	−2.15547
$999$	1.32773e7	0.420915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.a.1.4	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.a.1.4	✓	111	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-10.7598 q^{2} -8.37500 q^{3} +83.7726 q^{4} +78.2630 q^{5} +90.1130 q^{6} -21.6310 q^{7} -557.061 q^{8} -172.859 q^{9} +O(q^{10})\)	\(q-10.7598 q^{2} -8.37500 q^{3} +83.7726 q^{4} +78.2630 q^{5} +90.1130 q^{6} -21.6310 q^{7} -557.061 q^{8} -172.859 q^{9} -842.092 q^{10} +133.688 q^{11} -701.595 q^{12} +1056.68 q^{13} +232.745 q^{14} -655.452 q^{15} +3313.12 q^{16} -609.825 q^{17} +1859.93 q^{18} +194.599 q^{19} +6556.29 q^{20} +181.160 q^{21} -1438.46 q^{22} +308.413 q^{23} +4665.38 q^{24} +3000.10 q^{25} -11369.7 q^{26} +3482.82 q^{27} -1812.09 q^{28} -5346.67 q^{29} +7052.51 q^{30} -3753.75 q^{31} -17822.5 q^{32} -1119.64 q^{33} +6561.58 q^{34} -1692.91 q^{35} -14480.9 q^{36} +3812.21 q^{37} -2093.84 q^{38} -8849.71 q^{39} -43597.3 q^{40} -10069.0 q^{41} -1949.24 q^{42} -7669.49 q^{43} +11199.4 q^{44} -13528.5 q^{45} -3318.45 q^{46} +1397.26 q^{47} -27747.4 q^{48} -16339.1 q^{49} -32280.4 q^{50} +5107.28 q^{51} +88521.1 q^{52} -26884.2 q^{53} -37474.3 q^{54} +10462.9 q^{55} +12049.8 q^{56} -1629.77 q^{57} +57528.9 q^{58} +4522.19 q^{59} -54908.9 q^{60} +12346.8 q^{61} +40389.5 q^{62} +3739.13 q^{63} +85745.9 q^{64} +82699.2 q^{65} +12047.1 q^{66} -35521.1 q^{67} -51086.6 q^{68} -2582.95 q^{69} +18215.3 q^{70} +55629.3 q^{71} +96293.3 q^{72} +30278.9 q^{73} -41018.5 q^{74} -25125.8 q^{75} +16302.1 q^{76} -2891.82 q^{77} +95220.9 q^{78} -32783.4 q^{79} +259295. q^{80} +12836.2 q^{81} +108340. q^{82} -103387. q^{83} +15176.2 q^{84} -47726.8 q^{85} +82521.9 q^{86} +44778.3 q^{87} -74472.6 q^{88} +77761.7 q^{89} +145564. q^{90} -22857.2 q^{91} +25836.5 q^{92} +31437.6 q^{93} -15034.2 q^{94} +15229.9 q^{95} +149263. q^{96} -115894. q^{97} +175805. q^{98} -23109.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9} - 950 q^{10} - 1832 q^{11} - 4143 q^{12} - 4369 q^{13} - 4777 q^{14} - 3487 q^{15} + 26274 q^{16} - 13648 q^{17} - 10269 q^{18} - 5446 q^{19} - 26032 q^{20} - 8428 q^{21} - 8248 q^{22} - 24142 q^{23} - 18577 q^{24} + 58062 q^{25} - 17656 q^{26} - 33269 q^{27} - 23512 q^{28} - 33752 q^{29} - 12418 q^{30} - 13781 q^{31} - 44076 q^{32} - 39186 q^{33} - 7207 q^{34} - 30833 q^{35} + 120044 q^{36} - 61582 q^{37} - 91259 q^{38} - 20077 q^{39} - 66032 q^{40} - 54181 q^{41} - 69252 q^{42} - 38600 q^{43} - 95712 q^{44} - 190880 q^{45} - 9354 q^{46} - 83886 q^{47} - 173886 q^{48} + 194148 q^{49} - 70896 q^{50} - 60673 q^{51} - 145186 q^{52} - 286874 q^{53} - 116519 q^{54} - 74821 q^{55} - 240407 q^{56} - 95180 q^{57} - 66900 q^{58} - 135740 q^{59} - 144550 q^{60} - 227450 q^{61} - 308766 q^{62} - 249721 q^{63} + 347514 q^{64} - 290374 q^{65} - 178980 q^{66} - 91006 q^{67} - 521943 q^{68} - 414510 q^{69} - 165057 q^{70} - 236165 q^{71} - 527945 q^{72} - 184618 q^{73} - 206443 q^{74} - 243897 q^{75} - 221676 q^{76} - 751131 q^{77} - 306839 q^{78} - 107446 q^{79} - 856691 q^{80} + 382187 q^{81} - 244614 q^{82} - 499547 q^{83} - 330289 q^{84} - 287103 q^{85} - 272441 q^{86} - 391281 q^{87} - 588937 q^{88} - 740774 q^{89} - 687179 q^{90} - 237213 q^{91} - 1367678 q^{92} - 754880 q^{93} - 32851 q^{94} - 295814 q^{95} - 816078 q^{96} - 320770 q^{97} - 661922 q^{98} - 547439 q^{99}+O(q^{100}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9 - 950 * q^10 - 1832 * q^11 - 4143 * q^12 - 4369 * q^13 - 4777 * q^14 - 3487 * q^15 + 26274 * q^16 - 13648 * q^17 - 10269 * q^18 - 5446 * q^19 - 26032 * q^20 - 8428 * q^21 - 8248 * q^22 - 24142 * q^23 - 18577 * q^24 + 58062 * q^25 - 17656 * q^26 - 33269 * q^27 - 23512 * q^28 - 33752 * q^29 - 12418 * q^30 - 13781 * q^31 - 44076 * q^32 - 39186 * q^33 - 7207 * q^34 - 30833 * q^35 + 120044 * q^36 - 61582 * q^37 - 91259 * q^38 - 20077 * q^39 - 66032 * q^40 - 54181 * q^41 - 69252 * q^42 - 38600 * q^43 - 95712 * q^44 - 190880 * q^45 - 9354 * q^46 - 83886 * q^47 - 173886 * q^48 + 194148 * q^49 - 70896 * q^50 - 60673 * q^51 - 145186 * q^52 - 286874 * q^53 - 116519 * q^54 - 74821 * q^55 - 240407 * q^56 - 95180 * q^57 - 66900 * q^58 - 135740 * q^59 - 144550 * q^60 - 227450 * q^61 - 308766 * q^62 - 249721 * q^63 + 347514 * q^64 - 290374 * q^65 - 178980 * q^66 - 91006 * q^67 - 521943 * q^68 - 414510 * q^69 - 165057 * q^70 - 236165 * q^71 - 527945 * q^72 - 184618 * q^73 - 206443 * q^74 - 243897 * q^75 - 221676 * q^76 - 751131 * q^77 - 306839 * q^78 - 107446 * q^79 - 856691 * q^80 + 382187 * q^81 - 244614 * q^82 - 499547 * q^83 - 330289 * q^84 - 287103 * q^85 - 272441 * q^86 - 391281 * q^87 - 588937 * q^88 - 740774 * q^89 - 687179 * q^90 - 237213 * q^91 - 1367678 * q^92 - 754880 * q^93 - 32851 * q^94 - 295814 * q^95 - 816078 * q^96 - 320770 * q^97 - 661922 * q^98 - 547439 * q^99

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