LMFDB - Embedded newform 547.6.a.a.1.20

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			1.20
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)

$f(q)$	$=$	$q-8.10730 q^{2} +18.6684 q^{3} +33.7283 q^{4} -66.0394 q^{5} -151.350 q^{6} +35.8802 q^{7} -14.0116 q^{8} +105.509 q^{9} +O(q^{10})$	\(q-8.10730 q^{2} +18.6684 q^{3} +33.7283 q^{4} -66.0394 q^{5} -151.350 q^{6} +35.8802 q^{7} -14.0116 q^{8} +105.509 q^{9} +535.401 q^{10} +2.87864 q^{11} +629.653 q^{12} +453.880 q^{13} -290.891 q^{14} -1232.85 q^{15} -965.708 q^{16} +429.773 q^{17} -855.394 q^{18} -1086.69 q^{19} -2227.39 q^{20} +669.825 q^{21} -23.3380 q^{22} -1173.50 q^{23} -261.574 q^{24} +1236.20 q^{25} -3679.74 q^{26} -2566.73 q^{27} +1210.18 q^{28} +6482.71 q^{29} +9995.08 q^{30} -2006.45 q^{31} +8277.66 q^{32} +53.7396 q^{33} -3484.30 q^{34} -2369.50 q^{35} +3558.64 q^{36} +9600.13 q^{37} +8810.08 q^{38} +8473.21 q^{39} +925.317 q^{40} -1607.03 q^{41} -5430.47 q^{42} +6693.01 q^{43} +97.0915 q^{44} -6967.76 q^{45} +9513.90 q^{46} +3053.09 q^{47} -18028.2 q^{48} -15519.6 q^{49} -10022.2 q^{50} +8023.18 q^{51} +15308.6 q^{52} -2800.44 q^{53} +20809.3 q^{54} -190.104 q^{55} -502.739 q^{56} -20286.7 q^{57} -52557.3 q^{58} -51247.3 q^{59} -41581.9 q^{60} +21314.6 q^{61} +16266.8 q^{62} +3785.69 q^{63} -36206.8 q^{64} -29974.0 q^{65} -435.683 q^{66} +35371.6 q^{67} +14495.5 q^{68} -21907.3 q^{69} +19210.3 q^{70} +5386.61 q^{71} -1478.35 q^{72} -51756.8 q^{73} -77831.1 q^{74} +23077.9 q^{75} -36652.0 q^{76} +103.286 q^{77} -68694.9 q^{78} +46093.8 q^{79} +63774.8 q^{80} -73555.5 q^{81} +13028.7 q^{82} -73023.1 q^{83} +22592.1 q^{84} -28382.0 q^{85} -54262.2 q^{86} +121022. q^{87} -40.3343 q^{88} +108194. q^{89} +56489.7 q^{90} +16285.3 q^{91} -39580.1 q^{92} -37457.1 q^{93} -24752.3 q^{94} +71764.0 q^{95} +154531. q^{96} +158709. q^{97} +125822. q^{98} +303.723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.10730	−1.43318	−0.716591	−	0.697494i	$-0.754298\pi$
$2$	−8.10730	−1.43318	−0.716591	+	0.697494i	$0.754298\pi$
$3$	18.6684	1.19758	0.598789	−	0.800907i	$-0.295649\pi$
$3$	18.6684	1.19758	0.598789	+	0.800907i	$0.295649\pi$
$4$	33.7283	1.05401
$5$	−66.0394	−1.18135	−0.590674	−	0.806910i	$-0.701138\pi$
$5$	−66.0394	−1.18135	−0.590674	+	0.806910i	$0.701138\pi$
$6$	−151.350	−1.71635
$7$	35.8802	0.276764	0.138382	−	0.990379i	$-0.455810\pi$
$7$	35.8802	0.276764	0.138382	+	0.990379i	$0.455810\pi$
$8$	−14.0116	−0.0774039
$9$	105.509	0.434194
$10$	535.401	1.69309
$11$	2.87864	0.00717308	0.00358654	−	0.999994i	$-0.498858\pi$
$11$	2.87864	0.00717308	0.00358654	+	0.999994i	$0.498858\pi$
$12$	629.653	1.26226
$13$	453.880	0.744874	0.372437	−	0.928058i	$-0.378522\pi$
$13$	453.880	0.744874	0.372437	+	0.928058i	$0.378522\pi$
$14$	−290.891	−0.396653
$15$	−1232.85	−1.41476
$16$	−965.708	−0.943075
$17$	429.773	0.360676	0.180338	−	0.983605i	$-0.442281\pi$
$17$	429.773	0.360676	0.180338	+	0.983605i	$0.442281\pi$
$18$	−855.394	−0.622279
$19$	−1086.69	−0.690589	−0.345295	−	0.938494i	$-0.612221\pi$
$19$	−1086.69	−0.690589	−0.345295	+	0.938494i	$0.612221\pi$
$20$	−2227.39	−1.24515
$21$	669.825	0.331446
$22$	−23.3380	−0.0102803
$23$	−1173.50	−0.462554	−0.231277	−	0.972888i	$-0.574290\pi$
$23$	−1173.50	−0.462554	−0.231277	+	0.972888i	$0.574290\pi$
$24$	−261.574	−0.0926972
$25$	1236.20	0.395584
$26$	−3679.74	−1.06754
$27$	−2566.73	−0.677597
$28$	1210.18	0.291712
$29$	6482.71	1.43140	0.715701	−	0.698406i	$-0.246107\pi$
$29$	6482.71	1.43140	0.715701	+	0.698406i	$0.246107\pi$
$30$	9995.08	2.02760
$31$	−2006.45	−0.374993	−0.187496	−	0.982265i	$-0.560037\pi$
$31$	−2006.45	−0.374993	−0.187496	+	0.982265i	$0.560037\pi$
$32$	8277.66	1.42900
$33$	53.7396	0.00859032
$34$	−3484.30	−0.516914
$35$	−2369.50	−0.326955
$36$	3558.64	0.457644
$37$	9600.13	1.15285	0.576425	−	0.817150i	$-0.304447\pi$
$37$	9600.13	1.15285	0.576425	+	0.817150i	$0.304447\pi$
$38$	8810.08	0.989740
$39$	8473.21	0.892045
$40$	925.317	0.0914409
$41$	−1607.03	−0.149302	−0.0746510	−	0.997210i	$-0.523784\pi$
$41$	−1607.03	−0.149302	−0.0746510	+	0.997210i	$0.523784\pi$
$42$	−5430.47	−0.475023
$43$	6693.01	0.552014	0.276007	−	0.961156i	$-0.410989\pi$
$43$	6693.01	0.552014	0.276007	+	0.961156i	$0.410989\pi$
$44$	97.0915	0.00756048
$45$	−6967.76	−0.512934
$46$	9513.90	0.662924
$47$	3053.09	0.201602	0.100801	−	0.994907i	$-0.467859\pi$
$47$	3053.09	0.201602	0.100801	+	0.994907i	$0.467859\pi$
$48$	−18028.2	−1.12941
$49$	−15519.6	−0.923402
$50$	−10022.2	−0.566943
$51$	8023.18	0.431938
$52$	15308.6	0.785103
$53$	−2800.44	−0.136942	−0.0684709	−	0.997653i	$-0.521812\pi$
$53$	−2800.44	−0.136942	−0.0684709	+	0.997653i	$0.521812\pi$
$54$	20809.3	0.971119
$55$	−190.104	−0.00847390
$56$	−502.739	−0.0214226
$57$	−20286.7	−0.827035
$58$	−52557.3	−2.05146
$59$	−51247.3	−1.91664	−0.958321	−	0.285693i	$-0.907776\pi$
$59$	−51247.3	−1.91664	−0.958321	+	0.285693i	$0.907776\pi$
$60$	−41581.9	−1.49117
$61$	21314.6	0.733420	0.366710	−	0.930335i	$-0.380484\pi$
$61$	21314.6	0.733420	0.366710	+	0.930335i	$0.380484\pi$
$62$	16266.8	0.537433
$63$	3785.69	0.120169
$64$	−36206.8	−1.10494
$65$	−29974.0	−0.879955
$66$	−435.683	−0.0123115
$67$	35371.6	0.962649	0.481325	−	0.876542i	$-0.340156\pi$
$67$	35371.6	0.962649	0.481325	+	0.876542i	$0.340156\pi$
$68$	14495.5	0.380156
$69$	−21907.3	−0.553945
$70$	19210.3	0.468585
$71$	5386.61	0.126815	0.0634073	−	0.997988i	$-0.479803\pi$
$71$	5386.61	0.126815	0.0634073	+	0.997988i	$0.479803\pi$
$72$	−1478.35	−0.0336083
$73$	−51756.8	−1.13674	−0.568368	−	0.822774i	$-0.692425\pi$
$73$	−51756.8	−1.13674	−0.568368	+	0.822774i	$0.692425\pi$
$74$	−77831.1	−1.65224
$75$	23077.9	0.473743
$76$	−36652.0	−0.727887
$77$	103.286	0.00198525
$78$	−68694.9	−1.27846
$79$	46093.8	0.830950	0.415475	−	0.909605i	$-0.363615\pi$
$79$	46093.8	0.830950	0.415475	+	0.909605i	$0.363615\pi$
$80$	63774.8	1.11410
$81$	−73555.5	−1.24567
$82$	13028.7	0.213977
$83$	−73023.1	−1.16350	−0.581748	−	0.813369i	$-0.697631\pi$
$83$	−73023.1	−1.16350	−0.581748	+	0.813369i	$0.697631\pi$
$84$	22592.1	0.349347
$85$	−28382.0	−0.426084
$86$	−54262.2	−0.791136
$87$	121022.	1.71422
$88$	−40.3343	−0.000555224 0
$89$	108194.	1.44786	0.723932	−	0.689871i	$-0.242333\pi$
$89$	108194.	1.44786	0.723932	+	0.689871i	$0.242333\pi$
$90$	56489.7	0.735128
$91$	16285.3	0.206154
$92$	−39580.1	−0.487536
$93$	−37457.1	−0.449083
$94$	−24752.3	−0.288932
$95$	71764.0	0.815827
$96$	154531.	1.71134
$97$	158709.	1.71266	0.856331	−	0.516427i	$-0.172738\pi$
$97$	158709.	1.71266	0.856331	+	0.516427i	$0.172738\pi$
$98$	125822.	1.32340
$99$	303.723	0.00311451
$100$	41694.9	0.416949
$101$	−168004.	−1.63876	−0.819380	−	0.573250i	$-0.805682\pi$
$101$	−168004.	−1.63876	−0.819380	+	0.573250i	$0.805682\pi$
$102$	−65046.3	−0.619045
$103$	171855.	1.59613	0.798067	−	0.602569i	$-0.205856\pi$
$103$	171855.	1.59613	0.798067	+	0.602569i	$0.205856\pi$
$104$	−6359.58	−0.0576561
$105$	−44234.9	−0.391554
$106$	22704.0	0.196262
$107$	51905.2	0.438280	0.219140	−	0.975693i	$-0.429675\pi$
$107$	51905.2	0.438280	0.219140	+	0.975693i	$0.429675\pi$
$108$	−86571.5	−0.714193
$109$	−4230.39	−0.0341047	−0.0170524	−	0.999855i	$-0.505428\pi$
$109$	−4230.39	−0.0341047	−0.0170524	+	0.999855i	$0.505428\pi$
$110$	1541.23	0.0121446
$111$	179219.	1.38063
$112$	−34649.8	−0.261009
$113$	−185739.	−1.36838	−0.684190	−	0.729304i	$-0.739844\pi$
$113$	−185739.	−1.36838	−0.684190	+	0.729304i	$0.739844\pi$
$114$	164470.	1.18529
$115$	77497.1	0.546438
$116$	218651.	1.50871
$117$	47888.5	0.323420
$118$	415477.	2.74690
$119$	15420.3	0.0998221
$120$	17274.2	0.109508
$121$	−161043.	−0.999949
$122$	−172804.	−1.05112
$123$	−30000.8	−0.178801
$124$	−67673.9	−0.395246
$125$	124735.	0.714026
$126$	−30691.7	−0.172224
$127$	72295.4	0.397742	0.198871	−	0.980026i	$-0.436272\pi$
$127$	72295.4	0.397742	0.198871	+	0.980026i	$0.436272\pi$
$128$	28653.9	0.154582
$129$	124948.	0.661080
$130$	243008.	1.26114
$131$	−368733.	−1.87730	−0.938650	−	0.344871i	$-0.887923\pi$
$131$	−368733.	−1.87730	−0.938650	+	0.344871i	$0.887923\pi$
$132$	1812.54	0.00905427
$133$	−38990.5	−0.191130
$134$	−286768.	−1.37965
$135$	169506.	0.800478
$136$	−6021.81	−0.0279177
$137$	−317735.	−1.44632	−0.723159	−	0.690682i	$-0.757311\pi$
$137$	−317735.	−1.44632	−0.723159	+	0.690682i	$0.757311\pi$
$138$	177609.	0.793904
$139$	−34287.8	−0.150523	−0.0752614	−	0.997164i	$-0.523979\pi$
$139$	−34287.8	−0.150523	−0.0752614	+	0.997164i	$0.523979\pi$
$140$	−79919.3	−0.344613
$141$	56996.3	0.241434
$142$	−43670.8	−0.181748
$143$	1306.56	0.00534304
$144$	−101891.	−0.409477
$145$	−428114.	−1.69099
$146$	419607.	1.62915
$147$	−289726.	−1.10585
$148$	323796.	1.21511
$149$	−100422.	−0.370563	−0.185282	−	0.982685i	$-0.559320\pi$
$149$	−100422.	−0.370563	−0.185282	+	0.982685i	$0.559320\pi$
$150$	−187099.	−0.678959
$151$	−463554.	−1.65447	−0.827234	−	0.561858i	$-0.810087\pi$
$151$	−463554.	−1.65447	−0.827234	+	0.561858i	$0.810087\pi$
$152$	15226.2	0.0534543
$153$	45345.0	0.156603
$154$	−837.371	−0.00284522
$155$	132504.	0.442997
$156$	285787.	0.940223
$157$	183410.	0.593845	0.296922	−	0.954902i	$-0.404040\pi$
$157$	183410.	0.593845	0.296922	+	0.954902i	$0.404040\pi$
$158$	−373696.	−1.19090
$159$	−52279.7	−0.163999
$160$	−546651.	−1.68815
$161$	−42105.3	−0.128018
$162$	596337.	1.78527
$163$	664731.	1.95964	0.979821	−	0.199877i	$-0.0640542\pi$
$163$	664731.	1.95964	0.979821	+	0.199877i	$0.0640542\pi$
$164$	−54202.5	−0.157366
$165$	−3548.93	−0.0101482
$166$	592020.	1.66750
$167$	−194158.	−0.538722	−0.269361	−	0.963039i	$-0.586812\pi$
$167$	−194158.	−0.538722	−0.269361	+	0.963039i	$0.586812\pi$
$168$	−9385.32	−0.0256552
$169$	−165286.	−0.445163
$170$	230101.	0.610656
$171$	−114655.	−0.299850
$172$	225744.	0.581827
$173$	−490750.	−1.24665	−0.623325	−	0.781963i	$-0.714219\pi$
$173$	−490750.	−1.24665	−0.623325	+	0.781963i	$0.714219\pi$
$174$	−981160.	−2.45678
$175$	44355.0	0.109483
$176$	−2779.93	−0.00676475
$177$	−956705.	−2.29533
$178$	−877160.	−2.07505
$179$	−230724.	−0.538221	−0.269110	−	0.963109i	$-0.586730\pi$
$179$	−230724.	−0.538221	−0.269110	+	0.963109i	$0.586730\pi$
$180$	−235010.	−0.540637
$181$	−584973.	−1.32721	−0.663605	−	0.748083i	$-0.730974\pi$
$181$	−584973.	−1.32721	−0.663605	+	0.748083i	$0.730974\pi$
$182$	−132030.	−0.295456
$183$	397910.	0.878328
$184$	16442.6	0.0358035
$185$	−633987.	−1.36192
$186$	303676.	0.643618
$187$	1237.16	0.00258716
$188$	102976.	0.212490
$189$	−92094.9	−0.187534
$190$	−581812.	−1.16923
$191$	22241.9	0.0441151	0.0220576	−	0.999757i	$-0.492978\pi$
$191$	22241.9	0.0441151	0.0220576	+	0.999757i	$0.492978\pi$
$192$	−675922.	−1.32326
$193$	66816.8	0.129120	0.0645598	−	0.997914i	$-0.479436\pi$
$193$	66816.8	0.129120	0.0645598	+	0.997914i	$0.479436\pi$
$194$	−1.28670e6	−2.45456
$195$	−559566.	−1.05382
$196$	−523450.	−0.973273
$197$	−424341.	−0.779021	−0.389511	−	0.921022i	$-0.627356\pi$
$197$	−424341.	−0.779021	−0.389511	+	0.921022i	$0.627356\pi$
$198$	−2462.37	−0.00446365
$199$	26602.4	0.0476198	0.0238099	−	0.999717i	$-0.492420\pi$
$199$	26602.4	0.0476198	0.0238099	+	0.999717i	$0.492420\pi$
$200$	−17321.1	−0.0306197
$201$	660332.	1.15285
$202$	1.36206e6	2.34864
$203$	232601.	0.396161
$204$	270608.	0.455266
$205$	106128.	0.176378
$206$	−1.39328e6	−2.28755
$207$	−123815.	−0.200838
$208$	−438316.	−0.702472
$209$	−3128.17	−0.00495365
$210$	358625.	0.561167
$211$	−250553.	−0.387430	−0.193715	−	0.981058i	$-0.562054\pi$
$211$	−250553.	−0.387430	−0.193715	+	0.981058i	$0.562054\pi$
$212$	−94453.9	−0.144338
$213$	100559.	0.151870
$214$	−420811.	−0.628135
$215$	−442002.	−0.652121
$216$	35964.0	0.0524486
$217$	−71991.6	−0.103785
$218$	34297.1	0.0488782
$219$	−966216.	−1.36133
$220$	−6411.86	−0.00893156
$221$	195066.	0.268658
$222$	−1.45298e6	−1.97869
$223$	−1.12164e6	−1.51040	−0.755202	−	0.655492i	$-0.772461\pi$
$223$	−1.12164e6	−1.51040	−0.755202	+	0.655492i	$0.772461\pi$
$224$	297004.	0.395496
$225$	130430.	0.171760
$226$	1.50584e6	1.96114
$227$	−70668.8	−0.0910256	−0.0455128	−	0.998964i	$-0.514492\pi$
$227$	−70668.8	−0.0910256	−0.0455128	+	0.998964i	$0.514492\pi$
$228$	−684235.	−0.871702
$229$	−706815.	−0.890671	−0.445335	−	0.895364i	$-0.646916\pi$
$229$	−706815.	−0.890671	−0.445335	+	0.895364i	$0.646916\pi$
$230$	−628292.	−0.783144
$231$	1928.19	0.00237749
$232$	−90833.2	−0.110796
$233$	521610.	0.629442	0.314721	−	0.949184i	$-0.398089\pi$
$233$	521610.	0.629442	0.314721	+	0.949184i	$0.398089\pi$
$234$	−388246.	−0.463519
$235$	−201624.	−0.238162
$236$	−1.72848e6	−2.02016
$237$	860498.	0.995128
$238$	−125017.	−0.143063
$239$	−881626.	−0.998366	−0.499183	−	0.866497i	$-0.666366\pi$
$239$	−881626.	−0.998366	−0.499183	+	0.866497i	$0.666366\pi$
$240$	1.19057e6	1.33422
$241$	−174402.	−0.193423	−0.0967115	−	0.995312i	$-0.530832\pi$
$241$	−174402.	−0.193423	−0.0967115	+	0.995312i	$0.530832\pi$
$242$	1.30562e6	1.43311
$243$	−749448.	−0.814190
$244$	718905.	0.773031
$245$	1.02491e6	1.09086
$246$	243225.	0.256254
$247$	−493225.	−0.514402
$248$	28113.5	0.0290259
$249$	−1.36322e6	−1.39338
$250$	−1.01127e6	−1.02333
$251$	−1.42566e6	−1.42834	−0.714168	−	0.699974i	$-0.753195\pi$
$251$	−1.42566e6	−1.42834	−0.714168	+	0.699974i	$0.753195\pi$
$252$	127685.	0.126659
$253$	−3378.08	−0.00331794
$254$	−586121.	−0.570037
$255$	−529846.	−0.510269
$256$	926310.	0.883398
$257$	94860.5	0.0895886	0.0447943	−	0.998996i	$-0.485737\pi$
$257$	94860.5	0.0895886	0.0447943	+	0.998996i	$0.485737\pi$
$258$	−1.01299e6	−0.947448
$259$	344455.	0.319067
$260$	−1.01097e6	−0.927480
$261$	683986.	0.621506
$262$	2.98943e6	2.69051
$263$	444433.	0.396202	0.198101	−	0.980182i	$-0.436523\pi$
$263$	444433.	0.396202	0.198101	+	0.980182i	$0.436523\pi$
$264$	−752.977	−0.000664924 0
$265$	184939.	0.161776
$266$	316107.	0.273924
$267$	2.01981e6	1.73393
$268$	1.19302e6	1.01464
$269$	−485135.	−0.408773	−0.204386	−	0.978890i	$-0.565520\pi$
$269$	−485135.	−0.408773	−0.204386	+	0.978890i	$0.565520\pi$
$270$	−1.37423e6	−1.14723
$271$	362672.	0.299979	0.149989	−	0.988688i	$-0.452076\pi$
$271$	362672.	0.299979	0.149989	+	0.988688i	$0.452076\pi$
$272$	−415036.	−0.340144
$273$	304020.	0.246886
$274$	2.57597e6	2.07284
$275$	3558.57	0.00283755
$276$	−738896.	−0.583863
$277$	−23505.7	−0.0184066	−0.00920331	−	0.999958i	$-0.502930\pi$
$277$	−23505.7	−0.0184066	−0.00920331	+	0.999958i	$0.502930\pi$
$278$	277981.	0.215726
$279$	−211698.	−0.162820
$280$	33200.5	0.0253075
$281$	−2.17751e6	−1.64511	−0.822553	−	0.568688i	$-0.807451\pi$
$281$	−2.17751e6	−1.64511	−0.822553	+	0.568688i	$0.807451\pi$
$282$	−462086.	−0.346019
$283$	257328.	0.190995	0.0954974	−	0.995430i	$-0.469556\pi$
$283$	257328.	0.190995	0.0954974	+	0.995430i	$0.469556\pi$
$284$	181681.	0.133664
$285$	1.33972e6	0.977016
$286$	−10592.6	−0.00765754
$287$	−57660.7	−0.0413214
$288$	873368.	0.620463
$289$	−1.23515e6	−0.869913
$290$	3.47085e6	2.42349
$291$	2.96284e6	2.05105
$292$	−1.74567e6	−1.19813
$293$	1.24809e6	0.849329	0.424664	−	0.905351i	$-0.360392\pi$
$293$	1.24809e6	0.849329	0.424664	+	0.905351i	$0.360392\pi$
$294$	2.34890e6	1.58488
$295$	3.38434e6	2.26422
$296$	−134513.	−0.0892351
$297$	−7388.70	−0.00486046
$298$	814150.	0.531084
$299$	−532627.	−0.344545
$300$	778376.	0.499329
$301$	240146.	0.152778
$302$	3.75817e6	2.37115
$303$	−3.13636e6	−1.96254
$304$	1.04942e6	0.651277
$305$	−1.40760e6	−0.866425
$306$	−367626.	−0.224441
$307$	−2.21309e6	−1.34015	−0.670076	−	0.742293i	$-0.733738\pi$
$307$	−2.21309e6	−1.34015	−0.670076	+	0.742293i	$0.733738\pi$
$308$	3483.66	0.00209247
$309$	3.20826e6	1.91150
$310$	−1.07425e6	−0.634895
$311$	−3.30834e6	−1.93959	−0.969794	−	0.243924i	$-0.921565\pi$
$311$	−3.30834e6	−1.93959	−0.969794	+	0.243924i	$0.921565\pi$
$312$	−118723.	−0.0690477
$313$	−85138.2	−0.0491206	−0.0245603	−	0.999698i	$-0.507819\pi$
$313$	−85138.2	−0.0491206	−0.0245603	+	0.999698i	$0.507819\pi$
$314$	−1.48696e6	−0.851087
$315$	−250004.	−0.141962
$316$	1.55466e6	0.875828
$317$	−1.09017e6	−0.609324	−0.304662	−	0.952461i	$-0.598543\pi$
$317$	−1.09017e6	−0.609324	−0.304662	+	0.952461i	$0.598543\pi$
$318$	423847.	0.235040
$319$	18661.4	0.0102676
$320$	2.39107e6	1.30532
$321$	968987.	0.524875
$322$	341360.	0.183474
$323$	−467029.	−0.249079
$324$	−2.48090e6	−1.31295
$325$	561086.	0.294660
$326$	−5.38917e6	−2.80852
$327$	−78974.7	−0.0408431
$328$	22517.1	0.0115565
$329$	109545.	0.0557962
$330$	28772.2	0.0145442
$331$	3.72110e6	1.86681	0.933407	−	0.358819i	$-0.116820\pi$
$331$	3.72110e6	1.86681	0.933407	+	0.358819i	$0.116820\pi$
$332$	−2.46294e6	−1.22634
$333$	1.01290e6	0.500561
$334$	1.57410e6	0.772086
$335$	−2.33592e6	−1.13722
$336$	−646856.	−0.312579
$337$	625893.	0.300210	0.150105	−	0.988670i	$-0.452039\pi$
$337$	625893.	0.300210	0.150105	+	0.988670i	$0.452039\pi$
$338$	1.34002e6	0.637999
$339$	−3.46745e6	−1.63874
$340$	−957275.	−0.449096
$341$	−5775.83	−0.00268985
$342$	929544.	0.429739
$343$	−1.15988e6	−0.532328
$344$	−93779.7	−0.0427280
$345$	1.44675e6	0.654402
$346$	3.97865e6	1.78668
$347$	2.32946e6	1.03856	0.519280	−	0.854604i	$-0.326200\pi$
$347$	2.32946e6	1.03856	0.519280	+	0.854604i	$0.326200\pi$
$348$	4.08186e6	1.80680
$349$	−1.50413e6	−0.661032	−0.330516	−	0.943800i	$-0.607223\pi$
$349$	−1.50413e6	−0.661032	−0.330516	+	0.943800i	$0.607223\pi$
$350$	−359600.	−0.156909
$351$	−1.16499e6	−0.504724
$352$	23828.4	0.0102503
$353$	206100.	0.0880322	0.0440161	−	0.999031i	$-0.485985\pi$
$353$	206100.	0.0880322	0.0440161	+	0.999031i	$0.485985\pi$
$354$	7.75629e6	3.28962
$355$	−355728.	−0.149812
$356$	3.64919e6	1.52606
$357$	287873.	0.119545
$358$	1.87055e6	0.771368
$359$	1.81740e6	0.744243	0.372121	−	0.928184i	$-0.378631\pi$
$359$	1.81740e6	0.744243	0.372121	+	0.928184i	$0.378631\pi$
$360$	97629.4	0.0397031
$361$	−1.29521e6	−0.523086
$362$	4.74255e6	1.90213
$363$	−3.00641e6	−1.19752
$364$	549275.	0.217288
$365$	3.41798e6	1.34288
$366$	−3.22597e6	−1.25880
$367$	−1.02606e6	−0.397655	−0.198827	−	0.980035i	$-0.563713\pi$
$367$	−1.02606e6	−0.397655	−0.198827	+	0.980035i	$0.563713\pi$
$368$	1.13326e6	0.436223
$369$	−169557.	−0.0648260
$370$	5.13992e6	1.95188
$371$	−100480.	−0.0379006
$372$	−1.26336e6	−0.473338
$373$	−1.55505e6	−0.578726	−0.289363	−	0.957219i	$-0.593444\pi$
$373$	−1.55505e6	−0.578726	−0.289363	+	0.957219i	$0.593444\pi$
$374$	−10030.0	−0.00370786
$375$	2.32861e6	0.855102
$376$	−42778.7	−0.0156048
$377$	2.94237e6	1.06621
$378$	746641.	0.268771
$379$	−1.90135e6	−0.679931	−0.339966	−	0.940438i	$-0.610415\pi$
$379$	−1.90135e6	−0.679931	−0.339966	+	0.940438i	$0.610415\pi$
$380$	2.42048e6	0.859888
$381$	1.34964e6	0.476327
$382$	−180321.	−0.0632250
$383$	−596383.	−0.207744	−0.103872	−	0.994591i	$-0.533123\pi$
$383$	−596383.	−0.207744	−0.103872	+	0.994591i	$0.533123\pi$
$384$	534922.	0.185124
$385$	−6820.95	−0.00234527
$386$	−541703.	−0.185052
$387$	706173.	0.239681
$388$	5.35297e6	1.80516
$389$	−5.43740e6	−1.82187	−0.910935	−	0.412550i	$-0.864638\pi$
$389$	−5.43740e6	−1.82187	−0.910935	+	0.412550i	$0.864638\pi$
$390$	4.53657e6	1.51031
$391$	−504338.	−0.166832
$392$	217455.	0.0714749
$393$	−6.88365e6	−2.24821
$394$	3.44026e6	1.11648
$395$	−3.04401e6	−0.981641
$396$	10244.0	0.00328272
$397$	−2.09846e6	−0.668228	−0.334114	−	0.942533i	$-0.608437\pi$
$397$	−2.09846e6	−0.668228	−0.334114	+	0.942533i	$0.608437\pi$
$398$	−215673.	−0.0682479
$399$	−727890.	−0.228893
$400$	−1.19381e6	−0.373065
$401$	2.41081e6	0.748689	0.374344	−	0.927290i	$-0.377868\pi$
$401$	2.41081e6	0.748689	0.374344	+	0.927290i	$0.377868\pi$
$402$	−5.35350e6	−1.65224
$403$	−910685.	−0.279322
$404$	−5.66648e6	−1.72727
$405$	4.85756e6	1.47157
$406$	−1.88576e6	−0.567770
$407$	27635.3	0.00826949
$408$	−112418.	−0.0334337
$409$	−5.17619e6	−1.53004	−0.765018	−	0.644009i	$-0.777270\pi$
$409$	−5.17619e6	−1.53004	−0.765018	+	0.644009i	$0.777270\pi$
$410$	−860407.	−0.252781
$411$	−5.93160e6	−1.73208
$412$	5.79637e6	1.68234
$413$	−1.83876e6	−0.530457
$414$	1.00380e6	0.287838
$415$	4.82240e6	1.37449
$416$	3.75706e6	1.06443
$417$	−640098.	−0.180263
$418$	25361.0	0.00709948
$419$	1.65667e6	0.461000	0.230500	−	0.973072i	$-0.425964\pi$
$419$	1.65667e6	0.461000	0.230500	+	0.973072i	$0.425964\pi$
$420$	−1.49197e6	−0.412701
$421$	5.20299e6	1.43070	0.715349	−	0.698767i	$-0.246268\pi$
$421$	5.20299e6	1.43070	0.715349	+	0.698767i	$0.246268\pi$
$422$	2.03131e6	0.555258
$423$	322129.	0.0875344
$424$	39238.6	0.0105998
$425$	531286.	0.142678
$426$	−815264.	−0.217658
$427$	764772.	0.202984
$428$	1.75067e6	0.461951
$429$	24391.3	0.00639870
$430$	3.58344e6	0.934607
$431$	225719.	0.0585295	0.0292647	−	0.999572i	$-0.490683\pi$
$431$	225719.	0.0585295	0.0292647	+	0.999572i	$0.490683\pi$
$432$	2.47872e6	0.639025
$433$	1.01704e6	0.260687	0.130344	−	0.991469i	$-0.458392\pi$
$433$	1.01704e6	0.260687	0.130344	+	0.991469i	$0.458392\pi$
$434$	583657.	0.148742
$435$	−7.99221e6	−2.02509
$436$	−142684.	−0.0359467
$437$	1.27522e6	0.319435
$438$	7.83340e6	1.95103
$439$	−6.12650e6	−1.51723	−0.758615	−	0.651539i	$-0.774124\pi$
$439$	−6.12650e6	−1.51723	−0.758615	+	0.651539i	$0.774124\pi$
$440$	2663.65	0.000655913 0
$441$	−1.63746e6	−0.400935
$442$	−1.58145e6	−0.385036
$443$	6.88324e6	1.66642	0.833208	−	0.552959i	$-0.186501\pi$
$443$	6.88324e6	1.66642	0.833208	+	0.552959i	$0.186501\pi$
$444$	6.04475e6	1.45519
$445$	−7.14506e6	−1.71043
$446$	9.09351e6	2.16468
$447$	−1.87471e6	−0.443779
$448$	−1.29910e6	−0.305808
$449$	1.46672e6	0.343346	0.171673	−	0.985154i	$-0.445083\pi$
$449$	1.46672e6	0.343346	0.171673	+	0.985154i	$0.445083\pi$
$450$	−1.05744e6	−0.246163
$451$	−4626.07	−0.00107095
$452$	−6.26465e6	−1.44228
$453$	−8.65382e6	−1.98135
$454$	572933.	0.130456
$455$	−1.07547e6	−0.243540
$456$	284249.	0.0640157
$457$	3.11138e6	0.696888	0.348444	−	0.937330i	$-0.386710\pi$
$457$	3.11138e6	0.696888	0.348444	+	0.937330i	$0.386710\pi$
$458$	5.73036e6	1.27649
$459$	−1.10311e6	−0.244393
$460$	2.61384e6	0.575950
$461$	3.23952e6	0.709952	0.354976	−	0.934875i	$-0.384489\pi$
$461$	3.23952e6	0.709952	0.354976	+	0.934875i	$0.384489\pi$
$462$	−15632.4	−0.00340738
$463$	3.38717e6	0.734318	0.367159	−	0.930158i	$-0.380331\pi$
$463$	3.38717e6	0.734318	0.367159	+	0.930158i	$0.380331\pi$
$464$	−6.26041e6	−1.34992
$465$	2.47365e6	0.530524
$466$	−4.22884e6	−0.902104
$467$	−3.39059e6	−0.719421	−0.359710	−	0.933064i	$-0.617125\pi$
$467$	−3.39059e6	−0.719421	−0.359710	+	0.933064i	$0.617125\pi$
$468$	1.61520e6	0.340887
$469$	1.26914e6	0.266427
$470$	1.63463e6	0.341330
$471$	3.42396e6	0.711175
$472$	718057.	0.148356
$473$	19266.7	0.00395964
$474$	−6.97631e6	−1.42620
$475$	−1.34336e6	−0.273186
$476$	520102.	0.105213
$477$	−295472.	−0.0594593
$478$	7.14761e6	1.43084
$479$	−7.46979e6	−1.48754	−0.743772	−	0.668434i	$-0.766965\pi$
$479$	−7.46979e6	−1.48754	−0.743772	+	0.668434i	$0.766965\pi$
$480$	−1.02051e7	−2.02169
$481$	4.35731e6	0.858728
$482$	1.41393e6	0.277210
$483$	−786039.	−0.153312
$484$	−5.43169e6	−1.05395
$485$	−1.04810e7	−2.02325
$486$	6.07600e6	1.16688
$487$	5.44780e6	1.04088	0.520438	−	0.853900i	$-0.325769\pi$
$487$	5.44780e6	1.04088	0.520438	+	0.853900i	$0.325769\pi$
$488$	−298652.	−0.0567696
$489$	1.24095e7	2.34682
$490$	−8.30921e6	−1.56340
$491$	1.73472e6	0.324733	0.162367	−	0.986731i	$-0.448087\pi$
$491$	1.73472e6	0.324733	0.162367	+	0.986731i	$0.448087\pi$
$492$	−1.01187e6	−0.188458
$493$	2.78610e6	0.516273
$494$	3.99872e6	0.737231
$495$	−20057.7	−0.00367932
$496$	1.93764e6	0.353646
$497$	193272.	0.0350977
$498$	1.10521e7	1.99696
$499$	5.93085e6	1.06627	0.533133	−	0.846031i	$-0.321014\pi$
$499$	5.93085e6	1.06627	0.533133	+	0.846031i	$0.321014\pi$
$500$	4.20710e6	0.752590
$501$	−3.62462e6	−0.645161
$502$	1.15582e7	2.04707
$503$	1.72481e6	0.303963	0.151981	−	0.988383i	$-0.451435\pi$
$503$	1.72481e6	0.303963	0.151981	+	0.988383i	$0.451435\pi$
$504$	−53043.5	−0.00930156
$505$	1.10949e7	1.93595
$506$	27387.1	0.00475521
$507$	−3.08562e6	−0.533118
$508$	2.43840e6	0.419224
$509$	−1.63945e6	−0.280481	−0.140240	−	0.990117i	$-0.544788\pi$
$509$	−1.63945e6	−0.280481	−0.140240	+	0.990117i	$0.544788\pi$
$510$	4.29562e6	0.731308
$511$	−1.85704e6	−0.314608
$512$	−8.42680e6	−1.42065
$513$	2.78923e6	0.467941
$514$	−769063.	−0.128397
$515$	−1.13492e7	−1.88559
$516$	4.21427e6	0.696784
$517$	8788.75	0.00144611
$518$	−2.79260e6	−0.457281
$519$	−9.16151e6	−1.49296
$520$	419983.	0.0681119
$521$	1.04653e7	1.68911	0.844555	−	0.535469i	$-0.179865\pi$
$521$	1.04653e7	1.68911	0.844555	+	0.535469i	$0.179865\pi$
$522$	−5.54527e6	−0.890731
$523$	4.98851e6	0.797475	0.398737	−	0.917065i	$-0.369449\pi$
$523$	4.98851e6	0.797475	0.398737	+	0.917065i	$0.369449\pi$
$524$	−1.24367e7	−1.97869
$525$	828038.	0.131115
$526$	−3.60315e6	−0.567829
$527$	−862317.	−0.135251
$528$	−51896.8	−0.00810131
$529$	−5.05925e6	−0.786043
$530$	−1.49936e6	−0.231854
$531$	−5.40706e6	−0.832195
$532$	−1.31508e6	−0.201453
$533$	−729401.	−0.111211
$534$	−1.63752e7	−2.48504
$535$	−3.42779e6	−0.517761
$536$	−495613.	−0.0745128
$537$	−4.30725e6	−0.644562
$538$	3.93313e6	0.585845
$539$	−44675.4	−0.00662363
$540$	5.71713e6	0.843711
$541$	3.42646e6	0.503329	0.251665	−	0.967815i	$-0.419022\pi$
$541$	3.42646e6	0.503329	0.251665	+	0.967815i	$0.419022\pi$
$542$	−2.94029e6	−0.429924
$543$	−1.09205e7	−1.58944
$544$	3.55752e6	0.515406
$545$	279373.	0.0402896
$546$	−2.46478e6	−0.353832
$547$	−299209.	−0.0427569
$547$	−299209.	−0.0427569
$548$	−1.07167e7	−1.52443
$549$	2.24889e6	0.318447
$550$	−28850.4	−0.00406673
$551$	−7.04467e6	−0.988512
$552$	306957.	0.0428775
$553$	1.65385e6	0.229977
$554$	190568.	0.0263800
$555$	−1.18355e7	−1.63100
$556$	−1.15647e6	−0.158652
$557$	−372433.	−0.0508640	−0.0254320	−	0.999677i	$-0.508096\pi$
$557$	−372433.	−0.0508640	−0.0254320	+	0.999677i	$0.508096\pi$
$558$	1.71630e6	0.233350
$559$	3.03782e6	0.411181
$560$	2.28825e6	0.308343
$561$	23095.8	0.00309832
$562$	1.76537e7	2.35774
$563$	5.80123e6	0.771345	0.385673	−	0.922636i	$-0.373969\pi$
$563$	5.80123e6	0.771345	0.385673	+	0.922636i	$0.373969\pi$
$564$	1.92239e6	0.254474
$565$	1.22661e7	1.61653
$566$	−2.08624e6	−0.273730
$567$	−2.63919e6	−0.344756
$568$	−75475.0	−0.00981594
$569$	−1.02494e6	−0.132715	−0.0663573	−	0.997796i	$-0.521138\pi$
$569$	−1.02494e6	−0.132715	−0.0663573	+	0.997796i	$0.521138\pi$
$570$	−1.08615e7	−1.40024
$571$	−1.12031e7	−1.43797	−0.718983	−	0.695028i	$-0.755392\pi$
$571$	−1.12031e7	−1.43797	−0.718983	+	0.695028i	$0.755392\pi$
$572$	44067.9	0.00563160
$573$	415220.	0.0528313
$574$	467472.	0.0592210
$575$	−1.45068e6	−0.182979
$576$	−3.82014e6	−0.479759
$577$	4.15912e6	0.520070	0.260035	−	0.965599i	$-0.416266\pi$
$577$	4.15912e6	0.520070	0.260035	+	0.965599i	$0.416266\pi$
$578$	1.00137e7	1.24674
$579$	1.24736e6	0.154631
$580$	−1.44396e7	−1.78231
$581$	−2.62008e6	−0.322014
$582$	−2.40206e7	−2.93952
$583$	−8061.44	−0.000982294 0
$584$	725195.	0.0879878
$585$	−3.16253e6	−0.382071
$586$	−1.01186e7	−1.21724
$587$	2.98328e6	0.357354	0.178677	−	0.983908i	$-0.442818\pi$
$587$	2.98328e6	0.357354	0.178677	+	0.983908i	$0.442818\pi$
$588$	−9.77197e6	−1.16557
$589$	2.18038e6	0.258966
$590$	−2.74379e7	−3.24504
$591$	−7.92176e6	−0.932939
$592$	−9.27093e6	−1.08722
$593$	−1.07570e7	−1.25619	−0.628093	−	0.778139i	$-0.716164\pi$
$593$	−1.07570e7	−1.25619	−0.628093	+	0.778139i	$0.716164\pi$
$594$	59902.4	0.00696591
$595$	−1.01835e6	−0.117925
$596$	−3.38705e6	−0.390577
$597$	496624.	0.0570285
$598$	4.31817e6	0.493795
$599$	−1.63803e7	−1.86533	−0.932664	−	0.360745i	$-0.882522\pi$
$599$	−1.63803e7	−1.86533	−0.932664	+	0.360745i	$0.882522\pi$
$600$	−323358.	−0.0366695
$601$	1.05876e7	1.19566	0.597832	−	0.801621i	$-0.296029\pi$
$601$	1.05876e7	1.19566	0.597832	+	0.801621i	$0.296029\pi$
$602$	−1.94694e6	−0.218958
$603$	3.73203e6	0.417976
$604$	−1.56349e7	−1.74382
$605$	1.06352e7	1.18129
$606$	2.54274e7	2.81268
$607$	−1.92232e6	−0.211765	−0.105883	−	0.994379i	$-0.533767\pi$
$607$	−1.92232e6	−0.211765	−0.105883	+	0.994379i	$0.533767\pi$
$608$	−8.99521e6	−0.986853
$609$	4.34229e6	0.474433
$610$	1.14119e7	1.24174
$611$	1.38574e6	0.150168
$612$	1.52941e6	0.165061
$613$	9.73459e6	1.04632	0.523162	−	0.852233i	$-0.324752\pi$
$613$	9.73459e6	1.04632	0.523162	+	0.852233i	$0.324752\pi$
$614$	1.79422e7	1.92068
$615$	1.98123e6	0.211226
$616$	−1447.20	−0.000153666 0
$617$	−6.83902e6	−0.723238	−0.361619	−	0.932326i	$-0.617776\pi$
$617$	−6.83902e6	−0.723238	−0.361619	+	0.932326i	$0.617776\pi$
$618$	−2.60103e7	−2.73952
$619$	6.35589e6	0.666729	0.333365	−	0.942798i	$-0.391816\pi$
$619$	6.35589e6	0.666729	0.333365	+	0.942798i	$0.391816\pi$
$620$	4.46914e6	0.466923
$621$	3.01206e6	0.313426
$622$	2.68217e7	2.77978
$623$	3.88202e6	0.400716
$624$	−8.18265e6	−0.841265
$625$	−1.21006e7	−1.23910
$626$	690241.	0.0703987
$627$	−58398.0	−0.00593238
$628$	6.18609e6	0.625917
$629$	4.12588e6	0.415806
$630$	2.02686e6	0.203457
$631$	−5.10937e6	−0.510850	−0.255425	−	0.966829i	$-0.582215\pi$
$631$	−5.10937e6	−0.510850	−0.255425	+	0.966829i	$0.582215\pi$
$632$	−645848.	−0.0643187
$633$	−4.67742e6	−0.463978
$634$	8.83837e6	0.873271
$635$	−4.77435e6	−0.469872
$636$	−1.76330e6	−0.172856
$637$	−7.04404e6	−0.687818
$638$	−151293.	−0.0147153
$639$	568336.	0.0550622
$640$	−1.89229e6	−0.182615
$641$	9.01181e6	0.866297	0.433149	−	0.901323i	$-0.357403\pi$
$641$	9.01181e6	0.866297	0.433149	+	0.901323i	$0.357403\pi$
$642$	−7.85587e6	−0.752240
$643$	1.92557e6	0.183668	0.0918339	−	0.995774i	$-0.470727\pi$
$643$	1.92557e6	0.183668	0.0918339	+	0.995774i	$0.470727\pi$
$644$	−1.42014e6	−0.134932
$645$	−8.25147e6	−0.780966
$646$	3.78634e6	0.356975
$647$	−1.04628e7	−0.982627	−0.491313	−	0.870983i	$-0.663483\pi$
$647$	−1.04628e7	−0.982627	−0.491313	+	0.870983i	$0.663483\pi$
$648$	1.03063e6	0.0964196
$649$	−147523.	−0.0137482
$650$	−4.54889e6	−0.422301
$651$	−1.34397e6	−0.124290
$652$	2.24202e7	2.06548
$653$	2.02105e7	1.85478	0.927391	−	0.374093i	$-0.122046\pi$
$653$	2.02105e7	1.85478	0.927391	+	0.374093i	$0.122046\pi$
$654$	640271.	0.0585355
$655$	2.43509e7	2.21775
$656$	1.55193e6	0.140803
$657$	−5.46081e6	−0.493564
$658$	−888118.	−0.0799661
$659$	8.97832e6	0.805344	0.402672	−	0.915344i	$-0.368082\pi$
$659$	8.97832e6	0.805344	0.402672	+	0.915344i	$0.368082\pi$
$660$	−119699.	−0.0106962
$661$	1.00581e7	0.895389	0.447694	−	0.894187i	$-0.352245\pi$
$661$	1.00581e7	0.895389	0.447694	+	0.894187i	$0.352245\pi$
$662$	−3.01681e7	−2.67548
$663$	3.64156e6	0.321739
$664$	1.02317e6	0.0900591
$665$	2.57491e6	0.225791
$666$	−8.21190e6	−0.717394
$667$	−7.60745e6	−0.662102
$668$	−6.54862e6	−0.567817
$669$	−2.09393e7	−1.80883
$670$	1.89380e7	1.62985
$671$	61357.1	0.00526088
$672$	5.54459e6	0.473637
$673$	1.00338e7	0.853941	0.426971	−	0.904265i	$-0.359581\pi$
$673$	1.00338e7	0.853941	0.426971	+	0.904265i	$0.359581\pi$
$674$	−5.07430e6	−0.430256
$675$	−3.17300e6	−0.268046
$676$	−5.57481e6	−0.469206
$677$	5.13087e6	0.430248	0.215124	−	0.976587i	$-0.430984\pi$
$677$	5.13087e6	0.430248	0.215124	+	0.976587i	$0.430984\pi$
$678$	2.81116e7	2.34862
$679$	5.69450e6	0.474003
$680$	397677.	0.0329805
$681$	−1.31927e6	−0.109010
$682$	46826.4	0.00385505
$683$	2.16786e7	1.77819	0.889096	−	0.457721i	$-0.151334\pi$
$683$	2.16786e7	1.77819	0.889096	+	0.457721i	$0.151334\pi$
$684$	−3.86712e6	−0.316044
$685$	2.09830e7	1.70860
$686$	9.40353e6	0.762923
$687$	−1.31951e7	−1.06665
$688$	−6.46349e6	−0.520590
$689$	−1.27106e6	−0.102004
$690$	−1.17292e7	−0.937877
$691$	1.28254e7	1.02183	0.510914	−	0.859632i	$-0.329307\pi$
$691$	1.28254e7	1.02183	0.510914	+	0.859632i	$0.329307\pi$
$692$	−1.65521e7	−1.31398
$693$	10897.6	0.000861983 0
$694$	−1.88856e7	−1.48845
$695$	2.26434e6	0.177820
$696$	−1.69571e6	−0.132687
$697$	−690661.	−0.0538496
$698$	1.21944e7	0.947378
$699$	9.73762e6	0.753806
$700$	1.49602e6	0.115396
$701$	1.52774e6	0.117423	0.0587115	−	0.998275i	$-0.481301\pi$
$701$	1.52774e6	0.117423	0.0587115	+	0.998275i	$0.481301\pi$
$702$	9.44492e6	0.723361
$703$	−1.04323e7	−0.796146
$704$	−104226.	−0.00792584
$705$	−3.76400e6	−0.285218
$706$	−1.67092e6	−0.126166
$707$	−6.02800e6	−0.453550
$708$	−3.22680e7	−2.41930
$709$	8.36685e6	0.625095	0.312548	−	0.949902i	$-0.398818\pi$
$709$	8.36685e6	0.625095	0.312548	+	0.949902i	$0.398818\pi$
$710$	2.88399e6	0.214708
$711$	4.86332e6	0.360793
$712$	−1.51597e6	−0.112070
$713$	2.35456e6	0.173455
$714$	−2.33387e6	−0.171329
$715$	−86284.2	−0.00631199
$716$	−7.78193e6	−0.567289
$717$	−1.64585e7	−1.19562
$718$	−1.47342e7	−1.06663
$719$	2.46295e6	0.177678	0.0888390	−	0.996046i	$-0.471684\pi$
$719$	2.46295e6	0.177678	0.0888390	+	0.996046i	$0.471684\pi$
$720$	6.72882e6	0.483735
$721$	6.16619e6	0.441752
$722$	1.05007e7	0.749678
$723$	−3.25580e6	−0.231639
$724$	−1.97301e7	−1.39889
$725$	8.01393e6	0.566240
$726$	2.43739e7	1.71626
$727$	1.23376e7	0.865753	0.432877	−	0.901453i	$-0.357499\pi$
$727$	1.23376e7	0.865753	0.432877	+	0.901453i	$0.357499\pi$
$728$	−228183.	−0.0159571
$729$	3.88301e6	0.270613
$730$	−2.77106e7	−1.92459
$731$	2.87648e6	0.199098
$732$	1.34208e7	0.925765
$733$	−515330.	−0.0354262	−0.0177131	−	0.999843i	$-0.505639\pi$
$733$	−515330.	−0.0354262	−0.0177131	+	0.999843i	$0.505639\pi$
$734$	8.31855e6	0.569911
$735$	1.91333e7	1.30639
$736$	−9.71381e6	−0.660991
$737$	101822.	0.00690515
$738$	1.37465e6	0.0929074
$739$	−3.80857e6	−0.256537	−0.128269	−	0.991739i	$-0.540942\pi$
$739$	−3.80857e6	−0.256537	−0.128269	+	0.991739i	$0.540942\pi$
$740$	−2.13833e7	−1.43547
$741$	−9.20772e6	−0.616037
$742$	814622.	0.0543184
$743$	2.76495e7	1.83745	0.918724	−	0.394901i	$-0.129221\pi$
$743$	2.76495e7	1.83745	0.918724	+	0.394901i	$0.129221\pi$
$744$	524834.	0.0347608
$745$	6.63179e6	0.437764
$746$	1.26073e7	0.829420
$747$	−7.70461e6	−0.505183
$748$	41727.3	0.00272688
$749$	1.86237e6	0.121300
$750$	−1.88787e7	−1.22552
$751$	−5.66758e6	−0.366689	−0.183344	−	0.983049i	$-0.558692\pi$
$751$	−5.66758e6	−0.366689	−0.183344	+	0.983049i	$0.558692\pi$
$752$	−2.94840e6	−0.190126
$753$	−2.66147e7	−1.71055
$754$	−2.38547e7	−1.52808
$755$	3.06128e7	1.95450
$756$	−3.10620e6	−0.197663
$757$	−2.33218e7	−1.47918	−0.739592	−	0.673056i	$-0.764981\pi$
$757$	−2.33218e7	−1.47918	−0.739592	+	0.673056i	$0.764981\pi$
$758$	1.54148e7	0.974465
$759$	−63063.3	−0.00397349
$760$	−1.00553e6	−0.0631481
$761$	1.56059e7	0.976846	0.488423	−	0.872607i	$-0.337572\pi$
$761$	1.56059e7	0.976846	0.488423	+	0.872607i	$0.337572\pi$
$762$	−1.09419e7	−0.682663
$763$	−151787.	−0.00943896
$764$	750179.	0.0464977
$765$	−2.99456e6	−0.185003
$766$	4.83505e6	0.297735
$767$	−2.32601e7	−1.42766
$768$	1.72927e7	1.05794
$769$	−1.36055e7	−0.829657	−0.414828	−	0.909900i	$-0.636158\pi$
$769$	−1.36055e7	−0.829657	−0.414828	+	0.909900i	$0.636158\pi$
$770$	55299.4	0.00336120
$771$	1.77089e6	0.107289
$772$	2.25361e6	0.136093
$773$	−1.46811e7	−0.883711	−0.441855	−	0.897086i	$-0.645680\pi$
$773$	−1.46811e7	−0.883711	−0.441855	+	0.897086i	$0.645680\pi$
$774$	−5.72516e6	−0.343507
$775$	−2.48037e6	−0.148341
$776$	−2.22376e6	−0.132567
$777$	6.43041e6	0.382108
$778$	4.40826e7	2.61107
$779$	1.74634e6	0.103106
$780$	−1.88732e7	−1.11073
$781$	15506.1	0.000909651 0
$782$	4.08882e6	0.239101
$783$	−1.66394e7	−0.969914
$784$	1.49874e7	0.870837
$785$	−1.21123e7	−0.701537
$786$	5.58078e7	3.22210
$787$	1.01553e6	0.0584459	0.0292230	−	0.999573i	$-0.490697\pi$
$787$	1.01553e6	0.0584459	0.0292230	+	0.999573i	$0.490697\pi$
$788$	−1.43123e7	−0.821095
$789$	8.29685e6	0.474483
$790$	2.46787e7	1.40687
$791$	−6.66435e6	−0.378718
$792$	−4255.64	−0.000241075 0
$793$	9.67428e6	0.546306
$794$	1.70128e7	0.957692
$795$	3.45252e6	0.193739
$796$	897252.	0.0501917
$797$	−8.64329e6	−0.481985	−0.240992	−	0.970527i	$-0.577473\pi$
$797$	−8.64329e6	−0.481985	−0.240992	+	0.970527i	$0.577473\pi$
$798$	5.90122e6	0.328046
$799$	1.31214e6	0.0727131
$800$	1.02328e7	0.565289
$801$	1.14154e7	0.628654
$802$	−1.95451e7	−1.07301
$803$	−148989.	−0.00815390
$804$	2.22718e7	1.21511
$805$	2.78061e6	0.151234
$806$	7.38320e6	0.400320
$807$	−9.05669e6	−0.489537
$808$	2.35400e6	0.126846
$809$	−2.74211e7	−1.47304	−0.736519	−	0.676417i	$-0.763532\pi$
$809$	−2.74211e7	−1.47304	−0.736519	+	0.676417i	$0.763532\pi$
$810$	−3.93817e7	−2.10903
$811$	6.65865e6	0.355495	0.177748	−	0.984076i	$-0.443119\pi$
$811$	6.65865e6	0.355495	0.177748	+	0.984076i	$0.443119\pi$
$812$	7.84523e6	0.417557
$813$	6.77050e6	0.359248
$814$	−224048.	−0.0118517
$815$	−4.38984e7	−2.31502
$816$	−7.74805e6	−0.407350
$817$	−7.27319e6	−0.381215
$818$	4.19649e7	2.19282
$819$	1.71825e6	0.0895109
$820$	3.57950e6	0.185903
$821$	2.40462e7	1.24506	0.622528	−	0.782597i	$-0.286105\pi$
$821$	2.40462e7	1.24506	0.622528	+	0.782597i	$0.286105\pi$
$822$	4.80893e7	2.48238
$823$	−2.64199e7	−1.35967	−0.679833	−	0.733367i	$-0.737948\pi$
$823$	−2.64199e7	−1.35967	−0.679833	+	0.733367i	$0.737948\pi$
$824$	−2.40796e6	−0.123547
$825$	66432.8	0.00339819
$826$	1.49074e7	0.760242
$827$	−1.19287e7	−0.606497	−0.303248	−	0.952912i	$-0.598071\pi$
$827$	−1.19287e7	−0.606497	−0.303248	+	0.952912i	$0.598071\pi$
$828$	−4.17606e6	−0.211685
$829$	5.39739e6	0.272771	0.136385	−	0.990656i	$-0.456451\pi$
$829$	5.39739e6	0.272771	0.136385	+	0.990656i	$0.456451\pi$
$830$	−3.90966e7	−1.96990
$831$	−438814.	−0.0220434
$832$	−1.64335e7	−0.823043
$833$	−6.66992e6	−0.333049
$834$	5.18946e6	0.258349
$835$	1.28221e7	0.636418
$836$	−105508.	−0.00522119
$837$	5.15001e6	0.254094
$838$	−1.34311e7	−0.660696
$839$	2.43729e7	1.19537	0.597685	−	0.801731i	$-0.296087\pi$
$839$	2.43729e7	1.19537	0.597685	+	0.801731i	$0.296087\pi$
$840$	619801.	0.0303078
$841$	2.15144e7	1.04891
$842$	−4.21822e7	−2.05045
$843$	−4.06506e7	−1.97014
$844$	−8.45072e6	−0.408355
$845$	1.09154e7	0.525893
$846$	−2.61160e6	−0.125453
$847$	−5.77824e6	−0.276750
$848$	2.70441e6	0.129146
$849$	4.80391e6	0.228731
$850$	−4.30729e6	−0.204483
$851$	−1.12657e7	−0.533256
$852$	3.39169e6	0.160073
$853$	−1.43940e7	−0.677342	−0.338671	−	0.940905i	$-0.609977\pi$
$853$	−1.43940e7	−0.677342	−0.338671	+	0.940905i	$0.609977\pi$
$854$	−6.20024e6	−0.290913
$855$	7.57176e6	0.354227
$856$	−727275.	−0.0339246
$857$	−2.60195e6	−0.121017	−0.0605086	−	0.998168i	$-0.519272\pi$
$857$	−2.60195e6	−0.121017	−0.0605086	+	0.998168i	$0.519272\pi$
$858$	−197748.	−0.00917050
$859$	−1.59609e7	−0.738029	−0.369014	−	0.929424i	$-0.620305\pi$
$859$	−1.59609e7	−0.738029	−0.369014	+	0.929424i	$0.620305\pi$
$860$	−1.49080e7	−0.687341
$861$	−1.07643e6	−0.0494856
$862$	−1.82997e6	−0.0838833
$863$	−9.15557e6	−0.418464	−0.209232	−	0.977866i	$-0.567096\pi$
$863$	−9.15557e6	−0.418464	−0.209232	+	0.977866i	$0.567096\pi$
$864$	−2.12465e7	−0.968287
$865$	3.24088e7	1.47273
$866$	−8.24547e6	−0.373612
$867$	−2.30583e7	−1.04179
$868$	−2.42815e6	−0.109390
$869$	132687.	0.00596047
$870$	6.47952e7	2.90232
$871$	1.60545e7	0.717052
$872$	59274.6	0.00263984
$873$	1.67452e7	0.743627
$874$	−1.03386e7	−0.457808
$875$	4.47552e6	0.197617
$876$	−3.25888e7	−1.43485
$877$	−3.57910e6	−0.157136	−0.0785679	−	0.996909i	$-0.525035\pi$
$877$	−3.57910e6	−0.157136	−0.0785679	+	0.996909i	$0.525035\pi$
$878$	4.96694e7	2.17447
$879$	2.32998e7	1.01714
$880$	183585.	0.00799152
$881$	−2.76944e7	−1.20213	−0.601065	−	0.799200i	$-0.705257\pi$
$881$	−2.76944e7	−1.20213	−0.601065	+	0.799200i	$0.705257\pi$
$882$	1.32754e7	0.574613
$883$	−1.63016e7	−0.703605	−0.351803	−	0.936074i	$-0.614431\pi$
$883$	−1.63016e7	−0.703605	−0.351803	+	0.936074i	$0.614431\pi$
$884$	6.57922e6	0.283168
$885$	6.31802e7	2.71158
$886$	−5.58045e7	−2.38828
$887$	−2.61670e7	−1.11672	−0.558361	−	0.829598i	$-0.688570\pi$
$887$	−2.61670e7	−1.11672	−0.558361	+	0.829598i	$0.688570\pi$
$888$	−2.51115e6	−0.106866
$889$	2.59397e6	0.110081
$890$	5.79271e7	2.45136
$891$	−211740.	−0.00893528
$892$	−3.78311e7	−1.59198
$893$	−3.31775e6	−0.139224
$894$	1.51989e7	0.636015
$895$	1.52369e7	0.635826
$896$	1.02811e6	0.0427827
$897$	−9.94330e6	−0.412619
$898$	−1.18912e7	−0.492077
$899$	−1.30072e7	−0.536766
$900$	4.39919e6	0.181037
$901$	−1.20355e6	−0.0493916
$902$	37504.9	0.00153487
$903$	4.48315e6	0.182963
$904$	2.60250e6	0.105918
$905$	3.86313e7	1.56790
$906$	7.01591e7	2.83964
$907$	1.11300e7	0.449237	0.224619	−	0.974447i	$-0.427886\pi$
$907$	1.11300e7	0.449237	0.224619	+	0.974447i	$0.427886\pi$
$908$	−2.38354e6	−0.0959417
$909$	−1.77259e7	−0.711540
$910$	8.71916e6	0.349037
$911$	−1.01072e7	−0.403493	−0.201747	−	0.979438i	$-0.564662\pi$
$911$	−1.01072e7	−0.403493	−0.201747	+	0.979438i	$0.564662\pi$
$912$	1.95910e7	0.779956
$913$	−210207.	−0.00834585
$914$	−2.52249e7	−0.998766
$915$	−2.62777e7	−1.03761
$916$	−2.38397e7	−0.938774
$917$	−1.32302e7	−0.519569
$918$	8.94327e6	0.350259
$919$	−1.29271e7	−0.504907	−0.252453	−	0.967609i	$-0.581237\pi$
$919$	−1.29271e7	−0.504907	−0.252453	+	0.967609i	$0.581237\pi$
$920$	−1.08586e6	−0.0422964
$921$	−4.13149e7	−1.60494
$922$	−2.62638e7	−1.01749
$923$	2.44487e6	0.0944609
$924$	65034.4	0.00250590
$925$	1.18677e7	0.456049
$926$	−2.74608e7	−1.05241
$927$	1.81323e7	0.693032
$928$	5.36617e7	2.04548
$929$	−3.32136e7	−1.26263	−0.631316	−	0.775525i	$-0.717485\pi$
$929$	−3.32136e7	−1.26263	−0.631316	+	0.775525i	$0.717485\pi$
$930$	−2.00546e7	−0.760337
$931$	1.68649e7	0.637691
$932$	1.75930e7	0.663437
$933$	−6.17615e7	−2.32281
$934$	2.74885e7	1.03106
$935$	−81701.4	−0.00305633
$936$	−670994.	−0.0250339
$937$	1.08647e7	0.404268	0.202134	−	0.979358i	$-0.435212\pi$
$937$	1.08647e7	0.404268	0.202134	+	0.979358i	$0.435212\pi$
$938$	−1.02893e7	−0.381837
$939$	−1.58939e6	−0.0588258
$940$	−6.80044e6	−0.251025
$941$	−4.32555e7	−1.59246	−0.796228	−	0.604997i	$-0.793174\pi$
$941$	−4.32555e7	−1.59246	−0.796228	+	0.604997i	$0.793174\pi$
$942$	−2.77591e7	−1.01924
$943$	1.88585e6	0.0690603
$944$	4.94900e7	1.80754
$945$	6.08189e6	0.221543
$946$	−156201.	−0.00567488
$947$	1.59967e7	0.579635	0.289818	−	0.957082i	$-0.406405\pi$
$947$	1.59967e7	0.579635	0.289818	+	0.957082i	$0.406405\pi$
$948$	2.90231e7	1.04887
$949$	−2.34914e7	−0.846725
$950$	1.08910e7	0.391525
$951$	−2.03518e7	−0.729713
$952$	−216064.	−0.00772662
$953$	3.49936e7	1.24812	0.624060	−	0.781376i	$-0.285482\pi$
$953$	3.49936e7	1.24812	0.624060	+	0.781376i	$0.285482\pi$
$954$	2.39548e6	0.0852160
$955$	−1.46884e6	−0.0521153
$956$	−2.97357e7	−1.05229
$957$	348378.	0.0122962
$958$	6.05598e7	2.13192
$959$	−1.14004e7	−0.400289
$960$	4.46375e7	1.56323
$961$	−2.46033e7	−0.859380
$962$	−3.53260e7	−1.23071
$963$	5.47647e6	0.190299
$964$	−5.88227e6	−0.203870
$965$	−4.41254e6	−0.152535
$966$	6.37265e6	0.219724
$967$	4.00687e6	0.137797	0.0688984	−	0.997624i	$-0.478052\pi$
$967$	4.00687e6	0.137797	0.0688984	+	0.997624i	$0.478052\pi$
$968$	2.25647e6	0.0773999
$969$	−8.71868e6	−0.298292
$970$	8.49728e7	2.89968
$971$	2.35829e7	0.802691	0.401345	−	0.915927i	$-0.368543\pi$
$971$	2.35829e7	0.802691	0.401345	+	0.915927i	$0.368543\pi$
$972$	−2.52776e7	−0.858163
$973$	−1.23025e6	−0.0416593
$974$	−4.41669e7	−1.49176
$975$	1.04746e7	0.352878
$976$	−2.05837e7	−0.691670
$977$	−2.26595e7	−0.759477	−0.379738	−	0.925094i	$-0.623986\pi$
$977$	−2.26595e7	−0.759477	−0.379738	+	0.925094i	$0.623986\pi$
$978$	−1.00607e8	−3.36343
$979$	311451.	0.0103856
$980$	3.45683e7	1.14977
$981$	−446345.	−0.0148081
$982$	−1.40639e7	−0.465401
$983$	−3.46232e7	−1.14283	−0.571417	−	0.820660i	$-0.693606\pi$
$983$	−3.46232e7	−1.14283	−0.571417	+	0.820660i	$0.693606\pi$
$984$	420358.	0.0138399
$985$	2.80232e7	0.920295
$986$	−2.25877e7	−0.739912
$987$	2.04504e6	0.0668203
$988$	−1.66356e7	−0.542184
$989$	−7.85423e6	−0.255337
$990$	162613.	0.00527313
$991$	−2.37811e7	−0.769215	−0.384608	−	0.923080i	$-0.625663\pi$
$991$	−2.37811e7	−0.769215	−0.384608	+	0.923080i	$0.625663\pi$
$992$	−1.66087e7	−0.535865
$993$	6.94670e7	2.23566
$994$	−1.56692e6	−0.0503014
$995$	−1.75680e6	−0.0562556
$996$	−4.59792e7	−1.46863
$997$	−3.66617e7	−1.16809	−0.584043	−	0.811723i	$-0.698530\pi$
$997$	−3.66617e7	−1.16809	−0.584043	+	0.811723i	$0.698530\pi$
$998$	−4.80832e7	−1.52815
$999$	−2.46410e7	−0.781168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.a.1.20	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.a.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-8.10730 q^{2} +18.6684 q^{3} +33.7283 q^{4} -66.0394 q^{5} -151.350 q^{6} +35.8802 q^{7} -14.0116 q^{8} +105.509 q^{9} +O(q^{10})\)	\(q-8.10730 q^{2} +18.6684 q^{3} +33.7283 q^{4} -66.0394 q^{5} -151.350 q^{6} +35.8802 q^{7} -14.0116 q^{8} +105.509 q^{9} +535.401 q^{10} +2.87864 q^{11} +629.653 q^{12} +453.880 q^{13} -290.891 q^{14} -1232.85 q^{15} -965.708 q^{16} +429.773 q^{17} -855.394 q^{18} -1086.69 q^{19} -2227.39 q^{20} +669.825 q^{21} -23.3380 q^{22} -1173.50 q^{23} -261.574 q^{24} +1236.20 q^{25} -3679.74 q^{26} -2566.73 q^{27} +1210.18 q^{28} +6482.71 q^{29} +9995.08 q^{30} -2006.45 q^{31} +8277.66 q^{32} +53.7396 q^{33} -3484.30 q^{34} -2369.50 q^{35} +3558.64 q^{36} +9600.13 q^{37} +8810.08 q^{38} +8473.21 q^{39} +925.317 q^{40} -1607.03 q^{41} -5430.47 q^{42} +6693.01 q^{43} +97.0915 q^{44} -6967.76 q^{45} +9513.90 q^{46} +3053.09 q^{47} -18028.2 q^{48} -15519.6 q^{49} -10022.2 q^{50} +8023.18 q^{51} +15308.6 q^{52} -2800.44 q^{53} +20809.3 q^{54} -190.104 q^{55} -502.739 q^{56} -20286.7 q^{57} -52557.3 q^{58} -51247.3 q^{59} -41581.9 q^{60} +21314.6 q^{61} +16266.8 q^{62} +3785.69 q^{63} -36206.8 q^{64} -29974.0 q^{65} -435.683 q^{66} +35371.6 q^{67} +14495.5 q^{68} -21907.3 q^{69} +19210.3 q^{70} +5386.61 q^{71} -1478.35 q^{72} -51756.8 q^{73} -77831.1 q^{74} +23077.9 q^{75} -36652.0 q^{76} +103.286 q^{77} -68694.9 q^{78} +46093.8 q^{79} +63774.8 q^{80} -73555.5 q^{81} +13028.7 q^{82} -73023.1 q^{83} +22592.1 q^{84} -28382.0 q^{85} -54262.2 q^{86} +121022. q^{87} -40.3343 q^{88} +108194. q^{89} +56489.7 q^{90} +16285.3 q^{91} -39580.1 q^{92} -37457.1 q^{93} -24752.3 q^{94} +71764.0 q^{95} +154531. q^{96} +158709. q^{97} +125822. q^{98} +303.723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) \) 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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