LMFDB - Embedded newform 547.6.a.a.1.15

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			1.15
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)

$f(q)$	$=$	$q-8.79797 q^{2} -13.8260 q^{3} +45.4043 q^{4} -43.4417 q^{5} +121.641 q^{6} -186.463 q^{7} -117.931 q^{8} -51.8414 q^{9} +O(q^{10})$	\(q-8.79797 q^{2} -13.8260 q^{3} +45.4043 q^{4} -43.4417 q^{5} +121.641 q^{6} -186.463 q^{7} -117.931 q^{8} -51.8414 q^{9} +382.199 q^{10} -551.979 q^{11} -627.760 q^{12} +407.053 q^{13} +1640.50 q^{14} +600.625 q^{15} -415.386 q^{16} -565.793 q^{17} +456.100 q^{18} -1631.94 q^{19} -1972.44 q^{20} +2578.04 q^{21} +4856.29 q^{22} +1574.40 q^{23} +1630.51 q^{24} -1237.82 q^{25} -3581.24 q^{26} +4076.48 q^{27} -8466.22 q^{28} -4102.84 q^{29} -5284.28 q^{30} +2450.32 q^{31} +7428.34 q^{32} +7631.66 q^{33} +4977.83 q^{34} +8100.26 q^{35} -2353.82 q^{36} +5272.67 q^{37} +14357.8 q^{38} -5627.92 q^{39} +5123.11 q^{40} -6251.37 q^{41} -22681.5 q^{42} -16417.4 q^{43} -25062.2 q^{44} +2252.08 q^{45} -13851.5 q^{46} -26001.1 q^{47} +5743.14 q^{48} +17961.4 q^{49} +10890.3 q^{50} +7822.66 q^{51} +18482.0 q^{52} -481.576 q^{53} -35864.8 q^{54} +23978.9 q^{55} +21989.7 q^{56} +22563.2 q^{57} +36096.6 q^{58} +48308.2 q^{59} +27271.0 q^{60} +56329.1 q^{61} -21557.8 q^{62} +9666.51 q^{63} -52062.0 q^{64} -17683.1 q^{65} -67143.1 q^{66} +28986.6 q^{67} -25689.5 q^{68} -21767.7 q^{69} -71265.9 q^{70} +51188.4 q^{71} +6113.70 q^{72} -31587.1 q^{73} -46388.8 q^{74} +17114.1 q^{75} -74097.1 q^{76} +102924. q^{77} +49514.3 q^{78} +69518.0 q^{79} +18045.1 q^{80} -43764.0 q^{81} +54999.4 q^{82} +91479.7 q^{83} +117054. q^{84} +24579.0 q^{85} +144440. q^{86} +56725.8 q^{87} +65095.3 q^{88} -58076.5 q^{89} -19813.7 q^{90} -75900.3 q^{91} +71484.5 q^{92} -33878.1 q^{93} +228757. q^{94} +70894.2 q^{95} -102704. q^{96} +115486. q^{97} -158024. q^{98} +28615.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.79797	−1.55528	−0.777638	−	0.628712i	$-0.783582\pi$
$2$	−8.79797	−1.55528	−0.777638	+	0.628712i	$0.783582\pi$
$3$	−13.8260	−0.886939	−0.443469	−	0.896289i	$-0.646253\pi$
$3$	−13.8260	−0.886939	−0.443469	+	0.896289i	$0.646253\pi$
$4$	45.4043	1.41888
$5$	−43.4417	−0.777108	−0.388554	−	0.921426i	$-0.627025\pi$
$5$	−43.4417	−0.777108	−0.388554	+	0.921426i	$0.627025\pi$
$6$	121.641	1.37944
$7$	−186.463	−1.43829	−0.719147	−	0.694858i	$-0.755467\pi$
$7$	−186.463	−1.43829	−0.719147	+	0.694858i	$0.755467\pi$
$8$	−117.931	−0.651482
$9$	−51.8414	−0.213339
$10$	382.199	1.20862
$11$	−551.979	−1.37544	−0.687718	−	0.725978i	$-0.741388\pi$
$11$	−551.979	−1.37544	−0.687718	+	0.725978i	$0.741388\pi$
$12$	−627.760	−1.25846
$13$	407.053	0.668025	0.334012	−	0.942569i	$-0.391597\pi$
$13$	407.053	0.668025	0.334012	+	0.942569i	$0.391597\pi$
$14$	1640.50	2.23694
$15$	600.625	0.689248
$16$	−415.386	−0.405651
$17$	−565.793	−0.474827	−0.237414	−	0.971409i	$-0.576300\pi$
$17$	−565.793	−0.474827	−0.237414	+	0.971409i	$0.576300\pi$
$18$	456.100	0.331802
$19$	−1631.94	−1.03710	−0.518549	−	0.855048i	$-0.673528\pi$
$19$	−1631.94	−1.03710	−0.518549	+	0.855048i	$0.673528\pi$
$20$	−1972.44	−1.10263
$21$	2578.04	1.27568
$22$	4856.29	2.13918
$23$	1574.40	0.620577	0.310288	−	0.950642i	$-0.399574\pi$
$23$	1574.40	0.620577	0.310288	+	0.950642i	$0.399574\pi$
$24$	1630.51	0.577824
$25$	−1237.82	−0.396103
$26$	−3581.24	−1.03896
$27$	4076.48	1.07616
$28$	−8466.22	−2.04077
$29$	−4102.84	−0.905918	−0.452959	−	0.891531i	$-0.649632\pi$
$29$	−4102.84	−0.905918	−0.452959	+	0.891531i	$0.649632\pi$
$30$	−5284.28	−1.07197
$31$	2450.32	0.457950	0.228975	−	0.973432i	$-0.426463\pi$
$31$	2450.32	0.457950	0.228975	+	0.973432i	$0.426463\pi$
$32$	7428.34	1.28238
$33$	7631.66	1.21993
$34$	4977.83	0.738487
$35$	8100.26	1.11771
$36$	−2353.82	−0.302704
$37$	5272.67	0.633179	0.316590	−	0.948563i	$-0.397462\pi$
$37$	5272.67	0.633179	0.316590	+	0.948563i	$0.397462\pi$
$38$	14357.8	1.61297
$39$	−5627.92	−0.592497
$40$	5123.11	0.506272
$41$	−6251.37	−0.580785	−0.290393	−	0.956908i	$-0.593786\pi$
$41$	−6251.37	−0.580785	−0.290393	+	0.956908i	$0.593786\pi$
$42$	−22681.5	−1.98403
$43$	−16417.4	−1.35405	−0.677023	−	0.735961i	$-0.736730\pi$
$43$	−16417.4	−1.35405	−0.677023	+	0.735961i	$0.736730\pi$
$44$	−25062.2	−1.95159
$45$	2252.08	0.165788
$46$	−13851.5	−0.965168
$47$	−26001.1	−1.71691	−0.858453	−	0.512893i	$-0.828574\pi$
$47$	−26001.1	−1.71691	−0.858453	+	0.512893i	$0.828574\pi$
$48$	5743.14	0.359788
$49$	17961.4	1.06869
$50$	10890.3	0.616049
$51$	7822.66	0.421143
$52$	18482.0	0.947850
$53$	−481.576	−0.0235492	−0.0117746	−	0.999931i	$-0.503748\pi$
$53$	−481.576	−0.0235492	−0.0117746	+	0.999931i	$0.503748\pi$
$54$	−35864.8	−1.67372
$55$	23978.9	1.06886
$56$	21989.7	0.937021
$57$	22563.2	0.919843
$58$	36096.6	1.40895
$59$	48308.2	1.80672	0.903360	−	0.428883i	$-0.141093\pi$
$59$	48308.2	1.80672	0.903360	+	0.428883i	$0.141093\pi$
$60$	27271.0	0.977963
$61$	56329.1	1.93824	0.969122	−	0.246581i	$-0.0793072\pi$
$61$	56329.1	1.93824	0.969122	+	0.246581i	$0.0793072\pi$
$62$	−21557.8	−0.712239
$63$	9666.51	0.306844
$64$	−52062.0	−1.58881
$65$	−17683.1	−0.519128
$66$	−67143.1	−1.89733
$67$	28986.6	0.788880	0.394440	−	0.918922i	$-0.370939\pi$
$67$	28986.6	0.788880	0.394440	+	0.918922i	$0.370939\pi$
$68$	−25689.5	−0.673725
$69$	−21767.7	−0.550414
$70$	−71265.9	−1.73835
$71$	51188.4	1.20511	0.602554	−	0.798078i	$-0.294150\pi$
$71$	51188.4	1.20511	0.602554	+	0.798078i	$0.294150\pi$
$72$	6113.70	0.138987
$73$	−31587.1	−0.693748	−0.346874	−	0.937912i	$-0.612757\pi$
$73$	−31587.1	−0.693748	−0.346874	+	0.937912i	$0.612757\pi$
$74$	−46388.8	−0.984769
$75$	17114.1	0.351319
$76$	−74097.1	−1.47152
$77$	102924.	1.97828
$78$	49514.3	0.921497
$79$	69518.0	1.25323	0.626613	−	0.779330i	$-0.284441\pi$
$79$	69518.0	1.25323	0.626613	+	0.779330i	$0.284441\pi$
$80$	18045.1	0.315235
$81$	−43764.0	−0.741147
$82$	54999.4	0.903282
$83$	91479.7	1.45757	0.728785	−	0.684742i	$-0.240085\pi$
$83$	91479.7	1.45757	0.728785	+	0.684742i	$0.240085\pi$
$84$	117054.	1.81004
$85$	24579.0	0.368992
$86$	144440.	2.10592
$87$	56725.8	0.803494
$88$	65095.3	0.896072
$89$	−58076.5	−0.777187	−0.388593	−	0.921409i	$-0.627039\pi$
$89$	−58076.5	−0.777187	−0.388593	+	0.921409i	$0.627039\pi$
$90$	−19813.7	−0.257846
$91$	−75900.3	−0.960816
$92$	71484.5	0.880527
$93$	−33878.1	−0.406174
$94$	228757.	2.67026
$95$	70894.2	0.805938
$96$	−102704.	−1.13739
$97$	115486.	1.24623	0.623117	−	0.782129i	$-0.285866\pi$
$97$	115486.	1.24623	0.623117	+	0.782129i	$0.285866\pi$
$98$	−158024.	−1.66210
$99$	28615.4	0.293435
$100$	−56202.4	−0.562024
$101$	29400.6	0.286782	0.143391	−	0.989666i	$-0.454199\pi$
$101$	29400.6	0.286782	0.143391	+	0.989666i	$0.454199\pi$
$102$	−68823.6	−0.654993
$103$	23920.3	0.222164	0.111082	−	0.993811i	$-0.464568\pi$
$103$	23920.3	0.222164	0.111082	+	0.993811i	$0.464568\pi$
$104$	−48004.1	−0.435206
$105$	−111994.	−0.991340
$106$	4236.89	0.0366255
$107$	−17267.6	−0.145805	−0.0729024	−	0.997339i	$-0.523226\pi$
$107$	−17267.6	−0.145805	−0.0729024	+	0.997339i	$0.523226\pi$
$108$	185090.	1.52694
$109$	−51837.4	−0.417905	−0.208952	−	0.977926i	$-0.567005\pi$
$109$	−51837.4	−0.417905	−0.208952	+	0.977926i	$0.567005\pi$
$110$	−210965.	−1.66238
$111$	−72900.1	−0.561591
$112$	77454.2	0.583445
$113$	−24785.8	−0.182603	−0.0913014	−	0.995823i	$-0.529103\pi$
$113$	−24785.8	−0.182603	−0.0913014	+	0.995823i	$0.529103\pi$
$114$	−198510.	−1.43061
$115$	−68394.6	−0.482255
$116$	−186286.	−1.28539
$117$	−21102.2	−0.142516
$118$	−425014.	−2.80995
$119$	105499.	0.682941
$120$	−70832.2	−0.449032
$121$	143629.	0.891826
$122$	−495582.	−3.01451
$123$	86431.5	0.515121
$124$	111255.	0.649779
$125$	189528.	1.08492
$126$	−85045.7	−0.477228
$127$	178500.	0.982038	0.491019	−	0.871149i	$-0.336625\pi$
$127$	178500.	0.982038	0.491019	+	0.871149i	$0.336625\pi$
$128$	220333.	1.18865
$129$	226987.	1.20096
$130$	155575.	0.807387
$131$	−297397.	−1.51411	−0.757056	−	0.653350i	$-0.773363\pi$
$131$	−297397.	−1.51411	−0.757056	+	0.653350i	$0.773363\pi$
$132$	346510.	1.73094
$133$	304296.	1.49165
$134$	−255024.	−1.22693
$135$	−177089.	−0.836291
$136$	66724.4	0.309341
$137$	−421352.	−1.91798	−0.958988	−	0.283445i	$-0.908523\pi$
$137$	−421352.	−1.91798	−0.958988	+	0.283445i	$0.908523\pi$
$138$	191511.	0.856045
$139$	76325.5	0.335068	0.167534	−	0.985866i	$-0.446420\pi$
$139$	76325.5	0.335068	0.167534	+	0.985866i	$0.446420\pi$
$140$	367787.	1.58590
$141$	359491.	1.52279
$142$	−450354.	−1.87428
$143$	−224685.	−0.918826
$144$	21534.2	0.0865412
$145$	178234.	0.703997
$146$	277902.	1.07897
$147$	−248335.	−0.947860
$148$	239402.	0.898408
$149$	65873.3	0.243077	0.121539	−	0.992587i	$-0.461217\pi$
$149$	65873.3	0.243077	0.121539	+	0.992587i	$0.461217\pi$
$150$	−150570.	−0.546398
$151$	123394.	0.440404	0.220202	−	0.975454i	$-0.429328\pi$
$151$	123394.	0.440404	0.220202	+	0.975454i	$0.429328\pi$
$152$	192456.	0.675651
$153$	29331.5	0.101299
$154$	−905519.	−3.07677
$155$	−106446.	−0.355877
$156$	−255532.	−0.840685
$157$	−94544.3	−0.306116	−0.153058	−	0.988217i	$-0.548912\pi$
$157$	−94544.3	−0.306116	−0.153058	+	0.988217i	$0.548912\pi$
$158$	−611617.	−1.94911
$159$	6658.28	0.0208867
$160$	−322700.	−0.996549
$161$	−293567.	−0.892571
$162$	385034.	1.15269
$163$	−61355.3	−0.180877	−0.0904384	−	0.995902i	$-0.528827\pi$
$163$	−61355.3	−0.180877	−0.0904384	+	0.995902i	$0.528827\pi$
$164$	−283839.	−0.824068
$165$	−331532.	−0.948016
$166$	−804836.	−2.26692
$167$	73977.2	0.205261	0.102631	−	0.994720i	$-0.467274\pi$
$167$	73977.2	0.205261	0.102631	+	0.994720i	$0.467274\pi$
$168$	−304030.	−0.831081
$169$	−205601.	−0.553743
$170$	−216245.	−0.573885
$171$	84602.1	0.221254
$172$	−745422.	−1.92124
$173$	−278824.	−0.708297	−0.354148	−	0.935189i	$-0.615229\pi$
$173$	−278824.	−0.708297	−0.354148	+	0.935189i	$0.615229\pi$
$174$	−499072.	−1.24966
$175$	230808.	0.569712
$176$	229284.	0.557947
$177$	−667910.	−1.60245
$178$	510955.	1.20874
$179$	37481.1	0.0874338	0.0437169	−	0.999044i	$-0.486080\pi$
$179$	37481.1	0.0874338	0.0437169	+	0.999044i	$0.486080\pi$
$180$	102254.	0.235234
$181$	121276.	0.275155	0.137577	−	0.990491i	$-0.456068\pi$
$181$	121276.	0.275155	0.137577	+	0.990491i	$0.456068\pi$
$182$	667769.	1.49433
$183$	−778807.	−1.71910
$184$	−185670.	−0.404294
$185$	−229054.	−0.492049
$186$	298059.	0.631713
$187$	312306.	0.653094
$188$	−1.18056e6	−2.43609
$189$	−760113.	−1.54783
$190$	−623725.	−1.25346
$191$	149374.	0.296272	0.148136	−	0.988967i	$-0.452673\pi$
$191$	149374.	0.296272	0.148136	+	0.988967i	$0.452673\pi$
$192$	719810.	1.40917
$193$	63152.6	0.122039	0.0610194	−	0.998137i	$-0.480565\pi$
$193$	63152.6	0.122039	0.0610194	+	0.998137i	$0.480565\pi$
$194$	−1.01604e6	−1.93824
$195$	244486.	0.460435
$196$	815526.	1.51634
$197$	−351878.	−0.645991	−0.322996	−	0.946400i	$-0.604690\pi$
$197$	−351878.	−0.645991	−0.322996	+	0.946400i	$0.604690\pi$
$198$	−251757.	−0.456372
$199$	−879316.	−1.57403	−0.787013	−	0.616936i	$-0.788374\pi$
$199$	−879316.	−1.57403	−0.787013	+	0.616936i	$0.788374\pi$
$200$	145977.	0.258054
$201$	−400770.	−0.699688
$202$	−258666.	−0.446026
$203$	765027.	1.30298
$204$	355183.	0.597553
$205$	271570.	0.451333
$206$	−210450.	−0.345527
$207$	−81619.1	−0.132393
$208$	−169084.	−0.270985
$209$	900796.	1.42646
$210$	985323.	1.54181
$211$	72006.2	0.111343	0.0556716	−	0.998449i	$-0.482270\pi$
$211$	72006.2	0.111343	0.0556716	+	0.998449i	$0.482270\pi$
$212$	−21865.6	−0.0334135
$213$	−707732.	−1.06886
$214$	151920.	0.226767
$215$	713200.	1.05224
$216$	−480742.	−0.701097
$217$	−456894.	−0.658667
$218$	456064.	0.649957
$219$	436723.	0.615312
$220$	1.08874e6	1.51659
$221$	−230308.	−0.317196
$222$	641373.	0.873430
$223$	598812.	0.806359	0.403179	−	0.915121i	$-0.367905\pi$
$223$	598812.	0.806359	0.403179	+	0.915121i	$0.367905\pi$
$224$	−1.38511e6	−1.84444
$225$	64170.4	0.0845043
$226$	218065.	0.283998
$227$	335000.	0.431499	0.215750	−	0.976449i	$-0.430781\pi$
$227$	335000.	0.431499	0.215750	+	0.976449i	$0.430781\pi$
$228$	1.02447e6	1.30515
$229$	−679999.	−0.856879	−0.428440	−	0.903570i	$-0.640937\pi$
$229$	−679999.	−0.856879	−0.428440	+	0.903570i	$0.640937\pi$
$230$	601733.	0.750040
$231$	−1.42302e6	−1.75461
$232$	483850.	0.590189
$233$	−911115.	−1.09947	−0.549735	−	0.835339i	$-0.685271\pi$
$233$	−911115.	−1.09947	−0.549735	+	0.835339i	$0.685271\pi$
$234$	185657.	0.221652
$235$	1.12953e6	1.33422
$236$	2.19340e6	2.56353
$237$	−961157.	−1.11154
$238$	−928181.	−1.06216
$239$	−1.15484e6	−1.30775	−0.653877	−	0.756601i	$-0.726859\pi$
$239$	−1.15484e6	−1.30775	−0.653877	+	0.756601i	$0.726859\pi$
$240$	−249491.	−0.279594
$241$	1.29738e6	1.43888	0.719441	−	0.694554i	$-0.244398\pi$
$241$	1.29738e6	1.43888	0.719441	+	0.694554i	$0.244398\pi$
$242$	−1.26365e6	−1.38704
$243$	−385503.	−0.418806
$244$	2.55759e6	2.75015
$245$	−780274.	−0.830486
$246$	−760422.	−0.801156
$247$	−664286.	−0.692808
$248$	−288968.	−0.298346
$249$	−1.26480e6	−1.29278
$250$	−1.66746e6	−1.68736
$251$	125137.	0.125372	0.0626861	−	0.998033i	$-0.480033\pi$
$251$	125137.	0.125372	0.0626861	+	0.998033i	$0.480033\pi$
$252$	438901.	0.435377
$253$	−869035.	−0.853564
$254$	−1.57044e6	−1.52734
$255$	−339830.	−0.327273
$256$	−272499.	−0.259876
$257$	−912599.	−0.861881	−0.430940	−	0.902380i	$-0.641818\pi$
$257$	−912599.	−0.861881	−0.430940	+	0.902380i	$0.641818\pi$
$258$	−1.99703e6	−1.86782
$259$	−983158.	−0.910697
$260$	−802887.	−0.736582
$261$	212697.	0.193268
$262$	2.61649e6	2.35486
$263$	1.06655e6	0.950809	0.475404	−	0.879767i	$-0.342302\pi$
$263$	1.06655e6	0.950809	0.475404	+	0.879767i	$0.342302\pi$
$264$	−900008.	−0.794761
$265$	20920.5	0.0183002
$266$	−2.67719e6	−2.31993
$267$	802966.	0.689317
$268$	1.31612e6	1.11933
$269$	902434.	0.760387	0.380193	−	0.924907i	$-0.375857\pi$
$269$	902434.	0.760387	0.380193	+	0.924907i	$0.375857\pi$
$270$	1.55803e6	1.30066
$271$	1.75695e6	1.45324	0.726619	−	0.687041i	$-0.241091\pi$
$271$	1.75695e6	1.45324	0.726619	+	0.687041i	$0.241091\pi$
$272$	235023.	0.192614
$273$	1.04940e6	0.852185
$274$	3.70704e6	2.98298
$275$	683251.	0.544814
$276$	−988346.	−0.780973
$277$	−1.13717e6	−0.890487	−0.445244	−	0.895409i	$-0.646883\pi$
$277$	−1.13717e6	−0.890487	−0.445244	+	0.895409i	$0.646883\pi$
$278$	−671510.	−0.521123
$279$	−127028.	−0.0976988
$280$	−955270.	−0.728167
$281$	−1.40232e6	−1.05945	−0.529726	−	0.848169i	$-0.677705\pi$
$281$	−1.40232e6	−1.05945	−0.529726	+	0.848169i	$0.677705\pi$
$282$	−3.16279e6	−2.36836
$283$	2.31818e6	1.72060	0.860301	−	0.509787i	$-0.170276\pi$
$283$	2.31818e6	1.72060	0.860301	+	0.509787i	$0.170276\pi$
$284$	2.32418e6	1.70991
$285$	−980184.	−0.714818
$286$	1.97677e6	1.42903
$287$	1.16565e6	0.835340
$288$	−385096.	−0.273582
$289$	−1.09973e6	−0.774539
$290$	−1.56810e6	−1.09491
$291$	−1.59671e6	−1.10533
$292$	−1.43419e6	−0.984349
$293$	1.01419e6	0.690158	0.345079	−	0.938574i	$-0.387852\pi$
$293$	1.01419e6	0.690158	0.345079	+	0.938574i	$0.387852\pi$
$294$	2.18484e6	1.47418
$295$	−2.09859e6	−1.40402
$296$	−621811.	−0.412505
$297$	−2.25013e6	−1.48019
$298$	−579552.	−0.378052
$299$	640864.	0.414561
$300$	777055.	0.498481
$301$	3.06124e6	1.94752
$302$	−1.08562e6	−0.684950
$303$	−406493.	−0.254358
$304$	677885.	0.420700
$305$	−2.44703e6	−1.50623
$306$	−258058.	−0.157548
$307$	−3.19700e6	−1.93596	−0.967980	−	0.251026i	$-0.919232\pi$
$307$	−3.19700e6	−1.93596	−0.967980	+	0.251026i	$0.919232\pi$
$308$	4.67317e6	2.80695
$309$	−330723.	−0.197046
$310$	936508.	0.553487
$311$	2.27674e6	1.33479	0.667394	−	0.744704i	$-0.267410\pi$
$311$	2.27674e6	1.33479	0.667394	+	0.744704i	$0.267410\pi$
$312$	663705.	0.386001
$313$	−242283.	−0.139786	−0.0698928	−	0.997555i	$-0.522266\pi$
$313$	−242283.	−0.139786	−0.0698928	+	0.997555i	$0.522266\pi$
$314$	831798.	0.476095
$315$	−419929.	−0.238451
$316$	3.15642e6	1.77818
$317$	−1.83573e6	−1.02603	−0.513017	−	0.858379i	$-0.671472\pi$
$317$	−1.83573e6	−1.02603	−0.513017	+	0.858379i	$0.671472\pi$
$318$	−58579.3	−0.0324845
$319$	2.26468e6	1.24603
$320$	2.26166e6	1.23467
$321$	238742.	0.129320
$322$	2.58280e6	1.38819
$323$	923340.	0.492442
$324$	−1.98707e6	−1.05160
$325$	−503859.	−0.264607
$326$	539802.	0.281313
$327$	716705.	0.370656
$328$	737229.	0.378371
$329$	4.84823e6	2.46941
$330$	2.91681e6	1.47443
$331$	1.95085e6	0.978708	0.489354	−	0.872085i	$-0.337233\pi$
$331$	1.95085e6	0.978708	0.489354	+	0.872085i	$0.337233\pi$
$332$	4.15357e6	2.06812
$333$	−273343.	−0.135082
$334$	−650849.	−0.319238
$335$	−1.25923e6	−0.613045
$336$	−1.07088e6	−0.517480
$337$	2.21967e6	1.06467	0.532334	−	0.846535i	$-0.321315\pi$
$337$	2.21967e6	1.06467	0.532334	+	0.846535i	$0.321315\pi$
$338$	1.80887e6	0.861223
$339$	342689.	0.161958
$340$	1.11599e6	0.523557
$341$	−1.35252e6	−0.629881
$342$	−744327.	−0.344111
$343$	−215257.	−0.0987922
$344$	1.93612e6	0.882137
$345$	945624.	0.427731
$346$	2.45309e6	1.10160
$347$	−3.34622e6	−1.49187	−0.745934	−	0.666020i	$-0.767997\pi$
$347$	−3.34622e6	−1.49187	−0.745934	+	0.666020i	$0.767997\pi$
$348$	2.57560e6	1.14007
$349$	4.29684e6	1.88837	0.944183	−	0.329422i	$-0.106854\pi$
$349$	4.29684e6	1.88837	0.944183	+	0.329422i	$0.106854\pi$
$350$	−2.03064e6	−0.886060
$351$	1.65934e6	0.718900
$352$	−4.10029e6	−1.76383
$353$	−2.01321e6	−0.859909	−0.429954	−	0.902851i	$-0.641470\pi$
$353$	−2.01321e6	−0.859909	−0.429954	+	0.902851i	$0.641470\pi$
$354$	5.87625e6	2.49225
$355$	−2.22371e6	−0.936499
$356$	−2.63692e6	−1.10274
$357$	−1.45864e6	−0.605727
$358$	−329757.	−0.135984
$359$	1.47513e6	0.604078	0.302039	−	0.953296i	$-0.402333\pi$
$359$	1.47513e6	0.604078	0.302039	+	0.953296i	$0.402333\pi$
$360$	−265589.	−0.108008
$361$	187127.	0.0755734
$362$	−1.06698e6	−0.427942
$363$	−1.98582e6	−0.790995
$364$	−3.44620e6	−1.36329
$365$	1.37219e6	0.539118
$366$	6.85192e6	2.67368
$367$	1.72663e6	0.669166	0.334583	−	0.942366i	$-0.391405\pi$
$367$	1.72663e6	0.669166	0.334583	+	0.942366i	$0.391405\pi$
$368$	−653984.	−0.251737
$369$	324080.	0.123904
$370$	2.01521e6	0.765272
$371$	89796.1	0.0338706
$372$	−1.53821e6	−0.576314
$373$	844176.	0.314167	0.157084	−	0.987585i	$-0.449791\pi$
$373$	844176.	0.314167	0.157084	+	0.987585i	$0.449791\pi$
$374$	−2.74766e6	−1.01574
$375$	−2.62042e6	−0.962260
$376$	3.06632e6	1.11853
$377$	−1.67007e6	−0.605176
$378$	6.68745e6	2.40730
$379$	−1.77398e6	−0.634381	−0.317191	−	0.948362i	$-0.602740\pi$
$379$	−1.77398e6	−0.634381	−0.317191	+	0.948362i	$0.602740\pi$
$380$	3.21890e6	1.14353
$381$	−2.46794e6	−0.871008
$382$	−1.31419e6	−0.460785
$383$	−5.56374e6	−1.93807	−0.969036	−	0.246920i	$-0.920582\pi$
$383$	−5.56374e6	−1.93807	−0.969036	+	0.246920i	$0.920582\pi$
$384$	−3.04633e6	−1.05426
$385$	−4.47117e6	−1.53734
$386$	−555615.	−0.189804
$387$	851103.	0.288871
$388$	5.24356e6	1.76826
$389$	2.19308e6	0.734820	0.367410	−	0.930059i	$-0.380245\pi$
$389$	2.19308e6	0.734820	0.367410	+	0.930059i	$0.380245\pi$
$390$	−2.15098e6	−0.716103
$391$	−890785.	−0.294667
$392$	−2.11820e6	−0.696230
$393$	4.11181e6	1.34293
$394$	3.09581e6	1.00470
$395$	−3.01998e6	−0.973893
$396$	1.29926e6	0.416350
$397$	−4.54141e6	−1.44615	−0.723076	−	0.690768i	$-0.757273\pi$
$397$	−4.54141e6	−1.44615	−0.723076	+	0.690768i	$0.757273\pi$
$398$	7.73619e6	2.44805
$399$	−4.20720e6	−1.32300
$400$	514174.	0.160679
$401$	−3.18373e6	−0.988724	−0.494362	−	0.869256i	$-0.664598\pi$
$401$	−3.18373e6	−0.988724	−0.494362	+	0.869256i	$0.664598\pi$
$402$	3.52596e6	1.08821
$403$	997409.	0.305922
$404$	1.33491e6	0.406911
$405$	1.90118e6	0.575952
$406$	−6.73068e6	−2.02649
$407$	−2.91040e6	−0.870898
$408$	−922533.	−0.274367
$409$	4.19739e6	1.24071	0.620356	−	0.784320i	$-0.286988\pi$
$409$	4.19739e6	1.24071	0.620356	+	0.784320i	$0.286988\pi$
$410$	−2.38927e6	−0.701948
$411$	5.82561e6	1.70113
$412$	1.08609e6	0.315225
$413$	−9.00769e6	−2.59859
$414$	718083.	0.205908
$415$	−3.97403e6	−1.13269
$416$	3.02373e6	0.856662
$417$	−1.05528e6	−0.297185
$418$	−7.92517e6	−2.21854
$419$	−2.97499e6	−0.827847	−0.413924	−	0.910312i	$-0.635842\pi$
$419$	−2.97499e6	−0.827847	−0.413924	+	0.910312i	$0.635842\pi$
$420$	−5.08502e6	−1.40660
$421$	5.57102e6	1.53190	0.765949	−	0.642902i	$-0.222270\pi$
$421$	5.57102e6	1.53190	0.765949	+	0.642902i	$0.222270\pi$
$422$	−633508.	−0.173169
$423$	1.34793e6	0.366283
$424$	56792.7	0.0153418
$425$	700351.	0.188080
$426$	6.22660e6	1.66237
$427$	−1.05033e7	−2.78776
$428$	−784022.	−0.206880
$429$	3.10649e6	0.814942
$430$	−6.27471e6	−1.63653
$431$	5.97410e6	1.54910	0.774550	−	0.632513i	$-0.217976\pi$
$431$	5.97410e6	1.54910	0.774550	+	0.632513i	$0.217976\pi$
$432$	−1.69331e6	−0.436544
$433$	−3.41305e6	−0.874829	−0.437414	−	0.899260i	$-0.644106\pi$
$433$	−3.41305e6	−0.874829	−0.437414	+	0.899260i	$0.644106\pi$
$434$	4.01974e6	1.02441
$435$	−2.46427e6	−0.624402
$436$	−2.35364e6	−0.592959
$437$	−2.56933e6	−0.643599
$438$	−3.84228e6	−0.956981
$439$	3.24277e6	0.803073	0.401536	−	0.915843i	$-0.368476\pi$
$439$	3.24277e6	0.803073	0.401536	+	0.915843i	$0.368476\pi$
$440$	−2.82785e6	−0.696345
$441$	−931146.	−0.227993
$442$	2.02624e6	0.493328
$443$	7.40983e6	1.79390	0.896951	−	0.442129i	$-0.145777\pi$
$443$	7.40983e6	1.79390	0.896951	+	0.442129i	$0.145777\pi$
$444$	−3.30998e6	−0.796833
$445$	2.52294e6	0.603958
$446$	−5.26833e6	−1.25411
$447$	−910766.	−0.215595
$448$	9.70763e6	2.28517
$449$	2.16421e6	0.506622	0.253311	−	0.967385i	$-0.418480\pi$
$449$	2.16421e6	0.506622	0.253311	+	0.967385i	$0.418480\pi$
$450$	−564570.	−0.131428
$451$	3.45062e6	0.798834
$452$	−1.12538e6	−0.259092
$453$	−1.70605e6	−0.390611
$454$	−2.94732e6	−0.671101
$455$	3.29724e6	0.746658
$456$	−2.66090e6	−0.599261
$457$	−1.92523e6	−0.431213	−0.215606	−	0.976480i	$-0.569173\pi$
$457$	−1.92523e6	−0.431213	−0.215606	+	0.976480i	$0.569173\pi$
$458$	5.98261e6	1.33268
$459$	−2.30645e6	−0.510989
$460$	−3.10541e6	−0.684265
$461$	−6.45894e6	−1.41550	−0.707749	−	0.706464i	$-0.750289\pi$
$461$	−6.45894e6	−1.41550	−0.707749	+	0.706464i	$0.750289\pi$
$462$	1.25197e7	2.72891
$463$	2.06254e6	0.447147	0.223574	−	0.974687i	$-0.428228\pi$
$463$	2.06254e6	0.447147	0.223574	+	0.974687i	$0.428228\pi$
$464$	1.70426e6	0.367487
$465$	1.47172e6	0.315641
$466$	8.01596e6	1.70998
$467$	−899380.	−0.190832	−0.0954159	−	0.995437i	$-0.530418\pi$
$467$	−899380.	−0.190832	−0.0954159	+	0.995437i	$0.530418\pi$
$468$	−958132.	−0.202214
$469$	−5.40493e6	−1.13464
$470$	−9.93757e6	−2.07508
$471$	1.30717e6	0.271506
$472$	−5.69702e6	−1.17705
$473$	9.06206e6	1.86241
$474$	8.45623e6	1.72874
$475$	2.02005e6	0.410798
$476$	4.79013e6	0.969014
$477$	24965.6	0.00502396
$478$	1.01602e7	2.03392
$479$	3.96615e6	0.789824	0.394912	−	0.918719i	$-0.370775\pi$
$479$	3.96615e6	0.789824	0.394912	+	0.918719i	$0.370775\pi$
$480$	4.46165e6	0.883878
$481$	2.14626e6	0.422979
$482$	−1.14143e7	−2.23786
$483$	4.05886e6	0.791656
$484$	6.52139e6	1.26540
$485$	−5.01690e6	−0.968458
$486$	3.39165e6	0.651358
$487$	−3.84515e6	−0.734667	−0.367333	−	0.930089i	$-0.619729\pi$
$487$	−3.84515e6	−0.734667	−0.367333	+	0.930089i	$0.619729\pi$
$488$	−6.64294e6	−1.26273
$489$	848299.	0.160427
$490$	6.86483e6	1.29163
$491$	−3.96139e6	−0.741555	−0.370778	−	0.928722i	$-0.620909\pi$
$491$	−3.96139e6	−0.741555	−0.370778	+	0.928722i	$0.620909\pi$
$492$	3.92436e6	0.730898
$493$	2.32136e6	0.430155
$494$	5.84437e6	1.07751
$495$	−1.24310e6	−0.228030
$496$	−1.01783e6	−0.185768
$497$	−9.54475e6	−1.73330
$498$	1.11277e7	2.01062
$499$	−581979.	−0.104630	−0.0523150	−	0.998631i	$-0.516660\pi$
$499$	−581979.	−0.104630	−0.0523150	+	0.998631i	$0.516660\pi$
$500$	8.60540e6	1.53938
$501$	−1.02281e6	−0.182054
$502$	−1.10095e6	−0.194988
$503$	2.97660e6	0.524567	0.262283	−	0.964991i	$-0.415524\pi$
$503$	2.97660e6	0.524567	0.262283	+	0.964991i	$0.415524\pi$
$504$	−1.13998e6	−0.199903
$505$	−1.27721e6	−0.222861
$506$	7.64575e6	1.32753
$507$	2.84264e6	0.491136
$508$	8.10466e6	1.39340
$509$	7.55784e6	1.29301	0.646507	−	0.762908i	$-0.276229\pi$
$509$	7.55784e6	1.29301	0.646507	+	0.762908i	$0.276229\pi$
$510$	2.98981e6	0.509001
$511$	5.88981e6	0.997814
$512$	−4.65321e6	−0.784473
$513$	−6.65257e6	−1.11608
$514$	8.02902e6	1.34046
$515$	−1.03914e6	−0.172646
$516$	1.03062e7	1.70402
$517$	1.43520e7	2.36149
$518$	8.64980e6	1.41639
$519$	3.85503e6	0.628216
$520$	2.08538e6	0.338202
$521$	1.12498e6	0.181573	0.0907867	−	0.995870i	$-0.471062\pi$
$521$	1.12498e6	0.181573	0.0907867	+	0.995870i	$0.471062\pi$
$522$	−1.87130e6	−0.300585
$523$	−7.05280e6	−1.12748	−0.563738	−	0.825953i	$-0.690637\pi$
$523$	−7.05280e6	−1.12748	−0.563738	+	0.825953i	$0.690637\pi$
$524$	−1.35031e7	−2.14835
$525$	−3.19115e6	−0.505300
$526$	−9.38351e6	−1.47877
$527$	−1.38637e6	−0.217447
$528$	−3.17009e6	−0.494865
$529$	−3.95761e6	−0.614885
$530$	−184058.	−0.0284619
$531$	−2.50437e6	−0.385444
$532$	1.38164e7	2.11648
$533$	−2.54464e6	−0.387979
$534$	−7.06447e6	−1.07208
$535$	750132.	0.113306
$536$	−3.41842e6	−0.513941
$537$	−518214.	−0.0775485
$538$	−7.93959e6	−1.18261
$539$	−9.91432e6	−1.46991
$540$	−8.04061e6	−1.18660
$541$	1.20876e7	1.77560	0.887800	−	0.460229i	$-0.152233\pi$
$541$	1.20876e7	1.77560	0.887800	+	0.460229i	$0.152233\pi$
$542$	−1.54576e7	−2.26019
$543$	−1.67676e6	−0.244045
$544$	−4.20291e6	−0.608909
$545$	2.25190e6	0.324757
$546$	−9.23258e6	−1.32538
$547$	−299209.	−0.0427569
$547$	−299209.	−0.0427569
$548$	−1.91312e7	−2.72139
$549$	−2.92018e6	−0.413504
$550$	−6.01122e6	−0.847337
$551$	6.69558e6	0.939527
$552$	2.56708e6	0.358584
$553$	−1.29625e7	−1.80251
$554$	1.00048e7	1.38495
$555$	3.16690e6	0.436417
$556$	3.46551e6	0.475423
$557$	2.12463e6	0.290165	0.145083	−	0.989420i	$-0.453655\pi$
$557$	2.12463e6	0.290165	0.145083	+	0.989420i	$0.453655\pi$
$558$	1.11759e6	0.151949
$559$	−6.68276e6	−0.904537
$560$	−3.36474e6	−0.453400
$561$	−4.31794e6	−0.579255
$562$	1.23376e7	1.64774
$563$	−1.41731e7	−1.88448	−0.942242	−	0.334933i	$-0.891286\pi$
$563$	−1.41731e7	−1.88448	−0.942242	+	0.334933i	$0.891286\pi$
$564$	1.63224e7	2.16066
$565$	1.07674e6	0.141902
$566$	−2.03952e7	−2.67601
$567$	8.16036e6	1.06599
$568$	−6.03669e6	−0.785106
$569$	−8.62295e6	−1.11654	−0.558271	−	0.829658i	$-0.688535\pi$
$569$	−8.62295e6	−1.11654	−0.558271	+	0.829658i	$0.688535\pi$
$570$	8.62363e6	1.11174
$571$	1.34899e7	1.73148	0.865741	−	0.500493i	$-0.166848\pi$
$571$	1.34899e7	1.73148	0.865741	+	0.500493i	$0.166848\pi$
$572$	−1.02016e7	−1.30371
$573$	−2.06524e6	−0.262775
$574$	−1.02554e7	−1.29918
$575$	−1.94883e6	−0.245812
$576$	2.69897e6	0.338955
$577$	2.57643e6	0.322165	0.161083	−	0.986941i	$-0.448501\pi$
$577$	2.57643e6	0.322165	0.161083	+	0.986941i	$0.448501\pi$
$578$	9.67544e6	1.20462
$579$	−873149.	−0.108241
$580$	8.09259e6	0.998890
$581$	−1.70576e7	−2.09641
$582$	1.40478e7	1.71910
$583$	265820.	0.0323904
$584$	3.72509e6	0.451964
$585$	916715.	0.110750
$586$	−8.92277e6	−1.07339
$587$	1.57020e6	0.188088	0.0940439	−	0.995568i	$-0.470021\pi$
$587$	1.57020e6	0.188088	0.0940439	+	0.995568i	$0.470021\pi$
$588$	−1.12755e7	−1.34490
$589$	−3.99877e6	−0.474939
$590$	1.84633e7	2.18364
$591$	4.86507e6	0.572955
$592$	−2.19020e6	−0.256850
$593$	−6.20691e6	−0.724835	−0.362417	−	0.932016i	$-0.618048\pi$
$593$	−6.20691e6	−0.724835	−0.362417	+	0.932016i	$0.618048\pi$
$594$	1.97966e7	2.30210
$595$	−4.58307e6	−0.530719
$596$	2.99093e6	0.344898
$597$	1.21574e7	1.39607
$598$	−5.63831e6	−0.644756
$599$	−6.99929e6	−0.797052	−0.398526	−	0.917157i	$-0.630478\pi$
$599$	−6.99929e6	−0.797052	−0.398526	+	0.917157i	$0.630478\pi$
$600$	−2.01828e6	−0.228878
$601$	1.00721e7	1.13745	0.568725	−	0.822528i	$-0.307437\pi$
$601$	1.00721e7	1.13745	0.568725	+	0.822528i	$0.307437\pi$
$602$	−2.69327e7	−3.02893
$603$	−1.50271e6	−0.168299
$604$	5.60261e6	0.624882
$605$	−6.23950e6	−0.693045
$606$	3.57631e6	0.395598
$607$	950803.	0.104741	0.0523707	−	0.998628i	$-0.483322\pi$
$607$	950803.	0.104741	0.0523707	+	0.998628i	$0.483322\pi$
$608$	−1.21226e7	−1.32996
$609$	−1.05773e7	−1.15566
$610$	2.15289e7	2.34260
$611$	−1.05838e7	−1.14694
$612$	1.33178e6	0.143732
$613$	1.05634e7	1.13541	0.567704	−	0.823233i	$-0.307832\pi$
$613$	1.05634e7	1.13541	0.567704	+	0.823233i	$0.307832\pi$
$614$	2.81271e7	3.01095
$615$	−3.75473e6	−0.400305
$616$	−1.21379e7	−1.28881
$617$	−2.46898e6	−0.261098	−0.130549	−	0.991442i	$-0.541674\pi$
$617$	−2.46898e6	−0.261098	−0.130549	+	0.991442i	$0.541674\pi$
$618$	2.90969e6	0.306461
$619$	3.07503e6	0.322570	0.161285	−	0.986908i	$-0.448436\pi$
$619$	3.07503e6	0.322570	0.161285	+	0.986908i	$0.448436\pi$
$620$	−4.83310e6	−0.504948
$621$	6.41801e6	0.667838
$622$	−2.00307e7	−2.07597
$623$	1.08291e7	1.11782
$624$	2.33776e6	0.240347
$625$	−4.36523e6	−0.447000
$626$	2.13160e6	0.217405
$627$	−1.24544e7	−1.26519
$628$	−4.29272e6	−0.434344
$629$	−2.98324e6	−0.300651
$630$	3.69453e6	0.370858
$631$	1.46219e7	1.46194	0.730970	−	0.682410i	$-0.239068\pi$
$631$	1.46219e7	1.46194	0.730970	+	0.682410i	$0.239068\pi$
$632$	−8.19831e6	−0.816454
$633$	−995558.	−0.0987546
$634$	1.61507e7	1.59577
$635$	−7.75432e6	−0.763150
$636$	302315.	0.0296358
$637$	7.31125e6	0.713910
$638$	−1.99246e7	−1.93793
$639$	−2.65368e6	−0.257097
$640$	−9.57163e6	−0.923711
$641$	−1.67922e7	−1.61422	−0.807111	−	0.590399i	$-0.798970\pi$
$641$	−1.67922e7	−1.61422	−0.807111	+	0.590399i	$0.798970\pi$
$642$	−2.10044e6	−0.201128
$643$	7.51028e6	0.716356	0.358178	−	0.933653i	$-0.383398\pi$
$643$	7.51028e6	0.716356	0.358178	+	0.933653i	$0.383398\pi$
$644$	−1.33292e7	−1.26646
$645$	−9.86071e6	−0.933274
$646$	−8.12352e6	−0.765884
$647$	1.03551e7	0.972509	0.486255	−	0.873817i	$-0.338363\pi$
$647$	1.03551e7	0.972509	0.486255	+	0.873817i	$0.338363\pi$
$648$	5.16112e6	0.482844
$649$	−2.66651e7	−2.48503
$650$	4.43294e6	0.411536
$651$	6.31701e6	0.584197
$652$	−2.78579e6	−0.256643
$653$	−4.05475e6	−0.372118	−0.186059	−	0.982539i	$-0.559572\pi$
$653$	−4.05475e6	−0.372118	−0.186059	+	0.982539i	$0.559572\pi$
$654$	−6.30555e6	−0.576472
$655$	1.29194e7	1.17663
$656$	2.59674e6	0.235596
$657$	1.63752e6	0.148004
$658$	−4.26546e7	−3.84062
$659$	4.85685e6	0.435653	0.217827	−	0.975987i	$-0.430103\pi$
$659$	4.85685e6	0.435653	0.217827	+	0.975987i	$0.430103\pi$
$660$	−1.50530e7	−1.34513
$661$	1.49899e7	1.33443	0.667213	−	0.744867i	$-0.267487\pi$
$661$	1.49899e7	1.33443	0.667213	+	0.744867i	$0.267487\pi$
$662$	−1.71635e7	−1.52216
$663$	3.18424e6	0.281334
$664$	−1.07883e7	−0.949580
$665$	−1.32191e7	−1.15917
$666$	2.40486e6	0.210090
$667$	−6.45950e6	−0.562192
$668$	3.35888e6	0.291242
$669$	−8.27918e6	−0.715191
$670$	1.10787e7	0.953455
$671$	−3.10925e7	−2.66593
$672$	1.91506e7	1.63591
$673$	6.81489e6	0.579991	0.289995	−	0.957028i	$-0.406346\pi$
$673$	6.81489e6	0.579991	0.289995	+	0.957028i	$0.406346\pi$
$674$	−1.95286e7	−1.65585
$675$	−5.04595e6	−0.426269
$676$	−9.33516e6	−0.785697
$677$	−2.73891e6	−0.229671	−0.114835	−	0.993385i	$-0.536634\pi$
$677$	−2.73891e6	−0.229671	−0.114835	+	0.993385i	$0.536634\pi$
$678$	−3.01497e6	−0.251889
$679$	−2.15338e7	−1.79245
$680$	−2.89862e6	−0.240392
$681$	−4.63171e6	−0.382713
$682$	1.18995e7	0.979640
$683$	−1.11890e7	−0.917785	−0.458893	−	0.888492i	$-0.651754\pi$
$683$	−1.11890e7	−0.917785	−0.458893	+	0.888492i	$0.651754\pi$
$684$	3.84130e6	0.313934
$685$	1.83042e7	1.49048
$686$	1.89383e6	0.153649
$687$	9.40168e6	0.760000
$688$	6.81957e6	0.549270
$689$	−196027.	−0.0157314
$690$	−8.31957e6	−0.665240
$691$	−1.38311e7	−1.10195	−0.550973	−	0.834523i	$-0.685743\pi$
$691$	−1.38311e7	−1.10195	−0.550973	+	0.834523i	$0.685743\pi$
$692$	−1.26598e7	−1.00499
$693$	−5.33570e6	−0.422045
$694$	2.94399e7	2.32027
$695$	−3.31571e6	−0.260384
$696$	−6.68972e6	−0.523462
$697$	3.53698e6	0.275773
$698$	−3.78035e7	−2.93693
$699$	1.25971e7	0.975163
$700$	1.04797e7	0.808356
$701$	9.68003e6	0.744015	0.372007	−	0.928230i	$-0.378670\pi$
$701$	9.68003e6	0.744015	0.372007	+	0.928230i	$0.378670\pi$
$702$	−1.45989e7	−1.11809
$703$	−8.60469e6	−0.656669
$704$	2.87371e7	2.18530
$705$	−1.56169e7	−1.18337
$706$	1.77122e7	1.33740
$707$	−5.48212e6	−0.412477
$708$	−3.03260e7	−2.27369
$709$	1.44639e6	0.108061	0.0540306	−	0.998539i	$-0.482793\pi$
$709$	1.44639e6	0.108061	0.0540306	+	0.998539i	$0.482793\pi$
$710$	1.95641e7	1.45652
$711$	−3.60391e6	−0.267362
$712$	6.84900e6	0.506323
$713$	3.85778e6	0.284193
$714$	1.28330e7	0.942072
$715$	9.76067e6	0.714027
$716$	1.70180e6	0.124058
$717$	1.59668e7	1.15990
$718$	−1.29781e7	−0.939509
$719$	−2.79686e6	−0.201766	−0.100883	−	0.994898i	$-0.532167\pi$
$719$	−2.79686e6	−0.201766	−0.100883	+	0.994898i	$0.532167\pi$
$720$	−935483.	−0.0672519
$721$	−4.46025e6	−0.319537
$722$	−1.64634e6	−0.117538
$723$	−1.79376e7	−1.27620
$724$	5.50643e6	0.390413
$725$	5.07858e6	0.358837
$726$	1.74712e7	1.23022
$727$	−3.97974e6	−0.279266	−0.139633	−	0.990203i	$-0.544592\pi$
$727$	−3.97974e6	−0.279266	−0.139633	+	0.990203i	$0.544592\pi$
$728$	8.95098e6	0.625954
$729$	1.59646e7	1.11260
$730$	−1.20725e7	−0.838477
$731$	9.28886e6	0.642938
$732$	−3.53612e7	−2.43921
$733$	−1.67218e7	−1.14954	−0.574770	−	0.818315i	$-0.694909\pi$
$733$	−1.67218e7	−1.14954	−0.574770	+	0.818315i	$0.694909\pi$
$734$	−1.51908e7	−1.04074
$735$	1.07881e7	0.736590
$736$	1.16952e7	0.795816
$737$	−1.60000e7	−1.08505
$738$	−2.85125e6	−0.192706
$739$	−2.28135e7	−1.53667	−0.768337	−	0.640046i	$-0.778915\pi$
$739$	−2.28135e7	−1.53667	−0.768337	+	0.640046i	$0.778915\pi$
$740$	−1.04000e7	−0.698161
$741$	9.18442e6	0.614478
$742$	−790024.	−0.0526781
$743$	−2.63726e6	−0.175259	−0.0876296	−	0.996153i	$-0.527929\pi$
$743$	−2.63726e6	−0.175259	−0.0876296	+	0.996153i	$0.527929\pi$
$744$	3.99527e6	0.264615
$745$	−2.86165e6	−0.188897
$746$	−7.42704e6	−0.488617
$747$	−4.74244e6	−0.310957
$748$	1.41800e7	0.926666
$749$	3.21976e6	0.209710
$750$	2.30544e7	1.49658
$751$	2.15460e7	1.39401	0.697005	−	0.717066i	$-0.254516\pi$
$751$	2.15460e7	1.39401	0.697005	+	0.717066i	$0.254516\pi$
$752$	1.08005e7	0.696464
$753$	−1.73014e6	−0.111197
$754$	1.46932e7	0.941216
$755$	−5.36044e6	−0.342242
$756$	−3.45124e7	−2.19619
$757$	4.83490e6	0.306653	0.153327	−	0.988176i	$-0.451001\pi$
$757$	4.83490e6	0.306653	0.153327	+	0.988176i	$0.451001\pi$
$758$	1.56074e7	0.986638
$759$	1.20153e7	0.757059
$760$	−8.36060e6	−0.525054
$761$	2.87223e7	1.79786	0.898932	−	0.438088i	$-0.144344\pi$
$761$	2.87223e7	1.79786	0.898932	+	0.438088i	$0.144344\pi$
$762$	2.17129e7	1.35466
$763$	9.66576e6	0.601069
$764$	6.78221e6	0.420376
$765$	−1.27421e6	−0.0787205
$766$	4.89496e7	3.01424
$767$	1.96640e7	1.20693
$768$	3.76758e6	0.230494
$769$	2.54982e7	1.55487	0.777435	−	0.628964i	$-0.216521\pi$
$769$	2.54982e7	1.55487	0.777435	+	0.628964i	$0.216521\pi$
$770$	3.93372e7	2.39099
$771$	1.26176e7	0.764436
$772$	2.86740e6	0.173159
$773$	5.69488e6	0.342796	0.171398	−	0.985202i	$-0.445172\pi$
$773$	5.69488e6	0.342796	0.171398	+	0.985202i	$0.445172\pi$
$774$	−7.48798e6	−0.449275
$775$	−3.03306e6	−0.181395
$776$	−1.36193e7	−0.811898
$777$	1.35932e7	0.807733
$778$	−1.92947e7	−1.14285
$779$	1.02019e7	0.602332
$780$	1.11007e7	0.653304
$781$	−2.82549e7	−1.65755
$782$	7.83710e6	0.458288
$783$	−1.67251e7	−0.974911
$784$	−7.46093e6	−0.433514
$785$	4.10716e6	0.237885
$786$	−3.61756e7	−2.08862
$787$	−2.40888e7	−1.38637	−0.693183	−	0.720761i	$-0.743792\pi$
$787$	−2.40888e7	−1.38637	−0.693183	+	0.720761i	$0.743792\pi$
$788$	−1.59768e7	−0.916587
$789$	−1.47462e7	−0.843310
$790$	2.65697e7	1.51467
$791$	4.62164e6	0.262636
$792$	−3.37463e6	−0.191167
$793$	2.29289e7	1.29480
$794$	3.99552e7	2.24917
$795$	−289247.	−0.0162312
$796$	−3.99247e7	−2.23336
$797$	3.51358e7	1.95932	0.979658	−	0.200677i	$-0.0643141\pi$
$797$	3.51358e7	1.95932	0.979658	+	0.200677i	$0.0643141\pi$
$798$	3.70148e7	2.05764
$799$	1.47112e7	0.815233
$800$	−9.19496e6	−0.507955
$801$	3.01077e6	0.165804
$802$	2.80104e7	1.53774
$803$	1.74354e7	0.954207
$804$	−1.81967e7	−0.992777
$805$	1.27530e7	0.693624
$806$	−8.77518e6	−0.475793
$807$	−1.24771e7	−0.674417
$808$	−3.46723e6	−0.186833
$809$	−1.94816e7	−1.04653	−0.523266	−	0.852169i	$-0.675287\pi$
$809$	−1.94816e7	−1.04653	−0.523266	+	0.852169i	$0.675287\pi$
$810$	−1.67265e7	−0.895764
$811$	−3.71286e6	−0.198224	−0.0991120	−	0.995076i	$-0.531600\pi$
$811$	−3.71286e6	−0.198224	−0.0991120	+	0.995076i	$0.531600\pi$
$812$	3.47355e7	1.84877
$813$	−2.42916e7	−1.28893
$814$	2.56057e7	1.35449
$815$	2.66538e6	0.140561
$816$	−3.24943e6	−0.170837
$817$	2.67922e7	1.40428
$818$	−3.69285e7	−1.92965
$819$	3.93478e6	0.204980
$820$	1.23305e7	0.640390
$821$	−2.09769e7	−1.08614	−0.543068	−	0.839689i	$-0.682737\pi$
$821$	−2.09769e7	−1.08614	−0.543068	+	0.839689i	$0.682737\pi$
$822$	−5.12536e7	−2.64572
$823$	1.47411e7	0.758629	0.379314	−	0.925268i	$-0.376160\pi$
$823$	1.47411e7	0.758629	0.379314	+	0.925268i	$0.376160\pi$
$824$	−2.82094e6	−0.144736
$825$	−9.44663e6	−0.483217
$826$	7.92494e7	4.04153
$827$	−1.92837e6	−0.0980453	−0.0490227	−	0.998798i	$-0.515611\pi$
$827$	−1.92837e6	−0.0980453	−0.0490227	+	0.998798i	$0.515611\pi$
$828$	−3.70586e6	−0.187851
$829$	1.75331e7	0.886081	0.443041	−	0.896502i	$-0.353900\pi$
$829$	1.75331e7	0.886081	0.443041	+	0.896502i	$0.353900\pi$
$830$	3.49634e7	1.76165
$831$	1.57226e7	0.789808
$832$	−2.11920e7	−1.06136
$833$	−1.01625e7	−0.507442
$834$	9.28430e6	0.462204
$835$	−3.21369e6	−0.159510
$836$	4.09000e7	2.02399
$837$	9.98868e6	0.492827
$838$	2.61739e7	1.28753
$839$	−434728.	−0.0213213	−0.0106606	−	0.999943i	$-0.503393\pi$
$839$	−434728.	−0.0213213	−0.0106606	+	0.999943i	$0.503393\pi$
$840$	1.32076e7	0.645840
$841$	−3.67789e6	−0.179312
$842$	−4.90137e7	−2.38252
$843$	1.93885e7	0.939668
$844$	3.26939e6	0.157983
$845$	8.93164e6	0.430318
$846$	−1.18591e7	−0.569672
$847$	−2.67816e7	−1.28271
$848$	200040.	0.00955274
$849$	−3.20511e7	−1.52607
$850$	−6.16167e6	−0.292517
$851$	8.30130e6	0.392936
$852$	−3.21341e7	−1.51659
$853$	2.89773e7	1.36359	0.681797	−	0.731541i	$-0.261199\pi$
$853$	2.89773e7	1.36359	0.681797	+	0.731541i	$0.261199\pi$
$854$	9.24077e7	4.33574
$855$	−3.67526e6	−0.171938
$856$	2.03638e6	0.0949891
$857$	2.21450e7	1.02997	0.514984	−	0.857200i	$-0.327798\pi$
$857$	2.21450e7	1.02997	0.514984	+	0.857200i	$0.327798\pi$
$858$	−2.73308e7	−1.26746
$859$	−3.43337e7	−1.58759	−0.793793	−	0.608188i	$-0.791897\pi$
$859$	−3.43337e7	−1.58759	−0.793793	+	0.608188i	$0.791897\pi$
$860$	3.23824e7	1.49301
$861$	−1.61163e7	−0.740895
$862$	−5.25600e7	−2.40928
$863$	−4.78380e6	−0.218648	−0.109324	−	0.994006i	$-0.534869\pi$
$863$	−4.78380e6	−0.218648	−0.109324	+	0.994006i	$0.534869\pi$
$864$	3.02815e7	1.38004
$865$	1.21126e7	0.550423
$866$	3.00279e7	1.36060
$867$	1.52049e7	0.686969
$868$	−2.07449e7	−0.934572
$869$	−3.83724e7	−1.72373
$870$	2.16805e7	0.971118
$871$	1.17991e7	0.526991
$872$	6.11323e6	0.272257
$873$	−5.98695e6	−0.265871
$874$	2.26048e7	1.00097
$875$	−3.53400e7	−1.56044
$876$	1.98291e7	0.873058
$877$	−2.86518e6	−0.125792	−0.0628961	−	0.998020i	$-0.520034\pi$
$877$	−2.86518e6	−0.125792	−0.0628961	+	0.998020i	$0.520034\pi$
$878$	−2.85298e7	−1.24900
$879$	−1.40221e7	−0.612128
$880$	−9.96050e6	−0.433585
$881$	2.31484e7	1.00480	0.502402	−	0.864634i	$-0.332450\pi$
$881$	2.31484e7	1.00480	0.502402	+	0.864634i	$0.332450\pi$
$882$	8.19220e6	0.354592
$883$	2.34495e7	1.01212	0.506060	−	0.862498i	$-0.331101\pi$
$883$	2.34495e7	1.01212	0.506060	+	0.862498i	$0.331101\pi$
$884$	−1.04570e7	−0.450065
$885$	2.90151e7	1.24528
$886$	−6.51915e7	−2.79001
$887$	4.18967e7	1.78801	0.894006	−	0.448056i	$-0.147883\pi$
$887$	4.18967e7	1.78801	0.894006	+	0.448056i	$0.147883\pi$
$888$	8.59716e6	0.365866
$889$	−3.32836e7	−1.41246
$890$	−2.21968e7	−0.939322
$891$	2.41568e7	1.01940
$892$	2.71886e7	1.14413
$893$	4.24321e7	1.78060
$894$	8.01289e6	0.335309
$895$	−1.62824e6	−0.0679455
$896$	−4.10839e7	−1.70963
$897$	−8.86060e6	−0.367690
$898$	−1.90407e7	−0.787938
$899$	−1.00533e7	−0.414866
$900$	2.91361e6	0.119902
$901$	272473.	0.0111818
$902$	−3.03585e7	−1.24241
$903$	−4.23247e7	−1.72733
$904$	2.92301e6	0.118962
$905$	−5.26841e6	−0.213825
$906$	1.50097e7	0.607509
$907$	5.72010e6	0.230880	0.115440	−	0.993314i	$-0.463172\pi$
$907$	5.72010e6	0.230880	0.115440	+	0.993314i	$0.463172\pi$
$908$	1.52104e7	0.612248
$909$	−1.52417e6	−0.0611819
$910$	−2.90090e7	−1.16126
$911$	2.31636e6	0.0924722	0.0462361	−	0.998931i	$-0.485277\pi$
$911$	2.31636e6	0.0924722	0.0462361	+	0.998931i	$0.485277\pi$
$912$	−9.37245e6	−0.373135
$913$	−5.04948e7	−2.00480
$914$	1.69381e7	0.670655
$915$	3.38327e7	1.33593
$916$	−3.08749e7	−1.21581
$917$	5.54535e7	2.17774
$918$	2.02920e7	0.794729
$919$	−4.67828e7	−1.82725	−0.913623	−	0.406561i	$-0.866728\pi$
$919$	−4.67828e7	−1.82725	−0.913623	+	0.406561i	$0.866728\pi$
$920$	8.06582e6	0.314180
$921$	4.42017e7	1.71708
$922$	5.68256e7	2.20149
$923$	2.08364e7	0.805042
$924$	−6.46113e7	−2.48960
$925$	−6.52663e6	−0.250804
$926$	−1.81462e7	−0.695438
$927$	−1.24006e6	−0.0473963
$928$	−3.04773e7	−1.16173
$929$	2.22909e7	0.847400	0.423700	−	0.905803i	$-0.360731\pi$
$929$	2.22909e7	0.847400	0.423700	+	0.905803i	$0.360731\pi$
$930$	−1.29482e7	−0.490909
$931$	−2.93120e7	−1.10833
$932$	−4.13685e7	−1.56002
$933$	−3.14782e7	−1.18388
$934$	7.91272e6	0.296796
$935$	−1.35671e7	−0.507525
$936$	2.48860e6	0.0928465
$937$	−2.64328e7	−0.983543	−0.491772	−	0.870724i	$-0.663651\pi$
$937$	−2.64328e7	−0.983543	−0.491772	+	0.870724i	$0.663651\pi$
$938$	4.75525e7	1.76468
$939$	3.34981e6	0.123981
$940$	5.12855e7	1.89311
$941$	−4.17151e7	−1.53574	−0.767872	−	0.640603i	$-0.778685\pi$
$941$	−4.17151e7	−1.53574	−0.767872	+	0.640603i	$0.778685\pi$
$942$	−1.15005e7	−0.422268
$943$	−9.84216e6	−0.360422
$944$	−2.00666e7	−0.732898
$945$	3.30206e7	1.20283
$946$	−7.97278e7	−2.89656
$947$	−2.17948e7	−0.789728	−0.394864	−	0.918740i	$-0.629208\pi$
$947$	−2.17948e7	−0.789728	−0.394864	+	0.918740i	$0.629208\pi$
$948$	−4.36407e7	−1.57714
$949$	−1.28576e7	−0.463441
$950$	−1.77723e7	−0.638904
$951$	2.53809e7	0.910029
$952$	−1.24416e7	−0.444923
$953$	−5.74138e6	−0.204778	−0.102389	−	0.994744i	$-0.532649\pi$
$953$	−5.74138e6	−0.204778	−0.102389	+	0.994744i	$0.532649\pi$
$954$	−219647.	−0.00781365
$955$	−6.48905e6	−0.230236
$956$	−5.24346e7	−1.85555
$957$	−3.13115e7	−1.10516
$958$	−3.48941e7	−1.22839
$959$	7.85665e7	2.75861
$960$	−3.12697e7	−1.09508
$961$	−2.26251e7	−0.790282
$962$	−1.88827e7	−0.657850
$963$	895176.	0.0311059
$964$	5.89067e7	2.04161
$965$	−2.74346e6	−0.0948374
$966$	−3.57098e7	−1.23124
$967$	1.90367e7	0.654676	0.327338	−	0.944907i	$-0.393848\pi$
$967$	1.90367e7	0.654676	0.327338	+	0.944907i	$0.393848\pi$
$968$	−1.69383e7	−0.581008
$969$	−1.27661e7	−0.436766
$970$	4.41385e7	1.50622
$971$	3.27586e7	1.11501	0.557503	−	0.830175i	$-0.311759\pi$
$971$	3.27586e7	1.11501	0.557503	+	0.830175i	$0.311759\pi$
$972$	−1.75035e7	−0.594237
$973$	−1.42319e7	−0.481926
$974$	3.38295e7	1.14261
$975$	6.96636e6	0.234690
$976$	−2.33984e7	−0.786250
$977$	−3.52853e7	−1.18265	−0.591327	−	0.806432i	$-0.701396\pi$
$977$	−3.52853e7	−1.18265	−0.591327	+	0.806432i	$0.701396\pi$
$978$	−7.46331e6	−0.249508
$979$	3.20570e7	1.06897
$980$	−3.54278e7	−1.17836
$981$	2.68733e6	0.0891555
$982$	3.48522e7	1.15332
$983$	2.85757e7	0.943220	0.471610	−	0.881807i	$-0.343673\pi$
$983$	2.85757e7	0.943220	0.471610	+	0.881807i	$0.343673\pi$
$984$	−1.01929e7	−0.335592
$985$	1.52862e7	0.502005
$986$	−2.04232e7	−0.669009
$987$	−6.70317e7	−2.19022
$988$	−3.01614e7	−0.983014
$989$	−2.58476e7	−0.840290
$990$	1.09368e7	0.354650
$991$	−560137.	−0.0181180	−0.00905900	−	0.999959i	$-0.502884\pi$
$991$	−560137.	−0.0181180	−0.00905900	+	0.999959i	$0.502884\pi$
$992$	1.82018e7	0.587267
$993$	−2.69724e7	−0.868054
$994$	8.39744e7	2.69576
$995$	3.81989e7	1.22319
$996$	−5.74273e7	−1.83430
$997$	−7.55749e6	−0.240791	−0.120395	−	0.992726i	$-0.538416\pi$
$997$	−7.55749e6	−0.240791	−0.120395	+	0.992726i	$0.538416\pi$
$998$	5.12024e6	0.162728
$999$	2.14940e7	0.681401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.a.1.15	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.a.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-8.79797 q^{2} -13.8260 q^{3} +45.4043 q^{4} -43.4417 q^{5} +121.641 q^{6} -186.463 q^{7} -117.931 q^{8} -51.8414 q^{9} +O(q^{10})\)	\(q-8.79797 q^{2} -13.8260 q^{3} +45.4043 q^{4} -43.4417 q^{5} +121.641 q^{6} -186.463 q^{7} -117.931 q^{8} -51.8414 q^{9} +382.199 q^{10} -551.979 q^{11} -627.760 q^{12} +407.053 q^{13} +1640.50 q^{14} +600.625 q^{15} -415.386 q^{16} -565.793 q^{17} +456.100 q^{18} -1631.94 q^{19} -1972.44 q^{20} +2578.04 q^{21} +4856.29 q^{22} +1574.40 q^{23} +1630.51 q^{24} -1237.82 q^{25} -3581.24 q^{26} +4076.48 q^{27} -8466.22 q^{28} -4102.84 q^{29} -5284.28 q^{30} +2450.32 q^{31} +7428.34 q^{32} +7631.66 q^{33} +4977.83 q^{34} +8100.26 q^{35} -2353.82 q^{36} +5272.67 q^{37} +14357.8 q^{38} -5627.92 q^{39} +5123.11 q^{40} -6251.37 q^{41} -22681.5 q^{42} -16417.4 q^{43} -25062.2 q^{44} +2252.08 q^{45} -13851.5 q^{46} -26001.1 q^{47} +5743.14 q^{48} +17961.4 q^{49} +10890.3 q^{50} +7822.66 q^{51} +18482.0 q^{52} -481.576 q^{53} -35864.8 q^{54} +23978.9 q^{55} +21989.7 q^{56} +22563.2 q^{57} +36096.6 q^{58} +48308.2 q^{59} +27271.0 q^{60} +56329.1 q^{61} -21557.8 q^{62} +9666.51 q^{63} -52062.0 q^{64} -17683.1 q^{65} -67143.1 q^{66} +28986.6 q^{67} -25689.5 q^{68} -21767.7 q^{69} -71265.9 q^{70} +51188.4 q^{71} +6113.70 q^{72} -31587.1 q^{73} -46388.8 q^{74} +17114.1 q^{75} -74097.1 q^{76} +102924. q^{77} +49514.3 q^{78} +69518.0 q^{79} +18045.1 q^{80} -43764.0 q^{81} +54999.4 q^{82} +91479.7 q^{83} +117054. q^{84} +24579.0 q^{85} +144440. q^{86} +56725.8 q^{87} +65095.3 q^{88} -58076.5 q^{89} -19813.7 q^{90} -75900.3 q^{91} +71484.5 q^{92} -33878.1 q^{93} +228757. q^{94} +70894.2 q^{95} -102704. q^{96} +115486. q^{97} -158024. q^{98} +28615.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) \) 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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