LMFDB - Embedded newform 547.6.a.a.1.6

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			1.6
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.6698 q^{2} -9.29200 q^{3} +81.8438 q^{4} +43.9375 q^{5} +99.1434 q^{6} -209.001 q^{7} -531.821 q^{8} -156.659 q^{9} +O(q^{10})$	\(q-10.6698 q^{2} -9.29200 q^{3} +81.8438 q^{4} +43.9375 q^{5} +99.1434 q^{6} -209.001 q^{7} -531.821 q^{8} -156.659 q^{9} -468.803 q^{10} +261.363 q^{11} -760.493 q^{12} -780.301 q^{13} +2229.99 q^{14} -408.267 q^{15} +3055.41 q^{16} +886.109 q^{17} +1671.51 q^{18} -79.2700 q^{19} +3596.01 q^{20} +1942.03 q^{21} -2788.69 q^{22} +429.352 q^{23} +4941.68 q^{24} -1194.50 q^{25} +8325.62 q^{26} +3713.63 q^{27} -17105.4 q^{28} +7988.07 q^{29} +4356.11 q^{30} -428.863 q^{31} -15582.2 q^{32} -2428.59 q^{33} -9454.57 q^{34} -9182.97 q^{35} -12821.5 q^{36} -2657.40 q^{37} +845.792 q^{38} +7250.56 q^{39} -23366.9 q^{40} +1490.04 q^{41} -20721.0 q^{42} -4236.29 q^{43} +21391.0 q^{44} -6883.19 q^{45} -4581.09 q^{46} -12372.9 q^{47} -28390.8 q^{48} +26874.3 q^{49} +12745.0 q^{50} -8233.73 q^{51} -63862.8 q^{52} +11881.9 q^{53} -39623.5 q^{54} +11483.7 q^{55} +111151. q^{56} +736.577 q^{57} -85230.8 q^{58} -8280.56 q^{59} -33414.1 q^{60} -12397.8 q^{61} +4575.86 q^{62} +32741.8 q^{63} +68484.9 q^{64} -34284.5 q^{65} +25912.5 q^{66} +23817.7 q^{67} +72522.5 q^{68} -3989.54 q^{69} +97980.1 q^{70} +57008.5 q^{71} +83314.5 q^{72} +31196.0 q^{73} +28353.9 q^{74} +11099.3 q^{75} -6487.76 q^{76} -54625.1 q^{77} -77361.7 q^{78} +91810.6 q^{79} +134247. q^{80} +3561.03 q^{81} -15898.4 q^{82} +68350.6 q^{83} +158943. q^{84} +38933.4 q^{85} +45200.2 q^{86} -74225.1 q^{87} -138999. q^{88} -57948.7 q^{89} +73442.0 q^{90} +163083. q^{91} +35139.8 q^{92} +3984.99 q^{93} +132016. q^{94} -3482.92 q^{95} +144789. q^{96} -64628.0 q^{97} -286742. q^{98} -40944.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) $ 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9} - 950 q^{10} - 1832 q^{11} - 4143 q^{12} - 4369 q^{13} - 4777 q^{14} - 3487 q^{15} + 26274 q^{16} - 13648 q^{17} - 10269 q^{18} - 5446 q^{19} - 26032 q^{20} - 8428 q^{21} - 8248 q^{22} - 24142 q^{23} - 18577 q^{24} + 58062 q^{25} - 17656 q^{26} - 33269 q^{27} - 23512 q^{28} - 33752 q^{29} - 12418 q^{30} - 13781 q^{31} - 44076 q^{32} - 39186 q^{33} - 7207 q^{34} - 30833 q^{35} + 120044 q^{36} - 61582 q^{37} - 91259 q^{38} - 20077 q^{39} - 66032 q^{40} - 54181 q^{41} - 69252 q^{42} - 38600 q^{43} - 95712 q^{44} - 190880 q^{45} - 9354 q^{46} - 83886 q^{47} - 173886 q^{48} + 194148 q^{49} - 70896 q^{50} - 60673 q^{51} - 145186 q^{52} - 286874 q^{53} - 116519 q^{54} - 74821 q^{55} - 240407 q^{56} - 95180 q^{57} - 66900 q^{58} - 135740 q^{59} - 144550 q^{60} - 227450 q^{61} - 308766 q^{62} - 249721 q^{63} + 347514 q^{64} - 290374 q^{65} - 178980 q^{66} - 91006 q^{67} - 521943 q^{68} - 414510 q^{69} - 165057 q^{70} - 236165 q^{71} - 527945 q^{72} - 184618 q^{73} - 206443 q^{74} - 243897 q^{75} - 221676 q^{76} - 751131 q^{77} - 306839 q^{78} - 107446 q^{79} - 856691 q^{80} + 382187 q^{81} - 244614 q^{82} - 499547 q^{83} - 330289 q^{84} - 287103 q^{85} - 272441 q^{86} - 391281 q^{87} - 588937 q^{88} - 740774 q^{89} - 687179 q^{90} - 237213 q^{91} - 1367678 q^{92} - 754880 q^{93} - 32851 q^{94} - 295814 q^{95} - 816078 q^{96} - 320770 q^{97} - 661922 q^{98} - 547439 q^{99}+O(q^{100}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9 - 950 * q^10 - 1832 * q^11 - 4143 * q^12 - 4369 * q^13 - 4777 * q^14 - 3487 * q^15 + 26274 * q^16 - 13648 * q^17 - 10269 * q^18 - 5446 * q^19 - 26032 * q^20 - 8428 * q^21 - 8248 * q^22 - 24142 * q^23 - 18577 * q^24 + 58062 * q^25 - 17656 * q^26 - 33269 * q^27 - 23512 * q^28 - 33752 * q^29 - 12418 * q^30 - 13781 * q^31 - 44076 * q^32 - 39186 * q^33 - 7207 * q^34 - 30833 * q^35 + 120044 * q^36 - 61582 * q^37 - 91259 * q^38 - 20077 * q^39 - 66032 * q^40 - 54181 * q^41 - 69252 * q^42 - 38600 * q^43 - 95712 * q^44 - 190880 * q^45 - 9354 * q^46 - 83886 * q^47 - 173886 * q^48 + 194148 * q^49 - 70896 * q^50 - 60673 * q^51 - 145186 * q^52 - 286874 * q^53 - 116519 * q^54 - 74821 * q^55 - 240407 * q^56 - 95180 * q^57 - 66900 * q^58 - 135740 * q^59 - 144550 * q^60 - 227450 * q^61 - 308766 * q^62 - 249721 * q^63 + 347514 * q^64 - 290374 * q^65 - 178980 * q^66 - 91006 * q^67 - 521943 * q^68 - 414510 * q^69 - 165057 * q^70 - 236165 * q^71 - 527945 * q^72 - 184618 * q^73 - 206443 * q^74 - 243897 * q^75 - 221676 * q^76 - 751131 * q^77 - 306839 * q^78 - 107446 * q^79 - 856691 * q^80 + 382187 * q^81 - 244614 * q^82 - 499547 * q^83 - 330289 * q^84 - 287103 * q^85 - 272441 * q^86 - 391281 * q^87 - 588937 * q^88 - 740774 * q^89 - 687179 * q^90 - 237213 * q^91 - 1367678 * q^92 - 754880 * q^93 - 32851 * q^94 - 295814 * q^95 - 816078 * q^96 - 320770 * q^97 - 661922 * q^98 - 547439 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−10.6698	−1.88617	−0.943083	−	0.332559i	$-0.892088\pi$
$2$	−10.6698	−1.88617	−0.943083	+	0.332559i	$0.892088\pi$
$3$	−9.29200	−0.596082	−0.298041	−	0.954553i	$-0.596333\pi$
$3$	−9.29200	−0.596082	−0.298041	+	0.954553i	$0.596333\pi$
$4$	81.8438	2.55762
$5$	43.9375	0.785978	0.392989	−	0.919543i	$-0.371441\pi$
$5$	43.9375	0.785978	0.392989	+	0.919543i	$0.371441\pi$
$6$	99.1434	1.12431
$7$	−209.001	−1.61214	−0.806070	−	0.591820i	$-0.798409\pi$
$7$	−209.001	−1.61214	−0.806070	+	0.591820i	$0.798409\pi$
$8$	−531.821	−2.93793
$9$	−156.659	−0.644686
$10$	−468.803	−1.48248
$11$	261.363	0.651273	0.325637	−	0.945495i	$-0.394421\pi$
$11$	261.363	0.651273	0.325637	+	0.945495i	$0.394421\pi$
$12$	−760.493	−1.52455
$13$	−780.301	−1.28057	−0.640286	−	0.768137i	$-0.721184\pi$
$13$	−780.301	−1.28057	−0.640286	+	0.768137i	$0.721184\pi$
$14$	2229.99	3.04076
$15$	−408.267	−0.468507
$16$	3055.41	2.98379
$17$	886.109	0.743644	0.371822	−	0.928304i	$-0.378733\pi$
$17$	886.109	0.743644	0.371822	+	0.928304i	$0.378733\pi$
$18$	1671.51	1.21598
$19$	−79.2700	−0.0503761	−0.0251881	−	0.999683i	$-0.508018\pi$
$19$	−79.2700	−0.0503761	−0.0251881	+	0.999683i	$0.508018\pi$
$20$	3596.01	2.01023
$21$	1942.03	0.960968
$22$	−2788.69	−1.22841
$23$	429.352	0.169237	0.0846183	−	0.996413i	$-0.473033\pi$
$23$	429.352	0.169237	0.0846183	+	0.996413i	$0.473033\pi$
$24$	4941.68	1.75124
$25$	−1194.50	−0.382239
$26$	8325.62	2.41537
$27$	3713.63	0.980368
$28$	−17105.4	−4.12324
$29$	7988.07	1.76379	0.881895	−	0.471446i	$-0.156268\pi$
$29$	7988.07	1.76379	0.881895	+	0.471446i	$0.156268\pi$
$30$	4356.11	0.883682
$31$	−428.863	−0.0801520	−0.0400760	−	0.999197i	$-0.512760\pi$
$31$	−428.863	−0.0801520	−0.0400760	+	0.999197i	$0.512760\pi$
$32$	−15582.2	−2.69000
$33$	−2428.59	−0.388212
$34$	−9454.57	−1.40263
$35$	−9182.97	−1.26711
$36$	−12821.5	−1.64886
$37$	−2657.40	−0.319119	−0.159560	−	0.987188i	$-0.551007\pi$
$37$	−2657.40	−0.319119	−0.159560	+	0.987188i	$0.551007\pi$
$38$	845.792	0.0950177
$39$	7250.56	0.763326
$40$	−23366.9	−2.30914
$41$	1490.04	0.138433	0.0692164	−	0.997602i	$-0.477950\pi$
$41$	1490.04	0.138433	0.0692164	+	0.997602i	$0.477950\pi$
$42$	−20721.0	−1.81254
$43$	−4236.29	−0.349393	−0.174697	−	0.984622i	$-0.555894\pi$
$43$	−4236.29	−0.349393	−0.174697	+	0.984622i	$0.555894\pi$
$44$	21391.0	1.66571
$45$	−6883.19	−0.506709
$46$	−4581.09	−0.319208
$47$	−12372.9	−0.817012	−0.408506	−	0.912756i	$-0.633950\pi$
$47$	−12372.9	−0.817012	−0.408506	+	0.912756i	$0.633950\pi$
$48$	−28390.8	−1.77859
$49$	26874.3	1.59899
$50$	12745.0	0.720965
$51$	−8233.73	−0.443273
$52$	−63862.8	−3.27521
$53$	11881.9	0.581025	0.290512	−	0.956871i	$-0.406174\pi$
$53$	11881.9	0.581025	0.290512	+	0.956871i	$0.406174\pi$
$54$	−39623.5	−1.84914
$55$	11483.7	0.511886
$56$	111151.	4.73635
$57$	736.577	0.0300283
$58$	−85230.8	−3.32680
$59$	−8280.56	−0.309692	−0.154846	−	0.987939i	$-0.549488\pi$
$59$	−8280.56	−0.309692	−0.154846	+	0.987939i	$0.549488\pi$
$60$	−33414.1	−1.19826
$61$	−12397.8	−0.426599	−0.213300	−	0.976987i	$-0.568421\pi$
$61$	−12397.8	−0.426599	−0.213300	+	0.976987i	$0.568421\pi$
$62$	4575.86	0.151180
$63$	32741.8	1.03932
$64$	68484.9	2.08999
$65$	−34284.5	−1.00650
$66$	25912.5	0.732232
$67$	23817.7	0.648207	0.324103	−	0.946022i	$-0.394937\pi$
$67$	23817.7	0.648207	0.324103	+	0.946022i	$0.394937\pi$
$68$	72522.5	1.90196
$69$	−3989.54	−0.100879
$70$	97980.1	2.38997
$71$	57008.5	1.34213	0.671064	−	0.741399i	$-0.265838\pi$
$71$	57008.5	1.34213	0.671064	+	0.741399i	$0.265838\pi$
$72$	83314.5	1.89404
$73$	31196.0	0.685159	0.342580	−	0.939489i	$-0.388699\pi$
$73$	31196.0	0.685159	0.342580	+	0.939489i	$0.388699\pi$
$74$	28353.9	0.601912
$75$	11099.3	0.227846
$76$	−6487.76	−0.128843
$77$	−54625.1	−1.04994
$78$	−77361.7	−1.43976
$79$	91810.6	1.65510	0.827552	−	0.561390i	$-0.189733\pi$
$79$	91810.6	1.65510	0.827552	+	0.561390i	$0.189733\pi$
$80$	134247.	2.34520
$81$	3561.03	0.0603063
$82$	−15898.4	−0.261107
$83$	68350.6	1.08905	0.544524	−	0.838745i	$-0.316710\pi$
$83$	68350.6	1.08905	0.544524	+	0.838745i	$0.316710\pi$
$84$	158943.	2.45779
$85$	38933.4	0.584488
$86$	45200.2	0.659013
$87$	−74225.1	−1.05136
$88$	−138999.	−1.91339
$89$	−57948.7	−0.775476	−0.387738	−	0.921770i	$-0.626744\pi$
$89$	−57948.7	−0.775476	−0.387738	+	0.921770i	$0.626744\pi$
$90$	73442.0	0.955737
$91$	163083.	2.06446
$92$	35139.8	0.432843
$93$	3984.99	0.0477772
$94$	132016.	1.54102
$95$	−3482.92	−0.0395945
$96$	144789.	1.60346
$97$	−64628.0	−0.697415	−0.348707	−	0.937232i	$-0.613379\pi$
$97$	−64628.0	−0.697415	−0.348707	+	0.937232i	$0.613379\pi$
$98$	−286742.	−3.01597
$99$	−40944.9	−0.419867
$100$	−97762.1	−0.977621
$101$	24233.8	0.236384	0.118192	−	0.992991i	$-0.462290\pi$
$101$	24233.8	0.236384	0.118192	+	0.992991i	$0.462290\pi$
$102$	87851.9	0.836086
$103$	−42820.2	−0.397700	−0.198850	−	0.980030i	$-0.563721\pi$
$103$	−42820.2	−0.397700	−0.198850	+	0.980030i	$0.563721\pi$
$104$	414981.	3.76222
$105$	85328.1	0.755299
$106$	−126777.	−1.09591
$107$	−123392.	−1.04190	−0.520952	−	0.853586i	$-0.674423\pi$
$107$	−123392.	−1.04190	−0.520952	+	0.853586i	$0.674423\pi$
$108$	303937.	2.50741
$109$	45662.6	0.368124	0.184062	−	0.982915i	$-0.441075\pi$
$109$	45662.6	0.368124	0.184062	+	0.982915i	$0.441075\pi$
$110$	−122528.	−0.965502
$111$	24692.6	0.190221
$112$	−638582.	−4.81029
$113$	−149801.	−1.10362	−0.551810	−	0.833970i	$-0.686063\pi$
$113$	−149801.	−1.10362	−0.551810	+	0.833970i	$0.686063\pi$
$114$	−7859.10	−0.0566383
$115$	18864.7	0.133016
$116$	653774.	4.51110
$117$	122241.	0.825567
$118$	88351.6	0.584130
$119$	−185197.	−1.19886
$120$	217125.	1.37644
$121$	−92740.1	−0.575843
$122$	132282.	0.804637
$123$	−13845.5	−0.0825173
$124$	−35099.8	−0.204998
$125$	−189788.	−1.08641
$126$	−349347.	−1.96034
$127$	256822.	1.41293	0.706467	−	0.707746i	$-0.250288\pi$
$127$	256822.	1.41293	0.706467	+	0.707746i	$0.250288\pi$
$128$	−232089.	−1.25207
$129$	39363.6	0.208267
$130$	365807.	1.89843
$131$	140687.	0.716271	0.358135	−	0.933670i	$-0.383413\pi$
$131$	140687.	0.716271	0.358135	+	0.933670i	$0.383413\pi$
$132$	−198765.	−0.992899
$133$	16567.5	0.0812134
$134$	−254130.	−1.22262
$135$	163168.	0.770548
$136$	−471252.	−2.18477
$137$	158201.	0.720123	0.360062	−	0.932929i	$-0.382756\pi$
$137$	158201.	0.720123	0.360062	+	0.932929i	$0.382756\pi$
$138$	42567.5	0.190274
$139$	−289721.	−1.27187	−0.635935	−	0.771742i	$-0.719385\pi$
$139$	−289721.	−1.27187	−0.635935	+	0.771742i	$0.719385\pi$
$140$	−751569.	−3.24077
$141$	114969.	0.487006
$142$	−608267.	−2.53148
$143$	−203942.	−0.834002
$144$	−478656.	−1.92361
$145$	350976.	1.38630
$146$	−332854.	−1.29232
$147$	−249716.	−0.953132
$148$	−217492.	−0.816186
$149$	287545.	1.06106	0.530530	−	0.847666i	$-0.321993\pi$
$149$	287545.	1.06106	0.530530	+	0.847666i	$0.321993\pi$
$150$	−118426.	−0.429755
$151$	−168047.	−0.599776	−0.299888	−	0.953974i	$-0.596949\pi$
$151$	−168047.	−0.599776	−0.299888	+	0.953974i	$0.596949\pi$
$152$	42157.5	0.148001
$153$	−138817.	−0.479417
$154$	582837.	1.98037
$155$	−18843.2	−0.0629977
$156$	593413.	1.95230
$157$	−152862.	−0.494939	−0.247469	−	0.968896i	$-0.579599\pi$
$157$	−152862.	−0.494939	−0.247469	+	0.968896i	$0.579599\pi$
$158$	−979597.	−3.12180
$159$	−110406.	−0.346339
$160$	−684641.	−2.11428
$161$	−89734.9	−0.272833
$162$	−37995.3	−0.113748
$163$	510518.	1.50502	0.752510	−	0.658581i	$-0.228843\pi$
$163$	510518.	1.50502	0.752510	+	0.658581i	$0.228843\pi$
$164$	121951.	0.354058
$165$	−106706.	−0.305126
$166$	−729285.	−2.05412
$167$	−564866.	−1.56731	−0.783654	−	0.621197i	$-0.786647\pi$
$167$	−564866.	−1.56731	−0.783654	+	0.621197i	$0.786647\pi$
$168$	−1.03282e6	−2.82325
$169$	237577.	0.639863
$170$	−415410.	−1.10244
$171$	12418.3	0.0324768
$172$	−346714.	−0.893615
$173$	−199141.	−0.505878	−0.252939	−	0.967482i	$-0.581397\pi$
$173$	−199141.	−0.505878	−0.252939	+	0.967482i	$0.581397\pi$
$174$	791964.	1.98304
$175$	249651.	0.616222
$176$	798571.	1.94326
$177$	76942.9	0.184602
$178$	618299.	1.46268
$179$	−627853.	−1.46462	−0.732311	−	0.680971i	$-0.761558\pi$
$179$	−627853.	−1.46462	−0.732311	+	0.680971i	$0.761558\pi$
$180$	−563347.	−1.29597
$181$	307897.	0.698568	0.349284	−	0.937017i	$-0.386425\pi$
$181$	307897.	0.698568	0.349284	+	0.937017i	$0.386425\pi$
$182$	−1.74006e6	−3.89391
$183$	115200.	0.254288
$184$	−228339.	−0.497205
$185$	−116760.	−0.250821
$186$	−42518.9	−0.0901156
$187$	231597.	0.484315
$188$	−1.01265e6	−2.08960
$189$	−776151.	−1.58049
$190$	37162.0	0.0746818
$191$	896776.	1.77869	0.889345	−	0.457236i	$-0.151161\pi$
$191$	896776.	1.77869	0.889345	+	0.457236i	$0.151161\pi$
$192$	−636362.	−1.24581
$193$	−45522.6	−0.0879698	−0.0439849	−	0.999032i	$-0.514005\pi$
$193$	−45522.6	−0.0879698	−0.0439849	+	0.999032i	$0.514005\pi$
$194$	689565.	1.31544
$195$	318571.	0.599957
$196$	2.19949e6	4.08962
$197$	874152.	1.60480	0.802401	−	0.596786i	$-0.203556\pi$
$197$	874152.	1.60480	0.802401	+	0.596786i	$0.203556\pi$
$198$	436872.	0.791938
$199$	470663.	0.842514	0.421257	−	0.906941i	$-0.361589\pi$
$199$	470663.	0.842514	0.421257	+	0.906941i	$0.361589\pi$
$200$	635259.	1.12299
$201$	−221314.	−0.386384
$202$	−258569.	−0.445859
$203$	−1.66951e6	−2.84348
$204$	−673879.	−1.13372
$205$	65468.7	0.108805
$206$	456881.	0.750128
$207$	−67261.8	−0.109104
$208$	−2.38414e6	−3.82096
$209$	−20718.3	−0.0328086
$210$	−910431.	−1.42462
$211$	264902.	0.409619	0.204809	−	0.978802i	$-0.434343\pi$
$211$	264902.	0.409619	0.204809	+	0.978802i	$0.434343\pi$
$212$	972456.	1.48604
$213$	−529723.	−0.800019
$214$	1.31656e6	1.96520
$215$	−186132.	−0.274615
$216$	−1.97499e6	−2.88025
$217$	89632.6	0.129216
$218$	−487209.	−0.694343
$219$	−289873.	−0.408411
$220$	939866.	1.30921
$221$	−691432.	−0.952289
$222$	−263464.	−0.358789
$223$	−611142.	−0.822962	−0.411481	−	0.911418i	$-0.634988\pi$
$223$	−611142.	−0.822962	−0.411481	+	0.911418i	$0.634988\pi$
$224$	3.25668e6	4.33666
$225$	187128.	0.246424
$226$	1.59834e6	2.08161
$227$	1.22844e6	1.58230	0.791148	−	0.611625i	$-0.209484\pi$
$227$	1.22844e6	1.58230	0.791148	+	0.611625i	$0.209484\pi$
$228$	60284.2	0.0768010
$229$	494170.	0.622712	0.311356	−	0.950293i	$-0.399217\pi$
$229$	494170.	0.622712	0.311356	+	0.950293i	$0.399217\pi$
$230$	−201282.	−0.250891
$231$	507577.	0.625852
$232$	−4.24823e6	−5.18188
$233$	−342697.	−0.413543	−0.206771	−	0.978389i	$-0.566296\pi$
$233$	−342697.	−0.413543	−0.206771	+	0.978389i	$0.566296\pi$
$234$	−1.30428e6	−1.55715
$235$	−543636.	−0.642153
$236$	−677712.	−0.792073
$237$	−853104.	−0.986577
$238$	1.97601e6	2.26124
$239$	1.73111e6	1.96034	0.980168	−	0.198167i	$-0.0634990\pi$
$239$	1.73111e6	1.96034	0.980168	+	0.198167i	$0.0634990\pi$
$240$	−1.24742e6	−1.39793
$241$	−655352.	−0.726828	−0.363414	−	0.931628i	$-0.618389\pi$
$241$	−655352.	−0.726828	−0.363414	+	0.931628i	$0.618389\pi$
$242$	989515.	1.08614
$243$	−935501.	−1.01632
$244$	−1.01468e6	−1.09108
$245$	1.18079e6	1.25677
$246$	147728.	0.155641
$247$	61854.4	0.0645102
$248$	228078.	0.235481
$249$	−635114.	−0.649162
$250$	2.02499e6	2.04915
$251$	−1.05369e6	−1.05567	−0.527837	−	0.849346i	$-0.676997\pi$
$251$	−1.05369e6	−1.05567	−0.527837	+	0.849346i	$0.676997\pi$
$252$	2.67971e6	2.65819
$253$	112217.	0.110219
$254$	−2.74022e6	−2.66503
$255$	−361769.	−0.348403
$256$	284815.	0.271620
$257$	−1489.15	−0.00140639	−0.000703193	−	1.00000i	$-0.500224\pi$
$257$	−1489.15	−0.00140639	−0.000703193		1.00000i	$0.500224\pi$
$258$	−420000.	−0.392826
$259$	555399.	0.514465
$260$	−2.80597e6	−2.57424
$261$	−1.25140e6	−1.13709
$262$	−1.50110e6	−1.35100
$263$	−1.17068e6	−1.04364	−0.521820	−	0.853056i	$-0.674747\pi$
$263$	−1.17068e6	−1.04364	−0.521820	+	0.853056i	$0.674747\pi$
$264$	1.29158e6	1.14054
$265$	522059.	0.456673
$266$	−176771.	−0.153182
$267$	538459.	0.462248
$268$	1.94933e6	1.65787
$269$	−2.07952e6	−1.75220	−0.876098	−	0.482133i	$-0.839862\pi$
$269$	−2.07952e6	−1.75220	−0.876098	+	0.482133i	$0.839862\pi$
$270$	−1.74096e6	−1.45338
$271$	−506743.	−0.419145	−0.209572	−	0.977793i	$-0.567207\pi$
$271$	−506743.	−0.419145	−0.209572	+	0.977793i	$0.567207\pi$
$272$	2.70742e6	2.21888
$273$	−1.51537e6	−1.23059
$274$	−1.68796e6	−1.35827
$275$	−312198.	−0.248942
$276$	−326519.	−0.258010
$277$	−2.03878e6	−1.59650	−0.798252	−	0.602323i	$-0.794242\pi$
$277$	−2.03878e6	−1.59650	−0.798252	+	0.602323i	$0.794242\pi$
$278$	3.09125e6	2.39896
$279$	67185.1	0.0516729
$280$	4.88370e6	3.72266
$281$	−1.01983e6	−0.770477	−0.385239	−	0.922817i	$-0.625881\pi$
$281$	−1.01983e6	−0.770477	−0.385239	+	0.922817i	$0.625881\pi$
$282$	−1.22670e6	−0.918574
$283$	−1.63409e6	−1.21285	−0.606427	−	0.795139i	$-0.707398\pi$
$283$	−1.63409e6	−1.21285	−0.606427	+	0.795139i	$0.707398\pi$
$284$	4.66579e6	3.43265
$285$	32363.3	0.0236016
$286$	2.17601e6	1.57306
$287$	−311420.	−0.223173
$288$	2.44108e6	1.73421
$289$	−634667.	−0.446994
$290$	−3.74483e6	−2.61479
$291$	600523.	0.415717
$292$	2.55320e6	1.75238
$293$	648490.	0.441300	0.220650	−	0.975353i	$-0.429182\pi$
$293$	648490.	0.441300	0.220650	+	0.975353i	$0.429182\pi$
$294$	2.66441e6	1.79776
$295$	−363827.	−0.243411
$296$	1.41326e6	0.937549
$297$	970607.	0.638487
$298$	−3.06804e6	−2.00134
$299$	−335024.	−0.216720
$300$	908406.	0.582742
$301$	885387.	0.563271
$302$	1.79302e6	1.13128
$303$	−225180.	−0.140904
$304$	−242202.	−0.150312
$305$	−544729.	−0.335298
$306$	1.48114e6	0.904259
$307$	−1.34624e6	−0.815223	−0.407611	−	0.913156i	$-0.633638\pi$
$307$	−1.34624e6	−0.815223	−0.407611	+	0.913156i	$0.633638\pi$
$308$	−4.47073e6	−2.68535
$309$	397885.	0.237062
$310$	201052.	0.118824
$311$	−2.77623e6	−1.62763	−0.813813	−	0.581127i	$-0.802612\pi$
$311$	−2.77623e6	−1.62763	−0.813813	+	0.581127i	$0.802612\pi$
$312$	−3.85600e6	−2.24259
$313$	−1.26612e6	−0.730491	−0.365246	−	0.930911i	$-0.619015\pi$
$313$	−1.26612e6	−0.730491	−0.365246	+	0.930911i	$0.619015\pi$
$314$	1.63100e6	0.933536
$315$	1.43859e6	0.816886
$316$	7.51413e6	4.23312
$317$	−1.78034e6	−0.995075	−0.497538	−	0.867442i	$-0.665762\pi$
$317$	−1.78034e6	−0.995075	−0.497538	+	0.867442i	$0.665762\pi$
$318$	1.17801e6	0.653252
$319$	2.08779e6	1.14871
$320$	3.00906e6	1.64269
$321$	1.14656e6	0.621060
$322$	957450.	0.514608
$323$	−70241.9	−0.0374619
$324$	291448.	0.154240
$325$	932067.	0.489484
$326$	−5.44711e6	−2.83871
$327$	−424297.	−0.219432
$328$	−792436.	−0.406705
$329$	2.58595e6	1.31714
$330$	1.13853e6	0.575518
$331$	−2.43066e6	−1.21942	−0.609711	−	0.792624i	$-0.708714\pi$
$331$	−2.43066e6	−1.21942	−0.609711	+	0.792624i	$0.708714\pi$
$332$	5.59407e6	2.78537
$333$	416306.	0.205732
$334$	6.02699e6	2.95620
$335$	1.04649e6	0.509476
$336$	5.93370e6	2.86733
$337$	2.44213e6	1.17137	0.585684	−	0.810539i	$-0.300826\pi$
$337$	2.44213e6	1.17137	0.585684	+	0.810539i	$0.300826\pi$
$338$	−2.53489e6	−1.20689
$339$	1.39195e6	0.657848
$340$	3.18646e6	1.49490
$341$	−112089.	−0.0522008
$342$	−132501.	−0.0612566
$343$	−2.10407e6	−0.965662
$344$	2.25295e6	1.02649
$345$	−175291.	−0.0792886
$346$	2.12479e6	0.954169
$347$	−1.67434e6	−0.746483	−0.373241	−	0.927734i	$-0.621754\pi$
$347$	−1.67434e6	−0.746483	−0.373241	+	0.927734i	$0.621754\pi$
$348$	−6.07487e6	−2.68899
$349$	1.44976e6	0.637136	0.318568	−	0.947900i	$-0.396798\pi$
$349$	1.44976e6	0.637136	0.318568	+	0.947900i	$0.396798\pi$
$350$	−2.66371e6	−1.16230
$351$	−2.89775e6	−1.25543
$352$	−4.07261e6	−1.75193
$353$	−1.61900e6	−0.691527	−0.345764	−	0.938322i	$-0.612380\pi$
$353$	−1.61900e6	−0.691527	−0.345764	+	0.938322i	$0.612380\pi$
$354$	−820963.	−0.348189
$355$	2.50481e6	1.05488
$356$	−4.74274e6	−1.98337
$357$	1.72085e6	0.714618
$358$	6.69904e6	2.76252
$359$	−325273.	−0.133202	−0.0666011	−	0.997780i	$-0.521216\pi$
$359$	−325273.	−0.133202	−0.0666011	+	0.997780i	$0.521216\pi$
$360$	3.66063e6	1.48867
$361$	−2.46982e6	−0.997462
$362$	−3.28519e6	−1.31761
$363$	861741.	0.343250
$364$	1.33474e7	5.28010
$365$	1.37067e6	0.538520
$366$	−1.22916e6	−0.479630
$367$	353185.	0.136879	0.0684395	−	0.997655i	$-0.478198\pi$
$367$	353185.	0.136879	0.0684395	+	0.997655i	$0.478198\pi$
$368$	1.31185e6	0.504967
$369$	−233428.	−0.0892457
$370$	1.24580e6	0.473090
$371$	−2.48332e6	−0.936693
$372$	326147.	0.122196
$373$	1.41871e6	0.527987	0.263993	−	0.964525i	$-0.414960\pi$
$373$	1.41871e6	0.527987	0.263993	+	0.964525i	$0.414960\pi$
$374$	−2.47108e6	−0.913498
$375$	1.76351e6	0.647589
$376$	6.58019e6	2.40032
$377$	−6.23310e6	−2.25866
$378$	8.28135e6	2.98107
$379$	−607479.	−0.217237	−0.108618	−	0.994084i	$-0.534643\pi$
$379$	−607479.	−0.217237	−0.108618	+	0.994084i	$0.534643\pi$
$380$	−285056.	−0.101268
$381$	−2.38639e6	−0.842225
$382$	−9.56838e6	−3.35490
$383$	−2.39923e6	−0.835746	−0.417873	−	0.908505i	$-0.637224\pi$
$383$	−2.39923e6	−0.835746	−0.417873	+	0.908505i	$0.637224\pi$
$384$	2.15657e6	0.746338
$385$	−2.40009e6	−0.825232
$386$	485715.	0.165926
$387$	663652.	0.225249
$388$	−5.28940e6	−1.78372
$389$	−4.46259e6	−1.49525	−0.747623	−	0.664123i	$-0.768805\pi$
$389$	−4.46259e6	−1.49525	−0.747623	+	0.664123i	$0.768805\pi$
$390$	−3.39908e6	−1.13162
$391$	380453.	0.125852
$392$	−1.42923e7	−4.69773
$393$	−1.30727e6	−0.426956
$394$	−9.32699e6	−3.02692
$395$	4.03393e6	1.30087
$396$	−3.35108e6	−1.07386
$397$	−813957.	−0.259194	−0.129597	−	0.991567i	$-0.541368\pi$
$397$	−813957.	−0.259194	−0.129597	+	0.991567i	$0.541368\pi$
$398$	−5.02186e6	−1.58912
$399$	−153945.	−0.0484098
$400$	−3.64967e6	−1.14052
$401$	3.12582e6	0.970739	0.485370	−	0.874309i	$-0.338685\pi$
$401$	3.12582e6	0.970739	0.485370	+	0.874309i	$0.338685\pi$
$402$	2.36137e6	0.728785
$403$	334642.	0.102640
$404$	1.98338e6	0.604580
$405$	156463.	0.0473994
$406$	1.78133e7	5.36326
$407$	−694548.	−0.207834
$408$	4.37887e6	1.30230
$409$	−1.85255e6	−0.547597	−0.273799	−	0.961787i	$-0.588280\pi$
$409$	−1.85255e6	−0.547597	−0.273799	+	0.961787i	$0.588280\pi$
$410$	−698535.	−0.205224
$411$	−1.47000e6	−0.429253
$412$	−3.50457e6	−1.01717
$413$	1.73064e6	0.499266
$414$	717667.	0.205789
$415$	3.00315e6	0.855968
$416$	1.21588e7	3.44474
$417$	2.69209e6	0.758139
$418$	221059.	0.0618825
$419$	2.99758e6	0.834133	0.417067	−	0.908876i	$-0.363058\pi$
$419$	2.99758e6	0.834133	0.417067	+	0.908876i	$0.363058\pi$
$420$	6.98358e6	1.93177
$421$	1.33208e6	0.366291	0.183145	−	0.983086i	$-0.441372\pi$
$421$	1.33208e6	0.366291	0.183145	+	0.983086i	$0.441372\pi$
$422$	−2.82644e6	−0.772608
$423$	1.93833e6	0.526716
$424$	−6.31903e6	−1.70701
$425$	−1.05845e6	−0.284250
$426$	5.65202e6	1.50897
$427$	2.59115e6	0.687738
$428$	−1.00989e7	−2.66479
$429$	1.89503e6	0.497133
$430$	1.98598e6	0.517970
$431$	221436.	0.0574190	0.0287095	−	0.999588i	$-0.490860\pi$
$431$	221436.	0.0574190	0.0287095	+	0.999588i	$0.490860\pi$
$432$	1.13466e7	2.92522
$433$	−2.15443e6	−0.552220	−0.276110	−	0.961126i	$-0.589045\pi$
$433$	−2.15443e6	−0.552220	−0.276110	+	0.961126i	$0.589045\pi$
$434$	−956359.	−0.243723
$435$	−3.26127e6	−0.826348
$436$	3.73720e6	0.941521
$437$	−34034.8	−0.00852548
$438$	3.09288e6	0.770331
$439$	3.22054e6	0.797568	0.398784	−	0.917045i	$-0.369432\pi$
$439$	3.22054e6	0.797568	0.398784	+	0.917045i	$0.369432\pi$
$440$	−6.10725e6	−1.50388
$441$	−4.21009e6	−1.03085
$442$	7.37741e6	1.79617
$443$	3.19669e6	0.773911	0.386956	−	0.922098i	$-0.373527\pi$
$443$	3.19669e6	0.773911	0.386956	+	0.922098i	$0.373527\pi$
$444$	2.02094e6	0.486514
$445$	−2.54612e6	−0.609507
$446$	6.52074e6	1.55224
$447$	−2.67187e6	−0.632479
$448$	−1.43134e7	−3.36936
$449$	−5.10546e6	−1.19514	−0.597571	−	0.801816i	$-0.703867\pi$
$449$	−5.10546e6	−1.19514	−0.597571	+	0.801816i	$0.703867\pi$
$450$	−1.99661e6	−0.464796
$451$	389442.	0.0901575
$452$	−1.22603e7	−2.82264
$453$	1.56150e6	0.357516
$454$	−1.31071e7	−2.98447
$455$	7.16548e6	1.62262
$456$	−391727.	−0.0882209
$457$	−1.38784e6	−0.310849	−0.155425	−	0.987848i	$-0.549675\pi$
$457$	−1.38784e6	−0.310849	−0.155425	+	0.987848i	$0.549675\pi$
$458$	−5.27267e6	−1.17454
$459$	3.29068e6	0.729045
$460$	1.54396e6	0.340205
$461$	3.77116e6	0.826461	0.413230	−	0.910626i	$-0.364400\pi$
$461$	3.77116e6	0.826461	0.413230	+	0.910626i	$0.364400\pi$
$462$	−5.41572e6	−1.18046
$463$	7.67938e6	1.66484	0.832422	−	0.554142i	$-0.186953\pi$
$463$	7.67938e6	1.66484	0.832422	+	0.554142i	$0.186953\pi$
$464$	2.44068e7	5.26279
$465$	175091.	0.0375518
$466$	3.65649e6	0.780010
$467$	7.96999e6	1.69109	0.845543	−	0.533908i	$-0.179277\pi$
$467$	7.96999e6	1.69109	0.845543	+	0.533908i	$0.179277\pi$
$468$	1.00047e7	2.11148
$469$	−4.97792e6	−1.04500
$470$	5.80047e6	1.21121
$471$	1.42040e6	0.295024
$472$	4.40378e6	0.909851
$473$	−1.10721e6	−0.227550
$474$	9.10242e6	1.86085
$475$	94687.7	0.0192557
$476$	−1.51573e7	−3.06622
$477$	−1.86140e6	−0.374579
$478$	−1.84706e7	−3.69752
$479$	−3.27651e6	−0.652488	−0.326244	−	0.945286i	$-0.605783\pi$
$479$	−3.27651e6	−0.652488	−0.326244	+	0.945286i	$0.605783\pi$
$480$	6.36169e6	1.26029
$481$	2.07358e6	0.408655
$482$	6.99245e6	1.37092
$483$	833817.	0.162631
$484$	−7.59021e6	−1.47279
$485$	−2.83959e6	−0.548153
$486$	9.98157e6	1.91694
$487$	−6.79152e6	−1.29761	−0.648805	−	0.760954i	$-0.724731\pi$
$487$	−6.79152e6	−1.29761	−0.648805	+	0.760954i	$0.724731\pi$
$488$	6.59342e6	1.25332
$489$	−4.74373e6	−0.897115
$490$	−1.25987e7	−2.37048
$491$	−6.12309e6	−1.14622	−0.573109	−	0.819479i	$-0.694263\pi$
$491$	−6.12309e6	−1.14622	−0.573109	+	0.819479i	$0.694263\pi$
$492$	−1.13317e6	−0.211048
$493$	7.07830e6	1.31163
$494$	−659972.	−0.121677
$495$	−1.79901e6	−0.330006
$496$	−1.31035e6	−0.239157
$497$	−1.19148e7	−2.16370
$498$	6.77651e6	1.22443
$499$	7.92151e6	1.42415	0.712076	−	0.702102i	$-0.247755\pi$
$499$	7.92151e6	1.42415	0.712076	+	0.702102i	$0.247755\pi$
$500$	−1.55330e7	−2.77862
$501$	5.24874e6	0.934245
$502$	1.12426e7	1.99117
$503$	−1.12048e7	−1.97462	−0.987311	−	0.158800i	$-0.949237\pi$
$503$	−1.12048e7	−1.97462	−0.987311	+	0.158800i	$0.949237\pi$
$504$	−1.74128e7	−3.05346
$505$	1.06477e6	0.185792
$506$	−1.19733e6	−0.207892
$507$	−2.20756e6	−0.381411
$508$	2.10192e7	3.61375
$509$	−5.65186e6	−0.966934	−0.483467	−	0.875362i	$-0.660623\pi$
$509$	−5.65186e6	−0.966934	−0.483467	+	0.875362i	$0.660623\pi$
$510$	3.85999e6	0.657145
$511$	−6.51998e6	−1.10457
$512$	4.38794e6	0.739751
$513$	−294379.	−0.0493871
$514$	15888.8	0.00265268
$515$	−1.88141e6	−0.312583
$516$	3.22167e6	0.532668
$517$	−3.23383e6	−0.532098
$518$	−5.92598e6	−0.970366
$519$	1.85042e6	0.301545
$520$	1.82332e7	2.95702
$521$	4.62211e6	0.746013	0.373007	−	0.927829i	$-0.378327\pi$
$521$	4.62211e6	0.746013	0.373007	+	0.927829i	$0.378327\pi$
$522$	1.33521e7	2.14474
$523$	7.51331e6	1.20109	0.600547	−	0.799589i	$-0.294949\pi$
$523$	7.51331e6	1.20109	0.600547	+	0.799589i	$0.294949\pi$
$524$	1.15144e7	1.83195
$525$	−2.31975e6	−0.367319
$526$	1.24909e7	1.96848
$527$	−380019.	−0.0596045
$528$	−7.42032e6	−1.15835
$529$	−6.25200e6	−0.971359
$530$	−5.57025e6	−0.861360
$531$	1.29722e6	0.199654
$532$	1.35595e6	0.207713
$533$	−1.16268e6	−0.177273
$534$	−5.74523e6	−0.871875
$535$	−5.42153e6	−0.818913
$536$	−1.26668e7	−1.90438
$537$	5.83401e6	0.873035
$538$	2.21880e7	3.30493
$539$	7.02396e6	1.04138
$540$	1.33543e7	1.97077
$541$	−5.34819e6	−0.785622	−0.392811	−	0.919619i	$-0.628497\pi$
$541$	−5.34819e6	−0.785622	−0.392811	+	0.919619i	$0.628497\pi$
$542$	5.40682e6	0.790577
$543$	−2.86098e6	−0.416404
$544$	−1.38075e7	−2.00040
$545$	2.00630e6	0.289337
$546$	1.61687e7	2.32109
$547$	−299209.	−0.0427569
$547$	−299209.	−0.0427569
$548$	1.29477e7	1.84180
$549$	1.94222e6	0.275023
$550$	3.33107e6	0.469545
$551$	−633214.	−0.0888529
$552$	2.12172e6	0.296375
$553$	−1.91885e7	−2.66826
$554$	2.17533e7	3.01127
$555$	1.08493e6	0.149510
$556$	−2.37119e7	−3.25296
$557$	4.37828e6	0.597951	0.298976	−	0.954261i	$-0.403355\pi$
$557$	4.37828e6	0.597951	0.298976	+	0.954261i	$0.403355\pi$
$558$	−716849.	−0.0974635
$559$	3.30558e6	0.447423
$560$	−2.80577e7	−3.78078
$561$	−2.15200e6	−0.288692
$562$	1.08813e7	1.45325
$563$	−4.24951e6	−0.565025	−0.282513	−	0.959264i	$-0.591168\pi$
$563$	−4.24951e6	−0.565025	−0.282513	+	0.959264i	$0.591168\pi$
$564$	9.40953e6	1.24558
$565$	−6.58189e6	−0.867421
$566$	1.74353e7	2.28764
$567$	−744257.	−0.0972222
$568$	−3.03184e7	−3.94307
$569$	−1.09634e7	−1.41959	−0.709797	−	0.704407i	$-0.751213\pi$
$569$	−1.09634e7	−1.41959	−0.709797	+	0.704407i	$0.751213\pi$
$570$	−345309.	−0.0445165
$571$	9.73184e6	1.24912	0.624561	−	0.780976i	$-0.285278\pi$
$571$	9.73184e6	1.24912	0.624561	+	0.780976i	$0.285278\pi$
$572$	−1.66914e7	−2.13306
$573$	−8.33284e6	−1.06025
$574$	3.32277e6	0.420941
$575$	−512860.	−0.0646888
$576$	−1.07288e7	−1.34739
$577$	−1.29220e7	−1.61581	−0.807906	−	0.589312i	$-0.799399\pi$
$577$	−1.29220e7	−1.61581	−0.807906	+	0.589312i	$0.799399\pi$
$578$	6.77175e6	0.843104
$579$	422996.	0.0524372
$580$	2.87252e7	3.54563
$581$	−1.42853e7	−1.75570
$582$	−6.40744e6	−0.784110
$583$	3.10548e6	0.378406
$584$	−1.65907e7	−2.01295
$585$	5.37096e6	0.648877
$586$	−6.91923e6	−0.832365
$587$	−8.72616e6	−1.04527	−0.522634	−	0.852557i	$-0.675051\pi$
$587$	−8.72616e6	−1.04527	−0.522634	+	0.852557i	$0.675051\pi$
$588$	−2.04377e7	−2.43775
$589$	33995.9	0.00403775
$590$	3.88195e6	0.459113
$591$	−8.12262e6	−0.956594
$592$	−8.11945e6	−0.952187
$593$	4.04314e6	0.472153	0.236076	−	0.971735i	$-0.424138\pi$
$593$	4.04314e6	0.472153	0.236076	+	0.971735i	$0.424138\pi$
$594$	−1.03561e7	−1.20429
$595$	−8.13711e6	−0.942276
$596$	2.35338e7	2.71379
$597$	−4.37340e6	−0.502208
$598$	3.57463e6	0.408769
$599$	7.75545e6	0.883161	0.441580	−	0.897222i	$-0.354418\pi$
$599$	7.75545e6	0.883161	0.441580	+	0.897222i	$0.354418\pi$
$600$	−5.90282e6	−0.669394
$601$	−1.41271e7	−1.59539	−0.797696	−	0.603060i	$-0.793948\pi$
$601$	−1.41271e7	−1.59539	−0.797696	+	0.603060i	$0.793948\pi$
$602$	−9.44687e6	−1.06242
$603$	−3.73126e6	−0.417890
$604$	−1.37536e7	−1.53400
$605$	−4.07477e6	−0.452600
$606$	2.40262e6	0.265769
$607$	−2.61167e6	−0.287704	−0.143852	−	0.989599i	$-0.545949\pi$
$607$	−2.61167e6	−0.287704	−0.143852	+	0.989599i	$0.545949\pi$
$608$	1.23520e6	0.135512
$609$	1.55131e7	1.69494
$610$	5.81212e6	0.632427
$611$	9.65462e6	1.04624
$612$	−1.13613e7	−1.22617
$613$	−1.48753e7	−1.59888	−0.799440	−	0.600746i	$-0.794870\pi$
$613$	−1.48753e7	−1.59888	−0.799440	+	0.600746i	$0.794870\pi$
$614$	1.43640e7	1.53764
$615$	−608335.	−0.0648568
$616$	2.90508e7	3.08466
$617$	8.07851e6	0.854315	0.427158	−	0.904177i	$-0.359515\pi$
$617$	8.07851e6	0.854315	0.427158	+	0.904177i	$0.359515\pi$
$618$	−4.24534e6	−0.447138
$619$	−3.95799e6	−0.415192	−0.207596	−	0.978215i	$-0.566564\pi$
$619$	−3.95799e6	−0.415192	−0.207596	+	0.978215i	$0.566564\pi$
$620$	−1.54220e6	−0.161124
$621$	1.59446e6	0.165914
$622$	2.96217e7	3.06997
$623$	1.21113e7	1.25018
$624$	2.21534e7	2.27761
$625$	−4.60600e6	−0.471655
$626$	1.35092e7	1.37783
$627$	192514.	0.0195566
$628$	−1.25108e7	−1.26586
$629$	−2.35475e6	−0.237311
$630$	−1.53494e7	−1.54078
$631$	−8.94896e6	−0.894744	−0.447372	−	0.894348i	$-0.647640\pi$
$631$	−8.94896e6	−0.894744	−0.447372	+	0.894348i	$0.647640\pi$
$632$	−4.88268e7	−4.86257
$633$	−2.46147e6	−0.244166
$634$	1.89959e7	1.87688
$635$	1.12841e7	1.11054
$636$	−9.03607e6	−0.885802
$637$	−2.09700e7	−2.04763
$638$	−2.22762e7	−2.16665
$639$	−8.93088e6	−0.865251
$640$	−1.01974e7	−0.984101
$641$	8.26183e6	0.794203	0.397101	−	0.917775i	$-0.370016\pi$
$641$	8.26183e6	0.794203	0.397101	+	0.917775i	$0.370016\pi$
$642$	−1.22335e7	−1.17142
$643$	−2.22452e6	−0.212182	−0.106091	−	0.994356i	$-0.533833\pi$
$643$	−2.22452e6	−0.212182	−0.106091	+	0.994356i	$0.533833\pi$
$644$	−7.34425e6	−0.697803
$645$	1.72954e6	0.163693
$646$	749464.	0.0706593
$647$	−1.52713e7	−1.43422	−0.717108	−	0.696962i	$-0.754535\pi$
$647$	−1.52713e7	−1.43422	−0.717108	+	0.696962i	$0.754535\pi$
$648$	−1.89383e6	−0.177175
$649$	−2.16423e6	−0.201694
$650$	−9.94493e6	−0.923248
$651$	−832866.	−0.0770234
$652$	4.17827e7	3.84927
$653$	1.90099e6	0.174461	0.0872304	−	0.996188i	$-0.472198\pi$
$653$	1.90099e6	0.174461	0.0872304	+	0.996188i	$0.472198\pi$
$654$	4.52714e6	0.413885
$655$	6.18146e6	0.562973
$656$	4.55268e6	0.413055
$657$	−4.88712e6	−0.441713
$658$	−2.75915e7	−2.48434
$659$	1.76323e7	1.58160	0.790799	−	0.612076i	$-0.209666\pi$
$659$	1.76323e7	1.58160	0.790799	+	0.612076i	$0.209666\pi$
$660$	−8.73324e6	−0.780397
$661$	1.30960e7	1.16583	0.582914	−	0.812534i	$-0.301912\pi$
$661$	1.30960e7	1.16583	0.582914	+	0.812534i	$0.301912\pi$
$662$	2.59345e7	2.30003
$663$	6.42479e6	0.567642
$664$	−3.63503e7	−3.19954
$665$	727934.	0.0638319
$666$	−4.44188e6	−0.388044
$667$	3.42970e6	0.298498
$668$	−4.62308e7	−4.00858
$669$	5.67873e6	0.490553
$670$	−1.11658e7	−0.960956
$671$	−3.24033e6	−0.277833
$672$	−3.02611e7	−2.58501
$673$	−607633.	−0.0517135	−0.0258567	−	0.999666i	$-0.508231\pi$
$673$	−607633.	−0.0517135	−0.0258567	+	0.999666i	$0.508231\pi$
$674$	−2.60569e7	−2.20940
$675$	−4.43592e6	−0.374735
$676$	1.94442e7	1.63653
$677$	3.81284e6	0.319725	0.159863	−	0.987139i	$-0.448895\pi$
$677$	3.81284e6	0.319725	0.159863	+	0.987139i	$0.448895\pi$
$678$	−1.48518e7	−1.24081
$679$	1.35073e7	1.12433
$680$	−2.07056e7	−1.71718
$681$	−1.14146e7	−0.943178
$682$	1.19596e6	0.0984594
$683$	3.64852e6	0.299271	0.149636	−	0.988741i	$-0.452190\pi$
$683$	3.64852e6	0.299271	0.149636	+	0.988741i	$0.452190\pi$
$684$	1.01636e6	0.0830632
$685$	6.95094e6	0.566001
$686$	2.24499e7	1.82140
$687$	−4.59182e6	−0.371188
$688$	−1.29436e7	−1.04252
$689$	−9.27143e6	−0.744044
$690$	1.87031e6	0.149551
$691$	1.21733e7	0.969870	0.484935	−	0.874550i	$-0.338843\pi$
$691$	1.21733e7	0.969870	0.484935	+	0.874550i	$0.338843\pi$
$692$	−1.62985e7	−1.29384
$693$	8.55751e6	0.676884
$694$	1.78648e7	1.40799
$695$	−1.27296e7	−0.999662
$696$	3.94745e7	3.08883
$697$	1.32034e6	0.102945
$698$	−1.54686e7	−1.20174
$699$	3.18434e6	0.246505
$700$	2.04323e7	1.57606
$701$	−2.52439e6	−0.194027	−0.0970133	−	0.995283i	$-0.530929\pi$
$701$	−2.52439e6	−0.194027	−0.0970133	+	0.995283i	$0.530929\pi$
$702$	3.09183e7	2.36795
$703$	210652.	0.0160760
$704$	1.78995e7	1.36116
$705$	5.05147e6	0.382776
$706$	1.72743e7	1.30433
$707$	−5.06488e6	−0.381084
$708$	6.29730e6	0.472141
$709$	3.15243e6	0.235521	0.117760	−	0.993042i	$-0.462429\pi$
$709$	3.15243e6	0.235521	0.117760	+	0.993042i	$0.462429\pi$
$710$	−2.67257e7	−1.98968
$711$	−1.43829e7	−1.06702
$712$	3.08183e7	2.27829
$713$	−184133.	−0.0135646
$714$	−1.83611e7	−1.34789
$715$	−8.96071e6	−0.655507
$716$	−5.13859e7	−3.74594
$717$	−1.60855e7	−1.16852
$718$	3.47058e6	0.251241
$719$	−2.26233e7	−1.63205	−0.816025	−	0.578017i	$-0.803827\pi$
$719$	−2.26233e7	−1.63205	−0.816025	+	0.578017i	$0.803827\pi$
$720$	−2.10309e7	−1.51192
$721$	8.94945e6	0.641148
$722$	2.63523e7	1.88138
$723$	6.08953e6	0.433249
$724$	2.51994e7	1.78667
$725$	−9.54172e6	−0.674189
$726$	−9.19458e6	−0.647426
$727$	2.19466e7	1.54004	0.770020	−	0.638019i	$-0.220246\pi$
$727$	2.19466e7	1.54004	0.770020	+	0.638019i	$0.220246\pi$
$728$	−8.67313e7	−6.06523
$729$	7.82735e6	0.545501
$730$	−1.46248e7	−1.01574
$731$	−3.75381e6	−0.259824
$732$	9.42844e6	0.650372
$733$	−5.16298e6	−0.354928	−0.177464	−	0.984127i	$-0.556789\pi$
$733$	−5.16298e6	−0.354928	−0.177464	+	0.984127i	$0.556789\pi$
$734$	−3.76839e6	−0.258176
$735$	−1.09719e7	−0.749140
$736$	−6.69024e6	−0.455247
$737$	6.22509e6	0.422160
$738$	2.49062e6	0.168332
$739$	2.66105e7	1.79243	0.896213	−	0.443624i	$-0.146307\pi$
$739$	2.66105e7	1.79243	0.896213	+	0.443624i	$0.146307\pi$
$740$	−9.55606e6	−0.641504
$741$	−574752.	−0.0384534
$742$	2.64964e7	1.76676
$743$	1.53356e7	1.01913	0.509565	−	0.860432i	$-0.329806\pi$
$743$	1.53356e7	1.01913	0.509565	+	0.860432i	$0.329806\pi$
$744$	−2.11930e6	−0.140366
$745$	1.26340e7	0.833970
$746$	−1.51373e7	−0.995870
$747$	−1.07077e7	−0.702094
$748$	1.89547e7	1.23869
$749$	2.57890e7	1.67969
$750$	−1.88162e7	−1.22146
$751$	1.95128e7	1.26246	0.631232	−	0.775594i	$-0.282550\pi$
$751$	1.95128e7	1.26246	0.631232	+	0.775594i	$0.282550\pi$
$752$	−3.78043e7	−2.43779
$753$	9.79091e6	0.629268
$754$	6.65057e7	4.26020
$755$	−7.38358e6	−0.471411
$756$	−6.35232e7	−4.04229
$757$	−2.02590e7	−1.28493	−0.642463	−	0.766317i	$-0.722087\pi$
$757$	−2.02590e7	−1.28493	−0.642463	+	0.766317i	$0.722087\pi$
$758$	6.48165e6	0.409744
$759$	−1.04272e6	−0.0656997
$760$	1.85229e6	0.116326
$761$	2.67363e7	1.67355	0.836777	−	0.547544i	$-0.184437\pi$
$761$	2.67363e7	1.67355	0.836777	+	0.547544i	$0.184437\pi$
$762$	2.54622e7	1.58858
$763$	−9.54351e6	−0.593467
$764$	7.33955e7	4.54921
$765$	−6.09926e6	−0.376811
$766$	2.55992e7	1.57636
$767$	6.46133e6	0.396582
$768$	−2.64650e6	−0.161908
$769$	−3.17188e7	−1.93420	−0.967099	−	0.254399i	$-0.918122\pi$
$769$	−3.17188e7	−1.93420	−0.967099	+	0.254399i	$0.918122\pi$
$770$	2.56084e7	1.55652
$771$	13837.1	0.000838321 0
$772$	−3.72574e6	−0.224993
$773$	−2.46943e7	−1.48644	−0.743220	−	0.669047i	$-0.766703\pi$
$773$	−2.46943e7	−1.48644	−0.743220	+	0.669047i	$0.766703\pi$
$774$	−7.08100e6	−0.424857
$775$	512275.	0.0306372
$776$	3.43705e7	2.04895
$777$	−5.16077e6	−0.306663
$778$	4.76147e7	2.82028
$779$	−118116.	−0.00697371
$780$	2.60731e7	1.53446
$781$	1.48999e7	0.874092
$782$	−4.05934e6	−0.237377
$783$	2.96647e7	1.72916
$784$	8.21119e7	4.77107
$785$	−6.71639e6	−0.389011
$786$	1.39482e7	0.805310
$787$	2.16538e7	1.24623	0.623113	−	0.782132i	$-0.285868\pi$
$787$	2.16538e7	1.24623	0.623113	+	0.782132i	$0.285868\pi$
$788$	7.15439e7	4.10447
$789$	1.08780e7	0.622095
$790$	−4.30410e7	−2.45366
$791$	3.13086e7	1.77919
$792$	2.17754e7	1.23354
$793$	9.67402e6	0.546291
$794$	8.68473e6	0.488883
$795$	−4.85097e6	−0.272214
$796$	3.85208e7	2.15483
$797$	1.23045e7	0.686149	0.343074	−	0.939308i	$-0.388532\pi$
$797$	1.23045e7	0.686149	0.343074	+	0.939308i	$0.388532\pi$
$798$	1.64256e6	0.0913089
$799$	−1.09638e7	−0.607566
$800$	1.86128e7	1.02822
$801$	9.07817e6	0.499939
$802$	−3.33517e7	−1.83097
$803$	8.15349e6	0.446226
$804$	−1.81132e7	−0.988224
$805$	−3.94273e6	−0.214441
$806$	−3.57055e6	−0.193597
$807$	1.93229e7	1.04445
$808$	−1.28880e7	−0.694478
$809$	−2.26044e7	−1.21429	−0.607143	−	0.794593i	$-0.707684\pi$
$809$	−2.26044e7	−1.21429	−0.607143	+	0.794593i	$0.707684\pi$
$810$	−1.66942e6	−0.0894031
$811$	3.06246e7	1.63500	0.817501	−	0.575927i	$-0.195359\pi$
$811$	3.06246e7	1.63500	0.817501	+	0.575927i	$0.195359\pi$
$812$	−1.36639e8	−7.27252
$813$	4.70865e6	0.249845
$814$	7.41066e6	0.392009
$815$	2.24309e7	1.18291
$816$	−2.51574e7	−1.32263
$817$	335811.	0.0176011
$818$	1.97663e7	1.03286
$819$	−2.55484e7	−1.33093
$820$	5.35821e6	0.278282
$821$	−1.59866e7	−0.827751	−0.413875	−	0.910334i	$-0.635825\pi$
$821$	−1.59866e7	−0.827751	−0.413875	+	0.910334i	$0.635825\pi$
$822$	1.56846e7	0.809641
$823$	3.54599e6	0.182490	0.0912448	−	0.995828i	$-0.470915\pi$
$823$	3.54599e6	0.182490	0.0912448	+	0.995828i	$0.470915\pi$
$824$	2.27727e7	1.16841
$825$	2.90094e6	0.148390
$826$	−1.84655e7	−0.941698
$827$	2.44364e7	1.24244	0.621218	−	0.783638i	$-0.286638\pi$
$827$	2.44364e7	1.24244	0.621218	+	0.783638i	$0.286638\pi$
$828$	−5.50496e6	−0.279048
$829$	−2.98629e7	−1.50920	−0.754599	−	0.656186i	$-0.772169\pi$
$829$	−2.98629e7	−1.50920	−0.754599	+	0.656186i	$0.772169\pi$
$830$	−3.20429e7	−1.61450
$831$	1.89443e7	0.951648
$832$	−5.34389e7	−2.67639
$833$	2.38136e7	1.18908
$834$	−2.87239e7	−1.42998
$835$	−2.48188e7	−1.23187
$836$	−1.69566e6	−0.0839119
$837$	−1.59264e6	−0.0785784
$838$	−3.19834e7	−1.57331
$839$	−9.55459e6	−0.468605	−0.234303	−	0.972164i	$-0.575281\pi$
$839$	−9.55459e6	−0.468605	−0.234303	+	0.972164i	$0.575281\pi$
$840$	−4.53793e7	−2.21901
$841$	4.32981e7	2.11095
$842$	−1.42130e7	−0.690885
$843$	9.47621e6	0.459268
$844$	2.16806e7	1.04765
$845$	1.04385e7	0.502918
$846$	−2.06815e7	−0.993474
$847$	1.93828e7	0.928340
$848$	3.63039e7	1.73366
$849$	1.51839e7	0.722961
$850$	1.12935e7	0.536141
$851$	−1.14096e6	−0.0540067
$852$	−4.33546e7	−2.04614
$853$	−1.46978e7	−0.691641	−0.345821	−	0.938301i	$-0.612399\pi$
$853$	−1.46978e7	−0.691641	−0.345821	+	0.938301i	$0.612399\pi$
$854$	−2.76470e7	−1.29719
$855$	545631.	0.0255260
$856$	6.56225e7	3.06103
$857$	1.46595e7	0.681814	0.340907	−	0.940097i	$-0.389266\pi$
$857$	1.46595e7	0.681814	0.340907	+	0.940097i	$0.389266\pi$
$858$	−2.02195e7	−0.937676
$859$	−1.38347e7	−0.639717	−0.319859	−	0.947465i	$-0.603635\pi$
$859$	−1.38347e7	−0.639717	−0.319859	+	0.947465i	$0.603635\pi$
$860$	−1.52337e7	−0.702361
$861$	2.89371e6	0.133029
$862$	−2.36267e6	−0.108302
$863$	1.52301e7	0.696105	0.348052	−	0.937475i	$-0.386843\pi$
$863$	1.52301e7	0.696105	0.348052	+	0.937475i	$0.386843\pi$
$864$	−5.78664e7	−2.63719
$865$	−8.74976e6	−0.397609
$866$	2.29872e7	1.04158
$867$	5.89733e6	0.266445
$868$	7.33587e6	0.330486
$869$	2.39959e7	1.07792
$870$	3.47969e7	1.55863
$871$	−1.85850e7	−0.830075
$872$	−2.42843e7	−1.08152
$873$	1.01245e7	0.449614
$874$	363143.	0.0160805
$875$	3.96658e7	1.75144
$876$	−2.37243e7	−1.04456
$877$	2.19135e7	0.962081	0.481041	−	0.876698i	$-0.340259\pi$
$877$	2.19135e7	0.962081	0.481041	+	0.876698i	$0.340259\pi$
$878$	−3.43624e7	−1.50435
$879$	−6.02577e6	−0.263051
$880$	3.50872e7	1.52736
$881$	−3.57089e6	−0.155002	−0.0775009	−	0.996992i	$-0.524694\pi$
$881$	−3.57089e6	−0.155002	−0.0775009	+	0.996992i	$0.524694\pi$
$882$	4.49207e7	1.94435
$883$	2.48614e7	1.07306	0.536530	−	0.843882i	$-0.319735\pi$
$883$	2.48614e7	1.07306	0.536530	+	0.843882i	$0.319735\pi$
$884$	−5.65894e7	−2.43559
$885$	3.38068e6	0.145093
$886$	−3.41079e7	−1.45972
$887$	−2.95182e7	−1.25974	−0.629870	−	0.776700i	$-0.716892\pi$
$887$	−2.95182e7	−1.25974	−0.629870	+	0.776700i	$0.716892\pi$
$888$	−1.31321e7	−0.558856
$889$	−5.36759e7	−2.27785
$890$	2.71665e7	1.14963
$891$	930722.	0.0392759
$892$	−5.00182e7	−2.10482
$893$	980803.	0.0411579
$894$	2.85082e7	1.19296
$895$	−2.75863e7	−1.15116
$896$	4.85067e7	2.01852
$897$	3.11304e6	0.129183
$898$	5.44741e7	2.25423
$899$	−3.42579e6	−0.141371
$900$	1.53153e7	0.630259
$901$	1.05286e7	0.432075
$902$	−4.15526e6	−0.170052
$903$	−8.22702e6	−0.335756
$904$	7.96675e7	3.24235
$905$	1.35282e7	0.549059
$906$	−1.66608e7	−0.674334
$907$	7.90160e6	0.318931	0.159465	−	0.987204i	$-0.449023\pi$
$907$	7.90160e6	0.318931	0.159465	+	0.987204i	$0.449023\pi$
$908$	1.00540e8	4.04691
$909$	−3.79643e6	−0.152393
$910$	−7.64539e7	−3.06053
$911$	−3.66252e7	−1.46212	−0.731062	−	0.682312i	$-0.760975\pi$
$911$	−3.66252e7	−1.46212	−0.731062	+	0.682312i	$0.760975\pi$
$912$	2.25054e6	0.0895983
$913$	1.78643e7	0.709268
$914$	1.48080e7	0.586313
$915$	5.06162e6	0.199865
$916$	4.04447e7	1.59266
$917$	−2.94038e7	−1.15473
$918$	−3.51108e7	−1.37510
$919$	−2.18212e7	−0.852295	−0.426147	−	0.904654i	$-0.640129\pi$
$919$	−2.18212e7	−0.852295	−0.426147	+	0.904654i	$0.640129\pi$
$920$	−1.00326e7	−0.390792
$921$	1.25093e7	0.485940
$922$	−4.02373e7	−1.55884
$923$	−4.44838e7	−1.71869
$924$	4.15420e7	1.60069
$925$	3.17426e6	0.121980
$926$	−8.19371e7	−3.14017
$927$	6.70816e6	0.256392
$928$	−1.24471e8	−4.74460
$929$	1.41465e6	0.0537787	0.0268894	−	0.999638i	$-0.491440\pi$
$929$	1.41465e6	0.0537787	0.0268894	+	0.999638i	$0.491440\pi$
$930$	−1.86818e6	−0.0708289
$931$	−2.13032e6	−0.0805511
$932$	−2.80476e7	−1.05768
$933$	2.57967e7	0.970199
$934$	−8.50379e7	−3.18967
$935$	1.01758e7	0.380661
$936$	−6.50104e7	−2.42545
$937$	2.71676e7	1.01088	0.505442	−	0.862860i	$-0.331329\pi$
$937$	2.71676e7	1.01088	0.505442	+	0.862860i	$0.331329\pi$
$938$	5.31133e7	1.97104
$939$	1.17648e7	0.435433
$940$	−4.44932e7	−1.64238
$941$	2.39151e7	0.880436	0.440218	−	0.897891i	$-0.354901\pi$
$941$	2.39151e7	0.880436	0.440218	+	0.897891i	$0.354901\pi$
$942$	−1.51553e7	−0.556464
$943$	639753.	0.0234279
$944$	−2.53005e7	−0.924056
$945$	−3.41021e7	−1.24223
$946$	1.18137e7	0.429198
$947$	7.28782e6	0.264072	0.132036	−	0.991245i	$-0.457849\pi$
$947$	7.28782e6	0.264072	0.132036	+	0.991245i	$0.457849\pi$
$948$	−6.98213e7	−2.52329
$949$	−2.43423e7	−0.877396
$950$	−1.01030e6	−0.0363194
$951$	1.65430e7	0.593147
$952$	9.84920e7	3.52215
$953$	2.29798e7	0.819623	0.409811	−	0.912170i	$-0.365595\pi$
$953$	2.29798e7	0.819623	0.409811	+	0.912170i	$0.365595\pi$
$954$	1.98607e7	0.706517
$955$	3.94021e7	1.39801
$956$	1.41681e8	5.01379
$957$	−1.93997e7	−0.684725
$958$	3.49596e7	1.23070
$959$	−3.30640e7	−1.16094
$960$	−2.79602e7	−0.979178
$961$	−2.84452e7	−0.993576
$962$	−2.21246e7	−0.770791
$963$	1.93304e7	0.671701
$964$	−5.36365e7	−1.85895
$965$	−2.00015e6	−0.0691423
$966$	−8.89663e6	−0.306749
$967$	−5.25893e7	−1.80855	−0.904276	−	0.426948i	$-0.859589\pi$
$967$	−5.25893e7	−1.80855	−0.904276	+	0.426948i	$0.859589\pi$
$968$	4.93212e7	1.69178
$969$	652687.	0.0223304
$970$	3.02978e7	1.03391
$971$	−5.33382e7	−1.81548	−0.907738	−	0.419537i	$-0.862192\pi$
$971$	−5.33382e7	−1.81548	−0.907738	+	0.419537i	$0.862192\pi$
$972$	−7.65649e7	−2.59935
$973$	6.05519e7	2.05043
$974$	7.24639e7	2.44751
$975$	−8.66076e6	−0.291773
$976$	−3.78803e7	−1.27288
$977$	4.03613e7	1.35278	0.676392	−	0.736542i	$-0.263543\pi$
$977$	4.03613e7	1.35278	0.676392	+	0.736542i	$0.263543\pi$
$978$	5.06145e7	1.69211
$979$	−1.51457e7	−0.505047
$980$	9.66403e7	3.21435
$981$	−7.15344e6	−0.237324
$982$	6.53319e7	2.16196
$983$	−1.54483e7	−0.509914	−0.254957	−	0.966952i	$-0.582061\pi$
$983$	−1.54483e7	−0.509914	−0.254957	+	0.966952i	$0.582061\pi$
$984$	7.36332e6	0.242430
$985$	3.84080e7	1.26134
$986$	−7.55238e7	−2.47395
$987$	−2.40287e7	−0.785122
$988$	5.06240e6	0.164993
$989$	−1.81886e6	−0.0591301
$990$	1.91951e7	0.622446
$991$	−1.07434e7	−0.347504	−0.173752	−	0.984789i	$-0.555589\pi$
$991$	−1.07434e7	−0.347504	−0.173752	+	0.984789i	$0.555589\pi$
$992$	6.68261e6	0.215609
$993$	2.25857e7	0.726875
$994$	1.27128e8	4.08109
$995$	2.06798e7	0.662198
$996$	−5.19801e7	−1.66031
$997$	−4.08911e7	−1.30284	−0.651420	−	0.758717i	$-0.725826\pi$
$997$	−4.08911e7	−1.30284	−0.651420	+	0.758717i	$0.725826\pi$
$998$	−8.45206e7	−2.68619
$999$	−9.86861e6	−0.312855

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.a.1.6	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.a.1.6	✓	111	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-10.6698 q^{2} -9.29200 q^{3} +81.8438 q^{4} +43.9375 q^{5} +99.1434 q^{6} -209.001 q^{7} -531.821 q^{8} -156.659 q^{9} +O(q^{10})\)	\(q-10.6698 q^{2} -9.29200 q^{3} +81.8438 q^{4} +43.9375 q^{5} +99.1434 q^{6} -209.001 q^{7} -531.821 q^{8} -156.659 q^{9} -468.803 q^{10} +261.363 q^{11} -760.493 q^{12} -780.301 q^{13} +2229.99 q^{14} -408.267 q^{15} +3055.41 q^{16} +886.109 q^{17} +1671.51 q^{18} -79.2700 q^{19} +3596.01 q^{20} +1942.03 q^{21} -2788.69 q^{22} +429.352 q^{23} +4941.68 q^{24} -1194.50 q^{25} +8325.62 q^{26} +3713.63 q^{27} -17105.4 q^{28} +7988.07 q^{29} +4356.11 q^{30} -428.863 q^{31} -15582.2 q^{32} -2428.59 q^{33} -9454.57 q^{34} -9182.97 q^{35} -12821.5 q^{36} -2657.40 q^{37} +845.792 q^{38} +7250.56 q^{39} -23366.9 q^{40} +1490.04 q^{41} -20721.0 q^{42} -4236.29 q^{43} +21391.0 q^{44} -6883.19 q^{45} -4581.09 q^{46} -12372.9 q^{47} -28390.8 q^{48} +26874.3 q^{49} +12745.0 q^{50} -8233.73 q^{51} -63862.8 q^{52} +11881.9 q^{53} -39623.5 q^{54} +11483.7 q^{55} +111151. q^{56} +736.577 q^{57} -85230.8 q^{58} -8280.56 q^{59} -33414.1 q^{60} -12397.8 q^{61} +4575.86 q^{62} +32741.8 q^{63} +68484.9 q^{64} -34284.5 q^{65} +25912.5 q^{66} +23817.7 q^{67} +72522.5 q^{68} -3989.54 q^{69} +97980.1 q^{70} +57008.5 q^{71} +83314.5 q^{72} +31196.0 q^{73} +28353.9 q^{74} +11099.3 q^{75} -6487.76 q^{76} -54625.1 q^{77} -77361.7 q^{78} +91810.6 q^{79} +134247. q^{80} +3561.03 q^{81} -15898.4 q^{82} +68350.6 q^{83} +158943. q^{84} +38933.4 q^{85} +45200.2 q^{86} -74225.1 q^{87} -138999. q^{88} -57948.7 q^{89} +73442.0 q^{90} +163083. q^{91} +35139.8 q^{92} +3984.99 q^{93} +132016. q^{94} -3482.92 q^{95} +144789. q^{96} -64628.0 q^{97} -286742. q^{98} -40944.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) \) 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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