LMFDB - Embedded newform 546.8.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,8,Mod(1,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	546.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:	$170.562223914$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5672x^{3} - 117684x^{2} + 1695035x + 39011360 $ x^5 - 5672x^3 - 117684x^2 + 1695035*x + 39011360
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-57.6599$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -455.940 q^{5} -216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -455.940 q^{5} -216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +3647.52 q^{10} -5884.22 q^{11} +1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -12310.4 q^{15} +4096.00 q^{16} +3935.44 q^{17} -5832.00 q^{18} +43343.4 q^{19} -29180.2 q^{20} -9261.00 q^{21} +47073.8 q^{22} -25466.3 q^{23} -13824.0 q^{24} +129757. q^{25} +17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -159093. q^{29} +98483.1 q^{30} +288214. q^{31} -32768.0 q^{32} -158874. q^{33} -31483.5 q^{34} +156388. q^{35} +46656.0 q^{36} +13534.1 q^{37} -346748. q^{38} -59319.0 q^{39} +233441. q^{40} +217366. q^{41} +74088.0 q^{42} +363727. q^{43} -376590. q^{44} -332381. q^{45} +203731. q^{46} +1.04659e6 q^{47} +110592. q^{48} +117649. q^{49} -1.03805e6 q^{50} +106257. q^{51} -140608. q^{52} -857306. q^{53} -157464. q^{54} +2.68285e6 q^{55} +175616. q^{56} +1.17027e6 q^{57} +1.27274e6 q^{58} +1.12738e6 q^{59} -787865. q^{60} -1.04392e6 q^{61} -2.30571e6 q^{62} -250047. q^{63} +262144. q^{64} +1.00170e6 q^{65} +1.27099e6 q^{66} +1.23985e6 q^{67} +251868. q^{68} -687591. q^{69} -1.25110e6 q^{70} +2.22410e6 q^{71} -373248. q^{72} -2.32432e6 q^{73} -108273. q^{74} +3.50343e6 q^{75} +2.77398e6 q^{76} +2.01829e6 q^{77} +474552. q^{78} -4.89794e6 q^{79} -1.86753e6 q^{80} +531441. q^{81} -1.73893e6 q^{82} -1.87602e6 q^{83} -592704. q^{84} -1.79432e6 q^{85} -2.90981e6 q^{86} -4.29551e6 q^{87} +3.01272e6 q^{88} +1.55573e6 q^{89} +2.65904e6 q^{90} +753571. q^{91} -1.62985e6 q^{92} +7.78178e6 q^{93} -8.37269e6 q^{94} -1.97620e7 q^{95} -884736. q^{96} +1.58513e7 q^{97} -941192. q^{98} -4.28960e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} + 56 q^{5} - 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9}+O(q^{10}) $ 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 + 56 * q^5 - 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9	\( 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} + 56 q^{5} - 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9} - 448 q^{10} - 3679 q^{11} + 8640 q^{12} - 10985 q^{13} + 13720 q^{14} + 1512 q^{15} + 20480 q^{16} + 409 q^{17} - 29160 q^{18} + 33730 q^{19} + 3584 q^{20} - 46305 q^{21} + 29432 q^{22} - 142142 q^{23} - 69120 q^{24} + 153981 q^{25} + 87880 q^{26} + 98415 q^{27} - 109760 q^{28} + 88028 q^{29} - 12096 q^{30} + 244543 q^{31} - 163840 q^{32} - 99333 q^{33} - 3272 q^{34} - 19208 q^{35} + 233280 q^{36} + 730963 q^{37} - 269840 q^{38} - 296595 q^{39} - 28672 q^{40} + 479512 q^{41} + 370440 q^{42} - 406536 q^{43} - 235456 q^{44} + 40824 q^{45} + 1137136 q^{46} + 1138945 q^{47} + 552960 q^{48} + 588245 q^{49} - 1231848 q^{50} + 11043 q^{51} - 703040 q^{52} + 297595 q^{53} - 787320 q^{54} - 1834423 q^{55} + 878080 q^{56} + 910710 q^{57} - 704224 q^{58} + 941652 q^{59} + 96768 q^{60} - 2985259 q^{61} - 1956344 q^{62} - 1250235 q^{63} + 1310720 q^{64} - 123032 q^{65} + 794664 q^{66} - 2333504 q^{67} + 26176 q^{68} - 3837834 q^{69} + 153664 q^{70} - 11322272 q^{71} - 1866240 q^{72} - 6631604 q^{73} - 5847704 q^{74} + 4157487 q^{75} + 2158720 q^{76} + 1261897 q^{77} + 2372760 q^{78} - 10600265 q^{79} + 229376 q^{80} + 2657205 q^{81} - 3836096 q^{82} - 2425229 q^{83} - 2963520 q^{84} - 12267705 q^{85} + 3252288 q^{86} + 2376756 q^{87} + 1883648 q^{88} - 1581837 q^{89} - 326592 q^{90} + 3767855 q^{91} - 9097088 q^{92} + 6602661 q^{93} - 9111560 q^{94} - 11507718 q^{95} - 4423680 q^{96} + 5298407 q^{97} - 4705960 q^{98} - 2681991 q^{99}+O(q^{100}) \) 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 + 56 * q^5 - 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9 - 448 * q^10 - 3679 * q^11 + 8640 * q^12 - 10985 * q^13 + 13720 * q^14 + 1512 * q^15 + 20480 * q^16 + 409 * q^17 - 29160 * q^18 + 33730 * q^19 + 3584 * q^20 - 46305 * q^21 + 29432 * q^22 - 142142 * q^23 - 69120 * q^24 + 153981 * q^25 + 87880 * q^26 + 98415 * q^27 - 109760 * q^28 + 88028 * q^29 - 12096 * q^30 + 244543 * q^31 - 163840 * q^32 - 99333 * q^33 - 3272 * q^34 - 19208 * q^35 + 233280 * q^36 + 730963 * q^37 - 269840 * q^38 - 296595 * q^39 - 28672 * q^40 + 479512 * q^41 + 370440 * q^42 - 406536 * q^43 - 235456 * q^44 + 40824 * q^45 + 1137136 * q^46 + 1138945 * q^47 + 552960 * q^48 + 588245 * q^49 - 1231848 * q^50 + 11043 * q^51 - 703040 * q^52 + 297595 * q^53 - 787320 * q^54 - 1834423 * q^55 + 878080 * q^56 + 910710 * q^57 - 704224 * q^58 + 941652 * q^59 + 96768 * q^60 - 2985259 * q^61 - 1956344 * q^62 - 1250235 * q^63 + 1310720 * q^64 - 123032 * q^65 + 794664 * q^66 - 2333504 * q^67 + 26176 * q^68 - 3837834 * q^69 + 153664 * q^70 - 11322272 * q^71 - 1866240 * q^72 - 6631604 * q^73 - 5847704 * q^74 + 4157487 * q^75 + 2158720 * q^76 + 1261897 * q^77 + 2372760 * q^78 - 10600265 * q^79 + 229376 * q^80 + 2657205 * q^81 - 3836096 * q^82 - 2425229 * q^83 - 2963520 * q^84 - 12267705 * q^85 + 3252288 * q^86 + 2376756 * q^87 + 1883648 * q^88 - 1581837 * q^89 - 326592 * q^90 + 3767855 * q^91 - 9097088 * q^92 + 6602661 * q^93 - 9111560 * q^94 - 11507718 * q^95 - 4423680 * q^96 + 5298407 * q^97 - 4705960 * q^98 - 2681991 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	−455.940	−1.63122	−0.815611	−	0.578601i	$-0.803599\pi$
$5$	−455.940	−1.63122	−0.815611	+	0.578601i	$0.803599\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	3647.52	1.15345
$11$	−5884.22	−1.33295	−0.666476	−	0.745527i	$-0.732198\pi$
$11$	−5884.22	−1.33295	−0.666476	+	0.745527i	$0.732198\pi$
$12$	1728.00	0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	2744.00	0.267261
$15$	−12310.4	−0.941786
$16$	4096.00	0.250000
$17$	3935.44	0.194277	0.0971386	−	0.995271i	$-0.469031\pi$
$17$	3935.44	0.194277	0.0971386	+	0.995271i	$0.469031\pi$
$18$	−5832.00	−0.235702
$19$	43343.4	1.44973	0.724863	−	0.688893i	$-0.241903\pi$
$19$	43343.4	1.44973	0.724863	+	0.688893i	$0.241903\pi$
$20$	−29180.2	−0.815611
$21$	−9261.00	−0.218218
$22$	47073.8	0.942539
$23$	−25466.3	−0.436434	−0.218217	−	0.975900i	$-0.570024\pi$
$23$	−25466.3	−0.436434	−0.218217	+	0.975900i	$0.570024\pi$
$24$	−13824.0	−0.204124
$25$	129757.	1.66088
$26$	17576.0	0.196116
$27$	19683.0	0.192450
$28$	−21952.0	−0.188982
$29$	−159093.	−1.21132	−0.605658	−	0.795725i	$-0.707090\pi$
$29$	−159093.	−1.21132	−0.605658	+	0.795725i	$0.707090\pi$
$30$	98483.1	0.665944
$31$	288214.	1.73760	0.868798	−	0.495166i	$-0.164893\pi$
$31$	288214.	1.73760	0.868798	+	0.495166i	$0.164893\pi$
$32$	−32768.0	−0.176777
$33$	−158874.	−0.769580
$34$	−31483.5	−0.137375
$35$	156388.	0.616544
$36$	46656.0	0.166667
$37$	13534.1	0.0439261	0.0219630	−	0.999759i	$-0.493008\pi$
$37$	13534.1	0.0439261	0.0219630	+	0.999759i	$0.493008\pi$
$38$	−346748.	−1.02511
$39$	−59319.0	−0.160128
$40$	233441.	0.576724
$41$	217366.	0.492548	0.246274	−	0.969200i	$-0.420794\pi$
$41$	217366.	0.492548	0.246274	+	0.969200i	$0.420794\pi$
$42$	74088.0	0.154303
$43$	363727.	0.697647	0.348823	−	0.937188i	$-0.386581\pi$
$43$	363727.	0.697647	0.348823	+	0.937188i	$0.386581\pi$
$44$	−376590.	−0.666476
$45$	−332381.	−0.543741
$46$	203731.	0.308606
$47$	1.04659e6	1.47039	0.735195	−	0.677855i	$-0.237090\pi$
$47$	1.04659e6	1.47039	0.735195	+	0.677855i	$0.237090\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	−1.03805e6	−1.17442
$51$	106257.	0.112166
$52$	−140608.	−0.138675
$53$	−857306.	−0.790988	−0.395494	−	0.918468i	$-0.629427\pi$
$53$	−857306.	−0.790988	−0.395494	+	0.918468i	$0.629427\pi$
$54$	−157464.	−0.136083
$55$	2.68285e6	2.17434
$56$	175616.	0.133631
$57$	1.17027e6	0.837000
$58$	1.27274e6	0.856530
$59$	1.12738e6	0.714641	0.357321	−	0.933982i	$-0.383690\pi$
$59$	1.12738e6	0.714641	0.357321	+	0.933982i	$0.383690\pi$
$60$	−787865.	−0.470893
$61$	−1.04392e6	−0.588859	−0.294430	−	0.955673i	$-0.595130\pi$
$61$	−1.04392e6	−0.588859	−0.294430	+	0.955673i	$0.595130\pi$
$62$	−2.30571e6	−1.22867
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	1.00170e6	0.452420
$66$	1.27099e6	0.544175
$67$	1.23985e6	0.503625	0.251813	−	0.967776i	$-0.418973\pi$
$67$	1.23985e6	0.503625	0.251813	+	0.967776i	$0.418973\pi$
$68$	251868.	0.0971386
$69$	−687591.	−0.251976
$70$	−1.25110e6	−0.435962
$71$	2.22410e6	0.737480	0.368740	−	0.929533i	$-0.379789\pi$
$71$	2.22410e6	0.737480	0.368740	+	0.929533i	$0.379789\pi$
$72$	−373248.	−0.117851
$73$	−2.32432e6	−0.699303	−0.349652	−	0.936880i	$-0.613700\pi$
$73$	−2.32432e6	−0.699303	−0.349652	+	0.936880i	$0.613700\pi$
$74$	−108273.	−0.0310604
$75$	3.50343e6	0.958912
$76$	2.77398e6	0.724863
$77$	2.01829e6	0.503808
$78$	474552.	0.113228
$79$	−4.89794e6	−1.11768	−0.558841	−	0.829275i	$-0.688754\pi$
$79$	−4.89794e6	−1.11768	−0.558841	+	0.829275i	$0.688754\pi$
$80$	−1.86753e6	−0.407805
$81$	531441.	0.111111
$82$	−1.73893e6	−0.348284
$83$	−1.87602e6	−0.360135	−0.180067	−	0.983654i	$-0.557632\pi$
$83$	−1.87602e6	−0.360135	−0.180067	+	0.983654i	$0.557632\pi$
$84$	−592704.	−0.109109
$85$	−1.79432e6	−0.316909
$86$	−2.90981e6	−0.493311
$87$	−4.29551e6	−0.699354
$88$	3.01272e6	0.471270
$89$	1.55573e6	0.233922	0.116961	−	0.993137i	$-0.462685\pi$
$89$	1.55573e6	0.233922	0.116961	+	0.993137i	$0.462685\pi$
$90$	2.65904e6	0.384483
$91$	753571.	0.104828
$92$	−1.62985e6	−0.218217
$93$	7.78178e6	1.00320
$94$	−8.37269e6	−1.03972
$95$	−1.97620e7	−2.36482
$96$	−884736.	−0.102062
$97$	1.58513e7	1.76345	0.881727	−	0.471759i	$-0.156381\pi$
$97$	1.58513e7	1.76345	0.881727	+	0.471759i	$0.156381\pi$
$98$	−941192.	−0.101015
$99$	−4.28960e6	−0.444317
$100$	8.30442e6	0.830442
$101$	−7.28475e6	−0.703542	−0.351771	−	0.936086i	$-0.614420\pi$
$101$	−7.28475e6	−0.703542	−0.351771	+	0.936086i	$0.614420\pi$
$102$	−850054.	−0.0793133
$103$	−1.55479e7	−1.40198	−0.700989	−	0.713172i	$-0.747258\pi$
$103$	−1.55479e7	−1.40198	−0.700989	+	0.713172i	$0.747258\pi$
$104$	1.12486e6	0.0980581
$105$	4.22246e6	0.355962
$106$	6.85844e6	0.559313
$107$	3.48081e6	0.274687	0.137343	−	0.990523i	$-0.456144\pi$
$107$	3.48081e6	0.274687	0.137343	+	0.990523i	$0.456144\pi$
$108$	1.25971e6	0.0962250
$109$	−1.64941e7	−1.21994	−0.609968	−	0.792426i	$-0.708818\pi$
$109$	−1.64941e7	−1.21994	−0.609968	+	0.792426i	$0.708818\pi$
$110$	−2.14628e7	−1.53749
$111$	365420.	0.0253607
$112$	−1.40493e6	−0.0944911
$113$	−2.37010e7	−1.54523	−0.772613	−	0.634877i	$-0.781051\pi$
$113$	−2.37010e7	−1.54523	−0.772613	+	0.634877i	$0.781051\pi$
$114$	−9.36218e6	−0.591848
$115$	1.16111e7	0.711921
$116$	−1.01819e7	−0.605658
$117$	−1.60161e6	−0.0924500
$118$	−9.01904e6	−0.505328
$119$	−1.34985e6	−0.0734298
$120$	6.30292e6	0.332972
$121$	1.51369e7	0.776761
$122$	8.35133e6	0.416386
$123$	5.86889e6	0.284373
$124$	1.84457e7	0.868798
$125$	−2.35409e7	−1.07805
$126$	2.00038e6	0.0890871
$127$	1.00671e7	0.436106	0.218053	−	0.975937i	$-0.430029\pi$
$127$	1.00671e7	0.436106	0.218053	+	0.975937i	$0.430029\pi$
$128$	−2.09715e6	−0.0883883
$129$	9.82062e6	0.402787
$130$	−8.01361e6	−0.319909
$131$	4.08175e7	1.58634	0.793171	−	0.608999i	$-0.208429\pi$
$131$	4.08175e7	1.58634	0.793171	+	0.608999i	$0.208429\pi$
$132$	−1.01679e7	−0.384790
$133$	−1.48668e7	−0.547945
$134$	−9.91880e6	−0.356117
$135$	−8.97427e6	−0.313929
$136$	−2.01494e6	−0.0686873
$137$	−3.85578e7	−1.28112	−0.640560	−	0.767908i	$-0.721298\pi$
$137$	−3.85578e7	−1.28112	−0.640560	+	0.767908i	$0.721298\pi$
$138$	5.50073e6	0.178174
$139$	1.77039e6	0.0559137	0.0279568	−	0.999609i	$-0.491100\pi$
$139$	1.77039e6	0.0559137	0.0279568	+	0.999609i	$0.491100\pi$
$140$	1.00088e7	0.308272
$141$	2.82578e7	0.848930
$142$	−1.77928e7	−0.521477
$143$	1.29276e7	0.369694
$144$	2.98598e6	0.0833333
$145$	7.25369e7	1.97593
$146$	1.85945e7	0.494482
$147$	3.17652e6	0.0824786
$148$	866180.	0.0219630
$149$	3.26016e7	0.807398	0.403699	−	0.914892i	$-0.367724\pi$
$149$	3.26016e7	0.807398	0.403699	+	0.914892i	$0.367724\pi$
$150$	−2.80274e7	−0.678053
$151$	−1.88700e7	−0.446017	−0.223009	−	0.974816i	$-0.571588\pi$
$151$	−1.88700e7	−0.446017	−0.223009	+	0.974816i	$0.571588\pi$
$152$	−2.21918e7	−0.512555
$153$	2.86893e6	0.0647590
$154$	−1.61463e7	−0.356246
$155$	−1.31408e8	−2.83441
$156$	−3.79642e6	−0.0800641
$157$	7.51582e7	1.54998	0.774992	−	0.631970i	$-0.217754\pi$
$157$	7.51582e7	1.54998	0.774992	+	0.631970i	$0.217754\pi$
$158$	3.91835e7	0.790321
$159$	−2.31472e7	−0.456677
$160$	1.49403e7	0.288362
$161$	8.73495e6	0.164957
$162$	−4.25153e6	−0.0785674
$163$	6.65345e7	1.20335	0.601673	−	0.798742i	$-0.294501\pi$
$163$	6.65345e7	1.20335	0.601673	+	0.798742i	$0.294501\pi$
$164$	1.39114e7	0.246274
$165$	7.24370e7	1.25536
$166$	1.50082e7	0.254654
$167$	5.97482e7	0.992698	0.496349	−	0.868123i	$-0.334674\pi$
$167$	5.97482e7	0.992698	0.496349	+	0.868123i	$0.334674\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	1.43546e7	0.224089
$171$	3.15974e7	0.483242
$172$	2.32785e7	0.348823
$173$	7.15653e7	1.05085	0.525425	−	0.850840i	$-0.323906\pi$
$173$	7.15653e7	1.05085	0.525425	+	0.850840i	$0.323906\pi$
$174$	3.43641e7	0.494518
$175$	−4.45065e7	−0.627756
$176$	−2.41018e7	−0.333238
$177$	3.04393e7	0.412598
$178$	−1.24459e7	−0.165408
$179$	−9.50978e7	−1.23932	−0.619662	−	0.784869i	$-0.712730\pi$
$179$	−9.50978e7	−1.23932	−0.619662	+	0.784869i	$0.712730\pi$
$180$	−2.12724e7	−0.271870
$181$	−8.86505e7	−1.11124	−0.555618	−	0.831438i	$-0.687518\pi$
$181$	−8.86505e7	−1.11124	−0.555618	+	0.831438i	$0.687518\pi$
$182$	−6.02857e6	−0.0741249
$183$	−2.81857e7	−0.339978
$184$	1.30388e7	0.154303
$185$	−6.17073e6	−0.0716532
$186$	−6.22542e7	−0.709371
$187$	−2.31570e7	−0.258962
$188$	6.69816e7	0.735195
$189$	−6.75127e6	−0.0727393
$190$	1.58096e8	1.67218
$191$	−3.86537e7	−0.401397	−0.200698	−	0.979653i	$-0.564321\pi$
$191$	−3.86537e7	−0.401397	−0.200698	+	0.979653i	$0.564321\pi$
$192$	7.07789e6	0.0721688
$193$	−1.92263e8	−1.92506	−0.962530	−	0.271175i	$-0.912588\pi$
$193$	−1.92263e8	−1.92506	−0.962530	+	0.271175i	$0.912588\pi$
$194$	−1.26811e8	−1.24695
$195$	2.70459e7	0.261205
$196$	7.52954e6	0.0714286
$197$	1.90240e8	1.77284	0.886422	−	0.462878i	$-0.153183\pi$
$197$	1.90240e8	1.77284	0.886422	+	0.462878i	$0.153183\pi$
$198$	3.43168e7	0.314180
$199$	1.27855e7	0.115009	0.0575046	−	0.998345i	$-0.481686\pi$
$199$	1.27855e7	0.115009	0.0575046	+	0.998345i	$0.481686\pi$
$200$	−6.64354e7	−0.587212
$201$	3.34759e7	0.290768
$202$	5.82780e7	0.497479
$203$	5.45689e7	0.457835
$204$	6.80043e6	0.0560830
$205$	−9.91061e7	−0.803456
$206$	1.24383e8	0.991348
$207$	−1.85650e7	−0.145478
$208$	−8.99891e6	−0.0693375
$209$	−2.55042e8	−1.93241
$210$	−3.37797e7	−0.251703
$211$	2.42052e8	1.77386	0.886931	−	0.461902i	$-0.152833\pi$
$211$	2.42052e8	1.77386	0.886931	+	0.461902i	$0.152833\pi$
$212$	−5.48676e7	−0.395494
$213$	6.00507e7	0.425784
$214$	−2.78465e7	−0.194233
$215$	−1.65838e8	−1.13802
$216$	−1.00777e7	−0.0680414
$217$	−9.88574e7	−0.656750
$218$	1.31953e8	0.862625
$219$	−6.27566e7	−0.403743
$220$	1.71703e8	1.08717
$221$	−8.64615e6	−0.0538828
$222$	−2.92336e6	−0.0179327
$223$	−2.16593e8	−1.30791	−0.653953	−	0.756535i	$-0.726891\pi$
$223$	−2.16593e8	−1.30791	−0.653953	+	0.756535i	$0.726891\pi$
$224$	1.12394e7	0.0668153
$225$	9.45926e7	0.553628
$226$	1.89608e8	1.09264
$227$	2.08865e8	1.18516	0.592579	−	0.805513i	$-0.298110\pi$
$227$	2.08865e8	1.18516	0.592579	+	0.805513i	$0.298110\pi$
$228$	7.48975e7	0.418500
$229$	−6.63565e7	−0.365140	−0.182570	−	0.983193i	$-0.558442\pi$
$229$	−6.63565e7	−0.365140	−0.182570	+	0.983193i	$0.558442\pi$
$230$	−9.28890e7	−0.503404
$231$	5.44938e7	0.290874
$232$	8.14556e7	0.428265
$233$	−2.53103e8	−1.31085	−0.655423	−	0.755262i	$-0.727509\pi$
$233$	−2.53103e8	−1.31085	−0.655423	+	0.755262i	$0.727509\pi$
$234$	1.28129e7	0.0653720
$235$	−4.77181e8	−2.39853
$236$	7.21523e7	0.357321
$237$	−1.32244e8	−0.645294
$238$	1.07988e7	0.0519227
$239$	−3.08522e8	−1.46182	−0.730909	−	0.682475i	$-0.760904\pi$
$239$	−3.08522e8	−1.46182	−0.730909	+	0.682475i	$0.760904\pi$
$240$	−5.04234e7	−0.235447
$241$	8.07648e7	0.371674	0.185837	−	0.982581i	$-0.440500\pi$
$241$	8.07648e7	0.371674	0.185837	+	0.982581i	$0.440500\pi$
$242$	−1.21095e8	−0.549253
$243$	1.43489e7	0.0641500
$244$	−6.68107e7	−0.294430
$245$	−5.36409e7	−0.233032
$246$	−4.69511e7	−0.201082
$247$	−9.52256e7	−0.402082
$248$	−1.47566e8	−0.614333
$249$	−5.06526e7	−0.207924
$250$	1.88328e8	0.762296
$251$	2.94997e7	0.117750	0.0588749	−	0.998265i	$-0.481249\pi$
$251$	2.94997e7	0.117750	0.0588749	+	0.998265i	$0.481249\pi$
$252$	−1.60030e7	−0.0629941
$253$	1.49849e8	0.581746
$254$	−8.05370e7	−0.308374
$255$	−4.84468e7	−0.182968
$256$	1.67772e7	0.0625000
$257$	−4.78260e8	−1.75751	−0.878755	−	0.477273i	$-0.841625\pi$
$257$	−4.78260e8	−1.75751	−0.878755	+	0.477273i	$0.841625\pi$
$258$	−7.85650e7	−0.284813
$259$	−4.64218e6	−0.0166025
$260$	6.41089e7	0.226210
$261$	−1.15979e8	−0.403772
$262$	−3.26540e8	−1.12171
$263$	−2.32484e8	−0.788039	−0.394020	−	0.919102i	$-0.628916\pi$
$263$	−2.32484e8	−0.788039	−0.394020	+	0.919102i	$0.628916\pi$
$264$	8.13435e7	0.272088
$265$	3.90880e8	1.29028
$266$	1.18934e8	0.387456
$267$	4.20048e7	0.135055
$268$	7.93504e7	0.251813
$269$	−4.52563e8	−1.41758	−0.708788	−	0.705421i	$-0.750758\pi$
$269$	−4.52563e8	−1.41758	−0.708788	+	0.705421i	$0.750758\pi$
$270$	7.17942e7	0.221981
$271$	−4.28998e8	−1.30937	−0.654685	−	0.755902i	$-0.727199\pi$
$271$	−4.28998e8	−1.30937	−0.654685	+	0.755902i	$0.727199\pi$
$272$	1.61195e7	0.0485693
$273$	2.03464e7	0.0605228
$274$	3.08462e8	0.905889
$275$	−7.63517e8	−2.21388
$276$	−4.40058e7	−0.125988
$277$	8.43291e7	0.238396	0.119198	−	0.992871i	$-0.461968\pi$
$277$	8.43291e7	0.238396	0.119198	+	0.992871i	$0.461968\pi$
$278$	−1.41632e7	−0.0395369
$279$	2.10108e8	0.579199
$280$	−8.00704e7	−0.217981
$281$	1.26695e8	0.340633	0.170317	−	0.985389i	$-0.445521\pi$
$281$	1.26695e8	0.340633	0.170317	+	0.985389i	$0.445521\pi$
$282$	−2.26063e8	−0.600285
$283$	3.03473e8	0.795916	0.397958	−	0.917404i	$-0.369719\pi$
$283$	3.03473e8	0.795916	0.397958	+	0.917404i	$0.369719\pi$
$284$	1.42342e8	0.368740
$285$	−5.33575e8	−1.36533
$286$	−1.03421e8	−0.261413
$287$	−7.45567e7	−0.186166
$288$	−2.38879e7	−0.0589256
$289$	−3.94851e8	−0.962256
$290$	−5.80295e8	−1.39719
$291$	4.27986e8	1.01813
$292$	−1.48756e8	−0.349652
$293$	−4.53547e8	−1.05338	−0.526691	−	0.850057i	$-0.676567\pi$
$293$	−4.53547e8	−1.05338	−0.526691	+	0.850057i	$0.676567\pi$
$294$	−2.54122e7	−0.0583212
$295$	−5.14018e8	−1.16574
$296$	−6.92944e6	−0.0155302
$297$	−1.15819e8	−0.256527
$298$	−2.60813e8	−0.570916
$299$	5.59495e7	0.121045
$300$	2.24219e8	0.479456
$301$	−1.24758e8	−0.263686
$302$	1.50960e8	0.315382
$303$	−1.96688e8	−0.406190
$304$	1.77535e8	0.362431
$305$	4.75964e8	0.960560
$306$	−2.29515e7	−0.0457916
$307$	2.28775e8	0.451258	0.225629	−	0.974213i	$-0.427556\pi$
$307$	2.28775e8	0.451258	0.225629	+	0.974213i	$0.427556\pi$
$308$	1.29170e8	0.251904
$309$	−4.19793e8	−0.809432
$310$	1.05127e9	2.00423
$311$	−5.17405e8	−0.975370	−0.487685	−	0.873020i	$-0.662159\pi$
$311$	−5.17405e8	−0.975370	−0.487685	+	0.873020i	$0.662159\pi$
$312$	3.03713e7	0.0566139
$313$	−3.41723e8	−0.629896	−0.314948	−	0.949109i	$-0.601987\pi$
$313$	−3.41723e8	−0.629896	−0.314948	+	0.949109i	$0.601987\pi$
$314$	−6.01265e8	−1.09600
$315$	1.14007e8	0.205515
$316$	−3.13468e8	−0.558841
$317$	1.45960e7	0.0257352	0.0128676	−	0.999917i	$-0.495904\pi$
$317$	1.45960e7	0.0257352	0.0128676	+	0.999917i	$0.495904\pi$
$318$	1.85178e8	0.322920
$319$	9.36138e8	1.61463
$320$	−1.19522e8	−0.203903
$321$	9.39820e7	0.158590
$322$	−6.98796e7	−0.116642
$323$	1.70575e8	0.281649
$324$	3.40122e7	0.0555556
$325$	−2.85075e8	−0.460647
$326$	−5.32276e8	−0.850894
$327$	−4.45342e8	−0.704330
$328$	−1.11292e8	−0.174142
$329$	−3.58979e8	−0.555755
$330$	−5.79496e8	−0.887671
$331$	−6.62869e8	−1.00468	−0.502342	−	0.864669i	$-0.667528\pi$
$331$	−6.62869e8	−1.00468	−0.502342	+	0.864669i	$0.667528\pi$
$332$	−1.20066e8	−0.180067
$333$	9.86633e6	0.0146420
$334$	−4.77985e8	−0.701943
$335$	−5.65298e8	−0.821524
$336$	−3.79331e7	−0.0545545
$337$	−2.26174e8	−0.321913	−0.160957	−	0.986961i	$-0.551458\pi$
$337$	−2.26174e8	−0.321913	−0.160957	+	0.986961i	$0.551458\pi$
$338$	−3.86145e7	−0.0543928
$339$	−6.39927e8	−0.892137
$340$	−1.14837e8	−0.158455
$341$	−1.69591e9	−2.31613
$342$	−2.52779e8	−0.341704
$343$	−4.03536e7	−0.0539949
$344$	−1.86228e8	−0.246655
$345$	3.13501e8	0.411028
$346$	−5.72522e8	−0.743064
$347$	2.85603e8	0.366953	0.183476	−	0.983024i	$-0.441265\pi$
$347$	2.85603e8	0.366953	0.183476	+	0.983024i	$0.441265\pi$
$348$	−2.74913e8	−0.349677
$349$	−7.54063e8	−0.949552	−0.474776	−	0.880107i	$-0.657471\pi$
$349$	−7.54063e8	−0.949552	−0.474776	+	0.880107i	$0.657471\pi$
$350$	3.56052e8	0.443890
$351$	−4.32436e7	−0.0533761
$352$	1.92814e8	0.235635
$353$	−4.45378e8	−0.538911	−0.269455	−	0.963013i	$-0.586844\pi$
$353$	−4.45378e8	−0.538911	−0.269455	+	0.963013i	$0.586844\pi$
$354$	−2.43514e8	−0.291751
$355$	−1.01406e9	−1.20299
$356$	9.95670e7	0.116961
$357$	−3.64461e7	−0.0423947
$358$	7.60783e8	0.876335
$359$	5.21140e8	0.594461	0.297231	−	0.954806i	$-0.403937\pi$
$359$	5.21140e8	0.594461	0.297231	+	0.954806i	$0.403937\pi$
$360$	1.70179e8	0.192241
$361$	9.84783e8	1.10170
$362$	7.09204e8	0.785763
$363$	4.08695e8	0.448463
$364$	4.82285e7	0.0524142
$365$	1.05975e9	1.14072
$366$	2.25486e8	0.240401
$367$	−5.20784e8	−0.549954	−0.274977	−	0.961451i	$-0.588670\pi$
$367$	−5.20784e8	−0.549954	−0.274977	+	0.961451i	$0.588670\pi$
$368$	−1.04310e8	−0.109109
$369$	1.58460e8	0.164183
$370$	4.93658e7	0.0506664
$371$	2.94056e8	0.298965
$372$	4.98034e8	0.501601
$373$	5.96037e8	0.594692	0.297346	−	0.954770i	$-0.403899\pi$
$373$	5.96037e8	0.594692	0.297346	+	0.954770i	$0.403899\pi$
$374$	1.85256e8	0.183114
$375$	−6.35606e8	−0.622412
$376$	−5.35852e8	−0.519862
$377$	3.49527e8	0.335959
$378$	5.40102e7	0.0514344
$379$	2.69873e8	0.254638	0.127319	−	0.991862i	$-0.459363\pi$
$379$	2.69873e8	0.254638	0.127319	+	0.991862i	$0.459363\pi$
$380$	−1.26477e9	−1.18241
$381$	2.71812e8	0.251786
$382$	3.09229e8	0.283830
$383$	1.90595e9	1.73346	0.866732	−	0.498774i	$-0.166216\pi$
$383$	1.90595e9	1.73346	0.866732	+	0.498774i	$0.166216\pi$
$384$	−5.66231e7	−0.0510310
$385$	−9.20219e8	−0.821823
$386$	1.53810e9	1.36122
$387$	2.65157e8	0.232549
$388$	1.01448e9	0.881727
$389$	2.53924e8	0.218716	0.109358	−	0.994002i	$-0.465121\pi$
$389$	2.53924e8	0.218716	0.109358	+	0.994002i	$0.465121\pi$
$390$	−2.16367e8	−0.184700
$391$	−1.00221e8	−0.0847892
$392$	−6.02363e7	−0.0505076
$393$	1.10207e9	0.915875
$394$	−1.52192e9	−1.25359
$395$	2.23317e9	1.82319
$396$	−2.74534e8	−0.222159
$397$	−1.67330e9	−1.34217	−0.671086	−	0.741380i	$-0.734172\pi$
$397$	−1.67330e9	−1.34217	−0.671086	+	0.741380i	$0.734172\pi$
$398$	−1.02284e8	−0.0813238
$399$	−4.01404e8	−0.316356
$400$	5.31483e8	0.415221
$401$	3.39640e8	0.263035	0.131517	−	0.991314i	$-0.458015\pi$
$401$	3.39640e8	0.263035	0.131517	+	0.991314i	$0.458015\pi$
$402$	−2.67808e8	−0.205604
$403$	−6.33206e8	−0.481923
$404$	−4.66224e8	−0.351771
$405$	−2.42305e8	−0.181247
$406$	−4.36551e8	−0.323738
$407$	−7.96374e7	−0.0585513
$408$	−5.44035e7	−0.0396566
$409$	−1.14971e7	−0.00830914	−0.00415457	−	0.999991i	$-0.501322\pi$
$409$	−1.14971e7	−0.00830914	−0.00415457	+	0.999991i	$0.501322\pi$
$410$	7.92849e8	0.568129
$411$	−1.04106e9	−0.739655
$412$	−9.95065e8	−0.700989
$413$	−3.86691e8	−0.270109
$414$	1.48520e8	0.102869
$415$	8.55355e8	0.587460
$416$	7.19913e7	0.0490290
$417$	4.78006e7	0.0322818
$418$	2.04034e9	1.36642
$419$	2.70835e9	1.79869	0.899345	−	0.437240i	$-0.144044\pi$
$419$	2.70835e9	1.79869	0.899345	+	0.437240i	$0.144044\pi$
$420$	2.70238e8	0.177981
$421$	9.85178e8	0.643468	0.321734	−	0.946830i	$-0.395734\pi$
$421$	9.85178e8	0.643468	0.321734	+	0.946830i	$0.395734\pi$
$422$	−1.93642e9	−1.25431
$423$	7.62962e8	0.490130
$424$	4.38940e8	0.279657
$425$	5.10649e8	0.322672
$426$	−4.80406e8	−0.301075
$427$	3.58063e8	0.222568
$428$	2.22772e8	0.137343
$429$	3.49046e8	0.213443
$430$	1.32670e9	0.804700
$431$	4.73523e8	0.284886	0.142443	−	0.989803i	$-0.454504\pi$
$431$	4.73523e8	0.284886	0.142443	+	0.989803i	$0.454504\pi$
$432$	8.06216e7	0.0481125
$433$	5.87970e8	0.348055	0.174027	−	0.984741i	$-0.444322\pi$
$433$	5.87970e8	0.348055	0.174027	+	0.984741i	$0.444322\pi$
$434$	7.90859e8	0.464392
$435$	1.95850e9	1.14080
$436$	−1.05562e9	−0.609968
$437$	−1.10380e9	−0.632710
$438$	5.02053e8	0.285489
$439$	8.36320e8	0.471788	0.235894	−	0.971779i	$-0.424198\pi$
$439$	8.36320e8	0.471788	0.235894	+	0.971779i	$0.424198\pi$
$440$	−1.37362e9	−0.768745
$441$	8.57661e7	0.0476190
$442$	6.91692e7	0.0381009
$443$	8.05861e8	0.440400	0.220200	−	0.975455i	$-0.429329\pi$
$443$	8.05861e8	0.440400	0.220200	+	0.975455i	$0.429329\pi$
$444$	2.33869e7	0.0126804
$445$	−7.09322e8	−0.381578
$446$	1.73274e9	0.924829
$447$	8.80244e8	0.466151
$448$	−8.99154e7	−0.0472456
$449$	1.50590e8	0.0785117	0.0392558	−	0.999229i	$-0.487501\pi$
$449$	1.50590e8	0.0785117	0.0392558	+	0.999229i	$0.487501\pi$
$450$	−7.56741e8	−0.391474
$451$	−1.27903e9	−0.656543
$452$	−1.51686e9	−0.772613
$453$	−5.09489e8	−0.257508
$454$	−1.67092e9	−0.838033
$455$	−3.43583e8	−0.170999
$456$	−5.99180e8	−0.295924
$457$	−3.21544e9	−1.57592	−0.787958	−	0.615729i	$-0.788862\pi$
$457$	−3.21544e9	−1.57592	−0.787958	+	0.615729i	$0.788862\pi$
$458$	5.30852e8	0.258193
$459$	7.74612e7	0.0373886
$460$	7.43112e8	0.355961
$461$	−1.78668e9	−0.849365	−0.424683	−	0.905342i	$-0.639614\pi$
$461$	−1.78668e9	−0.849365	−0.424683	+	0.905342i	$0.639614\pi$
$462$	−4.35950e8	−0.205679
$463$	1.29965e9	0.608548	0.304274	−	0.952585i	$-0.401586\pi$
$463$	1.29965e9	0.608548	0.304274	+	0.952585i	$0.401586\pi$
$464$	−6.51644e8	−0.302829
$465$	−3.54803e9	−1.63645
$466$	2.02482e9	0.926907
$467$	−3.20933e9	−1.45816	−0.729081	−	0.684428i	$-0.760052\pi$
$467$	−3.20933e9	−1.45816	−0.729081	+	0.684428i	$0.760052\pi$
$468$	−1.02503e8	−0.0462250
$469$	−4.25269e8	−0.190352
$470$	3.81745e9	1.69602
$471$	2.02927e9	0.894884
$472$	−5.77218e8	−0.252664
$473$	−2.14025e9	−0.929930
$474$	1.05795e9	0.456292
$475$	5.62410e9	2.40783
$476$	−8.63907e7	−0.0367149
$477$	−6.24976e8	−0.263663
$478$	2.46818e9	1.03366
$479$	1.44297e9	0.599908	0.299954	−	0.953954i	$-0.403029\pi$
$479$	1.44297e9	0.599908	0.299954	+	0.953954i	$0.403029\pi$
$480$	4.03387e8	0.166486
$481$	−2.97343e7	−0.0121829
$482$	−6.46119e8	−0.262814
$483$	2.35844e8	0.0952378
$484$	9.68760e8	0.388380
$485$	−7.22726e9	−2.87659
$486$	−1.14791e8	−0.0453609
$487$	−4.74430e9	−1.86132	−0.930660	−	0.365886i	$-0.880766\pi$
$487$	−4.74430e9	−1.86132	−0.930660	+	0.365886i	$0.880766\pi$
$488$	5.34485e8	0.208193
$489$	1.79643e9	0.694752
$490$	4.29127e8	0.164778
$491$	−1.06123e9	−0.404600	−0.202300	−	0.979324i	$-0.564842\pi$
$491$	−1.06123e9	−0.404600	−0.202300	+	0.979324i	$0.564842\pi$
$492$	3.75609e8	0.142186
$493$	−6.26100e8	−0.235331
$494$	7.61804e8	0.284315
$495$	1.95580e9	0.724780
$496$	1.18052e9	0.434399
$497$	−7.62866e8	−0.278741
$498$	4.05221e8	0.147024
$499$	2.04058e9	0.735192	0.367596	−	0.929986i	$-0.380181\pi$
$499$	2.04058e9	0.735192	0.367596	+	0.929986i	$0.380181\pi$
$500$	−1.50662e9	−0.539025
$501$	1.61320e9	0.573134
$502$	−2.35998e8	−0.0832616
$503$	−2.23807e9	−0.784124	−0.392062	−	0.919939i	$-0.628238\pi$
$503$	−2.23807e9	−0.784124	−0.392062	+	0.919939i	$0.628238\pi$
$504$	1.28024e8	0.0445435
$505$	3.32141e9	1.14763
$506$	−1.19880e9	−0.411357
$507$	1.30324e8	0.0444116
$508$	6.44296e8	0.218053
$509$	−4.61138e9	−1.54995	−0.774977	−	0.631989i	$-0.782239\pi$
$509$	−4.61138e9	−1.54995	−0.774977	+	0.631989i	$0.782239\pi$
$510$	3.87574e8	0.129378
$511$	7.97241e8	0.264312
$512$	−1.34218e8	−0.0441942
$513$	8.53129e8	0.279000
$514$	3.82608e9	1.24275
$515$	7.08891e9	2.28694
$516$	6.28520e8	0.201393
$517$	−6.15835e9	−1.95996
$518$	3.71375e7	0.0117397
$519$	1.93226e9	0.606709
$520$	−5.12871e8	−0.159954
$521$	−5.72655e9	−1.77403	−0.887014	−	0.461742i	$-0.847225\pi$
$521$	−5.72655e9	−1.77403	−0.887014	+	0.461742i	$0.847225\pi$
$522$	9.27830e8	0.285510
$523$	−1.24237e9	−0.379746	−0.189873	−	0.981809i	$-0.560808\pi$
$523$	−1.24237e9	−0.379746	−0.189873	+	0.981809i	$0.560808\pi$
$524$	2.61232e9	0.793171
$525$	−1.20168e9	−0.362435
$526$	1.85987e9	0.557228
$527$	1.13425e9	0.337575
$528$	−6.50748e8	−0.192395
$529$	−2.75629e9	−0.809525
$530$	−3.12704e9	−0.912364
$531$	8.21860e8	0.238214
$532$	−9.51475e8	−0.273972
$533$	−4.77554e8	−0.136608
$534$	−3.36039e8	−0.0954981
$535$	−1.58704e9	−0.448075
$536$	−6.34803e8	−0.178058
$537$	−2.56764e9	−0.715524
$538$	3.62051e9	1.00238
$539$	−6.92273e8	−0.190422
$540$	−5.74354e8	−0.156964
$541$	−5.68333e8	−0.154317	−0.0771583	−	0.997019i	$-0.524585\pi$
$541$	−5.68333e8	−0.154317	−0.0771583	+	0.997019i	$0.524585\pi$
$542$	3.43198e9	0.925865
$543$	−2.39356e9	−0.641572
$544$	−1.28956e8	−0.0343437
$545$	7.52034e9	1.98999
$546$	−1.62771e8	−0.0427960
$547$	1.56087e9	0.407767	0.203884	−	0.978995i	$-0.434644\pi$
$547$	1.56087e9	0.407767	0.203884	+	0.978995i	$0.434644\pi$
$548$	−2.46770e9	−0.640560
$549$	−7.61015e8	−0.196286
$550$	6.10813e9	1.56545
$551$	−6.89563e9	−1.75608
$552$	3.52047e8	0.0890868
$553$	1.67999e9	0.422444
$554$	−6.74633e8	−0.168571
$555$	−1.66610e8	−0.0413690
$556$	1.13305e8	0.0279568
$557$	6.98294e9	1.71216	0.856081	−	0.516841i	$-0.172892\pi$
$557$	6.98294e9	1.71216	0.856081	+	0.516841i	$0.172892\pi$
$558$	−1.68086e9	−0.409555
$559$	−7.99108e8	−0.193492
$560$	6.40563e8	0.154136
$561$	−6.25238e8	−0.149512
$562$	−1.01356e9	−0.240864
$563$	7.84821e9	1.85349	0.926747	−	0.375685i	$-0.122593\pi$
$563$	7.84821e9	1.85349	0.926747	+	0.375685i	$0.122593\pi$
$564$	1.80850e9	0.424465
$565$	1.08062e10	2.52061
$566$	−2.42778e9	−0.562797
$567$	−1.82284e8	−0.0419961
$568$	−1.13874e9	−0.260738
$569$	−1.66504e9	−0.378906	−0.189453	−	0.981890i	$-0.560671\pi$
$569$	−1.66504e9	−0.378906	−0.189453	+	0.981890i	$0.560671\pi$
$570$	4.26860e9	0.965436
$571$	5.73417e9	1.28897	0.644487	−	0.764616i	$-0.277071\pi$
$571$	5.73417e9	1.28897	0.644487	+	0.764616i	$0.277071\pi$
$572$	8.27368e8	0.184847
$573$	−1.04365e9	−0.231746
$574$	5.96453e8	0.131639
$575$	−3.30443e9	−0.724867
$576$	1.91103e8	0.0416667
$577$	6.97791e9	1.51220	0.756102	−	0.654454i	$-0.227102\pi$
$577$	6.97791e9	1.51220	0.756102	+	0.654454i	$0.227102\pi$
$578$	3.15881e9	0.680418
$579$	−5.19109e9	−1.11143
$580$	4.64236e9	0.987963
$581$	6.43476e8	0.136118
$582$	−3.42388e9	−0.719927
$583$	5.04457e9	1.05435
$584$	1.19005e9	0.247241
$585$	7.30240e8	0.150807
$586$	3.62838e9	0.744853
$587$	−3.31486e9	−0.676443	−0.338222	−	0.941066i	$-0.609825\pi$
$587$	−3.31486e9	−0.676443	−0.338222	+	0.941066i	$0.609825\pi$
$588$	2.03297e8	0.0412393
$589$	1.24922e10	2.51904
$590$	4.11214e9	0.824302
$591$	5.13648e9	1.02355
$592$	5.54355e7	0.0109815
$593$	−4.36773e9	−0.860130	−0.430065	−	0.902798i	$-0.641509\pi$
$593$	−4.36773e9	−0.860130	−0.430065	+	0.902798i	$0.641509\pi$
$594$	9.26553e8	0.181392
$595$	6.15453e8	0.119780
$596$	2.08651e9	0.403699
$597$	3.45209e8	0.0664006
$598$	−4.47596e8	−0.0855918
$599$	3.11092e9	0.591419	0.295709	−	0.955278i	$-0.404444\pi$
$599$	3.11092e9	0.591419	0.295709	+	0.955278i	$0.404444\pi$
$600$	−1.79376e9	−0.339027
$601$	−3.39502e9	−0.637942	−0.318971	−	0.947764i	$-0.603337\pi$
$601$	−3.39502e9	−0.637942	−0.318971	+	0.947764i	$0.603337\pi$
$602$	9.98066e8	0.186454
$603$	9.03851e8	0.167875
$604$	−1.20768e9	−0.223009
$605$	−6.90151e9	−1.26707
$606$	1.57351e9	0.287220
$607$	5.51527e9	1.00094	0.500468	−	0.865755i	$-0.333161\pi$
$607$	5.51527e9	1.00094	0.500468	+	0.865755i	$0.333161\pi$
$608$	−1.42028e9	−0.256278
$609$	1.47336e9	0.264331
$610$	−3.80771e9	−0.679218
$611$	−2.29935e9	−0.407813
$612$	1.83612e8	0.0323795
$613$	3.43949e9	0.603090	0.301545	−	0.953452i	$-0.402498\pi$
$613$	3.43949e9	0.603090	0.301545	+	0.953452i	$0.402498\pi$
$614$	−1.83020e9	−0.319088
$615$	−2.67586e9	−0.463875
$616$	−1.03336e9	−0.178123
$617$	−6.57508e9	−1.12695	−0.563473	−	0.826135i	$-0.690535\pi$
$617$	−6.57508e9	−1.12695	−0.563473	+	0.826135i	$0.690535\pi$
$618$	3.35834e9	0.572355
$619$	6.90676e9	1.17046	0.585230	−	0.810867i	$-0.301004\pi$
$619$	6.90676e9	1.17046	0.585230	+	0.810867i	$0.301004\pi$
$620$	−8.41014e9	−1.41720
$621$	−5.01254e8	−0.0839918
$622$	4.13924e9	0.689691
$623$	−5.33617e8	−0.0884141
$624$	−2.42971e8	−0.0400320
$625$	5.96032e8	0.0976539
$626$	2.73378e9	0.445403
$627$	−6.88614e9	−1.11568
$628$	4.81012e9	0.774992
$629$	5.32625e7	0.00853383
$630$	−9.12052e8	−0.145321
$631$	−5.61238e9	−0.889292	−0.444646	−	0.895706i	$-0.646671\pi$
$631$	−5.61238e9	−0.889292	−0.444646	+	0.895706i	$0.646671\pi$
$632$	2.50774e9	0.395160
$633$	6.53540e9	1.02414
$634$	−1.16768e8	−0.0181975
$635$	−4.59001e9	−0.711386
$636$	−1.48142e9	−0.228339
$637$	−2.58475e8	−0.0396214
$638$	−7.48910e9	−1.14171
$639$	1.62137e9	0.245827
$640$	9.56176e8	0.144181
$641$	7.28301e9	1.09221	0.546107	−	0.837715i	$-0.316109\pi$
$641$	7.28301e9	1.09221	0.546107	+	0.837715i	$0.316109\pi$
$642$	−7.51856e8	−0.112140
$643$	1.15494e10	1.71324	0.856622	−	0.515944i	$-0.172559\pi$
$643$	1.15494e10	1.71324	0.856622	+	0.515944i	$0.172559\pi$
$644$	5.59037e8	0.0824784
$645$	−4.47762e9	−0.657034
$646$	−1.36460e9	−0.199156
$647$	−6.75450e9	−0.980457	−0.490228	−	0.871594i	$-0.663087\pi$
$647$	−6.75450e9	−0.980457	−0.490228	+	0.871594i	$0.663087\pi$
$648$	−2.72098e8	−0.0392837
$649$	−6.63375e9	−0.952583
$650$	2.28060e9	0.325726
$651$	−2.66915e9	−0.379175
$652$	4.25821e9	0.601673
$653$	−7.52603e9	−1.05772	−0.528859	−	0.848710i	$-0.677380\pi$
$653$	−7.52603e9	−1.05772	−0.528859	+	0.848710i	$0.677380\pi$
$654$	3.56273e9	0.498037
$655$	−1.86103e10	−2.58768
$656$	8.90333e8	0.123137
$657$	−1.69443e9	−0.233101
$658$	2.87183e9	0.392978
$659$	−5.38057e9	−0.732367	−0.366184	−	0.930543i	$-0.619336\pi$
$659$	−5.38057e9	−0.732367	−0.366184	+	0.930543i	$0.619336\pi$
$660$	4.63597e9	0.627678
$661$	−9.86609e9	−1.32874	−0.664370	−	0.747404i	$-0.731300\pi$
$661$	−9.86609e9	−1.32874	−0.664370	+	0.747404i	$0.731300\pi$
$662$	5.30295e9	0.710419
$663$	−2.33446e8	−0.0311092
$664$	9.60524e8	0.127327
$665$	6.77838e9	0.893820
$666$	−7.89307e7	−0.0103535
$667$	4.05151e9	0.528660
$668$	3.82388e9	0.496349
$669$	−5.84800e9	−0.755120
$670$	4.52238e9	0.580905
$671$	6.14263e9	0.784921
$672$	3.03464e8	0.0385758
$673$	3.50113e9	0.442747	0.221374	−	0.975189i	$-0.428946\pi$
$673$	3.50113e9	0.442747	0.221374	+	0.975189i	$0.428946\pi$
$674$	1.80940e9	0.227627
$675$	2.55400e9	0.319637
$676$	3.08916e8	0.0384615
$677$	−4.70192e9	−0.582392	−0.291196	−	0.956663i	$-0.594053\pi$
$677$	−4.70192e9	−0.582392	−0.291196	+	0.956663i	$0.594053\pi$
$678$	5.11941e9	0.630836
$679$	−5.43700e9	−0.666523
$680$	9.18694e8	0.112044
$681$	5.63937e9	0.684251
$682$	1.35673e10	1.63775
$683$	−8.58388e9	−1.03089	−0.515444	−	0.856923i	$-0.672373\pi$
$683$	−8.58388e9	−1.03089	−0.515444	+	0.856923i	$0.672373\pi$
$684$	2.02223e9	0.241621
$685$	1.75800e10	2.08979
$686$	3.22829e8	0.0381802
$687$	−1.79162e9	−0.210814
$688$	1.48982e9	0.174412
$689$	1.88350e9	0.219381
$690$	−2.50800e9	−0.290641
$691$	−1.01783e10	−1.17355	−0.586776	−	0.809749i	$-0.699603\pi$
$691$	−1.01783e10	−1.17355	−0.586776	+	0.809749i	$0.699603\pi$
$692$	4.58018e9	0.525425
$693$	1.47133e9	0.167936
$694$	−2.28483e9	−0.259475
$695$	−8.07194e8	−0.0912076
$696$	2.19930e9	0.247259
$697$	8.55431e8	0.0956909
$698$	6.03251e9	0.671435
$699$	−6.83378e9	−0.756817
$700$	−2.84842e9	−0.313878
$701$	1.52640e10	1.67362	0.836810	−	0.547494i	$-0.184418\pi$
$701$	1.52640e10	1.67362	0.836810	+	0.547494i	$0.184418\pi$
$702$	3.45948e8	0.0377426
$703$	5.86613e8	0.0636807
$704$	−1.54251e9	−0.166619
$705$	−1.28839e10	−1.38479
$706$	3.56302e9	0.381068
$707$	2.49867e9	0.265914
$708$	1.94811e9	0.206299
$709$	5.17614e9	0.545437	0.272718	−	0.962094i	$-0.412077\pi$
$709$	5.17614e9	0.545437	0.272718	+	0.962094i	$0.412077\pi$
$710$	8.11246e9	0.850645
$711$	−3.57060e9	−0.372561
$712$	−7.96536e8	−0.0827038
$713$	−7.33975e9	−0.758347
$714$	2.91569e8	0.0299776
$715$	−5.89423e9	−0.603053
$716$	−6.08626e9	−0.619662
$717$	−8.33009e9	−0.843981
$718$	−4.16912e9	−0.420348
$719$	4.81984e9	0.483594	0.241797	−	0.970327i	$-0.422263\pi$
$719$	4.81984e9	0.483594	0.241797	+	0.970327i	$0.422263\pi$
$720$	−1.36143e9	−0.135935
$721$	5.33293e9	0.529898
$722$	−7.87826e9	−0.779023
$723$	2.18065e9	0.214586
$724$	−5.67363e9	−0.555618
$725$	−2.06434e10	−2.01186
$726$	−3.26956e9	−0.317111
$727$	1.54657e10	1.49279	0.746395	−	0.665504i	$-0.231783\pi$
$727$	1.54657e10	1.49279	0.746395	+	0.665504i	$0.231783\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−8.47800e9	−0.806610
$731$	1.43142e9	0.135537
$732$	−1.80389e9	−0.169989
$733$	−1.62015e10	−1.51947	−0.759735	−	0.650233i	$-0.774671\pi$
$733$	−1.62015e10	−1.51947	−0.759735	+	0.650233i	$0.774671\pi$
$734$	4.16627e9	0.388876
$735$	−1.44831e9	−0.134541
$736$	8.34481e8	0.0771514
$737$	−7.29555e9	−0.671308
$738$	−1.26768e9	−0.116095
$739$	−1.59561e10	−1.45436	−0.727179	−	0.686448i	$-0.759169\pi$
$739$	−1.59561e10	−1.45436	−0.727179	+	0.686448i	$0.759169\pi$
$740$	−3.94927e8	−0.0358266
$741$	−2.57109e9	−0.232142
$742$	−2.35245e9	−0.211401
$743$	−1.56651e10	−1.40111	−0.700557	−	0.713596i	$-0.747065\pi$
$743$	−1.56651e10	−1.40111	−0.700557	+	0.713596i	$0.747065\pi$
$744$	−3.98427e9	−0.354685
$745$	−1.48644e10	−1.31704
$746$	−4.76829e9	−0.420511
$747$	−1.36762e9	−0.120045
$748$	−1.48205e9	−0.129481
$749$	−1.19392e9	−0.103822
$750$	5.08484e9	0.440112
$751$	1.99485e10	1.71858	0.859291	−	0.511488i	$-0.170905\pi$
$751$	1.99485e10	1.71858	0.859291	+	0.511488i	$0.170905\pi$
$752$	4.28682e9	0.367598
$753$	7.96493e8	0.0679828
$754$	−2.79622e9	−0.237559
$755$	8.60357e9	0.727553
$756$	−4.32081e8	−0.0363696
$757$	1.55566e9	0.130341	0.0651703	−	0.997874i	$-0.479241\pi$
$757$	1.55566e9	0.130341	0.0651703	+	0.997874i	$0.479241\pi$
$758$	−2.15899e9	−0.180056
$759$	4.04594e9	0.335871
$760$	1.01182e10	0.836092
$761$	1.29730e10	1.06707	0.533535	−	0.845778i	$-0.320863\pi$
$761$	1.29730e10	1.06707	0.533535	+	0.845778i	$0.320863\pi$
$762$	−2.17450e9	−0.178040
$763$	5.65749e9	0.461092
$764$	−2.47383e9	−0.200698
$765$	−1.30806e9	−0.105636
$766$	−1.52476e10	−1.22574
$767$	−2.47685e9	−0.198206
$768$	4.52985e8	0.0360844
$769$	1.57338e10	1.24765	0.623824	−	0.781565i	$-0.285578\pi$
$769$	1.57338e10	1.24765	0.623824	+	0.781565i	$0.285578\pi$
$770$	7.36175e9	0.581117
$771$	−1.29130e10	−1.01470
$772$	−1.23048e10	−0.962530
$773$	2.10722e10	1.64090	0.820448	−	0.571721i	$-0.193724\pi$
$773$	2.10722e10	1.64090	0.820448	+	0.571721i	$0.193724\pi$
$774$	−2.12125e9	−0.164437
$775$	3.73977e10	2.88595
$776$	−8.11587e9	−0.623475
$777$	−1.25339e8	−0.00958545
$778$	−2.03139e9	−0.154655
$779$	9.42141e9	0.714060
$780$	1.73094e9	0.130602
$781$	−1.30871e10	−0.983025
$782$	8.01769e8	0.0599550
$783$	−3.13143e9	−0.233118
$784$	4.81890e8	0.0357143
$785$	−3.42676e10	−2.52837
$786$	−8.81658e9	−0.647622
$787$	1.85046e10	1.35322	0.676610	−	0.736342i	$-0.263448\pi$
$787$	1.85046e10	1.35322	0.676610	+	0.736342i	$0.263448\pi$
$788$	1.21754e10	0.886422
$789$	−6.27707e9	−0.454975
$790$	−1.78653e10	−1.28919
$791$	8.12944e9	0.584041
$792$	2.19627e9	0.157090
$793$	2.29348e9	0.163320
$794$	1.33864e10	0.949059
$795$	1.05538e10	0.744942
$796$	8.18274e8	0.0575046
$797$	9.77176e9	0.683705	0.341852	−	0.939754i	$-0.388946\pi$
$797$	9.77176e9	0.683705	0.341852	+	0.939754i	$0.388946\pi$
$798$	3.21123e9	0.223698
$799$	4.11878e9	0.285663
$800$	−4.25187e9	−0.293606
$801$	1.13413e9	0.0779739
$802$	−2.71712e9	−0.185994
$803$	1.36768e10	0.932137
$804$	2.14246e9	0.145384
$805$	−3.98262e9	−0.269081
$806$	5.06565e9	0.340771
$807$	−1.22192e10	−0.818438
$808$	3.72979e9	0.248740
$809$	−7.32888e9	−0.486651	−0.243326	−	0.969945i	$-0.578238\pi$
$809$	−7.32888e9	−0.486651	−0.243326	+	0.969945i	$0.578238\pi$
$810$	1.93844e9	0.128161
$811$	3.61721e9	0.238123	0.119061	−	0.992887i	$-0.462011\pi$
$811$	3.61721e9	0.238123	0.119061	+	0.992887i	$0.462011\pi$
$812$	3.49241e9	0.228917
$813$	−1.15829e10	−0.755965
$814$	6.37099e8	0.0414020
$815$	−3.03358e10	−1.96292
$816$	4.35228e8	0.0280415
$817$	1.57652e10	1.01140
$818$	9.19767e7	0.00587545
$819$	5.49353e8	0.0349428
$820$	−6.34279e9	−0.401728
$821$	−7.09513e9	−0.447465	−0.223733	−	0.974651i	$-0.571824\pi$
$821$	−7.09513e9	−0.447465	−0.223733	+	0.974651i	$0.571824\pi$
$822$	8.32848e9	0.523015
$823$	2.03485e10	1.27242	0.636212	−	0.771514i	$-0.280500\pi$
$823$	2.03485e10	1.27242	0.636212	+	0.771514i	$0.280500\pi$
$824$	7.96052e9	0.495674
$825$	−2.06149e10	−1.27818
$826$	3.09353e9	0.190996
$827$	−2.87459e9	−0.176729	−0.0883643	−	0.996088i	$-0.528164\pi$
$827$	−2.87459e9	−0.176729	−0.0883643	+	0.996088i	$0.528164\pi$
$828$	−1.18816e9	−0.0727391
$829$	4.69741e9	0.286363	0.143182	−	0.989696i	$-0.454267\pi$
$829$	4.69741e9	0.286363	0.143182	+	0.989696i	$0.454267\pi$
$830$	−6.84284e9	−0.415397
$831$	2.27689e9	0.137638
$832$	−5.75930e8	−0.0346688
$833$	4.63000e8	0.0277539
$834$	−3.82405e8	−0.0228267
$835$	−2.72416e10	−1.61931
$836$	−1.63227e10	−0.966207
$837$	5.67291e9	0.334401
$838$	−2.16668e10	−1.27187
$839$	2.29211e10	1.33989	0.669943	−	0.742412i	$-0.266318\pi$
$839$	2.29211e10	1.33989	0.669943	+	0.742412i	$0.266318\pi$
$840$	−2.16190e9	−0.125852
$841$	8.06067e9	0.467289
$842$	−7.88142e9	−0.455001
$843$	3.42076e9	0.196665
$844$	1.54913e10	0.886931
$845$	−2.20074e9	−0.125479
$846$	−6.10369e9	−0.346574
$847$	−5.19195e9	−0.293588
$848$	−3.51152e9	−0.197747
$849$	8.19376e9	0.459522
$850$	−4.08519e9	−0.228164
$851$	−3.44663e8	−0.0191708
$852$	3.84324e9	0.212892
$853$	−5.34219e9	−0.294712	−0.147356	−	0.989084i	$-0.547076\pi$
$853$	−5.34219e9	−0.294712	−0.147356	+	0.989084i	$0.547076\pi$
$854$	−2.86451e9	−0.157379
$855$	−1.44065e10	−0.788275
$856$	−1.78218e9	−0.0971164
$857$	−2.95807e10	−1.60537	−0.802685	−	0.596403i	$-0.796596\pi$
$857$	−2.95807e10	−1.60537	−0.802685	+	0.596403i	$0.796596\pi$
$858$	−2.79237e9	−0.150927
$859$	−1.83784e10	−0.989309	−0.494654	−	0.869090i	$-0.664705\pi$
$859$	−1.83784e10	−0.989309	−0.494654	+	0.869090i	$0.664705\pi$
$860$	−1.06136e10	−0.569008
$861$	−2.01303e9	−0.107483
$862$	−3.78818e9	−0.201445
$863$	−3.26077e10	−1.72696	−0.863480	−	0.504383i	$-0.831720\pi$
$863$	−3.26077e10	−1.72696	−0.863480	+	0.504383i	$0.831720\pi$
$864$	−6.44973e8	−0.0340207
$865$	−3.26295e10	−1.71417
$866$	−4.70376e9	−0.246112
$867$	−1.06610e10	−0.555559
$868$	−6.32687e9	−0.328375
$869$	2.88205e10	1.48982
$870$	−1.56680e10	−0.806669
$871$	−2.72395e9	−0.139680
$872$	8.44500e9	0.431312
$873$	1.15556e10	0.587818
$874$	8.83039e9	0.447394
$875$	8.07455e9	0.407465
$876$	−4.01642e9	−0.201871
$877$	1.58001e10	0.790971	0.395485	−	0.918472i	$-0.370576\pi$
$877$	1.58001e10	0.790971	0.395485	+	0.918472i	$0.370576\pi$
$878$	−6.69056e9	−0.333604
$879$	−1.22458e10	−0.608170
$880$	1.09890e10	0.543585
$881$	3.47303e10	1.71117	0.855584	−	0.517665i	$-0.173198\pi$
$881$	3.47303e10	1.71117	0.855584	+	0.517665i	$0.173198\pi$
$882$	−6.86129e8	−0.0336718
$883$	1.49003e9	0.0728338	0.0364169	−	0.999337i	$-0.488406\pi$
$883$	1.49003e9	0.0728338	0.0364169	+	0.999337i	$0.488406\pi$
$884$	−5.53354e8	−0.0269414
$885$	−1.38785e10	−0.673040
$886$	−6.44688e9	−0.311410
$887$	1.22026e10	0.587110	0.293555	−	0.955942i	$-0.405162\pi$
$887$	1.22026e10	0.587110	0.293555	+	0.955942i	$0.405162\pi$
$888$	−1.87095e8	−0.00896637
$889$	−3.45302e9	−0.164833
$890$	5.67458e9	0.269816
$891$	−3.12712e9	−0.148106
$892$	−1.38619e10	−0.653953
$893$	4.53627e10	2.13166
$894$	−7.04195e9	−0.329619
$895$	4.33589e10	2.02161
$896$	7.19323e8	0.0334077
$897$	1.51064e9	0.0698854
$898$	−1.20472e9	−0.0555161
$899$	−4.58528e10	−2.10478
$900$	6.05393e9	0.276814
$901$	−3.37387e9	−0.153671
$902$	1.02323e10	0.464246
$903$	−3.36847e9	−0.152239
$904$	1.21349e10	0.546320
$905$	4.04194e10	1.81267
$906$	4.07591e9	0.182086
$907$	2.29729e10	1.02233	0.511165	−	0.859483i	$-0.329214\pi$
$907$	2.29729e10	1.02233	0.511165	+	0.859483i	$0.329214\pi$
$908$	1.33674e10	0.592579
$909$	−5.31059e9	−0.234514
$910$	2.74867e9	0.120914
$911$	−1.16204e10	−0.509223	−0.254611	−	0.967043i	$-0.581948\pi$
$911$	−1.16204e10	−0.509223	−0.254611	+	0.967043i	$0.581948\pi$
$912$	4.79344e9	0.209250
$913$	1.10389e10	0.480042
$914$	2.57235e10	1.11434
$915$	1.28510e10	0.554579
$916$	−4.24681e9	−0.182570
$917$	−1.40004e10	−0.599581
$918$	−6.19690e8	−0.0264378
$919$	1.92705e10	0.819008	0.409504	−	0.912308i	$-0.365702\pi$
$919$	1.92705e10	0.819008	0.409504	+	0.912308i	$0.365702\pi$
$920$	−5.94490e9	−0.251702
$921$	6.17693e9	0.260534
$922$	1.42935e10	0.600592
$923$	−4.88635e9	−0.204540
$924$	3.48760e9	0.145437
$925$	1.75613e9	0.0729561
$926$	−1.03972e10	−0.430308
$927$	−1.13344e10	−0.467326
$928$	5.21316e9	0.214133
$929$	−3.62513e10	−1.48344	−0.741718	−	0.670712i	$-0.765989\pi$
$929$	−3.62513e10	−1.48344	−0.741718	+	0.670712i	$0.765989\pi$
$930$	2.83842e10	1.15714
$931$	5.09931e9	0.207104
$932$	−1.61986e10	−0.655423
$933$	−1.39699e10	−0.563130
$934$	2.56747e10	1.03108
$935$	1.05582e10	0.422425
$936$	8.20026e8	0.0326860
$937$	−2.90289e10	−1.15277	−0.576384	−	0.817179i	$-0.695537\pi$
$937$	−2.90289e10	−1.15277	−0.576384	+	0.817179i	$0.695537\pi$
$938$	3.40215e9	0.134599
$939$	−9.22651e9	−0.363670
$940$	−3.05396e10	−1.19927
$941$	−1.86325e9	−0.0728965	−0.0364482	−	0.999336i	$-0.511604\pi$
$941$	−1.86325e9	−0.0728965	−0.0364482	+	0.999336i	$0.511604\pi$
$942$	−1.62342e10	−0.632779
$943$	−5.53552e9	−0.214965
$944$	4.61775e9	0.178660
$945$	3.07818e9	0.118654
$946$	1.71220e10	0.657560
$947$	1.62304e10	0.621016	0.310508	−	0.950571i	$-0.399501\pi$
$947$	1.62304e10	0.621016	0.310508	+	0.950571i	$0.399501\pi$
$948$	−8.46363e9	−0.322647
$949$	5.10653e9	0.193952
$950$	−4.49928e10	−1.70259
$951$	3.94093e8	0.0148582
$952$	6.91126e8	0.0259614
$953$	1.13776e10	0.425819	0.212910	−	0.977072i	$-0.431706\pi$
$953$	1.13776e10	0.425819	0.212910	+	0.977072i	$0.431706\pi$
$954$	4.99981e9	0.186438
$955$	1.76238e10	0.654767
$956$	−1.97454e10	−0.730909
$957$	2.52757e10	0.932205
$958$	−1.15438e10	−0.424199
$959$	1.32253e10	0.484218
$960$	−3.22710e9	−0.117723
$961$	5.55546e10	2.01924
$962$	2.37875e8	0.00861461
$963$	2.53751e9	0.0915622
$964$	5.16895e9	0.185837
$965$	8.76603e10	3.14020
$966$	−1.88675e9	−0.0673433
$967$	−4.26241e10	−1.51587	−0.757935	−	0.652330i	$-0.773792\pi$
$967$	−4.26241e10	−1.51587	−0.757935	+	0.652330i	$0.773792\pi$
$968$	−7.75008e9	−0.274626
$969$	4.60554e9	0.162610
$970$	5.78180e10	2.03405
$971$	1.63507e10	0.573152	0.286576	−	0.958058i	$-0.407483\pi$
$971$	1.63507e10	0.573152	0.286576	+	0.958058i	$0.407483\pi$
$972$	9.18330e8	0.0320750
$973$	−6.07245e8	−0.0211334
$974$	3.79544e10	1.31615
$975$	−7.69703e9	−0.265954
$976$	−4.27588e9	−0.147215
$977$	5.13840e10	1.76278	0.881388	−	0.472392i	$-0.156609\pi$
$977$	5.13840e10	1.76278	0.881388	+	0.472392i	$0.156609\pi$
$978$	−1.43715e10	−0.491264
$979$	−9.15428e9	−0.311806
$980$	−3.43302e9	−0.116516
$981$	−1.20242e10	−0.406645
$982$	8.48987e9	0.286095
$983$	2.77404e10	0.931485	0.465742	−	0.884920i	$-0.345787\pi$
$983$	2.77404e10	0.931485	0.465742	+	0.884920i	$0.345787\pi$
$984$	−3.00487e9	−0.100541
$985$	−8.67382e10	−2.89190
$986$	5.00880e9	0.166404
$987$	−9.69244e9	−0.320866
$988$	−6.09444e9	−0.201041
$989$	−9.26279e9	−0.304477
$990$	−1.56464e10	−0.512497
$991$	−3.30174e10	−1.07767	−0.538834	−	0.842412i	$-0.681135\pi$
$991$	−3.30174e10	−1.07767	−0.538834	+	0.842412i	$0.681135\pi$
$992$	−9.44419e9	−0.307167
$993$	−1.78975e10	−0.580055
$994$	6.10293e9	0.197100
$995$	−5.82944e9	−0.187606
$996$	−3.24177e9	−0.103962
$997$	6.20690e9	0.198354	0.0991771	−	0.995070i	$-0.468379\pi$
$997$	6.20690e9	0.198354	0.0991771	+	0.995070i	$0.468379\pi$
$998$	−1.63246e10	−0.519859
$999$	2.66391e8	0.00845357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.j.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.j.1.1	✓	5	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -455.940 q^{5} -216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -455.940 q^{5} -216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +3647.52 q^{10} -5884.22 q^{11} +1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -12310.4 q^{15} +4096.00 q^{16} +3935.44 q^{17} -5832.00 q^{18} +43343.4 q^{19} -29180.2 q^{20} -9261.00 q^{21} +47073.8 q^{22} -25466.3 q^{23} -13824.0 q^{24} +129757. q^{25} +17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -159093. q^{29} +98483.1 q^{30} +288214. q^{31} -32768.0 q^{32} -158874. q^{33} -31483.5 q^{34} +156388. q^{35} +46656.0 q^{36} +13534.1 q^{37} -346748. q^{38} -59319.0 q^{39} +233441. q^{40} +217366. q^{41} +74088.0 q^{42} +363727. q^{43} -376590. q^{44} -332381. q^{45} +203731. q^{46} +1.04659e6 q^{47} +110592. q^{48} +117649. q^{49} -1.03805e6 q^{50} +106257. q^{51} -140608. q^{52} -857306. q^{53} -157464. q^{54} +2.68285e6 q^{55} +175616. q^{56} +1.17027e6 q^{57} +1.27274e6 q^{58} +1.12738e6 q^{59} -787865. q^{60} -1.04392e6 q^{61} -2.30571e6 q^{62} -250047. q^{63} +262144. q^{64} +1.00170e6 q^{65} +1.27099e6 q^{66} +1.23985e6 q^{67} +251868. q^{68} -687591. q^{69} -1.25110e6 q^{70} +2.22410e6 q^{71} -373248. q^{72} -2.32432e6 q^{73} -108273. q^{74} +3.50343e6 q^{75} +2.77398e6 q^{76} +2.01829e6 q^{77} +474552. q^{78} -4.89794e6 q^{79} -1.86753e6 q^{80} +531441. q^{81} -1.73893e6 q^{82} -1.87602e6 q^{83} -592704. q^{84} -1.79432e6 q^{85} -2.90981e6 q^{86} -4.29551e6 q^{87} +3.01272e6 q^{88} +1.55573e6 q^{89} +2.65904e6 q^{90} +753571. q^{91} -1.62985e6 q^{92} +7.78178e6 q^{93} -8.37269e6 q^{94} -1.97620e7 q^{95} -884736. q^{96} +1.58513e7 q^{97} -941192. q^{98} -4.28960e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} + 56 q^{5} - 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 + 56 * q^5 - 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9	\( 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} + 56 q^{5} - 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9} - 448 q^{10} - 3679 q^{11} + 8640 q^{12} - 10985 q^{13} + 13720 q^{14} + 1512 q^{15} + 20480 q^{16} + 409 q^{17} - 29160 q^{18} + 33730 q^{19} + 3584 q^{20} - 46305 q^{21} + 29432 q^{22} - 142142 q^{23} - 69120 q^{24} + 153981 q^{25} + 87880 q^{26} + 98415 q^{27} - 109760 q^{28} + 88028 q^{29} - 12096 q^{30} + 244543 q^{31} - 163840 q^{32} - 99333 q^{33} - 3272 q^{34} - 19208 q^{35} + 233280 q^{36} + 730963 q^{37} - 269840 q^{38} - 296595 q^{39} - 28672 q^{40} + 479512 q^{41} + 370440 q^{42} - 406536 q^{43} - 235456 q^{44} + 40824 q^{45} + 1137136 q^{46} + 1138945 q^{47} + 552960 q^{48} + 588245 q^{49} - 1231848 q^{50} + 11043 q^{51} - 703040 q^{52} + 297595 q^{53} - 787320 q^{54} - 1834423 q^{55} + 878080 q^{56} + 910710 q^{57} - 704224 q^{58} + 941652 q^{59} + 96768 q^{60} - 2985259 q^{61} - 1956344 q^{62} - 1250235 q^{63} + 1310720 q^{64} - 123032 q^{65} + 794664 q^{66} - 2333504 q^{67} + 26176 q^{68} - 3837834 q^{69} + 153664 q^{70} - 11322272 q^{71} - 1866240 q^{72} - 6631604 q^{73} - 5847704 q^{74} + 4157487 q^{75} + 2158720 q^{76} + 1261897 q^{77} + 2372760 q^{78} - 10600265 q^{79} + 229376 q^{80} + 2657205 q^{81} - 3836096 q^{82} - 2425229 q^{83} - 2963520 q^{84} - 12267705 q^{85} + 3252288 q^{86} + 2376756 q^{87} + 1883648 q^{88} - 1581837 q^{89} - 326592 q^{90} + 3767855 q^{91} - 9097088 q^{92} + 6602661 q^{93} - 9111560 q^{94} - 11507718 q^{95} - 4423680 q^{96} + 5298407 q^{97} - 4705960 q^{98} - 2681991 q^{99}+O(q^{100}) \) 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 + 56 * q^5 - 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9 - 448 * q^10 - 3679 * q^11 + 8640 * q^12 - 10985 * q^13 + 13720 * q^14 + 1512 * q^15 + 20480 * q^16 + 409 * q^17 - 29160 * q^18 + 33730 * q^19 + 3584 * q^20 - 46305 * q^21 + 29432 * q^22 - 142142 * q^23 - 69120 * q^24 + 153981 * q^25 + 87880 * q^26 + 98415 * q^27 - 109760 * q^28 + 88028 * q^29 - 12096 * q^30 + 244543 * q^31 - 163840 * q^32 - 99333 * q^33 - 3272 * q^34 - 19208 * q^35 + 233280 * q^36 + 730963 * q^37 - 269840 * q^38 - 296595 * q^39 - 28672 * q^40 + 479512 * q^41 + 370440 * q^42 - 406536 * q^43 - 235456 * q^44 + 40824 * q^45 + 1137136 * q^46 + 1138945 * q^47 + 552960 * q^48 + 588245 * q^49 - 1231848 * q^50 + 11043 * q^51 - 703040 * q^52 + 297595 * q^53 - 787320 * q^54 - 1834423 * q^55 + 878080 * q^56 + 910710 * q^57 - 704224 * q^58 + 941652 * q^59 + 96768 * q^60 - 2985259 * q^61 - 1956344 * q^62 - 1250235 * q^63 + 1310720 * q^64 - 123032 * q^65 + 794664 * q^66 - 2333504 * q^67 + 26176 * q^68 - 3837834 * q^69 + 153664 * q^70 - 11322272 * q^71 - 1866240 * q^72 - 6631604 * q^73 - 5847704 * q^74 + 4157487 * q^75 + 2158720 * q^76 + 1261897 * q^77 + 2372760 * q^78 - 10600265 * q^79 + 229376 * q^80 + 2657205 * q^81 - 3836096 * q^82 - 2425229 * q^83 - 2963520 * q^84 - 12267705 * q^85 + 3252288 * q^86 + 2376756 * q^87 + 1883648 * q^88 - 1581837 * q^89 - 326592 * q^90 + 3767855 * q^91 - 9097088 * q^92 + 6602661 * q^93 - 9111560 * q^94 - 11507718 * q^95 - 4423680 * q^96 + 5298407 * q^97 - 4705960 * q^98 - 2681991 * q^99

Introduction

L-functions

Modular forms

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