LMFDB - Embedded newform 546.8.a.h.1.2

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} - 2x^{4} - 115603x^{3} - 20346254x^{2} - 1048249124x - 14570595462 $ x^5 - 2x^4 - 115603x^3 - 20346254x^2 - 1048249124x - 14570595462
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			1.2
Root			$-22.4181$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -94.6099 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -94.6099 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +756.879 q^{10} +1324.10 q^{11} -1728.00 q^{12} +2197.00 q^{13} +2744.00 q^{14} +2554.47 q^{15} +4096.00 q^{16} +20374.3 q^{17} -5832.00 q^{18} -29444.4 q^{19} -6055.03 q^{20} +9261.00 q^{21} -10592.8 q^{22} -75728.3 q^{23} +13824.0 q^{24} -69174.0 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} -564.123 q^{29} -20435.7 q^{30} +112843. q^{31} -32768.0 q^{32} -35750.7 q^{33} -162994. q^{34} +32451.2 q^{35} +46656.0 q^{36} +543269. q^{37} +235555. q^{38} -59319.0 q^{39} +48440.3 q^{40} +309422. q^{41} -74088.0 q^{42} +171238. q^{43} +84742.4 q^{44} -68970.6 q^{45} +605826. q^{46} -1.12381e6 q^{47} -110592. q^{48} +117649. q^{49} +553392. q^{50} -550105. q^{51} +140608. q^{52} -183347. q^{53} +157464. q^{54} -125273. q^{55} +175616. q^{56} +794998. q^{57} +4512.98 q^{58} -190284. q^{59} +163486. q^{60} -1.05184e6 q^{61} -902746. q^{62} -250047. q^{63} +262144. q^{64} -207858. q^{65} +286005. q^{66} -2.91774e6 q^{67} +1.30395e6 q^{68} +2.04466e6 q^{69} -259610. q^{70} +2.43981e6 q^{71} -373248. q^{72} +3.92018e6 q^{73} -4.34615e6 q^{74} +1.86770e6 q^{75} -1.88444e6 q^{76} -454166. q^{77} +474552. q^{78} +710665. q^{79} -387522. q^{80} +531441. q^{81} -2.47537e6 q^{82} +3.70523e6 q^{83} +592704. q^{84} -1.92761e6 q^{85} -1.36990e6 q^{86} +15231.3 q^{87} -677939. q^{88} +3.75600e6 q^{89} +551765. q^{90} -753571. q^{91} -4.84661e6 q^{92} -3.04677e6 q^{93} +8.99050e6 q^{94} +2.78573e6 q^{95} +884736. q^{96} +1.49969e7 q^{97} -941192. q^{98} +965269. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 40 q^{2} - 135 q^{3} + 320 q^{4} + 168 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 + 168 * q^5 + 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9	\( 5 q - 40 q^{2} - 135 q^{3} + 320 q^{4} + 168 q^{5} + 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9} - 1344 q^{10} + 2257 q^{11} - 8640 q^{12} + 10985 q^{13} + 13720 q^{14} - 4536 q^{15} + 20480 q^{16} - 18721 q^{17} - 29160 q^{18} - 67260 q^{19} + 10752 q^{20} + 46305 q^{21} - 18056 q^{22} + 53144 q^{23} + 69120 q^{24} + 68469 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} - 29936 q^{29} + 36288 q^{30} - 61969 q^{31} - 163840 q^{32} - 60939 q^{33} + 149768 q^{34} - 57624 q^{35} + 233280 q^{36} + 302731 q^{37} + 538080 q^{38} - 296595 q^{39} - 86016 q^{40} - 142308 q^{41} - 370440 q^{42} + 267382 q^{43} + 144448 q^{44} + 122472 q^{45} - 425152 q^{46} - 191523 q^{47} - 552960 q^{48} + 588245 q^{49} - 547752 q^{50} + 505467 q^{51} + 703040 q^{52} - 1242769 q^{53} + 787320 q^{54} - 2575465 q^{55} + 878080 q^{56} + 1816020 q^{57} + 239488 q^{58} - 72504 q^{59} - 290304 q^{60} + 678535 q^{61} + 495752 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 369096 q^{65} + 487512 q^{66} + 617640 q^{67} - 1198144 q^{68} - 1434888 q^{69} + 460992 q^{70} + 4351036 q^{71} - 1866240 q^{72} - 433356 q^{73} - 2421848 q^{74} - 1848663 q^{75} - 4304640 q^{76} - 774151 q^{77} + 2372760 q^{78} - 9421619 q^{79} + 688128 q^{80} + 2657205 q^{81} + 1138464 q^{82} - 5145733 q^{83} + 2963520 q^{84} + 6871191 q^{85} - 2139056 q^{86} + 808272 q^{87} - 1155584 q^{88} - 580687 q^{89} - 979776 q^{90} - 3767855 q^{91} + 3401216 q^{92} + 1673163 q^{93} + 1532184 q^{94} + 20602500 q^{95} + 4423680 q^{96} + 12998753 q^{97} - 4705960 q^{98} + 1645353 q^{99}+O(q^{100}) \) 5 * q - 40 * q^2 - 135 * q^3 + 320 * q^4 + 168 * q^5 + 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9 - 1344 * q^10 + 2257 * q^11 - 8640 * q^12 + 10985 * q^13 + 13720 * q^14 - 4536 * q^15 + 20480 * q^16 - 18721 * q^17 - 29160 * q^18 - 67260 * q^19 + 10752 * q^20 + 46305 * q^21 - 18056 * q^22 + 53144 * q^23 + 69120 * q^24 + 68469 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 - 29936 * q^29 + 36288 * q^30 - 61969 * q^31 - 163840 * q^32 - 60939 * q^33 + 149768 * q^34 - 57624 * q^35 + 233280 * q^36 + 302731 * q^37 + 538080 * q^38 - 296595 * q^39 - 86016 * q^40 - 142308 * q^41 - 370440 * q^42 + 267382 * q^43 + 144448 * q^44 + 122472 * q^45 - 425152 * q^46 - 191523 * q^47 - 552960 * q^48 + 588245 * q^49 - 547752 * q^50 + 505467 * q^51 + 703040 * q^52 - 1242769 * q^53 + 787320 * q^54 - 2575465 * q^55 + 878080 * q^56 + 1816020 * q^57 + 239488 * q^58 - 72504 * q^59 - 290304 * q^60 + 678535 * q^61 + 495752 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 369096 * q^65 + 487512 * q^66 + 617640 * q^67 - 1198144 * q^68 - 1434888 * q^69 + 460992 * q^70 + 4351036 * q^71 - 1866240 * q^72 - 433356 * q^73 - 2421848 * q^74 - 1848663 * q^75 - 4304640 * q^76 - 774151 * q^77 + 2372760 * q^78 - 9421619 * q^79 + 688128 * q^80 + 2657205 * q^81 + 1138464 * q^82 - 5145733 * q^83 + 2963520 * q^84 + 6871191 * q^85 - 2139056 * q^86 + 808272 * q^87 - 1155584 * q^88 - 580687 * q^89 - 979776 * q^90 - 3767855 * q^91 + 3401216 * q^92 + 1673163 * q^93 + 1532184 * q^94 + 20602500 * q^95 + 4423680 * q^96 + 12998753 * q^97 - 4705960 * q^98 + 1645353 * 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
$5$	−94.6099	−0.338487	−0.169243	−	0.985574i	$-0.554132\pi$
$5$	−94.6099	−0.338487	−0.169243	+	0.985574i	$0.554132\pi$
$6$	216.000	0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	756.879	0.239346
$11$	1324.10	0.299948	0.149974	−	0.988690i	$-0.452081\pi$
$11$	1324.10	0.299948	0.149974	+	0.988690i	$0.452081\pi$
$12$	−1728.00	−0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	2744.00	0.267261
$15$	2554.47	0.195425
$16$	4096.00	0.250000
$17$	20374.3	1.00580	0.502899	−	0.864345i	$-0.332267\pi$
$17$	20374.3	1.00580	0.502899	+	0.864345i	$0.332267\pi$
$18$	−5832.00	−0.235702
$19$	−29444.4	−0.984837	−0.492419	−	0.870358i	$-0.663887\pi$
$19$	−29444.4	−0.984837	−0.492419	+	0.870358i	$0.663887\pi$
$20$	−6055.03	−0.169243
$21$	9261.00	0.218218
$22$	−10592.8	−0.212095
$23$	−75728.3	−1.29781	−0.648904	−	0.760870i	$-0.724773\pi$
$23$	−75728.3	−1.29781	−0.648904	+	0.760870i	$0.724773\pi$
$24$	13824.0	0.204124
$25$	−69174.0	−0.885427
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	−564.123	−0.00429517	−0.00214759	−	0.999998i	$-0.500684\pi$
$29$	−564.123	−0.00429517	−0.00214759	+	0.999998i	$0.500684\pi$
$30$	−20435.7	−0.138187
$31$	112843.	0.680315	0.340157	−	0.940369i	$-0.389520\pi$
$31$	112843.	0.680315	0.340157	+	0.940369i	$0.389520\pi$
$32$	−32768.0	−0.176777
$33$	−35750.7	−0.173175
$34$	−162994.	−0.711206
$35$	32451.2	0.127936
$36$	46656.0	0.166667
$37$	543269.	1.76323	0.881615	−	0.471969i	$-0.156457\pi$
$37$	543269.	1.76323	0.881615	+	0.471969i	$0.156457\pi$
$38$	235555.	0.696385
$39$	−59319.0	−0.160128
$40$	48440.3	0.119673
$41$	309422.	0.701144	0.350572	−	0.936536i	$-0.385987\pi$
$41$	309422.	0.701144	0.350572	+	0.936536i	$0.385987\pi$
$42$	−74088.0	−0.154303
$43$	171238.	0.328444	0.164222	−	0.986423i	$-0.447489\pi$
$43$	171238.	0.328444	0.164222	+	0.986423i	$0.447489\pi$
$44$	84742.4	0.149974
$45$	−68970.6	−0.112829
$46$	605826.	0.917690
$47$	−1.12381e6	−1.57889	−0.789444	−	0.613823i	$-0.789631\pi$
$47$	−1.12381e6	−1.57889	−0.789444	+	0.613823i	$0.789631\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	553392.	0.626091
$51$	−550105.	−0.580698
$52$	140608.	0.138675
$53$	−183347.	−0.169164	−0.0845822	−	0.996417i	$-0.526956\pi$
$53$	−183347.	−0.169164	−0.0845822	+	0.996417i	$0.526956\pi$
$54$	157464.	0.136083
$55$	−125273.	−0.101528
$56$	175616.	0.133631
$57$	794998.	0.568596
$58$	4512.98	0.00303715
$59$	−190284.	−0.120620	−0.0603100	−	0.998180i	$-0.519209\pi$
$59$	−190284.	−0.120620	−0.0603100	+	0.998180i	$0.519209\pi$
$60$	163486.	0.0977127
$61$	−1.05184e6	−0.593329	−0.296665	−	0.954982i	$-0.595874\pi$
$61$	−1.05184e6	−0.593329	−0.296665	+	0.954982i	$0.595874\pi$
$62$	−902746.	−0.481055
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	−207858.	−0.0938793
$66$	286005.	0.122453
$67$	−2.91774e6	−1.18518	−0.592591	−	0.805503i	$-0.701895\pi$
$67$	−2.91774e6	−1.18518	−0.592591	+	0.805503i	$0.701895\pi$
$68$	1.30395e6	0.502899
$69$	2.04466e6	0.749290
$70$	−259610.	−0.0904644
$71$	2.43981e6	0.809005	0.404502	−	0.914537i	$-0.367445\pi$
$71$	2.43981e6	0.809005	0.404502	+	0.914537i	$0.367445\pi$
$72$	−373248.	−0.117851
$73$	3.92018e6	1.17944	0.589720	−	0.807608i	$-0.299238\pi$
$73$	3.92018e6	1.17944	0.589720	+	0.807608i	$0.299238\pi$
$74$	−4.34615e6	−1.24679
$75$	1.86770e6	0.511201
$76$	−1.88444e6	−0.492419
$77$	−454166.	−0.113370
$78$	474552.	0.113228
$79$	710665.	0.162170	0.0810849	−	0.996707i	$-0.474162\pi$
$79$	710665.	0.162170	0.0810849	+	0.996707i	$0.474162\pi$
$80$	−387522.	−0.0846217
$81$	531441.	0.111111
$82$	−2.47537e6	−0.495784
$83$	3.70523e6	0.711283	0.355641	−	0.934622i	$-0.384262\pi$
$83$	3.70523e6	0.711283	0.355641	+	0.934622i	$0.384262\pi$
$84$	592704.	0.109109
$85$	−1.92761e6	−0.340449
$86$	−1.36990e6	−0.232245
$87$	15231.3	0.00247982
$88$	−677939.	−0.106048
$89$	3.75600e6	0.564756	0.282378	−	0.959303i	$-0.408877\pi$
$89$	3.75600e6	0.564756	0.282378	+	0.959303i	$0.408877\pi$
$90$	551765.	0.0797821
$91$	−753571.	−0.104828
$92$	−4.84661e6	−0.648904
$93$	−3.04677e6	−0.392780
$94$	8.99050e6	1.11644
$95$	2.78573e6	0.333354
$96$	884736.	0.102062
$97$	1.49969e7	1.66840	0.834201	−	0.551461i	$-0.185929\pi$
$97$	1.49969e7	1.66840	0.834201	+	0.551461i	$0.185929\pi$
$98$	−941192.	−0.101015
$99$	965269.	0.0999827
$100$	−4.42713e6	−0.442713
$101$	7.85722e6	0.758830	0.379415	−	0.925227i	$-0.376125\pi$
$101$	7.85722e6	0.758830	0.379415	+	0.925227i	$0.376125\pi$
$102$	4.40084e6	0.410615
$103$	−1.54358e7	−1.39187	−0.695937	−	0.718103i	$-0.745011\pi$
$103$	−1.54358e7	−1.39187	−0.695937	+	0.718103i	$0.745011\pi$
$104$	−1.12486e6	−0.0980581
$105$	−876182.	−0.0738638
$106$	1.46678e6	0.119617
$107$	2.32267e7	1.83292	0.916461	−	0.400124i	$-0.131033\pi$
$107$	2.32267e7	1.83292	0.916461	+	0.400124i	$0.131033\pi$
$108$	−1.25971e6	−0.0962250
$109$	−5.14370e6	−0.380437	−0.190219	−	0.981742i	$-0.560920\pi$
$109$	−5.14370e6	−0.380437	−0.190219	+	0.981742i	$0.560920\pi$
$110$	1.00218e6	0.0717915
$111$	−1.46683e7	−1.01800
$112$	−1.40493e6	−0.0944911
$113$	−1.90737e6	−0.124354	−0.0621770	−	0.998065i	$-0.519804\pi$
$113$	−1.90737e6	−0.124354	−0.0621770	+	0.998065i	$0.519804\pi$
$114$	−6.35998e6	−0.402058
$115$	7.16465e6	0.439291
$116$	−36103.9	−0.00214759
$117$	1.60161e6	0.0924500
$118$	1.52227e6	0.0852913
$119$	−6.98837e6	−0.380156
$120$	−1.30789e6	−0.0690933
$121$	−1.77339e7	−0.910031
$122$	8.41473e6	0.419547
$123$	−8.35439e6	−0.404806
$124$	7.22197e6	0.340157
$125$	1.39359e7	0.638192
$126$	2.00038e6	0.0890871
$127$	1.74467e7	0.755787	0.377894	−	0.925849i	$-0.376649\pi$
$127$	1.74467e7	0.755787	0.377894	+	0.925849i	$0.376649\pi$
$128$	−2.09715e6	−0.0883883
$129$	−4.62343e6	−0.189627
$130$	1.66286e6	0.0663827
$131$	−5.45835e6	−0.212135	−0.106067	−	0.994359i	$-0.533826\pi$
$131$	−5.45835e6	−0.212135	−0.106067	+	0.994359i	$0.533826\pi$
$132$	−2.28804e6	−0.0865876
$133$	1.00994e7	0.372234
$134$	2.33419e7	0.838050
$135$	1.86221e6	0.0651418
$136$	−1.04316e7	−0.355603
$137$	5.24700e7	1.74337	0.871684	−	0.490068i	$-0.163028\pi$
$137$	5.24700e7	1.74337	0.871684	+	0.490068i	$0.163028\pi$
$138$	−1.63573e7	−0.529828
$139$	1.85310e7	0.585256	0.292628	−	0.956226i	$-0.405470\pi$
$139$	1.85310e7	0.585256	0.292628	+	0.956226i	$0.405470\pi$
$140$	2.07688e6	0.0639680
$141$	3.03429e7	0.911571
$142$	−1.95184e7	−0.572053
$143$	2.90905e6	0.0831907
$144$	2.98598e6	0.0833333
$145$	53371.6	0.00145386
$146$	−3.13614e7	−0.833991
$147$	−3.17652e6	−0.0824786
$148$	3.47692e7	0.881615
$149$	−2.30216e7	−0.570143	−0.285071	−	0.958506i	$-0.592017\pi$
$149$	−2.30216e7	−0.570143	−0.285071	+	0.958506i	$0.592017\pi$
$150$	−1.49416e7	−0.361474
$151$	1.04062e6	0.0245965	0.0122983	−	0.999924i	$-0.496085\pi$
$151$	1.04062e6	0.0245965	0.0122983	+	0.999924i	$0.496085\pi$
$152$	1.50755e7	0.348193
$153$	1.48528e7	0.335266
$154$	3.63333e6	0.0801645
$155$	−1.06761e7	−0.230277
$156$	−3.79642e6	−0.0800641
$157$	1.43458e7	0.295853	0.147927	−	0.988998i	$-0.452740\pi$
$157$	1.43458e7	0.295853	0.147927	+	0.988998i	$0.452740\pi$
$158$	−5.68532e6	−0.114671
$159$	4.95038e6	0.0976671
$160$	3.10018e6	0.0598366
$161$	2.59748e7	0.490526
$162$	−4.25153e6	−0.0785674
$163$	−3.60889e7	−0.652706	−0.326353	−	0.945248i	$-0.605820\pi$
$163$	−3.60889e7	−0.652706	−0.326353	+	0.945248i	$0.605820\pi$
$164$	1.98030e7	0.350572
$165$	3.38237e6	0.0586175
$166$	−2.96419e7	−0.502953
$167$	−8.56161e7	−1.42248	−0.711242	−	0.702947i	$-0.751867\pi$
$167$	−8.56161e7	−1.42248	−0.711242	+	0.702947i	$0.751867\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	1.54209e7	0.240734
$171$	−2.14649e7	−0.328279
$172$	1.09592e7	0.164222
$173$	7.98695e7	1.17279	0.586394	−	0.810026i	$-0.300547\pi$
$173$	7.98695e7	1.17279	0.586394	+	0.810026i	$0.300547\pi$
$174$	−121851.	−0.00175350
$175$	2.37267e7	0.334660
$176$	5.42351e6	0.0749870
$177$	5.13766e6	0.0696400
$178$	−3.00480e7	−0.399343
$179$	−6.67759e7	−0.870230	−0.435115	−	0.900375i	$-0.643292\pi$
$179$	−6.67759e7	−0.870230	−0.435115	+	0.900375i	$0.643292\pi$
$180$	−4.41412e6	−0.0564144
$181$	−2.09504e7	−0.262613	−0.131307	−	0.991342i	$-0.541917\pi$
$181$	−2.09504e7	−0.262613	−0.131307	+	0.991342i	$0.541917\pi$
$182$	6.02857e6	0.0741249
$183$	2.83997e7	0.342559
$184$	3.87729e7	0.458845
$185$	−5.13986e7	−0.596830
$186$	2.43741e7	0.277737
$187$	2.69775e7	0.301687
$188$	−7.19240e7	−0.789444
$189$	6.75127e6	0.0727393
$190$	−2.22858e7	−0.235717
$191$	8.53602e7	0.886419	0.443209	−	0.896418i	$-0.353840\pi$
$191$	8.53602e7	0.886419	0.443209	+	0.896418i	$0.353840\pi$
$192$	−7.07789e6	−0.0721688
$193$	−1.93577e8	−1.93822	−0.969112	−	0.246620i	$-0.920680\pi$
$193$	−1.93577e8	−1.93822	−0.969112	+	0.246620i	$0.920680\pi$
$194$	−1.19975e8	−1.17974
$195$	5.61216e6	0.0542012
$196$	7.52954e6	0.0714286
$197$	−1.66590e7	−0.155245	−0.0776223	−	0.996983i	$-0.524733\pi$
$197$	−1.66590e7	−0.155245	−0.0776223	+	0.996983i	$0.524733\pi$
$198$	−7.72215e6	−0.0706985
$199$	−6.67056e7	−0.600035	−0.300018	−	0.953934i	$-0.596993\pi$
$199$	−6.67056e7	−0.600035	−0.300018	+	0.953934i	$0.596993\pi$
$200$	3.54171e7	0.313046
$201$	7.87790e7	0.684265
$202$	−6.28578e7	−0.536574
$203$	193494.	0.00162342
$204$	−3.52067e7	−0.290349
$205$	−2.92744e7	−0.237328
$206$	1.23487e8	0.984203
$207$	−5.52059e7	−0.432603
$208$	8.99891e6	0.0693375
$209$	−3.89873e7	−0.295400
$210$	7.00946e6	0.0522296
$211$	−4.00654e7	−0.293617	−0.146808	−	0.989165i	$-0.546900\pi$
$211$	−4.00654e7	−0.293617	−0.146808	+	0.989165i	$0.546900\pi$
$212$	−1.17342e7	−0.0845822
$213$	−6.58747e7	−0.467079
$214$	−1.85814e8	−1.29607
$215$	−1.62008e7	−0.111174
$216$	1.00777e7	0.0680414
$217$	−3.87052e7	−0.257135
$218$	4.11496e7	0.269010
$219$	−1.05845e8	−0.680950
$220$	−8.01747e6	−0.0507642
$221$	4.47622e7	0.278958
$222$	1.17346e8	0.719836
$223$	−3.09249e7	−0.186741	−0.0933707	−	0.995631i	$-0.529764\pi$
$223$	−3.09249e7	−0.186741	−0.0933707	+	0.995631i	$0.529764\pi$
$224$	1.12394e7	0.0668153
$225$	−5.04278e7	−0.295142
$226$	1.52589e7	0.0879316
$227$	−2.79864e8	−1.58802	−0.794012	−	0.607902i	$-0.792011\pi$
$227$	−2.79864e8	−1.58802	−0.794012	+	0.607902i	$0.792011\pi$
$228$	5.08799e7	0.284298
$229$	−1.80908e8	−0.995483	−0.497741	−	0.867326i	$-0.665837\pi$
$229$	−1.80908e8	−0.995483	−0.497741	+	0.867326i	$0.665837\pi$
$230$	−5.73172e7	−0.310626
$231$	1.22625e7	0.0654541
$232$	288831.	0.00151857
$233$	−1.51602e8	−0.785160	−0.392580	−	0.919718i	$-0.628417\pi$
$233$	−1.51602e8	−0.785160	−0.392580	+	0.919718i	$0.628417\pi$
$234$	−1.28129e7	−0.0653720
$235$	1.06324e8	0.534432
$236$	−1.21782e7	−0.0603100
$237$	−1.91879e7	−0.0936288
$238$	5.59070e7	0.268811
$239$	−3.43015e7	−0.162525	−0.0812625	−	0.996693i	$-0.525895\pi$
$239$	−3.43015e7	−0.162525	−0.0812625	+	0.996693i	$0.525895\pi$
$240$	1.04631e7	0.0488563
$241$	9.16493e6	0.0421764	0.0210882	−	0.999778i	$-0.493287\pi$
$241$	9.16493e6	0.0421764	0.0210882	+	0.999778i	$0.493287\pi$
$242$	1.41871e8	0.643489
$243$	−1.43489e7	−0.0641500
$244$	−6.73178e7	−0.296665
$245$	−1.11308e7	−0.0483552
$246$	6.68351e7	0.286241
$247$	−6.46893e7	−0.273145
$248$	−5.77758e7	−0.240528
$249$	−1.00041e8	−0.410659
$250$	−1.11488e8	−0.451270
$251$	2.26855e8	0.905505	0.452753	−	0.891636i	$-0.350442\pi$
$251$	2.26855e8	0.905505	0.452753	+	0.891636i	$0.350442\pi$
$252$	−1.60030e7	−0.0629941
$253$	−1.00272e8	−0.389275
$254$	−1.39573e8	−0.534422
$255$	5.20454e7	0.196558
$256$	1.67772e7	0.0625000
$257$	3.40238e8	1.25031	0.625154	−	0.780501i	$-0.285036\pi$
$257$	3.40238e8	1.25031	0.625154	+	0.780501i	$0.285036\pi$
$258$	3.69874e7	0.134087
$259$	−1.86341e8	−0.666438
$260$	−1.33029e7	−0.0469397
$261$	−411245.	−0.00143172
$262$	4.36668e7	0.150002
$263$	5.47113e8	1.85452	0.927260	−	0.374418i	$-0.122157\pi$
$263$	5.47113e8	1.85452	0.927260	+	0.374418i	$0.122157\pi$
$264$	1.83044e7	0.0612267
$265$	1.73465e7	0.0572599
$266$	−8.07953e7	−0.263209
$267$	−1.01412e8	−0.326062
$268$	−1.86736e8	−0.592591
$269$	−4.79385e8	−1.50159	−0.750796	−	0.660535i	$-0.770330\pi$
$269$	−4.79385e8	−1.50159	−0.750796	+	0.660535i	$0.770330\pi$
$270$	−1.48977e7	−0.0460622
$271$	−2.61111e8	−0.796954	−0.398477	−	0.917178i	$-0.630461\pi$
$271$	−2.61111e8	−0.796954	−0.398477	+	0.917178i	$0.630461\pi$
$272$	8.34530e7	0.251449
$273$	2.03464e7	0.0605228
$274$	−4.19760e8	−1.23275
$275$	−9.15932e7	−0.265582
$276$	1.30858e8	0.374645
$277$	−6.16644e8	−1.74323	−0.871616	−	0.490189i	$-0.836928\pi$
$277$	−6.16644e8	−1.74323	−0.871616	+	0.490189i	$0.836928\pi$
$278$	−1.48248e8	−0.413839
$279$	8.22628e7	0.226772
$280$	−1.66150e7	−0.0452322
$281$	−8.97581e7	−0.241325	−0.120662	−	0.992694i	$-0.538502\pi$
$281$	−8.97581e7	−0.241325	−0.120662	+	0.992694i	$0.538502\pi$
$282$	−2.42743e8	−0.644578
$283$	−3.55705e7	−0.0932905	−0.0466452	−	0.998912i	$-0.514853\pi$
$283$	−3.55705e7	−0.0932905	−0.0466452	+	0.998912i	$0.514853\pi$
$284$	1.56148e8	0.404502
$285$	−7.52147e7	−0.192462
$286$	−2.32724e7	−0.0588247
$287$	−1.06132e8	−0.265008
$288$	−2.38879e7	−0.0589256
$289$	4.77180e6	0.0116289
$290$	−426973.	−0.00102803
$291$	−4.04916e8	−0.963252
$292$	2.50892e8	0.589720
$293$	−5.57987e8	−1.29595	−0.647973	−	0.761663i	$-0.724383\pi$
$293$	−5.57987e8	−1.29595	−0.647973	+	0.761663i	$0.724383\pi$
$294$	2.54122e7	0.0583212
$295$	1.80027e7	0.0408283
$296$	−2.78154e8	−0.623396
$297$	−2.60622e7	−0.0577251
$298$	1.84173e8	0.403152
$299$	−1.66375e8	−0.359947
$300$	1.19533e8	0.255601
$301$	−5.87347e7	−0.124140
$302$	−8.32498e6	−0.0173924
$303$	−2.12145e8	−0.438110
$304$	−1.20604e8	−0.246209
$305$	9.95146e7	0.200834
$306$	−1.18823e8	−0.237069
$307$	−1.70305e8	−0.335925	−0.167963	−	0.985793i	$-0.553719\pi$
$307$	−1.70305e8	−0.335925	−0.167963	+	0.985793i	$0.553719\pi$
$308$	−2.90666e7	−0.0566849
$309$	4.16768e8	0.803599
$310$	8.54087e7	0.162831
$311$	2.28330e8	0.430430	0.215215	−	0.976567i	$-0.430955\pi$
$311$	2.28330e8	0.430430	0.215215	+	0.976567i	$0.430955\pi$
$312$	3.03713e7	0.0566139
$313$	−7.75820e8	−1.43007	−0.715033	−	0.699091i	$-0.753588\pi$
$313$	−7.75820e8	−1.43007	−0.715033	+	0.699091i	$0.753588\pi$
$314$	−1.14767e8	−0.209200
$315$	2.36569e7	0.0426453
$316$	4.54825e7	0.0810849
$317$	−2.19011e8	−0.386153	−0.193076	−	0.981184i	$-0.561846\pi$
$317$	−2.19011e8	−0.386153	−0.193076	+	0.981184i	$0.561846\pi$
$318$	−3.96030e7	−0.0690611
$319$	−746955.	−0.00128833
$320$	−2.48014e7	−0.0423108
$321$	−6.27121e8	−1.05824
$322$	−2.07798e8	−0.346854
$323$	−5.99907e8	−0.990547
$324$	3.40122e7	0.0555556
$325$	−1.51975e8	−0.245573
$326$	2.88712e8	0.461533
$327$	1.38880e8	0.219645
$328$	−1.58424e8	−0.247892
$329$	3.85468e8	0.596764
$330$	−2.70589e7	−0.0414488
$331$	−3.59245e8	−0.544494	−0.272247	−	0.962227i	$-0.587767\pi$
$331$	−3.59245e8	−0.544494	−0.272247	+	0.962227i	$0.587767\pi$
$332$	2.37135e8	0.355641
$333$	3.96043e8	0.587743
$334$	6.84929e8	1.00585
$335$	2.76047e8	0.401168
$336$	3.79331e7	0.0545545
$337$	2.90850e8	0.413965	0.206983	−	0.978345i	$-0.433636\pi$
$337$	2.90850e8	0.413965	0.206983	+	0.978345i	$0.433636\pi$
$338$	−3.86145e7	−0.0543928
$339$	5.14989e7	0.0717959
$340$	−1.23367e8	−0.170225
$341$	1.49416e8	0.204059
$342$	1.71720e8	0.232128
$343$	−4.03536e7	−0.0539949
$344$	−8.76739e7	−0.116122
$345$	−1.93445e8	−0.253625
$346$	−6.38956e8	−0.829287
$347$	−4.82060e8	−0.619367	−0.309683	−	0.950840i	$-0.600223\pi$
$347$	−4.82060e8	−0.619367	−0.309683	+	0.950840i	$0.600223\pi$
$348$	974804.	0.00123991
$349$	−8.16083e8	−1.02765	−0.513825	−	0.857895i	$-0.671772\pi$
$349$	−8.16083e8	−1.02765	−0.513825	+	0.857895i	$0.671772\pi$
$350$	−1.89813e8	−0.236640
$351$	−4.32436e7	−0.0533761
$352$	−4.33881e7	−0.0530238
$353$	1.22709e8	0.148479	0.0742396	−	0.997240i	$-0.476347\pi$
$353$	1.22709e8	0.148479	0.0742396	+	0.997240i	$0.476347\pi$
$354$	−4.11013e7	−0.0492429
$355$	−2.30830e8	−0.273837
$356$	2.40384e8	0.282378
$357$	1.88686e8	0.219483
$358$	5.34207e8	0.615346
$359$	−1.22667e9	−1.39926	−0.699628	−	0.714508i	$-0.746651\pi$
$359$	−1.22667e9	−1.39926	−0.699628	+	0.714508i	$0.746651\pi$
$360$	3.53130e7	0.0398910
$361$	−2.69012e7	−0.0300951
$362$	1.67603e8	0.185696
$363$	4.78816e8	0.525407
$364$	−4.82285e7	−0.0524142
$365$	−3.70888e8	−0.399225
$366$	−2.27198e8	−0.242226
$367$	−5.65265e7	−0.0596927	−0.0298464	−	0.999554i	$-0.509502\pi$
$367$	−5.65265e7	−0.0596927	−0.0298464	+	0.999554i	$0.509502\pi$
$368$	−3.10183e8	−0.324452
$369$	2.25568e8	0.233715
$370$	4.11189e8	0.422022
$371$	6.28881e7	0.0639381
$372$	−1.94993e8	−0.196390
$373$	8.24280e8	0.822421	0.411210	−	0.911540i	$-0.365106\pi$
$373$	8.24280e8	0.822421	0.411210	+	0.911540i	$0.365106\pi$
$374$	−2.15820e8	−0.213325
$375$	−3.76270e8	−0.368460
$376$	5.75392e8	0.558221
$377$	−1.23938e6	−0.00119127
$378$	−5.40102e7	−0.0514344
$379$	−6.79304e8	−0.640954	−0.320477	−	0.947256i	$-0.603843\pi$
$379$	−6.79304e8	−0.640954	−0.320477	+	0.947256i	$0.603843\pi$
$380$	1.78287e8	0.166677
$381$	−4.71060e8	−0.436354
$382$	−6.82882e8	−0.626793
$383$	−1.55501e9	−1.41429	−0.707145	−	0.707068i	$-0.750017\pi$
$383$	−1.55501e9	−1.41429	−0.707145	+	0.707068i	$0.750017\pi$
$384$	5.66231e7	0.0510310
$385$	4.29686e7	0.0383741
$386$	1.54862e9	1.37053
$387$	1.24833e8	0.109481
$388$	9.59802e8	0.834201
$389$	1.06041e9	0.913375	0.456687	−	0.889627i	$-0.349036\pi$
$389$	1.06041e9	0.913375	0.456687	+	0.889627i	$0.349036\pi$
$390$	−4.48973e7	−0.0383261
$391$	−1.54291e9	−1.30533
$392$	−6.02363e7	−0.0505076
$393$	1.47375e8	0.122476
$394$	1.33272e8	0.109774
$395$	−6.72359e7	−0.0548923
$396$	6.17772e7	0.0499914
$397$	1.21622e9	0.975539	0.487770	−	0.872972i	$-0.337811\pi$
$397$	1.21622e9	0.975539	0.487770	+	0.872972i	$0.337811\pi$
$398$	5.33645e8	0.424289
$399$	−2.72684e8	−0.214909
$400$	−2.83337e8	−0.221357
$401$	1.96120e9	1.51885	0.759426	−	0.650594i	$-0.225480\pi$
$401$	1.96120e9	1.51885	0.759426	+	0.650594i	$0.225480\pi$
$402$	−6.30232e8	−0.483849
$403$	2.47917e8	0.188685
$404$	5.02862e8	0.379415
$405$	−5.02796e7	−0.0376096
$406$	−1.54795e6	−0.00114793
$407$	7.19342e8	0.528878
$408$	2.81654e8	0.205308
$409$	−1.01242e9	−0.731695	−0.365848	−	0.930675i	$-0.619221\pi$
$409$	−1.01242e9	−0.731695	−0.365848	+	0.930675i	$0.619221\pi$
$410$	2.34195e8	0.167816
$411$	−1.41669e9	−1.00653
$412$	−9.87893e8	−0.695937
$413$	6.52673e7	0.0455901
$414$	4.41647e8	0.305897
$415$	−3.50552e8	−0.240760
$416$	−7.19913e7	−0.0490290
$417$	−5.00336e8	−0.337898
$418$	3.11898e8	0.208879
$419$	8.76436e8	0.582065	0.291032	−	0.956713i	$-0.406001\pi$
$419$	8.76436e8	0.582065	0.291032	+	0.956713i	$0.406001\pi$
$420$	−5.60757e7	−0.0369319
$421$	3.92314e8	0.256240	0.128120	−	0.991759i	$-0.459106\pi$
$421$	3.92314e8	0.256240	0.128120	+	0.991759i	$0.459106\pi$
$422$	3.20523e8	0.207618
$423$	−8.19259e8	−0.526296
$424$	9.38738e7	0.0598087
$425$	−1.40937e9	−0.890560
$426$	5.26998e8	0.330275
$427$	3.60782e8	0.224257
$428$	1.48651e9	0.916461
$429$	−7.85443e7	−0.0480301
$430$	1.29607e8	0.0786117
$431$	2.09801e9	1.26222	0.631112	−	0.775692i	$-0.282599\pi$
$431$	2.09801e9	1.26222	0.631112	+	0.775692i	$0.282599\pi$
$432$	−8.06216e7	−0.0481125
$433$	−1.93518e9	−1.14555	−0.572774	−	0.819713i	$-0.694133\pi$
$433$	−1.93518e9	−1.14555	−0.572774	+	0.819713i	$0.694133\pi$
$434$	3.09642e8	0.181822
$435$	−1.44103e6	−0.000839386 0
$436$	−3.29197e8	−0.190219
$437$	2.22977e9	1.27813
$438$	8.46759e8	0.481505
$439$	−2.03616e9	−1.14865	−0.574324	−	0.818628i	$-0.694735\pi$
$439$	−2.03616e9	−1.14865	−0.574324	+	0.818628i	$0.694735\pi$
$440$	6.41397e7	0.0358957
$441$	8.57661e7	0.0476190
$442$	−3.58098e8	−0.197253
$443$	−7.18571e8	−0.392696	−0.196348	−	0.980534i	$-0.562908\pi$
$443$	−7.18571e8	−0.392696	−0.196348	+	0.980534i	$0.562908\pi$
$444$	−9.38769e8	−0.509001
$445$	−3.55355e8	−0.191162
$446$	2.47399e8	0.132046
$447$	6.21583e8	0.329172
$448$	−8.99154e7	−0.0472456
$449$	−2.18420e9	−1.13875	−0.569377	−	0.822077i	$-0.692815\pi$
$449$	−2.18420e9	−1.13875	−0.569377	+	0.822077i	$0.692815\pi$
$450$	4.03423e8	0.208697
$451$	4.09705e8	0.210307
$452$	−1.22072e8	−0.0621770
$453$	−2.80968e7	−0.0142008
$454$	2.23891e9	1.12290
$455$	7.12953e7	0.0354830
$456$	−4.07039e8	−0.201029
$457$	−1.81374e9	−0.888930	−0.444465	−	0.895796i	$-0.646606\pi$
$457$	−1.81374e9	−0.888930	−0.444465	+	0.895796i	$0.646606\pi$
$458$	1.44726e9	0.703913
$459$	−4.01027e8	−0.193566
$460$	4.58537e8	0.219646
$461$	−1.06405e9	−0.505836	−0.252918	−	0.967488i	$-0.581390\pi$
$461$	−1.06405e9	−0.505836	−0.252918	+	0.967488i	$0.581390\pi$
$462$	−9.80999e7	−0.0462830
$463$	2.25325e9	1.05506	0.527529	−	0.849537i	$-0.323119\pi$
$463$	2.25325e9	1.05506	0.527529	+	0.849537i	$0.323119\pi$
$464$	−2.31065e6	−0.00107379
$465$	2.88254e8	0.132951
$466$	1.21281e9	0.555192
$467$	−6.05384e8	−0.275056	−0.137528	−	0.990498i	$-0.543916\pi$
$467$	−6.05384e8	−0.275056	−0.137528	+	0.990498i	$0.543916\pi$
$468$	1.02503e8	0.0462250
$469$	1.00079e9	0.447957
$470$	−8.50590e8	−0.377901
$471$	−3.87337e8	−0.170811
$472$	9.74253e7	0.0426456
$473$	2.26736e8	0.0985160
$474$	1.53504e8	0.0662055
$475$	2.03678e9	0.872001
$476$	−4.47256e8	−0.190078
$477$	−1.33660e8	−0.0563881
$478$	2.74412e8	0.114922
$479$	4.00554e8	0.166528	0.0832639	−	0.996528i	$-0.473466\pi$
$479$	4.00554e8	0.166528	0.0832639	+	0.996528i	$0.473466\pi$
$480$	−8.37048e7	−0.0345466
$481$	1.19356e9	0.489032
$482$	−7.33194e7	−0.0298232
$483$	−7.01320e8	−0.283205
$484$	−1.13497e9	−0.455016
$485$	−1.41886e9	−0.564732
$486$	1.14791e8	0.0453609
$487$	1.03192e9	0.404849	0.202424	−	0.979298i	$-0.435118\pi$
$487$	1.03192e9	0.404849	0.202424	+	0.979298i	$0.435118\pi$
$488$	5.38543e8	0.209774
$489$	9.74401e8	0.376840
$490$	8.90461e7	0.0341923
$491$	−1.14135e9	−0.435145	−0.217572	−	0.976044i	$-0.569814\pi$
$491$	−1.14135e9	−0.435145	−0.217572	+	0.976044i	$0.569814\pi$
$492$	−5.34681e8	−0.202403
$493$	−1.14936e7	−0.00432007
$494$	5.17514e8	0.193143
$495$	−9.13240e7	−0.0338428
$496$	4.62206e8	0.170079
$497$	−8.36853e8	−0.305775
$498$	8.00331e8	0.290380
$499$	−4.61122e9	−1.66136	−0.830681	−	0.556749i	$-0.812049\pi$
$499$	−4.61122e9	−1.66136	−0.830681	+	0.556749i	$0.812049\pi$
$500$	8.91900e8	0.319096
$501$	2.31163e9	0.821272
$502$	−1.81484e9	−0.640289
$503$	−2.66458e9	−0.933559	−0.466779	−	0.884374i	$-0.654586\pi$
$503$	−2.66458e9	−0.933559	−0.466779	+	0.884374i	$0.654586\pi$
$504$	1.28024e8	0.0445435
$505$	−7.43371e8	−0.256854
$506$	8.02174e8	0.275259
$507$	−1.30324e8	−0.0444116
$508$	1.11659e9	0.377894
$509$	1.81775e9	0.610975	0.305487	−	0.952196i	$-0.401181\pi$
$509$	1.81775e9	0.610975	0.305487	+	0.952196i	$0.401181\pi$
$510$	−4.16363e8	−0.138988
$511$	−1.34462e9	−0.445787
$512$	−1.34218e8	−0.0441942
$513$	5.79553e8	0.189532
$514$	−2.72190e9	−0.884101
$515$	1.46038e9	0.471131
$516$	−2.95899e8	−0.0948135
$517$	−1.48804e9	−0.473585
$518$	1.49073e9	0.471243
$519$	−2.15648e9	−0.677110
$520$	1.06423e8	0.0331913
$521$	−4.23102e9	−1.31073	−0.655364	−	0.755313i	$-0.727485\pi$
$521$	−4.23102e9	−1.31073	−0.655364	+	0.755313i	$0.727485\pi$
$522$	3.28996e6	0.00101238
$523$	2.21055e8	0.0675686	0.0337843	−	0.999429i	$-0.489244\pi$
$523$	2.21055e8	0.0675686	0.0337843	+	0.999429i	$0.489244\pi$
$524$	−3.49334e8	−0.106067
$525$	−6.40620e8	−0.193216
$526$	−4.37690e9	−1.31134
$527$	2.29910e9	0.684259
$528$	−1.46435e8	−0.0432938
$529$	2.32995e9	0.684308
$530$	−1.38772e8	−0.0404889
$531$	−1.38717e8	−0.0402067
$532$	6.46363e8	0.186117
$533$	6.79800e8	0.194462
$534$	8.11296e8	0.230561
$535$	−2.19747e9	−0.620420
$536$	1.49388e9	0.419025
$537$	1.80295e9	0.502428
$538$	3.83508e9	1.06179
$539$	1.55779e8	0.0428497
$540$	1.19181e8	0.0325709
$541$	−2.02094e9	−0.548735	−0.274367	−	0.961625i	$-0.588468\pi$
$541$	−2.02094e9	−0.548735	−0.274367	+	0.961625i	$0.588468\pi$
$542$	2.08889e9	0.563531
$543$	5.65660e8	0.151620
$544$	−6.67624e8	−0.177802
$545$	4.86645e8	0.128773
$546$	−1.62771e8	−0.0427960
$547$	3.40680e9	0.890003	0.445002	−	0.895530i	$-0.353203\pi$
$547$	3.40680e9	0.890003	0.445002	+	0.895530i	$0.353203\pi$
$548$	3.35808e9	0.871684
$549$	−7.66792e8	−0.197776
$550$	7.32746e8	0.187795
$551$	1.66102e7	0.00423005
$552$	−1.04687e9	−0.264914
$553$	−2.43758e8	−0.0612944
$554$	4.93315e9	1.23265
$555$	1.38776e9	0.344580
$556$	1.18598e9	0.292628
$557$	5.53623e8	0.135744	0.0678721	−	0.997694i	$-0.478379\pi$
$557$	5.53623e8	0.135744	0.0678721	+	0.997694i	$0.478379\pi$
$558$	−6.58102e8	−0.160352
$559$	3.76210e8	0.0910938
$560$	1.32920e8	0.0319840
$561$	−7.28394e8	−0.174179
$562$	7.18065e8	0.170642
$563$	−1.10747e9	−0.261550	−0.130775	−	0.991412i	$-0.541747\pi$
$563$	−1.10747e9	−0.261550	−0.130775	+	0.991412i	$0.541747\pi$
$564$	1.94195e9	0.455786
$565$	1.80456e8	0.0420922
$566$	2.84564e8	0.0659663
$567$	−1.82284e8	−0.0419961
$568$	−1.24918e9	−0.286026
$569$	2.20280e9	0.501283	0.250641	−	0.968080i	$-0.419358\pi$
$569$	2.20280e9	0.501283	0.250641	+	0.968080i	$0.419358\pi$
$570$	6.01717e8	0.136091
$571$	7.02617e9	1.57940	0.789700	−	0.613493i	$-0.210236\pi$
$571$	7.02617e9	1.57940	0.789700	+	0.613493i	$0.210236\pi$
$572$	1.86179e8	0.0415953
$573$	−2.30473e9	−0.511774
$574$	8.49053e8	0.187389
$575$	5.23843e9	1.14911
$576$	1.91103e8	0.0416667
$577$	6.03163e9	1.30713	0.653566	−	0.756870i	$-0.273272\pi$
$577$	6.03163e9	1.30713	0.653566	+	0.756870i	$0.273272\pi$
$578$	−3.81744e7	−0.00822289
$579$	5.22659e9	1.11903
$580$	3.41578e6	0.000726929 0
$581$	−1.27090e9	−0.268840
$582$	3.23933e9	0.681122
$583$	−2.42770e8	−0.0507406
$584$	−2.00713e9	−0.416995
$585$	−1.51528e8	−0.0312931
$586$	4.46389e9	0.916373
$587$	7.08606e9	1.44601	0.723005	−	0.690843i	$-0.242760\pi$
$587$	7.08606e9	1.44601	0.723005	+	0.690843i	$0.242760\pi$
$588$	−2.03297e8	−0.0412393
$589$	−3.32260e9	−0.669999
$590$	−1.44022e8	−0.0288700
$591$	4.49792e8	0.0896305
$592$	2.22523e9	0.440807
$593$	1.57287e9	0.309742	0.154871	−	0.987935i	$-0.450504\pi$
$593$	1.57287e9	0.309742	0.154871	+	0.987935i	$0.450504\pi$
$594$	2.08498e8	0.0408178
$595$	6.61169e8	0.128678
$596$	−1.47338e9	−0.285071
$597$	1.80105e9	0.346431
$598$	1.33100e9	0.254521
$599$	6.84506e9	1.30132	0.650659	−	0.759370i	$-0.274493\pi$
$599$	6.84506e9	1.30132	0.650659	+	0.759370i	$0.274493\pi$
$600$	−9.56261e8	−0.180737
$601$	−2.28938e9	−0.430188	−0.215094	−	0.976593i	$-0.569006\pi$
$601$	−2.28938e9	−0.430188	−0.215094	+	0.976593i	$0.569006\pi$
$602$	4.69877e8	0.0877802
$603$	−2.12703e9	−0.395061
$604$	6.65998e7	0.0122983
$605$	1.67781e9	0.308033
$606$	1.69716e9	0.309791
$607$	−1.01054e10	−1.83398	−0.916989	−	0.398913i	$-0.869388\pi$
$607$	−1.01054e10	−1.83398	−0.916989	+	0.398913i	$0.869388\pi$
$608$	9.64833e8	0.174096
$609$	−5.22434e6	−0.000937283 0
$610$	−7.96117e8	−0.142011
$611$	−2.46902e9	−0.437905
$612$	9.50581e8	0.167633
$613$	−8.35923e9	−1.46573	−0.732866	−	0.680373i	$-0.761818\pi$
$613$	−8.35923e9	−1.46573	−0.732866	+	0.680373i	$0.761818\pi$
$614$	1.36244e9	0.237535
$615$	7.90408e8	0.137021
$616$	2.32533e8	0.0400823
$617$	−5.39470e9	−0.924632	−0.462316	−	0.886715i	$-0.652981\pi$
$617$	−5.39470e9	−0.924632	−0.462316	+	0.886715i	$0.652981\pi$
$618$	−3.33414e9	−0.568230
$619$	−8.60502e9	−1.45826	−0.729130	−	0.684376i	$-0.760075\pi$
$619$	−8.60502e9	−1.45826	−0.729130	+	0.684376i	$0.760075\pi$
$620$	−6.83270e8	−0.115139
$621$	1.49056e9	0.249763
$622$	−1.82664e9	−0.304360
$623$	−1.28831e9	−0.213458
$624$	−2.42971e8	−0.0400320
$625$	4.08574e9	0.669407
$626$	6.20656e9	1.01121
$627$	1.05266e9	0.170549
$628$	9.18132e8	0.147927
$629$	1.10687e10	1.77345
$630$	−1.89255e8	−0.0301548
$631$	−7.64873e9	−1.21195	−0.605977	−	0.795482i	$-0.707218\pi$
$631$	−7.64873e9	−1.21195	−0.605977	+	0.795482i	$0.707218\pi$
$632$	−3.63860e8	−0.0573357
$633$	1.08177e9	0.169520
$634$	1.75209e9	0.273051
$635$	−1.65063e9	−0.255824
$636$	3.16824e8	0.0488336
$637$	2.58475e8	0.0396214
$638$	5.97564e6	0.000910986 0
$639$	1.77862e9	0.269668
$640$	1.98411e8	0.0299183
$641$	4.30252e9	0.645238	0.322619	−	0.946529i	$-0.395437\pi$
$641$	4.30252e9	0.645238	0.322619	+	0.946529i	$0.395437\pi$
$642$	5.01696e9	0.748287
$643$	1.01691e10	1.50850	0.754249	−	0.656589i	$-0.228001\pi$
$643$	1.01691e10	1.50850	0.754249	+	0.656589i	$0.228001\pi$
$644$	1.66239e9	0.245263
$645$	4.37422e8	0.0641862
$646$	4.79926e9	0.700423
$647$	7.07522e9	1.02701	0.513505	−	0.858086i	$-0.328347\pi$
$647$	7.07522e9	1.02701	0.513505	+	0.858086i	$0.328347\pi$
$648$	−2.72098e8	−0.0392837
$649$	−2.51955e8	−0.0361798
$650$	1.21580e9	0.173646
$651$	1.04504e9	0.148457
$652$	−2.30969e9	−0.326353
$653$	−1.91463e9	−0.269084	−0.134542	−	0.990908i	$-0.542956\pi$
$653$	−1.91463e9	−0.269084	−0.134542	+	0.990908i	$0.542956\pi$
$654$	−1.11104e9	−0.155313
$655$	5.16413e8	0.0718047
$656$	1.26739e9	0.175286
$657$	2.85781e9	0.393147
$658$	−3.08374e9	−0.421976
$659$	1.29809e10	1.76687	0.883435	−	0.468553i	$-0.155224\pi$
$659$	1.29809e10	1.76687	0.883435	+	0.468553i	$0.155224\pi$
$660$	2.16472e8	0.0293087
$661$	−7.43966e9	−1.00195	−0.500977	−	0.865461i	$-0.667026\pi$
$661$	−7.43966e9	−1.00195	−0.500977	+	0.865461i	$0.667026\pi$
$662$	2.87396e9	0.385015
$663$	−1.20858e9	−0.161057
$664$	−1.89708e9	−0.251476
$665$	−9.55505e8	−0.125996
$666$	−3.16835e9	−0.415597
$667$	4.27201e7	0.00557431
$668$	−5.47943e9	−0.711242
$669$	8.34971e8	0.107815
$670$	−2.20838e9	−0.283669
$671$	−1.39274e9	−0.177968
$672$	−3.03464e8	−0.0385758
$673$	8.82885e9	1.11648	0.558241	−	0.829679i	$-0.311477\pi$
$673$	8.82885e9	1.11648	0.558241	+	0.829679i	$0.311477\pi$
$674$	−2.32680e9	−0.292718
$675$	1.36155e9	0.170400
$676$	3.08916e8	0.0384615
$677$	−1.14377e9	−0.141670	−0.0708348	−	0.997488i	$-0.522566\pi$
$677$	−1.14377e9	−0.141670	−0.0708348	+	0.997488i	$0.522566\pi$
$678$	−4.11992e8	−0.0507673
$679$	−5.14394e9	−0.630597
$680$	9.86935e8	0.120367
$681$	7.55634e9	0.916846
$682$	−1.19533e9	−0.144292
$683$	9.28527e9	1.11512	0.557561	−	0.830136i	$-0.311737\pi$
$683$	9.28527e9	1.11512	0.557561	+	0.830136i	$0.311737\pi$
$684$	−1.37376e9	−0.164140
$685$	−4.96418e9	−0.590107
$686$	3.22829e8	0.0381802
$687$	4.88452e9	0.574742
$688$	7.01391e8	0.0821109
$689$	−4.02814e8	−0.0469178
$690$	1.54756e9	0.179340
$691$	−1.34607e10	−1.55200	−0.776002	−	0.630730i	$-0.782755\pi$
$691$	−1.34607e10	−1.55200	−0.776002	+	0.630730i	$0.782755\pi$
$692$	5.11165e9	0.586394
$693$	−3.31087e8	−0.0377899
$694$	3.85648e9	0.437958
$695$	−1.75321e9	−0.198102
$696$	−7.79843e6	−0.000876748 0
$697$	6.30424e9	0.705209
$698$	6.52866e9	0.726658
$699$	4.09324e9	0.453312
$700$	1.51851e9	0.167330
$701$	1.41681e10	1.55346	0.776728	−	0.629836i	$-0.216878\pi$
$701$	1.41681e10	1.55346	0.776728	+	0.629836i	$0.216878\pi$
$702$	3.45948e8	0.0377426
$703$	−1.59962e10	−1.73649
$704$	3.47105e8	0.0374935
$705$	−2.87074e9	−0.308555
$706$	−9.81674e8	−0.104991
$707$	−2.69503e9	−0.286811
$708$	3.28810e8	0.0348200
$709$	1.63246e9	0.172020	0.0860102	−	0.996294i	$-0.472588\pi$
$709$	1.63246e9	0.172020	0.0860102	+	0.996294i	$0.472588\pi$
$710$	1.84664e9	0.193632
$711$	5.18075e8	0.0540566
$712$	−1.92307e9	−0.199671
$713$	−8.54543e9	−0.882918
$714$	−1.50949e9	−0.155198
$715$	−2.75225e8	−0.0281589
$716$	−4.27366e9	−0.435115
$717$	9.26139e8	0.0938338
$718$	9.81335e9	0.989423
$719$	6.38166e9	0.640298	0.320149	−	0.947367i	$-0.396267\pi$
$719$	6.38166e9	0.640298	0.320149	+	0.947367i	$0.396267\pi$
$720$	−2.82504e8	−0.0282072
$721$	5.29449e9	0.526079
$722$	2.15210e8	0.0212805
$723$	−2.47453e8	−0.0243505
$724$	−1.34082e9	−0.131307
$725$	3.90226e7	0.00380306
$726$	−3.83053e9	−0.371519
$727$	−1.09886e10	−1.06065	−0.530324	−	0.847795i	$-0.677930\pi$
$727$	−1.09886e10	−1.06065	−0.530324	+	0.847795i	$0.677930\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	2.96710e9	0.282295
$731$	3.48885e9	0.330348
$732$	1.81758e9	0.171279
$733$	2.28155e9	0.213977	0.106988	−	0.994260i	$-0.465879\pi$
$733$	2.28155e9	0.213977	0.106988	+	0.994260i	$0.465879\pi$
$734$	4.52212e8	0.0422091
$735$	3.00531e8	0.0279179
$736$	2.48146e9	0.229422
$737$	−3.86338e9	−0.355493
$738$	−1.80455e9	−0.165261
$739$	−4.97990e9	−0.453905	−0.226953	−	0.973906i	$-0.572876\pi$
$739$	−4.97990e9	−0.453905	−0.226953	+	0.973906i	$0.572876\pi$
$740$	−3.28951e9	−0.298415
$741$	1.74661e9	0.157700
$742$	−5.03105e8	−0.0452111
$743$	−2.10030e10	−1.87854	−0.939269	−	0.343182i	$-0.888495\pi$
$743$	−2.10030e10	−1.87854	−0.939269	+	0.343182i	$0.888495\pi$
$744$	1.55995e9	0.138869
$745$	2.17807e9	0.192986
$746$	−6.59424e9	−0.581539
$747$	2.70112e9	0.237094
$748$	1.72656e9	0.150844
$749$	−7.96675e9	−0.692780
$750$	3.01016e9	0.260541
$751$	−8.37140e9	−0.721204	−0.360602	−	0.932720i	$-0.617429\pi$
$751$	−8.37140e9	−0.721204	−0.360602	+	0.932720i	$0.617429\pi$
$752$	−4.60314e9	−0.394722
$753$	−6.12510e9	−0.522794
$754$	9.91502e6	0.000842353 0
$755$	−9.84532e7	−0.00832560
$756$	4.32081e8	0.0363696
$757$	−2.49702e8	−0.0209212	−0.0104606	−	0.999945i	$-0.503330\pi$
$757$	−2.49702e8	−0.0209212	−0.0104606	+	0.999945i	$0.503330\pi$
$758$	5.43443e9	0.453223
$759$	2.70734e9	0.224748
$760$	−1.42629e9	−0.117859
$761$	−1.50925e10	−1.24141	−0.620705	−	0.784044i	$-0.713153\pi$
$761$	−1.50925e10	−1.24141	−0.620705	+	0.784044i	$0.713153\pi$
$762$	3.76848e9	0.308549
$763$	1.76429e9	0.143792
$764$	5.46306e9	0.443209
$765$	−1.40523e9	−0.113483
$766$	1.24401e10	1.00005
$767$	−4.18053e8	−0.0334540
$768$	−4.52985e8	−0.0360844
$769$	8.38661e9	0.665035	0.332517	−	0.943097i	$-0.392102\pi$
$769$	8.38661e9	0.665035	0.332517	+	0.943097i	$0.392102\pi$
$770$	−3.43749e8	−0.0271346
$771$	−9.18643e9	−0.721866
$772$	−1.23890e10	−0.969112
$773$	−5.39417e9	−0.420046	−0.210023	−	0.977696i	$-0.567354\pi$
$773$	−5.39417e9	−0.420046	−0.210023	+	0.977696i	$0.567354\pi$
$774$	−9.98660e8	−0.0774149
$775$	−7.80582e9	−0.602369
$776$	−7.67842e9	−0.589869
$777$	5.03121e9	0.384768
$778$	−8.48326e9	−0.645854
$779$	−9.11073e9	−0.690513
$780$	3.59179e8	0.0271006
$781$	3.23054e9	0.242659
$782$	1.23433e10	0.923010
$783$	1.11036e7	0.000826606 0
$784$	4.81890e8	0.0357143
$785$	−1.35726e9	−0.100142
$786$	−1.17900e9	−0.0866036
$787$	−1.16965e10	−0.855348	−0.427674	−	0.903933i	$-0.640667\pi$
$787$	−1.16965e10	−0.855348	−0.427674	+	0.903933i	$0.640667\pi$
$788$	−1.06617e9	−0.0776223
$789$	−1.47720e10	−1.07071
$790$	5.37887e8	0.0388147
$791$	6.54227e8	0.0470014
$792$	−4.94217e8	−0.0353492
$793$	−2.31090e9	−0.164560
$794$	−9.72975e9	−0.689810
$795$	−4.68355e8	−0.0330590
$796$	−4.26916e9	−0.300018
$797$	4.10488e9	0.287208	0.143604	−	0.989635i	$-0.454131\pi$
$797$	4.10488e9	0.287208	0.143604	+	0.989635i	$0.454131\pi$
$798$	2.18147e9	0.151964
$799$	−2.28968e10	−1.58804
$800$	2.26669e9	0.156523
$801$	2.73813e9	0.188252
$802$	−1.56896e10	−1.07399
$803$	5.19071e9	0.353771
$804$	5.04186e9	0.342133
$805$	−2.45747e9	−0.166036
$806$	−1.98333e9	−0.133421
$807$	1.29434e10	0.866944
$808$	−4.02290e9	−0.268287
$809$	−2.31078e10	−1.53440	−0.767202	−	0.641406i	$-0.778351\pi$
$809$	−2.31078e10	−1.53440	−0.767202	+	0.641406i	$0.778351\pi$
$810$	4.02237e8	0.0265940
$811$	−7.48090e9	−0.492472	−0.246236	−	0.969210i	$-0.579194\pi$
$811$	−7.48090e9	−0.492472	−0.246236	+	0.969210i	$0.579194\pi$
$812$	1.23836e7	0.000811711 0
$813$	7.05000e9	0.460121
$814$	−5.75474e9	−0.373973
$815$	3.41437e9	0.220932
$816$	−2.25323e9	−0.145174
$817$	−5.04200e9	−0.323463
$818$	8.09938e9	0.517387
$819$	−5.49353e8	−0.0349428
$820$	−1.87356e9	−0.118664
$821$	1.60564e10	1.01262	0.506310	−	0.862352i	$-0.331009\pi$
$821$	1.60564e10	1.01262	0.506310	+	0.862352i	$0.331009\pi$
$822$	1.13335e10	0.711727
$823$	2.57871e10	1.61251	0.806257	−	0.591565i	$-0.201490\pi$
$823$	2.57871e10	1.61251	0.806257	+	0.591565i	$0.201490\pi$
$824$	7.90315e9	0.492102
$825$	2.47302e9	0.153334
$826$	−5.22139e8	−0.0322371
$827$	−2.84574e10	−1.74955	−0.874774	−	0.484531i	$-0.838990\pi$
$827$	−2.84574e10	−1.74955	−0.874774	+	0.484531i	$0.838990\pi$
$828$	−3.53318e9	−0.216301
$829$	−1.51982e10	−0.926510	−0.463255	−	0.886225i	$-0.653319\pi$
$829$	−1.51982e10	−0.926510	−0.463255	+	0.886225i	$0.653319\pi$
$830$	2.80441e9	0.170243
$831$	1.66494e10	1.00646
$832$	5.75930e8	0.0346688
$833$	2.39701e9	0.143685
$834$	4.00269e9	0.238930
$835$	8.10013e9	0.481492
$836$	−2.49519e9	−0.147700
$837$	−2.22109e9	−0.130927
$838$	−7.01149e9	−0.411582
$839$	−1.48884e10	−0.870323	−0.435161	−	0.900352i	$-0.643309\pi$
$839$	−1.48884e10	−0.870323	−0.435161	+	0.900352i	$0.643309\pi$
$840$	4.48605e8	0.0261148
$841$	−1.72496e10	−0.999982
$842$	−3.13851e9	−0.181189
$843$	2.42347e9	0.139329
$844$	−2.56419e9	−0.146808
$845$	−4.56664e8	−0.0260374
$846$	6.55407e9	0.372147
$847$	6.08274e9	0.343959
$848$	−7.50991e8	−0.0422911
$849$	9.60403e8	0.0538613
$850$	1.12749e10	0.629721
$851$	−4.11408e10	−2.28834
$852$	−4.21598e9	−0.233539
$853$	−1.18952e8	−0.00656224	−0.00328112	−	0.999995i	$-0.501044\pi$
$853$	−1.18952e8	−0.00656224	−0.00328112	+	0.999995i	$0.501044\pi$
$854$	−2.88625e9	−0.158574
$855$	2.03080e9	0.111118
$856$	−1.18921e10	−0.648036
$857$	2.28908e10	1.24231	0.621153	−	0.783690i	$-0.286665\pi$
$857$	2.28908e10	1.24231	0.621153	+	0.783690i	$0.286665\pi$
$858$	6.28354e8	0.0339624
$859$	1.17093e10	0.630313	0.315156	−	0.949040i	$-0.397943\pi$
$859$	1.17093e10	0.630313	0.315156	+	0.949040i	$0.397943\pi$
$860$	−1.03685e9	−0.0555869
$861$	2.86555e9	0.153002
$862$	−1.67840e10	−0.892527
$863$	3.13708e10	1.66145	0.830726	−	0.556681i	$-0.187926\pi$
$863$	3.13708e10	1.66145	0.830726	+	0.556681i	$0.187926\pi$
$864$	6.44973e8	0.0340207
$865$	−7.55645e9	−0.396973
$866$	1.54814e10	0.810025
$867$	−1.28839e8	−0.00671396
$868$	−2.47714e9	−0.128567
$869$	9.40991e8	0.0486425
$870$	1.15283e7	0.000593535 0
$871$	−6.41028e9	−0.328710
$872$	2.63357e9	0.134505
$873$	1.09327e10	0.556134
$874$	−1.78382e10	−0.903775
$875$	−4.78003e9	−0.241214
$876$	−6.77407e9	−0.340475
$877$	8.87220e9	0.444153	0.222077	−	0.975029i	$-0.428716\pi$
$877$	8.87220e9	0.444153	0.222077	+	0.975029i	$0.428716\pi$
$878$	1.62893e10	0.812217
$879$	1.50656e10	0.748215
$880$	−5.13118e8	−0.0253821
$881$	−3.21155e9	−0.158233	−0.0791167	−	0.996865i	$-0.525210\pi$
$881$	−3.21155e9	−0.158233	−0.0791167	+	0.996865i	$0.525210\pi$
$882$	−6.86129e8	−0.0336718
$883$	1.08651e10	0.531092	0.265546	−	0.964098i	$-0.414448\pi$
$883$	1.08651e10	0.531092	0.265546	+	0.964098i	$0.414448\pi$
$884$	2.86478e9	0.139479
$885$	−4.86074e8	−0.0235722
$886$	5.74857e9	0.277678
$887$	−1.20373e10	−0.579159	−0.289580	−	0.957154i	$-0.593515\pi$
$887$	−1.20373e10	−0.579159	−0.289580	+	0.957154i	$0.593515\pi$
$888$	7.51015e9	0.359918
$889$	−5.98421e9	−0.285661
$890$	2.84284e9	0.135172
$891$	7.03681e8	0.0333276
$892$	−1.97919e9	−0.0933707
$893$	3.30899e10	1.55495
$894$	−4.97266e9	−0.232760
$895$	6.31766e9	0.294561
$896$	7.19323e8	0.0334077
$897$	4.49213e9	0.207816
$898$	1.74736e10	0.805220
$899$	−6.36575e7	−0.00292207
$900$	−3.22738e9	−0.147571
$901$	−3.73557e9	−0.170145
$902$	−3.27764e9	−0.148709
$903$	1.58584e9	0.0716723
$904$	9.76573e8	0.0439658
$905$	1.98211e9	0.0888910
$906$	2.24774e8	0.0100415
$907$	−5.76307e9	−0.256465	−0.128232	−	0.991744i	$-0.540930\pi$
$907$	−5.76307e9	−0.256465	−0.128232	+	0.991744i	$0.540930\pi$
$908$	−1.79113e10	−0.794012
$909$	5.72791e9	0.252943
$910$	−5.70362e8	−0.0250903
$911$	−2.18155e10	−0.955984	−0.477992	−	0.878364i	$-0.658635\pi$
$911$	−2.18155e10	−0.955984	−0.477992	+	0.878364i	$0.658635\pi$
$912$	3.25631e9	0.142149
$913$	4.90610e9	0.213348
$914$	1.45099e10	0.628568
$915$	−2.68689e9	−0.115952
$916$	−1.15781e10	−0.497741
$917$	1.87221e9	0.0801793
$918$	3.20821e9	0.136872
$919$	−3.19137e10	−1.35635	−0.678176	−	0.734899i	$-0.737229\pi$
$919$	−3.19137e10	−1.35635	−0.678176	+	0.734899i	$0.737229\pi$
$920$	−3.66830e9	−0.155313
$921$	4.59823e9	0.193947
$922$	8.51242e9	0.357680
$923$	5.36025e9	0.224377
$924$	7.84799e8	0.0327270
$925$	−3.75801e10	−1.56121
$926$	−1.80260e10	−0.746039
$927$	−1.12527e10	−0.463958
$928$	1.84852e7	0.000759286 0
$929$	3.06149e10	1.25279	0.626393	−	0.779507i	$-0.284530\pi$
$929$	3.06149e10	1.25279	0.626393	+	0.779507i	$0.284530\pi$
$930$	−2.30604e9	−0.0940104
$931$	−3.46410e9	−0.140691
$932$	−9.70250e9	−0.392580
$933$	−6.16492e9	−0.248509
$934$	4.84307e9	0.194494
$935$	−2.55234e9	−0.102117
$936$	−8.20026e8	−0.0326860
$937$	3.43405e10	1.36370	0.681849	−	0.731493i	$-0.261176\pi$
$937$	3.43405e10	1.36370	0.681849	+	0.731493i	$0.261176\pi$
$938$	−8.00629e9	−0.316753
$939$	2.09471e10	0.825649
$940$	6.80472e9	0.267216
$941$	−1.34737e10	−0.527136	−0.263568	−	0.964641i	$-0.584899\pi$
$941$	−1.34737e10	−0.527136	−0.263568	+	0.964641i	$0.584899\pi$
$942$	3.09870e9	0.120782
$943$	−2.34320e10	−0.909951
$944$	−7.79402e8	−0.0301550
$945$	−6.38737e8	−0.0246213
$946$	−1.81389e9	−0.0696614
$947$	−1.38553e10	−0.530140	−0.265070	−	0.964229i	$-0.585395\pi$
$947$	−1.38553e10	−0.530140	−0.265070	+	0.964229i	$0.585395\pi$
$948$	−1.22803e9	−0.0468144
$949$	8.61264e9	0.327118
$950$	−1.62943e10	−0.616598
$951$	5.91330e9	0.222945
$952$	3.57805e9	0.134405
$953$	−1.85798e10	−0.695369	−0.347684	−	0.937612i	$-0.613032\pi$
$953$	−1.85798e10	−0.695369	−0.347684	+	0.937612i	$0.613032\pi$
$954$	1.06928e9	0.0398724
$955$	−8.07592e9	−0.300041
$956$	−2.19529e9	−0.0812625
$957$	2.01678e7	0.000743817 0
$958$	−3.20443e9	−0.117753
$959$	−1.79972e10	−0.658931
$960$	6.69638e8	0.0244282
$961$	−1.47790e10	−0.537172
$962$	−9.54850e9	−0.345798
$963$	1.69323e10	0.610974
$964$	5.86555e8	0.0210882
$965$	1.83143e10	0.656063
$966$	5.61056e9	0.200256
$967$	3.37775e10	1.20126	0.600628	−	0.799529i	$-0.294917\pi$
$967$	3.37775e10	1.20126	0.600628	+	0.799529i	$0.294917\pi$
$968$	9.07977e9	0.321745
$969$	1.61975e10	0.571893
$970$	1.13508e10	0.399326
$971$	−4.95770e10	−1.73785	−0.868926	−	0.494941i	$-0.835190\pi$
$971$	−4.95770e10	−1.73785	−0.868926	+	0.494941i	$0.835190\pi$
$972$	−9.18330e8	−0.0320750
$973$	−6.35612e9	−0.221206
$974$	−8.25532e9	−0.286271
$975$	4.10333e9	0.141782
$976$	−4.30834e9	−0.148332
$977$	−6.16987e9	−0.211663	−0.105831	−	0.994384i	$-0.533750\pi$
$977$	−6.16987e9	−0.211663	−0.105831	+	0.994384i	$0.533750\pi$
$978$	−7.79521e9	−0.266466
$979$	4.97332e9	0.169398
$980$	−7.12369e8	−0.0241776
$981$	−3.74976e9	−0.126812
$982$	9.13081e9	0.307694
$983$	3.56759e9	0.119795	0.0598973	−	0.998205i	$-0.480923\pi$
$983$	3.56759e9	0.119795	0.0598973	+	0.998205i	$0.480923\pi$
$984$	4.27745e9	0.143120
$985$	1.57610e9	0.0525482
$986$	9.19487e7	0.00305475
$987$	−1.04076e10	−0.344542
$988$	−4.14011e9	−0.136572
$989$	−1.29676e10	−0.426257
$990$	7.30592e8	0.0239305
$991$	−2.61000e9	−0.0851887	−0.0425943	−	0.999092i	$-0.513562\pi$
$991$	−2.61000e9	−0.0851887	−0.0425943	+	0.999092i	$0.513562\pi$
$992$	−3.69765e9	−0.120264
$993$	9.69962e9	0.314364
$994$	6.69483e9	0.216216
$995$	6.31101e9	0.203104
$996$	−6.40265e9	−0.205330
$997$	5.27101e10	1.68446	0.842230	−	0.539118i	$-0.181242\pi$
$997$	5.27101e10	1.68446	0.842230	+	0.539118i	$0.181242\pi$
$998$	3.68898e10	1.17476
$999$	−1.06932e10	−0.339334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.h.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.h.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -94.6099 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -94.6099 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +756.879 q^{10} +1324.10 q^{11} -1728.00 q^{12} +2197.00 q^{13} +2744.00 q^{14} +2554.47 q^{15} +4096.00 q^{16} +20374.3 q^{17} -5832.00 q^{18} -29444.4 q^{19} -6055.03 q^{20} +9261.00 q^{21} -10592.8 q^{22} -75728.3 q^{23} +13824.0 q^{24} -69174.0 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} -564.123 q^{29} -20435.7 q^{30} +112843. q^{31} -32768.0 q^{32} -35750.7 q^{33} -162994. q^{34} +32451.2 q^{35} +46656.0 q^{36} +543269. q^{37} +235555. q^{38} -59319.0 q^{39} +48440.3 q^{40} +309422. q^{41} -74088.0 q^{42} +171238. q^{43} +84742.4 q^{44} -68970.6 q^{45} +605826. q^{46} -1.12381e6 q^{47} -110592. q^{48} +117649. q^{49} +553392. q^{50} -550105. q^{51} +140608. q^{52} -183347. q^{53} +157464. q^{54} -125273. q^{55} +175616. q^{56} +794998. q^{57} +4512.98 q^{58} -190284. q^{59} +163486. q^{60} -1.05184e6 q^{61} -902746. q^{62} -250047. q^{63} +262144. q^{64} -207858. q^{65} +286005. q^{66} -2.91774e6 q^{67} +1.30395e6 q^{68} +2.04466e6 q^{69} -259610. q^{70} +2.43981e6 q^{71} -373248. q^{72} +3.92018e6 q^{73} -4.34615e6 q^{74} +1.86770e6 q^{75} -1.88444e6 q^{76} -454166. q^{77} +474552. q^{78} +710665. q^{79} -387522. q^{80} +531441. q^{81} -2.47537e6 q^{82} +3.70523e6 q^{83} +592704. q^{84} -1.92761e6 q^{85} -1.36990e6 q^{86} +15231.3 q^{87} -677939. q^{88} +3.75600e6 q^{89} +551765. q^{90} -753571. q^{91} -4.84661e6 q^{92} -3.04677e6 q^{93} +8.99050e6 q^{94} +2.78573e6 q^{95} +884736. q^{96} +1.49969e7 q^{97} -941192. q^{98} +965269. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 40 q^{2} - 135 q^{3} + 320 q^{4} + 168 q^{5} + 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q - 40 * q^2 - 135 * q^3 + 320 * q^4 + 168 * q^5 + 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9	\( 5 q - 40 q^{2} - 135 q^{3} + 320 q^{4} + 168 q^{5} + 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9} - 1344 q^{10} + 2257 q^{11} - 8640 q^{12} + 10985 q^{13} + 13720 q^{14} - 4536 q^{15} + 20480 q^{16} - 18721 q^{17} - 29160 q^{18} - 67260 q^{19} + 10752 q^{20} + 46305 q^{21} - 18056 q^{22} + 53144 q^{23} + 69120 q^{24} + 68469 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} - 29936 q^{29} + 36288 q^{30} - 61969 q^{31} - 163840 q^{32} - 60939 q^{33} + 149768 q^{34} - 57624 q^{35} + 233280 q^{36} + 302731 q^{37} + 538080 q^{38} - 296595 q^{39} - 86016 q^{40} - 142308 q^{41} - 370440 q^{42} + 267382 q^{43} + 144448 q^{44} + 122472 q^{45} - 425152 q^{46} - 191523 q^{47} - 552960 q^{48} + 588245 q^{49} - 547752 q^{50} + 505467 q^{51} + 703040 q^{52} - 1242769 q^{53} + 787320 q^{54} - 2575465 q^{55} + 878080 q^{56} + 1816020 q^{57} + 239488 q^{58} - 72504 q^{59} - 290304 q^{60} + 678535 q^{61} + 495752 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 369096 q^{65} + 487512 q^{66} + 617640 q^{67} - 1198144 q^{68} - 1434888 q^{69} + 460992 q^{70} + 4351036 q^{71} - 1866240 q^{72} - 433356 q^{73} - 2421848 q^{74} - 1848663 q^{75} - 4304640 q^{76} - 774151 q^{77} + 2372760 q^{78} - 9421619 q^{79} + 688128 q^{80} + 2657205 q^{81} + 1138464 q^{82} - 5145733 q^{83} + 2963520 q^{84} + 6871191 q^{85} - 2139056 q^{86} + 808272 q^{87} - 1155584 q^{88} - 580687 q^{89} - 979776 q^{90} - 3767855 q^{91} + 3401216 q^{92} + 1673163 q^{93} + 1532184 q^{94} + 20602500 q^{95} + 4423680 q^{96} + 12998753 q^{97} - 4705960 q^{98} + 1645353 q^{99}+O(q^{100}) \) 5 * q - 40 * q^2 - 135 * q^3 + 320 * q^4 + 168 * q^5 + 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9 - 1344 * q^10 + 2257 * q^11 - 8640 * q^12 + 10985 * q^13 + 13720 * q^14 - 4536 * q^15 + 20480 * q^16 - 18721 * q^17 - 29160 * q^18 - 67260 * q^19 + 10752 * q^20 + 46305 * q^21 - 18056 * q^22 + 53144 * q^23 + 69120 * q^24 + 68469 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 - 29936 * q^29 + 36288 * q^30 - 61969 * q^31 - 163840 * q^32 - 60939 * q^33 + 149768 * q^34 - 57624 * q^35 + 233280 * q^36 + 302731 * q^37 + 538080 * q^38 - 296595 * q^39 - 86016 * q^40 - 142308 * q^41 - 370440 * q^42 + 267382 * q^43 + 144448 * q^44 + 122472 * q^45 - 425152 * q^46 - 191523 * q^47 - 552960 * q^48 + 588245 * q^49 - 547752 * q^50 + 505467 * q^51 + 703040 * q^52 - 1242769 * q^53 + 787320 * q^54 - 2575465 * q^55 + 878080 * q^56 + 1816020 * q^57 + 239488 * q^58 - 72504 * q^59 - 290304 * q^60 + 678535 * q^61 + 495752 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 369096 * q^65 + 487512 * q^66 + 617640 * q^67 - 1198144 * q^68 - 1434888 * q^69 + 460992 * q^70 + 4351036 * q^71 - 1866240 * q^72 - 433356 * q^73 - 2421848 * q^74 - 1848663 * q^75 - 4304640 * q^76 - 774151 * q^77 + 2372760 * q^78 - 9421619 * q^79 + 688128 * q^80 + 2657205 * q^81 + 1138464 * q^82 - 5145733 * q^83 + 2963520 * q^84 + 6871191 * q^85 - 2139056 * q^86 + 808272 * q^87 - 1155584 * q^88 - 580687 * q^89 - 979776 * q^90 - 3767855 * q^91 + 3401216 * q^92 + 1673163 * q^93 + 1532184 * q^94 + 20602500 * q^95 + 4423680 * q^96 + 12998753 * q^97 - 4705960 * q^98 + 1645353 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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