LMFDB - Embedded newform 546.8.a.h.1.4

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			1.4
Root			$414.514$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +286.499 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +286.499 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -2291.99 q^{10} -7273.74 q^{11} -1728.00 q^{12} +2197.00 q^{13} +2744.00 q^{14} -7735.46 q^{15} +4096.00 q^{16} -486.888 q^{17} -5832.00 q^{18} +7558.69 q^{19} +18335.9 q^{20} +9261.00 q^{21} +58189.9 q^{22} +93411.4 q^{23} +13824.0 q^{24} +3956.50 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} -27607.9 q^{29} +61883.7 q^{30} +77979.4 q^{31} -32768.0 q^{32} +196391. q^{33} +3895.11 q^{34} -98269.1 q^{35} +46656.0 q^{36} +79888.2 q^{37} -60469.6 q^{38} -59319.0 q^{39} -146687. q^{40} +382405. q^{41} -74088.0 q^{42} -953411. q^{43} -465519. q^{44} +208858. q^{45} -747291. q^{46} +415816. q^{47} -110592. q^{48} +117649. q^{49} -31652.0 q^{50} +13146.0 q^{51} +140608. q^{52} -1.95424e6 q^{53} +157464. q^{54} -2.08392e6 q^{55} +175616. q^{56} -204085. q^{57} +220863. q^{58} +103360. q^{59} -495070. q^{60} +1.35192e6 q^{61} -623835. q^{62} -250047. q^{63} +262144. q^{64} +629438. q^{65} -1.57113e6 q^{66} +2.14550e6 q^{67} -31160.8 q^{68} -2.52211e6 q^{69} +786152. q^{70} +707729. q^{71} -373248. q^{72} +1.84707e6 q^{73} -639106. q^{74} -106826. q^{75} +483756. q^{76} +2.49489e6 q^{77} +474552. q^{78} -4.61854e6 q^{79} +1.17350e6 q^{80} +531441. q^{81} -3.05924e6 q^{82} -1.48072e6 q^{83} +592704. q^{84} -139493. q^{85} +7.62729e6 q^{86} +745414. q^{87} +3.72415e6 q^{88} -3.27708e6 q^{89} -1.67086e6 q^{90} -753571. q^{91} +5.97833e6 q^{92} -2.10544e6 q^{93} -3.32653e6 q^{94} +2.16556e6 q^{95} +884736. q^{96} -1.91640e6 q^{97} -941192. q^{98} -5.30256e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	286.499	1.02501	0.512504	−	0.858685i	$-0.328718\pi$
$5$	286.499	1.02501	0.512504	+	0.858685i	$0.328718\pi$
$6$	216.000	0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−2291.99	−0.724791
$11$	−7273.74	−1.64772	−0.823860	−	0.566794i	$-0.808184\pi$
$11$	−7273.74	−1.64772	−0.823860	+	0.566794i	$0.808184\pi$
$12$	−1728.00	−0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	2744.00	0.267261
$15$	−7735.46	−0.591789
$16$	4096.00	0.250000
$17$	−486.888	−0.0240358	−0.0120179	−	0.999928i	$-0.503826\pi$
$17$	−486.888	−0.0240358	−0.0120179	+	0.999928i	$0.503826\pi$
$18$	−5832.00	−0.235702
$19$	7558.69	0.252819	0.126409	−	0.991978i	$-0.459655\pi$
$19$	7558.69	0.252819	0.126409	+	0.991978i	$0.459655\pi$
$20$	18335.9	0.512504
$21$	9261.00	0.218218
$22$	58189.9	1.16511
$23$	93411.4	1.60086	0.800428	−	0.599429i	$-0.204606\pi$
$23$	93411.4	1.60086	0.800428	+	0.599429i	$0.204606\pi$
$24$	13824.0	0.204124
$25$	3956.50	0.0506432
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	−27607.9	−0.210204	−0.105102	−	0.994461i	$-0.533517\pi$
$29$	−27607.9	−0.210204	−0.105102	+	0.994461i	$0.533517\pi$
$30$	61883.7	0.418458
$31$	77979.4	0.470126	0.235063	−	0.971980i	$-0.424470\pi$
$31$	77979.4	0.470126	0.235063	+	0.971980i	$0.424470\pi$
$32$	−32768.0	−0.176777
$33$	196391.	0.951311
$34$	3895.11	0.0169959
$35$	−98269.1	−0.387417
$36$	46656.0	0.166667
$37$	79888.2	0.259284	0.129642	−	0.991561i	$-0.458617\pi$
$37$	79888.2	0.259284	0.129642	+	0.991561i	$0.458617\pi$
$38$	−60469.6	−0.178770
$39$	−59319.0	−0.160128
$40$	−146687.	−0.362395
$41$	382405.	0.866523	0.433262	−	0.901268i	$-0.357363\pi$
$41$	382405.	0.866523	0.433262	+	0.901268i	$0.357363\pi$
$42$	−74088.0	−0.154303
$43$	−953411.	−1.82869	−0.914346	−	0.404934i	$-0.867295\pi$
$43$	−953411.	−1.82869	−0.914346	+	0.404934i	$0.867295\pi$
$44$	−465519.	−0.823860
$45$	208858.	0.341670
$46$	−747291.	−1.13198
$47$	415816.	0.584196	0.292098	−	0.956388i	$-0.405647\pi$
$47$	415816.	0.584196	0.292098	+	0.956388i	$0.405647\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	−31652.0	−0.0358102
$51$	13146.0	0.0138771
$52$	140608.	0.138675
$53$	−1.95424e6	−1.80307	−0.901533	−	0.432710i	$-0.857557\pi$
$53$	−1.95424e6	−1.80307	−0.901533	+	0.432710i	$0.857557\pi$
$54$	157464.	0.136083
$55$	−2.08392e6	−1.68893
$56$	175616.	0.133631
$57$	−204085.	−0.145965
$58$	220863.	0.148637
$59$	103360.	0.0655194	0.0327597	−	0.999463i	$-0.489570\pi$
$59$	103360.	0.0655194	0.0327597	+	0.999463i	$0.489570\pi$
$60$	−495070.	−0.295895
$61$	1.35192e6	0.762598	0.381299	−	0.924452i	$-0.375477\pi$
$61$	1.35192e6	0.762598	0.381299	+	0.924452i	$0.375477\pi$
$62$	−623835.	−0.332429
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	629438.	0.284286
$66$	−1.57113e6	−0.672679
$67$	2.14550e6	0.871498	0.435749	−	0.900068i	$-0.356484\pi$
$67$	2.14550e6	0.871498	0.435749	+	0.900068i	$0.356484\pi$
$68$	−31160.8	−0.0120179
$69$	−2.52211e6	−0.924255
$70$	786152.	0.273945
$71$	707729.	0.234673	0.117336	−	0.993092i	$-0.462564\pi$
$71$	707729.	0.234673	0.117336	+	0.993092i	$0.462564\pi$
$72$	−373248.	−0.117851
$73$	1.84707e6	0.555718	0.277859	−	0.960622i	$-0.410375\pi$
$73$	1.84707e6	0.555718	0.277859	+	0.960622i	$0.410375\pi$
$74$	−639106.	−0.183342
$75$	−106826.	−0.0292389
$76$	483756.	0.126409
$77$	2.49489e6	0.622780
$78$	474552.	0.113228
$79$	−4.61854e6	−1.05393	−0.526963	−	0.849888i	$-0.676669\pi$
$79$	−4.61854e6	−1.05393	−0.526963	+	0.849888i	$0.676669\pi$
$80$	1.17350e6	0.256252
$81$	531441.	0.111111
$82$	−3.05924e6	−0.612724
$83$	−1.48072e6	−0.284249	−0.142125	−	0.989849i	$-0.545393\pi$
$83$	−1.48072e6	−0.284249	−0.142125	+	0.989849i	$0.545393\pi$
$84$	592704.	0.109109
$85$	−139493.	−0.0246369
$86$	7.62729e6	1.29308
$87$	745414.	0.121361
$88$	3.72415e6	0.582557
$89$	−3.27708e6	−0.492744	−0.246372	−	0.969175i	$-0.579239\pi$
$89$	−3.27708e6	−0.492744	−0.246372	+	0.969175i	$0.579239\pi$
$90$	−1.67086e6	−0.241597
$91$	−753571.	−0.104828
$92$	5.97833e6	0.800428
$93$	−2.10544e6	−0.271427
$94$	−3.32653e6	−0.413089
$95$	2.16556e6	0.259141
$96$	884736.	0.102062
$97$	−1.91640e6	−0.213199	−0.106599	−	0.994302i	$-0.533996\pi$
$97$	−1.91640e6	−0.213199	−0.106599	+	0.994302i	$0.533996\pi$
$98$	−941192.	−0.101015
$99$	−5.30256e6	−0.549240
$100$	253216.	0.0253216
$101$	3.17244e6	0.306386	0.153193	−	0.988196i	$-0.451044\pi$
$101$	3.17244e6	0.306386	0.153193	+	0.988196i	$0.451044\pi$
$102$	−105168.	−0.00981256
$103$	5.79940e6	0.522941	0.261470	−	0.965211i	$-0.415793\pi$
$103$	5.79940e6	0.522941	0.261470	+	0.965211i	$0.415793\pi$
$104$	−1.12486e6	−0.0980581
$105$	2.65326e6	0.223675
$106$	1.56339e7	1.27496
$107$	2.24258e7	1.76972	0.884859	−	0.465859i	$-0.154255\pi$
$107$	2.24258e7	1.76972	0.884859	+	0.465859i	$0.154255\pi$
$108$	−1.25971e6	−0.0962250
$109$	6.12864e6	0.453285	0.226643	−	0.973978i	$-0.427225\pi$
$109$	6.12864e6	0.453285	0.226643	+	0.973978i	$0.427225\pi$
$110$	1.66713e7	1.19425
$111$	−2.15698e6	−0.149698
$112$	−1.40493e6	−0.0944911
$113$	−2.44304e6	−0.159278	−0.0796390	−	0.996824i	$-0.525377\pi$
$113$	−2.44304e6	−0.159278	−0.0796390	+	0.996824i	$0.525377\pi$
$114$	1.63268e6	0.103213
$115$	2.67622e7	1.64089
$116$	−1.76691e6	−0.105102
$117$	1.60161e6	0.0924500
$118$	−826879.	−0.0463292
$119$	167003.	0.00908467
$120$	3.96056e6	0.209229
$121$	3.34201e7	1.71498
$122$	−1.08153e7	−0.539238
$123$	−1.03249e7	−0.500287
$124$	4.99068e6	0.235063
$125$	−2.12492e7	−0.973099
$126$	2.00038e6	0.0890871
$127$	−2.59595e7	−1.12456	−0.562281	−	0.826946i	$-0.690076\pi$
$127$	−2.59595e7	−1.12456	−0.562281	+	0.826946i	$0.690076\pi$
$128$	−2.09715e6	−0.0883883
$129$	2.57421e7	1.05580
$130$	−5.03550e6	−0.201021
$131$	6.48196e6	0.251917	0.125958	−	0.992036i	$-0.459799\pi$
$131$	6.48196e6	0.251917	0.125958	+	0.992036i	$0.459799\pi$
$132$	1.25690e7	0.475656
$133$	−2.59263e6	−0.0955565
$134$	−1.71640e7	−0.616242
$135$	−5.63915e6	−0.197263
$136$	249287.	0.00849793
$137$	−1.90119e7	−0.631690	−0.315845	−	0.948811i	$-0.602288\pi$
$137$	−1.90119e7	−0.631690	−0.315845	+	0.948811i	$0.602288\pi$
$138$	2.01769e7	0.653547
$139$	9.32918e6	0.294640	0.147320	−	0.989089i	$-0.452935\pi$
$139$	9.32918e6	0.294640	0.147320	+	0.989089i	$0.452935\pi$
$140$	−6.28922e6	−0.193708
$141$	−1.12270e7	−0.337286
$142$	−5.66184e6	−0.165939
$143$	−1.59804e7	−0.456995
$144$	2.98598e6	0.0833333
$145$	−7.90963e6	−0.215461
$146$	−1.47766e7	−0.392952
$147$	−3.17652e6	−0.0824786
$148$	5.11284e6	0.129642
$149$	−2.93110e7	−0.725903	−0.362951	−	0.931808i	$-0.618231\pi$
$149$	−2.93110e7	−0.725903	−0.362951	+	0.931808i	$0.618231\pi$
$150$	854604.	0.0206750
$151$	1.20316e7	0.284383	0.142192	−	0.989839i	$-0.454585\pi$
$151$	1.20316e7	0.284383	0.142192	+	0.989839i	$0.454585\pi$
$152$	−3.87005e6	−0.0893849
$153$	−354941.	−0.00801192
$154$	−1.99591e7	−0.440372
$155$	2.23410e7	0.481883
$156$	−3.79642e6	−0.0800641
$157$	7.87072e7	1.62318	0.811588	−	0.584230i	$-0.198604\pi$
$157$	7.87072e7	1.62318	0.811588	+	0.584230i	$0.198604\pi$
$158$	3.69483e7	0.745238
$159$	5.27644e7	1.04100
$160$	−9.38799e6	−0.181198
$161$	−3.20401e7	−0.605067
$162$	−4.25153e6	−0.0785674
$163$	−6.71948e7	−1.21529	−0.607644	−	0.794210i	$-0.707885\pi$
$163$	−6.71948e7	−1.21529	−0.607644	+	0.794210i	$0.707885\pi$
$164$	2.44739e7	0.433262
$165$	5.62658e7	0.975103
$166$	1.18458e7	0.200995
$167$	−3.44521e7	−0.572412	−0.286206	−	0.958168i	$-0.592394\pi$
$167$	−3.44521e7	−0.572412	−0.286206	+	0.958168i	$0.592394\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	1.11594e6	0.0174209
$171$	5.51029e6	0.0842729
$172$	−6.10183e7	−0.914346
$173$	1.22202e8	1.79439	0.897195	−	0.441634i	$-0.145601\pi$
$173$	1.22202e8	1.79439	0.897195	+	0.441634i	$0.145601\pi$
$174$	−5.96331e6	−0.0858153
$175$	−1.35708e6	−0.0191413
$176$	−2.97932e7	−0.411930
$177$	−2.79072e6	−0.0378276
$178$	2.62166e7	0.348423
$179$	−1.20328e8	−1.56813	−0.784064	−	0.620680i	$-0.786857\pi$
$179$	−1.20328e8	−1.56813	−0.784064	+	0.620680i	$0.786857\pi$
$180$	1.33669e7	0.170835
$181$	4.45779e7	0.558784	0.279392	−	0.960177i	$-0.409867\pi$
$181$	4.45779e7	0.558784	0.279392	+	0.960177i	$0.409867\pi$
$182$	6.02857e6	0.0741249
$183$	−3.65018e7	−0.440286
$184$	−4.78266e7	−0.565988
$185$	2.28879e7	0.265769
$186$	1.68436e7	0.191928
$187$	3.54150e6	0.0396042
$188$	2.66122e7	0.292098
$189$	6.75127e6	0.0727393
$190$	−1.73244e7	−0.183241
$191$	−6.53353e7	−0.678471	−0.339236	−	0.940701i	$-0.610168\pi$
$191$	−6.53353e7	−0.678471	−0.339236	+	0.940701i	$0.610168\pi$
$192$	−7.07789e6	−0.0721688
$193$	3.69388e7	0.369855	0.184928	−	0.982752i	$-0.440795\pi$
$193$	3.69388e7	0.369855	0.184928	+	0.982752i	$0.440795\pi$
$194$	1.53312e7	0.150754
$195$	−1.69948e7	−0.164133
$196$	7.52954e6	0.0714286
$197$	−2.99384e7	−0.278995	−0.139497	−	0.990222i	$-0.544549\pi$
$197$	−2.99384e7	−0.278995	−0.139497	+	0.990222i	$0.544549\pi$
$198$	4.24204e7	0.388371
$199$	−2.11520e8	−1.90268	−0.951338	−	0.308148i	$-0.900291\pi$
$199$	−2.11520e8	−1.90268	−0.951338	+	0.308148i	$0.900291\pi$
$200$	−2.02573e6	−0.0179051
$201$	−5.79285e7	−0.503160
$202$	−2.53795e7	−0.216647
$203$	9.46951e6	0.0794496
$204$	841343.	0.00693853
$205$	1.09559e8	0.888194
$206$	−4.63952e7	−0.369775
$207$	6.80969e7	0.533619
$208$	8.99891e6	0.0693375
$209$	−5.49800e7	−0.416574
$210$	−2.12261e7	−0.158162
$211$	−2.44899e8	−1.79472	−0.897362	−	0.441295i	$-0.854519\pi$
$211$	−2.44899e8	−1.79472	−0.897362	+	0.441295i	$0.854519\pi$
$212$	−1.25071e8	−0.901533
$213$	−1.91087e7	−0.135488
$214$	−1.79406e8	−1.25138
$215$	−2.73151e8	−1.87443
$216$	1.00777e7	0.0680414
$217$	−2.67469e7	−0.177691
$218$	−4.90291e7	−0.320521
$219$	−4.98710e7	−0.320844
$220$	−1.33371e8	−0.844464
$221$	−1.06969e6	−0.00666632
$222$	1.72558e7	0.105852
$223$	−2.77688e8	−1.67683	−0.838417	−	0.545029i	$-0.816519\pi$
$223$	−2.77688e8	−1.67683	−0.838417	+	0.545029i	$0.816519\pi$
$224$	1.12394e7	0.0668153
$225$	2.88429e6	0.0168811
$226$	1.95443e7	0.112626
$227$	−4.70536e7	−0.266995	−0.133497	−	0.991049i	$-0.542621\pi$
$227$	−4.70536e7	−0.266995	−0.133497	+	0.991049i	$0.542621\pi$
$228$	−1.30614e7	−0.0729825
$229$	1.93003e8	1.06204	0.531019	−	0.847360i	$-0.321809\pi$
$229$	1.93003e8	1.06204	0.531019	+	0.847360i	$0.321809\pi$
$230$	−2.14098e8	−1.16029
$231$	−6.73621e7	−0.359562
$232$	1.41353e7	0.0743183
$233$	1.12228e8	0.581240	0.290620	−	0.956839i	$-0.406139\pi$
$233$	1.12228e8	0.581240	0.290620	+	0.956839i	$0.406139\pi$
$234$	−1.28129e7	−0.0653720
$235$	1.19131e8	0.598806
$236$	6.61503e6	0.0327597
$237$	1.24701e8	0.608484
$238$	−1.33602e6	−0.00642383
$239$	1.79741e7	0.0851637	0.0425819	−	0.999093i	$-0.486442\pi$
$239$	1.79741e7	0.0851637	0.0425819	+	0.999093i	$0.486442\pi$
$240$	−3.16845e7	−0.147947
$241$	−2.53678e7	−0.116741	−0.0583704	−	0.998295i	$-0.518590\pi$
$241$	−2.53678e7	−0.116741	−0.0583704	+	0.998295i	$0.518590\pi$
$242$	−2.67361e8	−1.21267
$243$	−1.43489e7	−0.0641500
$244$	8.65227e7	0.381299
$245$	3.37063e7	0.146430
$246$	8.25995e7	0.353757
$247$	1.66065e7	0.0701193
$248$	−3.99255e7	−0.166215
$249$	3.99794e7	0.164111
$250$	1.69993e8	0.688085
$251$	2.86610e8	1.14402	0.572010	−	0.820247i	$-0.306164\pi$
$251$	2.86610e8	1.14402	0.572010	+	0.820247i	$0.306164\pi$
$252$	−1.60030e7	−0.0629941
$253$	−6.79450e8	−2.63776
$254$	2.07676e8	0.795185
$255$	3.76631e6	0.0142241
$256$	1.67772e7	0.0625000
$257$	−5.32391e7	−0.195643	−0.0978216	−	0.995204i	$-0.531187\pi$
$257$	−5.32391e7	−0.195643	−0.0978216	+	0.995204i	$0.531187\pi$
$258$	−2.05937e8	−0.746560
$259$	−2.74016e7	−0.0980003
$260$	4.02840e7	0.142143
$261$	−2.01262e7	−0.0700679
$262$	−5.18557e7	−0.178132
$263$	−3.84710e8	−1.30403	−0.652017	−	0.758204i	$-0.726077\pi$
$263$	−3.84710e8	−1.30403	−0.652017	+	0.758204i	$0.726077\pi$
$264$	−1.00552e8	−0.336339
$265$	−5.59886e8	−1.84816
$266$	2.07411e7	0.0675686
$267$	8.84811e7	0.284486
$268$	1.37312e8	0.435749
$269$	6.15549e8	1.92810	0.964050	−	0.265723i	$-0.0856105\pi$
$269$	6.15549e8	1.92810	0.964050	+	0.265723i	$0.0856105\pi$
$270$	4.51132e7	0.139486
$271$	−2.77745e8	−0.847722	−0.423861	−	0.905727i	$-0.639326\pi$
$271$	−2.77745e8	−0.847722	−0.423861	+	0.905727i	$0.639326\pi$
$272$	−1.99429e6	−0.00600894
$273$	2.03464e7	0.0605228
$274$	1.52095e8	0.446672
$275$	−2.87786e7	−0.0834458
$276$	−1.61415e8	−0.462127
$277$	−2.44162e8	−0.690237	−0.345118	−	0.938559i	$-0.612161\pi$
$277$	−2.44162e8	−0.690237	−0.345118	+	0.938559i	$0.612161\pi$
$278$	−7.46335e7	−0.208342
$279$	5.68470e7	0.156709
$280$	5.03138e7	0.136973
$281$	1.36202e8	0.366193	0.183097	−	0.983095i	$-0.441388\pi$
$281$	1.36202e8	0.366193	0.183097	+	0.983095i	$0.441388\pi$
$282$	8.98163e7	0.238497
$283$	−6.68072e8	−1.75215	−0.876074	−	0.482177i	$-0.839846\pi$
$283$	−6.68072e8	−1.75215	−0.876074	+	0.482177i	$0.839846\pi$
$284$	4.52947e7	0.117336
$285$	−5.84700e7	−0.149615
$286$	1.27843e8	0.323144
$287$	−1.31165e8	−0.327515
$288$	−2.38879e7	−0.0589256
$289$	−4.10102e8	−0.999422
$290$	6.32770e7	0.152354
$291$	5.17428e7	0.123090
$292$	1.18213e8	0.277859
$293$	5.17810e8	1.20264	0.601318	−	0.799010i	$-0.294643\pi$
$293$	5.17810e8	1.20264	0.601318	+	0.799010i	$0.294643\pi$
$294$	2.54122e7	0.0583212
$295$	2.96125e7	0.0671580
$296$	−4.09028e7	−0.0916709
$297$	1.43169e8	0.317104
$298$	2.34488e8	0.513291
$299$	2.05225e8	0.443998
$300$	−6.83683e6	−0.0146194
$301$	3.27020e8	0.691181
$302$	−9.62529e7	−0.201089
$303$	−8.56558e7	−0.176892
$304$	3.09604e7	0.0632047
$305$	3.87323e8	0.781670
$306$	2.83953e6	0.00566528
$307$	1.12227e8	0.221367	0.110683	−	0.993856i	$-0.464696\pi$
$307$	1.12227e8	0.221367	0.110683	+	0.993856i	$0.464696\pi$
$308$	1.59673e8	0.311390
$309$	−1.56584e8	−0.301920
$310$	−1.78728e8	−0.340743
$311$	−1.42544e8	−0.268713	−0.134356	−	0.990933i	$-0.542897\pi$
$311$	−1.42544e8	−0.268713	−0.134356	+	0.990933i	$0.542897\pi$
$312$	3.03713e7	0.0566139
$313$	3.60635e8	0.664757	0.332378	−	0.943146i	$-0.392149\pi$
$313$	3.60635e8	0.664757	0.332378	+	0.943146i	$0.392149\pi$
$314$	−6.29657e8	−1.14776
$315$	−7.16381e7	−0.129139
$316$	−2.95587e8	−0.526963
$317$	4.03611e6	0.00711632	0.00355816	−	0.999994i	$-0.498867\pi$
$317$	4.03611e6	0.00711632	0.00355816	+	0.999994i	$0.498867\pi$
$318$	−4.22115e8	−0.736099
$319$	2.00813e8	0.346357
$320$	7.51039e7	0.128126
$321$	−6.05496e8	−1.02175
$322$	2.56321e8	0.427847
$323$	−3.68024e6	−0.00607669
$324$	3.40122e7	0.0555556
$325$	8.69243e6	0.0140459
$326$	5.37558e8	0.859338
$327$	−1.65473e8	−0.261704
$328$	−1.95791e8	−0.306362
$329$	−1.42625e8	−0.220805
$330$	−4.50126e8	−0.689502
$331$	−1.03951e9	−1.57554	−0.787772	−	0.615967i	$-0.788766\pi$
$331$	−1.03951e9	−1.57554	−0.787772	+	0.615967i	$0.788766\pi$
$332$	−9.47660e7	−0.142125
$333$	5.82385e7	0.0864282
$334$	2.75617e8	0.404756
$335$	6.14683e8	0.893293
$336$	3.79331e7	0.0545545
$337$	−1.36656e9	−1.94502	−0.972510	−	0.232862i	$-0.925191\pi$
$337$	−1.36656e9	−1.94502	−0.972510	+	0.232862i	$0.925191\pi$
$338$	−3.86145e7	−0.0543928
$339$	6.59620e7	0.0919591
$340$	−8.92754e6	−0.0123184
$341$	−5.67202e8	−0.774635
$342$	−4.40823e7	−0.0595899
$343$	−4.03536e7	−0.0539949
$344$	4.88146e8	0.646540
$345$	−7.22580e8	−0.947369
$346$	−9.77616e8	−1.26883
$347$	−7.05636e8	−0.906624	−0.453312	−	0.891352i	$-0.649758\pi$
$347$	−7.05636e8	−0.906624	−0.453312	+	0.891352i	$0.649758\pi$
$348$	4.77065e7	0.0606806
$349$	8.18343e8	1.03050	0.515248	−	0.857041i	$-0.327700\pi$
$349$	8.18343e8	1.03050	0.515248	+	0.857041i	$0.327700\pi$
$350$	1.08566e7	0.0135350
$351$	−4.32436e7	−0.0533761
$352$	2.38346e8	0.291278
$353$	−1.56557e9	−1.89435	−0.947176	−	0.320713i	$-0.896077\pi$
$353$	−1.56557e9	−1.89435	−0.947176	+	0.320713i	$0.896077\pi$
$354$	2.23257e7	0.0267482
$355$	2.02764e8	0.240542
$356$	−2.09733e8	−0.246372
$357$	−4.50907e6	−0.00524503
$358$	9.62625e8	1.10883
$359$	6.13475e8	0.699787	0.349894	−	0.936789i	$-0.386218\pi$
$359$	6.13475e8	0.699787	0.349894	+	0.936789i	$0.386218\pi$
$360$	−1.06935e8	−0.120798
$361$	−8.36738e8	−0.936083
$362$	−3.56623e8	−0.395120
$363$	−9.02343e8	−0.990144
$364$	−4.82285e7	−0.0524142
$365$	5.29184e8	0.569616
$366$	2.92014e8	0.311329
$367$	−1.24200e9	−1.31157	−0.655786	−	0.754947i	$-0.727663\pi$
$367$	−1.24200e9	−1.31157	−0.655786	+	0.754947i	$0.727663\pi$
$368$	3.82613e8	0.400214
$369$	2.78773e8	0.288841
$370$	−1.83103e8	−0.187927
$371$	6.70303e8	0.681495
$372$	−1.34748e8	−0.135714
$373$	−1.37944e9	−1.37633	−0.688164	−	0.725555i	$-0.741583\pi$
$373$	−1.37944e9	−1.37633	−0.688164	+	0.725555i	$0.741583\pi$
$374$	−2.83320e7	−0.0280044
$375$	5.73728e8	0.561819
$376$	−2.12898e8	−0.206545
$377$	−6.06546e7	−0.0583000
$378$	−5.40102e7	−0.0514344
$379$	−1.85577e9	−1.75101	−0.875503	−	0.483213i	$-0.839470\pi$
$379$	−1.85577e9	−1.75101	−0.875503	+	0.483213i	$0.839470\pi$
$380$	1.38596e8	0.129571
$381$	7.00907e8	0.649266
$382$	5.22683e8	0.479751
$383$	−8.28081e8	−0.753143	−0.376571	−	0.926388i	$-0.622897\pi$
$383$	−8.28081e8	−0.753143	−0.376571	+	0.926388i	$0.622897\pi$
$384$	5.66231e7	0.0510310
$385$	7.14783e8	0.638355
$386$	−2.95510e8	−0.261527
$387$	−6.95037e8	−0.609564
$388$	−1.22650e8	−0.106599
$389$	7.67763e8	0.661308	0.330654	−	0.943752i	$-0.392731\pi$
$389$	7.67763e8	0.661308	0.330654	+	0.943752i	$0.392731\pi$
$390$	1.35959e8	0.116059
$391$	−4.54809e7	−0.0384778
$392$	−6.02363e7	−0.0505076
$393$	−1.75013e8	−0.145444
$394$	2.39507e8	0.197279
$395$	−1.32321e9	−1.08028
$396$	−3.39364e8	−0.274620
$397$	−2.75062e8	−0.220630	−0.110315	−	0.993897i	$-0.535186\pi$
$397$	−2.75062e8	−0.220630	−0.110315	+	0.993897i	$0.535186\pi$
$398$	1.69216e9	1.34540
$399$	7.00011e7	0.0551696
$400$	1.62058e7	0.0126608
$401$	3.93891e8	0.305050	0.152525	−	0.988300i	$-0.451260\pi$
$401$	3.93891e8	0.305050	0.152525	+	0.988300i	$0.451260\pi$
$402$	4.63428e8	0.355788
$403$	1.71321e8	0.130389
$404$	2.03036e8	0.153193
$405$	1.52257e8	0.113890
$406$	−7.57561e7	−0.0561793
$407$	−5.81086e8	−0.427228
$408$	−6.73074e6	−0.00490628
$409$	−7.27662e8	−0.525894	−0.262947	−	0.964810i	$-0.584694\pi$
$409$	−7.27662e8	−0.525894	−0.262947	+	0.964810i	$0.584694\pi$
$410$	−8.76468e8	−0.628048
$411$	5.13322e8	0.364706
$412$	3.71161e8	0.261470
$413$	−3.54524e7	−0.0247640
$414$	−5.44775e8	−0.377325
$415$	−4.24224e8	−0.291358
$416$	−7.19913e7	−0.0490290
$417$	−2.51888e8	−0.170111
$418$	4.39840e8	0.294563
$419$	1.19808e9	0.795678	0.397839	−	0.917455i	$-0.369760\pi$
$419$	1.19808e9	0.795678	0.397839	+	0.917455i	$0.369760\pi$
$420$	1.69809e8	0.111838
$421$	−6.87385e8	−0.448965	−0.224482	−	0.974478i	$-0.572069\pi$
$421$	−6.87385e8	−0.448965	−0.224482	+	0.974478i	$0.572069\pi$
$422$	1.95919e9	1.26906
$423$	3.03130e8	0.194732
$424$	1.00057e9	0.637480
$425$	−1.92637e6	−0.00121725
$426$	1.52870e8	0.0958048
$427$	−4.63708e8	−0.288235
$428$	1.43525e9	0.884859
$429$	4.31471e8	0.263846
$430$	2.18521e9	1.32542
$431$	−8.01087e8	−0.481958	−0.240979	−	0.970530i	$-0.577468\pi$
$431$	−8.01087e8	−0.481958	−0.240979	+	0.970530i	$0.577468\pi$
$432$	−8.06216e7	−0.0481125
$433$	2.85988e9	1.69294	0.846468	−	0.532440i	$-0.178725\pi$
$433$	2.85988e9	1.69294	0.846468	+	0.532440i	$0.178725\pi$
$434$	2.13975e8	0.125646
$435$	2.13560e8	0.124396
$436$	3.92233e8	0.226643
$437$	7.06068e8	0.404726
$438$	3.98968e8	0.226871
$439$	2.77164e8	0.156355	0.0781774	−	0.996939i	$-0.475090\pi$
$439$	2.77164e8	0.156355	0.0781774	+	0.996939i	$0.475090\pi$
$440$	1.06697e9	0.597126
$441$	8.57661e7	0.0476190
$442$	8.55755e6	0.00471380
$443$	−6.14846e8	−0.336011	−0.168005	−	0.985786i	$-0.553733\pi$
$443$	−6.14846e8	−0.336011	−0.168005	+	0.985786i	$0.553733\pi$
$444$	−1.38047e8	−0.0748490
$445$	−9.38878e8	−0.505067
$446$	2.22150e9	1.18570
$447$	7.91397e8	0.419100
$448$	−8.99154e7	−0.0472456
$449$	−3.37531e9	−1.75975	−0.879877	−	0.475202i	$-0.842375\pi$
$449$	−3.37531e9	−1.75975	−0.879877	+	0.475202i	$0.842375\pi$
$450$	−2.30743e7	−0.0119367
$451$	−2.78152e9	−1.42779
$452$	−1.56354e8	−0.0796390
$453$	−3.24853e8	−0.164189
$454$	3.76429e8	0.188794
$455$	−2.15897e8	−0.107450
$456$	1.04491e8	0.0516064
$457$	−2.75501e9	−1.35026	−0.675129	−	0.737700i	$-0.735912\pi$
$457$	−2.75501e9	−1.35026	−0.675129	+	0.737700i	$0.735912\pi$
$458$	−1.54403e9	−0.750974
$459$	9.58342e6	0.00462569
$460$	1.71278e9	0.820446
$461$	2.91509e8	0.138579	0.0692897	−	0.997597i	$-0.477927\pi$
$461$	2.91509e8	0.138579	0.0692897	+	0.997597i	$0.477927\pi$
$462$	5.38897e8	0.254249
$463$	1.70265e9	0.797244	0.398622	−	0.917115i	$-0.369489\pi$
$463$	1.70265e9	0.797244	0.398622	+	0.917115i	$0.369489\pi$
$464$	−1.13082e8	−0.0525510
$465$	−6.03207e8	−0.278215
$466$	−8.97823e8	−0.410998
$467$	9.91486e8	0.450482	0.225241	−	0.974303i	$-0.427683\pi$
$467$	9.91486e8	0.450482	0.225241	+	0.974303i	$0.427683\pi$
$468$	1.02503e8	0.0462250
$469$	−7.35906e8	−0.329395
$470$	−9.53046e8	−0.423420
$471$	−2.12509e9	−0.937141
$472$	−5.29202e7	−0.0231646
$473$	6.93486e9	3.01317
$474$	−9.97605e8	−0.430263
$475$	2.99060e7	0.0128036
$476$	1.06882e7	0.00454233
$477$	−1.42464e9	−0.601022
$478$	−1.43793e8	−0.0602199
$479$	−8.43734e8	−0.350777	−0.175388	−	0.984499i	$-0.556118\pi$
$479$	−8.43734e8	−0.350777	−0.175388	+	0.984499i	$0.556118\pi$
$480$	2.53476e8	0.104615
$481$	1.75514e8	0.0719126
$482$	2.02942e8	0.0825482
$483$	8.65083e8	0.349335
$484$	2.13889e9	0.857490
$485$	−5.49046e8	−0.218531
$486$	1.14791e8	0.0453609
$487$	−3.88433e9	−1.52393	−0.761964	−	0.647620i	$-0.775765\pi$
$487$	−3.88433e9	−1.52393	−0.761964	+	0.647620i	$0.775765\pi$
$488$	−6.92182e8	−0.269619
$489$	1.81426e9	0.701646
$490$	−2.69650e8	−0.103542
$491$	3.18143e9	1.21293	0.606467	−	0.795109i	$-0.292586\pi$
$491$	3.18143e9	1.21293	0.606467	+	0.795109i	$0.292586\pi$
$492$	−6.60796e8	−0.250144
$493$	1.34420e7	0.00505241
$494$	−1.32852e8	−0.0495818
$495$	−1.51918e9	−0.562976
$496$	3.19404e8	0.117531
$497$	−2.42751e8	−0.0886980
$498$	−3.19835e8	−0.116044
$499$	−2.06218e9	−0.742977	−0.371489	−	0.928437i	$-0.621153\pi$
$499$	−2.06218e9	−0.742977	−0.371489	+	0.928437i	$0.621153\pi$
$500$	−1.35995e9	−0.486550
$501$	9.30208e8	0.330482
$502$	−2.29288e9	−0.808944
$503$	1.82569e9	0.639645	0.319822	−	0.947478i	$-0.396377\pi$
$503$	1.82569e9	0.639645	0.319822	+	0.947478i	$0.396377\pi$
$504$	1.28024e8	0.0445435
$505$	9.08899e8	0.314048
$506$	5.43560e9	1.86518
$507$	−1.30324e8	−0.0444116
$508$	−1.66141e9	−0.562281
$509$	−1.78116e9	−0.598674	−0.299337	−	0.954147i	$-0.596766\pi$
$509$	−1.78116e9	−0.598674	−0.299337	+	0.954147i	$0.596766\pi$
$510$	−3.01304e7	−0.0100580
$511$	−6.33547e8	−0.210042
$512$	−1.34218e8	−0.0441942
$513$	−1.48778e8	−0.0486550
$514$	4.25913e8	0.138341
$515$	1.66152e9	0.536019
$516$	1.64749e9	0.527898
$517$	−3.02454e9	−0.962592
$518$	2.19213e8	0.0692967
$519$	−3.29945e9	−1.03599
$520$	−3.22272e8	−0.100510
$521$	−5.49297e9	−1.70167	−0.850835	−	0.525433i	$-0.823903\pi$
$521$	−5.49297e9	−1.70167	−0.850835	+	0.525433i	$0.823903\pi$
$522$	1.61009e8	0.0495455
$523$	2.70055e9	0.825461	0.412730	−	0.910853i	$-0.364575\pi$
$523$	2.70055e9	0.825461	0.412730	+	0.910853i	$0.364575\pi$
$524$	4.14846e8	0.125958
$525$	3.66412e7	0.0110513
$526$	3.07768e9	0.922091
$527$	−3.79672e7	−0.0112998
$528$	8.04417e8	0.237828
$529$	5.32086e9	1.56274
$530$	4.47909e9	1.30685
$531$	7.53493e7	0.0218398
$532$	−1.65928e8	−0.0477782
$533$	8.40144e8	0.240330
$534$	−7.07848e8	−0.201162
$535$	6.42495e9	1.81398
$536$	−1.09850e9	−0.308121
$537$	3.24886e9	0.905359
$538$	−4.92439e9	−1.36337
$539$	−8.55748e8	−0.235389
$540$	−3.60906e8	−0.0986315
$541$	−2.92568e9	−0.794394	−0.397197	−	0.917733i	$-0.630017\pi$
$541$	−2.92568e9	−0.794394	−0.397197	+	0.917733i	$0.630017\pi$
$542$	2.22196e9	0.599430
$543$	−1.20360e9	−0.322614
$544$	1.59544e7	0.00424896
$545$	1.75585e9	0.464621
$546$	−1.62771e8	−0.0427960
$547$	−1.88475e9	−0.492379	−0.246189	−	0.969222i	$-0.579178\pi$
$547$	−1.88475e9	−0.492379	−0.246189	+	0.969222i	$0.579178\pi$
$548$	−1.21676e9	−0.315845
$549$	9.85548e8	0.254199
$550$	2.30228e8	0.0590051
$551$	−2.08680e8	−0.0531435
$552$	1.29132e9	0.326773
$553$	1.58416e9	0.398347
$554$	1.95329e9	0.488071
$555$	−6.17972e8	−0.153442
$556$	5.97068e8	0.147320
$557$	5.81620e9	1.42609	0.713044	−	0.701120i	$-0.247316\pi$
$557$	5.81620e9	1.42609	0.713044	+	0.701120i	$0.247316\pi$
$558$	−4.54776e8	−0.110810
$559$	−2.09464e9	−0.507188
$560$	−4.02510e8	−0.0968542
$561$	−9.56204e7	−0.0228655
$562$	−1.08961e9	−0.258938
$563$	−2.28643e9	−0.539982	−0.269991	−	0.962863i	$-0.587021\pi$
$563$	−2.28643e9	−0.539982	−0.269991	+	0.962863i	$0.587021\pi$
$564$	−7.18530e8	−0.168643
$565$	−6.99927e8	−0.163261
$566$	5.34457e9	1.23896
$567$	−1.82284e8	−0.0419961
$568$	−3.62357e8	−0.0829694
$569$	3.34243e9	0.760623	0.380312	−	0.924858i	$-0.375817\pi$
$569$	3.34243e9	0.760623	0.380312	+	0.924858i	$0.375817\pi$
$570$	4.67760e8	0.105794
$571$	1.72538e9	0.387844	0.193922	−	0.981017i	$-0.437879\pi$
$571$	1.72538e9	0.387844	0.193922	+	0.981017i	$0.437879\pi$
$572$	−1.02275e9	−0.228498
$573$	1.76405e9	0.391715
$574$	1.04932e9	0.231588
$575$	3.69582e8	0.0810725
$576$	1.91103e8	0.0416667
$577$	3.44012e8	0.0745518	0.0372759	−	0.999305i	$-0.488132\pi$
$577$	3.44012e8	0.0745518	0.0372759	+	0.999305i	$0.488132\pi$
$578$	3.28081e9	0.706698
$579$	−9.97347e8	−0.213536
$580$	−5.06216e8	−0.107730
$581$	5.07887e8	0.107436
$582$	−4.13942e8	−0.0870381
$583$	1.42146e10	2.97095
$584$	−9.45702e8	−0.196476
$585$	4.58860e8	0.0947621
$586$	−4.14248e9	−0.850392
$587$	−5.07469e9	−1.03556	−0.517781	−	0.855513i	$-0.673242\pi$
$587$	−5.07469e9	−1.03556	−0.517781	+	0.855513i	$0.673242\pi$
$588$	−2.03297e8	−0.0412393
$589$	5.89422e8	0.118857
$590$	−2.36900e8	−0.0474878
$591$	8.08336e8	0.161078
$592$	3.27222e8	0.0648211
$593$	−2.73044e9	−0.537702	−0.268851	−	0.963182i	$-0.586644\pi$
$593$	−2.73044e9	−0.537702	−0.268851	+	0.963182i	$0.586644\pi$
$594$	−1.14535e9	−0.224226
$595$	4.78460e7	0.00931186
$596$	−1.87590e9	−0.362951
$597$	5.71103e9	1.09851
$598$	−1.64180e9	−0.313954
$599$	2.44705e9	0.465211	0.232605	−	0.972571i	$-0.425275\pi$
$599$	2.44705e9	0.465211	0.232605	+	0.972571i	$0.425275\pi$
$600$	5.46947e7	0.0103375
$601$	5.35264e9	1.00579	0.502895	−	0.864347i	$-0.332268\pi$
$601$	5.35264e9	1.00579	0.502895	+	0.864347i	$0.332268\pi$
$602$	−2.61616e9	−0.488739
$603$	1.56407e9	0.290499
$604$	7.70023e8	0.142192
$605$	9.57482e9	1.75787
$606$	6.85247e8	0.125081
$607$	1.35285e9	0.245522	0.122761	−	0.992436i	$-0.460825\pi$
$607$	1.35285e9	0.245522	0.122761	+	0.992436i	$0.460825\pi$
$608$	−2.47683e8	−0.0446925
$609$	−2.55677e8	−0.0458702
$610$	−3.09858e9	−0.552724
$611$	9.13548e8	0.162027
$612$	−2.27163e7	−0.00400596
$613$	2.96610e9	0.520084	0.260042	−	0.965597i	$-0.416264\pi$
$613$	2.96610e9	0.520084	0.260042	+	0.965597i	$0.416264\pi$
$614$	−8.97815e8	−0.156530
$615$	−2.95808e9	−0.512799
$616$	−1.27739e9	−0.220186
$617$	1.47761e9	0.253257	0.126628	−	0.991950i	$-0.459584\pi$
$617$	1.47761e9	0.253257	0.126628	+	0.991950i	$0.459584\pi$
$618$	1.25267e9	0.213490
$619$	7.86514e9	1.33287	0.666437	−	0.745561i	$-0.267818\pi$
$619$	7.86514e9	1.33287	0.666437	+	0.745561i	$0.267818\pi$
$620$	1.42982e9	0.240941
$621$	−1.83862e9	−0.308085
$622$	1.14035e9	0.190008
$623$	1.12404e9	0.186240
$624$	−2.42971e8	−0.0400320
$625$	−6.39696e9	−1.04808
$626$	−2.88508e9	−0.470054
$627$	1.48446e9	0.240509
$628$	5.03726e9	0.811588
$629$	−3.88966e7	−0.00623210
$630$	5.73105e8	0.0913150
$631$	−4.39200e9	−0.695921	−0.347960	−	0.937509i	$-0.613126\pi$
$631$	−4.39200e9	−0.695921	−0.347960	+	0.937509i	$0.613126\pi$
$632$	2.36469e9	0.372619
$633$	6.61226e9	1.03618
$634$	−3.22889e7	−0.00503199
$635$	−7.43736e9	−1.15269
$636$	3.37692e9	0.520500
$637$	2.58475e8	0.0396214
$638$	−1.60650e9	−0.244911
$639$	5.15935e8	0.0782243
$640$	−6.00831e8	−0.0905988
$641$	1.71712e9	0.257513	0.128756	−	0.991676i	$-0.458902\pi$
$641$	1.71712e9	0.257513	0.128756	+	0.991676i	$0.458902\pi$
$642$	4.84396e9	0.722484
$643$	−1.05089e10	−1.55891	−0.779454	−	0.626460i	$-0.784503\pi$
$643$	−1.05089e10	−1.55891	−0.779454	+	0.626460i	$0.784503\pi$
$644$	−2.05057e9	−0.302533
$645$	7.37508e9	1.08220
$646$	2.94419e7	0.00429687
$647$	1.20317e9	0.174647	0.0873237	−	0.996180i	$-0.472169\pi$
$647$	1.20317e9	0.174647	0.0873237	+	0.996180i	$0.472169\pi$
$648$	−2.72098e8	−0.0392837
$649$	−7.51813e8	−0.107958
$650$	−6.95395e7	−0.00993195
$651$	7.22167e8	0.102590
$652$	−4.30047e9	−0.607644
$653$	1.24383e10	1.74809	0.874044	−	0.485847i	$-0.161489\pi$
$653$	1.24383e10	1.74809	0.874044	+	0.485847i	$0.161489\pi$
$654$	1.32379e9	0.185053
$655$	1.85707e9	0.258217
$656$	1.56633e9	0.216631
$657$	1.34652e9	0.185239
$658$	1.14100e9	0.156133
$659$	−9.07674e9	−1.23547	−0.617733	−	0.786388i	$-0.711949\pi$
$659$	−9.07674e9	−1.23547	−0.617733	+	0.786388i	$0.711949\pi$
$660$	3.60101e9	0.487551
$661$	−1.10523e10	−1.48849	−0.744245	−	0.667907i	$-0.767190\pi$
$661$	−1.10523e10	−1.48849	−0.744245	+	0.667907i	$0.767190\pi$
$662$	8.31608e9	1.11408
$663$	2.88817e7	0.00384880
$664$	7.58128e8	0.100497
$665$	−7.42786e8	−0.0979462
$666$	−4.65908e8	−0.0611139
$667$	−2.57889e9	−0.336506
$668$	−2.20494e9	−0.286206
$669$	7.49758e9	0.968121
$670$	−4.91746e9	−0.631654
$671$	−9.83349e9	−1.25655
$672$	−3.03464e8	−0.0385758
$673$	−8.65278e9	−1.09422	−0.547108	−	0.837062i	$-0.684271\pi$
$673$	−8.65278e9	−1.09422	−0.547108	+	0.837062i	$0.684271\pi$
$674$	1.09325e10	1.37534
$675$	−7.78758e7	−0.00974629
$676$	3.08916e8	0.0384615
$677$	−2.68196e9	−0.332194	−0.166097	−	0.986109i	$-0.553116\pi$
$677$	−2.68196e9	−0.332194	−0.166097	+	0.986109i	$0.553116\pi$
$678$	−5.27696e8	−0.0650249
$679$	6.57325e8	0.0805816
$680$	7.14203e7	0.00871045
$681$	1.27045e9	0.154149
$682$	4.53761e9	0.547750
$683$	−3.30657e9	−0.397105	−0.198552	−	0.980090i	$-0.563624\pi$
$683$	−3.30657e9	−0.397105	−0.198552	+	0.980090i	$0.563624\pi$
$684$	3.52658e8	0.0421364
$685$	−5.44689e9	−0.647488
$686$	3.22829e8	0.0381802
$687$	−5.21108e9	−0.613168
$688$	−3.90517e9	−0.457173
$689$	−4.29346e9	−0.500081
$690$	5.78064e9	0.669891
$691$	6.24227e9	0.719730	0.359865	−	0.933004i	$-0.382823\pi$
$691$	6.24227e9	0.719730	0.359865	+	0.933004i	$0.382823\pi$
$692$	7.82093e9	0.897195
$693$	1.81878e9	0.207593
$694$	5.64509e9	0.641080
$695$	2.67280e9	0.302009
$696$	−3.81652e8	−0.0429077
$697$	−1.86189e8	−0.0208275
$698$	−6.54674e9	−0.728671
$699$	−3.03015e9	−0.335579
$700$	−8.68531e7	−0.00957067
$701$	−1.50309e9	−0.164805	−0.0824026	−	0.996599i	$-0.526259\pi$
$701$	−1.50309e9	−0.164805	−0.0824026	+	0.996599i	$0.526259\pi$
$702$	3.45948e8	0.0377426
$703$	6.03850e8	0.0655520
$704$	−1.90677e9	−0.205965
$705$	−3.21653e9	−0.345721
$706$	1.25246e10	1.33951
$707$	−1.08815e9	−0.115803
$708$	−1.78606e8	−0.0189138
$709$	−9.79607e9	−1.03226	−0.516131	−	0.856510i	$-0.672628\pi$
$709$	−9.79607e9	−1.03226	−0.516131	+	0.856510i	$0.672628\pi$
$710$	−1.62211e9	−0.170089
$711$	−3.36692e9	−0.351309
$712$	1.67786e9	0.174211
$713$	7.28416e9	0.752604
$714$	3.60726e7	0.00370880
$715$	−4.57837e9	−0.468424
$716$	−7.70100e9	−0.784064
$717$	−4.85301e8	−0.0491693
$718$	−4.90780e9	−0.494824
$719$	−3.81708e9	−0.382984	−0.191492	−	0.981494i	$-0.561333\pi$
$719$	−3.81708e9	−0.382984	−0.191492	+	0.981494i	$0.561333\pi$
$720$	8.55481e8	0.0854174
$721$	−1.98919e9	−0.197653
$722$	6.69390e9	0.661910
$723$	6.84930e8	0.0674003
$724$	2.85298e9	0.279392
$725$	−1.09231e8	−0.0106454
$726$	7.21874e9	0.700138
$727$	−1.47969e9	−0.142824	−0.0714118	−	0.997447i	$-0.522750\pi$
$727$	−1.47969e9	−0.142824	−0.0714118	+	0.997447i	$0.522750\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	−4.23348e9	−0.402779
$731$	4.64205e8	0.0439540
$732$	−2.33611e9	−0.220143
$733$	1.46127e10	1.37046	0.685231	−	0.728326i	$-0.259701\pi$
$733$	1.46127e10	1.37046	0.685231	+	0.728326i	$0.259701\pi$
$734$	9.93604e9	0.927421
$735$	−9.10070e8	−0.0845413
$736$	−3.06090e9	−0.282994
$737$	−1.56058e10	−1.43598
$738$	−2.23019e9	−0.204241
$739$	1.24191e10	1.13197	0.565983	−	0.824417i	$-0.308497\pi$
$739$	1.24191e10	1.13197	0.565983	+	0.824417i	$0.308497\pi$
$740$	1.46482e9	0.132884
$741$	−4.48374e8	−0.0404834
$742$	−5.36243e9	−0.481890
$743$	9.00227e9	0.805176	0.402588	−	0.915381i	$-0.368111\pi$
$743$	9.00227e9	0.805176	0.402588	+	0.915381i	$0.368111\pi$
$744$	1.07799e9	0.0959640
$745$	−8.39756e9	−0.744057
$746$	1.10355e10	0.973211
$747$	−1.07944e9	−0.0947498
$748$	2.26656e8	0.0198021
$749$	−7.69204e9	−0.668890
$750$	−4.58982e9	−0.397266
$751$	−1.53601e10	−1.32329	−0.661643	−	0.749819i	$-0.730140\pi$
$751$	−1.53601e10	−1.32329	−0.661643	+	0.749819i	$0.730140\pi$
$752$	1.70318e9	0.146049
$753$	−7.73847e9	−0.660500
$754$	4.85237e8	0.0412244
$755$	3.44704e9	0.291496
$756$	4.32081e8	0.0363696
$757$	−1.01560e10	−0.850916	−0.425458	−	0.904978i	$-0.639887\pi$
$757$	−1.01560e10	−0.850916	−0.425458	+	0.904978i	$0.639887\pi$
$758$	1.48462e10	1.23815
$759$	1.83451e10	1.52291
$760$	−1.10876e9	−0.0916203
$761$	−1.91857e9	−0.157809	−0.0789044	−	0.996882i	$-0.525142\pi$
$761$	−1.91857e9	−0.157809	−0.0789044	+	0.996882i	$0.525142\pi$
$762$	−5.60725e9	−0.459100
$763$	−2.10212e9	−0.171326
$764$	−4.18146e9	−0.339236
$765$	−1.01690e8	−0.00821229
$766$	6.62465e9	0.532552
$767$	2.27082e8	0.0181718
$768$	−4.52985e8	−0.0360844
$769$	−1.84491e10	−1.46296	−0.731482	−	0.681861i	$-0.761171\pi$
$769$	−1.84491e10	−1.46296	−0.731482	+	0.681861i	$0.761171\pi$
$770$	−5.71827e9	−0.451385
$771$	1.43746e9	0.112955
$772$	2.36408e9	0.184928
$773$	5.50771e9	0.428887	0.214444	−	0.976736i	$-0.431206\pi$
$773$	5.50771e9	0.428887	0.214444	+	0.976736i	$0.431206\pi$
$774$	5.56029e9	0.431027
$775$	3.08526e8	0.0238087
$776$	9.81196e8	0.0753772
$777$	7.39845e8	0.0565805
$778$	−6.14210e9	−0.467615
$779$	2.89048e9	0.219073
$780$	−1.08767e9	−0.0820664
$781$	−5.14784e9	−0.386675
$782$	3.63847e8	0.0272079
$783$	5.43407e8	0.0404537
$784$	4.81890e8	0.0357143
$785$	2.25495e10	1.66377
$786$	1.40010e9	0.102845
$787$	−1.47559e10	−1.07908	−0.539540	−	0.841960i	$-0.681402\pi$
$787$	−1.47559e10	−1.07908	−0.539540	+	0.841960i	$0.681402\pi$
$788$	−1.91606e9	−0.139497
$789$	1.03872e10	0.752884
$790$	1.05857e10	0.763876
$791$	8.37962e8	0.0602014
$792$	2.71491e9	0.194186
$793$	2.97016e9	0.211507
$794$	2.20050e9	0.156009
$795$	1.51169e10	1.06703
$796$	−1.35373e10	−0.951338
$797$	2.21948e10	1.55291	0.776455	−	0.630173i	$-0.217016\pi$
$797$	2.21948e10	1.55291	0.776455	+	0.630173i	$0.217016\pi$
$798$	−5.60009e8	−0.0390108
$799$	−2.02456e8	−0.0140416
$800$	−1.29647e8	−0.00895254
$801$	−2.38899e9	−0.164248
$802$	−3.15113e9	−0.215703
$803$	−1.34351e10	−0.915667
$804$	−3.70742e9	−0.251580
$805$	−9.17945e9	−0.620199
$806$	−1.37057e9	−0.0921992
$807$	−1.66198e10	−1.11319
$808$	−1.62429e9	−0.108324
$809$	5.77961e9	0.383777	0.191888	−	0.981417i	$-0.438539\pi$
$809$	5.77961e9	0.383777	0.191888	+	0.981417i	$0.438539\pi$
$810$	−1.21806e9	−0.0805323
$811$	−1.23208e9	−0.0811081	−0.0405540	−	0.999177i	$-0.512912\pi$
$811$	−1.23208e9	−0.0811081	−0.0405540	+	0.999177i	$0.512912\pi$
$812$	6.06049e8	0.0397248
$813$	7.49911e9	0.489433
$814$	4.64869e9	0.302096
$815$	−1.92512e10	−1.24568
$816$	5.38459e7	0.00346926
$817$	−7.20654e9	−0.462328
$818$	5.82130e9	0.371863
$819$	−5.49353e8	−0.0349428
$820$	7.01175e9	0.444097
$821$	−2.40571e10	−1.51720	−0.758600	−	0.651557i	$-0.774116\pi$
$821$	−2.40571e10	−1.51720	−0.758600	+	0.651557i	$0.774116\pi$
$822$	−4.10657e9	−0.257886
$823$	−3.28905e9	−0.205670	−0.102835	−	0.994698i	$-0.532791\pi$
$823$	−3.28905e9	−0.205670	−0.102835	+	0.994698i	$0.532791\pi$
$824$	−2.96929e9	−0.184888
$825$	7.77021e8	0.0481775
$826$	2.83619e8	0.0175108
$827$	8.13899e9	0.500381	0.250191	−	0.968197i	$-0.419507\pi$
$827$	8.13899e9	0.500381	0.250191	+	0.968197i	$0.419507\pi$
$828$	4.35820e9	0.266809
$829$	−8.31583e9	−0.506949	−0.253475	−	0.967342i	$-0.581573\pi$
$829$	−8.31583e9	−0.506949	−0.253475	+	0.967342i	$0.581573\pi$
$830$	3.39379e9	0.206021
$831$	6.59236e9	0.398508
$832$	5.75930e8	0.0346688
$833$	−5.72819e7	−0.00343368
$834$	2.01510e9	0.120286
$835$	−9.87049e9	−0.586727
$836$	−3.51872e9	−0.208287
$837$	−1.53487e9	−0.0904757
$838$	−9.58465e9	−0.562629
$839$	−1.55841e10	−0.910991	−0.455495	−	0.890238i	$-0.650538\pi$
$839$	−1.55841e10	−0.910991	−0.455495	+	0.890238i	$0.650538\pi$
$840$	−1.35847e9	−0.0790812
$841$	−1.64877e10	−0.955814
$842$	5.49908e9	0.317466
$843$	−3.67745e9	−0.211422
$844$	−1.56735e10	−0.897362
$845$	1.38287e9	0.0788468
$846$	−2.42504e9	−0.137696
$847$	−1.14631e10	−0.648202
$848$	−8.00455e9	−0.450767
$849$	1.80379e10	1.01160
$850$	1.54110e7	0.000860725 0
$851$	7.46246e9	0.415077
$852$	−1.22296e9	−0.0677442
$853$	−4.91293e9	−0.271031	−0.135516	−	0.990775i	$-0.543269\pi$
$853$	−4.91293e9	−0.271031	−0.135516	+	0.990775i	$0.543269\pi$
$854$	3.70966e9	0.203813
$855$	1.57869e9	0.0863805
$856$	−1.14820e10	−0.625690
$857$	4.11423e9	0.223283	0.111642	−	0.993749i	$-0.464389\pi$
$857$	4.11423e9	0.223283	0.111642	+	0.993749i	$0.464389\pi$
$858$	−3.45177e9	−0.186568
$859$	−2.39728e10	−1.29046	−0.645228	−	0.763990i	$-0.723238\pi$
$859$	−2.39728e10	−1.29046	−0.645228	+	0.763990i	$0.723238\pi$
$860$	−1.74817e10	−0.937213
$861$	3.54145e9	0.189091
$862$	6.40869e9	0.340796
$863$	−1.48740e10	−0.787750	−0.393875	−	0.919164i	$-0.628866\pi$
$863$	−1.48740e10	−0.787750	−0.393875	+	0.919164i	$0.628866\pi$
$864$	6.44973e8	0.0340207
$865$	3.50107e10	1.83927
$866$	−2.28790e10	−1.19709
$867$	1.10727e10	0.577017
$868$	−1.71180e9	−0.0888454
$869$	3.35941e10	1.73657
$870$	−1.70848e9	−0.0879615
$871$	4.71366e9	0.241710
$872$	−3.13787e9	−0.160261
$873$	−1.39706e9	−0.0710663
$874$	−5.64854e9	−0.286185
$875$	7.28847e9	0.367797
$876$	−3.19174e9	−0.160422
$877$	1.97247e9	0.0987441	0.0493720	−	0.998780i	$-0.484278\pi$
$877$	1.97247e9	0.0987441	0.0493720	+	0.998780i	$0.484278\pi$
$878$	−2.21731e9	−0.110560
$879$	−1.39809e10	−0.694342
$880$	−8.53572e9	−0.422232
$881$	−1.30892e10	−0.644906	−0.322453	−	0.946585i	$-0.604507\pi$
$881$	−1.30892e10	−0.644906	−0.322453	+	0.946585i	$0.604507\pi$
$882$	−6.86129e8	−0.0336718
$883$	−1.45556e9	−0.0711489	−0.0355745	−	0.999367i	$-0.511326\pi$
$883$	−1.45556e9	−0.0711489	−0.0355745	+	0.999367i	$0.511326\pi$
$884$	−6.84604e7	−0.00333316
$885$	−7.99537e8	−0.0387737
$886$	4.91877e9	0.237596
$887$	2.66963e10	1.28445	0.642227	−	0.766515i	$-0.278011\pi$
$887$	2.66963e10	1.28445	0.642227	+	0.766515i	$0.278011\pi$
$888$	1.10437e9	0.0529262
$889$	8.90411e9	0.425044
$890$	7.51102e9	0.357136
$891$	−3.86556e9	−0.183080
$892$	−1.77720e10	−0.838417
$893$	3.14303e9	0.147696
$894$	−6.33117e9	−0.296349
$895$	−3.44739e10	−1.60735
$896$	7.19323e8	0.0334077
$897$	−5.54107e9	−0.256342
$898$	2.70025e10	1.24433
$899$	−2.15285e9	−0.0988222
$900$	1.84595e8	0.00844054
$901$	9.51495e8	0.0433381
$902$	2.22521e10	1.00960
$903$	−8.82954e9	−0.399053
$904$	1.25084e9	0.0563132
$905$	1.27715e10	0.572759
$906$	2.59883e9	0.116099
$907$	−1.53023e10	−0.680974	−0.340487	−	0.940249i	$-0.610592\pi$
$907$	−1.53023e10	−0.680974	−0.340487	+	0.940249i	$0.610592\pi$
$908$	−3.01143e9	−0.133497
$909$	2.31271e9	0.102129
$910$	1.72718e9	0.0759787
$911$	2.39474e10	1.04941	0.524704	−	0.851285i	$-0.324176\pi$
$911$	2.39474e10	1.04941	0.524704	+	0.851285i	$0.324176\pi$
$912$	−8.35931e8	−0.0364912
$913$	1.07704e10	0.468363
$914$	2.20401e10	0.954776
$915$	−1.04577e10	−0.451297
$916$	1.23522e10	0.531019
$917$	−2.22331e9	−0.0952156
$918$	−7.66674e7	−0.00327085
$919$	−2.14021e9	−0.0909602	−0.0454801	−	0.998965i	$-0.514482\pi$
$919$	−2.14021e9	−0.0909602	−0.0454801	+	0.998965i	$0.514482\pi$
$920$	−1.37023e10	−0.580143
$921$	−3.03013e9	−0.127806
$922$	−2.33207e9	−0.0979905
$923$	1.55488e9	0.0650866
$924$	−4.31117e9	−0.179781
$925$	3.16078e8	0.0131310
$926$	−1.36212e10	−0.563736
$927$	4.22776e9	0.174314
$928$	9.04656e8	0.0371591
$929$	−3.77051e10	−1.54292	−0.771462	−	0.636275i	$-0.780474\pi$
$929$	−3.77051e10	−1.54292	−0.771462	+	0.636275i	$0.780474\pi$
$930$	4.82566e9	0.196728
$931$	8.89273e8	0.0361170
$932$	7.18259e9	0.290620
$933$	3.84869e9	0.155141
$934$	−7.93189e9	−0.318539
$935$	1.01463e9	0.0405947
$936$	−8.20026e8	−0.0326860
$937$	−2.05357e10	−0.815494	−0.407747	−	0.913095i	$-0.633685\pi$
$937$	−2.05357e10	−0.815494	−0.407747	+	0.913095i	$0.633685\pi$
$938$	5.88725e9	0.232918
$939$	−9.73715e9	−0.383798
$940$	7.62437e9	0.299403
$941$	−1.75144e10	−0.685221	−0.342611	−	0.939477i	$-0.611311\pi$
$941$	−1.75144e10	−0.685221	−0.342611	+	0.939477i	$0.611311\pi$
$942$	1.70008e10	0.662659
$943$	3.57210e10	1.38718
$944$	4.23362e8	0.0163798
$945$	1.93423e9	0.0745584
$946$	−5.54789e10	−2.13063
$947$	1.04432e10	0.399585	0.199792	−	0.979838i	$-0.435973\pi$
$947$	1.04432e10	0.399585	0.199792	+	0.979838i	$0.435973\pi$
$948$	7.98084e9	0.304242
$949$	4.05802e9	0.154128
$950$	−2.39248e8	−0.00905348
$951$	−1.08975e8	−0.00410861
$952$	−8.55053e7	−0.00321191
$953$	−2.79917e10	−1.04762	−0.523810	−	0.851835i	$-0.675490\pi$
$953$	−2.79917e10	−1.04762	−0.523810	+	0.851835i	$0.675490\pi$
$954$	1.13971e10	0.424987
$955$	−1.87185e10	−0.695439
$956$	1.15034e9	0.0425819
$957$	−5.42194e9	−0.199969
$958$	6.74987e9	0.248037
$959$	6.52109e9	0.238756
$960$	−2.02781e9	−0.0739736
$961$	−2.14318e10	−0.778982
$962$	−1.40411e9	−0.0508499
$963$	1.63484e10	0.589906
$964$	−1.62354e9	−0.0583704
$965$	1.05829e10	0.379105
$966$	−6.92066e9	−0.247017
$967$	2.21951e10	0.789342	0.394671	−	0.918822i	$-0.370859\pi$
$967$	2.21951e10	0.789342	0.394671	+	0.918822i	$0.370859\pi$
$968$	−1.71111e10	−0.606337
$969$	9.93664e7	0.00350838
$970$	4.39237e9	0.154525
$971$	−9.20084e9	−0.322523	−0.161261	−	0.986912i	$-0.551556\pi$
$971$	−9.20084e9	−0.322523	−0.161261	+	0.986912i	$0.551556\pi$
$972$	−9.18330e8	−0.0320750
$973$	−3.19991e9	−0.111364
$974$	3.10746e10	1.07758
$975$	−2.34696e8	−0.00810940
$976$	5.53745e9	0.190650
$977$	−1.16366e10	−0.399205	−0.199602	−	0.979877i	$-0.563965\pi$
$977$	−1.16366e10	−0.399205	−0.199602	+	0.979877i	$0.563965\pi$
$978$	−1.45141e10	−0.496139
$979$	2.38366e10	0.811904
$980$	2.15720e9	0.0732149
$981$	4.46778e9	0.151095
$982$	−2.54514e10	−0.857674
$983$	3.50013e10	1.17529	0.587647	−	0.809117i	$-0.300054\pi$
$983$	3.50013e10	1.17529	0.587647	+	0.809117i	$0.300054\pi$
$984$	5.28637e9	0.176878
$985$	−8.57730e9	−0.285972
$986$	−1.07536e8	−0.00357259
$987$	3.85087e9	0.127482
$988$	1.06281e9	0.0350596
$989$	−8.90594e10	−2.92747
$990$	1.21534e10	0.398084
$991$	−9.09045e7	−0.00296707	−0.00148353	−	0.999999i	$-0.500472\pi$
$991$	−9.09045e7	−0.00296707	−0.00148353	+	0.999999i	$0.500472\pi$
$992$	−2.55523e9	−0.0831073
$993$	2.80668e10	0.909641
$994$	1.94201e9	0.0627190
$995$	−6.06001e10	−1.95026
$996$	2.55868e9	0.0820557
$997$	1.78558e10	0.570620	0.285310	−	0.958435i	$-0.407903\pi$
$997$	1.78558e10	0.570620	0.285310	+	0.958435i	$0.407903\pi$
$998$	1.64975e10	0.525364
$999$	−1.57244e9	−0.0498993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.h.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.h.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +286.499 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +286.499 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -2291.99 q^{10} -7273.74 q^{11} -1728.00 q^{12} +2197.00 q^{13} +2744.00 q^{14} -7735.46 q^{15} +4096.00 q^{16} -486.888 q^{17} -5832.00 q^{18} +7558.69 q^{19} +18335.9 q^{20} +9261.00 q^{21} +58189.9 q^{22} +93411.4 q^{23} +13824.0 q^{24} +3956.50 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} -27607.9 q^{29} +61883.7 q^{30} +77979.4 q^{31} -32768.0 q^{32} +196391. q^{33} +3895.11 q^{34} -98269.1 q^{35} +46656.0 q^{36} +79888.2 q^{37} -60469.6 q^{38} -59319.0 q^{39} -146687. q^{40} +382405. q^{41} -74088.0 q^{42} -953411. q^{43} -465519. q^{44} +208858. q^{45} -747291. q^{46} +415816. q^{47} -110592. q^{48} +117649. q^{49} -31652.0 q^{50} +13146.0 q^{51} +140608. q^{52} -1.95424e6 q^{53} +157464. q^{54} -2.08392e6 q^{55} +175616. q^{56} -204085. q^{57} +220863. q^{58} +103360. q^{59} -495070. q^{60} +1.35192e6 q^{61} -623835. q^{62} -250047. q^{63} +262144. q^{64} +629438. q^{65} -1.57113e6 q^{66} +2.14550e6 q^{67} -31160.8 q^{68} -2.52211e6 q^{69} +786152. q^{70} +707729. q^{71} -373248. q^{72} +1.84707e6 q^{73} -639106. q^{74} -106826. q^{75} +483756. q^{76} +2.49489e6 q^{77} +474552. q^{78} -4.61854e6 q^{79} +1.17350e6 q^{80} +531441. q^{81} -3.05924e6 q^{82} -1.48072e6 q^{83} +592704. q^{84} -139493. q^{85} +7.62729e6 q^{86} +745414. q^{87} +3.72415e6 q^{88} -3.27708e6 q^{89} -1.67086e6 q^{90} -753571. q^{91} +5.97833e6 q^{92} -2.10544e6 q^{93} -3.32653e6 q^{94} +2.16556e6 q^{95} +884736. q^{96} -1.91640e6 q^{97} -941192. q^{98} -5.30256e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 40 q^{2} - 135 q^{3} + 320 q^{4} + 168 q^{5} + 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 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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Database

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