LMFDB - Embedded newform 546.8.a.o.1.5

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:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 280157x^{4} + 23551285x^{3} + 13122885428x^{2} - 1144917710924x - 95027285980032 $ x^6 - x^5 - 280157x^4 + 23551285x^3 + 13122885428x^2 - 1144917710924x - 95027285980032
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$213.623$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +207.623 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +207.623 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -1660.98 q^{10} +6014.21 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -5605.81 q^{15} +4096.00 q^{16} +34727.4 q^{17} -5832.00 q^{18} +52926.0 q^{19} +13287.8 q^{20} +9261.00 q^{21} -48113.6 q^{22} -6854.88 q^{23} +13824.0 q^{24} -35017.9 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +38077.2 q^{29} +44846.5 q^{30} +54456.2 q^{31} -32768.0 q^{32} -162384. q^{33} -277819. q^{34} -71214.5 q^{35} +46656.0 q^{36} +380108. q^{37} -423408. q^{38} +59319.0 q^{39} -106303. q^{40} +543214. q^{41} -74088.0 q^{42} -315988. q^{43} +384909. q^{44} +151357. q^{45} +54839.0 q^{46} +247257. q^{47} -110592. q^{48} +117649. q^{49} +280143. q^{50} -937641. q^{51} -140608. q^{52} +1.71712e6 q^{53} +157464. q^{54} +1.24868e6 q^{55} +175616. q^{56} -1.42900e6 q^{57} -304617. q^{58} +2.89085e6 q^{59} -358772. q^{60} -3.16503e6 q^{61} -435650. q^{62} -250047. q^{63} +262144. q^{64} -456147. q^{65} +1.29907e6 q^{66} +3.45251e6 q^{67} +2.22256e6 q^{68} +185082. q^{69} +569716. q^{70} +891205. q^{71} -373248. q^{72} -3.57538e6 q^{73} -3.04086e6 q^{74} +945483. q^{75} +3.38726e6 q^{76} -2.06287e6 q^{77} -474552. q^{78} -6.08855e6 q^{79} +850422. q^{80} +531441. q^{81} -4.34571e6 q^{82} -7.76927e6 q^{83} +592704. q^{84} +7.21020e6 q^{85} +2.52790e6 q^{86} -1.02808e6 q^{87} -3.07927e6 q^{88} +2.26396e6 q^{89} -1.21085e6 q^{90} +753571. q^{91} -438712. q^{92} -1.47032e6 q^{93} -1.97806e6 q^{94} +1.09886e7 q^{95} +884736. q^{96} -7.93808e6 q^{97} -941192. q^{98} +4.38436e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 35 q^{5} + 1296 q^{6} - 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) $ 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 35 * q^5 + 1296 * q^6 - 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 35 q^{5} + 1296 q^{6} - 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 280 q^{10} + 5606 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} + 945 q^{15} + 24576 q^{16} + 22022 q^{17} - 34992 q^{18} - 5779 q^{19} - 2240 q^{20} + 55566 q^{21} - 44848 q^{22} - 110789 q^{23} + 82944 q^{24} + 91769 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} + 30693 q^{29} - 7560 q^{30} + 180467 q^{31} - 196608 q^{32} - 151362 q^{33} - 176176 q^{34} + 12005 q^{35} + 279936 q^{36} - 322222 q^{37} + 46232 q^{38} + 355914 q^{39} + 17920 q^{40} - 212652 q^{41} - 444528 q^{42} - 329299 q^{43} + 358784 q^{44} - 25515 q^{45} + 886312 q^{46} + 1322861 q^{47} - 663552 q^{48} + 705894 q^{49} - 734152 q^{50} - 594594 q^{51} - 843648 q^{52} - 168719 q^{53} + 944784 q^{54} - 2252362 q^{55} + 1053696 q^{56} + 156033 q^{57} - 245544 q^{58} + 1943712 q^{59} + 60480 q^{60} - 1085922 q^{61} - 1443736 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 76895 q^{65} + 1210896 q^{66} + 885066 q^{67} + 1409408 q^{68} + 2991303 q^{69} - 96040 q^{70} + 1626164 q^{71} - 2239488 q^{72} - 4750115 q^{73} + 2577776 q^{74} - 2477763 q^{75} - 369856 q^{76} - 1922858 q^{77} - 2847312 q^{78} + 1794289 q^{79} - 143360 q^{80} + 3188646 q^{81} + 1701216 q^{82} - 8454255 q^{83} + 3556224 q^{84} - 18529504 q^{85} + 2634392 q^{86} - 828711 q^{87} - 2870272 q^{88} - 6055411 q^{89} + 204120 q^{90} + 4521426 q^{91} - 7090496 q^{92} - 4872609 q^{93} - 10582888 q^{94} - 3766747 q^{95} + 5308416 q^{96} - 9823899 q^{97} - 5647152 q^{98} + 4086774 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 35 * q^5 + 1296 * q^6 - 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 280 * q^10 + 5606 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 + 945 * q^15 + 24576 * q^16 + 22022 * q^17 - 34992 * q^18 - 5779 * q^19 - 2240 * q^20 + 55566 * q^21 - 44848 * q^22 - 110789 * q^23 + 82944 * q^24 + 91769 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 + 30693 * q^29 - 7560 * q^30 + 180467 * q^31 - 196608 * q^32 - 151362 * q^33 - 176176 * q^34 + 12005 * q^35 + 279936 * q^36 - 322222 * q^37 + 46232 * q^38 + 355914 * q^39 + 17920 * q^40 - 212652 * q^41 - 444528 * q^42 - 329299 * q^43 + 358784 * q^44 - 25515 * q^45 + 886312 * q^46 + 1322861 * q^47 - 663552 * q^48 + 705894 * q^49 - 734152 * q^50 - 594594 * q^51 - 843648 * q^52 - 168719 * q^53 + 944784 * q^54 - 2252362 * q^55 + 1053696 * q^56 + 156033 * q^57 - 245544 * q^58 + 1943712 * q^59 + 60480 * q^60 - 1085922 * q^61 - 1443736 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 76895 * q^65 + 1210896 * q^66 + 885066 * q^67 + 1409408 * q^68 + 2991303 * q^69 - 96040 * q^70 + 1626164 * q^71 - 2239488 * q^72 - 4750115 * q^73 + 2577776 * q^74 - 2477763 * q^75 - 369856 * q^76 - 1922858 * q^77 - 2847312 * q^78 + 1794289 * q^79 - 143360 * q^80 + 3188646 * q^81 + 1701216 * q^82 - 8454255 * q^83 + 3556224 * q^84 - 18529504 * q^85 + 2634392 * q^86 - 828711 * q^87 - 2870272 * q^88 - 6055411 * q^89 + 204120 * q^90 + 4521426 * q^91 - 7090496 * q^92 - 4872609 * q^93 - 10582888 * q^94 - 3766747 * q^95 + 5308416 * q^96 - 9823899 * q^97 - 5647152 * q^98 + 4086774 * 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
$5$	207.623	0.742813	0.371406	−	0.928470i	$-0.378876\pi$
$5$	207.623	0.742813	0.371406	+	0.928470i	$0.378876\pi$
$6$	216.000	0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−1660.98	−0.525248
$11$	6014.21	1.36240	0.681199	−	0.732099i	$-0.261459\pi$
$11$	6014.21	1.36240	0.681199	+	0.732099i	$0.261459\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	2744.00	0.267261
$15$	−5605.81	−0.428863
$16$	4096.00	0.250000
$17$	34727.4	1.71436	0.857179	−	0.515019i	$-0.172215\pi$
$17$	34727.4	1.71436	0.857179	+	0.515019i	$0.172215\pi$
$18$	−5832.00	−0.235702
$19$	52926.0	1.77024	0.885118	−	0.465367i	$-0.154078\pi$
$19$	52926.0	1.77024	0.885118	+	0.465367i	$0.154078\pi$
$20$	13287.8	0.371406
$21$	9261.00	0.218218
$22$	−48113.6	−0.963361
$23$	−6854.88	−0.117477	−0.0587384	−	0.998273i	$-0.518708\pi$
$23$	−6854.88	−0.117477	−0.0587384	+	0.998273i	$0.518708\pi$
$24$	13824.0	0.204124
$25$	−35017.9	−0.448229
$26$	17576.0	0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	38077.2	0.289916	0.144958	−	0.989438i	$-0.453695\pi$
$29$	38077.2	0.289916	0.144958	+	0.989438i	$0.453695\pi$
$30$	44846.5	0.303252
$31$	54456.2	0.328308	0.164154	−	0.986435i	$-0.447511\pi$
$31$	54456.2	0.328308	0.164154	+	0.986435i	$0.447511\pi$
$32$	−32768.0	−0.176777
$33$	−162384.	−0.786581
$34$	−277819.	−1.21223
$35$	−71214.5	−0.280757
$36$	46656.0	0.166667
$37$	380108.	1.23367	0.616837	−	0.787091i	$-0.288414\pi$
$37$	380108.	1.23367	0.616837	+	0.787091i	$0.288414\pi$
$38$	−423408.	−1.25175
$39$	59319.0	0.160128
$40$	−106303.	−0.262624
$41$	543214.	1.23091	0.615457	−	0.788171i	$-0.288972\pi$
$41$	543214.	1.23091	0.615457	+	0.788171i	$0.288972\pi$
$42$	−74088.0	−0.154303
$43$	−315988.	−0.606081	−0.303041	−	0.952978i	$-0.598002\pi$
$43$	−315988.	−0.606081	−0.303041	+	0.952978i	$0.598002\pi$
$44$	384909.	0.681199
$45$	151357.	0.247604
$46$	54839.0	0.0830687
$47$	247257.	0.347381	0.173691	−	0.984800i	$-0.444431\pi$
$47$	247257.	0.347381	0.173691	+	0.984800i	$0.444431\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	280143.	0.316946
$51$	−937641.	−0.989785
$52$	−140608.	−0.138675
$53$	1.71712e6	1.58429	0.792145	−	0.610332i	$-0.208964\pi$
$53$	1.71712e6	1.58429	0.792145	+	0.610332i	$0.208964\pi$
$54$	157464.	0.136083
$55$	1.24868e6	1.01201
$56$	175616.	0.133631
$57$	−1.42900e6	−1.02205
$58$	−304617.	−0.205001
$59$	2.89085e6	1.83250	0.916248	−	0.400612i	$-0.131202\pi$
$59$	2.89085e6	1.83250	0.916248	+	0.400612i	$0.131202\pi$
$60$	−358772.	−0.214432
$61$	−3.16503e6	−1.78535	−0.892674	−	0.450704i	$-0.851173\pi$
$61$	−3.16503e6	−1.78535	−0.892674	+	0.450704i	$0.851173\pi$
$62$	−435650.	−0.232149
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	−456147.	−0.206019
$66$	1.29907e6	0.556196
$67$	3.45251e6	1.40241	0.701203	−	0.712962i	$-0.252647\pi$
$67$	3.45251e6	1.40241	0.701203	+	0.712962i	$0.252647\pi$
$68$	2.22256e6	0.857179
$69$	185082.	0.0678253
$70$	569716.	0.198525
$71$	891205.	0.295511	0.147755	−	0.989024i	$-0.452795\pi$
$71$	891205.	0.295511	0.147755	+	0.989024i	$0.452795\pi$
$72$	−373248.	−0.117851
$73$	−3.57538e6	−1.07570	−0.537852	−	0.843040i	$-0.680764\pi$
$73$	−3.57538e6	−1.07570	−0.537852	+	0.843040i	$0.680764\pi$
$74$	−3.04086e6	−0.872339
$75$	945483.	0.258785
$76$	3.38726e6	0.885118
$77$	−2.06287e6	−0.514938
$78$	−474552.	−0.113228
$79$	−6.08855e6	−1.38937	−0.694686	−	0.719313i	$-0.744457\pi$
$79$	−6.08855e6	−1.38937	−0.694686	+	0.719313i	$0.744457\pi$
$80$	850422.	0.185703
$81$	531441.	0.111111
$82$	−4.34571e6	−0.870387
$83$	−7.76927e6	−1.49144	−0.745722	−	0.666257i	$-0.767895\pi$
$83$	−7.76927e6	−1.49144	−0.745722	+	0.666257i	$0.767895\pi$
$84$	592704.	0.109109
$85$	7.21020e6	1.27345
$86$	2.52790e6	0.428564
$87$	−1.02808e6	−0.167383
$88$	−3.07927e6	−0.481680
$89$	2.26396e6	0.340411	0.170205	−	0.985409i	$-0.445557\pi$
$89$	2.26396e6	0.340411	0.170205	+	0.985409i	$0.445557\pi$
$90$	−1.21085e6	−0.175083
$91$	753571.	0.104828
$92$	−438712.	−0.0587384
$93$	−1.47032e6	−0.189549
$94$	−1.97806e6	−0.245636
$95$	1.09886e7	1.31495
$96$	884736.	0.102062
$97$	−7.93808e6	−0.883109	−0.441555	−	0.897234i	$-0.645573\pi$
$97$	−7.93808e6	−0.883109	−0.441555	+	0.897234i	$0.645573\pi$
$98$	−941192.	−0.101015
$99$	4.38436e6	0.454133
$100$	−2.24114e6	−0.224114
$101$	−5.96508e6	−0.576091	−0.288046	−	0.957617i	$-0.593005\pi$
$101$	−5.96508e6	−0.576091	−0.288046	+	0.957617i	$0.593005\pi$
$102$	7.50112e6	0.699883
$103$	−7.50959e6	−0.677152	−0.338576	−	0.940939i	$-0.609945\pi$
$103$	−7.50959e6	−0.677152	−0.338576	+	0.940939i	$0.609945\pi$
$104$	1.12486e6	0.0980581
$105$	1.92279e6	0.162095
$106$	−1.37370e7	−1.12026
$107$	7.89212e6	0.622803	0.311401	−	0.950278i	$-0.399202\pi$
$107$	7.89212e6	0.622803	0.311401	+	0.950278i	$0.399202\pi$
$108$	−1.25971e6	−0.0962250
$109$	2.15285e7	1.59228	0.796142	−	0.605110i	$-0.206871\pi$
$109$	2.15285e7	1.59228	0.796142	+	0.605110i	$0.206871\pi$
$110$	−9.98948e6	−0.715597
$111$	−1.02629e7	−0.712262
$112$	−1.40493e6	−0.0944911
$113$	2.82163e6	0.183961	0.0919806	−	0.995761i	$-0.470680\pi$
$113$	2.82163e6	0.183961	0.0919806	+	0.995761i	$0.470680\pi$
$114$	1.14320e7	0.722696
$115$	−1.42323e6	−0.0872633
$116$	2.43694e6	0.144958
$117$	−1.60161e6	−0.0924500
$118$	−2.31268e7	−1.29577
$119$	−1.19115e7	−0.647966
$120$	2.87017e6	0.151626
$121$	1.66835e7	0.856127
$122$	2.53202e7	1.26243
$123$	−1.46668e7	−0.710668
$124$	3.48520e6	0.164154
$125$	−2.34910e7	−1.07576
$126$	2.00038e6	0.0890871
$127$	−3.15619e7	−1.36726	−0.683628	−	0.729831i	$-0.739599\pi$
$127$	−3.15619e7	−1.36726	−0.683628	+	0.729831i	$0.739599\pi$
$128$	−2.09715e6	−0.0883883
$129$	8.53168e6	0.349921
$130$	3.64917e6	0.145678
$131$	−2.82238e7	−1.09690	−0.548449	−	0.836184i	$-0.684781\pi$
$131$	−2.82238e7	−1.09690	−0.548449	+	0.836184i	$0.684781\pi$
$132$	−1.03925e7	−0.393290
$133$	−1.81536e7	−0.669086
$134$	−2.76201e7	−0.991651
$135$	−4.08663e6	−0.142954
$136$	−1.77804e7	−0.606117
$137$	−4.31212e7	−1.43275	−0.716373	−	0.697718i	$-0.754199\pi$
$137$	−4.31212e7	−1.43275	−0.716373	+	0.697718i	$0.754199\pi$
$138$	−1.48065e6	−0.0479597
$139$	−3.57357e7	−1.12863	−0.564314	−	0.825561i	$-0.690859\pi$
$139$	−3.57357e7	−1.12863	−0.564314	+	0.825561i	$0.690859\pi$
$140$	−4.55773e6	−0.140378
$141$	−6.67594e6	−0.200561
$142$	−7.12964e6	−0.208958
$143$	−1.32132e7	−0.377861
$144$	2.98598e6	0.0833333
$145$	7.90568e6	0.215353
$146$	2.86031e7	0.760637
$147$	−3.17652e6	−0.0824786
$148$	2.43269e7	0.616837
$149$	−5.38797e6	−0.133436	−0.0667180	−	0.997772i	$-0.521253\pi$
$149$	−5.38797e6	−0.133436	−0.0667180	+	0.997772i	$0.521253\pi$
$150$	−7.56386e6	−0.182989
$151$	−2.30602e7	−0.545058	−0.272529	−	0.962148i	$-0.587860\pi$
$151$	−2.30602e7	−0.545058	−0.272529	+	0.962148i	$0.587860\pi$
$152$	−2.70981e7	−0.625873
$153$	2.53163e7	0.571452
$154$	1.65030e7	0.364116
$155$	1.13063e7	0.243872
$156$	3.79642e6	0.0800641
$157$	6.41210e7	1.32237	0.661183	−	0.750225i	$-0.270055\pi$
$157$	6.41210e7	1.32237	0.661183	+	0.750225i	$0.270055\pi$
$158$	4.87084e7	0.982435
$159$	−4.63622e7	−0.914691
$160$	−6.80338e6	−0.131312
$161$	2.35122e6	0.0444021
$162$	−4.25153e6	−0.0785674
$163$	1.01817e8	1.84146	0.920732	−	0.390196i	$-0.127593\pi$
$163$	1.01817e8	1.84146	0.920732	+	0.390196i	$0.127593\pi$
$164$	3.47657e7	0.615457
$165$	−3.37145e7	−0.584282
$166$	6.21542e7	1.05461
$167$	6.24702e7	1.03792	0.518962	−	0.854797i	$-0.326319\pi$
$167$	6.24702e7	1.03792	0.518962	+	0.854797i	$0.326319\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	−5.76816e7	−0.900463
$171$	3.85830e7	0.590079
$172$	−2.02232e7	−0.303041
$173$	−7.26932e7	−1.06741	−0.533707	−	0.845670i	$-0.679201\pi$
$173$	−7.26932e7	−1.06741	−0.533707	+	0.845670i	$0.679201\pi$
$174$	8.22467e6	0.118358
$175$	1.20111e7	0.169415
$176$	2.46342e7	0.340599
$177$	−7.80529e7	−1.05799
$178$	−1.81117e7	−0.240707
$179$	3.79654e7	0.494769	0.247385	−	0.968917i	$-0.420429\pi$
$179$	3.79654e7	0.494769	0.247385	+	0.968917i	$0.420429\pi$
$180$	9.68684e6	0.123802
$181$	6.27262e7	0.786274	0.393137	−	0.919480i	$-0.371390\pi$
$181$	6.27262e7	0.786274	0.393137	+	0.919480i	$0.371390\pi$
$182$	−6.02857e6	−0.0741249
$183$	8.54557e7	1.03077
$184$	3.50970e6	0.0415343
$185$	7.89189e7	0.916389
$186$	1.17625e7	0.134031
$187$	2.08858e8	2.33564
$188$	1.58244e7	0.173691
$189$	6.75127e6	0.0727393
$190$	−8.79090e7	−0.929813
$191$	1.20365e6	0.0124992	0.00624959	−	0.999980i	$-0.498011\pi$
$191$	1.20365e6	0.0124992	0.00624959	+	0.999980i	$0.498011\pi$
$192$	−7.07789e6	−0.0721688
$193$	−9.12604e7	−0.913759	−0.456880	−	0.889528i	$-0.651033\pi$
$193$	−9.12604e7	−0.913759	−0.456880	+	0.889528i	$0.651033\pi$
$194$	6.35046e7	0.624452
$195$	1.23160e7	0.118945
$196$	7.52954e6	0.0714286
$197$	−6.45294e7	−0.601348	−0.300674	−	0.953727i	$-0.597212\pi$
$197$	−6.45294e7	−0.601348	−0.300674	+	0.953727i	$0.597212\pi$
$198$	−3.50748e7	−0.321120
$199$	1.52687e8	1.37346	0.686732	−	0.726910i	$-0.259044\pi$
$199$	1.52687e8	1.37346	0.686732	+	0.726910i	$0.259044\pi$
$200$	1.79292e7	0.158473
$201$	−9.32179e7	−0.809679
$202$	4.77206e7	0.407358
$203$	−1.30605e7	−0.109578
$204$	−6.00090e7	−0.494892
$205$	1.12783e8	0.914338
$206$	6.00767e7	0.478819
$207$	−4.99721e6	−0.0391590
$208$	−8.99891e6	−0.0693375
$209$	3.18308e8	2.41176
$210$	−1.53823e7	−0.114619
$211$	−1.30649e8	−0.957452	−0.478726	−	0.877964i	$-0.658901\pi$
$211$	−1.30649e8	−0.957452	−0.478726	+	0.877964i	$0.658901\pi$
$212$	1.09896e8	0.792145
$213$	−2.40625e7	−0.170613
$214$	−6.31370e7	−0.440388
$215$	−6.56062e7	−0.450205
$216$	1.00777e7	0.0680414
$217$	−1.86785e7	−0.124089
$218$	−1.72228e8	−1.12591
$219$	9.65353e7	0.621058
$220$	7.99158e7	0.506003
$221$	−7.62962e7	−0.475477
$222$	8.21032e7	0.503645
$223$	−1.40192e8	−0.846558	−0.423279	−	0.905999i	$-0.639121\pi$
$223$	−1.40192e8	−0.846558	−0.423279	+	0.905999i	$0.639121\pi$
$224$	1.12394e7	0.0668153
$225$	−2.55280e7	−0.149410
$226$	−2.25731e7	−0.130080
$227$	6.92735e7	0.393076	0.196538	−	0.980496i	$-0.437030\pi$
$227$	6.92735e7	0.393076	0.196538	+	0.980496i	$0.437030\pi$
$228$	−9.14560e7	−0.511023
$229$	1.72899e8	0.951413	0.475706	−	0.879604i	$-0.342192\pi$
$229$	1.72899e8	0.951413	0.475706	+	0.879604i	$0.342192\pi$
$230$	1.13858e7	0.0617045
$231$	5.56976e7	0.297300
$232$	−1.94955e7	−0.102501
$233$	−4.25492e7	−0.220367	−0.110183	−	0.993911i	$-0.535144\pi$
$233$	−4.25492e7	−0.220367	−0.110183	+	0.993911i	$0.535144\pi$
$234$	1.28129e7	0.0653720
$235$	5.13361e7	0.258039
$236$	1.85014e8	0.916248
$237$	1.64391e8	0.802155
$238$	9.52921e7	0.458181
$239$	3.87336e8	1.83525	0.917626	−	0.397445i	$-0.130103\pi$
$239$	3.87336e8	1.83525	0.917626	+	0.397445i	$0.130103\pi$
$240$	−2.29614e7	−0.107216
$241$	2.71446e8	1.24917	0.624587	−	0.780955i	$-0.285267\pi$
$241$	2.71446e8	1.24917	0.624587	+	0.780955i	$0.285267\pi$
$242$	−1.33468e8	−0.605373
$243$	−1.43489e7	−0.0641500
$244$	−2.02562e8	−0.892674
$245$	2.44266e7	0.106116
$246$	1.17334e8	0.502518
$247$	−1.16278e8	−0.490975
$248$	−2.78816e7	−0.116074
$249$	2.09770e8	0.861086
$250$	1.87928e8	0.760679
$251$	−2.94055e8	−1.17374	−0.586868	−	0.809683i	$-0.699639\pi$
$251$	−2.94055e8	−1.17374	−0.586868	+	0.809683i	$0.699639\pi$
$252$	−1.60030e7	−0.0629941
$253$	−4.12266e7	−0.160050
$254$	2.52495e8	0.966796
$255$	−1.94675e8	−0.735225
$256$	1.67772e7	0.0625000
$257$	−1.23885e8	−0.455252	−0.227626	−	0.973749i	$-0.573096\pi$
$257$	−1.23885e8	−0.455252	−0.227626	+	0.973749i	$0.573096\pi$
$258$	−6.82534e7	−0.247432
$259$	−1.30377e8	−0.466285
$260$	−2.91934e7	−0.103010
$261$	2.77583e7	0.0966385
$262$	2.25790e8	0.775624
$263$	−1.71767e7	−0.0582229	−0.0291115	−	0.999576i	$-0.509268\pi$
$263$	−1.71767e7	−0.0582229	−0.0291115	+	0.999576i	$0.509268\pi$
$264$	8.31404e7	0.278098
$265$	3.56513e8	1.17683
$266$	1.45229e8	0.473115
$267$	−6.11268e7	−0.196536
$268$	2.20961e8	0.701203
$269$	−6.86262e7	−0.214960	−0.107480	−	0.994207i	$-0.534278\pi$
$269$	−6.86262e7	−0.214960	−0.107480	+	0.994207i	$0.534278\pi$
$270$	3.26931e7	0.101084
$271$	−3.43319e8	−1.04787	−0.523933	−	0.851760i	$-0.675536\pi$
$271$	−3.43319e8	−1.04787	−0.523933	+	0.851760i	$0.675536\pi$
$272$	1.42244e8	0.428589
$273$	−2.03464e7	−0.0605228
$274$	3.44970e8	1.01310
$275$	−2.10605e8	−0.610666
$276$	1.18452e7	0.0339126
$277$	−1.97091e8	−0.557171	−0.278585	−	0.960411i	$-0.589866\pi$
$277$	−1.97091e8	−0.557171	−0.278585	+	0.960411i	$0.589866\pi$
$278$	2.85886e8	0.798060
$279$	3.96986e7	0.109436
$280$	3.64618e7	0.0992626
$281$	1.97465e8	0.530905	0.265453	−	0.964124i	$-0.414479\pi$
$281$	1.97465e8	0.530905	0.265453	+	0.964124i	$0.414479\pi$
$282$	5.34075e7	0.141818
$283$	3.16127e8	0.829104	0.414552	−	0.910026i	$-0.363938\pi$
$283$	3.16127e8	0.829104	0.414552	+	0.910026i	$0.363938\pi$
$284$	5.70371e7	0.147755
$285$	−2.96693e8	−0.759189
$286$	1.05706e8	0.267188
$287$	−1.86322e8	−0.465242
$288$	−2.38879e7	−0.0589256
$289$	7.95655e8	1.93902
$290$	−6.32454e7	−0.152278
$291$	2.14328e8	0.509863
$292$	−2.28824e8	−0.537852
$293$	2.62124e8	0.608795	0.304397	−	0.952545i	$-0.401545\pi$
$293$	2.62124e8	0.608795	0.304397	+	0.952545i	$0.401545\pi$
$294$	2.54122e7	0.0583212
$295$	6.00205e8	1.36120
$296$	−1.94615e8	−0.436170
$297$	−1.18378e8	−0.262194
$298$	4.31038e7	0.0943535
$299$	1.50602e7	0.0325822
$300$	6.05109e7	0.129393
$301$	1.08384e8	0.229077
$302$	1.84481e8	0.385415
$303$	1.61057e8	0.332606
$304$	2.16785e8	0.442559
$305$	−6.57131e8	−1.32618
$306$	−2.02530e8	−0.404078
$307$	1.08771e8	0.214550	0.107275	−	0.994229i	$-0.465788\pi$
$307$	1.08771e8	0.214550	0.107275	+	0.994229i	$0.465788\pi$
$308$	−1.32024e8	−0.257469
$309$	2.02759e8	0.390954
$310$	−9.04507e7	−0.172443
$311$	4.84541e8	0.913418	0.456709	−	0.889616i	$-0.349028\pi$
$311$	4.84541e8	0.913418	0.456709	+	0.889616i	$0.349028\pi$
$312$	−3.03713e7	−0.0566139
$313$	−9.05085e8	−1.66834	−0.834169	−	0.551509i	$-0.814052\pi$
$313$	−9.05085e8	−1.66834	−0.834169	+	0.551509i	$0.814052\pi$
$314$	−5.12968e8	−0.935054
$315$	−5.19154e7	−0.0935856
$316$	−3.89667e8	−0.694686
$317$	−2.69773e8	−0.475654	−0.237827	−	0.971308i	$-0.576435\pi$
$317$	−2.69773e8	−0.475654	−0.237827	+	0.971308i	$0.576435\pi$
$318$	3.70898e8	0.646784
$319$	2.29004e8	0.394980
$320$	5.44270e7	0.0928516
$321$	−2.13087e8	−0.359575
$322$	−1.88098e7	−0.0313970
$323$	1.83798e9	3.03482
$324$	3.40122e7	0.0555556
$325$	7.69343e7	0.124316
$326$	−8.14535e8	−1.30211
$327$	−5.81269e8	−0.919305
$328$	−2.78126e8	−0.435194
$329$	−8.48092e7	−0.131298
$330$	2.69716e8	0.413150
$331$	1.09982e9	1.66695	0.833476	−	0.552556i	$-0.186347\pi$
$331$	1.09982e9	1.66695	0.833476	+	0.552556i	$0.186347\pi$
$332$	−4.97233e8	−0.745722
$333$	2.77098e8	0.411225
$334$	−4.99762e8	−0.733923
$335$	7.16820e8	1.04173
$336$	3.79331e7	0.0545545
$337$	−1.23542e8	−0.175837	−0.0879185	−	0.996128i	$-0.528021\pi$
$337$	−1.23542e8	−0.175837	−0.0879185	+	0.996128i	$0.528021\pi$
$338$	−3.86145e7	−0.0543928
$339$	−7.61841e7	−0.106210
$340$	4.61453e8	0.636723
$341$	3.27511e8	0.447286
$342$	−3.08664e8	−0.417249
$343$	−4.03536e7	−0.0539949
$344$	1.61786e8	0.214282
$345$	3.84271e7	0.0503815
$346$	5.81546e8	0.754775
$347$	5.21630e8	0.670208	0.335104	−	0.942181i	$-0.391229\pi$
$347$	5.21630e8	0.670208	0.335104	+	0.942181i	$0.391229\pi$
$348$	−6.57973e7	−0.0836914
$349$	1.42212e9	1.79080	0.895399	−	0.445265i	$-0.146891\pi$
$349$	1.42212e9	1.79080	0.895399	+	0.445265i	$0.146891\pi$
$350$	−9.60891e7	−0.119794
$351$	4.32436e7	0.0533761
$352$	−1.97073e8	−0.240840
$353$	−6.66924e8	−0.806984	−0.403492	−	0.914983i	$-0.632204\pi$
$353$	−6.66924e8	−0.806984	−0.403492	+	0.914983i	$0.632204\pi$
$354$	6.24423e8	0.748113
$355$	1.85034e8	0.219509
$356$	1.44893e8	0.170205
$357$	3.21611e8	0.374103
$358$	−3.03724e8	−0.349855
$359$	1.19741e7	0.0136588	0.00682938	−	0.999977i	$-0.497826\pi$
$359$	1.19741e7	0.0136588	0.00682938	+	0.999977i	$0.497826\pi$
$360$	−7.74947e7	−0.0875413
$361$	1.90728e9	2.13373
$362$	−5.01809e8	−0.555979
$363$	−4.50454e8	−0.494285
$364$	4.82285e7	0.0524142
$365$	−7.42330e8	−0.799046
$366$	−6.83645e8	−0.728865
$367$	1.22893e9	1.29777	0.648883	−	0.760888i	$-0.275236\pi$
$367$	1.22893e9	1.29777	0.648883	+	0.760888i	$0.275236\pi$
$368$	−2.80776e7	−0.0293692
$369$	3.96003e8	0.410304
$370$	−6.31351e8	−0.647985
$371$	−5.88972e8	−0.598806
$372$	−9.41004e7	−0.0947744
$373$	1.00237e8	0.100011	0.0500056	−	0.998749i	$-0.484076\pi$
$373$	1.00237e8	0.100011	0.0500056	+	0.998749i	$0.484076\pi$
$374$	−1.67086e9	−1.65154
$375$	6.34257e8	0.621092
$376$	−1.26596e8	−0.122818
$377$	−8.36555e7	−0.0804081
$378$	−5.40102e7	−0.0514344
$379$	−2.58823e8	−0.244212	−0.122106	−	0.992517i	$-0.538965\pi$
$379$	−2.58823e8	−0.244212	−0.122106	+	0.992517i	$0.538965\pi$
$380$	7.03272e8	0.657477
$381$	8.52171e8	0.789386
$382$	−9.62916e6	−0.00883826
$383$	1.49638e8	0.136096	0.0680482	−	0.997682i	$-0.478323\pi$
$383$	1.49638e8	0.136096	0.0680482	+	0.997682i	$0.478323\pi$
$384$	5.66231e7	0.0510310
$385$	−4.28299e8	−0.382503
$386$	7.30083e8	0.646125
$387$	−2.30355e8	−0.202027
$388$	−5.08037e8	−0.441555
$389$	−6.70347e8	−0.577399	−0.288700	−	0.957420i	$-0.593223\pi$
$389$	−6.70347e8	−0.577399	−0.288700	+	0.957420i	$0.593223\pi$
$390$	−9.85277e7	−0.0841070
$391$	−2.38052e8	−0.201397
$392$	−6.02363e7	−0.0505076
$393$	7.62043e8	0.633294
$394$	5.16235e8	0.425217
$395$	−1.26412e9	−1.03204
$396$	2.80599e8	0.227066
$397$	2.34074e9	1.87753	0.938764	−	0.344561i	$-0.111972\pi$
$397$	2.34074e9	1.87753	0.938764	+	0.344561i	$0.111972\pi$
$398$	−1.22150e9	−0.971186
$399$	4.90147e8	0.386297
$400$	−1.43433e8	−0.112057
$401$	−1.63080e9	−1.26298	−0.631490	−	0.775384i	$-0.717556\pi$
$401$	−1.63080e9	−1.26298	−0.631490	+	0.775384i	$0.717556\pi$
$402$	7.45743e8	0.572530
$403$	−1.19640e8	−0.0910563
$404$	−3.81765e8	−0.288046
$405$	1.10339e8	0.0825348
$406$	1.04484e8	0.0774832
$407$	2.28604e9	1.68075
$408$	4.80072e8	0.349942
$409$	−7.75449e7	−0.0560431	−0.0280215	−	0.999607i	$-0.508921\pi$
$409$	−7.75449e7	−0.0560431	−0.0280215	+	0.999607i	$0.508921\pi$
$410$	−9.02268e8	−0.646535
$411$	1.16427e9	0.827196
$412$	−4.80614e8	−0.338576
$413$	−9.91560e8	−0.692618
$414$	3.99776e7	0.0276896
$415$	−1.61308e9	−1.10786
$416$	7.19913e7	0.0490290
$417$	9.64864e8	0.651613
$418$	−2.54646e9	−1.70538
$419$	1.02443e9	0.680350	0.340175	−	0.940362i	$-0.389514\pi$
$419$	1.02443e9	0.680350	0.340175	+	0.940362i	$0.389514\pi$
$420$	1.23059e8	0.0810475
$421$	6.42828e8	0.419863	0.209931	−	0.977716i	$-0.432676\pi$
$421$	6.42828e8	0.419863	0.209931	+	0.977716i	$0.432676\pi$
$422$	1.04519e9	0.677021
$423$	1.80250e8	0.115794
$424$	−8.79165e8	−0.560131
$425$	−1.21608e9	−0.768425
$426$	1.92500e8	0.120642
$427$	1.08560e9	0.674798
$428$	5.05096e8	0.311401
$429$	3.56757e8	0.218158
$430$	5.24850e8	0.318343
$431$	2.61988e8	0.157620	0.0788099	−	0.996890i	$-0.474888\pi$
$431$	2.61988e8	0.157620	0.0788099	+	0.996890i	$0.474888\pi$
$432$	−8.06216e7	−0.0481125
$433$	−2.75196e9	−1.62905	−0.814526	−	0.580127i	$-0.803003\pi$
$433$	−2.75196e9	−1.62905	−0.814526	+	0.580127i	$0.803003\pi$
$434$	1.49428e8	0.0877441
$435$	−2.13453e8	−0.124334
$436$	1.37782e9	0.796142
$437$	−3.62801e8	−0.207962
$438$	−7.72283e8	−0.439154
$439$	2.13790e9	1.20604	0.603021	−	0.797725i	$-0.293964\pi$
$439$	2.13790e9	1.20604	0.603021	+	0.797725i	$0.293964\pi$
$440$	−6.39327e8	−0.357798
$441$	8.57661e7	0.0476190
$442$	6.10369e8	0.336213
$443$	1.92799e9	1.05364	0.526819	−	0.849977i	$-0.323385\pi$
$443$	1.92799e9	1.05364	0.526819	+	0.849977i	$0.323385\pi$
$444$	−6.56826e8	−0.356131
$445$	4.70048e8	0.252861
$446$	1.12154e9	0.598607
$447$	1.45475e8	0.0770393
$448$	−8.99154e7	−0.0472456
$449$	−2.84525e9	−1.48340	−0.741700	−	0.670731i	$-0.765980\pi$
$449$	−2.84525e9	−1.48340	−0.741700	+	0.670731i	$0.765980\pi$
$450$	2.04224e8	0.105649
$451$	3.26700e9	1.67699
$452$	1.80585e8	0.0919806
$453$	6.22624e8	0.314690
$454$	−5.54188e8	−0.277947
$455$	1.56458e8	0.0778680
$456$	7.31648e8	0.361348
$457$	−1.14239e9	−0.559896	−0.279948	−	0.960015i	$-0.590317\pi$
$457$	−1.14239e9	−0.559896	−0.279948	+	0.960015i	$0.590317\pi$
$458$	−1.38319e9	−0.672750
$459$	−6.83540e8	−0.329928
$460$	−9.10865e7	−0.0436317
$461$	1.81415e9	0.862420	0.431210	−	0.902252i	$-0.358087\pi$
$461$	1.81415e9	0.862420	0.431210	+	0.902252i	$0.358087\pi$
$462$	−4.45580e8	−0.210223
$463$	2.75366e9	1.28937	0.644683	−	0.764450i	$-0.276989\pi$
$463$	2.75366e9	1.28937	0.644683	+	0.764450i	$0.276989\pi$
$464$	1.55964e8	0.0724789
$465$	−3.05271e8	−0.140799
$466$	3.40394e8	0.155823
$467$	−1.80484e9	−0.820032	−0.410016	−	0.912078i	$-0.634477\pi$
$467$	−1.80484e9	−0.820032	−0.410016	+	0.912078i	$0.634477\pi$
$468$	−1.02503e8	−0.0462250
$469$	−1.18421e9	−0.530060
$470$	−4.10689e8	−0.182461
$471$	−1.73127e9	−0.763468
$472$	−1.48011e9	−0.647885
$473$	−1.90042e9	−0.825724
$474$	−1.31513e9	−0.567209
$475$	−1.85335e9	−0.793471
$476$	−7.62336e8	−0.323983
$477$	1.25178e9	0.528097
$478$	−3.09869e9	−1.29772
$479$	−3.18571e8	−0.132444	−0.0662219	−	0.997805i	$-0.521095\pi$
$479$	−3.18571e8	−0.132444	−0.0662219	+	0.997805i	$0.521095\pi$
$480$	1.83691e8	0.0758130
$481$	−8.35096e8	−0.342160
$482$	−2.17156e9	−0.883300
$483$	−6.34830e7	−0.0256356
$484$	1.06774e9	0.428064
$485$	−1.64812e9	−0.655985
$486$	1.14791e8	0.0453609
$487$	2.28719e9	0.897328	0.448664	−	0.893701i	$-0.351900\pi$
$487$	2.28719e9	0.897328	0.448664	+	0.893701i	$0.351900\pi$
$488$	1.62049e9	0.631216
$489$	−2.74906e9	−1.06317
$490$	−1.95413e8	−0.0750354
$491$	−2.32407e9	−0.886061	−0.443030	−	0.896507i	$-0.646097\pi$
$491$	−2.32407e9	−0.886061	−0.443030	+	0.896507i	$0.646097\pi$
$492$	−9.38674e8	−0.355334
$493$	1.32232e9	0.497019
$494$	9.30227e8	0.347172
$495$	9.10291e8	0.337336
$496$	2.23053e8	0.0820770
$497$	−3.05683e8	−0.111693
$498$	−1.67816e9	−0.608880
$499$	8.53805e8	0.307615	0.153807	−	0.988101i	$-0.450847\pi$
$499$	8.53805e8	0.307615	0.153807	+	0.988101i	$0.450847\pi$
$500$	−1.50342e9	−0.537882
$501$	−1.68670e9	−0.599246
$502$	2.35244e9	0.829956
$503$	−9.91489e7	−0.0347376	−0.0173688	−	0.999849i	$-0.505529\pi$
$503$	−9.91489e7	−0.0347376	−0.0173688	+	0.999849i	$0.505529\pi$
$504$	1.28024e8	0.0445435
$505$	−1.23848e9	−0.427928
$506$	3.29813e8	0.113173
$507$	−1.30324e8	−0.0444116
$508$	−2.01996e9	−0.683628
$509$	2.78008e9	0.934425	0.467213	−	0.884145i	$-0.345258\pi$
$509$	2.78008e9	0.934425	0.467213	+	0.884145i	$0.345258\pi$
$510$	1.55740e9	0.519883
$511$	1.22636e9	0.406578
$512$	−1.34218e8	−0.0441942
$513$	−1.04174e9	−0.340682
$514$	9.91077e8	0.321911
$515$	−1.55916e9	−0.502997
$516$	5.46027e8	0.174961
$517$	1.48705e9	0.473271
$518$	1.04302e9	0.329713
$519$	1.96272e9	0.616271
$520$	2.33547e8	0.0728388
$521$	−1.77507e9	−0.549900	−0.274950	−	0.961459i	$-0.588661\pi$
$521$	−1.77507e9	−0.549900	−0.274950	+	0.961459i	$0.588661\pi$
$522$	−2.22066e8	−0.0683338
$523$	−1.94650e9	−0.594976	−0.297488	−	0.954726i	$-0.596149\pi$
$523$	−1.94650e9	−0.594976	−0.297488	+	0.954726i	$0.596149\pi$
$524$	−1.80632e9	−0.548449
$525$	−3.24301e8	−0.0978116
$526$	1.37413e8	0.0411698
$527$	1.89113e9	0.562838
$528$	−6.65123e8	−0.196645
$529$	−3.35784e9	−0.986199
$530$	−2.85210e9	−0.832146
$531$	2.10743e9	0.610832
$532$	−1.16183e9	−0.334543
$533$	−1.19344e9	−0.341394
$534$	4.89015e8	0.138972
$535$	1.63858e9	0.462626
$536$	−1.76769e9	−0.495825
$537$	−1.02507e9	−0.285655
$538$	5.49009e8	0.151999
$539$	7.07565e8	0.194628
$540$	−2.61545e8	−0.0714772
$541$	5.80094e9	1.57510	0.787550	−	0.616251i	$-0.211349\pi$
$541$	5.80094e9	1.57510	0.787550	+	0.616251i	$0.211349\pi$
$542$	2.74655e9	0.740953
$543$	−1.69361e9	−0.453955
$544$	−1.13795e9	−0.303058
$545$	4.46980e9	1.18277
$546$	1.62771e8	0.0427960
$547$	−6.09103e9	−1.59124	−0.795619	−	0.605798i	$-0.792854\pi$
$547$	−6.09103e9	−1.59124	−0.795619	+	0.605798i	$0.792854\pi$
$548$	−2.75976e9	−0.716373
$549$	−2.30730e9	−0.595116
$550$	1.68484e9	0.431806
$551$	2.01527e9	0.513219
$552$	−9.47618e7	−0.0239799
$553$	2.08837e9	0.525133
$554$	1.57673e9	0.393979
$555$	−2.13081e9	−0.529077
$556$	−2.28708e9	−0.564314
$557$	−7.07163e8	−0.173391	−0.0866955	−	0.996235i	$-0.527631\pi$
$557$	−7.07163e8	−0.173391	−0.0866955	+	0.996235i	$0.527631\pi$
$558$	−3.17589e8	−0.0773830
$559$	6.94226e8	0.168097
$560$	−2.91695e8	−0.0701892
$561$	−5.63916e9	−1.34848
$562$	−1.57972e9	−0.375407
$563$	6.20728e9	1.46596	0.732979	−	0.680251i	$-0.238129\pi$
$563$	6.20728e9	1.46596	0.732979	+	0.680251i	$0.238129\pi$
$564$	−4.27260e8	−0.100280
$565$	5.85835e8	0.136649
$566$	−2.52902e9	−0.586265
$567$	−1.82284e8	−0.0419961
$568$	−4.56297e8	−0.104479
$569$	6.01960e9	1.36986	0.684928	−	0.728611i	$-0.259834\pi$
$569$	6.01960e9	1.36986	0.684928	+	0.728611i	$0.259834\pi$
$570$	2.37354e9	0.536828
$571$	−5.91706e9	−1.33009	−0.665043	−	0.746805i	$-0.731587\pi$
$571$	−5.91706e9	−1.33009	−0.665043	+	0.746805i	$0.731587\pi$
$572$	−8.45645e8	−0.188931
$573$	−3.24984e7	−0.00721641
$574$	1.49058e9	0.328975
$575$	2.40043e8	0.0526565
$576$	1.91103e8	0.0416667
$577$	−7.87031e9	−1.70560	−0.852799	−	0.522240i	$-0.825097\pi$
$577$	−7.87031e9	−1.70560	−0.852799	+	0.522240i	$0.825097\pi$
$578$	−6.36524e9	−1.37110
$579$	2.46403e9	0.527559
$580$	5.05963e8	0.107677
$581$	2.66486e9	0.563713
$582$	−1.71463e9	−0.360528
$583$	1.03271e10	2.15843
$584$	1.83060e9	0.380318
$585$	−3.32531e8	−0.0686731
$586$	−2.09700e9	−0.430483
$587$	−8.08166e8	−0.164918	−0.0824588	−	0.996594i	$-0.526277\pi$
$587$	−8.08166e8	−0.164918	−0.0824588	+	0.996594i	$0.526277\pi$
$588$	−2.03297e8	−0.0412393
$589$	2.88215e9	0.581183
$590$	−4.80164e9	−0.962515
$591$	1.74229e9	0.347189
$592$	1.55692e9	0.308419
$593$	−4.93894e9	−0.972618	−0.486309	−	0.873787i	$-0.661657\pi$
$593$	−4.93894e9	−0.972618	−0.486309	+	0.873787i	$0.661657\pi$
$594$	9.47021e8	0.185399
$595$	−2.47310e9	−0.481318
$596$	−3.44830e8	−0.0667180
$597$	−4.12256e9	−0.792970
$598$	−1.20481e8	−0.0230391
$599$	−5.58028e9	−1.06087	−0.530435	−	0.847726i	$-0.677971\pi$
$599$	−5.58028e9	−1.06087	−0.530435	+	0.847726i	$0.677971\pi$
$600$	−4.84087e8	−0.0914943
$601$	−9.90101e9	−1.86045	−0.930226	−	0.366986i	$-0.880390\pi$
$601$	−9.90101e9	−1.86045	−0.930226	+	0.366986i	$0.880390\pi$
$602$	−8.67071e8	−0.161982
$603$	2.51688e9	0.467469
$604$	−1.47585e9	−0.272529
$605$	3.46387e9	0.635942
$606$	−1.28846e9	−0.235188
$607$	−9.39565e9	−1.70516	−0.852582	−	0.522593i	$-0.824965\pi$
$607$	−9.39565e9	−1.70516	−0.852582	+	0.522593i	$0.824965\pi$
$608$	−1.73428e9	−0.312936
$609$	3.52633e8	0.0632648
$610$	5.25704e9	0.937750
$611$	−5.43224e8	−0.0963462
$612$	1.62024e9	0.285726
$613$	−9.79892e9	−1.71817	−0.859086	−	0.511831i	$-0.828967\pi$
$613$	−9.79892e9	−1.71817	−0.859086	+	0.511831i	$0.828967\pi$
$614$	−8.70166e8	−0.151710
$615$	−3.04515e9	−0.527894
$616$	1.05619e9	0.182058
$617$	−8.61672e9	−1.47688	−0.738438	−	0.674322i	$-0.764436\pi$
$617$	−8.61672e9	−1.47688	−0.738438	+	0.674322i	$0.764436\pi$
$618$	−1.62207e9	−0.276446
$619$	8.64399e9	1.46486	0.732432	−	0.680841i	$-0.238385\pi$
$619$	8.64399e9	1.46486	0.732432	+	0.680841i	$0.238385\pi$
$620$	7.23606e8	0.121936
$621$	1.34925e8	0.0226084
$622$	−3.87633e9	−0.645884
$623$	−7.76537e8	−0.128663
$624$	2.42971e8	0.0400320
$625$	−2.14149e9	−0.350862
$626$	7.24068e9	1.17969
$627$	−8.59430e9	−1.39243
$628$	4.10375e9	0.661183
$629$	1.32002e10	2.11496
$630$	4.15323e8	0.0661750
$631$	1.06371e10	1.68547	0.842733	−	0.538331i	$-0.180945\pi$
$631$	1.06371e10	1.68547	0.842733	+	0.538331i	$0.180945\pi$
$632$	3.11734e9	0.491217
$633$	3.52752e9	0.552785
$634$	2.15818e9	0.336338
$635$	−6.55296e9	−1.01562
$636$	−2.96718e9	−0.457345
$637$	−2.58475e8	−0.0396214
$638$	−1.83203e9	−0.279293
$639$	6.49689e8	0.0985037
$640$	−4.35416e8	−0.0656560
$641$	−1.17937e10	−1.76868	−0.884338	−	0.466848i	$-0.845390\pi$
$641$	−1.17937e10	−1.76868	−0.884338	+	0.466848i	$0.845390\pi$
$642$	1.70470e9	0.254258
$643$	4.33461e9	0.643002	0.321501	−	0.946909i	$-0.395813\pi$
$643$	4.33461e9	0.643002	0.321501	+	0.946909i	$0.395813\pi$
$644$	1.50478e8	0.0222010
$645$	1.77137e9	0.259926
$646$	−1.47039e10	−2.14594
$647$	5.28936e8	0.0767783	0.0383891	−	0.999263i	$-0.487777\pi$
$647$	5.28936e8	0.0767783	0.0383891	+	0.999263i	$0.487777\pi$
$648$	−2.72098e8	−0.0392837
$649$	1.73861e10	2.49659
$650$	−6.15474e8	−0.0879049
$651$	5.04319e8	0.0716427
$652$	6.51628e9	0.920732
$653$	7.35629e8	0.103386	0.0516931	−	0.998663i	$-0.483538\pi$
$653$	7.35629e8	0.103386	0.0516931	+	0.998663i	$0.483538\pi$
$654$	4.65015e9	0.650047
$655$	−5.85990e9	−0.814790
$656$	2.22500e9	0.307728
$657$	−2.60645e9	−0.358568
$658$	6.78473e8	0.0928415
$659$	−8.45209e9	−1.15044	−0.575222	−	0.817998i	$-0.695084\pi$
$659$	−8.45209e9	−1.15044	−0.575222	+	0.817998i	$0.695084\pi$
$660$	−2.15773e9	−0.292141
$661$	−7.19273e9	−0.968698	−0.484349	−	0.874875i	$-0.660943\pi$
$661$	−7.19273e9	−0.968698	−0.484349	+	0.874875i	$0.660943\pi$
$662$	−8.79855e9	−1.17871
$663$	2.06000e9	0.274517
$664$	3.97787e9	0.527305
$665$	−3.76910e9	−0.497006
$666$	−2.21679e9	−0.290780
$667$	−2.61014e8	−0.0340584
$668$	3.99809e9	0.518962
$669$	3.78519e9	0.488760
$670$	−5.73456e9	−0.736611
$671$	−1.90351e10	−2.43235
$672$	−3.03464e8	−0.0385758
$673$	6.51630e9	0.824040	0.412020	−	0.911175i	$-0.364823\pi$
$673$	6.51630e9	0.824040	0.412020	+	0.911175i	$0.364823\pi$
$674$	9.88336e8	0.124336
$675$	6.89257e8	0.0862617
$676$	3.08916e8	0.0384615
$677$	−1.88362e9	−0.233309	−0.116655	−	0.993173i	$-0.537217\pi$
$677$	−1.88362e9	−0.233309	−0.116655	+	0.993173i	$0.537217\pi$
$678$	6.09473e8	0.0751018
$679$	2.72276e9	0.333784
$680$	−3.69162e9	−0.450231
$681$	−1.87038e9	−0.226943
$682$	−2.62009e9	−0.316279
$683$	−5.63688e9	−0.676965	−0.338482	−	0.940973i	$-0.609914\pi$
$683$	−5.63688e9	−0.676965	−0.338482	+	0.940973i	$0.609914\pi$
$684$	2.46931e9	0.295039
$685$	−8.95294e9	−1.06426
$686$	3.22829e8	0.0381802
$687$	−4.66828e9	−0.549298
$688$	−1.29429e9	−0.151520
$689$	−3.77251e9	−0.439403
$690$	−3.07417e8	−0.0356251
$691$	2.25906e9	0.260468	0.130234	−	0.991483i	$-0.458427\pi$
$691$	2.25906e9	0.260468	0.130234	+	0.991483i	$0.458427\pi$
$692$	−4.65237e9	−0.533707
$693$	−1.50383e9	−0.171646
$694$	−4.17304e9	−0.473909
$695$	−7.41954e9	−0.838359
$696$	5.26379e8	0.0591788
$697$	1.88644e10	2.11023
$698$	−1.13769e10	−1.26628
$699$	1.14883e9	0.127229
$700$	7.68713e8	0.0847073
$701$	9.71911e9	1.06565	0.532824	−	0.846226i	$-0.321131\pi$
$701$	9.71911e9	1.06565	0.532824	+	0.846226i	$0.321131\pi$
$702$	−3.45948e8	−0.0377426
$703$	2.01176e10	2.18389
$704$	1.57659e9	0.170300
$705$	−1.38608e9	−0.148979
$706$	5.33540e9	0.570624
$707$	2.04602e9	0.217742
$708$	−4.99538e9	−0.528996
$709$	−2.07035e9	−0.218163	−0.109082	−	0.994033i	$-0.534791\pi$
$709$	−2.07035e9	−0.218163	−0.109082	+	0.994033i	$0.534791\pi$
$710$	−1.48027e9	−0.155217
$711$	−4.43855e9	−0.463124
$712$	−1.15915e9	−0.120353
$713$	−3.73291e8	−0.0385686
$714$	−2.57289e9	−0.264531
$715$	−2.74336e9	−0.280680
$716$	2.42979e9	0.247385
$717$	−1.04581e10	−1.05958
$718$	−9.57925e7	−0.00965820
$719$	1.69928e10	1.70496	0.852478	−	0.522763i	$-0.175099\pi$
$719$	1.69928e10	1.70496	0.852478	+	0.522763i	$0.175099\pi$
$720$	6.19958e8	0.0619011
$721$	2.57579e9	0.255939
$722$	−1.52583e10	−1.50878
$723$	−7.32903e9	−0.721211
$724$	4.01447e9	0.393137
$725$	−1.33338e9	−0.129949
$726$	3.60363e9	0.349512
$727$	1.13993e10	1.10029	0.550146	−	0.835069i	$-0.314572\pi$
$727$	1.13993e10	1.10029	0.550146	+	0.835069i	$0.314572\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	5.93864e9	0.565011
$731$	−1.09735e10	−1.03904
$732$	5.46916e9	0.515385
$733$	7.32894e9	0.687349	0.343675	−	0.939089i	$-0.388328\pi$
$733$	7.32894e9	0.687349	0.343675	+	0.939089i	$0.388328\pi$
$734$	−9.83145e9	−0.917659
$735$	−6.59518e8	−0.0612662
$736$	2.24621e8	0.0207672
$737$	2.07641e10	1.91063
$738$	−3.16802e9	−0.290129
$739$	7.60945e9	0.693582	0.346791	−	0.937942i	$-0.387271\pi$
$739$	7.60945e9	0.693582	0.346791	+	0.937942i	$0.387271\pi$
$740$	5.05081e9	0.458195
$741$	3.13951e9	0.283465
$742$	4.71178e9	0.423420
$743$	9.49392e9	0.849151	0.424575	−	0.905393i	$-0.360423\pi$
$743$	9.49392e9	0.849151	0.424575	+	0.905393i	$0.360423\pi$
$744$	7.52803e8	0.0670156
$745$	−1.11866e9	−0.0991180
$746$	−8.01898e8	−0.0707186
$747$	−5.66380e9	−0.497148
$748$	1.33669e10	1.16782
$749$	−2.70700e9	−0.235397
$750$	−5.07406e9	−0.439178
$751$	−4.49759e8	−0.0387472	−0.0193736	−	0.999812i	$-0.506167\pi$
$751$	−4.49759e8	−0.0387472	−0.0193736	+	0.999812i	$0.506167\pi$
$752$	1.01276e9	0.0868453
$753$	7.93948e9	0.677656
$754$	6.69244e8	0.0568571
$755$	−4.78781e9	−0.404876
$756$	4.32081e8	0.0363696
$757$	1.41944e10	1.18927	0.594636	−	0.803995i	$-0.297296\pi$
$757$	1.41944e10	1.18927	0.594636	+	0.803995i	$0.297296\pi$
$758$	2.07059e9	0.172684
$759$	1.11312e9	0.0924050
$760$	−5.62617e9	−0.464906
$761$	6.81336e9	0.560422	0.280211	−	0.959939i	$-0.409596\pi$
$761$	6.81336e9	0.560422	0.280211	+	0.959939i	$0.409596\pi$
$762$	−6.81737e9	−0.558180
$763$	−7.38427e9	−0.601827
$764$	7.70333e7	0.00624959
$765$	5.25623e9	0.424482
$766$	−1.19711e9	−0.0962347
$767$	−6.35119e9	−0.508243
$768$	−4.52985e8	−0.0360844
$769$	−2.17198e10	−1.72232	−0.861159	−	0.508336i	$-0.830261\pi$
$769$	−2.17198e10	−1.72232	−0.861159	+	0.508336i	$0.830261\pi$
$770$	3.42639e9	0.270470
$771$	3.34488e9	0.262840
$772$	−5.84067e9	−0.456880
$773$	−1.70914e10	−1.33091	−0.665456	−	0.746437i	$-0.731763\pi$
$773$	−1.70914e10	−1.33091	−0.665456	+	0.746437i	$0.731763\pi$
$774$	1.84284e9	0.142855
$775$	−1.90694e9	−0.147157
$776$	4.06430e9	0.312226
$777$	3.52018e9	0.269210
$778$	5.36278e9	0.408283
$779$	2.87501e10	2.17901
$780$	7.88222e8	0.0594726
$781$	5.35989e9	0.402603
$782$	1.90442e9	0.142409
$783$	−7.49473e8	−0.0557943
$784$	4.81890e8	0.0357143
$785$	1.33130e10	0.982271
$786$	−6.09634e9	−0.447807
$787$	−1.04002e10	−0.760556	−0.380278	−	0.924872i	$-0.624172\pi$
$787$	−1.04002e10	−0.760556	−0.380278	+	0.924872i	$0.624172\pi$
$788$	−4.12988e9	−0.300674
$789$	4.63770e8	0.0336150
$790$	1.01130e10	0.729765
$791$	−9.67821e8	−0.0695308
$792$	−2.24479e9	−0.160560
$793$	6.95356e9	0.495166
$794$	−1.87259e10	−1.32761
$795$	−9.62584e9	−0.679444
$796$	9.77200e9	0.686732
$797$	2.52208e10	1.76463	0.882317	−	0.470655i	$-0.155982\pi$
$797$	2.52208e10	1.76463	0.882317	+	0.470655i	$0.155982\pi$
$798$	−3.92118e9	−0.273153
$799$	8.58660e9	0.595535
$800$	1.14747e9	0.0792364
$801$	1.65042e9	0.113470
$802$	1.30464e10	0.893061
$803$	−2.15031e10	−1.46554
$804$	−5.96595e9	−0.404840
$805$	4.88167e8	0.0329824
$806$	9.57123e8	0.0643865
$807$	1.85291e9	0.124107
$808$	3.05412e9	0.203679
$809$	−7.89147e9	−0.524008	−0.262004	−	0.965067i	$-0.584383\pi$
$809$	−7.89147e9	−0.524008	−0.262004	+	0.965067i	$0.584383\pi$
$810$	−8.82713e8	−0.0583609
$811$	1.94161e10	1.27817	0.639084	−	0.769137i	$-0.279313\pi$
$811$	1.94161e10	1.27817	0.639084	+	0.769137i	$0.279313\pi$
$812$	−8.35870e8	−0.0547889
$813$	9.26962e9	0.604986
$814$	−1.82884e10	−1.18847
$815$	2.11395e10	1.36786
$816$	−3.84058e9	−0.247446
$817$	−1.67240e10	−1.07291
$818$	6.20360e8	0.0396284
$819$	5.49353e8	0.0349428
$820$	7.21814e9	0.457169
$821$	1.61394e9	0.101785	0.0508927	−	0.998704i	$-0.483793\pi$
$821$	1.61394e9	0.101785	0.0508927	+	0.998704i	$0.483793\pi$
$822$	−9.31418e9	−0.584916
$823$	1.12066e10	0.700765	0.350383	−	0.936607i	$-0.386052\pi$
$823$	1.12066e10	0.700765	0.350383	+	0.936607i	$0.386052\pi$
$824$	3.84491e9	0.239409
$825$	5.68633e9	0.352568
$826$	7.93248e9	0.489755
$827$	2.13726e10	1.31398	0.656988	−	0.753901i	$-0.271830\pi$
$827$	2.13726e10	1.31398	0.656988	+	0.753901i	$0.271830\pi$
$828$	−3.19821e8	−0.0195795
$829$	1.28193e10	0.781490	0.390745	−	0.920499i	$-0.372217\pi$
$829$	1.28193e10	0.781490	0.390745	+	0.920499i	$0.372217\pi$
$830$	1.29046e10	0.783378
$831$	5.32147e9	0.321683
$832$	−5.75930e8	−0.0346688
$833$	4.08565e9	0.244908
$834$	−7.71891e9	−0.460760
$835$	1.29702e10	0.770983
$836$	2.03717e10	1.20588
$837$	−1.07186e9	−0.0631829
$838$	−8.19542e9	−0.481080
$839$	−2.08260e10	−1.21742	−0.608708	−	0.793394i	$-0.708312\pi$
$839$	−2.08260e10	−1.21742	−0.608708	+	0.793394i	$0.708312\pi$
$840$	−9.84470e8	−0.0573093
$841$	−1.58000e10	−0.915949
$842$	−5.14262e9	−0.296888
$843$	−5.33154e9	−0.306518
$844$	−8.36153e9	−0.478726
$845$	1.00215e9	0.0571395
$846$	−1.44200e9	−0.0818785
$847$	−5.72244e9	−0.323586
$848$	7.03332e9	0.396073
$849$	−8.53543e9	−0.478684
$850$	9.72865e9	0.543358
$851$	−2.60559e9	−0.144928
$852$	−1.54000e9	−0.0853067
$853$	2.59066e10	1.42918	0.714592	−	0.699542i	$-0.246612\pi$
$853$	2.59066e10	1.42918	0.714592	+	0.699542i	$0.246612\pi$
$854$	−8.68483e9	−0.477154
$855$	8.01070e9	0.438318
$856$	−4.04077e9	−0.220194
$857$	2.59753e9	0.140970	0.0704852	−	0.997513i	$-0.477545\pi$
$857$	2.59753e9	0.140970	0.0704852	+	0.997513i	$0.477545\pi$
$858$	−2.85405e9	−0.154261
$859$	7.29241e9	0.392550	0.196275	−	0.980549i	$-0.437115\pi$
$859$	7.29241e9	0.392550	0.196275	+	0.980549i	$0.437115\pi$
$860$	−4.19880e9	−0.225103
$861$	5.03071e9	0.268607
$862$	−2.09590e9	−0.111454
$863$	−8.48875e9	−0.449579	−0.224789	−	0.974407i	$-0.572169\pi$
$863$	−8.48875e9	−0.449579	−0.224789	+	0.974407i	$0.572169\pi$
$864$	6.44973e8	0.0340207
$865$	−1.50928e10	−0.792888
$866$	2.20157e10	1.15191
$867$	−2.14827e10	−1.11949
$868$	−1.19542e9	−0.0620444
$869$	−3.66178e10	−1.89288
$870$	1.70763e9	0.0879175
$871$	−7.58517e9	−0.388957
$872$	−1.10226e10	−0.562957
$873$	−5.78686e9	−0.294370
$874$	2.90241e9	0.147051
$875$	8.05742e9	0.406600
$876$	6.17826e9	0.310529
$877$	−1.55916e10	−0.780534	−0.390267	−	0.920702i	$-0.627617\pi$
$877$	−1.55916e10	−0.780534	−0.390267	+	0.920702i	$0.627617\pi$
$878$	−1.71032e10	−0.852800
$879$	−7.07736e9	−0.351488
$880$	5.11461e9	0.253002
$881$	5.07568e9	0.250080	0.125040	−	0.992152i	$-0.460094\pi$
$881$	5.07568e9	0.250080	0.125040	+	0.992152i	$0.460094\pi$
$882$	−6.86129e8	−0.0336718
$883$	3.05160e9	0.149164	0.0745821	−	0.997215i	$-0.476238\pi$
$883$	3.05160e9	0.149164	0.0745821	+	0.997215i	$0.476238\pi$
$884$	−4.88295e9	−0.237739
$885$	−1.62055e10	−0.785890
$886$	−1.54239e10	−0.745035
$887$	−2.17073e10	−1.04442	−0.522208	−	0.852818i	$-0.674892\pi$
$887$	−2.17073e10	−1.04442	−0.522208	+	0.852818i	$0.674892\pi$
$888$	5.25461e9	0.251823
$889$	1.08257e10	0.516774
$890$	−3.76039e9	−0.178800
$891$	3.19620e9	0.151378
$892$	−8.97229e9	−0.423279
$893$	1.30863e10	0.614946
$894$	−1.16380e9	−0.0544750
$895$	7.88248e9	0.367521
$896$	7.19323e8	0.0334077
$897$	−4.06624e8	−0.0188114
$898$	2.27620e10	1.04892
$899$	2.07354e9	0.0951817
$900$	−1.63379e9	−0.0747048
$901$	5.96311e10	2.71604
$902$	−2.61360e10	−1.18581
$903$	−2.92636e9	−0.132258
$904$	−1.44468e9	−0.0650401
$905$	1.30234e10	0.584054
$906$	−4.98100e9	−0.222519
$907$	−3.62371e10	−1.61261	−0.806303	−	0.591503i	$-0.798535\pi$
$907$	−3.62371e10	−1.61261	−0.806303	+	0.591503i	$0.798535\pi$
$908$	4.43350e9	0.196538
$909$	−4.34854e9	−0.192030
$910$	−1.25167e9	−0.0550610
$911$	−6.74898e9	−0.295749	−0.147875	−	0.989006i	$-0.547243\pi$
$911$	−6.74898e9	−0.295749	−0.147875	+	0.989006i	$0.547243\pi$
$912$	−5.85319e9	−0.255511
$913$	−4.67260e10	−2.03194
$914$	9.13912e9	0.395906
$915$	1.77425e10	0.765670
$916$	1.10656e10	0.475706
$917$	9.68076e9	0.414588
$918$	5.46832e9	0.233294
$919$	2.08819e10	0.887495	0.443748	−	0.896152i	$-0.353649\pi$
$919$	2.08819e10	0.887495	0.443748	+	0.896152i	$0.353649\pi$
$920$	7.28692e8	0.0308522
$921$	−2.93681e9	−0.123870
$922$	−1.45132e10	−0.609823
$923$	−1.95798e9	−0.0819600
$924$	3.56464e9	0.148650
$925$	−1.33106e10	−0.552968
$926$	−2.20293e10	−0.911720
$927$	−5.47449e9	−0.225717
$928$	−1.24771e9	−0.0512503
$929$	3.30579e10	1.35276	0.676379	−	0.736554i	$-0.263548\pi$
$929$	3.30579e10	1.35276	0.676379	+	0.736554i	$0.263548\pi$
$930$	2.44217e9	0.0995602
$931$	6.22669e9	0.252891
$932$	−2.72315e9	−0.110183
$933$	−1.30826e10	−0.527362
$934$	1.44388e10	0.579850
$935$	4.33636e10	1.73494
$936$	8.20026e8	0.0326860
$937$	−1.14567e10	−0.454958	−0.227479	−	0.973783i	$-0.573048\pi$
$937$	−1.14567e10	−0.454958	−0.227479	+	0.973783i	$0.573048\pi$
$938$	9.47370e9	0.374809
$939$	2.44373e10	0.963216
$940$	3.28551e9	0.129020
$941$	3.23385e10	1.26519	0.632595	−	0.774483i	$-0.281990\pi$
$941$	3.23385e10	1.26519	0.632595	+	0.774483i	$0.281990\pi$
$942$	1.38501e10	0.539854
$943$	−3.72367e9	−0.144604
$944$	1.18409e10	0.458124
$945$	1.40172e9	0.0540317
$946$	1.52033e10	0.583875
$947$	−1.66823e10	−0.638308	−0.319154	−	0.947703i	$-0.603399\pi$
$947$	−1.66823e10	−0.638308	−0.319154	+	0.947703i	$0.603399\pi$
$948$	1.05210e10	0.401077
$949$	7.85511e9	0.298346
$950$	1.48268e10	0.561069
$951$	7.28387e9	0.274619
$952$	6.09869e9	0.229091
$953$	−8.32406e9	−0.311537	−0.155769	−	0.987794i	$-0.549785\pi$
$953$	−8.32406e9	−0.311537	−0.155769	+	0.987794i	$0.549785\pi$
$954$	−1.00142e10	−0.373421
$955$	2.49904e8	0.00928456
$956$	2.47895e10	0.917626
$957$	−6.18310e9	−0.228042
$958$	2.54857e9	0.0936520
$959$	1.47906e10	0.541527
$960$	−1.46953e9	−0.0536079
$961$	−2.45471e10	−0.892214
$962$	6.68077e9	0.241943
$963$	5.75336e9	0.207601
$964$	1.73725e10	0.624587
$965$	−1.89477e10	−0.678752
$966$	5.07864e8	0.0181271
$967$	7.54962e9	0.268493	0.134246	−	0.990948i	$-0.457139\pi$
$967$	7.54962e9	0.268493	0.134246	+	0.990948i	$0.457139\pi$
$968$	−8.54195e9	−0.302687
$969$	−4.96255e10	−1.75215
$970$	1.31850e10	0.463851
$971$	3.33532e10	1.16915	0.584576	−	0.811339i	$-0.301261\pi$
$971$	3.33532e10	1.16915	0.584576	+	0.811339i	$0.301261\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.22573e10	0.426581
$974$	−1.82975e10	−0.634507
$975$	−2.07723e9	−0.0717741
$976$	−1.29639e10	−0.446337
$977$	2.93235e8	0.0100597	0.00502985	−	0.999987i	$-0.498399\pi$
$977$	2.93235e8	0.0100597	0.00502985	+	0.999987i	$0.498399\pi$
$978$	2.19924e10	0.751774
$979$	1.36159e10	0.463775
$980$	1.56330e9	0.0530581
$981$	1.56943e10	0.530761
$982$	1.85925e10	0.626540
$983$	7.58465e9	0.254682	0.127341	−	0.991859i	$-0.459356\pi$
$983$	7.58465e9	0.254682	0.127341	+	0.991859i	$0.459356\pi$
$984$	7.50939e9	0.251259
$985$	−1.33978e10	−0.446689
$986$	−1.05786e10	−0.351445
$987$	2.28985e9	0.0758048
$988$	−7.44181e9	−0.245488
$989$	2.16606e9	0.0712005
$990$	−7.28233e9	−0.238532
$991$	3.08473e10	1.00684	0.503419	−	0.864042i	$-0.332075\pi$
$991$	3.08473e10	1.00684	0.503419	+	0.864042i	$0.332075\pi$
$992$	−1.78442e9	−0.0580372
$993$	−2.96951e10	−0.962415
$994$	2.44547e9	0.0789786
$995$	3.17014e10	1.02023
$996$	1.34253e10	0.430543
$997$	−8.74206e9	−0.279371	−0.139685	−	0.990196i	$-0.544609\pi$
$997$	−8.74206e9	−0.279371	−0.139685	+	0.990196i	$0.544609\pi$
$998$	−6.83044e9	−0.217516
$999$	−7.48166e9	−0.237421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.o.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.o.1.5	✓	6	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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +207.623 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +207.623 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -1660.98 q^{10} +6014.21 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -5605.81 q^{15} +4096.00 q^{16} +34727.4 q^{17} -5832.00 q^{18} +52926.0 q^{19} +13287.8 q^{20} +9261.00 q^{21} -48113.6 q^{22} -6854.88 q^{23} +13824.0 q^{24} -35017.9 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +38077.2 q^{29} +44846.5 q^{30} +54456.2 q^{31} -32768.0 q^{32} -162384. q^{33} -277819. q^{34} -71214.5 q^{35} +46656.0 q^{36} +380108. q^{37} -423408. q^{38} +59319.0 q^{39} -106303. q^{40} +543214. q^{41} -74088.0 q^{42} -315988. q^{43} +384909. q^{44} +151357. q^{45} +54839.0 q^{46} +247257. q^{47} -110592. q^{48} +117649. q^{49} +280143. q^{50} -937641. q^{51} -140608. q^{52} +1.71712e6 q^{53} +157464. q^{54} +1.24868e6 q^{55} +175616. q^{56} -1.42900e6 q^{57} -304617. q^{58} +2.89085e6 q^{59} -358772. q^{60} -3.16503e6 q^{61} -435650. q^{62} -250047. q^{63} +262144. q^{64} -456147. q^{65} +1.29907e6 q^{66} +3.45251e6 q^{67} +2.22256e6 q^{68} +185082. q^{69} +569716. q^{70} +891205. q^{71} -373248. q^{72} -3.57538e6 q^{73} -3.04086e6 q^{74} +945483. q^{75} +3.38726e6 q^{76} -2.06287e6 q^{77} -474552. q^{78} -6.08855e6 q^{79} +850422. q^{80} +531441. q^{81} -4.34571e6 q^{82} -7.76927e6 q^{83} +592704. q^{84} +7.21020e6 q^{85} +2.52790e6 q^{86} -1.02808e6 q^{87} -3.07927e6 q^{88} +2.26396e6 q^{89} -1.21085e6 q^{90} +753571. q^{91} -438712. q^{92} -1.47032e6 q^{93} -1.97806e6 q^{94} +1.09886e7 q^{95} +884736. q^{96} -7.93808e6 q^{97} -941192. q^{98} +4.38436e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 35 q^{5} + 1296 q^{6} - 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 35 * q^5 + 1296 * q^6 - 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 35 q^{5} + 1296 q^{6} - 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 280 q^{10} + 5606 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} + 945 q^{15} + 24576 q^{16} + 22022 q^{17} - 34992 q^{18} - 5779 q^{19} - 2240 q^{20} + 55566 q^{21} - 44848 q^{22} - 110789 q^{23} + 82944 q^{24} + 91769 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} + 30693 q^{29} - 7560 q^{30} + 180467 q^{31} - 196608 q^{32} - 151362 q^{33} - 176176 q^{34} + 12005 q^{35} + 279936 q^{36} - 322222 q^{37} + 46232 q^{38} + 355914 q^{39} + 17920 q^{40} - 212652 q^{41} - 444528 q^{42} - 329299 q^{43} + 358784 q^{44} - 25515 q^{45} + 886312 q^{46} + 1322861 q^{47} - 663552 q^{48} + 705894 q^{49} - 734152 q^{50} - 594594 q^{51} - 843648 q^{52} - 168719 q^{53} + 944784 q^{54} - 2252362 q^{55} + 1053696 q^{56} + 156033 q^{57} - 245544 q^{58} + 1943712 q^{59} + 60480 q^{60} - 1085922 q^{61} - 1443736 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 76895 q^{65} + 1210896 q^{66} + 885066 q^{67} + 1409408 q^{68} + 2991303 q^{69} - 96040 q^{70} + 1626164 q^{71} - 2239488 q^{72} - 4750115 q^{73} + 2577776 q^{74} - 2477763 q^{75} - 369856 q^{76} - 1922858 q^{77} - 2847312 q^{78} + 1794289 q^{79} - 143360 q^{80} + 3188646 q^{81} + 1701216 q^{82} - 8454255 q^{83} + 3556224 q^{84} - 18529504 q^{85} + 2634392 q^{86} - 828711 q^{87} - 2870272 q^{88} - 6055411 q^{89} + 204120 q^{90} + 4521426 q^{91} - 7090496 q^{92} - 4872609 q^{93} - 10582888 q^{94} - 3766747 q^{95} + 5308416 q^{96} - 9823899 q^{97} - 5647152 q^{98} + 4086774 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 35 * q^5 + 1296 * q^6 - 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 280 * q^10 + 5606 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 + 945 * q^15 + 24576 * q^16 + 22022 * q^17 - 34992 * q^18 - 5779 * q^19 - 2240 * q^20 + 55566 * q^21 - 44848 * q^22 - 110789 * q^23 + 82944 * q^24 + 91769 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 + 30693 * q^29 - 7560 * q^30 + 180467 * q^31 - 196608 * q^32 - 151362 * q^33 - 176176 * q^34 + 12005 * q^35 + 279936 * q^36 - 322222 * q^37 + 46232 * q^38 + 355914 * q^39 + 17920 * q^40 - 212652 * q^41 - 444528 * q^42 - 329299 * q^43 + 358784 * q^44 - 25515 * q^45 + 886312 * q^46 + 1322861 * q^47 - 663552 * q^48 + 705894 * q^49 - 734152 * q^50 - 594594 * q^51 - 843648 * q^52 - 168719 * q^53 + 944784 * q^54 - 2252362 * q^55 + 1053696 * q^56 + 156033 * q^57 - 245544 * q^58 + 1943712 * q^59 + 60480 * q^60 - 1085922 * q^61 - 1443736 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 76895 * q^65 + 1210896 * q^66 + 885066 * q^67 + 1409408 * q^68 + 2991303 * q^69 - 96040 * q^70 + 1626164 * q^71 - 2239488 * q^72 - 4750115 * q^73 + 2577776 * q^74 - 2477763 * q^75 - 369856 * q^76 - 1922858 * q^77 - 2847312 * q^78 + 1794289 * q^79 - 143360 * q^80 + 3188646 * q^81 + 1701216 * q^82 - 8454255 * q^83 + 3556224 * q^84 - 18529504 * q^85 + 2634392 * q^86 - 828711 * q^87 - 2870272 * q^88 - 6055411 * q^89 + 204120 * q^90 + 4521426 * q^91 - 7090496 * q^92 - 4872609 * q^93 - 10582888 * q^94 - 3766747 * q^95 + 5308416 * q^96 - 9823899 * q^97 - 5647152 * q^98 + 4086774 * q^99

Introduction

L-functions

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