LMFDB - Embedded newform 546.8.a.n.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} - 309949x^{4} - 14548431x^{3} + 25221499020x^{2} + 1862570808000x - 308009568384000 $ x^6 - x^5 - 309949x^4 - 14548431x^3 + 25221499020x^2 + 1862570808000x - 308009568384000
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-309.836$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +279.836 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +279.836 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -2238.69 q^{10} +2560.01 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -7555.57 q^{15} +4096.00 q^{16} +28146.9 q^{17} -5832.00 q^{18} -39913.7 q^{19} +17909.5 q^{20} -9261.00 q^{21} -20480.0 q^{22} +92990.7 q^{23} +13824.0 q^{24} +183.186 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} -46635.8 q^{29} +60444.6 q^{30} +17816.9 q^{31} -32768.0 q^{32} -69120.1 q^{33} -225176. q^{34} +95983.7 q^{35} +46656.0 q^{36} +174128. q^{37} +319310. q^{38} -59319.0 q^{39} -143276. q^{40} +298372. q^{41} +74088.0 q^{42} +401578. q^{43} +163840. q^{44} +204000. q^{45} -743925. q^{46} +1.14534e6 q^{47} -110592. q^{48} +117649. q^{49} -1465.49 q^{50} -759967. q^{51} +140608. q^{52} +513232. q^{53} +157464. q^{54} +716382. q^{55} -175616. q^{56} +1.07767e6 q^{57} +373086. q^{58} -771678. q^{59} -483557. q^{60} -662661. q^{61} -142535. q^{62} +250047. q^{63} +262144. q^{64} +614800. q^{65} +552961. q^{66} -1.81101e6 q^{67} +1.80140e6 q^{68} -2.51075e6 q^{69} -767870. q^{70} +4.08717e6 q^{71} -373248. q^{72} +3.10343e6 q^{73} -1.39302e6 q^{74} -4946.02 q^{75} -2.55448e6 q^{76} +878082. q^{77} +474552. q^{78} +2.56597e6 q^{79} +1.14621e6 q^{80} +531441. q^{81} -2.38698e6 q^{82} -3.71429e6 q^{83} -592704. q^{84} +7.87653e6 q^{85} -3.21263e6 q^{86} +1.25917e6 q^{87} -1.31072e6 q^{88} -6.74927e6 q^{89} -1.63200e6 q^{90} +753571. q^{91} +5.95140e6 q^{92} -481055. q^{93} -9.16271e6 q^{94} -1.11693e7 q^{95} +884736. q^{96} -3.02051e6 q^{97} -941192. q^{98} +1.86624e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 181 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 - 181 * q^5 + 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 181 q^{5} + 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 1448 q^{10} - 6130 q^{11} - 10368 q^{12} + 13182 q^{13} - 16464 q^{14} + 4887 q^{15} + 24576 q^{16} - 34610 q^{17} - 34992 q^{18} - 4085 q^{19} - 11584 q^{20} - 55566 q^{21} + 49040 q^{22} + 1515 q^{23} + 82944 q^{24} + 156609 q^{25} - 105456 q^{26} - 118098 q^{27} + 131712 q^{28} - 59395 q^{29} - 39096 q^{30} + 478241 q^{31} - 196608 q^{32} + 165510 q^{33} + 276880 q^{34} - 62083 q^{35} + 279936 q^{36} + 574310 q^{37} + 32680 q^{38} - 355914 q^{39} + 92672 q^{40} + 201552 q^{41} + 444528 q^{42} + 728605 q^{43} - 392320 q^{44} - 131949 q^{45} - 12120 q^{46} + 227615 q^{47} - 663552 q^{48} + 705894 q^{49} - 1252872 q^{50} + 934470 q^{51} + 843648 q^{52} + 26321 q^{53} + 944784 q^{54} + 2115010 q^{55} - 1053696 q^{56} + 110295 q^{57} + 475160 q^{58} + 478280 q^{59} + 312768 q^{60} - 501406 q^{61} - 3825928 q^{62} + 1500282 q^{63} + 1572864 q^{64} - 397657 q^{65} - 1324080 q^{66} - 3156366 q^{67} - 2215040 q^{68} - 40905 q^{69} + 496664 q^{70} - 2003644 q^{71} - 2239488 q^{72} + 3659111 q^{73} - 4594480 q^{74} - 4228443 q^{75} - 261440 q^{76} - 2102590 q^{77} + 2847312 q^{78} + 1131065 q^{79} - 741376 q^{80} + 3188646 q^{81} - 1612416 q^{82} - 9629297 q^{83} - 3556224 q^{84} + 895068 q^{85} - 5828840 q^{86} + 1603665 q^{87} + 3138560 q^{88} - 21977377 q^{89} + 1055592 q^{90} + 4521426 q^{91} + 96960 q^{92} - 12912507 q^{93} - 1820920 q^{94} - 19325507 q^{95} + 5308416 q^{96} - 26386649 q^{97} - 5647152 q^{98} - 4468770 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 181 * q^5 + 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 1448 * q^10 - 6130 * q^11 - 10368 * q^12 + 13182 * q^13 - 16464 * q^14 + 4887 * q^15 + 24576 * q^16 - 34610 * q^17 - 34992 * q^18 - 4085 * q^19 - 11584 * q^20 - 55566 * q^21 + 49040 * q^22 + 1515 * q^23 + 82944 * q^24 + 156609 * q^25 - 105456 * q^26 - 118098 * q^27 + 131712 * q^28 - 59395 * q^29 - 39096 * q^30 + 478241 * q^31 - 196608 * q^32 + 165510 * q^33 + 276880 * q^34 - 62083 * q^35 + 279936 * q^36 + 574310 * q^37 + 32680 * q^38 - 355914 * q^39 + 92672 * q^40 + 201552 * q^41 + 444528 * q^42 + 728605 * q^43 - 392320 * q^44 - 131949 * q^45 - 12120 * q^46 + 227615 * q^47 - 663552 * q^48 + 705894 * q^49 - 1252872 * q^50 + 934470 * q^51 + 843648 * q^52 + 26321 * q^53 + 944784 * q^54 + 2115010 * q^55 - 1053696 * q^56 + 110295 * q^57 + 475160 * q^58 + 478280 * q^59 + 312768 * q^60 - 501406 * q^61 - 3825928 * q^62 + 1500282 * q^63 + 1572864 * q^64 - 397657 * q^65 - 1324080 * q^66 - 3156366 * q^67 - 2215040 * q^68 - 40905 * q^69 + 496664 * q^70 - 2003644 * q^71 - 2239488 * q^72 + 3659111 * q^73 - 4594480 * q^74 - 4228443 * q^75 - 261440 * q^76 - 2102590 * q^77 + 2847312 * q^78 + 1131065 * q^79 - 741376 * q^80 + 3188646 * q^81 - 1612416 * q^82 - 9629297 * q^83 - 3556224 * q^84 + 895068 * q^85 - 5828840 * q^86 + 1603665 * q^87 + 3138560 * q^88 - 21977377 * q^89 + 1055592 * q^90 + 4521426 * q^91 + 96960 * q^92 - 12912507 * q^93 - 1820920 * q^94 - 19325507 * q^95 + 5308416 * q^96 - 26386649 * q^97 - 5647152 * q^98 - 4468770 * 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
$5$	279.836	1.00117	0.500586	−	0.865687i	$-0.333118\pi$
$5$	279.836	1.00117	0.500586	+	0.865687i	$0.333118\pi$
$6$	216.000	0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−2238.69	−0.707935
$11$	2560.01	0.579918	0.289959	−	0.957039i	$-0.406358\pi$
$11$	2560.01	0.579918	0.289959	+	0.957039i	$0.406358\pi$
$12$	−1728.00	−0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−2744.00	−0.267261
$15$	−7555.57	−0.578027
$16$	4096.00	0.250000
$17$	28146.9	1.38950	0.694752	−	0.719249i	$-0.255514\pi$
$17$	28146.9	1.38950	0.694752	+	0.719249i	$0.255514\pi$
$18$	−5832.00	−0.235702
$19$	−39913.7	−1.33501	−0.667505	−	0.744605i	$-0.732638\pi$
$19$	−39913.7	−1.33501	−0.667505	+	0.744605i	$0.732638\pi$
$20$	17909.5	0.500586
$21$	−9261.00	−0.218218
$22$	−20480.0	−0.410064
$23$	92990.7	1.59365	0.796823	−	0.604213i	$-0.206512\pi$
$23$	92990.7	1.59365	0.796823	+	0.604213i	$0.206512\pi$
$24$	13824.0	0.204124
$25$	183.186	0.00234478
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	21952.0	0.188982
$29$	−46635.8	−0.355080	−0.177540	−	0.984114i	$-0.556814\pi$
$29$	−46635.8	−0.355080	−0.177540	+	0.984114i	$0.556814\pi$
$30$	60444.6	0.408727
$31$	17816.9	0.107415	0.0537076	−	0.998557i	$-0.482896\pi$
$31$	17816.9	0.107415	0.0537076	+	0.998557i	$0.482896\pi$
$32$	−32768.0	−0.176777
$33$	−69120.1	−0.334816
$34$	−225176.	−0.982528
$35$	95983.7	0.378407
$36$	46656.0	0.166667
$37$	174128.	0.565148	0.282574	−	0.959245i	$-0.408812\pi$
$37$	174128.	0.565148	0.282574	+	0.959245i	$0.408812\pi$
$38$	319310.	0.943994
$39$	−59319.0	−0.160128
$40$	−143276.	−0.353968
$41$	298372.	0.676105	0.338053	−	0.941127i	$-0.390232\pi$
$41$	298372.	0.676105	0.338053	+	0.941127i	$0.390232\pi$
$42$	74088.0	0.154303
$43$	401578.	0.770248	0.385124	−	0.922865i	$-0.374159\pi$
$43$	401578.	0.770248	0.385124	+	0.922865i	$0.374159\pi$
$44$	163840.	0.289959
$45$	204000.	0.333724
$46$	−743925.	−1.12688
$47$	1.14534e6	1.60913	0.804565	−	0.593864i	$-0.202398\pi$
$47$	1.14534e6	1.60913	0.804565	+	0.593864i	$0.202398\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	−1465.49	−0.00165801
$51$	−759967.	−0.802231
$52$	140608.	0.138675
$53$	513232.	0.473531	0.236765	−	0.971567i	$-0.423913\pi$
$53$	513232.	0.473531	0.236765	+	0.971567i	$0.423913\pi$
$54$	157464.	0.136083
$55$	716382.	0.580597
$56$	−175616.	−0.133631
$57$	1.07767e6	0.770768
$58$	373086.	0.251080
$59$	−771678.	−0.489164	−0.244582	−	0.969629i	$-0.578651\pi$
$59$	−771678.	−0.489164	−0.244582	+	0.969629i	$0.578651\pi$
$60$	−483557.	−0.289013
$61$	−662661.	−0.373798	−0.186899	−	0.982379i	$-0.559844\pi$
$61$	−662661.	−0.373798	−0.186899	+	0.982379i	$0.559844\pi$
$62$	−142535.	−0.0759540
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	614800.	0.277675
$66$	552961.	0.236750
$67$	−1.81101e6	−0.735631	−0.367815	−	0.929899i	$-0.619894\pi$
$67$	−1.81101e6	−0.735631	−0.367815	+	0.929899i	$0.619894\pi$
$68$	1.80140e6	0.694752
$69$	−2.51075e6	−0.920092
$70$	−767870.	−0.267574
$71$	4.08717e6	1.35525	0.677624	−	0.735409i	$-0.263010\pi$
$71$	4.08717e6	1.35525	0.677624	+	0.735409i	$0.263010\pi$
$72$	−373248.	−0.117851
$73$	3.10343e6	0.933711	0.466856	−	0.884334i	$-0.345387\pi$
$73$	3.10343e6	0.933711	0.466856	+	0.884334i	$0.345387\pi$
$74$	−1.39302e6	−0.399620
$75$	−4946.02	−0.00135376
$76$	−2.55448e6	−0.667505
$77$	878082.	0.219188
$78$	474552.	0.113228
$79$	2.56597e6	0.585540	0.292770	−	0.956183i	$-0.405423\pi$
$79$	2.56597e6	0.585540	0.292770	+	0.956183i	$0.405423\pi$
$80$	1.14621e6	0.250293
$81$	531441.	0.111111
$82$	−2.38698e6	−0.478079
$83$	−3.71429e6	−0.713022	−0.356511	−	0.934291i	$-0.616034\pi$
$83$	−3.71429e6	−0.713022	−0.356511	+	0.934291i	$0.616034\pi$
$84$	−592704.	−0.109109
$85$	7.87653e6	1.39113
$86$	−3.21263e6	−0.544648
$87$	1.25917e6	0.205006
$88$	−1.31072e6	−0.205032
$89$	−6.74927e6	−1.01483	−0.507414	−	0.861703i	$-0.669398\pi$
$89$	−6.74927e6	−1.01483	−0.507414	+	0.861703i	$0.669398\pi$
$90$	−1.63200e6	−0.235978
$91$	753571.	0.104828
$92$	5.95140e6	0.796823
$93$	−481055.	−0.0620161
$94$	−9.16271e6	−1.13783
$95$	−1.11693e7	−1.33657
$96$	884736.	0.102062
$97$	−3.02051e6	−0.336031	−0.168015	−	0.985784i	$-0.553736\pi$
$97$	−3.02051e6	−0.336031	−0.168015	+	0.985784i	$0.553736\pi$
$98$	−941192.	−0.101015
$99$	1.86624e6	0.193306
$100$	11723.9	0.00117239
$101$	−1.48941e7	−1.43844	−0.719218	−	0.694784i	$-0.755500\pi$
$101$	−1.48941e7	−1.43844	−0.719218	+	0.694784i	$0.755500\pi$
$102$	6.07974e6	0.567263
$103$	8.09003e6	0.729491	0.364745	−	0.931107i	$-0.381156\pi$
$103$	8.09003e6	0.729491	0.364745	+	0.931107i	$0.381156\pi$
$104$	−1.12486e6	−0.0980581
$105$	−2.59156e6	−0.218474
$106$	−4.10586e6	−0.334837
$107$	−1.51959e7	−1.19918	−0.599589	−	0.800308i	$-0.704669\pi$
$107$	−1.51959e7	−1.19918	−0.599589	+	0.800308i	$0.704669\pi$
$108$	−1.25971e6	−0.0962250
$109$	−1.67416e7	−1.23824	−0.619118	−	0.785298i	$-0.712510\pi$
$109$	−1.67416e7	−1.23824	−0.619118	+	0.785298i	$0.712510\pi$
$110$	−5.73105e6	−0.410544
$111$	−4.70145e6	−0.326288
$112$	1.40493e6	0.0944911
$113$	9.23394e6	0.602022	0.301011	−	0.953621i	$-0.402676\pi$
$113$	9.23394e6	0.602022	0.301011	+	0.953621i	$0.402676\pi$
$114$	−8.62136e6	−0.545015
$115$	2.60221e7	1.59551
$116$	−2.98469e6	−0.177540
$117$	1.60161e6	0.0924500
$118$	6.17342e6	0.345891
$119$	9.65440e6	0.525183
$120$	3.86845e6	0.204363
$121$	−1.29335e7	−0.663695
$122$	5.30129e6	0.264315
$123$	−8.05604e6	−0.390350
$124$	1.14028e6	0.0537076
$125$	−2.18109e7	−0.998824
$126$	−2.00038e6	−0.0890871
$127$	−3.03925e7	−1.31660	−0.658300	−	0.752756i	$-0.728724\pi$
$127$	−3.03925e7	−1.31660	−0.658300	+	0.752756i	$0.728724\pi$
$128$	−2.09715e6	−0.0883883
$129$	−1.08426e7	−0.444703
$130$	−4.91840e6	−0.196346
$131$	6.25622e6	0.243143	0.121572	−	0.992583i	$-0.461207\pi$
$131$	6.25622e6	0.243143	0.121572	+	0.992583i	$0.461207\pi$
$132$	−4.42369e6	−0.167408
$133$	−1.36904e7	−0.504586
$134$	1.44881e7	0.520170
$135$	−5.50801e6	−0.192676
$136$	−1.44112e7	−0.491264
$137$	5.70117e7	1.89427	0.947135	−	0.320836i	$-0.103964\pi$
$137$	5.70117e7	1.89427	0.947135	+	0.320836i	$0.103964\pi$
$138$	2.00860e7	0.650603
$139$	5.71171e6	0.180391	0.0901953	−	0.995924i	$-0.471251\pi$
$139$	5.71171e6	0.180391	0.0901953	+	0.995924i	$0.471251\pi$
$140$	6.14296e6	0.189204
$141$	−3.09241e7	−0.929032
$142$	−3.26974e7	−0.958305
$143$	5.62433e6	0.160840
$144$	2.98598e6	0.0833333
$145$	−1.30504e7	−0.355496
$146$	−2.48275e7	−0.660233
$147$	−3.17652e6	−0.0824786
$148$	1.11442e7	0.282574
$149$	−2.84900e7	−0.705571	−0.352786	−	0.935704i	$-0.614766\pi$
$149$	−2.84900e7	−0.705571	−0.352786	+	0.935704i	$0.614766\pi$
$150$	39568.2	0.000957253 0
$151$	2.15191e6	0.0508633	0.0254316	−	0.999677i	$-0.491904\pi$
$151$	2.15191e6	0.0508633	0.0254316	+	0.999677i	$0.491904\pi$
$152$	2.04358e7	0.471997
$153$	2.05191e7	0.463168
$154$	−7.02466e6	−0.154990
$155$	4.98580e6	0.107541
$156$	−3.79642e6	−0.0800641
$157$	−3.13987e7	−0.647535	−0.323767	−	0.946137i	$-0.604950\pi$
$157$	−3.13987e7	−0.647535	−0.323767	+	0.946137i	$0.604950\pi$
$158$	−2.05277e7	−0.414039
$159$	−1.38573e7	−0.273393
$160$	−9.16967e6	−0.176984
$161$	3.18958e7	0.602342
$162$	−4.25153e6	−0.0785674
$163$	8.19841e7	1.48277	0.741384	−	0.671081i	$-0.234170\pi$
$163$	8.19841e7	1.48277	0.741384	+	0.671081i	$0.234170\pi$
$164$	1.90958e7	0.338053
$165$	−1.93423e7	−0.335208
$166$	2.97143e7	0.504183
$167$	7.19173e7	1.19488	0.597442	−	0.801912i	$-0.296184\pi$
$167$	7.19173e7	1.19488	0.597442	+	0.801912i	$0.296184\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	−6.30122e7	−0.983679
$171$	−2.90971e7	−0.445003
$172$	2.57010e7	0.385124
$173$	−9.57835e7	−1.40647	−0.703233	−	0.710959i	$-0.748261\pi$
$173$	−9.57835e7	−1.40647	−0.703233	+	0.710959i	$0.748261\pi$
$174$	−1.00733e7	−0.144961
$175$	62832.8	0.000886244 0
$176$	1.04858e7	0.144979
$177$	2.08353e7	0.282419
$178$	5.39942e7	0.717591
$179$	−1.84562e7	−0.240523	−0.120262	−	0.992742i	$-0.538373\pi$
$179$	−1.84562e7	−0.240523	−0.120262	+	0.992742i	$0.538373\pi$
$180$	1.30560e7	0.166862
$181$	3.44041e6	0.0431256	0.0215628	−	0.999767i	$-0.493136\pi$
$181$	3.44041e6	0.0431256	0.0215628	+	0.999767i	$0.493136\pi$
$182$	−6.02857e6	−0.0741249
$183$	1.78919e7	0.215812
$184$	−4.76112e7	−0.563439
$185$	4.87273e7	0.565810
$186$	3.84844e6	0.0438520
$187$	7.20563e7	0.805799
$188$	7.33016e7	0.804565
$189$	−6.75127e6	−0.0727393
$190$	8.93543e7	0.945101
$191$	1.63094e8	1.69364	0.846821	−	0.531878i	$-0.178513\pi$
$191$	1.63094e8	1.69364	0.846821	+	0.531878i	$0.178513\pi$
$192$	−7.07789e6	−0.0721688
$193$	2.63577e7	0.263911	0.131955	−	0.991256i	$-0.457874\pi$
$193$	2.63577e7	0.263911	0.131955	+	0.991256i	$0.457874\pi$
$194$	2.41641e7	0.237610
$195$	−1.65996e7	−0.160316
$196$	7.52954e6	0.0714286
$197$	2.18273e7	0.203408	0.101704	−	0.994815i	$-0.467571\pi$
$197$	2.18273e7	0.203408	0.101704	+	0.994815i	$0.467571\pi$
$198$	−1.49300e7	−0.136688
$199$	1.32706e7	0.119372	0.0596861	−	0.998217i	$-0.480990\pi$
$199$	1.32706e7	0.119372	0.0596861	+	0.998217i	$0.480990\pi$
$200$	−93791.2	−0.000829005 0
$201$	4.88974e7	0.424717
$202$	1.19153e8	1.01713
$203$	−1.59961e7	−0.134208
$204$	−4.86379e7	−0.401115
$205$	8.34952e7	0.676898
$206$	−6.47202e7	−0.515828
$207$	6.77902e7	0.531215
$208$	8.99891e6	0.0693375
$209$	−1.02179e8	−0.774196
$210$	2.07325e7	0.154484
$211$	−1.51096e8	−1.10730	−0.553648	−	0.832751i	$-0.686765\pi$
$211$	−1.51096e8	−1.10730	−0.553648	+	0.832751i	$0.686765\pi$
$212$	3.28469e7	0.236765
$213$	−1.10354e8	−0.782453
$214$	1.21567e8	0.847948
$215$	1.12376e8	0.771151
$216$	1.00777e7	0.0680414
$217$	6.11119e6	0.0405991
$218$	1.33933e8	0.875565
$219$	−8.37927e7	−0.539078
$220$	4.58484e7	0.290299
$221$	6.18388e7	0.385379
$222$	3.76116e7	0.230721
$223$	1.84949e8	1.11683	0.558414	−	0.829563i	$-0.311410\pi$
$223$	1.84949e8	1.11683	0.558414	+	0.829563i	$0.311410\pi$
$224$	−1.12394e7	−0.0668153
$225$	133543.	0.000781593 0
$226$	−7.38715e7	−0.425694
$227$	−1.72543e8	−0.979056	−0.489528	−	0.871988i	$-0.662831\pi$
$227$	−1.72543e8	−0.979056	−0.489528	+	0.871988i	$0.662831\pi$
$228$	6.89709e7	0.385384
$229$	2.47492e8	1.36187	0.680936	−	0.732343i	$-0.261573\pi$
$229$	2.47492e8	1.36187	0.680936	+	0.732343i	$0.261573\pi$
$230$	−2.08177e8	−1.12820
$231$	−2.37082e7	−0.126548
$232$	2.38775e7	0.125540
$233$	2.54274e8	1.31691	0.658456	−	0.752619i	$-0.271210\pi$
$233$	2.54274e8	1.31691	0.658456	+	0.752619i	$0.271210\pi$
$234$	−1.28129e7	−0.0653720
$235$	3.20507e8	1.61102
$236$	−4.93874e7	−0.244582
$237$	−6.92811e7	−0.338061
$238$	−7.72352e7	−0.371361
$239$	−3.01822e8	−1.43008	−0.715038	−	0.699086i	$-0.753590\pi$
$239$	−3.01822e8	−1.43008	−0.715038	+	0.699086i	$0.753590\pi$
$240$	−3.09476e7	−0.144507
$241$	−2.89194e8	−1.33085	−0.665426	−	0.746464i	$-0.731750\pi$
$241$	−2.89194e8	−1.33085	−0.665426	+	0.746464i	$0.731750\pi$
$242$	1.03468e8	0.469303
$243$	−1.43489e7	−0.0641500
$244$	−4.24103e7	−0.186899
$245$	3.29224e7	0.143025
$246$	6.44483e7	0.276019
$247$	−8.76904e7	−0.370265
$248$	−9.12224e6	−0.0379770
$249$	1.00286e8	0.411663
$250$	1.74487e8	0.706275
$251$	9.14850e7	0.365167	0.182584	−	0.983190i	$-0.441554\pi$
$251$	9.14850e7	0.365167	0.182584	+	0.983190i	$0.441554\pi$
$252$	1.60030e7	0.0629941
$253$	2.38057e8	0.924184
$254$	2.43140e8	0.930976
$255$	−2.12666e8	−0.803171
$256$	1.67772e7	0.0625000
$257$	1.32553e7	0.0487105	0.0243553	−	0.999703i	$-0.492247\pi$
$257$	1.32553e7	0.0487105	0.0243553	+	0.999703i	$0.492247\pi$
$258$	8.67409e7	0.314452
$259$	5.97259e7	0.213606
$260$	3.93472e7	0.138838
$261$	−3.39975e7	−0.118360
$262$	−5.00497e7	−0.171928
$263$	1.46280e8	0.495836	0.247918	−	0.968781i	$-0.420254\pi$
$263$	1.46280e8	0.495836	0.247918	+	0.968781i	$0.420254\pi$
$264$	3.53895e7	0.118375
$265$	1.43621e8	0.474086
$266$	1.09523e8	0.356796
$267$	1.82230e8	0.585911
$268$	−1.15905e8	−0.367815
$269$	3.81607e8	1.19532	0.597659	−	0.801751i	$-0.296098\pi$
$269$	3.81607e8	1.19532	0.597659	+	0.801751i	$0.296098\pi$
$270$	4.40641e7	0.136242
$271$	4.51657e8	1.37853	0.689265	−	0.724509i	$-0.257933\pi$
$271$	4.51657e8	1.37853	0.689265	+	0.724509i	$0.257933\pi$
$272$	1.15290e8	0.347376
$273$	−2.03464e7	−0.0605228
$274$	−4.56093e8	−1.33945
$275$	468957.	0.00135978
$276$	−1.60688e8	−0.460046
$277$	−3.54408e8	−1.00190	−0.500950	−	0.865476i	$-0.667016\pi$
$277$	−3.54408e8	−1.00190	−0.500950	+	0.865476i	$0.667016\pi$
$278$	−4.56936e7	−0.127555
$279$	1.29885e7	0.0358050
$280$	−4.91437e7	−0.133787
$281$	1.42190e8	0.382293	0.191147	−	0.981562i	$-0.438779\pi$
$281$	1.42190e8	0.382293	0.191147	+	0.981562i	$0.438779\pi$
$282$	2.47393e8	0.656925
$283$	5.88634e8	1.54381	0.771903	−	0.635741i	$-0.219305\pi$
$283$	5.88634e8	1.54381	0.771903	+	0.635741i	$0.219305\pi$
$284$	2.61579e8	0.677624
$285$	3.01571e8	0.771671
$286$	−4.49947e7	−0.113731
$287$	1.02342e8	0.255544
$288$	−2.38879e7	−0.0589256
$289$	3.81912e8	0.930723
$290$	1.04403e8	0.251374
$291$	8.15537e7	0.194007
$292$	1.98620e8	0.466856
$293$	6.25283e8	1.45225	0.726123	−	0.687565i	$-0.241320\pi$
$293$	6.25283e8	1.45225	0.726123	+	0.687565i	$0.241320\pi$
$294$	2.54122e7	0.0583212
$295$	−2.15943e8	−0.489737
$296$	−8.91535e7	−0.199810
$297$	−5.03886e7	−0.111605
$298$	2.27920e8	0.498914
$299$	2.04300e8	0.441998
$300$	−316545.	−0.000676880 0
$301$	1.37741e8	0.291126
$302$	−1.72153e7	−0.0359658
$303$	4.02142e8	0.830482
$304$	−1.63487e8	−0.333752
$305$	−1.85436e8	−0.374236
$306$	−1.64153e8	−0.327509
$307$	−9.23330e8	−1.82126	−0.910632	−	0.413219i	$-0.864404\pi$
$307$	−9.23330e8	−1.82126	−0.910632	+	0.413219i	$0.864404\pi$
$308$	5.61972e7	0.109594
$309$	−2.18431e8	−0.421172
$310$	−3.98864e7	−0.0760430
$311$	−6.10893e8	−1.15161	−0.575803	−	0.817589i	$-0.695310\pi$
$311$	−6.10893e8	−1.15161	−0.575803	+	0.817589i	$0.695310\pi$
$312$	3.03713e7	0.0566139
$313$	1.90029e8	0.350280	0.175140	−	0.984544i	$-0.443962\pi$
$313$	1.90029e8	0.350280	0.175140	+	0.984544i	$0.443962\pi$
$314$	2.51190e8	0.457876
$315$	6.99722e7	0.126136
$316$	1.64222e8	0.292770
$317$	−8.54838e8	−1.50722	−0.753610	−	0.657322i	$-0.771689\pi$
$317$	−8.54838e8	−1.50722	−0.753610	+	0.657322i	$0.771689\pi$
$318$	1.10858e8	0.193318
$319$	−1.19388e8	−0.205917
$320$	7.33573e7	0.125146
$321$	4.10290e8	0.692346
$322$	−2.55166e8	−0.425920
$323$	−1.12345e9	−1.85500
$324$	3.40122e7	0.0555556
$325$	402460.	0.000650325 0
$326$	−6.55873e8	−1.04848
$327$	4.52022e8	0.714896
$328$	−1.52766e8	−0.239039
$329$	3.92851e8	0.608194
$330$	1.54738e8	0.237028
$331$	9.39361e8	1.42375	0.711876	−	0.702305i	$-0.247846\pi$
$331$	9.39361e8	1.42375	0.711876	+	0.702305i	$0.247846\pi$
$332$	−2.37715e8	−0.356511
$333$	1.26939e8	0.188383
$334$	−5.75339e8	−0.844911
$335$	−5.06787e8	−0.736493
$336$	−3.79331e7	−0.0545545
$337$	7.50225e8	1.06779	0.533897	−	0.845550i	$-0.320727\pi$
$337$	7.50225e8	1.06779	0.533897	+	0.845550i	$0.320727\pi$
$338$	−3.86145e7	−0.0543928
$339$	−2.49316e8	−0.347578
$340$	5.04098e8	0.695566
$341$	4.56113e7	0.0622919
$342$	2.32777e8	0.314665
$343$	4.03536e7	0.0539949
$344$	−2.05608e8	−0.272324
$345$	−7.02598e8	−0.921170
$346$	7.66268e8	0.994522
$347$	8.09047e7	0.103949	0.0519745	−	0.998648i	$-0.483449\pi$
$347$	8.09047e7	0.103949	0.0519745	+	0.998648i	$0.483449\pi$
$348$	8.05866e7	0.102503
$349$	−9.59619e7	−0.120840	−0.0604198	−	0.998173i	$-0.519244\pi$
$349$	−9.59619e7	−0.120840	−0.0604198	+	0.998173i	$0.519244\pi$
$350$	−502662.	−0.000626669 0
$351$	−4.32436e7	−0.0533761
$352$	−8.38863e7	−0.102516
$353$	1.17451e9	1.42116	0.710582	−	0.703614i	$-0.248432\pi$
$353$	1.17451e9	1.42116	0.710582	+	0.703614i	$0.248432\pi$
$354$	−1.66682e8	−0.199700
$355$	1.14374e9	1.35684
$356$	−4.31954e8	−0.507414
$357$	−2.60669e8	−0.303215
$358$	1.47650e8	0.170076
$359$	4.58909e8	0.523475	0.261738	−	0.965139i	$-0.415705\pi$
$359$	4.58909e8	0.523475	0.261738	+	0.965139i	$0.415705\pi$
$360$	−1.04448e8	−0.117989
$361$	6.99232e8	0.782251
$362$	−2.75233e7	−0.0304944
$363$	3.49206e8	0.383185
$364$	4.82285e7	0.0524142
$365$	8.68453e8	0.934805
$366$	−1.43135e8	−0.152602
$367$	7.19580e8	0.759885	0.379943	−	0.925010i	$-0.375944\pi$
$367$	7.19580e8	0.759885	0.379943	+	0.925010i	$0.375944\pi$
$368$	3.80890e8	0.398412
$369$	2.17513e8	0.225368
$370$	−3.89818e8	−0.400088
$371$	1.76039e8	0.178978
$372$	−3.07875e7	−0.0310081
$373$	1.01612e9	1.01382	0.506911	−	0.861998i	$-0.330787\pi$
$373$	1.01612e9	1.01382	0.506911	+	0.861998i	$0.330787\pi$
$374$	−5.76451e8	−0.569786
$375$	5.88895e8	0.576671
$376$	−5.86413e8	−0.568914
$377$	−1.02459e8	−0.0984815
$378$	5.40102e7	0.0514344
$379$	1.28264e9	1.21023	0.605116	−	0.796137i	$-0.293127\pi$
$379$	1.28264e9	1.21023	0.605116	+	0.796137i	$0.293127\pi$
$380$	−7.14835e8	−0.668287
$381$	8.20598e8	0.760139
$382$	−1.30475e9	−1.19759
$383$	−1.22709e9	−1.11605	−0.558023	−	0.829825i	$-0.688440\pi$
$383$	−1.22709e9	−1.11605	−0.558023	+	0.829825i	$0.688440\pi$
$384$	5.66231e7	0.0510310
$385$	2.45719e8	0.219445
$386$	−2.10862e8	−0.186613
$387$	2.92751e8	0.256749
$388$	−1.93312e8	−0.168015
$389$	−3.68027e8	−0.316998	−0.158499	−	0.987359i	$-0.550665\pi$
$389$	−3.68027e8	−0.316998	−0.158499	+	0.987359i	$0.550665\pi$
$390$	1.32797e8	0.113360
$391$	2.61740e9	2.21438
$392$	−6.02363e7	−0.0505076
$393$	−1.68918e8	−0.140379
$394$	−1.74618e8	−0.143831
$395$	7.18050e8	0.586226
$396$	1.19440e8	0.0966530
$397$	8.80873e8	0.706556	0.353278	−	0.935518i	$-0.385067\pi$
$397$	8.80873e8	0.706556	0.353278	+	0.935518i	$0.385067\pi$
$398$	−1.06164e8	−0.0844090
$399$	3.69641e8	0.291323
$400$	750330.	0.000586195 0
$401$	−2.11104e9	−1.63490	−0.817451	−	0.575998i	$-0.804613\pi$
$401$	−2.11104e9	−1.63490	−0.817451	+	0.575998i	$0.804613\pi$
$402$	−3.91179e8	−0.300320
$403$	3.91437e7	0.0297916
$404$	−9.53225e8	−0.719218
$405$	1.48716e8	0.111241
$406$	1.27969e8	0.0948991
$407$	4.45768e8	0.327740
$408$	3.89103e8	0.283631
$409$	−2.00534e7	−0.0144929	−0.00724647	−	0.999974i	$-0.502307\pi$
$409$	−2.00534e7	−0.0144929	−0.00724647	+	0.999974i	$0.502307\pi$
$410$	−6.67962e8	−0.478639
$411$	−1.53932e9	−1.09366
$412$	5.17762e8	0.364745
$413$	−2.64686e8	−0.184886
$414$	−5.42322e8	−0.375626
$415$	−1.03939e9	−0.713857
$416$	−7.19913e7	−0.0490290
$417$	−1.54216e8	−0.104149
$418$	8.17434e8	0.547439
$419$	1.63482e9	1.08573	0.542863	−	0.839821i	$-0.317340\pi$
$419$	1.63482e9	1.08573	0.542863	+	0.839821i	$0.317340\pi$
$420$	−1.65860e8	−0.109237
$421$	−1.42488e9	−0.930659	−0.465330	−	0.885137i	$-0.654064\pi$
$421$	−1.42488e9	−0.930659	−0.465330	+	0.885137i	$0.654064\pi$
$422$	1.20877e9	0.782977
$423$	8.34952e8	0.536377
$424$	−2.62775e8	−0.167418
$425$	5.15612e6	0.00325808
$426$	8.82829e8	0.553278
$427$	−2.27293e8	−0.141282
$428$	−9.72539e8	−0.599589
$429$	−1.51857e8	−0.0928612
$430$	−8.99009e8	−0.545286
$431$	1.99523e9	1.20039	0.600196	−	0.799853i	$-0.295089\pi$
$431$	1.99523e9	1.20039	0.600196	+	0.799853i	$0.295089\pi$
$432$	−8.06216e7	−0.0481125
$433$	1.58828e9	0.940198	0.470099	−	0.882614i	$-0.344218\pi$
$433$	1.58828e9	0.940198	0.470099	+	0.882614i	$0.344218\pi$
$434$	−4.88895e7	−0.0287079
$435$	3.52360e8	0.205246
$436$	−1.07146e9	−0.619118
$437$	−3.71160e9	−2.12753
$438$	6.70342e8	0.381186
$439$	2.59955e9	1.46647	0.733233	−	0.679977i	$-0.238010\pi$
$439$	2.59955e9	1.46647	0.733233	+	0.679977i	$0.238010\pi$
$440$	−3.66787e8	−0.205272
$441$	8.57661e7	0.0476190
$442$	−4.94711e8	−0.272504
$443$	−9.53546e8	−0.521109	−0.260555	−	0.965459i	$-0.583905\pi$
$443$	−9.53546e8	−0.521109	−0.260555	+	0.965459i	$0.583905\pi$
$444$	−3.00893e8	−0.163144
$445$	−1.88869e9	−1.01602
$446$	−1.47960e9	−0.789716
$447$	7.69231e8	0.407362
$448$	8.99154e7	0.0472456
$449$	−2.42551e9	−1.26456	−0.632281	−	0.774739i	$-0.717881\pi$
$449$	−2.42551e9	−1.26456	−0.632281	+	0.774739i	$0.717881\pi$
$450$	−1.06834e6	−0.000552670 0
$451$	7.63834e8	0.392086
$452$	5.90972e8	0.301011
$453$	−5.81015e7	−0.0293659
$454$	1.38035e9	0.692297
$455$	2.10876e8	0.104951
$456$	−5.51767e8	−0.272508
$457$	2.17272e9	1.06487	0.532435	−	0.846471i	$-0.321277\pi$
$457$	2.17272e9	1.06487	0.532435	+	0.846471i	$0.321277\pi$
$458$	−1.97993e9	−0.962989
$459$	−5.54016e8	−0.267410
$460$	1.66542e9	0.797757
$461$	−2.12021e9	−1.00792	−0.503959	−	0.863727i	$-0.668124\pi$
$461$	−2.12021e9	−1.00792	−0.503959	+	0.863727i	$0.668124\pi$
$462$	1.89666e8	0.0894833
$463$	3.93415e8	0.184212	0.0921058	−	0.995749i	$-0.470640\pi$
$463$	3.93415e8	0.184212	0.0921058	+	0.995749i	$0.470640\pi$
$464$	−1.91020e8	−0.0887700
$465$	−1.34617e8	−0.0620888
$466$	−2.03419e9	−0.931197
$467$	9.61470e8	0.436844	0.218422	−	0.975854i	$-0.429909\pi$
$467$	9.61470e8	0.436844	0.218422	+	0.975854i	$0.429909\pi$
$468$	1.02503e8	0.0462250
$469$	−6.21178e8	−0.278042
$470$	−2.56405e9	−1.13916
$471$	8.47766e8	0.373854
$472$	3.95099e8	0.172945
$473$	1.02804e9	0.446681
$474$	5.54249e8	0.239046
$475$	−7.31163e6	−0.00313030
$476$	6.17882e8	0.262592
$477$	3.74146e8	0.157844
$478$	2.41458e9	1.01122
$479$	2.40837e9	1.00126	0.500631	−	0.865661i	$-0.333101\pi$
$479$	2.40837e9	1.00126	0.500631	+	0.865661i	$0.333101\pi$
$480$	2.47581e8	0.102182
$481$	3.82559e8	0.156744
$482$	2.31355e9	0.941054
$483$	−8.61187e8	−0.347762
$484$	−8.27747e8	−0.331848
$485$	−8.45247e8	−0.336424
$486$	1.14791e8	0.0453609
$487$	1.59522e8	0.0625849	0.0312924	−	0.999510i	$-0.490038\pi$
$487$	1.59522e8	0.0625849	0.0312924	+	0.999510i	$0.490038\pi$
$488$	3.39283e8	0.132158
$489$	−2.21357e9	−0.856077
$490$	−2.63379e8	−0.101134
$491$	−2.15830e9	−0.822861	−0.411430	−	0.911441i	$-0.634971\pi$
$491$	−2.15830e9	−0.822861	−0.411430	+	0.911441i	$0.634971\pi$
$492$	−5.15587e8	−0.195175
$493$	−1.31265e9	−0.493385
$494$	7.01523e8	0.261817
$495$	5.22242e8	0.193532
$496$	7.29779e7	0.0268538
$497$	1.40190e9	0.512235
$498$	−8.02287e8	−0.291090
$499$	1.32331e8	0.0476771	0.0238385	−	0.999716i	$-0.492411\pi$
$499$	1.32331e8	0.0476771	0.0238385	+	0.999716i	$0.492411\pi$
$500$	−1.39590e9	−0.499412
$501$	−1.94177e9	−0.689867
$502$	−7.31880e8	−0.258212
$503$	2.43934e8	0.0854641	0.0427320	−	0.999087i	$-0.486394\pi$
$503$	2.43934e8	0.0854641	0.0427320	+	0.999087i	$0.486394\pi$
$504$	−1.28024e8	−0.0445435
$505$	−4.16792e9	−1.44012
$506$	−1.90445e9	−0.653497
$507$	−1.30324e8	−0.0444116
$508$	−1.94512e9	−0.658300
$509$	−4.52294e9	−1.52023	−0.760114	−	0.649790i	$-0.774857\pi$
$509$	−4.52294e9	−1.52023	−0.760114	+	0.649790i	$0.774857\pi$
$510$	1.70133e9	0.567928
$511$	1.06448e9	0.352910
$512$	−1.34218e8	−0.0441942
$513$	7.85621e8	0.256923
$514$	−1.06042e8	−0.0344436
$515$	2.26388e9	0.730346
$516$	−6.93927e8	−0.222351
$517$	2.93207e9	0.933164
$518$	−4.77807e8	−0.151042
$519$	2.58616e9	0.812024
$520$	−3.14777e8	−0.0981730
$521$	5.65921e9	1.75317	0.876585	−	0.481247i	$-0.159816\pi$
$521$	5.65921e9	1.75317	0.876585	+	0.481247i	$0.159816\pi$
$522$	2.71980e8	0.0836932
$523$	2.35283e8	0.0719177	0.0359588	−	0.999353i	$-0.488551\pi$
$523$	2.35283e8	0.0719177	0.0359588	+	0.999353i	$0.488551\pi$
$524$	4.00398e8	0.121572
$525$	−1.69649e6	−0.000511673 0
$526$	−1.17024e9	−0.350609
$527$	5.01490e8	0.149254
$528$	−2.83116e8	−0.0837039
$529$	5.24244e9	1.53971
$530$	−1.14897e9	−0.335229
$531$	−5.62553e8	−0.163055
$532$	−8.76186e8	−0.252293
$533$	6.55523e8	0.187518
$534$	−1.45784e9	−0.414301
$535$	−4.25237e9	−1.20058
$536$	9.27239e8	0.260085
$537$	4.98318e8	0.138866
$538$	−3.05286e9	−0.845217
$539$	3.01182e8	0.0828454
$540$	−3.52513e8	−0.0963378
$541$	−7.29719e9	−1.98137	−0.990684	−	0.136179i	$-0.956518\pi$
$541$	−7.29719e9	−1.98137	−0.990684	+	0.136179i	$0.956518\pi$
$542$	−3.61326e9	−0.974768
$543$	−9.28910e7	−0.0248986
$544$	−9.22319e8	−0.245632
$545$	−4.68489e9	−1.23969
$546$	1.62771e8	0.0427960
$547$	2.17324e9	0.567744	0.283872	−	0.958862i	$-0.408381\pi$
$547$	2.17324e9	0.567744	0.283872	+	0.958862i	$0.408381\pi$
$548$	3.64875e9	0.947135
$549$	−4.83080e8	−0.124599
$550$	−3.75166e6	−0.000961510 0
$551$	1.86141e9	0.474035
$552$	1.28550e9	0.325302
$553$	8.80127e8	0.221313
$554$	2.83526e9	0.708450
$555$	−1.31564e9	−0.326671
$556$	3.65549e8	0.0901953
$557$	6.93052e9	1.69931	0.849655	−	0.527339i	$-0.176810\pi$
$557$	6.93052e9	1.69931	0.849655	+	0.527339i	$0.176810\pi$
$558$	−1.03908e8	−0.0253180
$559$	8.82268e8	0.213628
$560$	3.93149e8	0.0946018
$561$	−1.94552e9	−0.465228
$562$	−1.13752e9	−0.270322
$563$	−8.07916e9	−1.90804	−0.954019	−	0.299746i	$-0.903098\pi$
$563$	−8.07916e9	−1.90804	−0.954019	+	0.299746i	$0.903098\pi$
$564$	−1.97914e9	−0.464516
$565$	2.58399e9	0.602727
$566$	−4.70907e9	−1.09164
$567$	1.82284e8	0.0419961
$568$	−2.09263e9	−0.479152
$569$	−3.32999e9	−0.757791	−0.378895	−	0.925439i	$-0.623696\pi$
$569$	−3.32999e9	−0.757791	−0.378895	+	0.925439i	$0.623696\pi$
$570$	−2.41257e9	−0.545654
$571$	−1.32724e9	−0.298348	−0.149174	−	0.988811i	$-0.547661\pi$
$571$	−1.32724e9	−0.298348	−0.149174	+	0.988811i	$0.547661\pi$
$572$	3.59957e8	0.0804201
$573$	−4.40354e9	−0.977825
$574$	−8.18732e8	−0.180697
$575$	1.70346e7	0.00373675
$576$	1.91103e8	0.0416667
$577$	−5.58863e9	−1.21113	−0.605563	−	0.795797i	$-0.707052\pi$
$577$	−5.58863e9	−1.21113	−0.605563	+	0.795797i	$0.707052\pi$
$578$	−3.05529e9	−0.658121
$579$	−7.11658e8	−0.152369
$580$	−8.35224e8	−0.177748
$581$	−1.27400e9	−0.269497
$582$	−6.52430e8	−0.137184
$583$	1.31388e9	0.274609
$584$	−1.58896e9	−0.330117
$585$	4.48189e8	0.0925584
$586$	−5.00227e9	−1.02689
$587$	−4.33912e9	−0.885459	−0.442730	−	0.896655i	$-0.645990\pi$
$587$	−4.33912e9	−0.885459	−0.442730	+	0.896655i	$0.645990\pi$
$588$	−2.03297e8	−0.0412393
$589$	−7.11137e8	−0.143400
$590$	1.72755e9	0.346296
$591$	−5.89337e8	−0.117438
$592$	7.13228e8	0.141287
$593$	3.08526e9	0.607576	0.303788	−	0.952740i	$-0.401749\pi$
$593$	3.08526e9	0.607576	0.303788	+	0.952740i	$0.401749\pi$
$594$	4.03109e8	0.0789168
$595$	2.70165e9	0.525799
$596$	−1.82336e9	−0.352786
$597$	−3.58305e8	−0.0689196
$598$	−1.63440e9	−0.312540
$599$	8.71948e9	1.65766	0.828832	−	0.559497i	$-0.189006\pi$
$599$	8.71948e9	1.65766	0.828832	+	0.559497i	$0.189006\pi$
$600$	2.53236e6	0.000478626 0
$601$	1.23552e9	0.232161	0.116080	−	0.993240i	$-0.462967\pi$
$601$	1.23552e9	0.232161	0.116080	+	0.993240i	$0.462967\pi$
$602$	−1.10193e9	−0.205857
$603$	−1.32023e9	−0.245210
$604$	1.37722e8	0.0254316
$605$	−3.61927e9	−0.664473
$606$	−3.21714e9	−0.587239
$607$	−6.05863e9	−1.09955	−0.549774	−	0.835314i	$-0.685286\pi$
$607$	−6.05863e9	−1.09955	−0.549774	+	0.835314i	$0.685286\pi$
$608$	1.30789e9	0.235999
$609$	4.31894e8	0.0774848
$610$	1.48349e9	0.264625
$611$	2.51631e9	0.446292
$612$	1.31322e9	0.231584
$613$	3.49905e9	0.613534	0.306767	−	0.951785i	$-0.400753\pi$
$613$	3.49905e9	0.613534	0.306767	+	0.951785i	$0.400753\pi$
$614$	7.38664e9	1.28783
$615$	−2.25437e9	−0.390807
$616$	−4.49578e8	−0.0774948
$617$	−7.81385e9	−1.33927	−0.669633	−	0.742692i	$-0.733549\pi$
$617$	−7.81385e9	−1.33927	−0.669633	+	0.742692i	$0.733549\pi$
$618$	1.74745e9	0.297813
$619$	2.70673e9	0.458699	0.229350	−	0.973344i	$-0.426340\pi$
$619$	2.70673e9	0.458699	0.229350	+	0.973344i	$0.426340\pi$
$620$	3.19091e8	0.0537705
$621$	−1.83034e9	−0.306697
$622$	4.88714e9	0.814308
$623$	−2.31500e9	−0.383569
$624$	−2.42971e8	−0.0400320
$625$	−6.11779e9	−1.00234
$626$	−1.52023e9	−0.247685
$627$	2.75884e9	0.446982
$628$	−2.00952e9	−0.323767
$629$	4.90117e9	0.785276
$630$	−5.59777e8	−0.0891915
$631$	5.09138e9	0.806739	0.403369	−	0.915037i	$-0.367839\pi$
$631$	5.09138e9	0.806739	0.403369	+	0.915037i	$0.367839\pi$
$632$	−1.31377e9	−0.207019
$633$	4.07959e9	0.639298
$634$	6.83871e9	1.06577
$635$	−8.50492e9	−1.31814
$636$	−8.86865e8	−0.136697
$637$	2.58475e8	0.0396214
$638$	9.55103e8	0.145606
$639$	2.97955e9	0.451749
$640$	−5.86859e8	−0.0884919
$641$	8.82947e8	0.132413	0.0662066	−	0.997806i	$-0.478910\pi$
$641$	8.82947e8	0.132413	0.0662066	+	0.997806i	$0.478910\pi$
$642$	−3.28232e9	−0.489563
$643$	−7.25074e9	−1.07558	−0.537792	−	0.843078i	$-0.680741\pi$
$643$	−7.25074e9	−1.07558	−0.537792	+	0.843078i	$0.680741\pi$
$644$	2.04133e9	0.301171
$645$	−3.03415e9	−0.445224
$646$	8.98759e9	1.31168
$647$	−5.67018e9	−0.823060	−0.411530	−	0.911396i	$-0.635006\pi$
$647$	−5.67018e9	−0.823060	−0.411530	+	0.911396i	$0.635006\pi$
$648$	−2.72098e8	−0.0392837
$649$	−1.97550e9	−0.283675
$650$	−3.21968e6	−0.000459849 0
$651$	−1.65002e8	−0.0234399
$652$	5.24698e9	0.741384
$653$	−5.30139e9	−0.745064	−0.372532	−	0.928019i	$-0.621510\pi$
$653$	−5.30139e9	−0.745064	−0.372532	+	0.928019i	$0.621510\pi$
$654$	−3.61618e9	−0.505508
$655$	1.75071e9	0.243428
$656$	1.22213e9	0.169026
$657$	2.26240e9	0.311237
$658$	−3.14281e9	−0.430058
$659$	2.99984e9	0.408318	0.204159	−	0.978938i	$-0.434554\pi$
$659$	2.99984e9	0.408318	0.204159	+	0.978938i	$0.434554\pi$
$660$	−1.23791e9	−0.167604
$661$	−8.35348e8	−0.112503	−0.0562513	−	0.998417i	$-0.517915\pi$
$661$	−8.35348e8	−0.112503	−0.0562513	+	0.998417i	$0.517915\pi$
$662$	−7.51489e9	−1.00675
$663$	−1.66965e9	−0.222499
$664$	1.90172e9	0.252091
$665$	−3.83107e9	−0.505177
$666$	−1.01551e9	−0.133207
$667$	−4.33669e9	−0.565872
$668$	4.60271e9	0.597442
$669$	−4.99363e9	−0.644801
$670$	4.05429e9	0.520779
$671$	−1.69642e9	−0.216772
$672$	3.03464e8	0.0385758
$673$	−2.38575e9	−0.301698	−0.150849	−	0.988557i	$-0.548201\pi$
$673$	−2.38575e9	−0.301698	−0.150849	+	0.988557i	$0.548201\pi$
$674$	−6.00180e9	−0.755044
$675$	−3.60565e6	−0.000451253 0
$676$	3.08916e8	0.0384615
$677$	−1.11650e10	−1.38292	−0.691460	−	0.722415i	$-0.743032\pi$
$677$	−1.11650e10	−1.38292	−0.691460	+	0.722415i	$0.743032\pi$
$678$	1.99453e9	0.245774
$679$	−1.03603e9	−0.127008
$680$	−4.03278e9	−0.491840
$681$	4.65867e9	0.565258
$682$	−3.64890e8	−0.0440471
$683$	1.10269e10	1.32428	0.662142	−	0.749378i	$-0.269647\pi$
$683$	1.10269e10	1.32428	0.662142	+	0.749378i	$0.269647\pi$
$684$	−1.86221e9	−0.222502
$685$	1.59539e10	1.89649
$686$	−3.22829e8	−0.0381802
$687$	−6.68228e9	−0.786278
$688$	1.64486e9	0.192562
$689$	1.12757e9	0.131334
$690$	5.62078e9	0.651366
$691$	1.11798e10	1.28903	0.644513	−	0.764593i	$-0.277060\pi$
$691$	1.11798e10	1.28903	0.644513	+	0.764593i	$0.277060\pi$
$692$	−6.13015e9	−0.703233
$693$	6.40122e8	0.0730628
$694$	−6.47237e8	−0.0735031
$695$	1.59834e9	0.180602
$696$	−6.44693e8	−0.0724804
$697$	8.39826e9	0.939452
$698$	7.67695e8	0.0854466
$699$	−6.86541e9	−0.760319
$700$	4.02130e6	0.000443122 0
$701$	3.29175e9	0.360922	0.180461	−	0.983582i	$-0.442241\pi$
$701$	3.29175e9	0.360922	0.180461	+	0.983582i	$0.442241\pi$
$702$	3.45948e8	0.0377426
$703$	−6.95009e9	−0.754478
$704$	6.71090e8	0.0724897
$705$	−8.65369e9	−0.930120
$706$	−9.39606e9	−1.00492
$707$	−5.10869e9	−0.543678
$708$	1.33346e9	0.141209
$709$	6.20927e9	0.654302	0.327151	−	0.944972i	$-0.393911\pi$
$709$	6.20927e9	0.654302	0.327151	+	0.944972i	$0.393911\pi$
$710$	−9.14990e9	−0.959428
$711$	1.87059e9	0.195180
$712$	3.45563e9	0.358796
$713$	1.65680e9	0.171182
$714$	2.08535e9	0.214405
$715$	1.57389e9	0.161029
$716$	−1.18120e9	−0.120262
$717$	8.14921e9	0.825654
$718$	−3.67127e9	−0.370153
$719$	−7.72606e9	−0.775188	−0.387594	−	0.921830i	$-0.626694\pi$
$719$	−7.72606e9	−0.775188	−0.387594	+	0.921830i	$0.626694\pi$
$720$	8.35586e8	0.0834310
$721$	2.77488e9	0.275722
$722$	−5.59386e9	−0.553135
$723$	7.80824e9	0.768367
$724$	2.20186e8	0.0215628
$725$	−8.54302e6	−0.000832585 0
$726$	−2.79365e9	−0.270952
$727$	−9.18547e9	−0.886606	−0.443303	−	0.896372i	$-0.646193\pi$
$727$	−9.18547e9	−0.886606	−0.443303	+	0.896372i	$0.646193\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−6.94762e9	−0.661007
$731$	1.13032e10	1.07026
$732$	1.14508e9	0.107906
$733$	6.66593e9	0.625169	0.312584	−	0.949890i	$-0.398805\pi$
$733$	6.66593e9	0.625169	0.312584	+	0.949890i	$0.398805\pi$
$734$	−5.75664e9	−0.537320
$735$	−8.88905e8	−0.0825753
$736$	−3.04712e9	−0.281720
$737$	−4.63620e9	−0.426605
$738$	−1.74010e9	−0.159360
$739$	1.64955e10	1.50352	0.751761	−	0.659436i	$-0.229205\pi$
$739$	1.64955e10	1.50352	0.751761	+	0.659436i	$0.229205\pi$
$740$	3.11854e9	0.282905
$741$	2.36764e9	0.213773
$742$	−1.40831e9	−0.126556
$743$	9.53888e9	0.853172	0.426586	−	0.904447i	$-0.359716\pi$
$743$	9.53888e9	0.853172	0.426586	+	0.904447i	$0.359716\pi$
$744$	2.46300e8	0.0219260
$745$	−7.97254e9	−0.706398
$746$	−8.12892e9	−0.716881
$747$	−2.70772e9	−0.237674
$748$	4.61160e9	0.402899
$749$	−5.21220e9	−0.453247
$750$	−4.71116e9	−0.407768
$751$	3.93662e9	0.339143	0.169572	−	0.985518i	$-0.445762\pi$
$751$	3.93662e9	0.339143	0.169572	+	0.985518i	$0.445762\pi$
$752$	4.69131e9	0.402283
$753$	−2.47009e9	−0.210829
$754$	8.19671e8	0.0696369
$755$	6.02181e8	0.0509229
$756$	−4.32081e8	−0.0363696
$757$	7.01490e8	0.0587741	0.0293871	−	0.999568i	$-0.490644\pi$
$757$	7.01490e8	0.0587741	0.0293871	+	0.999568i	$0.490644\pi$
$758$	−1.02612e10	−0.855764
$759$	−6.42753e9	−0.533578
$760$	5.71868e9	0.472550
$761$	7.22381e9	0.594183	0.297091	−	0.954849i	$-0.403983\pi$
$761$	7.22381e9	0.594183	0.297091	+	0.954849i	$0.403983\pi$
$762$	−6.56478e9	−0.537499
$763$	−5.74236e9	−0.468009
$764$	1.04380e10	0.846821
$765$	5.74199e9	0.463711
$766$	9.81676e9	0.789164
$767$	−1.69538e9	−0.135670
$768$	−4.52985e8	−0.0360844
$769$	1.72423e10	1.36727	0.683634	−	0.729825i	$-0.260398\pi$
$769$	1.72423e10	1.36727	0.683634	+	0.729825i	$0.260398\pi$
$770$	−1.96575e9	−0.155171
$771$	−3.57893e8	−0.0281230
$772$	1.68689e9	0.131955
$773$	4.66763e9	0.363470	0.181735	−	0.983348i	$-0.441829\pi$
$773$	4.66763e9	0.363470	0.181735	+	0.983348i	$0.441829\pi$
$774$	−2.34200e9	−0.181549
$775$	3.26380e6	0.000251865 0
$776$	1.54650e9	0.118805
$777$	−1.61260e9	−0.123325
$778$	2.94422e9	0.224151
$779$	−1.19091e10	−0.902607
$780$	−1.06237e9	−0.0801579
$781$	1.04632e10	0.785932
$782$	−2.09392e10	−1.56580
$783$	9.17932e8	0.0683352
$784$	4.81890e8	0.0357143
$785$	−8.78649e9	−0.648294
$786$	1.35134e9	0.0992628
$787$	1.36927e10	1.00133	0.500664	−	0.865642i	$-0.333089\pi$
$787$	1.36927e10	1.00133	0.500664	+	0.865642i	$0.333089\pi$
$788$	1.39695e9	0.101704
$789$	−3.94955e9	−0.286271
$790$	−5.74440e9	−0.414524
$791$	3.16724e9	0.227543
$792$	−9.55517e8	−0.0683440
$793$	−1.45587e9	−0.103673
$794$	−7.04698e9	−0.499610
$795$	−3.87776e9	−0.273714
$796$	8.49316e8	0.0596861
$797$	1.35135e10	0.945508	0.472754	−	0.881194i	$-0.343260\pi$
$797$	1.35135e10	0.945508	0.472754	+	0.881194i	$0.343260\pi$
$798$	−2.95713e9	−0.205996
$799$	3.22378e10	2.23589
$800$	−6.00264e6	−0.000414503 0
$801$	−4.92022e9	−0.338276
$802$	1.68883e10	1.15605
$803$	7.94481e9	0.541476
$804$	3.12943e9	0.212358
$805$	8.92559e9	0.603047
$806$	−3.13149e8	−0.0210658
$807$	−1.03034e10	−0.690117
$808$	7.62580e9	0.508564
$809$	4.22437e9	0.280506	0.140253	−	0.990116i	$-0.455208\pi$
$809$	4.22437e9	0.280506	0.140253	+	0.990116i	$0.455208\pi$
$810$	−1.18973e9	−0.0786595
$811$	−1.56128e10	−1.02780	−0.513898	−	0.857851i	$-0.671799\pi$
$811$	−1.56128e10	−1.02780	−0.513898	+	0.857851i	$0.671799\pi$
$812$	−1.02375e9	−0.0671038
$813$	−1.21947e10	−0.795895
$814$	−3.56615e9	−0.231747
$815$	2.29421e10	1.48451
$816$	−3.11283e9	−0.200558
$817$	−1.60285e10	−1.02829
$818$	1.60427e8	0.0102481
$819$	5.49353e8	0.0349428
$820$	5.34369e9	0.338449
$821$	1.92012e9	0.121095	0.0605475	−	0.998165i	$-0.480715\pi$
$821$	1.92012e9	0.121095	0.0605475	+	0.998165i	$0.480715\pi$
$822$	1.23145e10	0.773332
$823$	−3.34965e9	−0.209459	−0.104730	−	0.994501i	$-0.533398\pi$
$823$	−3.34965e9	−0.209459	−0.104730	+	0.994501i	$0.533398\pi$
$824$	−4.14210e9	−0.257914
$825$	−1.26618e7	−0.000785069 0
$826$	2.11748e9	0.130734
$827$	1.16687e10	0.717389	0.358695	−	0.933455i	$-0.383222\pi$
$827$	1.16687e10	0.717389	0.358695	+	0.933455i	$0.383222\pi$
$828$	4.33857e9	0.265608
$829$	2.62032e10	1.59740	0.798700	−	0.601730i	$-0.205522\pi$
$829$	2.62032e10	1.59740	0.798700	+	0.601730i	$0.205522\pi$
$830$	8.31514e9	0.504773
$831$	9.56902e9	0.578447
$832$	5.75930e8	0.0346688
$833$	3.31146e9	0.198501
$834$	1.23373e9	0.0736442
$835$	2.01251e10	1.19628
$836$	−6.53948e9	−0.387098
$837$	−3.50689e8	−0.0206720
$838$	−1.30785e10	−0.767724
$839$	1.62942e10	0.952505	0.476252	−	0.879309i	$-0.341995\pi$
$839$	1.62942e10	0.952505	0.476252	+	0.879309i	$0.341995\pi$
$840$	1.32688e9	0.0772421
$841$	−1.50750e10	−0.873918
$842$	1.13990e10	0.658076
$843$	−3.83913e9	−0.220717
$844$	−9.67013e9	−0.553648
$845$	1.35071e9	0.0770132
$846$	−6.67961e9	−0.379276
$847$	−4.43621e9	−0.250853
$848$	2.10220e9	0.118383
$849$	−1.58931e10	−0.891316
$850$	−4.12490e7	−0.00230381
$851$	1.61923e10	0.900646
$852$	−7.06263e9	−0.391226
$853$	6.90940e9	0.381170	0.190585	−	0.981671i	$-0.438962\pi$
$853$	6.90940e9	0.381170	0.190585	+	0.981671i	$0.438962\pi$
$854$	1.81834e9	0.0999018
$855$	−8.14241e9	−0.445525
$856$	7.78032e9	0.423974
$857$	−1.27157e10	−0.690093	−0.345047	−	0.938586i	$-0.612137\pi$
$857$	−1.27157e10	−0.690093	−0.345047	+	0.938586i	$0.612137\pi$
$858$	1.21486e9	0.0656628
$859$	1.62162e8	0.00872915	0.00436457	−	0.999990i	$-0.498611\pi$
$859$	1.62162e8	0.00872915	0.00436457	+	0.999990i	$0.498611\pi$
$860$	7.19207e9	0.385575
$861$	−2.76322e9	−0.147538
$862$	−1.59619e10	−0.848806
$863$	−3.35161e10	−1.77507	−0.887535	−	0.460739i	$-0.847584\pi$
$863$	−3.35161e10	−1.77507	−0.887535	+	0.460739i	$0.847584\pi$
$864$	6.44973e8	0.0340207
$865$	−2.68037e10	−1.40811
$866$	−1.27062e10	−0.664820
$867$	−1.03116e10	−0.537353
$868$	3.91116e8	0.0202995
$869$	6.56889e9	0.339565
$870$	−2.81888e9	−0.145131
$871$	−3.97880e9	−0.204027
$872$	8.57168e9	0.437782
$873$	−2.20195e9	−0.112010
$874$	2.96928e10	1.50439
$875$	−7.48115e9	−0.377520
$876$	−5.36273e9	−0.269539
$877$	−3.27104e9	−0.163752	−0.0818761	−	0.996643i	$-0.526091\pi$
$877$	−3.27104e9	−0.163752	−0.0818761	+	0.996643i	$0.526091\pi$
$878$	−2.07964e10	−1.03695
$879$	−1.68827e10	−0.838455
$880$	2.93430e9	0.145149
$881$	1.42712e10	0.703146	0.351573	−	0.936160i	$-0.385647\pi$
$881$	1.42712e10	0.703146	0.351573	+	0.936160i	$0.385647\pi$
$882$	−6.86129e8	−0.0336718
$883$	−7.00203e9	−0.342264	−0.171132	−	0.985248i	$-0.554743\pi$
$883$	−7.00203e9	−0.342264	−0.171132	+	0.985248i	$0.554743\pi$
$884$	3.95769e9	0.192690
$885$	5.83047e9	0.282750
$886$	7.62837e9	0.368480
$887$	7.78550e9	0.374588	0.187294	−	0.982304i	$-0.440028\pi$
$887$	7.78550e9	0.374588	0.187294	+	0.982304i	$0.440028\pi$
$888$	2.40714e9	0.115360
$889$	−1.04246e10	−0.497628
$890$	1.51095e10	0.718432
$891$	1.36049e9	0.0644353
$892$	1.18368e10	0.558414
$893$	−4.57147e10	−2.14820
$894$	−6.15385e9	−0.288048
$895$	−5.16471e9	−0.240805
$896$	−7.19323e8	−0.0334077
$897$	−5.51611e9	−0.255188
$898$	1.94040e10	0.894180
$899$	−8.30904e8	−0.0381410
$900$	8.54672e6	0.000390797 0
$901$	1.44459e10	0.657973
$902$	−6.11067e9	−0.277246
$903$	−3.71902e9	−0.168082
$904$	−4.72778e9	−0.212847
$905$	9.62750e8	0.0431761
$906$	4.64812e8	0.0207649
$907$	3.28147e10	1.46030	0.730151	−	0.683286i	$-0.239450\pi$
$907$	3.28147e10	1.46030	0.730151	+	0.683286i	$0.239450\pi$
$908$	−1.10428e10	−0.489528
$909$	−1.08578e10	−0.479479
$910$	−1.68701e9	−0.0742118
$911$	2.61726e10	1.14692	0.573460	−	0.819234i	$-0.305601\pi$
$911$	2.61726e10	1.14692	0.573460	+	0.819234i	$0.305601\pi$
$912$	4.41414e9	0.192692
$913$	−9.50861e9	−0.413494
$914$	−1.73817e10	−0.752977
$915$	5.00678e9	0.216065
$916$	1.58395e10	0.680936
$917$	2.14588e9	0.0918995
$918$	4.43213e9	0.189088
$919$	2.20658e10	0.937811	0.468906	−	0.883248i	$-0.344648\pi$
$919$	2.20658e10	0.937811	0.468906	+	0.883248i	$0.344648\pi$
$920$	−1.33233e10	−0.564099
$921$	2.49299e10	1.05151
$922$	1.69617e10	0.712706
$923$	8.97952e9	0.375878
$924$	−1.51733e9	−0.0632742
$925$	3.18978e7	0.00132515
$926$	−3.14732e9	−0.130257
$927$	5.89763e9	0.243164
$928$	1.52816e9	0.0627699
$929$	1.08178e10	0.442673	0.221337	−	0.975197i	$-0.428958\pi$
$929$	1.08178e10	0.442673	0.221337	+	0.975197i	$0.428958\pi$
$930$	1.07693e9	0.0439034
$931$	−4.69581e9	−0.190716
$932$	1.62736e10	0.658456
$933$	1.64941e10	0.664880
$934$	−7.69176e9	−0.308896
$935$	2.01640e10	0.806743
$936$	−8.20026e8	−0.0326860
$937$	9.93137e9	0.394385	0.197193	−	0.980365i	$-0.436818\pi$
$937$	9.93137e9	0.394385	0.197193	+	0.980365i	$0.436818\pi$
$938$	4.96942e9	0.196606
$939$	−5.13079e9	−0.202234
$940$	2.05124e10	0.805508
$941$	9.73478e9	0.380857	0.190429	−	0.981701i	$-0.439012\pi$
$941$	9.73478e9	0.380857	0.190429	+	0.981701i	$0.439012\pi$
$942$	−6.78212e9	−0.264355
$943$	2.77458e10	1.07747
$944$	−3.16079e9	−0.122291
$945$	−1.88925e9	−0.0728245
$946$	−8.22434e9	−0.315851
$947$	−2.83066e7	−0.00108308	−0.000541542	−	1.00000i	$-0.500172\pi$
$947$	−2.83066e7	−0.00108308	−0.000541542		1.00000i	$0.500172\pi$
$948$	−4.43399e9	−0.169031
$949$	6.81824e9	0.258965
$950$	5.84930e7	0.00221346
$951$	2.30806e10	0.870194
$952$	−4.94305e9	−0.185680
$953$	−2.75785e10	−1.03216	−0.516079	−	0.856541i	$-0.672609\pi$
$953$	−2.75785e10	−1.03216	−0.516079	+	0.856541i	$0.672609\pi$
$954$	−2.99317e9	−0.111612
$955$	4.56396e10	1.69563
$956$	−1.93166e10	−0.715038
$957$	3.22347e9	0.118886
$958$	−1.92669e10	−0.708000
$959$	1.95550e10	0.715967
$960$	−1.98065e9	−0.0722533
$961$	−2.71952e10	−0.988462
$962$	−3.06047e9	−0.110835
$963$	−1.10778e10	−0.399726
$964$	−1.85084e10	−0.665426
$965$	7.37584e9	0.264220
$966$	6.88949e9	0.245905
$967$	−4.41143e9	−0.156887	−0.0784434	−	0.996919i	$-0.524995\pi$
$967$	−4.41143e9	−0.156887	−0.0784434	+	0.996919i	$0.524995\pi$
$968$	6.62197e9	0.234652
$969$	3.03331e10	1.07099
$970$	6.76197e9	0.237888
$971$	2.60422e10	0.912872	0.456436	−	0.889756i	$-0.349126\pi$
$971$	2.60422e10	0.912872	0.456436	+	0.889756i	$0.349126\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.95912e9	0.0681813
$974$	−1.27618e9	−0.0442542
$975$	−1.08664e7	−0.000375465 0
$976$	−2.71426e9	−0.0934495
$977$	−3.42675e9	−0.117558	−0.0587789	−	0.998271i	$-0.518721\pi$
$977$	−3.42675e9	−0.117558	−0.0587789	+	0.998271i	$0.518721\pi$
$978$	1.77086e10	0.605338
$979$	−1.72782e10	−0.588516
$980$	2.10704e9	0.0715123
$981$	−1.22046e10	−0.412745
$982$	1.72664e10	0.581850
$983$	1.62156e9	0.0544498	0.0272249	−	0.999629i	$-0.491333\pi$
$983$	1.62156e9	0.0544498	0.0272249	+	0.999629i	$0.491333\pi$
$984$	4.12469e9	0.138009
$985$	6.10806e9	0.203646
$986$	1.05012e10	0.348876
$987$	−1.06070e10	−0.351141
$988$	−5.61219e9	−0.185133
$989$	3.73430e10	1.22750
$990$	−4.17794e9	−0.136848
$991$	1.76672e10	0.576646	0.288323	−	0.957533i	$-0.406902\pi$
$991$	1.76672e10	0.576646	0.288323	+	0.957533i	$0.406902\pi$
$992$	−5.83823e8	−0.0189885
$993$	−2.53627e10	−0.822004
$994$	−1.12152e10	−0.362205
$995$	3.71358e9	0.119512
$996$	6.41830e9	0.205832
$997$	1.44755e10	0.462595	0.231298	−	0.972883i	$-0.425703\pi$
$997$	1.44755e10	0.462595	0.231298	+	0.972883i	$0.425703\pi$
$998$	−1.05865e9	−0.0337128
$999$	−3.42736e9	−0.108763

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.n.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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +279.836 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +279.836 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -2238.69 q^{10} +2560.01 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -7555.57 q^{15} +4096.00 q^{16} +28146.9 q^{17} -5832.00 q^{18} -39913.7 q^{19} +17909.5 q^{20} -9261.00 q^{21} -20480.0 q^{22} +92990.7 q^{23} +13824.0 q^{24} +183.186 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} -46635.8 q^{29} +60444.6 q^{30} +17816.9 q^{31} -32768.0 q^{32} -69120.1 q^{33} -225176. q^{34} +95983.7 q^{35} +46656.0 q^{36} +174128. q^{37} +319310. q^{38} -59319.0 q^{39} -143276. q^{40} +298372. q^{41} +74088.0 q^{42} +401578. q^{43} +163840. q^{44} +204000. q^{45} -743925. q^{46} +1.14534e6 q^{47} -110592. q^{48} +117649. q^{49} -1465.49 q^{50} -759967. q^{51} +140608. q^{52} +513232. q^{53} +157464. q^{54} +716382. q^{55} -175616. q^{56} +1.07767e6 q^{57} +373086. q^{58} -771678. q^{59} -483557. q^{60} -662661. q^{61} -142535. q^{62} +250047. q^{63} +262144. q^{64} +614800. q^{65} +552961. q^{66} -1.81101e6 q^{67} +1.80140e6 q^{68} -2.51075e6 q^{69} -767870. q^{70} +4.08717e6 q^{71} -373248. q^{72} +3.10343e6 q^{73} -1.39302e6 q^{74} -4946.02 q^{75} -2.55448e6 q^{76} +878082. q^{77} +474552. q^{78} +2.56597e6 q^{79} +1.14621e6 q^{80} +531441. q^{81} -2.38698e6 q^{82} -3.71429e6 q^{83} -592704. q^{84} +7.87653e6 q^{85} -3.21263e6 q^{86} +1.25917e6 q^{87} -1.31072e6 q^{88} -6.74927e6 q^{89} -1.63200e6 q^{90} +753571. q^{91} +5.95140e6 q^{92} -481055. q^{93} -9.16271e6 q^{94} -1.11693e7 q^{95} +884736. q^{96} -3.02051e6 q^{97} -941192. q^{98} +1.86624e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 181 q^{5} + 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 181 * q^5 + 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 181 q^{5} + 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 1448 q^{10} - 6130 q^{11} - 10368 q^{12} + 13182 q^{13} - 16464 q^{14} + 4887 q^{15} + 24576 q^{16} - 34610 q^{17} - 34992 q^{18} - 4085 q^{19} - 11584 q^{20} - 55566 q^{21} + 49040 q^{22} + 1515 q^{23} + 82944 q^{24} + 156609 q^{25} - 105456 q^{26} - 118098 q^{27} + 131712 q^{28} - 59395 q^{29} - 39096 q^{30} + 478241 q^{31} - 196608 q^{32} + 165510 q^{33} + 276880 q^{34} - 62083 q^{35} + 279936 q^{36} + 574310 q^{37} + 32680 q^{38} - 355914 q^{39} + 92672 q^{40} + 201552 q^{41} + 444528 q^{42} + 728605 q^{43} - 392320 q^{44} - 131949 q^{45} - 12120 q^{46} + 227615 q^{47} - 663552 q^{48} + 705894 q^{49} - 1252872 q^{50} + 934470 q^{51} + 843648 q^{52} + 26321 q^{53} + 944784 q^{54} + 2115010 q^{55} - 1053696 q^{56} + 110295 q^{57} + 475160 q^{58} + 478280 q^{59} + 312768 q^{60} - 501406 q^{61} - 3825928 q^{62} + 1500282 q^{63} + 1572864 q^{64} - 397657 q^{65} - 1324080 q^{66} - 3156366 q^{67} - 2215040 q^{68} - 40905 q^{69} + 496664 q^{70} - 2003644 q^{71} - 2239488 q^{72} + 3659111 q^{73} - 4594480 q^{74} - 4228443 q^{75} - 261440 q^{76} - 2102590 q^{77} + 2847312 q^{78} + 1131065 q^{79} - 741376 q^{80} + 3188646 q^{81} - 1612416 q^{82} - 9629297 q^{83} - 3556224 q^{84} + 895068 q^{85} - 5828840 q^{86} + 1603665 q^{87} + 3138560 q^{88} - 21977377 q^{89} + 1055592 q^{90} + 4521426 q^{91} + 96960 q^{92} - 12912507 q^{93} - 1820920 q^{94} - 19325507 q^{95} + 5308416 q^{96} - 26386649 q^{97} - 5647152 q^{98} - 4468770 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 181 * q^5 + 1296 * q^6 + 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 1448 * q^10 - 6130 * q^11 - 10368 * q^12 + 13182 * q^13 - 16464 * q^14 + 4887 * q^15 + 24576 * q^16 - 34610 * q^17 - 34992 * q^18 - 4085 * q^19 - 11584 * q^20 - 55566 * q^21 + 49040 * q^22 + 1515 * q^23 + 82944 * q^24 + 156609 * q^25 - 105456 * q^26 - 118098 * q^27 + 131712 * q^28 - 59395 * q^29 - 39096 * q^30 + 478241 * q^31 - 196608 * q^32 + 165510 * q^33 + 276880 * q^34 - 62083 * q^35 + 279936 * q^36 + 574310 * q^37 + 32680 * q^38 - 355914 * q^39 + 92672 * q^40 + 201552 * q^41 + 444528 * q^42 + 728605 * q^43 - 392320 * q^44 - 131949 * q^45 - 12120 * q^46 + 227615 * q^47 - 663552 * q^48 + 705894 * q^49 - 1252872 * q^50 + 934470 * q^51 + 843648 * q^52 + 26321 * q^53 + 944784 * q^54 + 2115010 * q^55 - 1053696 * q^56 + 110295 * q^57 + 475160 * q^58 + 478280 * q^59 + 312768 * q^60 - 501406 * q^61 - 3825928 * q^62 + 1500282 * q^63 + 1572864 * q^64 - 397657 * q^65 - 1324080 * q^66 - 3156366 * q^67 - 2215040 * q^68 - 40905 * q^69 + 496664 * q^70 - 2003644 * q^71 - 2239488 * q^72 + 3659111 * q^73 - 4594480 * q^74 - 4228443 * q^75 - 261440 * q^76 - 2102590 * q^77 + 2847312 * q^78 + 1131065 * q^79 - 741376 * q^80 + 3188646 * q^81 - 1612416 * q^82 - 9629297 * q^83 - 3556224 * q^84 + 895068 * q^85 - 5828840 * q^86 + 1603665 * q^87 + 3138560 * q^88 - 21977377 * q^89 + 1055592 * q^90 + 4521426 * q^91 + 96960 * q^92 - 12912507 * q^93 - 1820920 * q^94 - 19325507 * q^95 + 5308416 * q^96 - 26386649 * q^97 - 5647152 * q^98 - 4468770 * q^99

Introduction

L-functions

Modular forms

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