LMFDB - Embedded newform 546.8.a.n.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	546.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$170.562223914$
Analytic rank:	$0$
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			1.4
Root			$-193.695$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +163.695 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +163.695 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -1309.56 q^{10} -5270.71 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -4419.76 q^{15} +4096.00 q^{16} -22465.3 q^{17} -5832.00 q^{18} +52382.4 q^{19} +10476.5 q^{20} -9261.00 q^{21} +42165.7 q^{22} -49077.8 q^{23} +13824.0 q^{24} -51329.0 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} -251211. q^{29} +35358.1 q^{30} -61456.3 q^{31} -32768.0 q^{32} +142309. q^{33} +179722. q^{34} +56147.3 q^{35} +46656.0 q^{36} +455742. q^{37} -419059. q^{38} -59319.0 q^{39} -83811.7 q^{40} -398400. q^{41} +74088.0 q^{42} +566931. q^{43} -337325. q^{44} +119333. q^{45} +392622. q^{46} +695284. q^{47} -110592. q^{48} +117649. q^{49} +410632. q^{50} +606563. q^{51} +140608. q^{52} +2.12926e6 q^{53} +157464. q^{54} -862787. q^{55} -175616. q^{56} -1.41432e6 q^{57} +2.00968e6 q^{58} +237754. q^{59} -282864. q^{60} +1.97343e6 q^{61} +491650. q^{62} +250047. q^{63} +262144. q^{64} +359637. q^{65} -1.13847e6 q^{66} -2.27193e6 q^{67} -1.43778e6 q^{68} +1.32510e6 q^{69} -449178. q^{70} -4.73935e6 q^{71} -373248. q^{72} +171509. q^{73} -3.64593e6 q^{74} +1.38588e6 q^{75} +3.35247e6 q^{76} -1.80785e6 q^{77} +474552. q^{78} -4.20339e6 q^{79} +670494. q^{80} +531441. q^{81} +3.18720e6 q^{82} -5.78958e6 q^{83} -592704. q^{84} -3.67745e6 q^{85} -4.53544e6 q^{86} +6.78268e6 q^{87} +2.69860e6 q^{88} +3.98718e6 q^{89} -954668. q^{90} +753571. q^{91} -3.14098e6 q^{92} +1.65932e6 q^{93} -5.56227e6 q^{94} +8.57472e6 q^{95} +884736. q^{96} -121519. q^{97} -941192. q^{98} -3.84235e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	163.695	0.585652	0.292826	−	0.956166i	$-0.405404\pi$
$5$	163.695	0.585652	0.292826	+	0.956166i	$0.405404\pi$
$6$	216.000	0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−1309.56	−0.414119
$11$	−5270.71	−1.19397	−0.596987	−	0.802251i	$-0.703635\pi$
$11$	−5270.71	−1.19397	−0.596987	+	0.802251i	$0.703635\pi$
$12$	−1728.00	−0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−2744.00	−0.267261
$15$	−4419.76	−0.338126
$16$	4096.00	0.250000
$17$	−22465.3	−1.10902	−0.554512	−	0.832176i	$-0.687095\pi$
$17$	−22465.3	−1.10902	−0.554512	+	0.832176i	$0.687095\pi$
$18$	−5832.00	−0.235702
$19$	52382.4	1.75205	0.876027	−	0.482261i	$-0.160184\pi$
$19$	52382.4	1.75205	0.876027	+	0.482261i	$0.160184\pi$
$20$	10476.5	0.292826
$21$	−9261.00	−0.218218
$22$	42165.7	0.844266
$23$	−49077.8	−0.841080	−0.420540	−	0.907274i	$-0.638159\pi$
$23$	−49077.8	−0.841080	−0.420540	+	0.907274i	$0.638159\pi$
$24$	13824.0	0.204124
$25$	−51329.0	−0.657012
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	21952.0	0.188982
$29$	−251211.	−1.91269	−0.956345	−	0.292238i	$-0.905600\pi$
$29$	−251211.	−1.91269	−0.956345	+	0.292238i	$0.905600\pi$
$30$	35358.1	0.239091
$31$	−61456.3	−0.370510	−0.185255	−	0.982690i	$-0.559311\pi$
$31$	−61456.3	−0.370510	−0.185255	+	0.982690i	$0.559311\pi$
$32$	−32768.0	−0.176777
$33$	142309.	0.689341
$34$	179722.	0.784198
$35$	56147.3	0.221356
$36$	46656.0	0.166667
$37$	455742.	1.47915	0.739576	−	0.673073i	$-0.235026\pi$
$37$	455742.	1.47915	0.739576	+	0.673073i	$0.235026\pi$
$38$	−419059.	−1.23889
$39$	−59319.0	−0.160128
$40$	−83811.7	−0.207059
$41$	−398400.	−0.902767	−0.451383	−	0.892330i	$-0.649069\pi$
$41$	−398400.	−0.902767	−0.451383	+	0.892330i	$0.649069\pi$
$42$	74088.0	0.154303
$43$	566931.	1.08740	0.543701	−	0.839279i	$-0.317022\pi$
$43$	566931.	1.08740	0.543701	+	0.839279i	$0.317022\pi$
$44$	−337325.	−0.596987
$45$	119333.	0.195217
$46$	392622.	0.594733
$47$	695284.	0.976832	0.488416	−	0.872611i	$-0.337575\pi$
$47$	695284.	0.976832	0.488416	+	0.872611i	$0.337575\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	410632.	0.464577
$51$	606563.	0.640295
$52$	140608.	0.138675
$53$	2.12926e6	1.96455	0.982273	−	0.187454i	$-0.0600235\pi$
$53$	2.12926e6	1.96455	0.982273	+	0.187454i	$0.0600235\pi$
$54$	157464.	0.136083
$55$	−862787.	−0.699253
$56$	−175616.	−0.133631
$57$	−1.41432e6	−1.01155
$58$	2.00968e6	1.35248
$59$	237754.	0.150711	0.0753557	−	0.997157i	$-0.475991\pi$
$59$	237754.	0.150711	0.0753557	+	0.997157i	$0.475991\pi$
$60$	−282864.	−0.169063
$61$	1.97343e6	1.11318	0.556591	−	0.830786i	$-0.312109\pi$
$61$	1.97343e6	1.11318	0.556591	+	0.830786i	$0.312109\pi$
$62$	491650.	0.261990
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	359637.	0.162431
$66$	−1.13847e6	−0.487437
$67$	−2.27193e6	−0.922855	−0.461428	−	0.887178i	$-0.652663\pi$
$67$	−2.27193e6	−0.922855	−0.461428	+	0.887178i	$0.652663\pi$
$68$	−1.43778e6	−0.554512
$69$	1.32510e6	0.485598
$70$	−449178.	−0.156522
$71$	−4.73935e6	−1.57150	−0.785750	−	0.618544i	$-0.787723\pi$
$71$	−4.73935e6	−1.57150	−0.785750	+	0.618544i	$0.787723\pi$
$72$	−373248.	−0.117851
$73$	171509.	0.0516008	0.0258004	−	0.999667i	$-0.491787\pi$
$73$	171509.	0.0516008	0.0258004	+	0.999667i	$0.491787\pi$
$74$	−3.64593e6	−1.04592
$75$	1.38588e6	0.379326
$76$	3.35247e6	0.876027
$77$	−1.80785e6	−0.451279
$78$	474552.	0.113228
$79$	−4.20339e6	−0.959190	−0.479595	−	0.877490i	$-0.659216\pi$
$79$	−4.20339e6	−0.959190	−0.479595	+	0.877490i	$0.659216\pi$
$80$	670494.	0.146413
$81$	531441.	0.111111
$82$	3.18720e6	0.638352
$83$	−5.78958e6	−1.11141	−0.555704	−	0.831380i	$-0.687551\pi$
$83$	−5.78958e6	−1.11141	−0.555704	+	0.831380i	$0.687551\pi$
$84$	−592704.	−0.109109
$85$	−3.67745e6	−0.649502
$86$	−4.53544e6	−0.768910
$87$	6.78268e6	1.10429
$88$	2.69860e6	0.422133
$89$	3.98718e6	0.599517	0.299758	−	0.954015i	$-0.403094\pi$
$89$	3.98718e6	0.599517	0.299758	+	0.954015i	$0.403094\pi$
$90$	−954668.	−0.138040
$91$	753571.	0.104828
$92$	−3.14098e6	−0.420540
$93$	1.65932e6	0.213914
$94$	−5.56227e6	−0.690724
$95$	8.57472e6	1.02609
$96$	884736.	0.102062
$97$	−121519.	−0.0135190	−0.00675950	−	0.999977i	$-0.502152\pi$
$97$	−121519.	−0.0135190	−0.00675950	+	0.999977i	$0.502152\pi$
$98$	−941192.	−0.101015
$99$	−3.84235e6	−0.397991
$100$	−3.28506e6	−0.328506
$101$	1.25924e7	1.21614	0.608070	−	0.793883i	$-0.291944\pi$
$101$	1.25924e7	1.21614	0.608070	+	0.793883i	$0.291944\pi$
$102$	−4.85250e6	−0.452757
$103$	2.03686e6	0.183667	0.0918333	−	0.995774i	$-0.470727\pi$
$103$	2.03686e6	0.183667	0.0918333	+	0.995774i	$0.470727\pi$
$104$	−1.12486e6	−0.0980581
$105$	−1.51598e6	−0.127800
$106$	−1.70340e7	−1.38914
$107$	−7.81636e6	−0.616824	−0.308412	−	0.951253i	$-0.599798\pi$
$107$	−7.81636e6	−0.616824	−0.308412	+	0.951253i	$0.599798\pi$
$108$	−1.25971e6	−0.0962250
$109$	−1.90675e7	−1.41027	−0.705133	−	0.709075i	$-0.749113\pi$
$109$	−1.90675e7	−1.41027	−0.705133	+	0.709075i	$0.749113\pi$
$110$	6.90230e6	0.494446
$111$	−1.23050e7	−0.853988
$112$	1.40493e6	0.0944911
$113$	−3.15325e6	−0.205582	−0.102791	−	0.994703i	$-0.532777\pi$
$113$	−3.15325e6	−0.205582	−0.102791	+	0.994703i	$0.532777\pi$
$114$	1.13146e7	0.715273
$115$	−8.03377e6	−0.492580
$116$	−1.60775e7	−0.956345
$117$	1.60161e6	0.0924500
$118$	−1.90203e6	−0.106569
$119$	−7.70559e6	−0.419171
$120$	2.26292e6	0.119546
$121$	8.29319e6	0.425572
$122$	−1.57874e7	−0.787139
$123$	1.07568e7	0.521213
$124$	−3.93320e6	−0.185255
$125$	−2.11909e7	−0.970432
$126$	−2.00038e6	−0.0890871
$127$	−2.78397e7	−1.20601	−0.603007	−	0.797736i	$-0.706031\pi$
$127$	−2.78397e7	−1.20601	−0.603007	+	0.797736i	$0.706031\pi$
$128$	−2.09715e6	−0.0883883
$129$	−1.53071e7	−0.627812
$130$	−2.87710e6	−0.114856
$131$	2.12651e7	0.826453	0.413226	−	0.910628i	$-0.364402\pi$
$131$	2.12651e7	0.826453	0.413226	+	0.910628i	$0.364402\pi$
$132$	9.10778e6	0.344670
$133$	1.79672e7	0.662214
$134$	1.81755e7	0.652557
$135$	−3.22200e6	−0.112709
$136$	1.15022e7	0.392099
$137$	3.85459e7	1.28072	0.640362	−	0.768073i	$-0.278784\pi$
$137$	3.85459e7	1.28072	0.640362	+	0.768073i	$0.278784\pi$
$138$	−1.06008e7	−0.343369
$139$	4.29822e7	1.35749	0.678746	−	0.734373i	$-0.262524\pi$
$139$	4.29822e7	1.35749	0.678746	+	0.734373i	$0.262524\pi$
$140$	3.59343e6	0.110678
$141$	−1.87727e7	−0.563974
$142$	3.79148e7	1.11122
$143$	−1.15797e7	−0.331149
$144$	2.98598e6	0.0833333
$145$	−4.11218e7	−1.12017
$146$	−1.37207e6	−0.0364873
$147$	−3.17652e6	−0.0824786
$148$	2.91675e7	0.739576
$149$	−3.13094e7	−0.775395	−0.387697	−	0.921787i	$-0.626729\pi$
$149$	−3.13094e7	−0.775395	−0.387697	+	0.921787i	$0.626729\pi$
$150$	−1.10871e7	−0.268224
$151$	−2.29410e7	−0.542243	−0.271121	−	0.962545i	$-0.587395\pi$
$151$	−2.29410e7	−0.542243	−0.271121	+	0.962545i	$0.587395\pi$
$152$	−2.68198e7	−0.619445
$153$	−1.63772e7	−0.369674
$154$	1.44628e7	0.319103
$155$	−1.00601e7	−0.216990
$156$	−3.79642e6	−0.0800641
$157$	3.22158e7	0.664386	0.332193	−	0.943211i	$-0.392211\pi$
$157$	3.22158e7	0.664386	0.332193	+	0.943211i	$0.392211\pi$
$158$	3.36271e7	0.678250
$159$	−5.74899e7	−1.13423
$160$	−5.36395e6	−0.103530
$161$	−1.68337e7	−0.317898
$162$	−4.25153e6	−0.0785674
$163$	2.59908e7	0.470070	0.235035	−	0.971987i	$-0.424480\pi$
$163$	2.59908e7	0.470070	0.235035	+	0.971987i	$0.424480\pi$
$164$	−2.54976e7	−0.451383
$165$	2.32953e7	0.403714
$166$	4.63166e7	0.785884
$167$	−3.81590e7	−0.634000	−0.317000	−	0.948426i	$-0.602676\pi$
$167$	−3.81590e7	−0.634000	−0.317000	+	0.948426i	$0.602676\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	2.94196e7	0.459267
$171$	3.81868e7	0.584018
$172$	3.62836e7	0.543701
$173$	1.11532e8	1.63772	0.818859	−	0.573994i	$-0.194607\pi$
$173$	1.11532e8	1.63772	0.818859	+	0.573994i	$0.194607\pi$
$174$	−5.42615e7	−0.780853
$175$	−1.76059e7	−0.248327
$176$	−2.15888e7	−0.298493
$177$	−6.41937e6	−0.0870133
$178$	−3.18975e7	−0.423922
$179$	2.73660e7	0.356637	0.178318	−	0.983973i	$-0.442934\pi$
$179$	2.73660e7	0.356637	0.178318	+	0.983973i	$0.442934\pi$
$180$	7.63734e6	0.0976087
$181$	−5.19179e7	−0.650791	−0.325396	−	0.945578i	$-0.605497\pi$
$181$	−5.19179e7	−0.650791	−0.325396	+	0.945578i	$0.605497\pi$
$182$	−6.02857e6	−0.0741249
$183$	−5.32825e7	−0.642696
$184$	2.51278e7	0.297367
$185$	7.46025e7	0.866268
$186$	−1.32746e7	−0.151260
$187$	1.18408e8	1.32414
$188$	4.44982e7	0.488416
$189$	−6.75127e6	−0.0727393
$190$	−6.85978e7	−0.725558
$191$	−2.97235e6	−0.0308662	−0.0154331	−	0.999881i	$-0.504913\pi$
$191$	−2.97235e6	−0.0308662	−0.0154331	+	0.999881i	$0.504913\pi$
$192$	−7.07789e6	−0.0721688
$193$	−1.32811e8	−1.32979	−0.664893	−	0.746938i	$-0.731523\pi$
$193$	−1.32811e8	−1.32979	−0.664893	+	0.746938i	$0.731523\pi$
$194$	972156.	0.00955938
$195$	−9.71021e6	−0.0937794
$196$	7.52954e6	0.0714286
$197$	7.63908e7	0.711885	0.355942	−	0.934508i	$-0.384160\pi$
$197$	7.63908e7	0.711885	0.355942	+	0.934508i	$0.384160\pi$
$198$	3.07388e7	0.281422
$199$	1.57883e8	1.42020	0.710099	−	0.704102i	$-0.248650\pi$
$199$	1.57883e8	1.42020	0.710099	+	0.704102i	$0.248650\pi$
$200$	2.62805e7	0.232289
$201$	6.13422e7	0.532811
$202$	−1.00739e8	−0.859941
$203$	−8.61652e7	−0.722929
$204$	3.88200e7	0.320147
$205$	−6.52159e7	−0.528707
$206$	−1.62948e7	−0.129872
$207$	−3.57777e7	−0.280360
$208$	8.99891e6	0.0693375
$209$	−2.76092e8	−2.09191
$210$	1.21278e7	0.0903681
$211$	1.73623e8	1.27239	0.636194	−	0.771529i	$-0.280508\pi$
$211$	1.73623e8	1.27239	0.636194	+	0.771529i	$0.280508\pi$
$212$	1.36272e8	0.982273
$213$	1.27962e8	0.907306
$214$	6.25309e7	0.436160
$215$	9.28036e7	0.636839
$216$	1.00777e7	0.0680414
$217$	−2.10795e7	−0.140040
$218$	1.52540e8	0.997209
$219$	−4.63074e6	−0.0297918
$220$	−5.52184e7	−0.349626
$221$	−4.93562e7	−0.307588
$222$	9.84402e7	0.603861
$223$	9.30286e7	0.561758	0.280879	−	0.959743i	$-0.409374\pi$
$223$	9.30286e7	0.561758	0.280879	+	0.959743i	$0.409374\pi$
$224$	−1.12394e7	−0.0668153
$225$	−3.74189e7	−0.219004
$226$	2.52260e7	0.145368
$227$	2.42913e8	1.37835	0.689175	−	0.724595i	$-0.257973\pi$
$227$	2.42913e8	1.37835	0.689175	+	0.724595i	$0.257973\pi$
$228$	−9.05168e7	−0.505775
$229$	3.02548e8	1.66483	0.832416	−	0.554151i	$-0.186957\pi$
$229$	3.02548e8	1.66483	0.832416	+	0.554151i	$0.186957\pi$
$230$	6.42702e7	0.348307
$231$	4.88120e7	0.260546
$232$	1.28620e8	0.676238
$233$	−3.07648e8	−1.59334	−0.796670	−	0.604415i	$-0.793407\pi$
$233$	−3.07648e8	−1.59334	−0.796670	+	0.604415i	$0.793407\pi$
$234$	−1.28129e7	−0.0653720
$235$	1.13814e8	0.572084
$236$	1.52163e7	0.0753557
$237$	1.13491e8	0.553789
$238$	6.16447e7	0.296399
$239$	3.42979e8	1.62508	0.812540	−	0.582906i	$-0.198084\pi$
$239$	3.42979e8	1.62508	0.812540	+	0.582906i	$0.198084\pi$
$240$	−1.81033e7	−0.0845316
$241$	−2.96164e8	−1.36293	−0.681463	−	0.731852i	$-0.738656\pi$
$241$	−2.96164e8	−1.36293	−0.681463	+	0.731852i	$0.738656\pi$
$242$	−6.63455e7	−0.300925
$243$	−1.43489e7	−0.0641500
$244$	1.26299e8	0.556591
$245$	1.92585e7	0.0836646
$246$	−8.60543e7	−0.368553
$247$	1.15084e8	0.485933
$248$	3.14656e7	0.130995
$249$	1.56319e8	0.641672
$250$	1.69528e8	0.686199
$251$	2.71379e8	1.08323	0.541613	−	0.840628i	$-0.317814\pi$
$251$	2.71379e8	1.08323	0.541613	+	0.840628i	$0.317814\pi$
$252$	1.60030e7	0.0629941
$253$	2.58675e8	1.00423
$254$	2.22718e8	0.852780
$255$	9.92911e7	0.374990
$256$	1.67772e7	0.0625000
$257$	8.20843e7	0.301644	0.150822	−	0.988561i	$-0.451808\pi$
$257$	8.20843e7	0.301644	0.150822	+	0.988561i	$0.451808\pi$
$258$	1.22457e8	0.443930
$259$	1.56319e8	0.559067
$260$	2.30168e7	0.0812153
$261$	−1.83132e8	−0.637564
$262$	−1.70121e8	−0.584390
$263$	2.88293e7	0.0977213	0.0488607	−	0.998806i	$-0.484441\pi$
$263$	2.88293e7	0.0977213	0.0488607	+	0.998806i	$0.484441\pi$
$264$	−7.28623e7	−0.243719
$265$	3.48548e8	1.15054
$266$	−1.43737e8	−0.468256
$267$	−1.07654e8	−0.346131
$268$	−1.45404e8	−0.461428
$269$	−2.55221e8	−0.799435	−0.399718	−	0.916638i	$-0.630892\pi$
$269$	−2.55221e8	−0.799435	−0.399718	+	0.916638i	$0.630892\pi$
$270$	2.57760e7	0.0796972
$271$	−2.33565e8	−0.712878	−0.356439	−	0.934319i	$-0.616009\pi$
$271$	−2.33565e8	−0.712878	−0.356439	+	0.934319i	$0.616009\pi$
$272$	−9.20178e7	−0.277256
$273$	−2.03464e7	−0.0605228
$274$	−3.08367e8	−0.905609
$275$	2.70540e8	0.784454
$276$	8.48064e7	0.242799
$277$	−1.03520e8	−0.292647	−0.146324	−	0.989237i	$-0.546744\pi$
$277$	−1.03520e8	−0.292647	−0.146324	+	0.989237i	$0.546744\pi$
$278$	−3.43858e8	−0.959892
$279$	−4.48016e7	−0.123503
$280$	−2.87474e7	−0.0782610
$281$	−6.76758e7	−0.181954	−0.0909769	−	0.995853i	$-0.528999\pi$
$281$	−6.76758e7	−0.181954	−0.0909769	+	0.995853i	$0.528999\pi$
$282$	1.50181e8	0.398790
$283$	8.46969e7	0.222134	0.111067	−	0.993813i	$-0.464573\pi$
$283$	8.46969e7	0.222134	0.111067	+	0.993813i	$0.464573\pi$
$284$	−3.03318e8	−0.785750
$285$	−2.31517e8	−0.592416
$286$	9.26380e7	0.234157
$287$	−1.36651e8	−0.341214
$288$	−2.38879e7	−0.0589256
$289$	9.43502e7	0.229932
$290$	3.28975e8	0.792081
$291$	3.28103e6	0.00780520
$292$	1.09766e7	0.0258004
$293$	2.45235e8	0.569568	0.284784	−	0.958592i	$-0.408078\pi$
$293$	2.45235e8	0.569568	0.284784	+	0.958592i	$0.408078\pi$
$294$	2.54122e7	0.0583212
$295$	3.89191e7	0.0882645
$296$	−2.33340e8	−0.522959
$297$	1.03743e8	0.229780
$298$	2.50475e8	0.548287
$299$	−1.07824e8	−0.233274
$300$	8.86966e7	0.189663
$301$	1.94457e8	0.410999
$302$	1.83528e8	0.383424
$303$	−3.39995e8	−0.702139
$304$	2.14558e8	0.438014
$305$	3.23040e8	0.651938
$306$	1.31018e8	0.261399
$307$	5.47835e8	1.08060	0.540301	−	0.841472i	$-0.318311\pi$
$307$	5.47835e8	1.08060	0.540301	+	0.841472i	$0.318311\pi$
$308$	−1.15703e8	−0.225640
$309$	−5.49951e7	−0.106040
$310$	8.04806e7	0.153435
$311$	9.10046e8	1.71554	0.857772	−	0.514030i	$-0.171848\pi$
$311$	9.10046e8	1.71554	0.857772	+	0.514030i	$0.171848\pi$
$312$	3.03713e7	0.0566139
$313$	−1.38241e8	−0.254819	−0.127410	−	0.991850i	$-0.540666\pi$
$313$	−1.38241e8	−0.254819	−0.127410	+	0.991850i	$0.540666\pi$
$314$	−2.57727e8	−0.469792
$315$	4.09314e7	0.0737852
$316$	−2.69017e8	−0.479595
$317$	6.63179e7	0.116929	0.0584647	−	0.998289i	$-0.481380\pi$
$317$	6.63179e7	0.116929	0.0584647	+	0.998289i	$0.481380\pi$
$318$	4.59919e8	0.802023
$319$	1.32406e9	2.28370
$320$	4.29116e7	0.0732065
$321$	2.11042e8	0.356124
$322$	1.34669e8	0.224788
$323$	−1.17679e9	−1.94307
$324$	3.40122e7	0.0555556
$325$	−1.12770e8	−0.182222
$326$	−2.07926e8	−0.332389
$327$	5.14823e8	0.814218
$328$	2.03981e8	0.319176
$329$	2.38482e8	0.369208
$330$	−1.86362e8	−0.285469
$331$	4.26707e8	0.646744	0.323372	−	0.946272i	$-0.395184\pi$
$331$	4.26707e8	0.646744	0.323372	+	0.946272i	$0.395184\pi$
$332$	−3.70533e8	−0.555704
$333$	3.32236e8	0.493050
$334$	3.05272e8	0.448306
$335$	−3.71903e8	−0.540472
$336$	−3.79331e7	−0.0545545
$337$	8.89325e8	1.26577	0.632887	−	0.774244i	$-0.281870\pi$
$337$	8.89325e8	1.26577	0.632887	+	0.774244i	$0.281870\pi$
$338$	−3.86145e7	−0.0543928
$339$	8.51378e7	0.118693
$340$	−2.35357e8	−0.324751
$341$	3.23918e8	0.442379
$342$	−3.05494e8	−0.412963
$343$	4.03536e7	0.0539949
$344$	−2.90268e8	−0.384455
$345$	2.16912e8	0.284391
$346$	−8.92258e8	−1.15804
$347$	−6.54816e7	−0.0841330	−0.0420665	−	0.999115i	$-0.513394\pi$
$347$	−6.54816e7	−0.0841330	−0.0420665	+	0.999115i	$0.513394\pi$
$348$	4.34092e8	0.552146
$349$	1.08393e9	1.36494	0.682470	−	0.730913i	$-0.260906\pi$
$349$	1.08393e9	1.36494	0.682470	+	0.730913i	$0.260906\pi$
$350$	1.40847e8	0.175594
$351$	−4.32436e7	−0.0533761
$352$	1.72711e8	0.211067
$353$	−1.33202e9	−1.61176	−0.805879	−	0.592080i	$-0.798307\pi$
$353$	−1.33202e9	−1.61176	−0.805879	+	0.592080i	$0.798307\pi$
$354$	5.13549e7	0.0615277
$355$	−7.75806e8	−0.920352
$356$	2.55180e8	0.299758
$357$	2.08051e8	0.242009
$358$	−2.18928e8	−0.252180
$359$	9.91147e8	1.13060	0.565298	−	0.824887i	$-0.308761\pi$
$359$	9.91147e8	1.13060	0.565298	+	0.824887i	$0.308761\pi$
$360$	−6.10987e7	−0.0690198
$361$	1.85004e9	2.06970
$362$	4.15343e8	0.460179
$363$	−2.23916e8	−0.245704
$364$	4.82285e7	0.0524142
$365$	2.80751e7	0.0302201
$366$	4.26260e8	0.454455
$367$	−5.86649e8	−0.619509	−0.309754	−	0.950817i	$-0.600247\pi$
$367$	−5.86649e8	−0.619509	−0.309754	+	0.950817i	$0.600247\pi$
$368$	−2.01022e8	−0.210270
$369$	−2.90433e8	−0.300922
$370$	−5.96820e8	−0.612544
$371$	7.30335e8	0.742529
$372$	1.06196e8	0.106957
$373$	−5.90219e8	−0.588887	−0.294444	−	0.955669i	$-0.595134\pi$
$373$	−5.90219e8	−0.588887	−0.294444	+	0.955669i	$0.595134\pi$
$374$	−9.47263e8	−0.936311
$375$	5.72155e8	0.560279
$376$	−3.55985e8	−0.345362
$377$	−5.51909e8	−0.530485
$378$	5.40102e7	0.0514344
$379$	−8.68959e8	−0.819903	−0.409951	−	0.912107i	$-0.634454\pi$
$379$	−8.68959e8	−0.819903	−0.409951	+	0.912107i	$0.634454\pi$
$380$	5.48782e8	0.513047
$381$	7.51673e8	0.696292
$382$	2.37788e7	0.0218257
$383$	8.24830e8	0.750185	0.375093	−	0.926987i	$-0.377611\pi$
$383$	8.24830e8	0.750185	0.375093	+	0.926987i	$0.377611\pi$
$384$	5.66231e7	0.0510310
$385$	−2.95936e8	−0.264293
$386$	1.06248e9	0.940301
$387$	4.13292e8	0.362467
$388$	−7.77724e6	−0.00675950
$389$	−2.56156e8	−0.220638	−0.110319	−	0.993896i	$-0.535187\pi$
$389$	−2.56156e8	−0.220638	−0.110319	+	0.993896i	$0.535187\pi$
$390$	7.76817e7	0.0663120
$391$	1.10255e9	0.932777
$392$	−6.02363e7	−0.0505076
$393$	−5.74158e8	−0.477153
$394$	−6.11127e8	−0.503378
$395$	−6.88072e8	−0.561752
$396$	−2.45910e8	−0.198996
$397$	1.47527e9	1.18332	0.591661	−	0.806187i	$-0.298472\pi$
$397$	1.47527e9	1.18332	0.591661	+	0.806187i	$0.298472\pi$
$398$	−1.26306e9	−1.00423
$399$	−4.85113e8	−0.382330
$400$	−2.10244e8	−0.164253
$401$	−1.33908e7	−0.0103705	−0.00518527	−	0.999987i	$-0.501651\pi$
$401$	−1.33908e7	−0.0103705	−0.00518527	+	0.999987i	$0.501651\pi$
$402$	−4.90737e8	−0.376754
$403$	−1.35019e8	−0.102761
$404$	8.05914e8	0.608070
$405$	8.69941e7	0.0650725
$406$	6.89322e8	0.511188
$407$	−2.40208e9	−1.76607
$408$	−3.10560e8	−0.226378
$409$	−1.60374e9	−1.15905	−0.579525	−	0.814955i	$-0.696762\pi$
$409$	−1.60374e9	−1.15905	−0.579525	+	0.814955i	$0.696762\pi$
$410$	5.21727e8	0.373852
$411$	−1.04074e9	−0.739427
$412$	1.30359e8	0.0918333
$413$	8.15497e7	0.0569636
$414$	2.86221e8	0.198244
$415$	−9.47723e8	−0.650898
$416$	−7.19913e7	−0.0490290
$417$	−1.16052e9	−0.783748
$418$	2.20874e9	1.47920
$419$	1.13848e9	0.756094	0.378047	−	0.925786i	$-0.376596\pi$
$419$	1.13848e9	0.756094	0.378047	+	0.925786i	$0.376596\pi$
$420$	−9.70225e7	−0.0638999
$421$	1.94357e9	1.26944	0.634722	−	0.772740i	$-0.281115\pi$
$421$	1.94357e9	1.26944	0.634722	+	0.772740i	$0.281115\pi$
$422$	−1.38899e9	−0.899715
$423$	5.06862e8	0.325611
$424$	−1.09018e9	−0.694572
$425$	1.15312e9	0.728641
$426$	−1.02370e9	−0.641562
$427$	6.76885e8	0.420744
$428$	−5.00247e8	−0.308412
$429$	3.12653e8	0.191189
$430$	−7.42428e8	−0.450314
$431$	2.34044e9	1.40808	0.704040	−	0.710161i	$-0.251378\pi$
$431$	2.34044e9	1.40808	0.704040	+	0.710161i	$0.251378\pi$
$432$	−8.06216e7	−0.0481125
$433$	2.27893e9	1.34903	0.674517	−	0.738259i	$-0.264352\pi$
$433$	2.27893e9	1.34903	0.674517	+	0.738259i	$0.264352\pi$
$434$	1.68636e8	0.0990231
$435$	1.11029e9	0.646731
$436$	−1.22032e9	−0.705133
$437$	−2.57081e9	−1.47362
$438$	3.70459e7	0.0210659
$439$	7.25236e8	0.409123	0.204561	−	0.978854i	$-0.434423\pi$
$439$	7.25236e8	0.409123	0.204561	+	0.978854i	$0.434423\pi$
$440$	4.41747e8	0.247223
$441$	8.57661e7	0.0476190
$442$	3.94850e8	0.217497
$443$	−1.61185e9	−0.880869	−0.440434	−	0.897785i	$-0.645176\pi$
$443$	−1.61185e9	−0.880869	−0.440434	+	0.897785i	$0.645176\pi$
$444$	−7.87521e8	−0.426994
$445$	6.52681e8	0.351108
$446$	−7.44229e8	−0.397223
$447$	8.45354e8	0.447674
$448$	8.99154e7	0.0472456
$449$	−2.02351e8	−0.105498	−0.0527489	−	0.998608i	$-0.516798\pi$
$449$	−2.02351e8	−0.105498	−0.0527489	+	0.998608i	$0.516798\pi$
$450$	2.99351e8	0.154859
$451$	2.09985e9	1.07788
$452$	−2.01808e8	−0.102791
$453$	6.19408e8	0.313064
$454$	−1.94330e9	−0.974640
$455$	1.23356e8	0.0613930
$456$	7.24134e8	0.357637
$457$	1.04166e9	0.510529	0.255265	−	0.966871i	$-0.417837\pi$
$457$	1.04166e9	0.510529	0.255265	+	0.966871i	$0.417837\pi$
$458$	−2.42039e9	−1.17721
$459$	4.42184e8	0.213432
$460$	−5.14161e8	−0.246290
$461$	1.70038e9	0.808336	0.404168	−	0.914685i	$-0.367561\pi$
$461$	1.70038e9	0.808336	0.404168	+	0.914685i	$0.367561\pi$
$462$	−3.90496e8	−0.184234
$463$	−2.03413e9	−0.952459	−0.476229	−	0.879321i	$-0.657997\pi$
$463$	−2.03413e9	−0.952459	−0.476229	+	0.879321i	$0.657997\pi$
$464$	−1.02896e9	−0.478173
$465$	2.71622e8	0.125279
$466$	2.46118e9	1.12666
$467$	5.11441e8	0.232373	0.116187	−	0.993227i	$-0.462933\pi$
$467$	5.11441e8	0.232373	0.116187	+	0.993227i	$0.462933\pi$
$468$	1.02503e8	0.0462250
$469$	−7.79273e8	−0.348807
$470$	−9.10515e8	−0.404524
$471$	−8.69828e8	−0.383584
$472$	−1.21730e8	−0.0532846
$473$	−2.98813e9	−1.29833
$474$	−9.07932e8	−0.391588
$475$	−2.68874e9	−1.15112
$476$	−4.93158e8	−0.209586
$477$	1.55223e9	0.654849
$478$	−2.74383e9	−1.14910
$479$	−1.29845e9	−0.539823	−0.269911	−	0.962885i	$-0.586994\pi$
$479$	−1.29845e9	−0.539823	−0.269911	+	0.962885i	$0.586994\pi$
$480$	1.44827e8	0.0597729
$481$	1.00126e9	0.410243
$482$	2.36931e9	0.963735
$483$	4.54509e8	0.183539
$484$	5.30764e8	0.212786
$485$	−1.98921e7	−0.00791743
$486$	1.14791e8	0.0453609
$487$	2.56798e9	1.00749	0.503745	−	0.863852i	$-0.331955\pi$
$487$	2.56798e9	1.00749	0.503745	+	0.863852i	$0.331955\pi$
$488$	−1.01039e9	−0.393570
$489$	−7.01750e8	−0.271395
$490$	−1.54068e8	−0.0591598
$491$	1.95588e9	0.745686	0.372843	−	0.927894i	$-0.378383\pi$
$491$	1.95588e9	0.745686	0.372843	+	0.927894i	$0.378383\pi$
$492$	6.88435e8	0.260606
$493$	5.64351e9	2.12122
$494$	−9.20673e8	−0.343606
$495$	−6.28972e8	−0.233084
$496$	−2.51725e8	−0.0926276
$497$	−1.62560e9	−0.593971
$498$	−1.25055e9	−0.453730
$499$	2.60857e9	0.939831	0.469916	−	0.882711i	$-0.344284\pi$
$499$	2.60857e9	0.939831	0.469916	+	0.882711i	$0.344284\pi$
$500$	−1.35622e9	−0.485216
$501$	1.03029e9	0.366040
$502$	−2.17104e9	−0.765956
$503$	4.35188e9	1.52472	0.762359	−	0.647155i	$-0.224041\pi$
$503$	4.35188e9	1.52472	0.762359	+	0.647155i	$0.224041\pi$
$504$	−1.28024e8	−0.0445435
$505$	2.06131e9	0.712235
$506$	−2.06940e9	−0.710096
$507$	−1.30324e8	−0.0444116
$508$	−1.78174e9	−0.603007
$509$	1.78817e8	0.0601029	0.0300515	−	0.999548i	$-0.490433\pi$
$509$	1.78817e8	0.0601029	0.0300515	+	0.999548i	$0.490433\pi$
$510$	−7.94329e8	−0.265158
$511$	5.88276e7	0.0195033
$512$	−1.34218e8	−0.0441942
$513$	−1.03104e9	−0.337183
$514$	−6.56675e8	−0.213294
$515$	3.33423e8	0.107565
$516$	−9.79656e8	−0.313906
$517$	−3.66464e9	−1.16631
$518$	−1.25055e9	−0.395320
$519$	−3.01137e9	−0.945537
$520$	−1.84134e8	−0.0574279
$521$	−1.26414e9	−0.391618	−0.195809	−	0.980642i	$-0.562733\pi$
$521$	−1.26414e9	−0.391618	−0.195809	+	0.980642i	$0.562733\pi$
$522$	1.46506e9	0.450826
$523$	1.42499e9	0.435567	0.217784	−	0.975997i	$-0.430117\pi$
$523$	1.42499e9	0.435567	0.217784	+	0.975997i	$0.430117\pi$
$524$	1.36097e9	0.413226
$525$	4.75358e8	0.143372
$526$	−2.30635e8	−0.0690994
$527$	1.38063e9	0.410905
$528$	5.82898e8	0.172335
$529$	−9.96199e8	−0.292585
$530$	−2.78838e9	−0.813555
$531$	1.73323e8	0.0502372
$532$	1.14990e9	0.331107
$533$	−8.75284e8	−0.250382
$534$	8.61232e8	0.244752
$535$	−1.27950e9	−0.361244
$536$	1.16323e9	0.326279
$537$	−7.38882e8	−0.205904
$538$	2.04177e9	0.565286
$539$	−6.20093e8	−0.170568
$540$	−2.06208e8	−0.0563544
$541$	1.23506e9	0.335350	0.167675	−	0.985842i	$-0.446374\pi$
$541$	1.23506e9	0.335350	0.167675	+	0.985842i	$0.446374\pi$
$542$	1.86852e9	0.504081
$543$	1.40178e9	0.375735
$544$	7.36142e8	0.196049
$545$	−3.12125e9	−0.825925
$546$	1.62771e8	0.0427960
$547$	−2.28518e9	−0.596986	−0.298493	−	0.954412i	$-0.596484\pi$
$547$	−2.28518e9	−0.596986	−0.298493	+	0.954412i	$0.596484\pi$
$548$	2.46694e9	0.640362
$549$	1.43863e9	0.371061
$550$	−2.16432e9	−0.554693
$551$	−1.31590e10	−3.35114
$552$	−6.78451e8	−0.171685
$553$	−1.44176e9	−0.362540
$554$	8.28159e8	0.206933
$555$	−2.01427e9	−0.500140
$556$	2.75086e9	0.678746
$557$	−2.92764e9	−0.717834	−0.358917	−	0.933369i	$-0.616854\pi$
$557$	−2.92764e9	−0.717834	−0.358917	+	0.933369i	$0.616854\pi$
$558$	3.58413e8	0.0873301
$559$	1.24555e9	0.301591
$560$	2.29979e8	0.0553389
$561$	−3.19701e9	−0.764495
$562$	5.41406e8	0.128661
$563$	−6.25385e9	−1.47696	−0.738479	−	0.674277i	$-0.764456\pi$
$563$	−6.25385e9	−1.47696	−0.738479	+	0.674277i	$0.764456\pi$
$564$	−1.20145e9	−0.281987
$565$	−5.16171e8	−0.120399
$566$	−6.77575e8	−0.157072
$567$	1.82284e8	0.0419961
$568$	2.42655e9	0.555609
$569$	3.72579e9	0.847863	0.423932	−	0.905694i	$-0.360650\pi$
$569$	3.72579e9	0.847863	0.423932	+	0.905694i	$0.360650\pi$
$570$	1.85214e9	0.418901
$571$	3.16634e9	0.711757	0.355878	−	0.934532i	$-0.384182\pi$
$571$	3.16634e9	0.711757	0.355878	+	0.934532i	$0.384182\pi$
$572$	−7.41104e8	−0.165574
$573$	8.02535e7	0.0178206
$574$	1.09321e9	0.241275
$575$	2.51911e9	0.552599
$576$	1.91103e8	0.0416667
$577$	1.01383e9	0.219710	0.109855	−	0.993948i	$-0.464961\pi$
$577$	1.01383e9	0.219710	0.109855	+	0.993948i	$0.464961\pi$
$578$	−7.54801e8	−0.162587
$579$	3.58589e9	0.767753
$580$	−2.63180e9	−0.560086
$581$	−1.98582e9	−0.420073
$582$	−2.62482e7	−0.00551911
$583$	−1.12227e10	−2.34562
$584$	−8.78126e7	−0.0182436
$585$	2.62176e8	0.0541436
$586$	−1.96188e9	−0.402745
$587$	6.54765e9	1.33614	0.668070	−	0.744098i	$-0.267121\pi$
$587$	6.54765e9	1.33614	0.668070	+	0.744098i	$0.267121\pi$
$588$	−2.03297e8	−0.0412393
$589$	−3.21923e9	−0.649155
$590$	−3.11353e8	−0.0624124
$591$	−2.06255e9	−0.411007
$592$	1.86672e9	0.369788
$593$	−2.05802e9	−0.405282	−0.202641	−	0.979253i	$-0.564952\pi$
$593$	−2.05802e9	−0.405282	−0.202641	+	0.979253i	$0.564952\pi$
$594$	−8.29947e8	−0.162479
$595$	−1.26136e9	−0.245489
$596$	−2.00380e9	−0.387697
$597$	−4.26284e9	−0.819952
$598$	8.62591e8	0.164949
$599$	1.42414e9	0.270744	0.135372	−	0.990795i	$-0.456777\pi$
$599$	1.42414e9	0.270744	0.135372	+	0.990795i	$0.456777\pi$
$600$	−7.09573e8	−0.134112
$601$	−8.70514e9	−1.63574	−0.817872	−	0.575401i	$-0.804846\pi$
$601$	−8.70514e9	−1.63574	−0.817872	+	0.575401i	$0.804846\pi$
$602$	−1.55566e9	−0.290621
$603$	−1.65624e9	−0.307618
$604$	−1.46823e9	−0.271121
$605$	1.35755e9	0.249237
$606$	2.71996e9	0.496487
$607$	−3.45603e9	−0.627217	−0.313608	−	0.949552i	$-0.601538\pi$
$607$	−3.45603e9	−0.627217	−0.313608	+	0.949552i	$0.601538\pi$
$608$	−1.71647e9	−0.309722
$609$	2.32646e9	0.417383
$610$	−2.58432e9	−0.460990
$611$	1.52754e9	0.270924
$612$	−1.04814e9	−0.184837
$613$	−5.23825e9	−0.918491	−0.459245	−	0.888310i	$-0.651880\pi$
$613$	−5.23825e9	−0.918491	−0.459245	+	0.888310i	$0.651880\pi$
$614$	−4.38268e9	−0.764100
$615$	1.76083e9	0.305249
$616$	9.25621e8	0.159551
$617$	2.35982e9	0.404465	0.202233	−	0.979338i	$-0.435180\pi$
$617$	2.35982e9	0.404465	0.202233	+	0.979338i	$0.435180\pi$
$618$	4.39961e8	0.0749815
$619$	−2.49856e8	−0.0423422	−0.0211711	−	0.999776i	$-0.506739\pi$
$619$	−2.49856e8	−0.0423422	−0.0211711	+	0.999776i	$0.506739\pi$
$620$	−6.43845e8	−0.108495
$621$	9.65997e8	0.161866
$622$	−7.28037e9	−1.21307
$623$	1.36760e9	0.226596
$624$	−2.42971e8	−0.0400320
$625$	5.41235e8	0.0886760
$626$	1.10593e9	0.180184
$627$	7.45449e9	1.20776
$628$	2.06181e9	0.332193
$629$	−1.02384e10	−1.64041
$630$	−3.27451e8	−0.0521740
$631$	−2.24587e9	−0.355863	−0.177931	−	0.984043i	$-0.556940\pi$
$631$	−2.24587e9	−0.355863	−0.177931	+	0.984043i	$0.556940\pi$
$632$	2.15213e9	0.339125
$633$	−4.68783e9	−0.734614
$634$	−5.30543e8	−0.0826815
$635$	−4.55722e9	−0.706304
$636$	−3.67935e9	−0.567116
$637$	2.58475e8	0.0396214
$638$	−1.05925e10	−1.61482
$639$	−3.45498e9	−0.523833
$640$	−3.43293e8	−0.0517648
$641$	7.70352e9	1.15528	0.577639	−	0.816293i	$-0.303974\pi$
$641$	7.70352e9	1.15528	0.577639	+	0.816293i	$0.303974\pi$
$642$	−1.68833e9	−0.251817
$643$	1.11370e10	1.65208	0.826040	−	0.563612i	$-0.190589\pi$
$643$	1.11370e10	1.65208	0.826040	+	0.563612i	$0.190589\pi$
$644$	−1.07735e9	−0.158949
$645$	−2.50570e9	−0.367679
$646$	9.41428e9	1.37396
$647$	3.47641e9	0.504621	0.252311	−	0.967646i	$-0.418809\pi$
$647$	3.47641e9	0.504621	0.252311	+	0.967646i	$0.418809\pi$
$648$	−2.72098e8	−0.0392837
$649$	−1.25313e9	−0.179945
$650$	9.02159e8	0.128851
$651$	5.69147e8	0.0808520
$652$	1.66341e9	0.235035
$653$	−6.56133e9	−0.922137	−0.461069	−	0.887364i	$-0.652534\pi$
$653$	−6.56133e9	−0.922137	−0.461069	+	0.887364i	$0.652534\pi$
$654$	−4.11858e9	−0.575739
$655$	3.48099e9	0.484014
$656$	−1.63185e9	−0.225692
$657$	1.25030e8	0.0172003
$658$	−1.90786e9	−0.261069
$659$	9.00640e9	1.22589	0.612946	−	0.790125i	$-0.289984\pi$
$659$	9.00640e9	1.22589	0.612946	+	0.790125i	$0.289984\pi$
$660$	1.49090e9	0.201857
$661$	−2.34847e9	−0.316286	−0.158143	−	0.987416i	$-0.550551\pi$
$661$	−2.34847e9	−0.316286	−0.158143	+	0.987416i	$0.550551\pi$
$662$	−3.41366e9	−0.457317
$663$	1.33262e9	0.177586
$664$	2.96426e9	0.392942
$665$	2.94113e9	0.387827
$666$	−2.65789e9	−0.348639
$667$	1.23288e10	1.60873
$668$	−2.44218e9	−0.317000
$669$	−2.51177e9	−0.324331
$670$	2.97523e9	0.382171
$671$	−1.04014e10	−1.32911
$672$	3.03464e8	0.0385758
$673$	−9.83171e9	−1.24330	−0.621651	−	0.783295i	$-0.713538\pi$
$673$	−9.83171e9	−1.24330	−0.621651	+	0.783295i	$0.713538\pi$
$674$	−7.11460e9	−0.895037
$675$	1.01031e9	0.126442
$676$	3.08916e8	0.0384615
$677$	1.52500e9	0.188891	0.0944454	−	0.995530i	$-0.469892\pi$
$677$	1.52500e9	0.188891	0.0944454	+	0.995530i	$0.469892\pi$
$678$	−6.81102e8	−0.0839283
$679$	−4.16812e7	−0.00510970
$680$	1.88285e9	0.229634
$681$	−6.55864e9	−0.795791
$682$	−2.59135e9	−0.312810
$683$	7.39570e9	0.888192	0.444096	−	0.895979i	$-0.353525\pi$
$683$	7.39570e9	0.888192	0.444096	+	0.895979i	$0.353525\pi$
$684$	2.44395e9	0.292009
$685$	6.30975e9	0.750059
$686$	−3.22829e8	−0.0381802
$687$	−8.16880e9	−0.961191
$688$	2.32215e9	0.271851
$689$	4.67798e9	0.544867
$690$	−1.73529e9	−0.201095
$691$	1.35463e10	1.56188	0.780939	−	0.624607i	$-0.214741\pi$
$691$	1.35463e10	1.56188	0.780939	+	0.624607i	$0.214741\pi$
$692$	7.13807e9	0.818859
$693$	−1.31792e9	−0.150426
$694$	5.23853e8	0.0594910
$695$	7.03597e9	0.795018
$696$	−3.47273e9	−0.390426
$697$	8.95016e9	1.00119
$698$	−8.67147e9	−0.965159
$699$	8.30649e9	0.919915
$700$	−1.12678e9	−0.124164
$701$	−1.40084e10	−1.53594	−0.767972	−	0.640484i	$-0.778734\pi$
$701$	−1.40084e10	−1.53594	−0.767972	+	0.640484i	$0.778734\pi$
$702$	3.45948e8	0.0377426
$703$	2.38728e10	2.59155
$704$	−1.38168e9	−0.149247
$705$	−3.07299e9	−0.330293
$706$	1.06562e10	1.13968
$707$	4.31919e9	0.459658
$708$	−4.10839e8	−0.0435067
$709$	−1.46074e10	−1.53926	−0.769631	−	0.638489i	$-0.779560\pi$
$709$	−1.46074e10	−1.53926	−0.769631	+	0.638489i	$0.779560\pi$
$710$	6.20645e9	0.650787
$711$	−3.06427e9	−0.319730
$712$	−2.04144e9	−0.211961
$713$	3.01614e9	0.311629
$714$	−1.66441e9	−0.171126
$715$	−1.89554e9	−0.193938
$716$	1.75142e9	0.178318
$717$	−9.26043e9	−0.938240
$718$	−7.92917e9	−0.799452
$719$	9.84644e9	0.987935	0.493967	−	0.869480i	$-0.335546\pi$
$719$	9.84644e9	0.987935	0.493967	+	0.869480i	$0.335546\pi$
$720$	4.88790e8	0.0488043
$721$	6.98641e8	0.0694194
$722$	−1.48003e10	−1.46350
$723$	7.99643e9	0.786886
$724$	−3.32274e9	−0.325396
$725$	1.28944e10	1.25666
$726$	1.79133e9	0.173739
$727$	3.21172e9	0.310004	0.155002	−	0.987914i	$-0.450462\pi$
$727$	3.21172e9	0.310004	0.155002	+	0.987914i	$0.450462\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−2.24601e8	−0.0213689
$731$	−1.27363e10	−1.20595
$732$	−3.41008e9	−0.321348
$733$	6.86076e9	0.643441	0.321720	−	0.946835i	$-0.395739\pi$
$733$	6.86076e9	0.643441	0.321720	+	0.946835i	$0.395739\pi$
$734$	4.69320e9	0.438059
$735$	−5.19980e8	−0.0483038
$736$	1.60818e9	0.148683
$737$	1.19747e10	1.10186
$738$	2.32347e9	0.212784
$739$	−1.63305e9	−0.148849	−0.0744243	−	0.997227i	$-0.523712\pi$
$739$	−1.63305e9	−0.148849	−0.0744243	+	0.997227i	$0.523712\pi$
$740$	4.77456e9	0.433134
$741$	−3.10727e9	−0.280553
$742$	−5.84268e9	−0.525047
$743$	9.07348e9	0.811546	0.405773	−	0.913974i	$-0.367002\pi$
$743$	9.07348e9	0.811546	0.405773	+	0.913974i	$0.367002\pi$
$744$	−8.49572e8	−0.0756301
$745$	−5.12518e9	−0.454111
$746$	4.72175e9	0.416406
$747$	−4.22060e9	−0.370469
$748$	7.57811e9	0.662072
$749$	−2.68101e9	−0.233138
$750$	−4.57724e9	−0.396177
$751$	7.11955e9	0.613356	0.306678	−	0.951813i	$-0.400783\pi$
$751$	7.11955e9	0.613356	0.306678	+	0.951813i	$0.400783\pi$
$752$	2.84788e9	0.244208
$753$	−7.32724e9	−0.625401
$754$	4.41528e9	0.375110
$755$	−3.75533e9	−0.317566
$756$	−4.32081e8	−0.0363696
$757$	1.28153e10	1.07373	0.536863	−	0.843669i	$-0.319609\pi$
$757$	1.28153e10	1.07373	0.536863	+	0.843669i	$0.319609\pi$
$758$	6.95168e9	0.579759
$759$	−6.98421e9	−0.579791
$760$	−4.39026e9	−0.362779
$761$	−1.61016e10	−1.32441	−0.662204	−	0.749323i	$-0.730379\pi$
$761$	−1.61016e10	−1.32441	−0.662204	+	0.749323i	$0.730379\pi$
$762$	−6.01338e9	−0.492353
$763$	−6.54015e9	−0.533031
$764$	−1.90231e8	−0.0154331
$765$	−2.68086e9	−0.216501
$766$	−6.59864e9	−0.530461
$767$	5.22346e8	0.0417998
$768$	−4.52985e8	−0.0360844
$769$	−1.67748e10	−1.33020	−0.665098	−	0.746757i	$-0.731610\pi$
$769$	−1.67748e10	−1.33020	−0.665098	+	0.746757i	$0.731610\pi$
$770$	2.36749e9	0.186883
$771$	−2.21628e9	−0.174154
$772$	−8.49988e9	−0.664893
$773$	−2.19178e10	−1.70674	−0.853372	−	0.521302i	$-0.825446\pi$
$773$	−2.19178e10	−1.70674	−0.853372	+	0.521302i	$0.825446\pi$
$774$	−3.30634e9	−0.256303
$775$	3.15449e9	0.243430
$776$	6.22180e7	0.00477969
$777$	−4.22062e9	−0.322777
$778$	2.04925e9	0.156015
$779$	−2.08691e10	−1.58170
$780$	−6.21453e8	−0.0468897
$781$	2.49797e10	1.87633
$782$	−8.82036e9	−0.659573
$783$	4.94458e9	0.368098
$784$	4.81890e8	0.0357143
$785$	5.27356e9	0.389099
$786$	4.59326e9	0.337398
$787$	5.84025e9	0.427090	0.213545	−	0.976933i	$-0.431499\pi$
$787$	5.84025e9	0.427090	0.213545	+	0.976933i	$0.431499\pi$
$788$	4.88901e9	0.355942
$789$	−7.78392e8	−0.0564194
$790$	5.50458e9	0.397218
$791$	−1.08157e9	−0.0777025
$792$	1.96728e9	0.140711
$793$	4.33562e9	0.308741
$794$	−1.18021e10	−0.836736
$795$	−9.41080e9	−0.664265
$796$	1.01045e10	0.710099
$797$	−2.26519e10	−1.58490	−0.792449	−	0.609939i	$-0.791194\pi$
$797$	−2.26519e10	−1.58490	−0.792449	+	0.609939i	$0.791194\pi$
$798$	3.88091e9	0.270348
$799$	−1.56198e10	−1.08333
$800$	1.68195e9	0.116144
$801$	2.90666e9	0.199839
$802$	1.07126e8	0.00733307
$803$	−9.03973e8	−0.0616100
$804$	3.92590e9	0.266405
$805$	−2.75558e9	−0.186178
$806$	1.08016e9	0.0726631
$807$	6.89097e9	0.461554
$808$	−6.44731e9	−0.429971
$809$	4.95125e9	0.328772	0.164386	−	0.986396i	$-0.447436\pi$
$809$	4.95125e9	0.328772	0.164386	+	0.986396i	$0.447436\pi$
$810$	−6.95953e8	−0.0460132
$811$	−1.15283e9	−0.0758912	−0.0379456	−	0.999280i	$-0.512081\pi$
$811$	−1.15283e9	−0.0758912	−0.0379456	+	0.999280i	$0.512081\pi$
$812$	−5.51457e9	−0.361465
$813$	6.30625e9	0.411580
$814$	1.92166e10	1.24880
$815$	4.25455e9	0.275297
$816$	2.48448e9	0.160074
$817$	2.96972e10	1.90519
$818$	1.28299e10	0.819572
$819$	5.49353e8	0.0349428
$820$	−4.17382e9	−0.264354
$821$	4.96304e9	0.313002	0.156501	−	0.987678i	$-0.449979\pi$
$821$	4.96304e9	0.313002	0.156501	+	0.987678i	$0.449979\pi$
$822$	8.32591e9	0.522854
$823$	6.27158e9	0.392173	0.196086	−	0.980587i	$-0.437177\pi$
$823$	6.27158e9	0.392173	0.196086	+	0.980587i	$0.437177\pi$
$824$	−1.04287e9	−0.0649359
$825$	−7.30459e9	−0.452905
$826$	−6.52398e8	−0.0402793
$827$	2.39717e10	1.47377	0.736883	−	0.676020i	$-0.236297\pi$
$827$	2.39717e10	1.47377	0.736883	+	0.676020i	$0.236297\pi$
$828$	−2.28977e9	−0.140180
$829$	2.05178e10	1.25080	0.625402	−	0.780303i	$-0.284935\pi$
$829$	2.05178e10	1.25080	0.625402	+	0.780303i	$0.284935\pi$
$830$	7.58179e9	0.460255
$831$	2.79504e9	0.168960
$832$	5.75930e8	0.0346688
$833$	−2.64302e9	−0.158432
$834$	9.28416e9	0.554194
$835$	−6.24643e9	−0.371304
$836$	−1.76699e10	−1.04595
$837$	1.20964e9	0.0713048
$838$	−9.10783e9	−0.534639
$839$	−3.66375e9	−0.214170	−0.107085	−	0.994250i	$-0.534152\pi$
$839$	−3.66375e9	−0.214170	−0.107085	+	0.994250i	$0.534152\pi$
$840$	7.76180e8	0.0451840
$841$	4.58568e10	2.65839
$842$	−1.55486e10	−0.897633
$843$	1.82725e9	0.105051
$844$	1.11119e10	0.636194
$845$	7.90123e8	0.0450502
$846$	−4.05490e9	−0.230241
$847$	2.84456e9	0.160851
$848$	8.72143e9	0.491137
$849$	−2.28682e9	−0.128249
$850$	−9.22497e9	−0.515227
$851$	−2.23668e10	−1.24408
$852$	8.18959e9	0.453653
$853$	−1.72029e10	−0.949029	−0.474515	−	0.880248i	$-0.657376\pi$
$853$	−1.72029e10	−0.949029	−0.474515	+	0.880248i	$0.657376\pi$
$854$	−5.41508e9	−0.297511
$855$	6.25097e9	0.342031
$856$	4.00198e9	0.218080
$857$	1.48518e10	0.806023	0.403011	−	0.915195i	$-0.367963\pi$
$857$	1.48518e10	0.806023	0.403011	+	0.915195i	$0.367963\pi$
$858$	−2.50122e9	−0.135191
$859$	3.08576e10	1.66106	0.830532	−	0.556971i	$-0.188037\pi$
$859$	3.08576e10	1.66106	0.830532	+	0.556971i	$0.188037\pi$
$860$	5.93943e9	0.318420
$861$	3.68958e9	0.197000
$862$	−1.87235e10	−0.995662
$863$	5.38886e9	0.285404	0.142702	−	0.989766i	$-0.454421\pi$
$863$	5.38886e9	0.285404	0.142702	+	0.989766i	$0.454421\pi$
$864$	6.44973e8	0.0340207
$865$	1.82573e10	0.959133
$866$	−1.82314e10	−0.953911
$867$	−2.54745e9	−0.132752
$868$	−1.34909e9	−0.0700199
$869$	2.21548e10	1.14525
$870$	−8.88232e9	−0.457308
$871$	−4.99144e9	−0.255954
$872$	9.76256e9	0.498604
$873$	−8.85877e7	−0.00450633
$874$	2.05665e10	1.04201
$875$	−7.26849e9	−0.366789
$876$	−2.96367e8	−0.0148959
$877$	3.70901e10	1.85678	0.928388	−	0.371612i	$-0.121195\pi$
$877$	3.70901e10	1.85678	0.928388	+	0.371612i	$0.121195\pi$
$878$	−5.80189e9	−0.289293
$879$	−6.62134e9	−0.328840
$880$	−3.53398e9	−0.174813
$881$	1.57370e10	0.775364	0.387682	−	0.921793i	$-0.373276\pi$
$881$	1.57370e10	0.775364	0.387682	+	0.921793i	$0.373276\pi$
$882$	−6.86129e8	−0.0336718
$883$	−6.37601e9	−0.311664	−0.155832	−	0.987784i	$-0.549806\pi$
$883$	−6.37601e9	−0.311664	−0.155832	+	0.987784i	$0.549806\pi$
$884$	−3.15880e9	−0.153794
$885$	−1.05082e9	−0.0509595
$886$	1.28948e10	0.622868
$887$	−3.31440e10	−1.59467	−0.797336	−	0.603535i	$-0.793758\pi$
$887$	−3.31440e10	−1.59467	−0.797336	+	0.603535i	$0.793758\pi$
$888$	6.30017e9	0.301931
$889$	−9.54903e9	−0.455830
$890$	−5.22145e9	−0.248271
$891$	−2.80107e9	−0.132664
$892$	5.95383e9	0.280879
$893$	3.64206e10	1.71146
$894$	−6.76283e9	−0.316553
$895$	4.47967e9	0.208865
$896$	−7.19323e8	−0.0334077
$897$	2.91124e9	0.134681
$898$	1.61881e9	0.0745982
$899$	1.54385e10	0.708672
$900$	−2.39481e9	−0.109502
$901$	−4.78343e10	−2.17873
$902$	−1.67988e10	−0.762176
$903$	−5.25034e9	−0.237291
$904$	1.61446e9	0.0726840
$905$	−8.49868e9	−0.381137
$906$	−4.95527e9	−0.221370
$907$	4.10407e9	0.182637	0.0913186	−	0.995822i	$-0.470892\pi$
$907$	4.10407e9	0.182637	0.0913186	+	0.995822i	$0.470892\pi$
$908$	1.55464e10	0.689175
$909$	9.17986e9	0.405380
$910$	−9.86845e8	−0.0434114
$911$	−5.15866e9	−0.226060	−0.113030	−	0.993592i	$-0.536056\pi$
$911$	−5.15866e9	−0.226060	−0.113030	+	0.993592i	$0.536056\pi$
$912$	−5.79307e9	−0.252887
$913$	3.05152e10	1.32699
$914$	−8.33331e9	−0.360999
$915$	−8.72207e9	−0.376397
$916$	1.93631e10	0.832416
$917$	7.29393e9	0.312370
$918$	−3.53747e9	−0.150919
$919$	−2.30947e10	−0.981539	−0.490769	−	0.871290i	$-0.663284\pi$
$919$	−2.30947e10	−0.981539	−0.490769	+	0.871290i	$0.663284\pi$
$920$	4.11329e9	0.174153
$921$	−1.47915e10	−0.623885
$922$	−1.36030e10	−0.571580
$923$	−1.04123e10	−0.435856
$924$	3.12397e9	0.130273
$925$	−2.33928e10	−0.971820
$926$	1.62731e10	0.673490
$927$	1.48487e9	0.0612222
$928$	8.23167e9	0.338119
$929$	−1.64796e10	−0.674358	−0.337179	−	0.941441i	$-0.609473\pi$
$929$	−1.64796e10	−0.674358	−0.337179	+	0.941441i	$0.609473\pi$
$930$	−2.17298e9	−0.0885859
$931$	6.16274e9	0.250294
$932$	−1.96895e10	−0.796670
$933$	−2.45712e10	−0.990470
$934$	−4.09153e9	−0.164313
$935$	1.93828e10	0.775488
$936$	−8.20026e8	−0.0326860
$937$	1.96988e10	0.782259	0.391130	−	0.920336i	$-0.372084\pi$
$937$	1.96988e10	0.782259	0.391130	+	0.920336i	$0.372084\pi$
$938$	6.23418e9	0.246643
$939$	3.73251e9	0.147120
$940$	7.28412e9	0.286042
$941$	5.05262e8	0.0197676	0.00988378	−	0.999951i	$-0.496854\pi$
$941$	5.05262e8	0.0197676	0.00988378	+	0.999951i	$0.496854\pi$
$942$	6.95862e9	0.271235
$943$	1.95526e10	0.759299
$944$	9.73842e8	0.0376779
$945$	−1.10515e9	−0.0425999
$946$	2.39050e10	0.918057
$947$	1.39479e10	0.533685	0.266842	−	0.963740i	$-0.414020\pi$
$947$	1.39479e10	0.533685	0.266842	+	0.963740i	$0.414020\pi$
$948$	7.26345e9	0.276894
$949$	3.76805e8	0.0143115
$950$	2.15099e10	0.813965
$951$	−1.79058e9	−0.0675092
$952$	3.94526e9	0.148199
$953$	2.19351e9	0.0820945	0.0410472	−	0.999157i	$-0.486931\pi$
$953$	2.19351e9	0.0820945	0.0410472	+	0.999157i	$0.486931\pi$
$954$	−1.24178e10	−0.463048
$955$	−4.86558e8	−0.0180769
$956$	2.19506e10	0.812540
$957$	−3.57495e10	−1.31850
$958$	1.03876e10	0.381712
$959$	1.32212e10	0.484068
$960$	−1.15861e9	−0.0422658
$961$	−2.37357e10	−0.862722
$962$	−8.01011e9	−0.290085
$963$	−5.69813e9	−0.205608
$964$	−1.89545e10	−0.681463
$965$	−2.17404e10	−0.778792
$966$	−3.63607e9	−0.129781
$967$	−4.23873e10	−1.50745	−0.753725	−	0.657190i	$-0.771745\pi$
$967$	−4.23873e10	−1.50745	−0.753725	+	0.657190i	$0.771745\pi$
$968$	−4.24611e9	−0.150462
$969$	3.17732e10	1.12183
$970$	1.59137e8	0.00559847
$971$	−1.05709e10	−0.370549	−0.185275	−	0.982687i	$-0.559317\pi$
$971$	−1.05709e10	−0.370549	−0.185275	+	0.982687i	$0.559317\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.47429e10	0.513084
$974$	−2.05439e10	−0.712403
$975$	3.04479e9	0.105206
$976$	8.08315e9	0.278296
$977$	3.10150e10	1.06400	0.531999	−	0.846745i	$-0.321441\pi$
$977$	3.10150e10	1.06400	0.531999	+	0.846745i	$0.321441\pi$
$978$	5.61400e9	0.191905
$979$	−2.10153e10	−0.715807
$980$	1.23255e9	0.0418323
$981$	−1.39002e10	−0.470089
$982$	−1.56470e10	−0.527280
$983$	4.80210e10	1.61248	0.806238	−	0.591591i	$-0.201500\pi$
$983$	4.80210e10	1.61248	0.806238	+	0.591591i	$0.201500\pi$
$984$	−5.50748e9	−0.184276
$985$	1.25048e10	0.416917
$986$	−4.51481e10	−1.49993
$987$	−6.43903e9	−0.213162
$988$	7.36538e9	0.242966
$989$	−2.78237e10	−0.914592
$990$	5.03177e9	0.164815
$991$	−3.84836e10	−1.25608	−0.628041	−	0.778180i	$-0.716143\pi$
$991$	−3.84836e10	−1.25608	−0.628041	+	0.778180i	$0.716143\pi$
$992$	2.01380e9	0.0654976
$993$	−1.15211e10	−0.373398
$994$	1.30048e10	0.420001
$995$	2.58446e10	0.831742
$996$	1.00044e10	0.320836
$997$	−2.76267e9	−0.0882868	−0.0441434	−	0.999025i	$-0.514056\pi$
$997$	−2.76267e9	−0.0882868	−0.0441434	+	0.999025i	$0.514056\pi$
$998$	−2.08685e10	−0.664561
$999$	−8.97036e9	−0.284663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.n.1.4	✓	6

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

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +163.695 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +163.695 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -1309.56 q^{10} -5270.71 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -4419.76 q^{15} +4096.00 q^{16} -22465.3 q^{17} -5832.00 q^{18} +52382.4 q^{19} +10476.5 q^{20} -9261.00 q^{21} +42165.7 q^{22} -49077.8 q^{23} +13824.0 q^{24} -51329.0 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} -251211. q^{29} +35358.1 q^{30} -61456.3 q^{31} -32768.0 q^{32} +142309. q^{33} +179722. q^{34} +56147.3 q^{35} +46656.0 q^{36} +455742. q^{37} -419059. q^{38} -59319.0 q^{39} -83811.7 q^{40} -398400. q^{41} +74088.0 q^{42} +566931. q^{43} -337325. q^{44} +119333. q^{45} +392622. q^{46} +695284. q^{47} -110592. q^{48} +117649. q^{49} +410632. q^{50} +606563. q^{51} +140608. q^{52} +2.12926e6 q^{53} +157464. q^{54} -862787. q^{55} -175616. q^{56} -1.41432e6 q^{57} +2.00968e6 q^{58} +237754. q^{59} -282864. q^{60} +1.97343e6 q^{61} +491650. q^{62} +250047. q^{63} +262144. q^{64} +359637. q^{65} -1.13847e6 q^{66} -2.27193e6 q^{67} -1.43778e6 q^{68} +1.32510e6 q^{69} -449178. q^{70} -4.73935e6 q^{71} -373248. q^{72} +171509. q^{73} -3.64593e6 q^{74} +1.38588e6 q^{75} +3.35247e6 q^{76} -1.80785e6 q^{77} +474552. q^{78} -4.20339e6 q^{79} +670494. q^{80} +531441. q^{81} +3.18720e6 q^{82} -5.78958e6 q^{83} -592704. q^{84} -3.67745e6 q^{85} -4.53544e6 q^{86} +6.78268e6 q^{87} +2.69860e6 q^{88} +3.98718e6 q^{89} -954668. q^{90} +753571. q^{91} -3.14098e6 q^{92} +1.65932e6 q^{93} -5.56227e6 q^{94} +8.57472e6 q^{95} +884736. q^{96} -121519. q^{97} -941192. q^{98} -3.84235e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 181 q^{5} + 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 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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