LMFDB - Embedded newform 546.8.a.n.1.3

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			1.3
Root			$83.4678$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -113.468 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -113.468 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +907.742 q^{10} -3827.20 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} +3063.63 q^{15} +4096.00 q^{16} -36941.0 q^{17} -5832.00 q^{18} -56827.3 q^{19} -7261.94 q^{20} -9261.00 q^{21} +30617.6 q^{22} +42283.4 q^{23} +13824.0 q^{24} -65250.1 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} +158520. q^{29} -24509.0 q^{30} +98296.8 q^{31} -32768.0 q^{32} +103335. q^{33} +295528. q^{34} -38919.5 q^{35} +46656.0 q^{36} +352941. q^{37} +454619. q^{38} -59319.0 q^{39} +58095.5 q^{40} -786907. q^{41} +74088.0 q^{42} -744062. q^{43} -244941. q^{44} -82718.0 q^{45} -338267. q^{46} -498725. q^{47} -110592. q^{48} +117649. q^{49} +522000. q^{50} +997408. q^{51} +140608. q^{52} -664787. q^{53} +157464. q^{54} +434264. q^{55} -175616. q^{56} +1.53434e6 q^{57} -1.26816e6 q^{58} +1.39438e6 q^{59} +196072. q^{60} -1.33040e6 q^{61} -786374. q^{62} +250047. q^{63} +262144. q^{64} -249289. q^{65} -826676. q^{66} +2.54161e6 q^{67} -2.36423e6 q^{68} -1.14165e6 q^{69} +311356. q^{70} -5.37482e6 q^{71} -373248. q^{72} +3.59276e6 q^{73} -2.82353e6 q^{74} +1.76175e6 q^{75} -3.63695e6 q^{76} -1.31273e6 q^{77} +474552. q^{78} +5.53769e6 q^{79} -464764. q^{80} +531441. q^{81} +6.29525e6 q^{82} -5.11360e6 q^{83} -592704. q^{84} +4.19162e6 q^{85} +5.95249e6 q^{86} -4.28003e6 q^{87} +1.95953e6 q^{88} -7.66025e6 q^{89} +661744. q^{90} +753571. q^{91} +2.70614e6 q^{92} -2.65401e6 q^{93} +3.98980e6 q^{94} +6.44807e6 q^{95} +884736. q^{96} -1.56564e7 q^{97} -941192. q^{98} -2.79003e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−113.468	−0.405955	−0.202977	−	0.979183i	$-0.565062\pi$
$5$	−113.468	−0.405955	−0.202977	+	0.979183i	$0.565062\pi$
$6$	216.000	0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	907.742	0.287053
$11$	−3827.20	−0.866976	−0.433488	−	0.901159i	$-0.642717\pi$
$11$	−3827.20	−0.866976	−0.433488	+	0.901159i	$0.642717\pi$
$12$	−1728.00	−0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−2744.00	−0.267261
$15$	3063.63	0.234378
$16$	4096.00	0.250000
$17$	−36941.0	−1.82363	−0.911817	−	0.410596i	$-0.865321\pi$
$17$	−36941.0	−1.82363	−0.911817	+	0.410596i	$0.865321\pi$
$18$	−5832.00	−0.235702
$19$	−56827.3	−1.90073	−0.950364	−	0.311142i	$-0.899289\pi$
$19$	−56827.3	−1.90073	−0.950364	+	0.311142i	$0.899289\pi$
$20$	−7261.94	−0.202977
$21$	−9261.00	−0.218218
$22$	30617.6	0.613045
$23$	42283.4	0.724641	0.362320	−	0.932054i	$-0.381985\pi$
$23$	42283.4	0.724641	0.362320	+	0.932054i	$0.381985\pi$
$24$	13824.0	0.204124
$25$	−65250.1	−0.835201
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	21952.0	0.188982
$29$	158520.	1.20695	0.603476	−	0.797381i	$-0.293782\pi$
$29$	158520.	1.20695	0.603476	+	0.797381i	$0.293782\pi$
$30$	−24509.0	−0.165730
$31$	98296.8	0.592616	0.296308	−	0.955092i	$-0.404245\pi$
$31$	98296.8	0.592616	0.296308	+	0.955092i	$0.404245\pi$
$32$	−32768.0	−0.176777
$33$	103335.	0.500549
$34$	295528.	1.28950
$35$	−38919.5	−0.153436
$36$	46656.0	0.166667
$37$	352941.	1.14550	0.572751	−	0.819729i	$-0.305876\pi$
$37$	352941.	1.14550	0.572751	+	0.819729i	$0.305876\pi$
$38$	454619.	1.34402
$39$	−59319.0	−0.160128
$40$	58095.5	0.143527
$41$	−786907.	−1.78312	−0.891558	−	0.452906i	$-0.850387\pi$
$41$	−786907.	−1.78312	−0.891558	+	0.452906i	$0.850387\pi$
$42$	74088.0	0.154303
$43$	−744062.	−1.42715	−0.713575	−	0.700579i	$-0.752925\pi$
$43$	−744062.	−1.42715	−0.713575	+	0.700579i	$0.752925\pi$
$44$	−244941.	−0.433488
$45$	−82718.0	−0.135318
$46$	−338267.	−0.512398
$47$	−498725.	−0.700678	−0.350339	−	0.936623i	$-0.613934\pi$
$47$	−498725.	−0.700678	−0.350339	+	0.936623i	$0.613934\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	522000.	0.590576
$51$	997408.	1.05288
$52$	140608.	0.138675
$53$	−664787.	−0.613362	−0.306681	−	0.951812i	$-0.599218\pi$
$53$	−664787.	−0.613362	−0.306681	+	0.951812i	$0.599218\pi$
$54$	157464.	0.136083
$55$	434264.	0.351953
$56$	−175616.	−0.133631
$57$	1.53434e6	1.09739
$58$	−1.26816e6	−0.853445
$59$	1.39438e6	0.883894	0.441947	−	0.897041i	$-0.354288\pi$
$59$	1.39438e6	0.883894	0.441947	+	0.897041i	$0.354288\pi$
$60$	196072.	0.117189
$61$	−1.33040e6	−0.750462	−0.375231	−	0.926931i	$-0.622437\pi$
$61$	−1.33040e6	−0.750462	−0.375231	+	0.926931i	$0.622437\pi$
$62$	−786374.	−0.419043
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	−249289.	−0.112592
$66$	−826676.	−0.353942
$67$	2.54161e6	1.03240	0.516198	−	0.856469i	$-0.327347\pi$
$67$	2.54161e6	1.03240	0.516198	+	0.856469i	$0.327347\pi$
$68$	−2.36423e6	−0.911817
$69$	−1.14165e6	−0.418372
$70$	311356.	0.108496
$71$	−5.37482e6	−1.78221	−0.891107	−	0.453792i	$-0.850071\pi$
$71$	−5.37482e6	−1.78221	−0.891107	+	0.453792i	$0.850071\pi$
$72$	−373248.	−0.117851
$73$	3.59276e6	1.08093	0.540466	−	0.841366i	$-0.318248\pi$
$73$	3.59276e6	1.08093	0.540466	+	0.841366i	$0.318248\pi$
$74$	−2.82353e6	−0.809992
$75$	1.76175e6	0.482203
$76$	−3.63695e6	−0.950364
$77$	−1.31273e6	−0.327686
$78$	474552.	0.113228
$79$	5.53769e6	1.26367	0.631835	−	0.775103i	$-0.282302\pi$
$79$	5.53769e6	1.26367	0.631835	+	0.775103i	$0.282302\pi$
$80$	−464764.	−0.101489
$81$	531441.	0.111111
$82$	6.29525e6	1.26085
$83$	−5.11360e6	−0.981643	−0.490822	−	0.871260i	$-0.663303\pi$
$83$	−5.11360e6	−0.981643	−0.490822	+	0.871260i	$0.663303\pi$
$84$	−592704.	−0.109109
$85$	4.19162e6	0.740313
$86$	5.95249e6	1.00915
$87$	−4.28003e6	−0.696835
$88$	1.95953e6	0.306522
$89$	−7.66025e6	−1.15180	−0.575901	−	0.817519i	$-0.695349\pi$
$89$	−7.66025e6	−1.15180	−0.575901	+	0.817519i	$0.695349\pi$
$90$	661744.	0.0956844
$91$	753571.	0.104828
$92$	2.70614e6	0.362320
$93$	−2.65401e6	−0.342147
$94$	3.98980e6	0.495454
$95$	6.44807e6	0.771609
$96$	884736.	0.102062
$97$	−1.56564e7	−1.74177	−0.870884	−	0.491488i	$-0.836453\pi$
$97$	−1.56564e7	−1.74177	−0.870884	+	0.491488i	$0.836453\pi$
$98$	−941192.	−0.101015
$99$	−2.79003e6	−0.288992
$100$	−4.17600e6	−0.417600
$101$	−103574.	−0.0100029	−0.00500147	−	0.999987i	$-0.501592\pi$
$101$	−103574.	−0.0100029	−0.00500147	+	0.999987i	$0.501592\pi$
$102$	−7.97926e6	−0.744496
$103$	−1.64565e7	−1.48391	−0.741954	−	0.670451i	$-0.766101\pi$
$103$	−1.64565e7	−1.48391	−0.741954	+	0.670451i	$0.766101\pi$
$104$	−1.12486e6	−0.0980581
$105$	1.05083e6	0.0885866
$106$	5.31829e6	0.433712
$107$	−7.14120e6	−0.563544	−0.281772	−	0.959481i	$-0.590922\pi$
$107$	−7.14120e6	−0.563544	−0.281772	+	0.959481i	$0.590922\pi$
$108$	−1.25971e6	−0.0962250
$109$	5.81181e6	0.429851	0.214926	−	0.976630i	$-0.431049\pi$
$109$	5.81181e6	0.429851	0.214926	+	0.976630i	$0.431049\pi$
$110$	−3.47411e6	−0.248868
$111$	−9.52940e6	−0.661356
$112$	1.40493e6	0.0944911
$113$	−1.89753e7	−1.23713	−0.618564	−	0.785735i	$-0.712285\pi$
$113$	−1.89753e7	−1.23713	−0.618564	+	0.785735i	$0.712285\pi$
$114$	−1.22747e7	−0.775969
$115$	−4.79781e6	−0.294171
$116$	1.01453e7	0.603476
$117$	1.60161e6	0.0924500
$118$	−1.11551e7	−0.625008
$119$	−1.26708e7	−0.689269
$120$	−1.56858e6	−0.0828652
$121$	−4.83968e6	−0.248352
$122$	1.06432e7	0.530657
$123$	2.12465e7	1.02948
$124$	6.29099e6	0.296308
$125$	1.62685e7	0.745008
$126$	−2.00038e6	−0.0890871
$127$	3.95319e7	1.71252	0.856258	−	0.516548i	$-0.172783\pi$
$127$	3.95319e7	1.71252	0.856258	+	0.516548i	$0.172783\pi$
$128$	−2.09715e6	−0.0883883
$129$	2.00897e7	0.823965
$130$	1.99431e6	0.0796143
$131$	−2.42781e6	−0.0943551	−0.0471775	−	0.998887i	$-0.515023\pi$
$131$	−2.42781e6	−0.0943551	−0.0471775	+	0.998887i	$0.515023\pi$
$132$	6.61341e6	0.250274
$133$	−1.94918e7	−0.718407
$134$	−2.03329e7	−0.730015
$135$	2.23339e6	0.0781260
$136$	1.89138e7	0.644752
$137$	4.16766e7	1.38475	0.692374	−	0.721539i	$-0.256565\pi$
$137$	4.16766e7	1.38475	0.692374	+	0.721539i	$0.256565\pi$
$138$	9.13322e6	0.295833
$139$	−5.96582e7	−1.88416	−0.942082	−	0.335383i	$-0.891134\pi$
$139$	−5.96582e7	−1.88416	−0.942082	+	0.335383i	$0.891134\pi$
$140$	−2.49084e6	−0.0767182
$141$	1.34656e7	0.404537
$142$	4.29986e7	1.26022
$143$	−8.40837e6	−0.240456
$144$	2.98598e6	0.0833333
$145$	−1.79869e7	−0.489968
$146$	−2.87421e7	−0.764335
$147$	−3.17652e6	−0.0824786
$148$	2.25882e7	0.572751
$149$	1.78622e7	0.442366	0.221183	−	0.975232i	$-0.429008\pi$
$149$	1.78622e7	0.442366	0.221183	+	0.975232i	$0.429008\pi$
$150$	−1.40940e7	−0.340969
$151$	−3.78116e7	−0.893729	−0.446865	−	0.894602i	$-0.647459\pi$
$151$	−3.78116e7	−0.893729	−0.446865	+	0.894602i	$0.647459\pi$
$152$	2.90956e7	0.672009
$153$	−2.69300e7	−0.607878
$154$	1.05018e7	0.231709
$155$	−1.11535e7	−0.240575
$156$	−3.79642e6	−0.0800641
$157$	−1.14825e7	−0.236804	−0.118402	−	0.992966i	$-0.537777\pi$
$157$	−1.14825e7	−0.236804	−0.118402	+	0.992966i	$0.537777\pi$
$158$	−4.43015e7	−0.893549
$159$	1.79492e7	0.354125
$160$	3.71811e6	0.0717633
$161$	1.45032e7	0.273888
$162$	−4.25153e6	−0.0785674
$163$	3.82479e7	0.691752	0.345876	−	0.938280i	$-0.387582\pi$
$163$	3.82479e7	0.691752	0.345876	+	0.938280i	$0.387582\pi$
$164$	−5.03620e7	−0.891558
$165$	−1.17251e7	−0.203200
$166$	4.09088e7	0.694127
$167$	4.21224e7	0.699851	0.349926	−	0.936778i	$-0.386207\pi$
$167$	4.21224e7	0.699851	0.349926	+	0.936778i	$0.386207\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	−3.35329e7	−0.523480
$171$	−4.14271e7	−0.633576
$172$	−4.76199e7	−0.713575
$173$	−2.41841e7	−0.355114	−0.177557	−	0.984110i	$-0.556819\pi$
$173$	−2.41841e7	−0.355114	−0.177557	+	0.984110i	$0.556819\pi$
$174$	3.42403e7	0.492736
$175$	−2.23808e7	−0.315676
$176$	−1.56762e7	−0.216744
$177$	−3.76484e7	−0.510317
$178$	6.12820e7	0.814447
$179$	−3.53619e7	−0.460840	−0.230420	−	0.973091i	$-0.574010\pi$
$179$	−3.53619e7	−0.460840	−0.230420	+	0.973091i	$0.574010\pi$
$180$	−5.29395e6	−0.0676591
$181$	2.96542e7	0.371716	0.185858	−	0.982577i	$-0.440494\pi$
$181$	2.96542e7	0.371716	0.185858	+	0.982577i	$0.440494\pi$
$182$	−6.02857e6	−0.0741249
$183$	3.59209e7	0.433280
$184$	−2.16491e7	−0.256199
$185$	−4.00474e7	−0.465022
$186$	2.12321e7	0.241934
$187$	1.41381e8	1.58105
$188$	−3.19184e7	−0.350339
$189$	−6.75127e6	−0.0727393
$190$	−5.15846e7	−0.545610
$191$	−1.47397e8	−1.53064	−0.765319	−	0.643651i	$-0.777419\pi$
$191$	−1.47397e8	−1.53064	−0.765319	+	0.643651i	$0.777419\pi$
$192$	−7.07789e6	−0.0721688
$193$	−9.04774e7	−0.905919	−0.452960	−	0.891531i	$-0.649632\pi$
$193$	−9.04774e7	−0.905919	−0.452960	+	0.891531i	$0.649632\pi$
$194$	1.25251e8	1.23162
$195$	6.73080e6	0.0650048
$196$	7.52954e6	0.0714286
$197$	−5.91676e7	−0.551382	−0.275691	−	0.961246i	$-0.588907\pi$
$197$	−5.91676e7	−0.551382	−0.275691	+	0.961246i	$0.588907\pi$
$198$	2.23203e7	0.204348
$199$	4.33390e7	0.389846	0.194923	−	0.980819i	$-0.437554\pi$
$199$	4.33390e7	0.389846	0.194923	+	0.980819i	$0.437554\pi$
$200$	3.34080e7	0.295288
$201$	−6.86234e7	−0.596055
$202$	828596.	0.00707315
$203$	5.43723e7	0.456185
$204$	6.38341e7	0.526438
$205$	8.92886e7	0.723865
$206$	1.31652e8	1.04928
$207$	3.08246e7	0.241547
$208$	8.99891e6	0.0693375
$209$	2.17490e8	1.64789
$210$	−8.40660e6	−0.0626402
$211$	2.26404e8	1.65918	0.829592	−	0.558369i	$-0.188573\pi$
$211$	2.26404e8	1.65918	0.829592	+	0.558369i	$0.188573\pi$
$212$	−4.25464e7	−0.306681
$213$	1.45120e8	1.02896
$214$	5.71296e7	0.398486
$215$	8.44270e7	0.579358
$216$	1.00777e7	0.0680414
$217$	3.37158e7	0.223988
$218$	−4.64945e7	−0.303951
$219$	−9.70046e7	−0.624077
$220$	2.77929e7	0.175977
$221$	−8.11595e7	−0.505785
$222$	7.62352e7	0.467649
$223$	1.76572e8	1.06624	0.533121	−	0.846039i	$-0.321019\pi$
$223$	1.76572e8	1.06624	0.533121	+	0.846039i	$0.321019\pi$
$224$	−1.12394e7	−0.0668153
$225$	−4.75673e7	−0.278400
$226$	1.51803e8	0.874781
$227$	5.10006e7	0.289391	0.144695	−	0.989476i	$-0.453780\pi$
$227$	5.10006e7	0.289391	0.144695	+	0.989476i	$0.453780\pi$
$228$	9.81977e7	0.548693
$229$	−3.09360e8	−1.70232	−0.851158	−	0.524909i	$-0.824099\pi$
$229$	−3.09360e8	−1.70232	−0.851158	+	0.524909i	$0.824099\pi$
$230$	3.83825e7	0.208011
$231$	3.54437e7	0.189190
$232$	−8.11621e7	−0.426722
$233$	1.46068e8	0.756501	0.378250	−	0.925703i	$-0.376526\pi$
$233$	1.46068e8	0.756501	0.378250	+	0.925703i	$0.376526\pi$
$234$	−1.28129e7	−0.0653720
$235$	5.65892e7	0.284443
$236$	8.92406e7	0.441947
$237$	−1.49518e8	−0.729580
$238$	1.01366e8	0.487387
$239$	9.61072e7	0.455369	0.227684	−	0.973735i	$-0.426885\pi$
$239$	9.61072e7	0.455369	0.227684	+	0.973735i	$0.426885\pi$
$240$	1.25486e7	0.0585945
$241$	3.91257e8	1.80054	0.900270	−	0.435333i	$-0.143369\pi$
$241$	3.91257e8	1.80054	0.900270	+	0.435333i	$0.143369\pi$
$242$	3.87175e7	0.175612
$243$	−1.43489e7	−0.0641500
$244$	−8.51458e7	−0.375231
$245$	−1.33494e7	−0.0579935
$246$	−1.69972e8	−0.727954
$247$	−1.24850e8	−0.527167
$248$	−5.03280e7	−0.209521
$249$	1.38067e8	0.566752
$250$	−1.30148e8	−0.526800
$251$	1.97659e8	0.788967	0.394483	−	0.918903i	$-0.370924\pi$
$251$	1.97659e8	0.788967	0.394483	+	0.918903i	$0.370924\pi$
$252$	1.60030e7	0.0629941
$253$	−1.61827e8	−0.628246
$254$	−3.16255e8	−1.21093
$255$	−1.13174e8	−0.427420
$256$	1.67772e7	0.0625000
$257$	−1.30951e8	−0.481219	−0.240610	−	0.970622i	$-0.577347\pi$
$257$	−1.30951e8	−0.481219	−0.240610	+	0.970622i	$0.577347\pi$
$258$	−1.60717e8	−0.582631
$259$	1.21059e8	0.432959
$260$	−1.59545e7	−0.0562958
$261$	1.15561e8	0.402318
$262$	1.94225e7	0.0667191
$263$	−3.42123e8	−1.15968	−0.579839	−	0.814731i	$-0.696884\pi$
$263$	−3.42123e8	−1.15968	−0.579839	+	0.814731i	$0.696884\pi$
$264$	−5.29073e7	−0.176971
$265$	7.54319e7	0.248997
$266$	1.55934e8	0.507991
$267$	2.06827e8	0.664993
$268$	1.62663e8	0.516198
$269$	1.20771e8	0.378295	0.189148	−	0.981949i	$-0.439428\pi$
$269$	1.20771e8	0.378295	0.189148	+	0.981949i	$0.439428\pi$
$270$	−1.78671e7	−0.0552434
$271$	5.29161e8	1.61508	0.807542	−	0.589809i	$-0.200797\pi$
$271$	5.29161e8	1.61508	0.807542	+	0.589809i	$0.200797\pi$
$272$	−1.51310e8	−0.455909
$273$	−2.03464e7	−0.0605228
$274$	−3.33413e8	−0.979165
$275$	2.49725e8	0.724099
$276$	−7.30658e7	−0.209186
$277$	3.39180e8	0.958850	0.479425	−	0.877583i	$-0.340845\pi$
$277$	3.39180e8	0.958850	0.479425	+	0.877583i	$0.340845\pi$
$278$	4.77266e8	1.33230
$279$	7.16584e7	0.197539
$280$	1.99268e7	0.0542480
$281$	6.33478e8	1.70317	0.851587	−	0.524213i	$-0.175640\pi$
$281$	6.33478e8	1.70317	0.851587	+	0.524213i	$0.175640\pi$
$282$	−1.07725e8	−0.286051
$283$	5.96829e8	1.56530	0.782650	−	0.622463i	$-0.213868\pi$
$283$	5.96829e8	1.56530	0.782650	+	0.622463i	$0.213868\pi$
$284$	−3.43989e8	−0.891107
$285$	−1.74098e8	−0.445489
$286$	6.72669e7	0.170028
$287$	−2.69909e8	−0.673955
$288$	−2.38879e7	−0.0589256
$289$	9.54302e8	2.32564
$290$	1.43895e8	0.346460
$291$	4.22722e8	1.00561
$292$	2.29937e8	0.540466
$293$	1.70024e8	0.394887	0.197443	−	0.980314i	$-0.436736\pi$
$293$	1.70024e8	0.394887	0.197443	+	0.980314i	$0.436736\pi$
$294$	2.54122e7	0.0583212
$295$	−1.58218e8	−0.358821
$296$	−1.80706e8	−0.404996
$297$	7.53309e7	0.166850
$298$	−1.42897e8	−0.312800
$299$	9.28967e7	0.200979
$300$	1.12752e8	0.241102
$301$	−2.55213e8	−0.539412
$302$	3.02493e8	0.631962
$303$	2.79651e6	0.00577520
$304$	−2.32765e8	−0.475182
$305$	1.50958e8	0.304654
$306$	2.15440e8	0.429835
$307$	4.12442e8	0.813540	0.406770	−	0.913531i	$-0.366655\pi$
$307$	4.12442e8	0.813540	0.406770	+	0.913531i	$0.366655\pi$
$308$	−8.40148e7	−0.163843
$309$	4.44325e8	0.856735
$310$	8.92282e7	0.170112
$311$	−7.47583e8	−1.40928	−0.704641	−	0.709564i	$-0.748892\pi$
$311$	−7.47583e8	−1.40928	−0.704641	+	0.709564i	$0.748892\pi$
$312$	3.03713e7	0.0566139
$313$	2.27958e8	0.420194	0.210097	−	0.977681i	$-0.432622\pi$
$313$	2.27958e8	0.420194	0.210097	+	0.977681i	$0.432622\pi$
$314$	9.18604e7	0.167446
$315$	−2.83723e7	−0.0511455
$316$	3.54412e8	0.631835
$317$	−1.72903e8	−0.304856	−0.152428	−	0.988315i	$-0.548709\pi$
$317$	−1.72903e8	−0.304856	−0.152428	+	0.988315i	$0.548709\pi$
$318$	−1.43594e8	−0.250404
$319$	−6.06687e8	−1.04640
$320$	−2.97449e7	−0.0507443
$321$	1.92812e8	0.325362
$322$	−1.16026e8	−0.193668
$323$	2.09926e9	3.46623
$324$	3.40122e7	0.0555556
$325$	−1.43354e8	−0.231643
$326$	−3.05983e8	−0.489143
$327$	−1.56919e8	−0.248175
$328$	4.02896e8	0.630427
$329$	−1.71063e8	−0.264831
$330$	9.38011e7	0.143684
$331$	−6.78468e8	−1.02833	−0.514164	−	0.857692i	$-0.671898\pi$
$331$	−6.78468e8	−1.02833	−0.514164	+	0.857692i	$0.671898\pi$
$332$	−3.27271e8	−0.490822
$333$	2.57294e8	0.381834
$334$	−3.36979e8	−0.494869
$335$	−2.88391e8	−0.419106
$336$	−3.79331e7	−0.0545545
$337$	−5.33477e8	−0.759295	−0.379648	−	0.925131i	$-0.623955\pi$
$337$	−5.33477e8	−0.759295	−0.379648	+	0.925131i	$0.623955\pi$
$338$	−3.86145e7	−0.0543928
$339$	5.12333e8	0.714256
$340$	2.68264e8	0.370157
$341$	−3.76202e8	−0.513784
$342$	3.31417e8	0.448006
$343$	4.03536e7	0.0539949
$344$	3.80960e8	0.504573
$345$	1.29541e8	0.169840
$346$	1.93473e8	0.251104
$347$	5.83712e8	0.749972	0.374986	−	0.927030i	$-0.377647\pi$
$347$	5.83712e8	0.749972	0.374986	+	0.927030i	$0.377647\pi$
$348$	−2.73922e8	−0.348417
$349$	−1.00692e9	−1.26796	−0.633978	−	0.773351i	$-0.718579\pi$
$349$	−1.00692e9	−1.26796	−0.633978	+	0.773351i	$0.718579\pi$
$350$	1.79046e8	0.223217
$351$	−4.32436e7	−0.0533761
$352$	1.25410e8	0.153261
$353$	−1.61837e8	−0.195825	−0.0979123	−	0.995195i	$-0.531216\pi$
$353$	−1.61837e8	−0.195825	−0.0979123	+	0.995195i	$0.531216\pi$
$354$	3.01187e8	0.360848
$355$	6.09869e8	0.723498
$356$	−4.90256e8	−0.575901
$357$	3.42111e8	0.397950
$358$	2.82895e8	0.325863
$359$	−1.36320e9	−1.55500	−0.777500	−	0.628883i	$-0.783512\pi$
$359$	−1.36320e9	−1.55500	−0.777500	+	0.628883i	$0.783512\pi$
$360$	4.23516e7	0.0478422
$361$	2.33548e9	2.61276
$362$	−2.37233e8	−0.262843
$363$	1.30671e8	0.143386
$364$	4.82285e7	0.0524142
$365$	−4.07663e8	−0.438810
$366$	−2.87367e8	−0.306375
$367$	9.23714e8	0.975452	0.487726	−	0.872997i	$-0.337826\pi$
$367$	9.23714e8	0.975452	0.487726	+	0.872997i	$0.337826\pi$
$368$	1.73193e8	0.181160
$369$	−5.73655e8	−0.594372
$370$	3.20379e8	0.328820
$371$	−2.28022e8	−0.231829
$372$	−1.69857e8	−0.171074
$373$	−7.84082e7	−0.0782313	−0.0391157	−	0.999235i	$-0.512454\pi$
$373$	−7.84082e7	−0.0782313	−0.0391157	+	0.999235i	$0.512454\pi$
$374$	−1.13105e9	−1.11797
$375$	−4.39248e8	−0.430131
$376$	2.55347e8	0.247727
$377$	3.48268e8	0.334749
$378$	5.40102e7	0.0514344
$379$	1.54173e8	0.145469	0.0727346	−	0.997351i	$-0.476827\pi$
$379$	1.54173e8	0.145469	0.0727346	+	0.997351i	$0.476827\pi$
$380$	4.12677e8	0.385805
$381$	−1.06736e9	−0.988722
$382$	1.17918e9	1.08232
$383$	5.09223e8	0.463140	0.231570	−	0.972818i	$-0.425614\pi$
$383$	5.09223e8	0.463140	0.231570	+	0.972818i	$0.425614\pi$
$384$	5.66231e7	0.0510310
$385$	1.48953e8	0.133026
$386$	7.23819e8	0.640582
$387$	−5.42421e8	−0.475716
$388$	−1.00201e9	−0.870884
$389$	2.44111e7	0.0210263	0.0105132	−	0.999945i	$-0.496653\pi$
$389$	2.44111e7	0.0210263	0.0105132	+	0.999945i	$0.496653\pi$
$390$	−5.38464e7	−0.0459653
$391$	−1.56199e9	−1.32148
$392$	−6.02363e7	−0.0505076
$393$	6.55509e7	0.0544759
$394$	4.73341e8	0.389886
$395$	−6.28349e8	−0.512993
$396$	−1.78562e8	−0.144496
$397$	5.09478e8	0.408657	0.204329	−	0.978902i	$-0.434499\pi$
$397$	5.09478e8	0.408657	0.204329	+	0.978902i	$0.434499\pi$
$398$	−3.46712e8	−0.275663
$399$	5.26278e8	0.414773
$400$	−2.67264e8	−0.208800
$401$	9.01074e8	0.697839	0.348919	−	0.937153i	$-0.386549\pi$
$401$	9.01074e8	0.697839	0.348919	+	0.937153i	$0.386549\pi$
$402$	5.48987e8	0.421474
$403$	2.15958e8	0.164362
$404$	−6.62877e6	−0.00500147
$405$	−6.03014e7	−0.0451061
$406$	−4.34978e8	−0.322572
$407$	−1.35078e9	−0.993123
$408$	−5.10673e8	−0.372248
$409$	1.63738e9	1.18337	0.591683	−	0.806171i	$-0.298464\pi$
$409$	1.63738e9	1.18337	0.591683	+	0.806171i	$0.298464\pi$
$410$	−7.14308e8	−0.511850
$411$	−1.12527e9	−0.799485
$412$	−1.05322e9	−0.741954
$413$	4.78274e8	0.334081
$414$	−2.46597e8	−0.170799
$415$	5.80229e8	0.398503
$416$	−7.19913e7	−0.0490290
$417$	1.61077e9	1.08782
$418$	−1.73992e9	−1.16523
$419$	1.35298e8	0.0898548	0.0449274	−	0.998990i	$-0.485694\pi$
$419$	1.35298e8	0.0898548	0.0449274	+	0.998990i	$0.485694\pi$
$420$	6.72528e7	0.0442933
$421$	−1.92665e9	−1.25839	−0.629196	−	0.777247i	$-0.716616\pi$
$421$	−1.92665e9	−1.25839	−0.629196	+	0.777247i	$0.716616\pi$
$422$	−1.81123e9	−1.17322
$423$	−3.63570e8	−0.233559
$424$	3.40371e8	0.216856
$425$	2.41041e9	1.52310
$426$	−1.16096e9	−0.727586
$427$	−4.56328e8	−0.283648
$428$	−4.57037e8	−0.281772
$429$	2.27026e8	0.138827
$430$	−6.75416e8	−0.409668
$431$	2.85171e9	1.71567	0.857837	−	0.513922i	$-0.171808\pi$
$431$	2.85171e9	1.71567	0.857837	+	0.513922i	$0.171808\pi$
$432$	−8.06216e7	−0.0481125
$433$	1.71853e8	0.101730	0.0508650	−	0.998706i	$-0.483802\pi$
$433$	1.71853e8	0.101730	0.0508650	+	0.998706i	$0.483802\pi$
$434$	−2.69726e8	−0.158383
$435$	4.85646e8	0.282883
$436$	3.71956e8	0.214926
$437$	−2.40286e9	−1.37734
$438$	7.76037e8	0.441289
$439$	9.19463e8	0.518691	0.259345	−	0.965785i	$-0.416493\pi$
$439$	9.19463e8	0.518691	0.259345	+	0.965785i	$0.416493\pi$
$440$	−2.22343e8	−0.124434
$441$	8.57661e7	0.0476190
$442$	6.49276e8	0.357644
$443$	−2.59886e9	−1.42027	−0.710134	−	0.704067i	$-0.751366\pi$
$443$	−2.59886e9	−1.42027	−0.710134	+	0.704067i	$0.751366\pi$
$444$	−6.09882e8	−0.330678
$445$	8.69192e8	0.467579
$446$	−1.41258e9	−0.753947
$447$	−4.82278e8	−0.255400
$448$	8.99154e7	0.0472456
$449$	5.80704e8	0.302756	0.151378	−	0.988476i	$-0.451629\pi$
$449$	5.80704e8	0.302756	0.151378	+	0.988476i	$0.451629\pi$
$450$	3.80538e8	0.196859
$451$	3.01165e9	1.54592
$452$	−1.21442e9	−0.618564
$453$	1.02091e9	0.515995
$454$	−4.08005e8	−0.204630
$455$	−8.55060e7	−0.0425556
$456$	−7.85581e8	−0.387984
$457$	−2.67969e9	−1.31334	−0.656672	−	0.754176i	$-0.728036\pi$
$457$	−2.67969e9	−1.31334	−0.656672	+	0.754176i	$0.728036\pi$
$458$	2.47488e9	1.20372
$459$	7.27110e8	0.350959
$460$	−3.07060e8	−0.147086
$461$	2.97997e9	1.41664	0.708319	−	0.705892i	$-0.249454\pi$
$461$	2.97997e9	1.41664	0.708319	+	0.705892i	$0.249454\pi$
$462$	−2.83550e8	−0.133777
$463$	2.53656e9	1.18771	0.593856	−	0.804571i	$-0.297605\pi$
$463$	2.53656e9	1.18771	0.593856	+	0.804571i	$0.297605\pi$
$464$	6.49297e8	0.301738
$465$	3.01145e8	0.138896
$466$	−1.16854e9	−0.534927
$467$	−1.87235e9	−0.850703	−0.425351	−	0.905028i	$-0.639849\pi$
$467$	−1.87235e9	−0.850703	−0.425351	+	0.905028i	$0.639849\pi$
$468$	1.02503e8	0.0462250
$469$	8.71771e8	0.390209
$470$	−4.52714e8	−0.201132
$471$	3.10029e8	0.136719
$472$	−7.13925e8	−0.312504
$473$	2.84768e9	1.23730
$474$	1.19614e9	0.515891
$475$	3.70799e9	1.58749
$476$	−8.10930e8	−0.344635
$477$	−4.84630e8	−0.204454
$478$	−7.68858e8	−0.321994
$479$	−2.75021e9	−1.14338	−0.571691	−	0.820469i	$-0.693713\pi$
$479$	−2.75021e9	−1.14338	−0.571691	+	0.820469i	$0.693713\pi$
$480$	−1.00389e8	−0.0414326
$481$	7.75411e8	0.317705
$482$	−3.13006e9	−1.27317
$483$	−3.91587e8	−0.158130
$484$	−3.09740e8	−0.124176
$485$	1.77650e9	0.707079
$486$	1.14791e8	0.0453609
$487$	3.55069e9	1.39303	0.696516	−	0.717541i	$-0.254732\pi$
$487$	3.55069e9	1.39303	0.696516	+	0.717541i	$0.254732\pi$
$488$	6.81167e8	0.265329
$489$	−1.03269e9	−0.399383
$490$	1.06795e8	0.0410076
$491$	−1.46470e9	−0.558425	−0.279213	−	0.960229i	$-0.590073\pi$
$491$	−1.46470e9	−0.558425	−0.279213	+	0.960229i	$0.590073\pi$
$492$	1.35977e9	0.514741
$493$	−5.85588e9	−2.20104
$494$	9.98797e8	0.372763
$495$	3.16579e8	0.117318
$496$	4.02624e8	0.148154
$497$	−1.84356e9	−0.673614
$498$	−1.10454e9	−0.400754
$499$	−1.64336e9	−0.592081	−0.296040	−	0.955175i	$-0.595666\pi$
$499$	−1.64336e9	−0.592081	−0.296040	+	0.955175i	$0.595666\pi$
$500$	1.04118e9	0.372504
$501$	−1.13731e9	−0.404059
$502$	−1.58127e9	−0.557884
$503$	2.63997e9	0.924934	0.462467	−	0.886636i	$-0.346964\pi$
$503$	2.63997e9	0.924934	0.462467	+	0.886636i	$0.346964\pi$
$504$	−1.28024e8	−0.0445435
$505$	1.17524e7	0.00406074
$506$	1.29462e9	0.444237
$507$	−1.30324e8	−0.0444116
$508$	2.53004e9	0.856258
$509$	1.19059e9	0.400177	0.200088	−	0.979778i	$-0.435877\pi$
$509$	1.19059e9	0.400177	0.200088	+	0.979778i	$0.435877\pi$
$510$	9.05389e8	0.302232
$511$	1.23232e9	0.408554
$512$	−1.34218e8	−0.0441942
$513$	1.11853e9	0.365795
$514$	1.04761e9	0.340273
$515$	1.86728e9	0.602400
$516$	1.28574e9	0.411982
$517$	1.90872e9	0.607471
$518$	−9.68470e8	−0.306148
$519$	6.52970e8	0.205025
$520$	1.27636e8	0.0398071
$521$	−3.82843e8	−0.118601	−0.0593005	−	0.998240i	$-0.518887\pi$
$521$	−3.82843e8	−0.118601	−0.0593005	+	0.998240i	$0.518887\pi$
$522$	−9.24487e8	−0.284482
$523$	−5.99389e9	−1.83212	−0.916058	−	0.401046i	$-0.868647\pi$
$523$	−5.99389e9	−1.83212	−0.916058	+	0.401046i	$0.868647\pi$
$524$	−1.55380e8	−0.0471775
$525$	6.04281e8	0.182256
$526$	2.73698e9	0.820016
$527$	−3.63119e9	−1.08072
$528$	4.23258e8	0.125137
$529$	−1.61694e9	−0.474896
$530$	−6.03455e8	−0.176068
$531$	1.01651e9	0.294631
$532$	−1.24747e9	−0.359204
$533$	−1.72883e9	−0.494548
$534$	−1.65461e9	−0.470221
$535$	8.10296e8	0.228773
$536$	−1.30130e9	−0.365007
$537$	9.54772e8	0.266066
$538$	−9.66171e8	−0.267495
$539$	−4.50267e8	−0.123854
$540$	1.42937e8	0.0390630
$541$	3.40349e9	0.924132	0.462066	−	0.886846i	$-0.347108\pi$
$541$	3.40349e9	0.924132	0.462066	+	0.886846i	$0.347108\pi$
$542$	−4.23329e9	−1.14204
$543$	−8.00662e8	−0.214610
$544$	1.21048e9	0.322376
$545$	−6.59453e8	−0.174500
$546$	1.62771e8	0.0427960
$547$	−2.88099e8	−0.0752638	−0.0376319	−	0.999292i	$-0.511981\pi$
$547$	−2.88099e8	−0.0752638	−0.0376319	+	0.999292i	$0.511981\pi$
$548$	2.66730e9	0.692374
$549$	−9.69864e8	−0.250154
$550$	−1.99780e9	−0.512015
$551$	−9.00826e9	−2.29409
$552$	5.84526e8	0.147917
$553$	1.89943e9	0.477622
$554$	−2.71344e9	−0.678009
$555$	1.08128e9	0.268481
$556$	−3.81813e9	−0.942082
$557$	−8.55398e8	−0.209737	−0.104868	−	0.994486i	$-0.533442\pi$
$557$	−8.55398e8	−0.209737	−0.104868	+	0.994486i	$0.533442\pi$
$558$	−5.73267e8	−0.139681
$559$	−1.63470e9	−0.395820
$560$	−1.59414e8	−0.0383591
$561$	−3.81728e9	−0.912819
$562$	−5.06782e9	−1.20433
$563$	9.35132e8	0.220848	0.110424	−	0.993885i	$-0.464779\pi$
$563$	9.35132e8	0.220848	0.110424	+	0.993885i	$0.464779\pi$
$564$	8.61796e8	0.202268
$565$	2.15309e9	0.502218
$566$	−4.77463e9	−1.10683
$567$	1.82284e8	0.0419961
$568$	2.75191e9	0.630108
$569$	1.19108e9	0.271049	0.135524	−	0.990774i	$-0.456728\pi$
$569$	1.19108e9	0.271049	0.135524	+	0.990774i	$0.456728\pi$
$570$	1.39278e9	0.315008
$571$	−4.44856e9	−0.999983	−0.499992	−	0.866030i	$-0.666664\pi$
$571$	−4.44856e9	−0.999983	−0.499992	+	0.866030i	$0.666664\pi$
$572$	−5.38135e8	−0.120228
$573$	3.97973e9	0.883714
$574$	2.15927e9	0.476558
$575$	−2.75900e9	−0.605221
$576$	1.91103e8	0.0416667
$577$	7.29923e9	1.58184	0.790918	−	0.611922i	$-0.209603\pi$
$577$	7.29923e9	1.58184	0.790918	+	0.611922i	$0.209603\pi$
$578$	−7.63441e9	−1.64448
$579$	2.44289e9	0.523033
$580$	−1.15116e9	−0.244984
$581$	−1.75397e9	−0.371026
$582$	−3.38178e9	−0.711074
$583$	2.54427e9	0.531770
$584$	−1.83949e9	−0.382167
$585$	−1.81731e8	−0.0375305
$586$	−1.36019e9	−0.279227
$587$	2.04418e9	0.417145	0.208572	−	0.978007i	$-0.433118\pi$
$587$	2.04418e9	0.417145	0.208572	+	0.978007i	$0.433118\pi$
$588$	−2.03297e8	−0.0412393
$589$	−5.58595e9	−1.12640
$590$	1.26574e9	0.253725
$591$	1.59753e9	0.318340
$592$	1.44565e9	0.286376
$593$	−6.01899e9	−1.18531	−0.592655	−	0.805456i	$-0.701920\pi$
$593$	−6.01899e9	−1.18531	−0.592655	+	0.805456i	$0.701920\pi$
$594$	−6.02647e8	−0.117981
$595$	1.43772e9	0.279812
$596$	1.14318e9	0.221183
$597$	−1.17015e9	−0.225078
$598$	−7.43174e8	−0.142114
$599$	−4.49081e9	−0.853750	−0.426875	−	0.904311i	$-0.640386\pi$
$599$	−4.49081e9	−0.853750	−0.426875	+	0.904311i	$0.640386\pi$
$600$	−9.02017e8	−0.170485
$601$	−6.69638e8	−0.125829	−0.0629143	−	0.998019i	$-0.520039\pi$
$601$	−6.69638e8	−0.125829	−0.0629143	+	0.998019i	$0.520039\pi$
$602$	2.04171e9	0.381422
$603$	1.85283e9	0.344132
$604$	−2.41994e9	−0.446865
$605$	5.49148e8	0.100820
$606$	−2.23721e7	−0.00408369
$607$	8.39969e9	1.52441	0.762207	−	0.647333i	$-0.224116\pi$
$607$	8.39969e9	1.52441	0.762207	+	0.647333i	$0.224116\pi$
$608$	1.86212e9	0.336004
$609$	−1.46805e9	−0.263379
$610$	−1.20766e9	−0.215423
$611$	−1.09570e9	−0.194333
$612$	−1.72352e9	−0.303939
$613$	−3.69061e9	−0.647122	−0.323561	−	0.946207i	$-0.604880\pi$
$613$	−3.69061e9	−0.647122	−0.323561	+	0.946207i	$0.604880\pi$
$614$	−3.29954e9	−0.575259
$615$	−2.41079e9	−0.417923
$616$	6.72118e8	0.115855
$617$	−8.35635e9	−1.43225	−0.716125	−	0.697972i	$-0.754086\pi$
$617$	−8.35635e9	−1.43225	−0.716125	+	0.697972i	$0.754086\pi$
$618$	−3.55460e9	−0.605803
$619$	5.90457e9	1.00062	0.500312	−	0.865845i	$-0.333219\pi$
$619$	5.90457e9	1.00062	0.500312	+	0.865845i	$0.333219\pi$
$620$	−7.13825e8	−0.120288
$621$	−8.32265e8	−0.139457
$622$	5.98066e9	0.996513
$623$	−2.62747e9	−0.435340
$624$	−2.42971e8	−0.0400320
$625$	3.25172e9	0.532761
$626$	−1.82366e9	−0.297122
$627$	−5.87223e9	−0.951407
$628$	−7.34883e8	−0.118402
$629$	−1.30380e10	−2.08898
$630$	2.26978e8	0.0361653
$631$	1.02737e9	0.162789	0.0813944	−	0.996682i	$-0.474063\pi$
$631$	1.02737e9	0.162789	0.0813944	+	0.996682i	$0.474063\pi$
$632$	−2.83530e9	−0.446775
$633$	−6.11290e9	−0.957931
$634$	1.38322e9	0.215565
$635$	−4.48560e9	−0.695204
$636$	1.14875e9	0.177062
$637$	2.58475e8	0.0396214
$638$	4.85350e9	0.739916
$639$	−3.91825e9	−0.594072
$640$	2.37959e8	0.0358817
$641$	9.46369e9	1.41924	0.709622	−	0.704582i	$-0.248866\pi$
$641$	9.46369e9	1.41924	0.709622	+	0.704582i	$0.248866\pi$
$642$	−1.54250e9	−0.230066
$643$	−1.09823e10	−1.62913	−0.814563	−	0.580075i	$-0.803023\pi$
$643$	−1.09823e10	−1.62913	−0.814563	+	0.580075i	$0.803023\pi$
$644$	9.28206e8	0.136944
$645$	−2.27953e9	−0.334492
$646$	−1.67941e10	−2.45100
$647$	−3.36347e9	−0.488228	−0.244114	−	0.969747i	$-0.578497\pi$
$647$	−3.36347e9	−0.488228	−0.244114	+	0.969747i	$0.578497\pi$
$648$	−2.72098e8	−0.0392837
$649$	−5.33659e9	−0.766315
$650$	1.14684e9	0.163796
$651$	−9.10327e8	−0.129319
$652$	2.44786e9	0.345876
$653$	6.26787e8	0.0880895	0.0440447	−	0.999030i	$-0.485976\pi$
$653$	6.26787e8	0.0880895	0.0440447	+	0.999030i	$0.485976\pi$
$654$	1.25535e9	0.175486
$655$	2.75478e8	0.0383039
$656$	−3.22317e9	−0.445779
$657$	2.61912e9	0.360311
$658$	1.36850e9	0.187264
$659$	6.73142e9	0.916236	0.458118	−	0.888891i	$-0.348524\pi$
$659$	6.73142e9	0.916236	0.458118	+	0.888891i	$0.348524\pi$
$660$	−7.50409e8	−0.101600
$661$	8.92439e8	0.120191	0.0600957	−	0.998193i	$-0.480859\pi$
$661$	8.92439e8	0.120191	0.0600957	+	0.998193i	$0.480859\pi$
$662$	5.42774e9	0.727137
$663$	2.19131e9	0.292015
$664$	2.61816e9	0.347063
$665$	2.21169e9	0.291641
$666$	−2.05835e9	−0.269997
$667$	6.70276e9	0.874607
$668$	2.69583e9	0.349926
$669$	−4.76746e9	−0.615595
$670$	2.30712e9	0.296353
$671$	5.09173e9	0.650633
$672$	3.03464e8	0.0385758
$673$	7.99740e9	1.01134	0.505669	−	0.862728i	$-0.331246\pi$
$673$	7.99740e9	1.01134	0.505669	+	0.862728i	$0.331246\pi$
$674$	4.26781e9	0.536903
$675$	1.28432e9	0.160734
$676$	3.08916e8	0.0384615
$677$	6.29402e8	0.0779592	0.0389796	−	0.999240i	$-0.487589\pi$
$677$	6.29402e8	0.0779592	0.0389796	+	0.999240i	$0.487589\pi$
$678$	−4.09867e9	−0.505055
$679$	−5.37014e9	−0.658327
$680$	−2.14611e9	−0.261740
$681$	−1.37702e9	−0.167080
$682$	3.00961e9	0.363300
$683$	6.50089e9	0.780729	0.390364	−	0.920660i	$-0.372349\pi$
$683$	6.50089e9	0.780729	0.390364	+	0.920660i	$0.372349\pi$
$684$	−2.65134e9	−0.316788
$685$	−4.72896e9	−0.562145
$686$	−3.22829e8	−0.0381802
$687$	8.35272e9	0.982833
$688$	−3.04768e9	−0.356787
$689$	−1.46054e9	−0.170116
$690$	−1.03633e9	−0.120095
$691$	7.64042e9	0.880935	0.440468	−	0.897768i	$-0.354813\pi$
$691$	7.64042e9	0.880935	0.440468	+	0.897768i	$0.354813\pi$
$692$	−1.54778e9	−0.177557
$693$	−9.56981e8	−0.109229
$694$	−4.66969e9	−0.530310
$695$	6.76929e9	0.764885
$696$	2.19138e9	0.246368
$697$	2.90692e10	3.25175
$698$	8.05532e9	0.896580
$699$	−3.94384e9	−0.436766
$700$	−1.43237e9	−0.157838
$701$	7.48269e7	0.00820436	0.00410218	−	0.999992i	$-0.498694\pi$
$701$	7.48269e7	0.00820436	0.00410218	+	0.999992i	$0.498694\pi$
$702$	3.45948e8	0.0377426
$703$	−2.00567e10	−2.17729
$704$	−1.00328e9	−0.108372
$705$	−1.52791e9	−0.164224
$706$	1.29470e9	0.138469
$707$	−3.55261e7	−0.00378076
$708$	−2.40950e9	−0.255158
$709$	4.53424e9	0.477796	0.238898	−	0.971045i	$-0.423214\pi$
$709$	4.53424e9	0.477796	0.238898	+	0.971045i	$0.423214\pi$
$710$	−4.87896e9	−0.511591
$711$	4.03697e9	0.421223
$712$	3.92205e9	0.407224
$713$	4.15633e9	0.429434
$714$	−2.73689e9	−0.281393
$715$	9.54079e8	0.0976142
$716$	−2.26316e9	−0.230420
$717$	−2.59489e9	−0.262907
$718$	1.09056e10	1.09955
$719$	−1.88677e9	−0.189307	−0.0946536	−	0.995510i	$-0.530174\pi$
$719$	−1.88677e9	−0.189307	−0.0946536	+	0.995510i	$0.530174\pi$
$720$	−3.38813e8	−0.0338296
$721$	−5.64458e9	−0.560865
$722$	−1.86838e10	−1.84750
$723$	−1.05639e10	−1.03954
$724$	1.89787e9	0.185858
$725$	−1.03434e10	−1.00805
$726$	−1.04537e9	−0.101389
$727$	1.04020e10	1.00403	0.502014	−	0.864859i	$-0.332592\pi$
$727$	1.04020e10	1.00403	0.502014	+	0.864859i	$0.332592\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	3.26130e9	0.310285
$731$	2.74864e10	2.60260
$732$	2.29894e9	0.216640
$733$	−1.80922e10	−1.69679	−0.848394	−	0.529366i	$-0.822430\pi$
$733$	−1.80922e10	−1.69679	−0.848394	+	0.529366i	$0.822430\pi$
$734$	−7.38971e9	−0.689749
$735$	3.60433e8	0.0334826
$736$	−1.38554e9	−0.128100
$737$	−9.72725e9	−0.895064
$738$	4.58924e9	0.420285
$739$	2.67865e9	0.244152	0.122076	−	0.992521i	$-0.461045\pi$
$739$	2.67865e9	0.244152	0.122076	+	0.992521i	$0.461045\pi$
$740$	−2.56303e9	−0.232511
$741$	3.37094e9	0.304360
$742$	1.82418e9	0.163928
$743$	2.77097e8	0.0247840	0.0123920	−	0.999923i	$-0.496055\pi$
$743$	2.77097e8	0.0247840	0.0123920	+	0.999923i	$0.496055\pi$
$744$	1.35885e9	0.120967
$745$	−2.02678e9	−0.179581
$746$	6.27266e8	0.0553179
$747$	−3.72782e9	−0.327214
$748$	9.04838e9	0.790524
$749$	−2.44943e9	−0.213000
$750$	3.51399e9	0.304148
$751$	1.25214e10	1.07873	0.539367	−	0.842071i	$-0.318663\pi$
$751$	1.25214e10	1.07873	0.539367	+	0.842071i	$0.318663\pi$
$752$	−2.04278e9	−0.175169
$753$	−5.33679e9	−0.455510
$754$	−2.78614e9	−0.236703
$755$	4.29040e9	0.362814
$756$	−4.32081e8	−0.0363696
$757$	−9.37050e9	−0.785104	−0.392552	−	0.919730i	$-0.628408\pi$
$757$	−9.37050e9	−0.785104	−0.392552	+	0.919730i	$0.628408\pi$
$758$	−1.23338e9	−0.102862
$759$	4.36934e9	0.362718
$760$	−3.30141e9	−0.272805
$761$	−1.28866e10	−1.05997	−0.529984	−	0.848008i	$-0.677802\pi$
$761$	−1.28866e10	−1.05997	−0.529984	+	0.848008i	$0.677802\pi$
$762$	8.53889e9	0.699132
$763$	1.99345e9	0.162469
$764$	−9.43342e9	−0.765319
$765$	3.05569e9	0.246771
$766$	−4.07378e9	−0.327489
$767$	3.06346e9	0.245148
$768$	−4.52985e8	−0.0360844
$769$	2.35638e9	0.186855	0.0934273	−	0.995626i	$-0.470218\pi$
$769$	2.35638e9	0.186855	0.0934273	+	0.995626i	$0.470218\pi$
$770$	−1.19162e9	−0.0940634
$771$	3.53568e9	0.277832
$772$	−5.79055e9	−0.452960
$773$	−1.60854e10	−1.25258	−0.626288	−	0.779592i	$-0.715426\pi$
$773$	−1.60854e10	−1.25258	−0.626288	+	0.779592i	$0.715426\pi$
$774$	4.33937e9	0.336382
$775$	−6.41387e9	−0.494953
$776$	8.01607e9	0.615808
$777$	−3.26859e9	−0.249969
$778$	−1.95289e8	−0.0148679
$779$	4.47178e10	3.38922
$780$	4.30771e8	0.0325024
$781$	2.05705e10	1.54514
$782$	1.24960e10	0.934428
$783$	−3.12014e9	−0.232278
$784$	4.81890e8	0.0357143
$785$	1.30290e9	0.0961318
$786$	−5.24407e8	−0.0385203
$787$	−1.42841e10	−1.04458	−0.522288	−	0.852769i	$-0.674921\pi$
$787$	−1.42841e10	−1.04458	−0.522288	+	0.852769i	$0.674921\pi$
$788$	−3.78673e9	−0.275691
$789$	9.23732e9	0.669540
$790$	5.02679e9	0.362740
$791$	−6.50853e9	−0.467590
$792$	1.42850e9	0.102174
$793$	−2.92290e9	−0.208141
$794$	−4.07583e9	−0.288964
$795$	−2.03666e9	−0.143759
$796$	2.77370e9	0.194923
$797$	4.63692e9	0.324433	0.162217	−	0.986755i	$-0.448136\pi$
$797$	4.63692e9	0.324433	0.162217	+	0.986755i	$0.448136\pi$
$798$	−4.21022e9	−0.293289
$799$	1.84234e10	1.27778
$800$	2.13811e9	0.147644
$801$	−5.58432e9	−0.383934
$802$	−7.20859e9	−0.493447
$803$	−1.37502e10	−0.937143
$804$	−4.39190e9	−0.298027
$805$	−1.64565e9	−0.111186
$806$	−1.72766e9	−0.116222
$807$	−3.26083e9	−0.218409
$808$	5.30301e7	0.00353658
$809$	−1.37884e10	−0.915577	−0.457789	−	0.889061i	$-0.651358\pi$
$809$	−1.37884e10	−0.915577	−0.457789	+	0.889061i	$0.651358\pi$
$810$	4.82411e8	0.0318948
$811$	2.64001e10	1.73793	0.868967	−	0.494871i	$-0.164785\pi$
$811$	2.64001e10	1.73793	0.868967	+	0.494871i	$0.164785\pi$
$812$	3.47983e9	0.228093
$813$	−1.42873e10	−0.932470
$814$	1.08062e10	0.702244
$815$	−4.33990e9	−0.280820
$816$	4.08538e9	0.263219
$817$	4.22831e10	2.71262
$818$	−1.30991e10	−0.836766
$819$	5.49353e8	0.0349428
$820$	5.71447e9	0.361932
$821$	−2.32509e10	−1.46635	−0.733177	−	0.680037i	$-0.761964\pi$
$821$	−2.32509e10	−1.46635	−0.733177	+	0.680037i	$0.761964\pi$
$822$	9.00215e9	0.565321
$823$	1.26784e10	0.792800	0.396400	−	0.918078i	$-0.370259\pi$
$823$	1.26784e10	0.792800	0.396400	+	0.918078i	$0.370259\pi$
$824$	8.42573e9	0.524641
$825$	−6.74258e9	−0.418059
$826$	−3.82619e9	−0.236231
$827$	1.11464e10	0.685279	0.342639	−	0.939467i	$-0.388679\pi$
$827$	1.11464e10	0.685279	0.342639	+	0.939467i	$0.388679\pi$
$828$	1.97278e9	0.120773
$829$	1.52385e9	0.0928968	0.0464484	−	0.998921i	$-0.485210\pi$
$829$	1.52385e9	0.0928968	0.0464484	+	0.998921i	$0.485210\pi$
$830$	−4.64183e9	−0.281784
$831$	−9.15785e9	−0.553592
$832$	5.75930e8	0.0346688
$833$	−4.34608e9	−0.260519
$834$	−1.28862e10	−0.769207
$835$	−4.77954e9	−0.284108
$836$	1.39193e10	0.823943
$837$	−1.93478e9	−0.114049
$838$	−1.08238e9	−0.0635369
$839$	1.97275e10	1.15320	0.576602	−	0.817025i	$-0.304378\pi$
$839$	1.97275e10	1.15320	0.576602	+	0.817025i	$0.304378\pi$
$840$	−5.38022e8	−0.0313201
$841$	7.87863e9	0.456736
$842$	1.54132e10	0.889818
$843$	−1.71039e10	−0.983328
$844$	1.44898e10	0.829592
$845$	−5.47687e8	−0.0312273
$846$	2.90856e9	0.165151
$847$	−1.66001e9	−0.0938683
$848$	−2.72297e9	−0.153341
$849$	−1.61144e10	−0.903726
$850$	−1.92832e10	−1.07700
$851$	1.49235e10	0.830078
$852$	9.28770e9	0.514481
$853$	1.83654e9	0.101316	0.0506582	−	0.998716i	$-0.483868\pi$
$853$	1.83654e9	0.101316	0.0506582	+	0.998716i	$0.483868\pi$
$854$	3.65063e9	0.200570
$855$	4.70065e9	0.257203
$856$	3.65629e9	0.199243
$857$	1.24123e10	0.673627	0.336813	−	0.941571i	$-0.390651\pi$
$857$	1.24123e10	0.673627	0.336813	+	0.941571i	$0.390651\pi$
$858$	−1.81621e9	−0.0981657
$859$	5.30403e9	0.285516	0.142758	−	0.989758i	$-0.454403\pi$
$859$	5.30403e9	0.285516	0.142758	+	0.989758i	$0.454403\pi$
$860$	5.40333e9	0.289679
$861$	7.28754e9	0.389108
$862$	−2.28137e10	−1.21316
$863$	2.55569e10	1.35354	0.676770	−	0.736195i	$-0.263379\pi$
$863$	2.55569e10	1.35354	0.676770	+	0.736195i	$0.263379\pi$
$864$	6.44973e8	0.0340207
$865$	2.74411e9	0.144160
$866$	−1.37482e9	−0.0719340
$867$	−2.57661e10	−1.34271
$868$	2.15781e9	0.111994
$869$	−2.11939e10	−1.09557
$870$	−3.88517e9	−0.200029
$871$	5.58391e9	0.286335
$872$	−2.97565e9	−0.151975
$873$	−1.14135e10	−0.580589
$874$	1.92228e10	0.973930
$875$	5.58008e9	0.281587
$876$	−6.20829e9	−0.312038
$877$	2.75111e10	1.37724	0.688621	−	0.725122i	$-0.258217\pi$
$877$	2.75111e10	1.37724	0.688621	+	0.725122i	$0.258217\pi$
$878$	−7.35570e9	−0.366770
$879$	−4.59064e9	−0.227988
$880$	1.77875e9	0.0879883
$881$	−2.66910e10	−1.31507	−0.657536	−	0.753424i	$-0.728401\pi$
$881$	−2.66910e10	−1.31507	−0.657536	+	0.753424i	$0.728401\pi$
$882$	−6.86129e8	−0.0336718
$883$	7.52996e9	0.368070	0.184035	−	0.982920i	$-0.441084\pi$
$883$	7.52996e9	0.368070	0.184035	+	0.982920i	$0.441084\pi$
$884$	−5.19421e9	−0.252893
$885$	4.27188e9	0.207165
$886$	2.07909e10	1.00428
$887$	2.61087e9	0.125618	0.0628092	−	0.998026i	$-0.479994\pi$
$887$	2.61087e9	0.125618	0.0628092	+	0.998026i	$0.479994\pi$
$888$	4.87905e9	0.233825
$889$	1.35594e10	0.647270
$890$	−6.95353e9	−0.330629
$891$	−2.03393e9	−0.0963307
$892$	1.13006e10	0.533121
$893$	2.83412e10	1.33180
$894$	3.85823e9	0.180595
$895$	4.01244e9	0.187080
$896$	−7.19323e8	−0.0334077
$897$	−2.50821e9	−0.116035
$898$	−4.64563e9	−0.214081
$899$	1.55820e10	0.715260
$900$	−3.04431e9	−0.139200
$901$	2.45579e10	1.11855
$902$	−2.40932e10	−1.09313
$903$	6.89076e9	0.311429
$904$	9.71536e9	0.437391
$905$	−3.36479e9	−0.150900
$906$	−8.16731e9	−0.364863
$907$	−9.59738e9	−0.427098	−0.213549	−	0.976932i	$-0.568502\pi$
$907$	−9.59738e9	−0.427098	−0.213549	+	0.976932i	$0.568502\pi$
$908$	3.26404e9	0.144695
$909$	−7.55058e7	−0.00333432
$910$	6.84048e8	0.0300914
$911$	2.70205e10	1.18408	0.592038	−	0.805910i	$-0.298324\pi$
$911$	2.70205e10	1.18408	0.592038	+	0.805910i	$0.298324\pi$
$912$	6.28465e9	0.274346
$913$	1.95708e10	0.851061
$914$	2.14375e10	0.928674
$915$	−4.07586e9	−0.175892
$916$	−1.97991e10	−0.851158
$917$	−8.32739e8	−0.0356629
$918$	−5.81688e9	−0.248165
$919$	5.19047e9	0.220599	0.110299	−	0.993898i	$-0.464819\pi$
$919$	5.19047e9	0.220599	0.110299	+	0.993898i	$0.464819\pi$
$920$	2.45648e9	0.104005
$921$	−1.11359e10	−0.469697
$922$	−2.38398e10	−1.00171
$923$	−1.18085e10	−0.494297
$924$	2.26840e9	0.0945949
$925$	−2.30294e10	−0.956724
$926$	−2.02925e10	−0.839840
$927$	−1.19968e10	−0.494636
$928$	−5.19437e9	−0.213361
$929$	3.23414e10	1.32344	0.661719	−	0.749752i	$-0.269827\pi$
$929$	3.23414e10	1.32344	0.661719	+	0.749752i	$0.269827\pi$
$930$	−2.40916e9	−0.0982144
$931$	−6.68568e9	−0.271532
$932$	9.34835e9	0.378250
$933$	2.01847e10	0.813649
$934$	1.49788e10	0.601538
$935$	−1.60422e10	−0.641834
$936$	−8.20026e8	−0.0326860
$937$	−7.25331e9	−0.288037	−0.144018	−	0.989575i	$-0.546002\pi$
$937$	−7.25331e9	−0.288037	−0.144018	+	0.989575i	$0.546002\pi$
$938$	−6.97417e9	−0.275920
$939$	−6.15486e9	−0.242599
$940$	3.62171e9	0.142222
$941$	−2.51889e10	−0.985473	−0.492737	−	0.870179i	$-0.664003\pi$
$941$	−2.51889e10	−0.985473	−0.492737	+	0.870179i	$0.664003\pi$
$942$	−2.48023e9	−0.0966749
$943$	−3.32731e10	−1.29212
$944$	5.71140e9	0.220974
$945$	7.66052e8	0.0295289
$946$	−2.27814e10	−0.874906
$947$	−2.22847e10	−0.852671	−0.426335	−	0.904565i	$-0.640196\pi$
$947$	−2.22847e10	−0.852671	−0.426335	+	0.904565i	$0.640196\pi$
$948$	−9.56912e9	−0.364790
$949$	7.89330e9	0.299797
$950$	−2.96639e10	−1.12252
$951$	4.66837e9	0.176008
$952$	6.48744e9	0.243693
$953$	−2.43375e10	−0.910857	−0.455429	−	0.890272i	$-0.650514\pi$
$953$	−2.43375e10	−0.910857	−0.455429	+	0.890272i	$0.650514\pi$
$954$	3.87704e9	0.144571
$955$	1.67248e10	0.621370
$956$	6.15086e9	0.227684
$957$	1.63806e10	0.604139
$958$	2.20017e10	0.808494
$959$	1.42951e10	0.523385
$960$	8.03112e8	0.0292973
$961$	−1.78504e10	−0.648806
$962$	−6.20329e9	−0.224651
$963$	−5.20593e9	−0.187848
$964$	2.50405e10	0.900270
$965$	1.02663e10	0.367762
$966$	3.13269e9	0.111814
$967$	−3.42527e10	−1.21815	−0.609076	−	0.793112i	$-0.708460\pi$
$967$	−3.42527e10	−1.21815	−0.609076	+	0.793112i	$0.708460\pi$
$968$	2.47792e9	0.0878058
$969$	−5.66801e10	−2.00123
$970$	−1.42120e10	−0.499980
$971$	1.06157e10	0.372117	0.186059	−	0.982539i	$-0.440429\pi$
$971$	1.06157e10	0.372117	0.186059	+	0.982539i	$0.440429\pi$
$972$	−9.18330e8	−0.0320750
$973$	−2.04628e10	−0.712147
$974$	−2.84055e10	−0.985023
$975$	3.87057e9	0.133739
$976$	−5.44933e9	−0.187616
$977$	3.29891e10	1.13172	0.565860	−	0.824501i	$-0.308544\pi$
$977$	3.29891e10	1.13172	0.565860	+	0.824501i	$0.308544\pi$
$978$	8.26154e9	0.282407
$979$	2.93173e10	0.998585
$980$	−8.54360e8	−0.0289968
$981$	4.23681e9	0.143284
$982$	1.17176e10	0.394866
$983$	1.51536e10	0.508837	0.254418	−	0.967094i	$-0.418116\pi$
$983$	1.51536e10	0.508837	0.254418	+	0.967094i	$0.418116\pi$
$984$	−1.08782e10	−0.363977
$985$	6.71362e9	0.223836
$986$	4.68471e10	1.55637
$987$	4.61869e9	0.152900
$988$	−7.99038e9	−0.263583
$989$	−3.14615e10	−1.03417
$990$	−2.53263e9	−0.0829561
$991$	−8.21417e9	−0.268106	−0.134053	−	0.990974i	$-0.542799\pi$
$991$	−8.21417e9	−0.268106	−0.134053	+	0.990974i	$0.542799\pi$
$992$	−3.22099e9	−0.104761
$993$	1.83186e10	0.593705
$994$	1.47485e10	0.476317
$995$	−4.91758e9	−0.158260
$996$	8.83630e9	0.283376
$997$	9.33193e9	0.298221	0.149111	−	0.988821i	$-0.452359\pi$
$997$	9.33193e9	0.298221	0.149111	+	0.988821i	$0.452359\pi$
$998$	1.31469e10	0.418664
$999$	−6.94693e9	−0.220452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.n.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.n.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -113.468 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -113.468 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +907.742 q^{10} -3827.20 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} +3063.63 q^{15} +4096.00 q^{16} -36941.0 q^{17} -5832.00 q^{18} -56827.3 q^{19} -7261.94 q^{20} -9261.00 q^{21} +30617.6 q^{22} +42283.4 q^{23} +13824.0 q^{24} -65250.1 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} +158520. q^{29} -24509.0 q^{30} +98296.8 q^{31} -32768.0 q^{32} +103335. q^{33} +295528. q^{34} -38919.5 q^{35} +46656.0 q^{36} +352941. q^{37} +454619. q^{38} -59319.0 q^{39} +58095.5 q^{40} -786907. q^{41} +74088.0 q^{42} -744062. q^{43} -244941. q^{44} -82718.0 q^{45} -338267. q^{46} -498725. q^{47} -110592. q^{48} +117649. q^{49} +522000. q^{50} +997408. q^{51} +140608. q^{52} -664787. q^{53} +157464. q^{54} +434264. q^{55} -175616. q^{56} +1.53434e6 q^{57} -1.26816e6 q^{58} +1.39438e6 q^{59} +196072. q^{60} -1.33040e6 q^{61} -786374. q^{62} +250047. q^{63} +262144. q^{64} -249289. q^{65} -826676. q^{66} +2.54161e6 q^{67} -2.36423e6 q^{68} -1.14165e6 q^{69} +311356. q^{70} -5.37482e6 q^{71} -373248. q^{72} +3.59276e6 q^{73} -2.82353e6 q^{74} +1.76175e6 q^{75} -3.63695e6 q^{76} -1.31273e6 q^{77} +474552. q^{78} +5.53769e6 q^{79} -464764. q^{80} +531441. q^{81} +6.29525e6 q^{82} -5.11360e6 q^{83} -592704. q^{84} +4.19162e6 q^{85} +5.95249e6 q^{86} -4.28003e6 q^{87} +1.95953e6 q^{88} -7.66025e6 q^{89} +661744. q^{90} +753571. q^{91} +2.70614e6 q^{92} -2.65401e6 q^{93} +3.98980e6 q^{94} +6.44807e6 q^{95} +884736. q^{96} -1.56564e7 q^{97} -941192. q^{98} -2.79003e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 181 q^{5} + 1296 q^{6} + 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 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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