LMFDB - Embedded newform 546.8.a.q.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} - 367021x^{4} - 17702143x^{3} + 34815194576x^{2} + 1422988371620x - 933871993059968 $ x^6 - x^5 - 367021x^4 - 17702143x^3 + 34815194576x^2 + 1422988371620x - 933871993059968
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$180.926$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +182.926 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +182.926 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +1463.41 q^{10} +3961.32 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -4939.00 q^{15} +4096.00 q^{16} -35665.6 q^{17} +5832.00 q^{18} +46854.3 q^{19} +11707.3 q^{20} -9261.00 q^{21} +31690.5 q^{22} +49170.5 q^{23} -13824.0 q^{24} -44663.0 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} +120077. q^{29} -39512.0 q^{30} +176117. q^{31} +32768.0 q^{32} -106956. q^{33} -285325. q^{34} +62743.7 q^{35} +46656.0 q^{36} +71904.5 q^{37} +374834. q^{38} +59319.0 q^{39} +93658.2 q^{40} -72808.6 q^{41} -74088.0 q^{42} +881838. q^{43} +253524. q^{44} +133353. q^{45} +393364. q^{46} -630654. q^{47} -110592. q^{48} +117649. q^{49} -357304. q^{50} +962971. q^{51} -140608. q^{52} -786307. q^{53} -157464. q^{54} +724628. q^{55} +175616. q^{56} -1.26507e6 q^{57} +960618. q^{58} -384980. q^{59} -316096. q^{60} -1.71564e6 q^{61} +1.40894e6 q^{62} +250047. q^{63} +262144. q^{64} -401889. q^{65} -855645. q^{66} -592009. q^{67} -2.28260e6 q^{68} -1.32760e6 q^{69} +501949. q^{70} -933329. q^{71} +373248. q^{72} -1.70766e6 q^{73} +575236. q^{74} +1.20590e6 q^{75} +2.99867e6 q^{76} +1.35873e6 q^{77} +474552. q^{78} +3.67639e6 q^{79} +749265. q^{80} +531441. q^{81} -582469. q^{82} -1.90923e6 q^{83} -592704. q^{84} -6.52417e6 q^{85} +7.05471e6 q^{86} -3.24209e6 q^{87} +2.02819e6 q^{88} +8.98136e6 q^{89} +1.06683e6 q^{90} -753571. q^{91} +3.14691e6 q^{92} -4.75516e6 q^{93} -5.04523e6 q^{94} +8.57087e6 q^{95} -884736. q^{96} -7.16753e6 q^{97} +941192. q^{98} +2.88780e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 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 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 104 q^{10} + 10054 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} - 351 q^{15} + 24576 q^{16} + 21222 q^{17} + 34992 q^{18} + 9527 q^{19} + 832 q^{20} - 55566 q^{21} + 80432 q^{22} + 33229 q^{23} - 82944 q^{24} + 265321 q^{25} - 105456 q^{26} - 118098 q^{27} + 131712 q^{28} + 174185 q^{29} - 2808 q^{30} + 119045 q^{31} + 196608 q^{32} - 271458 q^{33} + 169776 q^{34} + 4459 q^{35} + 279936 q^{36} + 56562 q^{37} + 76216 q^{38} + 355914 q^{39} + 6656 q^{40} + 101632 q^{41} - 444528 q^{42} + 441323 q^{43} + 643456 q^{44} + 9477 q^{45} + 265832 q^{46} - 892849 q^{47} - 663552 q^{48} + 705894 q^{49} + 2122568 q^{50} - 572994 q^{51} - 843648 q^{52} + 2093965 q^{53} - 944784 q^{54} - 331222 q^{55} + 1053696 q^{56} - 257229 q^{57} + 1393480 q^{58} - 136204 q^{59} - 22464 q^{60} - 3989946 q^{61} + 952360 q^{62} + 1500282 q^{63} + 1572864 q^{64} - 28561 q^{65} - 2171664 q^{66} - 2218250 q^{67} + 1358208 q^{68} - 897183 q^{69} + 35672 q^{70} + 2045928 q^{71} + 2239488 q^{72} - 8557479 q^{73} + 452496 q^{74} - 7163667 q^{75} + 609728 q^{76} + 3448522 q^{77} + 2847312 q^{78} - 8559709 q^{79} + 53248 q^{80} + 3188646 q^{81} + 813056 q^{82} + 2496351 q^{83} - 3556224 q^{84} + 5335304 q^{85} + 3530584 q^{86} - 4702995 q^{87} + 5147648 q^{88} - 2446683 q^{89} + 75816 q^{90} - 4521426 q^{91} + 2126656 q^{92} - 3214215 q^{93} - 7142792 q^{94} + 16410211 q^{95} - 5308416 q^{96} + 5786889 q^{97} + 5647152 q^{98} + 7329366 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 104 * q^10 + 10054 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 - 351 * q^15 + 24576 * q^16 + 21222 * q^17 + 34992 * q^18 + 9527 * q^19 + 832 * q^20 - 55566 * q^21 + 80432 * q^22 + 33229 * q^23 - 82944 * q^24 + 265321 * q^25 - 105456 * q^26 - 118098 * q^27 + 131712 * q^28 + 174185 * q^29 - 2808 * q^30 + 119045 * q^31 + 196608 * q^32 - 271458 * q^33 + 169776 * q^34 + 4459 * q^35 + 279936 * q^36 + 56562 * q^37 + 76216 * q^38 + 355914 * q^39 + 6656 * q^40 + 101632 * q^41 - 444528 * q^42 + 441323 * q^43 + 643456 * q^44 + 9477 * q^45 + 265832 * q^46 - 892849 * q^47 - 663552 * q^48 + 705894 * q^49 + 2122568 * q^50 - 572994 * q^51 - 843648 * q^52 + 2093965 * q^53 - 944784 * q^54 - 331222 * q^55 + 1053696 * q^56 - 257229 * q^57 + 1393480 * q^58 - 136204 * q^59 - 22464 * q^60 - 3989946 * q^61 + 952360 * q^62 + 1500282 * q^63 + 1572864 * q^64 - 28561 * q^65 - 2171664 * q^66 - 2218250 * q^67 + 1358208 * q^68 - 897183 * q^69 + 35672 * q^70 + 2045928 * q^71 + 2239488 * q^72 - 8557479 * q^73 + 452496 * q^74 - 7163667 * q^75 + 609728 * q^76 + 3448522 * q^77 + 2847312 * q^78 - 8559709 * q^79 + 53248 * q^80 + 3188646 * q^81 + 813056 * q^82 + 2496351 * q^83 - 3556224 * q^84 + 5335304 * q^85 + 3530584 * q^86 - 4702995 * q^87 + 5147648 * q^88 - 2446683 * q^89 + 75816 * q^90 - 4521426 * q^91 + 2126656 * q^92 - 3214215 * q^93 - 7142792 * q^94 + 16410211 * q^95 - 5308416 * q^96 + 5786889 * q^97 + 5647152 * q^98 + 7329366 * 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
$5$	182.926	0.654456	0.327228	−	0.944945i	$-0.393885\pi$
$5$	182.926	0.654456	0.327228	+	0.944945i	$0.393885\pi$
$6$	−216.000	−0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	1463.41	0.462771
$11$	3961.32	0.897357	0.448679	−	0.893693i	$-0.351895\pi$
$11$	3961.32	0.897357	0.448679	+	0.893693i	$0.351895\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	2744.00	0.267261
$15$	−4939.00	−0.377851
$16$	4096.00	0.250000
$17$	−35665.6	−1.76067	−0.880336	−	0.474351i	$-0.842683\pi$
$17$	−35665.6	−1.76067	−0.880336	+	0.474351i	$0.842683\pi$
$18$	5832.00	0.235702
$19$	46854.3	1.56715	0.783577	−	0.621295i	$-0.213393\pi$
$19$	46854.3	1.56715	0.783577	+	0.621295i	$0.213393\pi$
$20$	11707.3	0.327228
$21$	−9261.00	−0.218218
$22$	31690.5	0.634527
$23$	49170.5	0.842670	0.421335	−	0.906905i	$-0.361562\pi$
$23$	49170.5	0.842670	0.421335	+	0.906905i	$0.361562\pi$
$24$	−13824.0	−0.204124
$25$	−44663.0	−0.571687
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	21952.0	0.188982
$29$	120077.	0.914256	0.457128	−	0.889401i	$-0.348878\pi$
$29$	120077.	0.914256	0.457128	+	0.889401i	$0.348878\pi$
$30$	−39512.0	−0.267181
$31$	176117.	1.06178	0.530891	−	0.847440i	$-0.321857\pi$
$31$	176117.	1.06178	0.530891	+	0.847440i	$0.321857\pi$
$32$	32768.0	0.176777
$33$	−106956.	−0.518089
$34$	−285325.	−1.24498
$35$	62743.7	0.247361
$36$	46656.0	0.166667
$37$	71904.5	0.233373	0.116686	−	0.993169i	$-0.462773\pi$
$37$	71904.5	0.233373	0.116686	+	0.993169i	$0.462773\pi$
$38$	374834.	1.10814
$39$	59319.0	0.160128
$40$	93658.2	0.231385
$41$	−72808.6	−0.164983	−0.0824915	−	0.996592i	$-0.526288\pi$
$41$	−72808.6	−0.164983	−0.0824915	+	0.996592i	$0.526288\pi$
$42$	−74088.0	−0.154303
$43$	881838.	1.69141	0.845706	−	0.533649i	$-0.179180\pi$
$43$	881838.	1.69141	0.845706	+	0.533649i	$0.179180\pi$
$44$	253524.	0.448679
$45$	133353.	0.218152
$46$	393364.	0.595858
$47$	−630654.	−0.886031	−0.443015	−	0.896514i	$-0.646091\pi$
$47$	−630654.	−0.886031	−0.443015	+	0.896514i	$0.646091\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	−357304.	−0.404244
$51$	962971.	1.01652
$52$	−140608.	−0.138675
$53$	−786307.	−0.725482	−0.362741	−	0.931890i	$-0.618159\pi$
$53$	−786307.	−0.725482	−0.362741	+	0.931890i	$0.618159\pi$
$54$	−157464.	−0.136083
$55$	724628.	0.587281
$56$	175616.	0.133631
$57$	−1.26507e6	−0.904796
$58$	960618.	0.646476
$59$	−384980.	−0.244037	−0.122019	−	0.992528i	$-0.538937\pi$
$59$	−384980.	−0.244037	−0.122019	+	0.992528i	$0.538937\pi$
$60$	−316096.	−0.188925
$61$	−1.71564e6	−0.967771	−0.483885	−	0.875131i	$-0.660775\pi$
$61$	−1.71564e6	−0.967771	−0.483885	+	0.875131i	$0.660775\pi$
$62$	1.40894e6	0.750794
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	−401889.	−0.181514
$66$	−855645.	−0.366344
$67$	−592009.	−0.240473	−0.120237	−	0.992745i	$-0.538365\pi$
$67$	−592009.	−0.240473	−0.120237	+	0.992745i	$0.538365\pi$
$68$	−2.28260e6	−0.880336
$69$	−1.32760e6	−0.486516
$70$	501949.	0.174911
$71$	−933329.	−0.309479	−0.154739	−	0.987955i	$-0.549454\pi$
$71$	−933329.	−0.309479	−0.154739	+	0.987955i	$0.549454\pi$
$72$	373248.	0.117851
$73$	−1.70766e6	−0.513775	−0.256887	−	0.966441i	$-0.582697\pi$
$73$	−1.70766e6	−0.513775	−0.256887	+	0.966441i	$0.582697\pi$
$74$	575236.	0.165019
$75$	1.20590e6	0.330064
$76$	2.99867e6	0.783577
$77$	1.35873e6	0.339169
$78$	474552.	0.113228
$79$	3.67639e6	0.838932	0.419466	−	0.907771i	$-0.362217\pi$
$79$	3.67639e6	0.838932	0.419466	+	0.907771i	$0.362217\pi$
$80$	749265.	0.163614
$81$	531441.	0.111111
$82$	−582469.	−0.116661
$83$	−1.90923e6	−0.366510	−0.183255	−	0.983065i	$-0.558663\pi$
$83$	−1.90923e6	−0.366510	−0.183255	+	0.983065i	$0.558663\pi$
$84$	−592704.	−0.109109
$85$	−6.52417e6	−1.15228
$86$	7.05471e6	1.19601
$87$	−3.24209e6	−0.527846
$88$	2.02819e6	0.317264
$89$	8.98136e6	1.35045	0.675223	−	0.737614i	$-0.264048\pi$
$89$	8.98136e6	1.35045	0.675223	+	0.737614i	$0.264048\pi$
$90$	1.06683e6	0.154257
$91$	−753571.	−0.104828
$92$	3.14691e6	0.421335
$93$	−4.75516e6	−0.613021
$94$	−5.04523e6	−0.626518
$95$	8.57087e6	1.02563
$96$	−884736.	−0.102062
$97$	−7.16753e6	−0.797386	−0.398693	−	0.917084i	$-0.630536\pi$
$97$	−7.16753e6	−0.797386	−0.398693	+	0.917084i	$0.630536\pi$
$98$	941192.	0.101015
$99$	2.88780e6	0.299119
$100$	−2.85843e6	−0.285843
$101$	5.83931e6	0.563945	0.281973	−	0.959422i	$-0.409011\pi$
$101$	5.83931e6	0.563945	0.281973	+	0.959422i	$0.409011\pi$
$102$	7.70377e6	0.718791
$103$	1.84954e7	1.66776	0.833878	−	0.551949i	$-0.186116\pi$
$103$	1.84954e7	1.66776	0.833878	+	0.551949i	$0.186116\pi$
$104$	−1.12486e6	−0.0980581
$105$	−1.69408e6	−0.142814
$106$	−6.29046e6	−0.512993
$107$	1.19931e7	0.946429	0.473215	−	0.880947i	$-0.343094\pi$
$107$	1.19931e7	0.946429	0.473215	+	0.880947i	$0.343094\pi$
$108$	−1.25971e6	−0.0962250
$109$	−830639.	−0.0614355	−0.0307178	−	0.999528i	$-0.509779\pi$
$109$	−830639.	−0.0614355	−0.0307178	+	0.999528i	$0.509779\pi$
$110$	5.79703e6	0.415270
$111$	−1.94142e6	−0.134738
$112$	1.40493e6	0.0944911
$113$	1.07261e6	0.0699303	0.0349652	−	0.999389i	$-0.488868\pi$
$113$	1.07261e6	0.0699303	0.0349652	+	0.999389i	$0.488868\pi$
$114$	−1.01205e7	−0.639788
$115$	8.99457e6	0.551491
$116$	7.68494e6	0.457128
$117$	−1.60161e6	−0.0924500
$118$	−3.07984e6	−0.172561
$119$	−1.22333e7	−0.665471
$120$	−2.52877e6	−0.133590
$121$	−3.79513e6	−0.194750
$122$	−1.37251e7	−0.684317
$123$	1.96583e6	0.0952529
$124$	1.12715e7	0.530891
$125$	−2.24611e7	−1.02860
$126$	2.00038e6	0.0890871
$127$	−1.12134e7	−0.485762	−0.242881	−	0.970056i	$-0.578092\pi$
$127$	−1.12134e7	−0.485762	−0.242881	+	0.970056i	$0.578092\pi$
$128$	2.09715e6	0.0883883
$129$	−2.38096e7	−0.976537
$130$	−3.21511e6	−0.128349
$131$	1.37935e7	0.536073	0.268037	−	0.963409i	$-0.413625\pi$
$131$	1.37935e7	0.536073	0.268037	+	0.963409i	$0.413625\pi$
$132$	−6.84516e6	−0.259045
$133$	1.60710e7	0.592328
$134$	−4.73607e6	−0.170040
$135$	−3.60053e6	−0.125950
$136$	−1.82608e7	−0.622491
$137$	−8.84906e6	−0.294019	−0.147009	−	0.989135i	$-0.546965\pi$
$137$	−8.84906e6	−0.294019	−0.147009	+	0.989135i	$0.546965\pi$
$138$	−1.06208e7	−0.344019
$139$	3.94389e7	1.24558	0.622792	−	0.782387i	$-0.285998\pi$
$139$	3.94389e7	1.24558	0.622792	+	0.782387i	$0.285998\pi$
$140$	4.01559e6	0.123681
$141$	1.70277e7	0.511550
$142$	−7.46664e6	−0.218834
$143$	−8.70301e6	−0.248882
$144$	2.98598e6	0.0833333
$145$	2.19653e7	0.598340
$146$	−1.36613e7	−0.363294
$147$	−3.17652e6	−0.0824786
$148$	4.60189e6	0.116686
$149$	3.04585e7	0.754322	0.377161	−	0.926148i	$-0.376900\pi$
$149$	3.04585e7	0.754322	0.377161	+	0.926148i	$0.376900\pi$
$150$	9.64722e6	0.233390
$151$	6.68784e7	1.58076	0.790381	−	0.612615i	$-0.209882\pi$
$151$	6.68784e7	1.58076	0.790381	+	0.612615i	$0.209882\pi$
$152$	2.39894e7	0.554072
$153$	−2.60002e7	−0.586891
$154$	1.08699e7	0.239829
$155$	3.22164e7	0.694890
$156$	3.79642e6	0.0800641
$157$	−9.11088e7	−1.87893	−0.939467	−	0.342640i	$-0.888679\pi$
$157$	−9.11088e7	−1.87893	−0.939467	+	0.342640i	$0.888679\pi$
$158$	2.94111e7	0.593215
$159$	2.12303e7	0.418857
$160$	5.99412e6	0.115693
$161$	1.68655e7	0.318499
$162$	4.25153e6	0.0785674
$163$	6.97149e7	1.26087	0.630433	−	0.776244i	$-0.282877\pi$
$163$	6.97149e7	1.26087	0.630433	+	0.776244i	$0.282877\pi$
$164$	−4.65975e6	−0.0824915
$165$	−1.95650e7	−0.339067
$166$	−1.52739e7	−0.259162
$167$	8.71160e7	1.44741	0.723703	−	0.690112i	$-0.242439\pi$
$167$	8.71160e7	1.44741	0.723703	+	0.690112i	$0.242439\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	−5.21934e7	−0.814787
$171$	3.41568e7	0.522384
$172$	5.64376e7	0.845706
$173$	−3.43576e7	−0.504500	−0.252250	−	0.967662i	$-0.581170\pi$
$173$	−3.43576e7	−0.504500	−0.252250	+	0.967662i	$0.581170\pi$
$174$	−2.59367e7	−0.373243
$175$	−1.53194e7	−0.216077
$176$	1.62256e7	0.224339
$177$	1.03945e7	0.140895
$178$	7.18509e7	0.954909
$179$	−1.26368e8	−1.64684	−0.823420	−	0.567432i	$-0.807937\pi$
$179$	−1.26368e8	−1.64684	−0.823420	+	0.567432i	$0.807937\pi$
$180$	8.53460e6	0.109076
$181$	1.22054e8	1.52995	0.764974	−	0.644061i	$-0.222752\pi$
$181$	1.22054e8	1.52995	0.764974	+	0.644061i	$0.222752\pi$
$182$	−6.02857e6	−0.0741249
$183$	4.63224e7	0.558743
$184$	2.51753e7	0.297929
$185$	1.31532e7	0.152732
$186$	−3.80413e7	−0.433471
$187$	−1.41283e8	−1.57995
$188$	−4.03619e7	−0.443015
$189$	−6.75127e6	−0.0727393
$190$	6.85669e7	0.725232
$191$	2.62440e6	0.0272530	0.0136265	−	0.999907i	$-0.495662\pi$
$191$	2.62440e6	0.0272530	0.0136265	+	0.999907i	$0.495662\pi$
$192$	−7.07789e6	−0.0721688
$193$	7.07430e7	0.708325	0.354163	−	0.935184i	$-0.384766\pi$
$193$	7.07430e7	0.708325	0.354163	+	0.935184i	$0.384766\pi$
$194$	−5.73403e7	−0.563837
$195$	1.08510e7	0.104797
$196$	7.52954e6	0.0714286
$197$	1.07462e8	1.00144	0.500719	−	0.865610i	$-0.333069\pi$
$197$	1.07462e8	1.00144	0.500719	+	0.865610i	$0.333069\pi$
$198$	2.31024e7	0.211509
$199$	−1.19494e8	−1.07488	−0.537439	−	0.843303i	$-0.680608\pi$
$199$	−1.19494e8	−1.07488	−0.537439	+	0.843303i	$0.680608\pi$
$200$	−2.28675e7	−0.202122
$201$	1.59843e7	0.138837
$202$	4.67145e7	0.398769
$203$	4.11865e7	0.345556
$204$	6.16302e7	0.508262
$205$	−1.33186e7	−0.107974
$206$	1.47963e8	1.17928
$207$	3.58453e7	0.280890
$208$	−8.99891e6	−0.0693375
$209$	1.85605e8	1.40630
$210$	−1.35526e7	−0.100985
$211$	9.51023e7	0.696951	0.348476	−	0.937318i	$-0.386699\pi$
$211$	9.51023e7	0.696951	0.348476	+	0.937318i	$0.386699\pi$
$212$	−5.03236e7	−0.362741
$213$	2.51999e7	0.178678
$214$	9.59448e7	0.669226
$215$	1.61311e8	1.10696
$216$	−1.00777e7	−0.0680414
$217$	6.04082e7	0.401316
$218$	−6.64511e6	−0.0434415
$219$	4.61070e7	0.296628
$220$	4.63762e7	0.293640
$221$	7.83573e7	0.488322
$222$	−1.55314e7	−0.0952740
$223$	2.98610e8	1.80317	0.901587	−	0.432597i	$-0.142403\pi$
$223$	2.98610e8	1.80317	0.901587	+	0.432597i	$0.142403\pi$
$224$	1.12394e7	0.0668153
$225$	−3.25594e7	−0.190562
$226$	8.58085e6	0.0494482
$227$	4.11865e7	0.233703	0.116851	−	0.993149i	$-0.462720\pi$
$227$	4.11865e7	0.233703	0.116851	+	0.993149i	$0.462720\pi$
$228$	−8.09642e7	−0.452398
$229$	−2.28974e8	−1.25997	−0.629986	−	0.776606i	$-0.716940\pi$
$229$	−2.28974e8	−1.25997	−0.629986	+	0.776606i	$0.716940\pi$
$230$	7.19566e7	0.389963
$231$	−3.66858e7	−0.195819
$232$	6.14795e7	0.323238
$233$	3.16684e8	1.64014	0.820069	−	0.572264i	$-0.193935\pi$
$233$	3.16684e8	1.64014	0.820069	+	0.572264i	$0.193935\pi$
$234$	−1.28129e7	−0.0653720
$235$	−1.15363e8	−0.579869
$236$	−2.46387e7	−0.122019
$237$	−9.92626e7	−0.484358
$238$	−9.78664e7	−0.470559
$239$	2.77147e8	1.31316	0.656580	−	0.754257i	$-0.272003\pi$
$239$	2.77147e8	1.31316	0.656580	+	0.754257i	$0.272003\pi$
$240$	−2.02302e7	−0.0944626
$241$	1.08077e8	0.497361	0.248681	−	0.968586i	$-0.420003\pi$
$241$	1.08077e8	0.497361	0.248681	+	0.968586i	$0.420003\pi$
$242$	−3.03611e7	−0.137709
$243$	−1.43489e7	−0.0641500
$244$	−1.09801e8	−0.483885
$245$	2.15211e7	0.0934938
$246$	1.57267e7	0.0673540
$247$	−1.02939e8	−0.434650
$248$	9.01720e7	0.375397
$249$	5.15493e7	0.211605
$250$	−1.79689e8	−0.727330
$251$	5.96208e7	0.237980	0.118990	−	0.992895i	$-0.462034\pi$
$251$	5.96208e7	0.237980	0.118990	+	0.992895i	$0.462034\pi$
$252$	1.60030e7	0.0629941
$253$	1.94780e8	0.756176
$254$	−8.97070e7	−0.343485
$255$	1.76153e8	0.665271
$256$	1.67772e7	0.0625000
$257$	4.27487e8	1.57093	0.785466	−	0.618905i	$-0.212424\pi$
$257$	4.27487e8	1.57093	0.785466	+	0.618905i	$0.212424\pi$
$258$	−1.90477e8	−0.690516
$259$	2.46632e7	0.0882066
$260$	−2.57209e7	−0.0907568
$261$	8.75363e7	0.304752
$262$	1.10348e8	0.379061
$263$	−2.17144e8	−0.736041	−0.368021	−	0.929818i	$-0.619964\pi$
$263$	−2.17144e8	−0.736041	−0.368021	+	0.929818i	$0.619964\pi$
$264$	−5.47613e7	−0.183172
$265$	−1.43836e8	−0.474796
$266$	1.28568e8	0.418839
$267$	−2.42497e8	−0.779680
$268$	−3.78886e7	−0.120237
$269$	−6.07894e7	−0.190412	−0.0952061	−	0.995458i	$-0.530351\pi$
$269$	−6.07894e7	−0.190412	−0.0952061	+	0.995458i	$0.530351\pi$
$270$	−2.88043e7	−0.0890602
$271$	7.05492e7	0.215327	0.107664	−	0.994187i	$-0.465663\pi$
$271$	7.05492e7	0.215327	0.107664	+	0.994187i	$0.465663\pi$
$272$	−1.46086e8	−0.440168
$273$	2.03464e7	0.0605228
$274$	−7.07925e7	−0.207903
$275$	−1.76924e8	−0.513007
$276$	−8.49667e7	−0.243258
$277$	−2.77984e6	−0.00785852	−0.00392926	−	0.999992i	$-0.501251\pi$
$277$	−2.77984e6	−0.00785852	−0.00392926	+	0.999992i	$0.501251\pi$
$278$	3.15511e8	0.880761
$279$	1.28389e8	0.353928
$280$	3.21248e7	0.0874554
$281$	−1.06623e8	−0.286667	−0.143334	−	0.989674i	$-0.545782\pi$
$281$	−1.06623e8	−0.286667	−0.143334	+	0.989674i	$0.545782\pi$
$282$	1.36221e8	0.361721
$283$	−5.32045e8	−1.39539	−0.697695	−	0.716394i	$-0.745791\pi$
$283$	−5.32045e8	−1.39539	−0.697695	+	0.716394i	$0.745791\pi$
$284$	−5.97331e7	−0.154739
$285$	−2.31413e8	−0.592150
$286$	−6.96241e7	−0.175986
$287$	−2.49733e7	−0.0623577
$288$	2.38879e7	0.0589256
$289$	8.61697e8	2.09996
$290$	1.75722e8	0.423091
$291$	1.93523e8	0.460371
$292$	−1.09291e8	−0.256887
$293$	4.50077e8	1.04532	0.522661	−	0.852540i	$-0.324939\pi$
$293$	4.50077e8	1.04532	0.522661	+	0.852540i	$0.324939\pi$
$294$	−2.54122e7	−0.0583212
$295$	−7.04230e7	−0.159712
$296$	3.68151e7	0.0825097
$297$	−7.79706e7	−0.172696
$298$	2.43668e8	0.533386
$299$	−1.08028e8	−0.233715
$300$	7.71777e7	0.165032
$301$	3.02471e8	0.639294
$302$	5.35027e8	1.11777
$303$	−1.57661e8	−0.325594
$304$	1.91915e8	0.391788
$305$	−3.13836e8	−0.633364
$306$	−2.08002e8	−0.414994
$307$	5.17742e7	0.102124	0.0510621	−	0.998695i	$-0.483739\pi$
$307$	5.17742e7	0.102124	0.0510621	+	0.998695i	$0.483739\pi$
$308$	8.69588e7	0.169585
$309$	−4.99375e8	−0.962879
$310$	2.57731e8	0.491362
$311$	−1.24416e8	−0.234539	−0.117270	−	0.993100i	$-0.537414\pi$
$311$	−1.24416e8	−0.234539	−0.117270	+	0.993100i	$0.537414\pi$
$312$	3.03713e7	0.0566139
$313$	−6.96323e8	−1.28353	−0.641764	−	0.766902i	$-0.721797\pi$
$313$	−6.96323e8	−1.28353	−0.641764	+	0.766902i	$0.721797\pi$
$314$	−7.28870e8	−1.32861
$315$	4.57401e7	0.0824537
$316$	2.35289e8	0.419466
$317$	−2.96628e8	−0.523004	−0.261502	−	0.965203i	$-0.584218\pi$
$317$	−2.96628e8	−0.523004	−0.261502	+	0.965203i	$0.584218\pi$
$318$	1.69842e8	0.296177
$319$	4.75664e8	0.820414
$320$	4.79530e7	0.0818070
$321$	−3.23814e8	−0.546421
$322$	1.34924e8	0.225213
$323$	−1.67109e9	−2.75924
$324$	3.40122e7	0.0555556
$325$	9.81247e7	0.158557
$326$	5.57719e8	0.891567
$327$	2.24273e7	0.0354698
$328$	−3.72780e7	−0.0583303
$329$	−2.16314e8	−0.334888
$330$	−1.56520e8	−0.239756
$331$	4.70178e8	0.712630	0.356315	−	0.934366i	$-0.384033\pi$
$331$	4.70178e8	0.712630	0.356315	+	0.934366i	$0.384033\pi$
$332$	−1.22191e8	−0.183255
$333$	5.24184e7	0.0777909
$334$	6.96928e8	1.02347
$335$	−1.08294e8	−0.157379
$336$	−3.79331e7	−0.0545545
$337$	−2.50685e8	−0.356799	−0.178400	−	0.983958i	$-0.557092\pi$
$337$	−2.50685e8	−0.356799	−0.178400	+	0.983958i	$0.557092\pi$
$338$	3.86145e7	0.0543928
$339$	−2.89604e7	−0.0403743
$340$	−4.17547e8	−0.576141
$341$	6.97656e8	0.952798
$342$	2.73254e8	0.369382
$343$	4.03536e7	0.0539949
$344$	4.51501e8	0.598004
$345$	−2.42853e8	−0.318403
$346$	−2.74860e8	−0.356735
$347$	−7.17287e8	−0.921594	−0.460797	−	0.887505i	$-0.652436\pi$
$347$	−7.17287e8	−0.921594	−0.460797	+	0.887505i	$0.652436\pi$
$348$	−2.07493e8	−0.263923
$349$	9.32096e8	1.17374	0.586869	−	0.809682i	$-0.300360\pi$
$349$	9.32096e8	1.17374	0.586869	+	0.809682i	$0.300360\pi$
$350$	−1.22555e8	−0.152790
$351$	4.32436e7	0.0533761
$352$	1.29804e8	0.158632
$353$	−6.86106e8	−0.830195	−0.415097	−	0.909777i	$-0.636252\pi$
$353$	−6.86106e8	−0.830195	−0.415097	+	0.909777i	$0.636252\pi$
$354$	8.31557e7	0.0996279
$355$	−1.70730e8	−0.202540
$356$	5.74807e8	0.675223
$357$	3.30299e8	0.384210
$358$	−1.01094e9	−1.16449
$359$	3.38800e8	0.386467	0.193233	−	0.981153i	$-0.438103\pi$
$359$	3.38800e8	0.386467	0.193233	+	0.981153i	$0.438103\pi$
$360$	6.82768e7	0.0771284
$361$	1.30145e9	1.45597
$362$	9.76431e8	1.08184
$363$	1.02469e8	0.112439
$364$	−4.82285e7	−0.0524142
$365$	−3.12376e8	−0.336243
$366$	3.70579e8	0.395091
$367$	−1.09475e9	−1.15607	−0.578033	−	0.816013i	$-0.696180\pi$
$367$	−1.09475e9	−1.15607	−0.578033	+	0.816013i	$0.696180\pi$
$368$	2.01402e8	0.210667
$369$	−5.30774e7	−0.0549943
$370$	1.05226e8	0.107998
$371$	−2.69703e8	−0.274206
$372$	−3.04330e8	−0.306510
$373$	−5.25220e8	−0.524035	−0.262018	−	0.965063i	$-0.584388\pi$
$373$	−5.25220e8	−0.524035	−0.262018	+	0.965063i	$0.584388\pi$
$374$	−1.13026e9	−1.11719
$375$	6.06451e8	0.593863
$376$	−3.22895e8	−0.313259
$377$	−2.63810e8	−0.253569
$378$	−5.40102e7	−0.0514344
$379$	−4.96096e8	−0.468089	−0.234045	−	0.972226i	$-0.575196\pi$
$379$	−4.96096e8	−0.468089	−0.234045	+	0.972226i	$0.575196\pi$
$380$	5.48536e8	0.512817
$381$	3.02761e8	0.280455
$382$	2.09952e7	0.0192708
$383$	1.52741e9	1.38919	0.694594	−	0.719402i	$-0.255584\pi$
$383$	1.52741e9	1.38919	0.694594	+	0.719402i	$0.255584\pi$
$384$	−5.66231e7	−0.0510310
$385$	2.48548e8	0.221971
$386$	5.65944e8	0.500861
$387$	6.42860e8	0.563804
$388$	−4.58722e8	−0.398693
$389$	−1.30037e9	−1.12007	−0.560033	−	0.828470i	$-0.689211\pi$
$389$	−1.30037e9	−1.12007	−0.560033	+	0.828470i	$0.689211\pi$
$390$	8.68080e7	0.0741026
$391$	−1.75370e9	−1.48366
$392$	6.02363e7	0.0505076
$393$	−3.72424e8	−0.309502
$394$	8.59698e8	0.708124
$395$	6.72508e8	0.549045
$396$	1.84819e8	0.149560
$397$	4.21261e8	0.337897	0.168949	−	0.985625i	$-0.445963\pi$
$397$	4.21261e8	0.337897	0.168949	+	0.985625i	$0.445963\pi$
$398$	−9.55949e8	−0.760053
$399$	−4.33917e8	−0.341981
$400$	−1.82940e8	−0.142922
$401$	−1.05933e9	−0.820397	−0.410199	−	0.911996i	$-0.634541\pi$
$401$	−1.05933e9	−0.820397	−0.410199	+	0.911996i	$0.634541\pi$
$402$	1.27874e8	0.0981728
$403$	−3.86929e8	−0.294486
$404$	3.73716e8	0.281973
$405$	9.72144e7	0.0727174
$406$	3.29492e8	0.244345
$407$	2.84837e8	0.209419
$408$	4.93041e8	0.359396
$409$	−1.90948e9	−1.38001	−0.690006	−	0.723804i	$-0.742392\pi$
$409$	−1.90948e9	−1.38001	−0.690006	+	0.723804i	$0.742392\pi$
$410$	−1.06549e8	−0.0763492
$411$	2.38925e8	0.169752
$412$	1.18370e9	0.833878
$413$	−1.32048e8	−0.0922375
$414$	2.86763e8	0.198619
$415$	−3.49249e8	−0.239865
$416$	−7.19913e7	−0.0490290
$417$	−1.06485e9	−0.719138
$418$	1.48484e9	0.994402
$419$	1.68175e9	1.11689	0.558446	−	0.829541i	$-0.311398\pi$
$419$	1.68175e9	1.11689	0.558446	+	0.829541i	$0.311398\pi$
$420$	−1.08421e8	−0.0714070
$421$	−2.89394e8	−0.189018	−0.0945089	−	0.995524i	$-0.530128\pi$
$421$	−2.89394e8	−0.189018	−0.0945089	+	0.995524i	$0.530128\pi$
$422$	7.60818e8	0.492819
$423$	−4.59747e8	−0.295344
$424$	−4.02589e8	−0.256497
$425$	1.59293e9	1.00655
$426$	2.01599e8	0.126344
$427$	−5.88466e8	−0.365783
$428$	7.67558e8	0.473215
$429$	2.34981e8	0.143692
$430$	1.29049e9	0.782735
$431$	2.53501e9	1.52514	0.762569	−	0.646907i	$-0.223938\pi$
$431$	2.53501e9	1.52514	0.762569	+	0.646907i	$0.223938\pi$
$432$	−8.06216e7	−0.0481125
$433$	2.03208e9	1.20291	0.601455	−	0.798907i	$-0.294588\pi$
$433$	2.03208e9	1.20291	0.601455	+	0.798907i	$0.294588\pi$
$434$	4.83265e8	0.283773
$435$	−5.93062e8	−0.345452
$436$	−5.31609e7	−0.0307178
$437$	2.30385e9	1.32059
$438$	3.68856e8	0.209748
$439$	1.48051e9	0.835189	0.417595	−	0.908633i	$-0.362873\pi$
$439$	1.48051e9	0.835189	0.417595	+	0.908633i	$0.362873\pi$
$440$	3.71010e8	0.207635
$441$	8.57661e7	0.0476190
$442$	6.26859e8	0.345296
$443$	7.70309e8	0.420971	0.210485	−	0.977597i	$-0.432496\pi$
$443$	7.70309e8	0.420971	0.210485	+	0.977597i	$0.432496\pi$
$444$	−1.24251e8	−0.0673689
$445$	1.64293e9	0.883808
$446$	2.38888e9	1.27504
$447$	−8.22380e8	−0.435508
$448$	8.99154e7	0.0472456
$449$	7.82205e8	0.407810	0.203905	−	0.978991i	$-0.434637\pi$
$449$	7.82205e8	0.407810	0.203905	+	0.978991i	$0.434637\pi$
$450$	−2.60475e8	−0.134748
$451$	−2.88418e8	−0.148049
$452$	6.86468e7	0.0349652
$453$	−1.80572e9	−0.912654
$454$	3.29492e8	0.165253
$455$	−1.37848e8	−0.0686057
$456$	−6.47713e8	−0.319894
$457$	−1.73248e8	−0.0849106	−0.0424553	−	0.999098i	$-0.513518\pi$
$457$	−1.73248e8	−0.0849106	−0.0424553	+	0.999098i	$0.513518\pi$
$458$	−1.83179e9	−0.890935
$459$	7.02006e8	0.338841
$460$	5.75653e8	0.275745
$461$	9.33126e8	0.443595	0.221798	−	0.975093i	$-0.428808\pi$
$461$	9.33126e8	0.443595	0.221798	+	0.975093i	$0.428808\pi$
$462$	−2.93486e8	−0.138465
$463$	9.33958e8	0.437315	0.218657	−	0.975802i	$-0.429832\pi$
$463$	9.33958e8	0.437315	0.218657	+	0.975802i	$0.429832\pi$
$464$	4.91836e8	0.228564
$465$	−8.69843e8	−0.401195
$466$	2.53347e9	1.15975
$467$	−4.19058e9	−1.90399	−0.951996	−	0.306112i	$-0.900972\pi$
$467$	−4.19058e9	−1.90399	−0.951996	+	0.306112i	$0.900972\pi$
$468$	−1.02503e8	−0.0462250
$469$	−2.03059e8	−0.0908903
$470$	−9.22905e8	−0.410029
$471$	2.45994e9	1.08480
$472$	−1.97110e8	−0.0862803
$473$	3.49324e9	1.51780
$474$	−7.94101e8	−0.342493
$475$	−2.09265e9	−0.895921
$476$	−7.82931e8	−0.332736
$477$	−5.73218e8	−0.241827
$478$	2.21718e9	0.928544
$479$	−1.47647e9	−0.613832	−0.306916	−	0.951737i	$-0.599297\pi$
$479$	−1.47647e9	−0.613832	−0.306916	+	0.951737i	$0.599297\pi$
$480$	−1.61841e8	−0.0667952
$481$	−1.57974e8	−0.0647259
$482$	8.64612e8	0.351687
$483$	−4.55368e8	−0.183886
$484$	−2.42889e8	−0.0973752
$485$	−1.31113e9	−0.521854
$486$	−1.14791e8	−0.0453609
$487$	4.68279e7	0.0183719	0.00918594	−	0.999958i	$-0.497076\pi$
$487$	4.68279e7	0.0183719	0.00918594	+	0.999958i	$0.497076\pi$
$488$	−8.78409e8	−0.342159
$489$	−1.88230e9	−0.727961
$490$	1.72169e8	0.0661101
$491$	1.13424e9	0.432433	0.216217	−	0.976345i	$-0.430628\pi$
$491$	1.13424e9	0.432433	0.216217	+	0.976345i	$0.430628\pi$
$492$	1.25813e8	0.0476265
$493$	−4.28263e9	−1.60970
$494$	−8.23511e8	−0.307344
$495$	5.28254e8	0.195760
$496$	7.21376e8	0.265446
$497$	−3.20132e8	−0.116972
$498$	4.12395e8	0.149627
$499$	−3.52134e9	−1.26869	−0.634345	−	0.773050i	$-0.718730\pi$
$499$	−3.52134e9	−1.26869	−0.634345	+	0.773050i	$0.718730\pi$
$500$	−1.43751e9	−0.514300
$501$	−2.35213e9	−0.835660
$502$	4.76967e8	0.168277
$503$	−2.27544e9	−0.797218	−0.398609	−	0.917121i	$-0.630507\pi$
$503$	−2.27544e9	−0.797218	−0.398609	+	0.917121i	$0.630507\pi$
$504$	1.28024e8	0.0445435
$505$	1.06816e9	0.369077
$506$	1.55824e9	0.534697
$507$	−1.30324e8	−0.0444116
$508$	−7.17656e8	−0.242881
$509$	9.06030e7	0.0304530	0.0152265	−	0.999884i	$-0.495153\pi$
$509$	9.06030e7	0.0304530	0.0152265	+	0.999884i	$0.495153\pi$
$510$	1.40922e9	0.470417
$511$	−5.85729e8	−0.194189
$512$	1.34218e8	0.0441942
$513$	−9.22233e8	−0.301599
$514$	3.41990e9	1.11082
$515$	3.38328e9	1.09147
$516$	−1.52382e9	−0.488268
$517$	−2.49822e9	−0.795086
$518$	1.97306e8	0.0623715
$519$	9.27654e8	0.291273
$520$	−2.05767e8	−0.0641747
$521$	2.46442e9	0.763454	0.381727	−	0.924275i	$-0.375330\pi$
$521$	2.46442e9	0.763454	0.381727	+	0.924275i	$0.375330\pi$
$522$	7.00290e8	0.215492
$523$	−4.61350e9	−1.41018	−0.705090	−	0.709118i	$-0.749093\pi$
$523$	−4.61350e9	−1.41018	−0.705090	+	0.709118i	$0.749093\pi$
$524$	8.82783e8	0.268037
$525$	4.13624e8	0.124752
$526$	−1.73715e9	−0.520460
$527$	−6.28132e9	−1.86945
$528$	−4.38090e8	−0.129522
$529$	−9.87085e8	−0.289908
$530$	−1.15069e9	−0.335732
$531$	−2.80651e8	−0.0813458
$532$	1.02854e9	0.296164
$533$	1.59960e8	0.0457580
$534$	−1.93997e9	−0.551317
$535$	2.19385e9	0.619396
$536$	−3.03109e8	−0.0850201
$537$	3.41193e9	0.950803
$538$	−4.86315e8	−0.134642
$539$	4.66045e8	0.128194
$540$	−2.30434e8	−0.0629751
$541$	5.72039e9	1.55323	0.776614	−	0.629976i	$-0.216935\pi$
$541$	5.72039e9	1.55323	0.776614	+	0.629976i	$0.216935\pi$
$542$	5.64393e8	0.152260
$543$	−3.29546e9	−0.883316
$544$	−1.16869e9	−0.311246
$545$	−1.51946e8	−0.0402069
$546$	1.62771e8	0.0427960
$547$	−1.98970e9	−0.519796	−0.259898	−	0.965636i	$-0.583689\pi$
$547$	−1.98970e9	−0.519796	−0.259898	+	0.965636i	$0.583689\pi$
$548$	−5.66340e8	−0.147009
$549$	−1.25070e9	−0.322590
$550$	−1.41540e9	−0.362751
$551$	5.62613e9	1.43278
$552$	−6.79733e8	−0.172009
$553$	1.26100e9	0.317087
$554$	−2.22387e7	−0.00555681
$555$	−3.55137e8	−0.0881800
$556$	2.52409e9	0.622792
$557$	−5.84384e9	−1.43286	−0.716432	−	0.697657i	$-0.754226\pi$
$557$	−5.84384e9	−1.43286	−0.716432	+	0.697657i	$0.754226\pi$
$558$	1.02712e9	0.250265
$559$	−1.93740e9	−0.469113
$560$	2.56998e8	0.0618403
$561$	3.81464e9	0.912185
$562$	−8.52983e8	−0.202704
$563$	−3.09890e9	−0.731860	−0.365930	−	0.930642i	$-0.619249\pi$
$563$	−3.09890e9	−0.731860	−0.365930	+	0.930642i	$0.619249\pi$
$564$	1.08977e9	0.255775
$565$	1.96208e8	0.0457663
$566$	−4.25636e9	−0.986690
$567$	1.82284e8	0.0419961
$568$	−4.77865e8	−0.109417
$569$	1.40217e9	0.319087	0.159543	−	0.987191i	$-0.448998\pi$
$569$	1.40217e9	0.319087	0.159543	+	0.987191i	$0.448998\pi$
$570$	−1.85131e9	−0.418713
$571$	5.22715e8	0.117500	0.0587501	−	0.998273i	$-0.481288\pi$
$571$	5.22715e8	0.117500	0.0587501	+	0.998273i	$0.481288\pi$
$572$	−5.56993e8	−0.124441
$573$	−7.08589e7	−0.0157345
$574$	−1.99787e8	−0.0440935
$575$	−2.19611e9	−0.481743
$576$	1.91103e8	0.0416667
$577$	−3.10717e9	−0.673364	−0.336682	−	0.941618i	$-0.609305\pi$
$577$	−3.10717e9	−0.673364	−0.336682	+	0.941618i	$0.609305\pi$
$578$	6.89357e9	1.48490
$579$	−1.91006e9	−0.408952
$580$	1.40578e9	0.299170
$581$	−6.54868e8	−0.138528
$582$	1.54819e9	0.325532
$583$	−3.11481e9	−0.651016
$584$	−8.74324e8	−0.181647
$585$	−2.92977e8	−0.0605045
$586$	3.60062e9	0.739155
$587$	−7.02518e9	−1.43359	−0.716794	−	0.697285i	$-0.754391\pi$
$587$	−7.02518e9	−1.43359	−0.716794	+	0.697285i	$0.754391\pi$
$588$	−2.03297e8	−0.0412393
$589$	8.25184e9	1.66398
$590$	−5.63384e8	−0.112933
$591$	−2.90148e9	−0.578181
$592$	2.94521e8	0.0583432
$593$	2.56327e9	0.504782	0.252391	−	0.967625i	$-0.418783\pi$
$593$	2.56327e9	0.504782	0.252391	+	0.967625i	$0.418783\pi$
$594$	−6.23765e8	−0.122115
$595$	−2.23779e9	−0.435522
$596$	1.94935e9	0.377161
$597$	3.22633e9	0.620581
$598$	−8.64221e8	−0.165261
$599$	−3.77344e9	−0.717370	−0.358685	−	0.933459i	$-0.616775\pi$
$599$	−3.77344e9	−0.717370	−0.358685	+	0.933459i	$0.616775\pi$
$600$	6.17422e8	0.116695
$601$	6.94724e9	1.30542	0.652712	−	0.757606i	$-0.273631\pi$
$601$	6.94724e9	1.30542	0.652712	+	0.757606i	$0.273631\pi$
$602$	2.41976e9	0.452049
$603$	−4.31575e8	−0.0801577
$604$	4.28022e9	0.790381
$605$	−6.94229e8	−0.127456
$606$	−1.26129e9	−0.230230
$607$	−4.38390e9	−0.795611	−0.397805	−	0.917470i	$-0.630228\pi$
$607$	−4.38390e9	−0.795611	−0.397805	+	0.917470i	$0.630228\pi$
$608$	1.53532e9	0.277036
$609$	−1.11204e9	−0.199507
$610$	−2.51069e9	−0.447856
$611$	1.38555e9	0.245741
$612$	−1.66401e9	−0.293445
$613$	−2.26333e9	−0.396858	−0.198429	−	0.980115i	$-0.563584\pi$
$613$	−2.26333e9	−0.396858	−0.198429	+	0.980115i	$0.563584\pi$
$614$	4.14193e8	0.0722127
$615$	3.59602e8	0.0623389
$616$	6.95671e8	0.119914
$617$	−4.55416e9	−0.780566	−0.390283	−	0.920695i	$-0.627623\pi$
$617$	−4.55416e9	−0.780566	−0.390283	+	0.920695i	$0.627623\pi$
$618$	−3.99500e9	−0.680858
$619$	6.48895e9	1.09966	0.549828	−	0.835278i	$-0.314693\pi$
$619$	6.48895e9	1.09966	0.549828	+	0.835278i	$0.314693\pi$
$620$	2.06185e9	0.347445
$621$	−9.67823e8	−0.162172
$622$	−9.95330e8	−0.165844
$623$	3.08061e9	0.510420
$624$	2.42971e8	0.0400320
$625$	−6.19429e8	−0.101487
$626$	−5.57058e9	−0.907591
$627$	−5.01132e9	−0.811925
$628$	−5.83096e9	−0.939467
$629$	−2.56452e9	−0.410893
$630$	3.65921e8	0.0583036
$631$	−4.12166e9	−0.653084	−0.326542	−	0.945183i	$-0.605883\pi$
$631$	−4.12166e9	−0.653084	−0.326542	+	0.945183i	$0.605883\pi$
$632$	1.88231e9	0.296607
$633$	−2.56776e9	−0.402385
$634$	−2.37302e9	−0.369820
$635$	−2.05122e9	−0.317910
$636$	1.35874e9	0.209429
$637$	−2.58475e8	−0.0396214
$638$	3.80531e9	0.580120
$639$	−6.80397e8	−0.103160
$640$	3.83624e8	0.0578463
$641$	−3.92731e9	−0.588968	−0.294484	−	0.955656i	$-0.595148\pi$
$641$	−3.92731e9	−0.588968	−0.294484	+	0.955656i	$0.595148\pi$
$642$	−2.59051e9	−0.386378
$643$	−3.10296e9	−0.460296	−0.230148	−	0.973156i	$-0.573921\pi$
$643$	−3.10296e9	−0.460296	−0.230148	+	0.973156i	$0.573921\pi$
$644$	1.07939e9	0.159250
$645$	−4.35540e9	−0.639101
$646$	−1.33687e10	−1.95108
$647$	−1.28622e10	−1.86702	−0.933510	−	0.358552i	$-0.883271\pi$
$647$	−1.28622e10	−1.86702	−0.933510	+	0.358552i	$0.883271\pi$
$648$	2.72098e8	0.0392837
$649$	−1.52503e9	−0.218989
$650$	7.84998e8	0.112117
$651$	−1.63102e9	−0.231700
$652$	4.46175e9	0.630433
$653$	−9.22985e9	−1.29717	−0.648587	−	0.761140i	$-0.724640\pi$
$653$	−9.22985e9	−1.29717	−0.648587	+	0.761140i	$0.724640\pi$
$654$	1.79418e8	0.0250809
$655$	2.52319e9	0.350837
$656$	−2.98224e8	−0.0412457
$657$	−1.24489e9	−0.171258
$658$	−1.73052e9	−0.236802
$659$	−2.95484e9	−0.402193	−0.201097	−	0.979571i	$-0.564450\pi$
$659$	−2.95484e9	−0.402193	−0.201097	+	0.979571i	$0.564450\pi$
$660$	−1.25216e9	−0.169533
$661$	−1.03249e10	−1.39053	−0.695265	−	0.718754i	$-0.744713\pi$
$661$	−1.03249e10	−1.39053	−0.695265	+	0.718754i	$0.744713\pi$
$662$	3.76142e9	0.503906
$663$	−2.11565e9	−0.281933
$664$	−9.77528e8	−0.129581
$665$	2.93981e9	0.387653
$666$	4.19347e8	0.0550065
$667$	5.90426e9	0.770416
$668$	5.57543e9	0.723703
$669$	−8.06248e9	−1.04106
$670$	−8.66352e8	−0.111284
$671$	−6.79621e9	−0.868436
$672$	−3.03464e8	−0.0385758
$673$	6.90398e9	0.873065	0.436533	−	0.899688i	$-0.356206\pi$
$673$	6.90398e9	0.873065	0.436533	+	0.899688i	$0.356206\pi$
$674$	−2.00548e9	−0.252295
$675$	8.79103e8	0.110021
$676$	3.08916e8	0.0384615
$677$	−7.94792e9	−0.984449	−0.492224	−	0.870468i	$-0.663816\pi$
$677$	−7.94792e9	−0.984449	−0.492224	+	0.870468i	$0.663816\pi$
$678$	−2.31683e8	−0.0285489
$679$	−2.45846e9	−0.301384
$680$	−3.34038e9	−0.407393
$681$	−1.11203e9	−0.134928
$682$	5.58125e9	0.673730
$683$	1.08255e10	1.30009	0.650047	−	0.759894i	$-0.274749\pi$
$683$	1.08255e10	1.30009	0.650047	+	0.759894i	$0.274749\pi$
$684$	2.18603e9	0.261192
$685$	−1.61872e9	−0.192422
$686$	3.22829e8	0.0381802
$687$	6.18229e9	0.727445
$688$	3.61201e9	0.422853
$689$	1.72752e9	0.201212
$690$	−1.94283e9	−0.225145
$691$	3.22486e9	0.371824	0.185912	−	0.982566i	$-0.440476\pi$
$691$	3.22486e9	0.371824	0.185912	+	0.982566i	$0.440476\pi$
$692$	−2.19888e9	−0.252250
$693$	9.90516e8	0.113056
$694$	−5.73830e9	−0.651666
$695$	7.21441e9	0.815181
$696$	−1.65995e9	−0.186622
$697$	2.59676e9	0.290481
$698$	7.45676e9	0.829959
$699$	−8.55047e9	−0.946935
$700$	−9.80443e8	−0.108039
$701$	−4.66557e9	−0.511554	−0.255777	−	0.966736i	$-0.582331\pi$
$701$	−4.66557e9	−0.511554	−0.255777	+	0.966736i	$0.582331\pi$
$702$	3.45948e8	0.0377426
$703$	3.36903e9	0.365731
$704$	1.03844e9	0.112170
$705$	3.11480e9	0.334787
$706$	−5.48885e9	−0.587036
$707$	2.00288e9	0.213151
$708$	6.65246e8	0.0704475
$709$	8.75909e9	0.922991	0.461495	−	0.887143i	$-0.347313\pi$
$709$	8.75909e9	0.922991	0.461495	+	0.887143i	$0.347313\pi$
$710$	−1.36584e9	−0.143218
$711$	2.68009e9	0.279644
$712$	4.59846e9	0.477455
$713$	8.65977e9	0.894732
$714$	2.64239e9	0.271678
$715$	−1.59201e9	−0.162882
$716$	−8.08755e9	−0.823420
$717$	−7.48297e9	−0.758153
$718$	2.71040e9	0.273273
$719$	−1.13424e10	−1.13803	−0.569013	−	0.822329i	$-0.692674\pi$
$719$	−1.13424e10	−1.13803	−0.569013	+	0.822329i	$0.692674\pi$
$720$	5.46214e8	0.0545380
$721$	6.34391e9	0.630352
$722$	1.04116e10	1.02953
$723$	−2.91807e9	−0.287152
$724$	7.81145e9	0.764974
$725$	−5.36301e9	−0.522668
$726$	8.19749e8	0.0795065
$727$	−8.56279e9	−0.826503	−0.413252	−	0.910617i	$-0.635607\pi$
$727$	−8.56279e9	−0.826503	−0.413252	+	0.910617i	$0.635607\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−2.49901e9	−0.237760
$731$	−3.14513e10	−2.97802
$732$	2.96463e9	0.279371
$733$	−5.77607e9	−0.541712	−0.270856	−	0.962620i	$-0.587307\pi$
$733$	−5.77607e9	−0.541712	−0.270856	+	0.962620i	$0.587307\pi$
$734$	−8.75798e9	−0.817462
$735$	−5.81069e8	−0.0539786
$736$	1.61122e9	0.148964
$737$	−2.34514e9	−0.215790
$738$	−4.24620e8	−0.0388868
$739$	1.28018e10	1.16685	0.583425	−	0.812167i	$-0.301712\pi$
$739$	1.28018e10	1.16685	0.583425	+	0.812167i	$0.301712\pi$
$740$	8.41806e8	0.0763661
$741$	2.77935e9	0.250945
$742$	−2.15763e9	−0.193893
$743$	−1.96648e10	−1.75885	−0.879425	−	0.476038i	$-0.842072\pi$
$743$	−1.96648e10	−1.75885	−0.879425	+	0.476038i	$0.842072\pi$
$744$	−2.43464e9	−0.216736
$745$	5.57166e9	0.493671
$746$	−4.20176e9	−0.370549
$747$	−1.39183e9	−0.122170
$748$	−9.04210e9	−0.789976
$749$	4.11363e9	0.357717
$750$	4.85161e9	0.419924
$751$	9.14519e9	0.787867	0.393934	−	0.919139i	$-0.371114\pi$
$751$	9.14519e9	0.787867	0.393934	+	0.919139i	$0.371114\pi$
$752$	−2.58316e9	−0.221508
$753$	−1.60976e9	−0.137398
$754$	−2.11048e9	−0.179300
$755$	1.22338e10	1.03454
$756$	−4.32081e8	−0.0363696
$757$	−1.46791e9	−0.122989	−0.0614943	−	0.998107i	$-0.519587\pi$
$757$	−1.46791e9	−0.122989	−0.0614943	+	0.998107i	$0.519587\pi$
$758$	−3.96877e9	−0.330989
$759$	−5.25906e9	−0.436578
$760$	4.38828e9	0.362616
$761$	4.96452e9	0.408348	0.204174	−	0.978935i	$-0.434549\pi$
$761$	4.96452e9	0.408348	0.204174	+	0.978935i	$0.434549\pi$
$762$	2.42209e9	0.198311
$763$	−2.84909e8	−0.0232204
$764$	1.67962e8	0.0136265
$765$	−4.75612e9	−0.384094
$766$	1.22193e10	0.982305
$767$	8.45802e8	0.0676838
$768$	−4.52985e8	−0.0360844
$769$	−8.77630e9	−0.695936	−0.347968	−	0.937506i	$-0.613128\pi$
$769$	−8.77630e9	−0.695936	−0.347968	+	0.937506i	$0.613128\pi$
$770$	1.98838e9	0.156957
$771$	−1.15422e10	−0.906978
$772$	4.52755e9	0.354163
$773$	−9.51150e9	−0.740663	−0.370332	−	0.928900i	$-0.620756\pi$
$773$	−9.51150e9	−0.740663	−0.370332	+	0.928900i	$0.620756\pi$
$774$	5.14288e9	0.398670
$775$	−7.86593e9	−0.607007
$776$	−3.66978e9	−0.281919
$777$	−6.65908e8	−0.0509261
$778$	−1.04030e10	−0.792006
$779$	−3.41139e9	−0.258554
$780$	6.94464e8	0.0523984
$781$	−3.69721e9	−0.277713
$782$	−1.40296e10	−1.04911
$783$	−2.36348e9	−0.175949
$784$	4.81890e8	0.0357143
$785$	−1.66662e10	−1.22968
$786$	−2.97939e9	−0.218851
$787$	1.22117e10	0.893024	0.446512	−	0.894778i	$-0.352666\pi$
$787$	1.22117e10	0.893024	0.446512	+	0.894778i	$0.352666\pi$
$788$	6.87758e9	0.500719
$789$	5.86288e9	0.424953
$790$	5.38006e9	0.388233
$791$	3.67904e8	0.0264312
$792$	1.47855e9	0.105755
$793$	3.76927e9	0.268411
$794$	3.37009e9	0.238929
$795$	3.88357e9	0.274124
$796$	−7.64759e9	−0.537439
$797$	−5.98021e9	−0.418420	−0.209210	−	0.977871i	$-0.567089\pi$
$797$	−5.98021e9	−0.418420	−0.209210	+	0.977871i	$0.567089\pi$
$798$	−3.47134e9	−0.241817
$799$	2.24927e10	1.56001
$800$	−1.46352e9	−0.101061
$801$	6.54741e9	0.450148
$802$	−8.47461e9	−0.580108
$803$	−6.76460e9	−0.461039
$804$	1.02299e9	0.0694186
$805$	3.08514e9	0.208444
$806$	−3.09543e9	−0.208233
$807$	1.64131e9	0.109935
$808$	2.98973e9	0.199385
$809$	8.49553e9	0.564119	0.282060	−	0.959397i	$-0.408982\pi$
$809$	8.49553e9	0.564119	0.282060	+	0.959397i	$0.408982\pi$
$810$	7.77715e8	0.0514189
$811$	−2.73867e10	−1.80288	−0.901441	−	0.432903i	$-0.857489\pi$
$811$	−2.73867e10	−1.80288	−0.901441	+	0.432903i	$0.857489\pi$
$812$	2.63594e9	0.172778
$813$	−1.90483e9	−0.124319
$814$	2.27869e9	0.148081
$815$	1.27527e10	0.825181
$816$	3.94433e9	0.254131
$817$	4.13179e10	2.65070
$818$	−1.52758e10	−0.975816
$819$	−5.49353e8	−0.0349428
$820$	−8.52390e8	−0.0539871
$821$	−8.80748e9	−0.555457	−0.277729	−	0.960660i	$-0.589582\pi$
$821$	−8.80748e9	−0.555457	−0.277729	+	0.960660i	$0.589582\pi$
$822$	1.91140e9	0.120033
$823$	2.89145e10	1.80807	0.904037	−	0.427455i	$-0.140590\pi$
$823$	2.89145e10	1.80807	0.904037	+	0.427455i	$0.140590\pi$
$824$	9.46962e9	0.589641
$825$	4.77696e9	0.296185
$826$	−1.05639e9	−0.0652218
$827$	2.50014e9	0.153708	0.0768539	−	0.997042i	$-0.475513\pi$
$827$	2.50014e9	0.153708	0.0768539	+	0.997042i	$0.475513\pi$
$828$	2.29410e9	0.140445
$829$	−1.64084e10	−1.00029	−0.500144	−	0.865942i	$-0.666720\pi$
$829$	−1.64084e10	−1.00029	−0.500144	+	0.865942i	$0.666720\pi$
$830$	−2.79399e9	−0.169610
$831$	7.50557e7	0.00453712
$832$	−5.75930e8	−0.0346688
$833$	−4.19602e9	−0.251525
$834$	−8.51881e9	−0.508508
$835$	1.59358e10	0.947264
$836$	1.18787e10	0.703148
$837$	−3.46651e9	−0.204340
$838$	1.34540e10	0.789763
$839$	−2.11082e10	−1.23391	−0.616956	−	0.786997i	$-0.711634\pi$
$839$	−2.11082e10	−1.23391	−0.616956	+	0.786997i	$0.711634\pi$
$840$	−8.67368e8	−0.0504924
$841$	−2.83133e9	−0.164136
$842$	−2.31515e9	−0.133656
$843$	2.87882e9	0.165507
$844$	6.08655e9	0.348476
$845$	8.82949e8	0.0503428
$846$	−3.67798e9	−0.208839
$847$	−1.30173e9	−0.0736087
$848$	−3.22071e9	−0.181370
$849$	1.43652e10	0.805629
$850$	1.27435e10	0.711740
$851$	3.53558e9	0.196656
$852$	1.61279e9	0.0893388
$853$	1.55639e10	0.858614	0.429307	−	0.903159i	$-0.358758\pi$
$853$	1.55639e10	0.858614	0.429307	+	0.903159i	$0.358758\pi$
$854$	−4.70773e9	−0.258648
$855$	6.24816e9	0.341878
$856$	6.14046e9	0.334613
$857$	−2.12614e10	−1.15388	−0.576939	−	0.816787i	$-0.695753\pi$
$857$	−2.12614e10	−1.15388	−0.576939	+	0.816787i	$0.695753\pi$
$858$	1.87985e9	0.101606
$859$	3.32648e10	1.79064	0.895322	−	0.445420i	$-0.146945\pi$
$859$	3.32648e10	1.79064	0.895322	+	0.445420i	$0.146945\pi$
$860$	1.03239e10	0.553478
$861$	6.74280e8	0.0360022
$862$	2.02801e10	1.07844
$863$	3.43661e10	1.82009	0.910044	−	0.414512i	$-0.136048\pi$
$863$	3.43661e10	1.82009	0.910044	+	0.414512i	$0.136048\pi$
$864$	−6.44973e8	−0.0340207
$865$	−6.28489e9	−0.330173
$866$	1.62566e10	0.850586
$867$	−2.32658e10	−1.21242
$868$	3.86612e9	0.200658
$869$	1.45634e10	0.752822
$870$	−4.74450e9	−0.244271
$871$	1.30064e9	0.0666953
$872$	−4.25287e8	−0.0217207
$873$	−5.22513e9	−0.265795
$874$	1.84308e10	0.933800
$875$	−7.70417e9	−0.388774
$876$	2.95084e9	0.148314
$877$	2.01140e10	1.00693	0.503466	−	0.864015i	$-0.332058\pi$
$877$	2.01140e10	1.00693	0.503466	+	0.864015i	$0.332058\pi$
$878$	1.18441e10	0.590568
$879$	−1.21521e10	−0.603517
$880$	2.96808e9	0.146820
$881$	−2.02562e10	−0.998029	−0.499014	−	0.866594i	$-0.666305\pi$
$881$	−2.02562e10	−0.998029	−0.499014	+	0.866594i	$0.666305\pi$
$882$	6.86129e8	0.0336718
$883$	5.52142e9	0.269891	0.134945	−	0.990853i	$-0.456914\pi$
$883$	5.52142e9	0.269891	0.134945	+	0.990853i	$0.456914\pi$
$884$	5.01487e9	0.244161
$885$	1.90142e9	0.0922097
$886$	6.16247e9	0.297671
$887$	−3.10218e10	−1.49257	−0.746284	−	0.665628i	$-0.768164\pi$
$887$	−3.10218e10	−1.49257	−0.746284	+	0.665628i	$0.768164\pi$
$888$	−9.94008e8	−0.0476370
$889$	−3.84619e9	−0.183601
$890$	1.31434e10	0.624946
$891$	2.10521e9	0.0997063
$892$	1.91111e10	0.901587
$893$	−2.95488e10	−1.38855
$894$	−6.57904e9	−0.307951
$895$	−2.31160e10	−1.07778
$896$	7.19323e8	0.0334077
$897$	2.91675e9	0.134935
$898$	6.25764e9	0.288366
$899$	2.11477e10	0.970741
$900$	−2.08380e9	−0.0952811
$901$	2.80441e10	1.27734
$902$	−2.30734e9	−0.104686
$903$	−8.16670e9	−0.369096
$904$	5.49174e8	0.0247241
$905$	2.23268e10	1.00128
$906$	−1.44457e10	−0.645344
$907$	5.10220e9	0.227056	0.113528	−	0.993535i	$-0.463785\pi$
$907$	5.10220e9	0.227056	0.113528	+	0.993535i	$0.463785\pi$
$908$	2.63593e9	0.116851
$909$	4.25686e9	0.187982
$910$	−1.10278e9	−0.0485115
$911$	−1.43685e10	−0.629646	−0.314823	−	0.949150i	$-0.601945\pi$
$911$	−1.43685e10	−0.629646	−0.314823	+	0.949150i	$0.601945\pi$
$912$	−5.18171e9	−0.226199
$913$	−7.56309e9	−0.328890
$914$	−1.38598e9	−0.0600408
$915$	8.47357e9	0.365673
$916$	−1.46543e10	−0.629986
$917$	4.73116e9	0.202617
$918$	5.61605e9	0.239597
$919$	2.34317e10	0.995862	0.497931	−	0.867217i	$-0.334093\pi$
$919$	2.34317e10	0.995862	0.497931	+	0.867217i	$0.334093\pi$
$920$	4.60522e9	0.194981
$921$	−1.39790e9	−0.0589614
$922$	7.46501e9	0.313669
$923$	2.05052e9	0.0858339
$924$	−2.34789e9	−0.0979097
$925$	−3.21147e9	−0.133416
$926$	7.47167e9	0.309228
$927$	1.34831e10	0.555919
$928$	3.93469e9	0.161619
$929$	−2.86727e10	−1.17331	−0.586656	−	0.809836i	$-0.699556\pi$
$929$	−2.86727e10	−1.17331	−0.586656	+	0.809836i	$0.699556\pi$
$930$	−6.95875e9	−0.283688
$931$	5.51236e9	0.223879
$932$	2.02678e10	0.820069
$933$	3.35924e9	0.135411
$934$	−3.35246e10	−1.34633
$935$	−2.58443e10	−1.03401
$936$	−8.20026e8	−0.0326860
$937$	−2.30512e10	−0.915388	−0.457694	−	0.889110i	$-0.651324\pi$
$937$	−2.30512e10	−0.915388	−0.457694	+	0.889110i	$0.651324\pi$
$938$	−1.62447e9	−0.0642692
$939$	1.88007e10	0.741045
$940$	−7.38324e9	−0.289934
$941$	3.90728e10	1.52866	0.764330	−	0.644825i	$-0.223070\pi$
$941$	3.90728e10	1.52866	0.764330	+	0.644825i	$0.223070\pi$
$942$	1.96795e10	0.767071
$943$	−3.58004e9	−0.139026
$944$	−1.57688e9	−0.0610094
$945$	−1.23498e9	−0.0476047
$946$	2.79459e10	1.07325
$947$	−2.53616e10	−0.970400	−0.485200	−	0.874403i	$-0.661253\pi$
$947$	−2.53616e10	−0.970400	−0.485200	+	0.874403i	$0.661253\pi$
$948$	−6.35280e9	−0.242179
$949$	3.75174e9	0.142495
$950$	−1.67412e10	−0.633512
$951$	8.00896e9	0.301956
$952$	−6.26345e9	−0.235280
$953$	3.52515e10	1.31933	0.659664	−	0.751561i	$-0.270699\pi$
$953$	3.52515e10	1.31933	0.659664	+	0.751561i	$0.270699\pi$
$954$	−4.58574e9	−0.170998
$955$	4.80072e8	0.0178359
$956$	1.77374e10	0.656580
$957$	−1.28429e10	−0.473666
$958$	−1.18117e10	−0.434045
$959$	−3.03523e9	−0.111129
$960$	−1.29473e9	−0.0472313
$961$	3.50463e9	0.127383
$962$	−1.26379e9	−0.0457682
$963$	8.74297e9	0.315476
$964$	6.91690e9	0.248681
$965$	1.29407e10	0.463568
$966$	−3.64295e9	−0.130027
$967$	5.11070e10	1.81756	0.908778	−	0.417280i	$-0.137017\pi$
$967$	5.11070e10	1.81756	0.908778	+	0.417280i	$0.137017\pi$
$968$	−1.94311e9	−0.0688547
$969$	4.51193e10	1.59305
$970$	−1.04890e10	−0.369007
$971$	−3.58094e10	−1.25525	−0.627623	−	0.778517i	$-0.715972\pi$
$971$	−3.58094e10	−1.25525	−0.627623	+	0.778517i	$0.715972\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.35275e10	0.470787
$974$	3.74623e8	0.0129909
$975$	−2.64937e9	−0.0915432
$976$	−7.02727e9	−0.241943
$977$	1.64617e10	0.564735	0.282368	−	0.959306i	$-0.408880\pi$
$977$	1.64617e10	0.564735	0.282368	+	0.959306i	$0.408880\pi$
$978$	−1.50584e10	−0.514746
$979$	3.55780e10	1.21183
$980$	1.37735e9	0.0467469
$981$	−6.05536e8	−0.0204785
$982$	9.07391e9	0.305777
$983$	2.31524e10	0.777425	0.388712	−	0.921359i	$-0.372920\pi$
$983$	2.31524e10	0.777425	0.388712	+	0.921359i	$0.372920\pi$
$984$	1.00651e9	0.0336770
$985$	1.96576e10	0.655397
$986$	−3.42610e10	−1.13823
$987$	5.84049e9	0.193348
$988$	−6.58808e9	−0.217325
$989$	4.33604e10	1.42530
$990$	4.22603e9	0.138423
$991$	5.71792e10	1.86629	0.933147	−	0.359495i	$-0.117051\pi$
$991$	5.71792e10	1.86629	0.933147	+	0.359495i	$0.117051\pi$
$992$	5.77101e9	0.187698
$993$	−1.26948e10	−0.411437
$994$	−2.56106e9	−0.0827117
$995$	−2.18585e10	−0.703460
$996$	3.29916e9	0.105802
$997$	5.60393e10	1.79085	0.895425	−	0.445212i	$-0.146872\pi$
$997$	5.60393e10	1.79085	0.895425	+	0.445212i	$0.146872\pi$
$998$	−2.81707e10	−0.897100
$999$	−1.41530e9	−0.0449126

Twists

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

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

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +182.926 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +182.926 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +1463.41 q^{10} +3961.32 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -4939.00 q^{15} +4096.00 q^{16} -35665.6 q^{17} +5832.00 q^{18} +46854.3 q^{19} +11707.3 q^{20} -9261.00 q^{21} +31690.5 q^{22} +49170.5 q^{23} -13824.0 q^{24} -44663.0 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} +120077. q^{29} -39512.0 q^{30} +176117. q^{31} +32768.0 q^{32} -106956. q^{33} -285325. q^{34} +62743.7 q^{35} +46656.0 q^{36} +71904.5 q^{37} +374834. q^{38} +59319.0 q^{39} +93658.2 q^{40} -72808.6 q^{41} -74088.0 q^{42} +881838. q^{43} +253524. q^{44} +133353. q^{45} +393364. q^{46} -630654. q^{47} -110592. q^{48} +117649. q^{49} -357304. q^{50} +962971. q^{51} -140608. q^{52} -786307. q^{53} -157464. q^{54} +724628. q^{55} +175616. q^{56} -1.26507e6 q^{57} +960618. q^{58} -384980. q^{59} -316096. q^{60} -1.71564e6 q^{61} +1.40894e6 q^{62} +250047. q^{63} +262144. q^{64} -401889. q^{65} -855645. q^{66} -592009. q^{67} -2.28260e6 q^{68} -1.32760e6 q^{69} +501949. q^{70} -933329. q^{71} +373248. q^{72} -1.70766e6 q^{73} +575236. q^{74} +1.20590e6 q^{75} +2.99867e6 q^{76} +1.35873e6 q^{77} +474552. q^{78} +3.67639e6 q^{79} +749265. q^{80} +531441. q^{81} -582469. q^{82} -1.90923e6 q^{83} -592704. q^{84} -6.52417e6 q^{85} +7.05471e6 q^{86} -3.24209e6 q^{87} +2.02819e6 q^{88} +8.98136e6 q^{89} +1.06683e6 q^{90} -753571. q^{91} +3.14691e6 q^{92} -4.75516e6 q^{93} -5.04523e6 q^{94} +8.57087e6 q^{95} -884736. q^{96} -7.16753e6 q^{97} +941192. q^{98} +2.88780e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 104 q^{10} + 10054 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} - 351 q^{15} + 24576 q^{16} + 21222 q^{17} + 34992 q^{18} + 9527 q^{19} + 832 q^{20} - 55566 q^{21} + 80432 q^{22} + 33229 q^{23} - 82944 q^{24} + 265321 q^{25} - 105456 q^{26} - 118098 q^{27} + 131712 q^{28} + 174185 q^{29} - 2808 q^{30} + 119045 q^{31} + 196608 q^{32} - 271458 q^{33} + 169776 q^{34} + 4459 q^{35} + 279936 q^{36} + 56562 q^{37} + 76216 q^{38} + 355914 q^{39} + 6656 q^{40} + 101632 q^{41} - 444528 q^{42} + 441323 q^{43} + 643456 q^{44} + 9477 q^{45} + 265832 q^{46} - 892849 q^{47} - 663552 q^{48} + 705894 q^{49} + 2122568 q^{50} - 572994 q^{51} - 843648 q^{52} + 2093965 q^{53} - 944784 q^{54} - 331222 q^{55} + 1053696 q^{56} - 257229 q^{57} + 1393480 q^{58} - 136204 q^{59} - 22464 q^{60} - 3989946 q^{61} + 952360 q^{62} + 1500282 q^{63} + 1572864 q^{64} - 28561 q^{65} - 2171664 q^{66} - 2218250 q^{67} + 1358208 q^{68} - 897183 q^{69} + 35672 q^{70} + 2045928 q^{71} + 2239488 q^{72} - 8557479 q^{73} + 452496 q^{74} - 7163667 q^{75} + 609728 q^{76} + 3448522 q^{77} + 2847312 q^{78} - 8559709 q^{79} + 53248 q^{80} + 3188646 q^{81} + 813056 q^{82} + 2496351 q^{83} - 3556224 q^{84} + 5335304 q^{85} + 3530584 q^{86} - 4702995 q^{87} + 5147648 q^{88} - 2446683 q^{89} + 75816 q^{90} - 4521426 q^{91} + 2126656 q^{92} - 3214215 q^{93} - 7142792 q^{94} + 16410211 q^{95} - 5308416 q^{96} + 5786889 q^{97} + 5647152 q^{98} + 7329366 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 104 * q^10 + 10054 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 - 351 * q^15 + 24576 * q^16 + 21222 * q^17 + 34992 * q^18 + 9527 * q^19 + 832 * q^20 - 55566 * q^21 + 80432 * q^22 + 33229 * q^23 - 82944 * q^24 + 265321 * q^25 - 105456 * q^26 - 118098 * q^27 + 131712 * q^28 + 174185 * q^29 - 2808 * q^30 + 119045 * q^31 + 196608 * q^32 - 271458 * q^33 + 169776 * q^34 + 4459 * q^35 + 279936 * q^36 + 56562 * q^37 + 76216 * q^38 + 355914 * q^39 + 6656 * q^40 + 101632 * q^41 - 444528 * q^42 + 441323 * q^43 + 643456 * q^44 + 9477 * q^45 + 265832 * q^46 - 892849 * q^47 - 663552 * q^48 + 705894 * q^49 + 2122568 * q^50 - 572994 * q^51 - 843648 * q^52 + 2093965 * q^53 - 944784 * q^54 - 331222 * q^55 + 1053696 * q^56 - 257229 * q^57 + 1393480 * q^58 - 136204 * q^59 - 22464 * q^60 - 3989946 * q^61 + 952360 * q^62 + 1500282 * q^63 + 1572864 * q^64 - 28561 * q^65 - 2171664 * q^66 - 2218250 * q^67 + 1358208 * q^68 - 897183 * q^69 + 35672 * q^70 + 2045928 * q^71 + 2239488 * q^72 - 8557479 * q^73 + 452496 * q^74 - 7163667 * q^75 + 609728 * q^76 + 3448522 * q^77 + 2847312 * q^78 - 8559709 * q^79 + 53248 * q^80 + 3188646 * q^81 + 813056 * q^82 + 2496351 * q^83 - 3556224 * q^84 + 5335304 * q^85 + 3530584 * q^86 - 4702995 * q^87 + 5147648 * q^88 - 2446683 * q^89 + 75816 * q^90 - 4521426 * q^91 + 2126656 * q^92 - 3214215 * q^93 - 7142792 * q^94 + 16410211 * q^95 - 5308416 * q^96 + 5786889 * q^97 + 5647152 * q^98 + 7329366 * q^99

Introduction

L-functions

Modular forms

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