LMFDB - Embedded newform 546.8.a.q.1.6

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			1.6
Root			$527.645$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +529.645 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +529.645 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +4237.16 q^{10} +3727.68 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -14300.4 q^{15} +4096.00 q^{16} +24121.3 q^{17} +5832.00 q^{18} +9818.46 q^{19} +33897.3 q^{20} -9261.00 q^{21} +29821.5 q^{22} -36040.5 q^{23} -13824.0 q^{24} +202398. q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} -159862. q^{29} -114403. q^{30} +222746. q^{31} +32768.0 q^{32} -100647. q^{33} +192971. q^{34} +181668. q^{35} +46656.0 q^{36} +219687. q^{37} +78547.7 q^{38} +59319.0 q^{39} +271178. q^{40} -29299.4 q^{41} -74088.0 q^{42} -79448.9 q^{43} +238572. q^{44} +386111. q^{45} -288324. q^{46} +652464. q^{47} -110592. q^{48} +117649. q^{49} +1.61919e6 q^{50} -651276. q^{51} -140608. q^{52} +586529. q^{53} -157464. q^{54} +1.97435e6 q^{55} +175616. q^{56} -265098. q^{57} -1.27890e6 q^{58} -1.11075e6 q^{59} -915226. q^{60} +370461. q^{61} +1.78197e6 q^{62} +250047. q^{63} +262144. q^{64} -1.16363e6 q^{65} -805180. q^{66} -3.54571e6 q^{67} +1.54377e6 q^{68} +973093. q^{69} +1.45334e6 q^{70} +3.51099e6 q^{71} +373248. q^{72} -6.04121e6 q^{73} +1.75749e6 q^{74} -5.46476e6 q^{75} +628381. q^{76} +1.27860e6 q^{77} +474552. q^{78} -4.72429e6 q^{79} +2.16942e6 q^{80} +531441. q^{81} -234395. q^{82} +2.27200e6 q^{83} -592704. q^{84} +1.27757e7 q^{85} -635591. q^{86} +4.31628e6 q^{87} +1.90857e6 q^{88} -2.77728e6 q^{89} +3.08889e6 q^{90} -753571. q^{91} -2.30659e6 q^{92} -6.01415e6 q^{93} +5.21971e6 q^{94} +5.20029e6 q^{95} -884736. q^{96} +3.86868e6 q^{97} +941192. q^{98} +2.71748e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	529.645	1.89491	0.947457	−	0.319883i	$-0.103644\pi$
$5$	529.645	1.89491	0.947457	+	0.319883i	$0.103644\pi$
$6$	−216.000	−0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	4237.16	1.33991
$11$	3727.68	0.844432	0.422216	−	0.906495i	$-0.361252\pi$
$11$	3727.68	0.844432	0.422216	+	0.906495i	$0.361252\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	2744.00	0.267261
$15$	−14300.4	−1.09403
$16$	4096.00	0.250000
$17$	24121.3	1.19078	0.595388	−	0.803438i	$-0.296998\pi$
$17$	24121.3	1.19078	0.595388	+	0.803438i	$0.296998\pi$
$18$	5832.00	0.235702
$19$	9818.46	0.328402	0.164201	−	0.986427i	$-0.447495\pi$
$19$	9818.46	0.328402	0.164201	+	0.986427i	$0.447495\pi$
$20$	33897.3	0.947457
$21$	−9261.00	−0.218218
$22$	29821.5	0.597104
$23$	−36040.5	−0.617651	−0.308825	−	0.951119i	$-0.599936\pi$
$23$	−36040.5	−0.617651	−0.308825	+	0.951119i	$0.599936\pi$
$24$	−13824.0	−0.204124
$25$	202398.	2.59070
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	21952.0	0.188982
$29$	−159862.	−1.21717	−0.608587	−	0.793487i	$-0.708263\pi$
$29$	−159862.	−1.21717	−0.608587	+	0.793487i	$0.708263\pi$
$30$	−114403.	−0.773596
$31$	222746.	1.34290	0.671452	−	0.741048i	$-0.265671\pi$
$31$	222746.	1.34290	0.671452	+	0.741048i	$0.265671\pi$
$32$	32768.0	0.176777
$33$	−100647.	−0.487533
$34$	192971.	0.842006
$35$	181668.	0.716210
$36$	46656.0	0.166667
$37$	219687.	0.713013	0.356507	−	0.934293i	$-0.383968\pi$
$37$	219687.	0.713013	0.356507	+	0.934293i	$0.383968\pi$
$38$	78547.7	0.232215
$39$	59319.0	0.160128
$40$	271178.	0.669953
$41$	−29299.4	−0.0663919	−0.0331959	−	0.999449i	$-0.510569\pi$
$41$	−29299.4	−0.0663919	−0.0331959	+	0.999449i	$0.510569\pi$
$42$	−74088.0	−0.154303
$43$	−79448.9	−0.152387	−0.0761936	−	0.997093i	$-0.524277\pi$
$43$	−79448.9	−0.152387	−0.0761936	+	0.997093i	$0.524277\pi$
$44$	238572.	0.422216
$45$	386111.	0.631638
$46$	−288324.	−0.436745
$47$	652464.	0.916673	0.458336	−	0.888779i	$-0.348446\pi$
$47$	652464.	0.916673	0.458336	+	0.888779i	$0.348446\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	1.61919e6	1.83190
$51$	−651276.	−0.687495
$52$	−140608.	−0.138675
$53$	586529.	0.541158	0.270579	−	0.962698i	$-0.412785\pi$
$53$	586529.	0.541158	0.270579	+	0.962698i	$0.412785\pi$
$54$	−157464.	−0.136083
$55$	1.97435e6	1.60013
$56$	175616.	0.133631
$57$	−265098.	−0.189603
$58$	−1.27890e6	−0.860672
$59$	−1.11075e6	−0.704100	−0.352050	−	0.935981i	$-0.614515\pi$
$59$	−1.11075e6	−0.704100	−0.352050	+	0.935981i	$0.614515\pi$
$60$	−915226.	−0.547015
$61$	370461.	0.208972	0.104486	−	0.994526i	$-0.466680\pi$
$61$	370461.	0.208972	0.104486	+	0.994526i	$0.466680\pi$
$62$	1.78197e6	0.949576
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	−1.16363e6	−0.525555
$66$	−805180.	−0.344738
$67$	−3.54571e6	−1.44026	−0.720130	−	0.693839i	$-0.755918\pi$
$67$	−3.54571e6	−1.44026	−0.720130	+	0.693839i	$0.755918\pi$
$68$	1.54377e6	0.595388
$69$	973093.	0.356601
$70$	1.45334e6	0.506437
$71$	3.51099e6	1.16419	0.582097	−	0.813119i	$-0.302232\pi$
$71$	3.51099e6	1.16419	0.582097	+	0.813119i	$0.302232\pi$
$72$	373248.	0.117851
$73$	−6.04121e6	−1.81758	−0.908791	−	0.417251i	$-0.862994\pi$
$73$	−6.04121e6	−1.81758	−0.908791	+	0.417251i	$0.862994\pi$
$74$	1.75749e6	0.504177
$75$	−5.46476e6	−1.49574
$76$	628381.	0.164201
$77$	1.27860e6	0.319165
$78$	474552.	0.113228
$79$	−4.72429e6	−1.07806	−0.539028	−	0.842288i	$-0.681208\pi$
$79$	−4.72429e6	−1.07806	−0.539028	+	0.842288i	$0.681208\pi$
$80$	2.16942e6	0.473729
$81$	531441.	0.111111
$82$	−234395.	−0.0469461
$83$	2.27200e6	0.436149	0.218075	−	0.975932i	$-0.430022\pi$
$83$	2.27200e6	0.436149	0.218075	+	0.975932i	$0.430022\pi$
$84$	−592704.	−0.109109
$85$	1.27757e7	2.25642
$86$	−635591.	−0.107754
$87$	4.31628e6	0.702735
$88$	1.90857e6	0.298552
$89$	−2.77728e6	−0.417595	−0.208797	−	0.977959i	$-0.566955\pi$
$89$	−2.77728e6	−0.417595	−0.208797	+	0.977959i	$0.566955\pi$
$90$	3.08889e6	0.446636
$91$	−753571.	−0.104828
$92$	−2.30659e6	−0.308825
$93$	−6.01415e6	−0.775326
$94$	5.21971e6	0.648185
$95$	5.20029e6	0.622293
$96$	−884736.	−0.102062
$97$	3.86868e6	0.430390	0.215195	−	0.976571i	$-0.430961\pi$
$97$	3.86868e6	0.430390	0.215195	+	0.976571i	$0.430961\pi$
$98$	941192.	0.101015
$99$	2.71748e6	0.281477
$100$	1.29535e7	1.29535
$101$	−4.17061e6	−0.402786	−0.201393	−	0.979511i	$-0.564547\pi$
$101$	−4.17061e6	−0.402786	−0.201393	+	0.979511i	$0.564547\pi$
$102$	−5.21021e6	−0.486133
$103$	5.54746e6	0.500223	0.250111	−	0.968217i	$-0.419533\pi$
$103$	5.54746e6	0.500223	0.250111	+	0.968217i	$0.419533\pi$
$104$	−1.12486e6	−0.0980581
$105$	−4.90504e6	−0.413504
$106$	4.69223e6	0.382657
$107$	−2.37587e7	−1.87490	−0.937452	−	0.348115i	$-0.886822\pi$
$107$	−2.37587e7	−1.87490	−0.937452	+	0.348115i	$0.886822\pi$
$108$	−1.25971e6	−0.0962250
$109$	1.37063e7	1.01374	0.506870	−	0.862022i	$-0.330802\pi$
$109$	1.37063e7	1.01374	0.506870	+	0.862022i	$0.330802\pi$
$110$	1.57948e7	1.13146
$111$	−5.93154e6	−0.411658
$112$	1.40493e6	0.0944911
$113$	−2.23664e6	−0.145821	−0.0729107	−	0.997338i	$-0.523229\pi$
$113$	−2.23664e6	−0.145821	−0.0729107	+	0.997338i	$0.523229\pi$
$114$	−2.12079e6	−0.134070
$115$	−1.90886e7	−1.17040
$116$	−1.02312e7	−0.608587
$117$	−1.60161e6	−0.0924500
$118$	−8.88600e6	−0.497874
$119$	8.27362e6	0.450071
$120$	−7.32181e6	−0.386798
$121$	−5.59154e6	−0.286934
$122$	2.96369e6	0.147765
$123$	791083.	0.0383314
$124$	1.42558e7	0.671452
$125$	6.58208e7	3.01424
$126$	2.00038e6	0.0890871
$127$	−9.41494e6	−0.407854	−0.203927	−	0.978986i	$-0.565370\pi$
$127$	−9.41494e6	−0.407854	−0.203927	+	0.978986i	$0.565370\pi$
$128$	2.09715e6	0.0883883
$129$	2.14512e6	0.0879808
$130$	−9.30903e6	−0.371623
$131$	−1.62654e7	−0.632145	−0.316072	−	0.948735i	$-0.602364\pi$
$131$	−1.62654e7	−0.632145	−0.316072	+	0.948735i	$0.602364\pi$
$132$	−6.44144e6	−0.243767
$133$	3.36773e6	0.124124
$134$	−2.83656e7	−1.01842
$135$	−1.04250e7	−0.364676
$136$	1.23501e7	0.421003
$137$	−2.09518e7	−0.696146	−0.348073	−	0.937467i	$-0.613164\pi$
$137$	−2.09518e7	−0.696146	−0.348073	+	0.937467i	$0.613164\pi$
$138$	7.78474e6	0.252155
$139$	−2.42651e7	−0.766355	−0.383177	−	0.923675i	$-0.625170\pi$
$139$	−2.42651e7	−0.766355	−0.383177	+	0.923675i	$0.625170\pi$
$140$	1.16268e7	0.358105
$141$	−1.76165e7	−0.529241
$142$	2.80879e7	0.823210
$143$	−8.18972e6	−0.234203
$144$	2.98598e6	0.0833333
$145$	−8.46701e7	−2.30644
$146$	−4.83297e7	−1.28522
$147$	−3.17652e6	−0.0824786
$148$	1.40599e7	0.356507
$149$	4.42973e7	1.09705	0.548523	−	0.836135i	$-0.315190\pi$
$149$	4.42973e7	1.09705	0.548523	+	0.836135i	$0.315190\pi$
$150$	−4.37181e7	−1.05765
$151$	−5.68350e7	−1.34337	−0.671687	−	0.740835i	$-0.734430\pi$
$151$	−5.68350e7	−1.34337	−0.671687	+	0.740835i	$0.734430\pi$
$152$	5.02705e6	0.116108
$153$	1.75845e7	0.396926
$154$	1.02288e7	0.225684
$155$	1.17976e8	2.54469
$156$	3.79642e6	0.0800641
$157$	7.78930e7	1.60639	0.803193	−	0.595719i	$-0.203133\pi$
$157$	7.78930e7	1.60639	0.803193	+	0.595719i	$0.203133\pi$
$158$	−3.77943e7	−0.762301
$159$	−1.58363e7	−0.312438
$160$	1.73554e7	0.334977
$161$	−1.23619e7	−0.233450
$162$	4.25153e6	0.0785674
$163$	−5.14450e7	−0.930436	−0.465218	−	0.885196i	$-0.654024\pi$
$163$	−5.14450e7	−0.930436	−0.465218	+	0.885196i	$0.654024\pi$
$164$	−1.87516e6	−0.0331959
$165$	−5.33074e7	−0.923834
$166$	1.81760e7	0.308404
$167$	2.40929e7	0.400296	0.200148	−	0.979766i	$-0.435858\pi$
$167$	2.40929e7	0.400296	0.200148	+	0.979766i	$0.435858\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	1.02206e8	1.59553
$171$	7.15766e6	0.109467
$172$	−5.08473e6	−0.0761936
$173$	8.78537e7	1.29003	0.645013	−	0.764171i	$-0.276852\pi$
$173$	8.78537e7	1.29003	0.645013	+	0.764171i	$0.276852\pi$
$174$	3.45302e7	0.496909
$175$	6.94227e7	0.979193
$176$	1.52686e7	0.211108
$177$	2.99903e7	0.406512
$178$	−2.22183e7	−0.295284
$179$	7.47061e7	0.973578	0.486789	−	0.873520i	$-0.338168\pi$
$179$	7.47061e7	0.973578	0.486789	+	0.873520i	$0.338168\pi$
$180$	2.47111e7	0.315819
$181$	5.00109e7	0.626887	0.313444	−	0.949607i	$-0.398517\pi$
$181$	5.00109e7	0.626887	0.313444	+	0.949607i	$0.398517\pi$
$182$	−6.02857e6	−0.0741249
$183$	−1.00024e7	−0.120650
$184$	−1.84527e7	−0.218373
$185$	1.16356e8	1.35110
$186$	−4.81132e7	−0.548238
$187$	8.99168e7	1.00553
$188$	4.17577e7	0.458336
$189$	−6.75127e6	−0.0727393
$190$	4.16023e7	0.440028
$191$	1.78752e8	1.85624	0.928119	−	0.372284i	$-0.121425\pi$
$191$	1.78752e8	1.85624	0.928119	+	0.372284i	$0.121425\pi$
$192$	−7.07789e6	−0.0721688
$193$	2.51808e7	0.252127	0.126063	−	0.992022i	$-0.459766\pi$
$193$	2.51808e7	0.252127	0.126063	+	0.992022i	$0.459766\pi$
$194$	3.09495e7	0.304332
$195$	3.14180e7	0.303429
$196$	7.52954e6	0.0714286
$197$	1.23584e8	1.15168	0.575839	−	0.817563i	$-0.304675\pi$
$197$	1.23584e8	1.15168	0.575839	+	0.817563i	$0.304675\pi$
$198$	2.17399e7	0.199035
$199$	2.90019e7	0.260880	0.130440	−	0.991456i	$-0.458361\pi$
$199$	2.90019e7	0.260880	0.130440	+	0.991456i	$0.458361\pi$
$200$	1.03628e8	0.915951
$201$	9.57341e7	0.831535
$202$	−3.33649e7	−0.284813
$203$	−5.48327e7	−0.460048
$204$	−4.16817e7	−0.343748
$205$	−1.55183e7	−0.125807
$206$	4.43797e7	0.353711
$207$	−2.62735e7	−0.205884
$208$	−8.99891e6	−0.0693375
$209$	3.66001e7	0.277313
$210$	−3.92403e7	−0.292392
$211$	−6.62659e7	−0.485625	−0.242813	−	0.970073i	$-0.578070\pi$
$211$	−6.62659e7	−0.485625	−0.242813	+	0.970073i	$0.578070\pi$
$212$	3.75379e7	0.270579
$213$	−9.47968e7	−0.672148
$214$	−1.90069e8	−1.32576
$215$	−4.20797e7	−0.288761
$216$	−1.00777e7	−0.0680414
$217$	7.64020e7	0.507570
$218$	1.09650e8	0.716823
$219$	1.63113e8	1.04938
$220$	1.26358e8	0.800063
$221$	−5.29946e7	−0.330262
$222$	−4.74523e7	−0.291086
$223$	2.82014e8	1.70296	0.851479	−	0.524389i	$-0.175706\pi$
$223$	2.82014e8	1.70296	0.851479	+	0.524389i	$0.175706\pi$
$224$	1.12394e7	0.0668153
$225$	1.47548e8	0.863567
$226$	−1.78931e7	−0.103111
$227$	−1.19805e8	−0.679805	−0.339903	−	0.940461i	$-0.610394\pi$
$227$	−1.19805e8	−0.679805	−0.339903	+	0.940461i	$0.610394\pi$
$228$	−1.69663e7	−0.0948015
$229$	1.03961e7	0.0572064	0.0286032	−	0.999591i	$-0.490894\pi$
$229$	1.03961e7	0.0572064	0.0286032	+	0.999591i	$0.490894\pi$
$230$	−1.52709e8	−0.827595
$231$	−3.45221e7	−0.184270
$232$	−8.18494e7	−0.430336
$233$	−1.76469e8	−0.913952	−0.456976	−	0.889479i	$-0.651067\pi$
$233$	−1.76469e8	−0.913952	−0.456976	+	0.889479i	$0.651067\pi$
$234$	−1.28129e7	−0.0653720
$235$	3.45574e8	1.73702
$236$	−7.10880e7	−0.352050
$237$	1.27556e8	0.622416
$238$	6.61890e7	0.318248
$239$	2.48570e8	1.17776	0.588878	−	0.808222i	$-0.299570\pi$
$239$	2.48570e8	1.17776	0.588878	+	0.808222i	$0.299570\pi$
$240$	−5.85745e7	−0.273507
$241$	−3.65205e7	−0.168065	−0.0840326	−	0.996463i	$-0.526780\pi$
$241$	−3.65205e7	−0.168065	−0.0840326	+	0.996463i	$0.526780\pi$
$242$	−4.47323e7	−0.202893
$243$	−1.43489e7	−0.0641500
$244$	2.37095e7	0.104486
$245$	6.23122e7	0.270702
$246$	6.32867e6	0.0271044
$247$	−2.15712e7	−0.0910823
$248$	1.14046e8	0.474788
$249$	−6.13440e7	−0.251811
$250$	5.26566e8	2.13139
$251$	3.43704e8	1.37191	0.685957	−	0.727643i	$-0.259384\pi$
$251$	3.43704e8	1.37191	0.685957	+	0.727643i	$0.259384\pi$
$252$	1.60030e7	0.0629941
$253$	−1.34348e8	−0.521564
$254$	−7.53195e7	−0.288396
$255$	−3.44945e8	−1.30274
$256$	1.67772e7	0.0625000
$257$	−2.72290e8	−1.00061	−0.500306	−	0.865849i	$-0.666779\pi$
$257$	−2.72290e8	−1.00061	−0.500306	+	0.865849i	$0.666779\pi$
$258$	1.71610e7	0.0622118
$259$	7.53525e7	0.269494
$260$	−7.44723e7	−0.262777
$261$	−1.16539e8	−0.405724
$262$	−1.30124e8	−0.446994
$263$	3.55067e8	1.20355	0.601777	−	0.798664i	$-0.294460\pi$
$263$	3.55067e8	1.20355	0.601777	+	0.798664i	$0.294460\pi$
$264$	−5.15315e7	−0.172369
$265$	3.10652e8	1.02545
$266$	2.69418e7	0.0877691
$267$	7.49867e7	0.241099
$268$	−2.26925e8	−0.720130
$269$	2.87140e8	0.899417	0.449709	−	0.893175i	$-0.351528\pi$
$269$	2.87140e8	0.899417	0.449709	+	0.893175i	$0.351528\pi$
$270$	−8.34000e7	−0.257865
$271$	−5.05877e8	−1.54402	−0.772009	−	0.635611i	$-0.780748\pi$
$271$	−5.05877e8	−1.54402	−0.772009	+	0.635611i	$0.780748\pi$
$272$	9.88010e7	0.297694
$273$	2.03464e7	0.0605228
$274$	−1.67615e8	−0.492250
$275$	7.54478e8	2.18767
$276$	6.22779e7	0.178300
$277$	3.57253e8	1.00994	0.504971	−	0.863136i	$-0.331503\pi$
$277$	3.57253e8	1.00994	0.504971	+	0.863136i	$0.331503\pi$
$278$	−1.94121e8	−0.541895
$279$	1.62382e8	0.447635
$280$	9.30141e7	0.253219
$281$	−3.11274e8	−0.836893	−0.418447	−	0.908241i	$-0.637425\pi$
$281$	−3.11274e8	−0.836893	−0.418447	+	0.908241i	$0.637425\pi$
$282$	−1.40932e8	−0.374230
$283$	−3.45216e8	−0.905396	−0.452698	−	0.891664i	$-0.649538\pi$
$283$	−3.45216e8	−0.905396	−0.452698	+	0.891664i	$0.649538\pi$
$284$	2.24703e8	0.582097
$285$	−1.40408e8	−0.359281
$286$	−6.55178e7	−0.165607
$287$	−1.00497e7	−0.0250938
$288$	2.38879e7	0.0589256
$289$	1.71501e8	0.417949
$290$	−6.77361e8	−1.63090
$291$	−1.04454e8	−0.248486
$292$	−3.86638e8	−0.908791
$293$	−7.03438e8	−1.63376	−0.816882	−	0.576805i	$-0.804299\pi$
$293$	−7.03438e8	−1.63376	−0.816882	+	0.576805i	$0.804299\pi$
$294$	−2.54122e7	−0.0583212
$295$	−5.88303e8	−1.33421
$296$	1.12480e8	0.252088
$297$	−7.33720e7	−0.162511
$298$	3.54378e8	0.775729
$299$	7.91809e7	0.171306
$300$	−3.49745e8	−0.747871
$301$	−2.72510e7	−0.0575969
$302$	−4.54680e8	−0.949909
$303$	1.12606e8	0.232549
$304$	4.02164e7	0.0821005
$305$	1.96213e8	0.395984
$306$	1.40676e8	0.280669
$307$	3.64374e8	0.718726	0.359363	−	0.933198i	$-0.382994\pi$
$307$	3.64374e8	0.718726	0.359363	+	0.933198i	$0.382994\pi$
$308$	8.18301e7	0.159583
$309$	−1.49781e8	−0.288804
$310$	9.43812e8	1.79937
$311$	−1.04616e9	−1.97214	−0.986071	−	0.166325i	$-0.946810\pi$
$311$	−1.04616e9	−1.97214	−0.986071	+	0.166325i	$0.946810\pi$
$312$	3.03713e7	0.0566139
$313$	5.12995e8	0.945601	0.472800	−	0.881170i	$-0.343243\pi$
$313$	5.12995e8	0.945601	0.472800	+	0.881170i	$0.343243\pi$
$314$	6.23144e8	1.13589
$315$	1.32436e8	0.238737
$316$	−3.02354e8	−0.539028
$317$	9.43433e8	1.66343	0.831714	−	0.555205i	$-0.187360\pi$
$317$	9.43433e8	1.66343	0.831714	+	0.555205i	$0.187360\pi$
$318$	−1.26690e8	−0.220927
$319$	−5.95915e8	−1.02782
$320$	1.38843e8	0.236864
$321$	6.41484e8	1.08248
$322$	−9.88951e7	−0.165074
$323$	2.36834e8	0.391053
$324$	3.40122e7	0.0555556
$325$	−4.44669e8	−0.718531
$326$	−4.11560e8	−0.657917
$327$	−3.70069e8	−0.585283
$328$	−1.50013e7	−0.0234731
$329$	2.23795e8	0.346470
$330$	−4.26459e8	−0.653249
$331$	−6.52039e8	−0.988270	−0.494135	−	0.869385i	$-0.664515\pi$
$331$	−6.52039e8	−0.988270	−0.494135	+	0.869385i	$0.664515\pi$
$332$	1.45408e8	0.218075
$333$	1.60152e8	0.237671
$334$	1.92743e8	0.283052
$335$	−1.87796e9	−2.72917
$336$	−3.79331e7	−0.0545545
$337$	−5.31387e8	−0.756322	−0.378161	−	0.925740i	$-0.623443\pi$
$337$	−5.31387e8	−0.756322	−0.378161	+	0.925740i	$0.623443\pi$
$338$	3.86145e7	0.0543928
$339$	6.03893e7	0.0841901
$340$	8.17648e8	1.12821
$341$	8.30329e8	1.13399
$342$	5.72612e7	0.0774051
$343$	4.03536e7	0.0539949
$344$	−4.06779e7	−0.0538770
$345$	5.15393e8	0.675728
$346$	7.02830e8	0.912187
$347$	−4.68034e8	−0.601345	−0.300673	−	0.953727i	$-0.597211\pi$
$347$	−4.68034e8	−0.601345	−0.300673	+	0.953727i	$0.597211\pi$
$348$	2.76242e8	0.351368
$349$	5.87418e7	0.0739704	0.0369852	−	0.999316i	$-0.488225\pi$
$349$	5.87418e7	0.0739704	0.0369852	+	0.999316i	$0.488225\pi$
$350$	5.55381e8	0.692394
$351$	4.32436e7	0.0533761
$352$	1.22149e8	0.149276
$353$	6.26384e8	0.757930	0.378965	−	0.925411i	$-0.376280\pi$
$353$	6.26384e8	0.757930	0.378965	+	0.925411i	$0.376280\pi$
$354$	2.39922e8	0.287448
$355$	1.85958e9	2.20605
$356$	−1.77746e8	−0.208797
$357$	−2.23388e8	−0.259849
$358$	5.97649e8	0.688423
$359$	−6.26958e8	−0.715167	−0.357584	−	0.933881i	$-0.616399\pi$
$359$	−6.26958e8	−0.715167	−0.357584	+	0.933881i	$0.616399\pi$
$360$	1.97689e8	0.223318
$361$	−7.97470e8	−0.892152
$362$	4.00087e8	0.443276
$363$	1.50971e8	0.165662
$364$	−4.82285e7	−0.0524142
$365$	−3.19970e9	−3.44416
$366$	−8.00195e7	−0.0853124
$367$	−1.88762e8	−0.199335	−0.0996676	−	0.995021i	$-0.531778\pi$
$367$	−1.88762e8	−0.199335	−0.0996676	+	0.995021i	$0.531778\pi$
$368$	−1.47622e8	−0.154413
$369$	−2.13593e7	−0.0221306
$370$	9.30847e8	0.955371
$371$	2.01180e8	0.204539
$372$	−3.84906e8	−0.387663
$373$	−5.38574e8	−0.537358	−0.268679	−	0.963230i	$-0.586587\pi$
$373$	−5.38574e8	−0.537358	−0.268679	+	0.963230i	$0.586587\pi$
$374$	7.19334e8	0.711017
$375$	−1.77716e9	−1.74027
$376$	3.34062e8	0.324093
$377$	3.51217e8	0.337583
$378$	−5.40102e7	−0.0514344
$379$	−1.41681e9	−1.33682	−0.668411	−	0.743792i	$-0.733025\pi$
$379$	−1.41681e9	−1.33682	−0.668411	+	0.743792i	$0.733025\pi$
$380$	3.32819e8	0.311147
$381$	2.54203e8	0.235474
$382$	1.43001e9	1.31256
$383$	−2.11756e8	−0.192593	−0.0962965	−	0.995353i	$-0.530700\pi$
$383$	−2.11756e8	−0.192593	−0.0962965	+	0.995353i	$0.530700\pi$
$384$	−5.66231e7	−0.0510310
$385$	6.77201e8	0.604791
$386$	2.01447e8	0.178281
$387$	−5.79183e7	−0.0507957
$388$	2.47596e8	0.215195
$389$	1.97233e9	1.69885	0.849427	−	0.527706i	$-0.176948\pi$
$389$	1.97233e9	1.69885	0.849427	+	0.527706i	$0.176948\pi$
$390$	2.51344e8	0.214557
$391$	−8.69345e8	−0.735484
$392$	6.02363e7	0.0505076
$393$	4.39167e8	0.364969
$394$	9.88674e8	0.814360
$395$	−2.50219e9	−2.04282
$396$	1.73919e8	0.140739
$397$	−1.50693e9	−1.20872	−0.604359	−	0.796712i	$-0.706571\pi$
$397$	−1.50693e9	−1.20872	−0.604359	+	0.796712i	$0.706571\pi$
$398$	2.32015e8	0.184470
$399$	−9.09287e7	−0.0716632
$400$	8.29024e8	0.647675
$401$	1.47465e9	1.14205	0.571023	−	0.820934i	$-0.306547\pi$
$401$	1.47465e9	1.14205	0.571023	+	0.820934i	$0.306547\pi$
$402$	7.65873e8	0.587984
$403$	−4.89374e8	−0.372455
$404$	−2.66919e8	−0.201393
$405$	2.81475e8	0.210546
$406$	−4.38662e8	−0.325303
$407$	8.18923e8	0.602091
$408$	−3.33454e8	−0.243066
$409$	6.90014e8	0.498685	0.249342	−	0.968415i	$-0.419786\pi$
$409$	6.90014e8	0.498685	0.249342	+	0.968415i	$0.419786\pi$
$410$	−1.24146e8	−0.0889589
$411$	5.65700e8	0.401920
$412$	3.55037e8	0.250111
$413$	−3.80987e8	−0.266125
$414$	−2.10188e8	−0.145582
$415$	1.20335e9	0.826465
$416$	−7.19913e7	−0.0490290
$417$	6.55157e8	0.442455
$418$	2.92801e8	0.196090
$419$	2.48002e9	1.64704	0.823522	−	0.567284i	$-0.192006\pi$
$419$	2.48002e9	1.64704	0.823522	+	0.567284i	$0.192006\pi$
$420$	−3.13922e8	−0.206752
$421$	6.39837e8	0.417909	0.208955	−	0.977925i	$-0.432994\pi$
$421$	6.39837e8	0.417909	0.208955	+	0.977925i	$0.432994\pi$
$422$	−5.30127e8	−0.343389
$423$	4.75646e8	0.305558
$424$	3.00303e8	0.191328
$425$	4.88212e9	3.08495
$426$	−7.58374e8	−0.475281
$427$	1.27068e8	0.0789840
$428$	−1.52056e9	−0.937452
$429$	2.21123e8	0.135217
$430$	−3.36638e8	−0.204185
$431$	−9.03517e8	−0.543583	−0.271792	−	0.962356i	$-0.587616\pi$
$431$	−9.03517e8	−0.543583	−0.271792	+	0.962356i	$0.587616\pi$
$432$	−8.06216e7	−0.0481125
$433$	6.85293e8	0.405666	0.202833	−	0.979213i	$-0.434985\pi$
$433$	6.85293e8	0.405666	0.202833	+	0.979213i	$0.434985\pi$
$434$	6.11216e8	0.358906
$435$	2.28609e9	1.33162
$436$	8.77202e8	0.506870
$437$	−3.53862e8	−0.202838
$438$	1.30490e9	0.742025
$439$	6.71521e8	0.378821	0.189410	−	0.981898i	$-0.439342\pi$
$439$	6.71521e8	0.378821	0.189410	+	0.981898i	$0.439342\pi$
$440$	1.01087e9	0.565730
$441$	8.57661e7	0.0476190
$442$	−4.23957e8	−0.233531
$443$	−2.23297e9	−1.22031	−0.610155	−	0.792282i	$-0.708893\pi$
$443$	−2.23297e9	−1.22031	−0.610155	+	0.792282i	$0.708893\pi$
$444$	−3.79619e8	−0.205829
$445$	−1.47097e9	−0.791307
$446$	2.25611e9	1.20417
$447$	−1.19603e9	−0.633380
$448$	8.99154e7	0.0472456
$449$	−3.27633e9	−1.70815	−0.854075	−	0.520150i	$-0.825876\pi$
$449$	−3.27633e9	−1.70815	−0.854075	+	0.520150i	$0.825876\pi$
$450$	1.18039e9	0.610634
$451$	−1.09219e8	−0.0560634
$452$	−1.43145e8	−0.0729107
$453$	1.53455e9	0.775597
$454$	−9.58440e8	−0.480695
$455$	−3.99125e8	−0.198641
$456$	−1.35730e8	−0.0670348
$457$	3.24483e9	1.59032	0.795161	−	0.606398i	$-0.207386\pi$
$457$	3.24483e9	1.59032	0.795161	+	0.606398i	$0.207386\pi$
$458$	8.31685e7	0.0404510
$459$	−4.74780e8	−0.229165
$460$	−1.22167e9	−0.585198
$461$	2.24985e9	1.06955	0.534775	−	0.844994i	$-0.320396\pi$
$461$	2.24985e9	1.06955	0.534775	+	0.844994i	$0.320396\pi$
$462$	−2.76177e8	−0.130299
$463$	−1.87496e9	−0.877929	−0.438964	−	0.898504i	$-0.644655\pi$
$463$	−1.87496e9	−0.877929	−0.438964	+	0.898504i	$0.644655\pi$
$464$	−6.54795e8	−0.304293
$465$	−3.18536e9	−1.46918
$466$	−1.41175e9	−0.646262
$467$	−1.48428e9	−0.674385	−0.337192	−	0.941436i	$-0.609477\pi$
$467$	−1.48428e9	−0.674385	−0.337192	+	0.941436i	$0.609477\pi$
$468$	−1.02503e8	−0.0462250
$469$	−1.21618e9	−0.544367
$470$	2.76459e9	1.22826
$471$	−2.10311e9	−0.927447
$472$	−5.68704e8	−0.248937
$473$	−2.96161e8	−0.128681
$474$	1.02045e9	0.440115
$475$	1.98724e9	0.850791
$476$	5.29512e8	0.225036
$477$	4.27580e8	0.180386
$478$	1.98856e9	0.832799
$479$	−1.16314e9	−0.483568	−0.241784	−	0.970330i	$-0.577733\pi$
$479$	−1.16314e9	−0.483568	−0.241784	+	0.970330i	$0.577733\pi$
$480$	−4.68596e8	−0.193399
$481$	−4.82652e8	−0.197754
$482$	−2.92164e8	−0.118840
$483$	3.33771e8	0.134782
$484$	−3.57858e8	−0.143467
$485$	2.04903e9	0.815552
$486$	−1.14791e8	−0.0453609
$487$	1.04706e9	0.410790	0.205395	−	0.978679i	$-0.434152\pi$
$487$	1.04706e9	0.410790	0.205395	+	0.978679i	$0.434152\pi$
$488$	1.89676e8	0.0738827
$489$	1.38901e9	0.537187
$490$	4.98497e8	0.191415
$491$	2.44817e8	0.0933374	0.0466687	−	0.998910i	$-0.485139\pi$
$491$	2.44817e8	0.0933374	0.0466687	+	0.998910i	$0.485139\pi$
$492$	5.06293e7	0.0191657
$493$	−3.85609e9	−1.44938
$494$	−1.72569e8	−0.0644049
$495$	1.43930e9	0.533376
$496$	9.12370e8	0.335726
$497$	1.20427e9	0.440024
$498$	−4.90752e8	−0.178057
$499$	−1.10896e9	−0.399543	−0.199771	−	0.979843i	$-0.564020\pi$
$499$	−1.10896e9	−0.399543	−0.199771	+	0.979843i	$0.564020\pi$
$500$	4.21253e9	1.50712
$501$	−6.50509e8	−0.231111
$502$	2.74963e9	0.970089
$503$	−3.69487e9	−1.29453	−0.647264	−	0.762266i	$-0.724087\pi$
$503$	−3.69487e9	−1.29453	−0.647264	+	0.762266i	$0.724087\pi$
$504$	1.28024e8	0.0445435
$505$	−2.20894e9	−0.763245
$506$	−1.07478e9	−0.368802
$507$	−1.30324e8	−0.0444116
$508$	−6.02556e8	−0.203927
$509$	2.94308e8	0.0989213	0.0494606	−	0.998776i	$-0.484250\pi$
$509$	2.94308e8	0.0989213	0.0494606	+	0.998776i	$0.484250\pi$
$510$	−2.75956e9	−0.921180
$511$	−2.07214e9	−0.686982
$512$	1.34218e8	0.0441942
$513$	−1.93257e8	−0.0632010
$514$	−2.17832e9	−0.707539
$515$	2.93818e9	0.947880
$516$	1.37288e8	0.0439904
$517$	2.43218e9	0.774068
$518$	6.02820e8	0.190561
$519$	−2.37205e9	−0.744797
$520$	−5.95778e8	−0.185812
$521$	−4.14682e9	−1.28465	−0.642323	−	0.766434i	$-0.722029\pi$
$521$	−4.14682e9	−1.28465	−0.642323	+	0.766434i	$0.722029\pi$
$522$	−9.32316e8	−0.286891
$523$	−1.27950e9	−0.391096	−0.195548	−	0.980694i	$-0.562649\pi$
$523$	−1.27950e9	−0.391096	−0.195548	+	0.980694i	$0.562649\pi$
$524$	−1.04099e9	−0.316072
$525$	−1.87441e9	−0.565337
$526$	2.84054e9	0.851041
$527$	5.37295e9	1.59910
$528$	−4.12252e8	−0.121883
$529$	−2.10591e9	−0.618507
$530$	2.48522e9	0.725101
$531$	−8.09737e8	−0.234700
$532$	2.15535e8	0.0620621
$533$	6.43707e7	0.0184138
$534$	5.99893e8	0.170482
$535$	−1.25837e10	−3.55278
$536$	−1.81540e9	−0.509209
$537$	−2.01707e9	−0.562095
$538$	2.29712e9	0.635984
$539$	4.38558e8	0.120633
$540$	−6.67200e8	−0.182338
$541$	1.56702e9	0.425486	0.212743	−	0.977108i	$-0.431760\pi$
$541$	1.56702e9	0.425486	0.212743	+	0.977108i	$0.431760\pi$
$542$	−4.04702e9	−1.09179
$543$	−1.35029e9	−0.361934
$544$	7.90408e8	0.210502
$545$	7.25946e9	1.92095
$546$	1.62771e8	0.0427960
$547$	−1.56165e8	−0.0407971	−0.0203986	−	0.999792i	$-0.506494\pi$
$547$	−1.56165e8	−0.0407971	−0.0203986	+	0.999792i	$0.506494\pi$
$548$	−1.34092e9	−0.348073
$549$	2.70066e8	0.0696573
$550$	6.03582e9	1.54692
$551$	−1.56960e9	−0.399722
$552$	4.98224e8	0.126077
$553$	−1.62043e9	−0.407467
$554$	2.85802e9	0.714137
$555$	−3.14161e9	−0.780057
$556$	−1.55296e9	−0.383177
$557$	3.69047e9	0.904875	0.452438	−	0.891796i	$-0.350554\pi$
$557$	3.69047e9	0.904875	0.452438	+	0.891796i	$0.350554\pi$
$558$	1.29906e9	0.316525
$559$	1.74549e8	0.0422646
$560$	7.44113e8	0.179053
$561$	−2.42775e9	−0.580543
$562$	−2.49019e9	−0.591773
$563$	−4.93440e9	−1.16535	−0.582673	−	0.812706i	$-0.697993\pi$
$563$	−4.93440e9	−1.16535	−0.582673	+	0.812706i	$0.697993\pi$
$564$	−1.12746e9	−0.264621
$565$	−1.18462e9	−0.276319
$566$	−2.76173e9	−0.640212
$567$	1.82284e8	0.0419961
$568$	1.79763e9	0.411605
$569$	−7.09618e9	−1.61485	−0.807424	−	0.589972i	$-0.799139\pi$
$569$	−7.09618e9	−1.61485	−0.807424	+	0.589972i	$0.799139\pi$
$570$	−1.12326e9	−0.254050
$571$	4.29669e9	0.965845	0.482922	−	0.875663i	$-0.339575\pi$
$571$	4.29669e9	0.965845	0.482922	+	0.875663i	$0.339575\pi$
$572$	−5.24142e8	−0.117102
$573$	−4.82630e9	−1.07170
$574$	−8.03975e7	−0.0177440
$575$	−7.29454e9	−1.60015
$576$	1.91103e8	0.0416667
$577$	7.52264e9	1.63025	0.815126	−	0.579284i	$-0.196668\pi$
$577$	7.52264e9	1.63025	0.815126	+	0.579284i	$0.196668\pi$
$578$	1.37201e9	0.295535
$579$	−6.79882e8	−0.145566
$580$	−5.41889e9	−1.15322
$581$	7.79296e8	0.164849
$582$	−8.35635e8	−0.175706
$583$	2.18640e9	0.456971
$584$	−3.09310e9	−0.642612
$585$	−8.48286e8	−0.175185
$586$	−5.62750e9	−1.15525
$587$	−6.87873e9	−1.40370	−0.701851	−	0.712324i	$-0.747643\pi$
$587$	−6.87873e9	−1.40370	−0.701851	+	0.712324i	$0.747643\pi$
$588$	−2.03297e8	−0.0412393
$589$	2.18703e9	0.441012
$590$	−4.70642e9	−0.943429
$591$	−3.33677e9	−0.664922
$592$	8.99837e8	0.178253
$593$	7.09887e9	1.39797	0.698985	−	0.715137i	$-0.253636\pi$
$593$	7.09887e9	1.39797	0.698985	+	0.715137i	$0.253636\pi$
$594$	−5.86976e8	−0.114913
$595$	4.38208e9	0.852847
$596$	2.83503e9	0.548523
$597$	−7.83051e8	−0.150619
$598$	6.33447e8	0.121131
$599$	6.05066e9	1.15029	0.575147	−	0.818050i	$-0.304945\pi$
$599$	6.05066e9	1.15029	0.575147	+	0.818050i	$0.304945\pi$
$600$	−2.79796e9	−0.528824
$601$	−2.45316e9	−0.460962	−0.230481	−	0.973077i	$-0.574030\pi$
$601$	−2.45316e9	−0.460962	−0.230481	+	0.973077i	$0.574030\pi$
$602$	−2.18008e8	−0.0407272
$603$	−2.58482e9	−0.480087
$604$	−3.63744e9	−0.671687
$605$	−2.96153e9	−0.543716
$606$	9.00851e8	0.164437
$607$	−9.44990e9	−1.71501	−0.857506	−	0.514475i	$-0.827987\pi$
$607$	−9.44990e9	−1.71501	−0.857506	+	0.514475i	$0.827987\pi$
$608$	3.21731e8	0.0580538
$609$	1.48048e9	0.265609
$610$	1.56970e9	0.280003
$611$	−1.43346e9	−0.254239
$612$	1.12541e9	0.198463
$613$	3.84994e9	0.675060	0.337530	−	0.941315i	$-0.390409\pi$
$613$	3.84994e9	0.675060	0.337530	+	0.941315i	$0.390409\pi$
$614$	2.91500e9	0.508216
$615$	4.18993e8	0.0726347
$616$	6.54641e8	0.112842
$617$	7.81668e9	1.33975	0.669876	−	0.742473i	$-0.266347\pi$
$617$	7.81668e9	1.33975	0.669876	+	0.742473i	$0.266347\pi$
$618$	−1.19825e9	−0.204215
$619$	4.99558e9	0.846582	0.423291	−	0.905994i	$-0.360875\pi$
$619$	4.99558e9	0.846582	0.423291	+	0.905994i	$0.360875\pi$
$620$	7.55049e9	1.27234
$621$	7.09385e8	0.118867
$622$	−8.36931e9	−1.39452
$623$	−9.52608e8	−0.157836
$624$	2.42971e8	0.0400320
$625$	1.90492e10	3.12103
$626$	4.10396e9	0.668641
$627$	−9.88203e8	−0.160107
$628$	4.98515e9	0.803193
$629$	5.29914e9	0.849040
$630$	1.05949e9	0.168812
$631$	3.39241e9	0.537533	0.268767	−	0.963205i	$-0.413384\pi$
$631$	3.39241e9	0.537533	0.268767	+	0.963205i	$0.413384\pi$
$632$	−2.41883e9	−0.381150
$633$	1.78918e9	0.280376
$634$	7.54747e9	1.17622
$635$	−4.98657e9	−0.772848
$636$	−1.01352e9	−0.156219
$637$	−2.58475e8	−0.0396214
$638$	−4.76732e9	−0.726779
$639$	2.55951e9	0.388065
$640$	1.11075e9	0.167488
$641$	8.25496e9	1.23798	0.618988	−	0.785401i	$-0.287543\pi$
$641$	8.25496e9	1.23798	0.618988	+	0.785401i	$0.287543\pi$
$642$	5.13187e9	0.765426
$643$	−3.80038e9	−0.563753	−0.281876	−	0.959451i	$-0.590957\pi$
$643$	−3.80038e9	−0.563753	−0.281876	+	0.959451i	$0.590957\pi$
$644$	−7.91161e8	−0.116725
$645$	1.13615e9	0.166716
$646$	1.89468e9	0.276516
$647$	−6.58053e9	−0.955204	−0.477602	−	0.878576i	$-0.658494\pi$
$647$	−6.58053e9	−0.955204	−0.477602	+	0.878576i	$0.658494\pi$
$648$	2.72098e8	0.0392837
$649$	−4.14053e9	−0.594565
$650$	−3.55736e9	−0.508078
$651$	−2.06286e9	−0.293046
$652$	−3.29248e9	−0.465218
$653$	−6.68693e9	−0.939790	−0.469895	−	0.882722i	$-0.655708\pi$
$653$	−6.68693e9	−0.939790	−0.469895	+	0.882722i	$0.655708\pi$
$654$	−2.96056e9	−0.413858
$655$	−8.61491e9	−1.19786
$656$	−1.20010e8	−0.0165980
$657$	−4.40404e9	−0.605861
$658$	1.79036e9	0.244991
$659$	8.02087e8	0.109175	0.0545874	−	0.998509i	$-0.482616\pi$
$659$	8.02087e8	0.109175	0.0545874	+	0.998509i	$0.482616\pi$
$660$	−3.41167e9	−0.461917
$661$	7.97403e9	1.07392	0.536961	−	0.843607i	$-0.319572\pi$
$661$	7.97403e9	1.07392	0.536961	+	0.843607i	$0.319572\pi$
$662$	−5.21631e9	−0.698812
$663$	1.43085e9	0.190677
$664$	1.16326e9	0.154202
$665$	1.78370e9	0.235205
$666$	1.28121e9	0.168059
$667$	5.76151e9	0.751788
$668$	1.54195e9	0.200148
$669$	−7.61438e9	−0.983203
$670$	−1.50237e10	−1.92981
$671$	1.38096e9	0.176463
$672$	−3.03464e8	−0.0385758
$673$	−1.27130e10	−1.60766	−0.803831	−	0.594857i	$-0.797209\pi$
$673$	−1.27130e10	−1.60766	−0.803831	+	0.594857i	$0.797209\pi$
$674$	−4.25110e9	−0.534800
$675$	−3.98381e9	−0.498580
$676$	3.08916e8	0.0384615
$677$	−5.15085e9	−0.637997	−0.318999	−	0.947755i	$-0.603347\pi$
$677$	−5.15085e9	−0.637997	−0.318999	+	0.947755i	$0.603347\pi$
$678$	4.83114e8	0.0595314
$679$	1.32696e9	0.162672
$680$	6.54118e9	0.797765
$681$	3.23474e9	0.392486
$682$	6.64263e9	0.801853
$683$	−1.06047e10	−1.27358	−0.636790	−	0.771037i	$-0.719738\pi$
$683$	−1.06047e10	−1.27358	−0.636790	+	0.771037i	$0.719738\pi$
$684$	4.58090e8	0.0547337
$685$	−1.10970e10	−1.31914
$686$	3.22829e8	0.0381802
$687$	−2.80694e8	−0.0330281
$688$	−3.25423e8	−0.0380968
$689$	−1.28860e9	−0.150090
$690$	4.12315e9	0.477812
$691$	−8.18703e9	−0.943959	−0.471979	−	0.881610i	$-0.656460\pi$
$691$	−8.18703e9	−0.943959	−0.471979	+	0.881610i	$0.656460\pi$
$692$	5.62264e9	0.645013
$693$	9.32096e8	0.106388
$694$	−3.74427e9	−0.425215
$695$	−1.28519e10	−1.45218
$696$	2.20993e9	0.248454
$697$	−7.06741e8	−0.0790579
$698$	4.69934e8	0.0523050
$699$	4.76467e9	0.527670
$700$	4.44305e9	0.489596
$701$	−1.01784e10	−1.11601	−0.558005	−	0.829838i	$-0.688433\pi$
$701$	−1.01784e10	−1.11601	−0.558005	+	0.829838i	$0.688433\pi$
$702$	3.45948e8	0.0377426
$703$	2.15698e9	0.234155
$704$	9.77190e8	0.105554
$705$	−9.33050e9	−1.00287
$706$	5.01107e9	0.535937
$707$	−1.43052e9	−0.152239
$708$	1.91938e9	0.203256
$709$	6.47872e9	0.682696	0.341348	−	0.939937i	$-0.389117\pi$
$709$	6.47872e9	0.682696	0.341348	+	0.939937i	$0.389117\pi$
$710$	1.48766e10	1.55991
$711$	−3.44400e9	−0.359352
$712$	−1.42197e9	−0.147642
$713$	−8.02789e9	−0.829446
$714$	−1.78710e9	−0.183741
$715$	−4.33764e9	−0.443795
$716$	4.78119e9	0.486789
$717$	−6.71138e9	−0.679978
$718$	−5.01566e9	−0.505700
$719$	2.52939e9	0.253784	0.126892	−	0.991917i	$-0.459500\pi$
$719$	2.52939e9	0.253784	0.126892	+	0.991917i	$0.459500\pi$
$720$	1.58151e9	0.157910
$721$	1.90278e9	0.189067
$722$	−6.37976e9	−0.630847
$723$	9.86055e8	0.0970325
$724$	3.20070e9	0.313444
$725$	−3.23558e10	−3.15333
$726$	1.20777e9	0.117140
$727$	−1.55617e10	−1.50205	−0.751027	−	0.660272i	$-0.770441\pi$
$727$	−1.55617e10	−1.50205	−0.751027	+	0.660272i	$0.770441\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−2.55976e10	−2.43539
$731$	−1.91642e9	−0.181459
$732$	−6.40156e8	−0.0603250
$733$	−9.41674e9	−0.883155	−0.441577	−	0.897223i	$-0.645581\pi$
$733$	−9.41674e9	−0.883155	−0.441577	+	0.897223i	$0.645581\pi$
$734$	−1.51010e9	−0.140951
$735$	−1.68243e9	−0.156290
$736$	−1.18097e9	−0.109186
$737$	−1.32173e10	−1.21620
$738$	−1.70874e8	−0.0156487
$739$	2.34008e8	0.0213292	0.0106646	−	0.999943i	$-0.496605\pi$
$739$	2.34008e8	0.0213292	0.0106646	+	0.999943i	$0.496605\pi$
$740$	7.44677e9	0.675550
$741$	5.82421e8	0.0525864
$742$	1.60944e9	0.144631
$743$	1.99362e10	1.78312	0.891561	−	0.452901i	$-0.149611\pi$
$743$	1.99362e10	1.78312	0.891561	+	0.452901i	$0.149611\pi$
$744$	−3.07925e9	−0.274119
$745$	2.34618e10	2.07881
$746$	−4.30859e9	−0.379970
$747$	1.65629e9	0.145383
$748$	5.75467e9	0.502765
$749$	−8.14923e9	−0.708647
$750$	−1.42173e10	−1.23056
$751$	1.01576e10	0.875091	0.437545	−	0.899196i	$-0.355848\pi$
$751$	1.01576e10	0.875091	0.437545	+	0.899196i	$0.355848\pi$
$752$	2.67249e9	0.229168
$753$	−9.28001e9	−0.792074
$754$	2.80974e9	0.238707
$755$	−3.01024e10	−2.54558
$756$	−4.32081e8	−0.0363696
$757$	−4.40537e9	−0.369102	−0.184551	−	0.982823i	$-0.559083\pi$
$757$	−4.40537e9	−0.369102	−0.184551	+	0.982823i	$0.559083\pi$
$758$	−1.13345e10	−0.945276
$759$	3.62738e9	0.301125
$760$	2.66255e9	0.220014
$761$	−2.28127e9	−0.187642	−0.0938210	−	0.995589i	$-0.529908\pi$
$761$	−2.28127e9	−0.187642	−0.0938210	+	0.995589i	$0.529908\pi$
$762$	2.03363e9	0.166506
$763$	4.70125e9	0.383158
$764$	1.14401e10	0.928119
$765$	9.31352e9	0.752140
$766$	−1.69405e9	−0.136184
$767$	2.44032e9	0.195282
$768$	−4.52985e8	−0.0360844
$769$	−1.11493e10	−0.884112	−0.442056	−	0.896987i	$-0.645751\pi$
$769$	−1.11493e10	−0.884112	−0.442056	+	0.896987i	$0.645751\pi$
$770$	5.41761e9	0.427652
$771$	7.35182e9	0.577703
$772$	1.61157e9	0.126063
$773$	−2.11163e10	−1.64433	−0.822167	−	0.569247i	$-0.807235\pi$
$773$	−2.11163e10	−1.64433	−0.822167	+	0.569247i	$0.807235\pi$
$774$	−4.63346e8	−0.0359180
$775$	4.50835e10	3.47906
$776$	1.98076e9	0.152166
$777$	−2.03452e9	−0.155592
$778$	1.57786e10	1.20127
$779$	−2.87675e8	−0.0218032
$780$	2.01075e9	0.151715
$781$	1.30879e10	0.983084
$782$	−6.95476e9	−0.520066
$783$	3.14657e9	0.234245
$784$	4.81890e8	0.0357143
$785$	4.12556e10	3.04396
$786$	3.51334e9	0.258072
$787$	−6.54202e9	−0.478410	−0.239205	−	0.970969i	$-0.576887\pi$
$787$	−6.54202e9	−0.478410	−0.239205	+	0.970969i	$0.576887\pi$
$788$	7.90939e9	0.575839
$789$	−9.58681e9	−0.694872
$790$	−2.00175e10	−1.44449
$791$	−7.67167e8	−0.0551153
$792$	1.39135e9	0.0995173
$793$	−8.13903e8	−0.0579584
$794$	−1.20554e10	−0.854693
$795$	−8.38761e9	−0.592043
$796$	1.85612e9	0.130440
$797$	9.86813e9	0.690447	0.345224	−	0.938520i	$-0.387803\pi$
$797$	9.86813e9	0.690447	0.345224	+	0.938520i	$0.387803\pi$
$798$	−7.27430e8	−0.0506735
$799$	1.57383e10	1.09155
$800$	6.63219e9	0.457975
$801$	−2.02464e9	−0.139198
$802$	1.17972e10	0.807549
$803$	−2.25197e10	−1.53483
$804$	6.12698e9	0.415767
$805$	−6.54741e9	−0.442368
$806$	−3.91499e9	−0.263365
$807$	−7.75279e9	−0.519279
$808$	−2.13535e9	−0.142406
$809$	−2.46408e10	−1.63619	−0.818097	−	0.575081i	$-0.804971\pi$
$809$	−2.46408e10	−1.63619	−0.818097	+	0.575081i	$0.804971\pi$
$810$	2.25180e9	0.148879
$811$	2.37028e9	0.156037	0.0780184	−	0.996952i	$-0.475141\pi$
$811$	2.37028e9	0.156037	0.0780184	+	0.996952i	$0.475141\pi$
$812$	−3.50929e9	−0.230024
$813$	1.36587e10	0.891439
$814$	6.55138e9	0.425743
$815$	−2.72476e10	−1.76310
$816$	−2.66763e9	−0.171874
$817$	−7.80066e8	−0.0500442
$818$	5.52011e9	0.352623
$819$	−5.49353e8	−0.0349428
$820$	−9.93169e8	−0.0629035
$821$	−1.17171e10	−0.738956	−0.369478	−	0.929239i	$-0.620464\pi$
$821$	−1.17171e10	−0.738956	−0.369478	+	0.929239i	$0.620464\pi$
$822$	4.52560e9	0.284200
$823$	1.94300e10	1.21499	0.607496	−	0.794323i	$-0.292174\pi$
$823$	1.94300e10	1.21499	0.607496	+	0.794323i	$0.292174\pi$
$824$	2.84030e9	0.176856
$825$	−2.03709e10	−1.26305
$826$	−3.04790e9	−0.188179
$827$	−1.04477e10	−0.642319	−0.321159	−	0.947025i	$-0.604073\pi$
$827$	−1.04477e10	−0.642319	−0.321159	+	0.947025i	$0.604073\pi$
$828$	−1.68150e9	−0.102942
$829$	8.73946e9	0.532775	0.266387	−	0.963866i	$-0.414170\pi$
$829$	8.73946e9	0.532775	0.266387	+	0.963866i	$0.414170\pi$
$830$	9.62682e9	0.584399
$831$	−9.64582e9	−0.583090
$832$	−5.75930e8	−0.0346688
$833$	2.83785e9	0.170111
$834$	5.24126e9	0.312863
$835$	1.27607e10	0.758527
$836$	2.34241e9	0.138657
$837$	−4.38432e9	−0.258442
$838$	1.98401e10	1.16464
$839$	9.85221e9	0.575926	0.287963	−	0.957642i	$-0.407022\pi$
$839$	9.85221e9	0.575926	0.287963	+	0.957642i	$0.407022\pi$
$840$	−2.51138e9	−0.146196
$841$	8.30601e9	0.481511
$842$	5.11870e9	0.295506
$843$	8.40439e9	0.483181
$844$	−4.24102e9	−0.242813
$845$	2.55649e9	0.145763
$846$	3.80517e9	0.216062
$847$	−1.91790e9	−0.108451
$848$	2.40242e9	0.135290
$849$	9.32084e9	0.522731
$850$	3.90570e10	2.18139
$851$	−7.91761e9	−0.440393
$852$	−6.06699e9	−0.336074
$853$	−2.69371e10	−1.48604	−0.743019	−	0.669270i	$-0.766607\pi$
$853$	−2.69371e10	−1.48604	−0.743019	+	0.669270i	$0.766607\pi$
$854$	1.01654e9	0.0558501
$855$	3.79101e9	0.207431
$856$	−1.21644e10	−0.662879
$857$	−2.42559e10	−1.31639	−0.658194	−	0.752848i	$-0.728680\pi$
$857$	−2.42559e10	−1.31639	−0.658194	+	0.752848i	$0.728680\pi$
$858$	1.76898e9	0.0956131
$859$	−1.59346e10	−0.857761	−0.428880	−	0.903361i	$-0.641092\pi$
$859$	−1.59346e10	−0.857761	−0.428880	+	0.903361i	$0.641092\pi$
$860$	−2.69310e9	−0.144380
$861$	2.71342e8	0.0144879
$862$	−7.22814e9	−0.384371
$863$	1.82541e10	0.966767	0.483384	−	0.875409i	$-0.339408\pi$
$863$	1.82541e10	0.966767	0.483384	+	0.875409i	$0.339408\pi$
$864$	−6.44973e8	−0.0340207
$865$	4.65312e10	2.44449
$866$	5.48234e9	0.286849
$867$	−4.63052e9	−0.241303
$868$	4.88973e9	0.253785
$869$	−1.76107e10	−0.910345
$870$	1.82887e10	0.941600
$871$	7.78992e9	0.399456
$872$	7.01761e9	0.358411
$873$	2.82027e9	0.143463
$874$	−2.83090e9	−0.143428
$875$	2.25765e10	1.13928
$876$	1.04392e10	0.524691
$877$	2.98698e10	1.49532	0.747660	−	0.664082i	$-0.231177\pi$
$877$	2.98698e10	1.49532	0.747660	+	0.664082i	$0.231177\pi$
$878$	5.37217e9	0.267867
$879$	1.89928e10	0.943254
$880$	8.08693e9	0.400032
$881$	−3.44603e10	−1.69787	−0.848933	−	0.528501i	$-0.822754\pi$
$881$	−3.44603e10	−1.69787	−0.848933	+	0.528501i	$0.822754\pi$
$882$	6.86129e8	0.0336718
$883$	2.69143e10	1.31559	0.657794	−	0.753197i	$-0.271490\pi$
$883$	2.69143e10	1.31559	0.657794	+	0.753197i	$0.271490\pi$
$884$	−3.39165e9	−0.165131
$885$	1.58842e10	0.770306
$886$	−1.78638e10	−0.862889
$887$	−3.92756e10	−1.88969	−0.944844	−	0.327522i	$-0.893787\pi$
$887$	−3.92756e10	−1.88969	−0.944844	+	0.327522i	$0.893787\pi$
$888$	−3.03695e9	−0.145543
$889$	−3.22932e9	−0.154154
$890$	−1.17678e10	−0.559538
$891$	1.98104e9	0.0938258
$892$	1.80489e10	0.851479
$893$	6.40619e9	0.301037
$894$	−9.56821e9	−0.447867
$895$	3.95677e10	1.84485
$896$	7.19323e8	0.0334077
$897$	−2.13789e9	−0.0989033
$898$	−2.62107e10	−1.20784
$899$	−3.56087e10	−1.63455
$900$	9.44310e9	0.431783
$901$	1.41479e10	0.644398
$902$	−8.73751e8	−0.0396428
$903$	7.35777e8	0.0332536
$904$	−1.14516e9	−0.0515557
$905$	2.64880e10	1.18790
$906$	1.22764e10	0.548430
$907$	7.28341e9	0.324123	0.162061	−	0.986781i	$-0.448186\pi$
$907$	7.28341e9	0.324123	0.162061	+	0.986781i	$0.448186\pi$
$908$	−7.66752e9	−0.339903
$909$	−3.04037e9	−0.134262
$910$	−3.19300e9	−0.140460
$911$	3.07735e10	1.34854	0.674269	−	0.738486i	$-0.264459\pi$
$911$	3.07735e10	1.34854	0.674269	+	0.738486i	$0.264459\pi$
$912$	−1.08584e9	−0.0474007
$913$	8.46930e9	0.368298
$914$	2.59586e10	1.12453
$915$	−5.29774e9	−0.228621
$916$	6.65348e8	0.0286032
$917$	−5.57905e9	−0.238928
$918$	−3.79824e9	−0.162044
$919$	1.31495e10	0.558863	0.279431	−	0.960166i	$-0.409854\pi$
$919$	1.31495e10	0.558863	0.279431	+	0.960166i	$0.409854\pi$
$920$	−9.77339e9	−0.413797
$921$	−9.83811e9	−0.414957
$922$	1.79988e10	0.756286
$923$	−7.71365e9	−0.322890
$924$	−2.20941e9	−0.0921351
$925$	4.44642e10	1.84720
$926$	−1.49997e10	−0.620790
$927$	4.04410e9	0.166741
$928$	−5.23836e9	−0.215168
$929$	5.08773e9	0.208195	0.104097	−	0.994567i	$-0.466805\pi$
$929$	5.08773e9	0.208195	0.104097	+	0.994567i	$0.466805\pi$
$930$	−2.54829e10	−1.03886
$931$	1.15513e9	0.0469146
$932$	−1.12940e10	−0.456976
$933$	2.82464e10	1.13862
$934$	−1.18743e10	−0.476862
$935$	4.76239e10	1.90539
$936$	−8.20026e8	−0.0326860
$937$	−2.49041e10	−0.988968	−0.494484	−	0.869187i	$-0.664643\pi$
$937$	−2.49041e10	−0.988968	−0.494484	+	0.869187i	$0.664643\pi$
$938$	−9.72942e9	−0.384926
$939$	−1.38509e10	−0.545943
$940$	2.21168e10	0.868508
$941$	−4.73818e9	−0.185374	−0.0926868	−	0.995695i	$-0.529546\pi$
$941$	−4.73818e9	−0.185374	−0.0926868	+	0.995695i	$0.529546\pi$
$942$	−1.68249e10	−0.655804
$943$	1.05596e9	0.0410070
$944$	−4.54963e9	−0.176025
$945$	−3.57577e9	−0.137835
$946$	−2.36928e9	−0.0909910
$947$	3.83034e10	1.46559	0.732794	−	0.680450i	$-0.238216\pi$
$947$	3.83034e10	1.46559	0.732794	+	0.680450i	$0.238216\pi$
$948$	8.16357e9	0.311208
$949$	1.32725e10	0.504107
$950$	1.58979e10	0.601600
$951$	−2.54727e10	−0.960380
$952$	4.23609e9	0.159124
$953$	2.03440e10	0.761397	0.380698	−	0.924699i	$-0.375684\pi$
$953$	2.03440e10	0.761397	0.380698	+	0.924699i	$0.375684\pi$
$954$	3.42064e9	0.127552
$955$	9.46749e10	3.51741
$956$	1.59085e10	0.588878
$957$	1.60897e10	0.593412
$958$	−9.30512e9	−0.341934
$959$	−7.18648e9	−0.263118
$960$	−3.74877e9	−0.136754
$961$	2.21034e10	0.803391
$962$	−3.86121e9	−0.139833
$963$	−1.73201e10	−0.624968
$964$	−2.33732e9	−0.0840326
$965$	1.33369e10	0.477759
$966$	2.67017e9	0.0953056
$967$	1.63326e10	0.580848	0.290424	−	0.956898i	$-0.406204\pi$
$967$	1.63326e10	0.580848	0.290424	+	0.956898i	$0.406204\pi$
$968$	−2.86287e9	−0.101447
$969$	−6.39453e9	−0.225775
$970$	1.63922e10	0.576682
$971$	−2.46533e10	−0.864188	−0.432094	−	0.901829i	$-0.642225\pi$
$971$	−2.46533e10	−0.864188	−0.432094	+	0.901829i	$0.642225\pi$
$972$	−9.18330e8	−0.0320750
$973$	−8.32292e9	−0.289655
$974$	8.37648e9	0.290473
$975$	1.20061e10	0.414844
$976$	1.51741e9	0.0522430
$977$	2.98530e10	1.02413	0.512067	−	0.858946i	$-0.328880\pi$
$977$	2.98530e10	1.02413	0.512067	+	0.858946i	$0.328880\pi$
$978$	1.11121e10	0.379849
$979$	−1.03528e10	−0.352631
$980$	3.98798e9	0.135351
$981$	9.99187e9	0.337913
$982$	1.95853e9	0.0659995
$983$	−2.65165e10	−0.890389	−0.445194	−	0.895434i	$-0.646865\pi$
$983$	−2.65165e10	−0.890389	−0.445194	+	0.895434i	$0.646865\pi$
$984$	4.05035e8	0.0135522
$985$	6.54557e10	2.18233
$986$	−3.08487e10	−1.02487
$987$	−6.04247e9	−0.200034
$988$	−1.38055e9	−0.0455411
$989$	2.86338e9	0.0941221
$990$	1.15144e10	0.377153
$991$	−3.95353e10	−1.29041	−0.645205	−	0.764010i	$-0.723228\pi$
$991$	−3.95353e10	−1.29041	−0.645205	+	0.764010i	$0.723228\pi$
$992$	7.29896e9	0.237394
$993$	1.76051e10	0.570578
$994$	9.63416e9	0.311144
$995$	1.53607e10	0.494345
$996$	−3.92602e9	−0.125905
$997$	2.19110e10	0.700211	0.350105	−	0.936710i	$-0.386146\pi$
$997$	2.19110e10	0.700211	0.350105	+	0.936710i	$0.386146\pi$
$998$	−8.87167e9	−0.282520
$999$	−4.32409e9	−0.137219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.q.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.q.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +529.645 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +529.645 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +4237.16 q^{10} +3727.68 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -14300.4 q^{15} +4096.00 q^{16} +24121.3 q^{17} +5832.00 q^{18} +9818.46 q^{19} +33897.3 q^{20} -9261.00 q^{21} +29821.5 q^{22} -36040.5 q^{23} -13824.0 q^{24} +202398. q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} -159862. q^{29} -114403. q^{30} +222746. q^{31} +32768.0 q^{32} -100647. q^{33} +192971. q^{34} +181668. q^{35} +46656.0 q^{36} +219687. q^{37} +78547.7 q^{38} +59319.0 q^{39} +271178. q^{40} -29299.4 q^{41} -74088.0 q^{42} -79448.9 q^{43} +238572. q^{44} +386111. q^{45} -288324. q^{46} +652464. q^{47} -110592. q^{48} +117649. q^{49} +1.61919e6 q^{50} -651276. q^{51} -140608. q^{52} +586529. q^{53} -157464. q^{54} +1.97435e6 q^{55} +175616. q^{56} -265098. q^{57} -1.27890e6 q^{58} -1.11075e6 q^{59} -915226. q^{60} +370461. q^{61} +1.78197e6 q^{62} +250047. q^{63} +262144. q^{64} -1.16363e6 q^{65} -805180. q^{66} -3.54571e6 q^{67} +1.54377e6 q^{68} +973093. q^{69} +1.45334e6 q^{70} +3.51099e6 q^{71} +373248. q^{72} -6.04121e6 q^{73} +1.75749e6 q^{74} -5.46476e6 q^{75} +628381. q^{76} +1.27860e6 q^{77} +474552. q^{78} -4.72429e6 q^{79} +2.16942e6 q^{80} +531441. q^{81} -234395. q^{82} +2.27200e6 q^{83} -592704. q^{84} +1.27757e7 q^{85} -635591. q^{86} +4.31628e6 q^{87} +1.90857e6 q^{88} -2.77728e6 q^{89} +3.08889e6 q^{90} -753571. q^{91} -2.30659e6 q^{92} -6.01415e6 q^{93} +5.21971e6 q^{94} +5.20029e6 q^{95} -884736. q^{96} +3.86868e6 q^{97} +941192. q^{98} +2.71748e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 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

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