LMFDB - Embedded newform 546.8.a.r.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$170.562223914$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 264981x^{4} + 17519669x^{3} + 15113237808x^{2} - 1787613752904x - 21984668630064 $ x^6 - x^5 - 264981x^4 + 17519669x^3 + 15113237808x^2 - 1787613752904x - 21984668630064
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-298.282$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +332.282 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +332.282 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2658.26 q^{10} +4538.16 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -8971.62 q^{15} +4096.00 q^{16} -1683.55 q^{17} +5832.00 q^{18} +43035.4 q^{19} +21266.1 q^{20} +9261.00 q^{21} +36305.3 q^{22} +80014.0 q^{23} -13824.0 q^{24} +32286.5 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} -175048. q^{29} -71773.0 q^{30} -177686. q^{31} +32768.0 q^{32} -122530. q^{33} -13468.4 q^{34} -113973. q^{35} +46656.0 q^{36} +207013. q^{37} +344283. q^{38} -59319.0 q^{39} +170129. q^{40} +418774. q^{41} +74088.0 q^{42} +511110. q^{43} +290443. q^{44} +242234. q^{45} +640112. q^{46} -154485. q^{47} -110592. q^{48} +117649. q^{49} +258292. q^{50} +45456.0 q^{51} +140608. q^{52} -58699.1 q^{53} -157464. q^{54} +1.50795e6 q^{55} -175616. q^{56} -1.16196e6 q^{57} -1.40038e6 q^{58} +249612. q^{59} -574184. q^{60} -926699. q^{61} -1.42149e6 q^{62} -250047. q^{63} +262144. q^{64} +730024. q^{65} -980243. q^{66} -3.22459e6 q^{67} -107747. q^{68} -2.16038e6 q^{69} -911783. q^{70} -720569. q^{71} +373248. q^{72} +6.11222e6 q^{73} +1.65610e6 q^{74} -871736. q^{75} +2.75427e6 q^{76} -1.55659e6 q^{77} -474552. q^{78} -1.62450e6 q^{79} +1.36103e6 q^{80} +531441. q^{81} +3.35020e6 q^{82} +8.58284e6 q^{83} +592704. q^{84} -559415. q^{85} +4.08888e6 q^{86} +4.72629e6 q^{87} +2.32354e6 q^{88} -7.22166e6 q^{89} +1.93787e6 q^{90} -753571. q^{91} +5.12089e6 q^{92} +4.79753e6 q^{93} -1.23588e6 q^{94} +1.42999e7 q^{95} -884736. q^{96} -6.97736e6 q^{97} +941192. q^{98} +3.30832e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 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 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 1624 q^{10} - 2690 q^{11} - 10368 q^{12} + 13182 q^{13} - 16464 q^{14} - 5481 q^{15} + 24576 q^{16} + 2910 q^{17} + 34992 q^{18} - 13055 q^{19} + 12992 q^{20} + 55566 q^{21} - 21520 q^{22} + 11581 q^{23} - 82944 q^{24} + 68081 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} - 92335 q^{29} - 43848 q^{30} - 83081 q^{31} + 196608 q^{32} + 72630 q^{33} + 23280 q^{34} - 69629 q^{35} + 279936 q^{36} - 265114 q^{37} - 104440 q^{38} - 355914 q^{39} + 103936 q^{40} - 367468 q^{41} + 444528 q^{42} + 454955 q^{43} - 172160 q^{44} + 147987 q^{45} + 92648 q^{46} + 733973 q^{47} - 663552 q^{48} + 705894 q^{49} + 544648 q^{50} - 78570 q^{51} + 843648 q^{52} - 1577379 q^{53} - 944784 q^{54} + 2231118 q^{55} - 1053696 q^{56} + 352485 q^{57} - 738680 q^{58} + 2062708 q^{59} - 350784 q^{60} - 271270 q^{61} - 664648 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 445991 q^{65} + 581040 q^{66} - 758674 q^{67} + 186240 q^{68} - 312687 q^{69} - 557032 q^{70} - 6138216 q^{71} + 2239488 q^{72} + 6361979 q^{73} - 2120912 q^{74} - 1838187 q^{75} - 835520 q^{76} + 922670 q^{77} - 2847312 q^{78} - 899781 q^{79} + 831488 q^{80} + 3188646 q^{81} - 2939744 q^{82} + 3313561 q^{83} + 3556224 q^{84} + 5307940 q^{85} + 3639640 q^{86} + 2493045 q^{87} - 1377280 q^{88} + 11210703 q^{89} + 1183896 q^{90} - 4521426 q^{91} + 741184 q^{92} + 2243187 q^{93} + 5871784 q^{94} + 12912395 q^{95} - 5308416 q^{96} + 28682643 q^{97} + 5647152 q^{98} - 1961010 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 1624 * q^10 - 2690 * q^11 - 10368 * q^12 + 13182 * q^13 - 16464 * q^14 - 5481 * q^15 + 24576 * q^16 + 2910 * q^17 + 34992 * q^18 - 13055 * q^19 + 12992 * q^20 + 55566 * q^21 - 21520 * q^22 + 11581 * q^23 - 82944 * q^24 + 68081 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 - 92335 * q^29 - 43848 * q^30 - 83081 * q^31 + 196608 * q^32 + 72630 * q^33 + 23280 * q^34 - 69629 * q^35 + 279936 * q^36 - 265114 * q^37 - 104440 * q^38 - 355914 * q^39 + 103936 * q^40 - 367468 * q^41 + 444528 * q^42 + 454955 * q^43 - 172160 * q^44 + 147987 * q^45 + 92648 * q^46 + 733973 * q^47 - 663552 * q^48 + 705894 * q^49 + 544648 * q^50 - 78570 * q^51 + 843648 * q^52 - 1577379 * q^53 - 944784 * q^54 + 2231118 * q^55 - 1053696 * q^56 + 352485 * q^57 - 738680 * q^58 + 2062708 * q^59 - 350784 * q^60 - 271270 * q^61 - 664648 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 445991 * q^65 + 581040 * q^66 - 758674 * q^67 + 186240 * q^68 - 312687 * q^69 - 557032 * q^70 - 6138216 * q^71 + 2239488 * q^72 + 6361979 * q^73 - 2120912 * q^74 - 1838187 * q^75 - 835520 * q^76 + 922670 * q^77 - 2847312 * q^78 - 899781 * q^79 + 831488 * q^80 + 3188646 * q^81 - 2939744 * q^82 + 3313561 * q^83 + 3556224 * q^84 + 5307940 * q^85 + 3639640 * q^86 + 2493045 * q^87 - 1377280 * q^88 + 11210703 * q^89 + 1183896 * q^90 - 4521426 * q^91 + 741184 * q^92 + 2243187 * q^93 + 5871784 * q^94 + 12912395 * q^95 - 5308416 * q^96 + 28682643 * q^97 + 5647152 * q^98 - 1961010 * 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
$5$	332.282	1.18881	0.594405	−	0.804166i	$-0.297388\pi$
$5$	332.282	1.18881	0.594405	+	0.804166i	$0.297388\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	2658.26	0.840615
$11$	4538.16	1.02803	0.514015	−	0.857781i	$-0.328158\pi$
$11$	4538.16	1.02803	0.514015	+	0.857781i	$0.328158\pi$
$12$	−1728.00	−0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−2744.00	−0.267261
$15$	−8971.62	−0.686359
$16$	4096.00	0.250000
$17$	−1683.55	−0.0831105	−0.0415552	−	0.999136i	$-0.513231\pi$
$17$	−1683.55	−0.0831105	−0.0415552	+	0.999136i	$0.513231\pi$
$18$	5832.00	0.235702
$19$	43035.4	1.43942	0.719712	−	0.694273i	$-0.244274\pi$
$19$	43035.4	1.43942	0.719712	+	0.694273i	$0.244274\pi$
$20$	21266.1	0.594405
$21$	9261.00	0.218218
$22$	36305.3	0.726927
$23$	80014.0	1.37126	0.685628	−	0.727952i	$-0.259528\pi$
$23$	80014.0	1.37126	0.685628	+	0.727952i	$0.259528\pi$
$24$	−13824.0	−0.204124
$25$	32286.5	0.413267
$26$	17576.0	0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	−175048.	−1.33279	−0.666397	−	0.745597i	$-0.732165\pi$
$29$	−175048.	−1.33279	−0.666397	+	0.745597i	$0.732165\pi$
$30$	−71773.0	−0.485329
$31$	−177686.	−1.07124	−0.535622	−	0.844458i	$-0.679923\pi$
$31$	−177686.	−1.07124	−0.535622	+	0.844458i	$0.679923\pi$
$32$	32768.0	0.176777
$33$	−122530.	−0.593533
$34$	−13468.4	−0.0587680
$35$	−113973.	−0.449328
$36$	46656.0	0.166667
$37$	207013.	0.671880	0.335940	−	0.941883i	$-0.390946\pi$
$37$	207013.	0.671880	0.335940	+	0.941883i	$0.390946\pi$
$38$	344283.	1.01783
$39$	−59319.0	−0.160128
$40$	170129.	0.420308
$41$	418774.	0.948935	0.474468	−	0.880273i	$-0.342641\pi$
$41$	418774.	0.948935	0.474468	+	0.880273i	$0.342641\pi$
$42$	74088.0	0.154303
$43$	511110.	0.980336	0.490168	−	0.871628i	$-0.336935\pi$
$43$	511110.	0.980336	0.490168	+	0.871628i	$0.336935\pi$
$44$	290443.	0.514015
$45$	242234.	0.396270
$46$	640112.	0.969624
$47$	−154485.	−0.217042	−0.108521	−	0.994094i	$-0.534612\pi$
$47$	−154485.	−0.217042	−0.108521	+	0.994094i	$0.534612\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	258292.	0.292224
$51$	45456.0	0.0479839
$52$	140608.	0.138675
$53$	−58699.1	−0.0541584	−0.0270792	−	0.999633i	$-0.508621\pi$
$53$	−58699.1	−0.0541584	−0.0270792	+	0.999633i	$0.508621\pi$
$54$	−157464.	−0.136083
$55$	1.50795e6	1.22213
$56$	−175616.	−0.133631
$57$	−1.16196e6	−0.831051
$58$	−1.40038e6	−0.942428
$59$	249612.	0.158228	0.0791140	−	0.996866i	$-0.474791\pi$
$59$	249612.	0.158228	0.0791140	+	0.996866i	$0.474791\pi$
$60$	−574184.	−0.343180
$61$	−926699.	−0.522738	−0.261369	−	0.965239i	$-0.584174\pi$
$61$	−926699.	−0.522738	−0.261369	+	0.965239i	$0.584174\pi$
$62$	−1.42149e6	−0.757484
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	730024.	0.329716
$66$	−980243.	−0.419692
$67$	−3.22459e6	−1.30982	−0.654912	−	0.755705i	$-0.727294\pi$
$67$	−3.22459e6	−1.30982	−0.654912	+	0.755705i	$0.727294\pi$
$68$	−107747.	−0.0415552
$69$	−2.16038e6	−0.791695
$70$	−911783.	−0.317723
$71$	−720569.	−0.238930	−0.119465	−	0.992838i	$-0.538118\pi$
$71$	−720569.	−0.238930	−0.119465	+	0.992838i	$0.538118\pi$
$72$	373248.	0.117851
$73$	6.11222e6	1.83895	0.919474	−	0.393152i	$-0.128615\pi$
$73$	6.11222e6	1.83895	0.919474	+	0.393152i	$0.128615\pi$
$74$	1.65610e6	0.475091
$75$	−871736.	−0.238600
$76$	2.75427e6	0.719712
$77$	−1.55659e6	−0.388559
$78$	−474552.	−0.113228
$79$	−1.62450e6	−0.370702	−0.185351	−	0.982672i	$-0.559342\pi$
$79$	−1.62450e6	−0.370702	−0.185351	+	0.982672i	$0.559342\pi$
$80$	1.36103e6	0.297202
$81$	531441.	0.111111
$82$	3.35020e6	0.670999
$83$	8.58284e6	1.64762	0.823811	−	0.566864i	$-0.191844\pi$
$83$	8.58284e6	1.64762	0.823811	+	0.566864i	$0.191844\pi$
$84$	592704.	0.109109
$85$	−559415.	−0.0988025
$86$	4.08888e6	0.693202
$87$	4.72629e6	0.769489
$88$	2.32354e6	0.363464
$89$	−7.22166e6	−1.08586	−0.542928	−	0.839780i	$-0.682684\pi$
$89$	−7.22166e6	−1.08586	−0.542928	+	0.839780i	$0.682684\pi$
$90$	1.93787e6	0.280205
$91$	−753571.	−0.104828
$92$	5.12089e6	0.685628
$93$	4.79753e6	0.618483
$94$	−1.23588e6	−0.153472
$95$	1.42999e7	1.71120
$96$	−884736.	−0.102062
$97$	−6.97736e6	−0.776230	−0.388115	−	0.921611i	$-0.626874\pi$
$97$	−6.97736e6	−0.776230	−0.388115	+	0.921611i	$0.626874\pi$
$98$	941192.	0.101015
$99$	3.30832e6	0.342677
$100$	2.06634e6	0.206634
$101$	−430774.	−0.0416030	−0.0208015	−	0.999784i	$-0.506622\pi$
$101$	−430774.	−0.0416030	−0.0208015	+	0.999784i	$0.506622\pi$
$102$	363648.	0.0339297
$103$	−1.71937e7	−1.55039	−0.775193	−	0.631724i	$-0.782347\pi$
$103$	−1.71937e7	−1.55039	−0.775193	+	0.631724i	$0.782347\pi$
$104$	1.12486e6	0.0980581
$105$	3.07727e6	0.259419
$106$	−469593.	−0.0382958
$107$	−7.23378e6	−0.570850	−0.285425	−	0.958401i	$-0.592135\pi$
$107$	−7.23378e6	−0.570850	−0.285425	+	0.958401i	$0.592135\pi$
$108$	−1.25971e6	−0.0962250
$109$	531822.	0.0393345	0.0196673	−	0.999807i	$-0.493739\pi$
$109$	531822.	0.0393345	0.0196673	+	0.999807i	$0.493739\pi$
$110$	1.20636e7	0.864178
$111$	−5.58935e6	−0.387910
$112$	−1.40493e6	−0.0944911
$113$	1.31514e7	0.857426	0.428713	−	0.903441i	$-0.358967\pi$
$113$	1.31514e7	0.857426	0.428713	+	0.903441i	$0.358967\pi$
$114$	−9.29565e6	−0.587642
$115$	2.65872e7	1.63016
$116$	−1.12030e7	−0.666397
$117$	1.60161e6	0.0924500
$118$	1.99689e6	0.111884
$119$	577459.	0.0314128
$120$	−4.59347e6	−0.242665
$121$	1.10776e6	0.0568458
$122$	−7.41359e6	−0.369632
$123$	−1.13069e7	−0.547868
$124$	−1.13719e7	−0.535622
$125$	−1.52313e7	−0.697513
$126$	−2.00038e6	−0.0890871
$127$	−414009.	−0.0179348	−0.00896740	−	0.999960i	$-0.502854\pi$
$127$	−414009.	−0.0179348	−0.00896740	+	0.999960i	$0.502854\pi$
$128$	2.09715e6	0.0883883
$129$	−1.38000e7	−0.565997
$130$	5.84019e6	0.233145
$131$	4.64364e7	1.80472	0.902358	−	0.430988i	$-0.141835\pi$
$131$	4.64364e7	1.80472	0.902358	+	0.430988i	$0.141835\pi$
$132$	−7.84195e6	−0.296767
$133$	−1.47611e7	−0.544051
$134$	−2.57967e7	−0.926186
$135$	−6.54031e6	−0.228786
$136$	−861980.	−0.0293840
$137$	8.72739e6	0.289976	0.144988	−	0.989433i	$-0.453686\pi$
$137$	8.72739e6	0.289976	0.144988	+	0.989433i	$0.453686\pi$
$138$	−1.72830e7	−0.559813
$139$	−1.17087e7	−0.369790	−0.184895	−	0.982758i	$-0.559195\pi$
$139$	−1.17087e7	−0.369790	−0.184895	+	0.982758i	$0.559195\pi$
$140$	−7.29426e6	−0.224664
$141$	4.17110e6	0.125310
$142$	−5.76455e6	−0.168949
$143$	9.97035e6	0.285124
$144$	2.98598e6	0.0833333
$145$	−5.81652e7	−1.58444
$146$	4.88978e7	1.30033
$147$	−3.17652e6	−0.0824786
$148$	1.32488e7	0.335940
$149$	5.25065e7	1.30035	0.650176	−	0.759784i	$-0.274695\pi$
$149$	5.25065e7	1.30035	0.650176	+	0.759784i	$0.274695\pi$
$150$	−6.97389e6	−0.168716
$151$	−1.06827e6	−0.0252501	−0.0126251	−	0.999920i	$-0.504019\pi$
$151$	−1.06827e6	−0.0252501	−0.0126251	+	0.999920i	$0.504019\pi$
$152$	2.20341e7	0.508913
$153$	−1.22731e6	−0.0277035
$154$	−1.24527e7	−0.274753
$155$	−5.90420e7	−1.27350
$156$	−3.79642e6	−0.0800641
$157$	1.85891e7	0.383362	0.191681	−	0.981457i	$-0.438606\pi$
$157$	1.85891e7	0.383362	0.191681	+	0.981457i	$0.438606\pi$
$158$	−1.29960e7	−0.262126
$159$	1.58488e6	0.0312684
$160$	1.08882e7	0.210154
$161$	−2.74448e7	−0.518286
$162$	4.25153e6	0.0785674
$163$	7.81618e7	1.41364	0.706818	−	0.707395i	$-0.250130\pi$
$163$	7.81618e7	1.41364	0.706818	+	0.707395i	$0.250130\pi$
$164$	2.68016e7	0.474468
$165$	−4.07147e7	−0.705598
$166$	6.86627e7	1.16504
$167$	−2.97299e7	−0.493954	−0.246977	−	0.969021i	$-0.579437\pi$
$167$	−2.97299e7	−0.493954	−0.246977	+	0.969021i	$0.579437\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	−4.47532e6	−0.0698639
$171$	3.13728e7	0.479808
$172$	3.27111e7	0.490168
$173$	1.04807e8	1.53897	0.769485	−	0.638665i	$-0.220513\pi$
$173$	1.04807e8	1.53897	0.769485	+	0.638665i	$0.220513\pi$
$174$	3.78103e7	0.544111
$175$	−1.10743e7	−0.156200
$176$	1.85883e7	0.257008
$177$	−6.73952e6	−0.0913529
$178$	−5.77733e7	−0.767816
$179$	1.32769e8	1.73026	0.865131	−	0.501546i	$-0.167235\pi$
$179$	1.32769e8	1.73026	0.865131	+	0.501546i	$0.167235\pi$
$180$	1.55030e7	0.198135
$181$	−6.86420e7	−0.860428	−0.430214	−	0.902727i	$-0.641562\pi$
$181$	−6.86420e7	−0.860428	−0.430214	+	0.902727i	$0.641562\pi$
$182$	−6.02857e6	−0.0741249
$183$	2.50209e7	0.301803
$184$	4.09671e7	0.484812
$185$	6.87868e7	0.798737
$186$	3.83803e7	0.437333
$187$	−7.64024e6	−0.0854401
$188$	−9.88706e6	−0.108521
$189$	6.75127e6	0.0727393
$190$	1.14399e8	1.21000
$191$	−5.98203e7	−0.621200	−0.310600	−	0.950541i	$-0.600530\pi$
$191$	−5.98203e7	−0.621200	−0.310600	+	0.950541i	$0.600530\pi$
$192$	−7.07789e6	−0.0721688
$193$	1.48627e8	1.48815	0.744076	−	0.668095i	$-0.232890\pi$
$193$	1.48627e8	1.48815	0.744076	+	0.668095i	$0.232890\pi$
$194$	−5.58189e7	−0.548877
$195$	−1.97107e7	−0.190362
$196$	7.52954e6	0.0714286
$197$	4.01516e7	0.374172	0.187086	−	0.982344i	$-0.440096\pi$
$197$	4.01516e7	0.374172	0.187086	+	0.982344i	$0.440096\pi$
$198$	2.64666e7	0.242309
$199$	1.22948e8	1.10595	0.552976	−	0.833197i	$-0.313492\pi$
$199$	1.22948e8	1.10595	0.552976	+	0.833197i	$0.313492\pi$
$200$	1.65307e7	0.146112
$201$	8.70640e7	0.756228
$202$	−3.44619e6	−0.0294178
$203$	6.00413e7	0.503749
$204$	2.90918e6	0.0239919
$205$	1.39151e8	1.12810
$206$	−1.37550e8	−1.09629
$207$	5.83302e7	0.457085
$208$	8.99891e6	0.0693375
$209$	1.95302e8	1.47977
$210$	2.46181e7	0.183437
$211$	−2.00000e8	−1.46569	−0.732843	−	0.680397i	$-0.761807\pi$
$211$	−2.00000e8	−1.46569	−0.732843	+	0.680397i	$0.761807\pi$
$212$	−3.75674e6	−0.0270792
$213$	1.94554e7	0.137946
$214$	−5.78702e7	−0.403652
$215$	1.69833e8	1.16543
$216$	−1.00777e7	−0.0680414
$217$	6.09464e7	0.404892
$218$	4.25458e6	0.0278137
$219$	−1.65030e8	−1.06172
$220$	9.65089e7	0.611066
$221$	−3.69877e6	−0.0230507
$222$	−4.47148e7	−0.274294
$223$	−1.90121e8	−1.14805	−0.574027	−	0.818836i	$-0.694620\pi$
$223$	−1.90121e8	−1.14805	−0.574027	+	0.818836i	$0.694620\pi$
$224$	−1.12394e7	−0.0668153
$225$	2.35369e7	0.137756
$226$	1.05211e8	0.606292
$227$	1.97080e8	1.11828	0.559141	−	0.829073i	$-0.311131\pi$
$227$	1.97080e8	1.11828	0.559141	+	0.829073i	$0.311131\pi$
$228$	−7.43652e7	−0.415526
$229$	1.92885e8	1.06139	0.530694	−	0.847564i	$-0.321931\pi$
$229$	1.92885e8	1.06139	0.530694	+	0.847564i	$0.321931\pi$
$230$	2.12698e8	1.15270
$231$	4.20279e7	0.224335
$232$	−8.96244e7	−0.471214
$233$	2.15169e8	1.11438	0.557191	−	0.830385i	$-0.311879\pi$
$233$	2.15169e8	1.11438	0.557191	+	0.830385i	$0.311879\pi$
$234$	1.28129e7	0.0653720
$235$	−5.13327e7	−0.258022
$236$	1.59752e7	0.0791140
$237$	4.38615e7	0.214025
$238$	4.61967e6	0.0222122
$239$	−1.36102e8	−0.644868	−0.322434	−	0.946592i	$-0.604501\pi$
$239$	−1.36102e8	−0.644868	−0.322434	+	0.946592i	$0.604501\pi$
$240$	−3.67478e7	−0.171590
$241$	3.48180e8	1.60230	0.801150	−	0.598464i	$-0.204222\pi$
$241$	3.48180e8	1.60230	0.801150	+	0.598464i	$0.204222\pi$
$242$	8.86211e6	0.0401960
$243$	−1.43489e7	−0.0641500
$244$	−5.93087e7	−0.261369
$245$	3.90927e7	0.169830
$246$	−9.04553e7	−0.387401
$247$	9.45488e7	0.399224
$248$	−9.09754e7	−0.378742
$249$	−2.31737e8	−0.951255
$250$	−1.21851e8	−0.493216
$251$	5.30641e6	0.0211808	0.0105904	−	0.999944i	$-0.496629\pi$
$251$	5.30641e6	0.0211808	0.0105904	+	0.999944i	$0.496629\pi$
$252$	−1.60030e7	−0.0629941
$253$	3.63116e8	1.40969
$254$	−3.31207e6	−0.0126818
$255$	1.51042e7	0.0570437
$256$	1.67772e7	0.0625000
$257$	1.37965e8	0.506995	0.253498	−	0.967336i	$-0.418419\pi$
$257$	1.37965e8	0.506995	0.253498	+	0.967336i	$0.418419\pi$
$258$	−1.10400e8	−0.400221
$259$	−7.10055e7	−0.253947
$260$	4.67215e7	0.164858
$261$	−1.27610e8	−0.444265
$262$	3.71491e8	1.27613
$263$	5.05702e8	1.71415	0.857077	−	0.515189i	$-0.172278\pi$
$263$	5.05702e8	1.71415	0.857077	+	0.515189i	$0.172278\pi$
$264$	−6.27356e7	−0.209846
$265$	−1.95047e7	−0.0643840
$266$	−1.18089e8	−0.384702
$267$	1.94985e8	0.626919
$268$	−2.06374e8	−0.654912
$269$	−4.93505e7	−0.154582	−0.0772909	−	0.997009i	$-0.524627\pi$
$269$	−4.93505e7	−0.154582	−0.0772909	+	0.997009i	$0.524627\pi$
$270$	−5.23225e7	−0.161776
$271$	−1.26125e8	−0.384953	−0.192476	−	0.981302i	$-0.561652\pi$
$271$	−1.26125e8	−0.384953	−0.192476	+	0.981302i	$0.561652\pi$
$272$	−6.89584e6	−0.0207776
$273$	2.03464e7	0.0605228
$274$	6.98191e7	0.205044
$275$	1.46522e8	0.424851
$276$	−1.38264e8	−0.395847
$277$	−2.88014e8	−0.814207	−0.407103	−	0.913382i	$-0.633461\pi$
$277$	−2.88014e8	−0.814207	−0.407103	+	0.913382i	$0.633461\pi$
$278$	−9.36693e7	−0.261481
$279$	−1.29533e8	−0.357081
$280$	−5.83541e7	−0.158861
$281$	−8.91246e7	−0.239621	−0.119811	−	0.992797i	$-0.538229\pi$
$281$	−8.91246e7	−0.239621	−0.119811	+	0.992797i	$0.538229\pi$
$282$	3.33688e7	0.0886072
$283$	2.68924e7	0.0705304	0.0352652	−	0.999378i	$-0.488772\pi$
$283$	2.68924e7	0.0705304	0.0352652	+	0.999378i	$0.488772\pi$
$284$	−4.61164e7	−0.119465
$285$	−3.86098e8	−0.987961
$286$	7.97628e7	0.201613
$287$	−1.43640e8	−0.358664
$288$	2.38879e7	0.0589256
$289$	−4.07504e8	−0.993093
$290$	−4.65322e8	−1.12037
$291$	1.88389e8	0.448156
$292$	3.91182e8	0.919474
$293$	−1.31694e8	−0.305865	−0.152933	−	0.988237i	$-0.548872\pi$
$293$	−1.31694e8	−0.305865	−0.152933	+	0.988237i	$0.548872\pi$
$294$	−2.54122e7	−0.0583212
$295$	8.29416e7	0.188103
$296$	1.05991e8	0.237545
$297$	−8.93247e7	−0.197844
$298$	4.20052e8	0.919488
$299$	1.75791e8	0.380318
$300$	−5.57911e7	−0.119300
$301$	−1.75311e8	−0.370532
$302$	−8.54620e6	−0.0178545
$303$	1.16309e7	0.0240195
$304$	1.76273e8	0.359856
$305$	−3.07926e8	−0.621436
$306$	−9.81849e6	−0.0195893
$307$	7.59154e7	0.149743	0.0748714	−	0.997193i	$-0.476145\pi$
$307$	7.59154e7	0.149743	0.0748714	+	0.997193i	$0.476145\pi$
$308$	−9.96218e7	−0.194279
$309$	4.64231e8	0.895116
$310$	−4.72336e8	−0.900504
$311$	4.40832e8	0.831021	0.415511	−	0.909588i	$-0.363603\pi$
$311$	4.40832e8	0.831021	0.415511	+	0.909588i	$0.363603\pi$
$312$	−3.03713e7	−0.0566139
$313$	8.94209e8	1.64829	0.824146	−	0.566378i	$-0.191656\pi$
$313$	8.94209e8	1.64829	0.824146	+	0.566378i	$0.191656\pi$
$314$	1.48713e8	0.271078
$315$	−8.30862e7	−0.149776
$316$	−1.03968e8	−0.185351
$317$	−9.27330e8	−1.63503	−0.817517	−	0.575904i	$-0.804650\pi$
$317$	−9.27330e8	−1.63503	−0.817517	+	0.575904i	$0.804650\pi$
$318$	1.26790e7	0.0221101
$319$	−7.94395e8	−1.37015
$320$	8.71058e7	0.148601
$321$	1.95312e8	0.329580
$322$	−2.19558e8	−0.366483
$323$	−7.24525e7	−0.119631
$324$	3.40122e7	0.0555556
$325$	7.09335e7	0.114620
$326$	6.25294e8	0.999592
$327$	−1.43592e7	−0.0227098
$328$	2.14413e8	0.335499
$329$	5.29885e7	0.0820344
$330$	−3.25718e8	−0.498933
$331$	−9.99764e8	−1.51530	−0.757651	−	0.652660i	$-0.773653\pi$
$331$	−9.99764e8	−1.51530	−0.757651	+	0.652660i	$0.773653\pi$
$332$	5.49302e8	0.823811
$333$	1.50912e8	0.223960
$334$	−2.37840e8	−0.349278
$335$	−1.07148e9	−1.55713
$336$	3.79331e7	0.0545545
$337$	9.36583e8	1.33304	0.666518	−	0.745489i	$-0.267784\pi$
$337$	9.36583e8	1.33304	0.666518	+	0.745489i	$0.267784\pi$
$338$	3.86145e7	0.0543928
$339$	−3.55087e8	−0.495035
$340$	−3.58026e7	−0.0494013
$341$	−8.06370e8	−1.10127
$342$	2.50983e8	0.339275
$343$	−4.03536e7	−0.0539949
$344$	2.61688e8	0.346601
$345$	−7.17855e8	−0.941174
$346$	8.38458e8	1.08822
$347$	−2.89119e8	−0.371469	−0.185735	−	0.982600i	$-0.559466\pi$
$347$	−2.89119e8	−0.371469	−0.185735	+	0.982600i	$0.559466\pi$
$348$	3.02482e8	0.384745
$349$	1.05672e9	1.33067	0.665333	−	0.746546i	$-0.268289\pi$
$349$	1.05672e9	1.33067	0.665333	+	0.746546i	$0.268289\pi$
$350$	−8.85942e7	−0.110450
$351$	−4.32436e7	−0.0533761
$352$	1.48707e8	0.181732
$353$	2.62139e8	0.317191	0.158595	−	0.987344i	$-0.449303\pi$
$353$	2.62139e8	0.317191	0.158595	+	0.987344i	$0.449303\pi$
$354$	−5.39162e7	−0.0645963
$355$	−2.39432e8	−0.284043
$356$	−4.62186e8	−0.542928
$357$	−1.55914e7	−0.0181362
$358$	1.06215e9	1.22348
$359$	−1.58381e8	−0.180664	−0.0903322	−	0.995912i	$-0.528793\pi$
$359$	−1.58381e8	−0.180664	−0.0903322	+	0.995912i	$0.528793\pi$
$360$	1.24024e8	0.140103
$361$	9.58176e8	1.07194
$362$	−5.49136e8	−0.608415
$363$	−2.99096e7	−0.0328199
$364$	−4.82285e7	−0.0524142
$365$	2.03098e9	2.18616
$366$	2.00167e8	0.213407
$367$	−4.26484e8	−0.450372	−0.225186	−	0.974316i	$-0.572299\pi$
$367$	−4.26484e8	−0.450372	−0.225186	+	0.974316i	$0.572299\pi$
$368$	3.27737e8	0.342814
$369$	3.05287e8	0.316312
$370$	5.50294e8	0.564792
$371$	2.01338e7	0.0204700
$372$	3.07042e8	0.309241
$373$	−1.71354e9	−1.70967	−0.854836	−	0.518898i	$-0.826342\pi$
$373$	−1.71354e9	−1.70967	−0.854836	+	0.518898i	$0.826342\pi$
$374$	−6.11220e7	−0.0604153
$375$	4.11246e8	0.402709
$376$	−7.90965e7	−0.0767361
$377$	−3.84580e8	−0.369651
$378$	5.40102e7	0.0514344
$379$	−5.98355e8	−0.564575	−0.282288	−	0.959330i	$-0.591093\pi$
$379$	−5.98355e8	−0.564575	−0.282288	+	0.959330i	$0.591093\pi$
$380$	9.15194e8	0.855600
$381$	1.11782e7	0.0103547
$382$	−4.78562e8	−0.439255
$383$	−1.16290e9	−1.05766	−0.528829	−	0.848728i	$-0.677369\pi$
$383$	−1.16290e9	−1.05766	−0.528829	+	0.848728i	$0.677369\pi$
$384$	−5.66231e7	−0.0510310
$385$	−5.17227e8	−0.461922
$386$	1.18902e9	1.05228
$387$	3.72599e8	0.326779
$388$	−4.46551e8	−0.388115
$389$	−1.04953e9	−0.904004	−0.452002	−	0.892017i	$-0.649290\pi$
$389$	−1.04953e9	−0.904004	−0.452002	+	0.892017i	$0.649290\pi$
$390$	−1.57685e8	−0.134606
$391$	−1.34708e8	−0.113966
$392$	6.02363e7	0.0505076
$393$	−1.25378e9	−1.04195
$394$	3.21213e8	0.264579
$395$	−5.39793e8	−0.440694
$396$	2.11733e8	0.171338
$397$	−1.09871e9	−0.881284	−0.440642	−	0.897683i	$-0.645249\pi$
$397$	−1.09871e9	−0.881284	−0.440642	+	0.897683i	$0.645249\pi$
$398$	9.83586e8	0.782027
$399$	3.98551e8	0.314108
$400$	1.32246e8	0.103317
$401$	1.80907e9	1.40104	0.700520	−	0.713633i	$-0.252951\pi$
$401$	1.80907e9	1.40104	0.700520	+	0.713633i	$0.252951\pi$
$402$	6.96512e8	0.534734
$403$	−3.90377e8	−0.297110
$404$	−2.75695e7	−0.0208015
$405$	1.76588e8	0.132090
$406$	4.80331e8	0.356204
$407$	9.39459e8	0.690713
$408$	2.32735e7	0.0169649
$409$	8.35953e8	0.604157	0.302079	−	0.953283i	$-0.402319\pi$
$409$	8.35953e8	0.604157	0.302079	+	0.953283i	$0.402319\pi$
$410$	1.11321e9	0.797689
$411$	−2.35639e8	−0.167418
$412$	−1.10040e9	−0.775193
$413$	−8.56169e7	−0.0598045
$414$	4.66641e8	0.323208
$415$	2.85193e9	1.95871
$416$	7.19913e7	0.0490290
$417$	3.16134e8	0.213498
$418$	1.56241e9	1.04636
$419$	−6.07516e8	−0.403467	−0.201734	−	0.979440i	$-0.564658\pi$
$419$	−6.07516e8	−0.403467	−0.201734	+	0.979440i	$0.564658\pi$
$420$	1.96945e8	0.129710
$421$	2.06243e9	1.34708	0.673539	−	0.739152i	$-0.264773\pi$
$421$	2.06243e9	1.34708	0.673539	+	0.739152i	$0.264773\pi$
$422$	−1.60000e9	−1.03640
$423$	−1.12620e8	−0.0723475
$424$	−3.00539e7	−0.0191479
$425$	−5.43561e7	−0.0343469
$426$	1.55643e8	0.0975429
$427$	3.17858e8	0.197576
$428$	−4.62962e8	−0.285425
$429$	−2.69199e8	−0.164617
$430$	1.35866e9	0.824085
$431$	−1.90276e8	−0.114476	−0.0572378	−	0.998361i	$-0.518229\pi$
$431$	−1.90276e8	−0.114476	−0.0572378	+	0.998361i	$0.518229\pi$
$432$	−8.06216e7	−0.0481125
$433$	−2.84375e9	−1.68339	−0.841693	−	0.539957i	$-0.818441\pi$
$433$	−2.84375e9	−1.68339	−0.841693	+	0.539957i	$0.818441\pi$
$434$	4.87571e8	0.286302
$435$	1.57046e9	0.914776
$436$	3.40366e7	0.0196673
$437$	3.44343e9	1.97382
$438$	−1.32024e9	−0.750747
$439$	−2.56732e9	−1.44828	−0.724142	−	0.689651i	$-0.757764\pi$
$439$	−2.56732e9	−1.44828	−0.724142	+	0.689651i	$0.757764\pi$
$440$	7.72071e8	0.432089
$441$	8.57661e7	0.0476190
$442$	−2.95901e7	−0.0162993
$443$	8.11793e7	0.0443641	0.0221821	−	0.999754i	$-0.492939\pi$
$443$	8.11793e7	0.0443641	0.0221821	+	0.999754i	$0.492939\pi$
$444$	−3.57718e8	−0.193955
$445$	−2.39963e9	−1.29087
$446$	−1.52097e9	−0.811797
$447$	−1.41767e9	−0.750759
$448$	−8.99154e7	−0.0472456
$449$	1.41154e9	0.735920	0.367960	−	0.929842i	$-0.380056\pi$
$449$	1.41154e9	0.735920	0.367960	+	0.929842i	$0.380056\pi$
$450$	1.88295e8	0.0974081
$451$	1.90047e9	0.975534
$452$	8.41688e8	0.428713
$453$	2.88434e7	0.0145782
$454$	1.57664e9	0.790745
$455$	−2.50398e8	−0.124621
$456$	−5.94922e8	−0.293821
$457$	−2.45874e8	−0.120505	−0.0602526	−	0.998183i	$-0.519191\pi$
$457$	−2.45874e8	−0.120505	−0.0602526	+	0.998183i	$0.519191\pi$
$458$	1.54308e9	0.750515
$459$	3.31374e7	0.0159946
$460$	1.70158e9	0.815081
$461$	7.67759e8	0.364982	0.182491	−	0.983208i	$-0.441584\pi$
$461$	7.67759e8	0.364982	0.182491	+	0.983208i	$0.441584\pi$
$462$	3.36224e8	0.158628
$463$	−3.13479e9	−1.46783	−0.733914	−	0.679242i	$-0.762309\pi$
$463$	−3.13479e9	−1.46783	−0.733914	+	0.679242i	$0.762309\pi$
$464$	−7.16995e8	−0.333199
$465$	1.59414e9	0.735258
$466$	1.72135e9	0.787986
$467$	−3.05486e9	−1.38798	−0.693989	−	0.719985i	$-0.744148\pi$
$467$	−3.05486e9	−1.38798	−0.693989	+	0.719985i	$0.744148\pi$
$468$	1.02503e8	0.0462250
$469$	1.10604e9	0.495067
$470$	−4.10662e8	−0.182449
$471$	−5.01905e8	−0.221334
$472$	1.27801e8	0.0559420
$473$	2.31950e9	1.00782
$474$	3.50892e8	0.151339
$475$	1.38946e9	0.594867
$476$	3.69574e7	0.0157064
$477$	−4.27917e7	−0.0180528
$478$	−1.08881e9	−0.455990
$479$	8.05606e8	0.334926	0.167463	−	0.985878i	$-0.446443\pi$
$479$	8.05606e8	0.334926	0.167463	+	0.985878i	$0.446443\pi$
$480$	−2.93982e8	−0.121332
$481$	4.54808e8	0.186346
$482$	2.78544e9	1.13300
$483$	7.41009e8	0.299232
$484$	7.08969e7	0.0284229
$485$	−2.31845e9	−0.922789
$486$	−1.14791e8	−0.0453609
$487$	−3.88945e9	−1.52594	−0.762969	−	0.646435i	$-0.776259\pi$
$487$	−3.88945e9	−1.52594	−0.762969	+	0.646435i	$0.776259\pi$
$488$	−4.74470e8	−0.184816
$489$	−2.11037e9	−0.816164
$490$	3.12741e8	0.120088
$491$	3.09826e8	0.118122	0.0590612	−	0.998254i	$-0.481189\pi$
$491$	3.09826e8	0.118122	0.0590612	+	0.998254i	$0.481189\pi$
$492$	−7.23642e8	−0.273934
$493$	2.94702e8	0.110769
$494$	7.56391e8	0.282294
$495$	1.09930e9	0.407377
$496$	−7.27803e8	−0.267811
$497$	2.47155e8	0.0903072
$498$	−1.85389e9	−0.672639
$499$	−5.94530e8	−0.214201	−0.107101	−	0.994248i	$-0.534157\pi$
$499$	−5.94530e8	−0.214201	−0.107101	+	0.994248i	$0.534157\pi$
$500$	−9.74804e8	−0.348757
$501$	8.02708e8	0.285184
$502$	4.24512e7	0.0149771
$503$	−2.00206e9	−0.701437	−0.350718	−	0.936481i	$-0.614063\pi$
$503$	−2.00206e9	−0.701437	−0.350718	+	0.936481i	$0.614063\pi$
$504$	−1.28024e8	−0.0445435
$505$	−1.43139e8	−0.0494580
$506$	2.90493e9	0.996803
$507$	−1.30324e8	−0.0444116
$508$	−2.64966e7	−0.00896740
$509$	1.22512e9	0.411782	0.205891	−	0.978575i	$-0.433991\pi$
$509$	1.22512e9	0.411782	0.205891	+	0.978575i	$0.433991\pi$
$510$	1.20834e8	0.0403360
$511$	−2.09649e9	−0.695057
$512$	1.34218e8	0.0441942
$513$	−8.47066e8	−0.277017
$514$	1.10372e9	0.358500
$515$	−5.71317e9	−1.84311
$516$	−8.83199e8	−0.282999
$517$	−7.01080e8	−0.223126
$518$	−5.68044e8	−0.179567
$519$	−2.82980e9	−0.888525
$520$	3.73772e8	0.116572
$521$	2.07737e9	0.643548	0.321774	−	0.946816i	$-0.395721\pi$
$521$	2.07737e9	0.643548	0.321774	+	0.946816i	$0.395721\pi$
$522$	−1.02088e9	−0.314143
$523$	6.24365e8	0.190846	0.0954229	−	0.995437i	$-0.469580\pi$
$523$	6.24365e8	0.190846	0.0954229	+	0.995437i	$0.469580\pi$
$524$	2.97193e9	0.902358
$525$	2.99005e8	0.0901824
$526$	4.04562e9	1.21209
$527$	2.99145e8	0.0890316
$528$	−5.01885e8	−0.148383
$529$	2.99741e9	0.880341
$530$	−1.56037e8	−0.0455264
$531$	1.81967e8	0.0527426
$532$	−9.44714e8	−0.272025
$533$	9.20047e8	0.263187
$534$	1.55988e9	0.443299
$535$	−2.40366e9	−0.678632
$536$	−1.65099e9	−0.463093
$537$	−3.58477e9	−0.998967
$538$	−3.94804e8	−0.109306
$539$	5.33910e8	0.146861
$540$	−4.18580e8	−0.114393
$541$	−1.27993e9	−0.347534	−0.173767	−	0.984787i	$-0.555594\pi$
$541$	−1.27993e9	−0.347534	−0.173767	+	0.984787i	$0.555594\pi$
$542$	−1.00900e9	−0.272203
$543$	1.85333e9	0.496769
$544$	−5.51667e7	−0.0146920
$545$	1.76715e8	0.0467612
$546$	1.62771e8	0.0427960
$547$	−1.66165e9	−0.434093	−0.217047	−	0.976161i	$-0.569642\pi$
$547$	−1.66165e9	−0.434093	−0.217047	+	0.976161i	$0.569642\pi$
$548$	5.58553e8	0.144988
$549$	−6.75563e8	−0.174246
$550$	1.17217e9	0.300415
$551$	−7.53325e9	−1.91846
$552$	−1.10611e9	−0.279906
$553$	5.57204e8	0.140112
$554$	−2.30411e9	−0.575731
$555$	−1.85724e9	−0.461151
$556$	−7.49354e8	−0.184895
$557$	−4.23236e9	−1.03774	−0.518871	−	0.854852i	$-0.673648\pi$
$557$	−4.23236e9	−1.03774	−0.518871	+	0.854852i	$0.673648\pi$
$558$	−1.03627e9	−0.252495
$559$	1.12291e9	0.271896
$560$	−4.66833e8	−0.112332
$561$	2.06287e8	0.0493289
$562$	−7.12997e8	−0.169438
$563$	2.29041e9	0.540922	0.270461	−	0.962731i	$-0.412824\pi$
$563$	2.29041e9	0.540922	0.270461	+	0.962731i	$0.412824\pi$
$564$	2.66951e8	0.0626548
$565$	4.36997e9	1.01932
$566$	2.15139e8	0.0498725
$567$	−1.82284e8	−0.0419961
$568$	−3.68931e8	−0.0844746
$569$	5.70558e9	1.29839	0.649197	−	0.760620i	$-0.275105\pi$
$569$	5.70558e9	1.29839	0.649197	+	0.760620i	$0.275105\pi$
$570$	−3.08878e9	−0.698594
$571$	−5.78089e8	−0.129948	−0.0649738	−	0.997887i	$-0.520696\pi$
$571$	−5.78089e8	−0.129948	−0.0649738	+	0.997887i	$0.520696\pi$
$572$	6.38102e8	0.142562
$573$	1.61515e9	0.358650
$574$	−1.14912e9	−0.253614
$575$	2.58337e9	0.566695
$576$	1.91103e8	0.0416667
$577$	1.85447e9	0.401888	0.200944	−	0.979603i	$-0.435599\pi$
$577$	1.85447e9	0.401888	0.200944	+	0.979603i	$0.435599\pi$
$578$	−3.26003e9	−0.702223
$579$	−4.01293e9	−0.859185
$580$	−3.72257e9	−0.792219
$581$	−2.94391e9	−0.622743
$582$	1.50711e9	0.316894
$583$	−2.66386e8	−0.0556765
$584$	3.12946e9	0.650166
$585$	5.32188e8	0.109905
$586$	−1.05355e9	−0.216279
$587$	1.59026e7	0.00324516	0.00162258	−	0.999999i	$-0.499484\pi$
$587$	1.59026e7	0.00324516	0.00162258	+	0.999999i	$0.499484\pi$
$588$	−2.03297e8	−0.0412393
$589$	−7.64681e9	−1.54197
$590$	6.63533e8	0.133009
$591$	−1.08409e9	−0.216028
$592$	8.47925e8	0.167970
$593$	4.72446e9	0.930380	0.465190	−	0.885211i	$-0.345986\pi$
$593$	4.72446e9	0.930380	0.465190	+	0.885211i	$0.345986\pi$
$594$	−7.14597e8	−0.139897
$595$	1.91879e8	0.0373438
$596$	3.36041e9	0.650176
$597$	−3.31960e9	−0.638522
$598$	1.40633e9	0.268925
$599$	6.54444e9	1.24417	0.622084	−	0.782951i	$-0.286286\pi$
$599$	6.54444e9	1.24417	0.622084	+	0.782951i	$0.286286\pi$
$600$	−4.46329e8	−0.0843579
$601$	9.35203e9	1.75730	0.878649	−	0.477468i	$-0.158445\pi$
$601$	9.35203e9	1.75730	0.878649	+	0.477468i	$0.158445\pi$
$602$	−1.40249e9	−0.262006
$603$	−2.35073e9	−0.436608
$604$	−6.83696e7	−0.0126251
$605$	3.68090e8	0.0675788
$606$	9.30472e7	0.0169844
$607$	7.23440e9	1.31293	0.656466	−	0.754355i	$-0.272050\pi$
$607$	7.23440e9	1.31293	0.656466	+	0.754355i	$0.272050\pi$
$608$	1.41018e9	0.254456
$609$	−1.62112e9	−0.290840
$610$	−2.46340e9	−0.439422
$611$	−3.39404e8	−0.0601968
$612$	−7.85479e7	−0.0138517
$613$	1.45381e9	0.254916	0.127458	−	0.991844i	$-0.459318\pi$
$613$	1.45381e9	0.254916	0.127458	+	0.991844i	$0.459318\pi$
$614$	6.07323e8	0.105884
$615$	−3.75709e9	−0.651311
$616$	−7.96974e8	−0.137376
$617$	−4.53208e9	−0.776782	−0.388391	−	0.921495i	$-0.626969\pi$
$617$	−4.53208e9	−0.776782	−0.388391	+	0.921495i	$0.626969\pi$
$618$	3.71385e9	0.632943
$619$	−1.04972e10	−1.77891	−0.889457	−	0.457019i	$-0.848917\pi$
$619$	−1.04972e10	−1.77891	−0.889457	+	0.457019i	$0.848917\pi$
$620$	−3.77869e9	−0.636752
$621$	−1.57491e9	−0.263898
$622$	3.52666e9	0.587621
$623$	2.47703e9	0.410415
$624$	−2.42971e8	−0.0400320
$625$	−7.58348e9	−1.24248
$626$	7.15368e9	1.16552
$627$	−5.27315e9	−0.854346
$628$	1.18970e9	0.191681
$629$	−3.48518e8	−0.0558403
$630$	−6.64690e8	−0.105908
$631$	−1.90313e9	−0.301554	−0.150777	−	0.988568i	$-0.548178\pi$
$631$	−1.90313e9	−0.301554	−0.150777	+	0.988568i	$0.548178\pi$
$632$	−8.31744e8	−0.131063
$633$	5.40000e9	0.846215
$634$	−7.41864e9	−1.15614
$635$	−1.37568e8	−0.0213210
$636$	1.01432e8	0.0156342
$637$	2.58475e8	0.0396214
$638$	−6.35516e9	−0.968845
$639$	−5.25295e8	−0.0796434
$640$	6.96846e8	0.105077
$641$	−1.28685e10	−1.92986	−0.964930	−	0.262506i	$-0.915451\pi$
$641$	−1.28685e10	−1.92986	−0.964930	+	0.262506i	$0.915451\pi$
$642$	1.56250e9	0.233048
$643$	−1.15273e9	−0.170998	−0.0854989	−	0.996338i	$-0.527248\pi$
$643$	−1.15273e9	−0.170998	−0.0854989	+	0.996338i	$0.527248\pi$
$644$	−1.75647e9	−0.259143
$645$	−4.58549e9	−0.672863
$646$	−5.79620e8	−0.0845920
$647$	−5.76076e9	−0.836209	−0.418105	−	0.908399i	$-0.637305\pi$
$647$	−5.76076e9	−0.836209	−0.418105	+	0.908399i	$0.637305\pi$
$648$	2.72098e8	0.0392837
$649$	1.13278e9	0.162663
$650$	5.67468e8	0.0810484
$651$	−1.64555e9	−0.233765
$652$	5.00235e9	0.706818
$653$	3.72855e8	0.0524015	0.0262008	−	0.999657i	$-0.491659\pi$
$653$	3.72855e8	0.0524015	0.0262008	+	0.999657i	$0.491659\pi$
$654$	−1.14874e8	−0.0160582
$655$	1.54300e10	2.14546
$656$	1.71530e9	0.237234
$657$	4.45581e9	0.612982
$658$	4.23908e8	0.0580070
$659$	−5.88562e9	−0.801113	−0.400556	−	0.916272i	$-0.631183\pi$
$659$	−5.88562e9	−0.801113	−0.400556	+	0.916272i	$0.631183\pi$
$660$	−2.60574e9	−0.352799
$661$	−1.29378e8	−0.0174244	−0.00871218	−	0.999962i	$-0.502773\pi$
$661$	−1.29378e8	−0.0174244	−0.00871218	+	0.999962i	$0.502773\pi$
$662$	−7.99811e9	−1.07148
$663$	9.98667e7	0.0133083
$664$	4.39441e9	0.582522
$665$	−4.90487e9	−0.646773
$666$	1.20730e9	0.158364
$667$	−1.40063e10	−1.82760
$668$	−1.90272e9	−0.246977
$669$	5.13326e9	0.662829
$670$	−8.57180e9	−1.10106
$671$	−4.20551e9	−0.537390
$672$	3.03464e8	0.0385758
$673$	7.40929e9	0.936967	0.468483	−	0.883472i	$-0.344801\pi$
$673$	7.40929e9	0.936967	0.468483	+	0.883472i	$0.344801\pi$
$674$	7.49267e9	0.942599
$675$	−6.35496e8	−0.0795334
$676$	3.08916e8	0.0384615
$677$	−1.34737e10	−1.66888	−0.834441	−	0.551098i	$-0.814209\pi$
$677$	−1.34737e10	−1.66888	−0.834441	+	0.551098i	$0.814209\pi$
$678$	−2.84070e9	−0.350043
$679$	2.39324e9	0.293387
$680$	−2.86421e8	−0.0349320
$681$	−5.32115e9	−0.645640
$682$	−6.45096e9	−0.778716
$683$	−1.01931e10	−1.22415	−0.612074	−	0.790801i	$-0.709664\pi$
$683$	−1.01931e10	−1.22415	−0.612074	+	0.790801i	$0.709664\pi$
$684$	2.00786e9	0.239904
$685$	2.89996e9	0.344726
$686$	−3.22829e8	−0.0381802
$687$	−5.20789e9	−0.612793
$688$	2.09351e9	0.245084
$689$	−1.28962e8	−0.0150208
$690$	−5.74284e9	−0.665510
$691$	1.25240e10	1.44401	0.722005	−	0.691888i	$-0.243221\pi$
$691$	1.25240e10	1.44401	0.722005	+	0.691888i	$0.243221\pi$
$692$	6.70767e9	0.769485
$693$	−1.13475e9	−0.129520
$694$	−2.31295e9	−0.262669
$695$	−3.89058e9	−0.439610
$696$	2.41986e9	0.272056
$697$	−7.05029e8	−0.0788665
$698$	8.45373e9	0.940923
$699$	−5.80956e9	−0.643388
$700$	−7.08754e8	−0.0781002
$701$	−2.19973e9	−0.241188	−0.120594	−	0.992702i	$-0.538480\pi$
$701$	−2.19973e9	−0.241188	−0.120594	+	0.992702i	$0.538480\pi$
$702$	−3.45948e8	−0.0377426
$703$	8.90889e9	0.967119
$704$	1.18965e9	0.128504
$705$	1.38598e9	0.148969
$706$	2.09711e9	0.224288
$707$	1.47756e8	0.0157245
$708$	−4.31329e8	−0.0456765
$709$	−9.24653e9	−0.974355	−0.487177	−	0.873303i	$-0.661974\pi$
$709$	−9.24653e9	−0.974355	−0.487177	+	0.873303i	$0.661974\pi$
$710$	−1.91546e9	−0.200848
$711$	−1.18426e9	−0.123567
$712$	−3.69749e9	−0.383908
$713$	−1.42174e10	−1.46895
$714$	−1.24731e8	−0.0128242
$715$	3.31297e9	0.338958
$716$	8.49723e9	0.865131
$717$	3.67474e9	0.372314
$718$	−1.26705e9	−0.127749
$719$	−5.78088e9	−0.580020	−0.290010	−	0.957024i	$-0.593659\pi$
$719$	−5.78088e9	−0.580020	−0.290010	+	0.957024i	$0.593659\pi$
$720$	9.92190e8	0.0990674
$721$	5.89745e9	0.585991
$722$	7.66541e9	0.757975
$723$	−9.40085e9	−0.925088
$724$	−4.39309e9	−0.430214
$725$	−5.65168e9	−0.550801
$726$	−2.39277e8	−0.0232072
$727$	8.21685e9	0.793113	0.396556	−	0.918010i	$-0.370205\pi$
$727$	8.21685e9	0.793113	0.396556	+	0.918010i	$0.370205\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	1.62479e10	1.54585
$731$	−8.60482e8	−0.0814762
$732$	1.60134e9	0.150901
$733$	−2.05550e10	−1.92776	−0.963881	−	0.266332i	$-0.914188\pi$
$733$	−2.05550e10	−1.92776	−0.963881	+	0.266332i	$0.914188\pi$
$734$	−3.41187e9	−0.318461
$735$	−1.05550e9	−0.0980513
$736$	2.62190e9	0.242406
$737$	−1.46337e10	−1.34654
$738$	2.44229e9	0.223666
$739$	−1.95410e10	−1.78111	−0.890555	−	0.454876i	$-0.849683\pi$
$739$	−1.95410e10	−1.78111	−0.890555	+	0.454876i	$0.849683\pi$
$740$	4.40235e9	0.399368
$741$	−2.55282e9	−0.230492
$742$	1.61070e8	0.0144744
$743$	−1.92668e10	−1.72325	−0.861625	−	0.507546i	$-0.830553\pi$
$743$	−1.92668e10	−1.72325	−0.861625	+	0.507546i	$0.830553\pi$
$744$	2.45634e9	0.218667
$745$	1.74470e10	1.54587
$746$	−1.37083e10	−1.20892
$747$	6.25689e9	0.549207
$748$	−4.88976e8	−0.0427200
$749$	2.48119e9	0.215761
$750$	3.28996e9	0.284759
$751$	1.09052e10	0.939497	0.469749	−	0.882800i	$-0.344345\pi$
$751$	1.09052e10	0.939497	0.469749	+	0.882800i	$0.344345\pi$
$752$	−6.32772e8	−0.0542606
$753$	−1.43273e8	−0.0122287
$754$	−3.07664e9	−0.261383
$755$	−3.54969e8	−0.0300176
$756$	4.32081e8	0.0363696
$757$	7.82173e7	0.00655341	0.00327670	−	0.999995i	$-0.498957\pi$
$757$	7.82173e7	0.00655341	0.00327670	+	0.999995i	$0.498957\pi$
$758$	−4.78684e9	−0.399215
$759$	−9.80415e9	−0.813886
$760$	7.32155e9	0.605000
$761$	−1.53822e10	−1.26524	−0.632618	−	0.774464i	$-0.718020\pi$
$761$	−1.53822e10	−1.26524	−0.632618	+	0.774464i	$0.718020\pi$
$762$	8.94259e7	0.00732185
$763$	−1.82415e8	−0.0148670
$764$	−3.82850e9	−0.310600
$765$	−4.07814e8	−0.0329342
$766$	−9.30317e9	−0.747877
$767$	5.48397e8	0.0438845
$768$	−4.52985e8	−0.0360844
$769$	2.14405e10	1.70017	0.850087	−	0.526643i	$-0.176549\pi$
$769$	2.14405e10	1.70017	0.850087	+	0.526643i	$0.176549\pi$
$770$	−4.13782e9	−0.326628
$771$	−3.72506e9	−0.292714
$772$	9.51213e9	0.744076
$773$	−4.61629e9	−0.359472	−0.179736	−	0.983715i	$-0.557524\pi$
$773$	−4.61629e9	−0.359472	−0.179736	+	0.983715i	$0.557524\pi$
$774$	2.98080e9	0.231067
$775$	−5.73688e9	−0.442710
$776$	−3.57241e9	−0.274439
$777$	1.91715e9	0.146616
$778$	−8.39622e9	−0.639227
$779$	1.80221e10	1.36592
$780$	−1.26148e9	−0.0951809
$781$	−3.27006e9	−0.245628
$782$	−1.07766e9	−0.0805859
$783$	3.44546e9	0.256496
$784$	4.81890e8	0.0357143
$785$	6.17682e9	0.455744
$786$	−1.00303e10	−0.736772
$787$	−6.13485e9	−0.448634	−0.224317	−	0.974516i	$-0.572015\pi$
$787$	−6.13485e9	−0.448634	−0.224317	+	0.974516i	$0.572015\pi$
$788$	2.56970e9	0.187086
$789$	−1.36540e10	−0.989667
$790$	−4.31834e9	−0.311618
$791$	−4.51092e9	−0.324077
$792$	1.69386e9	0.121155
$793$	−2.03596e9	−0.144981
$794$	−8.78967e9	−0.623162
$795$	5.26626e8	0.0371721
$796$	7.86869e9	0.552976
$797$	−1.81940e10	−1.27298	−0.636492	−	0.771283i	$-0.719615\pi$
$797$	−1.81940e10	−1.27298	−0.636492	+	0.771283i	$0.719615\pi$
$798$	3.18841e9	0.222108
$799$	2.60084e8	0.0180385
$800$	1.05796e9	0.0730561
$801$	−5.26459e9	−0.361952
$802$	1.44726e10	0.990685
$803$	2.77383e10	1.89049
$804$	5.57210e9	0.378114
$805$	−9.11942e9	−0.616143
$806$	−3.12302e9	−0.210088
$807$	1.33246e9	0.0892479
$808$	−2.20556e8	−0.0147089
$809$	1.69125e10	1.12302	0.561511	−	0.827469i	$-0.310220\pi$
$809$	1.69125e10	1.12302	0.561511	+	0.827469i	$0.310220\pi$
$810$	1.41271e9	0.0934017
$811$	1.42003e10	0.934813	0.467407	−	0.884042i	$-0.345188\pi$
$811$	1.42003e10	0.934813	0.467407	+	0.884042i	$0.345188\pi$
$812$	3.84265e9	0.251875
$813$	3.40536e9	0.222253
$814$	7.51567e9	0.488408
$815$	2.59718e10	1.68054
$816$	1.86188e8	0.0119960
$817$	2.19958e10	1.41112
$818$	6.68762e9	0.427204
$819$	−5.49353e8	−0.0349428
$820$	8.90569e9	0.564052
$821$	−8.40863e9	−0.530303	−0.265152	−	0.964207i	$-0.585422\pi$
$821$	−8.40863e9	−0.530303	−0.265152	+	0.964207i	$0.585422\pi$
$822$	−1.88512e9	−0.118382
$823$	−8.48016e9	−0.530279	−0.265140	−	0.964210i	$-0.585418\pi$
$823$	−8.48016e9	−0.530279	−0.265140	+	0.964210i	$0.585418\pi$
$824$	−8.80319e9	−0.548144
$825$	−3.95608e9	−0.245288
$826$	−6.84935e8	−0.0422882
$827$	−1.81973e10	−1.11876	−0.559381	−	0.828911i	$-0.688961\pi$
$827$	−1.81973e10	−1.11876	−0.559381	+	0.828911i	$0.688961\pi$
$828$	3.73313e9	0.228543
$829$	−5.46488e9	−0.333150	−0.166575	−	0.986029i	$-0.553271\pi$
$829$	−5.46488e9	−0.333150	−0.166575	+	0.986029i	$0.553271\pi$
$830$	2.28154e10	1.38502
$831$	7.77638e9	0.470082
$832$	5.75930e8	0.0346688
$833$	−1.98068e8	−0.0118729
$834$	2.52907e9	0.150966
$835$	−9.87873e9	−0.587217
$836$	1.24993e10	0.739885
$837$	3.49740e9	0.206161
$838$	−4.86013e9	−0.285294
$839$	1.14912e9	0.0671737	0.0335868	−	0.999436i	$-0.489307\pi$
$839$	1.14912e9	0.0671737	0.0335868	+	0.999436i	$0.489307\pi$
$840$	1.57556e9	0.0917186
$841$	1.33918e10	0.776342
$842$	1.64995e10	0.952528
$843$	2.40637e9	0.138346
$844$	−1.28000e10	−0.732843
$845$	1.60386e9	0.0914469
$846$	−9.00958e8	−0.0511574
$847$	−3.79963e8	−0.0214857
$848$	−2.40432e8	−0.0135396
$849$	−7.26094e8	−0.0407208
$850$	−4.34849e8	−0.0242869
$851$	1.65639e10	0.921319
$852$	1.24514e9	0.0689732
$853$	1.87086e10	1.03210	0.516048	−	0.856560i	$-0.327403\pi$
$853$	1.87086e10	1.03210	0.516048	+	0.856560i	$0.327403\pi$
$854$	2.54286e9	0.139708
$855$	1.04246e10	0.570400
$856$	−3.70369e9	−0.201826
$857$	−1.77412e10	−0.962832	−0.481416	−	0.876492i	$-0.659877\pi$
$857$	−1.77412e10	−0.962832	−0.481416	+	0.876492i	$0.659877\pi$
$858$	−2.15359e9	−0.116401
$859$	1.69542e10	0.912643	0.456322	−	0.889815i	$-0.349167\pi$
$859$	1.69542e10	0.912643	0.456322	+	0.889815i	$0.349167\pi$
$860$	1.08693e10	0.582716
$861$	3.87827e9	0.207075
$862$	−1.52220e9	−0.0809464
$863$	−3.76730e10	−1.99523	−0.997613	−	0.0690540i	$-0.978002\pi$
$863$	−3.76730e10	−1.99523	−0.997613	+	0.0690540i	$0.978002\pi$
$864$	−6.44973e8	−0.0340207
$865$	3.48256e10	1.82954
$866$	−2.27500e10	−1.19033
$867$	1.10026e10	0.573362
$868$	3.90057e9	0.202446
$869$	−7.37225e9	−0.381093
$870$	1.25637e10	0.646844
$871$	−7.08443e9	−0.363280
$872$	2.72293e8	0.0139068
$873$	−5.08650e9	−0.258743
$874$	2.75475e10	1.39570
$875$	5.22434e9	0.263635
$876$	−1.05619e10	−0.530858
$877$	−1.32929e10	−0.665461	−0.332730	−	0.943022i	$-0.607970\pi$
$877$	−1.32929e10	−0.665461	−0.332730	+	0.943022i	$0.607970\pi$
$878$	−2.05385e10	−1.02409
$879$	3.55574e9	0.176591
$880$	6.17657e9	0.305533
$881$	1.63851e10	0.807299	0.403650	−	0.914914i	$-0.367742\pi$
$881$	1.63851e10	0.807299	0.403650	+	0.914914i	$0.367742\pi$
$882$	6.86129e8	0.0336718
$883$	2.98014e10	1.45671	0.728357	−	0.685198i	$-0.240284\pi$
$883$	2.98014e10	1.45671	0.728357	+	0.685198i	$0.240284\pi$
$884$	−2.36721e8	−0.0115254
$885$	−2.23942e9	−0.108601
$886$	6.49434e8	0.0313702
$887$	−1.54252e10	−0.742163	−0.371081	−	0.928600i	$-0.621013\pi$
$887$	−1.54252e10	−0.742163	−0.371081	+	0.928600i	$0.621013\pi$
$888$	−2.86175e9	−0.137147
$889$	1.42005e8	0.00677872
$890$	−1.91970e10	−0.912786
$891$	2.41177e9	0.114226
$892$	−1.21677e10	−0.574027
$893$	−6.64834e9	−0.312416
$894$	−1.13414e10	−0.530866
$895$	4.41169e10	2.05695
$896$	−7.19323e8	−0.0334077
$897$	−4.74635e9	−0.219577
$898$	1.12923e10	0.520374
$899$	3.11036e10	1.42775
$900$	1.50636e9	0.0688779
$901$	9.88231e7	0.00450113
$902$	1.52037e10	0.689807
$903$	4.73339e9	0.213927
$904$	6.73351e9	0.303146
$905$	−2.28085e10	−1.02289
$906$	2.30747e8	0.0103083
$907$	−2.20805e10	−0.982614	−0.491307	−	0.870987i	$-0.663481\pi$
$907$	−2.20805e10	−0.982614	−0.491307	+	0.870987i	$0.663481\pi$
$908$	1.26131e10	0.559141
$909$	−3.14034e8	−0.0138677
$910$	−2.00319e9	−0.0881204
$911$	−4.36513e10	−1.91286	−0.956428	−	0.291967i	$-0.905690\pi$
$911$	−4.36513e10	−1.91286	−0.956428	+	0.291967i	$0.905690\pi$
$912$	−4.75937e9	−0.207763
$913$	3.89503e10	1.69381
$914$	−1.96699e9	−0.0852100
$915$	8.31399e9	0.358786
$916$	1.23446e10	0.530694
$917$	−1.59277e10	−0.682118
$918$	2.65099e8	0.0113099
$919$	1.67550e9	0.0712099	0.0356049	−	0.999366i	$-0.488664\pi$
$919$	1.67550e9	0.0712099	0.0356049	+	0.999366i	$0.488664\pi$
$920$	1.36127e10	0.576349
$921$	−2.04972e9	−0.0864540
$922$	6.14207e9	0.258081
$923$	−1.58309e9	−0.0662673
$924$	2.68979e9	0.112167
$925$	6.68373e9	0.277666
$926$	−2.50783e10	−1.03791
$927$	−1.25342e10	−0.516795
$928$	−5.73596e9	−0.235607
$929$	2.20950e10	0.904149	0.452074	−	0.891980i	$-0.350684\pi$
$929$	2.20950e10	0.904149	0.452074	+	0.891980i	$0.350684\pi$
$930$	1.27531e10	0.519906
$931$	5.06307e9	0.205632
$932$	1.37708e10	0.557191
$933$	−1.19025e10	−0.479790
$934$	−2.44389e10	−0.981449
$935$	−2.53872e9	−0.101572
$936$	8.20026e8	0.0326860
$937$	3.17830e10	1.26214	0.631069	−	0.775727i	$-0.282617\pi$
$937$	3.17830e10	1.26214	0.631069	+	0.775727i	$0.282617\pi$
$938$	8.84828e9	0.350065
$939$	−2.41437e10	−0.951642
$940$	−3.28530e9	−0.129011
$941$	−2.50884e10	−0.981544	−0.490772	−	0.871288i	$-0.663285\pi$
$941$	−2.50884e10	−0.981544	−0.490772	+	0.871288i	$0.663285\pi$
$942$	−4.01524e9	−0.156507
$943$	3.35078e10	1.30123
$944$	1.02241e9	0.0395570
$945$	2.24333e9	0.0864731
$946$	1.85560e10	0.712633
$947$	−2.13366e10	−0.816396	−0.408198	−	0.912893i	$-0.633843\pi$
$947$	−2.13366e10	−0.816396	−0.408198	+	0.912893i	$0.633843\pi$
$948$	2.80714e9	0.107012
$949$	1.34286e10	0.510032
$950$	1.11157e10	0.420634
$951$	2.50379e10	0.943988
$952$	2.95659e8	0.0111061
$953$	−3.59693e10	−1.34619	−0.673097	−	0.739555i	$-0.735036\pi$
$953$	−3.59693e10	−1.34619	−0.673097	+	0.739555i	$0.735036\pi$
$954$	−3.42333e8	−0.0127653
$955$	−1.98772e10	−0.738489
$956$	−8.71050e9	−0.322434
$957$	2.14487e10	0.791058
$958$	6.44485e9	0.236828
$959$	−2.99349e9	−0.109601
$960$	−2.35186e9	−0.0857949
$961$	4.05984e9	0.147563
$962$	3.63846e9	0.131766
$963$	−5.27342e9	−0.190283
$964$	2.22835e10	0.801150
$965$	4.93861e10	1.76913
$966$	5.92807e9	0.211589
$967$	3.68747e10	1.31140	0.655702	−	0.755020i	$-0.272373\pi$
$967$	3.68747e10	1.31140	0.655702	+	0.755020i	$0.272373\pi$
$968$	5.67175e8	0.0200980
$969$	1.95622e9	0.0690691
$970$	−1.85476e10	−0.652510
$971$	3.88100e10	1.36043	0.680215	−	0.733013i	$-0.261886\pi$
$971$	3.88100e10	1.36043	0.680215	+	0.733013i	$0.261886\pi$
$972$	−9.18330e8	−0.0320750
$973$	4.01607e9	0.139768
$974$	−3.11156e10	−1.07900
$975$	−1.91520e9	−0.0661758
$976$	−3.79576e9	−0.130685
$977$	1.23536e10	0.423801	0.211901	−	0.977291i	$-0.432035\pi$
$977$	1.23536e10	0.423801	0.211901	+	0.977291i	$0.432035\pi$
$978$	−1.68829e10	−0.577115
$979$	−3.27731e10	−1.11629
$980$	2.50193e9	0.0849149
$981$	3.87698e8	0.0131115
$982$	2.47860e9	0.0835251
$983$	1.39366e9	0.0467972	0.0233986	−	0.999726i	$-0.492551\pi$
$983$	1.39366e9	0.0467972	0.0233986	+	0.999726i	$0.492551\pi$
$984$	−5.78914e9	−0.193701
$985$	1.33417e10	0.444819
$986$	2.35762e9	0.0783257
$987$	−1.43069e9	−0.0473626
$988$	6.05112e9	0.199612
$989$	4.08960e10	1.34429
$990$	8.79437e9	0.288059
$991$	3.93376e10	1.28396	0.641978	−	0.766723i	$-0.278114\pi$
$991$	3.93376e10	1.28396	0.641978	+	0.766723i	$0.278114\pi$
$992$	−5.82243e9	−0.189371
$993$	2.69936e10	0.874860
$994$	1.97724e9	0.0638568
$995$	4.08535e10	1.31477
$996$	−1.48311e10	−0.475628
$997$	5.24317e10	1.67556	0.837781	−	0.546006i	$-0.183853\pi$
$997$	5.24317e10	1.67556	0.837781	+	0.546006i	$0.183853\pi$
$998$	−4.75624e9	−0.151463
$999$	−4.07464e9	−0.129303

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.r.1.5	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +332.282 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +332.282 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +2658.26 q^{10} +4538.16 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} -8971.62 q^{15} +4096.00 q^{16} -1683.55 q^{17} +5832.00 q^{18} +43035.4 q^{19} +21266.1 q^{20} +9261.00 q^{21} +36305.3 q^{22} +80014.0 q^{23} -13824.0 q^{24} +32286.5 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} -175048. q^{29} -71773.0 q^{30} -177686. q^{31} +32768.0 q^{32} -122530. q^{33} -13468.4 q^{34} -113973. q^{35} +46656.0 q^{36} +207013. q^{37} +344283. q^{38} -59319.0 q^{39} +170129. q^{40} +418774. q^{41} +74088.0 q^{42} +511110. q^{43} +290443. q^{44} +242234. q^{45} +640112. q^{46} -154485. q^{47} -110592. q^{48} +117649. q^{49} +258292. q^{50} +45456.0 q^{51} +140608. q^{52} -58699.1 q^{53} -157464. q^{54} +1.50795e6 q^{55} -175616. q^{56} -1.16196e6 q^{57} -1.40038e6 q^{58} +249612. q^{59} -574184. q^{60} -926699. q^{61} -1.42149e6 q^{62} -250047. q^{63} +262144. q^{64} +730024. q^{65} -980243. q^{66} -3.22459e6 q^{67} -107747. q^{68} -2.16038e6 q^{69} -911783. q^{70} -720569. q^{71} +373248. q^{72} +6.11222e6 q^{73} +1.65610e6 q^{74} -871736. q^{75} +2.75427e6 q^{76} -1.55659e6 q^{77} -474552. q^{78} -1.62450e6 q^{79} +1.36103e6 q^{80} +531441. q^{81} +3.35020e6 q^{82} +8.58284e6 q^{83} +592704. q^{84} -559415. q^{85} +4.08888e6 q^{86} +4.72629e6 q^{87} +2.32354e6 q^{88} -7.22166e6 q^{89} +1.93787e6 q^{90} -753571. q^{91} +5.12089e6 q^{92} +4.79753e6 q^{93} -1.23588e6 q^{94} +1.42999e7 q^{95} -884736. q^{96} -6.97736e6 q^{97} +941192. q^{98} +3.30832e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 1624 q^{10} - 2690 q^{11} - 10368 q^{12} + 13182 q^{13} - 16464 q^{14} - 5481 q^{15} + 24576 q^{16} + 2910 q^{17} + 34992 q^{18} - 13055 q^{19} + 12992 q^{20} + 55566 q^{21} - 21520 q^{22} + 11581 q^{23} - 82944 q^{24} + 68081 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} - 92335 q^{29} - 43848 q^{30} - 83081 q^{31} + 196608 q^{32} + 72630 q^{33} + 23280 q^{34} - 69629 q^{35} + 279936 q^{36} - 265114 q^{37} - 104440 q^{38} - 355914 q^{39} + 103936 q^{40} - 367468 q^{41} + 444528 q^{42} + 454955 q^{43} - 172160 q^{44} + 147987 q^{45} + 92648 q^{46} + 733973 q^{47} - 663552 q^{48} + 705894 q^{49} + 544648 q^{50} - 78570 q^{51} + 843648 q^{52} - 1577379 q^{53} - 944784 q^{54} + 2231118 q^{55} - 1053696 q^{56} + 352485 q^{57} - 738680 q^{58} + 2062708 q^{59} - 350784 q^{60} - 271270 q^{61} - 664648 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 445991 q^{65} + 581040 q^{66} - 758674 q^{67} + 186240 q^{68} - 312687 q^{69} - 557032 q^{70} - 6138216 q^{71} + 2239488 q^{72} + 6361979 q^{73} - 2120912 q^{74} - 1838187 q^{75} - 835520 q^{76} + 922670 q^{77} - 2847312 q^{78} - 899781 q^{79} + 831488 q^{80} + 3188646 q^{81} - 2939744 q^{82} + 3313561 q^{83} + 3556224 q^{84} + 5307940 q^{85} + 3639640 q^{86} + 2493045 q^{87} - 1377280 q^{88} + 11210703 q^{89} + 1183896 q^{90} - 4521426 q^{91} + 741184 q^{92} + 2243187 q^{93} + 5871784 q^{94} + 12912395 q^{95} - 5308416 q^{96} + 28682643 q^{97} + 5647152 q^{98} - 1961010 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 203 * q^5 - 1296 * q^6 - 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 1624 * q^10 - 2690 * q^11 - 10368 * q^12 + 13182 * q^13 - 16464 * q^14 - 5481 * q^15 + 24576 * q^16 + 2910 * q^17 + 34992 * q^18 - 13055 * q^19 + 12992 * q^20 + 55566 * q^21 - 21520 * q^22 + 11581 * q^23 - 82944 * q^24 + 68081 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 - 92335 * q^29 - 43848 * q^30 - 83081 * q^31 + 196608 * q^32 + 72630 * q^33 + 23280 * q^34 - 69629 * q^35 + 279936 * q^36 - 265114 * q^37 - 104440 * q^38 - 355914 * q^39 + 103936 * q^40 - 367468 * q^41 + 444528 * q^42 + 454955 * q^43 - 172160 * q^44 + 147987 * q^45 + 92648 * q^46 + 733973 * q^47 - 663552 * q^48 + 705894 * q^49 + 544648 * q^50 - 78570 * q^51 + 843648 * q^52 - 1577379 * q^53 - 944784 * q^54 + 2231118 * q^55 - 1053696 * q^56 + 352485 * q^57 - 738680 * q^58 + 2062708 * q^59 - 350784 * q^60 - 271270 * q^61 - 664648 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 445991 * q^65 + 581040 * q^66 - 758674 * q^67 + 186240 * q^68 - 312687 * q^69 - 557032 * q^70 - 6138216 * q^71 + 2239488 * q^72 + 6361979 * q^73 - 2120912 * q^74 - 1838187 * q^75 - 835520 * q^76 + 922670 * q^77 - 2847312 * q^78 - 899781 * q^79 + 831488 * q^80 + 3188646 * q^81 - 2939744 * q^82 + 3313561 * q^83 + 3556224 * q^84 + 5307940 * q^85 + 3639640 * q^86 + 2493045 * q^87 - 1377280 * q^88 + 11210703 * q^89 + 1183896 * q^90 - 4521426 * q^91 + 741184 * q^92 + 2243187 * q^93 + 5871784 * q^94 + 12912395 * q^95 - 5308416 * q^96 + 28682643 * q^97 + 5647152 * q^98 - 1961010 * q^99

Introduction

L-functions

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