LMFDB - Embedded newform 546.8.a.l.1.2

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:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 122890x^{3} - 6160660x^{2} + 3465881625x + 278845474950 $ x^5 - 2x^4 - 122890x^3 - 6160660x^2 + 3465881625x + 278845474950
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-231.824$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -223.551 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -223.551 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -1788.41 q^{10} +3707.45 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +6035.88 q^{15} +4096.00 q^{16} -5322.98 q^{17} +5832.00 q^{18} -847.191 q^{19} -14307.3 q^{20} +9261.00 q^{21} +29659.6 q^{22} -6779.82 q^{23} -13824.0 q^{24} -28150.0 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +114612. q^{29} +48287.0 q^{30} -107586. q^{31} +32768.0 q^{32} -100101. q^{33} -42583.9 q^{34} +76678.0 q^{35} +46656.0 q^{36} +500720. q^{37} -6777.53 q^{38} +59319.0 q^{39} -114458. q^{40} -193490. q^{41} +74088.0 q^{42} +528743. q^{43} +237277. q^{44} -162969. q^{45} -54238.6 q^{46} -270082. q^{47} -110592. q^{48} +117649. q^{49} -225200. q^{50} +143721. q^{51} -140608. q^{52} +166841. q^{53} -157464. q^{54} -828803. q^{55} -175616. q^{56} +22874.2 q^{57} +916897. q^{58} +2.73954e6 q^{59} +386296. q^{60} -6760.78 q^{61} -860691. q^{62} -250047. q^{63} +262144. q^{64} +491142. q^{65} -800808. q^{66} +1.33318e6 q^{67} -340671. q^{68} +183055. q^{69} +613424. q^{70} -1.97912e6 q^{71} +373248. q^{72} -1.51276e6 q^{73} +4.00576e6 q^{74} +760049. q^{75} -54220.2 q^{76} -1.27165e6 q^{77} +474552. q^{78} +1.03335e6 q^{79} -915665. q^{80} +531441. q^{81} -1.54792e6 q^{82} -6.46458e6 q^{83} +592704. q^{84} +1.18996e6 q^{85} +4.22994e6 q^{86} -3.09453e6 q^{87} +1.89821e6 q^{88} -1.08910e7 q^{89} -1.30375e6 q^{90} +753571. q^{91} -433909. q^{92} +2.90483e6 q^{93} -2.16065e6 q^{94} +189390. q^{95} -884736. q^{96} +7.47976e6 q^{97} +941192. q^{98} +2.70273e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) $ 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} - 2000 q^{10} + 659 q^{11} - 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 6750 q^{15} + 20480 q^{16} + 24575 q^{17} + 29160 q^{18} - 6446 q^{19} - 16000 q^{20} + 46305 q^{21} + 5272 q^{22} + 30268 q^{23} - 69120 q^{24} + 38965 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} + 130950 q^{29} + 54000 q^{30} + 262979 q^{31} + 163840 q^{32} - 17793 q^{33} + 196600 q^{34} + 85750 q^{35} + 233280 q^{36} - 101549 q^{37} - 51568 q^{38} + 296595 q^{39} - 128000 q^{40} - 247328 q^{41} + 370440 q^{42} - 19092 q^{43} + 42176 q^{44} - 182250 q^{45} + 242144 q^{46} - 126419 q^{47} - 552960 q^{48} + 588245 q^{49} + 311720 q^{50} - 663525 q^{51} - 703040 q^{52} - 302793 q^{53} - 787320 q^{54} + 943985 q^{55} - 878080 q^{56} + 174042 q^{57} + 1047600 q^{58} - 2798636 q^{59} + 432000 q^{60} - 2493751 q^{61} + 2103832 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 549250 q^{65} - 142344 q^{66} + 160188 q^{67} + 1572800 q^{68} - 817236 q^{69} + 686000 q^{70} + 3846088 q^{71} + 1866240 q^{72} + 5655872 q^{73} - 812392 q^{74} - 1052055 q^{75} - 412544 q^{76} - 226037 q^{77} + 2372760 q^{78} + 5647991 q^{79} - 1024000 q^{80} + 2657205 q^{81} - 1978624 q^{82} - 4607669 q^{83} + 2963520 q^{84} + 3873935 q^{85} - 152736 q^{86} - 3535650 q^{87} + 337408 q^{88} - 17424029 q^{89} - 1458000 q^{90} + 3767855 q^{91} + 1937152 q^{92} - 7100433 q^{93} - 1011352 q^{94} - 24593720 q^{95} - 4423680 q^{96} - 18380577 q^{97} + 4705960 q^{98} + 480411 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 - 2000 * q^10 + 659 * q^11 - 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 6750 * q^15 + 20480 * q^16 + 24575 * q^17 + 29160 * q^18 - 6446 * q^19 - 16000 * q^20 + 46305 * q^21 + 5272 * q^22 + 30268 * q^23 - 69120 * q^24 + 38965 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 + 130950 * q^29 + 54000 * q^30 + 262979 * q^31 + 163840 * q^32 - 17793 * q^33 + 196600 * q^34 + 85750 * q^35 + 233280 * q^36 - 101549 * q^37 - 51568 * q^38 + 296595 * q^39 - 128000 * q^40 - 247328 * q^41 + 370440 * q^42 - 19092 * q^43 + 42176 * q^44 - 182250 * q^45 + 242144 * q^46 - 126419 * q^47 - 552960 * q^48 + 588245 * q^49 + 311720 * q^50 - 663525 * q^51 - 703040 * q^52 - 302793 * q^53 - 787320 * q^54 + 943985 * q^55 - 878080 * q^56 + 174042 * q^57 + 1047600 * q^58 - 2798636 * q^59 + 432000 * q^60 - 2493751 * q^61 + 2103832 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 549250 * q^65 - 142344 * q^66 + 160188 * q^67 + 1572800 * q^68 - 817236 * q^69 + 686000 * q^70 + 3846088 * q^71 + 1866240 * q^72 + 5655872 * q^73 - 812392 * q^74 - 1052055 * q^75 - 412544 * q^76 - 226037 * q^77 + 2372760 * q^78 + 5647991 * q^79 - 1024000 * q^80 + 2657205 * q^81 - 1978624 * q^82 - 4607669 * q^83 + 2963520 * q^84 + 3873935 * q^85 - 152736 * q^86 - 3535650 * q^87 + 337408 * q^88 - 17424029 * q^89 - 1458000 * q^90 + 3767855 * q^91 + 1937152 * q^92 - 7100433 * q^93 - 1011352 * q^94 - 24593720 * q^95 - 4423680 * q^96 - 18380577 * q^97 + 4705960 * q^98 + 480411 * 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
$5$	−223.551	−0.799800	−0.399900	−	0.916559i	$-0.630955\pi$
$5$	−223.551	−0.799800	−0.399900	+	0.916559i	$0.630955\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−1788.41	−0.565544
$11$	3707.45	0.839848	0.419924	−	0.907559i	$-0.362057\pi$
$11$	3707.45	0.839848	0.419924	+	0.907559i	$0.362057\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	6035.88	0.461765
$16$	4096.00	0.250000
$17$	−5322.98	−0.262775	−0.131387	−	0.991331i	$-0.541943\pi$
$17$	−5322.98	−0.262775	−0.131387	+	0.991331i	$0.541943\pi$
$18$	5832.00	0.235702
$19$	−847.191	−0.0283363	−0.0141682	−	0.999900i	$-0.504510\pi$
$19$	−847.191	−0.0283363	−0.0141682	+	0.999900i	$0.504510\pi$
$20$	−14307.3	−0.399900
$21$	9261.00	0.218218
$22$	29659.6	0.593862
$23$	−6779.82	−0.116191	−0.0580953	−	0.998311i	$-0.518503\pi$
$23$	−6779.82	−0.116191	−0.0580953	+	0.998311i	$0.518503\pi$
$24$	−13824.0	−0.204124
$25$	−28150.0	−0.360319
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	114612.	0.872645	0.436322	−	0.899790i	$-0.356281\pi$
$29$	114612.	0.872645	0.436322	+	0.899790i	$0.356281\pi$
$30$	48287.0	0.326517
$31$	−107586.	−0.648621	−0.324311	−	0.945951i	$-0.605132\pi$
$31$	−107586.	−0.648621	−0.324311	+	0.945951i	$0.605132\pi$
$32$	32768.0	0.176777
$33$	−100101.	−0.484886
$34$	−42583.9	−0.185810
$35$	76678.0	0.302296
$36$	46656.0	0.166667
$37$	500720.	1.62513	0.812567	−	0.582868i	$-0.198070\pi$
$37$	500720.	1.62513	0.812567	+	0.582868i	$0.198070\pi$
$38$	−6777.53	−0.0200368
$39$	59319.0	0.160128
$40$	−114458.	−0.282772
$41$	−193490.	−0.438446	−0.219223	−	0.975675i	$-0.570352\pi$
$41$	−193490.	−0.438446	−0.219223	+	0.975675i	$0.570352\pi$
$42$	74088.0	0.154303
$43$	528743.	1.01416	0.507078	−	0.861900i	$-0.330726\pi$
$43$	528743.	1.01416	0.507078	+	0.861900i	$0.330726\pi$
$44$	237277.	0.419924
$45$	−162969.	−0.266600
$46$	−54238.6	−0.0821592
$47$	−270082.	−0.379448	−0.189724	−	0.981837i	$-0.560759\pi$
$47$	−270082.	−0.379448	−0.189724	+	0.981837i	$0.560759\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	−225200.	−0.254784
$51$	143721.	0.151713
$52$	−140608.	−0.138675
$53$	166841.	0.153935	0.0769674	−	0.997034i	$-0.475476\pi$
$53$	166841.	0.153935	0.0769674	+	0.997034i	$0.475476\pi$
$54$	−157464.	−0.136083
$55$	−828803.	−0.671710
$56$	−175616.	−0.133631
$57$	22874.2	0.0163600
$58$	916897.	0.617053
$59$	2.73954e6	1.73659	0.868293	−	0.496052i	$-0.165218\pi$
$59$	2.73954e6	1.73659	0.868293	+	0.496052i	$0.165218\pi$
$60$	386296.	0.230882
$61$	−6760.78	−0.00381366	−0.00190683	−	0.999998i	$-0.500607\pi$
$61$	−6760.78	−0.00381366	−0.00190683	+	0.999998i	$0.500607\pi$
$62$	−860691.	−0.458645
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	491142.	0.221825
$66$	−800808.	−0.342866
$67$	1.33318e6	0.541535	0.270767	−	0.962645i	$-0.412723\pi$
$67$	1.33318e6	0.541535	0.270767	+	0.962645i	$0.412723\pi$
$68$	−340671.	−0.131387
$69$	183055.	0.0670827
$70$	613424.	0.213756
$71$	−1.97912e6	−0.656249	−0.328125	−	0.944634i	$-0.606417\pi$
$71$	−1.97912e6	−0.656249	−0.328125	+	0.944634i	$0.606417\pi$
$72$	373248.	0.117851
$73$	−1.51276e6	−0.455135	−0.227568	−	0.973762i	$-0.573077\pi$
$73$	−1.51276e6	−0.455135	−0.227568	+	0.973762i	$0.573077\pi$
$74$	4.00576e6	1.14914
$75$	760049.	0.208031
$76$	−54220.2	−0.0141682
$77$	−1.27165e6	−0.317433
$78$	474552.	0.113228
$79$	1.03335e6	0.235805	0.117902	−	0.993025i	$-0.462383\pi$
$79$	1.03335e6	0.235805	0.117902	+	0.993025i	$0.462383\pi$
$80$	−915665.	−0.199950
$81$	531441.	0.111111
$82$	−1.54792e6	−0.310028
$83$	−6.46458e6	−1.24099	−0.620493	−	0.784212i	$-0.713068\pi$
$83$	−6.46458e6	−1.24099	−0.620493	+	0.784212i	$0.713068\pi$
$84$	592704.	0.109109
$85$	1.18996e6	0.210167
$86$	4.22994e6	0.717117
$87$	−3.09453e6	−0.503822
$88$	1.89821e6	0.296931
$89$	−1.08910e7	−1.63758	−0.818791	−	0.574092i	$-0.805355\pi$
$89$	−1.08910e7	−1.63758	−0.818791	+	0.574092i	$0.805355\pi$
$90$	−1.30375e6	−0.188515
$91$	753571.	0.104828
$92$	−433909.	−0.0580953
$93$	2.90483e6	0.374482
$94$	−2.16065e6	−0.268310
$95$	189390.	0.0226634
$96$	−884736.	−0.102062
$97$	7.47976e6	0.832122	0.416061	−	0.909337i	$-0.363410\pi$
$97$	7.47976e6	0.832122	0.416061	+	0.909337i	$0.363410\pi$
$98$	941192.	0.101015
$99$	2.70273e6	0.279949
$100$	−1.80160e6	−0.180160
$101$	−6.63393e6	−0.640687	−0.320343	−	0.947301i	$-0.603798\pi$
$101$	−6.63393e6	−0.640687	−0.320343	+	0.947301i	$0.603798\pi$
$102$	1.14976e6	0.107277
$103$	9.42132e6	0.849535	0.424768	−	0.905302i	$-0.360356\pi$
$103$	9.42132e6	0.849535	0.424768	+	0.905302i	$0.360356\pi$
$104$	−1.12486e6	−0.0980581
$105$	−2.07031e6	−0.174531
$106$	1.33473e6	0.108848
$107$	−2.00792e7	−1.58454	−0.792270	−	0.610170i	$-0.791101\pi$
$107$	−2.00792e7	−1.58454	−0.792270	+	0.610170i	$0.791101\pi$
$108$	−1.25971e6	−0.0962250
$109$	−1.99527e7	−1.47573	−0.737867	−	0.674947i	$-0.764167\pi$
$109$	−1.99527e7	−1.47573	−0.737867	+	0.674947i	$0.764167\pi$
$110$	−6.63043e6	−0.474971
$111$	−1.35194e7	−0.938271
$112$	−1.40493e6	−0.0944911
$113$	−1.26125e7	−0.822295	−0.411148	−	0.911569i	$-0.634872\pi$
$113$	−1.26125e7	−0.822295	−0.411148	+	0.911569i	$0.634872\pi$
$114$	182993.	0.0115683
$115$	1.51564e6	0.0929293
$116$	7.33517e6	0.436322
$117$	−1.60161e6	−0.0924500
$118$	2.19163e7	1.22795
$119$	1.82578e6	0.0993196
$120$	3.09037e6	0.163259
$121$	−5.74201e6	−0.294656
$122$	−54086.3	−0.00269667
$123$	5.22424e6	0.253137
$124$	−6.88553e6	−0.324311
$125$	2.37579e7	1.08798
$126$	−2.00038e6	−0.0890871
$127$	−3.28621e7	−1.42358	−0.711790	−	0.702392i	$-0.752115\pi$
$127$	−3.28621e7	−1.42358	−0.711790	+	0.702392i	$0.752115\pi$
$128$	2.09715e6	0.0883883
$129$	−1.42761e7	−0.585523
$130$	3.92913e6	0.156854
$131$	−1.60922e7	−0.625413	−0.312707	−	0.949850i	$-0.601236\pi$
$131$	−1.60922e7	−0.625413	−0.312707	+	0.949850i	$0.601236\pi$
$132$	−6.40647e6	−0.242443
$133$	290587.	0.0107101
$134$	1.06654e7	0.382923
$135$	4.40015e6	0.153922
$136$	−2.72537e6	−0.0929050
$137$	4.48542e6	0.149032	0.0745162	−	0.997220i	$-0.476259\pi$
$137$	4.48542e6	0.149032	0.0745162	+	0.997220i	$0.476259\pi$
$138$	1.46444e6	0.0474346
$139$	−3.78403e7	−1.19510	−0.597548	−	0.801833i	$-0.703858\pi$
$139$	−3.78403e7	−1.19510	−0.597548	+	0.801833i	$0.703858\pi$
$140$	4.90739e6	0.151148
$141$	7.29220e6	0.219074
$142$	−1.58330e7	−0.464038
$143$	−8.14526e6	−0.232932
$144$	2.98598e6	0.0833333
$145$	−2.56216e7	−0.697942
$146$	−1.21021e7	−0.321829
$147$	−3.17652e6	−0.0824786
$148$	3.20461e7	0.812567
$149$	6.07663e7	1.50491	0.752456	−	0.658643i	$-0.228869\pi$
$149$	6.07663e7	1.50491	0.752456	+	0.658643i	$0.228869\pi$
$150$	6.08039e6	0.147100
$151$	−3.29904e7	−0.779773	−0.389886	−	0.920863i	$-0.627486\pi$
$151$	−3.29904e7	−0.779773	−0.389886	+	0.920863i	$0.627486\pi$
$152$	−433762.	−0.0100184
$153$	−3.88046e6	−0.0875916
$154$	−1.01732e7	−0.224459
$155$	2.40510e7	0.518768
$156$	3.79642e6	0.0800641
$157$	−2.58988e7	−0.534110	−0.267055	−	0.963681i	$-0.586051\pi$
$157$	−2.58988e7	−0.534110	−0.267055	+	0.963681i	$0.586051\pi$
$158$	8.26680e6	0.166739
$159$	−4.50471e6	−0.0888744
$160$	−7.32532e6	−0.141386
$161$	2.32548e6	0.0439159
$162$	4.25153e6	0.0785674
$163$	−4.88552e6	−0.0883596	−0.0441798	−	0.999024i	$-0.514067\pi$
$163$	−4.88552e6	−0.0883596	−0.0441798	+	0.999024i	$0.514067\pi$
$164$	−1.23834e7	−0.219223
$165$	2.23777e7	0.387812
$166$	−5.17167e7	−0.877510
$167$	−8.22156e7	−1.36599	−0.682993	−	0.730425i	$-0.739322\pi$
$167$	−8.22156e7	−1.36599	−0.682993	+	0.730425i	$0.739322\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	9.51967e6	0.148611
$171$	−617602.	−0.00944545
$172$	3.38395e7	0.507078
$173$	6.15776e7	0.904194	0.452097	−	0.891969i	$-0.350676\pi$
$173$	6.15776e7	0.904194	0.452097	+	0.891969i	$0.350676\pi$
$174$	−2.47562e7	−0.356256
$175$	9.65543e6	0.136188
$176$	1.51857e7	0.209962
$177$	−7.39677e7	−1.00262
$178$	−8.71281e7	−1.15795
$179$	8.02038e7	1.04522	0.522612	−	0.852571i	$-0.324958\pi$
$179$	8.02038e7	1.04522	0.522612	+	0.852571i	$0.324958\pi$
$180$	−1.04300e7	−0.133300
$181$	4.88590e7	0.612449	0.306224	−	0.951959i	$-0.400934\pi$
$181$	4.88590e7	0.612449	0.306224	+	0.951959i	$0.400934\pi$
$182$	6.02857e6	0.0741249
$183$	182541.	0.00220182
$184$	−3.47127e6	−0.0410796
$185$	−1.11936e8	−1.29978
$186$	2.32387e7	0.264799
$187$	−1.97347e7	−0.220691
$188$	−1.72852e7	−0.189724
$189$	6.75127e6	0.0727393
$190$	1.51512e6	0.0160255
$191$	−8.29971e7	−0.861879	−0.430939	−	0.902381i	$-0.641818\pi$
$191$	−8.29971e7	−0.861879	−0.430939	+	0.902381i	$0.641818\pi$
$192$	−7.07789e6	−0.0721688
$193$	−6.75634e7	−0.676489	−0.338245	−	0.941058i	$-0.609833\pi$
$193$	−6.75634e7	−0.676489	−0.338245	+	0.941058i	$0.609833\pi$
$194$	5.98381e7	0.588399
$195$	−1.32608e7	−0.128071
$196$	7.52954e6	0.0714286
$197$	2.08766e7	0.194548	0.0972742	−	0.995258i	$-0.468988\pi$
$197$	2.08766e7	0.194548	0.0972742	+	0.995258i	$0.468988\pi$
$198$	2.16218e7	0.197954
$199$	−6.60055e7	−0.593737	−0.296869	−	0.954918i	$-0.595942\pi$
$199$	−6.60055e7	−0.593737	−0.296869	+	0.954918i	$0.595942\pi$
$200$	−1.44128e7	−0.127392
$201$	−3.59958e7	−0.312655
$202$	−5.30714e7	−0.453034
$203$	−3.93119e7	−0.329829
$204$	9.19812e6	0.0758566
$205$	4.32550e7	0.350669
$206$	7.53706e7	0.600712
$207$	−4.94249e6	−0.0387302
$208$	−8.99891e6	−0.0693375
$209$	−3.14092e6	−0.0237982
$210$	−1.65624e7	−0.123412
$211$	3.57733e7	0.262162	0.131081	−	0.991372i	$-0.458155\pi$
$211$	3.57733e7	0.262162	0.131081	+	0.991372i	$0.458155\pi$
$212$	1.06778e7	0.0769674
$213$	5.34364e7	0.378886
$214$	−1.60634e8	−1.12044
$215$	−1.18201e8	−0.811123
$216$	−1.00777e7	−0.0680414
$217$	3.69021e7	0.245156
$218$	−1.59621e8	−1.04350
$219$	4.08446e7	0.262772
$220$	−5.30434e7	−0.335855
$221$	1.16946e7	0.0728807
$222$	−1.08156e8	−0.663458
$223$	−2.51998e8	−1.52170	−0.760852	−	0.648925i	$-0.775219\pi$
$223$	−2.51998e8	−1.52170	−0.760852	+	0.648925i	$0.775219\pi$
$224$	−1.12394e7	−0.0668153
$225$	−2.05213e7	−0.120106
$226$	−1.00900e8	−0.581451
$227$	−9.82486e7	−0.557488	−0.278744	−	0.960365i	$-0.589918\pi$
$227$	−9.82486e7	−0.557488	−0.278744	+	0.960365i	$0.589918\pi$
$228$	1.46395e6	0.00818000
$229$	−2.73707e8	−1.50613	−0.753063	−	0.657949i	$-0.771424\pi$
$229$	−2.73707e8	−1.50613	−0.753063	+	0.657949i	$0.771424\pi$
$230$	1.21251e7	0.0657109
$231$	3.43347e7	0.183270
$232$	5.86814e7	0.308526
$233$	−4.03236e7	−0.208840	−0.104420	−	0.994533i	$-0.533299\pi$
$233$	−4.03236e7	−0.208840	−0.104420	+	0.994533i	$0.533299\pi$
$234$	−1.28129e7	−0.0653720
$235$	6.03770e7	0.303483
$236$	1.75331e8	0.868293
$237$	−2.79005e7	−0.136142
$238$	1.46063e7	0.0702296
$239$	2.14738e7	0.101746	0.0508729	−	0.998705i	$-0.483800\pi$
$239$	2.14738e7	0.101746	0.0508729	+	0.998705i	$0.483800\pi$
$240$	2.47230e7	0.115441
$241$	−9.25323e7	−0.425827	−0.212914	−	0.977071i	$-0.568295\pi$
$241$	−9.25323e7	−0.425827	−0.212914	+	0.977071i	$0.568295\pi$
$242$	−4.59361e7	−0.208353
$243$	−1.43489e7	−0.0641500
$244$	−432690.	−0.00190683
$245$	−2.63006e7	−0.114257
$246$	4.17939e7	0.178995
$247$	1.86128e6	0.00785909
$248$	−5.50842e7	−0.229322
$249$	1.74544e8	0.716484
$250$	1.90063e8	0.769321
$251$	8.47223e7	0.338174	0.169087	−	0.985601i	$-0.445918\pi$
$251$	8.47223e7	0.338174	0.169087	+	0.985601i	$0.445918\pi$
$252$	−1.60030e7	−0.0629941
$253$	−2.51358e7	−0.0975824
$254$	−2.62897e8	−1.00662
$255$	−3.21289e7	−0.121340
$256$	1.67772e7	0.0625000
$257$	−2.14537e8	−0.788380	−0.394190	−	0.919029i	$-0.628975\pi$
$257$	−2.14537e8	−0.788380	−0.394190	+	0.919029i	$0.628975\pi$
$258$	−1.14208e8	−0.414028
$259$	−1.71747e8	−0.614243
$260$	3.14331e7	0.110912
$261$	8.35522e7	0.290882
$262$	−1.28738e8	−0.442234
$263$	−1.16062e6	−0.00393409	−0.00196705	−	0.999998i	$-0.500626\pi$
$263$	−1.16062e6	−0.00393409	−0.00196705	+	0.999998i	$0.500626\pi$
$264$	−5.12517e7	−0.171433
$265$	−3.72975e7	−0.123117
$266$	2.32469e6	0.00757321
$267$	2.94057e8	0.945459
$268$	8.53234e7	0.270767
$269$	1.37359e8	0.430253	0.215126	−	0.976586i	$-0.430984\pi$
$269$	1.37359e8	0.430253	0.215126	+	0.976586i	$0.430984\pi$
$270$	3.52012e7	0.108839
$271$	−1.44269e8	−0.440332	−0.220166	−	0.975462i	$-0.570660\pi$
$271$	−1.44269e8	−0.440332	−0.220166	+	0.975462i	$0.570660\pi$
$272$	−2.18029e7	−0.0656937
$273$	−2.03464e7	−0.0605228
$274$	3.58833e7	0.105382
$275$	−1.04364e8	−0.302613
$276$	1.17155e7	0.0335413
$277$	−1.86550e8	−0.527371	−0.263685	−	0.964609i	$-0.584938\pi$
$277$	−1.86550e8	−0.527371	−0.263685	+	0.964609i	$0.584938\pi$
$278$	−3.02722e8	−0.845060
$279$	−7.84304e7	−0.216207
$280$	3.92591e7	0.106878
$281$	−1.43449e8	−0.385680	−0.192840	−	0.981230i	$-0.561770\pi$
$281$	−1.43449e8	−0.385680	−0.192840	+	0.981230i	$0.561770\pi$
$282$	5.83376e7	0.154909
$283$	1.55861e8	0.408775	0.204388	−	0.978890i	$-0.434480\pi$
$283$	1.55861e8	0.408775	0.204388	+	0.978890i	$0.434480\pi$
$284$	−1.26664e8	−0.328125
$285$	−5.11354e6	−0.0130847
$286$	−6.51621e7	−0.164708
$287$	6.63672e7	0.165717
$288$	2.38879e7	0.0589256
$289$	−3.82005e8	−0.930949
$290$	−2.04973e8	−0.493519
$291$	−2.01954e8	−0.480426
$292$	−9.68167e7	−0.227568
$293$	−2.48565e8	−0.577302	−0.288651	−	0.957434i	$-0.593207\pi$
$293$	−2.48565e8	−0.577302	−0.288651	+	0.957434i	$0.593207\pi$
$294$	−2.54122e7	−0.0583212
$295$	−6.12428e8	−1.38892
$296$	2.56369e8	0.574571
$297$	−7.29737e7	−0.161629
$298$	4.86131e8	1.06413
$299$	1.48953e7	0.0322255
$300$	4.86431e7	0.104015
$301$	−1.81359e8	−0.383315
$302$	−2.63923e8	−0.551383
$303$	1.79116e8	0.369901
$304$	−3.47009e6	−0.00708409
$305$	1.51138e6	0.00305017
$306$	−3.10436e7	−0.0619366
$307$	3.67829e8	0.725540	0.362770	−	0.931879i	$-0.381831\pi$
$307$	3.67829e8	0.725540	0.362770	+	0.931879i	$0.381831\pi$
$308$	−8.13859e7	−0.158716
$309$	−2.54376e8	−0.490479
$310$	1.92408e8	0.366824
$311$	4.48616e7	0.0845694	0.0422847	−	0.999106i	$-0.486536\pi$
$311$	4.48616e7	0.0845694	0.0422847	+	0.999106i	$0.486536\pi$
$312$	3.03713e7	0.0566139
$313$	3.44280e8	0.634610	0.317305	−	0.948324i	$-0.397222\pi$
$313$	3.44280e8	0.634610	0.317305	+	0.948324i	$0.397222\pi$
$314$	−2.07190e8	−0.377673
$315$	5.58983e7	0.100765
$316$	6.61344e7	0.117902
$317$	−2.45491e8	−0.432840	−0.216420	−	0.976300i	$-0.569438\pi$
$317$	−2.45491e8	−0.432840	−0.216420	+	0.976300i	$0.569438\pi$
$318$	−3.60376e7	−0.0628437
$319$	4.24918e8	0.732888
$320$	−5.86026e7	−0.0999750
$321$	5.42139e8	0.914835
$322$	1.86038e7	0.0310532
$323$	4.50959e6	0.00744608
$324$	3.40122e7	0.0555556
$325$	6.18455e7	0.0999346
$326$	−3.90841e7	−0.0624797
$327$	5.38722e8	0.852015
$328$	−9.90671e7	−0.155014
$329$	9.26380e7	0.143418
$330$	1.79022e8	0.274225
$331$	3.78784e8	0.574108	0.287054	−	0.957914i	$-0.407324\pi$
$331$	3.78784e8	0.574108	0.287054	+	0.957914i	$0.407324\pi$
$332$	−4.13733e8	−0.620493
$333$	3.65025e8	0.541711
$334$	−6.57725e8	−0.965898
$335$	−2.98033e8	−0.433120
$336$	3.79331e7	0.0545545
$337$	1.21640e9	1.73130	0.865648	−	0.500654i	$-0.166907\pi$
$337$	1.21640e9	1.73130	0.865648	+	0.500654i	$0.166907\pi$
$338$	3.86145e7	0.0543928
$339$	3.40538e8	0.474752
$340$	7.61573e7	0.105084
$341$	−3.98871e8	−0.544743
$342$	−4.94082e6	−0.00667894
$343$	−4.03536e7	−0.0539949
$344$	2.70716e8	0.358558
$345$	−4.09222e7	−0.0536527
$346$	4.92621e8	0.639362
$347$	5.22321e8	0.671096	0.335548	−	0.942023i	$-0.391079\pi$
$347$	5.22321e8	0.671096	0.335548	+	0.942023i	$0.391079\pi$
$348$	−1.98050e8	−0.251911
$349$	3.39559e8	0.427588	0.213794	−	0.976879i	$-0.431418\pi$
$349$	3.39559e8	0.427588	0.213794	+	0.976879i	$0.431418\pi$
$350$	7.72435e7	0.0962994
$351$	4.32436e7	0.0533761
$352$	1.21486e8	0.148465
$353$	5.05955e8	0.612209	0.306105	−	0.951998i	$-0.400974\pi$
$353$	5.05955e8	0.612209	0.306105	+	0.951998i	$0.400974\pi$
$354$	−5.91741e8	−0.708958
$355$	4.42435e8	0.524869
$356$	−6.97025e8	−0.818791
$357$	−4.92962e7	−0.0573422
$358$	6.41630e8	0.739085
$359$	−1.16756e8	−0.133183	−0.0665913	−	0.997780i	$-0.521212\pi$
$359$	−1.16756e8	−0.133183	−0.0665913	+	0.997780i	$0.521212\pi$
$360$	−8.34400e7	−0.0942574
$361$	−8.93154e8	−0.999197
$362$	3.90872e8	0.433066
$363$	1.55034e8	0.170120
$364$	4.82285e7	0.0524142
$365$	3.38179e8	0.364017
$366$	1.46033e6	0.00155692
$367$	−1.43967e9	−1.52031	−0.760157	−	0.649740i	$-0.774878\pi$
$367$	−1.43967e9	−1.52031	−0.760157	+	0.649740i	$0.774878\pi$
$368$	−2.77702e7	−0.0290476
$369$	−1.41054e8	−0.146149
$370$	−8.95492e8	−0.919085
$371$	−5.72264e7	−0.0581819
$372$	1.85909e8	0.187241
$373$	−1.15250e8	−0.114990	−0.0574950	−	0.998346i	$-0.518311\pi$
$373$	−1.15250e8	−0.114990	−0.0574950	+	0.998346i	$0.518311\pi$
$374$	−1.57877e8	−0.156052
$375$	−6.41463e8	−0.628148
$376$	−1.38282e8	−0.134155
$377$	−2.51803e8	−0.242028
$378$	5.40102e7	0.0514344
$379$	1.15820e8	0.109282	0.0546408	−	0.998506i	$-0.482599\pi$
$379$	1.15820e8	0.109282	0.0546408	+	0.998506i	$0.482599\pi$
$380$	1.21210e7	0.0113317
$381$	8.87276e8	0.821905
$382$	−6.63977e8	−0.609440
$383$	−6.45665e8	−0.587234	−0.293617	−	0.955923i	$-0.594859\pi$
$383$	−6.45665e8	−0.587234	−0.293617	+	0.955923i	$0.594859\pi$
$384$	−5.66231e7	−0.0510310
$385$	2.84280e8	0.253883
$386$	−5.40507e8	−0.478350
$387$	3.85454e8	0.338052
$388$	4.78705e8	0.416061
$389$	−3.15611e8	−0.271850	−0.135925	−	0.990719i	$-0.543401\pi$
$389$	−3.15611e8	−0.271850	−0.135925	+	0.990719i	$0.543401\pi$
$390$	−1.06087e8	−0.0905596
$391$	3.60889e7	0.0305320
$392$	6.02363e7	0.0505076
$393$	4.34491e8	0.361083
$394$	1.67013e8	0.137566
$395$	−2.31006e8	−0.188597
$396$	1.72975e8	0.139975
$397$	−5.55156e8	−0.445295	−0.222648	−	0.974899i	$-0.571470\pi$
$397$	−5.55156e8	−0.445295	−0.222648	+	0.974899i	$0.571470\pi$
$398$	−5.28044e8	−0.419836
$399$	−7.84584e6	−0.00618350
$400$	−1.15302e8	−0.0900799
$401$	−2.99200e8	−0.231716	−0.115858	−	0.993266i	$-0.536962\pi$
$401$	−2.99200e8	−0.231716	−0.115858	+	0.993266i	$0.536962\pi$
$402$	−2.87967e8	−0.221081
$403$	2.36367e8	0.179895
$404$	−4.24571e8	−0.320343
$405$	−1.18804e8	−0.0888667
$406$	−3.14496e8	−0.233224
$407$	1.85639e9	1.36486
$408$	7.35849e7	0.0536387
$409$	−3.78639e8	−0.273649	−0.136824	−	0.990595i	$-0.543690\pi$
$409$	−3.78639e8	−0.273649	−0.136824	+	0.990595i	$0.543690\pi$
$410$	3.46040e8	0.247960
$411$	−1.21106e8	−0.0860439
$412$	6.02964e8	0.424768
$413$	−9.39663e8	−0.656368
$414$	−3.95399e7	−0.0273864
$415$	1.44516e9	0.992542
$416$	−7.19913e7	−0.0490290
$417$	1.02169e9	0.689989
$418$	−2.51273e7	−0.0168279
$419$	6.14549e8	0.408139	0.204069	−	0.978956i	$-0.434583\pi$
$419$	6.14549e8	0.408139	0.204069	+	0.978956i	$0.434583\pi$
$420$	−1.32500e8	−0.0872654
$421$	−1.34731e9	−0.879996	−0.439998	−	0.897999i	$-0.645021\pi$
$421$	−1.34731e9	−0.879996	−0.439998	+	0.897999i	$0.645021\pi$
$422$	2.86186e8	0.185377
$423$	−1.96889e8	−0.126483
$424$	8.54226e7	0.0544242
$425$	1.49842e8	0.0946829
$426$	4.27491e8	0.267913
$427$	2.31895e6	0.00144143
$428$	−1.28507e9	−0.792270
$429$	2.19922e8	0.134483
$430$	−9.45608e8	−0.573550
$431$	−1.75053e9	−1.05317	−0.526585	−	0.850122i	$-0.676528\pi$
$431$	−1.75053e9	−1.05317	−0.526585	+	0.850122i	$0.676528\pi$
$432$	−8.06216e7	−0.0481125
$433$	2.79533e8	0.165472	0.0827361	−	0.996571i	$-0.473634\pi$
$433$	2.79533e8	0.165472	0.0827361	+	0.996571i	$0.473634\pi$
$434$	2.95217e8	0.173351
$435$	6.91784e8	0.402957
$436$	−1.27697e9	−0.737867
$437$	5.74381e6	0.00329242
$438$	3.26756e8	0.185808
$439$	9.31660e8	0.525571	0.262786	−	0.964854i	$-0.415359\pi$
$439$	9.31660e8	0.525571	0.262786	+	0.964854i	$0.415359\pi$
$440$	−4.24347e8	−0.237485
$441$	8.57661e7	0.0476190
$442$	9.35568e7	0.0515344
$443$	−2.72631e9	−1.48992	−0.744958	−	0.667112i	$-0.767530\pi$
$443$	−2.72631e9	−1.48992	−0.744958	+	0.667112i	$0.767530\pi$
$444$	−8.65244e8	−0.469136
$445$	2.43470e9	1.30974
$446$	−2.01598e9	−1.07601
$447$	−1.64069e9	−0.868861
$448$	−8.99154e7	−0.0472456
$449$	−8.07255e8	−0.420871	−0.210435	−	0.977608i	$-0.567488\pi$
$449$	−8.07255e8	−0.420871	−0.210435	+	0.977608i	$0.567488\pi$
$450$	−1.64171e8	−0.0849281
$451$	−7.17355e8	−0.368228
$452$	−8.07202e8	−0.411148
$453$	8.90740e8	0.450202
$454$	−7.85989e8	−0.394204
$455$	−1.68462e8	−0.0838419
$456$	1.17116e7	0.00578413
$457$	−1.56428e9	−0.766669	−0.383334	−	0.923610i	$-0.625224\pi$
$457$	−1.56428e9	−0.766669	−0.383334	+	0.923610i	$0.625224\pi$
$458$	−2.18965e9	−1.06499
$459$	1.04772e8	0.0505711
$460$	9.70007e7	0.0464646
$461$	−3.03297e8	−0.144183	−0.0720916	−	0.997398i	$-0.522967\pi$
$461$	−3.03297e8	−0.144183	−0.0720916	+	0.997398i	$0.522967\pi$
$462$	2.74677e8	0.129591
$463$	7.12250e7	0.0333502	0.0166751	−	0.999861i	$-0.494692\pi$
$463$	7.12250e7	0.0333502	0.0166751	+	0.999861i	$0.494692\pi$
$464$	4.69451e8	0.218161
$465$	−6.49378e8	−0.299511
$466$	−3.22589e8	−0.147672
$467$	1.56816e9	0.712493	0.356246	−	0.934392i	$-0.384056\pi$
$467$	1.56816e9	0.712493	0.356246	+	0.934392i	$0.384056\pi$
$468$	−1.02503e8	−0.0462250
$469$	−4.57280e8	−0.204681
$470$	4.83016e8	0.214595
$471$	6.99268e8	0.308369
$472$	1.40265e9	0.613976
$473$	1.96029e9	0.851737
$474$	−2.23204e8	−0.0962669
$475$	2.38484e7	0.0102101
$476$	1.16850e8	0.0496598
$477$	1.21627e8	0.0513116
$478$	1.71791e8	0.0719451
$479$	3.95349e9	1.64364	0.821819	−	0.569749i	$-0.192960\pi$
$479$	3.95349e9	1.64364	0.821819	+	0.569749i	$0.192960\pi$
$480$	1.97784e8	0.0816293
$481$	−1.10008e9	−0.450731
$482$	−7.40258e8	−0.301105
$483$	−6.27879e7	−0.0253549
$484$	−3.67489e8	−0.147328
$485$	−1.67211e9	−0.665531
$486$	−1.14791e8	−0.0453609
$487$	3.30775e9	1.29772	0.648861	−	0.760907i	$-0.275246\pi$
$487$	3.30775e9	1.29772	0.648861	+	0.760907i	$0.275246\pi$
$488$	−3.46152e6	−0.00134833
$489$	1.31909e8	0.0510145
$490$	−2.10404e8	−0.0807920
$491$	9.54688e8	0.363979	0.181989	−	0.983300i	$-0.441746\pi$
$491$	9.54688e8	0.363979	0.181989	+	0.983300i	$0.441746\pi$
$492$	3.34351e8	0.126568
$493$	−6.10078e8	−0.229309
$494$	1.48902e7	0.00555721
$495$	−6.04198e8	−0.223903
$496$	−4.40674e8	−0.162155
$497$	6.78840e8	0.248039
$498$	1.39635e9	0.506631
$499$	−5.78352e8	−0.208372	−0.104186	−	0.994558i	$-0.533224\pi$
$499$	−5.78352e8	−0.208372	−0.104186	+	0.994558i	$0.533224\pi$
$500$	1.52050e9	0.543992
$501$	2.21982e9	0.788653
$502$	6.77779e8	0.239125
$503$	−3.78503e9	−1.32611	−0.663057	−	0.748568i	$-0.730742\pi$
$503$	−3.78503e9	−1.32611	−0.663057	+	0.748568i	$0.730742\pi$
$504$	−1.28024e8	−0.0445435
$505$	1.48302e9	0.512422
$506$	−2.01087e8	−0.0690012
$507$	−1.30324e8	−0.0444116
$508$	−2.10317e9	−0.711790
$509$	4.97723e7	0.0167292	0.00836460	−	0.999965i	$-0.497337\pi$
$509$	4.97723e7	0.0167292	0.00836460	+	0.999965i	$0.497337\pi$
$510$	−2.57031e8	−0.0858005
$511$	5.18877e8	0.172025
$512$	1.34218e8	0.0441942
$513$	1.66753e7	0.00545333
$514$	−1.71629e9	−0.557469
$515$	−2.10615e9	−0.679459
$516$	−9.13668e8	−0.292762
$517$	−1.00131e9	−0.318679
$518$	−1.37398e9	−0.434335
$519$	−1.66260e9	−0.522037
$520$	2.51464e8	0.0784269
$521$	−3.23429e9	−1.00195	−0.500976	−	0.865461i	$-0.667025\pi$
$521$	−3.23429e9	−1.00195	−0.500976	+	0.865461i	$0.667025\pi$
$522$	6.68418e8	0.205684
$523$	−5.04124e9	−1.54093	−0.770463	−	0.637485i	$-0.779975\pi$
$523$	−5.04124e9	−1.54093	−0.770463	+	0.637485i	$0.779975\pi$
$524$	−1.02990e9	−0.312707
$525$	−2.60697e8	−0.0786281
$526$	−9.28495e6	−0.00278182
$527$	5.72680e8	0.170441
$528$	−4.10014e8	−0.121222
$529$	−3.35886e9	−0.986500
$530$	−2.98380e8	−0.0870570
$531$	1.99713e9	0.578862
$532$	1.85975e7	0.00535507
$533$	4.25098e8	0.121603
$534$	2.35246e9	0.668540
$535$	4.48873e9	1.26732
$536$	6.82587e8	0.191462
$537$	−2.16550e9	−0.603460
$538$	1.09887e9	0.304235
$539$	4.36177e8	0.119978
$540$	2.81610e8	0.0769608
$541$	1.15462e9	0.313508	0.156754	−	0.987638i	$-0.449897\pi$
$541$	1.15462e9	0.313508	0.156754	+	0.987638i	$0.449897\pi$
$542$	−1.15415e9	−0.311362
$543$	−1.31919e9	−0.353597
$544$	−1.74424e8	−0.0464525
$545$	4.46044e9	1.18029
$546$	−1.62771e8	−0.0427960
$547$	4.59022e9	1.19916	0.599581	−	0.800314i	$-0.295334\pi$
$547$	4.59022e9	1.19916	0.599581	+	0.800314i	$0.295334\pi$
$548$	2.87067e8	0.0745162
$549$	−4.92861e6	−0.00127122
$550$	−8.34916e8	−0.213980
$551$	−9.70984e7	−0.0247276
$552$	9.37243e7	0.0237173
$553$	−3.54439e8	−0.0891259
$554$	−1.49240e9	−0.372907
$555$	3.02228e9	0.750430
$556$	−2.42178e9	−0.597548
$557$	5.53417e9	1.35694	0.678468	−	0.734630i	$-0.262644\pi$
$557$	5.53417e9	1.35694	0.678468	+	0.734630i	$0.262644\pi$
$558$	−6.27444e8	−0.152882
$559$	−1.16165e9	−0.281276
$560$	3.14073e8	0.0755740
$561$	5.32836e8	0.127416
$562$	−1.14760e9	−0.272717
$563$	−1.51012e9	−0.356641	−0.178321	−	0.983972i	$-0.557066\pi$
$563$	−1.51012e9	−0.356641	−0.178321	+	0.983972i	$0.557066\pi$
$564$	4.66701e8	0.109537
$565$	2.81954e9	0.657672
$566$	1.24689e9	0.289048
$567$	−1.82284e8	−0.0419961
$568$	−1.01331e9	−0.232019
$569$	2.00672e9	0.456660	0.228330	−	0.973584i	$-0.426673\pi$
$569$	2.00672e9	0.456660	0.228330	+	0.973584i	$0.426673\pi$
$570$	−4.09083e7	−0.00925230
$571$	−4.95810e9	−1.11452	−0.557261	−	0.830337i	$-0.688148\pi$
$571$	−4.95810e9	−1.11452	−0.557261	+	0.830337i	$0.688148\pi$
$572$	−5.21297e8	−0.116466
$573$	2.24092e9	0.497606
$574$	5.30938e8	0.117180
$575$	1.90852e8	0.0418657
$576$	1.91103e8	0.0416667
$577$	5.46115e8	0.118350	0.0591750	−	0.998248i	$-0.481153\pi$
$577$	5.46115e8	0.118350	0.0591750	+	0.998248i	$0.481153\pi$
$578$	−3.05604e9	−0.658281
$579$	1.82421e9	0.390571
$580$	−1.63979e9	−0.348971
$581$	2.21735e9	0.469049
$582$	−1.61563e9	−0.339712
$583$	6.18554e8	0.129282
$584$	−7.74534e8	−0.160915
$585$	3.58042e8	0.0739416
$586$	−1.98852e9	−0.408214
$587$	−3.28998e9	−0.671367	−0.335683	−	0.941975i	$-0.608967\pi$
$587$	−3.28998e9	−0.671367	−0.335683	+	0.941975i	$0.608967\pi$
$588$	−2.03297e8	−0.0412393
$589$	9.11462e7	0.0183796
$590$	−4.89942e9	−0.982116
$591$	−5.63668e8	−0.112323
$592$	2.05095e9	0.406283
$593$	7.13873e9	1.40582	0.702910	−	0.711279i	$-0.251884\pi$
$593$	7.13873e9	1.40582	0.702910	+	0.711279i	$0.251884\pi$
$594$	−5.83789e8	−0.114289
$595$	−4.08156e8	−0.0794358
$596$	3.88905e9	0.752456
$597$	1.78215e9	0.342794
$598$	1.19162e8	0.0227869
$599$	8.67322e9	1.64887	0.824435	−	0.565956i	$-0.191493\pi$
$599$	8.67322e9	1.64887	0.824435	+	0.565956i	$0.191493\pi$
$600$	3.89145e8	0.0735499
$601$	−6.48192e7	−0.0121799	−0.00608994	−	0.999981i	$-0.501939\pi$
$601$	−6.48192e7	−0.0121799	−0.00608994	+	0.999981i	$0.501939\pi$
$602$	−1.45087e9	−0.271045
$603$	9.71887e8	0.180512
$604$	−2.11138e9	−0.389886
$605$	1.28363e9	0.235666
$606$	1.43293e9	0.261559
$607$	7.01589e9	1.27328	0.636638	−	0.771163i	$-0.280325\pi$
$607$	7.01589e9	1.27328	0.636638	+	0.771163i	$0.280325\pi$
$608$	−2.77608e7	−0.00500921
$609$	1.06142e9	0.190427
$610$	1.20910e7	0.00215680
$611$	5.93369e8	0.105240
$612$	−2.48349e8	−0.0437958
$613$	6.35211e9	1.11380	0.556899	−	0.830580i	$-0.311991\pi$
$613$	6.35211e9	1.11380	0.556899	+	0.830580i	$0.311991\pi$
$614$	2.94263e9	0.513034
$615$	−1.16788e9	−0.202459
$616$	−6.51087e8	−0.112229
$617$	4.08336e9	0.699874	0.349937	−	0.936773i	$-0.386203\pi$
$617$	4.08336e9	0.699874	0.349937	+	0.936773i	$0.386203\pi$
$618$	−2.03501e9	−0.346821
$619$	−8.14644e9	−1.38055	−0.690273	−	0.723549i	$-0.742509\pi$
$619$	−8.14644e9	−1.38055	−0.690273	+	0.723549i	$0.742509\pi$
$620$	1.53927e9	0.259384
$621$	1.33447e8	0.0223609
$622$	3.58893e8	0.0597996
$623$	3.73562e9	0.618948
$624$	2.42971e8	0.0400320
$625$	−3.11188e9	−0.509850
$626$	2.75424e9	0.448737
$627$	8.48047e7	0.0137399
$628$	−1.65752e9	−0.267055
$629$	−2.66533e9	−0.427044
$630$	4.47186e8	0.0712519
$631$	1.12053e10	1.77550	0.887750	−	0.460325i	$-0.152267\pi$
$631$	1.12053e10	1.77550	0.887750	+	0.460325i	$0.152267\pi$
$632$	5.29075e8	0.0833696
$633$	−9.65879e8	−0.151360
$634$	−1.96393e9	−0.306064
$635$	7.34635e9	1.13858
$636$	−2.88301e8	−0.0444372
$637$	−2.58475e8	−0.0396214
$638$	3.39935e9	0.518230
$639$	−1.44278e9	−0.218750
$640$	−4.68820e8	−0.0706930
$641$	8.72371e9	1.30827	0.654136	−	0.756377i	$-0.273032\pi$
$641$	8.72371e9	1.30827	0.654136	+	0.756377i	$0.273032\pi$
$642$	4.33711e9	0.646886
$643$	6.26395e9	0.929202	0.464601	−	0.885520i	$-0.346198\pi$
$643$	6.26395e9	0.929202	0.464601	+	0.885520i	$0.346198\pi$
$644$	1.48831e8	0.0219580
$645$	3.19143e9	0.468302
$646$	3.60767e7	0.00526517
$647$	7.54789e9	1.09562	0.547811	−	0.836602i	$-0.315461\pi$
$647$	7.54789e9	1.09562	0.547811	+	0.836602i	$0.315461\pi$
$648$	2.72098e8	0.0392837
$649$	1.01567e10	1.45847
$650$	4.94764e8	0.0706645
$651$	−9.96357e8	−0.141541
$652$	−3.12673e8	−0.0441798
$653$	1.04105e10	1.46310	0.731550	−	0.681788i	$-0.238797\pi$
$653$	1.04105e10	1.46310	0.731550	+	0.681788i	$0.238797\pi$
$654$	4.30977e9	0.602466
$655$	3.59744e9	0.500206
$656$	−7.92537e8	−0.109611
$657$	−1.10280e9	−0.151712
$658$	7.41104e8	0.101412
$659$	−5.19413e9	−0.706990	−0.353495	−	0.935436i	$-0.615007\pi$
$659$	−5.19413e9	−0.706990	−0.353495	+	0.935436i	$0.615007\pi$
$660$	1.43217e9	0.193906
$661$	−4.90935e9	−0.661178	−0.330589	−	0.943775i	$-0.607247\pi$
$661$	−4.90935e9	−0.661178	−0.330589	+	0.943775i	$0.607247\pi$
$662$	3.03027e9	0.405955
$663$	−3.15754e8	−0.0420777
$664$	−3.30987e9	−0.438755
$665$	−6.49609e7	−0.00856597
$666$	2.92020e9	0.383048
$667$	−7.77050e8	−0.101393
$668$	−5.26180e9	−0.682993
$669$	6.80395e9	0.878556
$670$	−2.38427e9	−0.306262
$671$	−2.50652e7	−0.00320290
$672$	3.03464e8	0.0385758
$673$	4.04854e8	0.0511972	0.0255986	−	0.999672i	$-0.491851\pi$
$673$	4.04854e8	0.0511972	0.0255986	+	0.999672i	$0.491851\pi$
$674$	9.73119e9	1.22421
$675$	5.54076e8	0.0693435
$676$	3.08916e8	0.0384615
$677$	3.66555e9	0.454025	0.227012	−	0.973892i	$-0.427104\pi$
$677$	3.66555e9	0.454025	0.227012	+	0.973892i	$0.427104\pi$
$678$	2.72431e9	0.335701
$679$	−2.56556e9	−0.314512
$680$	6.09259e8	0.0743054
$681$	2.65271e9	0.321866
$682$	−3.19096e9	−0.385191
$683$	6.67383e9	0.801499	0.400749	−	0.916188i	$-0.368750\pi$
$683$	6.67383e9	0.801499	0.400749	+	0.916188i	$0.368750\pi$
$684$	−3.95266e7	−0.00472272
$685$	−1.00272e9	−0.119196
$686$	−3.22829e8	−0.0381802
$687$	7.39008e9	0.869562
$688$	2.16573e9	0.253539
$689$	−3.66550e8	−0.0426939
$690$	−3.27377e8	−0.0379382
$691$	−9.07458e9	−1.04629	−0.523147	−	0.852243i	$-0.675242\pi$
$691$	−9.07458e9	−1.04629	−0.523147	+	0.852243i	$0.675242\pi$
$692$	3.94097e9	0.452097
$693$	−9.27036e8	−0.105811
$694$	4.17857e9	0.474537
$695$	8.45924e9	0.955838
$696$	−1.58440e9	−0.178128
$697$	1.02995e9	0.115213
$698$	2.71647e9	0.302351
$699$	1.08874e9	0.120574
$700$	6.17948e8	0.0680940
$701$	−2.65100e9	−0.290668	−0.145334	−	0.989383i	$-0.546426\pi$
$701$	−2.65100e9	−0.290668	−0.145334	+	0.989383i	$0.546426\pi$
$702$	3.45948e8	0.0377426
$703$	−4.24206e8	−0.0460503
$704$	9.71885e8	0.104981
$705$	−1.63018e9	−0.175216
$706$	4.04764e9	0.432897
$707$	2.27544e9	0.242157
$708$	−4.73393e9	−0.501309
$709$	−1.59598e10	−1.68176	−0.840882	−	0.541219i	$-0.817963\pi$
$709$	−1.59598e10	−1.68176	−0.840882	+	0.541219i	$0.817963\pi$
$710$	3.53948e9	0.371138
$711$	7.53312e8	0.0786016
$712$	−5.57620e9	−0.578973
$713$	7.29416e8	0.0753637
$714$	−3.94369e8	−0.0405471
$715$	1.82088e9	0.186299
$716$	5.13304e9	0.522612
$717$	−5.79793e8	−0.0587430
$718$	−9.34045e8	−0.0941743
$719$	1.08770e10	1.09133	0.545666	−	0.838003i	$-0.316277\pi$
$719$	1.08770e10	1.09133	0.545666	+	0.838003i	$0.316277\pi$
$720$	−6.67520e8	−0.0666500
$721$	−3.23151e9	−0.321094
$722$	−7.14523e9	−0.706539
$723$	2.49837e9	0.245852
$724$	3.12698e9	0.306224
$725$	−3.22633e9	−0.314431
$726$	1.24028e9	0.120293
$727$	−1.85850e10	−1.79388	−0.896940	−	0.442153i	$-0.854215\pi$
$727$	−1.85850e10	−1.79388	−0.896940	+	0.442153i	$0.854215\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	2.70543e9	0.257399
$731$	−2.81449e9	−0.266495
$732$	1.16826e7	0.00110091
$733$	1.47641e10	1.38466	0.692330	−	0.721581i	$-0.256584\pi$
$733$	1.47641e10	1.38466	0.692330	+	0.721581i	$0.256584\pi$
$734$	−1.15174e10	−1.07502
$735$	7.10115e8	0.0659664
$736$	−2.22161e8	−0.0205398
$737$	4.94269e9	0.454807
$738$	−1.12844e9	−0.103343
$739$	1.82788e10	1.66607	0.833035	−	0.553220i	$-0.186601\pi$
$739$	1.82788e10	1.66607	0.833035	+	0.553220i	$0.186601\pi$
$740$	−7.16393e9	−0.649891
$741$	−5.02545e7	−0.00453745
$742$	−4.57812e8	−0.0411408
$743$	−1.17979e10	−1.05522	−0.527612	−	0.849486i	$-0.676912\pi$
$743$	−1.17979e10	−1.05522	−0.527612	+	0.849486i	$0.676912\pi$
$744$	1.48727e9	0.132399
$745$	−1.35844e10	−1.20363
$746$	−9.22000e8	−0.0813102
$747$	−4.71268e9	−0.413662
$748$	−1.26302e9	−0.110345
$749$	6.88717e9	0.598900
$750$	−5.13170e9	−0.444168
$751$	−6.79474e9	−0.585373	−0.292687	−	0.956208i	$-0.594549\pi$
$751$	−6.79474e9	−0.585373	−0.292687	+	0.956208i	$0.594549\pi$
$752$	−1.10625e9	−0.0948620
$753$	−2.28750e9	−0.195245
$754$	−2.01442e9	−0.171140
$755$	7.37503e9	0.623663
$756$	4.32081e8	0.0363696
$757$	−1.81738e10	−1.52268	−0.761341	−	0.648352i	$-0.775459\pi$
$757$	−1.81738e10	−1.52268	−0.761341	+	0.648352i	$0.775459\pi$
$758$	9.26562e8	0.0772738
$759$	6.78667e8	0.0563392
$760$	9.69679e7	0.00801273
$761$	2.81062e9	0.231183	0.115592	−	0.993297i	$-0.463124\pi$
$761$	2.81062e9	0.231183	0.115592	+	0.993297i	$0.463124\pi$
$762$	7.09821e9	0.581174
$763$	6.84376e9	0.557775
$764$	−5.31182e9	−0.430939
$765$	8.67480e8	0.0700558
$766$	−5.16532e9	−0.415237
$767$	−6.01878e9	−0.481642
$768$	−4.52985e8	−0.0360844
$769$	−1.77729e10	−1.40934	−0.704671	−	0.709534i	$-0.748906\pi$
$769$	−1.77729e10	−1.40934	−0.704671	+	0.709534i	$0.748906\pi$
$770$	2.27424e9	0.179522
$771$	5.79249e9	0.455171
$772$	−4.32406e9	−0.338245
$773$	8.49608e9	0.661592	0.330796	−	0.943702i	$-0.392683\pi$
$773$	8.49608e9	0.661592	0.330796	+	0.943702i	$0.392683\pi$
$774$	3.08363e9	0.239039
$775$	3.02855e9	0.233711
$776$	3.82964e9	0.294199
$777$	4.63717e9	0.354633
$778$	−2.52489e9	−0.192227
$779$	1.63923e8	0.0124239
$780$	−8.48693e8	−0.0640353
$781$	−7.33750e9	−0.551150
$782$	2.88711e8	0.0215894
$783$	−2.25591e9	−0.167941
$784$	4.81890e8	0.0357143
$785$	5.78970e9	0.427182
$786$	3.47593e9	0.255324
$787$	1.09652e10	0.801869	0.400935	−	0.916107i	$-0.368685\pi$
$787$	1.09652e10	0.801869	0.400935	+	0.916107i	$0.368685\pi$
$788$	1.33610e9	0.0972742
$789$	3.13367e7	0.00227135
$790$	−1.84805e9	−0.133358
$791$	4.32610e9	0.310798
$792$	1.38380e9	0.0989770
$793$	1.48534e7	0.00105772
$794$	−4.44124e9	−0.314871
$795$	1.00703e9	0.0710817
$796$	−4.22435e9	−0.296869
$797$	−1.08261e10	−0.757471	−0.378736	−	0.925505i	$-0.623641\pi$
$797$	−1.08261e10	−0.757471	−0.378736	+	0.925505i	$0.623641\pi$
$798$	−6.27667e7	−0.00437239
$799$	1.43764e9	0.0997094
$800$	−9.22418e8	−0.0636961
$801$	−7.93955e9	−0.545861
$802$	−2.39360e9	−0.163848
$803$	−5.60848e9	−0.382244
$804$	−2.30373e9	−0.156328
$805$	−5.19863e8	−0.0351240
$806$	1.89094e9	0.127205
$807$	−3.70869e9	−0.248407
$808$	−3.39657e9	−0.226517
$809$	−1.70536e10	−1.13239	−0.566196	−	0.824270i	$-0.691586\pi$
$809$	−1.70536e10	−1.13239	−0.566196	+	0.824270i	$0.691586\pi$
$810$	−9.50433e8	−0.0628382
$811$	−1.39453e10	−0.918023	−0.459011	−	0.888430i	$-0.651796\pi$
$811$	−1.39453e10	−0.918023	−0.459011	+	0.888430i	$0.651796\pi$
$812$	−2.51596e9	−0.164914
$813$	3.89526e9	0.254226
$814$	1.48511e10	0.965105
$815$	1.09216e9	0.0706701
$816$	5.88679e8	0.0379283
$817$	−4.47946e8	−0.0287375
$818$	−3.02911e9	−0.193499
$819$	5.49353e8	0.0349428
$820$	2.76832e9	0.175335
$821$	1.11715e10	0.704545	0.352273	−	0.935897i	$-0.385409\pi$
$821$	1.11715e10	0.704545	0.352273	+	0.935897i	$0.385409\pi$
$822$	−9.68850e8	−0.0608422
$823$	−1.07780e9	−0.0673965	−0.0336983	−	0.999432i	$-0.510729\pi$
$823$	−1.07780e9	−0.0673965	−0.0336983	+	0.999432i	$0.510729\pi$
$824$	4.82372e9	0.300356
$825$	2.81784e9	0.174714
$826$	−7.51731e9	−0.464122
$827$	−2.40146e10	−1.47641	−0.738204	−	0.674577i	$-0.764326\pi$
$827$	−2.40146e10	−1.47641	−0.738204	+	0.674577i	$0.764326\pi$
$828$	−3.16319e8	−0.0193651
$829$	−3.06915e10	−1.87102	−0.935508	−	0.353305i	$-0.885058\pi$
$829$	−3.06915e10	−1.87102	−0.935508	+	0.353305i	$0.885058\pi$
$830$	1.15613e10	0.701833
$831$	5.03685e9	0.304478
$832$	−5.75930e8	−0.0346688
$833$	−6.26244e8	−0.0375393
$834$	8.17350e9	0.487896
$835$	1.83794e10	1.09252
$836$	−2.01019e8	−0.0118991
$837$	2.11762e9	0.124827
$838$	4.91640e9	0.288598
$839$	−3.65874e9	−0.213877	−0.106939	−	0.994266i	$-0.534105\pi$
$839$	−3.65874e9	−0.213877	−0.106939	+	0.994266i	$0.534105\pi$
$840$	−1.06000e9	−0.0617059
$841$	−4.11394e9	−0.238491
$842$	−1.07785e10	−0.622251
$843$	3.87313e9	0.222672
$844$	2.28949e9	0.131081
$845$	−1.07904e9	−0.0615231
$846$	−1.57512e9	−0.0894368
$847$	1.96951e9	0.111370
$848$	6.83380e8	0.0384837
$849$	−4.20824e9	−0.236006
$850$	1.19873e9	0.0669509
$851$	−3.39479e9	−0.188825
$852$	3.41993e9	0.189443
$853$	−9.74468e9	−0.537583	−0.268792	−	0.963198i	$-0.586624\pi$
$853$	−9.74468e9	−0.537583	−0.268792	+	0.963198i	$0.586624\pi$
$854$	1.85516e7	0.00101924
$855$	1.38066e8	0.00755447
$856$	−1.02806e10	−0.560220
$857$	3.19200e10	1.73233	0.866165	−	0.499759i	$-0.166578\pi$
$857$	3.19200e10	1.73233	0.866165	+	0.499759i	$0.166578\pi$
$858$	1.75938e9	0.0950940
$859$	2.02111e9	0.108796	0.0543980	−	0.998519i	$-0.482676\pi$
$859$	2.02111e9	0.108796	0.0543980	+	0.998519i	$0.482676\pi$
$860$	−7.56486e9	−0.405561
$861$	−1.79191e9	−0.0956767
$862$	−1.40042e10	−0.744704
$863$	1.61680e10	0.856284	0.428142	−	0.903711i	$-0.359168\pi$
$863$	1.61680e10	0.856284	0.428142	+	0.903711i	$0.359168\pi$
$864$	−6.44973e8	−0.0340207
$865$	−1.37657e10	−0.723175
$866$	2.23626e9	0.117006
$867$	1.03141e10	0.537484
$868$	2.36174e9	0.122578
$869$	3.83109e9	0.198040
$870$	5.53428e9	0.284933
$871$	−2.92899e9	−0.150195
$872$	−1.02158e10	−0.521751
$873$	5.45275e9	0.277374
$874$	4.59505e7	0.00232809
$875$	−8.14895e9	−0.411219
$876$	2.61405e9	0.131386
$877$	1.14782e10	0.574612	0.287306	−	0.957839i	$-0.407240\pi$
$877$	1.14782e10	0.574612	0.287306	+	0.957839i	$0.407240\pi$
$878$	7.45328e9	0.371635
$879$	6.71125e9	0.333305
$880$	−3.39478e9	−0.167928
$881$	−2.78517e10	−1.37226	−0.686129	−	0.727480i	$-0.740691\pi$
$881$	−2.78517e10	−1.37226	−0.686129	+	0.727480i	$0.740691\pi$
$882$	6.86129e8	0.0336718
$883$	−3.43236e10	−1.67776	−0.838882	−	0.544313i	$-0.816790\pi$
$883$	−3.43236e10	−1.67776	−0.838882	+	0.544313i	$0.816790\pi$
$884$	7.48454e8	0.0364403
$885$	1.65355e10	0.801894
$886$	−2.18104e10	−1.05353
$887$	3.67327e10	1.76734	0.883670	−	0.468111i	$-0.155065\pi$
$887$	3.67327e10	1.76734	0.883670	+	0.468111i	$0.155065\pi$
$888$	−6.92196e9	−0.331729
$889$	1.12717e10	0.538063
$890$	1.94776e10	0.926125
$891$	1.97029e9	0.0933164
$892$	−1.61279e10	−0.760852
$893$	2.28811e8	0.0107522
$894$	−1.31255e10	−0.614378
$895$	−1.79296e10	−0.835970
$896$	−7.19323e8	−0.0334077
$897$	−4.02172e8	−0.0186054
$898$	−6.45804e9	−0.297600
$899$	−1.23307e10	−0.566016
$900$	−1.31336e9	−0.0600532
$901$	−8.88092e8	−0.0404502
$902$	−5.73884e9	−0.260376
$903$	4.89669e9	0.221307
$904$	−6.45762e9	−0.290725
$905$	−1.09225e10	−0.489837
$906$	7.12592e9	0.318341
$907$	6.68095e9	0.297312	0.148656	−	0.988889i	$-0.452505\pi$
$907$	6.68095e9	0.297312	0.148656	+	0.988889i	$0.452505\pi$
$908$	−6.28791e9	−0.278744
$909$	−4.83613e9	−0.213562
$910$	−1.34769e9	−0.0592851
$911$	−3.25671e10	−1.42713	−0.713567	−	0.700587i	$-0.752922\pi$
$911$	−3.25671e10	−1.42713	−0.713567	+	0.700587i	$0.752922\pi$
$912$	9.36926e7	0.00409000
$913$	−2.39671e10	−1.04224
$914$	−1.25142e10	−0.542117
$915$	−4.08072e7	−0.00176102
$916$	−1.75172e10	−0.753063
$917$	5.51964e9	0.236384
$918$	8.38178e8	0.0357591
$919$	2.33408e10	0.991998	0.495999	−	0.868323i	$-0.334802\pi$
$919$	2.33408e10	0.991998	0.495999	+	0.868323i	$0.334802\pi$
$920$	7.76006e8	0.0328555
$921$	−9.93138e9	−0.418891
$922$	−2.42638e9	−0.101953
$923$	4.34814e9	0.182011
$924$	2.19742e9	0.0916349
$925$	−1.40952e10	−0.585567
$926$	5.69800e8	0.0235822
$927$	6.86814e9	0.283178
$928$	3.75561e9	0.154263
$929$	−2.81419e10	−1.15159	−0.575795	−	0.817594i	$-0.695307\pi$
$929$	−2.81419e10	−1.15159	−0.575795	+	0.817594i	$0.695307\pi$
$930$	−5.19502e9	−0.211786
$931$	−9.96712e7	−0.00404805
$932$	−2.58071e9	−0.104420
$933$	−1.21126e9	−0.0488262
$934$	1.25453e10	0.503809
$935$	4.41171e9	0.176509
$936$	−8.20026e8	−0.0326860
$937$	−1.69089e10	−0.671472	−0.335736	−	0.941956i	$-0.608985\pi$
$937$	−1.69089e10	−0.671472	−0.335736	+	0.941956i	$0.608985\pi$
$938$	−3.65824e9	−0.144731
$939$	−9.29556e9	−0.366392
$940$	3.86413e9	0.151741
$941$	1.28772e9	0.0503798	0.0251899	−	0.999683i	$-0.491981\pi$
$941$	1.28772e9	0.0503798	0.0251899	+	0.999683i	$0.491981\pi$
$942$	5.59414e9	0.218050
$943$	1.31183e9	0.0509433
$944$	1.12212e10	0.434146
$945$	−1.50925e9	−0.0581769
$946$	1.56823e10	0.602269
$947$	3.25118e10	1.24399	0.621993	−	0.783023i	$-0.286323\pi$
$947$	3.25118e10	1.24399	0.621993	+	0.783023i	$0.286323\pi$
$948$	−1.78563e9	−0.0680710
$949$	3.32354e9	0.126232
$950$	1.90787e8	0.00721966
$951$	6.62825e9	0.249900
$952$	9.34801e8	0.0351148
$953$	−5.91066e9	−0.221213	−0.110606	−	0.993864i	$-0.535279\pi$
$953$	−5.91066e9	−0.221213	−0.110606	+	0.993864i	$0.535279\pi$
$954$	9.73016e8	0.0362828
$955$	1.85541e10	0.689331
$956$	1.37432e9	0.0508729
$957$	−1.14728e10	−0.423133
$958$	3.16279e10	1.16223
$959$	−1.53850e9	−0.0563290
$960$	1.58227e9	0.0577206
$961$	−1.59378e10	−0.579290
$962$	−8.80066e9	−0.318715
$963$	−1.46377e10	−0.528180
$964$	−5.92207e9	−0.212914
$965$	1.51039e10	0.541056
$966$	−5.02304e8	−0.0179286
$967$	−3.91881e10	−1.39368	−0.696838	−	0.717229i	$-0.745410\pi$
$967$	−3.91881e10	−1.39368	−0.696838	+	0.717229i	$0.745410\pi$
$968$	−2.93991e9	−0.104177
$969$	−1.21759e8	−0.00429900
$970$	−1.33769e10	−0.470602
$971$	3.00821e10	1.05449	0.527243	−	0.849715i	$-0.323226\pi$
$971$	3.00821e10	1.05449	0.527243	+	0.849715i	$0.323226\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.29792e10	0.451704
$974$	2.64620e10	0.917627
$975$	−1.66983e9	−0.0576973
$976$	−2.76922e7	−0.000953416 0
$977$	−3.20746e10	−1.10035	−0.550175	−	0.835050i	$-0.685439\pi$
$977$	−3.20746e10	−1.10035	−0.550175	+	0.835050i	$0.685439\pi$
$978$	1.05527e9	0.0360727
$979$	−4.03778e10	−1.37532
$980$	−1.68324e9	−0.0571286
$981$	−1.45455e10	−0.491911
$982$	7.63750e9	0.257372
$983$	5.21892e10	1.75244	0.876221	−	0.481910i	$-0.160057\pi$
$983$	5.21892e10	1.75244	0.876221	+	0.481910i	$0.160057\pi$
$984$	2.67481e9	0.0894974
$985$	−4.66698e9	−0.155600
$986$	−4.88063e9	−0.162146
$987$	−2.50122e9	−0.0828024
$988$	1.19122e8	0.00392954
$989$	−3.58478e9	−0.117835
$990$	−4.83358e9	−0.158324
$991$	−1.74474e10	−0.569474	−0.284737	−	0.958606i	$-0.591906\pi$
$991$	−1.74474e10	−0.569474	−0.284737	+	0.958606i	$0.591906\pi$
$992$	−3.52539e9	−0.114661
$993$	−1.02272e10	−0.331461
$994$	5.43072e9	0.175390
$995$	1.47556e10	0.474871
$996$	1.11708e10	0.358242
$997$	−3.30188e9	−0.105519	−0.0527593	−	0.998607i	$-0.516802\pi$
$997$	−3.30188e9	−0.105519	−0.0527593	+	0.998607i	$0.516802\pi$
$998$	−4.62681e9	−0.147341
$999$	−9.85567e9	−0.312757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.l.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.l.1.2	✓	5	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -223.551 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -223.551 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -1788.41 q^{10} +3707.45 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +6035.88 q^{15} +4096.00 q^{16} -5322.98 q^{17} +5832.00 q^{18} -847.191 q^{19} -14307.3 q^{20} +9261.00 q^{21} +29659.6 q^{22} -6779.82 q^{23} -13824.0 q^{24} -28150.0 q^{25} -17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +114612. q^{29} +48287.0 q^{30} -107586. q^{31} +32768.0 q^{32} -100101. q^{33} -42583.9 q^{34} +76678.0 q^{35} +46656.0 q^{36} +500720. q^{37} -6777.53 q^{38} +59319.0 q^{39} -114458. q^{40} -193490. q^{41} +74088.0 q^{42} +528743. q^{43} +237277. q^{44} -162969. q^{45} -54238.6 q^{46} -270082. q^{47} -110592. q^{48} +117649. q^{49} -225200. q^{50} +143721. q^{51} -140608. q^{52} +166841. q^{53} -157464. q^{54} -828803. q^{55} -175616. q^{56} +22874.2 q^{57} +916897. q^{58} +2.73954e6 q^{59} +386296. q^{60} -6760.78 q^{61} -860691. q^{62} -250047. q^{63} +262144. q^{64} +491142. q^{65} -800808. q^{66} +1.33318e6 q^{67} -340671. q^{68} +183055. q^{69} +613424. q^{70} -1.97912e6 q^{71} +373248. q^{72} -1.51276e6 q^{73} +4.00576e6 q^{74} +760049. q^{75} -54220.2 q^{76} -1.27165e6 q^{77} +474552. q^{78} +1.03335e6 q^{79} -915665. q^{80} +531441. q^{81} -1.54792e6 q^{82} -6.46458e6 q^{83} +592704. q^{84} +1.18996e6 q^{85} +4.22994e6 q^{86} -3.09453e6 q^{87} +1.89821e6 q^{88} -1.08910e7 q^{89} -1.30375e6 q^{90} +753571. q^{91} -433909. q^{92} +2.90483e6 q^{93} -2.16065e6 q^{94} +189390. q^{95} -884736. q^{96} +7.47976e6 q^{97} +941192. q^{98} +2.70273e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} - 135 q^{3} + 320 q^{4} - 250 q^{5} - 1080 q^{6} - 1715 q^{7} + 2560 q^{8} + 3645 q^{9} - 2000 q^{10} + 659 q^{11} - 8640 q^{12} - 10985 q^{13} - 13720 q^{14} + 6750 q^{15} + 20480 q^{16} + 24575 q^{17} + 29160 q^{18} - 6446 q^{19} - 16000 q^{20} + 46305 q^{21} + 5272 q^{22} + 30268 q^{23} - 69120 q^{24} + 38965 q^{25} - 87880 q^{26} - 98415 q^{27} - 109760 q^{28} + 130950 q^{29} + 54000 q^{30} + 262979 q^{31} + 163840 q^{32} - 17793 q^{33} + 196600 q^{34} + 85750 q^{35} + 233280 q^{36} - 101549 q^{37} - 51568 q^{38} + 296595 q^{39} - 128000 q^{40} - 247328 q^{41} + 370440 q^{42} - 19092 q^{43} + 42176 q^{44} - 182250 q^{45} + 242144 q^{46} - 126419 q^{47} - 552960 q^{48} + 588245 q^{49} + 311720 q^{50} - 663525 q^{51} - 703040 q^{52} - 302793 q^{53} - 787320 q^{54} + 943985 q^{55} - 878080 q^{56} + 174042 q^{57} + 1047600 q^{58} - 2798636 q^{59} + 432000 q^{60} - 2493751 q^{61} + 2103832 q^{62} - 1250235 q^{63} + 1310720 q^{64} + 549250 q^{65} - 142344 q^{66} + 160188 q^{67} + 1572800 q^{68} - 817236 q^{69} + 686000 q^{70} + 3846088 q^{71} + 1866240 q^{72} + 5655872 q^{73} - 812392 q^{74} - 1052055 q^{75} - 412544 q^{76} - 226037 q^{77} + 2372760 q^{78} + 5647991 q^{79} - 1024000 q^{80} + 2657205 q^{81} - 1978624 q^{82} - 4607669 q^{83} + 2963520 q^{84} + 3873935 q^{85} - 152736 q^{86} - 3535650 q^{87} + 337408 q^{88} - 17424029 q^{89} - 1458000 q^{90} + 3767855 q^{91} + 1937152 q^{92} - 7100433 q^{93} - 1011352 q^{94} - 24593720 q^{95} - 4423680 q^{96} - 18380577 q^{97} + 4705960 q^{98} + 480411 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 - 135 * q^3 + 320 * q^4 - 250 * q^5 - 1080 * q^6 - 1715 * q^7 + 2560 * q^8 + 3645 * q^9 - 2000 * q^10 + 659 * q^11 - 8640 * q^12 - 10985 * q^13 - 13720 * q^14 + 6750 * q^15 + 20480 * q^16 + 24575 * q^17 + 29160 * q^18 - 6446 * q^19 - 16000 * q^20 + 46305 * q^21 + 5272 * q^22 + 30268 * q^23 - 69120 * q^24 + 38965 * q^25 - 87880 * q^26 - 98415 * q^27 - 109760 * q^28 + 130950 * q^29 + 54000 * q^30 + 262979 * q^31 + 163840 * q^32 - 17793 * q^33 + 196600 * q^34 + 85750 * q^35 + 233280 * q^36 - 101549 * q^37 - 51568 * q^38 + 296595 * q^39 - 128000 * q^40 - 247328 * q^41 + 370440 * q^42 - 19092 * q^43 + 42176 * q^44 - 182250 * q^45 + 242144 * q^46 - 126419 * q^47 - 552960 * q^48 + 588245 * q^49 + 311720 * q^50 - 663525 * q^51 - 703040 * q^52 - 302793 * q^53 - 787320 * q^54 + 943985 * q^55 - 878080 * q^56 + 174042 * q^57 + 1047600 * q^58 - 2798636 * q^59 + 432000 * q^60 - 2493751 * q^61 + 2103832 * q^62 - 1250235 * q^63 + 1310720 * q^64 + 549250 * q^65 - 142344 * q^66 + 160188 * q^67 + 1572800 * q^68 - 817236 * q^69 + 686000 * q^70 + 3846088 * q^71 + 1866240 * q^72 + 5655872 * q^73 - 812392 * q^74 - 1052055 * q^75 - 412544 * q^76 - 226037 * q^77 + 2372760 * q^78 + 5647991 * q^79 - 1024000 * q^80 + 2657205 * q^81 - 1978624 * q^82 - 4607669 * q^83 + 2963520 * q^84 + 3873935 * q^85 - 152736 * q^86 - 3535650 * q^87 + 337408 * q^88 - 17424029 * q^89 - 1458000 * q^90 + 3767855 * q^91 + 1937152 * q^92 - 7100433 * q^93 - 1011352 * q^94 - 24593720 * q^95 - 4423680 * q^96 - 18380577 * q^97 + 4705960 * q^98 + 480411 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more