LMFDB - Embedded newform 354.8.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.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:	$110.584299021$
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} - x^{4} - 6162x^{3} - 12837x^{2} + 3760259x - 17264060 $ x^5 - x^4 - 6162x^3 - 12837x^2 + 3760259*x - 17264060
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.85925$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -301.683 q^{5} +216.000 q^{6} +1135.68 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -301.683 q^{5} +216.000 q^{6} +1135.68 q^{7} +512.000 q^{8} +729.000 q^{9} -2413.47 q^{10} -4671.11 q^{11} +1728.00 q^{12} -5448.90 q^{13} +9085.42 q^{14} -8145.45 q^{15} +4096.00 q^{16} +32160.1 q^{17} +5832.00 q^{18} -44141.1 q^{19} -19307.7 q^{20} +30663.3 q^{21} -37368.9 q^{22} -31126.7 q^{23} +13824.0 q^{24} +12887.8 q^{25} -43591.2 q^{26} +19683.0 q^{27} +72683.4 q^{28} -171161. q^{29} -65163.6 q^{30} +153757. q^{31} +32768.0 q^{32} -126120. q^{33} +257281. q^{34} -342615. q^{35} +46656.0 q^{36} -123880. q^{37} -353129. q^{38} -147120. q^{39} -154462. q^{40} -175979. q^{41} +245306. q^{42} -256606. q^{43} -298951. q^{44} -219927. q^{45} -249013. q^{46} +377328. q^{47} +110592. q^{48} +466221. q^{49} +103103. q^{50} +868324. q^{51} -348729. q^{52} +852261. q^{53} +157464. q^{54} +1.40920e6 q^{55} +581467. q^{56} -1.19181e6 q^{57} -1.36929e6 q^{58} +205379. q^{59} -521309. q^{60} -1.99375e6 q^{61} +1.23006e6 q^{62} +827909. q^{63} +262144. q^{64} +1.64384e6 q^{65} -1.00896e6 q^{66} -1.94039e6 q^{67} +2.05825e6 q^{68} -840420. q^{69} -2.74092e6 q^{70} +674666. q^{71} +373248. q^{72} -4.47921e6 q^{73} -991044. q^{74} +347972. q^{75} -2.82503e6 q^{76} -5.30488e6 q^{77} -1.17696e6 q^{78} -2.14344e6 q^{79} -1.23570e6 q^{80} +531441. q^{81} -1.40783e6 q^{82} -92386.6 q^{83} +1.96245e6 q^{84} -9.70218e6 q^{85} -2.05285e6 q^{86} -4.62135e6 q^{87} -2.39161e6 q^{88} -1.19788e7 q^{89} -1.75942e6 q^{90} -6.18819e6 q^{91} -1.99211e6 q^{92} +4.15144e6 q^{93} +3.01863e6 q^{94} +1.33166e7 q^{95} +884736. q^{96} +6.76114e6 q^{97} +3.72977e6 q^{98} -3.40524e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 164 q^{5} + 1080 q^{6} - 76 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) $ 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 164 * q^5 + 1080 * q^6 - 76 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 164 q^{5} + 1080 q^{6} - 76 q^{7} + 2560 q^{8} + 3645 q^{9} + 1312 q^{10} - 15730 q^{11} + 8640 q^{12} - 21854 q^{13} - 608 q^{14} + 4428 q^{15} + 20480 q^{16} - 34548 q^{17} + 29160 q^{18} - 43828 q^{19} + 10496 q^{20} - 2052 q^{21} - 125840 q^{22} - 110582 q^{23} + 69120 q^{24} - 174577 q^{25} - 174832 q^{26} + 98415 q^{27} - 4864 q^{28} - 307558 q^{29} + 35424 q^{30} - 277994 q^{31} + 163840 q^{32} - 424710 q^{33} - 276384 q^{34} - 764338 q^{35} + 233280 q^{36} - 853778 q^{37} - 350624 q^{38} - 590058 q^{39} + 83968 q^{40} + 131342 q^{41} - 16416 q^{42} - 721996 q^{43} - 1006720 q^{44} + 119556 q^{45} - 884656 q^{46} - 358832 q^{47} + 552960 q^{48} - 207141 q^{49} - 1396616 q^{50} - 932796 q^{51} - 1398656 q^{52} + 1006180 q^{53} + 787320 q^{54} + 81944 q^{55} - 38912 q^{56} - 1183356 q^{57} - 2460464 q^{58} + 1026895 q^{59} + 283392 q^{60} + 101158 q^{61} - 2223952 q^{62} - 55404 q^{63} + 1310720 q^{64} - 3138378 q^{65} - 3397680 q^{66} - 6362512 q^{67} - 2211072 q^{68} - 2985714 q^{69} - 6114704 q^{70} - 8877414 q^{71} + 1866240 q^{72} - 4881862 q^{73} - 6830224 q^{74} - 4713579 q^{75} - 2804992 q^{76} - 2205694 q^{77} - 4720464 q^{78} - 2769432 q^{79} + 671744 q^{80} + 2657205 q^{81} + 1050736 q^{82} - 1430156 q^{83} - 131328 q^{84} - 7564814 q^{85} - 5775968 q^{86} - 8304066 q^{87} - 8053760 q^{88} - 17172176 q^{89} + 956448 q^{90} - 932474 q^{91} - 7077248 q^{92} - 7505838 q^{93} - 2870656 q^{94} + 15962708 q^{95} + 4423680 q^{96} + 20863830 q^{97} - 1657128 q^{98} - 11467170 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 164 * q^5 + 1080 * q^6 - 76 * q^7 + 2560 * q^8 + 3645 * q^9 + 1312 * q^10 - 15730 * q^11 + 8640 * q^12 - 21854 * q^13 - 608 * q^14 + 4428 * q^15 + 20480 * q^16 - 34548 * q^17 + 29160 * q^18 - 43828 * q^19 + 10496 * q^20 - 2052 * q^21 - 125840 * q^22 - 110582 * q^23 + 69120 * q^24 - 174577 * q^25 - 174832 * q^26 + 98415 * q^27 - 4864 * q^28 - 307558 * q^29 + 35424 * q^30 - 277994 * q^31 + 163840 * q^32 - 424710 * q^33 - 276384 * q^34 - 764338 * q^35 + 233280 * q^36 - 853778 * q^37 - 350624 * q^38 - 590058 * q^39 + 83968 * q^40 + 131342 * q^41 - 16416 * q^42 - 721996 * q^43 - 1006720 * q^44 + 119556 * q^45 - 884656 * q^46 - 358832 * q^47 + 552960 * q^48 - 207141 * q^49 - 1396616 * q^50 - 932796 * q^51 - 1398656 * q^52 + 1006180 * q^53 + 787320 * q^54 + 81944 * q^55 - 38912 * q^56 - 1183356 * q^57 - 2460464 * q^58 + 1026895 * q^59 + 283392 * q^60 + 101158 * q^61 - 2223952 * q^62 - 55404 * q^63 + 1310720 * q^64 - 3138378 * q^65 - 3397680 * q^66 - 6362512 * q^67 - 2211072 * q^68 - 2985714 * q^69 - 6114704 * q^70 - 8877414 * q^71 + 1866240 * q^72 - 4881862 * q^73 - 6830224 * q^74 - 4713579 * q^75 - 2804992 * q^76 - 2205694 * q^77 - 4720464 * q^78 - 2769432 * q^79 + 671744 * q^80 + 2657205 * q^81 + 1050736 * q^82 - 1430156 * q^83 - 131328 * q^84 - 7564814 * q^85 - 5775968 * q^86 - 8304066 * q^87 - 8053760 * q^88 - 17172176 * q^89 + 956448 * q^90 - 932474 * q^91 - 7077248 * q^92 - 7505838 * q^93 - 2870656 * q^94 + 15962708 * q^95 + 4423680 * q^96 + 20863830 * q^97 - 1657128 * q^98 - 11467170 * 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
$5$	−301.683	−1.07934	−0.539668	−	0.841878i	$-0.681450\pi$
$5$	−301.683	−1.07934	−0.539668	+	0.841878i	$0.681450\pi$
$6$	216.000	0.408248
$7$	1135.68	1.25145	0.625723	−	0.780045i	$-0.284804\pi$
$7$	1135.68	1.25145	0.625723	+	0.780045i	$0.284804\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−2413.47	−0.763205
$11$	−4671.11	−1.05815	−0.529073	−	0.848576i	$-0.677460\pi$
$11$	−4671.11	−1.05815	−0.529073	+	0.848576i	$0.677460\pi$
$12$	1728.00	0.288675
$13$	−5448.90	−0.687871	−0.343935	−	0.938993i	$-0.611760\pi$
$13$	−5448.90	−0.687871	−0.343935	+	0.938993i	$0.611760\pi$
$14$	9085.42	0.884906
$15$	−8145.45	−0.623154
$16$	4096.00	0.250000
$17$	32160.1	1.58762	0.793810	−	0.608166i	$-0.208094\pi$
$17$	32160.1	1.58762	0.793810	+	0.608166i	$0.208094\pi$
$18$	5832.00	0.235702
$19$	−44141.1	−1.47640	−0.738202	−	0.674579i	$-0.764325\pi$
$19$	−44141.1	−1.47640	−0.738202	+	0.674579i	$0.764325\pi$
$20$	−19307.7	−0.539668
$21$	30663.3	0.722522
$22$	−37368.9	−0.748223
$23$	−31126.7	−0.533440	−0.266720	−	0.963774i	$-0.585940\pi$
$23$	−31126.7	−0.533440	−0.266720	+	0.963774i	$0.585940\pi$
$24$	13824.0	0.204124
$25$	12887.8	0.164964
$26$	−43591.2	−0.486398
$27$	19683.0	0.192450
$28$	72683.4	0.625723
$29$	−171161.	−1.30320	−0.651601	−	0.758562i	$-0.725902\pi$
$29$	−171161.	−1.30320	−0.651601	+	0.758562i	$0.725902\pi$
$30$	−65163.6	−0.440637
$31$	153757.	0.926978	0.463489	−	0.886103i	$-0.346597\pi$
$31$	153757.	0.926978	0.463489	+	0.886103i	$0.346597\pi$
$32$	32768.0	0.176777
$33$	−126120.	−0.610921
$34$	257281.	1.12262
$35$	−342615.	−1.35073
$36$	46656.0	0.166667
$37$	−123880.	−0.402065	−0.201033	−	0.979585i	$-0.564430\pi$
$37$	−123880.	−0.402065	−0.201033	+	0.979585i	$0.564430\pi$
$38$	−353129.	−1.04398
$39$	−147120.	−0.397142
$40$	−154462.	−0.381603
$41$	−175979.	−0.398765	−0.199382	−	0.979922i	$-0.563894\pi$
$41$	−175979.	−0.398765	−0.199382	+	0.979922i	$0.563894\pi$
$42$	245306.	0.510901
$43$	−256606.	−0.492184	−0.246092	−	0.969246i	$-0.579147\pi$
$43$	−256606.	−0.492184	−0.246092	+	0.969246i	$0.579147\pi$
$44$	−298951.	−0.529073
$45$	−219927.	−0.359778
$46$	−249013.	−0.377199
$47$	377328.	0.530124	0.265062	−	0.964231i	$-0.414608\pi$
$47$	377328.	0.530124	0.265062	+	0.964231i	$0.414608\pi$
$48$	110592.	0.144338
$49$	466221.	0.566116
$50$	103103.	0.116647
$51$	868324.	0.916613
$52$	−348729.	−0.343935
$53$	852261.	0.786334	0.393167	−	0.919467i	$-0.371379\pi$
$53$	852261.	0.786334	0.393167	+	0.919467i	$0.371379\pi$
$54$	157464.	0.136083
$55$	1.40920e6	1.14209
$56$	581467.	0.442453
$57$	−1.19181e6	−0.852403
$58$	−1.36929e6	−0.921503
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−521309.	−0.311577
$61$	−1.99375e6	−1.12465	−0.562324	−	0.826917i	$-0.690093\pi$
$61$	−1.99375e6	−1.12465	−0.562324	+	0.826917i	$0.690093\pi$
$62$	1.23006e6	0.655473
$63$	827909.	0.417149
$64$	262144.	0.125000
$65$	1.64384e6	0.742443
$66$	−1.00896e6	−0.431987
$67$	−1.94039e6	−0.788182	−0.394091	−	0.919071i	$-0.628940\pi$
$67$	−1.94039e6	−0.788182	−0.394091	+	0.919071i	$0.628940\pi$
$68$	2.05825e6	0.793810
$69$	−840420.	−0.307982
$70$	−2.74092e6	−0.955110
$71$	674666.	0.223710	0.111855	−	0.993725i	$-0.464321\pi$
$71$	674666.	0.223710	0.111855	+	0.993725i	$0.464321\pi$
$72$	373248.	0.117851
$73$	−4.47921e6	−1.34763	−0.673816	−	0.738899i	$-0.735346\pi$
$73$	−4.47921e6	−1.34763	−0.673816	+	0.738899i	$0.735346\pi$
$74$	−991044.	−0.284303
$75$	347972.	0.0952423
$76$	−2.82503e6	−0.738202
$77$	−5.30488e6	−1.32421
$78$	−1.17696e6	−0.280822
$79$	−2.14344e6	−0.489120	−0.244560	−	0.969634i	$-0.578644\pi$
$79$	−2.14344e6	−0.489120	−0.244560	+	0.969634i	$0.578644\pi$
$80$	−1.23570e6	−0.269834
$81$	531441.	0.111111
$82$	−1.40783e6	−0.281969
$83$	−92386.6	−0.0177352	−0.00886759	−	0.999961i	$-0.502823\pi$
$83$	−92386.6	−0.0177352	−0.00886759	+	0.999961i	$0.502823\pi$
$84$	1.96245e6	0.361261
$85$	−9.70218e6	−1.71357
$86$	−2.05285e6	−0.348027
$87$	−4.62135e6	−0.752404
$88$	−2.39161e6	−0.374111
$89$	−1.19788e7	−1.80115	−0.900574	−	0.434704i	$-0.856853\pi$
$89$	−1.19788e7	−1.80115	−0.900574	+	0.434704i	$0.856853\pi$
$90$	−1.75942e6	−0.254402
$91$	−6.18819e6	−0.860833
$92$	−1.99211e6	−0.266720
$93$	4.15144e6	0.535191
$94$	3.01863e6	0.374854
$95$	1.33166e7	1.59354
$96$	884736.	0.102062
$97$	6.76114e6	0.752175	0.376088	−	0.926584i	$-0.377269\pi$
$97$	6.76114e6	0.752175	0.376088	+	0.926584i	$0.377269\pi$
$98$	3.72977e6	0.400305
$99$	−3.40524e6	−0.352716
$100$	824822.	0.0824822
$101$	−1.70403e7	−1.64571	−0.822853	−	0.568255i	$-0.807619\pi$
$101$	−1.70403e7	−1.64571	−0.822853	+	0.568255i	$0.807619\pi$
$102$	6.94659e6	0.648143
$103$	−1.25721e7	−1.13364	−0.566822	−	0.823840i	$-0.691827\pi$
$103$	−1.25721e7	−1.13364	−0.566822	+	0.823840i	$0.691827\pi$
$104$	−2.78984e6	−0.243199
$105$	−9.25061e6	−0.779844
$106$	6.81809e6	0.556022
$107$	9.71129e6	0.766361	0.383181	−	0.923673i	$-0.374829\pi$
$107$	9.71129e6	0.766361	0.383181	+	0.923673i	$0.374829\pi$
$108$	1.25971e6	0.0962250
$109$	−1.05755e7	−0.782186	−0.391093	−	0.920351i	$-0.627903\pi$
$109$	−1.05755e7	−0.782186	−0.391093	+	0.920351i	$0.627903\pi$
$110$	1.12736e7	0.807583
$111$	−3.34477e6	−0.232133
$112$	4.65174e6	0.312861
$113$	1.44188e7	0.940059	0.470029	−	0.882651i	$-0.344243\pi$
$113$	1.44188e7	0.940059	0.470029	+	0.882651i	$0.344243\pi$
$114$	−9.53447e6	−0.602740
$115$	9.39040e6	0.575760
$116$	−1.09543e7	−0.651601
$117$	−3.97225e6	−0.229290
$118$	1.64303e6	0.0920575
$119$	3.65235e7	1.98682
$120$	−4.17047e6	−0.220318
$121$	2.33211e6	0.119674
$122$	−1.59500e7	−0.795246
$123$	−4.75143e6	−0.230227
$124$	9.84046e6	0.463489
$125$	1.96810e7	0.901283
$126$	6.62327e6	0.294969
$127$	−2.64338e7	−1.14511	−0.572554	−	0.819867i	$-0.694047\pi$
$127$	−2.64338e7	−1.14511	−0.572554	+	0.819867i	$0.694047\pi$
$128$	2.09715e6	0.0883883
$129$	−6.92837e6	−0.284163
$130$	1.31507e7	0.524987
$131$	−2.29456e7	−0.891763	−0.445881	−	0.895092i	$-0.647110\pi$
$131$	−2.29456e7	−0.891763	−0.445881	+	0.895092i	$0.647110\pi$
$132$	−8.07168e6	−0.305461
$133$	−5.01300e7	−1.84764
$134$	−1.55231e7	−0.557329
$135$	−5.93803e6	−0.207718
$136$	1.64660e7	0.561308
$137$	3.45276e7	1.14721	0.573607	−	0.819131i	$-0.305544\pi$
$137$	3.45276e7	1.14721	0.573607	+	0.819131i	$0.305544\pi$
$138$	−6.72336e6	−0.217776
$139$	4.18516e7	1.32178	0.660892	−	0.750481i	$-0.270178\pi$
$139$	4.18516e7	1.32178	0.660892	+	0.750481i	$0.270178\pi$
$140$	−2.19274e7	−0.675365
$141$	1.01879e7	0.306067
$142$	5.39733e6	0.158187
$143$	2.54524e7	0.727868
$144$	2.98598e6	0.0833333
$145$	5.16364e7	1.40659
$146$	−3.58337e7	−0.952920
$147$	1.25880e7	0.326847
$148$	−7.92835e6	−0.201033
$149$	7.13008e7	1.76580	0.882902	−	0.469557i	$-0.155586\pi$
$149$	7.13008e7	1.76580	0.882902	+	0.469557i	$0.155586\pi$
$150$	2.78378e6	0.0673465
$151$	−7.55179e7	−1.78497	−0.892484	−	0.451078i	$-0.851040\pi$
$151$	−7.55179e7	−1.78497	−0.892484	+	0.451078i	$0.851040\pi$
$152$	−2.26002e7	−0.521988
$153$	2.34447e7	0.529207
$154$	−4.24390e7	−0.936360
$155$	−4.63860e7	−1.00052
$156$	−9.41569e6	−0.198571
$157$	−4.10964e7	−0.847530	−0.423765	−	0.905772i	$-0.639292\pi$
$157$	−4.10964e7	−0.847530	−0.423765	+	0.905772i	$0.639292\pi$
$158$	−1.71475e7	−0.345860
$159$	2.30110e7	0.453990
$160$	−9.88556e6	−0.190801
$161$	−3.53499e7	−0.667571
$162$	4.25153e6	0.0785674
$163$	−3.64090e7	−0.658494	−0.329247	−	0.944244i	$-0.606795\pi$
$163$	−3.64090e7	−0.658494	−0.329247	+	0.944244i	$0.606795\pi$
$164$	−1.12626e7	−0.199382
$165$	3.80483e7	0.659389
$166$	−739093.	−0.0125407
$167$	−3.07198e7	−0.510400	−0.255200	−	0.966888i	$-0.582141\pi$
$167$	−3.07198e7	−0.510400	−0.255200	+	0.966888i	$0.582141\pi$
$168$	1.56996e7	0.255450
$169$	−3.30580e7	−0.526834
$170$	−7.76174e7	−1.21168
$171$	−3.21788e7	−0.492135
$172$	−1.64228e7	−0.246092
$173$	6.27008e7	0.920686	0.460343	−	0.887741i	$-0.347726\pi$
$173$	6.27008e7	0.920686	0.460343	+	0.887741i	$0.347726\pi$
$174$	−3.69708e7	−0.532030
$175$	1.46364e7	0.206444
$176$	−1.91329e7	−0.264537
$177$	5.54523e6	0.0751646
$178$	−9.58306e7	−1.27360
$179$	−1.18647e8	−1.54622	−0.773110	−	0.634272i	$-0.781300\pi$
$179$	−1.18647e8	−1.54622	−0.773110	+	0.634272i	$0.781300\pi$
$180$	−1.40753e7	−0.179889
$181$	5.19181e7	0.650795	0.325397	−	0.945577i	$-0.394502\pi$
$181$	5.19181e7	0.650795	0.325397	+	0.945577i	$0.394502\pi$
$182$	−4.95055e7	−0.608701
$183$	−5.38313e7	−0.649316
$184$	−1.59369e7	−0.188599
$185$	3.73727e7	0.433963
$186$	3.32116e7	0.378437
$187$	−1.50224e8	−1.67993
$188$	2.41490e7	0.265062
$189$	2.23535e7	0.240841
$190$	1.06533e8	1.12680
$191$	−1.13067e7	−0.117413	−0.0587067	−	0.998275i	$-0.518698\pi$
$191$	−1.13067e7	−0.117413	−0.0587067	+	0.998275i	$0.518698\pi$
$192$	7.07789e6	0.0721688
$193$	1.43625e8	1.43807	0.719035	−	0.694974i	$-0.244584\pi$
$193$	1.43625e8	1.43807	0.719035	+	0.694974i	$0.244584\pi$
$194$	5.40891e7	0.531868
$195$	4.43837e7	0.428650
$196$	2.98381e7	0.283058
$197$	−1.82068e8	−1.69669	−0.848344	−	0.529445i	$-0.822400\pi$
$197$	−1.82068e8	−1.69669	−0.848344	+	0.529445i	$0.822400\pi$
$198$	−2.72419e7	−0.249408
$199$	1.23417e7	0.111017	0.0555083	−	0.998458i	$-0.482322\pi$
$199$	1.23417e7	0.111017	0.0555083	+	0.998458i	$0.482322\pi$
$200$	6.59858e6	0.0583237
$201$	−5.23904e7	−0.455057
$202$	−1.36322e8	−1.16369
$203$	−1.94384e8	−1.63089
$204$	5.55727e7	0.458306
$205$	5.30899e7	0.430401
$206$	−1.00577e8	−0.801607
$207$	−2.26913e7	−0.177813
$208$	−2.23187e7	−0.171968
$209$	2.06188e8	1.56225
$210$	−7.40049e7	−0.551433
$211$	−2.10765e7	−0.154458	−0.0772288	−	0.997013i	$-0.524607\pi$
$211$	−2.10765e7	−0.154458	−0.0772288	+	0.997013i	$0.524607\pi$
$212$	5.45447e7	0.393167
$213$	1.82160e7	0.129159
$214$	7.76903e7	0.541899
$215$	7.74139e7	0.531232
$216$	1.00777e7	0.0680414
$217$	1.74619e8	1.16006
$218$	−8.46044e7	−0.553089
$219$	−1.20939e8	−0.778056
$220$	9.01886e7	0.571047
$221$	−1.75237e8	−1.09208
$222$	−2.67582e7	−0.164143
$223$	−1.54533e7	−0.0933157	−0.0466579	−	0.998911i	$-0.514857\pi$
$223$	−1.54533e7	−0.0933157	−0.0466579	+	0.998911i	$0.514857\pi$
$224$	3.72139e7	0.221226
$225$	9.39524e6	0.0549882
$226$	1.15351e8	0.664722
$227$	3.36414e8	1.90890	0.954451	−	0.298367i	$-0.0964419\pi$
$227$	3.36414e8	1.90890	0.954451	+	0.298367i	$0.0964419\pi$
$228$	−7.62758e7	−0.426201
$229$	−1.31785e6	−0.00725175	−0.00362588	−	0.999993i	$-0.501154\pi$
$229$	−1.31785e6	−0.00725175	−0.00362588	+	0.999993i	$0.501154\pi$
$230$	7.51232e7	0.407124
$231$	−1.43232e8	−0.764535
$232$	−8.76345e7	−0.460752
$233$	−2.77425e8	−1.43681	−0.718406	−	0.695624i	$-0.755128\pi$
$233$	−2.77425e8	−1.43681	−0.718406	+	0.695624i	$0.755128\pi$
$234$	−3.17780e7	−0.162133
$235$	−1.13834e8	−0.572181
$236$	1.31443e7	0.0650945
$237$	−5.78728e7	−0.282394
$238$	2.92188e8	1.40489
$239$	−2.16538e8	−1.02599	−0.512994	−	0.858392i	$-0.671464\pi$
$239$	−2.16538e8	−1.02599	−0.512994	+	0.858392i	$0.671464\pi$
$240$	−3.33638e7	−0.155789
$241$	9.94757e7	0.457781	0.228890	−	0.973452i	$-0.426490\pi$
$241$	9.94757e7	0.457781	0.228890	+	0.973452i	$0.426490\pi$
$242$	1.86569e7	0.0846225
$243$	1.43489e7	0.0641500
$244$	−1.27600e8	−0.562324
$245$	−1.40651e8	−0.611029
$246$	−3.80114e7	−0.162795
$247$	2.40520e8	1.01558
$248$	7.87237e7	0.327736
$249$	−2.49444e6	−0.0102394
$250$	1.57448e8	0.637303
$251$	2.71169e8	1.08239	0.541193	−	0.840898i	$-0.317973\pi$
$251$	2.71169e8	1.08239	0.541193	+	0.840898i	$0.317973\pi$
$252$	5.29862e7	0.208574
$253$	1.45396e8	0.564457
$254$	−2.11470e8	−0.809713
$255$	−2.61959e8	−0.989333
$256$	1.67772e7	0.0625000
$257$	4.43798e7	0.163087	0.0815435	−	0.996670i	$-0.474015\pi$
$257$	4.43798e7	0.163087	0.0815435	+	0.996670i	$0.474015\pi$
$258$	−5.54270e7	−0.200933
$259$	−1.40688e8	−0.503163
$260$	1.05206e8	0.371222
$261$	−1.24776e8	−0.434401
$262$	−1.83565e8	−0.630571
$263$	2.90398e8	0.984348	0.492174	−	0.870497i	$-0.336202\pi$
$263$	2.90398e8	0.984348	0.492174	+	0.870497i	$0.336202\pi$
$264$	−6.45734e7	−0.215993
$265$	−2.57113e8	−0.848718
$266$	−4.01040e8	−1.30648
$267$	−3.23428e8	−1.03989
$268$	−1.24185e8	−0.394091
$269$	2.90781e8	0.910822	0.455411	−	0.890281i	$-0.349492\pi$
$269$	2.90781e8	0.910822	0.455411	+	0.890281i	$0.349492\pi$
$270$	−4.75043e7	−0.146879
$271$	4.84825e8	1.47976	0.739882	−	0.672737i	$-0.234881\pi$
$271$	4.84825e8	1.47976	0.739882	+	0.672737i	$0.234881\pi$
$272$	1.31728e8	0.396905
$273$	−1.67081e8	−0.497002
$274$	2.76221e8	0.811203
$275$	−6.02006e7	−0.174557
$276$	−5.37869e7	−0.153991
$277$	3.21955e8	0.910156	0.455078	−	0.890452i	$-0.349611\pi$
$277$	3.21955e8	0.910156	0.455078	+	0.890452i	$0.349611\pi$
$278$	3.34813e8	0.934642
$279$	1.12089e8	0.308993
$280$	−1.75419e8	−0.477555
$281$	−6.61132e7	−0.177753	−0.0888763	−	0.996043i	$-0.528328\pi$
$281$	−6.61132e7	−0.177753	−0.0888763	+	0.996043i	$0.528328\pi$
$282$	8.15029e7	0.216422
$283$	−2.73822e8	−0.718150	−0.359075	−	0.933309i	$-0.616908\pi$
$283$	−2.73822e8	−0.718150	−0.359075	+	0.933309i	$0.616908\pi$
$284$	4.31786e7	0.111855
$285$	3.59549e8	0.920028
$286$	2.03619e8	0.514681
$287$	−1.99855e8	−0.499032
$288$	2.38879e7	0.0589256
$289$	6.23935e8	1.52054
$290$	4.13092e8	0.994611
$291$	1.82551e8	0.434269
$292$	−2.86669e8	−0.673816
$293$	−5.22338e8	−1.21315	−0.606575	−	0.795026i	$-0.707457\pi$
$293$	−5.22338e8	−1.21315	−0.606575	+	0.795026i	$0.707457\pi$
$294$	1.00704e8	0.231116
$295$	−6.19594e7	−0.140517
$296$	−6.34268e7	−0.142152
$297$	−9.19415e7	−0.203640
$298$	5.70407e8	1.24861
$299$	1.69606e8	0.366938
$300$	2.22702e7	0.0476211
$301$	−2.91422e8	−0.615942
$302$	−6.04143e8	−1.26216
$303$	−4.60088e8	−0.950149
$304$	−1.80802e8	−0.369101
$305$	6.01482e8	1.21387
$306$	1.87558e8	0.374206
$307$	−8.19072e8	−1.61561	−0.807807	−	0.589447i	$-0.799346\pi$
$307$	−8.19072e8	−1.61561	−0.807807	+	0.589447i	$0.799346\pi$
$308$	−3.39512e8	−0.662106
$309$	−3.39446e8	−0.654509
$310$	−3.71088e8	−0.707475
$311$	1.44622e8	0.272630	0.136315	−	0.990666i	$-0.456474\pi$
$311$	1.44622e8	0.272630	0.136315	+	0.990666i	$0.456474\pi$
$312$	−7.53256e7	−0.140411
$313$	−5.80229e8	−1.06953	−0.534767	−	0.845000i	$-0.679601\pi$
$313$	−5.80229e8	−1.06953	−0.534767	+	0.845000i	$0.679601\pi$
$314$	−3.28771e8	−0.599294
$315$	−2.49766e8	−0.450243
$316$	−1.37180e8	−0.244560
$317$	9.21783e8	1.62525	0.812627	−	0.582785i	$-0.198037\pi$
$317$	9.21783e8	1.62525	0.812627	+	0.582785i	$0.198037\pi$
$318$	1.84088e8	0.321019
$319$	7.99512e8	1.37898
$320$	−7.90845e7	−0.134917
$321$	2.62205e8	0.442459
$322$	−2.82799e8	−0.472044
$323$	−1.41958e9	−2.34397
$324$	3.40122e7	0.0555556
$325$	−7.02246e7	−0.113474
$326$	−2.91272e8	−0.465626
$327$	−2.85540e8	−0.451595
$328$	−9.01011e7	−0.140985
$329$	4.28524e8	0.663421
$330$	3.04386e8	0.466258
$331$	−7.95181e8	−1.20523	−0.602613	−	0.798034i	$-0.705874\pi$
$331$	−7.95181e8	−1.20523	−0.602613	+	0.798034i	$0.705874\pi$
$332$	−5.91274e6	−0.00886759
$333$	−9.03089e7	−0.134022
$334$	−2.45758e8	−0.360907
$335$	5.85382e8	0.850712
$336$	1.25597e8	0.180631
$337$	5.45195e8	0.775974	0.387987	−	0.921665i	$-0.373171\pi$
$337$	5.45195e8	0.775974	0.387987	+	0.921665i	$0.373171\pi$
$338$	−2.64464e8	−0.372528
$339$	3.89308e8	0.542743
$340$	−6.20939e8	−0.856787
$341$	−7.18217e8	−0.980879
$342$	−2.57431e8	−0.347992
$343$	−4.05803e8	−0.542982
$344$	−1.31382e8	−0.174013
$345$	2.53541e8	0.332415
$346$	5.01606e8	0.651023
$347$	1.01654e9	1.30609	0.653043	−	0.757320i	$-0.273492\pi$
$347$	1.01654e9	1.30609	0.653043	+	0.757320i	$0.273492\pi$
$348$	−2.95766e8	−0.376202
$349$	8.45370e8	1.06453	0.532265	−	0.846578i	$-0.321341\pi$
$349$	8.45370e8	1.06453	0.532265	+	0.846578i	$0.321341\pi$
$350$	1.17092e8	0.145978
$351$	−1.07251e8	−0.132381
$352$	−1.53063e8	−0.187056
$353$	6.07823e8	0.735472	0.367736	−	0.929930i	$-0.380133\pi$
$353$	6.07823e8	0.735472	0.367736	+	0.929930i	$0.380133\pi$
$354$	4.43619e7	0.0531494
$355$	−2.03536e8	−0.241458
$356$	−7.66645e8	−0.900574
$357$	9.86136e8	1.14709
$358$	−9.49176e8	−1.09334
$359$	3.32888e8	0.379724	0.189862	−	0.981811i	$-0.439196\pi$
$359$	3.32888e8	0.379724	0.189862	+	0.981811i	$0.439196\pi$
$360$	−1.12603e8	−0.127201
$361$	1.05456e9	1.17977
$362$	4.15345e8	0.460181
$363$	6.29670e7	0.0690940
$364$	−3.96044e8	−0.430416
$365$	1.35130e9	1.45455
$366$	−4.30650e8	−0.459136
$367$	6.74036e8	0.711790	0.355895	−	0.934526i	$-0.384176\pi$
$367$	6.74036e8	0.711790	0.355895	+	0.934526i	$0.384176\pi$
$368$	−1.27495e8	−0.133360
$369$	−1.28289e8	−0.132922
$370$	2.98981e8	0.306858
$371$	9.67894e8	0.984054
$372$	2.65692e8	0.267596
$373$	1.49754e8	0.149416	0.0747079	−	0.997205i	$-0.476198\pi$
$373$	1.49754e8	0.149416	0.0747079	+	0.997205i	$0.476198\pi$
$374$	−1.20179e9	−1.18789
$375$	5.31386e8	0.520356
$376$	1.93192e8	0.187427
$377$	9.32639e8	0.896435
$378$	1.78828e8	0.170300
$379$	1.31546e9	1.24120	0.620598	−	0.784129i	$-0.286890\pi$
$379$	1.31546e9	1.24120	0.620598	+	0.784129i	$0.286890\pi$
$380$	8.52264e8	0.796768
$381$	−7.13712e8	−0.661128
$382$	−9.04532e7	−0.0830237
$383$	5.40536e8	0.491619	0.245810	−	0.969318i	$-0.420946\pi$
$383$	5.40536e8	0.491619	0.245810	+	0.969318i	$0.420946\pi$
$384$	5.66231e7	0.0510310
$385$	1.60039e9	1.42927
$386$	1.14900e9	1.01687
$387$	−1.87066e8	−0.164061
$388$	4.32713e8	0.376088
$389$	7.41820e7	0.0638961	0.0319481	−	0.999490i	$-0.489829\pi$
$389$	7.41820e7	0.0638961	0.0319481	+	0.999490i	$0.489829\pi$
$390$	3.55070e8	0.303101
$391$	−1.00104e9	−0.846900
$392$	2.38705e8	0.200152
$393$	−6.19530e8	−0.514859
$394$	−1.45654e9	−1.19974
$395$	6.46639e8	0.527925
$396$	−2.17935e8	−0.176358
$397$	1.38996e9	1.11490	0.557448	−	0.830212i	$-0.311780\pi$
$397$	1.38996e9	1.11490	0.557448	+	0.830212i	$0.311780\pi$
$398$	9.87334e7	0.0785006
$399$	−1.35351e9	−1.06674
$400$	5.27886e7	0.0412411
$401$	−7.49870e8	−0.580738	−0.290369	−	0.956915i	$-0.593778\pi$
$401$	−7.49870e8	−0.580738	−0.290369	+	0.956915i	$0.593778\pi$
$402$	−4.19123e8	−0.321774
$403$	−8.37807e8	−0.637641
$404$	−1.09058e9	−0.822853
$405$	−1.60327e8	−0.119926
$406$	−1.55507e9	−1.15321
$407$	5.78659e8	0.425444
$408$	4.44582e8	0.324072
$409$	2.55782e9	1.84858	0.924292	−	0.381687i	$-0.124657\pi$
$409$	2.55782e9	1.84858	0.924292	+	0.381687i	$0.124657\pi$
$410$	4.24719e8	0.304339
$411$	9.32245e8	0.662344
$412$	−8.04613e8	−0.566822
$413$	2.33244e8	0.162924
$414$	−1.81531e8	−0.125733
$415$	2.78715e7	0.0191422
$416$	−1.78549e8	−0.121600
$417$	1.12999e9	0.763132
$418$	1.64950e9	1.10468
$419$	1.95097e8	0.129569	0.0647846	−	0.997899i	$-0.479364\pi$
$419$	1.95097e8	0.129569	0.0647846	+	0.997899i	$0.479364\pi$
$420$	−5.92039e8	−0.389922
$421$	−1.31461e9	−0.858639	−0.429320	−	0.903153i	$-0.641247\pi$
$421$	−1.31461e9	−0.858639	−0.429320	+	0.903153i	$0.641247\pi$
$422$	−1.68612e8	−0.109218
$423$	2.75072e8	0.176708
$424$	4.36358e8	0.278011
$425$	4.14475e8	0.261901
$426$	1.45728e8	0.0913291
$427$	−2.26426e9	−1.40744
$428$	6.21522e8	0.383181
$429$	6.87215e8	0.420235
$430$	6.19311e8	0.375638
$431$	2.44393e9	1.47034	0.735172	−	0.677881i	$-0.237102\pi$
$431$	2.44393e9	1.47034	0.735172	+	0.677881i	$0.237102\pi$
$432$	8.06216e7	0.0481125
$433$	−8.60828e8	−0.509576	−0.254788	−	0.966997i	$-0.582006\pi$
$433$	−8.60828e8	−0.509576	−0.254788	+	0.966997i	$0.582006\pi$
$434$	1.39695e9	0.820288
$435$	1.39418e9	0.812097
$436$	−6.76835e8	−0.391093
$437$	1.37397e9	0.787573
$438$	−9.67509e8	−0.550169
$439$	1.36561e9	0.770372	0.385186	−	0.922839i	$-0.374137\pi$
$439$	1.36561e9	0.770372	0.385186	+	0.922839i	$0.374137\pi$
$440$	7.21509e8	0.403792
$441$	3.39875e8	0.188705
$442$	−1.40190e9	−0.772215
$443$	−2.14086e9	−1.16997	−0.584987	−	0.811043i	$-0.698900\pi$
$443$	−2.14086e9	−1.16997	−0.584987	+	0.811043i	$0.698900\pi$
$444$	−2.14065e8	−0.116066
$445$	3.61381e9	1.94404
$446$	−1.23627e8	−0.0659842
$447$	1.92512e9	1.01949
$448$	2.97711e8	0.156431
$449$	−2.37411e9	−1.23777	−0.618883	−	0.785483i	$-0.712415\pi$
$449$	−2.37411e9	−1.23777	−0.618883	+	0.785483i	$0.712415\pi$
$450$	7.51619e7	0.0388825
$451$	8.22016e8	0.421952
$452$	9.22804e8	0.470029
$453$	−2.03898e9	−1.03055
$454$	2.69131e9	1.34980
$455$	1.86687e9	0.929127
$456$	−6.10206e8	−0.301370
$457$	−9.88001e8	−0.484229	−0.242114	−	0.970248i	$-0.577841\pi$
$457$	−9.88001e8	−0.484229	−0.242114	+	0.970248i	$0.577841\pi$
$458$	−1.05428e7	−0.00512776
$459$	6.33008e8	0.305538
$460$	6.00986e8	0.287880
$461$	6.51414e8	0.309673	0.154837	−	0.987940i	$-0.450515\pi$
$461$	6.51414e8	0.309673	0.154837	+	0.987940i	$0.450515\pi$
$462$	−1.14585e9	−0.540608
$463$	2.04953e8	0.0959668	0.0479834	−	0.998848i	$-0.484721\pi$
$463$	2.04953e8	0.0959668	0.0479834	+	0.998848i	$0.484721\pi$
$464$	−7.01076e8	−0.325801
$465$	−1.25242e9	−0.577651
$466$	−2.21940e9	−1.01598
$467$	2.65276e9	1.20528	0.602642	−	0.798012i	$-0.294115\pi$
$467$	2.65276e9	1.20528	0.602642	+	0.798012i	$0.294115\pi$
$468$	−2.54224e8	−0.114645
$469$	−2.20365e9	−0.986367
$470$	−9.10670e8	−0.404593
$471$	−1.10960e9	−0.489322
$472$	1.05154e8	0.0460287
$473$	1.19864e9	0.520803
$474$	−4.62982e8	−0.199683
$475$	−5.68884e8	−0.243554
$476$	2.33751e9	0.993410
$477$	6.21298e8	0.262111
$478$	−1.73231e9	−0.725483
$479$	2.63790e9	1.09669	0.548344	−	0.836253i	$-0.315258\pi$
$479$	2.63790e9	1.09669	0.548344	+	0.836253i	$0.315258\pi$
$480$	−2.66910e8	−0.110159
$481$	6.75012e8	0.276569
$482$	7.95806e8	0.323700
$483$	−9.54447e8	−0.385422
$484$	1.49255e8	0.0598371
$485$	−2.03972e9	−0.811849
$486$	1.14791e8	0.0453609
$487$	2.76833e9	1.08609	0.543046	−	0.839703i	$-0.317271\pi$
$487$	2.76833e9	1.08609	0.543046	+	0.839703i	$0.317271\pi$
$488$	−1.02080e9	−0.397623
$489$	−9.83042e8	−0.380182
$490$	−1.12521e9	−0.432063
$491$	7.16454e7	0.0273151	0.0136576	−	0.999907i	$-0.495653\pi$
$491$	7.16454e7	0.0273151	0.0136576	+	0.999907i	$0.495653\pi$
$492$	−3.04091e8	−0.115113
$493$	−5.50456e9	−2.06899
$494$	1.92416e9	0.718120
$495$	1.02730e9	0.380698
$496$	6.29790e8	0.231745
$497$	7.66203e8	0.279960
$498$	−1.99555e7	−0.00724036
$499$	−2.00958e9	−0.724023	−0.362012	−	0.932174i	$-0.617910\pi$
$499$	−2.00958e9	−0.724023	−0.362012	+	0.932174i	$0.617910\pi$
$500$	1.25958e9	0.450642
$501$	−8.29435e8	−0.294680
$502$	2.16935e9	0.765363
$503$	−3.78878e9	−1.32743	−0.663715	−	0.747986i	$-0.731021\pi$
$503$	−3.78878e9	−1.32743	−0.663715	+	0.747986i	$0.731021\pi$
$504$	4.23889e8	0.147484
$505$	5.14077e9	1.77627
$506$	1.16317e9	0.399132
$507$	−8.92567e8	−0.304168
$508$	−1.69176e9	−0.572554
$509$	−2.11995e9	−0.712548	−0.356274	−	0.934382i	$-0.615953\pi$
$509$	−2.11995e9	−0.712548	−0.356274	+	0.934382i	$0.615953\pi$
$510$	−2.09567e9	−0.699564
$511$	−5.08694e9	−1.68649
$512$	1.34218e8	0.0441942
$513$	−8.68829e8	−0.284134
$514$	3.55038e8	0.115320
$515$	3.79278e9	1.22358
$516$	−4.43416e8	−0.142081
$517$	−1.76254e9	−0.560948
$518$	−1.12551e9	−0.355790
$519$	1.69292e9	0.531558
$520$	8.41647e8	0.262493
$521$	3.27765e9	1.01538	0.507692	−	0.861539i	$-0.330499\pi$
$521$	3.27765e9	1.01538	0.507692	+	0.861539i	$0.330499\pi$
$522$	−9.98211e8	−0.307168
$523$	5.82438e8	0.178030	0.0890152	−	0.996030i	$-0.471628\pi$
$523$	5.82438e8	0.178030	0.0890152	+	0.996030i	$0.471628\pi$
$524$	−1.46852e9	−0.445881
$525$	3.95184e8	0.119191
$526$	2.32318e9	0.696039
$527$	4.94485e9	1.47169
$528$	−5.16588e8	−0.152730
$529$	−2.43596e9	−0.715442
$530$	−2.05690e9	−0.600134
$531$	1.49721e8	0.0433963
$532$	−3.20832e9	−0.923820
$533$	9.58890e8	0.274299
$534$	−2.58743e9	−0.735315
$535$	−2.92973e9	−0.827161
$536$	−9.93478e8	−0.278664
$537$	−3.20347e9	−0.892711
$538$	2.32625e9	0.644049
$539$	−2.17777e9	−0.599034
$540$	−3.80034e8	−0.103859
$541$	4.50224e9	1.22247	0.611235	−	0.791449i	$-0.290673\pi$
$541$	4.50224e9	1.22247	0.611235	+	0.791449i	$0.290673\pi$
$542$	3.87860e9	1.04635
$543$	1.40179e9	0.375737
$544$	1.05382e9	0.280654
$545$	3.19047e9	0.844241
$546$	−1.33665e9	−0.351434
$547$	6.56028e8	0.171383	0.0856913	−	0.996322i	$-0.472690\pi$
$547$	6.56028e8	0.171383	0.0856913	+	0.996322i	$0.472690\pi$
$548$	2.20977e9	0.573607
$549$	−1.45344e9	−0.374883
$550$	−4.81605e8	−0.123430
$551$	7.55523e9	1.92405
$552$	−4.30295e8	−0.108888
$553$	−2.43425e9	−0.612108
$554$	2.57564e9	0.643577
$555$	1.00906e9	0.250549
$556$	2.67850e9	0.660892
$557$	−2.48635e9	−0.609634	−0.304817	−	0.952411i	$-0.598595\pi$
$557$	−2.48635e9	−0.609634	−0.304817	+	0.952411i	$0.598595\pi$
$558$	8.96712e8	0.218491
$559$	1.39822e9	0.338559
$560$	−1.40335e9	−0.337682
$561$	−4.05604e9	−0.969911
$562$	−5.28905e8	−0.125690
$563$	3.41490e9	0.806488	0.403244	−	0.915092i	$-0.367883\pi$
$563$	3.41490e9	0.806488	0.403244	+	0.915092i	$0.367883\pi$
$564$	6.52024e8	0.153033
$565$	−4.34992e9	−1.01464
$566$	−2.19057e9	−0.507809
$567$	6.03546e8	0.139050
$568$	3.45429e8	0.0790933
$569$	6.17518e9	1.40526	0.702630	−	0.711555i	$-0.252009\pi$
$569$	6.17518e9	1.40526	0.702630	+	0.711555i	$0.252009\pi$
$570$	2.87639e9	0.650558
$571$	−4.79360e9	−1.07755	−0.538773	−	0.842451i	$-0.681112\pi$
$571$	−4.79360e9	−1.07755	−0.538773	+	0.842451i	$0.681112\pi$
$572$	1.62895e9	0.363934
$573$	−3.05280e8	−0.0677886
$574$	−1.59884e9	−0.352869
$575$	−4.01156e8	−0.0879986
$576$	1.91103e8	0.0416667
$577$	−7.13696e9	−1.54667	−0.773335	−	0.633997i	$-0.781413\pi$
$577$	−7.13696e9	−1.54667	−0.773335	+	0.633997i	$0.781413\pi$
$578$	4.99148e9	1.07518
$579$	3.87788e9	0.830270
$580$	3.30473e9	0.703296
$581$	−1.04921e8	−0.0221946
$582$	1.46041e9	0.307074
$583$	−3.98101e9	−0.832057
$584$	−2.29336e9	−0.476460
$585$	1.19836e9	0.247481
$586$	−4.17870e9	−0.857827
$587$	−7.43241e9	−1.51669	−0.758344	−	0.651854i	$-0.773991\pi$
$587$	−7.43241e9	−1.51669	−0.758344	+	0.651854i	$0.773991\pi$
$588$	8.05630e8	0.163424
$589$	−6.78701e9	−1.36860
$590$	−4.95675e8	−0.0993609
$591$	−4.91584e9	−0.979583
$592$	−5.07414e8	−0.100516
$593$	8.66039e9	1.70548	0.852738	−	0.522338i	$-0.174940\pi$
$593$	8.66039e9	1.70548	0.852738	+	0.522338i	$0.174940\pi$
$594$	−7.35532e8	−0.143996
$595$	−1.10185e10	−2.14444
$596$	4.56325e9	0.882902
$597$	3.33225e8	0.0640955
$598$	1.35685e9	0.259464
$599$	9.96657e8	0.189475	0.0947375	−	0.995502i	$-0.469799\pi$
$599$	9.96657e8	0.189475	0.0947375	+	0.995502i	$0.469799\pi$
$600$	1.78162e8	0.0336732
$601$	5.07972e9	0.954507	0.477253	−	0.878766i	$-0.341632\pi$
$601$	5.07972e9	0.954507	0.477253	+	0.878766i	$0.341632\pi$
$602$	−2.33138e9	−0.435537
$603$	−1.41454e9	−0.262727
$604$	−4.83315e9	−0.892484
$605$	−7.03560e8	−0.129169
$606$	−3.68070e9	−0.671857
$607$	−2.53911e9	−0.460809	−0.230405	−	0.973095i	$-0.574005\pi$
$607$	−2.53911e9	−0.460809	−0.230405	+	0.973095i	$0.574005\pi$
$608$	−1.44641e9	−0.260994
$609$	−5.24836e9	−0.941593
$610$	4.81185e9	0.858337
$611$	−2.05602e9	−0.364656
$612$	1.50046e9	0.264603
$613$	−3.50806e8	−0.0615114	−0.0307557	−	0.999527i	$-0.509791\pi$
$613$	−3.50806e8	−0.0615114	−0.0307557	+	0.999527i	$0.509791\pi$
$614$	−6.55258e9	−1.14241
$615$	1.43343e9	0.248492
$616$	−2.71610e9	−0.468180
$617$	−6.37312e9	−1.09233	−0.546165	−	0.837678i	$-0.683913\pi$
$617$	−6.37312e9	−1.09233	−0.546165	+	0.837678i	$0.683913\pi$
$618$	−2.71557e9	−0.462808
$619$	−1.30998e9	−0.221997	−0.110998	−	0.993821i	$-0.535405\pi$
$619$	−1.30998e9	−0.221997	−0.110998	+	0.993821i	$0.535405\pi$
$620$	−2.96870e9	−0.500260
$621$	−6.12666e8	−0.102661
$622$	1.15698e9	0.192778
$623$	−1.36041e10	−2.25404
$624$	−6.02604e8	−0.0992856
$625$	−6.94428e9	−1.13775
$626$	−4.64184e9	−0.756275
$627$	5.56707e9	0.901967
$628$	−2.63017e9	−0.423765
$629$	−3.98401e9	−0.638327
$630$	−1.99813e9	−0.318370
$631$	9.00316e9	1.42657	0.713283	−	0.700876i	$-0.247207\pi$
$631$	9.00316e9	1.42657	0.713283	+	0.700876i	$0.247207\pi$
$632$	−1.09744e9	−0.172930
$633$	−5.69065e8	−0.0891762
$634$	7.37426e9	1.14923
$635$	7.97463e9	1.23595
$636$	1.47271e9	0.226995
$637$	−2.54039e9	−0.389415
$638$	6.39610e9	0.975086
$639$	4.91832e8	0.0745699
$640$	−6.32676e8	−0.0954007
$641$	5.46685e9	0.819849	0.409924	−	0.912120i	$-0.365555\pi$
$641$	5.46685e9	0.819849	0.409924	+	0.912120i	$0.365555\pi$
$642$	2.09764e9	0.312866
$643$	−2.22009e9	−0.329331	−0.164665	−	0.986349i	$-0.552654\pi$
$643$	−2.22009e9	−0.329331	−0.164665	+	0.986349i	$0.552654\pi$
$644$	−2.26239e9	−0.333785
$645$	2.09017e9	0.306707
$646$	−1.13567e10	−1.65744
$647$	1.15227e10	1.67259	0.836297	−	0.548277i	$-0.184716\pi$
$647$	1.15227e10	1.67259	0.836297	+	0.548277i	$0.184716\pi$
$648$	2.72098e8	0.0392837
$649$	−9.59348e8	−0.137759
$650$	−5.61796e8	−0.0802384
$651$	4.71470e9	0.669763
$652$	−2.33017e9	−0.329247
$653$	−6.28515e9	−0.883323	−0.441661	−	0.897182i	$-0.645611\pi$
$653$	−6.28515e9	−0.883323	−0.441661	+	0.897182i	$0.645611\pi$
$654$	−2.28432e9	−0.319326
$655$	6.92230e9	0.962511
$656$	−7.20809e8	−0.0996912
$657$	−3.26534e9	−0.449211
$658$	3.42819e9	0.469109
$659$	−4.64452e9	−0.632181	−0.316091	−	0.948729i	$-0.602370\pi$
$659$	−4.64452e9	−0.632181	−0.316091	+	0.948729i	$0.602370\pi$
$660$	2.43509e9	0.329694
$661$	−4.47481e8	−0.0602656	−0.0301328	−	0.999546i	$-0.509593\pi$
$661$	−4.47481e8	−0.0602656	−0.0301328	+	0.999546i	$0.509593\pi$
$662$	−6.36145e9	−0.852223
$663$	−4.73141e9	−0.630511
$664$	−4.73019e7	−0.00627033
$665$	1.51234e10	1.99422
$666$	−7.22471e8	−0.0947677
$667$	5.32768e9	0.695180
$668$	−1.96607e9	−0.255200
$669$	−4.17240e8	−0.0538759
$670$	4.68306e9	0.601544
$671$	9.31304e9	1.19004
$672$	1.00478e9	0.127725
$673$	4.04486e9	0.511506	0.255753	−	0.966742i	$-0.417677\pi$
$673$	4.04486e9	0.511506	0.255753	+	0.966742i	$0.417677\pi$
$674$	4.36156e9	0.548696
$675$	2.53672e8	0.0317474
$676$	−2.11571e9	−0.263417
$677$	−1.05428e10	−1.30586	−0.652928	−	0.757420i	$-0.726459\pi$
$677$	−1.05428e10	−1.30586	−0.652928	+	0.757420i	$0.726459\pi$
$678$	3.11446e9	0.383777
$679$	7.67848e9	0.941306
$680$	−4.96751e9	−0.605840
$681$	9.08318e9	1.10211
$682$	−5.74574e9	−0.693586
$683$	−6.52217e9	−0.783285	−0.391642	−	0.920118i	$-0.628093\pi$
$683$	−6.52217e9	−0.783285	−0.391642	+	0.920118i	$0.628093\pi$
$684$	−2.05945e9	−0.246067
$685$	−1.04164e10	−1.23823
$686$	−3.24642e9	−0.383946
$687$	−3.55821e7	−0.00418680
$688$	−1.05106e9	−0.123046
$689$	−4.64388e9	−0.540896
$690$	2.02833e9	0.235053
$691$	−8.06410e9	−0.929785	−0.464892	−	0.885367i	$-0.653907\pi$
$691$	−8.06410e9	−0.929785	−0.464892	+	0.885367i	$0.653907\pi$
$692$	4.01285e9	0.460343
$693$	−3.86726e9	−0.441404
$694$	8.13233e9	0.923543
$695$	−1.26259e10	−1.42665
$696$	−2.36613e9	−0.266015
$697$	−5.65950e9	−0.633087
$698$	6.76296e9	0.752736
$699$	−7.49048e9	−0.829544
$700$	9.36732e8	0.103222
$701$	6.07255e9	0.665822	0.332911	−	0.942958i	$-0.391969\pi$
$701$	6.07255e9	0.665822	0.332911	+	0.942958i	$0.391969\pi$
$702$	−8.58005e8	−0.0936074
$703$	5.46822e9	0.593611
$704$	−1.22450e9	−0.132268
$705$	−3.07351e9	−0.330349
$706$	4.86259e9	0.520057
$707$	−1.93523e10	−2.05951
$708$	3.54895e8	0.0375823
$709$	−4.55216e9	−0.479684	−0.239842	−	0.970812i	$-0.577096\pi$
$709$	−4.55216e9	−0.479684	−0.239842	+	0.970812i	$0.577096\pi$
$710$	−1.62828e9	−0.170736
$711$	−1.56257e9	−0.163040
$712$	−6.13316e9	−0.636802
$713$	−4.78595e9	−0.494487
$714$	7.88909e9	0.811116
$715$	−7.67857e9	−0.785614
$716$	−7.59341e9	−0.773110
$717$	−5.84653e9	−0.592354
$718$	2.66311e9	0.268505
$719$	−1.43826e10	−1.44307	−0.721533	−	0.692380i	$-0.756562\pi$
$719$	−1.43826e10	−1.44307	−0.721533	+	0.692380i	$0.756562\pi$
$720$	−9.00822e8	−0.0899446
$721$	−1.42778e10	−1.41869
$722$	8.43651e9	0.834224
$723$	2.68584e9	0.264300
$724$	3.32276e9	0.325397
$725$	−2.20590e9	−0.214982
$726$	5.03736e8	0.0488568
$727$	−1.75058e10	−1.68971	−0.844855	−	0.534995i	$-0.820314\pi$
$727$	−1.75058e10	−1.68971	−0.844855	+	0.534995i	$0.820314\pi$
$728$	−3.16835e9	−0.304350
$729$	3.87420e8	0.0370370
$730$	1.08104e10	1.02852
$731$	−8.25249e9	−0.781402
$732$	−3.44520e9	−0.324658
$733$	−5.64835e9	−0.529734	−0.264867	−	0.964285i	$-0.585328\pi$
$733$	−5.64835e9	−0.529734	−0.264867	+	0.964285i	$0.585328\pi$
$734$	5.39229e9	0.503312
$735$	−3.79758e9	−0.352778
$736$	−1.01996e9	−0.0942997
$737$	9.06376e9	0.834012
$738$	−1.02631e9	−0.0939897
$739$	−1.19335e9	−0.108771	−0.0543854	−	0.998520i	$-0.517320\pi$
$739$	−1.19335e9	−0.108771	−0.0543854	+	0.998520i	$0.517320\pi$
$740$	2.39185e9	0.216982
$741$	6.49405e9	0.586343
$742$	7.74315e9	0.695831
$743$	−1.85757e10	−1.66144	−0.830718	−	0.556693i	$-0.812070\pi$
$743$	−1.85757e10	−1.66144	−0.830718	+	0.556693i	$0.812070\pi$
$744$	2.12554e9	0.189219
$745$	−2.15103e10	−1.90589
$746$	1.19803e9	0.105653
$747$	−6.73498e7	−0.00591173
$748$	−9.61431e9	−0.839967
$749$	1.10289e10	0.959059
$750$	4.25109e9	0.367947
$751$	−2.06739e10	−1.78108	−0.890540	−	0.454906i	$-0.849673\pi$
$751$	−2.06739e10	−1.78108	−0.890540	+	0.454906i	$0.849673\pi$
$752$	1.54554e9	0.132531
$753$	7.32157e9	0.624916
$754$	7.46111e9	0.633875
$755$	2.27825e10	1.92658
$756$	1.43063e9	0.120420
$757$	−1.47964e9	−0.123971	−0.0619854	−	0.998077i	$-0.519743\pi$
$757$	−1.47964e9	−0.123971	−0.0619854	+	0.998077i	$0.519743\pi$
$758$	1.05237e10	0.877658
$759$	3.92570e9	0.325890
$760$	6.81811e9	0.563400
$761$	2.60961e9	0.214649	0.107325	−	0.994224i	$-0.465772\pi$
$761$	2.60961e9	0.214649	0.107325	+	0.994224i	$0.465772\pi$
$762$	−5.70970e9	−0.467488
$763$	−1.20104e10	−0.978863
$764$	−7.23626e8	−0.0587067
$765$	−7.07289e9	−0.571191
$766$	4.32429e9	0.347627
$767$	−1.11909e9	−0.0895532
$768$	4.52985e8	0.0360844
$769$	1.38692e10	1.09979	0.549895	−	0.835234i	$-0.314668\pi$
$769$	1.38692e10	1.09979	0.549895	+	0.835234i	$0.314668\pi$
$770$	1.28031e10	1.01065
$771$	1.19825e9	0.0941583
$772$	9.19201e9	0.719035
$773$	−6.18087e8	−0.0481306	−0.0240653	−	0.999710i	$-0.507661\pi$
$773$	−6.18087e8	−0.0481306	−0.0240653	+	0.999710i	$0.507661\pi$
$774$	−1.49653e9	−0.116009
$775$	1.98160e9	0.152918
$776$	3.46170e9	0.265934
$777$	−3.79858e9	−0.290501
$778$	5.93456e8	0.0451814
$779$	7.76789e9	0.588738
$780$	2.84056e9	0.214325
$781$	−3.15144e9	−0.236718
$782$	−8.00830e9	−0.598848
$783$	−3.36896e9	−0.250801
$784$	1.90964e9	0.141529
$785$	1.23981e10	0.914769
$786$	−4.95624e9	−0.364061
$787$	−3.19955e8	−0.0233980	−0.0116990	−	0.999932i	$-0.503724\pi$
$787$	−3.19955e8	−0.0233980	−0.0116990	+	0.999932i	$0.503724\pi$
$788$	−1.16524e10	−0.848344
$789$	7.84075e9	0.568313
$790$	5.17311e9	0.373299
$791$	1.63751e10	1.17643
$792$	−1.74348e9	−0.124704
$793$	1.08637e10	0.773613
$794$	1.11197e10	0.788351
$795$	−6.94205e9	−0.490008
$796$	7.89867e8	0.0555083
$797$	4.73537e9	0.331322	0.165661	−	0.986183i	$-0.447024\pi$
$797$	4.73537e9	0.331322	0.165661	+	0.986183i	$0.447024\pi$
$798$	−1.08281e10	−0.754296
$799$	1.21349e10	0.841635
$800$	4.22309e8	0.0291619
$801$	−8.73256e9	−0.600382
$802$	−5.99896e9	−0.410644
$803$	2.09229e10	1.42599
$804$	−3.35299e9	−0.227528
$805$	1.06645e10	0.720533
$806$	−6.70246e9	−0.450881
$807$	7.85110e9	0.525863
$808$	−8.72463e9	−0.581845
$809$	7.18254e9	0.476934	0.238467	−	0.971151i	$-0.423355\pi$
$809$	7.18254e9	0.476934	0.238467	+	0.971151i	$0.423355\pi$
$810$	−1.28262e9	−0.0848006
$811$	−1.70884e10	−1.12494	−0.562468	−	0.826819i	$-0.690148\pi$
$811$	−1.70884e10	−1.12494	−0.562468	+	0.826819i	$0.690148\pi$
$812$	−1.24406e10	−0.815444
$813$	1.30903e10	0.854342
$814$	4.62928e9	0.300834
$815$	1.09840e10	0.710736
$816$	3.55665e9	0.229153
$817$	1.13269e10	0.726663
$818$	2.04626e10	1.30715
$819$	−4.51119e9	−0.286944
$820$	3.39775e9	0.215200
$821$	3.28768e8	0.0207343	0.0103671	−	0.999946i	$-0.496700\pi$
$821$	3.28768e8	0.0207343	0.0103671	+	0.999946i	$0.496700\pi$
$822$	7.45796e9	0.468348
$823$	−7.05433e9	−0.441119	−0.220560	−	0.975373i	$-0.570788\pi$
$823$	−7.05433e9	−0.441119	−0.220560	+	0.975373i	$0.570788\pi$
$824$	−6.43690e9	−0.400804
$825$	−1.62542e9	−0.100780
$826$	1.86595e9	0.115205
$827$	1.16823e10	0.718223	0.359112	−	0.933295i	$-0.383080\pi$
$827$	1.16823e10	0.718223	0.359112	+	0.933295i	$0.383080\pi$
$828$	−1.45225e9	−0.0889066
$829$	9.52275e8	0.0580526	0.0290263	−	0.999579i	$-0.490759\pi$
$829$	9.52275e8	0.0580526	0.0290263	+	0.999579i	$0.490759\pi$
$830$	2.22972e8	0.0135356
$831$	8.69278e9	0.525479
$832$	−1.42840e9	−0.0859839
$833$	1.49937e10	0.898777
$834$	9.03995e9	0.539616
$835$	9.26765e9	0.550893
$836$	1.31960e10	0.781126
$837$	3.02640e9	0.178397
$838$	1.56078e9	0.0916192
$839$	−1.24238e10	−0.726250	−0.363125	−	0.931740i	$-0.618290\pi$
$839$	−1.24238e10	−0.726250	−0.363125	+	0.931740i	$0.618290\pi$
$840$	−4.73631e9	−0.275716
$841$	1.20462e10	0.698337
$842$	−1.05169e10	−0.607150
$843$	−1.78506e9	−0.102625
$844$	−1.34889e9	−0.0772288
$845$	9.97306e9	0.568630
$846$	2.20058e9	0.124951
$847$	2.64853e9	0.149766
$848$	3.49086e9	0.196583
$849$	−7.39318e9	−0.414624
$850$	3.31580e9	0.185192
$851$	3.85599e9	0.214478
$852$	1.16582e9	0.0645794
$853$	−2.39952e10	−1.32374	−0.661870	−	0.749618i	$-0.730237\pi$
$853$	−2.39952e10	−1.32374	−0.661870	+	0.749618i	$0.730237\pi$
$854$	−1.81141e10	−0.995207
$855$	9.70782e9	0.531178
$856$	4.97218e9	0.270950
$857$	−3.46085e9	−0.187823	−0.0939117	−	0.995581i	$-0.529937\pi$
$857$	−3.46085e9	−0.187823	−0.0939117	+	0.995581i	$0.529937\pi$
$858$	5.49772e9	0.297151
$859$	1.26036e10	0.678452	0.339226	−	0.940705i	$-0.389835\pi$
$859$	1.26036e10	0.678452	0.339226	+	0.940705i	$0.389835\pi$
$860$	4.95449e9	0.265616
$861$	−5.39609e9	−0.288116
$862$	1.95515e10	1.03969
$863$	3.66738e10	1.94231	0.971154	−	0.238455i	$-0.0766408\pi$
$863$	3.66738e10	1.94231	0.971154	+	0.238455i	$0.0766408\pi$
$864$	6.44973e8	0.0340207
$865$	−1.89158e10	−0.993729
$866$	−6.88663e9	−0.360325
$867$	1.68463e10	0.877883
$868$	1.11756e10	0.580032
$869$	1.00122e10	0.517561
$870$	1.11535e10	0.574239
$871$	1.05730e10	0.542167
$872$	−5.41468e9	−0.276544
$873$	4.92887e9	0.250725
$874$	1.09917e10	0.556898
$875$	2.23512e10	1.12791
$876$	−7.74008e9	−0.389028
$877$	1.79731e10	0.899755	0.449878	−	0.893090i	$-0.351468\pi$
$877$	1.79731e10	0.899755	0.449878	+	0.893090i	$0.351468\pi$
$878$	1.09249e10	0.544735
$879$	−1.41031e10	−0.700413
$880$	5.77207e9	0.285524
$881$	2.29477e10	1.13064	0.565319	−	0.824873i	$-0.308753\pi$
$881$	2.29477e10	1.13064	0.565319	+	0.824873i	$0.308753\pi$
$882$	2.71900e9	0.133435
$883$	2.79362e10	1.36554	0.682772	−	0.730632i	$-0.260774\pi$
$883$	2.79362e10	1.36554	0.682772	+	0.730632i	$0.260774\pi$
$884$	−1.12152e10	−0.546039
$885$	−1.67290e9	−0.0811278
$886$	−1.71269e10	−0.827296
$887$	−2.58342e10	−1.24298	−0.621489	−	0.783423i	$-0.713472\pi$
$887$	−2.58342e10	−1.24298	−0.621489	+	0.783423i	$0.713472\pi$
$888$	−1.71252e9	−0.0820713
$889$	−3.00203e10	−1.43304
$890$	2.89105e10	1.37464
$891$	−2.48242e9	−0.117572
$892$	−9.89013e8	−0.0466579
$893$	−1.66557e10	−0.782677
$894$	1.54010e10	0.720887
$895$	3.57938e10	1.66889
$896$	2.38169e9	0.110613
$897$	4.57936e9	0.211852
$898$	−1.89929e10	−0.875233
$899$	−2.63172e10	−1.20804
$900$	6.01295e8	0.0274941
$901$	2.74088e10	1.24840
$902$	6.57613e9	0.298365
$903$	−7.86840e9	−0.355614
$904$	7.38243e9	0.332361
$905$	−1.56628e10	−0.702426
$906$	−1.63119e10	−0.728711
$907$	−2.67696e10	−1.19129	−0.595643	−	0.803249i	$-0.703103\pi$
$907$	−2.67696e10	−1.19129	−0.595643	+	0.803249i	$0.703103\pi$
$908$	2.15305e10	0.954451
$909$	−1.24224e10	−0.548569
$910$	1.49350e10	0.656992
$911$	2.60539e8	0.0114172	0.00570859	−	0.999984i	$-0.498183\pi$
$911$	2.60539e8	0.0114172	0.00570859	+	0.999984i	$0.498183\pi$
$912$	−4.88165e9	−0.213101
$913$	4.31548e8	0.0187664
$914$	−7.90401e9	−0.342402
$915$	1.62400e10	0.700829
$916$	−8.43426e7	−0.00362588
$917$	−2.60588e10	−1.11599
$918$	5.06406e9	0.216048
$919$	2.46531e10	1.04777	0.523886	−	0.851789i	$-0.324482\pi$
$919$	2.46531e10	1.04777	0.523886	+	0.851789i	$0.324482\pi$
$920$	4.80789e9	0.203562
$921$	−2.21149e10	−0.932775
$922$	5.21131e9	0.218972
$923$	−3.67619e9	−0.153883
$924$	−9.16683e9	−0.382267
$925$	−1.59655e9	−0.0663265
$926$	1.63963e9	0.0678588
$927$	−9.16504e9	−0.377881
$928$	−5.60861e9	−0.230376
$929$	−1.78065e10	−0.728657	−0.364328	−	0.931271i	$-0.618701\pi$
$929$	−1.78065e10	−0.728657	−0.364328	+	0.931271i	$0.618701\pi$
$930$	−1.00194e10	−0.408461
$931$	−2.05795e10	−0.835817
$932$	−1.77552e10	−0.718406
$933$	3.90480e9	0.157403
$934$	2.12221e10	0.852264
$935$	4.53199e10	1.81321
$936$	−2.03379e9	−0.0810664
$937$	−2.66222e9	−0.105720	−0.0528599	−	0.998602i	$-0.516834\pi$
$937$	−2.66222e9	−0.105720	−0.0528599	+	0.998602i	$0.516834\pi$
$938$	−1.76292e10	−0.697466
$939$	−1.56662e10	−0.617496
$940$	−7.28536e9	−0.286090
$941$	−2.43738e10	−0.953584	−0.476792	−	0.879016i	$-0.658200\pi$
$941$	−2.43738e10	−0.953584	−0.476792	+	0.879016i	$0.658200\pi$
$942$	−8.87682e9	−0.346003
$943$	5.47763e9	0.212717
$944$	8.41232e8	0.0325472
$945$	−6.74369e9	−0.259948
$946$	9.58909e9	0.368263
$947$	7.53708e9	0.288389	0.144194	−	0.989549i	$-0.453941\pi$
$947$	7.53708e9	0.288389	0.144194	+	0.989549i	$0.453941\pi$
$948$	−3.70386e9	−0.141197
$949$	2.44068e10	0.926997
$950$	−4.55107e9	−0.172219
$951$	2.48881e10	0.938341
$952$	1.87001e10	0.702447
$953$	−8.68215e9	−0.324939	−0.162470	−	0.986714i	$-0.551946\pi$
$953$	−8.68215e9	−0.324939	−0.162470	+	0.986714i	$0.551946\pi$
$954$	4.97039e9	0.185341
$955$	3.41103e9	0.126728
$956$	−1.38585e10	−0.512994
$957$	2.15868e10	0.796154
$958$	2.11032e10	0.775476
$959$	3.92122e10	1.43568
$960$	−2.13528e9	−0.0778943
$961$	−3.87133e9	−0.140711
$962$	5.40009e9	0.195564
$963$	7.07953e9	0.255454
$964$	6.36645e9	0.228890
$965$	−4.33293e10	−1.55216
$966$	−7.63557e9	−0.272535
$967$	−5.44262e9	−0.193560	−0.0967800	−	0.995306i	$-0.530854\pi$
$967$	−5.44262e9	−0.193560	−0.0967800	+	0.995306i	$0.530854\pi$
$968$	1.19404e9	0.0423112
$969$	−3.83287e10	−1.35329
$970$	−1.63178e10	−0.574064
$971$	−3.13299e10	−1.09823	−0.549113	−	0.835748i	$-0.685034\pi$
$971$	−3.13299e10	−1.09823	−0.549113	+	0.835748i	$0.685034\pi$
$972$	9.18330e8	0.0320750
$973$	4.75299e10	1.65414
$974$	2.21467e10	0.767984
$975$	−1.89606e9	−0.0655144
$976$	−8.16641e9	−0.281162
$977$	9.24858e9	0.317281	0.158641	−	0.987336i	$-0.449289\pi$
$977$	9.24858e9	0.317281	0.158641	+	0.987336i	$0.449289\pi$
$978$	−7.86434e9	−0.268829
$979$	5.59544e10	1.90588
$980$	−9.00167e9	−0.305515
$981$	−7.70957e9	−0.260729
$982$	5.73163e8	0.0193147
$983$	−4.09767e10	−1.37594	−0.687971	−	0.725738i	$-0.741498\pi$
$983$	−4.09767e10	−1.37594	−0.687971	+	0.725738i	$0.741498\pi$
$984$	−2.43273e9	−0.0813975
$985$	5.49269e10	1.83130
$986$	−4.40365e10	−1.46300
$987$	1.15701e10	0.383026
$988$	1.53933e10	0.507788
$989$	7.98730e9	0.262551
$990$	8.21843e9	0.269194
$991$	−1.20101e10	−0.392001	−0.196001	−	0.980604i	$-0.562795\pi$
$991$	−1.20101e10	−0.392001	−0.196001	+	0.980604i	$0.562795\pi$
$992$	5.03832e9	0.163868
$993$	−2.14699e10	−0.695837
$994$	6.12963e9	0.197962
$995$	−3.72328e9	−0.119824
$996$	−1.59644e8	−0.00511971
$997$	−5.81852e10	−1.85943	−0.929714	−	0.368283i	$-0.879946\pi$
$997$	−5.81852e10	−1.85943	−0.929714	+	0.368283i	$0.879946\pi$
$998$	−1.60766e10	−0.511962
$999$	−2.43834e9	−0.0773775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.b.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.b.1.1	✓	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -301.683 q^{5} +216.000 q^{6} +1135.68 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -301.683 q^{5} +216.000 q^{6} +1135.68 q^{7} +512.000 q^{8} +729.000 q^{9} -2413.47 q^{10} -4671.11 q^{11} +1728.00 q^{12} -5448.90 q^{13} +9085.42 q^{14} -8145.45 q^{15} +4096.00 q^{16} +32160.1 q^{17} +5832.00 q^{18} -44141.1 q^{19} -19307.7 q^{20} +30663.3 q^{21} -37368.9 q^{22} -31126.7 q^{23} +13824.0 q^{24} +12887.8 q^{25} -43591.2 q^{26} +19683.0 q^{27} +72683.4 q^{28} -171161. q^{29} -65163.6 q^{30} +153757. q^{31} +32768.0 q^{32} -126120. q^{33} +257281. q^{34} -342615. q^{35} +46656.0 q^{36} -123880. q^{37} -353129. q^{38} -147120. q^{39} -154462. q^{40} -175979. q^{41} +245306. q^{42} -256606. q^{43} -298951. q^{44} -219927. q^{45} -249013. q^{46} +377328. q^{47} +110592. q^{48} +466221. q^{49} +103103. q^{50} +868324. q^{51} -348729. q^{52} +852261. q^{53} +157464. q^{54} +1.40920e6 q^{55} +581467. q^{56} -1.19181e6 q^{57} -1.36929e6 q^{58} +205379. q^{59} -521309. q^{60} -1.99375e6 q^{61} +1.23006e6 q^{62} +827909. q^{63} +262144. q^{64} +1.64384e6 q^{65} -1.00896e6 q^{66} -1.94039e6 q^{67} +2.05825e6 q^{68} -840420. q^{69} -2.74092e6 q^{70} +674666. q^{71} +373248. q^{72} -4.47921e6 q^{73} -991044. q^{74} +347972. q^{75} -2.82503e6 q^{76} -5.30488e6 q^{77} -1.17696e6 q^{78} -2.14344e6 q^{79} -1.23570e6 q^{80} +531441. q^{81} -1.40783e6 q^{82} -92386.6 q^{83} +1.96245e6 q^{84} -9.70218e6 q^{85} -2.05285e6 q^{86} -4.62135e6 q^{87} -2.39161e6 q^{88} -1.19788e7 q^{89} -1.75942e6 q^{90} -6.18819e6 q^{91} -1.99211e6 q^{92} +4.15144e6 q^{93} +3.01863e6 q^{94} +1.33166e7 q^{95} +884736. q^{96} +6.76114e6 q^{97} +3.72977e6 q^{98} -3.40524e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 164 q^{5} + 1080 q^{6} - 76 q^{7} + 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 164 * q^5 + 1080 * q^6 - 76 * q^7 + 2560 * q^8 + 3645 * q^9	\( 5 q + 40 q^{2} + 135 q^{3} + 320 q^{4} + 164 q^{5} + 1080 q^{6} - 76 q^{7} + 2560 q^{8} + 3645 q^{9} + 1312 q^{10} - 15730 q^{11} + 8640 q^{12} - 21854 q^{13} - 608 q^{14} + 4428 q^{15} + 20480 q^{16} - 34548 q^{17} + 29160 q^{18} - 43828 q^{19} + 10496 q^{20} - 2052 q^{21} - 125840 q^{22} - 110582 q^{23} + 69120 q^{24} - 174577 q^{25} - 174832 q^{26} + 98415 q^{27} - 4864 q^{28} - 307558 q^{29} + 35424 q^{30} - 277994 q^{31} + 163840 q^{32} - 424710 q^{33} - 276384 q^{34} - 764338 q^{35} + 233280 q^{36} - 853778 q^{37} - 350624 q^{38} - 590058 q^{39} + 83968 q^{40} + 131342 q^{41} - 16416 q^{42} - 721996 q^{43} - 1006720 q^{44} + 119556 q^{45} - 884656 q^{46} - 358832 q^{47} + 552960 q^{48} - 207141 q^{49} - 1396616 q^{50} - 932796 q^{51} - 1398656 q^{52} + 1006180 q^{53} + 787320 q^{54} + 81944 q^{55} - 38912 q^{56} - 1183356 q^{57} - 2460464 q^{58} + 1026895 q^{59} + 283392 q^{60} + 101158 q^{61} - 2223952 q^{62} - 55404 q^{63} + 1310720 q^{64} - 3138378 q^{65} - 3397680 q^{66} - 6362512 q^{67} - 2211072 q^{68} - 2985714 q^{69} - 6114704 q^{70} - 8877414 q^{71} + 1866240 q^{72} - 4881862 q^{73} - 6830224 q^{74} - 4713579 q^{75} - 2804992 q^{76} - 2205694 q^{77} - 4720464 q^{78} - 2769432 q^{79} + 671744 q^{80} + 2657205 q^{81} + 1050736 q^{82} - 1430156 q^{83} - 131328 q^{84} - 7564814 q^{85} - 5775968 q^{86} - 8304066 q^{87} - 8053760 q^{88} - 17172176 q^{89} + 956448 q^{90} - 932474 q^{91} - 7077248 q^{92} - 7505838 q^{93} - 2870656 q^{94} + 15962708 q^{95} + 4423680 q^{96} + 20863830 q^{97} - 1657128 q^{98} - 11467170 q^{99}+O(q^{100}) \) 5 * q + 40 * q^2 + 135 * q^3 + 320 * q^4 + 164 * q^5 + 1080 * q^6 - 76 * q^7 + 2560 * q^8 + 3645 * q^9 + 1312 * q^10 - 15730 * q^11 + 8640 * q^12 - 21854 * q^13 - 608 * q^14 + 4428 * q^15 + 20480 * q^16 - 34548 * q^17 + 29160 * q^18 - 43828 * q^19 + 10496 * q^20 - 2052 * q^21 - 125840 * q^22 - 110582 * q^23 + 69120 * q^24 - 174577 * q^25 - 174832 * q^26 + 98415 * q^27 - 4864 * q^28 - 307558 * q^29 + 35424 * q^30 - 277994 * q^31 + 163840 * q^32 - 424710 * q^33 - 276384 * q^34 - 764338 * q^35 + 233280 * q^36 - 853778 * q^37 - 350624 * q^38 - 590058 * q^39 + 83968 * q^40 + 131342 * q^41 - 16416 * q^42 - 721996 * q^43 - 1006720 * q^44 + 119556 * q^45 - 884656 * q^46 - 358832 * q^47 + 552960 * q^48 - 207141 * q^49 - 1396616 * q^50 - 932796 * q^51 - 1398656 * q^52 + 1006180 * q^53 + 787320 * q^54 + 81944 * q^55 - 38912 * q^56 - 1183356 * q^57 - 2460464 * q^58 + 1026895 * q^59 + 283392 * q^60 + 101158 * q^61 - 2223952 * q^62 - 55404 * q^63 + 1310720 * q^64 - 3138378 * q^65 - 3397680 * q^66 - 6362512 * q^67 - 2211072 * q^68 - 2985714 * q^69 - 6114704 * q^70 - 8877414 * q^71 + 1866240 * q^72 - 4881862 * q^73 - 6830224 * q^74 - 4713579 * q^75 - 2804992 * q^76 - 2205694 * q^77 - 4720464 * q^78 - 2769432 * q^79 + 671744 * q^80 + 2657205 * q^81 + 1050736 * q^82 - 1430156 * q^83 - 131328 * q^84 - 7564814 * q^85 - 5775968 * q^86 - 8304066 * q^87 - 8053760 * q^88 - 17172176 * q^89 + 956448 * q^90 - 932474 * q^91 - 7077248 * q^92 - 7505838 * q^93 - 2870656 * q^94 + 15962708 * q^95 + 4423680 * q^96 + 20863830 * q^97 - 1657128 * q^98 - 11467170 * q^99

Introduction

L-functions

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