LMFDB - Embedded newform 546.8.a.o.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$170.562223914$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 280157x^{4} + 23551285x^{3} + 13122885428x^{2} - 1144917710924x - 95027285980032 $ x^6 - x^5 - 280157x^4 + 23551285x^3 + 13122885428x^2 - 1144917710924x - 95027285980032
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$177.668$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +171.668 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +171.668 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -1373.34 q^{10} +1694.14 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -4635.04 q^{15} +4096.00 q^{16} -20973.3 q^{17} -5832.00 q^{18} +10494.7 q^{19} +10986.8 q^{20} +9261.00 q^{21} -13553.1 q^{22} +12199.9 q^{23} +13824.0 q^{24} -48655.1 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +158093. q^{29} +37080.3 q^{30} -224307. q^{31} -32768.0 q^{32} -45741.9 q^{33} +167787. q^{34} -58882.1 q^{35} +46656.0 q^{36} -188764. q^{37} -83957.7 q^{38} +59319.0 q^{39} -87894.0 q^{40} +542955. q^{41} -74088.0 q^{42} +788341. q^{43} +108425. q^{44} +125146. q^{45} -97598.9 q^{46} -145783. q^{47} -110592. q^{48} +117649. q^{49} +389241. q^{50} +566280. q^{51} -140608. q^{52} -1.52364e6 q^{53} +157464. q^{54} +290830. q^{55} +175616. q^{56} -283357. q^{57} -1.26474e6 q^{58} -703660. q^{59} -296642. q^{60} +2.23041e6 q^{61} +1.79446e6 q^{62} -250047. q^{63} +262144. q^{64} -377155. q^{65} +365935. q^{66} -1.70631e6 q^{67} -1.34229e6 q^{68} -329396. q^{69} +471057. q^{70} +253067. q^{71} -373248. q^{72} +1.79195e6 q^{73} +1.51011e6 q^{74} +1.31369e6 q^{75} +671662. q^{76} -581091. q^{77} -474552. q^{78} +3.18342e6 q^{79} +703152. q^{80} +531441. q^{81} -4.34364e6 q^{82} +6.07357e6 q^{83} +592704. q^{84} -3.60045e6 q^{85} -6.30673e6 q^{86} -4.26850e6 q^{87} -867401. q^{88} -2.56995e6 q^{89} -1.00117e6 q^{90} +753571. q^{91} +780791. q^{92} +6.05630e6 q^{93} +1.16627e6 q^{94} +1.80161e6 q^{95} +884736. q^{96} -1.29031e7 q^{97} -941192. q^{98} +1.23503e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 35 q^{5} + 1296 q^{6} - 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) $ 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 35 * q^5 + 1296 * q^6 - 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 35 q^{5} + 1296 q^{6} - 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 280 q^{10} + 5606 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} + 945 q^{15} + 24576 q^{16} + 22022 q^{17} - 34992 q^{18} - 5779 q^{19} - 2240 q^{20} + 55566 q^{21} - 44848 q^{22} - 110789 q^{23} + 82944 q^{24} + 91769 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} + 30693 q^{29} - 7560 q^{30} + 180467 q^{31} - 196608 q^{32} - 151362 q^{33} - 176176 q^{34} + 12005 q^{35} + 279936 q^{36} - 322222 q^{37} + 46232 q^{38} + 355914 q^{39} + 17920 q^{40} - 212652 q^{41} - 444528 q^{42} - 329299 q^{43} + 358784 q^{44} - 25515 q^{45} + 886312 q^{46} + 1322861 q^{47} - 663552 q^{48} + 705894 q^{49} - 734152 q^{50} - 594594 q^{51} - 843648 q^{52} - 168719 q^{53} + 944784 q^{54} - 2252362 q^{55} + 1053696 q^{56} + 156033 q^{57} - 245544 q^{58} + 1943712 q^{59} + 60480 q^{60} - 1085922 q^{61} - 1443736 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 76895 q^{65} + 1210896 q^{66} + 885066 q^{67} + 1409408 q^{68} + 2991303 q^{69} - 96040 q^{70} + 1626164 q^{71} - 2239488 q^{72} - 4750115 q^{73} + 2577776 q^{74} - 2477763 q^{75} - 369856 q^{76} - 1922858 q^{77} - 2847312 q^{78} + 1794289 q^{79} - 143360 q^{80} + 3188646 q^{81} + 1701216 q^{82} - 8454255 q^{83} + 3556224 q^{84} - 18529504 q^{85} + 2634392 q^{86} - 828711 q^{87} - 2870272 q^{88} - 6055411 q^{89} + 204120 q^{90} + 4521426 q^{91} - 7090496 q^{92} - 4872609 q^{93} - 10582888 q^{94} - 3766747 q^{95} + 5308416 q^{96} - 9823899 q^{97} - 5647152 q^{98} + 4086774 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 35 * q^5 + 1296 * q^6 - 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 280 * q^10 + 5606 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 + 945 * q^15 + 24576 * q^16 + 22022 * q^17 - 34992 * q^18 - 5779 * q^19 - 2240 * q^20 + 55566 * q^21 - 44848 * q^22 - 110789 * q^23 + 82944 * q^24 + 91769 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 + 30693 * q^29 - 7560 * q^30 + 180467 * q^31 - 196608 * q^32 - 151362 * q^33 - 176176 * q^34 + 12005 * q^35 + 279936 * q^36 - 322222 * q^37 + 46232 * q^38 + 355914 * q^39 + 17920 * q^40 - 212652 * q^41 - 444528 * q^42 - 329299 * q^43 + 358784 * q^44 - 25515 * q^45 + 886312 * q^46 + 1322861 * q^47 - 663552 * q^48 + 705894 * q^49 - 734152 * q^50 - 594594 * q^51 - 843648 * q^52 - 168719 * q^53 + 944784 * q^54 - 2252362 * q^55 + 1053696 * q^56 + 156033 * q^57 - 245544 * q^58 + 1943712 * q^59 + 60480 * q^60 - 1085922 * q^61 - 1443736 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 76895 * q^65 + 1210896 * q^66 + 885066 * q^67 + 1409408 * q^68 + 2991303 * q^69 - 96040 * q^70 + 1626164 * q^71 - 2239488 * q^72 - 4750115 * q^73 + 2577776 * q^74 - 2477763 * q^75 - 369856 * q^76 - 1922858 * q^77 - 2847312 * q^78 + 1794289 * q^79 - 143360 * q^80 + 3188646 * q^81 + 1701216 * q^82 - 8454255 * q^83 + 3556224 * q^84 - 18529504 * q^85 + 2634392 * q^86 - 828711 * q^87 - 2870272 * q^88 - 6055411 * q^89 + 204120 * q^90 + 4521426 * q^91 - 7090496 * q^92 - 4872609 * q^93 - 10582888 * q^94 - 3766747 * q^95 + 5308416 * q^96 - 9823899 * q^97 - 5647152 * q^98 + 4086774 * 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
$5$	171.668	0.614178	0.307089	−	0.951681i	$-0.400645\pi$
$5$	171.668	0.614178	0.307089	+	0.951681i	$0.400645\pi$
$6$	216.000	0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	−1373.34	−0.434289
$11$	1694.14	0.383774	0.191887	−	0.981417i	$-0.438539\pi$
$11$	1694.14	0.383774	0.191887	+	0.981417i	$0.438539\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	2744.00	0.267261
$15$	−4635.04	−0.354596
$16$	4096.00	0.250000
$17$	−20973.3	−1.03537	−0.517686	−	0.855571i	$-0.673206\pi$
$17$	−20973.3	−1.03537	−0.517686	+	0.855571i	$0.673206\pi$
$18$	−5832.00	−0.235702
$19$	10494.7	0.351021	0.175510	−	0.984478i	$-0.443842\pi$
$19$	10494.7	0.351021	0.175510	+	0.984478i	$0.443842\pi$
$20$	10986.8	0.307089
$21$	9261.00	0.218218
$22$	−13553.1	−0.271369
$23$	12199.9	0.209078	0.104539	−	0.994521i	$-0.466663\pi$
$23$	12199.9	0.209078	0.104539	+	0.994521i	$0.466663\pi$
$24$	13824.0	0.204124
$25$	−48655.1	−0.622785
$26$	17576.0	0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	158093.	1.20370	0.601850	−	0.798609i	$-0.294430\pi$
$29$	158093.	1.20370	0.601850	+	0.798609i	$0.294430\pi$
$30$	37080.3	0.250737
$31$	−224307.	−1.35231	−0.676157	−	0.736758i	$-0.736356\pi$
$31$	−224307.	−1.35231	−0.676157	+	0.736758i	$0.736356\pi$
$32$	−32768.0	−0.176777
$33$	−45741.9	−0.221572
$34$	167787.	0.732119
$35$	−58882.1	−0.232137
$36$	46656.0	0.166667
$37$	−188764.	−0.612651	−0.306325	−	0.951927i	$-0.599100\pi$
$37$	−188764.	−0.612651	−0.306325	+	0.951927i	$0.599100\pi$
$38$	−83957.7	−0.248209
$39$	59319.0	0.160128
$40$	−87894.0	−0.217145
$41$	542955.	1.23033	0.615164	−	0.788400i	$-0.289090\pi$
$41$	542955.	1.23033	0.615164	+	0.788400i	$0.289090\pi$
$42$	−74088.0	−0.154303
$43$	788341.	1.51208	0.756039	−	0.654526i	$-0.227132\pi$
$43$	788341.	1.51208	0.756039	+	0.654526i	$0.227132\pi$
$44$	108425.	0.191887
$45$	125146.	0.204726
$46$	−97598.9	−0.147840
$47$	−145783.	−0.204817	−0.102408	−	0.994742i	$-0.532655\pi$
$47$	−145783.	−0.204817	−0.102408	+	0.994742i	$0.532655\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	389241.	0.440376
$51$	566280.	0.597772
$52$	−140608.	−0.138675
$53$	−1.52364e6	−1.40578	−0.702890	−	0.711299i	$-0.748107\pi$
$53$	−1.52364e6	−1.40578	−0.702890	+	0.711299i	$0.748107\pi$
$54$	157464.	0.136083
$55$	290830.	0.235706
$56$	175616.	0.133631
$57$	−283357.	−0.202662
$58$	−1.26474e6	−0.851145
$59$	−703660.	−0.446047	−0.223024	−	0.974813i	$-0.571593\pi$
$59$	−703660.	−0.446047	−0.223024	+	0.974813i	$0.571593\pi$
$60$	−296642.	−0.177298
$61$	2.23041e6	1.25815	0.629073	−	0.777346i	$-0.283435\pi$
$61$	2.23041e6	1.25815	0.629073	+	0.777346i	$0.283435\pi$
$62$	1.79446e6	0.956230
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	−377155.	−0.170342
$66$	365935.	0.156675
$67$	−1.70631e6	−0.693102	−0.346551	−	0.938031i	$-0.612647\pi$
$67$	−1.70631e6	−0.693102	−0.346551	+	0.938031i	$0.612647\pi$
$68$	−1.34229e6	−0.517686
$69$	−329396.	−0.120711
$70$	471057.	0.164146
$71$	253067.	0.0839134	0.0419567	−	0.999119i	$-0.486641\pi$
$71$	253067.	0.0839134	0.0419567	+	0.999119i	$0.486641\pi$
$72$	−373248.	−0.117851
$73$	1.79195e6	0.539132	0.269566	−	0.962982i	$-0.413120\pi$
$73$	1.79195e6	0.539132	0.269566	+	0.962982i	$0.413120\pi$
$74$	1.51011e6	0.433209
$75$	1.31369e6	0.359565
$76$	671662.	0.175510
$77$	−581091.	−0.145053
$78$	−474552.	−0.113228
$79$	3.18342e6	0.726440	0.363220	−	0.931703i	$-0.381677\pi$
$79$	3.18342e6	0.726440	0.363220	+	0.931703i	$0.381677\pi$
$80$	703152.	0.153545
$81$	531441.	0.111111
$82$	−4.34364e6	−0.869973
$83$	6.07357e6	1.16593	0.582963	−	0.812499i	$-0.301893\pi$
$83$	6.07357e6	1.16593	0.582963	+	0.812499i	$0.301893\pi$
$84$	592704.	0.109109
$85$	−3.60045e6	−0.635903
$86$	−6.30673e6	−1.06920
$87$	−4.26850e6	−0.694957
$88$	−867401.	−0.135685
$89$	−2.56995e6	−0.386420	−0.193210	−	0.981157i	$-0.561890\pi$
$89$	−2.56995e6	−0.386420	−0.193210	+	0.981157i	$0.561890\pi$
$90$	−1.00117e6	−0.144763
$91$	753571.	0.104828
$92$	780791.	0.104539
$93$	6.05630e6	0.780759
$94$	1.16627e6	0.144827
$95$	1.80161e6	0.215589
$96$	884736.	0.102062
$97$	−1.29031e7	−1.43546	−0.717731	−	0.696320i	$-0.754819\pi$
$97$	−1.29031e7	−1.43546	−0.717731	+	0.696320i	$0.754819\pi$
$98$	−941192.	−0.101015
$99$	1.23503e6	0.127925
$100$	−3.11393e6	−0.311393
$101$	1.73674e7	1.67729	0.838646	−	0.544676i	$-0.183348\pi$
$101$	1.73674e7	1.67729	0.838646	+	0.544676i	$0.183348\pi$
$102$	−4.53024e6	−0.422689
$103$	−1.87740e7	−1.69288	−0.846439	−	0.532486i	$-0.821258\pi$
$103$	−1.87740e7	−1.69288	−0.846439	+	0.532486i	$0.821258\pi$
$104$	1.12486e6	0.0980581
$105$	1.58982e6	0.134025
$106$	1.21891e7	0.994036
$107$	−1.06131e7	−0.837531	−0.418765	−	0.908094i	$-0.637537\pi$
$107$	−1.06131e7	−0.837531	−0.418765	+	0.908094i	$0.637537\pi$
$108$	−1.25971e6	−0.0962250
$109$	−7.18763e6	−0.531610	−0.265805	−	0.964027i	$-0.585638\pi$
$109$	−7.18763e6	−0.531610	−0.265805	+	0.964027i	$0.585638\pi$
$110$	−2.32664e6	−0.166669
$111$	5.09662e6	0.353714
$112$	−1.40493e6	−0.0944911
$113$	−1.29753e7	−0.845943	−0.422972	−	0.906143i	$-0.639013\pi$
$113$	−1.29753e7	−0.845943	−0.422972	+	0.906143i	$0.639013\pi$
$114$	2.26686e6	0.143304
$115$	2.09433e6	0.128411
$116$	1.01179e7	0.601850
$117$	−1.60161e6	−0.0924500
$118$	5.62928e6	0.315403
$119$	7.19386e6	0.391334
$120$	2.37314e6	0.125369
$121$	−1.66171e7	−0.852717
$122$	−1.78433e7	−0.889644
$123$	−1.46598e7	−0.710330
$124$	−1.43557e7	−0.676157
$125$	−2.17641e7	−0.996679
$126$	2.00038e6	0.0890871
$127$	−2.77002e7	−1.19997	−0.599983	−	0.800012i	$-0.704826\pi$
$127$	−2.77002e7	−1.19997	−0.599983	+	0.800012i	$0.704826\pi$
$128$	−2.09715e6	−0.0883883
$129$	−2.12852e7	−0.872999
$130$	3.01724e6	0.120450
$131$	−2.36444e7	−0.918923	−0.459461	−	0.888198i	$-0.651958\pi$
$131$	−2.36444e7	−0.918923	−0.459461	+	0.888198i	$0.651958\pi$
$132$	−2.92748e6	−0.110786
$133$	−3.59969e6	−0.132673
$134$	1.36505e7	0.490097
$135$	−3.37894e6	−0.118199
$136$	1.07384e7	0.366059
$137$	4.74725e7	1.57732	0.788661	−	0.614828i	$-0.210775\pi$
$137$	4.74725e7	1.57732	0.788661	+	0.614828i	$0.210775\pi$
$138$	2.63517e6	0.0853555
$139$	2.61963e7	0.827349	0.413674	−	0.910425i	$-0.364245\pi$
$139$	2.61963e7	0.827349	0.413674	+	0.910425i	$0.364245\pi$
$140$	−3.76846e6	−0.116069
$141$	3.93615e6	0.118251
$142$	−2.02454e6	−0.0593357
$143$	−3.72203e6	−0.106440
$144$	2.98598e6	0.0833333
$145$	2.71394e7	0.739286
$146$	−1.43356e7	−0.381224
$147$	−3.17652e6	−0.0824786
$148$	−1.20809e7	−0.306325
$149$	−1.57443e7	−0.389917	−0.194958	−	0.980812i	$-0.562457\pi$
$149$	−1.57443e7	−0.389917	−0.194958	+	0.980812i	$0.562457\pi$
$150$	−1.05095e7	−0.254251
$151$	−5.24476e7	−1.23967	−0.619835	−	0.784732i	$-0.712801\pi$
$151$	−5.24476e7	−1.23967	−0.619835	+	0.784732i	$0.712801\pi$
$152$	−5.37329e6	−0.124105
$153$	−1.52896e7	−0.345124
$154$	4.64873e6	0.102568
$155$	−3.85064e7	−0.830561
$156$	3.79642e6	0.0800641
$157$	8.84905e7	1.82494	0.912468	−	0.409148i	$-0.134174\pi$
$157$	8.84905e7	1.82494	0.912468	+	0.409148i	$0.134174\pi$
$158$	−2.54674e7	−0.513670
$159$	4.11383e7	0.811627
$160$	−5.62522e6	−0.108572
$161$	−4.18455e6	−0.0790239
$162$	−4.25153e6	−0.0785674
$163$	4.24885e7	0.768448	0.384224	−	0.923240i	$-0.374469\pi$
$163$	4.24885e7	0.768448	0.384224	+	0.923240i	$0.374469\pi$
$164$	3.47491e7	0.615164
$165$	−7.85241e6	−0.136085
$166$	−4.85886e7	−0.824434
$167$	3.70645e7	0.615815	0.307907	−	0.951416i	$-0.400371\pi$
$167$	3.70645e7	0.615815	0.307907	+	0.951416i	$0.400371\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	2.88036e7	0.449651
$171$	7.65064e6	0.117007
$172$	5.04538e7	0.756039
$173$	−4.25981e7	−0.625503	−0.312751	−	0.949835i	$-0.601251\pi$
$173$	−4.25981e7	−0.625503	−0.312751	+	0.949835i	$0.601251\pi$
$174$	3.41480e7	0.491409
$175$	1.66887e7	0.235391
$176$	6.93921e6	0.0959435
$177$	1.89988e7	0.257526
$178$	2.05596e7	0.273240
$179$	−1.24098e8	−1.61726	−0.808629	−	0.588318i	$-0.799790\pi$
$179$	−1.24098e8	−1.61726	−0.808629	+	0.588318i	$0.799790\pi$
$180$	8.00934e6	0.102363
$181$	1.07665e8	1.34958	0.674792	−	0.738008i	$-0.264234\pi$
$181$	1.07665e8	1.34958	0.674792	+	0.738008i	$0.264234\pi$
$182$	−6.02857e6	−0.0741249
$183$	−6.02212e7	−0.726391
$184$	−6.24633e6	−0.0739201
$185$	−3.24047e7	−0.376277
$186$	−4.84504e7	−0.552080
$187$	−3.55318e7	−0.397349
$188$	−9.33014e6	−0.102408
$189$	6.75127e6	0.0727393
$190$	−1.44128e7	−0.152445
$191$	1.61947e8	1.68173	0.840865	−	0.541244i	$-0.182047\pi$
$191$	1.61947e8	1.68173	0.840865	+	0.541244i	$0.182047\pi$
$192$	−7.07789e6	−0.0721688
$193$	5.99410e7	0.600169	0.300084	−	0.953913i	$-0.402985\pi$
$193$	5.99410e7	0.600169	0.300084	+	0.953913i	$0.402985\pi$
$194$	1.03224e8	1.01502
$195$	1.01832e7	0.0983472
$196$	7.52954e6	0.0714286
$197$	1.40300e7	0.130746	0.0653728	−	0.997861i	$-0.479176\pi$
$197$	1.40300e7	0.130746	0.0653728	+	0.997861i	$0.479176\pi$
$198$	−9.88024e6	−0.0904564
$199$	−1.92014e7	−0.172721	−0.0863607	−	0.996264i	$-0.527524\pi$
$199$	−1.92014e7	−0.172721	−0.0863607	+	0.996264i	$0.527524\pi$
$200$	2.49114e7	0.220188
$201$	4.60705e7	0.400163
$202$	−1.38939e8	−1.18602
$203$	−5.42257e7	−0.454956
$204$	3.62419e7	0.298886
$205$	9.32080e7	0.755640
$206$	1.50192e8	1.19705
$207$	8.89370e6	0.0696925
$208$	−8.99891e6	−0.0693375
$209$	1.77795e7	0.134713
$210$	−1.27185e7	−0.0947697
$211$	2.10461e8	1.54235	0.771174	−	0.636624i	$-0.219670\pi$
$211$	2.10461e8	1.54235	0.771174	+	0.636624i	$0.219670\pi$
$212$	−9.75131e7	−0.702890
$213$	−6.83281e6	−0.0484474
$214$	8.49052e7	0.592224
$215$	1.35333e8	0.928686
$216$	1.00777e7	0.0680414
$217$	7.69374e7	0.511126
$218$	5.75011e7	0.375905
$219$	−4.83826e7	−0.311268
$220$	1.86131e7	0.117853
$221$	4.60784e7	0.287161
$222$	−4.07730e7	−0.250114
$223$	1.22482e8	0.739613	0.369806	−	0.929109i	$-0.379424\pi$
$223$	1.22482e8	0.739613	0.369806	+	0.929109i	$0.379424\pi$
$224$	1.12394e7	0.0668153
$225$	−3.54696e7	−0.207595
$226$	1.03802e8	0.598172
$227$	2.34218e8	1.32901	0.664506	−	0.747283i	$-0.268642\pi$
$227$	2.34218e8	1.32901	0.664506	+	0.747283i	$0.268642\pi$
$228$	−1.81349e7	−0.101331
$229$	2.33393e7	0.128429	0.0642146	−	0.997936i	$-0.479546\pi$
$229$	2.33393e7	0.128429	0.0642146	+	0.997936i	$0.479546\pi$
$230$	−1.67546e7	−0.0908002
$231$	1.56895e7	0.0837464
$232$	−8.09434e7	−0.425572
$233$	−9.13322e7	−0.473019	−0.236509	−	0.971629i	$-0.576003\pi$
$233$	−9.13322e7	−0.473019	−0.236509	+	0.971629i	$0.576003\pi$
$234$	1.28129e7	0.0653720
$235$	−2.50263e7	−0.125794
$236$	−4.50343e7	−0.223024
$237$	−8.59524e7	−0.419410
$238$	−5.75509e7	−0.276715
$239$	1.66174e8	0.787356	0.393678	−	0.919248i	$-0.371203\pi$
$239$	1.66174e8	0.787356	0.393678	+	0.919248i	$0.371203\pi$
$240$	−1.89851e7	−0.0886490
$241$	−7.36920e7	−0.339126	−0.169563	−	0.985519i	$-0.554236\pi$
$241$	−7.36920e7	−0.339126	−0.169563	+	0.985519i	$0.554236\pi$
$242$	1.32936e8	0.602962
$243$	−1.43489e7	−0.0641500
$244$	1.42747e8	0.629073
$245$	2.01966e7	0.0877397
$246$	1.17278e8	0.502279
$247$	−2.30569e7	−0.0973557
$248$	1.14845e8	0.478115
$249$	−1.63986e8	−0.673147
$250$	1.74113e8	0.704759
$251$	3.56563e8	1.42324	0.711620	−	0.702565i	$-0.247962\pi$
$251$	3.56563e8	1.42324	0.711620	+	0.702565i	$0.247962\pi$
$252$	−1.60030e7	−0.0629941
$253$	2.06683e7	0.0802385
$254$	2.21601e8	0.848505
$255$	9.72122e7	0.367139
$256$	1.67772e7	0.0625000
$257$	−4.91137e8	−1.80483	−0.902416	−	0.430867i	$-0.858208\pi$
$257$	−4.91137e8	−1.80483	−0.902416	+	0.430867i	$0.858208\pi$
$258$	1.70282e8	0.617304
$259$	6.47460e7	0.231560
$260$	−2.41379e7	−0.0851712
$261$	1.15249e8	0.401233
$262$	1.89155e8	0.649777
$263$	−6.44317e7	−0.218401	−0.109200	−	0.994020i	$-0.534829\pi$
$263$	−6.44317e7	−0.218401	−0.109200	+	0.994020i	$0.534829\pi$
$264$	2.34198e7	0.0783375
$265$	−2.61560e8	−0.863399
$266$	2.87975e7	0.0938143
$267$	6.93887e7	0.223100
$268$	−1.09204e8	−0.346551
$269$	−3.21815e8	−1.00803	−0.504015	−	0.863695i	$-0.668144\pi$
$269$	−3.21815e8	−1.00803	−0.504015	+	0.863695i	$0.668144\pi$
$270$	2.70315e7	0.0835790
$271$	4.45913e8	1.36100	0.680500	−	0.732748i	$-0.261763\pi$
$271$	4.45913e8	1.36100	0.680500	+	0.732748i	$0.261763\pi$
$272$	−8.59068e7	−0.258843
$273$	−2.03464e7	−0.0605228
$274$	−3.79780e8	−1.11534
$275$	−8.24287e7	−0.239009
$276$	−2.10814e7	−0.0603555
$277$	3.93581e8	1.11264	0.556321	−	0.830968i	$-0.312213\pi$
$277$	3.93581e8	1.11264	0.556321	+	0.830968i	$0.312213\pi$
$278$	−2.09571e8	−0.585024
$279$	−1.63520e8	−0.450771
$280$	3.01476e7	0.0820730
$281$	2.31618e8	0.622732	0.311366	−	0.950290i	$-0.399214\pi$
$281$	2.31618e8	0.622732	0.311366	+	0.950290i	$0.399214\pi$
$282$	−3.14892e7	−0.0836161
$283$	2.94888e8	0.773400	0.386700	−	0.922206i	$-0.373615\pi$
$283$	2.94888e8	0.773400	0.386700	+	0.922206i	$0.373615\pi$
$284$	1.61963e7	0.0419567
$285$	−4.86434e7	−0.124471
$286$	2.97763e7	0.0752643
$287$	−1.86234e8	−0.465020
$288$	−2.38879e7	−0.0589256
$289$	2.95426e7	0.0719956
$290$	−2.17115e8	−0.522754
$291$	3.48383e8	0.828764
$292$	1.14685e8	0.269566
$293$	1.48803e8	0.345600	0.172800	−	0.984957i	$-0.444719\pi$
$293$	1.48803e8	0.345600	0.172800	+	0.984957i	$0.444719\pi$
$294$	2.54122e7	0.0583212
$295$	−1.20796e8	−0.273953
$296$	9.66471e7	0.216605
$297$	−3.33458e7	−0.0738573
$298$	1.25955e8	0.275713
$299$	−2.68031e7	−0.0579877
$300$	8.40760e7	0.179783
$301$	−2.70401e8	−0.571512
$302$	4.19581e8	0.876580
$303$	−4.68919e8	−0.968385
$304$	4.29863e7	0.0877552
$305$	3.82891e8	0.772726
$306$	1.22317e8	0.244040
$307$	6.83955e8	1.34910	0.674548	−	0.738231i	$-0.264338\pi$
$307$	6.83955e8	1.34910	0.674548	+	0.738231i	$0.264338\pi$
$308$	−3.71898e7	−0.0725265
$309$	5.06897e8	0.977383
$310$	3.08051e8	0.587296
$311$	2.84735e8	0.536760	0.268380	−	0.963313i	$-0.413512\pi$
$311$	2.84735e8	0.536760	0.268380	+	0.963313i	$0.413512\pi$
$312$	−3.03713e7	−0.0566139
$313$	6.48147e8	1.19473	0.597363	−	0.801971i	$-0.296215\pi$
$313$	6.48147e8	1.19473	0.597363	+	0.801971i	$0.296215\pi$
$314$	−7.07924e8	−1.29042
$315$	−4.29251e7	−0.0773792
$316$	2.03739e8	0.363220
$317$	9.78427e8	1.72513	0.862564	−	0.505949i	$-0.168857\pi$
$317$	9.78427e8	1.72513	0.862564	+	0.505949i	$0.168857\pi$
$318$	−3.29107e8	−0.573907
$319$	2.67831e8	0.461949
$320$	4.50017e7	0.0767723
$321$	2.86555e8	0.483549
$322$	3.34764e7	0.0558783
$323$	−2.20109e8	−0.363437
$324$	3.40122e7	0.0555556
$325$	1.06895e8	0.172730
$326$	−3.39908e8	−0.543375
$327$	1.94066e8	0.306925
$328$	−2.77993e8	−0.434986
$329$	5.00037e7	0.0774135
$330$	6.28193e7	0.0962264
$331$	6.28217e8	0.952164	0.476082	−	0.879401i	$-0.342057\pi$
$331$	6.28217e8	0.952164	0.476082	+	0.879401i	$0.342057\pi$
$332$	3.88709e8	0.582963
$333$	−1.37609e8	−0.204217
$334$	−2.96516e8	−0.435447
$335$	−2.92919e8	−0.425688
$336$	3.79331e7	0.0545545
$337$	1.86224e7	0.0265051	0.0132526	−	0.999912i	$-0.495781\pi$
$337$	1.86224e7	0.0265051	0.0132526	+	0.999912i	$0.495781\pi$
$338$	−3.86145e7	−0.0543928
$339$	3.50332e8	0.488406
$340$	−2.30429e8	−0.317951
$341$	−3.80008e8	−0.518983
$342$	−6.12052e7	−0.0827364
$343$	−4.03536e7	−0.0539949
$344$	−4.03630e8	−0.534601
$345$	−5.65468e7	−0.0741380
$346$	3.40785e8	0.442297
$347$	5.06343e8	0.650567	0.325283	−	0.945617i	$-0.394540\pi$
$347$	5.06343e8	0.650567	0.325283	+	0.945617i	$0.394540\pi$
$348$	−2.73184e8	−0.347478
$349$	−6.97208e7	−0.0877958	−0.0438979	−	0.999036i	$-0.513978\pi$
$349$	−6.97208e7	−0.0877958	−0.0438979	+	0.999036i	$0.513978\pi$
$350$	−1.33510e8	−0.166446
$351$	4.32436e7	0.0533761
$352$	−5.55137e7	−0.0678423
$353$	−9.89614e8	−1.19744	−0.598721	−	0.800958i	$-0.704324\pi$
$353$	−9.89614e8	−1.19744	−0.598721	+	0.800958i	$0.704324\pi$
$354$	−1.51991e8	−0.182098
$355$	4.34435e7	0.0515377
$356$	−1.64477e8	−0.193210
$357$	−1.94234e8	−0.225937
$358$	9.92785e8	1.14357
$359$	−2.47481e8	−0.282300	−0.141150	−	0.989988i	$-0.545080\pi$
$359$	−2.47481e8	−0.282300	−0.141150	+	0.989988i	$0.545080\pi$
$360$	−6.40747e7	−0.0723816
$361$	−7.83733e8	−0.876784
$362$	−8.61320e8	−0.954299
$363$	4.48660e8	0.492317
$364$	4.82285e7	0.0524142
$365$	3.07620e8	0.331123
$366$	4.81770e8	0.513636
$367$	1.23427e9	1.30340	0.651702	−	0.758475i	$-0.274055\pi$
$367$	1.23427e9	1.30340	0.651702	+	0.758475i	$0.274055\pi$
$368$	4.99706e7	0.0522694
$369$	3.95814e8	0.410109
$370$	2.59238e8	0.266068
$371$	5.22609e8	0.531335
$372$	3.87603e8	0.390379
$373$	1.37074e9	1.36765	0.683823	−	0.729648i	$-0.260316\pi$
$373$	1.37074e9	1.36765	0.683823	+	0.729648i	$0.260316\pi$
$374$	2.84255e8	0.280968
$375$	5.87630e8	0.575433
$376$	7.46411e7	0.0724137
$377$	−3.47329e8	−0.333846
$378$	−5.40102e7	−0.0514344
$379$	2.00505e9	1.89186	0.945929	−	0.324374i	$-0.105154\pi$
$379$	2.00505e9	1.89186	0.945929	+	0.324374i	$0.105154\pi$
$380$	1.15303e8	0.107795
$381$	7.47904e8	0.692801
$382$	−1.29558e9	−1.18916
$383$	−1.98529e9	−1.80563	−0.902813	−	0.430033i	$-0.858502\pi$
$383$	−1.98529e9	−1.80563	−0.902813	+	0.430033i	$0.858502\pi$
$384$	5.66231e7	0.0510310
$385$	−9.97547e7	−0.0890883
$386$	−4.79528e8	−0.424383
$387$	5.74700e8	0.504026
$388$	−8.25796e8	−0.717731
$389$	−3.75275e8	−0.323240	−0.161620	−	0.986853i	$-0.551672\pi$
$389$	−3.75275e8	−0.323240	−0.161620	+	0.986853i	$0.551672\pi$
$390$	−8.14654e7	−0.0695420
$391$	−2.55872e8	−0.216473
$392$	−6.02363e7	−0.0505076
$393$	6.38399e8	0.530540
$394$	−1.12240e8	−0.0924511
$395$	5.46492e8	0.446163
$396$	7.90419e7	0.0639623
$397$	−2.22322e9	−1.78326	−0.891632	−	0.452760i	$-0.850439\pi$
$397$	−2.22322e9	−1.78326	−0.891632	+	0.452760i	$0.850439\pi$
$398$	1.53611e8	0.122132
$399$	9.71915e7	0.0765990
$400$	−1.99291e8	−0.155696
$401$	2.76196e8	0.213900	0.106950	−	0.994264i	$-0.465891\pi$
$401$	2.76196e8	0.213900	0.106950	+	0.994264i	$0.465891\pi$
$402$	−3.68564e8	−0.282958
$403$	4.92803e8	0.375064
$404$	1.11151e9	0.838646
$405$	9.12314e7	0.0682420
$406$	4.33806e8	0.321702
$407$	−3.19793e8	−0.235119
$408$	−2.89936e8	−0.211344
$409$	9.68254e8	0.699774	0.349887	−	0.936792i	$-0.386220\pi$
$409$	9.68254e8	0.699774	0.349887	+	0.936792i	$0.386220\pi$
$410$	−7.45664e8	−0.534318
$411$	−1.28176e9	−0.910667
$412$	−1.20153e9	−0.846439
$413$	2.41356e8	0.168590
$414$	−7.11496e7	−0.0492800
$415$	1.04264e9	0.716086
$416$	7.19913e7	0.0490290
$417$	−7.07301e8	−0.477670
$418$	−1.42236e8	−0.0952563
$419$	1.62109e9	1.07661	0.538305	−	0.842750i	$-0.319065\pi$
$419$	1.62109e9	1.07661	0.538305	+	0.842750i	$0.319065\pi$
$420$	1.01748e8	0.0670123
$421$	1.99121e9	1.30055	0.650277	−	0.759697i	$-0.274653\pi$
$421$	1.99121e9	1.30055	0.650277	+	0.759697i	$0.274653\pi$
$422$	−1.68369e9	−1.09061
$423$	−1.06276e8	−0.0682723
$424$	7.80105e8	0.497018
$425$	1.02046e9	0.644815
$426$	5.46624e7	0.0342575
$427$	−7.65032e8	−0.475535
$428$	−6.79241e8	−0.418765
$429$	1.00495e8	0.0614530
$430$	−1.08266e9	−0.656680
$431$	−2.26685e9	−1.36380	−0.681902	−	0.731443i	$-0.738847\pi$
$431$	−2.26685e9	−1.36380	−0.681902	+	0.731443i	$0.738847\pi$
$432$	−8.06216e7	−0.0481125
$433$	9.16832e8	0.542728	0.271364	−	0.962477i	$-0.412525\pi$
$433$	9.16832e8	0.542728	0.271364	+	0.962477i	$0.412525\pi$
$434$	−6.15499e8	−0.361421
$435$	−7.32764e8	−0.426827
$436$	−4.60009e8	−0.265805
$437$	1.28034e8	0.0733906
$438$	3.87061e8	0.220100
$439$	3.31884e9	1.87223	0.936117	−	0.351689i	$-0.114392\pi$
$439$	3.31884e9	1.87223	0.936117	+	0.351689i	$0.114392\pi$
$440$	−1.48905e8	−0.0833345
$441$	8.57661e7	0.0476190
$442$	−3.68628e8	−0.203053
$443$	−2.35341e8	−0.128613	−0.0643064	−	0.997930i	$-0.520484\pi$
$443$	−2.35341e8	−0.128613	−0.0643064	+	0.997930i	$0.520484\pi$
$444$	3.26184e8	0.176857
$445$	−4.41178e8	−0.237331
$446$	−9.79854e8	−0.522985
$447$	4.25097e8	0.225119
$448$	−8.99154e7	−0.0472456
$449$	−6.40150e8	−0.333749	−0.166874	−	0.985978i	$-0.553367\pi$
$449$	−6.40150e8	−0.333749	−0.166874	+	0.985978i	$0.553367\pi$
$450$	2.83757e8	0.146792
$451$	9.19844e8	0.472168
$452$	−8.30416e8	−0.422972
$453$	1.41609e9	0.715724
$454$	−1.87374e9	−0.939754
$455$	1.29364e8	0.0643834
$456$	1.45079e8	0.0716518
$457$	−2.53582e9	−1.24283	−0.621414	−	0.783482i	$-0.713442\pi$
$457$	−2.53582e9	−1.24283	−0.621414	+	0.783482i	$0.713442\pi$
$458$	−1.86714e8	−0.0908131
$459$	4.12818e8	0.199257
$460$	1.34037e8	0.0642054
$461$	1.02375e9	0.486678	0.243339	−	0.969941i	$-0.421757\pi$
$461$	1.02375e9	0.486678	0.243339	+	0.969941i	$0.421757\pi$
$462$	−1.25516e8	−0.0592176
$463$	3.74262e8	0.175244	0.0876218	−	0.996154i	$-0.472073\pi$
$463$	3.74262e8	0.175244	0.0876218	+	0.996154i	$0.472073\pi$
$464$	6.47547e8	0.300925
$465$	1.03967e9	0.479525
$466$	7.30658e8	0.334475
$467$	1.82832e9	0.830696	0.415348	−	0.909663i	$-0.363660\pi$
$467$	1.82832e9	0.830696	0.415348	+	0.909663i	$0.363660\pi$
$468$	−1.02503e8	−0.0462250
$469$	5.85266e8	0.261968
$470$	2.00211e8	0.0889498
$471$	−2.38924e9	−1.05363
$472$	3.60274e8	0.157702
$473$	1.33556e9	0.580297
$474$	6.87619e8	0.296568
$475$	−5.10621e8	−0.218611
$476$	4.60407e8	0.195667
$477$	−1.11073e9	−0.468593
$478$	−1.32939e9	−0.556745
$479$	3.58054e9	1.48859	0.744294	−	0.667852i	$-0.232786\pi$
$479$	3.58054e9	1.48859	0.744294	+	0.667852i	$0.232786\pi$
$480$	1.51881e8	0.0626843
$481$	4.14714e8	0.169919
$482$	5.89536e8	0.239798
$483$	1.12983e8	0.0456245
$484$	−1.06349e9	−0.426359
$485$	−2.21504e9	−0.881629
$486$	1.14791e8	0.0453609
$487$	−1.35548e9	−0.531792	−0.265896	−	0.964002i	$-0.585668\pi$
$487$	−1.35548e9	−0.531792	−0.265896	+	0.964002i	$0.585668\pi$
$488$	−1.14197e9	−0.444822
$489$	−1.14719e9	−0.443664
$490$	−1.61573e8	−0.0620414
$491$	−7.80432e7	−0.0297543	−0.0148772	−	0.999889i	$-0.504736\pi$
$491$	−7.80432e7	−0.0297543	−0.0148772	+	0.999889i	$0.504736\pi$
$492$	−9.38227e8	−0.355165
$493$	−3.31573e9	−1.24628
$494$	1.84455e8	0.0688408
$495$	2.12015e8	0.0785685
$496$	−9.18763e8	−0.338078
$497$	−8.68019e7	−0.0317163
$498$	1.31189e9	0.475987
$499$	2.67821e8	0.0964925	0.0482462	−	0.998835i	$-0.484637\pi$
$499$	2.67821e8	0.0964925	0.0482462	+	0.998835i	$0.484637\pi$
$500$	−1.39290e9	−0.498340
$501$	−1.00074e9	−0.355541
$502$	−2.85250e9	−1.00638
$503$	−2.09448e9	−0.733818	−0.366909	−	0.930257i	$-0.619584\pi$
$503$	−2.09448e9	−0.733818	−0.366909	+	0.930257i	$0.619584\pi$
$504$	1.28024e8	0.0445435
$505$	2.98142e9	1.03016
$506$	−1.65346e8	−0.0567372
$507$	−1.30324e8	−0.0444116
$508$	−1.77281e9	−0.599983
$509$	−4.46893e9	−1.50207	−0.751037	−	0.660260i	$-0.770446\pi$
$509$	−4.46893e9	−1.50207	−0.751037	+	0.660260i	$0.770446\pi$
$510$	−7.77698e8	−0.259606
$511$	−6.14638e8	−0.203773
$512$	−1.34218e8	−0.0441942
$513$	−2.06567e8	−0.0675540
$514$	3.92909e9	1.27621
$515$	−3.22289e9	−1.03973
$516$	−1.36225e9	−0.436500
$517$	−2.46978e8	−0.0786034
$518$	−5.17968e8	−0.163738
$519$	1.15015e9	0.361134
$520$	1.93103e8	0.0602251
$521$	−2.88227e9	−0.892899	−0.446449	−	0.894809i	$-0.647312\pi$
$521$	−2.88227e9	−0.892899	−0.446449	+	0.894809i	$0.647312\pi$
$522$	−9.21996e8	−0.283715
$523$	2.98917e9	0.913682	0.456841	−	0.889548i	$-0.348981\pi$
$523$	2.98917e9	0.913682	0.456841	+	0.889548i	$0.348981\pi$
$524$	−1.51324e9	−0.459461
$525$	−4.50595e8	−0.135903
$526$	5.15454e8	0.154433
$527$	4.70447e9	1.40015
$528$	−1.87359e8	−0.0553930
$529$	−3.25599e9	−0.956287
$530$	2.09248e9	0.610515
$531$	−5.12968e8	−0.148682
$532$	−2.30380e8	−0.0663367
$533$	−1.19287e9	−0.341231
$534$	−5.55109e8	−0.157755
$535$	−1.82194e9	−0.514393
$536$	8.73633e8	0.245049
$537$	3.35065e9	0.933725
$538$	2.57452e9	0.712784
$539$	1.99314e8	0.0548249
$540$	−2.16252e8	−0.0590993
$541$	7.04229e9	1.91216	0.956078	−	0.293111i	$-0.0946905\pi$
$541$	7.04229e9	1.91216	0.956078	+	0.293111i	$0.0946905\pi$
$542$	−3.56731e9	−0.962372
$543$	−2.90696e9	−0.779182
$544$	6.87255e8	0.183030
$545$	−1.23389e9	−0.326503
$546$	1.62771e8	0.0427960
$547$	1.46289e9	0.382169	0.191084	−	0.981574i	$-0.438800\pi$
$547$	1.46289e9	0.382169	0.191084	+	0.981574i	$0.438800\pi$
$548$	3.03824e9	0.788661
$549$	1.62597e9	0.419382
$550$	6.59430e8	0.169005
$551$	1.65914e9	0.422524
$552$	1.68651e8	0.0426778
$553$	−1.09191e9	−0.274568
$554$	−3.14865e9	−0.786757
$555$	8.74927e8	0.217243
$556$	1.67656e9	0.413674
$557$	−3.80835e9	−0.933778	−0.466889	−	0.884316i	$-0.654625\pi$
$557$	−3.80835e9	−0.933778	−0.466889	+	0.884316i	$0.654625\pi$
$558$	1.30816e9	0.318743
$559$	−1.73198e9	−0.419375
$560$	−2.41181e8	−0.0580344
$561$	9.59360e8	0.229410
$562$	−1.85295e9	−0.440338
$563$	3.74743e9	0.885023	0.442512	−	0.896763i	$-0.354088\pi$
$563$	3.74743e9	0.885023	0.442512	+	0.896763i	$0.354088\pi$
$564$	2.51914e8	0.0591255
$565$	−2.22744e9	−0.519560
$566$	−2.35910e9	−0.546876
$567$	−1.82284e8	−0.0419961
$568$	−1.29570e8	−0.0296679
$569$	−4.22817e9	−0.962187	−0.481094	−	0.876669i	$-0.659760\pi$
$569$	−4.22817e9	−0.962187	−0.481094	+	0.876669i	$0.659760\pi$
$570$	3.89147e8	0.0880140
$571$	8.68265e9	1.95176	0.975879	−	0.218313i	$-0.0700552\pi$
$571$	8.68265e9	1.95176	0.975879	+	0.218313i	$0.0700552\pi$
$572$	−2.38210e8	−0.0532199
$573$	−4.37257e9	−0.970948
$574$	1.48987e9	0.328819
$575$	−5.93585e8	−0.130210
$576$	1.91103e8	0.0416667
$577$	−5.32869e8	−0.115480	−0.0577398	−	0.998332i	$-0.518389\pi$
$577$	−5.32869e8	−0.115480	−0.0577398	+	0.998332i	$0.518389\pi$
$578$	−2.36341e8	−0.0509086
$579$	−1.61841e9	−0.346508
$580$	1.73692e9	0.369643
$581$	−2.08323e9	−0.440678
$582$	−2.78706e9	−0.586025
$583$	−2.58127e9	−0.539502
$584$	−9.17477e8	−0.190612
$585$	−2.74946e8	−0.0567808
$586$	−1.19042e9	−0.244376
$587$	−3.93668e9	−0.803335	−0.401668	−	0.915786i	$-0.631569\pi$
$587$	−3.93668e9	−0.803335	−0.401668	+	0.915786i	$0.631569\pi$
$588$	−2.03297e8	−0.0412393
$589$	−2.35404e9	−0.474690
$590$	9.66368e8	0.193714
$591$	−3.78811e8	−0.0754860
$592$	−7.73177e8	−0.153163
$593$	6.94785e9	1.36823	0.684115	−	0.729374i	$-0.260189\pi$
$593$	6.94785e9	1.36823	0.684115	+	0.729374i	$0.260189\pi$
$594$	2.66766e8	0.0522250
$595$	1.23496e9	0.240349
$596$	−1.00764e9	−0.194958
$597$	5.18437e8	0.0997208
$598$	2.14425e8	0.0410035
$599$	−5.99653e9	−1.14000	−0.570002	−	0.821643i	$-0.693058\pi$
$599$	−5.99653e9	−1.14000	−0.570002	+	0.821643i	$0.693058\pi$
$600$	−6.72608e8	−0.127126
$601$	−6.28284e9	−1.18058	−0.590290	−	0.807192i	$-0.700986\pi$
$601$	−6.28284e9	−1.18058	−0.590290	+	0.807192i	$0.700986\pi$
$602$	2.16321e9	0.404120
$603$	−1.24390e9	−0.231034
$604$	−3.35665e9	−0.619835
$605$	−2.85262e9	−0.523720
$606$	3.75135e9	0.684752
$607$	−7.30503e9	−1.32575	−0.662875	−	0.748730i	$-0.730664\pi$
$607$	−7.30503e9	−1.32575	−0.662875	+	0.748730i	$0.730664\pi$
$608$	−3.43891e8	−0.0620523
$609$	1.46409e9	0.262669
$610$	−3.06313e9	−0.546400
$611$	3.20286e8	0.0568060
$612$	−9.78532e8	−0.172562
$613$	4.41149e9	0.773523	0.386762	−	0.922180i	$-0.373594\pi$
$613$	4.41149e9	0.773523	0.386762	+	0.922180i	$0.373594\pi$
$614$	−5.47164e9	−0.953955
$615$	−2.51662e9	−0.436269
$616$	2.97519e8	0.0512840
$617$	−2.41016e9	−0.413093	−0.206546	−	0.978437i	$-0.566222\pi$
$617$	−2.41016e9	−0.413093	−0.206546	+	0.978437i	$0.566222\pi$
$618$	−4.05517e9	−0.691114
$619$	5.13179e9	0.869664	0.434832	−	0.900512i	$-0.356808\pi$
$619$	5.13179e9	0.869664	0.434832	+	0.900512i	$0.356808\pi$
$620$	−2.46441e9	−0.415281
$621$	−2.40130e8	−0.0402370
$622$	−2.27788e9	−0.379547
$623$	8.81493e8	0.146053
$624$	2.42971e8	0.0400320
$625$	6.49834e7	0.0106469
$626$	−5.18518e9	−0.844799
$627$	−4.80048e8	−0.0777764
$628$	5.66339e9	0.912468
$629$	3.95901e9	0.634321
$630$	3.43401e8	0.0547153
$631$	4.70902e9	0.746153	0.373077	−	0.927801i	$-0.378303\pi$
$631$	4.70902e9	0.746153	0.373077	+	0.927801i	$0.378303\pi$
$632$	−1.62991e9	−0.256835
$633$	−5.68244e9	−0.890475
$634$	−7.82742e9	−1.21985
$635$	−4.75523e9	−0.736993
$636$	2.63285e9	0.405814
$637$	−2.58475e8	−0.0396214
$638$	−2.14265e9	−0.326647
$639$	1.84486e8	0.0279711
$640$	−3.60014e8	−0.0542862
$641$	−1.95843e9	−0.293700	−0.146850	−	0.989159i	$-0.546914\pi$
$641$	−1.95843e9	−0.293700	−0.146850	+	0.989159i	$0.546914\pi$
$642$	−2.29244e9	−0.341921
$643$	−4.61007e9	−0.683864	−0.341932	−	0.939725i	$-0.611081\pi$
$643$	−4.61007e9	−0.683864	−0.341932	+	0.939725i	$0.611081\pi$
$644$	−2.67811e8	−0.0395119
$645$	−3.65399e9	−0.536177
$646$	1.76087e9	0.256989
$647$	6.49512e9	0.942806	0.471403	−	0.881918i	$-0.343748\pi$
$647$	6.49512e9	0.942806	0.471403	+	0.881918i	$0.343748\pi$
$648$	−2.72098e8	−0.0392837
$649$	−1.19210e9	−0.171181
$650$	−8.55162e8	−0.122138
$651$	−2.07731e9	−0.295099
$652$	2.71926e9	0.384224
$653$	−2.97797e9	−0.418527	−0.209264	−	0.977859i	$-0.567107\pi$
$653$	−2.97797e9	−0.418527	−0.209264	+	0.977859i	$0.567107\pi$
$654$	−1.55253e9	−0.217029
$655$	−4.05899e9	−0.564382
$656$	2.22394e9	0.307582
$657$	1.30633e9	0.179711
$658$	−4.00030e8	−0.0547396
$659$	1.37668e9	0.187385	0.0936926	−	0.995601i	$-0.470133\pi$
$659$	1.37668e9	0.187385	0.0936926	+	0.995601i	$0.470133\pi$
$660$	−5.02554e8	−0.0680423
$661$	5.98276e9	0.805743	0.402871	−	0.915257i	$-0.368012\pi$
$661$	5.98276e9	0.805743	0.402871	+	0.915257i	$0.368012\pi$
$662$	−5.02574e9	−0.673282
$663$	−1.24412e9	−0.165792
$664$	−3.10967e9	−0.412217
$665$	−6.17951e8	−0.0814851
$666$	1.10087e9	0.144403
$667$	1.92871e9	0.251667
$668$	2.37213e9	0.307907
$669$	−3.30701e9	−0.427016
$670$	2.34336e9	0.301007
$671$	3.77864e9	0.482844
$672$	−3.03464e8	−0.0385758
$673$	−5.04918e9	−0.638511	−0.319256	−	0.947669i	$-0.603433\pi$
$673$	−5.04918e9	−0.638511	−0.319256	+	0.947669i	$0.603433\pi$
$674$	−1.48979e8	−0.0187420
$675$	9.57678e8	0.119855
$676$	3.08916e8	0.0384615
$677$	1.35193e10	1.67453	0.837264	−	0.546798i	$-0.184154\pi$
$677$	1.35193e10	1.67453	0.837264	+	0.546798i	$0.184154\pi$
$678$	−2.80265e9	−0.345355
$679$	4.42575e9	0.542554
$680$	1.84343e9	0.224826
$681$	−6.32388e9	−0.767306
$682$	3.04007e9	0.366976
$683$	−9.73772e9	−1.16946	−0.584729	−	0.811229i	$-0.698799\pi$
$683$	−9.73772e9	−1.16946	−0.584729	+	0.811229i	$0.698799\pi$
$684$	4.89641e8	0.0585035
$685$	8.14951e9	0.968757
$686$	3.22829e8	0.0381802
$687$	−6.30161e8	−0.0741486
$688$	3.22904e9	0.378020
$689$	3.34744e9	0.389893
$690$	4.52374e8	0.0524235
$691$	−1.34748e10	−1.55363	−0.776817	−	0.629726i	$-0.783167\pi$
$691$	−1.34748e10	−1.55363	−0.776817	+	0.629726i	$0.783167\pi$
$692$	−2.72628e9	−0.312751
$693$	−4.23615e8	−0.0483510
$694$	−4.05075e9	−0.460020
$695$	4.49707e9	0.508139
$696$	2.18547e9	0.245704
$697$	−1.13876e10	−1.27385
$698$	5.57767e8	0.0620810
$699$	2.46597e9	0.273097
$700$	1.06808e9	0.117695
$701$	5.14835e9	0.564488	0.282244	−	0.959343i	$-0.408921\pi$
$701$	5.14835e9	0.564488	0.282244	+	0.959343i	$0.408921\pi$
$702$	−3.45948e8	−0.0377426
$703$	−1.98102e9	−0.215053
$704$	4.44109e8	0.0479718
$705$	6.75711e8	0.0726272
$706$	7.91691e9	0.846719
$707$	−5.95700e9	−0.633957
$708$	1.21593e9	0.128763
$709$	1.56598e10	1.65015	0.825077	−	0.565021i	$-0.191132\pi$
$709$	1.56598e10	1.65015	0.825077	+	0.565021i	$0.191132\pi$
$710$	−3.47548e8	−0.0364427
$711$	2.32072e9	0.242147
$712$	1.31581e9	0.136620
$713$	−2.73652e9	−0.282738
$714$	1.55387e9	0.159761
$715$	−6.38954e8	−0.0653730
$716$	−7.94228e9	−0.808629
$717$	−4.48670e9	−0.454580
$718$	1.97985e9	0.199616
$719$	2.97991e9	0.298986	0.149493	−	0.988763i	$-0.452236\pi$
$719$	2.97991e9	0.298986	0.149493	+	0.988763i	$0.452236\pi$
$720$	5.12598e8	0.0511815
$721$	6.43947e9	0.639848
$722$	6.26986e9	0.619980
$723$	1.98968e9	0.195794
$724$	6.89056e9	0.674792
$725$	−7.69201e9	−0.749647
$726$	−3.58928e9	−0.348120
$727$	1.70164e10	1.64247	0.821237	−	0.570587i	$-0.193284\pi$
$727$	1.70164e10	1.64247	0.821237	+	0.570587i	$0.193284\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−2.46096e9	−0.234139
$731$	−1.65341e10	−1.56556
$732$	−3.85416e9	−0.363196
$733$	7.75056e9	0.726891	0.363446	−	0.931615i	$-0.381600\pi$
$733$	7.75056e9	0.726891	0.363446	+	0.931615i	$0.381600\pi$
$734$	−9.87417e9	−0.921646
$735$	−5.45307e8	−0.0506566
$736$	−3.99765e8	−0.0369600
$737$	−2.89074e9	−0.265995
$738$	−3.16652e9	−0.289991
$739$	3.87487e9	0.353185	0.176592	−	0.984284i	$-0.443493\pi$
$739$	3.87487e9	0.353185	0.176592	+	0.984284i	$0.443493\pi$
$740$	−2.07390e9	−0.188138
$741$	6.22536e8	0.0562083
$742$	−4.18087e9	−0.375710
$743$	4.07152e9	0.364163	0.182081	−	0.983283i	$-0.441717\pi$
$743$	4.07152e9	0.364163	0.182081	+	0.983283i	$0.441717\pi$
$744$	−3.10082e9	−0.276040
$745$	−2.70280e9	−0.239478
$746$	−1.09659e10	−0.967071
$747$	4.42763e9	0.388642
$748$	−2.27404e9	−0.198674
$749$	3.64031e9	0.316557
$750$	−4.70104e9	−0.406893
$751$	4.94226e9	0.425781	0.212890	−	0.977076i	$-0.431712\pi$
$751$	4.94226e9	0.425781	0.212890	+	0.977076i	$0.431712\pi$
$752$	−5.97129e8	−0.0512042
$753$	−9.62720e9	−0.821708
$754$	2.77863e9	0.236065
$755$	−9.00357e9	−0.761379
$756$	4.32081e8	0.0363696
$757$	3.49772e9	0.293055	0.146528	−	0.989207i	$-0.453190\pi$
$757$	3.49772e9	0.293055	0.146528	+	0.989207i	$0.453190\pi$
$758$	−1.60404e10	−1.33775
$759$	−5.58044e8	−0.0463257
$760$	−9.22422e8	−0.0762223
$761$	−2.12628e9	−0.174894	−0.0874470	−	0.996169i	$-0.527871\pi$
$761$	−2.12628e9	−0.174894	−0.0874470	+	0.996169i	$0.527871\pi$
$762$	−5.98323e9	−0.489884
$763$	2.46536e9	0.200930
$764$	1.03646e10	0.840865
$765$	−2.62473e9	−0.211968
$766$	1.58823e10	1.27677
$767$	1.54594e9	0.123711
$768$	−4.52985e8	−0.0360844
$769$	2.50591e10	1.98711	0.993557	−	0.113336i	$-0.0361537\pi$
$769$	2.50591e10	1.98711	0.993557	+	0.113336i	$0.0361537\pi$
$770$	7.98038e8	0.0629950
$771$	1.32607e10	1.04202
$772$	3.83622e9	0.300084
$773$	2.07244e10	1.61381	0.806907	−	0.590678i	$-0.201140\pi$
$773$	2.07244e10	1.61381	0.806907	+	0.590678i	$0.201140\pi$
$774$	−4.59760e9	−0.356400
$775$	1.09137e10	0.842201
$776$	6.60637e9	0.507512
$777$	−1.74814e9	−0.133691
$778$	3.00220e9	0.228566
$779$	5.69816e9	0.431870
$780$	6.51723e8	0.0491736
$781$	4.28731e8	0.0322038
$782$	2.04697e9	0.153070
$783$	−3.11174e9	−0.231652
$784$	4.81890e8	0.0357143
$785$	1.51910e10	1.12084
$786$	−5.10719e9	−0.375149
$787$	6.64380e8	0.0485853	0.0242927	−	0.999705i	$-0.492267\pi$
$787$	6.64380e8	0.0485853	0.0242927	+	0.999705i	$0.492267\pi$
$788$	8.97923e8	0.0653728
$789$	1.73966e9	0.126094
$790$	−4.37193e9	−0.315485
$791$	4.45051e9	0.319736
$792$	−6.32335e8	−0.0452282
$793$	−4.90022e9	−0.348947
$794$	1.77858e10	1.26096
$795$	7.06213e9	0.498484
$796$	−1.22889e9	−0.0863607
$797$	−9.65249e9	−0.675360	−0.337680	−	0.941261i	$-0.609642\pi$
$797$	−9.65249e9	−0.675360	−0.337680	+	0.941261i	$0.609642\pi$
$798$	−7.77532e8	−0.0541637
$799$	3.05757e9	0.212062
$800$	1.59433e9	0.110094
$801$	−1.87349e9	−0.128807
$802$	−2.20956e9	−0.151250
$803$	3.03582e9	0.206905
$804$	2.94851e9	0.200081
$805$	−7.18354e8	−0.0485347
$806$	−3.94242e9	−0.265210
$807$	8.68900e9	0.581986
$808$	−8.89208e9	−0.593012
$809$	−1.73819e10	−1.15419	−0.577096	−	0.816677i	$-0.695814\pi$
$809$	−1.73819e10	−1.15419	−0.577096	+	0.816677i	$0.695814\pi$
$810$	−7.29851e8	−0.0482544
$811$	3.30117e9	0.217317	0.108659	−	0.994079i	$-0.465344\pi$
$811$	3.30117e9	0.217317	0.108659	+	0.994079i	$0.465344\pi$
$812$	−3.47045e9	−0.227478
$813$	−1.20397e10	−0.785773
$814$	2.55834e9	0.166255
$815$	7.29391e9	0.471964
$816$	2.31948e9	0.149443
$817$	8.27341e9	0.530771
$818$	−7.74603e9	−0.494815
$819$	5.49353e8	0.0349428
$820$	5.96531e9	0.377820
$821$	−4.06886e9	−0.256609	−0.128304	−	0.991735i	$-0.540953\pi$
$821$	−4.06886e9	−0.256609	−0.128304	+	0.991735i	$0.540953\pi$
$822$	1.02541e10	0.643939
$823$	9.79157e9	0.612284	0.306142	−	0.951986i	$-0.400962\pi$
$823$	9.79157e9	0.612284	0.306142	+	0.951986i	$0.400962\pi$
$824$	9.61227e9	0.598523
$825$	2.22557e9	0.137992
$826$	−1.93084e9	−0.119211
$827$	−2.22006e10	−1.36489	−0.682443	−	0.730939i	$-0.739082\pi$
$827$	−2.22006e10	−1.36489	−0.682443	+	0.730939i	$0.739082\pi$
$828$	5.69197e8	0.0348463
$829$	−2.57752e10	−1.57131	−0.785654	−	0.618667i	$-0.787673\pi$
$829$	−2.57752e10	−1.57131	−0.785654	+	0.618667i	$0.787673\pi$
$830$	−8.34110e9	−0.506349
$831$	−1.06267e10	−0.642384
$832$	−5.75930e8	−0.0346688
$833$	−2.46749e9	−0.147910
$834$	5.65841e9	0.337764
$835$	6.36278e9	0.378220
$836$	1.13789e9	0.0673563
$837$	4.41504e9	0.260253
$838$	−1.29687e10	−0.761279
$839$	2.54748e10	1.48917	0.744585	−	0.667528i	$-0.232647\pi$
$839$	2.54748e10	1.48917	0.744585	+	0.667528i	$0.232647\pi$
$840$	−8.13986e8	−0.0473849
$841$	7.74337e9	0.448894
$842$	−1.59296e10	−0.919631
$843$	−6.25370e9	−0.359534
$844$	1.34695e10	0.771174
$845$	8.28609e8	0.0472445
$846$	8.50209e8	0.0482758
$847$	5.69965e9	0.322297
$848$	−6.24084e9	−0.351445
$849$	−7.96197e9	−0.446523
$850$	−8.16368e9	−0.455953
$851$	−2.30289e9	−0.128091
$852$	−4.37300e8	−0.0242237
$853$	−1.64039e10	−0.904952	−0.452476	−	0.891777i	$-0.649459\pi$
$853$	−1.64039e10	−0.904952	−0.452476	+	0.891777i	$0.649459\pi$
$854$	6.12026e9	0.336254
$855$	1.31337e9	0.0718631
$856$	5.43393e9	0.296112
$857$	−2.51635e9	−0.136565	−0.0682824	−	0.997666i	$-0.521752\pi$
$857$	−2.51635e9	−0.136565	−0.0682824	+	0.997666i	$0.521752\pi$
$858$	−8.03959e8	−0.0434539
$859$	−5.14244e7	−0.00276817	−0.00138409	−	0.999999i	$-0.500441\pi$
$859$	−5.14244e7	−0.00276817	−0.00138409	+	0.999999i	$0.500441\pi$
$860$	8.66130e9	0.464343
$861$	5.02831e9	0.268479
$862$	1.81348e10	0.964355
$863$	3.01957e10	1.59922	0.799608	−	0.600522i	$-0.205041\pi$
$863$	3.01957e10	1.59922	0.799608	+	0.600522i	$0.205041\pi$
$864$	6.44973e8	0.0340207
$865$	−7.31274e9	−0.384170
$866$	−7.33465e9	−0.383766
$867$	−7.97650e8	−0.0415667
$868$	4.92399e9	0.255563
$869$	5.39317e9	0.278789
$870$	5.86212e9	0.301812
$871$	3.74877e9	0.192232
$872$	3.68007e9	0.187953
$873$	−9.40633e9	−0.478487
$874$	−1.02427e9	−0.0518950
$875$	7.46508e9	0.376709
$876$	−3.09649e9	−0.155634
$877$	−1.36203e10	−0.681847	−0.340924	−	0.940091i	$-0.610740\pi$
$877$	−1.36203e10	−0.681847	−0.340924	+	0.940091i	$0.610740\pi$
$878$	−2.65507e10	−1.32387
$879$	−4.01767e9	−0.199532
$880$	1.19124e9	0.0589264
$881$	−2.02201e9	−0.0996249	−0.0498125	−	0.998759i	$-0.515862\pi$
$881$	−2.02201e9	−0.0996249	−0.0498125	+	0.998759i	$0.515862\pi$
$882$	−6.86129e8	−0.0336718
$883$	1.31759e10	0.644047	0.322023	−	0.946732i	$-0.395637\pi$
$883$	1.31759e10	0.644047	0.322023	+	0.946732i	$0.395637\pi$
$884$	2.94902e9	0.143580
$885$	3.26149e9	0.158167
$886$	1.88273e9	0.0909430
$887$	3.47315e10	1.67105	0.835527	−	0.549449i	$-0.185162\pi$
$887$	3.47315e10	1.67105	0.835527	+	0.549449i	$0.185162\pi$
$888$	−2.60947e9	−0.125057
$889$	9.50115e9	0.453545
$890$	3.52943e9	0.167818
$891$	9.00337e8	0.0426416
$892$	7.83884e9	0.369806
$893$	−1.52995e9	−0.0718950
$894$	−3.40077e9	−0.159183
$895$	−2.13037e10	−0.993285
$896$	7.19323e8	0.0334077
$897$	7.23683e8	0.0334792
$898$	5.12120e9	0.235996
$899$	−3.54613e10	−1.62778
$900$	−2.27005e9	−0.103798
$901$	3.19559e10	1.45551
$902$	−7.35875e9	−0.333873
$903$	7.30082e9	0.329963
$904$	6.64333e9	0.299086
$905$	1.84826e10	0.828884
$906$	−1.13287e10	−0.506093
$907$	4.03558e10	1.79589	0.897946	−	0.440106i	$-0.145059\pi$
$907$	4.03558e10	1.79589	0.897946	+	0.440106i	$0.145059\pi$
$908$	1.49899e10	0.664506
$909$	1.26608e10	0.559097
$910$	−1.03491e9	−0.0455259
$911$	−3.47148e10	−1.52125	−0.760625	−	0.649192i	$-0.775107\pi$
$911$	−3.47148e10	−1.52125	−0.760625	+	0.649192i	$0.775107\pi$
$912$	−1.16063e9	−0.0506655
$913$	1.02895e10	0.447452
$914$	2.02865e10	0.878813
$915$	−1.03381e10	−0.446133
$916$	1.49371e9	0.0642146
$917$	8.11003e9	0.347320
$918$	−3.30255e9	−0.140896
$919$	−2.00429e10	−0.851837	−0.425918	−	0.904762i	$-0.640049\pi$
$919$	−2.00429e10	−0.851837	−0.425918	+	0.904762i	$0.640049\pi$
$920$	−1.07229e9	−0.0454001
$921$	−1.84668e10	−0.778901
$922$	−8.19002e9	−0.344133
$923$	−5.55988e8	−0.0232734
$924$	1.00413e9	0.0418732
$925$	9.18433e9	0.381550
$926$	−2.99410e9	−0.123916
$927$	−1.36862e10	−0.564292
$928$	−5.18038e9	−0.212786
$929$	−3.48271e10	−1.42516	−0.712578	−	0.701593i	$-0.752472\pi$
$929$	−3.48271e10	−1.42516	−0.712578	+	0.701593i	$0.752472\pi$
$930$	−8.31738e9	−0.339075
$931$	1.23469e9	0.0501458
$932$	−5.84526e9	−0.236509
$933$	−7.68785e9	−0.309898
$934$	−1.46265e10	−0.587391
$935$	−6.09968e9	−0.244043
$936$	8.20026e8	0.0326860
$937$	3.21486e10	1.27666	0.638328	−	0.769764i	$-0.279626\pi$
$937$	3.21486e10	1.27666	0.638328	+	0.769764i	$0.279626\pi$
$938$	−4.68213e9	−0.185239
$939$	−1.75000e10	−0.689776
$940$	−1.60169e9	−0.0628970
$941$	2.29993e10	0.899809	0.449905	−	0.893077i	$-0.351458\pi$
$941$	2.29993e10	0.899809	0.449905	+	0.893077i	$0.351458\pi$
$942$	1.91139e10	0.745027
$943$	6.62398e9	0.257234
$944$	−2.88219e9	−0.111512
$945$	1.15898e9	0.0446749
$946$	−1.06845e10	−0.410332
$947$	2.31237e10	0.884773	0.442387	−	0.896824i	$-0.354132\pi$
$947$	2.31237e10	0.884773	0.442387	+	0.896824i	$0.354132\pi$
$948$	−5.50096e9	−0.209705
$949$	−3.93691e9	−0.149528
$950$	4.08497e9	0.154581
$951$	−2.64175e10	−0.996003
$952$	−3.68326e9	−0.138357
$953$	1.18708e10	0.444278	0.222139	−	0.975015i	$-0.428696\pi$
$953$	1.18708e10	0.444278	0.222139	+	0.975015i	$0.428696\pi$
$954$	8.88588e9	0.331345
$955$	2.78011e10	1.03288
$956$	1.06352e10	0.393678
$957$	−7.23145e9	−0.266706
$958$	−2.86443e10	−1.05259
$959$	−1.62831e10	−0.596172
$960$	−1.21505e9	−0.0443245
$961$	2.28011e10	0.828752
$962$	−3.31771e9	−0.120151
$963$	−7.73698e9	−0.279177
$964$	−4.71629e9	−0.169563
$965$	1.02899e10	0.368610
$966$	−9.03863e8	−0.0322614
$967$	1.48625e10	0.528567	0.264283	−	0.964445i	$-0.414865\pi$
$967$	1.48625e10	0.528567	0.264283	+	0.964445i	$0.414865\pi$
$968$	8.50793e9	0.301481
$969$	5.94295e9	0.209831
$970$	1.77203e10	0.623406
$971$	2.35412e10	0.825204	0.412602	−	0.910912i	$-0.364620\pi$
$971$	2.35412e10	0.825204	0.412602	+	0.910912i	$0.364620\pi$
$972$	−9.18330e8	−0.0320750
$973$	−8.98534e9	−0.312708
$974$	1.08438e10	0.376034
$975$	−2.88617e9	−0.0997255
$976$	9.13578e9	0.314537
$977$	−1.24156e10	−0.425930	−0.212965	−	0.977060i	$-0.568312\pi$
$977$	−1.24156e10	−0.425930	−0.212965	+	0.977060i	$0.568312\pi$
$978$	9.17751e9	0.313718
$979$	−4.35386e9	−0.148298
$980$	1.29258e9	0.0438699
$981$	−5.23978e9	−0.177203
$982$	6.24346e8	0.0210395
$983$	1.76047e10	0.591140	0.295570	−	0.955321i	$-0.404490\pi$
$983$	1.76047e10	0.591140	0.295570	+	0.955321i	$0.404490\pi$
$984$	7.50581e9	0.251139
$985$	2.40851e9	0.0803011
$986$	2.65258e10	0.881251
$987$	−1.35010e9	−0.0446947
$988$	−1.47564e9	−0.0486778
$989$	9.61765e9	0.316142
$990$	−1.69612e9	−0.0555563
$991$	−2.24252e10	−0.731945	−0.365972	−	0.930626i	$-0.619264\pi$
$991$	−2.24252e10	−0.731945	−0.365972	+	0.930626i	$0.619264\pi$
$992$	7.35010e9	0.239058
$993$	−1.69619e10	−0.549732
$994$	6.94416e8	0.0224268
$995$	−3.29626e9	−0.106082
$996$	−1.04951e10	−0.336574
$997$	−5.23515e10	−1.67300	−0.836500	−	0.547967i	$-0.815402\pi$
$997$	−5.23515e10	−1.67300	−0.836500	+	0.547967i	$0.815402\pi$
$998$	−2.14257e9	−0.0682305
$999$	3.71544e9	0.117905

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.o.1.4	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +171.668 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +171.668 q^{5} +216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} -1373.34 q^{10} +1694.14 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -4635.04 q^{15} +4096.00 q^{16} -20973.3 q^{17} -5832.00 q^{18} +10494.7 q^{19} +10986.8 q^{20} +9261.00 q^{21} -13553.1 q^{22} +12199.9 q^{23} +13824.0 q^{24} -48655.1 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} +158093. q^{29} +37080.3 q^{30} -224307. q^{31} -32768.0 q^{32} -45741.9 q^{33} +167787. q^{34} -58882.1 q^{35} +46656.0 q^{36} -188764. q^{37} -83957.7 q^{38} +59319.0 q^{39} -87894.0 q^{40} +542955. q^{41} -74088.0 q^{42} +788341. q^{43} +108425. q^{44} +125146. q^{45} -97598.9 q^{46} -145783. q^{47} -110592. q^{48} +117649. q^{49} +389241. q^{50} +566280. q^{51} -140608. q^{52} -1.52364e6 q^{53} +157464. q^{54} +290830. q^{55} +175616. q^{56} -283357. q^{57} -1.26474e6 q^{58} -703660. q^{59} -296642. q^{60} +2.23041e6 q^{61} +1.79446e6 q^{62} -250047. q^{63} +262144. q^{64} -377155. q^{65} +365935. q^{66} -1.70631e6 q^{67} -1.34229e6 q^{68} -329396. q^{69} +471057. q^{70} +253067. q^{71} -373248. q^{72} +1.79195e6 q^{73} +1.51011e6 q^{74} +1.31369e6 q^{75} +671662. q^{76} -581091. q^{77} -474552. q^{78} +3.18342e6 q^{79} +703152. q^{80} +531441. q^{81} -4.34364e6 q^{82} +6.07357e6 q^{83} +592704. q^{84} -3.60045e6 q^{85} -6.30673e6 q^{86} -4.26850e6 q^{87} -867401. q^{88} -2.56995e6 q^{89} -1.00117e6 q^{90} +753571. q^{91} +780791. q^{92} +6.05630e6 q^{93} +1.16627e6 q^{94} +1.80161e6 q^{95} +884736. q^{96} -1.29031e7 q^{97} -941192. q^{98} +1.23503e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 35 q^{5} + 1296 q^{6} - 2058 q^{7} - 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 35 * q^5 + 1296 * q^6 - 2058 * q^7 - 3072 * q^8 + 4374 * q^9	\( 6 q - 48 q^{2} - 162 q^{3} + 384 q^{4} - 35 q^{5} + 1296 q^{6} - 2058 q^{7} - 3072 q^{8} + 4374 q^{9} + 280 q^{10} + 5606 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} + 945 q^{15} + 24576 q^{16} + 22022 q^{17} - 34992 q^{18} - 5779 q^{19} - 2240 q^{20} + 55566 q^{21} - 44848 q^{22} - 110789 q^{23} + 82944 q^{24} + 91769 q^{25} + 105456 q^{26} - 118098 q^{27} - 131712 q^{28} + 30693 q^{29} - 7560 q^{30} + 180467 q^{31} - 196608 q^{32} - 151362 q^{33} - 176176 q^{34} + 12005 q^{35} + 279936 q^{36} - 322222 q^{37} + 46232 q^{38} + 355914 q^{39} + 17920 q^{40} - 212652 q^{41} - 444528 q^{42} - 329299 q^{43} + 358784 q^{44} - 25515 q^{45} + 886312 q^{46} + 1322861 q^{47} - 663552 q^{48} + 705894 q^{49} - 734152 q^{50} - 594594 q^{51} - 843648 q^{52} - 168719 q^{53} + 944784 q^{54} - 2252362 q^{55} + 1053696 q^{56} + 156033 q^{57} - 245544 q^{58} + 1943712 q^{59} + 60480 q^{60} - 1085922 q^{61} - 1443736 q^{62} - 1500282 q^{63} + 1572864 q^{64} + 76895 q^{65} + 1210896 q^{66} + 885066 q^{67} + 1409408 q^{68} + 2991303 q^{69} - 96040 q^{70} + 1626164 q^{71} - 2239488 q^{72} - 4750115 q^{73} + 2577776 q^{74} - 2477763 q^{75} - 369856 q^{76} - 1922858 q^{77} - 2847312 q^{78} + 1794289 q^{79} - 143360 q^{80} + 3188646 q^{81} + 1701216 q^{82} - 8454255 q^{83} + 3556224 q^{84} - 18529504 q^{85} + 2634392 q^{86} - 828711 q^{87} - 2870272 q^{88} - 6055411 q^{89} + 204120 q^{90} + 4521426 q^{91} - 7090496 q^{92} - 4872609 q^{93} - 10582888 q^{94} - 3766747 q^{95} + 5308416 q^{96} - 9823899 q^{97} - 5647152 q^{98} + 4086774 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 - 162 * q^3 + 384 * q^4 - 35 * q^5 + 1296 * q^6 - 2058 * q^7 - 3072 * q^8 + 4374 * q^9 + 280 * q^10 + 5606 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 + 945 * q^15 + 24576 * q^16 + 22022 * q^17 - 34992 * q^18 - 5779 * q^19 - 2240 * q^20 + 55566 * q^21 - 44848 * q^22 - 110789 * q^23 + 82944 * q^24 + 91769 * q^25 + 105456 * q^26 - 118098 * q^27 - 131712 * q^28 + 30693 * q^29 - 7560 * q^30 + 180467 * q^31 - 196608 * q^32 - 151362 * q^33 - 176176 * q^34 + 12005 * q^35 + 279936 * q^36 - 322222 * q^37 + 46232 * q^38 + 355914 * q^39 + 17920 * q^40 - 212652 * q^41 - 444528 * q^42 - 329299 * q^43 + 358784 * q^44 - 25515 * q^45 + 886312 * q^46 + 1322861 * q^47 - 663552 * q^48 + 705894 * q^49 - 734152 * q^50 - 594594 * q^51 - 843648 * q^52 - 168719 * q^53 + 944784 * q^54 - 2252362 * q^55 + 1053696 * q^56 + 156033 * q^57 - 245544 * q^58 + 1943712 * q^59 + 60480 * q^60 - 1085922 * q^61 - 1443736 * q^62 - 1500282 * q^63 + 1572864 * q^64 + 76895 * q^65 + 1210896 * q^66 + 885066 * q^67 + 1409408 * q^68 + 2991303 * q^69 - 96040 * q^70 + 1626164 * q^71 - 2239488 * q^72 - 4750115 * q^73 + 2577776 * q^74 - 2477763 * q^75 - 369856 * q^76 - 1922858 * q^77 - 2847312 * q^78 + 1794289 * q^79 - 143360 * q^80 + 3188646 * q^81 + 1701216 * q^82 - 8454255 * q^83 + 3556224 * q^84 - 18529504 * q^85 + 2634392 * q^86 - 828711 * q^87 - 2870272 * q^88 - 6055411 * q^89 + 204120 * q^90 + 4521426 * q^91 - 7090496 * q^92 - 4872609 * q^93 - 10582888 * q^94 - 3766747 * q^95 + 5308416 * q^96 - 9823899 * q^97 - 5647152 * q^98 + 4086774 * q^99

Introduction

L-functions

Modular forms

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