LMFDB - Embedded newform 546.8.a.s.1.3

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2 x^{6} - 313738 x^{5} + 10691268 x^{4} + 29687523333 x^{3} - 2032748091218 x^{2} + \cdots + 81\!\cdots\!96 $ x^7 - 2x^6 - 313738x^5 + 10691268x^4 + 29687523333x^3 - 2032748091218x^2 - 846237116901940x + 81946324586652296
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{6}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-235.941$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -146.941 q^{5} +216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -146.941 q^{5} +216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -1175.53 q^{10} -860.123 q^{11} +1728.00 q^{12} +2197.00 q^{13} +2744.00 q^{14} -3967.41 q^{15} +4096.00 q^{16} -6993.73 q^{17} +5832.00 q^{18} +1292.75 q^{19} -9404.24 q^{20} +9261.00 q^{21} -6880.99 q^{22} +64599.6 q^{23} +13824.0 q^{24} -56533.3 q^{25} +17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} -43549.7 q^{29} -31739.3 q^{30} +144074. q^{31} +32768.0 q^{32} -23223.3 q^{33} -55949.8 q^{34} -50400.8 q^{35} +46656.0 q^{36} +193704. q^{37} +10342.0 q^{38} +59319.0 q^{39} -75233.9 q^{40} +24308.3 q^{41} +74088.0 q^{42} +81716.9 q^{43} -55047.9 q^{44} -107120. q^{45} +516797. q^{46} +1.04890e6 q^{47} +110592. q^{48} +117649. q^{49} -452266. q^{50} -188831. q^{51} +140608. q^{52} -1.17808e6 q^{53} +157464. q^{54} +126388. q^{55} +175616. q^{56} +34904.1 q^{57} -348398. q^{58} +793618. q^{59} -253914. q^{60} +933838. q^{61} +1.15260e6 q^{62} +250047. q^{63} +262144. q^{64} -322830. q^{65} -185787. q^{66} -2.55872e6 q^{67} -447599. q^{68} +1.74419e6 q^{69} -403207. q^{70} +5.60813e6 q^{71} +373248. q^{72} -3.30544e6 q^{73} +1.54963e6 q^{74} -1.52640e6 q^{75} +82735.7 q^{76} -295022. q^{77} +474552. q^{78} +8.17331e6 q^{79} -601871. q^{80} +531441. q^{81} +194467. q^{82} -6.14973e6 q^{83} +592704. q^{84} +1.02767e6 q^{85} +653735. q^{86} -1.17584e6 q^{87} -440383. q^{88} +1.25444e6 q^{89} -856961. q^{90} +753571. q^{91} +4.13437e6 q^{92} +3.89001e6 q^{93} +8.39118e6 q^{94} -189958. q^{95} +884736. q^{96} -1.47204e7 q^{97} +941192. q^{98} -627030. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 56 q^{2} + 189 q^{3} + 448 q^{4} + 625 q^{5} + 1512 q^{6} + 2401 q^{7} + 3584 q^{8} + 5103 q^{9}+O(q^{10}) $ 7 * q + 56 * q^2 + 189 * q^3 + 448 * q^4 + 625 * q^5 + 1512 * q^6 + 2401 * q^7 + 3584 * q^8 + 5103 * q^9	\( 7 q + 56 q^{2} + 189 q^{3} + 448 q^{4} + 625 q^{5} + 1512 q^{6} + 2401 q^{7} + 3584 q^{8} + 5103 q^{9} + 5000 q^{10} + 4678 q^{11} + 12096 q^{12} + 15379 q^{13} + 19208 q^{14} + 16875 q^{15} + 28672 q^{16} + 38552 q^{17} + 40824 q^{18} + 60231 q^{19} + 40000 q^{20} + 64827 q^{21} + 37424 q^{22} + 82047 q^{23} + 96768 q^{24} + 136408 q^{25} + 123032 q^{26} + 137781 q^{27} + 153664 q^{28} + 87523 q^{29} + 135000 q^{30} - 3191 q^{31} + 229376 q^{32} + 126306 q^{33} + 308416 q^{34} + 214375 q^{35} + 326592 q^{36} + 360916 q^{37} + 481848 q^{38} + 415233 q^{39} + 320000 q^{40} + 814350 q^{41} + 518616 q^{42} + 840057 q^{43} + 299392 q^{44} + 455625 q^{45} + 656376 q^{46} + 472723 q^{47} + 774144 q^{48} + 823543 q^{49} + 1091264 q^{50} + 1040904 q^{51} + 984256 q^{52} + 2185687 q^{53} + 1102248 q^{54} + 298354 q^{55} + 1229312 q^{56} + 1626237 q^{57} + 700184 q^{58} + 2046232 q^{59} + 1080000 q^{60} + 2744560 q^{61} - 25528 q^{62} + 1750329 q^{63} + 1835008 q^{64} + 1373125 q^{65} + 1010448 q^{66} + 1960358 q^{67} + 2467328 q^{68} + 2215269 q^{69} + 1715000 q^{70} + 2774656 q^{71} + 2612736 q^{72} + 3696313 q^{73} + 2887328 q^{74} + 3683016 q^{75} + 3854784 q^{76} + 1604554 q^{77} + 3321864 q^{78} + 1532089 q^{79} + 2560000 q^{80} + 3720087 q^{81} + 6514800 q^{82} + 7473863 q^{83} + 4148928 q^{84} - 1656624 q^{85} + 6720456 q^{86} + 2363121 q^{87} + 2395136 q^{88} + 14077309 q^{89} + 3645000 q^{90} + 5274997 q^{91} + 5251008 q^{92} - 86157 q^{93} + 3781784 q^{94} - 1704679 q^{95} + 6193152 q^{96} + 8273673 q^{97} + 6588344 q^{98} + 3410262 q^{99}+O(q^{100}) \) 7 * q + 56 * q^2 + 189 * q^3 + 448 * q^4 + 625 * q^5 + 1512 * q^6 + 2401 * q^7 + 3584 * q^8 + 5103 * q^9 + 5000 * q^10 + 4678 * q^11 + 12096 * q^12 + 15379 * q^13 + 19208 * q^14 + 16875 * q^15 + 28672 * q^16 + 38552 * q^17 + 40824 * q^18 + 60231 * q^19 + 40000 * q^20 + 64827 * q^21 + 37424 * q^22 + 82047 * q^23 + 96768 * q^24 + 136408 * q^25 + 123032 * q^26 + 137781 * q^27 + 153664 * q^28 + 87523 * q^29 + 135000 * q^30 - 3191 * q^31 + 229376 * q^32 + 126306 * q^33 + 308416 * q^34 + 214375 * q^35 + 326592 * q^36 + 360916 * q^37 + 481848 * q^38 + 415233 * q^39 + 320000 * q^40 + 814350 * q^41 + 518616 * q^42 + 840057 * q^43 + 299392 * q^44 + 455625 * q^45 + 656376 * q^46 + 472723 * q^47 + 774144 * q^48 + 823543 * q^49 + 1091264 * q^50 + 1040904 * q^51 + 984256 * q^52 + 2185687 * q^53 + 1102248 * q^54 + 298354 * q^55 + 1229312 * q^56 + 1626237 * q^57 + 700184 * q^58 + 2046232 * q^59 + 1080000 * q^60 + 2744560 * q^61 - 25528 * q^62 + 1750329 * q^63 + 1835008 * q^64 + 1373125 * q^65 + 1010448 * q^66 + 1960358 * q^67 + 2467328 * q^68 + 2215269 * q^69 + 1715000 * q^70 + 2774656 * q^71 + 2612736 * q^72 + 3696313 * q^73 + 2887328 * q^74 + 3683016 * q^75 + 3854784 * q^76 + 1604554 * q^77 + 3321864 * q^78 + 1532089 * q^79 + 2560000 * q^80 + 3720087 * q^81 + 6514800 * q^82 + 7473863 * q^83 + 4148928 * q^84 - 1656624 * q^85 + 6720456 * q^86 + 2363121 * q^87 + 2395136 * q^88 + 14077309 * q^89 + 3645000 * q^90 + 5274997 * q^91 + 5251008 * q^92 - 86157 * q^93 + 3781784 * q^94 - 1704679 * q^95 + 6193152 * q^96 + 8273673 * q^97 + 6588344 * q^98 + 3410262 * 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
$5$	−146.941	−0.525713	−0.262856	−	0.964835i	$-0.584665\pi$
$5$	−146.941	−0.525713	−0.262856	+	0.964835i	$0.584665\pi$
$6$	216.000	0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−1175.53	−0.371735
$11$	−860.123	−0.194844	−0.0974218	−	0.995243i	$-0.531060\pi$
$11$	−860.123	−0.194844	−0.0974218	+	0.995243i	$0.531060\pi$
$12$	1728.00	0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	2744.00	0.267261
$15$	−3967.41	−0.303520
$16$	4096.00	0.250000
$17$	−6993.73	−0.345253	−0.172627	−	0.984987i	$-0.555225\pi$
$17$	−6993.73	−0.345253	−0.172627	+	0.984987i	$0.555225\pi$
$18$	5832.00	0.235702
$19$	1292.75	0.0432390	0.0216195	−	0.999766i	$-0.493118\pi$
$19$	1292.75	0.0432390	0.0216195	+	0.999766i	$0.493118\pi$
$20$	−9404.24	−0.262856
$21$	9261.00	0.218218
$22$	−6880.99	−0.137775
$23$	64599.6	1.10709	0.553544	−	0.832820i	$-0.313275\pi$
$23$	64599.6	1.10709	0.553544	+	0.832820i	$0.313275\pi$
$24$	13824.0	0.204124
$25$	−56533.3	−0.723626
$26$	17576.0	0.196116
$27$	19683.0	0.192450
$28$	21952.0	0.188982
$29$	−43549.7	−0.331583	−0.165791	−	0.986161i	$-0.553018\pi$
$29$	−43549.7	−0.331583	−0.165791	+	0.986161i	$0.553018\pi$
$30$	−31739.3	−0.214621
$31$	144074.	0.868602	0.434301	−	0.900768i	$-0.356995\pi$
$31$	144074.	0.868602	0.434301	+	0.900768i	$0.356995\pi$
$32$	32768.0	0.176777
$33$	−23223.3	−0.112493
$34$	−55949.8	−0.244131
$35$	−50400.8	−0.198701
$36$	46656.0	0.166667
$37$	193704.	0.628684	0.314342	−	0.949310i	$-0.398216\pi$
$37$	193704.	0.628684	0.314342	+	0.949310i	$0.398216\pi$
$38$	10342.0	0.0305746
$39$	59319.0	0.160128
$40$	−75233.9	−0.185868
$41$	24308.3	0.0550822	0.0275411	−	0.999621i	$-0.491232\pi$
$41$	24308.3	0.0550822	0.0275411	+	0.999621i	$0.491232\pi$
$42$	74088.0	0.154303
$43$	81716.9	0.156737	0.0783686	−	0.996924i	$-0.475029\pi$
$43$	81716.9	0.156737	0.0783686	+	0.996924i	$0.475029\pi$
$44$	−55047.9	−0.0974218
$45$	−107120.	−0.175238
$46$	516797.	0.782830
$47$	1.04890e6	1.47364	0.736818	−	0.676091i	$-0.236327\pi$
$47$	1.04890e6	1.47364	0.736818	+	0.676091i	$0.236327\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	−452266.	−0.511681
$51$	−188831.	−0.199332
$52$	140608.	0.138675
$53$	−1.17808e6	−1.08695	−0.543474	−	0.839426i	$-0.682891\pi$
$53$	−1.17808e6	−1.08695	−0.543474	+	0.839426i	$0.682891\pi$
$54$	157464.	0.136083
$55$	126388.	0.102432
$56$	175616.	0.133631
$57$	34904.1	0.0249640
$58$	−348398.	−0.234465
$59$	793618.	0.503071	0.251536	−	0.967848i	$-0.419064\pi$
$59$	793618.	0.503071	0.251536	+	0.967848i	$0.419064\pi$
$60$	−253914.	−0.151760
$61$	933838.	0.526765	0.263383	−	0.964691i	$-0.415162\pi$
$61$	933838.	0.526765	0.263383	+	0.964691i	$0.415162\pi$
$62$	1.15260e6	0.614195
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	−322830.	−0.145807
$66$	−185787.	−0.0795446
$67$	−2.55872e6	−1.03935	−0.519674	−	0.854364i	$-0.673947\pi$
$67$	−2.55872e6	−1.03935	−0.519674	+	0.854364i	$0.673947\pi$
$68$	−447599.	−0.172627
$69$	1.74419e6	0.639178
$70$	−403207.	−0.140503
$71$	5.60813e6	1.85958	0.929788	−	0.368096i	$-0.119990\pi$
$71$	5.60813e6	1.85958	0.929788	+	0.368096i	$0.119990\pi$
$72$	373248.	0.117851
$73$	−3.30544e6	−0.994487	−0.497243	−	0.867611i	$-0.665654\pi$
$73$	−3.30544e6	−0.994487	−0.497243	+	0.867611i	$0.665654\pi$
$74$	1.54963e6	0.444546
$75$	−1.52640e6	−0.417786
$76$	82735.7	0.0216195
$77$	−295022.	−0.0736440
$78$	474552.	0.113228
$79$	8.17331e6	1.86511	0.932553	−	0.361034i	$-0.117576\pi$
$79$	8.17331e6	1.86511	0.932553	+	0.361034i	$0.117576\pi$
$80$	−601871.	−0.131428
$81$	531441.	0.111111
$82$	194467.	0.0389490
$83$	−6.14973e6	−1.18055	−0.590273	−	0.807204i	$-0.700980\pi$
$83$	−6.14973e6	−1.18055	−0.590273	+	0.807204i	$0.700980\pi$
$84$	592704.	0.109109
$85$	1.02767e6	0.181504
$86$	653735.	0.110830
$87$	−1.17584e6	−0.191439
$88$	−440383.	−0.0688876
$89$	1.25444e6	0.188618	0.0943091	−	0.995543i	$-0.469936\pi$
$89$	1.25444e6	0.188618	0.0943091	+	0.995543i	$0.469936\pi$
$90$	−856961.	−0.123912
$91$	753571.	0.104828
$92$	4.13437e6	0.553544
$93$	3.89001e6	0.501488
$94$	8.39118e6	1.04202
$95$	−189958.	−0.0227313
$96$	884736.	0.102062
$97$	−1.47204e7	−1.63764	−0.818819	−	0.574052i	$-0.805371\pi$
$97$	−1.47204e7	−1.63764	−0.818819	+	0.574052i	$0.805371\pi$
$98$	941192.	0.101015
$99$	−627030.	−0.0649479
$100$	−3.61813e6	−0.361813
$101$	1.39541e7	1.34765	0.673827	−	0.738889i	$-0.264649\pi$
$101$	1.39541e7	1.34765	0.673827	+	0.738889i	$0.264649\pi$
$102$	−1.51065e6	−0.140949
$103$	1.28933e7	1.16261	0.581305	−	0.813686i	$-0.302542\pi$
$103$	1.28933e7	1.16261	0.581305	+	0.813686i	$0.302542\pi$
$104$	1.12486e6	0.0980581
$105$	−1.36082e6	−0.114720
$106$	−9.42463e6	−0.768588
$107$	4.77623e6	0.376914	0.188457	−	0.982081i	$-0.439651\pi$
$107$	4.77623e6	0.376914	0.188457	+	0.982081i	$0.439651\pi$
$108$	1.25971e6	0.0962250
$109$	2.23191e7	1.65076	0.825379	−	0.564579i	$-0.190961\pi$
$109$	2.23191e7	1.65076	0.825379	+	0.564579i	$0.190961\pi$
$110$	1.01110e6	0.0724302
$111$	5.23000e6	0.362971
$112$	1.40493e6	0.0944911
$113$	−9.14136e6	−0.595986	−0.297993	−	0.954568i	$-0.596317\pi$
$113$	−9.14136e6	−0.595986	−0.297993	+	0.954568i	$0.596317\pi$
$114$	279233.	0.0176522
$115$	−9.49234e6	−0.582011
$116$	−2.78718e6	−0.165791
$117$	1.60161e6	0.0924500
$118$	6.34895e6	0.355725
$119$	−2.39885e6	−0.130493
$120$	−2.03132e6	−0.107311
$121$	−1.87474e7	−0.962036
$122$	7.47070e6	0.372479
$123$	656325.	0.0318017
$124$	9.22076e6	0.434301
$125$	1.97869e7	0.906132
$126$	2.00038e6	0.0890871
$127$	2.97171e7	1.28734	0.643671	−	0.765302i	$-0.277411\pi$
$127$	2.97171e7	1.28734	0.643671	+	0.765302i	$0.277411\pi$
$128$	2.09715e6	0.0883883
$129$	2.20636e6	0.0904923
$130$	−2.58264e6	−0.103101
$131$	3.28866e7	1.27811	0.639056	−	0.769160i	$-0.279325\pi$
$131$	3.28866e7	1.27811	0.639056	+	0.769160i	$0.279325\pi$
$132$	−1.48629e6	−0.0562465
$133$	443412.	0.0163428
$134$	−2.04698e7	−0.734931
$135$	−2.89224e6	−0.101173
$136$	−3.58079e6	−0.122065
$137$	−6.99124e6	−0.232291	−0.116145	−	0.993232i	$-0.537054\pi$
$137$	−6.99124e6	−0.232291	−0.116145	+	0.993232i	$0.537054\pi$
$138$	1.39535e7	0.451967
$139$	4.59875e7	1.45241	0.726203	−	0.687481i	$-0.241283\pi$
$139$	4.59875e7	1.45241	0.726203	+	0.687481i	$0.241283\pi$
$140$	−3.22565e6	−0.0993504
$141$	2.83202e7	0.850804
$142$	4.48650e7	1.31492
$143$	−1.88969e6	−0.0540399
$144$	2.98598e6	0.0833333
$145$	6.39925e6	0.174317
$146$	−2.64435e7	−0.703208
$147$	3.17652e6	0.0824786
$148$	1.23970e7	0.314342
$149$	6.29891e7	1.55996	0.779980	−	0.625805i	$-0.215229\pi$
$149$	6.29891e7	1.55996	0.779980	+	0.625805i	$0.215229\pi$
$150$	−1.22112e7	−0.295419
$151$	−3.86546e6	−0.0913654	−0.0456827	−	0.998956i	$-0.514546\pi$
$151$	−3.86546e6	−0.0913654	−0.0456827	+	0.998956i	$0.514546\pi$
$152$	661886.	0.0152873
$153$	−5.09843e6	−0.115084
$154$	−2.36018e6	−0.0520742
$155$	−2.11705e7	−0.456635
$156$	3.79642e6	0.0800641
$157$	−2.07992e7	−0.428942	−0.214471	−	0.976730i	$-0.568803\pi$
$157$	−2.07992e7	−0.428942	−0.214471	+	0.976730i	$0.568803\pi$
$158$	6.53865e7	1.31883
$159$	−3.18081e7	−0.627549
$160$	−4.81497e6	−0.0929338
$161$	2.21577e7	0.418440
$162$	4.25153e6	0.0785674
$163$	−7.86751e7	−1.42292	−0.711461	−	0.702726i	$-0.751966\pi$
$163$	−7.86751e7	−1.42292	−0.711461	+	0.702726i	$0.751966\pi$
$164$	1.55573e6	0.0275411
$165$	3.41246e6	0.0591390
$166$	−4.91979e7	−0.834772
$167$	−2.41230e7	−0.400796	−0.200398	−	0.979715i	$-0.564224\pi$
$167$	−2.41230e7	−0.400796	−0.200398	+	0.979715i	$0.564224\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	8.22134e6	0.128343
$171$	942411.	0.0144130
$172$	5.22988e6	0.0783686
$173$	1.19101e8	1.74886	0.874431	−	0.485150i	$-0.161235\pi$
$173$	1.19101e8	1.74886	0.874431	+	0.485150i	$0.161235\pi$
$174$	−9.40673e6	−0.135368
$175$	−1.93909e7	−0.273505
$176$	−3.52307e6	−0.0487109
$177$	2.14277e7	0.290448
$178$	1.00355e7	0.133373
$179$	1.18823e8	1.54851	0.774255	−	0.632874i	$-0.218125\pi$
$179$	1.18823e8	1.54851	0.774255	+	0.632874i	$0.218125\pi$
$180$	−6.85569e6	−0.0876188
$181$	−1.42466e8	−1.78582	−0.892909	−	0.450237i	$-0.851340\pi$
$181$	−1.42466e8	−1.78582	−0.892909	+	0.450237i	$0.851340\pi$
$182$	6.02857e6	0.0741249
$183$	2.52136e7	0.304128
$184$	3.30750e7	0.391415
$185$	−2.84631e7	−0.330507
$186$	3.11201e7	0.354605
$187$	6.01547e6	0.0672704
$188$	6.71294e7	0.736818
$189$	6.75127e6	0.0727393
$190$	−1.51966e6	−0.0160734
$191$	−7.40924e7	−0.769409	−0.384704	−	0.923040i	$-0.625697\pi$
$191$	−7.40924e7	−0.769409	−0.384704	+	0.923040i	$0.625697\pi$
$192$	7.07789e6	0.0721688
$193$	−2.35315e7	−0.235613	−0.117807	−	0.993037i	$-0.537586\pi$
$193$	−2.35315e7	−0.235613	−0.117807	+	0.993037i	$0.537586\pi$
$194$	−1.17763e8	−1.15798
$195$	−8.71641e6	−0.0841814
$196$	7.52954e6	0.0714286
$197$	−5.13571e7	−0.478596	−0.239298	−	0.970946i	$-0.576917\pi$
$197$	−5.13571e7	−0.478596	−0.239298	+	0.970946i	$0.576917\pi$
$198$	−5.01624e6	−0.0459251
$199$	−6.16739e7	−0.554774	−0.277387	−	0.960758i	$-0.589468\pi$
$199$	−6.16739e7	−0.554774	−0.277387	+	0.960758i	$0.589468\pi$
$200$	−2.89450e7	−0.255840
$201$	−6.90855e7	−0.600068
$202$	1.11633e8	0.952935
$203$	−1.49375e7	−0.125327
$204$	−1.20852e7	−0.0996660
$205$	−3.57190e6	−0.0289574
$206$	1.03146e8	0.822090
$207$	4.70931e7	0.369029
$208$	8.99891e6	0.0693375
$209$	−1.11192e6	−0.00842484
$210$	−1.08866e7	−0.0811193
$211$	5.25722e7	0.385272	0.192636	−	0.981270i	$-0.438296\pi$
$211$	5.25722e7	0.385272	0.192636	+	0.981270i	$0.438296\pi$
$212$	−7.53970e7	−0.543474
$213$	1.51419e8	1.07363
$214$	3.82098e7	0.266518
$215$	−1.20076e7	−0.0823988
$216$	1.00777e7	0.0680414
$217$	4.94175e7	0.328301
$218$	1.78553e8	1.16726
$219$	−8.92468e7	−0.574167
$220$	8.08880e6	0.0512159
$221$	−1.53652e7	−0.0957560
$222$	4.18400e7	0.256659
$223$	−9.84523e7	−0.594510	−0.297255	−	0.954798i	$-0.596071\pi$
$223$	−9.84523e7	−0.594510	−0.297255	+	0.954798i	$0.596071\pi$
$224$	1.12394e7	0.0668153
$225$	−4.12128e7	−0.241209
$226$	−7.31309e7	−0.421426
$227$	9.82532e7	0.557515	0.278757	−	0.960362i	$-0.410077\pi$
$227$	9.82532e7	0.557515	0.278757	+	0.960362i	$0.410077\pi$
$228$	2.23386e6	0.0124820
$229$	1.15317e8	0.634555	0.317278	−	0.948333i	$-0.397231\pi$
$229$	1.15317e8	0.634555	0.317278	+	0.948333i	$0.397231\pi$
$230$	−7.59387e7	−0.411544
$231$	−7.96560e6	−0.0425184
$232$	−2.22974e7	−0.117232
$233$	3.21868e8	1.66699	0.833493	−	0.552530i	$-0.186338\pi$
$233$	3.21868e8	1.66699	0.833493	+	0.552530i	$0.186338\pi$
$234$	1.28129e7	0.0653720
$235$	−1.54126e8	−0.774710
$236$	5.07916e7	0.251536
$237$	2.20679e8	1.07682
$238$	−1.91908e7	−0.0922728
$239$	−6.98475e7	−0.330947	−0.165473	−	0.986214i	$-0.552915\pi$
$239$	−6.98475e7	−0.330947	−0.165473	+	0.986214i	$0.552915\pi$
$240$	−1.62505e7	−0.0758801
$241$	2.43136e8	1.11890	0.559448	−	0.828865i	$-0.311013\pi$
$241$	2.43136e8	1.11890	0.559448	+	0.828865i	$0.311013\pi$
$242$	−1.49979e8	−0.680262
$243$	1.43489e7	0.0641500
$244$	5.97656e7	0.263383
$245$	−1.72875e7	−0.0751018
$246$	5.25060e6	0.0224872
$247$	2.84016e6	0.0119923
$248$	7.37661e7	0.307097
$249$	−1.66043e8	−0.681589
$250$	1.58295e8	0.640732
$251$	1.11913e7	0.0446706	0.0223353	−	0.999751i	$-0.492890\pi$
$251$	1.11913e7	0.0446706	0.0223353	+	0.999751i	$0.492890\pi$
$252$	1.60030e7	0.0629941
$253$	−5.55636e7	−0.215709
$254$	2.37737e8	0.910288
$255$	2.77470e7	0.104791
$256$	1.67772e7	0.0625000
$257$	−5.16700e8	−1.89877	−0.949385	−	0.314115i	$-0.898292\pi$
$257$	−5.16700e8	−1.89877	−0.949385	+	0.314115i	$0.898292\pi$
$258$	1.76508e7	0.0639877
$259$	6.64404e7	0.237620
$260$	−2.06611e7	−0.0729033
$261$	−3.17477e7	−0.110528
$262$	2.63093e8	0.903762
$263$	2.94522e8	0.998327	0.499164	−	0.866508i	$-0.333641\pi$
$263$	2.94522e8	0.998327	0.499164	+	0.866508i	$0.333641\pi$
$264$	−1.18903e7	−0.0397723
$265$	1.73108e8	0.571422
$266$	3.54729e6	0.0115561
$267$	3.38698e7	0.108899
$268$	−1.63758e8	−0.519674
$269$	−5.63496e8	−1.76505	−0.882527	−	0.470261i	$-0.844160\pi$
$269$	−5.63496e8	−1.76505	−0.882527	+	0.470261i	$0.844160\pi$
$270$	−2.31380e7	−0.0715405
$271$	4.86410e8	1.48460	0.742301	−	0.670067i	$-0.233735\pi$
$271$	4.86410e8	1.48460	0.742301	+	0.670067i	$0.233735\pi$
$272$	−2.86463e7	−0.0863133
$273$	2.03464e7	0.0605228
$274$	−5.59299e7	−0.164254
$275$	4.86256e7	0.140994
$276$	1.11628e8	0.319589
$277$	4.33684e8	1.22601	0.613005	−	0.790079i	$-0.289961\pi$
$277$	4.33684e8	1.22601	0.613005	+	0.790079i	$0.289961\pi$
$278$	3.67900e8	1.02701
$279$	1.05030e8	0.289534
$280$	−2.58052e7	−0.0702513
$281$	6.96558e8	1.87277	0.936387	−	0.350970i	$-0.114148\pi$
$281$	6.96558e8	1.87277	0.936387	+	0.350970i	$0.114148\pi$
$282$	2.26562e8	0.601610
$283$	8.38792e7	0.219989	0.109995	−	0.993932i	$-0.464917\pi$
$283$	8.38792e7	0.219989	0.109995	+	0.993932i	$0.464917\pi$
$284$	3.58920e8	0.929788
$285$	−5.12885e6	−0.0131239
$286$	−1.51175e7	−0.0382120
$287$	8.33776e6	0.0208191
$288$	2.38879e7	0.0589256
$289$	−3.61426e8	−0.880800
$290$	5.11940e7	0.123261
$291$	−3.97450e8	−0.945491
$292$	−2.11548e8	−0.497243
$293$	−5.45402e8	−1.26672	−0.633359	−	0.773858i	$-0.718324\pi$
$293$	−5.45402e8	−1.26672	−0.633359	+	0.773858i	$0.718324\pi$
$294$	2.54122e7	0.0583212
$295$	−1.16615e8	−0.264471
$296$	9.91763e7	0.222273
$297$	−1.69298e7	−0.0374977
$298$	5.03913e8	1.10306
$299$	1.41925e8	0.307051
$300$	−9.76895e7	−0.208893
$301$	2.80289e7	0.0592411
$302$	−3.09237e7	−0.0646051
$303$	3.76762e8	0.778068
$304$	5.29508e6	0.0108097
$305$	−1.37219e8	−0.276927
$306$	−4.07874e7	−0.0813770
$307$	−5.58697e8	−1.10203	−0.551014	−	0.834496i	$-0.685759\pi$
$307$	−5.58697e8	−1.10203	−0.551014	+	0.834496i	$0.685759\pi$
$308$	−1.88814e7	−0.0368220
$309$	3.48119e8	0.671233
$310$	−1.69364e8	−0.322890
$311$	3.29697e8	0.621518	0.310759	−	0.950489i	$-0.399417\pi$
$311$	3.29697e8	0.621518	0.310759	+	0.950489i	$0.399417\pi$
$312$	3.03713e7	0.0566139
$313$	−5.46095e8	−1.00661	−0.503307	−	0.864108i	$-0.667883\pi$
$313$	−5.46095e8	−1.00661	−0.503307	+	0.864108i	$0.667883\pi$
$314$	−1.66394e8	−0.303308
$315$	−3.67422e7	−0.0662336
$316$	5.23092e8	0.932553
$317$	−3.45362e8	−0.608929	−0.304465	−	0.952524i	$-0.598478\pi$
$317$	−3.45362e8	−0.608929	−0.304465	+	0.952524i	$0.598478\pi$
$318$	−2.54465e8	−0.443744
$319$	3.74581e7	0.0646068
$320$	−3.85198e7	−0.0657141
$321$	1.28958e8	0.217611
$322$	1.77261e8	0.295882
$323$	−9.04111e6	−0.0149284
$324$	3.40122e7	0.0555556
$325$	−1.24204e8	−0.200698
$326$	−6.29401e8	−1.00616
$327$	6.02615e8	0.953066
$328$	1.24459e7	0.0194745
$329$	3.59772e8	0.556982
$330$	2.72997e7	0.0418176
$331$	1.17260e9	1.77726	0.888629	−	0.458628i	$-0.151659\pi$
$331$	1.17260e9	1.77726	0.888629	+	0.458628i	$0.151659\pi$
$332$	−3.93583e8	−0.590273
$333$	1.41210e8	0.209561
$334$	−1.92984e8	−0.283406
$335$	3.75982e8	0.546399
$336$	3.79331e7	0.0545545
$337$	−1.06004e9	−1.50875	−0.754374	−	0.656445i	$-0.772059\pi$
$337$	−1.06004e9	−1.50875	−0.754374	+	0.656445i	$0.772059\pi$
$338$	3.86145e7	0.0543928
$339$	−2.46817e8	−0.344093
$340$	6.57707e7	0.0907520
$341$	−1.23922e8	−0.169242
$342$	7.53929e6	0.0101915
$343$	4.03536e7	0.0539949
$344$	4.18390e7	0.0554150
$345$	−2.56293e8	−0.336024
$346$	9.52811e8	1.23663
$347$	1.39251e9	1.78914	0.894570	−	0.446928i	$-0.147482\pi$
$347$	1.39251e9	1.78914	0.894570	+	0.446928i	$0.147482\pi$
$348$	−7.52539e7	−0.0957197
$349$	1.04895e9	1.32089	0.660445	−	0.750874i	$-0.270368\pi$
$349$	1.04895e9	1.32089	0.660445	+	0.750874i	$0.270368\pi$
$350$	−1.55127e8	−0.193397
$351$	4.32436e7	0.0533761
$352$	−2.81845e7	−0.0344438
$353$	2.80613e8	0.339545	0.169772	−	0.985483i	$-0.445697\pi$
$353$	2.80613e8	0.339545	0.169772	+	0.985483i	$0.445697\pi$
$354$	1.71422e8	0.205378
$355$	−8.24065e8	−0.977603
$356$	8.02839e7	0.0943091
$357$	−6.47689e7	−0.0753404
$358$	9.50582e8	1.09496
$359$	−9.49222e8	−1.08277	−0.541386	−	0.840774i	$-0.682100\pi$
$359$	−9.49222e8	−1.08277	−0.541386	+	0.840774i	$0.682100\pi$
$360$	−5.48455e7	−0.0619559
$361$	−8.92201e8	−0.998130
$362$	−1.13973e9	−1.26276
$363$	−5.06179e8	−0.555432
$364$	4.82285e7	0.0524142
$365$	4.85705e8	0.522814
$366$	2.01709e8	0.215051
$367$	1.04101e9	1.09932	0.549661	−	0.835388i	$-0.314757\pi$
$367$	1.04101e9	1.09932	0.549661	+	0.835388i	$0.314757\pi$
$368$	2.64600e8	0.276772
$369$	1.77208e7	0.0183607
$370$	−2.27705e8	−0.233704
$371$	−4.04081e8	−0.410828
$372$	2.48961e8	0.250744
$373$	−2.65062e8	−0.264464	−0.132232	−	0.991219i	$-0.542214\pi$
$373$	−2.65062e8	−0.264464	−0.132232	+	0.991219i	$0.542214\pi$
$374$	4.81238e7	0.0475674
$375$	5.34245e8	0.523156
$376$	5.37035e8	0.521009
$377$	−9.56787e7	−0.0919645
$378$	5.40102e7	0.0514344
$379$	2.10298e9	1.98426	0.992131	−	0.125207i	$-0.0399596\pi$
$379$	2.10298e9	1.98426	0.992131	+	0.125207i	$0.0399596\pi$
$380$	−1.21573e7	−0.0113656
$381$	8.02363e8	0.743247
$382$	−5.92739e8	−0.544054
$383$	8.46404e7	0.0769807	0.0384903	−	0.999259i	$-0.487745\pi$
$383$	8.46404e7	0.0769807	0.0384903	+	0.999259i	$0.487745\pi$
$384$	5.66231e7	0.0510310
$385$	4.33509e7	0.0387156
$386$	−1.88252e8	−0.166604
$387$	5.95716e7	0.0522457
$388$	−9.42104e8	−0.818819
$389$	−6.31353e8	−0.543812	−0.271906	−	0.962324i	$-0.587654\pi$
$389$	−6.31353e8	−0.543812	−0.271906	+	0.962324i	$0.587654\pi$
$390$	−6.97312e7	−0.0595253
$391$	−4.51792e8	−0.382226
$392$	6.02363e7	0.0505076
$393$	8.87938e8	0.737919
$394$	−4.10857e8	−0.338418
$395$	−1.20100e9	−0.980510
$396$	−4.01299e7	−0.0324739
$397$	1.73468e7	0.0139140	0.00695701	−	0.999976i	$-0.497785\pi$
$397$	1.73468e7	0.0139140	0.00695701	+	0.999976i	$0.497785\pi$
$398$	−4.93391e8	−0.392284
$399$	1.19721e7	0.00943552
$400$	−2.31560e8	−0.180906
$401$	−1.19311e9	−0.924005	−0.462002	−	0.886879i	$-0.652869\pi$
$401$	−1.19311e9	−0.924005	−0.462002	+	0.886879i	$0.652869\pi$
$402$	−5.52684e8	−0.424312
$403$	3.16532e8	0.240907
$404$	8.93065e8	0.673827
$405$	−7.80906e7	−0.0584125
$406$	−1.19500e8	−0.0886193
$407$	−1.66609e8	−0.122495
$408$	−9.66813e7	−0.0704745
$409$	−1.78877e9	−1.29278	−0.646389	−	0.763008i	$-0.723722\pi$
$409$	−1.78877e9	−1.29278	−0.646389	+	0.763008i	$0.723722\pi$
$410$	−2.85752e7	−0.0204760
$411$	−1.88763e8	−0.134113
$412$	8.25172e8	0.581305
$413$	2.72211e8	0.190143
$414$	3.76745e8	0.260943
$415$	9.03649e8	0.620628
$416$	7.19913e7	0.0490290
$417$	1.24166e9	0.838547
$418$	−8.89536e6	−0.00595726
$419$	−1.86344e9	−1.23756	−0.618779	−	0.785565i	$-0.712372\pi$
$419$	−1.86344e9	−1.23756	−0.618779	+	0.785565i	$0.712372\pi$
$420$	−8.70926e7	−0.0573600
$421$	5.10202e8	0.333238	0.166619	−	0.986021i	$-0.446715\pi$
$421$	5.10202e8	0.333238	0.166619	+	0.986021i	$0.446715\pi$
$422$	4.20577e8	0.272428
$423$	7.64646e8	0.491212
$424$	−6.03176e8	−0.384294
$425$	3.95379e8	0.249834
$426$	1.21136e9	0.759168
$427$	3.20306e8	0.199099
$428$	3.05679e8	0.188457
$429$	−5.10217e7	−0.0312000
$430$	−9.60606e7	−0.0582647
$431$	−9.26408e8	−0.557355	−0.278678	−	0.960385i	$-0.589896\pi$
$431$	−9.26408e8	−0.557355	−0.278678	+	0.960385i	$0.589896\pi$
$432$	8.06216e7	0.0481125
$433$	1.65223e9	0.978053	0.489026	−	0.872269i	$-0.337352\pi$
$433$	1.65223e9	0.978053	0.489026	+	0.872269i	$0.337352\pi$
$434$	3.95340e8	0.232144
$435$	1.72780e8	0.100642
$436$	1.42842e9	0.825379
$437$	8.35108e7	0.0478694
$438$	−7.13975e8	−0.405998
$439$	−2.60328e9	−1.46857	−0.734287	−	0.678840i	$-0.762483\pi$
$439$	−2.60328e9	−1.46857	−0.734287	+	0.678840i	$0.762483\pi$
$440$	6.47104e7	0.0362151
$441$	8.57661e7	0.0476190
$442$	−1.22922e8	−0.0677097
$443$	−3.24687e9	−1.77440	−0.887199	−	0.461386i	$-0.847352\pi$
$443$	−3.24687e9	−1.77440	−0.887199	+	0.461386i	$0.847352\pi$
$444$	3.34720e8	0.181485
$445$	−1.84328e8	−0.0991590
$446$	−7.87618e8	−0.420382
$447$	1.70071e9	0.900643
$448$	8.99154e7	0.0472456
$449$	−1.82286e8	−0.0950367	−0.0475184	−	0.998870i	$-0.515131\pi$
$449$	−1.82286e8	−0.0950367	−0.0475184	+	0.998870i	$0.515131\pi$
$450$	−3.29702e8	−0.170560
$451$	−2.09082e7	−0.0107324
$452$	−5.85047e8	−0.297993
$453$	−1.04367e8	−0.0527499
$454$	7.86026e8	0.394223
$455$	−1.10731e8	−0.0551097
$456$	1.78709e7	0.00882612
$457$	−3.21006e9	−1.57328	−0.786640	−	0.617412i	$-0.788181\pi$
$457$	−3.21006e9	−1.57328	−0.786640	+	0.617412i	$0.788181\pi$
$458$	9.22536e8	0.448698
$459$	−1.37658e8	−0.0664440
$460$	−6.07510e8	−0.291005
$461$	2.10076e8	0.0998672	0.0499336	−	0.998753i	$-0.484099\pi$
$461$	2.10076e8	0.0998672	0.0499336	+	0.998753i	$0.484099\pi$
$462$	−6.37248e7	−0.0300650
$463$	5.03211e8	0.235622	0.117811	−	0.993036i	$-0.462412\pi$
$463$	5.03211e8	0.235622	0.117811	+	0.993036i	$0.462412\pi$
$464$	−1.78380e8	−0.0828957
$465$	−5.71603e8	−0.263639
$466$	2.57494e9	1.17874
$467$	9.95306e8	0.452218	0.226109	−	0.974102i	$-0.427400\pi$
$467$	9.95306e8	0.452218	0.226109	+	0.974102i	$0.427400\pi$
$468$	1.02503e8	0.0462250
$469$	−8.77642e8	−0.392837
$470$	−1.23301e9	−0.547803
$471$	−5.61579e8	−0.247650
$472$	4.06333e8	0.177863
$473$	−7.02866e7	−0.0305393
$474$	1.76544e9	0.761426
$475$	−7.30831e7	−0.0312888
$476$	−1.53526e8	−0.0652467
$477$	−8.58819e8	−0.362316
$478$	−5.58780e8	−0.234015
$479$	3.50883e9	1.45877	0.729386	−	0.684102i	$-0.239806\pi$
$479$	3.50883e9	1.45877	0.729386	+	0.684102i	$0.239806\pi$
$480$	−1.30004e8	−0.0536553
$481$	4.25567e8	0.174365
$482$	1.94509e9	0.791179
$483$	5.98257e8	0.241586
$484$	−1.19983e9	−0.481018
$485$	2.16303e9	0.860927
$486$	1.14791e8	0.0453609
$487$	6.11421e8	0.239877	0.119939	−	0.992781i	$-0.461730\pi$
$487$	6.11421e8	0.239877	0.119939	+	0.992781i	$0.461730\pi$
$488$	4.78125e8	0.186240
$489$	−2.12423e9	−0.821524
$490$	−1.38300e8	−0.0531050
$491$	4.60032e9	1.75389	0.876945	−	0.480590i	$-0.159578\pi$
$491$	4.60032e9	1.75389	0.876945	+	0.480590i	$0.159578\pi$
$492$	4.20048e7	0.0159009
$493$	3.04575e8	0.114480
$494$	2.27213e7	0.00847986
$495$	9.21365e7	0.0341439
$496$	5.90129e8	0.217151
$497$	1.92359e9	0.702853
$498$	−1.32834e9	−0.481956
$499$	1.96291e8	0.0707211	0.0353605	−	0.999375i	$-0.488742\pi$
$499$	1.96291e8	0.0707211	0.0353605	+	0.999375i	$0.488742\pi$
$500$	1.26636e9	0.453066
$501$	−6.51321e8	−0.231400
$502$	8.95303e7	0.0315869
$503$	5.09592e8	0.178540	0.0892699	−	0.996007i	$-0.471547\pi$
$503$	5.09592e8	0.178540	0.0892699	+	0.996007i	$0.471547\pi$
$504$	1.28024e8	0.0445435
$505$	−2.05044e9	−0.708479
$506$	−4.44509e8	−0.152529
$507$	1.30324e8	0.0444116
$508$	1.90190e9	0.643671
$509$	−4.45556e9	−1.49758	−0.748791	−	0.662806i	$-0.769365\pi$
$509$	−4.45556e9	−1.49758	−0.748791	+	0.662806i	$0.769365\pi$
$510$	2.21976e8	0.0740987
$511$	−1.13377e9	−0.375881
$512$	1.34218e8	0.0441942
$513$	2.54451e7	0.00832134
$514$	−4.13360e9	−1.34263
$515$	−1.89456e9	−0.611199
$516$	1.41207e8	0.0452461
$517$	−9.02181e8	−0.287129
$518$	5.31523e8	0.168023
$519$	3.21574e9	1.00971
$520$	−1.65289e8	−0.0515504
$521$	−3.86999e9	−1.19889	−0.599443	−	0.800418i	$-0.704611\pi$
$521$	−3.86999e9	−1.19889	−0.599443	+	0.800418i	$0.704611\pi$
$522$	−2.53982e8	−0.0781548
$523$	1.64751e9	0.503585	0.251792	−	0.967781i	$-0.418980\pi$
$523$	1.64751e9	0.503585	0.251792	+	0.967781i	$0.418980\pi$
$524$	2.10474e9	0.639056
$525$	−5.23555e8	−0.157908
$526$	2.35618e9	0.705924
$527$	−1.00762e9	−0.299888
$528$	−9.51228e7	−0.0281233
$529$	7.68280e8	0.225645
$530$	1.38487e9	0.404057
$531$	5.78548e8	0.167690
$532$	2.83783e7	0.00817140
$533$	5.34054e7	0.0152771
$534$	2.70958e8	0.0770030
$535$	−7.01825e8	−0.198148
$536$	−1.31007e9	−0.367465
$537$	3.20822e9	0.894033
$538$	−4.50797e9	−1.24808
$539$	−1.01193e8	−0.0278348
$540$	−1.85104e8	−0.0505867
$541$	−2.57675e9	−0.699651	−0.349825	−	0.936815i	$-0.613759\pi$
$541$	−2.57675e9	−0.699651	−0.349825	+	0.936815i	$0.613759\pi$
$542$	3.89128e9	1.04977
$543$	−3.84659e9	−1.03104
$544$	−2.29171e8	−0.0610327
$545$	−3.27959e9	−0.867825
$546$	1.62771e8	0.0427960
$547$	−2.06135e9	−0.538512	−0.269256	−	0.963069i	$-0.586778\pi$
$547$	−2.06135e9	−0.538512	−0.269256	+	0.963069i	$0.586778\pi$
$548$	−4.47439e8	−0.116145
$549$	6.80768e8	0.175588
$550$	3.89005e8	0.0996978
$551$	−5.62987e7	−0.0143373
$552$	8.93025e8	0.225983
$553$	2.80345e9	0.704943
$554$	3.46947e9	0.866920
$555$	−7.68503e8	−0.190818
$556$	2.94320e9	0.726203
$557$	−4.12809e9	−1.01218	−0.506088	−	0.862482i	$-0.668909\pi$
$557$	−4.12809e9	−1.01218	−0.506088	+	0.862482i	$0.668909\pi$
$558$	8.40242e8	0.204732
$559$	1.79532e8	0.0434711
$560$	−2.06442e8	−0.0496752
$561$	1.62418e8	0.0388386
$562$	5.57247e9	1.32425
$563$	−1.55611e9	−0.367502	−0.183751	−	0.982973i	$-0.558824\pi$
$563$	−1.55611e9	−0.367502	−0.183751	+	0.982973i	$0.558824\pi$
$564$	1.81249e9	0.425402
$565$	1.34324e9	0.313318
$566$	6.71034e8	0.155556
$567$	1.82284e8	0.0419961
$568$	2.87136e9	0.657459
$569$	−2.40166e9	−0.546536	−0.273268	−	0.961938i	$-0.588105\pi$
$569$	−2.40166e9	−0.546536	−0.273268	+	0.961938i	$0.588105\pi$
$570$	−4.10308e7	−0.00928001
$571$	−5.12675e9	−1.15243	−0.576216	−	0.817297i	$-0.695471\pi$
$571$	−5.12675e9	−1.15243	−0.576216	+	0.817297i	$0.695471\pi$
$572$	−1.20940e8	−0.0270200
$573$	−2.00050e9	−0.444218
$574$	6.67021e7	0.0147213
$575$	−3.65203e9	−0.801118
$576$	1.91103e8	0.0416667
$577$	−2.62083e9	−0.567968	−0.283984	−	0.958829i	$-0.591656\pi$
$577$	−2.62083e9	−0.567968	−0.283984	+	0.958829i	$0.591656\pi$
$578$	−2.89141e9	−0.622820
$579$	−6.35351e8	−0.136031
$580$	4.09552e8	0.0871587
$581$	−2.10936e9	−0.446205
$582$	−3.17960e9	−0.668563
$583$	1.01329e9	0.211785
$584$	−1.69238e9	−0.351604
$585$	−2.35343e8	−0.0486022
$586$	−4.36322e9	−0.895705
$587$	−1.39647e9	−0.284969	−0.142484	−	0.989797i	$-0.545509\pi$
$587$	−1.39647e9	−0.284969	−0.142484	+	0.989797i	$0.545509\pi$
$588$	2.03297e8	0.0412393
$589$	1.86252e8	0.0375575
$590$	−9.32922e8	−0.187009
$591$	−1.38664e9	−0.276317
$592$	7.93411e8	0.157171
$593$	4.51899e7	0.00889918	0.00444959	−	0.999990i	$-0.498584\pi$
$593$	4.51899e7	0.00889918	0.00444959	+	0.999990i	$0.498584\pi$
$594$	−1.35438e8	−0.0265149
$595$	3.52490e8	0.0686021
$596$	4.03130e9	0.779980
$597$	−1.66520e9	−0.320299
$598$	1.13540e9	0.217118
$599$	5.40320e9	1.02720	0.513602	−	0.858028i	$-0.328311\pi$
$599$	5.40320e9	1.02720	0.513602	+	0.858028i	$0.328311\pi$
$600$	−7.81516e8	−0.147710
$601$	−6.29501e9	−1.18287	−0.591433	−	0.806354i	$-0.701438\pi$
$601$	−6.29501e9	−1.18287	−0.591433	+	0.806354i	$0.701438\pi$
$602$	2.24231e8	0.0418898
$603$	−1.86531e9	−0.346450
$604$	−2.47389e8	−0.0456827
$605$	2.75476e9	0.505755
$606$	3.01409e9	0.550177
$607$	−7.33585e9	−1.33134	−0.665672	−	0.746245i	$-0.731855\pi$
$607$	−7.33585e9	−1.33134	−0.665672	+	0.746245i	$0.731855\pi$
$608$	4.23607e7	0.00764364
$609$	−4.03314e8	−0.0723573
$610$	−1.09775e9	−0.195817
$611$	2.30443e9	0.408713
$612$	−3.26300e8	−0.0575422
$613$	−1.01333e10	−1.77681	−0.888403	−	0.459065i	$-0.848185\pi$
$613$	−1.01333e10	−1.77681	−0.888403	+	0.459065i	$0.848185\pi$
$614$	−4.46958e9	−0.779251
$615$	−9.64412e7	−0.0167186
$616$	−1.51051e8	−0.0260371
$617$	1.01800e10	1.74481	0.872405	−	0.488783i	$-0.162559\pi$
$617$	1.01800e10	1.74481	0.872405	+	0.488783i	$0.162559\pi$
$618$	2.78495e9	0.474634
$619$	5.13939e8	0.0870952	0.0435476	−	0.999051i	$-0.486134\pi$
$619$	5.13939e8	0.0870952	0.0435476	+	0.999051i	$0.486134\pi$
$620$	−1.35491e9	−0.228318
$621$	1.27151e9	0.213059
$622$	2.63758e9	0.439480
$623$	4.30272e8	0.0712910
$624$	2.42971e8	0.0400320
$625$	1.50916e9	0.247261
$626$	−4.36876e9	−0.711784
$627$	−3.00218e7	−0.00486408
$628$	−1.33115e9	−0.214471
$629$	−1.35471e9	−0.217055
$630$	−2.93938e8	−0.0468342
$631$	−6.37569e9	−1.01024	−0.505120	−	0.863049i	$-0.668552\pi$
$631$	−6.37569e9	−1.01024	−0.505120	+	0.863049i	$0.668552\pi$
$632$	4.18474e9	0.659414
$633$	1.41945e9	0.222437
$634$	−2.76289e9	−0.430578
$635$	−4.36667e9	−0.676772
$636$	−2.03572e9	−0.313775
$637$	2.58475e8	0.0396214
$638$	2.99665e8	0.0456839
$639$	4.08833e9	0.619858
$640$	−3.08158e8	−0.0464669
$641$	−8.43237e9	−1.26458	−0.632290	−	0.774732i	$-0.717885\pi$
$641$	−8.43237e9	−1.26458	−0.632290	+	0.774732i	$0.717885\pi$
$642$	1.03167e9	0.153874
$643$	−5.35176e9	−0.793886	−0.396943	−	0.917843i	$-0.629929\pi$
$643$	−5.35176e9	−0.793886	−0.396943	+	0.917843i	$0.629929\pi$
$644$	1.41809e9	0.209220
$645$	−3.24205e8	−0.0475730
$646$	−7.23289e7	−0.0105560
$647$	−7.75566e9	−1.12578	−0.562890	−	0.826532i	$-0.690311\pi$
$647$	−7.75566e9	−1.12578	−0.562890	+	0.826532i	$0.690311\pi$
$648$	2.72098e8	0.0392837
$649$	−6.82610e8	−0.0980203
$650$	−9.93629e8	−0.141915
$651$	1.33427e9	0.189545
$652$	−5.03521e9	−0.711461
$653$	−3.76746e9	−0.529484	−0.264742	−	0.964319i	$-0.585287\pi$
$653$	−3.76746e9	−0.529484	−0.264742	+	0.964319i	$0.585287\pi$
$654$	4.82092e9	0.673919
$655$	−4.83239e9	−0.671920
$656$	9.95669e7	0.0137706
$657$	−2.40966e9	−0.331496
$658$	2.87817e9	0.393846
$659$	−4.66635e9	−0.635153	−0.317577	−	0.948233i	$-0.602869\pi$
$659$	−4.66635e9	−0.635153	−0.317577	+	0.948233i	$0.602869\pi$
$660$	2.18398e8	0.0295695
$661$	−4.36906e9	−0.588415	−0.294207	−	0.955742i	$-0.595056\pi$
$661$	−4.36906e9	−0.588415	−0.294207	+	0.955742i	$0.595056\pi$
$662$	9.38076e9	1.25671
$663$	−4.14861e8	−0.0552848
$664$	−3.14866e9	−0.417386
$665$	−6.51554e7	−0.00859162
$666$	1.12968e9	0.148182
$667$	−2.81329e9	−0.367092
$668$	−1.54387e9	−0.200398
$669$	−2.65821e9	−0.343240
$670$	3.00785e9	0.386362
$671$	−8.03216e8	−0.102637
$672$	3.03464e8	0.0385758
$673$	−1.35735e10	−1.71648	−0.858239	−	0.513250i	$-0.828441\pi$
$673$	−1.35735e10	−1.71648	−0.858239	+	0.513250i	$0.828441\pi$
$674$	−8.48030e9	−1.06685
$675$	−1.11274e9	−0.139262
$676$	3.08916e8	0.0384615
$677$	−9.92852e9	−1.22977	−0.614886	−	0.788616i	$-0.710798\pi$
$677$	−9.92852e9	−1.22977	−0.614886	+	0.788616i	$0.710798\pi$
$678$	−1.97453e9	−0.243310
$679$	−5.04909e9	−0.618969
$680$	5.26166e8	0.0641714
$681$	2.65284e9	0.321881
$682$	−9.91374e8	−0.119672
$683$	5.40081e8	0.0648614	0.0324307	−	0.999474i	$-0.489675\pi$
$683$	5.40081e8	0.0648614	0.0324307	+	0.999474i	$0.489675\pi$
$684$	6.03143e7	0.00720649
$685$	1.02730e9	0.122118
$686$	3.22829e8	0.0381802
$687$	3.11356e9	0.366361
$688$	3.34712e8	0.0391843
$689$	−2.58824e9	−0.301465
$690$	−2.05035e9	−0.237605
$691$	5.06049e9	0.583471	0.291735	−	0.956499i	$-0.405767\pi$
$691$	5.06049e9	0.583471	0.291735	+	0.956499i	$0.405767\pi$
$692$	7.62249e9	0.874431
$693$	−2.15071e8	−0.0245480
$694$	1.11401e10	1.26511
$695$	−6.75746e9	−0.763548
$696$	−6.02031e8	−0.0676841
$697$	−1.70006e8	−0.0190173
$698$	8.39162e9	0.934010
$699$	8.69043e9	0.962434
$700$	−1.24102e9	−0.136752
$701$	7.70944e9	0.845298	0.422649	−	0.906294i	$-0.361100\pi$
$701$	7.70944e9	0.845298	0.422649	+	0.906294i	$0.361100\pi$
$702$	3.45948e8	0.0377426
$703$	2.50410e8	0.0271836
$704$	−2.25476e8	−0.0243555
$705$	−4.16141e9	−0.447279
$706$	2.24491e9	0.240094
$707$	4.78627e9	0.509365
$708$	1.37137e9	0.145224
$709$	−4.13749e9	−0.435989	−0.217994	−	0.975950i	$-0.569951\pi$
$709$	−4.13749e9	−0.435989	−0.217994	+	0.975950i	$0.569951\pi$
$710$	−6.59252e9	−0.691270
$711$	5.95835e9	0.621702
$712$	6.42271e8	0.0666866
$713$	9.30715e9	0.961620
$714$	−5.18152e8	−0.0532737
$715$	2.77674e8	0.0284095
$716$	7.60466e9	0.774255
$717$	−1.88588e9	−0.191072
$718$	−7.59377e9	−0.765636
$719$	1.29208e10	1.29640	0.648199	−	0.761471i	$-0.275522\pi$
$719$	1.29208e10	1.29640	0.648199	+	0.761471i	$0.275522\pi$
$720$	−4.38764e8	−0.0438094
$721$	4.42241e9	0.439425
$722$	−7.13760e9	−0.705785
$723$	6.56468e9	0.645995
$724$	−9.11785e9	−0.892909
$725$	2.46201e9	0.239942
$726$	−4.04943e9	−0.392750
$727$	−1.04841e10	−1.01195	−0.505976	−	0.862547i	$-0.668868\pi$
$727$	−1.04841e10	−1.01195	−0.505976	+	0.862547i	$0.668868\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	3.88564e9	0.369686
$731$	−5.71506e8	−0.0541140
$732$	1.61367e9	0.152064
$733$	−1.74356e10	−1.63520	−0.817602	−	0.575783i	$-0.804697\pi$
$733$	−1.74356e10	−1.63520	−0.817602	+	0.575783i	$0.804697\pi$
$734$	8.32810e9	0.777338
$735$	−4.66762e8	−0.0433601
$736$	2.11680e9	0.195707
$737$	2.20082e9	0.202511
$738$	1.41766e8	0.0129830
$739$	−1.42818e10	−1.30175	−0.650873	−	0.759187i	$-0.725597\pi$
$739$	−1.42818e10	−1.30175	−0.650873	+	0.759187i	$0.725597\pi$
$740$	−1.82164e9	−0.165254
$741$	7.66843e7	0.00692378
$742$	−3.23265e9	−0.290499
$743$	−7.02759e9	−0.628559	−0.314279	−	0.949331i	$-0.601763\pi$
$743$	−7.02759e9	−0.628559	−0.314279	+	0.949331i	$0.601763\pi$
$744$	1.99169e9	0.177303
$745$	−9.25569e9	−0.820091
$746$	−2.12050e9	−0.187005
$747$	−4.48316e9	−0.393515
$748$	3.84990e8	0.0336352
$749$	1.63825e9	0.142460
$750$	4.27396e9	0.369927
$751$	−1.03905e10	−0.895154	−0.447577	−	0.894246i	$-0.647713\pi$
$751$	−1.03905e10	−0.895154	−0.447577	+	0.894246i	$0.647713\pi$
$752$	4.29628e9	0.368409
$753$	3.02165e8	0.0257906
$754$	−7.65429e8	−0.0650288
$755$	5.67995e8	0.0480320
$756$	4.32081e8	0.0363696
$757$	1.89829e10	1.59048	0.795238	−	0.606297i	$-0.207346\pi$
$757$	1.89829e10	1.59048	0.795238	+	0.606297i	$0.207346\pi$
$758$	1.68239e10	1.40308
$759$	−1.50022e9	−0.124540
$760$	−9.72583e7	−0.00803672
$761$	−3.28926e9	−0.270552	−0.135276	−	0.990808i	$-0.543192\pi$
$761$	−3.28926e9	−0.270552	−0.135276	+	0.990808i	$0.543192\pi$
$762$	6.41890e9	0.525555
$763$	7.65544e9	0.623928
$764$	−4.74192e9	−0.384704
$765$	7.49169e8	0.0605013
$766$	6.77123e8	0.0544336
$767$	1.74358e9	0.139527
$768$	4.52985e8	0.0360844
$769$	5.01064e9	0.397329	0.198665	−	0.980068i	$-0.436340\pi$
$769$	5.01064e9	0.397329	0.198665	+	0.980068i	$0.436340\pi$
$770$	3.46808e8	0.0273761
$771$	−1.39509e10	−1.09626
$772$	−1.50602e9	−0.117807
$773$	9.75075e9	0.759294	0.379647	−	0.925131i	$-0.376045\pi$
$773$	9.75075e9	0.759294	0.379647	+	0.925131i	$0.376045\pi$
$774$	4.76573e8	0.0369433
$775$	−8.14500e9	−0.628543
$776$	−7.53683e9	−0.578992
$777$	1.79389e9	0.137190
$778$	−5.05083e9	−0.384533
$779$	3.14245e7	0.00238170
$780$	−5.57850e8	−0.0420907
$781$	−4.82368e9	−0.362327
$782$	−3.61434e9	−0.270274
$783$	−8.57189e8	−0.0638132
$784$	4.81890e8	0.0357143
$785$	3.05626e9	0.225500
$786$	7.10350e9	0.521787
$787$	−9.14727e9	−0.668929	−0.334464	−	0.942408i	$-0.608555\pi$
$787$	−9.14727e9	−0.668929	−0.334464	+	0.942408i	$0.608555\pi$
$788$	−3.28686e9	−0.239298
$789$	7.95210e9	0.576384
$790$	−9.60797e9	−0.693325
$791$	−3.13549e9	−0.225262
$792$	−3.21039e8	−0.0229625
$793$	2.05164e9	0.146098
$794$	1.38774e8	0.00983869
$795$	4.67392e9	0.329911
$796$	−3.94713e9	−0.277387
$797$	−2.59698e10	−1.81704	−0.908520	−	0.417842i	$-0.862787\pi$
$797$	−2.59698e10	−1.81704	−0.908520	+	0.417842i	$0.862787\pi$
$798$	9.57769e7	0.00667192
$799$	−7.33570e9	−0.508778
$800$	−1.85248e9	−0.127920
$801$	9.14484e8	0.0628727
$802$	−9.54486e9	−0.653370
$803$	2.84308e9	0.193769
$804$	−4.42147e9	−0.300034
$805$	−3.25587e9	−0.219979
$806$	2.53225e9	0.170347
$807$	−1.52144e10	−1.01905
$808$	7.14452e9	0.476468
$809$	−1.70238e9	−0.113041	−0.0565207	−	0.998401i	$-0.518001\pi$
$809$	−1.70238e9	−0.113041	−0.0565207	+	0.998401i	$0.518001\pi$
$810$	−6.24725e8	−0.0413039
$811$	7.47713e9	0.492223	0.246112	−	0.969241i	$-0.420847\pi$
$811$	7.47713e9	0.492223	0.246112	+	0.969241i	$0.420847\pi$
$812$	−9.56003e8	−0.0626633
$813$	1.31331e10	0.857135
$814$	−1.33287e9	−0.0866171
$815$	1.15606e10	0.748048
$816$	−7.73451e8	−0.0498330
$817$	1.05639e8	0.00677716
$818$	−1.43102e10	−0.914132
$819$	5.49353e8	0.0349428
$820$	−2.28601e8	−0.0144787
$821$	2.21297e10	1.39564	0.697822	−	0.716271i	$-0.254153\pi$
$821$	2.21297e10	1.39564	0.697822	+	0.716271i	$0.254153\pi$
$822$	−1.51011e9	−0.0948323
$823$	2.42798e10	1.51826	0.759131	−	0.650938i	$-0.225624\pi$
$823$	2.42798e10	1.51826	0.759131	+	0.650938i	$0.225624\pi$
$824$	6.60137e9	0.411045
$825$	1.31289e9	0.0814029
$826$	2.17769e9	0.134451
$827$	1.92778e10	1.18519	0.592594	−	0.805501i	$-0.298104\pi$
$827$	1.92778e10	1.18519	0.592594	+	0.805501i	$0.298104\pi$
$828$	3.01396e9	0.184515
$829$	5.28251e9	0.322032	0.161016	−	0.986952i	$-0.448523\pi$
$829$	5.28251e9	0.322032	0.161016	+	0.986952i	$0.448523\pi$
$830$	7.22920e9	0.438851
$831$	1.17095e10	0.707837
$832$	5.75930e8	0.0346688
$833$	−8.22805e8	−0.0493219
$834$	9.93330e9	0.592942
$835$	3.54466e9	0.210704
$836$	−7.11629e7	−0.00421242
$837$	2.83582e9	0.167163
$838$	−1.49075e10	−0.875086
$839$	1.23531e10	0.722122	0.361061	−	0.932542i	$-0.382415\pi$
$839$	1.23531e10	0.722122	0.361061	+	0.932542i	$0.382415\pi$
$840$	−6.96741e8	−0.0405596
$841$	−1.53533e10	−0.890053
$842$	4.08161e9	0.235635
$843$	1.88071e10	1.08125
$844$	3.36462e9	0.192636
$845$	−7.09257e8	−0.0404395
$846$	6.11717e9	0.347339
$847$	−6.43034e9	−0.363615
$848$	−4.82541e9	−0.271737
$849$	2.26474e9	0.127011
$850$	3.16303e9	0.176659
$851$	1.25132e10	0.696008
$852$	9.69085e9	0.536813
$853$	−1.13110e10	−0.623994	−0.311997	−	0.950083i	$-0.600998\pi$
$853$	−1.13110e10	−0.623994	−0.311997	+	0.950083i	$0.600998\pi$
$854$	2.56245e9	0.140784
$855$	−1.38479e8	−0.00757709
$856$	2.44543e9	0.133259
$857$	2.08230e10	1.13008	0.565042	−	0.825062i	$-0.308860\pi$
$857$	2.08230e10	1.13008	0.565042	+	0.825062i	$0.308860\pi$
$858$	−4.08173e8	−0.0220617
$859$	−2.61381e10	−1.40701	−0.703507	−	0.710688i	$-0.748384\pi$
$859$	−2.61381e10	−1.40701	−0.703507	+	0.710688i	$0.748384\pi$
$860$	−7.68485e8	−0.0411994
$861$	2.25119e8	0.0120199
$862$	−7.41127e9	−0.394110
$863$	−8.01988e9	−0.424747	−0.212373	−	0.977189i	$-0.568119\pi$
$863$	−8.01988e9	−0.424747	−0.212373	+	0.977189i	$0.568119\pi$
$864$	6.44973e8	0.0340207
$865$	−1.75009e10	−0.919399
$866$	1.32178e10	0.691588
$867$	−9.75851e9	−0.508530
$868$	3.16272e9	0.164150
$869$	−7.03006e9	−0.363404
$870$	1.38224e9	0.0711648
$871$	−5.62151e9	−0.288264
$872$	1.14274e10	0.583631
$873$	−1.07312e10	−0.545879
$874$	6.68086e8	0.0338487
$875$	6.78689e9	0.342486
$876$	−5.71180e9	−0.287084
$877$	2.33068e10	1.16677	0.583383	−	0.812198i	$-0.301729\pi$
$877$	2.33068e10	1.16677	0.583383	+	0.812198i	$0.301729\pi$
$878$	−2.08263e10	−1.03844
$879$	−1.47259e10	−0.731340
$880$	5.17684e8	0.0256080
$881$	−2.23918e10	−1.10325	−0.551624	−	0.834093i	$-0.685992\pi$
$881$	−2.23918e10	−1.10325	−0.551624	+	0.834093i	$0.685992\pi$
$882$	6.86129e8	0.0336718
$883$	−9.84908e9	−0.481430	−0.240715	−	0.970596i	$-0.577382\pi$
$883$	−9.84908e9	−0.481430	−0.240715	+	0.970596i	$0.577382\pi$
$884$	−9.83374e8	−0.0478780
$885$	−3.14861e9	−0.152692
$886$	−2.59749e10	−1.25469
$887$	2.27012e10	1.09224	0.546119	−	0.837708i	$-0.316105\pi$
$887$	2.27012e10	1.09224	0.546119	+	0.837708i	$0.316105\pi$
$888$	2.67776e9	0.128329
$889$	1.01930e10	0.486569
$890$	−1.47463e9	−0.0701160
$891$	−4.57105e8	−0.0216493
$892$	−6.30095e9	−0.297255
$893$	1.35596e9	0.0637185
$894$	1.36056e10	0.636851
$895$	−1.74600e10	−0.814072
$896$	7.19323e8	0.0334077
$897$	3.83198e9	0.177276
$898$	−1.45829e9	−0.0672011
$899$	−6.27440e9	−0.288014
$900$	−2.63762e9	−0.120604
$901$	8.23916e9	0.375272
$902$	−1.67265e8	−0.00758897
$903$	7.56780e8	0.0342029
$904$	−4.68038e9	−0.210713
$905$	2.09342e10	0.938828
$906$	−8.34939e8	−0.0372998
$907$	−4.42625e9	−0.196975	−0.0984874	−	0.995138i	$-0.531400\pi$
$907$	−4.42625e9	−0.196975	−0.0984874	+	0.995138i	$0.531400\pi$
$908$	6.28821e9	0.278757
$909$	1.01726e10	0.449218
$910$	−8.85845e8	−0.0389684
$911$	2.35239e10	1.03085	0.515424	−	0.856935i	$-0.327635\pi$
$911$	2.35239e10	1.03085	0.515424	+	0.856935i	$0.327635\pi$
$912$	1.42967e8	0.00624101
$913$	5.28953e9	0.230022
$914$	−2.56805e10	−1.11248
$915$	−3.70492e9	−0.159884
$916$	7.38029e9	0.317278
$917$	1.12801e10	0.483081
$918$	−1.10126e9	−0.0469830
$919$	3.64332e10	1.54843	0.774217	−	0.632920i	$-0.218144\pi$
$919$	3.64332e10	1.54843	0.774217	+	0.632920i	$0.218144\pi$
$920$	−4.86008e9	−0.205772
$921$	−1.50848e10	−0.636256
$922$	1.68061e9	0.0706168
$923$	1.23211e10	0.515753
$924$	−5.09799e8	−0.0212592
$925$	−1.09507e10	−0.454932
$926$	4.02568e9	0.166610
$927$	9.39922e9	0.387537
$928$	−1.42704e9	−0.0586161
$929$	1.50294e10	0.615017	0.307508	−	0.951545i	$-0.400505\pi$
$929$	1.50294e10	0.615017	0.307508	+	0.951545i	$0.400505\pi$
$930$	−4.57282e9	−0.186421
$931$	1.52090e8	0.00617700
$932$	2.05995e10	0.833493
$933$	8.90182e9	0.358834
$934$	7.96245e9	0.319766
$935$	−8.83921e8	−0.0353649
$936$	8.20026e8	0.0326860
$937$	−4.31957e10	−1.71535	−0.857673	−	0.514195i	$-0.828091\pi$
$937$	−4.31957e10	−1.71535	−0.857673	+	0.514195i	$0.828091\pi$
$938$	−7.02113e9	−0.277778
$939$	−1.47446e10	−0.581169
$940$	−9.86408e9	−0.387355
$941$	1.17512e10	0.459746	0.229873	−	0.973221i	$-0.426169\pi$
$941$	1.17512e10	0.459746	0.229873	+	0.973221i	$0.426169\pi$
$942$	−4.49263e9	−0.175115
$943$	1.57031e9	0.0609809
$944$	3.25066e9	0.125768
$945$	−9.92040e8	−0.0382400
$946$	−5.62293e8	−0.0215945
$947$	3.21746e10	1.23109	0.615543	−	0.788103i	$-0.288937\pi$
$947$	3.21746e10	1.23109	0.615543	+	0.788103i	$0.288937\pi$
$948$	1.41235e10	0.538409
$949$	−7.26205e9	−0.275821
$950$	−5.84665e8	−0.0221246
$951$	−9.32477e9	−0.351566
$952$	−1.22821e9	−0.0461364
$953$	1.62686e10	0.608872	0.304436	−	0.952533i	$-0.401532\pi$
$953$	1.62686e10	0.608872	0.304436	+	0.952533i	$0.401532\pi$
$954$	−6.87055e9	−0.256196
$955$	1.08872e10	0.404488
$956$	−4.47024e9	−0.165473
$957$	1.01137e9	0.0373008
$958$	2.80706e10	1.03151
$959$	−2.39799e9	−0.0877977
$960$	−1.04003e9	−0.0379401
$961$	−6.75517e9	−0.245530
$962$	3.40454e9	0.123295
$963$	3.48187e9	0.125638
$964$	1.55607e10	0.559448
$965$	3.45775e9	0.123865
$966$	4.78605e9	0.170827
$967$	−1.59929e9	−0.0568768	−0.0284384	−	0.999596i	$-0.509053\pi$
$967$	−1.59929e9	−0.0568768	−0.0284384	+	0.999596i	$0.509053\pi$
$968$	−9.59865e9	−0.340131
$969$	−2.44110e8	−0.00861891
$970$	1.73042e10	0.608768
$971$	−2.99783e10	−1.05085	−0.525424	−	0.850841i	$-0.676093\pi$
$971$	−2.99783e10	−1.05085	−0.525424	+	0.850841i	$0.676093\pi$
$972$	9.18330e8	0.0320750
$973$	1.57737e10	0.548958
$974$	4.89137e9	0.169619
$975$	−3.35350e9	−0.115873
$976$	3.82500e9	0.131691
$977$	4.68270e10	1.60644	0.803221	−	0.595681i	$-0.203118\pi$
$977$	4.68270e10	1.60644	0.803221	+	0.595681i	$0.203118\pi$
$978$	−1.69938e10	−0.580905
$979$	−1.07897e9	−0.0367511
$980$	−1.10640e9	−0.0375509
$981$	1.62706e10	0.550253
$982$	3.68025e10	1.24019
$983$	2.42251e10	0.813447	0.406723	−	0.913551i	$-0.366671\pi$
$983$	2.42251e10	0.813447	0.406723	+	0.913551i	$0.366671\pi$
$984$	3.36038e8	0.0112436
$985$	7.54648e9	0.251604
$986$	2.43660e9	0.0809496
$987$	9.71384e9	0.321574
$988$	1.81770e8	0.00599617
$989$	5.27888e9	0.173522
$990$	7.37092e8	0.0241434
$991$	−2.36766e10	−0.772791	−0.386395	−	0.922333i	$-0.626280\pi$
$991$	−2.36766e10	−0.772791	−0.386395	+	0.922333i	$0.626280\pi$
$992$	4.72103e9	0.153549
$993$	3.16601e10	1.02610
$994$	1.53887e10	0.496992
$995$	9.06244e9	0.291652
$996$	−1.06267e10	−0.340794
$997$	−1.20295e10	−0.384429	−0.192215	−	0.981353i	$-0.561567\pi$
$997$	−1.20295e10	−0.384429	−0.192215	+	0.981353i	$0.561567\pi$
$998$	1.57033e9	0.0500074
$999$	3.81267e9	0.120990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.s.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.s.1.3	✓	7	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -146.941 q^{5} +216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -146.941 q^{5} +216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -1175.53 q^{10} -860.123 q^{11} +1728.00 q^{12} +2197.00 q^{13} +2744.00 q^{14} -3967.41 q^{15} +4096.00 q^{16} -6993.73 q^{17} +5832.00 q^{18} +1292.75 q^{19} -9404.24 q^{20} +9261.00 q^{21} -6880.99 q^{22} +64599.6 q^{23} +13824.0 q^{24} -56533.3 q^{25} +17576.0 q^{26} +19683.0 q^{27} +21952.0 q^{28} -43549.7 q^{29} -31739.3 q^{30} +144074. q^{31} +32768.0 q^{32} -23223.3 q^{33} -55949.8 q^{34} -50400.8 q^{35} +46656.0 q^{36} +193704. q^{37} +10342.0 q^{38} +59319.0 q^{39} -75233.9 q^{40} +24308.3 q^{41} +74088.0 q^{42} +81716.9 q^{43} -55047.9 q^{44} -107120. q^{45} +516797. q^{46} +1.04890e6 q^{47} +110592. q^{48} +117649. q^{49} -452266. q^{50} -188831. q^{51} +140608. q^{52} -1.17808e6 q^{53} +157464. q^{54} +126388. q^{55} +175616. q^{56} +34904.1 q^{57} -348398. q^{58} +793618. q^{59} -253914. q^{60} +933838. q^{61} +1.15260e6 q^{62} +250047. q^{63} +262144. q^{64} -322830. q^{65} -185787. q^{66} -2.55872e6 q^{67} -447599. q^{68} +1.74419e6 q^{69} -403207. q^{70} +5.60813e6 q^{71} +373248. q^{72} -3.30544e6 q^{73} +1.54963e6 q^{74} -1.52640e6 q^{75} +82735.7 q^{76} -295022. q^{77} +474552. q^{78} +8.17331e6 q^{79} -601871. q^{80} +531441. q^{81} +194467. q^{82} -6.14973e6 q^{83} +592704. q^{84} +1.02767e6 q^{85} +653735. q^{86} -1.17584e6 q^{87} -440383. q^{88} +1.25444e6 q^{89} -856961. q^{90} +753571. q^{91} +4.13437e6 q^{92} +3.89001e6 q^{93} +8.39118e6 q^{94} -189958. q^{95} +884736. q^{96} -1.47204e7 q^{97} +941192. q^{98} -627030. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 56 q^{2} + 189 q^{3} + 448 q^{4} + 625 q^{5} + 1512 q^{6} + 2401 q^{7} + 3584 q^{8} + 5103 q^{9}+O(q^{10}) \) 7 * q + 56 * q^2 + 189 * q^3 + 448 * q^4 + 625 * q^5 + 1512 * q^6 + 2401 * q^7 + 3584 * q^8 + 5103 * q^9	\( 7 q + 56 q^{2} + 189 q^{3} + 448 q^{4} + 625 q^{5} + 1512 q^{6} + 2401 q^{7} + 3584 q^{8} + 5103 q^{9} + 5000 q^{10} + 4678 q^{11} + 12096 q^{12} + 15379 q^{13} + 19208 q^{14} + 16875 q^{15} + 28672 q^{16} + 38552 q^{17} + 40824 q^{18} + 60231 q^{19} + 40000 q^{20} + 64827 q^{21} + 37424 q^{22} + 82047 q^{23} + 96768 q^{24} + 136408 q^{25} + 123032 q^{26} + 137781 q^{27} + 153664 q^{28} + 87523 q^{29} + 135000 q^{30} - 3191 q^{31} + 229376 q^{32} + 126306 q^{33} + 308416 q^{34} + 214375 q^{35} + 326592 q^{36} + 360916 q^{37} + 481848 q^{38} + 415233 q^{39} + 320000 q^{40} + 814350 q^{41} + 518616 q^{42} + 840057 q^{43} + 299392 q^{44} + 455625 q^{45} + 656376 q^{46} + 472723 q^{47} + 774144 q^{48} + 823543 q^{49} + 1091264 q^{50} + 1040904 q^{51} + 984256 q^{52} + 2185687 q^{53} + 1102248 q^{54} + 298354 q^{55} + 1229312 q^{56} + 1626237 q^{57} + 700184 q^{58} + 2046232 q^{59} + 1080000 q^{60} + 2744560 q^{61} - 25528 q^{62} + 1750329 q^{63} + 1835008 q^{64} + 1373125 q^{65} + 1010448 q^{66} + 1960358 q^{67} + 2467328 q^{68} + 2215269 q^{69} + 1715000 q^{70} + 2774656 q^{71} + 2612736 q^{72} + 3696313 q^{73} + 2887328 q^{74} + 3683016 q^{75} + 3854784 q^{76} + 1604554 q^{77} + 3321864 q^{78} + 1532089 q^{79} + 2560000 q^{80} + 3720087 q^{81} + 6514800 q^{82} + 7473863 q^{83} + 4148928 q^{84} - 1656624 q^{85} + 6720456 q^{86} + 2363121 q^{87} + 2395136 q^{88} + 14077309 q^{89} + 3645000 q^{90} + 5274997 q^{91} + 5251008 q^{92} - 86157 q^{93} + 3781784 q^{94} - 1704679 q^{95} + 6193152 q^{96} + 8273673 q^{97} + 6588344 q^{98} + 3410262 q^{99}+O(q^{100}) \) 7 * q + 56 * q^2 + 189 * q^3 + 448 * q^4 + 625 * q^5 + 1512 * q^6 + 2401 * q^7 + 3584 * q^8 + 5103 * q^9 + 5000 * q^10 + 4678 * q^11 + 12096 * q^12 + 15379 * q^13 + 19208 * q^14 + 16875 * q^15 + 28672 * q^16 + 38552 * q^17 + 40824 * q^18 + 60231 * q^19 + 40000 * q^20 + 64827 * q^21 + 37424 * q^22 + 82047 * q^23 + 96768 * q^24 + 136408 * q^25 + 123032 * q^26 + 137781 * q^27 + 153664 * q^28 + 87523 * q^29 + 135000 * q^30 - 3191 * q^31 + 229376 * q^32 + 126306 * q^33 + 308416 * q^34 + 214375 * q^35 + 326592 * q^36 + 360916 * q^37 + 481848 * q^38 + 415233 * q^39 + 320000 * q^40 + 814350 * q^41 + 518616 * q^42 + 840057 * q^43 + 299392 * q^44 + 455625 * q^45 + 656376 * q^46 + 472723 * q^47 + 774144 * q^48 + 823543 * q^49 + 1091264 * q^50 + 1040904 * q^51 + 984256 * q^52 + 2185687 * q^53 + 1102248 * q^54 + 298354 * q^55 + 1229312 * q^56 + 1626237 * q^57 + 700184 * q^58 + 2046232 * q^59 + 1080000 * q^60 + 2744560 * q^61 - 25528 * q^62 + 1750329 * q^63 + 1835008 * q^64 + 1373125 * q^65 + 1010448 * q^66 + 1960358 * q^67 + 2467328 * q^68 + 2215269 * q^69 + 1715000 * q^70 + 2774656 * q^71 + 2612736 * q^72 + 3696313 * q^73 + 2887328 * q^74 + 3683016 * q^75 + 3854784 * q^76 + 1604554 * q^77 + 3321864 * q^78 + 1532089 * q^79 + 2560000 * q^80 + 3720087 * q^81 + 6514800 * q^82 + 7473863 * q^83 + 4148928 * q^84 - 1656624 * q^85 + 6720456 * q^86 + 2363121 * q^87 + 2395136 * q^88 + 14077309 * q^89 + 3645000 * q^90 + 5274997 * q^91 + 5251008 * q^92 - 86157 * q^93 + 3781784 * q^94 - 1704679 * q^95 + 6193152 * q^96 + 8273673 * q^97 + 6588344 * q^98 + 3410262 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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