LMFDB - Embedded newform 546.8.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$170.562223914$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5672x^{3} - 117684x^{2} + 1695035x + 39011360 $ x^5 - 5672x^3 - 117684x^2 + 1695035*x + 39011360
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-20.7333$ 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)

$f(q)$	$=$	$q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -251.667 q^{5} -216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -251.667 q^{5} -216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +2013.33 q^{10} +6935.03 q^{11} +1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -6795.00 q^{15} +4096.00 q^{16} +3533.29 q^{17} -5832.00 q^{18} +5190.95 q^{19} -16106.7 q^{20} -9261.00 q^{21} -55480.2 q^{22} -40997.6 q^{23} -13824.0 q^{24} -14788.9 q^{25} +17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -70252.8 q^{29} +54360.0 q^{30} -288221. q^{31} -32768.0 q^{32} +187246. q^{33} -28266.3 q^{34} +86321.7 q^{35} +46656.0 q^{36} +288649. q^{37} -41527.6 q^{38} -59319.0 q^{39} +128853. q^{40} +8236.51 q^{41} +74088.0 q^{42} +284453. q^{43} +443842. q^{44} -183465. q^{45} +327981. q^{46} +254392. q^{47} +110592. q^{48} +117649. q^{49} +118311. q^{50} +95398.8 q^{51} -140608. q^{52} +679737. q^{53} -157464. q^{54} -1.74532e6 q^{55} +175616. q^{56} +140156. q^{57} +562022. q^{58} +1.06690e6 q^{59} -434880. q^{60} +2.93017e6 q^{61} +2.30577e6 q^{62} -250047. q^{63} +262144. q^{64} +552912. q^{65} -1.49797e6 q^{66} +1.20866e6 q^{67} +226131. q^{68} -1.10694e6 q^{69} -690573. q^{70} -2.99805e6 q^{71} -373248. q^{72} -1.35994e6 q^{73} -2.30919e6 q^{74} -399300. q^{75} +332221. q^{76} -2.37872e6 q^{77} +474552. q^{78} -565403. q^{79} -1.03083e6 q^{80} +531441. q^{81} -65892.1 q^{82} +2.10144e6 q^{83} -592704. q^{84} -889211. q^{85} -2.27563e6 q^{86} -1.89682e6 q^{87} -3.55074e6 q^{88} +6.47234e6 q^{89} +1.46772e6 q^{90} +753571. q^{91} -2.62385e6 q^{92} -7.78196e6 q^{93} -2.03513e6 q^{94} -1.30639e6 q^{95} -884736. q^{96} -4.68279e6 q^{97} -941192. q^{98} +5.05564e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} + 56 q^{5} - 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9}+O(q^{10}) $ 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 + 56 * q^5 - 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9	\( 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} + 56 q^{5} - 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9} - 448 q^{10} - 3679 q^{11} + 8640 q^{12} - 10985 q^{13} + 13720 q^{14} + 1512 q^{15} + 20480 q^{16} + 409 q^{17} - 29160 q^{18} + 33730 q^{19} + 3584 q^{20} - 46305 q^{21} + 29432 q^{22} - 142142 q^{23} - 69120 q^{24} + 153981 q^{25} + 87880 q^{26} + 98415 q^{27} - 109760 q^{28} + 88028 q^{29} - 12096 q^{30} + 244543 q^{31} - 163840 q^{32} - 99333 q^{33} - 3272 q^{34} - 19208 q^{35} + 233280 q^{36} + 730963 q^{37} - 269840 q^{38} - 296595 q^{39} - 28672 q^{40} + 479512 q^{41} + 370440 q^{42} - 406536 q^{43} - 235456 q^{44} + 40824 q^{45} + 1137136 q^{46} + 1138945 q^{47} + 552960 q^{48} + 588245 q^{49} - 1231848 q^{50} + 11043 q^{51} - 703040 q^{52} + 297595 q^{53} - 787320 q^{54} - 1834423 q^{55} + 878080 q^{56} + 910710 q^{57} - 704224 q^{58} + 941652 q^{59} + 96768 q^{60} - 2985259 q^{61} - 1956344 q^{62} - 1250235 q^{63} + 1310720 q^{64} - 123032 q^{65} + 794664 q^{66} - 2333504 q^{67} + 26176 q^{68} - 3837834 q^{69} + 153664 q^{70} - 11322272 q^{71} - 1866240 q^{72} - 6631604 q^{73} - 5847704 q^{74} + 4157487 q^{75} + 2158720 q^{76} + 1261897 q^{77} + 2372760 q^{78} - 10600265 q^{79} + 229376 q^{80} + 2657205 q^{81} - 3836096 q^{82} - 2425229 q^{83} - 2963520 q^{84} - 12267705 q^{85} + 3252288 q^{86} + 2376756 q^{87} + 1883648 q^{88} - 1581837 q^{89} - 326592 q^{90} + 3767855 q^{91} - 9097088 q^{92} + 6602661 q^{93} - 9111560 q^{94} - 11507718 q^{95} - 4423680 q^{96} + 5298407 q^{97} - 4705960 q^{98} - 2681991 q^{99}+O(q^{100}) \) 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 + 56 * q^5 - 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9 - 448 * q^10 - 3679 * q^11 + 8640 * q^12 - 10985 * q^13 + 13720 * q^14 + 1512 * q^15 + 20480 * q^16 + 409 * q^17 - 29160 * q^18 + 33730 * q^19 + 3584 * q^20 - 46305 * q^21 + 29432 * q^22 - 142142 * q^23 - 69120 * q^24 + 153981 * q^25 + 87880 * q^26 + 98415 * q^27 - 109760 * q^28 + 88028 * q^29 - 12096 * q^30 + 244543 * q^31 - 163840 * q^32 - 99333 * q^33 - 3272 * q^34 - 19208 * q^35 + 233280 * q^36 + 730963 * q^37 - 269840 * q^38 - 296595 * q^39 - 28672 * q^40 + 479512 * q^41 + 370440 * q^42 - 406536 * q^43 - 235456 * q^44 + 40824 * q^45 + 1137136 * q^46 + 1138945 * q^47 + 552960 * q^48 + 588245 * q^49 - 1231848 * q^50 + 11043 * q^51 - 703040 * q^52 + 297595 * q^53 - 787320 * q^54 - 1834423 * q^55 + 878080 * q^56 + 910710 * q^57 - 704224 * q^58 + 941652 * q^59 + 96768 * q^60 - 2985259 * q^61 - 1956344 * q^62 - 1250235 * q^63 + 1310720 * q^64 - 123032 * q^65 + 794664 * q^66 - 2333504 * q^67 + 26176 * q^68 - 3837834 * q^69 + 153664 * q^70 - 11322272 * q^71 - 1866240 * q^72 - 6631604 * q^73 - 5847704 * q^74 + 4157487 * q^75 + 2158720 * q^76 + 1261897 * q^77 + 2372760 * q^78 - 10600265 * q^79 + 229376 * q^80 + 2657205 * q^81 - 3836096 * q^82 - 2425229 * q^83 - 2963520 * q^84 - 12267705 * q^85 + 3252288 * q^86 + 2376756 * q^87 + 1883648 * q^88 - 1581837 * q^89 - 326592 * q^90 + 3767855 * q^91 - 9097088 * q^92 + 6602661 * q^93 - 9111560 * q^94 - 11507718 * q^95 - 4423680 * q^96 + 5298407 * q^97 - 4705960 * q^98 - 2681991 * 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
$5$	−251.667	−0.900390	−0.450195	−	0.892930i	$-0.648646\pi$
$5$	−251.667	−0.900390	−0.450195	+	0.892930i	$0.648646\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	2013.33	0.636672
$11$	6935.03	1.57099	0.785496	−	0.618867i	$-0.212408\pi$
$11$	6935.03	1.57099	0.785496	+	0.618867i	$0.212408\pi$
$12$	1728.00	0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	2744.00	0.267261
$15$	−6795.00	−0.519840
$16$	4096.00	0.250000
$17$	3533.29	0.174425	0.0872124	−	0.996190i	$-0.472204\pi$
$17$	3533.29	0.174425	0.0872124	+	0.996190i	$0.472204\pi$
$18$	−5832.00	−0.235702
$19$	5190.95	0.173624	0.0868118	−	0.996225i	$-0.472332\pi$
$19$	5190.95	0.173624	0.0868118	+	0.996225i	$0.472332\pi$
$20$	−16106.7	−0.450195
$21$	−9261.00	−0.218218
$22$	−55480.2	−1.11086
$23$	−40997.6	−0.702605	−0.351303	−	0.936262i	$-0.614261\pi$
$23$	−40997.6	−0.702605	−0.351303	+	0.936262i	$0.614261\pi$
$24$	−13824.0	−0.204124
$25$	−14788.9	−0.189298
$26$	17576.0	0.196116
$27$	19683.0	0.192450
$28$	−21952.0	−0.188982
$29$	−70252.8	−0.534897	−0.267449	−	0.963572i	$-0.586181\pi$
$29$	−70252.8	−0.534897	−0.267449	+	0.963572i	$0.586181\pi$
$30$	54360.0	0.367583
$31$	−288221.	−1.73764	−0.868819	−	0.495130i	$-0.835120\pi$
$31$	−288221.	−1.73764	−0.868819	+	0.495130i	$0.835120\pi$
$32$	−32768.0	−0.176777
$33$	187246.	0.907013
$34$	−28266.3	−0.123337
$35$	86321.7	0.340315
$36$	46656.0	0.166667
$37$	288649.	0.936837	0.468418	−	0.883507i	$-0.344824\pi$
$37$	288649.	0.936837	0.468418	+	0.883507i	$0.344824\pi$
$38$	−41527.6	−0.122770
$39$	−59319.0	−0.160128
$40$	128853.	0.318336
$41$	8236.51	0.0186638	0.00933190	−	0.999956i	$-0.497030\pi$
$41$	8236.51	0.0186638	0.00933190	+	0.999956i	$0.497030\pi$
$42$	74088.0	0.154303
$43$	284453.	0.545597	0.272798	−	0.962071i	$-0.412051\pi$
$43$	284453.	0.545597	0.272798	+	0.962071i	$0.412051\pi$
$44$	443842.	0.785496
$45$	−183465.	−0.300130
$46$	327981.	0.496817
$47$	254392.	0.357405	0.178702	−	0.983903i	$-0.442810\pi$
$47$	254392.	0.357405	0.178702	+	0.983903i	$0.442810\pi$
$48$	110592.	0.144338
$49$	117649.	0.142857
$50$	118311.	0.133854
$51$	95398.8	0.100704
$52$	−140608.	−0.138675
$53$	679737.	0.627155	0.313578	−	0.949563i	$-0.398472\pi$
$53$	679737.	0.627155	0.313578	+	0.949563i	$0.398472\pi$
$54$	−157464.	−0.136083
$55$	−1.74532e6	−1.41451
$56$	175616.	0.133631
$57$	140156.	0.100242
$58$	562022.	0.378229
$59$	1.06690e6	0.676304	0.338152	−	0.941092i	$-0.390198\pi$
$59$	1.06690e6	0.676304	0.338152	+	0.941092i	$0.390198\pi$
$60$	−434880.	−0.259920
$61$	2.93017e6	1.65287	0.826435	−	0.563032i	$-0.190365\pi$
$61$	2.93017e6	1.65287	0.826435	+	0.563032i	$0.190365\pi$
$62$	2.30577e6	1.22870
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	552912.	0.249723
$66$	−1.49797e6	−0.641355
$67$	1.20866e6	0.490957	0.245479	−	0.969402i	$-0.421055\pi$
$67$	1.20866e6	0.490957	0.245479	+	0.969402i	$0.421055\pi$
$68$	226131.	0.0872124
$69$	−1.10694e6	−0.405649
$70$	−690573.	−0.240639
$71$	−2.99805e6	−0.994111	−0.497056	−	0.867719i	$-0.665585\pi$
$71$	−2.99805e6	−0.994111	−0.497056	+	0.867719i	$0.665585\pi$
$72$	−373248.	−0.117851
$73$	−1.35994e6	−0.409156	−0.204578	−	0.978850i	$-0.565582\pi$
$73$	−1.35994e6	−0.409156	−0.204578	+	0.978850i	$0.565582\pi$
$74$	−2.30919e6	−0.662444
$75$	−399300.	−0.109291
$76$	332221.	0.0868118
$77$	−2.37872e6	−0.593779
$78$	474552.	0.113228
$79$	−565403.	−0.129022	−0.0645109	−	0.997917i	$-0.520549\pi$
$79$	−565403.	−0.129022	−0.0645109	+	0.997917i	$0.520549\pi$
$80$	−1.03083e6	−0.225098
$81$	531441.	0.111111
$82$	−65892.1	−0.0131973
$83$	2.10144e6	0.403408	0.201704	−	0.979447i	$-0.435352\pi$
$83$	2.10144e6	0.403408	0.201704	+	0.979447i	$0.435352\pi$
$84$	−592704.	−0.109109
$85$	−889211.	−0.157050
$86$	−2.27563e6	−0.385795
$87$	−1.89682e6	−0.308823
$88$	−3.55074e6	−0.555429
$89$	6.47234e6	0.973188	0.486594	−	0.873628i	$-0.338239\pi$
$89$	6.47234e6	0.973188	0.486594	+	0.873628i	$0.338239\pi$
$90$	1.46772e6	0.212224
$91$	753571.	0.104828
$92$	−2.62385e6	−0.351303
$93$	−7.78196e6	−1.00323
$94$	−2.03513e6	−0.252723
$95$	−1.30639e6	−0.156329
$96$	−884736.	−0.102062
$97$	−4.68279e6	−0.520959	−0.260479	−	0.965479i	$-0.583881\pi$
$97$	−4.68279e6	−0.520959	−0.260479	+	0.965479i	$0.583881\pi$
$98$	−941192.	−0.101015
$99$	5.05564e6	0.523664
$100$	−946489.	−0.0946489
$101$	−1.10597e7	−1.06812	−0.534060	−	0.845446i	$-0.679334\pi$
$101$	−1.10597e7	−1.06812	−0.534060	+	0.845446i	$0.679334\pi$
$102$	−763191.	−0.0712086
$103$	−6.69767e6	−0.603940	−0.301970	−	0.953318i	$-0.597644\pi$
$103$	−6.69767e6	−0.603940	−0.301970	+	0.953318i	$0.597644\pi$
$104$	1.12486e6	0.0980581
$105$	2.33069e6	0.196481
$106$	−5.43789e6	−0.443466
$107$	−1.95155e7	−1.54006	−0.770029	−	0.638009i	$-0.779758\pi$
$107$	−1.95155e7	−1.54006	−0.770029	+	0.638009i	$0.779758\pi$
$108$	1.25971e6	0.0962250
$109$	−1.70235e7	−1.25909	−0.629545	−	0.776964i	$-0.716758\pi$
$109$	−1.70235e7	−1.25909	−0.629545	+	0.776964i	$0.716758\pi$
$110$	1.39625e7	1.00021
$111$	7.79352e6	0.540883
$112$	−1.40493e6	−0.0944911
$113$	1.11219e7	0.725110	0.362555	−	0.931962i	$-0.381904\pi$
$113$	1.11219e7	0.725110	0.362555	+	0.931962i	$0.381904\pi$
$114$	−1.12124e6	−0.0708816
$115$	1.03177e7	0.632619
$116$	−4.49618e6	−0.267449
$117$	−1.60161e6	−0.0924500
$118$	−8.53520e6	−0.478219
$119$	−1.21192e6	−0.0659264
$120$	3.47904e6	0.183791
$121$	2.86075e7	1.46802
$122$	−2.34414e7	−1.16876
$123$	222386.	0.0107755
$124$	−1.84461e7	−0.868819
$125$	2.33833e7	1.07083
$126$	2.00038e6	0.0890871
$127$	2.81859e7	1.22101	0.610504	−	0.792013i	$-0.290967\pi$
$127$	2.81859e7	1.22101	0.610504	+	0.792013i	$0.290967\pi$
$128$	−2.09715e6	−0.0883883
$129$	7.68024e6	0.315000
$130$	−4.42329e6	−0.176581
$131$	−3.21524e7	−1.24958	−0.624789	−	0.780793i	$-0.714815\pi$
$131$	−3.21524e7	−1.24958	−0.624789	+	0.780793i	$0.714815\pi$
$132$	1.19837e7	0.453506
$133$	−1.78049e6	−0.0656236
$134$	−9.66931e6	−0.347159
$135$	−4.95356e6	−0.173280
$136$	−1.80904e6	−0.0616685
$137$	−1.69595e7	−0.563496	−0.281748	−	0.959488i	$-0.590914\pi$
$137$	−1.69595e7	−0.563496	−0.281748	+	0.959488i	$0.590914\pi$
$138$	8.85549e6	0.286837
$139$	5.15015e7	1.62655	0.813276	−	0.581878i	$-0.197682\pi$
$139$	5.15015e7	1.62655	0.813276	+	0.581878i	$0.197682\pi$
$140$	5.52459e6	0.170158
$141$	6.86858e6	0.206348
$142$	2.39844e7	0.702943
$143$	−1.52363e7	−0.435715
$144$	2.98598e6	0.0833333
$145$	1.76803e7	0.481616
$146$	1.08795e7	0.289317
$147$	3.17652e6	0.0824786
$148$	1.84735e7	0.468418
$149$	−1.98903e7	−0.492594	−0.246297	−	0.969194i	$-0.579214\pi$
$149$	−1.98903e7	−0.492594	−0.246297	+	0.969194i	$0.579214\pi$
$150$	3.19440e6	0.0772805
$151$	6.76658e7	1.59937	0.799687	−	0.600418i	$-0.204999\pi$
$151$	6.76658e7	1.59937	0.799687	+	0.600418i	$0.204999\pi$
$152$	−2.65776e6	−0.0613852
$153$	2.57577e6	0.0581416
$154$	1.90297e7	0.419865
$155$	7.25355e7	1.56455
$156$	−3.79642e6	−0.0800641
$157$	−7.01512e6	−0.144673	−0.0723363	−	0.997380i	$-0.523045\pi$
$157$	−7.01512e6	−0.144673	−0.0723363	+	0.997380i	$0.523045\pi$
$158$	4.52322e6	0.0912322
$159$	1.83529e7	0.362088
$160$	8.24661e6	0.159168
$161$	1.40622e7	0.265560
$162$	−4.25153e6	−0.0785674
$163$	−3.60262e7	−0.651571	−0.325786	−	0.945444i	$-0.605629\pi$
$163$	−3.60262e7	−0.651571	−0.325786	+	0.945444i	$0.605629\pi$
$164$	527137.	0.00933190
$165$	−4.71235e7	−0.816665
$166$	−1.68116e7	−0.285253
$167$	−7.32229e7	−1.21658	−0.608288	−	0.793717i	$-0.708143\pi$
$167$	−7.32229e7	−1.21658	−0.608288	+	0.793717i	$0.708143\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	7.11369e6	0.111051
$171$	3.78420e6	0.0578746
$172$	1.82050e7	0.272798
$173$	−8.04650e7	−1.18153	−0.590766	−	0.806843i	$-0.701174\pi$
$173$	−8.04650e7	−1.18153	−0.590766	+	0.806843i	$0.701174\pi$
$174$	1.51746e7	0.218371
$175$	5.07259e6	0.0715478
$176$	2.84059e7	0.392748
$177$	2.88063e7	0.390464
$178$	−5.17788e7	−0.688148
$179$	−1.43295e8	−1.86743	−0.933715	−	0.358016i	$-0.883453\pi$
$179$	−1.43295e8	−1.86743	−0.933715	+	0.358016i	$0.883453\pi$
$180$	−1.17418e7	−0.150065
$181$	−1.37748e8	−1.72668	−0.863339	−	0.504624i	$-0.831631\pi$
$181$	−1.37748e8	−1.72668	−0.863339	+	0.504624i	$0.831631\pi$
$182$	−6.02857e6	−0.0741249
$183$	7.91147e7	0.954285
$184$	2.09908e7	0.248408
$185$	−7.26433e7	−0.843518
$186$	6.22557e7	0.709387
$187$	2.45035e7	0.274020
$188$	1.62811e7	0.178702
$189$	−6.75127e6	−0.0727393
$190$	1.04511e7	0.110541
$191$	3.36027e7	0.348945	0.174473	−	0.984662i	$-0.444178\pi$
$191$	3.36027e7	0.348945	0.174473	+	0.984662i	$0.444178\pi$
$192$	7.07789e6	0.0721688
$193$	3.17594e7	0.317996	0.158998	−	0.987279i	$-0.449174\pi$
$193$	3.17594e7	0.317996	0.158998	+	0.987279i	$0.449174\pi$
$194$	3.74623e7	0.368373
$195$	1.49286e7	0.144178
$196$	7.52954e6	0.0714286
$197$	−1.15390e8	−1.07532	−0.537659	−	0.843163i	$-0.680691\pi$
$197$	−1.15390e8	−1.07532	−0.537659	+	0.843163i	$0.680691\pi$
$198$	−4.04451e7	−0.370286
$199$	1.08761e6	0.00978338	0.00489169	−	0.999988i	$-0.498443\pi$
$199$	1.08761e6	0.00978338	0.00489169	+	0.999988i	$0.498443\pi$
$200$	7.57191e6	0.0669269
$201$	3.26339e7	0.283454
$202$	8.84780e7	0.755275
$203$	2.40967e7	0.202172
$204$	6.10553e6	0.0503521
$205$	−2.07286e6	−0.0168047
$206$	5.35814e7	0.427050
$207$	−2.98873e7	−0.234202
$208$	−8.99891e6	−0.0693375
$209$	3.59994e7	0.272761
$210$	−1.86455e7	−0.138933
$211$	−1.70584e6	−0.0125011	−0.00625056	−	0.999980i	$-0.501990\pi$
$211$	−1.70584e6	−0.0125011	−0.00625056	+	0.999980i	$0.501990\pi$
$212$	4.35031e7	0.313578
$213$	−8.09474e7	−0.573950
$214$	1.56124e8	1.08899
$215$	−7.15875e7	−0.491250
$216$	−1.00777e7	−0.0680414
$217$	9.88597e7	0.656765
$218$	1.36188e8	0.890310
$219$	−3.67183e7	−0.236227
$220$	−1.11700e8	−0.707253
$221$	−7.76264e6	−0.0483767
$222$	−6.23482e7	−0.382462
$223$	6.10969e7	0.368937	0.184469	−	0.982838i	$-0.440944\pi$
$223$	6.10969e7	0.368937	0.184469	+	0.982838i	$0.440944\pi$
$224$	1.12394e7	0.0668153
$225$	−1.07811e7	−0.0630992
$226$	−8.89751e7	−0.512730
$227$	−1.32246e8	−0.750396	−0.375198	−	0.926945i	$-0.622425\pi$
$227$	−1.32246e8	−0.750396	−0.375198	+	0.926945i	$0.622425\pi$
$228$	8.96996e6	0.0501208
$229$	1.01733e8	0.559809	0.279904	−	0.960028i	$-0.409697\pi$
$229$	1.01733e8	0.559809	0.279904	+	0.960028i	$0.409697\pi$
$230$	−8.25419e7	−0.447329
$231$	−6.42253e7	−0.342819
$232$	3.59694e7	0.189115
$233$	−7.05503e7	−0.365387	−0.182694	−	0.983170i	$-0.558482\pi$
$233$	−7.05503e7	−0.365387	−0.182694	+	0.983170i	$0.558482\pi$
$234$	1.28129e7	0.0653720
$235$	−6.40219e7	−0.321804
$236$	6.82816e7	0.338152
$237$	−1.52659e7	−0.0744908
$238$	9.69535e6	0.0466170
$239$	1.77323e7	0.0840180	0.0420090	−	0.999117i	$-0.486624\pi$
$239$	1.77323e7	0.0840180	0.0420090	+	0.999117i	$0.486624\pi$
$240$	−2.78323e7	−0.129960
$241$	−2.54626e8	−1.17177	−0.585886	−	0.810394i	$-0.699253\pi$
$241$	−2.54626e8	−1.17177	−0.585886	+	0.810394i	$0.699253\pi$
$242$	−2.28860e8	−1.03804
$243$	1.43489e7	0.0641500
$244$	1.87531e8	0.826435
$245$	−2.96083e7	−0.128627
$246$	−1.77909e6	−0.00761946
$247$	−1.14045e7	−0.0481545
$248$	1.47569e8	0.614348
$249$	5.67390e7	0.232908
$250$	−1.87067e8	−0.757192
$251$	−2.53930e8	−1.01358	−0.506788	−	0.862071i	$-0.669167\pi$
$251$	−2.53930e8	−1.01358	−0.506788	+	0.862071i	$0.669167\pi$
$252$	−1.60030e7	−0.0629941
$253$	−2.84320e8	−1.10379
$254$	−2.25487e8	−0.863382
$255$	−2.40087e7	−0.0906730
$256$	1.67772e7	0.0625000
$257$	−1.29185e8	−0.474729	−0.237364	−	0.971421i	$-0.576284\pi$
$257$	−1.29185e8	−0.474729	−0.237364	+	0.971421i	$0.576284\pi$
$258$	−6.14419e7	−0.222739
$259$	−9.90066e7	−0.354091
$260$	3.53863e7	0.124862
$261$	−5.12143e7	−0.178299
$262$	2.57219e8	0.883586
$263$	−3.61265e6	−0.0122456	−0.00612282	−	0.999981i	$-0.501949\pi$
$263$	−3.61265e6	−0.0122456	−0.00612282	+	0.999981i	$0.501949\pi$
$264$	−9.58699e7	−0.320677
$265$	−1.71067e8	−0.564684
$266$	1.42440e7	0.0464029
$267$	1.74753e8	0.561870
$268$	7.73545e7	0.245479
$269$	−5.05729e8	−1.58411	−0.792055	−	0.610450i	$-0.790988\pi$
$269$	−5.05729e8	−1.58411	−0.792055	+	0.610450i	$0.790988\pi$
$270$	3.96284e7	0.122528
$271$	−4.25958e8	−1.30009	−0.650047	−	0.759894i	$-0.725251\pi$
$271$	−4.25958e8	−1.30009	−0.650047	+	0.759894i	$0.725251\pi$
$272$	1.44724e7	0.0436062
$273$	2.03464e7	0.0605228
$274$	1.35676e8	0.398452
$275$	−1.02561e8	−0.297385
$276$	−7.08439e7	−0.202825
$277$	−1.25232e8	−0.354026	−0.177013	−	0.984209i	$-0.556643\pi$
$277$	−1.25232e8	−0.354026	−0.177013	+	0.984209i	$0.556643\pi$
$278$	−4.12012e8	−1.15015
$279$	−2.10113e8	−0.579212
$280$	−4.41967e7	−0.120320
$281$	5.86467e8	1.57678	0.788390	−	0.615176i	$-0.210915\pi$
$281$	5.86467e8	1.57678	0.788390	+	0.615176i	$0.210915\pi$
$282$	−5.49486e7	−0.145910
$283$	−3.31438e7	−0.0869260	−0.0434630	−	0.999055i	$-0.513839\pi$
$283$	−3.31438e7	−0.0869260	−0.0434630	+	0.999055i	$0.513839\pi$
$284$	−1.91875e8	−0.497056
$285$	−3.52725e7	−0.0902566
$286$	1.21890e8	0.308097
$287$	−2.82512e6	−0.00705425
$288$	−2.38879e7	−0.0589256
$289$	−3.97855e8	−0.969576
$290$	−1.41442e8	−0.340554
$291$	−1.26435e8	−0.300776
$292$	−8.70361e7	−0.204578
$293$	2.85209e8	0.662409	0.331204	−	0.943559i	$-0.392545\pi$
$293$	2.85209e8	0.662409	0.331204	+	0.943559i	$0.392545\pi$
$294$	−2.54122e7	−0.0583212
$295$	−2.68503e8	−0.608937
$296$	−1.47788e8	−0.331222
$297$	1.36502e8	0.302338
$298$	1.59122e8	0.348317
$299$	9.00718e7	0.194868
$300$	−2.55552e7	−0.0546455
$301$	−9.75675e7	−0.206216
$302$	−5.41326e8	−1.13093
$303$	−2.98613e8	−0.616680
$304$	2.12621e7	0.0434059
$305$	−7.37427e8	−1.48823
$306$	−2.06061e7	−0.0411123
$307$	−1.61743e8	−0.319037	−0.159518	−	0.987195i	$-0.550994\pi$
$307$	−1.61743e8	−0.319037	−0.159518	+	0.987195i	$0.550994\pi$
$308$	−1.52238e8	−0.296890
$309$	−1.80837e8	−0.348685
$310$	−5.80284e8	−1.10630
$311$	−2.35974e8	−0.444839	−0.222419	−	0.974951i	$-0.571395\pi$
$311$	−2.35974e8	−0.444839	−0.222419	+	0.974951i	$0.571395\pi$
$312$	3.03713e7	0.0566139
$313$	−4.68223e7	−0.0863074	−0.0431537	−	0.999068i	$-0.513741\pi$
$313$	−4.68223e7	−0.0863074	−0.0431537	+	0.999068i	$0.513741\pi$
$314$	5.61210e7	0.102299
$315$	6.29285e7	0.113438
$316$	−3.61858e7	−0.0645109
$317$	−5.38537e8	−0.949529	−0.474764	−	0.880113i	$-0.657467\pi$
$317$	−5.38537e8	−0.949529	−0.474764	+	0.880113i	$0.657467\pi$
$318$	−1.46823e8	−0.256035
$319$	−4.87205e8	−0.840319
$320$	−6.59729e7	−0.112549
$321$	−5.26919e8	−0.889153
$322$	−1.12497e8	−0.187779
$323$	1.83411e7	0.0302843
$324$	3.40122e7	0.0555556
$325$	3.24912e7	0.0525017
$326$	2.88210e8	0.460730
$327$	−4.59635e8	−0.726935
$328$	−4.21709e6	−0.00659865
$329$	−8.72564e7	−0.135086
$330$	3.76988e8	0.577469
$331$	9.09442e8	1.37841	0.689203	−	0.724569i	$-0.257961\pi$
$331$	9.09442e8	1.37841	0.689203	+	0.724569i	$0.257961\pi$
$332$	1.34492e8	0.201704
$333$	2.10425e8	0.312279
$334$	5.85783e8	0.860249
$335$	−3.04180e8	−0.442053
$336$	−3.79331e7	−0.0545545
$337$	1.79739e8	0.255822	0.127911	−	0.991786i	$-0.459173\pi$
$337$	1.79739e8	0.255822	0.127911	+	0.991786i	$0.459173\pi$
$338$	−3.86145e7	−0.0543928
$339$	3.00291e8	0.418642
$340$	−5.69095e7	−0.0785252
$341$	−1.99882e9	−2.72981
$342$	−3.02736e7	−0.0409235
$343$	−4.03536e7	−0.0539949
$344$	−1.45640e8	−0.192898
$345$	2.78579e8	0.365243
$346$	6.43720e8	0.835470
$347$	1.45690e7	0.0187187	0.00935934	−	0.999956i	$-0.497021\pi$
$347$	1.45690e7	0.0187187	0.00935934	+	0.999956i	$0.497021\pi$
$348$	−1.21397e8	−0.154412
$349$	−1.24811e9	−1.57168	−0.785839	−	0.618431i	$-0.787769\pi$
$349$	−1.24811e9	−1.57168	−0.785839	+	0.618431i	$0.787769\pi$
$350$	−4.05807e7	−0.0505919
$351$	−4.32436e7	−0.0533761
$352$	−2.27247e8	−0.277715
$353$	2.12266e8	0.256843	0.128422	−	0.991720i	$-0.459009\pi$
$353$	2.12266e8	0.256843	0.128422	+	0.991720i	$0.459009\pi$
$354$	−2.30450e8	−0.276100
$355$	7.54510e8	0.895088
$356$	4.14230e8	0.486594
$357$	−3.27218e7	−0.0380626
$358$	1.14636e9	1.32047
$359$	5.08137e8	0.579630	0.289815	−	0.957083i	$-0.406406\pi$
$359$	5.08137e8	0.579630	0.289815	+	0.957083i	$0.406406\pi$
$360$	9.39341e7	0.106112
$361$	−8.66926e8	−0.969855
$362$	1.10199e9	1.22095
$363$	7.72402e8	0.847559
$364$	4.82285e7	0.0524142
$365$	3.42251e8	0.368400
$366$	−6.32917e8	−0.674781
$367$	−1.57790e8	−0.166628	−0.0833139	−	0.996523i	$-0.526550\pi$
$367$	−1.57790e8	−0.166628	−0.0833139	+	0.996523i	$0.526550\pi$
$368$	−1.67926e8	−0.175651
$369$	6.00442e6	0.00622126
$370$	5.81147e8	0.596458
$371$	−2.33150e8	−0.237042
$372$	−4.98045e8	−0.501613
$373$	−3.67655e8	−0.366825	−0.183413	−	0.983036i	$-0.558714\pi$
$373$	−3.67655e8	−0.366825	−0.183413	+	0.983036i	$0.558714\pi$
$374$	−1.96028e8	−0.193761
$375$	6.31350e8	0.618245
$376$	−1.30249e8	−0.126362
$377$	1.54345e8	0.148354
$378$	5.40102e7	0.0514344
$379$	−9.04041e8	−0.853004	−0.426502	−	0.904487i	$-0.640254\pi$
$379$	−9.04041e8	−0.853004	−0.426502	+	0.904487i	$0.640254\pi$
$380$	−8.36088e7	−0.0781645
$381$	7.61018e8	0.704949
$382$	−2.68822e8	−0.246742
$383$	−2.12799e9	−1.93541	−0.967707	−	0.252079i	$-0.918886\pi$
$383$	−2.12799e9	−1.93541	−0.967707	+	0.252079i	$0.918886\pi$
$384$	−5.66231e7	−0.0510310
$385$	5.98643e8	0.534633
$386$	−2.54075e8	−0.224857
$387$	2.07367e8	0.181866
$388$	−2.99698e8	−0.260479
$389$	−1.73532e9	−1.49471	−0.747353	−	0.664428i	$-0.768675\pi$
$389$	−1.73532e9	−1.49471	−0.747353	+	0.664428i	$0.768675\pi$
$390$	−1.19429e8	−0.101949
$391$	−1.44857e8	−0.122552
$392$	−6.02363e7	−0.0505076
$393$	−8.68114e8	−0.721445
$394$	9.23120e8	0.760364
$395$	1.42293e8	0.116170
$396$	3.23561e8	0.261832
$397$	1.90708e9	1.52969	0.764843	−	0.644217i	$-0.222816\pi$
$397$	1.90708e9	1.52969	0.764843	+	0.644217i	$0.222816\pi$
$398$	−8.70091e6	−0.00691789
$399$	−4.80734e7	−0.0378878
$400$	−6.05753e7	−0.0473244
$401$	2.12546e9	1.64607	0.823034	−	0.567992i	$-0.192280\pi$
$401$	2.12546e9	1.64607	0.823034	+	0.567992i	$0.192280\pi$
$402$	−2.61071e8	−0.200433
$403$	6.33221e8	0.481934
$404$	−7.07824e8	−0.534060
$405$	−1.33746e8	−0.100043
$406$	−1.92774e8	−0.142957
$407$	2.00179e9	1.47176
$408$	−4.88442e7	−0.0356043
$409$	3.09769e8	0.223875	0.111938	−	0.993715i	$-0.464294\pi$
$409$	3.09769e8	0.223875	0.111938	+	0.993715i	$0.464294\pi$
$410$	1.65828e7	0.0118827
$411$	−4.57906e8	−0.325334
$412$	−4.28651e8	−0.301970
$413$	−3.65947e8	−0.255619
$414$	2.39098e8	0.165606
$415$	−5.28864e8	−0.363225
$416$	7.19913e7	0.0490290
$417$	1.39054e9	0.939090
$418$	−2.87995e8	−0.192871
$419$	−1.81985e9	−1.20861	−0.604305	−	0.796753i	$-0.706549\pi$
$419$	−1.81985e9	−1.20861	−0.604305	+	0.796753i	$0.706549\pi$
$420$	1.49164e8	0.0982406
$421$	4.07380e8	0.266080	0.133040	−	0.991111i	$-0.457526\pi$
$421$	4.07380e8	0.266080	0.133040	+	0.991111i	$0.457526\pi$
$422$	1.36467e7	0.00883962
$423$	1.85452e8	0.119135
$424$	−3.48025e8	−0.221733
$425$	−5.22534e7	−0.0330182
$426$	6.47579e8	0.405844
$427$	−1.00505e9	−0.624726
$428$	−1.24899e9	−0.770029
$429$	−4.11379e8	−0.251560
$430$	5.72700e8	0.347366
$431$	1.22921e9	0.739527	0.369764	−	0.929126i	$-0.379439\pi$
$431$	1.22921e9	0.739527	0.369764	+	0.929126i	$0.379439\pi$
$432$	8.06216e7	0.0481125
$433$	2.38026e8	0.140902	0.0704509	−	0.997515i	$-0.477556\pi$
$433$	2.38026e8	0.140902	0.0704509	+	0.997515i	$0.477556\pi$
$434$	−7.90877e8	−0.464403
$435$	4.77367e8	0.278061
$436$	−1.08950e9	−0.629545
$437$	−2.12816e8	−0.121989
$438$	2.93747e8	0.167037
$439$	−2.18758e9	−1.23407	−0.617033	−	0.786937i	$-0.711665\pi$
$439$	−2.18758e9	−1.23407	−0.617033	+	0.786937i	$0.711665\pi$
$440$	8.93602e8	0.500103
$441$	8.57661e7	0.0476190
$442$	6.21011e7	0.0342075
$443$	7.00372e8	0.382751	0.191375	−	0.981517i	$-0.438705\pi$
$443$	7.00372e8	0.382751	0.191375	+	0.981517i	$0.438705\pi$
$444$	4.98785e8	0.270441
$445$	−1.62887e9	−0.876248
$446$	−4.88775e8	−0.260878
$447$	−5.37038e8	−0.284399
$448$	−8.99154e7	−0.0472456
$449$	2.41556e9	1.25937	0.629687	−	0.776849i	$-0.283183\pi$
$449$	2.41556e9	1.25937	0.629687	+	0.776849i	$0.283183\pi$
$450$	8.62488e7	0.0446179
$451$	5.71205e7	0.0293207
$452$	7.11801e8	0.362555
$453$	1.82698e9	0.923398
$454$	1.05796e9	0.530610
$455$	−1.89649e8	−0.0943865
$456$	−7.17596e7	−0.0354408
$457$	−7.67101e8	−0.375964	−0.187982	−	0.982173i	$-0.560195\pi$
$457$	−7.67101e8	−0.375964	−0.187982	+	0.982173i	$0.560195\pi$
$458$	−8.13868e8	−0.395844
$459$	6.95458e7	0.0335681
$460$	6.60335e8	0.316309
$461$	−2.40905e9	−1.14523	−0.572614	−	0.819825i	$-0.694071\pi$
$461$	−2.40905e9	−1.14523	−0.572614	+	0.819825i	$0.694071\pi$
$462$	5.13802e8	0.242409
$463$	1.53195e9	0.717315	0.358658	−	0.933469i	$-0.383235\pi$
$463$	1.53195e9	0.717315	0.358658	+	0.933469i	$0.383235\pi$
$464$	−2.87755e8	−0.133724
$465$	1.95846e9	0.903294
$466$	5.64403e8	0.258368
$467$	4.71604e8	0.214273	0.107137	−	0.994244i	$-0.465832\pi$
$467$	4.71604e8	0.214273	0.107137	+	0.994244i	$0.465832\pi$
$468$	−1.02503e8	−0.0462250
$469$	−4.14572e8	−0.185564
$470$	5.12175e8	0.227550
$471$	−1.89408e8	−0.0835268
$472$	−5.46253e8	−0.239109
$473$	1.97269e9	0.857128
$474$	1.22127e8	0.0526729
$475$	−7.67683e7	−0.0328666
$476$	−7.75628e7	−0.0329632
$477$	4.95528e8	0.209052
$478$	−1.41858e8	−0.0594097
$479$	−1.55082e9	−0.644744	−0.322372	−	0.946613i	$-0.604480\pi$
$479$	−1.55082e9	−0.644744	−0.322372	+	0.946613i	$0.604480\pi$
$480$	2.22659e8	0.0918957
$481$	−6.34162e8	−0.259832
$482$	2.03701e9	0.828568
$483$	3.79679e8	0.153321
$484$	1.83088e9	0.734008
$485$	1.17850e9	0.469066
$486$	−1.14791e8	−0.0453609
$487$	4.23914e9	1.66313	0.831566	−	0.555426i	$-0.187445\pi$
$487$	4.23914e9	1.66313	0.831566	+	0.555426i	$0.187445\pi$
$488$	−1.50025e9	−0.584378
$489$	−9.72707e8	−0.376185
$490$	2.36867e8	0.0909531
$491$	−4.19200e9	−1.59822	−0.799108	−	0.601187i	$-0.794695\pi$
$491$	−4.19200e9	−1.59822	−0.799108	+	0.601187i	$0.794695\pi$
$492$	1.42327e7	0.00538777
$493$	−2.48223e8	−0.0932993
$494$	9.12361e7	0.0340504
$495$	−1.27234e9	−0.471502
$496$	−1.18055e9	−0.434409
$497$	1.02833e9	0.375739
$498$	−4.53912e8	−0.164691
$499$	−2.55636e9	−0.921022	−0.460511	−	0.887654i	$-0.652334\pi$
$499$	−2.55636e9	−0.921022	−0.460511	+	0.887654i	$0.652334\pi$
$500$	1.49653e9	0.535416
$501$	−1.97702e9	−0.702390
$502$	2.03144e9	0.716707
$503$	3.40746e9	1.19383	0.596916	−	0.802304i	$-0.296393\pi$
$503$	3.40746e9	1.19383	0.596916	+	0.802304i	$0.296393\pi$
$504$	1.28024e8	0.0445435
$505$	2.78337e9	0.961725
$506$	2.27456e9	0.780495
$507$	1.30324e8	0.0444116
$508$	1.80389e9	0.610504
$509$	−1.85676e9	−0.624086	−0.312043	−	0.950068i	$-0.601013\pi$
$509$	−1.85676e9	−0.624086	−0.312043	+	0.950068i	$0.601013\pi$
$510$	1.92070e8	0.0641155
$511$	4.66459e8	0.154647
$512$	−1.34218e8	−0.0441942
$513$	1.02173e8	0.0334139
$514$	1.03348e9	0.335684
$515$	1.68558e9	0.543781
$516$	4.91536e8	0.157500
$517$	1.76421e9	0.561480
$518$	7.92053e8	0.250380
$519$	−2.17256e9	−0.682158
$520$	−2.83091e8	−0.0882905
$521$	−4.88865e9	−1.51446	−0.757229	−	0.653150i	$-0.773447\pi$
$521$	−4.88865e9	−1.51446	−0.757229	+	0.653150i	$0.773447\pi$
$522$	4.09714e8	0.126076
$523$	2.83241e9	0.865767	0.432883	−	0.901450i	$-0.357496\pi$
$523$	2.83241e9	0.865767	0.432883	+	0.901450i	$0.357496\pi$
$524$	−2.05775e9	−0.624789
$525$	1.36960e8	0.0413082
$526$	2.89012e7	0.00865897
$527$	−1.01837e9	−0.303087
$528$	7.66959e8	0.226753
$529$	−1.72402e9	−0.506346
$530$	1.36854e9	0.399292
$531$	7.77770e8	0.225435
$532$	−1.13952e8	−0.0328118
$533$	−1.80956e7	−0.00517640
$534$	−1.39803e9	−0.397302
$535$	4.91141e9	1.38665
$536$	−6.18836e8	−0.173580
$537$	−3.86896e9	−1.07816
$538$	4.04583e9	1.12013
$539$	8.15899e8	0.224427
$540$	−3.17028e8	−0.0866401
$541$	1.15617e9	0.313929	0.156965	−	0.987604i	$-0.449829\pi$
$541$	1.15617e9	0.313929	0.156965	+	0.987604i	$0.449829\pi$
$542$	3.40767e9	0.919305
$543$	−3.71921e9	−0.996898
$544$	−1.15779e8	−0.0308342
$545$	4.28425e9	1.13367
$546$	−1.62771e8	−0.0427960
$547$	4.72294e9	1.23383	0.616917	−	0.787028i	$-0.288381\pi$
$547$	4.72294e9	1.23383	0.616917	+	0.787028i	$0.288381\pi$
$548$	−1.08541e9	−0.281748
$549$	2.13610e9	0.550957
$550$	8.20491e8	0.210283
$551$	−3.64678e8	−0.0928708
$552$	5.66751e8	0.143419
$553$	1.93933e8	0.0487657
$554$	1.00185e9	0.250334
$555$	−1.96137e9	−0.487006
$556$	3.29609e9	0.813276
$557$	−3.75863e9	−0.921587	−0.460794	−	0.887507i	$-0.652435\pi$
$557$	−3.75863e9	−0.921587	−0.460794	+	0.887507i	$0.652435\pi$
$558$	1.68090e9	0.409565
$559$	−6.24944e8	−0.151321
$560$	3.53574e8	0.0850789
$561$	6.61594e8	0.158205
$562$	−4.69173e9	−1.11495
$563$	−7.13132e8	−0.168419	−0.0842094	−	0.996448i	$-0.526836\pi$
$563$	−7.13132e8	−0.168419	−0.0842094	+	0.996448i	$0.526836\pi$
$564$	4.39589e8	0.103174
$565$	−2.79901e9	−0.652882
$566$	2.65150e8	0.0614659
$567$	−1.82284e8	−0.0419961
$568$	1.53500e9	0.351471
$569$	−4.30301e9	−0.979217	−0.489609	−	0.871942i	$-0.662860\pi$
$569$	−4.30301e9	−0.979217	−0.489609	+	0.871942i	$0.662860\pi$
$570$	2.82180e8	0.0638211
$571$	4.59909e9	1.03382	0.516911	−	0.856039i	$-0.327082\pi$
$571$	4.59909e9	1.03382	0.516911	+	0.856039i	$0.327082\pi$
$572$	−9.75121e8	−0.217857
$573$	9.07273e8	0.201464
$574$	2.26010e7	0.00498811
$575$	6.06309e8	0.133002
$576$	1.91103e8	0.0416667
$577$	−9.60905e8	−0.208240	−0.104120	−	0.994565i	$-0.533203\pi$
$577$	−9.60905e8	−0.208240	−0.104120	+	0.994565i	$0.533203\pi$
$578$	3.18284e9	0.685594
$579$	8.57504e8	0.183595
$580$	1.13154e9	0.240808
$581$	−7.20795e8	−0.152474
$582$	1.01148e9	0.212681
$583$	4.71399e9	0.985256
$584$	6.96289e8	0.144659
$585$	4.03073e8	0.0832411
$586$	−2.28167e9	−0.468394
$587$	7.63413e9	1.55785	0.778926	−	0.627116i	$-0.215765\pi$
$587$	7.63413e9	1.55785	0.778926	+	0.627116i	$0.215765\pi$
$588$	2.03297e8	0.0412393
$589$	−1.49614e9	−0.301695
$590$	2.14803e9	0.430584
$591$	−3.11553e9	−0.620835
$592$	1.18231e9	0.234209
$593$	−8.34954e9	−1.64426	−0.822132	−	0.569297i	$-0.807215\pi$
$593$	−8.34954e9	−1.64426	−0.822132	+	0.569297i	$0.807215\pi$
$594$	−1.09202e9	−0.213785
$595$	3.05000e8	0.0593594
$596$	−1.27298e9	−0.246297
$597$	2.93656e7	0.00564844
$598$	−7.20574e8	−0.137792
$599$	1.70616e8	0.0324358	0.0162179	−	0.999868i	$-0.494837\pi$
$599$	1.70616e8	0.0324358	0.0162179	+	0.999868i	$0.494837\pi$
$600$	2.04442e8	0.0386402
$601$	6.88290e9	1.29333	0.646667	−	0.762772i	$-0.276162\pi$
$601$	6.88290e9	1.29333	0.646667	+	0.762772i	$0.276162\pi$
$602$	7.80540e8	0.145817
$603$	8.81116e8	0.163652
$604$	4.33061e9	0.799687
$605$	−7.19955e9	−1.32179
$606$	2.38890e9	0.436058
$607$	−2.87762e9	−0.522243	−0.261122	−	0.965306i	$-0.584092\pi$
$607$	−2.87762e9	−0.522243	−0.261122	+	0.965306i	$0.584092\pi$
$608$	−1.70097e8	−0.0306926
$609$	6.50611e8	0.116724
$610$	5.89941e9	1.05234
$611$	−5.58899e8	−0.0991263
$612$	1.64849e8	0.0290708
$613$	−4.83038e9	−0.846974	−0.423487	−	0.905902i	$-0.639194\pi$
$613$	−4.83038e9	−0.846974	−0.423487	+	0.905902i	$0.639194\pi$
$614$	1.29394e9	0.225593
$615$	−5.59671e7	−0.00970219
$616$	1.21790e9	0.209933
$617$	7.92314e9	1.35800	0.678999	−	0.734139i	$-0.262414\pi$
$617$	7.92314e9	1.35800	0.678999	+	0.734139i	$0.262414\pi$
$618$	1.44670e9	0.246557
$619$	1.07147e9	0.181578	0.0907892	−	0.995870i	$-0.471061\pi$
$619$	1.07147e9	0.181578	0.0907892	+	0.995870i	$0.471061\pi$
$620$	4.64227e9	0.782276
$621$	−8.06956e8	−0.135216
$622$	1.88779e9	0.314549
$623$	−2.22001e9	−0.367830
$624$	−2.42971e8	−0.0400320
$625$	−4.72942e9	−0.774869
$626$	3.74579e8	0.0610285
$627$	9.71983e8	0.157479
$628$	−4.48968e8	−0.0723363
$629$	1.01988e9	0.163408
$630$	−5.03428e8	−0.0802131
$631$	8.28876e9	1.31337	0.656685	−	0.754165i	$-0.271958\pi$
$631$	8.28876e9	1.31337	0.656685	+	0.754165i	$0.271958\pi$
$632$	2.89486e8	0.0456161
$633$	−4.60576e7	−0.00721752
$634$	4.30829e9	0.671418
$635$	−7.09344e9	−1.09938
$636$	1.17458e9	0.181044
$637$	−2.58475e8	−0.0396214
$638$	3.89764e9	0.594195
$639$	−2.18558e9	−0.331370
$640$	5.27783e8	0.0795840
$641$	−6.03889e9	−0.905636	−0.452818	−	0.891603i	$-0.649581\pi$
$641$	−6.03889e9	−0.905636	−0.452818	+	0.891603i	$0.649581\pi$
$642$	4.21536e9	0.628726
$643$	4.04616e9	0.600212	0.300106	−	0.953906i	$-0.402978\pi$
$643$	4.04616e9	0.600212	0.300106	+	0.953906i	$0.402978\pi$
$644$	8.99980e8	0.132780
$645$	−1.93286e9	−0.283623
$646$	−1.46729e8	−0.0214142
$647$	−1.01485e10	−1.47311	−0.736556	−	0.676377i	$-0.763549\pi$
$647$	−1.01485e10	−1.47311	−0.736556	+	0.676377i	$0.763549\pi$
$648$	−2.72098e8	−0.0392837
$649$	7.39898e9	1.06247
$650$	−2.59929e8	−0.0371243
$651$	2.66921e9	0.379184
$652$	−2.30568e9	−0.325786
$653$	2.38202e9	0.334772	0.167386	−	0.985891i	$-0.446467\pi$
$653$	2.38202e9	0.334772	0.167386	+	0.985891i	$0.446467\pi$
$654$	3.67708e9	0.514021
$655$	8.09168e9	1.12511
$656$	3.37368e7	0.00466595
$657$	−9.91395e8	−0.136385
$658$	6.98051e8	0.0955205
$659$	−1.40084e10	−1.90674	−0.953368	−	0.301812i	$-0.902409\pi$
$659$	−1.40084e10	−1.90674	−0.953368	+	0.301812i	$0.902409\pi$
$660$	−3.01591e9	−0.408333
$661$	−3.36924e8	−0.0453760	−0.0226880	−	0.999743i	$-0.507222\pi$
$661$	−3.36924e8	−0.0453760	−0.0226880	+	0.999743i	$0.507222\pi$
$662$	−7.27554e9	−0.974680
$663$	−2.09591e8	−0.0279303
$664$	−1.07594e9	−0.142626
$665$	4.48091e8	0.0590868
$666$	−1.68340e9	−0.220815
$667$	2.88020e9	0.375821
$668$	−4.68626e9	−0.608288
$669$	1.64962e9	0.213006
$670$	2.43344e9	0.312579
$671$	2.03208e10	2.59665
$672$	3.03464e8	0.0385758
$673$	−6.58816e9	−0.833127	−0.416563	−	0.909107i	$-0.636766\pi$
$673$	−6.58816e9	−0.833127	−0.416563	+	0.909107i	$0.636766\pi$
$674$	−1.43791e9	−0.180893
$675$	−2.91090e8	−0.0364304
$676$	3.08916e8	0.0384615
$677$	−6.29588e9	−0.779823	−0.389911	−	0.920852i	$-0.627494\pi$
$677$	−6.29588e9	−0.779823	−0.389911	+	0.920852i	$0.627494\pi$
$678$	−2.40233e9	−0.296025
$679$	1.60620e9	0.196904
$680$	4.55276e8	0.0555257
$681$	−3.57063e9	−0.433241
$682$	1.59905e10	1.93027
$683$	4.25942e8	0.0511538	0.0255769	−	0.999673i	$-0.491858\pi$
$683$	4.25942e8	0.0511538	0.0255769	+	0.999673i	$0.491858\pi$
$684$	2.42189e8	0.0289373
$685$	4.26814e9	0.507366
$686$	3.22829e8	0.0381802
$687$	2.74680e9	0.323206
$688$	1.16512e9	0.136399
$689$	−1.49338e9	−0.173942
$690$	−2.22863e9	−0.258265
$691$	1.11504e10	1.28563	0.642815	−	0.766021i	$-0.277766\pi$
$691$	1.11504e10	1.28563	0.642815	+	0.766021i	$0.277766\pi$
$692$	−5.14976e9	−0.590766
$693$	−1.73408e9	−0.197926
$694$	−1.16552e8	−0.0132361
$695$	−1.29612e10	−1.46453
$696$	9.71174e8	0.109185
$697$	2.91020e7	0.00325543
$698$	9.98488e9	1.11134
$699$	−1.90486e9	−0.210956
$700$	3.24646e8	0.0357739
$701$	−1.31586e10	−1.44277	−0.721385	−	0.692534i	$-0.756494\pi$
$701$	−1.31586e10	−1.44277	−0.721385	+	0.692534i	$0.756494\pi$
$702$	3.45948e8	0.0377426
$703$	1.49836e9	0.162657
$704$	1.81798e9	0.196374
$705$	−1.72859e9	−0.185794
$706$	−1.69813e9	−0.181616
$707$	3.79349e9	0.403712
$708$	1.84360e9	0.195232
$709$	1.43701e9	0.151425	0.0757124	−	0.997130i	$-0.475877\pi$
$709$	1.43701e9	0.151425	0.0757124	+	0.997130i	$0.475877\pi$
$710$	−6.03608e9	−0.632923
$711$	−4.12179e8	−0.0430073
$712$	−3.31384e9	−0.344074
$713$	1.18164e10	1.22087
$714$	2.61774e8	0.0269143
$715$	3.83446e9	0.392313
$716$	−9.17086e9	−0.933715
$717$	4.78772e8	0.0485078
$718$	−4.06510e9	−0.409860
$719$	7.52557e8	0.0755072	0.0377536	−	0.999287i	$-0.487980\pi$
$719$	7.52557e8	0.0755072	0.0377536	+	0.999287i	$0.487980\pi$
$720$	−7.51473e8	−0.0750325
$721$	2.29730e9	0.228268
$722$	6.93541e9	0.685791
$723$	−6.87490e9	−0.676523
$724$	−8.81589e9	−0.863339
$725$	1.03896e9	0.101255
$726$	−6.17921e9	−0.599315
$727$	−4.19798e9	−0.405200	−0.202600	−	0.979262i	$-0.564939\pi$
$727$	−4.19798e9	−0.405200	−0.202600	+	0.979262i	$0.564939\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−2.73801e9	−0.260498
$731$	1.00506e9	0.0951655
$732$	5.06334e9	0.477143
$733$	−1.61340e10	−1.51314	−0.756570	−	0.653913i	$-0.773126\pi$
$733$	−1.61340e10	−1.51314	−0.756570	+	0.653913i	$0.773126\pi$
$734$	1.26232e9	0.117824
$735$	−7.99425e8	−0.0742629
$736$	1.34341e9	0.124204
$737$	8.38212e9	0.771290
$738$	−4.80353e7	−0.00439910
$739$	1.59667e10	1.45532	0.727661	−	0.685937i	$-0.240608\pi$
$739$	1.59667e10	1.45532	0.727661	+	0.685937i	$0.240608\pi$
$740$	−4.64917e9	−0.421759
$741$	−3.07922e8	−0.0278020
$742$	1.86520e9	0.167614
$743$	−1.18458e10	−1.05951	−0.529755	−	0.848151i	$-0.677716\pi$
$743$	−1.18458e10	−1.05951	−0.529755	+	0.848151i	$0.677716\pi$
$744$	3.98436e9	0.354694
$745$	5.00573e9	0.443527
$746$	2.94124e9	0.259385
$747$	1.53195e9	0.134469
$748$	1.56822e9	0.137010
$749$	6.69383e9	0.582087
$750$	−5.05080e9	−0.437165
$751$	2.43069e9	0.209406	0.104703	−	0.994504i	$-0.466611\pi$
$751$	2.43069e9	0.209406	0.104703	+	0.994504i	$0.466611\pi$
$752$	1.04199e9	0.0893512
$753$	−6.85612e9	−0.585189
$754$	−1.23476e9	−0.104902
$755$	−1.70292e10	−1.44006
$756$	−4.32081e8	−0.0363696
$757$	−1.34156e10	−1.12402	−0.562011	−	0.827130i	$-0.689972\pi$
$757$	−1.34156e10	−1.12402	−0.562011	+	0.827130i	$0.689972\pi$
$758$	7.23233e9	0.603165
$759$	−7.67663e9	−0.637272
$760$	6.68871e8	0.0552707
$761$	−7.21735e9	−0.593651	−0.296826	−	0.954932i	$-0.595928\pi$
$761$	−7.21735e9	−0.593651	−0.296826	+	0.954932i	$0.595928\pi$
$762$	−6.08815e9	−0.498474
$763$	5.83906e9	0.475891
$764$	2.15057e9	0.174473
$765$	−6.48235e8	−0.0523501
$766$	1.70239e10	1.36854
$767$	−2.34398e9	−0.187573
$768$	4.52985e8	0.0360844
$769$	−1.38066e10	−1.09483	−0.547414	−	0.836862i	$-0.684388\pi$
$769$	−1.38066e10	−1.09483	−0.547414	+	0.836862i	$0.684388\pi$
$770$	−4.78915e9	−0.378042
$771$	−3.48799e9	−0.274085
$772$	2.03260e9	0.158998
$773$	9.76421e9	0.760342	0.380171	−	0.924916i	$-0.375865\pi$
$773$	9.76421e9	0.760342	0.380171	+	0.924916i	$0.375865\pi$
$774$	−1.65893e9	−0.128598
$775$	4.26246e9	0.328931
$776$	2.39759e9	0.184187
$777$	−2.67318e9	−0.204435
$778$	1.38825e10	1.05692
$779$	4.27553e7	0.00324048
$780$	9.55431e8	0.0720889
$781$	−2.07916e10	−1.56174
$782$	1.15885e9	0.0866571
$783$	−1.38278e9	−0.102941
$784$	4.81890e8	0.0357143
$785$	1.76547e9	0.130262
$786$	6.94492e9	0.510138
$787$	−8.95294e9	−0.654717	−0.327359	−	0.944900i	$-0.606159\pi$
$787$	−8.95294e9	−0.654717	−0.327359	+	0.944900i	$0.606159\pi$
$788$	−7.38496e9	−0.537659
$789$	−9.75416e7	−0.00707002
$790$	−1.13834e9	−0.0821445
$791$	−3.81481e9	−0.274066
$792$	−2.58849e9	−0.185143
$793$	−6.43759e9	−0.458424
$794$	−1.52566e10	−1.08165
$795$	−4.61881e9	−0.326021
$796$	6.96073e7	0.00489169
$797$	1.29583e10	0.906660	0.453330	−	0.891343i	$-0.350236\pi$
$797$	1.29583e10	0.906660	0.453330	+	0.891343i	$0.350236\pi$
$798$	3.84587e8	0.0267907
$799$	8.98840e8	0.0623403
$800$	4.84602e8	0.0334634
$801$	4.71834e9	0.324396
$802$	−1.70037e10	−1.16395
$803$	−9.43122e9	−0.642781
$804$	2.08857e9	0.141727
$805$	−3.53898e9	−0.239107
$806$	−5.06577e9	−0.340779
$807$	−1.36547e10	−0.914586
$808$	5.66259e9	0.377638
$809$	−3.31421e9	−0.220070	−0.110035	−	0.993928i	$-0.535096\pi$
$809$	−3.31421e9	−0.220070	−0.110035	+	0.993928i	$0.535096\pi$
$810$	1.06997e9	0.0707413
$811$	1.73663e10	1.14323	0.571615	−	0.820522i	$-0.306317\pi$
$811$	1.73663e10	1.14323	0.571615	+	0.820522i	$0.306317\pi$
$812$	1.54219e9	0.101086
$813$	−1.15009e10	−0.750609
$814$	−1.60143e10	−1.04069
$815$	9.06659e9	0.586668
$816$	3.90754e8	0.0251760
$817$	1.47658e9	0.0947285
$818$	−2.47815e9	−0.158304
$819$	5.49353e8	0.0349428
$820$	−1.32663e8	−0.00840235
$821$	9.16526e9	0.578021	0.289011	−	0.957326i	$-0.406674\pi$
$821$	9.16526e9	0.578021	0.289011	+	0.957326i	$0.406674\pi$
$822$	3.66325e9	0.230046
$823$	−1.23495e10	−0.772239	−0.386119	−	0.922449i	$-0.626185\pi$
$823$	−1.23495e10	−0.772239	−0.386119	+	0.922449i	$0.626185\pi$
$824$	3.42921e9	0.213525
$825$	−2.76916e9	−0.171695
$826$	2.92757e9	0.180750
$827$	1.08370e10	0.666255	0.333127	−	0.942882i	$-0.391896\pi$
$827$	1.08370e10	0.666255	0.333127	+	0.942882i	$0.391896\pi$
$828$	−1.91279e9	−0.117101
$829$	1.78237e9	0.108657	0.0543283	−	0.998523i	$-0.482698\pi$
$829$	1.78237e9	0.108657	0.0543283	+	0.998523i	$0.482698\pi$
$830$	4.23091e9	0.256839
$831$	−3.38126e9	−0.204397
$832$	−5.75930e8	−0.0346688
$833$	4.15688e8	0.0249178
$834$	−1.11243e10	−0.664037
$835$	1.84278e10	1.09539
$836$	2.30396e9	0.136381
$837$	−5.67305e9	−0.334408
$838$	1.45588e10	0.854616
$839$	2.24227e10	1.31075	0.655377	−	0.755302i	$-0.272510\pi$
$839$	2.24227e10	1.31075	0.655377	+	0.755302i	$0.272510\pi$
$840$	−1.19331e9	−0.0694666
$841$	−1.23144e10	−0.713885
$842$	−3.25904e9	−0.188147
$843$	1.58346e10	0.910354
$844$	−1.09173e8	−0.00625056
$845$	−1.21475e9	−0.0692608
$846$	−1.48361e9	−0.0842411
$847$	−9.81236e9	−0.554858
$848$	2.78420e9	0.156789
$849$	−8.94882e8	−0.0501867
$850$	4.18027e8	0.0233474
$851$	−1.18339e10	−0.658226
$852$	−5.18063e9	−0.286975
$853$	2.99743e10	1.65359	0.826796	−	0.562502i	$-0.190161\pi$
$853$	2.99743e10	1.65359	0.826796	+	0.562502i	$0.190161\pi$
$854$	8.04039e9	0.441748
$855$	−9.52357e8	−0.0521097
$856$	9.99195e9	0.544493
$857$	2.58131e10	1.40090	0.700450	−	0.713701i	$-0.252982\pi$
$857$	2.58131e10	1.40090	0.700450	+	0.713701i	$0.252982\pi$
$858$	3.29103e9	0.177880
$859$	−2.65860e9	−0.143112	−0.0715562	−	0.997437i	$-0.522797\pi$
$859$	−2.65860e9	−0.143112	−0.0715562	+	0.997437i	$0.522797\pi$
$860$	−4.58160e9	−0.245625
$861$	−7.62783e7	−0.00407277
$862$	−9.83364e9	−0.522925
$863$	−3.64194e9	−0.192884	−0.0964418	−	0.995339i	$-0.530746\pi$
$863$	−3.64194e9	−0.192884	−0.0964418	+	0.995339i	$0.530746\pi$
$864$	−6.44973e8	−0.0340207
$865$	2.02504e10	1.06384
$866$	−1.90421e9	−0.0996327
$867$	−1.07421e10	−0.559785
$868$	6.32702e9	0.328383
$869$	−3.92108e9	−0.202692
$870$	−3.81894e9	−0.196619
$871$	−2.65543e9	−0.136167
$872$	8.71604e9	0.445155
$873$	−3.41375e9	−0.173653
$874$	1.70253e9	0.0862592
$875$	−8.02048e9	−0.404736
$876$	−2.34997e9	−0.118113
$877$	−8.39113e9	−0.420070	−0.210035	−	0.977694i	$-0.567358\pi$
$877$	−8.39113e9	−0.420070	−0.210035	+	0.977694i	$0.567358\pi$
$878$	1.75006e10	0.872616
$879$	7.70064e9	0.382442
$880$	−7.14881e9	−0.353626
$881$	−2.31554e10	−1.14087	−0.570435	−	0.821343i	$-0.693225\pi$
$881$	−2.31554e10	−1.14087	−0.570435	+	0.821343i	$0.693225\pi$
$882$	−6.86129e8	−0.0336718
$883$	2.66795e7	0.00130411	0.000652055	−	1.00000i	$-0.499792\pi$
$883$	2.66795e7	0.00130411	0.000652055		1.00000i	$0.499792\pi$
$884$	−4.96809e8	−0.0241884
$885$	−7.24959e9	−0.351570
$886$	−5.60298e9	−0.270646
$887$	5.10941e9	0.245832	0.122916	−	0.992417i	$-0.460775\pi$
$887$	5.10941e9	0.245832	0.122916	+	0.992417i	$0.460775\pi$
$888$	−3.99028e9	−0.191231
$889$	−9.66775e9	−0.461497
$890$	1.30310e10	0.619601
$891$	3.68556e9	0.174555
$892$	3.91020e9	0.184469
$893$	1.32053e9	0.0620540
$894$	4.29630e9	0.201101
$895$	3.60625e10	1.68142
$896$	7.19323e8	0.0334077
$897$	2.43194e9	0.112507
$898$	−1.93245e10	−0.890513
$899$	2.02483e10	0.929457
$900$	−6.89990e8	−0.0315496
$901$	2.40171e9	0.109391
$902$	−4.56964e8	−0.0207328
$903$	−2.63432e9	−0.119059
$904$	−5.69441e9	−0.256365
$905$	3.46667e10	1.55468
$906$	−1.46158e10	−0.652941
$907$	4.00769e9	0.178348	0.0891741	−	0.996016i	$-0.471577\pi$
$907$	4.00769e9	0.178348	0.0891741	+	0.996016i	$0.471577\pi$
$908$	−8.46371e9	−0.375198
$909$	−8.06255e9	−0.356040
$910$	1.51719e9	0.0667414
$911$	−1.71929e10	−0.753415	−0.376707	−	0.926332i	$-0.622944\pi$
$911$	−1.71929e10	−0.753415	−0.376707	+	0.926332i	$0.622944\pi$
$912$	5.74077e8	0.0250604
$913$	1.45736e10	0.633751
$914$	6.13681e9	0.265846
$915$	−1.99105e10	−0.859229
$916$	6.51094e9	0.279904
$917$	1.10283e10	0.472296
$918$	−5.56366e8	−0.0237362
$919$	−1.75106e10	−0.744214	−0.372107	−	0.928190i	$-0.621365\pi$
$919$	−1.75106e10	−0.744214	−0.372107	+	0.928190i	$0.621365\pi$
$920$	−5.28268e9	−0.223664
$921$	−4.36706e9	−0.184196
$922$	1.92724e10	0.809799
$923$	6.58672e9	0.275717
$924$	−4.11042e9	−0.171409
$925$	−4.26880e9	−0.177341
$926$	−1.22556e10	−0.507218
$927$	−4.88260e9	−0.201313
$928$	2.30204e9	0.0945574
$929$	3.67318e10	1.50310	0.751549	−	0.659678i	$-0.229307\pi$
$929$	3.67318e10	1.50310	0.751549	+	0.659678i	$0.229307\pi$
$930$	−1.56677e10	−0.638725
$931$	6.10710e8	0.0248034
$932$	−4.51522e9	−0.182694
$933$	−6.37130e9	−0.256828
$934$	−3.77283e9	−0.151514
$935$	−6.16671e9	−0.246725
$936$	8.20026e8	0.0326860
$937$	−1.19505e10	−0.474567	−0.237283	−	0.971440i	$-0.576257\pi$
$937$	−1.19505e10	−0.474567	−0.237283	+	0.971440i	$0.576257\pi$
$938$	3.31657e9	0.131214
$939$	−1.26420e9	−0.0498296
$940$	−4.09740e9	−0.160902
$941$	1.33467e9	0.0522167	0.0261083	−	0.999659i	$-0.491689\pi$
$941$	1.33467e9	0.0522167	0.0261083	+	0.999659i	$0.491689\pi$
$942$	1.51527e9	0.0590624
$943$	−3.37677e8	−0.0131133
$944$	4.37002e9	0.169076
$945$	1.69907e9	0.0654937
$946$	−1.57815e10	−0.606081
$947$	−2.67182e10	−1.02231	−0.511155	−	0.859489i	$-0.670782\pi$
$947$	−2.67182e10	−1.02231	−0.511155	+	0.859489i	$0.670782\pi$
$948$	−9.77016e8	−0.0372454
$949$	2.98779e9	0.113480
$950$	6.14147e8	0.0232402
$951$	−1.45405e10	−0.548211
$952$	6.20502e8	0.0233085
$953$	−2.98289e10	−1.11638	−0.558191	−	0.829713i	$-0.688504\pi$
$953$	−2.98289e10	−1.11638	−0.558191	+	0.829713i	$0.688504\pi$
$954$	−3.96422e9	−0.147822
$955$	−8.45668e9	−0.314187
$956$	1.13487e9	0.0420090
$957$	−1.31545e10	−0.485159
$958$	1.24066e10	0.455903
$959$	5.81710e9	0.212981
$960$	−1.78127e9	−0.0649801
$961$	5.55585e10	2.01938
$962$	5.07329e9	0.183729
$963$	−1.42268e10	−0.513353
$964$	−1.62961e10	−0.585886
$965$	−7.99279e9	−0.286321
$966$	−3.03743e9	−0.108414
$967$	−1.52547e10	−0.542515	−0.271257	−	0.962507i	$-0.587439\pi$
$967$	−1.52547e10	−0.542515	−0.271257	+	0.962507i	$0.587439\pi$
$968$	−1.46470e10	−0.519022
$969$	4.95210e8	0.0174846
$970$	−9.42801e9	−0.331680
$971$	1.08089e10	0.378893	0.189446	−	0.981891i	$-0.439331\pi$
$971$	1.08089e10	0.378893	0.189446	+	0.981891i	$0.439331\pi$
$972$	9.18330e8	0.0320750
$973$	−1.76650e10	−0.614779
$974$	−3.39131e10	−1.17601
$975$	8.77262e8	0.0303119
$976$	1.20020e10	0.413218
$977$	3.59918e10	1.23473	0.617366	−	0.786676i	$-0.288200\pi$
$977$	3.59918e10	1.23473	0.617366	+	0.786676i	$0.288200\pi$
$978$	7.78166e9	0.266003
$979$	4.48859e10	1.52887
$980$	−1.89493e9	−0.0643136
$981$	−1.24101e10	−0.419696
$982$	3.35360e10	1.13011
$983$	−2.16979e10	−0.728585	−0.364293	−	0.931285i	$-0.618689\pi$
$983$	−2.16979e10	−0.728585	−0.364293	+	0.931285i	$0.618689\pi$
$984$	−1.13862e8	−0.00380973
$985$	2.90398e10	0.968205
$986$	1.98579e9	0.0659726
$987$	−2.35592e9	−0.0779921
$988$	−7.29889e8	−0.0240773
$989$	−1.16619e10	−0.383339
$990$	1.01787e10	0.333402
$991$	−3.26123e10	−1.06445	−0.532224	−	0.846604i	$-0.678643\pi$
$991$	−3.26123e10	−1.06445	−0.532224	+	0.846604i	$0.678643\pi$
$992$	9.44441e9	0.307174
$993$	2.45549e10	0.795823
$994$	−8.22665e9	−0.265687
$995$	−2.73716e8	−0.00880886
$996$	3.63130e9	0.116454
$997$	4.15307e10	1.32720	0.663599	−	0.748088i	$-0.269028\pi$
$997$	4.15307e10	1.32720	0.663599	+	0.748088i	$0.269028\pi$
$998$	2.04509e10	0.651261
$999$	5.68148e9	0.180294

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.j.1.2	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -251.667 q^{5} -216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -251.667 q^{5} -216.000 q^{6} -343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +2013.33 q^{10} +6935.03 q^{11} +1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} -6795.00 q^{15} +4096.00 q^{16} +3533.29 q^{17} -5832.00 q^{18} +5190.95 q^{19} -16106.7 q^{20} -9261.00 q^{21} -55480.2 q^{22} -40997.6 q^{23} -13824.0 q^{24} -14788.9 q^{25} +17576.0 q^{26} +19683.0 q^{27} -21952.0 q^{28} -70252.8 q^{29} +54360.0 q^{30} -288221. q^{31} -32768.0 q^{32} +187246. q^{33} -28266.3 q^{34} +86321.7 q^{35} +46656.0 q^{36} +288649. q^{37} -41527.6 q^{38} -59319.0 q^{39} +128853. q^{40} +8236.51 q^{41} +74088.0 q^{42} +284453. q^{43} +443842. q^{44} -183465. q^{45} +327981. q^{46} +254392. q^{47} +110592. q^{48} +117649. q^{49} +118311. q^{50} +95398.8 q^{51} -140608. q^{52} +679737. q^{53} -157464. q^{54} -1.74532e6 q^{55} +175616. q^{56} +140156. q^{57} +562022. q^{58} +1.06690e6 q^{59} -434880. q^{60} +2.93017e6 q^{61} +2.30577e6 q^{62} -250047. q^{63} +262144. q^{64} +552912. q^{65} -1.49797e6 q^{66} +1.20866e6 q^{67} +226131. q^{68} -1.10694e6 q^{69} -690573. q^{70} -2.99805e6 q^{71} -373248. q^{72} -1.35994e6 q^{73} -2.30919e6 q^{74} -399300. q^{75} +332221. q^{76} -2.37872e6 q^{77} +474552. q^{78} -565403. q^{79} -1.03083e6 q^{80} +531441. q^{81} -65892.1 q^{82} +2.10144e6 q^{83} -592704. q^{84} -889211. q^{85} -2.27563e6 q^{86} -1.89682e6 q^{87} -3.55074e6 q^{88} +6.47234e6 q^{89} +1.46772e6 q^{90} +753571. q^{91} -2.62385e6 q^{92} -7.78196e6 q^{93} -2.03513e6 q^{94} -1.30639e6 q^{95} -884736. q^{96} -4.68279e6 q^{97} -941192. q^{98} +5.05564e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} + 56 q^{5} - 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9}+O(q^{10}) \) 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 + 56 * q^5 - 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9	\( 5 q - 40 q^{2} + 135 q^{3} + 320 q^{4} + 56 q^{5} - 1080 q^{6} - 1715 q^{7} - 2560 q^{8} + 3645 q^{9} - 448 q^{10} - 3679 q^{11} + 8640 q^{12} - 10985 q^{13} + 13720 q^{14} + 1512 q^{15} + 20480 q^{16} + 409 q^{17} - 29160 q^{18} + 33730 q^{19} + 3584 q^{20} - 46305 q^{21} + 29432 q^{22} - 142142 q^{23} - 69120 q^{24} + 153981 q^{25} + 87880 q^{26} + 98415 q^{27} - 109760 q^{28} + 88028 q^{29} - 12096 q^{30} + 244543 q^{31} - 163840 q^{32} - 99333 q^{33} - 3272 q^{34} - 19208 q^{35} + 233280 q^{36} + 730963 q^{37} - 269840 q^{38} - 296595 q^{39} - 28672 q^{40} + 479512 q^{41} + 370440 q^{42} - 406536 q^{43} - 235456 q^{44} + 40824 q^{45} + 1137136 q^{46} + 1138945 q^{47} + 552960 q^{48} + 588245 q^{49} - 1231848 q^{50} + 11043 q^{51} - 703040 q^{52} + 297595 q^{53} - 787320 q^{54} - 1834423 q^{55} + 878080 q^{56} + 910710 q^{57} - 704224 q^{58} + 941652 q^{59} + 96768 q^{60} - 2985259 q^{61} - 1956344 q^{62} - 1250235 q^{63} + 1310720 q^{64} - 123032 q^{65} + 794664 q^{66} - 2333504 q^{67} + 26176 q^{68} - 3837834 q^{69} + 153664 q^{70} - 11322272 q^{71} - 1866240 q^{72} - 6631604 q^{73} - 5847704 q^{74} + 4157487 q^{75} + 2158720 q^{76} + 1261897 q^{77} + 2372760 q^{78} - 10600265 q^{79} + 229376 q^{80} + 2657205 q^{81} - 3836096 q^{82} - 2425229 q^{83} - 2963520 q^{84} - 12267705 q^{85} + 3252288 q^{86} + 2376756 q^{87} + 1883648 q^{88} - 1581837 q^{89} - 326592 q^{90} + 3767855 q^{91} - 9097088 q^{92} + 6602661 q^{93} - 9111560 q^{94} - 11507718 q^{95} - 4423680 q^{96} + 5298407 q^{97} - 4705960 q^{98} - 2681991 q^{99}+O(q^{100}) \) 5 * q - 40 * q^2 + 135 * q^3 + 320 * q^4 + 56 * q^5 - 1080 * q^6 - 1715 * q^7 - 2560 * q^8 + 3645 * q^9 - 448 * q^10 - 3679 * q^11 + 8640 * q^12 - 10985 * q^13 + 13720 * q^14 + 1512 * q^15 + 20480 * q^16 + 409 * q^17 - 29160 * q^18 + 33730 * q^19 + 3584 * q^20 - 46305 * q^21 + 29432 * q^22 - 142142 * q^23 - 69120 * q^24 + 153981 * q^25 + 87880 * q^26 + 98415 * q^27 - 109760 * q^28 + 88028 * q^29 - 12096 * q^30 + 244543 * q^31 - 163840 * q^32 - 99333 * q^33 - 3272 * q^34 - 19208 * q^35 + 233280 * q^36 + 730963 * q^37 - 269840 * q^38 - 296595 * q^39 - 28672 * q^40 + 479512 * q^41 + 370440 * q^42 - 406536 * q^43 - 235456 * q^44 + 40824 * q^45 + 1137136 * q^46 + 1138945 * q^47 + 552960 * q^48 + 588245 * q^49 - 1231848 * q^50 + 11043 * q^51 - 703040 * q^52 + 297595 * q^53 - 787320 * q^54 - 1834423 * q^55 + 878080 * q^56 + 910710 * q^57 - 704224 * q^58 + 941652 * q^59 + 96768 * q^60 - 2985259 * q^61 - 1956344 * q^62 - 1250235 * q^63 + 1310720 * q^64 - 123032 * q^65 + 794664 * q^66 - 2333504 * q^67 + 26176 * q^68 - 3837834 * q^69 + 153664 * q^70 - 11322272 * q^71 - 1866240 * q^72 - 6631604 * q^73 - 5847704 * q^74 + 4157487 * q^75 + 2158720 * q^76 + 1261897 * q^77 + 2372760 * q^78 - 10600265 * q^79 + 229376 * q^80 + 2657205 * q^81 - 3836096 * q^82 - 2425229 * q^83 - 2963520 * q^84 - 12267705 * q^85 + 3252288 * q^86 + 2376756 * q^87 + 1883648 * q^88 - 1581837 * q^89 - 326592 * q^90 + 3767855 * q^91 - 9097088 * q^92 + 6602661 * q^93 - 9111560 * q^94 - 11507718 * q^95 - 4423680 * q^96 + 5298407 * q^97 - 4705960 * q^98 - 2681991 * q^99

Introduction

L-functions

Modular forms

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