LMFDB - Embedded newform 546.8.a.q.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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 367021x^{4} - 17702143x^{3} + 34815194576x^{2} + 1422988371620x - 933871993059968 $ x^6 - x^5 - 367021x^4 - 17702143x^3 + 34815194576x^2 + 1422988371620x - 933871993059968
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-264.243$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -262.243 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -262.243 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -2097.94 q^{10} +8089.34 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} +7080.55 q^{15} +4096.00 q^{16} +36358.9 q^{17} +5832.00 q^{18} +7942.87 q^{19} -16783.5 q^{20} -9261.00 q^{21} +64714.7 q^{22} +80499.5 q^{23} -13824.0 q^{24} -9353.86 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} -98927.0 q^{29} +56644.4 q^{30} -315959. q^{31} +32768.0 q^{32} -218412. q^{33} +290871. q^{34} -89949.2 q^{35} +46656.0 q^{36} -533705. q^{37} +63543.0 q^{38} +59319.0 q^{39} -134268. q^{40} +293184. q^{41} -74088.0 q^{42} +438998. q^{43} +517718. q^{44} -191175. q^{45} +643996. q^{46} -410797. q^{47} -110592. q^{48} +117649. q^{49} -74830.9 q^{50} -981690. q^{51} -140608. q^{52} +1.31693e6 q^{53} -157464. q^{54} -2.12137e6 q^{55} +175616. q^{56} -214457. q^{57} -791416. q^{58} +1.45055e6 q^{59} +453155. q^{60} -1.08338e6 q^{61} -2.52767e6 q^{62} +250047. q^{63} +262144. q^{64} +576147. q^{65} -1.74730e6 q^{66} +258422. q^{67} +2.32697e6 q^{68} -2.17349e6 q^{69} -719593. q^{70} +2.75251e6 q^{71} +373248. q^{72} +574512. q^{73} -4.26964e6 q^{74} +252554. q^{75} +508344. q^{76} +2.77464e6 q^{77} +474552. q^{78} -2.14531e6 q^{79} -1.07415e6 q^{80} +531441. q^{81} +2.34547e6 q^{82} +5.48945e6 q^{83} -592704. q^{84} -9.53485e6 q^{85} +3.51198e6 q^{86} +2.67103e6 q^{87} +4.14174e6 q^{88} -8.91294e6 q^{89} -1.52940e6 q^{90} -753571. q^{91} +5.15196e6 q^{92} +8.53089e6 q^{93} -3.28637e6 q^{94} -2.08296e6 q^{95} -884736. q^{96} -1.12731e7 q^{97} +941192. q^{98} +5.89713e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) $ 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 104 q^{10} + 10054 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} - 351 q^{15} + 24576 q^{16} + 21222 q^{17} + 34992 q^{18} + 9527 q^{19} + 832 q^{20} - 55566 q^{21} + 80432 q^{22} + 33229 q^{23} - 82944 q^{24} + 265321 q^{25} - 105456 q^{26} - 118098 q^{27} + 131712 q^{28} + 174185 q^{29} - 2808 q^{30} + 119045 q^{31} + 196608 q^{32} - 271458 q^{33} + 169776 q^{34} + 4459 q^{35} + 279936 q^{36} + 56562 q^{37} + 76216 q^{38} + 355914 q^{39} + 6656 q^{40} + 101632 q^{41} - 444528 q^{42} + 441323 q^{43} + 643456 q^{44} + 9477 q^{45} + 265832 q^{46} - 892849 q^{47} - 663552 q^{48} + 705894 q^{49} + 2122568 q^{50} - 572994 q^{51} - 843648 q^{52} + 2093965 q^{53} - 944784 q^{54} - 331222 q^{55} + 1053696 q^{56} - 257229 q^{57} + 1393480 q^{58} - 136204 q^{59} - 22464 q^{60} - 3989946 q^{61} + 952360 q^{62} + 1500282 q^{63} + 1572864 q^{64} - 28561 q^{65} - 2171664 q^{66} - 2218250 q^{67} + 1358208 q^{68} - 897183 q^{69} + 35672 q^{70} + 2045928 q^{71} + 2239488 q^{72} - 8557479 q^{73} + 452496 q^{74} - 7163667 q^{75} + 609728 q^{76} + 3448522 q^{77} + 2847312 q^{78} - 8559709 q^{79} + 53248 q^{80} + 3188646 q^{81} + 813056 q^{82} + 2496351 q^{83} - 3556224 q^{84} + 5335304 q^{85} + 3530584 q^{86} - 4702995 q^{87} + 5147648 q^{88} - 2446683 q^{89} + 75816 q^{90} - 4521426 q^{91} + 2126656 q^{92} - 3214215 q^{93} - 7142792 q^{94} + 16410211 q^{95} - 5308416 q^{96} + 5786889 q^{97} + 5647152 q^{98} + 7329366 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 104 * q^10 + 10054 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 - 351 * q^15 + 24576 * q^16 + 21222 * q^17 + 34992 * q^18 + 9527 * q^19 + 832 * q^20 - 55566 * q^21 + 80432 * q^22 + 33229 * q^23 - 82944 * q^24 + 265321 * q^25 - 105456 * q^26 - 118098 * q^27 + 131712 * q^28 + 174185 * q^29 - 2808 * q^30 + 119045 * q^31 + 196608 * q^32 - 271458 * q^33 + 169776 * q^34 + 4459 * q^35 + 279936 * q^36 + 56562 * q^37 + 76216 * q^38 + 355914 * q^39 + 6656 * q^40 + 101632 * q^41 - 444528 * q^42 + 441323 * q^43 + 643456 * q^44 + 9477 * q^45 + 265832 * q^46 - 892849 * q^47 - 663552 * q^48 + 705894 * q^49 + 2122568 * q^50 - 572994 * q^51 - 843648 * q^52 + 2093965 * q^53 - 944784 * q^54 - 331222 * q^55 + 1053696 * q^56 - 257229 * q^57 + 1393480 * q^58 - 136204 * q^59 - 22464 * q^60 - 3989946 * q^61 + 952360 * q^62 + 1500282 * q^63 + 1572864 * q^64 - 28561 * q^65 - 2171664 * q^66 - 2218250 * q^67 + 1358208 * q^68 - 897183 * q^69 + 35672 * q^70 + 2045928 * q^71 + 2239488 * q^72 - 8557479 * q^73 + 452496 * q^74 - 7163667 * q^75 + 609728 * q^76 + 3448522 * q^77 + 2847312 * q^78 - 8559709 * q^79 + 53248 * q^80 + 3188646 * q^81 + 813056 * q^82 + 2496351 * q^83 - 3556224 * q^84 + 5335304 * q^85 + 3530584 * q^86 - 4702995 * q^87 + 5147648 * q^88 - 2446683 * q^89 + 75816 * q^90 - 4521426 * q^91 + 2126656 * q^92 - 3214215 * q^93 - 7142792 * q^94 + 16410211 * q^95 - 5308416 * q^96 + 5786889 * q^97 + 5647152 * q^98 + 7329366 * 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
$5$	−262.243	−0.938227	−0.469114	−	0.883138i	$-0.655427\pi$
$5$	−262.243	−0.938227	−0.469114	+	0.883138i	$0.655427\pi$
$6$	−216.000	−0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−2097.94	−0.663427
$11$	8089.34	1.83248	0.916239	−	0.400632i	$-0.131209\pi$
$11$	8089.34	1.83248	0.916239	+	0.400632i	$0.131209\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	2744.00	0.267261
$15$	7080.55	0.541686
$16$	4096.00	0.250000
$17$	36358.9	1.79490	0.897448	−	0.441120i	$-0.145419\pi$
$17$	36358.9	1.79490	0.897448	+	0.441120i	$0.145419\pi$
$18$	5832.00	0.235702
$19$	7942.87	0.265668	0.132834	−	0.991138i	$-0.457592\pi$
$19$	7942.87	0.265668	0.132834	+	0.991138i	$0.457592\pi$
$20$	−16783.5	−0.469114
$21$	−9261.00	−0.218218
$22$	64714.7	1.29576
$23$	80499.5	1.37958	0.689788	−	0.724012i	$-0.257704\pi$
$23$	80499.5	1.37958	0.689788	+	0.724012i	$0.257704\pi$
$24$	−13824.0	−0.204124
$25$	−9353.86	−0.119729
$26$	−17576.0	−0.196116
$27$	−19683.0	−0.192450
$28$	21952.0	0.188982
$29$	−98927.0	−0.753220	−0.376610	−	0.926372i	$-0.622910\pi$
$29$	−98927.0	−0.753220	−0.376610	+	0.926372i	$0.622910\pi$
$30$	56644.4	0.383030
$31$	−315959.	−1.90487	−0.952434	−	0.304745i	$-0.901429\pi$
$31$	−315959.	−1.90487	−0.952434	+	0.304745i	$0.901429\pi$
$32$	32768.0	0.176777
$33$	−218412.	−1.05798
$34$	290871.	1.26918
$35$	−89949.2	−0.354617
$36$	46656.0	0.166667
$37$	−533705.	−1.73219	−0.866094	−	0.499881i	$-0.833377\pi$
$37$	−533705.	−1.73219	−0.866094	+	0.499881i	$0.833377\pi$
$38$	63543.0	0.187856
$39$	59319.0	0.160128
$40$	−134268.	−0.331713
$41$	293184.	0.664350	0.332175	−	0.943218i	$-0.392217\pi$
$41$	293184.	0.664350	0.332175	+	0.943218i	$0.392217\pi$
$42$	−74088.0	−0.154303
$43$	438998.	0.842021	0.421010	−	0.907056i	$-0.361676\pi$
$43$	438998.	0.842021	0.421010	+	0.907056i	$0.361676\pi$
$44$	517718.	0.916239
$45$	−191175.	−0.312742
$46$	643996.	0.975507
$47$	−410797.	−0.577145	−0.288572	−	0.957458i	$-0.593181\pi$
$47$	−410797.	−0.577145	−0.288572	+	0.957458i	$0.593181\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	−74830.9	−0.0846615
$51$	−981690.	−1.03628
$52$	−140608.	−0.138675
$53$	1.31693e6	1.21506	0.607529	−	0.794298i	$-0.292161\pi$
$53$	1.31693e6	1.21506	0.607529	+	0.794298i	$0.292161\pi$
$54$	−157464.	−0.136083
$55$	−2.12137e6	−1.71928
$56$	175616.	0.133631
$57$	−214457.	−0.153384
$58$	−791416.	−0.532607
$59$	1.45055e6	0.919497	0.459748	−	0.888049i	$-0.347940\pi$
$59$	1.45055e6	0.919497	0.459748	+	0.888049i	$0.347940\pi$
$60$	453155.	0.270843
$61$	−1.08338e6	−0.611119	−0.305559	−	0.952173i	$-0.598843\pi$
$61$	−1.08338e6	−0.611119	−0.305559	+	0.952173i	$0.598843\pi$
$62$	−2.52767e6	−1.34694
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	576147.	0.260217
$66$	−1.74730e6	−0.748106
$67$	258422.	0.104970	0.0524852	−	0.998622i	$-0.483286\pi$
$67$	258422.	0.104970	0.0524852	+	0.998622i	$0.483286\pi$
$68$	2.32697e6	0.897448
$69$	−2.17349e6	−0.796498
$70$	−719593.	−0.250752
$71$	2.75251e6	0.912694	0.456347	−	0.889802i	$-0.349158\pi$
$71$	2.75251e6	0.912694	0.456347	+	0.889802i	$0.349158\pi$
$72$	373248.	0.117851
$73$	574512.	0.172850	0.0864250	−	0.996258i	$-0.472456\pi$
$73$	574512.	0.172850	0.0864250	+	0.996258i	$0.472456\pi$
$74$	−4.26964e6	−1.22484
$75$	252554.	0.0691258
$76$	508344.	0.132834
$77$	2.77464e6	0.692612
$78$	474552.	0.113228
$79$	−2.14531e6	−0.489547	−0.244774	−	0.969580i	$-0.578714\pi$
$79$	−2.14531e6	−0.489547	−0.244774	+	0.969580i	$0.578714\pi$
$80$	−1.07415e6	−0.234557
$81$	531441.	0.111111
$82$	2.34547e6	0.469767
$83$	5.48945e6	1.05379	0.526897	−	0.849929i	$-0.323355\pi$
$83$	5.48945e6	1.05379	0.526897	+	0.849929i	$0.323355\pi$
$84$	−592704.	−0.109109
$85$	−9.53485e6	−1.68402
$86$	3.51198e6	0.595398
$87$	2.67103e6	0.434872
$88$	4.14174e6	0.647879
$89$	−8.91294e6	−1.34016	−0.670079	−	0.742290i	$-0.733740\pi$
$89$	−8.91294e6	−1.34016	−0.670079	+	0.742290i	$0.733740\pi$
$90$	−1.52940e6	−0.221142
$91$	−753571.	−0.104828
$92$	5.15196e6	0.689788
$93$	8.53089e6	1.09978
$94$	−3.28637e6	−0.408103
$95$	−2.08296e6	−0.249257
$96$	−884736.	−0.102062
$97$	−1.12731e7	−1.25413	−0.627064	−	0.778967i	$-0.715744\pi$
$97$	−1.12731e7	−1.25413	−0.627064	+	0.778967i	$0.715744\pi$
$98$	941192.	0.101015
$99$	5.89713e6	0.610826
$100$	−598647.	−0.0598647
$101$	9.54170e6	0.921512	0.460756	−	0.887527i	$-0.347578\pi$
$101$	9.54170e6	0.921512	0.460756	+	0.887527i	$0.347578\pi$
$102$	−7.85352e6	−0.732763
$103$	1.57024e7	1.41591	0.707955	−	0.706257i	$-0.249618\pi$
$103$	1.57024e7	1.41591	0.707955	+	0.706257i	$0.249618\pi$
$104$	−1.12486e6	−0.0980581
$105$	2.42863e6	0.204738
$106$	1.05354e7	0.859175
$107$	1.39745e7	1.10279	0.551395	−	0.834244i	$-0.314096\pi$
$107$	1.39745e7	1.10279	0.551395	+	0.834244i	$0.314096\pi$
$108$	−1.25971e6	−0.0962250
$109$	2.91571e6	0.215651	0.107825	−	0.994170i	$-0.465611\pi$
$109$	2.91571e6	0.215651	0.107825	+	0.994170i	$0.465611\pi$
$110$	−1.69710e7	−1.21572
$111$	1.44100e7	1.00008
$112$	1.40493e6	0.0944911
$113$	−462016.	−0.0301219	−0.0150610	−	0.999887i	$-0.504794\pi$
$113$	−462016.	−0.0301219	−0.0150610	+	0.999887i	$0.504794\pi$
$114$	−1.71566e6	−0.108459
$115$	−2.11104e7	−1.29436
$116$	−6.33133e6	−0.376610
$117$	−1.60161e6	−0.0924500
$118$	1.16044e7	0.650182
$119$	1.24711e7	0.678407
$120$	3.62524e6	0.191515
$121$	4.59503e7	2.35798
$122$	−8.66702e6	−0.432126
$123$	−7.91598e6	−0.383563
$124$	−2.02214e7	−0.952434
$125$	2.29407e7	1.05056
$126$	2.00038e6	0.0890871
$127$	4.31989e7	1.87137	0.935685	−	0.352836i	$-0.114783\pi$
$127$	4.31989e7	1.87137	0.935685	+	0.352836i	$0.114783\pi$
$128$	2.09715e6	0.0883883
$129$	−1.18529e7	−0.486141
$130$	4.60917e6	0.184002
$131$	−3.79145e7	−1.47352	−0.736760	−	0.676154i	$-0.763645\pi$
$131$	−3.79145e7	−1.47352	−0.736760	+	0.676154i	$0.763645\pi$
$132$	−1.39784e7	−0.528991
$133$	2.72440e6	0.100413
$134$	2.06737e6	0.0742253
$135$	5.16172e6	0.180562
$136$	1.86157e7	0.634592
$137$	1.99944e7	0.664333	0.332166	−	0.943221i	$-0.392220\pi$
$137$	1.99944e7	0.664333	0.332166	+	0.943221i	$0.392220\pi$
$138$	−1.73879e7	−0.563209
$139$	5.72515e7	1.80815	0.904076	−	0.427371i	$-0.140560\pi$
$139$	5.72515e7	1.80815	0.904076	+	0.427371i	$0.140560\pi$
$140$	−5.75675e6	−0.177308
$141$	1.10915e7	0.333215
$142$	2.20201e7	0.645372
$143$	−1.77723e7	−0.508238
$144$	2.98598e6	0.0833333
$145$	2.59429e7	0.706692
$146$	4.59610e6	0.122223
$147$	−3.17652e6	−0.0824786
$148$	−3.41571e7	−0.866094
$149$	−7.54723e7	−1.86911	−0.934557	−	0.355813i	$-0.884204\pi$
$149$	−7.54723e7	−1.86911	−0.934557	+	0.355813i	$0.884204\pi$
$150$	2.02043e6	0.0488793
$151$	−1.79894e7	−0.425203	−0.212602	−	0.977139i	$-0.568194\pi$
$151$	−1.79894e7	−0.425203	−0.212602	+	0.977139i	$0.568194\pi$
$152$	4.06675e6	0.0939279
$153$	2.65056e7	0.598299
$154$	2.21972e7	0.489750
$155$	8.28579e7	1.78720
$156$	3.79642e6	0.0800641
$157$	−2.15622e7	−0.444677	−0.222338	−	0.974970i	$-0.571369\pi$
$157$	−2.15622e7	−0.444677	−0.222338	+	0.974970i	$0.571369\pi$
$158$	−1.71625e7	−0.346162
$159$	−3.55571e7	−0.701514
$160$	−8.59316e6	−0.165857
$161$	2.76113e7	0.521431
$162$	4.25153e6	0.0785674
$163$	−3.58850e7	−0.649017	−0.324509	−	0.945883i	$-0.605199\pi$
$163$	−3.58850e7	−0.649017	−0.324509	+	0.945883i	$0.605199\pi$
$164$	1.87638e7	0.332175
$165$	5.72770e7	0.992627
$166$	4.39156e7	0.745145
$167$	−6.65864e7	−1.10631	−0.553156	−	0.833077i	$-0.686577\pi$
$167$	−6.65864e7	−1.10631	−0.553156	+	0.833077i	$0.686577\pi$
$168$	−4.74163e6	−0.0771517
$169$	4.82681e6	0.0769231
$170$	−7.62788e7	−1.19078
$171$	5.79035e6	0.0885561
$172$	2.80959e7	0.421010
$173$	−1.04765e8	−1.53835	−0.769173	−	0.639040i	$-0.779332\pi$
$173$	−1.04765e8	−1.53835	−0.769173	+	0.639040i	$0.779332\pi$
$174$	2.13682e7	0.307501
$175$	−3.20837e6	−0.0452535
$176$	3.31339e7	0.458120
$177$	−3.91648e7	−0.530872
$178$	−7.13035e7	−0.947635
$179$	9.04976e7	1.17937	0.589687	−	0.807632i	$-0.299251\pi$
$179$	9.04976e7	1.17937	0.589687	+	0.807632i	$0.299251\pi$
$180$	−1.22352e7	−0.156371
$181$	−365955.	−0.00458726	−0.00229363	−	0.999997i	$-0.500730\pi$
$181$	−365955.	−0.00458726	−0.00229363	+	0.999997i	$0.500730\pi$
$182$	−6.02857e6	−0.0741249
$183$	2.92512e7	0.352830
$184$	4.12157e7	0.487754
$185$	1.39960e8	1.62519
$186$	6.82471e7	0.777659
$187$	2.94119e8	3.28911
$188$	−2.62910e7	−0.288572
$189$	−6.75127e6	−0.0727393
$190$	−1.66637e7	−0.176252
$191$	4.38236e7	0.455084	0.227542	−	0.973768i	$-0.426931\pi$
$191$	4.38236e7	0.455084	0.227542	+	0.973768i	$0.426931\pi$
$192$	−7.07789e6	−0.0721688
$193$	1.53764e8	1.53958	0.769791	−	0.638295i	$-0.220360\pi$
$193$	1.53764e8	1.53958	0.769791	+	0.638295i	$0.220360\pi$
$194$	−9.01848e7	−0.886803
$195$	−1.55560e7	−0.150237
$196$	7.52954e6	0.0714286
$197$	−9.46327e7	−0.881880	−0.440940	−	0.897537i	$-0.645355\pi$
$197$	−9.46327e7	−0.881880	−0.440940	+	0.897537i	$0.645355\pi$
$198$	4.71770e7	0.431919
$199$	−9.12893e7	−0.821172	−0.410586	−	0.911822i	$-0.634676\pi$
$199$	−9.12893e7	−0.821172	−0.410586	+	0.911822i	$0.634676\pi$
$200$	−4.78918e6	−0.0423307
$201$	−6.97738e6	−0.0606047
$202$	7.63336e7	0.651608
$203$	−3.39320e7	−0.284690
$204$	−6.28282e7	−0.518142
$205$	−7.68854e7	−0.623312
$206$	1.25619e8	1.00120
$207$	5.86841e7	0.459859
$208$	−8.99891e6	−0.0693375
$209$	6.42526e7	0.486831
$210$	1.94290e7	0.144772
$211$	2.32329e8	1.70261	0.851306	−	0.524670i	$-0.175811\pi$
$211$	2.32329e8	1.70261	0.851306	+	0.524670i	$0.175811\pi$
$212$	8.42834e7	0.607529
$213$	−7.43179e7	−0.526944
$214$	1.11796e8	0.779790
$215$	−1.15124e8	−0.790007
$216$	−1.00777e7	−0.0680414
$217$	−1.08374e8	−0.719972
$218$	2.33256e7	0.152488
$219$	−1.55118e7	−0.0997950
$220$	−1.35768e8	−0.859641
$221$	−7.98805e7	−0.497815
$222$	1.15280e8	0.707163
$223$	3.59293e7	0.216961	0.108480	−	0.994099i	$-0.465401\pi$
$223$	3.59293e7	0.216961	0.108480	+	0.994099i	$0.465401\pi$
$224$	1.12394e7	0.0668153
$225$	−6.81897e6	−0.0399098
$226$	−3.69613e6	−0.0212994
$227$	−1.12121e8	−0.636202	−0.318101	−	0.948057i	$-0.603045\pi$
$227$	−1.12121e8	−0.636202	−0.318101	+	0.948057i	$0.603045\pi$
$228$	−1.37253e7	−0.0766918
$229$	1.33685e7	0.0735628	0.0367814	−	0.999323i	$-0.488289\pi$
$229$	1.33685e7	0.0735628	0.0367814	+	0.999323i	$0.488289\pi$
$230$	−1.68883e8	−0.915248
$231$	−7.49154e7	−0.399879
$232$	−5.06506e7	−0.266304
$233$	−2.46179e7	−0.127499	−0.0637493	−	0.997966i	$-0.520306\pi$
$233$	−2.46179e7	−0.127499	−0.0637493	+	0.997966i	$0.520306\pi$
$234$	−1.28129e7	−0.0653720
$235$	1.07728e8	0.541493
$236$	9.28351e7	0.459748
$237$	5.79233e7	0.282640
$238$	9.97688e7	0.479706
$239$	3.25624e8	1.54285	0.771425	−	0.636320i	$-0.219544\pi$
$239$	3.25624e8	1.54285	0.771425	+	0.636320i	$0.219544\pi$
$240$	2.90019e7	0.135421
$241$	−3.13928e8	−1.44467	−0.722337	−	0.691541i	$-0.756932\pi$
$241$	−3.13928e8	−1.44467	−0.722337	+	0.691541i	$0.756932\pi$
$242$	3.67602e8	1.66734
$243$	−1.43489e7	−0.0641500
$244$	−6.93362e7	−0.305559
$245$	−3.08526e7	−0.134032
$246$	−6.33278e7	−0.271220
$247$	−1.74505e7	−0.0736831
$248$	−1.61771e8	−0.673472
$249$	−1.48215e8	−0.608408
$250$	1.83525e8	0.742859
$251$	1.69788e8	0.677717	0.338858	−	0.940837i	$-0.389959\pi$
$251$	1.69788e8	0.677717	0.338858	+	0.940837i	$0.389959\pi$
$252$	1.60030e7	0.0629941
$253$	6.51188e8	2.52804
$254$	3.45591e8	1.32326
$255$	2.57441e8	0.972270
$256$	1.67772e7	0.0625000
$257$	−2.46021e7	−0.0904080	−0.0452040	−	0.998978i	$-0.514394\pi$
$257$	−2.46021e7	−0.0904080	−0.0452040	+	0.998978i	$0.514394\pi$
$258$	−9.48235e7	−0.343753
$259$	−1.83061e8	−0.654706
$260$	3.68734e7	0.130109
$261$	−7.21178e7	−0.251073
$262$	−3.03316e8	−1.04194
$263$	3.74298e8	1.26874	0.634369	−	0.773030i	$-0.281260\pi$
$263$	3.74298e8	1.26874	0.634369	+	0.773030i	$0.281260\pi$
$264$	−1.11827e8	−0.374053
$265$	−3.45355e8	−1.14000
$266$	2.17952e7	0.0710028
$267$	2.40649e8	0.773741
$268$	1.65390e7	0.0524852
$269$	5.22987e7	0.163817	0.0819083	−	0.996640i	$-0.473899\pi$
$269$	5.22987e7	0.163817	0.0819083	+	0.996640i	$0.473899\pi$
$270$	4.12938e7	0.127677
$271$	1.27694e8	0.389743	0.194871	−	0.980829i	$-0.437571\pi$
$271$	1.27694e8	0.389743	0.194871	+	0.980829i	$0.437571\pi$
$272$	1.48926e8	0.448724
$273$	2.03464e7	0.0605228
$274$	1.59955e8	0.469754
$275$	−7.56666e7	−0.219402
$276$	−1.39103e8	−0.398249
$277$	3.96501e8	1.12089	0.560447	−	0.828190i	$-0.310629\pi$
$277$	3.96501e8	1.12089	0.560447	+	0.828190i	$0.310629\pi$
$278$	4.58012e8	1.27856
$279$	−2.30334e8	−0.634956
$280$	−4.60540e7	−0.125376
$281$	−9.05068e7	−0.243337	−0.121669	−	0.992571i	$-0.538825\pi$
$281$	−9.05068e7	−0.243337	−0.121669	+	0.992571i	$0.538825\pi$
$282$	8.87321e7	0.235618
$283$	6.65988e8	1.74668	0.873341	−	0.487109i	$-0.161949\pi$
$283$	6.65988e8	1.74668	0.873341	+	0.487109i	$0.161949\pi$
$284$	1.76161e8	0.456347
$285$	5.62399e7	0.143909
$286$	−1.42178e8	−0.359379
$287$	1.00562e8	0.251101
$288$	2.38879e7	0.0589256
$289$	9.11630e8	2.22165
$290$	2.07543e8	0.499707
$291$	3.04374e8	0.724072
$292$	3.67688e7	0.0864250
$293$	−8.54906e7	−0.198555	−0.0992776	−	0.995060i	$-0.531653\pi$
$293$	−8.54906e7	−0.198555	−0.0992776	+	0.995060i	$0.531653\pi$
$294$	−2.54122e7	−0.0583212
$295$	−3.80396e8	−0.862697
$296$	−2.73257e8	−0.612421
$297$	−1.59223e8	−0.352661
$298$	−6.03779e8	−1.32166
$299$	−1.76857e8	−0.382625
$300$	1.61635e7	0.0345629
$301$	1.50576e8	0.318254
$302$	−1.43915e8	−0.300664
$303$	−2.57626e8	−0.532035
$304$	3.25340e7	0.0664171
$305$	2.84108e8	0.573368
$306$	2.12045e8	0.423061
$307$	6.78551e7	0.133844	0.0669219	−	0.997758i	$-0.478682\pi$
$307$	6.78551e7	0.133844	0.0669219	+	0.997758i	$0.478682\pi$
$308$	1.77577e8	0.346306
$309$	−4.23965e8	−0.817476
$310$	6.62863e8	1.26374
$311$	−1.14569e7	−0.0215976	−0.0107988	−	0.999942i	$-0.503437\pi$
$311$	−1.14569e7	−0.0215976	−0.0107988	+	0.999942i	$0.503437\pi$
$312$	3.03713e7	0.0566139
$313$	−2.31158e8	−0.426092	−0.213046	−	0.977042i	$-0.568338\pi$
$313$	−2.31158e8	−0.426092	−0.213046	+	0.977042i	$0.568338\pi$
$314$	−1.72498e8	−0.314434
$315$	−6.55730e7	−0.118206
$316$	−1.37300e8	−0.244774
$317$	8.98774e8	1.58468	0.792342	−	0.610077i	$-0.208861\pi$
$317$	8.98774e8	1.58468	0.792342	+	0.610077i	$0.208861\pi$
$318$	−2.84457e8	−0.496045
$319$	−8.00254e8	−1.38026
$320$	−6.87453e7	−0.117278
$321$	−3.77311e8	−0.636696
$322$	2.20890e8	0.368707
$323$	2.88794e8	0.476847
$324$	3.40122e7	0.0555556
$325$	2.05504e7	0.0332070
$326$	−2.87080e8	−0.458924
$327$	−7.87241e7	−0.124506
$328$	1.50110e8	0.234883
$329$	−1.40903e8	−0.218140
$330$	4.58216e8	0.701894
$331$	−9.20059e8	−1.39450	−0.697249	−	0.716829i	$-0.745593\pi$
$331$	−9.20059e8	−1.39450	−0.697249	+	0.716829i	$0.745593\pi$
$332$	3.51325e8	0.526897
$333$	−3.89071e8	−0.577396
$334$	−5.32691e8	−0.782281
$335$	−6.77691e7	−0.0984861
$336$	−3.79331e7	−0.0545545
$337$	−1.14771e9	−1.63353	−0.816765	−	0.576970i	$-0.804235\pi$
$337$	−1.14771e9	−1.63353	−0.816765	+	0.576970i	$0.804235\pi$
$338$	3.86145e7	0.0543928
$339$	1.24744e7	0.0173909
$340$	−6.10230e8	−0.842010
$341$	−2.55590e9	−3.49063
$342$	4.63228e7	0.0626186
$343$	4.03536e7	0.0539949
$344$	2.24767e8	0.297699
$345$	5.69980e8	0.747297
$346$	−8.38119e8	−1.08778
$347$	1.20200e9	1.54437	0.772187	−	0.635396i	$-0.219163\pi$
$347$	1.20200e9	1.54437	0.772187	+	0.635396i	$0.219163\pi$
$348$	1.70946e8	0.217436
$349$	−7.46699e7	−0.0940279	−0.0470140	−	0.998894i	$-0.514971\pi$
$349$	−7.46699e7	−0.0940279	−0.0470140	+	0.998894i	$0.514971\pi$
$350$	−2.56670e7	−0.0319990
$351$	4.32436e7	0.0533761
$352$	2.65072e8	0.323939
$353$	1.09945e9	1.33035	0.665173	−	0.746689i	$-0.268358\pi$
$353$	1.09945e9	1.33035	0.665173	+	0.746689i	$0.268358\pi$
$354$	−3.13319e8	−0.375383
$355$	−7.21826e8	−0.856315
$356$	−5.70428e8	−0.670079
$357$	−3.36720e8	−0.391678
$358$	7.23981e8	0.833943
$359$	−5.37432e8	−0.613046	−0.306523	−	0.951863i	$-0.599166\pi$
$359$	−5.37432e8	−0.613046	−0.306523	+	0.951863i	$0.599166\pi$
$360$	−9.78815e7	−0.110571
$361$	−8.30783e8	−0.929420
$362$	−2.92764e6	−0.00324368
$363$	−1.24066e9	−1.36138
$364$	−4.82285e7	−0.0524142
$365$	−1.50662e8	−0.162173
$366$	2.34010e8	0.249488
$367$	8.15959e8	0.861662	0.430831	−	0.902433i	$-0.358220\pi$
$367$	8.15959e8	0.861662	0.430831	+	0.902433i	$0.358220\pi$
$368$	3.29726e8	0.344894
$369$	2.13731e8	0.221450
$370$	1.11968e9	1.14918
$371$	4.51707e8	0.459248
$372$	5.45977e8	0.549888
$373$	−6.16286e8	−0.614896	−0.307448	−	0.951565i	$-0.599475\pi$
$373$	−6.16286e8	−0.614896	−0.307448	+	0.951565i	$0.599475\pi$
$374$	2.35296e9	2.32575
$375$	−6.19398e8	−0.606542
$376$	−2.10328e8	−0.204051
$377$	2.17343e8	0.208906
$378$	−5.40102e7	−0.0514344
$379$	4.67684e8	0.441281	0.220641	−	0.975355i	$-0.429185\pi$
$379$	4.67684e8	0.441281	0.220641	+	0.975355i	$0.429185\pi$
$380$	−1.33309e8	−0.124629
$381$	−1.16637e9	−1.08044
$382$	3.50589e8	0.321793
$383$	1.42413e9	1.29525	0.647626	−	0.761958i	$-0.275762\pi$
$383$	1.42413e9	1.29525	0.647626	+	0.761958i	$0.275762\pi$
$384$	−5.66231e7	−0.0510310
$385$	−7.27630e8	−0.649827
$386$	1.23011e9	1.08865
$387$	3.20029e8	0.280674
$388$	−7.21478e8	−0.627064
$389$	−1.84423e8	−0.158852	−0.0794260	−	0.996841i	$-0.525309\pi$
$389$	−1.84423e8	−0.158852	−0.0794260	+	0.996841i	$0.525309\pi$
$390$	−1.24448e8	−0.106233
$391$	2.92687e9	2.47619
$392$	6.02363e7	0.0505076
$393$	1.02369e9	0.850738
$394$	−7.57062e8	−0.623583
$395$	5.62591e8	0.459307
$396$	3.77416e8	0.305413
$397$	1.13782e9	0.912653	0.456327	−	0.889812i	$-0.349165\pi$
$397$	1.13782e9	0.912653	0.456327	+	0.889812i	$0.349165\pi$
$398$	−7.30315e8	−0.580656
$399$	−7.35589e7	−0.0579736
$400$	−3.83134e7	−0.0299324
$401$	−2.16316e9	−1.67526	−0.837631	−	0.546237i	$-0.816060\pi$
$401$	−2.16316e9	−1.67526	−0.837631	+	0.546237i	$0.816060\pi$
$402$	−5.58191e7	−0.0428540
$403$	6.94162e8	0.528315
$404$	6.10669e8	0.460756
$405$	−1.39366e8	−0.104247
$406$	−2.71456e8	−0.201307
$407$	−4.31732e9	−3.17420
$408$	−5.02625e8	−0.366382
$409$	1.67587e9	1.21118	0.605590	−	0.795777i	$-0.292937\pi$
$409$	1.67587e9	1.21118	0.605590	+	0.795777i	$0.292937\pi$
$410$	−6.15083e8	−0.440748
$411$	−5.39848e8	−0.383553
$412$	1.00495e9	0.707955
$413$	4.97538e8	0.347537
$414$	4.69473e8	0.325169
$415$	−1.43957e9	−0.988698
$416$	−7.19913e7	−0.0490290
$417$	−1.54579e9	−1.04394
$418$	5.14021e8	0.344242
$419$	1.95050e9	1.29538	0.647689	−	0.761905i	$-0.275736\pi$
$419$	1.95050e9	1.29538	0.647689	+	0.761905i	$0.275736\pi$
$420$	1.55432e8	0.102369
$421$	2.04077e9	1.33293	0.666464	−	0.745537i	$-0.267807\pi$
$421$	2.04077e9	1.33293	0.666464	+	0.745537i	$0.267807\pi$
$422$	1.85864e9	1.20393
$423$	−2.99471e8	−0.192382
$424$	6.74267e8	0.429588
$425$	−3.40096e8	−0.214902
$426$	−5.94543e8	−0.372606
$427$	−3.71599e8	−0.230981
$428$	8.94367e8	0.551395
$429$	4.79852e8	0.293431
$430$	−9.20991e8	−0.558619
$431$	−1.76452e8	−0.106159	−0.0530795	−	0.998590i	$-0.516904\pi$
$431$	−1.76452e8	−0.106159	−0.0530795	+	0.998590i	$0.516904\pi$
$432$	−8.06216e7	−0.0481125
$433$	−9.70906e8	−0.574737	−0.287369	−	0.957820i	$-0.592780\pi$
$433$	−9.70906e8	−0.574737	−0.287369	+	0.957820i	$0.592780\pi$
$434$	−8.66992e8	−0.509097
$435$	−7.00457e8	−0.408009
$436$	1.86605e8	0.107825
$437$	6.39397e8	0.366510
$438$	−1.24095e8	−0.0705657
$439$	−2.81547e9	−1.58827	−0.794137	−	0.607738i	$-0.792077\pi$
$439$	−2.81547e9	−1.58827	−0.794137	+	0.607738i	$0.792077\pi$
$440$	−1.08614e9	−0.607858
$441$	8.57661e7	0.0476190
$442$	−6.39044e8	−0.352008
$443$	3.55508e7	0.0194283	0.00971417	−	0.999953i	$-0.496908\pi$
$443$	3.55508e7	0.0194283	0.00971417	+	0.999953i	$0.496908\pi$
$444$	9.22242e8	0.500040
$445$	2.33735e9	1.25737
$446$	2.87434e8	0.153415
$447$	2.03775e9	1.07913
$448$	8.99154e7	0.0472456
$449$	1.95787e9	1.02075	0.510377	−	0.859951i	$-0.329506\pi$
$449$	1.95787e9	1.02075	0.510377	+	0.859951i	$0.329506\pi$
$450$	−5.45517e7	−0.0282205
$451$	2.37167e9	1.21741
$452$	−2.95690e7	−0.0150610
$453$	4.85713e8	0.245491
$454$	−8.96965e8	−0.449863
$455$	1.97618e8	0.0983530
$456$	−1.09802e8	−0.0542293
$457$	2.17951e9	1.06820	0.534100	−	0.845422i	$-0.320651\pi$
$457$	2.17951e9	1.06820	0.534100	+	0.845422i	$0.320651\pi$
$458$	1.06948e8	0.0520168
$459$	−7.15652e8	−0.345428
$460$	−1.35106e9	−0.647178
$461$	−8.06597e8	−0.383445	−0.191723	−	0.981449i	$-0.561407\pi$
$461$	−8.06597e8	−0.383445	−0.191723	+	0.981449i	$0.561407\pi$
$462$	−5.99323e8	−0.282758
$463$	1.67835e9	0.785866	0.392933	−	0.919567i	$-0.371460\pi$
$463$	1.67835e9	0.785866	0.392933	+	0.919567i	$0.371460\pi$
$464$	−4.05205e8	−0.188305
$465$	−2.23716e9	−1.03184
$466$	−1.96943e8	−0.0901552
$467$	2.87764e9	1.30746	0.653728	−	0.756729i	$-0.273204\pi$
$467$	2.87764e9	1.30746	0.653728	+	0.756729i	$0.273204\pi$
$468$	−1.02503e8	−0.0462250
$469$	8.86386e7	0.0396751
$470$	8.61827e8	0.382893
$471$	5.82180e8	0.256734
$472$	7.42681e8	0.325091
$473$	3.55120e9	1.54298
$474$	4.63386e8	0.199857
$475$	−7.42965e7	−0.0318083
$476$	7.98150e8	0.339203
$477$	9.60041e8	0.405019
$478$	2.60499e9	1.09096
$479$	−9.17628e8	−0.381498	−0.190749	−	0.981639i	$-0.561092\pi$
$479$	−9.17628e8	−0.381498	−0.190749	+	0.981639i	$0.561092\pi$
$480$	2.32015e8	0.0957574
$481$	1.17255e9	0.480423
$482$	−2.51142e9	−1.02154
$483$	−7.45505e8	−0.301048
$484$	2.94082e9	1.17899
$485$	2.95628e9	1.17666
$486$	−1.14791e8	−0.0453609
$487$	−3.05087e9	−1.19694	−0.598469	−	0.801146i	$-0.704224\pi$
$487$	−3.05087e9	−1.19694	−0.598469	+	0.801146i	$0.704224\pi$
$488$	−5.54690e8	−0.216063
$489$	9.68895e8	0.374710
$490$	−2.46821e8	−0.0947753
$491$	8.68118e8	0.330974	0.165487	−	0.986212i	$-0.447080\pi$
$491$	8.68118e8	0.330974	0.165487	+	0.986212i	$0.447080\pi$
$492$	−5.06622e8	−0.191781
$493$	−3.59688e9	−1.35195
$494$	−1.39604e8	−0.0521018
$495$	−1.54648e9	−0.573094
$496$	−1.29417e9	−0.476217
$497$	9.44112e8	0.344966
$498$	−1.18572e9	−0.430209
$499$	−3.54412e9	−1.27690	−0.638450	−	0.769664i	$-0.720424\pi$
$499$	−3.54412e9	−1.27690	−0.638450	+	0.769664i	$0.720424\pi$
$500$	1.46820e9	0.525280
$501$	1.79783e9	0.638730
$502$	1.35830e9	0.479218
$503$	−3.81317e9	−1.33597	−0.667987	−	0.744173i	$-0.732844\pi$
$503$	−3.81317e9	−1.33597	−0.667987	+	0.744173i	$0.732844\pi$
$504$	1.28024e8	0.0445435
$505$	−2.50224e9	−0.864588
$506$	5.20950e9	1.78760
$507$	−1.30324e8	−0.0444116
$508$	2.76473e9	0.935685
$509$	5.60514e9	1.88397	0.941985	−	0.335654i	$-0.108957\pi$
$509$	5.60514e9	1.88397	0.941985	+	0.335654i	$0.108957\pi$
$510$	2.05953e9	0.687499
$511$	1.97058e8	0.0653311
$512$	1.34218e8	0.0441942
$513$	−1.56339e8	−0.0511279
$514$	−1.96817e8	−0.0639281
$515$	−4.11784e9	−1.32845
$516$	−7.58588e8	−0.243070
$517$	−3.32308e9	−1.05760
$518$	−1.46449e9	−0.462947
$519$	2.82865e9	0.888165
$520$	2.94987e8	0.0920008
$521$	−2.78007e9	−0.861240	−0.430620	−	0.902533i	$-0.641705\pi$
$521$	−2.78007e9	−0.861240	−0.430620	+	0.902533i	$0.641705\pi$
$522$	−5.76942e8	−0.177536
$523$	4.86040e8	0.148565	0.0742824	−	0.997237i	$-0.476333\pi$
$523$	4.86040e8	0.148565	0.0742824	+	0.997237i	$0.476333\pi$
$524$	−2.42653e9	−0.736760
$525$	8.66261e7	0.0261271
$526$	2.99438e9	0.897133
$527$	−1.14879e10	−3.41904
$528$	−8.94616e8	−0.264495
$529$	3.07534e9	0.903229
$530$	−2.76284e9	−0.806102
$531$	1.05745e9	0.306499
$532$	1.74362e8	0.0502066
$533$	−6.44126e8	−0.184258
$534$	1.92520e9	0.547117
$535$	−3.66470e9	−1.03467
$536$	1.32312e8	0.0371127
$537$	−2.44343e9	−0.680912
$538$	4.18390e8	0.115836
$539$	9.51703e8	0.261783
$540$	3.30350e8	0.0902810
$541$	−2.92864e9	−0.795197	−0.397599	−	0.917559i	$-0.630156\pi$
$541$	−2.92864e9	−0.795197	−0.397599	+	0.917559i	$0.630156\pi$
$542$	1.02155e9	0.275590
$543$	9.88079e6	0.00264845
$544$	1.19141e9	0.317296
$545$	−7.64622e8	−0.202329
$546$	1.62771e8	0.0427960
$547$	4.76852e9	1.24574	0.622871	−	0.782325i	$-0.285966\pi$
$547$	4.76852e9	1.24574	0.622871	+	0.782325i	$0.285966\pi$
$548$	1.27964e9	0.332166
$549$	−7.89783e8	−0.203706
$550$	−6.05333e8	−0.155140
$551$	−7.85764e8	−0.200107
$552$	−1.11282e9	−0.281605
$553$	−7.35840e8	−0.185031
$554$	3.17200e9	0.792592
$555$	−3.77892e9	−0.938302
$556$	3.66410e9	0.904076
$557$	2.40126e9	0.588769	0.294385	−	0.955687i	$-0.404885\pi$
$557$	2.40126e9	0.588769	0.294385	+	0.955687i	$0.404885\pi$
$558$	−1.84267e9	−0.448982
$559$	−9.64478e8	−0.233535
$560$	−3.68432e8	−0.0886542
$561$	−7.94122e9	−1.89897
$562$	−7.24054e8	−0.172066
$563$	5.35882e8	0.126558	0.0632790	−	0.997996i	$-0.479844\pi$
$563$	5.35882e8	0.126558	0.0632790	+	0.997996i	$0.479844\pi$
$564$	7.09857e8	0.166607
$565$	1.21160e8	0.0282612
$566$	5.32791e9	1.23509
$567$	1.82284e8	0.0419961
$568$	1.40929e9	0.322686
$569$	2.50427e9	0.569887	0.284943	−	0.958544i	$-0.408025\pi$
$569$	2.50427e9	0.569887	0.284943	+	0.958544i	$0.408025\pi$
$570$	4.49919e8	0.101759
$571$	−3.94023e9	−0.885717	−0.442859	−	0.896591i	$-0.646036\pi$
$571$	−3.94023e9	−0.885717	−0.442859	+	0.896591i	$0.646036\pi$
$572$	−1.13743e9	−0.254119
$573$	−1.18324e9	−0.262743
$574$	8.04498e8	0.177555
$575$	−7.52981e8	−0.165176
$576$	1.91103e8	0.0416667
$577$	−5.67394e9	−1.22962	−0.614808	−	0.788677i	$-0.710766\pi$
$577$	−5.67394e9	−1.22962	−0.614808	+	0.788677i	$0.710766\pi$
$578$	7.29304e9	1.57095
$579$	−4.15162e9	−0.888879
$580$	1.66034e9	0.353346
$581$	1.88288e9	0.398297
$582$	2.43499e9	0.511996
$583$	1.06531e10	2.22657
$584$	2.94150e8	0.0611117
$585$	4.20011e8	0.0867391
$586$	−6.83924e8	−0.140400
$587$	7.19268e9	1.46777	0.733884	−	0.679275i	$-0.237706\pi$
$587$	7.19268e9	1.46777	0.733884	+	0.679275i	$0.237706\pi$
$588$	−2.03297e8	−0.0412393
$589$	−2.50962e9	−0.506063
$590$	−3.04316e9	−0.610019
$591$	2.55508e9	0.509154
$592$	−2.18605e9	−0.433047
$593$	2.65660e9	0.523161	0.261581	−	0.965182i	$-0.415756\pi$
$593$	2.65660e9	0.523161	0.261581	+	0.965182i	$0.415756\pi$
$594$	−1.27378e9	−0.249369
$595$	−3.27045e9	−0.636500
$596$	−4.83023e9	−0.934557
$597$	2.46481e9	0.474104
$598$	−1.41486e9	−0.270557
$599$	4.83838e9	0.919826	0.459913	−	0.887964i	$-0.347881\pi$
$599$	4.83838e9	0.919826	0.459913	+	0.887964i	$0.347881\pi$
$600$	1.29308e8	0.0244397
$601$	−6.40961e9	−1.20440	−0.602201	−	0.798345i	$-0.705709\pi$
$601$	−6.40961e9	−1.20440	−0.602201	+	0.798345i	$0.705709\pi$
$602$	1.20461e9	0.225039
$603$	1.88389e8	0.0349901
$604$	−1.15132e9	−0.212602
$605$	−1.20501e10	−2.21232
$606$	−2.06101e9	−0.376206
$607$	−4.61181e9	−0.836973	−0.418486	−	0.908223i	$-0.637439\pi$
$607$	−4.61181e9	−0.836973	−0.418486	+	0.908223i	$0.637439\pi$
$608$	2.60272e8	0.0469640
$609$	9.16163e8	0.164366
$610$	2.27286e9	0.405433
$611$	9.02521e8	0.160071
$612$	1.69636e9	0.299149
$613$	−1.68984e9	−0.296301	−0.148151	−	0.988965i	$-0.547332\pi$
$613$	−1.68984e9	−0.296301	−0.148151	+	0.988965i	$0.547332\pi$
$614$	5.42841e8	0.0946418
$615$	2.07591e9	0.359869
$616$	1.42062e9	0.244875
$617$	−1.03250e10	−1.76966	−0.884831	−	0.465912i	$-0.845726\pi$
$617$	−1.03250e10	−1.76966	−0.884831	+	0.465912i	$0.845726\pi$
$618$	−3.39172e9	−0.578043
$619$	2.48042e9	0.420347	0.210174	−	0.977664i	$-0.432597\pi$
$619$	2.48042e9	0.420347	0.210174	+	0.977664i	$0.432597\pi$
$620$	5.30290e9	0.893600
$621$	−1.58447e9	−0.265499
$622$	−9.16551e7	−0.0152718
$623$	−3.05714e9	−0.506532
$624$	2.42971e8	0.0400320
$625$	−5.28525e9	−0.865935
$626$	−1.84926e9	−0.301292
$627$	−1.73482e9	−0.281072
$628$	−1.37998e9	−0.222338
$629$	−1.94049e10	−3.10910
$630$	−5.24584e8	−0.0835839
$631$	−1.66794e9	−0.264288	−0.132144	−	0.991231i	$-0.542186\pi$
$631$	−1.66794e9	−0.264288	−0.132144	+	0.991231i	$0.542186\pi$
$632$	−1.09840e9	−0.173081
$633$	−6.27290e9	−0.983003
$634$	7.19019e9	1.12054
$635$	−1.13286e10	−1.75577
$636$	−2.27565e9	−0.350757
$637$	−2.58475e8	−0.0396214
$638$	−6.40204e9	−0.975991
$639$	2.00658e9	0.304231
$640$	−5.49962e8	−0.0829284
$641$	5.95360e9	0.892846	0.446423	−	0.894822i	$-0.352698\pi$
$641$	5.95360e9	0.892846	0.446423	+	0.894822i	$0.352698\pi$
$642$	−3.01849e9	−0.450212
$643$	−8.74492e9	−1.29723	−0.648616	−	0.761116i	$-0.724652\pi$
$643$	−8.74492e9	−1.29723	−0.648616	+	0.761116i	$0.724652\pi$
$644$	1.76712e9	0.260715
$645$	3.10834e9	0.456111
$646$	2.31035e9	0.337182
$647$	−7.84651e9	−1.13897	−0.569484	−	0.822002i	$-0.692857\pi$
$647$	−7.84651e9	−1.13897	−0.569484	+	0.822002i	$0.692857\pi$
$648$	2.72098e8	0.0392837
$649$	1.17340e10	1.68496
$650$	1.64403e8	0.0234809
$651$	2.92610e9	0.415676
$652$	−2.29664e9	−0.324509
$653$	−1.36993e10	−1.92532	−0.962662	−	0.270708i	$-0.912742\pi$
$653$	−1.36993e10	−1.92532	−0.962662	+	0.270708i	$0.912742\pi$
$654$	−6.29792e8	−0.0880390
$655$	9.94280e9	1.38250
$656$	1.20088e9	0.166088
$657$	4.18819e8	0.0576167
$658$	−1.12723e9	−0.154248
$659$	5.88214e9	0.800638	0.400319	−	0.916376i	$-0.368899\pi$
$659$	5.88214e9	0.800638	0.400319	+	0.916376i	$0.368899\pi$
$660$	3.66573e9	0.496314
$661$	−1.06870e10	−1.43929	−0.719646	−	0.694341i	$-0.755696\pi$
$661$	−1.06870e10	−1.43929	−0.719646	+	0.694341i	$0.755696\pi$
$662$	−7.36047e9	−0.986059
$663$	2.15677e9	0.287413
$664$	2.81060e9	0.372572
$665$	−7.14455e8	−0.0942104
$666$	−3.11257e9	−0.408281
$667$	−7.96357e9	−1.03912
$668$	−4.26153e9	−0.553156
$669$	−9.70091e8	−0.125262
$670$	−5.42153e8	−0.0696402
$671$	−8.76381e9	−1.11986
$672$	−3.03464e8	−0.0385758
$673$	9.41563e9	1.19068	0.595342	−	0.803472i	$-0.297016\pi$
$673$	9.41563e9	1.19068	0.595342	+	0.803472i	$0.297016\pi$
$674$	−9.18168e9	−1.15508
$675$	1.84112e8	0.0230419
$676$	3.08916e8	0.0384615
$677$	1.00850e8	0.0124916	0.00624579	−	0.999980i	$-0.498012\pi$
$677$	1.00850e8	0.0124916	0.00624579	+	0.999980i	$0.498012\pi$
$678$	9.97955e7	0.0122972
$679$	−3.86667e9	−0.474016
$680$	−4.88184e9	−0.595391
$681$	3.02726e9	0.367311
$682$	−2.04472e10	−2.46825
$683$	−5.72351e9	−0.687369	−0.343685	−	0.939085i	$-0.611675\pi$
$683$	−5.72351e9	−0.687369	−0.343685	+	0.939085i	$0.611675\pi$
$684$	3.70582e8	0.0442781
$685$	−5.24337e9	−0.623295
$686$	3.22829e8	0.0381802
$687$	−3.60950e8	−0.0424715
$688$	1.79813e9	0.210505
$689$	−2.89329e9	−0.336996
$690$	4.55984e9	0.528418
$691$	1.06363e10	1.22636	0.613180	−	0.789943i	$-0.289890\pi$
$691$	1.06363e10	1.22636	0.613180	+	0.789943i	$0.289890\pi$
$692$	−6.70495e9	−0.769173
$693$	2.02272e9	0.230871
$694$	9.61602e9	1.09204
$695$	−1.50138e10	−1.69646
$696$	1.36757e9	0.153750
$697$	1.06599e10	1.19244
$698$	−5.97360e8	−0.0664878
$699$	6.64684e8	0.0736114
$700$	−2.05336e8	−0.0226267
$701$	−1.82601e9	−0.200212	−0.100106	−	0.994977i	$-0.531918\pi$
$701$	−1.82601e9	−0.200212	−0.100106	+	0.994977i	$0.531918\pi$
$702$	3.45948e8	0.0377426
$703$	−4.23915e9	−0.460188
$704$	2.12057e9	0.229060
$705$	−2.90867e9	−0.312631
$706$	8.79562e9	0.940697
$707$	3.27280e9	0.348299
$708$	−2.50655e9	−0.265436
$709$	6.35699e9	0.669869	0.334935	−	0.942241i	$-0.391286\pi$
$709$	6.35699e9	0.669869	0.334935	+	0.942241i	$0.391286\pi$
$710$	−5.77461e9	−0.605506
$711$	−1.56393e9	−0.163182
$712$	−4.56343e9	−0.473818
$713$	−2.54345e10	−2.62791
$714$	−2.69376e9	−0.276958
$715$	4.66065e9	0.476843
$716$	5.79185e9	0.589687
$717$	−8.79185e9	−0.890765
$718$	−4.29946e9	−0.433489
$719$	1.31687e10	1.32127	0.660633	−	0.750709i	$-0.270288\pi$
$719$	1.31687e10	1.32127	0.660633	+	0.750709i	$0.270288\pi$
$720$	−7.83052e8	−0.0781856
$721$	5.38592e9	0.535164
$722$	−6.64626e9	−0.657199
$723$	8.47604e9	0.834083
$724$	−2.34211e7	−0.00229363
$725$	9.25350e8	0.0901826
$726$	−9.92526e9	−0.962640
$727$	−7.56453e9	−0.730149	−0.365074	−	0.930978i	$-0.618956\pi$
$727$	−7.56453e9	−0.730149	−0.365074	+	0.930978i	$0.618956\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−1.20529e9	−0.114673
$731$	1.59615e10	1.51134
$732$	1.87208e9	0.176415
$733$	5.51700e9	0.517415	0.258707	−	0.965956i	$-0.416703\pi$
$733$	5.51700e9	0.517415	0.258707	+	0.965956i	$0.416703\pi$
$734$	6.52767e9	0.609287
$735$	8.33019e8	0.0773837
$736$	2.63781e9	0.243877
$737$	2.09046e9	0.192356
$738$	1.70985e9	0.156589
$739$	−9.43656e9	−0.860118	−0.430059	−	0.902801i	$-0.641507\pi$
$739$	−9.43656e9	−0.860118	−0.430059	+	0.902801i	$0.641507\pi$
$740$	8.95745e9	0.812593
$741$	4.71163e8	0.0425410
$742$	3.61365e9	0.324738
$743$	−1.76347e10	−1.57727	−0.788637	−	0.614859i	$-0.789213\pi$
$743$	−1.76347e10	−1.57727	−0.788637	+	0.614859i	$0.789213\pi$
$744$	4.36782e9	0.388830
$745$	1.97921e10	1.75365
$746$	−4.93029e9	−0.434797
$747$	4.00181e9	0.351265
$748$	1.88236e10	1.64455
$749$	4.79325e9	0.416815
$750$	−4.95519e9	−0.428890
$751$	1.51261e10	1.30313	0.651564	−	0.758593i	$-0.274113\pi$
$751$	1.51261e10	1.30313	0.651564	+	0.758593i	$0.274113\pi$
$752$	−1.68262e9	−0.144286
$753$	−4.58427e9	−0.391280
$754$	1.73874e9	0.147719
$755$	4.71758e9	0.398937
$756$	−4.32081e8	−0.0363696
$757$	8.50906e9	0.712929	0.356464	−	0.934309i	$-0.383982\pi$
$757$	8.50906e9	0.712929	0.356464	+	0.934309i	$0.383982\pi$
$758$	3.74147e9	0.312033
$759$	−1.75821e10	−1.45957
$760$	−1.06647e9	−0.0881258
$761$	1.27843e9	0.105155	0.0525777	−	0.998617i	$-0.483256\pi$
$761$	1.27843e9	0.105155	0.0525777	+	0.998617i	$0.483256\pi$
$762$	−9.33097e9	−0.763984
$763$	1.00009e9	0.0815083
$764$	2.80471e9	0.227542
$765$	−6.95090e9	−0.561340
$766$	1.13931e10	0.915882
$767$	−3.18686e9	−0.255023
$768$	−4.52985e8	−0.0360844
$769$	6.26123e9	0.496498	0.248249	−	0.968696i	$-0.420145\pi$
$769$	6.26123e9	0.496498	0.248249	+	0.968696i	$0.420145\pi$
$770$	−5.82104e9	−0.459497
$771$	6.64258e8	0.0521971
$772$	9.84087e9	0.769791
$773$	−3.35252e9	−0.261062	−0.130531	−	0.991444i	$-0.541668\pi$
$773$	−3.35252e9	−0.261062	−0.130531	+	0.991444i	$0.541668\pi$
$774$	2.56024e9	0.198466
$775$	2.95544e9	0.228069
$776$	−5.77182e9	−0.443401
$777$	4.94264e9	0.377994
$778$	−1.47539e9	−0.112325
$779$	2.32872e9	0.176497
$780$	−9.95582e8	−0.0751183
$781$	2.22660e10	1.67249
$782$	2.34150e10	1.75093
$783$	1.94718e9	0.144957
$784$	4.81890e8	0.0357143
$785$	5.65453e9	0.417208
$786$	8.18954e9	0.601562
$787$	−2.38346e9	−0.174300	−0.0871499	−	0.996195i	$-0.527776\pi$
$787$	−2.38346e9	−0.174300	−0.0871499	+	0.996195i	$0.527776\pi$
$788$	−6.05649e9	−0.440940
$789$	−1.01060e10	−0.732506
$790$	4.50073e9	0.324779
$791$	−1.58471e8	−0.0113850
$792$	3.01933e9	0.215960
$793$	2.38018e9	0.169494
$794$	9.10254e9	0.645343
$795$	9.32458e9	0.658179
$796$	−5.84252e9	−0.410586
$797$	−1.33613e10	−0.934855	−0.467427	−	0.884031i	$-0.654819\pi$
$797$	−1.33613e10	−0.934855	−0.467427	+	0.884031i	$0.654819\pi$
$798$	−5.88471e8	−0.0409935
$799$	−1.49361e10	−1.03591
$800$	−3.06507e8	−0.0211654
$801$	−6.49754e9	−0.446719
$802$	−1.73053e10	−1.18459
$803$	4.64743e9	0.316744
$804$	−4.46552e8	−0.0303024
$805$	−7.24086e9	−0.489220
$806$	5.55330e9	0.373575
$807$	−1.41207e9	−0.0945796
$808$	4.88535e9	0.325804
$809$	−7.57292e9	−0.502856	−0.251428	−	0.967876i	$-0.580900\pi$
$809$	−7.57292e9	−0.502856	−0.251428	+	0.967876i	$0.580900\pi$
$810$	−1.11493e9	−0.0737141
$811$	−9.58451e7	−0.00630953	−0.00315476	−	0.999995i	$-0.501004\pi$
$811$	−9.58451e7	−0.00630953	−0.00315476	+	0.999995i	$0.501004\pi$
$812$	−2.17165e9	−0.142345
$813$	−3.44774e9	−0.225018
$814$	−3.45386e10	−2.24450
$815$	9.41057e9	0.608926
$816$	−4.02100e9	−0.259071
$817$	3.48690e9	0.223698
$818$	1.34069e10	0.856433
$819$	−5.49353e8	−0.0349428
$820$	−4.92066e9	−0.311656
$821$	3.05920e10	1.92933	0.964667	−	0.263472i	$-0.0848677\pi$
$821$	3.05920e10	1.92933	0.964667	+	0.263472i	$0.0848677\pi$
$822$	−4.31878e9	−0.271213
$823$	−2.67508e10	−1.67278	−0.836388	−	0.548137i	$-0.815337\pi$
$823$	−2.67508e10	−1.67278	−0.836388	+	0.548137i	$0.815337\pi$
$824$	8.03963e9	0.500600
$825$	2.04300e9	0.126672
$826$	3.98031e9	0.245746
$827$	1.13389e10	0.697112	0.348556	−	0.937288i	$-0.386672\pi$
$827$	1.13389e10	0.697112	0.348556	+	0.937288i	$0.386672\pi$
$828$	3.75578e9	0.229929
$829$	7.95356e9	0.484865	0.242432	−	0.970168i	$-0.422055\pi$
$829$	7.95356e9	0.484865	0.242432	+	0.970168i	$0.422055\pi$
$830$	−1.15165e10	−0.699115
$831$	−1.07055e10	−0.647149
$832$	−5.75930e8	−0.0346688
$833$	4.27759e9	0.256414
$834$	−1.23663e10	−0.738175
$835$	1.74618e10	1.03797
$836$	4.11217e9	0.243416
$837$	6.21902e9	0.366592
$838$	1.56040e10	0.915970
$839$	1.58689e10	0.927640	0.463820	−	0.885929i	$-0.346478\pi$
$839$	1.58689e10	0.927640	0.463820	+	0.885929i	$0.346478\pi$
$840$	1.24346e9	0.0723858
$841$	−7.46332e9	−0.432659
$842$	1.63262e10	0.942522
$843$	2.44368e9	0.140491
$844$	1.48691e10	0.851306
$845$	−1.26579e9	−0.0721713
$846$	−2.39577e9	−0.136034
$847$	1.57609e10	0.891231
$848$	5.39414e9	0.303764
$849$	−1.79817e10	−1.00845
$850$	−2.72077e9	−0.151959
$851$	−4.29629e10	−2.38968
$852$	−4.75634e9	−0.263472
$853$	1.04522e10	0.576615	0.288308	−	0.957538i	$-0.406907\pi$
$853$	1.04522e10	0.576615	0.288308	+	0.957538i	$0.406907\pi$
$854$	−2.97279e9	−0.163328
$855$	−1.51848e9	−0.0830858
$856$	7.15494e9	0.389895
$857$	2.43883e10	1.32358	0.661789	−	0.749690i	$-0.269798\pi$
$857$	2.43883e10	1.32358	0.661789	+	0.749690i	$0.269798\pi$
$858$	3.83881e9	0.207487
$859$	−1.53166e10	−0.824493	−0.412246	−	0.911072i	$-0.635256\pi$
$859$	−1.53166e10	−0.824493	−0.412246	+	0.911072i	$0.635256\pi$
$860$	−7.36793e9	−0.395003
$861$	−2.71518e9	−0.144973
$862$	−1.41162e9	−0.0750657
$863$	−6.85504e9	−0.363055	−0.181528	−	0.983386i	$-0.558104\pi$
$863$	−6.85504e9	−0.363055	−0.181528	+	0.983386i	$0.558104\pi$
$864$	−6.44973e8	−0.0340207
$865$	2.74738e10	1.44332
$866$	−7.76725e9	−0.406401
$867$	−2.46140e10	−1.28267
$868$	−6.93593e9	−0.359986
$869$	−1.73541e10	−0.897085
$870$	−5.60366e9	−0.288506
$871$	−5.67752e8	−0.0291136
$872$	1.49284e9	0.0762441
$873$	−8.21809e9	−0.418043
$874$	5.11517e9	0.259161
$875$	7.86865e9	0.397075
$876$	−9.92757e8	−0.0498975
$877$	1.83666e10	0.919453	0.459726	−	0.888061i	$-0.347947\pi$
$877$	1.83666e10	0.919453	0.459726	+	0.888061i	$0.347947\pi$
$878$	−2.25238e10	−1.12308
$879$	2.30825e9	0.114636
$880$	−8.68913e9	−0.429820
$881$	3.29732e9	0.162460	0.0812299	−	0.996695i	$-0.474115\pi$
$881$	3.29732e9	0.162460	0.0812299	+	0.996695i	$0.474115\pi$
$882$	6.86129e8	0.0336718
$883$	−2.94976e10	−1.44186	−0.720932	−	0.693005i	$-0.756286\pi$
$883$	−2.94976e10	−1.44186	−0.720932	+	0.693005i	$0.756286\pi$
$884$	−5.11235e9	−0.248907
$885$	1.02707e10	0.498078
$886$	2.84406e8	0.0137379
$887$	−2.61083e9	−0.125616	−0.0628081	−	0.998026i	$-0.520006\pi$
$887$	−2.61083e9	−0.125616	−0.0628081	+	0.998026i	$0.520006\pi$
$888$	7.37794e9	0.353581
$889$	1.48172e10	0.707312
$890$	1.86988e10	0.889097
$891$	4.29901e9	0.203609
$892$	2.29947e9	0.108480
$893$	−3.26291e9	−0.153329
$894$	1.63020e10	0.763063
$895$	−2.37323e10	−1.10652
$896$	7.19323e8	0.0334077
$897$	4.77515e9	0.220909
$898$	1.56629e10	0.721782
$899$	3.12569e10	1.43478
$900$	−4.36414e8	−0.0199549
$901$	4.78821e10	2.18090
$902$	1.89733e10	0.860837
$903$	−4.06556e9	−0.183744
$904$	−2.36552e8	−0.0106497
$905$	9.59690e7	0.00430389
$906$	3.88570e9	0.173588
$907$	2.81292e10	1.25179	0.625896	−	0.779907i	$-0.284733\pi$
$907$	2.81292e10	1.25179	0.625896	+	0.779907i	$0.284733\pi$
$908$	−7.17572e9	−0.318101
$909$	6.95590e9	0.307171
$910$	1.58095e9	0.0695460
$911$	−3.77491e10	−1.65422	−0.827108	−	0.562043i	$-0.810016\pi$
$911$	−3.77491e10	−1.65422	−0.827108	+	0.562043i	$0.810016\pi$
$912$	−8.78418e8	−0.0383459
$913$	4.44060e10	1.93105
$914$	1.74361e10	0.755331
$915$	−7.67091e9	−0.331034
$916$	8.55584e8	0.0367814
$917$	−1.30047e10	−0.556938
$918$	−5.72522e9	−0.244254
$919$	−2.24933e10	−0.955981	−0.477990	−	0.878365i	$-0.658635\pi$
$919$	−2.24933e10	−0.955981	−0.477990	+	0.878365i	$0.658635\pi$
$920$	−1.08085e10	−0.457624
$921$	−1.83209e9	−0.0772747
$922$	−6.45278e9	−0.271137
$923$	−6.04727e9	−0.253136
$924$	−4.79459e9	−0.199940
$925$	4.99220e9	0.207394
$926$	1.34268e10	0.555691
$927$	1.14470e10	0.471970
$928$	−3.24164e9	−0.133152
$929$	1.01665e10	0.416020	0.208010	−	0.978127i	$-0.433301\pi$
$929$	1.01665e10	0.416020	0.208010	+	0.978127i	$0.433301\pi$
$930$	−1.78973e10	−0.729621
$931$	9.34471e8	0.0379526
$932$	−1.57555e9	−0.0637493
$933$	3.09336e8	0.0124694
$934$	2.30211e10	0.924512
$935$	−7.71306e10	−3.08593
$936$	−8.20026e8	−0.0326860
$937$	2.91223e10	1.15648	0.578240	−	0.815867i	$-0.303740\pi$
$937$	2.91223e10	1.15648	0.578240	+	0.815867i	$0.303740\pi$
$938$	7.09109e8	0.0280545
$939$	6.24125e9	0.246004
$940$	6.89462e9	0.270746
$941$	−6.31351e9	−0.247006	−0.123503	−	0.992344i	$-0.539413\pi$
$941$	−6.31351e9	−0.247006	−0.123503	+	0.992344i	$0.539413\pi$
$942$	4.65744e9	0.181539
$943$	2.36012e10	0.916521
$944$	5.94145e9	0.229874
$945$	1.77047e9	0.0682460
$946$	2.84096e10	1.09105
$947$	1.94677e10	0.744885	0.372443	−	0.928055i	$-0.378520\pi$
$947$	1.94677e10	0.744885	0.372443	+	0.928055i	$0.378520\pi$
$948$	3.70709e9	0.141320
$949$	−1.26220e9	−0.0479400
$950$	−5.94372e8	−0.0224919
$951$	−2.42669e10	−0.914918
$952$	6.38520e9	0.239853
$953$	−1.40644e10	−0.526376	−0.263188	−	0.964745i	$-0.584774\pi$
$953$	−1.40644e10	−0.526376	−0.263188	+	0.964745i	$0.584774\pi$
$954$	7.68033e9	0.286392
$955$	−1.14924e10	−0.426972
$956$	2.08399e10	0.771425
$957$	2.16069e10	0.796893
$958$	−7.34102e9	−0.269760
$959$	6.85807e9	0.251094
$960$	1.85612e9	0.0677107
$961$	7.23175e10	2.62852
$962$	9.38040e9	0.339710
$963$	1.01874e10	0.367597
$964$	−2.00914e10	−0.722337
$965$	−4.03234e10	−1.44448
$966$	−5.96404e9	−0.212873
$967$	−2.63668e10	−0.937703	−0.468852	−	0.883277i	$-0.655332\pi$
$967$	−2.63668e10	−0.937703	−0.468852	+	0.883277i	$0.655332\pi$
$968$	2.35265e10	0.833670
$969$	−7.79743e9	−0.275308
$970$	2.36503e10	0.832023
$971$	−1.38855e10	−0.486735	−0.243368	−	0.969934i	$-0.578252\pi$
$971$	−1.38855e10	−0.486735	−0.243368	+	0.969934i	$0.578252\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.96373e10	0.683417
$974$	−2.44069e10	−0.846364
$975$	−5.54862e8	−0.0191721
$976$	−4.43752e9	−0.152780
$977$	2.36190e9	0.0810270	0.0405135	−	0.999179i	$-0.487101\pi$
$977$	2.36190e9	0.0810270	0.0405135	+	0.999179i	$0.487101\pi$
$978$	7.75116e9	0.264960
$979$	−7.20998e10	−2.45581
$980$	−1.97456e9	−0.0670162
$981$	2.12555e9	0.0718836
$982$	6.94494e9	0.234034
$983$	4.42618e10	1.48625	0.743125	−	0.669153i	$-0.233343\pi$
$983$	4.42618e10	1.48625	0.743125	+	0.669153i	$0.233343\pi$
$984$	−4.05298e9	−0.135610
$985$	2.48167e10	0.827404
$986$	−2.87750e10	−0.955974
$987$	3.80439e9	0.125943
$988$	−1.11683e9	−0.0368416
$989$	3.53391e10	1.16163
$990$	−1.23718e10	−0.405238
$991$	4.03463e10	1.31688	0.658440	−	0.752634i	$-0.271217\pi$
$991$	4.03463e10	1.31688	0.658440	+	0.752634i	$0.271217\pi$
$992$	−1.03533e10	−0.336736
$993$	2.48416e10	0.805114
$994$	7.55290e9	0.243928
$995$	2.39399e10	0.770446
$996$	−9.48577e9	−0.304204
$997$	−2.59706e10	−0.829944	−0.414972	−	0.909834i	$-0.636209\pi$
$997$	−2.59706e10	−0.829944	−0.414972	+	0.909834i	$0.636209\pi$
$998$	−2.83530e10	−0.902904
$999$	1.05049e10	0.333360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.q.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.q.1.3	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -262.243 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -262.243 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -2097.94 q^{10} +8089.34 q^{11} -1728.00 q^{12} -2197.00 q^{13} +2744.00 q^{14} +7080.55 q^{15} +4096.00 q^{16} +36358.9 q^{17} +5832.00 q^{18} +7942.87 q^{19} -16783.5 q^{20} -9261.00 q^{21} +64714.7 q^{22} +80499.5 q^{23} -13824.0 q^{24} -9353.86 q^{25} -17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} -98927.0 q^{29} +56644.4 q^{30} -315959. q^{31} +32768.0 q^{32} -218412. q^{33} +290871. q^{34} -89949.2 q^{35} +46656.0 q^{36} -533705. q^{37} +63543.0 q^{38} +59319.0 q^{39} -134268. q^{40} +293184. q^{41} -74088.0 q^{42} +438998. q^{43} +517718. q^{44} -191175. q^{45} +643996. q^{46} -410797. q^{47} -110592. q^{48} +117649. q^{49} -74830.9 q^{50} -981690. q^{51} -140608. q^{52} +1.31693e6 q^{53} -157464. q^{54} -2.12137e6 q^{55} +175616. q^{56} -214457. q^{57} -791416. q^{58} +1.45055e6 q^{59} +453155. q^{60} -1.08338e6 q^{61} -2.52767e6 q^{62} +250047. q^{63} +262144. q^{64} +576147. q^{65} -1.74730e6 q^{66} +258422. q^{67} +2.32697e6 q^{68} -2.17349e6 q^{69} -719593. q^{70} +2.75251e6 q^{71} +373248. q^{72} +574512. q^{73} -4.26964e6 q^{74} +252554. q^{75} +508344. q^{76} +2.77464e6 q^{77} +474552. q^{78} -2.14531e6 q^{79} -1.07415e6 q^{80} +531441. q^{81} +2.34547e6 q^{82} +5.48945e6 q^{83} -592704. q^{84} -9.53485e6 q^{85} +3.51198e6 q^{86} +2.67103e6 q^{87} +4.14174e6 q^{88} -8.91294e6 q^{89} -1.52940e6 q^{90} -753571. q^{91} +5.15196e6 q^{92} +8.53089e6 q^{93} -3.28637e6 q^{94} -2.08296e6 q^{95} -884736. q^{96} -1.12731e7 q^{97} +941192. q^{98} +5.89713e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 13 q^{5} - 1296 q^{6} + 2058 q^{7} + 3072 q^{8} + 4374 q^{9} + 104 q^{10} + 10054 q^{11} - 10368 q^{12} - 13182 q^{13} + 16464 q^{14} - 351 q^{15} + 24576 q^{16} + 21222 q^{17} + 34992 q^{18} + 9527 q^{19} + 832 q^{20} - 55566 q^{21} + 80432 q^{22} + 33229 q^{23} - 82944 q^{24} + 265321 q^{25} - 105456 q^{26} - 118098 q^{27} + 131712 q^{28} + 174185 q^{29} - 2808 q^{30} + 119045 q^{31} + 196608 q^{32} - 271458 q^{33} + 169776 q^{34} + 4459 q^{35} + 279936 q^{36} + 56562 q^{37} + 76216 q^{38} + 355914 q^{39} + 6656 q^{40} + 101632 q^{41} - 444528 q^{42} + 441323 q^{43} + 643456 q^{44} + 9477 q^{45} + 265832 q^{46} - 892849 q^{47} - 663552 q^{48} + 705894 q^{49} + 2122568 q^{50} - 572994 q^{51} - 843648 q^{52} + 2093965 q^{53} - 944784 q^{54} - 331222 q^{55} + 1053696 q^{56} - 257229 q^{57} + 1393480 q^{58} - 136204 q^{59} - 22464 q^{60} - 3989946 q^{61} + 952360 q^{62} + 1500282 q^{63} + 1572864 q^{64} - 28561 q^{65} - 2171664 q^{66} - 2218250 q^{67} + 1358208 q^{68} - 897183 q^{69} + 35672 q^{70} + 2045928 q^{71} + 2239488 q^{72} - 8557479 q^{73} + 452496 q^{74} - 7163667 q^{75} + 609728 q^{76} + 3448522 q^{77} + 2847312 q^{78} - 8559709 q^{79} + 53248 q^{80} + 3188646 q^{81} + 813056 q^{82} + 2496351 q^{83} - 3556224 q^{84} + 5335304 q^{85} + 3530584 q^{86} - 4702995 q^{87} + 5147648 q^{88} - 2446683 q^{89} + 75816 q^{90} - 4521426 q^{91} + 2126656 q^{92} - 3214215 q^{93} - 7142792 q^{94} + 16410211 q^{95} - 5308416 q^{96} + 5786889 q^{97} + 5647152 q^{98} + 7329366 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 162 * q^3 + 384 * q^4 + 13 * q^5 - 1296 * q^6 + 2058 * q^7 + 3072 * q^8 + 4374 * q^9 + 104 * q^10 + 10054 * q^11 - 10368 * q^12 - 13182 * q^13 + 16464 * q^14 - 351 * q^15 + 24576 * q^16 + 21222 * q^17 + 34992 * q^18 + 9527 * q^19 + 832 * q^20 - 55566 * q^21 + 80432 * q^22 + 33229 * q^23 - 82944 * q^24 + 265321 * q^25 - 105456 * q^26 - 118098 * q^27 + 131712 * q^28 + 174185 * q^29 - 2808 * q^30 + 119045 * q^31 + 196608 * q^32 - 271458 * q^33 + 169776 * q^34 + 4459 * q^35 + 279936 * q^36 + 56562 * q^37 + 76216 * q^38 + 355914 * q^39 + 6656 * q^40 + 101632 * q^41 - 444528 * q^42 + 441323 * q^43 + 643456 * q^44 + 9477 * q^45 + 265832 * q^46 - 892849 * q^47 - 663552 * q^48 + 705894 * q^49 + 2122568 * q^50 - 572994 * q^51 - 843648 * q^52 + 2093965 * q^53 - 944784 * q^54 - 331222 * q^55 + 1053696 * q^56 - 257229 * q^57 + 1393480 * q^58 - 136204 * q^59 - 22464 * q^60 - 3989946 * q^61 + 952360 * q^62 + 1500282 * q^63 + 1572864 * q^64 - 28561 * q^65 - 2171664 * q^66 - 2218250 * q^67 + 1358208 * q^68 - 897183 * q^69 + 35672 * q^70 + 2045928 * q^71 + 2239488 * q^72 - 8557479 * q^73 + 452496 * q^74 - 7163667 * q^75 + 609728 * q^76 + 3448522 * q^77 + 2847312 * q^78 - 8559709 * q^79 + 53248 * q^80 + 3188646 * q^81 + 813056 * q^82 + 2496351 * q^83 - 3556224 * q^84 + 5335304 * q^85 + 3530584 * q^86 - 4702995 * q^87 + 5147648 * q^88 - 2446683 * q^89 + 75816 * q^90 - 4521426 * q^91 + 2126656 * q^92 - 3214215 * q^93 - 7142792 * q^94 + 16410211 * q^95 - 5308416 * q^96 + 5786889 * q^97 + 5647152 * q^98 + 7329366 * q^99

Introduction

L-functions

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