LMFDB - Embedded newform 177.6.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.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:	$28.3879361069$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + \cdots - 14846072 $ x^11 - 5x^10 - 238x^9 + 1067x^8 + 20782x^7 - 79077x^6 - 813818x^5 + 2364885x^4 + 13849341x^3 - 23890558x^2 - 74443300x - 14846072
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$5.75393$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.75393 q^{2} +9.00000 q^{3} -9.40015 q^{4} -8.06966 q^{5} +42.7854 q^{6} -28.8581 q^{7} -196.813 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.75393 q^{2} +9.00000 q^{3} -9.40015 q^{4} -8.06966 q^{5} +42.7854 q^{6} -28.8581 q^{7} -196.813 q^{8} +81.0000 q^{9} -38.3626 q^{10} +556.758 q^{11} -84.6013 q^{12} -1129.41 q^{13} -137.189 q^{14} -72.6270 q^{15} -634.832 q^{16} +447.456 q^{17} +385.068 q^{18} -1350.14 q^{19} +75.8560 q^{20} -259.723 q^{21} +2646.79 q^{22} -4466.66 q^{23} -1771.32 q^{24} -3059.88 q^{25} -5369.15 q^{26} +729.000 q^{27} +271.270 q^{28} -2943.74 q^{29} -345.264 q^{30} +1113.75 q^{31} +3280.08 q^{32} +5010.83 q^{33} +2127.18 q^{34} +232.875 q^{35} -761.412 q^{36} -5875.21 q^{37} -6418.45 q^{38} -10164.7 q^{39} +1588.22 q^{40} -638.732 q^{41} -1234.70 q^{42} -9932.25 q^{43} -5233.61 q^{44} -653.643 q^{45} -21234.2 q^{46} +25092.0 q^{47} -5713.49 q^{48} -15974.2 q^{49} -14546.5 q^{50} +4027.11 q^{51} +10616.6 q^{52} +19396.9 q^{53} +3465.62 q^{54} -4492.85 q^{55} +5679.66 q^{56} -12151.2 q^{57} -13994.3 q^{58} +3481.00 q^{59} +682.704 q^{60} +7814.71 q^{61} +5294.71 q^{62} -2337.51 q^{63} +35907.9 q^{64} +9113.98 q^{65} +23821.1 q^{66} +36824.7 q^{67} -4206.15 q^{68} -40199.9 q^{69} +1107.07 q^{70} +24174.9 q^{71} -15941.9 q^{72} -78229.0 q^{73} -27930.3 q^{74} -27538.9 q^{75} +12691.5 q^{76} -16067.0 q^{77} -48322.3 q^{78} +4205.35 q^{79} +5122.88 q^{80} +6561.00 q^{81} -3036.49 q^{82} -36905.9 q^{83} +2441.43 q^{84} -3610.82 q^{85} -47217.2 q^{86} -26493.7 q^{87} -109578. q^{88} +6625.63 q^{89} -3107.37 q^{90} +32592.7 q^{91} +41987.2 q^{92} +10023.8 q^{93} +119286. q^{94} +10895.1 q^{95} +29520.7 q^{96} +88314.2 q^{97} -75940.3 q^{98} +45097.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) $ 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9} - 399 q^{10} - 698 q^{11} + 1350 q^{12} - 1556 q^{13} - 1679 q^{14} - 1728 q^{15} - 2662 q^{16} - 4793 q^{17} - 486 q^{18} - 3753 q^{19} - 11023 q^{20} - 3339 q^{21} - 9534 q^{22} - 7323 q^{23} - 5589 q^{24} + 7867 q^{25} - 4844 q^{26} + 8019 q^{27} + 3650 q^{28} - 15467 q^{29} - 3591 q^{30} - 5151 q^{31} - 15368 q^{32} - 6282 q^{33} + 8452 q^{34} - 23285 q^{35} + 12150 q^{36} + 8623 q^{37} + 15205 q^{38} - 14004 q^{39} + 41530 q^{40} - 6369 q^{41} - 15111 q^{42} - 20506 q^{43} - 55632 q^{44} - 15552 q^{45} - 45191 q^{46} - 47899 q^{47} - 23958 q^{48} - 10322 q^{49} - 102147 q^{50} - 43137 q^{51} - 292 q^{52} - 80048 q^{53} - 4374 q^{54} - 2114 q^{55} - 108126 q^{56} - 33777 q^{57} - 58294 q^{58} + 38291 q^{59} - 99207 q^{60} - 82527 q^{61} - 67438 q^{62} - 30051 q^{63} - 51411 q^{64} - 167646 q^{65} - 85806 q^{66} - 166976 q^{67} - 136533 q^{68} - 65907 q^{69} + 76140 q^{70} - 183560 q^{71} - 50301 q^{72} - 36809 q^{73} - 116686 q^{74} + 70803 q^{75} + 55580 q^{76} - 164885 q^{77} - 43596 q^{78} - 281518 q^{79} - 32683 q^{80} + 72171 q^{81} + 178815 q^{82} - 254691 q^{83} + 32850 q^{84} + 4763 q^{85} + 349324 q^{86} - 139203 q^{87} + 251285 q^{88} - 89687 q^{89} - 32319 q^{90} + 34897 q^{91} - 20240 q^{92} - 46359 q^{93} + 96548 q^{94} - 155113 q^{95} - 138312 q^{96} - 45828 q^{97} + 465864 q^{98} - 56538 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9 - 399 * q^10 - 698 * q^11 + 1350 * q^12 - 1556 * q^13 - 1679 * q^14 - 1728 * q^15 - 2662 * q^16 - 4793 * q^17 - 486 * q^18 - 3753 * q^19 - 11023 * q^20 - 3339 * q^21 - 9534 * q^22 - 7323 * q^23 - 5589 * q^24 + 7867 * q^25 - 4844 * q^26 + 8019 * q^27 + 3650 * q^28 - 15467 * q^29 - 3591 * q^30 - 5151 * q^31 - 15368 * q^32 - 6282 * q^33 + 8452 * q^34 - 23285 * q^35 + 12150 * q^36 + 8623 * q^37 + 15205 * q^38 - 14004 * q^39 + 41530 * q^40 - 6369 * q^41 - 15111 * q^42 - 20506 * q^43 - 55632 * q^44 - 15552 * q^45 - 45191 * q^46 - 47899 * q^47 - 23958 * q^48 - 10322 * q^49 - 102147 * q^50 - 43137 * q^51 - 292 * q^52 - 80048 * q^53 - 4374 * q^54 - 2114 * q^55 - 108126 * q^56 - 33777 * q^57 - 58294 * q^58 + 38291 * q^59 - 99207 * q^60 - 82527 * q^61 - 67438 * q^62 - 30051 * q^63 - 51411 * q^64 - 167646 * q^65 - 85806 * q^66 - 166976 * q^67 - 136533 * q^68 - 65907 * q^69 + 76140 * q^70 - 183560 * q^71 - 50301 * q^72 - 36809 * q^73 - 116686 * q^74 + 70803 * q^75 + 55580 * q^76 - 164885 * q^77 - 43596 * q^78 - 281518 * q^79 - 32683 * q^80 + 72171 * q^81 + 178815 * q^82 - 254691 * q^83 + 32850 * q^84 + 4763 * q^85 + 349324 * q^86 - 139203 * q^87 + 251285 * q^88 - 89687 * q^89 - 32319 * q^90 + 34897 * q^91 - 20240 * q^92 - 46359 * q^93 + 96548 * q^94 - 155113 * q^95 - 138312 * q^96 - 45828 * q^97 + 465864 * q^98 - 56538 * 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 $

$2$	4.75393	0.840384	0.420192	−	0.907435i	$-0.361963\pi$
$2$	4.75393	0.840384	0.420192	+	0.907435i	$0.361963\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−9.40015	−0.293755
$5$	−8.06966	−0.144355	−0.0721773	−	0.997392i	$-0.522995\pi$
$5$	−8.06966	−0.144355	−0.0721773	+	0.997392i	$0.522995\pi$
$6$	42.7854	0.485196
$7$	−28.8581	−0.222599	−0.111299	−	0.993787i	$-0.535501\pi$
$7$	−28.8581	−0.222599	−0.111299	+	0.993787i	$0.535501\pi$
$8$	−196.813	−1.08725
$9$	81.0000	0.333333
$10$	−38.3626	−0.121313
$11$	556.758	1.38735	0.693673	−	0.720290i	$-0.255991\pi$
$11$	556.758	1.38735	0.693673	+	0.720290i	$0.255991\pi$
$12$	−84.6013	−0.169599
$13$	−1129.41	−1.85351	−0.926754	−	0.375670i	$-0.877413\pi$
$13$	−1129.41	−1.85351	−0.926754	+	0.375670i	$0.877413\pi$
$14$	−137.189	−0.187068
$15$	−72.6270	−0.0833431
$16$	−634.832	−0.619954
$17$	447.456	0.375516	0.187758	−	0.982215i	$-0.439878\pi$
$17$	447.456	0.375516	0.187758	+	0.982215i	$0.439878\pi$
$18$	385.068	0.280128
$19$	−1350.14	−0.858012	−0.429006	−	0.903302i	$-0.641136\pi$
$19$	−1350.14	−0.858012	−0.429006	+	0.903302i	$0.641136\pi$
$20$	75.8560	0.0424048
$21$	−259.723	−0.128517
$22$	2646.79	1.16590
$23$	−4466.66	−1.76061	−0.880304	−	0.474409i	$-0.842662\pi$
$23$	−4466.66	−1.76061	−0.880304	+	0.474409i	$0.842662\pi$
$24$	−1771.32	−0.627725
$25$	−3059.88	−0.979162
$26$	−5369.15	−1.55766
$27$	729.000	0.192450
$28$	271.270	0.0653894
$29$	−2943.74	−0.649987	−0.324994	−	0.945716i	$-0.605362\pi$
$29$	−2943.74	−0.649987	−0.324994	+	0.945716i	$0.605362\pi$
$30$	−345.264	−0.0700402
$31$	1113.75	0.208154	0.104077	−	0.994569i	$-0.466811\pi$
$31$	1113.75	0.208154	0.104077	+	0.994569i	$0.466811\pi$
$32$	3280.08	0.566252
$33$	5010.83	0.800985
$34$	2127.18	0.315578
$35$	232.875	0.0321331
$36$	−761.412	−0.0979182
$37$	−5875.21	−0.705536	−0.352768	−	0.935711i	$-0.614759\pi$
$37$	−5875.21	−0.705536	−0.352768	+	0.935711i	$0.614759\pi$
$38$	−6418.45	−0.721060
$39$	−10164.7	−1.07012
$40$	1588.22	0.156950
$41$	−638.732	−0.0593415	−0.0296708	−	0.999560i	$-0.509446\pi$
$41$	−638.732	−0.0593415	−0.0296708	+	0.999560i	$0.509446\pi$
$42$	−1234.70	−0.108004
$43$	−9932.25	−0.819175	−0.409587	−	0.912271i	$-0.634327\pi$
$43$	−9932.25	−0.819175	−0.409587	+	0.912271i	$0.634327\pi$
$44$	−5233.61	−0.407540
$45$	−653.643	−0.0481182
$46$	−21234.2	−1.47959
$47$	25092.0	1.65688	0.828440	−	0.560078i	$-0.189229\pi$
$47$	25092.0	1.65688	0.828440	+	0.560078i	$0.189229\pi$
$48$	−5713.49	−0.357930
$49$	−15974.2	−0.950450
$50$	−14546.5	−0.822872
$51$	4027.11	0.216804
$52$	10616.6	0.544476
$53$	19396.9	0.948509	0.474255	−	0.880388i	$-0.342718\pi$
$53$	19396.9	0.948509	0.474255	+	0.880388i	$0.342718\pi$
$54$	3465.62	0.161732
$55$	−4492.85	−0.200270
$56$	5679.66	0.242021
$57$	−12151.2	−0.495374
$58$	−13994.3	−0.546239
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	682.704	0.0244824
$61$	7814.71	0.268898	0.134449	−	0.990920i	$-0.457073\pi$
$61$	7814.71	0.268898	0.134449	+	0.990920i	$0.457073\pi$
$62$	5294.71	0.174929
$63$	−2337.51	−0.0741996
$64$	35907.9	1.09582
$65$	9113.98	0.267562
$66$	23821.1	0.673135
$67$	36824.7	1.00220	0.501098	−	0.865391i	$-0.332930\pi$
$67$	36824.7	1.00220	0.501098	+	0.865391i	$0.332930\pi$
$68$	−4206.15	−0.110310
$69$	−40199.9	−1.01649
$70$	1107.07	0.0270042
$71$	24174.9	0.569141	0.284570	−	0.958655i	$-0.408149\pi$
$71$	24174.9	0.569141	0.284570	+	0.958655i	$0.408149\pi$
$72$	−15941.9	−0.362417
$73$	−78229.0	−1.71815	−0.859075	−	0.511850i	$-0.828960\pi$
$73$	−78229.0	−1.71815	−0.859075	+	0.511850i	$0.828960\pi$
$74$	−27930.3	−0.592921
$75$	−27538.9	−0.565319
$76$	12691.5	0.252045
$77$	−16067.0	−0.308822
$78$	−48322.3	−0.899314
$79$	4205.35	0.0758115	0.0379057	−	0.999281i	$-0.487931\pi$
$79$	4205.35	0.0758115	0.0379057	+	0.999281i	$0.487931\pi$
$80$	5122.88	0.0894931
$81$	6561.00	0.111111
$82$	−3036.49	−0.0498697
$83$	−36905.9	−0.588032	−0.294016	−	0.955801i	$-0.594992\pi$
$83$	−36905.9	−0.588032	−0.294016	+	0.955801i	$0.594992\pi$
$84$	2441.43	0.0377526
$85$	−3610.82	−0.0542074
$86$	−47217.2	−0.688421
$87$	−26493.7	−0.375270
$88$	−109578.	−1.50839
$89$	6625.63	0.0886650	0.0443325	−	0.999017i	$-0.485884\pi$
$89$	6625.63	0.0886650	0.0443325	+	0.999017i	$0.485884\pi$
$90$	−3107.37	−0.0404377
$91$	32592.7	0.412588
$92$	41987.2	0.517187
$93$	10023.8	0.120178
$94$	119286.	1.39242
$95$	10895.1	0.123858
$96$	29520.7	0.326926
$97$	88314.2	0.953018	0.476509	−	0.879170i	$-0.341902\pi$
$97$	88314.2	0.953018	0.476509	+	0.879170i	$0.341902\pi$
$98$	−75940.3	−0.798743
$99$	45097.4	0.462449
$100$	28763.3	0.287633
$101$	−123051.	−1.20028	−0.600138	−	0.799896i	$-0.704888\pi$
$101$	−123051.	−1.20028	−0.600138	+	0.799896i	$0.704888\pi$
$102$	19144.6	0.182199
$103$	87267.1	0.810509	0.405254	−	0.914204i	$-0.367183\pi$
$103$	87267.1	0.810509	0.405254	+	0.914204i	$0.367183\pi$
$104$	222284.	2.01523
$105$	2095.88	0.0185521
$106$	92211.3	0.797112
$107$	−2531.40	−0.0213748	−0.0106874	−	0.999943i	$-0.503402\pi$
$107$	−2531.40	−0.0213748	−0.0106874	+	0.999943i	$0.503402\pi$
$108$	−6852.71	−0.0565331
$109$	−158752.	−1.27983	−0.639914	−	0.768446i	$-0.721030\pi$
$109$	−158752.	−1.27983	−0.639914	+	0.768446i	$0.721030\pi$
$110$	−21358.7	−0.168304
$111$	−52876.9	−0.407341
$112$	18320.1	0.138001
$113$	−45254.3	−0.333399	−0.166699	−	0.986008i	$-0.553311\pi$
$113$	−45254.3	−0.333399	−0.166699	+	0.986008i	$0.553311\pi$
$114$	−57766.1	−0.416304
$115$	36044.4	0.254152
$116$	27671.6	0.190937
$117$	−91482.4	−0.617836
$118$	16548.4	0.109409
$119$	−12912.7	−0.0835893
$120$	14294.0	0.0906149
$121$	148929.	0.924731
$122$	37150.6	0.225978
$123$	−5748.58	−0.0342608
$124$	−10469.5	−0.0611463
$125$	49909.9	0.285701
$126$	−11112.3	−0.0623561
$127$	−60121.1	−0.330764	−0.165382	−	0.986230i	$-0.552886\pi$
$127$	−60121.1	−0.330764	−0.165382	+	0.986230i	$0.552886\pi$
$128$	65741.1	0.354660
$129$	−89390.3	−0.472951
$130$	43327.2	0.224855
$131$	339921.	1.73061	0.865307	−	0.501243i	$-0.167124\pi$
$131$	339921.	1.73061	0.865307	+	0.501243i	$0.167124\pi$
$132$	−47102.5	−0.235293
$133$	38962.4	0.190992
$134$	175062.	0.842229
$135$	−5882.78	−0.0277810
$136$	−88065.4	−0.408280
$137$	67355.2	0.306598	0.153299	−	0.988180i	$-0.451010\pi$
$137$	67355.2	0.306598	0.153299	+	0.988180i	$0.451010\pi$
$138$	−191108.	−0.854240
$139$	308422.	1.35397	0.676983	−	0.735999i	$-0.263287\pi$
$139$	308422.	1.35397	0.676983	+	0.735999i	$0.263287\pi$
$140$	−2189.06	−0.00943926
$141$	225828.	0.956600
$142$	114926.	0.478297
$143$	−628810.	−2.57146
$144$	−51421.4	−0.206651
$145$	23755.0	0.0938286
$146$	−371895.	−1.44391
$147$	−143768.	−0.548742
$148$	55227.8	0.207254
$149$	386065.	1.42460	0.712302	−	0.701873i	$-0.247653\pi$
$149$	386065.	1.42460	0.712302	+	0.701873i	$0.247653\pi$
$150$	−130918.	−0.475085
$151$	361671.	1.29084	0.645418	−	0.763829i	$-0.276683\pi$
$151$	361671.	1.29084	0.645418	+	0.763829i	$0.276683\pi$
$152$	265725.	0.932875
$153$	36244.0	0.125172
$154$	−76381.3	−0.259529
$155$	−8987.62	−0.0300480
$156$	95549.8	0.314354
$157$	−125710.	−0.407026	−0.203513	−	0.979072i	$-0.565236\pi$
$157$	−125710.	−0.407026	−0.203513	+	0.979072i	$0.565236\pi$
$158$	19992.0	0.0637107
$159$	174572.	0.547622
$160$	−26469.1	−0.0817410
$161$	128899.	0.391909
$162$	31190.5	0.0933760
$163$	312195.	0.920358	0.460179	−	0.887826i	$-0.347785\pi$
$163$	312195.	0.920358	0.460179	+	0.887826i	$0.347785\pi$
$164$	6004.17	0.0174318
$165$	−40435.7	−0.115626
$166$	−175448.	−0.494173
$167$	−696281.	−1.93194	−0.965969	−	0.258656i	$-0.916720\pi$
$167$	−696281.	−1.93194	−0.965969	+	0.258656i	$0.916720\pi$
$168$	51117.0	0.139731
$169$	904280.	2.43549
$170$	−17165.6	−0.0455550
$171$	−109361.	−0.286004
$172$	93364.6	0.240636
$173$	−467449.	−1.18746	−0.593730	−	0.804664i	$-0.702345\pi$
$173$	−467449.	−1.18746	−0.593730	+	0.804664i	$0.702345\pi$
$174$	−125949.	−0.315371
$175$	88302.3	0.217960
$176$	−353448.	−0.860091
$177$	31329.0	0.0751646
$178$	31497.8	0.0745127
$179$	−205080.	−0.478400	−0.239200	−	0.970970i	$-0.576885\pi$
$179$	−205080.	−0.478400	−0.239200	+	0.970970i	$0.576885\pi$
$180$	6144.34	0.0141349
$181$	184862.	0.419421	0.209711	−	0.977763i	$-0.432748\pi$
$181$	184862.	0.419421	0.209711	+	0.977763i	$0.432748\pi$
$182$	154943.	0.346733
$183$	70332.4	0.155249
$184$	879098.	1.91422
$185$	47411.0	0.101847
$186$	47652.4	0.100996
$187$	249125.	0.520971
$188$	−235869.	−0.486716
$189$	−21037.6	−0.0428391
$190$	51794.7	0.104088
$191$	−272484.	−0.540453	−0.270226	−	0.962797i	$-0.587099\pi$
$191$	−272484.	−0.540453	−0.270226	+	0.962797i	$0.587099\pi$
$192$	323171.	0.632673
$193$	−270438.	−0.522606	−0.261303	−	0.965257i	$-0.584152\pi$
$193$	−270438.	−0.522606	−0.261303	+	0.965257i	$0.584152\pi$
$194$	419840.	0.800901
$195$	82025.8	0.154477
$196$	150160.	0.279199
$197$	−707478.	−1.29882	−0.649408	−	0.760440i	$-0.724983\pi$
$197$	−707478.	−1.29882	−0.649408	+	0.760440i	$0.724983\pi$
$198$	214390.	0.388635
$199$	−1.02712e6	−1.83861	−0.919303	−	0.393550i	$-0.871247\pi$
$199$	−1.02712e6	−1.83861	−0.919303	+	0.393550i	$0.871247\pi$
$200$	602226.	1.06459
$201$	331423.	0.578618
$202$	−584975.	−1.00869
$203$	84950.8	0.144686
$204$	−37855.4	−0.0636872
$205$	5154.35	0.00856622
$206$	414862.	0.681138
$207$	−361799.	−0.586870
$208$	716988.	1.14909
$209$	−751699.	−1.19036
$210$	9963.65	0.0155909
$211$	−806769.	−1.24751	−0.623753	−	0.781621i	$-0.714393\pi$
$211$	−806769.	−1.24751	−0.623753	+	0.781621i	$0.714393\pi$
$212$	−182333.	−0.278629
$213$	217575.	0.328594
$214$	−12034.1	−0.0179630
$215$	80149.9	0.118252
$216$	−143477.	−0.209242
$217$	−32140.8	−0.0463349
$218$	−754694.	−1.07555
$219$	−704061.	−0.991974
$220$	42233.5	0.0588302
$221$	−505363.	−0.696021
$222$	−251373.	−0.342323
$223$	−337189.	−0.454058	−0.227029	−	0.973888i	$-0.572901\pi$
$223$	−337189.	−0.454058	−0.227029	+	0.973888i	$0.572901\pi$
$224$	−94656.9	−0.126047
$225$	−247850.	−0.326387
$226$	−215136.	−0.280183
$227$	−259818.	−0.334661	−0.167331	−	0.985901i	$-0.553515\pi$
$227$	−259818.	−0.334661	−0.167331	+	0.985901i	$0.553515\pi$
$228$	114223.	0.145518
$229$	227371.	0.286515	0.143257	−	0.989685i	$-0.454242\pi$
$229$	227371.	0.286515	0.143257	+	0.989685i	$0.454242\pi$
$230$	171353.	0.213585
$231$	−144603.	−0.178298
$232$	579368.	0.706699
$233$	265219.	0.320048	0.160024	−	0.987113i	$-0.448843\pi$
$233$	265219.	0.320048	0.160024	+	0.987113i	$0.448843\pi$
$234$	−434901.	−0.519219
$235$	−202484.	−0.239178
$236$	−32721.9	−0.0382436
$237$	37848.2	0.0437698
$238$	−61386.2	−0.0702471
$239$	−245730.	−0.278268	−0.139134	−	0.990274i	$-0.544432\pi$
$239$	−245730.	−0.278268	−0.139134	+	0.990274i	$0.544432\pi$
$240$	46106.0	0.0516689
$241$	1.23701e6	1.37193	0.685963	−	0.727636i	$-0.259381\pi$
$241$	1.23701e6	1.37193	0.685963	+	0.727636i	$0.259381\pi$
$242$	707997.	0.777129
$243$	59049.0	0.0641500
$244$	−73459.4	−0.0789902
$245$	128906.	0.137202
$246$	−27328.4	−0.0287923
$247$	1.52486e6	1.59033
$248$	−219202.	−0.226316
$249$	−332153.	−0.339500
$250$	237268.	0.240099
$251$	−412168.	−0.412943	−0.206472	−	0.978453i	$-0.566198\pi$
$251$	−412168.	−0.412943	−0.206472	+	0.978453i	$0.566198\pi$
$252$	21972.9	0.0217965
$253$	−2.48685e6	−2.44258
$254$	−285812.	−0.277969
$255$	−32497.4	−0.0312967
$256$	−836524.	−0.797772
$257$	−1.57045e6	−1.48317	−0.741585	−	0.670859i	$-0.765926\pi$
$257$	−1.57045e6	−1.48317	−0.741585	+	0.670859i	$0.765926\pi$
$258$	−424955.	−0.397460
$259$	169547.	0.157051
$260$	−85672.7	−0.0785976
$261$	−238443.	−0.216662
$262$	1.61596e6	1.45438
$263$	1.39983e6	1.24792	0.623959	−	0.781457i	$-0.285523\pi$
$263$	1.39983e6	1.24792	0.623959	+	0.781457i	$0.285523\pi$
$264$	−986198.	−0.870872
$265$	−156526.	−0.136922
$266$	185224.	0.160507
$267$	59630.7	0.0511908
$268$	−346158.	−0.294400
$269$	−1.66101e6	−1.39956	−0.699780	−	0.714358i	$-0.746719\pi$
$269$	−1.66101e6	−1.39956	−0.699780	+	0.714358i	$0.746719\pi$
$270$	−27966.3	−0.0233467
$271$	−2.02912e6	−1.67836	−0.839178	−	0.543856i	$-0.816964\pi$
$271$	−2.02912e6	−1.67836	−0.839178	+	0.543856i	$0.816964\pi$
$272$	−284060.	−0.232802
$273$	293334.	0.238208
$274$	320202.	0.257660
$275$	−1.70361e6	−1.35844
$276$	377885.	0.298598
$277$	−1.82153e6	−1.42638	−0.713191	−	0.700970i	$-0.752751\pi$
$277$	−1.82153e6	−1.42638	−0.713191	+	0.700970i	$0.752751\pi$
$278$	1.46621e6	1.13785
$279$	90214.1	0.0693847
$280$	−45833.0	−0.0349368
$281$	−1.98485e6	−1.49955	−0.749777	−	0.661691i	$-0.769839\pi$
$281$	−1.98485e6	−1.49955	−0.749777	+	0.661691i	$0.769839\pi$
$282$	1.07357e6	0.803912
$283$	2.17263e6	1.61258	0.806289	−	0.591522i	$-0.201473\pi$
$283$	2.17263e6	1.61258	0.806289	+	0.591522i	$0.201473\pi$
$284$	−227248.	−0.167188
$285$	98056.3	0.0715094
$286$	−2.98932e6	−2.16101
$287$	18432.6	0.0132093
$288$	265686.	0.188751
$289$	−1.21964e6	−0.858988
$290$	112930.	0.0788521
$291$	794828.	0.550225
$292$	735365.	0.504714
$293$	−1.73848e6	−1.18305	−0.591523	−	0.806288i	$-0.701473\pi$
$293$	−1.73848e6	−1.18305	−0.591523	+	0.806288i	$0.701473\pi$
$294$	−683463.	−0.461154
$295$	−28090.5	−0.0187934
$296$	1.15632e6	0.767094
$297$	405877.	0.266995
$298$	1.83532e6	1.19721
$299$	5.04470e6	3.26330
$300$	258870.	0.166065
$301$	286626.	0.182347
$302$	1.71936e6	1.08480
$303$	−1.10746e6	−0.692980
$304$	857110.	0.531928
$305$	−63062.1	−0.0388167
$306$	172301.	0.105193
$307$	1.20069e6	0.727082	0.363541	−	0.931578i	$-0.381568\pi$
$307$	1.20069e6	0.727082	0.363541	+	0.931578i	$0.381568\pi$
$308$	151032.	0.0907178
$309$	785404.	0.467947
$310$	−42726.5	−0.0252519
$311$	1.20148e6	0.704395	0.352197	−	0.935926i	$-0.385435\pi$
$311$	1.20148e6	0.704395	0.352197	+	0.935926i	$0.385435\pi$
$312$	2.00055e6	1.16349
$313$	−1.09781e6	−0.633385	−0.316693	−	0.948528i	$-0.602572\pi$
$313$	−1.09781e6	−0.633385	−0.316693	+	0.948528i	$0.602572\pi$
$314$	−597619.	−0.342058
$315$	18862.9	0.0107110
$316$	−39531.0	−0.0222700
$317$	36761.0	0.0205466	0.0102733	−	0.999947i	$-0.496730\pi$
$317$	36761.0	0.0205466	0.0102733	+	0.999947i	$0.496730\pi$
$318$	829902.	0.460213
$319$	−1.63895e6	−0.901758
$320$	−289765.	−0.158187
$321$	−22782.6	−0.0123407
$322$	612778.	0.329354
$323$	−604127.	−0.322197
$324$	−61674.4	−0.0326394
$325$	3.45587e6	1.81488
$326$	1.48415e6	0.773454
$327$	−1.42876e6	−0.738910
$328$	125711.	0.0645191
$329$	−724108.	−0.368819
$330$	−192228.	−0.0971701
$331$	2.44095e6	1.22459	0.612293	−	0.790631i	$-0.290247\pi$
$331$	2.44095e6	1.22459	0.612293	+	0.790631i	$0.290247\pi$
$332$	346921.	0.172737
$333$	−475892.	−0.235179
$334$	−3.31007e6	−1.62357
$335$	−297163.	−0.144671
$336$	164881.	0.0796748
$337$	−532207.	−0.255274	−0.127637	−	0.991821i	$-0.540739\pi$
$337$	−532207.	−0.255274	−0.127637	+	0.991821i	$0.540739\pi$
$338$	4.29888e6	2.04675
$339$	−407289.	−0.192488
$340$	33942.3	0.0159237
$341$	620092.	0.288782
$342$	−519895.	−0.240353
$343$	946003.	0.434168
$344$	1.95480e6	0.890648
$345$	324400.	0.146735
$346$	−2.22222e6	−0.997923
$347$	−3.36260e6	−1.49917	−0.749587	−	0.661906i	$-0.769748\pi$
$347$	−3.36260e6	−1.49917	−0.749587	+	0.661906i	$0.769748\pi$
$348$	249045.	0.110237
$349$	3.19465e6	1.40398	0.701989	−	0.712188i	$-0.252296\pi$
$349$	3.19465e6	1.40398	0.701989	+	0.712188i	$0.252296\pi$
$350$	419783.	0.183170
$351$	−823342.	−0.356708
$352$	1.82621e6	0.785587
$353$	3.86212e6	1.64964	0.824821	−	0.565394i	$-0.191276\pi$
$353$	3.86212e6	1.64964	0.824821	+	0.565394i	$0.191276\pi$
$354$	148936.	0.0631671
$355$	−195084.	−0.0821580
$356$	−62281.9	−0.0260458
$357$	−116215.	−0.0482603
$358$	−974936.	−0.402039
$359$	3.20790e6	1.31367	0.656833	−	0.754036i	$-0.271896\pi$
$359$	3.20790e6	1.31367	0.656833	+	0.754036i	$0.271896\pi$
$360$	128646.	0.0523165
$361$	−653232.	−0.263815
$362$	878819.	0.352475
$363$	1.34036e6	0.533894
$364$	−306376.	−0.121200
$365$	631282.	0.248023
$366$	334355.	0.130468
$367$	−3.71516e6	−1.43983	−0.719917	−	0.694060i	$-0.755820\pi$
$367$	−3.71516e6	−1.43983	−0.719917	+	0.694060i	$0.755820\pi$
$368$	2.83558e6	1.09150
$369$	−51737.3	−0.0197805
$370$	225388.	0.0855908
$371$	−559756.	−0.211137
$372$	−94225.1	−0.0353028
$373$	−106590.	−0.0396684	−0.0198342	−	0.999803i	$-0.506314\pi$
$373$	−106590.	−0.0396684	−0.0198342	+	0.999803i	$0.506314\pi$
$374$	1.18432e6	0.437815
$375$	449189.	0.164950
$376$	−4.93845e6	−1.80144
$377$	3.32470e6	1.20476
$378$	−100011.	−0.0360013
$379$	2.90777e6	1.03983	0.519914	−	0.854219i	$-0.325964\pi$
$379$	2.90777e6	1.03983	0.519914	+	0.854219i	$0.325964\pi$
$380$	−102416.	−0.0363838
$381$	−541090.	−0.190966
$382$	−1.29537e6	−0.454188
$383$	4.43725e6	1.54567	0.772835	−	0.634608i	$-0.218838\pi$
$383$	4.43725e6	1.54567	0.772835	+	0.634608i	$0.218838\pi$
$384$	591670.	0.204763
$385$	129655.	0.0445798
$386$	−1.28564e6	−0.439190
$387$	−804512.	−0.273058
$388$	−830167.	−0.279954
$389$	−2.41971e6	−0.810755	−0.405378	−	0.914149i	$-0.632860\pi$
$389$	−2.41971e6	−0.810755	−0.405378	+	0.914149i	$0.632860\pi$
$390$	389945.	0.129820
$391$	−1.99863e6	−0.661137
$392$	3.14394e6	1.03338
$393$	3.05929e6	0.999170
$394$	−3.36330e6	−1.09150
$395$	−33935.8	−0.0109437
$396$	−423922.	−0.135847
$397$	−435661.	−0.138731	−0.0693654	−	0.997591i	$-0.522097\pi$
$397$	−435661.	−0.138731	−0.0693654	+	0.997591i	$0.522097\pi$
$398$	−4.88286e6	−1.54514
$399$	350661.	0.110270
$400$	1.94251e6	0.607035
$401$	2.31919e6	0.720237	0.360119	−	0.932906i	$-0.382736\pi$
$401$	2.31919e6	0.720237	0.360119	+	0.932906i	$0.382736\pi$
$402$	1.57556e6	0.486261
$403$	−1.25789e6	−0.385815
$404$	1.15670e6	0.352587
$405$	−52945.1	−0.0160394
$406$	403850.	0.121592
$407$	−3.27107e6	−0.978823
$408$	−792588.	−0.235720
$409$	−293179.	−0.0866612	−0.0433306	−	0.999061i	$-0.513797\pi$
$409$	−293179.	−0.0866612	−0.0433306	+	0.999061i	$0.513797\pi$
$410$	24503.4	0.00719891
$411$	606197.	0.177015
$412$	−820324.	−0.238091
$413$	−100455.	−0.0289799
$414$	−1.71997e6	−0.493196
$415$	297818.	0.0848851
$416$	−3.70456e6	−1.04955
$417$	2.77579e6	0.781713
$418$	−3.57353e6	−1.00036
$419$	989556.	0.275363	0.137681	−	0.990477i	$-0.456035\pi$
$419$	989556.	0.275363	0.137681	+	0.990477i	$0.456035\pi$
$420$	−19701.5	−0.00544976
$421$	−1.03799e6	−0.285421	−0.142711	−	0.989764i	$-0.545582\pi$
$421$	−1.03799e6	−0.285421	−0.142711	+	0.989764i	$0.545582\pi$
$422$	−3.83532e6	−1.04838
$423$	2.03245e6	0.552293
$424$	−3.81756e6	−1.03127
$425$	−1.36916e6	−0.367691
$426$	1.03433e6	0.276145
$427$	−225518.	−0.0598564
$428$	23795.6	0.00627895
$429$	−5.65929e6	−1.48463
$430$	381027.	0.0993767
$431$	−6.08956e6	−1.57904	−0.789519	−	0.613726i	$-0.789670\pi$
$431$	−6.08956e6	−1.57904	−0.789519	+	0.613726i	$0.789670\pi$
$432$	−462793.	−0.119310
$433$	679052.	0.174054	0.0870269	−	0.996206i	$-0.472263\pi$
$433$	679052.	0.174054	0.0870269	+	0.996206i	$0.472263\pi$
$434$	−152795.	−0.0389391
$435$	213795.	0.0541720
$436$	1.49229e6	0.375956
$437$	6.03059e6	1.51062
$438$	−3.34706e6	−0.833639
$439$	−6.18297e6	−1.53121	−0.765606	−	0.643309i	$-0.777561\pi$
$439$	−6.18297e6	−1.53121	−0.765606	+	0.643309i	$0.777561\pi$
$440$	884254.	0.217743
$441$	−1.29391e6	−0.316817
$442$	−2.40246e6	−0.584925
$443$	226949.	0.0549437	0.0274719	−	0.999623i	$-0.491254\pi$
$443$	226949.	0.0549437	0.0274719	+	0.999623i	$0.491254\pi$
$444$	497051.	0.119658
$445$	−53466.6	−0.0127992
$446$	−1.60297e6	−0.381583
$447$	3.47458e6	0.822496
$448$	−1.03623e6	−0.243929
$449$	−418434.	−0.0979515	−0.0489758	−	0.998800i	$-0.515596\pi$
$449$	−418434.	−0.0979515	−0.0489758	+	0.998800i	$0.515596\pi$
$450$	−1.17826e6	−0.274291
$451$	−355619.	−0.0823273
$452$	425397.	0.0979374
$453$	3.25504e6	0.745265
$454$	−1.23516e6	−0.281244
$455$	−263012.	−0.0595590
$456$	2.39152e6	0.538595
$457$	6.90035e6	1.54554	0.772770	−	0.634686i	$-0.218871\pi$
$457$	6.90035e6	1.54554	0.772770	+	0.634686i	$0.218871\pi$
$458$	1.08091e6	0.240782
$459$	326196.	0.0722681
$460$	−338823.	−0.0746583
$461$	373717.	0.0819013	0.0409507	−	0.999161i	$-0.486961\pi$
$461$	373717.	0.0819013	0.0409507	+	0.999161i	$0.486961\pi$
$462$	−687432.	−0.149839
$463$	−5.19758e6	−1.12680	−0.563402	−	0.826183i	$-0.690508\pi$
$463$	−5.19758e6	−1.12680	−0.563402	+	0.826183i	$0.690508\pi$
$464$	1.86878e6	0.402962
$465$	−80888.6	−0.0173482
$466$	1.26083e6	0.268963
$467$	−6.54913e6	−1.38961	−0.694803	−	0.719200i	$-0.744508\pi$
$467$	−6.54913e6	−1.38961	−0.694803	+	0.719200i	$0.744508\pi$
$468$	859948.	0.181492
$469$	−1.06269e6	−0.223087
$470$	−962596.	−0.201001
$471$	−1.13139e6	−0.234997
$472$	−685107.	−0.141548
$473$	−5.52986e6	−1.13648
$474$	179928.	0.0367834
$475$	4.13125e6	0.840133
$476$	121382.	0.0245548
$477$	1.57115e6	0.316170
$478$	−1.16818e6	−0.233852
$479$	−2.70999e6	−0.539671	−0.269836	−	0.962906i	$-0.586969\pi$
$479$	−2.70999e6	−0.539671	−0.269836	+	0.962906i	$0.586969\pi$
$480$	−238222.	−0.0471932
$481$	6.63554e6	1.30772
$482$	5.88066e6	1.15294
$483$	1.16009e6	0.226269
$484$	−1.39995e6	−0.271644
$485$	−712666.	−0.137572
$486$	280715.	0.0539107
$487$	−3.13993e6	−0.599925	−0.299963	−	0.953951i	$-0.596974\pi$
$487$	−3.13993e6	−0.599925	−0.299963	+	0.953951i	$0.596974\pi$
$488$	−1.53804e6	−0.292360
$489$	2.80975e6	0.531369
$490$	612812.	0.115302
$491$	−51374.3	−0.00961705	−0.00480853	−	0.999988i	$-0.501531\pi$
$491$	−51374.3	−0.00961705	−0.00480853	+	0.999988i	$0.501531\pi$
$492$	54037.5	0.0100643
$493$	−1.31720e6	−0.244081
$494$	7.24908e6	1.33649
$495$	−363921.	−0.0667566
$496$	−707048.	−0.129046
$497$	−697643.	−0.126690
$498$	−1.57903e6	−0.285311
$499$	4.49962e6	0.808955	0.404477	−	0.914548i	$-0.367453\pi$
$499$	4.49962e6	0.808955	0.404477	+	0.914548i	$0.367453\pi$
$500$	−469160.	−0.0839260
$501$	−6.26653e6	−1.11541
$502$	−1.95942e6	−0.347031
$503$	1.70528e6	0.300521	0.150260	−	0.988646i	$-0.451989\pi$
$503$	1.70528e6	0.300521	0.150260	+	0.988646i	$0.451989\pi$
$504$	460053.	0.0806735
$505$	992979.	0.173265
$506$	−1.18223e7	−2.05270
$507$	8.13852e6	1.40613
$508$	565147.	0.0971634
$509$	616751.	0.105515	0.0527576	−	0.998607i	$-0.483199\pi$
$509$	616751.	0.105515	0.0527576	+	0.998607i	$0.483199\pi$
$510$	−154490.	−0.0263012
$511$	2.25754e6	0.382458
$512$	−6.08049e6	−1.02509
$513$	−984249.	−0.165125
$514$	−7.46580e6	−1.24643
$515$	−704216.	−0.117001
$516$	840282.	0.138931
$517$	1.39702e7	2.29867
$518$	806017.	0.131983
$519$	−4.20704e6	−0.685581
$520$	−1.79375e6	−0.290907
$521$	1.06106e7	1.71255	0.856277	−	0.516517i	$-0.172772\pi$
$521$	1.06106e7	1.71255	0.856277	+	0.516517i	$0.172772\pi$
$522$	−1.13354e6	−0.182080
$523$	−8.38687e6	−1.34074	−0.670371	−	0.742026i	$-0.733865\pi$
$523$	−8.38687e6	−1.34074	−0.670371	+	0.742026i	$0.733865\pi$
$524$	−3.19531e6	−0.508376
$525$	794721.	0.125839
$526$	6.65470e6	1.04873
$527$	498356.	0.0781652
$528$	−3.18103e6	−0.496574
$529$	1.35147e7	2.09974
$530$	−744114.	−0.115067
$531$	281961.	0.0433963
$532$	−366252.	−0.0561049
$533$	721391.	0.109990
$534$	283480.	0.0430199
$535$	20427.6	0.00308555
$536$	−7.24760e6	−1.08964
$537$	−1.84572e6	−0.276204
$538$	−7.89633e6	−1.17617
$539$	−8.89377e6	−1.31860
$540$	55299.0	0.00816081
$541$	−3.78138e6	−0.555465	−0.277733	−	0.960658i	$-0.589583\pi$
$541$	−3.78138e6	−0.555465	−0.277733	+	0.960658i	$0.589583\pi$
$542$	−9.64629e6	−1.41046
$543$	1.66376e6	0.242153
$544$	1.46769e6	0.212636
$545$	1.28107e6	0.184749
$546$	1.39449e6	0.200186
$547$	−3.06265e6	−0.437652	−0.218826	−	0.975764i	$-0.570223\pi$
$547$	−3.06265e6	−0.437652	−0.218826	+	0.975764i	$0.570223\pi$
$548$	−633149.	−0.0900647
$549$	632992.	0.0896328
$550$	−8.09886e6	−1.14161
$551$	3.97445e6	0.557697
$552$	7.91188e6	1.10518
$553$	−121359.	−0.0168755
$554$	−8.65941e6	−1.19871
$555$	426699.	0.0588016
$556$	−2.89921e6	−0.397734
$557$	2.10567e6	0.287576	0.143788	−	0.989608i	$-0.454072\pi$
$557$	2.10567e6	0.287576	0.143788	+	0.989608i	$0.454072\pi$
$558$	428872.	0.0583098
$559$	1.12176e7	1.51835
$560$	−147837.	−0.0199210
$561$	2.24212e6	0.300783
$562$	−9.43584e6	−1.26020
$563$	−3.85100e6	−0.512039	−0.256019	−	0.966672i	$-0.582411\pi$
$563$	−3.85100e6	−0.512039	−0.256019	+	0.966672i	$0.582411\pi$
$564$	−2.12282e6	−0.281006
$565$	365187.	0.0481276
$566$	1.03286e7	1.35518
$567$	−189338.	−0.0247332
$568$	−4.75795e6	−0.618799
$569$	7.28749e6	0.943621	0.471810	−	0.881700i	$-0.343601\pi$
$569$	7.28749e6	0.943621	0.471810	+	0.881700i	$0.343601\pi$
$570$	466153.	0.0600954
$571$	9.75125e6	1.25161	0.625807	−	0.779978i	$-0.284770\pi$
$571$	9.75125e6	1.25161	0.625807	+	0.779978i	$0.284770\pi$
$572$	5.91091e6	0.755377
$573$	−2.45236e6	−0.312031
$574$	87627.2	0.0111009
$575$	1.36674e7	1.72392
$576$	2.90854e6	0.365274
$577$	−3.33348e6	−0.416829	−0.208415	−	0.978041i	$-0.566830\pi$
$577$	−3.33348e6	−0.416829	−0.208415	+	0.978041i	$0.566830\pi$
$578$	−5.79808e6	−0.721880
$579$	−2.43394e6	−0.301727
$580$	−223301.	−0.0275626
$581$	1.06504e6	0.130895
$582$	3.77856e6	0.462401
$583$	1.07994e7	1.31591
$584$	1.53965e7	1.86806
$585$	738232.	0.0891874
$586$	−8.26464e6	−0.994214
$587$	1.65752e6	0.198548	0.0992738	−	0.995060i	$-0.468348\pi$
$587$	1.65752e6	0.198548	0.0992738	+	0.995060i	$0.468348\pi$
$588$	1.35144e6	0.161196
$589$	−1.50372e6	−0.178599
$590$	−133540.	−0.0157936
$591$	−6.36730e6	−0.749872
$592$	3.72977e6	0.437400
$593$	−1.21542e7	−1.41935	−0.709677	−	0.704527i	$-0.751159\pi$
$593$	−1.21542e7	−1.41935	−0.709677	+	0.704527i	$0.751159\pi$
$594$	1.92951e6	0.224378
$595$	104201.	0.0120665
$596$	−3.62906e6	−0.418484
$597$	−9.24409e6	−1.06152
$598$	2.39821e7	2.74243
$599$	6.59980e6	0.751560	0.375780	−	0.926709i	$-0.377375\pi$
$599$	6.59980e6	0.751560	0.375780	+	0.926709i	$0.377375\pi$
$600$	5.42003e6	0.614644
$601$	−2.88369e6	−0.325658	−0.162829	−	0.986654i	$-0.552062\pi$
$601$	−2.88369e6	−0.325658	−0.162829	+	0.986654i	$0.552062\pi$
$602$	1.36260e6	0.153242
$603$	2.98280e6	0.334065
$604$	−3.39976e6	−0.379189
$605$	−1.20181e6	−0.133489
$606$	−5.26478e6	−0.582369
$607$	−1.26616e7	−1.39482	−0.697410	−	0.716673i	$-0.745664\pi$
$607$	−1.26616e7	−1.39482	−0.697410	+	0.716673i	$0.745664\pi$
$608$	−4.42855e6	−0.485851
$609$	764557.	0.0835347
$610$	−299793.	−0.0326209
$611$	−2.83393e7	−3.07104
$612$	−340699.	−0.0367698
$613$	2.13203e6	0.229162	0.114581	−	0.993414i	$-0.463447\pi$
$613$	2.13203e6	0.229162	0.114581	+	0.993414i	$0.463447\pi$
$614$	5.70798e6	0.611028
$615$	46389.1	0.00494571
$616$	3.16220e6	0.335767
$617$	1.12243e7	1.18698	0.593492	−	0.804840i	$-0.297749\pi$
$617$	1.12243e7	1.18698	0.593492	+	0.804840i	$0.297749\pi$
$618$	3.73376e6	0.393255
$619$	−1.62425e7	−1.70383	−0.851916	−	0.523679i	$-0.824559\pi$
$619$	−1.62425e7	−1.70383	−0.851916	+	0.523679i	$0.824559\pi$
$620$	84485.0	0.00882674
$621$	−3.25619e6	−0.338829
$622$	5.71176e6	0.591962
$623$	−191203.	−0.0197367
$624$	6.45289e6	0.663426
$625$	9.15937e6	0.937920
$626$	−5.21893e6	−0.532287
$627$	−6.76530e6	−0.687255
$628$	1.18170e6	0.119566
$629$	−2.62890e6	−0.264940
$630$	89672.8	0.00900139
$631$	1.11288e7	1.11270	0.556348	−	0.830950i	$-0.312202\pi$
$631$	1.11288e7	1.11270	0.556348	+	0.830950i	$0.312202\pi$
$632$	−827670.	−0.0824261
$633$	−7.26092e6	−0.720248
$634$	174759.	0.0172670
$635$	485157.	0.0477472
$636$	−1.64100e6	−0.160867
$637$	1.80415e7	1.76167
$638$	−7.79147e6	−0.757823
$639$	1.95817e6	0.189714
$640$	−530509.	−0.0511968
$641$	2.41239e6	0.231901	0.115950	−	0.993255i	$-0.463009\pi$
$641$	2.41239e6	0.231901	0.115950	+	0.993255i	$0.463009\pi$
$642$	−108307.	−0.0103710
$643$	7.10405e6	0.677608	0.338804	−	0.940857i	$-0.389978\pi$
$643$	7.10405e6	0.677608	0.338804	+	0.940857i	$0.389978\pi$
$644$	−1.21167e6	−0.115125
$645$	721349.	0.0682726
$646$	−2.87198e6	−0.270769
$647$	−4.34524e6	−0.408088	−0.204044	−	0.978962i	$-0.565409\pi$
$647$	−4.34524e6	−0.408088	−0.204044	+	0.978962i	$0.565409\pi$
$648$	−1.29129e6	−0.120806
$649$	1.93808e6	0.180617
$650$	1.64290e7	1.52520
$651$	−289268.	−0.0267514
$652$	−2.93468e6	−0.270359
$653$	−1.74836e7	−1.60453	−0.802263	−	0.596971i	$-0.796371\pi$
$653$	−1.74836e7	−1.60453	−0.802263	+	0.596971i	$0.796371\pi$
$654$	−6.79225e6	−0.620968
$655$	−2.74305e6	−0.249822
$656$	405488.	0.0367890
$657$	−6.33655e6	−0.572716
$658$	−3.44236e6	−0.309950
$659$	−1.73557e7	−1.55678	−0.778392	−	0.627779i	$-0.783964\pi$
$659$	−1.73557e7	−1.55678	−0.778392	+	0.627779i	$0.783964\pi$
$660$	380101.	0.0339656
$661$	5.32811e6	0.474318	0.237159	−	0.971471i	$-0.423784\pi$
$661$	5.32811e6	0.474318	0.237159	+	0.971471i	$0.423784\pi$
$662$	1.16041e7	1.02912
$663$	−4.54826e6	−0.401848
$664$	7.26358e6	0.639338
$665$	−314413.	−0.0275706
$666$	−2.26236e6	−0.197640
$667$	1.31487e7	1.14437
$668$	6.54514e6	0.567516
$669$	−3.03470e6	−0.262150
$670$	−1.41269e6	−0.121580
$671$	4.35091e6	0.373055
$672$	−851912.	−0.0727732
$673$	9.87967e6	0.840823	0.420412	−	0.907333i	$-0.361886\pi$
$673$	9.87967e6	0.840823	0.420412	+	0.907333i	$0.361886\pi$
$674$	−2.53008e6	−0.214528
$675$	−2.23065e6	−0.188440
$676$	−8.50036e6	−0.715436
$677$	1.67635e7	1.40570	0.702849	−	0.711339i	$-0.251911\pi$
$677$	1.67635e7	1.40570	0.702849	+	0.711339i	$0.251911\pi$
$678$	−1.93622e6	−0.161764
$679$	−2.54858e6	−0.212141
$680$	710658.	0.0589370
$681$	−2.33837e6	−0.193217
$682$	2.94787e6	0.242688
$683$	4.71929e6	0.387102	0.193551	−	0.981090i	$-0.438000\pi$
$683$	4.71929e6	0.387102	0.193551	+	0.981090i	$0.438000\pi$
$684$	1.02801e6	0.0840150
$685$	−543534.	−0.0442589
$686$	4.49723e6	0.364868
$687$	2.04634e6	0.165419
$688$	6.30532e6	0.507850
$689$	−2.19071e7	−1.75807
$690$	1.54217e6	0.123313
$691$	−1.44431e7	−1.15071	−0.575353	−	0.817905i	$-0.695135\pi$
$691$	−1.44431e7	−1.15071	−0.575353	+	0.817905i	$0.695135\pi$
$692$	4.39409e6	0.348822
$693$	−1.30143e6	−0.102941
$694$	−1.59856e7	−1.25988
$695$	−2.48886e6	−0.195451
$696$	5.21431e6	0.408013
$697$	−285804.	−0.0222837
$698$	1.51872e7	1.17988
$699$	2.38697e6	0.184780
$700$	−830055.	−0.0640268
$701$	−40301.8	−0.00309763	−0.00154881	−	0.999999i	$-0.500493\pi$
$701$	−40301.8	−0.00309763	−0.00154881	+	0.999999i	$0.500493\pi$
$702$	−3.91411e6	−0.299771
$703$	7.93233e6	0.605358
$704$	1.99920e7	1.52029
$705$	−1.82236e6	−0.138090
$706$	1.83603e7	1.38633
$707$	3.55102e6	0.267180
$708$	−294497.	−0.0220800
$709$	2.32913e7	1.74011	0.870056	−	0.492953i	$-0.164082\pi$
$709$	2.32913e7	1.74011	0.870056	+	0.492953i	$0.164082\pi$
$710$	−927414.	−0.0690443
$711$	340634.	0.0252705
$712$	−1.30401e6	−0.0964011
$713$	−4.97476e6	−0.366478
$714$	−552476.	−0.0405572
$715$	5.07428e6	0.371201
$716$	1.92778e6	0.140532
$717$	−2.21157e6	−0.160658
$718$	1.52501e7	1.10398
$719$	2.22695e7	1.60653	0.803265	−	0.595622i	$-0.203094\pi$
$719$	2.22695e7	1.60653	0.803265	+	0.595622i	$0.203094\pi$
$720$	414954.	0.0298310
$721$	−2.51836e6	−0.180418
$722$	−3.10542e6	−0.221706
$723$	1.11331e7	0.792082
$724$	−1.73773e6	−0.123207
$725$	9.00750e6	0.636443
$726$	6.37198e6	0.448676
$727$	−2.97421e6	−0.208706	−0.104353	−	0.994540i	$-0.533277\pi$
$727$	−2.97421e6	−0.208706	−0.104353	+	0.994540i	$0.533277\pi$
$728$	−6.41468e6	−0.448587
$729$	531441.	0.0370370
$730$	3.00107e6	0.208434
$731$	−4.44425e6	−0.307613
$732$	−661135.	−0.0456050
$733$	6.38381e6	0.438854	0.219427	−	0.975629i	$-0.429581\pi$
$733$	6.38381e6	0.438854	0.219427	+	0.975629i	$0.429581\pi$
$734$	−1.76616e7	−1.21001
$735$	1.16016e6	0.0792135
$736$	−1.46510e7	−0.996948
$737$	2.05025e7	1.39039
$738$	−245955.	−0.0166232
$739$	−2.18800e7	−1.47379	−0.736897	−	0.676005i	$-0.763710\pi$
$739$	−2.18800e7	−1.47379	−0.736897	+	0.676005i	$0.763710\pi$
$740$	−445670.	−0.0299181
$741$	1.37237e7	0.918178
$742$	−2.66104e6	−0.177436
$743$	−1.15290e7	−0.766157	−0.383079	−	0.923716i	$-0.625136\pi$
$743$	−1.15290e7	−0.766157	−0.383079	+	0.923716i	$0.625136\pi$
$744$	−1.97282e6	−0.130664
$745$	−3.11541e6	−0.205648
$746$	−506722.	−0.0333367
$747$	−2.98938e6	−0.196011
$748$	−2.34181e6	−0.153038
$749$	73051.5	0.00475800
$750$	2.13541e6	0.138621
$751$	−1.87579e6	−0.121363	−0.0606813	−	0.998157i	$-0.519327\pi$
$751$	−1.87579e6	−0.121363	−0.0606813	+	0.998157i	$0.519327\pi$
$752$	−1.59292e7	−1.02719
$753$	−3.70951e6	−0.238413
$754$	1.58054e7	1.01246
$755$	−2.91856e6	−0.186338
$756$	197756.	0.0125842
$757$	−1.76953e7	−1.12232	−0.561161	−	0.827707i	$-0.689645\pi$
$757$	−1.76953e7	−1.12232	−0.561161	+	0.827707i	$0.689645\pi$
$758$	1.38233e7	0.873855
$759$	−2.23816e7	−1.41022
$760$	−2.14431e6	−0.134665
$761$	8.98396e6	0.562349	0.281175	−	0.959657i	$-0.409276\pi$
$761$	8.98396e6	0.562349	0.281175	+	0.959657i	$0.409276\pi$
$762$	−2.57230e6	−0.160485
$763$	4.58127e6	0.284888
$764$	2.56139e6	0.158760
$765$	−292476.	−0.0180691
$766$	2.10944e7	1.29896
$767$	−3.93149e6	−0.241306
$768$	−7.52872e6	−0.460594
$769$	−1.93851e7	−1.18210	−0.591049	−	0.806636i	$-0.701286\pi$
$769$	−1.93851e7	−1.18210	−0.591049	+	0.806636i	$0.701286\pi$
$770$	616372.	0.0374641
$771$	−1.41340e7	−0.856309
$772$	2.54216e6	0.153518
$773$	1.11176e7	0.669207	0.334604	−	0.942359i	$-0.391398\pi$
$773$	1.11176e7	0.669207	0.334604	+	0.942359i	$0.391398\pi$
$774$	−3.82460e6	−0.229474
$775$	−3.40796e6	−0.203817
$776$	−1.73814e7	−1.03617
$777$	1.52593e6	0.0906737
$778$	−1.15031e7	−0.681346
$779$	862374.	0.0509158
$780$	−771055.	−0.0453784
$781$	1.34596e7	0.789596
$782$	−9.50136e6	−0.555609
$783$	−2.14599e6	−0.125090
$784$	1.01409e7	0.589235
$785$	1.01444e6	0.0587560
$786$	1.45437e7	0.839686
$787$	3.09807e7	1.78302	0.891508	−	0.453006i	$-0.149648\pi$
$787$	3.09807e7	1.78302	0.891508	+	0.453006i	$0.149648\pi$
$788$	6.65040e6	0.381533
$789$	1.25985e7	0.720486
$790$	−161328.	−0.00919693
$791$	1.30595e6	0.0742141
$792$	−8.87578e6	−0.502798
$793$	−8.82603e6	−0.498405
$794$	−2.07110e6	−0.116587
$795$	−1.40873e6	−0.0790517
$796$	9.65509e6	0.540099
$797$	1.87042e6	0.104302	0.0521511	−	0.998639i	$-0.483392\pi$
$797$	1.87042e6	0.104302	0.0521511	+	0.998639i	$0.483392\pi$
$798$	1.66702e6	0.0926688
$799$	1.12276e7	0.622185
$800$	−1.00367e7	−0.554452
$801$	536676.	0.0295550
$802$	1.10253e7	0.605276
$803$	−4.35547e7	−2.38367
$804$	−3.11542e6	−0.169972
$805$	−1.04017e6	−0.0565739
$806$	−5.97991e6	−0.324233
$807$	−1.49491e7	−0.808037
$808$	2.42181e7	1.30500
$809$	2.51924e7	1.35331	0.676656	−	0.736299i	$-0.263428\pi$
$809$	2.51924e7	1.35331	0.676656	+	0.736299i	$0.263428\pi$
$810$	−251697.	−0.0134792
$811$	−4.70372e6	−0.251125	−0.125562	−	0.992086i	$-0.540073\pi$
$811$	−4.70372e6	−0.251125	−0.125562	+	0.992086i	$0.540073\pi$
$812$	−798550.	−0.0425023
$813$	−1.82621e7	−0.969000
$814$	−1.55504e7	−0.822587
$815$	−2.51931e6	−0.132858
$816$	−2.55654e6	−0.134409
$817$	1.34099e7	0.702862
$818$	−1.39375e6	−0.0728287
$819$	2.64001e6	0.137529
$820$	−48451.6	−0.00251637
$821$	−2.56227e6	−0.132668	−0.0663341	−	0.997797i	$-0.521130\pi$
$821$	−2.56227e6	−0.132668	−0.0663341	+	0.997797i	$0.521130\pi$
$822$	2.88182e6	0.148760
$823$	−1.26515e7	−0.651092	−0.325546	−	0.945526i	$-0.605548\pi$
$823$	−1.26515e7	−0.651092	−0.325546	+	0.945526i	$0.605548\pi$
$824$	−1.71753e7	−0.881226
$825$	−1.53325e7	−0.784294
$826$	−477556.	−0.0243542
$827$	2.53615e7	1.28947	0.644735	−	0.764406i	$-0.276968\pi$
$827$	2.53615e7	1.28947	0.644735	+	0.764406i	$0.276968\pi$
$828$	3.40097e6	0.172396
$829$	−3.29273e7	−1.66406	−0.832032	−	0.554728i	$-0.812822\pi$
$829$	−3.29273e7	−1.66406	−0.832032	+	0.554728i	$0.812822\pi$
$830$	1.41581e6	0.0713361
$831$	−1.63937e7	−0.823522
$832$	−4.05548e7	−2.03111
$833$	−7.14776e6	−0.356909
$834$	1.31959e7	0.656939
$835$	5.61875e6	0.278884
$836$	7.06609e6	0.349674
$837$	811927.	0.0400593
$838$	4.70428e6	0.231411
$839$	7.45341e6	0.365553	0.182776	−	0.983155i	$-0.441492\pi$
$839$	7.45341e6	0.365553	0.182776	+	0.983155i	$0.441492\pi$
$840$	−412497.	−0.0201708
$841$	−1.18455e7	−0.577516
$842$	−4.93451e6	−0.239863
$843$	−1.78637e7	−0.865768
$844$	7.58375e6	0.366461
$845$	−7.29723e6	−0.351574
$846$	9.66214e6	0.464139
$847$	−4.29780e6	−0.205844
$848$	−1.23138e7	−0.588032
$849$	1.95537e7	0.931022
$850$	−6.50890e6	−0.309001
$851$	2.62425e7	1.24217
$852$	−2.04523e6	−0.0965259
$853$	8.47401e6	0.398764	0.199382	−	0.979922i	$-0.436106\pi$
$853$	8.47401e6	0.398764	0.199382	+	0.979922i	$0.436106\pi$
$854$	−1.07210e6	−0.0503024
$855$	882506.	0.0412860
$856$	498214.	0.0232398
$857$	400864.	0.0186443	0.00932213	−	0.999957i	$-0.497033\pi$
$857$	400864.	0.0186443	0.00932213	+	0.999957i	$0.497033\pi$
$858$	−2.69039e7	−1.24766
$859$	−3.38025e7	−1.56302	−0.781512	−	0.623890i	$-0.785551\pi$
$859$	−3.38025e7	−1.56302	−0.781512	+	0.623890i	$0.785551\pi$
$860$	−753421.	−0.0347369
$861$	165893.	0.00762642
$862$	−2.89493e7	−1.32700
$863$	−1.70141e7	−0.777648	−0.388824	−	0.921312i	$-0.627119\pi$
$863$	−1.70141e7	−0.777648	−0.388824	+	0.921312i	$0.627119\pi$
$864$	2.39118e6	0.108975
$865$	3.77216e6	0.171415
$866$	3.22817e6	0.146272
$867$	−1.09768e7	−0.495937
$868$	302129.	0.0136111
$869$	2.34137e6	0.105177
$870$	1.01637e6	0.0455253
$871$	−4.15903e7	−1.85758
$872$	3.12444e7	1.39149
$873$	7.15345e6	0.317673
$874$	2.86690e7	1.26950
$875$	−1.44030e6	−0.0635967
$876$	6.61828e6	0.291397
$877$	2.44197e7	1.07212	0.536058	−	0.844181i	$-0.319913\pi$
$877$	2.44197e7	1.07212	0.536058	+	0.844181i	$0.319913\pi$
$878$	−2.93934e7	−1.28681
$879$	−1.56464e7	−0.683032
$880$	2.85221e6	0.124158
$881$	2.05768e7	0.893180	0.446590	−	0.894739i	$-0.352638\pi$
$881$	2.05768e7	0.893180	0.446590	+	0.894739i	$0.352638\pi$
$882$	−6.15116e6	−0.266248
$883$	−1.69532e7	−0.731727	−0.365864	−	0.930668i	$-0.619226\pi$
$883$	−1.69532e7	−0.731727	−0.365864	+	0.930668i	$0.619226\pi$
$884$	4.75048e6	0.204459
$885$	−252814.	−0.0108503
$886$	1.07890e6	0.0461738
$887$	−2.25912e7	−0.964118	−0.482059	−	0.876139i	$-0.660111\pi$
$887$	−2.25912e7	−0.964118	−0.482059	+	0.876139i	$0.660111\pi$
$888$	1.04069e7	0.442882
$889$	1.73498e6	0.0736276
$890$	−254177.	−0.0107562
$891$	3.65289e6	0.154150
$892$	3.16962e6	0.133381
$893$	−3.38776e7	−1.42162
$894$	1.65179e7	0.691212
$895$	1.65493e6	0.0690592
$896$	−1.89716e6	−0.0789469
$897$	4.54023e7	1.88407
$898$	−1.98921e6	−0.0823169
$899$	−3.27861e6	−0.135298
$900$	2.32983e6	0.0958778
$901$	8.67924e6	0.356180
$902$	−1.69059e6	−0.0691865
$903$	2.57963e6	0.105278
$904$	8.90665e6	0.362488
$905$	−1.49177e6	−0.0605454
$906$	1.54742e7	0.626309
$907$	−3.60866e6	−0.145656	−0.0728279	−	0.997345i	$-0.523202\pi$
$907$	−3.60866e6	−0.145656	−0.0728279	+	0.997345i	$0.523202\pi$
$908$	2.44233e6	0.0983082
$909$	−9.96712e6	−0.400092
$910$	−1.25034e6	−0.0500524
$911$	−3.83128e7	−1.52950	−0.764748	−	0.644329i	$-0.777137\pi$
$911$	−3.83128e7	−1.52950	−0.764748	+	0.644329i	$0.777137\pi$
$912$	7.71399e6	0.307109
$913$	−2.05477e7	−0.815804
$914$	3.28038e7	1.29885
$915$	−567559.	−0.0224108
$916$	−2.13732e6	−0.0841650
$917$	−9.80948e6	−0.385232
$918$	1.55071e6	0.0607329
$919$	−4.24918e7	−1.65965	−0.829824	−	0.558026i	$-0.811559\pi$
$919$	−4.24918e7	−1.65965	−0.829824	+	0.558026i	$0.811559\pi$
$920$	−7.09402e6	−0.276327
$921$	1.08062e7	0.419781
$922$	1.77663e6	0.0688286
$923$	−2.73035e7	−1.05491
$924$	1.35929e6	0.0523759
$925$	1.79774e7	0.690834
$926$	−2.47089e7	−0.946948
$927$	7.06864e6	0.270170
$928$	−9.65571e6	−0.368056
$929$	−2.93992e7	−1.11762	−0.558812	−	0.829294i	$-0.688743\pi$
$929$	−2.93992e7	−1.11762	−0.558812	+	0.829294i	$0.688743\pi$
$930$	−384539.	−0.0145792
$931$	2.15674e7	0.815498
$932$	−2.49310e6	−0.0940156
$933$	1.08133e7	0.406682
$934$	−3.11341e7	−1.16780
$935$	−2.01035e6	−0.0752045
$936$	1.80050e7	0.671742
$937$	−8.24040e6	−0.306619	−0.153310	−	0.988178i	$-0.548993\pi$
$937$	−8.24040e6	−0.306619	−0.153310	+	0.988178i	$0.548993\pi$
$938$	−5.05196e6	−0.187479
$939$	−9.88032e6	−0.365685
$940$	1.90338e6	0.0702597
$941$	1.23397e7	0.454286	0.227143	−	0.973861i	$-0.427062\pi$
$941$	1.23397e7	0.454286	0.227143	+	0.973861i	$0.427062\pi$
$942$	−5.37857e6	−0.197487
$943$	2.85299e6	0.104477
$944$	−2.20985e6	−0.0807111
$945$	169766.	0.00618402
$946$	−2.62886e7	−0.955079
$947$	2.68109e7	0.971485	0.485743	−	0.874102i	$-0.338549\pi$
$947$	2.68109e7	0.971485	0.485743	+	0.874102i	$0.338549\pi$
$948$	−355779.	−0.0128576
$949$	8.83529e7	3.18460
$950$	1.96397e7	0.706034
$951$	330849.	0.0118626
$952$	2.54140e6	0.0908826
$953$	2.06693e6	0.0737214	0.0368607	−	0.999320i	$-0.488264\pi$
$953$	2.06693e6	0.0737214	0.0368607	+	0.999320i	$0.488264\pi$
$954$	7.46911e6	0.265704
$955$	2.19885e6	0.0780168
$956$	2.30990e6	0.0817424
$957$	−1.47506e7	−0.520630
$958$	−1.28831e7	−0.453531
$959$	−1.94374e6	−0.0682484
$960$	−2.60788e6	−0.0913293
$961$	−2.73887e7	−0.956672
$962$	3.15449e7	1.09898
$963$	−205044.	−0.00712493
$964$	−1.16281e7	−0.403010
$965$	2.18234e6	0.0754406
$966$	5.51500e6	0.190153
$967$	1.24136e6	0.0426904	0.0213452	−	0.999772i	$-0.493205\pi$
$967$	1.24136e6	0.0426904	0.0213452	+	0.999772i	$0.493205\pi$
$968$	−2.93112e7	−1.00541
$969$	−5.43714e6	−0.186021
$970$	−3.38796e6	−0.115614
$971$	2.08971e7	0.711277	0.355639	−	0.934624i	$-0.384263\pi$
$971$	2.08971e7	0.711277	0.355639	+	0.934624i	$0.384263\pi$
$972$	−555069.	−0.0188444
$973$	−8.90046e6	−0.301391
$974$	−1.49270e7	−0.504167
$975$	3.11028e7	1.04782
$976$	−4.96103e6	−0.166705
$977$	4.79889e7	1.60844	0.804220	−	0.594332i	$-0.202584\pi$
$977$	4.79889e7	1.60844	0.804220	+	0.594332i	$0.202584\pi$
$978$	1.33574e7	0.446554
$979$	3.68888e6	0.123009
$980$	−1.21174e6	−0.0403036
$981$	−1.28589e7	−0.426610
$982$	−244230.	−0.00808202
$983$	−5.71930e7	−1.88781	−0.943907	−	0.330212i	$-0.892880\pi$
$983$	−5.71930e7	−1.88781	−0.943907	+	0.330212i	$0.892880\pi$
$984$	1.13140e6	0.0372501
$985$	5.70911e6	0.187490
$986$	−6.26186e6	−0.205121
$987$	−6.51697e6	−0.212938
$988$	−1.43339e7	−0.467167
$989$	4.43639e7	1.44225
$990$	−1.73006e6	−0.0561012
$991$	5.03427e7	1.62837	0.814184	−	0.580607i	$-0.197185\pi$
$991$	5.03427e7	1.62837	0.814184	+	0.580607i	$0.197185\pi$
$992$	3.65320e6	0.117868
$993$	2.19686e7	0.707015
$994$	−3.31655e6	−0.106468
$995$	8.28852e6	0.265411
$996$	3.12229e6	0.0997298
$997$	−2.10591e7	−0.670968	−0.335484	−	0.942046i	$-0.608900\pi$
$997$	−2.10591e7	−0.670968	−0.335484	+	0.942046i	$0.608900\pi$
$998$	2.13909e7	0.679833
$999$	−4.28303e6	−0.135780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.a.1.8	✓	11
3.2	odd	2		531.6.a.b.1.4		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.a.1.8	✓	11	1.1	even	1	trivial
531.6.a.b.1.4		11	3.2	odd	2

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+4.75393 q^{2} +9.00000 q^{3} -9.40015 q^{4} -8.06966 q^{5} +42.7854 q^{6} -28.8581 q^{7} -196.813 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.75393 q^{2} +9.00000 q^{3} -9.40015 q^{4} -8.06966 q^{5} +42.7854 q^{6} -28.8581 q^{7} -196.813 q^{8} +81.0000 q^{9} -38.3626 q^{10} +556.758 q^{11} -84.6013 q^{12} -1129.41 q^{13} -137.189 q^{14} -72.6270 q^{15} -634.832 q^{16} +447.456 q^{17} +385.068 q^{18} -1350.14 q^{19} +75.8560 q^{20} -259.723 q^{21} +2646.79 q^{22} -4466.66 q^{23} -1771.32 q^{24} -3059.88 q^{25} -5369.15 q^{26} +729.000 q^{27} +271.270 q^{28} -2943.74 q^{29} -345.264 q^{30} +1113.75 q^{31} +3280.08 q^{32} +5010.83 q^{33} +2127.18 q^{34} +232.875 q^{35} -761.412 q^{36} -5875.21 q^{37} -6418.45 q^{38} -10164.7 q^{39} +1588.22 q^{40} -638.732 q^{41} -1234.70 q^{42} -9932.25 q^{43} -5233.61 q^{44} -653.643 q^{45} -21234.2 q^{46} +25092.0 q^{47} -5713.49 q^{48} -15974.2 q^{49} -14546.5 q^{50} +4027.11 q^{51} +10616.6 q^{52} +19396.9 q^{53} +3465.62 q^{54} -4492.85 q^{55} +5679.66 q^{56} -12151.2 q^{57} -13994.3 q^{58} +3481.00 q^{59} +682.704 q^{60} +7814.71 q^{61} +5294.71 q^{62} -2337.51 q^{63} +35907.9 q^{64} +9113.98 q^{65} +23821.1 q^{66} +36824.7 q^{67} -4206.15 q^{68} -40199.9 q^{69} +1107.07 q^{70} +24174.9 q^{71} -15941.9 q^{72} -78229.0 q^{73} -27930.3 q^{74} -27538.9 q^{75} +12691.5 q^{76} -16067.0 q^{77} -48322.3 q^{78} +4205.35 q^{79} +5122.88 q^{80} +6561.00 q^{81} -3036.49 q^{82} -36905.9 q^{83} +2441.43 q^{84} -3610.82 q^{85} -47217.2 q^{86} -26493.7 q^{87} -109578. q^{88} +6625.63 q^{89} -3107.37 q^{90} +32592.7 q^{91} +41987.2 q^{92} +10023.8 q^{93} +119286. q^{94} +10895.1 q^{95} +29520.7 q^{96} +88314.2 q^{97} -75940.3 q^{98} +45097.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9} - 399 q^{10} - 698 q^{11} + 1350 q^{12} - 1556 q^{13} - 1679 q^{14} - 1728 q^{15} - 2662 q^{16} - 4793 q^{17} - 486 q^{18} - 3753 q^{19} - 11023 q^{20} - 3339 q^{21} - 9534 q^{22} - 7323 q^{23} - 5589 q^{24} + 7867 q^{25} - 4844 q^{26} + 8019 q^{27} + 3650 q^{28} - 15467 q^{29} - 3591 q^{30} - 5151 q^{31} - 15368 q^{32} - 6282 q^{33} + 8452 q^{34} - 23285 q^{35} + 12150 q^{36} + 8623 q^{37} + 15205 q^{38} - 14004 q^{39} + 41530 q^{40} - 6369 q^{41} - 15111 q^{42} - 20506 q^{43} - 55632 q^{44} - 15552 q^{45} - 45191 q^{46} - 47899 q^{47} - 23958 q^{48} - 10322 q^{49} - 102147 q^{50} - 43137 q^{51} - 292 q^{52} - 80048 q^{53} - 4374 q^{54} - 2114 q^{55} - 108126 q^{56} - 33777 q^{57} - 58294 q^{58} + 38291 q^{59} - 99207 q^{60} - 82527 q^{61} - 67438 q^{62} - 30051 q^{63} - 51411 q^{64} - 167646 q^{65} - 85806 q^{66} - 166976 q^{67} - 136533 q^{68} - 65907 q^{69} + 76140 q^{70} - 183560 q^{71} - 50301 q^{72} - 36809 q^{73} - 116686 q^{74} + 70803 q^{75} + 55580 q^{76} - 164885 q^{77} - 43596 q^{78} - 281518 q^{79} - 32683 q^{80} + 72171 q^{81} + 178815 q^{82} - 254691 q^{83} + 32850 q^{84} + 4763 q^{85} + 349324 q^{86} - 139203 q^{87} + 251285 q^{88} - 89687 q^{89} - 32319 q^{90} + 34897 q^{91} - 20240 q^{92} - 46359 q^{93} + 96548 q^{94} - 155113 q^{95} - 138312 q^{96} - 45828 q^{97} + 465864 q^{98} - 56538 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9 - 399 * q^10 - 698 * q^11 + 1350 * q^12 - 1556 * q^13 - 1679 * q^14 - 1728 * q^15 - 2662 * q^16 - 4793 * q^17 - 486 * q^18 - 3753 * q^19 - 11023 * q^20 - 3339 * q^21 - 9534 * q^22 - 7323 * q^23 - 5589 * q^24 + 7867 * q^25 - 4844 * q^26 + 8019 * q^27 + 3650 * q^28 - 15467 * q^29 - 3591 * q^30 - 5151 * q^31 - 15368 * q^32 - 6282 * q^33 + 8452 * q^34 - 23285 * q^35 + 12150 * q^36 + 8623 * q^37 + 15205 * q^38 - 14004 * q^39 + 41530 * q^40 - 6369 * q^41 - 15111 * q^42 - 20506 * q^43 - 55632 * q^44 - 15552 * q^45 - 45191 * q^46 - 47899 * q^47 - 23958 * q^48 - 10322 * q^49 - 102147 * q^50 - 43137 * q^51 - 292 * q^52 - 80048 * q^53 - 4374 * q^54 - 2114 * q^55 - 108126 * q^56 - 33777 * q^57 - 58294 * q^58 + 38291 * q^59 - 99207 * q^60 - 82527 * q^61 - 67438 * q^62 - 30051 * q^63 - 51411 * q^64 - 167646 * q^65 - 85806 * q^66 - 166976 * q^67 - 136533 * q^68 - 65907 * q^69 + 76140 * q^70 - 183560 * q^71 - 50301 * q^72 - 36809 * q^73 - 116686 * q^74 + 70803 * q^75 + 55580 * q^76 - 164885 * q^77 - 43596 * q^78 - 281518 * q^79 - 32683 * q^80 + 72171 * q^81 + 178815 * q^82 - 254691 * q^83 + 32850 * q^84 + 4763 * q^85 + 349324 * q^86 - 139203 * q^87 + 251285 * q^88 - 89687 * q^89 - 32319 * q^90 + 34897 * q^91 - 20240 * q^92 - 46359 * q^93 + 96548 * q^94 - 155113 * q^95 - 138312 * q^96 - 45828 * q^97 + 465864 * q^98 - 56538 * q^99

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