LMFDB - Embedded newform 177.6.a.a.1.5

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			1.5
Root			$-1.75662$ 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)

$f(q)$	$=$	$q-2.75662 q^{2} +9.00000 q^{3} -24.4011 q^{4} +5.39522 q^{5} -24.8096 q^{6} -153.490 q^{7} +155.476 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-2.75662 q^{2} +9.00000 q^{3} -24.4011 q^{4} +5.39522 q^{5} -24.8096 q^{6} -153.490 q^{7} +155.476 q^{8} +81.0000 q^{9} -14.8726 q^{10} +761.180 q^{11} -219.609 q^{12} +217.951 q^{13} +423.115 q^{14} +48.5570 q^{15} +352.245 q^{16} -1059.30 q^{17} -223.286 q^{18} -2368.63 q^{19} -131.649 q^{20} -1381.41 q^{21} -2098.28 q^{22} +3572.52 q^{23} +1399.29 q^{24} -3095.89 q^{25} -600.809 q^{26} +729.000 q^{27} +3745.33 q^{28} +538.264 q^{29} -133.853 q^{30} -6089.90 q^{31} -5946.24 q^{32} +6850.62 q^{33} +2920.08 q^{34} -828.115 q^{35} -1976.49 q^{36} -12608.0 q^{37} +6529.41 q^{38} +1961.56 q^{39} +838.829 q^{40} -3786.34 q^{41} +3808.03 q^{42} +20706.6 q^{43} -18573.6 q^{44} +437.013 q^{45} -9848.09 q^{46} -19719.4 q^{47} +3170.20 q^{48} +6752.30 q^{49} +8534.19 q^{50} -9533.67 q^{51} -5318.24 q^{52} -18054.4 q^{53} -2009.58 q^{54} +4106.74 q^{55} -23864.1 q^{56} -21317.7 q^{57} -1483.79 q^{58} +3481.00 q^{59} -1184.84 q^{60} -8691.16 q^{61} +16787.5 q^{62} -12432.7 q^{63} +5119.69 q^{64} +1175.90 q^{65} -18884.6 q^{66} -26644.1 q^{67} +25847.9 q^{68} +32152.7 q^{69} +2282.80 q^{70} -16613.0 q^{71} +12593.6 q^{72} -57940.7 q^{73} +34755.4 q^{74} -27863.0 q^{75} +57797.1 q^{76} -116834. q^{77} -5407.28 q^{78} -34743.3 q^{79} +1900.44 q^{80} +6561.00 q^{81} +10437.5 q^{82} -58060.2 q^{83} +33707.9 q^{84} -5715.14 q^{85} -57080.3 q^{86} +4844.38 q^{87} +118345. q^{88} -27715.2 q^{89} -1204.68 q^{90} -33453.4 q^{91} -87173.4 q^{92} -54809.1 q^{93} +54358.8 q^{94} -12779.3 q^{95} -53516.2 q^{96} +64764.4 q^{97} -18613.5 q^{98} +61655.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.75662	−0.487306	−0.243653	−	0.969862i	$-0.578346\pi$
$2$	−2.75662	−0.487306	−0.243653	+	0.969862i	$0.578346\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−24.4011	−0.762533
$5$	5.39522	0.0965127	0.0482563	−	0.998835i	$-0.484634\pi$
$5$	5.39522	0.0965127	0.0482563	+	0.998835i	$0.484634\pi$
$6$	−24.8096	−0.281346
$7$	−153.490	−1.18396	−0.591979	−	0.805954i	$-0.701653\pi$
$7$	−153.490	−1.18396	−0.591979	+	0.805954i	$0.701653\pi$
$8$	155.476	0.858893
$9$	81.0000	0.333333
$10$	−14.8726	−0.0470312
$11$	761.180	1.89673	0.948366	−	0.317180i	$-0.102736\pi$
$11$	761.180	1.89673	0.948366	+	0.317180i	$0.102736\pi$
$12$	−219.609	−0.440249
$13$	217.951	0.357685	0.178843	−	0.983878i	$-0.442765\pi$
$13$	217.951	0.357685	0.178843	+	0.983878i	$0.442765\pi$
$14$	423.115	0.576950
$15$	48.5570	0.0557216
$16$	352.245	0.343989
$17$	−1059.30	−0.888987	−0.444493	−	0.895782i	$-0.646616\pi$
$17$	−1059.30	−0.888987	−0.444493	+	0.895782i	$0.646616\pi$
$18$	−223.286	−0.162435
$19$	−2368.63	−1.50527	−0.752633	−	0.658440i	$-0.771217\pi$
$19$	−2368.63	−1.50527	−0.752633	+	0.658440i	$0.771217\pi$
$20$	−131.649	−0.0735941
$21$	−1381.41	−0.683558
$22$	−2098.28	−0.924288
$23$	3572.52	1.40817	0.704086	−	0.710115i	$-0.251357\pi$
$23$	3572.52	1.40817	0.704086	+	0.710115i	$0.251357\pi$
$24$	1399.29	0.495882
$25$	−3095.89	−0.990685
$26$	−600.809	−0.174302
$27$	729.000	0.192450
$28$	3745.33	0.902806
$29$	538.264	0.118850	0.0594251	−	0.998233i	$-0.481073\pi$
$29$	538.264	0.118850	0.0594251	+	0.998233i	$0.481073\pi$
$30$	−133.853	−0.0271535
$31$	−6089.90	−1.13817	−0.569084	−	0.822279i	$-0.692702\pi$
$31$	−6089.90	−1.13817	−0.569084	+	0.822279i	$0.692702\pi$
$32$	−5946.24	−1.02652
$33$	6850.62	1.09508
$34$	2920.08	0.433208
$35$	−828.115	−0.114267
$36$	−1976.49	−0.254178
$37$	−12608.0	−1.51406	−0.757028	−	0.653383i	$-0.773349\pi$
$37$	−12608.0	−1.51406	−0.757028	+	0.653383i	$0.773349\pi$
$38$	6529.41	0.733526
$39$	1961.56	0.206510
$40$	838.829	0.0828940
$41$	−3786.34	−0.351771	−0.175886	−	0.984411i	$-0.556279\pi$
$41$	−3786.34	−0.351771	−0.175886	+	0.984411i	$0.556279\pi$
$42$	3808.03	0.333102
$43$	20706.6	1.70780	0.853902	−	0.520434i	$-0.174230\pi$
$43$	20706.6	1.70780	0.853902	+	0.520434i	$0.174230\pi$
$44$	−18573.6	−1.44632
$45$	437.013	0.0321709
$46$	−9848.09	−0.686211
$47$	−19719.4	−1.30211	−0.651056	−	0.759029i	$-0.725674\pi$
$47$	−19719.4	−1.30211	−0.651056	+	0.759029i	$0.725674\pi$
$48$	3170.20	0.198602
$49$	6752.30	0.401755
$50$	8534.19	0.482767
$51$	−9533.67	−0.513257
$52$	−5318.24	−0.272747
$53$	−18054.4	−0.882865	−0.441433	−	0.897294i	$-0.645530\pi$
$53$	−18054.4	−0.882865	−0.441433	+	0.897294i	$0.645530\pi$
$54$	−2009.58	−0.0937821
$55$	4106.74	0.183059
$56$	−23864.1	−1.01689
$57$	−21317.7	−0.869066
$58$	−1483.79	−0.0579165
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−1184.84	−0.0424896
$61$	−8691.16	−0.299056	−0.149528	−	0.988757i	$-0.547775\pi$
$61$	−8691.16	−0.299056	−0.149528	+	0.988757i	$0.547775\pi$
$62$	16787.5	0.554636
$63$	−12432.7	−0.394652
$64$	5119.69	0.156241
$65$	1175.90	0.0345212
$66$	−18884.6	−0.533638
$67$	−26644.1	−0.725128	−0.362564	−	0.931959i	$-0.618099\pi$
$67$	−26644.1	−0.725128	−0.362564	+	0.931959i	$0.618099\pi$
$68$	25847.9	0.677881
$69$	32152.7	0.813008
$70$	2282.80	0.0556829
$71$	−16613.0	−0.391114	−0.195557	−	0.980692i	$-0.562651\pi$
$71$	−16613.0	−0.391114	−0.195557	+	0.980692i	$0.562651\pi$
$72$	12593.6	0.286298
$73$	−57940.7	−1.27255	−0.636277	−	0.771460i	$-0.719527\pi$
$73$	−57940.7	−1.27255	−0.636277	+	0.771460i	$0.719527\pi$
$74$	34755.4	0.737808
$75$	−27863.0	−0.571972
$76$	57797.1	1.14782
$77$	−116834.	−2.24565
$78$	−5407.28	−0.100633
$79$	−34743.3	−0.626331	−0.313165	−	0.949699i	$-0.601389\pi$
$79$	−34743.3	−0.626331	−0.313165	+	0.949699i	$0.601389\pi$
$80$	1900.44	0.0331993
$81$	6561.00	0.111111
$82$	10437.5	0.171420
$83$	−58060.2	−0.925088	−0.462544	−	0.886596i	$-0.653063\pi$
$83$	−58060.2	−0.925088	−0.462544	+	0.886596i	$0.653063\pi$
$84$	33707.9	0.521236
$85$	−5715.14	−0.0857985
$86$	−57080.3	−0.832223
$87$	4844.38	0.0686182
$88$	118345.	1.62909
$89$	−27715.2	−0.370888	−0.185444	−	0.982655i	$-0.559372\pi$
$89$	−27715.2	−0.370888	−0.185444	+	0.982655i	$0.559372\pi$
$90$	−1204.68	−0.0156771
$91$	−33453.4	−0.423484
$92$	−87173.4	−1.07378
$93$	−54809.1	−0.657121
$94$	54358.8	0.634527
$95$	−12779.3	−0.145277
$96$	−53516.2	−0.592662
$97$	64764.4	0.698887	0.349444	−	0.936957i	$-0.386371\pi$
$97$	64764.4	0.698887	0.349444	+	0.936957i	$0.386371\pi$
$98$	−18613.5	−0.195778
$99$	61655.6	0.632244
$100$	75543.0	0.755430
$101$	74064.2	0.722445	0.361222	−	0.932480i	$-0.382360\pi$
$101$	74064.2	0.722445	0.361222	+	0.932480i	$0.382360\pi$
$102$	26280.7	0.250113
$103$	−92839.9	−0.862266	−0.431133	−	0.902288i	$-0.641886\pi$
$103$	−92839.9	−0.862266	−0.431133	+	0.902288i	$0.641886\pi$
$104$	33886.2	0.307213
$105$	−7453.03	−0.0659720
$106$	49769.2	0.430225
$107$	140418.	1.18567	0.592834	−	0.805324i	$-0.298009\pi$
$107$	140418.	1.18567	0.592834	+	0.805324i	$0.298009\pi$
$108$	−17788.4	−0.146750
$109$	87790.6	0.707753	0.353876	−	0.935292i	$-0.384863\pi$
$109$	87790.6	0.707753	0.353876	+	0.935292i	$0.384863\pi$
$110$	−11320.7	−0.0892055
$111$	−113472.	−0.874140
$112$	−54066.2	−0.407269
$113$	−48010.0	−0.353700	−0.176850	−	0.984238i	$-0.556591\pi$
$113$	−48010.0	−0.353700	−0.176850	+	0.984238i	$0.556591\pi$
$114$	58764.7	0.423501
$115$	19274.6	0.135906
$116$	−13134.2	−0.0906273
$117$	17654.1	0.119228
$118$	−9595.79	−0.0634418
$119$	162592.	1.05252
$120$	7549.46	0.0478589
$121$	418344.	2.59759
$122$	23958.2	0.145732
$123$	−34077.1	−0.203095
$124$	148600.	0.867890
$125$	−33563.1	−0.192126
$126$	34272.3	0.192317
$127$	198782.	1.09362	0.546812	−	0.837255i	$-0.315841\pi$
$127$	198782.	1.09362	0.546812	+	0.837255i	$0.315841\pi$
$128$	176167.	0.950384
$129$	186360.	0.986001
$130$	−3241.50	−0.0168224
$131$	−28009.5	−0.142603	−0.0713013	−	0.997455i	$-0.522715\pi$
$131$	−28009.5	−0.142603	−0.0713013	+	0.997455i	$0.522715\pi$
$132$	−167162.	−0.835033
$133$	363562.	1.78217
$134$	73447.8	0.353359
$135$	3933.12	0.0185739
$136$	−164695.	−0.763544
$137$	−169288.	−0.770593	−0.385296	−	0.922793i	$-0.625901\pi$
$137$	−169288.	−0.770593	−0.385296	+	0.922793i	$0.625901\pi$
$138$	−88632.8	−0.396184
$139$	−20974.7	−0.0920786	−0.0460393	−	0.998940i	$-0.514660\pi$
$139$	−20974.7	−0.0920786	−0.0460393	+	0.998940i	$0.514660\pi$
$140$	20206.9	0.0871322
$141$	−177474.	−0.751775
$142$	45795.8	0.190592
$143$	165900.	0.678433
$144$	28531.8	0.114663
$145$	2904.05	0.0114706
$146$	159720.	0.620124
$147$	60770.7	0.231953
$148$	307648.	1.15452
$149$	1132.13	0.00417762	0.00208881	−	0.999998i	$-0.499335\pi$
$149$	1132.13	0.00417762	0.00208881	+	0.999998i	$0.499335\pi$
$150$	76807.7	0.278726
$151$	−338574.	−1.20840	−0.604200	−	0.796833i	$-0.706507\pi$
$151$	−338574.	−1.20840	−0.604200	+	0.796833i	$0.706507\pi$
$152$	−368266.	−1.29286
$153$	−85803.0	−0.296329
$154$	322066.	1.09432
$155$	−32856.4	−0.109848
$156$	−47864.2	−0.157470
$157$	124948.	0.404558	0.202279	−	0.979328i	$-0.435165\pi$
$157$	124948.	0.404558	0.202279	+	0.979328i	$0.435165\pi$
$158$	95774.1	0.305215
$159$	−162490.	−0.509722
$160$	−32081.3	−0.0990723
$161$	−548348.	−1.66722
$162$	−18086.2	−0.0541451
$163$	−280389.	−0.826595	−0.413297	−	0.910596i	$-0.635623\pi$
$163$	−280389.	−0.826595	−0.413297	+	0.910596i	$0.635623\pi$
$164$	92390.7	0.268237
$165$	36960.6	0.105689
$166$	160050.	0.450801
$167$	−613337.	−1.70180	−0.850900	−	0.525328i	$-0.823942\pi$
$167$	−613337.	−1.70180	−0.850900	+	0.525328i	$0.823942\pi$
$168$	−214777.	−0.587103
$169$	−323790.	−0.872061
$170$	15754.5	0.0418101
$171$	−191859.	−0.501756
$172$	−505263.	−1.30226
$173$	−490483.	−1.24597	−0.622986	−	0.782233i	$-0.714081\pi$
$173$	−490483.	−1.24597	−0.622986	+	0.782233i	$0.714081\pi$
$174$	−13354.1	−0.0334381
$175$	475190.	1.17293
$176$	268122.	0.652455
$177$	31329.0	0.0751646
$178$	76400.2	0.180736
$179$	480903.	1.12183	0.560913	−	0.827875i	$-0.310450\pi$
$179$	480903.	1.12183	0.560913	+	0.827875i	$0.310450\pi$
$180$	−10663.6	−0.0245314
$181$	230617.	0.523234	0.261617	−	0.965172i	$-0.415744\pi$
$181$	230617.	0.523234	0.261617	+	0.965172i	$0.415744\pi$
$182$	92218.4	0.206366
$183$	−78220.4	−0.172660
$184$	555443.	1.20947
$185$	−68022.9	−0.146125
$186$	151088.	0.320219
$187$	−806315.	−1.68617
$188$	481174.	0.992904
$189$	−111894.	−0.227853
$190$	35227.6	0.0707945
$191$	788835.	1.56460	0.782299	−	0.622903i	$-0.214047\pi$
$191$	788835.	1.56460	0.782299	+	0.622903i	$0.214047\pi$
$192$	46077.2	0.0902055
$193$	693991.	1.34110	0.670549	−	0.741865i	$-0.266059\pi$
$193$	693991.	1.34110	0.670549	+	0.741865i	$0.266059\pi$
$194$	−178531.	−0.340572
$195$	10583.1	0.0199308
$196$	−164763.	−0.306352
$197$	514963.	0.945388	0.472694	−	0.881227i	$-0.343282\pi$
$197$	514963.	0.945388	0.472694	+	0.881227i	$0.343282\pi$
$198$	−169961.	−0.308096
$199$	−402836.	−0.721100	−0.360550	−	0.932740i	$-0.617411\pi$
$199$	−402836.	−0.721100	−0.360550	+	0.932740i	$0.617411\pi$
$200$	−481337.	−0.850893
$201$	−239797.	−0.418653
$202$	−204167.	−0.352052
$203$	−82618.3	−0.140714
$204$	232632.	0.391375
$205$	−20428.2	−0.0339504
$206$	255924.	0.420188
$207$	289375.	0.469391
$208$	76772.2	0.123040
$209$	−1.80296e6	−2.85509
$210$	20545.2	0.0321486
$211$	−621140.	−0.960469	−0.480235	−	0.877140i	$-0.659449\pi$
$211$	−621140.	−0.960469	−0.480235	+	0.877140i	$0.659449\pi$
$212$	440547.	0.673214
$213$	−149517.	−0.225810
$214$	−387079.	−0.577783
$215$	111717.	0.164825
$216$	113342.	0.165294
$217$	934742.	1.34754
$218$	−242005.	−0.344892
$219$	−521466.	−0.734710
$220$	−100209.	−0.139588
$221$	−230875.	−0.317977
$222$	312799.	0.425974
$223$	507140.	0.682913	0.341457	−	0.939898i	$-0.389080\pi$
$223$	507140.	0.682913	0.341457	+	0.939898i	$0.389080\pi$
$224$	912691.	1.21536
$225$	−250767.	−0.330228
$226$	132345.	0.172360
$227$	−1.48547e6	−1.91337	−0.956686	−	0.291121i	$-0.905972\pi$
$227$	−1.48547e6	−1.91337	−0.956686	+	0.291121i	$0.905972\pi$
$228$	520174.	0.662692
$229$	−460323.	−0.580062	−0.290031	−	0.957017i	$-0.593666\pi$
$229$	−460323.	−0.580062	−0.290031	+	0.957017i	$0.593666\pi$
$230$	−53132.6	−0.0662280
$231$	−1.05150e6	−1.29653
$232$	83687.2	0.102080
$233$	1.45102e6	1.75099	0.875496	−	0.483225i	$-0.160535\pi$
$233$	1.45102e6	1.75099	0.875496	+	0.483225i	$0.160535\pi$
$234$	−48665.5	−0.0581007
$235$	−106390.	−0.125670
$236$	−84940.1	−0.0992733
$237$	−312690.	−0.361612
$238$	−448204.	−0.512900
$239$	536002.	0.606976	0.303488	−	0.952835i	$-0.401849\pi$
$239$	536002.	0.606976	0.303488	+	0.952835i	$0.401849\pi$
$240$	17104.0	0.0191676
$241$	−1.55236e6	−1.72166	−0.860832	−	0.508889i	$-0.830056\pi$
$241$	−1.55236e6	−1.72166	−0.860832	+	0.508889i	$0.830056\pi$
$242$	−1.15322e6	−1.26582
$243$	59049.0	0.0641500
$244$	212073.	0.228040
$245$	36430.2	0.0387745
$246$	93937.5	0.0989695
$247$	−516246.	−0.538412
$248$	−946835.	−0.977564
$249$	−522542.	−0.534100
$250$	92520.6	0.0936243
$251$	1.35415e6	1.35669	0.678347	−	0.734742i	$-0.262697\pi$
$251$	1.35415e6	1.35669	0.678347	+	0.734742i	$0.262697\pi$
$252$	303371.	0.300935
$253$	2.71934e6	2.67092
$254$	−547967.	−0.532930
$255$	−51436.2	−0.0495358
$256$	−649455.	−0.619368
$257$	1.62655e6	1.53615	0.768075	−	0.640360i	$-0.221215\pi$
$257$	1.62655e6	1.53615	0.768075	+	0.640360i	$0.221215\pi$
$258$	−513722.	−0.480484
$259$	1.93521e6	1.79258
$260$	−28693.1	−0.0263235
$261$	43599.4	0.0396168
$262$	77211.6	0.0694911
$263$	−210060.	−0.187264	−0.0936319	−	0.995607i	$-0.529848\pi$
$263$	−210060.	−0.187264	−0.0936319	+	0.995607i	$0.529848\pi$
$264$	1.06511e6	0.940555
$265$	−97407.7	−0.0852076
$266$	−1.00220e6	−0.868463
$267$	−249437.	−0.214132
$268$	650145.	0.552934
$269$	−1.70569e6	−1.43721	−0.718606	−	0.695418i	$-0.755219\pi$
$269$	−1.70569e6	−1.43721	−0.718606	+	0.695418i	$0.755219\pi$
$270$	−10842.1	−0.00905116
$271$	496417.	0.410604	0.205302	−	0.978699i	$-0.434182\pi$
$271$	496417.	0.410604	0.205302	+	0.978699i	$0.434182\pi$
$272$	−373132.	−0.305802
$273$	−301081.	−0.244499
$274$	466663.	0.375515
$275$	−2.35653e6	−1.87906
$276$	−784560.	−0.619946
$277$	−964655.	−0.755392	−0.377696	−	0.925930i	$-0.623284\pi$
$277$	−964655.	−0.755392	−0.377696	+	0.925930i	$0.623284\pi$
$278$	57819.2	0.0448704
$279$	−493282.	−0.379389
$280$	−128752.	−0.0981430
$281$	−304671.	−0.230179	−0.115089	−	0.993355i	$-0.536715\pi$
$281$	−304671.	−0.230179	−0.115089	+	0.993355i	$0.536715\pi$
$282$	489229.	0.366344
$283$	−1.20302e6	−0.892908	−0.446454	−	0.894807i	$-0.647313\pi$
$283$	−1.20302e6	−0.892908	−0.446454	+	0.894807i	$0.647313\pi$
$284$	405375.	0.298237
$285$	−115014.	−0.0838759
$286$	−457324.	−0.330604
$287$	581167.	0.416482
$288$	−481646.	−0.342174
$289$	−297748.	−0.209703
$290$	−8005.37	−0.00558967
$291$	582880.	0.403503
$292$	1.41381e6	0.970365
$293$	−1.44326e6	−0.982146	−0.491073	−	0.871118i	$-0.663395\pi$
$293$	−1.44326e6	−0.982146	−0.491073	+	0.871118i	$0.663395\pi$
$294$	−167522.	−0.113032
$295$	18780.8	0.0125649
$296$	−1.96024e6	−1.30041
$297$	554900.	0.365026
$298$	−3120.84	−0.00203578
$299$	778636.	0.503682
$300$	679887.	0.436148
$301$	−3.17827e6	−2.02197
$302$	933318.	0.588861
$303$	666577.	0.417104
$304$	−834339.	−0.517796
$305$	−46890.7	−0.0288627
$306$	236526.	0.144403
$307$	−591937.	−0.358451	−0.179226	−	0.983808i	$-0.557359\pi$
$307$	−591937.	−0.358451	−0.179226	+	0.983808i	$0.557359\pi$
$308$	2.85087e6	1.71238
$309$	−835559.	−0.497830
$310$	90572.5	0.0535294
$311$	1.22564e6	0.718560	0.359280	−	0.933230i	$-0.383022\pi$
$311$	1.22564e6	0.718560	0.359280	+	0.933230i	$0.383022\pi$
$312$	304976.	0.177370
$313$	2.29772e6	1.32567	0.662835	−	0.748766i	$-0.269353\pi$
$313$	2.29772e6	1.32567	0.662835	+	0.748766i	$0.269353\pi$
$314$	−344435.	−0.197144
$315$	−67077.3	−0.0380890
$316$	847774.	0.477598
$317$	−2.05515e6	−1.14867	−0.574335	−	0.818620i	$-0.694739\pi$
$317$	−2.05515e6	−1.14867	−0.574335	+	0.818620i	$0.694739\pi$
$318$	447923.	0.248391
$319$	409716.	0.225427
$320$	27621.9	0.0150792
$321$	1.26376e6	0.684546
$322$	1.51159e6	0.812444
$323$	2.50908e6	1.33816
$324$	−160095.	−0.0847259
$325$	−674754.	−0.354354
$326$	772927.	0.402805
$327$	790115.	0.408621
$328$	−588686.	−0.302134
$329$	3.02673e6	1.54165
$330$	−101886.	−0.0515028
$331$	1.63165e6	0.818570	0.409285	−	0.912407i	$-0.365778\pi$
$331$	1.63165e6	0.818570	0.409285	+	0.912407i	$0.365778\pi$
$332$	1.41673e6	0.705410
$333$	−1.02125e6	−0.504685
$334$	1.69074e6	0.829297
$335$	−143751.	−0.0699841
$336$	−486596.	−0.235137
$337$	−1.28987e6	−0.618689	−0.309344	−	0.950950i	$-0.600110\pi$
$337$	−1.28987e6	−0.618689	−0.309344	+	0.950950i	$0.600110\pi$
$338$	892566.	0.424961
$339$	−432090.	−0.204209
$340$	139455.	0.0654241
$341$	−4.63551e6	−2.15880
$342$	528883.	0.244509
$343$	1.54330e6	0.708296
$344$	3.21939e6	1.46682
$345$	173471.	0.0784656
$346$	1.35207e6	0.607170
$347$	3.13549e6	1.39792	0.698959	−	0.715161i	$-0.253647\pi$
$347$	3.13549e6	1.39792	0.698959	+	0.715161i	$0.253647\pi$
$348$	−118208.	−0.0523237
$349$	−4.47945e6	−1.96862	−0.984308	−	0.176458i	$-0.943536\pi$
$349$	−4.47945e6	−1.96862	−0.984308	+	0.176458i	$0.943536\pi$
$350$	−1.30992e6	−0.571575
$351$	158886.	0.0688366
$352$	−4.52616e6	−1.94703
$353$	−749388.	−0.320088	−0.160044	−	0.987110i	$-0.551164\pi$
$353$	−749388.	−0.320088	−0.160044	+	0.987110i	$0.551164\pi$
$354$	−86362.1	−0.0366282
$355$	−89631.0	−0.0377474
$356$	676279.	0.282814
$357$	1.46333e6	0.607674
$358$	−1.32567e6	−0.546672
$359$	−320342.	−0.131183	−0.0655916	−	0.997847i	$-0.520893\pi$
$359$	−320342.	−0.131183	−0.0655916	+	0.997847i	$0.520893\pi$
$360$	67945.1	0.0276313
$361$	3.13432e6	1.26583
$362$	−635724.	−0.254975
$363$	3.76510e6	1.49972
$364$	816299.	0.322921
$365$	−312603.	−0.122818
$366$	215624.	0.0841384
$367$	2.58137e6	1.00043	0.500214	−	0.865902i	$-0.333255\pi$
$367$	2.58137e6	1.00043	0.500214	+	0.865902i	$0.333255\pi$
$368$	1.25840e6	0.484396
$369$	−306694.	−0.117257
$370$	187513.	0.0712078
$371$	2.77118e6	1.04527
$372$	1.33740e6	0.501077
$373$	−5.10128e6	−1.89849	−0.949243	−	0.314543i	$-0.898149\pi$
$373$	−5.10128e6	−1.89849	−0.949243	+	0.314543i	$0.898149\pi$
$374$	2.22270e6	0.821680
$375$	−302068.	−0.110924
$376$	−3.06589e6	−1.11838
$377$	117315.	0.0425110
$378$	308450.	0.111034
$379$	−3.63450e6	−1.29971	−0.649855	−	0.760058i	$-0.725170\pi$
$379$	−3.63450e6	−1.29971	−0.649855	+	0.760058i	$0.725170\pi$
$380$	311828.	0.110779
$381$	1.78904e6	0.631404
$382$	−2.17452e6	−0.762438
$383$	−492940.	−0.171710	−0.0858552	−	0.996308i	$-0.527362\pi$
$383$	−492940.	−0.171710	−0.0858552	+	0.996308i	$0.527362\pi$
$384$	1.58550e6	0.548704
$385$	−630344.	−0.216734
$386$	−1.91307e6	−0.653525
$387$	1.67724e6	0.569268
$388$	−1.58032e6	−0.532924
$389$	2.72335e6	0.912494	0.456247	−	0.889853i	$-0.349193\pi$
$389$	2.72335e6	0.912494	0.456247	+	0.889853i	$0.349193\pi$
$390$	−29173.5	−0.00971240
$391$	−3.78436e6	−1.25185
$392$	1.04982e6	0.345065
$393$	−252086.	−0.0823317
$394$	−1.41956e6	−0.460693
$395$	−187448.	−0.0604489
$396$	−1.50446e6	−0.482107
$397$	4.08799e6	1.30177	0.650885	−	0.759177i	$-0.274398\pi$
$397$	4.08799e6	1.30177	0.650885	+	0.759177i	$0.274398\pi$
$398$	1.11047e6	0.351397
$399$	3.27206e6	1.02894
$400$	−1.09051e6	−0.340785
$401$	4.53424e6	1.40813	0.704067	−	0.710134i	$-0.251366\pi$
$401$	4.53424e6	1.40813	0.704067	+	0.710134i	$0.251366\pi$
$402$	661030.	0.204012
$403$	−1.32730e6	−0.407106
$404$	−1.80724e6	−0.550888
$405$	35398.0	0.0107236
$406$	227747.	0.0685706
$407$	−9.59696e6	−2.87176
$408$	−1.48226e6	−0.440832
$409$	4.51979e6	1.33601	0.668005	−	0.744156i	$-0.267148\pi$
$409$	4.51979e6	1.33601	0.668005	+	0.744156i	$0.267148\pi$
$410$	56312.6	0.0165442
$411$	−1.52359e6	−0.444902
$412$	2.26539e6	0.657506
$413$	−534300.	−0.154138
$414$	−797695.	−0.228737
$415$	−313248.	−0.0892827
$416$	−1.29599e6	−0.367171
$417$	−188772.	−0.0531616
$418$	4.97006e6	1.39130
$419$	1.11078e6	0.309095	0.154548	−	0.987985i	$-0.450608\pi$
$419$	1.11078e6	0.309095	0.154548	+	0.987985i	$0.450608\pi$
$420$	181862.	0.0503058
$421$	6.16251e6	1.69454	0.847270	−	0.531162i	$-0.178244\pi$
$421$	6.16251e6	1.69454	0.847270	+	0.531162i	$0.178244\pi$
$422$	1.71225e6	0.468042
$423$	−1.59727e6	−0.434038
$424$	−2.80704e6	−0.758286
$425$	3.27947e6	0.880706
$426$	412162.	0.110038
$427$	1.33401e6	0.354070
$428$	−3.42635e6	−0.904111
$429$	1.49310e6	0.391693
$430$	−307961.	−0.0803201
$431$	3.15040e6	0.816907	0.408453	−	0.912779i	$-0.366068\pi$
$431$	3.15040e6	0.816907	0.408453	+	0.912779i	$0.366068\pi$
$432$	256787.	0.0662008
$433$	1.13247e6	0.290273	0.145136	−	0.989412i	$-0.453638\pi$
$433$	1.13247e6	0.290273	0.145136	+	0.989412i	$0.453638\pi$
$434$	−2.57673e6	−0.656665
$435$	26136.5	0.00662253
$436$	−2.14218e6	−0.539685
$437$	−8.46199e6	−2.11967
$438$	1.43748e6	0.358028
$439$	−5.79846e6	−1.43599	−0.717995	−	0.696048i	$-0.754940\pi$
$439$	−5.79846e6	−1.43599	−0.717995	+	0.696048i	$0.754940\pi$
$440$	638500.	0.157228
$441$	546936.	0.133918
$442$	636434.	0.154952
$443$	−6.79918e6	−1.64607	−0.823033	−	0.567994i	$-0.807720\pi$
$443$	−6.79918e6	−1.64607	−0.823033	+	0.567994i	$0.807720\pi$
$444$	2.76883e6	0.666561
$445$	−149530.	−0.0357954
$446$	−1.39799e6	−0.332788
$447$	10189.1	0.00241195
$448$	−785823.	−0.184982
$449$	3.96539e6	0.928261	0.464131	−	0.885767i	$-0.346367\pi$
$449$	3.96539e6	0.928261	0.464131	+	0.885767i	$0.346367\pi$
$450$	691270.	0.160922
$451$	−2.88209e6	−0.667215
$452$	1.17149e6	0.269708
$453$	−3.04716e6	−0.697670
$454$	4.09488e6	0.932398
$455$	−180489.	−0.0408716
$456$	−3.31439e6	−0.746435
$457$	4.45488e6	0.997804	0.498902	−	0.866659i	$-0.333737\pi$
$457$	4.45488e6	0.997804	0.498902	+	0.866659i	$0.333737\pi$
$458$	1.26894e6	0.282667
$459$	−772227.	−0.171086
$460$	−470320.	−0.103633
$461$	302131.	0.0662129	0.0331065	−	0.999452i	$-0.489460\pi$
$461$	302131.	0.0662129	0.0331065	+	0.999452i	$0.489460\pi$
$462$	2.89860e6	0.631805
$463$	−6.99444e6	−1.51635	−0.758177	−	0.652049i	$-0.773910\pi$
$463$	−6.99444e6	−1.51635	−0.758177	+	0.652049i	$0.773910\pi$
$464$	189601.	0.0408832
$465$	−295707.	−0.0634205
$466$	−3.99992e6	−0.853269
$467$	737365.	0.156455	0.0782276	−	0.996936i	$-0.475074\pi$
$467$	737365.	0.156455	0.0782276	+	0.996936i	$0.475074\pi$
$468$	−430778.	−0.0909156
$469$	4.08962e6	0.858521
$470$	293278.	0.0612399
$471$	1.12453e6	0.233572
$472$	541213.	0.111818
$473$	1.57615e7	3.23925
$474$	861967.	0.176216
$475$	7.33303e6	1.49125
$476$	−3.96741e6	−0.802583
$477$	−1.46241e6	−0.294288
$478$	−1.47755e6	−0.295783
$479$	−1.30251e6	−0.259383	−0.129692	−	0.991554i	$-0.541399\pi$
$479$	−1.30251e6	−0.259383	−0.129692	+	0.991554i	$0.541399\pi$
$480$	−288732.	−0.0571994
$481$	−2.74793e6	−0.541555
$482$	4.27925e6	0.838977
$483$	−4.93513e6	−0.962567
$484$	−1.02080e7	−1.98075
$485$	349418.	0.0674515
$486$	−162776.	−0.0312607
$487$	−3.74819e6	−0.716142	−0.358071	−	0.933694i	$-0.616565\pi$
$487$	−3.74819e6	−0.716142	−0.358071	+	0.933694i	$0.616565\pi$
$488$	−1.35127e6	−0.256857
$489$	−2.52351e6	−0.477235
$490$	−100424.	−0.0188950
$491$	1.58539e6	0.296779	0.148389	−	0.988929i	$-0.452591\pi$
$491$	1.58539e6	0.296779	0.148389	+	0.988929i	$0.452591\pi$
$492$	831517.	0.154867
$493$	−570181.	−0.105656
$494$	1.42309e6	0.262371
$495$	332646.	0.0610195
$496$	−2.14514e6	−0.391517
$497$	2.54994e6	0.463062
$498$	1.44045e6	0.260270
$499$	−600537.	−0.107966	−0.0539831	−	0.998542i	$-0.517192\pi$
$499$	−600537.	−0.107966	−0.0539831	+	0.998542i	$0.517192\pi$
$500$	818975.	0.146503
$501$	−5.52004e6	−0.982534
$502$	−3.73287e6	−0.661125
$503$	2.49025e6	0.438858	0.219429	−	0.975628i	$-0.429581\pi$
$503$	2.49025e6	0.438858	0.219429	+	0.975628i	$0.429581\pi$
$504$	−1.93299e6	−0.338964
$505$	399593.	0.0697251
$506$	−7.49617e6	−1.30156
$507$	−2.91411e6	−0.503485
$508$	−4.85049e6	−0.833925
$509$	945025.	0.161677	0.0808386	−	0.996727i	$-0.474240\pi$
$509$	945025.	0.161677	0.0808386	+	0.996727i	$0.474240\pi$
$510$	141790.	0.0241391
$511$	8.89334e6	1.50665
$512$	−3.84704e6	−0.648562
$513$	−1.72673e6	−0.289689
$514$	−4.48377e6	−0.748575
$515$	−500892.	−0.0832196
$516$	−4.54737e6	−0.751858
$517$	−1.50100e7	−2.46976
$518$	−5.33463e6	−0.873533
$519$	−4.41434e6	−0.719363
$520$	182824.	0.0296500
$521$	−7.80138e6	−1.25915	−0.629575	−	0.776940i	$-0.716771\pi$
$521$	−7.80138e6	−1.25915	−0.629575	+	0.776940i	$0.716771\pi$
$522$	−120187.	−0.0193055
$523$	−5.57082e6	−0.890564	−0.445282	−	0.895390i	$-0.646897\pi$
$523$	−5.57082e6	−0.890564	−0.445282	+	0.895390i	$0.646897\pi$
$524$	683462.	0.108739
$525$	4.27671e6	0.677191
$526$	579055.	0.0912547
$527$	6.45101e6	1.01182
$528$	2.41310e6	0.376695
$529$	6.32659e6	0.982948
$530$	268516.	0.0415222
$531$	281961.	0.0433963
$532$	−8.87130e6	−1.35896
$533$	−825238.	−0.125823
$534$	687602.	0.104348
$535$	757586.	0.114432
$536$	−4.14253e6	−0.622807
$537$	4.32813e6	0.647686
$538$	4.70195e6	0.700362
$539$	5.13972e6	0.762022
$540$	−95972.2	−0.0141632
$541$	−4.82906e6	−0.709365	−0.354683	−	0.934987i	$-0.615411\pi$
$541$	−4.82906e6	−0.709365	−0.354683	+	0.934987i	$0.615411\pi$
$542$	−1.36843e6	−0.200090
$543$	2.07556e6	0.302089
$544$	6.29883e6	0.912563
$545$	473650.	0.0683071
$546$	829965.	0.119146
$547$	1.44580e6	0.206605	0.103302	−	0.994650i	$-0.467059\pi$
$547$	1.44580e6	0.206605	0.103302	+	0.994650i	$0.467059\pi$
$548$	4.13081e6	0.587602
$549$	−703984.	−0.0996855
$550$	6.49606e6	0.915679
$551$	−1.27495e6	−0.178901
$552$	4.99898e6	0.698287
$553$	5.33277e6	0.741549
$554$	2.65919e6	0.368107
$555$	−612206.	−0.0843656
$556$	511805.	0.0702129
$557$	5.82905e6	0.796085	0.398043	−	0.917367i	$-0.369690\pi$
$557$	5.82905e6	0.796085	0.398043	+	0.917367i	$0.369690\pi$
$558$	1.35979e6	0.184879
$559$	4.51304e6	0.610856
$560$	−291699.	−0.0393066
$561$	−7.25684e6	−0.973510
$562$	839862.	0.112168
$563$	−1.31388e7	−1.74696	−0.873482	−	0.486856i	$-0.838144\pi$
$563$	−1.31388e7	−1.74696	−0.873482	+	0.486856i	$0.838144\pi$
$564$	4.33056e6	0.573253
$565$	−259025.	−0.0341366
$566$	3.31627e6	0.435119
$567$	−1.00705e6	−0.131551
$568$	−2.58293e6	−0.335925
$569$	−1.52848e6	−0.197915	−0.0989576	−	0.995092i	$-0.531551\pi$
$569$	−1.52848e6	−0.197915	−0.0989576	+	0.995092i	$0.531551\pi$
$570$	317049.	0.0408732
$571$	1.28959e6	0.165524	0.0827621	−	0.996569i	$-0.473626\pi$
$571$	1.28959e6	0.165524	0.0827621	+	0.996569i	$0.473626\pi$
$572$	−4.04814e6	−0.517327
$573$	7.09952e6	0.903321
$574$	−1.60206e6	−0.202954
$575$	−1.10601e7	−1.39506
$576$	414695.	0.0520802
$577$	1.20588e7	1.50787	0.753937	−	0.656947i	$-0.228152\pi$
$577$	1.20588e7	1.50787	0.753937	+	0.656947i	$0.228152\pi$
$578$	820778.	0.102190
$579$	6.24592e6	0.774283
$580$	−70861.9	−0.00874668
$581$	8.91168e6	1.09527
$582$	−1.60678e6	−0.196629
$583$	−1.37427e7	−1.67456
$584$	−9.00840e6	−1.09299
$585$	95247.5	0.0115071
$586$	3.97852e6	0.478606
$587$	−8.94749e6	−1.07178	−0.535890	−	0.844288i	$-0.680024\pi$
$587$	−8.94749e6	−1.07178	−0.535890	+	0.844288i	$0.680024\pi$
$588$	−1.48287e6	−0.176872
$589$	1.44247e7	1.71325
$590$	−51771.4	−0.00612294
$591$	4.63466e6	0.545820
$592$	−4.44110e6	−0.520819
$593$	−5.05616e6	−0.590451	−0.295225	−	0.955428i	$-0.595395\pi$
$593$	−5.05616e6	−0.590451	−0.295225	+	0.955428i	$0.595395\pi$
$594$	−1.52965e6	−0.177879
$595$	877219.	0.101582
$596$	−27625.1	−0.00318557
$597$	−3.62552e6	−0.416327
$598$	−2.14640e6	−0.245447
$599$	−873873.	−0.0995133	−0.0497567	−	0.998761i	$-0.515845\pi$
$599$	−873873.	−0.0995133	−0.0497567	+	0.998761i	$0.515845\pi$
$600$	−4.33204e6	−0.491263
$601$	1.08755e7	1.22818	0.614091	−	0.789235i	$-0.289523\pi$
$601$	1.08755e7	1.22818	0.614091	+	0.789235i	$0.289523\pi$
$602$	8.76127e6	0.985317
$603$	−2.15818e6	−0.241709
$604$	8.26155e6	0.921445
$605$	2.25706e6	0.250700
$606$	−1.83750e6	−0.203257
$607$	−5.06183e6	−0.557617	−0.278809	−	0.960347i	$-0.589940\pi$
$607$	−5.06183e6	−0.557617	−0.278809	+	0.960347i	$0.589940\pi$
$608$	1.40845e7	1.54519
$609$	−743565.	−0.0812411
$610$	129260.	0.0140650
$611$	−4.29786e6	−0.465747
$612$	2.09368e6	0.225960
$613$	−5.66357e6	−0.608750	−0.304375	−	0.952552i	$-0.598448\pi$
$613$	−5.66357e6	−0.608750	−0.304375	+	0.952552i	$0.598448\pi$
$614$	1.63175e6	0.174675
$615$	−183853.	−0.0196013
$616$	−1.81649e7	−1.92877
$617$	−3.87368e6	−0.409648	−0.204824	−	0.978799i	$-0.565662\pi$
$617$	−3.87368e6	−0.409648	−0.204824	+	0.978799i	$0.565662\pi$
$618$	2.30332e6	0.242595
$619$	3.10004e6	0.325193	0.162596	−	0.986693i	$-0.448013\pi$
$619$	3.10004e6	0.325193	0.162596	+	0.986693i	$0.448013\pi$
$620$	801730.	0.0837624
$621$	2.60437e6	0.271003
$622$	−3.37863e6	−0.350158
$623$	4.25401e6	0.439115
$624$	690950.	0.0710371
$625$	9.49358e6	0.972143
$626$	−6.33393e6	−0.646007
$627$	−1.62266e7	−1.64838
$628$	−3.04887e6	−0.308489
$629$	1.33556e7	1.34597
$630$	184907.	0.0185610
$631$	6.13084e6	0.612981	0.306490	−	0.951874i	$-0.400845\pi$
$631$	6.13084e6	0.612981	0.306490	+	0.951874i	$0.400845\pi$
$632$	−5.40176e6	−0.537951
$633$	−5.59026e6	−0.554527
$634$	5.66527e6	0.559754
$635$	1.07247e6	0.105549
$636$	3.96493e6	0.388680
$637$	1.47167e6	0.143702
$638$	−1.12943e6	−0.109852
$639$	−1.34566e6	−0.130371
$640$	950459.	0.0917241
$641$	7.71788e6	0.741913	0.370956	−	0.928650i	$-0.379030\pi$
$641$	7.71788e6	0.741913	0.370956	+	0.928650i	$0.379030\pi$
$642$	−3.48371e6	−0.333583
$643$	1.95943e7	1.86897	0.934483	−	0.356007i	$-0.115862\pi$
$643$	1.95943e7	1.86897	0.934483	+	0.356007i	$0.115862\pi$
$644$	1.33803e7	1.27131
$645$	1.00545e6	0.0951616
$646$	−6.91659e6	−0.652094
$647$	−3.83076e6	−0.359769	−0.179885	−	0.983688i	$-0.557572\pi$
$647$	−3.83076e6	−0.359769	−0.179885	+	0.983688i	$0.557572\pi$
$648$	1.02008e6	0.0954325
$649$	2.64967e6	0.246933
$650$	1.86004e6	0.172679
$651$	8.41268e6	0.778004
$652$	6.84180e6	0.630306
$653$	5.17420e6	0.474854	0.237427	−	0.971405i	$-0.423696\pi$
$653$	5.17420e6	0.474854	0.237427	+	0.971405i	$0.423696\pi$
$654$	−2.17805e6	−0.199124
$655$	−151118.	−0.0137630
$656$	−1.33372e6	−0.121005
$657$	−4.69320e6	−0.424185
$658$	−8.34355e6	−0.751253
$659$	−237453.	−0.0212992	−0.0106496	−	0.999943i	$-0.503390\pi$
$659$	−237453.	−0.0212992	−0.0106496	+	0.999943i	$0.503390\pi$
$660$	−901878.	−0.0805913
$661$	1.38935e7	1.23683	0.618414	−	0.785852i	$-0.287775\pi$
$661$	1.38935e7	1.23683	0.618414	+	0.785852i	$0.287775\pi$
$662$	−4.49782e6	−0.398894
$663$	−2.07788e6	−0.183584
$664$	−9.02698e6	−0.794552
$665$	1.96150e6	0.172002
$666$	2.81519e6	0.245936
$667$	1.92296e6	0.167362
$668$	1.49661e7	1.29768
$669$	4.56426e6	0.394280
$670$	396267.	0.0341036
$671$	−6.61554e6	−0.567230
$672$	8.21422e6	0.701687
$673$	6.38741e6	0.543609	0.271805	−	0.962352i	$-0.412380\pi$
$673$	6.38741e6	0.543609	0.271805	+	0.962352i	$0.412380\pi$
$674$	3.55569e6	0.301491
$675$	−2.25690e6	−0.190657
$676$	7.90082e6	0.664975
$677$	2.23699e7	1.87583	0.937914	−	0.346867i	$-0.112754\pi$
$677$	2.23699e7	1.87583	0.937914	+	0.346867i	$0.112754\pi$
$678$	1.19111e6	0.0995123
$679$	−9.94071e6	−0.827453
$680$	−888568.	−0.0736917
$681$	−1.33692e7	−1.10469
$682$	1.27783e7	1.05200
$683$	−1.38765e6	−0.113823	−0.0569114	−	0.998379i	$-0.518125\pi$
$683$	−1.38765e6	−0.113823	−0.0569114	+	0.998379i	$0.518125\pi$
$684$	4.68157e6	0.382605
$685$	−913347.	−0.0743720
$686$	−4.25429e6	−0.345157
$687$	−4.14291e6	−0.334899
$688$	7.29380e6	0.587466
$689$	−3.93499e6	−0.315788
$690$	−478194.	−0.0382368
$691$	2.42471e7	1.93181	0.965905	−	0.258898i	$-0.0833594\pi$
$691$	2.42471e7	1.93181	0.965905	+	0.258898i	$0.0833594\pi$
$692$	1.19683e7	0.950095
$693$	−9.46354e6	−0.748550
$694$	−8.64336e6	−0.681214
$695$	−113163.	−0.00888675
$696$	753185.	0.0589357
$697$	4.01086e6	0.312720
$698$	1.23481e7	0.959318
$699$	1.30592e7	1.01094
$700$	−1.15951e7	−0.894397
$701$	−1.41759e7	−1.08957	−0.544784	−	0.838577i	$-0.683388\pi$
$701$	−1.41759e7	−1.08957	−0.544784	+	0.838577i	$0.683388\pi$
$702$	−437990.	−0.0335445
$703$	2.98637e7	2.27906
$704$	3.89701e6	0.296346
$705$	−957514.	−0.0725558
$706$	2.06578e6	0.155981
$707$	−1.13681e7	−0.855344
$708$	−764461.	−0.0573155
$709$	2.10353e7	1.57157	0.785783	−	0.618502i	$-0.212260\pi$
$709$	2.10353e7	1.57157	0.785783	+	0.618502i	$0.212260\pi$
$710$	247078.	0.0183945
$711$	−2.81421e6	−0.208777
$712$	−4.30905e6	−0.318553
$713$	−2.17563e7	−1.60274
$714$	−4.03383e6	−0.296123
$715$	895068.	0.0654774
$716$	−1.17346e7	−0.855429
$717$	4.82401e6	0.350438
$718$	883062.	0.0639263
$719$	549187.	0.0396185	0.0198092	−	0.999804i	$-0.493694\pi$
$719$	549187.	0.0396185	0.0198092	+	0.999804i	$0.493694\pi$
$720$	153936.	0.0110664
$721$	1.42500e7	1.02089
$722$	−8.64012e6	−0.616846
$723$	−1.39712e7	−0.994003
$724$	−5.62731e6	−0.398983
$725$	−1.66641e6	−0.117743
$726$	−1.03789e7	−0.730822
$727$	−7.73782e6	−0.542979	−0.271489	−	0.962441i	$-0.587516\pi$
$727$	−7.73782e6	−0.542979	−0.271489	+	0.962441i	$0.587516\pi$
$728$	−5.20121e6	−0.363728
$729$	531441.	0.0370370
$730$	861727.	0.0598498
$731$	−2.19344e7	−1.51822
$732$	1.90866e6	0.131659
$733$	6.46053e6	0.444128	0.222064	−	0.975032i	$-0.428721\pi$
$733$	6.46053e6	0.444128	0.222064	+	0.975032i	$0.428721\pi$
$734$	−7.11586e6	−0.487514
$735$	327871.	0.0223864
$736$	−2.12431e7	−1.44552
$737$	−2.02810e7	−1.37537
$738$	845438.	0.0571401
$739$	−6.27646e6	−0.422770	−0.211385	−	0.977403i	$-0.567797\pi$
$739$	−6.27646e6	−0.422770	−0.211385	+	0.977403i	$0.567797\pi$
$740$	1.65983e6	0.111425
$741$	−4.64622e6	−0.310852
$742$	−7.63910e6	−0.509369
$743$	775801.	0.0515559	0.0257780	−	0.999668i	$-0.491794\pi$
$743$	775801.	0.0515559	0.0257780	+	0.999668i	$0.491794\pi$
$744$	−8.52152e6	−0.564397
$745$	6108.07	0.000403193 0
$746$	1.40623e7	0.925144
$747$	−4.70288e6	−0.308363
$748$	1.96749e7	1.28576
$749$	−2.15528e7	−1.40378
$750$	832686.	0.0540540
$751$	−2.78444e7	−1.80151	−0.900756	−	0.434325i	$-0.856987\pi$
$751$	−2.78444e7	−1.80151	−0.900756	+	0.434325i	$0.856987\pi$
$752$	−6.94605e6	−0.447913
$753$	1.21873e7	0.783288
$754$	−323394.	−0.0207159
$755$	−1.82668e6	−0.116626
$756$	2.73034e6	0.173745
$757$	2.30184e7	1.45994	0.729970	−	0.683479i	$-0.239534\pi$
$757$	2.30184e7	1.45994	0.729970	+	0.683479i	$0.239534\pi$
$758$	1.00189e7	0.633356
$759$	2.44740e7	1.54206
$760$	−1.98688e6	−0.124778
$761$	2.41431e7	1.51123	0.755616	−	0.655015i	$-0.227338\pi$
$761$	2.41431e7	1.51123	0.755616	+	0.655015i	$0.227338\pi$
$762$	−4.93170e6	−0.307687
$763$	−1.34750e7	−0.837949
$764$	−1.92484e7	−1.19306
$765$	−462926.	−0.0285995
$766$	1.35885e6	0.0836755
$767$	758688.	0.0465667
$768$	−5.84509e6	−0.357592
$769$	1.52125e7	0.927651	0.463825	−	0.885927i	$-0.346476\pi$
$769$	1.52125e7	0.927651	0.463825	+	0.885927i	$0.346476\pi$
$770$	1.73762e6	0.105616
$771$	1.46389e7	0.886897
$772$	−1.69341e7	−1.02263
$773$	−1.47219e7	−0.886168	−0.443084	−	0.896480i	$-0.646116\pi$
$773$	−1.47219e7	−0.886168	−0.443084	+	0.896480i	$0.646116\pi$
$774$	−4.62350e6	−0.277408
$775$	1.88537e7	1.12757
$776$	1.00693e7	0.600269
$777$	1.74169e7	1.03494
$778$	−7.50725e6	−0.444664
$779$	8.96845e6	0.529509
$780$	−258238.	−0.0151979
$781$	−1.26455e7	−0.741837
$782$	1.04320e7	0.610032
$783$	392394.	0.0228727
$784$	2.37846e6	0.138199
$785$	674123.	0.0390450
$786$	694905.	0.0401207
$787$	−8.62728e6	−0.496520	−0.248260	−	0.968693i	$-0.579859\pi$
$787$	−8.62728e6	−0.496520	−0.248260	+	0.968693i	$0.579859\pi$
$788$	−1.25656e7	−0.720889
$789$	−1.89054e6	−0.108117
$790$	516723.	0.0294571
$791$	7.36907e6	0.418766
$792$	9.58598e6	0.543030
$793$	−1.89425e6	−0.106968
$794$	−1.12690e7	−0.634360
$795$	−876669.	−0.0491947
$796$	9.82962e6	0.549863
$797$	−3.78019e6	−0.210798	−0.105399	−	0.994430i	$-0.533612\pi$
$797$	−3.78019e6	−0.210798	−0.105399	+	0.994430i	$0.533612\pi$
$798$	−9.01982e6	−0.501407
$799$	2.08887e7	1.15756
$800$	1.84089e7	1.01696
$801$	−2.24493e6	−0.123629
$802$	−1.24992e7	−0.686192
$803$	−4.41033e7	−2.41369
$804$	5.85131e6	0.319237
$805$	−2.95846e6	−0.160907
$806$	3.65887e6	0.198385
$807$	−1.53513e7	−0.829774
$808$	1.15152e7	0.620503
$809$	4.91572e6	0.264068	0.132034	−	0.991245i	$-0.457849\pi$
$809$	4.91572e6	0.264068	0.132034	+	0.991245i	$0.457849\pi$
$810$	−97578.9	−0.00522569
$811$	1.59029e7	0.849032	0.424516	−	0.905421i	$-0.360444\pi$
$811$	1.59029e7	0.849032	0.424516	+	0.905421i	$0.360444\pi$
$812$	2.01597e6	0.107299
$813$	4.46775e6	0.237062
$814$	2.64551e7	1.39942
$815$	−1.51276e6	−0.0797769
$816$	−3.35819e6	−0.176555
$817$	−4.90464e7	−2.57070
$818$	−1.24593e7	−0.651046
$819$	−2.70973e6	−0.141161
$820$	498468.	0.0258883
$821$	−4.00292e6	−0.207262	−0.103631	−	0.994616i	$-0.533046\pi$
$821$	−4.00292e6	−0.207262	−0.103631	+	0.994616i	$0.533046\pi$
$822$	4.19996e6	0.216803
$823$	−223649.	−0.0115098	−0.00575489	−	0.999983i	$-0.501832\pi$
$823$	−223649.	−0.0115098	−0.00575489	+	0.999983i	$0.501832\pi$
$824$	−1.44344e7	−0.740594
$825$	−2.12088e7	−1.08488
$826$	1.47286e6	0.0751124
$827$	1.68423e7	0.856325	0.428163	−	0.903702i	$-0.359161\pi$
$827$	1.68423e7	0.856325	0.428163	+	0.903702i	$0.359161\pi$
$828$	−7.06104e6	−0.357926
$829$	2.09362e6	0.105806	0.0529032	−	0.998600i	$-0.483153\pi$
$829$	2.09362e6	0.105806	0.0529032	+	0.998600i	$0.483153\pi$
$830$	863504.	0.0435080
$831$	−8.68189e6	−0.436126
$832$	1.11584e6	0.0558849
$833$	−7.15269e6	−0.357155
$834$	520373.	0.0259060
$835$	−3.30909e6	−0.164245
$836$	4.39940e7	2.17710
$837$	−4.43954e6	−0.219040
$838$	−3.06199e6	−0.150624
$839$	−1.59903e7	−0.784244	−0.392122	−	0.919913i	$-0.628259\pi$
$839$	−1.59903e7	−0.784244	−0.392122	+	0.919913i	$0.628259\pi$
$840$	−1.15877e6	−0.0566629
$841$	−2.02214e7	−0.985875
$842$	−1.69877e7	−0.825760
$843$	−2.74204e6	−0.132894
$844$	1.51565e7	0.732389
$845$	−1.74692e6	−0.0841649
$846$	4.40306e6	0.211509
$847$	−6.42118e7	−3.07543
$848$	−6.35959e6	−0.303696
$849$	−1.08272e7	−0.515521
$850$	−9.04024e6	−0.429173
$851$	−4.50424e7	−2.13205
$852$	3.64838e6	0.172187
$853$	3.34429e7	1.57373	0.786867	−	0.617122i	$-0.211702\pi$
$853$	3.34429e7	1.57373	0.786867	+	0.617122i	$0.211702\pi$
$854$	−3.67736e6	−0.172540
$855$	−1.03512e6	−0.0484258
$856$	2.18317e7	1.01836
$857$	−2.16267e7	−1.00586	−0.502932	−	0.864326i	$-0.667745\pi$
$857$	−2.16267e7	−1.00586	−0.502932	+	0.864326i	$0.667745\pi$
$858$	−4.11591e6	−0.190875
$859$	8.97034e6	0.414788	0.207394	−	0.978258i	$-0.433502\pi$
$859$	8.97034e6	0.414788	0.207394	+	0.978258i	$0.433502\pi$
$860$	−2.72601e6	−0.125684
$861$	5.23050e6	0.240456
$862$	−8.68445e6	−0.398084
$863$	2.02065e7	0.923557	0.461778	−	0.886995i	$-0.347212\pi$
$863$	2.02065e7	0.923557	0.461778	+	0.886995i	$0.347212\pi$
$864$	−4.33481e6	−0.197554
$865$	−2.64626e6	−0.120252
$866$	−3.12178e6	−0.141452
$867$	−2.67973e6	−0.121072
$868$	−2.28087e7	−1.02755
$869$	−2.64459e7	−1.18798
$870$	−72048.3	−0.00322720
$871$	−5.80713e6	−0.259368
$872$	1.36493e7	0.607884
$873$	5.24592e6	0.232962
$874$	2.33265e7	1.03293
$875$	5.15161e6	0.227469
$876$	1.27243e7	0.560240
$877$	−3.46086e7	−1.51945	−0.759724	−	0.650246i	$-0.774666\pi$
$877$	−3.46086e7	−1.51945	−0.759724	+	0.650246i	$0.774666\pi$
$878$	1.59842e7	0.699767
$879$	−1.29894e7	−0.567042
$880$	1.44658e6	0.0629702
$881$	3.00593e7	1.30479	0.652393	−	0.757881i	$-0.273765\pi$
$881$	3.00593e7	1.30479	0.652393	+	0.757881i	$0.273765\pi$
$882$	−1.50770e6	−0.0652592
$883$	3.54978e7	1.53214	0.766072	−	0.642755i	$-0.222208\pi$
$883$	3.54978e7	1.53214	0.766072	+	0.642755i	$0.222208\pi$
$884$	5.63359e6	0.242468
$885$	169027.	0.00725434
$886$	1.87427e7	0.802137
$887$	2.49795e6	0.106604	0.0533021	−	0.998578i	$-0.483025\pi$
$887$	2.49795e6	0.106604	0.0533021	+	0.998578i	$0.483025\pi$
$888$	−1.76422e7	−0.750793
$889$	−3.05112e7	−1.29480
$890$	412196.	0.0174433
$891$	4.99410e6	0.210748
$892$	−1.23747e7	−0.520744
$893$	4.67079e7	1.96003
$894$	−28087.6	−0.00117536
$895$	2.59458e6	0.108270
$896$	−2.70399e7	−1.12521
$897$	7.00773e6	0.290801
$898$	−1.09311e7	−0.452347
$899$	−3.27798e6	−0.135272
$900$	6.11898e6	0.251810
$901$	1.91250e7	0.784855
$902$	7.94482e6	0.325138
$903$	−2.86044e7	−1.16738
$904$	−7.46441e6	−0.303791
$905$	1.24423e6	0.0504987
$906$	8.39987e6	0.339979
$907$	−1.00612e7	−0.406101	−0.203050	−	0.979168i	$-0.565085\pi$
$907$	−1.00612e7	−0.406101	−0.203050	+	0.979168i	$0.565085\pi$
$908$	3.62471e7	1.45901
$909$	5.99920e6	0.240815
$910$	497538.	0.0199170
$911$	2.02381e7	0.807932	0.403966	−	0.914774i	$-0.367631\pi$
$911$	2.02381e7	0.807932	0.403966	+	0.914774i	$0.367631\pi$
$912$	−7.50905e6	−0.298949
$913$	−4.41943e7	−1.75464
$914$	−1.22804e7	−0.486236
$915$	−422017.	−0.0166639
$916$	1.12324e7	0.442316
$917$	4.29919e6	0.168836
$918$	2.12874e6	0.0833710
$919$	−1.76993e7	−0.691301	−0.345650	−	0.938363i	$-0.612342\pi$
$919$	−1.76993e7	−0.691301	−0.345650	+	0.938363i	$0.612342\pi$
$920$	2.99674e6	0.116729
$921$	−5.32744e6	−0.206952
$922$	−832860.	−0.0322660
$923$	−3.62083e6	−0.139896
$924$	2.56578e7	0.988644
$925$	3.90330e7	1.49995
$926$	1.92810e7	0.738928
$927$	−7.52003e6	−0.287422
$928$	−3.20065e6	−0.122002
$929$	4.09764e7	1.55774	0.778868	−	0.627187i	$-0.215794\pi$
$929$	4.09764e7	1.55774	0.778868	+	0.627187i	$0.215794\pi$
$930$	815153.	0.0309052
$931$	−1.59937e7	−0.604749
$932$	−3.54065e7	−1.33519
$933$	1.10308e7	0.414861
$934$	−2.03263e6	−0.0762416
$935$	−4.35025e6	−0.162737
$936$	2.74479e6	0.102404
$937$	3.39931e7	1.26486	0.632429	−	0.774618i	$-0.282058\pi$
$937$	3.39931e7	1.26486	0.632429	+	0.774618i	$0.282058\pi$
$938$	−1.12735e7	−0.418362
$939$	2.06794e7	0.765376
$940$	2.59604e6	0.0958278
$941$	1.43970e7	0.530027	0.265013	−	0.964245i	$-0.414624\pi$
$941$	1.43970e7	0.530027	0.265013	+	0.964245i	$0.414624\pi$
$942$	−3.09991e6	−0.113821
$943$	−1.35268e7	−0.495354
$944$	1.22616e6	0.0447836
$945$	−603696.	−0.0219907
$946$	−4.34484e7	−1.57850
$947$	−4.96509e7	−1.79909	−0.899544	−	0.436831i	$-0.856101\pi$
$947$	−4.96509e7	−1.79909	−0.899544	+	0.436831i	$0.856101\pi$
$948$	7.62997e6	0.275741
$949$	−1.26282e7	−0.455174
$950$	−2.02144e7	−0.726693
$951$	−1.84964e7	−0.663185
$952$	2.52792e7	0.904004
$953$	−4.52874e7	−1.61527	−0.807635	−	0.589683i	$-0.799253\pi$
$953$	−4.52874e7	−1.61527	−0.807635	+	0.589683i	$0.799253\pi$
$954$	4.03131e6	0.143408
$955$	4.25594e6	0.151004
$956$	−1.30790e7	−0.462839
$957$	3.68744e6	0.130150
$958$	3.59052e6	0.126399
$959$	2.59841e7	0.912349
$960$	248597.	0.00870597
$961$	8.45779e6	0.295426
$962$	7.57499e6	0.263903
$963$	1.13739e7	0.395223
$964$	3.78791e7	1.31283
$965$	3.74423e6	0.129433
$966$	1.36043e7	0.469065
$967$	−2.67183e7	−0.918846	−0.459423	−	0.888218i	$-0.651944\pi$
$967$	−2.67183e7	−0.918846	−0.459423	+	0.888218i	$0.651944\pi$
$968$	6.50426e7	2.23105
$969$	2.25817e7	0.772588
$970$	−963213.	−0.0328695
$971$	1.78197e7	0.606529	0.303265	−	0.952906i	$-0.401923\pi$
$971$	1.78197e7	0.606529	0.303265	+	0.952906i	$0.401923\pi$
$972$	−1.44086e6	−0.0489165
$973$	3.21941e6	0.109017
$974$	1.03323e7	0.348980
$975$	−6.07278e6	−0.204586
$976$	−3.06142e6	−0.102872
$977$	5.43351e7	1.82114	0.910572	−	0.413351i	$-0.135642\pi$
$977$	5.43351e7	1.82114	0.910572	+	0.413351i	$0.135642\pi$
$978$	6.95634e6	0.232559
$979$	−2.10962e7	−0.703475
$980$	−888934.	−0.0295668
$981$	7.11104e6	0.235918
$982$	−4.37032e6	−0.144622
$983$	−5.43884e7	−1.79524	−0.897620	−	0.440769i	$-0.854706\pi$
$983$	−5.43884e7	−1.79524	−0.897620	+	0.440769i	$0.854706\pi$
$984$	−5.29818e6	−0.174437
$985$	2.77834e6	0.0912419
$986$	1.57177e6	0.0514870
$987$	2.72406e7	0.890070
$988$	1.25970e7	0.410557
$989$	7.39749e7	2.40488
$990$	−916977.	−0.0297352
$991$	3.77447e7	1.22088	0.610439	−	0.792064i	$-0.290993\pi$
$991$	3.77447e7	1.22088	0.610439	+	0.792064i	$0.290993\pi$
$992$	3.62121e7	1.16835
$993$	1.46848e7	0.472602
$994$	−7.02921e6	−0.225653
$995$	−2.17339e6	−0.0695953
$996$	1.27506e7	0.407269
$997$	−3.51167e7	−1.11886	−0.559431	−	0.828877i	$-0.688980\pi$
$997$	−3.51167e7	−1.11886	−0.559431	+	0.828877i	$0.688980\pi$
$998$	1.65545e6	0.0526126
$999$	−9.19123e6	−0.291380

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.a.1.5	✓	11
3.2	odd	2		531.6.a.b.1.7		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.a.1.5	✓	11	1.1	even	1	trivial
531.6.a.b.1.7		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)

\(f(q)\)	\(=\)	\(q-2.75662 q^{2} +9.00000 q^{3} -24.4011 q^{4} +5.39522 q^{5} -24.8096 q^{6} -153.490 q^{7} +155.476 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-2.75662 q^{2} +9.00000 q^{3} -24.4011 q^{4} +5.39522 q^{5} -24.8096 q^{6} -153.490 q^{7} +155.476 q^{8} +81.0000 q^{9} -14.8726 q^{10} +761.180 q^{11} -219.609 q^{12} +217.951 q^{13} +423.115 q^{14} +48.5570 q^{15} +352.245 q^{16} -1059.30 q^{17} -223.286 q^{18} -2368.63 q^{19} -131.649 q^{20} -1381.41 q^{21} -2098.28 q^{22} +3572.52 q^{23} +1399.29 q^{24} -3095.89 q^{25} -600.809 q^{26} +729.000 q^{27} +3745.33 q^{28} +538.264 q^{29} -133.853 q^{30} -6089.90 q^{31} -5946.24 q^{32} +6850.62 q^{33} +2920.08 q^{34} -828.115 q^{35} -1976.49 q^{36} -12608.0 q^{37} +6529.41 q^{38} +1961.56 q^{39} +838.829 q^{40} -3786.34 q^{41} +3808.03 q^{42} +20706.6 q^{43} -18573.6 q^{44} +437.013 q^{45} -9848.09 q^{46} -19719.4 q^{47} +3170.20 q^{48} +6752.30 q^{49} +8534.19 q^{50} -9533.67 q^{51} -5318.24 q^{52} -18054.4 q^{53} -2009.58 q^{54} +4106.74 q^{55} -23864.1 q^{56} -21317.7 q^{57} -1483.79 q^{58} +3481.00 q^{59} -1184.84 q^{60} -8691.16 q^{61} +16787.5 q^{62} -12432.7 q^{63} +5119.69 q^{64} +1175.90 q^{65} -18884.6 q^{66} -26644.1 q^{67} +25847.9 q^{68} +32152.7 q^{69} +2282.80 q^{70} -16613.0 q^{71} +12593.6 q^{72} -57940.7 q^{73} +34755.4 q^{74} -27863.0 q^{75} +57797.1 q^{76} -116834. q^{77} -5407.28 q^{78} -34743.3 q^{79} +1900.44 q^{80} +6561.00 q^{81} +10437.5 q^{82} -58060.2 q^{83} +33707.9 q^{84} -5715.14 q^{85} -57080.3 q^{86} +4844.38 q^{87} +118345. q^{88} -27715.2 q^{89} -1204.68 q^{90} -33453.4 q^{91} -87173.4 q^{92} -54809.1 q^{93} +54358.8 q^{94} -12779.3 q^{95} -53516.2 q^{96} +64764.4 q^{97} -18613.5 q^{98} +61655.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more