LMFDB - Embedded newform 177.6.a.d.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:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + \cdots - 6400833792 $ x^13 - 331x^11 - 41x^10 + 41990x^9 + 7229x^8 - 2592364x^7 - 312100x^6 + 81977088x^5 - 3773728x^4 - 1245415104x^3 + 453320896x^2 + 6872784896*x - 6400833792
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-6.06926$ 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)

$f(q)$	$=$	$q-6.06926 q^{2} -9.00000 q^{3} +4.83596 q^{4} +26.0687 q^{5} +54.6234 q^{6} -152.673 q^{7} +164.866 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-6.06926 q^{2} -9.00000 q^{3} +4.83596 q^{4} +26.0687 q^{5} +54.6234 q^{6} -152.673 q^{7} +164.866 q^{8} +81.0000 q^{9} -158.218 q^{10} +105.236 q^{11} -43.5237 q^{12} -582.342 q^{13} +926.616 q^{14} -234.618 q^{15} -1155.36 q^{16} -1069.36 q^{17} -491.610 q^{18} +390.786 q^{19} +126.067 q^{20} +1374.06 q^{21} -638.707 q^{22} -400.841 q^{23} -1483.79 q^{24} -2445.42 q^{25} +3534.39 q^{26} -729.000 q^{27} -738.323 q^{28} -4917.03 q^{29} +1423.96 q^{30} -6824.95 q^{31} +1736.51 q^{32} -947.126 q^{33} +6490.22 q^{34} -3980.00 q^{35} +391.713 q^{36} +15771.2 q^{37} -2371.78 q^{38} +5241.08 q^{39} +4297.83 q^{40} -3504.92 q^{41} -8339.54 q^{42} +10247.6 q^{43} +508.919 q^{44} +2111.56 q^{45} +2432.81 q^{46} +7721.01 q^{47} +10398.3 q^{48} +6502.19 q^{49} +14841.9 q^{50} +9624.22 q^{51} -2816.18 q^{52} +17958.4 q^{53} +4424.49 q^{54} +2743.37 q^{55} -25170.6 q^{56} -3517.07 q^{57} +29842.7 q^{58} +3481.00 q^{59} -1134.61 q^{60} +45574.7 q^{61} +41422.4 q^{62} -12366.6 q^{63} +26432.3 q^{64} -15180.9 q^{65} +5748.36 q^{66} +20668.2 q^{67} -5171.38 q^{68} +3607.57 q^{69} +24155.7 q^{70} -39463.9 q^{71} +13354.1 q^{72} -2618.86 q^{73} -95719.8 q^{74} +22008.8 q^{75} +1889.83 q^{76} -16066.8 q^{77} -31809.5 q^{78} +5265.20 q^{79} -30118.8 q^{80} +6561.00 q^{81} +21272.3 q^{82} +98001.8 q^{83} +6644.91 q^{84} -27876.8 q^{85} -62195.3 q^{86} +44253.3 q^{87} +17349.8 q^{88} +35159.0 q^{89} -12815.6 q^{90} +88908.2 q^{91} -1938.45 q^{92} +61424.5 q^{93} -46860.9 q^{94} +10187.3 q^{95} -15628.6 q^{96} +126268. q^{97} -39463.5 q^{98} +8524.14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) $ 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9} + 137 q^{10} + 250 q^{11} - 2214 q^{12} + 1054 q^{13} - 575 q^{14} + 126 q^{15} + 922 q^{16} + 271 q^{17} + 671 q^{19} - 5491 q^{20} - 3357 q^{21} + 1094 q^{22} + 3975 q^{23} - 1107 q^{24} + 15569 q^{25} + 4622 q^{26} - 9477 q^{27} + 21214 q^{28} - 10613 q^{29} - 1233 q^{30} + 25597 q^{31} + 15966 q^{32} - 2250 q^{33} + 31796 q^{34} + 6729 q^{35} + 19926 q^{36} + 17585 q^{37} + 34903 q^{38} - 9486 q^{39} + 31382 q^{40} + 12537 q^{41} + 5175 q^{42} + 26644 q^{43} + 6654 q^{44} - 1134 q^{45} + 149005 q^{46} + 52087 q^{47} - 8298 q^{48} + 95384 q^{49} + 121821 q^{50} - 2439 q^{51} + 263630 q^{52} + 20014 q^{53} + 120932 q^{55} + 126688 q^{56} - 6039 q^{57} + 86066 q^{58} + 45253 q^{59} + 49419 q^{60} - 11667 q^{61} + 164794 q^{62} + 30213 q^{63} + 151893 q^{64} - 28674 q^{65} - 9846 q^{66} + 1106 q^{67} - 4043 q^{68} - 35775 q^{69} + 56066 q^{70} + 21230 q^{71} + 9963 q^{72} + 81131 q^{73} + 102042 q^{74} - 140121 q^{75} + 73900 q^{76} - 104655 q^{77} - 41598 q^{78} - 13470 q^{79} - 191969 q^{80} + 85293 q^{81} + 79909 q^{82} - 76149 q^{83} - 190926 q^{84} + 10035 q^{85} - 321496 q^{86} + 95517 q^{87} - 276779 q^{88} - 190205 q^{89} + 11097 q^{90} + 80601 q^{91} + 45672 q^{92} - 230373 q^{93} + 36768 q^{94} + 9875 q^{95} - 143694 q^{96} + 160850 q^{97} - 116644 q^{98} + 20250 q^{99}+O(q^{100}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9 + 137 * q^10 + 250 * q^11 - 2214 * q^12 + 1054 * q^13 - 575 * q^14 + 126 * q^15 + 922 * q^16 + 271 * q^17 + 671 * q^19 - 5491 * q^20 - 3357 * q^21 + 1094 * q^22 + 3975 * q^23 - 1107 * q^24 + 15569 * q^25 + 4622 * q^26 - 9477 * q^27 + 21214 * q^28 - 10613 * q^29 - 1233 * q^30 + 25597 * q^31 + 15966 * q^32 - 2250 * q^33 + 31796 * q^34 + 6729 * q^35 + 19926 * q^36 + 17585 * q^37 + 34903 * q^38 - 9486 * q^39 + 31382 * q^40 + 12537 * q^41 + 5175 * q^42 + 26644 * q^43 + 6654 * q^44 - 1134 * q^45 + 149005 * q^46 + 52087 * q^47 - 8298 * q^48 + 95384 * q^49 + 121821 * q^50 - 2439 * q^51 + 263630 * q^52 + 20014 * q^53 + 120932 * q^55 + 126688 * q^56 - 6039 * q^57 + 86066 * q^58 + 45253 * q^59 + 49419 * q^60 - 11667 * q^61 + 164794 * q^62 + 30213 * q^63 + 151893 * q^64 - 28674 * q^65 - 9846 * q^66 + 1106 * q^67 - 4043 * q^68 - 35775 * q^69 + 56066 * q^70 + 21230 * q^71 + 9963 * q^72 + 81131 * q^73 + 102042 * q^74 - 140121 * q^75 + 73900 * q^76 - 104655 * q^77 - 41598 * q^78 - 13470 * q^79 - 191969 * q^80 + 85293 * q^81 + 79909 * q^82 - 76149 * q^83 - 190926 * q^84 + 10035 * q^85 - 321496 * q^86 + 95517 * q^87 - 276779 * q^88 - 190205 * q^89 + 11097 * q^90 + 80601 * q^91 + 45672 * q^92 - 230373 * q^93 + 36768 * q^94 + 9875 * q^95 - 143694 * q^96 + 160850 * q^97 - 116644 * q^98 + 20250 * 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 $

$2$	−6.06926	−1.07290	−0.536452	−	0.843931i	$-0.680236\pi$
$2$	−6.06926	−1.07290	−0.536452	+	0.843931i	$0.680236\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	4.83596	0.151124
$5$	26.0687	0.466331	0.233166	−	0.972437i	$-0.425092\pi$
$5$	26.0687	0.466331	0.233166	+	0.972437i	$0.425092\pi$
$6$	54.6234	0.619442
$7$	−152.673	−1.17766	−0.588828	−	0.808258i	$-0.700411\pi$
$7$	−152.673	−1.17766	−0.588828	+	0.808258i	$0.700411\pi$
$8$	164.866	0.910763
$9$	81.0000	0.333333
$10$	−158.218	−0.500329
$11$	105.236	0.262231	0.131115	−	0.991367i	$-0.458144\pi$
$11$	105.236	0.262231	0.131115	+	0.991367i	$0.458144\pi$
$12$	−43.5237	−0.0872514
$13$	−582.342	−0.955696	−0.477848	−	0.878443i	$-0.658583\pi$
$13$	−582.342	−0.955696	−0.477848	+	0.878443i	$0.658583\pi$
$14$	926.616	1.26351
$15$	−234.618	−0.269236
$16$	−1155.36	−1.12829
$17$	−1069.36	−0.897431	−0.448715	−	0.893675i	$-0.648118\pi$
$17$	−1069.36	−0.897431	−0.448715	+	0.893675i	$0.648118\pi$
$18$	−491.610	−0.357635
$19$	390.786	0.248345	0.124172	−	0.992261i	$-0.460372\pi$
$19$	390.786	0.248345	0.124172	+	0.992261i	$0.460372\pi$
$20$	126.067	0.0704737
$21$	1374.06	0.679920
$22$	−638.707	−0.281349
$23$	−400.841	−0.157998	−0.0789992	−	0.996875i	$-0.525172\pi$
$23$	−400.841	−0.157998	−0.0789992	+	0.996875i	$0.525172\pi$
$24$	−1483.79	−0.525829
$25$	−2445.42	−0.782535
$26$	3534.39	1.02537
$27$	−729.000	−0.192450
$28$	−738.323	−0.177972
$29$	−4917.03	−1.08569	−0.542847	−	0.839831i	$-0.682654\pi$
$29$	−4917.03	−1.08569	−0.542847	+	0.839831i	$0.682654\pi$
$30$	1423.96	0.288865
$31$	−6824.95	−1.27554	−0.637772	−	0.770226i	$-0.720144\pi$
$31$	−6824.95	−1.27554	−0.637772	+	0.770226i	$0.720144\pi$
$32$	1736.51	0.299779
$33$	−947.126	−0.151399
$34$	6490.22	0.962857
$35$	−3980.00	−0.549178
$36$	391.713	0.0503746
$37$	15771.2	1.89392	0.946960	−	0.321352i	$-0.104137\pi$
$37$	15771.2	1.89392	0.946960	+	0.321352i	$0.104137\pi$
$38$	−2371.78	−0.266450
$39$	5241.08	0.551771
$40$	4297.83	0.424717
$41$	−3504.92	−0.325625	−0.162813	−	0.986657i	$-0.552057\pi$
$41$	−3504.92	−0.325625	−0.162813	+	0.986657i	$0.552057\pi$
$42$	−8339.54	−0.729489
$43$	10247.6	0.845182	0.422591	−	0.906320i	$-0.361121\pi$
$43$	10247.6	0.845182	0.422591	+	0.906320i	$0.361121\pi$
$44$	508.919	0.0396293
$45$	2111.56	0.155444
$46$	2432.81	0.169517
$47$	7721.01	0.509835	0.254917	−	0.966963i	$-0.417952\pi$
$47$	7721.01	0.509835	0.254917	+	0.966963i	$0.417952\pi$
$48$	10398.3	0.651416
$49$	6502.19	0.386874
$50$	14841.9	0.839586
$51$	9624.22	0.518132
$52$	−2816.18	−0.144428
$53$	17958.4	0.878169	0.439084	−	0.898446i	$-0.355303\pi$
$53$	17958.4	0.878169	0.439084	+	0.898446i	$0.355303\pi$
$54$	4424.49	0.206481
$55$	2743.37	0.122286
$56$	−25170.6	−1.07257
$57$	−3517.07	−0.143382
$58$	29842.7	1.16485
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−1134.61	−0.0406880
$61$	45574.7	1.56819	0.784095	−	0.620640i	$-0.213127\pi$
$61$	45574.7	1.56819	0.784095	+	0.620640i	$0.213127\pi$
$62$	41422.4	1.36854
$63$	−12366.6	−0.392552
$64$	26432.3	0.806651
$65$	−15180.9	−0.445671
$66$	5748.36	0.162437
$67$	20668.2	0.562490	0.281245	−	0.959636i	$-0.409253\pi$
$67$	20668.2	0.562490	0.281245	+	0.959636i	$0.409253\pi$
$68$	−5171.38	−0.135623
$69$	3607.57	0.0912204
$70$	24155.7	0.589215
$71$	−39463.9	−0.929081	−0.464541	−	0.885552i	$-0.653781\pi$
$71$	−39463.9	−0.929081	−0.464541	+	0.885552i	$0.653781\pi$
$72$	13354.1	0.303588
$73$	−2618.86	−0.0575181	−0.0287590	−	0.999586i	$-0.509156\pi$
$73$	−2618.86	−0.0575181	−0.0287590	+	0.999586i	$0.509156\pi$
$74$	−95719.8	−2.03199
$75$	22008.8	0.451797
$76$	1889.83	0.0375308
$77$	−16066.8	−0.308818
$78$	−31809.5	−0.591998
$79$	5265.20	0.0949177	0.0474589	−	0.998873i	$-0.484888\pi$
$79$	5265.20	0.0949177	0.0474589	+	0.998873i	$0.484888\pi$
$80$	−30118.8	−0.526154
$81$	6561.00	0.111111
$82$	21272.3	0.349365
$83$	98001.8	1.56149	0.780744	−	0.624851i	$-0.214840\pi$
$83$	98001.8	1.56149	0.780744	+	0.624851i	$0.214840\pi$
$84$	6644.91	0.102752
$85$	−27876.8	−0.418500
$86$	−62195.3	−0.906800
$87$	44253.3	0.626826
$88$	17349.8	0.238830
$89$	35159.0	0.470501	0.235251	−	0.971935i	$-0.424409\pi$
$89$	35159.0	0.470501	0.235251	+	0.971935i	$0.424409\pi$
$90$	−12815.6	−0.166776
$91$	88908.2	1.12548
$92$	−1938.45	−0.0238773
$93$	61424.5	0.736435
$94$	−46860.9	−0.547004
$95$	10187.3	0.115811
$96$	−15628.6	−0.173078
$97$	126268.	1.36258	0.681291	−	0.732012i	$-0.261419\pi$
$97$	126268.	1.36258	0.681291	+	0.732012i	$0.261419\pi$
$98$	−39463.5	−0.415079
$99$	8524.14	0.0874103
$100$	−11826.0	−0.118260
$101$	−67402.7	−0.657467	−0.328733	−	0.944423i	$-0.606622\pi$
$101$	−67402.7	−0.657467	−0.328733	+	0.944423i	$0.606622\pi$
$102$	−58411.9	−0.555906
$103$	−122149.	−1.13448	−0.567240	−	0.823553i	$-0.691989\pi$
$103$	−122149.	−1.13448	−0.567240	+	0.823553i	$0.691989\pi$
$104$	−96008.2	−0.870412
$105$	35820.0	0.317068
$106$	−108994.	−0.942191
$107$	108415.	0.915444	0.457722	−	0.889095i	$-0.348666\pi$
$107$	108415.	0.915444	0.457722	+	0.889095i	$0.348666\pi$
$108$	−3525.42	−0.0290838
$109$	−135107.	−1.08921	−0.544604	−	0.838694i	$-0.683320\pi$
$109$	−135107.	−1.08921	−0.544604	+	0.838694i	$0.683320\pi$
$110$	−16650.2	−0.131202
$111$	−141941.	−1.09346
$112$	176393.	1.32873
$113$	−140109.	−1.03222	−0.516108	−	0.856523i	$-0.672620\pi$
$113$	−140109.	−1.03222	−0.516108	+	0.856523i	$0.672620\pi$
$114$	21346.0	0.153835
$115$	−10449.4	−0.0736795
$116$	−23778.6	−0.164074
$117$	−47169.7	−0.318565
$118$	−21127.1	−0.139680
$119$	163263.	1.05686
$120$	−38680.5	−0.245210
$121$	−149976.	−0.931235
$122$	−276605.	−1.68252
$123$	31544.3	0.188000
$124$	−33005.2	−0.192765
$125$	−145214.	−0.831252
$126$	75055.9	0.421171
$127$	300303.	1.65215	0.826076	−	0.563559i	$-0.190568\pi$
$127$	300303.	1.65215	0.826076	+	0.563559i	$0.190568\pi$
$128$	−215993.	−1.16524
$129$	−92228.3	−0.487966
$130$	92136.8	0.478162
$131$	−24226.5	−0.123342	−0.0616712	−	0.998097i	$-0.519643\pi$
$131$	−24226.5	−0.123342	−0.0616712	+	0.998097i	$0.519643\pi$
$132$	−4580.27	−0.0228800
$133$	−59662.7	−0.292465
$134$	−125441.	−0.603498
$135$	−19004.1	−0.0897454
$136$	−176300.	−0.817347
$137$	−238971.	−1.08779	−0.543894	−	0.839154i	$-0.683051\pi$
$137$	−238971.	−1.08779	−0.543894	+	0.839154i	$0.683051\pi$
$138$	−21895.3	−0.0978708
$139$	13346.3	0.0585901	0.0292951	−	0.999571i	$-0.490674\pi$
$139$	13346.3	0.0585901	0.0292951	+	0.999571i	$0.490674\pi$
$140$	−19247.1	−0.0829938
$141$	−69489.1	−0.294353
$142$	239517.	0.996815
$143$	−61283.5	−0.250613
$144$	−93584.5	−0.376095
$145$	−128181.	−0.506293
$146$	15894.5	0.0617114
$147$	−58519.7	−0.223362
$148$	76269.1	0.286216
$149$	231222.	0.853225	0.426612	−	0.904435i	$-0.359707\pi$
$149$	231222.	0.853225	0.426612	+	0.904435i	$0.359707\pi$
$150$	−133577.	−0.484735
$151$	444904.	1.58790	0.793951	−	0.607981i	$-0.208020\pi$
$151$	444904.	1.58790	0.793951	+	0.607981i	$0.208020\pi$
$152$	64427.2	0.226183
$153$	−86618.0	−0.299144
$154$	97513.6	0.331332
$155$	−177918.	−0.594825
$156$	25345.7	0.0833858
$157$	356448.	1.15411	0.577054	−	0.816706i	$-0.304202\pi$
$157$	356448.	1.15411	0.577054	+	0.816706i	$0.304202\pi$
$158$	−31955.9	−0.101838
$159$	−161626.	−0.507011
$160$	45268.5	0.139796
$161$	61197.8	0.186068
$162$	−39820.4	−0.119212
$163$	110391.	0.325437	0.162718	−	0.986673i	$-0.447974\pi$
$163$	110391.	0.325437	0.162718	+	0.986673i	$0.447974\pi$
$164$	−16949.7	−0.0492098
$165$	−24690.3	−0.0706021
$166$	−594799.	−1.67533
$167$	164938.	0.457645	0.228823	−	0.973468i	$-0.426512\pi$
$167$	164938.	0.457645	0.228823	+	0.973468i	$0.426512\pi$
$168$	226536.	0.619246
$169$	−32170.9	−0.0866457
$170$	169191.	0.449010
$171$	31653.7	0.0827816
$172$	49556.9	0.127727
$173$	432927.	1.09976	0.549881	−	0.835243i	$-0.314673\pi$
$173$	432927.	1.09976	0.549881	+	0.835243i	$0.314673\pi$
$174$	−268585.	−0.672525
$175$	373351.	0.921558
$176$	−121586.	−0.295871
$177$	−31329.0	−0.0751646
$178$	−213389.	−0.504803
$179$	331441.	0.773168	0.386584	−	0.922254i	$-0.373655\pi$
$179$	331441.	0.773168	0.386584	+	0.922254i	$0.373655\pi$
$180$	10211.4	0.0234912
$181$	136830.	0.310444	0.155222	−	0.987880i	$-0.450391\pi$
$181$	136830.	0.310444	0.155222	+	0.987880i	$0.450391\pi$
$182$	−539607.	−1.20753
$183$	−410172.	−0.905395
$184$	−66085.0	−0.143899
$185$	411136.	0.883194
$186$	−372802.	−0.790125
$187$	−112535.	−0.235334
$188$	37338.5	0.0770482
$189$	111299.	0.226640
$190$	−61829.3	−0.124254
$191$	777758.	1.54263	0.771314	−	0.636455i	$-0.219600\pi$
$191$	777758.	1.54263	0.771314	+	0.636455i	$0.219600\pi$
$192$	−237891.	−0.465720
$193$	−402573.	−0.777949	−0.388974	−	0.921249i	$-0.627171\pi$
$193$	−402573.	−0.777949	−0.388974	+	0.921249i	$0.627171\pi$
$194$	−766352.	−1.46192
$195$	136628.	0.257308
$196$	31444.4	0.0584659
$197$	−335493.	−0.615910	−0.307955	−	0.951401i	$-0.599645\pi$
$197$	−335493.	−0.615910	−0.307955	+	0.951401i	$0.599645\pi$
$198$	−51735.2	−0.0937828
$199$	642899.	1.15083	0.575413	−	0.817863i	$-0.304841\pi$
$199$	642899.	1.15083	0.575413	+	0.817863i	$0.304841\pi$
$200$	−403166.	−0.712704
$201$	−186013.	−0.324754
$202$	409085.	0.705399
$203$	750700.	1.27858
$204$	46542.4	0.0783021
$205$	−91368.7	−0.151849
$206$	741354.	1.21719
$207$	−32468.1	−0.0526661
$208$	672817.	1.07830
$209$	41124.8	0.0651236
$210$	−217401.	−0.340183
$211$	905267.	1.39982	0.699908	−	0.714233i	$-0.253224\pi$
$211$	905267.	1.39982	0.699908	+	0.714233i	$0.253224\pi$
$212$	86846.2	0.132712
$213$	355175.	0.536405
$214$	−658002.	−0.982184
$215$	267141.	0.394135
$216$	−120187.	−0.175276
$217$	1.04199e6	1.50215
$218$	819998.	1.16861
$219$	23569.7	0.0332081
$220$	13266.8	0.0184804
$221$	622732.	0.857671
$222$	861478.	1.17317
$223$	−156940.	−0.211335	−0.105667	−	0.994402i	$-0.533698\pi$
$223$	−156940.	−0.211335	−0.105667	+	0.994402i	$0.533698\pi$
$224$	−265119.	−0.353037
$225$	−198079.	−0.260845
$226$	850360.	1.10747
$227$	784043.	1.00989	0.504946	−	0.863151i	$-0.331512\pi$
$227$	784043.	1.00989	0.504946	+	0.863151i	$0.331512\pi$
$228$	−17008.4	−0.0216684
$229$	−664454.	−0.837290	−0.418645	−	0.908150i	$-0.637495\pi$
$229$	−664454.	−0.837290	−0.418645	+	0.908150i	$0.637495\pi$
$230$	63420.2	0.0790511
$231$	144601.	0.178296
$232$	−810650.	−0.988811
$233$	−984844.	−1.18844	−0.594220	−	0.804302i	$-0.702539\pi$
$233$	−984844.	−1.18844	−0.594220	+	0.804302i	$0.702539\pi$
$234$	286285.	0.341790
$235$	201277.	0.237752
$236$	16834.0	0.0196746
$237$	−47386.8	−0.0548008
$238$	−990884.	−1.13391
$239$	−1.51318e6	−1.71355	−0.856774	−	0.515692i	$-0.827535\pi$
$239$	−1.51318e6	−1.71355	−0.856774	+	0.515692i	$0.827535\pi$
$240$	271070.	0.303775
$241$	392563.	0.435378	0.217689	−	0.976018i	$-0.430148\pi$
$241$	392563.	0.435378	0.217689	+	0.976018i	$0.430148\pi$
$242$	910246.	0.999126
$243$	−59049.0	−0.0641500
$244$	220397.	0.236991
$245$	169504.	0.180411
$246$	−191451.	−0.201706
$247$	−227571.	−0.237342
$248$	−1.12520e6	−1.16172
$249$	−882016.	−0.901526
$250$	881340.	0.891853
$251$	−239322.	−0.239772	−0.119886	−	0.992788i	$-0.538253\pi$
$251$	−239322.	−0.239772	−0.119886	+	0.992788i	$0.538253\pi$
$252$	−59804.2	−0.0593240
$253$	−42183.0	−0.0414320
$254$	−1.82262e6	−1.77260
$255$	250891.	0.241621
$256$	465084.	0.443539
$257$	−118296.	−0.111721	−0.0558607	−	0.998439i	$-0.517790\pi$
$257$	−118296.	−0.111721	−0.0558607	+	0.998439i	$0.517790\pi$
$258$	559758.	0.523541
$259$	−2.40785e6	−2.23039
$260$	−73414.2	−0.0673514
$261$	−398279.	−0.361898
$262$	147037.	0.132335
$263$	170441.	0.151944	0.0759722	−	0.997110i	$-0.475794\pi$
$263$	170441.	0.151944	0.0759722	+	0.997110i	$0.475794\pi$
$264$	−156149.	−0.137889
$265$	468152.	0.409517
$266$	362108.	0.313787
$267$	−316431.	−0.271644
$268$	99950.4	0.0850056
$269$	1.16647e6	0.982867	0.491433	−	0.870915i	$-0.336473\pi$
$269$	1.16647e6	0.982867	0.491433	+	0.870915i	$0.336473\pi$
$270$	115341.	0.0962883
$271$	25230.7	0.0208692	0.0104346	−	0.999946i	$-0.496678\pi$
$271$	25230.7	0.0208692	0.0104346	+	0.999946i	$0.496678\pi$
$272$	1.23550e6	1.01256
$273$	−800173.	−0.649797
$274$	1.45038e6	1.16709
$275$	−257347.	−0.205205
$276$	17446.1	0.0137856
$277$	−118869.	−0.0930824	−0.0465412	−	0.998916i	$-0.514820\pi$
$277$	−118869.	−0.0930824	−0.0465412	+	0.998916i	$0.514820\pi$
$278$	−81002.3	−0.0628616
$279$	−552821.	−0.425181
$280$	−656165.	−0.500171
$281$	−492378.	−0.371991	−0.185996	−	0.982551i	$-0.559551\pi$
$281$	−492378.	−0.371991	−0.185996	+	0.982551i	$0.559551\pi$
$282$	421748.	0.315813
$283$	532204.	0.395014	0.197507	−	0.980302i	$-0.436716\pi$
$283$	532204.	0.395014	0.197507	+	0.980302i	$0.436716\pi$
$284$	−190846.	−0.140406
$285$	−91685.5	−0.0668634
$286$	371946.	0.268884
$287$	535108.	0.383475
$288$	140657.	0.0999265
$289$	−276330.	−0.194618
$290$	777962.	0.543204
$291$	−1.13641e6	−0.786687
$292$	−12664.7	−0.00869235
$293$	170024.	0.115702	0.0578510	−	0.998325i	$-0.481575\pi$
$293$	170024.	0.115702	0.0578510	+	0.998325i	$0.481575\pi$
$294$	355172.	0.239646
$295$	90745.1	0.0607111
$296$	2.60014e6	1.72491
$297$	−76717.2	−0.0504663
$298$	−1.40335e6	−0.915428
$299$	233427.	0.150998
$300$	106434.	0.0682773
$301$	−1.56453e6	−0.995334
$302$	−2.70024e6	−1.70367
$303$	606624.	0.379589
$304$	−451500.	−0.280204
$305$	1.18807e6	0.731296
$306$	525708.	0.320952
$307$	−118160.	−0.0715522	−0.0357761	−	0.999360i	$-0.511390\pi$
$307$	−118160.	−0.0715522	−0.0357761	+	0.999360i	$0.511390\pi$
$308$	−77698.4	−0.0466697
$309$	1.09934e6	0.654992
$310$	1.07983e6	0.638191
$311$	−2.00186e6	−1.17363	−0.586816	−	0.809720i	$-0.699619\pi$
$311$	−2.00186e6	−1.17363	−0.586816	+	0.809720i	$0.699619\pi$
$312$	864074.	0.502533
$313$	3.40535e6	1.96472	0.982361	−	0.186992i	$-0.0598739\pi$
$313$	3.40535e6	1.96472	0.982361	+	0.186992i	$0.0598739\pi$
$314$	−2.16337e6	−1.23825
$315$	−322380.	−0.183059
$316$	25462.3	0.0143443
$317$	−394188.	−0.220321	−0.110160	−	0.993914i	$-0.535136\pi$
$317$	−394188.	−0.220321	−0.110160	+	0.993914i	$0.535136\pi$
$318$	980948.	0.543974
$319$	−517450.	−0.284703
$320$	689056.	0.376166
$321$	−975739.	−0.528532
$322$	−371426.	−0.199633
$323$	−417890.	−0.222872
$324$	31728.7	0.0167915
$325$	1.42407e6	0.747866
$326$	−669995.	−0.349162
$327$	1.21596e6	0.628854
$328$	−577841.	−0.296568
$329$	−1.17879e6	−0.600410
$330$	149852.	0.0757493
$331$	−2.27331e6	−1.14048	−0.570240	−	0.821478i	$-0.693150\pi$
$331$	−2.27331e6	−1.14048	−0.570240	+	0.821478i	$0.693150\pi$
$332$	473933.	0.235978
$333$	1.27747e6	0.631307
$334$	−1.00105e6	−0.491010
$335$	538792.	0.262307
$336$	−1.58754e6	−0.767144
$337$	−1.15578e6	−0.554370	−0.277185	−	0.960817i	$-0.589402\pi$
$337$	−1.15578e6	−0.554370	−0.277185	+	0.960817i	$0.589402\pi$
$338$	195254.	0.0929626
$339$	1.26098e6	0.595950
$340$	−134811.	−0.0632453
$341$	−718232.	−0.334487
$342$	−192114.	−0.0888167
$343$	1.57327e6	0.722051
$344$	1.68948e6	0.769761
$345$	94044.6	0.0425389
$346$	−2.62755e6	−1.17994
$347$	3.28503e6	1.46459	0.732295	−	0.680988i	$-0.238449\pi$
$347$	3.28503e6	1.46459	0.732295	+	0.680988i	$0.238449\pi$
$348$	214007.	0.0947284
$349$	3.89003e6	1.70958	0.854790	−	0.518974i	$-0.173686\pi$
$349$	3.89003e6	1.70958	0.854790	+	0.518974i	$0.173686\pi$
$350$	−2.26597e6	−0.988743
$351$	424527.	0.183924
$352$	182744.	0.0786114
$353$	−2.80229e6	−1.19695	−0.598476	−	0.801141i	$-0.704227\pi$
$353$	−2.80229e6	−1.19695	−0.598476	+	0.801141i	$0.704227\pi$
$354$	190144.	0.0806444
$355$	−1.02877e6	−0.433259
$356$	170027.	0.0711040
$357$	−1.46936e6	−0.610181
$358$	−2.01160e6	−0.829536
$359$	671218.	0.274870	0.137435	−	0.990511i	$-0.456114\pi$
$359$	671218.	0.274870	0.137435	+	0.990511i	$0.456114\pi$
$360$	348125.	0.141572
$361$	−2.32339e6	−0.938325
$362$	−830455.	−0.333077
$363$	1.34979e6	0.537649
$364$	429957.	0.170087
$365$	−68270.2	−0.0268225
$366$	2.48944e6	0.971403
$367$	−642875.	−0.249150	−0.124575	−	0.992210i	$-0.539757\pi$
$367$	−642875.	−0.249150	−0.124575	+	0.992210i	$0.539757\pi$
$368$	463117.	0.178267
$369$	−283898.	−0.108542
$370$	−2.49529e6	−0.947582
$371$	−2.74177e6	−1.03418
$372$	297047.	0.111293
$373$	−3.08089e6	−1.14658	−0.573290	−	0.819352i	$-0.694333\pi$
$373$	−3.08089e6	−1.14658	−0.573290	+	0.819352i	$0.694333\pi$
$374$	683006.	0.252491
$375$	1.30692e6	0.479923
$376$	1.27293e6	0.464339
$377$	2.86339e6	1.03759
$378$	−675503.	−0.243163
$379$	−2.66225e6	−0.952030	−0.476015	−	0.879437i	$-0.657919\pi$
$379$	−2.66225e6	−0.952030	−0.476015	+	0.879437i	$0.657919\pi$
$380$	49265.3	0.0175018
$381$	−2.70272e6	−0.953870
$382$	−4.72042e6	−1.65509
$383$	944201.	0.328903	0.164451	−	0.986385i	$-0.447415\pi$
$383$	944201.	0.328903	0.164451	+	0.986385i	$0.447415\pi$
$384$	1.94394e6	0.672751
$385$	−418840.	−0.144011
$386$	2.44332e6	0.834664
$387$	830054.	0.281727
$388$	610626.	0.205919
$389$	−3.17438e6	−1.06362	−0.531808	−	0.846865i	$-0.678487\pi$
$389$	−3.17438e6	−1.06362	−0.531808	+	0.846865i	$0.678487\pi$
$390$	−829232.	−0.276067
$391$	428643.	0.141793
$392$	1.07199e6	0.352351
$393$	218038.	0.0712118
$394$	2.03619e6	0.660813
$395$	137257.	0.0442631
$396$	41222.4	0.0132098
$397$	3.57862e6	1.13957	0.569783	−	0.821795i	$-0.307027\pi$
$397$	3.57862e6	1.13957	0.569783	+	0.821795i	$0.307027\pi$
$398$	−3.90192e6	−1.23473
$399$	536964.	0.168855
$400$	2.82535e6	0.882923
$401$	−4.84786e6	−1.50553	−0.752764	−	0.658290i	$-0.771280\pi$
$401$	−4.84786e6	−1.50553	−0.752764	+	0.658290i	$0.771280\pi$
$402$	1.12896e6	0.348430
$403$	3.97445e6	1.21903
$404$	−325957.	−0.0993589
$405$	171037.	0.0518146
$406$	−4.55620e6	−1.37179
$407$	1.65971e6	0.496644
$408$	1.58670e6	0.471895
$409$	−2.38119e6	−0.703859	−0.351930	−	0.936026i	$-0.614474\pi$
$409$	−2.38119e6	−0.703859	−0.351930	+	0.936026i	$0.614474\pi$
$410$	554541.	0.162920
$411$	2.15074e6	0.628035
$412$	−590708.	−0.171447
$413$	−531456.	−0.153318
$414$	197058.	0.0565057
$415$	2.55478e6	0.728171
$416$	−1.01124e6	−0.286498
$417$	−120117.	−0.0338270
$418$	−249598.	−0.0698714
$419$	−510637.	−0.142095	−0.0710473	−	0.997473i	$-0.522634\pi$
$419$	−510637.	−0.142095	−0.0710473	+	0.997473i	$0.522634\pi$
$420$	173224.	0.0479165
$421$	−2.82268e6	−0.776168	−0.388084	−	0.921624i	$-0.626863\pi$
$421$	−2.82268e6	−0.776168	−0.388084	+	0.921624i	$0.626863\pi$
$422$	−5.49431e6	−1.50187
$423$	625402.	0.169945
$424$	2.96072e6	0.799804
$425$	2.61503e6	0.702271
$426$	−2.15565e6	−0.575512
$427$	−6.95804e6	−1.84679
$428$	524293.	0.138345
$429$	551551.	0.144691
$430$	−1.62135e6	−0.422869
$431$	−2.25262e6	−0.584111	−0.292056	−	0.956401i	$-0.594339\pi$
$431$	−2.25262e6	−0.584111	−0.292056	+	0.956401i	$0.594339\pi$
$432$	842261.	0.217139
$433$	−720129.	−0.184582	−0.0922912	−	0.995732i	$-0.529419\pi$
$433$	−720129.	−0.184582	−0.0922912	+	0.995732i	$0.529419\pi$
$434$	−6.32410e6	−1.61166
$435$	1.15362e6	0.292309
$436$	−653371.	−0.164605
$437$	−156643.	−0.0392381
$438$	−143051.	−0.0356291
$439$	1.48562e6	0.367913	0.183957	−	0.982934i	$-0.441109\pi$
$439$	1.48562e6	0.367913	0.183957	+	0.982934i	$0.441109\pi$
$440$	452288.	0.111374
$441$	526678.	0.128958
$442$	−3.77952e6	−0.920199
$443$	5.34112e6	1.29307	0.646536	−	0.762884i	$-0.276217\pi$
$443$	5.34112e6	1.29307	0.646536	+	0.762884i	$0.276217\pi$
$444$	−686422.	−0.165247
$445$	916548.	0.219409
$446$	952508.	0.226742
$447$	−2.08100e6	−0.492609
$448$	−4.03552e6	−0.949957
$449$	−2.91837e6	−0.683163	−0.341582	−	0.939852i	$-0.610963\pi$
$449$	−2.91837e6	−0.683163	−0.341582	+	0.939852i	$0.610963\pi$
$450$	1.20220e6	0.279862
$451$	−368845.	−0.0853890
$452$	−677563.	−0.155992
$453$	−4.00414e6	−0.916776
$454$	−4.75856e6	−1.08352
$455$	2.31772e6	0.524847
$456$	−579845.	−0.130587
$457$	4.95434e6	1.10967	0.554837	−	0.831959i	$-0.312781\pi$
$457$	4.95434e6	1.10967	0.554837	+	0.831959i	$0.312781\pi$
$458$	4.03274e6	0.898332
$459$	779562.	0.172711
$460$	−50532.9	−0.0111347
$461$	8.92176e6	1.95523	0.977616	−	0.210396i	$-0.0674755\pi$
$461$	8.92176e6	1.95523	0.977616	+	0.210396i	$0.0674755\pi$
$462$	−877622.	−0.191295
$463$	−4.66737e6	−1.01186	−0.505929	−	0.862575i	$-0.668850\pi$
$463$	−4.66737e6	−1.01186	−0.505929	+	0.862575i	$0.668850\pi$
$464$	5.68096e6	1.22497
$465$	1.60126e6	0.343423
$466$	5.97728e6	1.27508
$467$	−1.63053e6	−0.345968	−0.172984	−	0.984925i	$-0.555341\pi$
$467$	−1.63053e6	−0.345968	−0.172984	+	0.984925i	$0.555341\pi$
$468$	−228111.	−0.0481428
$469$	−3.15548e6	−0.662420
$470$	−1.22160e6	−0.255085
$471$	−3.20803e6	−0.666325
$472$	573898.	0.118571
$473$	1.07842e6	0.221633
$474$	287603.	0.0587960
$475$	−955637.	−0.194339
$476$	789532.	0.159717
$477$	1.45463e6	0.292723
$478$	9.18390e6	1.83847
$479$	−2.82698e6	−0.562969	−0.281484	−	0.959566i	$-0.590827\pi$
$479$	−2.82698e6	−0.562969	−0.281484	+	0.959566i	$0.590827\pi$
$480$	−407416.	−0.0807115
$481$	−9.18425e6	−1.81001
$482$	−2.38257e6	−0.467119
$483$	−550780.	−0.107426
$484$	−725280.	−0.140732
$485$	3.29163e6	0.635414
$486$	358384.	0.0688268
$487$	9.05496e6	1.73007	0.865036	−	0.501710i	$-0.167296\pi$
$487$	9.05496e6	1.73007	0.865036	+	0.501710i	$0.167296\pi$
$488$	7.51370e6	1.42825
$489$	−993523.	−0.187891
$490$	−1.02876e6	−0.193564
$491$	5.23566e6	0.980094	0.490047	−	0.871696i	$-0.336980\pi$
$491$	5.23566e6	0.980094	0.490047	+	0.871696i	$0.336980\pi$
$492$	152547.	0.0284113
$493$	5.25807e6	0.974336
$494$	1.38119e6	0.254645
$495$	222213.	0.0407621
$496$	7.88530e6	1.43918
$497$	6.02508e6	1.09414
$498$	5.35319e6	0.967251
$499$	6.52056e6	1.17229	0.586143	−	0.810208i	$-0.300646\pi$
$499$	6.52056e6	1.17229	0.586143	+	0.810208i	$0.300646\pi$
$500$	−702248.	−0.125622
$501$	−1.48444e6	−0.264222
$502$	1.45251e6	0.257252
$503$	8.90079e6	1.56859	0.784294	−	0.620390i	$-0.213026\pi$
$503$	8.90079e6	1.56859	0.784294	+	0.620390i	$0.213026\pi$
$504$	−2.03882e6	−0.357522
$505$	−1.75710e6	−0.306597
$506$	256020.	0.0444526
$507$	289539.	0.0500249
$508$	1.45225e6	0.249679
$509$	4.51848e6	0.773033	0.386516	−	0.922283i	$-0.373678\pi$
$509$	4.51848e6	0.773033	0.386516	+	0.922283i	$0.373678\pi$
$510$	−1.52272e6	−0.259236
$511$	399830.	0.0677365
$512$	4.08906e6	0.689364
$513$	−284883.	−0.0477940
$514$	717968.	0.119866
$515$	−3.18426e6	−0.529043
$516$	−446012.	−0.0737433
$517$	812530.	0.133694
$518$	1.46139e7	2.39299
$519$	−3.89634e6	−0.634948
$520$	−2.50281e6	−0.405900
$521$	−3.74138e6	−0.603862	−0.301931	−	0.953330i	$-0.597631\pi$
$521$	−3.74138e6	−0.603862	−0.301931	+	0.953330i	$0.597631\pi$
$522$	2.41726e6	0.388282
$523$	−1.64299e6	−0.262653	−0.131326	−	0.991339i	$-0.541924\pi$
$523$	−1.64299e6	−0.262653	−0.131326	+	0.991339i	$0.541924\pi$
$524$	−117158.	−0.0186400
$525$	−3.36016e6	−0.532062
$526$	−1.03445e6	−0.163022
$527$	7.29831e6	1.14471
$528$	1.09428e6	0.170821
$529$	−6.27567e6	−0.975037
$530$	−2.84134e6	−0.439373
$531$	281961.	0.0433963
$532$	−288526.	−0.0441984
$533$	2.04106e6	0.311199
$534$	1.92050e6	0.291448
$535$	2.82625e6	0.426900
$536$	3.40747e6	0.512295
$537$	−2.98297e6	−0.446389
$538$	−7.07964e6	−1.05452
$539$	684267.	0.101450
$540$	−91903.0	−0.0135627
$541$	896593.	0.131705	0.0658525	−	0.997829i	$-0.479023\pi$
$541$	896593.	0.131705	0.0658525	+	0.997829i	$0.479023\pi$
$542$	−153132.	−0.0223907
$543$	−1.23147e6	−0.179235
$544$	−1.85695e6	−0.269031
$545$	−3.52205e6	−0.507931
$546$	4.85646e6	0.697170
$547$	−3.23932e6	−0.462898	−0.231449	−	0.972847i	$-0.574347\pi$
$547$	−3.23932e6	−0.462898	−0.231449	+	0.972847i	$0.574347\pi$
$548$	−1.15566e6	−0.164391
$549$	3.69155e6	0.522730
$550$	1.56191e6	0.220165
$551$	−1.92151e6	−0.269627
$552$	594765.	0.0830802
$553$	−803857.	−0.111780
$554$	721445.	0.0998685
$555$	−3.70022e6	−0.509912
$556$	64542.3	0.00885436
$557$	−1.14366e6	−0.156192	−0.0780958	−	0.996946i	$-0.524884\pi$
$557$	−1.14366e6	−0.156192	−0.0780958	+	0.996946i	$0.524884\pi$
$558$	3.35522e6	0.456179
$559$	−5.96760e6	−0.807737
$560$	4.59835e6	0.619629
$561$	1.01282e6	0.135870
$562$	2.98837e6	0.399111
$563$	3.50782e6	0.466408	0.233204	−	0.972428i	$-0.425079\pi$
$563$	3.50782e6	0.466408	0.233204	+	0.972428i	$0.425079\pi$
$564$	−336047.	−0.0444838
$565$	−3.65247e6	−0.481354
$566$	−3.23009e6	−0.423812
$567$	−1.00169e6	−0.130851
$568$	−6.50624e6	−0.846173
$569$	2.53909e6	0.328774	0.164387	−	0.986396i	$-0.447435\pi$
$569$	2.53909e6	0.328774	0.164387	+	0.986396i	$0.447435\pi$
$570$	556464.	0.0717381
$571$	1.08743e7	1.39576	0.697882	−	0.716212i	$-0.254126\pi$
$571$	1.08743e7	1.39576	0.697882	+	0.716212i	$0.254126\pi$
$572$	−296365.	−0.0378736
$573$	−6.99983e6	−0.890637
$574$	−3.24771e6	−0.411432
$575$	980226.	0.123639
$576$	2.14102e6	0.268884
$577$	−207945.	−0.0260021	−0.0130011	−	0.999915i	$-0.504138\pi$
$577$	−207945.	−0.0260021	−0.0130011	+	0.999915i	$0.504138\pi$
$578$	1.67712e6	0.208807
$579$	3.62315e6	0.449149
$580$	−619876.	−0.0765130
$581$	−1.49623e7	−1.83890
$582$	6.89717e6	0.844040
$583$	1.88987e6	0.230283
$584$	−431759.	−0.0523853
$585$	−1.22965e6	−0.148557
$586$	−1.03192e6	−0.124137
$587$	−1.05248e7	−1.26071	−0.630357	−	0.776305i	$-0.717092\pi$
$587$	−1.05248e7	−1.26071	−0.630357	+	0.776305i	$0.717092\pi$
$588$	−282999.	−0.0337553
$589$	−2.66709e6	−0.316774
$590$	−550756.	−0.0651372
$591$	3.01943e6	0.355596
$592$	−1.82215e7	−2.13688
$593$	−1.40794e7	−1.64418	−0.822089	−	0.569359i	$-0.807191\pi$
$593$	−1.40794e7	−1.64418	−0.822089	+	0.569359i	$0.807191\pi$
$594$	465617.	0.0541456
$595$	4.25604e6	0.492849
$596$	1.11818e6	0.128943
$597$	−5.78609e6	−0.664430
$598$	−1.41673e6	−0.162007
$599$	−7.81286e6	−0.889699	−0.444849	−	0.895605i	$-0.646743\pi$
$599$	−7.81286e6	−0.889699	−0.444849	+	0.895605i	$0.646743\pi$
$600$	3.62850e6	0.411480
$601$	1.10899e7	1.25239	0.626196	−	0.779666i	$-0.284611\pi$
$601$	1.10899e7	1.25239	0.626196	+	0.779666i	$0.284611\pi$
$602$	9.49557e6	1.06790
$603$	1.67412e6	0.187497
$604$	2.15154e6	0.239970
$605$	−3.90969e6	−0.434264
$606$	−3.68176e6	−0.407262
$607$	729204.	0.0803299	0.0401649	−	0.999193i	$-0.487212\pi$
$607$	729204.	0.0803299	0.0401649	+	0.999193i	$0.487212\pi$
$608$	678603.	0.0744486
$609$	−6.75630e6	−0.738186
$610$	−7.21072e6	−0.784611
$611$	−4.49627e6	−0.487247
$612$	−418881.	−0.0452077
$613$	1.53130e7	1.64593	0.822963	−	0.568096i	$-0.192320\pi$
$613$	1.53130e7	1.64593	0.822963	+	0.568096i	$0.192320\pi$
$614$	717142.	0.0767687
$615$	822318.	0.0876702
$616$	−2.64886e6	−0.281260
$617$	2.52522e6	0.267046	0.133523	−	0.991046i	$-0.457371\pi$
$617$	2.52522e6	0.267046	0.133523	+	0.991046i	$0.457371\pi$
$618$	−6.67219e6	−0.702744
$619$	6.17194e6	0.647433	0.323717	−	0.946154i	$-0.395068\pi$
$619$	6.17194e6	0.647433	0.323717	+	0.946154i	$0.395068\pi$
$620$	−860402.	−0.0898923
$621$	292213.	0.0304068
$622$	1.21498e7	1.25920
$623$	−5.36784e6	−0.554089
$624$	−6.05535e6	−0.622555
$625$	3.85642e6	0.394897
$626$	−2.06680e7	−2.10796
$627$	−370124.	−0.0375991
$628$	1.72377e6	0.174413
$629$	−1.68651e7	−1.69966
$630$	1.95661e6	0.196405
$631$	8.46974e6	0.846831	0.423416	−	0.905936i	$-0.360831\pi$
$631$	8.46974e6	0.846831	0.423416	+	0.905936i	$0.360831\pi$
$632$	868051.	0.0864475
$633$	−8.14741e6	−0.808184
$634$	2.39243e6	0.236383
$635$	7.82850e6	0.770449
$636$	−781615.	−0.0766214
$637$	−3.78650e6	−0.369734
$638$	3.14054e6	0.305459
$639$	−3.19657e6	−0.309694
$640$	−5.63066e6	−0.543387
$641$	2.80019e6	0.269180	0.134590	−	0.990901i	$-0.457028\pi$
$641$	2.80019e6	0.269180	0.134590	+	0.990901i	$0.457028\pi$
$642$	5.92202e6	0.567064
$643$	−2.94663e6	−0.281059	−0.140530	−	0.990076i	$-0.544880\pi$
$643$	−2.94663e6	−0.281059	−0.140530	+	0.990076i	$0.544880\pi$
$644$	295950.	0.0281193
$645$	−2.40427e6	−0.227554
$646$	2.53629e6	0.239121
$647$	247037.	0.0232007	0.0116003	−	0.999933i	$-0.496307\pi$
$647$	247037.	0.0232007	0.0116003	+	0.999933i	$0.496307\pi$
$648$	1.08168e6	0.101196
$649$	366327.	0.0341395
$650$	−8.64307e6	−0.802388
$651$	−9.37790e6	−0.867267
$652$	533849.	0.0491812
$653$	4.06721e6	0.373262	0.186631	−	0.982430i	$-0.440243\pi$
$653$	4.06721e6	0.373262	0.186631	+	0.982430i	$0.440243\pi$
$654$	−7.37998e6	−0.674700
$655$	−631553.	−0.0575184
$656$	4.04946e6	0.367398
$657$	−212127.	−0.0191727
$658$	7.15441e6	0.644183
$659$	−1.80835e7	−1.62207	−0.811034	−	0.584998i	$-0.801095\pi$
$659$	−1.80835e7	−1.62207	−0.811034	+	0.584998i	$0.801095\pi$
$660$	−119402.	−0.0106697
$661$	5.40254e6	0.480944	0.240472	−	0.970656i	$-0.422698\pi$
$661$	5.40254e6	0.480944	0.240472	+	0.970656i	$0.422698\pi$
$662$	1.37973e7	1.22363
$663$	−5.60459e6	−0.495176
$664$	1.61571e7	1.42215
$665$	−1.55533e6	−0.136385
$666$	−7.75331e6	−0.677332
$667$	1.97095e6	0.171538
$668$	797633.	0.0691611
$669$	1.41246e6	0.122014
$670$	−3.27007e6	−0.281430
$671$	4.79611e6	0.411228
$672$	2.38607e6	0.203826
$673$	−1.78587e7	−1.51989	−0.759946	−	0.649986i	$-0.774775\pi$
$673$	−1.78587e7	−1.51989	−0.759946	+	0.649986i	$0.774775\pi$
$674$	7.01472e6	0.594786
$675$	1.78271e6	0.150599
$676$	−155577.	−0.0130942
$677$	−1.84660e7	−1.54846	−0.774231	−	0.632903i	$-0.781863\pi$
$677$	−1.84660e7	−1.54846	−0.774231	+	0.632903i	$0.781863\pi$
$678$	−7.65324e6	−0.639398
$679$	−1.92777e7	−1.60465
$680$	−4.59592e6	−0.381154
$681$	−7.05639e6	−0.583062
$682$	4.35914e6	0.358872
$683$	−1.20352e7	−0.987193	−0.493596	−	0.869691i	$-0.664318\pi$
$683$	−1.20352e7	−0.987193	−0.493596	+	0.869691i	$0.664318\pi$
$684$	153076.	0.0125103
$685$	−6.22967e6	−0.507270
$686$	−9.54859e6	−0.774692
$687$	5.98008e6	0.483410
$688$	−1.18397e7	−0.953607
$689$	−1.04579e7	−0.839262
$690$	−570782.	−0.0456402
$691$	9.13181e6	0.727548	0.363774	−	0.931487i	$-0.381488\pi$
$691$	9.13181e6	0.727548	0.363774	+	0.931487i	$0.381488\pi$
$692$	2.09362e6	0.166200
$693$	−1.30141e6	−0.102939
$694$	−1.99377e7	−1.57136
$695$	347921.	0.0273224
$696$	7.29585e6	0.570890
$697$	3.74801e6	0.292226
$698$	−2.36096e7	−1.83422
$699$	8.86359e6	0.686146
$700$	1.80551e6	0.139269
$701$	−1.78286e7	−1.37032	−0.685160	−	0.728393i	$-0.740268\pi$
$701$	−1.78286e7	−1.37032	−0.685160	+	0.728393i	$0.740268\pi$
$702$	−2.57657e6	−0.197333
$703$	6.16318e6	0.470345
$704$	2.78164e6	0.211529
$705$	−1.81149e6	−0.137266
$706$	1.70079e7	1.28422
$707$	1.02906e7	0.774270
$708$	−151506.	−0.0113592
$709$	1.63081e7	1.21839	0.609197	−	0.793019i	$-0.291492\pi$
$709$	1.63081e7	1.21839	0.609197	+	0.793019i	$0.291492\pi$
$710$	6.24388e6	0.464846
$711$	426481.	0.0316392
$712$	5.79651e6	0.428515
$713$	2.73572e6	0.201534
$714$	8.91796e6	0.654666
$715$	−1.59758e6	−0.116869
$716$	1.60284e6	0.116844
$717$	1.36186e7	0.989317
$718$	−4.07380e6	−0.294909
$719$	−2.01650e7	−1.45471	−0.727356	−	0.686261i	$-0.759251\pi$
$719$	−2.01650e7	−1.45471	−0.727356	+	0.686261i	$0.759251\pi$
$720$	−2.43963e6	−0.175385
$721$	1.86489e7	1.33603
$722$	1.41012e7	1.00673
$723$	−3.53306e6	−0.251366
$724$	661703.	0.0469155
$725$	1.20242e7	0.849595
$726$	−8.19221e6	−0.576846
$727$	−2.39725e7	−1.68220	−0.841098	−	0.540883i	$-0.818090\pi$
$727$	−2.39725e7	−1.68220	−0.841098	+	0.540883i	$0.818090\pi$
$728$	1.46579e7	1.02505
$729$	531441.	0.0370370
$730$	414350.	0.0287779
$731$	−1.09583e7	−0.758492
$732$	−1.98358e6	−0.136827
$733$	872995.	0.0600139	0.0300069	−	0.999550i	$-0.490447\pi$
$733$	872995.	0.0600139	0.0300069	+	0.999550i	$0.490447\pi$
$734$	3.90178e6	0.267315
$735$	−1.52553e6	−0.104161
$736$	−696064.	−0.0473647
$737$	2.17504e6	0.147502
$738$	1.72305e6	0.116455
$739$	1.39258e7	0.938015	0.469007	−	0.883194i	$-0.344612\pi$
$739$	1.39258e7	0.938015	0.469007	+	0.883194i	$0.344612\pi$
$740$	1.98824e6	0.133472
$741$	2.04814e6	0.137029
$742$	1.66405e7	1.10958
$743$	−2.00248e7	−1.33075	−0.665374	−	0.746510i	$-0.731728\pi$
$743$	−2.00248e7	−1.33075	−0.665374	+	0.746510i	$0.731728\pi$
$744$	1.01268e7	0.670718
$745$	6.02766e6	0.397885
$746$	1.86988e7	1.23017
$747$	7.93815e6	0.520496
$748$	−544216.	−0.0355646
$749$	−1.65522e7	−1.07808
$750$	−7.93206e6	−0.514912
$751$	1.08500e7	0.701986	0.350993	−	0.936378i	$-0.385844\pi$
$751$	1.08500e7	0.701986	0.350993	+	0.936378i	$0.385844\pi$
$752$	−8.92058e6	−0.575239
$753$	2.15390e6	0.138432
$754$	−1.73787e7	−1.11324
$755$	1.15981e7	0.740488
$756$	538238.	0.0342507
$757$	2.29213e7	1.45378	0.726892	−	0.686751i	$-0.240964\pi$
$757$	2.29213e7	1.45378	0.726892	+	0.686751i	$0.240964\pi$
$758$	1.61579e7	1.02144
$759$	379647.	0.0239208
$760$	1.67953e6	0.105476
$761$	1.09281e7	0.684042	0.342021	−	0.939692i	$-0.388889\pi$
$761$	1.09281e7	0.684042	0.342021	+	0.939692i	$0.388889\pi$
$762$	1.64035e7	1.02341
$763$	2.06272e7	1.28271
$764$	3.76121e6	0.233128
$765$	−2.25802e6	−0.139500
$766$	−5.73061e6	−0.352881
$767$	−2.02713e6	−0.124421
$768$	−4.18576e6	−0.256077
$769$	−1.73650e7	−1.05891	−0.529453	−	0.848339i	$-0.677603\pi$
$769$	−1.73650e7	−1.05891	−0.529453	+	0.848339i	$0.677603\pi$
$770$	2.54205e6	0.154510
$771$	1.06466e6	0.0645024
$772$	−1.94683e6	−0.117567
$773$	−1.45083e7	−0.873308	−0.436654	−	0.899629i	$-0.643837\pi$
$773$	−1.45083e7	−0.873308	−0.436654	+	0.899629i	$0.643837\pi$
$774$	−5.03782e6	−0.302267
$775$	1.66899e7	0.998158
$776$	2.08172e7	1.24099
$777$	2.16707e7	1.28771
$778$	1.92662e7	1.14116
$779$	−1.36967e6	−0.0808674
$780$	660728.	0.0388854
$781$	−4.15303e6	−0.243634
$782$	−2.60155e6	−0.152130
$783$	3.58451e6	0.208942
$784$	−7.51240e6	−0.436504
$785$	9.29213e6	0.538197
$786$	−1.32333e6	−0.0764034
$787$	1.28648e6	0.0740401	0.0370200	−	0.999315i	$-0.488213\pi$
$787$	1.28648e6	0.0740401	0.0370200	+	0.999315i	$0.488213\pi$
$788$	−1.62243e6	−0.0930787
$789$	−1.53397e6	−0.0877252
$790$	−833049.	−0.0474900
$791$	2.13910e7	1.21560
$792$	1.40534e6	0.0796100
$793$	−2.65400e7	−1.49871
$794$	−2.17196e7	−1.22265
$795$	−4.21337e6	−0.236435
$796$	3.10903e6	0.173917
$797$	1.58057e6	0.0881389	0.0440694	−	0.999028i	$-0.485968\pi$
$797$	1.58057e6	0.0881389	0.0440694	+	0.999028i	$0.485968\pi$
$798$	−3.25898e6	−0.181165
$799$	−8.25653e6	−0.457541
$800$	−4.24650e6	−0.234588
$801$	2.84788e6	0.156834
$802$	2.94229e7	1.61529
$803$	−275599.	−0.0150830
$804$	−899554.	−0.0490780
$805$	1.59535e6	0.0867692
$806$	−2.41220e7	−1.30790
$807$	−1.04983e7	−0.567458
$808$	−1.11124e7	−0.598796
$809$	−7.43750e6	−0.399536	−0.199768	−	0.979843i	$-0.564019\pi$
$809$	−7.43750e6	−0.399536	−0.199768	+	0.979843i	$0.564019\pi$
$810$	−1.03807e6	−0.0555921
$811$	2.65806e7	1.41910	0.709551	−	0.704654i	$-0.248898\pi$
$811$	2.65806e7	1.41910	0.709551	+	0.704654i	$0.248898\pi$
$812$	3.63036e6	0.193223
$813$	−227077.	−0.0120489
$814$	−1.00732e7	−0.532852
$815$	2.87776e6	0.151761
$816$	−1.11195e7	−0.584601
$817$	4.00461e6	0.209897
$818$	1.44521e7	0.755174
$819$	7.20156e6	0.375160
$820$	−441855.	−0.0229480
$821$	−1.67822e7	−0.868942	−0.434471	−	0.900686i	$-0.643065\pi$
$821$	−1.67822e7	−0.868942	−0.434471	+	0.900686i	$0.643065\pi$
$822$	−1.30534e7	−0.673822
$823$	1.25067e7	0.643642	0.321821	−	0.946801i	$-0.395705\pi$
$823$	1.25067e7	0.643642	0.321821	+	0.946801i	$0.395705\pi$
$824$	−2.01382e7	−1.03324
$825$	2.31612e6	0.118475
$826$	3.22555e6	0.164495
$827$	2.95809e7	1.50400	0.752000	−	0.659163i	$-0.229089\pi$
$827$	2.95809e7	1.50400	0.752000	+	0.659163i	$0.229089\pi$
$828$	−157015.	−0.00795911
$829$	2.33450e7	1.17980	0.589898	−	0.807478i	$-0.299168\pi$
$829$	2.33450e7	1.17980	0.589898	+	0.807478i	$0.299168\pi$
$830$	−1.55056e7	−0.781257
$831$	1.06982e6	0.0537411
$832$	−1.53927e7	−0.770913
$833$	−6.95317e6	−0.347193
$834$	729021.	0.0362932
$835$	4.29971e6	0.213414
$836$	198878.	0.00984173
$837$	4.97539e6	0.245478
$838$	3.09919e6	0.152454
$839$	−2.47748e7	−1.21508	−0.607541	−	0.794289i	$-0.707844\pi$
$839$	−2.47748e7	−1.21508	−0.607541	+	0.794289i	$0.707844\pi$
$840$	5.90549e6	0.288774
$841$	3.66603e6	0.178733
$842$	1.71316e7	0.832754
$843$	4.43140e6	0.214769
$844$	4.37784e6	0.211545
$845$	−838655.	−0.0404056
$846$	−3.79573e6	−0.182335
$847$	2.28974e7	1.09667
$848$	−2.07485e7	−0.990825
$849$	−4.78984e6	−0.228061
$850$	−1.58713e7	−0.753470
$851$	−6.32176e6	−0.299236
$852$	1.71761e6	0.0810636
$853$	−7.94099e6	−0.373682	−0.186841	−	0.982390i	$-0.559825\pi$
$853$	−7.94099e6	−0.373682	−0.186841	+	0.982390i	$0.559825\pi$
$854$	4.22302e7	1.98143
$855$	825170.	0.0386036
$856$	1.78740e7	0.833752
$857$	2.65740e7	1.23596	0.617981	−	0.786193i	$-0.287951\pi$
$857$	2.65740e7	1.23596	0.617981	+	0.786193i	$0.287951\pi$
$858$	−3.34751e6	−0.155240
$859$	−2.41374e7	−1.11611	−0.558057	−	0.829803i	$-0.688453\pi$
$859$	−2.41374e7	−1.11611	−0.558057	+	0.829803i	$0.688453\pi$
$860$	1.29188e6	0.0595631
$861$	−4.81597e6	−0.221399
$862$	1.36718e7	0.626696
$863$	2.16716e7	0.990522	0.495261	−	0.868744i	$-0.335072\pi$
$863$	2.16716e7	0.990522	0.495261	+	0.868744i	$0.335072\pi$
$864$	−1.26591e6	−0.0576926
$865$	1.12858e7	0.512853
$866$	4.37065e6	0.198039
$867$	2.48697e6	0.112363
$868$	5.03902e6	0.227011
$869$	554090.	0.0248903
$870$	−7.00165e6	−0.313619
$871$	−1.20359e7	−0.537569
$872$	−2.22745e7	−0.992009
$873$	1.02277e7	0.454194
$874$	950708.	0.0420987
$875$	2.21703e7	0.978929
$876$	113982.	0.00501853
$877$	760211.	0.0333761	0.0166880	−	0.999861i	$-0.494688\pi$
$877$	760211.	0.0333761	0.0166880	+	0.999861i	$0.494688\pi$
$878$	−9.01660e6	−0.394736
$879$	−1.53022e6	−0.0668006
$880$	−3.16959e6	−0.137974
$881$	2.14521e7	0.931171	0.465585	−	0.885003i	$-0.345844\pi$
$881$	2.14521e7	0.931171	0.465585	+	0.885003i	$0.345844\pi$
$882$	−3.19655e6	−0.138360
$883$	2.44065e7	1.05343	0.526713	−	0.850043i	$-0.323424\pi$
$883$	2.44065e7	1.05343	0.526713	+	0.850043i	$0.323424\pi$
$884$	3.01151e6	0.129614
$885$	−816706.	−0.0350516
$886$	−3.24166e7	−1.38734
$887$	−3.14967e7	−1.34417	−0.672087	−	0.740472i	$-0.734602\pi$
$887$	−3.14967e7	−1.34417	−0.672087	+	0.740472i	$0.734602\pi$
$888$	−2.34012e7	−0.995878
$889$	−4.58482e7	−1.94567
$890$	−5.56277e6	−0.235405
$891$	690455.	0.0291368
$892$	−758954.	−0.0319377
$893$	3.01726e6	0.126615
$894$	1.26301e7	0.528523
$895$	8.64024e6	0.360552
$896$	3.29764e7	1.37225
$897$	−2.10084e6	−0.0871790
$898$	1.77124e7	0.732969
$899$	3.35585e7	1.38485
$900$	−957904.	−0.0394199
$901$	−1.92040e7	−0.788096
$902$	2.23861e6	0.0916143
$903$	1.40808e7	0.574656
$904$	−2.30992e7	−0.940104
$905$	3.56697e6	0.144770
$906$	2.43022e7	0.983613
$907$	1.45980e7	0.589215	0.294608	−	0.955618i	$-0.404811\pi$
$907$	1.45980e7	0.589215	0.294608	+	0.955618i	$0.404811\pi$
$908$	3.79160e6	0.152619
$909$	−5.45962e6	−0.219156
$910$	−1.40669e7	−0.563110
$911$	−4.38637e7	−1.75109	−0.875546	−	0.483135i	$-0.839498\pi$
$911$	−4.38637e7	−1.75109	−0.875546	+	0.483135i	$0.839498\pi$
$912$	4.06350e6	0.161776
$913$	1.03133e7	0.409470
$914$	−3.00692e7	−1.19057
$915$	−1.06926e7	−0.422214
$916$	−3.21327e6	−0.126534
$917$	3.69874e6	0.145255
$918$	−4.73137e6	−0.185302
$919$	7.90937e6	0.308925	0.154463	−	0.987999i	$-0.450635\pi$
$919$	7.90937e6	0.308925	0.154463	+	0.987999i	$0.450635\pi$
$920$	−1.72275e6	−0.0671046
$921$	1.06344e6	0.0413107
$922$	−5.41485e7	−2.09778
$923$	2.29815e7	0.887919
$924$	699285.	0.0269448
$925$	−3.85674e7	−1.48206
$926$	2.83275e7	1.08563
$927$	−9.89407e6	−0.378160
$928$	−8.53846e6	−0.325469
$929$	−2.76806e7	−1.05229	−0.526146	−	0.850394i	$-0.676364\pi$
$929$	−2.76806e7	−1.05229	−0.526146	+	0.850394i	$0.676364\pi$
$930$	−9.71845e6	−0.368460
$931$	2.54097e6	0.0960782
$932$	−4.76267e6	−0.179602
$933$	1.80167e7	0.677597
$934$	9.89610e6	0.371190
$935$	−2.93365e6	−0.109744
$936$	−7.77666e6	−0.290137
$937$	−5.16566e6	−0.192211	−0.0961053	−	0.995371i	$-0.530639\pi$
$937$	−5.16566e6	−0.192211	−0.0961053	+	0.995371i	$0.530639\pi$
$938$	1.91514e7	0.710713
$939$	−3.06482e7	−1.13433
$940$	973367.	0.0359300
$941$	−2.70233e7	−0.994865	−0.497433	−	0.867503i	$-0.665724\pi$
$941$	−2.70233e7	−0.994865	−0.497433	+	0.867503i	$0.665724\pi$
$942$	1.94704e7	0.714903
$943$	1.40492e6	0.0514483
$944$	−4.02182e6	−0.146890
$945$	2.90142e6	0.105689
$946$	−6.54520e6	−0.237791
$947$	−2.07792e7	−0.752930	−0.376465	−	0.926431i	$-0.622860\pi$
$947$	−2.07792e7	−0.752930	−0.376465	+	0.926431i	$0.622860\pi$
$948$	−229161.	−0.00828170
$949$	1.52507e6	0.0549698
$950$	5.80001e6	0.208507
$951$	3.54769e6	0.127202
$952$	2.69164e7	0.962553
$953$	4.60122e7	1.64112	0.820560	−	0.571560i	$-0.193661\pi$
$953$	4.60122e7	1.64112	0.820560	+	0.571560i	$0.193661\pi$
$954$	−8.82854e6	−0.314064
$955$	2.02751e7	0.719375
$956$	−7.31769e6	−0.258958
$957$	4.65705e6	0.164373
$958$	1.71577e7	0.604012
$959$	3.64846e7	1.28104
$960$	−6.20151e6	−0.217180
$961$	1.79508e7	0.627010
$962$	5.57417e7	1.94197
$963$	8.78165e6	0.305148
$964$	1.89842e6	0.0657960
$965$	−1.04945e7	−0.362782
$966$	3.34283e6	0.115258
$967$	3.55492e7	1.22254	0.611271	−	0.791422i	$-0.290659\pi$
$967$	3.55492e7	1.22254	0.611271	+	0.791422i	$0.290659\pi$
$968$	−2.47260e7	−0.848134
$969$	3.76101e6	0.128675
$970$	−1.99778e7	−0.681739
$971$	2.58132e7	0.878606	0.439303	−	0.898339i	$-0.355225\pi$
$971$	2.58132e7	0.878606	0.439303	+	0.898339i	$0.355225\pi$
$972$	−285559.	−0.00969460
$973$	−2.03763e6	−0.0689990
$974$	−5.49569e7	−1.85620
$975$	−1.28167e7	−0.431780
$976$	−5.26553e7	−1.76937
$977$	2.97056e7	0.995641	0.497820	−	0.867280i	$-0.334134\pi$
$977$	2.97056e7	0.995641	0.497820	+	0.867280i	$0.334134\pi$
$978$	6.02995e6	0.201589
$979$	3.70000e6	0.123380
$980$	819714.	0.0272645
$981$	−1.09436e7	−0.363069
$982$	−3.17766e7	−1.05155
$983$	3.72568e7	1.22976	0.614882	−	0.788619i	$-0.289204\pi$
$983$	3.72568e7	1.22976	0.614882	+	0.788619i	$0.289204\pi$
$984$	5.20057e6	0.171223
$985$	−8.74586e6	−0.287218
$986$	−3.19126e7	−1.04537
$987$	1.06091e7	0.346647
$988$	−1.10052e6	−0.0358680
$989$	−4.10765e6	−0.133537
$990$	−1.34867e6	−0.0437339
$991$	5.24786e7	1.69745	0.848727	−	0.528831i	$-0.177370\pi$
$991$	5.24786e7	1.69745	0.848727	+	0.528831i	$0.177370\pi$
$992$	−1.18516e7	−0.382382
$993$	2.04598e7	0.658457
$994$	−3.65678e7	−1.17391
$995$	1.67595e7	0.536666
$996$	−4.26540e6	−0.136242
$997$	1.26015e7	0.401500	0.200750	−	0.979643i	$-0.435662\pi$
$997$	1.26015e7	0.401500	0.200750	+	0.979643i	$0.435662\pi$
$998$	−3.95750e7	−1.25775
$999$	−1.14972e7	−0.364485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.d.1.5	✓	13
3.2	odd	2		531.6.a.e.1.9		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.d.1.5	✓	13	1.1	even	1	trivial
531.6.a.e.1.9		13	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)

\(f(q)\)	\(=\)	\(q-6.06926 q^{2} -9.00000 q^{3} +4.83596 q^{4} +26.0687 q^{5} +54.6234 q^{6} -152.673 q^{7} +164.866 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-6.06926 q^{2} -9.00000 q^{3} +4.83596 q^{4} +26.0687 q^{5} +54.6234 q^{6} -152.673 q^{7} +164.866 q^{8} +81.0000 q^{9} -158.218 q^{10} +105.236 q^{11} -43.5237 q^{12} -582.342 q^{13} +926.616 q^{14} -234.618 q^{15} -1155.36 q^{16} -1069.36 q^{17} -491.610 q^{18} +390.786 q^{19} +126.067 q^{20} +1374.06 q^{21} -638.707 q^{22} -400.841 q^{23} -1483.79 q^{24} -2445.42 q^{25} +3534.39 q^{26} -729.000 q^{27} -738.323 q^{28} -4917.03 q^{29} +1423.96 q^{30} -6824.95 q^{31} +1736.51 q^{32} -947.126 q^{33} +6490.22 q^{34} -3980.00 q^{35} +391.713 q^{36} +15771.2 q^{37} -2371.78 q^{38} +5241.08 q^{39} +4297.83 q^{40} -3504.92 q^{41} -8339.54 q^{42} +10247.6 q^{43} +508.919 q^{44} +2111.56 q^{45} +2432.81 q^{46} +7721.01 q^{47} +10398.3 q^{48} +6502.19 q^{49} +14841.9 q^{50} +9624.22 q^{51} -2816.18 q^{52} +17958.4 q^{53} +4424.49 q^{54} +2743.37 q^{55} -25170.6 q^{56} -3517.07 q^{57} +29842.7 q^{58} +3481.00 q^{59} -1134.61 q^{60} +45574.7 q^{61} +41422.4 q^{62} -12366.6 q^{63} +26432.3 q^{64} -15180.9 q^{65} +5748.36 q^{66} +20668.2 q^{67} -5171.38 q^{68} +3607.57 q^{69} +24155.7 q^{70} -39463.9 q^{71} +13354.1 q^{72} -2618.86 q^{73} -95719.8 q^{74} +22008.8 q^{75} +1889.83 q^{76} -16066.8 q^{77} -31809.5 q^{78} +5265.20 q^{79} -30118.8 q^{80} +6561.00 q^{81} +21272.3 q^{82} +98001.8 q^{83} +6644.91 q^{84} -27876.8 q^{85} -62195.3 q^{86} +44253.3 q^{87} +17349.8 q^{88} +35159.0 q^{89} -12815.6 q^{90} +88908.2 q^{91} -1938.45 q^{92} +61424.5 q^{93} -46860.9 q^{94} +10187.3 q^{95} -15628.6 q^{96} +126268. q^{97} -39463.5 q^{98} +8524.14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9}+O(q^{10}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9	\( 13 q - 117 q^{3} + 246 q^{4} - 14 q^{5} + 373 q^{7} + 123 q^{8} + 1053 q^{9} + 137 q^{10} + 250 q^{11} - 2214 q^{12} + 1054 q^{13} - 575 q^{14} + 126 q^{15} + 922 q^{16} + 271 q^{17} + 671 q^{19} - 5491 q^{20} - 3357 q^{21} + 1094 q^{22} + 3975 q^{23} - 1107 q^{24} + 15569 q^{25} + 4622 q^{26} - 9477 q^{27} + 21214 q^{28} - 10613 q^{29} - 1233 q^{30} + 25597 q^{31} + 15966 q^{32} - 2250 q^{33} + 31796 q^{34} + 6729 q^{35} + 19926 q^{36} + 17585 q^{37} + 34903 q^{38} - 9486 q^{39} + 31382 q^{40} + 12537 q^{41} + 5175 q^{42} + 26644 q^{43} + 6654 q^{44} - 1134 q^{45} + 149005 q^{46} + 52087 q^{47} - 8298 q^{48} + 95384 q^{49} + 121821 q^{50} - 2439 q^{51} + 263630 q^{52} + 20014 q^{53} + 120932 q^{55} + 126688 q^{56} - 6039 q^{57} + 86066 q^{58} + 45253 q^{59} + 49419 q^{60} - 11667 q^{61} + 164794 q^{62} + 30213 q^{63} + 151893 q^{64} - 28674 q^{65} - 9846 q^{66} + 1106 q^{67} - 4043 q^{68} - 35775 q^{69} + 56066 q^{70} + 21230 q^{71} + 9963 q^{72} + 81131 q^{73} + 102042 q^{74} - 140121 q^{75} + 73900 q^{76} - 104655 q^{77} - 41598 q^{78} - 13470 q^{79} - 191969 q^{80} + 85293 q^{81} + 79909 q^{82} - 76149 q^{83} - 190926 q^{84} + 10035 q^{85} - 321496 q^{86} + 95517 q^{87} - 276779 q^{88} - 190205 q^{89} + 11097 q^{90} + 80601 q^{91} + 45672 q^{92} - 230373 q^{93} + 36768 q^{94} + 9875 q^{95} - 143694 q^{96} + 160850 q^{97} - 116644 q^{98} + 20250 q^{99}+O(q^{100}) \) 13 * q - 117 * q^3 + 246 * q^4 - 14 * q^5 + 373 * q^7 + 123 * q^8 + 1053 * q^9 + 137 * q^10 + 250 * q^11 - 2214 * q^12 + 1054 * q^13 - 575 * q^14 + 126 * q^15 + 922 * q^16 + 271 * q^17 + 671 * q^19 - 5491 * q^20 - 3357 * q^21 + 1094 * q^22 + 3975 * q^23 - 1107 * q^24 + 15569 * q^25 + 4622 * q^26 - 9477 * q^27 + 21214 * q^28 - 10613 * q^29 - 1233 * q^30 + 25597 * q^31 + 15966 * q^32 - 2250 * q^33 + 31796 * q^34 + 6729 * q^35 + 19926 * q^36 + 17585 * q^37 + 34903 * q^38 - 9486 * q^39 + 31382 * q^40 + 12537 * q^41 + 5175 * q^42 + 26644 * q^43 + 6654 * q^44 - 1134 * q^45 + 149005 * q^46 + 52087 * q^47 - 8298 * q^48 + 95384 * q^49 + 121821 * q^50 - 2439 * q^51 + 263630 * q^52 + 20014 * q^53 + 120932 * q^55 + 126688 * q^56 - 6039 * q^57 + 86066 * q^58 + 45253 * q^59 + 49419 * q^60 - 11667 * q^61 + 164794 * q^62 + 30213 * q^63 + 151893 * q^64 - 28674 * q^65 - 9846 * q^66 + 1106 * q^67 - 4043 * q^68 - 35775 * q^69 + 56066 * q^70 + 21230 * q^71 + 9963 * q^72 + 81131 * q^73 + 102042 * q^74 - 140121 * q^75 + 73900 * q^76 - 104655 * q^77 - 41598 * q^78 - 13470 * q^79 - 191969 * q^80 + 85293 * q^81 + 79909 * q^82 - 76149 * q^83 - 190926 * q^84 + 10035 * q^85 - 321496 * q^86 + 95517 * q^87 - 276779 * q^88 - 190205 * q^89 + 11097 * q^90 + 80601 * q^91 + 45672 * q^92 - 230373 * q^93 + 36768 * q^94 + 9875 * q^95 - 143694 * q^96 + 160850 * q^97 - 116644 * q^98 + 20250 * q^99

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