LMFDB - Embedded newform 177.6.a.a.1.6

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			1.6
Root			$-0.216241$ 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)

$f(q)$	$=$	$q-1.21624 q^{2} +9.00000 q^{3} -30.5208 q^{4} +0.914506 q^{5} -10.9462 q^{6} +61.7584 q^{7} +76.0403 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-1.21624 q^{2} +9.00000 q^{3} -30.5208 q^{4} +0.914506 q^{5} -10.9462 q^{6} +61.7584 q^{7} +76.0403 q^{8} +81.0000 q^{9} -1.11226 q^{10} -311.532 q^{11} -274.687 q^{12} -150.260 q^{13} -75.1131 q^{14} +8.23055 q^{15} +884.181 q^{16} +1232.93 q^{17} -98.5155 q^{18} -266.956 q^{19} -27.9114 q^{20} +555.825 q^{21} +378.898 q^{22} -1920.26 q^{23} +684.363 q^{24} -3124.16 q^{25} +182.752 q^{26} +729.000 q^{27} -1884.91 q^{28} -2981.52 q^{29} -10.0103 q^{30} -8356.31 q^{31} -3508.67 q^{32} -2803.79 q^{33} -1499.54 q^{34} +56.4784 q^{35} -2472.18 q^{36} +8500.15 q^{37} +324.682 q^{38} -1352.34 q^{39} +69.5393 q^{40} +13953.0 q^{41} -676.018 q^{42} -11289.0 q^{43} +9508.19 q^{44} +74.0750 q^{45} +2335.50 q^{46} -24855.4 q^{47} +7957.63 q^{48} -12992.9 q^{49} +3799.74 q^{50} +11096.3 q^{51} +4586.04 q^{52} -35346.4 q^{53} -886.640 q^{54} -284.898 q^{55} +4696.13 q^{56} -2402.60 q^{57} +3626.25 q^{58} +3481.00 q^{59} -251.203 q^{60} -46879.0 q^{61} +10163.3 q^{62} +5002.43 q^{63} -24026.4 q^{64} -137.413 q^{65} +3410.08 q^{66} +37659.9 q^{67} -37629.8 q^{68} -17282.3 q^{69} -68.6913 q^{70} -56413.7 q^{71} +6159.26 q^{72} +66253.6 q^{73} -10338.2 q^{74} -28117.5 q^{75} +8147.69 q^{76} -19239.7 q^{77} +1644.77 q^{78} -51579.2 q^{79} +808.588 q^{80} +6561.00 q^{81} -16970.2 q^{82} -28845.7 q^{83} -16964.2 q^{84} +1127.52 q^{85} +13730.1 q^{86} -26833.7 q^{87} -23689.0 q^{88} -9518.85 q^{89} -90.0930 q^{90} -9279.79 q^{91} +58607.8 q^{92} -75206.8 q^{93} +30230.2 q^{94} -244.132 q^{95} -31578.0 q^{96} +96360.6 q^{97} +15802.5 q^{98} -25234.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.21624	−0.215003	−0.107502	−	0.994205i	$-0.534285\pi$
$2$	−1.21624	−0.215003	−0.107502	+	0.994205i	$0.534285\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−30.5208	−0.953774
$5$	0.914506	0.0163592	0.00817959	−	0.999967i	$-0.497396\pi$
$5$	0.914506	0.0163592	0.00817959	+	0.999967i	$0.497396\pi$
$6$	−10.9462	−0.124132
$7$	61.7584	0.476377	0.238188	−	0.971219i	$-0.423446\pi$
$7$	61.7584	0.476377	0.238188	+	0.971219i	$0.423446\pi$
$8$	76.0403	0.420067
$9$	81.0000	0.333333
$10$	−1.11226	−0.00351727
$11$	−311.532	−0.776284	−0.388142	−	0.921599i	$-0.626883\pi$
$11$	−311.532	−0.776284	−0.388142	+	0.921599i	$0.626883\pi$
$12$	−274.687	−0.550661
$13$	−150.260	−0.246595	−0.123297	−	0.992370i	$-0.539347\pi$
$13$	−150.260	−0.246595	−0.123297	+	0.992370i	$0.539347\pi$
$14$	−75.1131	−0.102422
$15$	8.23055	0.00944497
$16$	884.181	0.863458
$17$	1232.93	1.03470	0.517350	−	0.855774i	$-0.326918\pi$
$17$	1232.93	1.03470	0.517350	+	0.855774i	$0.326918\pi$
$18$	−98.5155	−0.0716677
$19$	−266.956	−0.169651	−0.0848253	−	0.996396i	$-0.527033\pi$
$19$	−266.956	−0.169651	−0.0848253	+	0.996396i	$0.527033\pi$
$20$	−27.9114	−0.0156029
$21$	555.825	0.275036
$22$	378.898	0.166904
$23$	−1920.26	−0.756903	−0.378451	−	0.925621i	$-0.623543\pi$
$23$	−1920.26	−0.756903	−0.378451	+	0.925621i	$0.623543\pi$
$24$	684.363	0.242526
$25$	−3124.16	−0.999732
$26$	182.752	0.0530187
$27$	729.000	0.192450
$28$	−1884.91	−0.454356
$29$	−2981.52	−0.658329	−0.329165	−	0.944273i	$-0.606767\pi$
$29$	−2981.52	−0.658329	−0.329165	+	0.944273i	$0.606767\pi$
$30$	−10.0103	−0.00203070
$31$	−8356.31	−1.56175	−0.780873	−	0.624689i	$-0.785226\pi$
$31$	−8356.31	−1.56175	−0.780873	+	0.624689i	$0.785226\pi$
$32$	−3508.67	−0.605713
$33$	−2803.79	−0.448188
$34$	−1499.54	−0.222464
$35$	56.4784	0.00779313
$36$	−2472.18	−0.317925
$37$	8500.15	1.02076	0.510378	−	0.859950i	$-0.329505\pi$
$37$	8500.15	1.02076	0.510378	+	0.859950i	$0.329505\pi$
$38$	324.682	0.0364754
$39$	−1352.34	−0.142372
$40$	69.5393	0.00687195
$41$	13953.0	1.29631	0.648155	−	0.761509i	$-0.275541\pi$
$41$	13953.0	1.29631	0.648155	+	0.761509i	$0.275541\pi$
$42$	−676.018	−0.0591337
$43$	−11289.0	−0.931071	−0.465535	−	0.885029i	$-0.654138\pi$
$43$	−11289.0	−0.931071	−0.465535	+	0.885029i	$0.654138\pi$
$44$	9508.19	0.740400
$45$	74.0750	0.00545306
$46$	2335.50	0.162736
$47$	−24855.4	−1.64126	−0.820628	−	0.571463i	$-0.806376\pi$
$47$	−24855.4	−1.64126	−0.820628	+	0.571463i	$0.806376\pi$
$48$	7957.63	0.498518
$49$	−12992.9	−0.773065
$50$	3799.74	0.214946
$51$	11096.3	0.597385
$52$	4586.04	0.235196
$53$	−35346.4	−1.72844	−0.864222	−	0.503111i	$-0.832189\pi$
$53$	−35346.4	−1.72844	−0.864222	+	0.503111i	$0.832189\pi$
$54$	−886.640	−0.0413774
$55$	−284.898	−0.0126994
$56$	4696.13	0.200110
$57$	−2402.60	−0.0979478
$58$	3626.25	0.141543
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−251.203	−0.00900837
$61$	−46879.0	−1.61307	−0.806536	−	0.591185i	$-0.798660\pi$
$61$	−46879.0	−1.61307	−0.806536	+	0.591185i	$0.798660\pi$
$62$	10163.3	0.335780
$63$	5002.43	0.158792
$64$	−24026.4	−0.733228
$65$	−137.413	−0.00403409
$66$	3410.08	0.0963618
$67$	37659.9	1.02492	0.512462	−	0.858710i	$-0.328734\pi$
$67$	37659.9	1.02492	0.512462	+	0.858710i	$0.328734\pi$
$68$	−37629.8	−0.986870
$69$	−17282.3	−0.436998
$70$	−68.6913	−0.00167555
$71$	−56413.7	−1.32812	−0.664062	−	0.747677i	$-0.731169\pi$
$71$	−56413.7	−1.32812	−0.664062	+	0.747677i	$0.731169\pi$
$72$	6159.26	0.140022
$73$	66253.6	1.45513	0.727566	−	0.686037i	$-0.240651\pi$
$73$	66253.6	1.45513	0.727566	+	0.686037i	$0.240651\pi$
$74$	−10338.2	−0.219466
$75$	−28117.5	−0.577196
$76$	8147.69	0.161808
$77$	−19239.7	−0.369804
$78$	1644.77	0.0306103
$79$	−51579.2	−0.929837	−0.464918	−	0.885354i	$-0.653916\pi$
$79$	−51579.2	−0.929837	−0.464918	+	0.885354i	$0.653916\pi$
$80$	808.588	0.0141255
$81$	6561.00	0.111111
$82$	−16970.2	−0.278710
$83$	−28845.7	−0.459606	−0.229803	−	0.973237i	$-0.573808\pi$
$83$	−28845.7	−0.459606	−0.229803	+	0.973237i	$0.573808\pi$
$84$	−16964.2	−0.262322
$85$	1127.52	0.0169269
$86$	13730.1	0.200183
$87$	−26833.7	−0.380087
$88$	−23689.0	−0.326092
$89$	−9518.85	−0.127382	−0.0636912	−	0.997970i	$-0.520287\pi$
$89$	−9518.85	−0.127382	−0.0636912	+	0.997970i	$0.520287\pi$
$90$	−90.0930	−0.00117242
$91$	−9279.79	−0.117472
$92$	58607.8	0.721914
$93$	−75206.8	−0.901675
$94$	30230.2	0.352875
$95$	−244.132	−0.00277534
$96$	−31578.0	−0.349709
$97$	96360.6	1.03985	0.519924	−	0.854212i	$-0.325960\pi$
$97$	96360.6	1.03985	0.519924	+	0.854212i	$0.325960\pi$
$98$	15802.5	0.166211
$99$	−25234.1	−0.258761
$100$	95351.8	0.953518
$101$	−2640.59	−0.0257571	−0.0128785	−	0.999917i	$-0.504099\pi$
$101$	−2640.59	−0.0257571	−0.0128785	+	0.999917i	$0.504099\pi$
$102$	−13495.8	−0.128440
$103$	117451.	1.09085	0.545425	−	0.838160i	$-0.316368\pi$
$103$	117451.	1.09085	0.545425	+	0.838160i	$0.316368\pi$
$104$	−11425.8	−0.103586
$105$	508.305	0.00449937
$106$	42989.7	0.371621
$107$	−228868.	−1.93253	−0.966263	−	0.257558i	$-0.917082\pi$
$107$	−228868.	−1.93253	−0.966263	+	0.257558i	$0.917082\pi$
$108$	−22249.6	−0.183554
$109$	163809.	1.32060	0.660301	−	0.751001i	$-0.270429\pi$
$109$	163809.	1.32060	0.660301	+	0.751001i	$0.270429\pi$
$110$	346.504	0.00273040
$111$	76501.3	0.589334
$112$	54605.6	0.411331
$113$	16245.7	0.119686	0.0598430	−	0.998208i	$-0.480940\pi$
$113$	16245.7	0.119686	0.0598430	+	0.998208i	$0.480940\pi$
$114$	2922.14	0.0210591
$115$	−1756.09	−0.0123823
$116$	90998.4	0.627897
$117$	−12171.0	−0.0821983
$118$	−4233.73	−0.0279910
$119$	76143.5	0.492908
$120$	625.854	0.00396752
$121$	−63998.8	−0.397382
$122$	57016.2	0.346816
$123$	125577.	0.748424
$124$	255041.	1.48955
$125$	−5714.90	−0.0327140
$126$	−6084.16	−0.0341408
$127$	285457.	1.57047	0.785237	−	0.619195i	$-0.212541\pi$
$127$	285457.	1.57047	0.785237	+	0.619195i	$0.212541\pi$
$128$	141499.	0.763360
$129$	−101601.	−0.537554
$130$	167.128	0.000867341 0
$131$	153837.	0.783217	0.391609	−	0.920132i	$-0.371919\pi$
$131$	153837.	0.783217	0.391609	+	0.920132i	$0.371919\pi$
$132$	85573.7	0.427470
$133$	−16486.8	−0.0808176
$134$	−45803.5	−0.220362
$135$	666.675	0.00314832
$136$	93752.1	0.434644
$137$	−281641.	−1.28202	−0.641010	−	0.767532i	$-0.721484\pi$
$137$	−281641.	−1.28202	−0.641010	+	0.767532i	$0.721484\pi$
$138$	21019.5	0.0939559
$139$	171456.	0.752689	0.376344	−	0.926480i	$-0.377181\pi$
$139$	171456.	0.752689	0.376344	+	0.926480i	$0.377181\pi$
$140$	−1723.76	−0.00743289
$141$	−223699.	−0.947580
$142$	68612.7	0.285551
$143$	46810.7	0.191428
$144$	71618.7	0.287819
$145$	−2726.62	−0.0107697
$146$	−80580.4	−0.312858
$147$	−116936.	−0.446329
$148$	−259431.	−0.973570
$149$	246577.	0.909885	0.454942	−	0.890521i	$-0.349660\pi$
$149$	246577.	0.909885	0.454942	+	0.890521i	$0.349660\pi$
$150$	34197.6	0.124099
$151$	161787.	0.577433	0.288717	−	0.957415i	$-0.406771\pi$
$151$	161787.	0.577433	0.288717	+	0.957415i	$0.406771\pi$
$152$	−20299.4	−0.0712646
$153$	99867.0	0.344900
$154$	23400.1	0.0795090
$155$	−7641.90	−0.0255489
$156$	41274.4	0.135790
$157$	−212289.	−0.687351	−0.343675	−	0.939089i	$-0.611672\pi$
$157$	−212289.	−0.687351	−0.343675	+	0.939089i	$0.611672\pi$
$158$	62732.7	0.199918
$159$	−318117.	−0.997917
$160$	−3208.70	−0.00990897
$161$	−118592.	−0.360571
$162$	−7979.76	−0.0238892
$163$	428153.	1.26221	0.631103	−	0.775699i	$-0.282603\pi$
$163$	428153.	1.26221	0.631103	+	0.775699i	$0.282603\pi$
$164$	−425857.	−1.23639
$165$	−2564.08	−0.00733199
$166$	35083.3	0.0988166
$167$	260524.	0.722863	0.361432	−	0.932399i	$-0.382288\pi$
$167$	260524.	0.722863	0.361432	+	0.932399i	$0.382288\pi$
$168$	42265.1	0.115534
$169$	−348715.	−0.939191
$170$	−1371.33	−0.00363932
$171$	−21623.4	−0.0565502
$172$	344547.	0.888031
$173$	375123.	0.952924	0.476462	−	0.879195i	$-0.341919\pi$
$173$	375123.	0.952924	0.476462	+	0.879195i	$0.341919\pi$
$174$	32636.3	0.0817198
$175$	−192943.	−0.476249
$176$	−275451.	−0.670289
$177$	31329.0	0.0751646
$178$	11577.2	0.0273876
$179$	−569801.	−1.32920	−0.664601	−	0.747199i	$-0.731398\pi$
$179$	−569801.	−1.32920	−0.664601	+	0.747199i	$0.731398\pi$
$180$	−2260.82	−0.00520098
$181$	−532297.	−1.20770	−0.603848	−	0.797099i	$-0.706367\pi$
$181$	−532297.	−1.20770	−0.603848	+	0.797099i	$0.706367\pi$
$182$	11286.5	0.0252569
$183$	−421911.	−0.931308
$184$	−146017.	−0.317950
$185$	7773.43	0.0166987
$186$	91469.6	0.193863
$187$	−384096.	−0.803222
$188$	758606.	1.56539
$189$	45021.9	0.0916788
$190$	296.924	0.000596707 0
$191$	−756470.	−1.50040	−0.750202	−	0.661209i	$-0.770044\pi$
$191$	−756470.	−1.50040	−0.750202	+	0.661209i	$0.770044\pi$
$192$	−216238.	−0.423329
$193$	715629.	1.38291	0.691456	−	0.722418i	$-0.256969\pi$
$193$	715629.	1.38291	0.691456	+	0.722418i	$0.256969\pi$
$194$	−117198.	−0.223571
$195$	−1236.72	−0.00232908
$196$	396553.	0.737329
$197$	330788.	0.607273	0.303637	−	0.952788i	$-0.401799\pi$
$197$	330788.	0.607273	0.303637	+	0.952788i	$0.401799\pi$
$198$	30690.7	0.0556345
$199$	−145072.	−0.259687	−0.129844	−	0.991534i	$-0.541448\pi$
$199$	−145072.	−0.259687	−0.129844	+	0.991534i	$0.541448\pi$
$200$	−237562.	−0.419955
$201$	338939.	0.591740
$202$	3211.59	0.00553785
$203$	−184134.	−0.313613
$204$	−338669.	−0.569770
$205$	12760.1	0.0212065
$206$	−142849.	−0.234536
$207$	−155541.	−0.252301
$208$	−132857.	−0.212924
$209$	83165.2	0.131697
$210$	−618.222	−0.000967378 0
$211$	836441.	1.29339	0.646695	−	0.762749i	$-0.276151\pi$
$211$	836441.	1.29339	0.646695	+	0.762749i	$0.276151\pi$
$212$	1.07880e6	1.64854
$213$	−507724.	−0.766793
$214$	278358.	0.415499
$215$	−10323.8	−0.0152315
$216$	55433.4	0.0808420
$217$	−516072.	−0.743980
$218$	−199231.	−0.283933
$219$	596283.	0.840121
$220$	8695.29	0.0121123
$221$	−185259.	−0.255152
$222$	−93044.0	−0.126709
$223$	734281.	0.988781	0.494391	−	0.869240i	$-0.335391\pi$
$223$	734281.	0.988781	0.494391	+	0.869240i	$0.335391\pi$
$224$	−216690.	−0.288548
$225$	−253057.	−0.333244
$226$	−19758.7	−0.0257329
$227$	370264.	0.476922	0.238461	−	0.971152i	$-0.423357\pi$
$227$	370264.	0.476922	0.238461	+	0.971152i	$0.423357\pi$
$228$	73329.2	0.0934200
$229$	−690656.	−0.870309	−0.435154	−	0.900356i	$-0.643306\pi$
$229$	−690656.	−0.870309	−0.435154	+	0.900356i	$0.643306\pi$
$230$	2135.83	0.00266223
$231$	−173157.	−0.213506
$232$	−226716.	−0.276543
$233$	−924763.	−1.11594	−0.557970	−	0.829861i	$-0.688419\pi$
$233$	−924763.	−1.11594	−0.557970	+	0.829861i	$0.688419\pi$
$234$	14802.9	0.0176729
$235$	−22730.4	−0.0268496
$236$	−106243.	−0.124171
$237$	−464213.	−0.536841
$238$	−92608.9	−0.105977
$239$	−568443.	−0.643713	−0.321856	−	0.946788i	$-0.604307\pi$
$239$	−568443.	−0.643713	−0.321856	+	0.946788i	$0.604307\pi$
$240$	7277.30	0.00815534
$241$	−292121.	−0.323981	−0.161990	−	0.986792i	$-0.551791\pi$
$241$	−292121.	−0.323981	−0.161990	+	0.986792i	$0.551791\pi$
$242$	77838.0	0.0854384
$243$	59049.0	0.0641500
$244$	1.43078e6	1.53851
$245$	−11882.1	−0.0126467
$246$	−152732.	−0.160914
$247$	40112.7	0.0418350
$248$	−635417.	−0.656039
$249$	−259611.	−0.265353
$250$	6950.69	0.00703360
$251$	−1.76450e6	−1.76781	−0.883907	−	0.467663i	$-0.845096\pi$
$251$	−1.76450e6	−1.76781	−0.883907	+	0.467663i	$0.845096\pi$
$252$	−152678.	−0.151452
$253$	598222.	0.587572
$254$	−347184.	−0.337657
$255$	10147.7	0.00977272
$256$	596748.	0.569103
$257$	−824695.	−0.778862	−0.389431	−	0.921056i	$-0.627328\pi$
$257$	−824695.	−0.778862	−0.389431	+	0.921056i	$0.627328\pi$
$258$	123571.	0.115576
$259$	524955.	0.486265
$260$	4193.96	0.00384761
$261$	−241503.	−0.219443
$262$	−187103.	−0.168394
$263$	−915456.	−0.816109	−0.408055	−	0.912958i	$-0.633793\pi$
$263$	−915456.	−0.816109	−0.408055	+	0.912958i	$0.633793\pi$
$264$	−213201.	−0.188269
$265$	−32324.4	−0.0282759
$266$	20051.9	0.0173760
$267$	−85669.7	−0.0735443
$268$	−1.14941e6	−0.977546
$269$	1.00139e6	0.843769	0.421884	−	0.906650i	$-0.361369\pi$
$269$	1.00139e6	0.843769	0.421884	+	0.906650i	$0.361369\pi$
$270$	−810.837	−0.000676899 0
$271$	−2.25170e6	−1.86246	−0.931232	−	0.364428i	$-0.881265\pi$
$271$	−2.25170e6	−1.86246	−0.931232	+	0.364428i	$0.881265\pi$
$272$	1.09013e6	0.893421
$273$	−83518.2	−0.0678226
$274$	342544.	0.275638
$275$	973277.	0.776077
$276$	527470.	0.416797
$277$	5282.15	0.00413629	0.00206815	−	0.999998i	$-0.499342\pi$
$277$	5282.15	0.00413629	0.00206815	+	0.999998i	$0.499342\pi$
$278$	−208532.	−0.161830
$279$	−676861.	−0.520582
$280$	4294.63	0.00327364
$281$	−2.48246e6	−1.87550	−0.937748	−	0.347317i	$-0.887093\pi$
$281$	−2.48246e6	−1.87550	−0.937748	+	0.347317i	$0.887093\pi$
$282$	272072.	0.203733
$283$	−87005.1	−0.0645771	−0.0322886	−	0.999479i	$-0.510280\pi$
$283$	−87005.1	−0.0645771	−0.0322886	+	0.999479i	$0.510280\pi$
$284$	1.72179e6	1.26673
$285$	−2197.19	−0.00160234
$286$	−56933.1	−0.0411576
$287$	861716.	0.617532
$288$	−284202.	−0.201904
$289$	100250.	0.0706059
$290$	3316.23	0.00231552
$291$	867245.	0.600357
$292$	−2.02211e6	−1.38787
$293$	165504.	0.112626	0.0563131	−	0.998413i	$-0.482065\pi$
$293$	165504.	0.112626	0.0563131	+	0.998413i	$0.482065\pi$
$294$	142223.	0.0959622
$295$	3183.39	0.00212978
$296$	646354.	0.428786
$297$	−227107.	−0.149396
$298$	−299897.	−0.195628
$299$	288538.	0.186648
$300$	858167.	0.550514
$301$	−697188.	−0.443541
$302$	−196772.	−0.124150
$303$	−23765.3	−0.0148709
$304$	−236037.	−0.146486
$305$	−42871.1	−0.0263885
$306$	−121462.	−0.0741546
$307$	746565.	0.452087	0.226043	−	0.974117i	$-0.427421\pi$
$307$	746565.	0.452087	0.226043	+	0.974117i	$0.427421\pi$
$308$	587210.	0.352709
$309$	1.05706e6	0.629802
$310$	9294.39	0.00549309
$311$	638206.	0.374162	0.187081	−	0.982344i	$-0.440097\pi$
$311$	638206.	0.374162	0.187081	+	0.982344i	$0.440097\pi$
$312$	−102832.	−0.0598057
$313$	1.55232e6	0.895615	0.447808	−	0.894130i	$-0.352205\pi$
$313$	1.55232e6	0.895615	0.447808	+	0.894130i	$0.352205\pi$
$314$	258195.	0.147782
$315$	4574.75	0.00259771
$316$	1.57424e6	0.886854
$317$	1.97404e6	1.10334	0.551669	−	0.834063i	$-0.313991\pi$
$317$	1.97404e6	1.10334	0.551669	+	0.834063i	$0.313991\pi$
$318$	386907.	0.214555
$319$	928840.	0.511051
$320$	−21972.3	−0.0119950
$321$	−2.05981e6	−1.11574
$322$	144237.	0.0775239
$323$	−329137.	−0.175538
$324$	−200247.	−0.105975
$325$	469436.	0.246529
$326$	−520737.	−0.271378
$327$	1.47428e6	0.762450
$328$	1.06099e6	0.544537
$329$	−1.53503e6	−0.781857
$330$	3118.54	0.00157640
$331$	−2.40736e6	−1.20774	−0.603868	−	0.797084i	$-0.706375\pi$
$331$	−2.40736e6	−1.20774	−0.603868	+	0.797084i	$0.706375\pi$
$332$	880391.	0.438360
$333$	688512.	0.340252
$334$	−316860.	−0.155418
$335$	34440.2	0.0167669
$336$	491450.	0.237482
$337$	1.90636e6	0.914389	0.457194	−	0.889367i	$-0.348854\pi$
$337$	1.90636e6	0.914389	0.457194	+	0.889367i	$0.348854\pi$
$338$	424121.	0.201929
$339$	146212.	0.0691007
$340$	−34412.7	−0.0161444
$341$	2.60326e6	1.21236
$342$	26299.3	0.0121585
$343$	−1.84039e6	−0.844647
$344$	−858416.	−0.391112
$345$	−15804.8	−0.00714893
$346$	−456240.	−0.204882
$347$	3.72382e6	1.66022	0.830110	−	0.557600i	$-0.188278\pi$
$347$	3.72382e6	1.66022	0.830110	+	0.557600i	$0.188278\pi$
$348$	818985.	0.362517
$349$	−99542.3	−0.0437466	−0.0218733	−	0.999761i	$-0.506963\pi$
$349$	−99542.3	−0.0437466	−0.0218733	+	0.999761i	$0.506963\pi$
$350$	234665.	0.102395
$351$	−109539.	−0.0474572
$352$	1.09306e6	0.470206
$353$	528656.	0.225806	0.112903	−	0.993606i	$-0.463985\pi$
$353$	528656.	0.225806	0.112903	+	0.993606i	$0.463985\pi$
$354$	−38103.6	−0.0161606
$355$	−51590.7	−0.0217270
$356$	290523.	0.121494
$357$	685292.	0.284580
$358$	693016.	0.285782
$359$	−1.49351e6	−0.611605	−0.305803	−	0.952095i	$-0.598925\pi$
$359$	−1.49351e6	−0.611605	−0.305803	+	0.952095i	$0.598925\pi$
$360$	5632.68	0.00229065
$361$	−2.40483e6	−0.971219
$362$	647402.	0.259658
$363$	−575990.	−0.229429
$364$	283226.	0.112042
$365$	60589.3	0.0238048
$366$	513146.	0.200234
$367$	154208.	0.0597642	0.0298821	−	0.999553i	$-0.490487\pi$
$367$	154208.	0.0597642	0.0298821	+	0.999553i	$0.490487\pi$
$368$	−1.69786e6	−0.653554
$369$	1.13019e6	0.432103
$370$	−9454.36	−0.00359028
$371$	−2.18293e6	−0.823390
$372$	2.29537e6	0.859994
$373$	−443333.	−0.164990	−0.0824951	−	0.996591i	$-0.526289\pi$
$373$	−443333.	−0.164990	−0.0824951	+	0.996591i	$0.526289\pi$
$374$	467153.	0.172695
$375$	−51434.1	−0.0188874
$376$	−1.89001e6	−0.689438
$377$	448003.	0.162341
$378$	−54757.4	−0.0197112
$379$	2.52046e6	0.901324	0.450662	−	0.892695i	$-0.351188\pi$
$379$	2.52046e6	0.901324	0.450662	+	0.892695i	$0.351188\pi$
$380$	7451.11	0.00264705
$381$	2.56911e6	0.906714
$382$	920049.	0.322591
$383$	3.56075e6	1.24035	0.620175	−	0.784463i	$-0.287062\pi$
$383$	3.56075e6	1.24035	0.620175	+	0.784463i	$0.287062\pi$
$384$	1.27349e6	0.440726
$385$	−17594.8	−0.00604969
$386$	−870377.	−0.297330
$387$	−914405.	−0.310357
$388$	−2.94100e6	−0.991780
$389$	1.66815e6	0.558933	0.279467	−	0.960155i	$-0.409842\pi$
$389$	1.66815e6	0.558933	0.279467	+	0.960155i	$0.409842\pi$
$390$	1504.15	0.000500760 0
$391$	−2.36754e6	−0.783168
$392$	−987984.	−0.324739
$393$	1.38453e6	0.452191
$394$	−402318.	−0.130566
$395$	−47169.4	−0.0152114
$396$	770163.	0.246800
$397$	−4.98663e6	−1.58793	−0.793964	−	0.607964i	$-0.791986\pi$
$397$	−4.98663e6	−1.58793	−0.793964	+	0.607964i	$0.791986\pi$
$398$	176443.	0.0558336
$399$	−148381.	−0.0466601
$400$	−2.76233e6	−0.863227
$401$	1.72114e6	0.534509	0.267255	−	0.963626i	$-0.413884\pi$
$401$	1.72114e6	0.534509	0.267255	+	0.963626i	$0.413884\pi$
$402$	−412231.	−0.127226
$403$	1.25562e6	0.385119
$404$	80592.7	0.0245664
$405$	6000.07	0.00181769
$406$	223951.	0.0674277
$407$	−2.64807e6	−0.792397
$408$	843769.	0.250942
$409$	4.38543e6	1.29630	0.648148	−	0.761515i	$-0.275544\pi$
$409$	4.38543e6	1.29630	0.648148	+	0.761515i	$0.275544\pi$
$410$	−15519.4	−0.00455947
$411$	−2.53477e6	−0.740175
$412$	−3.58470e6	−1.04042
$413$	214981.	0.0620190
$414$	189175.	0.0542455
$415$	−26379.5	−0.00751877
$416$	527211.	0.149366
$417$	1.54310e6	0.434565
$418$	−101149.	−0.0283153
$419$	5.77647e6	1.60741	0.803706	−	0.595026i	$-0.202858\pi$
$419$	5.77647e6	1.60741	0.803706	+	0.595026i	$0.202858\pi$
$420$	−15513.9	−0.00429138
$421$	−624265.	−0.171658	−0.0858290	−	0.996310i	$-0.527354\pi$
$421$	−624265.	−0.171658	−0.0858290	+	0.996310i	$0.527354\pi$
$422$	−1.01731e6	−0.278083
$423$	−2.01329e6	−0.547085
$424$	−2.68775e6	−0.726062
$425$	−3.85186e6	−1.03442
$426$	617514.	0.164863
$427$	−2.89517e6	−0.768431
$428$	6.98522e6	1.84319
$429$	421296.	0.110521
$430$	12556.2	0.00327483
$431$	1.51781e6	0.393573	0.196787	−	0.980446i	$-0.436949\pi$
$431$	1.51781e6	0.393573	0.196787	+	0.980446i	$0.436949\pi$
$432$	644568.	0.166173
$433$	6.06106e6	1.55356	0.776781	−	0.629770i	$-0.216851\pi$
$433$	6.06106e6	1.55356	0.776781	+	0.629770i	$0.216851\pi$
$434$	627668.	0.159958
$435$	−24539.6	−0.00621790
$436$	−4.99958e6	−1.25956
$437$	512624.	0.128409
$438$	−725223.	−0.180629
$439$	4.36235e6	1.08034	0.540168	−	0.841557i	$-0.318361\pi$
$439$	4.36235e6	1.08034	0.540168	+	0.841557i	$0.318361\pi$
$440$	−21663.7	−0.00533459
$441$	−1.05243e6	−0.257688
$442$	225320.	0.0548585
$443$	−6.36182e6	−1.54018	−0.770091	−	0.637934i	$-0.779789\pi$
$443$	−6.36182e6	−1.54018	−0.770091	+	0.637934i	$0.779789\pi$
$444$	−2.33488e6	−0.562091
$445$	−8705.04	−0.00208387
$446$	−893063.	−0.212591
$447$	2.21919e6	0.525322
$448$	−1.48383e6	−0.349293
$449$	−4.13291e6	−0.967475	−0.483737	−	0.875213i	$-0.660721\pi$
$449$	−4.13291e6	−0.967475	−0.483737	+	0.875213i	$0.660721\pi$
$450$	307779.	0.0716485
$451$	−4.34681e6	−1.00630
$452$	−495832.	−0.114153
$453$	1.45609e6	0.333381
$454$	−450330.	−0.102540
$455$	−8486.42	−0.00192175
$456$	−182695.	−0.0411447
$457$	−4.22694e6	−0.946751	−0.473375	−	0.880861i	$-0.656965\pi$
$457$	−4.22694e6	−0.946751	−0.473375	+	0.880861i	$0.656965\pi$
$458$	840005.	0.187119
$459$	898803.	0.199128
$460$	53597.1	0.0118099
$461$	5.51414e6	1.20844	0.604220	−	0.796817i	$-0.293485\pi$
$461$	5.51414e6	1.20844	0.604220	+	0.796817i	$0.293485\pi$
$462$	210601.	0.0459045
$463$	−1.86964e6	−0.405327	−0.202664	−	0.979248i	$-0.564960\pi$
$463$	−1.86964e6	−0.405327	−0.202664	+	0.979248i	$0.564960\pi$
$464$	−2.63621e6	−0.568440
$465$	−68777.1	−0.0147507
$466$	1.12473e6	0.239930
$467$	4.32669e6	0.918045	0.459022	−	0.888425i	$-0.348200\pi$
$467$	4.32669e6	0.918045	0.459022	+	0.888425i	$0.348200\pi$
$468$	371469.	0.0783986
$469$	2.32581e6	0.488250
$470$	27645.7	0.00577274
$471$	−1.91060e6	−0.396842
$472$	264696.	0.0546881
$473$	3.51687e6	0.722776
$474$	564594.	0.115423
$475$	834013.	0.169605
$476$	−2.32396e6	−0.470122
$477$	−2.86306e6	−0.576148
$478$	691364.	0.138400
$479$	−3.34586e6	−0.666298	−0.333149	−	0.942874i	$-0.608111\pi$
$479$	−3.34586e6	−0.666298	−0.333149	+	0.942874i	$0.608111\pi$
$480$	−28878.3	−0.00572095
$481$	−1.27723e6	−0.251713
$482$	355289.	0.0696569
$483$	−1.06733e6	−0.208176
$484$	1.95329e6	0.379013
$485$	88122.3	0.0170111
$486$	−71817.8	−0.0137925
$487$	1.41911e6	0.271139	0.135570	−	0.990768i	$-0.456714\pi$
$487$	1.41911e6	0.271139	0.135570	+	0.990768i	$0.456714\pi$
$488$	−3.56469e6	−0.677599
$489$	3.85338e6	0.728735
$490$	14451.5	0.00271908
$491$	−3.66412e6	−0.685908	−0.342954	−	0.939352i	$-0.611427\pi$
$491$	−3.66412e6	−0.685908	−0.342954	+	0.939352i	$0.611427\pi$
$492$	−3.83271e6	−0.713827
$493$	−3.67600e6	−0.681174
$494$	−48786.7	−0.00899464
$495$	−23076.7	−0.00423312
$496$	−7.38849e6	−1.34850
$497$	−3.48402e6	−0.632688
$498$	315749.	0.0570518
$499$	−1.94309e6	−0.349335	−0.174667	−	0.984627i	$-0.555885\pi$
$499$	−1.94309e6	−0.349335	−0.174667	+	0.984627i	$0.555885\pi$
$500$	174423.	0.0312017
$501$	2.34471e6	0.417345
$502$	2.14605e6	0.380085
$503$	2.10114e6	0.370285	0.185142	−	0.982712i	$-0.440725\pi$
$503$	2.10114e6	0.370285	0.185142	+	0.982712i	$0.440725\pi$
$504$	380386.	0.0667035
$505$	−2414.83	−0.000421365 0
$506$	−727582.	−0.126330
$507$	−3.13844e6	−0.542242
$508$	−8.71235e6	−1.49788
$509$	−2.83832e6	−0.485587	−0.242793	−	0.970078i	$-0.578064\pi$
$509$	−2.83832e6	−0.485587	−0.242793	+	0.970078i	$0.578064\pi$
$510$	−12342.0	−0.00210117
$511$	4.09172e6	0.693192
$512$	−5.25376e6	−0.885718
$513$	−194611.	−0.0326493
$514$	1.00303e6	0.167458
$515$	107410.	0.0178454
$516$	3.10093e6	0.512705
$517$	7.74326e6	1.27408
$518$	−638472.	−0.104548
$519$	3.37611e6	0.550171
$520$	−10449.0	−0.00169459
$521$	6.04781e6	0.976121	0.488060	−	0.872810i	$-0.337705\pi$
$521$	6.04781e6	0.976121	0.488060	+	0.872810i	$0.337705\pi$
$522$	293726.	0.0471809
$523$	1.00745e7	1.61053	0.805265	−	0.592915i	$-0.202023\pi$
$523$	1.00745e7	1.61053	0.805265	+	0.592915i	$0.202023\pi$
$524$	−4.69522e6	−0.747012
$525$	−1.73649e6	−0.274963
$526$	1.11342e6	0.175466
$527$	−1.03027e7	−1.61594
$528$	−2.47906e6	−0.386992
$529$	−2.74895e6	−0.427098
$530$	39314.3	0.00607940
$531$	281961.	0.0433963
$532$	503188.	0.0770817
$533$	−2.09658e6	−0.319663
$534$	104195.	0.0158122
$535$	−209301.	−0.0316145
$536$	2.86367e6	0.430537
$537$	−5.12821e6	−0.767415
$538$	−1.21793e6	−0.181413
$539$	4.04770e6	0.600118
$540$	−20347.4	−0.00300279
$541$	2.90078e6	0.426110	0.213055	−	0.977040i	$-0.431659\pi$
$541$	2.90078e6	0.426110	0.213055	+	0.977040i	$0.431659\pi$
$542$	2.73861e6	0.400435
$543$	−4.79068e6	−0.697264
$544$	−4.32593e6	−0.626732
$545$	149804.	0.0216040
$546$	101578.	0.0145821
$547$	−6.58103e6	−0.940428	−0.470214	−	0.882552i	$-0.655823\pi$
$547$	−6.58103e6	−0.940428	−0.470214	+	0.882552i	$0.655823\pi$
$548$	8.59591e6	1.22276
$549$	−3.79720e6	−0.537691
$550$	−1.18374e6	−0.166859
$551$	795935.	0.111686
$552$	−1.31415e6	−0.183569
$553$	−3.18545e6	−0.442953
$554$	−6424.37	−0.000889316 0
$555$	69960.9	0.00964102
$556$	−5.23296e6	−0.717895
$557$	−8.57629e6	−1.17128	−0.585641	−	0.810571i	$-0.699157\pi$
$557$	−8.57629e6	−1.17128	−0.585641	+	0.810571i	$0.699157\pi$
$558$	823227.	0.111927
$559$	1.69628e6	0.229597
$560$	49937.1	0.00672904
$561$	−3.45686e6	−0.463741
$562$	3.01927e6	0.403237
$563$	−6.42359e6	−0.854096	−0.427048	−	0.904229i	$-0.640446\pi$
$563$	−6.42359e6	−0.854096	−0.427048	+	0.904229i	$0.640446\pi$
$564$	6.82745e6	0.903776
$565$	14856.8	0.00195796
$566$	105819.	0.0138843
$567$	405197.	0.0529308
$568$	−4.28972e6	−0.557902
$569$	1.17161e7	1.51706	0.758531	−	0.651638i	$-0.225918\pi$
$569$	1.17161e7	1.51706	0.758531	+	0.651638i	$0.225918\pi$
$570$	2672.32	0.000344509 0
$571$	−4.99504e6	−0.641134	−0.320567	−	0.947226i	$-0.603873\pi$
$571$	−4.99504e6	−0.641134	−0.320567	+	0.947226i	$0.603873\pi$
$572$	−1.42870e6	−0.182579
$573$	−6.80823e6	−0.866258
$574$	−1.04805e6	−0.132771
$575$	5.99920e6	0.756700
$576$	−1.94614e6	−0.244409
$577$	495976.	0.0620185	0.0310093	−	0.999519i	$-0.490128\pi$
$577$	495976.	0.0620185	0.0310093	+	0.999519i	$0.490128\pi$
$578$	−121929.	−0.0151805
$579$	6.44066e6	0.798425
$580$	83218.5	0.0102719
$581$	−1.78146e6	−0.218945
$582$	−1.05478e6	−0.129079
$583$	1.10115e7	1.34176
$584$	5.03795e6	0.611254
$585$	−11130.5	−0.00134470
$586$	−201293.	−0.0242150
$587$	−202428.	−0.0242480	−0.0121240	−	0.999927i	$-0.503859\pi$
$587$	−202428.	−0.0242480	−0.0121240	+	0.999927i	$0.503859\pi$
$588$	3.56898e6	0.425697
$589$	2.23077e6	0.264951
$590$	−3871.77	−0.000457910 0
$591$	2.97709e6	0.350609
$592$	7.51567e6	0.881380
$593$	7.95364e6	0.928815	0.464407	−	0.885622i	$-0.346267\pi$
$593$	7.95364e6	0.928815	0.464407	+	0.885622i	$0.346267\pi$
$594$	276217.	0.0321206
$595$	69633.7	0.00806356
$596$	−7.52571e6	−0.867824
$597$	−1.30565e6	−0.149931
$598$	−350931.	−0.0401300
$599$	−1.68592e7	−1.91986	−0.959930	−	0.280241i	$-0.909586\pi$
$599$	−1.68592e7	−1.91986	−0.959930	+	0.280241i	$0.909586\pi$
$600$	−2.13806e6	−0.242461
$601$	5.03561e6	0.568677	0.284339	−	0.958724i	$-0.408226\pi$
$601$	5.03561e6	0.568677	0.284339	+	0.958724i	$0.408226\pi$
$602$	847948.	0.0953626
$603$	3.05045e6	0.341641
$604$	−4.93787e6	−0.550741
$605$	−58527.3	−0.00650085
$606$	28904.3	0.00319728
$607$	9.93216e6	1.09414	0.547069	−	0.837088i	$-0.315744\pi$
$607$	9.93216e6	1.09414	0.547069	+	0.837088i	$0.315744\pi$
$608$	936659.	0.102760
$609$	−1.65721e6	−0.181065
$610$	52141.6	0.00567362
$611$	3.73477e6	0.404725
$612$	−3.04802e6	−0.328957
$613$	1.09871e7	1.18095	0.590477	−	0.807054i	$-0.298940\pi$
$613$	1.09871e7	1.18095	0.590477	+	0.807054i	$0.298940\pi$
$614$	−908003.	−0.0972000
$615$	114841.	0.0122436
$616$	−1.46299e6	−0.155343
$617$	6.30095e6	0.666336	0.333168	−	0.942867i	$-0.391882\pi$
$617$	6.30095e6	0.666336	0.333168	+	0.942867i	$0.391882\pi$
$618$	−1.28564e6	−0.135409
$619$	5.08049e6	0.532941	0.266470	−	0.963843i	$-0.414143\pi$
$619$	5.08049e6	0.532941	0.266470	+	0.963843i	$0.414143\pi$
$620$	233236.	0.0243679
$621$	−1.39987e6	−0.145666
$622$	−776212.	−0.0804460
$623$	−587869.	−0.0606820
$624$	−1.19571e6	−0.122932
$625$	9.75779e6	0.999197
$626$	−1.88800e6	−0.192560
$627$	748487.	0.0760353
$628$	6.47922e6	0.655577
$629$	1.04801e7	1.05618
$630$	−5564.00	−0.000558516 0
$631$	−7.62504e6	−0.762376	−0.381188	−	0.924498i	$-0.624485\pi$
$631$	−7.62504e6	−0.762376	−0.381188	+	0.924498i	$0.624485\pi$
$632$	−3.92210e6	−0.390594
$633$	7.52797e6	0.746739
$634$	−2.40091e6	−0.237221
$635$	261052.	0.0256917
$636$	9.70918e6	0.951787
$637$	1.95231e6	0.190634
$638$	−1.12969e6	−0.109878
$639$	−4.56951e6	−0.442708
$640$	129402.	0.0124879
$641$	−7.34805e6	−0.706362	−0.353181	−	0.935555i	$-0.614900\pi$
$641$	−7.34805e6	−0.706362	−0.353181	+	0.935555i	$0.614900\pi$
$642$	2.50523e6	0.239888
$643$	−4.91274e6	−0.468594	−0.234297	−	0.972165i	$-0.575279\pi$
$643$	−4.91274e6	−0.468594	−0.234297	+	0.972165i	$0.575279\pi$
$644$	3.61952e6	0.343903
$645$	−92914.3	−0.00879394
$646$	400310.	0.0377411
$647$	5.02847e6	0.472254	0.236127	−	0.971722i	$-0.424122\pi$
$647$	5.02847e6	0.472254	0.236127	+	0.971722i	$0.424122\pi$
$648$	498900.	0.0466741
$649$	−1.08444e6	−0.101064
$650$	−570947.	−0.0530045
$651$	−4.64465e6	−0.429537
$652$	−1.30676e7	−1.20386
$653$	5.06290e6	0.464639	0.232320	−	0.972639i	$-0.425368\pi$
$653$	5.06290e6	0.464639	0.232320	+	0.972639i	$0.425368\pi$
$654$	−1.79308e6	−0.163929
$655$	140685.	0.0128128
$656$	1.23370e7	1.11931
$657$	5.36654e6	0.485044
$658$	1.86697e6	0.168102
$659$	−176951.	−0.0158723	−0.00793615	−	0.999969i	$-0.502526\pi$
$659$	−176951.	−0.0158723	−0.00793615	+	0.999969i	$0.502526\pi$
$660$	78257.6	0.00699305
$661$	1.83120e7	1.63016	0.815082	−	0.579346i	$-0.196692\pi$
$661$	1.83120e7	1.63016	0.815082	+	0.579346i	$0.196692\pi$
$662$	2.92794e6	0.259667
$663$	−1.66733e6	−0.147312
$664$	−2.19343e6	−0.193065
$665$	−15077.2	−0.00132211
$666$	−837396.	−0.0731552
$667$	5.72530e6	0.498291
$668$	−7.95138e6	−0.689448
$669$	6.60853e6	0.570873
$670$	−41887.5	−0.00360494
$671$	1.46043e7	1.25220
$672$	−1.95021e6	−0.166593
$673$	1.31732e7	1.12112	0.560561	−	0.828113i	$-0.310586\pi$
$673$	1.31732e7	1.12112	0.560561	+	0.828113i	$0.310586\pi$
$674$	−2.31860e6	−0.196596
$675$	−2.27752e6	−0.192399
$676$	1.06430e7	0.895776
$677$	−5.29079e6	−0.443658	−0.221829	−	0.975086i	$-0.571203\pi$
$677$	−5.29079e6	−0.443658	−0.221829	+	0.975086i	$0.571203\pi$
$678$	−177829.	−0.0148569
$679$	5.95107e6	0.495360
$680$	85736.8	0.00711042
$681$	3.33238e6	0.275351
$682$	−3.16619e6	−0.260661
$683$	−1.28101e7	−1.05076	−0.525378	−	0.850869i	$-0.676076\pi$
$683$	−1.28101e7	−1.05076	−0.525378	+	0.850869i	$0.676076\pi$
$684$	659963.	0.0539361
$685$	−257563.	−0.0209728
$686$	2.23836e6	0.181602
$687$	−6.21591e6	−0.502473
$688$	−9.98148e6	−0.803940
$689$	5.31113e6	0.426225
$690$	19222.4	0.00153704
$691$	−2.41425e7	−1.92348	−0.961739	−	0.273969i	$-0.911664\pi$
$691$	−2.41425e7	−1.92348	−0.961739	+	0.273969i	$0.911664\pi$
$692$	−1.14490e7	−0.908874
$693$	−1.55842e6	−0.123268
$694$	−4.52907e6	−0.356952
$695$	156797.	0.0123134
$696$	−2.04044e6	−0.159662
$697$	1.72030e7	1.34129
$698$	121067.	0.00940565
$699$	−8.32286e6	−0.644288
$700$	5.88877e6	0.454234
$701$	−1.34383e7	−1.03288	−0.516441	−	0.856323i	$-0.672743\pi$
$701$	−1.34383e7	−1.03288	−0.516441	+	0.856323i	$0.672743\pi$
$702$	133226.	0.0102034
$703$	−2.26916e6	−0.173172
$704$	7.48499e6	0.569193
$705$	−204574.	−0.0155016
$706$	−642973.	−0.0485491
$707$	−163078.	−0.0122701
$708$	−956185.	−0.0716900
$709$	4.97439e6	0.371642	0.185821	−	0.982584i	$-0.440506\pi$
$709$	4.97439e6	0.371642	0.185821	+	0.982584i	$0.440506\pi$
$710$	62746.7	0.00467138
$711$	−4.17791e6	−0.309946
$712$	−723816.	−0.0535092
$713$	1.60463e7	1.18209
$714$	−833480.	−0.0611856
$715$	42808.6	0.00313160
$716$	1.73908e7	1.26776
$717$	−5.11599e6	−0.371648
$718$	1.81647e6	0.131497
$719$	−2.75626e6	−0.198837	−0.0994185	−	0.995046i	$-0.531698\pi$
$719$	−2.75626e6	−0.198837	−0.0994185	+	0.995046i	$0.531698\pi$
$720$	65495.7	0.00470849
$721$	7.25360e6	0.519655
$722$	2.92486e6	0.208815
$723$	−2.62908e6	−0.187050
$724$	1.62461e7	1.15187
$725$	9.31477e6	0.658153
$726$	700542.	0.0493279
$727$	−1.11365e7	−0.781470	−0.390735	−	0.920503i	$-0.627779\pi$
$727$	−1.11365e7	−0.781470	−0.390735	+	0.920503i	$0.627779\pi$
$728$	−705638.	−0.0493462
$729$	531441.	0.0370370
$730$	−73691.2	−0.00511810
$731$	−1.39185e7	−0.963380
$732$	1.28770e7	0.888257
$733$	2.89889e6	0.199284	0.0996419	−	0.995023i	$-0.468230\pi$
$733$	2.89889e6	0.199284	0.0996419	+	0.995023i	$0.468230\pi$
$734$	−187554.	−0.0128495
$735$	−106939.	−0.00730158
$736$	6.73755e6	0.458466
$737$	−1.17322e7	−0.795633
$738$	−1.37459e6	−0.0929035
$739$	2.76654e7	1.86348	0.931741	−	0.363123i	$-0.118290\pi$
$739$	2.76654e7	1.86348	0.931741	+	0.363123i	$0.118290\pi$
$740$	−237251.	−0.0159268
$741$	361014.	0.0241534
$742$	2.65497e6	0.177031
$743$	−1.08048e7	−0.718033	−0.359017	−	0.933331i	$-0.616888\pi$
$743$	−1.08048e7	−0.718033	−0.359017	+	0.933331i	$0.616888\pi$
$744$	−5.71875e6	−0.378764
$745$	225496.	0.0148850
$746$	539200.	0.0354734
$747$	−2.33650e6	−0.153202
$748$	1.17229e7	0.766092
$749$	−1.41345e7	−0.920611
$750$	62556.2	0.00406085
$751$	−2.36060e7	−1.52729	−0.763645	−	0.645636i	$-0.776592\pi$
$751$	−2.36060e7	−1.52729	−0.763645	+	0.645636i	$0.776592\pi$
$752$	−2.19767e7	−1.41716
$753$	−1.58805e7	−1.02065
$754$	−544879.	−0.0349037
$755$	147955.	0.00944633
$756$	−1.37410e6	−0.0874408
$757$	2.12366e7	1.34693	0.673464	−	0.739220i	$-0.264806\pi$
$757$	2.12366e7	1.34693	0.673464	+	0.739220i	$0.264806\pi$
$758$	−3.06548e6	−0.193787
$759$	5.38400e6	0.339235
$760$	−18563.9	−0.00116583
$761$	−2.37074e7	−1.48396	−0.741982	−	0.670420i	$-0.766114\pi$
$761$	−2.37074e7	−1.48396	−0.741982	+	0.670420i	$0.766114\pi$
$762$	−3.12466e6	−0.194946
$763$	1.01166e7	0.629104
$764$	2.30880e7	1.43105
$765$	91329.0	0.00564228
$766$	−4.33073e6	−0.266679
$767$	−523054.	−0.0321039
$768$	5.37073e6	0.328572
$769$	1.33593e7	0.814644	0.407322	−	0.913285i	$-0.366463\pi$
$769$	1.33593e7	0.814644	0.407322	+	0.913285i	$0.366463\pi$
$770$	21399.5	0.00130070
$771$	−7.42226e6	−0.449676
$772$	−2.18415e7	−1.31899
$773$	−1.28438e7	−0.773117	−0.386558	−	0.922265i	$-0.626336\pi$
$773$	−1.28438e7	−0.773117	−0.386558	+	0.922265i	$0.626336\pi$
$774$	1.11214e6	0.0667277
$775$	2.61065e7	1.56133
$776$	7.32729e6	0.436806
$777$	4.72460e6	0.280745
$778$	−2.02887e6	−0.120172
$779$	−3.72484e6	−0.219920
$780$	37745.6	0.00222142
$781$	1.75747e7	1.03100
$782$	2.87950e6	0.168384
$783$	−2.17353e6	−0.126696
$784$	−1.14881e7	−0.667509
$785$	−194139.	−0.0112445
$786$	−1.68392e6	−0.0972224
$787$	−5.78070e6	−0.332693	−0.166347	−	0.986067i	$-0.553197\pi$
$787$	−5.78070e6	−0.332693	−0.166347	+	0.986067i	$0.553197\pi$
$788$	−1.00959e7	−0.579201
$789$	−8.23911e6	−0.471181
$790$	57369.4	0.00327049
$791$	1.00331e6	0.0570157
$792$	−1.91881e6	−0.108697
$793$	7.04403e6	0.397776
$794$	6.06495e6	0.341410
$795$	−290920.	−0.0163251
$796$	4.42771e6	0.247683
$797$	−4.78906e6	−0.267057	−0.133529	−	0.991045i	$-0.542631\pi$
$797$	−4.78906e6	−0.267057	−0.133529	+	0.991045i	$0.542631\pi$
$798$	180467.	0.0100321
$799$	−3.06449e7	−1.69821
$800$	1.09616e7	0.605551
$801$	−771027.	−0.0424608
$802$	−2.09332e6	−0.114921
$803$	−2.06401e7	−1.12960
$804$	−1.03447e7	−0.564386
$805$	−108453.	−0.00589864
$806$	−1.52713e6	−0.0828017
$807$	9.01253e6	0.487150
$808$	−200791.	−0.0108197
$809$	−1.17461e7	−0.630987	−0.315494	−	0.948928i	$-0.602170\pi$
$809$	−1.17461e7	−0.630987	−0.315494	+	0.948928i	$0.602170\pi$
$810$	−7297.53	−0.000390808 0
$811$	2.70056e6	0.144179	0.0720893	−	0.997398i	$-0.477033\pi$
$811$	2.70056e6	0.144179	0.0720893	+	0.997398i	$0.477033\pi$
$812$	5.61991e6	0.299116
$813$	−2.02653e7	−1.07529
$814$	3.22069e6	0.170368
$815$	391548.	0.0206486
$816$	9.81117e6	0.515817
$817$	3.01365e6	0.157957
$818$	−5.33374e6	−0.278708
$819$	−751663.	−0.0391574
$820$	−389448.	−0.0202262
$821$	2.05695e7	1.06504	0.532520	−	0.846418i	$-0.321245\pi$
$821$	2.05695e7	1.06504	0.532520	+	0.846418i	$0.321245\pi$
$822$	3.08289e6	0.159140
$823$	−3.85189e7	−1.98232	−0.991162	−	0.132654i	$-0.957650\pi$
$823$	−3.85189e7	−1.98232	−0.991162	+	0.132654i	$0.957650\pi$
$824$	8.93103e6	0.458230
$825$	8.75949e6	0.448068
$826$	−261469.	−0.0133343
$827$	726695.	0.0369478	0.0184739	−	0.999829i	$-0.494119\pi$
$827$	726695.	0.0369478	0.0184739	+	0.999829i	$0.494119\pi$
$828$	4.74723e6	0.240638
$829$	1.92752e7	0.974120	0.487060	−	0.873369i	$-0.338069\pi$
$829$	1.92752e7	0.974120	0.487060	+	0.873369i	$0.338069\pi$
$830$	32083.8	0.00161656
$831$	47539.4	0.00238809
$832$	3.61020e6	0.180810
$833$	−1.60193e7	−0.799891
$834$	−1.87679e6	−0.0934328
$835$	238250.	0.0118254
$836$	−2.53827e6	−0.125609
$837$	−6.09175e6	−0.300558
$838$	−7.02558e6	−0.345599
$839$	−2.47117e7	−1.21199	−0.605994	−	0.795470i	$-0.707224\pi$
$839$	−2.47117e7	−1.21199	−0.605994	+	0.795470i	$0.707224\pi$
$840$	38651.7	0.00189004
$841$	−1.16217e7	−0.566602
$842$	759257.	0.0369070
$843$	−2.23421e7	−1.08282
$844$	−2.55288e7	−1.23360
$845$	−318902.	−0.0153644
$846$	2.44864e6	0.117625
$847$	−3.95246e6	−0.189304
$848$	−3.12526e7	−1.49244
$849$	−783046.	−0.0372836
$850$	4.68479e6	0.222404
$851$	−1.63225e7	−0.772613
$852$	1.54961e7	0.731347
$853$	2.66298e7	1.25313	0.626563	−	0.779370i	$-0.284461\pi$
$853$	2.66298e7	1.25313	0.626563	+	0.779370i	$0.284461\pi$
$854$	3.52123e6	0.165215
$855$	−19774.7	−0.000925114 0
$856$	−1.74032e7	−0.811791
$857$	5.12844e6	0.238525	0.119262	−	0.992863i	$-0.461947\pi$
$857$	5.12844e6	0.238525	0.119262	+	0.992863i	$0.461947\pi$
$858$	−512398.	−0.0237623
$859$	2.30168e7	1.06430	0.532148	−	0.846651i	$-0.321385\pi$
$859$	2.30168e7	1.06430	0.532148	+	0.846651i	$0.321385\pi$
$860$	315091.	0.0145274
$861$	7.75544e6	0.356532
$862$	−1.84603e6	−0.0846194
$863$	−3.81545e7	−1.74389	−0.871944	−	0.489606i	$-0.837141\pi$
$863$	−3.81545e7	−1.74389	−0.871944	+	0.489606i	$0.837141\pi$
$864$	−2.55782e6	−0.116570
$865$	343052.	0.0155891
$866$	−7.37171e6	−0.334021
$867$	902253.	0.0407644
$868$	1.57509e7	0.709589
$869$	1.60686e7	0.721818
$870$	29846.0	0.00133687
$871$	−5.65876e6	−0.252741
$872$	1.24561e7	0.554742
$873$	7.80521e6	0.346616
$874$	−623474.	−0.0276083
$875$	−352943.	−0.0155842
$876$	−1.81990e7	−0.801285
$877$	−3.38162e7	−1.48466	−0.742328	−	0.670036i	$-0.766278\pi$
$877$	−3.38162e7	−1.48466	−0.742328	+	0.670036i	$0.766278\pi$
$878$	−5.30566e6	−0.232275
$879$	1.48954e6	0.0650248
$880$	−251901.	−0.0109654
$881$	2.86617e7	1.24412	0.622059	−	0.782970i	$-0.286296\pi$
$881$	2.86617e7	1.24412	0.622059	+	0.782970i	$0.286296\pi$
$882$	1.28000e6	0.0554038
$883$	−4.01713e7	−1.73386	−0.866930	−	0.498430i	$-0.833910\pi$
$883$	−4.01713e7	−1.73386	−0.866930	+	0.498430i	$0.833910\pi$
$884$	5.65425e6	0.243357
$885$	28650.5	0.00122963
$886$	7.73751e6	0.331144
$887$	−1.88137e7	−0.802906	−0.401453	−	0.915880i	$-0.631495\pi$
$887$	−1.88137e7	−0.802906	−0.401453	+	0.915880i	$0.631495\pi$
$888$	5.81718e6	0.247560
$889$	1.76293e7	0.748138
$890$	10587.4	0.000448039 0
$891$	−2.04396e6	−0.0862538
$892$	−2.24108e7	−0.943074
$893$	6.63529e6	0.278440
$894$	−2.69907e6	−0.112946
$895$	−521086.	−0.0217446
$896$	8.73876e6	0.363647
$897$	2.59684e6	0.107762
$898$	5.02661e6	0.208010
$899$	2.49146e7	1.02814
$900$	7.72350e6	0.317839
$901$	−4.35795e7	−1.78842
$902$	5.28677e6	0.216359
$903$	−6.27469e6	−0.256078
$904$	1.23533e6	0.0502762
$905$	−486789.	−0.0197569
$906$	−1.77095e6	−0.0716780
$907$	−8.85338e6	−0.357348	−0.178674	−	0.983908i	$-0.557181\pi$
$907$	−8.85338e6	−0.357348	−0.178674	+	0.983908i	$0.557181\pi$
$908$	−1.13007e7	−0.454875
$909$	−213887.	−0.00858570
$910$	10321.5	0.000413181 0
$911$	1.12187e7	0.447864	0.223932	−	0.974605i	$-0.428111\pi$
$911$	1.12187e7	0.447864	0.223932	+	0.974605i	$0.428111\pi$
$912$	−2.12433e6	−0.0845738
$913$	8.98634e6	0.356785
$914$	5.14098e6	0.203554
$915$	−385840.	−0.0152354
$916$	2.10794e7	0.830078
$917$	9.50072e6	0.373107
$918$	−1.09316e6	−0.0428132
$919$	2.15141e7	0.840299	0.420149	−	0.907455i	$-0.361978\pi$
$919$	2.15141e7	0.840299	0.420149	+	0.907455i	$0.361978\pi$
$920$	−133533.	−0.00520140
$921$	6.71909e6	0.261012
$922$	−6.70652e6	−0.259818
$923$	8.47671e6	0.327509
$924$	5.28489e6	0.203637
$925$	−2.65558e7	−1.02048
$926$	2.27393e6	0.0871466
$927$	9.51355e6	0.363616
$928$	1.04612e7	0.398759
$929$	1.34111e7	0.509831	0.254916	−	0.966963i	$-0.417952\pi$
$929$	1.34111e7	0.509831	0.254916	+	0.966963i	$0.417952\pi$
$930$	83649.5	0.00317144
$931$	3.46853e6	0.131151
$932$	2.82245e7	1.06435
$933$	5.74385e6	0.216023
$934$	−5.26230e6	−0.197382
$935$	−351258.	−0.0131401
$936$	−925489.	−0.0345288
$937$	−3.24101e7	−1.20596	−0.602978	−	0.797758i	$-0.706019\pi$
$937$	−3.24101e7	−1.20596	−0.602978	+	0.797758i	$0.706019\pi$
$938$	−2.82875e6	−0.104975
$939$	1.39709e7	0.517084
$940$	693749.	0.0256084
$941$	−3.91775e6	−0.144232	−0.0721162	−	0.997396i	$-0.522975\pi$
$941$	−3.91775e6	−0.144232	−0.0721162	+	0.997396i	$0.522975\pi$
$942$	2.32375e6	0.0853223
$943$	−2.67934e7	−0.981180
$944$	3.07783e6	0.112413
$945$	41172.7	0.00149979
$946$	−4.27736e6	−0.155399
$947$	−3.42000e7	−1.23923	−0.619614	−	0.784907i	$-0.712711\pi$
$947$	−3.42000e7	−1.23923	−0.619614	+	0.784907i	$0.712711\pi$
$948$	1.41681e7	0.512025
$949$	−9.95525e6	−0.358828
$950$	−1.01436e6	−0.0364656
$951$	1.77664e7	0.637013
$952$	5.78998e6	0.207054
$953$	4.25014e7	1.51590	0.757951	−	0.652312i	$-0.226201\pi$
$953$	4.25014e7	1.51590	0.757951	+	0.652312i	$0.226201\pi$
$954$	3.48217e6	0.123874
$955$	−691796.	−0.0245454
$956$	1.73493e7	0.613956
$957$	8.35956e6	0.295055
$958$	4.06937e6	0.143256
$959$	−1.73937e7	−0.610725
$960$	−197751.	−0.00692532
$961$	4.11988e7	1.43905
$962$	1.55342e6	0.0541191
$963$	−1.85383e7	−0.644175
$964$	8.91574e6	0.309005
$965$	654447.	0.0226233
$966$	1.29813e6	0.0447584
$967$	2.74628e7	0.944450	0.472225	−	0.881478i	$-0.343451\pi$
$967$	2.74628e7	0.944450	0.472225	+	0.881478i	$0.343451\pi$
$968$	−4.86649e6	−0.166927
$969$	−2.96223e6	−0.101347
$970$	−107178.	−0.00365743
$971$	4.50046e7	1.53183	0.765913	−	0.642945i	$-0.222287\pi$
$971$	4.50046e7	1.53183	0.765913	+	0.642945i	$0.222287\pi$
$972$	−1.80222e6	−0.0611846
$973$	1.05888e7	0.358564
$974$	−1.72598e6	−0.0582958
$975$	4.22492e6	0.142334
$976$	−4.14495e7	−1.39282
$977$	−1.02124e7	−0.342287	−0.171144	−	0.985246i	$-0.554746\pi$
$977$	−1.02124e7	−0.342287	−0.171144	+	0.985246i	$0.554746\pi$
$978$	−4.68664e6	−0.156680
$979$	2.96543e6	0.0988850
$980$	362650.	0.0120621
$981$	1.32685e7	0.440201
$982$	4.45645e6	0.147472
$983$	1.34161e7	0.442835	0.221418	−	0.975179i	$-0.428932\pi$
$983$	1.34161e7	0.442835	0.221418	+	0.975179i	$0.428932\pi$
$984$	9.54893e6	0.314389
$985$	302507.	0.00993449
$986$	4.47090e6	0.146455
$987$	−1.38153e7	−0.451405
$988$	−1.22427e6	−0.0399011
$989$	2.16777e7	0.704730
$990$	28066.8	0.000910135 0
$991$	−4.37148e7	−1.41398	−0.706992	−	0.707222i	$-0.749948\pi$
$991$	−4.37148e7	−1.41398	−0.706992	+	0.707222i	$0.749948\pi$
$992$	2.93195e7	0.945971
$993$	−2.16663e7	−0.697287
$994$	4.23741e6	0.136030
$995$	−132669.	−0.00424827
$996$	7.92352e6	0.253087
$997$	−3.11427e7	−0.992243	−0.496121	−	0.868253i	$-0.665243\pi$
$997$	−3.11427e7	−0.992243	−0.496121	+	0.868253i	$0.665243\pi$
$998$	2.36327e6	0.0751081
$999$	6.19661e6	0.196445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.a.1.6	✓	11
3.2	odd	2		531.6.a.b.1.6		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.a.1.6	✓	11	1.1	even	1	trivial
531.6.a.b.1.6		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)

\(f(q)\)	\(=\)	\(q-1.21624 q^{2} +9.00000 q^{3} -30.5208 q^{4} +0.914506 q^{5} -10.9462 q^{6} +61.7584 q^{7} +76.0403 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-1.21624 q^{2} +9.00000 q^{3} -30.5208 q^{4} +0.914506 q^{5} -10.9462 q^{6} +61.7584 q^{7} +76.0403 q^{8} +81.0000 q^{9} -1.11226 q^{10} -311.532 q^{11} -274.687 q^{12} -150.260 q^{13} -75.1131 q^{14} +8.23055 q^{15} +884.181 q^{16} +1232.93 q^{17} -98.5155 q^{18} -266.956 q^{19} -27.9114 q^{20} +555.825 q^{21} +378.898 q^{22} -1920.26 q^{23} +684.363 q^{24} -3124.16 q^{25} +182.752 q^{26} +729.000 q^{27} -1884.91 q^{28} -2981.52 q^{29} -10.0103 q^{30} -8356.31 q^{31} -3508.67 q^{32} -2803.79 q^{33} -1499.54 q^{34} +56.4784 q^{35} -2472.18 q^{36} +8500.15 q^{37} +324.682 q^{38} -1352.34 q^{39} +69.5393 q^{40} +13953.0 q^{41} -676.018 q^{42} -11289.0 q^{43} +9508.19 q^{44} +74.0750 q^{45} +2335.50 q^{46} -24855.4 q^{47} +7957.63 q^{48} -12992.9 q^{49} +3799.74 q^{50} +11096.3 q^{51} +4586.04 q^{52} -35346.4 q^{53} -886.640 q^{54} -284.898 q^{55} +4696.13 q^{56} -2402.60 q^{57} +3626.25 q^{58} +3481.00 q^{59} -251.203 q^{60} -46879.0 q^{61} +10163.3 q^{62} +5002.43 q^{63} -24026.4 q^{64} -137.413 q^{65} +3410.08 q^{66} +37659.9 q^{67} -37629.8 q^{68} -17282.3 q^{69} -68.6913 q^{70} -56413.7 q^{71} +6159.26 q^{72} +66253.6 q^{73} -10338.2 q^{74} -28117.5 q^{75} +8147.69 q^{76} -19239.7 q^{77} +1644.77 q^{78} -51579.2 q^{79} +808.588 q^{80} +6561.00 q^{81} -16970.2 q^{82} -28845.7 q^{83} -16964.2 q^{84} +1127.52 q^{85} +13730.1 q^{86} -26833.7 q^{87} -23689.0 q^{88} -9518.85 q^{89} -90.0930 q^{90} -9279.79 q^{91} +58607.8 q^{92} -75206.8 q^{93} +30230.2 q^{94} -244.132 q^{95} -31578.0 q^{96} +96360.6 q^{97} +15802.5 q^{98} -25234.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9} - 399 q^{10} - 698 q^{11} + 1350 q^{12} - 1556 q^{13} - 1679 q^{14} - 1728 q^{15} - 2662 q^{16} - 4793 q^{17} - 486 q^{18} - 3753 q^{19} - 11023 q^{20} - 3339 q^{21} - 9534 q^{22} - 7323 q^{23} - 5589 q^{24} + 7867 q^{25} - 4844 q^{26} + 8019 q^{27} + 3650 q^{28} - 15467 q^{29} - 3591 q^{30} - 5151 q^{31} - 15368 q^{32} - 6282 q^{33} + 8452 q^{34} - 23285 q^{35} + 12150 q^{36} + 8623 q^{37} + 15205 q^{38} - 14004 q^{39} + 41530 q^{40} - 6369 q^{41} - 15111 q^{42} - 20506 q^{43} - 55632 q^{44} - 15552 q^{45} - 45191 q^{46} - 47899 q^{47} - 23958 q^{48} - 10322 q^{49} - 102147 q^{50} - 43137 q^{51} - 292 q^{52} - 80048 q^{53} - 4374 q^{54} - 2114 q^{55} - 108126 q^{56} - 33777 q^{57} - 58294 q^{58} + 38291 q^{59} - 99207 q^{60} - 82527 q^{61} - 67438 q^{62} - 30051 q^{63} - 51411 q^{64} - 167646 q^{65} - 85806 q^{66} - 166976 q^{67} - 136533 q^{68} - 65907 q^{69} + 76140 q^{70} - 183560 q^{71} - 50301 q^{72} - 36809 q^{73} - 116686 q^{74} + 70803 q^{75} + 55580 q^{76} - 164885 q^{77} - 43596 q^{78} - 281518 q^{79} - 32683 q^{80} + 72171 q^{81} + 178815 q^{82} - 254691 q^{83} + 32850 q^{84} + 4763 q^{85} + 349324 q^{86} - 139203 q^{87} + 251285 q^{88} - 89687 q^{89} - 32319 q^{90} + 34897 q^{91} - 20240 q^{92} - 46359 q^{93} + 96548 q^{94} - 155113 q^{95} - 138312 q^{96} - 45828 q^{97} + 465864 q^{98} - 56538 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9 - 399 * q^10 - 698 * q^11 + 1350 * q^12 - 1556 * q^13 - 1679 * q^14 - 1728 * q^15 - 2662 * q^16 - 4793 * q^17 - 486 * q^18 - 3753 * q^19 - 11023 * q^20 - 3339 * q^21 - 9534 * q^22 - 7323 * q^23 - 5589 * q^24 + 7867 * q^25 - 4844 * q^26 + 8019 * q^27 + 3650 * q^28 - 15467 * q^29 - 3591 * q^30 - 5151 * q^31 - 15368 * q^32 - 6282 * q^33 + 8452 * q^34 - 23285 * q^35 + 12150 * q^36 + 8623 * q^37 + 15205 * q^38 - 14004 * q^39 + 41530 * q^40 - 6369 * q^41 - 15111 * q^42 - 20506 * q^43 - 55632 * q^44 - 15552 * q^45 - 45191 * q^46 - 47899 * q^47 - 23958 * q^48 - 10322 * q^49 - 102147 * q^50 - 43137 * q^51 - 292 * q^52 - 80048 * q^53 - 4374 * q^54 - 2114 * q^55 - 108126 * q^56 - 33777 * q^57 - 58294 * q^58 + 38291 * q^59 - 99207 * q^60 - 82527 * q^61 - 67438 * q^62 - 30051 * q^63 - 51411 * q^64 - 167646 * q^65 - 85806 * q^66 - 166976 * q^67 - 136533 * q^68 - 65907 * q^69 + 76140 * q^70 - 183560 * q^71 - 50301 * q^72 - 36809 * q^73 - 116686 * q^74 + 70803 * q^75 + 55580 * q^76 - 164885 * q^77 - 43596 * q^78 - 281518 * q^79 - 32683 * q^80 + 72171 * q^81 + 178815 * q^82 - 254691 * q^83 + 32850 * q^84 + 4763 * q^85 + 349324 * q^86 - 139203 * q^87 + 251285 * q^88 - 89687 * q^89 - 32319 * q^90 + 34897 * q^91 - 20240 * q^92 - 46359 * q^93 + 96548 * q^94 - 155113 * q^95 - 138312 * q^96 - 45828 * q^97 + 465864 * q^98 - 56538 * q^99

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