LMFDB - Embedded newform 177.6.a.c.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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + \cdots + 49172480 $ x^12 - 2x^11 - 269x^10 + 143x^9 + 25384x^8 + 8539x^7 - 1009736x^6 - 720516x^5 + 15565376x^4 + 6775664x^3 - 75006848x^2 + 21512960*x + 49172480
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.70991$ 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)

$f(q)$	$=$	$q+0.290087 q^{2} +9.00000 q^{3} -31.9158 q^{4} +87.1048 q^{5} +2.61079 q^{6} +167.610 q^{7} -18.5412 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+0.290087 q^{2} +9.00000 q^{3} -31.9158 q^{4} +87.1048 q^{5} +2.61079 q^{6} +167.610 q^{7} -18.5412 q^{8} +81.0000 q^{9} +25.2680 q^{10} +252.804 q^{11} -287.243 q^{12} -289.403 q^{13} +48.6216 q^{14} +783.943 q^{15} +1015.93 q^{16} -227.568 q^{17} +23.4971 q^{18} -1162.71 q^{19} -2780.02 q^{20} +1508.49 q^{21} +73.3353 q^{22} -1231.89 q^{23} -166.871 q^{24} +4462.24 q^{25} -83.9520 q^{26} +729.000 q^{27} -5349.42 q^{28} +1975.28 q^{29} +227.412 q^{30} +7791.87 q^{31} +888.026 q^{32} +2275.24 q^{33} -66.0147 q^{34} +14599.6 q^{35} -2585.18 q^{36} +7046.70 q^{37} -337.287 q^{38} -2604.62 q^{39} -1615.03 q^{40} -11251.3 q^{41} +437.594 q^{42} +18519.7 q^{43} -8068.46 q^{44} +7055.49 q^{45} -357.355 q^{46} -20101.5 q^{47} +9143.36 q^{48} +11286.1 q^{49} +1294.44 q^{50} -2048.11 q^{51} +9236.53 q^{52} +37357.8 q^{53} +211.474 q^{54} +22020.5 q^{55} -3107.69 q^{56} -10464.4 q^{57} +573.003 q^{58} -3481.00 q^{59} -25020.2 q^{60} -998.231 q^{61} +2260.32 q^{62} +13576.4 q^{63} -32252.1 q^{64} -25208.3 q^{65} +660.018 q^{66} -19664.7 q^{67} +7263.03 q^{68} -11087.0 q^{69} +4235.17 q^{70} +21610.0 q^{71} -1501.84 q^{72} +46265.2 q^{73} +2044.16 q^{74} +40160.2 q^{75} +37108.8 q^{76} +42372.5 q^{77} -755.568 q^{78} -85014.5 q^{79} +88492.2 q^{80} +6561.00 q^{81} -3263.86 q^{82} +75468.7 q^{83} -48144.8 q^{84} -19822.3 q^{85} +5372.32 q^{86} +17777.5 q^{87} -4687.29 q^{88} +105603. q^{89} +2046.71 q^{90} -48506.8 q^{91} +39316.7 q^{92} +70126.8 q^{93} -5831.19 q^{94} -101277. q^{95} +7992.23 q^{96} -109794. q^{97} +3273.97 q^{98} +20477.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9} + 601 q^{10} + 1480 q^{11} + 1782 q^{12} + 472 q^{13} + 1065 q^{14} + 1422 q^{15} + 6370 q^{16} + 1565 q^{17} + 1782 q^{18} + 3939 q^{19} + 8033 q^{20} + 3717 q^{21} - 1738 q^{22} + 7245 q^{23} + 6507 q^{24} + 9690 q^{25} + 3764 q^{26} + 8748 q^{27} + 12154 q^{28} + 10003 q^{29} + 5409 q^{30} + 7295 q^{31} + 11628 q^{32} + 13320 q^{33} - 16344 q^{34} + 11015 q^{35} + 16038 q^{36} + 6741 q^{37} + 3035 q^{38} + 4248 q^{39} + 5572 q^{40} + 34025 q^{41} + 9585 q^{42} - 6336 q^{43} + 41168 q^{44} + 12798 q^{45} + 2345 q^{46} + 66167 q^{47} + 57330 q^{48} + 28319 q^{49} + 31173 q^{50} + 14085 q^{51} + 16440 q^{52} + 62290 q^{53} + 16038 q^{54} + 55764 q^{55} + 107306 q^{56} + 35451 q^{57} + 37952 q^{58} - 41772 q^{59} + 72297 q^{60} + 68469 q^{61} + 99190 q^{62} + 33453 q^{63} + 68525 q^{64} + 80156 q^{65} - 15642 q^{66} + 113310 q^{67} + 33887 q^{68} + 65205 q^{69} + 32034 q^{70} + 84520 q^{71} + 58563 q^{72} + 135895 q^{73} - 31962 q^{74} + 87210 q^{75} - 61848 q^{76} - 3799 q^{77} + 33876 q^{78} + 14122 q^{79} + 77609 q^{80} + 78732 q^{81} - 1501 q^{82} + 114463 q^{83} + 109386 q^{84} - 101097 q^{85} - 203536 q^{86} + 90027 q^{87} - 244967 q^{88} + 189109 q^{89} + 48681 q^{90} - 168249 q^{91} - 71946 q^{92} + 65655 q^{93} - 472284 q^{94} + 21923 q^{95} + 104652 q^{96} - 76192 q^{97} - 17544 q^{98} + 119880 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9 + 601 * q^10 + 1480 * q^11 + 1782 * q^12 + 472 * q^13 + 1065 * q^14 + 1422 * q^15 + 6370 * q^16 + 1565 * q^17 + 1782 * q^18 + 3939 * q^19 + 8033 * q^20 + 3717 * q^21 - 1738 * q^22 + 7245 * q^23 + 6507 * q^24 + 9690 * q^25 + 3764 * q^26 + 8748 * q^27 + 12154 * q^28 + 10003 * q^29 + 5409 * q^30 + 7295 * q^31 + 11628 * q^32 + 13320 * q^33 - 16344 * q^34 + 11015 * q^35 + 16038 * q^36 + 6741 * q^37 + 3035 * q^38 + 4248 * q^39 + 5572 * q^40 + 34025 * q^41 + 9585 * q^42 - 6336 * q^43 + 41168 * q^44 + 12798 * q^45 + 2345 * q^46 + 66167 * q^47 + 57330 * q^48 + 28319 * q^49 + 31173 * q^50 + 14085 * q^51 + 16440 * q^52 + 62290 * q^53 + 16038 * q^54 + 55764 * q^55 + 107306 * q^56 + 35451 * q^57 + 37952 * q^58 - 41772 * q^59 + 72297 * q^60 + 68469 * q^61 + 99190 * q^62 + 33453 * q^63 + 68525 * q^64 + 80156 * q^65 - 15642 * q^66 + 113310 * q^67 + 33887 * q^68 + 65205 * q^69 + 32034 * q^70 + 84520 * q^71 + 58563 * q^72 + 135895 * q^73 - 31962 * q^74 + 87210 * q^75 - 61848 * q^76 - 3799 * q^77 + 33876 * q^78 + 14122 * q^79 + 77609 * q^80 + 78732 * q^81 - 1501 * q^82 + 114463 * q^83 + 109386 * q^84 - 101097 * q^85 - 203536 * q^86 + 90027 * q^87 - 244967 * q^88 + 189109 * q^89 + 48681 * q^90 - 168249 * q^91 - 71946 * q^92 + 65655 * q^93 - 472284 * q^94 + 21923 * q^95 + 104652 * q^96 - 76192 * q^97 - 17544 * q^98 + 119880 * 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 $

$2$	0.290087	0.0512807	0.0256403	−	0.999671i	$-0.491838\pi$
$2$	0.290087	0.0512807	0.0256403	+	0.999671i	$0.491838\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−31.9158	−0.997370
$5$	87.1048	1.55818	0.779089	−	0.626913i	$-0.215682\pi$
$5$	87.1048	1.55818	0.779089	+	0.626913i	$0.215682\pi$
$6$	2.61079	0.0296069
$7$	167.610	1.29287	0.646435	−	0.762969i	$-0.276259\pi$
$7$	167.610	1.29287	0.646435	+	0.762969i	$0.276259\pi$
$8$	−18.5412	−0.102427
$9$	81.0000	0.333333
$10$	25.2680	0.0799044
$11$	252.804	0.629945	0.314972	−	0.949101i	$-0.398005\pi$
$11$	252.804	0.629945	0.314972	+	0.949101i	$0.398005\pi$
$12$	−287.243	−0.575832
$13$	−289.403	−0.474946	−0.237473	−	0.971394i	$-0.576319\pi$
$13$	−289.403	−0.474946	−0.237473	+	0.971394i	$0.576319\pi$
$14$	48.6216	0.0662993
$15$	783.943	0.899614
$16$	1015.93	0.992118
$17$	−227.568	−0.190981	−0.0954903	−	0.995430i	$-0.530442\pi$
$17$	−227.568	−0.190981	−0.0954903	+	0.995430i	$0.530442\pi$
$18$	23.4971	0.0170936
$19$	−1162.71	−0.738902	−0.369451	−	0.929250i	$-0.620454\pi$
$19$	−1162.71	−0.738902	−0.369451	+	0.929250i	$0.620454\pi$
$20$	−2780.02	−1.55408
$21$	1508.49	0.746439
$22$	73.3353	0.0323040
$23$	−1231.89	−0.485570	−0.242785	−	0.970080i	$-0.578061\pi$
$23$	−1231.89	−0.485570	−0.242785	+	0.970080i	$0.578061\pi$
$24$	−166.871	−0.0591360
$25$	4462.24	1.42792
$26$	−83.9520	−0.0243555
$27$	729.000	0.192450
$28$	−5349.42	−1.28947
$29$	1975.28	0.436147	0.218073	−	0.975932i	$-0.430023\pi$
$29$	1975.28	0.436147	0.218073	+	0.975932i	$0.430023\pi$
$30$	227.412	0.0461328
$31$	7791.87	1.45626	0.728128	−	0.685441i	$-0.240391\pi$
$31$	7791.87	1.45626	0.728128	+	0.685441i	$0.240391\pi$
$32$	888.026	0.153303
$33$	2275.24	0.363699
$34$	−66.0147	−0.00979362
$35$	14599.6	2.01452
$36$	−2585.18	−0.332457
$37$	7046.70	0.846216	0.423108	−	0.906079i	$-0.360939\pi$
$37$	7046.70	0.846216	0.423108	+	0.906079i	$0.360939\pi$
$38$	−337.287	−0.0378914
$39$	−2604.62	−0.274210
$40$	−1615.03	−0.159599
$41$	−11251.3	−1.04530	−0.522652	−	0.852546i	$-0.675057\pi$
$41$	−11251.3	−1.04530	−0.522652	+	0.852546i	$0.675057\pi$
$42$	437.594	0.0382779
$43$	18519.7	1.52743	0.763716	−	0.645552i	$-0.223373\pi$
$43$	18519.7	1.52743	0.763716	+	0.645552i	$0.223373\pi$
$44$	−8068.46	−0.628288
$45$	7055.49	0.519393
$46$	−357.355	−0.0249003
$47$	−20101.5	−1.32735	−0.663673	−	0.748023i	$-0.731003\pi$
$47$	−20101.5	−1.32735	−0.663673	+	0.748023i	$0.731003\pi$
$48$	9143.36	0.572799
$49$	11286.1	0.671514
$50$	1294.44	0.0732246
$51$	−2048.11	−0.110263
$52$	9236.53	0.473697
$53$	37357.8	1.82681	0.913403	−	0.407058i	$-0.133445\pi$
$53$	37357.8	1.82681	0.913403	+	0.407058i	$0.133445\pi$
$54$	211.474	0.00986897
$55$	22020.5	0.981566
$56$	−3107.69	−0.132424
$57$	−10464.4	−0.426605
$58$	573.003	0.0223659
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−25020.2	−0.897249
$61$	−998.231	−0.0343484	−0.0171742	−	0.999853i	$-0.505467\pi$
$61$	−998.231	−0.0343484	−0.0171742	+	0.999853i	$0.505467\pi$
$62$	2260.32	0.0746778
$63$	13576.4	0.430957
$64$	−32252.1	−0.984256
$65$	−25208.3	−0.740050
$66$	660.018	0.0186507
$67$	−19664.7	−0.535181	−0.267590	−	0.963533i	$-0.586227\pi$
$67$	−19664.7	−0.535181	−0.267590	+	0.963533i	$0.586227\pi$
$68$	7263.03	0.190478
$69$	−11087.0	−0.280344
$70$	4235.17	0.103306
$71$	21610.0	0.508755	0.254378	−	0.967105i	$-0.418129\pi$
$71$	21610.0	0.508755	0.254378	+	0.967105i	$0.418129\pi$
$72$	−1501.84	−0.0341422
$73$	46265.2	1.01613	0.508063	−	0.861320i	$-0.330362\pi$
$73$	46265.2	1.01613	0.508063	+	0.861320i	$0.330362\pi$
$74$	2044.16	0.0433945
$75$	40160.2	0.824409
$76$	37108.8	0.736958
$77$	42372.5	0.814437
$78$	−755.568	−0.0140617
$79$	−85014.5	−1.53259	−0.766294	−	0.642490i	$-0.777901\pi$
$79$	−85014.5	−1.53259	−0.766294	+	0.642490i	$0.777901\pi$
$80$	88492.2	1.54590
$81$	6561.00	0.111111
$82$	−3263.86	−0.0536039
$83$	75468.7	1.20246	0.601231	−	0.799075i	$-0.294677\pi$
$83$	75468.7	1.20246	0.601231	+	0.799075i	$0.294677\pi$
$84$	−48144.8	−0.744476
$85$	−19822.3	−0.297582
$86$	5372.32	0.0783278
$87$	17777.5	0.251810
$88$	−4687.29	−0.0645231
$89$	105603.	1.41319	0.706596	−	0.707617i	$-0.250230\pi$
$89$	105603.	1.41319	0.706596	+	0.707617i	$0.250230\pi$
$90$	2046.71	0.0266348
$91$	−48506.8	−0.614043
$92$	39316.7	0.484293
$93$	70126.8	0.840769
$94$	−5831.19	−0.0680672
$95$	−101277.	−1.15134
$96$	7992.23	0.0885095
$97$	−109794.	−1.18481	−0.592404	−	0.805641i	$-0.701821\pi$
$97$	−109794.	−1.18481	−0.592404	+	0.805641i	$0.701821\pi$
$98$	3273.97	0.0344357
$99$	20477.1	0.209982
$100$	−142416.	−1.42416
$101$	96278.1	0.939126	0.469563	−	0.882899i	$-0.344411\pi$
$101$	96278.1	0.939126	0.469563	+	0.882899i	$0.344411\pi$
$102$	−594.132	−0.00565435
$103$	−120043.	−1.11492	−0.557459	−	0.830205i	$-0.688223\pi$
$103$	−120043.	−1.11492	−0.557459	+	0.830205i	$0.688223\pi$
$104$	5365.87	0.0486470
$105$	131397.	1.16308
$106$	10837.0	0.0936798
$107$	−37527.7	−0.316878	−0.158439	−	0.987369i	$-0.550646\pi$
$107$	−37527.7	−0.316878	−0.158439	+	0.987369i	$0.550646\pi$
$108$	−23266.7	−0.191944
$109$	−100498.	−0.810201	−0.405101	−	0.914272i	$-0.632763\pi$
$109$	−100498.	−0.810201	−0.405101	+	0.914272i	$0.632763\pi$
$110$	6387.85	0.0503354
$111$	63420.3	0.488563
$112$	170280.	1.28268
$113$	−96992.3	−0.714564	−0.357282	−	0.933997i	$-0.616297\pi$
$113$	−96992.3	−0.714564	−0.357282	+	0.933997i	$0.616297\pi$
$114$	−3035.58	−0.0218766
$115$	−107303.	−0.756604
$116$	−63042.6	−0.435000
$117$	−23441.6	−0.158315
$118$	−1009.79	−0.00667618
$119$	−38142.7	−0.246913
$120$	−14535.2	−0.0921444
$121$	−97141.1	−0.603170
$122$	−289.574	−0.00176141
$123$	−101262.	−0.603506
$124$	−248684.	−1.45243
$125$	116480.	0.666772
$126$	3938.35	0.0220998
$127$	22759.5	0.125214	0.0626071	−	0.998038i	$-0.480058\pi$
$127$	22759.5	0.125214	0.0626071	+	0.998038i	$0.480058\pi$
$128$	−37772.8	−0.203776
$129$	166677.	0.881863
$130$	−7312.62	−0.0379503
$131$	−218805.	−1.11398	−0.556992	−	0.830518i	$-0.688045\pi$
$131$	−218805.	−1.11398	−0.556992	+	0.830518i	$0.688045\pi$
$132$	−72616.1	−0.362742
$133$	−194882.	−0.955304
$134$	−5704.48	−0.0274444
$135$	63499.4	0.299871
$136$	4219.38	0.0195615
$137$	−377313.	−1.71752	−0.858758	−	0.512382i	$-0.828763\pi$
$137$	−377313.	−1.71752	−0.858758	+	0.512382i	$0.828763\pi$
$138$	−3216.20	−0.0143762
$139$	−5026.98	−0.0220683	−0.0110342	−	0.999939i	$-0.503512\pi$
$139$	−5026.98	−0.0220683	−0.0110342	+	0.999939i	$0.503512\pi$
$140$	−465960.	−2.00922
$141$	−180914.	−0.766343
$142$	6268.79	0.0260893
$143$	−73162.2	−0.299190
$144$	82290.2	0.330706
$145$	172056.	0.679594
$146$	13421.0	0.0521076
$147$	101575.	0.387699
$148$	−224901.	−0.843991
$149$	−165819.	−0.611884	−0.305942	−	0.952050i	$-0.598971\pi$
$149$	−165819.	−0.611884	−0.305942	+	0.952050i	$0.598971\pi$
$150$	11650.0	0.0422763
$151$	305526.	1.09045	0.545225	−	0.838290i	$-0.316444\pi$
$151$	305526.	1.09045	0.545225	+	0.838290i	$0.316444\pi$
$152$	21558.0	0.0756831
$153$	−18433.0	−0.0636602
$154$	12291.7	0.0417649
$155$	678709.	2.26910
$156$	83128.8	0.273489
$157$	−412996.	−1.33720	−0.668600	−	0.743622i	$-0.733106\pi$
$157$	−412996.	−1.33720	−0.668600	+	0.743622i	$0.733106\pi$
$158$	−24661.6	−0.0785921
$159$	336221.	1.05471
$160$	77351.3	0.238873
$161$	−206477.	−0.627779
$162$	1903.26	0.00569785
$163$	234544.	0.691441	0.345721	−	0.938337i	$-0.387634\pi$
$163$	234544.	0.691441	0.345721	+	0.938337i	$0.387634\pi$
$164$	359094.	1.04255
$165$	198184.	0.566707
$166$	21892.5	0.0616631
$167$	138449.	0.384148	0.192074	−	0.981380i	$-0.438479\pi$
$167$	138449.	0.384148	0.192074	+	0.981380i	$0.438479\pi$
$168$	−27969.2	−0.0764552
$169$	−287539.	−0.774427
$170$	−5750.19	−0.0152602
$171$	−94179.3	−0.246301
$172$	−591071.	−1.52342
$173$	150940.	0.383433	0.191717	−	0.981450i	$-0.438595\pi$
$173$	150940.	0.383433	0.191717	+	0.981450i	$0.438595\pi$
$174$	5157.02	0.0129130
$175$	747917.	1.84611
$176$	256831.	0.624979
$177$	−31329.0	−0.0751646
$178$	30634.1	0.0724694
$179$	2851.21	0.00665114	0.00332557	−	0.999994i	$-0.498941\pi$
$179$	2851.21	0.00665114	0.00332557	+	0.999994i	$0.498941\pi$
$180$	−225182.	−0.518027
$181$	340696.	0.772985	0.386492	−	0.922293i	$-0.373687\pi$
$181$	340696.	0.772985	0.386492	+	0.922293i	$0.373687\pi$
$182$	−14071.2	−0.0314886
$183$	−8984.08	−0.0198311
$184$	22840.7	0.0497352
$185$	613801.	1.31856
$186$	20342.9	0.0431152
$187$	−57530.2	−0.120307
$188$	641557.	1.32386
$189$	122188.	0.248813
$190$	−29379.3	−0.0590415
$191$	−101124.	−0.200571	−0.100286	−	0.994959i	$-0.531976\pi$
$191$	−101124.	−0.200571	−0.100286	+	0.994959i	$0.531976\pi$
$192$	−290269.	−0.568261
$193$	344995.	0.666683	0.333342	−	0.942806i	$-0.391824\pi$
$193$	344995.	0.666683	0.333342	+	0.942806i	$0.391824\pi$
$194$	−31849.8	−0.0607578
$195$	−226875.	−0.427268
$196$	−360207.	−0.669748
$197$	−506599.	−0.930034	−0.465017	−	0.885302i	$-0.653952\pi$
$197$	−506599.	−0.930034	−0.465017	+	0.885302i	$0.653952\pi$
$198$	5940.16	0.0107680
$199$	−221500.	−0.396498	−0.198249	−	0.980152i	$-0.563525\pi$
$199$	−221500.	−0.396498	−0.198249	+	0.980152i	$0.563525\pi$
$200$	−82735.3	−0.146257
$201$	−176982.	−0.308987
$202$	27929.1	0.0481591
$203$	331076.	0.563882
$204$	65367.3	0.109973
$205$	−980041.	−1.62877
$206$	−34822.9	−0.0571737
$207$	−99782.9	−0.161857
$208$	−294012.	−0.471202
$209$	−293937.	−0.465467
$210$	38116.5	0.0596438
$211$	−969455.	−1.49907	−0.749534	−	0.661966i	$-0.769723\pi$
$211$	−969455.	−1.49907	−0.749534	+	0.661966i	$0.769723\pi$
$212$	−1.19231e6	−1.82200
$213$	194490.	0.293730
$214$	−10886.3	−0.0162497
$215$	1.61315e6	2.38001
$216$	−13516.5	−0.0197120
$217$	1.30600e6	1.88275
$218$	−29153.3	−0.0415477
$219$	416387.	0.586660
$220$	−702801.	−0.978985
$221$	65858.8	0.0907054
$222$	18397.4	0.0250539
$223$	−1.33305e6	−1.79509	−0.897544	−	0.440925i	$-0.854650\pi$
$223$	−1.33305e6	−1.79509	−0.897544	+	0.440925i	$0.854650\pi$
$224$	148842.	0.198201
$225$	361442.	0.475973
$226$	−28136.2	−0.0366433
$227$	734891.	0.946582	0.473291	−	0.880906i	$-0.343066\pi$
$227$	734891.	0.946582	0.473291	+	0.880906i	$0.343066\pi$
$228$	333979.	0.425483
$229$	315332.	0.397355	0.198677	−	0.980065i	$-0.436335\pi$
$229$	315332.	0.397355	0.198677	+	0.980065i	$0.436335\pi$
$230$	−31127.3	−0.0387992
$231$	381353.	0.470215
$232$	−36624.0	−0.0446730
$233$	447622.	0.540159	0.270079	−	0.962838i	$-0.412950\pi$
$233$	447622.	0.540159	0.270079	+	0.962838i	$0.412950\pi$
$234$	−6800.12	−0.00811852
$235$	−1.75094e6	−2.06824
$236$	111099.	0.129847
$237$	−765131.	−0.884840
$238$	−11064.7	−0.0126619
$239$	220701.	0.249925	0.124962	−	0.992161i	$-0.460119\pi$
$239$	220701.	0.249925	0.124962	+	0.992161i	$0.460119\pi$
$240$	796430.	0.892523
$241$	643890.	0.714117	0.357058	−	0.934082i	$-0.383780\pi$
$241$	643890.	0.714117	0.357058	+	0.934082i	$0.383780\pi$
$242$	−28179.4	−0.0309310
$243$	59049.0	0.0641500
$244$	31859.4	0.0342581
$245$	983077.	1.04634
$246$	−29374.7	−0.0309482
$247$	336491.	0.350938
$248$	−144471.	−0.149159
$249$	679218.	0.694242
$250$	33789.5	0.0341925
$251$	1.13484e6	1.13697	0.568485	−	0.822693i	$-0.307530\pi$
$251$	1.13484e6	1.13697	0.568485	+	0.822693i	$0.307530\pi$
$252$	−433303.	−0.429824
$253$	−311426.	−0.305882
$254$	6602.25	0.00642107
$255$	−178401.	−0.171809
$256$	1.02111e6	0.973807
$257$	157266.	0.148526	0.0742630	−	0.997239i	$-0.476340\pi$
$257$	157266.	0.148526	0.0742630	+	0.997239i	$0.476340\pi$
$258$	48350.9	0.0452226
$259$	1.18110e6	1.09405
$260$	804546.	0.738104
$261$	159997.	0.145382
$262$	−63472.6	−0.0571259
$263$	−943147.	−0.840794	−0.420397	−	0.907340i	$-0.638109\pi$
$263$	−943147.	−0.840794	−0.420397	+	0.907340i	$0.638109\pi$
$264$	−42185.6	−0.0372524
$265$	3.25405e6	2.84649
$266$	−56532.7	−0.0489886
$267$	950427.	0.815907
$268$	627616.	0.533773
$269$	528620.	0.445413	0.222707	−	0.974885i	$-0.428511\pi$
$269$	528620.	0.445413	0.222707	+	0.974885i	$0.428511\pi$
$270$	18420.4	0.0153776
$271$	1.81630e6	1.50233	0.751163	−	0.660117i	$-0.229493\pi$
$271$	1.81630e6	1.50233	0.751163	+	0.660117i	$0.229493\pi$
$272$	−231193.	−0.189475
$273$	−436561.	−0.354518
$274$	−109454.	−0.0880754
$275$	1.12807e6	0.899509
$276$	353851.	0.279607
$277$	−1.67266e6	−1.30981	−0.654905	−	0.755711i	$-0.727291\pi$
$277$	−1.67266e6	−1.30981	−0.654905	+	0.755711i	$0.727291\pi$
$278$	−1458.26	−0.00113168
$279$	631142.	0.485418
$280$	−270695.	−0.206340
$281$	461678.	0.348798	0.174399	−	0.984675i	$-0.444202\pi$
$281$	461678.	0.348798	0.174399	+	0.984675i	$0.444202\pi$
$282$	−52480.7	−0.0392986
$283$	880352.	0.653417	0.326708	−	0.945125i	$-0.394061\pi$
$283$	880352.	0.653417	0.326708	+	0.945125i	$0.394061\pi$
$284$	−689702.	−0.507418
$285$	−911497.	−0.664726
$286$	−21223.4	−0.0153426
$287$	−1.88583e6	−1.35144
$288$	71930.1	0.0511010
$289$	−1.36807e6	−0.963526
$290$	49911.3	0.0348501
$291$	−988143.	−0.684049
$292$	−1.47659e6	−1.01345
$293$	−2.64738e6	−1.80155	−0.900777	−	0.434281i	$-0.857002\pi$
$293$	−2.64738e6	−1.80155	−0.900777	+	0.434281i	$0.857002\pi$
$294$	29465.7	0.0198815
$295$	−303212.	−0.202857
$296$	−130654.	−0.0866750
$297$	184294.	0.121233
$298$	−48102.0	−0.0313778
$299$	356512.	0.230619
$300$	−1.28175e6	−0.822241
$301$	3.10408e6	1.97477
$302$	88629.2	0.0559190
$303$	866503.	0.542205
$304$	−1.18123e6	−0.733077
$305$	−86950.7	−0.0535209
$306$	−5347.19	−0.00326454
$307$	−2.30973e6	−1.39867	−0.699336	−	0.714794i	$-0.746521\pi$
$307$	−2.30973e6	−1.39867	−0.699336	+	0.714794i	$0.746521\pi$
$308$	−1.35236e6	−0.812295
$309$	−1.08038e6	−0.643698
$310$	196885.	0.116361
$311$	−2.74862e6	−1.61144	−0.805719	−	0.592298i	$-0.798221\pi$
$311$	−2.74862e6	−1.61144	−0.805719	+	0.592298i	$0.798221\pi$
$312$	48292.8	0.0280864
$313$	−2.11318e6	−1.21920	−0.609601	−	0.792708i	$-0.708670\pi$
$313$	−2.11318e6	−1.21920	−0.609601	+	0.792708i	$0.708670\pi$
$314$	−119805.	−0.0685725
$315$	1.18257e6	0.671507
$316$	2.71331e6	1.52856
$317$	1.75231e6	0.979407	0.489703	−	0.871889i	$-0.337105\pi$
$317$	1.75231e6	0.979407	0.489703	+	0.871889i	$0.337105\pi$
$318$	97533.4	0.0540861
$319$	499358.	0.274748
$320$	−2.80931e6	−1.53365
$321$	−337749.	−0.182950
$322$	−59896.3	−0.0321929
$323$	264595.	0.141116
$324$	−209400.	−0.110819
$325$	−1.29138e6	−0.678184
$326$	68038.2	0.0354576
$327$	−904485.	−0.467770
$328$	208612.	0.107067
$329$	−3.36922e6	−1.71609
$330$	57490.7	0.0290611
$331$	−971356.	−0.487313	−0.243657	−	0.969862i	$-0.578347\pi$
$331$	−971356.	−0.487313	−0.243657	+	0.969862i	$0.578347\pi$
$332$	−2.40865e6	−1.19930
$333$	570782.	0.282072
$334$	40162.3	0.0196994
$335$	−1.71289e6	−0.833907
$336$	1.53252e6	0.740556
$337$	1.02817e6	0.493164	0.246582	−	0.969122i	$-0.420693\pi$
$337$	1.02817e6	0.493164	0.246582	+	0.969122i	$0.420693\pi$
$338$	−83411.5	−0.0397131
$339$	−872931.	−0.412554
$340$	632645.	0.296799
$341$	1.96982e6	0.917360
$342$	−27320.2	−0.0126305
$343$	−925352.	−0.424690
$344$	−343376.	−0.156450
$345$	−965730.	−0.436825
$346$	43785.9	0.0196627
$347$	2.24381e6	1.00038	0.500188	−	0.865917i	$-0.333264\pi$
$347$	2.24381e6	1.00038	0.500188	+	0.865917i	$0.333264\pi$
$348$	−567384.	−0.251147
$349$	2.31221e6	1.01616	0.508081	−	0.861309i	$-0.330355\pi$
$349$	2.31221e6	1.01616	0.508081	+	0.861309i	$0.330355\pi$
$350$	216961.	0.0946700
$351$	−210974.	−0.0914034
$352$	224497.	0.0965724
$353$	−749517.	−0.320144	−0.160072	−	0.987105i	$-0.551173\pi$
$353$	−749517.	−0.320144	−0.160072	+	0.987105i	$0.551173\pi$
$354$	−9088.15	−0.00385449
$355$	1.88234e6	0.792731
$356$	−3.37041e6	−1.40948
$357$	−343285.	−0.142555
$358$	827.099	0.000341075 0
$359$	2.49839e6	1.02312	0.511558	−	0.859249i	$-0.329069\pi$
$359$	2.49839e6	1.02312	0.511558	+	0.859249i	$0.329069\pi$
$360$	−130817.	−0.0531996
$361$	−1.12421e6	−0.454024
$362$	98831.7	0.0396392
$363$	−874270.	−0.348240
$364$	1.54814e6	0.612429
$365$	4.02992e6	1.58330
$366$	−2606.17	−0.00101695
$367$	−2.57748e6	−0.998920	−0.499460	−	0.866337i	$-0.666468\pi$
$367$	−2.57748e6	−0.998920	−0.499460	+	0.866337i	$0.666468\pi$
$368$	−1.25151e6	−0.481742
$369$	−911354.	−0.348435
$370$	178056.	0.0676164
$371$	6.26155e6	2.36182
$372$	−2.23816e6	−0.838558
$373$	−999728.	−0.372057	−0.186029	−	0.982544i	$-0.559562\pi$
$373$	−999728.	−0.372057	−0.186029	+	0.982544i	$0.559562\pi$
$374$	−16688.8	−0.00616944
$375$	1.04832e6	0.384961
$376$	372706.	0.135955
$377$	−571650.	−0.207146
$378$	35445.1	0.0127593
$379$	−3.57477e6	−1.27835	−0.639175	−	0.769062i	$-0.720724\pi$
$379$	−3.57477e6	−1.27835	−0.639175	+	0.769062i	$0.720724\pi$
$380$	3.23235e6	1.14831
$381$	204836.	0.0722925
$382$	−29334.7	−0.0102854
$383$	−47574.2	−0.0165720	−0.00828599	−	0.999966i	$-0.502638\pi$
$383$	−47574.2	−0.0165720	−0.00828599	+	0.999966i	$0.502638\pi$
$384$	−339955.	−0.117650
$385$	3.69085e6	1.26904
$386$	100079.	0.0341880
$387$	1.50009e6	0.509144
$388$	3.50416e6	1.18169
$389$	−4.27552e6	−1.43257	−0.716284	−	0.697809i	$-0.754158\pi$
$389$	−4.27552e6	−1.43257	−0.716284	+	0.697809i	$0.754158\pi$
$390$	−65813.6	−0.0219106
$391$	280339.	0.0927344
$392$	−209258.	−0.0687809
$393$	−1.96925e6	−0.643159
$394$	−146958.	−0.0476928
$395$	−7.40517e6	−2.38804
$396$	−653545.	−0.209429
$397$	−4.92533e6	−1.56841	−0.784204	−	0.620504i	$-0.786928\pi$
$397$	−4.92533e6	−1.56841	−0.784204	+	0.620504i	$0.786928\pi$
$398$	−64254.3	−0.0203327
$399$	−1.75393e6	−0.551545
$400$	4.53332e6	1.41666
$401$	−3.08195e6	−0.957117	−0.478559	−	0.878056i	$-0.658841\pi$
$401$	−3.08195e6	−0.957117	−0.478559	+	0.878056i	$0.658841\pi$
$402$	−51340.4	−0.0158451
$403$	−2.25499e6	−0.691642
$404$	−3.07280e6	−0.936657
$405$	571495.	0.173131
$406$	96041.0	0.0289162
$407$	1.78143e6	0.533069
$408$	37974.5	0.0112938
$409$	−4.03756e6	−1.19347	−0.596734	−	0.802439i	$-0.703535\pi$
$409$	−4.03756e6	−1.19347	−0.596734	+	0.802439i	$0.703535\pi$
$410$	−284297.	−0.0835244
$411$	−3.39582e6	−0.991608
$412$	3.83126e6	1.11199
$413$	−583451.	−0.168317
$414$	−28945.8	−0.00830012
$415$	6.57369e6	1.87365
$416$	−256997.	−0.0728106
$417$	−45242.8	−0.0127412
$418$	−85267.5	−0.0238695
$419$	3.20507e6	0.891873	0.445936	−	0.895065i	$-0.352871\pi$
$419$	3.20507e6	0.891873	0.445936	+	0.895065i	$0.352871\pi$
$420$	−4.19364e6	−1.16003
$421$	3.86174e6	1.06189	0.530943	−	0.847408i	$-0.321838\pi$
$421$	3.86174e6	1.06189	0.530943	+	0.847408i	$0.321838\pi$
$422$	−281227.	−0.0768733
$423$	−1.62822e6	−0.442449
$424$	−692659.	−0.187113
$425$	−1.01546e6	−0.272705
$426$	56419.1	0.0150627
$427$	−167314.	−0.0444080
$428$	1.19773e6	0.316045
$429$	−658460.	−0.172737
$430$	467955.	0.122049
$431$	4.57174e6	1.18547	0.592733	−	0.805399i	$-0.298049\pi$
$431$	4.57174e6	1.18547	0.592733	+	0.805399i	$0.298049\pi$
$432$	740612.	0.190933
$433$	6.35435e6	1.62874	0.814370	−	0.580346i	$-0.197083\pi$
$433$	6.35435e6	1.62874	0.814370	+	0.580346i	$0.197083\pi$
$434$	378853.	0.0965487
$435$	1.54850e6	0.392364
$436$	3.20749e6	0.808070
$437$	1.43233e6	0.358788
$438$	120789.	0.0300843
$439$	−5.50122e6	−1.36238	−0.681189	−	0.732108i	$-0.738537\pi$
$439$	−5.50122e6	−1.36238	−0.681189	+	0.732108i	$0.738537\pi$
$440$	−408285.	−0.100538
$441$	914177.	0.223838
$442$	19104.8	0.00465144
$443$	3.19936e6	0.774558	0.387279	−	0.921963i	$-0.373415\pi$
$443$	3.19936e6	0.774558	0.387279	+	0.921963i	$0.373415\pi$
$444$	−2.02411e6	−0.487278
$445$	9.19852e6	2.20200
$446$	−386702.	−0.0920533
$447$	−1.49237e6	−0.353271
$448$	−5.40578e6	−1.27252
$449$	−4.16986e6	−0.976124	−0.488062	−	0.872809i	$-0.662296\pi$
$449$	−4.16986e6	−0.976124	−0.488062	+	0.872809i	$0.662296\pi$
$450$	104850.	0.0244082
$451$	−2.84437e6	−0.658484
$452$	3.09559e6	0.712685
$453$	2.74973e6	0.629571
$454$	213183.	0.0485414
$455$	−4.22517e6	−0.956789
$456$	194022.	0.0436957
$457$	5.33516e6	1.19497	0.597485	−	0.801880i	$-0.296167\pi$
$457$	5.33516e6	1.19497	0.597485	+	0.801880i	$0.296167\pi$
$458$	91473.7	0.0203766
$459$	−165897.	−0.0367542
$460$	3.42468e6	0.754614
$461$	−5.91111e6	−1.29544	−0.647719	−	0.761879i	$-0.724277\pi$
$461$	−5.91111e6	−1.29544	−0.647719	+	0.761879i	$0.724277\pi$
$462$	110626.	0.0241130
$463$	−7.25730e6	−1.57334	−0.786670	−	0.617373i	$-0.788197\pi$
$463$	−7.25730e6	−1.57334	−0.786670	+	0.617373i	$0.788197\pi$
$464$	2.00674e6	0.432709
$465$	6.10838e6	1.31007
$466$	129849.	0.0276997
$467$	8.09273e6	1.71713	0.858565	−	0.512706i	$-0.171357\pi$
$467$	8.09273e6	1.71713	0.858565	+	0.512706i	$0.171357\pi$
$468$	748159.	0.157899
$469$	−3.29600e6	−0.691919
$470$	−507925.	−0.106061
$471$	−3.71696e6	−0.772033
$472$	64541.9	0.0133348
$473$	4.68185e6	0.962198
$474$	−221955.	−0.0453752
$475$	−5.18829e6	−1.05509
$476$	1.21736e6	0.246264
$477$	3.02599e6	0.608935
$478$	64022.6	0.0128163
$479$	4.31869e6	0.860030	0.430015	−	0.902822i	$-0.358508\pi$
$479$	4.31869e6	0.860030	0.430015	+	0.902822i	$0.358508\pi$
$480$	696162.	0.137914
$481$	−2.03933e6	−0.401907
$482$	186784.	0.0366204
$483$	−1.85829e6	−0.362448
$484$	3.10034e6	0.601583
$485$	−9.56356e6	−1.84614
$486$	17129.4	0.00328966
$487$	−134182.	−0.0256372	−0.0128186	−	0.999918i	$-0.504080\pi$
$487$	−134182.	−0.0256372	−0.0128186	+	0.999918i	$0.504080\pi$
$488$	18508.4	0.00351819
$489$	2.11090e6	0.399204
$490$	285178.	0.0536570
$491$	3.28974e6	0.615825	0.307913	−	0.951415i	$-0.400370\pi$
$491$	3.28974e6	0.615825	0.307913	+	0.951415i	$0.400370\pi$
$492$	3.23185e6	0.601919
$493$	−449510.	−0.0832956
$494$	97611.7	0.0179964
$495$	1.78366e6	0.327189
$496$	7.91599e6	1.44478
$497$	3.62205e6	0.657755
$498$	197033.	0.0356012
$499$	9.24373e6	1.66187	0.830933	−	0.556373i	$-0.187807\pi$
$499$	9.24373e6	1.66187	0.830933	+	0.556373i	$0.187807\pi$
$500$	−3.71757e6	−0.665019
$501$	1.24604e6	0.221788
$502$	329202.	0.0583046
$503$	−5.84762e6	−1.03053	−0.515263	−	0.857032i	$-0.672306\pi$
$503$	−5.84762e6	−1.03053	−0.515263	+	0.857032i	$0.672306\pi$
$504$	−251723.	−0.0441414
$505$	8.38628e6	1.46333
$506$	−90340.9	−0.0156858
$507$	−2.58785e6	−0.447115
$508$	−726389.	−0.124885
$509$	−9.97745e6	−1.70697	−0.853483	−	0.521120i	$-0.825514\pi$
$509$	−9.97745e6	−1.70697	−0.853483	+	0.521120i	$0.825514\pi$
$510$	−51751.7	−0.00881048
$511$	7.75451e6	1.31372
$512$	1.50494e6	0.253714
$513$	−847614.	−0.142202
$514$	45620.9	0.00761652
$515$	−1.04563e7	−1.73724
$516$	−5.31964e6	−0.879544
$517$	−5.08174e6	−0.836154
$518$	342621.	0.0561035
$519$	1.35846e6	0.221375
$520$	467393.	0.0758007
$521$	6.29007e6	1.01522	0.507611	−	0.861586i	$-0.330529\pi$
$521$	6.29007e6	1.01522	0.507611	+	0.861586i	$0.330529\pi$
$522$	46413.2	0.00745531
$523$	777756.	0.124334	0.0621669	−	0.998066i	$-0.480199\pi$
$523$	777756.	0.124334	0.0621669	+	0.998066i	$0.480199\pi$
$524$	6.98335e6	1.11106
$525$	6.73125e6	1.06585
$526$	−273595.	−0.0431165
$527$	−1.77318e6	−0.278117
$528$	2.31148e6	0.360832
$529$	−4.91880e6	−0.764222
$530$	943958.	0.145970
$531$	−281961.	−0.0433963
$532$	6.21981e6	0.952792
$533$	3.25615e6	0.496463
$534$	275707.	0.0418403
$535$	−3.26884e6	−0.493753
$536$	364607.	0.0548167
$537$	25660.9	0.00384004
$538$	153346.	0.0228411
$539$	2.85318e6	0.423017
$540$	−2.02664e6	−0.299083
$541$	3.53668e6	0.519520	0.259760	−	0.965673i	$-0.416357\pi$
$541$	3.53668e6	0.519520	0.259760	+	0.965673i	$0.416357\pi$
$542$	526885.	0.0770403
$543$	3.06627e6	0.446283
$544$	−202086.	−0.0292779
$545$	−8.75389e6	−1.26244
$546$	−126641.	−0.0181799
$547$	−7.93013e6	−1.13321	−0.566607	−	0.823988i	$-0.691744\pi$
$547$	−7.93013e6	−1.13321	−0.566607	+	0.823988i	$0.691744\pi$
$548$	1.20423e7	1.71300
$549$	−80856.7	−0.0114495
$550$	327240.	0.0461275
$551$	−2.29667e6	−0.322270
$552$	205566.	0.0287146
$553$	−1.42493e7	−1.98144
$554$	−485217.	−0.0671679
$555$	5.52421e6	0.761268
$556$	160440.	0.0220103
$557$	−1.08864e7	−1.48678	−0.743392	−	0.668857i	$-0.766784\pi$
$557$	−1.08864e7	−1.48678	−0.743392	+	0.668857i	$0.766784\pi$
$558$	183086.	0.0248926
$559$	−5.35964e6	−0.725447
$560$	1.48322e7	1.99864
$561$	−517772.	−0.0694594
$562$	133927.	0.0178866
$563$	3.05550e6	0.406267	0.203133	−	0.979151i	$-0.434887\pi$
$563$	3.05550e6	0.406267	0.203133	+	0.979151i	$0.434887\pi$
$564$	5.77401e6	0.764328
$565$	−8.44850e6	−1.11342
$566$	255379.	0.0335077
$567$	1.09969e6	0.143652
$568$	−400675.	−0.0521100
$569$	7.58838e6	0.982581	0.491291	−	0.870996i	$-0.336525\pi$
$569$	7.58838e6	0.982581	0.491291	+	0.870996i	$0.336525\pi$
$570$	−264414.	−0.0340876
$571$	−6.32584e6	−0.811948	−0.405974	−	0.913885i	$-0.633068\pi$
$571$	−6.32584e6	−0.811948	−0.405974	+	0.913885i	$0.633068\pi$
$572$	2.33503e6	0.298403
$573$	−910112.	−0.115800
$574$	−547055.	−0.0693029
$575$	−5.49698e6	−0.693354
$576$	−2.61242e6	−0.328085
$577$	−2.66897e6	−0.333737	−0.166868	−	0.985979i	$-0.553365\pi$
$577$	−2.66897e6	−0.333737	−0.166868	+	0.985979i	$0.553365\pi$
$578$	−396860.	−0.0494103
$579$	3.10495e6	0.384910
$580$	−5.49131e6	−0.677807
$581$	1.26493e7	1.55463
$582$	−286648.	−0.0350785
$583$	9.44422e6	1.15079
$584$	−857811.	−0.104078
$585$	−2.04188e6	−0.246683
$586$	−767972.	−0.0923850
$587$	5.82526e6	0.697782	0.348891	−	0.937163i	$-0.386558\pi$
$587$	5.82526e6	0.697782	0.348891	+	0.937163i	$0.386558\pi$
$588$	−3.24186e6	−0.386679
$589$	−9.05967e6	−1.07603
$590$	−87957.9	−0.0104027
$591$	−4.55939e6	−0.536955
$592$	7.15894e6	0.839546
$593$	−1.39791e7	−1.63246	−0.816232	−	0.577724i	$-0.803941\pi$
$593$	−1.39791e7	−1.63246	−0.816232	+	0.577724i	$0.803941\pi$
$594$	53461.4	0.00621691
$595$	−3.32241e6	−0.384735
$596$	5.29226e6	0.610275
$597$	−1.99350e6	−0.228918
$598$	103419.	0.0118263
$599$	−1.42274e7	−1.62016	−0.810081	−	0.586319i	$-0.800577\pi$
$599$	−1.42274e7	−1.62016	−0.810081	+	0.586319i	$0.800577\pi$
$600$	−744617.	−0.0844413
$601$	8.29425e6	0.936679	0.468340	−	0.883549i	$-0.344852\pi$
$601$	8.29425e6	0.936679	0.468340	+	0.883549i	$0.344852\pi$
$602$	900455.	0.101268
$603$	−1.59284e6	−0.178394
$604$	−9.75111e6	−1.08758
$605$	−8.46145e6	−0.939845
$606$	251362.	0.0278046
$607$	6.09959e6	0.671938	0.335969	−	0.941873i	$-0.390936\pi$
$607$	6.09959e6	0.671938	0.335969	+	0.941873i	$0.390936\pi$
$608$	−1.03251e6	−0.113276
$609$	2.97969e6	0.325557
$610$	−25223.3	−0.00274459
$611$	5.81743e6	0.630417
$612$	588306.	0.0634928
$613$	−9.06279e6	−0.974116	−0.487058	−	0.873370i	$-0.661930\pi$
$613$	−9.06279e6	−0.974116	−0.487058	+	0.873370i	$0.661930\pi$
$614$	−670024.	−0.0717248
$615$	−8.82037e6	−0.940370
$616$	−785637.	−0.0834200
$617$	1.70732e7	1.80552	0.902760	−	0.430145i	$-0.141537\pi$
$617$	1.70732e7	1.80552	0.902760	+	0.430145i	$0.141537\pi$
$618$	−313406.	−0.0330093
$619$	8.30455e6	0.871143	0.435572	−	0.900154i	$-0.356546\pi$
$619$	8.30455e6	0.871143	0.435572	+	0.900154i	$0.356546\pi$
$620$	−2.16616e7	−2.26314
$621$	−898046.	−0.0934479
$622$	−797340.	−0.0826357
$623$	1.77001e7	1.82707
$624$	−2.64611e6	−0.272049
$625$	−3.79852e6	−0.388968
$626$	−613007.	−0.0625216
$627$	−2.64544e6	−0.268738
$628$	1.31811e7	1.33368
$629$	−1.60360e6	−0.161611
$630$	343049.	0.0344354
$631$	1.07615e7	1.07597	0.537983	−	0.842956i	$-0.319186\pi$
$631$	1.07615e7	1.07597	0.537983	+	0.842956i	$0.319186\pi$
$632$	1.57627e6	0.156978
$633$	−8.72509e6	−0.865488
$634$	508323.	0.0502246
$635$	1.98246e6	0.195106
$636$	−1.07308e7	−1.05193
$637$	−3.26624e6	−0.318933
$638$	144857.	0.0140893
$639$	1.75041e6	0.169585
$640$	−3.29019e6	−0.317520
$641$	−1.33893e7	−1.28711	−0.643553	−	0.765402i	$-0.722540\pi$
$641$	−1.33893e7	−1.28711	−0.643553	+	0.765402i	$0.722540\pi$
$642$	−97976.8	−0.00938179
$643$	−2.78332e6	−0.265482	−0.132741	−	0.991151i	$-0.542378\pi$
$643$	−2.78332e6	−0.265482	−0.132741	+	0.991151i	$0.542378\pi$
$644$	6.58988e6	0.626128
$645$	1.45184e7	1.37410
$646$	76755.8	0.00723652
$647$	2.39129e6	0.224580	0.112290	−	0.993675i	$-0.464181\pi$
$647$	2.39129e6	0.224580	0.112290	+	0.993675i	$0.464181\pi$
$648$	−121649.	−0.0113807
$649$	−880011.	−0.0820118
$650$	−374614.	−0.0347777
$651$	1.17540e7	1.08701
$652$	−7.48567e6	−0.689623
$653$	1.02862e7	0.943997	0.471998	−	0.881599i	$-0.343533\pi$
$653$	1.02862e7	0.943997	0.471998	+	0.881599i	$0.343533\pi$
$654$	−262380.	−0.0239876
$655$	−1.90590e7	−1.73579
$656$	−1.14305e7	−1.03706
$657$	3.74748e6	0.338708
$658$	−977367.	−0.0880021
$659$	1.52742e7	1.37007	0.685036	−	0.728509i	$-0.259786\pi$
$659$	1.52742e7	1.37007	0.685036	+	0.728509i	$0.259786\pi$
$660$	−6.32521e6	−0.565217
$661$	−2.48992e6	−0.221657	−0.110829	−	0.993840i	$-0.535350\pi$
$661$	−2.48992e6	−0.221657	−0.110829	+	0.993840i	$0.535350\pi$
$662$	−281778.	−0.0249898
$663$	592729.	0.0523688
$664$	−1.39928e6	−0.123164
$665$	−1.69751e7	−1.48853
$666$	165577.	0.0144648
$667$	−2.43332e6	−0.211780
$668$	−4.41872e6	−0.383138
$669$	−1.19975e7	−1.03639
$670$	−496888.	−0.0427633
$671$	−252357.	−0.0216376
$672$	1.33958e6	0.114431
$673$	1.62042e7	1.37908	0.689542	−	0.724246i	$-0.257812\pi$
$673$	1.62042e7	1.37908	0.689542	+	0.724246i	$0.257812\pi$
$674$	298260.	0.0252898
$675$	3.25298e6	0.274803
$676$	9.17706e6	0.772390
$677$	8.11683e6	0.680636	0.340318	−	0.940310i	$-0.389465\pi$
$677$	8.11683e6	0.680636	0.340318	+	0.940310i	$0.389465\pi$
$678$	−253226.	−0.0211560
$679$	−1.84025e7	−1.53180
$680$	367529.	0.0304803
$681$	6.61402e6	0.546510
$682$	571419.	0.0470429
$683$	−1.39257e7	−1.14226	−0.571131	−	0.820859i	$-0.693495\pi$
$683$	−1.39257e7	−1.14226	−0.571131	+	0.820859i	$0.693495\pi$
$684$	3.00581e6	0.245653
$685$	−3.28658e7	−2.67619
$686$	−268433.	−0.0217784
$687$	2.83798e6	0.229413
$688$	1.88147e7	1.51539
$689$	−1.08115e7	−0.867633
$690$	−280146.	−0.0224007
$691$	2.03394e7	1.62048	0.810238	−	0.586101i	$-0.199338\pi$
$691$	2.03394e7	1.62048	0.810238	+	0.586101i	$0.199338\pi$
$692$	−4.81739e6	−0.382425
$693$	3.43217e6	0.271479
$694$	650902.	0.0513000
$695$	−437874.	−0.0343864
$696$	−329616.	−0.0257920
$697$	2.56043e6	0.199633
$698$	670742.	0.0521095
$699$	4.02859e6	0.311861
$700$	−2.38704e7	−1.84126
$701$	2.46892e6	0.189763	0.0948815	−	0.995489i	$-0.469753\pi$
$701$	2.46892e6	0.189763	0.0948815	+	0.995489i	$0.469753\pi$
$702$	−61201.0	−0.00468723
$703$	−8.19325e6	−0.625270
$704$	−8.15347e6	−0.620027
$705$	−1.57584e7	−1.19410
$706$	−217426.	−0.0164172
$707$	1.61372e7	1.21417
$708$	999892.	0.0749669
$709$	1.05339e7	0.786994	0.393497	−	0.919326i	$-0.371265\pi$
$709$	1.05339e7	0.786994	0.393497	+	0.919326i	$0.371265\pi$
$710$	546042.	0.0406518
$711$	−6.88617e6	−0.510862
$712$	−1.95800e6	−0.144748
$713$	−9.59871e6	−0.707113
$714$	−99582.5	−0.00731034
$715$	−6.37278e6	−0.466191
$716$	−90998.7	−0.00663365
$717$	1.98631e6	0.144294
$718$	724752.	0.0524660
$719$	1.89639e7	1.36806	0.684029	−	0.729455i	$-0.260226\pi$
$719$	1.89639e7	1.36806	0.684029	+	0.729455i	$0.260226\pi$
$720$	7.16787e6	0.515299
$721$	−2.01204e7	−1.44144
$722$	−326119.	−0.0232827
$723$	5.79501e6	0.412296
$724$	−1.08736e7	−0.770952
$725$	8.81416e6	0.622782
$726$	−253615.	−0.0178580
$727$	−579638.	−0.0406744	−0.0203372	−	0.999793i	$-0.506474\pi$
$727$	−579638.	−0.0406744	−0.0203372	+	0.999793i	$0.506474\pi$
$728$	899373.	0.0628943
$729$	531441.	0.0370370
$730$	1.16903e6	0.0811929
$731$	−4.21449e6	−0.291710
$732$	286735.	0.0197789
$733$	−1.22334e7	−0.840980	−0.420490	−	0.907297i	$-0.638142\pi$
$733$	−1.22334e7	−0.840980	−0.420490	+	0.907297i	$0.638142\pi$
$734$	−747696.	−0.0512253
$735$	8.84769e6	0.604104
$736$	−1.09395e6	−0.0744393
$737$	−4.97132e6	−0.337134
$738$	−264372.	−0.0178680
$739$	1.16099e7	0.782017	0.391008	−	0.920387i	$-0.372126\pi$
$739$	1.16099e7	0.782017	0.391008	+	0.920387i	$0.372126\pi$
$740$	−1.95900e7	−1.31509
$741$	3.02842e6	0.202614
$742$	1.81640e6	0.121116
$743$	2.39450e7	1.59127	0.795634	−	0.605777i	$-0.207138\pi$
$743$	2.39450e7	1.59127	0.795634	+	0.605777i	$0.207138\pi$
$744$	−1.30023e6	−0.0861171
$745$	−1.44436e7	−0.953424
$746$	−290008.	−0.0190793
$747$	6.11297e6	0.400821
$748$	1.83612e6	0.119991
$749$	−6.29002e6	−0.409683
$750$	304105.	0.0197411
$751$	1.54209e6	0.0997720	0.0498860	−	0.998755i	$-0.484114\pi$
$751$	1.54209e6	0.0997720	0.0498860	+	0.998755i	$0.484114\pi$
$752$	−2.04217e7	−1.31688
$753$	1.02135e7	0.656430
$754$	−165828.	−0.0106226
$755$	2.66128e7	1.69911
$756$	−3.89973e6	−0.248159
$757$	−2.03724e7	−1.29212	−0.646059	−	0.763288i	$-0.723584\pi$
$757$	−2.03724e7	−1.29212	−0.646059	+	0.763288i	$0.723584\pi$
$758$	−1.03699e6	−0.0655546
$759$	−2.80284e6	−0.176601
$760$	1.87780e6	0.117928
$761$	−6.63887e6	−0.415559	−0.207779	−	0.978176i	$-0.566624\pi$
$761$	−6.63887e6	−0.415559	−0.207779	+	0.978176i	$0.566624\pi$
$762$	59420.3	0.00370721
$763$	−1.68445e7	−1.04749
$764$	3.22744e6	0.200044
$765$	−1.60560e6	−0.0991939
$766$	−13800.7	−0.000849822 0
$767$	1.00741e6	0.0618327
$768$	9.18999e6	0.562227
$769$	−1.86945e7	−1.13998	−0.569992	−	0.821650i	$-0.693054\pi$
$769$	−1.86945e7	−1.13998	−0.569992	+	0.821650i	$0.693054\pi$
$770$	1.07067e6	0.0650771
$771$	1.41540e6	0.0857515
$772$	−1.10108e7	−0.664930
$773$	2.02459e7	1.21867	0.609337	−	0.792911i	$-0.291436\pi$
$773$	2.02459e7	1.21867	0.609337	+	0.792911i	$0.291436\pi$
$774$	435158.	0.0261093
$775$	3.47692e7	2.07941
$776$	2.03570e6	0.121356
$777$	1.06299e7	0.631649
$778$	−1.24027e6	−0.0734630
$779$	1.30820e7	0.772377
$780$	7.24091e6	0.426144
$781$	5.46310e6	0.320488
$782$	81322.7	0.00475548
$783$	1.43998e6	0.0839365
$784$	1.14659e7	0.666221
$785$	−3.59739e7	−2.08359
$786$	−571253.	−0.0329816
$787$	1.82754e7	1.05179	0.525895	−	0.850550i	$-0.323730\pi$
$787$	1.82754e7	1.05179	0.525895	+	0.850550i	$0.323730\pi$
$788$	1.61685e7	0.927588
$789$	−8.48832e6	−0.485433
$790$	−2.14815e6	−0.122461
$791$	−1.62569e7	−0.923839
$792$	−379670.	−0.0215077
$793$	288891.	0.0163136
$794$	−1.42878e6	−0.0804290
$795$	2.92864e7	1.64342
$796$	7.06935e6	0.395455
$797$	−2.12442e7	−1.18466	−0.592331	−	0.805695i	$-0.701792\pi$
$797$	−2.12442e7	−1.18466	−0.592331	+	0.805695i	$0.701792\pi$
$798$	−508794.	−0.0282836
$799$	4.57446e6	0.253497
$800$	3.96259e6	0.218904
$801$	8.55384e6	0.471064
$802$	−894036.	−0.0490816
$803$	1.16960e7	0.640103
$804$	5.64854e6	0.308174
$805$	−1.79851e7	−0.978191
$806$	−654144.	−0.0354679
$807$	4.75758e6	0.257160
$808$	−1.78511e6	−0.0961915
$809$	1.25471e7	0.674020	0.337010	−	0.941501i	$-0.390584\pi$
$809$	1.25471e7	0.674020	0.337010	+	0.941501i	$0.390584\pi$
$810$	165783.	0.00887827
$811$	727251.	0.0388269	0.0194134	−	0.999812i	$-0.493820\pi$
$811$	727251.	0.0388269	0.0194134	+	0.999812i	$0.493820\pi$
$812$	−1.05666e7	−0.562399
$813$	1.63467e7	0.867368
$814$	516772.	0.0273362
$815$	2.04299e7	1.07739
$816$	−2.08074e6	−0.109394
$817$	−2.15330e7	−1.12862
$818$	−1.17125e6	−0.0612019
$819$	−3.92905e6	−0.204681
$820$	3.12788e7	1.62449
$821$	1.33577e7	0.691629	0.345815	−	0.938303i	$-0.387603\pi$
$821$	1.33577e7	0.691629	0.345815	+	0.938303i	$0.387603\pi$
$822$	−985084.	−0.0508503
$823$	−1.38719e7	−0.713896	−0.356948	−	0.934124i	$-0.616183\pi$
$823$	−1.38719e7	−0.713896	−0.356948	+	0.934124i	$0.616183\pi$
$824$	2.22573e6	0.114197
$825$	1.01527e7	0.519332
$826$	−169252.	−0.00863143
$827$	3.82559e7	1.94507	0.972533	−	0.232765i	$-0.0747773\pi$
$827$	3.82559e7	1.94507	0.972533	+	0.232765i	$0.0747773\pi$
$828$	3.18466e6	0.161431
$829$	1.78067e7	0.899907	0.449954	−	0.893052i	$-0.351441\pi$
$829$	1.78067e7	0.899907	0.449954	+	0.893052i	$0.351441\pi$
$830$	1.90694e6	0.0960821
$831$	−1.50539e7	−0.756219
$832$	9.33384e6	0.467468
$833$	−2.56837e6	−0.128246
$834$	−13124.4	−0.000653376 0
$835$	1.20596e7	0.598571
$836$	9.38126e6	0.464243
$837$	5.68027e6	0.280256
$838$	929751.	0.0457359
$839$	9.51395e6	0.466612	0.233306	−	0.972403i	$-0.425046\pi$
$839$	9.51395e6	0.466612	0.233306	+	0.972403i	$0.425046\pi$
$840$	−2.43625e6	−0.119131
$841$	−1.66094e7	−0.809776
$842$	1.12024e6	0.0544542
$843$	4.15510e6	0.201378
$844$	3.09410e7	1.49513
$845$	−2.50460e7	−1.20669
$846$	−472327.	−0.0226891
$847$	−1.62818e7	−0.779820
$848$	3.79529e7	1.81241
$849$	7.92317e6	0.377250
$850$	−294574.	−0.0139845
$851$	−8.68074e6	−0.410897
$852$	−6.20732e6	−0.292958
$853$	−1.04920e7	−0.493727	−0.246864	−	0.969050i	$-0.579400\pi$
$853$	−1.04920e7	−0.493727	−0.246864	+	0.969050i	$0.579400\pi$
$854$	−48535.6	−0.00227727
$855$	−8.20347e6	−0.383780
$856$	695808.	0.0324567
$857$	1.41436e7	0.657821	0.328911	−	0.944361i	$-0.393318\pi$
$857$	1.41436e7	0.657821	0.328911	+	0.944361i	$0.393318\pi$
$858$	−191011.	−0.00885808
$859$	3.56902e7	1.65031	0.825155	−	0.564906i	$-0.191088\pi$
$859$	3.56902e7	1.65031	0.825155	+	0.564906i	$0.191088\pi$
$860$	−5.14851e7	−2.37375
$861$	−1.69725e7	−0.780256
$862$	1.32621e6	0.0607915
$863$	1.25188e7	0.572183	0.286091	−	0.958202i	$-0.407644\pi$
$863$	1.25188e7	0.572183	0.286091	+	0.958202i	$0.407644\pi$
$864$	647371.	0.0295032
$865$	1.31476e7	0.597457
$866$	1.84332e6	0.0835229
$867$	−1.23126e7	−0.556292
$868$	−4.16820e7	−1.87780
$869$	−2.14920e7	−0.965445
$870$	449201.	0.0201207
$871$	5.69102e6	0.254182
$872$	1.86336e6	0.0829861
$873$	−8.89329e6	−0.394936
$874$	415500.	0.0183989
$875$	1.95233e7	0.862050
$876$	−1.32893e7	−0.585118
$877$	−3.08425e7	−1.35410	−0.677050	−	0.735937i	$-0.736742\pi$
$877$	−3.08425e7	−1.35410	−0.677050	+	0.735937i	$0.736742\pi$
$878$	−1.59583e6	−0.0698637
$879$	−2.38264e7	−1.04013
$880$	2.23712e7	0.973829
$881$	−1.52828e6	−0.0663379	−0.0331690	−	0.999450i	$-0.510560\pi$
$881$	−1.52828e6	−0.0663379	−0.0331690	+	0.999450i	$0.510560\pi$
$882$	265191.	0.0114786
$883$	1.20855e7	0.521632	0.260816	−	0.965389i	$-0.416008\pi$
$883$	1.20855e7	0.521632	0.260816	+	0.965389i	$0.416008\pi$
$884$	−2.10194e6	−0.0904669
$885$	−2.72891e6	−0.117120
$886$	928094.	0.0397198
$887$	1.34386e7	0.573516	0.286758	−	0.958003i	$-0.407422\pi$
$887$	1.34386e7	0.573516	0.286758	+	0.958003i	$0.407422\pi$
$888$	−1.17589e6	−0.0500418
$889$	3.81473e6	0.161886
$890$	2.66838e6	0.112920
$891$	1.65865e6	0.0699939
$892$	4.25456e7	1.79037
$893$	2.33722e7	0.980778
$894$	−432918.	−0.0181160
$895$	248354.	0.0103637
$896$	−6.33110e6	−0.263456
$897$	3.20860e6	0.133148
$898$	−1.20962e6	−0.0500563
$899$	1.53911e7	0.635141
$900$	−1.15357e7	−0.474721
$901$	−8.50146e6	−0.348884
$902$	−825116.	−0.0337675
$903$	2.79367e7	1.14014
$904$	1.79835e6	0.0731903
$905$	2.96763e7	1.20445
$906$	797662.	0.0322848
$907$	4.92075e6	0.198616	0.0993078	−	0.995057i	$-0.468337\pi$
$907$	4.92075e6	0.198616	0.0993078	+	0.995057i	$0.468337\pi$
$908$	−2.34547e7	−0.944093
$909$	7.79853e6	0.313042
$910$	−1.22567e6	−0.0490648
$911$	−4.20882e7	−1.68021	−0.840106	−	0.542422i	$-0.817507\pi$
$911$	−4.20882e7	−1.68021	−0.840106	+	0.542422i	$0.817507\pi$
$912$	−1.06311e7	−0.423242
$913$	1.90788e7	0.757485
$914$	1.54766e6	0.0612789
$915$	−782556.	−0.0309003
$916$	−1.00641e7	−0.396310
$917$	−3.66739e7	−1.44024
$918$	−48124.7	−0.00188478
$919$	−4.32245e7	−1.68827	−0.844134	−	0.536133i	$-0.819885\pi$
$919$	−4.32245e7	−1.68827	−0.844134	+	0.536133i	$0.819885\pi$
$920$	1.98953e6	0.0774963
$921$	−2.07876e7	−0.807523
$922$	−1.71474e6	−0.0664310
$923$	−6.25399e6	−0.241631
$924$	−1.21712e7	−0.468979
$925$	3.14441e7	1.20833
$926$	−2.10525e6	−0.0806820
$927$	−9.72346e6	−0.371639
$928$	1.75410e6	0.0668626
$929$	4.09390e6	0.155632	0.0778158	−	0.996968i	$-0.475205\pi$
$929$	4.09390e6	0.155632	0.0778158	+	0.996968i	$0.475205\pi$
$930$	1.77197e6	0.0671812
$931$	−1.31225e7	−0.496183
$932$	−1.42862e7	−0.538738
$933$	−2.47376e7	−0.930365
$934$	2.34760e6	0.0880556
$935$	−5.01115e6	−0.187460
$936$	434635.	0.0162157
$937$	1.35185e6	0.0503015	0.0251507	−	0.999684i	$-0.491993\pi$
$937$	1.35185e6	0.0503015	0.0251507	+	0.999684i	$0.491993\pi$
$938$	−956129.	−0.0354821
$939$	−1.90186e7	−0.703907
$940$	5.58827e7	2.06280
$941$	3.76790e7	1.38715	0.693577	−	0.720382i	$-0.256034\pi$
$941$	3.76790e7	1.38715	0.693577	+	0.720382i	$0.256034\pi$
$942$	−1.07824e6	−0.0395904
$943$	1.38603e7	0.507568
$944$	−3.53645e6	−0.129163
$945$	1.06431e7	0.387695
$946$	1.35814e6	0.0493422
$947$	2.29344e7	0.831024	0.415512	−	0.909588i	$-0.363603\pi$
$947$	2.29344e7	0.831024	0.415512	+	0.909588i	$0.363603\pi$
$948$	2.44198e7	0.882513
$949$	−1.33893e7	−0.482604
$950$	−1.50506e6	−0.0541058
$951$	1.57708e7	0.565461
$952$	707211.	0.0252905
$953$	3.44029e7	1.22705	0.613526	−	0.789675i	$-0.289751\pi$
$953$	3.44029e7	1.22705	0.613526	+	0.789675i	$0.289751\pi$
$954$	877800.	0.0312266
$955$	−8.80834e6	−0.312526
$956$	−7.04386e6	−0.249268
$957$	4.49422e6	0.158626
$958$	1.25280e6	0.0441029
$959$	−6.32415e7	−2.22052
$960$	−2.52838e7	−0.885451
$961$	3.20841e7	1.12068
$962$	−591585.	−0.0206101
$963$	−3.03974e6	−0.105626
$964$	−2.05503e7	−0.712239
$965$	3.00507e7	1.03881
$966$	−539067.	−0.0185866
$967$	4.00865e7	1.37858	0.689289	−	0.724486i	$-0.257923\pi$
$967$	4.00865e7	1.37858	0.689289	+	0.724486i	$0.257923\pi$
$968$	1.80111e6	0.0617806
$969$	2.38136e6	0.0814733
$970$	−2.77427e6	−0.0946714
$971$	3.52454e7	1.19965	0.599825	−	0.800131i	$-0.295237\pi$
$971$	3.52454e7	1.19965	0.599825	+	0.800131i	$0.295237\pi$
$972$	−1.88460e6	−0.0639813
$973$	−842572.	−0.0285315
$974$	−38924.5	−0.00131470
$975$	−1.16225e7	−0.391549
$976$	−1.01413e6	−0.0340777
$977$	−1.35507e7	−0.454178	−0.227089	−	0.973874i	$-0.572921\pi$
$977$	−1.35507e7	−0.454178	−0.227089	+	0.973874i	$0.572921\pi$
$978$	612344.	0.0204714
$979$	2.66969e7	0.890233
$980$	−3.13757e7	−1.04359
$981$	−8.14037e6	−0.270067
$982$	954311.	0.0315799
$983$	4.74375e7	1.56580	0.782902	−	0.622145i	$-0.213738\pi$
$983$	4.74375e7	1.56580	0.782902	+	0.622145i	$0.213738\pi$
$984$	1.87751e6	0.0618151
$985$	−4.41272e7	−1.44916
$986$	−130397.	−0.00427146
$987$	−3.03229e7	−0.990783
$988$	−1.07394e7	−0.350015
$989$	−2.28141e7	−0.741675
$990$	517416.	0.0167785
$991$	4.59032e7	1.48477	0.742385	−	0.669974i	$-0.233695\pi$
$991$	4.59032e7	1.48477	0.742385	+	0.669974i	$0.233695\pi$
$992$	6.91938e6	0.223248
$993$	−8.74220e6	−0.281351
$994$	1.05071e6	0.0337301
$995$	−1.92937e7	−0.617814
$996$	−2.16778e7	−0.692417
$997$	2.51295e6	0.0800655	0.0400327	−	0.999198i	$-0.487254\pi$
$997$	2.51295e6	0.0800655	0.0400327	+	0.999198i	$0.487254\pi$
$998$	2.68149e6	0.0852216
$999$	5.13704e6	0.162854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.c.1.5	✓	12
3.2	odd	2		531.6.a.c.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.c.1.5	✓	12	1.1	even	1	trivial
531.6.a.c.1.8		12	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)

\(f(q)\)	\(=\)	\(q+0.290087 q^{2} +9.00000 q^{3} -31.9158 q^{4} +87.1048 q^{5} +2.61079 q^{6} +167.610 q^{7} -18.5412 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+0.290087 q^{2} +9.00000 q^{3} -31.9158 q^{4} +87.1048 q^{5} +2.61079 q^{6} +167.610 q^{7} -18.5412 q^{8} +81.0000 q^{9} +25.2680 q^{10} +252.804 q^{11} -287.243 q^{12} -289.403 q^{13} +48.6216 q^{14} +783.943 q^{15} +1015.93 q^{16} -227.568 q^{17} +23.4971 q^{18} -1162.71 q^{19} -2780.02 q^{20} +1508.49 q^{21} +73.3353 q^{22} -1231.89 q^{23} -166.871 q^{24} +4462.24 q^{25} -83.9520 q^{26} +729.000 q^{27} -5349.42 q^{28} +1975.28 q^{29} +227.412 q^{30} +7791.87 q^{31} +888.026 q^{32} +2275.24 q^{33} -66.0147 q^{34} +14599.6 q^{35} -2585.18 q^{36} +7046.70 q^{37} -337.287 q^{38} -2604.62 q^{39} -1615.03 q^{40} -11251.3 q^{41} +437.594 q^{42} +18519.7 q^{43} -8068.46 q^{44} +7055.49 q^{45} -357.355 q^{46} -20101.5 q^{47} +9143.36 q^{48} +11286.1 q^{49} +1294.44 q^{50} -2048.11 q^{51} +9236.53 q^{52} +37357.8 q^{53} +211.474 q^{54} +22020.5 q^{55} -3107.69 q^{56} -10464.4 q^{57} +573.003 q^{58} -3481.00 q^{59} -25020.2 q^{60} -998.231 q^{61} +2260.32 q^{62} +13576.4 q^{63} -32252.1 q^{64} -25208.3 q^{65} +660.018 q^{66} -19664.7 q^{67} +7263.03 q^{68} -11087.0 q^{69} +4235.17 q^{70} +21610.0 q^{71} -1501.84 q^{72} +46265.2 q^{73} +2044.16 q^{74} +40160.2 q^{75} +37108.8 q^{76} +42372.5 q^{77} -755.568 q^{78} -85014.5 q^{79} +88492.2 q^{80} +6561.00 q^{81} -3263.86 q^{82} +75468.7 q^{83} -48144.8 q^{84} -19822.3 q^{85} +5372.32 q^{86} +17777.5 q^{87} -4687.29 q^{88} +105603. q^{89} +2046.71 q^{90} -48506.8 q^{91} +39316.7 q^{92} +70126.8 q^{93} -5831.19 q^{94} -101277. q^{95} +7992.23 q^{96} -109794. q^{97} +3273.97 q^{98} +20477.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9} + 601 q^{10} + 1480 q^{11} + 1782 q^{12} + 472 q^{13} + 1065 q^{14} + 1422 q^{15} + 6370 q^{16} + 1565 q^{17} + 1782 q^{18} + 3939 q^{19} + 8033 q^{20} + 3717 q^{21} - 1738 q^{22} + 7245 q^{23} + 6507 q^{24} + 9690 q^{25} + 3764 q^{26} + 8748 q^{27} + 12154 q^{28} + 10003 q^{29} + 5409 q^{30} + 7295 q^{31} + 11628 q^{32} + 13320 q^{33} - 16344 q^{34} + 11015 q^{35} + 16038 q^{36} + 6741 q^{37} + 3035 q^{38} + 4248 q^{39} + 5572 q^{40} + 34025 q^{41} + 9585 q^{42} - 6336 q^{43} + 41168 q^{44} + 12798 q^{45} + 2345 q^{46} + 66167 q^{47} + 57330 q^{48} + 28319 q^{49} + 31173 q^{50} + 14085 q^{51} + 16440 q^{52} + 62290 q^{53} + 16038 q^{54} + 55764 q^{55} + 107306 q^{56} + 35451 q^{57} + 37952 q^{58} - 41772 q^{59} + 72297 q^{60} + 68469 q^{61} + 99190 q^{62} + 33453 q^{63} + 68525 q^{64} + 80156 q^{65} - 15642 q^{66} + 113310 q^{67} + 33887 q^{68} + 65205 q^{69} + 32034 q^{70} + 84520 q^{71} + 58563 q^{72} + 135895 q^{73} - 31962 q^{74} + 87210 q^{75} - 61848 q^{76} - 3799 q^{77} + 33876 q^{78} + 14122 q^{79} + 77609 q^{80} + 78732 q^{81} - 1501 q^{82} + 114463 q^{83} + 109386 q^{84} - 101097 q^{85} - 203536 q^{86} + 90027 q^{87} - 244967 q^{88} + 189109 q^{89} + 48681 q^{90} - 168249 q^{91} - 71946 q^{92} + 65655 q^{93} - 472284 q^{94} + 21923 q^{95} + 104652 q^{96} - 76192 q^{97} - 17544 q^{98} + 119880 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9 + 601 * q^10 + 1480 * q^11 + 1782 * q^12 + 472 * q^13 + 1065 * q^14 + 1422 * q^15 + 6370 * q^16 + 1565 * q^17 + 1782 * q^18 + 3939 * q^19 + 8033 * q^20 + 3717 * q^21 - 1738 * q^22 + 7245 * q^23 + 6507 * q^24 + 9690 * q^25 + 3764 * q^26 + 8748 * q^27 + 12154 * q^28 + 10003 * q^29 + 5409 * q^30 + 7295 * q^31 + 11628 * q^32 + 13320 * q^33 - 16344 * q^34 + 11015 * q^35 + 16038 * q^36 + 6741 * q^37 + 3035 * q^38 + 4248 * q^39 + 5572 * q^40 + 34025 * q^41 + 9585 * q^42 - 6336 * q^43 + 41168 * q^44 + 12798 * q^45 + 2345 * q^46 + 66167 * q^47 + 57330 * q^48 + 28319 * q^49 + 31173 * q^50 + 14085 * q^51 + 16440 * q^52 + 62290 * q^53 + 16038 * q^54 + 55764 * q^55 + 107306 * q^56 + 35451 * q^57 + 37952 * q^58 - 41772 * q^59 + 72297 * q^60 + 68469 * q^61 + 99190 * q^62 + 33453 * q^63 + 68525 * q^64 + 80156 * q^65 - 15642 * q^66 + 113310 * q^67 + 33887 * q^68 + 65205 * q^69 + 32034 * q^70 + 84520 * q^71 + 58563 * q^72 + 135895 * q^73 - 31962 * q^74 + 87210 * q^75 - 61848 * q^76 - 3799 * q^77 + 33876 * q^78 + 14122 * q^79 + 77609 * q^80 + 78732 * q^81 - 1501 * q^82 + 114463 * q^83 + 109386 * q^84 - 101097 * q^85 - 203536 * q^86 + 90027 * q^87 - 244967 * q^88 + 189109 * q^89 + 48681 * q^90 - 168249 * q^91 - 71946 * q^92 + 65655 * q^93 - 472284 * q^94 + 21923 * q^95 + 104652 * q^96 - 76192 * q^97 - 17544 * q^98 + 119880 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more