LMFDB - Embedded newform 177.6.a.a.1.10

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			1.10
Root			$8.66878$ 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)

$f(q)$	$=$	$q+7.66878 q^{2} +9.00000 q^{3} +26.8102 q^{4} -109.801 q^{5} +69.0190 q^{6} +156.301 q^{7} -39.7996 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+7.66878 q^{2} +9.00000 q^{3} +26.8102 q^{4} -109.801 q^{5} +69.0190 q^{6} +156.301 q^{7} -39.7996 q^{8} +81.0000 q^{9} -842.036 q^{10} -426.905 q^{11} +241.292 q^{12} -123.969 q^{13} +1198.64 q^{14} -988.205 q^{15} -1163.14 q^{16} -852.404 q^{17} +621.171 q^{18} +232.142 q^{19} -2943.77 q^{20} +1406.71 q^{21} -3273.84 q^{22} -3642.90 q^{23} -358.197 q^{24} +8931.16 q^{25} -950.692 q^{26} +729.000 q^{27} +4190.45 q^{28} -8173.34 q^{29} -7578.33 q^{30} -9358.70 q^{31} -7646.28 q^{32} -3842.15 q^{33} -6536.90 q^{34} -17161.9 q^{35} +2171.62 q^{36} +6317.09 q^{37} +1780.24 q^{38} -1115.72 q^{39} +4370.02 q^{40} +13017.8 q^{41} +10787.7 q^{42} +23355.0 q^{43} -11445.4 q^{44} -8893.84 q^{45} -27936.6 q^{46} -8861.12 q^{47} -10468.3 q^{48} +7622.89 q^{49} +68491.1 q^{50} -7671.64 q^{51} -3323.64 q^{52} +23012.3 q^{53} +5590.54 q^{54} +46874.4 q^{55} -6220.71 q^{56} +2089.28 q^{57} -62679.6 q^{58} +3481.00 q^{59} -26493.9 q^{60} +13699.8 q^{61} -71769.8 q^{62} +12660.4 q^{63} -21417.1 q^{64} +13611.9 q^{65} -29464.6 q^{66} -1424.88 q^{67} -22853.1 q^{68} -32786.1 q^{69} -131611. q^{70} +34543.2 q^{71} -3223.77 q^{72} -50120.2 q^{73} +48444.4 q^{74} +80380.4 q^{75} +6223.76 q^{76} -66725.5 q^{77} -8556.23 q^{78} -69723.6 q^{79} +127713. q^{80} +6561.00 q^{81} +99830.8 q^{82} +49883.0 q^{83} +37714.0 q^{84} +93594.5 q^{85} +179104. q^{86} -73560.1 q^{87} +16990.7 q^{88} -50735.3 q^{89} -68204.9 q^{90} -19376.5 q^{91} -97666.8 q^{92} -84228.3 q^{93} -67954.0 q^{94} -25489.3 q^{95} -68816.5 q^{96} +21922.7 q^{97} +58458.2 q^{98} -34579.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.66878	1.35566	0.677831	−	0.735218i	$-0.262920\pi$
$2$	7.66878	1.35566	0.677831	+	0.735218i	$0.262920\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	26.8102	0.837818
$5$	−109.801	−1.96417	−0.982086	−	0.188434i	$-0.939659\pi$
$5$	−109.801	−1.96417	−0.982086	+	0.188434i	$0.939659\pi$
$6$	69.0190	0.782692
$7$	156.301	1.20563	0.602817	−	0.797879i	$-0.294045\pi$
$7$	156.301	1.20563	0.602817	+	0.797879i	$0.294045\pi$
$8$	−39.7996	−0.219864
$9$	81.0000	0.333333
$10$	−842.036	−2.66275
$11$	−426.905	−1.06377	−0.531887	−	0.846815i	$-0.678517\pi$
$11$	−426.905	−1.06377	−0.531887	+	0.846815i	$0.678517\pi$
$12$	241.292	0.483714
$13$	−123.969	−0.203449	−0.101724	−	0.994813i	$-0.532436\pi$
$13$	−123.969	−0.203449	−0.101724	+	0.994813i	$0.532436\pi$
$14$	1198.64	1.63443
$15$	−988.205	−1.13402
$16$	−1163.14	−1.13588
$17$	−852.404	−0.715358	−0.357679	−	0.933845i	$-0.616432\pi$
$17$	−852.404	−0.715358	−0.357679	+	0.933845i	$0.616432\pi$
$18$	621.171	0.451887
$19$	232.142	0.147526	0.0737631	−	0.997276i	$-0.476499\pi$
$19$	232.142	0.147526	0.0737631	+	0.997276i	$0.476499\pi$
$20$	−2943.77	−1.64562
$21$	1406.71	0.696073
$22$	−3273.84	−1.44212
$23$	−3642.90	−1.43591	−0.717956	−	0.696089i	$-0.754922\pi$
$23$	−3642.90	−1.43591	−0.717956	+	0.696089i	$0.754922\pi$
$24$	−358.197	−0.126938
$25$	8931.16	2.85797
$26$	−950.692	−0.275808
$27$	729.000	0.192450
$28$	4190.45	1.01010
$29$	−8173.34	−1.80470	−0.902349	−	0.431005i	$-0.858159\pi$
$29$	−8173.34	−1.80470	−0.902349	+	0.431005i	$0.858159\pi$
$30$	−7578.33	−1.53734
$31$	−9358.70	−1.74909	−0.874544	−	0.484947i	$-0.838839\pi$
$31$	−9358.70	−1.74909	−0.874544	+	0.484947i	$0.838839\pi$
$32$	−7646.28	−1.32000
$33$	−3842.15	−0.614171
$34$	−6536.90	−0.969783
$35$	−17161.9	−2.36807
$36$	2171.62	0.279273
$37$	6317.09	0.758600	0.379300	−	0.925274i	$-0.376165\pi$
$37$	6317.09	0.758600	0.379300	+	0.925274i	$0.376165\pi$
$38$	1780.24	0.199996
$39$	−1115.72	−0.117461
$40$	4370.02	0.431850
$41$	13017.8	1.20942	0.604712	−	0.796444i	$-0.293288\pi$
$41$	13017.8	1.20942	0.604712	+	0.796444i	$0.293288\pi$
$42$	10787.7	0.943640
$43$	23355.0	1.92623	0.963117	−	0.269084i	$-0.0867208\pi$
$43$	23355.0	1.92623	0.963117	+	0.269084i	$0.0867208\pi$
$44$	−11445.4	−0.891250
$45$	−8893.84	−0.654724
$46$	−27936.6	−1.94661
$47$	−8861.12	−0.585119	−0.292559	−	0.956247i	$-0.594507\pi$
$47$	−8861.12	−0.585119	−0.292559	+	0.956247i	$0.594507\pi$
$48$	−10468.3	−0.655800
$49$	7622.89	0.453554
$50$	68491.1	3.87444
$51$	−7671.64	−0.413012
$52$	−3323.64	−0.170453
$53$	23012.3	1.12531	0.562653	−	0.826693i	$-0.309781\pi$
$53$	23012.3	1.12531	0.562653	+	0.826693i	$0.309781\pi$
$54$	5590.54	0.260897
$55$	46874.4	2.08944
$56$	−6220.71	−0.265075
$57$	2089.28	0.0851743
$58$	−62679.6	−2.44656
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−26493.9	−0.950098
$61$	13699.8	0.471399	0.235699	−	0.971826i	$-0.424262\pi$
$61$	13699.8	0.471399	0.235699	+	0.971826i	$0.424262\pi$
$62$	−71769.8	−2.37117
$63$	12660.4	0.401878
$64$	−21417.1	−0.653599
$65$	13611.9	0.399609
$66$	−29464.6	−0.832607
$67$	−1424.88	−0.0387785	−0.0193893	−	0.999812i	$-0.506172\pi$
$67$	−1424.88	−0.0387785	−0.0193893	+	0.999812i	$0.506172\pi$
$68$	−22853.1	−0.599340
$69$	−32786.1	−0.829024
$70$	−131611.	−3.21031
$71$	34543.2	0.813235	0.406618	−	0.913598i	$-0.366708\pi$
$71$	34543.2	0.813235	0.406618	+	0.913598i	$0.366708\pi$
$72$	−3223.77	−0.0732880
$73$	−50120.2	−1.10079	−0.550397	−	0.834903i	$-0.685524\pi$
$73$	−50120.2	−1.10079	−0.550397	+	0.834903i	$0.685524\pi$
$74$	48444.4	1.02840
$75$	80380.4	1.65005
$76$	6223.76	0.123600
$77$	−66725.5	−1.28252
$78$	−8556.23	−0.159238
$79$	−69723.6	−1.25693	−0.628466	−	0.777837i	$-0.716317\pi$
$79$	−69723.6	−1.25693	−0.628466	+	0.777837i	$0.716317\pi$
$80$	127713.	2.23106
$81$	6561.00	0.111111
$82$	99830.8	1.63957
$83$	49883.0	0.794799	0.397399	−	0.917646i	$-0.369913\pi$
$83$	49883.0	0.794799	0.397399	+	0.917646i	$0.369913\pi$
$84$	37714.0	0.583183
$85$	93594.5	1.40509
$86$	179104.	2.61132
$87$	−73560.1	−1.04194
$88$	16990.7	0.233886
$89$	−50735.3	−0.678946	−0.339473	−	0.940616i	$-0.610249\pi$
$89$	−50735.3	−0.678946	−0.339473	+	0.940616i	$0.610249\pi$
$90$	−68204.9	−0.887584
$91$	−19376.5	−0.245285
$92$	−97666.8	−1.20303
$93$	−84228.3	−1.00984
$94$	−67954.0	−0.793223
$95$	−25489.3	−0.289767
$96$	−68816.5	−0.762104
$97$	21922.7	0.236573	0.118286	−	0.992980i	$-0.462260\pi$
$97$	21922.7	0.236573	0.118286	+	0.992980i	$0.462260\pi$
$98$	58458.2	0.614866
$99$	−34579.3	−0.354592
$100$	239446.	2.39446
$101$	136749.	1.33389	0.666944	−	0.745108i	$-0.267602\pi$
$101$	136749.	1.33389	0.666944	+	0.745108i	$0.267602\pi$
$102$	−58832.1	−0.559905
$103$	−45802.7	−0.425400	−0.212700	−	0.977118i	$-0.568226\pi$
$103$	−45802.7	−0.425400	−0.212700	+	0.977118i	$0.568226\pi$
$104$	4933.93	0.0447311
$105$	−154457.	−1.36721
$106$	176476.	1.52553
$107$	42126.7	0.355711	0.177856	−	0.984057i	$-0.443084\pi$
$107$	42126.7	0.355711	0.177856	+	0.984057i	$0.443084\pi$
$108$	19544.6	0.161238
$109$	−184019.	−1.48353	−0.741765	−	0.670660i	$-0.766011\pi$
$109$	−184019.	−1.48353	−0.741765	+	0.670660i	$0.766011\pi$
$110$	359470.	2.83257
$111$	56853.8	0.437978
$112$	−181800.	−1.36945
$113$	−180222.	−1.32773	−0.663867	−	0.747851i	$-0.731086\pi$
$113$	−180222.	−1.32773	−0.663867	+	0.747851i	$0.731086\pi$
$114$	16022.2	0.115468
$115$	399992.	2.82038
$116$	−219129.	−1.51201
$117$	−10041.5	−0.0678163
$118$	26695.0	0.176492
$119$	−133231.	−0.862460
$120$	39330.2	0.249329
$121$	21197.0	0.131616
$122$	105060.	0.639057
$123$	117160.	0.698261
$124$	−250908.	−1.46542
$125$	−637519.	−3.64937
$126$	97089.4	0.544811
$127$	−25072.4	−0.137939	−0.0689694	−	0.997619i	$-0.521971\pi$
$127$	−25072.4	−0.137939	−0.0689694	+	0.997619i	$0.521971\pi$
$128$	80437.6	0.433945
$129$	210195.	1.11211
$130$	104387.	0.541734
$131$	28027.7	0.142695	0.0713475	−	0.997452i	$-0.477270\pi$
$131$	28027.7	0.142695	0.0713475	+	0.997452i	$0.477270\pi$
$132$	−103009.	−0.514563
$133$	36283.9	0.177863
$134$	−10927.1	−0.0525705
$135$	−80044.6	−0.378005
$136$	33925.4	0.157281
$137$	193823.	0.882277	0.441139	−	0.897439i	$-0.354575\pi$
$137$	193823.	0.882277	0.441139	+	0.897439i	$0.354575\pi$
$138$	−251429.	−1.12388
$139$	−385667.	−1.69307	−0.846536	−	0.532331i	$-0.821316\pi$
$139$	−385667.	−1.69307	−0.846536	+	0.532331i	$0.821316\pi$
$140$	−460113.	−1.98401
$141$	−79750.1	−0.337818
$142$	264904.	1.10247
$143$	52923.1	0.216424
$144$	−94214.3	−0.378626
$145$	897438.	3.54474
$146$	−384361.	−1.49230
$147$	68606.0	0.261860
$148$	169362.	0.635569
$149$	−97076.0	−0.358217	−0.179109	−	0.983829i	$-0.557321\pi$
$149$	−97076.0	−0.358217	−0.179109	+	0.983829i	$0.557321\pi$
$150$	616420.	2.23691
$151$	28312.8	0.101051	0.0505255	−	0.998723i	$-0.483910\pi$
$151$	28312.8	0.101051	0.0505255	+	0.998723i	$0.483910\pi$
$152$	−9239.15	−0.0324357
$153$	−69044.8	−0.238453
$154$	−511703.	−1.73867
$155$	1.02759e6	3.43551
$156$	−29912.7	−0.0984112
$157$	−147457.	−0.477439	−0.238719	−	0.971089i	$-0.576728\pi$
$157$	−147457.	−0.477439	−0.238719	+	0.971089i	$0.576728\pi$
$158$	−534695.	−1.70398
$159$	207111.	0.649695
$160$	839565.	2.59271
$161$	−569388.	−1.73118
$162$	50314.9	0.150629
$163$	−140469.	−0.414105	−0.207053	−	0.978330i	$-0.566387\pi$
$163$	−140469.	−0.414105	−0.207053	+	0.978330i	$0.566387\pi$
$164$	349010.	1.01328
$165$	421870.	1.20634
$166$	382542.	1.07748
$167$	−33450.1	−0.0928125	−0.0464063	−	0.998923i	$-0.514777\pi$
$167$	−33450.1	−0.0928125	−0.0464063	+	0.998923i	$0.514777\pi$
$168$	−55986.3	−0.153041
$169$	−355925.	−0.958609
$170$	717755.	1.90482
$171$	18803.5	0.0491754
$172$	626152.	1.61383
$173$	359847.	0.914118	0.457059	−	0.889436i	$-0.348903\pi$
$173$	359847.	0.914118	0.457059	+	0.889436i	$0.348903\pi$
$174$	−564116.	−1.41252
$175$	1.39595e6	3.44567
$176$	496550.	1.20832
$177$	31329.0	0.0751646
$178$	−389078.	−0.920422
$179$	51692.7	0.120586	0.0602930	−	0.998181i	$-0.480796\pi$
$179$	51692.7	0.120586	0.0602930	+	0.998181i	$0.480796\pi$
$180$	−238446.	−0.548540
$181$	−649652.	−1.47395	−0.736977	−	0.675918i	$-0.763748\pi$
$181$	−649652.	−1.47395	−0.736977	+	0.675918i	$0.763748\pi$
$182$	−148594.	−0.332523
$183$	123298.	0.272162
$184$	144986.	0.315705
$185$	−693620.	−1.49002
$186$	−645928.	−1.36900
$187$	363896.	0.760980
$188$	−237568.	−0.490223
$189$	113943.	0.232024
$190$	−195472.	−0.392826
$191$	76790.3	0.152308	0.0761540	−	0.997096i	$-0.475736\pi$
$191$	76790.3	0.152308	0.0761540	+	0.997096i	$0.475736\pi$
$192$	−192754.	−0.377355
$193$	496266.	0.959006	0.479503	−	0.877540i	$-0.340817\pi$
$193$	496266.	0.959006	0.479503	+	0.877540i	$0.340817\pi$
$194$	168120.	0.320712
$195$	122507.	0.230714
$196$	204371.	0.379996
$197$	−442784.	−0.812879	−0.406439	−	0.913678i	$-0.633230\pi$
$197$	−442784.	−0.812879	−0.406439	+	0.913678i	$0.633230\pi$
$198$	−265181.	−0.480706
$199$	730332.	1.30734	0.653668	−	0.756781i	$-0.273229\pi$
$199$	730332.	1.30734	0.653668	+	0.756781i	$0.273229\pi$
$200$	−355457.	−0.628365
$201$	−12823.9	−0.0223888
$202$	1.04869e6	1.80830
$203$	−1.27750e6	−2.17581
$204$	−205678.	−0.346029
$205$	−1.42936e6	−2.37552
$206$	−351251.	−0.576699
$207$	−295075.	−0.478637
$208$	144194.	0.231093
$209$	−99102.5	−0.156935
$210$	−1.18450e6	−1.85347
$211$	960167.	1.48471	0.742353	−	0.670008i	$-0.233710\pi$
$211$	960167.	1.48471	0.742353	+	0.670008i	$0.233710\pi$
$212$	616964.	0.942801
$213$	310889.	0.469522
$214$	323060.	0.482224
$215$	−2.56439e6	−3.78345
$216$	−29013.9	−0.0423128
$217$	−1.46277e6	−2.10876
$218$	−1.41120e6	−2.01117
$219$	−451082.	−0.635543
$220$	1.25671e6	1.75057
$221$	105672.	0.145539
$222$	435999.	0.593750
$223$	−114848.	−0.154655	−0.0773273	−	0.997006i	$-0.524639\pi$
$223$	−114848.	−0.154655	−0.0773273	+	0.997006i	$0.524639\pi$
$224$	−1.19512e6	−1.59144
$225$	723424.	0.952657
$226$	−1.38208e6	−1.79996
$227$	−316011.	−0.407040	−0.203520	−	0.979071i	$-0.565238\pi$
$227$	−316011.	−0.407040	−0.203520	+	0.979071i	$0.565238\pi$
$228$	56013.9	0.0713606
$229$	−110133.	−0.138781	−0.0693903	−	0.997590i	$-0.522105\pi$
$229$	−110133.	−0.138781	−0.0693903	+	0.997590i	$0.522105\pi$
$230$	3.06745e6	3.82348
$231$	−600530.	−0.740465
$232$	325296.	0.396788
$233$	8645.45	0.0104327	0.00521636	−	0.999986i	$-0.498340\pi$
$233$	8645.45	0.0104327	0.00521636	+	0.999986i	$0.498340\pi$
$234$	−77006.1	−0.0919359
$235$	972956.	1.14927
$236$	93326.2	0.109075
$237$	−627512.	−0.725690
$238$	−1.02172e6	−1.16920
$239$	623677.	0.706261	0.353131	−	0.935574i	$-0.385117\pi$
$239$	623677.	0.706261	0.353131	+	0.935574i	$0.385117\pi$
$240$	1.14942e6	1.28810
$241$	−1.73477e6	−1.92398	−0.961988	−	0.273092i	$-0.911954\pi$
$241$	−1.73477e6	−1.92398	−0.961988	+	0.273092i	$0.911954\pi$
$242$	162555.	0.178427
$243$	59049.0	0.0641500
$244$	367293.	0.394946
$245$	−836997.	−0.890859
$246$	898477.	0.946606
$247$	−28778.4	−0.0300141
$248$	372473.	0.384561
$249$	448947.	0.458877
$250$	−4.88900e6	−4.94732
$251$	1.44679e6	1.44951	0.724755	−	0.689006i	$-0.241953\pi$
$251$	1.44679e6	1.44951	0.724755	+	0.689006i	$0.241953\pi$
$252$	339426.	0.336701
$253$	1.55517e6	1.52749
$254$	−192275.	−0.186998
$255$	842350.	0.811227
$256$	1.30221e6	1.24188
$257$	−177900.	−0.168013	−0.0840064	−	0.996465i	$-0.526772\pi$
$257$	−177900.	−0.168013	−0.0840064	+	0.996465i	$0.526772\pi$
$258$	1.61194e6	1.50765
$259$	987365.	0.914594
$260$	364937.	0.334799
$261$	−662041.	−0.601566
$262$	214938.	0.193446
$263$	−662979.	−0.591031	−0.295515	−	0.955338i	$-0.595491\pi$
$263$	−662979.	−0.591031	−0.295515	+	0.955338i	$0.595491\pi$
$264$	152916.	0.135034
$265$	−2.52676e6	−2.21029
$266$	278253.	0.241122
$267$	−456618.	−0.391990
$268$	−38201.3	−0.0324893
$269$	−1.10386e6	−0.930105	−0.465052	−	0.885283i	$-0.653965\pi$
$269$	−1.10386e6	−0.930105	−0.465052	+	0.885283i	$0.653965\pi$
$270$	−613844.	−0.512447
$271$	−1.65544e6	−1.36927	−0.684635	−	0.728886i	$-0.740039\pi$
$271$	−1.65544e6	−1.36927	−0.684635	+	0.728886i	$0.740039\pi$
$272$	991466.	0.812560
$273$	−174388.	−0.141615
$274$	1.48639e6	1.19607
$275$	−3.81276e6	−3.04024
$276$	−879001.	−0.694571
$277$	−87836.5	−0.0687821	−0.0343911	−	0.999408i	$-0.510949\pi$
$277$	−87836.5	−0.0687821	−0.0343911	+	0.999408i	$0.510949\pi$
$278$	−2.95760e6	−2.29523
$279$	−758055.	−0.583029
$280$	683037.	0.520654
$281$	−800455.	−0.604743	−0.302372	−	0.953190i	$-0.597778\pi$
$281$	−800455.	−0.604743	−0.302372	+	0.953190i	$0.597778\pi$
$282$	−611586.	−0.457967
$283$	−2.09590e6	−1.55563	−0.777813	−	0.628495i	$-0.783671\pi$
$283$	−2.09590e6	−1.55563	−0.777813	+	0.628495i	$0.783671\pi$
$284$	926108.	0.681343
$285$	−229404.	−0.167297
$286$	405855.	0.293397
$287$	2.03469e6	1.45812
$288$	−619348.	−0.440001
$289$	−693264.	−0.488263
$290$	6.88225e6	4.80547
$291$	197304.	0.136585
$292$	−1.34373e6	−0.922264
$293$	1.40390e6	0.955363	0.477681	−	0.878533i	$-0.341477\pi$
$293$	1.40390e6	0.955363	0.477681	+	0.878533i	$0.341477\pi$
$294$	526124.	0.354993
$295$	−382216.	−0.255713
$296$	−251418.	−0.166789
$297$	−311214.	−0.204724
$298$	−744455.	−0.485621
$299$	451607.	0.292135
$300$	2.15501e6	1.38244
$301$	3.65040e6	2.32233
$302$	217125.	0.136991
$303$	1.23074e6	0.770121
$304$	−270013.	−0.167572
$305$	−1.50424e6	−0.925908
$306$	−529489.	−0.323261
$307$	−1.33666e6	−0.809422	−0.404711	−	0.914445i	$-0.632628\pi$
$307$	−1.33666e6	−0.809422	−0.404711	+	0.914445i	$0.632628\pi$
$308$	−1.78892e6	−1.07452
$309$	−412224.	−0.245605
$310$	7.88037e6	4.65739
$311$	−2.02561e6	−1.18756	−0.593778	−	0.804629i	$-0.702364\pi$
$311$	−2.02561e6	−1.18756	−0.593778	+	0.804629i	$0.702364\pi$
$312$	44405.3	0.0258255
$313$	513441.	0.296231	0.148115	−	0.988970i	$-0.452679\pi$
$313$	513441.	0.296231	0.148115	+	0.988970i	$0.452679\pi$
$314$	−1.13082e6	−0.647245
$315$	−1.39011e6	−0.789358
$316$	−1.86930e6	−1.05308
$317$	4929.11	0.00275499	0.00137750	−	0.999999i	$-0.499562\pi$
$317$	4929.11	0.00275499	0.00137750	+	0.999999i	$0.499562\pi$
$318$	1.58829e6	0.880767
$319$	3.48924e6	1.91979
$320$	2.35161e6	1.28378
$321$	379140.	0.205370
$322$	−4.36651e6	−2.34690
$323$	−197879.	−0.105534
$324$	175902.	0.0930909
$325$	−1.10719e6	−0.581451
$326$	−1.07722e6	−0.561386
$327$	−1.65617e6	−0.856517
$328$	−518104.	−0.265909
$329$	−1.38500e6	−0.705439
$330$	3.23523e6	1.63538
$331$	−1.97213e6	−0.989386	−0.494693	−	0.869068i	$-0.664719\pi$
$331$	−1.97213e6	−0.989386	−0.494693	+	0.869068i	$0.664719\pi$
$332$	1.33737e6	0.665897
$333$	511684.	0.252867
$334$	−256522.	−0.125822
$335$	156453.	0.0761676
$336$	−1.63620e6	−0.790655
$337$	2.30193e6	1.10412	0.552062	−	0.833803i	$-0.313841\pi$
$337$	2.30193e6	1.10412	0.552062	+	0.833803i	$0.313841\pi$
$338$	−2.72951e6	−1.29955
$339$	−1.62200e6	−0.766567
$340$	2.50928e6	1.17721
$341$	3.99528e6	1.86063
$342$	144200.	0.0666652
$343$	−1.43548e6	−0.658814
$344$	−929521.	−0.423509
$345$	3.59993e6	1.62835
$346$	2.75958e6	1.23923
$347$	947055.	0.422232	0.211116	−	0.977461i	$-0.432290\pi$
$347$	947055.	0.422232	0.211116	+	0.977461i	$0.432290\pi$
$348$	−1.97216e6	−0.872959
$349$	1.96092e6	0.861781	0.430891	−	0.902404i	$-0.358199\pi$
$349$	1.96092e6	0.861781	0.430891	+	0.902404i	$0.358199\pi$
$350$	1.07052e7	4.67116
$351$	−90373.5	−0.0391538
$352$	3.26423e6	1.40419
$353$	2.49167e6	1.06427	0.532137	−	0.846658i	$-0.321389\pi$
$353$	2.49167e6	1.06427	0.532137	+	0.846658i	$0.321389\pi$
$354$	240255.	0.101898
$355$	−3.79286e6	−1.59733
$356$	−1.36022e6	−0.568834
$357$	−1.19908e6	−0.497942
$358$	396420.	0.163474
$359$	282969.	0.115878	0.0579392	−	0.998320i	$-0.481547\pi$
$359$	282969.	0.115878	0.0579392	+	0.998320i	$0.481547\pi$
$360$	353972.	0.143950
$361$	−2.42221e6	−0.978236
$362$	−4.98203e6	−1.99818
$363$	190773.	0.0759888
$364$	−519486.	−0.205504
$365$	5.50323e6	2.16215
$366$	945544.	0.368960
$367$	1.02276e6	0.396378	0.198189	−	0.980164i	$-0.436494\pi$
$367$	1.02276e6	0.396378	0.198189	+	0.980164i	$0.436494\pi$
$368$	4.23720e6	1.63102
$369$	1.05444e6	0.403141
$370$	−5.31922e6	−2.01996
$371$	3.59684e6	1.35671
$372$	−2.25818e6	−0.846059
$373$	3.02229e6	1.12477	0.562385	−	0.826876i	$-0.309884\pi$
$373$	3.02229e6	1.12477	0.562385	+	0.826876i	$0.309884\pi$
$374$	2.79064e6	1.03163
$375$	−5.73768e6	−2.10697
$376$	352669.	0.128646
$377$	1.01324e6	0.367164
$378$	873805.	0.314547
$379$	−529457.	−0.189336	−0.0946679	−	0.995509i	$-0.530179\pi$
$379$	−529457.	−0.189336	−0.0946679	+	0.995509i	$0.530179\pi$
$380$	−683372.	−0.242772
$381$	−225652.	−0.0796390
$382$	588887.	0.206478
$383$	−2.95011e6	−1.02764	−0.513820	−	0.857898i	$-0.671770\pi$
$383$	−2.95011e6	−1.02764	−0.513820	+	0.857898i	$0.671770\pi$
$384$	723939.	0.250538
$385$	7.32650e6	2.51910
$386$	3.80575e6	1.30009
$387$	1.89176e6	0.642078
$388$	587751.	0.198205
$389$	−2.96852e6	−0.994641	−0.497321	−	0.867567i	$-0.665683\pi$
$389$	−2.96852e6	−0.994641	−0.497321	+	0.867567i	$0.665683\pi$
$390$	939479.	0.312770
$391$	3.10522e6	1.02719
$392$	−303388.	−0.0997202
$393$	252249.	0.0823849
$394$	−3.39561e6	−1.10199
$395$	7.65569e6	2.46883
$396$	−927077.	−0.297083
$397$	1.04019e6	0.331234	0.165617	−	0.986190i	$-0.447038\pi$
$397$	1.04019e6	0.331234	0.165617	+	0.986190i	$0.447038\pi$
$398$	5.60075e6	1.77231
$399$	326555.	0.102689
$400$	−1.03882e7	−3.24631
$401$	3.31007e6	1.02796	0.513980	−	0.857802i	$-0.328171\pi$
$401$	3.31007e6	1.02796	0.513980	+	0.857802i	$0.328171\pi$
$402$	−98343.8	−0.0303516
$403$	1.16019e6	0.355850
$404$	3.66625e6	1.11756
$405$	−720401.	−0.218241
$406$	−9.79686e6	−2.94966
$407$	−2.69680e6	−0.806979
$408$	305328.	0.0908065
$409$	−5.21191e6	−1.54059	−0.770297	−	0.637685i	$-0.779892\pi$
$409$	−5.21191e6	−1.54059	−0.770297	+	0.637685i	$0.779892\pi$
$410$	−1.09615e7	−3.22040
$411$	1.74441e6	0.509383
$412$	−1.22798e6	−0.356408
$413$	544083.	0.156960
$414$	−2.26286e6	−0.648870
$415$	−5.47718e6	−1.56112
$416$	947903.	0.268553
$417$	−3.47100e6	−0.977496
$418$	−759995.	−0.212750
$419$	−3.41630e6	−0.950649	−0.475325	−	0.879810i	$-0.657669\pi$
$419$	−3.41630e6	−0.950649	−0.475325	+	0.879810i	$0.657669\pi$
$420$	−4.14102e6	−1.14547
$421$	5.70486e6	1.56870	0.784350	−	0.620319i	$-0.212997\pi$
$421$	5.70486e6	1.56870	0.784350	+	0.620319i	$0.212997\pi$
$422$	7.36331e6	2.01276
$423$	−717751.	−0.195040
$424$	−915881.	−0.247414
$425$	−7.61296e6	−2.04447
$426$	2.38414e6	0.636513
$427$	2.14128e6	0.568335
$428$	1.12942e6	0.298021
$429$	476308.	0.124952
$430$	−1.96658e7	−5.12908
$431$	−2.31113e6	−0.599281	−0.299640	−	0.954052i	$-0.596867\pi$
$431$	−2.31113e6	−0.599281	−0.299640	+	0.954052i	$0.596867\pi$
$432$	−847929.	−0.218600
$433$	−55388.5	−0.0141971	−0.00709856	−	0.999975i	$-0.502260\pi$
$433$	−55388.5	−0.0141971	−0.00709856	+	0.999975i	$0.502260\pi$
$434$	−1.12177e7	−2.85876
$435$	8.07694e6	2.04656
$436$	−4.93358e6	−1.24293
$437$	−845669.	−0.211835
$438$	−3.45925e6	−0.861582
$439$	−5.60645e6	−1.38844	−0.694219	−	0.719764i	$-0.744250\pi$
$439$	−5.60645e6	−1.38844	−0.694219	+	0.719764i	$0.744250\pi$
$440$	−1.86558e6	−0.459392
$441$	617454.	0.151185
$442$	810374.	0.197301
$443$	5.33809e6	1.29234	0.646170	−	0.763194i	$-0.276370\pi$
$443$	5.33809e6	1.29234	0.646170	+	0.763194i	$0.276370\pi$
$444$	1.52426e6	0.366946
$445$	5.57077e6	1.33357
$446$	−880747.	−0.209659
$447$	−873684.	−0.206817
$448$	−3.34751e6	−0.788001
$449$	−3.68121e6	−0.861737	−0.430869	−	0.902415i	$-0.641793\pi$
$449$	−3.68121e6	−0.861737	−0.430869	+	0.902415i	$0.641793\pi$
$450$	5.54778e6	1.29148
$451$	−5.55737e6	−1.28655
$452$	−4.83177e6	−1.11240
$453$	254815.	0.0583418
$454$	−2.42342e6	−0.551809
$455$	2.12755e6	0.481782
$456$	−83152.4	−0.0187268
$457$	3.14852e6	0.705205	0.352603	−	0.935773i	$-0.385297\pi$
$457$	3.14852e6	0.705205	0.352603	+	0.935773i	$0.385297\pi$
$458$	−844585.	−0.188139
$459$	−621403.	−0.137671
$460$	1.07239e7	2.36296
$461$	−3.05916e6	−0.670425	−0.335213	−	0.942143i	$-0.608808\pi$
$461$	−3.05916e6	−0.670425	−0.335213	+	0.942143i	$0.608808\pi$
$462$	−4.60533e6	−1.00382
$463$	8.35625e6	1.81159	0.905793	−	0.423721i	$-0.139276\pi$
$463$	8.35625e6	1.81159	0.905793	+	0.423721i	$0.139276\pi$
$464$	9.50674e6	2.04992
$465$	9.24832e6	1.98349
$466$	66300.1	0.0141432
$467$	1.16583e6	0.247367	0.123683	−	0.992322i	$-0.460529\pi$
$467$	1.16583e6	0.247367	0.123683	+	0.992322i	$0.460529\pi$
$468$	−269214.	−0.0568177
$469$	−222710.	−0.0467527
$470$	7.46138e6	1.55803
$471$	−1.32712e6	−0.275649
$472$	−138542.	−0.0286238
$473$	−9.97037e6	−2.04908
$474$	−4.81225e6	−0.983791
$475$	2.07330e6	0.421626
$476$	−3.57196e6	−0.722585
$477$	1.86400e6	0.375102
$478$	4.78284e6	0.957451
$479$	−1.23399e6	−0.245737	−0.122869	−	0.992423i	$-0.539209\pi$
$479$	−1.23399e6	−0.245737	−0.122869	+	0.992423i	$0.539209\pi$
$480$	7.55609e6	1.49690
$481$	−783124.	−0.154336
$482$	−1.33036e7	−2.60826
$483$	−5.12449e6	−0.999500
$484$	568294.	0.110271
$485$	−2.40712e6	−0.464669
$486$	452834.	0.0869657
$487$	1.60158e6	0.306004	0.153002	−	0.988226i	$-0.451106\pi$
$487$	1.60158e6	0.306004	0.153002	+	0.988226i	$0.451106\pi$
$488$	−545245.	−0.103644
$489$	−1.26422e6	−0.239084
$490$	−6.41875e6	−1.20770
$491$	1.78594e6	0.334321	0.167161	−	0.985930i	$-0.446540\pi$
$491$	1.78594e6	0.334321	0.167161	+	0.985930i	$0.446540\pi$
$492$	3.14109e6	0.585016
$493$	6.96699e6	1.29101
$494$	−220695.	−0.0406889
$495$	3.79683e6	0.696479
$496$	1.08855e7	1.98675
$497$	5.39912e6	0.980465
$498$	3.44287e6	0.622082
$499$	7.98618e6	1.43578	0.717889	−	0.696157i	$-0.245108\pi$
$499$	7.98618e6	1.43578	0.717889	+	0.696157i	$0.245108\pi$
$500$	−1.70920e7	−3.05751
$501$	−301051.	−0.0535853
$502$	1.10951e7	1.96505
$503$	−3.77866e6	−0.665914	−0.332957	−	0.942942i	$-0.608046\pi$
$503$	−3.77866e6	−0.665914	−0.332957	+	0.942942i	$0.608046\pi$
$504$	−503877.	−0.0883585
$505$	−1.50151e7	−2.61999
$506$	1.19263e7	2.07075
$507$	−3.20332e6	−0.553453
$508$	−672196.	−0.115568
$509$	−5.46200e6	−0.934452	−0.467226	−	0.884138i	$-0.654747\pi$
$509$	−5.46200e6	−0.934452	−0.467226	+	0.884138i	$0.654747\pi$
$510$	6.45980e6	1.09975
$511$	−7.83382e6	−1.32715
$512$	7.41233e6	1.24963
$513$	169231.	0.0283914
$514$	−1.36427e6	−0.227768
$515$	5.02916e6	0.835559
$516$	5.63537e6	0.931747
$517$	3.78286e6	0.622434
$518$	7.57189e6	1.23988
$519$	3.23862e6	0.527766
$520$	−541748.	−0.0878595
$521$	−3.79145e6	−0.611944	−0.305972	−	0.952041i	$-0.598981\pi$
$521$	−3.79145e6	−0.611944	−0.305972	+	0.952041i	$0.598981\pi$
$522$	−5.07705e6	−0.815520
$523$	2.52314e6	0.403355	0.201678	−	0.979452i	$-0.435361\pi$
$523$	2.52314e6	0.403355	0.201678	+	0.979452i	$0.435361\pi$
$524$	751426.	0.119552
$525$	1.25635e7	1.98936
$526$	−5.08424e6	−0.801238
$527$	7.97740e6	1.25122
$528$	4.46895e6	0.697623
$529$	6.83438e6	1.06184
$530$	−1.93772e7	−2.99641
$531$	281961.	0.0433963
$532$	972778.	0.149017
$533$	−1.61381e6	−0.246056
$534$	−3.50170e6	−0.531406
$535$	−4.62553e6	−0.698678
$536$	56709.6	0.00852599
$537$	465235.	0.0696204
$538$	−8.46523e6	−1.26091
$539$	−3.25425e6	−0.482480
$540$	−2.14601e6	−0.316699
$541$	3.18382e6	0.467687	0.233844	−	0.972274i	$-0.424870\pi$
$541$	3.18382e6	0.467687	0.233844	+	0.972274i	$0.424870\pi$
$542$	−1.26952e7	−1.85627
$543$	−5.84686e6	−0.850988
$544$	6.51772e6	0.944275
$545$	2.02054e7	2.91391
$546$	−1.33734e6	−0.191982
$547$	1.08153e7	1.54550	0.772749	−	0.634712i	$-0.218881\pi$
$547$	1.08153e7	1.54550	0.772749	+	0.634712i	$0.218881\pi$
$548$	5.19644e6	0.739188
$549$	1.10968e6	0.157133
$550$	−2.92392e7	−4.12153
$551$	−1.89737e6	−0.266240
$552$	1.30487e6	0.182272
$553$	−1.08978e7	−1.51540
$554$	−673599.	−0.0932453
$555$	−6.24258e6	−0.860264
$556$	−1.03398e7	−1.41849
$557$	−300600.	−0.0410536	−0.0205268	−	0.999789i	$-0.506534\pi$
$557$	−300600.	−0.0410536	−0.0205268	+	0.999789i	$0.506534\pi$
$558$	−5.81336e6	−0.790390
$559$	−2.89530e6	−0.391890
$560$	1.99617e7	2.68984
$561$	3.27506e6	0.439352
$562$	−6.13851e6	−0.819827
$563$	−9.21092e6	−1.22471	−0.612353	−	0.790584i	$-0.709777\pi$
$563$	−9.21092e6	−1.22471	−0.612353	+	0.790584i	$0.709777\pi$
$564$	−2.13811e6	−0.283030
$565$	1.97884e7	2.60790
$566$	−1.60730e7	−2.10890
$567$	1.02549e6	0.133959
$568$	−1.37480e6	−0.178801
$569$	−1.44126e6	−0.186621	−0.0933106	−	0.995637i	$-0.529745\pi$
$569$	−1.44126e6	−0.186621	−0.0933106	+	0.995637i	$0.529745\pi$
$570$	−1.75925e6	−0.226798
$571$	4.03264e6	0.517606	0.258803	−	0.965930i	$-0.416672\pi$
$571$	4.03264e6	0.517606	0.258803	+	0.965930i	$0.416672\pi$
$572$	1.41888e6	0.181324
$573$	691112.	0.0879351
$574$	1.56036e7	1.97672
$575$	−3.25353e7	−4.10379
$576$	−1.73479e6	−0.217866
$577$	2.52617e6	0.315880	0.157940	−	0.987449i	$-0.449515\pi$
$577$	2.52617e6	0.315880	0.157940	+	0.987449i	$0.449515\pi$
$578$	−5.31649e6	−0.661919
$579$	4.46639e6	0.553682
$580$	2.40605e7	2.96985
$581$	7.79674e6	0.958237
$582$	1.51308e6	0.185163
$583$	−9.82407e6	−1.19707
$584$	1.99477e6	0.242025
$585$	1.10256e6	0.133203
$586$	1.07662e7	1.29515
$587$	5.01886e6	0.601188	0.300594	−	0.953752i	$-0.402815\pi$
$587$	5.01886e6	0.601188	0.300594	+	0.953752i	$0.402815\pi$
$588$	1.83934e6	0.219391
$589$	−2.17255e6	−0.258036
$590$	−2.93113e6	−0.346661
$591$	−3.98505e6	−0.469316
$592$	−7.34766e6	−0.861678
$593$	−1.51902e7	−1.77390	−0.886948	−	0.461870i	$-0.847179\pi$
$593$	−1.51902e7	−1.77390	−0.886948	+	0.461870i	$0.847179\pi$
$594$	−2.38663e6	−0.277536
$595$	1.46289e7	1.69402
$596$	−2.60263e6	−0.300121
$597$	6.57299e6	0.754791
$598$	3.46328e6	0.396036
$599$	7.13948e6	0.813017	0.406509	−	0.913647i	$-0.366746\pi$
$599$	7.13948e6	0.813017	0.406509	+	0.913647i	$0.366746\pi$
$600$	−3.19911e6	−0.362786
$601$	8.80337e6	0.994175	0.497088	−	0.867700i	$-0.334403\pi$
$601$	8.80337e6	0.994175	0.497088	+	0.867700i	$0.334403\pi$
$602$	2.79941e7	3.14830
$603$	−115415.	−0.0129262
$604$	759072.	0.0846624
$605$	−2.32744e6	−0.258517
$606$	9.43825e6	1.04402
$607$	−9.90444e6	−1.09108	−0.545542	−	0.838084i	$-0.683676\pi$
$607$	−9.90444e6	−1.09108	−0.545542	+	0.838084i	$0.683676\pi$
$608$	−1.77502e6	−0.194735
$609$	−1.14975e7	−1.25620
$610$	−1.15357e7	−1.25522
$611$	1.09851e6	0.119042
$612$	−1.85110e6	−0.199780
$613$	7.13725e6	0.767149	0.383574	−	0.923510i	$-0.374693\pi$
$613$	7.13725e6	0.767149	0.383574	+	0.923510i	$0.374693\pi$
$614$	−1.02506e7	−1.09730
$615$	−1.28643e7	−1.37151
$616$	2.65565e6	0.281981
$617$	−6.15006e6	−0.650379	−0.325189	−	0.945649i	$-0.605428\pi$
$617$	−6.15006e6	−0.650379	−0.325189	+	0.945649i	$0.605428\pi$
$618$	−3.16125e6	−0.332957
$619$	−749330.	−0.0786043	−0.0393022	−	0.999227i	$-0.512513\pi$
$619$	−749330.	−0.0786043	−0.0393022	+	0.999227i	$0.512513\pi$
$620$	2.75499e7	2.87833
$621$	−2.65567e6	−0.276341
$622$	−1.55339e7	−1.60992
$623$	−7.92997e6	−0.818561
$624$	1.29774e6	0.133422
$625$	4.20901e7	4.31003
$626$	3.93747e6	0.401588
$627$	−891923.	−0.0906063
$628$	−3.95336e6	−0.400007
$629$	−5.38472e6	−0.542670
$630$	−1.06605e7	−1.07010
$631$	−2.06221e6	−0.206186	−0.103093	−	0.994672i	$-0.532874\pi$
$631$	−2.06221e6	−0.206186	−0.103093	+	0.994672i	$0.532874\pi$
$632$	2.77497e6	0.276354
$633$	8.64150e6	0.857196
$634$	37800.2	0.00373483
$635$	2.75296e6	0.270936
$636$	5.55267e6	0.544326
$637$	−945003.	−0.0922751
$638$	2.67582e7	2.60259
$639$	2.79800e6	0.271078
$640$	−8.83210e6	−0.852342
$641$	−3.59859e6	−0.345929	−0.172964	−	0.984928i	$-0.555335\pi$
$641$	−3.59859e6	−0.345929	−0.172964	+	0.984928i	$0.555335\pi$
$642$	2.90754e6	0.278412
$643$	1.37456e7	1.31110	0.655549	−	0.755153i	$-0.272437\pi$
$643$	1.37456e7	1.31110	0.655549	+	0.755153i	$0.272437\pi$
$644$	−1.52654e7	−1.45042
$645$	−2.30795e7	−2.18438
$646$	−1.51749e6	−0.143068
$647$	5.03818e6	0.473165	0.236583	−	0.971611i	$-0.423973\pi$
$647$	5.03818e6	0.473165	0.236583	+	0.971611i	$0.423973\pi$
$648$	−261125.	−0.0244293
$649$	−1.48606e6	−0.138492
$650$	−8.49078e6	−0.788251
$651$	−1.31649e7	−1.21749
$652$	−3.76599e6	−0.346945
$653$	1.53399e7	1.40780	0.703898	−	0.710301i	$-0.251441\pi$
$653$	1.53399e7	1.40780	0.703898	+	0.710301i	$0.251441\pi$
$654$	−1.27008e7	−1.16115
$655$	−3.07745e6	−0.280277
$656$	−1.51415e7	−1.37376
$657$	−4.05974e6	−0.366931
$658$	−1.06212e7	−0.956337
$659$	−3.56478e6	−0.319756	−0.159878	−	0.987137i	$-0.551110\pi$
$659$	−3.56478e6	−0.319756	−0.159878	+	0.987137i	$0.551110\pi$
$660$	1.13104e7	1.01069
$661$	−1.62245e7	−1.44434	−0.722168	−	0.691718i	$-0.756854\pi$
$661$	−1.62245e7	−1.44434	−0.722168	+	0.691718i	$0.756854\pi$
$662$	−1.51238e7	−1.34127
$663$	951047.	0.0840269
$664$	−1.98532e6	−0.174748
$665$	−3.98399e6	−0.349353
$666$	3.92399e6	0.342802
$667$	2.97747e7	2.59139
$668$	−896804.	−0.0777600
$669$	−1.03364e6	−0.0892899
$670$	1.19980e6	0.103258
$671$	−5.84850e6	−0.501462
$672$	−1.07561e7	−0.918819
$673$	3.40408e6	0.289709	0.144854	−	0.989453i	$-0.453729\pi$
$673$	3.40408e6	0.289709	0.144854	+	0.989453i	$0.453729\pi$
$674$	1.76530e7	1.49682
$675$	6.51082e6	0.550017
$676$	−9.54240e6	−0.803139
$677$	1.17767e7	0.987531	0.493766	−	0.869595i	$-0.335620\pi$
$677$	1.17767e7	0.987531	0.493766	+	0.869595i	$0.335620\pi$
$678$	−1.24387e7	−1.03921
$679$	3.42653e6	0.285220
$680$	−3.72502e6	−0.308928
$681$	−2.84410e6	−0.235005
$682$	3.06389e7	2.52239
$683$	1.47519e7	1.21003	0.605015	−	0.796214i	$-0.293167\pi$
$683$	1.47519e7	1.21003	0.605015	+	0.796214i	$0.293167\pi$
$684$	504125.	0.0412000
$685$	−2.12819e7	−1.73294
$686$	−1.10084e7	−0.893128
$687$	−991196.	−0.0801250
$688$	−2.71652e7	−2.18797
$689$	−2.85282e6	−0.228942
$690$	2.76071e7	2.20749
$691$	−1.18621e6	−0.0945079	−0.0472539	−	0.998883i	$-0.515047\pi$
$691$	−1.18621e6	−0.0945079	−0.0472539	+	0.998883i	$0.515047\pi$
$692$	9.64755e6	0.765864
$693$	−5.40477e6	−0.427508
$694$	7.26275e6	0.572404
$695$	4.23465e7	3.32549
$696$	2.92766e6	0.229086
$697$	−1.10964e7	−0.865171
$698$	1.50379e7	1.16828
$699$	77809.1	0.00602334
$700$	3.74256e7	2.88684
$701$	−1.36391e7	−1.04831	−0.524155	−	0.851623i	$-0.675619\pi$
$701$	−1.36391e7	−1.04831	−0.524155	+	0.851623i	$0.675619\pi$
$702$	−693055.	−0.0530792
$703$	1.46646e6	0.111913
$704$	9.14308e6	0.695282
$705$	8.75660e6	0.663534
$706$	1.91081e7	1.44280
$707$	2.13739e7	1.60818
$708$	839936.	0.0629743
$709$	−1.43919e7	−1.07524	−0.537618	−	0.843189i	$-0.680676\pi$
$709$	−1.43919e7	−1.07524	−0.537618	+	0.843189i	$0.680676\pi$
$710$	−2.90866e7	−2.16544
$711$	−5.64761e6	−0.418978
$712$	2.01925e6	0.149276
$713$	3.40928e7	2.51153
$714$	−9.19550e6	−0.675040
$715$	−5.81098e6	−0.425093
$716$	1.38589e6	0.101029
$717$	5.61310e6	0.407760
$718$	2.17003e6	0.157092
$719$	1.64117e7	1.18395	0.591974	−	0.805957i	$-0.298349\pi$
$719$	1.64117e7	1.18395	0.591974	+	0.805957i	$0.298349\pi$
$720$	1.03448e7	0.743687
$721$	−7.15899e6	−0.512877
$722$	−1.85754e7	−1.32616
$723$	−1.56129e7	−1.11081
$724$	−1.74173e7	−1.23491
$725$	−7.29974e7	−5.15778
$726$	1.46299e6	0.103015
$727$	−1.31438e7	−0.922328	−0.461164	−	0.887315i	$-0.652568\pi$
$727$	−1.31438e7	−0.922328	−0.461164	+	0.887315i	$0.652568\pi$
$728$	771176.	0.0539293
$729$	531441.	0.0370370
$730$	4.22030e7	2.93114
$731$	−1.99079e7	−1.37795
$732$	3.30564e6	0.228022
$733$	2.02772e6	0.139395	0.0696977	−	0.997568i	$-0.477797\pi$
$733$	2.02772e6	0.139395	0.0696977	+	0.997568i	$0.477797\pi$
$734$	7.84333e6	0.537354
$735$	−7.53298e6	−0.514338
$736$	2.78546e7	1.89541
$737$	608288.	0.0412516
$738$	8.08629e6	0.546523
$739$	−1.39245e7	−0.937929	−0.468964	−	0.883217i	$-0.655373\pi$
$739$	−1.39245e7	−0.937929	−0.468964	+	0.883217i	$0.655373\pi$
$740$	−1.85961e7	−1.24837
$741$	−259006.	−0.0173286
$742$	2.75834e7	1.83924
$743$	−1.13430e6	−0.0753800	−0.0376900	−	0.999289i	$-0.512000\pi$
$743$	−1.13430e6	−0.0753800	−0.0376900	+	0.999289i	$0.512000\pi$
$744$	3.35226e6	0.222026
$745$	1.06590e7	0.703600
$746$	2.31772e7	1.52481
$747$	4.04052e6	0.264933
$748$	9.75611e6	0.637562
$749$	6.58442e6	0.428858
$750$	−4.40010e7	−2.85633
$751$	−2.62894e7	−1.70091	−0.850456	−	0.526047i	$-0.823674\pi$
$751$	−2.62894e7	−1.70091	−0.850456	+	0.526047i	$0.823674\pi$
$752$	1.03067e7	0.664624
$753$	1.30211e7	0.836875
$754$	7.77033e6	0.497750
$755$	−3.10876e6	−0.198482
$756$	3.05484e6	0.194394
$757$	2.04231e7	1.29534	0.647668	−	0.761923i	$-0.275744\pi$
$757$	2.04231e7	1.29534	0.647668	+	0.761923i	$0.275744\pi$
$758$	−4.06029e6	−0.256675
$759$	1.39966e7	0.881895
$760$	1.01446e6	0.0637093
$761$	671201.	0.0420137	0.0210068	−	0.999779i	$-0.493313\pi$
$761$	671201.	0.0420137	0.0210068	+	0.999779i	$0.493313\pi$
$762$	−1.73047e6	−0.107964
$763$	−2.87623e7	−1.78860
$764$	2.05876e6	0.127606
$765$	7.58115e6	0.468362
$766$	−2.26237e7	−1.39313
$767$	−431537.	−0.0264868
$768$	1.17199e7	0.717000
$769$	5.15936e6	0.314616	0.157308	−	0.987550i	$-0.449719\pi$
$769$	5.15936e6	0.314616	0.157308	+	0.987550i	$0.449719\pi$
$770$	5.61853e7	3.41504
$771$	−1.60110e6	−0.0970022
$772$	1.33050e7	0.803472
$773$	1.30533e7	0.785727	0.392863	−	0.919597i	$-0.371485\pi$
$773$	1.30533e7	0.785727	0.392863	+	0.919597i	$0.371485\pi$
$774$	1.45075e7	0.870440
$775$	−8.35841e7	−4.99884
$776$	−872515.	−0.0520138
$777$	8.88629e6	0.528041
$778$	−2.27650e7	−1.34840
$779$	3.02198e6	0.178422
$780$	3.28443e6	0.193296
$781$	−1.47467e7	−0.865099
$782$	2.38133e7	1.39252
$783$	−5.95837e6	−0.347314
$784$	−8.86649e6	−0.515183
$785$	1.61909e7	0.937772
$786$	1.93444e6	0.111686
$787$	−1.77189e7	−1.01977	−0.509883	−	0.860244i	$-0.670311\pi$
$787$	−1.77189e7	−1.01977	−0.509883	+	0.860244i	$0.670311\pi$
$788$	−1.18711e7	−0.681045
$789$	−5.96681e6	−0.341232
$790$	5.87098e7	3.34690
$791$	−2.81688e7	−1.60076
$792$	1.37624e6	0.0779619
$793$	−1.69835e6	−0.0959056
$794$	7.97695e6	0.449041
$795$	−2.27409e7	−1.27611
$796$	1.95803e7	1.09531
$797$	1.81052e7	1.00962	0.504809	−	0.863231i	$-0.331563\pi$
$797$	1.81052e7	1.00962	0.504809	+	0.863231i	$0.331563\pi$
$798$	2.50428e6	0.139212
$799$	7.55326e6	0.418569
$800$	−6.82901e7	−3.77253
$801$	−4.10956e6	−0.226315
$802$	2.53842e7	1.39357
$803$	2.13966e7	1.17100
$804$	−343811.	−0.0187577
$805$	6.25191e7	3.40034
$806$	8.89725e6	0.482412
$807$	−9.93471e6	−0.536996
$808$	−5.44254e6	−0.293274
$809$	−1.50822e7	−0.810204	−0.405102	−	0.914272i	$-0.632764\pi$
$809$	−1.50822e7	−0.810204	−0.405102	+	0.914272i	$0.632764\pi$
$810$	−5.52460e6	−0.295861
$811$	3.23070e7	1.72482	0.862411	−	0.506209i	$-0.168954\pi$
$811$	3.23070e7	1.72482	0.862411	+	0.506209i	$0.168954\pi$
$812$	−3.42500e7	−1.82293
$813$	−1.48989e7	−0.790549
$814$	−2.06811e7	−1.09399
$815$	1.54235e7	0.813374
$816$	8.92319e6	0.469132
$817$	5.42167e6	0.284170
$818$	−3.99690e7	−2.08852
$819$	−1.56949e6	−0.0817617
$820$	−3.83215e7	−1.99025
$821$	−3.33802e7	−1.72835	−0.864175	−	0.503191i	$-0.832159\pi$
$821$	−3.33802e7	−1.72835	−0.864175	+	0.503191i	$0.832159\pi$
$822$	1.33775e7	0.690551
$823$	3.38256e7	1.74079	0.870393	−	0.492357i	$-0.163865\pi$
$823$	3.38256e7	1.74079	0.870393	+	0.492357i	$0.163865\pi$
$824$	1.82293e6	0.0935301
$825$	−3.43148e7	−1.75528
$826$	4.17245e6	0.212785
$827$	3.25009e7	1.65246	0.826231	−	0.563332i	$-0.190481\pi$
$827$	3.25009e7	1.65246	0.826231	+	0.563332i	$0.190481\pi$
$828$	−7.91101e6	−0.401011
$829$	−508321.	−0.0256893	−0.0128446	−	0.999918i	$-0.504089\pi$
$829$	−508321.	−0.0256893	−0.0128446	+	0.999918i	$0.504089\pi$
$830$	−4.20033e7	−2.11635
$831$	−790529.	−0.0397114
$832$	2.65506e6	0.132974
$833$	−6.49778e6	−0.324454
$834$	−2.66184e7	−1.32515
$835$	3.67284e6	0.182300
$836$	−2.65696e6	−0.131483
$837$	−6.82249e6	−0.336612
$838$	−2.61988e7	−1.28876
$839$	−583710.	−0.0286281	−0.0143140	−	0.999898i	$-0.504556\pi$
$839$	−583710.	−0.0286281	−0.0143140	+	0.999898i	$0.504556\pi$
$840$	6.14733e6	0.300600
$841$	4.62924e7	2.25694
$842$	4.37493e7	2.12663
$843$	−7.20409e6	−0.349149
$844$	2.57423e7	1.24391
$845$	3.90807e7	1.88287
$846$	−5.50427e6	−0.264408
$847$	3.31310e6	0.158681
$848$	−2.67665e7	−1.27821
$849$	−1.88631e7	−0.898141
$850$	−5.83821e7	−2.77161
$851$	−2.30125e7	−1.08928
$852$	8.33498e6	0.393374
$853$	9.83319e6	0.462724	0.231362	−	0.972868i	$-0.425682\pi$
$853$	9.83319e6	0.462724	0.231362	+	0.972868i	$0.425682\pi$
$854$	1.64210e7	0.770469
$855$	−2.06463e6	−0.0965890
$856$	−1.67662e6	−0.0782081
$857$	1.07762e7	0.501201	0.250601	−	0.968091i	$-0.419372\pi$
$857$	1.07762e7	0.501201	0.250601	+	0.968091i	$0.419372\pi$
$858$	3.65270e6	0.169393
$859$	−3.47029e7	−1.60466	−0.802329	−	0.596883i	$-0.796406\pi$
$859$	−3.47029e7	−1.60466	−0.802329	+	0.596883i	$0.796406\pi$
$860$	−6.87518e7	−3.16985
$861$	1.83122e7	0.841848
$862$	−1.77235e7	−0.812422
$863$	−2.34351e7	−1.07112	−0.535561	−	0.844496i	$-0.679900\pi$
$863$	−2.34351e7	−1.07112	−0.535561	+	0.844496i	$0.679900\pi$
$864$	−5.57414e6	−0.254035
$865$	−3.95114e7	−1.79548
$866$	−424762.	−0.0192465
$867$	−6.23937e6	−0.281899
$868$	−3.92172e7	−1.76676
$869$	2.97654e7	1.33709
$870$	6.19403e7	2.77444
$871$	176641.	0.00788944
$872$	7.32389e6	0.326175
$873$	1.77574e6	0.0788575
$874$	−6.48525e6	−0.287176
$875$	−9.96447e7	−4.39981
$876$	−1.20936e7	−0.532470
$877$	5.93447e6	0.260545	0.130273	−	0.991478i	$-0.458415\pi$
$877$	5.93447e6	0.260545	0.130273	+	0.991478i	$0.458415\pi$
$878$	−4.29946e7	−1.88225
$879$	1.26351e7	0.551579
$880$	−5.45215e7	−2.37335
$881$	−7.45973e6	−0.323805	−0.161902	−	0.986807i	$-0.551763\pi$
$881$	−7.45973e6	−0.323805	−0.161902	+	0.986807i	$0.551763\pi$
$882$	4.73512e6	0.204955
$883$	−2.46902e7	−1.06567	−0.532835	−	0.846219i	$-0.678873\pi$
$883$	−2.46902e7	−1.06567	−0.532835	+	0.846219i	$0.678873\pi$
$884$	2.83308e6	0.121935
$885$	−3.43994e6	−0.147636
$886$	4.09366e7	1.75198
$887$	2.56140e7	1.09312	0.546562	−	0.837419i	$-0.315936\pi$
$887$	2.56140e7	1.09312	0.546562	+	0.837419i	$0.315936\pi$
$888$	−2.26276e6	−0.0962955
$889$	−3.91883e6	−0.166304
$890$	4.27210e7	1.80787
$891$	−2.80092e6	−0.118197
$892$	−3.07911e6	−0.129572
$893$	−2.05704e6	−0.0863204
$894$	−6.70009e6	−0.280374
$895$	−5.67589e6	−0.236852
$896$	1.25725e7	0.523179
$897$	4.06447e6	0.168664
$898$	−2.82304e7	−1.16822
$899$	7.64919e7	3.15658
$900$	1.93951e7	0.798153
$901$	−1.96158e7	−0.804996
$902$	−4.26183e7	−1.74413
$903$	3.28536e7	1.34080
$904$	7.17275e6	0.291921
$905$	7.13321e7	2.89510
$906$	1.95412e6	0.0790918
$907$	−1.05309e7	−0.425055	−0.212528	−	0.977155i	$-0.568170\pi$
$907$	−1.05309e7	−0.425055	−0.212528	+	0.977155i	$0.568170\pi$
$908$	−8.47231e6	−0.341026
$909$	1.10766e7	0.444629
$910$	1.63157e7	0.653133
$911$	8.73649e6	0.348772	0.174386	−	0.984677i	$-0.444206\pi$
$911$	8.73649e6	0.348772	0.174386	+	0.984677i	$0.444206\pi$
$912$	−2.43012e6	−0.0967477
$913$	−2.12953e7	−0.845487
$914$	2.41453e7	0.956019
$915$	−1.35382e7	−0.534573
$916$	−2.95268e6	−0.116273
$917$	4.38074e6	0.172038
$918$	−4.76540e6	−0.186635
$919$	−1.11596e7	−0.435874	−0.217937	−	0.975963i	$-0.569933\pi$
$919$	−1.11596e7	−0.435874	−0.217937	+	0.975963i	$0.569933\pi$
$920$	−1.59195e7	−0.620099
$921$	−1.20299e7	−0.467320
$922$	−2.34600e7	−0.908870
$923$	−4.28229e6	−0.165452
$924$	−1.61003e7	−0.620375
$925$	5.64189e7	2.16806
$926$	6.40822e7	2.45590
$927$	−3.71002e6	−0.141800
$928$	6.24957e7	2.38221
$929$	334818.	0.0127283	0.00636415	−	0.999980i	$-0.497974\pi$
$929$	334818.	0.0127283	0.00636415	+	0.999980i	$0.497974\pi$
$930$	7.09233e7	2.68894
$931$	1.76959e6	0.0669112
$932$	231786.	0.00874073
$933$	−1.82305e7	−0.685636
$934$	8.94046e6	0.335345
$935$	−3.99560e7	−1.49469
$936$	399648.	0.0149104
$937$	−4.10034e6	−0.152571	−0.0762853	−	0.997086i	$-0.524306\pi$
$937$	−4.10034e6	−0.152571	−0.0762853	+	0.997086i	$0.524306\pi$
$938$	−1.70791e6	−0.0633808
$939$	4.62097e6	0.171029
$940$	2.60851e7	0.962882
$941$	−760066.	−0.0279819	−0.0139910	−	0.999902i	$-0.504454\pi$
$941$	−760066.	−0.0279819	−0.0139910	+	0.999902i	$0.504454\pi$
$942$	−1.01774e7	−0.373687
$943$	−4.74226e7	−1.73663
$944$	−4.04889e6	−0.147879
$945$	−1.25110e7	−0.455736
$946$	−7.64606e7	−2.77786
$947$	2.02978e7	0.735486	0.367743	−	0.929927i	$-0.380131\pi$
$947$	2.02978e7	0.735486	0.367743	+	0.929927i	$0.380131\pi$
$948$	−1.68237e7	−0.607997
$949$	6.21336e6	0.223955
$950$	1.58996e7	0.571582
$951$	44362.0	0.00159059
$952$	5.30256e6	0.189624
$953$	−7.64595e6	−0.272709	−0.136354	−	0.990660i	$-0.543539\pi$
$953$	−7.64595e6	−0.272709	−0.136354	+	0.990660i	$0.543539\pi$
$954$	1.42946e7	0.508511
$955$	−8.43161e6	−0.299159
$956$	1.67209e7	0.591718
$957$	3.14032e7	1.10839
$958$	−9.46316e6	−0.333137
$959$	3.02947e7	1.06370
$960$	2.11645e7	0.741191
$961$	5.89562e7	2.05931
$962$	−6.00561e6	−0.209228
$963$	3.41226e6	0.118570
$964$	−4.65095e7	−1.61194
$965$	−5.44903e7	−1.88365
$966$	−3.92986e7	−1.35498
$967$	−362592.	−0.0124696	−0.00623479	−	0.999981i	$-0.501985\pi$
$967$	−362592.	−0.0124696	−0.00623479	+	0.999981i	$0.501985\pi$
$968$	−843631.	−0.0289377
$969$	−1.78091e6	−0.0609301
$970$	−1.84597e7	−0.629934
$971$	−4.16836e7	−1.41879	−0.709393	−	0.704813i	$-0.751031\pi$
$971$	−4.16836e7	−1.41879	−0.709393	+	0.704813i	$0.751031\pi$
$972$	1.58311e6	0.0537460
$973$	−6.02800e7	−2.04123
$974$	1.22822e7	0.414838
$975$	−9.96470e6	−0.335701
$976$	−1.59347e7	−0.535452
$977$	−2.63657e7	−0.883695	−0.441847	−	0.897090i	$-0.645677\pi$
$977$	−2.63657e7	−0.883695	−0.441847	+	0.897090i	$0.645677\pi$
$978$	−9.69501e6	−0.324117
$979$	2.16592e7	0.722246
$980$	−2.24400e7	−0.746377
$981$	−1.49055e7	−0.494510
$982$	1.36960e7	0.453227
$983$	3.95927e6	0.130687	0.0653433	−	0.997863i	$-0.479186\pi$
$983$	3.95927e6	0.130687	0.0653433	+	0.997863i	$0.479186\pi$
$984$	−4.66294e6	−0.153522
$985$	4.86179e7	1.59663
$986$	5.34283e7	1.75017
$987$	−1.24650e7	−0.407286
$988$	−771555.	−0.0251463
$989$	−8.50800e7	−2.76590
$990$	2.91170e7	0.944189
$991$	−3.87210e7	−1.25246	−0.626228	−	0.779640i	$-0.715402\pi$
$991$	−3.87210e7	−1.25246	−0.626228	+	0.779640i	$0.715402\pi$
$992$	7.15592e7	2.30880
$993$	−1.77492e7	−0.571222
$994$	4.14047e7	1.32918
$995$	−8.01908e7	−2.56783
$996$	1.20363e7	0.384456
$997$	3.15392e7	1.00488	0.502438	−	0.864613i	$-0.332436\pi$
$997$	3.15392e7	1.00488	0.502438	+	0.864613i	$0.332436\pi$
$998$	6.12442e7	1.94643
$999$	4.60516e6	0.145993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.a.1.10	✓	11
3.2	odd	2		531.6.a.b.1.2		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.a.1.10	✓	11	1.1	even	1	trivial
531.6.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q+7.66878 q^{2} +9.00000 q^{3} +26.8102 q^{4} -109.801 q^{5} +69.0190 q^{6} +156.301 q^{7} -39.7996 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+7.66878 q^{2} +9.00000 q^{3} +26.8102 q^{4} -109.801 q^{5} +69.0190 q^{6} +156.301 q^{7} -39.7996 q^{8} +81.0000 q^{9} -842.036 q^{10} -426.905 q^{11} +241.292 q^{12} -123.969 q^{13} +1198.64 q^{14} -988.205 q^{15} -1163.14 q^{16} -852.404 q^{17} +621.171 q^{18} +232.142 q^{19} -2943.77 q^{20} +1406.71 q^{21} -3273.84 q^{22} -3642.90 q^{23} -358.197 q^{24} +8931.16 q^{25} -950.692 q^{26} +729.000 q^{27} +4190.45 q^{28} -8173.34 q^{29} -7578.33 q^{30} -9358.70 q^{31} -7646.28 q^{32} -3842.15 q^{33} -6536.90 q^{34} -17161.9 q^{35} +2171.62 q^{36} +6317.09 q^{37} +1780.24 q^{38} -1115.72 q^{39} +4370.02 q^{40} +13017.8 q^{41} +10787.7 q^{42} +23355.0 q^{43} -11445.4 q^{44} -8893.84 q^{45} -27936.6 q^{46} -8861.12 q^{47} -10468.3 q^{48} +7622.89 q^{49} +68491.1 q^{50} -7671.64 q^{51} -3323.64 q^{52} +23012.3 q^{53} +5590.54 q^{54} +46874.4 q^{55} -6220.71 q^{56} +2089.28 q^{57} -62679.6 q^{58} +3481.00 q^{59} -26493.9 q^{60} +13699.8 q^{61} -71769.8 q^{62} +12660.4 q^{63} -21417.1 q^{64} +13611.9 q^{65} -29464.6 q^{66} -1424.88 q^{67} -22853.1 q^{68} -32786.1 q^{69} -131611. q^{70} +34543.2 q^{71} -3223.77 q^{72} -50120.2 q^{73} +48444.4 q^{74} +80380.4 q^{75} +6223.76 q^{76} -66725.5 q^{77} -8556.23 q^{78} -69723.6 q^{79} +127713. q^{80} +6561.00 q^{81} +99830.8 q^{82} +49883.0 q^{83} +37714.0 q^{84} +93594.5 q^{85} +179104. q^{86} -73560.1 q^{87} +16990.7 q^{88} -50735.3 q^{89} -68204.9 q^{90} -19376.5 q^{91} -97666.8 q^{92} -84228.3 q^{93} -67954.0 q^{94} -25489.3 q^{95} -68816.5 q^{96} +21922.7 q^{97} +58458.2 q^{98} -34579.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) \) 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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