LMFDB - Embedded newform 177.6.a.b.1.11

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:	$12$
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} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + \cdots - 50564480 $ x^12 - 4x^11 - 283x^10 + 1045x^9 + 27968x^8 - 94393x^7 - 1130486x^6 + 3566264x^5 + 15496192x^4 - 53008480x^3 - 16576192x^2 + 120303168*x - 50564480
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			1.11
Root			$-8.78000$ 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)

$f(q)$	$=$	$q+8.78000 q^{2} -9.00000 q^{3} +45.0883 q^{4} -17.5207 q^{5} -79.0200 q^{6} +12.9559 q^{7} +114.916 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+8.78000 q^{2} -9.00000 q^{3} +45.0883 q^{4} -17.5207 q^{5} -79.0200 q^{6} +12.9559 q^{7} +114.916 q^{8} +81.0000 q^{9} -153.831 q^{10} -434.226 q^{11} -405.795 q^{12} -637.700 q^{13} +113.753 q^{14} +157.686 q^{15} -433.869 q^{16} -850.752 q^{17} +711.180 q^{18} +1822.12 q^{19} -789.977 q^{20} -116.603 q^{21} -3812.51 q^{22} +715.863 q^{23} -1034.24 q^{24} -2818.03 q^{25} -5599.00 q^{26} -729.000 q^{27} +584.162 q^{28} +1133.86 q^{29} +1384.48 q^{30} -9559.39 q^{31} -7486.66 q^{32} +3908.04 q^{33} -7469.60 q^{34} -226.997 q^{35} +3652.16 q^{36} -107.111 q^{37} +15998.2 q^{38} +5739.30 q^{39} -2013.40 q^{40} -6614.88 q^{41} -1023.78 q^{42} -2995.66 q^{43} -19578.5 q^{44} -1419.17 q^{45} +6285.27 q^{46} +10180.6 q^{47} +3904.82 q^{48} -16639.1 q^{49} -24742.3 q^{50} +7656.77 q^{51} -28752.8 q^{52} +11009.5 q^{53} -6400.62 q^{54} +7607.93 q^{55} +1488.84 q^{56} -16399.1 q^{57} +9955.28 q^{58} -3481.00 q^{59} +7109.80 q^{60} +2294.87 q^{61} -83931.4 q^{62} +1049.43 q^{63} -51849.1 q^{64} +11172.9 q^{65} +34312.6 q^{66} +23569.8 q^{67} -38359.0 q^{68} -6442.76 q^{69} -1993.03 q^{70} +56039.7 q^{71} +9308.16 q^{72} +56572.1 q^{73} -940.434 q^{74} +25362.2 q^{75} +82156.5 q^{76} -5625.81 q^{77} +50391.0 q^{78} +65746.0 q^{79} +7601.67 q^{80} +6561.00 q^{81} -58078.6 q^{82} -13649.8 q^{83} -5257.45 q^{84} +14905.7 q^{85} -26301.9 q^{86} -10204.7 q^{87} -49899.4 q^{88} +77607.3 q^{89} -12460.3 q^{90} -8262.00 q^{91} +32277.1 q^{92} +86034.5 q^{93} +89386.0 q^{94} -31924.8 q^{95} +67380.0 q^{96} +41043.1 q^{97} -146092. q^{98} -35172.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * 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 $

$2$	8.78000	1.55210	0.776049	−	0.630672i	$-0.217221\pi$
$2$	8.78000	1.55210	0.776049	+	0.630672i	$0.217221\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	45.0883	1.40901
$5$	−17.5207	−0.313419	−0.156710	−	0.987645i	$-0.550089\pi$
$5$	−17.5207	−0.313419	−0.156710	+	0.987645i	$0.550089\pi$
$6$	−79.0200	−0.896105
$7$	12.9559	0.0999364	0.0499682	−	0.998751i	$-0.484088\pi$
$7$	12.9559	0.0999364	0.0499682	+	0.998751i	$0.484088\pi$
$8$	114.916	0.634825
$9$	81.0000	0.333333
$10$	−153.831	−0.486457
$11$	−434.226	−1.08202	−0.541009	−	0.841017i	$-0.681958\pi$
$11$	−434.226	−1.08202	−0.541009	+	0.841017i	$0.681958\pi$
$12$	−405.795	−0.813493
$13$	−637.700	−1.04655	−0.523273	−	0.852165i	$-0.675289\pi$
$13$	−637.700	−1.04655	−0.523273	+	0.852165i	$0.675289\pi$
$14$	113.753	0.155111
$15$	157.686	0.180953
$16$	−433.869	−0.423700
$17$	−850.752	−0.713971	−0.356986	−	0.934110i	$-0.616196\pi$
$17$	−850.752	−0.713971	−0.356986	+	0.934110i	$0.616196\pi$
$18$	711.180	0.517366
$19$	1822.12	1.15796	0.578980	−	0.815341i	$-0.303451\pi$
$19$	1822.12	1.15796	0.578980	+	0.815341i	$0.303451\pi$
$20$	−789.977	−0.441611
$21$	−116.603	−0.0576983
$22$	−3812.51	−1.67940
$23$	715.863	0.282170	0.141085	−	0.989998i	$-0.454941\pi$
$23$	715.863	0.282170	0.141085	+	0.989998i	$0.454941\pi$
$24$	−1034.24	−0.366516
$25$	−2818.03	−0.901768
$26$	−5599.00	−1.62434
$27$	−729.000	−0.192450
$28$	584.162	0.140811
$29$	1133.86	0.250360	0.125180	−	0.992134i	$-0.460049\pi$
$29$	1133.86	0.250360	0.125180	+	0.992134i	$0.460049\pi$
$30$	1384.48	0.280856
$31$	−9559.39	−1.78659	−0.893297	−	0.449467i	$-0.851614\pi$
$31$	−9559.39	−1.78659	−0.893297	+	0.449467i	$0.851614\pi$
$32$	−7486.66	−1.29245
$33$	3908.04	0.624703
$34$	−7469.60	−1.10815
$35$	−226.997	−0.0313220
$36$	3652.16	0.469670
$37$	−107.111	−0.0128626	−0.00643132	−	0.999979i	$-0.502047\pi$
$37$	−107.111	−0.0128626	−0.00643132	+	0.999979i	$0.502047\pi$
$38$	15998.2	1.79727
$39$	5739.30	0.604223
$40$	−2013.40	−0.198966
$41$	−6614.88	−0.614557	−0.307279	−	0.951620i	$-0.599418\pi$
$41$	−6614.88	−0.614557	−0.307279	+	0.951620i	$0.599418\pi$
$42$	−1023.78	−0.0895535
$43$	−2995.66	−0.247070	−0.123535	−	0.992340i	$-0.539423\pi$
$43$	−2995.66	−0.247070	−0.123535	+	0.992340i	$0.539423\pi$
$44$	−19578.5	−1.52457
$45$	−1419.17	−0.104473
$46$	6285.27	0.437955
$47$	10180.6	0.672249	0.336125	−	0.941817i	$-0.390884\pi$
$47$	10180.6	0.672249	0.336125	+	0.941817i	$0.390884\pi$
$48$	3904.82	0.244623
$49$	−16639.1	−0.990013
$50$	−24742.3	−1.39963
$51$	7656.77	0.412212
$52$	−28752.8	−1.47459
$53$	11009.5	0.538367	0.269183	−	0.963089i	$-0.413246\pi$
$53$	11009.5	0.538367	0.269183	+	0.963089i	$0.413246\pi$
$54$	−6400.62	−0.298702
$55$	7607.93	0.339125
$56$	1488.84	0.0634421
$57$	−16399.1	−0.668549
$58$	9955.28	0.388583
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	7109.80	0.254964
$61$	2294.87	0.0789648	0.0394824	−	0.999220i	$-0.487429\pi$
$61$	2294.87	0.0789648	0.0394824	+	0.999220i	$0.487429\pi$
$62$	−83931.4	−2.77297
$63$	1049.43	0.0333121
$64$	−51849.1	−1.58231
$65$	11172.9	0.328007
$66$	34312.6	0.969601
$67$	23569.8	0.641459	0.320729	−	0.947171i	$-0.396072\pi$
$67$	23569.8	0.641459	0.320729	+	0.947171i	$0.396072\pi$
$68$	−38359.0	−1.00599
$69$	−6442.76	−0.162911
$70$	−1993.03	−0.0486148
$71$	56039.7	1.31932	0.659660	−	0.751564i	$-0.270700\pi$
$71$	56039.7	1.31932	0.659660	+	0.751564i	$0.270700\pi$
$72$	9308.16	0.211608
$73$	56572.1	1.24250	0.621248	−	0.783614i	$-0.286626\pi$
$73$	56572.1	1.24250	0.621248	+	0.783614i	$0.286626\pi$
$74$	−940.434	−0.0199641
$75$	25362.2	0.520636
$76$	82156.5	1.63158
$77$	−5625.81	−0.108133
$78$	50391.0	0.937814
$79$	65746.0	1.18523	0.592614	−	0.805487i	$-0.298096\pi$
$79$	65746.0	1.18523	0.592614	+	0.805487i	$0.298096\pi$
$80$	7601.67	0.132796
$81$	6561.00	0.111111
$82$	−58078.6	−0.953853
$83$	−13649.8	−0.217486	−0.108743	−	0.994070i	$-0.534682\pi$
$83$	−13649.8	−0.217486	−0.108743	+	0.994070i	$0.534682\pi$
$84$	−5257.45	−0.0812975
$85$	14905.7	0.223772
$86$	−26301.9	−0.383478
$87$	−10204.7	−0.144545
$88$	−49899.4	−0.686892
$89$	77607.3	1.03855	0.519275	−	0.854607i	$-0.326202\pi$
$89$	77607.3	1.03855	0.519275	+	0.854607i	$0.326202\pi$
$90$	−12460.3	−0.162152
$91$	−8262.00	−0.104588
$92$	32277.1	0.397580
$93$	86034.5	1.03149
$94$	89386.0	1.04340
$95$	−31924.8	−0.362927
$96$	67380.0	0.746196
$97$	41043.1	0.442906	0.221453	−	0.975171i	$-0.428920\pi$
$97$	41043.1	0.442906	0.221453	+	0.975171i	$0.428920\pi$
$98$	−146092.	−1.53660
$99$	−35172.3	−0.360673
$100$	−127060.	−1.27060
$101$	−175206.	−1.70901	−0.854505	−	0.519444i	$-0.826139\pi$
$101$	−175206.	−1.70901	−0.854505	+	0.519444i	$0.826139\pi$
$102$	67226.4	0.639793
$103$	6862.58	0.0637374	0.0318687	−	0.999492i	$-0.489854\pi$
$103$	6862.58	0.0637374	0.0318687	+	0.999492i	$0.489854\pi$
$104$	−73281.7	−0.664373
$105$	2042.97	0.0180838
$106$	96663.4	0.835598
$107$	−231771.	−1.95704	−0.978520	−	0.206152i	$-0.933906\pi$
$107$	−231771.	−1.95704	−0.978520	+	0.206152i	$0.933906\pi$
$108$	−32869.4	−0.271164
$109$	138570.	1.11713	0.558565	−	0.829461i	$-0.311352\pi$
$109$	138570.	1.11713	0.558565	+	0.829461i	$0.311352\pi$
$110$	66797.6	0.526356
$111$	963.999	0.00742624
$112$	−5621.17	−0.0423430
$113$	26310.1	0.193832	0.0969162	−	0.995293i	$-0.469102\pi$
$113$	26310.1	0.193832	0.0969162	+	0.995293i	$0.469102\pi$
$114$	−143984.	−1.03765
$115$	−12542.4	−0.0884373
$116$	51123.8	0.352759
$117$	−51653.7	−0.348848
$118$	−30563.2	−0.202066
$119$	−11022.3	−0.0713517
$120$	18120.6	0.114873
$121$	27501.6	0.170763
$122$	20149.0	0.122561
$123$	59533.9	0.354815
$124$	−431017.	−2.51733
$125$	104126.	0.596051
$126$	9214.00	0.0517037
$127$	−328460.	−1.80706	−0.903531	−	0.428522i	$-0.859035\pi$
$127$	−328460.	−1.80706	−0.903531	+	0.428522i	$0.859035\pi$
$128$	−215661.	−1.16345
$129$	26960.9	0.142646
$130$	98098.3	0.509100
$131$	57771.7	0.294128	0.147064	−	0.989127i	$-0.453018\pi$
$131$	57771.7	0.294128	0.147064	+	0.989127i	$0.453018\pi$
$132$	176207.	0.880214
$133$	23607.3	0.115722
$134$	206943.	0.995608
$135$	12772.6	0.0603175
$136$	−97764.7	−0.453247
$137$	116139.	0.528662	0.264331	−	0.964432i	$-0.414849\pi$
$137$	116139.	0.528662	0.264331	+	0.964432i	$0.414849\pi$
$138$	−56567.4	−0.252853
$139$	−433033.	−1.90101	−0.950504	−	0.310713i	$-0.899432\pi$
$139$	−433033.	−1.90101	−0.950504	+	0.310713i	$0.899432\pi$
$140$	−10234.9	−0.0441330
$141$	−91625.8	−0.388123
$142$	492029.	2.04771
$143$	276906.	1.13238
$144$	−35143.4	−0.141233
$145$	−19866.0	−0.0784675
$146$	496703.	1.92848
$147$	149752.	0.571584
$148$	−4829.46	−0.0181236
$149$	283234.	1.04515	0.522576	−	0.852593i	$-0.324971\pi$
$149$	283234.	1.04515	0.522576	+	0.852593i	$0.324971\pi$
$150$	222680.	0.808079
$151$	−118520.	−0.423009	−0.211505	−	0.977377i	$-0.567836\pi$
$151$	−118520.	−0.423009	−0.211505	+	0.977377i	$0.567836\pi$
$152$	209390.	0.735102
$153$	−68910.9	−0.237990
$154$	−49394.6	−0.167833
$155$	167487.	0.559953
$156$	258776.	0.851357
$157$	−189854.	−0.614712	−0.307356	−	0.951595i	$-0.599444\pi$
$157$	−189854.	−0.614712	−0.307356	+	0.951595i	$0.599444\pi$
$158$	577250.	1.83959
$159$	−99085.6	−0.310826
$160$	131171.	0.405078
$161$	9274.67	0.0281990
$162$	57605.6	0.172455
$163$	127496.	0.375861	0.187931	−	0.982182i	$-0.439822\pi$
$163$	127496.	0.375861	0.187931	+	0.982182i	$0.439822\pi$
$164$	−298254.	−0.865917
$165$	−68471.4	−0.195794
$166$	−119845.	−0.337559
$167$	201919.	0.560255	0.280128	−	0.959963i	$-0.409623\pi$
$167$	201919.	0.560255	0.280128	+	0.959963i	$0.409623\pi$
$168$	−13399.5	−0.0366283
$169$	35368.4	0.0952574
$170$	130872.	0.347317
$171$	147592.	0.385987
$172$	−135069.	−0.348125
$173$	−299080.	−0.759752	−0.379876	−	0.925037i	$-0.624033\pi$
$173$	−299080.	−0.759752	−0.379876	+	0.925037i	$0.624033\pi$
$174$	−89597.5	−0.224348
$175$	−36510.2	−0.0901195
$176$	188397.	0.458451
$177$	31329.0	0.0751646
$178$	681392.	1.61193
$179$	659619.	1.53872	0.769362	−	0.638813i	$-0.220574\pi$
$179$	659619.	1.53872	0.769362	+	0.638813i	$0.220574\pi$
$180$	−63988.2	−0.147204
$181$	−242677.	−0.550595	−0.275297	−	0.961359i	$-0.588776\pi$
$181$	−242677.	−0.550595	−0.275297	+	0.961359i	$0.588776\pi$
$182$	−72540.3	−0.162331
$183$	−20653.8	−0.0455903
$184$	82263.7	0.179128
$185$	1876.66	0.00403139
$186$	755382.	1.60097
$187$	369419.	0.772530
$188$	459028.	0.947207
$189$	−9444.88	−0.0192328
$190$	−280300.	−0.563299
$191$	202851.	0.402341	0.201171	−	0.979556i	$-0.435525\pi$
$191$	202851.	0.402341	0.201171	+	0.979556i	$0.435525\pi$
$192$	466642.	0.913546
$193$	−240767.	−0.465268	−0.232634	−	0.972564i	$-0.574734\pi$
$193$	−240767.	−0.465268	−0.232634	+	0.972564i	$0.574734\pi$
$194$	360359.	0.687433
$195$	−100556.	−0.189375
$196$	−750231.	−1.39494
$197$	−372003.	−0.682937	−0.341469	−	0.939893i	$-0.610924\pi$
$197$	−372003.	−0.682937	−0.341469	+	0.939893i	$0.610924\pi$
$198$	−308813.	−0.559800
$199$	−927046.	−1.65947	−0.829733	−	0.558160i	$-0.811508\pi$
$199$	−927046.	−1.65947	−0.829733	+	0.558160i	$0.811508\pi$
$200$	−323835.	−0.572465
$201$	−212128.	−0.370346
$202$	−1.53830e6	−2.65255
$203$	14690.2	0.0250200
$204$	345231.	0.580810
$205$	115897.	0.192614
$206$	60253.4	0.0989267
$207$	57984.9	0.0940565
$208$	276678.	0.443421
$209$	−791214.	−1.25293
$210$	17937.3	0.0280678
$211$	−372955.	−0.576701	−0.288350	−	0.957525i	$-0.593107\pi$
$211$	−372955.	−0.576701	−0.288350	+	0.957525i	$0.593107\pi$
$212$	496400.	0.758564
$213$	−504357.	−0.761710
$214$	−2.03495e6	−3.03752
$215$	52485.9	0.0774366
$216$	−83773.4	−0.122172
$217$	−123851.	−0.178546
$218$	1.21665e6	1.73390
$219$	−509149.	−0.717355
$220$	343029.	0.477831
$221$	542525.	0.747203
$222$	8463.91	0.0115263
$223$	−632099.	−0.851183	−0.425592	−	0.904915i	$-0.639934\pi$
$223$	−632099.	−0.851183	−0.425592	+	0.904915i	$0.639934\pi$
$224$	−96996.7	−0.129163
$225$	−228260.	−0.300589
$226$	231003.	0.300847
$227$	−890035.	−1.14642	−0.573208	−	0.819410i	$-0.694301\pi$
$227$	−890035.	−1.14642	−0.573208	+	0.819410i	$0.694301\pi$
$228$	−739409.	−0.941992
$229$	259318.	0.326771	0.163386	−	0.986562i	$-0.447758\pi$
$229$	259318.	0.326771	0.163386	+	0.986562i	$0.447758\pi$
$230$	−110122.	−0.137263
$231$	50632.3	0.0624306
$232$	130298.	0.158934
$233$	−476260.	−0.574717	−0.287358	−	0.957823i	$-0.592777\pi$
$233$	−476260.	−0.574717	−0.287358	+	0.957823i	$0.592777\pi$
$234$	−453519.	−0.541447
$235$	−178372.	−0.210696
$236$	−156952.	−0.183438
$237$	−591714.	−0.684291
$238$	−96775.7	−0.110745
$239$	−400093.	−0.453071	−0.226535	−	0.974003i	$-0.572740\pi$
$239$	−400093.	−0.453071	−0.226535	+	0.974003i	$0.572740\pi$
$240$	−68415.0	−0.0766696
$241$	66354.4	0.0735914	0.0367957	−	0.999323i	$-0.488285\pi$
$241$	66354.4	0.0735914	0.0367957	+	0.999323i	$0.488285\pi$
$242$	241464.	0.265041
$243$	−59049.0	−0.0641500
$244$	103472.	0.111262
$245$	291529.	0.310289
$246$	522707.	0.550707
$247$	−1.16197e6	−1.21186
$248$	−1.09852e6	−1.13417
$249$	122848.	0.125565
$250$	914224.	0.925129
$251$	−378287.	−0.378998	−0.189499	−	0.981881i	$-0.560686\pi$
$251$	−378287.	−0.378998	−0.189499	+	0.981881i	$0.560686\pi$
$252$	47317.1	0.0469371
$253$	−310846.	−0.305313
$254$	−2.88388e6	−2.80474
$255$	−134152.	−0.129195
$256$	−234337.	−0.223481
$257$	−6758.28	−0.00638268	−0.00319134	−	0.999995i	$-0.501016\pi$
$257$	−6758.28	−0.00638268	−0.00319134	+	0.999995i	$0.501016\pi$
$258$	236717.	0.221401
$259$	−1387.72	−0.00128545
$260$	503769.	0.462166
$261$	91842.6	0.0834532
$262$	507235.	0.456516
$263$	1.53754e6	1.37068	0.685342	−	0.728222i	$-0.259653\pi$
$263$	1.53754e6	1.37068	0.685342	+	0.728222i	$0.259653\pi$
$264$	449094.	0.396577
$265$	−192894.	−0.168734
$266$	207272.	0.179613
$267$	−698465.	−0.599607
$268$	1.06272e6	0.903822
$269$	760328.	0.640649	0.320325	−	0.947308i	$-0.396208\pi$
$269$	760328.	0.640649	0.320325	+	0.947308i	$0.396208\pi$
$270$	112143.	0.0936188
$271$	−621403.	−0.513985	−0.256992	−	0.966413i	$-0.582732\pi$
$271$	−621403.	−0.513985	−0.256992	+	0.966413i	$0.582732\pi$
$272$	369115.	0.302510
$273$	74358.0	0.0603839
$274$	1.01970e6	0.820536
$275$	1.22366e6	0.975730
$276$	−290493.	−0.229543
$277$	−317260.	−0.248437	−0.124219	−	0.992255i	$-0.539642\pi$
$277$	−317260.	−0.248437	−0.124219	+	0.992255i	$0.539642\pi$
$278$	−3.80203e6	−2.95055
$279$	−774310.	−0.595531
$280$	−26085.4	−0.0198840
$281$	−368043.	−0.278057	−0.139028	−	0.990288i	$-0.544398\pi$
$281$	−368043.	−0.278057	−0.139028	+	0.990288i	$0.544398\pi$
$282$	−804474.	−0.602406
$283$	−1.66530e6	−1.23602	−0.618010	−	0.786170i	$-0.712061\pi$
$283$	−1.66530e6	−1.23602	−0.618010	+	0.786170i	$0.712061\pi$
$284$	2.52674e6	1.85894
$285$	287323.	0.209536
$286$	2.43124e6	1.75757
$287$	−85701.9	−0.0614166
$288$	−606420.	−0.430816
$289$	−696078.	−0.490245
$290$	−174423.	−0.121789
$291$	−369388.	−0.255712
$292$	2.55074e6	1.75069
$293$	1.24407e6	0.846598	0.423299	−	0.905990i	$-0.360872\pi$
$293$	1.24407e6	0.846598	0.423299	+	0.905990i	$0.360872\pi$
$294$	1.31482e6	0.887155
$295$	60989.4	0.0408037
$296$	−12308.7	−0.00816552
$297$	316551.	0.208234
$298$	2.48679e6	1.62218
$299$	−456506.	−0.295303
$300$	1.14354e6	0.733582
$301$	−38811.5	−0.0246913
$302$	−1.04061e6	−0.656552
$303$	1.57685e6	0.986697
$304$	−790562.	−0.490628
$305$	−40207.6	−0.0247491
$306$	−605038.	−0.369385
$307$	1.88311e6	1.14033	0.570165	−	0.821530i	$-0.306879\pi$
$307$	1.88311e6	1.14033	0.570165	+	0.821530i	$0.306879\pi$
$308$	−253658.	−0.152361
$309$	−61763.2	−0.0367988
$310$	1.47053e6	0.869102
$311$	−3.10201e6	−1.81862	−0.909310	−	0.416119i	$-0.863390\pi$
$311$	−3.10201e6	−1.81862	−0.909310	+	0.416119i	$0.863390\pi$
$312$	659535.	0.383576
$313$	−2.33451e6	−1.34690	−0.673449	−	0.739234i	$-0.735188\pi$
$313$	−2.33451e6	−1.34690	−0.673449	+	0.739234i	$0.735188\pi$
$314$	−1.66692e6	−0.954094
$315$	−18386.7	−0.0104407
$316$	2.96438e6	1.67000
$317$	−103565.	−0.0578846	−0.0289423	−	0.999581i	$-0.509214\pi$
$317$	−103565.	−0.0578846	−0.0289423	+	0.999581i	$0.509214\pi$
$318$	−869971.	−0.482433
$319$	−492352.	−0.270894
$320$	908430.	0.495926
$321$	2.08594e6	1.12990
$322$	81431.6	0.0437676
$323$	−1.55018e6	−0.826751
$324$	295825.	0.156557
$325$	1.79706e6	0.943742
$326$	1.11942e6	0.583374
$327$	−1.24713e6	−0.644975
$328$	−760152.	−0.390136
$329$	131900.	0.0671822
$330$	−601179.	−0.303892
$331$	1.75769e6	0.881804	0.440902	−	0.897555i	$-0.354659\pi$
$331$	1.75769e6	0.881804	0.440902	+	0.897555i	$0.354659\pi$
$332$	−615446.	−0.306439
$333$	−8675.99	−0.00428754
$334$	1.77285e6	0.869572
$335$	−412958.	−0.201045
$336$	50590.6	0.0244468
$337$	−620309.	−0.297532	−0.148766	−	0.988872i	$-0.547530\pi$
$337$	−620309.	−0.297532	−0.148766	+	0.988872i	$0.547530\pi$
$338$	310534.	0.147849
$339$	−236791.	−0.111909
$340$	672075.	0.315297
$341$	4.15094e6	1.93313
$342$	1.29586e6	0.599090
$343$	−433326.	−0.198875
$344$	−344247.	−0.156846
$345$	112881.	0.0510593
$346$	−2.62592e6	−1.17921
$347$	495722.	0.221011	0.110506	−	0.993876i	$-0.464753\pi$
$347$	495722.	0.221011	0.110506	+	0.993876i	$0.464753\pi$
$348$	−460115.	−0.203666
$349$	−1.71145e6	−0.752142	−0.376071	−	0.926591i	$-0.622725\pi$
$349$	−1.71145e6	−0.752142	−0.376071	+	0.926591i	$0.622725\pi$
$350$	−320559.	−0.139874
$351$	464883.	0.201408
$352$	3.25091e6	1.39845
$353$	−2.42249e6	−1.03472	−0.517362	−	0.855767i	$-0.673086\pi$
$353$	−2.42249e6	−1.03472	−0.517362	+	0.855767i	$0.673086\pi$
$354$	275069.	0.116663
$355$	−981853.	−0.413500
$356$	3.49918e6	1.46333
$357$	99200.6	0.0411949
$358$	5.79146e6	2.38825
$359$	2.09761e6	0.858989	0.429495	−	0.903069i	$-0.358692\pi$
$359$	2.09761e6	0.858989	0.429495	+	0.903069i	$0.358692\pi$
$360$	−163085.	−0.0663221
$361$	844035.	0.340873
$362$	−2.13070e6	−0.854577
$363$	−247514.	−0.0985901
$364$	−372520.	−0.147366
$365$	−991180.	−0.389422
$366$	−181341.	−0.0707607
$367$	−4.92708e6	−1.90952	−0.954760	−	0.297376i	$-0.903888\pi$
$367$	−4.92708e6	−1.90952	−0.954760	+	0.297376i	$0.903888\pi$
$368$	−310590.	−0.119555
$369$	−535805.	−0.204852
$370$	16477.0	0.00625712
$371$	142638.	0.0538024
$372$	3.87915e6	1.45338
$373$	1.78212e6	0.663231	0.331616	−	0.943415i	$-0.392406\pi$
$373$	1.78212e6	0.663231	0.331616	+	0.943415i	$0.392406\pi$
$374$	3.24350e6	1.19904
$375$	−937132.	−0.344130
$376$	1.16991e6	0.426761
$377$	−723062.	−0.262013
$378$	−82926.0	−0.0298512
$379$	399928.	0.143016	0.0715079	−	0.997440i	$-0.477219\pi$
$379$	399928.	0.143016	0.0715079	+	0.997440i	$0.477219\pi$
$380$	−1.43944e6	−0.511368
$381$	2.95614e6	1.04331
$382$	1.78103e6	0.624473
$383$	1.37113e6	0.477618	0.238809	−	0.971067i	$-0.423243\pi$
$383$	1.37113e6	0.477618	0.238809	+	0.971067i	$0.423243\pi$
$384$	1.94095e6	0.671718
$385$	98567.9	0.0338909
$386$	−2.11393e6	−0.722142
$387$	−242648.	−0.0823568
$388$	1.85057e6	0.624059
$389$	3.29557e6	1.10422	0.552111	−	0.833771i	$-0.313822\pi$
$389$	3.29557e6	1.10422	0.552111	+	0.833771i	$0.313822\pi$
$390$	−882884.	−0.293929
$391$	−609022.	−0.201461
$392$	−1.91210e6	−0.628485
$393$	−519945.	−0.169815
$394$	−3.26618e6	−1.05999
$395$	−1.15191e6	−0.371473
$396$	−1.58586e6	−0.508192
$397$	2.44883e6	0.779798	0.389899	−	0.920858i	$-0.372510\pi$
$397$	2.44883e6	0.779798	0.389899	+	0.920858i	$0.372510\pi$
$398$	−8.13946e6	−2.57566
$399$	−212466.	−0.0668124
$400$	1.22265e6	0.382079
$401$	4.98383e6	1.54775	0.773877	−	0.633336i	$-0.218315\pi$
$401$	4.98383e6	1.54775	0.773877	+	0.633336i	$0.218315\pi$
$402$	−1.86248e6	−0.574814
$403$	6.09602e6	1.86975
$404$	−7.89973e6	−2.40801
$405$	−114953.	−0.0348243
$406$	128980.	0.0388336
$407$	46510.4	0.0139176
$408$	879882.	0.261682
$409$	−1.36543e6	−0.403611	−0.201805	−	0.979426i	$-0.564681\pi$
$409$	−1.36543e6	−0.403611	−0.201805	+	0.979426i	$0.564681\pi$
$410$	1.01758e6	0.298956
$411$	−1.04525e6	−0.305223
$412$	309422.	0.0898066
$413$	−45099.6	−0.0130106
$414$	509107.	0.145985
$415$	239153.	0.0681641
$416$	4.77425e6	1.35261
$417$	3.89730e6	1.09755
$418$	−6.94686e6	−1.94468
$419$	2.31238e6	0.643465	0.321732	−	0.946831i	$-0.395735\pi$
$419$	2.31238e6	0.643465	0.321732	+	0.946831i	$0.395735\pi$
$420$	92114.1	0.0254802
$421$	3.96201e6	1.08946	0.544728	−	0.838613i	$-0.316633\pi$
$421$	3.96201e6	1.08946	0.544728	+	0.838613i	$0.316633\pi$
$422$	−3.27455e6	−0.895097
$423$	824632.	0.224083
$424$	1.26516e6	0.341768
$425$	2.39744e6	0.643837
$426$	−4.42826e6	−1.18225
$427$	29732.2	0.00789146
$428$	−1.04502e7	−2.75749
$429$	−2.49216e6	−0.653781
$430$	460826.	0.120189
$431$	−3.23219e6	−0.838115	−0.419057	−	0.907960i	$-0.637639\pi$
$431$	−3.23219e6	−0.838115	−0.419057	+	0.907960i	$0.637639\pi$
$432$	316290.	0.0815411
$433$	−2.25277e6	−0.577426	−0.288713	−	0.957416i	$-0.593227\pi$
$433$	−2.25277e6	−0.577426	−0.288713	+	0.957416i	$0.593227\pi$
$434$	−1.08741e6	−0.277121
$435$	178794.	0.0453032
$436$	6.24790e6	1.57405
$437$	1.30439e6	0.326741
$438$	−4.47032e6	−1.11341
$439$	−6.68557e6	−1.65568	−0.827841	−	0.560963i	$-0.810431\pi$
$439$	−6.68557e6	−1.65568	−0.827841	+	0.560963i	$0.810431\pi$
$440$	874270.	0.215285
$441$	−1.34777e6	−0.330004
$442$	4.76337e6	1.15973
$443$	−6.04955e6	−1.46458	−0.732291	−	0.680992i	$-0.761549\pi$
$443$	−6.04955e6	−1.46458	−0.732291	+	0.680992i	$0.761549\pi$
$444$	43465.1	0.0104637
$445$	−1.35973e6	−0.325501
$446$	−5.54983e6	−1.32112
$447$	−2.54910e6	−0.603418
$448$	−671753.	−0.158130
$449$	−514041.	−0.120332	−0.0601661	−	0.998188i	$-0.519163\pi$
$449$	−514041.	−0.120332	−0.0601661	+	0.998188i	$0.519163\pi$
$450$	−2.00412e6	−0.466545
$451$	2.87235e6	0.664962
$452$	1.18628e6	0.273112
$453$	1.06668e6	0.244225
$454$	−7.81450e6	−1.77935
$455$	144756.	0.0327799
$456$	−1.88451e6	−0.424411
$457$	7.09850e6	1.58992	0.794962	−	0.606660i	$-0.207491\pi$
$457$	7.09850e6	1.58992	0.794962	+	0.606660i	$0.207491\pi$
$458$	2.27681e6	0.507182
$459$	620198.	0.137404
$460$	−565515.	−0.124609
$461$	538077.	0.117921	0.0589606	−	0.998260i	$-0.481221\pi$
$461$	538077.	0.117921	0.0589606	+	0.998260i	$0.481221\pi$
$462$	444551.	0.0968985
$463$	−5.69755e6	−1.23520	−0.617598	−	0.786494i	$-0.711894\pi$
$463$	−5.69755e6	−1.23520	−0.617598	+	0.786494i	$0.711894\pi$
$464$	−491946.	−0.106077
$465$	−1.50738e6	−0.323289
$466$	−4.18156e6	−0.892017
$467$	6.84726e6	1.45286	0.726431	−	0.687239i	$-0.241178\pi$
$467$	6.84726e6	1.45286	0.726431	+	0.687239i	$0.241178\pi$
$468$	−2.32898e6	−0.491531
$469$	305369.	0.0641051
$470$	−1.56610e6	−0.327021
$471$	1.70869e6	0.354904
$472$	−400021.	−0.0826471
$473$	1.30079e6	0.267335
$474$	−5.19525e6	−1.06209
$475$	−5.13479e6	−1.04421
$476$	−496977.	−0.100535
$477$	891770.	0.179456
$478$	−3.51281e6	−0.703210
$479$	2.13269e6	0.424706	0.212353	−	0.977193i	$-0.431887\pi$
$479$	2.13269e6	0.424706	0.212353	+	0.977193i	$0.431887\pi$
$480$	−1.18054e6	−0.233872
$481$	68304.7	0.0134613
$482$	582591.	0.114221
$483$	−83472.0	−0.0162807
$484$	1.24000e6	0.240607
$485$	−719103.	−0.138815
$486$	−518450.	−0.0995672
$487$	1.44011e6	0.275152	0.137576	−	0.990491i	$-0.456069\pi$
$487$	1.44011e6	0.275152	0.137576	+	0.990491i	$0.456069\pi$
$488$	263716.	0.0501288
$489$	−1.14746e6	−0.217004
$490$	2.55962e6	0.481599
$491$	193566.	0.0362347	0.0181174	−	0.999836i	$-0.494233\pi$
$491$	193566.	0.0362347	0.0181174	+	0.999836i	$0.494233\pi$
$492$	2.68428e6	0.499938
$493$	−964633.	−0.178750
$494$	−1.02021e7	−1.88092
$495$	616243.	0.113042
$496$	4.14752e6	0.756979
$497$	726047.	0.131848
$498$	1.07861e6	0.194890
$499$	1.09525e7	1.96908	0.984539	−	0.175165i	$-0.0560460\pi$
$499$	1.09525e7	1.96908	0.984539	+	0.175165i	$0.0560460\pi$
$500$	4.69486e6	0.839842
$501$	−1.81727e6	−0.323464
$502$	−3.32136e6	−0.588243
$503$	−1.09972e6	−0.193804	−0.0969022	−	0.995294i	$-0.530893\pi$
$503$	−1.09972e6	−0.193804	−0.0969022	+	0.995294i	$0.530893\pi$
$504$	120596.	0.0211474
$505$	3.06972e6	0.535636
$506$	−2.72923e6	−0.473875
$507$	−318316.	−0.0549969
$508$	−1.48097e7	−2.54617
$509$	5.13320e6	0.878201	0.439100	−	0.898438i	$-0.355297\pi$
$509$	5.13320e6	0.878201	0.439100	+	0.898438i	$0.355297\pi$
$510$	−1.17785e6	−0.200523
$511$	732944.	0.124171
$512$	4.84369e6	0.816586
$513$	−1.32833e6	−0.222850
$514$	−59337.6	−0.00990655
$515$	−120237.	−0.0199765
$516$	1.21562e6	0.200990
$517$	−4.42070e6	−0.727386
$518$	−12184.2	−0.00199514
$519$	2.69172e6	0.438643
$520$	1.28394e6	0.208227
$521$	9.05184e6	1.46097	0.730487	−	0.682926i	$-0.239293\pi$
$521$	9.05184e6	1.46097	0.730487	+	0.682926i	$0.239293\pi$
$522$	806378.	0.129528
$523$	974287.	0.155752	0.0778758	−	0.996963i	$-0.475186\pi$
$523$	974287.	0.155752	0.0778758	+	0.996963i	$0.475186\pi$
$524$	2.60483e6	0.414430
$525$	328592.	0.0520305
$526$	1.34996e7	2.12744
$527$	8.13267e6	1.27558
$528$	−1.69558e6	−0.264687
$529$	−5.92388e6	−0.920380
$530$	−1.69361e6	−0.261892
$531$	−281961.	−0.0433963
$532$	1.06441e6	0.163054
$533$	4.21831e6	0.643162
$534$	−6.13252e6	−0.930649
$535$	4.06078e6	0.613374
$536$	2.70854e6	0.407214
$537$	−5.93657e6	−0.888383
$538$	6.67568e6	0.994351
$539$	7.22516e6	1.07121
$540$	575894.	0.0849880
$541$	6.38853e6	0.938443	0.469222	−	0.883080i	$-0.344535\pi$
$541$	6.38853e6	0.938443	0.469222	+	0.883080i	$0.344535\pi$
$542$	−5.45592e6	−0.797755
$543$	2.18409e6	0.317886
$544$	6.36930e6	0.922771
$545$	−2.42784e6	−0.350130
$546$	652863.	0.0937218
$547$	−4.31658e6	−0.616838	−0.308419	−	0.951251i	$-0.599800\pi$
$547$	−4.31658e6	−0.616838	−0.308419	+	0.951251i	$0.599800\pi$
$548$	5.23653e6	0.744891
$549$	185884.	0.0263216
$550$	1.07437e7	1.51443
$551$	2.06603e6	0.289907
$552$	−740374.	−0.103420
$553$	851801.	0.118447
$554$	−2.78554e6	−0.385599
$555$	−16889.9	−0.00232753
$556$	−1.95247e7	−2.67854
$557$	6.96213e6	0.950833	0.475416	−	0.879761i	$-0.342297\pi$
$557$	6.96213e6	0.950833	0.475416	+	0.879761i	$0.342297\pi$
$558$	−6.79844e6	−0.924323
$559$	1.91033e6	0.258570
$560$	98486.7	0.0132711
$561$	−3.32477e6	−0.446020
$562$	−3.23142e6	−0.431571
$563$	−442629.	−0.0588530	−0.0294265	−	0.999567i	$-0.509368\pi$
$563$	−442629.	−0.0588530	−0.0294265	+	0.999567i	$0.509368\pi$
$564$	−4.13125e6	−0.546870
$565$	−460970.	−0.0607508
$566$	−1.46213e7	−1.91843
$567$	85003.9	0.0111040
$568$	6.43983e6	0.837537
$569$	4.56709e6	0.591369	0.295685	−	0.955286i	$-0.404452\pi$
$569$	4.56709e6	0.591369	0.295685	+	0.955286i	$0.404452\pi$
$570$	2.52270e6	0.325221
$571$	−1.20733e7	−1.54966	−0.774831	−	0.632169i	$-0.782165\pi$
$571$	−1.20733e7	−1.54966	−0.774831	+	0.632169i	$0.782165\pi$
$572$	1.24852e7	1.59554
$573$	−1.82566e6	−0.232292
$574$	−752463.	−0.0953247
$575$	−2.01732e6	−0.254452
$576$	−4.19978e6	−0.527436
$577$	−3.82492e6	−0.478280	−0.239140	−	0.970985i	$-0.576866\pi$
$577$	−3.82492e6	−0.478280	−0.239140	+	0.970985i	$0.576866\pi$
$578$	−6.11156e6	−0.760908
$579$	2.16690e6	0.268623
$580$	−895723.	−0.110562
$581$	−176846.	−0.0217347
$582$	−3.24323e6	−0.396890
$583$	−4.78062e6	−0.582522
$584$	6.50101e6	0.788767
$585$	905007.	0.109336
$586$	1.09230e7	1.31400
$587$	−1.24579e7	−1.49227	−0.746136	−	0.665793i	$-0.768093\pi$
$587$	−1.24579e7	−1.49227	−0.746136	+	0.665793i	$0.768093\pi$
$588$	6.75208e6	0.805368
$589$	−1.74184e7	−2.06880
$590$	535487.	0.0633314
$591$	3.34803e6	0.394294
$592$	46472.1	0.00544990
$593$	8.12876e6	0.949265	0.474633	−	0.880184i	$-0.342581\pi$
$593$	8.12876e6	0.949265	0.474633	+	0.880184i	$0.342581\pi$
$594$	2.77932e6	0.323200
$595$	193118.	0.0223630
$596$	1.27705e7	1.47263
$597$	8.34341e6	0.958094
$598$	−4.00812e6	−0.458340
$599$	−2.18535e6	−0.248860	−0.124430	−	0.992228i	$-0.539710\pi$
$599$	−2.18535e6	−0.248860	−0.124430	+	0.992228i	$0.539710\pi$
$600$	2.91452e6	0.330513
$601$	−3.56350e6	−0.402430	−0.201215	−	0.979547i	$-0.564489\pi$
$601$	−3.56350e6	−0.402430	−0.201215	+	0.979547i	$0.564489\pi$
$602$	−340765.	−0.0383234
$603$	1.90915e6	0.213820
$604$	−5.34388e6	−0.596025
$605$	−481845.	−0.0535204
$606$	1.38447e7	1.53145
$607$	1.07019e6	0.117893	0.0589464	−	0.998261i	$-0.481226\pi$
$607$	1.07019e6	0.117893	0.0589464	+	0.998261i	$0.481226\pi$
$608$	−1.36416e7	−1.49660
$609$	−132212.	−0.0144453
$610$	−353023.	−0.0384130
$611$	−6.49220e6	−0.703540
$612$	−3.10708e6	−0.335331
$613$	−1.33424e7	−1.43411	−0.717057	−	0.697015i	$-0.754511\pi$
$613$	−1.33424e7	−1.43411	−0.717057	+	0.697015i	$0.754511\pi$
$614$	1.65337e7	1.76991
$615$	−1.04307e6	−0.111206
$616$	−646493.	−0.0686455
$617$	−791902.	−0.0837449	−0.0418724	−	0.999123i	$-0.513332\pi$
$617$	−791902.	−0.0837449	−0.0418724	+	0.999123i	$0.513332\pi$
$618$	−542281.	−0.0571154
$619$	9.53469e6	1.00018	0.500092	−	0.865972i	$-0.333299\pi$
$619$	9.53469e6	1.00018	0.500092	+	0.865972i	$0.333299\pi$
$620$	7.55170e6	0.788979
$621$	−521864.	−0.0543035
$622$	−2.72356e7	−2.82268
$623$	1.00547e6	0.103789
$624$	−2.49010e6	−0.256009
$625$	6.98198e6	0.714955
$626$	−2.04970e7	−2.09052
$627$	7.12093e6	0.723382
$628$	−8.56022e6	−0.866136
$629$	91124.9	0.00918355
$630$	−161435.	−0.0162049
$631$	−1.67624e6	−0.167595	−0.0837977	−	0.996483i	$-0.526705\pi$
$631$	−1.67624e6	−0.167595	−0.0837977	+	0.996483i	$0.526705\pi$
$632$	7.55524e6	0.752412
$633$	3.35660e6	0.332958
$634$	−909296.	−0.0898426
$635$	5.75484e6	0.566368
$636$	−4.46760e6	−0.437957
$637$	1.06108e7	1.03609
$638$	−4.32285e6	−0.420454
$639$	4.53922e6	0.439773
$640$	3.77853e6	0.364647
$641$	−4.71863e6	−0.453598	−0.226799	−	0.973942i	$-0.572826\pi$
$641$	−4.71863e6	−0.453598	−0.226799	+	0.973942i	$0.572826\pi$
$642$	1.83145e7	1.75371
$643$	−1.25582e7	−1.19785	−0.598923	−	0.800807i	$-0.704404\pi$
$643$	−1.25582e7	−1.19785	−0.598923	+	0.800807i	$0.704404\pi$
$644$	418179.	0.0397327
$645$	−472373.	−0.0447080
$646$	−1.36105e7	−1.28320
$647$	1.79155e6	0.168256	0.0841278	−	0.996455i	$-0.473190\pi$
$647$	1.79155e6	0.168256	0.0841278	+	0.996455i	$0.473190\pi$
$648$	753961.	0.0705361
$649$	1.51154e6	0.140867
$650$	1.57781e7	1.46478
$651$	1.11466e6	0.103083
$652$	5.74859e6	0.529593
$653$	1.71252e7	1.57164	0.785821	−	0.618454i	$-0.212241\pi$
$653$	1.71252e7	1.57164	0.785821	+	0.618454i	$0.212241\pi$
$654$	−1.09498e7	−1.00106
$655$	−1.01220e6	−0.0921854
$656$	2.86999e6	0.260388
$657$	4.58234e6	0.414165
$658$	1.15808e6	0.104273
$659$	−1.46762e7	−1.31643	−0.658216	−	0.752829i	$-0.728689\pi$
$659$	−1.46762e7	−1.31643	−0.658216	+	0.752829i	$0.728689\pi$
$660$	−3.08726e6	−0.275876
$661$	−1.49380e7	−1.32981	−0.664904	−	0.746929i	$-0.731528\pi$
$661$	−1.49380e7	−1.32981	−0.664904	+	0.746929i	$0.731528\pi$
$662$	1.54325e7	1.36865
$663$	−4.88272e6	−0.431398
$664$	−1.56857e6	−0.138065
$665$	−413616.	−0.0362696
$666$	−76175.2	−0.00665469
$667$	811688.	0.0706438
$668$	9.10419e6	0.789406
$669$	5.68889e6	0.491431
$670$	−3.62577e6	−0.312042
$671$	−996493.	−0.0854413
$672$	872971.	0.0745721
$673$	8.30140e6	0.706502	0.353251	−	0.935529i	$-0.385076\pi$
$673$	8.30140e6	0.706502	0.353251	+	0.935529i	$0.385076\pi$
$674$	−5.44631e6	−0.461799
$675$	2.05434e6	0.173545
$676$	1.59470e6	0.134219
$677$	−287812.	−0.0241345	−0.0120672	−	0.999927i	$-0.503841\pi$
$677$	−287812.	−0.0241345	−0.0120672	+	0.999927i	$0.503841\pi$
$678$	−2.07902e6	−0.173694
$679$	531752.	0.0442624
$680$	1.71290e6	0.142056
$681$	8.01031e6	0.661884
$682$	3.64452e7	3.00040
$683$	−2.12554e7	−1.74348	−0.871742	−	0.489965i	$-0.837010\pi$
$683$	−2.12554e7	−1.74348	−0.871742	+	0.489965i	$0.837010\pi$
$684$	6.65468e6	0.543860
$685$	−2.03484e6	−0.165693
$686$	−3.80460e6	−0.308673
$687$	−2.33386e6	−0.188662
$688$	1.29972e6	0.104684
$689$	−7.02076e6	−0.563425
$690$	991099.	0.0792491
$691$	−2.41473e6	−0.192386	−0.0961932	−	0.995363i	$-0.530667\pi$
$691$	−2.41473e6	−0.192386	−0.0961932	+	0.995363i	$0.530667\pi$
$692$	−1.34850e7	−1.07050
$693$	−455691.	−0.0360443
$694$	4.35243e6	0.343031
$695$	7.58702e6	0.595812
$696$	−1.17268e6	−0.0917608
$697$	5.62762e6	0.438776
$698$	−1.50265e7	−1.16740
$699$	4.28634e6	0.331813
$700$	−1.64618e6	−0.126979
$701$	1.06511e7	0.818654	0.409327	−	0.912388i	$-0.365764\pi$
$701$	1.06511e7	0.818654	0.409327	+	0.912388i	$0.365764\pi$
$702$	4.08167e6	0.312605
$703$	−195170.	−0.0148944
$704$	2.25142e7	1.71209
$705$	1.60534e6	0.121645
$706$	−2.12694e7	−1.60599
$707$	−2.26995e6	−0.170792
$708$	1.41257e6	0.105908
$709$	1.04662e7	0.781943	0.390971	−	0.920403i	$-0.372139\pi$
$709$	1.04662e7	0.781943	0.390971	+	0.920403i	$0.372139\pi$
$710$	−8.62067e6	−0.641793
$711$	5.32543e6	0.395076
$712$	8.91828e6	0.659297
$713$	−6.84321e6	−0.504122
$714$	870981.	0.0639386
$715$	−4.85158e6	−0.354910
$716$	2.97411e7	2.16808
$717$	3.60083e6	0.261580
$718$	1.84170e7	1.33324
$719$	−1.40608e7	−1.01435	−0.507175	−	0.861843i	$-0.669310\pi$
$719$	−1.40608e7	−1.01435	−0.507175	+	0.861843i	$0.669310\pi$
$720$	615735.	0.0442652
$721$	88911.1	0.00636968
$722$	7.41063e6	0.529069
$723$	−597189.	−0.0424880
$724$	−1.09419e7	−0.775793
$725$	−3.19525e6	−0.225766
$726$	−2.17317e6	−0.153022
$727$	4.54577e6	0.318986	0.159493	−	0.987199i	$-0.449014\pi$
$727$	4.54577e6	0.318986	0.159493	+	0.987199i	$0.449014\pi$
$728$	−949432.	−0.0663950
$729$	531441.	0.0370370
$730$	−8.70256e6	−0.604421
$731$	2.54856e6	0.176401
$732$	−931247.	−0.0642373
$733$	−6.72753e6	−0.462483	−0.231241	−	0.972896i	$-0.574279\pi$
$733$	−6.72753e6	−0.462483	−0.231241	+	0.972896i	$0.574279\pi$
$734$	−4.32597e7	−2.96376
$735$	−2.62376e6	−0.179145
$736$	−5.35942e6	−0.364690
$737$	−1.02346e7	−0.694070
$738$	−4.70437e6	−0.317951
$739$	7.96547e6	0.536538	0.268269	−	0.963344i	$-0.413548\pi$
$739$	7.96547e6	0.536538	0.268269	+	0.963344i	$0.413548\pi$
$740$	84615.3	0.00568028
$741$	1.04577e7	0.699667
$742$	1.25237e6	0.0835067
$743$	3.70267e6	0.246061	0.123031	−	0.992403i	$-0.460739\pi$
$743$	3.70267e6	0.246061	0.123031	+	0.992403i	$0.460739\pi$
$744$	9.88670e6	0.654815
$745$	−4.96244e6	−0.327570
$746$	1.56470e7	1.02940
$747$	−1.10563e6	−0.0724952
$748$	1.66565e7	1.08850
$749$	−3.00281e6	−0.195580
$750$	−8.22801e6	−0.534124
$751$	−2.71608e7	−1.75728	−0.878642	−	0.477480i	$-0.841550\pi$
$751$	−2.71608e7	−1.75728	−0.878642	+	0.477480i	$0.841550\pi$
$752$	−4.41706e6	−0.284832
$753$	3.40459e6	0.218815
$754$	−6.34848e6	−0.406670
$755$	2.07655e6	0.132579
$756$	−425854.	−0.0270992
$757$	2.64905e7	1.68016	0.840078	−	0.542465i	$-0.182509\pi$
$757$	2.64905e7	1.68016	0.840078	+	0.542465i	$0.182509\pi$
$758$	3.51137e6	0.221975
$759$	2.79762e6	0.176272
$760$	−3.66866e6	−0.230395
$761$	−2.94938e7	−1.84616	−0.923080	−	0.384607i	$-0.874337\pi$
$761$	−2.94938e7	−1.84616	−0.923080	+	0.384607i	$0.874337\pi$
$762$	2.59549e7	1.61932
$763$	1.79531e6	0.111642
$764$	9.14623e6	0.566903
$765$	1.20737e6	0.0745908
$766$	1.20385e7	0.741310
$767$	2.21983e6	0.136249
$768$	2.10903e6	0.129027
$769$	9.58663e6	0.584588	0.292294	−	0.956329i	$-0.405581\pi$
$769$	9.58663e6	0.584588	0.292294	+	0.956329i	$0.405581\pi$
$770$	865426.	0.0526021
$771$	60824.5	0.00368504
$772$	−1.08558e7	−0.655567
$773$	6.41914e6	0.386392	0.193196	−	0.981160i	$-0.438115\pi$
$773$	6.41914e6	0.386392	0.193196	+	0.981160i	$0.438115\pi$
$774$	−2.13045e6	−0.127826
$775$	2.69386e7	1.61109
$776$	4.71649e6	0.281167
$777$	12489.5	0.000742152 0
$778$	2.89351e7	1.71386
$779$	−1.20531e7	−0.711633
$780$	−4.53392e6	−0.266832
$781$	−2.43339e7	−1.42753
$782$	−5.34721e6	−0.312687
$783$	−826584.	−0.0481817
$784$	7.21920e6	0.419468
$785$	3.32638e6	0.192663
$786$	−4.56512e6	−0.263570
$787$	3.15258e7	1.81438	0.907191	−	0.420719i	$-0.138222\pi$
$787$	3.15258e7	1.81438	0.907191	+	0.420719i	$0.138222\pi$
$788$	−1.67730e7	−0.962265
$789$	−1.38379e7	−0.791364
$790$	−1.01138e7	−0.576563
$791$	340872.	0.0193709
$792$	−4.04185e6	−0.228964
$793$	−1.46344e6	−0.0826402
$794$	2.15007e7	1.21032
$795$	1.73604e6	0.0974189
$796$	−4.17990e7	−2.33821
$797$	−2.66338e7	−1.48521	−0.742605	−	0.669730i	$-0.766410\pi$
$797$	−2.66338e7	−1.48521	−0.742605	+	0.669730i	$0.766410\pi$
$798$	−1.86545e6	−0.103699
$799$	−8.66120e6	−0.479967
$800$	2.10976e7	1.16549
$801$	6.28619e6	0.346183
$802$	4.37580e7	2.40227
$803$	−2.45651e7	−1.34440
$804$	−9.56451e6	−0.521822
$805$	−162498.	−0.00883811
$806$	5.35230e7	2.90204
$807$	−6.84295e6	−0.369879
$808$	−2.01338e7	−1.08492
$809$	−4.02522e6	−0.216231	−0.108116	−	0.994138i	$-0.534482\pi$
$809$	−4.02522e6	−0.216231	−0.108116	+	0.994138i	$0.534482\pi$
$810$	−1.00929e6	−0.0540508
$811$	−2.10486e7	−1.12375	−0.561876	−	0.827222i	$-0.689920\pi$
$811$	−2.10486e7	−1.12375	−0.561876	+	0.827222i	$0.689920\pi$
$812$	662357.	0.0352535
$813$	5.59263e6	0.296749
$814$	408361.	0.0216015
$815$	−2.23382e6	−0.117802
$816$	−3.32203e6	−0.174654
$817$	−5.45846e6	−0.286098
$818$	−1.19885e7	−0.626444
$819$	−669222.	−0.0348627
$820$	5.22561e6	0.271395
$821$	7.16356e6	0.370912	0.185456	−	0.982653i	$-0.440624\pi$
$821$	7.16356e6	0.370912	0.185456	+	0.982653i	$0.440624\pi$
$822$	−9.17733e6	−0.473737
$823$	−1.93310e7	−0.994846	−0.497423	−	0.867508i	$-0.665720\pi$
$823$	−1.93310e7	−0.994846	−0.497423	+	0.867508i	$0.665720\pi$
$824$	788617.	0.0404621
$825$	−1.10130e7	−0.563338
$826$	−395974.	−0.0201938
$827$	8.87409e6	0.451191	0.225595	−	0.974221i	$-0.427567\pi$
$827$	8.87409e6	0.451191	0.225595	+	0.974221i	$0.427567\pi$
$828$	2.61444e6	0.132527
$829$	8.50913e6	0.430030	0.215015	−	0.976611i	$-0.431020\pi$
$829$	8.50913e6	0.430030	0.215015	+	0.976611i	$0.431020\pi$
$830$	2.09976e6	0.105797
$831$	2.85534e6	0.143435
$832$	3.30642e7	1.65596
$833$	1.41558e7	0.706841
$834$	3.42182e7	1.70350
$835$	−3.53776e6	−0.175595
$836$	−3.56745e7	−1.76540
$837$	6.96879e6	0.343830
$838$	2.03027e7	0.998721
$839$	−3.61604e7	−1.77349	−0.886744	−	0.462261i	$-0.847038\pi$
$839$	−3.61604e7	−1.77349	−0.886744	+	0.462261i	$0.847038\pi$
$840$	234769.	0.0114800
$841$	−1.92255e7	−0.937320
$842$	3.47864e7	1.69094
$843$	3.31239e6	0.160536
$844$	−1.68159e7	−0.812578
$845$	−619678.	−0.0298555
$846$	7.24026e6	0.347799
$847$	356308.	0.0170654
$848$	−4.77668e6	−0.228106
$849$	1.49877e7	0.713617
$850$	2.10495e7	0.999298
$851$	−76676.8	−0.00362944
$852$	−2.27406e7	−1.07326
$853$	1.02908e7	0.484257	0.242128	−	0.970244i	$-0.422154\pi$
$853$	1.02908e7	0.484257	0.242128	+	0.970244i	$0.422154\pi$
$854$	261049.	0.0122483
$855$	−2.58591e6	−0.120976
$856$	−2.66341e7	−1.24238
$857$	1.01966e7	0.474244	0.237122	−	0.971480i	$-0.423796\pi$
$857$	1.01966e7	0.474244	0.237122	+	0.971480i	$0.423796\pi$
$858$	−2.18811e7	−1.01473
$859$	−3.60575e7	−1.66730	−0.833648	−	0.552296i	$-0.813752\pi$
$859$	−3.60575e7	−1.66730	−0.833648	+	0.552296i	$0.813752\pi$
$860$	2.36650e6	0.109109
$861$	771317.	0.0354589
$862$	−2.83786e7	−1.30084
$863$	−3.91789e7	−1.79071	−0.895354	−	0.445355i	$-0.853077\pi$
$863$	−3.91789e7	−1.79071	−0.895354	+	0.445355i	$0.853077\pi$
$864$	5.45778e6	0.248732
$865$	5.24008e6	0.238121
$866$	−1.97793e7	−0.896222
$867$	6.26470e6	0.283043
$868$	−5.58423e6	−0.251573
$869$	−2.85487e7	−1.28244
$870$	1.56981e6	0.0703151
$871$	−1.50305e7	−0.671316
$872$	1.59239e7	0.709181
$873$	3.32449e6	0.147635
$874$	1.14525e7	0.507135
$875$	1.34905e6	0.0595671
$876$	−2.29567e7	−1.01076
$877$	−3.90462e6	−0.171427	−0.0857137	−	0.996320i	$-0.527317\pi$
$877$	−3.90462e6	−0.171427	−0.0857137	+	0.996320i	$0.527317\pi$
$878$	−5.86993e7	−2.56978
$879$	−1.11967e7	−0.488783
$880$	−3.30084e6	−0.143687
$881$	3.06209e7	1.32916	0.664582	−	0.747215i	$-0.268610\pi$
$881$	3.06209e7	1.32916	0.664582	+	0.747215i	$0.268610\pi$
$882$	−1.18334e7	−0.512199
$883$	2.72635e7	1.17674	0.588368	−	0.808593i	$-0.299771\pi$
$883$	2.72635e7	1.17674	0.588368	+	0.808593i	$0.299771\pi$
$884$	2.44615e7	1.05282
$885$	−548905.	−0.0235580
$886$	−5.31150e7	−2.27318
$887$	7.45001e6	0.317942	0.158971	−	0.987283i	$-0.449182\pi$
$887$	7.45001e6	0.317942	0.158971	+	0.987283i	$0.449182\pi$
$888$	110778.	0.00471436
$889$	−4.25551e6	−0.180591
$890$	−1.19384e7	−0.505210
$891$	−2.84896e6	−0.120224
$892$	−2.85003e7	−1.19933
$893$	1.85504e7	0.778438
$894$	−2.23811e7	−0.936565
$895$	−1.15570e7	−0.482266
$896$	−2.79410e6	−0.116271
$897$	4.10855e6	0.170493
$898$	−4.51327e6	−0.186767
$899$	−1.08390e7	−0.447291
$900$	−1.02919e7	−0.423534
$901$	−9.36636e6	−0.384378
$902$	2.52193e7	1.03209
$903$	349304.	0.0142555
$904$	3.02344e6	0.123050
$905$	4.25186e6	0.172567
$906$	9.36546e6	0.379061
$907$	8.74302e6	0.352893	0.176447	−	0.984310i	$-0.443540\pi$
$907$	8.74302e6	0.352893	0.176447	+	0.984310i	$0.443540\pi$
$908$	−4.01302e7	−1.61531
$909$	−1.41916e7	−0.569670
$910$	1.27095e6	0.0508776
$911$	2.92020e7	1.16578	0.582891	−	0.812551i	$-0.301922\pi$
$911$	2.92020e7	1.16578	0.582891	+	0.812551i	$0.301922\pi$
$912$	7.11506e6	0.283264
$913$	5.92709e6	0.235323
$914$	6.23248e7	2.46772
$915$	361869.	0.0142889
$916$	1.16922e7	0.460424
$917$	748486.	0.0293941
$918$	5.44534e6	0.213264
$919$	3.40665e7	1.33057	0.665287	−	0.746588i	$-0.268309\pi$
$919$	3.40665e7	1.33057	0.665287	+	0.746588i	$0.268309\pi$
$920$	−1.44132e6	−0.0561422
$921$	−1.69480e7	−0.658370
$922$	4.72431e6	0.183025
$923$	−3.57365e7	−1.38073
$924$	2.28293e6	0.0879654
$925$	301842.	0.0115991
$926$	−5.00245e7	−1.91715
$927$	555869.	0.0212458
$928$	−8.48882e6	−0.323577
$929$	7.22466e6	0.274649	0.137325	−	0.990526i	$-0.456150\pi$
$929$	7.22466e6	0.274649	0.137325	+	0.990526i	$0.456150\pi$
$930$	−1.32348e7	−0.501776
$931$	−3.03186e7	−1.14640
$932$	−2.14737e7	−0.809782
$933$	2.79181e7	1.04998
$934$	6.01189e7	2.25499
$935$	−6.47247e6	−0.242126
$936$	−5.93581e6	−0.221458
$937$	2.02690e7	0.754194	0.377097	−	0.926174i	$-0.376922\pi$
$937$	2.02690e7	0.754194	0.377097	+	0.926174i	$0.376922\pi$
$938$	2.68114e6	0.0994974
$939$	2.10106e7	0.777632
$940$	−8.04248e6	−0.296873
$941$	−1.37966e7	−0.507923	−0.253962	−	0.967214i	$-0.581734\pi$
$941$	−1.37966e7	−0.507923	−0.253962	+	0.967214i	$0.581734\pi$
$942$	1.50023e7	0.550846
$943$	−4.73534e6	−0.173409
$944$	1.51030e6	0.0551610
$945$	165480.	0.00602792
$946$	1.14210e7	0.414930
$947$	3.23524e7	1.17228	0.586139	−	0.810210i	$-0.300647\pi$
$947$	3.23524e7	1.17228	0.586139	+	0.810210i	$0.300647\pi$
$948$	−2.66794e7	−0.964174
$949$	−3.60760e7	−1.30033
$950$	−4.50835e7	−1.62072
$951$	932081.	0.0334197
$952$	−1.26663e6	−0.0452958
$953$	−1.28170e7	−0.457146	−0.228573	−	0.973527i	$-0.573406\pi$
$953$	−1.28170e7	−0.457146	−0.228573	+	0.973527i	$0.573406\pi$
$954$	7.82974e6	0.278533
$955$	−3.55409e6	−0.126101
$956$	−1.80395e7	−0.638381
$957$	4.43117e6	0.156400
$958$	1.87250e7	0.659186
$959$	1.50470e6	0.0528326
$960$	−8.17587e6	−0.286323
$961$	6.27527e7	2.19192
$962$	599715.	0.0208933
$963$	−1.87735e7	−0.652347
$964$	2.99181e6	0.103691
$965$	4.21839e6	0.145824
$966$	−732884.	−0.0252693
$967$	−4.53561e7	−1.55980	−0.779901	−	0.625903i	$-0.784731\pi$
$967$	−4.53561e7	−1.55980	−0.779901	+	0.625903i	$0.784731\pi$
$968$	3.16036e6	0.108405
$969$	1.39516e7	0.477325
$970$	−6.31372e6	−0.215455
$971$	−6.25506e6	−0.212904	−0.106452	−	0.994318i	$-0.533949\pi$
$971$	−6.25506e6	−0.212904	−0.106452	+	0.994318i	$0.533949\pi$
$972$	−2.66242e6	−0.0903881
$973$	−5.61035e6	−0.189980
$974$	1.26442e7	0.427063
$975$	−1.61735e7	−0.544870
$976$	−995672.	−0.0334574
$977$	6.26249e6	0.209899	0.104950	−	0.994478i	$-0.466532\pi$
$977$	6.26249e6	0.209899	0.104950	+	0.994478i	$0.466532\pi$
$978$	−1.00747e7	−0.336811
$979$	−3.36991e7	−1.12373
$980$	1.31445e7	0.437200
$981$	1.12242e7	0.372377
$982$	1.69951e6	0.0562398
$983$	2.95453e7	0.975226	0.487613	−	0.873060i	$-0.337868\pi$
$983$	2.95453e7	0.975226	0.487613	+	0.873060i	$0.337868\pi$
$984$	6.84137e6	0.225245
$985$	6.51774e6	0.214046
$986$	−8.46948e6	−0.277437
$987$	−1.18710e6	−0.0387877
$988$	−5.23912e7	−1.70752
$989$	−2.14448e6	−0.0697158
$990$	5.41061e6	0.175452
$991$	−2.48240e7	−0.802947	−0.401474	−	0.915871i	$-0.631502\pi$
$991$	−2.48240e7	−0.802947	−0.401474	+	0.915871i	$0.631502\pi$
$992$	7.15679e7	2.30908
$993$	−1.58192e7	−0.509110
$994$	6.37469e6	0.204641
$995$	1.62425e7	0.520109
$996$	5.53901e6	0.176923
$997$	−2.40550e7	−0.766421	−0.383211	−	0.923661i	$-0.625182\pi$
$997$	−2.40550e7	−0.766421	−0.383211	+	0.923661i	$0.625182\pi$
$998$	9.61631e7	3.05620
$999$	78083.9	0.00247541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.b.1.11	✓	12
3.2	odd	2		531.6.a.d.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.b.1.11	✓	12	1.1	even	1	trivial
531.6.a.d.1.2		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)

\(f(q)\)	\(=\)	\(q+8.78000 q^{2} -9.00000 q^{3} +45.0883 q^{4} -17.5207 q^{5} -79.0200 q^{6} +12.9559 q^{7} +114.916 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+8.78000 q^{2} -9.00000 q^{3} +45.0883 q^{4} -17.5207 q^{5} -79.0200 q^{6} +12.9559 q^{7} +114.916 q^{8} +81.0000 q^{9} -153.831 q^{10} -434.226 q^{11} -405.795 q^{12} -637.700 q^{13} +113.753 q^{14} +157.686 q^{15} -433.869 q^{16} -850.752 q^{17} +711.180 q^{18} +1822.12 q^{19} -789.977 q^{20} -116.603 q^{21} -3812.51 q^{22} +715.863 q^{23} -1034.24 q^{24} -2818.03 q^{25} -5599.00 q^{26} -729.000 q^{27} +584.162 q^{28} +1133.86 q^{29} +1384.48 q^{30} -9559.39 q^{31} -7486.66 q^{32} +3908.04 q^{33} -7469.60 q^{34} -226.997 q^{35} +3652.16 q^{36} -107.111 q^{37} +15998.2 q^{38} +5739.30 q^{39} -2013.40 q^{40} -6614.88 q^{41} -1023.78 q^{42} -2995.66 q^{43} -19578.5 q^{44} -1419.17 q^{45} +6285.27 q^{46} +10180.6 q^{47} +3904.82 q^{48} -16639.1 q^{49} -24742.3 q^{50} +7656.77 q^{51} -28752.8 q^{52} +11009.5 q^{53} -6400.62 q^{54} +7607.93 q^{55} +1488.84 q^{56} -16399.1 q^{57} +9955.28 q^{58} -3481.00 q^{59} +7109.80 q^{60} +2294.87 q^{61} -83931.4 q^{62} +1049.43 q^{63} -51849.1 q^{64} +11172.9 q^{65} +34312.6 q^{66} +23569.8 q^{67} -38359.0 q^{68} -6442.76 q^{69} -1993.03 q^{70} +56039.7 q^{71} +9308.16 q^{72} +56572.1 q^{73} -940.434 q^{74} +25362.2 q^{75} +82156.5 q^{76} -5625.81 q^{77} +50391.0 q^{78} +65746.0 q^{79} +7601.67 q^{80} +6561.00 q^{81} -58078.6 q^{82} -13649.8 q^{83} -5257.45 q^{84} +14905.7 q^{85} -26301.9 q^{86} -10204.7 q^{87} -49899.4 q^{88} +77607.3 q^{89} -12460.3 q^{90} -8262.00 q^{91} +32277.1 q^{92} +86034.5 q^{93} +89386.0 q^{94} -31924.8 q^{95} +67380.0 q^{96} +41043.1 q^{97} -146092. q^{98} -35172.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * q^99

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