LMFDB - Embedded newform 165.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.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:	$26.4633302691$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.3368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 15x + 11 $ x^3 - x^2 - 15*x + 11
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			1.1
Root			$4.03932$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.07863 q^{2} +9.00000 q^{3} +33.2643 q^{4} -25.0000 q^{5} -72.7077 q^{6} -39.3760 q^{7} -10.2141 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-8.07863 q^{2} +9.00000 q^{3} +33.2643 q^{4} -25.0000 q^{5} -72.7077 q^{6} -39.3760 q^{7} -10.2141 q^{8} +81.0000 q^{9} +201.966 q^{10} +121.000 q^{11} +299.379 q^{12} -220.765 q^{13} +318.105 q^{14} -225.000 q^{15} -981.943 q^{16} -200.343 q^{17} -654.369 q^{18} +350.345 q^{19} -831.608 q^{20} -354.384 q^{21} -977.515 q^{22} +1385.09 q^{23} -91.9273 q^{24} +625.000 q^{25} +1783.48 q^{26} +729.000 q^{27} -1309.82 q^{28} +5506.64 q^{29} +1817.69 q^{30} -2450.86 q^{31} +8259.61 q^{32} +1089.00 q^{33} +1618.50 q^{34} +984.401 q^{35} +2694.41 q^{36} -4060.46 q^{37} -2830.31 q^{38} -1986.88 q^{39} +255.354 q^{40} +527.283 q^{41} +2862.94 q^{42} -12078.9 q^{43} +4024.99 q^{44} -2025.00 q^{45} -11189.6 q^{46} +563.023 q^{47} -8837.48 q^{48} -15256.5 q^{49} -5049.15 q^{50} -1803.09 q^{51} -7343.59 q^{52} -37203.0 q^{53} -5889.32 q^{54} -3025.00 q^{55} +402.192 q^{56} +3153.11 q^{57} -44486.2 q^{58} +2157.64 q^{59} -7484.48 q^{60} -39938.0 q^{61} +19799.6 q^{62} -3189.46 q^{63} -35304.2 q^{64} +5519.11 q^{65} -8797.63 q^{66} -38473.2 q^{67} -6664.29 q^{68} +12465.8 q^{69} -7952.62 q^{70} -13725.3 q^{71} -827.345 q^{72} -39736.3 q^{73} +32803.0 q^{74} +5625.00 q^{75} +11654.0 q^{76} -4764.50 q^{77} +16051.3 q^{78} +35672.9 q^{79} +24548.6 q^{80} +6561.00 q^{81} -4259.73 q^{82} -79999.7 q^{83} -11788.4 q^{84} +5008.58 q^{85} +97580.6 q^{86} +49559.8 q^{87} -1235.91 q^{88} -37783.0 q^{89} +16359.2 q^{90} +8692.83 q^{91} +46074.1 q^{92} -22057.7 q^{93} -4548.46 q^{94} -8758.63 q^{95} +74336.5 q^{96} -7616.35 q^{97} +123252. q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9	\( 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 252 q^{12} + 450 q^{13} - 1504 q^{14} - 675 q^{15} - 1360 q^{16} - 334 q^{17} - 162 q^{18} - 4036 q^{19} - 700 q^{20} - 2088 q^{21} - 242 q^{22} - 7060 q^{23} + 216 q^{24} + 1875 q^{25} + 2932 q^{26} + 2187 q^{27} - 8320 q^{28} + 4042 q^{29} + 450 q^{30} - 608 q^{31} - 3104 q^{32} + 3267 q^{33} - 3644 q^{34} + 5800 q^{35} + 2268 q^{36} + 2250 q^{37} - 12632 q^{38} + 4050 q^{39} - 600 q^{40} + 10654 q^{41} - 13536 q^{42} - 35528 q^{43} + 3388 q^{44} - 6075 q^{45} - 41800 q^{46} - 2100 q^{47} - 12240 q^{48} + 7667 q^{49} - 1250 q^{50} - 3006 q^{51} - 14520 q^{52} - 12826 q^{53} - 1458 q^{54} - 9075 q^{55} + 17088 q^{56} - 36324 q^{57} - 17196 q^{58} - 81876 q^{59} - 6300 q^{60} - 62298 q^{61} + 109184 q^{62} - 18792 q^{63} - 72256 q^{64} - 11250 q^{65} - 2178 q^{66} - 46148 q^{67} - 35832 q^{68} - 63540 q^{69} + 37600 q^{70} - 64724 q^{71} + 1944 q^{72} + 810 q^{73} - 44796 q^{74} + 16875 q^{75} + 44656 q^{76} - 28072 q^{77} + 26388 q^{78} + 43876 q^{79} + 34000 q^{80} + 19683 q^{81} + 56060 q^{82} - 101024 q^{83} - 74880 q^{84} + 8350 q^{85} + 24128 q^{86} + 36378 q^{87} + 2904 q^{88} + 60022 q^{89} + 4050 q^{90} - 28568 q^{91} + 38256 q^{92} - 5472 q^{93} + 74552 q^{94} + 100900 q^{95} - 27936 q^{96} - 319746 q^{97} + 431134 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 252 * q^12 + 450 * q^13 - 1504 * q^14 - 675 * q^15 - 1360 * q^16 - 334 * q^17 - 162 * q^18 - 4036 * q^19 - 700 * q^20 - 2088 * q^21 - 242 * q^22 - 7060 * q^23 + 216 * q^24 + 1875 * q^25 + 2932 * q^26 + 2187 * q^27 - 8320 * q^28 + 4042 * q^29 + 450 * q^30 - 608 * q^31 - 3104 * q^32 + 3267 * q^33 - 3644 * q^34 + 5800 * q^35 + 2268 * q^36 + 2250 * q^37 - 12632 * q^38 + 4050 * q^39 - 600 * q^40 + 10654 * q^41 - 13536 * q^42 - 35528 * q^43 + 3388 * q^44 - 6075 * q^45 - 41800 * q^46 - 2100 * q^47 - 12240 * q^48 + 7667 * q^49 - 1250 * q^50 - 3006 * q^51 - 14520 * q^52 - 12826 * q^53 - 1458 * q^54 - 9075 * q^55 + 17088 * q^56 - 36324 * q^57 - 17196 * q^58 - 81876 * q^59 - 6300 * q^60 - 62298 * q^61 + 109184 * q^62 - 18792 * q^63 - 72256 * q^64 - 11250 * q^65 - 2178 * q^66 - 46148 * q^67 - 35832 * q^68 - 63540 * q^69 + 37600 * q^70 - 64724 * q^71 + 1944 * q^72 + 810 * q^73 - 44796 * q^74 + 16875 * q^75 + 44656 * q^76 - 28072 * q^77 + 26388 * q^78 + 43876 * q^79 + 34000 * q^80 + 19683 * q^81 + 56060 * q^82 - 101024 * q^83 - 74880 * q^84 + 8350 * q^85 + 24128 * q^86 + 36378 * q^87 + 2904 * q^88 + 60022 * q^89 + 4050 * q^90 - 28568 * q^91 + 38256 * q^92 - 5472 * q^93 + 74552 * q^94 + 100900 * q^95 - 27936 * q^96 - 319746 * q^97 + 431134 * q^98 + 29403 * 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 $

$2$	−8.07863	−1.42811	−0.714057	−	0.700087i	$-0.753144\pi$
$2$	−8.07863	−1.42811	−0.714057	+	0.700087i	$0.753144\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	33.2643	1.03951
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−72.7077	−0.824522
$7$	−39.3760	−0.303730	−0.151865	−	0.988401i	$-0.548528\pi$
$7$	−39.3760	−0.303730	−0.151865	+	0.988401i	$0.548528\pi$
$8$	−10.2141	−0.0564257
$9$	81.0000	0.333333
$10$	201.966	0.638672
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	299.379	0.600162
$13$	−220.765	−0.362302	−0.181151	−	0.983455i	$-0.557982\pi$
$13$	−220.765	−0.362302	−0.181151	+	0.983455i	$0.557982\pi$
$14$	318.105	0.433761
$15$	−225.000	−0.258199
$16$	−981.943	−0.958928
$17$	−200.343	−0.168133	−0.0840664	−	0.996460i	$-0.526791\pi$
$17$	−200.343	−0.168133	−0.0840664	+	0.996460i	$0.526791\pi$
$18$	−654.369	−0.476038
$19$	350.345	0.222645	0.111322	−	0.993784i	$-0.464491\pi$
$19$	350.345	0.222645	0.111322	+	0.993784i	$0.464491\pi$
$20$	−831.608	−0.464883
$21$	−354.384	−0.175358
$22$	−977.515	−0.430593
$23$	1385.09	0.545957	0.272978	−	0.962020i	$-0.411991\pi$
$23$	1385.09	0.545957	0.272978	+	0.962020i	$0.411991\pi$
$24$	−91.9273	−0.0325774
$25$	625.000	0.200000
$26$	1783.48	0.517409
$27$	729.000	0.192450
$28$	−1309.82	−0.315730
$29$	5506.64	1.21588	0.607942	−	0.793982i	$-0.291995\pi$
$29$	5506.64	1.21588	0.607942	+	0.793982i	$0.291995\pi$
$30$	1817.69	0.368738
$31$	−2450.86	−0.458051	−0.229025	−	0.973420i	$-0.573554\pi$
$31$	−2450.86	−0.458051	−0.229025	+	0.973420i	$0.573554\pi$
$32$	8259.61	1.42588
$33$	1089.00	0.174078
$34$	1618.50	0.240113
$35$	984.401	0.135832
$36$	2694.41	0.346504
$37$	−4060.46	−0.487609	−0.243804	−	0.969824i	$-0.578395\pi$
$37$	−4060.46	−0.487609	−0.243804	+	0.969824i	$0.578395\pi$
$38$	−2830.31	−0.317962
$39$	−1986.88	−0.209175
$40$	255.354	0.0252343
$41$	527.283	0.0489874	0.0244937	−	0.999700i	$-0.492203\pi$
$41$	527.283	0.0489874	0.0244937	+	0.999700i	$0.492203\pi$
$42$	2862.94	0.250432
$43$	−12078.9	−0.996218	−0.498109	−	0.867114i	$-0.665972\pi$
$43$	−12078.9	−0.996218	−0.498109	+	0.867114i	$0.665972\pi$
$44$	4024.99	0.313424
$45$	−2025.00	−0.149071
$46$	−11189.6	−0.779689
$47$	563.023	0.0371776	0.0185888	−	0.999827i	$-0.494083\pi$
$47$	563.023	0.0371776	0.0185888	+	0.999827i	$0.494083\pi$
$48$	−8837.48	−0.553638
$49$	−15256.5	−0.907748
$50$	−5049.15	−0.285623
$51$	−1803.09	−0.0970715
$52$	−7343.59	−0.376617
$53$	−37203.0	−1.81923	−0.909617	−	0.415449i	$-0.863625\pi$
$53$	−37203.0	−1.81923	−0.909617	+	0.415449i	$0.863625\pi$
$54$	−5889.32	−0.274841
$55$	−3025.00	−0.134840
$56$	402.192	0.0171381
$57$	3153.11	0.128544
$58$	−44486.2	−1.73642
$59$	2157.64	0.0806955	0.0403477	−	0.999186i	$-0.487153\pi$
$59$	2157.64	0.0806955	0.0403477	+	0.999186i	$0.487153\pi$
$60$	−7484.48	−0.268400
$61$	−39938.0	−1.37424	−0.687119	−	0.726545i	$-0.741125\pi$
$61$	−39938.0	−1.37424	−0.687119	+	0.726545i	$0.741125\pi$
$62$	19799.6	0.654149
$63$	−3189.46	−0.101243
$64$	−35304.2	−1.07740
$65$	5519.11	0.162026
$66$	−8797.63	−0.248603
$67$	−38473.2	−1.04706	−0.523529	−	0.852008i	$-0.675385\pi$
$67$	−38473.2	−1.04706	−0.523529	+	0.852008i	$0.675385\pi$
$68$	−6664.29	−0.174776
$69$	12465.8	0.315208
$70$	−7952.62	−0.193984
$71$	−13725.3	−0.323129	−0.161564	−	0.986862i	$-0.551654\pi$
$71$	−13725.3	−0.323129	−0.161564	+	0.986862i	$0.551654\pi$
$72$	−827.345	−0.0188086
$73$	−39736.3	−0.872731	−0.436366	−	0.899769i	$-0.643735\pi$
$73$	−39736.3	−0.872731	−0.436366	+	0.899769i	$0.643735\pi$
$74$	32803.0	0.696361
$75$	5625.00	0.115470
$76$	11654.0	0.231441
$77$	−4764.50	−0.0915779
$78$	16051.3	0.298726
$79$	35672.9	0.643088	0.321544	−	0.946895i	$-0.395798\pi$
$79$	35672.9	0.643088	0.321544	+	0.946895i	$0.395798\pi$
$80$	24548.6	0.428846
$81$	6561.00	0.111111
$82$	−4259.73	−0.0699596
$83$	−79999.7	−1.27466	−0.637328	−	0.770593i	$-0.719960\pi$
$83$	−79999.7	−1.27466	−0.637328	+	0.770593i	$0.719960\pi$
$84$	−11788.4	−0.182287
$85$	5008.58	0.0751913
$86$	97580.6	1.42271
$87$	49559.8	0.701991
$88$	−1235.91	−0.0170130
$89$	−37783.0	−0.505616	−0.252808	−	0.967516i	$-0.581354\pi$
$89$	−37783.0	−0.505616	−0.252808	+	0.967516i	$0.581354\pi$
$90$	16359.2	0.212891
$91$	8692.83	0.110042
$92$	46074.1	0.567528
$93$	−22057.7	−0.264456
$94$	−4548.46	−0.0530939
$95$	−8758.63	−0.0995697
$96$	74336.5	0.823235
$97$	−7616.35	−0.0821897	−0.0410948	−	0.999155i	$-0.513085\pi$
$97$	−7616.35	−0.0821897	−0.0410948	+	0.999155i	$0.513085\pi$
$98$	123252.	1.29637
$99$	9801.00	0.100504
$100$	20790.2	0.207902
$101$	125963.	1.22868	0.614341	−	0.789041i	$-0.289422\pi$
$101$	125963.	1.22868	0.614341	+	0.789041i	$0.289422\pi$
$102$	14566.5	0.138629
$103$	−165220.	−1.53451	−0.767257	−	0.641340i	$-0.778379\pi$
$103$	−165220.	−1.53451	−0.767257	+	0.641340i	$0.778379\pi$
$104$	2254.92	0.0204431
$105$	8859.61	0.0784226
$106$	300550.	2.59807
$107$	−13152.3	−0.111056	−0.0555279	−	0.998457i	$-0.517684\pi$
$107$	−13152.3	−0.111056	−0.0555279	+	0.998457i	$0.517684\pi$
$108$	24249.7	0.200054
$109$	37970.9	0.306115	0.153057	−	0.988217i	$-0.451088\pi$
$109$	37970.9	0.306115	0.153057	+	0.988217i	$0.451088\pi$
$110$	24437.9	0.192567
$111$	−36544.2	−0.281521
$112$	38665.0	0.291255
$113$	−85189.7	−0.627612	−0.313806	−	0.949487i	$-0.601604\pi$
$113$	−85189.7	−0.627612	−0.313806	+	0.949487i	$0.601604\pi$
$114$	−25472.8	−0.183575
$115$	−34627.3	−0.244159
$116$	183175.	1.26392
$117$	−17881.9	−0.120767
$118$	−17430.8	−0.115242
$119$	7888.73	0.0510669
$120$	2298.18	0.0145691
$121$	14641.0	0.0909091
$122$	322645.	1.96257
$123$	4745.55	0.0282829
$124$	−81526.1	−0.476148
$125$	−15625.0	−0.0894427
$126$	25766.5	0.144587
$127$	−141237.	−0.777033	−0.388517	−	0.921442i	$-0.627012\pi$
$127$	−141237.	−0.777033	−0.388517	+	0.921442i	$0.627012\pi$
$128$	20902.2	0.112763
$129$	−108710.	−0.575167
$130$	−44586.9	−0.231392
$131$	210469.	1.07155	0.535773	−	0.844362i	$-0.320020\pi$
$131$	210469.	1.07155	0.535773	+	0.844362i	$0.320020\pi$
$132$	36224.9	0.180956
$133$	−13795.2	−0.0676237
$134$	310811.	1.49532
$135$	−18225.0	−0.0860663
$136$	2046.33	0.00948701
$137$	19565.1	0.0890594	0.0445297	−	0.999008i	$-0.485821\pi$
$137$	19565.1	0.0890594	0.0445297	+	0.999008i	$0.485821\pi$
$138$	−100707.	−0.450154
$139$	132498.	0.581663	0.290831	−	0.956774i	$-0.406068\pi$
$139$	132498.	0.581663	0.290831	+	0.956774i	$0.406068\pi$
$140$	32745.5	0.141199
$141$	5067.21	0.0214645
$142$	110882.	0.461465
$143$	−26712.5	−0.109238
$144$	−79537.3	−0.319643
$145$	−137666.	−0.543760
$146$	321015.	1.24636
$147$	−137309.	−0.524089
$148$	−135069.	−0.506874
$149$	−153316.	−0.565748	−0.282874	−	0.959157i	$-0.591288\pi$
$149$	−153316.	−0.565748	−0.282874	+	0.959157i	$0.591288\pi$
$150$	−45442.3	−0.164904
$151$	248151.	0.885672	0.442836	−	0.896603i	$-0.353972\pi$
$151$	248151.	0.885672	0.442836	+	0.896603i	$0.353972\pi$
$152$	−3578.47	−0.0125629
$153$	−16227.8	−0.0560443
$154$	38490.7	0.130784
$155$	61271.4	0.204846
$156$	−66092.3	−0.217440
$157$	−180692.	−0.585047	−0.292523	−	0.956258i	$-0.594495\pi$
$157$	−180692.	−0.585047	−0.292523	+	0.956258i	$0.594495\pi$
$158$	−288188.	−0.918403
$159$	−334827.	−1.05033
$160$	−206490.	−0.637675
$161$	−54539.4	−0.165823
$162$	−53003.9	−0.158679
$163$	−176045.	−0.518985	−0.259493	−	0.965745i	$-0.583555\pi$
$163$	−176045.	−0.518985	−0.259493	+	0.965745i	$0.583555\pi$
$164$	17539.7	0.0509229
$165$	−27225.0	−0.0778499
$166$	646288.	1.82035
$167$	293818.	0.815244	0.407622	−	0.913151i	$-0.366358\pi$
$167$	293818.	0.815244	0.407622	+	0.913151i	$0.366358\pi$
$168$	3619.73	0.00989471
$169$	−322556.	−0.868737
$170$	−40462.5	−0.107382
$171$	28378.0	0.0742148
$172$	−401795.	−1.03558
$173$	−20784.9	−0.0527999	−0.0263999	−	0.999651i	$-0.508404\pi$
$173$	−20784.9	−0.0527999	−0.0263999	+	0.999651i	$0.508404\pi$
$174$	−400375.	−1.00252
$175$	−24610.0	−0.0607459
$176$	−118815.	−0.289128
$177$	19418.8	0.0465896
$178$	305235.	0.722078
$179$	−229326.	−0.534958	−0.267479	−	0.963564i	$-0.586191\pi$
$179$	−229326.	−0.534958	−0.267479	+	0.963564i	$0.586191\pi$
$180$	−67360.3	−0.154961
$181$	−90807.3	−0.206027	−0.103014	−	0.994680i	$-0.532849\pi$
$181$	−90807.3	−0.206027	−0.103014	+	0.994680i	$0.532849\pi$
$182$	−70226.2	−0.157152
$183$	−359442.	−0.793416
$184$	−14147.5	−0.0308060
$185$	101512.	0.218065
$186$	178196.	0.377673
$187$	−24241.5	−0.0506939
$188$	18728.6	0.0386465
$189$	−28705.1	−0.0584528
$190$	70757.8	0.142197
$191$	−496794.	−0.985356	−0.492678	−	0.870212i	$-0.663982\pi$
$191$	−496794.	−0.985356	−0.492678	+	0.870212i	$0.663982\pi$
$192$	−317738.	−0.622036
$193$	271362.	0.524391	0.262196	−	0.965015i	$-0.415553\pi$
$193$	271362.	0.524391	0.262196	+	0.965015i	$0.415553\pi$
$194$	61529.7	0.117376
$195$	49672.0	0.0935460
$196$	−507498.	−0.943614
$197$	−190972.	−0.350594	−0.175297	−	0.984516i	$-0.556089\pi$
$197$	−190972.	−0.350594	−0.175297	+	0.984516i	$0.556089\pi$
$198$	−79178.7	−0.143531
$199$	602637.	1.07876	0.539378	−	0.842064i	$-0.318660\pi$
$199$	602637.	1.07876	0.539378	+	0.842064i	$0.318660\pi$
$200$	−6383.84	−0.0112851
$201$	−346258.	−0.604519
$202$	−1.01761e6	−1.75470
$203$	−216830.	−0.369300
$204$	−59978.6	−0.100907
$205$	−13182.1	−0.0219078
$206$	1.33476e6	2.19146
$207$	112192.	0.181986
$208$	216778.	0.347422
$209$	42391.8	0.0671299
$210$	−71573.6	−0.111996
$211$	918176.	1.41978	0.709888	−	0.704315i	$-0.248746\pi$
$211$	918176.	1.41978	0.709888	+	0.704315i	$0.248746\pi$
$212$	−1.23753e6	−1.89111
$213$	−123528.	−0.186559
$214$	106252.	0.158600
$215$	301971.	0.445522
$216$	−7446.11	−0.0108591
$217$	96505.0	0.139123
$218$	−306753.	−0.437167
$219$	−357627.	−0.503872
$220$	−100625.	−0.140168
$221$	44228.7	0.0609149
$222$	295227.	0.402044
$223$	959605.	1.29220	0.646101	−	0.763252i	$-0.276399\pi$
$223$	959605.	1.29220	0.646101	+	0.763252i	$0.276399\pi$
$224$	−325231.	−0.433083
$225$	50625.0	0.0666667
$226$	688217.	0.896301
$227$	−289954.	−0.373477	−0.186739	−	0.982410i	$-0.559792\pi$
$227$	−289954.	−0.373477	−0.186739	+	0.982410i	$0.559792\pi$
$228$	104886.	0.133623
$229$	111161.	0.140076	0.0700379	−	0.997544i	$-0.477688\pi$
$229$	111161.	0.140076	0.0700379	+	0.997544i	$0.477688\pi$
$230$	279741.	0.348688
$231$	−42880.5	−0.0528725
$232$	−56245.6	−0.0686071
$233$	−453216.	−0.546909	−0.273455	−	0.961885i	$-0.588166\pi$
$233$	−453216.	−0.546909	−0.273455	+	0.961885i	$0.588166\pi$
$234$	144462.	0.172470
$235$	−14075.6	−0.0166263
$236$	71772.5	0.0838838
$237$	321056.	0.371287
$238$	−63730.1	−0.0729294
$239$	1.26387e6	1.43123	0.715614	−	0.698496i	$-0.246147\pi$
$239$	1.26387e6	1.43123	0.715614	+	0.698496i	$0.246147\pi$
$240$	220937.	0.247594
$241$	134350.	0.149003	0.0745013	−	0.997221i	$-0.476264\pi$
$241$	134350.	0.149003	0.0745013	+	0.997221i	$0.476264\pi$
$242$	−118279.	−0.129829
$243$	59049.0	0.0641500
$244$	−1.32851e6	−1.42853
$245$	381413.	0.405957
$246$	−38337.6	−0.0403912
$247$	−77343.8	−0.0806646
$248$	25033.4	0.0258458
$249$	−719997.	−0.735923
$250$	126229.	0.127734
$251$	−1.43370e6	−1.43639	−0.718197	−	0.695840i	$-0.755032\pi$
$251$	−1.43370e6	−1.43639	−0.718197	+	0.695840i	$0.755032\pi$
$252$	−106095.	−0.105243
$253$	167596.	0.164612
$254$	1.14100e6	1.10969
$255$	45077.2	0.0434117
$256$	960873.	0.916360
$257$	−953935.	−0.900920	−0.450460	−	0.892797i	$-0.648740\pi$
$257$	−953935.	−0.900920	−0.450460	+	0.892797i	$0.648740\pi$
$258$	878226.	0.821404
$259$	159885.	0.148101
$260$	183590.	0.168428
$261$	446038.	0.405294
$262$	−1.70030e6	−1.53029
$263$	322280.	0.287306	0.143653	−	0.989628i	$-0.454115\pi$
$263$	322280.	0.287306	0.143653	+	0.989628i	$0.454115\pi$
$264$	−11123.2	−0.00982245
$265$	930075.	0.813586
$266$	111446.	0.0965744
$267$	−340047.	−0.291918
$268$	−1.27978e6	−1.08843
$269$	808737.	0.681438	0.340719	−	0.940165i	$-0.389329\pi$
$269$	808737.	0.681438	0.340719	+	0.940165i	$0.389329\pi$
$270$	147233.	0.122913
$271$	−909303.	−0.752117	−0.376058	−	0.926596i	$-0.622721\pi$
$271$	−909303.	−0.752117	−0.376058	+	0.926596i	$0.622721\pi$
$272$	196726.	0.161227
$273$	78235.5	0.0635327
$274$	−158059.	−0.127187
$275$	75625.0	0.0603023
$276$	414667.	0.327662
$277$	236933.	0.185535	0.0927675	−	0.995688i	$-0.470429\pi$
$277$	236933.	0.185535	0.0927675	+	0.995688i	$0.470429\pi$
$278$	−1.07040e6	−0.830681
$279$	−198519.	−0.152684
$280$	−10054.8	−0.00766441
$281$	−450779.	−0.340563	−0.170282	−	0.985395i	$-0.554468\pi$
$281$	−450779.	−0.340563	−0.170282	+	0.985395i	$0.554468\pi$
$282$	−40936.1	−0.0306538
$283$	683413.	0.507245	0.253622	−	0.967303i	$-0.418378\pi$
$283$	683413.	0.507245	0.253622	+	0.967303i	$0.418378\pi$
$284$	−456563.	−0.335896
$285$	−78827.6	−0.0574866
$286$	215801.	0.156005
$287$	−20762.3	−0.0148789
$288$	669028.	0.475295
$289$	−1.37972e6	−0.971731
$290$	1.11215e6	0.776551
$291$	−68547.1	−0.0474522
$292$	−1.32180e6	−0.907213
$293$	−1.81068e6	−1.23218	−0.616088	−	0.787678i	$-0.711283\pi$
$293$	−1.81068e6	−1.23218	−0.616088	+	0.787678i	$0.711283\pi$
$294$	1.10927e6	0.748459
$295$	−53941.0	−0.0360881
$296$	41474.1	0.0275136
$297$	88209.0	0.0580259
$298$	1.23859e6	0.807953
$299$	−305779.	−0.197801
$300$	187112.	0.120032
$301$	475617.	0.302581
$302$	−2.00472e6	−1.26484
$303$	1.13367e6	0.709380
$304$	−344019.	−0.213500
$305$	998450.	0.614578
$306$	131099.	0.0800376
$307$	−3.00860e6	−1.82187	−0.910937	−	0.412546i	$-0.864639\pi$
$307$	−3.00860e6	−1.82187	−0.910937	+	0.412546i	$0.864639\pi$
$308$	−158488.	−0.0951962
$309$	−1.48698e6	−0.885952
$310$	−494989.	−0.292544
$311$	−2.04083e6	−1.19648	−0.598241	−	0.801316i	$-0.704134\pi$
$311$	−2.04083e6	−1.19648	−0.598241	+	0.801316i	$0.704134\pi$
$312$	20294.3	0.0118029
$313$	−1.73940e6	−1.00355	−0.501774	−	0.864999i	$-0.667319\pi$
$313$	−1.73940e6	−1.00355	−0.501774	+	0.864999i	$0.667319\pi$
$314$	1.45975e6	0.835513
$315$	79736.5	0.0452773
$316$	1.18663e6	0.668497
$317$	106704.	0.0596392	0.0298196	−	0.999555i	$-0.490507\pi$
$317$	106704.	0.0596392	0.0298196	+	0.999555i	$0.490507\pi$
$318$	2.70495e6	1.50000
$319$	666304.	0.366603
$320$	882605.	0.481827
$321$	−118370.	−0.0641181
$322$	440604.	0.236815
$323$	−70189.3	−0.0374338
$324$	218247.	0.115501
$325$	−137978.	−0.0724604
$326$	1.42220e6	0.741170
$327$	341738.	0.176736
$328$	−5385.74	−0.00276415
$329$	−22169.6	−0.0112919
$330$	219941.	0.111179
$331$	1.54759e6	0.776402	0.388201	−	0.921575i	$-0.373097\pi$
$331$	1.54759e6	0.776402	0.388201	+	0.921575i	$0.373097\pi$
$332$	−2.66114e6	−1.32502
$333$	−328898.	−0.162536
$334$	−2.37365e6	−1.16426
$335$	961829.	0.468259
$336$	347985.	0.168156
$337$	1.22550e6	0.587814	0.293907	−	0.955834i	$-0.405044\pi$
$337$	1.22550e6	0.587814	0.293907	+	0.955834i	$0.405044\pi$
$338$	2.60581e6	1.24066
$339$	−766708.	−0.362352
$340$	166607.	0.0781621
$341$	−296553.	−0.138107
$342$	−229255.	−0.105987
$343$	1.26253e6	0.579440
$344$	123375.	0.0562123
$345$	−311645.	−0.140965
$346$	167914.	0.0754042
$347$	3.82684e6	1.70615	0.853074	−	0.521789i	$-0.174735\pi$
$347$	3.82684e6	1.70615	0.853074	+	0.521789i	$0.174735\pi$
$348$	1.64857e6	0.729727
$349$	456968.	0.200827	0.100413	−	0.994946i	$-0.467983\pi$
$349$	456968.	0.200827	0.100413	+	0.994946i	$0.467983\pi$
$350$	198815.	0.0867521
$351$	−160937.	−0.0697251
$352$	999413.	0.429920
$353$	4.32830e6	1.84876	0.924380	−	0.381474i	$-0.124583\pi$
$353$	4.32830e6	1.84876	0.924380	+	0.381474i	$0.124583\pi$
$354$	−156877.	−0.0665352
$355$	343132.	0.144508
$356$	−1.25683e6	−0.525594
$357$	70998.5	0.0294835
$358$	1.85264e6	0.763982
$359$	−845380.	−0.346191	−0.173095	−	0.984905i	$-0.555377\pi$
$359$	−845380.	−0.346191	−0.173095	+	0.984905i	$0.555377\pi$
$360$	20683.6	0.00841145
$361$	−2.35336e6	−0.950429
$362$	733599.	0.294230
$363$	131769.	0.0524864
$364$	289161.	0.114390
$365$	993408.	0.390297
$366$	2.90380e6	1.13309
$367$	2.96016e6	1.14723	0.573615	−	0.819125i	$-0.305540\pi$
$367$	2.96016e6	1.14723	0.573615	+	0.819125i	$0.305540\pi$
$368$	−1.36008e6	−0.523534
$369$	42709.9	0.0163291
$370$	−820075.	−0.311422
$371$	1.46491e6	0.552555
$372$	−733735.	−0.274904
$373$	1.02299e6	0.380713	0.190357	−	0.981715i	$-0.439036\pi$
$373$	1.02299e6	0.380713	0.190357	+	0.981715i	$0.439036\pi$
$374$	195839.	0.0723968
$375$	−140625.	−0.0516398
$376$	−5750.80	−0.00209777
$377$	−1.21567e6	−0.440517
$378$	231898.	0.0834772
$379$	−4.19402e6	−1.49980	−0.749899	−	0.661552i	$-0.769898\pi$
$379$	−4.19402e6	−1.49980	−0.749899	+	0.661552i	$0.769898\pi$
$380$	−291350.	−0.103504
$381$	−1.27113e6	−0.448620
$382$	4.01342e6	1.40720
$383$	−1.64287e6	−0.572276	−0.286138	−	0.958188i	$-0.592372\pi$
$383$	−1.64287e6	−0.572276	−0.286138	+	0.958188i	$0.592372\pi$
$384$	188120.	0.0651039
$385$	119113.	0.0409549
$386$	−2.19223e6	−0.748891
$387$	−978387.	−0.332073
$388$	−253353.	−0.0854371
$389$	769820.	0.257938	0.128969	−	0.991649i	$-0.458833\pi$
$389$	769820.	0.257938	0.128969	+	0.991649i	$0.458833\pi$
$390$	−401282.	−0.133594
$391$	−277493.	−0.0917933
$392$	155832.	0.0512203
$393$	1.89422e6	0.618657
$394$	1.54279e6	0.500688
$395$	−891822.	−0.287598
$396$	326024.	0.104475
$397$	4.86631e6	1.54961	0.774806	−	0.632199i	$-0.217847\pi$
$397$	4.86631e6	1.54961	0.774806	+	0.632199i	$0.217847\pi$
$398$	−4.86848e6	−1.54059
$399$	−124157.	−0.0390426
$400$	−613714.	−0.191786
$401$	717064.	0.222688	0.111344	−	0.993782i	$-0.464484\pi$
$401$	717064.	0.222688	0.111344	+	0.993782i	$0.464484\pi$
$402$	2.79730e6	0.863323
$403$	541062.	0.165953
$404$	4.19007e6	1.27723
$405$	−164025.	−0.0496904
$406$	1.75169e6	0.527402
$407$	−491316.	−0.147019
$408$	18417.0	0.00547733
$409$	−3.80091e6	−1.12352	−0.561758	−	0.827302i	$-0.689875\pi$
$409$	−3.80091e6	−1.12352	−0.561758	+	0.827302i	$0.689875\pi$
$410$	106493.	0.0312869
$411$	176086.	0.0514185
$412$	−5.49595e6	−1.59514
$413$	−84959.4	−0.0245096
$414$	−906361.	−0.259896
$415$	1.99999e6	0.570044
$416$	−1.82343e6	−0.516601
$417$	1.19248e6	0.335823
$418$	−342468.	−0.0958691
$419$	−1.55888e6	−0.433787	−0.216894	−	0.976195i	$-0.569592\pi$
$419$	−1.55888e6	−0.433787	−0.216894	+	0.976195i	$0.569592\pi$
$420$	294709.	0.0815212
$421$	4.13561e6	1.13719	0.568596	−	0.822617i	$-0.307487\pi$
$421$	4.13561e6	1.13719	0.568596	+	0.822617i	$0.307487\pi$
$422$	−7.41761e6	−2.02760
$423$	45604.9	0.0123925
$424$	379997.	0.102651
$425$	−125215.	−0.0336266
$426$	997935.	0.266427
$427$	1.57260e6	0.417397
$428$	−437502.	−0.115444
$429$	−240413.	−0.0630687
$430$	−2.43952e6	−0.636257
$431$	−5.25900e6	−1.36367	−0.681836	−	0.731505i	$-0.738818\pi$
$431$	−5.25900e6	−1.36367	−0.681836	+	0.731505i	$0.738818\pi$
$432$	−715836.	−0.184546
$433$	−694549.	−0.178026	−0.0890130	−	0.996030i	$-0.528371\pi$
$433$	−694549.	−0.178026	−0.0890130	+	0.996030i	$0.528371\pi$
$434$	−779629.	−0.198684
$435$	−1.23899e6	−0.313940
$436$	1.26308e6	0.318210
$437$	485260.	0.121554
$438$	2.88914e6	0.719586
$439$	−7.80969e6	−1.93407	−0.967036	−	0.254640i	$-0.918043\pi$
$439$	−7.80969e6	−1.93407	−0.967036	+	0.254640i	$0.918043\pi$
$440$	30897.8	0.00760844
$441$	−1.23578e6	−0.302583
$442$	−357307.	−0.0869934
$443$	−5.43876e6	−1.31671	−0.658356	−	0.752707i	$-0.728748\pi$
$443$	−5.43876e6	−1.31671	−0.658356	+	0.752707i	$0.728748\pi$
$444$	−1.21562e6	−0.292644
$445$	944575.	0.226119
$446$	−7.75229e6	−1.84541
$447$	−1.37985e6	−0.326635
$448$	1.39014e6	0.327238
$449$	5.46277e6	1.27878	0.639392	−	0.768881i	$-0.279186\pi$
$449$	5.46277e6	1.27878	0.639392	+	0.768881i	$0.279186\pi$
$450$	−408981.	−0.0952076
$451$	63801.3	0.0147703
$452$	−2.83378e6	−0.652409
$453$	2.23336e6	0.511343
$454$	2.34243e6	0.533368
$455$	−217321.	−0.0492122
$456$	−32206.3	−0.00725318
$457$	3.07144e6	0.687941	0.343970	−	0.938980i	$-0.388228\pi$
$457$	3.07144e6	0.687941	0.343970	+	0.938980i	$0.388228\pi$
$458$	−898028.	−0.200044
$459$	−146050.	−0.0323572
$460$	−1.15185e6	−0.253806
$461$	3.85641e6	0.845143	0.422572	−	0.906329i	$-0.361127\pi$
$461$	3.85641e6	0.845143	0.422572	+	0.906329i	$0.361127\pi$
$462$	346416.	0.0755080
$463$	3.20594e6	0.695029	0.347514	−	0.937675i	$-0.387026\pi$
$463$	3.20594e6	0.695029	0.347514	+	0.937675i	$0.387026\pi$
$464$	−5.40721e6	−1.16594
$465$	551442.	0.118268
$466$	3.66136e6	0.781049
$467$	−2.43952e6	−0.517622	−0.258811	−	0.965928i	$-0.583331\pi$
$467$	−2.43952e6	−0.517622	−0.258811	+	0.965928i	$0.583331\pi$
$468$	−594830.	−0.125539
$469$	1.51492e6	0.318023
$470$	113711.	0.0237443
$471$	−1.62623e6	−0.337777
$472$	−22038.5	−0.00455330
$473$	−1.46154e6	−0.300371
$474$	−2.59369e6	−0.530240
$475$	218966.	0.0445289
$476$	262413.	0.0530846
$477$	−3.01344e6	−0.606411
$478$	−1.02104e7	−2.04396
$479$	4.69186e6	0.934342	0.467171	−	0.884167i	$-0.345273\pi$
$479$	4.69186e6	0.934342	0.467171	+	0.884167i	$0.345273\pi$
$480$	−1.85841e6	−0.368162
$481$	896406.	0.176662
$482$	−1.08536e6	−0.212793
$483$	−490854.	−0.0957381
$484$	487023.	0.0945010
$485$	190409.	0.0367564
$486$	−477035.	−0.0916136
$487$	5.73305e6	1.09538	0.547688	−	0.836683i	$-0.315508\pi$
$487$	5.73305e6	1.09538	0.547688	+	0.836683i	$0.315508\pi$
$488$	407932.	0.0775423
$489$	−1.58441e6	−0.299636
$490$	−3.08130e6	−0.579754
$491$	−693872.	−0.129890	−0.0649449	−	0.997889i	$-0.520687\pi$
$491$	−693872.	−0.129890	−0.0649449	+	0.997889i	$0.520687\pi$
$492$	157858.	0.0294004
$493$	−1.10322e6	−0.204430
$494$	624832.	0.115198
$495$	−245025.	−0.0449467
$496$	2.40660e6	0.439238
$497$	540448.	0.0981438
$498$	5.81659e6	1.05098
$499$	1.23153e6	0.221407	0.110704	−	0.993853i	$-0.464690\pi$
$499$	1.23153e6	0.221407	0.110704	+	0.993853i	$0.464690\pi$
$500$	−519755.	−0.0929767
$501$	2.64436e6	0.470681
$502$	1.15823e7	2.05133
$503$	−7.61551e6	−1.34208	−0.671041	−	0.741420i	$-0.734153\pi$
$503$	−7.61551e6	−1.34208	−0.671041	+	0.741420i	$0.734153\pi$
$504$	32577.6	0.00571272
$505$	−3.14907e6	−0.549483
$506$	−1.35395e6	−0.235085
$507$	−2.90300e6	−0.501566
$508$	−4.69816e6	−0.807734
$509$	−1.55496e6	−0.266026	−0.133013	−	0.991114i	$-0.542465\pi$
$509$	−1.55496e6	−0.266026	−0.133013	+	0.991114i	$0.542465\pi$
$510$	−364163.	−0.0619969
$511$	1.56466e6	0.265074
$512$	−8.43141e6	−1.42143
$513$	255402.	0.0428480
$514$	7.70649e6	1.28662
$515$	4.13051e6	0.686255
$516$	−3.61616e6	−0.597892
$517$	68125.8	0.0112095
$518$	−1.29165e6	−0.211505
$519$	−187064.	−0.0304840
$520$	−56373.0	−0.00914245
$521$	−3.26766e6	−0.527403	−0.263701	−	0.964604i	$-0.584943\pi$
$521$	−3.26766e6	−0.527403	−0.263701	+	0.964604i	$0.584943\pi$
$522$	−3.60338e6	−0.578807
$523$	−8.35303e6	−1.33533	−0.667667	−	0.744460i	$-0.732707\pi$
$523$	−8.35303e6	−1.33533	−0.667667	+	0.744460i	$0.732707\pi$
$524$	7.00112e6	1.11388
$525$	−221490.	−0.0350717
$526$	−2.60358e6	−0.410305
$527$	491012.	0.0770133
$528$	−1.06934e6	−0.166928
$529$	−4.51787e6	−0.701931
$530$	−7.51374e6	−1.16189
$531$	174769.	0.0268985
$532$	−458888.	−0.0702956
$533$	−116405.	−0.0177482
$534$	2.74711e6	0.416892
$535$	328807.	0.0496657
$536$	392970.	0.0590810
$537$	−2.06393e6	−0.308858
$538$	−6.53349e6	−0.973172
$539$	−1.84604e6	−0.273696
$540$	−606243.	−0.0894668
$541$	4.72814e6	0.694540	0.347270	−	0.937765i	$-0.387109\pi$
$541$	4.72814e6	0.694540	0.347270	+	0.937765i	$0.387109\pi$
$542$	7.34593e6	1.07411
$543$	−817266.	−0.118950
$544$	−1.65476e6	−0.239738
$545$	−949272.	−0.136899
$546$	−632036.	−0.0907320
$547$	−3.84639e6	−0.549648	−0.274824	−	0.961495i	$-0.588620\pi$
$547$	−3.84639e6	−0.549648	−0.274824	+	0.961495i	$0.588620\pi$
$548$	650819.	0.0925782
$549$	−3.23498e6	−0.458079
$550$	−610947.	−0.0861185
$551$	1.92923e6	0.270710
$552$	−127328.	−0.0177859
$553$	−1.40466e6	−0.195325
$554$	−1.91409e6	−0.264965
$555$	913604.	0.125900
$556$	4.40745e6	0.604644
$557$	1.34095e7	1.83137	0.915684	−	0.401900i	$-0.131650\pi$
$557$	1.34095e7	1.83137	0.915684	+	0.401900i	$0.131650\pi$
$558$	1.60376e6	0.218050
$559$	2.66658e6	0.360932
$560$	−966625.	−0.130253
$561$	−218174.	−0.0292682
$562$	3.64168e6	0.486363
$563$	1.51163e6	0.200990	0.100495	−	0.994938i	$-0.467957\pi$
$563$	1.51163e6	0.200990	0.100495	+	0.994938i	$0.467957\pi$
$564$	168557.	0.0223126
$565$	2.12974e6	0.280677
$566$	−5.52105e6	−0.724403
$567$	−258346.	−0.0337477
$568$	140192.	0.0182328
$569$	1.39221e7	1.80271	0.901353	−	0.433085i	$-0.142575\pi$
$569$	1.39221e7	1.80271	0.901353	+	0.433085i	$0.142575\pi$
$570$	636820.	0.0820974
$571$	−3.44073e6	−0.441632	−0.220816	−	0.975316i	$-0.570872\pi$
$571$	−3.44073e6	−0.441632	−0.220816	+	0.975316i	$0.570872\pi$
$572$	−888574.	−0.113554
$573$	−4.47115e6	−0.568896
$574$	167731.	0.0212488
$575$	865681.	0.109191
$576$	−2.85964e6	−0.359133
$577$	3.96778e6	0.496144	0.248072	−	0.968742i	$-0.420203\pi$
$577$	3.96778e6	0.496144	0.248072	+	0.968742i	$0.420203\pi$
$578$	1.11463e7	1.38774
$579$	2.44226e6	0.302758
$580$	−4.57937e6	−0.565244
$581$	3.15007e6	0.387151
$582$	553767.	0.0677672
$583$	−4.50156e6	−0.548519
$584$	405872.	0.0492445
$585$	447048.	0.0540088
$586$	1.46278e7	1.75969
$587$	3.64595e6	0.436733	0.218366	−	0.975867i	$-0.429927\pi$
$587$	3.64595e6	0.436733	0.218366	+	0.975867i	$0.429927\pi$
$588$	−4.56748e6	−0.544796
$589$	−858645.	−0.101982
$590$	435770.	0.0515380
$591$	−1.71875e6	−0.202416
$592$	3.98714e6	0.467582
$593$	−486759.	−0.0568431	−0.0284215	−	0.999596i	$-0.509048\pi$
$593$	−486759.	−0.0568431	−0.0284215	+	0.999596i	$0.509048\pi$
$594$	−712608.	−0.0828676
$595$	−197218.	−0.0228378
$596$	−5.09997e6	−0.588101
$597$	5.42373e6	0.622820
$598$	2.47027e6	0.282483
$599$	1.37413e7	1.56481	0.782404	−	0.622771i	$-0.213993\pi$
$599$	1.37413e7	1.56481	0.782404	+	0.622771i	$0.213993\pi$
$600$	−57454.5	−0.00651548
$601$	7.84470e6	0.885911	0.442955	−	0.896544i	$-0.353930\pi$
$601$	7.84470e6	0.885911	0.442955	+	0.896544i	$0.353930\pi$
$602$	−3.84234e6	−0.432120
$603$	−3.11633e6	−0.349019
$604$	8.25457e6	0.920666
$605$	−366025.	−0.0406558
$606$	−9.15848e6	−1.01308
$607$	−3.41681e6	−0.376399	−0.188200	−	0.982131i	$-0.560265\pi$
$607$	−3.41681e6	−0.376399	−0.188200	+	0.982131i	$0.560265\pi$
$608$	2.89371e6	0.317465
$609$	−1.95147e6	−0.213215
$610$	−8.06611e6	−0.877687
$611$	−124296.	−0.0134695
$612$	−539807.	−0.0582586
$613$	−1.32402e7	−1.42313	−0.711564	−	0.702621i	$-0.752013\pi$
$613$	−1.32402e7	−1.42313	−0.711564	+	0.702621i	$0.752013\pi$
$614$	2.43054e7	2.60184
$615$	−118639.	−0.0126485
$616$	48665.3	0.00516735
$617$	1.72143e7	1.82044	0.910220	−	0.414126i	$-0.135913\pi$
$617$	1.72143e7	1.82044	0.910220	+	0.414126i	$0.135913\pi$
$618$	1.20128e7	1.26524
$619$	1.60142e7	1.67988	0.839940	−	0.542679i	$-0.182590\pi$
$619$	1.60142e7	1.67988	0.839940	+	0.542679i	$0.182590\pi$
$620$	2.03815e6	0.212940
$621$	1.00973e6	0.105069
$622$	1.64871e7	1.70871
$623$	1.48774e6	0.153571
$624$	1.95100e6	0.200584
$625$	390625.	0.0400000
$626$	1.40520e7	1.43318
$627$	381526.	0.0387574
$628$	−6.01061e6	−0.608162
$629$	813486.	0.0819830
$630$	−644162.	−0.0646612
$631$	−7.75049e6	−0.774918	−0.387459	−	0.921887i	$-0.626647\pi$
$631$	−7.75049e6	−0.774918	−0.387459	+	0.921887i	$0.626647\pi$
$632$	−364368.	−0.0362867
$633$	8.26358e6	0.819708
$634$	−862021.	−0.0851716
$635$	3.53093e6	0.347500
$636$	−1.11378e7	−1.09183
$637$	3.36810e6	0.328879
$638$	−5.38282e6	−0.523550
$639$	−1.11175e6	−0.107710
$640$	−522556.	−0.0504293
$641$	8.77648e6	0.843675	0.421838	−	0.906671i	$-0.361385\pi$
$641$	8.77648e6	0.843675	0.421838	+	0.906671i	$0.361385\pi$
$642$	956272.	0.0915680
$643$	−1.51011e7	−1.44040	−0.720198	−	0.693768i	$-0.755949\pi$
$643$	−1.51011e7	−1.44040	−0.720198	+	0.693768i	$0.755949\pi$
$644$	−1.81422e6	−0.172375
$645$	2.71774e6	0.257222
$646$	567034.	0.0534598
$647$	1.57910e7	1.48303	0.741516	−	0.670936i	$-0.234107\pi$
$647$	1.57910e7	1.48303	0.741516	+	0.670936i	$0.234107\pi$
$648$	−67015.0	−0.00626952
$649$	261075.	0.0243306
$650$	1.11467e6	0.103482
$651$	868545.	0.0803230
$652$	−5.85603e6	−0.539491
$653$	1.33260e7	1.22297	0.611484	−	0.791256i	$-0.290573\pi$
$653$	1.33260e7	1.22297	0.611484	+	0.791256i	$0.290573\pi$
$654$	−2.76078e6	−0.252399
$655$	−5.26173e6	−0.479210
$656$	−517762.	−0.0469754
$657$	−3.21864e6	−0.290910
$658$	179100.	0.0161262
$659$	−882213.	−0.0791334	−0.0395667	−	0.999217i	$-0.512598\pi$
$659$	−882213.	−0.0791334	−0.0395667	+	0.999217i	$0.512598\pi$
$660$	−905622.	−0.0809258
$661$	−5.59700e6	−0.498255	−0.249127	−	0.968471i	$-0.580144\pi$
$661$	−5.59700e6	−0.498255	−0.249127	+	0.968471i	$0.580144\pi$
$662$	−1.25024e7	−1.10879
$663$	398058.	0.0351692
$664$	817128.	0.0719234
$665$	344880.	0.0302422
$666$	2.65704e6	0.232120
$667$	7.62720e6	0.663820
$668$	9.77367e6	0.847454
$669$	8.63644e6	0.746053
$670$	−7.77027e6	−0.668727
$671$	−4.83250e6	−0.414348
$672$	−2.92708e6	−0.250041
$673$	1.29320e6	0.110060	0.0550300	−	0.998485i	$-0.482475\pi$
$673$	1.29320e6	0.110060	0.0550300	+	0.998485i	$0.482475\pi$
$674$	−9.90040e6	−0.839466
$675$	455625.	0.0384900
$676$	−1.07296e7	−0.903062
$677$	1.48798e7	1.24775	0.623873	−	0.781526i	$-0.285558\pi$
$677$	1.48798e7	1.24775	0.623873	+	0.781526i	$0.285558\pi$
$678$	6.19395e6	0.517480
$679$	299902.	0.0249634
$680$	−51158.4	−0.00424272
$681$	−2.60958e6	−0.215627
$682$	2.39575e6	0.197233
$683$	8.62925e6	0.707817	0.353909	−	0.935280i	$-0.384852\pi$
$683$	8.62925e6	0.707817	0.353909	+	0.935280i	$0.384852\pi$
$684$	943974.	0.0771471
$685$	−489127.	−0.0398286
$686$	−1.01996e7	−0.827506
$687$	1.00045e6	0.0808729
$688$	1.18607e7	0.955302
$689$	8.21310e6	0.659112
$690$	2.51767e6	0.201315
$691$	−1.79734e7	−1.43198	−0.715988	−	0.698113i	$-0.754023\pi$
$691$	−1.79734e7	−1.43198	−0.715988	+	0.698113i	$0.754023\pi$
$692$	−691396.	−0.0548860
$693$	−385925.	−0.0305260
$694$	−3.09157e7	−2.43658
$695$	−3.31244e6	−0.260127
$696$	−506211.	−0.0396103
$697$	−105638.	−0.00823639
$698$	−3.69167e6	−0.286804
$699$	−4.07894e6	−0.315758
$700$	−818636.	−0.0631460
$701$	−2.13485e7	−1.64086	−0.820432	−	0.571744i	$-0.806267\pi$
$701$	−2.13485e7	−1.64086	−0.820432	+	0.571744i	$0.806267\pi$
$702$	1.30015e6	0.0995754
$703$	−1.42256e6	−0.108563
$704$	−4.27181e6	−0.324848
$705$	−126680.	−0.00959922
$706$	−3.49667e7	−2.64024
$707$	−4.95992e6	−0.373187
$708$	645953.	0.0484303
$709$	6.90604e6	0.515957	0.257979	−	0.966151i	$-0.416944\pi$
$709$	6.90604e6	0.515957	0.257979	+	0.966151i	$0.416944\pi$
$710$	−2.77204e6	−0.206373
$711$	2.88950e6	0.214363
$712$	385921.	0.0285298
$713$	−3.39466e6	−0.250076
$714$	−573571.	−0.0421058
$715$	667813.	0.0488528
$716$	−7.62837e6	−0.556095
$717$	1.13749e7	0.826320
$718$	6.82951e6	0.494400
$719$	−1.71863e7	−1.23983	−0.619913	−	0.784670i	$-0.712832\pi$
$719$	−1.71863e7	−1.23983	−0.619913	+	0.784670i	$0.712832\pi$
$720$	1.98843e6	0.142949
$721$	6.50573e6	0.466077
$722$	1.90119e7	1.35732
$723$	1.20915e6	0.0860266
$724$	−3.02065e6	−0.214167
$725$	3.44165e6	0.243177
$726$	−1.06451e6	−0.0749566
$727$	−2.43516e7	−1.70880	−0.854401	−	0.519615i	$-0.826075\pi$
$727$	−2.43516e7	−1.70880	−0.854401	+	0.519615i	$0.826075\pi$
$728$	−88789.8	−0.00620919
$729$	531441.	0.0370370
$730$	−8.02538e6	−0.557389
$731$	2.41992e6	0.167497
$732$	−1.19566e7	−0.824765
$733$	−1.93102e7	−1.32747	−0.663737	−	0.747966i	$-0.731031\pi$
$733$	−1.93102e7	−1.32747	−0.663737	+	0.747966i	$0.731031\pi$
$734$	−2.39141e7	−1.63838
$735$	3.43272e6	0.234380
$736$	1.14403e7	0.778472
$737$	−4.65525e6	−0.315700
$738$	−345038.	−0.0233199
$739$	−9.23336e6	−0.621940	−0.310970	−	0.950420i	$-0.600654\pi$
$739$	−9.23336e6	−0.621940	−0.310970	+	0.950420i	$0.600654\pi$
$740$	3.37672e6	0.226681
$741$	−696094.	−0.0465717
$742$	−1.18345e7	−0.789112
$743$	8.02302e6	0.533170	0.266585	−	0.963811i	$-0.414105\pi$
$743$	8.02302e6	0.533170	0.266585	+	0.963811i	$0.414105\pi$
$744$	225300.	0.0149221
$745$	3.83291e6	0.253010
$746$	−8.26434e6	−0.543702
$747$	−6.47998e6	−0.424885
$748$	−806379.	−0.0526969
$749$	517885.	0.0337309
$750$	1.13606e6	0.0737475
$751$	1.19930e6	0.0775938	0.0387969	−	0.999247i	$-0.487647\pi$
$751$	1.19930e6	0.0775938	0.0387969	+	0.999247i	$0.487647\pi$
$752$	−552856.	−0.0356507
$753$	−1.29033e7	−0.829302
$754$	9.82096e6	0.629109
$755$	−6.20377e6	−0.396085
$756$	−954858.	−0.0607623
$757$	−1.40172e7	−0.889040	−0.444520	−	0.895769i	$-0.646626\pi$
$757$	−1.40172e7	−0.889040	−0.444520	+	0.895769i	$0.646626\pi$
$758$	3.38820e7	2.14188
$759$	1.50836e6	0.0950389
$760$	89461.9	0.00561829
$761$	−1.98659e7	−1.24350	−0.621750	−	0.783215i	$-0.713578\pi$
$761$	−1.98659e7	−1.24350	−0.621750	+	0.783215i	$0.713578\pi$
$762$	1.02690e7	0.640681
$763$	−1.49514e6	−0.0929761
$764$	−1.65255e7	−1.02429
$765$	405695.	0.0250638
$766$	1.32721e7	0.817275
$767$	−476331.	−0.0292361
$768$	8.64785e6	0.529060
$769$	−2.09738e7	−1.27897	−0.639486	−	0.768803i	$-0.720853\pi$
$769$	−2.09738e7	−1.27897	−0.639486	+	0.768803i	$0.720853\pi$
$770$	−962267.	−0.0584883
$771$	−8.58542e6	−0.520146
$772$	9.02668e6	0.545111
$773$	7.69041e6	0.462914	0.231457	−	0.972845i	$-0.425651\pi$
$773$	7.69041e6	0.462914	0.231457	+	0.972845i	$0.425651\pi$
$774$	7.90403e6	0.474238
$775$	−1.53178e6	−0.0916101
$776$	77794.4	0.00463761
$777$	1.43896e6	0.0855062
$778$	−6.21909e6	−0.368365
$779$	184731.	0.0109068
$780$	1.65231e6	0.0972421
$781$	−1.66076e6	−0.0974270
$782$	2.24177e6	0.131091
$783$	4.01434e6	0.233997
$784$	1.49810e7	0.870466
$785$	4.51731e6	0.261641
$786$	−1.53027e7	−0.883513
$787$	−1.39975e6	−0.0805589	−0.0402794	−	0.999188i	$-0.512825\pi$
$787$	−1.39975e6	−0.0805589	−0.0402794	+	0.999188i	$0.512825\pi$
$788$	−6.35256e6	−0.364446
$789$	2.90052e6	0.165876
$790$	7.20470e6	0.410722
$791$	3.35443e6	0.190624
$792$	−100109.	−0.00567100
$793$	8.81689e6	0.497889
$794$	−3.93131e7	−2.21302
$795$	8.37068e6	0.469724
$796$	2.00463e7	1.12138
$797$	1.22917e7	0.685432	0.342716	−	0.939439i	$-0.388653\pi$
$797$	1.22917e7	0.685432	0.342716	+	0.939439i	$0.388653\pi$
$798$	1.00302e6	0.0557573
$799$	−112798.	−0.00625078
$800$	5.16225e6	0.285177
$801$	−3.06042e6	−0.168539
$802$	−5.79290e6	−0.318024
$803$	−4.80810e6	−0.263138
$804$	−1.15181e7	−0.628404
$805$	1.36348e6	0.0741584
$806$	−4.37104e6	−0.236999
$807$	7.27863e6	0.393429
$808$	−1.28660e6	−0.0693292
$809$	−1.19607e7	−0.642515	−0.321258	−	0.946992i	$-0.604106\pi$
$809$	−1.19607e7	−0.642515	−0.321258	+	0.946992i	$0.604106\pi$
$810$	1.32510e6	0.0709636
$811$	−1.15112e7	−0.614565	−0.307282	−	0.951618i	$-0.599420\pi$
$811$	−1.15112e7	−0.614565	−0.307282	+	0.951618i	$0.599420\pi$
$812$	−7.21270e6	−0.383891
$813$	−8.18373e6	−0.434235
$814$	3.96916e6	0.209961
$815$	4.40113e6	0.232097
$816$	1.77053e6	0.0930846
$817$	−4.23177e6	−0.221803
$818$	3.07062e7	1.60451
$819$	704120.	0.0366806
$820$	−438493.	−0.0227734
$821$	2.77684e7	1.43778	0.718890	−	0.695124i	$-0.244651\pi$
$821$	2.77684e7	1.43778	0.718890	+	0.695124i	$0.244651\pi$
$822$	−1.42253e6	−0.0734315
$823$	−2.63447e7	−1.35580	−0.677898	−	0.735156i	$-0.737109\pi$
$823$	−2.63447e7	−1.35580	−0.677898	+	0.735156i	$0.737109\pi$
$824$	1.68758e6	0.0865860
$825$	680625.	0.0348155
$826$	686356.	0.0350025
$827$	−3.32551e7	−1.69081	−0.845406	−	0.534125i	$-0.820641\pi$
$827$	−3.32551e7	−1.69081	−0.845406	+	0.534125i	$0.820641\pi$
$828$	3.73200e6	0.189176
$829$	2.84581e7	1.43820	0.719101	−	0.694905i	$-0.244554\pi$
$829$	2.84581e7	1.43820	0.719101	+	0.694905i	$0.244554\pi$
$830$	−1.61572e7	−0.814087
$831$	2.13239e6	0.107119
$832$	7.79391e6	0.390344
$833$	3.05654e6	0.152622
$834$	−9.63360e6	−0.479594
$835$	−7.34545e6	−0.364588
$836$	1.41013e6	0.0697822
$837$	−1.78667e6	−0.0881519
$838$	1.25936e7	0.619498
$839$	−9.47931e6	−0.464913	−0.232457	−	0.972607i	$-0.574676\pi$
$839$	−9.47931e6	−0.464913	−0.232457	+	0.972607i	$0.574676\pi$
$840$	−90493.3	−0.00442505
$841$	9.81196e6	0.478372
$842$	−3.34101e7	−1.62404
$843$	−4.05701e6	−0.196624
$844$	3.05425e7	1.47587
$845$	8.06390e6	0.388511
$846$	−368425.	−0.0176980
$847$	−576505.	−0.0276118
$848$	3.65312e7	1.74451
$849$	6.15072e6	0.292858
$850$	1.01156e6	0.0480226
$851$	−5.62411e6	−0.266213
$852$	−4.10907e6	−0.193930
$853$	2.13145e7	1.00300	0.501501	−	0.865157i	$-0.332781\pi$
$853$	2.13145e7	1.00300	0.501501	+	0.865157i	$0.332781\pi$
$854$	−1.27045e7	−0.596090
$855$	−709449.	−0.0331899
$856$	134339.	0.00626640
$857$	2.21044e7	1.02808	0.514039	−	0.857767i	$-0.328149\pi$
$857$	2.21044e7	1.02808	0.514039	+	0.857767i	$0.328149\pi$
$858$	1.94221e6	0.0900693
$859$	−7.07193e6	−0.327006	−0.163503	−	0.986543i	$-0.552279\pi$
$859$	−7.07193e6	−0.327006	−0.163503	+	0.986543i	$0.552279\pi$
$860$	1.00449e7	0.463125
$861$	−186861.	−0.00859035
$862$	4.24855e7	1.94748
$863$	−5.45080e6	−0.249134	−0.124567	−	0.992211i	$-0.539754\pi$
$863$	−5.45080e6	−0.249134	−0.124567	+	0.992211i	$0.539754\pi$
$864$	6.02125e6	0.274412
$865$	519623.	0.0236128
$866$	5.61101e6	0.254241
$867$	−1.24175e7	−0.561029
$868$	3.21017e6	0.144620
$869$	4.31642e6	0.193898
$870$	1.00094e7	0.448342
$871$	8.49351e6	0.379351
$872$	−387840.	−0.0172727
$873$	−616924.	−0.0273966
$874$	−3.92023e6	−0.173593
$875$	615251.	0.0271664
$876$	−1.18962e7	−0.523780
$877$	−2.02823e7	−0.890467	−0.445234	−	0.895414i	$-0.646879\pi$
$877$	−2.02823e7	−0.890467	−0.445234	+	0.895414i	$0.646879\pi$
$878$	6.30917e7	2.76208
$879$	−1.62961e7	−0.711397
$880$	2.97038e6	0.129302
$881$	−6.58178e6	−0.285696	−0.142848	−	0.989745i	$-0.545626\pi$
$881$	−6.58178e6	−0.285696	−0.142848	+	0.989745i	$0.545626\pi$
$882$	9.98340e6	0.432123
$883$	−1.63860e7	−0.707247	−0.353623	−	0.935388i	$-0.615051\pi$
$883$	−1.63860e7	−0.707247	−0.353623	+	0.935388i	$0.615051\pi$
$884$	1.47124e6	0.0633217
$885$	−485469.	−0.0208355
$886$	4.39378e7	1.88042
$887$	−2.92929e6	−0.125013	−0.0625063	−	0.998045i	$-0.519909\pi$
$887$	−2.92929e6	−0.125013	−0.0625063	+	0.998045i	$0.519909\pi$
$888$	373267.	0.0158850
$889$	5.56136e6	0.236008
$890$	−7.63087e6	−0.322923
$891$	793881.	0.0335013
$892$	3.19206e7	1.34326
$893$	197252.	0.00827739
$894$	1.11473e7	0.466472
$895$	5.73314e6	0.239241
$896$	−823047.	−0.0342495
$897$	−2.75201e6	−0.114201
$898$	−4.41317e7	−1.82625
$899$	−1.34960e7	−0.556936
$900$	1.68401e6	0.0693007
$901$	7.45337e6	0.305873
$902$	−515427.	−0.0210936
$903$	4.28056e6	0.174695
$904$	870140.	0.0354134
$905$	2.27018e6	0.0921381
$906$	−1.80425e7	−0.730256
$907$	−7.88236e6	−0.318154	−0.159077	−	0.987266i	$-0.550852\pi$
$907$	−7.88236e6	−0.318154	−0.159077	+	0.987266i	$0.550852\pi$
$908$	−9.64512e6	−0.388234
$909$	1.02030e7	0.409561
$910$	1.75566e6	0.0702807
$911$	−2.16713e7	−0.865146	−0.432573	−	0.901599i	$-0.642394\pi$
$911$	−2.16713e7	−0.865146	−0.432573	+	0.901599i	$0.642394\pi$
$912$	−3.09617e6	−0.123264
$913$	−9.67996e6	−0.384323
$914$	−2.48130e7	−0.982458
$915$	8.98605e6	0.354827
$916$	3.69769e6	0.145610
$917$	−8.28745e6	−0.325460
$918$	1.17989e6	0.0462097
$919$	4.32037e7	1.68746	0.843728	−	0.536771i	$-0.180356\pi$
$919$	4.32037e7	1.68746	0.843728	+	0.536771i	$0.180356\pi$
$920$	353688.	0.0137769
$921$	−2.70774e7	−1.05186
$922$	−3.11545e7	−1.20696
$923$	3.03006e6	0.117070
$924$	−1.42639e6	−0.0549616
$925$	−2.53779e6	−0.0975217
$926$	−2.58996e7	−0.992580
$927$	−1.33829e7	−0.511504
$928$	4.54827e7	1.73371
$929$	3.70288e7	1.40767	0.703834	−	0.710364i	$-0.251470\pi$
$929$	3.70288e7	1.40767	0.703834	+	0.710364i	$0.251470\pi$
$930$	−4.45490e6	−0.168900
$931$	−5.34505e6	−0.202105
$932$	−1.50759e7	−0.568518
$933$	−1.83675e7	−0.690790
$934$	1.97080e7	0.739224
$935$	606038.	0.0226710
$936$	182648.	0.00681438
$937$	1.22598e7	0.456180	0.228090	−	0.973640i	$-0.426752\pi$
$937$	1.22598e7	0.456180	0.228090	+	0.973640i	$0.426752\pi$
$938$	−1.22385e7	−0.454173
$939$	−1.56546e7	−0.579399
$940$	−468215.	−0.0172833
$941$	−1.25646e7	−0.462565	−0.231283	−	0.972887i	$-0.574292\pi$
$941$	−1.25646e7	−0.462565	−0.231283	+	0.972887i	$0.574292\pi$
$942$	1.31377e7	0.482384
$943$	730335.	0.0267450
$944$	−2.11868e6	−0.0773812
$945$	717628.	0.0261409
$946$	1.18073e7	0.428964
$947$	3.16122e7	1.14546	0.572730	−	0.819744i	$-0.305884\pi$
$947$	3.16122e7	1.14546	0.572730	+	0.819744i	$0.305884\pi$
$948$	1.06797e7	0.385957
$949$	8.77237e6	0.316192
$950$	−1.76894e6	−0.0635924
$951$	960334.	0.0344327
$952$	−80576.6	−0.00288148
$953$	−2.84509e7	−1.01476	−0.507380	−	0.861722i	$-0.669386\pi$
$953$	−2.84509e7	−1.01476	−0.507380	+	0.861722i	$0.669386\pi$
$954$	2.43445e7	0.866024
$955$	1.24199e7	0.440665
$956$	4.20419e7	1.48778
$957$	5.99673e6	0.211658
$958$	−3.79038e7	−1.33435
$959$	−770395.	−0.0270500
$960$	7.94344e6	0.278183
$961$	−2.26225e7	−0.790190
$962$	−7.24174e6	−0.252293
$963$	−1.06533e6	−0.0370186
$964$	4.46905e6	0.154890
$965$	−6.78405e6	−0.234515
$966$	3.96543e6	0.136725
$967$	−4.73439e7	−1.62816	−0.814081	−	0.580751i	$-0.802759\pi$
$967$	−4.73439e7	−1.62816	−0.814081	+	0.580751i	$0.802759\pi$
$968$	−149545.	−0.00512961
$969$	−631704.	−0.0216124
$970$	−1.53824e6	−0.0524923
$971$	−4.33248e7	−1.47465	−0.737324	−	0.675539i	$-0.763911\pi$
$971$	−4.33248e7	−1.47465	−0.737324	+	0.675539i	$0.763911\pi$
$972$	1.96423e6	0.0666846
$973$	−5.21723e6	−0.176668
$974$	−4.63152e7	−1.56432
$975$	−1.24180e6	−0.0418350
$976$	3.92168e7	1.31780
$977$	−4.64678e7	−1.55745	−0.778727	−	0.627363i	$-0.784134\pi$
$977$	−4.64678e7	−1.55745	−0.778727	+	0.627363i	$0.784134\pi$
$978$	1.27998e7	0.427915
$979$	−4.57174e6	−0.152449
$980$	1.26875e7	0.421997
$981$	3.07564e6	0.102038
$982$	5.60553e6	0.185498
$983$	−1.02443e7	−0.338141	−0.169071	−	0.985604i	$-0.554077\pi$
$983$	−1.02443e7	−0.338141	−0.169071	+	0.985604i	$0.554077\pi$
$984$	−48471.7	−0.00159588
$985$	4.77430e6	0.156790
$986$	8.91250e6	0.291949
$987$	−199527.	−0.00651940
$988$	−2.57279e6	−0.0838517
$989$	−1.67303e7	−0.543892
$990$	1.97947e6	0.0641890
$991$	−6.52638e6	−0.211100	−0.105550	−	0.994414i	$-0.533660\pi$
$991$	−6.52638e6	−0.211100	−0.105550	+	0.994414i	$0.533660\pi$
$992$	−2.02431e7	−0.653127
$993$	1.39283e7	0.448256
$994$	−4.36608e6	−0.140161
$995$	−1.50659e7	−0.482434
$996$	−2.39502e7	−0.765000
$997$	1.08535e7	0.345804	0.172902	−	0.984939i	$-0.444686\pi$
$997$	1.08535e7	0.345804	0.172902	+	0.984939i	$0.444686\pi$
$998$	−9.94904e6	−0.316195
$999$	−2.96008e6	−0.0938403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.b.1.1	✓	3
3.2	odd	2		495.6.a.d.1.3		3
5.4	even	2		825.6.a.i.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.b.1.1	✓	3	1.1	even	1	trivial
495.6.a.d.1.3		3	3.2	odd	2
825.6.a.i.1.3		3	5.4	even	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q-8.07863 q^{2} +9.00000 q^{3} +33.2643 q^{4} -25.0000 q^{5} -72.7077 q^{6} -39.3760 q^{7} -10.2141 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-8.07863 q^{2} +9.00000 q^{3} +33.2643 q^{4} -25.0000 q^{5} -72.7077 q^{6} -39.3760 q^{7} -10.2141 q^{8} +81.0000 q^{9} +201.966 q^{10} +121.000 q^{11} +299.379 q^{12} -220.765 q^{13} +318.105 q^{14} -225.000 q^{15} -981.943 q^{16} -200.343 q^{17} -654.369 q^{18} +350.345 q^{19} -831.608 q^{20} -354.384 q^{21} -977.515 q^{22} +1385.09 q^{23} -91.9273 q^{24} +625.000 q^{25} +1783.48 q^{26} +729.000 q^{27} -1309.82 q^{28} +5506.64 q^{29} +1817.69 q^{30} -2450.86 q^{31} +8259.61 q^{32} +1089.00 q^{33} +1618.50 q^{34} +984.401 q^{35} +2694.41 q^{36} -4060.46 q^{37} -2830.31 q^{38} -1986.88 q^{39} +255.354 q^{40} +527.283 q^{41} +2862.94 q^{42} -12078.9 q^{43} +4024.99 q^{44} -2025.00 q^{45} -11189.6 q^{46} +563.023 q^{47} -8837.48 q^{48} -15256.5 q^{49} -5049.15 q^{50} -1803.09 q^{51} -7343.59 q^{52} -37203.0 q^{53} -5889.32 q^{54} -3025.00 q^{55} +402.192 q^{56} +3153.11 q^{57} -44486.2 q^{58} +2157.64 q^{59} -7484.48 q^{60} -39938.0 q^{61} +19799.6 q^{62} -3189.46 q^{63} -35304.2 q^{64} +5519.11 q^{65} -8797.63 q^{66} -38473.2 q^{67} -6664.29 q^{68} +12465.8 q^{69} -7952.62 q^{70} -13725.3 q^{71} -827.345 q^{72} -39736.3 q^{73} +32803.0 q^{74} +5625.00 q^{75} +11654.0 q^{76} -4764.50 q^{77} +16051.3 q^{78} +35672.9 q^{79} +24548.6 q^{80} +6561.00 q^{81} -4259.73 q^{82} -79999.7 q^{83} -11788.4 q^{84} +5008.58 q^{85} +97580.6 q^{86} +49559.8 q^{87} -1235.91 q^{88} -37783.0 q^{89} +16359.2 q^{90} +8692.83 q^{91} +46074.1 q^{92} -22057.7 q^{93} -4548.46 q^{94} -8758.63 q^{95} +74336.5 q^{96} -7616.35 q^{97} +123252. q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9	\( 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 252 q^{12} + 450 q^{13} - 1504 q^{14} - 675 q^{15} - 1360 q^{16} - 334 q^{17} - 162 q^{18} - 4036 q^{19} - 700 q^{20} - 2088 q^{21} - 242 q^{22} - 7060 q^{23} + 216 q^{24} + 1875 q^{25} + 2932 q^{26} + 2187 q^{27} - 8320 q^{28} + 4042 q^{29} + 450 q^{30} - 608 q^{31} - 3104 q^{32} + 3267 q^{33} - 3644 q^{34} + 5800 q^{35} + 2268 q^{36} + 2250 q^{37} - 12632 q^{38} + 4050 q^{39} - 600 q^{40} + 10654 q^{41} - 13536 q^{42} - 35528 q^{43} + 3388 q^{44} - 6075 q^{45} - 41800 q^{46} - 2100 q^{47} - 12240 q^{48} + 7667 q^{49} - 1250 q^{50} - 3006 q^{51} - 14520 q^{52} - 12826 q^{53} - 1458 q^{54} - 9075 q^{55} + 17088 q^{56} - 36324 q^{57} - 17196 q^{58} - 81876 q^{59} - 6300 q^{60} - 62298 q^{61} + 109184 q^{62} - 18792 q^{63} - 72256 q^{64} - 11250 q^{65} - 2178 q^{66} - 46148 q^{67} - 35832 q^{68} - 63540 q^{69} + 37600 q^{70} - 64724 q^{71} + 1944 q^{72} + 810 q^{73} - 44796 q^{74} + 16875 q^{75} + 44656 q^{76} - 28072 q^{77} + 26388 q^{78} + 43876 q^{79} + 34000 q^{80} + 19683 q^{81} + 56060 q^{82} - 101024 q^{83} - 74880 q^{84} + 8350 q^{85} + 24128 q^{86} + 36378 q^{87} + 2904 q^{88} + 60022 q^{89} + 4050 q^{90} - 28568 q^{91} + 38256 q^{92} - 5472 q^{93} + 74552 q^{94} + 100900 q^{95} - 27936 q^{96} - 319746 q^{97} + 431134 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 252 * q^12 + 450 * q^13 - 1504 * q^14 - 675 * q^15 - 1360 * q^16 - 334 * q^17 - 162 * q^18 - 4036 * q^19 - 700 * q^20 - 2088 * q^21 - 242 * q^22 - 7060 * q^23 + 216 * q^24 + 1875 * q^25 + 2932 * q^26 + 2187 * q^27 - 8320 * q^28 + 4042 * q^29 + 450 * q^30 - 608 * q^31 - 3104 * q^32 + 3267 * q^33 - 3644 * q^34 + 5800 * q^35 + 2268 * q^36 + 2250 * q^37 - 12632 * q^38 + 4050 * q^39 - 600 * q^40 + 10654 * q^41 - 13536 * q^42 - 35528 * q^43 + 3388 * q^44 - 6075 * q^45 - 41800 * q^46 - 2100 * q^47 - 12240 * q^48 + 7667 * q^49 - 1250 * q^50 - 3006 * q^51 - 14520 * q^52 - 12826 * q^53 - 1458 * q^54 - 9075 * q^55 + 17088 * q^56 - 36324 * q^57 - 17196 * q^58 - 81876 * q^59 - 6300 * q^60 - 62298 * q^61 + 109184 * q^62 - 18792 * q^63 - 72256 * q^64 - 11250 * q^65 - 2178 * q^66 - 46148 * q^67 - 35832 * q^68 - 63540 * q^69 + 37600 * q^70 - 64724 * q^71 + 1944 * q^72 + 810 * q^73 - 44796 * q^74 + 16875 * q^75 + 44656 * q^76 - 28072 * q^77 + 26388 * q^78 + 43876 * q^79 + 34000 * q^80 + 19683 * q^81 + 56060 * q^82 - 101024 * q^83 - 74880 * q^84 + 8350 * q^85 + 24128 * q^86 + 36378 * q^87 + 2904 * q^88 + 60022 * q^89 + 4050 * q^90 - 28568 * q^91 + 38256 * q^92 - 5472 * q^93 + 74552 * q^94 + 100900 * q^95 - 27936 * q^96 - 319746 * q^97 + 431134 * q^98 + 29403 * q^99

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