LMFDB - Embedded newform 165.6.c.b.34.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(34,165)]

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, 1, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.3
Character	$\chi$	$=$	165.34
Dual form			165.6.c.b.34.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.0460i q^{2} +9.00000i q^{3} -68.9227 q^{4} +(24.7608 - 50.1189i) q^{5} +90.4143 q^{6} +29.0524i q^{7} +370.927i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q-10.0460i q^{2} +9.00000i q^{3} -68.9227 q^{4} +(24.7608 - 50.1189i) q^{5} +90.4143 q^{6} +29.0524i q^{7} +370.927i q^{8} -81.0000 q^{9} +(-503.496 - 248.748i) q^{10} +121.000 q^{11} -620.305i q^{12} +1023.51i q^{13} +291.862 q^{14} +(451.070 + 222.848i) q^{15} +1520.82 q^{16} +1509.69i q^{17} +813.728i q^{18} -1643.04 q^{19} +(-1706.58 + 3454.33i) q^{20} -261.472 q^{21} -1215.57i q^{22} +1478.11i q^{23} -3338.34 q^{24} +(-1898.80 - 2481.97i) q^{25} +10282.2 q^{26} -729.000i q^{27} -2002.37i q^{28} +4572.33 q^{29} +(2238.73 - 4531.46i) q^{30} +7531.62 q^{31} -3408.50i q^{32} +1089.00i q^{33} +15166.4 q^{34} +(1456.07 + 719.362i) q^{35} +5582.74 q^{36} -4408.40i q^{37} +16506.0i q^{38} -9211.62 q^{39} +(18590.4 + 9184.46i) q^{40} +5629.62 q^{41} +2626.75i q^{42} -2283.11i q^{43} -8339.65 q^{44} +(-2005.63 + 4059.63i) q^{45} +14849.1 q^{46} -5980.48i q^{47} +13687.3i q^{48} +15963.0 q^{49} +(-24934.0 + 19075.4i) q^{50} -13587.2 q^{51} -70543.3i q^{52} +28498.0i q^{53} -7323.56 q^{54} +(2996.06 - 6064.38i) q^{55} -10776.3 q^{56} -14787.3i q^{57} -45933.7i q^{58} -25942.8 q^{59} +(-31089.0 - 15359.3i) q^{60} -51360.7 q^{61} -75662.8i q^{62} -2353.25i q^{63} +14424.2 q^{64} +(51297.3 + 25343.0i) q^{65} +10940.1 q^{66} +39180.2i q^{67} -104052. i q^{68} -13303.0 q^{69} +(7226.74 - 14627.8i) q^{70} +37560.3 q^{71} -30045.1i q^{72} +58687.6i q^{73} -44286.9 q^{74} +(22337.7 - 17089.2i) q^{75} +113242. q^{76} +3515.34i q^{77} +92540.2i q^{78} +8274.06 q^{79} +(37656.7 - 76221.5i) q^{80} +6561.00 q^{81} -56555.3i q^{82} -21355.4i q^{83} +18021.4 q^{84} +(75663.8 + 37381.1i) q^{85} -22936.2 q^{86} +41150.9i q^{87} +44882.1i q^{88} -78385.8 q^{89} +(40783.1 + 20148.6i) q^{90} -29735.5 q^{91} -101875. i q^{92} +67784.5i q^{93} -60080.1 q^{94} +(-40682.9 + 82347.1i) q^{95} +30676.5 q^{96} -64574.7i q^{97} -160364. i q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	10.0460i		−	1.77590i	−0.459936	−	0.887952i	$-0.652128\pi$
$2$		−	10.0460i		−	1.77590i	0.459936	−	0.887952i	$-0.347872\pi$
$3$			9.00000i			0.577350i
$3$			9.00000i			0.577350i
$4$	−68.9227			−2.15384
$5$	24.7608	−	50.1189i	0.442935	−	0.896554i
$5$	24.7608	−	50.1189i	0.442935	−	0.896554i
$6$	90.4143			1.02532
$7$			29.0524i			0.224098i	0.993703	+	0.112049i	$0.0357413\pi$
$7$			29.0524i			0.224098i	−0.993703	+	0.112049i	$0.964259\pi$
$8$			370.927i			2.04910i
$9$	−81.0000			−0.333333
$10$	−503.496	−	248.748i	−1.59219	−	0.786611i
$11$	121.000			0.301511
$11$	121.000			0.301511
$12$		−	620.305i		−	1.24352i
$13$			1023.51i			1.67971i	0.542809	+	0.839856i	$0.317361\pi$
$13$			1023.51i			1.67971i	−0.542809	+	0.839856i	$0.682639\pi$
$14$	291.862			0.397976
$15$	451.070	+	222.848i	0.517625	+	0.255729i
$16$	1520.82			1.48517
$17$			1509.69i			1.26696i	0.773757	+	0.633482i	$0.218375\pi$
$17$			1509.69i			1.26696i	−0.773757	+	0.633482i	$0.781625\pi$
$18$			813.728i			0.591968i
$19$	−1643.04			−1.04415			−0.522075	−	0.852900i	$-0.674842\pi$
$19$	−1643.04			−1.04415			−0.522075	+	0.852900i	$0.674842\pi$
$20$	−1706.58	+	3454.33i	−0.954010	+	1.93103i
$21$	−261.472			−0.129383
$22$		−	1215.57i		−	0.535455i
$23$			1478.11i			0.582622i	0.956628	+	0.291311i	$0.0940915\pi$
$23$			1478.11i			0.582622i	−0.956628	+	0.291311i	$0.905908\pi$
$24$	−3338.34			−1.18305
$25$	−1898.80	−	2481.97i	−0.607616	−	0.794231i
$26$	10282.2			2.98301
$27$		−	729.000i		−	0.192450i
$28$		−	2002.37i		−	0.482669i
$29$	4572.33			1.00958			0.504792	−	0.863241i	$-0.331569\pi$
$29$	4572.33			1.00958			0.504792	+	0.863241i	$0.331569\pi$
$30$	2238.73	−	4531.46i	0.454150	−	0.919253i
$31$	7531.62			1.40762			0.703808	−	0.710391i	$-0.251482\pi$
$31$	7531.62			1.40762			0.703808	+	0.710391i	$0.251482\pi$
$32$		−	3408.50i		−	0.588421i
$33$			1089.00i			0.174078i
$34$	15166.4			2.25001
$35$	1456.07	+	719.362i	0.200916	+	0.0992608i
$36$	5582.74			0.717945
$37$		−	4408.40i		−	0.529391i	−0.964332	−	0.264695i	$-0.914729\pi$
$37$		−	4408.40i		−	0.529391i	0.964332	−	0.264695i	$-0.0852714\pi$
$38$			16506.0i			1.85431i
$39$	−9211.62			−0.969783
$40$	18590.4	+	9184.46i	1.83713	+	0.907619i
$41$	5629.62			0.523021			0.261511	−	0.965201i	$-0.415779\pi$
$41$	5629.62			0.523021			0.261511	+	0.965201i	$0.415779\pi$
$42$			2626.75i			0.229771i
$43$		−	2283.11i		−	0.188302i	−0.995558	−	0.0941510i	$-0.969986\pi$
$43$		−	2283.11i		−	0.188302i	0.995558	−	0.0941510i	$-0.0300137\pi$
$44$	−8339.65			−0.649406
$45$	−2005.63	+	4059.63i	−0.147645	+	0.298851i
$46$	14849.1			1.03468
$47$		−	5980.48i		−	0.394904i	−0.980313	−	0.197452i	$-0.936733\pi$
$47$		−	5980.48i		−	0.394904i	0.980313	−	0.197452i	$-0.0632667\pi$
$48$			13687.3i			0.857464i
$49$	15963.0			0.949780
$50$	−24934.0	+	19075.4i	−1.41048	+	1.07907i
$51$	−13587.2			−0.731482
$52$		−	70543.3i		−	3.61782i
$53$			28498.0i			1.39356i	0.717287	+	0.696778i	$0.245384\pi$
$53$			28498.0i			1.39356i	−0.717287	+	0.696778i	$0.754616\pi$
$54$	−7323.56			−0.341773
$55$	2996.06	−	6064.38i	0.133550	−	0.270321i
$56$	−10776.3			−0.459199
$57$		−	14787.3i		−	0.602840i
$58$		−	45933.7i		−	1.79292i
$59$	−25942.8			−0.970258			−0.485129	−	0.874443i	$-0.661227\pi$
$59$	−25942.8			−0.970258			−0.485129	+	0.874443i	$0.661227\pi$
$60$	−31089.0	−	15359.3i	−1.11488	−	0.550798i
$61$	−51360.7			−1.76728			−0.883642	−	0.468163i	$-0.844916\pi$
$61$	−51360.7			−1.76728			−0.883642	+	0.468163i	$0.844916\pi$
$62$		−	75662.8i		−	2.49979i
$63$		−	2353.25i		−	0.0746992i
$64$	14424.2			0.440193
$65$	51297.3	+	25343.0i	1.50595	+	0.744004i
$66$	10940.1			0.309145
$67$			39180.2i			1.06630i	0.846020	+	0.533151i	$0.178992\pi$
$67$			39180.2i			1.06630i	−0.846020	+	0.533151i	$0.821008\pi$
$68$		−	104052.i		−	2.72883i
$69$	−13303.0			−0.336377
$70$	7226.74	−	14627.8i	0.176278	−	0.356807i
$71$	37560.3			0.884267			0.442133	−	0.896949i	$-0.354222\pi$
$71$	37560.3			0.884267			0.442133	+	0.896949i	$0.354222\pi$
$72$		−	30045.1i		−	0.683034i
$73$			58687.6i			1.28896i	0.764621	+	0.644480i	$0.222926\pi$
$73$			58687.6i			1.28896i	−0.764621	+	0.644480i	$0.777074\pi$
$74$	−44286.9			−0.940147
$75$	22337.7	−	17089.2i	0.458549	−	0.350808i
$76$	113242.			2.24893
$77$			3515.34i			0.0675680i
$78$			92540.2i			1.72224i
$79$	8274.06			0.149160			0.0745798	−	0.997215i	$-0.476238\pi$
$79$	8274.06			0.149160			0.0745798	+	0.997215i	$0.476238\pi$
$80$	37656.7	−	76221.5i	0.657835	−	1.33154i
$81$	6561.00			0.111111
$82$		−	56555.3i		−	0.928836i
$83$		−	21355.4i		−	0.340261i	−0.985422	−	0.170130i	$-0.945581\pi$
$83$		−	21355.4i		−	0.340261i	0.985422	−	0.170130i	$-0.0544188\pi$
$84$	18021.4			0.278669
$85$	75663.8	+	37381.1i	1.13590	+	0.561183i
$86$	−22936.2			−0.334406
$87$			41150.9i			0.582883i
$88$			44882.1i			0.617827i
$89$	−78385.8			−1.04897			−0.524484	−	0.851420i	$-0.675742\pi$
$89$	−78385.8			−1.04897			−0.524484	+	0.851420i	$0.675742\pi$
$90$	40783.1	+	20148.6i	0.530731	+	0.262204i
$91$	−29735.5			−0.376420
$92$		−	101875.i		−	1.25487i
$93$			67784.5i			0.812687i
$94$	−60080.1			−0.701312
$95$	−40682.9	+	82347.1i	−0.462491	+	0.936136i
$96$	30676.5			0.339725
$97$		−	64574.7i		−	0.696840i	−0.937339	−	0.348420i	$-0.886718\pi$
$97$		−	64574.7i		−	0.696840i	0.937339	−	0.348420i	$-0.113282\pi$
$98$		−	160364.i		−	1.68672i
$99$	−9801.00			−0.100504
$100$	130871.	+	171064.i	1.30871	+	1.71064i
$101$	48364.4			0.471762			0.235881	−	0.971782i	$-0.424203\pi$
$101$	48364.4			0.471762			0.235881	+	0.971782i	$0.424203\pi$
$102$			136497.i			1.29904i
$103$			121923.i			1.13238i	0.824273	+	0.566192i	$0.191584\pi$
$103$			121923.i			1.13238i	−0.824273	+	0.566192i	$0.808416\pi$
$104$	−379648.			−3.44190
$105$	−6474.26	+	13104.7i	−0.0573082	+	0.115999i
$106$	286291.			2.47482
$107$			191883.i			1.62023i	0.586269	+	0.810117i	$0.300596\pi$
$107$			191883.i			1.62023i	−0.586269	+	0.810117i	$0.699404\pi$
$108$			50244.7i			0.414506i
$109$	15660.0			0.126248			0.0631240	−	0.998006i	$-0.479894\pi$
$109$	15660.0			0.126248			0.0631240	+	0.998006i	$0.479894\pi$
$110$	−60923.0	−	30098.5i	−0.480064	−	0.237172i
$111$	39675.6			0.305644
$112$			44183.4i			0.332823i
$113$		−	15119.6i		−	0.111389i	−0.998448	−	0.0556947i	$-0.982263\pi$
$113$		−	15119.6i		−	0.111389i	0.998448	−	0.0556947i	$-0.0177374\pi$
$114$	−148554.			−1.07059
$115$	74081.2	+	36599.3i	0.522352	+	0.258064i
$116$	−315137.			−2.17448
$117$		−	82904.6i		−	0.559904i
$118$			260622.i			1.72309i
$119$	−43860.0			−0.283924
$120$	−82660.2	+	167314.i	−0.524014	+	1.06067i
$121$	14641.0			0.0909091
$122$			515971.i			3.13853i
$123$			50666.6i			0.301966i
$124$	−519099.			−3.03177
$125$	−171409.	+	33710.1i	−0.981205	+	0.192968i
$126$	−23640.8			−0.132659
$127$			223751.i			1.23099i	0.788140	+	0.615496i	$0.211044\pi$
$127$			223751.i			1.23099i	−0.788140	+	0.615496i	$0.788956\pi$
$128$		−	253978.i		−	1.37016i
$129$	20548.0			0.108716
$130$	254597.	−	515334.i	1.32128	−	2.67443i
$131$	269255.			1.37084			0.685418	−	0.728149i	$-0.259619\pi$
$131$	269255.			1.37084			0.685418	+	0.728149i	$0.259619\pi$
$132$		−	75056.9i		−	0.374935i
$133$		−	47734.1i		−	0.233991i
$134$	393606.			1.89365
$135$	−36536.7	−	18050.7i	−0.172542	−	0.0852430i
$136$	−559983.			−2.59614
$137$		−	172187.i		−	0.783790i	−0.920010	−	0.391895i	$-0.871820\pi$
$137$		−	172187.i		−	0.783790i	0.920010	−	0.391895i	$-0.128180\pi$
$138$			133642.i			0.597374i
$139$	350209.			1.53741			0.768707	−	0.639601i	$-0.220901\pi$
$139$	350209.			1.53741			0.768707	+	0.639601i	$0.220901\pi$
$140$	−100357.	−	49580.4i	−0.432739	−	0.213791i
$141$	53824.4			0.227998
$142$		−	377332.i		−	1.57037i
$143$			123845.i			0.506452i
$144$	−123186.			−0.495057
$145$	113215.	−	229160.i	0.447180	−	0.905146i
$146$	589578.			2.28907
$147$			143667.i			0.548356i
$148$			303839.i			1.14022i
$149$	−519184.			−1.91582			−0.957912	−	0.287062i	$-0.907322\pi$
$149$	−519184.			−1.91582			−0.957912	+	0.287062i	$0.907322\pi$
$150$	−171679.	−	224406.i	−0.623000	−	0.814340i
$151$	−230203.			−0.821617			−0.410808	−	0.911722i	$-0.634753\pi$
$151$	−230203.			−0.821617			−0.410808	+	0.911722i	$0.634753\pi$
$152$		−	609446.i		−	2.13957i
$153$		−	122285.i		−	0.422321i
$154$	35315.2			0.119994
$155$	186489.	−	377476.i	0.623483	−	1.26200i
$156$	634890.			2.08875
$157$			328864.i			1.06480i	0.846494	+	0.532399i	$0.178709\pi$
$157$			328864.i			1.06480i	−0.846494	+	0.532399i	$0.821291\pi$
$158$		−	83121.5i		−	0.264893i
$159$	−256482.			−0.804569
$160$	−170830.	−	84397.2i	−0.527551	−	0.260632i
$161$	−42942.7			−0.130564
$162$		−	65912.0i		−	0.197323i
$163$		−	246382.i		−	0.726341i	−0.931723	−	0.363171i	$-0.881694\pi$
$163$		−	246382.i		−	0.726341i	0.931723	−	0.363171i	$-0.118306\pi$
$164$	−388009.			−1.12650
$165$	54579.4	+	26964.6i	0.156070	+	0.0771052i
$166$	−214537.			−0.604270
$167$			581413.i			1.61322i	0.591084	+	0.806610i	$0.298700\pi$
$167$			581413.i			1.61322i	−0.591084	+	0.806610i	$0.701300\pi$
$168$		−	96986.9i		−	0.265118i
$169$	−676286.			−1.82143
$170$	375532.	−	760120.i	0.996608	−	2.01725i
$171$	133086.			0.348050
$172$			157358.i			0.405572i
$173$		−	264650.i		−	0.672290i	−0.941810	−	0.336145i	$-0.890877\pi$
$173$		−	264650.i		−	0.672290i	0.941810	−	0.336145i	$-0.109123\pi$
$174$	413404.			1.03515
$175$	72107.3	−	55164.8i	0.177985	−	0.136165i
$176$	184019.			0.447796
$177$		−	233485.i		−	0.560179i
$178$			787466.i			1.86287i
$179$	13886.5			0.0323937			0.0161969	−	0.999869i	$-0.494844\pi$
$179$	13886.5			0.0323937			0.0161969	+	0.999869i	$0.494844\pi$
$180$	138233.	−	279801.i	0.318003	−	0.643676i
$181$	−752593.			−1.70751			−0.853756	−	0.520673i	$-0.825681\pi$
$181$	−752593.			−1.70751			−0.853756	+	0.520673i	$0.825681\pi$
$182$			298724.i			0.668485i
$183$		−	462246.i		−	1.02034i
$184$	−548271.			−1.19385
$185$	−220944.	−	109156.i	−0.474627	−	0.234486i
$186$	680966.			1.44325
$187$			182672.i			0.382004i
$188$			412191.i			0.850558i
$189$	21179.2			0.0431276
$190$	827261.	+	408702.i	1.66249	+	0.821340i
$191$	−25416.1			−0.0504110			−0.0252055	−	0.999682i	$-0.508024\pi$
$191$	−25416.1			−0.0504110			−0.0252055	+	0.999682i	$0.508024\pi$
$192$			129818.i			0.254145i
$193$		−	489822.i		−	0.946553i	−0.880914	−	0.473277i	$-0.843071\pi$
$193$		−	489822.i		−	0.946553i	0.880914	−	0.473277i	$-0.156929\pi$
$194$	−648719.			−1.23752
$195$	−228087.	+	461676.i	−0.429551	+	0.869462i
$196$	−1.10021e6			−2.04567
$197$			324827.i			0.596329i	0.954515	+	0.298164i	$0.0963744\pi$
$197$			324827.i			0.596329i	−0.954515	+	0.298164i	$0.903626\pi$
$198$			98461.1i			0.178485i
$199$	398516.			0.713368			0.356684	−	0.934225i	$-0.383907\pi$
$199$	398516.			0.713368			0.356684	+	0.934225i	$0.383907\pi$
$200$	920630.	−	704316.i	1.62746	−	1.24507i
$201$	−352622.			−0.615629
$202$		−	485870.i		−	0.837803i
$203$			132837.i			0.226245i
$204$	936465.			1.57549
$205$	139394.	−	282150.i	0.231665	−	0.468917i
$206$	1.22485e6			2.01101
$207$		−	119727.i		−	0.194207i
$208$			1.55657e6i			2.49466i
$209$	−198807.			−0.314823
$210$	131650.	+	65040.6i	0.206002	+	0.101774i
$211$	−868645.			−1.34319			−0.671593	−	0.740920i	$-0.734390\pi$
$211$	−868645.			−1.34319			−0.671593	+	0.740920i	$0.734390\pi$
$212$		−	1.96416e6i		−	3.00149i
$213$			338043.i			0.510532i
$214$	1.92766e6			2.87738
$215$	−114427.	−	56531.6i	−0.168823	−	0.0834057i
$216$	270406.			0.394350
$217$			218812.i			0.315443i
$218$		−	157320.i		−	0.224204i
$219$	−528189.			−0.744181
$220$	−206497.	+	417974.i	−0.287645	+	0.582227i
$221$	−1.54518e6			−2.12814
$222$		−	398582.i		−	0.542794i
$223$		−	48571.9i		−	0.0654068i	−0.999465	−	0.0327034i	$-0.989588\pi$
$223$		−	48571.9i		−	0.0654068i	0.999465	−	0.0327034i	$-0.0104117\pi$
$224$	99025.1			0.131864
$225$	153803.	+	201040.i	0.202539	+	0.264744i
$226$	−151892.			−0.197817
$227$		−	78669.6i		−	0.101331i	−0.998716	−	0.0506655i	$-0.983866\pi$
$227$		−	78669.6i		−	0.101331i	0.998716	−	0.0506655i	$-0.0161342\pi$
$228$			1.01918e6i			1.29842i
$229$	324090.			0.408391			0.204196	−	0.978930i	$-0.434542\pi$
$229$	324090.			0.408391			0.204196	+	0.978930i	$0.434542\pi$
$230$	367677.	−	744222.i	0.458297	−	0.927647i
$231$	−31638.1			−0.0390104
$232$			1.69600e6i			2.06874i
$233$			1.26828e6i			1.53048i	0.643747	+	0.765238i	$0.277379\pi$
$233$			1.26828e6i			1.53048i	−0.643747	+	0.765238i	$0.722621\pi$
$234$	−832862.			−0.994336
$235$	−299735.	−	148082.i	−0.354053	−	0.174917i
$236$	1.78805e6			2.08978
$237$			74466.6i			0.0861173i
$238$			440619.i			0.504221i
$239$	1.35381e6			1.53307			0.766535	−	0.642202i	$-0.221979\pi$
$239$	1.35381e6			1.53307			0.766535	+	0.642202i	$0.221979\pi$
$240$	685994.	+	338910.i	0.768762	+	0.379801i
$241$	1.14198e6			1.26653			0.633264	−	0.773936i	$-0.281715\pi$
$241$	1.14198e6			1.26653			0.633264	+	0.773936i	$0.281715\pi$
$242$		−	147084.i		−	0.161446i
$243$			59049.0i			0.0641500i
$244$	3.53992e6			3.80644
$245$	395256.	−	800045.i	0.420691	−	0.851529i
$246$	508998.			0.536264
$247$		−	1.68167e6i		−	1.75387i
$248$			2.79368e6i			2.88434i
$249$	192198.			0.196449
$250$	338653.	+	1.72198e6i	0.342692	+	1.74253i
$251$	−321578.			−0.322183			−0.161091	−	0.986940i	$-0.551501\pi$
$251$	−321578.			−0.322183			−0.161091	+	0.986940i	$0.551501\pi$
$252$			162192.i			0.160890i
$253$			178851.i			0.175667i
$254$	2.24781e6			2.18612
$255$	−336430.	+	680974.i	−0.323999	+	0.655813i
$256$	−2.08990e6			−1.99308
$257$		−	1.44275e6i		−	1.36257i	−0.732018	−	0.681286i	$-0.761421\pi$
$257$		−	1.44275e6i		−	1.36257i	0.732018	−	0.681286i	$-0.238579\pi$
$258$		−	206425.i		−	0.193070i
$259$	128075.			0.118635
$260$	−3.53555e6	−	1.74671e6i	−3.24357	−	1.60246i
$261$	−370359.			−0.336528
$262$		−	2.70495e6i		−	2.43447i
$263$			838618.i			0.747610i	0.927507	+	0.373805i	$0.121947\pi$
$263$			838618.i			0.747610i	−0.927507	+	0.373805i	$0.878053\pi$
$264$	−403939.			−0.356703
$265$	1.42829e6	+	705634.i	1.24940	+	0.617255i
$266$	−479539.			−0.415546
$267$		−	705472.i		−	0.605622i
$268$		−	2.70041e6i		−	2.29664i
$269$	415262.			0.349898			0.174949	−	0.984577i	$-0.444024\pi$
$269$	415262.			0.349898			0.174949	+	0.984577i	$0.444024\pi$
$270$	−181337.	+	367048.i	−0.151383	+	0.306418i
$271$	647209.			0.535330			0.267665	−	0.963512i	$-0.413748\pi$
$271$	647209.			0.535330			0.267665	+	0.963512i	$0.413748\pi$
$272$			2.29595e6i			1.88166i
$273$		−	267620.i		−	0.217326i
$274$	−1.72980e6			−1.39193
$275$	−229755.	−	300318.i	−0.183203	−	0.239470i
$276$	916878.			0.724501
$277$		−	679011.i		−	0.531713i	−0.964013	−	0.265856i	$-0.914345\pi$
$277$		−	679011.i		−	0.531713i	0.964013	−	0.265856i	$-0.0856547\pi$
$278$		−	3.51821e6i		−	2.73030i
$279$	−610061.			−0.469205
$280$	−266831.	+	540097.i	−0.203395	+	0.411696i
$281$	−1.78685e6			−1.34997			−0.674983	−	0.737834i	$-0.735849\pi$
$281$	−1.78685e6			−1.34997			−0.674983	+	0.737834i	$0.735849\pi$
$282$		−	540721.i		−	0.404903i
$283$		−	872555.i		−	0.647630i	−0.946120	−	0.323815i	$-0.895034\pi$
$283$		−	872555.i		−	0.647630i	0.946120	−	0.323815i	$-0.104966\pi$
$284$	−2.58876e6			−1.90457
$285$	−741123.	−	366146.i	−0.540478	−	0.267019i
$286$	1.24415e6			0.899411
$287$			163554.i			0.117208i
$288$			276088.i			0.196140i
$289$	−859295.			−0.605198
$290$	−2.30215e6	−	1.13736e6i	−1.60745	−	0.794149i
$291$	581172.			0.402321
$292$		−	4.04491e6i		−	2.77621i
$293$			653130.i			0.444458i	0.974995	+	0.222229i	$0.0713332\pi$
$293$			653130.i			0.444458i	−0.974995	+	0.222229i	$0.928667\pi$
$294$	1.44328e6			0.973827
$295$	−642366.	+	1.30023e6i	−0.429762	+	0.869888i
$296$	1.63519e6			1.08477
$297$		−	88209.0i		−	0.0580259i
$298$			5.21574e6i			3.40232i
$299$	−1.51286e6			−0.978638
$300$	−1.53958e6	+	1.17784e6i	−0.987640	+	0.755582i
$301$	66329.8			0.0421980
$302$			2.31263e6i			1.45911i
$303$			435280.i			0.272372i
$304$	−2.49875e6			−1.55074
$305$	−1.27173e6	+	2.57414e6i	−0.782793	+	1.58447i
$306$	−1.22847e6			−0.750002
$307$			1.87392e6i			1.13476i	0.823456	+	0.567381i	$0.192043\pi$
$307$			1.87392e6i			1.13476i	−0.823456	+	0.567381i	$0.807957\pi$
$308$		−	242287.i		−	0.145530i
$309$	−1.09731e6			−0.653783
$310$	−3.79214e6	−	1.87348e6i	−2.24119	−	1.10725i
$311$	−1.60626e6			−0.941705			−0.470853	−	0.882212i	$-0.656054\pi$
$311$	−1.60626e6			−0.941705			−0.470853	+	0.882212i	$0.656054\pi$
$312$		−	3.41684e6i		−	1.98718i
$313$		−	2.58202e6i		−	1.48970i	−0.667234	−	0.744849i	$-0.732522\pi$
$313$		−	2.58202e6i		−	1.48970i	0.667234	−	0.744849i	$-0.267478\pi$
$314$	3.30377e6			1.89098
$315$	−117942.	−	58268.4i	−0.0669718	−	0.0330869i
$316$	−570271.			−0.321265
$317$			1.34588e6i			0.752242i	0.926571	+	0.376121i	$0.122742\pi$
$317$			1.34588e6i			0.752242i	−0.926571	+	0.376121i	$0.877258\pi$
$318$			2.57662e6i			1.42884i
$319$	553252.			0.304401
$320$	357156.	−	722926.i	0.194977	−	0.394656i
$321$	−1.72695e6			−0.935442
$322$			431403.i			0.231870i
$323$		−	2.48047e6i		−	1.32290i
$324$	−452202.			−0.239315
$325$	2.54033e6	−	1.94345e6i	1.33408	−	1.02062i
$326$	−2.47516e6			−1.28991
$327$			140940.i			0.0728893i
$328$			2.08818e6i			1.07172i
$329$	173748.			0.0884971
$330$	270887.	−	548307.i	0.136931	−	0.277165i
$331$	2.74357e6			1.37641			0.688203	−	0.725518i	$-0.258400\pi$
$331$	2.74357e6			1.37641			0.688203	+	0.725518i	$0.258400\pi$
$332$			1.47187e6i			0.732865i
$333$			357080.i			0.176464i
$334$	5.84089e6			2.86492
$335$	1.96367e6	+	970135.i	0.955996	+	0.472303i
$336$	−397650.			−0.192156
$337$		−	3.70365e6i		−	1.77646i	−0.459400	−	0.888229i	$-0.651936\pi$
$337$		−	3.70365e6i		−	1.77646i	0.459400	−	0.888229i	$-0.348064\pi$
$338$			6.79399e6i			3.23469i
$339$	136076.			0.0643107
$340$	−5.21495e6	−	2.57641e6i	−2.44654	−	1.20870i
$341$	911325.			0.424412
$342$		−	1.33698e6i		−	0.618103i
$343$			952047.i			0.436941i
$344$	846866.			0.385850
$345$	−329393.	+	666731.i	−0.148993	+	0.301580i
$346$	−2.65868e6			−1.19392
$347$			1.17221e6i			0.522616i	0.965255	+	0.261308i	$0.0841539\pi$
$347$			1.17221e6i			0.522616i	−0.965255	+	0.261308i	$0.915846\pi$
$348$		−	2.83624e6i		−	1.25543i
$349$	360082.			0.158248			0.0791240	−	0.996865i	$-0.474788\pi$
$349$	360082.			0.158248			0.0791240	+	0.996865i	$0.474788\pi$
$350$	−554187.	−	724392.i	−0.241817	−	0.316085i
$351$	746141.			0.323261
$352$		−	412428.i		−	0.177415i
$353$			998723.i			0.426588i	0.976988	+	0.213294i	$0.0684192\pi$
$353$			998723.i			0.426588i	−0.976988	+	0.213294i	$0.931581\pi$
$354$	−2.34560e6			−0.994824
$355$	930025.	−	1.88248e6i	0.391673	−	0.792793i
$356$	5.40256e6			2.25930
$357$		−	394740.i		−	0.163923i
$358$		−	139504.i		−	0.0575282i
$359$	−1.47706e6			−0.604871			−0.302436	−	0.953170i	$-0.597800\pi$
$359$	−1.47706e6			−0.604871			−0.302436	+	0.953170i	$0.597800\pi$
$360$	−1.50583e6	−	743941.i	−0.612376	−	0.302540i
$361$	223465.			0.0902489
$362$			7.56057e6i			3.03238i
$363$			131769.i			0.0524864i
$364$	2.04945e6			0.810746
$365$	2.94136e6	+	1.45316e6i	1.15562	+	0.570926i
$366$	−4.64374e6			−1.81203
$367$		−	3.21905e6i		−	1.24756i	−0.781599	−	0.623781i	$-0.785596\pi$
$367$		−	3.21905e6i		−	1.24756i	0.781599	−	0.623781i	$-0.214404\pi$
$368$			2.24793e6i			0.865294i
$369$	−455999.			−0.174340
$370$	−1.09658e6	+	2.21961e6i	−0.416424	+	0.842892i
$371$	−827935.			−0.312292
$372$		−	4.67190e6i		−	1.75039i
$373$		−	4.65790e6i		−	1.73348i	−0.498762	−	0.866739i	$-0.666212\pi$
$373$		−	4.65790e6i		−	1.73348i	0.498762	−	0.866739i	$-0.333788\pi$
$374$	1.83513e6			0.678403
$375$	−303391.	−	1.54269e6i	−0.111410	−	0.566499i
$376$	2.21832e6			0.809198
$377$			4.67984e6i			1.69581i
$378$		−	212767.i		−	0.0765905i
$379$	4.04644e6			1.44702			0.723510	−	0.690314i	$-0.242528\pi$
$379$	4.04644e6			1.44702			0.723510	+	0.690314i	$0.242528\pi$
$380$	2.80398e6	−	5.67558e6i	0.996129	−	2.01628i
$381$	−2.01376e6			−0.710714
$382$			255331.i			0.0895252i
$383$			824148.i			0.287084i	0.989644	+	0.143542i	$0.0458491\pi$
$383$			824148.i			0.287084i	−0.989644	+	0.143542i	$0.954151\pi$
$384$	2.28580e6			0.791062
$385$	176185.	+	87042.9i	0.0605783	+	0.0299283i
$386$	−4.92077e6			−1.68099
$387$			184932.i			0.0627674i
$388$			4.45066e6i			1.50088i
$389$	2.54462e6			0.852607			0.426303	−	0.904580i	$-0.359816\pi$
$389$	2.54462e6			0.852607			0.426303	+	0.904580i	$0.359816\pi$
$390$	4.63801e6	+	2.29137e6i	1.54408	+	0.762841i
$391$	−2.23148e6			−0.738162
$392$			5.92109e6i			1.94620i
$393$			2.42330e6i			0.791453i
$394$	3.26322e6			1.05902
$395$	204873.	−	414687.i	0.0660681	−	0.133730i
$396$	675512.			0.216469
$397$			5.17776e6i			1.64879i	0.566015	+	0.824395i	$0.308484\pi$
$397$			5.17776e6i			1.64879i	−0.566015	+	0.824395i	$0.691516\pi$
$398$		−	4.00351e6i		−	1.26687i
$399$	429607.			0.135095
$400$	−2.88773e6	−	3.77462e6i	−0.902414	−	1.17957i
$401$	−4.82239e6			−1.49762			−0.748809	−	0.662785i	$-0.769374\pi$
$401$	−4.82239e6			−1.49762			−0.748809	+	0.662785i	$0.769374\pi$
$402$			3.54245e6i			1.09330i
$403$			7.70871e6i			2.36439i
$404$	−3.33341e6			−1.01610
$405$	162456.	−	328830.i	0.0492150	−	0.0996171i
$406$	1.33449e6			0.401790
$407$		−	533416.i		−	0.159617i
$408$		−	5.03985e6i		−	1.49888i
$409$	3.68626e6			1.08963			0.544813	−	0.838558i	$-0.316601\pi$
$409$	3.68626e6			1.08963			0.544813	+	0.838558i	$0.316601\pi$
$410$	−2.83449e6	−	1.40036e6i	−0.832751	−	0.411414i
$411$	1.54968e6			0.452521
$412$		−	8.40329e6i		−	2.43897i
$413$		−	753702.i		−	0.217433i
$414$	−1.20278e6			−0.344894
$415$	−1.07031e6	−	528777.i	−0.305062	−	0.150713i
$416$	3.48864e6			0.988377
$417$			3.15188e6i			0.887626i
$418$			1.99722e6i			0.559095i
$419$	−1.31904e6			−0.367049			−0.183525	−	0.983015i	$-0.558751\pi$
$419$	−1.31904e6			−0.367049			−0.183525	+	0.983015i	$0.558751\pi$
$420$	446224.	−	903210.i	0.123432	−	0.249842i
$421$	−3.29518e6			−0.906095			−0.453048	−	0.891486i	$-0.649663\pi$
$421$	−3.29518e6			−0.906095			−0.453048	+	0.891486i	$0.649663\pi$
$422$			8.72643e6i			2.38537i
$423$			484419.i			0.131635i
$424$	−1.05707e7			−2.85553
$425$	3.74700e6	−	2.86659e6i	1.00626	−	0.769828i
$426$	3.39599e6			0.906655
$427$		−	1.49215e6i		−	0.396044i
$428$		−	1.32251e7i		−	3.48972i
$429$	−1.11461e6			−0.292400
$430$	−567919.	+	1.14953e6i	−0.148120	+	0.299813i
$431$	1.87137e6			0.485251			0.242625	−	0.970120i	$-0.421991\pi$
$431$	1.87137e6			0.485251			0.242625	+	0.970120i	$0.421991\pi$
$432$		−	1.10867e6i		−	0.285821i
$433$			4.31194e6i			1.10523i	0.833437	+	0.552615i	$0.186370\pi$
$433$			4.31194e6i			1.10523i	−0.833437	+	0.552615i	$0.813630\pi$
$434$	2.19819e6			0.560197
$435$	2.06244e6	+	1.01893e6i	0.522586	+	0.258180i
$436$	−1.07933e6			−0.271917
$437$		−	2.42859e6i		−	0.608345i
$438$			5.30620e6i			1.32159i
$439$	−1.13612e6			−0.281360			−0.140680	−	0.990055i	$-0.544929\pi$
$439$	−1.13612e6			−0.281360			−0.140680	+	0.990055i	$0.544929\pi$
$440$	2.24944e6	+	1.11132e6i	0.553915	+	0.273658i
$441$	−1.29300e6			−0.316593
$442$			1.55230e7i			3.77936i
$443$		−	875875.i		−	0.212047i	−0.994364	−	0.106024i	$-0.966188\pi$
$443$		−	875875.i		−	0.212047i	0.994364	−	0.106024i	$-0.0338119\pi$
$444$	−2.73455e6			−0.658306
$445$	−1.94090e6	+	3.92860e6i	−0.464625	+	0.940456i
$446$	−487955.			−0.116156
$447$		−	4.67266e6i		−	1.10610i
$448$			419059.i			0.0986461i
$449$	−4.08806e6			−0.956977			−0.478489	−	0.878094i	$-0.658815\pi$
$449$	−4.08806e6			−0.956977			−0.478489	+	0.878094i	$0.658815\pi$
$450$	2.01965e6	−	1.54511e6i	0.470159	−	0.359689i
$451$	681184.			0.157697
$452$			1.04208e6i			0.239915i
$453$		−	2.07183e6i		−	0.474361i
$454$	−790317.			−0.179954
$455$	−736277.	+	1.49031e6i	−0.166730	+	0.337480i
$456$	5.48501e6			1.23528
$457$		−	2.85279e6i		−	0.638968i	−0.947592	−	0.319484i	$-0.896490\pi$
$457$		−	2.85279e6i		−	0.638968i	0.947592	−	0.319484i	$-0.103510\pi$
$458$		−	3.25581e6i		−	0.725263i
$459$	1.10056e6			0.243827
$460$	−5.10588e6	−	2.52252e6i	−1.12506	−	0.555828i
$461$	6.16387e6			1.35083			0.675416	−	0.737437i	$-0.263964\pi$
$461$	6.16387e6			1.35083			0.675416	+	0.737437i	$0.263964\pi$
$462$			317837.i			0.0692787i
$463$		−	4.52412e6i		−	0.980804i	−0.871496	−	0.490402i	$-0.836850\pi$
$463$		−	4.52412e6i		−	0.980804i	0.871496	−	0.490402i	$-0.163150\pi$
$464$	6.95366e6			1.49940
$465$	3.39728e6	+	1.67840e6i	0.728617	+	0.359968i
$466$	1.27412e7			2.71798
$467$		−	2.23084e6i		−	0.473344i	−0.971590	−	0.236672i	$-0.923943\pi$
$467$		−	2.23084e6i		−	0.473344i	0.971590	−	0.236672i	$-0.0760567\pi$
$468$			5.71401e6i			1.20594i
$469$	−1.13828e6			−0.238956
$470$	−1.48763e6	+	3.01115e6i	−0.310636	+	0.628764i
$471$	−2.95977e6			−0.614761
$472$		−	9.62289e6i		−	1.98816i
$473$		−	276256.i		−	0.0567752i
$474$	748093.			0.152936
$475$	3.11980e6	+	4.07796e6i	0.634443	+	0.829296i
$476$	3.02295e6			0.611525
$477$		−	2.30834e6i		−	0.464518i
$478$		−	1.36004e7i		−	2.72259i
$479$	6.62215e6			1.31874			0.659372	−	0.751817i	$-0.270822\pi$
$479$	6.62215e6			1.31874			0.659372	+	0.751817i	$0.270822\pi$
$480$	759575.	−	1.53747e6i	0.150476	−	0.304581i
$481$	4.51205e6			0.889224
$482$		−	1.14723e7i		−	2.24923i
$483$		−	386484.i		−	0.0753813i
$484$	−1.00910e6			−0.195803
$485$	−3.23641e6	−	1.59892e6i	−0.624754	−	0.308655i
$486$	593208.			0.113924
$487$		−	2.17583e6i		−	0.415721i	−0.978158	−	0.207860i	$-0.933350\pi$
$487$		−	2.17583e6i		−	0.415721i	0.978158	−	0.207860i	$-0.0666500\pi$
$488$		−	1.90511e7i		−	3.62134i
$489$	2.21744e6			0.419353
$490$	−8.03728e6	−	3.97076e6i	−1.51223	−	0.747107i
$491$	7.67198e6			1.43616			0.718081	−	0.695959i	$-0.245021\pi$
$491$	7.67198e6			1.43616			0.718081	+	0.695959i	$0.245021\pi$
$492$		−	3.49208e6i		−	0.650386i
$493$			6.90278e6i			1.27911i
$494$	−1.68941e7			−3.11471
$495$	−242681.	+	491215.i	−0.0445167	+	0.0901070i
$496$	1.14542e7			2.09055
$497$			1.09122e6i			0.198162i
$498$		−	1.93083e6i		−	0.348875i
$499$	−6.65009e6			−1.19557			−0.597787	−	0.801655i	$-0.703953\pi$
$499$	−6.65009e6			−1.19557			−0.597787	+	0.801655i	$0.703953\pi$
$500$	1.18140e7	−	2.32339e6i	2.11335	−	0.415621i
$501$	−5.23272e6			−0.931393
$502$			3.23058e6i			0.572165i
$503$			4.18197e6i			0.736989i	0.929630	+	0.368495i	$0.120127\pi$
$503$			4.18197e6i			0.736989i	−0.929630	+	0.368495i	$0.879873\pi$
$504$	872882.			0.153066
$505$	1.19754e6	−	2.42397e6i	0.208960	−	0.422959i
$506$	1.79675e6			0.311968
$507$		−	6.08657e6i		−	1.05161i
$508$		−	1.54215e7i		−	2.65135i
$509$	1.01322e7			1.73345			0.866725	−	0.498787i	$-0.166221\pi$
$509$	1.01322e7			1.73345			0.866725	+	0.498787i	$0.166221\pi$
$510$	6.84108e6	+	3.37978e6i	1.16466	+	0.575392i
$511$	−1.70502e6			−0.288853
$512$			1.28679e7i			2.16936i
$513$			1.19777e6i			0.200947i
$514$	−1.44939e7			−2.41980
$515$	6.11066e6	+	3.01893e6i	1.01524	+	0.501573i
$516$	−1.41622e6			−0.234157
$517$		−	723639.i		−	0.119068i
$518$		−	1.28664e6i		−	0.210685i
$519$	2.38185e6			0.388147
$520$	−9.40042e6	+	1.90275e7i	−1.52454	+	3.08585i
$521$	−6.42546e6			−1.03707			−0.518537	−	0.855055i	$-0.673523\pi$
$521$	−6.42546e6			−1.03707			−0.518537	+	0.855055i	$0.673523\pi$
$522$			3.72063e6i			0.597641i
$523$		−	1.17398e6i		−	0.187674i	−0.995588	−	0.0938372i	$-0.970087\pi$
$523$		−	1.17398e6i		−	0.187674i	0.995588	−	0.0938372i	$-0.0299133\pi$
$524$	−1.85578e7			−2.95256
$525$	496483.	+	648965.i	0.0786151	+	0.102760i
$526$	8.42478e6			1.32768
$527$			1.13704e7i			1.78340i
$528$			1.65617e6i			0.258535i
$529$	4.25153e6			0.660551
$530$	7.08882e6	−	1.43486e7i	1.09619	−	2.21881i
$531$	2.10137e6			0.323419
$532$			3.28997e6i			0.503979i
$533$			5.76199e6i			0.878525i
$534$	−7.08719e6			−1.07553
$535$	9.61697e6	+	4.75119e6i	1.45263	+	0.717659i
$536$	−1.45330e7			−2.18496
$537$			124979.i			0.0187025i
$538$		−	4.17174e6i		−	0.621386i
$539$	1.93152e6			0.286370
$540$	2.51821e6	+	1.24410e6i	0.371627	+	0.183599i
$541$	−5.25283e6			−0.771614			−0.385807	−	0.922580i	$-0.626077\pi$
$541$	−5.25283e6			−0.771614			−0.385807	+	0.922580i	$0.626077\pi$
$542$		−	6.50188e6i		−	0.950694i
$543$		−	6.77334e6i		−	0.985833i
$544$	5.14576e6			0.745508
$545$	387754.	−	784860.i	0.0559197	−	0.113188i
$546$	−2.68852e6			−0.385950
$547$		−	1.13849e7i		−	1.62689i	−0.581640	−	0.813447i	$-0.697589\pi$
$547$		−	1.13849e7i		−	1.62689i	0.581640	−	0.813447i	$-0.302411\pi$
$548$			1.18676e7i			1.68815i
$549$	4.16022e6			0.589095
$550$	−3.01701e6	+	2.30813e6i	−0.425275	+	0.325351i
$551$	−7.51249e6			−1.05416
$552$		−	4.93444e6i		−	0.689271i
$553$			240382.i			0.0334263i
$554$	−6.82136e6			−0.944271
$555$	982400.	−	1.98849e6i	0.135380	−	0.274026i
$556$	−2.41374e7			−3.31134
$557$		−	4.54355e6i		−	0.620522i	−0.950651	−	0.310261i	$-0.899584\pi$
$557$		−	4.54355e6i		−	0.620522i	0.950651	−	0.310261i	$-0.100416\pi$
$558$			6.12869e6i			0.833263i
$559$	2.33679e6			0.316293
$560$	2.21442e6	+	1.09402e6i	0.298394	+	0.147419i
$561$	−1.64405e6			−0.220550
$562$			1.79508e7i			2.39741i
$563$		−	1.22077e7i		−	1.62317i	−0.584237	−	0.811583i	$-0.698606\pi$
$563$		−	1.22077e7i		−	1.62317i	0.584237	−	0.811583i	$-0.301394\pi$
$564$	−3.70972e6			−0.491070
$565$	−757777.	−	374374.i	−0.0998666	−	0.0493383i
$566$	−8.76572e6			−1.15013
$567$			190613.i			0.0248997i
$568$			1.39321e7i			1.81195i
$569$	1.58948e6			0.205814			0.102907	−	0.994691i	$-0.467186\pi$
$569$	1.58948e6			0.205814			0.102907	+	0.994691i	$0.467186\pi$
$570$	−3.67832e6	+	7.44535e6i	−0.474201	+	0.959838i
$571$	−692853.			−0.0889306			−0.0444653	−	0.999011i	$-0.514158\pi$
$571$	−692853.			−0.0889306			−0.0444653	+	0.999011i	$0.514158\pi$
$572$		−	8.53574e6i		−	1.09082i
$573$		−	228745.i		−	0.0291048i
$574$	1.64307e6			0.208150
$575$	3.66863e6	−	2.80664e6i	0.462737	−	0.354011i
$576$	−1.16836e6			−0.146731
$577$		−	1.24815e7i		−	1.56073i	−0.625324	−	0.780365i	$-0.715033\pi$
$577$		−	1.24815e7i		−	1.56073i	0.625324	−	0.780365i	$-0.284967\pi$
$578$			8.63250e6i			1.07477i
$579$	4.40840e6			0.546493
$580$	−7.80306e6	+	1.57943e7i	−0.963153	+	1.94954i
$581$	620425.			0.0762516
$582$		−	5.83847e6i		−	0.714483i
$583$			3.44825e6i			0.420173i
$584$	−2.17688e7			−2.64121
$585$	−4.15508e6	−	2.05279e6i	−0.501984	−	0.248001i
$586$	6.56136e6			0.789314
$587$			9.13291e6i			1.09399i	0.837135	+	0.546996i	$0.184229\pi$
$587$			9.13291e6i			1.09399i	−0.837135	+	0.546996i	$0.815771\pi$
$588$		−	9.90189e6i		−	1.18107i
$589$	−1.23747e7			−1.46976
$590$	1.30621e7	+	6.45323e6i	1.54484	+	0.763216i
$591$	−2.92344e6			−0.344291
$592$		−	6.70436e6i		−	0.786236i
$593$			1.08272e7i			1.26438i	0.774813	+	0.632191i	$0.217844\pi$
$593$			1.08272e7i			1.26438i	−0.774813	+	0.632191i	$0.782156\pi$
$594$	−886150.			−0.103048
$595$	−1.08601e6	+	2.19822e6i	−0.125760	+	0.254553i
$596$	3.57836e7			4.12637
$597$			3.58665e6i			0.411863i
$598$			1.51983e7i			1.73797i
$599$	−7.47502e6			−0.851227			−0.425614	−	0.904905i	$-0.639942\pi$
$599$	−7.47502e6			−0.851227			−0.425614	+	0.904905i	$0.639942\pi$
$600$	6.33885e6	+	8.28567e6i	0.718840	+	0.939614i
$601$	−1.02516e6			−0.115772			−0.0578861	−	0.998323i	$-0.518436\pi$
$601$	−1.02516e6			−0.115772			−0.0578861	+	0.998323i	$0.518436\pi$
$602$		−	666351.i		−	0.0749397i
$603$		−	3.17360e6i		−	0.355434i
$604$	1.58662e7			1.76963
$605$	362524.	−	733790.i	0.0402669	−	0.0815049i
$606$	4.37283e6			0.483706
$607$		−	1.33264e7i		−	1.46805i	−0.679123	−	0.734024i	$-0.737640\pi$
$607$		−	1.33264e7i		−	1.46805i	0.679123	−	0.734024i	$-0.262360\pi$
$608$			5.60028e6i			0.614399i
$609$	−1.19553e6			−0.130623
$610$	2.58599e7	+	1.27759e7i	2.81386	+	1.39017i
$611$	6.12110e6			0.663325
$612$			8.42819e6i			0.909611i
$613$		−	1.57435e7i		−	1.69220i	−0.533027	−	0.846098i	$-0.678946\pi$
$613$		−	1.57435e7i		−	1.69220i	0.533027	−	0.846098i	$-0.321054\pi$
$614$	1.88254e7			2.01523
$615$	2.53935e6	+	1.25455e6i	0.270729	+	0.133752i
$616$	−1.30394e6			−0.138454
$617$			5.87960e6i			0.621777i	0.950446	+	0.310888i	$0.100627\pi$
$617$			5.87960e6i			0.621777i	−0.950446	+	0.310888i	$0.899373\pi$
$618$			1.10236e7i			1.16106i
$619$	1.81138e6			0.190013			0.0950063	−	0.995477i	$-0.469713\pi$
$619$	1.81138e6			0.190013			0.0950063	+	0.995477i	$0.469713\pi$
$620$	−1.28533e7	+	2.60167e7i	−1.34288	+	2.71814i
$621$	1.07754e6			0.112126
$622$			1.61365e7i			1.67238i
$623$		−	2.27730e6i		−	0.235071i
$624$	−1.40092e7			−1.44029
$625$	−2.55473e6	+	9.42554e6i	−0.261605	+	0.965175i
$626$	−2.59390e7			−2.64556
$627$		−	1.78927e6i		−	0.181763i
$628$		−	2.26662e7i		−	2.29340i
$629$	6.65529e6			0.670719
$630$	−585366.	+	1.18485e6i	−0.0587592	+	0.118936i
$631$	−1.43835e7			−1.43811			−0.719054	−	0.694954i	$-0.755425\pi$
$631$	−1.43835e7			−1.43811			−0.719054	+	0.694954i	$0.755425\pi$
$632$			3.06907e6i			0.305643i
$633$		−	7.81780e6i		−	0.775489i
$634$	1.35207e7			1.33591
$635$	1.12141e7	+	5.54026e6i	1.10365	+	0.545250i
$636$	1.76774e7			1.73291
$637$			1.63383e7i			1.59536i
$638$		−	5.55798e6i		−	0.540587i
$639$	−3.04239e6			−0.294756
$640$	−1.27291e7	−	6.28871e6i	−1.22842	−	0.606893i
$641$	−3.80867e6			−0.366124			−0.183062	−	0.983101i	$-0.558601\pi$
$641$	−3.80867e6			−0.366124			−0.183062	+	0.983101i	$0.558601\pi$
$642$			1.73490e7i			1.66126i
$643$			483920.i			0.0461579i	0.999734	+	0.0230789i	$0.00734691\pi$
$643$			483920.i			0.0461579i	−0.999734	+	0.0230789i	$0.992653\pi$
$644$	2.95973e6			0.281214
$645$	508785.	−	1.02984e6i	0.0481543	−	0.0974699i
$646$	−2.49188e7			−2.34934
$647$		−	1.80652e7i		−	1.69661i	−0.529506	−	0.848306i	$-0.677623\pi$
$647$		−	1.80652e7i		−	1.69661i	0.529506	−	0.848306i	$-0.322377\pi$
$648$			2.43365e6i			0.227678i
$649$	−3.13908e6			−0.292544
$650$	−1.95239e7	−	2.55202e7i	−1.81252	−	2.36920i
$651$	−1.96931e6			−0.182121
$652$			1.69813e7i			1.56442i
$653$			2.03744e7i			1.86983i	0.354871	+	0.934915i	$0.384525\pi$
$653$			2.03744e7i			1.86983i	−0.354871	+	0.934915i	$0.615475\pi$
$654$	1.41588e6			0.129444
$655$	6.66698e6	−	1.34948e7i	0.607192	−	1.22903i
$656$	8.56161e6			0.776776
$657$		−	4.75370e6i		−	0.429653i
$658$		−	1.74547e6i		−	0.157162i
$659$	1.37586e7			1.23413			0.617066	−	0.786912i	$-0.288321\pi$
$659$	1.37586e7			1.23413			0.617066	+	0.786912i	$0.288321\pi$
$660$	−3.76176e6	−	1.85847e6i	−0.336149	−	0.166072i
$661$	−1.34803e7			−1.20004			−0.600019	−	0.799985i	$-0.704840\pi$
$661$	−1.34803e7			−1.20004			−0.600019	+	0.799985i	$0.704840\pi$
$662$		−	2.75620e7i		−	2.44437i
$663$		−	1.39066e7i		−	1.22868i
$664$	7.92127e6			0.697228
$665$	−2.39238e6	−	1.18194e6i	−0.209786	−	0.103643i
$666$	3.58724e6			0.313382
$667$			6.75840e6i			0.588206i
$668$		−	4.00726e7i		−	3.47461i
$669$	437147.			0.0377627
$670$	9.74601e6	−	1.97271e7i	0.838764	−	1.69776i
$671$	−6.21465e6			−0.532856
$672$			891226.i			0.0761315i
$673$		−	680925.i		−	0.0579511i	−0.999580	−	0.0289755i	$-0.990776\pi$
$673$		−	680925.i		−	0.0579511i	0.999580	−	0.0289755i	$-0.00922449\pi$
$674$	−3.72070e7			−3.15482
$675$	−1.80936e6	+	1.38423e6i	−0.152850	+	0.116936i
$676$	4.66115e7			3.92307
$677$		−	1.36705e7i		−	1.14634i	−0.819436	−	0.573171i	$-0.805713\pi$
$677$		−	1.36705e7i		−	1.14634i	0.819436	−	0.573171i	$-0.194287\pi$
$678$		−	1.36703e6i		−	0.114210i
$679$	1.87605e6			0.156160
$680$	−1.38657e7	+	2.80657e7i	−1.14992	+	2.32758i
$681$	708026.			0.0585034
$682$		−	9.15520e6i		−	0.753715i
$683$			6.79648e6i			0.557484i	0.960366	+	0.278742i	$0.0899174\pi$
$683$			6.79648e6i			0.557484i	−0.960366	+	0.278742i	$0.910083\pi$
$684$	−9.17264e6			−0.749642
$685$	−8.62983e6	−	4.26350e6i	−0.702709	−	0.347168i
$686$	9.56429e6			0.775966
$687$			2.91681e6i			0.235785i
$688$		−	3.47218e6i		−	0.279661i
$689$	−2.91680e7			−2.34077
$690$	6.69800e6	+	3.30909e6i	0.535577	+	0.264598i
$691$	9.11491e6			0.726202			0.363101	−	0.931750i	$-0.381718\pi$
$691$	9.11491e6			0.726202			0.363101	+	0.931750i	$0.381718\pi$
$692$			1.82404e7i			1.44800i
$693$		−	284743.i		−	0.0225227i
$694$	1.17761e7			0.928116
$695$	8.67148e6	−	1.75521e7i	0.680975	−	1.37837i
$696$	−1.52640e7			−1.19439
$697$			8.49896e6i			0.662649i
$698$		−	3.61740e6i		−	0.281033i
$699$	−1.14146e7			−0.883621
$700$	−4.96983e6	+	3.80211e6i	−0.383351	+	0.293278i
$701$	−1.03729e7			−0.797269			−0.398634	−	0.917110i	$-0.630516\pi$
$701$	−1.03729e7			−0.797269			−0.398634	+	0.917110i	$0.630516\pi$
$702$		−	7.49575e6i		−	0.574080i
$703$			7.24315e6i			0.552763i
$704$	1.74533e6			0.132723
$705$	1.33274e6	−	2.69762e6i	0.100988	−	0.204412i
$706$	1.00332e7			0.757579
$707$			1.40510e6i			0.105721i
$708$			1.60925e7i			1.20653i
$709$	−1.78828e7			−1.33604			−0.668022	−	0.744142i	$-0.732859\pi$
$709$	−1.78828e7			−1.33604			−0.668022	+	0.744142i	$0.732859\pi$
$710$	−1.89115e7	−	9.34306e6i	−1.40792	−	0.695574i
$711$	−670199.			−0.0497199
$712$		−	2.90754e7i		−	2.14944i
$713$			1.11326e7i			0.820108i
$714$	−3.96557e6			−0.291112
$715$	6.20697e6	+	3.06651e6i	0.454062	+	0.224326i
$716$	−957097.			−0.0697708
$717$			1.21843e7i			0.885119i
$718$			1.48386e7i			1.07419i
$719$	2.62904e7			1.89660			0.948298	−	0.317382i	$-0.102804\pi$
$719$	2.62904e7			1.89660			0.948298	+	0.317382i	$0.102804\pi$
$720$	−3.05019e6	+	6.17394e6i	−0.219278	+	0.443845i
$721$	−3.54217e6			−0.253765
$722$		−	2.24494e6i		−	0.160273i
$723$			1.02778e7i			0.731231i
$724$	5.18708e7			3.67770
$725$	−8.68194e6	−	1.13484e7i	−0.613440	−	0.801842i
$726$	1.32376e6			0.0932108
$727$		−	1.40763e7i		−	0.987763i	−0.869529	−	0.493882i	$-0.835578\pi$
$727$		−	1.40763e7i		−	0.987763i	0.869529	−	0.493882i	$-0.164422\pi$
$728$		−	1.10297e7i		−	0.771322i
$729$	−531441.			−0.0370370
$730$	1.45984e7	−	2.95490e7i	1.01391	−	2.05227i
$731$	3.44677e6			0.238572
$732$			3.18593e7i			2.19765i
$733$		−	5.60463e6i		−	0.385290i	−0.981269	−	0.192645i	$-0.938293\pi$
$733$		−	5.60463e6i		−	0.385290i	0.981269	−	0.192645i	$-0.0617065\pi$
$734$	−3.23387e7			−2.21555
$735$	7.20041e6	+	3.55731e6i	0.491630	+	0.242886i
$736$	5.03813e6			0.342827
$737$			4.74081e6i			0.321502i
$738$			4.58098e6i			0.309612i
$739$	1.92933e6			0.129956			0.0649778	−	0.997887i	$-0.479302\pi$
$739$	1.92933e6			0.129956			0.0649778	+	0.997887i	$0.479302\pi$
$740$	1.52280e7	+	7.52330e6i	1.02227	+	0.505044i
$741$	1.51350e7			1.01260
$742$			8.31746e6i			0.554601i
$743$		−	4.43790e6i		−	0.294921i	−0.989068	−	0.147460i	$-0.952890\pi$
$743$		−	4.43790e6i		−	0.294921i	0.989068	−	0.147460i	$-0.0471099\pi$
$744$	−2.51431e7			−1.66528
$745$	−1.28554e7	+	2.60209e7i	−0.848586	+	1.71764i
$746$	−4.67934e7			−3.07849
$747$			1.72978e6i			0.113420i
$748$		−	1.25903e7i		−	0.822774i
$749$	−5.57467e6			−0.363090
$750$	−1.54979e7	+	3.04787e6i	−1.00605	+	0.197853i
$751$	−1.11577e7			−0.721897			−0.360949	−	0.932586i	$-0.617547\pi$
$751$	−1.11577e7			−0.721897			−0.360949	+	0.932586i	$0.617547\pi$
$752$		−	9.09521e6i		−	0.586500i
$753$		−	2.89420e6i		−	0.186012i
$754$	4.70138e7			3.01160
$755$	−5.70003e6	+	1.15375e7i	−0.363923	+	0.736623i
$756$	−1.45973e6			−0.0928898
$757$		−	1.16077e7i		−	0.736216i	−0.929783	−	0.368108i	$-0.880006\pi$
$757$		−	1.16077e7i		−	0.736216i	0.929783	−	0.368108i	$-0.119994\pi$
$758$		−	4.06506e7i		−	2.56977i
$759$	−1.60966e6			−0.101422
$760$	−3.05447e7	−	1.50904e7i	−1.91824	−	0.947691i
$761$	−1.38952e6			−0.0869770			−0.0434885	−	0.999054i	$-0.513847\pi$
$761$	−1.38952e6			−0.0869770			−0.0434885	+	0.999054i	$0.513847\pi$
$762$			2.02303e7i			1.26216i
$763$			454960.i			0.0282919i
$764$	1.75175e6			0.108577
$765$	−6.12876e6	−	3.02787e6i	−0.378634	−	0.187061i
$766$	8.27942e6			0.509833
$767$		−	2.65528e7i		−	1.62975i
$768$		−	1.88091e7i		−	1.15071i
$769$	2.19019e7			1.33557			0.667784	−	0.744355i	$-0.267243\pi$
$769$	2.19019e7			1.33557			0.667784	+	0.744355i	$0.267243\pi$
$770$	874435.	−	1.76996e6i	0.0531497	−	0.107581i
$771$	1.29848e7			0.786681
$772$			3.37599e7i			2.03872i
$773$		−	9.21665e6i		−	0.554784i	−0.960757	−	0.277392i	$-0.910530\pi$
$773$		−	9.21665e6i		−	0.554784i	0.960757	−	0.277392i	$-0.0894701\pi$
$774$	1.85783e6			0.111469
$775$	−1.43010e7	−	1.86932e7i	−0.855290	−	1.11797i
$776$	2.39525e7			1.42789
$777$			1.15267e6i			0.0684941i
$778$		−	2.55633e7i		−	1.51415i
$779$	−9.24966e6			−0.546113
$780$	1.57204e7	−	3.18200e7i	0.925182	−	1.87268i
$781$	4.54480e6			0.266617
$782$			2.24175e7i			1.31090i
$783$		−	3.33323e6i		−	0.194294i
$784$	2.42767e7			1.41059
$785$	1.64823e7	+	8.14294e6i	0.954648	+	0.471636i
$786$	2.43445e7			1.40554
$787$			2.18581e7i			1.25798i	0.777412	+	0.628992i	$0.216532\pi$
$787$			2.18581e7i			1.25798i	−0.777412	+	0.628992i	$0.783468\pi$
$788$		−	2.23879e7i		−	1.28439i
$789$	−7.54756e6			−0.431633
$790$	−4.16595e6	−	2.05816e6i	−0.237491	−	0.117331i
$791$	439261.			0.0249621
$792$		−	3.63545e6i		−	0.205942i
$793$		−	5.25684e7i		−	2.96853i
$794$	5.20159e7			2.92809
$795$	−6.35070e6	+	1.28546e7i	−0.356372	+	0.721340i
$796$	−2.74668e7			−1.53648
$797$		−	2.79333e7i		−	1.55767i	−0.627226	−	0.778837i	$-0.715810\pi$
$797$		−	2.79333e7i		−	1.55767i	0.627226	−	0.778837i	$-0.284190\pi$
$798$		−	4.31585e6i		−	0.239916i
$799$	9.02865e6			0.500329
$800$	−8.45979e6	+	6.47206e6i	−0.467342	+	0.357534i
$801$	6.34925e6			0.349656
$802$			4.84459e7i			2.65963i
$803$			7.10120e6i			0.388636i
$804$	2.43037e7			1.32596
$805$	−1.06330e6	+	2.15224e6i	−0.0578316	+	0.117058i
$806$	7.74419e7			4.19893
$807$			3.73736e6i			0.202014i
$808$			1.79397e7i			0.966687i
$809$	−1.07778e7			−0.578974			−0.289487	−	0.957182i	$-0.593485\pi$
$809$	−1.07778e7			−0.578974			−0.289487	+	0.957182i	$0.593485\pi$
$810$	−3.30343e6	−	1.63204e6i	−0.176910	−	0.0874012i
$811$	−2.71394e7			−1.44893			−0.724467	−	0.689309i	$-0.757914\pi$
$811$	−2.71394e7			−1.44893			−0.724467	+	0.689309i	$0.757914\pi$
$812$		−	9.15550e6i		−	0.487295i
$813$			5.82488e6i			0.309073i
$814$	−5.35871e6			−0.283465
$815$	−1.23484e7	−	6.10064e6i	−0.651204	−	0.321722i
$816$	−2.06636e7			−1.08638
$817$			3.75122e6i			0.196616i
$818$		−	3.70322e7i		−	1.93507i
$819$	2.40858e6			0.125473
$820$	−9.60742e6	+	1.94466e7i	−0.498968	+	1.00997i
$821$	6.84095e6			0.354208			0.177104	−	0.984192i	$-0.443327\pi$
$821$	6.84095e6			0.354208			0.177104	+	0.984192i	$0.443327\pi$
$822$		−	1.55682e7i		−	0.803634i
$823$			1.95930e7i			1.00833i	0.863609	+	0.504163i	$0.168199\pi$
$823$			1.95930e7i			1.00833i	−0.863609	+	0.504163i	$0.831801\pi$
$824$	−4.52247e7			−2.32037
$825$	2.70287e6	−	2.06779e6i	0.138258	−	0.105772i
$826$	−7.57171e6			−0.386139
$827$			1.86828e7i			0.949902i	0.880012	+	0.474951i	$0.157534\pi$
$827$			1.86828e7i			0.949902i	−0.880012	+	0.474951i	$0.842466\pi$
$828$			8.25191e6i			0.418291i
$829$	1.58057e7			0.798779			0.399390	−	0.916781i	$-0.369222\pi$
$829$	1.58057e7			0.798779			0.399390	+	0.916781i	$0.369222\pi$
$830$	−5.31211e6	+	1.07523e7i	−0.267653	+	0.541760i
$831$	6.11109e6			0.306985
$832$			1.47634e7i			0.739397i
$833$			2.40991e7i			1.20334i
$834$	3.16639e7			1.57634
$835$	2.91398e7	+	1.43963e7i	1.44634	+	0.714552i
$836$	1.37023e7			0.678077
$837$		−	5.49055e6i		−	0.270896i
$838$			1.32512e7i			0.651844i
$839$	3.69461e7			1.81202			0.906011	−	0.423255i	$-0.139112\pi$
$839$	3.69461e7			1.81202			0.906011	+	0.423255i	$0.139112\pi$
$840$	−4.86087e6	−	2.40148e6i	−0.237693	−	0.117430i
$841$	395030.			0.0192593
$842$			3.31035e7i			1.60914i
$843$		−	1.60817e7i		−	0.779403i
$844$	5.98694e7			2.89300
$845$	−1.67454e7	+	3.38947e7i	−0.806778	+	1.63301i
$846$	4.86649e6			0.233771
$847$			425357.i			0.0203725i
$848$			4.33401e7i			2.06967i
$849$	7.85300e6			0.373909
$850$	−2.87979e7	−	3.76424e7i	−1.36714	−	1.78702i
$851$	6.51609e6			0.308435
$852$		−	2.32988e7i		−	1.09960i
$853$			2.39478e7i			1.12692i	0.826144	+	0.563459i	$0.190530\pi$
$853$			2.39478e7i			1.12692i	−0.826144	+	0.563459i	$0.809470\pi$
$854$	−1.49902e7			−0.703337
$855$	3.29532e6	−	6.67011e6i	0.154164	−	0.312045i
$856$	−7.11746e7			−3.32002
$857$			4.09428e6i			0.190426i	0.995457	+	0.0952129i	$0.0303532\pi$
$857$			4.09428e6i			0.190426i	−0.995457	+	0.0952129i	$0.969647\pi$
$858$			1.11974e7i			0.519275i
$859$	6.51782e6			0.301384			0.150692	−	0.988581i	$-0.451850\pi$
$859$	6.51782e6			0.301384			0.150692	+	0.988581i	$0.451850\pi$
$860$	7.88660e6	+	3.89632e6i	0.363617	+	0.179642i
$861$	−1.47199e6			−0.0676700
$862$		−	1.87998e7i		−	0.861759i
$863$			8.54609e6i			0.390607i	0.980743	+	0.195304i	$0.0625693\pi$
$863$			8.54609e6i			0.390607i	−0.980743	+	0.195304i	$0.937431\pi$
$864$	−2.48479e6			−0.113242
$865$	−1.32639e7	−	6.55295e6i	−0.602744	−	0.297781i
$866$	4.33178e7			1.96278
$867$		−	7.73365e6i		−	0.349411i
$868$		−	1.50811e7i		−	0.679413i
$869$	1.00116e6			0.0449733
$870$	1.02362e7	−	2.07193e7i	0.458502	−	0.928063i
$871$	−4.01015e7			−1.79108
$872$			5.80870e6i			0.258695i
$873$			5.23055e6i			0.232280i
$874$	−2.43977e7			−1.08036
$875$	−979360.	−	4.97986e6i	−0.0432436	−	0.219886i
$876$	3.64042e7			1.60284
$877$			3.63188e7i			1.59453i	0.603629	+	0.797266i	$0.293721\pi$
$877$			3.63188e7i			1.59453i	−0.603629	+	0.797266i	$0.706279\pi$
$878$			1.14135e7i			0.499668i
$879$	−5.87817e6			−0.256608
$880$	4.55646e6	−	9.22281e6i	0.198345	−	0.401473i
$881$	1.57431e7			0.683364			0.341682	−	0.939816i	$-0.389004\pi$
$881$	1.57431e7			0.683364			0.341682	+	0.939816i	$0.389004\pi$
$882$			1.29895e7i			0.562240i
$883$			1.30059e7i			0.561354i	0.959802	+	0.280677i	$0.0905590\pi$
$883$			1.30059e7i			0.561354i	−0.959802	+	0.280677i	$0.909441\pi$
$884$	1.06498e8			4.58365
$885$	−1.17020e7	−	5.78130e6i	−0.502230	−	0.248123i
$886$	−8.79907e6			−0.376576
$887$			3.12186e7i			1.33231i	0.745814	+	0.666154i	$0.232061\pi$
$887$			3.12186e7i			1.33231i	−0.745814	+	0.666154i	$0.767939\pi$
$888$			1.47167e7i			0.626295i
$889$	−6.50050e6			−0.275862
$890$	3.94669e7	+	1.94983e7i	1.67016	+	0.825129i
$891$	793881.			0.0335013
$892$			3.34771e6i			0.140876i
$893$			9.82614e6i			0.412339i
$894$	−4.69416e7			−1.96433
$895$	343842.	−	695977.i	0.0143483	−	0.0290427i
$896$	7.37868e6			0.307050
$897$		−	1.36158e7i		−	0.565017i
$898$			4.10688e7i			1.69950i
$899$	3.44370e7			1.42111
$900$	−1.06005e7	−	1.38562e7i	−0.436235	−	0.570214i
$901$	−4.30230e7			−1.76558
$902$		−	6.84319e6i		−	0.280054i
$903$			596968.i			0.0243631i
$904$	5.60827e6			0.228248
$905$	−1.86348e7	+	3.77191e7i	−0.756318	+	1.53088i
$906$	−2.08137e7			−0.842419
$907$		−	3.59253e7i		−	1.45005i	−0.688725	−	0.725023i	$-0.741829\pi$
$907$		−	3.59253e7i		−	1.45005i	0.688725	−	0.725023i	$-0.258171\pi$
$908$			5.42212e6i			0.218250i
$909$	−3.91752e6			−0.157254
$910$	1.49717e7	+	7.39666e6i	0.599333	+	0.296096i
$911$	−1.47634e7			−0.589372			−0.294686	−	0.955594i	$-0.595215\pi$
$911$	−1.47634e7			−0.589372			−0.294686	+	0.955594i	$0.595215\pi$
$912$		−	2.24888e7i		−	0.895321i
$913$		−	2.58400e6i		−	0.102592i
$914$	−2.86592e7			−1.13475
$915$	−2.31673e7	−	1.14456e7i	−0.914791	−	0.451946i
$916$	−2.23371e7			−0.879607
$917$			7.82251e6i			0.307201i
$918$		−	1.10563e7i		−	0.433014i
$919$	1.26772e7			0.495146			0.247573	−	0.968869i	$-0.420367\pi$
$919$	1.26772e7			0.495146			0.247573	+	0.968869i	$0.420367\pi$
$920$	−1.35756e7	+	2.74787e7i	−0.528799	+	1.07035i
$921$	−1.68653e7			−0.655155
$922$		−	6.19224e7i		−	2.39895i
$923$			3.84435e7i			1.48531i
$924$	2.18058e6			0.0840220
$925$	−1.09415e7	+	8.37067e6i	−0.420458	+	0.321666i
$926$	−4.54495e7			−1.74181
$927$		−	9.87580e6i		−	0.377462i
$928$		−	1.55848e7i		−	0.594060i
$929$	−1.20341e7			−0.457482			−0.228741	−	0.973487i	$-0.573461\pi$
$929$	−1.20341e7			−0.457482			−0.228741	+	0.973487i	$0.573461\pi$
$930$	1.68613e7	−	3.41292e7i	0.639268	−	1.29395i
$931$	−2.62277e7			−0.991713
$932$		−	8.74136e7i		−	3.29639i
$933$		−	1.44563e7i		−	0.543694i
$934$	−2.24111e7			−0.840614
$935$	9.15531e6	+	4.52311e6i	0.342487	+	0.169203i
$936$	3.07515e7			1.14730
$937$			4.51344e7i			1.67942i	0.543038	+	0.839708i	$0.317274\pi$
$937$			4.51344e7i			1.67942i	−0.543038	+	0.839708i	$0.682726\pi$
$938$			1.14352e7i			0.424362i
$939$	2.32381e7			0.860077
$940$	2.06586e7	+	1.02062e7i	0.762571	+	0.376742i
$941$	8.44095e6			0.310754			0.155377	−	0.987855i	$-0.450341\pi$
$941$	8.44095e6			0.310754			0.155377	+	0.987855i	$0.450341\pi$
$942$			2.97340e7i			1.09176i
$943$			8.32120e6i			0.304724i
$944$	−3.94543e7			−1.44100
$945$	524415.	−	1.06148e6i	0.0191027	−	0.0386662i
$946$	−2.77528e6			−0.100827
$947$		−	2.68109e7i		−	0.971485i	−0.874102	−	0.485743i	$-0.838549\pi$
$947$		−	2.68109e7i		−	0.971485i	0.874102	−	0.485743i	$-0.161451\pi$
$948$		−	5.13244e6i		−	0.185483i
$949$	−6.00675e7			−2.16508
$950$	4.09674e7	−	3.13416e7i	1.47275	−	1.12671i
$951$	−1.21129e7			−0.434307
$952$		−	1.62689e7i		−	0.581788i
$953$			1.42183e7i			0.507127i	0.967319	+	0.253563i	$0.0816027\pi$
$953$			1.42183e7i			0.507127i	−0.967319	+	0.253563i	$0.918397\pi$
$954$	−2.31896e7			−0.824940
$955$	−629324.	+	1.27383e6i	−0.0223288	+	0.0451962i
$956$	−9.33081e7			−3.30198
$957$			4.97926e6i			0.175746i
$958$		−	6.65263e7i		−	2.34196i
$959$	5.00246e6			0.175645
$960$	6.50633e6	+	3.21440e6i	0.227855	+	0.112570i
$961$	2.80961e7			0.981380
$962$		−	4.53282e7i		−	1.57918i
$963$		−	1.55425e7i		−	0.540078i
$964$	−7.87082e7			−2.72789
$965$	−2.45493e7	−	1.21284e7i	−0.848636	−	0.419262i
$966$	−3.88263e6			−0.133870
$967$		−	277112.i		−	0.00952993i	−0.999989	−	0.00476496i	$-0.998483\pi$
$967$		−	277112.i		−	0.00952993i	0.999989	−	0.00476496i	$-0.00151674\pi$
$968$			5.43074e6i			0.186282i
$969$	2.23242e7			0.763777
$970$	−1.60628e7	+	3.25131e7i	−0.548142	+	1.10950i
$971$	7.77514e6			0.264643			0.132321	−	0.991207i	$-0.457757\pi$
$971$	7.77514e6			0.264643			0.132321	+	0.991207i	$0.457757\pi$
$972$		−	4.06982e6i		−	0.138169i
$973$			1.01744e7i			0.344531i
$974$	−2.18584e7			−0.738280
$975$	1.74910e7	+	2.28630e7i	0.589256	+	0.770231i
$976$	−7.81102e7			−2.62472
$977$		−	4.83351e6i		−	0.162004i	−0.996714	−	0.0810020i	$-0.974188\pi$
$977$		−	4.83351e6i		−	0.162004i	0.996714	−	0.0810020i	$-0.0258120\pi$
$978$		−	2.22765e7i		−	0.744731i
$979$	−9.48468e6			−0.316276
$980$	−2.72421e7	+	5.51413e7i	−0.906100	+	1.83405i
$981$	−1.26846e6			−0.0420827
$982$		−	7.70729e7i		−	2.55049i
$983$		−	9.75876e6i		−	0.322115i	−0.986945	−	0.161057i	$-0.948510\pi$
$983$		−	9.75876e6i		−	0.322115i	0.986945	−	0.161057i	$-0.0514904\pi$
$984$	−1.87936e7			−0.618760
$985$	1.62799e7	+	8.04298e6i	0.534641	+	0.264135i
$986$	6.93455e7			2.27157
$987$			1.56373e6i			0.0510938i
$988$			1.15905e8i			3.77755i
$989$	3.37468e6			0.109709
$990$	4.93476e6	+	2.43798e6i	0.160021	+	0.0790574i
$991$	2.72969e7			0.882935			0.441468	−	0.897277i	$-0.354458\pi$
$991$	2.72969e7			0.882935			0.441468	+	0.897277i	$0.354458\pi$
$992$		−	2.56715e7i		−	0.828270i
$993$			2.46922e7i			0.794668i
$994$	1.09624e7			0.351917
$995$	9.86760e6	−	1.99732e7i	0.315976	−	0.639572i
$996$	−1.32468e7			−0.423120
$997$		−	4.85951e7i		−	1.54830i	−0.633004	−	0.774149i	$-0.718178\pi$
$997$		−	4.85951e7i		−	1.54830i	0.633004	−	0.774149i	$-0.281822\pi$
$998$			6.68070e7i			2.12322i
$999$	−3.21372e6			−0.101881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.c.b.34.3	✓	26
5.2	odd	4		825.6.a.y.1.12		13
5.3	odd	4		825.6.a.v.1.2		13
5.4	even	2	inner	165.6.c.b.34.24	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.c.b.34.3	✓	26	1.1	even	1	trivial
165.6.c.b.34.24	yes	26	5.4	even	2	inner
825.6.a.v.1.2		13	5.3	odd	4
825.6.a.y.1.12		13	5.2	odd	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-10.0460i q^{2} +9.00000i q^{3} -68.9227 q^{4} +(24.7608 - 50.1189i) q^{5} +90.4143 q^{6} +29.0524i q^{7} +370.927i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q-10.0460i q^{2} +9.00000i q^{3} -68.9227 q^{4} +(24.7608 - 50.1189i) q^{5} +90.4143 q^{6} +29.0524i q^{7} +370.927i q^{8} -81.0000 q^{9} +(-503.496 - 248.748i) q^{10} +121.000 q^{11} -620.305i q^{12} +1023.51i q^{13} +291.862 q^{14} +(451.070 + 222.848i) q^{15} +1520.82 q^{16} +1509.69i q^{17} +813.728i q^{18} -1643.04 q^{19} +(-1706.58 + 3454.33i) q^{20} -261.472 q^{21} -1215.57i q^{22} +1478.11i q^{23} -3338.34 q^{24} +(-1898.80 - 2481.97i) q^{25} +10282.2 q^{26} -729.000i q^{27} -2002.37i q^{28} +4572.33 q^{29} +(2238.73 - 4531.46i) q^{30} +7531.62 q^{31} -3408.50i q^{32} +1089.00i q^{33} +15166.4 q^{34} +(1456.07 + 719.362i) q^{35} +5582.74 q^{36} -4408.40i q^{37} +16506.0i q^{38} -9211.62 q^{39} +(18590.4 + 9184.46i) q^{40} +5629.62 q^{41} +2626.75i q^{42} -2283.11i q^{43} -8339.65 q^{44} +(-2005.63 + 4059.63i) q^{45} +14849.1 q^{46} -5980.48i q^{47} +13687.3i q^{48} +15963.0 q^{49} +(-24934.0 + 19075.4i) q^{50} -13587.2 q^{51} -70543.3i q^{52} +28498.0i q^{53} -7323.56 q^{54} +(2996.06 - 6064.38i) q^{55} -10776.3 q^{56} -14787.3i q^{57} -45933.7i q^{58} -25942.8 q^{59} +(-31089.0 - 15359.3i) q^{60} -51360.7 q^{61} -75662.8i q^{62} -2353.25i q^{63} +14424.2 q^{64} +(51297.3 + 25343.0i) q^{65} +10940.1 q^{66} +39180.2i q^{67} -104052. i q^{68} -13303.0 q^{69} +(7226.74 - 14627.8i) q^{70} +37560.3 q^{71} -30045.1i q^{72} +58687.6i q^{73} -44286.9 q^{74} +(22337.7 - 17089.2i) q^{75} +113242. q^{76} +3515.34i q^{77} +92540.2i q^{78} +8274.06 q^{79} +(37656.7 - 76221.5i) q^{80} +6561.00 q^{81} -56555.3i q^{82} -21355.4i q^{83} +18021.4 q^{84} +(75663.8 + 37381.1i) q^{85} -22936.2 q^{86} +41150.9i q^{87} +44882.1i q^{88} -78385.8 q^{89} +(40783.1 + 20148.6i) q^{90} -29735.5 q^{91} -101875. i q^{92} +67784.5i q^{93} -60080.1 q^{94} +(-40682.9 + 82347.1i) q^{95} +30676.5 q^{96} -64574.7i q^{97} -160364. i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

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