LMFDB - Embedded newform 165.6.f.a.131.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(131,165)]

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([1, 0, 1]))

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

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

chi := DirichletCharacter("165.131");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.f (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:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.20
Character	$\chi$	$=$	165.131
Dual form			165.6.f.a.131.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.89239 q^{2} +(14.9703 - 4.34640i) q^{3} +15.5051 q^{4} +25.0000i q^{5} +(-103.181 + 29.9571i) q^{6} +243.497i q^{7} +113.689 q^{8} +(205.218 - 130.134i) q^{9} +O(q^{10})$	\(q-6.89239 q^{2} +(14.9703 - 4.34640i) q^{3} +15.5051 q^{4} +25.0000i q^{5} +(-103.181 + 29.9571i) q^{6} +243.497i q^{7} +113.689 q^{8} +(205.218 - 130.134i) q^{9} -172.310i q^{10} +(391.706 - 87.2784i) q^{11} +(232.116 - 67.3914i) q^{12} +971.892i q^{13} -1678.28i q^{14} +(108.660 + 374.257i) q^{15} -1279.76 q^{16} -1343.78 q^{17} +(-1414.44 + 896.932i) q^{18} -1492.36i q^{19} +387.628i q^{20} +(1058.33 + 3645.21i) q^{21} +(-2699.79 + 601.557i) q^{22} +858.534i q^{23} +(1701.96 - 494.139i) q^{24} -625.000 q^{25} -6698.66i q^{26} +(2506.55 - 2840.09i) q^{27} +3775.44i q^{28} -6758.09 q^{29} +(-748.928 - 2579.52i) q^{30} +8922.59 q^{31} +5182.52 q^{32} +(5484.59 - 3009.09i) q^{33} +9261.88 q^{34} -6087.42 q^{35} +(3181.92 - 2017.73i) q^{36} -7807.55 q^{37} +10285.9i q^{38} +(4224.23 + 14549.5i) q^{39} +2842.23i q^{40} +5464.06 q^{41} +(-7294.46 - 25124.2i) q^{42} -2141.27i q^{43} +(6073.44 - 1353.26i) q^{44} +(3253.34 + 5130.44i) q^{45} -5917.36i q^{46} +655.436i q^{47} +(-19158.3 + 5562.33i) q^{48} -42483.7 q^{49} +4307.75 q^{50} +(-20116.8 + 5840.61i) q^{51} +15069.3i q^{52} +33167.8i q^{53} +(-17276.1 + 19575.0i) q^{54} +(2181.96 + 9792.65i) q^{55} +27683.0i q^{56} +(-6486.40 - 22341.1i) q^{57} +46579.4 q^{58} +5037.89i q^{59} +(1684.79 + 5802.89i) q^{60} +37289.1i q^{61} -61498.0 q^{62} +(31687.1 + 49969.8i) q^{63} +5232.19 q^{64} -24297.3 q^{65} +(-37802.0 + 20739.8i) q^{66} -12102.0 q^{67} -20835.5 q^{68} +(3731.53 + 12852.5i) q^{69} +41956.9 q^{70} -5434.63i q^{71} +(23331.0 - 14794.8i) q^{72} +27556.5i q^{73} +53812.7 q^{74} +(-9356.41 + 2716.50i) q^{75} -23139.2i q^{76} +(21252.0 + 95379.1i) q^{77} +(-29115.1 - 100281. i) q^{78} -17497.3i q^{79} -31993.9i q^{80} +(25179.5 - 53411.4i) q^{81} -37660.5 q^{82} -92352.9 q^{83} +(16409.6 + 56519.4i) q^{84} -33594.5i q^{85} +14758.5i q^{86} +(-101170. + 29373.4i) q^{87} +(44532.8 - 9922.62i) q^{88} -27945.3i q^{89} +(-22423.3 - 35361.0i) q^{90} -236653. q^{91} +13311.7i q^{92} +(133573. - 38781.1i) q^{93} -4517.52i q^{94} +37309.0 q^{95} +(77583.7 - 22525.3i) q^{96} +23926.4 q^{97} +292814. q^{98} +(69027.1 - 68885.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9}+O(q^{10}) $ 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9	$ 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9} + 2112 q^{12} + 1100 q^{15} + 13792 q^{16} - 9892 q^{22} - 50000 q^{25} - 10780 q^{27} + 2112 q^{31} + 6316 q^{33} + 69560 q^{34} - 17268 q^{36} - 7456 q^{37} - 100712 q^{42} + 61352 q^{48} - 233408 q^{49} - 15800 q^{55} - 93728 q^{58} + 62700 q^{60} + 212400 q^{64} + 203724 q^{66} + 182072 q^{67} - 122584 q^{69} + 6600 q^{70} - 27500 q^{75} - 489128 q^{78} + 194872 q^{81} - 237544 q^{82} - 641716 q^{88} + 168272 q^{91} + 433336 q^{93} + 949008 q^{97} + 328952 q^{99}+O(q^{100}) $ 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9 + 2112 * q^12 + 1100 * q^15 + 13792 * q^16 - 9892 * q^22 - 50000 * q^25 - 10780 * q^27 + 2112 * q^31 + 6316 * q^33 + 69560 * q^34 - 17268 * q^36 - 7456 * q^37 - 100712 * q^42 + 61352 * q^48 - 233408 * q^49 - 15800 * q^55 - 93728 * q^58 + 62700 * q^60 + 212400 * q^64 + 203724 * q^66 + 182072 * q^67 - 122584 * q^69 + 6600 * q^70 - 27500 * q^75 - 489128 * q^78 + 194872 * q^81 - 237544 * q^82 - 641716 * q^88 + 168272 * q^91 + 433336 * q^93 + 949008 * q^97 + 328952 * 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 $

$2$	−6.89239			−1.21841			−0.609207	−	0.793011i	$-0.708512\pi$
$2$	−6.89239			−1.21841			−0.609207	+	0.793011i	$0.708512\pi$
$3$	14.9703	−	4.34640i	0.960343	−	0.278822i
$3$	14.9703	−	4.34640i	0.960343	−	0.278822i
$4$	15.5051			0.484535
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$	−103.181	+	29.9571i	−1.17010	+	0.339721i
$7$			243.497i			1.87823i	0.343607	+	0.939113i	$0.388351\pi$
$7$			243.497i			1.87823i	−0.343607	+	0.939113i	$0.611649\pi$
$8$	113.689			0.628051
$9$	205.218	−	130.134i	0.844517	−	0.535529i
$10$		−	172.310i		−	0.544892i
$11$	391.706	−	87.2784i	0.976064	−	0.217483i
$11$	391.706	−	87.2784i	0.976064	−	0.217483i
$12$	232.116	−	67.3914i	0.465319	−	0.135099i
$13$			971.892i			1.59500i	0.603321	+	0.797498i	$0.293844\pi$
$13$			971.892i			1.59500i	−0.603321	+	0.797498i	$0.706156\pi$
$14$		−	1678.28i		−	2.28846i
$15$	108.660	+	374.257i	0.124693	+	0.429478i
$16$	−1279.76			−1.24976
$17$	−1343.78			−1.12773			−0.563867	−	0.825866i	$-0.690687\pi$
$17$	−1343.78			−1.12773			−0.563867	+	0.825866i	$0.690687\pi$
$18$	−1414.44	+	896.932i	−1.02897	+	0.652496i
$19$		−	1492.36i		−	0.948397i	−0.880418	−	0.474198i	$-0.842738\pi$
$19$		−	1492.36i		−	0.948397i	0.880418	−	0.474198i	$-0.157262\pi$
$20$			387.628i			0.216690i
$21$	1058.33	+	3645.21i	0.523690	+	1.80374i
$22$	−2699.79	+	601.557i	−1.18925	+	0.264984i
$23$			858.534i			0.338406i	0.985581	+	0.169203i	$0.0541193\pi$
$23$			858.534i			0.338406i	−0.985581	+	0.169203i	$0.945881\pi$
$24$	1701.96	−	494.139i	0.603144	−	0.175114i
$25$	−625.000			−0.200000
$26$		−	6698.66i		−	1.94337i
$27$	2506.55	−	2840.09i	0.661709	−	0.749761i
$28$			3775.44i			0.910066i
$29$	−6758.09			−1.49221			−0.746103	−	0.665831i	$-0.768077\pi$
$29$	−6758.09			−1.49221			−0.746103	+	0.665831i	$0.768077\pi$
$30$	−748.928	−	2579.52i	−0.151928	−	0.523283i
$31$	8922.59			1.66758			0.833790	−	0.552082i	$-0.186167\pi$
$31$	8922.59			1.66758			0.833790	+	0.552082i	$0.186167\pi$
$32$	5182.52			0.894676
$33$	5484.59	−	3009.09i	0.876717	−	0.481006i
$34$	9261.88			1.37405
$35$	−6087.42			−0.839969
$36$	3181.92	−	2017.73i	0.409198	−	0.259482i
$37$	−7807.55			−0.937585			−0.468792	−	0.883308i	$-0.655311\pi$
$37$	−7807.55			−0.937585			−0.468792	+	0.883308i	$0.655311\pi$
$38$			10285.9i			1.15554i
$39$	4224.23	+	14549.5i	0.444720	+	1.53174i
$40$			2842.23i			0.280873i
$41$	5464.06			0.507640			0.253820	−	0.967251i	$-0.418313\pi$
$41$	5464.06			0.507640			0.253820	+	0.967251i	$0.418313\pi$
$42$	−7294.46	−	25124.2i	−0.638072	−	2.19771i
$43$		−	2141.27i		−	0.176604i	−0.996094	−	0.0883019i	$-0.971856\pi$
$43$		−	2141.27i		−	0.176604i	0.996094	−	0.0883019i	$-0.0281440\pi$
$44$	6073.44	−	1353.26i	0.472937	−	0.105378i
$45$	3253.34	+	5130.44i	0.239496	+	0.377679i
$46$		−	5917.36i		−	0.412319i
$47$			655.436i			0.0432798i	0.999766	+	0.0216399i	$0.00688874\pi$
$47$			655.436i			0.0432798i	−0.999766	+	0.0216399i	$0.993111\pi$
$48$	−19158.3	+	5562.33i	−1.20020	+	0.348460i
$49$	−42483.7			−2.52774
$50$	4307.75			0.243683
$51$	−20116.8	+	5840.61i	−1.08301	+	0.314437i
$52$			15069.3i			0.772831i
$53$			33167.8i			1.62191i	0.585108	+	0.810955i	$0.301052\pi$
$53$			33167.8i			1.62191i	−0.585108	+	0.810955i	$0.698948\pi$
$54$	−17276.1	+	19575.0i	−0.806236	+	0.913520i
$55$	2181.96	+	9792.65i	0.0972613	+	0.436509i
$56$			27683.0i			1.17962i
$57$	−6486.40	−	22341.1i	−0.264434	−	0.910786i
$58$	46579.4			1.81813
$59$			5037.89i			0.188416i	0.995553	+	0.0942081i	$0.0300319\pi$
$59$			5037.89i			0.188416i	−0.995553	+	0.0942081i	$0.969968\pi$
$60$	1684.79	+	5802.89i	0.0604180	+	0.208097i
$61$			37289.1i			1.28309i	0.767085	+	0.641545i	$0.221706\pi$
$61$			37289.1i			1.28309i	−0.767085	+	0.641545i	$0.778294\pi$
$62$	−61498.0			−2.03180
$63$	31687.1	+	49969.8i	1.00584	+	1.58619i
$64$	5232.19			0.159674
$65$	−24297.3			−0.713304
$66$	−37802.0	+	20739.8i	−1.06821	+	0.586065i
$67$	−12102.0			−0.329359			−0.164680	−	0.986347i	$-0.552659\pi$
$67$	−12102.0			−0.329359			−0.164680	+	0.986347i	$0.552659\pi$
$68$	−20835.5			−0.546426
$69$	3731.53	+	12852.5i	0.0943549	+	0.324986i
$70$	41956.9			1.02343
$71$		−	5434.63i		−	0.127945i	−0.997952	−	0.0639726i	$-0.979623\pi$
$71$		−	5434.63i		−	0.127945i	0.997952	−	0.0639726i	$-0.0203770\pi$
$72$	23331.0	−	14794.8i	0.530399	−	0.336339i
$73$			27556.5i			0.605226i	0.953114	+	0.302613i	$0.0978589\pi$
$73$			27556.5i			0.605226i	−0.953114	+	0.302613i	$0.902141\pi$
$74$	53812.7			1.14237
$75$	−9356.41	+	2716.50i	−0.192069	+	0.0557643i
$76$		−	23139.2i		−	0.459531i
$77$	21252.0	+	95379.1i	0.408482	+	1.83327i
$78$	−29115.1	−	100281.i	−0.541853	−	1.86630i
$79$		−	17497.3i		−	0.315430i	−0.987485	−	0.157715i	$-0.949587\pi$
$79$		−	17497.3i		−	0.315430i	0.987485	−	0.157715i	$-0.0504128\pi$
$80$		−	31993.9i		−	0.558910i
$81$	25179.5	−	53411.4i	0.426418	−	0.904526i
$82$	−37660.5			−0.618516
$83$	−92352.9			−1.47148			−0.735742	−	0.677262i	$-0.763166\pi$
$83$	−92352.9			−1.47148			−0.735742	+	0.677262i	$0.763166\pi$
$84$	16409.6	+	56519.4i	0.253746	+	0.873975i
$85$		−	33594.5i		−	0.504338i
$86$			14758.5i			0.215177i
$87$	−101170.	+	29373.4i	−1.43303	+	0.416059i
$88$	44532.8	−	9922.62i	0.613018	−	0.136590i
$89$		−	27945.3i		−	0.373967i	−0.982363	−	0.186984i	$-0.940129\pi$
$89$		−	27945.3i		−	0.373967i	0.982363	−	0.186984i	$-0.0598711\pi$
$90$	−22423.3	−	35361.0i	−0.291805	−	0.460170i
$91$	−236653.			−2.99577
$92$			13311.7i			0.163969i
$93$	133573.	−	38781.1i	1.60145	−	0.464957i
$94$		−	4517.52i		−	0.0527328i
$95$	37309.0			0.424136
$96$	77583.7	−	22525.3i	0.859196	−	0.249455i
$97$	23926.4			0.258195			0.129098	−	0.991632i	$-0.458792\pi$
$97$	23926.4			0.258195			0.129098	+	0.991632i	$0.458792\pi$
$98$	292814.			3.07983
$99$	69027.1	−	68885.1i	0.707834	−	0.706378i
$100$	−9690.69			−0.0969069
$101$	−108206.			−1.05547			−0.527737	−	0.849408i	$-0.676959\pi$
$101$	−108206.			−1.05547			−0.527737	+	0.849408i	$0.676959\pi$
$102$	138653.	−	40255.8i	1.31956	−	0.383114i
$103$	107547.			0.998862			0.499431	−	0.866354i	$-0.333542\pi$
$103$	107547.			0.998862			0.499431	+	0.866354i	$0.333542\pi$
$104$			110494.i			1.00174i
$105$	−91130.3	+	26458.4i	−0.806658	+	0.234202i
$106$		−	228605.i		−	1.97616i
$107$	70895.5			0.598631			0.299315	−	0.954154i	$-0.403242\pi$
$107$	70895.5			0.598631			0.299315	+	0.954154i	$0.403242\pi$
$108$	38864.3	−	44035.9i	0.320621	−	0.363285i
$109$			19813.1i			0.159730i	0.996806	+	0.0798650i	$0.0254489\pi$
$109$			19813.1i			0.159730i	−0.996806	+	0.0798650i	$0.974551\pi$
$110$	−15038.9	−	67494.8i	−0.118505	−	0.531849i
$111$	−116881.	+	33934.7i	−0.900403	+	0.261419i
$112$		−	311616.i		−	2.34733i
$113$			190770.i			1.40545i	0.711462	+	0.702724i	$0.248033\pi$
$113$			190770.i			1.40545i	−0.711462	+	0.702724i	$0.751967\pi$
$114$	44706.9	+	153983.i	0.322190	+	1.10972i
$115$	−21463.3			−0.151340
$116$	−104785.			−0.723025
$117$	126476.	+	199449.i	0.854167	+	1.34700i
$118$		−	34723.1i		−	0.229569i
$119$		−	327207.i		−	2.11814i
$120$	12353.5	+	42549.0i	0.0783134	+	0.269734i
$121$	145816.	−	68374.9i	0.905402	−	0.424554i
$122$		−	257011.i		−	1.56334i
$123$	81798.4	−	23749.0i	0.487509	−	0.141541i
$124$	138346.			0.808000
$125$		−	15625.0i		−	0.0894427i
$126$	−218400.	−	344412.i	−1.22554	−	1.93264i
$127$		−	192590.i		−	1.05956i	−0.848137	−	0.529778i	$-0.822275\pi$
$127$		−	192590.i		−	1.05956i	0.848137	−	0.529778i	$-0.177725\pi$
$128$	−201903.			−1.08923
$129$	−9306.82	−	32055.4i	−0.0492410	−	0.169600i
$130$	167467.			0.869100
$131$	45996.1			0.234176			0.117088	−	0.993122i	$-0.462644\pi$
$131$	45996.1			0.234176			0.117088	+	0.993122i	$0.462644\pi$
$132$	85039.2	−	46656.3i	0.424800	−	0.233064i
$133$	363385.			1.78130
$134$	83411.7			0.401296
$135$	71002.3	+	62663.7i	0.335303	+	0.295925i
$136$	−152774.			−0.708274
$137$			132638.i			0.603762i	0.953346	+	0.301881i	$0.0976145\pi$
$137$			132638.i			0.603762i	−0.953346	+	0.301881i	$0.902385\pi$
$138$	−25719.2	−	88584.4i	−0.114963	−	0.395967i
$139$			230420.i			1.01154i	0.862669	+	0.505769i	$0.168791\pi$
$139$			230420.i			1.01154i	−0.862669	+	0.505769i	$0.831209\pi$
$140$	−94386.1			−0.406994
$141$	2848.79	+	9812.05i	0.0120674	+	0.0415635i
$142$			37457.6i			0.155890i
$143$	84825.2	+	380696.i	0.346884	+	1.55682i
$144$	−262628.	+	166539.i	−1.05544	+	0.669283i
$145$		−	168952.i		−	0.667335i
$146$		−	189931.i		−	0.737416i
$147$	−635992.	+	184651.i	−2.42749	+	0.704788i
$148$	−121057.			−0.454292
$149$	140787.			0.519512			0.259756	−	0.965674i	$-0.416358\pi$
$149$	140787.			0.519512			0.259756	+	0.965674i	$0.416358\pi$
$150$	64488.1	−	18723.2i	0.234019	−	0.0679441i
$151$		−	165078.i		−	0.589178i	−0.955624	−	0.294589i	$-0.904817\pi$
$151$		−	165078.i		−	0.589178i	0.955624	−	0.294589i	$-0.0951827\pi$
$152$		−	169666.i		−	0.595641i
$153$	−275768.	+	174871.i	−0.952390	+	0.603934i
$154$	−146477.	−	657390.i	−0.497701	−	2.23368i
$155$			223065.i			0.745764i
$156$	65497.2	+	225591.i	0.215482	+	0.742183i
$157$	−120750.			−0.390965			−0.195482	−	0.980707i	$-0.562627\pi$
$157$	−120750.			−0.390965			−0.195482	+	0.980707i	$0.562627\pi$
$158$			120598.i			0.384325i
$159$	144160.	+	496531.i	0.452224	+	1.55759i
$160$			129563.i			0.400111i
$161$	−209050.			−0.635603
$162$	−173547.	+	368132.i	−0.519553	+	1.10209i
$163$	214839.			0.633350			0.316675	−	0.948534i	$-0.397434\pi$
$163$	214839.			0.633350			0.316675	+	0.948534i	$0.397434\pi$
$164$	84720.9			0.245969
$165$	75227.3	+	137115.i	0.215112	+	0.392080i
$166$	636533.			1.79288
$167$	162717.			0.451483			0.225741	−	0.974187i	$-0.427520\pi$
$167$	162717.			0.451483			0.225741	+	0.974187i	$0.427520\pi$
$168$	120321.	+	414421.i	0.328904	+	1.13284i
$169$	−573281.			−1.54401
$170$			231547.i			0.614493i
$171$	−194206.	−	306259.i	−0.507894	−	0.800937i
$172$		−	33200.6i		−	0.0855707i
$173$	−492304.			−1.25060			−0.625300	−	0.780385i	$-0.715023\pi$
$173$	−492304.			−1.25060			−0.625300	+	0.780385i	$0.715023\pi$
$174$	697306.	−	202453.i	1.74602	−	0.506933i
$175$		−	152185.i		−	0.375645i
$176$	−501288.	+	111695.i	−1.21985	+	0.271802i
$177$	21896.7	+	75418.5i	0.0525345	+	0.180944i
$178$			192610.i			0.455647i
$179$		−	498524.i		−	1.16293i	−0.813571	−	0.581465i	$-0.802480\pi$
$179$		−	498524.i		−	1.16293i	0.813571	−	0.581465i	$-0.197520\pi$
$180$	50443.4	+	79548.0i	0.116044	+	0.182999i
$181$	25308.6			0.0574212			0.0287106	−	0.999588i	$-0.490860\pi$
$181$	25308.6			0.0574212			0.0287106	+	0.999588i	$0.490860\pi$
$182$	1.63110e6			3.65008
$183$	162073.	+	558227.i	0.357753	+	1.23221i
$184$			97606.1i			0.212536i
$185$		−	195189.i		−	0.419301i
$186$	−920641.	+	267295.i	−1.95123	+	0.566511i
$187$	−526367.	+	117283.i	−1.10074	+	0.245263i
$188$			10162.6i			0.0209706i
$189$	691553.	+	610337.i	1.40822	+	1.24284i
$190$	−257149.			−0.516774
$191$			115773.i			0.229627i	0.993387	+	0.114813i	$0.0366270\pi$
$191$			115773.i			0.229627i	−0.993387	+	0.114813i	$0.963373\pi$
$192$	78327.3	−	22741.2i	0.153342	−	0.0445205i
$193$		−	590165.i		−	1.14046i	−0.821485	−	0.570230i	$-0.806854\pi$
$193$		−	590165.i		−	1.14046i	0.821485	−	0.570230i	$-0.193146\pi$
$194$	−164910.			−0.314589
$195$	−363737.	+	105606.i	−0.685016	+	0.198885i
$196$	−658714.			−1.22478
$197$	−103711.			−0.190396			−0.0951981	−	0.995458i	$-0.530348\pi$
$197$	−103711.			−0.190396			−0.0951981	+	0.995458i	$0.530348\pi$
$198$	−475762.	+	474783.i	−0.862436	+	0.860662i
$199$	−184896.			−0.330975			−0.165488	−	0.986212i	$-0.552920\pi$
$199$	−184896.			−0.330975			−0.165488	+	0.986212i	$0.552920\pi$
$200$	−71055.8			−0.125610
$201$	−181170.	+	52600.1i	−0.316298	+	0.0918325i
$202$	745797.			1.28600
$203$		−	1.64557e6i		−	2.80270i
$204$	−311913.	+	90559.4i	−0.524756	+	0.152355i
$205$			136602.i			0.227024i
$206$	−741257.			−1.21703
$207$	111724.	+	176186.i	0.181226	+	0.285789i
$208$		−	1.24378e6i		−	1.99336i
$209$	−130251.	−	584567.i	−0.206260	−	0.925696i
$210$	628106.	−	182361.i	0.982844	−	0.285355i
$211$			205817.i			0.318255i	0.987258	+	0.159128i	$0.0508681\pi$
$211$			205817.i			0.318255i	−0.987258	+	0.159128i	$0.949132\pi$
$212$			514270.i			0.785872i
$213$	−23621.1	−	81357.8i	−0.0356739	−	0.122871i
$214$	−488640.			−0.729381
$215$	53531.7			0.0789797
$216$	284968.	−	322888.i	0.415587	−	0.470888i
$217$			2.17262e6i			3.13209i
$218$		−	136560.i		−	0.194617i
$219$	119772.	+	412529.i	0.168750	+	0.581224i
$220$	33831.5	+	151836.i	0.0471265	+	0.211504i
$221$		−	1.30601e6i		−	1.79873i
$222$	805591.	−	233892.i	1.09706	−	0.318517i
$223$	826428.			1.11287			0.556433	−	0.830893i	$-0.312170\pi$
$223$	826428.			1.11287			0.556433	+	0.830893i	$0.312170\pi$
$224$			1.26193e6i			1.68041i
$225$	−128261.	+	81333.5i	−0.168903	+	0.107106i
$226$		−	1.31487e6i		−	1.71242i
$227$	1.32913e6			1.71199			0.855996	−	0.516982i	$-0.172945\pi$
$227$	1.32913e6			1.71199			0.855996	+	0.516982i	$0.172945\pi$
$228$	−100572.	−	346400.i	−0.128127	−	0.441307i
$229$	639018.			0.805238			0.402619	−	0.915368i	$-0.368100\pi$
$229$	639018.			0.805238			0.402619	+	0.915368i	$0.368100\pi$
$230$	147934.			0.184395
$231$	732704.	+	1.33548e6i	0.903438	+	1.64667i
$232$	−768322.			−0.937181
$233$	−116508.			−0.140593			−0.0702966	−	0.997526i	$-0.522395\pi$
$233$	−116508.			−0.140593			−0.0702966	+	0.997526i	$0.522395\pi$
$234$	−871721.	−	1.37468e6i	−1.04073	−	1.64121i
$235$	−16385.9			−0.0193553
$236$			78113.0i			0.0912942i
$237$	−76050.3	−	261939.i	−0.0879488	−	0.302921i
$238$			2.25524e6i			2.58077i
$239$	−576197.			−0.652493			−0.326247	−	0.945285i	$-0.605784\pi$
$239$	−576197.			−0.652493			−0.326247	+	0.945285i	$0.605784\pi$
$240$	−139058.	−	478957.i	−0.155836	−	0.536745i
$241$			763924.i			0.847242i	0.905840	+	0.423621i	$0.139241\pi$
$241$			763924.i			0.847242i	−0.905840	+	0.423621i	$0.860759\pi$
$242$	−1.00502e6	+	471267.i	−1.10316	+	0.517283i
$243$	144797.	−	909023.i	0.157305	−	0.987550i
$244$			578171.i			0.621702i
$245$		−	1.06209e6i		−	1.13044i
$246$	−563787.	+	163687.i	−0.593988	+	0.172456i
$247$	1.45041e6			1.51269
$248$	1.01440e6			1.04732
$249$	−1.38255e6	+	401403.i	−1.41313	+	0.410282i
$250$			107694.i			0.108978i
$251$		−	734412.i		−	0.735792i	−0.929867	−	0.367896i	$-0.880078\pi$
$251$		−	734412.i		−	0.735792i	0.929867	−	0.367896i	$-0.119922\pi$
$252$	491312.	+	774787.i	0.487367	+	0.768566i
$253$	74931.5	+	336293.i	0.0735975	+	0.330306i
$254$			1.32740e6i			1.29098i
$255$	−146015.	−	502919.i	−0.140620	−	0.484337i
$256$	1.22416e6			1.16745
$257$		−	661763.i		−	0.624985i	−0.949920	−	0.312493i	$-0.898836\pi$
$257$		−	661763.i		−	0.624985i	0.949920	−	0.312493i	$-0.101164\pi$
$258$	64146.3	+	220938.i	0.0599960	+	0.206643i
$259$		−	1.90111e6i		−	1.76100i
$260$	−376732.			−0.345620
$261$	−1.38688e6	+	879454.i	−1.26019	+	0.799119i
$262$	−317023.			−0.285324
$263$	1.30932e6			1.16723			0.583616	−	0.812030i	$-0.301638\pi$
$263$	1.30932e6			1.16723			0.583616	+	0.812030i	$0.301638\pi$
$264$	623540.	−	342101.i	0.550623	−	0.302096i
$265$	−829195.			−0.725340
$266$	−2.50459e6			−2.17037
$267$	−121461.	−	418348.i	−0.104270	−	0.359137i
$268$	−187643.			−0.159586
$269$			1.59652e6i			1.34522i	0.739996	+	0.672611i	$0.234827\pi$
$269$			1.59652e6i			1.34522i	−0.739996	+	0.672611i	$0.765173\pi$
$270$	−489376.	−	431903.i	−0.408539	−	0.360560i
$271$			1.88153e6i			1.55628i	0.628092	+	0.778139i	$0.283836\pi$
$271$			1.88153e6i			1.55628i	−0.628092	+	0.778139i	$0.716164\pi$
$272$	1.71971e6			1.40940
$273$	−3.54275e6	+	1.02859e6i	−2.87696	+	0.835284i
$274$		−	914192.i		−	0.735633i
$275$	−244816.	+	54549.0i	−0.195213	+	0.0434966i
$276$	57857.8	+	199279.i	0.0457182	+	0.157467i
$277$		−	395451.i		−	0.309666i	−0.987941	−	0.154833i	$-0.950516\pi$
$277$		−	395451.i		−	0.309666i	0.987941	−	0.154833i	$-0.0494839\pi$
$278$		−	1.58814e6i		−	1.23247i
$279$	1.83107e6	−	1.16113e6i	1.40830	−	0.893037i
$280$	−692074.			−0.527543
$281$	−321106.			−0.242595			−0.121298	−	0.992616i	$-0.538706\pi$
$281$	−321106.			−0.242595			−0.121298	+	0.992616i	$0.538706\pi$
$282$	−19635.0	−	67628.5i	−0.0147030	−	0.0506415i
$283$			756857.i			0.561756i	0.959743	+	0.280878i	$0.0906256\pi$
$283$			756857.i			0.561756i	−0.959743	+	0.280878i	$0.909374\pi$
$284$		−	84264.5i		−	0.0619939i
$285$	558526.	−	162160.i	0.407316	−	0.118258i
$286$	−584649.	−	2.62391e6i	−0.422649	−	1.89685i
$287$			1.33048e6i			0.953463i
$288$	1.06354e6	−	674420.i	0.755569	−	0.479125i
$289$	385893.			0.271783
$290$			1.16449e6i			0.813091i
$291$	358185.	−	103994.i	0.247956	−	0.0719904i
$292$			427267.i			0.293253i
$293$	−782097.			−0.532221			−0.266110	−	0.963943i	$-0.585739\pi$
$293$	−782097.			−0.532221			−0.266110	+	0.963943i	$0.585739\pi$
$294$	4.38351e6	−	1.27269e6i	2.95769	−	0.858724i
$295$	−125947.			−0.0842623
$296$	−887635.			−0.588851
$297$	733951.	−	1.33125e6i	0.482810	−	0.875725i
$298$	−970357.			−0.632981
$299$	−834402.			−0.539756
$300$	−145072.	+	42119.6i	−0.0930639	+	0.0270198i
$301$	521392.			0.331702
$302$			1.13778e6i			0.717863i
$303$	−1.61987e6	+	470306.i	−1.01362	+	0.294289i
$304$			1.90986e6i			1.18527i
$305$	−932227.			−0.573815
$306$	1.90070e6	−	1.20528e6i	1.16041	−	0.735842i
$307$			786177.i			0.476074i	0.971256	+	0.238037i	$0.0765040\pi$
$307$			786177.i			0.476074i	−0.971256	+	0.238037i	$0.923496\pi$
$308$	329515.	+	1.47886e6i	0.197924	+	0.888283i
$309$	1.61001e6	−	467443.i	0.959250	−	0.278505i
$310$		−	1.53745e6i		−	0.908650i
$311$			906773.i			0.531616i	0.964026	+	0.265808i	$0.0856387\pi$
$311$			906773.i			0.531616i	−0.964026	+	0.265808i	$0.914361\pi$
$312$	480250.	+	1.65412e6i	0.279306	+	0.962012i
$313$	−1.26320e6			−0.728802			−0.364401	−	0.931242i	$-0.618726\pi$
$313$	−1.26320e6			−0.728802			−0.364401	+	0.931242i	$0.618726\pi$
$314$	832256.			0.476357
$315$	−1.24925e6	+	792177.i	−0.709368	+	0.449827i
$316$		−	271298.i		−	0.152837i
$317$			751865.i			0.420234i	0.977676	+	0.210117i	$0.0673845\pi$
$317$			751865.i			0.420234i	−0.977676	+	0.210117i	$0.932615\pi$
$318$	−993611.	−	3.42228e6i	−0.550996	−	1.89779i
$319$	−2.64718e6	+	589835.i	−1.45649	+	0.324529i
$320$			130805.i			0.0714083i
$321$	1.06132e6	−	308140.i	0.574891	−	0.166911i
$322$	1.44086e6			0.774428
$323$			2.00541e6i			1.06954i
$324$	390411.	−	828149.i	0.206614	−	0.438274i
$325$		−	607433.i		−	0.318999i
$326$	−1.48075e6			−0.771682
$327$	86115.8	+	296608.i	0.0445362	+	0.153396i
$328$	621205.			0.318824
$329$	−159596.			−0.0812893
$330$	−518496.	−	945050.i	−0.262096	−	0.477716i
$331$	1.59418e6			0.799772			0.399886	−	0.916565i	$-0.369050\pi$
$331$	1.59418e6			0.799772			0.399886	+	0.916565i	$0.369050\pi$
$332$	−1.43194e6			−0.712985
$333$	−1.60225e6	+	1.01602e6i	−0.791806	+	0.502104i
$334$	−1.12151e6			−0.550093
$335$		−	302550.i		−	0.147294i
$336$	−1.35441e6	−	4.66498e6i	−0.654488	−	2.25425i
$337$		−	3.51036e6i		−	1.68375i	−0.539676	−	0.841873i	$-0.681453\pi$
$337$		−	3.51036e6i		−	1.68375i	0.539676	−	0.841873i	$-0.318547\pi$
$338$	3.95128e6			1.88125
$339$	829165.	+	2.85588e6i	0.391870	+	1.34971i
$340$		−	520887.i		−	0.244369i
$341$	3.49503e6	−	778749.i	1.62766	−	0.362670i
$342$	1.33855e6	+	2.11086e6i	0.618826	+	0.975874i
$343$		−	6.25218e6i		−	2.86944i
$344$		−	243439.i		−	0.110916i
$345$	−321312.	+	93288.3i	−0.145338	+	0.0421968i
$346$	3.39315e6			1.52375
$347$	2.42448e6			1.08092			0.540461	−	0.841369i	$-0.318250\pi$
$347$	2.42448e6			1.08092			0.540461	+	0.841369i	$0.318250\pi$
$348$	−1.56866e6	+	455437.i	−0.694352	+	0.201595i
$349$			3.83807e6i			1.68674i	0.537331	+	0.843371i	$0.319433\pi$
$349$			3.83807e6i			1.68674i	−0.537331	+	0.843371i	$0.680567\pi$
$350$			1.04892e6i			0.457692i
$351$	2.76026e6	+	2.43610e6i	1.19587	+	1.05542i
$352$	2.03002e6	−	452322.i	0.873262	−	0.194577i
$353$			3.78339e6i			1.61601i	0.589174	+	0.808006i	$0.299453\pi$
$353$			3.78339e6i			1.61601i	−0.589174	+	0.808006i	$0.700547\pi$
$354$	−150921.	−	519814.i	−0.0640089	−	0.220465i
$355$	135866.			0.0572188
$356$		−	433295.i		−	0.181200i
$357$	−1.42217e6	−	4.89837e6i	−0.590583	−	2.03414i
$358$			3.43603e6i			1.41693i
$359$	4.05594e6			1.66095			0.830473	−	0.557059i	$-0.188070\pi$
$359$	4.05594e6			1.66095			0.830473	+	0.557059i	$0.188070\pi$
$360$	369870.	+	583276.i	0.150416	+	0.237202i
$361$	248955.			0.100543
$362$	−174437.			−0.0699628
$363$	1.88572e6	−	1.65736e6i	0.751122	−	0.660164i
$364$	−3.66932e6			−1.45155
$365$	−688913.			−0.270665
$366$	−1.11707e6	−	3.84752e6i	−0.435892	−	1.50134i
$367$	−3.09785e6			−1.20059			−0.600296	−	0.799778i	$-0.704951\pi$
$367$	−3.09785e6			−1.20059			−0.600296	+	0.799778i	$0.704951\pi$
$368$		−	1.09871e6i		−	0.422926i
$369$	1.12132e6	−	711058.i	0.428711	−	0.271856i
$370$			1.34532e6i			0.510882i
$371$	−8.07625e6			−3.04632
$372$	2.07107e6	−	601306.i	0.775957	−	0.225288i
$373$		−	2.19728e6i		−	0.817737i	−0.912593	−	0.408869i	$-0.865923\pi$
$373$		−	2.19728e6i		−	0.817737i	0.912593	−	0.408869i	$-0.134077\pi$
$374$	3.62793e6	−	808361.i	1.34116	−	0.298832i
$375$	−67912.5	−	233910.i	−0.0249386	−	0.0858957i
$376$			74516.0i			0.0271819i
$377$		−	6.56813e6i		−	2.38006i
$378$	−4.76646e6	−	4.20668e6i	−1.71580	−	1.51429i
$379$	−1.82958e6			−0.654266			−0.327133	−	0.944978i	$-0.606083\pi$
$379$	−1.82958e6			−0.654266			−0.327133	+	0.944978i	$0.606083\pi$
$380$	578481.			0.205509
$381$	−837072.	−	2.88312e6i	−0.295427	−	1.01754i
$382$		−	797951.i		−	0.279781i
$383$		−	4.31621e6i		−	1.50351i	−0.659444	−	0.751754i	$-0.729208\pi$
$383$		−	4.31621e6i		−	1.50351i	0.659444	−	0.751754i	$-0.270792\pi$
$384$	−3.02254e6	+	877551.i	−1.04603	+	0.303700i
$385$	−2.38448e6	+	531300.i	−0.819863	+	0.182679i
$386$			4.06765e6i			1.38955i
$387$	−278651.	−	439426.i	−0.0945765	−	0.149145i
$388$	370981.			0.125104
$389$			3.12937e6i			1.04853i	0.851554	+	0.524267i	$0.175661\pi$
$389$			3.12937e6i			1.04853i	−0.851554	+	0.524267i	$0.824339\pi$
$390$	2.50702e6	−	727877.i	0.834634	−	0.242324i
$391$		−	1.15368e6i		−	0.381632i
$392$	−4.82994e6			−1.58755
$393$	688574.	−	199918.i	0.224890	−	0.0652935i
$394$	714816.			0.231982
$395$	437433.			0.141065
$396$	1.07027e6	−	1.06807e6i	0.342970	−	0.342265i
$397$	4.26335e6			1.35761			0.678804	−	0.734319i	$-0.262499\pi$
$397$	4.26335e6			1.35761			0.678804	+	0.734319i	$0.262499\pi$
$398$	1.27438e6			0.403265
$399$	5.43997e6	−	1.57942e6i	1.71066	−	0.496666i
$400$	799847.			0.249952
$401$		−	1.61177e6i		−	0.500545i	−0.968175	−	0.250273i	$-0.919480\pi$
$401$		−	1.61177e6i		−	0.500545i	0.968175	−	0.250273i	$-0.0805202\pi$
$402$	1.24870e6	−	362541.i	0.385382	−	0.111890i
$403$			8.67179e6i			2.65978i
$404$	−1.67774e6			−0.511413
$405$	1.33528e6	+	629488.i	0.404517	+	0.190700i
$406$			1.13419e7i			3.41485i
$407$	−3.05826e6	+	681430.i	−0.915143	+	0.203909i
$408$	−2.28706e6	+	664015.i	−0.680186	+	0.197482i
$409$		−	783394.i		−	0.231564i	−0.993275	−	0.115782i	$-0.963063\pi$
$409$		−	783394.i		−	0.231564i	0.993275	−	0.115782i	$-0.0369375\pi$
$410$		−	941512.i		−	0.276609i
$411$	576497.	+	1.98562e6i	0.168342	+	0.579819i
$412$	1.66753e6			0.483983
$413$	−1.22671e6			−0.353888
$414$	−770046.	−	1.21435e6i	−0.220809	−	0.348210i
$415$		−	2.30882e6i		−	0.658067i
$416$			5.03685e6i			1.42701i
$417$	1.00150e6	+	3.44944e6i	0.282039	+	0.971424i
$418$	897741.	+	4.02907e6i	0.251310	+	1.12788i
$419$		−	1.11440e6i		−	0.310103i	−0.987906	−	0.155051i	$-0.950446\pi$
$419$		−	1.11440e6i		−	0.310103i	0.987906	−	0.155051i	$-0.0495543\pi$
$420$	−1.41298e6	+	410240.i	−0.390854	+	0.113479i
$421$	5.36727e6			1.47587			0.737935	−	0.674872i	$-0.235801\pi$
$421$	5.36727e6			1.47587			0.737935	+	0.674872i	$0.235801\pi$
$422$		−	1.41857e6i		−	0.387767i
$423$	85294.2	+	134507.i	0.0231776	+	0.0365505i
$424$			3.77082e6i			1.01864i
$425$	839864.			0.225547
$426$	162806.	+	560750.i	0.0434656	+	0.149708i
$427$	−9.07977e6			−2.40993
$428$	1.09924e6			0.290057
$429$	2.92451e6	+	5.33043e6i	0.767203	+	1.39836i
$430$	−368962.			−0.0962300
$431$	2.75713e6			0.714931			0.357466	−	0.933926i	$-0.383641\pi$
$431$	2.75713e6			0.714931			0.357466	+	0.933926i	$0.383641\pi$
$432$	−3.20777e6	+	3.63462e6i	−0.826978	+	0.937022i
$433$	6.39963e6			1.64035			0.820173	−	0.572116i	$-0.193877\pi$
$433$	6.39963e6			1.64035			0.820173	+	0.572116i	$0.193877\pi$
$434$		−	1.49746e7i		−	3.81619i
$435$	−734334.	−	2.52926e6i	−0.186067	−	0.640870i
$436$			307205.i			0.0773948i
$437$	1.28124e6			0.320943
$438$	−825514.	−	2.84331e6i	−0.205608	−	0.708172i
$439$		−	5.29258e6i		−	1.31071i	−0.755322	−	0.655354i	$-0.772519\pi$
$439$		−	5.29258e6i		−	1.31071i	0.755322	−	0.655354i	$-0.227481\pi$
$440$	248065.	+	1.11332e6i	0.0610850	+	0.274150i
$441$	−8.71840e6	+	5.52855e6i	−2.13472	+	1.35368i
$442$			9.00154e6i			2.19160i
$443$		−	2.43986e6i		−	0.590685i	−0.955392	−	0.295342i	$-0.904566\pi$
$443$		−	2.43986e6i		−	0.590685i	0.955392	−	0.295342i	$-0.0954337\pi$
$444$	−1.81225e6	+	526162.i	−0.436276	+	0.126667i
$445$	698632.			0.167243
$446$	−5.69607e6			−1.35593
$447$	2.10761e6	−	611915.i	0.498910	−	0.144851i
$448$			1.27402e6i			0.299904i
$449$			6.57938e6i			1.54017i	0.637940	+	0.770086i	$0.279787\pi$
$449$			6.57938e6i			1.54017i	−0.637940	+	0.770086i	$0.720213\pi$
$450$	884025.	−	560582.i	0.205794	−	0.130499i
$451$	2.14030e6	−	476894.i	0.495489	−	0.110403i
$452$			2.95792e6i			0.680989i
$453$	−717495.	−	2.47126e6i	−0.164276	−	0.565813i
$454$	−9.16087e6			−2.08592
$455$		−	5.91631e6i		−	1.33975i
$456$	−737435.	−	2.53994e6i	−0.166078	−	0.572020i
$457$		−	478720.i		−	0.107224i	−0.998562	−	0.0536119i	$-0.982927\pi$
$457$		−	478720.i		−	0.107224i	0.998562	−	0.0536119i	$-0.0170734\pi$
$458$	−4.40436e6			−0.981114
$459$	−3.36826e6	+	3.81646e6i	−0.746231	+	0.845531i
$460$	−332792.			−0.0733293
$461$	1.86485e6			0.408689			0.204344	−	0.978899i	$-0.434494\pi$
$461$	1.86485e6			0.408689			0.204344	+	0.978899i	$0.434494\pi$
$462$	−5.05008e6	−	9.20466e6i	−1.10076	−	2.00633i
$463$	−4.95502e6			−1.07422			−0.537110	−	0.843512i	$-0.680484\pi$
$463$	−4.95502e6			−1.07422			−0.537110	+	0.843512i	$0.680484\pi$
$464$	8.64870e6			1.86490
$465$	969528.	+	3.33934e6i	0.207935	+	0.716189i
$466$	803017.			0.171301
$467$			8.68761e6i			1.84335i	0.387962	+	0.921676i	$0.373179\pi$
$467$			8.68761e6i			1.84335i	−0.387962	+	0.921676i	$0.626821\pi$
$468$	1.96102e6	+	3.09248e6i	0.413873	+	0.652669i
$469$		−	2.94680e6i		−	0.618612i
$470$	112938.			0.0235828
$471$	−1.80766e6	+	524828.i	−0.375460	+	0.109010i
$472$			572754.i			0.118335i
$473$	−186887.	−	838748.i	−0.0384083	−	0.172377i
$474$	524169.	+	1.80539e6i	0.107158	+	0.369084i
$475$			932726.i			0.189679i
$476$		−	5.07337e6i		−	1.02631i
$477$	4.31624e6	+	6.80661e6i	0.868580	+	1.36973i
$478$	3.97138e6			0.795008
$479$	−2.40511e6			−0.478956			−0.239478	−	0.970902i	$-0.576976\pi$
$479$	−2.40511e6			−0.478956			−0.239478	+	0.970902i	$0.576976\pi$
$480$	563133.	+	1.93959e6i	0.111560	+	0.384244i
$481$		−	7.58810e6i		−	1.49544i
$482$		−	5.26526e6i		−	1.03229i
$483$	−3.12954e6	+	908616.i	−0.610397	+	0.177220i
$484$	2.26089e6	−	1.06016e6i	0.438699	−	0.205711i
$485$			598160.i			0.115468i
$486$	−997998.	+	6.26534e6i	−0.191663	+	1.20325i
$487$	−2.45855e6			−0.469739			−0.234870	−	0.972027i	$-0.575466\pi$
$487$	−2.45855e6			−0.469739			−0.234870	+	0.972027i	$0.575466\pi$
$488$			4.23937e6i			0.805846i
$489$	3.21619e6	−	933775.i	0.608233	−	0.176592i
$490$			7.32036e6i			1.37734i
$491$	8.97373e6			1.67985			0.839923	−	0.542706i	$-0.182600\pi$
$491$	8.97373e6			1.67985			0.839923	+	0.542706i	$0.182600\pi$
$492$	1.26829e6	−	368231.i	0.236215	−	0.0685816i
$493$	9.08139e6			1.68281
$494$	−9.99683e6			−1.84308
$495$	1.72213e6	+	1.72568e6i	0.315902	+	0.316553i
$496$	−1.14187e7			−2.08408
$497$	1.32331e6			0.240310
$498$	9.52906e6	−	2.76663e6i	1.72178	−	0.499893i
$499$	264084.			0.0474777			0.0237389	−	0.999718i	$-0.492443\pi$
$499$	264084.			0.0474777			0.0237389	+	0.999718i	$0.492443\pi$
$500$		−	242267.i		−	0.0433381i
$501$	2.43591e6	−	707233.i	0.433578	−	0.125883i
$502$			5.06185e6i			0.896500i
$503$	9.91864e6			1.74796			0.873982	−	0.485959i	$-0.161529\pi$
$503$	9.91864e6			1.74796			0.873982	+	0.485959i	$0.161529\pi$
$504$	3.60248e6	+	5.68103e6i	0.631722	+	0.996210i
$505$		−	2.70515e6i		−	0.472022i
$506$	−516457.	−	2.31786e6i	−0.0896722	−	0.402450i
$507$	−8.58217e6	+	2.49171e6i	−1.48278	+	0.430504i
$508$		−	2.98612e6i		−	0.513391i
$509$		−	5.33171e6i		−	0.912161i	−0.889938	−	0.456081i	$-0.849253\pi$
$509$		−	5.33171e6i		−	0.912161i	0.889938	−	0.456081i	$-0.150747\pi$
$510$	1.00640e6	+	3.46632e6i	0.171334	+	0.590124i
$511$	−6.70993e6			−1.13675
$512$	−1.97653e6			−0.333218
$513$	−4.23844e6	−	3.74068e6i	−0.711071	−	0.627563i
$514$			4.56113e6i			0.761491i
$515$			2.68868e6i			0.446705i
$516$	−144303.	−	497022.i	−0.0238590	−	0.0821772i
$517$	57205.4	+	256738.i	0.00941262	+	0.0422439i
$518$			1.31032e7i			2.14562i
$519$	−7.36992e6	+	2.13975e6i	−1.20100	+	0.348694i
$520$	−2.76234e6			−0.447991
$521$		−	5.98013e6i		−	0.965197i	−0.875842	−	0.482599i	$-0.839693\pi$
$521$		−	5.98013e6i		−	0.965197i	0.875842	−	0.482599i	$-0.160307\pi$
$522$	9.55891e6	−	6.06154e6i	1.53544	−	0.973659i
$523$		−	3.36356e6i		−	0.537707i	−0.963181	−	0.268853i	$-0.913355\pi$
$523$		−	3.36356e6i		−	0.537707i	0.963181	−	0.268853i	$-0.0866447\pi$
$524$	713175.			0.113467
$525$	−661459.	−	2.27826e6i	−0.104738	−	0.360748i
$526$	−9.02436e6			−1.42217
$527$	−1.19900e7			−1.88059
$528$	−7.01894e6	+	3.85090e6i	−1.09569	+	0.601142i
$529$	5.69926e6			0.885481
$530$	5.71514e6			0.883765
$531$	655598.	+	1.03386e6i	0.100902	+	0.159121i
$532$	5.63433e6			0.863104
$533$			5.31048e6i			0.809684i
$534$	837160.	+	2.88342e6i	0.127044	+	0.437578i
$535$			1.77239e6i			0.267716i
$536$	−1.37587e6			−0.206854
$537$	−2.16679e6	−	7.46304e6i	−0.324250	−	1.11681i
$538$		−	1.10039e7i		−	1.63904i
$539$	−1.66411e7	+	3.70791e6i	−2.46723	+	0.549739i
$540$	1.10090e6	+	971608.i	0.162466	+	0.143386i
$541$			938352.i			0.137839i	0.997622	+	0.0689196i	$0.0219552\pi$
$541$			938352.i			0.137839i	−0.997622	+	0.0689196i	$0.978045\pi$
$542$		−	1.29682e7i		−	1.89619i
$543$	378877.	−	110001.i	0.0551440	−	0.0160103i
$544$	−6.96418e6			−1.00896
$545$	−495328.			−0.0714335
$546$	2.44180e7	−	7.08943e6i	3.50533	−	1.01772i
$547$		−	4.17840e6i		−	0.597092i	−0.954395	−	0.298546i	$-0.903498\pi$
$547$		−	4.17840e6i		−	0.597092i	0.954395	−	0.298546i	$-0.0965017\pi$
$548$			2.05656e6i			0.292544i
$549$	4.85256e6	+	7.65238e6i	0.687132	+	1.08359i
$550$	1.68737e6	−	375973.i	0.237850	−	0.0529969i
$551$			1.00855e7i			1.41520i
$552$	424235.	+	1.46119e6i	0.0592597	+	0.204107i
$553$	4.26054e6			0.592450
$554$			2.72560e6i			0.377301i
$555$	−848369.	−	2.92203e6i	−0.116910	−	0.402672i
$556$			3.57268e6i			0.490126i
$557$	921794.			0.125891			0.0629457	−	0.998017i	$-0.479951\pi$
$557$	921794.			0.125891			0.0629457	+	0.998017i	$0.479951\pi$
$558$	−1.26205e7	+	8.00295e6i	−1.71589	+	1.08809i
$559$	2.08108e6			0.281683
$560$	7.79040e6			1.04976
$561$	−7.37010e6	+	4.04356e6i	−0.988704	+	0.542447i
$562$	2.21319e6			0.295582
$563$	2.04531e6			0.271949			0.135975	−	0.990712i	$-0.456583\pi$
$563$	2.04531e6			0.271949			0.135975	+	0.990712i	$0.456583\pi$
$564$	44170.7	+	152137.i	0.00584705	+	0.0201389i
$565$	−4.76926e6			−0.628536
$566$		−	5.21656e6i		−	0.684452i
$567$	1.30055e7	+	6.13113e6i	1.69891	+	0.800909i
$568$		−	617859.i		−	0.0803560i
$569$	700647.			0.0907233			0.0453616	−	0.998971i	$-0.485556\pi$
$569$	700647.			0.0907233			0.0453616	+	0.998971i	$0.485556\pi$
$570$	−3.84958e6	+	1.11767e6i	−0.496280	+	0.144088i
$571$			97880.9i			0.0125634i	0.999980	+	0.00628171i	$0.00199954\pi$
$571$			97880.9i			0.0125634i	−0.999980	+	0.00628171i	$0.998000\pi$
$572$	1.31522e6	+	5.90273e6i	0.168077	+	0.754333i
$573$	503194.	+	1.73315e6i	0.0640249	+	0.220520i
$574$		−	9.17020e6i		−	1.16171i
$575$		−	536584.i		−	0.0676812i
$576$	1.07374e6	−	680884.i	0.134847	−	0.0855100i
$577$	−8.70294e6			−1.08824			−0.544122	−	0.839006i	$-0.683137\pi$
$577$	−8.70294e6			−1.08824			−0.544122	+	0.839006i	$0.683137\pi$
$578$	−2.65973e6			−0.331144
$579$	−2.56509e6	−	8.83492e6i	−0.317985	−	1.09523i
$580$		−	2.61962e6i		−	0.323347i
$581$		−	2.24876e7i		−	2.76378i
$582$	−2.46875e6	+	716766.i	−0.302113	+	0.0877142i
$583$	2.89483e6	+	1.29920e7i	0.352738	+	1.58309i
$584$			3.13288e6i			0.380112i
$585$	−4.98623e6	+	3.16189e6i	−0.602397	+	0.381995i
$586$	5.39052e6			0.648466
$587$		−	8.71643e6i		−	1.04410i	−0.852914	−	0.522051i	$-0.825167\pi$
$587$		−	8.71643e6i		−	1.04410i	0.852914	−	0.522051i	$-0.174833\pi$
$588$	−9.86112e6	+	2.86303e6i	−1.17620	+	0.341494i
$589$		−	1.33157e7i		−	1.58153i
$590$	868078.			0.102666
$591$	−1.55258e6	+	450769.i	−0.182846	+	0.0530866i
$592$	9.99175e6			1.17176
$593$	8.54547e6			0.997928			0.498964	−	0.866623i	$-0.333714\pi$
$593$	8.54547e6			0.997928			0.498964	+	0.866623i	$0.333714\pi$
$594$	−5.05868e6	+	9.17549e6i	−0.588263	+	1.06700i
$595$	8.18016e6			0.947261
$596$	2.18291e6			0.251722
$597$	−2.76795e6	+	803633.i	−0.317850	+	0.0922831i
$598$	5.75103e6			0.657647
$599$		−	1.47272e7i		−	1.67707i	−0.544844	−	0.838537i	$-0.683411\pi$
$599$		−	1.47272e7i		−	1.67707i	0.544844	−	0.838537i	$-0.316589\pi$
$600$	−1.06372e6	+	308837.i	−0.120629	+	0.0350228i
$601$		−	1.20227e7i		−	1.35774i	−0.734258	−	0.678871i	$-0.762470\pi$
$601$		−	1.20227e7i		−	1.35774i	0.734258	−	0.678871i	$-0.237530\pi$
$602$	−3.59364e6			−0.404151
$603$	−2.48354e6	+	1.57488e6i	−0.278150	+	0.176381i
$604$		−	2.55955e6i		−	0.285477i
$605$	1.70937e6	+	3.64540e6i	0.189866	+	0.404908i
$606$	1.11648e7	−	3.24153e6i	1.23501	−	0.358566i
$607$			4.68497e6i			0.516101i	0.966131	+	0.258051i	$0.0830802\pi$
$607$			4.68497e6i			0.516101i	−0.966131	+	0.258051i	$0.916920\pi$
$608$		−	7.73419e6i		−	0.848508i
$609$	−7.15232e6	−	2.46346e7i	−0.781454	−	2.69155i
$610$	6.42528e6			0.699145
$611$	−637013.			−0.0690312
$612$	−4.27581e6	+	2.71139e6i	−0.461466	+	0.292627i
$613$		−	1.03086e7i		−	1.10802i	−0.832509	−	0.554012i	$-0.813096\pi$
$613$		−	1.03086e7i		−	1.10802i	0.832509	−	0.554012i	$-0.186904\pi$
$614$		−	5.41864e6i		−	0.580056i
$615$	593725.	+	2.04496e6i	0.0632991	+	0.218020i
$616$	2.41613e6	+	1.08436e7i	0.256547	+	1.15139i
$617$			4.31575e6i			0.456398i	0.973614	+	0.228199i	$0.0732837\pi$
$617$			4.31575e6i			0.456398i	−0.973614	+	0.228199i	$0.926716\pi$
$618$	−1.10968e7	+	3.22180e6i	−1.16876	+	0.339334i
$619$	1.43494e7			1.50524			0.752621	−	0.658454i	$-0.228789\pi$
$619$	1.43494e7			1.50524			0.752621	+	0.658454i	$0.228789\pi$
$620$			3.45864e6i			0.361349i
$621$	2.43831e6	+	2.15196e6i	0.253724	+	0.223926i
$622$		−	6.24984e6i		−	0.647728i
$623$	6.80459e6			0.702395
$624$	−5.40598e6	−	1.86198e7i	−0.555793	−	1.91431i
$625$	390625.			0.0400000
$626$	8.70644e6			0.887984
$627$	−4.49065e6	−	8.18500e6i	−0.456185	−	0.831476i
$628$	−1.87224e6			−0.189436
$629$	1.04916e7			1.05735
$630$	8.61029e6	−	5.46000e6i	0.864304	−	0.548076i
$631$	−4.60487e6			−0.460409			−0.230205	−	0.973142i	$-0.573940\pi$
$631$	−4.60487e6			−0.460409			−0.230205	+	0.973142i	$0.573940\pi$
$632$		−	1.98926e6i		−	0.198106i
$633$	894564.	+	3.08114e6i	0.0887364	+	0.305634i
$634$		−	5.18215e6i		−	0.512020i
$635$	4.81474e6			0.473848
$636$	2.23522e6	+	7.69876e6i	0.219118	+	0.754706i
$637$		−	4.12895e7i		−	4.03173i
$638$	1.82454e7	−	4.06537e6i	1.77461	−	0.395411i
$639$	−707227.	−	1.11528e6i	−0.0685183	−	0.108052i
$640$		−	5.04757e6i		−	0.487116i
$641$			1.84982e6i			0.177821i	0.996040	+	0.0889107i	$0.0283386\pi$
$641$			1.84982e6i			0.177821i	−0.996040	+	0.0889107i	$0.971661\pi$
$642$	−7.31506e6	+	2.12382e6i	−0.700455	+	0.203367i
$643$	1.77736e7			1.69530			0.847651	−	0.530555i	$-0.178016\pi$
$643$	1.77736e7			1.69530			0.847651	+	0.530555i	$0.178016\pi$
$644$	−3.24135e6			−0.307972
$645$	801384.	−	232670.i	0.0758475	−	0.0220212i
$646$		−	1.38221e7i		−	1.30314i
$647$			1.76228e7i			1.65506i	0.561419	+	0.827532i	$0.310256\pi$
$647$			1.76228e7i			1.65506i	−0.561419	+	0.827532i	$0.689744\pi$
$648$	2.86264e6	−	6.07230e6i	0.267812	−	0.568088i
$649$	439699.	+	1.97337e6i	0.0409773	+	0.183906i
$650$			4.18667e6i			0.388673i
$651$	9.44308e6	+	3.25247e7i	0.873295	+	3.00788i
$652$	3.33110e6			0.306880
$653$			1.07701e7i			0.988410i	0.869346	+	0.494205i	$0.164541\pi$
$653$			1.07701e7i			0.988410i	−0.869346	+	0.494205i	$0.835459\pi$
$654$	−593544.	−	2.04434e6i	−0.0542636	−	0.186900i
$655$			1.14990e6i			0.104727i
$656$	−6.99266e6			−0.634429
$657$	3.58603e6	+	5.65509e6i	0.324116	+	0.511123i
$658$	1.10000e6			0.0990441
$659$	−576365.			−0.0516992			−0.0258496	−	0.999666i	$-0.508229\pi$
$659$	−576365.			−0.0516992			−0.0258496	+	0.999666i	$0.508229\pi$
$660$	1.16641e6	+	2.12598e6i	0.104229	+	0.189976i
$661$	7.04939e6			0.627549			0.313775	−	0.949498i	$-0.398406\pi$
$661$	7.04939e6			0.627549			0.313775	+	0.949498i	$0.398406\pi$
$662$	−1.09877e7			−0.974454
$663$	−5.67645e6	−	1.95513e7i	−0.501525	−	1.72740i
$664$	−1.04995e7			−0.924166
$665$			9.08463e6i			0.796624i
$666$	1.10433e7	−	7.00284e6i	0.964748	−	0.611771i
$667$		−	5.80205e6i		−	0.504971i
$668$	2.52294e6			0.218759
$669$	1.23718e7	−	3.59199e6i	1.06873	−	0.310291i
$670$			2.08529e6i			0.179465i
$671$	3.25453e6	+	1.46064e7i	0.279050	+	1.25238i
$672$	5.48484e6	+	1.88914e7i	0.468534	+	1.61377i
$673$		−	2.48205e6i		−	0.211238i	−0.994407	−	0.105619i	$-0.966318\pi$
$673$		−	2.48205e6i		−	0.211238i	0.994407	−	0.105619i	$-0.0336824\pi$
$674$			2.41948e7i			2.05150i
$675$	−1.56659e6	+	1.77506e6i	−0.132342	+	0.149952i
$676$	−8.88879e6			−0.748128
$677$	−1.66672e7			−1.39762			−0.698812	−	0.715305i	$-0.746288\pi$
$677$	−1.66672e7			−1.39762			−0.698812	+	0.715305i	$0.746288\pi$
$678$	−5.71493e6	−	1.96839e7i	−0.477460	−	1.64451i
$679$			5.82600e6i			0.484949i
$680$		−	3.81934e6i		−	0.316750i
$681$	1.98974e7	−	5.77692e6i	1.64410	−	0.477341i
$682$	−2.40891e7	+	5.36744e6i	−1.98317	+	0.441882i
$683$		−	1.40720e7i		−	1.15426i	−0.816653	−	0.577129i	$-0.804173\pi$
$683$		−	1.40720e7i		−	1.15426i	0.816653	−	0.577129i	$-0.195827\pi$
$684$	−3.01119e6	−	4.74858e6i	−0.246092	−	0.388082i
$685$	−3.31594e6			−0.270011
$686$			4.30925e7i			3.49616i
$687$	9.56626e6	−	2.77743e6i	0.773304	−	0.224518i
$688$			2.74030e6i			0.220713i
$689$	−3.22355e7			−2.58694
$690$	2.21461e6	−	642980.i	0.177082	−	0.0514132i
$691$	1.11246e7			0.886319			0.443159	−	0.896443i	$-0.353858\pi$
$691$	1.11246e7			0.886319			0.443159	+	0.896443i	$0.353858\pi$
$692$	−7.63323e6			−0.605959
$693$	1.67733e7	+	1.68079e7i	1.32674	+	1.32947i
$694$	−1.67105e7			−1.31701
$695$	−5.76049e6			−0.452374
$696$	−1.15020e7	+	3.33944e6i	−0.900015	+	0.261306i
$697$	−7.34251e6			−0.572483
$698$		−	2.64535e7i		−	2.05515i
$699$	−1.74415e6	+	506389.i	−0.135018	+	0.0392005i
$700$		−	2.35965e6i		−	0.182013i
$701$	3.22831e6			0.248130			0.124065	−	0.992274i	$-0.460407\pi$
$701$	3.22831e6			0.248130			0.124065	+	0.992274i	$0.460407\pi$
$702$	−1.90248e7	−	1.67905e7i	−1.45706	−	1.28594i
$703$			1.16517e7i			0.889202i
$704$	2.04948e6	−	456657.i	0.155852	−	0.0347263i
$705$	−245301.	+	71219.7i	−0.0185877	+	0.00539669i
$706$		−	2.60766e7i		−	1.96897i
$707$		−	2.63478e7i		−	1.98242i
$708$	339510.	+	1.16937e6i	0.0254548	+	0.0876737i
$709$	−1.35291e6			−0.101077			−0.0505387	−	0.998722i	$-0.516094\pi$
$709$	−1.35291e6			−0.101077			−0.0505387	+	0.998722i	$0.516094\pi$
$710$	−936440.			−0.0697163
$711$	−2.27699e6	−	3.59076e6i	−0.168922	−	0.266386i
$712$		−	3.17708e6i		−	0.234870i
$713$			7.66034e6i			0.564319i
$714$	9.80216e6	+	3.37615e7i	0.719575	+	2.47843i
$715$	−9.51740e6	+	2.12063e6i	−0.696230	+	0.155131i
$716$		−	7.72968e6i		−	0.563480i
$717$	−8.62582e6	+	2.50438e6i	−0.626617	+	0.181929i
$718$	−2.79552e7			−2.02372
$719$			2.46313e7i			1.77691i	0.458964	+	0.888455i	$0.348221\pi$
$719$			2.46313e7i			1.77691i	−0.458964	+	0.888455i	$0.651779\pi$
$720$	−4.16348e6	−	6.56571e6i	−0.299312	−	0.472009i
$721$			2.61874e7i			1.87609i
$722$	−1.71589e6			−0.122503
$723$	3.32032e6	+	1.14361e7i	0.236229	+	0.813643i
$724$	392413.			0.0278225
$725$	4.22380e6			0.298441
$726$	−1.29971e7	+	1.14232e7i	−0.915178	+	0.804353i
$727$	−957627.			−0.0671986			−0.0335993	−	0.999435i	$-0.510697\pi$
$727$	−957627.			−0.0671986			−0.0335993	+	0.999435i	$0.510697\pi$
$728$	−2.69049e7			−1.88149
$729$	−1.78333e6	−	1.42377e7i	−0.124283	−	0.992247i
$730$	4.74826e6			0.329782
$731$			2.87740e6i			0.199162i
$732$	2.51296e6	+	8.65538e6i	0.173344	+	0.597047i
$733$		−	2.38370e6i		−	0.163867i	−0.996638	−	0.0819335i	$-0.973890\pi$
$733$		−	2.38370e6i		−	0.163867i	0.996638	−	0.0819335i	$-0.0261095\pi$
$734$	2.13516e7			1.46282
$735$	−4.61628e6	−	1.58998e7i	−0.315191	−	1.08561i
$736$			4.44937e6i			0.302764i
$737$	−4.74042e6	+	1.05624e6i	−0.321476	+	0.0716300i
$738$	−7.72859e6	+	4.90089e6i	−0.522347	+	0.331233i
$739$			1.46709e7i			0.988205i	0.869404	+	0.494102i	$0.164503\pi$
$739$			1.46709e7i			0.988205i	−0.869404	+	0.494102i	$0.835497\pi$
$740$		−	3.02642e6i		−	0.203166i
$741$	2.17131e7	−	6.30408e6i	1.45270	−	0.421771i
$742$	5.56647e7			3.71168
$743$	4.71697e6			0.313467			0.156733	−	0.987641i	$-0.449904\pi$
$743$	4.71697e6			0.313467			0.156733	+	0.987641i	$0.449904\pi$
$744$	1.51859e7	−	4.40900e6i	1.00579	−	0.292017i
$745$			3.51967e6i			0.232333i
$746$			1.51445e7i			0.996343i
$747$	−1.89524e7	+	1.20182e7i	−1.24269	+	0.788022i
$748$	−8.16138e6	+	1.81849e6i	−0.533347	+	0.118838i
$749$			1.72628e7i			1.12436i
$750$	468080.	+	1.61220e6i	0.0303855	+	0.104657i
$751$	−7.37092e6			−0.476894			−0.238447	−	0.971155i	$-0.576638\pi$
$751$	−7.37092e6			−0.476894			−0.238447	+	0.971155i	$0.576638\pi$
$752$		−	838797.i		−	0.0540894i
$753$	−3.19205e6	−	1.09943e7i	−0.205155	−	0.706613i
$754$			4.52702e7i			2.89990i
$755$	4.12695e6			0.263488
$756$	1.07226e7	+	9.46333e6i	0.682332	+	0.602199i
$757$	−1.10594e7			−0.701445			−0.350722	−	0.936479i	$-0.614064\pi$
$757$	−1.10594e7			−0.701445			−0.350722	+	0.936479i	$0.614064\pi$
$758$	1.26102e7			0.797167
$759$	2.58341e6	+	4.70871e6i	0.162775	+	0.296686i
$760$	4.24164e6			0.266379
$761$	6.41893e6			0.401792			0.200896	−	0.979613i	$-0.435615\pi$
$761$	6.41893e6			0.401792			0.200896	+	0.979613i	$0.435615\pi$
$762$	5.76943e6	+	1.98716e7i	0.359953	+	1.23978i
$763$	−4.82443e6			−0.300009
$764$			1.79507e6i			0.111262i
$765$	−4.37178e6	−	6.89419e6i	−0.270087	−	0.425922i
$766$			2.97490e7i			1.83190i
$767$	−4.89628e6			−0.300523
$768$	1.83261e7	−	5.32071e6i	1.12116	−	0.325512i
$769$		−	3.16914e7i		−	1.93253i	−0.257555	−	0.966264i	$-0.582917\pi$
$769$		−	3.16914e7i		−	1.93253i	0.257555	−	0.966264i	$-0.417083\pi$
$770$	1.64348e7	−	3.66193e6i	0.998934	−	0.222578i
$771$	−2.87629e6	−	9.90677e6i	−0.174259	−	0.600200i
$772$		−	9.15057e6i		−	0.552592i
$773$			9.09163e6i			0.547259i	0.961835	+	0.273630i	$0.0882243\pi$
$773$			9.09163e6i			0.547259i	−0.961835	+	0.273630i	$0.911776\pi$
$774$	1.92057e6	+	3.02870e6i	0.115233	+	0.181720i
$775$	−5.57662e6			−0.333516
$776$	2.72018e6			0.162160
$777$	−8.26300e6	−	2.84602e7i	−0.491004	−	1.69116i
$778$		−	2.15688e7i		−	1.27755i
$779$		−	8.15436e6i		−	0.481444i
$780$	−5.63978e6	+	1.63743e6i	−0.331914	+	0.0963665i
$781$	−474325.	−	2.12878e6i	−0.0278259	−	0.124883i
$782$			7.95163e6i			0.464986i
$783$	−1.69395e7	+	1.91936e7i	−0.987406	+	1.11880i
$784$	5.43687e7			3.15907
$785$		−	3.01875e6i		−	0.174845i
$786$	−4.74593e6	+	1.37791e6i	−0.274009	+	0.0795545i
$787$			2.70844e7i			1.55877i	0.626545	+	0.779385i	$0.284468\pi$
$787$			2.70844e7i			1.55877i	−0.626545	+	0.779385i	$0.715532\pi$
$788$	−1.60805e6			−0.0922536
$789$	1.96009e7	−	5.69083e6i	1.12094	−	0.325449i
$790$	−3.01496e6			−0.171875
$791$	−4.64520e7			−2.63975
$792$	7.84764e6	−	7.83150e6i	0.444556	−	0.443641i
$793$	−3.62410e7			−2.04652
$794$	−2.93847e7			−1.65413
$795$	−1.24133e7	+	3.60401e6i	−0.696575	+	0.202241i
$796$	−2.86684e6			−0.160369
$797$			1.20852e7i			0.673921i	0.941519	+	0.336961i	$0.109399\pi$
$797$			1.20852e7i			0.673921i	−0.941519	+	0.336961i	$0.890601\pi$
$798$	−3.74944e7	+	1.08860e7i	−2.08430	+	0.605146i
$799$		−	880763.i		−	0.0488081i
$800$	−3.23907e6			−0.178935
$801$	−3.63662e6	−	5.73487e6i	−0.200270	−	0.315822i
$802$			1.11090e7i			0.609872i
$803$	2.40509e6	+	1.07941e7i	0.131626	+	0.590739i
$804$	−2.80906e6	+	815571.i	−0.153257	+	0.0444960i
$805$		−	5.22626e6i		−	0.284250i
$806$		−	5.97694e7i		−	3.24072i
$807$	6.93912e6	+	2.39003e7i	0.375077	+	1.29187i
$808$	−1.23018e7			−0.662891
$809$	3.39581e6			0.182420			0.0912098	−	0.995832i	$-0.470927\pi$
$809$	3.39581e6			0.182420			0.0912098	+	0.995832i	$0.470927\pi$
$810$	−9.20331e6	−	4.33868e6i	−0.492869	−	0.232351i
$811$			1.16193e6i			0.0620339i	0.999519	+	0.0310169i	$0.00987458\pi$
$811$			1.16193e6i			0.0620339i	−0.999519	+	0.0310169i	$0.990125\pi$
$812$		−	2.55148e7i		−	1.35801i
$813$	8.17787e6	+	2.81670e7i	0.433924	+	1.49456i
$814$	2.10788e7	−	4.69669e6i	1.11502	−	0.248445i
$815$			5.37097e6i			0.283243i
$816$	2.57445e7	−	7.47456e6i	1.35350	−	0.392971i
$817$	−3.19555e6			−0.167491
$818$			5.39946e6i			0.282142i
$819$	−4.85653e7	+	3.07964e7i	−2.52997	+	1.60432i
$820$			2.11802e6i			0.110001i
$821$	8.96225e6			0.464044			0.232022	−	0.972711i	$-0.425466\pi$
$821$	8.96225e6			0.464044			0.232022	+	0.972711i	$0.425466\pi$
$822$	−3.97344e6	−	1.36857e7i	−0.205110	−	0.706459i
$823$	−2.49223e7			−1.28259			−0.641296	−	0.767294i	$-0.721603\pi$
$823$	−2.49223e7			−1.28259			−0.641296	+	0.767294i	$0.721603\pi$
$824$	1.22270e7			0.627336
$825$	−3.42787e6	+	1.88068e6i	−0.175343	+	0.0962012i
$826$	8.45496e6			0.431183
$827$	1.09561e7			0.557048			0.278524	−	0.960429i	$-0.410155\pi$
$827$	1.09561e7			0.557048			0.278524	+	0.960429i	$0.410155\pi$
$828$	1.73229e6	+	2.73179e6i	0.0878103	+	0.138475i
$829$	−3.01505e7			−1.52373			−0.761866	−	0.647735i	$-0.775717\pi$
$829$	−3.01505e7			−1.52373			−0.761866	+	0.647735i	$0.775717\pi$
$830$			1.59133e7i			0.801799i
$831$	−1.71879e6	−	5.92000e6i	−0.0863415	−	0.297385i
$832$			5.08513e6i			0.254679i
$833$	5.70888e7			2.85061
$834$	−6.90271e6	−	2.37749e7i	−0.343640	−	1.18360i
$835$			4.06792e6i			0.201909i
$836$	−2.01955e6	−	9.06377e6i	−0.0999401	−	0.448532i
$837$	2.23649e7	−	2.53410e7i	1.10345	−	1.25029i
$838$			7.68087e6i			0.377834i
$839$		−	3.07528e7i		−	1.50827i	−0.656718	−	0.754136i	$-0.728056\pi$
$839$		−	3.07528e7i		−	1.50827i	0.656718	−	0.754136i	$-0.271944\pi$
$840$	−1.03605e7	+	3.00803e6i	−0.506622	+	0.147090i
$841$	2.51606e7			1.22668
$842$	−3.69933e7			−1.79822
$843$	−4.80704e6	+	1.39566e6i	−0.232975	+	0.0676409i
$844$			3.19122e6i			0.154206i
$845$		−	1.43320e7i		−	0.690504i
$846$	−587881.	−	927075.i	−0.0282399	−	0.0445337i
$847$	1.66491e7	+	3.55057e7i	0.797409	+	1.70055i
$848$		−	4.24466e7i		−	2.02700i
$849$	3.28960e6	+	1.13303e7i	0.156630	+	0.539478i
$850$	−5.78867e6			−0.274809
$851$		−	6.70305e6i		−	0.317284i
$852$	−366247.	−	1.26146e6i	−0.0172852	−	0.0595354i
$853$		−	3.04053e7i		−	1.43079i	−0.698719	−	0.715397i	$-0.746246\pi$
$853$		−	3.04053e7i		−	1.43079i	0.698719	−	0.715397i	$-0.253754\pi$
$854$	6.25814e7			2.93630
$855$	7.65647e6	−	4.85516e6i	0.358190	−	0.227137i
$856$	8.06006e6			0.375970
$857$	1.83133e6			0.0851755			0.0425877	−	0.999093i	$-0.486440\pi$
$857$	1.83133e6			0.0851755			0.0425877	+	0.999093i	$0.486440\pi$
$858$	−2.01569e7	−	3.67395e7i	−0.934771	−	1.70378i
$859$	2.90723e7			1.34430			0.672151	−	0.740414i	$-0.265371\pi$
$859$	2.90723e7			1.34430			0.672151	+	0.740414i	$0.265371\pi$
$860$	830015.			0.0382684
$861$	5.78280e6	+	1.99177e7i	0.265846	+	0.915652i
$862$	−1.90032e7			−0.871083
$863$			9.40066e6i			0.429666i	0.976651	+	0.214833i	$0.0689208\pi$
$863$			9.40066e6i			0.429666i	−0.976651	+	0.214833i	$0.931079\pi$
$864$	1.29902e7	−	1.47188e7i	0.592015	−	0.670794i
$865$		−	1.23076e7i		−	0.559285i
$866$	−4.41088e7			−1.99862
$867$	5.77692e6	−	1.67724e6i	0.261005	−	0.0757790i
$868$			3.36867e7i			1.51761i
$869$	−1.52714e6	−	6.85380e6i	−0.0686007	−	0.307880i
$870$	5.06132e6	+	1.74326e7i	0.226707	+	0.780846i
$871$		−	1.17618e7i		−	0.525327i
$872$			2.25254e6i			0.100319i
$873$	4.91012e6	−	3.11363e6i	0.218050	−	0.138271i
$874$	−8.83084e6			−0.391042
$875$	3.80464e6			0.167994
$876$	1.85707e6	+	6.39630e6i	0.0817653	+	0.281623i
$877$		−	1.09284e7i		−	0.479798i	−0.970798	−	0.239899i	$-0.922886\pi$
$877$		−	1.09284e7i		−	0.479798i	0.970798	−	0.239899i	$-0.0771144\pi$
$878$			3.64785e7i			1.59699i
$879$	−1.17082e7	+	3.39931e6i	−0.511114	+	0.148395i
$880$	−2.79237e6	−	1.25322e7i	−0.121553	−	0.545532i
$881$		−	1.67518e7i		−	0.727145i	−0.931566	−	0.363572i	$-0.881557\pi$
$881$		−	1.67518e7i		−	0.727145i	0.931566	−	0.363572i	$-0.118443\pi$
$882$	6.00906e7	−	3.81049e7i	2.60097	−	1.64934i
$883$	1.84876e7			0.797955			0.398977	−	0.916961i	$-0.369365\pi$
$883$	1.84876e7			0.797955			0.398977	+	0.916961i	$0.369365\pi$
$884$		−	2.02498e7i		−	0.871547i
$885$	−1.88546e6	+	547417.i	−0.0809207	+	0.0234942i
$886$			1.68165e7i			0.719699i
$887$	3.92355e7			1.67444			0.837221	−	0.546864i	$-0.184179\pi$
$887$	3.92355e7			1.67444			0.837221	+	0.546864i	$0.184179\pi$
$888$	−1.32881e7	+	3.85802e6i	−0.565499	+	0.164184i
$889$	4.68950e7			1.99009
$890$	−4.81525e6			−0.203772
$891$	5.20131e6	−	2.31192e7i	0.219492	−	0.975614i
$892$	1.28139e7			0.539222
$893$	978147.			0.0410465
$894$	−1.45265e7	+	4.21756e6i	−0.607879	+	0.176489i
$895$	1.24631e7			0.520078
$896$		−	4.91627e7i		−	2.04581i
$897$	−1.24912e7	+	3.62665e6i	−0.518351	+	0.150496i
$898$		−	4.53477e7i		−	1.87657i
$899$	−6.02996e7			−2.48837
$900$	−1.98870e6	+	1.26108e6i	−0.0818395	+	0.0518965i
$901$		−	4.45703e7i		−	1.82908i
$902$	−1.47518e7	+	3.28694e6i	−0.603712	+	0.134517i
$903$	7.80538e6	−	2.26618e6i	0.318548	−	0.0924858i
$904$			2.16886e7i			0.882693i
$905$			632715.i			0.0256795i
$906$	4.94526e6	+	1.70329e7i	0.200156	+	0.689395i
$907$	−1.85378e6			−0.0748238			−0.0374119	−	0.999300i	$-0.511911\pi$
$907$	−1.85378e6			−0.0748238			−0.0374119	+	0.999300i	$0.511911\pi$
$908$	2.06083e7			0.829519
$909$	−2.22057e7	+	1.40812e7i	−0.891365	+	0.565236i
$910$			4.07776e7i			1.63237i
$911$			4.22257e7i			1.68570i	0.538148	+	0.842851i	$0.319124\pi$
$911$			4.22257e7i			1.68570i	−0.538148	+	0.842851i	$0.680876\pi$
$912$	8.30101e6	+	2.85911e7i	0.330479	+	1.13827i
$913$	−3.61752e7	+	8.06041e6i	−1.43626	+	0.320022i
$914$			3.29953e6i			0.130643i
$915$	−1.39557e7	+	4.05183e6i	−0.551059	+	0.159992i
$916$	9.90804e6			0.390166
$917$			1.11999e7i			0.439836i
$918$	2.32153e7	−	2.63046e7i	0.909219	−	1.03021i
$919$			2.60233e7i			1.01642i	0.861233	+	0.508210i	$0.169692\pi$
$919$			2.60233e7i			1.01642i	−0.861233	+	0.508210i	$0.830308\pi$
$920$	−2.44015e6			−0.0950490
$921$	3.41704e6	+	1.17693e7i	0.132740	+	0.457194i
$922$	−1.28533e7			−0.497952
$923$	5.28187e6			0.204072
$924$	1.13607e7	+	2.07068e7i	0.437747	+	0.797871i
$925$	4.87972e6			0.187517
$926$	3.41520e7			1.30885
$927$	2.20706e7	−	1.39955e7i	0.843556	−	0.534920i
$928$	−3.50239e7			−1.33504
$929$		−	1.02889e7i		−	0.391139i	−0.980690	−	0.195570i	$-0.937344\pi$
$929$		−	1.02889e7i		−	0.391139i	0.980690	−	0.195570i	$-0.0626555\pi$
$930$	−6.68237e6	−	2.30160e7i	−0.253351	−	0.872616i
$931$			6.34010e7i			2.39730i
$932$	−1.80646e6			−0.0681223
$933$	3.94120e6	+	1.35746e7i	0.148226	+	0.510533i
$934$		−	5.98784e7i		−	2.24597i
$935$	−2.93208e6	−	1.31592e7i	−0.109685	−	0.492266i
$936$	1.43789e7	+	2.26753e7i	0.536460	+	0.845985i
$937$			6.00306e6i			0.223369i	0.993744	+	0.111685i	$0.0356247\pi$
$937$			6.00306e6i			0.223369i	−0.993744	+	0.111685i	$0.964375\pi$
$938$			2.03105e7i			0.753726i
$939$	−1.89104e7	+	5.49035e6i	−0.699900	+	0.203206i
$940$	−254065.			−0.00937832
$941$	2.63324e7			0.969429			0.484714	−	0.874673i	$-0.338924\pi$
$941$	2.63324e7			0.969429			0.484714	+	0.874673i	$0.338924\pi$
$942$	1.24591e7	−	3.61732e6i	0.457466	−	0.132819i
$943$			4.69108e6i			0.171788i
$944$		−	6.44726e6i		−	0.235475i
$945$	−1.52584e7	+	1.72888e7i	−0.555815	+	0.629776i
$946$	1.28810e6	+	5.78098e6i	0.0467973	+	0.210026i
$947$		−	1.16852e7i		−	0.423412i	−0.977333	−	0.211706i	$-0.932098\pi$
$947$		−	1.16852e7i		−	0.423412i	0.977333	−	0.211706i	$-0.0679019\pi$
$948$	−1.17917e6	−	4.06140e6i	−0.0426143	−	0.146776i
$949$	−2.67820e7			−0.965333
$950$		−	6.42872e6i		−	0.231108i
$951$	3.26790e6	+	1.12556e7i	0.117170	+	0.403569i
$952$		−	3.71999e7i		−	1.33030i
$953$	−5.40223e6			−0.192682			−0.0963409	−	0.995348i	$-0.530714\pi$
$953$	−5.40223e6			−0.192682			−0.0963409	+	0.995348i	$0.530714\pi$
$954$	−2.97492e7	−	4.69139e7i	−1.05829	−	1.66890i
$955$	−2.89432e6			−0.102692
$956$	−8.93399e6			−0.316156
$957$	−3.70654e7	+	2.03357e7i	−1.30824	+	0.717760i
$958$	1.65770e7			0.583568
$959$	−3.22969e7			−1.13400
$960$	568530.	+	1.95818e6i	0.0199102	+	0.0685765i
$961$	5.09834e7			1.78082
$962$			5.23002e7i			1.82207i
$963$	1.45490e7	−	9.22588e6i	0.505554	−	0.320584i
$964$			1.18447e7i			0.410518i
$965$	1.47541e7			0.510029
$966$	2.15700e7	−	6.26254e6i	0.743717	−	0.215927i
$967$		−	3.12092e6i		−	0.107329i	−0.998559	−	0.0536645i	$-0.982910\pi$
$967$		−	3.12092e6i		−	0.107329i	0.998559	−	0.0536645i	$-0.0170901\pi$
$968$	1.65777e7	−	7.77350e6i	0.568639	−	0.266642i
$969$	8.71631e6	+	3.00215e7i	0.298211	+	1.02712i
$970$		−	4.12275e6i		−	0.140688i
$971$			3.50456e7i			1.19285i	0.802669	+	0.596425i	$0.203413\pi$
$971$			3.50456e7i			1.19285i	−0.802669	+	0.596425i	$0.796587\pi$
$972$	2.24509e6	−	1.40945e7i	0.0762199	−	0.478502i
$973$	−5.61064e7			−1.89990
$974$	1.69453e7			0.572337
$975$	−2.64015e6	−	9.09343e6i	−0.0889439	−	0.306349i
$976$		−	4.77209e7i		−	1.60356i
$977$			1.49893e7i			0.502394i	0.967936	+	0.251197i	$0.0808242\pi$
$977$			1.49893e7i			0.502394i	−0.967936	+	0.251197i	$0.919176\pi$
$978$	−2.21673e7	+	6.43595e6i	−0.741080	+	0.215162i
$979$	−2.43902e6	−	1.09463e7i	−0.0813315	−	0.365016i
$980$		−	1.64678e7i		−	0.547736i
$981$	2.57835e6	+	4.06600e6i	0.0855401	+	0.134895i
$982$	−6.18505e7			−2.04675
$983$			1.57856e7i			0.521048i	0.965467	+	0.260524i	$0.0838953\pi$
$983$			1.57856e7i			0.521048i	−0.965467	+	0.260524i	$0.916105\pi$
$984$	9.29961e6	−	2.70001e6i	0.306180	−	0.0888950i
$985$		−	2.59277e6i		−	0.0851478i
$986$	−6.25926e7			−2.05036
$987$	−2.38920e6	+	693670.i	−0.0780656	+	0.0226652i
$988$	2.24888e7			0.732951
$989$	1.83835e6			0.0597638
$990$	−1.18696e7	−	1.18941e7i	−0.384900	−	0.385693i
$991$	−3.53877e7			−1.14464			−0.572319	−	0.820031i	$-0.693956\pi$
$991$	−3.53877e7			−1.14464			−0.572319	+	0.820031i	$0.693956\pi$
$992$	4.62415e7			1.49194
$993$	2.38652e7	−	6.92893e6i	0.768055	−	0.222994i
$994$	−9.12080e6			−0.292797
$995$		−	4.62241e6i		−	0.148017i
$996$	−2.14365e7	+	6.22379e6i	−0.684710	+	0.198796i
$997$			2.31585e7i			0.737857i	0.929458	+	0.368929i	$0.120275\pi$
$997$			2.31585e7i			0.737857i	−0.929458	+	0.368929i	$0.879725\pi$
$998$	−1.82017e6			−0.0578476
$999$	−1.95700e7	+	2.21742e7i	−0.620408	+	0.702964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.f.a.131.20	yes	80
3.2	odd	2	inner	165.6.f.a.131.62	yes	80
11.10	odd	2	inner	165.6.f.a.131.61	yes	80
33.32	even	2	inner	165.6.f.a.131.19	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.f.a.131.19	✓	80	33.32	even	2	inner
165.6.f.a.131.20	yes	80	1.1	even	1	trivial
165.6.f.a.131.61	yes	80	11.10	odd	2	inner
165.6.f.a.131.62	yes	80	3.2	odd	2	inner

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

\(f(q)\)	\(=\)	\(q-6.89239 q^{2} +(14.9703 - 4.34640i) q^{3} +15.5051 q^{4} +25.0000i q^{5} +(-103.181 + 29.9571i) q^{6} +243.497i q^{7} +113.689 q^{8} +(205.218 - 130.134i) q^{9} +O(q^{10})\)	\(q-6.89239 q^{2} +(14.9703 - 4.34640i) q^{3} +15.5051 q^{4} +25.0000i q^{5} +(-103.181 + 29.9571i) q^{6} +243.497i q^{7} +113.689 q^{8} +(205.218 - 130.134i) q^{9} -172.310i q^{10} +(391.706 - 87.2784i) q^{11} +(232.116 - 67.3914i) q^{12} +971.892i q^{13} -1678.28i q^{14} +(108.660 + 374.257i) q^{15} -1279.76 q^{16} -1343.78 q^{17} +(-1414.44 + 896.932i) q^{18} -1492.36i q^{19} +387.628i q^{20} +(1058.33 + 3645.21i) q^{21} +(-2699.79 + 601.557i) q^{22} +858.534i q^{23} +(1701.96 - 494.139i) q^{24} -625.000 q^{25} -6698.66i q^{26} +(2506.55 - 2840.09i) q^{27} +3775.44i q^{28} -6758.09 q^{29} +(-748.928 - 2579.52i) q^{30} +8922.59 q^{31} +5182.52 q^{32} +(5484.59 - 3009.09i) q^{33} +9261.88 q^{34} -6087.42 q^{35} +(3181.92 - 2017.73i) q^{36} -7807.55 q^{37} +10285.9i q^{38} +(4224.23 + 14549.5i) q^{39} +2842.23i q^{40} +5464.06 q^{41} +(-7294.46 - 25124.2i) q^{42} -2141.27i q^{43} +(6073.44 - 1353.26i) q^{44} +(3253.34 + 5130.44i) q^{45} -5917.36i q^{46} +655.436i q^{47} +(-19158.3 + 5562.33i) q^{48} -42483.7 q^{49} +4307.75 q^{50} +(-20116.8 + 5840.61i) q^{51} +15069.3i q^{52} +33167.8i q^{53} +(-17276.1 + 19575.0i) q^{54} +(2181.96 + 9792.65i) q^{55} +27683.0i q^{56} +(-6486.40 - 22341.1i) q^{57} +46579.4 q^{58} +5037.89i q^{59} +(1684.79 + 5802.89i) q^{60} +37289.1i q^{61} -61498.0 q^{62} +(31687.1 + 49969.8i) q^{63} +5232.19 q^{64} -24297.3 q^{65} +(-37802.0 + 20739.8i) q^{66} -12102.0 q^{67} -20835.5 q^{68} +(3731.53 + 12852.5i) q^{69} +41956.9 q^{70} -5434.63i q^{71} +(23331.0 - 14794.8i) q^{72} +27556.5i q^{73} +53812.7 q^{74} +(-9356.41 + 2716.50i) q^{75} -23139.2i q^{76} +(21252.0 + 95379.1i) q^{77} +(-29115.1 - 100281. i) q^{78} -17497.3i q^{79} -31993.9i q^{80} +(25179.5 - 53411.4i) q^{81} -37660.5 q^{82} -92352.9 q^{83} +(16409.6 + 56519.4i) q^{84} -33594.5i q^{85} +14758.5i q^{86} +(-101170. + 29373.4i) q^{87} +(44532.8 - 9922.62i) q^{88} -27945.3i q^{89} +(-22423.3 - 35361.0i) q^{90} -236653. q^{91} +13311.7i q^{92} +(133573. - 38781.1i) q^{93} -4517.52i q^{94} +37309.0 q^{95} +(77583.7 - 22525.3i) q^{96} +23926.4 q^{97} +292814. q^{98} +(69027.1 - 68885.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9}+O(q^{10}) \) 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9	\( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9} + 2112 q^{12} + 1100 q^{15} + 13792 q^{16} - 9892 q^{22} - 50000 q^{25} - 10780 q^{27} + 2112 q^{31} + 6316 q^{33} + 69560 q^{34} - 17268 q^{36} - 7456 q^{37} - 100712 q^{42} + 61352 q^{48} - 233408 q^{49} - 15800 q^{55} - 93728 q^{58} + 62700 q^{60} + 212400 q^{64} + 203724 q^{66} + 182072 q^{67} - 122584 q^{69} + 6600 q^{70} - 27500 q^{75} - 489128 q^{78} + 194872 q^{81} - 237544 q^{82} - 641716 q^{88} + 168272 q^{91} + 433336 q^{93} + 949008 q^{97} + 328952 q^{99}+O(q^{100}) \) 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9 + 2112 * q^12 + 1100 * q^15 + 13792 * q^16 - 9892 * q^22 - 50000 * q^25 - 10780 * q^27 + 2112 * q^31 + 6316 * q^33 + 69560 * q^34 - 17268 * q^36 - 7456 * q^37 - 100712 * q^42 + 61352 * q^48 - 233408 * q^49 - 15800 * q^55 - 93728 * q^58 + 62700 * q^60 + 212400 * q^64 + 203724 * q^66 + 182072 * q^67 - 122584 * q^69 + 6600 * q^70 - 27500 * q^75 - 489128 * q^78 + 194872 * q^81 - 237544 * q^82 - 641716 * q^88 + 168272 * q^91 + 433336 * q^93 + 949008 * q^97 + 328952 * q^99

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