LMFDB - Embedded newform 33.5.b.a.23.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,5,Mod(23,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	33.b (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:	$3.41120878177$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 162x^{12} + 10041x^{10} + 298396x^{8} + 4418856x^{6} + 32113344x^{4} + 102865552x^{2} + 102193344 $ x^14 + 162x^12 + 10041x^10 + 298396x^8 + 4418856x^6 + 32113344x^4 + 102865552x^2 + 102193344
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{9}\cdot 11^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.14
Root			$7.08422i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.5.b.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.08422i q^{2} +(1.47928 + 8.87760i) q^{3} -34.1862 q^{4} -5.51941i q^{5} +(-62.8909 + 10.4795i) q^{6} +86.8582 q^{7} -128.835i q^{8} +(-76.6235 + 26.2648i) q^{9} +O(q^{10})$	\(q+7.08422i q^{2} +(1.47928 + 8.87760i) q^{3} -34.1862 q^{4} -5.51941i q^{5} +(-62.8909 + 10.4795i) q^{6} +86.8582 q^{7} -128.835i q^{8} +(-76.6235 + 26.2648i) q^{9} +39.1007 q^{10} +36.4829i q^{11} +(-50.5708 - 303.491i) q^{12} -166.850 q^{13} +615.323i q^{14} +(48.9991 - 8.16473i) q^{15} +365.716 q^{16} +57.8030i q^{17} +(-186.066 - 542.818i) q^{18} +469.895 q^{19} +188.688i q^{20} +(128.487 + 771.092i) q^{21} -258.453 q^{22} +403.013i q^{23} +(1143.74 - 190.582i) q^{24} +594.536 q^{25} -1182.00i q^{26} +(-346.516 - 641.380i) q^{27} -2969.35 q^{28} -583.701i q^{29} +(57.8408 + 347.120i) q^{30} +334.760 q^{31} +529.453i q^{32} +(-323.880 + 53.9682i) q^{33} -409.489 q^{34} -479.406i q^{35} +(2619.46 - 897.894i) q^{36} +793.796 q^{37} +3328.84i q^{38} +(-246.817 - 1481.22i) q^{39} -711.092 q^{40} +1525.28i q^{41} +(-5462.59 + 910.232i) q^{42} -578.739 q^{43} -1247.21i q^{44} +(144.966 + 422.916i) q^{45} -2855.03 q^{46} -3241.31i q^{47} +(540.994 + 3246.68i) q^{48} +5143.35 q^{49} +4211.82i q^{50} +(-513.152 + 85.5066i) q^{51} +5703.95 q^{52} -4293.98i q^{53} +(4543.67 - 2454.79i) q^{54} +201.364 q^{55} -11190.4i q^{56} +(695.104 + 4171.53i) q^{57} +4135.06 q^{58} +2286.12i q^{59} +(-1675.09 + 279.121i) q^{60} -4999.79 q^{61} +2371.51i q^{62} +(-6655.38 + 2281.32i) q^{63} +2100.69 q^{64} +920.911i q^{65} +(-382.323 - 2294.44i) q^{66} +1349.06 q^{67} -1976.06i q^{68} +(-3577.79 + 596.168i) q^{69} +3396.22 q^{70} +421.099i q^{71} +(3383.83 + 9871.78i) q^{72} -1400.57 q^{73} +5623.42i q^{74} +(879.483 + 5278.05i) q^{75} -16063.9 q^{76} +3168.84i q^{77} +(10493.3 - 1748.50i) q^{78} -3506.52 q^{79} -2018.54i q^{80} +(5181.32 - 4025.01i) q^{81} -10805.4 q^{82} +1461.59i q^{83} +(-4392.49 - 26360.7i) q^{84} +319.039 q^{85} -4099.91i q^{86} +(5181.86 - 863.454i) q^{87} +4700.27 q^{88} +694.642i q^{89} +(-2996.03 + 1026.97i) q^{90} -14492.3 q^{91} -13777.5i q^{92} +(495.202 + 2971.86i) q^{93} +22962.1 q^{94} -2593.54i q^{95} +(-4700.27 + 783.207i) q^{96} +6700.63 q^{97} +36436.6i q^{98} +(-958.217 - 2795.44i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9}+O(q^{10}) $ 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9	$ 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9} - 156 q^{10} - 100 q^{12} - 104 q^{13} + 151 q^{15} + 356 q^{16} - 34 q^{18} + 1072 q^{19} + 718 q^{21} + 1200 q^{24} - 1060 q^{25} - 1154 q^{27} - 1808 q^{28} - 3026 q^{30} + 3310 q^{31} - 605 q^{33} - 2304 q^{34} + 2644 q^{36} - 362 q^{37} + 4264 q^{39} + 1896 q^{40} - 7364 q^{42} - 6740 q^{43} + 3611 q^{45} - 4068 q^{46} - 2956 q^{48} + 7074 q^{49} - 7046 q^{51} + 13072 q^{52} + 20512 q^{54} + 726 q^{55} + 3876 q^{57} - 7848 q^{58} - 8416 q^{60} - 3560 q^{61} - 17662 q^{63} + 12020 q^{64} + 1210 q^{66} - 16514 q^{67} + 9833 q^{69} + 13320 q^{70} + 8160 q^{72} + 12664 q^{73} - 5386 q^{75} - 43736 q^{76} + 19096 q^{78} + 3052 q^{79} - 11611 q^{81} + 10200 q^{82} - 39184 q^{84} + 34884 q^{85} + 37068 q^{87} - 7260 q^{88} - 26686 q^{90} - 45856 q^{91} + 2719 q^{93} + 6120 q^{94} - 38368 q^{96} - 27854 q^{97} + 4235 q^{99}+O(q^{100}) $ 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9 - 156 * q^10 - 100 * q^12 - 104 * q^13 + 151 * q^15 + 356 * q^16 - 34 * q^18 + 1072 * q^19 + 718 * q^21 + 1200 * q^24 - 1060 * q^25 - 1154 * q^27 - 1808 * q^28 - 3026 * q^30 + 3310 * q^31 - 605 * q^33 - 2304 * q^34 + 2644 * q^36 - 362 * q^37 + 4264 * q^39 + 1896 * q^40 - 7364 * q^42 - 6740 * q^43 + 3611 * q^45 - 4068 * q^46 - 2956 * q^48 + 7074 * q^49 - 7046 * q^51 + 13072 * q^52 + 20512 * q^54 + 726 * q^55 + 3876 * q^57 - 7848 * q^58 - 8416 * q^60 - 3560 * q^61 - 17662 * q^63 + 12020 * q^64 + 1210 * q^66 - 16514 * q^67 + 9833 * q^69 + 13320 * q^70 + 8160 * q^72 + 12664 * q^73 - 5386 * q^75 - 43736 * q^76 + 19096 * q^78 + 3052 * q^79 - 11611 * q^81 + 10200 * q^82 - 39184 * q^84 + 34884 * q^85 + 37068 * q^87 - 7260 * q^88 - 26686 * q^90 - 45856 * q^91 + 2719 * q^93 + 6120 * q^94 - 38368 * q^96 - 27854 * q^97 + 4235 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

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 $

$2$			7.08422i			1.77106i	0.464587	+	0.885528i	$0.346203\pi$
$2$			7.08422i			1.77106i	−0.464587	+	0.885528i	$0.653797\pi$
$3$	1.47928	+	8.87760i	0.164364	+	0.986400i
$3$	1.47928	+	8.87760i	0.164364	+	0.986400i
$4$	−34.1862			−2.13664
$5$		−	5.51941i		−	0.220776i	−0.993889	−	0.110388i	$-0.964791\pi$
$5$		−	5.51941i		−	0.220776i	0.993889	−	0.110388i	$-0.0352094\pi$
$6$	−62.8909	+	10.4795i	−1.74697	+	0.291098i
$7$	86.8582			1.77262			0.886308	−	0.463096i	$-0.153262\pi$
$7$	86.8582			1.77262			0.886308	+	0.463096i	$0.153262\pi$
$8$		−	128.835i		−	2.01304i
$9$	−76.6235	+	26.2648i	−0.945969	+	0.324257i
$10$	39.1007			0.391007
$11$			36.4829i			0.301511i
$11$			36.4829i			0.301511i
$12$	−50.5708	−	303.491i	−0.351186	−	2.10758i
$13$	−166.850			−0.987276			−0.493638	−	0.869668i	$-0.664333\pi$
$13$	−166.850			−0.987276			−0.493638	+	0.869668i	$0.664333\pi$
$14$			615.323i			3.13940i
$15$	48.9991	−	8.16473i	0.217774	−	0.0362877i
$16$	365.716			1.42858
$17$			57.8030i			0.200010i	0.994987	+	0.100005i	$0.0318860\pi$
$17$			57.8030i			0.200010i	−0.994987	+	0.100005i	$0.968114\pi$
$18$	−186.066	−	542.818i	−0.574277	−	1.67536i
$19$	469.895			1.30165			0.650823	−	0.759229i	$-0.274424\pi$
$19$	469.895			1.30165			0.650823	+	0.759229i	$0.274424\pi$
$20$			188.688i			0.471719i
$21$	128.487	+	771.092i	0.291354	+	1.74851i
$22$	−258.453			−0.533993
$23$			403.013i			0.761840i	0.924608	+	0.380920i	$0.124393\pi$
$23$			403.013i			0.761840i	−0.924608	+	0.380920i	$0.875607\pi$
$24$	1143.74	−	190.582i	1.98567	−	0.330872i
$25$	594.536			0.951258
$26$		−	1182.00i		−	1.74852i
$27$	−346.516	−	641.380i	−0.475330	−	0.879807i
$28$	−2969.35			−3.78744
$29$		−	583.701i		−	0.694056i	−0.937855	−	0.347028i	$-0.887191\pi$
$29$		−	583.701i		−	0.694056i	0.937855	−	0.347028i	$-0.112809\pi$
$30$	57.8408	+	347.120i	0.0642675	+	0.385689i
$31$	334.760			0.348345			0.174173	−	0.984715i	$-0.444275\pi$
$31$	334.760			0.348345			0.174173	+	0.984715i	$0.444275\pi$
$32$			529.453i			0.517044i
$33$	−323.880	+	53.9682i	−0.297411	+	0.0495576i
$34$	−409.489			−0.354230
$35$		−	479.406i		−	0.391352i
$36$	2619.46	−	897.894i	2.02119	−	0.692820i
$37$	793.796			0.579836			0.289918	−	0.957051i	$-0.406372\pi$
$37$	793.796			0.579836			0.289918	+	0.957051i	$0.406372\pi$
$38$			3328.84i			2.30529i
$39$	−246.817	−	1481.22i	−0.162273	−	0.973848i
$40$	−711.092			−0.444433
$41$			1525.28i			0.907363i	0.891164	+	0.453682i	$0.149890\pi$
$41$			1525.28i			0.907363i	−0.891164	+	0.453682i	$0.850110\pi$
$42$	−5462.59	+	910.232i	−3.09670	+	0.516004i
$43$	−578.739			−0.313001			−0.156500	−	0.987678i	$-0.550021\pi$
$43$	−578.739			−0.313001			−0.156500	+	0.987678i	$0.550021\pi$
$44$		−	1247.21i		−	0.644220i
$45$	144.966	+	422.916i	0.0715883	+	0.208848i
$46$	−2855.03			−1.34926
$47$		−	3241.31i		−	1.46732i	−0.679518	−	0.733659i	$-0.737811\pi$
$47$		−	3241.31i		−	1.46732i	0.679518	−	0.733659i	$-0.262189\pi$
$48$	540.994	+	3246.68i	0.234807	+	1.40915i
$49$	5143.35			2.14217
$50$			4211.82i			1.68473i
$51$	−513.152	+	85.5066i	−0.197290	+	0.0328745i
$52$	5703.95			2.10945
$53$		−	4293.98i		−	1.52865i	−0.644830	−	0.764326i	$-0.723072\pi$
$53$		−	4293.98i		−	1.52865i	0.644830	−	0.764326i	$-0.276928\pi$
$54$	4543.67	−	2454.79i	1.55819	−	0.841836i
$55$	201.364			0.0665666
$56$		−	11190.4i		−	3.56836i
$57$	695.104	+	4171.53i	0.213944	+	1.28394i
$58$	4135.06			1.22921
$59$			2286.12i			0.656741i	0.944549	+	0.328371i	$0.106500\pi$
$59$			2286.12i			0.656741i	−0.944549	+	0.328371i	$0.893500\pi$
$60$	−1675.09	+	279.121i	−0.465303	+	0.0775336i
$61$	−4999.79			−1.34367			−0.671834	−	0.740702i	$-0.734493\pi$
$61$	−4999.79			−1.34367			−0.671834	+	0.740702i	$0.734493\pi$
$62$			2371.51i			0.616939i
$63$	−6655.38	+	2281.32i	−1.67684	+	0.574784i
$64$	2100.69			0.512864
$65$			920.911i			0.217967i
$66$	−382.323	−	2294.44i	−0.0877692	−	0.526731i
$67$	1349.06			0.300526			0.150263	−	0.988646i	$-0.451988\pi$
$67$	1349.06			0.300526			0.150263	+	0.988646i	$0.451988\pi$
$68$		−	1976.06i		−	0.427350i
$69$	−3577.79	+	596.168i	−0.751478	+	0.125219i
$70$	3396.22			0.693106
$71$			421.099i			0.0835349i	0.999127	+	0.0417675i	$0.0132989\pi$
$71$			421.099i			0.0835349i	−0.999127	+	0.0417675i	$0.986701\pi$
$72$	3383.83	+	9871.78i	0.652744	+	1.90428i
$73$	−1400.57			−0.262820			−0.131410	−	0.991328i	$-0.541950\pi$
$73$	−1400.57			−0.262820			−0.131410	+	0.991328i	$0.541950\pi$
$74$			5623.42i			1.02692i
$75$	879.483	+	5278.05i	0.156353	+	0.938320i
$76$	−16063.9			−2.78115
$77$			3168.84i			0.534464i
$78$	10493.3	−	1748.50i	1.72474	−	0.287394i
$79$	−3506.52			−0.561852			−0.280926	−	0.959729i	$-0.590641\pi$
$79$	−3506.52			−0.561852			−0.280926	+	0.959729i	$0.590641\pi$
$80$		−	2018.54i		−	0.315396i
$81$	5181.32	−	4025.01i	0.789715	−	0.613474i
$82$	−10805.4			−1.60699
$83$			1461.59i			0.212163i	0.994357	+	0.106081i	$0.0338304\pi$
$83$			1461.59i			0.212163i	−0.994357	+	0.106081i	$0.966170\pi$
$84$	−4392.49	−	26360.7i	−0.622518	−	3.73593i
$85$	319.039			0.0441576
$86$		−	4099.91i		−	0.554342i
$87$	5181.86	−	863.454i	0.684616	−	0.114078i
$88$	4700.27			0.606956
$89$			694.642i			0.0876963i	0.999038	+	0.0438481i	$0.0139618\pi$
$89$			694.642i			0.0876963i	−0.999038	+	0.0438481i	$0.986038\pi$
$90$	−2996.03	+	1026.97i	−0.369881	+	0.126787i
$91$	−14492.3			−1.75006
$92$		−	13777.5i		−	1.62777i
$93$	495.202	+	2971.86i	0.0572555	+	0.343608i
$94$	22962.1			2.59870
$95$		−	2593.54i		−	0.287373i
$96$	−4700.27	+	783.207i	−0.510012	+	0.0849834i
$97$	6700.63			0.712151			0.356075	−	0.934457i	$-0.384115\pi$
$97$	6700.63			0.712151			0.356075	+	0.934457i	$0.384115\pi$
$98$			36436.6i			3.79390i
$99$	−958.217	−	2795.44i	−0.0977672	−	0.285220i
$100$	−20324.9			−2.03249
$101$		−	17998.0i		−	1.76434i	−0.470933	−	0.882169i	$-0.656082\pi$
$101$		−	17998.0i		−	1.76434i	0.470933	−	0.882169i	$-0.343918\pi$
$102$	−605.748	−	3635.28i	−0.0582226	−	0.349412i
$103$	−10521.4			−0.991743			−0.495871	−	0.868396i	$-0.665151\pi$
$103$	−10521.4			−0.991743			−0.495871	+	0.868396i	$0.665151\pi$
$104$			21496.0i			1.98743i
$105$	4255.97	−	709.174i	0.386029	−	0.0643241i
$106$	30419.5			2.70733
$107$		−	12848.3i		−	1.12222i	−0.827740	−	0.561112i	$-0.810374\pi$
$107$		−	12848.3i		−	1.12222i	0.827740	−	0.561112i	$-0.189626\pi$
$108$	11846.1	+	21926.3i	1.01561	+	1.87983i
$109$	6835.33			0.575316			0.287658	−	0.957733i	$-0.407123\pi$
$109$	6835.33			0.575316			0.287658	+	0.957733i	$0.407123\pi$
$110$			1426.51i			0.117893i
$111$	1174.24	+	7047.00i	0.0953042	+	0.571950i
$112$	31765.4			2.53232
$113$			3948.82i			0.309250i	0.987973	+	0.154625i	$0.0494170\pi$
$113$			3948.82i			0.309250i	−0.987973	+	0.154625i	$0.950583\pi$
$114$	−29552.1	+	4924.27i	−2.27394	+	0.378906i
$115$	2224.40			0.168196
$116$			19954.5i			1.48294i
$117$	12784.6	−	4382.28i	0.933932	−	0.320131i
$118$	−16195.4			−1.16313
$119$			5020.67i			0.354542i
$120$	−1051.90	−	6312.79i	−0.0730487	−	0.438388i
$121$	−1331.00			−0.0909091
$122$		−	35419.6i		−	2.37971i
$123$	−13540.8	+	2256.31i	−0.895023	+	0.149138i
$124$	−11444.2			−0.744287
$125$		−	6731.12i		−	0.430792i
$126$	−16161.3	−	47148.2i	−1.01797	−	2.96978i
$127$	−6338.74			−0.393003			−0.196501	−	0.980504i	$-0.562958\pi$
$127$	−6338.74			−0.393003			−0.196501	+	0.980504i	$0.562958\pi$
$128$			23353.0i			1.42535i
$129$	−856.114	−	5137.81i	−0.0514461	−	0.308744i
$130$	−6523.94			−0.386032
$131$		−	22162.7i		−	1.29146i	−0.763568	−	0.645728i	$-0.776554\pi$
$131$		−	22162.7i		−	1.29146i	0.763568	−	0.645728i	$-0.223446\pi$
$132$	11072.2	−	1844.97i	0.635458	−	0.105887i
$133$	40814.2			2.30732
$134$			9557.06i			0.532249i
$135$	−3540.04	+	1912.56i	−0.194241	+	0.104942i
$136$	7447.05			0.402630
$137$			26756.3i			1.42556i	0.701389	+	0.712779i	$0.252564\pi$
$137$			26756.3i			1.42556i	−0.701389	+	0.712779i	$0.747436\pi$
$138$	−4223.38	−	25345.8i	−0.221770	−	1.33091i
$139$	−14831.1			−0.767614			−0.383807	−	0.923413i	$-0.625387\pi$
$139$	−14831.1			−0.767614			−0.383807	+	0.923413i	$0.625387\pi$
$140$			16389.1i			0.836176i
$141$	28775.0	−	4794.78i	1.44736	−	0.241174i
$142$	−2983.16			−0.147945
$143$		−	6087.15i		−	0.297675i
$144$	−28022.4	+	9605.46i	−1.35139	+	0.463226i
$145$	−3221.68			−0.153231
$146$		−	9921.93i		−	0.465469i
$147$	7608.43	+	45660.5i	0.352095	+	2.11303i
$148$	−27136.8			−1.23890
$149$			17492.4i			0.787913i	0.919129	+	0.393956i	$0.128894\pi$
$149$			17492.4i			0.787913i	−0.919129	+	0.393956i	$0.871106\pi$
$150$	−37390.9	+	6230.45i	−1.66182	+	0.276909i
$151$	−11316.3			−0.496305			−0.248153	−	0.968721i	$-0.579823\pi$
$151$	−11316.3			−0.496305			−0.248153	+	0.968721i	$0.579823\pi$
$152$		−	60538.8i		−	2.62027i
$153$	−1518.19	−	4429.07i	−0.0648548	−	0.189204i
$154$	−22448.7			−0.946565
$155$		−	1847.68i		−	0.0769065i
$156$	8437.71	+	50637.4i	0.346717	+	2.08076i
$157$	−34382.5			−1.39489			−0.697443	−	0.716641i	$-0.745679\pi$
$157$	−34382.5			−1.39489			−0.697443	+	0.716641i	$0.745679\pi$
$158$		−	24840.9i		−	0.995070i
$159$	38120.3	−	6351.99i	1.50786	−	0.251255i
$160$	2922.27			0.114151
$161$			35005.0i			1.35045i
$162$	28514.0	+	36705.6i	1.08650	+	1.39863i
$163$	−5455.01			−0.205315			−0.102657	−	0.994717i	$-0.532735\pi$
$163$	−5455.01			−0.205315			−0.102657	+	0.994717i	$0.532735\pi$
$164$		−	52143.4i		−	1.93870i
$165$	297.873	+	1787.63i	0.0109412	+	0.0656613i
$166$	−10354.2			−0.375752
$167$			19051.8i			0.683129i	0.939858	+	0.341565i	$0.110957\pi$
$167$			19051.8i			0.683129i	−0.939858	+	0.341565i	$0.889043\pi$
$168$	99343.5	−	16553.6i	3.51982	−	0.586509i
$169$	−722.223			−0.0252870
$170$			2260.14i			0.0782055i
$171$	−36005.0	+	12341.7i	−1.23132	+	0.422068i
$172$	19784.9			0.668769
$173$		−	15040.9i		−	0.502552i	−0.967915	−	0.251276i	$-0.919150\pi$
$173$		−	15040.9i		−	0.502552i	0.967915	−	0.251276i	$-0.0808502\pi$
$174$	6116.90	+	36709.4i	0.202038	+	1.21249i
$175$	51640.3			1.68621
$176$			13342.4i			0.430732i
$177$	−20295.2	+	3381.80i	−0.647809	+	0.107945i
$178$	−4921.00			−0.155315
$179$		−	24102.7i		−	0.752246i	−0.926570	−	0.376123i	$-0.877257\pi$
$179$		−	24102.7i		−	0.752246i	0.926570	−	0.376123i	$-0.122743\pi$
$180$	−4955.85	−	14457.9i	−0.152958	−	0.446231i
$181$	41085.0			1.25408			0.627041	−	0.778987i	$-0.284266\pi$
$181$	41085.0			1.25408			0.627041	+	0.778987i	$0.284266\pi$
$182$		−	102666.i		−	3.09945i
$183$	−7396.06	−	44386.1i	−0.220851	−	1.32539i
$184$	51922.1			1.53362
$185$		−	4381.28i		−	0.128014i
$186$	−21053.3	+	3508.12i	−0.608549	+	0.101403i
$187$	−2108.82			−0.0603054
$188$			110808.i			3.13512i
$189$	−30097.7	−	55709.1i	−0.842578	−	1.55956i
$190$	18373.2			0.508953
$191$			18699.5i			0.512582i	0.966600	+	0.256291i	$0.0825006\pi$
$191$			18699.5i			0.512582i	−0.966600	+	0.256291i	$0.917499\pi$
$192$	3107.50	+	18649.1i	0.0842964	+	0.505889i
$193$	−36749.5			−0.986592			−0.493296	−	0.869862i	$-0.664208\pi$
$193$	−36749.5			−0.986592			−0.493296	+	0.869862i	$0.664208\pi$
$194$			47468.7i			1.26126i
$195$	−8175.48	+	1362.28i	−0.215003	+	0.0358260i
$196$	−175831.			−4.57703
$197$			54900.2i			1.41463i	0.706901	+	0.707313i	$0.250093\pi$
$197$			54900.2i			1.41463i	−0.706901	+	0.707313i	$0.749907\pi$
$198$	19803.5	−	6788.22i	0.505141	−	0.173151i
$199$	34161.8			0.862651			0.431325	−	0.902196i	$-0.358046\pi$
$199$	34161.8			0.862651			0.431325	+	0.902196i	$0.358046\pi$
$200$		−	76597.0i		−	1.91492i
$201$	1995.64	+	11976.4i	0.0493957	+	0.296439i
$202$	127502.			3.12474
$203$		−	50699.2i		−	1.23029i
$204$	17542.7	−	2923.14i	0.421538	−	0.0702409i
$205$	8418.63			0.200324
$206$		−	74535.9i		−	1.75643i
$207$	−10585.1	−	30880.3i	−0.247032	−	0.720677i
$208$	−61019.5			−1.41040
$209$			17143.1i			0.392461i
$210$	5023.94	+	30150.3i	0.113922	+	0.683679i
$211$	−33399.0			−0.750184			−0.375092	−	0.926988i	$-0.622389\pi$
$211$	−33399.0			−0.750184			−0.375092	+	0.926988i	$0.622389\pi$
$212$			146795.i			3.26617i
$213$	−3738.35	+	622.922i	−0.0823988	+	0.0137301i
$214$	91020.5			1.98752
$215$			3194.30i			0.0691032i
$216$	−82632.0	+	44643.3i	−1.77109	+	0.956861i
$217$	29076.6			0.617483
$218$			48423.0i			1.01892i
$219$	−2071.83	−	12433.7i	−0.0431981	−	0.259246i
$220$	−6883.86			−0.142229
$221$		−	9644.41i		−	0.197465i
$222$	−49922.5	+	8318.59i	−1.01296	+	0.168789i
$223$	3798.36			0.0763811			0.0381906	−	0.999270i	$-0.487841\pi$
$223$	3798.36			0.0763811			0.0381906	+	0.999270i	$0.487841\pi$
$224$			45987.3i			0.916520i
$225$	−45555.4	+	15615.4i	−0.899860	+	0.308452i
$226$	−27974.3			−0.547699
$227$		−	56899.2i		−	1.10422i	−0.833772	−	0.552109i	$-0.813823\pi$
$227$		−	56899.2i		−	1.10422i	0.833772	−	0.552109i	$-0.186177\pi$
$228$	−23762.9	−	142609.i	−0.457120	−	2.74332i
$229$	37230.1			0.709943			0.354972	−	0.934877i	$-0.384490\pi$
$229$	37230.1			0.709943			0.354972	+	0.934877i	$0.384490\pi$
$230$			15758.1i			0.297885i
$231$	−28131.7	+	4687.58i	−0.527195	+	0.0878466i
$232$	−75201.0			−1.39716
$233$		−	53156.8i		−	0.979145i	−0.871962	−	0.489573i	$-0.837153\pi$
$233$		−	53156.8i		−	0.979145i	0.871962	−	0.489573i	$-0.162847\pi$
$234$	31045.0	+	90568.9i	0.566970	+	1.65404i
$235$	−17890.1			−0.323949
$236$		−	78153.6i		−	1.40322i
$237$	−5187.10	−	31129.4i	−0.0923482	−	0.554210i
$238$	−35567.5			−0.627913
$239$			67041.6i			1.17368i	0.809704	+	0.586839i	$0.199628\pi$
$239$			67041.6i			1.17368i	−0.809704	+	0.586839i	$0.800372\pi$
$240$	17919.7	−	2985.97i	0.311107	−	0.0518398i
$241$	−47173.6			−0.812204			−0.406102	−	0.913828i	$-0.633112\pi$
$241$	−47173.6			−0.812204			−0.406102	+	0.913828i	$0.633112\pi$
$242$		−	9429.10i		−	0.161005i
$243$	43397.0	+	40043.6i	0.734932	+	0.678141i
$244$	170924.			2.87093
$245$		−	28388.2i		−	0.472940i
$246$	−15984.2	−	95926.0i	−0.264131	−	1.58513i
$247$	−78401.7			−1.28508
$248$		−	43128.8i		−	0.701235i
$249$	−12975.4	+	2162.09i	−0.209277	+	0.0348719i
$250$	47684.7			0.762956
$251$			38550.2i			0.611898i	0.952048	+	0.305949i	$0.0989738\pi$
$251$			38550.2i			0.611898i	−0.952048	+	0.305949i	$0.901026\pi$
$252$	227522.	−	77989.5i	3.58280	−	1.22810i
$253$	−14703.1			−0.229703
$254$		−	44905.1i		−	0.696030i
$255$	471.946	+	2832.30i	0.00725792	+	0.0435570i
$256$	−131827.			−2.01152
$257$			40243.9i			0.609304i	0.952464	+	0.304652i	$0.0985402\pi$
$257$			40243.9i			0.609304i	−0.952464	+	0.304652i	$0.901460\pi$
$258$	36397.4	−	6064.90i	0.546803	−	0.0911138i
$259$	68947.6			1.02783
$260$		−	31482.4i		−	0.465716i
$261$	15330.8	+	44725.2i	0.225052	+	0.656555i
$262$	157005.			2.28724
$263$		−	23723.2i		−	0.342975i	−0.985186	−	0.171487i	$-0.945143\pi$
$263$		−	23723.2i		−	0.342975i	0.985186	−	0.171487i	$-0.0548572\pi$
$264$	6952.99	+	41727.1i	0.0997617	+	0.598701i
$265$	−23700.3			−0.337490
$266$			289137.i			4.08639i
$267$	−6166.75	+	1027.57i	−0.0865036	+	0.0144141i
$268$	−46119.3			−0.642115
$269$		−	3414.59i		−	0.0471882i	−0.999722	−	0.0235941i	$-0.992489\pi$
$269$		−	3414.59i		−	0.0471882i	0.999722	−	0.0235941i	$-0.00751093\pi$
$270$	−13549.0	−	25078.4i	−0.185858	−	0.344011i
$271$	111399.			1.51686			0.758428	−	0.651757i	$-0.225968\pi$
$271$	111399.			1.51686			0.758428	+	0.651757i	$0.225968\pi$
$272$			21139.5i			0.285730i
$273$	−21438.0	−	128656.i	−0.287647	−	1.72626i
$274$	−189547.			−2.52474
$275$			21690.4i			0.286815i
$276$	122311.	−	20380.7i	1.60564	−	0.267547i
$277$	−110761.			−1.44354			−0.721771	−	0.692132i	$-0.756671\pi$
$277$	−110761.			−1.44354			−0.721771	+	0.692132i	$0.756671\pi$
$278$		−	105067.i		−	1.35949i
$279$	−25650.5	+	8792.42i	−0.329524	+	0.112954i
$280$	−61764.2			−0.787809
$281$			136319.i			1.72640i	0.504859	+	0.863202i	$0.331545\pi$
$281$			136319.i			1.72640i	−0.504859	+	0.863202i	$0.668455\pi$
$282$	33967.3	+	203848.i	0.427133	+	2.56336i
$283$	−13996.7			−0.174765			−0.0873824	−	0.996175i	$-0.527850\pi$
$283$	−13996.7			−0.174765			−0.0873824	+	0.996175i	$0.527850\pi$
$284$		−	14395.8i		−	0.178484i
$285$	23024.4	−	3836.56i	0.283465	−	0.0472338i
$286$	43122.7			0.527198
$287$			132483.i			1.60841i
$288$	−13906.0	−	40568.5i	−0.167655	−	0.489107i
$289$	80179.8			0.959996
$290$		−	22823.1i		−	0.271381i
$291$	9912.07	+	59485.5i	0.117052	+	0.702465i
$292$	47880.1			0.561551
$293$			881.046i			0.0102627i	0.999987	+	0.00513137i	$0.00163337\pi$
$293$			881.046i			0.0102627i	−0.999987	+	0.00513137i	$0.998367\pi$
$294$	−323469.	+	53899.8i	−3.74230	+	0.623580i
$295$	12618.0			0.144993
$296$		−	102269.i		−	1.16724i
$297$	23399.4	−	12641.9i	0.265272	−	0.143318i
$298$	−123920.			−1.39544
$299$		−	67242.6i		−	0.752146i
$300$	−30066.2	−	180436.i	−0.334068	−	2.00485i
$301$	−50268.2			−0.554830
$302$		−	80166.8i		−	0.878984i
$303$	159779.	−	26624.0i	1.74034	−	0.289994i
$304$	171848.			1.85950
$305$			27595.9i			0.296650i
$306$	31376.5	−	10755.2i	0.335090	−	0.114861i
$307$	44732.9			0.474625			0.237312	−	0.971433i	$-0.423733\pi$
$307$	44732.9			0.474625			0.237312	+	0.971433i	$0.423733\pi$
$308$		−	108330.i		−	1.14195i
$309$	−15564.1	−	93404.8i	−0.163007	−	0.978255i
$310$	13089.4			0.136206
$311$		−	96960.7i		−	1.00248i	−0.865309	−	0.501239i	$-0.832878\pi$
$311$		−	96960.7i		−	1.00248i	0.865309	−	0.501239i	$-0.167122\pi$
$312$	−190833.	+	31798.6i	−1.96040	+	0.326662i
$313$	9368.88			0.0956310			0.0478155	−	0.998856i	$-0.484774\pi$
$313$	9368.88			0.0956310			0.0478155	+	0.998856i	$0.484774\pi$
$314$		−	243573.i		−	2.47042i
$315$	12591.5	+	36733.8i	0.126899	+	0.370207i
$316$	119874.			1.20047
$317$			50948.3i			0.507003i	0.967335	+	0.253502i	$0.0815824\pi$
$317$			50948.3i			0.507003i	−0.967335	+	0.253502i	$0.918418\pi$
$318$	44998.9	+	270052.i	0.444987	+	2.67051i
$319$	21295.1			0.209266
$320$		−	11594.6i		−	0.113228i
$321$	114062.	−	19006.2i	1.10696	−	0.184453i
$322$	−247983.			−2.39172
$323$			27161.3i			0.260343i
$324$	−177129.	+	137600.i	−1.68733	+	1.31077i
$325$	−99198.1			−0.939154
$326$		−	38644.5i		−	0.363624i
$327$	10111.3	+	60681.3i	0.0945612	+	0.567491i
$328$	196509.			1.82656
$329$		−	281534.i		−	2.60099i
$330$	−12664.0	+	2110.20i	−0.116290	+	0.0193774i
$331$	−135492.			−1.23668			−0.618340	−	0.785911i	$-0.712195\pi$
$331$	−135492.			−1.23668			−0.618340	+	0.785911i	$0.712195\pi$
$332$		−	49966.1i		−	0.453314i
$333$	−60823.4	+	20848.9i	−0.548507	+	0.188016i
$334$	−134967.			−1.20986
$335$		−	7446.03i		−	0.0663491i
$336$	46989.8	+	282000.i	0.416222	+	2.49788i
$337$	−28515.1			−0.251082			−0.125541	−	0.992088i	$-0.540067\pi$
$337$	−28515.1			−0.251082			−0.125541	+	0.992088i	$0.540067\pi$
$338$		−	5116.39i		−	0.0447847i
$339$	−35056.0	+	5841.39i	−0.305045	+	0.0508296i
$340$	−10906.7			−0.0943487
$341$			12213.0i			0.105030i
$342$	−87431.3	−	255067.i	−0.747506	−	2.18073i
$343$	238195.			2.02463
$344$			74561.7i			0.630085i
$345$	3290.49	+	19747.3i	0.0276454	+	0.165909i
$346$	106553.			0.890047
$347$			238395.i			1.97988i	0.141496	+	0.989939i	$0.454809\pi$
$347$			238395.i			1.97988i	−0.141496	+	0.989939i	$0.545191\pi$
$348$	−177148.	+	29518.2i	−1.46278	+	0.243743i
$349$	−31082.7			−0.255192			−0.127596	−	0.991826i	$-0.540726\pi$
$349$	−31082.7			−0.255192			−0.127596	+	0.991826i	$0.540726\pi$
$350$			365831.i			2.98638i
$351$	57816.0	+	107014.i	0.469282	+	0.868612i
$352$	−19316.0			−0.155895
$353$			107859.i			0.865577i	0.901496	+	0.432788i	$0.142470\pi$
$353$			107859.i			0.865577i	−0.901496	+	0.432788i	$0.857530\pi$
$354$	−23957.4	−	143776.i	−0.191176	−	1.14731i
$355$	2324.22			0.0184425
$356$		−	23747.2i		−	0.187375i
$357$	−44571.5	+	7426.95i	−0.349720	+	0.0582739i
$358$	170749.			1.33227
$359$		−	157141.i		−	1.21927i	−0.792681	−	0.609637i	$-0.791315\pi$
$359$		−	157141.i		−	1.21927i	0.792681	−	0.609637i	$-0.208685\pi$
$360$	54486.4	−	18676.7i	0.420420	−	0.144111i
$361$	90479.9			0.694285
$362$			291055.i			2.22105i
$363$	−1968.92	−	11816.1i	−0.0149422	−	0.0896727i
$364$	495435.			3.73924
$365$			7730.31i			0.0580245i
$366$	314441.	−	52395.3i	2.34734	−	0.391138i
$367$	220091.			1.63407			0.817033	−	0.576591i	$-0.195618\pi$
$367$	220091.			1.63407			0.817033	+	0.576591i	$0.195618\pi$
$368$			147388.i			1.08835i
$369$	−40061.2	−	116872.i	−0.294219	−	0.858337i
$370$	31038.0			0.226720
$371$		−	372968.i		−	2.70971i
$372$	−16929.1	−	101597.i	−0.122334	−	0.734165i
$373$	−271957.			−1.95471			−0.977355	−	0.211608i	$-0.932130\pi$
$373$	−271957.			−1.95471			−0.977355	+	0.211608i	$0.932130\pi$
$374$		−	14939.3i		−	0.106804i
$375$	59756.2	−	9957.18i	0.424933	−	0.0708066i
$376$	−417593.			−2.95378
$377$			97390.2i			0.685224i
$378$	394655.	−	213219.i	2.76207	−	1.49225i
$379$	−160684.			−1.11865			−0.559326	−	0.828948i	$-0.688940\pi$
$379$	−160684.			−1.11865			−0.559326	+	0.828948i	$0.688940\pi$
$380$			88663.2i			0.614011i
$381$	−9376.75	−	56272.8i	−0.0645955	−	0.387658i
$382$	−132471.			−0.907811
$383$		−	188579.i		−	1.28557i	−0.766047	−	0.642784i	$-0.777779\pi$
$383$		−	188579.i		−	1.28557i	0.766047	−	0.642784i	$-0.222221\pi$
$384$	−207319.	+	34545.5i	−1.40597	+	0.234277i
$385$	17490.1			0.117997
$386$		−	260342.i		−	1.74731i
$387$	44345.0	−	15200.5i	0.296089	−	0.101493i
$388$	−229069.			−1.52161
$389$			156066.i			1.03136i	0.856782	+	0.515678i	$0.172460\pi$
$389$			156066.i			1.03136i	−0.856782	+	0.515678i	$0.827540\pi$
$390$	−9650.70	−	57916.9i	−0.0634497	−	0.380782i
$391$	−23295.4			−0.152376
$392$		−	662642.i		−	4.31228i
$393$	196751.	−	32784.7i	1.27389	−	0.212269i
$394$	−388925.			−2.50538
$395$			19353.9i			0.124044i
$396$	32757.8	+	95565.6i	0.208893	+	0.609412i
$397$	−56319.0			−0.357334			−0.178667	−	0.983910i	$-0.557178\pi$
$397$	−56319.0			−0.357334			−0.178667	+	0.983910i	$0.557178\pi$
$398$			242010.i			1.52780i
$399$	60375.4	+	362332.i	0.379240	+	2.27594i
$400$	217431.			1.35894
$401$		−	184600.i		−	1.14801i	−0.818853	−	0.574003i	$-0.805390\pi$
$401$		−	184600.i		−	1.14801i	0.818853	−	0.574003i	$-0.194610\pi$
$402$	−84843.7	+	14137.5i	−0.525010	+	0.0874825i
$403$	−55854.6			−0.343913
$404$			615283.i			3.76975i
$405$	−22215.7	−	28597.8i	−0.135441	−	0.174350i
$406$	359164.			2.17892
$407$			28959.9i			0.174827i
$408$	11016.2	+	66111.9i	0.0661779	+	0.397154i
$409$	−29823.1			−0.178281			−0.0891407	−	0.996019i	$-0.528412\pi$
$409$	−29823.1			−0.178281			−0.0891407	+	0.996019i	$0.528412\pi$
$410$			59639.5i			0.354786i
$411$	−237532.	+	39579.9i	−1.40617	+	0.234310i
$412$	359686.			2.11899
$413$			198568.i			1.16415i
$414$	218763.	−	74987.0i	1.27636	−	0.437507i
$415$	8067.10			0.0468405
$416$		−	88339.0i		−	0.510465i
$417$	−21939.2	−	131664.i	−0.126168	−	0.757174i
$418$	−121446.			−0.695071
$419$		−	219062.i		−	1.24778i	−0.781511	−	0.623891i	$-0.785551\pi$
$419$		−	219062.i		−	1.24778i	0.781511	−	0.623891i	$-0.214449\pi$
$420$	−145495.	+	24243.9i	−0.824804	+	0.137437i
$421$	318263.			1.79565			0.897824	−	0.440354i	$-0.145147\pi$
$421$	318263.			1.79565			0.897824	+	0.440354i	$0.145147\pi$
$422$		−	236606.i		−	1.32862i
$423$	85132.3	+	248360.i	0.475788	+	1.38804i
$424$	−553215.			−3.07724
$425$			34366.0i			0.190262i
$426$	−4412.92	−	26483.3i	−0.0243168	−	0.145933i
$427$	−434272.			−2.38181
$428$			439236.i			2.39778i
$429$	54039.3	−	9004.58i	0.293626	−	0.0489270i
$430$	−22629.1			−0.122386
$431$		−	117207.i		−	0.630958i	−0.948933	−	0.315479i	$-0.897835\pi$
$431$		−	117207.i		−	0.630958i	0.948933	−	0.315479i	$-0.102165\pi$
$432$	−126726.	−	234563.i	−0.679046	−	1.25687i
$433$	−207642.			−1.10749			−0.553745	−	0.832686i	$-0.686802\pi$
$433$	−207642.			−1.10749			−0.553745	+	0.832686i	$0.686802\pi$
$434$			205985.i			1.09360i
$435$	−4765.76	−	28600.8i	−0.0251857	−	0.151147i
$436$	−233674.			−1.22924
$437$			189374.i			0.991646i
$438$	88082.9	−	14677.3i	0.459138	−	0.0765063i
$439$	119558.			0.620369			0.310184	−	0.950676i	$-0.399609\pi$
$439$	119558.			0.620369			0.310184	+	0.950676i	$0.399609\pi$
$440$		−	25942.7i		−	0.134002i
$441$	−394101.	+	135089.i	−2.02642	+	0.694613i
$442$	68323.1			0.349722
$443$		−	219826.i		−	1.12014i	−0.828445	−	0.560070i	$-0.810774\pi$
$443$		−	219826.i		−	1.12014i	0.828445	−	0.560070i	$-0.189226\pi$
$444$	−40142.9	−	240910.i	−0.203630	−	1.22205i
$445$	3834.01			0.0193613
$446$			26908.4i			0.135275i
$447$	−155291.	+	25876.2i	−0.777197	+	0.129504i
$448$	182462.			0.909111
$449$			291244.i			1.44466i	0.691551	+	0.722328i	$0.256928\pi$
$449$			291244.i			1.44466i	−0.691551	+	0.722328i	$0.743072\pi$
$450$	−110623.	−	322725.i	−0.546286	−	1.59370i
$451$	−55646.5			−0.273580
$452$		−	134995.i		−	0.660755i
$453$	−16739.9	−	100461.i	−0.0815747	−	0.489555i
$454$	403087.			1.95563
$455$			79988.7i			0.386372i
$456$	537439.	−	89553.6i	2.58464	−	0.430679i
$457$	253632.			1.21443			0.607214	−	0.794538i	$-0.292287\pi$
$457$	253632.			1.21443			0.607214	+	0.794538i	$0.292287\pi$
$458$			263747.i			1.25735i
$459$	37073.7	−	20029.7i	0.175971	−	0.0950711i
$460$	−76043.6			−0.359374
$461$			92929.1i			0.437270i	0.975807	+	0.218635i	$0.0701604\pi$
$461$			92929.1i			0.437270i	−0.975807	+	0.218635i	$0.929840\pi$
$462$	−33207.9	−	199291.i	−0.155581	−	0.933691i
$463$	11931.5			0.0556587			0.0278294	−	0.999613i	$-0.491140\pi$
$463$	11931.5			0.0556587			0.0278294	+	0.999613i	$0.491140\pi$
$464$		−	213469.i		−	0.991512i
$465$	16402.9	−	2733.23i	0.0758605	−	0.0126407i
$466$	376575.			1.73412
$467$		−	15703.0i		−	0.0720029i	−0.999352	−	0.0360015i	$-0.988538\pi$
$467$		−	15703.0i		−	0.0720029i	0.999352	−	0.0360015i	$-0.0114621\pi$
$468$	−437056.	+	149813.i	−1.99547	+	0.684004i
$469$	117177.			0.532718
$470$		−	126737.i		−	0.573732i
$471$	−50861.2	−	305234.i	−0.229269	−	1.37591i
$472$	294532.			1.32205
$473$		−	21114.0i		−	0.0943733i
$474$	220528.	−	36746.6i	0.981537	−	0.163554i
$475$	279369.			1.23820
$476$		−	171637.i		−	0.757527i
$477$	112781.	+	329020.i	0.495676	+	1.44606i
$478$	−474938.			−2.07865
$479$		−	141473.i		−	0.616599i	−0.951289	−	0.308299i	$-0.900240\pi$
$479$		−	141473.i		−	0.616599i	0.951289	−	0.308299i	$-0.0997599\pi$
$480$	4322.84	+	25942.7i	0.0187623	+	0.112599i
$481$	−132444.			−0.572458
$482$		−	334188.i		−	1.43846i
$483$	−310760.	+	51782.0i	−1.33208	+	0.221965i
$484$	45501.8			0.194240
$485$		−	36983.5i		−	0.157226i
$486$	−283677.	+	307434.i	−1.20103	+	1.30160i
$487$	208617.			0.879613			0.439807	−	0.898093i	$-0.355047\pi$
$487$	208617.			0.879613			0.439807	+	0.898093i	$0.355047\pi$
$488$			644147.i			2.70486i
$489$	−8069.46	−	48427.4i	−0.0337463	−	0.202522i
$490$	201108.			0.837603
$491$			457191.i			1.89642i	0.317644	+	0.948210i	$0.397108\pi$
$491$			457191.i			1.89642i	−0.317644	+	0.948210i	$0.602892\pi$
$492$	462908.	−	77134.5i	1.91234	−	0.318653i
$493$	33739.7			0.138818
$494$		−	555415.i		−	2.27595i
$495$	−15429.2	+	5288.79i	−0.0629699	+	0.0215847i
$496$	122427.			0.497638
$497$			36575.9i			0.148075i
$498$	−15316.7	−	91920.5i	−0.0617600	−	0.370641i
$499$	256989.			1.03208			0.516040	−	0.856564i	$-0.327406\pi$
$499$	256989.			1.03208			0.516040	+	0.856564i	$0.327406\pi$
$500$			230111.i			0.920445i
$501$	−169134.	+	28182.8i	−0.673838	+	0.112282i
$502$	−273098.			−1.08371
$503$		−	193555.i		−	0.765013i	−0.923953	−	0.382506i	$-0.875061\pi$
$503$		−	193555.i		−	0.765013i	0.923953	−	0.382506i	$-0.124939\pi$
$504$	293913.	+	857445.i	1.15706	+	3.37555i
$505$	−99338.4			−0.389524
$506$		−	104160.i		−	0.406817i
$507$	−1068.37	−	6411.61i	−0.00415628	−	0.0249431i
$508$	216697.			0.839704
$509$		−	443725.i		−	1.71269i	−0.516405	−	0.856344i	$-0.672730\pi$
$509$		−	443725.i		−	1.71269i	0.516405	−	0.856344i	$-0.327270\pi$
$510$	−20064.6	+	3343.37i	−0.0771419	+	0.0128542i
$511$	−121651.			−0.465879
$512$		−	560242.i		−	2.13715i
$513$	−162826.	−	301381.i	−0.618712	−	1.14520i
$514$	−285097.			−1.07911
$515$			58071.9i			0.218953i
$516$	29267.3	+	175642.i	0.109922	+	0.659674i
$517$	118252.			0.442413
$518$			488440.i			1.82034i
$519$	133527.	−	22249.6i	0.495717	−	0.0826015i
$520$	118645.			0.438778
$521$		−	340325.i		−	1.25377i	−0.779111	−	0.626885i	$-0.784329\pi$
$521$		−	340325.i		−	1.25377i	0.779111	−	0.626885i	$-0.215671\pi$
$522$	−316843.	+	108607.i	−1.16280	+	0.398580i
$523$	−371830.			−1.35938			−0.679690	−	0.733500i	$-0.737886\pi$
$523$	−371830.			−1.35938			−0.679690	+	0.733500i	$0.737886\pi$
$524$			757657.i			2.75937i
$525$	76390.3	+	458442.i	0.277153	+	1.66328i
$526$	168060.			0.607427
$527$			19350.1i			0.0696728i
$528$	−118448.	+	19737.0i	−0.424874	+	0.0707969i
$529$	117421.			0.419600
$530$		−	167898.i		−	0.597714i
$531$	−60044.5	−	175170.i	−0.212953	−	0.621257i
$532$	−1.39528e6			−4.92990
$533$		−	254492.i		−	0.895818i
$534$	−7279.51	−	43686.6i	−0.0255282	−	0.153203i
$535$	−70915.3			−0.247761
$536$		−	173806.i		−	0.604973i
$537$	213974.	−	35654.6i	0.742016	−	0.123642i
$538$	24189.7			0.0835729
$539$			187644.i			0.645888i
$540$	121020.	−	65383.2i	0.415022	−	0.224222i
$541$	536289.			1.83233			0.916166	−	0.400798i	$-0.131267\pi$
$541$	536289.			1.83233			0.916166	+	0.400798i	$0.131267\pi$
$542$			789178.i			2.68644i
$543$	60776.0	+	364736.i	0.206126	+	1.23703i
$544$	−30604.0			−0.103414
$545$		−	37727.0i		−	0.127016i
$546$	911430.	−	151872.i	3.05730	−	0.509439i
$547$	−411275.			−1.37454			−0.687270	−	0.726402i	$-0.741191\pi$
$547$	−411275.			−1.37454			−0.687270	+	0.726402i	$0.741191\pi$
$548$		−	914695.i		−	3.04590i
$549$	383101.	−	131319.i	1.27107	−	0.435694i
$550$	−153659.			−0.507965
$551$		−	274278.i		−	0.903415i
$552$	76807.2	+	460944.i	0.252071	+	1.51276i
$553$	−304570.			−0.995947
$554$		−	784659.i		−	2.55659i
$555$	38895.3	−	6481.13i	0.126273	−	0.0210409i
$556$	507017.			1.64011
$557$		−	279120.i		−	0.899663i	−0.893113	−	0.449832i	$-0.851484\pi$
$557$		−	279120.i		−	0.899663i	0.893113	−	0.449832i	$-0.148516\pi$
$558$	−62287.4	−	181714.i	−0.200047	−	0.583605i
$559$	96562.3			0.309018
$560$		−	175326.i		−	0.559076i
$561$	−3119.53	−	18721.3i	−0.00991204	−	0.0594853i
$562$	−965711.			−3.05756
$563$			382629.i			1.20715i	0.797306	+	0.603575i	$0.206258\pi$
$563$			382629.i			1.20715i	−0.797306	+	0.603575i	$0.793742\pi$
$564$	−983707.	+	163915.i	−3.09249	+	0.515301i
$565$	21795.2			0.0682752
$566$		−	99156.0i		−	0.309518i
$567$	450040.	−	349605.i	1.39986	−	1.08745i
$568$	54252.3			0.168159
$569$		−	64550.9i		−	0.199378i	−0.995019	−	0.0996892i	$-0.968215\pi$
$569$		−	64550.9i		−	0.199378i	0.995019	−	0.0996892i	$-0.0317849\pi$
$570$	27179.1	+	163110.i	0.0836536	+	0.502031i
$571$	205977.			0.631752			0.315876	−	0.948800i	$-0.397702\pi$
$571$	205977.			0.631752			0.315876	+	0.948800i	$0.397702\pi$
$572$			208096.i			0.636023i
$573$	−166007.	+	27661.7i	−0.505611	+	0.0842500i
$574$	−938538.			−2.84858
$575$			239606.i			0.724706i
$576$	−160962.	+	55174.3i	−0.485153	+	0.166300i
$577$	579244.			1.73984			0.869921	−	0.493191i	$-0.164170\pi$
$577$	579244.			1.73984			0.869921	+	0.493191i	$0.164170\pi$
$578$			568011.i			1.70021i
$579$	−54362.7	−	326248.i	−0.162160	−	0.973174i
$580$	110137.			0.327399
$581$			126951.i			0.376083i
$582$	−421408.	+	70219.3i	−1.24410	+	0.207305i
$583$	156657.			0.460906
$584$			180442.i			0.529068i
$585$	−24187.6	−	70563.4i	−0.0706774	−	0.206190i
$586$	−6241.52			−0.0181759
$587$		−	554602.i		−	1.60955i	−0.593578	−	0.804777i	$-0.702285\pi$
$587$		−	554602.i		−	1.60955i	0.593578	−	0.804777i	$-0.297715\pi$
$588$	−260103.	−	1.56096e6i	−0.752299	−	4.51478i
$589$	157302.			0.453423
$590$			89388.8i			0.256791i
$591$	−487382.	+	81212.5i	−1.39539	+	0.232513i
$592$	290304.			0.828340
$593$			308535.i			0.877395i	0.898635	+	0.438697i	$0.144560\pi$
$593$			308535.i			0.877395i	−0.898635	+	0.438697i	$0.855440\pi$
$594$	89558.0	+	165766.i	0.253823	+	0.469811i
$595$	27711.1			0.0782745
$596$		−	598000.i		−	1.68348i
$597$	50534.8	+	303275.i	0.141789	+	0.850918i
$598$	476361.			1.33209
$599$			540961.i			1.50769i	0.657052	+	0.753845i	$0.271803\pi$
$599$			540961.i			1.50769i	−0.657052	+	0.753845i	$0.728197\pi$
$600$	679997.	−	113308.i	1.88888	−	0.314745i
$601$	285642.			0.790812			0.395406	−	0.918506i	$-0.370604\pi$
$601$	285642.			0.790812			0.395406	+	0.918506i	$0.370604\pi$
$602$		−	356111.i		−	0.982635i
$603$	−103370.	+	35432.9i	−0.284289	+	0.0974478i
$604$	386859.			1.06042
$605$			7346.34i			0.0200706i
$606$	188610.	+	1.13191e6i	0.513595	+	3.08224i
$607$	−416023.			−1.12912			−0.564560	−	0.825392i	$-0.690954\pi$
$607$	−416023.			−1.12912			−0.564560	+	0.825392i	$0.690954\pi$
$608$			248787.i			0.673008i
$609$	450087.	−	74998.1i	1.21356	−	0.202216i
$610$	−195495.			−0.525384
$611$			540810.i			1.44865i
$612$	51901.0	+	151413.i	0.138571	+	0.404259i
$613$	135554.			0.360739			0.180369	−	0.983599i	$-0.442271\pi$
$613$	135554.			0.360739			0.180369	+	0.983599i	$0.442271\pi$
$614$			316898.i			0.840587i
$615$	12453.5	+	74737.2i	0.0329261	+	0.197600i
$616$	408257.			1.07590
$617$			530393.i			1.39324i	0.717439	+	0.696622i	$0.245314\pi$
$617$			530393.i			1.39324i	−0.717439	+	0.696622i	$0.754686\pi$
$618$	661700.	−	110259.i	1.73254	−	0.288694i
$619$	−449143.			−1.17220			−0.586102	−	0.810237i	$-0.699338\pi$
$619$	−449143.			−1.17220			−0.586102	+	0.810237i	$0.699338\pi$
$620$			63165.0i			0.164321i
$621$	258484.	−	139650.i	0.670272	−	0.362126i
$622$	686891.			1.77544
$623$			60335.4i			0.155452i
$624$	−90264.7	−	541707.i	−0.231819	−	1.39122i
$625$	334433.			0.856149
$626$			66371.2i			0.169368i
$627$	−152190.	+	25359.4i	−0.387124	+	0.0645065i
$628$	1.17541e6			2.98036
$629$			45883.8i			0.115973i
$630$	−260230.	+	89201.1i	−0.655656	+	0.224744i
$631$	−537734.			−1.35054			−0.675272	−	0.737569i	$-0.735974\pi$
$631$	−537734.			−1.35054			−0.675272	+	0.737569i	$0.735974\pi$
$632$			451761.i			1.13103i
$633$	−49406.3	−	296502.i	−0.123303	−	0.739982i
$634$	−360929.			−0.897931
$635$			34986.1i			0.0867658i
$636$	−1.30319e6	+	217150.i	−3.22175	+	0.536841i
$637$	−858165.			−2.11491
$638$			150859.i			0.370621i
$639$	−11060.1	−	32266.1i	−0.0270868	−	0.0790214i
$640$	128895.			0.314685
$641$			431615.i			1.05046i	0.850959	+	0.525232i	$0.176021\pi$
$641$			431615.i			1.05046i	−0.850959	+	0.525232i	$0.823979\pi$
$642$	134644.	+	808043.i	0.326677	+	1.96049i
$643$	−643756.			−1.55704			−0.778519	−	0.627621i	$-0.784029\pi$
$643$	−643756.			−1.55704			−0.778519	+	0.627621i	$0.784029\pi$
$644$		−	1.19669e6i		−	2.88542i
$645$	−28357.7	+	4725.25i	−0.0681634	+	0.0113581i
$646$	−192417.			−0.461082
$647$		−	165576.i		−	0.395539i	−0.980249	−	0.197770i	$-0.936630\pi$
$647$		−	165576.i		−	0.395539i	0.980249	−	0.197770i	$-0.0633698\pi$
$648$	−518561.	−	667534.i	−1.23495	−	1.58973i
$649$	−83404.1			−0.198015
$650$		−	702741.i		−	1.66329i
$651$	43012.4	+	258131.i	0.101492	+	0.609085i
$652$	186486.			0.438683
$653$		−	342054.i		−	0.802173i	−0.916040	−	0.401087i	$-0.868633\pi$
$653$		−	342054.i		−	0.802173i	0.916040	−	0.401087i	$-0.131367\pi$
$654$	−429879.	+	71630.9i	−1.00506	+	0.167473i
$655$	−122325.			−0.285123
$656$			557818.i			1.29624i
$657$	107316.	−	36785.7i	0.248620	−	0.0852213i
$658$	1.99445e6			4.60650
$659$		−	139528.i		−	0.321285i	−0.987013	−	0.160642i	$-0.948643\pi$
$659$		−	139528.i		−	0.321285i	0.987013	−	0.160642i	$-0.0513565\pi$
$660$	−10183.1	−	61112.2i	−0.0233773	−	0.140294i
$661$	272057.			0.622668			0.311334	−	0.950301i	$-0.399224\pi$
$661$	272057.			0.622668			0.311334	+	0.950301i	$0.399224\pi$
$662$		−	959855.i		−	2.19023i
$663$	85619.2	−	14266.7i	0.194780	−	0.0324562i
$664$	188303.			0.427093
$665$		−	225270.i		−	0.509402i
$666$	−147698.	−	430886.i	−0.332987	−	0.971436i
$667$	235239.			0.528759
$668$		−	651308.i		−	1.45960i
$669$	5618.82	+	33720.3i	0.0125543	+	0.0753423i
$670$	52749.3			0.117508
$671$		−	182407.i		−	0.405131i
$672$	−408257.	+	68027.9i	−0.904055	+	0.150643i
$673$	−574544.			−1.26851			−0.634254	−	0.773124i	$-0.718693\pi$
$673$	−574544.			−1.26851			−0.634254	+	0.773124i	$0.718693\pi$
$674$		−	202007.i		−	0.444680i
$675$	−206016.	−	381323.i	−0.452162	−	0.836924i
$676$	24690.0			0.0540292
$677$			311725.i			0.680134i	0.940401	+	0.340067i	$0.110450\pi$
$677$			311725.i			0.680134i	−0.940401	+	0.340067i	$0.889550\pi$
$678$	−41381.7	−	248345.i	−0.0900221	−	0.540251i
$679$	582004.			1.26237
$680$		−	41103.3i		−	0.0888912i
$681$	505128.	−	84169.6i	1.08920	−	0.181494i
$682$	−86519.6			−0.186014
$683$			532150.i			1.14076i	0.821382	+	0.570378i	$0.193203\pi$
$683$			532150.i			1.14076i	−0.821382	+	0.570378i	$0.806797\pi$
$684$	1.23087e6	−	421916.i	2.63088	−	0.901806i
$685$	147679.			0.314729
$686$			1.68743e6i			3.58572i
$687$	55073.7	+	330514.i	0.116689	+	0.700288i
$688$	−211654.			−0.447146
$689$			716449.i			1.50920i
$690$	−139894.	+	23310.6i	−0.293833	+	0.0489615i
$691$	−24193.6			−0.0506693			−0.0253347	−	0.999679i	$-0.508065\pi$
$691$	−24193.6			−0.0506693			−0.0253347	+	0.999679i	$0.508065\pi$
$692$			514190.i			1.07377i
$693$	−83229.0	−	242807.i	−0.173304	−	0.505586i
$694$	−1.68884e6			−3.50647
$695$			81858.7i			0.169471i
$696$	−111243.	−	667604.i	−0.229644	−	1.37816i
$697$	−88165.7			−0.181482
$698$		−	220196.i		−	0.451959i
$699$	471905.	−	78633.6i	0.965829	−	0.160936i
$700$	−1.76539e6			−3.60283
$701$			931.216i			0.00189502i	1.00000		0.000947511i	$0.000301602\pi$
$701$			931.216i			0.00189502i	−1.00000		0.000947511i	$0.999698\pi$
$702$	−758110.	+	409581.i	−1.53836	+	0.831124i
$703$	373000.			0.754742
$704$			76639.2i			0.154634i
$705$	−26464.4	−	158821.i	−0.0532456	−	0.319543i
$706$	−764094.			−1.53298
$707$		−	1.56328e6i		−	3.12749i
$708$	693816.	−	115611.i	1.38413	−	0.230638i
$709$	−163571.			−0.325396			−0.162698	−	0.986676i	$-0.552020\pi$
$709$	−163571.			−0.325396			−0.162698	+	0.986676i	$0.552020\pi$
$710$			16465.3i			0.0326627i
$711$	268681.	−	92098.0i	0.531494	−	0.182184i
$712$	89494.1			0.176536
$713$			134913.i			0.265383i
$714$	−52614.2	−	315754.i	−0.103206	−	0.619373i
$715$	−33597.5			−0.0657196
$716$			823980.i			1.60728i
$717$	−595169.	+	99173.1i	−1.15772	+	0.192910i
$718$	1.11322e6			2.15940
$719$			527824.i			1.02101i	0.859874	+	0.510506i	$0.170542\pi$
$719$			527824.i			1.02101i	−0.859874	+	0.510506i	$0.829458\pi$
$720$	53016.5	+	154667.i	0.102269	+	0.298355i
$721$	−913870.			−1.75798
$722$			640979.i			1.22962i
$723$	−69782.8	−	418788.i	−0.133497	−	0.801158i
$724$	−1.40454e6			−2.67951
$725$		−	347031.i		−	0.660226i
$726$	83707.7	−	13948.2i	0.158815	−	0.0264634i
$727$	750478.			1.41994			0.709969	−	0.704233i	$-0.248709\pi$
$727$	750478.			1.41994			0.709969	+	0.704233i	$0.248709\pi$
$728$			1.86711e6i			3.52295i
$729$	−291294.	+	444496.i	−0.548122	+	0.836398i
$730$	−54763.2			−0.102765
$731$		−	33452.9i		−	0.0626035i
$732$	252843.	+	1.51739e6i	0.471877	+	2.83188i
$733$	−413160.			−0.768972			−0.384486	−	0.923131i	$-0.625621\pi$
$733$	−413160.			−0.768972			−0.384486	+	0.923131i	$0.625621\pi$
$734$			1.55917e6i			2.89402i
$735$	252019.	−	41994.0i	0.466508	−	0.0777343i
$736$	−213376.			−0.393904
$737$			49217.7i			0.0906121i
$738$	827948.	−	283802.i	1.52016	−	0.521078i
$739$	−712815.			−1.30523			−0.652617	−	0.757688i	$-0.726329\pi$
$739$	−712815.			−1.30523			−0.652617	+	0.757688i	$0.726329\pi$
$740$			149779.i			0.273520i
$741$	−115978.	−	696019.i	−0.211222	−	1.26761i
$742$	2.64218e6			4.79905
$743$		−	771341.i		−	1.39723i	−0.715496	−	0.698617i	$-0.753799\pi$
$743$		−	771341.i		−	1.39723i	0.715496	−	0.698617i	$-0.246201\pi$
$744$	382880.	−	63799.3i	0.691698	−	0.115258i
$745$	96548.0			0.173953
$746$		−	1.92660e6i		−	3.46190i
$747$	−38388.4	−	111992.i	−0.0687952	−	0.200699i
$748$	72092.5			0.128851
$749$		−	1.11598e6i		−	1.98927i
$750$	70538.9	+	423326.i	0.125402	+	0.752579i
$751$	−156029.			−0.276646			−0.138323	−	0.990387i	$-0.544171\pi$
$751$	−156029.			−0.276646			−0.138323	+	0.990387i	$0.544171\pi$
$752$		−	1.18540e6i		−	2.09618i
$753$	−342233.	+	57026.4i	−0.603576	+	0.100574i
$754$	−689934.			−1.21357
$755$			62459.0i			0.109572i
$756$	1.02893e6	+	1.90448e6i	1.80028	+	3.33221i
$757$	−451862.			−0.788523			−0.394261	−	0.918998i	$-0.629000\pi$
$757$	−451862.			−0.788523			−0.394261	+	0.918998i	$0.629000\pi$
$758$		−	1.13832e6i		−	1.98119i
$759$	−21749.9	−	130528.i	−0.0377549	−	0.226579i
$760$	−334138.			−0.578495
$761$		−	690227.i		−	1.19185i	−0.803039	−	0.595926i	$-0.796785\pi$
$761$		−	690227.i		−	1.19185i	0.803039	−	0.595926i	$-0.203215\pi$
$762$	398649.	−	66427.0i	0.686564	−	0.114402i
$763$	593704.			1.01981
$764$		−	639265.i		−	1.09520i
$765$	−24445.9	+	8379.50i	−0.0417717	+	0.0143184i
$766$	1.33593e6			2.27681
$767$		−	381438.i		−	0.648385i
$768$	−195008.	−	1.17030e6i	−0.330621	−	1.98416i
$769$	340721.			0.576165			0.288082	−	0.957606i	$-0.406982\pi$
$769$	340721.			0.576165			0.288082	+	0.957606i	$0.406982\pi$
$770$			123904.i			0.208979i
$771$	−357270.	+	59531.9i	−0.601018	+	0.100148i
$772$	1.25633e6			2.10799
$773$			734245.i			1.22880i	0.788994	+	0.614402i	$0.210602\pi$
$773$			734245.i			1.22880i	−0.788994	+	0.614402i	$0.789398\pi$
$774$	107684.	+	314150.i	0.179749	+	0.524390i
$775$	199027.			0.331366
$776$		−	863274.i		−	1.43359i
$777$	101993.	+	612089.i	0.168938	+	1.01385i
$778$	−1.10561e6			−1.82659
$779$			716720.i			1.18107i
$780$	279488.	−	46571.2i	0.459383	−	0.0765470i
$781$	−15362.9			−0.0251867
$782$		−	165030.i		−	0.269866i
$783$	−374374.	+	202262.i	−0.610635	+	0.329906i
$784$	1.88100e6			3.06025
$785$			189771.i			0.307958i
$786$	232254.	+	1.39383e6i	0.375940	+	2.25613i
$787$	−649287.			−1.04830			−0.524152	−	0.851625i	$-0.675618\pi$
$787$	−649287.			−1.04830			−0.524152	+	0.851625i	$0.675618\pi$
$788$		−	1.87683e6i		−	3.02254i
$789$	210605.	−	35093.2i	0.338310	−	0.0563727i
$790$	−137107.			−0.219688
$791$			342987.i			0.548182i
$792$	−360151.	+	123452.i	−0.574161	+	0.196810i
$793$	834212.			1.32657
$794$		−	398976.i		−	0.632858i
$795$	−35059.2	−	210401.i	−0.0554713	−	0.332900i
$796$	−1.16786e6			−1.84317
$797$		−	263308.i		−	0.414522i	−0.978286	−	0.207261i	$-0.933545\pi$
$797$		−	263308.i		−	0.414522i	0.978286	−	0.207261i	$-0.0664550\pi$
$798$	−2.56684e6	+	427713.i	−4.03082	+	0.671656i
$799$	187357.			0.293479
$800$			314779.i			0.491842i
$801$	−18244.7	−	53225.9i	−0.0284361	−	0.0829579i
$802$	1.30775e6			2.03318
$803$		−	51096.7i		−	0.0792432i
$804$	−68223.2	−	409429.i	−0.105541	−	0.633383i
$805$	193207.			0.298147
$806$		−	395686.i		−	0.609089i
$807$	30313.3	−	5051.11i	0.0465464	−	0.00775604i
$808$	−2.31877e6			−3.55169
$809$			516170.i			0.788671i	0.918967	+	0.394335i	$0.129025\pi$
$809$			516170.i			0.788671i	−0.918967	+	0.394335i	$0.870975\pi$
$810$	202593.	−	157381.i	0.308784	−	0.239873i
$811$	403990.			0.614227			0.307114	−	0.951673i	$-0.400637\pi$
$811$	403990.			0.614227			0.307114	+	0.951673i	$0.400637\pi$
$812$			1.73321e6i			2.62869i
$813$	164791.	+	988959.i	0.249317	+	1.49623i
$814$	−205159.			−0.309629
$815$			30108.4i			0.0453286i
$816$	−187668.	+	31271.1i	−0.281844	+	0.0469638i
$817$	−271946.			−0.407417
$818$		−	211273.i		−	0.315746i
$819$	1.11045e6	−	380637.i	1.65550	−	0.567470i
$820$	−287801.			−0.428020
$821$			229139.i			0.339948i	0.985449	+	0.169974i	$0.0543684\pi$
$821$			229139.i			0.339948i	−0.985449	+	0.169974i	$0.945632\pi$
$822$	−280393.	−	1.68273e6i	−0.414976	−	2.49040i
$823$	520877.			0.769016			0.384508	−	0.923122i	$-0.374371\pi$
$823$	520877.			0.769016			0.384508	+	0.923122i	$0.374371\pi$
$824$			1.35552e6i			1.99642i
$825$	−192559.	+	32086.1i	−0.282914	+	0.0471421i
$826$	−1.40670e6			−2.06177
$827$			1.05248e6i			1.53888i	0.638720	+	0.769439i	$0.279464\pi$
$827$			1.05248e6i			1.53888i	−0.638720	+	0.769439i	$0.720536\pi$
$828$	361863.	+	1.05568e6i	0.527817	+	1.53982i
$829$	277222.			0.403383			0.201692	−	0.979449i	$-0.435356\pi$
$829$	277222.			0.403383			0.201692	+	0.979449i	$0.435356\pi$
$830$			57149.1i			0.0829571i
$831$	−163847.	−	983296.i	−0.237266	−	1.42391i
$832$	−350499.			−0.506338
$833$			297301.i			0.428456i
$834$	932738.	−	155422.i	1.34100	−	0.223451i
$835$	105155.			0.150819
$836$		−	586057.i		−	0.838547i
$837$	−116000.	−	214708.i	−0.165579	−	0.306477i
$838$	1.55188e6			2.20989
$839$			1.10943e6i			1.57607i	0.615629	+	0.788036i	$0.288902\pi$
$839$			1.10943e6i			1.57607i	−0.615629	+	0.788036i	$0.711098\pi$
$840$	−91366.3	−	548318.i	−0.129487	−	0.777094i
$841$	366574.			0.518287
$842$			2.25464e6i			3.18019i
$843$	−1.21018e6	+	201653.i	−1.70292	+	0.283759i
$844$	1.14178e6			1.60287
$845$			3986.25i			0.00558278i
$846$	−1.75944e6	+	603096.i	−2.45829	+	0.842647i
$847$	−115608.			−0.161147
$848$		−	1.57038e6i		−	2.18380i
$849$	−20705.0	−	124257.i	−0.0287250	−	0.172388i
$850$	−243456.			−0.336964
$851$			319910.i			0.441742i
$852$	127800.	−	21295.3i	0.176056	−	0.0293363i
$853$	669050.			0.919519			0.459759	−	0.888044i	$-0.347936\pi$
$853$	669050.			0.919519			0.459759	+	0.888044i	$0.347936\pi$
$854$		−	3.07648e6i		−	4.21831i
$855$	68118.9	+	198726.i	0.0931827	+	0.271846i
$856$	−1.65531e6			−2.25909
$857$			571270.i			0.777821i	0.921276	+	0.388910i	$0.127148\pi$
$857$			571270.i			0.777821i	−0.921276	+	0.388910i	$0.872852\pi$
$858$	63790.4	+	382826.i	0.0866524	+	0.520028i
$859$	1.13560e6			1.53900			0.769500	−	0.638646i	$-0.220505\pi$
$859$	1.13560e6			1.53900			0.769500	+	0.638646i	$0.220505\pi$
$860$		−	109201.i		−	0.147648i
$861$	−1.17613e6	+	195979.i	−1.58653	+	0.264364i
$862$	830322.			1.11746
$863$			449719.i			0.603837i	0.953334	+	0.301918i	$0.0976270\pi$
$863$			449719.i			0.603837i	−0.953334	+	0.301918i	$0.902373\pi$
$864$	339580.	−	183464.i	0.454899	−	0.245767i
$865$	−83016.8			−0.110952
$866$		−	1.47098e6i		−	1.96143i
$867$	118608.	+	711804.i	0.157789	+	0.946940i
$868$	−994019.			−1.31934
$869$		−	127928.i		−	0.169405i
$870$	202614.	−	33761.7i	0.267690	−	0.0446052i
$871$	−225091.			−0.296702
$872$		−	880628.i		−	1.15814i
$873$	−513425.	+	175991.i	−0.673672	+	0.230920i
$874$	−1.34156e6			−1.75626
$875$		−	584653.i		−	0.763628i
$876$	70827.8	+	425060.i	0.0922987	+	0.553914i
$877$	−784495.			−1.01998			−0.509989	−	0.860181i	$-0.670351\pi$
$877$	−784495.			−1.01998			−0.509989	+	0.860181i	$0.670351\pi$
$878$			846976.i			1.09871i
$879$	−7821.57	+	1303.31i	−0.0101232	+	0.00168682i
$880$	73642.0			0.0950955
$881$		−	133825.i		−	0.172419i	−0.996277	−	0.0862096i	$-0.972525\pi$
$881$		−	133825.i		−	0.172419i	0.996277	−	0.0862096i	$-0.0274755\pi$
$882$	−957001.	−	2.79190e6i	−1.23020	−	3.58891i
$883$	483132.			0.619647			0.309824	−	0.950794i	$-0.399730\pi$
$883$	483132.			0.619647			0.309824	+	0.950794i	$0.399730\pi$
$884$			329705.i			0.421912i
$885$	18665.5	+	112018.i	0.0238316	+	0.143021i
$886$	1.55730e6			1.98383
$887$		−	1.21635e6i		−	1.54601i	−0.634399	−	0.773005i	$-0.718753\pi$
$887$		−	1.21635e6i		−	1.54601i	0.634399	−	0.773005i	$-0.281247\pi$
$888$	907899.	−	151283.i	1.15136	−	0.191852i
$889$	−550572.			−0.696643
$890$			27161.0i			0.0342899i
$891$	146844.	+	189029.i	0.184970	+	0.238108i
$892$	−129851.			−0.163199
$893$		−	1.52307e6i		−	1.90993i
$894$	−183312.	−	1.10012e6i	−0.229360	−	1.37646i
$895$	−133033.			−0.166078
$896$			2.02840e6i			2.52661i
$897$	596952.	−	99470.3i	0.741916	−	0.123626i
$898$	−2.06324e6			−2.55856
$899$		−	195400.i		−	0.241771i
$900$	1.55737e6	−	533830.i	1.92267	−	0.659050i
$901$	248205.			0.305746
$902$		−	394212.i		−	0.484526i
$903$	−74360.5	−	446261.i	−0.0911941	−	0.547285i
$904$	508745.			0.622535
$905$		−	226765.i		−	0.276872i
$906$	711689.	−	118589.i	0.867029	−	0.144473i
$907$	−75811.7			−0.0921556			−0.0460778	−	0.998938i	$-0.514672\pi$
$907$	−75811.7			−0.0921556			−0.0460778	+	0.998938i	$0.514672\pi$
$908$			1.94517e6i			2.35931i
$909$	472715.	+	1.37907e6i	0.572099	+	1.66901i
$910$	−566657.			−0.684286
$911$			1.16667e6i			1.40575i	0.711311	+	0.702877i	$0.248102\pi$
$911$			1.16667e6i			1.40575i	−0.711311	+	0.702877i	$0.751898\pi$
$912$	254210.	+	1.52560e6i	0.305635	+	1.83421i
$913$	−53322.9			−0.0639694
$914$			1.79679e6i			2.15082i
$915$	−244985.	+	40821.9i	−0.292616	+	0.0487586i
$916$	−1.27276e6			−1.51689
$917$		−	1.92501e6i		−	2.28926i
$918$	141895.	+	262638.i	0.168376	+	0.311654i
$919$	−90255.3			−0.106867			−0.0534333	−	0.998571i	$-0.517016\pi$
$919$	−90255.3			−0.106867			−0.0534333	+	0.998571i	$0.517016\pi$
$920$		−	286580.i		−	0.338587i
$921$	66172.3	+	397121.i	0.0780112	+	0.468170i
$922$	−658330.			−0.774430
$923$		−	70260.3i		−	0.0824720i
$924$	961714.	−	160251.i	1.12642	−	0.187696i
$925$	471940.			0.551574
$926$			84525.4i			0.0985747i
$927$	806186.	−	276343.i	0.938158	−	0.321580i
$928$	309042.			0.358857
$929$		−	1.47067e6i		−	1.70406i	−0.523497	−	0.852028i	$-0.675373\pi$
$929$		−	1.47067e6i		−	1.70406i	0.523497	−	0.852028i	$-0.324627\pi$
$930$	19362.8	+	116202.i	0.0223873	+	0.134353i
$931$	2.41683e6			2.78835
$932$			1.81723e6i			2.09208i
$933$	860778.	−	143432.i	0.988844	−	0.164771i
$934$	111244.			0.127521
$935$			11639.4i			0.0133140i
$936$	−564590.	−	1.64710e6i	−0.644438	−	1.88005i
$937$	−537409.			−0.612105			−0.306052	−	0.952015i	$-0.599008\pi$
$937$	−537409.			−0.612105			−0.306052	+	0.952015i	$0.599008\pi$
$938$			830109.i			0.943473i
$939$	13859.2	+	83173.1i	0.0157183	+	0.0943304i
$940$	611594.			0.692162
$941$		−	932898.i		−	1.05355i	−0.850005	−	0.526775i	$-0.823401\pi$
$941$		−	932898.i		−	1.05355i	0.850005	−	0.526775i	$-0.176599\pi$
$942$	2.16235e6	−	360312.i	2.43682	−	0.406048i
$943$	−614707.			−0.691265
$944$			836069.i			0.938206i
$945$	−307481.	+	166122.i	−0.344314	+	0.186021i
$946$	149577.			0.167140
$947$		−	159383.i		−	0.177722i	−0.996044	−	0.0888609i	$-0.971677\pi$
$947$		−	159383.i		−	0.177722i	0.996044	−	0.0888609i	$-0.0283227\pi$
$948$	177327.	+	1.06420e6i	0.197314	+	1.18415i
$949$	233684.			0.259476
$950$			1.97911e6i			2.19292i
$951$	−452298.	+	75366.5i	−0.500108	+	0.0833331i
$952$	646837.			0.713709
$953$			792800.i			0.872927i	0.899722	+	0.436464i	$0.143769\pi$
$953$			792800.i			0.872927i	−0.899722	+	0.436464i	$0.856231\pi$
$954$	−2.33085e6	+	798964.i	−2.56105	+	0.877870i
$955$	103210.			0.113166
$956$		−	2.29190e6i		−	2.50772i
$957$	31501.3	+	189049.i	0.0343957	+	0.206420i
$958$	1.00223e6			1.09203
$959$			2.32400e6i			2.52697i
$960$	102932.	−	17151.6i	0.111688	−	0.0186107i
$961$	−811457.			−0.878655
$962$		−	938266.i		−	1.01385i
$963$	337460.	+	984485.i	0.363889	+	1.06159i
$964$	1.61269e6			1.73538
$965$			202836.i			0.217816i
$966$	−366835.	−	2.20149e6i	−0.393113	−	2.35919i
$967$	153688.			0.164357			0.0821783	−	0.996618i	$-0.473812\pi$
$967$	153688.			0.164357			0.0821783	+	0.996618i	$0.473812\pi$
$968$			171479.i			0.183004i
$969$	−241127.	+	40179.1i	−0.256802	+	0.0427910i
$970$	261999.			0.278456
$971$		−	587707.i		−	0.623336i	−0.950191	−	0.311668i	$-0.899112\pi$
$971$		−	587707.i		−	0.623336i	0.950191	−	0.311668i	$-0.100888\pi$
$972$	−1.48358e6	−	1.36894e6i	−1.57028	−	1.44894i
$973$	−1.28820e6			−1.36068
$974$			1.47789e6i			1.55784i
$975$	−146741.	−	880641.i	−0.154363	−	0.926381i
$976$	−1.82850e6			−1.91953
$977$		−	1.61099e6i		−	1.68773i	−0.536556	−	0.843865i	$-0.680275\pi$
$977$		−	1.61099e6i		−	1.68773i	0.536556	−	0.843865i	$-0.319725\pi$
$978$	343070.	−	57165.8i	0.358678	−	0.0597666i
$979$	−25342.5			−0.0264414
$980$			970485.i			1.01050i
$981$	−523746.	+	179529.i	−0.544231	+	0.186550i
$982$	−3.23884e6			−3.35866
$983$			299713.i			0.310169i	0.987901	+	0.155084i	$0.0495650\pi$
$983$			299713.i			0.310169i	−0.987901	+	0.155084i	$0.950435\pi$
$984$	290691.	+	1.74453e6i	0.300221	+	1.80172i
$985$	303017.			0.312316
$986$			239019.i			0.245855i
$987$	2.49934e6	−	416466.i	2.56562	−	0.427509i
$988$	2.68025e6			2.74576
$989$		−	233239.i		−	0.238456i
$990$	−37467.0	−	109304.i	−0.0382277	−	0.111523i
$991$	−635246.			−0.646836			−0.323418	−	0.946256i	$-0.604832\pi$
$991$	−635246.			−0.646836			−0.323418	+	0.946256i	$0.604832\pi$
$992$			177240.i			0.180110i
$993$	−200430.	−	1.20284e6i	−0.203266	−	1.21986i
$994$	−259112.			−0.262250
$995$		−	188553.i		−	0.190453i
$996$	443579.	−	73913.6i	0.447149	−	0.0745085i
$997$	−155118.			−0.156053			−0.0780265	−	0.996951i	$-0.524862\pi$
$997$	−155118.			−0.156053			−0.0780265	+	0.996951i	$0.524862\pi$
$998$			1.82057e6i			1.82787i
$999$	−275063.	−	509124.i	−0.275614	−	0.510144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.5.b.a.23.14	yes	14
3.2	odd	2	inner	33.5.b.a.23.1	✓	14
4.3	odd	2		528.5.i.d.353.7		14
12.11	even	2		528.5.i.d.353.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.b.a.23.1	✓	14	3.2	odd	2	inner
33.5.b.a.23.14	yes	14	1.1	even	1	trivial
528.5.i.d.353.7		14	4.3	odd	2
528.5.i.d.353.8		14	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+7.08422i q^{2} +(1.47928 + 8.87760i) q^{3} -34.1862 q^{4} -5.51941i q^{5} +(-62.8909 + 10.4795i) q^{6} +86.8582 q^{7} -128.835i q^{8} +(-76.6235 + 26.2648i) q^{9} +O(q^{10})\)	\(q+7.08422i q^{2} +(1.47928 + 8.87760i) q^{3} -34.1862 q^{4} -5.51941i q^{5} +(-62.8909 + 10.4795i) q^{6} +86.8582 q^{7} -128.835i q^{8} +(-76.6235 + 26.2648i) q^{9} +39.1007 q^{10} +36.4829i q^{11} +(-50.5708 - 303.491i) q^{12} -166.850 q^{13} +615.323i q^{14} +(48.9991 - 8.16473i) q^{15} +365.716 q^{16} +57.8030i q^{17} +(-186.066 - 542.818i) q^{18} +469.895 q^{19} +188.688i q^{20} +(128.487 + 771.092i) q^{21} -258.453 q^{22} +403.013i q^{23} +(1143.74 - 190.582i) q^{24} +594.536 q^{25} -1182.00i q^{26} +(-346.516 - 641.380i) q^{27} -2969.35 q^{28} -583.701i q^{29} +(57.8408 + 347.120i) q^{30} +334.760 q^{31} +529.453i q^{32} +(-323.880 + 53.9682i) q^{33} -409.489 q^{34} -479.406i q^{35} +(2619.46 - 897.894i) q^{36} +793.796 q^{37} +3328.84i q^{38} +(-246.817 - 1481.22i) q^{39} -711.092 q^{40} +1525.28i q^{41} +(-5462.59 + 910.232i) q^{42} -578.739 q^{43} -1247.21i q^{44} +(144.966 + 422.916i) q^{45} -2855.03 q^{46} -3241.31i q^{47} +(540.994 + 3246.68i) q^{48} +5143.35 q^{49} +4211.82i q^{50} +(-513.152 + 85.5066i) q^{51} +5703.95 q^{52} -4293.98i q^{53} +(4543.67 - 2454.79i) q^{54} +201.364 q^{55} -11190.4i q^{56} +(695.104 + 4171.53i) q^{57} +4135.06 q^{58} +2286.12i q^{59} +(-1675.09 + 279.121i) q^{60} -4999.79 q^{61} +2371.51i q^{62} +(-6655.38 + 2281.32i) q^{63} +2100.69 q^{64} +920.911i q^{65} +(-382.323 - 2294.44i) q^{66} +1349.06 q^{67} -1976.06i q^{68} +(-3577.79 + 596.168i) q^{69} +3396.22 q^{70} +421.099i q^{71} +(3383.83 + 9871.78i) q^{72} -1400.57 q^{73} +5623.42i q^{74} +(879.483 + 5278.05i) q^{75} -16063.9 q^{76} +3168.84i q^{77} +(10493.3 - 1748.50i) q^{78} -3506.52 q^{79} -2018.54i q^{80} +(5181.32 - 4025.01i) q^{81} -10805.4 q^{82} +1461.59i q^{83} +(-4392.49 - 26360.7i) q^{84} +319.039 q^{85} -4099.91i q^{86} +(5181.86 - 863.454i) q^{87} +4700.27 q^{88} +694.642i q^{89} +(-2996.03 + 1026.97i) q^{90} -14492.3 q^{91} -13777.5i q^{92} +(495.202 + 2971.86i) q^{93} +22962.1 q^{94} -2593.54i q^{95} +(-4700.27 + 783.207i) q^{96} +6700.63 q^{97} +36436.6i q^{98} +(-958.217 - 2795.44i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9}+O(q^{10}) \) 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9	\( 14 q - 5 q^{3} - 100 q^{4} - 2 q^{6} + 76 q^{7} - 67 q^{9} - 156 q^{10} - 100 q^{12} - 104 q^{13} + 151 q^{15} + 356 q^{16} - 34 q^{18} + 1072 q^{19} + 718 q^{21} + 1200 q^{24} - 1060 q^{25} - 1154 q^{27} - 1808 q^{28} - 3026 q^{30} + 3310 q^{31} - 605 q^{33} - 2304 q^{34} + 2644 q^{36} - 362 q^{37} + 4264 q^{39} + 1896 q^{40} - 7364 q^{42} - 6740 q^{43} + 3611 q^{45} - 4068 q^{46} - 2956 q^{48} + 7074 q^{49} - 7046 q^{51} + 13072 q^{52} + 20512 q^{54} + 726 q^{55} + 3876 q^{57} - 7848 q^{58} - 8416 q^{60} - 3560 q^{61} - 17662 q^{63} + 12020 q^{64} + 1210 q^{66} - 16514 q^{67} + 9833 q^{69} + 13320 q^{70} + 8160 q^{72} + 12664 q^{73} - 5386 q^{75} - 43736 q^{76} + 19096 q^{78} + 3052 q^{79} - 11611 q^{81} + 10200 q^{82} - 39184 q^{84} + 34884 q^{85} + 37068 q^{87} - 7260 q^{88} - 26686 q^{90} - 45856 q^{91} + 2719 q^{93} + 6120 q^{94} - 38368 q^{96} - 27854 q^{97} + 4235 q^{99}+O(q^{100}) \) 14 * q - 5 * q^3 - 100 * q^4 - 2 * q^6 + 76 * q^7 - 67 * q^9 - 156 * q^10 - 100 * q^12 - 104 * q^13 + 151 * q^15 + 356 * q^16 - 34 * q^18 + 1072 * q^19 + 718 * q^21 + 1200 * q^24 - 1060 * q^25 - 1154 * q^27 - 1808 * q^28 - 3026 * q^30 + 3310 * q^31 - 605 * q^33 - 2304 * q^34 + 2644 * q^36 - 362 * q^37 + 4264 * q^39 + 1896 * q^40 - 7364 * q^42 - 6740 * q^43 + 3611 * q^45 - 4068 * q^46 - 2956 * q^48 + 7074 * q^49 - 7046 * q^51 + 13072 * q^52 + 20512 * q^54 + 726 * q^55 + 3876 * q^57 - 7848 * q^58 - 8416 * q^60 - 3560 * q^61 - 17662 * q^63 + 12020 * q^64 + 1210 * q^66 - 16514 * q^67 + 9833 * q^69 + 13320 * q^70 + 8160 * q^72 + 12664 * q^73 - 5386 * q^75 - 43736 * q^76 + 19096 * q^78 + 3052 * q^79 - 11611 * q^81 + 10200 * q^82 - 39184 * q^84 + 34884 * q^85 + 37068 * q^87 - 7260 * q^88 - 26686 * q^90 - 45856 * q^91 + 2719 * q^93 + 6120 * q^94 - 38368 * q^96 - 27854 * q^97 + 4235 * q^99

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