LMFDB - Embedded newform 950.2.e.i.501.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, degree $2$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.1
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	950.501
Dual form			950.2.e.i.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.895644 - 1.55130i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.895644 + 1.55130i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.104356 + 0.180750i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.895644 - 1.55130i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.895644 + 1.55130i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.104356 + 0.180750i) q^{9} +0.791288 q^{11} +1.79129 q^{12} +(2.39564 - 4.14938i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.89564 - 3.28335i) q^{17} +0.208712 q^{18} +(-3.50000 + 2.59808i) q^{19} +(0.895644 + 1.55130i) q^{21} +(-0.395644 - 0.685275i) q^{22} +(2.29129 - 3.96863i) q^{23} +(-0.895644 - 1.55130i) q^{24} -4.79129 q^{26} -5.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-1.10436 + 1.91280i) q^{29} -0.208712 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.708712 - 1.22753i) q^{33} +(-1.89564 + 3.28335i) q^{34} +(-0.104356 - 0.180750i) q^{36} -5.58258 q^{37} +(4.00000 + 1.73205i) q^{38} -8.58258 q^{39} +(-1.18693 - 2.05583i) q^{41} +(0.895644 - 1.55130i) q^{42} +(-0.604356 - 1.04678i) q^{43} +(-0.395644 + 0.685275i) q^{44} -4.58258 q^{46} +(-3.08258 + 5.33918i) q^{47} +(-0.895644 + 1.55130i) q^{48} -6.00000 q^{49} +(-3.39564 + 5.88143i) q^{51} +(2.39564 + 4.14938i) q^{52} +(-2.29129 + 3.96863i) q^{53} +(2.50000 + 4.33013i) q^{54} -1.00000 q^{56} +(7.16515 + 3.10260i) q^{57} +2.20871 q^{58} +(2.29129 + 3.96863i) q^{59} +(6.18693 - 10.7161i) q^{61} +(0.104356 + 0.180750i) q^{62} +(0.104356 - 0.180750i) q^{63} +1.00000 q^{64} +(-0.708712 + 1.22753i) q^{66} +(-3.20871 + 5.55765i) q^{67} +3.79129 q^{68} -8.20871 q^{69} +(-2.29129 - 3.96863i) q^{71} +(-0.104356 + 0.180750i) q^{72} +(0.895644 + 1.55130i) q^{73} +(2.79129 + 4.83465i) q^{74} +(-0.500000 - 4.33013i) q^{76} -0.791288 q^{77} +(4.29129 + 7.43273i) q^{78} +(3.97822 + 6.89048i) q^{79} +(4.79129 + 8.29875i) q^{81} +(-1.18693 + 2.05583i) q^{82} -0.791288 q^{83} -1.79129 q^{84} +(-0.604356 + 1.04678i) q^{86} +3.95644 q^{87} +0.791288 q^{88} +(2.29129 - 3.96863i) q^{89} +(-2.39564 + 4.14938i) q^{91} +(2.29129 + 3.96863i) q^{92} +(0.186932 + 0.323775i) q^{93} +6.16515 q^{94} +1.79129 q^{96} +(-0.686932 - 1.18980i) q^{97} +(3.00000 + 5.19615i) q^{98} +(-0.0825757 + 0.143025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + q^{3} - 2 q^{4} + q^{6} - 4 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + q^3 - 2 * q^4 + q^6 - 4 * q^7 + 4 * q^8 - 5 * q^9	$ 4 q - 2 q^{2} + q^{3} - 2 q^{4} + q^{6} - 4 q^{7} + 4 q^{8} - 5 q^{9} - 6 q^{11} - 2 q^{12} + 5 q^{13} + 2 q^{14} - 2 q^{16} - 3 q^{17} + 10 q^{18} - 14 q^{19} - q^{21} + 3 q^{22} + q^{24} - 10 q^{26} - 20 q^{27} + 2 q^{28} - 9 q^{29} - 10 q^{31} - 2 q^{32} - 12 q^{33} - 3 q^{34} - 5 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{39} + 9 q^{41} - q^{42} - 7 q^{43} + 3 q^{44} + 6 q^{47} + q^{48} - 24 q^{49} - 9 q^{51} + 5 q^{52} + 10 q^{54} - 4 q^{56} - 8 q^{57} + 18 q^{58} + 11 q^{61} + 5 q^{62} + 5 q^{63} + 4 q^{64} - 12 q^{66} - 22 q^{67} + 6 q^{68} - 42 q^{69} - 5 q^{72} - q^{73} + 2 q^{74} - 2 q^{76} + 6 q^{77} + 8 q^{78} - 7 q^{79} + 10 q^{81} + 9 q^{82} + 6 q^{83} + 2 q^{84} - 7 q^{86} - 30 q^{87} - 6 q^{88} - 5 q^{91} - 13 q^{93} - 12 q^{94} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 18 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + q^3 - 2 * q^4 + q^6 - 4 * q^7 + 4 * q^8 - 5 * q^9 - 6 * q^11 - 2 * q^12 + 5 * q^13 + 2 * q^14 - 2 * q^16 - 3 * q^17 + 10 * q^18 - 14 * q^19 - q^21 + 3 * q^22 + q^24 - 10 * q^26 - 20 * q^27 + 2 * q^28 - 9 * q^29 - 10 * q^31 - 2 * q^32 - 12 * q^33 - 3 * q^34 - 5 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^39 + 9 * q^41 - q^42 - 7 * q^43 + 3 * q^44 + 6 * q^47 + q^48 - 24 * q^49 - 9 * q^51 + 5 * q^52 + 10 * q^54 - 4 * q^56 - 8 * q^57 + 18 * q^58 + 11 * q^61 + 5 * q^62 + 5 * q^63 + 4 * q^64 - 12 * q^66 - 22 * q^67 + 6 * q^68 - 42 * q^69 - 5 * q^72 - q^73 + 2 * q^74 - 2 * q^76 + 6 * q^77 + 8 * q^78 - 7 * q^79 + 10 * q^81 + 9 * q^82 + 6 * q^83 + 2 * q^84 - 7 * q^86 - 30 * q^87 - 6 * q^88 - 5 * q^91 - 13 * q^93 - 12 * q^94 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.895644	−	1.55130i	−0.517100	−	0.895644i	−0.999803	−	0.0198595i	$-0.993678\pi$
$3$	−0.895644	−	1.55130i	−0.517100	−	0.895644i	0.482703	−	0.875784i	$-0.339655\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.895644	+	1.55130i	−0.365645	+	0.633316i
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000			0.353553
$9$	−0.104356	+	0.180750i	−0.0347854	+	0.0602500i
$10$		0			0
$11$	0.791288			0.238582			0.119291	−	0.992859i	$-0.461938\pi$
$11$	0.791288			0.238582			0.119291	+	0.992859i	$0.461938\pi$
$12$	1.79129			0.517100
$13$	2.39564	−	4.14938i	0.664432	−	1.15083i	−0.315007	−	0.949089i	$-0.602007\pi$
$13$	2.39564	−	4.14938i	0.664432	−	1.15083i	0.979439	−	0.201741i	$-0.0646598\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.89564	−	3.28335i	−0.459761	−	0.796330i	0.539187	−	0.842186i	$-0.318732\pi$
$17$	−1.89564	−	3.28335i	−0.459761	−	0.796330i	−0.998948	+	0.0458564i	$0.985398\pi$
$18$	0.208712			0.0491939
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$20$		0			0
$21$	0.895644	+	1.55130i	0.195446	+	0.338522i
$22$	−0.395644	−	0.685275i	−0.0843516	−	0.146101i
$23$	2.29129	−	3.96863i	0.477767	−	0.827516i	−0.521909	−	0.853001i	$-0.674780\pi$
$23$	2.29129	−	3.96863i	0.477767	−	0.827516i	0.999675	+	0.0254855i	$0.00811315\pi$
$24$	−0.895644	−	1.55130i	−0.182823	−	0.316658i
$25$		0			0
$26$	−4.79129			−0.939649
$27$	−5.00000			−0.962250
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−1.10436	+	1.91280i	−0.205074	+	0.355198i	−0.950156	−	0.311774i	$-0.899077\pi$
$29$	−1.10436	+	1.91280i	−0.205074	+	0.355198i	0.745082	+	0.666972i	$0.232410\pi$
$30$		0			0
$31$	−0.208712			−0.0374858			−0.0187429	−	0.999824i	$-0.505966\pi$
$31$	−0.208712			−0.0374858			−0.0187429	+	0.999824i	$0.505966\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.708712	−	1.22753i	−0.123371	−	0.213685i
$34$	−1.89564	+	3.28335i	−0.325100	+	0.563090i
$35$		0			0
$36$	−0.104356	−	0.180750i	−0.0173927	−	0.0301250i
$37$	−5.58258			−0.917770			−0.458885	−	0.888496i	$-0.651751\pi$
$37$	−5.58258			−0.917770			−0.458885	+	0.888496i	$0.651751\pi$
$38$	4.00000	+	1.73205i	0.648886	+	0.280976i
$39$	−8.58258			−1.37431
$40$		0			0
$41$	−1.18693	−	2.05583i	−0.185368	−	0.321066i	0.758333	−	0.651868i	$-0.226014\pi$
$41$	−1.18693	−	2.05583i	−0.185368	−	0.321066i	−0.943700	+	0.330802i	$0.892681\pi$
$42$	0.895644	−	1.55130i	0.138201	−	0.239371i
$43$	−0.604356	−	1.04678i	−0.0921634	−	0.159632i	0.816258	−	0.577688i	$-0.196045\pi$
$43$	−0.604356	−	1.04678i	−0.0921634	−	0.159632i	−0.908421	+	0.418056i	$0.862712\pi$
$44$	−0.395644	+	0.685275i	−0.0596456	+	0.103309i
$45$		0			0
$46$	−4.58258			−0.675664
$47$	−3.08258	+	5.33918i	−0.449640	+	0.778799i	−0.998362	−	0.0572054i	$-0.981781\pi$
$47$	−3.08258	+	5.33918i	−0.449640	+	0.778799i	0.548723	+	0.836005i	$0.315114\pi$
$48$	−0.895644	+	1.55130i	−0.129275	+	0.223911i
$49$	−6.00000			−0.857143
$50$		0			0
$51$	−3.39564	+	5.88143i	−0.475485	+	0.823565i
$52$	2.39564	+	4.14938i	0.332216	+	0.575415i
$53$	−2.29129	+	3.96863i	−0.314733	+	0.545133i	−0.979381	−	0.202024i	$-0.935248\pi$
$53$	−2.29129	+	3.96863i	−0.314733	+	0.545133i	0.664648	+	0.747157i	$0.268582\pi$
$54$	2.50000	+	4.33013i	0.340207	+	0.589256i
$55$		0			0
$56$	−1.00000			−0.133631
$57$	7.16515	+	3.10260i	0.949047	+	0.410950i
$58$	2.20871			0.290018
$59$	2.29129	+	3.96863i	0.298300	+	0.516671i	0.975747	−	0.218900i	$-0.0702470\pi$
$59$	2.29129	+	3.96863i	0.298300	+	0.516671i	−0.677447	+	0.735572i	$0.736914\pi$
$60$		0			0
$61$	6.18693	−	10.7161i	0.792155	−	1.37205i	−0.132474	−	0.991186i	$-0.542292\pi$
$61$	6.18693	−	10.7161i	0.792155	−	1.37205i	0.924630	−	0.380867i	$-0.124374\pi$
$62$	0.104356	+	0.180750i	0.0132532	+	0.0229553i
$63$	0.104356	−	0.180750i	0.0131476	−	0.0227724i
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.708712	+	1.22753i	−0.0872364	+	0.151098i
$67$	−3.20871	+	5.55765i	−0.392007	+	0.678975i	−0.992714	−	0.120494i	$-0.961552\pi$
$67$	−3.20871	+	5.55765i	−0.392007	+	0.678975i	0.600708	+	0.799469i	$0.294886\pi$
$68$	3.79129			0.459761
$69$	−8.20871			−0.988213
$70$		0			0
$71$	−2.29129	−	3.96863i	−0.271926	−	0.470989i	0.697429	−	0.716654i	$-0.254327\pi$
$71$	−2.29129	−	3.96863i	−0.271926	−	0.470989i	−0.969355	+	0.245664i	$0.920994\pi$
$72$	−0.104356	+	0.180750i	−0.0122985	+	0.0213016i
$73$	0.895644	+	1.55130i	0.104827	+	0.181566i	0.913668	−	0.406462i	$-0.133238\pi$
$73$	0.895644	+	1.55130i	0.104827	+	0.181566i	−0.808840	+	0.588028i	$0.799904\pi$
$74$	2.79129	+	4.83465i	0.324481	+	0.562017i
$75$		0			0
$76$	−0.500000	−	4.33013i	−0.0573539	−	0.496700i
$77$	−0.791288			−0.0901756
$78$	4.29129	+	7.43273i	0.485893	+	0.841591i
$79$	3.97822	+	6.89048i	0.447585	+	0.775239i	0.998228	−	0.0595011i	$-0.0189510\pi$
$79$	3.97822	+	6.89048i	0.447585	+	0.775239i	−0.550644	+	0.834740i	$0.685618\pi$
$80$		0			0
$81$	4.79129	+	8.29875i	0.532365	+	0.922084i
$82$	−1.18693	+	2.05583i	−0.131075	+	0.227028i
$83$	−0.791288			−0.0868551			−0.0434276	−	0.999057i	$-0.513828\pi$
$83$	−0.791288			−0.0868551			−0.0434276	+	0.999057i	$0.513828\pi$
$84$	−1.79129			−0.195446
$85$		0			0
$86$	−0.604356	+	1.04678i	−0.0651694	+	0.112877i
$87$	3.95644			0.424175
$88$	0.791288			0.0843516
$89$	2.29129	−	3.96863i	0.242876	−	0.420674i	−0.718656	−	0.695365i	$-0.755243\pi$
$89$	2.29129	−	3.96863i	0.242876	−	0.420674i	0.961532	+	0.274692i	$0.0885758\pi$
$90$		0			0
$91$	−2.39564	+	4.14938i	−0.251132	+	0.434973i
$92$	2.29129	+	3.96863i	0.238883	+	0.413758i
$93$	0.186932	+	0.323775i	0.0193839	+	0.0335739i
$94$	6.16515			0.635887
$95$		0			0
$96$	1.79129			0.182823
$97$	−0.686932	−	1.18980i	−0.0697474	−	0.120806i	0.829043	−	0.559185i	$-0.188886\pi$
$97$	−0.686932	−	1.18980i	−0.0697474	−	0.120806i	−0.898790	+	0.438379i	$0.855553\pi$
$98$	3.00000	+	5.19615i	0.303046	+	0.524891i
$99$	−0.0825757	+	0.143025i	−0.00829917	+	0.0143746i
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	6.79129			0.672438
$103$	−13.1652			−1.29720			−0.648600	−	0.761129i	$-0.724645\pi$
$103$	−13.1652			−1.29720			−0.648600	+	0.761129i	$0.724645\pi$
$104$	2.39564	−	4.14938i	0.234912	−	0.406880i
$105$		0			0
$106$	4.58258			0.445099
$107$	−3.95644			−0.382483			−0.191242	−	0.981543i	$-0.561251\pi$
$107$	−3.95644			−0.382483			−0.191242	+	0.981543i	$0.561251\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$	−7.87386	−	13.6379i	−0.754179	−	1.30628i	−0.945781	−	0.324804i	$-0.894702\pi$
$109$	−7.87386	−	13.6379i	−0.754179	−	1.30628i	0.191602	−	0.981473i	$-0.438632\pi$
$110$		0			0
$111$	5.00000	+	8.66025i	0.474579	+	0.821995i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	−8.37386			−0.787747			−0.393873	−	0.919165i	$-0.628865\pi$
$113$	−8.37386			−0.787747			−0.393873	+	0.919165i	$0.628865\pi$
$114$	−0.895644	−	7.75650i	−0.0838847	−	0.726463i
$115$		0			0
$116$	−1.10436	−	1.91280i	−0.102537	−	0.177599i
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$	2.29129	−	3.96863i	0.210930	−	0.365342i
$119$	1.89564	+	3.28335i	0.173773	+	0.300984i
$120$		0			0
$121$	−10.3739			−0.943079
$122$	−12.3739			−1.12028
$123$	−2.12614	+	3.68258i	−0.191707	+	0.332047i
$124$	0.104356	−	0.180750i	0.00937145	−	0.0162318i
$125$		0			0
$126$	−0.208712			−0.0185936
$127$	−8.18693	+	14.1802i	−0.726473	+	1.25829i	0.231892	+	0.972741i	$0.425508\pi$
$127$	−8.18693	+	14.1802i	−0.726473	+	1.25829i	−0.958365	+	0.285546i	$0.907825\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.08258	+	1.87508i	−0.0953155	+	0.165091i
$130$		0			0
$131$	10.2695	+	17.7873i	0.897251	+	1.55408i	0.830994	+	0.556282i	$0.187772\pi$
$131$	10.2695	+	17.7873i	0.897251	+	1.55408i	0.0662573	+	0.997803i	$0.478894\pi$
$132$	1.41742			0.123371
$133$	3.50000	−	2.59808i	0.303488	−	0.225282i
$134$	6.41742			0.554381
$135$		0			0
$136$	−1.89564	−	3.28335i	−0.162550	−	0.281545i
$137$	10.6652	−	18.4726i	0.911185	−	1.57822i	0.0987932	−	0.995108i	$-0.468502\pi$
$137$	10.6652	−	18.4726i	0.911185	−	1.57822i	0.812392	−	0.583111i	$-0.198165\pi$
$138$	4.10436	+	7.10895i	0.349386	+	0.605154i
$139$	8.39564	−	14.5417i	0.712109	−	1.23341i	−0.251955	−	0.967739i	$-0.581073\pi$
$139$	8.39564	−	14.5417i	0.712109	−	1.23341i	0.964064	−	0.265670i	$-0.0855933\pi$
$140$		0			0
$141$	11.0436			0.930036
$142$	−2.29129	+	3.96863i	−0.192281	+	0.333040i
$143$	1.89564	−	3.28335i	0.158522	−	0.274568i
$144$	0.208712			0.0173927
$145$		0			0
$146$	0.895644	−	1.55130i	0.0741240	−	0.128387i
$147$	5.37386	+	9.30780i	0.443229	+	0.767695i
$148$	2.79129	−	4.83465i	0.229442	−	0.397406i
$149$	−2.37386	−	4.11165i	−0.194474	−	0.336840i	0.752254	−	0.658874i	$-0.228967\pi$
$149$	−2.37386	−	4.11165i	−0.194474	−	0.336840i	−0.946728	+	0.322034i	$0.895633\pi$
$150$		0			0
$151$	−11.7477			−0.956016			−0.478008	−	0.878355i	$-0.658641\pi$
$151$	−11.7477			−0.956016			−0.478008	+	0.878355i	$0.658641\pi$
$152$	−3.50000	+	2.59808i	−0.283887	+	0.210732i
$153$	0.791288			0.0639718
$154$	0.395644	+	0.685275i	0.0318819	+	0.0552211i
$155$		0			0
$156$	4.29129	−	7.43273i	0.343578	−	0.595095i
$157$	−7.47822	−	12.9527i	−0.596827	−	1.03373i	−0.993286	−	0.115682i	$-0.963095\pi$
$157$	−7.47822	−	12.9527i	−0.596827	−	1.03373i	0.396459	−	0.918052i	$-0.370239\pi$
$158$	3.97822	−	6.89048i	0.316490	−	0.548177i
$159$	8.20871			0.650993
$160$		0			0
$161$	−2.29129	+	3.96863i	−0.180579	+	0.312772i
$162$	4.79129	−	8.29875i	0.376439	−	0.652012i
$163$	−5.41742			−0.424325			−0.212163	−	0.977234i	$-0.568051\pi$
$163$	−5.41742			−0.424325			−0.212163	+	0.977234i	$0.568051\pi$
$164$	2.37386			0.185368
$165$		0			0
$166$	0.395644	+	0.685275i	0.0307079	+	0.0531877i
$167$	10.2695	−	17.7873i	0.794678	−	1.37642i	−0.128365	−	0.991727i	$-0.540973\pi$
$167$	10.2695	−	17.7873i	0.794678	−	1.37642i	0.923043	−	0.384696i	$-0.125694\pi$
$168$	0.895644	+	1.55130i	0.0691004	+	0.119685i
$169$	−4.97822	−	8.62253i	−0.382940	−	0.663271i
$170$		0			0
$171$	−0.104356	−	0.903750i	−0.00798031	−	0.0691115i
$172$	1.20871			0.0921634
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	0.920722	+	0.390218i	$0.127601\pi$
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	−0.122422	+	0.992478i	$0.539066\pi$
$174$	−1.97822	−	3.42638i	−0.149968	−	0.259753i
$175$		0			0
$176$	−0.395644	−	0.685275i	−0.0298228	−	0.0516546i
$177$	4.10436	−	7.10895i	0.308502	−	0.534342i
$178$	−4.58258			−0.343479
$179$	10.7477			0.803323			0.401661	−	0.915788i	$-0.368433\pi$
$179$	10.7477			0.803323			0.401661	+	0.915788i	$0.368433\pi$
$180$		0			0
$181$	10.6869	−	18.5103i	0.794353	−	1.37586i	−0.128896	−	0.991658i	$-0.541143\pi$
$181$	10.6869	−	18.5103i	0.794353	−	1.37586i	0.923249	−	0.384202i	$-0.125523\pi$
$182$	4.79129			0.355154
$183$	−22.1652			−1.63850
$184$	2.29129	−	3.96863i	0.168916	−	0.292571i
$185$		0			0
$186$	0.186932	−	0.323775i	0.0137065	−	0.0237404i
$187$	−1.50000	−	2.59808i	−0.109691	−	0.189990i
$188$	−3.08258	−	5.33918i	−0.224820	−	0.389400i
$189$	5.00000			0.363696
$190$		0			0
$191$	−6.95644			−0.503350			−0.251675	−	0.967812i	$-0.580981\pi$
$191$	−6.95644			−0.503350			−0.251675	+	0.967812i	$0.580981\pi$
$192$	−0.895644	−	1.55130i	−0.0646375	−	0.111955i
$193$	−12.3739	−	21.4322i	−0.890690	−	1.54272i	−0.839050	−	0.544055i	$-0.816888\pi$
$193$	−12.3739	−	21.4322i	−0.890690	−	1.54272i	−0.0516406	−	0.998666i	$-0.516445\pi$
$194$	−0.686932	+	1.18980i	−0.0493188	+	0.0854227i
$195$		0			0
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	24.7913			1.76631			0.883153	−	0.469085i	$-0.155416\pi$
$197$	24.7913			1.76631			0.883153	+	0.469085i	$0.155416\pi$
$198$	0.165151			0.0117368
$199$	2.79129	−	4.83465i	0.197869	−	0.342719i	−0.749968	−	0.661474i	$-0.769931\pi$
$199$	2.79129	−	4.83465i	0.197869	−	0.342719i	0.947837	+	0.318755i	$0.103265\pi$
$200$		0			0
$201$	11.4955			0.810827
$202$		0			0
$203$	1.10436	−	1.91280i	0.0775106	−	0.134252i
$204$	−3.39564	−	5.88143i	−0.237743	−	0.411782i
$205$		0			0
$206$	6.58258	+	11.4014i	0.458630	+	0.794370i
$207$	0.478220	+	0.828301i	0.0332386	+	0.0575709i
$208$	−4.79129			−0.332216
$209$	−2.76951	+	2.05583i	−0.191571	+	0.142204i
$210$		0			0
$211$	−0.521780	−	0.903750i	−0.0359208	−	0.0622167i	0.847506	−	0.530786i	$-0.178103\pi$
$211$	−0.521780	−	0.903750i	−0.0359208	−	0.0622167i	−0.883427	+	0.468569i	$0.844770\pi$
$212$	−2.29129	−	3.96863i	−0.157366	−	0.272566i
$213$	−4.10436	+	7.10895i	−0.281226	+	0.487097i
$214$	1.97822	+	3.42638i	0.135228	+	0.234222i
$215$		0			0
$216$	−5.00000			−0.340207
$217$	0.208712			0.0141683
$218$	−7.87386	+	13.6379i	−0.533285	+	0.923677i
$219$	1.60436	−	2.77883i	0.108412	−	0.187776i
$220$		0			0
$221$	−18.1652			−1.22192
$222$	5.00000	−	8.66025i	0.335578	−	0.581238i
$223$	−11.8956	−	20.6039i	−0.796591	−	1.37974i	−0.921824	−	0.387609i	$-0.873301\pi$
$223$	−11.8956	−	20.6039i	−0.796591	−	1.37974i	0.125233	−	0.992127i	$-0.460032\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	4.18693	+	7.25198i	0.278511	+	0.482394i
$227$	−19.7477			−1.31070			−0.655351	−	0.755324i	$-0.727479\pi$
$227$	−19.7477			−1.31070			−0.655351	+	0.755324i	$0.727479\pi$
$228$	−6.26951	+	4.65390i	−0.415208	+	0.308212i
$229$	11.3303			0.748727			0.374364	−	0.927282i	$-0.377861\pi$
$229$	11.3303			0.748727			0.374364	+	0.927282i	$0.377861\pi$
$230$		0			0
$231$	0.708712	+	1.22753i	0.0466298	+	0.0807652i
$232$	−1.10436	+	1.91280i	−0.0725045	+	0.125582i
$233$	4.58258	+	7.93725i	0.300215	+	0.519987i	0.976184	−	0.216942i	$-0.0696084\pi$
$233$	4.58258	+	7.93725i	0.300215	+	0.519987i	−0.675970	+	0.736929i	$0.736275\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$		0			0
$236$	−4.58258			−0.298300
$237$	7.12614	−	12.3428i	0.462892	−	0.801753i
$238$	1.89564	−	3.28335i	0.122876	−	0.212828i
$239$	7.41742			0.479793			0.239897	−	0.970798i	$-0.422886\pi$
$239$	7.41742			0.479793			0.239897	+	0.970798i	$0.422886\pi$
$240$		0			0
$241$	6.10436	−	10.5731i	0.393216	−	0.681070i	−0.599656	−	0.800258i	$-0.704696\pi$
$241$	6.10436	−	10.5731i	0.393216	−	0.681070i	0.992872	+	0.119188i	$0.0380291\pi$
$242$	5.18693	+	8.98403i	0.333429	+	0.577515i
$243$	1.08258	−	1.87508i	0.0694473	−	0.120286i
$244$	6.18693	+	10.7161i	0.396078	+	0.686027i
$245$		0			0
$246$	4.25227			0.271115
$247$	2.39564	+	20.7469i	0.152431	+	1.32009i
$248$	−0.208712			−0.0132532
$249$	0.708712	+	1.22753i	0.0449128	+	0.0777913i
$250$		0			0
$251$	14.0608	−	24.3540i	0.887510	−	1.53721i	0.0446995	−	0.999000i	$-0.485767\pi$
$251$	14.0608	−	24.3540i	0.887510	−	1.53721i	0.842810	−	0.538211i	$-0.180900\pi$
$252$	0.104356	+	0.180750i	0.00657381	+	0.0113862i
$253$	1.81307	−	3.14033i	0.113987	−	0.197431i
$254$	16.3739			1.02739
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.89564	−	13.6757i	0.492517	−	0.853064i	−0.507446	−	0.861683i	$-0.669410\pi$
$257$	7.89564	−	13.6757i	0.492517	−	0.853064i	0.999963	+	0.00861948i	$0.00274370\pi$
$258$	2.16515			0.134796
$259$	5.58258			0.346884
$260$		0			0
$261$	−0.230493	−	0.399225i	−0.0142671	−	0.0247114i
$262$	10.2695	−	17.7873i	0.634452	−	1.09890i
$263$	14.2913	+	24.7532i	0.881239	+	1.52635i	0.849965	+	0.526839i	$0.176623\pi$
$263$	14.2913	+	24.7532i	0.881239	+	1.52635i	0.0312735	+	0.999511i	$0.490044\pi$
$264$	−0.708712	−	1.22753i	−0.0436182	−	0.0755490i
$265$		0			0
$266$	−4.00000	−	1.73205i	−0.245256	−	0.106199i
$267$	−8.20871			−0.502365
$268$	−3.20871	−	5.55765i	−0.196003	−	0.339488i
$269$	14.0608	+	24.3540i	0.857302	+	1.48489i	0.874493	+	0.485038i	$0.161194\pi$
$269$	14.0608	+	24.3540i	0.857302	+	1.48489i	−0.0171912	+	0.999852i	$0.505472\pi$
$270$		0			0
$271$	−12.0608	−	20.8899i	−0.732641	−	1.26897i	−0.955751	−	0.294178i	$-0.904954\pi$
$271$	−12.0608	−	20.8899i	−0.732641	−	1.26897i	0.223109	−	0.974793i	$-0.428379\pi$
$272$	−1.89564	+	3.28335i	−0.114940	+	0.199082i
$273$	8.58258			0.519441
$274$	−21.3303			−1.28861
$275$		0			0
$276$	4.10436	−	7.10895i	0.247053	−	0.427909i
$277$	18.7477			1.12644			0.563221	−	0.826306i	$-0.309562\pi$
$277$	18.7477			1.12644			0.563221	+	0.826306i	$0.309562\pi$
$278$	−16.7913			−1.00707
$279$	0.0217804	−	0.0377247i	0.00130396	−	0.00225852i
$280$		0			0
$281$	−0.708712	+	1.22753i	−0.0422782	+	0.0732280i	−0.886390	−	0.462939i	$-0.846795\pi$
$281$	−0.708712	+	1.22753i	−0.0422782	+	0.0732280i	0.844112	+	0.536167i	$0.180128\pi$
$282$	−5.52178	−	9.56400i	−0.328817	−	0.569528i
$283$	10.0608	+	17.4258i	0.598052	+	1.03586i	0.993108	+	0.117200i	$0.0373918\pi$
$283$	10.0608	+	17.4258i	0.598052	+	1.03586i	−0.395056	+	0.918657i	$0.629275\pi$
$284$	4.58258			0.271926
$285$		0			0
$286$	−3.79129			−0.224184
$287$	1.18693	+	2.05583i	0.0700624	+	0.121352i
$288$	−0.104356	−	0.180750i	−0.00614924	−	0.0106508i
$289$	1.31307	−	2.27430i	0.0772393	−	0.133782i
$290$		0			0
$291$	−1.23049	+	2.13128i	−0.0721327	+	0.124938i
$292$	−1.79129			−0.104827
$293$	2.04356			0.119386			0.0596930	−	0.998217i	$-0.480988\pi$
$293$	2.04356			0.119386			0.0596930	+	0.998217i	$0.480988\pi$
$294$	5.37386	−	9.30780i	0.313410	−	0.542842i
$295$		0			0
$296$	−5.58258			−0.324481
$297$	−3.95644			−0.229576
$298$	−2.37386	+	4.11165i	−0.137514	+	0.238182i
$299$	−10.9782	−	19.0148i	−0.634887	−	1.09966i
$300$		0			0
$301$	0.604356	+	1.04678i	0.0348345	+	0.0603351i
$302$	5.87386	+	10.1738i	0.338003	+	0.585438i
$303$		0			0
$304$	4.00000	+	1.73205i	0.229416	+	0.0993399i
$305$		0			0
$306$	−0.395644	−	0.685275i	−0.0226175	−	0.0391746i
$307$	−10.2477	−	17.7496i	−0.584869	−	1.01302i	−0.994892	−	0.100947i	$-0.967813\pi$
$307$	−10.2477	−	17.7496i	−0.584869	−	1.01302i	0.410023	−	0.912075i	$-0.365521\pi$
$308$	0.395644	−	0.685275i	0.0225439	−	0.0390472i
$309$	11.7913	+	20.4231i	0.670783	+	1.16183i
$310$		0			0
$311$	−15.0000			−0.850572			−0.425286	−	0.905059i	$-0.639826\pi$
$311$	−15.0000			−0.850572			−0.425286	+	0.905059i	$0.639826\pi$
$312$	−8.58258			−0.485893
$313$	−7.87386	+	13.6379i	−0.445057	+	0.770861i	−0.998056	−	0.0623204i	$-0.980150\pi$
$313$	−7.87386	+	13.6379i	−0.445057	+	0.770861i	0.552999	+	0.833182i	$0.313483\pi$
$314$	−7.47822	+	12.9527i	−0.422020	+	0.730961i
$315$		0			0
$316$	−7.95644			−0.447585
$317$	−4.58258	+	7.93725i	−0.257383	+	0.445801i	−0.965540	−	0.260254i	$-0.916194\pi$
$317$	−4.58258	+	7.93725i	−0.257383	+	0.445801i	0.708157	+	0.706055i	$0.249527\pi$
$318$	−4.10436	−	7.10895i	−0.230161	−	0.398650i
$319$	−0.873864	+	1.51358i	−0.0489270	+	0.0847440i
$320$		0			0
$321$	3.54356	+	6.13763i	0.197782	+	0.342569i
$322$	4.58258			0.255377
$323$	15.1652	+	6.56670i	0.843812	+	0.365381i
$324$	−9.58258			−0.532365
$325$		0			0
$326$	2.70871	+	4.69163i	0.150022	+	0.259845i
$327$	−14.1044	+	24.4295i	−0.779973	+	1.35095i
$328$	−1.18693	−	2.05583i	−0.0655373	−	0.113514i
$329$	3.08258	−	5.33918i	0.169948	−	0.294358i
$330$		0			0
$331$	27.9129			1.53423			0.767115	−	0.641509i	$-0.221691\pi$
$331$	27.9129			1.53423			0.767115	+	0.641509i	$0.221691\pi$
$332$	0.395644	−	0.685275i	0.0217138	−	0.0376094i
$333$	0.582576	−	1.00905i	0.0319250	−	0.0552956i
$334$	−20.5390			−1.12384
$335$		0			0
$336$	0.895644	−	1.55130i	0.0488614	−	0.0846304i
$337$	6.66515	+	11.5444i	0.363074	+	0.628862i	0.988465	−	0.151449i	$-0.0483939\pi$
$337$	6.66515	+	11.5444i	0.363074	+	0.628862i	−0.625391	+	0.780311i	$0.715061\pi$
$338$	−4.97822	+	8.62253i	−0.270779	+	0.469004i
$339$	7.50000	+	12.9904i	0.407344	+	0.705541i
$340$		0			0
$341$	−0.165151			−0.00894345
$342$	−0.730493	+	0.542250i	−0.0395005	+	0.0293215i
$343$	13.0000			0.701934
$344$	−0.604356	−	1.04678i	−0.0325847	−	0.0564383i
$345$		0			0
$346$	10.5000	−	18.1865i	0.564483	−	0.977714i
$347$	−8.68693	−	15.0462i	−0.466339	−	0.807723i	0.532922	−	0.846164i	$-0.321094\pi$
$347$	−8.68693	−	15.0462i	−0.466339	−	0.807723i	−0.999261	+	0.0384417i	$0.987761\pi$
$348$	−1.97822	+	3.42638i	−0.106044	+	0.183673i
$349$	−14.5826			−0.780587			−0.390294	−	0.920690i	$-0.627627\pi$
$349$	−14.5826			−0.780587			−0.390294	+	0.920690i	$0.627627\pi$
$350$		0			0
$351$	−11.9782	+	20.7469i	−0.639350	+	1.10739i
$352$	−0.395644	+	0.685275i	−0.0210879	+	0.0365253i
$353$	13.7477			0.731718			0.365859	−	0.930670i	$-0.380775\pi$
$353$	13.7477			0.731718			0.365859	+	0.930670i	$0.380775\pi$
$354$	−8.20871			−0.436288
$355$		0			0
$356$	2.29129	+	3.96863i	0.121438	+	0.210337i
$357$	3.39564	−	5.88143i	0.179717	−	0.311278i
$358$	−5.37386	−	9.30780i	−0.284018	−	0.491933i
$359$	−7.35208	−	12.7342i	−0.388028	−	0.672084i	0.604156	−	0.796866i	$-0.293510\pi$
$359$	−7.35208	−	12.7342i	−0.388028	−	0.672084i	−0.992184	+	0.124782i	$0.960177\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$	−21.3739			−1.12339
$363$	9.29129	+	16.0930i	0.487666	+	0.844663i
$364$	−2.39564	−	4.14938i	−0.125566	−	0.217486i
$365$		0			0
$366$	11.0826	+	19.1956i	0.579296	+	1.00337i
$367$	−2.10436	+	3.64485i	−0.109846	+	0.190260i	−0.915708	−	0.401844i	$-0.868369\pi$
$367$	−2.10436	+	3.64485i	−0.109846	+	0.190260i	0.805861	+	0.592104i	$0.201703\pi$
$368$	−4.58258			−0.238883
$369$	0.495454			0.0257923
$370$		0			0
$371$	2.29129	−	3.96863i	0.118958	−	0.206041i
$372$	−0.373864			−0.0193839
$373$	−7.62614			−0.394866			−0.197433	−	0.980316i	$-0.563261\pi$
$373$	−7.62614			−0.394866			−0.197433	+	0.980316i	$0.563261\pi$
$374$	−1.50000	+	2.59808i	−0.0775632	+	0.134343i
$375$		0			0
$376$	−3.08258	+	5.33918i	−0.158972	+	0.275347i
$377$	5.29129	+	9.16478i	0.272515	+	0.472010i
$378$	−2.50000	−	4.33013i	−0.128586	−	0.222718i
$379$	23.1652			1.18991			0.594957	−	0.803758i	$-0.297169\pi$
$379$	23.1652			1.18991			0.594957	+	0.803758i	$0.297169\pi$
$380$		0			0
$381$	29.3303			1.50264
$382$	3.47822	+	6.02445i	0.177961	+	0.308238i
$383$	2.29129	+	3.96863i	0.117079	+	0.202787i	0.918609	−	0.395168i	$-0.129313\pi$
$383$	2.29129	+	3.96863i	0.117079	+	0.202787i	−0.801530	+	0.597955i	$0.795980\pi$
$384$	−0.895644	+	1.55130i	−0.0457056	+	0.0791645i
$385$		0			0
$386$	−12.3739	+	21.4322i	−0.629813	+	1.09087i
$387$	0.252273			0.0128238
$388$	1.37386			0.0697474
$389$	−16.1869	+	28.0366i	−0.820710	+	1.42151i	0.0844442	+	0.996428i	$0.473089\pi$
$389$	−16.1869	+	28.0366i	−0.820710	+	1.42151i	−0.905154	+	0.425083i	$0.860245\pi$
$390$		0			0
$391$	−17.3739			−0.878634
$392$	−6.00000			−0.303046
$393$	18.3956	−	31.8622i	0.927937	−	1.60723i
$394$	−12.3956	−	21.4699i	−0.624484	−	1.08164i
$395$		0			0
$396$	−0.0825757	−	0.143025i	−0.00414958	−	0.00718729i
$397$	10.2913	+	17.8250i	0.516505	+	0.894613i	0.999816	+	0.0191643i	$0.00610055\pi$
$397$	10.2913	+	17.8250i	0.516505	+	0.894613i	−0.483311	+	0.875448i	$0.660566\pi$
$398$	−5.58258			−0.279829
$399$	−7.16515	−	3.10260i	−0.358706	−	0.155324i
$400$		0			0
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	0.976050	−	0.217545i	$-0.0698049\pi$
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	−0.676425	+	0.736512i	$0.736472\pi$
$402$	−5.74773	−	9.95536i	−0.286671	−	0.496528i
$403$	−0.500000	+	0.866025i	−0.0249068	+	0.0431398i
$404$		0			0
$405$		0			0
$406$	−2.20871			−0.109617
$407$	−4.41742			−0.218964
$408$	−3.39564	+	5.88143i	−0.168109	+	0.291174i
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	−0.715523	−	0.698589i	$-0.753812\pi$
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	0.962757	+	0.270367i	$0.0871450\pi$
$410$		0			0
$411$	−38.2087			−1.88470
$412$	6.58258	−	11.4014i	0.324300	−	0.561704i
$413$	−2.29129	−	3.96863i	−0.112747	−	0.195283i
$414$	0.478220	−	0.828301i	0.0235032	−	0.0407088i
$415$		0			0
$416$	2.39564	+	4.14938i	0.117456	+	0.203440i
$417$	−30.0780			−1.47293
$418$	3.16515	+	1.37055i	0.154813	+	0.0670358i
$419$	4.74773			0.231942			0.115971	−	0.993253i	$-0.463002\pi$
$419$	4.74773			0.231942			0.115971	+	0.993253i	$0.463002\pi$
$420$		0			0
$421$	−10.0000	−	17.3205i	−0.487370	−	0.844150i	0.512524	−	0.858673i	$-0.328710\pi$
$421$	−10.0000	−	17.3205i	−0.487370	−	0.844150i	−0.999895	+	0.0145228i	$0.995377\pi$
$422$	−0.521780	+	0.903750i	−0.0253999	+	0.0439939i
$423$	−0.643371	−	1.11435i	−0.0312818	−	0.0541816i
$424$	−2.29129	+	3.96863i	−0.111275	+	0.192734i
$425$		0			0
$426$	8.20871			0.397713
$427$	−6.18693	+	10.7161i	−0.299407	+	0.518587i
$428$	1.97822	−	3.42638i	0.0956209	−	0.165620i
$429$	−6.79129			−0.327886
$430$		0			0
$431$	−6.39564	+	11.0776i	−0.308067	+	0.533588i	−0.977940	−	0.208888i	$-0.933016\pi$
$431$	−6.39564	+	11.0776i	−0.308067	+	0.533588i	0.669872	+	0.742476i	$0.266349\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	19.4564	−	33.6995i	0.935017	−	1.61950i	0.160413	−	0.987050i	$-0.448717\pi$
$433$	19.4564	−	33.6995i	0.935017	−	1.61950i	0.774604	−	0.632447i	$-0.217949\pi$
$434$	−0.104356	−	0.180750i	−0.00500925	−	0.00867628i
$435$		0			0
$436$	15.7477			0.754179
$437$	2.29129	+	19.8431i	0.109607	+	0.949226i
$438$	−3.20871			−0.153318
$439$	−5.66515	−	9.81233i	−0.270383	−	0.468317i	0.698577	−	0.715535i	$-0.253817\pi$
$439$	−5.66515	−	9.81233i	−0.270383	−	0.468317i	−0.968960	+	0.247218i	$0.920484\pi$
$440$		0			0
$441$	0.626136	−	1.08450i	0.0298160	−	0.0516429i
$442$	9.08258	+	15.7315i	0.432014	+	0.748270i
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	−0.426414	−	0.904528i	$-0.640223\pi$
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	0.996551	−	0.0829786i	$-0.0264433\pi$
$444$	−10.0000			−0.474579
$445$		0			0
$446$	−11.8956	+	20.6039i	−0.563275	+	0.975621i
$447$	−4.25227	+	7.36515i	−0.201126	+	0.348360i
$448$	−1.00000			−0.0472456
$449$	−33.3303			−1.57295			−0.786477	−	0.617619i	$-0.788097\pi$
$449$	−33.3303			−1.57295			−0.786477	+	0.617619i	$0.788097\pi$
$450$		0			0
$451$	−0.939205	−	1.62675i	−0.0442254	−	0.0766007i
$452$	4.18693	−	7.25198i	0.196937	−	0.341104i
$453$	10.5218	+	18.2243i	0.494356	+	0.856250i
$454$	9.87386	+	17.1020i	0.463403	+	0.802638i
$455$		0			0
$456$	7.16515	+	3.10260i	0.335539	+	0.145293i
$457$	6.74773			0.315645			0.157823	−	0.987467i	$-0.449553\pi$
$457$	6.74773			0.315645			0.157823	+	0.987467i	$0.449553\pi$
$458$	−5.66515	−	9.81233i	−0.264715	−	0.458500i
$459$	9.47822	+	16.4168i	0.442405	+	0.766269i
$460$		0			0
$461$	−4.10436	−	7.10895i	−0.191159	−	0.331097i	0.754476	−	0.656328i	$-0.227891\pi$
$461$	−4.10436	−	7.10895i	−0.191159	−	0.331097i	−0.945635	+	0.325231i	$0.894558\pi$
$462$	0.708712	−	1.22753i	0.0329723	−	0.0571097i
$463$	−4.95644			−0.230345			−0.115173	−	0.993345i	$-0.536742\pi$
$463$	−4.95644			−0.230345			−0.115173	+	0.993345i	$0.536742\pi$
$464$	2.20871			0.102537
$465$		0			0
$466$	4.58258	−	7.93725i	0.212284	−	0.367686i
$467$	24.3303			1.12587			0.562936	−	0.826500i	$-0.309672\pi$
$467$	24.3303			1.12587			0.562936	+	0.826500i	$0.309672\pi$
$468$	−1.00000			−0.0462250
$469$	3.20871	−	5.55765i	0.148165	−	0.256629i
$470$		0			0
$471$	−13.3956	+	23.2019i	−0.617239	+	1.06909i
$472$	2.29129	+	3.96863i	0.105465	+	0.182671i
$473$	−0.478220	−	0.828301i	−0.0219886	−	0.0380853i
$474$	−14.2523			−0.654629
$475$		0			0
$476$	−3.79129			−0.173773
$477$	−0.478220	−	0.828301i	−0.0218962	−	0.0379253i
$478$	−3.70871	−	6.42368i	−0.169633	−	0.293812i
$479$	−2.12614	+	3.68258i	−0.0971457	+	0.168261i	−0.910502	−	0.413504i	$-0.864305\pi$
$479$	−2.12614	+	3.68258i	−0.0971457	+	0.168261i	0.813356	+	0.581766i	$0.197638\pi$
$480$		0			0
$481$	−13.3739	+	23.1642i	−0.609796	+	1.05620i
$482$	−12.2087			−0.556092
$483$	8.20871			0.373509
$484$	5.18693	−	8.98403i	0.235770	−	0.408365i
$485$		0			0
$486$	−2.16515			−0.0982133
$487$	23.0000			1.04223			0.521115	−	0.853487i	$-0.325516\pi$
$487$	23.0000			1.04223			0.521115	+	0.853487i	$0.325516\pi$
$488$	6.18693	−	10.7161i	0.280069	−	0.485094i
$489$	4.85208	+	8.40405i	0.219419	+	0.380044i
$490$		0			0
$491$	20.2913	+	35.1455i	0.915733	+	1.58610i	0.805825	+	0.592154i	$0.201722\pi$
$491$	20.2913	+	35.1455i	0.915733	+	1.58610i	0.109908	+	0.993942i	$0.464944\pi$
$492$	−2.12614	−	3.68258i	−0.0958536	−	0.166023i
$493$	8.37386			0.377140
$494$	16.7695	−	12.4481i	0.754496	−	0.560068i
$495$		0			0
$496$	0.104356	+	0.180750i	0.00468573	+	0.00811592i
$497$	2.29129	+	3.96863i	0.102778	+	0.178017i
$498$	0.708712	−	1.22753i	0.0317582	−	0.0550067i
$499$	−8.66515	−	15.0085i	−0.387905	−	0.671872i	0.604262	−	0.796786i	$-0.293468\pi$
$499$	−8.66515	−	15.0085i	−0.387905	−	0.671872i	−0.992168	+	0.124914i	$0.960135\pi$
$500$		0			0
$501$	−36.7913			−1.64371
$502$	−28.1216			−1.25513
$503$	−2.29129	+	3.96863i	−0.102163	+	0.176952i	−0.912576	−	0.408908i	$-0.865910\pi$
$503$	−2.29129	+	3.96863i	−0.102163	+	0.176952i	0.810412	+	0.585860i	$0.199243\pi$
$504$	0.104356	−	0.180750i	0.00464839	−	0.00805125i
$505$		0			0
$506$	−3.62614			−0.161201
$507$	−8.91742	+	15.4454i	−0.396037	+	0.685956i
$508$	−8.18693	−	14.1802i	−0.363236	−	0.629144i
$509$	−15.7913	+	27.3513i	−0.699937	+	1.21233i	0.268551	+	0.963265i	$0.413455\pi$
$509$	−15.7913	+	27.3513i	−0.699937	+	1.21233i	−0.968488	+	0.249060i	$0.919878\pi$
$510$		0			0
$511$	−0.895644	−	1.55130i	−0.0396210	−	0.0686255i
$512$	1.00000			0.0441942
$513$	17.5000	−	12.9904i	0.772644	−	0.573539i
$514$	−15.7913			−0.696524
$515$		0			0
$516$	−1.08258	−	1.87508i	−0.0476577	−	0.0825456i
$517$	−2.43920	+	4.22483i	−0.107276	+	0.185808i
$518$	−2.79129	−	4.83465i	−0.122642	−	0.212422i
$519$	18.8085	−	32.5773i	0.825603	−	1.42999i
$520$		0			0
$521$	40.7477			1.78519			0.892595	−	0.450859i	$-0.148882\pi$
$521$	40.7477			1.78519			0.892595	+	0.450859i	$0.148882\pi$
$522$	−0.230493	+	0.399225i	−0.0100884	+	0.0174736i
$523$	−4.87386	+	8.44178i	−0.213119	+	0.369133i	−0.952689	−	0.303946i	$-0.901696\pi$
$523$	−4.87386	+	8.44178i	−0.213119	+	0.369133i	0.739570	+	0.673080i	$0.235029\pi$
$524$	−20.5390			−0.897251
$525$		0			0
$526$	14.2913	−	24.7532i	0.623130	−	1.07929i
$527$	0.395644	+	0.685275i	0.0172345	+	0.0298511i
$528$	−0.708712	+	1.22753i	−0.0308427	+	0.0534212i
$529$	1.00000	+	1.73205i	0.0434783	+	0.0753066i
$530$		0			0
$531$	−0.956439			−0.0415059
$532$	0.500000	+	4.33013i	0.0216777	+	0.187735i
$533$	−11.3739			−0.492657
$534$	4.10436	+	7.10895i	0.177613	+	0.307634i
$535$		0			0
$536$	−3.20871	+	5.55765i	−0.138595	+	0.240054i
$537$	−9.62614	−	16.6730i	−0.415398	−	0.719491i
$538$	14.0608	−	24.3540i	0.606204	−	1.04998i
$539$	−4.74773			−0.204499
$540$		0			0
$541$	−12.0608	+	20.8899i	−0.518534	+	0.898127i	0.481234	+	0.876592i	$0.340189\pi$
$541$	−12.0608	+	20.8899i	−0.518534	+	0.898127i	−0.999768	+	0.0215352i	$0.993145\pi$
$542$	−12.0608	+	20.8899i	−0.518056	+	0.897298i
$543$	−38.2867			−1.64304
$544$	3.79129			0.162550
$545$		0			0
$546$	−4.29129	−	7.43273i	−0.183650	−	0.318091i
$547$	−17.5826	+	30.4539i	−0.751777	+	1.30212i	0.195184	+	0.980767i	$0.437470\pi$
$547$	−17.5826	+	30.4539i	−0.751777	+	1.30212i	−0.946961	+	0.321349i	$0.895864\pi$
$548$	10.6652	+	18.4726i	0.455593	+	0.789110i
$549$	1.29129	+	2.23658i	0.0551108	+	0.0954547i
$550$		0			0
$551$	−1.10436	−	9.56400i	−0.0470472	−	0.407440i
$552$	−8.20871			−0.349386
$553$	−3.97822	−	6.89048i	−0.169171	−	0.293013i
$554$	−9.37386	−	16.2360i	−0.398257	−	0.689802i
$555$		0			0
$556$	8.39564	+	14.5417i	0.356055	+	0.616705i
$557$	6.47822	−	11.2206i	0.274491	−	0.475432i	−0.695516	−	0.718511i	$-0.744824\pi$
$557$	6.47822	−	11.2206i	0.274491	−	0.475432i	0.970007	+	0.243079i	$0.0781573\pi$
$558$	−0.0435608			−0.00184407
$559$	−5.79129			−0.244945
$560$		0			0
$561$	−2.68693	+	4.65390i	−0.113442	+	0.196488i
$562$	1.41742			0.0597904
$563$	−0.626136			−0.0263885			−0.0131943	−	0.999913i	$-0.504200\pi$
$563$	−0.626136			−0.0263885			−0.0131943	+	0.999913i	$0.504200\pi$
$564$	−5.52178	+	9.56400i	−0.232509	+	0.402717i
$565$		0			0
$566$	10.0608	−	17.4258i	0.422887	−	0.732461i
$567$	−4.79129	−	8.29875i	−0.201215	−	0.348515i
$568$	−2.29129	−	3.96863i	−0.0961403	−	0.166520i
$569$	−27.1652			−1.13882			−0.569411	−	0.822053i	$-0.692829\pi$
$569$	−27.1652			−1.13882			−0.569411	+	0.822053i	$0.692829\pi$
$570$		0			0
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	1.89564	+	3.28335i	0.0792609	+	0.137284i
$573$	6.23049	+	10.7915i	0.260283	+	0.450823i
$574$	1.18693	−	2.05583i	0.0495416	−	0.0858085i
$575$		0			0
$576$	−0.104356	+	0.180750i	−0.00434817	+	0.00753125i
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$	−2.62614			−0.109233
$579$	−22.1652	+	38.3912i	−0.921152	+	1.59548i
$580$		0			0
$581$	0.791288			0.0328282
$582$	2.46099			0.102011
$583$	−1.81307	+	3.14033i	−0.0750896	+	0.130059i
$584$	0.895644	+	1.55130i	0.0370620	+	0.0641933i
$585$		0			0
$586$	−1.02178	−	1.76978i	−0.0422094	−	0.0731088i
$587$	−22.7477	−	39.4002i	−0.938899	−	1.62622i	−0.767529	−	0.641014i	$-0.778514\pi$
$587$	−22.7477	−	39.4002i	−0.938899	−	1.62622i	−0.171370	−	0.985207i	$-0.554819\pi$
$588$	−10.7477			−0.443229
$589$	0.730493	−	0.542250i	0.0300994	−	0.0223430i
$590$		0			0
$591$	−22.2042	−	38.4587i	−0.913357	−	1.58198i
$592$	2.79129	+	4.83465i	0.114721	+	0.198703i
$593$	15.0826	−	26.1238i	0.619367	−	1.07278i	−0.370234	−	0.928938i	$-0.620723\pi$
$593$	15.0826	−	26.1238i	0.619367	−	1.07278i	0.989601	−	0.143837i	$-0.0459441\pi$
$594$	1.97822	+	3.42638i	0.0811673	+	0.140586i
$595$		0			0
$596$	4.74773			0.194474
$597$	−10.0000			−0.409273
$598$	−10.9782	+	19.0148i	−0.448933	+	0.777574i
$599$	−2.06080	+	3.56940i	−0.0842018	+	0.145842i	−0.905051	−	0.425303i	$-0.860167\pi$
$599$	−2.06080	+	3.56940i	−0.0842018	+	0.145842i	0.820849	+	0.571145i	$0.193501\pi$
$600$		0			0
$601$	−35.9129			−1.46492			−0.732458	−	0.680812i	$-0.761627\pi$
$601$	−35.9129			−1.46492			−0.732458	+	0.680812i	$0.761627\pi$
$602$	0.604356	−	1.04678i	0.0246317	−	0.0426634i
$603$	−0.669697	−	1.15995i	−0.0272722	−	0.0472368i
$604$	5.87386	−	10.1738i	0.239004	−	0.413967i
$605$		0			0
$606$		0			0
$607$	−22.7913			−0.925070			−0.462535	−	0.886601i	$-0.653060\pi$
$607$	−22.7913			−0.925070			−0.462535	+	0.886601i	$0.653060\pi$
$608$	−0.500000	−	4.33013i	−0.0202777	−	0.175610i
$609$	−3.95644			−0.160323
$610$		0			0
$611$	14.7695	+	25.5815i	0.597510	+	1.03492i
$612$	−0.395644	+	0.685275i	−0.0159930	+	0.0277006i
$613$	20.2477	+	35.0701i	0.817798	+	1.41647i	0.907301	+	0.420481i	$0.138139\pi$
$613$	20.2477	+	35.0701i	0.817798	+	1.41647i	−0.0895033	+	0.995987i	$0.528528\pi$
$614$	−10.2477	+	17.7496i	−0.413565	+	0.716315i
$615$		0			0
$616$	−0.791288			−0.0318819
$617$	16.5000	−	28.5788i	0.664265	−	1.15054i	−0.315219	−	0.949019i	$-0.602078\pi$
$617$	16.5000	−	28.5788i	0.664265	−	1.15054i	0.979484	−	0.201522i	$-0.0645887\pi$
$618$	11.7913	−	20.4231i	0.474315	−	0.821538i
$619$	−10.6261			−0.427100			−0.213550	−	0.976932i	$-0.568503\pi$
$619$	−10.6261			−0.427100			−0.213550	+	0.976932i	$0.568503\pi$
$620$		0			0
$621$	−11.4564	+	19.8431i	−0.459731	+	0.796278i
$622$	7.50000	+	12.9904i	0.300723	+	0.520867i
$623$	−2.29129	+	3.96863i	−0.0917985	+	0.159000i
$624$	4.29129	+	7.43273i	0.171789	+	0.297547i
$625$		0			0
$626$	15.7477			0.629406
$627$	5.66970	+	2.45505i	0.226426	+	0.0980453i
$628$	14.9564			0.596827
$629$	10.5826	+	18.3296i	0.421955	+	0.730847i
$630$		0			0
$631$	20.3956	−	35.3263i	0.811938	−	1.40632i	−0.0995683	−	0.995031i	$-0.531746\pi$
$631$	20.3956	−	35.3263i	0.811938	−	1.40632i	0.911506	−	0.411287i	$-0.134921\pi$
$632$	3.97822	+	6.89048i	0.158245	+	0.274089i
$633$	−0.934659	+	1.61888i	−0.0371494	+	0.0643446i
$634$	9.16515			0.363995
$635$		0			0
$636$	−4.10436	+	7.10895i	−0.162748	+	0.281888i
$637$	−14.3739	+	24.8963i	−0.569513	+	0.986426i
$638$	1.74773			0.0691932
$639$	0.956439			0.0378362
$640$		0			0
$641$	−19.9782	−	34.6033i	−0.789092	−	1.36675i	−0.926524	−	0.376237i	$-0.877218\pi$
$641$	−19.9782	−	34.6033i	−0.789092	−	1.36675i	0.137431	−	0.990511i	$-0.456115\pi$
$642$	3.54356	−	6.13763i	0.139853	−	0.242233i
$643$	12.7477	+	22.0797i	0.502721	+	0.870739i	0.999995	+	0.00314512i	$0.00100112\pi$
$643$	12.7477	+	22.0797i	0.502721	+	0.870739i	−0.497274	+	0.867594i	$0.665666\pi$
$644$	−2.29129	−	3.96863i	−0.0902894	−	0.156386i
$645$		0			0
$646$	−1.89564	−	16.4168i	−0.0745831	−	0.645909i
$647$	14.2087			0.558602			0.279301	−	0.960204i	$-0.409897\pi$
$647$	14.2087			0.558602			0.279301	+	0.960204i	$0.409897\pi$
$648$	4.79129	+	8.29875i	0.188220	+	0.326006i
$649$	1.81307	+	3.14033i	0.0711692	+	0.123269i
$650$		0			0
$651$	−0.186932	−	0.323775i	−0.00732643	−	0.0126898i
$652$	2.70871	−	4.69163i	0.106081	−	0.183738i
$653$	9.33030			0.365123			0.182561	−	0.983194i	$-0.441561\pi$
$653$	9.33030			0.365123			0.182561	+	0.983194i	$0.441561\pi$
$654$	28.2087			1.10305
$655$		0			0
$656$	−1.18693	+	2.05583i	−0.0463419	+	0.0802665i
$657$	−0.373864			−0.0145858
$658$	−6.16515			−0.240343
$659$	12.8739	−	22.2982i	0.501495	−	0.868614i	−0.498504	−	0.866887i	$-0.666117\pi$
$659$	12.8739	−	22.2982i	0.501495	−	0.868614i	0.999999	−	0.00172659i	$-0.000549590\pi$
$660$		0			0
$661$	10.9347	−	18.9394i	0.425309	−	0.736657i	−0.571140	−	0.820852i	$-0.693499\pi$
$661$	10.9347	−	18.9394i	0.425309	−	0.736657i	0.996449	+	0.0841958i	$0.0268321\pi$
$662$	−13.9564	−	24.1733i	−0.542432	−	0.939521i
$663$	16.2695	+	28.1796i	0.631855	+	1.09441i
$664$	−0.791288			−0.0307079
$665$		0			0
$666$	−1.16515			−0.0451487
$667$	5.06080	+	8.76555i	0.195955	+	0.339404i
$668$	10.2695	+	17.7873i	0.397339	+	0.688212i
$669$	−21.3085	+	36.9074i	−0.823835	+	1.42692i
$670$		0			0
$671$	4.89564	−	8.47950i	0.188994	−	0.327348i
$672$	−1.79129			−0.0691004
$673$	−1.79129			−0.0690491			−0.0345245	−	0.999404i	$-0.510992\pi$
$673$	−1.79129			−0.0690491			−0.0345245	+	0.999404i	$0.510992\pi$
$674$	6.66515	−	11.5444i	0.256732	−	0.444673i
$675$		0			0
$676$	9.95644			0.382940
$677$	47.2432			1.81570			0.907851	−	0.419292i	$-0.137722\pi$
$677$	47.2432			1.81570			0.907851	+	0.419292i	$0.137722\pi$
$678$	7.50000	−	12.9904i	0.288036	−	0.498893i
$679$	0.686932	+	1.18980i	0.0263620	+	0.0456604i
$680$		0			0
$681$	17.6869	+	30.6347i	0.677765	+	1.17392i
$682$	0.0825757	+	0.143025i	0.00316199	+	0.00547672i
$683$	−17.8348			−0.682432			−0.341216	−	0.939985i	$-0.610839\pi$
$683$	−17.8348			−0.682432			−0.341216	+	0.939985i	$0.610839\pi$
$684$	0.834849	+	0.361500i	0.0319212	+	0.0138223i
$685$		0			0
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	−10.1479	−	17.5767i	−0.387167	−	0.670593i
$688$	−0.604356	+	1.04678i	−0.0230409	+	0.0399079i
$689$	10.9782	+	19.0148i	0.418237	+	0.724407i
$690$		0			0
$691$	9.12159			0.347002			0.173501	−	0.984834i	$-0.444492\pi$
$691$	9.12159			0.347002			0.173501	+	0.984834i	$0.444492\pi$
$692$	−21.0000			−0.798300
$693$	0.0825757	−	0.143025i	0.00313679	−	0.00543308i
$694$	−8.68693	+	15.0462i	−0.329751	+	0.571146i
$695$		0			0
$696$	3.95644			0.149968
$697$	−4.50000	+	7.79423i	−0.170450	+	0.295227i
$698$	7.29129	+	12.6289i	0.275979	+	0.478010i
$699$	8.20871	−	14.2179i	0.310482	−	0.537771i
$700$		0			0
$701$	−4.97822	−	8.62253i	−0.188025	−	0.325668i	0.756567	−	0.653916i	$-0.226875\pi$
$701$	−4.97822	−	8.62253i	−0.188025	−	0.325668i	−0.944592	+	0.328248i	$0.893542\pi$
$702$	23.9564			0.904178
$703$	19.5390	−	14.5040i	0.736928	−	0.547027i
$704$	0.791288			0.0298228
$705$		0			0
$706$	−6.87386	−	11.9059i	−0.258701	−	0.448084i
$707$		0			0
$708$	4.10436	+	7.10895i	0.154251	+	0.267171i
$709$	−0.373864	+	0.647551i	−0.0140407	+	0.0243193i	−0.872960	−	0.487791i	$-0.837803\pi$
$709$	−0.373864	+	0.647551i	−0.0140407	+	0.0243193i	0.858920	+	0.512110i	$0.171136\pi$
$710$		0			0
$711$	−1.66061			−0.0622776
$712$	2.29129	−	3.96863i	0.0858696	−	0.148731i
$713$	−0.478220	+	0.828301i	−0.0179095	+	0.0310201i
$714$	−6.79129			−0.254158
$715$		0			0
$716$	−5.37386	+	9.30780i	−0.200831	+	0.347849i
$717$	−6.64337	−	11.5067i	−0.248101	−	0.429724i
$718$	−7.35208	+	12.7342i	−0.274377	+	0.475235i
$719$	−3.08258	−	5.33918i	−0.114961	−	0.199118i	0.802803	−	0.596244i	$-0.203341\pi$
$719$	−3.08258	−	5.33918i	−0.114961	−	0.199118i	−0.917764	+	0.397126i	$0.870008\pi$
$720$		0			0
$721$	13.1652			0.490296
$722$	−18.5000	+	4.33013i	−0.688499	+	0.161151i
$723$	−21.8693			−0.813329
$724$	10.6869	+	18.5103i	0.397177	+	0.687930i
$725$		0			0
$726$	9.29129	−	16.0930i	0.344832	−	0.597267i
$727$	−7.08258	−	12.2674i	−0.262678	−	0.454972i	0.704275	−	0.709928i	$-0.251272\pi$
$727$	−7.08258	−	12.2674i	−0.262678	−	0.454972i	−0.966953	+	0.254956i	$0.917939\pi$
$728$	−2.39564	+	4.14938i	−0.0887885	+	0.153786i
$729$	24.8693			0.921086
$730$		0			0
$731$	−2.29129	+	3.96863i	−0.0847463	+	0.146785i
$732$	11.0826	−	19.1956i	0.409624	−	0.709489i
$733$	−14.7477			−0.544720			−0.272360	−	0.962195i	$-0.587804\pi$
$733$	−14.7477			−0.544720			−0.272360	+	0.962195i	$0.587804\pi$
$734$	4.20871			0.155346
$735$		0			0
$736$	2.29129	+	3.96863i	0.0844580	+	0.146286i
$737$	−2.53901	+	4.39770i	−0.0935258	+	0.161991i
$738$	−0.247727	−	0.429076i	−0.00911896	−	0.0157945i
$739$	4.12614	+	7.14668i	0.151782	+	0.262895i	0.931883	−	0.362760i	$-0.118165\pi$
$739$	4.12614	+	7.14668i	0.151782	+	0.262895i	−0.780100	+	0.625654i	$0.784832\pi$
$740$		0			0
$741$	30.0390	−	22.2982i	1.10351	−	0.819144i
$742$	−4.58258			−0.168232
$743$	−14.2913	−	24.7532i	−0.524297	−	0.908108i	−0.999600	−	0.0282862i	$-0.990995\pi$
$743$	−14.2913	−	24.7532i	−0.524297	−	0.908108i	0.475303	−	0.879822i	$-0.342338\pi$
$744$	0.186932	+	0.323775i	0.00685325	+	0.0118702i
$745$		0			0
$746$	3.81307	+	6.60443i	0.139606	+	0.241805i
$747$	0.0825757	−	0.143025i	0.00302129	−	0.00523302i
$748$	3.00000			0.109691
$749$	3.95644			0.144565
$750$		0			0
$751$	−6.20871	+	10.7538i	−0.226559	+	0.392412i	−0.956786	−	0.290793i	$-0.906081\pi$
$751$	−6.20871	+	10.7538i	−0.226559	+	0.392412i	0.730227	+	0.683205i	$0.239414\pi$
$752$	6.16515			0.224820
$753$	−50.3739			−1.83573
$754$	5.29129	−	9.16478i	0.192697	−	0.333762i
$755$		0			0
$756$	−2.50000	+	4.33013i	−0.0909241	+	0.157485i
$757$	−9.12614	−	15.8069i	−0.331695	−	0.574513i	0.651149	−	0.758950i	$-0.274287\pi$
$757$	−9.12614	−	15.8069i	−0.331695	−	0.574513i	−0.982844	+	0.184437i	$0.940954\pi$
$758$	−11.5826	−	20.0616i	−0.420698	−	0.728670i
$759$	−6.49545			−0.235770
$760$		0			0
$761$	52.7477			1.91210			0.956052	−	0.293198i	$-0.0947194\pi$
$761$	52.7477			1.91210			0.956052	+	0.293198i	$0.0947194\pi$
$762$	−14.6652	−	25.4008i	−0.531262	−	0.920173i
$763$	7.87386	+	13.6379i	0.285053	+	0.493726i
$764$	3.47822	−	6.02445i	0.125838	−	0.217957i
$765$		0			0
$766$	2.29129	−	3.96863i	0.0827876	−	0.143392i
$767$	21.9564			0.792801
$768$	1.79129			0.0646375
$769$	−7.16515	+	12.4104i	−0.258382	+	0.447531i	−0.965809	−	0.259256i	$-0.916523\pi$
$769$	−7.16515	+	12.4104i	−0.258382	+	0.447531i	0.707427	+	0.706787i	$0.249856\pi$
$770$		0			0
$771$	−28.2867			−1.01872
$772$	24.7477			0.890690
$773$	−7.66515	+	13.2764i	−0.275696	+	0.477520i	−0.970311	−	0.241862i	$-0.922242\pi$
$773$	−7.66515	+	13.2764i	−0.275696	+	0.477520i	0.694614	+	0.719382i	$0.255575\pi$
$774$	−0.126136	−	0.218475i	−0.00453388	−	0.00785291i
$775$		0			0
$776$	−0.686932	−	1.18980i	−0.0246594	−	0.0427114i
$777$	−5.00000	−	8.66025i	−0.179374	−	0.310685i
$778$	32.3739			1.16066
$779$	9.49545	+	4.11165i	0.340210	+	0.147315i
$780$		0			0
$781$	−1.81307	−	3.14033i	−0.0648767	−	0.112370i
$782$	8.68693	+	15.0462i	0.310644	+	0.538051i
$783$	5.52178	−	9.56400i	0.197332	−	0.341790i
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$		0			0
$786$	−36.7913			−1.31230
$787$	3.74773			0.133592			0.0667960	−	0.997767i	$-0.478722\pi$
$787$	3.74773			0.133592			0.0667960	+	0.997767i	$0.478722\pi$
$788$	−12.3956	+	21.4699i	−0.441577	+	0.764833i
$789$	25.5998	−	44.3402i	0.911377	−	1.57855i
$790$		0			0
$791$	8.37386			0.297740
$792$	−0.0825757	+	0.143025i	−0.00293420	+	0.00508218i
$793$	−29.6434	−	51.3438i	−1.05267	−	1.82327i
$794$	10.2913	−	17.8250i	0.365224	−	0.632587i
$795$		0			0
$796$	2.79129	+	4.83465i	0.0989346	+	0.171360i
$797$	−6.46099			−0.228860			−0.114430	−	0.993431i	$-0.536504\pi$
$797$	−6.46099			−0.228860			−0.114430	+	0.993431i	$0.536504\pi$
$798$	0.895644	+	7.75650i	0.0317055	+	0.274577i
$799$	23.3739			0.826908
$800$		0			0
$801$	0.478220	+	0.828301i	0.0168971	+	0.0292666i
$802$	6.00000	−	10.3923i	0.211867	−	0.366965i
$803$	0.708712	+	1.22753i	0.0250099	+	0.0433184i
$804$	−5.74773	+	9.95536i	−0.202707	+	0.351098i
$805$		0			0
$806$	1.00000			0.0352235
$807$	25.1869	−	43.6250i	0.886622	−	1.53567i
$808$		0			0
$809$	29.5390			1.03854			0.519268	−	0.854611i	$-0.326205\pi$
$809$	29.5390			1.03854			0.519268	+	0.854611i	$0.326205\pi$
$810$		0			0
$811$	21.4347	−	37.1259i	0.752673	−	1.30367i	−0.193850	−	0.981031i	$-0.562098\pi$
$811$	21.4347	−	37.1259i	0.752673	−	1.30367i	0.946523	−	0.322636i	$-0.104569\pi$
$812$	1.10436	+	1.91280i	0.0387553	+	0.0671261i
$813$	−21.6044	+	37.4198i	−0.757698	+	1.31237i
$814$	2.20871	+	3.82560i	0.0774153	+	0.134087i
$815$		0			0
$816$	6.79129			0.237743
$817$	4.83485	+	2.09355i	0.169150	+	0.0732441i
$818$	−10.0000			−0.349642
$819$	−0.500000	−	0.866025i	−0.0174714	−	0.0302614i
$820$		0			0
$821$	−0.165151	+	0.286051i	−0.00576382	+	0.00998323i	−0.868893	−	0.495000i	$-0.835168\pi$
$821$	−0.165151	+	0.286051i	−0.00576382	+	0.00998323i	0.863129	+	0.504983i	$0.168501\pi$
$822$	19.1044	+	33.0897i	0.666341	+	1.15414i
$823$	−4.62614	+	8.01270i	−0.161257	+	0.279305i	−0.935320	−	0.353804i	$-0.884888\pi$
$823$	−4.62614	+	8.01270i	−0.161257	+	0.279305i	0.774063	+	0.633109i	$0.218221\pi$
$824$	−13.1652			−0.458630
$825$		0			0
$826$	−2.29129	+	3.96863i	−0.0797241	+	0.138086i
$827$	−8.45644	+	14.6470i	−0.294059	+	0.509325i	−0.974766	−	0.223231i	$-0.928340\pi$
$827$	−8.45644	+	14.6470i	−0.294059	+	0.509325i	0.680706	+	0.732556i	$0.261673\pi$
$828$	−0.956439			−0.0332386
$829$	−0.539015			−0.0187208			−0.00936038	−	0.999956i	$-0.502980\pi$
$829$	−0.539015			−0.0187208			−0.00936038	+	0.999956i	$0.502980\pi$
$830$		0			0
$831$	−16.7913	−	29.0834i	−0.582483	−	1.00889i
$832$	2.39564	−	4.14938i	0.0830540	−	0.143854i
$833$	11.3739	+	19.7001i	0.394081	+	0.682568i
$834$	15.0390	+	26.0483i	0.520758	+	0.901980i
$835$		0			0
$836$	−0.395644	−	3.42638i	−0.0136836	−	0.118504i
$837$	1.04356			0.0360707
$838$	−2.37386	−	4.11165i	−0.0820038	−	0.142035i
$839$	−14.5218	−	25.1525i	−0.501348	−	0.868359i	−0.999999	−	0.00155670i	$-0.999504\pi$
$839$	−14.5218	−	25.1525i	−0.501348	−	0.868359i	0.498651	−	0.866803i	$-0.333829\pi$
$840$		0			0
$841$	12.0608	+	20.8899i	0.415889	+	0.720342i
$842$	−10.0000	+	17.3205i	−0.344623	+	0.596904i
$843$	2.53901			0.0874483
$844$	1.04356			0.0359208
$845$		0			0
$846$	−0.643371	+	1.11435i	−0.0221196	+	0.0383122i
$847$	10.3739			0.356450
$848$	4.58258			0.157366
$849$	18.0218	−	31.2146i	0.618506	−	1.07128i
$850$		0			0
$851$	−12.7913	+	22.1552i	−0.438480	+	0.759469i
$852$	−4.10436	−	7.10895i	−0.140613	−	0.243549i
$853$	−17.5172	−	30.3407i	−0.599779	−	1.03885i	−0.992853	−	0.119341i	$-0.961922\pi$
$853$	−17.5172	−	30.3407i	−0.599779	−	1.03885i	0.393075	−	0.919507i	$-0.371411\pi$
$854$	12.3739			0.423425
$855$		0			0
$856$	−3.95644			−0.135228
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	0.839268	−	0.543718i	$-0.182984\pi$
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	−0.890507	+	0.454969i	$0.849650\pi$
$858$	3.39564	+	5.88143i	0.115925	+	0.200789i
$859$	16.8521	−	29.1887i	0.574986	−	0.995904i	−0.421058	−	0.907034i	$-0.638341\pi$
$859$	16.8521	−	29.1887i	0.574986	−	0.995904i	0.996043	−	0.0888704i	$-0.0283257\pi$
$860$		0			0
$861$	2.12614	−	3.68258i	0.0724585	−	0.125502i
$862$	12.7913			0.435673
$863$	−13.5826			−0.462356			−0.231178	−	0.972911i	$-0.574258\pi$
$863$	−13.5826			−0.462356			−0.231178	+	0.972911i	$0.574258\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$		0			0
$866$	−38.9129			−1.32231
$867$	−4.70417			−0.159762
$868$	−0.104356	+	0.180750i	−0.00354208	+	0.00613506i
$869$	3.14792	+	5.45235i	0.106786	+	0.184958i
$870$		0			0
$871$	15.3739	+	26.6283i	0.520923	+	0.902266i
$872$	−7.87386	−	13.6379i	−0.266643	−	0.461839i
$873$	0.286742			0.00970475
$874$	16.0390	−	11.9059i	0.542528	−	0.402722i
$875$		0			0
$876$	1.60436	+	2.77883i	0.0542062	+	0.0938878i
$877$	14.2477	+	24.6778i	0.481112	+	0.833310i	0.999765	−	0.0216749i	$-0.00689986\pi$
$877$	14.2477	+	24.6778i	0.481112	+	0.833310i	−0.518654	+	0.854985i	$0.673567\pi$
$878$	−5.66515	+	9.81233i	−0.191190	+	0.331150i
$879$	−1.83030	−	3.17018i	−0.0617346	−	0.106927i
$880$		0			0
$881$	3.79129			0.127732			0.0638659	−	0.997958i	$-0.479657\pi$
$881$	3.79129			0.127732			0.0638659	+	0.997958i	$0.479657\pi$
$882$	−1.25227			−0.0421662
$883$	1.37386	−	2.37960i	0.0462342	−	0.0800800i	−0.841982	−	0.539505i	$-0.818611\pi$
$883$	1.37386	−	2.37960i	0.0462342	−	0.0800800i	0.888216	+	0.459425i	$0.151945\pi$
$884$	9.08258	−	15.7315i	0.305480	−	0.529107i
$885$		0			0
$886$	−24.0000			−0.806296
$887$	−3.56080	+	6.16748i	−0.119560	+	0.207084i	−0.919593	−	0.392872i	$-0.871482\pi$
$887$	−3.56080	+	6.16748i	−0.119560	+	0.207084i	0.800034	+	0.599955i	$0.204815\pi$
$888$	5.00000	+	8.66025i	0.167789	+	0.290619i
$889$	8.18693	−	14.1802i	0.274581	−	0.475588i
$890$		0			0
$891$	3.79129	+	6.56670i	0.127013	+	0.219993i
$892$	23.7913			0.796591
$893$	−3.08258	−	26.6959i	−0.103154	−	0.893344i
$894$	8.50455			0.284435
$895$		0			0
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$	−19.6652	+	34.0610i	−0.656600	+	1.13727i
$898$	16.6652	+	28.8649i	0.556123	+	0.963234i
$899$	0.230493	−	0.399225i	0.00768736	−	0.0133149i
$900$		0			0
$901$	17.3739			0.578807
$902$	−0.939205	+	1.62675i	−0.0312721	+	0.0541649i
$903$	1.08258	−	1.87508i	0.0360259	−	0.0623986i
$904$	−8.37386			−0.278511
$905$		0			0
$906$	10.5218	−	18.2243i	0.349563	−	0.605460i
$907$	−17.4347	−	30.1977i	−0.578908	−	1.00270i	−0.995605	−	0.0936530i	$-0.970146\pi$
$907$	−17.4347	−	30.1977i	−0.578908	−	1.00270i	0.416697	−	0.909046i	$-0.363188\pi$
$908$	9.87386	−	17.1020i	0.327676	−	0.567551i
$909$		0			0
$910$		0			0
$911$	24.6606			0.817042			0.408521	−	0.912749i	$-0.366045\pi$
$911$	24.6606			0.817042			0.408521	+	0.912749i	$0.366045\pi$
$912$	−0.895644	−	7.75650i	−0.0296577	−	0.256844i
$913$	−0.626136			−0.0207221
$914$	−3.37386	−	5.84370i	−0.111597	−	0.193293i
$915$		0			0
$916$	−5.66515	+	9.81233i	−0.187182	+	0.324209i
$917$	−10.2695	−	17.7873i	−0.339129	−	0.587389i
$918$	9.47822	−	16.4168i	0.312828	−	0.541834i
$919$	−42.2087			−1.39234			−0.696168	−	0.717878i	$-0.745113\pi$
$919$	−42.2087			−1.39234			−0.696168	+	0.717878i	$0.745113\pi$
$920$		0			0
$921$	−18.3566	+	31.7946i	−0.604871	+	1.04767i
$922$	−4.10436	+	7.10895i	−0.135170	+	0.234121i
$923$	−21.9564			−0.722705
$924$	−1.41742			−0.0466298
$925$		0			0
$926$	2.47822	+	4.29240i	0.0814393	+	0.141057i
$927$	1.37386	−	2.37960i	0.0451236	−	0.0781564i
$928$	−1.10436	−	1.91280i	−0.0362523	−	0.0627908i
$929$	−26.0608	−	45.1386i	−0.855027	−	1.48095i	−0.876620	−	0.481183i	$-0.840207\pi$
$929$	−26.0608	−	45.1386i	−0.855027	−	1.48095i	0.0215930	−	0.999767i	$-0.493126\pi$
$930$		0			0
$931$	21.0000	−	15.5885i	0.688247	−	0.510891i
$932$	−9.16515			−0.300215
$933$	13.4347	+	23.2695i	0.439831	+	0.761810i
$934$	−12.1652	−	21.0707i	−0.398056	−	0.689453i
$935$		0			0
$936$	0.500000	+	0.866025i	0.0163430	+	0.0283069i
$937$	17.5608	−	30.4162i	0.573686	−	0.993654i	−0.422497	−	0.906364i	$-0.638846\pi$
$937$	17.5608	−	30.4162i	0.573686	−	0.993654i	0.996183	−	0.0872892i	$-0.0278204\pi$
$938$	−6.41742			−0.209536
$939$	28.2087			0.920557
$940$		0			0
$941$	15.7087	−	27.2083i	0.512089	−	0.886965i	−0.487812	−	0.872948i	$-0.662205\pi$
$941$	15.7087	−	27.2083i	0.512089	−	0.886965i	0.999902	−	0.0140163i	$-0.00446168\pi$
$942$	26.7913			0.872907
$943$	−10.8784			−0.354250
$944$	2.29129	−	3.96863i	0.0745751	−	0.129168i
$945$		0			0
$946$	−0.478220	+	0.828301i	−0.0155483	+	0.0269304i
$947$	9.70871	+	16.8160i	0.315491	+	0.546446i	0.979542	−	0.201241i	$-0.0644975\pi$
$947$	9.70871	+	16.8160i	0.315491	+	0.546446i	−0.664051	+	0.747687i	$0.731164\pi$
$948$	7.12614	+	12.3428i	0.231446	+	0.400876i
$949$	8.58258			0.278602
$950$		0			0
$951$	16.4174			0.532371
$952$	1.89564	+	3.28335i	0.0614382	+	0.106414i
$953$	−12.5608	−	21.7559i	−0.406884	−	0.704744i	0.587655	−	0.809112i	$-0.300051\pi$
$953$	−12.5608	−	21.7559i	−0.406884	−	0.704744i	−0.994539	+	0.104368i	$0.966718\pi$
$954$	−0.478220	+	0.828301i	−0.0154829	+	0.0268172i
$955$		0			0
$956$	−3.70871	+	6.42368i	−0.119948	+	0.207757i
$957$	3.13068			0.101201
$958$	4.25227			0.137385
$959$	−10.6652	+	18.4726i	−0.344396	+	0.596511i
$960$		0			0
$961$	−30.9564			−0.998595
$962$	26.7477			0.862381
$963$	0.412878	−	0.715126i	0.0133048	−	0.0230446i
$964$	6.10436	+	10.5731i	0.196608	+	0.340535i
$965$		0			0
$966$	−4.10436	−	7.10895i	−0.132055	−	0.228727i
$967$	−6.53901	−	11.3259i	−0.210281	−	0.364217i	0.741522	−	0.670929i	$-0.234104\pi$
$967$	−6.53901	−	11.3259i	−0.210281	−	0.364217i	−0.951802	+	0.306712i	$0.900771\pi$
$968$	−10.3739			−0.333429
$969$	−3.39564	−	29.4071i	−0.109084	−	0.944693i
$970$		0			0
$971$	23.4564	+	40.6277i	0.752753	+	1.30381i	0.946484	+	0.322752i	$0.104608\pi$
$971$	23.4564	+	40.6277i	0.752753	+	1.30381i	−0.193731	+	0.981055i	$0.562059\pi$
$972$	1.08258	+	1.87508i	0.0347236	+	0.0601431i
$973$	−8.39564	+	14.5417i	−0.269152	+	0.466185i
$974$	−11.5000	−	19.9186i	−0.368484	−	0.638233i
$975$		0			0
$976$	−12.3739			−0.396078
$977$	18.6261			0.595903			0.297951	−	0.954581i	$-0.403697\pi$
$977$	18.6261			0.595903			0.297951	+	0.954581i	$0.403697\pi$
$978$	4.85208	−	8.40405i	0.155153	−	0.268732i
$979$	1.81307	−	3.14033i	0.0579459	−	0.100365i
$980$		0			0
$981$	3.28674			0.104938
$982$	20.2913	−	35.1455i	0.647521	−	1.12154i
$983$	−20.2087	−	35.0025i	−0.644558	−	1.11641i	−0.984403	−	0.175926i	$-0.943708\pi$
$983$	−20.2087	−	35.0025i	−0.644558	−	1.11641i	0.339846	−	0.940481i	$-0.389625\pi$
$984$	−2.12614	+	3.68258i	−0.0677788	+	0.117396i
$985$		0			0
$986$	−4.18693	−	7.25198i	−0.133339	−	0.230950i
$987$	−11.0436			−0.351520
$988$	−19.1652	−	8.29875i	−0.609725	−	0.264019i
$989$	−5.53901			−0.176130
$990$		0			0
$991$	8.56080	+	14.8277i	0.271943	+	0.471018i	0.969359	−	0.245648i	$-0.0790006\pi$
$991$	8.56080	+	14.8277i	0.271943	+	0.471018i	−0.697417	+	0.716666i	$0.745667\pi$
$992$	0.104356	−	0.180750i	0.00331331	−	0.00573882i
$993$	−25.0000	−	43.3013i	−0.793351	−	1.37412i
$994$	2.29129	−	3.96863i	0.0726752	−	0.125877i
$995$		0			0
$996$	−1.41742			−0.0449128
$997$	0.500000	−	0.866025i	0.0158352	−	0.0274273i	−0.857999	−	0.513651i	$-0.828293\pi$
$997$	0.500000	−	0.866025i	0.0158352	−	0.0274273i	0.873834	+	0.486224i	$0.161626\pi$
$998$	−8.66515	+	15.0085i	−0.274291	+	0.475085i
$999$	27.9129			0.883124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.i.501.1	yes	4
5.2	odd	4		950.2.j.h.349.3		8
5.3	odd	4		950.2.j.h.349.2		8
5.4	even	2		950.2.e.j.501.2	yes	4
19.11	even	3	inner	950.2.e.i.201.1	✓	4
95.49	even	6		950.2.e.j.201.2	yes	4
95.68	odd	12		950.2.j.h.49.3		8
95.87	odd	12		950.2.j.h.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.i.201.1	✓	4	19.11	even	3	inner
950.2.e.i.501.1	yes	4	1.1	even	1	trivial
950.2.e.j.201.2	yes	4	95.49	even	6
950.2.e.j.501.2	yes	4	5.4	even	2
950.2.j.h.49.2		8	95.87	odd	12
950.2.j.h.49.3		8	95.68	odd	12
950.2.j.h.349.2		8	5.3	odd	4
950.2.j.h.349.3		8	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.895644 - 1.55130i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.895644 + 1.55130i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.104356 + 0.180750i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.895644 - 1.55130i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.895644 + 1.55130i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.104356 + 0.180750i) q^{9} +0.791288 q^{11} +1.79129 q^{12} +(2.39564 - 4.14938i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.89564 - 3.28335i) q^{17} +0.208712 q^{18} +(-3.50000 + 2.59808i) q^{19} +(0.895644 + 1.55130i) q^{21} +(-0.395644 - 0.685275i) q^{22} +(2.29129 - 3.96863i) q^{23} +(-0.895644 - 1.55130i) q^{24} -4.79129 q^{26} -5.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-1.10436 + 1.91280i) q^{29} -0.208712 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.708712 - 1.22753i) q^{33} +(-1.89564 + 3.28335i) q^{34} +(-0.104356 - 0.180750i) q^{36} -5.58258 q^{37} +(4.00000 + 1.73205i) q^{38} -8.58258 q^{39} +(-1.18693 - 2.05583i) q^{41} +(0.895644 - 1.55130i) q^{42} +(-0.604356 - 1.04678i) q^{43} +(-0.395644 + 0.685275i) q^{44} -4.58258 q^{46} +(-3.08258 + 5.33918i) q^{47} +(-0.895644 + 1.55130i) q^{48} -6.00000 q^{49} +(-3.39564 + 5.88143i) q^{51} +(2.39564 + 4.14938i) q^{52} +(-2.29129 + 3.96863i) q^{53} +(2.50000 + 4.33013i) q^{54} -1.00000 q^{56} +(7.16515 + 3.10260i) q^{57} +2.20871 q^{58} +(2.29129 + 3.96863i) q^{59} +(6.18693 - 10.7161i) q^{61} +(0.104356 + 0.180750i) q^{62} +(0.104356 - 0.180750i) q^{63} +1.00000 q^{64} +(-0.708712 + 1.22753i) q^{66} +(-3.20871 + 5.55765i) q^{67} +3.79129 q^{68} -8.20871 q^{69} +(-2.29129 - 3.96863i) q^{71} +(-0.104356 + 0.180750i) q^{72} +(0.895644 + 1.55130i) q^{73} +(2.79129 + 4.83465i) q^{74} +(-0.500000 - 4.33013i) q^{76} -0.791288 q^{77} +(4.29129 + 7.43273i) q^{78} +(3.97822 + 6.89048i) q^{79} +(4.79129 + 8.29875i) q^{81} +(-1.18693 + 2.05583i) q^{82} -0.791288 q^{83} -1.79129 q^{84} +(-0.604356 + 1.04678i) q^{86} +3.95644 q^{87} +0.791288 q^{88} +(2.29129 - 3.96863i) q^{89} +(-2.39564 + 4.14938i) q^{91} +(2.29129 + 3.96863i) q^{92} +(0.186932 + 0.323775i) q^{93} +6.16515 q^{94} +1.79129 q^{96} +(-0.686932 - 1.18980i) q^{97} +(3.00000 + 5.19615i) q^{98} +(-0.0825757 + 0.143025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + q^{6} - 4 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 + q^6 - 4 * q^7 + 4 * q^8 - 5 * q^9	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + q^{6} - 4 q^{7} + 4 q^{8} - 5 q^{9} - 6 q^{11} - 2 q^{12} + 5 q^{13} + 2 q^{14} - 2 q^{16} - 3 q^{17} + 10 q^{18} - 14 q^{19} - q^{21} + 3 q^{22} + q^{24} - 10 q^{26} - 20 q^{27} + 2 q^{28} - 9 q^{29} - 10 q^{31} - 2 q^{32} - 12 q^{33} - 3 q^{34} - 5 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{39} + 9 q^{41} - q^{42} - 7 q^{43} + 3 q^{44} + 6 q^{47} + q^{48} - 24 q^{49} - 9 q^{51} + 5 q^{52} + 10 q^{54} - 4 q^{56} - 8 q^{57} + 18 q^{58} + 11 q^{61} + 5 q^{62} + 5 q^{63} + 4 q^{64} - 12 q^{66} - 22 q^{67} + 6 q^{68} - 42 q^{69} - 5 q^{72} - q^{73} + 2 q^{74} - 2 q^{76} + 6 q^{77} + 8 q^{78} - 7 q^{79} + 10 q^{81} + 9 q^{82} + 6 q^{83} + 2 q^{84} - 7 q^{86} - 30 q^{87} - 6 q^{88} - 5 q^{91} - 13 q^{93} - 12 q^{94} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 18 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 + q^6 - 4 * q^7 + 4 * q^8 - 5 * q^9 - 6 * q^11 - 2 * q^12 + 5 * q^13 + 2 * q^14 - 2 * q^16 - 3 * q^17 + 10 * q^18 - 14 * q^19 - q^21 + 3 * q^22 + q^24 - 10 * q^26 - 20 * q^27 + 2 * q^28 - 9 * q^29 - 10 * q^31 - 2 * q^32 - 12 * q^33 - 3 * q^34 - 5 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^39 + 9 * q^41 - q^42 - 7 * q^43 + 3 * q^44 + 6 * q^47 + q^48 - 24 * q^49 - 9 * q^51 + 5 * q^52 + 10 * q^54 - 4 * q^56 - 8 * q^57 + 18 * q^58 + 11 * q^61 + 5 * q^62 + 5 * q^63 + 4 * q^64 - 12 * q^66 - 22 * q^67 + 6 * q^68 - 42 * q^69 - 5 * q^72 - q^73 + 2 * q^74 - 2 * q^76 + 6 * q^77 + 8 * q^78 - 7 * q^79 + 10 * q^81 + 9 * q^82 + 6 * q^83 + 2 * q^84 - 7 * q^86 - 30 * q^87 - 6 * q^88 - 5 * q^91 - 13 * q^93 - 12 * q^94 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 18 * q^99

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