LMFDB - Embedded newform 950.2.j.h.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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([3, 4]))

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

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (of order $6$, degree $2$, not 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.3
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	950.349
Dual form			950.2.j.h.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.55130	+	0.895644i	−0.895644	+	0.517100i	−0.875784	−	0.482703i	$-0.839655\pi$
$3$	−1.55130	+	0.895644i	−0.895644	+	0.517100i	−0.0198595	+	0.999803i	$0.506322\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.895644	+	1.55130i	−0.365645	+	0.633316i
$7$		−	1.00000i		−	0.377964i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$		−	1.00000i		−	0.377964i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$		−	1.00000i		−	0.353553i
$9$	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	$0.461938\pi$
$12$			1.79129i			0.517100i
$13$	−4.14938	−	2.39564i	−1.15083	−	0.664432i	−0.201741	−	0.979439i	$-0.564660\pi$
$13$	−4.14938	−	2.39564i	−1.15083	−	0.664432i	−0.949089	+	0.315007i	$0.897993\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.28335	−	1.89564i	0.796330	−	0.459761i	−0.0458564	−	0.998948i	$-0.514602\pi$
$17$	3.28335	−	1.89564i	0.796330	−	0.459761i	0.842186	+	0.539187i	$0.181268\pi$
$18$		−	0.208712i		−	0.0491939i
$19$	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
$22$	0.685275	−	0.395644i	0.146101	−	0.0843516i
$23$	−3.96863	−	2.29129i	−0.827516	−	0.477767i	0.0254855	−	0.999675i	$-0.491887\pi$
$23$	−3.96863	−	2.29129i	−0.827516	−	0.477767i	−0.853001	+	0.521909i	$0.825220\pi$
$24$	0.895644	+	1.55130i	0.182823	+	0.316658i
$25$		0			0
$26$	−4.79129			−0.939649
$27$		−	5.00000i		−	0.962250i
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	1.10436	−	1.91280i	0.205074	−	0.355198i	−0.745082	−	0.666972i	$-0.767590\pi$
$29$	1.10436	−	1.91280i	0.205074	−	0.355198i	0.950156	+	0.311774i	$0.100923\pi$
$30$		0			0
$31$	−0.208712			−0.0374858			−0.0187429	−	0.999824i	$-0.505966\pi$
$31$	−0.208712			−0.0374858			−0.0187429	+	0.999824i	$0.505966\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.22753	+	0.708712i	−0.213685	+	0.123371i
$34$	1.89564	−	3.28335i	0.325100	−	0.563090i
$35$		0			0
$36$	−0.104356	−	0.180750i	−0.0173927	−	0.0301250i
$37$		−	5.58258i		−	0.917770i	−0.888496	−	0.458885i	$-0.848249\pi$
$37$		−	5.58258i		−	0.917770i	0.888496	−	0.458885i	$-0.151751\pi$
$38$	1.73205	−	4.00000i	0.280976	−	0.648886i
$39$	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	$0.892681\pi$
$42$	1.55130	+	0.895644i	0.239371	+	0.138201i
$43$	−1.04678	+	0.604356i	−0.159632	+	0.0921634i	−0.577688	−	0.816258i	$-0.696045\pi$
$43$	−1.04678	+	0.604356i	−0.159632	+	0.0921634i	0.418056	+	0.908421i	$0.362712\pi$
$44$	0.395644	−	0.685275i	0.0596456	−	0.103309i
$45$		0			0
$46$	−4.58258			−0.675664
$47$	−5.33918	−	3.08258i	−0.778799	−	0.449640i	0.0572054	−	0.998362i	$-0.481781\pi$
$47$	−5.33918	−	3.08258i	−0.778799	−	0.449640i	−0.836005	+	0.548723i	$0.815114\pi$
$48$	1.55130	+	0.895644i	0.223911	+	0.129275i
$49$	6.00000			0.857143
$50$		0			0
$51$	−3.39564	+	5.88143i	−0.475485	+	0.823565i
$52$	−4.14938	+	2.39564i	−0.575415	+	0.332216i
$53$	3.96863	+	2.29129i	0.545133	+	0.314733i	0.747157	−	0.664648i	$-0.231418\pi$
$53$	3.96863	+	2.29129i	0.545133	+	0.314733i	−0.202024	+	0.979381i	$0.564752\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$		0			0
$56$	−1.00000			−0.133631
$57$	−3.10260	+	7.16515i	−0.410950	+	0.949047i
$58$		−	2.20871i		−	0.290018i
$59$	−2.29129	−	3.96863i	−0.298300	−	0.516671i	0.677447	−	0.735572i	$-0.263086\pi$
$59$	−2.29129	−	3.96863i	−0.298300	−	0.516671i	−0.975747	+	0.218900i	$0.929753\pi$
$60$		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	$-0.124374\pi$
$62$	−0.180750	+	0.104356i	−0.0229553	+	0.0132532i
$63$	−0.180750	−	0.104356i	−0.0227724	−	0.0131476i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−0.708712	+	1.22753i	−0.0872364	+	0.151098i
$67$	−5.55765	−	3.20871i	−0.678975	−	0.392007i	0.120494	−	0.992714i	$-0.461552\pi$
$67$	−5.55765	−	3.20871i	−0.678975	−	0.392007i	−0.799469	+	0.600708i	$0.794886\pi$
$68$		−	3.79129i		−	0.459761i
$69$	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	$0.920994\pi$
$72$	−0.180750	−	0.104356i	−0.0213016	−	0.0122985i
$73$	1.55130	−	0.895644i	0.181566	−	0.104827i	−0.406462	−	0.913668i	$-0.633238\pi$
$73$	1.55130	−	0.895644i	0.181566	−	0.104827i	0.588028	+	0.808840i	$0.299904\pi$
$74$	−2.79129	−	4.83465i	−0.324481	−	0.562017i
$75$		0			0
$76$	−0.500000	−	4.33013i	−0.0573539	−	0.496700i
$77$		−	0.791288i		−	0.0901756i
$78$	7.43273	−	4.29129i	0.841591	−	0.485893i
$79$	−3.97822	−	6.89048i	−0.447585	−	0.775239i	0.550644	−	0.834740i	$-0.314382\pi$
$79$	−3.97822	−	6.89048i	−0.447585	−	0.775239i	−0.998228	+	0.0595011i	$0.981049\pi$
$80$		0			0
$81$	4.79129	+	8.29875i	0.532365	+	0.922084i
$82$	−2.05583	−	1.18693i	−0.227028	−	0.131075i
$83$			0.791288i			0.0868551i	0.999057	+	0.0434276i	$0.0138278\pi$
$83$			0.791288i			0.0868551i	−0.999057	+	0.0434276i	$0.986172\pi$
$84$	1.79129			0.195446
$85$		0			0
$86$	−0.604356	+	1.04678i	−0.0651694	+	0.112877i
$87$			3.95644i			0.424175i
$88$		−	0.791288i		−	0.0843516i
$89$	−2.29129	+	3.96863i	−0.242876	+	0.420674i	−0.961532	−	0.274692i	$-0.911424\pi$
$89$	−2.29129	+	3.96863i	−0.242876	+	0.420674i	0.718656	+	0.695365i	$0.244757\pi$
$90$		0			0
$91$	−2.39564	+	4.14938i	−0.251132	+	0.434973i
$92$	−3.96863	+	2.29129i	−0.413758	+	0.238883i
$93$	0.323775	−	0.186932i	0.0335739	−	0.0193839i
$94$	−6.16515			−0.635887
$95$		0			0
$96$	1.79129			0.182823
$97$	1.18980	−	0.686932i	0.120806	−	0.0697474i	−0.438379	−	0.898790i	$-0.644447\pi$
$97$	1.18980	−	0.686932i	0.120806	−	0.0697474i	0.559185	+	0.829043i	$0.311114\pi$
$98$	5.19615	−	3.00000i	0.524891	−	0.303046i
$99$	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	$0.166667\pi$
$102$			6.79129i			0.672438i
$103$			13.1652i			1.29720i	0.761129	+	0.648600i	$0.224645\pi$
$103$			13.1652i			1.29720i	−0.761129	+	0.648600i	$0.775355\pi$
$104$	−2.39564	+	4.14938i	−0.234912	+	0.406880i
$105$		0			0
$106$	4.58258			0.445099
$107$		−	3.95644i		−	0.382483i	−0.981543	−	0.191242i	$-0.938749\pi$
$107$		−	3.95644i		−	0.382483i	0.981543	−	0.191242i	$-0.0612514\pi$
$108$	−4.33013	−	2.50000i	−0.416667	−	0.240563i
$109$	7.87386	+	13.6379i	0.754179	+	1.30628i	0.945781	+	0.324804i	$0.105298\pi$
$109$	7.87386	+	13.6379i	0.754179	+	1.30628i	−0.191602	+	0.981473i	$0.561368\pi$
$110$		0			0
$111$	5.00000	+	8.66025i	0.474579	+	0.821995i
$112$	−0.866025	+	0.500000i	−0.0818317	+	0.0472456i
$113$			8.37386i			0.787747i	0.919165	+	0.393873i	$0.128865\pi$
$113$			8.37386i			0.787747i	−0.919165	+	0.393873i	$0.871135\pi$
$114$	0.895644	+	7.75650i	0.0838847	+	0.726463i
$115$		0			0
$116$	−1.10436	−	1.91280i	−0.102537	−	0.177599i
$117$	−0.866025	+	0.500000i	−0.0800641	+	0.0462250i
$118$	−3.96863	−	2.29129i	−0.365342	−	0.210930i
$119$	−1.89564	−	3.28335i	−0.173773	−	0.300984i
$120$		0			0
$121$	−10.3739			−0.943079
$122$		−	12.3739i		−	1.12028i
$123$	3.68258	+	2.12614i	0.332047	+	0.191707i
$124$	−0.104356	+	0.180750i	−0.00937145	+	0.0162318i
$125$		0			0
$126$	−0.208712			−0.0185936
$127$	−14.1802	−	8.18693i	−1.25829	−	0.726473i	−0.285546	−	0.958365i	$-0.592175\pi$
$127$	−14.1802	−	8.18693i	−1.25829	−	0.726473i	−0.972741	+	0.231892i	$0.925508\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	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	$0.478894\pi$
$132$			1.41742i			0.123371i
$133$	−2.59808	−	3.50000i	−0.225282	−	0.303488i
$134$	−6.41742			−0.554381
$135$		0			0
$136$	−1.89564	−	3.28335i	−0.162550	−	0.281545i
$137$	18.4726	+	10.6652i	1.57822	+	0.911185i	0.995108	+	0.0987932i	$0.0314982\pi$
$137$	18.4726	+	10.6652i	1.57822	+	0.911185i	0.583111	+	0.812392i	$0.301835\pi$
$138$	7.10895	−	4.10436i	0.605154	−	0.349386i
$139$	−8.39564	+	14.5417i	−0.712109	+	1.23341i	0.251955	+	0.967739i	$0.418927\pi$
$139$	−8.39564	+	14.5417i	−0.712109	+	1.23341i	−0.964064	+	0.265670i	$0.914407\pi$
$140$		0			0
$141$	11.0436			0.930036
$142$	−3.96863	−	2.29129i	−0.333040	−	0.192281i
$143$	−3.28335	−	1.89564i	−0.274568	−	0.158522i
$144$	−0.208712			−0.0173927
$145$		0			0
$146$	0.895644	−	1.55130i	0.0741240	−	0.128387i
$147$	−9.30780	+	5.37386i	−0.767695	+	0.443229i
$148$	−4.83465	−	2.79129i	−0.397406	−	0.229442i
$149$	2.37386	+	4.11165i	0.194474	+	0.336840i	0.946728	−	0.322034i	$-0.104367\pi$
$149$	2.37386	+	4.11165i	0.194474	+	0.336840i	−0.752254	+	0.658874i	$0.771033\pi$
$150$		0			0
$151$	−11.7477			−0.956016			−0.478008	−	0.878355i	$-0.658641\pi$
$151$	−11.7477			−0.956016			−0.478008	+	0.878355i	$0.658641\pi$
$152$	−2.59808	−	3.50000i	−0.210732	−	0.283887i
$153$		−	0.791288i		−	0.0639718i
$154$	−0.395644	−	0.685275i	−0.0318819	−	0.0552211i
$155$		0			0
$156$	4.29129	−	7.43273i	0.343578	−	0.595095i
$157$	12.9527	−	7.47822i	1.03373	−	0.596827i	0.115682	−	0.993286i	$-0.463095\pi$
$157$	12.9527	−	7.47822i	1.03373	−	0.596827i	0.918052	+	0.396459i	$0.129761\pi$
$158$	−6.89048	−	3.97822i	−0.548177	−	0.316490i
$159$	−8.20871			−0.650993
$160$		0			0
$161$	−2.29129	+	3.96863i	−0.180579	+	0.312772i
$162$	8.29875	+	4.79129i	0.652012	+	0.376439i
$163$			5.41742i			0.424325i	0.977234	+	0.212163i	$0.0680507\pi$
$163$			5.41742i			0.424325i	−0.977234	+	0.212163i	$0.931949\pi$
$164$	−2.37386			−0.185368
$165$		0			0
$166$	0.395644	+	0.685275i	0.0307079	+	0.0531877i
$167$	17.7873	+	10.2695i	1.37642	+	0.794678i	0.991727	−	0.128365i	$-0.0409729\pi$
$167$	17.7873	+	10.2695i	1.37642	+	0.794678i	0.384696	+	0.923043i	$0.374306\pi$
$168$	1.55130	−	0.895644i	0.119685	−	0.0691004i
$169$	4.97822	+	8.62253i	0.382940	+	0.663271i
$170$		0			0
$171$	−0.104356	−	0.903750i	−0.00798031	−	0.0691115i
$172$			1.20871i			0.0921634i
$173$	18.1865	−	10.5000i	1.38270	−	0.798300i	0.390218	−	0.920722i	$-0.372399\pi$
$173$	18.1865	−	10.5000i	1.38270	−	0.798300i	0.992478	+	0.122422i	$0.0390662\pi$
$174$	1.97822	+	3.42638i	0.149968	+	0.259753i
$175$		0			0
$176$	−0.395644	−	0.685275i	−0.0298228	−	0.0516546i
$177$	7.10895	+	4.10436i	0.534342	+	0.308502i
$178$			4.58258i			0.343479i
$179$	−10.7477			−0.803323			−0.401661	−	0.915788i	$-0.631567\pi$
$179$	−10.7477			−0.803323			−0.401661	+	0.915788i	$0.631567\pi$
$180$		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	$-0.125523\pi$
$182$			4.79129i			0.355154i
$183$			22.1652i			1.63850i
$184$	−2.29129	+	3.96863i	−0.168916	+	0.292571i
$185$		0			0
$186$	0.186932	−	0.323775i	0.0137065	−	0.0237404i
$187$	2.59808	−	1.50000i	0.189990	−	0.109691i
$188$	−5.33918	+	3.08258i	−0.389400	+	0.224820i
$189$	−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	$0.580981\pi$
$192$	1.55130	−	0.895644i	0.111955	−	0.0646375i
$193$	−21.4322	+	12.3739i	−1.54272	+	0.890690i	−0.544055	+	0.839050i	$0.683112\pi$
$193$	−21.4322	+	12.3739i	−1.54272	+	0.890690i	−0.998666	+	0.0516406i	$0.983555\pi$
$194$	0.686932	−	1.18980i	0.0493188	−	0.0854227i
$195$		0			0
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$			24.7913i			1.76631i	0.469085	+	0.883153i	$0.344584\pi$
$197$			24.7913i			1.76631i	−0.469085	+	0.883153i	$0.655416\pi$
$198$		−	0.165151i		−	0.0117368i
$199$	−2.79129	+	4.83465i	−0.197869	+	0.342719i	−0.947837	−	0.318755i	$-0.896735\pi$
$199$	−2.79129	+	4.83465i	−0.197869	+	0.342719i	0.749968	+	0.661474i	$0.230069\pi$
$200$		0			0
$201$	11.4955			0.810827
$202$		0			0
$203$	−1.91280	−	1.10436i	−0.134252	−	0.0775106i
$204$	3.39564	+	5.88143i	0.237743	+	0.411782i
$205$		0			0
$206$	6.58258	+	11.4014i	0.458630	+	0.794370i
$207$	−0.828301	+	0.478220i	−0.0575709	+	0.0332386i
$208$			4.79129i			0.332216i
$209$	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	$0.844770\pi$
$212$	3.96863	−	2.29129i	0.272566	−	0.157366i
$213$	7.10895	+	4.10436i	0.487097	+	0.281226i
$214$	−1.97822	−	3.42638i	−0.135228	−	0.234222i
$215$		0			0
$216$	−5.00000			−0.340207
$217$			0.208712i			0.0141683i
$218$	13.6379	+	7.87386i	0.923677	+	0.533285i
$219$	−1.60436	+	2.77883i	−0.108412	+	0.187776i
$220$		0			0
$221$	−18.1652			−1.22192
$222$	8.66025	+	5.00000i	0.581238	+	0.335578i
$223$	−20.6039	+	11.8956i	−1.37974	+	0.796591i	−0.992127	−	0.125233i	$-0.960032\pi$
$223$	−20.6039	+	11.8956i	−1.37974	+	0.796591i	−0.387609	+	0.921824i	$0.626699\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$		0			0
$226$	4.18693	+	7.25198i	0.278511	+	0.482394i
$227$		−	19.7477i		−	1.31070i	−0.755324	−	0.655351i	$-0.772521\pi$
$227$		−	19.7477i		−	1.31070i	0.755324	−	0.655351i	$-0.227479\pi$
$228$	4.65390	+	6.26951i	0.308212	+	0.415208i
$229$	−11.3303			−0.748727			−0.374364	−	0.927282i	$-0.622139\pi$
$229$	−11.3303			−0.748727			−0.374364	+	0.927282i	$0.622139\pi$
$230$		0			0
$231$	0.708712	+	1.22753i	0.0466298	+	0.0807652i
$232$	−1.91280	−	1.10436i	−0.125582	−	0.0725045i
$233$	7.93725	−	4.58258i	0.519987	−	0.300215i	−0.216942	−	0.976184i	$-0.569608\pi$
$233$	7.93725	−	4.58258i	0.519987	−	0.300215i	0.736929	+	0.675970i	$0.236275\pi$
$234$	−0.500000	+	0.866025i	−0.0326860	+	0.0566139i
$235$		0			0
$236$	−4.58258			−0.298300
$237$	12.3428	+	7.12614i	0.801753	+	0.462892i
$238$	−3.28335	−	1.89564i	−0.212828	−	0.122876i
$239$	−7.41742			−0.479793			−0.239897	−	0.970798i	$-0.577114\pi$
$239$	−7.41742			−0.479793			−0.239897	+	0.970798i	$0.577114\pi$
$240$		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	$0.0380291\pi$
$242$	−8.98403	+	5.18693i	−0.577515	+	0.333429i
$243$	−1.87508	−	1.08258i	−0.120286	−	0.0694473i
$244$	−6.18693	−	10.7161i	−0.396078	−	0.686027i
$245$		0			0
$246$	4.25227			0.271115
$247$	−20.7469	+	2.39564i	−1.32009	+	0.152431i
$248$			0.208712i			0.0132532i
$249$	−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	$-0.180900\pi$
$252$	−0.180750	+	0.104356i	−0.0113862	+	0.00657381i
$253$	−3.14033	−	1.81307i	−0.197431	−	0.113987i
$254$	−16.3739			−1.02739
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.6757	+	7.89564i	0.853064	+	0.492517i	0.861683	−	0.507446i	$-0.169410\pi$
$257$	13.6757	+	7.89564i	0.853064	+	0.492517i	−0.00861948	+	0.999963i	$0.502744\pi$
$258$		−	2.16515i		−	0.134796i
$259$	−5.58258			−0.346884
$260$		0			0
$261$	−0.230493	−	0.399225i	−0.0142671	−	0.0247114i
$262$	17.7873	+	10.2695i	1.09890	+	0.634452i
$263$	24.7532	−	14.2913i	1.52635	−	0.881239i	0.526839	−	0.849965i	$-0.323377\pi$
$263$	24.7532	−	14.2913i	1.52635	−	0.881239i	0.999511	−	0.0312735i	$-0.00995629\pi$
$264$	0.708712	+	1.22753i	0.0436182	+	0.0755490i
$265$		0			0
$266$	−4.00000	−	1.73205i	−0.245256	−	0.106199i
$267$		−	8.20871i		−	0.502365i
$268$	−5.55765	+	3.20871i	−0.339488	+	0.196003i
$269$	−14.0608	−	24.3540i	−0.857302	−	1.48489i	−0.874493	−	0.485038i	$-0.838806\pi$
$269$	−14.0608	−	24.3540i	−0.857302	−	1.48489i	0.0171912	−	0.999852i	$-0.494528\pi$
$270$		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	$-0.428379\pi$
$272$	−3.28335	−	1.89564i	−0.199082	−	0.114940i
$273$		−	8.58258i		−	0.519441i
$274$	21.3303			1.28861
$275$		0			0
$276$	4.10436	−	7.10895i	0.247053	−	0.427909i
$277$			18.7477i			1.12644i	0.826306	+	0.563221i	$0.190438\pi$
$277$			18.7477i			1.12644i	−0.826306	+	0.563221i	$0.809562\pi$
$278$			16.7913i			1.00707i
$279$	−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	$0.180128\pi$
$282$	9.56400	−	5.52178i	0.569528	−	0.328817i
$283$	17.4258	−	10.0608i	1.03586	−	0.598052i	0.117200	−	0.993108i	$-0.462608\pi$
$283$	17.4258	−	10.0608i	1.03586	−	0.598052i	0.918657	+	0.395056i	$0.129275\pi$
$284$	−4.58258			−0.271926
$285$		0			0
$286$	−3.79129			−0.224184
$287$	−2.05583	+	1.18693i	−0.121352	+	0.0700624i
$288$	−0.180750	+	0.104356i	−0.0106508	+	0.00614924i
$289$	−1.31307	+	2.27430i	−0.0772393	+	0.133782i
$290$		0			0
$291$	−1.23049	+	2.13128i	−0.0721327	+	0.124938i
$292$		−	1.79129i		−	0.104827i
$293$		−	2.04356i		−	0.119386i	−0.998217	−	0.0596930i	$-0.980988\pi$
$293$		−	2.04356i		−	0.119386i	0.998217	−	0.0596930i	$-0.0190122\pi$
$294$	−5.37386	+	9.30780i	−0.313410	+	0.542842i
$295$		0			0
$296$	−5.58258			−0.324481
$297$		−	3.95644i		−	0.229576i
$298$	4.11165	+	2.37386i	0.238182	+	0.137514i
$299$	10.9782	+	19.0148i	0.634887	+	1.09966i
$300$		0			0
$301$	0.604356	+	1.04678i	0.0348345	+	0.0603351i
$302$	−10.1738	+	5.87386i	−0.585438	+	0.338003i
$303$		0			0
$304$	−4.00000	−	1.73205i	−0.229416	−	0.0993399i
$305$		0			0
$306$	−0.395644	−	0.685275i	−0.0226175	−	0.0391746i
$307$	17.7496	−	10.2477i	1.01302	−	0.584869i	0.100947	−	0.994892i	$-0.467813\pi$
$307$	17.7496	−	10.2477i	1.01302	−	0.584869i	0.912075	+	0.410023i	$0.134479\pi$
$308$	−0.685275	−	0.395644i	−0.0390472	−	0.0225439i
$309$	−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	$0.639826\pi$
$312$		−	8.58258i		−	0.485893i
$313$	13.6379	+	7.87386i	0.770861	+	0.445057i	0.833182	−	0.552999i	$-0.186517\pi$
$313$	13.6379	+	7.87386i	0.770861	+	0.445057i	−0.0623204	+	0.998056i	$0.519850\pi$
$314$	7.47822	−	12.9527i	0.422020	−	0.730961i
$315$		0			0
$316$	−7.95644			−0.447585
$317$	−7.93725	−	4.58258i	−0.445801	−	0.257383i	0.260254	−	0.965540i	$-0.416194\pi$
$317$	−7.93725	−	4.58258i	−0.445801	−	0.257383i	−0.706055	+	0.708157i	$0.749527\pi$
$318$	−7.10895	+	4.10436i	−0.398650	+	0.230161i
$319$	0.873864	−	1.51358i	0.0489270	−	0.0847440i
$320$		0			0
$321$	3.54356	+	6.13763i	0.197782	+	0.342569i
$322$			4.58258i			0.255377i
$323$	6.56670	−	15.1652i	0.365381	−	0.843812i
$324$	9.58258			0.532365
$325$		0			0
$326$	2.70871	+	4.69163i	0.150022	+	0.259845i
$327$	−24.4295	−	14.1044i	−1.35095	−	0.779973i
$328$	−2.05583	+	1.18693i	−0.113514	+	0.0655373i
$329$	−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	$0.221691\pi$
$332$	0.685275	+	0.395644i	0.0376094	+	0.0217138i
$333$	−1.00905	−	0.582576i	−0.0552956	−	0.0319250i
$334$	20.5390			1.12384
$335$		0			0
$336$	0.895644	−	1.55130i	0.0488614	−	0.0846304i
$337$	−11.5444	+	6.66515i	−0.628862	+	0.363074i	−0.780311	−	0.625391i	$-0.784939\pi$
$337$	−11.5444	+	6.66515i	−0.628862	+	0.363074i	0.151449	+	0.988465i	$0.451606\pi$
$338$	8.62253	+	4.97822i	0.469004	+	0.270779i
$339$	−7.50000	−	12.9904i	−0.407344	−	0.705541i
$340$		0			0
$341$	−0.165151			−0.00894345
$342$	−0.542250	−	0.730493i	−0.0293215	−	0.0395005i
$343$		−	13.0000i		−	0.701934i
$344$	0.604356	+	1.04678i	0.0325847	+	0.0564383i
$345$		0			0
$346$	10.5000	−	18.1865i	0.564483	−	0.977714i
$347$	15.0462	−	8.68693i	0.807723	−	0.466339i	−0.0384417	−	0.999261i	$-0.512239\pi$
$347$	15.0462	−	8.68693i	0.807723	−	0.466339i	0.846164	+	0.532922i	$0.178906\pi$
$348$	3.42638	+	1.97822i	0.183673	+	0.106044i
$349$	14.5826			0.780587			0.390294	−	0.920690i	$-0.372373\pi$
$349$	14.5826			0.780587			0.390294	+	0.920690i	$0.372373\pi$
$350$		0			0
$351$	−11.9782	+	20.7469i	−0.639350	+	1.10739i
$352$	−0.685275	−	0.395644i	−0.0365253	−	0.0210879i
$353$		−	13.7477i		−	0.731718i	−0.930670	−	0.365859i	$-0.880775\pi$
$353$		−	13.7477i		−	0.731718i	0.930670	−	0.365859i	$-0.119225\pi$
$354$	8.20871			0.436288
$355$		0			0
$356$	2.29129	+	3.96863i	0.121438	+	0.210337i
$357$	5.88143	+	3.39564i	0.311278	+	0.179717i
$358$	−9.30780	+	5.37386i	−0.491933	+	0.284018i
$359$	7.35208	+	12.7342i	0.388028	+	0.672084i	0.992184	−	0.124782i	$-0.0398230\pi$
$359$	7.35208	+	12.7342i	0.388028	+	0.672084i	−0.604156	+	0.796866i	$0.706490\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$		−	21.3739i		−	1.12339i
$363$	16.0930	−	9.29129i	0.844663	−	0.487666i
$364$	2.39564	+	4.14938i	0.125566	+	0.217486i
$365$		0			0
$366$	11.0826	+	19.1956i	0.579296	+	1.00337i
$367$	−3.64485	−	2.10436i	−0.190260	−	0.109846i	0.401844	−	0.915708i	$-0.368369\pi$
$367$	−3.64485	−	2.10436i	−0.190260	−	0.109846i	−0.592104	+	0.805861i	$0.701703\pi$
$368$			4.58258i			0.238883i
$369$	−0.495454			−0.0257923
$370$		0			0
$371$	2.29129	−	3.96863i	0.118958	−	0.206041i
$372$		−	0.373864i		−	0.0193839i
$373$			7.62614i			0.394866i	0.980316	+	0.197433i	$0.0632605\pi$
$373$			7.62614i			0.394866i	−0.980316	+	0.197433i	$0.936739\pi$
$374$	1.50000	−	2.59808i	0.0775632	−	0.134343i
$375$		0			0
$376$	−3.08258	+	5.33918i	−0.158972	+	0.275347i
$377$	−9.16478	+	5.29129i	−0.472010	+	0.272515i
$378$	−4.33013	+	2.50000i	−0.222718	+	0.128586i
$379$	−23.1652			−1.18991			−0.594957	−	0.803758i	$-0.702831\pi$
$379$	−23.1652			−1.18991			−0.594957	+	0.803758i	$0.702831\pi$
$380$		0			0
$381$	29.3303			1.50264
$382$	−6.02445	+	3.47822i	−0.308238	+	0.177961i
$383$	3.96863	−	2.29129i	0.202787	−	0.117079i	−0.395168	−	0.918609i	$-0.629313\pi$
$383$	3.96863	−	2.29129i	0.202787	−	0.117079i	0.597955	+	0.801530i	$0.295980\pi$
$384$	0.895644	−	1.55130i	0.0457056	−	0.0791645i
$385$		0			0
$386$	−12.3739	+	21.4322i	−0.629813	+	1.09087i
$387$			0.252273i			0.0128238i
$388$		−	1.37386i		−	0.0697474i
$389$	16.1869	−	28.0366i	0.820710	−	1.42151i	−0.0844442	−	0.996428i	$-0.526911\pi$
$389$	16.1869	−	28.0366i	0.820710	−	1.42151i	0.905154	−	0.425083i	$-0.139755\pi$
$390$		0			0
$391$	−17.3739			−0.878634
$392$		−	6.00000i		−	0.303046i
$393$	−31.8622	−	18.3956i	−1.60723	−	0.927937i
$394$	12.3956	+	21.4699i	0.624484	+	1.08164i
$395$		0			0
$396$	−0.0825757	−	0.143025i	−0.00414958	−	0.00718729i
$397$	−17.8250	+	10.2913i	−0.894613	+	0.516505i	−0.875448	−	0.483311i	$-0.839434\pi$
$397$	−17.8250	+	10.2913i	−0.894613	+	0.516505i	−0.0191643	+	0.999816i	$0.506101\pi$
$398$			5.58258i			0.279829i
$399$	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	$0.736472\pi$
$402$	9.95536	−	5.74773i	0.496528	−	0.286671i
$403$	0.866025	+	0.500000i	0.0431398	+	0.0249068i
$404$		0			0
$405$		0			0
$406$	−2.20871			−0.109617
$407$		−	4.41742i		−	0.218964i
$408$	5.88143	+	3.39564i	0.291174	+	0.168109i
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$		0			0
$411$	−38.2087			−1.88470
$412$	11.4014	+	6.58258i	0.561704	+	0.324300i
$413$	−3.96863	+	2.29129i	−0.195283	+	0.112747i
$414$	−0.478220	+	0.828301i	−0.0235032	+	0.0407088i
$415$		0			0
$416$	2.39564	+	4.14938i	0.117456	+	0.203440i
$417$		−	30.0780i		−	1.47293i
$418$	1.37055	−	3.16515i	0.0670358	−	0.154813i
$419$	−4.74773			−0.231942			−0.115971	−	0.993253i	$-0.536998\pi$
$419$	−4.74773			−0.231942			−0.115971	+	0.993253i	$0.536998\pi$
$420$		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	$0.995377\pi$
$422$	−0.903750	−	0.521780i	−0.0439939	−	0.0253999i
$423$	−1.11435	+	0.643371i	−0.0541816	+	0.0312818i
$424$	2.29129	−	3.96863i	0.111275	−	0.192734i
$425$		0			0
$426$	8.20871			0.397713
$427$	−10.7161	−	6.18693i	−0.518587	−	0.299407i
$428$	−3.42638	−	1.97822i	−0.165620	−	0.0956209i
$429$	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	$0.266349\pi$
$432$	−4.33013	+	2.50000i	−0.208333	+	0.120281i
$433$	−33.6995	−	19.4564i	−1.61950	−	0.935017i	−0.987050	−	0.160413i	$-0.948717\pi$
$433$	−33.6995	−	19.4564i	−1.61950	−	0.935017i	−0.632447	−	0.774604i	$-0.717949\pi$
$434$	0.104356	+	0.180750i	0.00500925	+	0.00867628i
$435$		0			0
$436$	15.7477			0.754179
$437$	−19.8431	+	2.29129i	−0.949226	+	0.109607i
$438$			3.20871i			0.153318i
$439$	5.66515	+	9.81233i	0.270383	+	0.468317i	0.968960	−	0.247218i	$-0.0795164\pi$
$439$	5.66515	+	9.81233i	0.270383	+	0.468317i	−0.698577	+	0.715535i	$0.746183\pi$
$440$		0			0
$441$	0.626136	−	1.08450i	0.0298160	−	0.0516429i
$442$	−15.7315	+	9.08258i	−0.748270	+	0.432014i
$443$	−20.7846	−	12.0000i	−0.987507	−	0.570137i	−0.0829786	−	0.996551i	$-0.526443\pi$
$443$	−20.7846	−	12.0000i	−0.987507	−	0.570137i	−0.904528	+	0.426414i	$0.859777\pi$
$444$	10.0000			0.474579
$445$		0			0
$446$	−11.8956	+	20.6039i	−0.563275	+	0.975621i
$447$	−7.36515	−	4.25227i	−0.348360	−	0.201126i
$448$			1.00000i			0.0472456i
$449$	33.3303			1.57295			0.786477	−	0.617619i	$-0.211903\pi$
$449$	33.3303			1.57295			0.786477	+	0.617619i	$0.211903\pi$
$450$		0			0
$451$	−0.939205	−	1.62675i	−0.0442254	−	0.0766007i
$452$	7.25198	+	4.18693i	0.341104	+	0.196937i
$453$	18.2243	−	10.5218i	0.856250	−	0.494356i
$454$	−9.87386	−	17.1020i	−0.463403	−	0.802638i
$455$		0			0
$456$	7.16515	+	3.10260i	0.335539	+	0.145293i
$457$			6.74773i			0.315645i	0.987467	+	0.157823i	$0.0504474\pi$
$457$			6.74773i			0.315645i	−0.987467	+	0.157823i	$0.949553\pi$
$458$	−9.81233	+	5.66515i	−0.458500	+	0.264715i
$459$	−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	$0.894558\pi$
$462$	1.22753	+	0.708712i	0.0571097	+	0.0329723i
$463$			4.95644i			0.230345i	0.993345	+	0.115173i	$0.0367421\pi$
$463$			4.95644i			0.230345i	−0.993345	+	0.115173i	$0.963258\pi$
$464$	−2.20871			−0.102537
$465$		0			0
$466$	4.58258	−	7.93725i	0.212284	−	0.367686i
$467$			24.3303i			1.12587i	0.826500	+	0.562936i	$0.190328\pi$
$467$			24.3303i			1.12587i	−0.826500	+	0.562936i	$0.809672\pi$
$468$			1.00000i			0.0462250i
$469$	−3.20871	+	5.55765i	−0.148165	+	0.256629i
$470$		0			0
$471$	−13.3956	+	23.2019i	−0.617239	+	1.06909i
$472$	−3.96863	+	2.29129i	−0.182671	+	0.105465i
$473$	−0.828301	+	0.478220i	−0.0380853	+	0.0219886i
$474$	14.2523			0.654629
$475$		0			0
$476$	−3.79129			−0.173773
$477$	0.828301	−	0.478220i	0.0379253	−	0.0218962i
$478$	−6.42368	+	3.70871i	−0.293812	+	0.169633i
$479$	2.12614	−	3.68258i	0.0971457	−	0.168261i	−0.813356	−	0.581766i	$-0.802362\pi$
$479$	2.12614	−	3.68258i	0.0971457	−	0.168261i	0.910502	+	0.413504i	$0.135695\pi$
$480$		0			0
$481$	−13.3739	+	23.1642i	−0.609796	+	1.05620i
$482$		−	12.2087i		−	0.556092i
$483$		−	8.20871i		−	0.373509i
$484$	−5.18693	+	8.98403i	−0.235770	+	0.408365i
$485$		0			0
$486$	−2.16515			−0.0982133
$487$			23.0000i			1.04223i	0.853487	+	0.521115i	$0.174484\pi$
$487$			23.0000i			1.04223i	−0.853487	+	0.521115i	$0.825516\pi$
$488$	−10.7161	−	6.18693i	−0.485094	−	0.280069i
$489$	−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	$0.464944\pi$
$492$	3.68258	−	2.12614i	0.166023	−	0.0958536i
$493$		−	8.37386i		−	0.377140i
$494$	−16.7695	+	12.4481i	−0.754496	+	0.560068i
$495$		0			0
$496$	0.104356	+	0.180750i	0.00468573	+	0.00811592i
$497$	−3.96863	+	2.29129i	−0.178017	+	0.102778i
$498$	−1.22753	−	0.708712i	−0.0550067	−	0.0317582i
$499$	8.66515	+	15.0085i	0.387905	+	0.671872i	0.992168	−	0.124914i	$-0.0398654\pi$
$499$	8.66515	+	15.0085i	0.387905	+	0.671872i	−0.604262	+	0.796786i	$0.706532\pi$
$500$		0			0
$501$	−36.7913			−1.64371
$502$		−	28.1216i		−	1.25513i
$503$	3.96863	+	2.29129i	0.176952	+	0.102163i	0.585860	−	0.810412i	$-0.300757\pi$
$503$	3.96863	+	2.29129i	0.176952	+	0.102163i	−0.408908	+	0.912576i	$0.634090\pi$
$504$	−0.104356	+	0.180750i	−0.00464839	+	0.00805125i
$505$		0			0
$506$	−3.62614			−0.161201
$507$	−15.4454	−	8.91742i	−0.685956	−	0.396037i
$508$	−14.1802	+	8.18693i	−0.629144	+	0.363236i
$509$	15.7913	−	27.3513i	0.699937	−	1.21233i	−0.268551	−	0.963265i	$-0.586545\pi$
$509$	15.7913	−	27.3513i	0.699937	−	1.21233i	0.968488	−	0.249060i	$-0.0801217\pi$
$510$		0			0
$511$	−0.895644	−	1.55130i	−0.0396210	−	0.0686255i
$512$			1.00000i			0.0441942i
$513$	−12.9904	−	17.5000i	−0.573539	−	0.772644i
$514$	15.7913			0.696524
$515$		0			0
$516$	−1.08258	−	1.87508i	−0.0476577	−	0.0825456i
$517$	−4.22483	−	2.43920i	−0.185808	−	0.107276i
$518$	−4.83465	+	2.79129i	−0.212422	+	0.122642i
$519$	−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	$0.148882\pi$
$522$	−0.399225	−	0.230493i	−0.0174736	−	0.0100884i
$523$	8.44178	+	4.87386i	0.369133	+	0.213119i	0.673080	−	0.739570i	$-0.264971\pi$
$523$	8.44178	+	4.87386i	0.369133	+	0.213119i	−0.303946	+	0.952689i	$0.598304\pi$
$524$	20.5390			0.897251
$525$		0			0
$526$	14.2913	−	24.7532i	0.623130	−	1.07929i
$527$	−0.685275	+	0.395644i	−0.0298511	+	0.0172345i
$528$	1.22753	+	0.708712i	0.0534212	+	0.0308427i
$529$	−1.00000	−	1.73205i	−0.0434783	−	0.0753066i
$530$		0			0
$531$	−0.956439			−0.0415059
$532$	−4.33013	+	0.500000i	−0.187735	+	0.0216777i
$533$			11.3739i			0.492657i
$534$	−4.10436	−	7.10895i	−0.177613	−	0.307634i
$535$		0			0
$536$	−3.20871	+	5.55765i	−0.138595	+	0.240054i
$537$	16.6730	−	9.62614i	0.719491	−	0.415398i
$538$	−24.3540	−	14.0608i	−1.04998	−	0.606204i
$539$	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	$0.993145\pi$
$542$	−20.8899	−	12.0608i	−0.897298	−	0.518056i
$543$			38.2867i			1.64304i
$544$	−3.79129			−0.162550
$545$		0			0
$546$	−4.29129	−	7.43273i	−0.183650	−	0.318091i
$547$	−30.4539	−	17.5826i	−1.30212	−	0.751777i	−0.321349	−	0.946961i	$-0.604136\pi$
$547$	−30.4539	−	17.5826i	−1.30212	−	0.751777i	−0.980767	+	0.195184i	$0.937470\pi$
$548$	18.4726	−	10.6652i	0.789110	−	0.455593i
$549$	−1.29129	−	2.23658i	−0.0551108	−	0.0954547i
$550$		0			0
$551$	−1.10436	−	9.56400i	−0.0470472	−	0.407440i
$552$		−	8.20871i		−	0.349386i
$553$	−6.89048	+	3.97822i	−0.293013	+	0.169171i
$554$	9.37386	+	16.2360i	0.398257	+	0.689802i
$555$		0			0
$556$	8.39564	+	14.5417i	0.356055	+	0.616705i
$557$	11.2206	+	6.47822i	0.475432	+	0.274491i	0.718511	−	0.695516i	$-0.244824\pi$
$557$	11.2206	+	6.47822i	0.475432	+	0.274491i	−0.243079	+	0.970007i	$0.578157\pi$
$558$			0.0435608i			0.00184407i
$559$	5.79129			0.244945
$560$		0			0
$561$	−2.68693	+	4.65390i	−0.113442	+	0.196488i
$562$			1.41742i			0.0597904i
$563$			0.626136i			0.0263885i	0.999913	+	0.0131943i	$0.00419998\pi$
$563$			0.626136i			0.0263885i	−0.999913	+	0.0131943i	$0.995800\pi$
$564$	5.52178	−	9.56400i	0.232509	−	0.402717i
$565$		0			0
$566$	10.0608	−	17.4258i	0.422887	−	0.732461i
$567$	8.29875	−	4.79129i	0.348515	−	0.201215i
$568$	−3.96863	+	2.29129i	−0.166520	+	0.0961403i
$569$	27.1652			1.13882			0.569411	−	0.822053i	$-0.307171\pi$
$569$	27.1652			1.13882			0.569411	+	0.822053i	$0.307171\pi$
$570$		0			0
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	−3.28335	+	1.89564i	−0.137284	+	0.0792609i
$573$	10.7915	−	6.23049i	0.450823	−	0.260283i
$574$	−1.18693	+	2.05583i	−0.0495416	+	0.0858085i
$575$		0			0
$576$	−0.104356	+	0.180750i	−0.00434817	+	0.00753125i
$577$			14.0000i			0.582828i	0.956597	+	0.291414i	$0.0941257\pi$
$577$			14.0000i			0.582828i	−0.956597	+	0.291414i	$0.905874\pi$
$578$			2.62614i			0.109233i
$579$	22.1652	−	38.3912i	0.921152	−	1.59548i
$580$		0			0
$581$	0.791288			0.0328282
$582$			2.46099i			0.102011i
$583$	3.14033	+	1.81307i	0.130059	+	0.0750896i
$584$	−0.895644	−	1.55130i	−0.0370620	−	0.0641933i
$585$		0			0
$586$	−1.02178	−	1.76978i	−0.0422094	−	0.0731088i
$587$	39.4002	−	22.7477i	1.62622	−	0.938899i	0.641014	−	0.767529i	$-0.278514\pi$
$587$	39.4002	−	22.7477i	1.62622	−	0.938899i	0.985207	−	0.171370i	$-0.0548195\pi$
$588$			10.7477i			0.443229i
$589$	−0.730493	+	0.542250i	−0.0300994	+	0.0223430i
$590$		0			0
$591$	−22.2042	−	38.4587i	−0.913357	−	1.58198i
$592$	−4.83465	+	2.79129i	−0.198703	+	0.114721i
$593$	−26.1238	−	15.0826i	−1.07278	−	0.619367i	−0.143837	−	0.989601i	$-0.545944\pi$
$593$	−26.1238	−	15.0826i	−1.07278	−	0.619367i	−0.928938	+	0.370234i	$0.879277\pi$
$594$	−1.97822	−	3.42638i	−0.0811673	−	0.140586i
$595$		0			0
$596$	4.74773			0.194474
$597$		−	10.0000i		−	0.409273i
$598$	19.0148	+	10.9782i	0.777574	+	0.448933i
$599$	2.06080	−	3.56940i	0.0842018	−	0.145842i	−0.820849	−	0.571145i	$-0.806499\pi$
$599$	2.06080	−	3.56940i	0.0842018	−	0.145842i	0.905051	+	0.425303i	$0.139833\pi$
$600$		0			0
$601$	−35.9129			−1.46492			−0.732458	−	0.680812i	$-0.761627\pi$
$601$	−35.9129			−1.46492			−0.732458	+	0.680812i	$0.761627\pi$
$602$	1.04678	+	0.604356i	0.0426634	+	0.0246317i
$603$	−1.15995	+	0.669697i	−0.0472368	+	0.0272722i
$604$	−5.87386	+	10.1738i	−0.239004	+	0.413967i
$605$		0			0
$606$		0			0
$607$		−	22.7913i		−	0.925070i	−0.886601	−	0.462535i	$-0.846940\pi$
$607$		−	22.7913i		−	0.925070i	0.886601	−	0.462535i	$-0.153060\pi$
$608$	−4.33013	+	0.500000i	−0.175610	+	0.0202777i
$609$	3.95644			0.160323
$610$		0			0
$611$	14.7695	+	25.5815i	0.597510	+	1.03492i
$612$	−0.685275	−	0.395644i	−0.0277006	−	0.0159930i
$613$	35.0701	−	20.2477i	1.41647	−	0.817798i	0.420481	−	0.907301i	$-0.361861\pi$
$613$	35.0701	−	20.2477i	1.41647	−	0.817798i	0.995987	+	0.0895033i	$0.0285280\pi$
$614$	10.2477	−	17.7496i	0.413565	−	0.716315i
$615$		0			0
$616$	−0.791288			−0.0318819
$617$	28.5788	+	16.5000i	1.15054	+	0.664265i	0.949019	−	0.315219i	$-0.102078\pi$
$617$	28.5788	+	16.5000i	1.15054	+	0.664265i	0.201522	+	0.979484i	$0.435411\pi$
$618$	−20.4231	−	11.7913i	−0.821538	−	0.474315i
$619$	10.6261			0.427100			0.213550	−	0.976932i	$-0.431497\pi$
$619$	10.6261			0.427100			0.213550	+	0.976932i	$0.431497\pi$
$620$		0			0
$621$	−11.4564	+	19.8431i	−0.459731	+	0.796278i
$622$	−12.9904	+	7.50000i	−0.520867	+	0.300723i
$623$	3.96863	+	2.29129i	0.159000	+	0.0917985i
$624$	−4.29129	−	7.43273i	−0.171789	−	0.297547i
$625$		0			0
$626$	15.7477			0.629406
$627$	−2.45505	+	5.66970i	−0.0980453	+	0.226426i
$628$		−	14.9564i		−	0.596827i
$629$	−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	$-0.134921\pi$
$632$	−6.89048	+	3.97822i	−0.274089	+	0.158245i
$633$	1.61888	+	0.934659i	0.0643446	+	0.0371494i
$634$	−9.16515			−0.363995
$635$		0			0
$636$	−4.10436	+	7.10895i	−0.162748	+	0.281888i
$637$	−24.8963	−	14.3739i	−0.986426	−	0.569513i
$638$		−	1.74773i		−	0.0691932i
$639$	−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	$-0.456115\pi$
$642$	6.13763	+	3.54356i	0.242233	+	0.139853i
$643$	22.0797	−	12.7477i	0.870739	−	0.502721i	0.00314512	−	0.999995i	$-0.498999\pi$
$643$	22.0797	−	12.7477i	0.870739	−	0.502721i	0.867594	+	0.497274i	$0.165666\pi$
$644$	2.29129	+	3.96863i	0.0902894	+	0.156386i
$645$		0			0
$646$	−1.89564	−	16.4168i	−0.0745831	−	0.645909i
$647$			14.2087i			0.558602i	0.960204	+	0.279301i	$0.0901027\pi$
$647$			14.2087i			0.558602i	−0.960204	+	0.279301i	$0.909897\pi$
$648$	8.29875	−	4.79129i	0.326006	−	0.188220i
$649$	−1.81307	−	3.14033i	−0.0711692	−	0.123269i
$650$		0			0
$651$	−0.186932	−	0.323775i	−0.00732643	−	0.0126898i
$652$	4.69163	+	2.70871i	0.183738	+	0.106081i
$653$		−	9.33030i		−	0.365123i	−0.983194	−	0.182561i	$-0.941561\pi$
$653$		−	9.33030i		−	0.365123i	0.983194	−	0.182561i	$-0.0584389\pi$
$654$	−28.2087			−1.10305
$655$		0			0
$656$	−1.18693	+	2.05583i	−0.0463419	+	0.0802665i
$657$		−	0.373864i		−	0.0145858i
$658$			6.16515i			0.240343i
$659$	−12.8739	+	22.2982i	−0.501495	+	0.868614i	0.498504	+	0.866887i	$0.333883\pi$
$659$	−12.8739	+	22.2982i	−0.501495	+	0.868614i	−0.999999	+	0.00172659i	$0.999450\pi$
$660$		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	$0.0268321\pi$
$662$	24.1733	−	13.9564i	0.939521	−	0.542432i
$663$	28.1796	−	16.2695i	1.09441	−	0.631855i
$664$	0.791288			0.0307079
$665$		0			0
$666$	−1.16515			−0.0451487
$667$	−8.76555	+	5.06080i	−0.339404	+	0.195955i
$668$	17.7873	−	10.2695i	0.688212	−	0.397339i
$669$	21.3085	−	36.9074i	0.823835	−	1.42692i
$670$		0			0
$671$	4.89564	−	8.47950i	0.188994	−	0.327348i
$672$		−	1.79129i		−	0.0691004i
$673$			1.79129i			0.0690491i	0.999404	+	0.0345245i	$0.0109917\pi$
$673$			1.79129i			0.0690491i	−0.999404	+	0.0345245i	$0.989008\pi$
$674$	−6.66515	+	11.5444i	−0.256732	+	0.444673i
$675$		0			0
$676$	9.95644			0.382940
$677$			47.2432i			1.81570i	0.419292	+	0.907851i	$0.362278\pi$
$677$			47.2432i			1.81570i	−0.419292	+	0.907851i	$0.637722\pi$
$678$	−12.9904	−	7.50000i	−0.498893	−	0.288036i
$679$	−0.686932	−	1.18980i	−0.0263620	−	0.0456604i
$680$		0			0
$681$	17.6869	+	30.6347i	0.677765	+	1.17392i
$682$	−0.143025	+	0.0825757i	−0.00547672	+	0.00316199i
$683$			17.8348i			0.682432i	0.939985	+	0.341216i	$0.110839\pi$
$683$			17.8348i			0.682432i	−0.939985	+	0.341216i	$0.889161\pi$
$684$	−0.834849	−	0.361500i	−0.0319212	−	0.0138223i
$685$		0			0
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	17.5767	−	10.1479i	0.670593	−	0.387167i
$688$	1.04678	+	0.604356i	0.0399079	+	0.0230409i
$689$	−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	$0.444492\pi$
$692$		−	21.0000i		−	0.798300i
$693$	−0.143025	−	0.0825757i	−0.00543308	−	0.00313679i
$694$	8.68693	−	15.0462i	0.329751	−	0.571146i
$695$		0			0
$696$	3.95644			0.149968
$697$	−7.79423	−	4.50000i	−0.295227	−	0.170450i
$698$	12.6289	−	7.29129i	0.478010	−	0.275979i
$699$	−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	$0.893542\pi$
$702$			23.9564i			0.904178i
$703$	−14.5040	−	19.5390i	−0.547027	−	0.736928i
$704$	−0.791288			−0.0298228
$705$		0			0
$706$	−6.87386	−	11.9059i	−0.258701	−	0.448084i
$707$		0			0
$708$	7.10895	−	4.10436i	0.267171	−	0.154251i
$709$	0.373864	−	0.647551i	0.0140407	−	0.0243193i	−0.858920	−	0.512110i	$-0.828864\pi$
$709$	0.373864	−	0.647551i	0.0140407	−	0.0243193i	0.872960	+	0.487791i	$0.162197\pi$
$710$		0			0
$711$	−1.66061			−0.0622776
$712$	3.96863	+	2.29129i	0.148731	+	0.0858696i
$713$	0.828301	+	0.478220i	0.0310201	+	0.0179095i
$714$	6.79129			0.254158
$715$		0			0
$716$	−5.37386	+	9.30780i	−0.200831	+	0.347849i
$717$	11.5067	−	6.64337i	0.429724	−	0.248101i
$718$	12.7342	+	7.35208i	0.475235	+	0.274377i
$719$	3.08258	+	5.33918i	0.114961	+	0.199118i	0.917764	−	0.397126i	$-0.129992\pi$
$719$	3.08258	+	5.33918i	0.114961	+	0.199118i	−0.802803	+	0.596244i	$0.796659\pi$
$720$		0			0
$721$	13.1652			0.490296
$722$	−4.33013	−	18.5000i	−0.161151	−	0.688499i
$723$			21.8693i			0.813329i
$724$	−10.6869	−	18.5103i	−0.397177	−	0.687930i
$725$		0			0
$726$	9.29129	−	16.0930i	0.344832	−	0.597267i
$727$	12.2674	−	7.08258i	0.454972	−	0.262678i	−0.254956	−	0.966953i	$-0.582061\pi$
$727$	12.2674	−	7.08258i	0.454972	−	0.262678i	0.709928	+	0.704275i	$0.248728\pi$
$728$	4.14938	+	2.39564i	0.153786	+	0.0887885i
$729$	−24.8693			−0.921086
$730$		0			0
$731$	−2.29129	+	3.96863i	−0.0847463	+	0.146785i
$732$	19.1956	+	11.0826i	0.709489	+	0.409624i
$733$			14.7477i			0.544720i	0.962195	+	0.272360i	$0.0878041\pi$
$733$			14.7477i			0.544720i	−0.962195	+	0.272360i	$0.912196\pi$
$734$	−4.20871			−0.155346
$735$		0			0
$736$	2.29129	+	3.96863i	0.0844580	+	0.146286i
$737$	−4.39770	−	2.53901i	−0.161991	−	0.0935258i
$738$	−0.429076	+	0.247727i	−0.0157945	+	0.00911896i
$739$	−4.12614	−	7.14668i	−0.151782	−	0.262895i	0.780100	−	0.625654i	$-0.215168\pi$
$739$	−4.12614	−	7.14668i	−0.151782	−	0.262895i	−0.931883	+	0.362760i	$0.881835\pi$
$740$		0			0
$741$	30.0390	−	22.2982i	1.10351	−	0.819144i
$742$		−	4.58258i		−	0.168232i
$743$	−24.7532	+	14.2913i	−0.908108	+	0.524297i	−0.879822	−	0.475303i	$-0.842338\pi$
$743$	−24.7532	+	14.2913i	−0.908108	+	0.524297i	−0.0282862	+	0.999600i	$0.509005\pi$
$744$	−0.186932	−	0.323775i	−0.00685325	−	0.0118702i
$745$		0			0
$746$	3.81307	+	6.60443i	0.139606	+	0.241805i
$747$	0.143025	+	0.0825757i	0.00523302	+	0.00302129i
$748$		−	3.00000i		−	0.109691i
$749$	−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	$0.239414\pi$
$752$			6.16515i			0.224820i
$753$			50.3739i			1.83573i
$754$	−5.29129	+	9.16478i	−0.192697	+	0.333762i
$755$		0			0
$756$	−2.50000	+	4.33013i	−0.0909241	+	0.157485i
$757$	15.8069	−	9.12614i	0.574513	−	0.331695i	−0.184437	−	0.982844i	$-0.559046\pi$
$757$	15.8069	−	9.12614i	0.574513	−	0.331695i	0.758950	+	0.651149i	$0.225713\pi$
$758$	−20.0616	+	11.5826i	−0.728670	+	0.420698i
$759$	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	$0.0947194\pi$
$762$	25.4008	−	14.6652i	0.920173	−	0.531262i
$763$	13.6379	−	7.87386i	0.493726	−	0.285053i
$764$	−3.47822	+	6.02445i	−0.125838	+	0.217957i
$765$		0			0
$766$	2.29129	−	3.96863i	0.0827876	−	0.143392i
$767$			21.9564i			0.792801i
$768$		−	1.79129i		−	0.0646375i
$769$	7.16515	−	12.4104i	0.258382	−	0.447531i	−0.707427	−	0.706787i	$-0.750144\pi$
$769$	7.16515	−	12.4104i	0.258382	−	0.447531i	0.965809	+	0.259256i	$0.0834774\pi$
$770$		0			0
$771$	−28.2867			−1.01872
$772$			24.7477i			0.890690i
$773$	13.2764	+	7.66515i	0.477520	+	0.275696i	0.719382	−	0.694614i	$-0.244425\pi$
$773$	13.2764	+	7.66515i	0.477520	+	0.275696i	−0.241862	+	0.970311i	$0.577758\pi$
$774$	0.126136	+	0.218475i	0.00453388	+	0.00785291i
$775$		0			0
$776$	−0.686932	−	1.18980i	−0.0246594	−	0.0427114i
$777$	8.66025	−	5.00000i	0.310685	−	0.179374i
$778$		−	32.3739i		−	1.16066i
$779$	−9.49545	−	4.11165i	−0.340210	−	0.147315i
$780$		0			0
$781$	−1.81307	−	3.14033i	−0.0648767	−	0.112370i
$782$	−15.0462	+	8.68693i	−0.538051	+	0.310644i
$783$	−9.56400	−	5.52178i	−0.341790	−	0.197332i
$784$	−3.00000	−	5.19615i	−0.107143	−	0.185577i
$785$		0			0
$786$	−36.7913			−1.31230
$787$			3.74773i			0.133592i	0.997767	+	0.0667960i	$0.0212777\pi$
$787$			3.74773i			0.133592i	−0.997767	+	0.0667960i	$0.978722\pi$
$788$	21.4699	+	12.3956i	0.764833	+	0.441577i
$789$	−25.5998	+	44.3402i	−0.911377	+	1.57855i
$790$		0			0
$791$	8.37386			0.297740
$792$	−0.143025	−	0.0825757i	−0.00508218	−	0.00293420i
$793$	−51.3438	+	29.6434i	−1.82327	+	1.05267i
$794$	−10.2913	+	17.8250i	−0.365224	+	0.632587i
$795$		0			0
$796$	2.79129	+	4.83465i	0.0989346	+	0.171360i
$797$		−	6.46099i		−	0.228860i	−0.993431	−	0.114430i	$-0.963496\pi$
$797$		−	6.46099i		−	0.228860i	0.993431	−	0.114430i	$-0.0365041\pi$
$798$	7.75650	−	0.895644i	0.274577	−	0.0317055i
$799$	−23.3739			−0.826908
$800$		0			0
$801$	0.478220	+	0.828301i	0.0168971	+	0.0292666i
$802$	10.3923	+	6.00000i	0.366965	+	0.211867i
$803$	1.22753	−	0.708712i	0.0433184	−	0.0250099i
$804$	5.74773	−	9.95536i	0.202707	−	0.351098i
$805$		0			0
$806$	1.00000			0.0352235
$807$	43.6250	+	25.1869i	1.53567	+	0.886622i
$808$		0			0
$809$	−29.5390			−1.03854			−0.519268	−	0.854611i	$-0.673795\pi$
$809$	−29.5390			−1.03854			−0.519268	+	0.854611i	$0.673795\pi$
$810$		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	$-0.104569\pi$
$812$	−1.91280	+	1.10436i	−0.0671261	+	0.0387553i
$813$	37.4198	+	21.6044i	1.31237	+	0.757698i
$814$	−2.20871	−	3.82560i	−0.0774153	−	0.134087i
$815$		0			0
$816$	6.79129			0.237743
$817$	−2.09355	+	4.83485i	−0.0732441	+	0.169150i
$818$			10.0000i			0.349642i
$819$	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	$0.168501\pi$
$822$	−33.0897	+	19.1044i	−1.15414	+	0.666341i
$823$	8.01270	+	4.62614i	0.279305	+	0.161257i	0.633109	−	0.774063i	$-0.281779\pi$
$823$	8.01270	+	4.62614i	0.279305	+	0.161257i	−0.353804	+	0.935320i	$0.615112\pi$
$824$	13.1652			0.458630
$825$		0			0
$826$	−2.29129	+	3.96863i	−0.0797241	+	0.138086i
$827$	−14.6470	−	8.45644i	−0.509325	−	0.294059i	0.223231	−	0.974766i	$-0.428340\pi$
$827$	−14.6470	−	8.45644i	−0.509325	−	0.294059i	−0.732556	+	0.680706i	$0.761673\pi$
$828$			0.956439i			0.0332386i
$829$	0.539015			0.0187208			0.00936038	−	0.999956i	$-0.497020\pi$
$829$	0.539015			0.0187208			0.00936038	+	0.999956i	$0.497020\pi$
$830$		0			0
$831$	−16.7913	−	29.0834i	−0.582483	−	1.00889i
$832$	4.14938	+	2.39564i	0.143854	+	0.0830540i
$833$	19.7001	−	11.3739i	0.682568	−	0.394081i
$834$	−15.0390	−	26.0483i	−0.520758	−	0.901980i
$835$		0			0
$836$	−0.395644	−	3.42638i	−0.0136836	−	0.118504i
$837$			1.04356i			0.0360707i
$838$	−4.11165	+	2.37386i	−0.142035	+	0.0820038i
$839$	14.5218	+	25.1525i	0.501348	+	0.868359i	0.999999	+	0.00155670i	$0.000495513\pi$
$839$	14.5218	+	25.1525i	0.501348	+	0.868359i	−0.498651	+	0.866803i	$0.666171\pi$
$840$		0			0
$841$	12.0608	+	20.8899i	0.415889	+	0.720342i
$842$	−17.3205	−	10.0000i	−0.596904	−	0.344623i
$843$		−	2.53901i		−	0.0874483i
$844$	−1.04356			−0.0359208
$845$		0			0
$846$	−0.643371	+	1.11435i	−0.0221196	+	0.0383122i
$847$			10.3739i			0.356450i
$848$		−	4.58258i		−	0.157366i
$849$	−18.0218	+	31.2146i	−0.618506	+	1.07128i
$850$		0			0
$851$	−12.7913	+	22.1552i	−0.438480	+	0.759469i
$852$	7.10895	−	4.10436i	0.243549	−	0.140613i
$853$	−30.3407	+	17.5172i	−1.03885	+	0.599779i	−0.919507	−	0.393075i	$-0.871411\pi$
$853$	−30.3407	+	17.5172i	−1.03885	+	0.599779i	−0.119341	+	0.992853i	$0.538078\pi$
$854$	−12.3739			−0.423425
$855$		0			0
$856$	−3.95644			−0.135228
$857$	2.59808	−	1.50000i	0.0887486	−	0.0512390i	−0.454969	−	0.890507i	$-0.650350\pi$
$857$	2.59808	−	1.50000i	0.0887486	−	0.0512390i	0.543718	+	0.839268i	$0.317016\pi$
$858$	5.88143	−	3.39564i	0.200789	−	0.115925i
$859$	−16.8521	+	29.1887i	−0.574986	+	0.995904i	0.421058	+	0.907034i	$0.361659\pi$
$859$	−16.8521	+	29.1887i	−0.574986	+	0.995904i	−0.996043	+	0.0888704i	$0.971674\pi$
$860$		0			0
$861$	2.12614	−	3.68258i	0.0724585	−	0.125502i
$862$			12.7913i			0.435673i
$863$			13.5826i			0.462356i	0.972911	+	0.231178i	$0.0742580\pi$
$863$			13.5826i			0.462356i	−0.972911	+	0.231178i	$0.925742\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$		0			0
$866$	−38.9129			−1.32231
$867$		−	4.70417i		−	0.159762i
$868$	0.180750	+	0.104356i	0.00613506	+	0.00354208i
$869$	−3.14792	−	5.45235i	−0.106786	−	0.184958i
$870$		0			0
$871$	15.3739	+	26.6283i	0.520923	+	0.902266i
$872$	13.6379	−	7.87386i	0.461839	−	0.266643i
$873$		−	0.286742i		−	0.00970475i
$874$	−16.0390	+	11.9059i	−0.542528	+	0.402722i
$875$		0			0
$876$	1.60436	+	2.77883i	0.0542062	+	0.0938878i
$877$	−24.6778	+	14.2477i	−0.833310	+	0.481112i	−0.854985	−	0.518654i	$-0.826433\pi$
$877$	−24.6778	+	14.2477i	−0.833310	+	0.481112i	0.0216749	+	0.999765i	$0.493100\pi$
$878$	9.81233	+	5.66515i	0.331150	+	0.191190i
$879$	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	$0.479657\pi$
$882$		−	1.25227i		−	0.0421662i
$883$	−2.37960	−	1.37386i	−0.0800800	−	0.0462342i	0.459425	−	0.888216i	$-0.348055\pi$
$883$	−2.37960	−	1.37386i	−0.0800800	−	0.0462342i	−0.539505	+	0.841982i	$0.681389\pi$
$884$	−9.08258	+	15.7315i	−0.305480	+	0.529107i
$885$		0			0
$886$	−24.0000			−0.806296
$887$	−6.16748	−	3.56080i	−0.207084	−	0.119560i	0.392872	−	0.919593i	$-0.371482\pi$
$887$	−6.16748	−	3.56080i	−0.207084	−	0.119560i	−0.599955	+	0.800034i	$0.704815\pi$
$888$	8.66025	−	5.00000i	0.290619	−	0.167789i
$889$	−8.18693	+	14.1802i	−0.274581	+	0.475588i
$890$		0			0
$891$	3.79129	+	6.56670i	0.127013	+	0.219993i
$892$			23.7913i			0.796591i
$893$	−26.6959	+	3.08258i	−0.893344	+	0.103154i
$894$	−8.50455			−0.284435
$895$		0			0
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$	−34.0610	−	19.6652i	−1.13727	−	0.656600i
$898$	28.8649	−	16.6652i	0.963234	−	0.556123i
$899$	−0.230493	+	0.399225i	−0.00768736	+	0.0133149i
$900$		0			0
$901$	17.3739			0.578807
$902$	−1.62675	−	0.939205i	−0.0541649	−	0.0312721i
$903$	−1.87508	−	1.08258i	−0.0623986	−	0.0360259i
$904$	8.37386			0.278511
$905$		0			0
$906$	10.5218	−	18.2243i	0.349563	−	0.605460i
$907$	30.1977	−	17.4347i	1.00270	−	0.578908i	0.0936530	−	0.995605i	$-0.470146\pi$
$907$	30.1977	−	17.4347i	1.00270	−	0.578908i	0.909046	+	0.416697i	$0.136812\pi$
$908$	−17.1020	−	9.87386i	−0.567551	−	0.327676i
$909$		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	$0.366045\pi$
$912$	7.75650	−	0.895644i	0.256844	−	0.0296577i
$913$			0.626136i			0.0207221i
$914$	3.37386	+	5.84370i	0.111597	+	0.193293i
$915$		0			0
$916$	−5.66515	+	9.81233i	−0.187182	+	0.324209i
$917$	17.7873	−	10.2695i	0.587389	−	0.339129i
$918$	−16.4168	−	9.47822i	−0.541834	−	0.312828i
$919$	42.2087			1.39234			0.696168	−	0.717878i	$-0.254887\pi$
$919$	42.2087			1.39234			0.696168	+	0.717878i	$0.254887\pi$
$920$		0			0
$921$	−18.3566	+	31.7946i	−0.604871	+	1.04767i
$922$	−7.10895	−	4.10436i	−0.234121	−	0.135170i
$923$			21.9564i			0.722705i
$924$	1.41742			0.0466298
$925$		0			0
$926$	2.47822	+	4.29240i	0.0814393	+	0.141057i
$927$	2.37960	+	1.37386i	0.0781564	+	0.0451236i
$928$	−1.91280	+	1.10436i	−0.0627908	+	0.0362523i
$929$	26.0608	+	45.1386i	0.855027	+	1.48095i	0.876620	+	0.481183i	$0.159793\pi$
$929$	26.0608	+	45.1386i	0.855027	+	1.48095i	−0.0215930	+	0.999767i	$0.506874\pi$
$930$		0			0
$931$	21.0000	−	15.5885i	0.688247	−	0.510891i
$932$		−	9.16515i		−	0.300215i
$933$	23.2695	−	13.4347i	0.761810	−	0.439831i
$934$	12.1652	+	21.0707i	0.398056	+	0.689453i
$935$		0			0
$936$	0.500000	+	0.866025i	0.0163430	+	0.0283069i
$937$	30.4162	+	17.5608i	0.993654	+	0.573686i	0.906364	−	0.422497i	$-0.138846\pi$
$937$	30.4162	+	17.5608i	0.993654	+	0.573686i	0.0872892	+	0.996183i	$0.472180\pi$
$938$			6.41742i			0.209536i
$939$	−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	$-0.00446168\pi$
$942$			26.7913i			0.872907i
$943$			10.8784i			0.354250i
$944$	−2.29129	+	3.96863i	−0.0745751	+	0.129168i
$945$		0			0
$946$	−0.478220	+	0.828301i	−0.0155483	+	0.0269304i
$947$	−16.8160	+	9.70871i	−0.546446	+	0.315491i	−0.747687	−	0.664051i	$-0.768836\pi$
$947$	−16.8160	+	9.70871i	−0.546446	+	0.315491i	0.201241	+	0.979542i	$0.435502\pi$
$948$	12.3428	−	7.12614i	0.400876	−	0.231446i
$949$	−8.58258			−0.278602
$950$		0			0
$951$	16.4174			0.532371
$952$	−3.28335	+	1.89564i	−0.106414	+	0.0614382i
$953$	−21.7559	+	12.5608i	−0.704744	+	0.406884i	−0.809112	−	0.587655i	$-0.800051\pi$
$953$	−21.7559	+	12.5608i	−0.704744	+	0.406884i	0.104368	+	0.994539i	$0.466718\pi$
$954$	0.478220	−	0.828301i	0.0154829	−	0.0268172i
$955$		0			0
$956$	−3.70871	+	6.42368i	−0.119948	+	0.207757i
$957$			3.13068i			0.101201i
$958$		−	4.25227i		−	0.137385i
$959$	10.6652	−	18.4726i	0.344396	−	0.596511i
$960$		0			0
$961$	−30.9564			−0.998595
$962$			26.7477i			0.862381i
$963$	−0.715126	−	0.412878i	−0.0230446	−	0.0133048i
$964$	−6.10436	−	10.5731i	−0.196608	−	0.340535i
$965$		0			0
$966$	−4.10436	−	7.10895i	−0.132055	−	0.228727i
$967$	11.3259	−	6.53901i	0.364217	−	0.210281i	−0.306712	−	0.951802i	$-0.599229\pi$
$967$	11.3259	−	6.53901i	0.364217	−	0.210281i	0.670929	+	0.741522i	$0.265896\pi$
$968$			10.3739i			0.333429i
$969$	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	$0.562059\pi$
$972$	−1.87508	+	1.08258i	−0.0601431	+	0.0347236i
$973$	14.5417	+	8.39564i	0.466185	+	0.269152i
$974$	11.5000	+	19.9186i	0.368484	+	0.638233i
$975$		0			0
$976$	−12.3739			−0.396078
$977$			18.6261i			0.595903i	0.954581	+	0.297951i	$0.0963034\pi$
$977$			18.6261i			0.595903i	−0.954581	+	0.297951i	$0.903697\pi$
$978$	−8.40405	−	4.85208i	−0.268732	−	0.155153i
$979$	−1.81307	+	3.14033i	−0.0579459	+	0.100365i
$980$		0			0
$981$	3.28674			0.104938
$982$	35.1455	+	20.2913i	1.12154	+	0.647521i
$983$	−35.0025	+	20.2087i	−1.11641	+	0.644558i	−0.940481	−	0.339846i	$-0.889625\pi$
$983$	−35.0025	+	20.2087i	−1.11641	+	0.644558i	−0.175926	+	0.984403i	$0.556292\pi$
$984$	2.12614	−	3.68258i	0.0677788	−	0.117396i
$985$		0			0
$986$	−4.18693	−	7.25198i	−0.133339	−	0.230950i
$987$		−	11.0436i		−	0.351520i
$988$	−8.29875	+	19.1652i	−0.264019	+	0.609725i
$989$	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	$0.745667\pi$
$992$	0.180750	+	0.104356i	0.00573882	+	0.00331331i
$993$	−43.3013	+	25.0000i	−1.37412	+	0.793351i
$994$	−2.29129	+	3.96863i	−0.0726752	+	0.125877i
$995$		0			0
$996$	−1.41742			−0.0449128
$997$	0.866025	+	0.500000i	0.0274273	+	0.0158352i	0.513651	−	0.857999i	$-0.328293\pi$
$997$	0.866025	+	0.500000i	0.0274273	+	0.0158352i	−0.486224	+	0.873834i	$0.661626\pi$
$998$	15.0085	+	8.66515i	0.475085	+	0.274291i
$999$	−27.9129			−0.883124

Twists

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

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

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.j (of order \(6\), degree \(2\), not minimal)

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

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