LMFDB - Embedded newform 950.2.q.f.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.8
Character	$\chi$	$=$	950.107
Dual form			950.2.q.f.293.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.824123 - 3.07567i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.59208 - 2.75757i) q^{6} +(3.29328 + 3.29328i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-6.18248 - 3.56945i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.824123 - 3.07567i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.59208 - 2.75757i) q^{6} +(3.29328 + 3.29328i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-6.18248 - 3.56945i) q^{9} +1.07205 q^{11} +(2.25155 - 2.25155i) q^{12} +(-0.991808 + 0.265754i) q^{13} +(2.32870 + 4.03343i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.62141 - 6.05120i) q^{17} +(-5.04797 - 5.04797i) q^{18} +(3.41662 - 2.70679i) q^{19} +(12.8431 - 7.41497i) q^{21} +(1.03552 + 0.277467i) q^{22} +(0.642278 + 2.39702i) q^{23} +(2.75757 - 1.59208i) q^{24} -1.02680 q^{26} +(-9.31894 + 9.31894i) q^{27} +(1.20542 + 4.49871i) q^{28} +(2.98775 - 5.17494i) q^{29} -0.124795i q^{31} +(0.258819 + 0.965926i) q^{32} +(0.883501 - 3.29727i) q^{33} +(3.13233 - 5.42535i) q^{34} +(-3.56945 - 6.18248i) q^{36} +(-3.61481 + 3.61481i) q^{37} +(4.00077 - 1.73028i) q^{38} +3.26949i q^{39} +(-4.79061 + 2.76586i) q^{41} +(14.3246 - 3.83827i) q^{42} +(-10.2706 - 2.75200i) q^{43} +(0.928423 + 0.536025i) q^{44} +2.48157i q^{46} +(-9.50178 + 2.54600i) q^{47} +(3.07567 - 0.824123i) q^{48} +14.6914i q^{49} +(-17.2752 - 9.97386i) q^{51} +(-0.991808 - 0.265754i) q^{52} +(1.72808 - 0.463037i) q^{53} +(-11.4133 + 6.58949i) q^{54} +4.65740i q^{56} +(-5.50949 - 12.7391i) q^{57} +(4.22532 - 4.22532i) q^{58} +(5.41804 + 9.38432i) q^{59} +(-3.14151 + 5.44125i) q^{61} +(0.0322994 - 0.120543i) q^{62} +(-8.60542 - 32.1159i) q^{63} +1.00000i q^{64} +(1.70679 - 2.95625i) q^{66} +(3.60991 + 13.4724i) q^{67} +(4.42978 - 4.42978i) q^{68} +7.90174 q^{69} +(9.49898 - 5.48424i) q^{71} +(-1.84769 - 6.89566i) q^{72} +(9.56263 + 2.56230i) q^{73} +(-4.42722 + 2.55606i) q^{74} +(4.31227 - 0.635843i) q^{76} +(3.53056 + 3.53056i) q^{77} +(-0.846205 + 3.15808i) q^{78} +(-3.35422 - 5.80968i) q^{79} +(10.2737 + 17.7945i) q^{81} +(-5.34323 + 1.43171i) q^{82} +(-3.38153 + 3.38153i) q^{83} +14.8299 q^{84} +(-9.20836 - 5.31645i) q^{86} +(-13.4541 - 13.4541i) q^{87} +(0.758054 + 0.758054i) q^{88} +(2.05933 - 3.56686i) q^{89} +(-4.14151 - 2.39110i) q^{91} +(-0.642278 + 2.39702i) q^{92} +(-0.383829 - 0.102847i) q^{93} -9.83697 q^{94} +3.18417 q^{96} +(-9.27072 - 2.48408i) q^{97} +(-3.80242 + 14.1908i) q^{98} +(-6.62793 - 3.82664i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{6}+O(q^{10}) $ 32 * q + 4 * q^6	$ 32 q + 4 q^{6} + 72 q^{11} + 16 q^{16} + 60 q^{21} + 8 q^{26} - 28 q^{36} - 84 q^{41} - 84 q^{51} - 52 q^{61} - 24 q^{71} + 16 q^{76} + 64 q^{81} - 36 q^{86} - 84 q^{91} + 8 q^{96}+O(q^{100}) $ 32 * q + 4 * q^6 + 72 * q^11 + 16 * q^16 + 60 * q^21 + 8 * q^26 - 28 * q^36 - 84 * q^41 - 84 * q^51 - 52 * q^61 - 24 * q^71 + 16 * q^76 + 64 * q^81 - 36 * q^86 - 84 * q^91 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	0.824123	−	3.07567i	0.475807	−	1.77574i	−0.142493	−	0.989796i	$-0.545512\pi$
$3$	0.824123	−	3.07567i	0.475807	−	1.77574i	0.618301	−	0.785942i	$-0.287821\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	1.59208	−	2.75757i	0.649965	−	1.12577i
$7$	3.29328	+	3.29328i	1.24474	+	1.24474i	0.958011	+	0.286733i	$0.0925692\pi$
$7$	3.29328	+	3.29328i	1.24474	+	1.24474i	0.286733	+	0.958011i	$0.407431\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−6.18248	−	3.56945i	−2.06083	−	1.18982i
$10$		0			0
$11$	1.07205			0.323235			0.161618	−	0.986853i	$-0.448329\pi$
$11$	1.07205			0.323235			0.161618	+	0.986853i	$0.448329\pi$
$12$	2.25155	−	2.25155i	0.649965	−	0.649965i
$13$	−0.991808	+	0.265754i	−0.275078	+	0.0737069i	−0.393721	−	0.919230i	$-0.628812\pi$
$13$	−0.991808	+	0.265754i	−0.275078	+	0.0737069i	0.118643	+	0.992937i	$0.462146\pi$
$14$	2.32870	+	4.03343i	0.622372	+	1.07798i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.62141	−	6.05120i	0.393250	−	1.46763i	−0.431489	−	0.902118i	$-0.642012\pi$
$17$	1.62141	−	6.05120i	0.393250	−	1.46763i	0.824740	−	0.565513i	$-0.191322\pi$
$18$	−5.04797	−	5.04797i	−1.18982	−	1.18982i
$19$	3.41662	−	2.70679i	0.783826	−	0.620981i
$19$	3.41662	−	2.70679i	0.783826	−	0.620981i
$20$		0			0
$21$	12.8431	−	7.41497i	2.80260	−	1.61808i
$22$	1.03552	+	0.277467i	0.220774	+	0.0591562i
$23$	0.642278	+	2.39702i	0.133924	+	0.499812i	1.00000		0.000100572i	$-3.20132e-5\pi$
$23$	0.642278	+	2.39702i	0.133924	+	0.499812i	−0.866076	+	0.499913i	$0.833365\pi$
$24$	2.75757	−	1.59208i	0.562886	−	0.324983i
$25$		0			0
$26$	−1.02680			−0.201371
$27$	−9.31894	+	9.31894i	−1.79343	+	1.79343i
$28$	1.20542	+	4.49871i	0.227804	+	0.850176i
$29$	2.98775	−	5.17494i	0.554811	−	0.960961i	−0.443107	−	0.896469i	$-0.646124\pi$
$29$	2.98775	−	5.17494i	0.554811	−	0.960961i	0.997918	−	0.0644926i	$-0.0205429\pi$
$30$		0			0
$31$		−	0.124795i		−	0.0224139i	−0.999937	−	0.0112070i	$-0.996433\pi$
$31$		−	0.124795i		−	0.0224139i	0.999937	−	0.0112070i	$-0.00356736\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	0.883501	−	3.29727i	0.153798	−	0.573981i
$34$	3.13233	−	5.42535i	0.537190	−	0.930440i
$35$		0			0
$36$	−3.56945	−	6.18248i	−0.594909	−	1.03041i
$37$	−3.61481	+	3.61481i	−0.594271	+	0.594271i	−0.938782	−	0.344511i	$-0.888045\pi$
$37$	−3.61481	+	3.61481i	−0.594271	+	0.594271i	0.344511	+	0.938782i	$0.388045\pi$
$38$	4.00077	−	1.73028i	0.649010	−	0.280688i
$39$			3.26949i			0.523537i
$40$		0			0
$41$	−4.79061	+	2.76586i	−0.748168	+	0.431955i	−0.825031	−	0.565087i	$-0.808843\pi$
$41$	−4.79061	+	2.76586i	−0.748168	+	0.431955i	0.0768637	+	0.997042i	$0.475509\pi$
$42$	14.3246	−	3.83827i	2.21034	−	0.592258i
$43$	−10.2706	−	2.75200i	−1.56625	−	0.419676i	−0.631615	−	0.775282i	$-0.717608\pi$
$43$	−10.2706	−	2.75200i	−1.56625	−	0.419676i	−0.934636	+	0.355606i	$0.884274\pi$
$44$	0.928423	+	0.536025i	0.139965	+	0.0808089i
$45$		0			0
$46$			2.48157i			0.365888i
$47$	−9.50178	+	2.54600i	−1.38598	+	0.371372i	−0.873289	−	0.487203i	$-0.838017\pi$
$47$	−9.50178	+	2.54600i	−1.38598	+	0.371372i	−0.512689	+	0.858574i	$0.671351\pi$
$48$	3.07567	−	0.824123i	0.443934	−	0.118952i
$49$			14.6914i			2.09877i
$50$		0			0
$51$	−17.2752	−	9.97386i	−2.41902	−	1.39662i
$52$	−0.991808	−	0.265754i	−0.137539	−	0.0368535i
$53$	1.72808	−	0.463037i	0.237370	−	0.0636031i	−0.138173	−	0.990408i	$-0.544123\pi$
$53$	1.72808	−	0.463037i	0.237370	−	0.0636031i	0.375543	+	0.926805i	$0.377456\pi$
$54$	−11.4133	+	6.58949i	−1.55316	+	0.896716i
$55$		0			0
$56$			4.65740i			0.622372i
$57$	−5.50949	−	12.7391i	−0.729749	−	1.68734i
$58$	4.22532	−	4.22532i	0.554811	−	0.554811i
$59$	5.41804	+	9.38432i	0.705369	+	1.22173i	0.966558	+	0.256447i	$0.0825520\pi$
$59$	5.41804	+	9.38432i	0.705369	+	1.22173i	−0.261189	+	0.965288i	$0.584115\pi$
$60$		0			0
$61$	−3.14151	+	5.44125i	−0.402229	+	0.696680i	−0.993995	−	0.109429i	$-0.965098\pi$
$61$	−3.14151	+	5.44125i	−0.402229	+	0.696680i	0.591766	+	0.806110i	$0.298431\pi$
$62$	0.0322994	−	0.120543i	0.00410203	−	0.0153090i
$63$	−8.60542	−	32.1159i	−1.08418	−	4.04622i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	1.70679	−	2.95625i	0.210092	−	0.363890i
$67$	3.60991	+	13.4724i	0.441021	+	1.64591i	0.726234	+	0.687448i	$0.241269\pi$
$67$	3.60991	+	13.4724i	0.441021	+	1.64591i	−0.285213	+	0.958464i	$0.592064\pi$
$68$	4.42978	−	4.42978i	0.537190	−	0.537190i
$69$	7.90174			0.951258
$70$		0			0
$71$	9.49898	−	5.48424i	1.12732	−	0.650859i	0.184061	−	0.982915i	$-0.441076\pi$
$71$	9.49898	−	5.48424i	1.12732	−	0.650859i	0.943260	+	0.332056i	$0.107742\pi$
$72$	−1.84769	−	6.89566i	−0.217752	−	0.812661i
$73$	9.56263	+	2.56230i	1.11922	+	0.299895i	0.770568	−	0.637357i	$-0.219972\pi$
$73$	9.56263	+	2.56230i	1.11922	+	0.299895i	0.348653	+	0.937252i	$0.386639\pi$
$74$	−4.42722	+	2.55606i	−0.514654	+	0.297136i
$75$		0			0
$76$	4.31227	−	0.635843i	0.494652	−	0.0729362i
$77$	3.53056	+	3.53056i	0.402345	+	0.402345i
$78$	−0.846205	+	3.15808i	−0.0958139	+	0.357582i
$79$	−3.35422	−	5.80968i	−0.377379	−	0.653640i	0.613301	−	0.789849i	$-0.289841\pi$
$79$	−3.35422	−	5.80968i	−0.377379	−	0.653640i	−0.990680	+	0.136210i	$0.956508\pi$
$80$		0			0
$81$	10.2737	+	17.7945i	1.14152	+	1.97717i
$82$	−5.34323	+	1.43171i	−0.590061	+	0.158106i
$83$	−3.38153	+	3.38153i	−0.371171	+	0.371171i	−0.867903	−	0.496733i	$-0.834533\pi$
$83$	−3.38153	+	3.38153i	−0.371171	+	0.371171i	0.496733	+	0.867903i	$0.334533\pi$
$84$	14.8299			1.61808
$85$		0			0
$86$	−9.20836	−	5.31645i	−0.992964	−	0.573288i
$87$	−13.4541	−	13.4541i	−1.44243	−	1.44243i
$88$	0.758054	+	0.758054i	0.0808089	+	0.0808089i
$89$	2.05933	−	3.56686i	0.218288	−	0.378086i	−0.735997	−	0.676985i	$-0.763286\pi$
$89$	2.05933	−	3.56686i	0.218288	−	0.378086i	0.954285	+	0.298899i	$0.0966194\pi$
$90$		0			0
$91$	−4.14151	−	2.39110i	−0.434148	−	0.250655i
$92$	−0.642278	+	2.39702i	−0.0669622	+	0.249906i
$93$	−0.383829	−	0.102847i	−0.0398012	−	0.0106647i
$94$	−9.83697			−1.01461
$95$		0			0
$96$	3.18417			0.324983
$97$	−9.27072	−	2.48408i	−0.941299	−	0.252220i	−0.244633	−	0.969616i	$-0.578667\pi$
$97$	−9.27072	−	2.48408i	−0.941299	−	0.252220i	−0.696666	+	0.717396i	$0.745334\pi$
$98$	−3.80242	+	14.1908i	−0.384102	+	1.43349i
$99$	−6.62793	−	3.82664i	−0.666132	−	0.384591i
$100$		0			0
$101$	0.398687	−	0.690546i	0.0396708	−	0.0687119i	−0.845508	−	0.533962i	$-0.820702\pi$
$101$	0.398687	−	0.690546i	0.0396708	−	0.0687119i	0.885179	+	0.465250i	$0.154036\pi$
$102$	−14.1052	−	14.1052i	−1.39662	−	1.39662i
$103$	6.27965	+	6.27965i	0.618752	+	0.618752i	0.945211	−	0.326459i	$-0.105856\pi$
$103$	6.27965	+	6.27965i	0.618752	+	0.618752i	−0.326459	+	0.945211i	$0.605856\pi$
$104$	−0.889231	−	0.513398i	−0.0871962	−	0.0503428i
$105$		0			0
$106$	1.78904			0.173767
$107$	1.96848	−	1.96848i	0.190300	−	0.190300i	−0.605526	−	0.795826i	$-0.707037\pi$
$107$	1.96848	−	1.96848i	0.190300	−	0.190300i	0.795826	+	0.605526i	$0.207037\pi$
$108$	−12.7299	+	3.41097i	−1.22494	+	0.328221i
$109$	0.951628	+	1.64827i	0.0911495	+	0.157875i	0.907995	−	0.418981i	$-0.137613\pi$
$109$	0.951628	+	1.64827i	0.0911495	+	0.157875i	−0.816846	+	0.576856i	$0.804279\pi$
$110$		0			0
$111$	8.13891	+	14.0970i	0.772511	+	1.33803i
$112$	−1.20542	+	4.49871i	−0.113902	+	0.425088i
$113$	−9.16841	−	9.16841i	−0.862491	−	0.862491i	0.129136	−	0.991627i	$-0.458780\pi$
$113$	−9.16841	−	9.16841i	−0.862491	−	0.862491i	−0.991627	+	0.129136i	$0.958780\pi$
$114$	−2.02463	−	13.7310i	−0.189624	−	1.28603i
$115$		0			0
$116$	5.17494	−	2.98775i	0.480481	−	0.277406i
$117$	7.08043	+	1.89719i	0.654586	+	0.175396i
$118$	2.80458	+	10.4669i	0.258183	+	0.963552i
$119$	25.2681	−	14.5885i	2.31632	−	1.33733i
$120$		0			0
$121$	−9.85071			−0.895519
$122$	−4.44276	+	4.44276i	−0.402229	+	0.402229i
$123$	4.55882	+	17.0137i	0.411055	+	1.53408i
$124$	0.0623977	−	0.108076i	0.00560348	−	0.00970550i
$125$		0			0
$126$		−	33.2488i		−	2.96204i
$127$	0.289180	+	1.07923i	0.0256606	+	0.0957666i	0.977569	−	0.210618i	$-0.0675475\pi$
$127$	0.289180	+	1.07923i	0.0256606	+	0.0957666i	−0.951908	+	0.306384i	$0.900881\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−16.9285	+	29.3210i	−1.49047	+	2.58157i
$130$		0			0
$131$	2.38173	+	4.12527i	0.208093	+	0.360427i	0.951114	−	0.308841i	$-0.0999411\pi$
$131$	2.38173	+	4.12527i	0.208093	+	0.360427i	−0.743021	+	0.669268i	$0.766608\pi$
$132$	2.41377	−	2.41377i	0.210092	−	0.210092i
$133$	20.1661	+	2.33765i	1.74862	+	0.202700i
$134$			13.9476i			1.20489i
$135$		0			0
$136$	5.42535	−	3.13233i	0.465220	−	0.268595i
$137$	−8.04836	+	2.15655i	−0.687618	+	0.184247i	−0.585678	−	0.810544i	$-0.699172\pi$
$137$	−8.04836	+	2.15655i	−0.687618	+	0.184247i	−0.101940	+	0.994791i	$0.532505\pi$
$138$	7.63249	+	2.04512i	0.649721	+	0.174092i
$139$	3.42658	+	1.97834i	0.290639	+	0.167800i	0.638230	−	0.769846i	$-0.279667\pi$
$139$	3.42658	+	1.97834i	0.290639	+	0.167800i	−0.347591	+	0.937646i	$0.613000\pi$
$140$		0			0
$141$			31.3225i			2.63783i
$142$	10.5947	−	2.83885i	0.889090	−	0.238231i
$143$	−1.06327	+	0.284902i	−0.0889150	+	0.0238247i
$144$		−	7.13891i		−	0.594909i
$145$		0			0
$146$	8.57362	+	4.94998i	0.709558	+	0.409664i
$147$	45.1859	+	12.1075i	3.72687	+	0.998612i
$148$	−4.93792	+	1.32311i	−0.405895	+	0.108759i
$149$	15.3791	−	8.87913i	1.25991	−	0.727407i	0.286850	−	0.957976i	$-0.407392\pi$
$149$	15.3791	−	8.87913i	1.25991	−	0.727407i	0.973056	+	0.230569i	$0.0740586\pi$
$150$		0			0
$151$		−	23.9042i		−	1.94529i	−0.232292	−	0.972646i	$-0.574622\pi$
$151$		−	23.9042i		−	1.94529i	0.232292	−	0.972646i	$-0.425378\pi$
$152$	4.32990	+	0.501921i	0.351202	+	0.0407112i
$153$	−31.6238	+	31.6238i	−2.55663	+	2.55663i
$154$	2.49649	+	4.32404i	0.201173	+	0.348441i
$155$		0			0
$156$	−1.63474	+	2.83146i	−0.130884	+	0.226698i
$157$	−3.18000	+	11.8679i	−0.253791	+	0.947163i	0.714967	+	0.699158i	$0.246442\pi$
$157$	−3.18000	+	11.8679i	−0.253791	+	0.947163i	−0.968759	+	0.248005i	$0.920225\pi$
$158$	−1.73627	−	6.47985i	−0.138130	−	0.515509i
$159$		−	5.69660i		−	0.451770i
$160$		0			0
$161$	−5.77884	+	10.0093i	−0.455437	+	0.788840i
$162$	5.31803	+	19.8472i	0.417824	+	1.55934i
$163$	−13.4213	+	13.4213i	−1.05124	+	1.05124i	−0.0526222	+	0.998614i	$0.516758\pi$
$163$	−13.4213	+	13.4213i	−1.05124	+	1.05124i	−0.998614	+	0.0526222i	$0.983242\pi$
$164$	−5.53172			−0.431955
$165$		0			0
$166$	−4.14151	+	2.39110i	−0.321443	+	0.185585i
$167$	2.54427	+	9.49536i	0.196882	+	0.734773i	0.991772	+	0.128019i	$0.0408619\pi$
$167$	2.54427	+	9.49536i	0.196882	+	0.734773i	−0.794890	+	0.606754i	$0.792471\pi$
$168$	14.3246	+	3.83827i	1.10517	+	0.296129i
$169$	−10.3453	+	5.97285i	−0.795790	+	0.459450i
$170$		0			0
$171$	−30.7849	+	4.53923i	−2.35418	+	0.347123i
$172$	−7.51860	−	7.51860i	−0.573288	−	0.573288i
$173$	0.114479	−	0.427241i	0.00870366	−	0.0324825i	−0.961437	−	0.275024i	$-0.911314\pi$
$173$	0.114479	−	0.427241i	0.00870366	−	0.0324825i	0.970141	+	0.242541i	$0.0779810\pi$
$174$	−9.51349	−	16.4779i	−0.721216	−	1.24918i
$175$		0			0
$176$	0.536025	+	0.928423i	0.0404044	+	0.0699825i
$177$	33.3282	−	8.93026i	2.50510	−	0.671240i
$178$	2.91233	−	2.91233i	0.218288	−	0.218288i
$179$	13.5736			1.01454			0.507271	−	0.861787i	$-0.330654\pi$
$179$	13.5736			1.01454			0.507271	+	0.861787i	$0.330654\pi$
$180$		0			0
$181$	−5.86320	−	3.38512i	−0.435808	−	0.251614i	0.266010	−	0.963970i	$-0.414295\pi$
$181$	−5.86320	−	3.38512i	−0.435808	−	0.251614i	−0.701818	+	0.712356i	$0.747628\pi$
$182$	−3.38153	−	3.38153i	−0.250655	−	0.250655i
$183$	14.1465	+	14.1465i	1.04574	+	1.04574i
$184$	−1.24079	+	2.14911i	−0.0914720	+	0.158434i
$185$		0			0
$186$	−0.344132	−	0.198684i	−0.0252330	−	0.0145683i
$187$	1.73824	−	6.48719i	0.127112	−	0.474390i
$188$	−9.50178	−	2.54600i	−0.692989	−	0.185686i
$189$	−61.3798			−4.46472
$190$		0			0
$191$	−4.89922			−0.354495			−0.177248	−	0.984166i	$-0.556719\pi$
$191$	−4.89922			−0.354495			−0.177248	+	0.984166i	$0.556719\pi$
$192$	3.07567	+	0.824123i	0.221967	+	0.0594759i
$193$	−4.74236	+	17.6987i	−0.341363	+	1.27398i	0.555442	+	0.831555i	$0.312549\pi$
$193$	−4.74236	+	17.6987i	−0.341363	+	1.27398i	−0.896804	+	0.442427i	$0.854118\pi$
$194$	−8.31190	−	4.79888i	−0.596759	−	0.344539i
$195$		0			0
$196$	−7.34570	+	12.7231i	−0.524693	+	0.908795i
$197$	−10.2427	−	10.2427i	−0.729763	−	0.729763i	0.240809	−	0.970572i	$-0.422587\pi$
$197$	−10.2427	−	10.2427i	−0.729763	−	0.729763i	−0.970572	+	0.240809i	$0.922587\pi$
$198$	−5.41168	−	5.41168i	−0.384591	−	0.384591i
$199$	2.42260	+	1.39869i	0.171733	+	0.0991503i	0.583403	−	0.812183i	$-0.301721\pi$
$199$	2.42260	+	1.39869i	0.171733	+	0.0991503i	−0.411670	+	0.911333i	$0.635054\pi$
$200$		0			0
$201$	44.4115			3.13255
$202$	0.563829	−	0.563829i	0.0396708	−	0.0396708i
$203$	26.8820	−	7.20302i	1.88675	−	0.505553i
$204$	−9.97386	−	17.2752i	−0.698310	−	1.20951i
$205$		0			0
$206$	4.44038	+	7.69097i	0.309376	+	0.535855i
$207$	4.58517	−	17.1121i	0.318691	−	1.18937i
$208$	−0.726054	−	0.726054i	−0.0503428	−	0.0503428i
$209$	3.66279	−	2.90182i	0.253360	−	0.200723i
$210$		0			0
$211$	7.30968	−	4.22024i	0.503219	−	0.290534i	−0.226823	−	0.973936i	$-0.572834\pi$
$211$	7.30968	−	4.22024i	0.503219	−	0.290534i	0.730042	+	0.683402i	$0.239501\pi$
$212$	1.72808	+	0.463037i	0.118685	+	0.0318015i
$213$	−9.03937	−	33.7354i	−0.619367	−	2.31151i
$214$	2.41088	−	1.39192i	0.164805	−	0.0951500i
$215$		0			0
$216$	−13.1790			−0.896716
$217$	0.410986	−	0.410986i	0.0278996	−	0.0278996i
$218$	0.492599	+	1.83840i	0.0333630	+	0.124512i
$219$	15.7616	−	27.2998i	1.06507	−	1.84475i
$220$		0			0
$221$			6.43252i			0.432698i
$222$	4.21301	+	15.7232i	0.282759	+	1.05527i
$223$	3.65330	−	13.6343i	0.244643	−	0.913020i	−0.728920	−	0.684599i	$-0.759977\pi$
$223$	3.65330	−	13.6343i	0.244643	−	0.913020i	0.973563	−	0.228421i	$-0.0733561\pi$
$224$	−2.32870	+	4.03343i	−0.155593	+	0.269495i
$225$		0			0
$226$	−6.48304	−	11.2290i	−0.431246	−	0.746939i
$227$	−0.972592	+	0.972592i	−0.0645532	+	0.0645532i	−0.738646	−	0.674093i	$-0.764535\pi$
$227$	−0.972592	+	0.972592i	−0.0645532	+	0.0645532i	0.674093	+	0.738646i	$0.264535\pi$
$228$	1.59820	−	13.7871i	0.105843	−	0.913075i
$229$			5.97961i			0.395144i	0.980288	+	0.197572i	$0.0633056\pi$
$229$			5.97961i			0.395144i	−0.980288	+	0.197572i	$0.936694\pi$
$230$		0			0
$231$	13.7685	−	7.94922i	0.905898	−	0.523021i
$232$	5.77189	−	1.54657i	0.378943	−	0.101538i
$233$	−5.48598	−	1.46996i	−0.359398	−	0.0963005i	0.0746016	−	0.997213i	$-0.476231\pi$
$233$	−5.48598	−	1.46996i	−0.359398	−	0.0963005i	−0.434000	+	0.900913i	$0.642898\pi$
$234$	6.34814	+	3.66510i	0.414991	+	0.239595i
$235$		0			0
$236$			10.8361i			0.705369i
$237$	−20.6329	+	5.52858i	−1.34025	+	0.359120i
$238$	28.1829	−	7.55157i	1.82682	−	0.489496i
$239$		−	26.0669i		−	1.68612i	−0.537816	−	0.843062i	$-0.680750\pi$
$239$		−	26.0669i		−	1.68612i	0.537816	−	0.843062i	$-0.319250\pi$
$240$		0			0
$241$	8.20920	+	4.73958i	0.528801	+	0.305304i	0.740528	−	0.672025i	$-0.234575\pi$
$241$	8.20920	+	4.73958i	0.528801	+	0.305304i	−0.211727	+	0.977329i	$0.567909\pi$
$242$	−9.51505	−	2.54955i	−0.611651	−	0.163891i
$243$	25.0069	−	6.70059i	1.60420	−	0.429843i
$244$	−5.44125	+	3.14151i	−0.348340	+	0.201114i
$245$		0			0
$246$			17.6139i			1.12302i
$247$	−2.66929	+	3.59260i	−0.169843	+	0.228592i
$248$	0.0882436	−	0.0882436i	0.00560348	−	0.00560348i
$249$	7.61366	+	13.1872i	0.482496	+	0.835707i
$250$		0			0
$251$	−8.16558	+	14.1432i	−0.515407	+	0.892710i	0.484433	+	0.874828i	$0.339026\pi$
$251$	−8.16558	+	14.1432i	−0.515407	+	0.892710i	−0.999840	+	0.0178824i	$0.994308\pi$
$252$	8.60542	−	32.1159i	0.542090	−	2.02311i
$253$	0.688555	+	2.56972i	0.0432891	+	0.161557i
$254$			1.11731i			0.0701060i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.57537	+	17.0755i	0.285404	+	1.06514i	0.948544	+	0.316646i	$0.102557\pi$
$257$	4.57537	+	17.0755i	0.285404	+	1.06514i	−0.663140	+	0.748496i	$0.730777\pi$
$258$	−23.9405	+	23.9405i	−1.49047	+	1.49047i
$259$	−23.8092			−1.47943
$260$		0			0
$261$	−36.9434	+	21.3293i	−2.28674	+	1.32025i
$262$	1.23287	+	4.60115i	0.0761672	+	0.284260i
$263$	−10.8358	−	2.90345i	−0.668165	−	0.179034i	−0.0912370	−	0.995829i	$-0.529082\pi$
$263$	−10.8358	−	2.90345i	−0.668165	−	0.179034i	−0.576928	+	0.816795i	$0.695749\pi$
$264$	2.95625	−	1.70679i	0.181945	−	0.105046i
$265$		0			0
$266$	18.8739	+	7.47737i	1.15724	+	0.458467i
$267$	−9.27334	−	9.27334i	−0.567519	−	0.567519i
$268$	−3.60991	+	13.4724i	−0.220510	+	0.822956i
$269$	16.1806	+	28.0256i	0.986549	+	1.70875i	0.634838	+	0.772645i	$0.281067\pi$
$269$	16.1806	+	28.0256i	0.986549	+	1.70875i	0.351711	+	0.936109i	$0.385600\pi$
$270$		0			0
$271$	−10.4444	−	18.0903i	−0.634453	−	1.09891i	−0.986631	−	0.162972i	$-0.947892\pi$
$271$	−10.4444	−	18.0903i	−0.634453	−	1.09891i	0.352177	−	0.935933i	$-0.385441\pi$
$272$	6.05120	−	1.62141i	0.366908	−	0.0983126i
$273$	−10.7673	+	10.7673i	−0.651669	+	0.651669i
$274$	−8.33228			−0.503371
$275$		0			0
$276$	6.84311	+	3.95087i	0.411907	+	0.237814i
$277$	1.18557	+	1.18557i	0.0712340	+	0.0712340i	0.741826	−	0.670592i	$-0.233960\pi$
$277$	1.18557	+	1.18557i	0.0712340	+	0.0712340i	−0.670592	+	0.741826i	$0.733960\pi$
$278$	2.79779	+	2.79779i	0.167800	+	0.167800i
$279$	−0.445451	+	0.771544i	−0.0266685	+	0.0461911i
$280$		0			0
$281$	−10.8651	−	6.27295i	−0.648156	−	0.374213i	0.139594	−	0.990209i	$-0.455420\pi$
$281$	−10.8651	−	6.27295i	−0.648156	−	0.374213i	−0.787749	+	0.615996i	$0.788754\pi$
$282$	−8.10687	+	30.2553i	−0.482757	+	1.80167i
$283$	10.6096	+	2.84283i	0.630675	+	0.168989i	0.559976	−	0.828509i	$-0.310810\pi$
$283$	10.6096	+	2.84283i	0.630675	+	0.168989i	0.0706990	+	0.997498i	$0.477477\pi$
$284$	10.9685			0.650859
$285$		0			0
$286$	−1.10078			−0.0650903
$287$	−24.8856	−	6.66807i	−1.46895	−	0.393604i
$288$	1.84769	−	6.89566i	0.108876	−	0.406331i
$289$	−19.2656	−	11.1230i	−1.13327	−	0.654293i
$290$		0			0
$291$	−15.2804	+	26.4665i	−0.895754	+	1.55149i
$292$	7.00033	+	7.00033i	0.409664	+	0.409664i
$293$	17.5445	+	17.5445i	1.02496	+	1.02496i	0.999680	+	0.0252772i	$0.00804685\pi$
$293$	17.5445	+	17.5445i	1.02496	+	1.02496i	0.0252772	+	0.999680i	$0.491953\pi$
$294$	40.5126	+	23.3899i	2.36274	+	1.36413i
$295$		0			0
$296$	−5.11211			−0.297136
$297$	−9.99038	+	9.99038i	−0.579700	+	0.579700i
$298$	17.1532	−	4.59618i	0.993656	−	0.266249i
$299$	−1.27403	−	2.20669i	−0.0736793	−	0.127616i
$300$		0			0
$301$	−24.7609	−	42.8871i	−1.42719	−	2.47197i
$302$	6.18685	−	23.0896i	0.356013	−	1.32866i
$303$	−1.79532	−	1.79532i	−0.103139	−	0.103139i
$304$	4.05246	+	1.60548i	0.232425	+	0.0920806i
$305$		0			0
$306$	−38.7311	+	22.3614i	−2.21411	+	1.27832i
$307$	−15.0693	−	4.03781i	−0.860051	−	0.230450i	−0.198270	−	0.980147i	$-0.563532\pi$
$307$	−15.0693	−	4.03781i	−0.860051	−	0.230450i	−0.661781	+	0.749697i	$0.730199\pi$
$308$	1.29228	+	4.82284i	0.0736343	+	0.274807i
$309$	24.4893	−	14.1389i	1.39315	−	0.804334i
$310$		0			0
$311$	15.7787			0.894726			0.447363	−	0.894353i	$-0.352363\pi$
$311$	15.7787			0.894726			0.447363	+	0.894353i	$0.352363\pi$
$312$	−2.31188	+	2.31188i	−0.130884	+	0.130884i
$313$	−6.89802	−	25.7438i	−0.389899	−	1.45512i	−0.830297	−	0.557321i	$-0.811829\pi$
$313$	−6.89802	−	25.7438i	−0.389899	−	1.45512i	0.440398	−	0.897803i	$-0.354837\pi$
$314$	−6.14328	+	10.6405i	−0.346686	+	0.600477i
$315$		0			0
$316$		−	6.70844i		−	0.377379i
$317$	2.34452	+	8.74986i	0.131681	+	0.491441i	0.999989	−	0.00458379i	$-0.00145907\pi$
$317$	2.34452	+	8.74986i	0.131681	+	0.491441i	−0.868308	+	0.496025i	$0.834792\pi$
$318$	1.47439	−	5.50249i	0.0826796	−	0.308564i
$319$	3.20302	−	5.54779i	0.179335	−	0.310617i
$320$		0			0
$321$	−4.43212	−	7.67665i	−0.247377	−	0.428469i
$322$	−8.17252	+	8.17252i	−0.455437	+	0.455437i
$323$	−10.8396	−	25.0634i	−0.603131	−	1.39457i
$324$			20.5473i			1.14152i
$325$		0			0
$326$	−16.4377	+	9.49029i	−0.910398	+	0.525618i
$327$	5.85378	−	1.56852i	0.323715	−	0.0867392i
$328$	−5.34323	−	1.43171i	−0.295031	−	0.0790532i
$329$	−39.6767	−	22.9074i	−2.18745	−	1.26292i
$330$		0			0
$331$		−	12.5890i		−	0.691952i	−0.938243	−	0.345976i	$-0.887548\pi$
$331$		−	12.5890i		−	0.691952i	0.938243	−	0.345976i	$-0.112452\pi$
$332$	−4.61925	+	1.23772i	−0.253514	+	0.0679289i
$333$	35.2514	−	9.44558i	1.93176	−	0.517615i
$334$			9.83032i			0.537891i
$335$		0			0
$336$	12.8431	+	7.41497i	0.700649	+	0.404520i
$337$	18.9250	+	5.07093i	1.03091	+	0.276231i	0.734341	−	0.678781i	$-0.237491\pi$
$337$	18.9250	+	5.07093i	1.03091	+	0.276231i	0.296567	+	0.955012i	$0.404158\pi$
$338$	−11.5387	+	3.09177i	−0.627620	+	0.168170i
$339$	−35.7549	+	20.6431i	−1.94194	+	1.12118i
$340$		0			0
$341$		−	0.133787i		−	0.00724497i
$342$	−30.9108	−	3.58317i	−1.67146	−	0.193756i
$343$	−25.3300	+	25.3300i	−1.36769	+	1.36769i
$344$	−5.31645	−	9.20836i	−0.286644	−	0.496482i
$345$		0			0
$346$	0.221156	−	0.383054i	0.0118894	−	0.0205931i
$347$	1.12287	−	4.19059i	0.0602786	−	0.224963i	−0.929215	−	0.369540i	$-0.879515\pi$
$347$	1.12287	−	4.19059i	0.0602786	−	0.224963i	0.989494	+	0.144577i	$0.0461821\pi$
$348$	−4.92455	−	18.3787i	−0.263983	−	0.985199i
$349$			9.97961i			0.534196i	0.963669	+	0.267098i	$0.0860648\pi$
$349$			9.97961i			0.534196i	−0.963669	+	0.267098i	$0.913935\pi$
$350$		0			0
$351$	6.76605	−	11.7191i	0.361145	−	0.625522i
$352$	0.277467	+	1.03552i	0.0147890	+	0.0551935i
$353$	−6.92781	+	6.92781i	−0.368730	+	0.368730i	−0.867014	−	0.498284i	$-0.833964\pi$
$353$	−6.92781	+	6.92781i	−0.368730	+	0.368730i	0.498284	+	0.867014i	$0.333964\pi$
$354$	34.5039			1.83386
$355$		0			0
$356$	3.56686	−	2.05933i	0.189043	−	0.109144i
$357$	−24.0455	−	89.7389i	−1.27262	−	4.74949i
$358$	13.1111	+	3.51312i	0.692945	+	0.185674i
$359$	−3.08522	+	1.78125i	−0.162832	+	0.0940109i	−0.579201	−	0.815184i	$-0.696636\pi$
$359$	−3.08522	+	1.78125i	−0.162832	+	0.0940109i	0.416370	+	0.909195i	$0.363302\pi$
$360$		0			0
$361$	4.34654	−	18.4962i	0.228765	−	0.973482i
$362$	−4.78728	−	4.78728i	−0.251614	−	0.251614i
$363$	−8.11819	+	30.2975i	−0.426095	+	1.59021i
$364$	−2.39110	−	4.14151i	−0.125328	−	0.217074i
$365$		0			0
$366$	10.0031	+	17.3258i	0.522869	+	0.905636i
$367$	−10.0892	+	2.70339i	−0.526652	+	0.141116i	−0.512342	−	0.858782i	$-0.671222\pi$
$367$	−10.0892	+	2.70339i	−0.526652	+	0.141116i	−0.0143103	+	0.999898i	$0.504555\pi$
$368$	−1.75474	+	1.75474i	−0.0914720	+	0.0914720i
$369$	39.4905			2.05579
$370$		0			0
$371$	7.21596	+	4.16614i	0.374634	+	0.216295i
$372$	−0.280982	−	0.280982i	−0.0145683	−	0.0145683i
$373$	0.728359	+	0.728359i	0.0377130	+	0.0377130i	0.725712	−	0.687999i	$-0.241511\pi$
$373$	0.728359	+	0.728359i	0.0377130	+	0.0377130i	−0.687999	+	0.725712i	$0.741511\pi$
$374$	3.35802	−	5.81625i	0.173639	−	0.300751i
$375$		0			0
$376$	−8.51907	−	4.91849i	−0.439337	−	0.253652i
$377$	−1.58801	+	5.92655i	−0.0817869	+	0.305233i
$378$	−59.2883	−	15.8863i	−3.04946	−	0.817101i
$379$	−16.9385			−0.870074			−0.435037	−	0.900413i	$-0.643265\pi$
$379$	−16.9385			−0.870074			−0.435037	+	0.900413i	$0.643265\pi$
$380$		0			0
$381$	3.55769			0.182266
$382$	−4.73229	−	1.26801i	−0.242125	−	0.0648772i
$383$	7.86581	−	29.3556i	0.401924	−	1.50000i	−0.407735	−	0.913100i	$-0.633681\pi$
$383$	7.86581	−	29.3556i	0.401924	−	1.50000i	0.809659	−	0.586901i	$-0.199652\pi$
$384$	2.75757	+	1.59208i	0.140722	+	0.0812456i
$385$		0			0
$386$	−9.16154	+	15.8682i	−0.466310	+	0.807673i
$387$	53.6746	+	53.6746i	2.72843	+	2.72843i
$388$	−6.78664	−	6.78664i	−0.344539	−	0.344539i
$389$	−16.0249	−	9.25199i	−0.812496	−	0.469095i	0.0353262	−	0.999376i	$-0.488753\pi$
$389$	−16.0249	−	9.25199i	−0.812496	−	0.469095i	−0.847822	+	0.530281i	$0.822086\pi$
$390$		0			0
$391$	15.5462			0.786206
$392$	−10.3884	+	10.3884i	−0.524693	+	0.524693i
$393$	14.6508	−	3.92567i	0.739036	−	0.198024i
$394$	−7.24269	−	12.5447i	−0.364882	−	0.631993i
$395$		0			0
$396$	−3.82664	−	6.62793i	−0.192296	−	0.333066i
$397$	0.111122	−	0.414714i	0.00557707	−	0.0208139i	−0.963081	−	0.269211i	$-0.913237\pi$
$397$	0.111122	−	0.414714i	0.00557707	−	0.0208139i	0.968658	+	0.248397i	$0.0799038\pi$
$398$	1.97804	+	1.97804i	0.0991503	+	0.0991503i
$399$	23.8092	−	60.0978i	1.19195	−	3.00865i
$400$		0			0
$401$	2.32217	−	1.34070i	0.115964	−	0.0669516i	−0.440896	−	0.897558i	$-0.645339\pi$
$401$	2.32217	−	1.34070i	0.115964	−	0.0669516i	0.556860	+	0.830606i	$0.312006\pi$
$402$	42.8983	+	11.4946i	2.13957	+	0.573296i
$403$	0.0331649	+	0.123773i	0.00165206	+	0.00616557i
$404$	0.690546	−	0.398687i	0.0343560	−	0.0198354i
$405$		0			0
$406$	27.8303			1.38120
$407$	−3.87526	+	3.87526i	−0.192090	+	0.192090i
$408$	−5.16285	−	19.2680i	−0.255599	−	0.953909i
$409$	2.42580	−	4.20160i	0.119948	−	0.207756i	−0.799799	−	0.600268i	$-0.795061\pi$
$409$	2.42580	−	4.20160i	0.119948	−	0.207756i	0.919747	+	0.392512i	$0.128394\pi$
$410$		0			0
$411$			26.5314i			1.30870i
$412$	2.29851	+	8.57816i	0.113239	+	0.422616i
$413$	−13.0621	+	48.7484i	−0.642743	+	2.39875i
$414$	8.85786	−	15.3423i	0.435340	−	0.754031i
$415$		0			0
$416$	−0.513398	−	0.889231i	−0.0251714	−	0.0435981i
$417$	8.90863	−	8.90863i	0.436258	−	0.436258i
$418$	4.28903	−	1.85494i	0.209783	−	0.0907283i
$419$		−	2.92276i		−	0.142786i	−0.997448	−	0.0713930i	$-0.977256\pi$
$419$		−	2.92276i		−	0.142786i	0.997448	−	0.0713930i	$-0.0227445\pi$
$420$		0			0
$421$	10.7018	−	6.17868i	0.521573	−	0.301130i	−0.216005	−	0.976392i	$-0.569303\pi$
$421$	10.7018	−	6.17868i	0.521573	−	0.301130i	0.737578	+	0.675262i	$0.235969\pi$
$422$	8.15289	−	2.18456i	0.396876	−	0.106343i
$423$	67.8324	+	18.1756i	3.29812	+	0.883729i
$424$	1.54935	+	0.894520i	0.0752433	+	0.0434417i
$425$		0			0
$426$		−	34.9254i		−	1.69214i
$427$	−28.2654	+	7.57370i	−1.36786	+	0.366517i
$428$	2.68899	−	0.720513i	0.129977	−	0.0348273i
$429$			3.50505i			0.169226i
$430$		0			0
$431$	19.5919	+	11.3114i	0.943706	+	0.544849i	0.891120	−	0.453767i	$-0.149920\pi$
$431$	19.5919	+	11.3114i	0.943706	+	0.544849i	0.0525861	+	0.998616i	$0.483254\pi$
$432$	−12.7299	−	3.41097i	−0.612468	−	0.164110i
$433$	−13.1912	+	3.53457i	−0.633929	+	0.169861i	−0.561452	−	0.827509i	$-0.689757\pi$
$433$	−13.1912	+	3.53457i	−0.633929	+	0.169861i	−0.0724768	+	0.997370i	$0.523090\pi$
$434$	0.503353	−	0.290611i	0.0241617	−	0.0139498i
$435$		0			0
$436$			1.90326i			0.0911495i
$437$	8.68265	+	6.45117i	0.415347	+	0.308601i
$438$	22.2902	−	22.2902i	1.06507	−	1.06507i
$439$	1.54319	+	2.67288i	0.0736522	+	0.127569i	0.900499	−	0.434857i	$-0.143201\pi$
$439$	1.54319	+	2.67288i	0.0736522	+	0.127569i	−0.826847	+	0.562427i	$0.809868\pi$
$440$		0			0
$441$	52.4403	−	90.8293i	2.49716	−	4.32520i
$442$	−1.66486	+	6.21334i	−0.0791893	+	0.295538i
$443$	−5.61941	−	20.9719i	−0.266986	−	0.996406i	−0.961023	−	0.276467i	$-0.910836\pi$
$443$	−5.61941	−	20.9719i	−0.266986	−	0.996406i	0.694037	−	0.719939i	$-0.255830\pi$
$444$			16.2778i			0.772511i
$445$		0			0
$446$	7.05763	−	12.2242i	0.334188	−	0.578831i
$447$	−14.6350	−	54.6185i	−0.692211	−	2.58337i
$448$	−3.29328	+	3.29328i	−0.155593	+	0.155593i
$449$	−1.17247			−0.0553322			−0.0276661	−	0.999617i	$-0.508808\pi$
$449$	−1.17247			−0.0553322			−0.0276661	+	0.999617i	$0.508808\pi$
$450$		0			0
$451$	−5.13578	+	2.96514i	−0.241834	+	0.139623i
$452$	−3.35587	−	12.5243i	−0.157847	−	0.589092i
$453$	−73.5212	−	19.7000i	−3.45433	−	0.925585i
$454$	−1.19118	+	0.687726i	−0.0559047	+	0.0322766i
$455$		0			0
$456$	5.11211	−	12.9037i	0.239397	−	0.604271i
$457$	−4.99712	−	4.99712i	−0.233755	−	0.233755i	0.580503	−	0.814258i	$-0.302856\pi$
$457$	−4.99712	−	4.99712i	−0.233755	−	0.233755i	−0.814258	+	0.580503i	$0.802856\pi$
$458$	−1.54764	+	5.77586i	−0.0723163	+	0.269888i
$459$	41.2809	+	71.5006i	1.92683	+	3.33736i
$460$		0			0
$461$	−8.72743	−	15.1164i	−0.406477	−	0.704039i	0.588015	−	0.808850i	$-0.299910\pi$
$461$	−8.72743	−	15.1164i	−0.406477	−	0.704039i	−0.994492	+	0.104811i	$0.966576\pi$
$462$	15.3567	−	4.11482i	0.714459	−	0.191439i
$463$	15.5618	−	15.5618i	0.723219	−	0.723219i	−0.246040	−	0.969260i	$-0.579130\pi$
$463$	15.5618	−	15.5618i	0.723219	−	0.723219i	0.969260	+	0.246040i	$0.0791296\pi$
$464$	5.97550			0.277406
$465$		0			0
$466$	−4.91859	−	2.83975i	−0.227849	−	0.131549i
$467$	11.1702	+	11.1702i	0.516896	+	0.516896i	0.916631	−	0.399735i	$-0.130898\pi$
$467$	11.1702	+	11.1702i	0.516896	+	0.516896i	−0.399735	+	0.916631i	$0.630898\pi$
$468$	5.18323	+	5.18323i	0.239595	+	0.239595i
$469$	−32.4799	+	56.2568i	−1.49978	+	2.59770i
$470$		0			0
$471$	33.8811	+	19.5612i	1.56116	+	0.901334i
$472$	−2.80458	+	10.4669i	−0.129091	+	0.481776i
$473$	−11.0106	−	2.95028i	−0.506268	−	0.135654i
$474$	−21.3608			−0.981133
$475$		0			0
$476$	29.1770			1.33733
$477$	−12.3366	−	3.30558i	−0.564854	−	0.151352i
$478$	6.74660	−	25.1787i	0.308582	−	1.15164i
$479$	11.0418	+	6.37497i	0.504511	+	0.291280i	0.730575	−	0.682833i	$-0.239252\pi$
$479$	11.0418	+	6.37497i	0.504511	+	0.291280i	−0.226063	+	0.974113i	$0.572586\pi$
$480$		0			0
$481$	2.62455	−	4.54585i	0.119669	−	0.207273i
$482$	6.70279	+	6.70279i	0.305304	+	0.305304i
$483$	26.0227	+	26.0227i	1.18407	+	1.18407i
$484$	−8.53096	−	4.92535i	−0.387771	−	0.223880i
$485$		0			0
$486$	25.8891			1.17435
$487$	21.5327	−	21.5327i	0.975741	−	0.975741i	−0.0239721	−	0.999713i	$-0.507631\pi$
$487$	21.5327	−	21.5327i	0.975741	−	0.975741i	0.999713	+	0.0239721i	$0.00763129\pi$
$488$	−6.06892	+	1.62616i	−0.274727	+	0.0736129i
$489$	30.2186	+	52.3402i	1.36653	+	2.36691i
$490$		0			0
$491$	−11.6144	−	20.1166i	−0.524148	−	0.907852i	−0.999605	−	0.0281123i	$-0.991050\pi$
$491$	−11.6144	−	20.1166i	−0.524148	−	0.907852i	0.475456	−	0.879739i	$-0.342283\pi$
$492$	−4.55882	+	17.0137i	−0.205527	+	0.767038i
$493$	−26.4702	−	26.4702i	−1.19216	−	1.19216i
$494$	−3.50817	+	2.77932i	−0.157840	+	0.125048i
$495$		0			0
$496$	0.108076	−	0.0623977i	0.00485275	−	0.00280174i
$497$	49.3439	+	13.2217i	2.21338	+	0.593073i
$498$	3.94112	+	14.7085i	0.176606	+	0.659102i
$499$	−28.3605	+	16.3739i	−1.26959	+	0.732998i	−0.974910	−	0.222598i	$-0.928546\pi$
$499$	−28.3605	+	16.3739i	−1.26959	+	0.732998i	−0.294680	+	0.955596i	$0.595213\pi$
$500$		0			0
$501$	31.3014			1.39844
$502$	−11.5479	+	11.5479i	−0.515407	+	0.515407i
$503$	1.88772	+	7.04507i	0.0841694	+	0.314124i	0.995156	−	0.0983124i	$-0.0313444\pi$
$503$	1.88772	+	7.04507i	0.0841694	+	0.314124i	−0.910986	+	0.412437i	$0.864678\pi$
$504$	16.6244	−	28.7943i	0.740509	−	1.28260i
$505$		0			0
$506$			2.66037i			0.118268i
$507$	9.84472	+	36.7410i	0.437219	+	1.63172i
$508$	−0.289180	+	1.07923i	−0.0128303	+	0.0478833i
$509$	10.2779	−	17.8019i	0.455561	−	0.789055i	−0.543159	−	0.839630i	$-0.682772\pi$
$509$	10.2779	−	17.8019i	0.455561	−	0.789055i	0.998720	+	0.0505748i	$0.0161053\pi$
$510$		0			0
$511$	23.0541	+	39.9308i	1.01985	+	1.76644i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−6.61480	+	57.0637i	−0.292051	+	2.51942i
$514$			17.6779i			0.779738i
$515$		0			0
$516$	−29.3210	+	16.9285i	−1.29078	+	0.745234i
$517$	−10.1864	+	2.72944i	−0.447997	+	0.120040i
$518$	−22.9979	−	6.16227i	−1.01047	−	0.270755i
$519$	−1.21971	−	0.704198i	−0.0535392	−	0.0309108i
$520$		0			0
$521$		−	11.0447i		−	0.483877i	−0.970292	−	0.241939i	$-0.922217\pi$
$521$		−	11.0447i		−	0.483877i	0.970292	−	0.241939i	$-0.0777833\pi$
$522$	−41.2050	+	11.0408i	−1.80349	+	0.483245i
$523$	13.6313	−	3.65248i	0.596053	−	0.159712i	0.0518350	−	0.998656i	$-0.483493\pi$
$523$	13.6313	−	3.65248i	0.596053	−	0.159712i	0.544218	+	0.838944i	$0.316826\pi$
$524$			4.76346i			0.208093i
$525$		0			0
$526$	−9.71513	−	5.60903i	−0.423600	−	0.244565i
$527$	−0.755161	−	0.202345i	−0.0328953	−	0.00881428i
$528$	3.29727	−	0.883501i	0.143495	−	0.0384495i
$529$	14.5854	−	8.42090i	0.634149	−	0.366126i
$530$		0			0
$531$		−	77.3578i		−	3.35704i
$532$	16.2955	+	12.1075i	0.706501	+	0.524928i
$533$	4.01633	−	4.01633i	0.173966	−	0.173966i
$534$	−6.55724	−	11.3575i	−0.283759	−	0.491486i
$535$		0			0
$536$	−6.97381	+	12.0790i	−0.301223	+	0.521733i
$537$	11.1863	−	41.7480i	0.482727	−	1.80156i
$538$	8.37570	+	31.2585i	0.361102	+	1.34765i
$539$			15.7499i			0.678398i
$540$		0			0
$541$	−9.17494	+	15.8915i	−0.394461	+	0.683227i	−0.993032	−	0.117843i	$-0.962402\pi$
$541$	−9.17494	+	15.8915i	−0.394461	+	0.683227i	0.598571	+	0.801070i	$0.295735\pi$
$542$	−5.40643	−	20.1771i	−0.232226	−	0.866679i
$543$	−15.2435	+	15.2435i	−0.654161	+	0.654161i
$544$	6.26466			0.268595
$545$		0			0
$546$	−13.1872	+	7.61366i	−0.564362	+	0.325834i
$547$	8.83208	+	32.9618i	0.377633	+	1.40934i	0.849460	+	0.527653i	$0.176928\pi$
$547$	8.83208	+	32.9618i	0.377633	+	1.40934i	−0.471827	+	0.881691i	$0.656405\pi$
$548$	−8.04836	−	2.15655i	−0.343809	−	0.0921234i
$549$	38.8446	−	22.4269i	1.65785	−	0.957158i
$550$		0			0
$551$	−3.79948	−	25.7680i	−0.161863	−	1.09775i
$552$	5.58737	+	5.58737i	0.237814	+	0.237814i
$553$	8.08652	−	30.1793i	0.343874	−	1.28335i
$554$	0.838324	+	1.45202i	0.0356170	+	0.0616904i
$555$		0			0
$556$	1.97834	+	3.42658i	0.0839002	+	0.145319i
$557$	31.2064	−	8.36172i	1.32226	−	0.354298i	0.472434	−	0.881366i	$-0.343376\pi$
$557$	31.2064	−	8.36172i	1.32226	−	0.354298i	0.849823	+	0.527068i	$0.176709\pi$
$558$	−0.629963	+	0.629963i	−0.0266685	+	0.0266685i
$559$	10.9178			0.461774
$560$		0			0
$561$	−18.5199	−	10.6925i	−0.781911	−	0.451437i
$562$	−8.87129	−	8.87129i	−0.374213	−	0.374213i
$563$	17.8915	+	17.8915i	0.754038	+	0.754038i	0.975230	−	0.221193i	$-0.0709949\pi$
$563$	17.8915	+	17.8915i	0.754038	+	0.754038i	−0.221193	+	0.975230i	$0.570995\pi$
$564$	−15.6613	+	27.1261i	−0.659459	+	1.14222i
$565$		0			0
$566$	9.51230	+	5.49193i	0.399832	+	0.230843i
$567$	−24.7682	+	92.4363i	−1.04017	+	3.88196i
$568$	10.5947	+	2.83885i	0.444545	+	0.119115i
$569$	10.9187			0.457736			0.228868	−	0.973457i	$-0.426498\pi$
$569$	10.9187			0.457736			0.228868	+	0.973457i	$0.426498\pi$
$570$		0			0
$571$	−14.8924			−0.623226			−0.311613	−	0.950209i	$-0.600869\pi$
$571$	−14.8924			−0.623226			−0.311613	+	0.950209i	$0.600869\pi$
$572$	−1.06327	−	0.284902i	−0.0444575	−	0.0119123i
$573$	−4.03756	+	15.0684i	−0.168672	+	0.629491i
$574$	−22.3118	−	12.8817i	−0.931277	−	0.537673i
$575$		0			0
$576$	3.56945	−	6.18248i	0.148727	−	0.257603i
$577$	10.9134	+	10.9134i	0.454330	+	0.454330i	0.896789	−	0.442459i	$-0.145894\pi$
$577$	10.9134	+	10.9134i	0.454330	+	0.454330i	−0.442459	+	0.896789i	$0.645894\pi$
$578$	−15.7303	−	15.7303i	−0.654293	−	0.654293i
$579$	50.5271	+	29.1719i	2.09984	+	1.21234i
$580$		0			0
$581$	−22.2726			−0.924024
$582$	−21.6098	+	21.6098i	−0.895754	+	0.895754i
$583$	1.85259	−	0.496400i	0.0767264	−	0.0205588i
$584$	4.94998	+	8.57362i	0.204832	+	0.354779i
$585$		0			0
$586$	12.4058	+	21.4875i	0.512479	+	0.887639i
$587$	10.9091	−	40.7134i	0.450268	−	1.68042i	−0.251372	−	0.967891i	$-0.580882\pi$
$587$	10.9091	−	40.7134i	0.450268	−	1.68042i	0.701639	−	0.712532i	$-0.252452\pi$
$588$	33.0784	+	33.0784i	1.36413	+	1.36413i
$589$	−0.337795	−	0.426378i	−0.0139186	−	0.0175686i
$590$		0			0
$591$	−39.9444	+	23.0619i	−1.64309	+	0.948641i
$592$	−4.93792	−	1.32311i	−0.202947	−	0.0543796i
$593$	−7.81003	−	29.1474i	−0.320720	−	1.19694i	−0.918545	−	0.395316i	$-0.870635\pi$
$593$	−7.81003	−	29.1474i	−0.320720	−	1.19694i	0.597826	−	0.801626i	$-0.296032\pi$
$594$	−12.2357	+	7.06426i	−0.502035	+	0.289850i
$595$		0			0
$596$	17.7583			0.727407
$597$	6.29841	−	6.29841i	0.257777	−	0.257777i
$598$	−0.659488	−	2.46124i	−0.0269685	−	0.100648i
$599$	−1.11766	+	1.93585i	−0.0456665	+	0.0790967i	−0.887955	−	0.459930i	$-0.847874\pi$
$599$	−1.11766	+	1.93585i	−0.0456665	+	0.0790967i	0.842289	+	0.539027i	$0.181208\pi$
$600$		0			0
$601$			6.81740i			0.278088i	0.990286	+	0.139044i	$0.0444029\pi$
$601$			6.81740i			0.278088i	−0.990286	+	0.139044i	$0.955597\pi$
$602$	−12.8172	−	47.8343i	−0.522389	−	1.94958i
$603$	25.7708	−	96.1780i	1.04947	−	3.91667i
$604$	11.9521	−	20.7016i	0.486323	−	0.842336i
$605$		0			0
$606$	−1.26949	−	2.19881i	−0.0515693	−	0.0893207i
$607$	3.64903	−	3.64903i	0.148110	−	0.148110i	−0.629163	−	0.777273i	$-0.716602\pi$
$607$	3.64903	−	3.64903i	0.148110	−	0.148110i	0.777273	+	0.629163i	$0.216602\pi$
$608$	3.49885	+	2.59963i	0.141897	+	0.105429i
$609$		−	88.6163i		−	3.59092i
$610$		0			0
$611$	8.74734	−	5.05028i	0.353879	−	0.204312i
$612$	−43.1989	+	11.5751i	−1.74621	+	0.467897i
$613$	−40.9385	−	10.9694i	−1.65349	−	0.443051i	−0.692903	−	0.721031i	$-0.743669\pi$
$613$	−40.9385	−	10.9694i	−1.65349	−	0.443051i	−0.960587	+	0.277980i	$0.910335\pi$
$614$	−13.5108	−	7.80045i	−0.545250	−	0.314800i
$615$		0			0
$616$			4.99297i			0.201173i
$617$	14.7224	−	3.94485i	0.592701	−	0.158814i	0.0500139	−	0.998749i	$-0.484073\pi$
$617$	14.7224	−	3.94485i	0.592701	−	0.158814i	0.542688	+	0.839935i	$0.317407\pi$
$618$	27.3143	−	7.31884i	1.09874	−	0.294407i
$619$		−	23.9577i		−	0.962943i	−0.876462	−	0.481472i	$-0.840102\pi$
$619$		−	23.9577i		−	0.962943i	0.876462	−	0.481472i	$-0.159898\pi$
$620$		0			0
$621$	−28.3230	−	16.3523i	−1.13656	−	0.656195i
$622$	15.2410	+	4.08382i	0.611109	+	0.163746i
$623$	18.5286	−	4.96473i	0.742333	−	0.198908i
$624$	−2.83146	+	1.63474i	−0.113349	+	0.0654421i
$625$		0			0
$626$		−	26.6519i		−	1.06522i
$627$	−5.90645	−	13.6570i	−0.235881	−	0.545407i
$628$	−8.68792	+	8.68792i	−0.346686	+	0.346686i
$629$	16.0128	+	27.7350i	0.638473	+	1.10587i
$630$		0			0
$631$	−12.9202	+	22.3784i	−0.514344	+	0.890869i	0.485518	+	0.874227i	$0.338631\pi$
$631$	−12.9202	+	22.3784i	−0.514344	+	0.890869i	−0.999862	+	0.0166425i	$0.994702\pi$
$632$	1.73627	−	6.47985i	0.0690652	−	0.257755i
$633$	−6.95600	−	25.9601i	−0.276476	−	1.03182i
$634$			9.05852i			0.359760i
$635$		0			0
$636$	2.84830	−	4.93340i	0.112942	−	0.195622i
$637$	−3.90430	−	14.5711i	−0.154694	−	0.577326i
$638$	4.52975	−	4.52975i	0.179335	−	0.179335i
$639$	−78.3029			−3.09762
$640$		0			0
$641$	−9.52113	+	5.49702i	−0.376062	+	0.217119i	−0.676103	−	0.736807i	$-0.736333\pi$
$641$	−9.52113	+	5.49702i	−0.376062	+	0.217119i	0.300042	+	0.953926i	$0.402999\pi$
$642$	−2.29423	−	8.56219i	−0.0905461	−	0.337923i
$643$	−31.8995	−	8.54744i	−1.25799	−	0.337078i	−0.432574	−	0.901599i	$-0.642394\pi$
$643$	−31.8995	−	8.54744i	−1.25799	−	0.337078i	−0.825419	+	0.564521i	$0.809061\pi$
$644$	−10.0093	+	5.77884i	−0.394420	+	0.227718i
$645$		0			0
$646$	−3.98334	−	27.0149i	−0.156722	−	1.06289i
$647$	−35.3490	−	35.3490i	−1.38971	−	1.38971i	−0.825912	−	0.563799i	$-0.809339\pi$
$647$	−35.3490	−	35.3490i	−1.38971	−	1.38971i	−0.563799	−	0.825912i	$-0.690661\pi$
$648$	−5.31803	+	19.8472i	−0.208912	+	0.779671i
$649$	5.80842	+	10.0605i	0.228000	+	0.394908i
$650$		0			0
$651$	−0.925354	−	1.60276i	−0.0362675	−	0.0628171i
$652$	−18.3338	+	4.91253i	−0.718008	+	0.192390i
$653$	11.6783	−	11.6783i	0.457006	−	0.457006i	−0.440665	−	0.897672i	$-0.645257\pi$
$653$	11.6783	−	11.6783i	0.457006	−	0.457006i	0.897672	+	0.440665i	$0.145257\pi$
$654$	6.06028			0.236976
$655$		0			0
$656$	−4.79061	−	2.76586i	−0.187042	−	0.107989i
$657$	−49.9747	−	49.9747i	−1.94970	−	1.94970i
$658$	−32.3959	−	32.3959i	−1.26292	−	1.26292i
$659$	24.7640	−	42.8925i	0.964669	−	1.67086i	0.254167	−	0.967160i	$-0.418199\pi$
$659$	24.7640	−	42.8925i	0.964669	−	1.67086i	0.710502	−	0.703695i	$-0.248468\pi$
$660$		0			0
$661$	13.1595	+	7.59767i	0.511847	+	0.295515i	0.733593	−	0.679590i	$-0.237842\pi$
$661$	13.1595	+	7.59767i	0.511847	+	0.295515i	−0.221745	+	0.975105i	$0.571175\pi$
$662$	3.25826	−	12.1600i	0.126636	−	0.472612i
$663$	19.7843	+	5.30119i	0.768358	+	0.205881i
$664$	−4.78220			−0.185585
$665$		0			0
$666$	36.4949			1.41415
$667$	14.3234	+	3.83794i	0.554603	+	0.148605i
$668$	−2.54427	+	9.49536i	−0.0984409	+	0.367386i
$669$	−38.9238	−	22.4727i	−1.50488	−	0.868843i
$670$		0			0
$671$	−3.36785	+	5.83329i	−0.130015	+	0.225192i
$672$	10.4864	+	10.4864i	0.404520	+	0.404520i
$673$	−23.3555	−	23.3555i	−0.900289	−	0.900289i	0.0951720	−	0.995461i	$-0.469660\pi$
$673$	−23.3555	−	23.3555i	−0.900289	−	0.900289i	−0.995461	+	0.0951720i	$0.969660\pi$
$674$	16.9677	+	9.79628i	0.653570	+	0.377339i
$675$		0			0
$676$	−11.9457			−0.459450
$677$	3.95095	−	3.95095i	0.151847	−	0.151847i	−0.627095	−	0.778943i	$-0.715756\pi$
$677$	3.95095	−	3.95095i	0.151847	−	0.151847i	0.778943	+	0.627095i	$0.215756\pi$
$678$	−39.8794	+	10.6856i	−1.53156	+	0.410380i
$679$	−22.3503	−	38.7119i	−0.857726	−	1.48562i
$680$		0			0
$681$	2.18983	+	3.79291i	0.0839147	+	0.145344i
$682$	0.0346266	−	0.129228i	0.00132592	−	0.00494840i
$683$	8.91512	+	8.91512i	0.341127	+	0.341127i	0.856791	−	0.515664i	$-0.172455\pi$
$683$	8.91512	+	8.91512i	0.341127	+	0.341127i	−0.515664	+	0.856791i	$0.672455\pi$
$684$	−28.9301	−	11.4614i	−1.10617	−	0.438237i
$685$		0			0
$686$	−31.0227	+	17.9110i	−1.18445	+	0.683845i
$687$	18.3913	+	4.92793i	0.701671	+	0.188012i
$688$	−2.75200	−	10.2706i	−0.104919	−	0.391563i
$689$	−1.59087	+	0.918488i	−0.0606073	+	0.0349916i
$690$		0			0
$691$	−21.0721			−0.801619			−0.400809	−	0.916162i	$-0.631271\pi$
$691$	−21.0721			−0.801619			−0.400809	+	0.916162i	$0.631271\pi$
$692$	0.312762	−	0.312762i	0.0118894	−	0.0118894i
$693$	−9.22544	−	34.4298i	−0.350446	−	1.30788i
$694$	2.16921	−	3.75718i	0.0823421	−	0.142621i
$695$		0			0
$696$		−	19.0270i		−	0.721216i
$697$	8.96920	+	33.4735i	0.339733	+	1.26790i
$698$	−2.58291	+	9.63956i	−0.0977647	+	0.364863i
$699$	−9.04223	+	15.6616i	−0.342009	+	0.592376i
$700$		0			0
$701$	16.9351	+	29.3324i	0.639628	+	1.10787i	0.985514	+	0.169592i	$0.0542451\pi$
$701$	16.9351	+	29.3324i	0.639628	+	1.10787i	−0.345886	+	0.938277i	$0.612422\pi$
$702$	9.56864	−	9.56864i	0.361145	−	0.361145i
$703$	−2.56588	+	22.1350i	−0.0967739	+	0.834836i
$704$			1.07205i			0.0404044i
$705$		0			0
$706$	−8.48480	+	4.89870i	−0.319330	+	0.184365i
$707$	3.58715	−	0.961174i	0.134909	−	0.0361487i
$708$	33.3282	+	8.93026i	1.25255	+	0.335620i
$709$	41.4264	+	23.9176i	1.55580	+	0.898243i	0.997651	+	0.0685042i	$0.0218227\pi$
$709$	41.4264	+	23.9176i	1.55580	+	0.898243i	0.558152	+	0.829739i	$0.311511\pi$
$710$		0			0
$711$			47.8909i			1.79605i
$712$	3.97831	−	1.06599i	0.149094	−	0.0399495i
$713$	0.299136	−	0.0801533i	0.0112027	−	0.00300177i
$714$		−	92.9045i		−	3.47686i
$715$		0			0
$716$	11.7551	+	6.78682i	0.439310	+	0.253635i
$717$	−80.1730	−	21.4823i	−2.99412	−	0.802271i
$718$	−3.44112	+	0.922044i	−0.128421	+	0.0344104i
$719$	−34.6899	+	20.0282i	−1.29372	+	0.746927i	−0.979311	−	0.202362i	$-0.935138\pi$
$719$	−34.6899	+	20.0282i	−1.29372	+	0.746927i	−0.314405	+	0.949289i	$0.601805\pi$
$720$		0			0
$721$			41.3613i			1.54038i
$722$	8.98559	−	16.7409i	0.334409	−	0.623033i
$723$	21.3428	−	21.3428i	0.793746	−	0.793746i
$724$	−3.38512	−	5.86320i	−0.125807	−	0.217904i
$725$		0			0
$726$	−15.6831	+	27.1640i	−0.582056	+	1.00815i
$727$	2.72289	−	10.1620i	0.100986	−	0.376887i	−0.896873	−	0.442289i	$-0.854166\pi$
$727$	2.72289	−	10.1620i	0.100986	−	0.376887i	0.997859	+	0.0654026i	$0.0208332\pi$
$728$	−1.23772	−	4.61925i	−0.0458731	−	0.171201i
$729$		−	20.7933i		−	0.770121i
$730$		0			0
$731$	−33.3058	+	57.6873i	−1.23186	+	2.13364i
$732$	5.17797	+	19.3245i	0.191383	+	0.714252i
$733$	−1.46892	+	1.46892i	−0.0542557	+	0.0542557i	−0.733714	−	0.679458i	$-0.762215\pi$
$733$	−1.46892	+	1.46892i	−0.0542557	+	0.0542557i	0.679458	+	0.733714i	$0.262215\pi$
$734$	−10.4451			−0.385536
$735$		0			0
$736$	−2.14911	+	1.24079i	−0.0792171	+	0.0457360i
$737$	3.87001	+	14.4431i	0.142554	+	0.532017i
$738$	38.1449	+	10.2209i	1.40413	+	0.376236i
$739$	−0.540874	+	0.312274i	−0.0198964	+	0.0114872i	−0.509915	−	0.860225i	$-0.670323\pi$
$739$	−0.540874	+	0.312274i	−0.0198964	+	0.0114872i	0.490019	+	0.871712i	$0.336990\pi$
$740$		0			0
$741$	8.84982	+	11.1706i	0.325106	+	0.410361i
$742$	5.89181	+	5.89181i	0.216295	+	0.216295i
$743$	13.1514	−	49.0817i	0.482478	−	1.80063i	−0.108682	−	0.994077i	$-0.534663\pi$
$743$	13.1514	−	49.0817i	0.482478	−	1.80063i	0.591159	−	0.806555i	$-0.298670\pi$
$744$	−0.198684	−	0.344132i	−0.00728413	−	0.0126165i
$745$		0			0
$746$	0.515028	+	0.892054i	0.0188565	+	0.0326604i
$747$	32.9764	−	8.83600i	1.20654	−	0.323292i
$748$	4.74895	−	4.74895i	0.173639	−	0.173639i
$749$	12.9655			0.473749
$750$		0			0
$751$	1.48564	+	0.857733i	0.0542117	+	0.0312991i	0.526861	−	0.849952i	$-0.323369\pi$
$751$	1.48564	+	0.857733i	0.0542117	+	0.0312991i	−0.472649	+	0.881251i	$0.656702\pi$
$752$	−6.95579	−	6.95579i	−0.253652	−	0.253652i
$753$	36.7703	+	36.7703i	1.33999	+	1.33999i
$754$	−3.06781	+	5.31360i	−0.111723	+	0.193510i
$755$		0			0
$756$	−53.1565	−	30.6899i	−1.93328	−	1.11618i
$757$	−7.94801	+	29.6624i	−0.288875	+	1.07810i	0.657085	+	0.753816i	$0.271789\pi$
$757$	−7.94801	+	29.6624i	−0.288875	+	1.07810i	−0.945961	+	0.324281i	$0.894878\pi$
$758$	−16.3614	−	4.38401i	−0.594271	−	0.159235i
$759$	8.47107			0.307480
$760$		0			0
$761$	−33.0759			−1.19900			−0.599500	−	0.800375i	$-0.704634\pi$
$761$	−33.0759			−1.19900			−0.599500	+	0.800375i	$0.704634\pi$
$762$	3.43646	+	0.920797i	0.124490	+	0.0333570i
$763$	−2.29423	+	8.56219i	−0.0830568	+	0.309972i
$764$	−4.24285	−	2.44961i	−0.153501	−	0.0886238i
$765$		0			0
$766$	15.1956	−	26.3195i	0.549038	−	0.950962i
$767$	−7.86758	−	7.86758i	−0.284082	−	0.284082i
$768$	2.25155	+	2.25155i	0.0812456	+	0.0812456i
$769$	−4.93644	−	2.85006i	−0.178013	−	0.102776i	0.408346	−	0.912827i	$-0.366106\pi$
$769$	−4.93644	−	2.85006i	−0.178013	−	0.102776i	−0.586359	+	0.810052i	$0.699439\pi$
$770$		0			0
$771$	56.2893			2.02721
$772$	−12.9564	+	12.9564i	−0.466310	+	0.466310i
$773$	−10.9859	+	2.94365i	−0.395134	+	0.105876i	−0.450914	−	0.892567i	$-0.648902\pi$
$773$	−10.9859	+	2.94365i	−0.395134	+	0.105876i	0.0557803	+	0.998443i	$0.482235\pi$
$774$	37.9537	+	65.7377i	1.36422	+	2.36289i
$775$		0			0
$776$	−4.79888	−	8.31190i	−0.172270	−	0.298380i
$777$	−19.6217	+	73.2291i	−0.703924	+	2.62708i
$778$	−13.0843	−	13.0843i	−0.469095	−	0.469095i
$779$	−8.88107	+	22.4171i	−0.318197	+	0.803175i
$780$		0			0
$781$	10.1834	−	5.87938i	0.364390	−	0.210381i
$782$	15.0165	+	4.02366i	0.536988	+	0.143886i
$783$	20.3823	+	76.0676i	0.728402	+	2.71843i
$784$	−12.7231	+	7.34570i	−0.454398	+	0.262347i
$785$		0			0
$786$	15.1676			0.541012
$787$	10.8007	−	10.8007i	0.385005	−	0.385005i	−0.487897	−	0.872901i	$-0.662236\pi$
$787$	10.8007	−	10.8007i	0.385005	−	0.385005i	0.872901	+	0.487897i	$0.162236\pi$
$788$	−3.74909	−	13.9918i	−0.133556	−	0.498437i
$789$	−17.8601	+	30.9346i	−0.635836	+	1.10130i
$790$		0			0
$791$		−	60.3883i		−	2.14716i
$792$	−1.98081	−	7.39249i	−0.0703851	−	0.262681i
$793$	1.66974	−	6.23154i	0.0592941	−	0.221288i
$794$	0.214672	−	0.371822i	0.00761842	−	0.0131955i
$795$		0			0
$796$	1.39869	+	2.42260i	0.0495751	+	0.0858667i
$797$	−25.2078	+	25.2078i	−0.892905	+	0.892905i	−0.994796	−	0.101891i	$-0.967511\pi$
$797$	−25.2078	+	25.2078i	−0.892905	+	0.892905i	0.101891	+	0.994796i	$0.467511\pi$
$798$	38.5523	−	51.8877i	1.36474	−	1.83680i
$799$			61.6253i			2.18015i
$800$		0			0
$801$	−25.4635	+	14.7014i	−0.899708	+	0.519447i
$802$	2.59004	−	0.694000i	0.0914576	−	0.0245060i
$803$	10.2516	+	2.74692i	0.361772	+	0.0969365i
$804$	38.4615	+	22.2058i	1.35643	+	0.783137i
$805$		0			0
$806$			0.128139i			0.00451351i
$807$	99.5324	−	26.6696i	3.50371	−	0.938815i
$808$	0.770204	−	0.206376i	0.0270957	−	0.00726027i
$809$		−	11.4475i		−	0.402473i	−0.979543	−	0.201236i	$-0.935504\pi$
$809$		−	11.4475i		−	0.402473i	0.979543	−	0.201236i	$-0.0644959\pi$
$810$		0			0
$811$	−4.22375	−	2.43858i	−0.148316	−	0.0856303i	0.424005	−	0.905660i	$-0.360624\pi$
$811$	−4.22375	−	2.43858i	−0.148316	−	0.0856303i	−0.572321	+	0.820029i	$0.693957\pi$
$812$	26.8820	+	7.20302i	0.943374	+	0.252776i
$813$	−64.2471	+	17.2150i	−2.25325	+	0.603755i
$814$	−4.74621	+	2.74022i	−0.166354	+	0.0960448i
$815$		0			0
$816$		−	19.9477i		−	0.698310i
$817$	−42.5398	+	18.3979i	−1.48828	+	0.643660i
$818$	3.43059	−	3.43059i	0.119948	−	0.119948i
$819$	17.0698	+	29.5658i	0.596469	+	1.03311i
$820$		0			0
$821$	10.9279	−	18.9278i	0.381388	−	0.660584i	−0.609873	−	0.792499i	$-0.708780\pi$
$821$	10.9279	−	18.9278i	0.381388	−	0.660584i	0.991261	+	0.131916i	$0.0421128\pi$
$822$	−6.86682	+	25.6273i	−0.239508	+	0.893855i
$823$	11.4739	+	42.8213i	0.399956	+	1.49266i	0.813172	+	0.582023i	$0.197739\pi$
$823$	11.4739	+	42.8213i	0.399956	+	1.49266i	−0.413216	+	0.910633i	$0.635595\pi$
$824$			8.88076i			0.309376i
$825$		0			0
$826$	−25.2340	+	43.7066i	−0.878003	+	1.52075i
$827$	−8.46359	−	31.5866i	−0.294308	−	1.09837i	−0.941765	−	0.336271i	$-0.890834\pi$
$827$	−8.46359	−	31.5866i	−0.294308	−	1.09837i	0.647457	−	0.762102i	$-0.275832\pi$
$828$	12.5269	−	12.5269i	0.435340	−	0.435340i
$829$	−46.3621			−1.61022			−0.805111	−	0.593125i	$-0.797894\pi$
$829$	−46.3621			−1.61022			−0.805111	+	0.593125i	$0.797894\pi$
$830$		0			0
$831$	4.62347	−	2.66936i	0.160387	−	0.0925992i
$832$	−0.265754	−	0.991808i	−0.00921337	−	0.0343848i
$833$	88.9006	+	23.8208i	3.08022	+	0.825343i
$834$	10.9108	−	6.29935i	0.377810	−	0.218129i
$835$		0			0
$836$	4.62298	−	0.681656i	0.159889	−	0.0235756i
$837$	1.16296	+	1.16296i	0.0401978	+	0.0401978i
$838$	0.756465	−	2.82317i	0.0261317	−	0.0975247i
$839$	−19.7543	−	34.2155i	−0.681996	−	1.18125i	−0.974371	−	0.224948i	$-0.927779\pi$
$839$	−19.7543	−	34.2155i	−0.681996	−	1.18125i	0.292375	−	0.956304i	$-0.405554\pi$
$840$		0			0
$841$	−3.35330	−	5.80809i	−0.115631	−	0.200279i
$842$	11.9363	−	3.19832i	0.411352	−	0.110221i
$843$	−28.2477	+	28.2477i	−0.972901	+	0.972901i
$844$	8.44049			0.290534
$845$		0			0
$846$	60.8169	+	35.1126i	2.09093	+	1.20720i
$847$	−32.4412	−	32.4412i	−1.11469	−	1.11469i
$848$	1.26504	+	1.26504i	0.0434417	+	0.0434417i
$849$	17.4872	−	30.2888i	0.600160	−	1.03951i
$850$		0			0
$851$	−10.9865	−	6.34304i	−0.376611	−	0.217437i
$852$	9.03937	−	33.7354i	0.309684	−	1.15575i
$853$	42.0422	+	11.2652i	1.43950	+	0.385712i	0.892358	−	0.451329i	$-0.149050\pi$
$853$	42.0422	+	11.2652i	1.43950	+	0.385712i	0.547140	+	0.837041i	$0.315717\pi$
$854$	−29.2625			−1.00134
$855$		0			0
$856$	2.78385			0.0951500
$857$	27.1473	+	7.27411i	0.927335	+	0.248479i	0.690718	−	0.723124i	$-0.257295\pi$
$857$	27.1473	+	7.27411i	0.927335	+	0.248479i	0.236617	+	0.971603i	$0.423961\pi$
$858$	−0.907175	+	3.38562i	−0.0309704	+	0.115583i
$859$	−0.904066	−	0.521963i	−0.0308463	−	0.0178091i	0.484498	−	0.874793i	$-0.339002\pi$
$859$	−0.904066	−	0.521963i	−0.0308463	−	0.0178091i	−0.515344	+	0.856983i	$0.672336\pi$
$860$		0			0
$861$	−41.0176	+	71.0445i	−1.39787	+	2.42119i
$862$	15.9967	+	15.9967i	0.544849	+	0.544849i
$863$	−15.5892	−	15.5892i	−0.530663	−	0.530663i	0.390107	−	0.920770i	$-0.372438\pi$
$863$	−15.5892	−	15.5892i	−0.530663	−	0.530663i	−0.920770	+	0.390107i	$0.872438\pi$
$864$	−11.4133	−	6.58949i	−0.388289	−	0.224179i
$865$		0			0
$866$	−13.6565			−0.464068
$867$	−50.0878	+	50.0878i	−1.70107	+	1.70107i
$868$	0.561417	−	0.150431i	0.0190558	−	0.00510597i
$869$	−3.59589	−	6.22827i	−0.121982	−	0.211280i
$870$		0			0
$871$	−7.16067	−	12.4027i	−0.242630	−	0.420248i
$872$	−0.492599	+	1.83840i	−0.0166815	+	0.0622562i
$873$	48.4492	+	48.4492i	1.63976	+	1.63976i
$874$	6.71711	+	8.47858i	0.227209	+	0.286792i
$875$		0			0
$876$	27.2998	−	15.7616i	0.922376	−	0.532534i
$877$	21.8099	+	5.84395i	0.736469	+	0.197336i	0.607508	−	0.794314i	$-0.292169\pi$
$877$	21.8099	+	5.84395i	0.736469	+	0.197336i	0.128961	+	0.991650i	$0.458836\pi$
$878$	0.798812	+	2.98121i	0.0269586	+	0.100611i
$879$	68.4197	−	39.5021i	2.30774	−	1.33237i
$880$		0			0
$881$	31.2152			1.05167			0.525833	−	0.850588i	$-0.323754\pi$
$881$	31.2152			1.05167			0.525833	+	0.850588i	$0.323754\pi$
$882$	74.1618	−	74.1618i	2.49716	−	2.49716i
$883$	2.26117	+	8.43880i	0.0760944	+	0.283988i	0.993479	−	0.114013i	$-0.0363706\pi$
$883$	2.26117	+	8.43880i	0.0760944	+	0.283988i	−0.917385	+	0.398001i	$0.869704\pi$
$884$	−3.21626	+	5.57073i	−0.108175	+	0.187364i
$885$		0			0
$886$		−	21.7117i		−	0.729420i
$887$	13.1580	+	49.1064i	0.441803	+	1.64883i	0.724243	+	0.689545i	$0.242190\pi$
$887$	13.1580	+	49.1064i	0.441803	+	1.64883i	−0.282440	+	0.959285i	$0.591144\pi$
$888$	−4.21301	+	15.7232i	−0.141379	+	0.527635i
$889$	−2.60187	+	4.50658i	−0.0872640	+	0.151146i
$890$		0			0
$891$	11.0139	+	19.0766i	0.368979	+	0.639090i
$892$	9.98099	−	9.98099i	0.334188	−	0.334188i
$893$	−25.5725	+	34.4181i	−0.855750	+	1.15176i
$894$		−	56.5453i		−	1.89116i
$895$		0			0
$896$	−4.03343	+	2.32870i	−0.134747	+	0.0777965i
$897$	−7.83701	+	2.09992i	−0.261670	+	0.0701143i
$898$	−1.13252	−	0.303457i	−0.0377926	−	0.0101265i
$899$	−0.645808	−	0.372857i	−0.0215389	−	0.0124355i
$900$		0			0
$901$		−	11.2077i		−	0.373383i
$902$	−5.72822	+	1.53487i	−0.190729	+	0.0511056i
$903$	−152.312	+	40.8120i	−5.06864	+	1.35814i
$904$		−	12.9661i		−	0.431246i
$905$		0			0
$906$	−65.9173	−	38.0574i	−2.18996	−	1.26437i
$907$	11.6009	+	3.10845i	0.385201	+	0.103214i	0.446222	−	0.894922i	$-0.352769\pi$
$907$	11.6009	+	3.10845i	0.385201	+	0.103214i	−0.0610211	+	0.998136i	$0.519436\pi$
$908$	−1.32859	+	0.355993i	−0.0440907	+	0.0118141i
$909$	−4.92975	+	2.84619i	−0.163509	+	0.0944022i
$910$		0			0
$911$		−	6.19741i		−	0.205330i	−0.994716	−	0.102665i	$-0.967263\pi$
$911$		−	6.19741i		−	0.205330i	0.994716	−	0.102665i	$-0.0327369\pi$
$912$	8.27765	−	11.1409i	0.274100	−	0.368912i
$913$	−3.62517	+	3.62517i	−0.119975	+	0.119975i
$914$	−3.53349	−	6.12019i	−0.116878	−	0.202438i
$915$		0			0
$916$	−2.98980	+	5.17849i	−0.0987859	+	0.171102i
$917$	−5.74199	+	21.4294i	−0.189617	+	0.707661i
$918$	21.3686	+	79.7486i	0.705268	+	2.63209i
$919$		−	41.7333i		−	1.37665i	−0.725401	−	0.688327i	$-0.758345\pi$
$919$		−	41.7333i		−	1.37665i	0.725401	−	0.688327i	$-0.241655\pi$
$920$		0			0
$921$	−24.8379	+	43.0205i	−0.818437	+	1.41757i
$922$	−4.51765	−	16.8601i	−0.148781	−	0.555258i
$923$	−7.96370	+	7.96370i	−0.262128	+	0.262128i
$924$	15.8984			0.523021
$925$		0			0
$926$	19.0593	−	11.0039i	0.626326	−	0.361610i
$927$	−16.4089	−	61.2387i	−0.538938	−	2.01134i
$928$	5.77189	+	1.54657i	0.189472	+	0.0507688i
$929$	6.53344	−	3.77208i	0.214355	−	0.123758i	−0.388979	−	0.921247i	$-0.627172\pi$
$929$	6.53344	−	3.77208i	0.214355	−	0.123758i	0.603334	+	0.797489i	$0.293839\pi$
$930$		0			0
$931$	39.7666	+	50.1949i	1.30330	+	1.64507i
$932$	−4.01601	−	4.01601i	−0.131549	−	0.131549i
$933$	13.0035	−	48.5299i	0.425717	−	1.58880i
$934$	7.89854	+	13.6807i	0.258448	+	0.447645i
$935$		0			0
$936$	3.66510	+	6.34814i	0.119797	+	0.207495i
$937$	−24.0876	+	6.45426i	−0.786908	+	0.210851i	−0.629828	−	0.776734i	$-0.716875\pi$
$937$	−24.0876	+	6.45426i	−0.786908	+	0.210851i	−0.157080	+	0.987586i	$0.550208\pi$
$938$	−45.9334	+	45.9334i	−1.49978	+	1.49978i
$939$	−84.8641			−2.76943
$940$		0			0
$941$	−9.25899	−	5.34568i	−0.301834	−	0.174264i	0.341432	−	0.939906i	$-0.389088\pi$
$941$	−9.25899	−	5.34568i	−0.301834	−	0.174264i	−0.643267	+	0.765642i	$0.722421\pi$
$942$	27.6638	+	27.6638i	0.901334	+	0.901334i
$943$	−9.70672	−	9.70672i	−0.316094	−	0.316094i
$944$	−5.41804	+	9.38432i	−0.176342	+	0.305434i
$945$		0			0
$946$	−9.87183	−	5.69951i	−0.320961	−	0.185307i
$947$	12.4176	−	46.3433i	0.403519	−	1.50595i	−0.403251	−	0.915089i	$-0.632120\pi$
$947$	12.4176	−	46.3433i	0.403519	−	1.50595i	0.806770	−	0.590865i	$-0.201214\pi$
$948$	−20.6329	−	5.52858i	−0.670126	−	0.179560i
$949$	−10.1652			−0.329978
$950$		0			0
$951$	28.8438			0.935326
$952$	28.1829	+	7.55157i	0.913412	+	0.244748i
$953$	−2.47980	+	9.25475i	−0.0803287	+	0.299791i	−0.994389	−	0.105788i	$-0.966263\pi$
$953$	−2.47980	+	9.25475i	−0.0803287	+	0.299791i	0.914060	+	0.405579i	$0.132930\pi$
$954$	−11.0607	−	6.38590i	−0.358103	−	0.206751i
$955$		0			0
$956$	13.0334	−	22.5746i	0.421531	−	0.730114i
$957$	−14.4235	−	14.4235i	−0.466245	−	0.466245i
$958$	9.01556	+	9.01556i	0.291280	+	0.291280i
$959$	−33.6077	−	19.4034i	−1.08525	−	0.626568i
$960$		0			0
$961$	30.9844			0.999498
$962$	3.71167	−	3.71167i	0.119669	−	0.119669i
$963$	−19.1965	+	5.14368i	−0.618597	+	0.165753i
$964$	4.73958	+	8.20920i	0.152652	+	0.264401i
$965$		0			0
$966$	18.4008	+	31.8711i	0.592036	+	1.02544i
$967$	−1.31004	+	4.88914i	−0.0421281	+	0.157224i	−0.983786	−	0.179348i	$-0.942601\pi$
$967$	−1.31004	+	4.88914i	−0.0421281	+	0.157224i	0.941658	+	0.336573i	$0.109268\pi$
$968$	−6.96550	−	6.96550i	−0.223880	−	0.223880i
$969$	−86.0200	+	12.6836i	−2.76336	+	0.407457i
$970$		0			0
$971$	9.02686	−	5.21166i	0.289686	−	0.167250i	−0.348114	−	0.937452i	$-0.613178\pi$
$971$	9.02686	−	5.21166i	0.289686	−	0.167250i	0.637800	+	0.770202i	$0.279845\pi$
$972$	25.0069	+	6.70059i	0.802098	+	0.214922i
$973$	4.76947	+	17.7999i	0.152902	+	0.570639i
$974$	26.3721	−	15.2259i	0.845016	−	0.487870i
$975$		0			0
$976$	−6.28301			−0.201114
$977$	37.9198	−	37.9198i	1.21316	−	1.21316i	0.243182	−	0.969981i	$-0.421809\pi$
$977$	37.9198	−	37.9198i	1.21316	−	1.21316i	0.969981	−	0.243182i	$-0.0781911\pi$
$978$	15.6423	+	58.3779i	0.500186	+	1.86672i
$979$	2.20770	−	3.82385i	0.0705585	−	0.122211i
$980$		0			0
$981$		−	13.5872i		−	0.433805i
$982$	−6.01203	−	22.4372i	−0.191852	−	0.716000i
$983$	−4.97503	+	18.5671i	−0.158679	+	0.592197i	0.840083	+	0.542457i	$0.182506\pi$
$983$	−4.97503	+	18.5671i	−0.158679	+	0.592197i	−0.998762	+	0.0497401i	$0.984161\pi$
$984$	−8.80696	+	15.2541i	−0.280756	+	0.486283i
$985$		0			0
$986$	−18.7172	−	32.4192i	−0.596078	−	1.03244i
$987$	−103.154	+	103.154i	−3.28343	+	3.28343i
$988$	−4.10797	+	1.77664i	−0.130692	+	0.0565224i
$989$		−	26.3863i		−	0.839036i
$990$		0			0
$991$	13.3023	−	7.68007i	0.422561	−	0.243966i	−0.273612	−	0.961840i	$-0.588218\pi$
$991$	13.3023	−	7.68007i	0.422561	−	0.243966i	0.696172	+	0.717875i	$0.254885\pi$
$992$	0.120543	−	0.0322994i	0.00382724	−	0.00102551i
$993$	−38.7195	−	10.3749i	−1.22873	−	0.329236i
$994$	44.2406	+	25.5423i	1.40323	+	0.810153i
$995$		0			0
$996$			15.2273i			0.482496i
$997$	−0.733543	+	0.196552i	−0.0232315	+	0.00622487i	−0.270416	−	0.962744i	$-0.587161\pi$
$997$	−0.733543	+	0.196552i	−0.0232315	+	0.00622487i	0.247185	+	0.968968i	$0.420495\pi$
$998$	−31.6320	+	8.47578i	−1.00129	+	0.268296i
$999$		−	67.3724i		−	2.13157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.f.107.8	yes	32
5.2	odd	4	inner	950.2.q.f.943.1	yes	32
5.3	odd	4	inner	950.2.q.f.943.8	yes	32
5.4	even	2	inner	950.2.q.f.107.1	✓	32
19.8	odd	6	inner	950.2.q.f.407.8	yes	32
95.8	even	12	inner	950.2.q.f.293.8	yes	32
95.27	even	12	inner	950.2.q.f.293.1	yes	32
95.84	odd	6	inner	950.2.q.f.407.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.f.107.1	✓	32	5.4	even	2	inner
950.2.q.f.107.8	yes	32	1.1	even	1	trivial
950.2.q.f.293.1	yes	32	95.27	even	12	inner
950.2.q.f.293.8	yes	32	95.8	even	12	inner
950.2.q.f.407.1	yes	32	95.84	odd	6	inner
950.2.q.f.407.8	yes	32	19.8	odd	6	inner
950.2.q.f.943.1	yes	32	5.2	odd	4	inner
950.2.q.f.943.8	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.824123 - 3.07567i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.59208 - 2.75757i) q^{6} +(3.29328 + 3.29328i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-6.18248 - 3.56945i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.824123 - 3.07567i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.59208 - 2.75757i) q^{6} +(3.29328 + 3.29328i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-6.18248 - 3.56945i) q^{9} +1.07205 q^{11} +(2.25155 - 2.25155i) q^{12} +(-0.991808 + 0.265754i) q^{13} +(2.32870 + 4.03343i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.62141 - 6.05120i) q^{17} +(-5.04797 - 5.04797i) q^{18} +(3.41662 - 2.70679i) q^{19} +(12.8431 - 7.41497i) q^{21} +(1.03552 + 0.277467i) q^{22} +(0.642278 + 2.39702i) q^{23} +(2.75757 - 1.59208i) q^{24} -1.02680 q^{26} +(-9.31894 + 9.31894i) q^{27} +(1.20542 + 4.49871i) q^{28} +(2.98775 - 5.17494i) q^{29} -0.124795i q^{31} +(0.258819 + 0.965926i) q^{32} +(0.883501 - 3.29727i) q^{33} +(3.13233 - 5.42535i) q^{34} +(-3.56945 - 6.18248i) q^{36} +(-3.61481 + 3.61481i) q^{37} +(4.00077 - 1.73028i) q^{38} +3.26949i q^{39} +(-4.79061 + 2.76586i) q^{41} +(14.3246 - 3.83827i) q^{42} +(-10.2706 - 2.75200i) q^{43} +(0.928423 + 0.536025i) q^{44} +2.48157i q^{46} +(-9.50178 + 2.54600i) q^{47} +(3.07567 - 0.824123i) q^{48} +14.6914i q^{49} +(-17.2752 - 9.97386i) q^{51} +(-0.991808 - 0.265754i) q^{52} +(1.72808 - 0.463037i) q^{53} +(-11.4133 + 6.58949i) q^{54} +4.65740i q^{56} +(-5.50949 - 12.7391i) q^{57} +(4.22532 - 4.22532i) q^{58} +(5.41804 + 9.38432i) q^{59} +(-3.14151 + 5.44125i) q^{61} +(0.0322994 - 0.120543i) q^{62} +(-8.60542 - 32.1159i) q^{63} +1.00000i q^{64} +(1.70679 - 2.95625i) q^{66} +(3.60991 + 13.4724i) q^{67} +(4.42978 - 4.42978i) q^{68} +7.90174 q^{69} +(9.49898 - 5.48424i) q^{71} +(-1.84769 - 6.89566i) q^{72} +(9.56263 + 2.56230i) q^{73} +(-4.42722 + 2.55606i) q^{74} +(4.31227 - 0.635843i) q^{76} +(3.53056 + 3.53056i) q^{77} +(-0.846205 + 3.15808i) q^{78} +(-3.35422 - 5.80968i) q^{79} +(10.2737 + 17.7945i) q^{81} +(-5.34323 + 1.43171i) q^{82} +(-3.38153 + 3.38153i) q^{83} +14.8299 q^{84} +(-9.20836 - 5.31645i) q^{86} +(-13.4541 - 13.4541i) q^{87} +(0.758054 + 0.758054i) q^{88} +(2.05933 - 3.56686i) q^{89} +(-4.14151 - 2.39110i) q^{91} +(-0.642278 + 2.39702i) q^{92} +(-0.383829 - 0.102847i) q^{93} -9.83697 q^{94} +3.18417 q^{96} +(-9.27072 - 2.48408i) q^{97} +(-3.80242 + 14.1908i) q^{98} +(-6.62793 - 3.82664i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{6}+O(q^{10}) \) 32 * q + 4 * q^6	\( 32 q + 4 q^{6} + 72 q^{11} + 16 q^{16} + 60 q^{21} + 8 q^{26} - 28 q^{36} - 84 q^{41} - 84 q^{51} - 52 q^{61} - 24 q^{71} + 16 q^{76} + 64 q^{81} - 36 q^{86} - 84 q^{91} + 8 q^{96}+O(q^{100}) \) 32 * q + 4 * q^6 + 72 * q^11 + 16 * q^16 + 60 * q^21 + 8 * q^26 - 28 * q^36 - 84 * q^41 - 84 * q^51 - 52 * q^61 - 24 * q^71 + 16 * q^76 + 64 * q^81 - 36 * q^86 - 84 * q^91 + 8 * q^96

Introduction

L-functions

Modular forms

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Database

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