LMFDB - Embedded newform 380.2.u.b.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(61,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("380.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 $ x^18 - 3x^17 + 21x^16 - 30x^15 + 192x^14 - 207x^13 + 1178x^12 - 705x^11 + 4413x^10 - 2224x^9 + 11430x^8 - 4101x^7 + 19237x^6 - 7125x^5 + 21573x^4 - 5266x^3 + 13851x^2 - 3285*x + 5329
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			321.2
Root			$0.443231 + 0.767698i$ of defining polynomial
Character	$\chi$	$=$	380.321
Dual form			380.2.u.b.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.679069 - 0.569806i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(0.460431 + 0.797489i) q^{7} +(-0.384489 - 2.18055i) q^{9} +O(q^{10})$	\(q+(-0.679069 - 0.569806i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(0.460431 + 0.797489i) q^{7} +(-0.384489 - 2.18055i) q^{9} +(1.03842 - 1.79860i) q^{11} +(3.22410 - 2.70534i) q^{13} +(0.833001 + 0.303188i) q^{15} +(0.340401 - 1.93051i) q^{17} +(0.207532 - 4.35396i) q^{19} +(0.141750 - 0.803906i) q^{21} +(-0.570023 - 0.207471i) q^{23} +(0.766044 - 0.642788i) q^{25} +(-2.31109 + 4.00292i) q^{27} +(-1.31313 - 7.44714i) q^{29} +(1.07398 + 1.86019i) q^{31} +(-1.73001 + 0.629673i) q^{33} +(-0.705421 - 0.591918i) q^{35} +3.88044 q^{37} -3.73090 q^{39} +(-4.50081 - 3.77663i) q^{41} +(-0.638807 + 0.232507i) q^{43} +(1.10709 + 1.91754i) q^{45} +(1.88450 + 10.6875i) q^{47} +(3.07601 - 5.32780i) q^{49} +(-1.33117 + 1.11699i) q^{51} +(4.25090 + 1.54720i) q^{53} +(-0.360640 + 2.04529i) q^{55} +(-2.62184 + 2.83838i) q^{57} +(-1.02661 + 5.82217i) q^{59} +(6.55984 + 2.38759i) q^{61} +(1.56193 - 1.31062i) q^{63} +(-2.10438 + 3.64489i) q^{65} +(1.32744 + 7.52828i) q^{67} +(0.268866 + 0.465690i) q^{69} +(-10.8097 + 3.93442i) q^{71} +(2.42577 + 2.03547i) q^{73} -0.886461 q^{75} +1.91248 q^{77} +(-2.36217 - 1.98209i) q^{79} +(-2.39169 + 0.870503i) q^{81} +(-5.06043 - 8.76492i) q^{83} +(0.340401 + 1.93051i) q^{85} +(-3.35172 + 5.80535i) q^{87} +(2.60677 - 2.18734i) q^{89} +(3.64195 + 1.32556i) q^{91} +(0.330641 - 1.87516i) q^{93} +(1.29412 + 4.16236i) q^{95} +(-3.29871 + 18.7079i) q^{97} +(-4.32119 - 1.57279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 15 * q^9	$ 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.679069	−	0.569806i	−0.392061	−	0.328978i	0.425355	−	0.905027i	$-0.360149\pi$
$3$	−0.679069	−	0.569806i	−0.392061	−	0.328978i	−0.817415	+	0.576049i	$0.804594\pi$
$4$		0			0
$5$	−0.939693	+	0.342020i	−0.420243	+	0.152956i
$5$	−0.939693	+	0.342020i	−0.420243	+	0.152956i
$6$		0			0
$7$	0.460431	+	0.797489i	0.174026	+	0.301423i	0.939824	−	0.341659i	$-0.110989\pi$
$7$	0.460431	+	0.797489i	0.174026	+	0.301423i	−0.765797	+	0.643082i	$0.777656\pi$
$8$		0			0
$9$	−0.384489	−	2.18055i	−0.128163	−	0.726849i
$10$		0			0
$11$	1.03842	−	1.79860i	0.313096	−	0.542298i	−0.665935	−	0.746010i	$-0.731967\pi$
$11$	1.03842	−	1.79860i	0.313096	−	0.542298i	0.979031	+	0.203712i	$0.0653005\pi$
$12$		0			0
$13$	3.22410	−	2.70534i	0.894203	−	0.750326i	−0.0748453	−	0.997195i	$-0.523846\pi$
$13$	3.22410	−	2.70534i	0.894203	−	0.750326i	0.969049	+	0.246869i	$0.0794019\pi$
$14$		0			0
$15$	0.833001	+	0.303188i	0.215080	+	0.0782827i
$16$		0			0
$17$	0.340401	−	1.93051i	0.0825594	−	0.468218i	−0.915297	−	0.402779i	$-0.868044\pi$
$17$	0.340401	−	1.93051i	0.0825594	−	0.468218i	0.997857	−	0.0654386i	$-0.0208447\pi$
$18$		0			0
$19$	0.207532	−	4.35396i	0.0476111	−	0.998866i
$19$	0.207532	−	4.35396i	0.0476111	−	0.998866i
$20$		0			0
$21$	0.141750	−	0.803906i	0.0309325	−	0.175427i
$22$		0			0
$23$	−0.570023	−	0.207471i	−0.118858	−	0.0432608i	0.281906	−	0.959442i	$-0.409033\pi$
$23$	−0.570023	−	0.207471i	−0.118858	−	0.0432608i	−0.400764	+	0.916181i	$0.631255\pi$
$24$		0			0
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$		0			0
$27$	−2.31109	+	4.00292i	−0.444769	+	0.770362i
$28$		0			0
$29$	−1.31313	−	7.44714i	−0.243843	−	1.38290i	−0.823165	−	0.567802i	$-0.807794\pi$
$29$	−1.31313	−	7.44714i	−0.243843	−	1.38290i	0.579323	−	0.815098i	$-0.303317\pi$
$30$		0			0
$31$	1.07398	+	1.86019i	0.192893	+	0.334100i	0.946208	−	0.323560i	$-0.104880\pi$
$31$	1.07398	+	1.86019i	0.192893	+	0.334100i	−0.753315	+	0.657660i	$0.771546\pi$
$32$		0			0
$33$	−1.73001	+	0.629673i	−0.301157	+	0.109612i
$34$		0			0
$35$	−0.705421	−	0.591918i	−0.119238	−	0.100052i
$36$		0			0
$37$	3.88044			0.637940			0.318970	−	0.947765i	$-0.396663\pi$
$37$	3.88044			0.637940			0.318970	+	0.947765i	$0.396663\pi$
$38$		0			0
$39$	−3.73090			−0.597422
$40$		0			0
$41$	−4.50081	−	3.77663i	−0.702909	−	0.589811i	0.219691	−	0.975570i	$-0.429495\pi$
$41$	−4.50081	−	3.77663i	−0.702909	−	0.589811i	−0.922600	+	0.385759i	$0.873940\pi$
$42$		0			0
$43$	−0.638807	+	0.232507i	−0.0974171	+	0.0354569i	−0.390269	−	0.920701i	$-0.627618\pi$
$43$	−0.638807	+	0.232507i	−0.0974171	+	0.0354569i	0.292852	+	0.956158i	$0.405396\pi$
$44$		0			0
$45$	1.10709	+	1.91754i	0.165036	+	0.285850i
$46$		0			0
$47$	1.88450	+	10.6875i	0.274883	+	1.55894i	0.739334	+	0.673339i	$0.235141\pi$
$47$	1.88450	+	10.6875i	0.274883	+	1.55894i	−0.464451	+	0.885599i	$0.653748\pi$
$48$		0			0
$49$	3.07601	−	5.32780i	0.439430	−	0.761114i
$50$		0			0
$51$	−1.33117	+	1.11699i	−0.186402	+	0.156410i
$52$		0			0
$53$	4.25090	+	1.54720i	0.583907	+	0.212525i	0.617047	−	0.786926i	$-0.288329\pi$
$53$	4.25090	+	1.54720i	0.583907	+	0.212525i	−0.0331407	+	0.999451i	$0.510551\pi$
$54$		0			0
$55$	−0.360640	+	2.04529i	−0.0486287	+	0.275787i
$56$		0			0
$57$	−2.62184	+	2.83838i	−0.347271	+	0.375953i
$58$		0			0
$59$	−1.02661	+	5.82217i	−0.133653	+	0.757982i	0.842136	+	0.539266i	$0.181298\pi$
$59$	−1.02661	+	5.82217i	−0.133653	+	0.757982i	−0.975788	+	0.218716i	$0.929813\pi$
$60$		0			0
$61$	6.55984	+	2.38759i	0.839902	+	0.305699i	0.725916	−	0.687783i	$-0.241416\pi$
$61$	6.55984	+	2.38759i	0.839902	+	0.305699i	0.113986	+	0.993482i	$0.463638\pi$
$62$		0			0
$63$	1.56193	−	1.31062i	0.196785	−	0.165122i
$64$		0			0
$65$	−2.10438	+	3.64489i	−0.261016	+	0.452093i
$66$		0			0
$67$	1.32744	+	7.52828i	0.162172	+	0.919726i	0.951932	+	0.306309i	$0.0990942\pi$
$67$	1.32744	+	7.52828i	0.162172	+	0.919726i	−0.789760	+	0.613417i	$0.789795\pi$
$68$		0			0
$69$	0.268866	+	0.465690i	0.0323677	+	0.0560625i
$70$		0			0
$71$	−10.8097	+	3.93442i	−1.28288	+	0.466930i	−0.891383	−	0.453251i	$-0.850264\pi$
$71$	−10.8097	+	3.93442i	−1.28288	+	0.466930i	−0.391495	+	0.920180i	$0.628042\pi$
$72$		0			0
$73$	2.42577	+	2.03547i	0.283915	+	0.238233i	0.773612	−	0.633660i	$-0.218448\pi$
$73$	2.42577	+	2.03547i	0.283915	+	0.238233i	−0.489697	+	0.871893i	$0.662892\pi$
$74$		0			0
$75$	−0.886461			−0.102360
$76$		0			0
$77$	1.91248			0.217948
$78$		0			0
$79$	−2.36217	−	1.98209i	−0.265765	−	0.223003i	0.500161	−	0.865933i	$-0.333274\pi$
$79$	−2.36217	−	1.98209i	−0.265765	−	0.223003i	−0.765925	+	0.642930i	$0.777719\pi$
$80$		0			0
$81$	−2.39169	+	0.870503i	−0.265743	+	0.0967225i
$82$		0			0
$83$	−5.06043	−	8.76492i	−0.555454	−	0.962075i	−0.997868	−	0.0652636i	$-0.979211\pi$
$83$	−5.06043	−	8.76492i	−0.555454	−	0.962075i	0.442414	−	0.896811i	$-0.354122\pi$
$84$		0			0
$85$	0.340401	+	1.93051i	0.0369217	+	0.209393i
$86$		0			0
$87$	−3.35172	+	5.80535i	−0.359342	+	0.622399i
$88$		0			0
$89$	2.60677	−	2.18734i	0.276317	−	0.231858i	−0.494089	−	0.869412i	$-0.664498\pi$
$89$	2.60677	−	2.18734i	0.276317	−	0.231858i	0.770406	+	0.637554i	$0.220054\pi$
$90$		0			0
$91$	3.64195	+	1.32556i	0.381780	+	0.138957i
$92$		0			0
$93$	0.330641	−	1.87516i	0.0342859	−	0.194445i
$94$		0			0
$95$	1.29412	+	4.16236i	0.132774	+	0.427049i
$96$		0			0
$97$	−3.29871	+	18.7079i	−0.334933	+	1.89950i	0.0929607	+	0.995670i	$0.470367\pi$
$97$	−3.29871	+	18.7079i	−0.334933	+	1.89950i	−0.427894	+	0.903829i	$0.640744\pi$
$98$		0			0
$99$	−4.32119	−	1.57279i	−0.434296	−	0.158071i
$100$		0			0
$101$	9.57643	−	8.03558i	0.952890	−	0.799570i	−0.0268917	−	0.999638i	$-0.508561\pi$
$101$	9.57643	−	8.03558i	0.952890	−	0.799570i	0.979782	+	0.200069i	$0.0641165\pi$
$102$		0			0
$103$	−0.347379	+	0.601678i	−0.0342283	+	0.0592851i	−0.882632	−	0.470064i	$-0.844231\pi$
$103$	−0.347379	+	0.601678i	−0.0342283	+	0.0592851i	0.848404	+	0.529350i	$0.177564\pi$
$104$		0			0
$105$	0.141750	+	0.803906i	0.0138334	+	0.0784532i
$106$		0			0
$107$	3.22893	+	5.59267i	0.312152	+	0.540664i	0.978828	−	0.204684i	$-0.0656167\pi$
$107$	3.22893	+	5.59267i	0.312152	+	0.540664i	−0.666676	+	0.745348i	$0.732283\pi$
$108$		0			0
$109$	1.58055	−	0.575274i	0.151389	−	0.0551013i	−0.265214	−	0.964190i	$-0.585443\pi$
$109$	1.58055	−	0.575274i	0.151389	−	0.0551013i	0.416603	+	0.909088i	$0.363220\pi$
$110$		0			0
$111$	−2.63508	−	2.21110i	−0.250111	−	0.209868i
$112$		0			0
$113$	−17.7924			−1.67376			−0.836882	−	0.547383i	$-0.815624\pi$
$113$	−17.7924			−1.67376			−0.836882	+	0.547383i	$0.815624\pi$
$114$		0			0
$115$	0.606605			0.0565663
$116$		0			0
$117$	−7.13875	−	5.99012i	−0.659978	−	0.553787i
$118$		0			0
$119$	1.69629	−	0.617400i	0.155499	−	0.0565970i
$120$		0			0
$121$	3.34336	+	5.79087i	0.303942	+	0.526443i
$122$		0			0
$123$	0.904414	+	5.12919i	0.0815482	+	0.462483i
$124$		0			0
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$		0			0
$127$	2.51384	−	2.10936i	0.223067	−	0.187176i	−0.524404	−	0.851469i	$-0.675712\pi$
$127$	2.51384	−	2.10936i	0.223067	−	0.187176i	0.747472	+	0.664294i	$0.231268\pi$
$128$		0			0
$129$	0.566278	+	0.206108i	0.0498580	+	0.0181468i
$130$		0			0
$131$	−1.19306	+	6.76619i	−0.104238	+	0.591164i	0.887284	+	0.461224i	$0.152590\pi$
$131$	−1.19306	+	6.76619i	−0.104238	+	0.591164i	−0.991522	+	0.129940i	$0.958521\pi$
$132$		0			0
$133$	3.56779	−	1.83919i	0.309366	−	0.159478i
$134$		0			0
$135$	0.802632	−	4.55195i	0.0690796	−	0.391770i
$136$		0			0
$137$	−3.71112	−	1.35074i	−0.317063	−	0.115401i	0.178587	−	0.983924i	$-0.442848\pi$
$137$	−3.71112	−	1.35074i	−0.317063	−	0.115401i	−0.495649	+	0.868523i	$0.665070\pi$
$138$		0			0
$139$	13.2455	−	11.1143i	1.12347	−	0.942701i	0.124693	−	0.992195i	$-0.460205\pi$
$139$	13.2455	−	11.1143i	1.12347	−	0.942701i	0.998774	+	0.0494941i	$0.0157609\pi$
$140$		0			0
$141$	4.81012	−	8.33138i	0.405085	−	0.701628i
$142$		0			0
$143$	−1.51785	−	8.60814i	−0.126929	−	0.719849i
$144$		0			0
$145$	3.78101	+	6.54891i	0.313996	+	0.543857i
$146$		0			0
$147$	−5.12464	+	1.86521i	−0.422673	+	0.153840i
$148$		0			0
$149$	−2.44856	−	2.05459i	−0.200594	−	0.168319i	0.536957	−	0.843609i	$-0.319574\pi$
$149$	−2.44856	−	2.05459i	−0.200594	−	0.168319i	−0.737551	+	0.675291i	$0.764018\pi$
$150$		0			0
$151$	−11.8963			−0.968110			−0.484055	−	0.875038i	$-0.660837\pi$
$151$	−11.8963			−0.968110			−0.484055	+	0.875038i	$0.660837\pi$
$152$		0			0
$153$	−4.34045			−0.350905
$154$		0			0
$155$	−1.64544	−	1.38068i	−0.132165	−	0.110899i
$156$		0			0
$157$	18.4402	−	6.71170i	1.47169	−	0.535652i	0.523132	−	0.852252i	$-0.324763\pi$
$157$	18.4402	−	6.71170i	1.47169	−	0.535652i	0.948559	+	0.316600i	$0.102541\pi$
$158$		0			0
$159$	−2.00505	−	3.47285i	−0.159011	−	0.275415i
$160$		0			0
$161$	−0.0969998	−	0.550113i	−0.00764465	−	0.0433550i
$162$		0			0
$163$	9.37242	−	16.2335i	0.734105	−	1.27151i	−0.221010	−	0.975271i	$-0.570935\pi$
$163$	9.37242	−	16.2335i	0.734105	−	1.27151i	0.955115	−	0.296235i	$-0.0957312\pi$
$164$		0			0
$165$	1.41032	−	1.18340i	0.109793	−	0.0921275i
$166$		0			0
$167$	4.73371	+	1.72293i	0.366306	+	0.133324i	0.518614	−	0.855009i	$-0.326448\pi$
$167$	4.73371	+	1.72293i	0.366306	+	0.133324i	−0.152308	+	0.988333i	$0.548671\pi$
$168$		0			0
$169$	0.818517	−	4.64204i	0.0629629	−	0.357080i
$170$		0			0
$171$	−9.57380	+	1.22152i	−0.732127	+	0.0934117i
$172$		0			0
$173$	−2.60163	+	14.7546i	−0.197799	+	1.12177i	0.710578	+	0.703618i	$0.248434\pi$
$173$	−2.60163	+	14.7546i	−0.197799	+	1.12177i	−0.908377	+	0.418153i	$0.862678\pi$
$174$		0			0
$175$	0.865327	+	0.314953i	0.0654125	+	0.0238082i
$176$		0			0
$177$	4.01464	−	3.36869i	0.301759	−	0.253206i
$178$		0			0
$179$	1.18715	−	2.05620i	0.0887316	−	0.153688i	−0.818244	−	0.574872i	$-0.805052\pi$
$179$	1.18715	−	2.05620i	0.0887316	−	0.153688i	0.906975	+	0.421184i	$0.138385\pi$
$180$		0			0
$181$	−2.19843	−	12.4679i	−0.163408	−	0.926732i	−0.950691	−	0.310140i	$-0.899624\pi$
$181$	−2.19843	−	12.4679i	−0.163408	−	0.926732i	0.787283	−	0.616592i	$-0.211487\pi$
$182$		0			0
$183$	−3.09412	−	5.35918i	−0.228724	−	0.396162i
$184$		0			0
$185$	−3.64642	+	1.32719i	−0.268090	+	0.0975768i
$186$		0			0
$187$	−3.11874	−	2.61693i	−0.228065	−	0.191369i
$188$		0			0
$189$	−4.25638			−0.309606
$190$		0			0
$191$	21.7998			1.57737			0.788687	−	0.614795i	$-0.210761\pi$
$191$	21.7998			1.57737			0.788687	+	0.614795i	$0.210761\pi$
$192$		0			0
$193$	−4.94729	−	4.15127i	−0.356114	−	0.298815i	0.447126	−	0.894471i	$-0.352448\pi$
$193$	−4.94729	−	4.15127i	−0.356114	−	0.298815i	−0.803240	+	0.595656i	$0.796892\pi$
$194$		0			0
$195$	3.50590	−	1.27604i	0.251063	−	0.0913794i
$196$		0			0
$197$	−4.73539	−	8.20194i	−0.337383	−	0.584364i	0.646557	−	0.762866i	$-0.276208\pi$
$197$	−4.73539	−	8.20194i	−0.337383	−	0.584364i	−0.983940	+	0.178502i	$0.942875\pi$
$198$		0			0
$199$	4.28855	+	24.3216i	0.304007	+	1.72411i	0.628142	+	0.778099i	$0.283816\pi$
$199$	4.28855	+	24.3216i	0.304007	+	1.72411i	−0.324135	+	0.946011i	$0.605073\pi$
$200$		0			0
$201$	3.38824	−	5.86860i	0.238988	−	0.413939i
$202$		0			0
$203$	5.33441	−	4.47610i	0.374402	−	0.314161i
$204$		0			0
$205$	5.52107	+	2.00950i	0.385608	+	0.140350i
$206$		0			0
$207$	−0.233233	+	1.32273i	−0.0162108	+	0.0919363i
$208$		0			0
$209$	−7.61552	−	4.89451i	−0.526776	−	0.338560i
$210$		0			0
$211$	−0.338736	+	1.92107i	−0.0233196	+	0.132252i	−0.994245	−	0.107130i	$-0.965834\pi$
$211$	−0.338736	+	1.92107i	−0.0233196	+	0.132252i	0.970925	+	0.239382i	$0.0769449\pi$
$212$		0			0
$213$	9.58240	+	3.48771i	0.656575	+	0.238974i
$214$		0			0
$215$	0.520760	−	0.436970i	0.0355156	−	0.0298011i
$216$		0			0
$217$	−0.988989	+	1.71298i	−0.0671369	+	0.116285i
$218$		0			0
$219$	−0.487446	−	2.76444i	−0.0329385	−	0.186804i
$220$		0			0
$221$	−4.12520	−	7.14506i	−0.277491	−	0.480628i
$222$		0			0
$223$	22.0336	−	8.01957i	1.47548	−	0.537030i	0.525896	−	0.850549i	$-0.323730\pi$
$223$	22.0336	−	8.01957i	1.47548	−	0.537030i	0.949582	+	0.313518i	$0.101508\pi$
$224$		0			0
$225$	−1.69617	−	1.42325i	−0.113078	−	0.0948834i
$226$		0			0
$227$	−4.14223			−0.274929			−0.137465	−	0.990507i	$-0.543895\pi$
$227$	−4.14223			−0.274929			−0.137465	+	0.990507i	$0.543895\pi$
$228$		0			0
$229$	0.644603			0.0425965			0.0212983	−	0.999773i	$-0.493220\pi$
$229$	0.644603			0.0425965			0.0212983	+	0.999773i	$0.493220\pi$
$230$		0			0
$231$	−1.29871	−	1.08975i	−0.0854488	−	0.0717000i
$232$		0			0
$233$	−1.96247	+	0.714281i	−0.128566	+	0.0467941i	−0.405502	−	0.914094i	$-0.632903\pi$
$233$	−1.96247	+	0.714281i	−0.128566	+	0.0467941i	0.276936	+	0.960888i	$0.410681\pi$
$234$		0			0
$235$	−5.42621	−	9.39847i	−0.353967	−	0.613088i
$236$		0			0
$237$	0.474665	+	2.69196i	0.0308328	+	0.174861i
$238$		0			0
$239$	3.10456	−	5.37725i	0.200817	−	0.347825i	−0.747975	−	0.663727i	$-0.768974\pi$
$239$	3.10456	−	5.37725i	0.200817	−	0.347825i	0.948792	+	0.315902i	$0.102307\pi$
$240$		0			0
$241$	−7.33621	+	6.15581i	−0.472567	+	0.396531i	−0.847730	−	0.530428i	$-0.822031\pi$
$241$	−7.33621	+	6.15581i	−0.472567	+	0.396531i	0.375163	+	0.926959i	$0.377587\pi$
$242$		0			0
$243$	15.1504	+	5.51430i	0.971899	+	0.353742i
$244$		0			0
$245$	−1.06829	+	6.05855i	−0.0682503	+	0.387067i
$246$		0			0
$247$	−11.1098	−	14.5990i	−0.706901	−	0.928913i
$248$		0			0
$249$	−1.55793	+	8.83544i	−0.0987296	+	0.559924i
$250$		0			0
$251$	−9.59301	−	3.49157i	−0.605506	−	0.220386i	0.0210300	−	0.999779i	$-0.493305\pi$
$251$	−9.59301	−	3.49157i	−0.605506	−	0.220386i	−0.626536	+	0.779393i	$0.715528\pi$
$252$		0			0
$253$	−0.965082	+	0.809800i	−0.0606742	+	0.0509117i
$254$		0			0
$255$	0.868862	−	1.50491i	0.0544102	−	0.0942413i
$256$		0			0
$257$	−0.128277	−	0.727493i	−0.00800168	−	0.0453798i	0.980545	−	0.196292i	$-0.0628900\pi$
$257$	−0.128277	−	0.727493i	−0.00800168	−	0.0453798i	−0.988547	+	0.150912i	$0.951779\pi$
$258$		0			0
$259$	1.78667	+	3.09461i	0.111018	+	0.192290i
$260$		0			0
$261$	−15.7340	+	5.72670i	−0.973908	+	0.354474i
$262$		0			0
$263$	−16.5311	−	13.8712i	−1.01935	−	0.855336i	−0.0298039	−	0.999556i	$-0.509488\pi$
$263$	−16.5311	−	13.8712i	−1.01935	−	0.855336i	−0.989546	+	0.144220i	$0.953933\pi$
$264$		0			0
$265$	−4.52372			−0.277890
$266$		0			0
$267$	−3.01654			−0.184609
$268$		0			0
$269$	−7.00867	−	5.88097i	−0.427326	−	0.358569i	0.403616	−	0.914929i	$-0.367753\pi$
$269$	−7.00867	−	5.88097i	−0.427326	−	0.358569i	−0.830942	+	0.556359i	$0.812198\pi$
$270$		0			0
$271$	4.87686	−	1.77503i	0.296248	−	0.107826i	−0.189620	−	0.981858i	$-0.560726\pi$
$271$	4.87686	−	1.77503i	0.296248	−	0.107826i	0.485868	+	0.874032i	$0.338503\pi$
$272$		0			0
$273$	−1.71782	−	2.97535i	−0.103967	−	0.180077i
$274$		0			0
$275$	−0.360640	−	2.04529i	−0.0217474	−	0.123336i
$276$		0			0
$277$	11.7053	−	20.2742i	0.703303	−	1.21816i	−0.263998	−	0.964523i	$-0.585041\pi$
$277$	11.7053	−	20.2742i	0.703303	−	1.21816i	0.967301	−	0.253633i	$-0.0816255\pi$
$278$		0			0
$279$	3.64330	−	3.05709i	0.218119	−	0.183023i
$280$		0			0
$281$	17.4286	+	6.34349i	1.03970	+	0.378421i	0.804767	−	0.593590i	$-0.202290\pi$
$281$	17.4286	+	6.34349i	1.03970	+	0.378421i	0.234935	+	0.972011i	$0.424512\pi$
$282$		0			0
$283$	−3.82002	+	21.6644i	−0.227077	+	1.28782i	0.631599	+	0.775295i	$0.282399\pi$
$283$	−3.82002	+	21.6644i	−0.227077	+	1.28782i	−0.858675	+	0.512520i	$0.828712\pi$
$284$		0			0
$285$	1.49294	−	3.56393i	0.0884341	−	0.211109i
$286$		0			0
$287$	0.939510	−	5.32823i	0.0554575	−	0.314515i
$288$		0			0
$289$	12.3638	+	4.50005i	0.727281	+	0.264709i
$290$		0			0
$291$	12.8999	−	10.8243i	0.756207	−	0.634533i
$292$		0			0
$293$	−11.7723	+	20.3902i	−0.687745	+	1.19121i	0.284821	+	0.958581i	$0.408066\pi$
$293$	−11.7723	+	20.3902i	−0.687745	+	1.19121i	−0.972566	+	0.232629i	$0.925267\pi$
$294$		0			0
$295$	−1.02661	−	5.82217i	−0.0597713	−	0.338980i
$296$		0			0
$297$	4.79977	+	8.31344i	0.278511	+	0.482395i
$298$		0			0
$299$	−2.39909	+	0.873197i	−0.138743	+	0.0504983i
$300$		0			0
$301$	−0.479548	−	0.402388i	−0.0276407	−	0.0231933i
$302$		0			0
$303$	−11.0818			−0.636631
$304$		0			0
$305$	−6.98084			−0.399722
$306$		0			0
$307$	2.98192	+	2.50213i	0.170187	+	0.142804i	0.723903	−	0.689902i	$-0.242346\pi$
$307$	2.98192	+	2.50213i	0.170187	+	0.142804i	−0.553716	+	0.832706i	$0.686791\pi$
$308$		0			0
$309$	0.578734	−	0.210642i	0.0329230	−	0.0119830i
$310$		0			0
$311$	12.5567	+	21.7489i	0.712028	+	1.23327i	0.964095	+	0.265559i	$0.0855564\pi$
$311$	12.5567	+	21.7489i	0.712028	+	1.23327i	−0.252067	+	0.967710i	$0.581110\pi$
$312$		0			0
$313$	4.10192	+	23.2631i	0.231854	+	1.31491i	0.849139	+	0.528169i	$0.177121\pi$
$313$	4.10192	+	23.2631i	0.231854	+	1.31491i	−0.617285	+	0.786740i	$0.711767\pi$
$314$		0			0
$315$	−1.01948	+	1.76579i	−0.0574411	+	0.0994910i
$316$		0			0
$317$	4.96644	−	4.16734i	0.278943	−	0.234061i	−0.492572	−	0.870271i	$-0.663943\pi$
$317$	4.96644	−	4.16734i	0.278943	−	0.234061i	0.771516	+	0.636210i	$0.219499\pi$
$318$		0			0
$319$	−14.7580	−	5.37148i	−0.826290	−	0.300745i
$320$		0			0
$321$	0.994074	−	5.63767i	0.0554838	−	0.314664i
$322$		0			0
$323$	−8.33472	−	1.88274i	−0.463756	−	0.104758i
$324$		0			0
$325$	0.730843	−	4.14482i	0.0405399	−	0.229913i
$326$		0			0
$327$	−1.40110	−	0.509958i	−0.0774809	−	0.0282008i
$328$		0			0
$329$	−7.65552	+	6.42374i	−0.422062	+	0.354152i
$330$		0			0
$331$	−9.62278	+	16.6671i	−0.528916	+	0.916109i	0.470515	+	0.882392i	$0.344068\pi$
$331$	−9.62278	+	16.6671i	−0.528916	+	0.916109i	−0.999431	+	0.0337175i	$0.989265\pi$
$332$		0			0
$333$	−1.49199	−	8.46148i	−0.0817604	−	0.463686i
$334$		0			0
$335$	−3.82221	−	6.62026i	−0.208830	−	0.361703i
$336$		0			0
$337$	−15.9785	+	5.81569i	−0.870402	+	0.316801i	−0.738330	−	0.674439i	$-0.764385\pi$
$337$	−15.9785	+	5.81569i	−0.870402	+	0.316801i	−0.132072	+	0.991240i	$0.542163\pi$
$338$		0			0
$339$	12.0822	+	10.1382i	0.656217	+	0.550631i
$340$		0			0
$341$	4.46099			0.241576
$342$		0			0
$343$	12.1112			0.653942
$344$		0			0
$345$	−0.411927	−	0.345648i	−0.0221774	−	0.0186090i
$346$		0			0
$347$	17.2902	−	6.29311i	0.928186	−	0.337832i	0.166696	−	0.986008i	$-0.446690\pi$
$347$	17.2902	−	6.29311i	0.928186	−	0.337832i	0.761490	+	0.648176i	$0.224468\pi$
$348$		0			0
$349$	15.7745	+	27.3223i	0.844392	+	1.46253i	0.886148	+	0.463402i	$0.153372\pi$
$349$	15.7745	+	27.3223i	0.844392	+	1.46253i	−0.0417557	+	0.999128i	$0.513295\pi$
$350$		0			0
$351$	3.37809	+	19.1581i	0.180309	+	1.02258i
$352$		0			0
$353$	−16.3730	+	28.3588i	−0.871444	+	1.50939i	−0.0109414	+	0.999940i	$0.503483\pi$
$353$	−16.3730	+	28.3588i	−0.871444	+	1.50939i	−0.860503	+	0.509446i	$0.829850\pi$
$354$		0			0
$355$	8.81217	−	7.39429i	0.467701	−	0.392448i
$356$		0			0
$357$	−1.50370	−	0.547302i	−0.0795842	−	0.0289663i
$358$		0			0
$359$	−2.42755	+	13.7673i	−0.128121	+	0.726612i	0.851284	+	0.524706i	$0.175825\pi$
$359$	−2.42755	+	13.7673i	−0.128121	+	0.726612i	−0.979405	+	0.201906i	$0.935286\pi$
$360$		0			0
$361$	−18.9139	−	1.80717i	−0.995466	−	0.0951143i
$362$		0			0
$363$	1.02930	−	5.83747i	0.0540244	−	0.306388i
$364$		0			0
$365$	−2.97565	−	1.08305i	−0.155753	−	0.0566893i
$366$		0			0
$367$	4.11551	−	3.45332i	0.214828	−	0.180262i	−0.529023	−	0.848607i	$-0.677442\pi$
$367$	4.11551	−	3.45332i	0.214828	−	0.180262i	0.743851	+	0.668345i	$0.232997\pi$
$368$		0			0
$369$	−6.50461	+	11.2663i	−0.338617	+	0.586501i
$370$		0			0
$371$	0.723369	+	4.10243i	0.0375555	+	0.212988i
$372$		0			0
$373$	16.1702	+	28.0076i	0.837260	+	1.45018i	0.892177	+	0.451686i	$0.149177\pi$
$373$	16.1702	+	28.0076i	0.837260	+	1.45018i	−0.0549172	+	0.998491i	$0.517490\pi$
$374$		0			0
$375$	0.833001	−	0.303188i	0.0430160	−	0.0156565i
$376$		0			0
$377$	−24.3807	−	20.4578i	−1.25567	−	1.05363i
$378$		0			0
$379$	−33.8059			−1.73649			−0.868247	−	0.496133i	$-0.834753\pi$
$379$	−33.8059			−1.73649			−0.868247	+	0.496133i	$0.834753\pi$
$380$		0			0
$381$	−2.90900			−0.149033
$382$		0			0
$383$	−0.548598	−	0.460328i	−0.0280320	−	0.0235217i	0.628664	−	0.777677i	$-0.283602\pi$
$383$	−0.548598	−	0.460328i	−0.0280320	−	0.0235217i	−0.656696	+	0.754155i	$0.728047\pi$
$384$		0			0
$385$	−1.79715	+	0.654108i	−0.0915911	+	0.0333364i
$386$		0			0
$387$	0.752607	+	1.30355i	0.0382571	+	0.0662633i
$388$		0			0
$389$	3.64903	+	20.6947i	0.185013	+	1.04926i	0.925938	+	0.377674i	$0.123276\pi$
$389$	3.64903	+	20.6947i	0.185013	+	1.04926i	−0.740925	+	0.671587i	$0.765613\pi$
$390$		0			0
$391$	−0.594562	+	1.02981i	−0.0300683	+	0.0520798i
$392$		0			0
$393$	4.66559	−	3.91489i	0.235348	−	0.197480i
$394$		0			0
$395$	2.89763	+	1.05465i	0.145796	+	0.0530652i
$396$		0			0
$397$	3.55616	−	20.1680i	0.178479	−	1.01220i	−0.755573	−	0.655064i	$-0.772642\pi$
$397$	3.55616	−	20.1680i	0.178479	−	1.01220i	0.934052	−	0.357138i	$-0.116247\pi$
$398$		0			0
$399$	−3.47075	−	0.784011i	−0.173755	−	0.0392497i
$400$		0			0
$401$	−2.62785	+	14.9033i	−0.131229	+	0.744235i	0.846183	+	0.532892i	$0.178895\pi$
$401$	−2.62785	+	14.9033i	−0.131229	+	0.744235i	−0.977412	+	0.211343i	$0.932216\pi$
$402$		0			0
$403$	8.49507	+	3.09195i	0.423170	+	0.154021i
$404$		0			0
$405$	1.94972	−	1.63601i	0.0968824	−	0.0812940i
$406$		0			0
$407$	4.02953	−	6.97935i	0.199736	−	0.345954i
$408$		0			0
$409$	−0.528547	−	2.99754i	−0.0261349	−	0.148219i	0.968948	−	0.247265i	$-0.0795319\pi$
$409$	−0.528547	−	2.99754i	−0.0261349	−	0.148219i	−0.995083	+	0.0990465i	$0.968421\pi$
$410$		0			0
$411$	1.75045	+	3.03186i	0.0863432	+	0.149551i
$412$		0			0
$413$	−5.11580	+	1.86200i	−0.251732	+	0.0916229i
$414$		0			0
$415$	7.75302	+	6.50556i	0.380581	+	0.319345i
$416$		0			0
$417$	−15.3276			−0.750595
$418$		0			0
$419$	−3.89744			−0.190402			−0.0952011	−	0.995458i	$-0.530349\pi$
$419$	−3.89744			−0.190402			−0.0952011	+	0.995458i	$0.530349\pi$
$420$		0			0
$421$	2.18162	+	1.83059i	0.106325	+	0.0892177i	0.694401	−	0.719589i	$-0.255670\pi$
$421$	2.18162	+	1.83059i	0.106325	+	0.0892177i	−0.588075	+	0.808806i	$0.700114\pi$
$422$		0			0
$423$	22.5801	−	8.21849i	1.09788	−	0.399597i
$424$		0			0
$425$	−0.980146	−	1.69766i	−0.0475441	−	0.0823488i
$426$		0			0
$427$	1.11628	+	6.33072i	0.0540204	+	0.306365i
$428$		0			0
$429$	−3.87425	+	6.71040i	−0.187051	+	0.323981i
$430$		0			0
$431$	18.4177	−	15.4543i	0.887152	−	0.744409i	−0.0804852	−	0.996756i	$-0.525647\pi$
$431$	18.4177	−	15.4543i	0.887152	−	0.744409i	0.967637	+	0.252347i	$0.0812025\pi$
$432$		0			0
$433$	13.7914	+	5.01965i	0.662771	+	0.241229i	0.651432	−	0.758707i	$-0.274168\pi$
$433$	13.7914	+	5.01965i	0.662771	+	0.241229i	0.0113389	+	0.999936i	$0.496391\pi$
$434$		0			0
$435$	1.16404	−	6.60161i	0.0558115	−	0.316523i
$436$		0			0
$437$	−1.02162	+	2.43880i	−0.0488707	+	0.116663i
$438$		0			0
$439$	−1.22539	+	6.94955i	−0.0584849	+	0.331684i	−0.999986	−	0.00532619i	$-0.998305\pi$
$439$	−1.22539	+	6.94955i	−0.0584849	+	0.331684i	0.941501	+	0.337010i	$0.109416\pi$
$440$		0			0
$441$	−12.8002	−	4.65890i	−0.609534	−	0.221852i
$442$		0			0
$443$	−7.89296	+	6.62298i	−0.375006	+	0.314667i	−0.810738	−	0.585409i	$-0.800934\pi$
$443$	−7.89296	+	6.62298i	−0.375006	+	0.314667i	0.435732	+	0.900076i	$0.356489\pi$
$444$		0			0
$445$	−1.70145	+	2.94699i	−0.0806564	+	0.139701i
$446$		0			0
$447$	0.492026	+	2.79042i	0.0232720	+	0.131982i
$448$		0			0
$449$	0.920622	+	1.59456i	0.0434468	+	0.0752521i	0.886931	−	0.461902i	$-0.152833\pi$
$449$	0.920622	+	1.59456i	0.0434468	+	0.0752521i	−0.843484	+	0.537154i	$0.819499\pi$
$450$		0			0
$451$	−11.4664	+	4.17343i	−0.539931	+	0.196519i
$452$		0			0
$453$	8.07843	+	6.77861i	0.379558	+	0.318487i
$454$		0			0
$455$	−3.87568			−0.181695
$456$		0			0
$457$	−10.3531			−0.484297			−0.242148	−	0.970239i	$-0.577852\pi$
$457$	−10.3531			−0.484297			−0.242148	+	0.970239i	$0.577852\pi$
$458$		0			0
$459$	6.94099	+	5.82418i	0.323978	+	0.271849i
$460$		0			0
$461$	12.3814	−	4.50647i	0.576660	−	0.209887i	−0.0371922	−	0.999308i	$-0.511841\pi$
$461$	12.3814	−	4.50647i	0.576660	−	0.209887i	0.613852	+	0.789421i	$0.289619\pi$
$462$		0			0
$463$	−15.0532	−	26.0728i	−0.699579	−	1.21171i	−0.968612	−	0.248576i	$-0.920037\pi$
$463$	−15.0532	−	26.0728i	−0.699579	−	1.21171i	0.269033	−	0.963131i	$-0.413296\pi$
$464$		0			0
$465$	0.330641	+	1.87516i	0.0153331	+	0.0869584i
$466$		0			0
$467$	20.3663	−	35.2754i	0.942438	−	1.63235i	0.181636	−	0.983366i	$-0.441861\pi$
$467$	20.3663	−	35.2754i	0.942438	−	1.63235i	0.760801	−	0.648985i	$-0.224806\pi$
$468$		0			0
$469$	−5.39253	+	4.52487i	−0.249004	+	0.208939i
$470$		0			0
$471$	−16.3466	−	5.94966i	−0.753210	−	0.274146i
$472$		0			0
$473$	−0.245165	+	1.39040i	−0.0112727	+	0.0639306i
$474$		0			0
$475$	−2.63969	−	3.46872i	−0.121117	−	0.159156i
$476$		0			0
$477$	1.73932	−	9.86418i	0.0796381	−	0.451650i
$478$		0			0
$479$	28.1142	+	10.2327i	1.28457	+	0.467545i	0.891941	−	0.452153i	$-0.149344\pi$
$479$	28.1142	+	10.2327i	1.28457	+	0.467545i	0.392628	+	0.919697i	$0.371566\pi$
$480$		0			0
$481$	12.5109	−	10.4979i	0.570448	−	0.478663i
$482$		0			0
$483$	−0.247588	+	0.428836i	−0.0112657	+	0.0195127i
$484$		0			0
$485$	−3.29871	−	18.7079i	−0.149787	−	0.849482i
$486$		0			0
$487$	−12.1450	−	21.0357i	−0.550341	−	0.953219i	−0.998250	−	0.0591397i	$-0.981164\pi$
$487$	−12.1450	−	21.0357i	−0.550341	−	0.953219i	0.447908	−	0.894079i	$-0.352169\pi$
$488$		0			0
$489$	−15.6145	+	5.68320i	−0.706111	+	0.257003i
$490$		0			0
$491$	6.17437	+	5.18091i	0.278645	+	0.233811i	0.771390	−	0.636363i	$-0.219562\pi$
$491$	6.17437	+	5.18091i	0.278645	+	0.233811i	−0.492745	+	0.870174i	$0.664006\pi$
$492$		0			0
$493$	−14.8238			−0.667630
$494$		0			0
$495$	4.59852			0.206688
$496$		0			0
$497$	−8.11479	−	6.80911i	−0.363998	−	0.305430i
$498$		0			0
$499$	9.34595	−	3.40165i	0.418382	−	0.152279i	−0.124247	−	0.992251i	$-0.539651\pi$
$499$	9.34595	−	3.40165i	0.418382	−	0.152279i	0.542629	+	0.839973i	$0.317429\pi$
$500$		0			0
$501$	−2.23278	−	3.86729i	−0.0997532	−	0.172778i
$502$		0			0
$503$	−1.97979	−	11.2279i	−0.0882744	−	0.500629i	−0.996602	−	0.0823692i	$-0.973751\pi$
$503$	−1.97979	−	11.2279i	−0.0882744	−	0.500629i	0.908328	−	0.418260i	$-0.137360\pi$
$504$		0			0
$505$	−6.25057	+	10.8263i	−0.278147	+	0.481764i
$506$		0			0
$507$	−3.20089	+	2.68587i	−0.142157	+	0.119284i
$508$		0			0
$509$	26.1717	+	9.52573i	1.16004	+	0.422220i	0.849112	−	0.528213i	$-0.177138\pi$
$509$	26.1717	+	9.52573i	1.16004	+	0.422220i	0.310929	+	0.950433i	$0.399360\pi$
$510$		0			0
$511$	−0.506361	+	2.87172i	−0.0224001	+	0.127037i
$512$		0			0
$513$	16.9489	+	10.8931i	0.748313	+	0.480942i
$514$		0			0
$515$	0.120643	−	0.684203i	0.00531618	−	0.0301496i
$516$		0			0
$517$	21.1795	+	7.70871i	0.931474	+	0.339029i
$518$		0			0
$519$	10.1740	−	8.53696i	0.446587	−	0.374731i
$520$		0			0
$521$	18.6901	−	32.3722i	0.818829	−	1.41825i	−0.0877173	−	0.996145i	$-0.527957\pi$
$521$	18.6901	−	32.3722i	0.818829	−	1.41825i	0.906546	−	0.422107i	$-0.138709\pi$
$522$		0			0
$523$	−6.76998	−	38.3944i	−0.296030	−	1.67887i	−0.662985	−	0.748633i	$-0.730711\pi$
$523$	−6.76998	−	38.3944i	−0.296030	−	1.67887i	0.366954	−	0.930239i	$-0.380401\pi$
$524$		0			0
$525$	−0.408154	−	0.706943i	−0.0178133	−	0.0308535i
$526$		0			0
$527$	3.95671	−	1.44012i	0.172357	−	0.0627328i
$528$		0			0
$529$	−17.3371	−	14.5476i	−0.753789	−	0.632504i
$530$		0			0
$531$	13.0902			0.568068
$532$		0			0
$533$	−24.7281			−1.07109
$534$		0			0
$535$	−4.94701	−	4.15103i	−0.213878	−	0.179465i
$536$		0			0
$537$	−1.97779	+	0.719857i	−0.0853480	+	0.0310641i
$538$		0			0
$539$	−6.38839	−	11.0650i	−0.275167	−	0.476604i
$540$		0			0
$541$	1.44443	+	8.19179i	0.0621011	+	0.352193i	0.999986	+	0.00524684i	$0.00167013\pi$
$541$	1.44443	+	8.19179i	0.0621011	+	0.352193i	−0.937885	+	0.346946i	$0.887219\pi$
$542$		0			0
$543$	−5.61141	+	9.71925i	−0.240809	+	0.417093i
$544$		0			0
$545$	−1.28848	+	1.08116i	−0.0551924	+	0.0463119i
$546$		0			0
$547$	−41.9506	−	15.2688i	−1.79368	−	0.652846i	−0.998947	−	0.0458869i	$-0.985389\pi$
$547$	−41.9506	−	15.2688i	−1.79368	−	0.652846i	−0.794733	−	0.606959i	$-0.792389\pi$
$548$		0			0
$549$	2.68406	−	15.2221i	0.114553	−	0.649662i
$550$		0			0
$551$	−32.6971	+	4.17180i	−1.39294	+	0.177725i
$552$		0			0
$553$	0.493085	−	2.79642i	0.0209681	−	0.118916i
$554$		0			0
$555$	3.23241	+	1.17650i	0.137208	+	0.0499397i
$556$		0			0
$557$	20.7113	−	17.3788i	0.877565	−	0.736365i	−0.0881117	−	0.996111i	$-0.528083\pi$
$557$	20.7113	−	17.3788i	0.877565	−	0.736365i	0.965677	+	0.259746i	$0.0836388\pi$
$558$		0			0
$559$	−1.43057	+	2.47781i	−0.0605065	+	0.104800i
$560$		0			0
$561$	0.626693	+	3.55415i	0.0264590	+	0.150056i
$562$		0			0
$563$	17.4197	+	30.1718i	0.734153	+	1.27159i	0.955094	+	0.296303i	$0.0957540\pi$
$563$	17.4197	+	30.1718i	0.734153	+	1.27159i	−0.220941	+	0.975287i	$0.570913\pi$
$564$		0			0
$565$	16.7193	−	6.08534i	0.703388	−	0.256012i
$566$		0			0
$567$	−1.79542	−	1.50654i	−0.0754007	−	0.0632687i
$568$		0			0
$569$	26.2259			1.09945			0.549723	−	0.835347i	$-0.314733\pi$
$569$	26.2259			1.09945			0.549723	+	0.835347i	$0.314733\pi$
$570$		0			0
$571$	−29.6016			−1.23879			−0.619393	−	0.785081i	$-0.712621\pi$
$571$	−29.6016			−1.23879			−0.619393	+	0.785081i	$0.712621\pi$
$572$		0			0
$573$	−14.8035	−	12.4216i	−0.618426	−	0.518921i
$574$		0			0
$575$	−0.570023	+	0.207471i	−0.0237716	+	0.00865215i
$576$		0			0
$577$	14.6753	+	25.4183i	0.610940	+	1.05818i	0.991082	+	0.133252i	$0.0425418\pi$
$577$	14.6753	+	25.4183i	0.610940	+	1.05818i	−0.380142	+	0.924928i	$0.624125\pi$
$578$		0			0
$579$	0.994131	+	5.63800i	0.0413147	+	0.234307i
$580$		0			0
$581$	4.65995	−	8.07127i	0.193327	−	0.334853i
$582$		0			0
$583$	7.19703	−	6.03902i	0.298071	−	0.250111i
$584$		0			0
$585$	8.75697	+	3.18728i	0.362056	+	0.131778i
$586$		0			0
$587$	0.701381	−	3.97773i	0.0289491	−	0.164179i	−0.966906	−	0.255133i	$-0.917881\pi$
$587$	0.701381	−	3.97773i	0.0289491	−	0.164179i	0.995855	+	0.0909546i	$0.0289918\pi$
$588$		0			0
$589$	8.32208	−	4.29002i	0.342905	−	0.176767i
$590$		0			0
$591$	−1.45786	+	8.26794i	−0.0599684	+	0.340097i
$592$		0			0
$593$	8.77518	+	3.19390i	0.360353	+	0.131158i	0.515851	−	0.856678i	$-0.327476\pi$
$593$	8.77518	+	3.19390i	0.360353	+	0.131158i	−0.155498	+	0.987836i	$0.549698\pi$
$594$		0			0
$595$	−1.38283	+	1.16033i	−0.0566905	+	0.0475690i
$596$		0			0
$597$	10.9464	−	18.9597i	0.448005	−	0.775967i
$598$		0			0
$599$	2.49742	+	14.1636i	0.102042	+	0.578707i	0.992361	+	0.123370i	$0.0393702\pi$
$599$	2.49742	+	14.1636i	0.102042	+	0.578707i	−0.890319	+	0.455337i	$0.849519\pi$
$600$		0			0
$601$	−22.6873	−	39.2956i	−0.925435	−	1.60290i	−0.790860	−	0.611997i	$-0.790366\pi$
$601$	−22.6873	−	39.2956i	−0.925435	−	1.60290i	−0.134575	−	0.990903i	$-0.542967\pi$
$602$		0			0
$603$	15.9054	−	5.78909i	0.647718	−	0.235750i
$604$		0			0
$605$	−5.12233	−	4.29814i	−0.208252	−	0.174744i
$606$		0			0
$607$	−5.07790			−0.206105			−0.103053	−	0.994676i	$-0.532861\pi$
$607$	−5.07790			−0.206105			−0.103053	+	0.994676i	$0.532861\pi$
$608$		0			0
$609$	−6.17294			−0.250140
$610$		0			0
$611$	34.9892	+	29.3594i	1.41551	+	1.18776i
$612$		0			0
$613$	−12.0467	+	4.38465i	−0.486563	+	0.177095i	−0.573641	−	0.819107i	$-0.694469\pi$
$613$	−12.0467	+	4.38465i	−0.486563	+	0.177095i	0.0870775	+	0.996202i	$0.472247\pi$
$614$		0			0
$615$	−2.60416	−	4.51053i	−0.105010	−	0.181882i
$616$		0			0
$617$	3.09892	+	17.5748i	0.124758	+	0.707536i	0.981452	+	0.191711i	$0.0614035\pi$
$617$	3.09892	+	17.5748i	0.124758	+	0.707536i	−0.856694	+	0.515825i	$0.827485\pi$
$618$		0			0
$619$	8.02039	−	13.8917i	0.322367	−	0.558355i	−0.658609	−	0.752485i	$-0.728855\pi$
$619$	8.02039	−	13.8917i	0.322367	−	0.558355i	0.980976	+	0.194130i	$0.0621883\pi$
$620$		0			0
$621$	2.14786	−	1.80227i	0.0861908	−	0.0723227i
$622$		0			0
$623$	2.94462	+	1.07175i	0.117974	+	0.0429389i
$624$		0			0
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$		0			0
$627$	2.38254	+	7.66308i	0.0951493	+	0.306034i
$628$		0			0
$629$	1.32091	−	7.49123i	0.0526680	−	0.298695i
$630$		0			0
$631$	−24.3557	−	8.86476i	−0.969586	−	0.352900i	−0.191803	−	0.981433i	$-0.561433\pi$
$631$	−24.3557	−	8.86476i	−0.969586	−	0.352900i	−0.777783	+	0.628533i	$0.783656\pi$
$632$		0			0
$633$	1.32466	−	1.11152i	0.0526506	−	0.0441791i
$634$		0			0
$635$	−1.64079	+	2.84194i	−0.0651129	+	0.112779i
$636$		0			0
$637$	−4.49616	−	25.4990i	−0.178144	−	1.01031i
$638$		0			0
$639$	12.7354	+	22.0584i	0.503805	+	0.872616i
$640$		0			0
$641$	−5.01574	+	1.82558i	−0.198110	+	0.0721061i	−0.439170	−	0.898404i	$-0.644727\pi$
$641$	−5.01574	+	1.82558i	−0.198110	+	0.0721061i	0.241060	+	0.970510i	$0.422505\pi$
$642$		0			0
$643$	−2.90330	−	2.43616i	−0.114495	−	0.0960727i	0.583743	−	0.811939i	$-0.301588\pi$
$643$	−2.90330	−	2.43616i	−0.114495	−	0.0960727i	−0.698238	+	0.715866i	$0.746032\pi$
$644$		0			0
$645$	−0.602620			−0.0237281
$646$		0			0
$647$	30.2823			1.19052			0.595260	−	0.803533i	$-0.297049\pi$
$647$	30.2823			1.19052			0.595260	+	0.803533i	$0.297049\pi$
$648$		0			0
$649$	9.40570	+	7.89232i	0.369206	+	0.309801i
$650$		0			0
$651$	1.64766	−	0.599698i	0.0645768	−	0.0235040i
$652$		0			0
$653$	−11.4949	−	19.9098i	−0.449831	−	0.779131i	0.548543	−	0.836122i	$-0.315183\pi$
$653$	−11.4949	−	19.9098i	−0.449831	−	0.779131i	−0.998375	+	0.0569914i	$0.981849\pi$
$654$		0			0
$655$	−1.19306	−	6.76619i	−0.0466168	−	0.264377i
$656$		0			0
$657$	3.50575	−	6.07213i	0.136772	−	0.236896i
$658$		0			0
$659$	0.410633	−	0.344562i	0.0159960	−	0.0134222i	−0.634755	−	0.772714i	$-0.718899\pi$
$659$	0.410633	−	0.344562i	0.0159960	−	0.0134222i	0.650751	+	0.759292i	$0.274454\pi$
$660$		0			0
$661$	28.0558	+	10.2115i	1.09124	+	0.397180i	0.824081	−	0.566472i	$-0.191692\pi$
$661$	28.0558	+	10.2115i	1.09124	+	0.397180i	0.267162	+	0.963652i	$0.413914\pi$
$662$		0			0
$663$	−1.27000	+	7.20255i	−0.0493229	+	0.279724i
$664$		0			0
$665$	−2.72358	+	2.94853i	−0.105616	+	0.114339i
$666$		0			0
$667$	−0.796553	+	4.51748i	−0.0308427	+	0.174917i
$668$		0			0
$669$	−19.5319	−	7.10904i	−0.755148	−	0.274851i
$670$		0			0
$671$	11.1062	−	9.31921i	0.428750	−	0.359764i
$672$		0			0
$673$	11.2524	−	19.4898i	0.433750	−	0.751277i	−0.563443	−	0.826155i	$-0.690523\pi$
$673$	11.2524	−	19.4898i	0.433750	−	0.751277i	0.997193	+	0.0748782i	$0.0238568\pi$
$674$		0			0
$675$	0.802632	+	4.55195i	0.0308933	+	0.175205i
$676$		0			0
$677$	8.55072	+	14.8103i	0.328631	+	0.569206i	0.982240	−	0.187626i	$-0.0600794\pi$
$677$	8.55072	+	14.8103i	0.328631	+	0.569206i	−0.653609	+	0.756832i	$0.726746\pi$
$678$		0			0
$679$	−16.4382	+	5.98300i	−0.630839	+	0.229607i
$680$		0			0
$681$	2.81286	+	2.36027i	0.107789	+	0.0904456i
$682$		0			0
$683$	−50.9124			−1.94811			−0.974054	−	0.226316i	$-0.927332\pi$
$683$	−50.9124			−1.94811			−0.974054	+	0.226316i	$0.927332\pi$
$684$		0			0
$685$	3.94929			0.150895
$686$		0			0
$687$	−0.437730	−	0.367299i	−0.0167004	−	0.0140133i
$688$		0			0
$689$	17.8910	−	6.51180i	0.681594	−	0.248080i
$690$		0			0
$691$	13.5121	+	23.4037i	0.514026	+	0.890318i	0.999868	+	0.0162718i	$0.00517971\pi$
$691$	13.5121	+	23.4037i	0.514026	+	0.890318i	−0.485842	+	0.874047i	$0.661487\pi$
$692$		0			0
$693$	−0.735330	−	4.17026i	−0.0279329	−	0.158415i
$694$		0			0
$695$	−8.64538	+	14.9742i	−0.327938	+	0.568005i
$696$		0			0
$697$	−8.82291	+	7.40330i	−0.334192	+	0.280420i
$698$		0			0
$699$	1.73965	+	0.633182i	0.0657998	+	0.0239492i
$700$		0			0
$701$	7.76496	−	44.0373i	0.293278	−	1.66326i	−0.380839	−	0.924641i	$-0.624365\pi$
$701$	7.76496	−	44.0373i	0.293278	−	1.66326i	0.674118	−	0.738624i	$-0.264524\pi$
$702$		0			0
$703$	0.805315	−	16.8953i	0.0303730	−	0.637217i
$704$		0			0
$705$	−1.67054	+	9.47409i	−0.0629161	+	0.356815i
$706$		0			0
$707$	10.8176	+	3.93727i	0.406837	+	0.148076i
$708$		0			0
$709$	−27.6472	+	23.1988i	−1.03831	+	0.871249i	−0.991817	−	0.127669i	$-0.959250\pi$
$709$	−27.6472	+	23.1988i	−1.03831	+	0.871249i	−0.0464974	+	0.998918i	$0.514806\pi$
$710$		0			0
$711$	−3.41382	+	5.91292i	−0.128028	+	0.221752i
$712$		0			0
$713$	−0.226258	−	1.28317i	−0.00847342	−	0.0480552i
$714$		0			0
$715$	4.37047	+	7.56987i	0.163446	+	0.283097i
$716$		0			0
$717$	−5.17220	+	1.88253i	−0.193159	+	0.0703042i
$718$		0			0
$719$	−17.5573	−	14.7323i	−0.654776	−	0.549423i	0.253740	−	0.967273i	$-0.418339\pi$
$719$	−17.5573	−	14.7323i	−0.654776	−	0.549423i	−0.908516	+	0.417850i	$0.862784\pi$
$720$		0			0
$721$	−0.639776			−0.0238265
$722$		0			0
$723$	8.48941			0.315725
$724$		0			0
$725$	−5.79285	−	4.86078i	−0.215141	−	0.180525i
$726$		0			0
$727$	−43.9640	+	16.0016i	−1.63053	+	0.593466i	−0.985347	−	0.170559i	$-0.945443\pi$
$727$	−43.9640	+	16.0016i	−1.63053	+	0.593466i	−0.645186	+	0.764025i	$0.723220\pi$
$728$		0			0
$729$	−3.32832	−	5.76481i	−0.123271	−	0.213512i
$730$		0			0
$731$	0.231406	+	1.31237i	0.00855887	+	0.0485398i
$732$		0			0
$733$	−9.44660	+	16.3620i	−0.348918	+	0.604344i	−0.986058	−	0.166405i	$-0.946784\pi$
$733$	−9.44660	+	16.3620i	−0.348918	+	0.604344i	0.637139	+	0.770749i	$0.280118\pi$
$734$		0			0
$735$	4.17764	−	3.50546i	0.154095	−	0.129301i
$736$		0			0
$737$	14.9188	+	5.43000i	0.549541	+	0.200017i
$738$		0			0
$739$	−3.11918	+	17.6897i	−0.114741	+	0.650727i	0.872138	+	0.489261i	$0.162733\pi$
$739$	−3.11918	+	17.6897i	−0.114741	+	0.650727i	−0.986878	+	0.161466i	$0.948378\pi$
$740$		0			0
$741$	−0.774282	+	16.2442i	−0.0284440	+	0.596745i
$742$		0			0
$743$	−0.940109	+	5.33163i	−0.0344893	+	0.195598i	−0.997184	−	0.0749906i	$-0.976107\pi$
$743$	−0.940109	+	5.33163i	−0.0344893	+	0.195598i	0.962695	+	0.270589i	$0.0872184\pi$
$744$		0			0
$745$	3.00361	+	1.09322i	0.110044	+	0.0400526i
$746$		0			0
$747$	−17.1666	+	14.4045i	−0.628094	+	0.527034i
$748$		0			0
$749$	−2.97340	+	5.15007i	−0.108646	+	0.188180i
$750$		0			0
$751$	−1.33116	−	7.54938i	−0.0485747	−	0.275481i	0.950840	−	0.309682i	$-0.100222\pi$
$751$	−1.33116	−	7.54938i	−0.0485747	−	0.275481i	−0.999415	+	0.0342010i	$0.989111\pi$
$752$		0			0
$753$	4.52480	+	7.83718i	0.164893	+	0.285603i
$754$		0			0
$755$	11.1789	−	4.06879i	0.406842	−	0.148078i
$756$		0			0
$757$	−5.89669	−	4.94791i	−0.214319	−	0.179835i	0.529308	−	0.848430i	$-0.322452\pi$
$757$	−5.89669	−	4.94791i	−0.214319	−	0.179835i	−0.743627	+	0.668595i	$0.766896\pi$
$758$		0			0
$759$	1.11679			0.0405368
$760$		0			0
$761$	25.8527			0.937161			0.468581	−	0.883421i	$-0.344766\pi$
$761$	25.8527			0.937161			0.468581	+	0.883421i	$0.344766\pi$
$762$		0			0
$763$	1.18651	+	0.995600i	0.0429545	+	0.0360431i
$764$		0			0
$765$	4.07869	−	1.48452i	0.147465	−	0.0536730i
$766$		0			0
$767$	12.4411	+	21.5486i	0.449221	+	0.778073i
$768$		0			0
$769$	−8.31408	−	47.1515i	−0.299814	−	1.70033i	−0.646966	−	0.762519i	$-0.723963\pi$
$769$	−8.31408	−	47.1515i	−0.299814	−	1.70033i	0.347153	−	0.937809i	$-0.387149\pi$
$770$		0			0
$771$	−0.327422	+	0.567111i	−0.0117918	+	0.0204240i
$772$		0			0
$773$	6.51612	−	5.46768i	0.234369	−	0.196659i	−0.518038	−	0.855358i	$-0.673337\pi$
$773$	6.51612	−	5.46768i	0.234369	−	0.196659i	0.752407	+	0.658699i	$0.228893\pi$
$774$		0			0
$775$	2.01843	+	0.734647i	0.0725040	+	0.0263893i
$776$		0			0
$777$	0.550053	−	3.11951i	0.0197331	−	0.111912i
$778$		0			0
$779$	−17.3774	+	18.8126i	−0.622608	+	0.674030i
$780$		0			0
$781$	−4.14861	+	23.5280i	−0.148449	+	0.841896i
$782$		0			0
$783$	32.8451	+	11.9546i	1.17379	+	0.427224i
$784$		0			0
$785$	−15.0326	+	12.6139i	−0.536537	+	0.450208i
$786$		0			0
$787$	−10.1390	+	17.5612i	−0.361415	+	0.625989i	−0.988194	−	0.153208i	$-0.951039\pi$
$787$	−10.1390	+	17.5612i	−0.361415	+	0.625989i	0.626779	+	0.779197i	$0.284373\pi$
$788$		0			0
$789$	3.32183	+	18.8390i	0.118260	+	0.670687i
$790$		0			0
$791$	−8.19215	−	14.1892i	−0.291279	−	0.504510i
$792$		0			0
$793$	27.6088	−	10.0488i	0.980417	−	0.356843i
$794$		0			0
$795$	3.07192	+	2.57764i	0.108950	+	0.0914196i
$796$		0			0
$797$	3.31162			0.117304			0.0586518	−	0.998278i	$-0.481320\pi$
$797$	3.31162			0.117304			0.0586518	+	0.998278i	$0.481320\pi$
$798$		0			0
$799$	21.2739			0.752617
$800$		0			0
$801$	−5.77187	−	4.84318i	−0.203939	−	0.171125i
$802$		0			0
$803$	6.17996	−	2.24932i	0.218086	−	0.0793769i
$804$		0			0
$805$	0.279300	+	0.483761i	0.00984402	+	0.0170503i
$806$		0			0
$807$	1.40835	+	7.98717i	0.0495764	+	0.281162i
$808$		0			0
$809$	20.6626	−	35.7886i	0.726457	−	1.25826i	−0.231914	−	0.972736i	$-0.574499\pi$
$809$	20.6626	−	35.7886i	0.726457	−	1.25826i	0.958371	−	0.285525i	$-0.0921679\pi$
$810$		0			0
$811$	−24.4629	+	20.5268i	−0.859007	+	0.720793i	−0.961754	−	0.273915i	$-0.911681\pi$
$811$	−24.4629	+	20.5268i	−0.859007	+	0.720793i	0.102747	+	0.994708i	$0.467237\pi$
$812$		0			0
$813$	−4.32315	−	1.57350i	−0.151619	−	0.0551850i
$814$		0			0
$815$	−3.25501	+	18.4601i	−0.114018	+	0.646628i
$816$		0			0
$817$	0.879751	+	2.82959i	0.0307786	+	0.0989948i
$818$		0			0
$819$	1.49016	−	8.45111i	0.0520704	−	0.295306i
$820$		0			0
$821$	−40.2952	−	14.6663i	−1.40631	−	0.511856i	−0.476268	−	0.879300i	$-0.658011\pi$
$821$	−40.2952	−	14.6663i	−1.40631	−	0.511856i	−0.930046	+	0.367444i	$0.880233\pi$
$822$		0			0
$823$	−24.2528	+	20.3505i	−0.845400	+	0.709375i	−0.958772	−	0.284177i	$-0.908280\pi$
$823$	−24.2528	+	20.3505i	−0.845400	+	0.709375i	0.113371	+	0.993553i	$0.463835\pi$
$824$		0			0
$825$	−0.920521	+	1.59439i	−0.0320484	+	0.0555095i
$826$		0			0
$827$	5.58719	+	31.6865i	0.194286	+	1.10185i	0.913432	+	0.406991i	$0.133422\pi$
$827$	5.58719	+	31.6865i	0.194286	+	1.10185i	−0.719147	+	0.694858i	$0.755467\pi$
$828$		0			0
$829$	−0.678996	−	1.17606i	−0.0235825	−	0.0408461i	0.853993	−	0.520284i	$-0.174174\pi$
$829$	−0.678996	−	1.17606i	−0.0235825	−	0.0408461i	−0.877576	+	0.479438i	$0.840841\pi$
$830$		0			0
$831$	−19.5010	+	7.09780i	−0.676484	+	0.246220i
$832$		0			0
$833$	−9.23830	−	7.75186i	−0.320088	−	0.268586i
$834$		0			0
$835$	−5.03751			−0.174330
$836$		0			0
$837$	−9.92826			−0.343171
$838$		0			0
$839$	−15.9336	−	13.3699i	−0.550088	−	0.461579i	0.324883	−	0.945754i	$-0.394675\pi$
$839$	−15.9336	−	13.3699i	−0.550088	−	0.461579i	−0.874971	+	0.484176i	$0.839120\pi$
$840$		0			0
$841$	−26.4846	+	9.63959i	−0.913261	+	0.332400i
$842$		0			0
$843$	−8.22065	−	14.2386i	−0.283134	−	0.490403i
$844$		0			0
$845$	0.818517	+	4.64204i	0.0281578	+	0.159691i
$846$		0			0
$847$	−3.07877	+	5.33259i	−0.105788	+	0.183230i
$848$		0			0
$849$	14.9386	−	12.5349i	0.512690	−	0.430198i
$850$		0			0
$851$	−2.21194	−	0.805079i	−0.0758242	−	0.0275978i
$852$		0			0
$853$	−2.73450	+	15.5081i	−0.0936277	+	0.530989i	0.901532	+	0.432713i	$0.142444\pi$
$853$	−2.73450	+	15.5081i	−0.0936277	+	0.530989i	−0.995159	+	0.0982755i	$0.968667\pi$
$854$		0			0
$855$	8.57865	−	4.42228i	0.293384	−	0.151239i
$856$		0			0
$857$	−7.88008	+	44.6901i	−0.269178	+	1.52659i	0.487689	+	0.873018i	$0.337840\pi$
$857$	−7.88008	+	44.6901i	−0.269178	+	1.52659i	−0.756867	+	0.653569i	$0.773271\pi$
$858$		0			0
$859$	−43.5839	−	15.8633i	−1.48706	−	0.541247i	−0.534389	−	0.845238i	$-0.679458\pi$
$859$	−43.5839	−	15.8633i	−1.48706	−	0.541247i	−0.952675	+	0.303991i	$0.901681\pi$
$860$		0			0
$861$	−3.67405	+	3.08289i	−0.125211	+	0.105065i
$862$		0			0
$863$	−17.9599	+	31.1075i	−0.611363	+	1.05891i	0.379648	+	0.925131i	$0.376045\pi$
$863$	−17.9599	+	31.1075i	−0.611363	+	1.05891i	−0.991011	+	0.133781i	$0.957288\pi$
$864$		0			0
$865$	−2.60163	−	14.7546i	−0.0884582	−	0.501671i
$866$		0			0
$867$	−5.83170	−	10.1008i	−0.198055	−	0.343041i
$868$		0			0
$869$	−6.01792	+	2.19034i	−0.204144	+	0.0743024i
$870$		0			0
$871$	24.6463	+	20.6807i	0.835109	+	0.700740i
$872$		0			0
$873$	42.0618			1.42358
$874$		0			0
$875$	−0.920861			−0.0311308
$876$		0			0
$877$	21.8730	+	18.3537i	0.738600	+	0.619759i	0.932461	−	0.361270i	$-0.117657\pi$
$877$	21.8730	+	18.3537i	0.738600	+	0.619759i	−0.193861	+	0.981029i	$0.562101\pi$
$878$		0			0
$879$	19.6127	−	7.13843i	0.661519	−	0.240773i
$880$		0			0
$881$	18.8728	+	32.6887i	0.635842	+	1.10131i	0.986336	+	0.164745i	$0.0526802\pi$
$881$	18.8728	+	32.6887i	0.635842	+	1.10131i	−0.350495	+	0.936565i	$0.613987\pi$
$882$		0			0
$883$	−0.870377	−	4.93615i	−0.0292905	−	0.166115i	0.966654	−	0.256087i	$-0.0824333\pi$
$883$	−0.870377	−	4.93615i	−0.0292905	−	0.166115i	−0.995944	+	0.0899721i	$0.971322\pi$
$884$		0			0
$885$	−2.62037	+	4.53862i	−0.0880829	+	0.152564i
$886$		0			0
$887$	−34.6671	+	29.0891i	−1.16401	+	0.976717i	−0.999953	−	0.00973474i	$-0.996901\pi$
$887$	−34.6671	+	29.0891i	−1.16401	+	0.976717i	−0.164053	+	0.986452i	$0.552457\pi$
$888$		0			0
$889$	2.83965	+	1.03355i	0.0952387	+	0.0346640i
$890$		0			0
$891$	−0.917894	+	5.20564i	−0.0307506	+	0.174395i
$892$		0			0
$893$	46.9242	−	5.98703i	1.57026	−	0.200348i
$894$		0			0
$895$	−0.412292	+	2.33822i	−0.0137814	+	0.0781582i
$896$		0			0
$897$	2.12670	+	0.774055i	0.0710084	+	0.0258449i
$898$		0			0
$899$	12.4428	−	10.4408i	0.414992	−	0.348219i
$900$		0			0
$901$	4.43391	−	7.67975i	0.147715	−	0.255850i
$902$		0			0
$903$	0.0963625	+	0.546499i	0.00320674	+	0.0181863i
$904$		0			0
$905$	6.33012	+	10.9641i	0.210420	+	0.364459i
$906$		0			0
$907$	8.79459	−	3.20097i	0.292019	−	0.106286i	−0.191856	−	0.981423i	$-0.561451\pi$
$907$	8.79459	−	3.20097i	0.292019	−	0.106286i	0.483876	+	0.875137i	$0.339229\pi$
$908$		0			0
$909$	−21.2040	−	17.7923i	−0.703292	−	0.590132i
$910$		0			0
$911$	55.7316			1.84647			0.923235	−	0.384235i	$-0.125535\pi$
$911$	55.7316			1.84647			0.923235	+	0.384235i	$0.125535\pi$
$912$		0			0
$913$	−21.0194			−0.695642
$914$		0			0
$915$	4.74047	+	3.97773i	0.156715	+	0.131500i
$916$		0			0
$917$	−5.94528	+	2.16391i	−0.196331	+	0.0714585i
$918$		0			0
$919$	−5.03798	−	8.72604i	−0.166188	−	0.287845i	0.770889	−	0.636970i	$-0.219812\pi$
$919$	−5.03798	−	8.72604i	−0.166188	−	0.287845i	−0.937076	+	0.349124i	$0.886479\pi$
$920$		0			0
$921$	−0.599201	−	3.39824i	−0.0197443	−	0.111976i
$922$		0			0
$923$	−24.2077	+	41.9289i	−0.796805	+	1.38011i
$924$		0			0
$925$	2.97259	−	2.49430i	0.0977381	−	0.0820120i
$926$		0			0
$927$	1.44555	+	0.526138i	0.0474781	+	0.0172806i
$928$		0			0
$929$	5.23530	−	29.6909i	0.171765	−	0.974125i	−0.770048	−	0.637986i	$-0.779768\pi$
$929$	5.23530	−	29.6909i	0.171765	−	0.974125i	0.941812	−	0.336139i	$-0.109121\pi$
$930$		0			0
$931$	−22.5586	−	14.4985i	−0.739330	−	0.475169i
$932$		0			0
$933$	3.86578	−	21.9239i	0.126560	−	0.717757i
$934$		0			0
$935$	3.82570	+	1.39244i	0.125114	+	0.0455377i
$936$		0			0
$937$	−8.04844	+	6.75344i	−0.262931	+	0.220625i	−0.764717	−	0.644367i	$-0.777121\pi$
$937$	−8.04844	+	6.75344i	−0.262931	+	0.220625i	0.501786	+	0.864992i	$0.332677\pi$
$938$		0			0
$939$	10.4700	−	18.1346i	0.341675	−	0.591799i
$940$		0			0
$941$	7.69310	+	43.6297i	0.250788	+	1.42229i	0.806657	+	0.591019i	$0.201274\pi$
$941$	7.69310	+	43.6297i	0.250788	+	1.42229i	−0.555870	+	0.831270i	$0.687615\pi$
$942$		0			0
$943$	1.78202	+	3.08656i	0.0580307	+	0.100512i
$944$		0			0
$945$	3.99969	−	1.45577i	0.130110	−	0.0473561i
$946$		0			0
$947$	24.4835	+	20.5441i	0.795606	+	0.667593i	0.947126	−	0.320861i	$-0.103972\pi$
$947$	24.4835	+	20.5441i	0.795606	+	0.667593i	−0.151520	+	0.988454i	$0.548417\pi$
$948$		0			0
$949$	13.3275			0.432630
$950$		0			0
$951$	−5.74713			−0.186364
$952$		0			0
$953$	−44.6219	−	37.4423i	−1.44545	−	1.21287i	−0.935820	−	0.352478i	$-0.885339\pi$
$953$	−44.6219	−	37.4423i	−1.44545	−	1.21287i	−0.509626	−	0.860396i	$-0.670216\pi$
$954$		0			0
$955$	−20.4851	+	7.45595i	−0.662881	+	0.241269i
$956$		0			0
$957$	6.96100	+	12.0568i	0.225017	+	0.389741i
$958$		0			0
$959$	−0.631515	−	3.58150i	−0.0203927	−	0.115653i
$960$		0			0
$961$	13.1931	−	22.8512i	0.425585	−	0.737134i
$962$		0			0
$963$	10.9536	−	9.19116i	0.352975	−	0.296181i
$964$		0			0
$965$	6.06875	+	2.20885i	0.195360	+	0.0711053i
$966$		0			0
$967$	−5.68462	+	32.2391i	−0.182805	+	1.03674i	0.745938	+	0.666015i	$0.232001\pi$
$967$	−5.68462	+	32.2391i	−0.182805	+	1.03674i	−0.928743	+	0.370724i	$0.879110\pi$
$968$		0			0
$969$	4.58705	+	6.02768i	0.147357	+	0.193637i
$970$		0			0
$971$	9.54906	−	54.1554i	0.306444	−	1.73793i	−0.310186	−	0.950676i	$-0.600391\pi$
$971$	9.54906	−	54.1554i	0.306444	−	1.73793i	0.616630	−	0.787253i	$-0.288498\pi$
$972$		0			0
$973$	14.9622	+	5.44578i	0.479665	+	0.174584i
$974$		0			0
$975$	−2.85804	+	2.39818i	−0.0915304	+	0.0768031i
$976$		0			0
$977$	2.76351	−	4.78654i	0.0884125	−	0.153135i	−0.818428	−	0.574609i	$-0.805154\pi$
$977$	2.76351	−	4.78654i	0.0884125	−	0.153135i	0.906840	+	0.421475i	$0.138487\pi$
$978$		0			0
$979$	−1.22722	−	6.95991i	−0.0392221	−	0.222440i
$980$		0			0
$981$	−1.86212	−	3.22528i	−0.0594529	−	0.102975i
$982$		0			0
$983$	26.2253	−	9.54522i	0.836456	−	0.304445i	0.111950	−	0.993714i	$-0.464290\pi$
$983$	26.2253	−	9.54522i	0.836456	−	0.304445i	0.724506	+	0.689269i	$0.242068\pi$
$984$		0			0
$985$	7.25504	+	6.08770i	0.231165	+	0.193970i
$986$		0			0
$987$	8.85891			0.281982
$988$		0			0
$989$	0.412373			0.0131127
$990$		0			0
$991$	−2.27230	−	1.90669i	−0.0721820	−	0.0605679i	0.605983	−	0.795478i	$-0.292780\pi$
$991$	−2.27230	−	1.90669i	−0.0721820	−	0.0605679i	−0.678165	+	0.734910i	$0.737224\pi$
$992$		0			0
$993$	16.0316	−	5.83502i	0.508747	−	0.185169i
$994$		0			0
$995$	−12.3484	−	21.3880i	−0.391470	−	0.678046i
$996$		0			0
$997$	1.28766	+	7.30269i	0.0407807	+	0.231279i	0.998385	−	0.0568076i	$-0.0180922\pi$
$997$	1.28766	+	7.30269i	0.0407807	+	0.231279i	−0.957604	+	0.288086i	$0.906981\pi$
$998$		0			0
$999$	−8.96803	+	15.5331i	−0.283736	+	0.491445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.b.321.2	yes	18
19.3	odd	18		7220.2.a.y.1.5		9
19.9	even	9	inner	380.2.u.b.161.2	✓	18
19.16	even	9		7220.2.a.w.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.b.161.2	✓	18	19.9	even	9	inner
380.2.u.b.321.2	yes	18	1.1	even	1	trivial
7220.2.a.w.1.5		9	19.16	even	9
7220.2.a.y.1.5		9	19.3	odd	18

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.679069 - 0.569806i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(0.460431 + 0.797489i) q^{7} +(-0.384489 - 2.18055i) q^{9} +O(q^{10})\)	\(q+(-0.679069 - 0.569806i) q^{3} +(-0.939693 + 0.342020i) q^{5} +(0.460431 + 0.797489i) q^{7} +(-0.384489 - 2.18055i) q^{9} +(1.03842 - 1.79860i) q^{11} +(3.22410 - 2.70534i) q^{13} +(0.833001 + 0.303188i) q^{15} +(0.340401 - 1.93051i) q^{17} +(0.207532 - 4.35396i) q^{19} +(0.141750 - 0.803906i) q^{21} +(-0.570023 - 0.207471i) q^{23} +(0.766044 - 0.642788i) q^{25} +(-2.31109 + 4.00292i) q^{27} +(-1.31313 - 7.44714i) q^{29} +(1.07398 + 1.86019i) q^{31} +(-1.73001 + 0.629673i) q^{33} +(-0.705421 - 0.591918i) q^{35} +3.88044 q^{37} -3.73090 q^{39} +(-4.50081 - 3.77663i) q^{41} +(-0.638807 + 0.232507i) q^{43} +(1.10709 + 1.91754i) q^{45} +(1.88450 + 10.6875i) q^{47} +(3.07601 - 5.32780i) q^{49} +(-1.33117 + 1.11699i) q^{51} +(4.25090 + 1.54720i) q^{53} +(-0.360640 + 2.04529i) q^{55} +(-2.62184 + 2.83838i) q^{57} +(-1.02661 + 5.82217i) q^{59} +(6.55984 + 2.38759i) q^{61} +(1.56193 - 1.31062i) q^{63} +(-2.10438 + 3.64489i) q^{65} +(1.32744 + 7.52828i) q^{67} +(0.268866 + 0.465690i) q^{69} +(-10.8097 + 3.93442i) q^{71} +(2.42577 + 2.03547i) q^{73} -0.886461 q^{75} +1.91248 q^{77} +(-2.36217 - 1.98209i) q^{79} +(-2.39169 + 0.870503i) q^{81} +(-5.06043 - 8.76492i) q^{83} +(0.340401 + 1.93051i) q^{85} +(-3.35172 + 5.80535i) q^{87} +(2.60677 - 2.18734i) q^{89} +(3.64195 + 1.32556i) q^{91} +(0.330641 - 1.87516i) q^{93} +(1.29412 + 4.16236i) q^{95} +(-3.29871 + 18.7079i) q^{97} +(-4.32119 - 1.57279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 15 * q^9	\( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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