LMFDB - Embedded newform 380.2.u.b.101.1

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			101.1
Root			$-0.838693 + 1.45266i$ of defining polynomial
Character	$\chi$	$=$	380.101
Dual form			380.2.u.b.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57623 - 0.573700i) q^{3} +(0.173648 + 0.984808i) q^{5} +(0.230636 - 0.399473i) q^{7} +(-0.142773 - 0.119801i) q^{9} +O(q^{10})$	\(q+(-1.57623 - 0.573700i) q^{3} +(0.173648 + 0.984808i) q^{5} +(0.230636 - 0.399473i) q^{7} +(-0.142773 - 0.119801i) q^{9} +(-0.642179 - 1.11229i) q^{11} +(5.58829 - 2.03397i) q^{13} +(0.291275 - 1.65190i) q^{15} +(4.26171 - 3.57600i) q^{17} +(-3.93062 - 1.88419i) q^{19} +(-0.592712 + 0.497345i) q^{21} +(0.379967 - 2.15490i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(2.67239 + 4.62872i) q^{27} +(-7.31767 - 6.14026i) q^{29} +(4.61929 - 8.00084i) q^{31} +(0.374101 + 2.12163i) q^{33} +(0.433454 + 0.157764i) q^{35} +8.90443 q^{37} -9.97531 q^{39} +(4.53095 + 1.64913i) q^{41} +(-0.655751 - 3.71895i) q^{43} +(0.0931885 - 0.161407i) q^{45} +(-5.24811 - 4.40369i) q^{47} +(3.39361 + 5.87791i) q^{49} +(-8.76897 + 3.19164i) q^{51} +(-1.37327 + 7.78821i) q^{53} +(0.983875 - 0.825569i) q^{55} +(5.11460 + 5.22492i) q^{57} +(-4.10588 + 3.44524i) q^{59} +(-1.76051 + 9.98434i) q^{61} +(-0.0807859 + 0.0294036i) q^{63} +(2.97347 + 5.15020i) q^{65} +(5.05696 + 4.24330i) q^{67} +(-1.83518 + 3.17863i) q^{69} +(1.19711 + 6.78912i) q^{71} +(-12.3010 - 4.47721i) q^{73} +1.67739 q^{75} -0.592438 q^{77} +(-1.30465 - 0.474853i) q^{79} +(-1.45971 - 8.27842i) q^{81} +(-0.0660497 + 0.114402i) q^{83} +(4.26171 + 3.57600i) q^{85} +(8.01165 + 13.8766i) q^{87} +(2.89456 - 1.05353i) q^{89} +(0.476344 - 2.70148i) q^{91} +(-11.8711 + 9.96105i) q^{93} +(1.17302 - 4.19810i) q^{95} +(0.447812 - 0.375759i) q^{97} +(-0.0415670 + 0.235738i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

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
$3$	−1.57623	−	0.573700i	−0.910035	−	0.331226i	−0.155768	−	0.987794i	$-0.549785\pi$
$3$	−1.57623	−	0.573700i	−0.910035	−	0.331226i	−0.754267	+	0.656568i	$0.772008\pi$
$4$		0			0
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$		0			0
$7$	0.230636	−	0.399473i	0.0871722	−	0.150987i	−0.819143	−	0.573590i	$-0.805550\pi$
$7$	0.230636	−	0.399473i	0.0871722	−	0.150987i	0.906315	+	0.422603i	$0.138884\pi$
$8$		0			0
$9$	−0.142773	−	0.119801i	−0.0475910	−	0.0399336i
$10$		0			0
$11$	−0.642179	−	1.11229i	−0.193624	−	0.335367i	0.752824	−	0.658221i	$-0.228691\pi$
$11$	−0.642179	−	1.11229i	−0.193624	−	0.335367i	−0.946449	+	0.322854i	$0.895358\pi$
$12$		0			0
$13$	5.58829	−	2.03397i	1.54991	−	0.564122i	0.581516	−	0.813535i	$-0.302460\pi$
$13$	5.58829	−	2.03397i	1.54991	−	0.564122i	0.968397	+	0.249412i	$0.0802375\pi$
$14$		0			0
$15$	0.291275	−	1.65190i	0.0752069	−	0.426519i
$16$		0			0
$17$	4.26171	−	3.57600i	1.03362	−	0.867307i	0.0423393	−	0.999103i	$-0.486519\pi$
$17$	4.26171	−	3.57600i	1.03362	−	0.867307i	0.991277	+	0.131796i	$0.0420745\pi$
$18$		0			0
$19$	−3.93062	−	1.88419i	−0.901747	−	0.432264i
$19$	−3.93062	−	1.88419i	−0.901747	−	0.432264i
$20$		0			0
$21$	−0.592712	+	0.497345i	−0.129340	+	0.108530i
$22$		0			0
$23$	0.379967	−	2.15490i	0.0792287	−	0.449328i	−0.919225	−	0.393733i	$-0.871183\pi$
$23$	0.379967	−	2.15490i	0.0792287	−	0.449328i	0.998453	−	0.0555949i	$-0.0177055\pi$
$24$		0			0
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$		0			0
$27$	2.67239	+	4.62872i	0.514302	+	0.890797i
$28$		0			0
$29$	−7.31767	−	6.14026i	−1.35886	−	1.14022i	−0.976333	−	0.216272i	$-0.930610\pi$
$29$	−7.31767	−	6.14026i	−1.35886	−	1.14022i	−0.382524	−	0.923945i	$-0.624945\pi$
$30$		0			0
$31$	4.61929	−	8.00084i	0.829648	−	1.43699i	−0.0686661	−	0.997640i	$-0.521874\pi$
$31$	4.61929	−	8.00084i	0.829648	−	1.43699i	0.898314	−	0.439353i	$-0.144792\pi$
$32$		0			0
$33$	0.374101	+	2.12163i	0.0651227	+	0.369329i
$34$		0			0
$35$	0.433454	+	0.157764i	0.0732671	+	0.0266670i
$36$		0			0
$37$	8.90443			1.46388			0.731940	−	0.681369i	$-0.238615\pi$
$37$	8.90443			1.46388			0.731940	+	0.681369i	$0.238615\pi$
$38$		0			0
$39$	−9.97531			−1.59733
$40$		0			0
$41$	4.53095	+	1.64913i	0.707615	+	0.257551i	0.670659	−	0.741766i	$-0.266012\pi$
$41$	4.53095	+	1.64913i	0.707615	+	0.257551i	0.0369563	+	0.999317i	$0.488234\pi$
$42$		0			0
$43$	−0.655751	−	3.71895i	−0.100001	−	0.567134i	−0.993100	−	0.117273i	$-0.962585\pi$
$43$	−0.655751	−	3.71895i	−0.100001	−	0.567134i	0.893099	−	0.449861i	$-0.148526\pi$
$44$		0			0
$45$	0.0931885	−	0.161407i	0.0138917	−	0.0240612i
$46$		0			0
$47$	−5.24811	−	4.40369i	−0.765516	−	0.642344i	0.174041	−	0.984738i	$-0.444318\pi$
$47$	−5.24811	−	4.40369i	−0.765516	−	0.642344i	−0.939556	+	0.342395i	$0.888762\pi$
$48$		0			0
$49$	3.39361	+	5.87791i	0.484802	+	0.839702i
$50$		0			0
$51$	−8.76897	+	3.19164i	−1.22790	+	0.446919i
$52$		0			0
$53$	−1.37327	+	7.78821i	−0.188633	+	1.06979i	0.732564	+	0.680698i	$0.238323\pi$
$53$	−1.37327	+	7.78821i	−0.188633	+	1.06979i	−0.921198	+	0.389095i	$0.872788\pi$
$54$		0			0
$55$	0.983875	−	0.825569i	0.132666	−	0.111320i
$56$		0			0
$57$	5.11460	+	5.22492i	0.677445	+	0.692057i
$58$		0			0
$59$	−4.10588	+	3.44524i	−0.534540	+	0.448532i	−0.869666	−	0.493641i	$-0.835666\pi$
$59$	−4.10588	+	3.44524i	−0.534540	+	0.448532i	0.335126	+	0.942173i	$0.391221\pi$
$60$		0			0
$61$	−1.76051	+	9.98434i	−0.225410	+	1.27836i	0.636490	+	0.771285i	$0.280386\pi$
$61$	−1.76051	+	9.98434i	−0.225410	+	1.27836i	−0.861900	+	0.507079i	$0.830725\pi$
$62$		0			0
$63$	−0.0807859	+	0.0294036i	−0.0101781	+	0.00370451i
$64$		0			0
$65$	2.97347	+	5.15020i	0.368813	+	0.638804i
$66$		0			0
$67$	5.05696	+	4.24330i	0.617807	+	0.518401i	0.897113	−	0.441801i	$-0.145660\pi$
$67$	5.05696	+	4.24330i	0.617807	+	0.518401i	−0.279307	+	0.960202i	$0.590105\pi$
$68$		0			0
$69$	−1.83518	+	3.17863i	−0.220930	+	0.382662i
$70$		0			0
$71$	1.19711	+	6.78912i	0.142070	+	0.805721i	0.969673	+	0.244406i	$0.0785931\pi$
$71$	1.19711	+	6.78912i	0.142070	+	0.805721i	−0.827603	+	0.561314i	$0.810296\pi$
$72$		0			0
$73$	−12.3010	−	4.47721i	−1.43973	−	0.524017i	−0.500024	−	0.866012i	$-0.666675\pi$
$73$	−12.3010	−	4.47721i	−1.43973	−	0.524017i	−0.939702	+	0.341994i	$0.888898\pi$
$74$		0			0
$75$	1.67739			0.193688
$76$		0			0
$77$	−0.592438			−0.0675146
$78$		0			0
$79$	−1.30465	−	0.474853i	−0.146784	−	0.0534251i	0.267583	−	0.963535i	$-0.413775\pi$
$79$	−1.30465	−	0.474853i	−0.146784	−	0.0534251i	−0.414368	+	0.910110i	$0.635997\pi$
$80$		0			0
$81$	−1.45971	−	8.27842i	−0.162190	−	0.919825i
$82$		0			0
$83$	−0.0660497	+	0.114402i	−0.00724990	+	0.0125572i	−0.869628	−	0.493708i	$-0.835641\pi$
$83$	−0.0660497	+	0.114402i	−0.00724990	+	0.0125572i	0.862378	+	0.506265i	$0.168974\pi$
$84$		0			0
$85$	4.26171	+	3.57600i	0.462247	+	0.387871i
$86$		0			0
$87$	8.01165	+	13.8766i	0.858939	+	1.48773i
$88$		0			0
$89$	2.89456	−	1.05353i	0.306823	−	0.111674i	−0.184020	−	0.982922i	$-0.558911\pi$
$89$	2.89456	−	1.05353i	0.306823	−	0.111674i	0.490843	+	0.871248i	$0.336689\pi$
$90$		0			0
$91$	0.476344	−	2.70148i	0.0499344	−	0.283192i
$92$		0			0
$93$	−11.8711	+	9.96105i	−1.23098	+	1.03291i
$94$		0			0
$95$	1.17302	−	4.19810i	0.120350	−	0.430716i
$96$		0			0
$97$	0.447812	−	0.375759i	0.0454684	−	0.0381525i	−0.619770	−	0.784783i	$-0.712774\pi$
$97$	0.447812	−	0.375759i	0.0454684	−	0.0381525i	0.665239	+	0.746631i	$0.268330\pi$
$98$		0			0
$99$	−0.0415670	+	0.235738i	−0.00417764	+	0.0236926i
$100$		0			0
$101$	−5.06052	+	1.84188i	−0.503541	+	0.183274i	−0.581286	−	0.813699i	$-0.697450\pi$
$101$	−5.06052	+	1.84188i	−0.503541	+	0.183274i	0.0777450	+	0.996973i	$0.475228\pi$
$102$		0			0
$103$	−1.26492	−	2.19090i	−0.124636	−	0.215876i	0.796955	−	0.604039i	$-0.206443\pi$
$103$	−1.26492	−	2.19090i	−0.124636	−	0.215876i	−0.921591	+	0.388163i	$0.873110\pi$
$104$		0			0
$105$	−0.592712	−	0.497345i	−0.0578428	−	0.0485359i
$106$		0			0
$107$	−3.63551	+	6.29689i	−0.351458	+	0.608743i	−0.986505	−	0.163730i	$-0.947647\pi$
$107$	−3.63551	+	6.29689i	−0.351458	+	0.608743i	0.635047	+	0.772473i	$0.280981\pi$
$108$		0			0
$109$	−1.19744	−	6.79102i	−0.114694	−	0.650462i	−0.986901	−	0.161325i	$-0.948423\pi$
$109$	−1.19744	−	6.79102i	−0.114694	−	0.650462i	0.872207	−	0.489136i	$-0.162688\pi$
$110$		0			0
$111$	−14.0354	−	5.10847i	−1.33218	−	0.484875i
$112$		0			0
$113$	9.85398			0.926984			0.463492	−	0.886101i	$-0.346596\pi$
$113$	9.85398			0.926984			0.463492	+	0.886101i	$0.346596\pi$
$114$		0			0
$115$	2.18815			0.204046
$116$		0			0
$117$	−1.04153	−	0.379086i	−0.0962894	−	0.0350465i
$118$		0			0
$119$	−0.445612	−	2.52719i	−0.0408492	−	0.231667i
$120$		0			0
$121$	4.67521	−	8.09771i	0.425019	−	0.736155i
$122$		0			0
$123$	−6.19569	−	5.19881i	−0.558647	−	0.468760i
$124$		0			0
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	18.1523	−	6.60689i	1.61075	−	0.586267i	0.629165	−	0.777271i	$-0.283397\pi$
$127$	18.1523	−	6.60689i	1.61075	−	0.586267i	0.981589	+	0.191005i	$0.0611746\pi$
$128$		0			0
$129$	−1.09995	+	6.23811i	−0.0968449	+	0.549235i
$130$		0			0
$131$	−7.55776	+	6.34171i	−0.660324	+	0.554078i	−0.910184	−	0.414204i	$-0.864060\pi$
$131$	−7.55776	+	6.34171i	−0.660324	+	0.554078i	0.249860	+	0.968282i	$0.419615\pi$
$132$		0			0
$133$	−1.65923	+	1.13562i	−0.143873	+	0.0984705i
$134$		0			0
$135$	−4.09434	+	3.43556i	−0.352385	+	0.295686i
$136$		0			0
$137$	1.85178	−	10.5020i	0.158208	−	0.897242i	−0.797586	−	0.603205i	$-0.793890\pi$
$137$	1.85178	−	10.5020i	0.158208	−	0.897242i	0.955794	−	0.294037i	$-0.0949989\pi$
$138$		0			0
$139$	−1.23752	+	0.450422i	−0.104965	+	0.0382043i	−0.393969	−	0.919124i	$-0.628898\pi$
$139$	−1.23752	+	0.450422i	−0.104965	+	0.0382043i	0.289004	+	0.957328i	$0.406676\pi$
$140$		0			0
$141$	5.74582	+	9.95205i	0.483885	+	0.838114i
$142$		0			0
$143$	−5.85104	−	4.90961i	−0.489289	−	0.410562i
$144$		0			0
$145$	4.77627	−	8.27274i	0.396648	−	0.687014i
$146$		0			0
$147$	−1.97695	−	11.2118i	−0.163056	−	0.924737i
$148$		0			0
$149$	−15.8692	−	5.77592i	−1.30006	−	0.473181i	−0.403041	−	0.915182i	$-0.632047\pi$
$149$	−15.8692	−	5.77592i	−1.30006	−	0.473181i	−0.897015	+	0.442001i	$0.854269\pi$
$150$		0			0
$151$	21.5094			1.75041			0.875206	−	0.483751i	$-0.160726\pi$
$151$	21.5094			1.75041			0.875206	+	0.483751i	$0.160726\pi$
$152$		0			0
$153$	−1.03686			−0.0838256
$154$		0			0
$155$	8.68142	+	3.15978i	0.697308	+	0.253799i
$156$		0			0
$157$	−0.0930096	−	0.527484i	−0.00742297	−	0.0420978i	0.980871	−	0.194657i	$-0.0623595\pi$
$157$	−0.0930096	−	0.527484i	−0.00742297	−	0.0420978i	−0.988294	+	0.152560i	$0.951248\pi$
$158$		0			0
$159$	6.63268	−	11.4881i	0.526006	−	0.911069i
$160$		0			0
$161$	−0.773192	−	0.648785i	−0.0609360	−	0.0511314i
$162$		0			0
$163$	2.35598	+	4.08068i	0.184535	+	0.319624i	0.943420	−	0.331601i	$-0.107589\pi$
$163$	2.35598	+	4.08068i	0.184535	+	0.319624i	−0.758885	+	0.651225i	$0.774255\pi$
$164$		0			0
$165$	−2.02444	+	0.736836i	−0.157602	+	0.0573626i
$166$		0			0
$167$	−2.67217	+	15.1546i	−0.206779	+	1.17270i	0.687837	+	0.725865i	$0.258560\pi$
$167$	−2.67217	+	15.1546i	−0.206779	+	1.17270i	−0.894616	+	0.446835i	$0.852551\pi$
$168$		0			0
$169$	17.1334	−	14.3766i	1.31795	−	1.10589i
$170$		0			0
$171$	0.335459	+	0.739904i	0.0256532	+	0.0565819i
$172$		0			0
$173$	−15.3406	+	12.8722i	−1.16632	+	0.978659i	−0.999973	−	0.00740809i	$-0.997642\pi$
$173$	−15.3406	+	12.8722i	−1.16632	+	0.978659i	−0.166348	+	0.986067i	$0.553197\pi$
$174$		0			0
$175$	−0.0800990	+	0.454264i	−0.00605492	+	0.0343392i
$176$		0			0
$177$	8.44833	−	3.07494i	0.635015	−	0.231127i
$178$		0			0
$179$	6.47084	+	11.2078i	0.483653	+	0.837712i	0.999824	−	0.0187736i	$-0.00597617\pi$
$179$	6.47084	+	11.2078i	0.483653	+	0.837712i	−0.516170	+	0.856486i	$0.672643\pi$
$180$		0			0
$181$	5.41021	+	4.53971i	0.402138	+	0.337434i	0.821319	−	0.570469i	$-0.193238\pi$
$181$	5.41021	+	4.53971i	0.402138	+	0.337434i	−0.419181	+	0.907903i	$0.637683\pi$
$182$		0			0
$183$	8.50298	−	14.7276i	0.628558	−	1.08869i
$184$		0			0
$185$	1.54624	+	8.76915i	0.113682	+	0.644721i
$186$		0			0
$187$	−6.71431	−	2.44381i	−0.490999	−	0.178709i
$188$		0			0
$189$	2.46540			0.179331
$190$		0			0
$191$	−23.1066			−1.67194			−0.835968	−	0.548778i	$-0.815093\pi$
$191$	−23.1066			−1.67194			−0.835968	+	0.548778i	$0.815093\pi$
$192$		0			0
$193$	7.11202	+	2.58856i	0.511934	+	0.186329i	0.585054	−	0.810994i	$-0.301073\pi$
$193$	7.11202	+	2.58856i	0.511934	+	0.186329i	−0.0731197	+	0.997323i	$0.523296\pi$
$194$		0			0
$195$	−1.73219	−	9.82376i	−0.124045	−	0.703494i
$196$		0			0
$197$	1.04381	−	1.80794i	0.0743687	−	0.128810i	−0.826443	−	0.563021i	$-0.809639\pi$
$197$	1.04381	−	1.80794i	0.0743687	−	0.128810i	0.900812	+	0.434210i	$0.142972\pi$
$198$		0			0
$199$	−8.17751	−	6.86174i	−0.579688	−	0.486416i	0.305157	−	0.952302i	$-0.401291\pi$
$199$	−8.17751	−	6.86174i	−0.579688	−	0.486416i	−0.884845	+	0.465886i	$0.845736\pi$
$200$		0			0
$201$	−5.53655	−	9.58958i	−0.390518	−	0.676397i
$202$		0			0
$203$	−4.14059	+	1.50705i	−0.290612	+	0.105774i
$204$		0			0
$205$	−0.837285	+	4.74848i	−0.0584785	+	0.331648i
$206$		0			0
$207$	−0.312408	+	0.262142i	−0.0217139	+	0.0182201i
$208$		0			0
$209$	0.428401	+	5.58197i	0.0296331	+	0.386113i
$210$		0			0
$211$	−1.92530	+	1.61552i	−0.132543	+	0.111217i	−0.706649	−	0.707564i	$-0.749794\pi$
$211$	−1.92530	+	1.61552i	−0.132543	+	0.111217i	0.574106	+	0.818781i	$0.305350\pi$
$212$		0			0
$213$	2.00801	−	11.3880i	0.137586	−	0.780292i
$214$		0			0
$215$	3.54858	−	1.29158i	0.242011	−	0.0880848i
$216$		0			0
$217$	−2.13075	−	3.69056i	−0.144645	−	0.250532i
$218$		0			0
$219$	16.8206	+	14.1142i	1.13663	+	0.953748i
$220$		0			0
$221$	16.5422	−	28.6519i	1.11275	−	1.92734i
$222$		0			0
$223$	−0.994453	−	5.63982i	−0.0665935	−	0.377671i	−0.999831	−	0.0184093i	$-0.994140\pi$
$223$	−0.994453	−	5.63982i	−0.0665935	−	0.377671i	0.933237	−	0.359261i	$-0.116971\pi$
$224$		0			0
$225$	0.175137	+	0.0637447i	0.0116758	+	0.00424965i
$226$		0			0
$227$	10.9014			0.723551			0.361775	−	0.932265i	$-0.382171\pi$
$227$	10.9014			0.723551			0.361775	+	0.932265i	$0.382171\pi$
$228$		0			0
$229$	0.764616			0.0505272			0.0252636	−	0.999681i	$-0.491957\pi$
$229$	0.764616			0.0505272			0.0252636	+	0.999681i	$0.491957\pi$
$230$		0			0
$231$	0.933817	+	0.339882i	0.0614407	+	0.0223626i
$232$		0			0
$233$	−2.23090	−	12.6520i	−0.146151	−	0.828863i	−0.966436	−	0.256908i	$-0.917296\pi$
$233$	−2.23090	−	12.6520i	−0.146151	−	0.828863i	0.820285	−	0.571955i	$-0.193815\pi$
$234$		0			0
$235$	3.42546	−	5.93307i	0.223452	−	0.387031i
$236$		0			0
$237$	1.78400	+	1.49695i	0.115883	+	0.0972375i
$238$		0			0
$239$	4.87692	+	8.44707i	0.315462	+	0.546396i	0.979536	−	0.201271i	$-0.0645073\pi$
$239$	4.87692	+	8.44707i	0.315462	+	0.546396i	−0.664074	+	0.747667i	$0.731174\pi$
$240$		0			0
$241$	−9.11167	+	3.31638i	−0.586934	+	0.213626i	−0.618380	−	0.785879i	$-0.712211\pi$
$241$	−9.11167	+	3.31638i	−0.586934	+	0.213626i	0.0314464	+	0.999505i	$0.489989\pi$
$242$		0			0
$243$	0.335840	−	1.90464i	0.0215441	−	0.122183i
$244$		0			0
$245$	−5.19932	+	4.36275i	−0.332172	+	0.278726i
$246$		0			0
$247$	−25.7979	−	2.53465i	−1.64148	−	0.161276i
$248$		0			0
$249$	0.169741	−	0.142430i	0.0107569	−	0.00902614i
$250$		0			0
$251$	2.48507	−	14.0935i	0.156856	−	0.889576i	−0.800213	−	0.599716i	$-0.795280\pi$
$251$	2.48507	−	14.0935i	0.156856	−	0.889576i	0.957069	−	0.289860i	$-0.0936087\pi$
$252$		0			0
$253$	−2.64088	+	0.961200i	−0.166030	+	0.0604301i
$254$		0			0
$255$	−4.66587	−	8.08153i	−0.292188	−	0.506085i
$256$		0			0
$257$	−12.5560	−	10.5357i	−0.783221	−	0.657201i	0.160836	−	0.986981i	$-0.448581\pi$
$257$	−12.5560	−	10.5357i	−0.783221	−	0.657201i	−0.944058	+	0.329780i	$0.893025\pi$
$258$		0			0
$259$	2.05368	−	3.55708i	0.127610	−	0.221026i
$260$		0			0
$261$	0.309159	+	1.75333i	0.0191365	+	0.108528i
$262$		0			0
$263$	28.3445	+	10.3166i	1.74780	+	0.636146i	0.999626	−	0.0273600i	$-0.00871003\pi$
$263$	28.3445	+	10.3166i	1.74780	+	0.636146i	0.748171	+	0.663506i	$0.230932\pi$
$264$		0			0
$265$	−7.90836			−0.485807
$266$		0			0
$267$	−5.16689			−0.316209
$268$		0			0
$269$	−10.0213	−	3.64747i	−0.611012	−	0.222390i	0.0179339	−	0.999839i	$-0.494291\pi$
$269$	−10.0213	−	3.64747i	−0.611012	−	0.222390i	−0.628946	+	0.777449i	$0.716513\pi$
$270$		0			0
$271$	5.03825	+	28.5733i	0.306052	+	1.73571i	0.618511	+	0.785776i	$0.287736\pi$
$271$	5.03825	+	28.5733i	0.306052	+	1.73571i	−0.312460	+	0.949931i	$0.601153\pi$
$272$		0			0
$273$	−2.30067	+	3.98487i	−0.139243	+	0.241175i
$274$		0			0
$275$	0.983875	+	0.825569i	0.0593299	+	0.0497837i
$276$		0			0
$277$	8.11556	+	14.0566i	0.487617	+	0.844577i	0.999899	−	0.0142406i	$-0.00453307\pi$
$277$	8.11556	+	14.0566i	0.487617	+	0.844577i	−0.512282	+	0.858817i	$0.671200\pi$
$278$		0			0
$279$	−1.61802	+	0.588910i	−0.0968681	+	0.0352571i
$280$		0			0
$281$	0.339000	−	1.92256i	0.0202230	−	0.114690i	−0.973025	−	0.230699i	$-0.925899\pi$
$281$	0.339000	−	1.92256i	0.0202230	−	0.114690i	0.993248	+	0.116008i	$0.0370099\pi$
$282$		0			0
$283$	15.3905	−	12.9142i	0.914873	−	0.767670i	−0.0581666	−	0.998307i	$-0.518525\pi$
$283$	15.3905	−	12.9142i	0.914873	−	0.767670i	0.973040	+	0.230637i	$0.0740810\pi$
$284$		0			0
$285$	−4.25740	+	5.94419i	−0.252186	+	0.352103i
$286$		0			0
$287$	1.70378	−	1.42964i	0.100571	−	0.0843892i
$288$		0			0
$289$	2.42238	−	13.7380i	0.142493	−	0.808117i
$290$		0			0
$291$	−0.921426	+	0.335371i	−0.0540149	+	0.0196598i
$292$		0			0
$293$	9.65324	+	16.7199i	0.563948	+	0.976787i	0.997147	+	0.0754882i	$0.0240515\pi$
$293$	9.65324	+	16.7199i	0.563948	+	0.976787i	−0.433199	+	0.901298i	$0.642615\pi$
$294$		0			0
$295$	−4.10588	−	3.44524i	−0.239053	−	0.200590i
$296$		0			0
$297$	3.43231	−	5.94493i	0.199163	−	0.344960i
$298$		0			0
$299$	−2.25964	−	12.8151i	−0.130678	−	0.741115i
$300$		0			0
$301$	−1.63686	−	0.595768i	−0.0943471	−	0.0343395i
$302$		0			0
$303$	9.03322			0.518945
$304$		0			0
$305$	−10.1384			−0.580521
$306$		0			0
$307$	−10.2195	−	3.71959i	−0.583257	−	0.212288i	0.0335038	−	0.999439i	$-0.489333\pi$
$307$	−10.2195	−	3.71959i	−0.583257	−	0.212288i	−0.616761	+	0.787150i	$0.711556\pi$
$308$		0			0
$309$	0.736878	+	4.17904i	0.0419195	+	0.237737i
$310$		0			0
$311$	8.62121	−	14.9324i	0.488864	−	0.846737i	−0.511054	−	0.859549i	$-0.670745\pi$
$311$	8.62121	−	14.9324i	0.488864	−	0.846737i	0.999918	+	0.0128113i	$0.00407807\pi$
$312$		0			0
$313$	6.00211	+	5.03637i	0.339259	+	0.284672i	0.796460	−	0.604691i	$-0.206703\pi$
$313$	6.00211	+	5.03637i	0.339259	+	0.284672i	−0.457201	+	0.889364i	$0.651148\pi$
$314$		0			0
$315$	−0.0429853	−	0.0744527i	−0.00242194	−	0.00419493i
$316$		0			0
$317$	−9.67697	+	3.52213i	−0.543513	+	0.197822i	−0.599162	−	0.800628i	$-0.704499\pi$
$317$	−9.67697	+	3.52213i	−0.543513	+	0.197822i	0.0556491	+	0.998450i	$0.482277\pi$
$318$		0			0
$319$	−2.13047	+	12.0825i	−0.119283	+	0.676490i
$320$		0			0
$321$	9.34291	−	7.83963i	0.521470	−	0.437566i
$322$		0			0
$323$	−23.4891	+	6.02602i	−1.30697	+	0.335297i
$324$		0			0
$325$	−4.55562	+	3.82262i	−0.252700	+	0.212041i
$326$		0			0
$327$	−2.00857	+	11.3912i	−0.111074	+	0.629933i
$328$		0			0
$329$	−2.96956	+	1.08083i	−0.163717	+	0.0595881i
$330$		0			0
$331$	16.7428	+	28.9993i	0.920266	+	1.59395i	0.799004	+	0.601326i	$0.205361\pi$
$331$	16.7428	+	28.9993i	0.920266	+	1.59395i	0.121262	+	0.992621i	$0.461306\pi$
$332$		0			0
$333$	−1.27131	−	1.06676i	−0.0696675	−	0.0584580i
$334$		0			0
$335$	−3.30070	+	5.71698i	−0.180336	+	0.312352i
$336$		0			0
$337$	−4.32250	−	24.5141i	−0.235462	−	1.33537i	−0.841639	−	0.540041i	$-0.818409\pi$
$337$	−4.32250	−	24.5141i	−0.235462	−	1.33537i	0.606177	−	0.795330i	$-0.292702\pi$
$338$		0			0
$339$	−15.5321	−	5.65322i	−0.843588	−	0.307041i
$340$		0			0
$341$	−11.8656			−0.642560
$342$		0			0
$343$	6.35966			0.343389
$344$		0			0
$345$	−3.44901	−	1.25534i	−0.185689	−	0.0675851i
$346$		0			0
$347$	4.38162	+	24.8494i	0.235218	+	1.33399i	0.842155	+	0.539236i	$0.181287\pi$
$347$	4.38162	+	24.8494i	0.235218	+	1.33399i	−0.606937	+	0.794750i	$0.707602\pi$
$348$		0			0
$349$	−14.2024	+	24.5992i	−0.760236	+	1.31677i	0.182493	+	0.983207i	$0.441583\pi$
$349$	−14.2024	+	24.5992i	−0.760236	+	1.31677i	−0.942729	+	0.333560i	$0.891750\pi$
$350$		0			0
$351$	24.3488	+	20.4311i	1.29964	+	1.09053i
$352$		0			0
$353$	15.0606	+	26.0858i	0.801596	+	1.38841i	0.918565	+	0.395270i	$0.129349\pi$
$353$	15.0606	+	26.0858i	0.801596	+	1.38841i	−0.116969	+	0.993136i	$0.537318\pi$
$354$		0			0
$355$	−6.47811	+	2.35784i	−0.343822	+	0.125141i
$356$		0			0
$357$	−0.747464	+	4.23908i	−0.0395600	+	0.224356i
$358$		0			0
$359$	−26.1437	+	21.9372i	−1.37981	+	1.15780i	−0.410530	+	0.911847i	$0.634656\pi$
$359$	−26.1437	+	21.9372i	−1.37981	+	1.15780i	−0.969282	+	0.245952i	$0.920899\pi$
$360$		0			0
$361$	11.8996	+	14.8121i	0.626296	+	0.779585i
$362$		0			0
$363$	−12.0148	+	10.0817i	−0.630616	+	0.529150i
$364$		0			0
$365$	2.27314	−	12.8916i	0.118981	−	0.674777i
$366$		0			0
$367$	−21.2362	+	7.72935i	−1.10852	+	0.403469i	−0.830451	−	0.557092i	$-0.811917\pi$
$367$	−21.2362	+	7.72935i	−1.10852	+	0.403469i	−0.278071	+	0.960561i	$0.589695\pi$
$368$		0			0
$369$	−0.449330	−	0.778263i	−0.0233912	−	0.0405147i
$370$		0			0
$371$	2.79446	+	2.34483i	0.145081	+	0.121737i
$372$		0			0
$373$	−6.05955	+	10.4955i	−0.313752	+	0.543434i	−0.979171	−	0.203036i	$-0.934919\pi$
$373$	−6.05955	+	10.4955i	−0.313752	+	0.543434i	0.665420	+	0.746469i	$0.268253\pi$
$374$		0			0
$375$	0.291275	+	1.65190i	0.0150414	+	0.0853039i
$376$		0			0
$377$	−53.3824	−	19.4296i	−2.74933	−	1.00068i
$378$		0			0
$379$	34.8034			1.78773			0.893866	−	0.448335i	$-0.147983\pi$
$379$	34.8034			1.78773			0.893866	+	0.448335i	$0.147983\pi$
$380$		0			0
$381$	−32.4025			−1.66003
$382$		0			0
$383$	25.9413	+	9.44187i	1.32554	+	0.482457i	0.905229	−	0.424924i	$-0.139699\pi$
$383$	25.9413	+	9.44187i	1.32554	+	0.482457i	0.420310	+	0.907381i	$0.361921\pi$
$384$		0			0
$385$	−0.102876	−	0.583438i	−0.00524304	−	0.0297347i
$386$		0			0
$387$	−0.351910	+	0.609525i	−0.0178886	+	0.0309839i
$388$		0			0
$389$	16.6736	+	13.9908i	0.845384	+	0.709362i	0.958768	−	0.284190i	$-0.0917246\pi$
$389$	16.6736	+	13.9908i	0.845384	+	0.709362i	−0.113384	+	0.993551i	$0.536169\pi$
$390$		0			0
$391$	−6.08662	−	10.5423i	−0.307813	−	0.533148i
$392$		0			0
$393$	15.5510	−	5.66009i	0.784443	−	0.285514i
$394$		0			0
$395$	0.241089	−	1.36728i	0.0121305	−	0.0687956i
$396$		0			0
$397$	0.534594	−	0.448577i	0.0268305	−	0.0225134i	−0.629274	−	0.777184i	$-0.716648\pi$
$397$	0.534594	−	0.448577i	0.0268305	−	0.0225134i	0.656104	+	0.754670i	$0.272203\pi$
$398$		0			0
$399$	3.26682	−	0.838091i	0.163546	−	0.0419570i
$400$		0			0
$401$	8.08896	−	6.78745i	0.403944	−	0.338949i	−0.418072	−	0.908414i	$-0.637294\pi$
$401$	8.08896	−	6.78745i	0.403944	−	0.338949i	0.822016	+	0.569465i	$0.192850\pi$
$402$		0			0
$403$	9.54044	−	54.1065i	0.475243	−	2.69524i
$404$		0			0
$405$	7.89918	−	2.87507i	0.392513	−	0.142863i
$406$		0			0
$407$	−5.71824	−	9.90428i	−0.283443	−	0.490937i
$408$		0			0
$409$	9.35982	+	7.85383i	0.462814	+	0.388347i	0.844165	−	0.536083i	$-0.180097\pi$
$409$	9.35982	+	7.85383i	0.462814	+	0.388347i	−0.381351	+	0.924430i	$0.624541\pi$
$410$		0			0
$411$	−8.94379	+	15.4911i	−0.441165	+	0.764119i
$412$		0			0
$413$	0.429318	+	2.43478i	0.0211254	+	0.119808i
$414$		0			0
$415$	−0.124133	−	0.0451807i	−0.00609344	−	0.00221783i
$416$		0			0
$417$	2.20902			0.108176
$418$		0			0
$419$	26.6471			1.30180			0.650899	−	0.759165i	$-0.274392\pi$
$419$	26.6471			1.30180			0.650899	+	0.759165i	$0.274392\pi$
$420$		0			0
$421$	−14.4385	−	5.25519i	−0.703690	−	0.256122i	−0.0347043	−	0.999398i	$-0.511049\pi$
$421$	−14.4385	−	5.25519i	−0.703690	−	0.256122i	−0.668985	+	0.743276i	$0.733271\pi$
$422$		0			0
$423$	0.221723	+	1.25746i	0.0107806	+	0.0611396i
$424$		0			0
$425$	−2.78163	+	4.81793i	−0.134929	+	0.233704i
$426$		0			0
$427$	3.58244	+	3.00603i	0.173366	+	0.145472i
$428$		0			0
$429$	6.40593	+	11.0954i	0.309281	+	0.535691i
$430$		0			0
$431$	−36.0199	+	13.1102i	−1.73502	+	0.631494i	−0.998967	−	0.0454340i	$-0.985533\pi$
$431$	−36.0199	+	13.1102i	−1.73502	+	0.631494i	−0.736049	+	0.676928i	$0.763311\pi$
$432$		0			0
$433$	−5.71443	+	32.4082i	−0.274618	+	1.55744i	0.465554	+	0.885019i	$0.345855\pi$
$433$	−5.71443	+	32.4082i	−0.274618	+	1.55744i	−0.740172	+	0.672417i	$0.765256\pi$
$434$		0			0
$435$	−12.2746	+	10.2996i	−0.588520	+	0.493827i
$436$		0			0
$437$	−5.55376	+	7.75418i	−0.265673	+	0.370933i
$438$		0			0
$439$	−18.1190	+	15.2037i	−0.864775	+	0.725632i	−0.962991	−	0.269533i	$-0.913131\pi$
$439$	−18.1190	+	15.2037i	−0.864775	+	0.725632i	0.0982162	+	0.995165i	$0.468686\pi$
$440$		0			0
$441$	0.219662	−	1.24577i	0.0104601	−	0.0593222i
$442$		0			0
$443$	15.5447	−	5.65781i	0.738551	−	0.268811i	0.0547713	−	0.998499i	$-0.482557\pi$
$443$	15.5447	−	5.65781i	0.738551	−	0.268811i	0.683780	+	0.729688i	$0.260335\pi$
$444$		0			0
$445$	1.54016	+	2.66764i	0.0730107	+	0.126458i
$446$		0			0
$447$	21.6998	+	18.2083i	1.02637	+	0.861224i
$448$		0			0
$449$	14.6752	−	25.4181i	0.692563	−	1.19955i	−0.278432	−	0.960456i	$-0.589815\pi$
$449$	14.6752	−	25.4181i	0.692563	−	1.19955i	0.970995	−	0.239099i	$-0.0768520\pi$
$450$		0			0
$451$	−1.07537	−	6.09875i	−0.0506374	−	0.287179i
$452$		0			0
$453$	−33.9037	−	12.3399i	−1.59294	−	0.579781i
$454$		0			0
$455$	2.74316			0.128601
$456$		0			0
$457$	−5.48753			−0.256696			−0.128348	−	0.991729i	$-0.540967\pi$
$457$	−5.48753			−0.256696			−0.128348	+	0.991729i	$0.540967\pi$
$458$		0			0
$459$	27.9412	+	10.1698i	1.30419	+	0.474685i
$460$		0			0
$461$	−5.76350	−	32.6864i	−0.268433	−	1.52236i	−0.759079	−	0.650999i	$-0.774350\pi$
$461$	−5.76350	−	32.6864i	−0.268433	−	1.52236i	0.490646	−	0.871359i	$-0.336761\pi$
$462$		0			0
$463$	6.07020	−	10.5139i	0.282106	−	0.488622i	−0.689797	−	0.724003i	$-0.742300\pi$
$463$	6.07020	−	10.5139i	0.282106	−	0.488622i	0.971903	+	0.235381i	$0.0756336\pi$
$464$		0			0
$465$	−11.8711	−	9.96105i	−0.550510	−	0.461933i
$466$		0			0
$467$	−10.2092	−	17.6828i	−0.472425	−	0.818264i	0.527077	−	0.849817i	$-0.323288\pi$
$467$	−10.2092	−	17.6828i	−0.472425	−	0.818264i	−0.999502	+	0.0315536i	$0.989955\pi$
$468$		0			0
$469$	2.86140	−	1.04147i	0.132127	−	0.0480904i
$470$		0			0
$471$	−0.156013	+	0.884793i	−0.00718870	+	0.0407691i
$472$		0			0
$473$	−3.71543	+	3.11761i	−0.170835	+	0.143348i
$474$		0			0
$475$	4.33801	+	0.426210i	0.199042	+	0.0195559i
$476$		0			0
$477$	1.12910	−	0.947428i	0.0516980	−	0.0433798i
$478$		0			0
$479$	1.98862	−	11.2780i	0.0908621	−	0.515305i	−0.905075	−	0.425252i	$-0.860185\pi$
$479$	1.98862	−	11.2780i	0.0908621	−	0.515305i	0.995937	−	0.0900526i	$-0.0287035\pi$
$480$		0			0
$481$	49.7606	−	18.1114i	2.26889	−	0.825807i
$482$		0			0
$483$	0.846518	+	1.46621i	0.0385179	+	0.0667150i
$484$		0			0
$485$	0.447812	+	0.375759i	0.0203341	+	0.0170623i
$486$		0			0
$487$	6.46021	−	11.1894i	0.292740	−	0.507041i	−0.681716	−	0.731617i	$-0.738766\pi$
$487$	6.46021	−	11.1894i	0.292740	−	0.507041i	0.974457	+	0.224575i	$0.0720995\pi$
$488$		0			0
$489$	−1.37248	−	7.78371i	−0.0620656	−	0.351992i
$490$		0			0
$491$	30.1324	+	10.9673i	1.35986	+	0.494947i	0.916010	−	0.401156i	$-0.131391\pi$
$491$	30.1324	+	10.9673i	1.35986	+	0.494947i	0.443846	+	0.896103i	$0.353614\pi$
$492$		0			0
$493$	−53.1433			−2.39346
$494$		0			0
$495$	−0.239375			−0.0107591
$496$		0			0
$497$	2.98817	+	1.08760i	0.134038	+	0.0487857i
$498$		0			0
$499$	−0.339187	−	1.92363i	−0.0151841	−	0.0861133i	0.976274	−	0.216539i	$-0.0694768\pi$
$499$	−0.339187	−	1.92363i	−0.0151841	−	0.0861133i	−0.991458	+	0.130425i	$0.958366\pi$
$500$		0			0
$501$	12.9062	−	22.3541i	0.576604	−	0.998708i
$502$		0			0
$503$	20.8314	+	17.4796i	0.928824	+	0.779376i	0.975606	−	0.219529i	$-0.0704521\pi$
$503$	20.8314	+	17.4796i	0.928824	+	0.779376i	−0.0467817	+	0.998905i	$0.514897\pi$
$504$		0			0
$505$	−2.69265	−	4.66380i	−0.119821	−	0.207537i
$506$		0			0
$507$	−35.2540	+	12.8314i	−1.56568	+	0.569863i
$508$		0			0
$509$	4.27733	−	24.2580i	0.189589	−	1.07521i	−0.730326	−	0.683098i	$-0.760632\pi$
$509$	4.27733	−	24.2580i	0.189589	−	1.07521i	0.919916	−	0.392116i	$-0.128257\pi$
$510$		0			0
$511$	−4.62558	+	3.88133i	−0.204624	+	0.171700i
$512$		0			0
$513$	−1.78277	−	23.2291i	−0.0787110	−	1.02559i
$514$		0			0
$515$	1.93797	−	1.62615i	0.0853970	−	0.0716566i
$516$		0			0
$517$	−1.52794	+	8.66536i	−0.0671986	+	0.381102i
$518$		0			0
$519$	31.5650	−	11.4887i	1.38555	−	0.504299i
$520$		0			0
$521$	0.800476	+	1.38646i	0.0350695	+	0.0607421i	0.883027	−	0.469321i	$-0.155501\pi$
$521$	0.800476	+	1.38646i	0.0350695	+	0.0607421i	−0.847958	+	0.530064i	$0.822168\pi$
$522$		0			0
$523$	−4.61410	−	3.87169i	−0.201760	−	0.169297i	0.536309	−	0.844021i	$-0.319818\pi$
$523$	−4.61410	−	3.87169i	−0.201760	−	0.169297i	−0.738070	+	0.674724i	$0.764262\pi$
$524$		0			0
$525$	0.386866	−	0.670071i	0.0168842	−	0.0292443i
$526$		0			0
$527$	−8.92493	−	50.6158i	−0.388776	−	2.20486i
$528$		0			0
$529$	17.1137	+	6.22888i	0.744074	+	0.270821i
$530$		0			0
$531$	0.998952			0.0433508
$532$		0			0
$533$	28.6745			1.24203
$534$		0			0
$535$	−6.83252	−	2.48684i	−0.295396	−	0.107515i
$536$		0			0
$537$	−3.76959	−	21.3784i	−0.162670	−	0.922546i
$538$		0			0
$539$	4.35861	−	7.54934i	0.187739	−	0.325173i
$540$		0			0
$541$	−17.7515	−	14.8952i	−0.763194	−	0.640396i	0.175762	−	0.984433i	$-0.443761\pi$
$541$	−17.7515	−	14.8952i	−0.763194	−	0.640396i	−0.938956	+	0.344037i	$0.888206\pi$
$542$		0			0
$543$	−5.92330	−	10.2595i	−0.254193	−	0.440275i
$544$		0			0
$545$	6.47992	−	2.35850i	0.277569	−	0.101027i
$546$		0			0
$547$	4.25083	−	24.1076i	0.181752	−	1.03077i	−0.748305	−	0.663355i	$-0.769132\pi$
$547$	4.25083	−	24.1076i	0.181752	−	1.03077i	0.930058	−	0.367414i	$-0.119757\pi$
$548$		0			0
$549$	1.44749	−	1.21459i	0.0617772	−	0.0518372i
$550$		0			0
$551$	17.1936	+	37.9230i	0.732472	+	1.61557i
$552$		0			0
$553$	−0.490590	+	0.411654i	−0.0208620	+	0.0175053i
$554$		0			0
$555$	2.59364	−	14.7093i	0.110094	−	0.624373i
$556$		0			0
$557$	−20.8341	+	7.58301i	−0.882771	+	0.321302i	−0.743327	−	0.668928i	$-0.766754\pi$
$557$	−20.8341	+	7.58301i	−0.882771	+	0.321302i	−0.139443	+	0.990230i	$0.544531\pi$
$558$		0			0
$559$	−11.2288	−	19.4488i	−0.474926	−	0.822596i
$560$		0			0
$561$	9.18127	+	7.70400i	0.387633	+	0.325263i
$562$		0			0
$563$	−0.331404	+	0.574008i	−0.0139670	+	0.0241916i	−0.872924	−	0.487855i	$-0.837779\pi$
$563$	−0.331404	+	0.574008i	−0.0139670	+	0.0241916i	0.858957	+	0.512047i	$0.171113\pi$
$564$		0			0
$565$	1.71112	+	9.70427i	0.0719876	+	0.408262i
$566$		0			0
$567$	−3.64367	−	1.32619i	−0.153020	−	0.0556947i
$568$		0			0
$569$	2.63574			0.110496			0.0552480	−	0.998473i	$-0.482405\pi$
$569$	2.63574			0.110496			0.0552480	+	0.998473i	$0.482405\pi$
$570$		0			0
$571$	−38.1084			−1.59479			−0.797393	−	0.603461i	$-0.793788\pi$
$571$	−38.1084			−1.59479			−0.797393	+	0.603461i	$0.793788\pi$
$572$		0			0
$573$	36.4213	+	13.2563i	1.52152	+	0.553788i
$574$		0			0
$575$	0.379967	+	2.15490i	0.0158457	+	0.0898656i
$576$		0			0
$577$	−21.8375	+	37.8237i	−0.909109	+	1.57462i	−0.0938036	+	0.995591i	$0.529903\pi$
$577$	−21.8375	+	37.8237i	−0.909109	+	1.57462i	−0.815305	+	0.579032i	$0.803431\pi$
$578$		0			0
$579$	−9.72510	−	8.16033i	−0.404161	−	0.339132i
$580$		0			0
$581$	0.0304669	+	0.0527702i	0.00126398	+	0.00218928i
$582$		0			0
$583$	9.54461	−	3.47395i	0.395297	−	0.143876i
$584$		0			0
$585$	0.192467	−	1.09153i	0.00795753	−	0.0451294i
$586$		0			0
$587$	28.1433	−	23.6150i	1.16160	−	0.974696i	0.161671	−	0.986845i	$-0.448312\pi$
$587$	28.1433	−	23.6150i	1.16160	−	0.974696i	0.999926	+	0.0121486i	$0.00386711\pi$
$588$		0			0
$589$	−33.2318	+	22.7447i	−1.36929	+	0.937177i
$590$		0			0
$591$	−2.68250	+	2.25089i	−0.110343	+	0.0925892i
$592$		0			0
$593$	−1.48665	+	8.43118i	−0.0610492	+	0.346227i	0.938948	+	0.344058i	$0.111802\pi$
$593$	−1.48665	+	8.43118i	−0.0610492	+	0.346227i	−0.999998	+	0.00216936i	$0.999309\pi$
$594$		0			0
$595$	2.41142	−	0.877685i	0.0988585	−	0.0359816i
$596$		0			0
$597$	8.95303	+	15.5071i	0.366423	+	0.634663i
$598$		0			0
$599$	16.3426	+	13.7131i	0.667740	+	0.560301i	0.912396	−	0.409310i	$-0.134230\pi$
$599$	16.3426	+	13.7131i	0.667740	+	0.560301i	−0.244655	+	0.969610i	$0.578675\pi$
$600$		0			0
$601$	5.27120	−	9.12999i	0.215017	−	0.372420i	−0.738261	−	0.674515i	$-0.764353\pi$
$601$	5.27120	−	9.12999i	0.215017	−	0.372420i	0.953278	+	0.302095i	$0.0976860\pi$
$602$		0			0
$603$	−0.213648	−	1.21166i	−0.00870041	−	0.0493425i
$604$		0			0
$605$	8.78653	+	3.19803i	0.357223	+	0.130019i
$606$		0			0
$607$	−5.51930			−0.224022			−0.112011	−	0.993707i	$-0.535729\pi$
$607$	−5.51930			−0.224022			−0.112011	+	0.993707i	$0.535729\pi$
$608$		0			0
$609$	7.39110			0.299502
$610$		0			0
$611$	−38.2850	−	13.9346i	−1.54884	−	0.563733i
$612$		0			0
$613$	−3.65334	−	20.7191i	−0.147557	−	0.836837i	−0.965279	−	0.261223i	$-0.915874\pi$
$613$	−3.65334	−	20.7191i	−0.147557	−	0.836837i	0.817722	−	0.575614i	$-0.195237\pi$
$614$		0			0
$615$	4.04395	−	7.00433i	0.163068	−	0.282442i
$616$		0			0
$617$	6.98028	+	5.85715i	0.281015	+	0.235800i	0.772390	−	0.635148i	$-0.219061\pi$
$617$	6.98028	+	5.85715i	0.281015	+	0.235800i	−0.491375	+	0.870948i	$0.663505\pi$
$618$		0			0
$619$	−5.64698	−	9.78086i	−0.226971	−	0.393126i	0.729938	−	0.683514i	$-0.239549\pi$
$619$	−5.64698	−	9.78086i	−0.226971	−	0.393126i	−0.956909	+	0.290388i	$0.906216\pi$
$620$		0			0
$621$	10.9899	−	3.99998i	0.441008	−	0.160514i
$622$		0			0
$623$	0.246731	−	1.39928i	0.00988507	−	0.0560610i
$624$		0			0
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$		0			0
$627$	2.52712	−	9.04423i	0.100923	−	0.361192i
$628$		0			0
$629$	37.9481	−	31.8422i	1.51309	−	1.26963i
$630$		0			0
$631$	−1.07783	+	6.11268i	−0.0429077	+	0.243342i	−0.998717	−	0.0506469i	$-0.983872\pi$
$631$	−1.07783	+	6.11268i	−0.0429077	+	0.243342i	0.955809	+	0.293989i	$0.0949828\pi$
$632$		0			0
$633$	3.96153	−	1.44188i	0.157457	−	0.0573096i
$634$		0			0
$635$	9.65863	+	16.7292i	0.383291	+	0.663879i
$636$		0			0
$637$	30.9200	+	25.9450i	1.22510	+	1.02798i
$638$		0			0
$639$	0.642428	−	1.11272i	0.0254141	−	0.0440185i
$640$		0			0
$641$	−2.93315	−	16.6347i	−0.115852	−	0.657032i	−0.986325	−	0.164814i	$-0.947298\pi$
$641$	−2.93315	−	16.6347i	−0.115852	−	0.657032i	0.870472	−	0.492218i	$-0.163814\pi$
$642$		0			0
$643$	−21.6034	−	7.86301i	−0.851957	−	0.310087i	−0.121119	−	0.992638i	$-0.538648\pi$
$643$	−21.6034	−	7.86301i	−0.851957	−	0.310087i	−0.730838	+	0.682551i	$0.760870\pi$
$644$		0			0
$645$	−6.33434			−0.249415
$646$		0			0
$647$	12.9497			0.509105			0.254553	−	0.967059i	$-0.418072\pi$
$647$	12.9497			0.509105			0.254553	+	0.967059i	$0.418072\pi$
$648$		0			0
$649$	6.46880	+	2.35445i	0.253923	+	0.0924203i
$650$		0			0
$651$	1.24127	+	7.03957i	0.0486491	+	0.275903i
$652$		0			0
$653$	−5.15557	+	8.92972i	−0.201753	+	0.349447i	−0.949093	−	0.314995i	$-0.897997\pi$
$653$	−5.15557	+	8.92972i	−0.201753	+	0.349447i	0.747340	+	0.664442i	$0.231331\pi$
$654$		0			0
$655$	−7.55776	−	6.34171i	−0.295306	−	0.247791i
$656$		0			0
$657$	1.21988	+	2.11290i	0.0475921	+	0.0824320i
$658$		0			0
$659$	17.7370	−	6.45573i	0.690934	−	0.251480i	0.0273992	−	0.999625i	$-0.491277\pi$
$659$	17.7370	−	6.45573i	0.690934	−	0.251480i	0.663535	+	0.748145i	$0.269055\pi$
$660$		0			0
$661$	−4.53848	+	25.7390i	−0.176526	+	1.00113i	0.759841	+	0.650109i	$0.225277\pi$
$661$	−4.53848	+	25.7390i	−0.176526	+	1.00113i	−0.936367	+	0.351022i	$0.885834\pi$
$662$		0			0
$663$	−42.5119	+	35.6717i	−1.65102	+	1.38537i
$664$		0			0
$665$	−1.40649	−	1.43682i	−0.0545412	−	0.0557176i
$666$		0			0
$667$	−16.0121	+	13.4358i	−0.619992	+	0.520235i
$668$		0			0
$669$	−1.66808	+	9.46016i	−0.0644918	+	0.365751i
$670$		0			0
$671$	12.2360	−	4.45354i	0.472366	−	0.171927i
$672$		0			0
$673$	2.44003	+	4.22625i	0.0940562	+	0.162910i	0.909214	−	0.416328i	$-0.136683\pi$
$673$	2.44003	+	4.22625i	0.0940562	+	0.162910i	−0.815158	+	0.579239i	$0.803350\pi$
$674$		0			0
$675$	−4.09434	−	3.43556i	−0.157591	−	0.132235i
$676$		0			0
$677$	5.91099	−	10.2381i	0.227178	−	0.393484i	−0.729793	−	0.683668i	$-0.760383\pi$
$677$	5.91099	−	10.2381i	0.227178	−	0.393484i	0.956971	+	0.290185i	$0.0937168\pi$
$678$		0			0
$679$	−0.0468240	−	0.265552i	−0.00179694	−	0.0101910i
$680$		0			0
$681$	−17.1831	−	6.25412i	−0.658456	−	0.239659i
$682$		0			0
$683$	−1.10522			−0.0422901			−0.0211450	−	0.999776i	$-0.506731\pi$
$683$	−1.10522			−0.0422901			−0.0211450	+	0.999776i	$0.506731\pi$
$684$		0			0
$685$	10.6640			0.407449
$686$		0			0
$687$	−1.20521	−	0.438660i	−0.0459816	−	0.0167359i
$688$		0			0
$689$	8.16676	+	46.3160i	0.311129	+	1.76450i
$690$		0			0
$691$	6.74026	−	11.6745i	0.256412	−	0.444118i	−0.708866	−	0.705343i	$-0.750793\pi$
$691$	6.74026	−	11.6745i	0.256412	−	0.444118i	0.965278	+	0.261225i	$0.0841264\pi$
$692$		0			0
$693$	0.0845843	+	0.0709746i	0.00321309	+	0.00269610i
$694$		0			0
$695$	−0.658472	−	1.14051i	−0.0249773	−	0.0432619i
$696$		0			0
$697$	25.2069	−	9.17454i	0.954778	−	0.347511i
$698$		0			0
$699$	−3.74207	+	21.2223i	−0.141538	+	0.802703i
$700$		0			0
$701$	19.0387	−	15.9754i	0.719082	−	0.603381i	−0.208049	−	0.978118i	$-0.566711\pi$
$701$	19.0387	−	15.9754i	0.719082	−	0.603381i	0.927131	+	0.374737i	$0.122267\pi$
$702$		0			0
$703$	−35.0000	−	16.7777i	−1.32005	−	0.632782i
$704$		0			0
$705$	−8.80311	+	7.38668i	−0.331544	+	0.278199i
$706$		0			0
$707$	−0.431357	+	2.44635i	−0.0162229	+	0.0920044i
$708$		0			0
$709$	−1.71534	+	0.624331i	−0.0644208	+	0.0234473i	−0.374030	−	0.927417i	$-0.622024\pi$
$709$	−1.71534	+	0.624331i	−0.0644208	+	0.0234473i	0.309609	+	0.950864i	$0.399802\pi$
$710$		0			0
$711$	0.129381	+	0.224094i	0.00485216	+	0.00840419i
$712$		0			0
$713$	−15.4858	−	12.9942i	−0.579950	−	0.486635i
$714$		0			0
$715$	3.81900	−	6.61470i	0.142822	−	0.247376i
$716$		0			0
$717$	−2.84105	−	16.1124i	−0.106101	−	0.601728i
$718$		0			0
$719$	−30.6963	−	11.1725i	−1.14478	−	0.416665i	−0.301141	−	0.953580i	$-0.597367\pi$
$719$	−30.6963	−	11.1725i	−1.14478	−	0.416665i	−0.843636	+	0.536915i	$0.819590\pi$
$720$		0			0
$721$	−1.16694			−0.0434592
$722$		0			0
$723$	16.2647			0.604889
$724$		0			0
$725$	8.97645	+	3.26716i	0.333377	+	0.121339i
$726$		0			0
$727$	2.76543	+	15.6835i	0.102564	+	0.581670i	0.992165	+	0.124932i	$0.0398713\pi$
$727$	2.76543	+	15.6835i	0.102564	+	0.581670i	−0.889601	+	0.456738i	$0.849018\pi$
$728$		0			0
$729$	−14.2313	+	24.6492i	−0.527083	+	0.912935i
$730$		0			0
$731$	−16.0936	−	13.5041i	−0.595242	−	0.499467i
$732$		0			0
$733$	−6.14652	−	10.6461i	−0.227027	−	0.393222i	0.729899	−	0.683555i	$-0.239567\pi$
$733$	−6.14652	−	10.6461i	−0.227027	−	0.393222i	−0.956926	+	0.290333i	$0.906234\pi$
$734$		0			0
$735$	10.6982	−	3.89383i	0.394610	−	0.143626i
$736$		0			0
$737$	1.47229	−	8.34975i	0.0542324	−	0.307567i
$738$		0			0
$739$	20.4726	−	17.1786i	0.753098	−	0.631924i	−0.183222	−	0.983071i	$-0.558653\pi$
$739$	20.4726	−	17.1786i	0.753098	−	0.631924i	0.936320	+	0.351147i	$0.114208\pi$
$740$		0			0
$741$	39.2092	+	18.7954i	1.44039	+	0.690467i
$742$		0			0
$743$	−10.9203	+	9.16320i	−0.400626	+	0.336165i	−0.820736	−	0.571308i	$-0.806436\pi$
$743$	−10.9203	+	9.16320i	−0.400626	+	0.336165i	0.420109	+	0.907473i	$0.361992\pi$
$744$		0			0
$745$	2.93251	−	16.6311i	0.107439	−	0.609316i
$746$		0			0
$747$	0.0231355	−	0.00842064i	0.000846485	−	0.000308095i
$748$		0			0
$749$	1.67696	+	2.90458i	0.0612747	+	0.106131i
$750$		0			0
$751$	−8.50411	−	7.13580i	−0.310319	−	0.260389i	0.474305	−	0.880361i	$-0.342700\pi$
$751$	−8.50411	−	7.13580i	−0.310319	−	0.260389i	−0.784624	+	0.619972i	$0.787144\pi$
$752$		0			0
$753$	−12.0025	+	20.7889i	−0.437395	+	0.757590i
$754$		0			0
$755$	3.73507	+	21.1826i	0.135933	+	0.770915i
$756$		0			0
$757$	−2.08443	−	0.758670i	−0.0757599	−	0.0275743i	0.303862	−	0.952716i	$-0.401724\pi$
$757$	−2.08443	−	0.758670i	−0.0757599	−	0.0275743i	−0.379622	+	0.925142i	$0.623946\pi$
$758$		0			0
$759$	4.71406			0.171110
$760$		0			0
$761$	−49.1007			−1.77990			−0.889950	−	0.456058i	$-0.849261\pi$
$761$	−49.1007			−1.77990			−0.889950	+	0.456058i	$0.849261\pi$
$762$		0			0
$763$	−2.98900	−	1.08791i	−0.108209	−	0.0393849i
$764$		0			0
$765$	−0.180050	−	1.02111i	−0.00650971	−	0.0369184i
$766$		0			0
$767$	−15.9373	+	27.6043i	−0.575463	+	0.996732i
$768$		0			0
$769$	24.6995	+	20.7254i	0.890687	+	0.747376i	0.968348	−	0.249604i	$-0.0803006\pi$
$769$	24.6995	+	20.7254i	0.890687	+	0.747376i	−0.0776605	+	0.996980i	$0.524745\pi$
$770$		0			0
$771$	13.7468	+	23.8101i	0.495077	+	0.857499i
$772$		0			0
$773$	5.75551	−	2.09483i	0.207011	−	0.0753459i	−0.236433	−	0.971648i	$-0.575979\pi$
$773$	5.75551	−	2.09483i	0.207011	−	0.0753459i	0.443445	+	0.896302i	$0.353756\pi$
$774$		0			0
$775$	−1.60426	+	9.09822i	−0.0576268	+	0.326818i
$776$		0			0
$777$	−5.27777	+	4.42857i	−0.189339	+	0.158874i
$778$		0			0
$779$	−14.7022	−	15.0193i	−0.526760	−	0.538122i
$780$		0			0
$781$	6.78270	−	5.69136i	0.242704	−	0.203653i
$782$		0			0
$783$	8.86583	−	50.2806i	0.316839	−	1.79688i
$784$		0			0
$785$	0.503319	−	0.183193i	0.0179642	−	0.00653844i
$786$		0			0
$787$	−7.55427	−	13.0844i	−0.269281	−	0.466408i	0.699396	−	0.714735i	$-0.253453\pi$
$787$	−7.55427	−	13.0844i	−0.269281	−	0.466408i	−0.968676	+	0.248327i	$0.920119\pi$
$788$		0			0
$789$	−38.7588	−	32.5225i	−1.37985	−	1.15783i
$790$		0			0
$791$	2.27268	−	3.93640i	0.0808073	−	0.139962i
$792$		0			0
$793$	10.4696	+	59.3763i	0.371788	+	2.10851i
$794$		0			0
$795$	12.4654	+	4.53702i	0.442101	+	0.160912i
$796$		0			0
$797$	34.3148			1.21549			0.607747	−	0.794131i	$-0.292074\pi$
$797$	34.3148			1.21549			0.607747	+	0.794131i	$0.292074\pi$
$798$		0			0
$799$	−38.1135			−1.34836
$800$		0			0
$801$	−0.539479	−	0.196354i	−0.0190616	−	0.00693784i
$802$		0			0
$803$	2.91952	+	16.5574i	0.103028	+	0.584299i
$804$		0			0
$805$	0.504665	−	0.874106i	0.0177871	−	0.0308082i
$806$		0			0
$807$	13.7034	+	11.4985i	0.482381	+	0.404766i
$808$		0			0
$809$	−11.4159	−	19.7729i	−0.401361	−	0.695177i	0.592530	−	0.805548i	$-0.298129\pi$
$809$	−11.4159	−	19.7729i	−0.401361	−	0.695177i	−0.993890	+	0.110372i	$0.964796\pi$
$810$		0			0
$811$	−37.4959	+	13.6474i	−1.31666	+	0.479225i	−0.902387	−	0.430927i	$-0.858187\pi$
$811$	−37.4959	+	13.6474i	−1.31666	+	0.479225i	−0.414274	+	0.910152i	$0.635964\pi$
$812$		0			0
$813$	8.45109	−	47.9285i	0.296393	−	1.68093i
$814$		0			0
$815$	−3.60958	+	3.02879i	−0.126438	+	0.106094i
$816$		0			0
$817$	−4.42971	+	15.8534i	−0.154976	+	0.554639i
$818$		0			0
$819$	−0.391649	+	0.328632i	−0.0136853	+	0.0114833i
$820$		0			0
$821$	−3.25236	+	18.4451i	−0.113508	+	0.643737i	0.873970	+	0.485980i	$0.161537\pi$
$821$	−3.25236	+	18.4451i	−0.113508	+	0.643737i	−0.987478	+	0.157757i	$0.949574\pi$
$822$		0			0
$823$	−4.59210	+	1.67139i	−0.160070	+	0.0582609i	−0.420813	−	0.907148i	$-0.638255\pi$
$823$	−4.59210	+	1.67139i	−0.160070	+	0.0582609i	0.260742	+	0.965408i	$0.416033\pi$
$824$		0			0
$825$	−1.07718	−	1.86573i	−0.0375027	−	0.0649565i
$826$		0			0
$827$	−15.1382	−	12.7024i	−0.526406	−	0.441707i	0.340452	−	0.940262i	$-0.389420\pi$
$827$	−15.1382	−	12.7024i	−0.526406	−	0.441707i	−0.866858	+	0.498555i	$0.833864\pi$
$828$		0			0
$829$	4.57583	−	7.92558i	0.158925	−	0.275267i	−0.775556	−	0.631279i	$-0.782530\pi$
$829$	4.57583	−	7.92558i	0.158925	−	0.275267i	0.934481	+	0.356012i	$0.115864\pi$
$830$		0			0
$831$	−4.72772	−	26.8122i	−0.164003	−	0.930106i
$832$		0			0
$833$	35.4820	+	12.9144i	1.22938	+	0.447457i
$834$		0			0
$835$	−15.3884			−0.532538
$836$		0			0
$837$	49.3782			1.70676
$838$		0			0
$839$	−45.4522	−	16.5433i	−1.56919	−	0.571137i	−0.596368	−	0.802711i	$-0.703390\pi$
$839$	−45.4522	−	16.5433i	−1.56919	−	0.571137i	−0.972817	+	0.231574i	$0.925612\pi$
$840$		0			0
$841$	10.8098	+	61.3053i	0.372751	+	2.11398i
$842$		0			0
$843$	−1.63731	+	2.83591i	−0.0563921	+	0.0976740i
$844$		0			0
$845$	17.1334	+	14.3766i	0.589407	+	0.494571i
$846$		0			0
$847$	−2.15654	−	3.73524i	−0.0740998	−	0.128345i
$848$		0			0
$849$	−31.6679	+	11.5262i	−1.08684	+	0.395577i
$850$		0			0
$851$	3.38339	−	19.1882i	0.115981	−	0.657762i
$852$		0			0
$853$	−3.09983	+	2.60107i	−0.106136	+	0.0890589i	−0.694312	−	0.719675i	$-0.744291\pi$
$853$	−3.09983	+	2.60107i	−0.106136	+	0.0890589i	0.588175	+	0.808734i	$0.299847\pi$
$854$		0			0
$855$	−0.670412	+	0.458846i	−0.0229276	+	0.0156922i
$856$		0			0
$857$	15.6271	−	13.1127i	0.533810	−	0.447920i	−0.335605	−	0.942003i	$-0.608941\pi$
$857$	15.6271	−	13.1127i	0.533810	−	0.447920i	0.869415	+	0.494083i	$0.164496\pi$
$858$		0			0
$859$	−8.99981	+	51.0405i	−0.307070	+	1.74148i	0.306530	+	0.951861i	$0.400832\pi$
$859$	−8.99981	+	51.0405i	−0.307070	+	1.74148i	−0.613600	+	0.789617i	$0.710279\pi$
$860$		0			0
$861$	−3.50573	+	1.27598i	−0.119475	+	0.0434854i
$862$		0			0
$863$	−9.45039	−	16.3686i	−0.321695	−	0.557192i	0.659143	−	0.752018i	$-0.270919\pi$
$863$	−9.45039	−	16.3686i	−0.321695	−	0.557192i	−0.980838	+	0.194826i	$0.937586\pi$
$864$		0			0
$865$	−15.3406	−	12.8722i	−0.521594	−	0.437670i
$866$		0			0
$867$	−11.6997	+	20.2645i	−0.397343	+	0.688217i
$868$		0			0
$869$	0.309645	+	1.75608i	0.0105040	+	0.0595710i
$870$		0			0
$871$	36.8905	+	13.4271i	1.24999	+	0.454959i
$872$		0			0
$873$	−0.108952			−0.00368746
$874$		0			0
$875$	−0.461272			−0.0155938
$876$		0			0
$877$	11.7646	+	4.28197i	0.397263	+	0.144592i	0.532923	−	0.846164i	$-0.321093\pi$
$877$	11.7646	+	4.28197i	0.397263	+	0.144592i	−0.135661	+	0.990755i	$0.543316\pi$
$878$		0			0
$879$	−5.62349	−	31.8924i	−0.189676	−	1.07570i
$880$		0			0
$881$	−8.19948	+	14.2019i	−0.276248	+	0.478475i	−0.970449	−	0.241306i	$-0.922424\pi$
$881$	−8.19948	+	14.2019i	−0.276248	+	0.478475i	0.694202	+	0.719781i	$0.255758\pi$
$882$		0			0
$883$	−16.8404	−	14.1307i	−0.566723	−	0.475537i	0.313834	−	0.949478i	$-0.398387\pi$
$883$	−16.8404	−	14.1307i	−0.566723	−	0.475537i	−0.880557	+	0.473941i	$0.842831\pi$
$884$		0			0
$885$	4.49526	+	7.78602i	0.151107	+	0.261724i
$886$		0			0
$887$	10.6896	−	3.89071i	0.358923	−	0.130637i	−0.156264	−	0.987715i	$-0.549945\pi$
$887$	10.6896	−	3.89071i	0.358923	−	0.130637i	0.515186	+	0.857078i	$0.327723\pi$
$888$		0			0
$889$	1.54729	−	8.77514i	0.0518946	−	0.294309i
$890$		0			0
$891$	−8.27059	+	6.93985i	−0.277075	+	0.232494i
$892$		0			0
$893$	12.3310	+	27.1977i	0.412640	+	0.910137i
$894$		0			0
$895$	−9.91391	+	8.31875i	−0.331385	+	0.278065i
$896$		0			0
$897$	−3.79029	+	21.4958i	−0.126554	+	0.717724i
$898$		0			0
$899$	−82.9296	+	30.1839i	−2.76586	+	1.00669i
$900$		0			0
$901$	21.9981	+	38.1019i	0.732865	+	1.26936i
$902$		0			0
$903$	2.23827	+	1.87813i	0.0744850	+	0.0625003i
$904$		0			0
$905$	−3.53127	+	6.11633i	−0.117383	+	0.203314i
$906$		0			0
$907$	8.68002	+	49.2269i	0.288215	+	1.63455i	0.693568	+	0.720391i	$0.256037\pi$
$907$	8.68002	+	49.2269i	0.288215	+	1.63455i	−0.405353	+	0.914160i	$0.632851\pi$
$908$		0			0
$909$	0.943165	+	0.343284i	0.0312828	+	0.0113860i
$910$		0			0
$911$	13.9854			0.463358			0.231679	−	0.972792i	$-0.425578\pi$
$911$	13.9854			0.463358			0.231679	+	0.972792i	$0.425578\pi$
$912$		0			0
$913$	0.169663			0.00561503
$914$		0			0
$915$	15.9804	+	5.81638i	0.528295	+	0.192284i
$916$		0			0
$917$	0.790253	+	4.48175i	0.0260965	+	0.148000i
$918$		0			0
$919$	4.97698	−	8.62038i	0.164175	−	0.284360i	−0.772187	−	0.635396i	$-0.780837\pi$
$919$	4.97698	−	8.62038i	0.164175	−	0.284360i	0.936362	+	0.351036i	$0.114170\pi$
$920$		0			0
$921$	13.9743	+	11.7258i	0.460469	+	0.386380i
$922$		0			0
$923$	20.4987	+	35.5047i	0.674722	+	1.16865i
$924$		0			0
$925$	−8.36743	+	3.04550i	−0.275119	+	0.100135i
$926$		0			0
$927$	−0.0818757	+	0.464340i	−0.00268915	+	0.0152509i
$928$		0			0
$929$	5.81808	−	4.88195i	0.190885	−	0.160171i	−0.542337	−	0.840161i	$-0.682460\pi$
$929$	5.81808	−	4.88195i	0.190885	−	0.160171i	0.733222	+	0.679990i	$0.238016\pi$
$930$		0			0
$931$	−2.26390	−	29.4981i	−0.0741962	−	0.966761i
$932$		0			0
$933$	−22.1557	+	18.5908i	−0.725345	+	0.608636i
$934$		0			0
$935$	1.24075	−	7.03667i	0.0405770	−	0.230124i
$936$		0			0
$937$	−9.13741	+	3.32575i	−0.298506	+	0.108647i	−0.486932	−	0.873440i	$-0.661884\pi$
$937$	−9.13741	+	3.32575i	−0.298506	+	0.108647i	0.188425	+	0.982088i	$0.439662\pi$
$938$		0			0
$939$	−6.57133	−	11.3819i	−0.214447	−	0.371433i
$940$		0			0
$941$	−12.7510	−	10.6994i	−0.415671	−	0.348789i	0.410842	−	0.911706i	$-0.365235\pi$
$941$	−12.7510	−	10.6994i	−0.415671	−	0.348789i	−0.826513	+	0.562917i	$0.809679\pi$
$942$		0			0
$943$	5.27533	−	9.13713i	0.171788	−	0.297546i
$944$		0			0
$945$	0.428112	+	2.42794i	0.0139265	+	0.0789810i
$946$		0			0
$947$	49.2017	+	17.9080i	1.59884	+	0.581930i	0.979190	−	0.202947i	$-0.0650520\pi$
$947$	49.2017	+	17.9080i	1.59884	+	0.581930i	0.619651	+	0.784878i	$0.287274\pi$
$948$		0			0
$949$	−77.8482			−2.52706
$950$		0			0
$951$	17.2737			0.560139
$952$		0			0
$953$	40.7403	+	14.8283i	1.31971	+	0.480335i	0.903365	−	0.428873i	$-0.141089\pi$
$953$	40.7403	+	14.8283i	1.31971	+	0.480335i	0.416343	+	0.909207i	$0.363311\pi$
$954$		0			0
$955$	−4.01242	−	22.7556i	−0.129839	−	0.736353i
$956$		0			0
$957$	10.2898	−	17.8225i	0.332623	−	0.576120i
$958$		0			0
$959$	−3.76816	−	3.16186i	−0.121680	−	0.102102i
$960$		0			0
$961$	−27.1756	−	47.0695i	−0.876632	−	1.51837i
$962$		0			0
$963$	1.27343	−	0.463489i	0.0410356	−	0.0149357i
$964$		0			0
$965$	−1.31425	+	7.45347i	−0.0423071	+	0.239936i
$966$		0			0
$967$	13.4494	−	11.2854i	0.432503	−	0.362913i	−0.400392	−	0.916344i	$-0.631126\pi$
$967$	13.4494	−	11.2854i	0.432503	−	0.362913i	0.832895	+	0.553431i	$0.186682\pi$
$968$		0			0
$969$	40.4812	+	3.97729i	1.30044	+	0.127769i
$970$		0			0
$971$	42.6182	−	35.7609i	1.36768	−	1.14762i	0.394158	−	0.919043i	$-0.371036\pi$
$971$	42.6182	−	35.7609i	1.36768	−	1.14762i	0.973525	−	0.228580i	$-0.0734083\pi$
$972$		0			0
$973$	−0.105486	+	0.598241i	−0.00338173	+	0.0191787i
$974$		0			0
$975$	9.37372	−	3.41176i	0.300199	−	0.109264i
$976$		0			0
$977$	2.82064	+	4.88548i	0.0902401	+	0.156300i	0.907612	−	0.419810i	$-0.137903\pi$
$977$	2.82064	+	4.88548i	0.0902401	+	0.156300i	−0.817372	+	0.576110i	$0.804570\pi$
$978$		0			0
$979$	−3.03065	−	2.54302i	−0.0968601	−	0.0812753i
$980$		0			0
$981$	−0.642608	+	1.11303i	−0.0205169	+	0.0355363i
$982$		0			0
$983$	2.66371	+	15.1066i	0.0849592	+	0.481827i	0.997365	+	0.0725415i	$0.0231110\pi$
$983$	2.66371	+	15.1066i	0.0849592	+	0.481827i	−0.912406	+	0.409286i	$0.865778\pi$
$984$		0			0
$985$	1.96173	+	0.714011i	0.0625059	+	0.0227503i
$986$		0			0
$987$	5.30077			0.168725
$988$		0			0
$989$	−8.26313			−0.262752
$990$		0			0
$991$	−40.5654	−	14.7646i	−1.28860	−	0.469013i	−0.395334	−	0.918537i	$-0.629371\pi$
$991$	−40.5654	−	14.7646i	−1.28860	−	0.469013i	−0.893268	+	0.449524i	$0.851593\pi$
$992$		0			0
$993$	−9.75350	−	55.3148i	−0.309518	−	1.75536i
$994$		0			0
$995$	5.33749	−	9.24480i	0.169210	−	0.293080i
$996$		0			0
$997$	−7.44517	−	6.24724i	−0.235791	−	0.197852i	0.517234	−	0.855844i	$-0.326962\pi$
$997$	−7.44517	−	6.24724i	−0.235791	−	0.197852i	−0.753025	+	0.657992i	$0.771406\pi$
$998$		0			0
$999$	23.7961	+	41.2161i	0.752876	+	1.30402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.b.101.1	✓	18
19.4	even	9		7220.2.a.w.1.8		9
19.15	odd	18		7220.2.a.y.1.2		9
19.16	even	9	inner	380.2.u.b.301.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.b.101.1	✓	18	1.1	even	1	trivial
380.2.u.b.301.1	yes	18	19.16	even	9	inner
7220.2.a.w.1.8		9	19.4	even	9
7220.2.a.y.1.2		9	19.15	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)

\(f(q)\)	\(=\)	\(q+(-1.57623 - 0.573700i) q^{3} +(0.173648 + 0.984808i) q^{5} +(0.230636 - 0.399473i) q^{7} +(-0.142773 - 0.119801i) q^{9} +O(q^{10})\)	\(q+(-1.57623 - 0.573700i) q^{3} +(0.173648 + 0.984808i) q^{5} +(0.230636 - 0.399473i) q^{7} +(-0.142773 - 0.119801i) q^{9} +(-0.642179 - 1.11229i) q^{11} +(5.58829 - 2.03397i) q^{13} +(0.291275 - 1.65190i) q^{15} +(4.26171 - 3.57600i) q^{17} +(-3.93062 - 1.88419i) q^{19} +(-0.592712 + 0.497345i) q^{21} +(0.379967 - 2.15490i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(2.67239 + 4.62872i) q^{27} +(-7.31767 - 6.14026i) q^{29} +(4.61929 - 8.00084i) q^{31} +(0.374101 + 2.12163i) q^{33} +(0.433454 + 0.157764i) q^{35} +8.90443 q^{37} -9.97531 q^{39} +(4.53095 + 1.64913i) q^{41} +(-0.655751 - 3.71895i) q^{43} +(0.0931885 - 0.161407i) q^{45} +(-5.24811 - 4.40369i) q^{47} +(3.39361 + 5.87791i) q^{49} +(-8.76897 + 3.19164i) q^{51} +(-1.37327 + 7.78821i) q^{53} +(0.983875 - 0.825569i) q^{55} +(5.11460 + 5.22492i) q^{57} +(-4.10588 + 3.44524i) q^{59} +(-1.76051 + 9.98434i) q^{61} +(-0.0807859 + 0.0294036i) q^{63} +(2.97347 + 5.15020i) q^{65} +(5.05696 + 4.24330i) q^{67} +(-1.83518 + 3.17863i) q^{69} +(1.19711 + 6.78912i) q^{71} +(-12.3010 - 4.47721i) q^{73} +1.67739 q^{75} -0.592438 q^{77} +(-1.30465 - 0.474853i) q^{79} +(-1.45971 - 8.27842i) q^{81} +(-0.0660497 + 0.114402i) q^{83} +(4.26171 + 3.57600i) q^{85} +(8.01165 + 13.8766i) q^{87} +(2.89456 - 1.05353i) q^{89} +(0.476344 - 2.70148i) q^{91} +(-11.8711 + 9.96105i) q^{93} +(1.17302 - 4.19810i) q^{95} +(0.447812 - 0.375759i) q^{97} +(-0.0415670 + 0.235738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 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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