LMFDB - Embedded newform 380.2.u.a.61.2

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} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 $ x^18 - 3x^17 + 3x^15 + 36x^14 + 72x^13 - 134x^12 - 741x^11 + 486x^10 + 5700x^9 + 11637x^8 + 13878x^7 + 13978x^6 + 10005x^5 + 5949x^4 + 2649x^3 + 819x^2 + 135x + 9
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			61.2
Root			$-0.344606 - 0.289159i$ of defining polynomial
Character	$\chi$	$=$	380.61
Dual form			380.2.u.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0781159 - 0.443017i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-1.06981 + 1.85297i) q^{7} +(2.62892 - 0.956847i) q^{9} +O(q^{10})$	\(q+(-0.0781159 - 0.443017i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-1.06981 + 1.85297i) q^{7} +(2.62892 - 0.956847i) q^{9} +(2.25634 + 3.90810i) q^{11} +(-0.155380 + 0.881206i) q^{13} +(0.344606 + 0.289159i) q^{15} +(-0.00854515 - 0.00311018i) q^{17} +(4.31164 + 0.640134i) q^{19} +(0.904468 + 0.329199i) q^{21} +(4.94633 + 4.15046i) q^{23} +(0.173648 - 0.984808i) q^{25} +(-1.30404 - 2.25866i) q^{27} +(-0.381463 + 0.138841i) q^{29} +(-0.920071 + 1.59361i) q^{31} +(1.55510 - 1.30488i) q^{33} +(-0.371542 - 2.10712i) q^{35} -6.75663 q^{37} +0.402527 q^{39} +(-1.24280 - 7.04829i) q^{41} +(1.04904 - 0.880252i) q^{43} +(-1.39882 + 2.42282i) q^{45} +(1.13486 - 0.413057i) q^{47} +(1.21100 + 2.09751i) q^{49} +(-0.000710351 + 0.00402860i) q^{51} +(1.90313 + 1.59691i) q^{53} +(-4.24054 - 1.54343i) q^{55} +(-0.0532169 - 1.96013i) q^{57} +(8.35638 + 3.04147i) q^{59} +(-4.44422 - 3.72914i) q^{61} +(-1.03944 + 5.89495i) q^{63} +(-0.447400 - 0.774919i) q^{65} +(-14.6860 + 5.34527i) q^{67} +(1.45234 - 2.51552i) q^{69} +(-5.71938 + 4.79913i) q^{71} +(-1.93685 - 10.9844i) q^{73} -0.449851 q^{75} -9.65546 q^{77} +(-1.27942 - 7.25594i) q^{79} +(5.53058 - 4.64071i) q^{81} +(-0.0758467 + 0.131370i) q^{83} +(0.00854515 - 0.00311018i) q^{85} +(0.0913074 + 0.158149i) q^{87} +(1.98885 - 11.2793i) q^{89} +(-1.46662 - 1.23064i) q^{91} +(0.777868 + 0.283121i) q^{93} +(-3.71438 + 2.28110i) q^{95} +(-7.85592 - 2.85932i) q^{97} +(9.67119 + 8.11509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 9 * q^9	$ 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^9 + 9 * q^13 - 3 * q^15 + 12 * q^17 + 18 * q^19 + 15 * q^21 - 9 * q^23 - 33 * q^29 - 18 * q^31 + 9 * q^33 + 12 * q^35 + 60 * q^37 - 84 * q^39 - 18 * q^41 + 18 * q^43 + 6 * q^45 - 15 * q^47 - 15 * q^49 - 9 * q^51 + 24 * q^53 + 3 * q^55 + 66 * q^57 + 48 * q^59 - 18 * q^61 - 54 * q^63 + 3 * q^65 - 36 * q^67 - 9 * q^69 + 18 * q^73 - 6 * q^75 + 9 * q^79 - 9 * q^81 - 30 * q^83 - 12 * q^85 - 9 * q^87 + 6 * q^89 + 30 * q^91 + 21 * q^95 + 21 * q^97 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.0781159	−	0.443017i	−0.0451002	−	0.255776i	0.953919	−	0.300066i	$-0.0970086\pi$
$3$	−0.0781159	−	0.443017i	−0.0451002	−	0.255776i	−0.999019	+	0.0442897i	$0.985898\pi$
$4$		0			0
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$		0			0
$7$	−1.06981	+	1.85297i	−0.404352	+	0.700357i	−0.994246	−	0.107123i	$-0.965836\pi$
$7$	−1.06981	+	1.85297i	−0.404352	+	0.700357i	0.589894	+	0.807481i	$0.299169\pi$
$8$		0			0
$9$	2.62892	−	0.956847i	0.876305	−	0.318949i
$10$		0			0
$11$	2.25634	+	3.90810i	0.680313	+	1.17834i	0.974885	+	0.222707i	$0.0714894\pi$
$11$	2.25634	+	3.90810i	0.680313	+	1.17834i	−0.294573	+	0.955629i	$0.595177\pi$
$12$		0			0
$13$	−0.155380	+	0.881206i	−0.0430947	+	0.244402i	−0.998744	−	0.0501049i	$-0.984044\pi$
$13$	−0.155380	+	0.881206i	−0.0430947	+	0.244402i	0.955649	+	0.294507i	$0.0951555\pi$
$14$		0			0
$15$	0.344606	+	0.289159i	0.0889769	+	0.0746605i
$16$		0			0
$17$	−0.00854515	−	0.00311018i	−0.00207250	−	0.000754330i	0.340984	−	0.940069i	$-0.389240\pi$
$17$	−0.00854515	−	0.00311018i	−0.00207250	−	0.000754330i	−0.343056	+	0.939315i	$0.611462\pi$
$18$		0			0
$19$	4.31164	+	0.640134i	0.989158	+	0.146857i
$19$	4.31164	+	0.640134i	0.989158	+	0.146857i
$20$		0			0
$21$	0.904468	+	0.329199i	0.197371	+	0.0718372i
$22$		0			0
$23$	4.94633	+	4.15046i	1.03138	+	0.865431i	0.991015	−	0.133754i	$-0.0427032\pi$
$23$	4.94633	+	4.15046i	1.03138	+	0.865431i	0.0403658	+	0.999185i	$0.487148\pi$
$24$		0			0
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$		0			0
$27$	−1.30404	−	2.25866i	−0.250962	−	0.434679i
$28$		0			0
$29$	−0.381463	+	0.138841i	−0.0708359	+	0.0257822i	−0.377195	−	0.926134i	$-0.623111\pi$
$29$	−0.381463	+	0.138841i	−0.0708359	+	0.0257822i	0.306359	+	0.951916i	$0.400889\pi$
$30$		0			0
$31$	−0.920071	+	1.59361i	−0.165250	+	0.286221i	−0.936744	−	0.350016i	$-0.886176\pi$
$31$	−0.920071	+	1.59361i	−0.165250	+	0.286221i	0.771494	+	0.636236i	$0.219510\pi$
$32$		0			0
$33$	1.55510	−	1.30488i	0.270708	−	0.227151i
$34$		0			0
$35$	−0.371542	−	2.10712i	−0.0628021	−	0.356169i
$36$		0			0
$37$	−6.75663			−1.11078			−0.555392	−	0.831589i	$-0.687432\pi$
$37$	−6.75663			−1.11078			−0.555392	+	0.831589i	$0.687432\pi$
$38$		0			0
$39$	0.402527			0.0644559
$40$		0			0
$41$	−1.24280	−	7.04829i	−0.194093	−	1.10076i	−0.913704	−	0.406380i	$-0.866791\pi$
$41$	−1.24280	−	7.04829i	−0.194093	−	1.10076i	0.719611	−	0.694378i	$-0.244320\pi$
$42$		0			0
$43$	1.04904	−	0.880252i	0.159978	−	0.134237i	−0.559285	−	0.828975i	$-0.688924\pi$
$43$	1.04904	−	0.880252i	0.159978	−	0.134237i	0.719263	+	0.694738i	$0.244480\pi$
$44$		0			0
$45$	−1.39882	+	2.42282i	−0.208523	+	0.361173i
$46$		0			0
$47$	1.13486	−	0.413057i	0.165537	−	0.0602505i	−0.257922	−	0.966166i	$-0.583038\pi$
$47$	1.13486	−	0.413057i	0.165537	−	0.0602505i	0.423459	+	0.905915i	$0.360816\pi$
$48$		0			0
$49$	1.21100	+	2.09751i	0.173000	+	0.299644i
$50$		0			0
$51$	−0.000710351		0.00402860i	−9.94691e−5		0.000564117i
$52$		0			0
$53$	1.90313	+	1.59691i	0.261415	+	0.219353i	0.764069	−	0.645135i	$-0.223199\pi$
$53$	1.90313	+	1.59691i	0.261415	+	0.219353i	−0.502654	+	0.864487i	$0.667643\pi$
$54$		0			0
$55$	−4.24054	−	1.54343i	−0.571794	−	0.208116i
$56$		0			0
$57$	−0.0532169	−	1.96013i	−0.00704875	−	0.259626i
$58$		0			0
$59$	8.35638	+	3.04147i	1.08791	+	0.395966i	0.822845	−	0.568265i	$-0.192385\pi$
$59$	8.35638	+	3.04147i	1.08791	+	0.395966i	0.265062	+	0.964231i	$0.414607\pi$
$60$		0			0
$61$	−4.44422	−	3.72914i	−0.569024	−	0.477468i	0.312298	−	0.949984i	$-0.398901\pi$
$61$	−4.44422	−	3.72914i	−0.569024	−	0.477468i	−0.881322	+	0.472517i	$0.843346\pi$
$62$		0			0
$63$	−1.03944	+	5.89495i	−0.130957	+	0.742694i
$64$		0			0
$65$	−0.447400	−	0.774919i	−0.0554931	−	0.0961169i
$66$		0			0
$67$	−14.6860	+	5.34527i	−1.79418	+	0.653029i	−0.795276	+	0.606247i	$0.792674\pi$
$67$	−14.6860	+	5.34527i	−1.79418	+	0.653029i	−0.998905	+	0.0467817i	$0.985103\pi$
$68$		0			0
$69$	1.45234	−	2.51552i	0.174841	−	0.302834i
$70$		0			0
$71$	−5.71938	+	4.79913i	−0.678766	+	0.569552i	−0.915646	−	0.401987i	$-0.868320\pi$
$71$	−5.71938	+	4.79913i	−0.678766	+	0.569552i	0.236879	+	0.971539i	$0.423875\pi$
$72$		0			0
$73$	−1.93685	−	10.9844i	−0.226691	−	1.28563i	−0.859426	−	0.511260i	$-0.829179\pi$
$73$	−1.93685	−	10.9844i	−0.226691	−	1.28563i	0.632735	−	0.774369i	$-0.281932\pi$
$74$		0			0
$75$	−0.449851			−0.0519444
$76$		0			0
$77$	−9.65546			−1.10034
$78$		0			0
$79$	−1.27942	−	7.25594i	−0.143946	−	0.816357i	−0.968208	−	0.250148i	$-0.919521\pi$
$79$	−1.27942	−	7.25594i	−0.143946	−	0.816357i	0.824262	−	0.566209i	$-0.191590\pi$
$80$		0			0
$81$	5.53058	−	4.64071i	0.614509	−	0.515634i
$82$		0			0
$83$	−0.0758467	+	0.131370i	−0.00832526	+	0.0144198i	−0.870158	−	0.492773i	$-0.835983\pi$
$83$	−0.0758467	+	0.131370i	−0.00832526	+	0.0144198i	0.861833	+	0.507193i	$0.169317\pi$
$84$		0			0
$85$	0.00854515	−	0.00311018i	0.000926852	−	0.000337346i
$86$		0			0
$87$	0.0913074	+	0.158149i	0.00978918	+	0.0169554i
$88$		0			0
$89$	1.98885	−	11.2793i	0.210817	−	1.19560i	−0.677202	−	0.735797i	$-0.736808\pi$
$89$	1.98885	−	11.2793i	0.210817	−	1.19560i	0.888019	−	0.459807i	$-0.152081\pi$
$90$		0			0
$91$	−1.46662	−	1.23064i	−0.153744	−	0.129006i
$92$		0			0
$93$	0.777868	+	0.283121i	0.0806612	+	0.0293583i
$94$		0			0
$95$	−3.71438	+	2.28110i	−0.381087	+	0.234036i
$96$		0			0
$97$	−7.85592	−	2.85932i	−0.797648	−	0.290320i	−0.0891365	−	0.996019i	$-0.528411\pi$
$97$	−7.85592	−	2.85932i	−0.797648	−	0.290320i	−0.708511	+	0.705699i	$0.750633\pi$
$98$		0			0
$99$	9.67119	+	8.11509i	0.971991	+	0.815597i
$100$		0			0
$101$	1.53748	−	8.71948i	0.152985	−	0.867621i	−0.807620	−	0.589703i	$-0.799245\pi$
$101$	1.53748	−	8.71948i	0.152985	−	0.867621i	0.960605	−	0.277918i	$-0.0896442\pi$
$102$		0			0
$103$	−8.48725	−	14.7003i	−0.836273	−	1.44847i	−0.892989	−	0.450078i	$-0.851396\pi$
$103$	−8.48725	−	14.7003i	−0.836273	−	1.44847i	0.0567161	−	0.998390i	$-0.481937\pi$
$104$		0			0
$105$	−0.904468	+	0.329199i	−0.0882670	+	0.0321266i
$106$		0			0
$107$	−3.73769	+	6.47387i	−0.361336	+	0.625853i	−0.988181	−	0.153291i	$-0.951013\pi$
$107$	−3.73769	+	6.47387i	−0.361336	+	0.625853i	0.626845	+	0.779144i	$0.284346\pi$
$108$		0			0
$109$	−0.821088	+	0.688975i	−0.0786460	+	0.0659918i	−0.681263	−	0.732039i	$-0.738569\pi$
$109$	−0.821088	+	0.688975i	−0.0786460	+	0.0659918i	0.602617	+	0.798030i	$0.294125\pi$
$110$		0			0
$111$	0.527800	+	2.99330i	0.0500966	+	0.284112i
$112$		0			0
$113$	18.3614			1.72729			0.863647	−	0.504097i	$-0.168175\pi$
$113$	18.3614			1.72729			0.863647	+	0.504097i	$0.168175\pi$
$114$		0			0
$115$	−6.45697			−0.602116
$116$		0			0
$117$	0.434697	+	2.46529i	0.0401878	+	0.227916i
$118$		0			0
$119$	0.0149048	−	0.0125066i	0.00136632	−	0.00114648i
$120$		0			0
$121$	−4.68216	+	8.10974i	−0.425651	+	0.737249i
$122$		0			0
$123$	−3.02543	+	1.10117i	−0.272794	+	0.0992889i
$124$		0			0
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$		0			0
$127$	1.45854	−	8.27177i	0.129424	−	0.734001i	−0.849157	−	0.528140i	$-0.822889\pi$
$127$	1.45854	−	8.27177i	0.129424	−	0.734001i	0.978581	−	0.205861i	$-0.0659994\pi$
$128$		0			0
$129$	−0.471913	−	0.395982i	−0.0415497	−	0.0348643i
$130$		0			0
$131$	17.0821	+	6.21737i	1.49247	+	0.543214i	0.954098	−	0.299495i	$-0.0968181\pi$
$131$	17.0821	+	6.21737i	1.49247	+	0.543214i	0.538370	+	0.842709i	$0.319040\pi$
$132$		0			0
$133$	−5.79880	+	7.30452i	−0.502820	+	0.633382i
$134$		0			0
$135$	2.45079	+	0.892014i	0.210930	+	0.0767723i
$136$		0			0
$137$	−12.1065	−	10.1585i	−1.03432	−	0.867901i	−0.0429651	−	0.999077i	$-0.513680\pi$
$137$	−12.1065	−	10.1585i	−1.03432	−	0.867901i	−0.991359	+	0.131175i	$0.958125\pi$
$138$		0			0
$139$	−1.06326	+	6.03005i	−0.0901845	+	0.511462i	0.905932	+	0.423422i	$0.139171\pi$
$139$	−1.06326	+	6.03005i	−0.0901845	+	0.511462i	−0.996117	+	0.0880396i	$0.971940\pi$
$140$		0			0
$141$	−0.271642	−	0.470498i	−0.0228764	−	0.0396231i
$142$		0			0
$143$	−3.79443	+	1.38106i	−0.317306	+	0.115490i
$144$		0			0
$145$	0.202972	−	0.351558i	0.0168559	−	0.0291953i
$146$		0			0
$147$	0.834634	−	0.700341i	0.0688395	−	0.0577632i
$148$		0			0
$149$	1.54257	+	8.74835i	0.126372	+	0.716693i	0.980483	+	0.196602i	$0.0629908\pi$
$149$	1.54257	+	8.74835i	0.126372	+	0.716693i	−0.854111	+	0.520091i	$0.825898\pi$
$150$		0			0
$151$	14.4216			1.17362			0.586808	−	0.809726i	$-0.300384\pi$
$151$	14.4216			1.17362			0.586808	+	0.809726i	$0.300384\pi$
$152$		0			0
$153$	−0.0254405			−0.00205674
$154$		0			0
$155$	−0.319537	−	1.81219i	−0.0256658	−	0.145558i
$156$		0			0
$157$	9.18908	−	7.71055i	0.733368	−	0.615369i	−0.197679	−	0.980267i	$-0.563340\pi$
$157$	9.18908	−	7.71055i	0.733368	−	0.615369i	0.931048	+	0.364898i	$0.118896\pi$
$158$		0			0
$159$	0.558796	−	0.967862i	0.0443154	−	0.0767565i
$160$		0			0
$161$	−12.9823	+	4.72518i	−1.02315	+	0.372397i
$162$		0			0
$163$	−3.03640	−	5.25920i	−0.237829	−	0.411932i	0.722262	−	0.691620i	$-0.243102\pi$
$163$	−3.03640	−	5.25920i	−0.237829	−	0.411932i	−0.960091	+	0.279687i	$0.909769\pi$
$164$		0			0
$165$	−0.352512	+	1.99920i	−0.0274430	+	0.155637i
$166$		0			0
$167$	6.34194	+	5.32152i	0.490754	+	0.411792i	0.854296	−	0.519786i	$-0.173988\pi$
$167$	6.34194	+	5.32152i	0.490754	+	0.411792i	−0.363542	+	0.931578i	$0.618433\pi$
$168$		0			0
$169$	11.4636	+	4.17242i	0.881817	+	0.320955i
$170$		0			0
$171$	11.9474	−	2.44272i	0.913644	−	0.186799i
$172$		0			0
$173$	19.7600	+	7.19207i	1.50233	+	0.546803i	0.956662	−	0.291200i	$-0.0940545\pi$
$173$	19.7600	+	7.19207i	1.50233	+	0.546803i	0.545666	+	0.838003i	$0.316277\pi$
$174$		0			0
$175$	1.63905	+	1.37533i	0.123901	+	0.103965i
$176$		0			0
$177$	0.694659	−	3.93961i	0.0522138	−	0.296119i
$178$		0			0
$179$	−5.30897	−	9.19540i	−0.396811	−	0.687296i	0.596520	−	0.802598i	$-0.296550\pi$
$179$	−5.30897	−	9.19540i	−0.396811	−	0.687296i	−0.993330	+	0.115302i	$0.963216\pi$
$180$		0			0
$181$	−11.7436	+	4.27432i	−0.872895	+	0.317708i	−0.739339	−	0.673333i	$-0.764862\pi$
$181$	−11.7436	+	4.27432i	−0.872895	+	0.317708i	−0.133556	+	0.991041i	$0.542640\pi$
$182$		0			0
$183$	−1.30491	+	2.26017i	−0.0964617	+	0.167077i
$184$		0			0
$185$	5.17588	−	4.34308i	0.380538	−	0.319310i
$186$		0			0
$187$	−0.00712589	−	0.0404129i	−0.000521097	−	0.00295529i
$188$		0			0
$189$	5.58031			0.405908
$190$		0			0
$191$	−5.16539			−0.373755			−0.186877	−	0.982383i	$-0.559837\pi$
$191$	−5.16539			−0.373755			−0.186877	+	0.982383i	$0.559837\pi$
$192$		0			0
$193$	3.30453	+	18.7409i	0.237866	+	1.34900i	0.836494	+	0.547976i	$0.184601\pi$
$193$	3.30453	+	18.7409i	0.237866	+	1.34900i	−0.598629	+	0.801027i	$0.704287\pi$
$194$		0			0
$195$	−0.308353	+	0.258739i	−0.0220817	+	0.0185287i
$196$		0			0
$197$	−11.2779	+	19.5339i	−0.803516	+	1.39173i	0.113773	+	0.993507i	$0.463706\pi$
$197$	−11.2779	+	19.5339i	−0.803516	+	1.39173i	−0.917288	+	0.398223i	$0.869627\pi$
$198$		0			0
$199$	−3.01263	+	1.09651i	−0.213559	+	0.0777293i	−0.446585	−	0.894741i	$-0.647360\pi$
$199$	−3.01263	+	1.09651i	−0.213559	+	0.0777293i	0.233025	+	0.972471i	$0.425138\pi$
$200$		0			0
$201$	3.51526	+	6.08860i	0.247947	+	0.429457i
$202$		0			0
$203$	0.150826	−	0.855375i	0.0105859	−	0.0600355i
$204$		0			0
$205$	5.48260	+	4.60044i	0.382921	+	0.321309i
$206$		0			0
$207$	16.9748	+	6.17833i	1.17983	+	0.429424i
$208$		0			0
$209$	7.22682	+	18.2947i	0.499890	+	1.26547i
$210$		0			0
$211$	−12.1660	−	4.42808i	−0.837545	−	0.304841i	−0.112593	−	0.993641i	$-0.535916\pi$
$211$	−12.1660	−	4.42808i	−0.837545	−	0.304841i	−0.724952	+	0.688800i	$0.758138\pi$
$212$		0			0
$213$	2.57287	+	2.15890i	0.176290	+	0.147925i
$214$		0			0
$215$	−0.237799	+	1.34862i	−0.0162177	+	0.0919754i
$216$		0			0
$217$	−1.96861	−	3.40973i	−0.133638	−	0.231468i
$218$		0			0
$219$	−4.71499	+	1.71611i	−0.318609	+	0.115964i
$220$		0			0
$221$	0.00406846	−	0.00704677i	0.000273674	−	0.000474017i
$222$		0			0
$223$	6.59373	−	5.53280i	0.441549	−	0.370504i	−0.394740	−	0.918793i	$-0.629165\pi$
$223$	6.59373	−	5.53280i	0.441549	−	0.370504i	0.836289	+	0.548289i	$0.184721\pi$
$224$		0			0
$225$	−0.485804	−	2.75513i	−0.0323869	−	0.183675i
$226$		0			0
$227$	7.99196			0.530445			0.265223	−	0.964187i	$-0.414555\pi$
$227$	7.99196			0.530445			0.265223	+	0.964187i	$0.414555\pi$
$228$		0			0
$229$	−11.9777			−0.791510			−0.395755	−	0.918356i	$-0.629517\pi$
$229$	−11.9777			−0.791510			−0.395755	+	0.918356i	$0.629517\pi$
$230$		0			0
$231$	0.754245	+	4.27754i	0.0496257	+	0.281441i
$232$		0			0
$233$	18.4257	−	15.4610i	1.20711	−	1.01288i	0.207709	−	0.978191i	$-0.433399\pi$
$233$	18.4257	−	15.4610i	1.20711	−	1.01288i	0.999398	−	0.0346928i	$-0.0110453\pi$
$234$		0			0
$235$	−0.603849	+	1.04590i	−0.0393907	+	0.0682268i
$236$		0			0
$237$	−3.11456	+	1.13361i	−0.202313	+	0.0736357i
$238$		0			0
$239$	4.44437	+	7.69788i	0.287483	+	0.497935i	0.973208	−	0.229926i	$-0.0738483\pi$
$239$	4.44437	+	7.69788i	0.287483	+	0.497935i	−0.685726	+	0.727860i	$0.740515\pi$
$240$		0			0
$241$	4.14103	−	23.4850i	0.266747	−	1.51280i	−0.497266	−	0.867598i	$-0.665663\pi$
$241$	4.14103	−	23.4850i	0.266747	−	1.51280i	0.764013	−	0.645201i	$-0.223226\pi$
$242$		0			0
$243$	−8.48164	−	7.11694i	−0.544097	−	0.456552i
$244$		0			0
$245$	−2.27593	−	0.828371i	−0.145404	−	0.0529227i
$246$		0			0
$247$	−1.23403	+	3.69998i	−0.0785197	+	0.235424i
$248$		0			0
$249$	0.0641241	+	0.0233393i	0.00406370	+	0.00147907i
$250$		0			0
$251$	2.90062	+	2.43391i	0.183086	+	0.153627i	0.729724	−	0.683741i	$-0.239648\pi$
$251$	2.90062	+	2.43391i	0.183086	+	0.153627i	−0.546639	+	0.837369i	$0.684093\pi$
$252$		0			0
$253$	−5.05981	+	28.6956i	−0.318107	+	1.80408i
$254$		0			0
$255$	−0.00204538	−	0.00354269i	−0.000128086	−	0.000221852i
$256$		0			0
$257$	6.30524	−	2.29492i	0.393310	−	0.143153i	−0.137792	−	0.990461i	$-0.544000\pi$
$257$	6.30524	−	2.29492i	0.393310	−	0.143153i	0.531102	+	0.847308i	$0.321778\pi$
$258$		0			0
$259$	7.22834	−	12.5198i	0.449147	−	0.777946i
$260$		0			0
$261$	−0.869985	+	0.730004i	−0.0538507	+	0.0451861i
$262$		0			0
$263$	−3.90776	−	22.1620i	−0.240963	−	1.36657i	−0.829684	−	0.558233i	$-0.811479\pi$
$263$	−3.90776	−	22.1620i	−0.240963	−	1.36657i	0.588721	−	0.808336i	$-0.299632\pi$
$264$		0			0
$265$	−2.48436			−0.152613
$266$		0			0
$267$	−5.15229			−0.315315
$268$		0			0
$269$	−4.97959	−	28.2406i	−0.303611	−	1.72186i	−0.629973	−	0.776617i	$-0.716934\pi$
$269$	−4.97959	−	28.2406i	−0.303611	−	1.72186i	0.326362	−	0.945245i	$-0.394177\pi$
$270$		0			0
$271$	9.15115	−	7.67872i	0.555892	−	0.466449i	−0.321038	−	0.947066i	$-0.604032\pi$
$271$	9.15115	−	7.67872i	0.555892	−	0.466449i	0.876931	+	0.480617i	$0.159587\pi$
$272$		0			0
$273$	−0.430629	+	0.745871i	−0.0260628	+	0.0451422i
$274$		0			0
$275$	4.24054	−	1.54343i	0.255714	−	0.0930723i
$276$		0			0
$277$	13.6617	+	23.6628i	0.820852	+	1.42176i	0.905049	+	0.425308i	$0.139834\pi$
$277$	13.6617	+	23.6628i	0.820852	+	1.42176i	−0.0841968	+	0.996449i	$0.526832\pi$
$278$		0			0
$279$	−0.893948	+	5.06983i	−0.0535193	+	0.303523i
$280$		0			0
$281$	−2.31699	−	1.94419i	−0.138220	−	0.115980i	0.571056	−	0.820911i	$-0.306534\pi$
$281$	−2.31699	−	1.94419i	−0.138220	−	0.115980i	−0.709276	+	0.704930i	$0.750978\pi$
$282$		0			0
$283$	−13.3558	−	4.86113i	−0.793923	−	0.288964i	−0.0869569	−	0.996212i	$-0.527714\pi$
$283$	−13.3558	−	4.86113i	−0.793923	−	0.288964i	−0.706966	+	0.707248i	$0.749936\pi$
$284$		0			0
$285$	1.30072	+	1.46734i	0.0770478	+	0.0869179i
$286$		0			0
$287$	14.3898	+	5.23748i	0.849406	+	0.309158i
$288$		0			0
$289$	−13.0227	−	10.9273i	−0.766041	−	0.642784i
$290$		0			0
$291$	−0.653056	+	3.70367i	−0.0382828	+	0.217113i
$292$		0			0
$293$	−0.0582602	−	0.100910i	−0.00340360	−	0.00589520i	0.864319	−	0.502945i	$-0.167750\pi$
$293$	−0.0582602	−	0.100910i	−0.00340360	−	0.00589520i	−0.867722	+	0.497050i	$0.834417\pi$
$294$		0			0
$295$	−8.35638	+	3.04147i	−0.486527	+	0.177081i
$296$		0			0
$297$	5.88471	−	10.1926i	0.341465	−	0.591435i
$298$		0			0
$299$	−4.42597	+	3.71383i	−0.255961	+	0.214776i
$300$		0			0
$301$	0.508801	+	2.88555i	0.0293268	+	0.166320i
$302$		0			0
$303$	−3.98298			−0.228816
$304$		0			0
$305$	5.80151			0.332194
$306$		0			0
$307$	−0.0503112	−	0.285329i	−0.00287141	−	0.0162846i	0.983338	−	0.181785i	$-0.0581873\pi$
$307$	−0.0503112	−	0.285329i	−0.00287141	−	0.0162846i	−0.986210	+	0.165500i	$0.947076\pi$
$308$		0			0
$309$	−5.84952	+	4.90833i	−0.332767	+	0.279225i
$310$		0			0
$311$	−10.4600	+	18.1173i	−0.593133	+	1.02734i	0.400674	+	0.916221i	$0.368776\pi$
$311$	−10.4600	+	18.1173i	−0.593133	+	1.02734i	−0.993807	+	0.111116i	$0.964557\pi$
$312$		0			0
$313$	−31.0335	+	11.2953i	−1.75412	+	0.638446i	−0.999836	−	0.0181073i	$-0.994236\pi$
$313$	−31.0335	+	11.2953i	−1.75412	+	0.638446i	−0.754280	+	0.656553i	$0.772014\pi$
$314$		0			0
$315$	−2.99295	−	5.18394i	−0.168633	−	0.292082i
$316$		0			0
$317$	0.452529	−	2.56642i	0.0254165	−	0.144144i	−0.969459	−	0.245255i	$-0.921128\pi$
$317$	0.452529	−	2.56642i	0.0254165	−	0.144144i	0.994875	+	0.101110i	$0.0322395\pi$
$318$		0			0
$319$	−1.40332	−	1.17752i	−0.0785706	−	0.0659286i
$320$		0			0
$321$	3.16001	+	1.15015i	0.176375	+	0.0641951i
$322$		0			0
$323$	−0.0348527	−	0.0188800i	−0.00193925	−	0.00105051i
$324$		0			0
$325$	0.840837	+	0.306040i	0.0466412	+	0.0169760i
$326$		0			0
$327$	0.369368	+	0.309936i	0.0204261	+	0.0171395i
$328$		0			0
$329$	−0.448711	+	2.54477i	−0.0247382	+	0.140297i
$330$		0			0
$331$	−9.50939	−	16.4708i	−0.522684	−	0.905314i	−0.999652	−	0.0263938i	$-0.991598\pi$
$331$	−9.50939	−	16.4708i	−0.522684	−	0.905314i	0.476968	−	0.878921i	$-0.341736\pi$
$332$		0			0
$333$	−17.7626	+	6.46506i	−0.973385	+	0.354283i
$334$		0			0
$335$	7.81426	−	13.5347i	0.426939	−	0.739480i
$336$		0			0
$337$	16.5519	−	13.8887i	0.901642	−	0.756568i	−0.0688686	−	0.997626i	$-0.521939\pi$
$337$	16.5519	−	13.8887i	0.901642	−	0.756568i	0.970511	+	0.241058i	$0.0774945\pi$
$338$		0			0
$339$	−1.43432	−	8.13441i	−0.0779014	−	0.441801i
$340$		0			0
$341$	−8.30398			−0.449686
$342$		0			0
$343$	−20.1596			−1.08851
$344$		0			0
$345$	0.504392	+	2.86055i	0.0271555	+	0.154007i
$346$		0			0
$347$	10.7429	−	9.01436i	0.576709	−	0.483916i	−0.307155	−	0.951659i	$-0.599377\pi$
$347$	10.7429	−	9.01436i	0.576709	−	0.483916i	0.883865	+	0.467743i	$0.154933\pi$
$348$		0			0
$349$	−10.0053	+	17.3296i	−0.535570	+	0.927634i	0.463566	+	0.886062i	$0.346570\pi$
$349$	−10.0053	+	17.3296i	−0.535570	+	0.927634i	−0.999136	+	0.0415713i	$0.986764\pi$
$350$		0			0
$351$	2.19296	−	0.798174i	0.117052	−	0.0426034i
$352$		0			0
$353$	6.53402	+	11.3173i	0.347771	+	0.602357i	0.985853	−	0.167611i	$-0.0536053\pi$
$353$	6.53402	+	11.3173i	0.347771	+	0.602357i	−0.638082	+	0.769968i	$0.720272\pi$
$354$		0			0
$355$	1.29648	−	7.35270i	0.0688100	−	0.390241i
$356$		0			0
$357$	−0.00670494	−	0.00562612i	−0.000354863	−	0.000297766i
$358$		0			0
$359$	−19.9748	−	7.27025i	−1.05423	−	0.383709i	−0.243973	−	0.969782i	$-0.578451\pi$
$359$	−19.9748	−	7.27025i	−1.05423	−	0.383709i	−0.810258	+	0.586073i	$0.800673\pi$
$360$		0			0
$361$	18.1805	+	5.52006i	0.956866	+	0.290529i
$362$		0			0
$363$	3.95851	+	1.44078i	0.207768	+	0.0756212i
$364$		0			0
$365$	8.54436	+	7.16957i	0.447232	+	0.375272i
$366$		0			0
$367$	3.75221	−	21.2799i	0.195864	−	1.11080i	−0.715319	−	0.698798i	$-0.753719\pi$
$367$	3.75221	−	21.2799i	0.195864	−	1.11080i	0.911183	−	0.412002i	$-0.135170\pi$
$368$		0			0
$369$	−10.0114	−	17.3402i	−0.521171	−	0.902694i
$370$		0			0
$371$	−4.99503	+	1.81804i	−0.259329	+	0.0943880i
$372$		0			0
$373$	9.22242	−	15.9737i	0.477519	−	0.827086i	−0.522149	−	0.852854i	$-0.674870\pi$
$373$	9.22242	−	15.9737i	0.477519	−	0.827086i	0.999668	+	0.0257676i	$0.00820299\pi$
$374$		0			0
$375$	0.344606	−	0.289159i	0.0177954	−	0.0149321i
$376$		0			0
$377$	−0.0630758	−	0.357721i	−0.00324857	−	0.0184235i
$378$		0			0
$379$	−28.0324			−1.43993			−0.719964	−	0.694012i	$-0.755842\pi$
$379$	−28.0324			−1.43993			−0.719964	+	0.694012i	$0.755842\pi$
$380$		0			0
$381$	−3.77847			−0.193577
$382$		0			0
$383$	−4.29445	−	24.3550i	−0.219436	−	1.24448i	−0.873040	−	0.487648i	$-0.837855\pi$
$383$	−4.29445	−	24.3550i	−0.219436	−	1.24448i	0.653604	−	0.756836i	$-0.273256\pi$
$384$		0			0
$385$	7.39651	−	6.20641i	0.376961	−	0.316308i
$386$		0			0
$387$	1.91558	−	3.31788i	0.0973744	−	0.168657i
$388$		0			0
$389$	−12.0959	+	4.40256i	−0.613289	+	0.223219i	−0.629942	−	0.776642i	$-0.716921\pi$
$389$	−12.0959	+	4.40256i	−0.613289	+	0.223219i	0.0166528	+	0.999861i	$0.494699\pi$
$390$		0			0
$391$	−0.0293584	−	0.0508503i	−0.00148472	−	0.00257161i
$392$		0			0
$393$	1.42002	−	8.05333i	0.0716305	−	0.406237i
$394$		0			0
$395$	5.64412	+	4.73598i	0.283986	+	0.238293i
$396$		0			0
$397$	−4.54281	−	1.65345i	−0.227997	−	0.0829842i	0.225495	−	0.974244i	$-0.427600\pi$
$397$	−4.54281	−	1.65345i	−0.227997	−	0.0829842i	−0.453493	+	0.891260i	$0.649822\pi$
$398$		0			0
$399$	3.68901	+	1.99837i	0.184681	+	0.100044i
$400$		0			0
$401$	−24.8719	−	9.05262i	−1.24204	−	0.452066i	−0.364336	−	0.931267i	$-0.618704\pi$
$401$	−24.8719	−	9.05262i	−1.24204	−	0.452066i	−0.877705	+	0.479201i	$0.840926\pi$
$402$		0			0
$403$	−1.26134	−	1.05839i	−0.0628316	−	0.0527220i
$404$		0			0
$405$	−1.25368	+	7.10997i	−0.0622959	+	0.353297i
$406$		0			0
$407$	−15.2453	−	26.4056i	−0.755680	−	1.30888i
$408$		0			0
$409$	−9.15328	+	3.33152i	−0.452601	+	0.164733i	−0.558254	−	0.829670i	$-0.688529\pi$
$409$	−9.15328	+	3.33152i	−0.452601	+	0.164733i	0.105654	+	0.994403i	$0.466306\pi$
$410$		0			0
$411$	−3.55469	+	6.15691i	−0.175340	+	0.303698i
$412$		0			0
$413$	−14.5755	+	12.2303i	−0.717215	+	0.601815i
$414$		0			0
$415$	−0.0263413	−	0.149389i	−0.00129304	−	0.00733321i
$416$		0			0
$417$	2.75447			0.134887
$418$		0			0
$419$	−12.5930			−0.615211			−0.307605	−	0.951514i	$-0.599528\pi$
$419$	−12.5930			−0.615211			−0.307605	+	0.951514i	$0.599528\pi$
$420$		0			0
$421$	−0.389772	−	2.21051i	−0.0189963	−	0.107734i	0.973835	−	0.227255i	$-0.0729751\pi$
$421$	−0.389772	−	2.21051i	−0.0189963	−	0.107734i	−0.992832	+	0.119521i	$0.961864\pi$
$422$		0			0
$423$	2.58823	−	2.17178i	0.125844	−	0.105596i
$424$		0			0
$425$	−0.00454678	+	0.00787525i	−0.000220551	+	0.000382006i
$426$		0			0
$427$	11.6645	−	4.24552i	0.564484	−	0.205455i
$428$		0			0
$429$	0.908238	+	1.57312i	0.0438502	+	0.0759507i
$430$		0			0
$431$	−1.94744	+	11.0445i	−0.0938051	+	0.531995i	0.901302	+	0.433192i	$0.142613\pi$
$431$	−1.94744	+	11.0445i	−0.0938051	+	0.531995i	−0.995107	+	0.0988036i	$0.968498\pi$
$432$		0			0
$433$	20.4565	+	17.1651i	0.983078	+	0.824900i	0.984551	−	0.175099i	$-0.0560244\pi$
$433$	20.4565	+	17.1651i	0.983078	+	0.824900i	−0.00147297	+	0.999999i	$0.500469\pi$
$434$		0			0
$435$	−0.171602	−	0.0624579i	−0.00822767	−	0.00299463i
$436$		0			0
$437$	18.6699	+	21.0616i	0.893103	+	1.00751i
$438$		0			0
$439$	2.65088	+	0.964842i	0.126520	+	0.0460494i	0.404504	−	0.914536i	$-0.367444\pi$
$439$	2.65088	+	0.964842i	0.126520	+	0.0460494i	−0.277984	+	0.960586i	$0.589666\pi$
$440$		0			0
$441$	5.19061	+	4.35544i	0.247172	+	0.207402i
$442$		0			0
$443$	0.321970	−	1.82598i	0.0152973	−	0.0867551i	−0.976203	−	0.216857i	$-0.930419\pi$
$443$	0.321970	−	1.82598i	0.0152973	−	0.0867551i	0.991501	+	0.130102i	$0.0415305\pi$
$444$		0			0
$445$	5.72665	+	9.91886i	0.271469	+	0.470199i
$446$		0			0
$447$	3.75517	−	1.36677i	0.177614	−	0.0646460i
$448$		0			0
$449$	−9.89875	+	17.1451i	−0.467151	+	0.809129i	−0.999296	−	0.0375242i	$-0.988053\pi$
$449$	−9.89875	+	17.1451i	−0.467151	+	0.809129i	0.532145	+	0.846653i	$0.321386\pi$
$450$		0			0
$451$	24.7412	−	20.7604i	1.16502	−	0.977567i
$452$		0			0
$453$	−1.12656	−	6.38903i	−0.0529303	−	0.300183i
$454$		0			0
$455$	1.91454			0.0897549
$456$		0			0
$457$	27.6117			1.29162			0.645811	−	0.763497i	$-0.276519\pi$
$457$	27.6117			1.29162			0.645811	+	0.763497i	$0.276519\pi$
$458$		0			0
$459$	0.00411836	+	0.0233564i	0.000192228	+	0.00109018i
$460$		0			0
$461$	−27.3590	+	22.9569i	−1.27424	+	1.06921i	−0.280226	+	0.959934i	$0.590409\pi$
$461$	−27.3590	+	22.9569i	−1.27424	+	1.06921i	−0.994011	+	0.109278i	$0.965146\pi$
$462$		0			0
$463$	−4.24784	+	7.35747i	−0.197414	+	0.341931i	−0.947689	−	0.319195i	$-0.896588\pi$
$463$	−4.24784	+	7.35747i	−0.197414	+	0.341931i	0.750275	+	0.661126i	$0.229921\pi$
$464$		0			0
$465$	−0.777868	+	0.283121i	−0.0360728	+	0.0131294i
$466$		0			0
$467$	8.09252	+	14.0167i	0.374477	+	0.648613i	0.990249	−	0.139311i	$-0.0444889\pi$
$467$	8.09252	+	14.0167i	0.374477	+	0.648613i	−0.615772	+	0.787925i	$0.711156\pi$
$468$		0			0
$469$	5.80666	−	32.9312i	0.268127	−	1.52062i
$470$		0			0
$471$	−4.13372	−	3.46860i	−0.190472	−	0.159825i
$472$		0			0
$473$	5.80711	+	2.11362i	0.267011	+	0.0971841i
$474$		0			0
$475$	1.37912	−	4.13498i	0.0632783	−	0.189726i
$476$		0			0
$477$	6.53116	+	2.37715i	0.299041	+	0.108842i
$478$		0			0
$479$	7.14947	+	5.99912i	0.326668	+	0.274107i	0.791340	−	0.611376i	$-0.209384\pi$
$479$	7.14947	+	5.99912i	0.326668	+	0.274107i	−0.464673	+	0.885482i	$0.653828\pi$
$480$		0			0
$481$	1.04985	−	5.95398i	0.0478689	−	0.271478i
$482$		0			0
$483$	3.10746	+	5.38228i	0.141394	+	0.244902i
$484$		0			0
$485$	7.85592	−	2.85932i	0.356719	−	0.129835i
$486$		0			0
$487$	−17.1310	+	29.6718i	−0.776281	+	1.34456i	0.157790	+	0.987473i	$0.449563\pi$
$487$	−17.1310	+	29.6718i	−0.776281	+	1.34456i	−0.934071	+	0.357086i	$0.883770\pi$
$488$		0			0
$489$	−2.09272	+	1.75600i	−0.0946362	+	0.0794092i
$490$		0			0
$491$	3.00626	+	17.0493i	0.135670	+	0.769425i	0.974391	+	0.224862i	$0.0721932\pi$
$491$	3.00626	+	17.0493i	0.135670	+	0.769425i	−0.838720	+	0.544563i	$0.816696\pi$
$492$		0			0
$493$	0.00369148			0.000166256
$494$		0			0
$495$	−12.6248			−0.567444
$496$		0			0
$497$	−2.77398	−	15.7320i	−0.124430	−	0.705678i
$498$		0			0
$499$	11.3552	−	9.52812i	0.508327	−	0.426537i	−0.352213	−	0.935920i	$-0.614571\pi$
$499$	11.3552	−	9.52812i	0.508327	−	0.426537i	0.860540	+	0.509383i	$0.170126\pi$
$500$		0			0
$501$	1.86212	−	3.22528i	0.0831933	−	0.144095i
$502$		0			0
$503$	−0.934331	+	0.340069i	−0.0416598	+	0.0151629i	−0.362766	−	0.931880i	$-0.618168\pi$
$503$	−0.934331	+	0.340069i	−0.0416598	+	0.0151629i	0.321106	+	0.947043i	$0.395945\pi$
$504$		0			0
$505$	4.42700	+	7.66778i	0.196999	+	0.341212i
$506$		0			0
$507$	0.952962	−	5.40451i	0.0423225	−	0.240023i
$508$		0			0
$509$	8.66391	+	7.26988i	0.384021	+	0.322232i	0.814279	−	0.580474i	$-0.197133\pi$
$509$	8.66391	+	7.26988i	0.384021	+	0.322232i	−0.430258	+	0.902706i	$0.641577\pi$
$510$		0			0
$511$	22.4259	+	8.16235i	0.992063	+	0.361081i
$512$		0			0
$513$	−4.17669	−	10.5733i	−0.184405	−	0.466822i
$514$		0			0
$515$	15.9508	+	5.80562i	0.702877	+	0.255826i
$516$		0			0
$517$	4.17491	+	3.50316i	0.183612	+	0.154069i
$518$		0			0
$519$	1.64264	−	9.31585i	0.0721037	−	0.408921i
$520$		0			0
$521$	−20.2138	−	35.0113i	−0.885582	−	1.53387i	−0.845045	−	0.534695i	$-0.820427\pi$
$521$	−20.2138	−	35.0113i	−0.885582	−	1.53387i	−0.0405365	−	0.999178i	$-0.512907\pi$
$522$		0			0
$523$	−26.2979	+	9.57167i	−1.14993	+	0.418540i	−0.845490	−	0.533992i	$-0.820691\pi$
$523$	−26.2979	+	9.57167i	−1.14993	+	0.418540i	−0.304439	+	0.952532i	$0.598469\pi$
$524$		0			0
$525$	0.481257	−	0.833562i	0.0210038	−	0.0363796i
$526$		0			0
$527$	0.0128186	−	0.0107560i	0.000558385	−	0.000468541i
$528$		0			0
$529$	3.24591	+	18.4085i	0.141127	+	0.800369i
$530$		0			0
$531$	24.8784			1.07963
$532$		0			0
$533$	6.40410			0.277392
$534$		0			0
$535$	−1.29809	−	7.36182i	−0.0561212	−	0.318279i
$536$		0			0
$537$	−3.65900	+	3.07027i	−0.157898	+	0.132492i
$538$		0			0
$539$	−5.46485	+	9.46540i	−0.235388	+	0.407703i
$540$		0			0
$541$	10.0543	−	3.65946i	0.432268	−	0.157333i	−0.116717	−	0.993165i	$-0.537237\pi$
$541$	10.0543	−	3.65946i	0.432268	−	0.157333i	0.548984	+	0.835833i	$0.315015\pi$
$542$		0			0
$543$	2.81096	+	4.86872i	0.120630	+	0.208937i
$544$		0			0
$545$	0.186126	−	1.05557i	0.00797274	−	0.0452157i
$546$		0			0
$547$	21.6218	+	18.1429i	0.924483	+	0.775734i	0.974819	−	0.222999i	$-0.0715846\pi$
$547$	21.6218	+	18.1429i	0.924483	+	0.775734i	−0.0503355	+	0.998732i	$0.516029\pi$
$548$		0			0
$549$	−15.2517	−	5.55116i	−0.650926	−	0.236918i
$550$		0			0
$551$	−1.73361	+	0.354445i	−0.0738542	+	0.0150999i
$552$		0			0
$553$	14.8138	+	5.39178i	0.629946	+	0.229282i
$554$		0			0
$555$	−2.32838	−	1.95374i	−0.0988341	−	0.0829317i
$556$		0			0
$557$	−4.01173	+	22.7517i	−0.169983	+	0.964019i	0.773795	+	0.633436i	$0.218356\pi$
$557$	−4.01173	+	22.7517i	−0.169983	+	0.964019i	−0.943777	+	0.330582i	$0.892755\pi$
$558$		0			0
$559$	0.612682	+	1.06120i	0.0259137	+	0.0448838i
$560$		0			0
$561$	−0.0173470	+	0.00631378i	−0.000732390	+	0.000266568i
$562$		0			0
$563$	17.5328	−	30.3677i	0.738918	−	1.27984i	−0.214064	−	0.976820i	$-0.568670\pi$
$563$	17.5328	−	30.3677i	0.738918	−	1.27984i	0.952983	−	0.303025i	$-0.0979965\pi$
$564$		0			0
$565$	−14.0656	+	11.8025i	−0.591746	+	0.496534i
$566$		0			0
$567$	2.68241	+	15.2127i	0.112651	+	0.638873i
$568$		0			0
$569$	19.9610			0.836811			0.418405	−	0.908260i	$-0.362589\pi$
$569$	19.9610			0.836811			0.418405	+	0.908260i	$0.362589\pi$
$570$		0			0
$571$	−13.1675			−0.551044			−0.275522	−	0.961295i	$-0.588851\pi$
$571$	−13.1675			−0.551044			−0.275522	+	0.961295i	$0.588851\pi$
$572$		0			0
$573$	0.403499	+	2.28836i	0.0168564	+	0.0955975i
$574$		0			0
$575$	4.94633	−	4.15046i	0.206276	−	0.173086i
$576$		0			0
$577$	9.96695	−	17.2633i	0.414930	−	0.718679i	−0.580491	−	0.814266i	$-0.697140\pi$
$577$	9.96695	−	17.2633i	0.414930	−	0.718679i	0.995421	+	0.0955871i	$0.0304729\pi$
$578$		0			0
$579$	8.04442	−	2.92793i	0.334315	−	0.121681i
$580$		0			0
$581$	−0.162284	−	0.281084i	−0.00673266	−	0.0116613i
$582$		0			0
$583$	−1.94679	+	11.0408i	−0.0806278	+	0.457263i
$584$		0			0
$585$	−1.91766	−	1.60910i	−0.0792853	−	0.0665283i
$586$		0			0
$587$	17.0954	+	6.22220i	0.705601	+	0.256818i	0.669800	−	0.742541i	$-0.266380\pi$
$587$	17.0954	+	6.22220i	0.705601	+	0.256818i	0.0358006	+	0.999359i	$0.488602\pi$
$588$		0			0
$589$	−4.98714	+	6.28210i	−0.205491	+	0.258849i
$590$		0			0
$591$	9.53482	+	3.47039i	0.392210	+	0.142753i
$592$		0			0
$593$	−3.42900	−	2.87727i	−0.140812	−	0.118155i	0.569661	−	0.821880i	$-0.307075\pi$
$593$	−3.42900	−	2.87727i	−0.140812	−	0.118155i	−0.710473	+	0.703724i	$0.751519\pi$
$594$		0			0
$595$	−0.00337864	+	0.0191612i	−0.000138511	+	0.000785534i
$596$		0			0
$597$	0.721105	+	1.24899i	0.0295129	+	0.0511178i
$598$		0			0
$599$	−13.0414	+	4.74670i	−0.532859	+	0.193945i	−0.594414	−	0.804159i	$-0.702616\pi$
$599$	−13.0414	+	4.74670i	−0.532859	+	0.193945i	0.0615555	+	0.998104i	$0.480394\pi$
$600$		0			0
$601$	−11.7807	+	20.4048i	−0.480545	+	0.832328i	−0.999751	−	0.0223210i	$-0.992894\pi$
$601$	−11.7807	+	20.4048i	−0.480545	+	0.832328i	0.519206	+	0.854649i	$0.326228\pi$
$602$		0			0
$603$	−33.4937	+	28.1045i	−1.36397	+	1.14450i
$604$		0			0
$605$	−1.62610	−	9.22206i	−0.0661103	−	0.374930i
$606$		0			0
$607$	39.7548			1.61360			0.806799	−	0.590826i	$-0.201198\pi$
$607$	39.7548			1.61360			0.806799	+	0.590826i	$0.201198\pi$
$608$		0			0
$609$	−0.390727			−0.0158331
$610$		0			0
$611$	0.187652	+	1.06423i	0.00759160	+	0.0430541i
$612$		0			0
$613$	30.8058	−	25.8492i	1.24424	−	1.04404i	0.247055	−	0.969001i	$-0.420537\pi$
$613$	30.8058	−	25.8492i	1.24424	−	1.04404i	0.997181	−	0.0750365i	$-0.0239073\pi$
$614$		0			0
$615$	1.60980	−	2.78825i	0.0649133	−	0.112433i
$616$		0			0
$617$	−1.58432	+	0.576645i	−0.0637823	+	0.0232149i	−0.373714	−	0.927544i	$-0.621916\pi$
$617$	−1.58432	+	0.576645i	−0.0637823	+	0.0232149i	0.309932	+	0.950759i	$0.399694\pi$
$618$		0			0
$619$	4.54040	+	7.86421i	0.182494	+	0.316089i	0.942729	−	0.333559i	$-0.108250\pi$
$619$	4.54040	+	7.86421i	0.182494	+	0.316089i	−0.760235	+	0.649648i	$0.774916\pi$
$620$		0			0
$621$	2.92428	−	16.5844i	0.117347	−	0.665510i
$622$		0			0
$623$	18.7725	+	15.7520i	0.752106	+	0.631092i
$624$		0			0
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$		0			0
$627$	7.54033	−	4.63071i	0.301132	−	0.184933i
$628$		0			0
$629$	0.0577364	+	0.0210143i	0.00230210	+	0.000837897i
$630$		0			0
$631$	5.65759	+	4.74728i	0.225225	+	0.188986i	0.748417	−	0.663229i	$-0.230814\pi$
$631$	5.65759	+	4.74728i	0.225225	+	0.188986i	−0.523192	+	0.852215i	$0.675259\pi$
$632$		0			0
$633$	−1.01135	+	5.73567i	−0.0401977	+	0.227972i
$634$		0			0
$635$	4.19969	+	7.27407i	0.166660	+	0.288663i
$636$		0			0
$637$	−2.03650	+	0.741226i	−0.0806891	+	0.0293684i
$638$		0			0
$639$	−10.4437	+	18.0891i	−0.413148	+	0.715594i
$640$		0			0
$641$	−1.25431	+	1.05249i	−0.0495424	+	0.0415710i	−0.667223	−	0.744858i	$-0.732517\pi$
$641$	−1.25431	+	1.05249i	−0.0495424	+	0.0415710i	0.617680	+	0.786429i	$0.288073\pi$
$642$		0			0
$643$	−1.84236	−	10.4486i	−0.0726557	−	0.412051i	−0.999344	−	0.0362197i	$-0.988468\pi$
$643$	−1.84236	−	10.4486i	−0.0726557	−	0.412051i	0.926688	−	0.375831i	$-0.122643\pi$
$644$		0			0
$645$	0.616039			0.0242565
$646$		0			0
$647$	−31.6557			−1.24451			−0.622257	−	0.782813i	$-0.713784\pi$
$647$	−31.6557			−1.24451			−0.622257	+	0.782813i	$0.713784\pi$
$648$		0			0
$649$	6.96847	+	39.5202i	0.273536	+	1.55130i
$650$		0			0
$651$	−1.35679	+	1.13848i	−0.0531768	+	0.0446206i
$652$		0			0
$653$	21.3857	−	37.0410i	0.836885	−	1.44953i	−0.0556007	−	0.998453i	$-0.517707\pi$
$653$	21.3857	−	37.0410i	0.836885	−	1.44953i	0.892486	−	0.451075i	$-0.148959\pi$
$654$		0			0
$655$	−17.0821	+	6.21737i	−0.667452	+	0.242933i
$656$		0			0
$657$	−15.6022	−	27.0238i	−0.608701	−	1.05430i
$658$		0			0
$659$	−4.87136	+	27.6269i	−0.189761	+	1.07619i	0.729922	+	0.683530i	$0.239556\pi$
$659$	−4.87136	+	27.6269i	−0.189761	+	1.07619i	−0.919684	+	0.392660i	$0.871555\pi$
$660$		0			0
$661$	28.0335	+	23.5229i	1.09038	+	0.914935i	0.996741	−	0.0806714i	$-0.0257064\pi$
$661$	28.0335	+	23.5229i	1.09038	+	0.914935i	0.0936364	+	0.995606i	$0.470151\pi$
$662$		0			0
$663$	−0.00343965	−	0.00125193i	−0.000133585	−	4.86210e-5i
$664$		0			0
$665$	−0.253115	−	9.32298i	−0.00981539	−	0.361530i
$666$		0			0
$667$	−2.46310	−	0.896494i	−0.0953715	−	0.0347124i
$668$		0			0
$669$	−2.96620	−	2.48894i	−0.114680	−	0.0962279i
$670$		0			0
$671$	4.54618	−	25.7827i	0.175503	−	0.995329i
$672$		0			0
$673$	18.4796	+	32.0075i	0.712335	+	1.23380i	0.963979	+	0.265980i	$0.0856954\pi$
$673$	18.4796	+	32.0075i	0.712335	+	1.23380i	−0.251644	+	0.967820i	$0.580971\pi$
$674$		0			0
$675$	−2.45079	+	0.892014i	−0.0943309	+	0.0343336i
$676$		0			0
$677$	4.75900	−	8.24282i	0.182903	−	0.316797i	−0.759965	−	0.649964i	$-0.774784\pi$
$677$	4.75900	−	8.24282i	0.182903	−	0.316797i	0.942868	+	0.333167i	$0.108117\pi$
$678$		0			0
$679$	13.7026	−	11.4979i	0.525858	−	0.441247i
$680$		0			0
$681$	−0.624299	−	3.54058i	−0.0239232	−	0.135675i
$682$		0			0
$683$	−47.2832			−1.80924			−0.904620	−	0.426218i	$-0.859846\pi$
$683$	−47.2832			−1.80924			−0.904620	+	0.426218i	$0.859846\pi$
$684$		0			0
$685$	15.8039			0.603834
$686$		0			0
$687$	0.935650	+	5.30634i	0.0356973	+	0.202449i
$688$		0			0
$689$	−1.70292	+	1.42892i	−0.0648760	+	0.0544374i
$690$		0			0
$691$	−22.4880	+	38.9504i	−0.855485	+	1.48174i	0.0207098	+	0.999786i	$0.493407\pi$
$691$	−22.4880	+	38.9504i	−0.855485	+	1.48174i	−0.876195	+	0.481958i	$0.839926\pi$
$692$		0			0
$693$	−25.3834	+	9.23880i	−0.964236	+	0.350953i
$694$		0			0
$695$	−3.06153	−	5.30273i	−0.116131	−	0.201144i
$696$		0			0
$697$	−0.0113015	+	0.0640940i	−0.000428075	+	0.00242773i
$698$		0			0
$699$	−8.28882	−	6.95515i	−0.313512	−	0.263068i
$700$		0			0
$701$	−37.2174	−	13.5460i	−1.40568	−	0.511626i	−0.475821	−	0.879542i	$-0.657849\pi$
$701$	−37.2174	−	13.5460i	−1.40568	−	0.511626i	−0.929859	+	0.367916i	$0.880071\pi$
$702$		0			0
$703$	−29.1322	−	4.32515i	−1.09874	−	0.163126i
$704$		0			0
$705$	0.510520	+	0.185814i	0.0192273	+	0.00699817i
$706$		0			0
$707$	14.5121	+	12.1771i	0.545785	+	0.457968i
$708$		0			0
$709$	2.81747	−	15.9787i	0.105812	−	0.600092i	−0.885080	−	0.465438i	$-0.845897\pi$
$709$	2.81747	−	15.9787i	0.105812	−	0.600092i	0.990893	−	0.134654i	$-0.0429922\pi$
$710$		0			0
$711$	−10.3063	−	17.8510i	−0.386516	−	0.669466i
$712$		0			0
$713$	−11.1652	+	4.06379i	−0.418139	+	0.152190i
$714$		0			0
$715$	2.01897	−	3.49697i	0.0755054	−	0.130779i
$716$		0			0
$717$	3.06312	−	2.57026i	0.114394	−	0.0959881i
$718$		0			0
$719$	−3.00667	−	17.0517i	−0.112130	−	0.635920i	−0.988131	−	0.153612i	$-0.950909\pi$
$719$	−3.00667	−	17.0517i	−0.112130	−	0.635920i	0.876001	−	0.482309i	$-0.160202\pi$
$720$		0			0
$721$	36.3191			1.35259
$722$		0			0
$723$	−10.7277			−0.398968
$724$		0			0
$725$	0.0704915	+	0.399777i	0.00261799	+	0.0148474i
$726$		0			0
$727$	−12.4738	+	10.4668i	−0.462628	+	0.388191i	−0.844097	−	0.536191i	$-0.819863\pi$
$727$	−12.4738	+	10.4668i	−0.462628	+	0.388191i	0.381469	+	0.924382i	$0.375418\pi$
$728$		0			0
$729$	8.33911	−	14.4438i	0.308856	−	0.534954i
$730$		0			0
$731$	−0.0117020	+	0.00425917i	−0.000432813	+	0.000157531i
$732$		0			0
$733$	−3.13699	−	5.43342i	−0.115867	−	0.200688i	0.802259	−	0.596976i	$-0.203631\pi$
$733$	−3.13699	−	5.43342i	−0.115867	−	0.200688i	−0.918126	+	0.396288i	$0.870298\pi$
$734$		0			0
$735$	−0.189196	+	1.07299i	−0.00697861	+	0.0395777i
$736$		0			0
$737$	−54.0265	−	45.3336i	−1.99009	−	1.66989i
$738$		0			0
$739$	40.7952	+	14.8482i	1.50068	+	0.546201i	0.956235	−	0.292598i	$-0.0945199\pi$
$739$	40.7952	+	14.8482i	1.50068	+	0.546201i	0.544440	+	0.838800i	$0.316742\pi$
$740$		0			0
$741$	1.73555	+	0.257671i	0.0637570	+	0.00946579i
$742$		0			0
$743$	50.4446	+	18.3603i	1.85063	+	0.673575i	0.984914	+	0.173043i	$0.0553599\pi$
$743$	50.4446	+	18.3603i	1.85063	+	0.673575i	0.865718	+	0.500532i	$0.166862\pi$
$744$		0			0
$745$	−6.80501	−	5.71008i	−0.249316	−	0.209201i
$746$		0			0
$747$	−0.0736932	+	0.417935i	−0.00269629	+	0.0152914i
$748$		0			0
$749$	−7.99727	−	13.8517i	−0.292214	−	0.506129i
$750$		0			0
$751$	49.2594	−	17.9290i	1.79750	−	0.654237i	0.798896	−	0.601470i	$-0.205418\pi$
$751$	49.2594	−	17.9290i	1.79750	−	0.654237i	0.998607	−	0.0527677i	$-0.0168043\pi$
$752$		0			0
$753$	0.851680	−	1.47515i	0.0310369	−	0.0537576i
$754$		0			0
$755$	−11.0476	+	9.27005i	−0.402064	+	0.337372i
$756$		0			0
$757$	1.15681	+	6.56062i	0.0420451	+	0.238450i	0.998587	−	0.0531460i	$-0.0169249\pi$
$757$	1.15681	+	6.56062i	0.0420451	+	0.238450i	−0.956542	+	0.291596i	$0.905814\pi$
$758$		0			0
$759$	13.1079			0.475786
$760$		0			0
$761$	11.7342			0.425364			0.212682	−	0.977121i	$-0.431780\pi$
$761$	11.7342			0.425364			0.212682	+	0.977121i	$0.431780\pi$
$762$		0			0
$763$	−0.398239	−	2.25853i	−0.0144172	−	0.0817642i
$764$		0			0
$765$	0.0194885	−	0.0163528i	0.000704609	−	0.000591237i
$766$		0			0
$767$	−3.97858	+	6.89110i	−0.143658	+	0.248823i
$768$		0			0
$769$	1.95903	−	0.713030i	0.0706446	−	0.0257125i	−0.306456	−	0.951885i	$-0.599143\pi$
$769$	1.95903	−	0.713030i	0.0706446	−	0.0257125i	0.377101	+	0.926172i	$0.376921\pi$
$770$		0			0
$771$	−1.50923	−	2.61406i	−0.0543535	−	0.0941431i
$772$		0			0
$773$	5.65027	−	32.0443i	0.203226	−	1.15255i	−0.696980	−	0.717090i	$-0.745474\pi$
$773$	5.65027	−	32.0443i	0.203226	−	1.15255i	0.900207	−	0.435463i	$-0.143415\pi$
$774$		0			0
$775$	1.40963	+	1.18282i	0.0506354	+	0.0424882i
$776$		0			0
$777$	−6.11116	−	2.22428i	−0.219236	−	0.0797956i
$778$		0			0
$779$	−0.846667	−	31.1852i	−0.0303350	−	1.11733i
$780$		0			0
$781$	−31.6604	−	11.5234i	−1.13290	−	0.412341i
$782$		0			0
$783$	0.811037	+	0.680541i	0.0289841	+	0.0243205i
$784$		0			0
$785$	−2.08300	+	11.8133i	−0.0743453	+	0.421633i
$786$		0			0
$787$	−20.4871	−	35.4846i	−0.730285	−	1.26489i	−0.956761	−	0.290874i	$-0.906054\pi$
$787$	−20.4871	−	35.4846i	−0.730285	−	1.26489i	0.226476	−	0.974017i	$-0.427279\pi$
$788$		0			0
$789$	−9.51290	+	3.46241i	−0.338668	+	0.123265i
$790$		0			0
$791$	−19.6433	+	34.0231i	−0.698434	+	1.20972i
$792$		0			0
$793$	3.97668	−	3.33683i	0.141216	−	0.118494i
$794$		0			0
$795$	0.194068	+	1.10061i	0.00688287	+	0.0390347i
$796$		0			0
$797$	−33.7920			−1.19697			−0.598487	−	0.801132i	$-0.704231\pi$
$797$	−33.7920			−1.19697			−0.598487	+	0.801132i	$0.704231\pi$
$798$		0			0
$799$	−0.0109823			−0.000388525
$800$		0			0
$801$	−5.56406	−	31.5554i	−0.196597	−	1.11495i
$802$		0			0
$803$	38.5580	−	32.3540i	1.36068	−	1.14175i
$804$		0			0
$805$	6.90776	−	11.9646i	0.243466	−	0.421696i
$806$		0			0
$807$	−12.1221	+	4.41208i	−0.426718	+	0.155313i
$808$		0			0
$809$	−7.46472	−	12.9293i	−0.262445	−	0.454569i	0.704446	−	0.709758i	$-0.251196\pi$
$809$	−7.46472	−	12.9293i	−0.262445	−	0.454569i	−0.966891	+	0.255189i	$0.917862\pi$
$810$		0			0
$811$	−6.28041	+	35.6180i	−0.220535	+	1.25072i	0.650504	+	0.759503i	$0.274558\pi$
$811$	−6.28041	+	35.6180i	−0.220535	+	1.25072i	−0.871039	+	0.491214i	$0.836553\pi$
$812$		0			0
$813$	−4.11666	−	3.45428i	−0.144377	−	0.121147i
$814$		0			0
$815$	5.70656	+	2.07702i	0.199892	+	0.0727548i
$816$		0			0
$817$	5.08657	−	3.12380i	0.177957	−	0.109288i
$818$		0			0
$819$	−5.03316	−	1.83192i	−0.175873	−	0.0640125i
$820$		0			0
$821$	−6.21404	−	5.21420i	−0.216872	−	0.181977i	0.527879	−	0.849319i	$-0.322987\pi$
$821$	−6.21404	−	5.21420i	−0.216872	−	0.181977i	−0.744751	+	0.667342i	$0.767432\pi$
$822$		0			0
$823$	−1.27345	+	7.22211i	−0.0443898	+	0.251747i	−0.998925	−	0.0463504i	$-0.985241\pi$
$823$	−1.27345	+	7.22211i	−0.0443898	+	0.251747i	0.954535	+	0.298097i	$0.0963520\pi$
$824$		0			0
$825$	−1.01502	−	1.75806i	−0.0353384	−	0.0612079i
$826$		0			0
$827$	−22.0689	+	8.03243i	−0.767412	+	0.279315i	−0.695913	−	0.718126i	$-0.745000\pi$
$827$	−22.0689	+	8.03243i	−0.767412	+	0.279315i	−0.0714983	+	0.997441i	$0.522778\pi$
$828$		0			0
$829$	13.3729	−	23.1625i	0.464459	−	0.804467i	−0.534718	−	0.845031i	$-0.679582\pi$
$829$	13.3729	−	23.1625i	0.464459	−	0.804467i	0.999177	+	0.0405640i	$0.0129155\pi$
$830$		0			0
$831$	9.41581	−	7.90080i	0.326631	−	0.274076i
$832$		0			0
$833$	−0.00382452	−	0.0216900i	−0.000132512	−	0.000751512i
$834$		0			0
$835$	−8.27882			−0.286500
$836$		0			0
$837$	4.79922			0.165885
$838$		0			0
$839$	2.51241	+	14.2486i	0.0867380	+	0.491916i	0.996968	+	0.0778127i	$0.0247936\pi$
$839$	2.51241	+	14.2486i	0.0867380	+	0.491916i	−0.910230	+	0.414103i	$0.864095\pi$
$840$		0			0
$841$	−22.0891	+	18.5349i	−0.761691	+	0.639135i
$842$		0			0
$843$	−0.680314	+	1.17834i	−0.0234313	+	0.0405841i
$844$		0			0
$845$	−11.4636	+	4.17242i	−0.394361	+	0.143536i
$846$		0			0
$847$	−10.0181	−	17.3518i	−0.344225	−	0.596216i
$848$		0			0
$849$	−1.11026	+	6.29660i	−0.0381040	+	0.216099i
$850$		0			0
$851$	−33.4205	−	28.0431i	−1.14564	−	0.961306i
$852$		0			0
$853$	−19.2436	−	7.00411i	−0.658889	−	0.239816i	−0.00913255	−	0.999958i	$-0.502907\pi$
$853$	−19.2436	−	7.00411i	−0.658889	−	0.239816i	−0.649757	+	0.760142i	$0.725129\pi$
$854$		0			0
$855$	−7.58212	+	9.55090i	−0.259303	+	0.326634i
$856$		0			0
$857$	−50.3628	−	18.3305i	−1.72036	−	0.626159i	−0.722488	−	0.691383i	$-0.757002\pi$
$857$	−50.3628	−	18.3305i	−1.72036	−	0.626159i	−0.997871	+	0.0652238i	$0.979224\pi$
$858$		0			0
$859$	−21.7374	−	18.2399i	−0.741672	−	0.622337i	0.191614	−	0.981470i	$-0.438628\pi$
$859$	−21.7374	−	18.2399i	−0.741672	−	0.622337i	−0.933286	+	0.359134i	$0.883072\pi$
$860$		0			0
$861$	1.19622	−	6.78408i	0.0407669	−	0.231201i
$862$		0			0
$863$	25.6593	+	44.4432i	0.873452	+	1.51286i	0.858403	+	0.512976i	$0.171457\pi$
$863$	25.6593	+	44.4432i	0.873452	+	1.51286i	0.0150485	+	0.999887i	$0.495210\pi$
$864$		0			0
$865$	−19.7600	+	7.19207i	−0.671862	+	0.244538i
$866$		0			0
$867$	−3.82372	+	6.62287i	−0.129860	+	0.224925i
$868$		0			0
$869$	25.4701	−	21.3720i	0.864014	−	0.724994i
$870$		0			0
$871$	−2.42837	−	13.7719i	−0.0822820	−	0.466645i
$872$		0			0
$873$	−23.3885			−0.791580
$874$		0			0
$875$	−2.13963			−0.0723326
$876$		0			0
$877$	4.28817	+	24.3194i	0.144801	+	0.821209i	0.967526	+	0.252770i	$0.0813415\pi$
$877$	4.28817	+	24.3194i	0.144801	+	0.821209i	−0.822725	+	0.568439i	$0.807547\pi$
$878$		0			0
$879$	−0.0401536	+	0.0336929i	−0.00135435	+	0.00113643i
$880$		0			0
$881$	−10.1551	+	17.5891i	−0.342133	+	0.592592i	−0.984829	−	0.173530i	$-0.944483\pi$
$881$	−10.1551	+	17.5891i	−0.342133	+	0.592592i	0.642696	+	0.766122i	$0.277816\pi$
$882$		0			0
$883$	42.6680	−	15.5299i	1.43589	−	0.522622i	0.497278	−	0.867591i	$-0.334333\pi$
$883$	42.6680	−	15.5299i	1.43589	−	0.522622i	0.938614	+	0.344969i	$0.112111\pi$
$884$		0			0
$885$	2.00019	+	3.46443i	0.0672357	+	0.116456i
$886$		0			0
$887$	−3.06102	+	17.3599i	−0.102779	+	0.582889i	0.889305	+	0.457315i	$0.151189\pi$
$887$	−3.06102	+	17.3599i	−0.102779	+	0.582889i	−0.992084	+	0.125575i	$0.959922\pi$
$888$		0			0
$889$	13.7670	+	11.5519i	0.461730	+	0.387438i
$890$		0			0
$891$	30.6152	+	11.1430i	1.02565	+	0.373305i
$892$		0			0
$893$	5.15754	−	1.05449i	0.172590	−	0.0352870i
$894$		0			0
$895$	9.97759	+	3.63155i	0.333514	+	0.121389i
$896$		0			0
$897$	1.99103	+	1.67067i	0.0664785	+	0.0557821i
$898$		0			0
$899$	0.129714	−	0.735647i	0.00432622	−	0.0245352i
$900$		0			0
$901$	−0.0112958	−	0.0195649i	−0.000376318	−	0.000651803i
$902$		0			0
$903$	1.23860	−	0.450815i	0.0412182	−	0.0150022i
$904$		0			0
$905$	6.24864	−	10.8230i	0.207712	−	0.359767i
$906$		0			0
$907$	−27.0126	+	22.6663i	−0.896940	+	0.752622i	−0.969590	−	0.244736i	$-0.921299\pi$
$907$	−27.0126	+	22.6663i	−0.896940	+	0.752622i	0.0726501	+	0.997357i	$0.476854\pi$
$908$		0			0
$909$	−4.30131	−	24.3939i	−0.142665	−	0.809095i
$910$		0			0
$911$	1.09159			0.0361660			0.0180830	−	0.999836i	$-0.494244\pi$
$911$	1.09159			0.0361660			0.0180830	+	0.999836i	$0.494244\pi$
$912$		0			0
$913$	−0.684544			−0.0226551
$914$		0			0
$915$	−0.453190	−	2.57017i	−0.0149820	−	0.0849672i
$916$		0			0
$917$	−29.7952	+	25.0012i	−0.983926	+	0.825612i
$918$		0			0
$919$	−2.43232	+	4.21291i	−0.0802350	+	0.138971i	−0.903351	−	0.428902i	$-0.858900\pi$
$919$	−2.43232	+	4.21291i	−0.0802350	+	0.138971i	0.823116	+	0.567874i	$0.192234\pi$
$920$		0			0
$921$	−0.122476	+	0.0445775i	−0.00403571	+	0.00146888i
$922$		0			0
$923$	−3.34034	−	5.78565i	−0.109949	−	0.190437i
$924$		0			0
$925$	−1.17328	+	6.65398i	−0.0385771	+	0.218782i
$926$		0			0
$927$	−36.3782	−	30.5250i	−1.19482	−	1.00257i
$928$		0			0
$929$	24.7981	+	9.02577i	0.813599	+	0.296126i	0.715110	−	0.699012i	$-0.246377\pi$
$929$	24.7981	+	9.02577i	0.813599	+	0.296126i	0.0984895	+	0.995138i	$0.468599\pi$
$930$		0			0
$931$	3.87870	+	9.81890i	0.127119	+	0.321802i
$932$		0			0
$933$	8.84336	+	3.21872i	0.289519	+	0.105376i
$934$		0			0
$935$	0.0314357	+	0.0263777i	0.00102806	+	0.000862642i
$936$		0			0
$937$	0.495573	−	2.81053i	0.0161897	−	0.0918162i	−0.975642	−	0.219367i	$-0.929601\pi$
$937$	0.495573	−	2.81053i	0.0161897	−	0.0918162i	0.991832	+	0.127551i	$0.0407118\pi$
$938$		0			0
$939$	7.42820	+	12.8660i	0.242410	+	0.419867i
$940$		0			0
$941$	39.2216	−	14.2755i	1.27859	−	0.465368i	0.388624	−	0.921397i	$-0.372951\pi$
$941$	39.2216	−	14.2755i	1.27859	−	0.465368i	0.889965	+	0.456028i	$0.150728\pi$
$942$		0			0
$943$	23.1063	−	40.0213i	0.752446	−	1.30327i
$944$		0			0
$945$	−4.27476	+	3.58695i	−0.139058	+	0.116684i
$946$		0			0
$947$	3.05892	+	17.3480i	0.0994016	+	0.563734i	0.993309	+	0.115483i	$0.0368417\pi$
$947$	3.05892	+	17.3480i	0.0994016	+	0.563734i	−0.893908	+	0.448251i	$0.852047\pi$
$948$		0			0
$949$	9.98048			0.323980
$950$		0			0
$951$	−1.17232			−0.0380150
$952$		0			0
$953$	3.46296	+	19.6394i	0.112176	+	0.636183i	0.988110	+	0.153751i	$0.0491353\pi$
$953$	3.46296	+	19.6394i	0.112176	+	0.636183i	−0.875934	+	0.482432i	$0.839754\pi$
$954$		0			0
$955$	3.95692	−	3.32025i	0.128043	−	0.107441i
$956$		0			0
$957$	−0.412041	+	0.713677i	−0.0133194	+	0.0230699i
$958$		0			0
$959$	31.7751	−	11.5652i	1.02607	−	0.373460i
$960$		0			0
$961$	13.8069	+	23.9143i	0.445385	+	0.771430i
$962$		0			0
$963$	−3.63157	+	20.5957i	−0.117026	+	0.663686i
$964$		0			0
$965$	−14.5779	−	12.2323i	−0.469278	−	0.393771i
$966$		0			0
$967$	−20.9538	−	7.62656i	−0.673829	−	0.245254i	−0.0176332	−	0.999845i	$-0.505613\pi$
$967$	−20.9538	−	7.62656i	−0.673829	−	0.245254i	−0.656196	+	0.754591i	$0.727835\pi$
$968$		0			0
$969$	−0.00564163	+	0.0169152i	−0.000181235	+	0.000543393i
$970$		0			0
$971$	−31.7102	−	11.5416i	−1.01763	−	0.370387i	−0.221271	−	0.975212i	$-0.571021\pi$
$971$	−31.7102	−	11.5416i	−1.01763	−	0.370387i	−0.796358	+	0.604826i	$0.793243\pi$
$972$		0			0
$973$	−10.0360	−	8.42122i	−0.321740	−	0.269972i
$974$		0			0
$975$	0.0698981	−	0.396412i	0.00223853	−	0.0126953i
$976$		0			0
$977$	−2.47596	−	4.28849i	−0.0792129	−	0.137201i	0.823698	−	0.567029i	$-0.191907\pi$
$977$	−2.47596	−	4.28849i	−0.0792129	−	0.137201i	−0.902911	+	0.429828i	$0.858574\pi$
$978$		0			0
$979$	48.5682	−	17.6774i	1.55225	−	0.564971i
$980$		0			0
$981$	−1.49933	+	2.59691i	−0.0478698	+	0.0829130i
$982$		0			0
$983$	−13.9610	+	11.7147i	−0.445288	+	0.373641i	−0.837684	−	0.546155i	$-0.816091\pi$
$983$	−13.9610	+	11.7147i	−0.445288	+	0.373641i	0.392396	+	0.919796i	$0.371646\pi$
$984$		0			0
$985$	−3.91677	−	22.2131i	−0.124799	−	0.707768i
$986$		0			0
$987$	1.16243			0.0370004
$988$		0			0
$989$	8.84236			0.281171
$990$		0			0
$991$	1.16408	+	6.60185i	0.0369784	+	0.209715i	0.997699	−	0.0678037i	$-0.0215992\pi$
$991$	1.16408	+	6.60185i	0.0369784	+	0.209715i	−0.960720	+	0.277518i	$0.910488\pi$
$992$		0			0
$993$	−6.55399	+	5.49945i	−0.207985	+	0.174520i
$994$		0			0
$995$	1.60299	−	2.77645i	0.0508181	−	0.0880195i
$996$		0			0
$997$	19.2083	−	6.99126i	0.608334	−	0.221415i	−0.0194403	−	0.999811i	$-0.506188\pi$
$997$	19.2083	−	6.99126i	0.608334	−	0.221415i	0.627774	+	0.778396i	$0.283966\pi$
$998$		0			0
$999$	8.81090	+	15.2609i	0.278764	+	0.482834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.a.61.2	✓	18
19.5	even	9	inner	380.2.u.a.81.2	yes	18
19.9	even	9		7220.2.a.v.1.5		9
19.10	odd	18		7220.2.a.x.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.a.61.2	✓	18	1.1	even	1	trivial
380.2.u.a.81.2	yes	18	19.5	even	9	inner
7220.2.a.v.1.5		9	19.9	even	9
7220.2.a.x.1.5		9	19.10	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)

\(f(q)\)	\(=\)	\(q+(-0.0781159 - 0.443017i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-1.06981 + 1.85297i) q^{7} +(2.62892 - 0.956847i) q^{9} +O(q^{10})\)	\(q+(-0.0781159 - 0.443017i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-1.06981 + 1.85297i) q^{7} +(2.62892 - 0.956847i) q^{9} +(2.25634 + 3.90810i) q^{11} +(-0.155380 + 0.881206i) q^{13} +(0.344606 + 0.289159i) q^{15} +(-0.00854515 - 0.00311018i) q^{17} +(4.31164 + 0.640134i) q^{19} +(0.904468 + 0.329199i) q^{21} +(4.94633 + 4.15046i) q^{23} +(0.173648 - 0.984808i) q^{25} +(-1.30404 - 2.25866i) q^{27} +(-0.381463 + 0.138841i) q^{29} +(-0.920071 + 1.59361i) q^{31} +(1.55510 - 1.30488i) q^{33} +(-0.371542 - 2.10712i) q^{35} -6.75663 q^{37} +0.402527 q^{39} +(-1.24280 - 7.04829i) q^{41} +(1.04904 - 0.880252i) q^{43} +(-1.39882 + 2.42282i) q^{45} +(1.13486 - 0.413057i) q^{47} +(1.21100 + 2.09751i) q^{49} +(-0.000710351 + 0.00402860i) q^{51} +(1.90313 + 1.59691i) q^{53} +(-4.24054 - 1.54343i) q^{55} +(-0.0532169 - 1.96013i) q^{57} +(8.35638 + 3.04147i) q^{59} +(-4.44422 - 3.72914i) q^{61} +(-1.03944 + 5.89495i) q^{63} +(-0.447400 - 0.774919i) q^{65} +(-14.6860 + 5.34527i) q^{67} +(1.45234 - 2.51552i) q^{69} +(-5.71938 + 4.79913i) q^{71} +(-1.93685 - 10.9844i) q^{73} -0.449851 q^{75} -9.65546 q^{77} +(-1.27942 - 7.25594i) q^{79} +(5.53058 - 4.64071i) q^{81} +(-0.0758467 + 0.131370i) q^{83} +(0.00854515 - 0.00311018i) q^{85} +(0.0913074 + 0.158149i) q^{87} +(1.98885 - 11.2793i) q^{89} +(-1.46662 - 1.23064i) q^{91} +(0.777868 + 0.283121i) q^{93} +(-3.71438 + 2.28110i) q^{95} +(-7.85592 - 2.85932i) q^{97} +(9.67119 + 8.11509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 9 * q^9	\( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^9 + 9 * q^13 - 3 * q^15 + 12 * q^17 + 18 * q^19 + 15 * q^21 - 9 * q^23 - 33 * q^29 - 18 * q^31 + 9 * q^33 + 12 * q^35 + 60 * q^37 - 84 * q^39 - 18 * q^41 + 18 * q^43 + 6 * q^45 - 15 * q^47 - 15 * q^49 - 9 * q^51 + 24 * q^53 + 3 * q^55 + 66 * q^57 + 48 * q^59 - 18 * q^61 - 54 * q^63 + 3 * q^65 - 36 * q^67 - 9 * q^69 + 18 * q^73 - 6 * q^75 + 9 * q^79 - 9 * q^81 - 30 * q^83 - 12 * q^85 - 9 * q^87 + 6 * q^89 + 30 * q^91 + 21 * q^95 + 21 * q^97 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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