LMFDB - Embedded newform 380.2.u.a.61.3

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			61.3
Root			$2.39653 + 2.01093i$ of defining polynomial
Character	$\chi$	$=$	380.61
Dual form			380.2.u.a.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.543249 + 3.08092i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(0.0481505 - 0.0833990i) q^{7} +(-6.37785 + 2.32135i) q^{9} +O(q^{10})$	\(q+(0.543249 + 3.08092i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(0.0481505 - 0.0833990i) q^{7} +(-6.37785 + 2.32135i) q^{9} +(0.190371 + 0.329733i) q^{11} +(-0.668410 + 3.79074i) q^{13} +(-2.39653 - 2.01093i) q^{15} +(2.49811 + 0.909237i) q^{17} +(-0.788719 - 4.28695i) q^{19} +(0.283103 + 0.103041i) q^{21} +(0.131397 + 0.110255i) q^{23} +(0.173648 - 0.984808i) q^{25} +(-5.92397 - 10.2606i) q^{27} +(-3.67797 + 1.33867i) q^{29} +(-1.23201 + 2.13390i) q^{31} +(-0.912460 + 0.765645i) q^{33} +(0.0167225 + 0.0948379i) q^{35} +6.92274 q^{37} -12.0421 q^{39} +(0.688068 + 3.90223i) q^{41} +(9.81139 - 8.23273i) q^{43} +(3.39358 - 5.87786i) q^{45} +(-10.5733 + 3.84836i) q^{47} +(3.49536 + 6.05415i) q^{49} +(-1.44419 + 8.19040i) q^{51} +(9.54161 + 8.00636i) q^{53} +(-0.357781 - 0.130222i) q^{55} +(12.7793 - 4.75886i) q^{57} +(5.79519 + 2.10928i) q^{59} +(-3.93179 - 3.29916i) q^{61} +(-0.113498 + 0.643680i) q^{63} +(-1.92461 - 3.33352i) q^{65} +(11.4515 - 4.16802i) q^{67} +(-0.268306 + 0.464720i) q^{69} +(1.30881 - 1.09822i) q^{71} +(0.258258 + 1.46465i) q^{73} +3.12844 q^{75} +0.0366658 q^{77} +(2.60810 + 14.7913i) q^{79} +(12.7961 - 10.7372i) q^{81} +(-5.46582 + 9.46708i) q^{83} +(-2.49811 + 0.909237i) q^{85} +(-6.12238 - 10.6043i) q^{87} +(-0.400265 + 2.27002i) q^{89} +(0.283960 + 0.238271i) q^{91} +(-7.24366 - 2.63648i) q^{93} +(3.35979 + 2.77701i) q^{95} +(1.37387 + 0.500047i) q^{97} +(-1.97958 - 1.66107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.543249	+	3.08092i	0.313645	+	1.77877i	0.579720	+	0.814816i	$0.303162\pi$
$3$	0.543249	+	3.08092i	0.313645	+	1.77877i	−0.266075	+	0.963952i	$0.585727\pi$
$4$		0			0
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$		0			0
$7$	0.0481505	−	0.0833990i	0.0181992	−	0.0315219i	−0.856782	−	0.515678i	$-0.827540\pi$
$7$	0.0481505	−	0.0833990i	0.0181992	−	0.0315219i	0.874982	+	0.484156i	$0.160873\pi$
$8$		0			0
$9$	−6.37785	+	2.32135i	−2.12595	+	0.773782i
$10$		0			0
$11$	0.190371	+	0.329733i	0.0573991	+	0.0994181i	0.893297	−	0.449467i	$-0.148386\pi$
$11$	0.190371	+	0.329733i	0.0573991	+	0.0994181i	−0.835898	+	0.548885i	$0.815053\pi$
$12$		0			0
$13$	−0.668410	+	3.79074i	−0.185384	+	1.05136i	0.740078	+	0.672521i	$0.234789\pi$
$13$	−0.668410	+	3.79074i	−0.185384	+	1.05136i	−0.925461	+	0.378842i	$0.876322\pi$
$14$		0			0
$15$	−2.39653	−	2.01093i	−0.618781	−	0.519219i
$16$		0			0
$17$	2.49811	+	0.909237i	0.605880	+	0.220522i	0.626700	−	0.779261i	$-0.284405\pi$
$17$	2.49811	+	0.909237i	0.605880	+	0.220522i	−0.0208196	+	0.999783i	$0.506628\pi$
$18$		0			0
$19$	−0.788719	−	4.28695i	−0.180945	−	0.983493i
$19$	−0.788719	−	4.28695i	−0.180945	−	0.983493i
$20$		0			0
$21$	0.283103	+	0.103041i	0.0617782	+	0.0224854i
$22$		0			0
$23$	0.131397	+	0.110255i	0.0273982	+	0.0229898i	0.656384	−	0.754427i	$-0.272085\pi$
$23$	0.131397	+	0.110255i	0.0273982	+	0.0229898i	−0.628986	+	0.777417i	$0.716530\pi$
$24$		0			0
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$		0			0
$27$	−5.92397	−	10.2606i	−1.14007	−	1.97466i
$28$		0			0
$29$	−3.67797	+	1.33867i	−0.682982	+	0.248585i	−0.660127	−	0.751154i	$-0.729498\pi$
$29$	−3.67797	+	1.33867i	−0.682982	+	0.248585i	−0.0228544	+	0.999739i	$0.507275\pi$
$30$		0			0
$31$	−1.23201	+	2.13390i	−0.221275	+	0.383260i	−0.955195	−	0.295976i	$-0.904355\pi$
$31$	−1.23201	+	2.13390i	−0.221275	+	0.383260i	0.733920	+	0.679236i	$0.237689\pi$
$32$		0			0
$33$	−0.912460	+	0.765645i	−0.158839	+	0.133282i
$34$		0			0
$35$	0.0167225	+	0.0948379i	0.00282661	+	0.0160305i
$36$		0			0
$37$	6.92274			1.13809			0.569046	−	0.822306i	$-0.307313\pi$
$37$	6.92274			1.13809			0.569046	+	0.822306i	$0.307313\pi$
$38$		0			0
$39$	−12.0421			−1.92828
$40$		0			0
$41$	0.688068	+	3.90223i	0.107458	+	0.609426i	0.990210	+	0.139586i	$0.0445772\pi$
$41$	0.688068	+	3.90223i	0.107458	+	0.609426i	−0.882752	+	0.469840i	$0.844312\pi$
$42$		0			0
$43$	9.81139	−	8.23273i	1.49622	−	1.25548i	0.609841	−	0.792524i	$-0.291233\pi$
$43$	9.81139	−	8.23273i	1.49622	−	1.25548i	0.886382	−	0.462956i	$-0.153211\pi$
$44$		0			0
$45$	3.39358	−	5.87786i	0.505885	−	0.876219i
$46$		0			0
$47$	−10.5733	+	3.84836i	−1.54227	+	0.561341i	−0.966589	−	0.256331i	$-0.917486\pi$
$47$	−10.5733	+	3.84836i	−1.54227	+	0.561341i	−0.575684	+	0.817672i	$0.695264\pi$
$48$		0			0
$49$	3.49536	+	6.05415i	0.499338	+	0.864878i
$50$		0			0
$51$	−1.44419	+	8.19040i	−0.202227	+	1.14689i
$52$		0			0
$53$	9.54161	+	8.00636i	1.31064	+	1.09976i	0.988200	+	0.153169i	$0.0489480\pi$
$53$	9.54161	+	8.00636i	1.31064	+	1.09976i	0.322442	+	0.946589i	$0.395496\pi$
$54$		0			0
$55$	−0.357781	−	0.130222i	−0.0482432	−	0.0175591i
$56$		0			0
$57$	12.7793	−	4.75886i	1.69265	−	0.630326i
$58$		0			0
$59$	5.79519	+	2.10928i	0.754469	+	0.274604i	0.690485	−	0.723346i	$-0.257397\pi$
$59$	5.79519	+	2.10928i	0.754469	+	0.274604i	0.0639842	+	0.997951i	$0.479619\pi$
$60$		0			0
$61$	−3.93179	−	3.29916i	−0.503414	−	0.422414i	0.355391	−	0.934718i	$-0.384348\pi$
$61$	−3.93179	−	3.29916i	−0.503414	−	0.422414i	−0.858804	+	0.512304i	$0.828792\pi$
$62$		0			0
$63$	−0.113498	+	0.643680i	−0.0142994	+	0.0810961i
$64$		0			0
$65$	−1.92461	−	3.33352i	−0.238719	−	0.413473i
$66$		0			0
$67$	11.4515	−	4.16802i	1.39903	−	0.509205i	0.471139	−	0.882059i	$-0.343843\pi$
$67$	11.4515	−	4.16802i	1.39903	−	0.509205i	0.927890	+	0.372854i	$0.121621\pi$
$68$		0			0
$69$	−0.268306	+	0.464720i	−0.0323003	+	0.0559457i
$70$		0			0
$71$	1.30881	−	1.09822i	0.155327	−	0.130335i	−0.561812	−	0.827265i	$-0.689896\pi$
$71$	1.30881	−	1.09822i	0.155327	−	0.130335i	0.717139	+	0.696930i	$0.245451\pi$
$72$		0			0
$73$	0.258258	+	1.46465i	0.0302268	+	0.171424i	0.996184	−	0.0872770i	$-0.0278165\pi$
$73$	0.258258	+	1.46465i	0.0302268	+	0.171424i	−0.965957	+	0.258701i	$0.916705\pi$
$74$		0			0
$75$	3.12844			0.361242
$76$		0			0
$77$	0.0366658			0.00417846
$78$		0			0
$79$	2.60810	+	14.7913i	0.293434	+	1.66415i	0.673500	+	0.739188i	$0.264790\pi$
$79$	2.60810	+	14.7913i	0.293434	+	1.66415i	−0.380066	+	0.924960i	$0.624099\pi$
$80$		0			0
$81$	12.7961	−	10.7372i	1.42179	−	1.19302i
$82$		0			0
$83$	−5.46582	+	9.46708i	−0.599952	+	1.03915i	0.392876	+	0.919592i	$0.371480\pi$
$83$	−5.46582	+	9.46708i	−0.599952	+	1.03915i	−0.992828	+	0.119555i	$0.961853\pi$
$84$		0			0
$85$	−2.49811	+	0.909237i	−0.270958	+	0.0986206i
$86$		0			0
$87$	−6.12238	−	10.6043i	−0.656389	−	1.13690i
$88$		0			0
$89$	−0.400265	+	2.27002i	−0.0424280	+	0.240621i	−0.998645	−	0.0520369i	$-0.983429\pi$
$89$	−0.400265	+	2.27002i	−0.0424280	+	0.240621i	0.956217	+	0.292658i	$0.0945398\pi$
$90$		0			0
$91$	0.283960	+	0.238271i	0.0297671	+	0.0249776i
$92$		0			0
$93$	−7.24366	−	2.63648i	−0.751132	−	0.273390i
$94$		0			0
$95$	3.35979	+	2.77701i	0.344707	+	0.284916i
$96$		0			0
$97$	1.37387	+	0.500047i	0.139495	+	0.0507721i	0.410824	−	0.911715i	$-0.365241\pi$
$97$	1.37387	+	0.500047i	0.139495	+	0.0507721i	−0.271329	+	0.962487i	$0.587463\pi$
$98$		0			0
$99$	−1.97958	−	1.66107i	−0.198956	−	0.166944i
$100$		0			0
$101$	1.75107	−	9.93081i	0.174238	−	0.988153i	−0.764782	−	0.644290i	$-0.777153\pi$
$101$	1.75107	−	9.93081i	0.174238	−	0.988153i	0.939020	−	0.343863i	$-0.111736\pi$
$102$		0			0
$103$	−6.02829	−	10.4413i	−0.593986	−	1.02881i	−0.993689	−	0.112169i	$-0.964220\pi$
$103$	−6.02829	−	10.4413i	−0.593986	−	1.02881i	0.399704	−	0.916644i	$-0.369113\pi$
$104$		0			0
$105$	−0.283103	+	0.103041i	−0.0276280	+	0.0100558i
$106$		0			0
$107$	8.14790	−	14.1126i	0.787688	−	1.36431i	−0.139693	−	0.990195i	$-0.544611\pi$
$107$	8.14790	−	14.1126i	0.787688	−	1.36431i	0.927380	−	0.374120i	$-0.122055\pi$
$108$		0			0
$109$	10.6753	−	8.95764i	1.02251	−	0.857986i	0.0325676	−	0.999470i	$-0.489632\pi$
$109$	10.6753	−	8.95764i	1.02251	−	0.857986i	0.989941	+	0.141483i	$0.0451871\pi$
$110$		0			0
$111$	3.76077	+	21.3284i	0.356957	+	2.02440i
$112$		0			0
$113$	−12.7951			−1.20366			−0.601830	−	0.798624i	$-0.705562\pi$
$113$	−12.7951			−1.20366			−0.601830	+	0.798624i	$0.705562\pi$
$114$		0			0
$115$	−0.171527			−0.0159950
$116$		0			0
$117$	−4.53661	−	25.7284i	−0.419410	−	2.37859i
$118$		0			0
$119$	0.196114	−	0.164560i	0.0179778	−	0.0150851i
$120$		0			0
$121$	5.42752	−	9.40074i	0.493411	−	0.854612i
$122$		0			0
$123$	−11.6486	+	4.23976i	−1.05032	+	0.382286i
$124$		0			0
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$		0			0
$127$	1.89784	−	10.7632i	0.168406	−	0.955076i	−0.777077	−	0.629405i	$-0.783299\pi$
$127$	1.89784	−	10.7632i	0.168406	−	0.955076i	0.945483	−	0.325671i	$-0.105590\pi$
$128$		0			0
$129$	30.6944	+	25.7556i	2.70249	+	2.26766i
$130$		0			0
$131$	−11.3585	−	4.13416i	−0.992399	−	0.361204i	−0.205750	−	0.978605i	$-0.565963\pi$
$131$	−11.3585	−	4.13416i	−0.992399	−	0.361204i	−0.786649	+	0.617401i	$0.788186\pi$
$132$		0			0
$133$	−0.395504	−	0.140640i	−0.0342946	−	0.0121950i
$134$		0			0
$135$	11.1334	+	4.05223i	0.958212	+	0.348761i
$136$		0			0
$137$	15.5123	+	13.0164i	1.32530	+	1.11206i	0.985151	+	0.171692i	$0.0549235\pi$
$137$	15.5123	+	13.0164i	1.32530	+	1.11206i	0.340154	+	0.940370i	$0.389521\pi$
$138$		0			0
$139$	3.51481	−	19.9335i	0.298123	−	1.69074i	−0.356110	−	0.934444i	$-0.615897\pi$
$139$	3.51481	−	19.9335i	0.298123	−	1.69074i	0.654233	−	0.756293i	$-0.272992\pi$
$140$		0			0
$141$	−17.6004	−	30.4848i	−1.48222	−	2.56728i
$142$		0			0
$143$	−1.37718	+	0.501252i	−0.115165	+	0.0419168i
$144$		0			0
$145$	1.95701	−	3.38963i	0.162521	−	0.281494i
$146$		0			0
$147$	−16.7535	+	14.0578i	−1.38180	+	1.15947i
$148$		0			0
$149$	1.84464	+	10.4615i	0.151119	+	0.857036i	0.962249	+	0.272171i	$0.0877416\pi$
$149$	1.84464	+	10.4615i	0.151119	+	0.857036i	−0.811130	+	0.584865i	$0.801147\pi$
$150$		0			0
$151$	−13.5660			−1.10399			−0.551993	−	0.833849i	$-0.686132\pi$
$151$	−13.5660			−1.10399			−0.551993	+	0.833849i	$0.686132\pi$
$152$		0			0
$153$	−18.0432			−1.45871
$154$		0			0
$155$	−0.427872	−	2.42658i	−0.0343675	−	0.194908i
$156$		0			0
$157$	−7.93595	+	6.65905i	−0.633358	+	0.531450i	−0.901970	−	0.431798i	$-0.857879\pi$
$157$	−7.93595	+	6.65905i	−0.633358	+	0.531450i	0.268613	+	0.963248i	$0.413435\pi$
$158$		0			0
$159$	−19.4835	+	33.7464i	−1.54514	+	2.67626i
$160$		0			0
$161$	0.0155220	−	0.00564955i	0.00122331	−	0.000445247i
$162$		0			0
$163$	1.38192	+	2.39355i	0.108240	+	0.187477i	0.915057	−	0.403324i	$-0.132145\pi$
$163$	1.38192	+	2.39355i	0.108240	+	0.187477i	−0.806817	+	0.590801i	$0.798812\pi$
$164$		0			0
$165$	0.206838	−	1.17304i	0.0161023	−	0.0913207i
$166$		0			0
$167$	−4.50618	−	3.78114i	−0.348699	−	0.292593i	0.451568	−	0.892236i	$-0.350865\pi$
$167$	−4.50618	−	3.78114i	−0.348699	−	0.292593i	−0.800267	+	0.599643i	$0.795309\pi$
$168$		0			0
$169$	−1.70696	−	0.621281i	−0.131304	−	0.0477908i
$170$		0			0
$171$	14.9818	+	25.5106i	1.14569	+	1.95085i
$172$		0			0
$173$	7.18765	+	2.61609i	0.546467	+	0.198898i	0.600476	−	0.799643i	$-0.294978\pi$
$173$	7.18765	+	2.61609i	0.546467	+	0.198898i	−0.0540090	+	0.998540i	$0.517200\pi$
$174$		0			0
$175$	−0.0737708	−	0.0619010i	−0.00557655	−	0.00467928i
$176$		0			0
$177$	−3.35028	+	19.0004i	−0.251822	+	1.42815i
$178$		0			0
$179$	0.180527	+	0.312681i	0.0134932	+	0.0233709i	0.872693	−	0.488269i	$-0.162372\pi$
$179$	0.180527	+	0.312681i	0.0134932	+	0.0233709i	−0.859200	+	0.511640i	$0.829038\pi$
$180$		0			0
$181$	−19.5568	+	7.11810i	−1.45365	+	0.529084i	−0.943607	−	0.331067i	$-0.892591\pi$
$181$	−19.5568	+	7.11810i	−1.45365	+	0.529084i	−0.510039	+	0.860151i	$0.670369\pi$
$182$		0			0
$183$	8.02850	−	13.9058i	0.593484	−	1.02794i
$184$		0			0
$185$	−5.30313	+	4.44985i	−0.389894	+	0.327160i
$186$		0			0
$187$	0.175763	+	0.996800i	0.0128530	+	0.0728932i
$188$		0			0
$189$	−1.14097			−0.0829932
$190$		0			0
$191$	−22.1534			−1.60296			−0.801481	−	0.598020i	$-0.795954\pi$
$191$	−22.1534			−1.60296			−0.801481	+	0.598020i	$0.795954\pi$
$192$		0			0
$193$	−1.32392	−	7.50831i	−0.0952977	−	0.540460i	−0.994656	−	0.103247i	$-0.967077\pi$
$193$	−1.32392	−	7.50831i	−0.0952977	−	0.540460i	0.899358	−	0.437213i	$-0.144034\pi$
$194$		0			0
$195$	9.22477	−	7.74050i	0.660599	−	0.554308i
$196$		0			0
$197$	1.99852	−	3.46154i	0.142389	−	0.246625i	−0.786007	−	0.618218i	$-0.787855\pi$
$197$	1.99852	−	3.46154i	0.142389	−	0.246625i	0.928396	+	0.371593i	$0.121188\pi$
$198$		0			0
$199$	11.7475	−	4.27573i	0.832756	−	0.303099i	0.109767	−	0.993957i	$-0.464990\pi$
$199$	11.7475	−	4.27573i	0.832756	−	0.303099i	0.722990	+	0.690859i	$0.242767\pi$
$200$		0			0
$201$	19.0624	+	33.0170i	1.34455	+	2.32884i
$202$		0			0
$203$	−0.0654520	+	0.371197i	−0.00459383	+	0.0260529i
$204$		0			0
$205$	−3.03539	−	2.54700i	−0.212001	−	0.177890i
$206$		0			0
$207$	−1.09397	−	0.398173i	−0.0760363	−	0.0276750i
$208$		0			0
$209$	1.26340	−	1.07618i	0.0873910	−	0.0744408i
$210$		0			0
$211$	18.7594	+	6.82787i	1.29145	+	0.470050i	0.894203	−	0.447661i	$-0.147743\pi$
$211$	18.7594	+	6.82787i	1.29145	+	0.470050i	0.397248	+	0.917711i	$0.369965\pi$
$212$		0			0
$213$	4.09454	+	3.43573i	0.280553	+	0.235412i
$214$		0			0
$215$	−2.22406	+	12.6133i	−0.151680	+	0.860218i
$216$		0			0
$217$	0.118643	+	0.205497i	0.00805404	+	0.0139500i
$218$		0			0
$219$	−4.37217	+	1.59134i	−0.295444	+	0.107533i
$220$		0			0
$221$	−5.11644	+	8.86194i	−0.344169	+	0.596118i
$222$		0			0
$223$	12.3057	−	10.3257i	0.824052	−	0.691462i	−0.129865	−	0.991532i	$-0.541455\pi$
$223$	12.3057	−	10.3257i	0.824052	−	0.691462i	0.953917	+	0.300070i	$0.0970101\pi$
$224$		0			0
$225$	1.17858	+	6.68405i	0.0785719	+	0.445604i
$226$		0			0
$227$	14.8532			0.985840			0.492920	−	0.870075i	$-0.335929\pi$
$227$	14.8532			0.985840			0.492920	+	0.870075i	$0.335929\pi$
$228$		0			0
$229$	−9.64786			−0.637548			−0.318774	−	0.947831i	$-0.603271\pi$
$229$	−9.64786			−0.637548			−0.318774	+	0.947831i	$0.603271\pi$
$230$		0			0
$231$	0.0199187	+	0.112964i	0.00131055	+	0.00743251i
$232$		0			0
$233$	−12.7259	+	10.6783i	−0.833701	+	0.699558i	−0.956138	−	0.292918i	$-0.905374\pi$
$233$	−12.7259	+	10.6783i	−0.833701	+	0.699558i	0.122437	+	0.992476i	$0.460929\pi$
$234$		0			0
$235$	5.62593	−	9.74440i	0.366995	−	0.635654i
$236$		0			0
$237$	−44.1538	+	16.0707i	−2.86810	+	1.04390i
$238$		0			0
$239$	−4.04101	−	6.99924i	−0.261391	−	0.452743i	0.705221	−	0.708988i	$-0.250848\pi$
$239$	−4.04101	−	6.99924i	−0.261391	−	0.452743i	−0.966612	+	0.256245i	$0.917515\pi$
$240$		0			0
$241$	1.91566	−	10.8643i	0.123399	−	0.699828i	−0.858847	−	0.512231i	$-0.828819\pi$
$241$	1.91566	−	10.8643i	0.123399	−	0.699828i	0.982246	−	0.187597i	$-0.0600699\pi$
$242$		0			0
$243$	12.8038	+	10.7436i	0.821361	+	0.689204i
$244$		0			0
$245$	−6.56913	−	2.39097i	−0.419687	−	0.152753i
$246$		0			0
$247$	16.7779	−	0.124393i	1.06755	−	0.00791493i
$248$		0			0
$249$	−32.1366	−	11.6968i	−2.03657	−	0.741252i
$250$		0			0
$251$	−21.4319	−	17.9835i	−1.35277	−	1.13511i	−0.978144	−	0.207930i	$-0.933327\pi$
$251$	−21.4319	−	17.9835i	−1.35277	−	1.13511i	−0.374624	−	0.927177i	$-0.622228\pi$
$252$		0			0
$253$	−0.0113405	+	0.0643154i	−0.000712974	+	0.00404347i
$254$		0			0
$255$	−4.15838	−	7.20252i	−0.260408	−	0.451039i
$256$		0			0
$257$	5.77465	−	2.10180i	0.360213	−	0.131107i	−0.155573	−	0.987824i	$-0.549722\pi$
$257$	5.77465	−	2.10180i	0.360213	−	0.131107i	0.515786	+	0.856718i	$0.327500\pi$
$258$		0			0
$259$	0.333333	−	0.577350i	0.0207123	−	0.0358748i
$260$		0			0
$261$	20.3500	−	17.0757i	1.25963	−	1.05696i
$262$		0			0
$263$	−3.32800	−	18.8740i	−0.205213	−	1.16382i	−0.897104	−	0.441820i	$-0.854333\pi$
$263$	−3.32800	−	18.8740i	−0.205213	−	1.16382i	0.691890	−	0.722003i	$-0.256778\pi$
$264$		0			0
$265$	−12.4557			−0.765147
$266$		0			0
$267$	−7.21117			−0.441316
$268$		0			0
$269$	−3.13375	−	17.7724i	−0.191068	−	1.08360i	−0.917908	−	0.396794i	$-0.870123\pi$
$269$	−3.13375	−	17.7724i	−0.191068	−	1.08360i	0.726839	−	0.686808i	$-0.240988\pi$
$270$		0			0
$271$	2.77161	−	2.32565i	0.168363	−	0.141273i	−0.554713	−	0.832042i	$-0.687172\pi$
$271$	2.77161	−	2.32565i	0.168363	−	0.141273i	0.723076	+	0.690768i	$0.242728\pi$
$272$		0			0
$273$	−0.579831	+	1.00430i	−0.0350930	+	0.0607828i
$274$		0			0
$275$	0.357781	−	0.130222i	0.0215750	−	0.00785266i
$276$		0			0
$277$	2.71265	+	4.69844i	0.162987	+	0.282302i	0.935939	−	0.352163i	$-0.114554\pi$
$277$	2.71265	+	4.69844i	0.162987	+	0.282302i	−0.772952	+	0.634465i	$0.781220\pi$
$278$		0			0
$279$	2.90404	−	16.4696i	0.173860	−	0.986010i
$280$		0			0
$281$	−13.8745	−	11.6421i	−0.827682	−	0.694507i	0.127076	−	0.991893i	$-0.459441\pi$
$281$	−13.8745	−	11.6421i	−0.827682	−	0.694507i	−0.954757	+	0.297386i	$0.903885\pi$
$282$		0			0
$283$	0.741940	+	0.270044i	0.0441037	+	0.0160524i	0.363978	−	0.931408i	$-0.381418\pi$
$283$	0.741940	+	0.270044i	0.0441037	+	0.0160524i	−0.319874	+	0.947460i	$0.603641\pi$
$284$		0			0
$285$	−6.73054	+	11.8598i	−0.398683	+	0.702517i
$286$		0			0
$287$	0.358573	+	0.130510i	0.0211659	+	0.00770375i
$288$		0			0
$289$	−7.60893	−	6.38465i	−0.447584	−	0.375568i
$290$		0			0
$291$	−0.794252	+	4.50443i	−0.0465599	+	0.264054i
$292$		0			0
$293$	11.9210	+	20.6478i	0.696433	+	1.20626i	0.969695	+	0.244318i	$0.0785640\pi$
$293$	11.9210	+	20.6478i	0.696433	+	1.20626i	−0.273262	+	0.961940i	$0.588103\pi$
$294$		0			0
$295$	−5.79519	+	2.10928i	−0.337409	+	0.122807i
$296$		0			0
$297$	2.25551	−	3.90665i	0.130878	−	0.226687i
$298$		0			0
$299$	−0.505777	+	0.424397i	−0.0292498	+	0.0245435i
$300$		0			0
$301$	−0.214179	−	1.21467i	−0.0123451	−	0.0700124i
$302$		0			0
$303$	31.5473			1.81234
$304$		0			0
$305$	5.13258			0.293891
$306$		0			0
$307$	−1.00580	−	5.70416i	−0.0574039	−	0.325554i	0.942560	−	0.334036i	$-0.108411\pi$
$307$	−1.00580	−	5.70416i	−0.0574039	−	0.325554i	−0.999964	+	0.00848295i	$0.997300\pi$
$308$		0			0
$309$	28.8939	−	24.2449i	1.64372	−	1.37924i
$310$		0			0
$311$	7.43736	−	12.8819i	0.421734	−	0.730464i	−0.574375	−	0.818592i	$-0.694755\pi$
$311$	7.43736	−	12.8819i	0.421734	−	0.730464i	0.996109	+	0.0881277i	$0.0280884\pi$
$312$		0			0
$313$	−1.57814	+	0.574396i	−0.0892017	+	0.0324668i	−0.386236	−	0.922400i	$-0.626225\pi$
$313$	−1.57814	+	0.574396i	−0.0892017	+	0.0324668i	0.297034	+	0.954867i	$0.404003\pi$
$314$		0			0
$315$	−0.326805	−	0.566043i	−0.0184134	−	0.0318929i
$316$		0			0
$317$	1.85471	−	10.5186i	0.104171	−	0.590781i	−0.887378	−	0.461043i	$-0.847475\pi$
$317$	1.85471	−	10.5186i	0.104171	−	0.590781i	0.991548	−	0.129738i	$-0.0414136\pi$
$318$		0			0
$319$	−1.14158	−	0.957902i	−0.0639164	−	0.0536322i
$320$		0			0
$321$	47.9060	+	17.4364i	2.67385	+	0.973203i
$322$		0			0
$323$	1.92754	−	11.4264i	0.107251	−	0.635781i
$324$		0			0
$325$	3.61708	+	1.31651i	0.200640	+	0.0730269i
$326$		0			0
$327$	33.3971	+	28.0235i	1.84686	+	1.54970i
$328$		0			0
$329$	−0.188159	+	1.06710i	−0.0103735	+	0.0588313i
$330$		0			0
$331$	−8.30178	−	14.3791i	−0.456307	−	0.790347i	0.542455	−	0.840085i	$-0.317495\pi$
$331$	−8.30178	−	14.3791i	−0.456307	−	0.790347i	−0.998762	+	0.0497378i	$0.984161\pi$
$332$		0			0
$333$	−44.1522	+	16.0701i	−2.41953	+	0.880635i
$334$		0			0
$335$	−6.09324	+	10.5538i	−0.332909	+	0.576616i
$336$		0			0
$337$	−3.48289	+	2.92249i	−0.189725	+	0.159198i	−0.732703	−	0.680549i	$-0.761741\pi$
$337$	−3.48289	+	2.92249i	−0.189725	+	0.159198i	0.542978	+	0.839747i	$0.317297\pi$
$338$		0			0
$339$	−6.95092	−	39.4206i	−0.377522	−	2.14103i
$340$		0			0
$341$	−0.938156			−0.0508040
$342$		0			0
$343$	1.34732			0.0727484
$344$		0			0
$345$	−0.0931817	−	0.528460i	−0.00501674	−	0.0284513i
$346$		0			0
$347$	−13.3065	+	11.1655i	−0.714332	+	0.599396i	−0.925811	−	0.377986i	$-0.876617\pi$
$347$	−13.3065	+	11.1655i	−0.714332	+	0.599396i	0.211479	+	0.977383i	$0.432172\pi$
$348$		0			0
$349$	−6.05950	+	10.4954i	−0.324358	+	0.561804i	−0.981382	−	0.192065i	$-0.938482\pi$
$349$	−6.05950	+	10.4954i	−0.324358	+	0.561804i	0.657024	+	0.753869i	$0.271815\pi$
$350$		0			0
$351$	42.8550	−	15.5979i	2.28743	−	0.832557i
$352$		0			0
$353$	16.3694	+	28.3526i	0.871255	+	1.50906i	0.860700	+	0.509113i	$0.170027\pi$
$353$	16.3694	+	28.3526i	0.871255	+	1.50906i	0.0105551	+	0.999944i	$0.496640\pi$
$354$		0			0
$355$	−0.296683	+	1.68257i	−0.0157463	+	0.0893017i
$356$		0			0
$357$	0.613533	+	0.514815i	0.0324716	+	0.0272469i
$358$		0			0
$359$	4.48402	+	1.63205i	0.236658	+	0.0861364i	0.457627	−	0.889145i	$-0.348700\pi$
$359$	4.48402	+	1.63205i	0.236658	+	0.0861364i	−0.220969	+	0.975281i	$0.570922\pi$
$360$		0			0
$361$	−17.7558	+	6.76240i	−0.934518	+	0.355916i
$362$		0			0
$363$	31.9114	+	11.6148i	1.67491	+	0.609618i
$364$		0			0
$365$	−1.13930	−	0.955983i	−0.0596335	−	0.0500385i
$366$		0			0
$367$	1.53048	−	8.67977i	0.0798903	−	0.453080i	−0.918452	−	0.395532i	$-0.870560\pi$
$367$	1.53048	−	8.67977i	0.0798903	−	0.453080i	0.998343	−	0.0575488i	$-0.0183285\pi$
$368$		0			0
$369$	−13.4468	−	23.2906i	−0.700014	−	1.21246i
$370$		0			0
$371$	1.12716	−	0.410251i	0.0585190	−	0.0212992i
$372$		0			0
$373$	11.0167	−	19.0814i	0.570422	−	0.987999i	−0.426101	−	0.904676i	$-0.640113\pi$
$373$	11.0167	−	19.0814i	0.570422	−	0.987999i	0.996523	−	0.0833236i	$-0.0265535\pi$
$374$		0			0
$375$	−2.39653	+	2.01093i	−0.123756	+	0.103844i
$376$		0			0
$377$	−2.61617	−	14.8370i	−0.134739	−	0.764145i
$378$		0			0
$379$	18.1470			0.932150			0.466075	−	0.884745i	$-0.345668\pi$
$379$	18.1470			0.932150			0.466075	+	0.884745i	$0.345668\pi$
$380$		0			0
$381$	34.1914			1.75168
$382$		0			0
$383$	5.44319	+	30.8699i	0.278134	+	1.57738i	0.728828	+	0.684697i	$0.240066\pi$
$383$	5.44319	+	30.8699i	0.278134	+	1.57738i	−0.450694	+	0.892679i	$0.648823\pi$
$384$		0			0
$385$	−0.0280877	+	0.0235684i	−0.00143148	+	0.00120115i
$386$		0			0
$387$	−43.4645	+	75.2827i	−2.20943	+	3.82684i
$388$		0			0
$389$	−23.5340	+	8.56568i	−1.19322	+	0.434297i	−0.860854	−	0.508852i	$-0.830070\pi$
$389$	−23.5340	+	8.56568i	−1.19322	+	0.434297i	−0.332368	+	0.943150i	$0.607848\pi$
$390$		0			0
$391$	0.227996	+	0.394901i	0.0115303	+	0.0199710i
$392$		0			0
$393$	6.56651	−	37.2405i	0.331237	−	1.87854i
$394$		0			0
$395$	−11.5056	−	9.65431i	−0.578908	−	0.485761i
$396$		0			0
$397$	23.3194	+	8.48755i	1.17037	+	0.425978i	0.852789	−	0.522255i	$-0.174909\pi$
$397$	23.3194	+	8.48755i	1.17037	+	0.425978i	0.317576	+	0.948233i	$0.397131\pi$
$398$		0			0
$399$	0.218443	−	1.29492i	0.0109358	−	0.0648270i
$400$		0			0
$401$	4.53343	+	1.65003i	0.226389	+	0.0823988i	0.452724	−	0.891651i	$-0.350452\pi$
$401$	4.53343	+	1.65003i	0.226389	+	0.0823988i	−0.226335	+	0.974049i	$0.572675\pi$
$402$		0			0
$403$	−7.26558	−	6.09655i	−0.361924	−	0.303691i
$404$		0			0
$405$	−2.90064	+	16.4504i	−0.144134	+	0.817424i
$406$		0			0
$407$	1.31789	+	2.28265i	0.0653254	+	0.113147i
$408$		0			0
$409$	−11.7988	+	4.29440i	−0.583411	+	0.212344i	−0.616829	−	0.787097i	$-0.711583\pi$
$409$	−11.7988	+	4.29440i	−0.583411	+	0.212344i	0.0334179	+	0.999441i	$0.489361\pi$
$410$		0			0
$411$	−31.6753	+	54.8632i	−1.56243	+	2.70620i
$412$		0			0
$413$	0.454953	−	0.381751i	0.0223868	−	0.0187847i
$414$		0			0
$415$	−1.89826	−	10.7656i	−0.0931819	−	0.528461i
$416$		0			0
$417$	63.3229			3.10093
$418$		0			0
$419$	20.7543			1.01391			0.506957	−	0.861971i	$-0.330770\pi$
$419$	20.7543			1.01391			0.506957	+	0.861971i	$0.330770\pi$
$420$		0			0
$421$	5.81159	+	32.9592i	0.283240	+	1.60633i	0.711507	+	0.702679i	$0.248013\pi$
$421$	5.81159	+	32.9592i	0.283240	+	1.60633i	−0.428267	+	0.903652i	$0.640876\pi$
$422$		0			0
$423$	58.5015	−	49.0886i	2.84444	−	2.38677i
$424$		0			0
$425$	1.32922	−	2.30227i	0.0644764	−	0.111676i
$426$		0			0
$427$	−0.464464	+	0.169051i	−0.0224770	+	0.00818095i
$428$		0			0
$429$	−2.29247	−	3.97067i	−0.110681	−	0.191706i
$430$		0			0
$431$	4.47549	−	25.3817i	0.215577	−	1.22260i	−0.664327	−	0.747442i	$-0.731282\pi$
$431$	4.47549	−	25.3817i	0.215577	−	1.22260i	0.879903	−	0.475153i	$-0.157607\pi$
$432$		0			0
$433$	−8.54685	−	7.17166i	−0.410735	−	0.344648i	0.413890	−	0.910327i	$-0.364170\pi$
$433$	−8.54685	−	7.17166i	−0.410735	−	0.344648i	−0.824626	+	0.565679i	$0.808614\pi$
$434$		0			0
$435$	11.5063	+	4.18796i	0.551686	+	0.200797i
$436$		0			0
$437$	0.369023	−	0.650253i	0.0176528	−	0.0311058i
$438$		0			0
$439$	−1.18318	−	0.430641i	−0.0564699	−	0.0205534i	0.313631	−	0.949545i	$-0.398455\pi$
$439$	−1.18318	−	0.430641i	−0.0564699	−	0.0205534i	−0.370101	+	0.928992i	$0.620677\pi$
$440$		0			0
$441$	−36.3467	−	30.4985i	−1.73079	−	1.45231i
$442$		0			0
$443$	−1.51072	+	8.56770i	−0.0717764	+	0.407064i	0.927658	+	0.373431i	$0.121819\pi$
$443$	−1.51072	+	8.56770i	−0.0717764	+	0.407064i	−0.999434	+	0.0336328i	$0.989292\pi$
$444$		0			0
$445$	−1.15252	−	1.99622i	−0.0546345	−	0.0946298i
$446$		0			0
$447$	−31.2288	+	11.3663i	−1.47707	+	0.537610i
$448$		0			0
$449$	17.5925	−	30.4710i	0.830240	−	1.43802i	−0.0676084	−	0.997712i	$-0.521537\pi$
$449$	17.5925	−	30.4710i	0.830240	−	1.43802i	0.897848	−	0.440305i	$-0.145130\pi$
$450$		0			0
$451$	−1.15570	+	0.969751i	−0.0544200	+	0.0456638i
$452$		0			0
$453$	−7.36971	−	41.7957i	−0.346259	−	1.96373i
$454$		0			0
$455$	−0.370683			−0.0173779
$456$		0			0
$457$	−1.11871			−0.0523311			−0.0261655	−	0.999658i	$-0.508330\pi$
$457$	−1.11871			−0.0523311			−0.0261655	+	0.999658i	$0.508330\pi$
$458$		0			0
$459$	−5.46938	−	31.0184i	−0.255289	−	1.44782i
$460$		0			0
$461$	−1.43612	+	1.20504i	−0.0668866	+	0.0561245i	−0.675618	−	0.737252i	$-0.736123\pi$
$461$	−1.43612	+	1.20504i	−0.0668866	+	0.0561245i	0.608731	+	0.793376i	$0.291679\pi$
$462$		0			0
$463$	−0.683989	+	1.18470i	−0.0317877	+	0.0550578i	−0.881482	−	0.472218i	$-0.843453\pi$
$463$	−0.683989	+	1.18470i	−0.0317877	+	0.0550578i	0.849694	+	0.527276i	$0.176787\pi$
$464$		0			0
$465$	7.24366	−	2.63648i	0.335916	−	0.122264i
$466$		0			0
$467$	6.20452	+	10.7465i	0.287111	+	0.497290i	0.973119	−	0.230303i	$-0.0739719\pi$
$467$	6.20452	+	10.7465i	0.287111	+	0.497290i	−0.686008	+	0.727594i	$0.740639\pi$
$468$		0			0
$469$	0.203788	−	1.15574i	0.00941006	−	0.0533671i
$470$		0			0
$471$	−24.8272	−	20.8325i	−1.14398	−	0.959910i
$472$		0			0
$473$	4.58241	+	1.66786i	0.210699	+	0.0766883i
$474$		0			0
$475$	−4.35878	+	0.0323164i	−0.199995	+	0.00148278i
$476$		0			0
$477$	−79.4405	−	28.9140i	−3.63733	−	1.32388i
$478$		0			0
$479$	24.6697	+	20.7003i	1.12719	+	0.945823i	0.998945	−	0.0459199i	$-0.0146219\pi$
$479$	24.6697	+	20.7003i	1.12719	+	0.945823i	0.128243	+	0.991743i	$0.459066\pi$
$480$		0			0
$481$	−4.62723	+	26.2423i	−0.210984	+	1.19655i
$482$		0			0
$483$	0.0258381	+	0.0447529i	0.00117568	+	0.00203633i
$484$		0			0
$485$	−1.37387	+	0.500047i	−0.0623842	+	0.0227060i
$486$		0			0
$487$	−14.6132	+	25.3108i	−0.662186	+	1.14694i	0.317854	+	0.948140i	$0.397038\pi$
$487$	−14.6132	+	25.3108i	−0.662186	+	1.14694i	−0.980040	+	0.198800i	$0.936295\pi$
$488$		0			0
$489$	−6.62360	+	5.55786i	−0.299529	+	0.251335i
$490$		0			0
$491$	0.782012	+	4.43501i	0.0352917	+	0.200149i	0.997356	−	0.0726747i	$-0.0231535\pi$
$491$	0.782012	+	4.43501i	0.0352917	+	0.200149i	−0.962064	+	0.272824i	$0.912042\pi$
$492$		0			0
$493$	−10.4051			−0.468623
$494$		0			0
$495$	2.58416			0.116149
$496$		0			0
$497$	−0.0285708	−	0.162033i	−0.00128158	−	0.00726819i
$498$		0			0
$499$	−7.44052	+	6.24334i	−0.333083	+	0.279490i	−0.793955	−	0.607977i	$-0.791981\pi$
$499$	−7.44052	+	6.24334i	−0.333083	+	0.279490i	0.460871	+	0.887467i	$0.347537\pi$
$500$		0			0
$501$	9.20139	−	15.9373i	0.411088	−	0.712025i
$502$		0			0
$503$	−2.63383	+	0.958636i	−0.117437	+	0.0427435i	−0.400070	−	0.916485i	$-0.631014\pi$
$503$	−2.63383	+	0.958636i	−0.117437	+	0.0427435i	0.282633	+	0.959228i	$0.408792\pi$
$504$		0			0
$505$	5.04201	+	8.73301i	0.224366	+	0.388614i
$506$		0			0
$507$	0.986813	−	5.59650i	0.0438259	−	0.248549i
$508$		0			0
$509$	−19.6233	−	16.4659i	−0.869788	−	0.729838i	0.0942658	−	0.995547i	$-0.469950\pi$
$509$	−19.6233	−	16.4659i	−0.869788	−	0.729838i	−0.964053	+	0.265709i	$0.914394\pi$
$510$		0			0
$511$	0.134586	+	0.0489852i	0.00595372	+	0.00216698i
$512$		0			0
$513$	−39.3144	+	33.4885i	−1.73577	+	1.47855i
$514$		0			0
$515$	11.3295	+	4.12360i	0.499237	+	0.181707i
$516$		0			0
$517$	−3.28178	−	2.75374i	−0.144333	−	0.121109i
$518$		0			0
$519$	−4.15528	+	23.5657i	−0.182396	+	1.03442i
$520$		0			0
$521$	−10.3772	−	17.9738i	−0.454632	−	0.787445i	0.544035	−	0.839062i	$-0.316896\pi$
$521$	−10.3772	−	17.9738i	−0.454632	−	0.787445i	−0.998667	+	0.0516173i	$0.983562\pi$
$522$		0			0
$523$	3.77430	−	1.37373i	0.165039	−	0.0600692i	−0.258180	−	0.966097i	$-0.583123\pi$
$523$	3.77430	−	1.37373i	0.165039	−	0.0600692i	0.423218	+	0.906028i	$0.360900\pi$
$524$		0			0
$525$	0.150636	−	0.260909i	0.00657429	−	0.0113870i
$526$		0			0
$527$	−5.01791	+	4.21052i	−0.218584	+	0.183413i
$528$		0			0
$529$	−3.98880	−	22.6216i	−0.173426	−	0.983548i
$530$		0			0
$531$	−41.8572			−1.81645
$532$		0			0
$533$	−15.2523			−0.660648
$534$		0			0
$535$	2.82974	+	16.0482i	0.122340	+	0.693826i
$536$		0			0
$537$	−0.865274	+	0.726051i	−0.0373393	+	0.0313314i
$538$		0			0
$539$	−1.33083	+	2.30507i	−0.0573231	+	0.0992864i
$540$		0			0
$541$	19.5001	−	7.09746i	0.838376	−	0.305144i	0.113084	−	0.993585i	$-0.463927\pi$
$541$	19.5001	−	7.09746i	0.838376	−	0.305144i	0.725292	+	0.688442i	$0.241705\pi$
$542$		0			0
$543$	−32.5545	−	56.3860i	−1.39705	−	2.41975i
$544$		0			0
$545$	−2.41989	+	13.7239i	−0.103657	+	0.587867i
$546$		0			0
$547$	15.0644	+	12.6405i	0.644105	+	0.540469i	0.905276	−	0.424824i	$-0.139664\pi$
$547$	15.0644	+	12.6405i	0.644105	+	0.540469i	−0.261170	+	0.965293i	$0.584108\pi$
$548$		0			0
$549$	32.7348	+	11.9145i	1.39709	+	0.508499i
$550$		0			0
$551$	8.63970	+	14.7114i	0.368063	+	0.626728i
$552$		0			0
$553$	1.35916	+	0.494693i	0.0577973	+	0.0210365i
$554$		0			0
$555$	−16.5905	−	13.9211i	−0.704229	−	0.590918i
$556$		0			0
$557$	3.86522	−	21.9207i	0.163775	−	0.928812i	−0.786544	−	0.617534i	$-0.788132\pi$
$557$	3.86522	−	21.9207i	0.163775	−	0.928812i	0.950319	−	0.311278i	$-0.100757\pi$
$558$		0			0
$559$	24.6501	+	42.6953i	1.04259	+	1.80582i
$560$		0			0
$561$	−2.97558	+	1.08302i	−0.125629	+	0.0457252i
$562$		0			0
$563$	−12.3888	+	21.4580i	−0.522125	+	0.904348i	0.477543	+	0.878608i	$0.341527\pi$
$563$	−12.3888	+	21.4580i	−0.522125	+	0.904348i	−0.999669	+	0.0257394i	$0.991806\pi$
$564$		0			0
$565$	9.80161	−	8.22452i	0.412357	−	0.346008i
$566$		0			0
$567$	−0.279334	−	1.58418i	−0.0117309	−	0.0665295i
$568$		0			0
$569$	41.6154			1.74461			0.872304	−	0.488963i	$-0.162625\pi$
$569$	41.6154			1.74461			0.872304	+	0.488963i	$0.162625\pi$
$570$		0			0
$571$	−12.1626			−0.508991			−0.254496	−	0.967074i	$-0.581909\pi$
$571$	−12.1626			−0.508991			−0.254496	+	0.967074i	$0.581909\pi$
$572$		0			0
$573$	−12.0348	−	68.2527i	−0.502761	−	2.85130i
$574$		0			0
$575$	0.131397	−	0.110255i	0.00547964	−	0.00459796i
$576$		0			0
$577$	−19.5319	+	33.8302i	−0.813122	+	1.40837i	0.0975473	+	0.995231i	$0.468900\pi$
$577$	−19.5319	+	33.8302i	−0.813122	+	1.40837i	−0.910669	+	0.413137i	$0.864433\pi$
$578$		0			0
$579$	22.4133	−	8.15776i	0.931463	−	0.339025i
$580$		0			0
$581$	0.526363	+	0.911688i	0.0218372	+	0.0378232i
$582$		0			0
$583$	−0.823511	+	4.67036i	−0.0341063	+	0.193427i
$584$		0			0
$585$	20.0131	+	16.7930i	0.827442	+	0.694306i
$586$		0			0
$587$	−5.69284	−	2.07203i	−0.234969	−	0.0855216i	0.221852	−	0.975080i	$-0.428790\pi$
$587$	−5.69284	−	2.07203i	−0.234969	−	0.0855216i	−0.456821	+	0.889559i	$0.651012\pi$
$588$		0			0
$589$	10.1196	+	3.59851i	0.416972	+	0.148274i
$590$		0			0
$591$	11.7504	+	4.27680i	0.483348	+	0.175924i
$592$		0			0
$593$	22.5998	+	18.9635i	0.928062	+	0.778736i	0.975468	−	0.220139i	$-0.0706513\pi$
$593$	22.5998	+	18.9635i	0.928062	+	0.778736i	−0.0474068	+	0.998876i	$0.515096\pi$
$594$		0			0
$595$	−0.0444555	+	0.252120i	−0.00182250	+	0.0103359i
$596$		0			0
$597$	19.5550	+	33.8702i	0.800332	+	1.38622i
$598$		0			0
$599$	−22.8429	+	8.31415i	−0.933337	+	0.339707i	−0.763531	−	0.645771i	$-0.776536\pi$
$599$	−22.8429	+	8.31415i	−0.933337	+	0.339707i	−0.169805	+	0.985478i	$0.554314\pi$
$600$		0			0
$601$	−14.5601	+	25.2188i	−0.593917	+	1.02869i	0.399781	+	0.916610i	$0.369086\pi$
$601$	−14.5601	+	25.2188i	−0.593917	+	1.02869i	−0.993699	+	0.112084i	$0.964247\pi$
$602$		0			0
$603$	−63.3608	+	53.1660i	−2.58025	+	2.16509i
$604$		0			0
$605$	1.88496	+	10.6901i	0.0766344	+	0.434615i
$606$		0			0
$607$	16.5543			0.671920			0.335960	−	0.941876i	$-0.390939\pi$
$607$	16.5543			0.671920			0.335960	+	0.941876i	$0.390939\pi$
$608$		0			0
$609$	−1.17918			−0.0477829
$610$		0			0
$611$	−7.52086	−	42.6529i	−0.304261	−	1.72555i
$612$		0			0
$613$	−25.2751	+	21.2083i	−1.02085	+	0.856596i	−0.989734	−	0.142920i	$-0.954351\pi$
$613$	−25.2751	+	21.2083i	−1.02085	+	0.856596i	−0.0311169	+	0.999516i	$0.509906\pi$
$614$		0			0
$615$	6.19812	−	10.7355i	0.249932	−	0.432895i
$616$		0			0
$617$	30.4129	−	11.0694i	1.22438	−	0.445637i	0.352708	−	0.935733i	$-0.385261\pi$
$617$	30.4129	−	11.0694i	1.22438	−	0.445637i	0.871668	+	0.490097i	$0.163039\pi$
$618$		0			0
$619$	20.8433	+	36.1016i	0.837762	+	1.45105i	0.891762	+	0.452505i	$0.149470\pi$
$619$	20.8433	+	36.1016i	0.837762	+	1.45105i	−0.0539997	+	0.998541i	$0.517197\pi$
$620$		0			0
$621$	0.352895	−	2.00137i	0.0141612	−	0.0803120i
$622$		0			0
$623$	0.170044	+	0.142684i	0.00681267	+	0.00571651i
$624$		0			0
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$		0			0
$627$	4.00195	+	3.30779i	0.159823	+	0.132100i
$628$		0			0
$629$	17.2937	+	6.29441i	0.689547	+	0.250975i
$630$		0			0
$631$	−4.22290	−	3.54344i	−0.168111	−	0.141062i	0.554851	−	0.831950i	$-0.312775\pi$
$631$	−4.22290	−	3.54344i	−0.168111	−	0.141062i	−0.722962	+	0.690888i	$0.757220\pi$
$632$		0			0
$633$	−10.8451	+	61.5054i	−0.431053	+	2.44462i
$634$		0			0
$635$	5.46460	+	9.46497i	0.216856	+	0.375606i
$636$		0			0
$637$	−25.2860	+	9.20337i	−1.00187	+	0.364651i
$638$		0			0
$639$	−5.79804	+	10.0425i	−0.229367	+	0.397275i
$640$		0			0
$641$	25.7780	−	21.6303i	1.01817	−	0.854346i	0.0287732	−	0.999586i	$-0.490840\pi$
$641$	25.7780	−	21.6303i	1.01817	−	0.854346i	0.989396	+	0.145240i	$0.0463955\pi$
$642$		0			0
$643$	−3.98328	−	22.5903i	−0.157085	−	0.890874i	−0.956855	−	0.290567i	$-0.906156\pi$
$643$	−3.98328	−	22.5903i	−0.157085	−	0.890874i	0.799769	−	0.600307i	$-0.204955\pi$
$644$		0			0
$645$	−40.0687			−1.57770
$646$		0			0
$647$	−21.5785			−0.848338			−0.424169	−	0.905583i	$-0.639434\pi$
$647$	−21.5785			−0.848338			−0.424169	+	0.905583i	$0.639434\pi$
$648$		0			0
$649$	0.407740	+	2.31241i	0.0160052	+	0.0907700i
$650$		0			0
$651$	−0.568665	+	0.477166i	−0.0222877	+	0.0187016i
$652$		0			0
$653$	−2.26943	+	3.93077i	−0.0888097	+	0.153823i	−0.907008	−	0.421113i	$-0.861640\pi$
$653$	−2.26943	+	3.93077i	−0.0888097	+	0.153823i	0.818199	+	0.574936i	$0.194973\pi$
$654$		0			0
$655$	11.3585	−	4.13416i	0.443814	−	0.161535i
$656$		0			0
$657$	−5.04709	−	8.74182i	−0.196906	−	0.341051i
$658$		0			0
$659$	4.81363	−	27.2994i	0.187512	−	1.06343i	−0.735173	−	0.677880i	$-0.762899\pi$
$659$	4.81363	−	27.2994i	0.187512	−	1.06343i	0.922685	−	0.385555i	$-0.125990\pi$
$660$		0			0
$661$	−9.11550	−	7.64881i	−0.354552	−	0.297504i	0.448063	−	0.894002i	$-0.352114\pi$
$661$	−9.11550	−	7.64881i	−0.354552	−	0.297504i	−0.802615	+	0.596498i	$0.796558\pi$
$662$		0			0
$663$	−30.0824	−	10.9491i	−1.16830	−	0.425228i
$664$		0			0
$665$	0.393376	−	0.146489i	0.0152545	−	0.00568059i
$666$		0			0
$667$	−0.630870	−	0.229618i	−0.0244274	−	0.00889084i
$668$		0			0
$669$	38.4978	+	32.3035i	1.48841	+	1.24892i
$670$		0			0
$671$	0.339342	−	1.92450i	0.0131001	−	0.0742946i
$672$		0			0
$673$	12.4259	+	21.5222i	0.478982	+	0.829621i	0.999710	−	0.0241016i	$-0.00767253\pi$
$673$	12.4259	+	21.5222i	0.478982	+	0.829621i	−0.520727	+	0.853723i	$0.674339\pi$
$674$		0			0
$675$	−11.1334	+	4.05223i	−0.428526	+	0.155971i
$676$		0			0
$677$	17.1730	−	29.7445i	0.660012	−	1.14317i	−0.320600	−	0.947215i	$-0.603885\pi$
$677$	17.1730	−	29.7445i	0.660012	−	1.14317i	0.980612	−	0.195959i	$-0.0627820\pi$
$678$		0			0
$679$	0.107856	−	0.0905018i	0.00413913	−	0.00347314i
$680$		0			0
$681$	8.06897	+	45.7614i	0.309204	+	1.75358i
$682$		0			0
$683$	−3.79403			−0.145175			−0.0725873	−	0.997362i	$-0.523126\pi$
$683$	−3.79403			−0.145175			−0.0725873	+	0.997362i	$0.523126\pi$
$684$		0			0
$685$	−20.2499			−0.773707
$686$		0			0
$687$	−5.24119	−	29.7242i	−0.199964	−	1.13405i
$688$		0			0
$689$	−36.7278	+	30.8183i	−1.39922	+	1.17408i
$690$		0			0
$691$	−9.26742	+	16.0516i	−0.352549	+	0.610633i	−0.986695	−	0.162580i	$-0.948018\pi$
$691$	−9.26742	+	16.0516i	−0.352549	+	0.610633i	0.634146	+	0.773213i	$0.281352\pi$
$692$		0			0
$693$	−0.233849	+	0.0851142i	−0.00888320	+	0.00323322i
$694$		0			0
$695$	10.1205	+	17.5292i	0.383892	+	0.664921i
$696$		0			0
$697$	−1.82918	+	10.3738i	−0.0692852	+	0.392936i
$698$		0			0
$699$	−39.8123	−	33.4064i	−1.50584	−	1.26355i
$700$		0			0
$701$	44.4694	+	16.1855i	1.67958	+	0.611319i	0.993253	−	0.115970i	$-0.0369975\pi$
$701$	44.4694	+	16.1855i	1.67958	+	0.611319i	0.686332	+	0.727288i	$0.259220\pi$
$702$		0			0
$703$	−5.46010	−	29.6774i	−0.205932	−	1.11931i
$704$		0			0
$705$	33.0780	+	12.0394i	1.24579	+	0.453430i
$706$		0			0
$707$	−0.743905	−	0.624211i	−0.0279774	−	0.0234759i
$708$		0			0
$709$	3.80759	−	21.5939i	0.142997	−	0.810977i	−0.825956	−	0.563734i	$-0.809364\pi$
$709$	3.80759	−	21.5939i	0.142997	−	0.810977i	0.968953	−	0.247243i	$-0.0795246\pi$
$710$		0			0
$711$	−50.9697	−	88.2821i	−1.91151	−	3.31084i
$712$		0			0
$713$	−0.397156	+	0.144553i	−0.0148736	+	0.00541355i
$714$		0			0
$715$	0.732781	−	1.26921i	0.0274045	−	0.0474659i
$716$		0			0
$717$	19.3688	−	16.2523i	0.723341	−	0.606955i
$718$		0			0
$719$	0.963680	+	5.46530i	0.0359392	+	0.203821i	0.997490	−	0.0708053i	$-0.0225569\pi$
$719$	0.963680	+	5.46530i	0.0359392	+	0.203821i	−0.961551	+	0.274627i	$0.911446\pi$
$720$		0			0
$721$	−1.16106			−0.0432401
$722$		0			0
$723$	34.5126			1.28354
$724$		0			0
$725$	0.679661	+	3.85455i	0.0252420	+	0.143154i
$726$		0			0
$727$	−1.18242	+	0.992168i	−0.0438535	+	0.0367975i	−0.664451	−	0.747332i	$-0.731335\pi$
$727$	−1.18242	+	0.992168i	−0.0438535	+	0.0367975i	0.620597	+	0.784129i	$0.286890\pi$
$728$		0			0
$729$	−1.08840	+	1.88516i	−0.0403110	+	0.0698207i
$730$		0			0
$731$	31.9954	−	11.6454i	1.18339	−	0.430720i
$732$		0			0
$733$	3.11148	+	5.38924i	0.114925	+	0.199056i	0.917750	−	0.397159i	$-0.130004\pi$
$733$	3.11148	+	5.38924i	0.114925	+	0.199056i	−0.802825	+	0.596215i	$0.796671\pi$
$734$		0			0
$735$	3.79770	−	21.5378i	0.140080	−	0.794435i
$736$		0			0
$737$	3.55438	+	2.98248i	0.130927	+	0.109861i
$738$		0			0
$739$	−19.5054	−	7.09939i	−0.717518	−	0.261155i	−0.0426465	−	0.999090i	$-0.513579\pi$
$739$	−19.5054	−	7.09939i	−0.717518	−	0.261155i	−0.674872	+	0.737935i	$0.735801\pi$
$740$		0			0
$741$	9.49782	+	51.6237i	0.348911	+	1.89645i
$742$		0			0
$743$	13.4428	+	4.89277i	0.493168	+	0.179498i	0.576618	−	0.817014i	$-0.304372\pi$
$743$	13.4428	+	4.89277i	0.493168	+	0.179498i	−0.0834508	+	0.996512i	$0.526594\pi$
$744$		0			0
$745$	−8.13757	−	6.82823i	−0.298138	−	0.250167i
$746$		0			0
$747$	12.8838	−	73.0677i	0.471394	−	2.67341i
$748$		0			0
$749$	−0.784651	−	1.35905i	−0.0286705	−	0.0496588i
$750$		0			0
$751$	−3.00729	+	1.09457i	−0.109738	+	0.0399412i	−0.396305	−	0.918119i	$-0.629708\pi$
$751$	−3.00729	+	1.09457i	−0.109738	+	0.0399412i	0.286568	+	0.958060i	$0.407486\pi$
$752$		0			0
$753$	43.7627	−	75.7993i	1.59480	−	2.76228i
$754$		0			0
$755$	10.3922	−	8.72005i	0.378209	−	0.317355i
$756$		0			0
$757$	−4.25324	−	24.1213i	−0.154587	−	0.876704i	−0.959163	−	0.282855i	$-0.908719\pi$
$757$	−4.25324	−	24.1213i	−0.154587	−	0.876704i	0.804576	−	0.593850i	$-0.202393\pi$
$758$		0			0
$759$	−0.204311			−0.00741602
$760$		0			0
$761$	−9.40561			−0.340953			−0.170477	−	0.985362i	$-0.554531\pi$
$761$	−9.40561			−0.340953			−0.170477	+	0.985362i	$0.554531\pi$
$762$		0			0
$763$	−0.233038	−	1.32162i	−0.00843654	−	0.0478460i
$764$		0			0
$765$	13.8219	−	11.5979i	0.499732	−	0.419325i
$766$		0			0
$767$	−11.8693	+	20.5582i	−0.428575	+	0.742314i
$768$		0			0
$769$	−38.8442	+	14.1381i	−1.40076	+	0.509834i	−0.928403	−	0.371575i	$-0.878818\pi$
$769$	−38.8442	+	14.1381i	−1.40076	+	0.509834i	−0.472354	+	0.881409i	$0.656596\pi$
$770$		0			0
$771$	9.61255	+	16.6494i	0.346187	+	0.599614i
$772$		0			0
$773$	3.57247	−	20.2605i	0.128493	−	0.728719i	−0.850679	−	0.525686i	$-0.823809\pi$
$773$	3.57247	−	20.2605i	0.128493	−	0.728719i	0.979172	−	0.203034i	$-0.0650801\pi$
$774$		0			0
$775$	1.88755	+	1.58384i	0.0678026	+	0.0568932i
$776$		0			0
$777$	1.95985	+	0.713327i	0.0703092	+	0.0255905i
$778$		0			0
$779$	16.1860	−	6.02748i	0.579922	−	0.215957i
$780$		0			0
$781$	0.611279	+	0.222487i	0.0218733	+	0.00796123i
$782$		0			0
$783$	35.5238	+	29.8080i	1.26952	+	1.06525i
$784$		0			0
$785$	1.79893	−	10.2023i	0.0642067	−	0.364134i
$786$		0			0
$787$	24.2543	+	42.0097i	0.864572	+	1.49748i	0.867471	+	0.497487i	$0.165744\pi$
$787$	24.2543	+	42.0097i	0.864572	+	1.49748i	−0.00289884	+	0.999996i	$0.500923\pi$
$788$		0			0
$789$	56.3414	−	20.5066i	2.00581	−	0.730054i
$790$		0			0
$791$	−0.616089	+	1.06710i	−0.0219056	+	0.0379416i
$792$		0			0
$793$	15.1343	−	12.6992i	0.537435	−	0.450962i
$794$		0			0
$795$	−6.76654	−	38.3749i	−0.239984	−	1.36102i
$796$		0			0
$797$	−31.5050			−1.11597			−0.557983	−	0.829852i	$-0.688425\pi$
$797$	−31.5050			−1.11597			−0.557983	+	0.829852i	$0.688425\pi$
$798$		0			0
$799$	−29.9123			−1.05822
$800$		0			0
$801$	−2.71666	−	15.4070i	−0.0959886	−	0.544379i
$802$		0			0
$803$	−0.433779	+	0.363983i	−0.0153077	+	0.0128447i
$804$		0			0
$805$	−0.00825909	+	0.0143052i	−0.000291095	+	0.000504191i
$806$		0			0
$807$	53.0529	−	19.3097i	1.86755	−	0.679732i
$808$		0			0
$809$	−2.48715	−	4.30786i	−0.0874434	−	0.151456i	0.818986	−	0.573813i	$-0.194536\pi$
$809$	−2.48715	−	4.30786i	−0.0874434	−	0.151456i	−0.906430	+	0.422357i	$0.861203\pi$
$810$		0			0
$811$	−0.601992	+	3.41407i	−0.0211388	+	0.119884i	−0.993551	−	0.113384i	$-0.963831\pi$
$811$	−0.601992	+	3.41407i	−0.0211388	+	0.119884i	0.972412	+	0.233268i	$0.0749420\pi$
$812$		0			0
$813$	8.67081	+	7.27568i	0.304099	+	0.255169i
$814$		0			0
$815$	−2.59715	−	0.945286i	−0.0909743	−	0.0331119i
$816$		0			0
$817$	−43.0317	−	35.5676i	−1.50549	−	1.24435i
$818$		0			0
$819$	−2.36416	−	0.860485i	−0.0826106	−	0.0300678i
$820$		0			0
$821$	−23.2019	−	19.4687i	−0.809753	−	0.679463i	0.140796	−	0.990039i	$-0.455034\pi$
$821$	−23.2019	−	19.4687i	−0.809753	−	0.679463i	−0.950549	+	0.310575i	$0.899478\pi$
$822$		0			0
$823$	−1.28291	+	7.27572i	−0.0447193	+	0.253616i	−0.998969	−	0.0453947i	$-0.985545\pi$
$823$	−1.28291	+	7.27572i	−0.0447193	+	0.253616i	0.954250	+	0.299010i	$0.0966566\pi$
$824$		0			0
$825$	0.595566	+	1.03155i	0.0207349	+	0.0359140i
$826$		0			0
$827$	0.751234	−	0.273427i	0.0261230	−	0.00950798i	−0.328926	−	0.944356i	$-0.606687\pi$
$827$	0.751234	−	0.273427i	0.0261230	−	0.00950798i	0.355049	+	0.934848i	$0.384464\pi$
$828$		0			0
$829$	−3.06501	+	5.30876i	−0.106452	+	0.184381i	−0.914331	−	0.404968i	$-0.867282\pi$
$829$	−3.06501	+	5.30876i	−0.106452	+	0.184381i	0.807878	+	0.589349i	$0.200616\pi$
$830$		0			0
$831$	−13.0019	+	10.9099i	−0.451029	+	0.378459i
$832$		0			0
$833$	3.22714	+	18.3020i	0.111814	+	0.634127i
$834$		0			0
$835$	5.88241			0.203569
$836$		0			0
$837$	29.1935			1.00908
$838$		0			0
$839$	−2.48329	−	14.0835i	−0.0857329	−	0.486215i	−0.997196	−	0.0748336i	$-0.976157\pi$
$839$	−2.48329	−	14.0835i	−0.0857329	−	0.486215i	0.911463	−	0.411382i	$-0.134954\pi$
$840$		0			0
$841$	−10.4799	+	8.79366i	−0.361375	+	0.303230i
$842$		0			0
$843$	28.3309	−	49.0706i	0.975769	−	1.69008i
$844$		0			0
$845$	1.70696	−	0.621281i	0.0587210	−	0.0213727i
$846$		0			0
$847$	−0.522675	−	0.905299i	−0.0179593	−	0.0311065i
$848$		0			0
$849$	−0.428925	+	2.43256i	−0.0147207	+	0.0834851i
$850$		0			0
$851$	0.909629	+	0.763269i	0.0311817	+	0.0261645i
$852$		0			0
$853$	9.34352	+	3.40076i	0.319916	+	0.116440i	0.496987	−	0.867758i	$-0.334440\pi$
$853$	9.34352	+	3.40076i	0.319916	+	0.116440i	−0.177070	+	0.984198i	$0.556662\pi$
$854$		0			0
$855$	−27.8747	−	9.91213i	−0.953293	−	0.338988i
$856$		0			0
$857$	−18.0975	−	6.58696i	−0.618199	−	0.225006i	0.0138877	−	0.999904i	$-0.495579\pi$
$857$	−18.0975	−	6.58696i	−0.618199	−	0.225006i	−0.632087	+	0.774897i	$0.717801\pi$
$858$		0			0
$859$	7.12685	+	5.98014i	0.243165	+	0.204040i	0.756222	−	0.654315i	$-0.227043\pi$
$859$	7.12685	+	5.98014i	0.243165	+	0.204040i	−0.513057	+	0.858354i	$0.671487\pi$
$860$		0			0
$861$	−0.207296	+	1.17563i	−0.00706462	+	0.0400654i
$862$		0			0
$863$	−1.36497	−	2.36419i	−0.0464640	−	0.0804780i	0.841858	−	0.539699i	$-0.181462\pi$
$863$	−1.36497	−	2.36419i	−0.0464640	−	0.0804780i	−0.888322	+	0.459221i	$0.848129\pi$
$864$		0			0
$865$	−7.18765	+	2.61609i	−0.244388	+	0.0889498i
$866$		0			0
$867$	15.5370	−	26.9109i	0.527665	−	0.913943i
$868$		0			0
$869$	−4.38066	+	3.67581i	−0.148604	+	0.124693i
$870$		0			0
$871$	8.14557	+	46.1958i	0.276002	+	1.56528i
$872$		0			0
$873$	−9.92311			−0.335846
$874$		0			0
$875$	0.0963009			0.00325556
$876$		0			0
$877$	7.85822	+	44.5662i	0.265353	+	1.50489i	0.768027	+	0.640417i	$0.221239\pi$
$877$	7.85822	+	44.5662i	0.265353	+	1.50489i	−0.502674	+	0.864476i	$0.667650\pi$
$878$		0			0
$879$	−57.1381	+	47.9445i	−1.92722	+	1.61713i
$880$		0			0
$881$	25.5981	−	44.3373i	0.862423	−	1.49376i	−0.00715990	−	0.999974i	$-0.502279\pi$
$881$	25.5981	−	44.3373i	0.862423	−	1.49376i	0.869583	−	0.493787i	$-0.164388\pi$
$882$		0			0
$883$	−25.3496	+	9.22650i	−0.853082	+	0.310496i	−0.731296	−	0.682060i	$-0.761084\pi$
$883$	−25.3496	+	9.22650i	−0.853082	+	0.310496i	−0.121786	+	0.992556i	$0.538862\pi$
$884$		0			0
$885$	−9.64673	−	16.7086i	−0.324271	−	0.561655i
$886$		0			0
$887$	0.683969	−	3.87898i	0.0229654	−	0.130243i	−0.971170	−	0.238390i	$-0.923380\pi$
$887$	0.683969	−	3.87898i	0.0229654	−	0.130243i	0.994135	+	0.108146i	$0.0344915\pi$
$888$		0			0
$889$	−0.806256	−	0.676529i	−0.0270409	−	0.0226900i
$890$		0			0
$891$	5.97642	+	2.17524i	0.200218	+	0.0728732i
$892$		0			0
$893$	24.8371	+	42.2919i	0.831142	+	1.41524i
$894$		0			0
$895$	−0.339279	−	0.123488i	−0.0113409	−	0.00412773i
$896$		0			0
$897$	−1.58229	−	1.32770i	−0.0528313	−	0.0443307i
$898$		0			0
$899$	1.67470	−	9.49767i	0.0558542	−	0.316765i
$900$		0			0
$901$	16.5563	+	28.6763i	0.551570	+	0.955347i
$902$		0			0
$903$	3.62594	−	1.31974i	0.120664	−	0.0439180i
$904$		0			0
$905$	10.4060	−	18.0237i	0.345906	−	0.599126i
$906$		0			0
$907$	34.9575	−	29.3328i	1.16074	−	0.973980i	0.160828	−	0.986982i	$-0.448583\pi$
$907$	34.9575	−	29.3328i	1.16074	−	0.973980i	0.999915	+	0.0130026i	$0.00413899\pi$
$908$		0			0
$909$	11.8848	+	67.4021i	0.394194	+	2.23559i
$910$		0			0
$911$	−27.8259			−0.921912			−0.460956	−	0.887423i	$-0.652493\pi$
$911$	−27.8259			−0.921912			−0.460956	+	0.887423i	$0.652493\pi$
$912$		0			0
$913$	−4.16214			−0.137747
$914$		0			0
$915$	2.78827	+	15.8131i	0.0921773	+	0.522763i
$916$		0			0
$917$	−0.891703	+	0.748228i	−0.0294466	+	0.0247087i
$918$		0			0
$919$	1.29817	−	2.24849i	0.0428225	−	0.0741708i	−0.843820	−	0.536627i	$-0.819698\pi$
$919$	1.29817	−	2.24849i	0.0428225	−	0.0741708i	0.886642	+	0.462456i	$0.153032\pi$
$920$		0			0
$921$	17.0276	−	6.19755i	0.561080	−	0.204216i
$922$		0			0
$923$	3.28825	+	5.69542i	0.108234	+	0.187467i
$924$		0			0
$925$	1.20212	−	6.81757i	0.0395255	−	0.224160i
$926$		0			0
$927$	62.6855	+	52.5994i	2.05886	+	1.72759i
$928$		0			0
$929$	−55.8543	−	20.3293i	−1.83252	−	0.666983i	−0.992163	−	0.124952i	$-0.960122\pi$
$929$	−55.8543	−	20.3293i	−1.83252	−	0.666983i	−0.840358	−	0.542031i	$-0.817655\pi$
$930$		0			0
$931$	23.1969	−	19.7595i	0.760249	−	0.647590i
$932$		0			0
$933$	43.7283	+	15.9158i	1.43160	+	0.521060i
$934$		0			0
$935$	−0.775373	−	0.650615i	−0.0253574	−	0.0212774i
$936$		0			0
$937$	9.27418	−	52.5965i	0.302974	−	1.71825i	−0.329916	−	0.944010i	$-0.607020\pi$
$937$	9.27418	−	52.5965i	0.302974	−	1.71825i	0.632890	−	0.774242i	$-0.281869\pi$
$938$		0			0
$939$	−2.62699	−	4.55008i	−0.0857285	−	0.148486i
$940$		0			0
$941$	31.7155	−	11.5435i	1.03390	−	0.376307i	0.231332	−	0.972875i	$-0.425692\pi$
$941$	31.7155	−	11.5435i	1.03390	−	0.376307i	0.802563	+	0.596568i	$0.203469\pi$
$942$		0			0
$943$	−0.339831	+	0.588605i	−0.0110664	+	0.0191676i
$944$		0			0
$945$	0.874032	−	0.733400i	0.0284322	−	0.0238575i
$946$		0			0
$947$	−2.95013	−	16.7310i	−0.0958665	−	0.543686i	−0.994478	−	0.104941i	$-0.966534\pi$
$947$	−2.95013	−	16.7310i	−0.0958665	−	0.543686i	0.898612	−	0.438744i	$-0.144577\pi$
$948$		0			0
$949$	−5.72474			−0.185833
$950$		0			0
$951$	33.4144			1.08354
$952$		0			0
$953$	0.446428	+	2.53182i	0.0144612	+	0.0820136i	0.991184	−	0.132491i	$-0.0422975\pi$
$953$	0.446428	+	2.53182i	0.0144612	+	0.0820136i	−0.976723	+	0.214504i	$0.931186\pi$
$954$		0			0
$955$	16.9705	−	14.2399i	0.549152	−	0.460793i
$956$		0			0
$957$	2.33105	−	4.03750i	0.0753522	−	0.130514i
$958$		0			0
$959$	1.83247	−	0.666966i	0.0591737	−	0.0215375i
$960$		0			0
$961$	12.4643	+	21.5888i	0.402075	+	0.696414i
$962$		0			0
$963$	−19.2059	+	108.922i	−0.618901	+	3.50996i
$964$		0			0
$965$	5.84043	+	4.90070i	0.188010	+	0.157759i
$966$		0			0
$967$	−44.3252	−	16.1330i	−1.42540	−	0.518804i	−0.489791	−	0.871840i	$-0.662927\pi$
$967$	−44.3252	−	16.1330i	−1.42540	−	0.518804i	−0.935610	+	0.353036i	$0.885149\pi$
$968$		0			0
$969$	36.2509	−	0.268767i	1.16455	−	0.00863405i
$970$		0			0
$971$	26.8824	+	9.78441i	0.862698	+	0.313997i	0.735207	−	0.677843i	$-0.237085\pi$
$971$	26.8824	+	9.78441i	0.862698	+	0.313997i	0.127492	+	0.991840i	$0.459307\pi$
$972$		0			0
$973$	−1.49319	−	1.25294i	−0.0478696	−	0.0401674i
$974$		0			0
$975$	−2.09108	+	11.8591i	−0.0669683	+	0.379796i
$976$		0			0
$977$	−2.73858	−	4.74336i	−0.0876150	−	0.151754i	0.818888	−	0.573954i	$-0.194591\pi$
$977$	−2.73858	−	4.74336i	−0.0876150	−	0.151754i	−0.906503	+	0.422200i	$0.861258\pi$
$978$		0			0
$979$	−0.824697	+	0.300165i	−0.0263574	+	0.00959332i
$980$		0			0
$981$	−47.2917	+	81.9116i	−1.50991	+	2.61523i
$982$		0			0
$983$	−27.4300	+	23.0165i	−0.874883	+	0.734114i	−0.965120	−	0.261807i	$-0.915682\pi$
$983$	−27.4300	+	23.0165i	−0.874883	+	0.734114i	0.0902377	+	0.995920i	$0.471237\pi$
$984$		0			0
$985$	0.694080	+	3.93632i	0.0221152	+	0.125422i
$986$		0			0
$987$	−3.38987			−0.107901
$988$		0			0
$989$	2.19689			0.0698571
$990$		0			0
$991$	9.47965	+	53.7617i	0.301131	+	1.70780i	0.641180	+	0.767390i	$0.278445\pi$
$991$	9.47965	+	53.7617i	0.301131	+	1.70780i	−0.340049	+	0.940408i	$0.610444\pi$
$992$		0			0
$993$	39.7909	−	33.3885i	1.26273	−	1.05955i
$994$		0			0
$995$	−6.25070	+	10.8265i	−0.198161	+	0.343224i
$996$		0			0
$997$	−34.0482	+	12.3925i	−1.07832	+	0.392475i	−0.819281	−	0.573392i	$-0.805627\pi$
$997$	−34.0482	+	12.3925i	−1.07832	+	0.392475i	−0.259036	+	0.965868i	$0.583405\pi$
$998$		0			0
$999$	−41.0101	−	71.0316i	−1.29750	−	2.24734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.a.61.3	✓	18
19.5	even	9	inner	380.2.u.a.81.3	yes	18
19.9	even	9		7220.2.a.v.1.9		9
19.10	odd	18		7220.2.a.x.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.a.61.3	✓	18	1.1	even	1	trivial
380.2.u.a.81.3	yes	18	19.5	even	9	inner
7220.2.a.v.1.9		9	19.9	even	9
7220.2.a.x.1.1		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)

\(f(q)\)	\(=\)	\(q+(0.543249 + 3.08092i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(0.0481505 - 0.0833990i) q^{7} +(-6.37785 + 2.32135i) q^{9} +O(q^{10})\)	\(q+(0.543249 + 3.08092i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(0.0481505 - 0.0833990i) q^{7} +(-6.37785 + 2.32135i) q^{9} +(0.190371 + 0.329733i) q^{11} +(-0.668410 + 3.79074i) q^{13} +(-2.39653 - 2.01093i) q^{15} +(2.49811 + 0.909237i) q^{17} +(-0.788719 - 4.28695i) q^{19} +(0.283103 + 0.103041i) q^{21} +(0.131397 + 0.110255i) q^{23} +(0.173648 - 0.984808i) q^{25} +(-5.92397 - 10.2606i) q^{27} +(-3.67797 + 1.33867i) q^{29} +(-1.23201 + 2.13390i) q^{31} +(-0.912460 + 0.765645i) q^{33} +(0.0167225 + 0.0948379i) q^{35} +6.92274 q^{37} -12.0421 q^{39} +(0.688068 + 3.90223i) q^{41} +(9.81139 - 8.23273i) q^{43} +(3.39358 - 5.87786i) q^{45} +(-10.5733 + 3.84836i) q^{47} +(3.49536 + 6.05415i) q^{49} +(-1.44419 + 8.19040i) q^{51} +(9.54161 + 8.00636i) q^{53} +(-0.357781 - 0.130222i) q^{55} +(12.7793 - 4.75886i) q^{57} +(5.79519 + 2.10928i) q^{59} +(-3.93179 - 3.29916i) q^{61} +(-0.113498 + 0.643680i) q^{63} +(-1.92461 - 3.33352i) q^{65} +(11.4515 - 4.16802i) q^{67} +(-0.268306 + 0.464720i) q^{69} +(1.30881 - 1.09822i) q^{71} +(0.258258 + 1.46465i) q^{73} +3.12844 q^{75} +0.0366658 q^{77} +(2.60810 + 14.7913i) q^{79} +(12.7961 - 10.7372i) q^{81} +(-5.46582 + 9.46708i) q^{83} +(-2.49811 + 0.909237i) q^{85} +(-6.12238 - 10.6043i) q^{87} +(-0.400265 + 2.27002i) q^{89} +(0.283960 + 0.238271i) q^{91} +(-7.24366 - 2.63648i) q^{93} +(3.35979 + 2.77701i) q^{95} +(1.37387 + 0.500047i) q^{97} +(-1.97958 - 1.66107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 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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