LMFDB - Embedded newform 380.2.u.a.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("380.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 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			301.1
Root			$0.128174 + 0.726910i$ of defining polynomial
Character	$\chi$	$=$	380.301
Dual form			380.2.u.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.693610 + 0.252453i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-2.32856 - 4.03318i) q^{7} +(-1.88077 + 1.57815i) q^{9} +O(q^{10})$	\(q+(-0.693610 + 0.252453i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-2.32856 - 4.03318i) q^{7} +(-1.88077 + 1.57815i) q^{9} +(-1.20808 + 2.09246i) q^{11} +(-2.11186 - 0.768655i) q^{13} +(-0.128174 - 0.726910i) q^{15} +(-0.901391 - 0.756357i) q^{17} +(-3.98240 - 1.77215i) q^{19} +(2.63330 + 2.20960i) q^{21} +(-0.255223 - 1.44744i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(2.01330 - 3.48713i) q^{27} +(-3.72314 + 3.12409i) q^{29} +(-3.60610 - 6.24595i) q^{31} +(0.309690 - 1.75634i) q^{33} +(4.37626 - 1.59283i) q^{35} +2.81439 q^{37} +1.65886 q^{39} +(-5.05804 + 1.84097i) q^{41} +(-1.33878 + 7.59257i) q^{43} +(-1.22759 - 2.12624i) q^{45} +(4.70570 - 3.94855i) q^{47} +(-7.34438 + 12.7208i) q^{49} +(0.816159 + 0.297058i) q^{51} +(0.390796 + 2.21632i) q^{53} +(-1.85089 - 1.55308i) q^{55} +(3.20962 + 0.223809i) q^{57} +(8.78120 + 7.36830i) q^{59} +(-0.285673 - 1.62013i) q^{61} +(10.7445 + 3.91067i) q^{63} +(1.12370 - 1.94630i) q^{65} +(1.80864 - 1.51763i) q^{67} +(0.542437 + 0.939529i) q^{69} +(1.11027 - 6.29664i) q^{71} +(3.18662 - 1.15983i) q^{73} +0.738124 q^{75} +11.2524 q^{77} +(2.11795 - 0.770872i) q^{79} +(0.762904 - 4.32665i) q^{81} +(-5.11094 - 8.85241i) q^{83} +(0.901391 - 0.756357i) q^{85} +(1.79372 - 3.10682i) q^{87} +(5.26955 + 1.91796i) q^{89} +(1.81747 + 10.3074i) q^{91} +(4.07804 + 3.42188i) q^{93} +(2.43676 - 3.61417i) q^{95} +(4.19849 + 3.52295i) q^{97} +(-1.03010 - 5.84198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$	$1$

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
$3$	−0.693610	+	0.252453i	−0.400456	+	0.145754i	−0.534394	−	0.845236i	$-0.679460\pi$
$3$	−0.693610	+	0.252453i	−0.400456	+	0.145754i	0.133938	+	0.990990i	$0.457238\pi$
$4$		0			0
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$6$		0			0
$7$	−2.32856	−	4.03318i	−0.880113	−	1.52440i	−0.851215	−	0.524818i	$-0.824134\pi$
$7$	−2.32856	−	4.03318i	−0.880113	−	1.52440i	−0.0288981	−	0.999582i	$-0.509200\pi$
$8$		0			0
$9$	−1.88077	+	1.57815i	−0.626924	+	0.526052i
$10$		0			0
$11$	−1.20808	+	2.09246i	−0.364251	+	0.630901i	−0.988656	−	0.150200i	$-0.952008\pi$
$11$	−1.20808	+	2.09246i	−0.364251	+	0.630901i	0.624405	+	0.781101i	$0.285342\pi$
$12$		0			0
$13$	−2.11186	−	0.768655i	−0.585725	−	0.213187i	0.0321229	−	0.999484i	$-0.489773\pi$
$13$	−2.11186	−	0.768655i	−0.585725	−	0.213187i	−0.617848	+	0.786297i	$0.711995\pi$
$14$		0			0
$15$	−0.128174	−	0.726910i	−0.0330944	−	0.187687i
$16$		0			0
$17$	−0.901391	−	0.756357i	−0.218620	−	0.183444i	0.526900	−	0.849927i	$-0.323354\pi$
$17$	−0.901391	−	0.756357i	−0.218620	−	0.183444i	−0.745520	+	0.666484i	$0.767799\pi$
$18$		0			0
$19$	−3.98240	−	1.77215i	−0.913625	−	0.406558i
$19$	−3.98240	−	1.77215i	−0.913625	−	0.406558i
$20$		0			0
$21$	2.63330	+	2.20960i	0.574634	+	0.482175i
$22$		0			0
$23$	−0.255223	−	1.44744i	−0.0532178	−	0.301813i	0.946568	−	0.322504i	$-0.104525\pi$
$23$	−0.255223	−	1.44744i	−0.0532178	−	0.301813i	−0.999786	+	0.0206909i	$0.993413\pi$
$24$		0			0
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$		0			0
$27$	2.01330	−	3.48713i	0.387459	−	0.671099i
$28$		0			0
$29$	−3.72314	+	3.12409i	−0.691370	+	0.580128i	−0.919304	−	0.393548i	$-0.871247\pi$
$29$	−3.72314	+	3.12409i	−0.691370	+	0.580128i	0.227934	+	0.973677i	$0.426803\pi$
$30$		0			0
$31$	−3.60610	−	6.24595i	−0.647675	−	1.12181i	−0.983677	−	0.179945i	$-0.942408\pi$
$31$	−3.60610	−	6.24595i	−0.647675	−	1.12181i	0.336002	−	0.941861i	$-0.390925\pi$
$32$		0			0
$33$	0.309690	−	1.75634i	0.0539100	−	0.305739i
$34$		0			0
$35$	4.37626	−	1.59283i	0.739723	−	0.269237i
$36$		0			0
$37$	2.81439			0.462683			0.231341	−	0.972873i	$-0.425689\pi$
$37$	2.81439			0.462683			0.231341	+	0.972873i	$0.425689\pi$
$38$		0			0
$39$	1.65886			0.265630
$40$		0			0
$41$	−5.05804	+	1.84097i	−0.789933	+	0.287512i	−0.705308	−	0.708901i	$-0.749191\pi$
$41$	−5.05804	+	1.84097i	−0.789933	+	0.287512i	−0.0846245	+	0.996413i	$0.526969\pi$
$42$		0			0
$43$	−1.33878	+	7.59257i	−0.204161	+	1.15786i	0.694593	+	0.719403i	$0.255585\pi$
$43$	−1.33878	+	7.59257i	−0.204161	+	1.15786i	−0.898754	+	0.438453i	$0.855526\pi$
$44$		0			0
$45$	−1.22759	−	2.12624i	−0.182998	−	0.316961i
$46$		0			0
$47$	4.70570	−	3.94855i	0.686396	−	0.575955i	−0.231471	−	0.972842i	$-0.574354\pi$
$47$	4.70570	−	3.94855i	0.686396	−	0.575955i	0.917868	+	0.396887i	$0.129909\pi$
$48$		0			0
$49$	−7.34438	+	12.7208i	−1.04920	+	1.81726i
$50$		0			0
$51$	0.816159	+	0.297058i	0.114285	+	0.0415964i
$52$		0			0
$53$	0.390796	+	2.21632i	0.0536800	+	0.304434i	0.999813	−	0.0193442i	$-0.00615783\pi$
$53$	0.390796	+	2.21632i	0.0536800	+	0.304434i	−0.946133	+	0.323779i	$0.895047\pi$
$54$		0			0
$55$	−1.85089	−	1.55308i	−0.249574	−	0.209417i
$56$		0			0
$57$	3.20962	+	0.223809i	0.425124	+	0.0296442i
$58$		0			0
$59$	8.78120	+	7.36830i	1.14322	+	0.959271i	0.999539	−	0.0303534i	$-0.00966327\pi$
$59$	8.78120	+	7.36830i	1.14322	+	0.959271i	0.143676	+	0.989625i	$0.454108\pi$
$60$		0			0
$61$	−0.285673	−	1.62013i	−0.0365767	−	0.207437i	0.961042	−	0.276401i	$-0.0891417\pi$
$61$	−0.285673	−	1.62013i	−0.0365767	−	0.207437i	−0.997619	+	0.0689641i	$0.978031\pi$
$62$		0			0
$63$	10.7445	+	3.91067i	1.35368	+	0.492698i
$64$		0			0
$65$	1.12370	−	1.94630i	0.139378	−	0.241409i
$66$		0			0
$67$	1.80864	−	1.51763i	0.220961	−	0.185408i	−0.525587	−	0.850740i	$-0.676154\pi$
$67$	1.80864	−	1.51763i	0.220961	−	0.185408i	0.746548	+	0.665332i	$0.231710\pi$
$68$		0			0
$69$	0.542437	+	0.939529i	0.0653018	+	0.113106i
$70$		0			0
$71$	1.11027	−	6.29664i	0.131764	−	0.747273i	−0.845294	−	0.534302i	$-0.820575\pi$
$71$	1.11027	−	6.29664i	0.131764	−	0.747273i	0.977058	−	0.212972i	$-0.0683142\pi$
$72$		0			0
$73$	3.18662	−	1.15983i	0.372966	−	0.135748i	−0.148735	−	0.988877i	$-0.547520\pi$
$73$	3.18662	−	1.15983i	0.372966	−	0.135748i	0.521700	+	0.853129i	$0.325298\pi$
$74$		0			0
$75$	0.738124			0.0852312
$76$		0			0
$77$	11.2524			1.28233
$78$		0			0
$79$	2.11795	−	0.770872i	0.238289	−	0.0867299i	−0.220116	−	0.975474i	$-0.570643\pi$
$79$	2.11795	−	0.770872i	0.238289	−	0.0867299i	0.458404	+	0.888744i	$0.348421\pi$
$80$		0			0
$81$	0.762904	−	4.32665i	0.0847671	−	0.480738i
$82$		0			0
$83$	−5.11094	−	8.85241i	−0.560999	−	0.971678i	−0.997410	−	0.0719307i	$-0.977084\pi$
$83$	−5.11094	−	8.85241i	−0.560999	−	0.971678i	0.436411	−	0.899747i	$-0.356249\pi$
$84$		0			0
$85$	0.901391	−	0.756357i	0.0977696	−	0.0820385i
$86$		0			0
$87$	1.79372	−	3.10682i	0.192307	−	0.333086i
$88$		0			0
$89$	5.26955	+	1.91796i	0.558571	+	0.203303i	0.605851	−	0.795578i	$-0.292833\pi$
$89$	5.26955	+	1.91796i	0.558571	+	0.203303i	−0.0472794	+	0.998882i	$0.515055\pi$
$90$		0			0
$91$	1.81747	+	10.3074i	0.190523	+	1.08051i
$92$		0			0
$93$	4.07804	+	3.42188i	0.422873	+	0.354833i
$94$		0			0
$95$	2.43676	−	3.61417i	0.250006	−	0.370806i
$96$		0			0
$97$	4.19849	+	3.52295i	0.426292	+	0.357701i	0.830550	−	0.556943i	$-0.188026\pi$
$97$	4.19849	+	3.52295i	0.426292	+	0.357701i	−0.404259	+	0.914645i	$0.632470\pi$
$98$		0			0
$99$	−1.03010	−	5.84198i	−0.103529	−	0.587141i
$100$		0			0
$101$	11.5198	+	4.19286i	1.14626	+	0.417205i	0.844171	−	0.536075i	$-0.180093\pi$
$101$	11.5198	+	4.19286i	1.14626	+	0.417205i	0.302090	+	0.953279i	$0.402316\pi$
$102$		0			0
$103$	−6.87149	+	11.9018i	−0.677068	+	1.17272i	0.298792	+	0.954318i	$0.403416\pi$
$103$	−6.87149	+	11.9018i	−0.677068	+	1.17272i	−0.975860	+	0.218398i	$0.929917\pi$
$104$		0			0
$105$	−2.63330	+	2.20960i	−0.256984	+	0.215635i
$106$		0			0
$107$	−7.57368	−	13.1180i	−0.732176	−	1.26817i	−0.955951	−	0.293525i	$-0.905172\pi$
$107$	−7.57368	−	13.1180i	−0.732176	−	1.26817i	0.223776	−	0.974641i	$-0.428162\pi$
$108$		0			0
$109$	−2.38654	+	13.5347i	−0.228589	+	1.29639i	0.627116	+	0.778926i	$0.284235\pi$
$109$	−2.38654	+	13.5347i	−0.228589	+	1.29639i	−0.855704	+	0.517465i	$0.826876\pi$
$110$		0			0
$111$	−1.95209	+	0.710502i	−0.185284	+	0.0674379i
$112$		0			0
$113$	−19.0463			−1.79173			−0.895865	−	0.444327i	$-0.853443\pi$
$113$	−19.0463			−1.79173			−0.895865	+	0.444327i	$0.853443\pi$
$114$		0			0
$115$	1.46977			0.137057
$116$		0			0
$117$	5.18499	−	1.88718i	0.479352	−	0.174470i
$118$		0			0
$119$	−0.951584	+	5.39670i	−0.0872315	+	0.494715i
$120$		0			0
$121$	2.58107	+	4.47055i	0.234643	+	0.406413i
$122$		0			0
$123$	3.04354	−	2.55384i	0.274427	−	0.230272i
$124$		0			0
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$		0			0
$127$	−11.2619	−	4.09901i	−0.999336	−	0.363729i	−0.210008	−	0.977700i	$-0.567349\pi$
$127$	−11.2619	−	4.09901i	−0.999336	−	0.363729i	−0.789328	+	0.613971i	$0.789571\pi$
$128$		0			0
$129$	−0.988183	−	5.60426i	−0.0870046	−	0.493428i
$130$		0			0
$131$	7.33068	+	6.15117i	0.640484	+	0.537430i	0.904167	−	0.427179i	$-0.140493\pi$
$131$	7.33068	+	6.15117i	0.640484	+	0.537430i	−0.263683	+	0.964609i	$0.584937\pi$
$132$		0			0
$133$	2.12586	+	20.1883i	0.184335	+	1.75055i
$134$		0			0
$135$	3.08455	+	2.58825i	0.265476	+	0.222761i
$136$		0			0
$137$	−1.98184	−	11.2395i	−0.169320	−	0.960259i	−0.944498	−	0.328517i	$-0.893451\pi$
$137$	−1.98184	−	11.2395i	−0.169320	−	0.960259i	0.775178	−	0.631742i	$-0.217660\pi$
$138$		0			0
$139$	−19.6728	−	7.16031i	−1.66862	−	0.607329i	−0.676941	−	0.736038i	$-0.736695\pi$
$139$	−19.6728	−	7.16031i	−1.66862	−	0.607329i	−0.991682	+	0.128708i	$0.958917\pi$
$140$		0			0
$141$	−2.26709	+	3.92672i	−0.190924	+	0.330689i
$142$		0			0
$143$	4.15969	−	3.49039i	0.347851	−	0.291881i
$144$		0			0
$145$	−2.43011	−	4.20907i	−0.201809	−	0.349544i
$146$		0			0
$147$	1.88272	−	10.6774i	0.155284	−	0.880658i
$148$		0			0
$149$	19.8946	−	7.24104i	1.62983	−	0.593209i	0.644609	−	0.764512i	$-0.277020\pi$
$149$	19.8946	−	7.24104i	1.62983	−	0.593209i	0.985218	+	0.171303i	$0.0547978\pi$
$150$		0			0
$151$	−16.7285			−1.36134			−0.680671	−	0.732589i	$-0.738312\pi$
$151$	−16.7285			−1.36134			−0.680671	+	0.732589i	$0.738312\pi$
$152$		0			0
$153$	2.88896			0.233559
$154$		0			0
$155$	6.77725	−	2.46672i	0.544362	−	0.198132i
$156$		0			0
$157$	3.44927	−	19.5618i	0.275282	−	1.56120i	−0.462784	−	0.886471i	$-0.653149\pi$
$157$	3.44927	−	19.5618i	0.275282	−	1.56120i	0.738065	−	0.674729i	$-0.235740\pi$
$158$		0			0
$159$	−0.830576	−	1.43860i	−0.0658690	−	0.114088i
$160$		0			0
$161$	−5.24350	+	4.39982i	−0.413246	+	0.346755i
$162$		0			0
$163$	2.78567	−	4.82492i	0.218191	−	0.377917i	−0.736064	−	0.676912i	$-0.763318\pi$
$163$	2.78567	−	4.82492i	0.218191	−	0.377917i	0.954255	+	0.298994i	$0.0966512\pi$
$164$		0			0
$165$	1.67588	+	0.609969i	0.130467	+	0.0474860i
$166$		0			0
$167$	3.98022	+	22.5730i	0.307999	+	1.74675i	0.609043	+	0.793137i	$0.291554\pi$
$167$	3.98022	+	22.5730i	0.307999	+	1.74675i	−0.301044	+	0.953610i	$0.597335\pi$
$168$		0			0
$169$	−6.08944	−	5.10965i	−0.468419	−	0.393050i
$170$		0			0
$171$	10.2867	−	2.95184i	0.786644	−	0.225733i
$172$		0			0
$173$	−19.5400	−	16.3960i	−1.48560	−	1.24657i	−0.899943	−	0.436008i	$-0.856392\pi$
$173$	−19.5400	−	16.3960i	−1.48560	−	1.24657i	−0.585658	−	0.810558i	$-0.699164\pi$
$174$		0			0
$175$	0.808700	+	4.58637i	0.0611320	+	0.346697i
$176$		0			0
$177$	−7.95088	−	2.89388i	−0.597625	−	0.217518i
$178$		0			0
$179$	−2.19869	+	3.80824i	−0.164338	+	0.284641i	−0.936420	−	0.350881i	$-0.885882\pi$
$179$	−2.19869	+	3.80824i	−0.164338	+	0.284641i	0.772082	+	0.635523i	$0.219215\pi$
$180$		0			0
$181$	5.64119	−	4.73352i	0.419306	−	0.351840i	−0.408593	−	0.912717i	$-0.633980\pi$
$181$	5.64119	−	4.73352i	0.419306	−	0.351840i	0.827899	+	0.560877i	$0.189536\pi$
$182$		0			0
$183$	0.607153	+	1.05162i	0.0448821	+	0.0777380i
$184$		0			0
$185$	−0.488714	+	2.77163i	−0.0359310	+	0.203775i
$186$		0			0
$187$	2.67160	−	0.972384i	0.195367	−	0.0711078i
$188$		0			0
$189$	−18.7523			−1.36403
$190$		0			0
$191$	−14.9154			−1.07924			−0.539620	−	0.841908i	$-0.681432\pi$
$191$	−14.9154			−1.07924			−0.539620	+	0.841908i	$0.681432\pi$
$192$		0			0
$193$	−21.4669	+	7.81332i	−1.54522	+	0.562415i	−0.967291	−	0.253670i	$-0.918362\pi$
$193$	−21.4669	+	7.81332i	−1.54522	+	0.562415i	−0.577932	+	0.816085i	$0.696140\pi$
$194$		0			0
$195$	−0.288058	+	1.63366i	−0.0206282	+	0.116989i
$196$		0			0
$197$	0.984224	+	1.70473i	0.0701231	+	0.121457i	0.898955	−	0.438041i	$-0.144327\pi$
$197$	0.984224	+	1.70473i	0.0701231	+	0.121457i	−0.828832	+	0.559498i	$0.810994\pi$
$198$		0			0
$199$	−5.86623	+	4.92235i	−0.415846	+	0.348936i	−0.826580	−	0.562819i	$-0.809717\pi$
$199$	−5.86623	+	4.92235i	−0.415846	+	0.348936i	0.410734	+	0.911755i	$0.365272\pi$
$200$		0			0
$201$	−0.871360	+	1.50924i	−0.0614610	+	0.106454i
$202$		0			0
$203$	21.2696	+	7.74149i	1.49283	+	0.543346i
$204$		0			0
$205$	−0.934687	−	5.30088i	−0.0652814	−	0.370229i
$206$		0			0
$207$	2.76431	+	2.31953i	0.192133	+	0.161218i
$208$		0			0
$209$	8.51922	−	6.19211i	0.589287	−	0.428317i
$210$		0			0
$211$	−1.93264	−	1.62168i	−0.133048	−	0.111641i	0.573835	−	0.818971i	$-0.305455\pi$
$211$	−1.93264	−	1.62168i	−0.133048	−	0.111641i	−0.706883	+	0.707330i	$0.749899\pi$
$212$		0			0
$213$	0.819515	+	4.64770i	0.0561522	+	0.318455i
$214$		0			0
$215$	−7.24475	−	2.63687i	−0.494088	−	0.179833i
$216$		0			0
$217$	−16.7940	+	29.0881i	−1.14005	+	1.97463i
$218$		0			0
$219$	−1.91747	+	1.60895i	−0.129570	+	0.108722i
$220$		0			0
$221$	1.32224	+	2.29018i	0.0889433	+	0.154054i
$222$		0			0
$223$	3.84787	−	21.8224i	0.257673	−	1.46133i	−0.531445	−	0.847093i	$-0.678351\pi$
$223$	3.84787	−	21.8224i	0.257673	−	1.46133i	0.789118	−	0.614242i	$-0.210538\pi$
$224$		0			0
$225$	2.30711	−	0.839719i	0.153807	−	0.0559812i
$226$		0			0
$227$	−14.4646			−0.960049			−0.480024	−	0.877255i	$-0.659372\pi$
$227$	−14.4646			−0.960049			−0.480024	+	0.877255i	$0.659372\pi$
$228$		0			0
$229$	17.0323			1.12553			0.562764	−	0.826618i	$-0.309738\pi$
$229$	17.0323			1.12553			0.562764	+	0.826618i	$0.309738\pi$
$230$		0			0
$231$	−7.80476	+	2.84070i	−0.513515	+	0.186904i
$232$		0			0
$233$	4.06307	−	23.0428i	0.266181	−	1.50958i	−0.499472	−	0.866330i	$-0.666473\pi$
$233$	4.06307	−	23.0428i	0.266181	−	1.50958i	0.765652	−	0.643255i	$-0.222416\pi$
$234$		0			0
$235$	3.07142	+	5.31986i	0.200358	+	0.347030i
$236$		0			0
$237$	−1.27442	+	1.06937i	−0.0827828	+	0.0694630i
$238$		0			0
$239$	−12.0058	+	20.7947i	−0.776593	+	1.34510i	0.157302	+	0.987551i	$0.449721\pi$
$239$	−12.0058	+	20.7947i	−0.776593	+	1.34510i	−0.933895	+	0.357548i	$0.883613\pi$
$240$		0			0
$241$	−23.6077	−	8.59251i	−1.52071	−	0.553492i	−0.559382	−	0.828910i	$-0.688962\pi$
$241$	−23.6077	−	8.59251i	−1.52071	−	0.553492i	−0.961325	+	0.275418i	$0.911184\pi$
$242$		0			0
$243$	2.66075	+	15.0899i	0.170687	+	0.968015i
$244$		0			0
$245$	−11.2522	−	9.44175i	−0.718879	−	0.603211i
$246$		0			0
$247$	7.04811	+	6.80362i	0.448460	+	0.432904i
$248$		0			0
$249$	5.77982	+	4.84984i	0.366281	+	0.307346i
$250$		0			0
$251$	−2.25159	−	12.7694i	−0.142119	−	0.805998i	−0.969635	−	0.244556i	$-0.921358\pi$
$251$	−2.25159	−	12.7694i	−0.142119	−	0.805998i	0.827516	−	0.561442i	$-0.189753\pi$
$252$		0			0
$253$	3.33705	+	1.21459i	0.209799	+	0.0763604i
$254$		0			0
$255$	−0.434269	+	0.752176i	−0.0271950	+	0.0471031i
$256$		0			0
$257$	−1.77328	+	1.48796i	−0.110614	+	0.0928163i	−0.696417	−	0.717637i	$-0.745224\pi$
$257$	−1.77328	+	1.48796i	−0.110614	+	0.0928163i	0.585803	+	0.810453i	$0.300779\pi$
$258$		0			0
$259$	−6.55348	−	11.3510i	−0.407213	−	0.705314i
$260$		0			0
$261$	2.07209	−	11.7514i	0.128259	−	0.727392i
$262$		0			0
$263$	7.50002	−	2.72978i	0.462471	−	0.168326i	−0.100268	−	0.994960i	$-0.531970\pi$
$263$	7.50002	−	2.72978i	0.462471	−	0.168326i	0.562739	+	0.826635i	$0.309748\pi$
$264$		0			0
$265$	−2.25051			−0.138247
$266$		0			0
$267$	−4.13921			−0.253315
$268$		0			0
$269$	21.9625	−	7.99371i	1.33908	−	0.487385i	0.429557	−	0.903040i	$-0.358670\pi$
$269$	21.9625	−	7.99371i	1.33908	−	0.487385i	0.909523	+	0.415654i	$0.136447\pi$
$270$		0			0
$271$	4.18967	−	23.7608i	0.254504	−	1.44336i	−0.542838	−	0.839837i	$-0.682650\pi$
$271$	4.18967	−	23.7608i	0.254504	−	1.44336i	0.797342	−	0.603527i	$-0.206239\pi$
$272$		0			0
$273$	−3.86275	−	6.69048i	−0.233784	−	0.404926i
$274$		0			0
$275$	1.85089	−	1.55308i	0.111613	−	0.0936544i
$276$		0			0
$277$	6.69101	−	11.5892i	0.402024	−	0.696326i	−0.591946	−	0.805978i	$-0.701640\pi$
$277$	6.69101	−	11.5892i	0.402024	−	0.696326i	0.993970	+	0.109652i	$0.0349735\pi$
$278$		0			0
$279$	16.6393	+	6.05622i	0.996171	+	0.362576i
$280$		0			0
$281$	0.871304	+	4.94141i	0.0519777	+	0.294780i	0.999705	−	0.0243024i	$-0.00773645\pi$
$281$	0.871304	+	4.94141i	0.0519777	+	0.294780i	−0.947727	+	0.319082i	$0.896625\pi$
$282$		0			0
$283$	2.46269	+	2.06644i	0.146392	+	0.122837i	0.713042	−	0.701121i	$-0.247317\pi$
$283$	2.46269	+	2.06644i	0.146392	+	0.122837i	−0.566651	+	0.823958i	$0.691761\pi$
$284$		0			0
$285$	−0.777753	+	3.12199i	−0.0460701	+	0.184931i
$286$		0			0
$287$	19.2029	+	16.1132i	1.13351	+	0.951130i
$288$		0			0
$289$	−2.71159	−	15.3782i	−0.159505	−	0.904599i
$290$		0			0
$291$	−3.80149	−	1.38363i	−0.222847	−	0.0811098i
$292$		0			0
$293$	−9.11970	+	15.7958i	−0.532779	+	0.922800i	0.466489	+	0.884527i	$0.345519\pi$
$293$	−9.11970	+	15.7958i	−0.532779	+	0.922800i	−0.999267	+	0.0382724i	$0.987815\pi$
$294$		0			0
$295$	−8.78120	+	7.36830i	−0.511261	+	0.428999i
$296$		0			0
$297$	4.86446	+	8.42549i	0.282265	+	0.488897i
$298$		0			0
$299$	−0.573588	+	3.25298i	−0.0331715	+	0.188125i
$300$		0			0
$301$	33.7397	−	12.2802i	1.94472	−	0.707821i
$302$		0			0
$303$	−9.04873			−0.519836
$304$		0			0
$305$	1.64513			0.0941996
$306$		0			0
$307$	−16.3329	+	5.94469i	−0.932167	+	0.339281i	−0.763068	−	0.646318i	$-0.776308\pi$
$307$	−16.3329	+	5.94469i	−0.932167	+	0.339281i	−0.169099	+	0.985599i	$0.554086\pi$
$308$		0			0
$309$	1.76149	−	9.98992i	0.100208	−	0.568307i
$310$		0			0
$311$	2.37948	+	4.12138i	0.134928	+	0.233702i	0.925570	−	0.378577i	$-0.123586\pi$
$311$	2.37948	+	4.12138i	0.134928	+	0.233702i	−0.790642	+	0.612279i	$0.790253\pi$
$312$		0			0
$313$	6.19056	−	5.19450i	0.349911	−	0.293611i	−0.450843	−	0.892603i	$-0.648877\pi$
$313$	6.19056	−	5.19450i	0.349911	−	0.293611i	0.800754	+	0.598993i	$0.204432\pi$
$314$		0			0
$315$	−5.71702	+	9.90216i	−0.322117	+	0.557924i
$316$		0			0
$317$	10.1397	+	3.69056i	0.569503	+	0.207282i	0.610691	−	0.791869i	$-0.290892\pi$
$317$	10.1397	+	3.69056i	0.569503	+	0.207282i	−0.0411875	+	0.999151i	$0.513114\pi$
$318$		0			0
$319$	−2.03917	−	11.5647i	−0.114171	−	0.647498i
$320$		0			0
$321$	8.56487	+	7.18678i	0.478044	+	0.401127i
$322$		0			0
$323$	2.24932	+	4.60951i	0.125156	+	0.256480i
$324$		0			0
$325$	1.72161	+	1.44460i	0.0954975	+	0.0801320i
$326$		0			0
$327$	−1.76156	−	9.99031i	−0.0974145	−	0.552465i
$328$		0			0
$329$	−26.8827	−	9.78450i	−1.48209	−	0.539437i
$330$		0			0
$331$	−11.4550	+	19.8406i	−0.629622	+	1.09054i	0.358006	+	0.933719i	$0.383457\pi$
$331$	−11.4550	+	19.8406i	−0.629622	+	1.09054i	−0.987628	+	0.156817i	$0.949877\pi$
$332$		0			0
$333$	−5.29322	+	4.44154i	−0.290067	+	0.243395i
$334$		0			0
$335$	1.18051	+	2.04470i	0.0644980	+	0.111714i
$336$		0			0
$337$	−5.07731	+	28.7949i	−0.276579	+	1.56856i	0.457322	+	0.889301i	$0.348809\pi$
$337$	−5.07731	+	28.7949i	−0.276579	+	1.56856i	−0.733901	+	0.679256i	$0.762303\pi$
$338$		0			0
$339$	13.2107	−	4.80831i	0.717509	−	0.261152i
$340$		0			0
$341$	17.4259			0.943664
$342$		0			0
$343$	35.8075			1.93342
$344$		0			0
$345$	−1.01945	+	0.371049i	−0.0548853	+	0.0199766i
$346$		0			0
$347$	−4.61087	+	26.1496i	−0.247525	+	1.40378i	0.567031	+	0.823696i	$0.308092\pi$
$347$	−4.61087	+	26.1496i	−0.247525	+	1.40378i	−0.814556	+	0.580085i	$0.803019\pi$
$348$		0			0
$349$	8.16447	+	14.1413i	0.437034	+	0.756965i	0.997459	−	0.0712400i	$-0.0226956\pi$
$349$	8.16447	+	14.1413i	0.437034	+	0.756965i	−0.560425	+	0.828205i	$0.689362\pi$
$350$		0			0
$351$	−6.93221	+	5.81682i	−0.370014	+	0.310479i
$352$		0			0
$353$	1.94078	−	3.36153i	0.103297	−	0.178916i	−0.809744	−	0.586783i	$-0.800394\pi$
$353$	1.94078	−	3.36153i	0.103297	−	0.178916i	0.913041	+	0.407867i	$0.133727\pi$
$354$		0			0
$355$	6.00818	+	2.18680i	0.318881	+	0.116063i
$356$		0			0
$357$	−0.702387	−	3.98343i	−0.0371743	−	0.210826i
$358$		0			0
$359$	0.264938	+	0.222310i	0.0139829	+	0.0117331i	0.649752	−	0.760146i	$-0.274873\pi$
$359$	0.264938	+	0.222310i	0.0139829	+	0.0117331i	−0.635769	+	0.771879i	$0.719317\pi$
$360$		0			0
$361$	12.7190	+	14.1148i	0.669420	+	0.742884i
$362$		0			0
$363$	−2.91886	−	2.44921i	−0.153200	−	0.128550i
$364$		0			0
$365$	0.588864	+	3.33961i	0.0308225	+	0.174803i
$366$		0			0
$367$	−3.13757	−	1.14198i	−0.163780	−	0.0596110i	0.258829	−	0.965923i	$-0.416663\pi$
$367$	−3.13757	−	1.14198i	−0.163780	−	0.0596110i	−0.422609	+	0.906312i	$0.638886\pi$
$368$		0			0
$369$	6.60767	−	11.4448i	0.343981	−	0.595793i
$370$		0			0
$371$	8.02882	−	6.73698i	0.416835	−	0.349766i
$372$		0			0
$373$	−10.4571	−	18.1123i	−0.541450	−	0.937818i	−0.998821	−	0.0485425i	$-0.984542\pi$
$373$	−10.4571	−	18.1123i	−0.541450	−	0.937818i	0.457372	−	0.889276i	$-0.348791\pi$
$374$		0			0
$375$	−0.128174	+	0.726910i	−0.00661887	+	0.0375375i
$376$		0			0
$377$	10.2641	−	3.73583i	0.528628	−	0.192405i
$378$		0			0
$379$	16.4497			0.844966			0.422483	−	0.906371i	$-0.361159\pi$
$379$	16.4497			0.844966			0.422483	+	0.906371i	$0.361159\pi$
$380$		0			0
$381$	8.84620			0.453205
$382$		0			0
$383$	22.2497	−	8.09821i	1.13690	−	0.413799i	0.296110	−	0.955154i	$-0.404311\pi$
$383$	22.2497	−	8.09821i	1.13690	−	0.413799i	0.840794	+	0.541354i	$0.182088\pi$
$384$		0			0
$385$	−1.95395	+	11.0814i	−0.0995827	+	0.564762i
$386$		0			0
$387$	−9.46433	−	16.3927i	−0.481099	−	0.833287i
$388$		0			0
$389$	−6.89298	+	5.78389i	−0.349488	+	0.293255i	−0.800584	−	0.599220i	$-0.795477\pi$
$389$	−6.89298	+	5.78389i	−0.349488	+	0.293255i	0.451097	+	0.892475i	$0.351033\pi$
$390$		0			0
$391$	−0.864728	+	1.49775i	−0.0437312	+	0.0757447i
$392$		0			0
$393$	−6.63751	−	2.41586i	−0.334818	−	0.121864i
$394$		0			0
$395$	0.391382	+	2.21964i	0.0196926	+	0.111682i
$396$		0			0
$397$	−3.47331	−	2.91445i	−0.174320	−	0.146272i	0.551453	−	0.834206i	$-0.314074\pi$
$397$	−3.47331	−	2.91445i	−0.174320	−	0.146272i	−0.725774	+	0.687934i	$0.758518\pi$
$398$		0			0
$399$	−6.57112	−	13.4661i	−0.328967	−	0.674149i
$400$		0			0
$401$	29.5693	+	24.8115i	1.47662	+	1.23903i	0.909707	+	0.415250i	$0.136306\pi$
$401$	29.5693	+	24.8115i	1.47662	+	1.23903i	0.566911	+	0.823779i	$0.308138\pi$
$402$		0			0
$403$	2.81461	+	15.9624i	0.140206	+	0.795146i
$404$		0			0
$405$	4.12844	+	1.50263i	0.205144	+	0.0746662i
$406$		0			0
$407$	−3.40002	+	5.88900i	−0.168533	+	0.291907i
$408$		0			0
$409$	13.6673	−	11.4682i	0.675804	−	0.567067i	−0.238973	−	0.971026i	$-0.576811\pi$
$409$	13.6673	−	11.4682i	0.675804	−	0.567067i	0.914777	+	0.403959i	$0.132366\pi$
$410$		0			0
$411$	4.21208	+	7.29554i	0.207767	+	0.359862i
$412$		0			0
$413$	9.27017	−	52.5737i	0.456155	−	2.58698i
$414$		0			0
$415$	9.60543	−	3.49609i	0.471512	−	0.171616i
$416$		0			0
$417$	15.4529			0.756731
$418$		0			0
$419$	6.36461			0.310931			0.155466	−	0.987841i	$-0.450312\pi$
$419$	6.36461			0.310931			0.155466	+	0.987841i	$0.450312\pi$
$420$		0			0
$421$	−24.0784	+	8.76384i	−1.17351	+	0.427123i	−0.853906	−	0.520427i	$-0.825773\pi$
$421$	−24.0784	+	8.76384i	−1.17351	+	0.427123i	−0.319606	+	0.947551i	$0.603550\pi$
$422$		0			0
$423$	−2.61892	+	14.8526i	−0.127336	+	0.722160i
$424$		0			0
$425$	0.588341	+	1.01904i	0.0285388	+	0.0494306i
$426$		0			0
$427$	−5.86908	+	4.92475i	−0.284025	+	0.238325i
$428$		0			0
$429$	−2.00404	+	3.47110i	−0.0967559	+	0.167586i
$430$		0			0
$431$	−0.258943	−	0.0942475i	−0.0124728	−	0.00453974i	0.335776	−	0.941942i	$-0.391001\pi$
$431$	−0.258943	−	0.0942475i	−0.0124728	−	0.00453974i	−0.348249	+	0.937402i	$0.613224\pi$
$432$		0			0
$433$	−0.448391	−	2.54295i	−0.0215483	−	0.122206i	0.972136	−	0.234417i	$-0.0753180\pi$
$433$	−0.448391	−	2.54295i	−0.0215483	−	0.122206i	−0.993684	+	0.112210i	$0.964207\pi$
$434$		0			0
$435$	2.74814	+	2.30596i	0.131763	+	0.110562i
$436$		0			0
$437$	−1.54868	+	6.21659i	−0.0740835	+	0.297380i
$438$		0			0
$439$	20.6138	+	17.2971i	0.983844	+	0.825543i	0.984665	−	0.174456i	$-0.0558168\pi$
$439$	20.6138	+	17.2971i	0.983844	+	0.825543i	−0.000820776		1.00000i	$0.500261\pi$
$440$		0			0
$441$	−6.26235	−	35.5155i	−0.298207	−	1.69122i
$442$		0			0
$443$	10.7671	+	3.91891i	0.511561	+	0.186193i	0.584887	−	0.811115i	$-0.301139\pi$
$443$	10.7671	+	3.91891i	0.511561	+	0.186193i	−0.0733256	+	0.997308i	$0.523361\pi$
$444$		0			0
$445$	−2.80387	+	4.85644i	−0.132916	+	0.230218i
$446$		0			0
$447$	−11.9711	+	10.0449i	−0.566211	+	0.475108i
$448$		0			0
$449$	−17.4065	−	30.1490i	−0.821464	−	1.42282i	−0.904592	−	0.426278i	$-0.859824\pi$
$449$	−17.4065	−	30.1490i	−0.821464	−	1.42282i	0.0831280	−	0.996539i	$-0.473509\pi$
$450$		0			0
$451$	2.25836	−	12.8078i	0.106342	−	0.603096i
$452$		0			0
$453$	11.6030	−	4.22316i	0.545158	−	0.198421i
$454$		0			0
$455$	−10.4664			−0.490672
$456$		0			0
$457$	−8.23172			−0.385064			−0.192532	−	0.981291i	$-0.561670\pi$
$457$	−8.23172			−0.385064			−0.192532	+	0.981291i	$0.561670\pi$
$458$		0			0
$459$	−4.45229	+	1.62050i	−0.207815	+	0.0756385i
$460$		0			0
$461$	−4.93548	+	27.9905i	−0.229868	+	1.30365i	0.623288	+	0.781992i	$0.285796\pi$
$461$	−4.93548	+	27.9905i	−0.229868	+	1.30365i	−0.853156	+	0.521655i	$0.825315\pi$
$462$		0			0
$463$	3.47770	+	6.02355i	0.161622	+	0.279938i	0.935451	−	0.353457i	$-0.114994\pi$
$463$	3.47770	+	6.02355i	0.161622	+	0.279938i	−0.773828	+	0.633395i	$0.781661\pi$
$464$		0			0
$465$	−4.07804	+	3.42188i	−0.189115	+	0.158686i
$466$		0			0
$467$	−16.3197	+	28.2665i	−0.755185	+	1.30802i	0.190098	+	0.981765i	$0.439119\pi$
$467$	−16.3197	+	28.2665i	−0.755185	+	1.30802i	−0.945282	+	0.326253i	$0.894214\pi$
$468$		0			0
$469$	−10.3324	−	3.76069i	−0.477106	−	0.173652i
$470$		0			0
$471$	2.54599	+	14.4390i	0.117313	+	0.665315i
$472$		0			0
$473$	−14.2698	−	11.9738i	−0.656127	−	0.550556i
$474$		0			0
$475$	3.13612	+	3.02733i	0.143895	+	0.138904i
$476$		0			0
$477$	−4.23269	−	3.55165i	−0.193801	−	0.162619i
$478$		0			0
$479$	−4.77539	−	27.0826i	−0.218193	−	1.23744i	−0.875278	−	0.483619i	$-0.839322\pi$
$479$	−4.77539	−	27.0826i	−0.218193	−	1.23744i	0.657085	−	0.753816i	$-0.271789\pi$
$480$		0			0
$481$	−5.94361	−	2.16330i	−0.271005	−	0.0986378i
$482$		0			0
$483$	2.52620	−	4.37550i	0.114946	−	0.199092i
$484$		0			0
$485$	−4.19849	+	3.52295i	−0.190644	+	0.159969i
$486$		0			0
$487$	−15.1932	−	26.3153i	−0.688468	−	1.19246i	−0.972333	−	0.233597i	$-0.924950\pi$
$487$	−15.1932	−	26.3153i	−0.688468	−	1.19246i	0.283866	−	0.958864i	$-0.408383\pi$
$488$		0			0
$489$	−0.714101	+	4.04987i	−0.0322928	+	0.183141i
$490$		0			0
$491$	−25.1763	+	9.16343i	−1.13619	+	0.413540i	−0.840536	−	0.541755i	$-0.817760\pi$
$491$	−25.1763	+	9.16343i	−1.13619	+	0.413540i	−0.295655	+	0.955295i	$0.595538\pi$
$492$		0			0
$493$	5.71893			0.257568
$494$		0			0
$495$	5.93211			0.266628
$496$		0			0
$497$	−27.9808	+	10.1842i	−1.25511	+	0.456823i
$498$		0			0
$499$	−1.02904	+	5.83598i	−0.0460662	+	0.261254i	−0.999139	−	0.0414868i	$-0.986791\pi$
$499$	−1.02904	+	5.83598i	−0.0460662	+	0.261254i	0.953073	+	0.302741i	$0.0979017\pi$
$500$		0			0
$501$	−8.45934	−	14.6520i	−0.377935	−	0.654603i
$502$		0			0
$503$	−11.6839	+	9.80400i	−0.520962	+	0.437139i	−0.864967	−	0.501829i	$-0.832661\pi$
$503$	−11.6839	+	9.80400i	−0.520962	+	0.437139i	0.344005	+	0.938968i	$0.388216\pi$
$504$		0			0
$505$	−6.12955	+	10.6167i	−0.272761	+	0.472436i
$506$		0			0
$507$	5.51365	+	2.00680i	0.244870	+	0.0891253i
$508$		0			0
$509$	−0.610129	−	3.46022i	−0.0270435	−	0.153371i	0.968296	−	0.249807i	$-0.0803670\pi$
$509$	−0.610129	−	3.46022i	−0.0270435	−	0.153371i	−0.995339	+	0.0964352i	$0.969256\pi$
$510$		0			0
$511$	−12.0981	−	10.1515i	−0.535187	−	0.449075i
$512$		0			0
$513$	−14.1975	+	10.3193i	−0.626833	+	0.455608i
$514$		0			0
$515$	−10.5277	−	8.83382i	−0.463907	−	0.389265i
$516$		0			0
$517$	2.57731	+	14.6167i	0.113350	+	0.642840i
$518$		0			0
$519$	17.6924	+	6.43950i	0.776609	+	0.282663i
$520$		0			0
$521$	20.2771	−	35.1209i	0.888355	−	1.53868i	0.0465357	−	0.998917i	$-0.485182\pi$
$521$	20.2771	−	35.1209i	0.888355	−	1.53868i	0.841819	−	0.539759i	$-0.181485\pi$
$522$		0			0
$523$	−18.5173	+	15.5379i	−0.809707	+	0.679425i	−0.950538	−	0.310609i	$-0.899467\pi$
$523$	−18.5173	+	15.5379i	−0.809707	+	0.679425i	0.140831	+	0.990034i	$0.455023\pi$
$524$		0			0
$525$	−1.71877	−	2.97699i	−0.0750131	−	0.129927i
$526$		0			0
$527$	−1.47366	+	8.35755i	−0.0641937	+	0.364061i
$528$		0			0
$529$	19.5830	−	7.12762i	0.851434	−	0.309897i
$530$		0			0
$531$	−28.1438			−1.22133
$532$		0			0
$533$	12.0970			0.523977
$534$		0			0
$535$	14.2339	−	5.18070i	0.615384	−	0.223981i
$536$		0			0
$537$	0.563629	−	3.19650i	0.0243224	−	0.137939i
$538$		0			0
$539$	−17.7452	−	30.7357i	−0.764342	−	1.32388i
$540$		0			0
$541$	25.9983	−	21.8152i	1.11775	−	0.937907i	0.119265	−	0.992862i	$-0.461946\pi$
$541$	25.9983	−	21.8152i	1.11775	−	0.937907i	0.998489	+	0.0549553i	$0.0175016\pi$
$542$		0			0
$543$	−2.71779	+	4.70735i	−0.116632	+	0.202012i
$544$		0			0
$545$	−12.9147	−	4.70056i	−0.553204	−	0.201350i
$546$		0			0
$547$	−0.241319	−	1.36859i	−0.0103181	−	0.0585167i	0.979214	−	0.202830i	$-0.0650138\pi$
$547$	−0.241319	−	1.36859i	−0.0103181	−	0.0585167i	−0.989532	+	0.144313i	$0.953903\pi$
$548$		0			0
$549$	3.09410	+	2.59626i	0.132053	+	0.110806i
$550$		0			0
$551$	20.3634	−	5.84340i	0.867509	−	0.248937i
$552$		0			0
$553$	−8.04085	−	6.74708i	−0.341932	−	0.286915i
$554$		0			0
$555$	−0.360731	−	2.04581i	−0.0153122	−	0.0868398i
$556$		0			0
$557$	−10.2344	−	3.72501i	−0.433645	−	0.157834i	0.115968	−	0.993253i	$-0.463003\pi$
$557$	−10.2344	−	3.72501i	−0.433645	−	0.157834i	−0.549614	+	0.835419i	$0.685225\pi$
$558$		0			0
$559$	8.66338	−	15.0054i	0.366422	−	0.634662i
$560$		0			0
$561$	−1.60757	+	1.34891i	−0.0678716	+	0.0569511i
$562$		0			0
$563$	−13.9598	−	24.1792i	−0.588337	−	1.01903i	−0.994450	−	0.105207i	$-0.966449\pi$
$563$	−13.9598	−	24.1792i	−0.588337	−	1.01903i	0.406113	−	0.913823i	$-0.366884\pi$
$564$		0			0
$565$	3.30736	−	18.7570i	0.139142	−	0.789113i
$566$		0			0
$567$	−19.2266	+	6.99792i	−0.807442	+	0.293885i
$568$		0			0
$569$	6.97102			0.292240			0.146120	−	0.989267i	$-0.453321\pi$
$569$	6.97102			0.292240			0.146120	+	0.989267i	$0.453321\pi$
$570$		0			0
$571$	−22.7164			−0.950652			−0.475326	−	0.879810i	$-0.657670\pi$
$571$	−22.7164			−0.950652			−0.475326	+	0.879810i	$0.657670\pi$
$572$		0			0
$573$	10.3455	−	3.76544i	0.432188	−	0.157304i
$574$		0			0
$575$	−0.255223	+	1.44744i	−0.0106436	+	0.0603626i
$576$		0			0
$577$	10.0668	+	17.4362i	0.419086	+	0.725879i	0.995848	−	0.0910337i	$-0.0290171\pi$
$577$	10.0668	+	17.4362i	0.419086	+	0.725879i	−0.576761	+	0.816913i	$0.695684\pi$
$578$		0			0
$579$	12.9172	−	10.8388i	0.536819	−	0.450445i
$580$		0			0
$581$	−23.8023	+	41.2267i	−0.987484	+	1.71037i
$582$		0			0
$583$	−5.10967	−	1.85977i	−0.211621	−	0.0770237i
$584$		0			0
$585$	0.958147	+	5.43392i	0.0396145	+	0.224665i
$586$		0			0
$587$	33.2219	+	27.8765i	1.37121	+	1.15059i	0.972337	+	0.233582i	$0.0750446\pi$
$587$	33.2219	+	27.8765i	1.37121	+	1.15059i	0.398878	+	0.917004i	$0.369400\pi$
$588$		0			0
$589$	3.29219	+	31.2644i	0.135652	+	1.28823i
$590$		0			0
$591$	−1.11303	−	0.933944i	−0.0457840	−	0.0384173i
$592$		0			0
$593$	−0.509542	−	2.88976i	−0.0209244	−	0.118668i	0.972557	−	0.232667i	$-0.0747452\pi$
$593$	−0.509542	−	2.88976i	−0.0209244	−	0.118668i	−0.993481	+	0.113999i	$0.963634\pi$
$594$		0			0
$595$	−5.14947	−	1.87425i	−0.211108	−	0.0768369i
$596$		0			0
$597$	2.82621	−	4.89514i	0.115669	−	0.200345i
$598$		0			0
$599$	−24.5081	+	20.5648i	−1.00138	+	0.840254i	−0.987174	−	0.159645i	$-0.948965\pi$
$599$	−24.5081	+	20.5648i	−1.00138	+	0.840254i	−0.0142009	+	0.999899i	$0.504520\pi$
$600$		0			0
$601$	−13.3118	−	23.0567i	−0.542998	−	0.940501i	−0.998730	−	0.0503835i	$-0.983956\pi$
$601$	−13.3118	−	23.0567i	−0.542998	−	0.940501i	0.455732	−	0.890117i	$-0.349378\pi$
$602$		0			0
$603$	−1.00659	+	5.70863i	−0.0409913	+	0.232473i
$604$		0			0
$605$	−4.85083	+	1.76556i	−0.197214	+	0.0717801i
$606$		0			0
$607$	7.23183			0.293531			0.146766	−	0.989171i	$-0.453114\pi$
$607$	7.23183			0.293531			0.146766	+	0.989171i	$0.453114\pi$
$608$		0			0
$609$	−16.7071			−0.677008
$610$		0			0
$611$	−12.9729	+	4.72173i	−0.524826	+	0.191021i
$612$		0			0
$613$	−8.33598	+	47.2757i	−0.336687	+	1.90945i	0.0732109	+	0.997316i	$0.476675\pi$
$613$	−8.33598	+	47.2757i	−0.336687	+	1.90945i	−0.409898	+	0.912131i	$0.634436\pi$
$614$		0			0
$615$	1.98653	+	3.44077i	0.0801047	+	0.138745i
$616$		0			0
$617$	−15.6781	+	13.1555i	−0.631175	+	0.529619i	−0.901294	−	0.433208i	$-0.857381\pi$
$617$	−15.6781	+	13.1555i	−0.631175	+	0.529619i	0.270119	+	0.962827i	$0.412937\pi$
$618$		0			0
$619$	19.9789	−	34.6044i	0.803019	−	1.39087i	−0.114601	−	0.993412i	$-0.536559\pi$
$619$	19.9789	−	34.6044i	0.803019	−	1.39087i	0.917620	−	0.397459i	$-0.130108\pi$
$620$		0			0
$621$	−5.56127	−	2.02414i	−0.223166	−	0.0812258i
$622$		0			0
$623$	−4.53498	−	25.7191i	−0.181690	−	1.03042i
$624$		0			0
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$		0			0
$627$	−4.34579	+	6.44562i	−0.173554	+	0.257413i
$628$		0			0
$629$	−2.53687	−	2.12868i	−0.101152	−	0.0848762i
$630$		0			0
$631$	−6.92667	−	39.2831i	−0.275746	−	1.56383i	−0.736581	−	0.676349i	$-0.763561\pi$
$631$	−6.92667	−	39.2831i	−0.275746	−	1.56383i	0.460835	−	0.887486i	$-0.347550\pi$
$632$		0			0
$633$	1.74990	+	0.636910i	0.0695521	+	0.0253149i
$634$		0			0
$635$	5.99235	−	10.3791i	0.237799	−	0.411881i
$636$		0			0
$637$	25.2883	−	21.2194i	1.00196	−	0.840742i
$638$		0			0
$639$	7.84891	+	13.5947i	0.310498	+	0.537798i
$640$		0			0
$641$	−5.64717	+	32.0267i	−0.223050	+	1.26498i	0.643328	+	0.765591i	$0.277553\pi$
$641$	−5.64717	+	32.0267i	−0.223050	+	1.26498i	−0.866378	+	0.499389i	$0.833558\pi$
$642$		0			0
$643$	3.52792	−	1.28406i	0.139128	−	0.0506383i	−0.271518	−	0.962433i	$-0.587526\pi$
$643$	3.52792	−	1.28406i	0.139128	−	0.0506383i	0.410645	+	0.911795i	$0.365303\pi$
$644$		0			0
$645$	5.69072			0.224072
$646$		0			0
$647$	25.9437			1.01995			0.509976	−	0.860188i	$-0.329654\pi$
$647$	25.9437			1.01995			0.509976	+	0.860188i	$0.329654\pi$
$648$		0			0
$649$	−26.0263	+	9.47280i	−1.02162	+	0.371840i
$650$		0			0
$651$	4.30512	−	24.4155i	0.168731	−	0.956920i
$652$		0			0
$653$	−3.60013	−	6.23560i	−0.140884	−	0.244018i	0.786946	−	0.617022i	$-0.211661\pi$
$653$	−3.60013	−	6.23560i	−0.140884	−	0.244018i	−0.927830	+	0.373004i	$0.878328\pi$
$654$		0			0
$655$	−7.33068	+	6.15117i	−0.286433	+	0.240346i
$656$		0			0
$657$	−4.16290	+	7.21036i	−0.162410	+	0.281303i
$658$		0			0
$659$	3.67127	+	1.33623i	0.143012	+	0.0520522i	0.412535	−	0.910942i	$-0.364644\pi$
$659$	3.67127	+	1.33623i	0.143012	+	0.0520522i	−0.269522	+	0.962994i	$0.586866\pi$
$660$		0			0
$661$	1.37423	+	7.79367i	0.0534515	+	0.303139i	0.999800	−	0.0200098i	$-0.00636975\pi$
$661$	1.37423	+	7.79367i	0.0534515	+	0.303139i	−0.946348	+	0.323149i	$0.895259\pi$
$662$		0			0
$663$	−1.49528	−	1.25469i	−0.0580719	−	0.0487281i
$664$		0			0
$665$	−20.2507	−	1.41210i	−0.785290	−	0.0547589i
$666$		0			0
$667$	5.47217	+	4.59170i	0.211883	+	0.177791i
$668$		0			0
$669$	2.84021	+	16.1076i	0.109809	+	0.622757i
$670$		0			0
$671$	3.73518	+	1.35949i	0.144195	+	0.0524827i
$672$		0			0
$673$	−12.3605	+	21.4089i	−0.476460	+	0.825254i	−0.999636	−	0.0269712i	$-0.991414\pi$
$673$	−12.3605	+	21.4089i	−0.476460	+	0.825254i	0.523176	+	0.852225i	$0.324747\pi$
$674$		0			0
$675$	−3.08455	+	2.58825i	−0.118724	+	0.0996216i
$676$		0			0
$677$	−3.62242	−	6.27421i	−0.139221	−	0.241138i	0.787981	−	0.615699i	$-0.211126\pi$
$677$	−3.62242	−	6.27421i	−0.139221	−	0.241138i	−0.927202	+	0.374562i	$0.877793\pi$
$678$		0			0
$679$	4.43227	−	25.1367i	0.170095	−	0.964657i
$680$		0			0
$681$	10.0328	−	3.65164i	0.384457	−	0.139931i
$682$		0			0
$683$	−28.2210			−1.07984			−0.539922	−	0.841715i	$-0.681546\pi$
$683$	−28.2210			−1.07984			−0.539922	+	0.841715i	$0.681546\pi$
$684$		0			0
$685$	11.4129			0.436066
$686$		0			0
$687$	−11.8138	+	4.29987i	−0.450724	+	0.164050i
$688$		0			0
$689$	0.878275	−	4.98094i	0.0334596	−	0.189759i
$690$		0			0
$691$	2.42568	+	4.20140i	0.0922772	+	0.159829i	0.908469	−	0.417952i	$-0.137252\pi$
$691$	2.42568	+	4.20140i	0.0922772	+	0.159829i	−0.816192	+	0.577781i	$0.803919\pi$
$692$		0			0
$693$	−21.1631	+	17.7580i	−0.803921	+	0.674570i
$694$		0			0
$695$	10.4677	−	18.1305i	0.397061	−	0.687730i
$696$		0			0
$697$	5.95171	+	2.16624i	0.225437	+	0.0820523i
$698$		0			0
$699$	2.99905	+	17.0085i	0.113434	+	0.643319i
$700$		0			0
$701$	7.95515	+	6.67517i	0.300462	+	0.252118i	0.780537	−	0.625110i	$-0.214946\pi$
$701$	7.95515	+	6.67517i	0.300462	+	0.252118i	−0.480075	+	0.877228i	$0.659390\pi$
$702$		0			0
$703$	−11.2080	−	4.98751i	−0.422719	−	0.188108i
$704$		0			0
$705$	−3.47339	−	2.91452i	−0.130815	−	0.109767i
$706$		0			0
$707$	−9.91393	−	56.2247i	−0.372852	−	2.11455i
$708$		0			0
$709$	11.7708	+	4.28424i	0.442063	+	0.160898i	0.553456	−	0.832879i	$-0.313309\pi$
$709$	11.7708	+	4.28424i	0.442063	+	0.160898i	−0.111392	+	0.993776i	$0.535531\pi$
$710$		0			0
$711$	−2.76683	+	4.79229i	−0.103764	+	0.179725i
$712$		0			0
$713$	−8.12030	+	6.81374i	−0.304108	+	0.255177i
$714$		0			0
$715$	2.71504	+	4.70259i	0.101537	+	0.175867i
$716$		0			0
$717$	3.07767	−	17.4543i	0.114938	−	0.651844i
$718$		0			0
$719$	−28.5351	+	10.3859i	−1.06418	+	0.387330i	−0.813997	−	0.580869i	$-0.802713\pi$
$719$	−28.5351	+	10.3859i	−1.06418	+	0.387330i	−0.250182	+	0.968199i	$0.580491\pi$
$720$		0			0
$721$	64.0027			2.38359
$722$		0			0
$723$	18.5438			0.689650
$724$		0			0
$725$	4.56711	−	1.66229i	0.169618	−	0.0617360i
$726$		0			0
$727$	4.79921	−	27.2176i	0.177993	−	1.00945i	−0.756640	−	0.653832i	$-0.773160\pi$
$727$	4.79921	−	27.2176i	0.177993	−	1.00945i	0.934633	−	0.355615i	$-0.115728\pi$
$728$		0			0
$729$	0.935075	+	1.61960i	0.0346324	+	0.0599851i
$730$		0			0
$731$	6.94946	−	5.83129i	0.257035	−	0.215678i
$732$		0			0
$733$	16.2769	−	28.1924i	0.601201	−	1.04131i	−0.391439	−	0.920204i	$-0.628023\pi$
$733$	16.2769	−	28.1924i	0.601201	−	1.04131i	0.992640	−	0.121106i	$-0.0386441\pi$
$734$		0			0
$735$	10.1883	+	3.70823i	0.375800	+	0.136780i
$736$		0			0
$737$	0.990593	+	5.61793i	0.0364890	+	0.206939i
$738$		0			0
$739$	3.18376	+	2.67150i	0.117117	+	0.0982725i	0.699465	−	0.714667i	$-0.253422\pi$
$739$	3.18376	+	2.67150i	0.117117	+	0.0982725i	−0.582348	+	0.812939i	$0.697866\pi$
$740$		0			0
$741$	−6.60624	−	2.93974i	−0.242686	−	0.107994i
$742$		0			0
$743$	5.58048	+	4.68258i	0.204728	+	0.171787i	0.739387	−	0.673281i	$-0.235115\pi$
$743$	5.58048	+	4.68258i	0.204728	+	0.171787i	−0.534659	+	0.845068i	$0.679560\pi$
$744$		0			0
$745$	3.67637	+	20.8497i	0.134692	+	0.763875i
$746$		0			0
$747$	23.5830	+	8.58350i	0.862856	+	0.314054i
$748$		0			0
$749$	−35.2715	+	61.0921i	−1.28879	+	2.23226i
$750$		0			0
$751$	8.54980	−	7.17413i	0.311987	−	0.261788i	−0.473326	−	0.880887i	$-0.656947\pi$
$751$	8.54980	−	7.17413i	0.311987	−	0.261788i	0.785313	+	0.619100i	$0.212502\pi$
$752$		0			0
$753$	4.78540	+	8.28856i	0.174390	+	0.302052i
$754$		0			0
$755$	2.90487	−	16.4743i	0.105719	−	0.599562i
$756$		0			0
$757$	1.18635	−	0.431797i	0.0431187	−	0.0156939i	−0.320371	−	0.947292i	$-0.603807\pi$
$757$	1.18635	−	0.431797i	0.0431187	−	0.0156939i	0.363489	+	0.931598i	$0.381585\pi$
$758$		0			0
$759$	−2.62124			−0.0951449
$760$		0			0
$761$	−42.2386			−1.53115			−0.765574	−	0.643347i	$-0.777545\pi$
$761$	−42.2386			−1.53115			−0.765574	+	0.643347i	$0.777545\pi$
$762$		0			0
$763$	60.1452	−	21.8911i	2.17740	−	0.792510i
$764$		0			0
$765$	−0.501663	+	2.84507i	−0.0181376	+	0.102864i
$766$		0			0
$767$	−12.8810	−	22.3106i	−0.465106	−	0.805588i
$768$		0			0
$769$	31.5317	−	26.4582i	1.13706	−	0.954109i	0.137724	−	0.990471i	$-0.456021\pi$
$769$	31.5317	−	26.4582i	1.13706	−	0.954109i	0.999339	+	0.0363619i	$0.0115769\pi$
$770$		0			0
$771$	0.854325	−	1.47973i	0.0307678	−	0.0532913i
$772$		0			0
$773$	29.6767	+	10.8014i	1.06740	+	0.388500i	0.815202	−	0.579176i	$-0.196626\pi$
$773$	29.6767	+	10.8014i	1.06740	+	0.388500i	0.252194	+	0.967677i	$0.418848\pi$
$774$		0			0
$775$	1.25239	+	7.10263i	0.0449870	+	0.255134i
$776$		0			0
$777$	7.41114	+	6.21869i	0.265873	+	0.223094i
$778$		0			0
$779$	23.4056	+	1.63209i	0.838592	+	0.0584758i
$780$		0			0
$781$	11.8342	+	9.93005i	0.423460	+	0.355325i
$782$		0			0
$783$	3.39832	+	19.2728i	0.121446	+	0.688754i
$784$		0			0
$785$	18.6656	+	6.79374i	0.666205	+	0.242479i
$786$		0			0
$787$	16.8936	−	29.2607i	0.602194	−	1.04303i	−0.390295	−	0.920690i	$-0.627627\pi$
$787$	16.8936	−	29.2607i	0.602194	−	1.04303i	0.992488	−	0.122340i	$-0.0390398\pi$
$788$		0			0
$789$	−4.51294	+	3.78681i	−0.160665	+	0.134814i
$790$		0			0
$791$	44.3506	+	76.8174i	1.57692	+	2.73131i
$792$		0			0
$793$	−0.642021	+	3.64108i	−0.0227988	+	0.129299i
$794$		0			0
$795$	1.56097	−	0.568148i	0.0553620	−	0.0201501i
$796$		0			0
$797$	−29.5303			−1.04602			−0.523008	−	0.852328i	$-0.675190\pi$
$797$	−29.5303			−1.04602			−0.523008	+	0.852328i	$0.675190\pi$
$798$		0			0
$799$	−7.22819			−0.255715
$800$		0			0
$801$	−12.9377	+	4.70892i	−0.457130	+	0.166382i
$802$		0			0
$803$	−1.42279	+	8.06906i	−0.0502092	+	0.284751i
$804$		0			0
$805$	−3.42245	−	5.92786i	−0.120626	−	0.208930i
$806$		0			0
$807$	−13.2154	+	11.0890i	−0.465204	+	0.390353i
$808$		0			0
$809$	11.7019	−	20.2682i	0.411416	−	0.712594i	−0.583629	−	0.812021i	$-0.698368\pi$
$809$	11.7019	−	20.2682i	0.411416	−	0.712594i	0.995045	+	0.0994270i	$0.0317010\pi$
$810$		0			0
$811$	−12.0309	−	4.37890i	−0.422463	−	0.153764i	0.122035	−	0.992526i	$-0.461058\pi$
$811$	−12.0309	−	4.37890i	−0.422463	−	0.153764i	−0.544499	+	0.838762i	$0.683280\pi$
$812$		0			0
$813$	3.09249	+	17.5384i	0.108459	+	0.615099i
$814$		0			0
$815$	4.26790	+	3.58119i	0.149498	+	0.125444i
$816$		0			0
$817$	18.7867	−	27.8641i	0.657263	−	0.974843i
$818$		0			0
$819$	−19.6849	−	16.5176i	−0.687846	−	0.577171i
$820$		0			0
$821$	3.24624	+	18.4103i	0.113294	+	0.642525i	0.987581	+	0.157114i	$0.0502189\pi$
$821$	3.24624	+	18.4103i	0.113294	+	0.642525i	−0.874286	+	0.485411i	$0.838670\pi$
$822$		0			0
$823$	−10.3012	−	3.74934i	−0.359078	−	0.130694i	0.156181	−	0.987729i	$-0.450082\pi$
$823$	−10.3012	−	3.74934i	−0.359078	−	0.130694i	−0.515258	+	0.857035i	$0.672304\pi$
$824$		0			0
$825$	−0.891715	+	1.54450i	−0.0310455	+	0.0537725i
$826$		0			0
$827$	0.757742	−	0.635821i	0.0263493	−	0.0221097i	−0.629518	−	0.776986i	$-0.716748\pi$
$827$	0.757742	−	0.635821i	0.0263493	−	0.0221097i	0.655867	+	0.754876i	$0.272303\pi$
$828$		0			0
$829$	−0.959825	−	1.66247i	−0.0333361	−	0.0577398i	0.848876	−	0.528592i	$-0.177280\pi$
$829$	−0.959825	−	1.66247i	−0.0333361	−	0.0577398i	−0.882212	+	0.470852i	$0.843947\pi$
$830$		0			0
$831$	−1.71523	+	9.72753i	−0.0595005	+	0.337444i
$832$		0			0
$833$	16.2417	−	5.91148i	0.562740	−	0.204821i
$834$		0			0
$835$	−22.9212			−0.793220
$836$		0			0
$837$	−29.0406			−1.00379
$838$		0			0
$839$	−25.4222	+	9.25293i	−0.877672	+	0.319447i	−0.741270	−	0.671207i	$-0.765776\pi$
$839$	−25.4222	+	9.25293i	−0.877672	+	0.319447i	−0.136402	+	0.990654i	$0.543554\pi$
$840$		0			0
$841$	−0.933934	+	5.29660i	−0.0322046	+	0.182641i
$842$		0			0
$843$	−1.85182	−	3.20745i	−0.0637801	−	0.110470i
$844$		0			0
$845$	6.08944	−	5.10965i	0.209483	−	0.175777i
$846$		0			0
$847$	12.0204	−	20.8199i	0.413024	−	0.715379i
$848$		0			0
$849$	−2.22983	−	0.811591i	−0.0765275	−	0.0278537i
$850$		0			0
$851$	−0.718298	−	4.07367i	−0.0246229	−	0.139644i
$852$		0			0
$853$	−21.4593	−	18.0065i	−0.734754	−	0.616532i	0.196669	−	0.980470i	$-0.436987\pi$
$853$	−21.4593	−	18.0065i	−0.734754	−	0.616532i	−0.931423	+	0.363938i	$0.881432\pi$
$854$		0			0
$855$	1.12072	+	10.6430i	0.0383279	+	0.363983i
$856$		0			0
$857$	3.37241	+	2.82979i	0.115199	+	0.0966639i	0.698568	−	0.715544i	$-0.253821\pi$
$857$	3.37241	+	2.82979i	0.115199	+	0.0966639i	−0.583368	+	0.812208i	$0.698266\pi$
$858$		0			0
$859$	4.40179	+	24.9638i	0.150187	+	0.851754i	0.963055	+	0.269305i	$0.0867941\pi$
$859$	4.40179	+	24.9638i	0.150187	+	0.851754i	−0.812868	+	0.582448i	$0.802095\pi$
$860$		0			0
$861$	−17.3872	−	6.32841i	−0.592553	−	0.215672i
$862$		0			0
$863$	18.5834	−	32.1873i	0.632585	−	1.09567i	−0.354436	−	0.935080i	$-0.615327\pi$
$863$	18.5834	−	32.1873i	0.632585	−	1.09567i	0.987021	−	0.160589i	$-0.0513395\pi$
$864$		0			0
$865$	19.5400	−	16.3960i	0.664381	−	0.557482i
$866$		0			0
$867$	5.76306	+	9.98191i	0.195724	+	0.339003i
$868$		0			0
$869$	−0.945644	+	5.36302i	−0.0320788	+	0.181928i
$870$		0			0
$871$	−4.98614	+	1.81480i	−0.168949	+	0.0614923i
$872$		0			0
$873$	−13.4562			−0.455422
$874$		0			0
$875$	−4.65712			−0.157439
$876$		0			0
$877$	28.6613	−	10.4318i	0.967822	−	0.352258i	0.190728	−	0.981643i	$-0.438915\pi$
$877$	28.6613	−	10.4318i	0.967822	−	0.352258i	0.777094	+	0.629385i	$0.216693\pi$
$878$		0			0
$879$	2.33782	−	13.2584i	0.0788526	−	0.447195i
$880$		0			0
$881$	26.1253	+	45.2503i	0.880183	+	1.52452i	0.851137	+	0.524944i	$0.175914\pi$
$881$	26.1253	+	45.2503i	0.880183	+	1.52452i	0.0290468	+	0.999578i	$0.490753\pi$
$882$		0			0
$883$	0.341169	−	0.286275i	0.0114812	−	0.00963391i	−0.637029	−	0.770840i	$-0.719837\pi$
$883$	0.341169	−	0.286275i	0.0114812	−	0.00963391i	0.648510	+	0.761206i	$0.275392\pi$
$884$		0			0
$885$	4.23058	−	7.32757i	0.142209	−	0.246314i
$886$		0			0
$887$	25.3696	+	9.23377i	0.851827	+	0.310040i	0.730785	−	0.682608i	$-0.239154\pi$
$887$	25.3696	+	9.23377i	0.851827	+	0.310040i	0.121042	+	0.992647i	$0.461376\pi$
$888$		0			0
$889$	9.69204	+	54.9663i	0.325061	+	1.84351i
$890$		0			0
$891$	8.13169	+	6.82329i	0.272422	+	0.228589i
$892$		0			0
$893$	−25.7374	+	7.38550i	−0.861268	+	0.247146i
$894$		0			0
$895$	−3.36859	−	2.82658i	−0.112599	−	0.0944822i
$896$		0			0
$897$	−0.423380	−	2.40110i	−0.0141362	−	0.0801705i
$898$		0			0
$899$	32.9389	+	11.9888i	1.09857	+	0.399848i
$900$		0			0
$901$	1.32407	−	2.29335i	0.0441110	−	0.0764026i
$902$		0			0
$903$	−20.3020	+	17.0354i	−0.675608	+	0.566902i
$904$		0			0
$905$	3.68203	+	6.37745i	0.122395	+	0.211994i
$906$		0			0
$907$	−3.65438	+	20.7250i	−0.121342	+	0.688164i	0.862072	+	0.506786i	$0.169167\pi$
$907$	−3.65438	+	20.7250i	−0.121342	+	0.688164i	−0.983414	+	0.181378i	$0.941944\pi$
$908$		0			0
$909$	−28.2830	+	10.2942i	−0.938089	+	0.341437i
$910$		0			0
$911$	−0.548483			−0.0181720			−0.00908602	−	0.999959i	$-0.502892\pi$
$911$	−0.548483			−0.0181720			−0.00908602	+	0.999959i	$0.502892\pi$
$912$		0			0
$913$	24.6978			0.817377
$914$		0			0
$915$	−1.14108	+	0.415317i	−0.0377228	+	0.0137300i
$916$		0			0
$917$	7.73887	−	43.8893i	0.255560	−	1.44935i
$918$		0			0
$919$	−1.82780	−	3.16584i	−0.0602936	−	0.104432i	0.834303	−	0.551306i	$-0.185870\pi$
$919$	−1.82780	−	3.16584i	−0.0602936	−	0.104432i	−0.894597	+	0.446875i	$0.852537\pi$
$920$		0			0
$921$	9.82790	−	8.24658i	0.323840	−	0.271734i
$922$		0			0
$923$	−7.18468	+	12.4442i	−0.236486	+	0.409607i
$924$		0			0
$925$	−2.64466	−	0.962578i	−0.0869559	−	0.0316494i
$926$		0			0
$927$	−5.85913	−	33.2288i	−0.192439	−	1.09138i
$928$		0			0
$929$	18.7251	+	15.7123i	0.614352	+	0.515502i	0.896022	−	0.444009i	$-0.146444\pi$
$929$	18.7251	+	15.7123i	0.614352	+	0.515502i	−0.281671	+	0.959511i	$0.590889\pi$
$930$		0			0
$931$	51.7914	−	37.6441i	1.69740	−	1.23374i
$932$		0			0
$933$	−2.69089	−	2.25792i	−0.0880956	−	0.0739210i
$934$		0			0
$935$	0.493692	+	2.79987i	0.0161455	+	0.0915655i
$936$		0			0
$937$	−27.4701	−	9.99830i	−0.897409	−	0.326630i	−0.148195	−	0.988958i	$-0.547346\pi$
$937$	−27.4701	−	9.99830i	−0.897409	−	0.326630i	−0.749214	+	0.662328i	$0.769569\pi$
$938$		0			0
$939$	−2.98247	+	5.16579i	−0.0973292	+	0.168579i
$940$		0			0
$941$	8.50084	−	7.13305i	0.277119	−	0.232531i	−0.493626	−	0.869675i	$-0.664329\pi$
$941$	8.50084	−	7.13305i	0.277119	−	0.232531i	0.770745	+	0.637144i	$0.219884\pi$
$942$		0			0
$943$	3.95564	+	6.85136i	0.128813	+	0.223111i
$944$		0			0
$945$	3.25631	−	18.4674i	0.105928	−	0.600746i
$946$		0			0
$947$	33.2851	−	12.1148i	1.08162	−	0.393677i	0.261110	−	0.965309i	$-0.415912\pi$
$947$	33.2851	−	12.1148i	1.08162	−	0.393677i	0.820510	+	0.571632i	$0.193689\pi$
$948$		0			0
$949$	−7.62122			−0.247395
$950$		0			0
$951$	−7.96470			−0.258273
$952$		0			0
$953$	47.9492	−	17.4521i	1.55323	−	0.565328i	0.584055	−	0.811714i	$-0.301465\pi$
$953$	47.9492	−	17.4521i	1.55323	−	0.565328i	0.969172	+	0.246386i	$0.0792430\pi$
$954$		0			0
$955$	2.59003	−	14.6888i	0.0838115	−	0.475319i
$956$		0			0
$957$	4.33393	+	7.50658i	0.140096	+	0.242653i
$958$		0			0
$959$	−40.7163	+	34.1651i	−1.31480	+	1.10325i
$960$		0			0
$961$	−10.5079	+	18.2003i	−0.338966	+	0.587106i
$962$		0			0
$963$	34.9466	+	12.7195i	1.12614	+	0.409881i
$964$		0			0
$965$	−3.96693	−	22.4976i	−0.127700	−	0.724222i
$966$		0			0
$967$	−5.84430	−	4.90395i	−0.187940	−	0.157700i	0.543963	−	0.839109i	$-0.316923\pi$
$967$	−5.84430	−	4.90395i	−0.187940	−	0.157700i	−0.731903	+	0.681409i	$0.761368\pi$
$968$		0			0
$969$	−2.72384	−	2.62936i	−0.0875023	−	0.0844671i
$970$		0			0
$971$	−21.1081	−	17.7118i	−0.677392	−	0.568400i	0.237851	−	0.971302i	$-0.423557\pi$
$971$	−21.1081	−	17.7118i	−0.677392	−	0.568400i	−0.915243	+	0.402902i	$0.868001\pi$
$972$		0			0
$973$	16.9304	+	96.0171i	0.542764	+	3.07817i
$974$		0			0
$975$	−1.55882	−	0.567363i	−0.0499221	−	0.0181702i
$976$		0			0
$977$	−3.64072	+	6.30591i	−0.116477	+	0.201744i	−0.918369	−	0.395725i	$-0.870493\pi$
$977$	−3.64072	+	6.30591i	−0.116477	+	0.201744i	0.801892	+	0.597469i	$0.203827\pi$
$978$		0			0
$979$	−10.3793	+	8.70928i	−0.331724	+	0.278350i
$980$		0			0
$981$	−16.8714	−	29.2220i	−0.538661	−	0.932988i
$982$		0			0
$983$	−0.827298	+	4.69184i	−0.0263867	+	0.149646i	−0.995155	−	0.0983230i	$-0.968652\pi$
$983$	−0.827298	+	4.69184i	−0.0263867	+	0.149646i	0.968768	+	0.247969i	$0.0797633\pi$
$984$		0			0
$985$	−1.84974	+	0.673249i	−0.0589375	+	0.0214515i
$986$		0			0
$987$	21.1162			0.672137
$988$		0			0
$989$	11.3315			0.360321
$990$		0			0
$991$	11.5436	−	4.20153i	0.366695	−	0.133466i	−0.152099	−	0.988365i	$-0.548603\pi$
$991$	11.5436	−	4.20153i	0.366695	−	0.133466i	0.518794	+	0.854899i	$0.326381\pi$
$992$		0			0
$993$	2.93645	−	16.6535i	0.0931856	−	0.528482i
$994$		0			0
$995$	−3.82891	−	6.63187i	−0.121385	−	0.210244i
$996$		0			0
$997$	25.4297	−	21.3381i	0.805367	−	0.675783i	−0.144130	−	0.989559i	$-0.546038\pi$
$997$	25.4297	−	21.3381i	0.805367	−	0.675783i	0.949497	+	0.313776i	$0.101594\pi$
$998$		0			0
$999$	5.66621	−	9.81416i	0.179271	−	0.310506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.a.301.1	yes	18
19.5	even	9		7220.2.a.v.1.7		9
19.6	even	9	inner	380.2.u.a.101.1	✓	18
19.14	odd	18		7220.2.a.x.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.a.101.1	✓	18	19.6	even	9	inner
380.2.u.a.301.1	yes	18	1.1	even	1	trivial
7220.2.a.v.1.7		9	19.5	even	9
7220.2.a.x.1.3		9	19.14	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)

\(f(q)\)	\(=\)	\(q+(-0.693610 + 0.252453i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-2.32856 - 4.03318i) q^{7} +(-1.88077 + 1.57815i) q^{9} +O(q^{10})\)	\(q+(-0.693610 + 0.252453i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-2.32856 - 4.03318i) q^{7} +(-1.88077 + 1.57815i) q^{9} +(-1.20808 + 2.09246i) q^{11} +(-2.11186 - 0.768655i) q^{13} +(-0.128174 - 0.726910i) q^{15} +(-0.901391 - 0.756357i) q^{17} +(-3.98240 - 1.77215i) q^{19} +(2.63330 + 2.20960i) q^{21} +(-0.255223 - 1.44744i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(2.01330 - 3.48713i) q^{27} +(-3.72314 + 3.12409i) q^{29} +(-3.60610 - 6.24595i) q^{31} +(0.309690 - 1.75634i) q^{33} +(4.37626 - 1.59283i) q^{35} +2.81439 q^{37} +1.65886 q^{39} +(-5.05804 + 1.84097i) q^{41} +(-1.33878 + 7.59257i) q^{43} +(-1.22759 - 2.12624i) q^{45} +(4.70570 - 3.94855i) q^{47} +(-7.34438 + 12.7208i) q^{49} +(0.816159 + 0.297058i) q^{51} +(0.390796 + 2.21632i) q^{53} +(-1.85089 - 1.55308i) q^{55} +(3.20962 + 0.223809i) q^{57} +(8.78120 + 7.36830i) q^{59} +(-0.285673 - 1.62013i) q^{61} +(10.7445 + 3.91067i) q^{63} +(1.12370 - 1.94630i) q^{65} +(1.80864 - 1.51763i) q^{67} +(0.542437 + 0.939529i) q^{69} +(1.11027 - 6.29664i) q^{71} +(3.18662 - 1.15983i) q^{73} +0.738124 q^{75} +11.2524 q^{77} +(2.11795 - 0.770872i) q^{79} +(0.762904 - 4.32665i) q^{81} +(-5.11094 - 8.85241i) q^{83} +(0.901391 - 0.756357i) q^{85} +(1.79372 - 3.10682i) q^{87} +(5.26955 + 1.91796i) q^{89} +(1.81747 + 10.3074i) q^{91} +(4.07804 + 3.42188i) q^{93} +(2.43676 - 3.61417i) q^{95} +(4.19849 + 3.52295i) q^{97} +(-1.03010 - 5.84198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more