LMFDB - Embedded newform 1320.2.bw.h.1081.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 13 x^{10} - 30 x^{9} + 96 x^{8} + 35 x^{7} + 177 x^{6} + 598 x^{5} + 1576 x^{4} + \cdots + 25 $ x^12 - x^11 + 13x^10 - 30x^9 + 96x^8 + 35x^7 + 177x^6 + 598x^5 + 1576x^4 + 450x^3 + 240x^2 + 100x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1081.1
Root			$0.129370 - 0.398160i$ of defining polynomial
Character	$\chi$	$=$	1320.1081
Dual form			1320.2.bw.h.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-0.688583 + 2.11924i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-0.688583 + 2.11924i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-1.91625 - 2.70703i) q^{11} +(-1.14771 + 0.833861i) q^{13} +(0.309017 - 0.951057i) q^{15} +(2.62621 + 1.90805i) q^{17} +(1.57227 + 4.83896i) q^{19} +2.22830 q^{21} -4.17220 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-0.174038 + 0.535634i) q^{29} +(-2.73949 + 1.99036i) q^{31} +(-1.98238 + 2.65898i) q^{33} +(-1.80273 + 1.30976i) q^{35} +(-0.907314 + 2.79242i) q^{37} +(1.14771 + 0.833861i) q^{39} +(3.41649 + 10.5149i) q^{41} -4.54160 q^{43} -1.00000 q^{45} +(0.845613 + 2.60253i) q^{47} +(1.64609 + 1.19595i) q^{49} +(1.00312 - 3.08729i) q^{51} +(-0.149477 + 0.108602i) q^{53} +(0.0408712 - 3.31637i) q^{55} +(4.11627 - 2.99064i) q^{57} +(-0.618480 + 1.90349i) q^{59} +(-5.16994 - 3.75618i) q^{61} +(-0.688583 - 2.11924i) q^{63} -1.41865 q^{65} -6.13724 q^{67} +(1.28928 + 3.96800i) q^{69} +(-8.05149 - 5.84975i) q^{71} +(-4.85287 + 14.9356i) q^{73} +(0.809017 - 0.587785i) q^{75} +(7.05633 - 2.19698i) q^{77} +(3.99092 - 2.89957i) q^{79} +(0.309017 - 0.951057i) q^{81} +(10.2660 + 7.45866i) q^{83} +(1.00312 + 3.08729i) q^{85} +0.563199 q^{87} +7.90696 q^{89} +(-0.976858 - 3.00646i) q^{91} +(2.73949 + 1.99036i) q^{93} +(-1.57227 + 4.83896i) q^{95} +(1.40017 - 1.01728i) q^{97} +(3.14143 + 1.06369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 3 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 3 * q^5 + 5 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} + 3 q^{5} + 5 q^{7} - 3 q^{9} + 6 q^{11} - 2 q^{13} - 3 q^{15} - 13 q^{17} - 12 q^{23} - 3 q^{25} + 3 q^{27} - 15 q^{29} - 3 q^{31} + 9 q^{33} + 5 q^{35} + 11 q^{37} + 2 q^{39} + 13 q^{41} + 10 q^{43} - 12 q^{45} + 14 q^{47} + 12 q^{49} - 12 q^{51} - 21 q^{53} - q^{55} + 5 q^{57} - 31 q^{59} - 39 q^{61} + 5 q^{63} - 8 q^{65} - 40 q^{67} + 7 q^{69} - q^{71} + 9 q^{73} + 3 q^{75} + 79 q^{77} + 39 q^{79} - 3 q^{81} - 17 q^{83} - 12 q^{85} - 40 q^{87} + 36 q^{89} + 17 q^{91} + 3 q^{93} + 3 q^{97} + 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 + 3 * q^5 + 5 * q^7 - 3 * q^9 + 6 * q^11 - 2 * q^13 - 3 * q^15 - 13 * q^17 - 12 * q^23 - 3 * q^25 + 3 * q^27 - 15 * q^29 - 3 * q^31 + 9 * q^33 + 5 * q^35 + 11 * q^37 + 2 * q^39 + 13 * q^41 + 10 * q^43 - 12 * q^45 + 14 * q^47 + 12 * q^49 - 12 * q^51 - 21 * q^53 - q^55 + 5 * q^57 - 31 * q^59 - 39 * q^61 + 5 * q^63 - 8 * q^65 - 40 * q^67 + 7 * q^69 - q^71 + 9 * q^73 + 3 * q^75 + 79 * q^77 + 39 * q^79 - 3 * q^81 - 17 * q^83 - 12 * q^85 - 40 * q^87 + 36 * q^89 + 17 * q^91 + 3 * q^93 + 3 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	−0.688583	+	2.11924i	−0.260260	+	0.800998i	0.732488	+	0.680780i	$0.238359\pi$
$7$	−0.688583	+	2.11924i	−0.260260	+	0.800998i	−0.992748	+	0.120217i	$0.961641\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−1.91625	−	2.70703i	−0.577771	−	0.816199i
$11$	−1.91625	−	2.70703i	−0.577771	−	0.816199i
$12$		0			0
$13$	−1.14771	+	0.833861i	−0.318318	+	0.231272i	−0.735457	−	0.677571i	$-0.763033\pi$
$13$	−1.14771	+	0.833861i	−0.318318	+	0.231272i	0.417139	+	0.908842i	$0.363033\pi$
$14$		0			0
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$		0			0
$17$	2.62621	+	1.90805i	0.636949	+	0.462771i	0.858801	−	0.512310i	$-0.171210\pi$
$17$	2.62621	+	1.90805i	0.636949	+	0.462771i	−0.221852	+	0.975080i	$0.571210\pi$
$18$		0			0
$19$	1.57227	+	4.83896i	0.360705	+	1.11013i	0.952627	+	0.304140i	$0.0983690\pi$
$19$	1.57227	+	4.83896i	0.360705	+	1.11013i	−0.591923	+	0.805995i	$0.701631\pi$
$20$		0			0
$21$	2.22830			0.486255
$22$		0			0
$23$	−4.17220			−0.869963			−0.434982	−	0.900439i	$-0.643245\pi$
$23$	−4.17220			−0.869963			−0.434982	+	0.900439i	$0.643245\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	−0.174038	+	0.535634i	−0.0323181	+	0.0994647i	−0.965914	−	0.258862i	$-0.916653\pi$
$29$	−0.174038	+	0.535634i	−0.0323181	+	0.0994647i	0.933596	+	0.358327i	$0.116653\pi$
$30$		0			0
$31$	−2.73949	+	1.99036i	−0.492028	+	0.357479i	−0.805964	−	0.591965i	$-0.798352\pi$
$31$	−2.73949	+	1.99036i	−0.492028	+	0.357479i	0.313936	+	0.949444i	$0.398352\pi$
$32$		0			0
$33$	−1.98238	+	2.65898i	−0.345088	+	0.462869i
$34$		0			0
$35$	−1.80273	+	1.30976i	−0.304718	+	0.221390i
$36$		0			0
$37$	−0.907314	+	2.79242i	−0.149161	+	0.459072i	−0.997523	−	0.0703461i	$-0.977590\pi$
$37$	−0.907314	+	2.79242i	−0.149161	+	0.459072i	0.848361	+	0.529418i	$0.177590\pi$
$38$		0			0
$39$	1.14771	+	0.833861i	0.183781	+	0.133525i
$40$		0			0
$41$	3.41649	+	10.5149i	0.533566	+	1.64215i	0.746726	+	0.665131i	$0.231624\pi$
$41$	3.41649	+	10.5149i	0.533566	+	1.64215i	−0.213160	+	0.977017i	$0.568376\pi$
$42$		0			0
$43$	−4.54160			−0.692587			−0.346293	−	0.938126i	$-0.612560\pi$
$43$	−4.54160			−0.692587			−0.346293	+	0.938126i	$0.612560\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	0.845613	+	2.60253i	0.123345	+	0.379618i	0.993596	−	0.112991i	$-0.0360432\pi$
$47$	0.845613	+	2.60253i	0.123345	+	0.379618i	−0.870251	+	0.492609i	$0.836043\pi$
$48$		0			0
$49$	1.64609	+	1.19595i	0.235155	+	0.170850i
$50$		0			0
$51$	1.00312	−	3.08729i	0.140465	−	0.432308i
$52$		0			0
$53$	−0.149477	+	0.108602i	−0.0205323	+	0.0149176i	−0.598004	−	0.801493i	$-0.704039\pi$
$53$	−0.149477	+	0.108602i	−0.0205323	+	0.0149176i	0.577472	+	0.816411i	$0.304039\pi$
$54$		0			0
$55$	0.0408712	−	3.31637i	0.00551107	−	0.447180i
$56$		0			0
$57$	4.11627	−	2.99064i	0.545213	−	0.396120i
$58$		0			0
$59$	−0.618480	+	1.90349i	−0.0805193	+	0.247813i	−0.983210	−	0.182477i	$-0.941589\pi$
$59$	−0.618480	+	1.90349i	−0.0805193	+	0.247813i	0.902691	+	0.430290i	$0.141589\pi$
$60$		0			0
$61$	−5.16994	−	3.75618i	−0.661943	−	0.480929i	0.205376	−	0.978683i	$-0.434158\pi$
$61$	−5.16994	−	3.75618i	−0.661943	−	0.480929i	−0.867318	+	0.497754i	$0.834158\pi$
$62$		0			0
$63$	−0.688583	−	2.11924i	−0.0867533	−	0.266999i
$64$		0			0
$65$	−1.41865			−0.175962
$66$		0			0
$67$	−6.13724			−0.749783			−0.374891	−	0.927069i	$-0.622320\pi$
$67$	−6.13724			−0.749783			−0.374891	+	0.927069i	$0.622320\pi$
$68$		0			0
$69$	1.28928	+	3.96800i	0.155211	+	0.477691i
$70$		0			0
$71$	−8.05149	−	5.84975i	−0.955537	−	0.694238i	−0.00342672	−	0.999994i	$-0.501091\pi$
$71$	−8.05149	−	5.84975i	−0.955537	−	0.694238i	−0.952110	+	0.305756i	$0.901091\pi$
$72$		0			0
$73$	−4.85287	+	14.9356i	−0.567986	+	1.74808i	0.0909242	+	0.995858i	$0.471018\pi$
$73$	−4.85287	+	14.9356i	−0.567986	+	1.74808i	−0.658910	+	0.752222i	$0.728982\pi$
$74$		0			0
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$		0			0
$77$	7.05633	−	2.19698i	0.804144	−	0.250369i
$78$		0			0
$79$	3.99092	−	2.89957i	0.449014	−	0.326228i	−0.340192	−	0.940356i	$-0.610492\pi$
$79$	3.99092	−	2.89957i	0.449014	−	0.326228i	0.789206	+	0.614128i	$0.210492\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	10.2660	+	7.45866i	1.12684	+	0.818694i	0.985231	−	0.171229i	$-0.0547739\pi$
$83$	10.2660	+	7.45866i	1.12684	+	0.818694i	0.141604	+	0.989923i	$0.454774\pi$
$84$		0			0
$85$	1.00312	+	3.08729i	0.108804	+	0.334864i
$86$		0			0
$87$	0.563199			0.0603813
$88$		0			0
$89$	7.90696			0.838136			0.419068	−	0.907955i	$-0.362357\pi$
$89$	7.90696			0.838136			0.419068	+	0.907955i	$0.362357\pi$
$90$		0			0
$91$	−0.976858	−	3.00646i	−0.102403	−	0.315163i
$92$		0			0
$93$	2.73949	+	1.99036i	0.284072	+	0.206391i
$94$		0			0
$95$	−1.57227	+	4.83896i	−0.161312	+	0.496467i
$96$		0			0
$97$	1.40017	−	1.01728i	0.142165	−	0.103289i	−0.514429	−	0.857533i	$-0.671996\pi$
$97$	1.40017	−	1.01728i	0.142165	−	0.103289i	0.656595	+	0.754244i	$0.271996\pi$
$98$		0			0
$99$	3.14143	+	1.06369i	0.315725	+	0.106905i
$100$		0			0
$101$	15.7928	−	11.4742i	1.57145	−	1.14172i	0.645692	−	0.763598i	$-0.276569\pi$
$101$	15.7928	−	11.4742i	1.57145	−	1.14172i	0.925754	−	0.378125i	$-0.123431\pi$
$102$		0			0
$103$	−4.08371	+	12.5684i	−0.402380	+	1.23840i	0.520683	+	0.853750i	$0.325677\pi$
$103$	−4.08371	+	12.5684i	−0.402380	+	1.23840i	−0.923063	+	0.384649i	$0.874323\pi$
$104$		0			0
$105$	1.80273	+	1.30976i	0.175929	+	0.127820i
$106$		0			0
$107$	1.89689	+	5.83804i	0.183380	+	0.564385i	0.999917	−	0.0129084i	$-0.00410898\pi$
$107$	1.89689	+	5.83804i	0.183380	+	0.564385i	−0.816537	+	0.577293i	$0.804109\pi$
$108$		0			0
$109$	5.97639			0.572434			0.286217	−	0.958165i	$-0.407602\pi$
$109$	5.97639			0.572434			0.286217	+	0.958165i	$0.407602\pi$
$110$		0			0
$111$	2.93613			0.278685
$112$		0			0
$113$	3.79514	+	11.6802i	0.357017	+	1.09878i	0.954831	+	0.297150i	$0.0960361\pi$
$113$	3.79514	+	11.6802i	0.357017	+	1.09878i	−0.597814	+	0.801635i	$0.703964\pi$
$114$		0			0
$115$	−3.37538	−	2.45236i	−0.314756	−	0.228683i
$116$		0			0
$117$	0.438387	−	1.34922i	0.0405289	−	0.124735i
$118$		0			0
$119$	−5.85198	+	4.25172i	−0.536451	+	0.389754i
$120$		0			0
$121$	−3.65597	+	10.3747i	−0.332361	+	0.943152i
$122$		0			0
$123$	8.94449	−	6.49855i	0.806498	−	0.585955i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	−1.91576	−	1.39188i	−0.169996	−	0.123509i	0.499534	−	0.866294i	$-0.333505\pi$
$127$	−1.91576	−	1.39188i	−0.169996	−	0.123509i	−0.669530	+	0.742785i	$0.733505\pi$
$128$		0			0
$129$	1.40343	+	4.31931i	0.123565	+	0.380294i
$130$		0			0
$131$	3.36399			0.293913			0.146957	−	0.989143i	$-0.453052\pi$
$131$	3.36399			0.293913			0.146957	+	0.989143i	$0.453052\pi$
$132$		0			0
$133$	−11.3376			−0.983092
$134$		0			0
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$		0			0
$137$	4.31214	+	3.13295i	0.368411	+	0.267666i	0.756552	−	0.653934i	$-0.226883\pi$
$137$	4.31214	+	3.13295i	0.368411	+	0.267666i	−0.388141	+	0.921600i	$0.626883\pi$
$138$		0			0
$139$	1.31493	−	4.04694i	0.111531	−	0.343257i	−0.879677	−	0.475572i	$-0.842241\pi$
$139$	1.31493	−	4.04694i	0.111531	−	0.343257i	0.991208	+	0.132315i	$0.0422410\pi$
$140$		0			0
$141$	2.21384	−	1.60845i	0.186439	−	0.135456i
$142$		0			0
$143$	4.45659	+	1.50900i	0.372678	+	0.126189i
$144$		0			0
$145$	−0.455637	+	0.331040i	−0.0378386	+	0.0274914i
$146$		0			0
$147$	0.628749	−	1.93509i	0.0518583	−	0.159604i
$148$		0			0
$149$	−16.5897	−	12.0531i	−1.35908	−	0.987428i	−0.998503	−	0.0546978i	$-0.982580\pi$
$149$	−16.5897	−	12.0531i	−1.35908	−	0.987428i	−0.360575	−	0.932730i	$-0.617420\pi$
$150$		0			0
$151$	−6.05855	−	18.6463i	−0.493038	−	1.51742i	−0.819992	−	0.572375i	$-0.806022\pi$
$151$	−6.05855	−	18.6463i	−0.493038	−	1.51742i	0.326954	−	0.945040i	$-0.393978\pi$
$152$		0			0
$153$	−3.24617			−0.262438
$154$		0			0
$155$	−3.38620			−0.271986
$156$		0			0
$157$	2.39906	+	7.38355i	0.191466	+	0.589271i	1.00000		0.000821645i	$0.000261538\pi$
$157$	2.39906	+	7.38355i	0.191466	+	0.589271i	−0.808534	+	0.588450i	$0.799738\pi$
$158$		0			0
$159$	0.149477	+	0.108602i	0.0118543	+	0.00861268i
$160$		0			0
$161$	2.87290	−	8.84189i	0.226417	−	0.696838i
$162$		0			0
$163$	−10.1896	+	7.40316i	−0.798109	+	0.579860i	−0.910359	−	0.413820i	$-0.864194\pi$
$163$	−10.1896	+	7.40316i	−0.798109	+	0.579860i	0.112250	+	0.993680i	$0.464194\pi$
$164$		0			0
$165$	−3.16669	+	0.985945i	−0.246526	+	0.0767557i
$166$		0			0
$167$	2.19961	−	1.59811i	0.170211	−	0.123666i	−0.499418	−	0.866361i	$-0.666453\pi$
$167$	2.19961	−	1.59811i	0.170211	−	0.123666i	0.669629	+	0.742695i	$0.266453\pi$
$168$		0			0
$169$	−3.39530	+	10.4497i	−0.261177	+	0.803821i
$170$		0			0
$171$	−4.11627	−	2.99064i	−0.314779	−	0.228700i
$172$		0			0
$173$	0.937736	+	2.88606i	0.0712948	+	0.219423i	0.980355	−	0.197243i	$-0.0631987\pi$
$173$	0.937736	+	2.88606i	0.0712948	+	0.219423i	−0.909060	+	0.416665i	$0.863199\pi$
$174$		0			0
$175$	−2.22830			−0.168444
$176$		0			0
$177$	2.00144			0.150438
$178$		0			0
$179$	−4.63529	−	14.2660i	−0.346458	−	1.06629i	−0.960799	−	0.277247i	$-0.910578\pi$
$179$	−4.63529	−	14.2660i	−0.346458	−	1.06629i	0.614340	−	0.789041i	$-0.289422\pi$
$180$		0			0
$181$	0.713985	+	0.518741i	0.0530701	+	0.0385577i	0.614004	−	0.789303i	$-0.289558\pi$
$181$	0.713985	+	0.518741i	0.0530701	+	0.0385577i	−0.560934	+	0.827861i	$0.689558\pi$
$182$		0			0
$183$	−1.97474	+	6.07763i	−0.145977	+	0.449271i
$184$		0			0
$185$	−2.37538	+	1.72581i	−0.174641	+	0.126884i
$186$		0			0
$187$	0.132675	−	10.7655i	0.00970215	−	0.787253i
$188$		0			0
$189$	−1.80273	+	1.30976i	−0.131130	+	0.0952712i
$190$		0			0
$191$	8.03275	−	24.7223i	0.581229	−	1.78884i	−0.0326838	−	0.999466i	$-0.510405\pi$
$191$	8.03275	−	24.7223i	0.581229	−	1.78884i	0.613913	−	0.789374i	$-0.289595\pi$
$192$		0			0
$193$	−16.2503	−	11.8066i	−1.16973	−	0.849855i	−0.178750	−	0.983895i	$-0.557205\pi$
$193$	−16.2503	−	11.8066i	−1.16973	−	0.849855i	−0.990976	+	0.134039i	$0.957205\pi$
$194$		0			0
$195$	0.438387	+	1.34922i	0.0313935	+	0.0966194i
$196$		0			0
$197$	1.50048			0.106905			0.0534523	−	0.998570i	$-0.482977\pi$
$197$	1.50048			0.106905			0.0534523	+	0.998570i	$0.482977\pi$
$198$		0			0
$199$	−17.4559			−1.23741			−0.618707	−	0.785622i	$-0.712343\pi$
$199$	−17.4559			−1.23741			−0.618707	+	0.785622i	$0.712343\pi$
$200$		0			0
$201$	1.89651	+	5.83686i	0.133770	+	0.411700i
$202$		0			0
$203$	−1.01530	−	0.737657i	−0.0712599	−	0.0517734i
$204$		0			0
$205$	−3.41649	+	10.5149i	−0.238618	+	0.734391i
$206$		0			0
$207$	3.37538	−	2.45236i	0.234605	−	0.170451i
$208$		0			0
$209$	10.0863	−	13.5288i	0.697686	−	0.935810i
$210$		0			0
$211$	16.9492	−	12.3143i	1.16683	−	0.847752i	0.176204	−	0.984354i	$-0.443618\pi$
$211$	16.9492	−	12.3143i	1.16683	−	0.847752i	0.990626	+	0.136602i	$0.0436181\pi$
$212$		0			0
$213$	−3.07540	+	9.46510i	−0.210723	+	0.648538i
$214$		0			0
$215$	−3.67423	−	2.66948i	−0.250580	−	0.182057i
$216$		0			0
$217$	−2.33168	−	7.17617i	−0.158285	−	0.487150i
$218$		0			0
$219$	15.7042			1.06119
$220$		0			0
$221$	−4.60518			−0.309778
$222$		0			0
$223$	0.842944	+	2.59431i	0.0564477	+	0.173728i	0.975305	−	0.220861i	$-0.0708868\pi$
$223$	0.842944	+	2.59431i	0.0564477	+	0.173728i	−0.918858	+	0.394589i	$0.870887\pi$
$224$		0			0
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$		0			0
$227$	−2.00347	+	6.16604i	−0.132975	+	0.409254i	−0.995270	−	0.0971525i	$-0.969027\pi$
$227$	−2.00347	+	6.16604i	−0.132975	+	0.409254i	0.862295	+	0.506407i	$0.169027\pi$
$228$		0			0
$229$	−9.17675	+	6.66730i	−0.606417	+	0.440588i	−0.848151	−	0.529755i	$-0.822284\pi$
$229$	−9.17675	+	6.66730i	−0.606417	+	0.440588i	0.241734	+	0.970343i	$0.422284\pi$
$230$		0			0
$231$	−4.26998	−	6.03207i	−0.280944	−	0.396881i
$232$		0			0
$233$	6.98326	−	5.07364i	0.457489	−	0.332385i	−0.335057	−	0.942198i	$-0.608755\pi$
$233$	6.98326	−	5.07364i	0.457489	−	0.332385i	0.792545	+	0.609813i	$0.208755\pi$
$234$		0			0
$235$	−0.845613	+	2.60253i	−0.0551617	+	0.169770i
$236$		0			0
$237$	−3.99092	−	2.89957i	−0.259238	−	0.188348i
$238$		0			0
$239$	2.11627	+	6.51320i	0.136890	+	0.421304i	0.995879	−	0.0906896i	$-0.0289071\pi$
$239$	2.11627	+	6.51320i	0.136890	+	0.421304i	−0.858989	+	0.511994i	$0.828907\pi$
$240$		0			0
$241$	−12.6826			−0.816959			−0.408480	−	0.912767i	$-0.633941\pi$
$241$	−12.6826			−0.816959			−0.408480	+	0.912767i	$0.633941\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	0.628749	+	1.93509i	0.0401693	+	0.123628i
$246$		0			0
$247$	−5.83954	−	4.24268i	−0.371561	−	0.269955i
$248$		0			0
$249$	3.92125	−	12.0684i	0.248499	−	0.764801i
$250$		0			0
$251$	17.7670	−	12.9084i	1.12144	−	0.814774i	0.137013	−	0.990569i	$-0.456250\pi$
$251$	17.7670	−	12.9084i	1.12144	−	0.814774i	0.984427	+	0.175795i	$0.0562497\pi$
$252$		0			0
$253$	7.99497	+	11.2942i	0.502640	+	0.710063i
$254$		0			0
$255$	2.62621	−	1.90805i	0.164460	−	0.119487i
$256$		0			0
$257$	6.35552	−	19.5603i	0.396447	−	1.22014i	−0.531383	−	0.847132i	$-0.678327\pi$
$257$	6.35552	−	19.5603i	0.396447	−	1.22014i	0.927829	−	0.373005i	$-0.121673\pi$
$258$		0			0
$259$	−5.29306	−	3.84563i	−0.328895	−	0.238956i
$260$		0			0
$261$	−0.174038	−	0.535634i	−0.0107727	−	0.0331549i
$262$		0			0
$263$	−0.215843			−0.0133094			−0.00665472	−	0.999978i	$-0.502118\pi$
$263$	−0.215843			−0.0133094			−0.00665472	+	0.999978i	$0.502118\pi$
$264$		0			0
$265$	−0.184764			−0.0113500
$266$		0			0
$267$	−2.44338	−	7.51997i	−0.149533	−	0.460214i
$268$		0			0
$269$	−16.3212	−	11.8581i	−0.995124	−	0.723000i	−0.0340869	−	0.999419i	$-0.510852\pi$
$269$	−16.3212	−	11.8581i	−0.995124	−	0.723000i	−0.961037	+	0.276419i	$0.910852\pi$
$270$		0			0
$271$	−2.12836	+	6.55043i	−0.129289	+	0.397910i	−0.994658	−	0.103225i	$-0.967084\pi$
$271$	−2.12836	+	6.55043i	−0.129289	+	0.397910i	0.865369	+	0.501135i	$0.167084\pi$
$272$		0			0
$273$	−2.55745	+	1.85809i	−0.154784	+	0.112457i
$274$		0			0
$275$	1.98238	−	2.65898i	0.119542	−	0.160342i
$276$		0			0
$277$	9.45086	−	6.86645i	0.567847	−	0.412565i	−0.266475	−	0.963842i	$-0.585859\pi$
$277$	9.45086	−	6.86645i	0.567847	−	0.412565i	0.834323	+	0.551277i	$0.185859\pi$
$278$		0			0
$279$	1.04639	−	3.22047i	0.0626460	−	0.192804i
$280$		0			0
$281$	7.98709	+	5.80296i	0.476470	+	0.346176i	0.799957	−	0.600057i	$-0.204855\pi$
$281$	7.98709	+	5.80296i	0.476470	+	0.346176i	−0.323487	+	0.946232i	$0.604855\pi$
$282$		0			0
$283$	−3.36440	−	10.3546i	−0.199993	−	0.615515i	−0.999882	−	0.0153669i	$-0.995108\pi$
$283$	−3.36440	−	10.3546i	−0.199993	−	0.615515i	0.799889	−	0.600148i	$-0.204892\pi$
$284$		0			0
$285$	5.08799			0.301386
$286$		0			0
$287$	−24.6361			−1.45422
$288$		0			0
$289$	−1.99698	−	6.14607i	−0.117469	−	0.361534i
$290$		0			0
$291$	−1.40017	−	1.01728i	−0.0820791	−	0.0596340i
$292$		0			0
$293$	4.15756	−	12.7956i	0.242887	−	0.747530i	−0.753090	−	0.657918i	$-0.771437\pi$
$293$	4.15756	−	12.7956i	0.242887	−	0.747530i	0.995977	−	0.0896118i	$-0.0285626\pi$
$294$		0			0
$295$	−1.61920	+	1.17642i	−0.0942736	+	0.0684938i
$296$		0			0
$297$	0.0408712	−	3.31637i	0.00237159	−	0.192435i
$298$		0			0
$299$	4.78848	−	3.47903i	0.276925	−	0.201198i
$300$		0			0
$301$	3.12727	−	9.62473i	0.180253	−	0.554760i
$302$		0			0
$303$	−15.7928	−	11.4742i	−0.907275	−	0.659174i
$304$		0			0
$305$	−1.97474	−	6.07763i	−0.113073	−	0.348004i
$306$		0			0
$307$	7.01371			0.400294			0.200147	−	0.979766i	$-0.435858\pi$
$307$	7.01371			0.400294			0.200147	+	0.979766i	$0.435858\pi$
$308$		0			0
$309$	13.2152			0.751785
$310$		0			0
$311$	4.04922	+	12.4622i	0.229610	+	0.706667i	0.997791	+	0.0664343i	$0.0211623\pi$
$311$	4.04922	+	12.4622i	0.229610	+	0.706667i	−0.768181	+	0.640233i	$0.778838\pi$
$312$		0			0
$313$	−7.32769	−	5.32388i	−0.414185	−	0.300923i	0.361109	−	0.932524i	$-0.382398\pi$
$313$	−7.32769	−	5.32388i	−0.414185	−	0.300923i	−0.775294	+	0.631600i	$0.782398\pi$
$314$		0			0
$315$	0.688583	−	2.11924i	0.0387973	−	0.119406i
$316$		0			0
$317$	8.48397	−	6.16397i	0.476507	−	0.346203i	−0.323465	−	0.946240i	$-0.604848\pi$
$317$	8.48397	−	6.16397i	0.476507	−	0.346203i	0.799972	+	0.600037i	$0.204848\pi$
$318$		0			0
$319$	1.78348	−	0.555283i	0.0998554	−	0.0310899i
$320$		0			0
$321$	4.96613	−	3.60811i	0.277183	−	0.201385i
$322$		0			0
$323$	−5.10387	+	15.7081i	−0.283987	+	0.874023i
$324$		0			0
$325$	−1.14771	−	0.833861i	−0.0636636	−	0.0462543i
$326$		0			0
$327$	−1.84681	−	5.68388i	−0.102129	−	0.314319i
$328$		0			0
$329$	−6.09766			−0.336175
$330$		0			0
$331$	21.9744			1.20782			0.603911	−	0.797052i	$-0.293608\pi$
$331$	21.9744			1.20782			0.603911	+	0.797052i	$0.293608\pi$
$332$		0			0
$333$	−0.907314	−	2.79242i	−0.0497205	−	0.153024i
$334$		0			0
$335$	−4.96513	−	3.60738i	−0.271274	−	0.197092i
$336$		0			0
$337$	5.00400	−	15.4007i	0.272585	−	0.838930i	−0.717263	−	0.696802i	$-0.754605\pi$
$337$	5.00400	−	15.4007i	0.272585	−	0.838930i	0.989848	−	0.142128i	$-0.0453945\pi$
$338$		0			0
$339$	9.93581	−	7.21879i	0.539639	−	0.392071i
$340$		0			0
$341$	10.6375	+	3.60186i	0.576053	+	0.195051i
$342$		0			0
$343$	−16.2871	+	11.8333i	−0.879421	+	0.638937i
$344$		0			0
$345$	−1.28928	+	3.96800i	−0.0694125	+	0.213630i
$346$		0			0
$347$	4.62593	+	3.36093i	0.248333	+	0.180424i	0.704988	−	0.709220i	$-0.250953\pi$
$347$	4.62593	+	3.36093i	0.248333	+	0.180424i	−0.456655	+	0.889644i	$0.650953\pi$
$348$		0			0
$349$	3.51103	+	10.8058i	0.187941	+	0.578423i	0.999987	−	0.00517122i	$-0.00164606\pi$
$349$	3.51103	+	10.8058i	0.187941	+	0.578423i	−0.812046	+	0.583594i	$0.801646\pi$
$350$		0			0
$351$	−1.41865			−0.0757219
$352$		0			0
$353$	2.83817			0.151060			0.0755302	−	0.997144i	$-0.475935\pi$
$353$	2.83817			0.151060			0.0755302	+	0.997144i	$0.475935\pi$
$354$		0			0
$355$	−3.07540	−	9.46510i	−0.163225	−	0.502355i
$356$		0			0
$357$	5.85198	+	4.25172i	0.309720	+	0.225025i
$358$		0			0
$359$	−7.20972	+	22.1892i	−0.380514	+	1.17110i	0.559168	+	0.829054i	$0.311121\pi$
$359$	−7.20972	+	22.1892i	−0.380514	+	1.17110i	−0.939682	+	0.342048i	$0.888879\pi$
$360$		0			0
$361$	−5.57220	+	4.04844i	−0.293274	+	0.213076i
$362$		0			0
$363$	10.9967	+	0.271088i	0.577175	+	0.0142284i
$364$		0			0
$365$	−12.7050	+	9.23071i	−0.665009	+	0.483157i
$366$		0			0
$367$	−0.458099	+	1.40988i	−0.0239126	+	0.0735954i	−0.962301	−	0.271988i	$-0.912319\pi$
$367$	−0.458099	+	1.40988i	−0.0239126	+	0.0735954i	0.938388	+	0.345583i	$0.112319\pi$
$368$		0			0
$369$	−8.94449	−	6.49855i	−0.465632	−	0.338301i
$370$		0			0
$371$	−0.127226	−	0.391560i	−0.00660522	−	0.0203288i
$372$		0			0
$373$	12.8594			0.665835			0.332917	−	0.942956i	$-0.391967\pi$
$373$	12.8594			0.665835			0.332917	+	0.942956i	$0.391967\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−0.246899	−	0.759877i	−0.0127159	−	0.0391357i
$378$		0			0
$379$	4.20467	+	3.05487i	0.215979	+	0.156918i	0.690515	−	0.723318i	$-0.257384\pi$
$379$	4.20467	+	3.05487i	0.215979	+	0.156918i	−0.474536	+	0.880236i	$0.657384\pi$
$380$		0			0
$381$	−0.731754	+	2.25211i	−0.0374889	+	0.115379i
$382$		0			0
$383$	−25.1750	+	18.2907i	−1.28638	+	0.934611i	−0.999726	−	0.0234226i	$-0.992544\pi$
$383$	−25.1750	+	18.2907i	−1.28638	+	0.934611i	−0.286656	+	0.958034i	$0.592544\pi$
$384$		0			0
$385$	7.00005	+	2.37021i	0.356755	+	0.120797i
$386$		0			0
$387$	3.67423	−	2.66948i	0.186772	−	0.135697i
$388$		0			0
$389$	11.0335	−	33.9576i	0.559421	−	1.72172i	−0.124551	−	0.992213i	$-0.539749\pi$
$389$	11.0335	−	33.9576i	0.559421	−	1.72172i	0.683972	−	0.729508i	$-0.260251\pi$
$390$		0			0
$391$	−10.9571	−	7.96077i	−0.554122	−	0.402594i
$392$		0			0
$393$	−1.03953	−	3.19935i	−0.0524374	−	0.161386i
$394$		0			0
$395$	4.93305			0.248209
$396$		0			0
$397$	−12.6893			−0.636858			−0.318429	−	0.947947i	$-0.603155\pi$
$397$	−12.6893			−0.636858			−0.318429	+	0.947947i	$0.603155\pi$
$398$		0			0
$399$	3.50350	+	10.7827i	0.175394	+	0.539809i
$400$		0			0
$401$	−2.32260	−	1.68747i	−0.115985	−	0.0842680i	0.528281	−	0.849070i	$-0.322837\pi$
$401$	−2.32260	−	1.68747i	−0.115985	−	0.0842680i	−0.644266	+	0.764802i	$0.722837\pi$
$402$		0			0
$403$	1.48447	−	4.56872i	0.0739465	−	0.227584i
$404$		0			0
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$		0			0
$407$	9.29781	−	2.89486i	0.460875	−	0.143493i
$408$		0			0
$409$	3.29035	−	2.39058i	0.162697	−	0.118206i	−0.503458	−	0.864020i	$-0.667939\pi$
$409$	3.29035	−	2.39058i	0.162697	−	0.118206i	0.666155	+	0.745814i	$0.267939\pi$
$410$		0			0
$411$	1.64709	−	5.06923i	0.0812450	−	0.250047i
$412$		0			0
$413$	−3.60807	−	2.62142i	−0.177542	−	0.128992i
$414$		0			0
$415$	3.92125	+	12.0684i	0.192486	+	0.592412i
$416$		0			0
$417$	−4.25521			−0.208378
$418$		0			0
$419$	−21.2623			−1.03873			−0.519366	−	0.854552i	$-0.673832\pi$
$419$	−21.2623			−1.03873			−0.519366	+	0.854552i	$0.673832\pi$
$420$		0			0
$421$	3.14353	+	9.67479i	0.153206	+	0.471521i	0.997975	−	0.0636115i	$-0.0202618\pi$
$421$	3.14353	+	9.67479i	0.153206	+	0.471521i	−0.844768	+	0.535132i	$0.820262\pi$
$422$		0			0
$423$	−2.21384	−	1.60845i	−0.107641	−	0.0782056i
$424$		0			0
$425$	−1.00312	+	3.08729i	−0.0486586	+	0.149756i
$426$		0			0
$427$	11.5202	−	8.36990i	0.557500	−	0.405048i
$428$		0			0
$429$	0.0579819	−	4.70477i	0.00279939	−	0.227149i
$430$		0			0
$431$	7.02620	−	5.10483i	0.338440	−	0.245891i	−0.405563	−	0.914067i	$-0.632925\pi$
$431$	7.02620	−	5.10483i	0.338440	−	0.245891i	0.744003	+	0.668176i	$0.232925\pi$
$432$		0			0
$433$	−1.73098	+	5.32740i	−0.0831854	+	0.256018i	−0.983995	−	0.178196i	$-0.942974\pi$
$433$	−1.73098	+	5.32740i	−0.0831854	+	0.256018i	0.900810	+	0.434214i	$0.142974\pi$
$434$		0			0
$435$	0.455637	+	0.331040i	0.0218461	+	0.0158722i
$436$		0			0
$437$	−6.55984	−	20.1891i	−0.313800	−	0.965776i
$438$		0			0
$439$	33.7039			1.60860			0.804300	−	0.594223i	$-0.202540\pi$
$439$	33.7039			1.60860			0.804300	+	0.594223i	$0.202540\pi$
$440$		0			0
$441$	−2.03467			−0.0968892
$442$		0			0
$443$	8.57131	+	26.3798i	0.407235	+	1.25334i	0.919014	+	0.394224i	$0.128987\pi$
$443$	8.57131	+	26.3798i	0.407235	+	1.25334i	−0.511779	+	0.859117i	$0.671013\pi$
$444$		0			0
$445$	6.39686	+	4.64759i	0.303240	+	0.220317i
$446$		0			0
$447$	−6.33669	+	19.5023i	−0.299715	+	0.922428i
$448$		0			0
$449$	−25.4148	+	18.4650i	−1.19940	+	0.871415i	−0.994226	−	0.107310i	$-0.965776\pi$
$449$	−25.4148	+	18.4650i	−1.19940	+	0.871415i	−0.205175	+	0.978725i	$0.565776\pi$
$450$		0			0
$451$	21.9172	−	29.3977i	1.03204	−	1.38428i
$452$		0			0
$453$	−15.8615	+	11.5241i	−0.745238	+	0.541447i
$454$		0			0
$455$	0.976858	−	3.00646i	0.0457958	−	0.140945i
$456$		0			0
$457$	−30.9556	−	22.4905i	−1.44804	−	1.05206i	−0.986284	−	0.165055i	$-0.947220\pi$
$457$	−30.9556	−	22.4905i	−1.44804	−	1.05206i	−0.461755	−	0.887007i	$-0.652780\pi$
$458$		0			0
$459$	1.00312	+	3.08729i	0.0468218	+	0.144103i
$460$		0			0
$461$	24.8934			1.15940			0.579700	−	0.814830i	$-0.303170\pi$
$461$	24.8934			1.15940			0.579700	+	0.814830i	$0.303170\pi$
$462$		0			0
$463$	−33.7713			−1.56949			−0.784743	−	0.619822i	$-0.787205\pi$
$463$	−33.7713			−1.56949			−0.784743	+	0.619822i	$0.787205\pi$
$464$		0			0
$465$	1.04639	+	3.22047i	0.0485254	+	0.149346i
$466$		0			0
$467$	18.1913	+	13.2167i	0.841792	+	0.611598i	0.922871	−	0.385110i	$-0.125836\pi$
$467$	18.1913	+	13.2167i	0.841792	+	0.611598i	−0.0810785	+	0.996708i	$0.525836\pi$
$468$		0			0
$469$	4.22600	−	13.0063i	0.195138	−	0.600574i
$470$		0			0
$471$	6.28082	−	4.56328i	0.289405	−	0.210265i
$472$		0			0
$473$	8.70283	+	12.2942i	0.400157	+	0.565289i
$474$		0			0
$475$	−4.11627	+	2.99064i	−0.188867	+	0.137220i
$476$		0			0
$477$	0.0570953	−	0.175721i	0.00261421	−	0.00804572i
$478$		0			0
$479$	16.5443	+	12.0202i	0.755930	+	0.549215i	0.897659	−	0.440690i	$-0.145266\pi$
$479$	16.5443	+	12.0202i	0.755930	+	0.549215i	−0.141729	+	0.989905i	$0.545266\pi$
$480$		0			0
$481$	−1.28716	−	3.96147i	−0.0586895	−	0.180628i
$482$		0			0
$483$	−9.29691			−0.423024
$484$		0			0
$485$	1.73070			0.0785870
$486$		0			0
$487$	11.7106	+	36.0416i	0.530658	+	1.63320i	0.752847	+	0.658195i	$0.228680\pi$
$487$	11.7106	+	36.0416i	0.530658	+	1.63320i	−0.222189	+	0.975004i	$0.571320\pi$
$488$		0			0
$489$	10.1896	+	7.40316i	0.460788	+	0.334782i
$490$		0			0
$491$	−6.56587	+	20.2077i	−0.296313	+	0.911959i	0.686464	+	0.727164i	$0.259162\pi$
$491$	−6.56587	+	20.2077i	−0.296313	+	0.911959i	−0.982777	+	0.184795i	$0.940838\pi$
$492$		0			0
$493$	−1.47908	+	1.07461i	−0.0666143	+	0.0483981i
$494$		0			0
$495$	1.91625	+	2.70703i	0.0861290	+	0.121672i
$496$		0			0
$497$	17.9412	−	13.0350i	0.804771	−	0.584700i
$498$		0			0
$499$	5.23838	−	16.1221i	0.234502	−	0.721723i	−0.762685	−	0.646770i	$-0.776119\pi$
$499$	5.23838	−	16.1221i	0.234502	−	0.721723i	0.997187	−	0.0749528i	$-0.0238806\pi$
$500$		0			0
$501$	−2.19961	−	1.59811i	−0.0982714	−	0.0713983i
$502$		0			0
$503$	1.56072	+	4.80340i	0.0695891	+	0.214173i	0.979803	−	0.199965i	$-0.0640829\pi$
$503$	1.56072	+	4.80340i	0.0695891	+	0.214173i	−0.910214	+	0.414138i	$0.864083\pi$
$504$		0			0
$505$	19.5210			0.868674
$506$		0			0
$507$	10.9874			0.487969
$508$		0			0
$509$	−1.14683	−	3.52957i	−0.0508322	−	0.156445i	0.922418	−	0.386193i	$-0.126210\pi$
$509$	−1.14683	−	3.52957i	−0.0508322	−	0.156445i	−0.973250	+	0.229747i	$0.926210\pi$
$510$		0			0
$511$	−28.3105	−	20.5688i	−1.25238	−	0.909910i
$512$		0			0
$513$	−1.57227	+	4.83896i	−0.0694176	+	0.213645i
$514$		0			0
$515$	−10.6913	+	7.76768i	−0.471115	+	0.342285i
$516$		0			0
$517$	5.42471	−	7.27619i	0.238578	−	0.320006i
$518$		0			0
$519$	2.45503	−	1.78368i	0.107764	−	0.0782949i
$520$		0			0
$521$	3.88569	−	11.9589i	0.170235	−	0.523930i	−0.829149	−	0.559028i	$-0.811174\pi$
$521$	3.88569	−	11.9589i	0.170235	−	0.523930i	0.999384	+	0.0350980i	$0.0111743\pi$
$522$		0			0
$523$	28.9375	+	21.0243i	1.26535	+	0.919328i	0.999007	−	0.0445509i	$-0.0141857\pi$
$523$	28.9375	+	21.0243i	1.26535	+	0.919328i	0.266340	+	0.963879i	$0.414186\pi$
$524$		0			0
$525$	0.688583	+	2.11924i	0.0300522	+	0.0924912i
$526$		0			0
$527$	−10.9922			−0.478828
$528$		0			0
$529$	−5.59277			−0.243164
$530$		0			0
$531$	−0.618480	−	1.90349i	−0.0268398	−	0.0826043i
$532$		0			0
$533$	−12.6891	−	9.21917i	−0.549626	−	0.399327i
$534$		0			0
$535$	−1.89689	+	5.83804i	−0.0820099	+	0.252401i
$536$		0			0
$537$	−12.1354	+	8.81685i	−0.523679	+	0.380475i
$538$		0			0
$539$	0.0831595	−	6.74774i	0.00358193	−	0.290646i
$540$		0			0
$541$	−11.8112	+	8.58130i	−0.507801	+	0.368939i	−0.811989	−	0.583673i	$-0.801615\pi$
$541$	−11.8112	+	8.58130i	−0.507801	+	0.368939i	0.304188	+	0.952612i	$0.401615\pi$
$542$		0			0
$543$	0.272718	−	0.839340i	0.0117035	−	0.0360195i
$544$		0			0
$545$	4.83500	+	3.51283i	0.207109	+	0.150473i
$546$		0			0
$547$	10.1338	+	31.1888i	0.433292	+	1.33354i	0.894827	+	0.446413i	$0.147299\pi$
$547$	10.1338	+	31.1888i	0.433292	+	1.33354i	−0.461535	+	0.887122i	$0.652701\pi$
$548$		0			0
$549$	6.39039			0.272735
$550$		0			0
$551$	−2.86555			−0.122076
$552$		0			0
$553$	3.39681	+	10.4543i	0.144447	+	0.444563i
$554$		0			0
$555$	2.37538	+	1.72581i	0.100829	+	0.0732567i
$556$		0			0
$557$	11.0736	−	34.0810i	0.469203	−	1.44406i	−0.384415	−	0.923160i	$-0.625597\pi$
$557$	11.0736	−	34.0810i	0.469203	−	1.44406i	0.853618	−	0.520899i	$-0.174403\pi$
$558$		0			0
$559$	5.21244	−	3.78706i	0.220463	−	0.160176i
$560$		0			0
$561$	−10.2796	+	3.20055i	−0.434006	+	0.135127i
$562$		0			0
$563$	16.3621	−	11.8877i	0.689578	−	0.501008i	−0.186943	−	0.982371i	$-0.559858\pi$
$563$	16.3621	−	11.8877i	0.689578	−	0.501008i	0.876522	+	0.481363i	$0.159858\pi$
$564$		0			0
$565$	−3.79514	+	11.6802i	−0.159663	+	0.491392i
$566$		0			0
$567$	1.80273	+	1.30976i	0.0757077	+	0.0550049i
$568$		0			0
$569$	0.706343	+	2.17390i	0.0296114	+	0.0911347i	0.964770	−	0.263095i	$-0.0847432\pi$
$569$	0.706343	+	2.17390i	0.0296114	+	0.0911347i	−0.935159	+	0.354229i	$0.884743\pi$
$570$		0			0
$571$	29.2507			1.22410			0.612051	−	0.790818i	$-0.290345\pi$
$571$	29.2507			1.22410			0.612051	+	0.790818i	$0.290345\pi$
$572$		0			0
$573$	−25.9945			−1.08594
$574$		0			0
$575$	−1.28928	−	3.96800i	−0.0537667	−	0.165477i
$576$		0			0
$577$	−23.2419	−	16.8862i	−0.967571	−	0.702981i	−0.0126743	−	0.999920i	$-0.504034\pi$
$577$	−23.2419	−	16.8862i	−0.967571	−	0.702981i	−0.954897	+	0.296938i	$0.904034\pi$
$578$		0			0
$579$	−6.20708	+	19.1034i	−0.257957	+	0.793911i
$580$		0			0
$581$	−22.8756	+	16.6201i	−0.949042	+	0.689519i
$582$		0			0
$583$	0.580424	+	0.196531i	0.0240387	+	0.00813949i
$584$		0			0
$585$	1.14771	−	0.833861i	0.0474520	−	0.0344759i
$586$		0			0
$587$	8.93356	−	27.4947i	0.368728	−	1.13483i	−0.578886	−	0.815408i	$-0.696512\pi$
$587$	8.93356	−	27.4947i	0.368728	−	1.13483i	0.947614	−	0.319419i	$-0.103488\pi$
$588$		0			0
$589$	−13.9385	−	10.1269i	−0.574326	−	0.417273i
$590$		0			0
$591$	−0.463673	−	1.42704i	−0.0190730	−	0.0587005i
$592$		0			0
$593$	18.0337			0.740555			0.370277	−	0.928921i	$-0.379263\pi$
$593$	18.0337			0.740555			0.370277	+	0.928921i	$0.379263\pi$
$594$		0			0
$595$	−7.23345			−0.296543
$596$		0			0
$597$	5.39416	+	16.6015i	0.220768	+	0.679455i
$598$		0			0
$599$	−10.3442	−	7.51552i	−0.422654	−	0.307076i	0.356051	−	0.934467i	$-0.384123\pi$
$599$	−10.3442	−	7.51552i	−0.422654	−	0.307076i	−0.778705	+	0.627391i	$0.784123\pi$
$600$		0			0
$601$	−10.5728	+	32.5398i	−0.431275	+	1.32733i	0.465582	+	0.885005i	$0.345845\pi$
$601$	−10.5728	+	32.5398i	−0.431275	+	1.32733i	−0.896856	+	0.442322i	$0.854155\pi$
$602$		0			0
$603$	4.96513	−	3.60738i	0.202196	−	0.146904i
$604$		0			0
$605$	−9.05583	+	6.24436i	−0.368172	+	0.253869i
$606$		0			0
$607$	−2.63541	+	1.91474i	−0.106968	+	0.0777169i	−0.639983	−	0.768389i	$-0.721059\pi$
$607$	−2.63541	+	1.91474i	−0.106968	+	0.0777169i	0.533015	+	0.846106i	$0.321059\pi$
$608$		0			0
$609$	−0.387809	+	1.19355i	−0.0157148	+	0.0483652i
$610$		0			0
$611$	−3.14067	−	2.28183i	−0.127058	−	0.0923129i
$612$		0			0
$613$	−9.89241	−	30.4457i	−0.399551	−	1.22969i	−0.925360	−	0.379089i	$-0.876238\pi$
$613$	−9.89241	−	30.4457i	−0.399551	−	1.22969i	0.525809	−	0.850602i	$-0.323762\pi$
$614$		0			0
$615$	11.0560			0.445821
$616$		0			0
$617$	3.25258			0.130944			0.0654720	−	0.997854i	$-0.479145\pi$
$617$	3.25258			0.130944			0.0654720	+	0.997854i	$0.479145\pi$
$618$		0			0
$619$	14.1210	+	43.4600i	0.567572	+	1.74681i	0.660184	+	0.751104i	$0.270478\pi$
$619$	14.1210	+	43.4600i	0.567572	+	1.74681i	−0.0926119	+	0.995702i	$0.529522\pi$
$620$		0			0
$621$	−3.37538	−	2.45236i	−0.135449	−	0.0984097i
$622$		0			0
$623$	−5.44460	+	16.7567i	−0.218133	+	0.671345i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−15.9835	−	5.41202i	−0.638321	−	0.216135i
$628$		0			0
$629$	−7.71089	+	5.60229i	−0.307453	+	0.223378i
$630$		0			0
$631$	4.22060	−	12.9897i	0.168020	−	0.517111i	−0.831227	−	0.555934i	$-0.812361\pi$
$631$	4.22060	−	12.9897i	0.168020	−	0.517111i	0.999246	+	0.0388228i	$0.0123608\pi$
$632$		0			0
$633$	−16.9492	−	12.3143i	−0.673670	−	0.489450i
$634$		0			0
$635$	−0.731754	−	2.25211i	−0.0290388	−	0.0893722i
$636$		0			0
$637$	−2.88649			−0.114367
$638$		0			0
$639$	9.95219			0.393703
$640$		0			0
$641$	10.3765	+	31.9355i	0.409846	+	1.26138i	0.916781	+	0.399391i	$0.130778\pi$
$641$	10.3765	+	31.9355i	0.409846	+	1.26138i	−0.506935	+	0.861984i	$0.669222\pi$
$642$		0			0
$643$	−16.9384	−	12.3065i	−0.667986	−	0.485320i	0.201364	−	0.979516i	$-0.435462\pi$
$643$	−16.9384	−	12.3065i	−0.667986	−	0.485320i	−0.869350	+	0.494196i	$0.835462\pi$
$644$		0			0
$645$	−1.40343	+	4.31931i	−0.0552600	+	0.170073i
$646$		0			0
$647$	−39.6610	+	28.8154i	−1.55924	+	1.13285i	−0.622602	+	0.782539i	$0.713924\pi$
$647$	−39.6610	+	28.8154i	−1.55924	+	1.13285i	−0.936633	+	0.350312i	$0.886076\pi$
$648$		0			0
$649$	6.33795	−	1.97331i	0.248786	−	0.0774594i
$650$		0			0
$651$	−6.10442	+	4.43512i	−0.239251	+	0.173826i
$652$		0			0
$653$	−14.5134	+	44.6678i	−0.567954	+	1.74798i	0.0910512	+	0.995846i	$0.470977\pi$
$653$	−14.5134	+	44.6678i	−0.567954	+	1.74798i	−0.659006	+	0.752138i	$0.729023\pi$
$654$		0			0
$655$	2.72153	+	1.97730i	0.106339	+	0.0772597i
$656$		0			0
$657$	−4.85287	−	14.9356i	−0.189329	−	0.582693i
$658$		0			0
$659$	−47.3426			−1.84421			−0.922103	−	0.386945i	$-0.873530\pi$
$659$	−47.3426			−1.84421			−0.922103	+	0.386945i	$0.873530\pi$
$660$		0			0
$661$	22.4135			0.871783			0.435891	−	0.899999i	$-0.356433\pi$
$661$	22.4135			0.871783			0.435891	+	0.899999i	$0.356433\pi$
$662$		0			0
$663$	1.42308	+	4.37979i	0.0552678	+	0.170097i
$664$		0			0
$665$	−9.17229	−	6.66406i	−0.355686	−	0.258421i
$666$		0			0
$667$	0.726121	−	2.23477i	0.0281155	−	0.0865307i
$668$		0			0
$669$	2.20686	−	1.60337i	0.0853220	−	0.0619900i
$670$		0			0
$671$	−0.261183	+	21.1929i	−0.0100829	+	0.818144i
$672$		0			0
$673$	20.6743	−	15.0208i	0.796937	−	0.579008i	−0.113077	−	0.993586i	$-0.536071\pi$
$673$	20.6743	−	15.0208i	0.796937	−	0.579008i	0.910014	+	0.414578i	$0.136071\pi$
$674$		0			0
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$		0			0
$677$	−40.6452	−	29.5305i	−1.56212	−	1.13495i	−0.934243	−	0.356636i	$-0.883924\pi$
$677$	−40.6452	−	29.5305i	−1.56212	−	1.13495i	−0.627878	−	0.778312i	$-0.716076\pi$
$678$		0			0
$679$	1.19173	+	3.66777i	0.0457344	+	0.140756i
$680$		0			0
$681$	6.48335			0.248443
$682$		0			0
$683$	23.7448			0.908570			0.454285	−	0.890856i	$-0.349895\pi$
$683$	23.7448			0.908570			0.454285	+	0.890856i	$0.349895\pi$
$684$		0			0
$685$	1.64709	+	5.06923i	0.0629321	+	0.193685i
$686$		0			0
$687$	9.17675	+	6.66730i	0.350115	+	0.254373i
$688$		0			0
$689$	0.0809982	−	0.249287i	0.00308579	−	0.00949707i
$690$		0			0
$691$	23.6779	−	17.2030i	0.900749	−	0.654433i	−0.0379090	−	0.999281i	$-0.512070\pi$
$691$	23.6779	−	17.2030i	0.900749	−	0.654433i	0.938658	+	0.344848i	$0.112070\pi$
$692$		0			0
$693$	−4.41734	+	5.92500i	−0.167801	+	0.225072i
$694$		0			0
$695$	3.44254	−	2.50115i	0.130583	−	0.0948740i
$696$		0			0
$697$	−11.0905	+	34.1331i	−0.420084	+	1.29288i
$698$		0			0
$699$	−6.98326	−	5.07364i	−0.264131	−	0.191903i
$700$		0			0
$701$	3.59814	+	11.0739i	0.135900	+	0.418257i	0.995729	−	0.0923252i	$-0.0294299\pi$
$701$	3.59814	+	11.0739i	0.135900	+	0.418257i	−0.859829	+	0.510582i	$0.829430\pi$
$702$		0			0
$703$	−14.9390			−0.563435
$704$		0			0
$705$	2.73646			0.103061
$706$		0			0
$707$	13.4418	+	41.3698i	0.505533	+	1.55587i
$708$		0			0
$709$	34.0145	+	24.7130i	1.27744	+	0.928117i	0.999473	−	0.0324730i	$-0.0103383\pi$
$709$	34.0145	+	24.7130i	1.27744	+	0.928117i	0.277970	+	0.960590i	$0.410338\pi$
$710$		0			0
$711$	−1.52440	+	4.69161i	−0.0571693	+	0.175949i
$712$		0			0
$713$	11.4297	−	8.30417i	0.428046	−	0.310994i
$714$		0			0
$715$	2.71849	+	3.84032i	0.101666	+	0.143620i
$716$		0			0
$717$	5.54046	−	4.02538i	0.206912	−	0.150331i
$718$		0			0
$719$	−2.64689	+	8.14629i	−0.0987123	+	0.303805i	−0.988203	−	0.153147i	$-0.951059\pi$
$719$	−2.64689	+	8.14629i	−0.0987123	+	0.303805i	0.889491	+	0.456953i	$0.151059\pi$
$720$		0			0
$721$	−23.8234	−	17.3087i	−0.887231	−	0.644611i
$722$		0			0
$723$	3.91914	+	12.0619i	0.145755	+	0.448586i
$724$		0			0
$725$	−0.563199			−0.0209167
$726$		0			0
$727$	34.5283			1.28059			0.640293	−	0.768131i	$-0.278813\pi$
$727$	34.5283			1.28059			0.640293	+	0.768131i	$0.278813\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−11.9272	−	8.66560i	−0.441143	−	0.320509i
$732$		0			0
$733$	−0.732201	+	2.25348i	−0.0270445	+	0.0832343i	−0.963668	−	0.267104i	$-0.913933\pi$
$733$	−0.732201	+	2.25348i	−0.0270445	+	0.0832343i	0.936623	+	0.350338i	$0.113933\pi$
$734$		0			0
$735$	1.64609	−	1.19595i	0.0607168	−	0.0441133i
$736$		0			0
$737$	11.7605	+	16.6137i	0.433203	+	0.611972i
$738$		0			0
$739$	15.9064	−	11.5567i	0.585128	−	0.425120i	−0.255441	−	0.966825i	$-0.582221\pi$
$739$	15.9064	−	11.5567i	0.585128	−	0.425120i	0.840569	+	0.541704i	$0.182221\pi$
$740$		0			0
$741$	−2.23051	+	6.86479i	−0.0819397	+	0.252185i
$742$		0			0
$743$	40.3887	+	29.3441i	1.48172	+	1.07653i	0.976998	+	0.213248i	$0.0684044\pi$
$743$	40.3887	+	29.3441i	1.48172	+	1.07653i	0.504720	+	0.863283i	$0.331596\pi$
$744$		0			0
$745$	−6.33669	−	19.5023i	−0.232158	−	0.714510i
$746$		0			0
$747$	−12.6894			−0.464282
$748$		0			0
$749$	−13.6784			−0.499797
$750$		0			0
$751$	7.96543	+	24.5151i	0.290663	+	0.894568i	0.984644	+	0.174575i	$0.0558550\pi$
$751$	7.96543	+	24.5151i	0.290663	+	0.894568i	−0.693981	+	0.719993i	$0.744145\pi$
$752$		0			0
$753$	−17.7670	−	12.9084i	−0.647464	−	0.470410i
$754$		0			0
$755$	6.05855	−	18.6463i	0.220493	−	0.678609i
$756$		0			0
$757$	3.47298	−	2.52327i	0.126228	−	0.0917097i	−0.522880	−	0.852406i	$-0.675142\pi$
$757$	3.47298	−	2.52327i	0.126228	−	0.0917097i	0.649108	+	0.760697i	$0.275142\pi$
$758$		0			0
$759$	8.27088	−	11.0938i	0.300214	−	0.402679i
$760$		0			0
$761$	7.79176	−	5.66105i	0.282451	−	0.205213i	−0.437535	−	0.899202i	$-0.644148\pi$
$761$	7.79176	−	5.66105i	0.282451	−	0.205213i	0.719986	+	0.693989i	$0.244148\pi$
$762$		0			0
$763$	−4.11524	+	12.6654i	−0.148982	+	0.458518i
$764$		0			0
$765$	−2.62621	−	1.90805i	−0.0949508	−	0.0689858i
$766$		0			0
$767$	−0.877407	−	2.70038i	−0.0316813	−	0.0975051i
$768$		0			0
$769$	35.6122			1.28421			0.642104	−	0.766617i	$-0.278062\pi$
$769$	35.6122			1.28421			0.642104	+	0.766617i	$0.278062\pi$
$770$		0			0
$771$	−20.5669			−0.740699
$772$		0			0
$773$	4.19521	+	12.9115i	0.150891	+	0.464395i	0.997721	−	0.0674679i	$-0.0214920\pi$
$773$	4.19521	+	12.9115i	0.150891	+	0.464395i	−0.846830	+	0.531863i	$0.821492\pi$
$774$		0			0
$775$	−2.73949	−	1.99036i	−0.0984055	−	0.0714958i
$776$		0			0
$777$	−2.02177	+	6.22236i	−0.0725305	+	0.223226i
$778$		0			0
$779$	−45.5095	+	33.0646i	−1.63055	+	1.18466i
$780$		0			0
$781$	−0.406758	+	33.0052i	−0.0145549	+	1.18102i
$782$		0			0
$783$	−0.455637	+	0.331040i	−0.0162832	+	0.0118304i
$784$		0			0
$785$	−2.39906	+	7.38355i	−0.0856261	+	0.263530i
$786$		0			0
$787$	−4.06661	−	2.95456i	−0.144959	−	0.105319i	0.512942	−	0.858423i	$-0.328556\pi$
$787$	−4.06661	−	2.95456i	−0.144959	−	0.105319i	−0.657901	+	0.753104i	$0.728556\pi$
$788$		0			0
$789$	0.0666991	+	0.205279i	0.00237455	+	0.00730812i
$790$		0			0
$791$	−27.3665			−0.973041
$792$		0			0
$793$	9.06573			0.321934
$794$		0			0
$795$	0.0570953	+	0.175721i	0.00202496	+	0.00623219i
$796$		0			0
$797$	−2.20999	−	1.60565i	−0.0782817	−	0.0568750i	0.547956	−	0.836507i	$-0.315406\pi$
$797$	−2.20999	−	1.60565i	−0.0782817	−	0.0568750i	−0.626238	+	0.779632i	$0.715406\pi$
$798$		0			0
$799$	−2.74500	+	8.44826i	−0.0971113	+	0.298878i
$800$		0			0
$801$	−6.39686	+	4.64759i	−0.226022	+	0.164215i
$802$		0			0
$803$	49.7304	−	15.4835i	1.75495	−	0.546401i
$804$		0			0
$805$	7.52136	−	5.46459i	0.265093	−	0.192601i
$806$		0			0
$807$	−6.23416	+	19.1868i	−0.219453	+	0.675407i
$808$		0			0
$809$	−7.63174	−	5.54478i	−0.268318	−	0.194944i	0.445488	−	0.895288i	$-0.353030\pi$
$809$	−7.63174	−	5.54478i	−0.268318	−	0.194944i	−0.713806	+	0.700344i	$0.753030\pi$
$810$		0			0
$811$	−0.0236378	−	0.0727495i	−0.000830034	−	0.00255458i	0.950641	−	0.310294i	$-0.100427\pi$
$811$	−0.0236378	−	0.0727495i	−0.000830034	−	0.00255458i	−0.951471	+	0.307739i	$0.900427\pi$
$812$		0			0
$813$	6.88753			0.241556
$814$		0			0
$815$	−12.5950			−0.441184
$816$		0			0
$817$	−7.14064	−	21.9766i	−0.249819	−	0.768865i
$818$		0			0
$819$	2.55745	+	1.85809i	0.0893644	+	0.0649271i
$820$		0			0
$821$	6.97324	−	21.4614i	0.243368	−	0.749009i	−0.752533	−	0.658555i	$-0.771168\pi$
$821$	6.97324	−	21.4614i	0.243368	−	0.749009i	0.995901	−	0.0904544i	$-0.0288319\pi$
$822$		0			0
$823$	−4.90390	+	3.56289i	−0.170939	+	0.124195i	−0.669966	−	0.742392i	$-0.733691\pi$
$823$	−4.90390	+	3.56289i	−0.170939	+	0.124195i	0.499026	+	0.866587i	$0.333691\pi$
$824$		0			0
$825$	−3.14143	−	1.06369i	−0.109370	−	0.0370328i
$826$		0			0
$827$	11.3453	−	8.24283i	0.394514	−	0.286631i	−0.372789	−	0.927916i	$-0.621598\pi$
$827$	11.3453	−	8.24283i	0.394514	−	0.286631i	0.767303	+	0.641285i	$0.221598\pi$
$828$		0			0
$829$	8.43078	−	25.9473i	0.292813	−	0.901186i	−0.691134	−	0.722727i	$-0.742889\pi$
$829$	8.43078	−	25.9473i	0.292813	−	0.901186i	0.983947	−	0.178460i	$-0.0571114\pi$
$830$		0			0
$831$	−9.45086	−	6.86645i	−0.327847	−	0.238195i
$832$		0			0
$833$	2.04103	+	6.28164i	0.0707174	+	0.217646i
$834$		0			0
$835$	2.71887			0.0940903
$836$		0			0
$837$	−3.38620			−0.117044
$838$		0			0
$839$	3.45457	+	10.6321i	0.119265	+	0.367060i	0.992813	−	0.119679i	$-0.0381864\pi$
$839$	3.45457	+	10.6321i	0.119265	+	0.367060i	−0.873548	+	0.486739i	$0.838186\pi$
$840$		0			0
$841$	23.2049	+	16.8593i	0.800168	+	0.581356i
$842$		0			0
$843$	3.05080	−	9.38939i	0.105075	−	0.323388i
$844$		0			0
$845$	−8.88902	+	6.45825i	−0.305792	+	0.222171i
$846$		0			0
$847$	−19.4690	−	14.8917i	−0.668962	−	0.511685i
$848$		0			0
$849$	−8.80812	+	6.39947i	−0.302294	+	0.219629i
$850$		0			0
$851$	3.78549	−	11.6505i	0.129765	−	0.399376i
$852$		0			0
$853$	3.24382	+	2.35677i	0.111066	+	0.0806944i	0.641932	−	0.766762i	$-0.278133\pi$
$853$	3.24382	+	2.35677i	0.111066	+	0.0806944i	−0.530866	+	0.847456i	$0.678133\pi$
$854$		0			0
$855$	−1.57227	−	4.83896i	−0.0537707	−	0.165489i
$856$		0			0
$857$	−14.6541			−0.500573			−0.250286	−	0.968172i	$-0.580525\pi$
$857$	−14.6541			−0.500573			−0.250286	+	0.968172i	$0.580525\pi$
$858$		0			0
$859$	−3.80881			−0.129955			−0.0649774	−	0.997887i	$-0.520698\pi$
$859$	−3.80881			−0.129955			−0.0649774	+	0.997887i	$0.520698\pi$
$860$		0			0
$861$	7.61297	+	23.4303i	0.259449	+	0.798503i
$862$		0			0
$863$	−21.7427	−	15.7970i	−0.740130	−	0.537736i	0.152622	−	0.988285i	$-0.451228\pi$
$863$	−21.7427	−	15.7970i	−0.740130	−	0.537736i	−0.892752	+	0.450549i	$0.851228\pi$
$864$		0			0
$865$	−0.937736	+	2.88606i	−0.0318840	+	0.0981288i
$866$		0			0
$867$	−5.22816	+	3.79848i	−0.177558	+	0.129003i
$868$		0			0
$869$	−15.4968	−	5.24722i	−0.525694	−	0.178000i
$870$		0			0
$871$	7.04378	−	5.11761i	0.238669	−	0.173403i
$872$		0			0
$873$	−0.534816	+	1.64599i	−0.0181008	+	0.0557084i
$874$		0			0
$875$	−1.80273	−	1.30976i	−0.0609435	−	0.0442781i
$876$		0			0
$877$	16.2411	+	49.9851i	0.548425	+	1.68788i	0.712705	+	0.701463i	$0.247470\pi$
$877$	16.2411	+	49.9851i	0.548425	+	1.68788i	−0.164281	+	0.986414i	$0.552530\pi$
$878$		0			0
$879$	−13.4541			−0.453797
$880$		0			0
$881$	48.5932			1.63715			0.818574	−	0.574401i	$-0.194765\pi$
$881$	48.5932			1.63715			0.818574	+	0.574401i	$0.194765\pi$
$882$		0			0
$883$	11.8781	+	36.5569i	0.399729	+	1.23024i	0.925217	+	0.379437i	$0.123882\pi$
$883$	11.8781	+	36.5569i	0.399729	+	1.23024i	−0.525489	+	0.850800i	$0.676118\pi$
$884$		0			0
$885$	1.61920	+	1.17642i	0.0544289	+	0.0395449i
$886$		0			0
$887$	−11.2198	+	34.5310i	−0.376724	+	1.15944i	0.565584	+	0.824691i	$0.308651\pi$
$887$	−11.2198	+	34.5310i	−0.376724	+	1.15944i	−0.942308	+	0.334747i	$0.891349\pi$
$888$		0			0
$889$	4.26889	−	3.10153i	0.143174	−	0.104022i
$890$		0			0
$891$	−3.16669	+	0.985945i	−0.106088	+	0.0330304i
$892$		0			0
$893$	−11.2640	+	8.18378i	−0.376936	+	0.273860i
$894$		0			0
$895$	4.63529	−	14.2660i	0.154941	−	0.476859i
$896$		0			0
$897$	−4.78848	−	3.47903i	−0.159883	−	0.116162i
$898$		0			0
$899$	−0.589328	−	1.81376i	−0.0196552	−	0.0604924i
$900$		0			0
$901$	−0.599777			−0.0199815
$902$		0			0
$903$	−10.1200			−0.336774
$904$		0			0
$905$	0.272718	+	0.839340i	0.00906546	+	0.0279006i
$906$		0			0
$907$	25.2413	+	18.3389i	0.838125	+	0.608934i	0.921846	−	0.387556i	$-0.126680\pi$
$907$	25.2413	+	18.3389i	0.838125	+	0.608934i	−0.0837211	+	0.996489i	$0.526680\pi$
$908$		0			0
$909$	−6.03233	+	18.5656i	−0.200080	+	0.615782i
$910$		0			0
$911$	2.64260	−	1.91996i	0.0875533	−	0.0636112i	−0.543147	−	0.839637i	$-0.682768\pi$
$911$	2.64260	−	1.91996i	0.0875533	−	0.0636112i	0.630701	+	0.776026i	$0.282768\pi$
$912$		0			0
$913$	0.518632	−	42.0829i	0.0171642	−	1.39274i
$914$		0			0
$915$	−5.16994	+	3.75618i	−0.170913	+	0.124175i
$916$		0			0
$917$	−2.31639	+	7.12910i	−0.0764938	+	0.235424i
$918$		0			0
$919$	35.6018	+	25.8662i	1.17439	+	0.853248i	0.991528	−	0.129890i	$-0.0414625\pi$
$919$	35.6018	+	25.8662i	1.17439	+	0.853248i	0.182866	+	0.983138i	$0.441462\pi$
$920$		0			0
$921$	−2.16736	−	6.67044i	−0.0714168	−	0.219798i
$922$		0			0
$923$	14.1187			0.464722
$924$		0			0
$925$	−2.93613			−0.0965393
$926$		0			0
$927$	−4.08371	−	12.5684i	−0.134127	−	0.412800i
$928$		0			0
$929$	−44.9130	−	32.6312i	−1.47355	−	1.07060i	−0.979566	−	0.201123i	$-0.935541\pi$
$929$	−44.9130	−	32.6312i	−1.47355	−	1.07060i	−0.493982	−	0.869472i	$-0.664459\pi$
$930$		0			0
$931$	−3.19907	+	9.84571i	−0.104845	+	0.322680i
$932$		0			0
$933$	10.6010	−	7.70207i	0.347061	−	0.252155i
$934$		0			0
$935$	6.43515	−	8.63150i	0.210452	−	0.282280i
$936$		0			0
$937$	26.1738	−	19.0164i	0.855060	−	0.621237i	−0.0714765	−	0.997442i	$-0.522771\pi$
$937$	26.1738	−	19.0164i	0.855060	−	0.621237i	0.926537	+	0.376205i	$0.122771\pi$
$938$		0			0
$939$	−2.79893	+	8.61422i	−0.0913396	+	0.281114i
$940$		0			0
$941$	6.67793	+	4.85180i	0.217694	+	0.158164i	0.691288	−	0.722579i	$-0.257044\pi$
$941$	6.67793	+	4.85180i	0.217694	+	0.158164i	−0.473594	+	0.880743i	$0.657044\pi$
$942$		0			0
$943$	−14.2543	−	43.8702i	−0.464183	−	1.42861i
$944$		0			0
$945$	−2.22830			−0.0724866
$946$		0			0
$947$	46.6243			1.51509			0.757543	−	0.652786i	$-0.226400\pi$
$947$	46.6243			1.51509			0.757543	+	0.652786i	$0.226400\pi$
$948$		0			0
$949$	−6.88452	−	21.1884i	−0.223481	−	0.687804i
$950$		0			0
$951$	−8.48397	−	6.16397i	−0.275112	−	0.199880i
$952$		0			0
$953$	1.72659	−	5.31389i	0.0559297	−	0.172134i	−0.919189	−	0.393816i	$-0.871155\pi$
$953$	1.72659	−	5.31389i	0.0559297	−	0.172134i	0.975119	+	0.221682i	$0.0711547\pi$
$954$		0			0
$955$	21.0300	−	15.2792i	0.680515	−	0.494423i
$956$		0			0
$957$	−1.07923	−	1.52459i	−0.0348865	−	0.0492831i
$958$		0			0
$959$	−9.60875	+	6.98117i	−0.310283	+	0.225434i
$960$		0			0
$961$	−6.03623	+	18.5776i	−0.194717	+	0.599277i
$962$		0			0
$963$	−4.96613	−	3.60811i	−0.160031	−	0.116270i
$964$		0			0
$965$	−6.20708	−	19.1034i	−0.199813	−	0.614961i
$966$		0			0
$967$	31.8742			1.02501			0.512503	−	0.858685i	$-0.328718\pi$
$967$	31.8742			1.02501			0.512503	+	0.858685i	$0.328718\pi$
$968$		0			0
$969$	16.5165			0.530586
$970$		0			0
$971$	−0.499291	−	1.53666i	−0.0160230	−	0.0493138i	0.942725	−	0.333570i	$-0.108253\pi$
$971$	−0.499291	−	1.53666i	−0.0160230	−	0.0493138i	−0.958748	+	0.284256i	$0.908253\pi$
$972$		0			0
$973$	7.67101	+	5.57331i	0.245921	+	0.178672i
$974$		0			0
$975$	−0.438387	+	1.34922i	−0.0140396	+	0.0432095i
$976$		0			0
$977$	−29.0215	+	21.0853i	−0.928479	+	0.674579i	−0.945620	−	0.325274i	$-0.894544\pi$
$977$	−29.0215	+	21.0853i	−0.928479	+	0.674579i	0.0171411	+	0.999853i	$0.494544\pi$
$978$		0			0
$979$	−15.1517	−	21.4043i	−0.484251	−	0.684086i
$980$		0			0
$981$	−4.83500	+	3.51283i	−0.154370	+	0.112156i
$982$		0			0
$983$	14.6828	−	45.1891i	0.468309	−	1.44131i	−0.386464	−	0.922305i	$-0.626304\pi$
$983$	14.6828	−	45.1891i	0.468309	−	1.44131i	0.854773	−	0.519002i	$-0.173696\pi$
$984$		0			0
$985$	1.21391	+	0.881958i	0.0386784	+	0.0281015i
$986$		0			0
$987$	1.88428	+	5.79922i	0.0599773	+	0.184591i
$988$		0			0
$989$	18.9484			0.602525
$990$		0			0
$991$	32.6557			1.03734			0.518671	−	0.854974i	$-0.326427\pi$
$991$	32.6557			1.03734			0.518671	+	0.854974i	$0.326427\pi$
$992$		0			0
$993$	−6.79046	−	20.8989i	−0.215489	−	0.663206i
$994$		0			0
$995$	−14.1221	−	10.2603i	−0.447701	−	0.325274i
$996$		0			0
$997$	−1.33430	+	4.10654i	−0.0422576	+	0.130055i	−0.969960	−	0.243266i	$-0.921781\pi$
$997$	−1.33430	+	4.10654i	−0.0422576	+	0.130055i	0.927702	+	0.373322i	$0.121781\pi$
$998$		0			0
$999$	−2.37538	+	1.72581i	−0.0751536	+	0.0546023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.h.1081.1	yes	12
11.4	even	5	inner	1320.2.bw.h.961.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.h.961.1	✓	12	11.4	even	5	inner
1320.2.bw.h.1081.1	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-0.688583 + 2.11924i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-0.688583 + 2.11924i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-1.91625 - 2.70703i) q^{11} +(-1.14771 + 0.833861i) q^{13} +(0.309017 - 0.951057i) q^{15} +(2.62621 + 1.90805i) q^{17} +(1.57227 + 4.83896i) q^{19} +2.22830 q^{21} -4.17220 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-0.174038 + 0.535634i) q^{29} +(-2.73949 + 1.99036i) q^{31} +(-1.98238 + 2.65898i) q^{33} +(-1.80273 + 1.30976i) q^{35} +(-0.907314 + 2.79242i) q^{37} +(1.14771 + 0.833861i) q^{39} +(3.41649 + 10.5149i) q^{41} -4.54160 q^{43} -1.00000 q^{45} +(0.845613 + 2.60253i) q^{47} +(1.64609 + 1.19595i) q^{49} +(1.00312 - 3.08729i) q^{51} +(-0.149477 + 0.108602i) q^{53} +(0.0408712 - 3.31637i) q^{55} +(4.11627 - 2.99064i) q^{57} +(-0.618480 + 1.90349i) q^{59} +(-5.16994 - 3.75618i) q^{61} +(-0.688583 - 2.11924i) q^{63} -1.41865 q^{65} -6.13724 q^{67} +(1.28928 + 3.96800i) q^{69} +(-8.05149 - 5.84975i) q^{71} +(-4.85287 + 14.9356i) q^{73} +(0.809017 - 0.587785i) q^{75} +(7.05633 - 2.19698i) q^{77} +(3.99092 - 2.89957i) q^{79} +(0.309017 - 0.951057i) q^{81} +(10.2660 + 7.45866i) q^{83} +(1.00312 + 3.08729i) q^{85} +0.563199 q^{87} +7.90696 q^{89} +(-0.976858 - 3.00646i) q^{91} +(2.73949 + 1.99036i) q^{93} +(-1.57227 + 4.83896i) q^{95} +(1.40017 - 1.01728i) q^{97} +(3.14143 + 1.06369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 3 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 3 * q^5 + 5 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} + 3 q^{5} + 5 q^{7} - 3 q^{9} + 6 q^{11} - 2 q^{13} - 3 q^{15} - 13 q^{17} - 12 q^{23} - 3 q^{25} + 3 q^{27} - 15 q^{29} - 3 q^{31} + 9 q^{33} + 5 q^{35} + 11 q^{37} + 2 q^{39} + 13 q^{41} + 10 q^{43} - 12 q^{45} + 14 q^{47} + 12 q^{49} - 12 q^{51} - 21 q^{53} - q^{55} + 5 q^{57} - 31 q^{59} - 39 q^{61} + 5 q^{63} - 8 q^{65} - 40 q^{67} + 7 q^{69} - q^{71} + 9 q^{73} + 3 q^{75} + 79 q^{77} + 39 q^{79} - 3 q^{81} - 17 q^{83} - 12 q^{85} - 40 q^{87} + 36 q^{89} + 17 q^{91} + 3 q^{93} + 3 q^{97} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 + 3 * q^5 + 5 * q^7 - 3 * q^9 + 6 * q^11 - 2 * q^13 - 3 * q^15 - 13 * q^17 - 12 * q^23 - 3 * q^25 + 3 * q^27 - 15 * q^29 - 3 * q^31 + 9 * q^33 + 5 * q^35 + 11 * q^37 + 2 * q^39 + 13 * q^41 + 10 * q^43 - 12 * q^45 + 14 * q^47 + 12 * q^49 - 12 * q^51 - 21 * q^53 - q^55 + 5 * q^57 - 31 * q^59 - 39 * q^61 + 5 * q^63 - 8 * q^65 - 40 * q^67 + 7 * q^69 - q^71 + 9 * q^73 + 3 * q^75 + 79 * q^77 + 39 * q^79 - 3 * q^81 - 17 * q^83 - 12 * q^85 - 40 * q^87 + 36 * q^89 + 17 * q^91 + 3 * q^93 + 3 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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