LMFDB - Embedded newform 819.2.n.f.100.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(100,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.100"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,-16,0,0,-9,12,0,8,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.8
Root			$0.904928 - 1.56738i$ of defining polynomial
Character	$\chi$	$=$	819.100
Dual form			819.2.n.f.172.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.904928 + 1.56738i) q^{2} +(-0.637789 + 1.10468i) q^{4} +(-1.98776 + 3.44291i) q^{5} +(-2.60384 + 0.469078i) q^{7} +1.31110 q^{8} -7.19513 q^{10} +0.286654 q^{11} +(3.60075 - 0.185985i) q^{13} +(-3.09151 - 3.65672i) q^{14} +(2.46203 + 4.26436i) q^{16} +(-2.30091 + 3.98530i) q^{17} -6.96749 q^{19} +(-2.53555 - 4.39170i) q^{20} +(0.259402 + 0.449297i) q^{22} +(-3.61929 - 6.26879i) q^{23} +(-5.40240 - 9.35723i) q^{25} +(3.54993 + 5.47545i) q^{26} +(1.14252 - 3.17559i) q^{28} +(-0.421754 + 0.730500i) q^{29} +(-0.212854 - 0.368675i) q^{31} +(-3.14482 + 5.44698i) q^{32} -8.32864 q^{34} +(3.56082 - 9.89718i) q^{35} +(2.18208 + 3.77948i) q^{37} +(-6.30507 - 10.9207i) q^{38} +(-2.60615 + 4.51399i) q^{40} +(0.509885 - 0.883147i) q^{41} +(0.585291 + 1.01375i) q^{43} +(-0.182825 + 0.316662i) q^{44} +(6.55039 - 11.3456i) q^{46} +(-2.71264 + 4.69843i) q^{47} +(6.55993 - 2.44280i) q^{49} +(9.77756 - 16.9352i) q^{50} +(-2.09107 + 4.09631i) q^{52} +(0.574226 + 0.994589i) q^{53} +(-0.569801 + 0.986924i) q^{55} +(-3.41389 + 0.615007i) q^{56} -1.52663 q^{58} +(-2.42927 + 4.20762i) q^{59} +8.16848 q^{61} +(0.385236 - 0.667248i) q^{62} -1.53522 q^{64} +(-6.51711 + 12.7667i) q^{65} +1.57387 q^{67} +(-2.93499 - 5.08356i) q^{68} +(18.7349 - 3.37507i) q^{70} +(3.22369 + 5.58359i) q^{71} +(8.24845 + 14.2867i) q^{73} +(-3.94925 + 6.84031i) q^{74} +(4.44379 - 7.69686i) q^{76} +(-0.746401 + 0.134463i) q^{77} +(-3.84412 + 6.65821i) q^{79} -19.5757 q^{80} +1.84564 q^{82} -13.3888 q^{83} +(-9.14733 - 15.8436i) q^{85} +(-1.05929 + 1.83475i) q^{86} +0.375832 q^{88} +(-1.10786 - 1.91886i) q^{89} +(-9.28853 + 2.17331i) q^{91} +9.23336 q^{92} -9.81898 q^{94} +(13.8497 - 23.9884i) q^{95} +(9.52241 + 16.4933i) q^{97} +(9.76507 + 8.07135i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 16 q^{4} - 9 q^{7} + 12 q^{8} + 8 q^{10} - 16 q^{11} - 5 q^{13} + 9 q^{14} - 20 q^{16} - 14 q^{19} - 12 q^{20} - 9 q^{22} + 14 q^{23} - 32 q^{25} - 4 q^{26} + 13 q^{28} + 9 q^{29} - 9 q^{31} - 17 q^{32}+ \cdots + 79 q^{98}+O(q^{100}) $ 20 * q - 16 * q^4 - 9 * q^7 + 12 * q^8 + 8 * q^10 - 16 * q^11 - 5 * q^13 + 9 * q^14 - 20 * q^16 - 14 * q^19 - 12 * q^20 - 9 * q^22 + 14 * q^23 - 32 * q^25 - 4 * q^26 + 13 * q^28 + 9 * q^29 - 9 * q^31 - 17 * q^32 + 12 * q^34 - 10 * q^35 + 18 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 - 10 * q^46 - 13 * q^47 - 21 * q^49 - 5 * q^50 - 2 * q^52 + 6 * q^53 - 19 * q^55 + 5 * q^56 + 15 * q^59 - 22 * q^62 + 72 * q^64 + 27 * q^65 + 44 * q^67 - 39 * q^68 + 30 * q^70 + 11 * q^71 + 3 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 + 96 * q^80 + 26 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 + 24 * q^88 - 2 * q^89 + 9 * q^91 - 66 * q^92 + 88 * q^94 + 36 * q^95 + 21 * q^97 + 79 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.904928	+	1.56738i	0.639881	+	1.10831i	0.985459	+	0.169916i	$0.0543496\pi$
$2$	0.904928	+	1.56738i	0.639881	+	1.10831i	−0.345578	+	0.938390i	$0.612317\pi$
$3$		0			0
$3$		0			0
$4$	−0.637789	+	1.10468i	−0.318895	+	0.552342i
$5$	−1.98776	+	3.44291i	−0.888954	+	1.53971i	−0.0478412	+	0.998855i	$0.515234\pi$
$5$	−1.98776	+	3.44291i	−0.888954	+	1.53971i	−0.841113	+	0.540859i	$0.818099\pi$
$6$		0			0
$7$	−2.60384	+	0.469078i	−0.984158	+	0.177295i
$7$	−2.60384	+	0.469078i	−0.984158	+	0.177295i
$8$	1.31110			0.463543
$9$		0			0
$10$	−7.19513			−2.27530
$11$	0.286654			0.0864295			0.0432148	−	0.999066i	$-0.486240\pi$
$11$	0.286654			0.0864295			0.0432148	+	0.999066i	$0.486240\pi$
$12$		0			0
$13$	3.60075	−	0.185985i	0.998669	−	0.0515830i
$13$	3.60075	−	0.185985i	0.998669	−	0.0515830i
$14$	−3.09151	−	3.65672i	−0.826240	−	0.977300i
$15$		0			0
$16$	2.46203	+	4.26436i	0.615507	+	1.06609i
$17$	−2.30091	+	3.98530i	−0.558053	+	0.966577i	0.439606	+	0.898191i	$0.355118\pi$
$17$	−2.30091	+	3.98530i	−0.558053	+	0.966577i	−0.997659	+	0.0683857i	$0.978215\pi$
$18$		0			0
$19$	−6.96749			−1.59845			−0.799225	−	0.601031i	$-0.794757\pi$
$19$	−6.96749			−1.59845			−0.799225	+	0.601031i	$0.794757\pi$
$20$	−2.53555	−	4.39170i	−0.566965	−	0.982013i
$21$		0			0
$22$	0.259402	+	0.449297i	0.0553046	+	0.0957904i
$23$	−3.61929	−	6.26879i	−0.754673	−	1.30713i	−0.945537	−	0.325516i	$-0.894462\pi$
$23$	−3.61929	−	6.26879i	−0.754673	−	1.30713i	0.190863	−	0.981617i	$-0.438871\pi$
$24$		0			0
$25$	−5.40240	−	9.35723i	−1.08048	−	1.87145i
$26$	3.54993	+	5.47545i	0.696199	+	1.07382i
$27$		0			0
$28$	1.14252	−	3.17559i	0.215915	−	0.600130i
$29$	−0.421754	+	0.730500i	−0.0783178	+	0.135650i	−0.902524	−	0.430639i	$-0.858288\pi$
$29$	−0.421754	+	0.730500i	−0.0783178	+	0.135650i	0.824206	+	0.566289i	$0.191622\pi$
$30$		0			0
$31$	−0.212854	−	0.368675i	−0.0382298	−	0.0662159i	0.846277	−	0.532742i	$-0.178839\pi$
$31$	−0.212854	−	0.368675i	−0.0382298	−	0.0662159i	−0.884507	+	0.466527i	$0.845505\pi$
$32$	−3.14482	+	5.44698i	−0.555930	+	0.962900i
$33$		0			0
$34$	−8.32864			−1.42835
$35$	3.56082	−	9.89718i	0.601888	−	1.67293i
$36$		0			0
$37$	2.18208	+	3.77948i	0.358732	+	0.621342i	0.987749	−	0.156049i	$-0.0498758\pi$
$37$	2.18208	+	3.77948i	0.358732	+	0.621342i	−0.629017	+	0.777391i	$0.716542\pi$
$38$	−6.30507	−	10.9207i	−1.02282	−	1.77157i
$39$		0			0
$40$	−2.60615	+	4.51399i	−0.412069	+	0.713724i
$41$	0.509885	−	0.883147i	0.0796307	−	0.137924i	−0.823460	−	0.567374i	$-0.807959\pi$
$41$	0.509885	−	0.883147i	0.0796307	−	0.137924i	0.903091	+	0.429450i	$0.141293\pi$
$42$		0			0
$43$	0.585291	+	1.01375i	0.0892560	+	0.154596i	0.907197	−	0.420706i	$-0.138218\pi$
$43$	0.585291	+	1.01375i	0.0892560	+	0.154596i	−0.817941	+	0.575302i	$0.804884\pi$
$44$	−0.182825	+	0.316662i	−0.0275619	+	0.0477386i
$45$		0			0
$46$	6.55039	−	11.3456i	0.965802	−	1.67282i
$47$	−2.71264	+	4.69843i	−0.395680	+	0.685337i	−0.993188	−	0.116526i	$-0.962824\pi$
$47$	−2.71264	+	4.69843i	−0.395680	+	0.685337i	0.597508	+	0.801863i	$0.296158\pi$
$48$		0			0
$49$	6.55993	−	2.44280i	0.937133	−	0.348972i
$50$	9.77756	−	16.9352i	1.38276	−	2.39500i
$51$		0			0
$52$	−2.09107	+	4.09631i	−0.289979	+	0.568056i
$53$	0.574226	+	0.994589i	0.0788760	+	0.136617i	0.902765	−	0.430134i	$-0.141534\pi$
$53$	0.574226	+	0.994589i	0.0788760	+	0.136617i	−0.823889	+	0.566751i	$0.808200\pi$
$54$		0			0
$55$	−0.569801	+	0.986924i	−0.0768319	+	0.133077i
$56$	−3.41389	+	0.615007i	−0.456200	+	0.0821838i
$57$		0			0
$58$	−1.52663			−0.200456
$59$	−2.42927	+	4.20762i	−0.316264	+	0.547785i	−0.979705	−	0.200443i	$-0.935762\pi$
$59$	−2.42927	+	4.20762i	−0.316264	+	0.547785i	0.663441	+	0.748228i	$0.269095\pi$
$60$		0			0
$61$	8.16848			1.04587			0.522933	−	0.852374i	$-0.324838\pi$
$61$	8.16848			1.04587			0.522933	+	0.852374i	$0.324838\pi$
$62$	0.385236	−	0.667248i	0.0489250	−	0.0847406i
$63$		0			0
$64$	−1.53522			−0.191902
$65$	−6.51711	+	12.7667i	−0.808348	+	1.58352i
$66$		0			0
$67$	1.57387			0.192279			0.0961397	−	0.995368i	$-0.469350\pi$
$67$	1.57387			0.192279			0.0961397	+	0.995368i	$0.469350\pi$
$68$	−2.93499	−	5.08356i	−0.355920	−	0.616472i
$69$		0			0
$70$	18.7349	−	3.37507i	2.23925	−	0.403399i
$71$	3.22369	+	5.58359i	0.382581	+	0.662650i	0.991430	−	0.130636i	$-0.0417019\pi$
$71$	3.22369	+	5.58359i	0.382581	+	0.662650i	−0.608849	+	0.793286i	$0.708369\pi$
$72$		0			0
$73$	8.24845	+	14.2867i	0.965408	+	1.67214i	0.708515	+	0.705696i	$0.249365\pi$
$73$	8.24845	+	14.2867i	0.965408	+	1.67214i	0.256893	+	0.966440i	$0.417301\pi$
$74$	−3.94925	+	6.84031i	−0.459092	+	0.795170i
$75$		0			0
$76$	4.44379	−	7.69686i	0.509737	−	0.882891i
$77$	−0.746401	+	0.134463i	−0.0850603	+	0.0153235i
$78$		0			0
$79$	−3.84412	+	6.65821i	−0.432497	+	0.749107i	−0.997088	−	0.0762639i	$-0.975701\pi$
$79$	−3.84412	+	6.65821i	−0.432497	+	0.749107i	0.564590	+	0.825371i	$0.309034\pi$
$80$	−19.5757			−2.18863
$81$		0			0
$82$	1.84564			0.203817
$83$	−13.3888			−1.46961			−0.734805	−	0.678279i	$-0.762726\pi$
$83$	−13.3888			−1.46961			−0.734805	+	0.678279i	$0.762726\pi$
$84$		0			0
$85$	−9.14733	−	15.8436i	−0.992168	−	1.71848i
$86$	−1.05929	+	1.83475i	−0.114226	+	0.197846i
$87$		0			0
$88$	0.375832			0.0400639
$89$	−1.10786	−	1.91886i	−0.117433	−	0.203399i	0.801317	−	0.598240i	$-0.204133\pi$
$89$	−1.10786	−	1.91886i	−0.117433	−	0.203399i	−0.918750	+	0.394841i	$0.870800\pi$
$90$		0			0
$91$	−9.28853	+	2.17331i	−0.973702	+	0.227825i
$92$	9.23336			0.962645
$93$		0			0
$94$	−9.81898			−1.01275
$95$	13.8497	−	23.9884i	1.42095	−	2.46116i
$96$		0			0
$97$	9.52241	+	16.4933i	0.966854	+	1.67464i	0.704549	+	0.709656i	$0.251150\pi$
$97$	9.52241	+	16.4933i	0.966854	+	1.67464i	0.262306	+	0.964985i	$0.415517\pi$
$98$	9.76507	+	8.07135i	0.986421	+	0.815330i
$99$		0			0
$100$	13.7824			1.37824
$101$	9.08855			0.904344			0.452172	−	0.891931i	$-0.350649\pi$
$101$	9.08855			0.904344			0.452172	+	0.891931i	$0.350649\pi$
$102$		0			0
$103$	2.34421	−	4.06029i	0.230982	−	0.400072i	−0.727116	−	0.686515i	$-0.759140\pi$
$103$	2.34421	−	4.06029i	0.230982	−	0.400072i	0.958097	+	0.286443i	$0.0924729\pi$
$104$	4.72094	−	0.243845i	0.462926	−	0.0239109i
$105$		0			0
$106$	−1.03927	+	1.80006i	−0.100943	+	0.174838i
$107$	7.25279	+	12.5622i	0.701154	+	1.21443i	0.968062	+	0.250712i	$0.0806648\pi$
$107$	7.25279	+	12.5622i	0.701154	+	1.21443i	−0.266908	+	0.963722i	$0.586002\pi$
$108$		0			0
$109$	2.09694	+	3.63200i	0.200850	+	0.347883i	0.948803	−	0.315870i	$-0.102296\pi$
$109$	2.09694	+	3.63200i	0.200850	+	0.347883i	−0.747952	+	0.663752i	$0.768963\pi$
$110$	−2.06251			−0.196653
$111$		0			0
$112$	−8.41104	−	9.94881i	−0.794768	−	0.940074i
$113$	−4.12305	−	7.14133i	−0.387864	−	0.671800i	0.604298	−	0.796758i	$-0.293454\pi$
$113$	−4.12305	−	7.14133i	−0.387864	−	0.671800i	−0.992162	+	0.124958i	$0.960120\pi$
$114$		0			0
$115$	28.7771			2.68348
$116$	−0.537981	−	0.931810i	−0.0499503	−	0.0865164i
$117$		0			0
$118$	−8.79326			−0.809485
$119$	4.12179	−	11.4564i	0.377843	−	1.05020i
$120$		0			0
$121$	−10.9178			−0.992530
$122$	7.39189	+	12.8031i	0.669230	+	1.15914i
$123$		0			0
$124$	0.543025			0.0487651
$125$	23.0771			2.06408
$126$		0			0
$127$	−3.92173	+	6.79263i	−0.347997	+	0.602748i	−0.985894	−	0.167374i	$-0.946471\pi$
$127$	−3.92173	+	6.79263i	−0.347997	+	0.602748i	0.637897	+	0.770122i	$0.279805\pi$
$128$	4.90037	+	8.48769i	0.433136	+	0.750213i
$129$		0			0
$130$	−25.9079	+	1.33819i	−2.27227	+	0.117367i
$131$	4.04277	−	7.00228i	0.353218	−	0.611792i	−0.633593	−	0.773666i	$-0.718421\pi$
$131$	4.04277	−	7.00228i	0.353218	−	0.611792i	0.986811	+	0.161874i	$0.0517540\pi$
$132$		0			0
$133$	18.1422	−	3.26829i	1.57313	−	0.283397i
$134$	1.42424	+	2.46686i	0.123036	+	0.213104i
$135$		0			0
$136$	−3.01672	+	5.22512i	−0.258682	+	0.448050i
$137$	0.754841	−	1.30742i	0.0644904	−	0.111701i	−0.831977	−	0.554809i	$-0.812791\pi$
$137$	0.754841	−	1.30742i	0.0644904	−	0.111701i	0.896468	+	0.443109i	$0.146124\pi$
$138$		0			0
$139$	2.02132	+	3.50104i	0.171446	+	0.296954i	0.938926	−	0.344120i	$-0.111823\pi$
$139$	2.02132	+	3.50104i	0.171446	+	0.296954i	−0.767479	+	0.641074i	$0.778489\pi$
$140$	8.66220	+	10.2459i	0.732089	+	0.865936i
$141$		0			0
$142$	−5.83441	+	10.1055i	−0.489613	+	0.848034i
$143$	1.03217	−	0.0533134i	0.0863145	−	0.00445829i
$144$		0			0
$145$	−1.67670	−	2.90412i	−0.139242	−	0.241174i
$146$	−14.9285	+	25.8569i	−1.23549	+	2.13993i
$147$		0			0
$148$	−5.56683			−0.457591
$149$	19.1947			1.57249			0.786247	−	0.617912i	$-0.212021\pi$
$149$	19.1947			1.57249			0.786247	+	0.617912i	$0.212021\pi$
$150$		0			0
$151$	−9.47334	−	16.4083i	−0.770929	−	1.33529i	−0.937054	−	0.349184i	$-0.886459\pi$
$151$	−9.47334	−	16.4083i	−0.770929	−	1.33529i	0.166125	−	0.986105i	$-0.446874\pi$
$152$	−9.13506			−0.740951
$153$		0			0
$154$	−0.886194	−	1.04822i	−0.0714116	−	0.0844676i
$155$	1.69242			0.135938
$156$		0			0
$157$	−9.31770	−	16.1387i	−0.743633	−	1.28801i	−0.950831	−	0.309711i	$-0.899768\pi$
$157$	−9.31770	−	16.1387i	−0.743633	−	1.28801i	0.207197	−	0.978299i	$-0.433566\pi$
$158$	−13.9146			−1.10699
$159$		0			0
$160$	−12.5023	−	21.6546i	−0.988394	−	1.71195i
$161$	12.3646	+	14.6252i	0.974465	+	1.15262i
$162$		0			0
$163$	10.7052			0.838500			0.419250	−	0.907871i	$-0.362293\pi$
$163$	10.7052			0.838500			0.419250	+	0.907871i	$0.362293\pi$
$164$	0.650398	+	1.12652i	0.0507876	+	0.0879667i
$165$		0			0
$166$	−12.1159	−	20.9853i	−0.940375	−	1.62878i
$167$	−0.0240620	+	0.0416766i	−0.00186197	+	0.00322503i	−0.866955	−	0.498387i	$-0.833926\pi$
$167$	−0.0240620	+	0.0416766i	−0.00186197	+	0.00322503i	0.865093	+	0.501612i	$0.167259\pi$
$168$		0			0
$169$	12.9308	−	1.33937i	0.994678	−	0.103029i
$170$	16.5554	−	28.6747i	1.26974	−	2.19925i
$171$		0			0
$172$	−1.49317			−0.113853
$173$	14.0297			1.06666			0.533330	−	0.845907i	$-0.320940\pi$
$173$	14.0297			1.06666			0.533330	+	0.845907i	$0.320940\pi$
$174$		0			0
$175$	18.4562	+	21.8306i	1.39516	+	1.65023i
$176$	0.705751	+	1.22240i	0.0531980	+	0.0921416i
$177$		0			0
$178$	2.00506	−	3.47287i	0.150286	−	0.260302i
$179$	−4.69863			−0.351192			−0.175596	−	0.984462i	$-0.556185\pi$
$179$	−4.69863			−0.351192			−0.175596	+	0.984462i	$0.556185\pi$
$180$		0			0
$181$	−22.0382			−1.63809			−0.819044	−	0.573730i	$-0.805496\pi$
$181$	−22.0382			−1.63809			−0.819044	+	0.573730i	$0.805496\pi$
$182$	−11.8118	−	12.5920i	−0.875552	−	0.933379i
$183$		0			0
$184$	−4.74524	−	8.21900i	−0.349824	−	0.605913i
$185$	−17.3498			−1.27559
$186$		0			0
$187$	−0.659567	+	1.14240i	−0.0482323	+	0.0835408i
$188$	−3.46019	−	5.99322i	−0.252360	−	0.437101i
$189$		0			0
$190$	50.1319			3.63695
$191$	−11.0974			−0.802982			−0.401491	−	0.915863i	$-0.631508\pi$
$191$	−11.0974			−0.802982			−0.401491	+	0.915863i	$0.631508\pi$
$192$		0			0
$193$	−0.486230			−0.0349996			−0.0174998	−	0.999847i	$-0.505571\pi$
$193$	−0.486230			−0.0349996			−0.0174998	+	0.999847i	$0.505571\pi$
$194$	−17.2342	+	29.8505i	−1.23734	+	2.14314i
$195$		0			0
$196$	−1.48533	+	8.80464i	−0.106095	+	0.628903i
$197$	8.53814	−	14.7885i	0.608317	−	1.05364i	−0.383200	−	0.923665i	$-0.625178\pi$
$197$	8.53814	−	14.7885i	0.608317	−	1.05364i	0.991518	−	0.129971i	$-0.0414886\pi$
$198$		0			0
$199$	−11.5849	+	20.0656i	−0.821230	+	1.42241i	0.0835360	+	0.996505i	$0.473379\pi$
$199$	−11.5849	+	20.0656i	−0.821230	+	1.42241i	−0.904766	+	0.425908i	$0.859955\pi$
$200$	−7.08308	−	12.2683i	−0.500849	−	0.867497i
$201$		0			0
$202$	8.22448	+	14.2452i	0.578673	+	1.00229i
$203$	0.755518	−	2.09994i	0.0530270	−	0.147387i
$204$		0			0
$205$	2.02706	+	3.51097i	0.141576	+	0.245217i
$206$	8.48536			0.591203
$207$		0			0
$208$	9.65826	+	14.8970i	0.669680	+	1.03292i
$209$	−1.99726			−0.138153
$210$		0			0
$211$	1.40788	−	2.43852i	0.0969224	−	0.167874i	−0.813487	−	0.581583i	$-0.802433\pi$
$211$	1.40788	−	2.43852i	0.0969224	−	0.167874i	0.910409	+	0.413709i	$0.135767\pi$
$212$	−1.46494			−0.100613
$213$		0			0
$214$	−13.1265	+	22.7358i	−0.897310	+	1.55419i
$215$	−4.65368			−0.317378
$216$		0			0
$217$	0.727175	+	0.860123i	0.0493639	+	0.0583890i
$218$	−3.79515	+	6.57340i	−0.257040	+	0.445207i
$219$		0			0
$220$	−0.726825	−	1.25890i	−0.0490026	−	0.0848749i
$221$	−7.54381	+	14.7780i	−0.507451	+	0.994076i
$222$		0			0
$223$	−8.16232	+	14.1375i	−0.546589	+	0.946720i	0.451916	+	0.892061i	$0.350741\pi$
$223$	−8.16232	+	14.1375i	−0.546589	+	0.946720i	−0.998505	+	0.0546597i	$0.982593\pi$
$224$	5.63353	−	15.6582i	0.376406	−	1.04621i
$225$		0			0
$226$	7.46213	−	12.9248i	0.496373	−	0.859744i
$227$	−3.10289	+	5.37436i	−0.205946	+	0.356709i	−0.950434	−	0.310927i	$-0.899360\pi$
$227$	−3.10289	+	5.37436i	−0.205946	+	0.356709i	0.744488	+	0.667636i	$0.232694\pi$
$228$		0			0
$229$	0.261463	−	0.452867i	0.0172779	−	0.0299263i	−0.857257	−	0.514889i	$-0.827833\pi$
$229$	0.261463	−	0.452867i	0.0172779	−	0.0299263i	0.874535	+	0.484962i	$0.161167\pi$
$230$	26.0412	+	45.1047i	1.71711	+	2.97412i
$231$		0			0
$232$	−0.552962	+	0.957758i	−0.0363037	+	0.0628799i
$233$	6.48273	−	11.2284i	0.424697	−	0.735598i	−0.571695	−	0.820466i	$-0.693714\pi$
$233$	6.48273	−	11.2284i	0.424697	−	0.735598i	0.996392	+	0.0848689i	$0.0270471\pi$
$234$		0			0
$235$	−10.7842	−	18.6787i	−0.703482	−	1.21847i
$236$	−3.09872	−	5.36715i	−0.201710	−	0.349371i
$237$		0			0
$238$	21.6864	−	3.90678i	1.40572	−	0.253239i
$239$	4.79605			0.310231			0.155116	−	0.987896i	$-0.450425\pi$
$239$	4.79605			0.310231			0.155116	+	0.987896i	$0.450425\pi$
$240$		0			0
$241$	−5.20975	+	9.02355i	−0.335589	+	0.581258i	−0.983598	−	0.180375i	$-0.942269\pi$
$241$	−5.20975	+	9.02355i	−0.335589	+	0.581258i	0.648008	+	0.761633i	$0.275602\pi$
$242$	−9.87985	−	17.1124i	−0.635101	−	1.10003i
$243$		0			0
$244$	−5.20977	+	9.02358i	−0.333521	+	0.577676i
$245$	−4.62924	+	27.4409i	−0.295751	+	1.75314i
$246$		0			0
$247$	−25.0882	+	1.29585i	−1.59632	+	0.0824529i
$248$	−0.279073	−	0.483369i	−0.0177212	−	0.0306940i
$249$		0			0
$250$	20.8831	+	36.1706i	1.32077	+	2.28763i
$251$	5.10645	+	8.84463i	0.322316	+	0.558268i	0.980966	−	0.194182i	$-0.0622052\pi$
$251$	5.10645	+	8.84463i	0.322316	+	0.558268i	−0.658649	+	0.752450i	$0.728872\pi$
$252$		0			0
$253$	−1.03748	−	1.79698i	−0.0652261	−	0.112975i
$254$	−14.1955			−0.890706
$255$		0			0
$256$	−10.4042	+	18.0206i	−0.650262	+	1.12629i
$257$	−3.18140	−	5.51035i	−0.198450	−	0.343726i	0.749576	−	0.661919i	$-0.230258\pi$
$257$	−3.18140	−	5.51035i	−0.198450	−	0.343726i	−0.948026	+	0.318192i	$0.896924\pi$
$258$		0			0
$259$	−7.45466	−	8.81758i	−0.463210	−	0.547898i
$260$	−9.94666	−	15.3418i	−0.616866	−	0.951460i
$261$		0			0
$262$	14.6337			0.904070
$263$	17.0135			1.04910			0.524550	−	0.851380i	$-0.324234\pi$
$263$	17.0135			1.04910			0.524550	+	0.851380i	$0.324234\pi$
$264$		0			0
$265$	−4.56570			−0.280469
$266$	21.5400	+	25.4782i	1.32070	+	1.56217i
$267$		0			0
$268$	−1.00380	+	1.73863i	−0.0613168	+	0.106204i
$269$	−4.53019	+	7.84653i	−0.276211	+	0.478411i	−0.970440	−	0.241343i	$-0.922412\pi$
$269$	−4.53019	+	7.84653i	−0.276211	+	0.478411i	0.694229	+	0.719754i	$0.255745\pi$
$270$		0			0
$271$	−1.11398	−	1.92947i	−0.0676696	−	0.117207i	0.830206	−	0.557457i	$-0.188223\pi$
$271$	−1.11398	−	1.92947i	−0.0676696	−	0.117207i	−0.897875	+	0.440250i	$0.854890\pi$
$272$	−22.6596			−1.37394
$273$		0			0
$274$	2.73231			0.165065
$275$	−1.54862	−	2.68229i	−0.0933854	−	0.161748i
$276$		0			0
$277$	3.90377	−	6.76153i	0.234555	−	0.406261i	−0.724588	−	0.689182i	$-0.757970\pi$
$277$	3.90377	−	6.76153i	0.234555	−	0.406261i	0.959143	+	0.282921i	$0.0913034\pi$
$278$	−3.65830	+	6.33637i	−0.219411	+	0.380030i
$279$		0			0
$280$	4.66858	−	12.9762i	0.279001	−	0.775475i
$281$	12.7531			0.760789			0.380394	−	0.924824i	$-0.375788\pi$
$281$	12.7531			0.760789			0.380394	+	0.924824i	$0.375788\pi$
$282$		0			0
$283$	16.3439			0.971542			0.485771	−	0.874086i	$-0.338539\pi$
$283$	16.3439			0.971542			0.485771	+	0.874086i	$0.338539\pi$
$284$	−8.22413			−0.488012
$285$		0			0
$286$	1.01760	+	1.56956i	0.0601721	+	0.0928101i
$287$	−0.913393	+	2.53875i	−0.0539159	+	0.149857i
$288$		0			0
$289$	−2.08840	−	3.61721i	−0.122847	−	0.212777i
$290$	3.03458	−	5.25604i	0.178196	−	0.308645i
$291$		0			0
$292$	−21.0431			−1.23145
$293$	−11.8319	−	20.4935i	−0.691227	−	1.19724i	−0.971436	−	0.237302i	$-0.923737\pi$
$293$	−11.8319	−	20.4935i	−0.691227	−	1.19724i	0.280209	−	0.959939i	$-0.409596\pi$
$294$		0			0
$295$	−9.65762	−	16.7275i	−0.562288	−	0.973912i
$296$	2.86093	+	4.95527i	0.166288	+	0.288019i
$297$		0			0
$298$	17.3699	+	30.0855i	1.00621	+	1.74280i
$299$	−14.1980	−	21.8992i	−0.821094	−	1.26646i
$300$		0			0
$301$	−1.99953	−	2.36510i	−0.115251	−	0.136322i
$302$	17.1454	−	29.6967i	0.986605	−	1.70885i
$303$		0			0
$304$	−17.1541	−	29.7119i	−0.983858	−	1.70409i
$305$	−16.2370	+	28.1233i	−0.929728	+	1.61034i
$306$		0			0
$307$	8.99691			0.513481			0.256740	−	0.966480i	$-0.417351\pi$
$307$	8.99691			0.513481			0.256740	+	0.966480i	$0.417351\pi$
$308$	0.327507	−	0.910296i	0.0186615	−	0.0518689i
$309$		0			0
$310$	1.53151	+	2.65266i	0.0869842	+	0.150661i
$311$	−15.4498	−	26.7598i	−0.876077	−	1.51741i	−0.855611	−	0.517619i	$-0.826819\pi$
$311$	−15.4498	−	26.7598i	−0.876077	−	1.51741i	−0.0204655	−	0.999791i	$-0.506515\pi$
$312$		0			0
$313$	3.74574	−	6.48782i	0.211722	−	0.366713i	−0.740532	−	0.672022i	$-0.765426\pi$
$313$	3.74574	−	6.48782i	0.211722	−	0.366713i	0.952254	+	0.305308i	$0.0987595\pi$
$314$	16.8637	−	29.2088i	0.951673	−	1.64835i
$315$		0			0
$316$	−4.90348	−	8.49307i	−0.275842	−	0.477773i
$317$	−8.11402	+	14.0539i	−0.455729	+	0.789346i	−0.998730	−	0.0503864i	$-0.983955\pi$
$317$	−8.11402	+	14.0539i	−0.455729	+	0.789346i	0.543001	+	0.839732i	$0.317288\pi$
$318$		0			0
$319$	−0.120898	+	0.209401i	−0.00676897	+	0.0117242i
$320$	3.05165	−	5.28562i	0.170593	−	0.295475i
$321$		0			0
$322$	−11.7342	+	32.6147i	−0.653919	+	1.81755i
$323$	16.0316	−	27.7675i	0.892021	−	1.54503i
$324$		0			0
$325$	−21.1930	−	32.6883i	−1.17558	−	1.81322i
$326$	9.68748	+	16.7792i	0.536540	+	0.929314i
$327$		0			0
$328$	0.668510	−	1.15789i	0.0369123	−	0.0639340i
$329$	4.85935	−	13.5064i	0.267904	−	0.744632i
$330$		0			0
$331$	5.58434			0.306943			0.153472	−	0.988153i	$-0.450955\pi$
$331$	5.58434			0.306943			0.153472	+	0.988153i	$0.450955\pi$
$332$	8.53922	−	14.7904i	0.468650	−	0.811726i
$333$		0			0
$334$	−0.0870976			−0.00476577
$335$	−3.12849	+	5.41870i	−0.170928	+	0.296055i
$336$		0			0
$337$	−0.504097			−0.0274599			−0.0137299	−	0.999906i	$-0.504371\pi$
$337$	−0.504097			−0.0274599			−0.0137299	+	0.999906i	$0.504371\pi$
$338$	13.8008	+	19.0555i	0.750663	+	1.03648i
$339$		0			0
$340$	23.3363			1.26559
$341$	−0.0610156	−	0.105682i	−0.00330418	−	0.00572301i
$342$		0			0
$343$	−15.9351	+	9.43778i	−0.860416	+	0.509592i
$344$	0.767374	+	1.32913i	0.0413740	+	0.0716619i
$345$		0			0
$346$	12.6959	+	21.9899i	0.682535	+	1.18219i
$347$	−6.06672	+	10.5079i	−0.325678	+	0.564092i	−0.981649	−	0.190694i	$-0.938926\pi$
$347$	−6.06672	+	10.5079i	−0.325678	+	0.564092i	0.655971	+	0.754786i	$0.272259\pi$
$348$		0			0
$349$	10.9086	−	18.8943i	0.583924	−	1.01139i	−0.411084	−	0.911597i	$-0.634850\pi$
$349$	10.9086	−	18.8943i	0.583924	−	1.01139i	0.995009	−	0.0997893i	$-0.0318169\pi$
$350$	−17.5152	+	48.6830i	−0.936229	+	2.60222i
$351$		0			0
$352$	−0.901476	+	1.56140i	−0.0480488	+	0.0832230i
$353$	12.0879			0.643375			0.321688	−	0.946846i	$-0.395750\pi$
$353$	12.0879			0.643375			0.321688	+	0.946846i	$0.395750\pi$
$354$		0			0
$355$	−25.6317			−1.36039
$356$	2.82631			0.149794
$357$		0			0
$358$	−4.25192	−	7.36454i	−0.224721	−	0.389228i
$359$	7.22027	−	12.5059i	0.381071	−	0.660035i	−0.610144	−	0.792290i	$-0.708889\pi$
$359$	7.22027	−	12.5059i	0.381071	−	0.660035i	0.991216	+	0.132255i	$0.0422218\pi$
$360$		0			0
$361$	29.5459			1.55505
$362$	−19.9430	−	34.5423i	−1.04818	−	1.81550i
$363$		0			0
$364$	3.52331	−	11.6470i	0.184671	−	0.610468i
$365$	−65.5838			−3.43281
$366$		0			0
$367$	24.3787			1.27256			0.636280	−	0.771459i	$-0.280472\pi$
$367$	24.3787			1.27256			0.636280	+	0.771459i	$0.280472\pi$
$368$	17.8216	−	30.8679i	0.929013	−	1.60910i
$369$		0			0
$370$	−15.7004	−	27.1938i	−0.816223	−	1.41374i
$371$	−1.96173	−	2.32039i	−0.101848	−	0.120469i
$372$		0			0
$373$	−8.40033			−0.434953			−0.217476	−	0.976066i	$-0.569782\pi$
$373$	−8.40033			−0.434953			−0.217476	+	0.976066i	$0.569782\pi$
$374$	−2.38744			−0.123452
$375$		0			0
$376$	−3.55654	+	6.16011i	−0.183415	+	0.317684i
$377$	−1.38277	+	2.70879i	−0.0712163	+	0.139510i
$378$		0			0
$379$	−1.82895	+	3.16783i	−0.0939467	+	0.162720i	−0.909169	−	0.416428i	$-0.863282\pi$
$379$	−1.82895	+	3.16783i	−0.0939467	+	0.162720i	0.815222	+	0.579149i	$0.196615\pi$
$380$	17.6664	+	30.5991i	0.906266	+	1.56970i
$381$		0			0
$382$	−10.0424	−	17.3939i	−0.513812	−	0.889949i
$383$	30.7052			1.56896			0.784481	−	0.620152i	$-0.212929\pi$
$383$	30.7052			1.56896			0.784481	+	0.620152i	$0.212929\pi$
$384$		0			0
$385$	1.02072	−	2.83707i	0.0520209	−	0.144590i
$386$	−0.440003	−	0.762108i	−0.0223956	−	0.0387903i
$387$		0			0
$388$	−24.2932			−1.23330
$389$	9.21889	+	15.9676i	0.467416	+	0.809589i	0.999307	−	0.0372241i	$-0.0118515\pi$
$389$	9.21889	+	15.9676i	0.467416	+	0.809589i	−0.531890	+	0.846813i	$0.678518\pi$
$390$		0			0
$391$	33.3106			1.68459
$392$	8.60072	−	3.20276i	0.434402	−	0.161764i
$393$		0			0
$394$	30.9056			1.55700
$395$	−15.2824	−	26.4699i	−0.768941	−	1.33184i
$396$		0			0
$397$	−2.26064			−0.113458			−0.0567290	−	0.998390i	$-0.518067\pi$
$397$	−2.26064			−0.113458			−0.0567290	+	0.998390i	$0.518067\pi$
$398$	−41.9339			−2.10196
$399$		0			0
$400$	26.6017	−	46.0755i	1.33009	−	2.30378i
$401$	14.2609	+	24.7005i	0.712153	+	1.23349i	0.964047	+	0.265731i	$0.0856132\pi$
$401$	14.2609	+	24.7005i	0.712153	+	1.23349i	−0.251894	+	0.967755i	$0.581053\pi$
$402$		0			0
$403$	−0.835004	−	1.28792i	−0.0415945	−	0.0641558i
$404$	−5.79658	+	10.0400i	−0.288391	+	0.499507i
$405$		0			0
$406$	3.97509	−	0.716108i	0.197281	−	0.0355398i
$407$	0.625503	+	1.08340i	0.0310051	+	0.0537023i
$408$		0			0
$409$	−5.42700	+	9.39983i	−0.268348	+	0.464792i	−0.968435	−	0.249265i	$-0.919811\pi$
$409$	−5.42700	+	9.39983i	−0.268348	+	0.464792i	0.700088	+	0.714057i	$0.253144\pi$
$410$	−3.66869	+	6.35436i	−0.181184	+	0.313819i
$411$		0			0
$412$	2.99022	+	5.17921i	0.147318	+	0.255162i
$413$	4.35172	−	12.0955i	0.214134	−	0.595179i
$414$		0			0
$415$	26.6137	−	46.0963i	1.30642	−	2.26278i
$416$	−10.3106	+	20.1981i	−0.505521	+	0.990294i
$417$		0			0
$418$	−1.80738	−	3.13047i	−0.0884017	−	0.153116i
$419$	7.68279	−	13.3070i	0.375329	−	0.650089i	−0.615047	−	0.788490i	$-0.710863\pi$
$419$	7.68279	−	13.3070i	0.375329	−	0.650089i	0.990376	+	0.138401i	$0.0441964\pi$
$420$		0			0
$421$	−3.33695			−0.162633			−0.0813166	−	0.996688i	$-0.525912\pi$
$421$	−3.33695			−0.162633			−0.0813166	+	0.996688i	$0.525912\pi$
$422$	5.09612			0.248075
$423$		0			0
$424$	0.752867	+	1.30400i	0.0365625	+	0.0633281i
$425$	49.7218			2.41186
$426$		0			0
$427$	−21.2694	+	3.83165i	−1.02930	+	0.185427i
$428$	−18.5030			−0.894377
$429$		0			0
$430$	−4.21124	−	7.29408i	−0.203084	−	0.351752i
$431$	4.26093			0.205242			0.102621	−	0.994721i	$-0.467277\pi$
$431$	4.26093			0.205242			0.102621	+	0.994721i	$0.467277\pi$
$432$		0			0
$433$	−5.56416	−	9.63741i	−0.267396	−	0.463144i	0.700792	−	0.713365i	$-0.252830\pi$
$433$	−5.56416	−	9.63741i	−0.267396	−	0.463144i	−0.968189	+	0.250221i	$0.919497\pi$
$434$	−0.690100	+	1.91811i	−0.0331259	+	0.0920722i
$435$		0			0
$436$	−5.34961			−0.256200
$437$	25.2173	+	43.6777i	1.20631	+	2.08939i
$438$		0			0
$439$	−20.5012	−	35.5092i	−0.978470	−	1.69476i	−0.667973	−	0.744186i	$-0.732838\pi$
$439$	−20.5012	−	35.5092i	−0.978470	−	1.69476i	−0.310497	−	0.950574i	$-0.600496\pi$
$440$	−0.747065	+	1.29395i	−0.0356149	+	0.0616869i
$441$		0			0
$442$	−29.9894	+	1.54900i	−1.42645	+	0.0736785i
$443$	7.92693	−	13.7298i	0.376620	−	0.652325i	−0.613948	−	0.789346i	$-0.710420\pi$
$443$	7.92693	−	13.7298i	0.376620	−	0.652325i	0.990568	+	0.137022i	$0.0437530\pi$
$444$		0			0
$445$	8.80862			0.417569
$446$	−29.5452			−1.39901
$447$		0			0
$448$	3.99746	−	0.720137i	0.188862	−	0.0340233i
$449$	7.54997	+	13.0769i	0.356305	+	0.617139i	0.987340	−	0.158616i	$-0.0507030\pi$
$449$	7.54997	+	13.0769i	0.356305	+	0.617139i	−0.631035	+	0.775754i	$0.717370\pi$
$450$		0			0
$451$	0.146161	−	0.253158i	0.00688244	−	0.0119207i
$452$	10.5185			0.494751
$453$		0			0
$454$	−11.2316			−0.527123
$455$	10.9809	−	36.2995i	0.514792	−	1.70175i
$456$		0			0
$457$	0.0139240	+	0.0241170i	0.000651335	+	0.00112815i	0.866351	−	0.499436i	$-0.166459\pi$
$457$	0.0139240	+	0.0241170i	0.000651335	+	0.00112815i	−0.865700	+	0.500564i	$0.833126\pi$
$458$	0.946420			0.0442233
$459$		0			0
$460$	−18.3537	+	31.7896i	−0.855747	+	1.48220i
$461$	−14.0543	−	24.3428i	−0.654575	−	1.13376i	−0.982000	−	0.188880i	$-0.939514\pi$
$461$	−14.0543	−	24.3428i	−0.654575	−	1.13376i	0.327425	−	0.944877i	$-0.393819\pi$
$462$		0			0
$463$	−0.266538			−0.0123871			−0.00619354	−	0.999981i	$-0.501971\pi$
$463$	−0.266538			−0.0123871			−0.00619354	+	0.999981i	$0.501971\pi$
$464$	−4.15349			−0.192821
$465$		0			0
$466$	23.4656			1.08702
$467$	18.5400	−	32.1123i	0.857931	−	1.48598i	−0.0159687	−	0.999872i	$-0.505083\pi$
$467$	18.5400	−	32.1123i	0.857931	−	1.48598i	0.873899	−	0.486107i	$-0.161583\pi$
$468$		0			0
$469$	−4.09811	+	0.738270i	−0.189233	+	0.0340901i
$470$	19.5178	−	33.8058i	0.900289	−	1.55935i
$471$		0			0
$472$	−3.18501	+	5.51660i	−0.146602	+	0.253922i
$473$	0.167776	+	0.290597i	0.00771436	+	0.0133617i
$474$		0			0
$475$	37.6411	+	65.1964i	1.72709	+	2.99141i
$476$	10.0268	+	11.8600i	0.459579	+	0.543603i
$477$		0			0
$478$	4.34008	+	7.51725i	0.198511	+	0.343831i
$479$	−28.7986			−1.31584			−0.657922	−	0.753086i	$-0.728564\pi$
$479$	−28.7986			−1.31584			−0.657922	+	0.753086i	$0.728564\pi$
$480$		0			0
$481$	8.56006	+	13.2031i	0.390305	+	0.602011i
$482$	−18.8578			−0.858949
$483$		0			0
$484$	6.96327	−	12.0607i	0.316512	−	0.548216i
$485$	−75.7132			−3.43796
$486$		0			0
$487$	6.86516	−	11.8908i	0.311090	−	0.538824i	−0.667508	−	0.744602i	$-0.732639\pi$
$487$	6.86516	−	11.8908i	0.311090	−	0.538824i	0.978599	+	0.205778i	$0.0659725\pi$
$488$	10.7097			0.484805
$489$		0			0
$490$	−47.1995	+	17.5763i	−2.13226	+	0.794016i
$491$	−13.7632	+	23.8386i	−0.621126	+	1.07582i	0.368150	+	0.929766i	$0.379991\pi$
$491$	−13.7632	+	23.8386i	−0.621126	+	1.07582i	−0.989276	+	0.146056i	$0.953342\pi$
$492$		0			0
$493$	−1.94084	−	3.36163i	−0.0874110	−	0.151400i
$494$	−24.7341	−	38.1501i	−1.11284	−	1.71645i
$495$		0			0
$496$	1.04811	−	1.81537i	0.0470614	−	0.0815127i
$497$	−11.0131	−	13.0266i	−0.494005	−	0.584323i
$498$		0			0
$499$	1.94567	−	3.37000i	0.0871001	−	0.150862i	−0.819184	−	0.573531i	$-0.805573\pi$
$499$	1.94567	−	3.37000i	0.0871001	−	0.150862i	0.906284	+	0.422669i	$0.138907\pi$
$500$	−14.7183	+	25.4929i	−0.658224	+	1.14008i
$501$		0			0
$502$	−9.24194	+	16.0075i	−0.412488	+	0.714450i
$503$	1.87991	+	3.25610i	0.0838212	+	0.145183i	0.904888	−	0.425649i	$-0.139954\pi$
$503$	1.87991	+	3.25610i	0.0838212	+	0.145183i	−0.821067	+	0.570832i	$0.806621\pi$
$504$		0			0
$505$	−18.0659	+	31.2910i	−0.803921	+	1.39243i
$506$	1.87770	−	3.25227i	0.0834738	−	0.144581i
$507$		0			0
$508$	−5.00247	−	8.66453i	−0.221949	−	0.384426i
$509$	−19.2740	−	33.3836i	−0.854307	−	1.47970i	−0.877286	−	0.479967i	$-0.840649\pi$
$509$	−19.2740	−	33.3836i	−0.854307	−	1.47970i	0.0229793	−	0.999736i	$-0.492685\pi$
$510$		0			0
$511$	−28.1792	−	33.3312i	−1.24657	−	1.47448i
$512$	−18.0587			−0.798088
$513$		0			0
$514$	5.75788	−	9.97294i	0.253969	−	0.439888i
$515$	9.31946	+	16.1418i	0.410664	+	0.711291i
$516$		0			0
$517$	−0.777591	+	1.34683i	−0.0341984	+	0.0592334i
$518$	7.07458	−	19.6636i	0.310839	−	0.863967i
$519$		0			0
$520$	−8.54457	+	16.7385i	−0.374704	+	0.734030i
$521$	6.92277	+	11.9906i	0.303292	+	0.525318i	0.976880	−	0.213790i	$-0.0685808\pi$
$521$	6.92277	+	11.9906i	0.303292	+	0.525318i	−0.673587	+	0.739108i	$0.735247\pi$
$522$		0			0
$523$	−10.0335	−	17.3786i	−0.438736	−	0.759913i	0.558856	−	0.829265i	$-0.311240\pi$
$523$	−10.0335	−	17.3786i	−0.438736	−	0.759913i	−0.997592	+	0.0693515i	$0.977907\pi$
$524$	5.15687	+	8.93196i	0.225279	+	0.390194i
$525$		0			0
$526$	15.3960	+	26.6667i	0.671299	+	1.16272i
$527$	1.95904			0.0853370
$528$		0			0
$529$	−14.6985	+	25.4585i	−0.639063	+	1.10689i
$530$	−4.13163	−	7.15619i	−0.179467	−	0.310845i
$531$		0			0
$532$	−7.96047	+	22.1259i	−0.345130	+	0.959278i
$533$	1.67172	−	3.27482i	0.0724101	−	0.141848i
$534$		0			0
$535$	−57.6673			−2.49318
$536$	2.06351			0.0891298
$537$		0			0
$538$	−16.3980			−0.706968
$539$	1.88043	−	0.700240i	0.0809960	−	0.0301615i
$540$		0			0
$541$	−18.9415	+	32.8076i	−0.814357	+	1.41051i	0.0954310	+	0.995436i	$0.469577\pi$
$541$	−18.9415	+	32.8076i	−0.814357	+	1.41051i	−0.909788	+	0.415072i	$0.863756\pi$
$542$	2.01615	−	3.49207i	0.0866009	−	0.149997i
$543$		0			0
$544$	−14.4719	−	25.0661i	−0.620478	−	1.07470i
$545$	−16.6728			−0.714186
$546$		0			0
$547$	29.3783			1.25613			0.628063	−	0.778162i	$-0.283848\pi$
$547$	29.3783			1.25613			0.628063	+	0.778162i	$0.283848\pi$
$548$	0.962858	+	1.66772i	0.0411313	+	0.0712415i
$549$		0			0
$550$	2.80278	−	4.85456i	0.119511	−	0.206999i
$551$	2.93857	−	5.08975i	0.125187	−	0.216831i
$552$		0			0
$553$	6.88624	−	19.1401i	0.292833	−	0.813919i
$554$	14.1305			0.600349
$555$		0			0
$556$	−5.15671			−0.218693
$557$	−1.02608			−0.0434763			−0.0217381	−	0.999764i	$-0.506920\pi$
$557$	−1.02608			−0.0434763			−0.0217381	+	0.999764i	$0.506920\pi$
$558$		0			0
$559$	2.29603	+	3.54142i	0.0971117	+	0.149786i
$560$	50.9720	−	9.18253i	2.15396	−	0.388033i
$561$		0			0
$562$	11.5407	+	19.9890i	0.486814	+	0.843187i
$563$	−18.1124	+	31.3716i	−0.763348	+	1.32216i	0.177768	+	0.984072i	$0.443112\pi$
$563$	−18.1124	+	31.3716i	−0.763348	+	1.32216i	−0.941116	+	0.338085i	$0.890221\pi$
$564$		0			0
$565$	32.7826			1.37917
$566$	14.7900	+	25.6171i	0.621671	+	1.07677i
$567$		0			0
$568$	4.22657	+	7.32064i	0.177343	+	0.307167i
$569$	1.41835	+	2.45666i	0.0594605	+	0.102989i	0.894223	−	0.447621i	$-0.147729\pi$
$569$	1.41835	+	2.45666i	0.0594605	+	0.102989i	−0.834763	+	0.550610i	$0.814395\pi$
$570$		0			0
$571$	2.29825	+	3.98069i	0.0961789	+	0.166587i	0.910100	−	0.414389i	$-0.136005\pi$
$571$	2.29825	+	3.98069i	0.0961789	+	0.166587i	−0.813921	+	0.580975i	$0.802671\pi$
$572$	−0.599413	+	1.17422i	−0.0250627	+	0.0490968i
$573$		0			0
$574$	−4.80574	+	0.865748i	−0.200588	+	0.0361356i
$575$	−39.1057	+	67.7330i	−1.63082	+	2.82466i
$576$		0			0
$577$	8.75176	+	15.1585i	0.364341	+	0.631056i	0.988670	−	0.150105i	$-0.0479611\pi$
$577$	8.75176	+	15.1585i	0.364341	+	0.631056i	−0.624329	+	0.781161i	$0.714628\pi$
$578$	3.77970	−	6.54662i	0.157215	−	0.272304i
$579$		0			0
$580$	4.27751			0.177614
$581$	34.8622	−	6.28038i	1.44633	−	0.260554i
$582$		0			0
$583$	0.164604	+	0.285103i	0.00681722	+	0.0118078i
$584$	10.8145	+	18.7313i	0.447509	+	0.775108i
$585$		0			0
$586$	21.4140	−	37.0902i	0.884606	−	1.53218i
$587$	0.671155	−	1.16247i	0.0277015	−	0.0479805i	−0.851842	−	0.523798i	$-0.824515\pi$
$587$	0.671155	−	1.16247i	0.0277015	−	0.0479805i	0.879544	+	0.475818i	$0.157848\pi$
$588$		0			0
$589$	1.48306	+	2.56874i	0.0611084	+	0.105843i
$590$	17.4789	−	30.2743i	0.719595	−	1.24638i
$591$		0			0
$592$	−10.7447	+	18.6104i	−0.441604	+	0.764881i
$593$	−22.0843	+	38.2512i	−0.906895	+	1.57079i	−0.0885427	+	0.996072i	$0.528221\pi$
$593$	−22.0843	+	38.2512i	−0.906895	+	1.57079i	−0.818353	+	0.574716i	$0.805112\pi$
$594$		0			0
$595$	31.2501	+	36.9635i	1.28113	+	1.51535i
$596$	−12.2422	+	21.2041i	−0.501460	+	0.868554i
$597$		0			0
$598$	21.4762	−	42.0710i	0.878227	−	1.72041i
$599$	−8.46583	−	14.6632i	−0.345904	−	0.599124i	0.639613	−	0.768697i	$-0.279095\pi$
$599$	−8.46583	−	14.6632i	−0.345904	−	0.599124i	−0.985518	+	0.169573i	$0.945761\pi$
$600$		0			0
$601$	7.56311	−	13.0997i	0.308506	−	0.534348i	−0.669530	−	0.742785i	$-0.733504\pi$
$601$	7.56311	−	13.0997i	0.308506	−	0.534348i	0.978036	+	0.208437i	$0.0668378\pi$
$602$	1.89758	−	5.27427i	0.0773398	−	0.214963i
$603$		0			0
$604$	24.1680			0.983381
$605$	21.7021	−	37.5891i	0.882314	−	1.52821i
$606$		0			0
$607$	47.7239			1.93705			0.968527	−	0.248910i	$-0.0800722\pi$
$607$	47.7239			1.93705			0.968527	+	0.248910i	$0.0800722\pi$
$608$	21.9115	−	37.9518i	0.888628	−	1.53915i
$609$		0			0
$610$	−58.7733			−2.37966
$611$	−8.89371	+	17.4224i	−0.359801	+	0.704835i
$612$		0			0
$613$	23.9708			0.968173			0.484086	−	0.875020i	$-0.339152\pi$
$613$	23.9708			0.968173			0.484086	+	0.875020i	$0.339152\pi$
$614$	8.14155	+	14.1016i	0.328566	+	0.569094i
$615$		0			0
$616$	−0.978606	+	0.176295i	−0.0394292	+	0.00710311i
$617$	1.41810	+	2.45623i	0.0570907	+	0.0988839i	0.893158	−	0.449743i	$-0.148484\pi$
$617$	1.41810	+	2.45623i	0.0570907	+	0.0988839i	−0.836068	+	0.548626i	$0.815151\pi$
$618$		0			0
$619$	0.658494	+	1.14055i	0.0264671	+	0.0458424i	0.878956	−	0.476904i	$-0.158241\pi$
$619$	0.658494	+	1.14055i	0.0264671	+	0.0458424i	−0.852488	+	0.522746i	$0.824908\pi$
$620$	−1.07940	+	1.86958i	−0.0433499	+	0.0750843i
$621$		0			0
$622$	27.9619	−	48.4314i	1.12117	−	1.94192i
$623$	3.78477	+	4.47674i	0.151634	+	0.179357i
$624$		0			0
$625$	−18.8598	+	32.6662i	−0.754393	+	1.30665i
$626$	13.5585			0.541907
$627$		0			0
$628$	23.7709			0.948562
$629$	−20.0831			−0.800766
$630$		0			0
$631$	−11.5676	−	20.0356i	−0.460497	−	0.797604i	0.538489	−	0.842633i	$-0.318995\pi$
$631$	−11.5676	−	20.0356i	−0.460497	−	0.797604i	−0.998986	+	0.0450286i	$0.985662\pi$
$632$	−5.04002	+	8.72957i	−0.200481	+	0.347244i
$633$		0			0
$634$	−29.3704			−1.16645
$635$	−15.5909	−	27.0043i	−0.618707	−	1.07163i
$636$		0			0
$637$	23.1664	−	10.0160i	0.917885	−	0.396848i
$638$	−0.437615			−0.0173253
$639$		0			0
$640$	−38.9631			−1.54015
$641$	−18.3262	+	31.7420i	−0.723843	+	1.25373i	0.235605	+	0.971849i	$0.424293\pi$
$641$	−18.3262	+	31.7420i	−0.723843	+	1.25373i	−0.959448	+	0.281884i	$0.909041\pi$
$642$		0			0
$643$	−1.86917	−	3.23749i	−0.0737127	−	0.127674i	0.826813	−	0.562477i	$-0.190151\pi$
$643$	−1.86917	−	3.23749i	−0.0737127	−	0.127674i	−0.900526	+	0.434803i	$0.856818\pi$
$644$	−24.0422	+	4.33117i	−0.947394	+	0.170672i
$645$		0			0
$646$	58.0297			2.28315
$647$	1.52619			0.0600006			0.0300003	−	0.999550i	$-0.490449\pi$
$647$	1.52619			0.0600006			0.0300003	+	0.999550i	$0.490449\pi$
$648$		0			0
$649$	−0.696361	+	1.20613i	−0.0273345	+	0.0473448i
$650$	32.0569	−	62.7981i	1.25737	−	2.46314i
$651$		0			0
$652$	−6.82769	+	11.8259i	−0.267393	+	0.463138i
$653$	4.47546	+	7.75172i	0.175138	+	0.303348i	0.940209	−	0.340598i	$-0.110629\pi$
$653$	4.47546	+	7.75172i	0.175138	+	0.303348i	−0.765071	+	0.643946i	$0.777296\pi$
$654$		0			0
$655$	16.0721	+	27.8377i	0.627990	+	1.08771i
$656$	5.02141			0.196053
$657$		0			0
$658$	25.5670	−	4.60587i	0.996707	−	0.179555i
$659$	−4.30599	−	7.45819i	−0.167737	−	0.290530i	0.769887	−	0.638181i	$-0.220313\pi$
$659$	−4.30599	−	7.45819i	−0.167737	−	0.290530i	−0.937624	+	0.347651i	$0.886979\pi$
$660$		0			0
$661$	−40.0783			−1.55887			−0.779433	−	0.626486i	$-0.784493\pi$
$661$	−40.0783			−1.55887			−0.779433	+	0.626486i	$0.784493\pi$
$662$	5.05343	+	8.75279i	0.196407	+	0.340187i
$663$		0			0
$664$	−17.5540			−0.681228
$665$	−24.8100	+	68.9585i	−0.962089	+	2.67409i
$666$		0			0
$667$	6.10580			0.236417
$668$	−0.0306930	−	0.0531618i	−0.00118755	−	0.00205689i
$669$		0			0
$670$	−11.3242			−0.437493
$671$	2.34153			0.0903938
$672$		0			0
$673$	−22.0131	+	38.1277i	−0.848541	+	1.46972i	0.0339689	+	0.999423i	$0.489185\pi$
$673$	−22.0131	+	38.1277i	−0.848541	+	1.46972i	−0.882510	+	0.470294i	$0.844148\pi$
$674$	−0.456171	−	0.790112i	−0.0175711	−	0.0304340i
$675$		0			0
$676$	−6.76755	+	15.1387i	−0.260291	+	0.582258i
$677$	12.0556	−	20.8809i	0.463334	−	0.802518i	−0.535791	−	0.844351i	$-0.679986\pi$
$677$	12.0556	−	20.8809i	0.463334	−	0.802518i	0.999125	+	0.0418328i	$0.0133197\pi$
$678$		0			0
$679$	−32.5314	−	38.4791i	−1.24844	−	1.47669i
$680$	−11.9931	−	20.7726i	−0.459913	−	0.796592i
$681$		0			0
$682$	0.110430	−	0.191270i	0.00422856	−	0.00732409i
$683$	−9.29276	+	16.0955i	−0.355578	+	0.615878i	−0.987217	−	0.159384i	$-0.949049\pi$
$683$	−9.29276	+	16.0955i	−0.355578	+	0.615878i	0.631639	+	0.775263i	$0.282382\pi$
$684$		0			0
$685$	3.00089	+	5.19769i	0.114658	+	0.198594i
$686$	−29.2127	−	16.4359i	−1.11535	−	0.627526i
$687$		0			0
$688$	−2.88201	+	4.99178i	−0.109875	+	0.190310i
$689$	2.25262	+	3.47447i	0.0858182	+	0.132367i
$690$		0			0
$691$	11.3187	+	19.6045i	0.430583	+	0.745792i	0.996924	−	0.0783796i	$-0.0249746\pi$
$691$	11.3187	+	19.6045i	0.430583	+	0.745792i	−0.566340	+	0.824171i	$0.691641\pi$
$692$	−8.94801	+	15.4984i	−0.340152	+	0.589161i
$693$		0			0
$694$	−21.9598			−0.833581
$695$	−16.0716			−0.609632
$696$		0			0
$697$	2.34640	+	4.06409i	0.0888763	+	0.153938i
$698$	39.4860			1.49457
$699$		0			0
$700$	−35.8870	+	6.46500i	−1.35640	+	0.244354i
$701$	−50.1432			−1.89388			−0.946941	−	0.321407i	$-0.895844\pi$
$701$	−50.1432			−1.89388			−0.946941	+	0.321407i	$0.895844\pi$
$702$		0			0
$703$	−15.2036	−	26.3335i	−0.573416	−	0.993185i
$704$	−0.440077			−0.0165860
$705$		0			0
$706$	10.9387	+	18.9464i	0.411683	+	0.713056i
$707$	−23.6651	+	4.26324i	−0.890018	+	0.160336i
$708$		0			0
$709$	−29.7112			−1.11583			−0.557913	−	0.829899i	$-0.688398\pi$
$709$	−29.7112			−1.11583			−0.557913	+	0.829899i	$0.688398\pi$
$710$	−23.1948	−	40.1746i	−0.870487	−	1.50773i
$711$		0			0
$712$	−1.45251	−	2.51582i	−0.0544351	−	0.0942843i
$713$	−1.54076	+	2.66868i	−0.0577020	+	0.0999428i
$714$		0			0
$715$	−1.86816	+	3.65964i	−0.0698651	+	0.136863i
$716$	2.99673	−	5.19049i	0.111993	−	0.193978i
$717$		0			0
$718$	26.1353			0.975361
$719$	29.8693			1.11394			0.556968	−	0.830534i	$-0.311965\pi$
$719$	29.8693			1.11394			0.556968	+	0.830534i	$0.311965\pi$
$720$		0			0
$721$	−4.19934	+	11.6719i	−0.156392	+	0.434686i
$722$	26.7369	+	46.3096i	0.995044	+	1.72347i
$723$		0			0
$724$	14.0557	−	24.3453i	0.522378	−	0.904785i
$725$	9.11394			0.338483
$726$		0			0
$727$	36.0210			1.33594			0.667972	−	0.744186i	$-0.267163\pi$
$727$	36.0210			1.33594			0.667972	+	0.744186i	$0.267163\pi$
$728$	−12.1782	+	2.84942i	−0.451353	+	0.105607i
$729$		0			0
$730$	−59.3486	−	102.795i	−2.19659	−	3.80461i
$731$	−5.38681			−0.199238
$732$		0			0
$733$	8.97642	−	15.5476i	0.331552	−	0.574265i	−0.651265	−	0.758851i	$-0.725761\pi$
$733$	8.97642	−	15.5476i	0.331552	−	0.574265i	0.982816	+	0.184586i	$0.0590945\pi$
$734$	22.0610	+	38.2108i	0.814286	+	1.41038i
$735$		0			0
$736$	45.5280			1.67818
$737$	0.451158			0.0166186
$738$		0			0
$739$	44.4938			1.63673			0.818366	−	0.574698i	$-0.194880\pi$
$739$	44.4938			1.63673			0.818366	+	0.574698i	$0.194880\pi$
$740$	11.0655	−	19.1661i	0.406777	−	0.704559i
$741$		0			0
$742$	1.86171	−	5.17457i	0.0683456	−	0.189964i
$743$	10.7390	−	18.6004i	0.393975	−	0.682384i	−0.598995	−	0.800753i	$-0.704433\pi$
$743$	10.7390	−	18.6004i	0.393975	−	0.682384i	0.992970	+	0.118368i	$0.0377664\pi$
$744$		0			0
$745$	−38.1546	+	66.0857i	−1.39788	+	2.42119i
$746$	−7.60169	−	13.1665i	−0.278318	−	0.482061i
$747$		0			0
$748$	−0.841329	−	1.45722i	−0.0307620	−	0.0532814i
$749$	−24.7777	−	29.3078i	−0.905359	−	1.07088i
$750$		0			0
$751$	−1.60018	−	2.77159i	−0.0583913	−	0.101137i	0.835352	−	0.549715i	$-0.185264\pi$
$751$	−1.60018	−	2.77159i	−0.0583913	−	0.101137i	−0.893743	+	0.448579i	$0.851930\pi$
$752$	−26.7144			−0.974174
$753$		0			0
$754$	−5.49701	+	0.283930i	−0.200189	+	0.0103401i
$755$	75.3230			2.74128
$756$		0			0
$757$	−12.8640	+	22.2811i	−0.467550	+	0.809821i	−0.999313	−	0.0370727i	$-0.988197\pi$
$757$	−12.8640	+	22.2811i	−0.467550	+	0.809821i	0.531762	+	0.846894i	$0.321530\pi$
$758$	−6.62026			−0.240459
$759$		0			0
$760$	18.1583	−	31.4512i	0.658672	−	1.14085i
$761$	−28.7496			−1.04217			−0.521087	−	0.853504i	$-0.674473\pi$
$761$	−28.7496			−1.04217			−0.521087	+	0.853504i	$0.674473\pi$
$762$		0			0
$763$	−7.16377	−	8.47351i	−0.259346	−	0.306762i
$764$	7.07782	−	12.2591i	0.256066	−	0.443520i
$765$		0			0
$766$	27.7860	+	48.1268i	1.00395	+	1.73889i
$767$	−7.96464	+	15.6024i	−0.287587	+	0.563370i
$768$		0			0
$769$	8.98213	−	15.5575i	0.323904	−	0.561018i	−0.657386	−	0.753554i	$-0.728338\pi$
$769$	8.98213	−	15.5575i	0.323904	−	0.561018i	0.981290	+	0.192536i	$0.0616712\pi$
$770$	5.37045	−	0.967480i	0.193538	−	0.0348656i
$771$		0			0
$772$	0.310112	−	0.537131i	0.0111612	−	0.0193318i
$773$	19.8326	−	34.3511i	0.713329	−	1.23552i	−0.250272	−	0.968176i	$-0.580520\pi$
$773$	19.8326	−	34.3511i	0.713329	−	1.23552i	0.963601	−	0.267346i	$-0.0861468\pi$
$774$		0			0
$775$	−2.29985	+	3.98345i	−0.0826130	+	0.143090i
$776$	12.4848	+	21.6243i	0.448179	+	0.776269i
$777$		0			0
$778$	−16.6849	+	28.8990i	−0.598182	+	1.03608i
$779$	−3.55262	+	6.15331i	−0.127286	+	0.220465i
$780$		0			0
$781$	0.924084	+	1.60056i	0.0330663	+	0.0572725i
$782$	30.1437	+	52.2105i	1.07794	+	1.86704i
$783$		0			0
$784$	26.5677	+	21.9596i	0.948848	+	0.784273i
$785$	74.0855			2.64422
$786$		0			0
$787$	19.7833	−	34.2657i	0.705199	−	1.22144i	−0.261421	−	0.965225i	$-0.584191\pi$
$787$	19.7833	−	34.2657i	0.705199	−	1.22144i	0.966620	−	0.256215i	$-0.0824756\pi$
$788$	10.8911	+	18.8639i	0.387978	+	0.671998i
$789$		0			0
$790$	27.6589	−	47.9067i	0.984061	−	1.70444i
$791$	14.0856	+	16.6608i	0.500826	+	0.592391i
$792$		0			0
$793$	29.4127	−	1.51922i	1.04447	−	0.0539489i
$794$	−2.04571	−	3.54328i	−0.0725996	−	0.125746i
$795$		0			0
$796$	−14.7774	−	25.5952i	−0.523772	−	0.907199i
$797$	9.72309	+	16.8409i	0.344409	+	0.596535i	0.985246	−	0.171142i	$-0.0547458\pi$
$797$	9.72309	+	16.8409i	0.344409	+	0.596535i	−0.640837	+	0.767677i	$0.721412\pi$
$798$		0			0
$799$	−12.4831	−	21.6214i	−0.441621	−	0.764909i
$800$	67.9582			2.40269
$801$		0			0
$802$	−25.8101	+	44.7044i	−0.911386	+	1.57857i
$803$	2.36445	+	4.09535i	0.0834398	+	0.144522i
$804$		0			0
$805$	−74.9309	+	13.4987i	−2.64097	+	0.475767i
$806$	1.26304	−	2.47424i	0.0444887	−	0.0871515i
$807$		0			0
$808$	11.9160			0.419203
$809$	17.3084			0.608531			0.304265	−	0.952587i	$-0.401589\pi$
$809$	17.3084			0.608531			0.304265	+	0.952587i	$0.401589\pi$
$810$		0			0
$811$	−2.62646			−0.0922275			−0.0461138	−	0.998936i	$-0.514684\pi$
$811$	−2.62646			−0.0922275			−0.0461138	+	0.998936i	$0.514684\pi$
$812$	1.83791	+	2.17393i	0.0644978	+	0.0762899i
$813$		0			0
$814$	−1.13207	+	1.96080i	−0.0396791	+	0.0687262i
$815$	−21.2795	+	36.8572i	−0.745388	+	1.29105i
$816$		0			0
$817$	−4.07801	−	7.06331i	−0.142671	−	0.247114i
$818$	−19.6442			−0.686842
$819$		0			0
$820$	−5.17135			−0.180591
$821$	−16.1977	−	28.0553i	−0.565305	−	0.979137i	−0.997021	−	0.0771274i	$-0.975425\pi$
$821$	−16.1977	−	28.0553i	−0.565305	−	0.979137i	0.431716	−	0.902009i	$-0.357908\pi$
$822$		0			0
$823$	20.5081	−	35.5210i	0.714866	−	1.23818i	−0.248145	−	0.968723i	$-0.579821\pi$
$823$	20.5081	−	35.5210i	0.714866	−	1.23818i	0.963011	−	0.269461i	$-0.0868457\pi$
$824$	3.07349	−	5.32344i	0.107070	−	0.185451i
$825$		0			0
$826$	22.8962	−	4.12472i	0.796661	−	0.143517i
$827$	44.2260			1.53789			0.768944	−	0.639316i	$-0.220782\pi$
$827$	44.2260			1.53789			0.768944	+	0.639316i	$0.220782\pi$
$828$		0			0
$829$	−5.49562			−0.190871			−0.0954354	−	0.995436i	$-0.530424\pi$
$829$	−5.49562			−0.190871			−0.0954354	+	0.995436i	$0.530424\pi$
$830$	96.3339			3.34380
$831$		0			0
$832$	−5.52794	+	0.285528i	−0.191647	+	0.00989890i
$833$	−5.35853	+	31.7640i	−0.185662	+	1.10056i
$834$		0			0
$835$	−0.0956591	−	0.165686i	−0.00331042	−	0.00573382i
$836$	1.27383	−	2.20634i	0.0440564	−	0.0763079i
$837$		0			0
$838$	27.8095			0.960663
$839$	21.4269	+	37.1125i	0.739739	+	1.28127i	0.952612	+	0.304186i	$0.0983846\pi$
$839$	21.4269	+	37.1125i	0.739739	+	1.28127i	−0.212873	+	0.977080i	$0.568282\pi$
$840$		0			0
$841$	14.1442	+	24.4986i	0.487733	+	0.844778i
$842$	−3.01970	−	5.23028i	−0.104066	−	0.180247i
$843$		0			0
$844$	1.79586	+	3.11052i	0.0618160	+	0.107069i
$845$	−21.0921	+	47.1819i	−0.725589	+	1.62311i
$846$		0			0
$847$	28.4282	−	5.12131i	0.976806	−	0.175970i
$848$	−2.82752	+	4.89741i	−0.0970975	+	0.168178i
$849$		0			0
$850$	44.9946	+	77.9330i	1.54330	+	2.67308i
$851$	15.7952	−	27.3580i	0.541451	−	0.937821i
$852$		0			0
$853$	−46.0876			−1.57801			−0.789004	−	0.614388i	$-0.789403\pi$
$853$	−46.0876			−1.57801			−0.789004	+	0.614388i	$0.789403\pi$
$854$	−25.2529	−	29.8699i	−0.864137	−	1.02213i
$855$		0			0
$856$	9.50913	+	16.4703i	0.325015	+	0.562943i
$857$	−3.33662	−	5.77919i	−0.113977	−	0.197413i	0.803394	−	0.595448i	$-0.203026\pi$
$857$	−3.33662	−	5.77919i	−0.113977	−	0.197413i	−0.917370	+	0.398035i	$0.869692\pi$
$858$		0			0
$859$	8.20940	−	14.2191i	0.280101	−	0.485149i	−0.691308	−	0.722560i	$-0.742965\pi$
$859$	8.20940	−	14.2191i	0.280101	−	0.485149i	0.971409	+	0.237411i	$0.0762987\pi$
$860$	2.96806	−	5.14084i	0.101210	−	0.175301i
$861$		0			0
$862$	3.85584	+	6.67851i	0.131330	+	0.227471i
$863$	−4.92500	+	8.53035i	−0.167649	+	0.290377i	−0.937593	−	0.347735i	$-0.886951\pi$
$863$	−4.92500	+	8.53035i	−0.167649	+	0.290377i	0.769944	+	0.638112i	$0.220284\pi$
$864$		0			0
$865$	−27.8878	+	48.3030i	−0.948213	+	1.64235i
$866$	10.0703	−	17.4423i	0.342204	−	0.592714i
$867$		0			0
$868$	−1.41395	+	0.254721i	−0.0479925	+	0.00864579i
$869$	−1.10193	+	1.90861i	−0.0373805	+	0.0647450i
$870$		0			0
$871$	5.66713	−	0.292717i	0.192023	−	0.00991834i
$872$	2.74929	+	4.76191i	0.0931027	+	0.161259i
$873$		0			0
$874$	−45.6397	+	79.0503i	−1.54379	+	2.67392i
$875$	−60.0890	+	10.8250i	−2.03138	+	0.365951i
$876$		0			0
$877$	6.04112			0.203994			0.101997	−	0.994785i	$-0.467477\pi$
$877$	6.04112			0.203994			0.101997	+	0.994785i	$0.467477\pi$
$878$	37.1043	−	64.2665i	1.25221	−	2.16889i
$879$		0			0
$880$	−5.61146			−0.189162
$881$	−15.5861	+	26.9959i	−0.525109	+	0.909516i	0.474463	+	0.880275i	$0.342642\pi$
$881$	−15.5861	+	26.9959i	−0.525109	+	0.909516i	−0.999572	+	0.0292404i	$0.990691\pi$
$882$		0			0
$883$	−18.2205			−0.613169			−0.306584	−	0.951844i	$-0.599186\pi$
$883$	−18.2205			−0.613169			−0.306584	+	0.951844i	$0.599186\pi$
$884$	−11.5136	−	17.7588i	−0.387246	−	0.597292i
$885$		0			0
$886$	28.6932			0.963967
$887$	3.70842	+	6.42317i	0.124517	+	0.215669i	0.921544	−	0.388274i	$-0.126929\pi$
$887$	3.70842	+	6.42317i	0.124517	+	0.215669i	−0.797027	+	0.603943i	$0.793595\pi$
$888$		0			0
$889$	7.02526	−	19.5265i	0.235620	−	0.654898i
$890$	7.97117	+	13.8065i	0.267194	+	0.462794i
$891$		0			0
$892$	−10.4117	−	18.0336i	−0.348609	−	0.603808i
$893$	18.9003	−	32.7363i	0.632474	−	1.09548i
$894$		0			0
$895$	9.33975	−	16.1769i	0.312194	−	0.540735i
$896$	−16.7412	−	19.8019i	−0.559283	−	0.661535i
$897$		0			0
$898$	−13.6644	+	23.6674i	−0.455986	+	0.789790i
$899$	0.359089			0.0119763
$900$		0			0
$901$	−5.28498			−0.176068
$902$	0.529060			0.0176158
$903$		0			0
$904$	−5.40573	−	9.36299i	−0.179792	−	0.311409i
$905$	43.8068	−	75.8756i	1.45619	−	2.52219i
$906$		0			0
$907$	−17.4144			−0.578234			−0.289117	−	0.957294i	$-0.593362\pi$
$907$	−17.4144			−0.578234			−0.289117	+	0.957294i	$0.593362\pi$
$908$	−3.95797	−	6.85541i	−0.131350	−	0.227505i
$909$		0			0
$910$	66.8321	−	15.6372i	2.21546	−	0.518369i
$911$	40.5753			1.34432			0.672159	−	0.740407i	$-0.265367\pi$
$911$	40.5753			1.34432			0.672159	+	0.740407i	$0.265367\pi$
$912$		0			0
$913$	−3.83795			−0.127018
$914$	−0.0252004	+	0.0436483i	−0.000833554	+	0.00144376i
$915$		0			0
$916$	0.333516	+	0.577667i	0.0110197	+	0.0190867i
$917$	−7.24209	+	20.1292i	−0.239155	+	0.664724i
$918$		0			0
$919$	−48.5466			−1.60140			−0.800702	−	0.599062i	$-0.795540\pi$
$919$	−48.5466			−1.60140			−0.800702	+	0.599062i	$0.795540\pi$
$920$	37.7297			1.24391
$921$		0			0
$922$	25.4363	−	44.0570i	0.837700	−	1.45094i
$923$	12.6462	+	19.5056i	0.416253	+	0.642033i
$924$		0			0
$925$	23.5770	−	40.8365i	0.775206	−	1.34270i
$926$	−0.241198	−	0.417767i	−0.00792625	−	0.0137287i
$927$		0			0
$928$	−2.65268	−	4.59458i	−0.0870785	−	0.150824i
$929$	8.13928			0.267041			0.133521	−	0.991046i	$-0.457372\pi$
$929$	8.13928			0.267041			0.133521	+	0.991046i	$0.457372\pi$
$930$		0			0
$931$	−45.7062	+	17.0202i	−1.49796	+	0.557815i
$932$	8.26922	+	14.3227i	0.270867	+	0.469156i
$933$		0			0
$934$	67.1096			2.19589
$935$	−2.62212	−	4.54165i	−0.0857526	−	0.148528i
$936$		0			0
$937$	30.6536			1.00141			0.500705	−	0.865618i	$-0.333074\pi$
$937$	30.6536			1.00141			0.500705	+	0.865618i	$0.333074\pi$
$938$	−4.86565	−	5.75522i	−0.158869	−	0.187915i
$939$		0			0
$940$	27.5121			0.897347
$941$	−4.34815	−	7.53122i	−0.141746	−	0.245511i	0.786408	−	0.617707i	$-0.211938\pi$
$941$	−4.34815	−	7.53122i	−0.141746	−	0.245511i	−0.928154	+	0.372196i	$0.878605\pi$
$942$		0			0
$943$	−7.38168			−0.240381
$944$	−23.9237			−0.778651
$945$		0			0
$946$	−0.303651	+	0.525938i	−0.00987254	+	0.0170997i
$947$	−5.73610	−	9.93522i	−0.186398	−	0.322851i	0.757649	−	0.652663i	$-0.226348\pi$
$947$	−5.73610	−	9.93522i	−0.186398	−	0.322851i	−0.944047	+	0.329812i	$0.893015\pi$
$948$		0			0
$949$	32.3577	+	49.9089i	1.05038	+	1.62011i
$950$	−68.1250	+	117.996i	−2.21027	+	3.82830i
$951$		0			0
$952$	5.40407	−	15.0204i	0.175147	−	0.486815i
$953$	23.1731	+	40.1370i	0.750650	+	1.30016i	0.947508	+	0.319731i	$0.103593\pi$
$953$	23.1731	+	40.1370i	0.750650	+	1.30016i	−0.196859	+	0.980432i	$0.563074\pi$
$954$		0			0
$955$	22.0590	−	38.2074i	0.713814	−	1.23636i
$956$	−3.05887	+	5.29812i	−0.0989310	+	0.171353i
$957$		0			0
$958$	−26.0607	−	45.1384i	−0.841983	−	1.45836i
$959$	−1.35220	+	3.75839i	−0.0436648	+	0.121365i
$960$		0			0
$961$	15.4094	−	26.6898i	0.497077	−	0.860963i
$962$	−12.9481	+	25.3648i	−0.417463	+	0.817793i
$963$		0			0
$964$	−6.64544	−	11.5102i	−0.214035	−	0.370720i
$965$	0.966511	−	1.67405i	0.0311131	−	0.0538894i
$966$		0			0
$967$	8.71419			0.280229			0.140115	−	0.990135i	$-0.455253\pi$
$967$	8.71419			0.280229			0.140115	+	0.990135i	$0.455253\pi$
$968$	−14.3144			−0.460081
$969$		0			0
$970$	−68.5149	−	118.671i	−2.19988	−	3.81031i
$971$	−40.0563			−1.28547			−0.642733	−	0.766090i	$-0.722200\pi$
$971$	−40.0563			−1.28547			−0.642733	+	0.766090i	$0.722200\pi$
$972$		0			0
$973$	−6.90545	−	8.16797i	−0.221379	−	0.261853i
$974$	24.8499			0.796243
$975$		0			0
$976$	20.1110	+	34.8333i	0.643738	+	1.11499i
$977$	42.3067			1.35351			0.676755	−	0.736208i	$-0.263386\pi$
$977$	42.3067			1.35351			0.676755	+	0.736208i	$0.263386\pi$
$978$		0			0
$979$	−0.317572	−	0.550050i	−0.0101496	−	0.0175797i
$980$	−27.3611	−	22.6154i	−0.874017	−	0.722422i
$981$		0			0
$982$	−49.8189			−1.58979
$983$	−2.44395	−	4.23305i	−0.0779501	−	0.135013i	0.824415	−	0.565985i	$-0.191504\pi$
$983$	−2.44395	−	4.23305i	−0.0779501	−	0.135013i	−0.902365	+	0.430972i	$0.858171\pi$
$984$		0			0
$985$	33.9436	+	58.7920i	1.08153	+	1.87327i
$986$	3.51264	−	6.08407i	0.111865	−	0.193756i
$987$		0			0
$988$	14.5695	−	28.5410i	0.463517	−	0.908009i
$989$	4.23667	−	7.33813i	0.134718	−	0.233339i
$990$		0			0
$991$	−18.5959			−0.590718			−0.295359	−	0.955386i	$-0.595439\pi$
$991$	−18.5959			−0.590718			−0.295359	+	0.955386i	$0.595439\pi$
$992$	2.67755			0.0850124
$993$		0			0
$994$	10.4516	−	29.0498i	0.331504	−	0.921405i
$995$	−46.0560	−	79.7713i	−1.46007	−	2.52892i
$996$		0			0
$997$	12.8181	−	22.2017i	0.405954	−	0.703133i	−0.588478	−	0.808513i	$-0.700273\pi$
$997$	12.8181	−	22.2017i	0.405954	−	0.703133i	0.994432	+	0.105380i	$0.0336059\pi$
$998$	7.04276			0.222935
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.f.100.8		20
3.2	odd	2		273.2.j.c.100.3	✓	20
7.4	even	3		819.2.s.f.802.3		20
13.3	even	3		819.2.s.f.289.3		20
21.11	odd	6		273.2.l.c.256.8	yes	20
39.29	odd	6		273.2.l.c.16.8	yes	20
91.81	even	3	inner	819.2.n.f.172.8		20
273.263	odd	6		273.2.j.c.172.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.3	✓	20	3.2	odd	2
273.2.j.c.172.3	yes	20	273.263	odd	6
273.2.l.c.16.8	yes	20	39.29	odd	6
273.2.l.c.256.8	yes	20	21.11	odd	6
819.2.n.f.100.8		20	1.1	even	1	trivial
819.2.n.f.172.8		20	91.81	even	3	inner
819.2.s.f.289.3		20	13.3	even	3
819.2.s.f.802.3		20	7.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.904928 + 1.56738i) q^{2} +(-0.637789 + 1.10468i) q^{4} +(-1.98776 + 3.44291i) q^{5} +(-2.60384 + 0.469078i) q^{7} +1.31110 q^{8} -7.19513 q^{10} +0.286654 q^{11} +(3.60075 - 0.185985i) q^{13} +(-3.09151 - 3.65672i) q^{14} +(2.46203 + 4.26436i) q^{16} +(-2.30091 + 3.98530i) q^{17} -6.96749 q^{19} +(-2.53555 - 4.39170i) q^{20} +(0.259402 + 0.449297i) q^{22} +(-3.61929 - 6.26879i) q^{23} +(-5.40240 - 9.35723i) q^{25} +(3.54993 + 5.47545i) q^{26} +(1.14252 - 3.17559i) q^{28} +(-0.421754 + 0.730500i) q^{29} +(-0.212854 - 0.368675i) q^{31} +(-3.14482 + 5.44698i) q^{32} -8.32864 q^{34} +(3.56082 - 9.89718i) q^{35} +(2.18208 + 3.77948i) q^{37} +(-6.30507 - 10.9207i) q^{38} +(-2.60615 + 4.51399i) q^{40} +(0.509885 - 0.883147i) q^{41} +(0.585291 + 1.01375i) q^{43} +(-0.182825 + 0.316662i) q^{44} +(6.55039 - 11.3456i) q^{46} +(-2.71264 + 4.69843i) q^{47} +(6.55993 - 2.44280i) q^{49} +(9.77756 - 16.9352i) q^{50} +(-2.09107 + 4.09631i) q^{52} +(0.574226 + 0.994589i) q^{53} +(-0.569801 + 0.986924i) q^{55} +(-3.41389 + 0.615007i) q^{56} -1.52663 q^{58} +(-2.42927 + 4.20762i) q^{59} +8.16848 q^{61} +(0.385236 - 0.667248i) q^{62} -1.53522 q^{64} +(-6.51711 + 12.7667i) q^{65} +1.57387 q^{67} +(-2.93499 - 5.08356i) q^{68} +(18.7349 - 3.37507i) q^{70} +(3.22369 + 5.58359i) q^{71} +(8.24845 + 14.2867i) q^{73} +(-3.94925 + 6.84031i) q^{74} +(4.44379 - 7.69686i) q^{76} +(-0.746401 + 0.134463i) q^{77} +(-3.84412 + 6.65821i) q^{79} -19.5757 q^{80} +1.84564 q^{82} -13.3888 q^{83} +(-9.14733 - 15.8436i) q^{85} +(-1.05929 + 1.83475i) q^{86} +0.375832 q^{88} +(-1.10786 - 1.91886i) q^{89} +(-9.28853 + 2.17331i) q^{91} +9.23336 q^{92} -9.81898 q^{94} +(13.8497 - 23.9884i) q^{95} +(9.52241 + 16.4933i) q^{97} +(9.76507 + 8.07135i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 16 q^{4} - 9 q^{7} + 12 q^{8} + 8 q^{10} - 16 q^{11} - 5 q^{13} + 9 q^{14} - 20 q^{16} - 14 q^{19} - 12 q^{20} - 9 q^{22} + 14 q^{23} - 32 q^{25} - 4 q^{26} + 13 q^{28} + 9 q^{29} - 9 q^{31} - 17 q^{32}+ \cdots + 79 q^{98}+O(q^{100}) \) 20 * q - 16 * q^4 - 9 * q^7 + 12 * q^8 + 8 * q^10 - 16 * q^11 - 5 * q^13 + 9 * q^14 - 20 * q^16 - 14 * q^19 - 12 * q^20 - 9 * q^22 + 14 * q^23 - 32 * q^25 - 4 * q^26 + 13 * q^28 + 9 * q^29 - 9 * q^31 - 17 * q^32 + 12 * q^34 - 10 * q^35 + 18 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 - 10 * q^46 - 13 * q^47 - 21 * q^49 - 5 * q^50 - 2 * q^52 + 6 * q^53 - 19 * q^55 + 5 * q^56 + 15 * q^59 - 22 * q^62 + 72 * q^64 + 27 * q^65 + 44 * q^67 - 39 * q^68 + 30 * q^70 + 11 * q^71 + 3 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 + 96 * q^80 + 26 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 + 24 * q^88 - 2 * q^89 + 9 * q^91 - 66 * q^92 + 88 * q^94 + 36 * q^95 + 21 * q^97 + 79 * q^98

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