LMFDB - Embedded newform 819.2.n.f.172.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			172.8
Root			$0.904928 + 1.56738i$ of defining polynomial
Character	$\chi$	$=$	819.172
Dual form			819.2.n.f.100.8

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

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

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	−0.345578	−	0.938390i	$-0.612317\pi$
$2$	0.904928	−	1.56738i	0.639881	−	1.10831i	0.985459	−	0.169916i	$-0.0543496\pi$
$3$		0			0
$3$		0			0
$4$	−0.637789	−	1.10468i	−0.318895	−	0.552342i
$5$	−1.98776	−	3.44291i	−0.888954	−	1.53971i	−0.841113	−	0.540859i	$-0.818099\pi$
$5$	−1.98776	−	3.44291i	−0.888954	−	1.53971i	−0.0478412	−	0.998855i	$-0.515234\pi$
$6$		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	−0.997659	−	0.0683857i	$-0.978215\pi$
$17$	−2.30091	−	3.98530i	−0.558053	−	0.966577i	0.439606	−	0.898191i	$-0.355118\pi$
$18$		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	0.190863	+	0.981617i	$0.438871\pi$
$23$	−3.61929	+	6.26879i	−0.754673	+	1.30713i	−0.945537	+	0.325516i	$0.894462\pi$
$24$		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	0.824206	−	0.566289i	$-0.191622\pi$
$29$	−0.421754	−	0.730500i	−0.0783178	−	0.135650i	−0.902524	+	0.430639i	$0.858288\pi$
$30$		0			0
$31$	−0.212854	+	0.368675i	−0.0382298	+	0.0662159i	−0.884507	−	0.466527i	$-0.845505\pi$
$31$	−0.212854	+	0.368675i	−0.0382298	+	0.0662159i	0.846277	+	0.532742i	$0.178839\pi$
$32$	−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	−0.629017	−	0.777391i	$-0.716542\pi$
$37$	2.18208	−	3.77948i	0.358732	−	0.621342i	0.987749	+	0.156049i	$0.0498758\pi$
$38$	−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	0.903091	−	0.429450i	$-0.141293\pi$
$41$	0.509885	+	0.883147i	0.0796307	+	0.137924i	−0.823460	+	0.567374i	$0.807959\pi$
$42$		0			0
$43$	0.585291	−	1.01375i	0.0892560	−	0.154596i	−0.817941	−	0.575302i	$-0.804884\pi$
$43$	0.585291	−	1.01375i	0.0892560	−	0.154596i	0.907197	+	0.420706i	$0.138218\pi$
$44$	−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	0.597508	−	0.801863i	$-0.296158\pi$
$47$	−2.71264	−	4.69843i	−0.395680	−	0.685337i	−0.993188	+	0.116526i	$0.962824\pi$
$48$		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	−0.823889	−	0.566751i	$-0.808200\pi$
$53$	0.574226	−	0.994589i	0.0788760	−	0.136617i	0.902765	+	0.430134i	$0.141534\pi$
$54$		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	0.663441	−	0.748228i	$-0.269095\pi$
$59$	−2.42927	−	4.20762i	−0.316264	−	0.547785i	−0.979705	+	0.200443i	$0.935762\pi$
$60$		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	−0.608849	−	0.793286i	$-0.708369\pi$
$71$	3.22369	−	5.58359i	0.382581	−	0.662650i	0.991430	+	0.130636i	$0.0417019\pi$
$72$		0			0
$73$	8.24845	−	14.2867i	0.965408	−	1.67214i	0.256893	−	0.966440i	$-0.417301\pi$
$73$	8.24845	−	14.2867i	0.965408	−	1.67214i	0.708515	−	0.705696i	$-0.249365\pi$
$74$	−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	0.564590	−	0.825371i	$-0.309034\pi$
$79$	−3.84412	−	6.65821i	−0.432497	−	0.749107i	−0.997088	+	0.0762639i	$0.975701\pi$
$80$	−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	−0.918750	−	0.394841i	$-0.870800\pi$
$89$	−1.10786	+	1.91886i	−0.117433	+	0.203399i	0.801317	+	0.598240i	$0.204133\pi$
$90$		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	0.262306	−	0.964985i	$-0.415517\pi$
$97$	9.52241	−	16.4933i	0.966854	−	1.67464i	0.704549	−	0.709656i	$-0.251150\pi$
$98$	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	0.958097	−	0.286443i	$-0.0924729\pi$
$103$	2.34421	+	4.06029i	0.230982	+	0.400072i	−0.727116	+	0.686515i	$0.759140\pi$
$104$	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	−0.266908	−	0.963722i	$-0.586002\pi$
$107$	7.25279	−	12.5622i	0.701154	−	1.21443i	0.968062	−	0.250712i	$-0.0806648\pi$
$108$		0			0
$109$	2.09694	−	3.63200i	0.200850	−	0.347883i	−0.747952	−	0.663752i	$-0.768963\pi$
$109$	2.09694	−	3.63200i	0.200850	−	0.347883i	0.948803	+	0.315870i	$0.102296\pi$
$110$	−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	−0.992162	−	0.124958i	$-0.960120\pi$
$113$	−4.12305	+	7.14133i	−0.387864	+	0.671800i	0.604298	+	0.796758i	$0.293454\pi$
$114$		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	0.637897	−	0.770122i	$-0.279805\pi$
$127$	−3.92173	−	6.79263i	−0.347997	−	0.602748i	−0.985894	+	0.167374i	$0.946471\pi$
$128$	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	0.986811	−	0.161874i	$-0.0517540\pi$
$131$	4.04277	+	7.00228i	0.353218	+	0.611792i	−0.633593	+	0.773666i	$0.718421\pi$
$132$		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	0.896468	−	0.443109i	$-0.146124\pi$
$137$	0.754841	+	1.30742i	0.0644904	+	0.111701i	−0.831977	+	0.554809i	$0.812791\pi$
$138$		0			0
$139$	2.02132	−	3.50104i	0.171446	−	0.296954i	−0.767479	−	0.641074i	$-0.778489\pi$
$139$	2.02132	−	3.50104i	0.171446	−	0.296954i	0.938926	+	0.344120i	$0.111823\pi$
$140$	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	0.166125	+	0.986105i	$0.446874\pi$
$151$	−9.47334	+	16.4083i	−0.770929	+	1.33529i	−0.937054	+	0.349184i	$0.886459\pi$
$152$	−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	0.207197	+	0.978299i	$0.433566\pi$
$157$	−9.31770	+	16.1387i	−0.743633	+	1.28801i	−0.950831	+	0.309711i	$0.899768\pi$
$158$	−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	0.865093	−	0.501612i	$-0.167259\pi$
$167$	−0.0240620	−	0.0416766i	−0.00186197	−	0.00322503i	−0.866955	+	0.498387i	$0.833926\pi$
$168$		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	0.991518	+	0.129971i	$0.0414886\pi$
$197$	8.53814	+	14.7885i	0.608317	+	1.05364i	−0.383200	+	0.923665i	$0.625178\pi$
$198$		0			0
$199$	−11.5849	−	20.0656i	−0.821230	−	1.42241i	−0.904766	−	0.425908i	$-0.859955\pi$
$199$	−11.5849	−	20.0656i	−0.821230	−	1.42241i	0.0835360	−	0.996505i	$-0.473379\pi$
$200$	−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	0.910409	−	0.413709i	$-0.135767\pi$
$211$	1.40788	+	2.43852i	0.0969224	+	0.167874i	−0.813487	+	0.581583i	$0.802433\pi$
$212$	−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	−0.998505	−	0.0546597i	$-0.982593\pi$
$223$	−8.16232	−	14.1375i	−0.546589	−	0.946720i	0.451916	−	0.892061i	$-0.350741\pi$
$224$	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	0.744488	−	0.667636i	$-0.232694\pi$
$227$	−3.10289	−	5.37436i	−0.205946	−	0.356709i	−0.950434	+	0.310927i	$0.899360\pi$
$228$		0			0
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	0.874535	−	0.484962i	$-0.161167\pi$
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	−0.857257	+	0.514889i	$0.827833\pi$
$230$	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	0.996392	−	0.0848689i	$-0.0270471\pi$
$233$	6.48273	+	11.2284i	0.424697	+	0.735598i	−0.571695	+	0.820466i	$0.693714\pi$
$234$		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	0.648008	−	0.761633i	$-0.275602\pi$
$241$	−5.20975	−	9.02355i	−0.335589	−	0.581258i	−0.983598	+	0.180375i	$0.942269\pi$
$242$	−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	−0.658649	−	0.752450i	$-0.728872\pi$
$251$	5.10645	−	8.84463i	0.322316	−	0.558268i	0.980966	+	0.194182i	$0.0622052\pi$
$252$		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	−0.948026	−	0.318192i	$-0.896924\pi$
$257$	−3.18140	+	5.51035i	−0.198450	+	0.343726i	0.749576	+	0.661919i	$0.230258\pi$
$258$		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	0.694229	−	0.719754i	$-0.255745\pi$
$269$	−4.53019	−	7.84653i	−0.276211	−	0.478411i	−0.970440	+	0.241343i	$0.922412\pi$
$270$		0			0
$271$	−1.11398	+	1.92947i	−0.0676696	+	0.117207i	−0.897875	−	0.440250i	$-0.854890\pi$
$271$	−1.11398	+	1.92947i	−0.0676696	+	0.117207i	0.830206	+	0.557457i	$0.188223\pi$
$272$	−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	0.959143	−	0.282921i	$-0.0913034\pi$
$277$	3.90377	+	6.76153i	0.234555	+	0.406261i	−0.724588	+	0.689182i	$0.757970\pi$
$278$	−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	0.280209	+	0.959939i	$0.409596\pi$
$293$	−11.8319	+	20.4935i	−0.691227	+	1.19724i	−0.971436	+	0.237302i	$0.923737\pi$
$294$		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	−0.0204655	+	0.999791i	$0.506515\pi$
$311$	−15.4498	+	26.7598i	−0.876077	+	1.51741i	−0.855611	+	0.517619i	$0.826819\pi$
$312$		0			0
$313$	3.74574	+	6.48782i	0.211722	+	0.366713i	0.952254	−	0.305308i	$-0.0987595\pi$
$313$	3.74574	+	6.48782i	0.211722	+	0.366713i	−0.740532	+	0.672022i	$0.765426\pi$
$314$	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	0.543001	−	0.839732i	$-0.317288\pi$
$317$	−8.11402	−	14.0539i	−0.455729	−	0.789346i	−0.998730	+	0.0503864i	$0.983955\pi$
$318$		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	0.655971	−	0.754786i	$-0.272259\pi$
$347$	−6.06672	−	10.5079i	−0.325678	−	0.564092i	−0.981649	+	0.190694i	$0.938926\pi$
$348$		0			0
$349$	10.9086	+	18.8943i	0.583924	+	1.01139i	0.995009	+	0.0997893i	$0.0318169\pi$
$349$	10.9086	+	18.8943i	0.583924	+	1.01139i	−0.411084	+	0.911597i	$0.634850\pi$
$350$	−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	0.991216	−	0.132255i	$-0.0422218\pi$
$359$	7.22027	+	12.5059i	0.381071	+	0.660035i	−0.610144	+	0.792290i	$0.708889\pi$
$360$		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	0.815222	−	0.579149i	$-0.196615\pi$
$379$	−1.82895	−	3.16783i	−0.0939467	−	0.162720i	−0.909169	+	0.416428i	$0.863282\pi$
$380$	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	−0.531890	−	0.846813i	$-0.678518\pi$
$389$	9.21889	−	15.9676i	0.467416	−	0.809589i	0.999307	+	0.0372241i	$0.0118515\pi$
$390$		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	−0.251894	−	0.967755i	$-0.581053\pi$
$401$	14.2609	−	24.7005i	0.712153	−	1.23349i	0.964047	−	0.265731i	$-0.0856132\pi$
$402$		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	0.700088	−	0.714057i	$-0.253144\pi$
$409$	−5.42700	−	9.39983i	−0.268348	−	0.464792i	−0.968435	+	0.249265i	$0.919811\pi$
$410$	−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	0.990376	−	0.138401i	$-0.0441964\pi$
$419$	7.68279	+	13.3070i	0.375329	+	0.650089i	−0.615047	+	0.788490i	$0.710863\pi$
$420$		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	−0.968189	−	0.250221i	$-0.919497\pi$
$433$	−5.56416	+	9.63741i	−0.267396	+	0.463144i	0.700792	+	0.713365i	$0.252830\pi$
$434$	−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	−0.310497	+	0.950574i	$0.600496\pi$
$439$	−20.5012	+	35.5092i	−0.978470	+	1.69476i	−0.667973	+	0.744186i	$0.732838\pi$
$440$	−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	0.990568	−	0.137022i	$-0.0437530\pi$
$443$	7.92693	+	13.7298i	0.376620	+	0.652325i	−0.613948	+	0.789346i	$0.710420\pi$
$444$		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	−0.631035	−	0.775754i	$-0.717370\pi$
$449$	7.54997	−	13.0769i	0.356305	−	0.617139i	0.987340	+	0.158616i	$0.0507030\pi$
$450$		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	−0.865700	−	0.500564i	$-0.833126\pi$
$457$	0.0139240	−	0.0241170i	0.000651335	−	0.00112815i	0.866351	+	0.499436i	$0.166459\pi$
$458$	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	0.327425	+	0.944877i	$0.393819\pi$
$461$	−14.0543	+	24.3428i	−0.654575	+	1.13376i	−0.982000	+	0.188880i	$0.939514\pi$
$462$		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	0.873899	+	0.486107i	$0.161583\pi$
$467$	18.5400	+	32.1123i	0.857931	+	1.48598i	−0.0159687	+	0.999872i	$0.505083\pi$
$468$		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	0.978599	−	0.205778i	$-0.0659725\pi$
$487$	6.86516	+	11.8908i	0.311090	+	0.538824i	−0.667508	+	0.744602i	$0.732639\pi$
$488$	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	−0.989276	−	0.146056i	$-0.953342\pi$
$491$	−13.7632	−	23.8386i	−0.621126	−	1.07582i	0.368150	−	0.929766i	$-0.379991\pi$
$492$		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	0.906284	−	0.422669i	$-0.138907\pi$
$499$	1.94567	+	3.37000i	0.0871001	+	0.150862i	−0.819184	+	0.573531i	$0.805573\pi$
$500$	−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	−0.821067	−	0.570832i	$-0.806621\pi$
$503$	1.87991	−	3.25610i	0.0838212	−	0.145183i	0.904888	+	0.425649i	$0.139954\pi$
$504$		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	0.0229793	+	0.999736i	$0.492685\pi$
$509$	−19.2740	+	33.3836i	−0.854307	+	1.47970i	−0.877286	+	0.479967i	$0.840649\pi$
$510$		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	−0.673587	−	0.739108i	$-0.735247\pi$
$521$	6.92277	−	11.9906i	0.303292	−	0.525318i	0.976880	+	0.213790i	$0.0685808\pi$
$522$		0			0
$523$	−10.0335	+	17.3786i	−0.438736	+	0.759913i	−0.997592	−	0.0693515i	$-0.977907\pi$
$523$	−10.0335	+	17.3786i	−0.438736	+	0.759913i	0.558856	+	0.829265i	$0.311240\pi$
$524$	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	−0.909788	−	0.415072i	$-0.863756\pi$
$541$	−18.9415	−	32.8076i	−0.814357	−	1.41051i	0.0954310	−	0.995436i	$-0.469577\pi$
$542$	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	−0.941116	−	0.338085i	$-0.890221\pi$
$563$	−18.1124	−	31.3716i	−0.763348	−	1.32216i	0.177768	−	0.984072i	$-0.443112\pi$
$564$		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	−0.834763	−	0.550610i	$-0.814395\pi$
$569$	1.41835	−	2.45666i	0.0594605	−	0.102989i	0.894223	+	0.447621i	$0.147729\pi$
$570$		0			0
$571$	2.29825	−	3.98069i	0.0961789	−	0.166587i	−0.813921	−	0.580975i	$-0.802671\pi$
$571$	2.29825	−	3.98069i	0.0961789	−	0.166587i	0.910100	+	0.414389i	$0.136005\pi$
$572$	−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	−0.624329	−	0.781161i	$-0.714628\pi$
$577$	8.75176	−	15.1585i	0.364341	−	0.631056i	0.988670	+	0.150105i	$0.0479611\pi$
$578$	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	0.879544	−	0.475818i	$-0.157848\pi$
$587$	0.671155	+	1.16247i	0.0277015	+	0.0479805i	−0.851842	+	0.523798i	$0.824515\pi$
$588$		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	−0.818353	−	0.574716i	$-0.805112\pi$
$593$	−22.0843	−	38.2512i	−0.906895	−	1.57079i	−0.0885427	−	0.996072i	$-0.528221\pi$
$594$		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	−0.985518	−	0.169573i	$-0.945761\pi$
$599$	−8.46583	+	14.6632i	−0.345904	+	0.599124i	0.639613	+	0.768697i	$0.279095\pi$
$600$		0			0
$601$	7.56311	+	13.0997i	0.308506	+	0.534348i	0.978036	−	0.208437i	$-0.0668378\pi$
$601$	7.56311	+	13.0997i	0.308506	+	0.534348i	−0.669530	+	0.742785i	$0.733504\pi$
$602$	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	−0.836068	−	0.548626i	$-0.815151\pi$
$617$	1.41810	−	2.45623i	0.0570907	−	0.0988839i	0.893158	+	0.449743i	$0.148484\pi$
$618$		0			0
$619$	0.658494	−	1.14055i	0.0264671	−	0.0458424i	−0.852488	−	0.522746i	$-0.824908\pi$
$619$	0.658494	−	1.14055i	0.0264671	−	0.0458424i	0.878956	+	0.476904i	$0.158241\pi$
$620$	−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	−0.998986	−	0.0450286i	$-0.985662\pi$
$631$	−11.5676	+	20.0356i	−0.460497	+	0.797604i	0.538489	+	0.842633i	$0.318995\pi$
$632$	−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	−0.959448	−	0.281884i	$-0.909041\pi$
$641$	−18.3262	−	31.7420i	−0.723843	−	1.25373i	0.235605	−	0.971849i	$-0.424293\pi$
$642$		0			0
$643$	−1.86917	+	3.23749i	−0.0737127	+	0.127674i	−0.900526	−	0.434803i	$-0.856818\pi$
$643$	−1.86917	+	3.23749i	−0.0737127	+	0.127674i	0.826813	+	0.562477i	$0.190151\pi$
$644$	−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	−0.765071	−	0.643946i	$-0.777296\pi$
$653$	4.47546	−	7.75172i	0.175138	−	0.303348i	0.940209	+	0.340598i	$0.110629\pi$
$654$		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	−0.937624	−	0.347651i	$-0.886979\pi$
$659$	−4.30599	+	7.45819i	−0.167737	+	0.290530i	0.769887	+	0.638181i	$0.220313\pi$
$660$		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	−0.882510	−	0.470294i	$-0.844148\pi$
$673$	−22.0131	−	38.1277i	−0.848541	−	1.46972i	0.0339689	−	0.999423i	$-0.489185\pi$
$674$	−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	0.999125	−	0.0418328i	$-0.0133197\pi$
$677$	12.0556	+	20.8809i	0.463334	+	0.802518i	−0.535791	+	0.844351i	$0.679986\pi$
$678$		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	0.631639	−	0.775263i	$-0.282382\pi$
$683$	−9.29276	−	16.0955i	−0.355578	−	0.615878i	−0.987217	+	0.159384i	$0.949049\pi$
$684$		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	−0.566340	−	0.824171i	$-0.691641\pi$
$691$	11.3187	−	19.6045i	0.430583	−	0.745792i	0.996924	+	0.0783796i	$0.0249746\pi$
$692$	−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	0.982816	−	0.184586i	$-0.0590945\pi$
$733$	8.97642	+	15.5476i	0.331552	+	0.574265i	−0.651265	+	0.758851i	$0.725761\pi$
$734$	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	0.992970	−	0.118368i	$-0.0377664\pi$
$743$	10.7390	+	18.6004i	0.393975	+	0.682384i	−0.598995	+	0.800753i	$0.704433\pi$
$744$		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	−0.893743	−	0.448579i	$-0.851930\pi$
$751$	−1.60018	+	2.77159i	−0.0583913	+	0.101137i	0.835352	+	0.549715i	$0.185264\pi$
$752$	−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	0.531762	−	0.846894i	$-0.321530\pi$
$757$	−12.8640	−	22.2811i	−0.467550	−	0.809821i	−0.999313	+	0.0370727i	$0.988197\pi$
$758$	−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	0.981290	−	0.192536i	$-0.0616712\pi$
$769$	8.98213	+	15.5575i	0.323904	+	0.561018i	−0.657386	+	0.753554i	$0.728338\pi$
$770$	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	0.963601	+	0.267346i	$0.0861468\pi$
$773$	19.8326	+	34.3511i	0.713329	+	1.23552i	−0.250272	+	0.968176i	$0.580520\pi$
$774$		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	0.966620	+	0.256215i	$0.0824756\pi$
$787$	19.7833	+	34.2657i	0.705199	+	1.22144i	−0.261421	+	0.965225i	$0.584191\pi$
$788$	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	−0.640837	−	0.767677i	$-0.721412\pi$
$797$	9.72309	−	16.8409i	0.344409	−	0.596535i	0.985246	+	0.171142i	$0.0547458\pi$
$798$		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	0.431716	+	0.902009i	$0.357908\pi$
$821$	−16.1977	+	28.0553i	−0.565305	+	0.979137i	−0.997021	+	0.0771274i	$0.975425\pi$
$822$		0			0
$823$	20.5081	+	35.5210i	0.714866	+	1.23818i	0.963011	+	0.269461i	$0.0868457\pi$
$823$	20.5081	+	35.5210i	0.714866	+	1.23818i	−0.248145	+	0.968723i	$0.579821\pi$
$824$	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	−0.212873	−	0.977080i	$-0.568282\pi$
$839$	21.4269	−	37.1125i	0.739739	−	1.28127i	0.952612	−	0.304186i	$-0.0983846\pi$
$840$		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	−0.917370	−	0.398035i	$-0.869692\pi$
$857$	−3.33662	+	5.77919i	−0.113977	+	0.197413i	0.803394	+	0.595448i	$0.203026\pi$
$858$		0			0
$859$	8.20940	+	14.2191i	0.280101	+	0.485149i	0.971409	−	0.237411i	$-0.0762987\pi$
$859$	8.20940	+	14.2191i	0.280101	+	0.485149i	−0.691308	+	0.722560i	$0.742965\pi$
$860$	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	0.769944	−	0.638112i	$-0.220284\pi$
$863$	−4.92500	−	8.53035i	−0.167649	−	0.290377i	−0.937593	+	0.347735i	$0.886951\pi$
$864$		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	−0.999572	−	0.0292404i	$-0.990691\pi$
$881$	−15.5861	−	26.9959i	−0.525109	−	0.909516i	0.474463	−	0.880275i	$-0.342642\pi$
$882$		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	−0.797027	−	0.603943i	$-0.793595\pi$
$887$	3.70842	−	6.42317i	0.124517	−	0.215669i	0.921544	+	0.388274i	$0.126929\pi$
$888$		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	−0.928154	−	0.372196i	$-0.878605\pi$
$941$	−4.34815	+	7.53122i	−0.141746	+	0.245511i	0.786408	+	0.617707i	$0.211938\pi$
$942$		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	−0.944047	−	0.329812i	$-0.893015\pi$
$947$	−5.73610	+	9.93522i	−0.186398	+	0.322851i	0.757649	+	0.652663i	$0.226348\pi$
$948$		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	−0.196859	−	0.980432i	$-0.563074\pi$
$953$	23.1731	−	40.1370i	0.750650	−	1.30016i	0.947508	−	0.319731i	$-0.103593\pi$
$954$		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	−0.902365	−	0.430972i	$-0.858171\pi$
$983$	−2.44395	+	4.23305i	−0.0779501	+	0.135013i	0.824415	+	0.565985i	$0.191504\pi$
$984$		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	0.994432	−	0.105380i	$-0.0336059\pi$
$997$	12.8181	+	22.2017i	0.405954	+	0.703133i	−0.588478	+	0.808513i	$0.700273\pi$
$998$	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.172.8		20
3.2	odd	2		273.2.j.c.172.3	yes	20
7.2	even	3		819.2.s.f.289.3		20
13.9	even	3		819.2.s.f.802.3		20
21.2	odd	6		273.2.l.c.16.8	yes	20
39.35	odd	6		273.2.l.c.256.8	yes	20
91.9	even	3	inner	819.2.n.f.100.8		20
273.191	odd	6		273.2.j.c.100.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.3	✓	20	273.191	odd	6
273.2.j.c.172.3	yes	20	3.2	odd	2
273.2.l.c.16.8	yes	20	21.2	odd	6
273.2.l.c.256.8	yes	20	39.35	odd	6
819.2.n.f.100.8		20	91.9	even	3	inner
819.2.n.f.172.8		20	1.1	even	1	trivial
819.2.s.f.289.3		20	7.2	even	3
819.2.s.f.802.3		20	13.9	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 $\F_{q}$

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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