LMFDB - Embedded newform 819.2.ct.b.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(127,819)]

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, 0, 5]))

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

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

chi := DirichletCharacter("819.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ct (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.8
Root			$2.60802i$ of defining polynomial
Character	$\chi$	$=$	819.127
Dual form			819.2.ct.b.316.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.25861 - 1.30401i) q^{2} +(2.40088 - 4.15844i) q^{4} -1.50528i q^{5} +(-0.866025 - 0.500000i) q^{7} -7.30704i q^{8} +(-1.96290 - 3.39983i) q^{10} +(-0.0753030 + 0.0434762i) q^{11} +(-1.30332 - 3.36175i) q^{13} -2.60802 q^{14} +(-4.72668 - 8.18685i) q^{16} +(-3.24732 + 5.62452i) q^{17} +(4.58318 + 2.64610i) q^{19} +(-6.25961 - 3.61399i) q^{20} +(-0.113387 + 0.196391i) q^{22} +(2.60110 + 4.50524i) q^{23} +2.73414 q^{25} +(-7.32743 - 5.89335i) q^{26} +(-4.15844 + 2.40088i) q^{28} +(-2.98801 - 5.17538i) q^{29} -2.00289i q^{31} +(-8.69531 - 5.02024i) q^{32} +16.9381i q^{34} +(-0.752639 + 1.30361i) q^{35} +(8.24566 - 4.76063i) q^{37} +13.8022 q^{38} -10.9991 q^{40} +(-5.57631 + 3.21948i) q^{41} +(3.40536 - 5.89825i) q^{43} +0.417524i q^{44} +(11.7498 + 6.78372i) q^{46} +1.83051i q^{47} +(0.500000 + 0.866025i) q^{49} +(6.17535 - 3.56534i) q^{50} +(-17.1088 - 2.65139i) q^{52} +3.28476 q^{53} +(0.0654437 + 0.113352i) q^{55} +(-3.65352 + 6.32808i) q^{56} +(-13.4975 - 7.79278i) q^{58} +(2.31669 + 1.33754i) q^{59} +(3.27278 - 5.66863i) q^{61} +(-2.61179 - 4.52375i) q^{62} -7.27901 q^{64} +(-5.06037 + 1.96185i) q^{65} +(-7.18333 + 4.14730i) q^{67} +(15.5928 + 27.0076i) q^{68} +3.92579i q^{70} +(11.1872 + 6.45892i) q^{71} +14.5507i q^{73} +(12.4158 - 21.5048i) q^{74} +(22.0073 - 12.7059i) q^{76} +0.0869524 q^{77} -11.6780 q^{79} +(-12.3235 + 7.11497i) q^{80} +(-8.39647 + 14.5431i) q^{82} +1.29310i q^{83} +(8.46647 + 4.88812i) q^{85} -17.7625i q^{86} +(0.317682 + 0.550241i) q^{88} +(-13.7225 + 7.92270i) q^{89} +(-0.552171 + 3.56302i) q^{91} +24.9797 q^{92} +(2.38701 + 4.13442i) q^{94} +(3.98312 - 6.89896i) q^{95} +(-5.08340 - 2.93490i) q^{97} +(2.25861 + 1.30401i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} - 4 q^{10} + 12 q^{11} + 4 q^{13} - 4 q^{14} - 10 q^{16} - 10 q^{17} - 6 q^{20} - 2 q^{22} + 2 q^{23} + 12 q^{25} - 20 q^{26} - 12 q^{29} - 30 q^{32} + 2 q^{35} + 18 q^{37} + 32 q^{38} - 60 q^{40}+ \cdots - 54 q^{97}+O(q^{100}) $ 16 * q + 6 * q^4 - 4 * q^10 + 12 * q^11 + 4 * q^13 - 4 * q^14 - 10 * q^16 - 10 * q^17 - 6 * q^20 - 2 * q^22 + 2 * q^23 + 12 * q^25 - 20 * q^26 - 12 * q^29 - 30 * q^32 + 2 * q^35 + 18 * q^37 + 32 * q^38 - 60 * q^40 - 18 * q^41 - 10 * q^43 + 30 * q^46 + 8 * q^49 + 24 * q^50 - 26 * q^52 - 12 * q^53 + 10 * q^55 - 12 * q^56 - 54 * q^58 + 60 * q^59 - 6 * q^61 - 16 * q^62 + 16 * q^64 + 20 * q^65 - 18 * q^67 + 20 * q^68 - 6 * q^71 - 18 * q^74 + 72 * q^76 + 16 * q^77 - 4 * q^79 - 30 * q^80 - 18 * q^82 - 24 * q^85 - 2 * q^88 - 78 * q^89 - 8 * q^91 + 20 * q^92 + 16 * q^94 + 4 * q^95 - 54 * q^97

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.25861	−	1.30401i	1.59708	−	0.922074i	0.605032	−	0.796201i	$-0.293160\pi$
$2$	2.25861	−	1.30401i	1.59708	−	0.922074i	0.992046	−	0.125872i	$-0.0401730\pi$
$3$		0			0
$3$		0			0
$4$	2.40088	−	4.15844i	1.20044	−	2.07922i
$5$		−	1.50528i		−	0.673181i	−0.941651	−	0.336590i	$-0.890726\pi$
$5$		−	1.50528i		−	0.673181i	0.941651	−	0.336590i	$-0.109274\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	7.30704i		−	2.58343i
$9$		0			0
$10$	−1.96290	−	3.39983i	−0.620722	−	1.07512i
$11$	−0.0753030	+	0.0434762i	−0.0227047	+	0.0131086i	−0.511309	−	0.859397i	$-0.670839\pi$
$11$	−0.0753030	+	0.0434762i	−0.0227047	+	0.0131086i	0.488605	+	0.872505i	$0.337506\pi$
$12$		0			0
$13$	−1.30332	−	3.36175i	−0.361475	−	0.932382i
$13$	−1.30332	−	3.36175i	−0.361475	−	0.932382i
$14$	−2.60802			−0.697022
$15$		0			0
$16$	−4.72668	−	8.18685i	−1.18167	−	2.04671i
$17$	−3.24732	+	5.62452i	−0.787591	+	1.36415i	0.139848	+	0.990173i	$0.455338\pi$
$17$	−3.24732	+	5.62452i	−0.787591	+	1.36415i	−0.927439	+	0.373974i	$0.877995\pi$
$18$		0			0
$19$	4.58318	+	2.64610i	1.05145	+	0.607057i	0.923056	−	0.384665i	$-0.125683\pi$
$19$	4.58318	+	2.64610i	1.05145	+	0.607057i	0.128398	+	0.991723i	$0.459016\pi$
$20$	−6.25961	−	3.61399i	−1.39969	−	0.808113i
$21$		0			0
$22$	−0.113387	+	0.196391i	−0.0241741	+	0.0418708i
$23$	2.60110	+	4.50524i	0.542367	+	0.939408i	0.998768	+	0.0496333i	$0.0158053\pi$
$23$	2.60110	+	4.50524i	0.542367	+	0.939408i	−0.456400	+	0.889775i	$0.650861\pi$
$24$		0			0
$25$	2.73414			0.546828
$26$	−7.32743	−	5.89335i	−1.43703	−	1.15578i
$27$		0			0
$28$	−4.15844	+	2.40088i	−0.785872	+	0.453723i
$29$	−2.98801	−	5.17538i	−0.554859	−	0.961045i	−0.997914	−	0.0645503i	$-0.979439\pi$
$29$	−2.98801	−	5.17538i	−0.554859	−	0.961045i	0.443055	−	0.896494i	$-0.353895\pi$
$30$		0			0
$31$		−	2.00289i		−	0.359730i	−0.983691	−	0.179865i	$-0.942434\pi$
$31$		−	2.00289i		−	0.359730i	0.983691	−	0.179865i	$-0.0575660\pi$
$32$	−8.69531	−	5.02024i	−1.53713	−	0.887461i
$33$		0			0
$34$			16.9381i			2.90487i
$35$	−0.752639	+	1.30361i	−0.127219	+	0.220350i
$36$		0			0
$37$	8.24566	−	4.76063i	1.35558	−	0.782643i	0.366554	−	0.930397i	$-0.380538\pi$
$37$	8.24566	−	4.76063i	1.35558	−	0.782643i	0.989024	+	0.147754i	$0.0472042\pi$
$38$	13.8022			2.23901
$39$		0			0
$40$	−10.9991			−1.73911
$41$	−5.57631	+	3.21948i	−0.870873	+	0.502799i	−0.867638	−	0.497196i	$-0.834363\pi$
$41$	−5.57631	+	3.21948i	−0.870873	+	0.502799i	−0.00323453	+	0.999995i	$0.501030\pi$
$42$		0			0
$43$	3.40536	−	5.89825i	0.519312	−	0.899475i	−0.480436	−	0.877030i	$-0.659522\pi$
$43$	3.40536	−	5.89825i	0.519312	−	0.899475i	0.999748	−	0.0224449i	$-0.00714502\pi$
$44$			0.417524i			0.0629441i
$45$		0			0
$46$	11.7498	+	6.78372i	1.73241	+	1.00021i
$47$			1.83051i			0.267008i	0.991048	+	0.133504i	$0.0426229\pi$
$47$			1.83051i			0.267008i	−0.991048	+	0.133504i	$0.957377\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	6.17535	−	3.56534i	0.873327	−	0.504216i
$51$		0			0
$52$	−17.1088	−	2.65139i	−2.37256	−	0.367682i
$53$	3.28476			0.451197			0.225598	−	0.974220i	$-0.427566\pi$
$53$	3.28476			0.451197			0.225598	+	0.974220i	$0.427566\pi$
$54$		0			0
$55$	0.0654437	+	0.113352i	0.00882443	+	0.0152844i
$56$	−3.65352	+	6.32808i	−0.488222	+	0.845625i
$57$		0			0
$58$	−13.4975	−	7.79278i	−1.77231	−	1.02324i
$59$	2.31669	+	1.33754i	0.301608	+	0.174133i	0.643165	−	0.765728i	$-0.277621\pi$
$59$	2.31669	+	1.33754i	0.301608	+	0.174133i	−0.341557	+	0.939861i	$0.610954\pi$
$60$		0			0
$61$	3.27278	−	5.66863i	0.419037	−	0.725794i	−0.576806	−	0.816881i	$-0.695701\pi$
$61$	3.27278	−	5.66863i	0.419037	−	0.725794i	0.995843	+	0.0910877i	$0.0290344\pi$
$62$	−2.61179	−	4.52375i	−0.331697	−	0.574516i
$63$		0			0
$64$	−7.27901			−0.909876
$65$	−5.06037	+	1.96185i	−0.627661	+	0.243338i
$66$		0			0
$67$	−7.18333	+	4.14730i	−0.877583	+	0.506673i	−0.869861	−	0.493297i	$-0.835791\pi$
$67$	−7.18333	+	4.14730i	−0.877583	+	0.506673i	−0.00772242	+	0.999970i	$0.502458\pi$
$68$	15.5928	+	27.0076i	1.89091	+	3.27515i
$69$		0			0
$70$			3.92579i			0.469222i
$71$	11.1872	+	6.45892i	1.32767	+	0.766533i	0.984940	−	0.172899i	$-0.0553134\pi$
$71$	11.1872	+	6.45892i	1.32767	+	0.766533i	0.342735	+	0.939432i	$0.388647\pi$
$72$		0			0
$73$			14.5507i			1.70303i	0.524334	+	0.851513i	$0.324314\pi$
$73$			14.5507i			1.70303i	−0.524334	+	0.851513i	$0.675686\pi$
$74$	12.4158	−	21.5048i	1.44331	−	2.49989i
$75$		0			0
$76$	22.0073	−	12.7059i	2.52441	−	1.45747i
$77$	0.0869524			0.00990914
$78$		0			0
$79$	−11.6780			−1.31387			−0.656936	−	0.753946i	$-0.728148\pi$
$79$	−11.6780			−1.31387			−0.656936	+	0.753946i	$0.728148\pi$
$80$	−12.3235	+	7.11497i	−1.37781	+	0.795478i
$81$		0			0
$82$	−8.39647	+	14.5431i	−0.927235	+	1.60602i
$83$			1.29310i			0.141937i	0.997479	+	0.0709683i	$0.0226089\pi$
$83$			1.29310i			0.141937i	−0.997479	+	0.0709683i	$0.977391\pi$
$84$		0			0
$85$	8.46647	+	4.88812i	0.918317	+	0.530191i
$86$		−	17.7625i		−	1.91538i
$87$		0			0
$88$	0.317682	+	0.550241i	0.0338650	+	0.0586559i
$89$	−13.7225	+	7.92270i	−1.45458	+	0.839805i	−0.998737	−	0.0502531i	$-0.983997\pi$
$89$	−13.7225	+	7.92270i	−1.45458	+	0.839805i	−0.455848	+	0.890058i	$0.650664\pi$
$90$		0			0
$91$	−0.552171	+	3.56302i	−0.0578833	+	0.373506i
$92$	24.9797			2.60432
$93$		0			0
$94$	2.38701	+	4.13442i	0.246201	+	0.426433i
$95$	3.98312	−	6.89896i	0.408659	−	0.707819i
$96$		0			0
$97$	−5.08340	−	2.93490i	−0.516141	−	0.297994i	0.219213	−	0.975677i	$-0.429651\pi$
$97$	−5.08340	−	2.93490i	−0.516141	−	0.297994i	−0.735354	+	0.677683i	$0.762984\pi$
$98$	2.25861	+	1.30401i	0.228154	+	0.131725i
$99$		0			0
$100$	6.56434	−	11.3698i	0.656434	−	1.13698i
$101$	3.34086	+	5.78654i	0.332428	+	0.575782i	0.982987	−	0.183673i	$-0.0587989\pi$
$101$	3.34086	+	5.78654i	0.332428	+	0.575782i	−0.650559	+	0.759455i	$0.725466\pi$
$102$		0			0
$103$	4.52273			0.445637			0.222819	−	0.974860i	$-0.428474\pi$
$103$	4.52273			0.445637			0.222819	+	0.974860i	$0.428474\pi$
$104$	−24.5644	+	9.52337i	−2.40874	+	0.933843i
$105$		0			0
$106$	7.41900	−	4.28336i	0.720597	−	0.416037i
$107$	−5.12241	−	8.87227i	−0.495202	−	0.857715i	0.504783	−	0.863246i	$-0.331573\pi$
$107$	−5.12241	−	8.87227i	−0.495202	−	0.857715i	−0.999985	+	0.00553163i	$0.998239\pi$
$108$		0			0
$109$			13.5552i			1.29835i	0.760637	+	0.649177i	$0.224887\pi$
$109$			13.5552i			1.29835i	−0.760637	+	0.649177i	$0.775113\pi$
$110$	0.295624	+	0.170678i	0.0281866	+	0.0162735i
$111$		0			0
$112$			9.45336i			0.893259i
$113$	6.69370	−	11.5938i	0.629691	−	1.09066i	−0.357923	−	0.933751i	$-0.616515\pi$
$113$	6.69370	−	11.5938i	0.629691	−	1.09066i	0.987614	−	0.156905i	$-0.0501517\pi$
$114$		0			0
$115$	6.78164	−	3.91538i	0.632391	−	0.365111i
$116$	−28.6954			−2.66430
$117$		0			0
$118$	6.97667			0.642255
$119$	5.62452	−	3.24732i	0.515599	−	0.297681i
$120$		0			0
$121$	−5.49622	+	9.51973i	−0.499656	+	0.865430i
$122$		−	17.0710i		−	1.54553i
$123$		0			0
$124$	−8.32891	−	4.80870i	−0.747958	−	0.431834i
$125$		−	11.6420i		−	1.04129i
$126$		0			0
$127$	6.47234	+	11.2104i	0.574328	+	0.994765i	0.996114	+	0.0880695i	$0.0280698\pi$
$127$	6.47234	+	11.2104i	0.574328	+	0.994765i	−0.421787	+	0.906695i	$0.638597\pi$
$128$	0.950172	−	0.548582i	0.0839841	−	0.0484883i
$129$		0			0
$130$	−8.87113	+	11.0298i	−0.778049	+	0.967379i
$131$	−5.84887			−0.511018			−0.255509	−	0.966807i	$-0.582243\pi$
$131$	−5.84887			−0.511018			−0.255509	+	0.966807i	$0.582243\pi$
$132$		0			0
$133$	−2.64610	−	4.58318i	−0.229446	−	0.397412i
$134$	−10.8162	+	18.7342i	−0.934379	+	1.61839i
$135$		0			0
$136$	41.0986	+	23.7283i	3.52417	+	2.03468i
$137$	4.42616	+	2.55545i	0.378153	+	0.218327i	0.677014	−	0.735970i	$-0.263274\pi$
$137$	4.42616	+	2.55545i	0.378153	+	0.218327i	−0.298862	+	0.954296i	$0.596607\pi$
$138$		0			0
$139$	9.66376	−	16.7381i	0.819669	−	1.41971i	−0.0862564	−	0.996273i	$-0.527490\pi$
$139$	9.66376	−	16.7381i	0.819669	−	1.41971i	0.905926	−	0.423436i	$-0.139176\pi$
$140$	3.61399	+	6.25961i	0.305438	+	0.529034i
$141$		0			0
$142$	33.6900			2.82720
$143$	0.244300	+	0.196487i	0.0204294	+	0.0164310i
$144$		0			0
$145$	−7.79039	+	4.49778i	−0.646957	+	0.373521i
$146$	18.9742	+	32.8643i	1.57031	+	2.71987i
$147$		0			0
$148$		−	45.7188i		−	3.75806i
$149$	8.23614	+	4.75514i	0.674731	+	0.389556i	0.797867	−	0.602834i	$-0.205962\pi$
$149$	8.23614	+	4.75514i	0.674731	+	0.389556i	−0.123136	+	0.992390i	$0.539295\pi$
$150$		0			0
$151$		−	12.7770i		−	1.03977i	−0.854235	−	0.519887i	$-0.825974\pi$
$151$		−	12.7770i		−	1.03977i	0.854235	−	0.519887i	$-0.174026\pi$
$152$	19.3352	−	33.4895i	1.56829	−	2.71636i
$153$		0			0
$154$	0.196391	−	0.113387i	0.0158257	−	0.00913696i
$155$	−3.01490			−0.242163
$156$		0			0
$157$	−2.57466			−0.205480			−0.102740	−	0.994708i	$-0.532761\pi$
$157$	−2.57466			−0.205480			−0.102740	+	0.994708i	$0.532761\pi$
$158$	−26.3759	+	15.2282i	−2.09836	+	1.21149i
$159$		0			0
$160$	−7.55685	+	13.0888i	−0.597421	+	1.03476i
$161$		−	5.20221i		−	0.409991i
$162$		0			0
$163$	−16.9135	−	9.76499i	−1.32476	−	0.764853i	−0.340280	−	0.940324i	$-0.610522\pi$
$163$	−16.9135	−	9.76499i	−1.32476	−	0.764853i	−0.984485	+	0.175471i	$0.943855\pi$
$164$			30.9183i			2.41432i
$165$		0			0
$166$	1.68622	+	2.92062i	0.130876	+	0.226684i
$167$	1.20942	−	0.698261i	0.0935881	−	0.0540331i	−0.452476	−	0.891777i	$-0.649459\pi$
$167$	1.20942	−	0.698261i	0.0935881	−	0.0540331i	0.546064	+	0.837744i	$0.316126\pi$
$168$		0			0
$169$	−9.60274	+	8.76284i	−0.738672	+	0.674065i
$170$	25.4966			1.95550
$171$		0			0
$172$	−16.3517	−	28.3220i	−1.24680	−	2.15953i
$173$	−8.59070	+	14.8795i	−0.653138	+	1.13127i	0.329219	+	0.944254i	$0.393215\pi$
$173$	−8.59070	+	14.8795i	−0.653138	+	1.13127i	−0.982357	+	0.187015i	$0.940119\pi$
$174$		0			0
$175$	−2.36783	−	1.36707i	−0.178991	−	0.103341i
$176$	0.711866	+	0.410996i	0.0536589	+	0.0309800i
$177$		0			0
$178$	−20.6625	+	35.7886i	−1.54872	+	2.68247i
$179$	0.718538	+	1.24454i	0.0537061	+	0.0930216i	0.891629	−	0.452768i	$-0.149563\pi$
$179$	0.718538	+	1.24454i	0.0537061	+	0.0930216i	−0.837923	+	0.545789i	$0.816230\pi$
$180$		0			0
$181$	4.31882			0.321015			0.160508	−	0.987035i	$-0.448687\pi$
$181$	4.31882			0.321015			0.160508	+	0.987035i	$0.448687\pi$
$182$	3.39907	+	8.76751i	0.251956	+	0.649891i
$183$		0			0
$184$	32.9200	−	19.0064i	2.42689	−	1.40117i
$185$	−7.16607	−	12.4120i	−0.526860	−	0.912549i
$186$		0			0
$187$		−	0.564724i		−	0.0412967i
$188$	7.61209	+	4.39484i	0.555169	+	0.320527i
$189$		0			0
$190$		−	20.7761i		−	1.50726i
$191$	−3.39359	+	5.87788i	−0.245552	+	0.425308i	−0.962287	−	0.272038i	$-0.912302\pi$
$191$	−3.39359	+	5.87788i	−0.245552	+	0.425308i	0.716735	+	0.697346i	$0.245636\pi$
$192$		0			0
$193$	−18.5112	+	10.6875i	−1.33247	+	0.769300i	−0.985677	−	0.168642i	$-0.946062\pi$
$193$	−18.5112	+	10.6875i	−1.33247	+	0.769300i	−0.346790	+	0.937943i	$0.612728\pi$
$194$	−15.3085			−1.09909
$195$		0			0
$196$	4.80176			0.342983
$197$	−19.7438	+	11.3991i	−1.40669	+	0.812153i	−0.995067	−	0.0992006i	$-0.968371\pi$
$197$	−19.7438	+	11.3991i	−1.40669	+	0.812153i	−0.411623	+	0.911354i	$0.635038\pi$
$198$		0			0
$199$	1.33183	−	2.30679i	0.0944107	−	0.163524i	−0.814952	−	0.579529i	$-0.803237\pi$
$199$	1.33183	−	2.30679i	0.0944107	−	0.163524i	0.909363	+	0.416005i	$0.136570\pi$
$200$		−	19.9785i		−	1.41269i
$201$		0			0
$202$	15.0914	+	8.71302i	1.06183	+	0.613046i
$203$			5.97602i			0.419434i
$204$		0			0
$205$	4.84621	+	8.39389i	0.338474	+	0.586255i
$206$	10.2151	−	5.89767i	0.711718	−	0.410910i
$207$		0			0
$208$	−21.3618	+	26.5600i	−1.48117	+	1.84160i
$209$	−0.460170			−0.0318306
$210$		0			0
$211$	12.0916	+	20.9432i	0.832419	+	1.44179i	0.896115	+	0.443823i	$0.146378\pi$
$211$	12.0916	+	20.9432i	0.832419	+	1.44179i	−0.0636958	+	0.997969i	$0.520289\pi$
$212$	7.88632	−	13.6595i	0.541635	−	0.938138i
$213$		0			0
$214$	−23.1390	−	13.3593i	−1.58175	−	0.913225i
$215$	−8.87850	−	5.12601i	−0.605509	−	0.349591i
$216$		0			0
$217$	−1.00144	+	1.73455i	−0.0679825	+	0.117749i
$218$	17.6761	+	30.6160i	1.19718	+	2.07357i
$219$		0			0
$220$	0.628490			0.0423728
$221$	23.1405	+	3.58615i	1.55660	+	0.241231i
$222$		0			0
$223$	−14.6428	+	8.45400i	−0.980551	+	0.566122i	−0.902437	−	0.430823i	$-0.858223\pi$
$223$	−14.6428	+	8.45400i	−0.980551	+	0.566122i	−0.0781148	+	0.996944i	$0.524890\pi$
$224$	5.02024	+	8.69531i	0.335429	+	0.580980i
$225$		0			0
$226$		−	34.9146i		−	2.32248i
$227$	−10.0833	−	5.82157i	−0.669249	−	0.386391i	0.126543	−	0.991961i	$-0.459612\pi$
$227$	−10.0833	−	5.82157i	−0.669249	−	0.386391i	−0.795792	+	0.605570i	$0.792945\pi$
$228$		0			0
$229$		−	7.90801i		−	0.522576i	−0.965261	−	0.261288i	$-0.915853\pi$
$229$		−	7.90801i		−	0.522576i	0.965261	−	0.261288i	$-0.0841473\pi$
$230$	10.2114	−	17.6866i	0.673319	−	1.16622i
$231$		0			0
$232$	−37.8167	+	21.8335i	−2.48279	+	1.43344i
$233$	−24.0854			−1.57789			−0.788945	−	0.614464i	$-0.789372\pi$
$233$	−24.0854			−1.57789			−0.788945	+	0.614464i	$0.789372\pi$
$234$		0			0
$235$	2.75543			0.179745
$236$	11.1242	−	6.42256i	0.724124	−	0.418073i
$237$		0			0
$238$	8.46907	−	14.6689i	0.548968	−	0.950841i
$239$		−	10.9354i		−	0.707352i	−0.935368	−	0.353676i	$-0.884932\pi$
$239$		−	10.9354i		−	0.707352i	0.935368	−	0.353676i	$-0.115068\pi$
$240$		0			0
$241$	17.2385	+	9.95268i	1.11043	+	0.641108i	0.938941	−	0.344077i	$-0.111808\pi$
$241$	17.2385	+	9.95268i	1.11043	+	0.641108i	0.171491	+	0.985186i	$0.445142\pi$
$242$			28.6685i			1.84288i
$243$		0			0
$244$	−15.7151	−	27.2194i	−1.00606	−	1.74254i
$245$	1.30361	−	0.752639i	0.0832845	−	0.0480843i
$246$		0			0
$247$	2.92220	−	18.8562i	0.185935	−	1.19979i
$248$	−14.6352			−0.929335
$249$		0			0
$250$	−15.1813	−	26.2948i	−0.960150	−	1.66303i
$251$	11.6942	−	20.2549i	0.738129	−	1.27848i	−0.215208	−	0.976568i	$-0.569043\pi$
$251$	11.6942	−	20.2549i	0.738129	−	1.27848i	0.953337	−	0.301909i	$-0.0976238\pi$
$252$		0			0
$253$	−0.391741	−	0.226172i	−0.0246286	−	0.0142193i
$254$	29.2370	+	16.8800i	1.83449	+	1.05914i
$255$		0			0
$256$	8.70972	−	15.0857i	0.544357	−	0.942855i
$257$	−6.02975	−	10.4438i	−0.376125	−	0.651468i	0.614369	−	0.789019i	$-0.289410\pi$
$257$	−6.02975	−	10.4438i	−0.376125	−	0.651468i	−0.990495	+	0.137550i	$0.956077\pi$
$258$		0			0
$259$	−9.52127			−0.591623
$260$	−3.99108	+	25.7534i	−0.247516	+	1.59716i
$261$		0			0
$262$	−13.2103	+	7.62698i	−0.816136	+	0.471196i
$263$	2.26613	+	3.92505i	0.139736	+	0.242029i	0.927396	−	0.374080i	$-0.122041\pi$
$263$	2.26613	+	3.92505i	0.139736	+	0.242029i	−0.787661	+	0.616109i	$0.788708\pi$
$264$		0			0
$265$		−	4.94448i		−	0.303737i
$266$	−11.9530	−	6.90108i	−0.732887	−	0.423132i
$267$		0			0
$268$			39.8286i			2.43292i
$269$	−13.9800	+	24.2140i	−0.852375	+	1.47636i	0.0266843	+	0.999644i	$0.491505\pi$
$269$	−13.9800	+	24.2140i	−0.852375	+	1.47636i	−0.879059	+	0.476713i	$0.841828\pi$
$270$		0			0
$271$	3.62825	−	2.09477i	0.220400	−	0.127248i	−0.385735	−	0.922609i	$-0.626052\pi$
$271$	3.62825	−	2.09477i	0.220400	−	0.127248i	0.606136	+	0.795361i	$0.292719\pi$
$272$	61.3962			3.72269
$273$		0			0
$274$	13.3293			0.805252
$275$	−0.205889	+	0.118870i	−0.0124156	+	0.00716813i
$276$		0			0
$277$	4.93402	−	8.54598i	0.296457	−	0.513478i	−0.678866	−	0.734262i	$-0.737528\pi$
$277$	4.93402	−	8.54598i	0.296457	−	0.513478i	0.975323	+	0.220784i	$0.0708616\pi$
$278$		−	50.4065i		−	3.02318i
$279$		0			0
$280$	9.52551	+	5.49956i	0.569258	+	0.328661i
$281$			2.76496i			0.164944i	0.996593	+	0.0824719i	$0.0262815\pi$
$281$			2.76496i			0.164944i	−0.996593	+	0.0824719i	$0.973719\pi$
$282$		0			0
$283$	−2.87040	−	4.97167i	−0.170627	−	0.295535i	0.768012	−	0.640435i	$-0.221246\pi$
$283$	−2.87040	−	4.97167i	−0.170627	−	0.295535i	−0.938639	+	0.344900i	$0.887913\pi$
$284$	53.7181	−	31.0142i	3.18759	−	1.84035i
$285$		0			0
$286$	0.807998	+	0.125218i	0.0477779	+	0.00740428i
$287$	6.43896			0.380080
$288$		0			0
$289$	−12.5902	−	21.8068i	−0.740598	−	1.28275i
$290$	−11.7303	+	20.3175i	−0.688827	+	1.19308i
$291$		0			0
$292$	60.5081	+	34.9344i	3.54097	+	2.04438i
$293$	−13.6845	−	7.90072i	−0.799454	−	0.461565i	0.0438259	−	0.999039i	$-0.486045\pi$
$293$	−13.6845	−	7.90072i	−0.799454	−	0.461565i	−0.843280	+	0.537474i	$0.819379\pi$
$294$		0			0
$295$	2.01337	−	3.48727i	0.117223	−	0.203036i
$296$	−34.7861	−	60.2513i	−2.02190	−	3.50204i
$297$		0			0
$298$	24.8030			1.43680
$299$	11.7554	−	14.6160i	0.679835	−	0.845266i
$300$		0			0
$301$	−5.89825	+	3.40536i	−0.339969	+	0.196281i
$302$	−16.6613	−	28.8582i	−0.958749	−	1.66060i
$303$		0			0
$304$		−	50.0291i		−	2.86937i
$305$	−8.53286	−	4.92645i	−0.488590	−	0.282088i
$306$		0			0
$307$		−	10.1195i		−	0.577549i	−0.957397	−	0.288774i	$-0.906752\pi$
$307$		−	10.1195i		−	0.577549i	0.957397	−	0.288774i	$-0.0932478\pi$
$308$	0.208762	−	0.361587i	0.0118953	−	0.0206033i
$309$		0			0
$310$	−6.80949	+	3.93146i	−0.386753	+	0.223292i
$311$	14.4989			0.822155			0.411077	−	0.911600i	$-0.365153\pi$
$311$	14.4989			0.822155			0.411077	+	0.911600i	$0.365153\pi$
$312$		0			0
$313$	13.2670			0.749897			0.374948	−	0.927046i	$-0.377660\pi$
$313$	13.2670			0.749897			0.374948	+	0.927046i	$0.377660\pi$
$314$	−5.81516	+	3.35738i	−0.328168	+	0.189468i
$315$		0			0
$316$	−28.0374	+	48.5621i	−1.57722	+	2.73183i
$317$		−	30.4190i		−	1.70850i	−0.519860	−	0.854252i	$-0.674016\pi$
$317$		−	30.4190i		−	1.70850i	0.519860	−	0.854252i	$-0.325984\pi$
$318$		0			0
$319$	0.450012	+	0.259814i	0.0251958	+	0.0145468i
$320$			10.9569i			0.612511i
$321$		0			0
$322$	−6.78372	−	11.7498i	−0.378042	−	0.654788i
$323$	−29.7661	+	17.1855i	−1.65623	+	0.956226i
$324$		0			0
$325$	−3.56345	−	9.19150i	−0.197664	−	0.509852i
$326$	−50.9345			−2.82100
$327$		0			0
$328$	23.5249	+	40.7463i	1.29894	+	2.24984i
$329$	0.915257	−	1.58527i	0.0504598	−	0.0873989i
$330$		0			0
$331$	8.05659	+	4.65147i	0.442830	+	0.255668i	0.704797	−	0.709409i	$-0.251038\pi$
$331$	8.05659	+	4.65147i	0.442830	+	0.255668i	−0.261967	+	0.965077i	$0.584371\pi$
$332$	5.37730	+	3.10459i	0.295118	+	0.170386i
$333$		0			0
$334$	1.82108	−	3.15420i	0.0996450	−	0.172590i
$335$	6.24283	+	10.8129i	0.341082	+	0.590772i
$336$		0			0
$337$	−13.3054			−0.724789			−0.362395	−	0.932025i	$-0.618041\pi$
$337$	−13.3054			−0.724789			−0.362395	+	0.932025i	$0.618041\pi$
$338$	−10.2620	+	32.3139i	−0.558180	+	1.75764i
$339$		0			0
$340$	40.6539	−	23.4716i	2.20477	−	1.27292i
$341$	0.0870780	+	0.150824i	0.00471554	+	0.00816755i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−43.0987	−	24.8831i	−2.32373	−	1.34160i
$345$		0			0
$346$			44.8094i			2.40897i
$347$	−8.43801	+	14.6151i	−0.452976	+	0.784578i	−0.998569	−	0.0534723i	$-0.982971\pi$
$347$	−8.43801	+	14.6151i	−0.452976	+	0.784578i	0.545593	+	0.838050i	$0.316304\pi$
$348$		0			0
$349$	−2.08469	+	1.20360i	−0.111591	+	0.0644271i	−0.554757	−	0.832013i	$-0.687189\pi$
$349$	−2.08469	+	1.20360i	−0.111591	+	0.0644271i	0.443166	+	0.896440i	$0.353855\pi$
$350$	−7.13069			−0.381151
$351$		0			0
$352$	0.873043			0.0465333
$353$	26.5988	−	15.3568i	1.41571	−	0.817361i	0.419793	−	0.907620i	$-0.362103\pi$
$353$	26.5988	−	15.3568i	1.41571	−	0.817361i	0.995918	+	0.0902583i	$0.0287693\pi$
$354$		0			0
$355$	9.72247	−	16.8398i	0.516015	−	0.893765i
$356$			76.0858i			4.03254i
$357$		0			0
$358$	3.24579	+	1.87396i	0.171546	+	0.0990419i
$359$		−	10.6322i		−	0.561145i	−0.959833	−	0.280572i	$-0.909476\pi$
$359$		−	10.6322i		−	0.561145i	0.959833	−	0.280572i	$-0.0905243\pi$
$360$		0			0
$361$	4.50371	+	7.80065i	0.237037	+	0.410561i
$362$	9.75453	−	5.63178i	0.512687	−	0.296000i
$363$		0			0
$364$	13.4909	+	10.8506i	0.707116	+	0.568723i
$365$	21.9028			1.14644
$366$		0			0
$367$	−13.1031	−	22.6953i	−0.683977	−	1.18468i	−0.973757	−	0.227590i	$-0.926915\pi$
$367$	−13.1031	−	22.6953i	−0.683977	−	1.18468i	0.289780	−	0.957093i	$-0.406418\pi$
$368$	24.5892	−	42.5897i	1.28180	−	2.22014i
$369$		0			0
$370$	−32.3707	−	18.6893i	−1.68287	−	0.971608i
$371$	−2.84469	−	1.64238i	−0.147689	−	0.0852682i
$372$		0			0
$373$	−9.10509	+	15.7705i	−0.471444	+	0.816565i	−0.999466	−	0.0326656i	$-0.989600\pi$
$373$	−9.10509	+	15.7705i	−0.471444	+	0.816565i	0.528022	+	0.849230i	$0.322934\pi$
$374$	−0.736405	−	1.27549i	−0.0380786	−	0.0659541i
$375$		0			0
$376$	13.3756			0.689796
$377$	−13.5040	+	16.7901i	−0.695493	+	0.864734i
$378$		0			0
$379$	−25.0235	+	14.4473i	−1.28537	+	0.742110i	−0.977825	−	0.209423i	$-0.932842\pi$
$379$	−25.0235	+	14.4473i	−1.28537	+	0.742110i	−0.307547	+	0.951533i	$0.599508\pi$
$380$	−19.1260	−	33.1271i	−0.981141	−	1.69939i
$381$		0			0
$382$			17.7011i			0.905668i
$383$	15.0050	+	8.66312i	0.766718	+	0.442665i	0.831702	−	0.555222i	$-0.187367\pi$
$383$	15.0050	+	8.66312i	0.766718	+	0.442665i	−0.0649848	+	0.997886i	$0.520700\pi$
$384$		0			0
$385$		−	0.130887i		−	0.00667064i
$386$	−27.8731	+	48.2776i	−1.41870	+	2.45727i
$387$		0			0
$388$	−24.4092	+	14.0927i	−1.23919	+	0.715448i
$389$	13.6737			0.693282			0.346641	−	0.937998i	$-0.387322\pi$
$389$	13.6737			0.693282			0.346641	+	0.937998i	$0.387322\pi$
$390$		0			0
$391$	−33.7865			−1.70865
$392$	6.32808	−	3.65352i	0.319616	−	0.184531i
$393$		0			0
$394$	−29.7291	+	51.4923i	−1.49773	+	2.59415i
$395$			17.5786i			0.884473i
$396$		0			0
$397$	−13.3743	−	7.72167i	−0.671238	−	0.387540i	0.125307	−	0.992118i	$-0.460008\pi$
$397$	−13.3743	−	7.72167i	−0.671238	−	0.387540i	−0.796546	+	0.604578i	$0.793342\pi$
$398$		−	6.94686i		−	0.348215i
$399$		0			0
$400$	−12.9234	−	22.3840i	−0.646170	−	1.11920i
$401$	−12.3265	+	7.11671i	−0.615556	+	0.355391i	−0.775137	−	0.631794i	$-0.782319\pi$
$401$	−12.3265	+	7.11671i	−0.615556	+	0.355391i	0.159581	+	0.987185i	$0.448986\pi$
$402$		0			0
$403$	−6.73322	+	2.61040i	−0.335405	+	0.130033i
$404$	32.0840			1.59624
$405$		0			0
$406$	7.79278	+	13.4975i	0.386749	+	0.669869i
$407$	−0.413948	+	0.716979i	−0.0205187	+	0.0355394i
$408$		0			0
$409$	12.1987	+	7.04291i	0.603185	+	0.348249i	0.770294	−	0.637689i	$-0.220110\pi$
$409$	12.1987	+	7.04291i	0.603185	+	0.348249i	−0.167108	+	0.985939i	$0.553443\pi$
$410$	21.8914	+	12.6390i	1.08114	+	0.624196i
$411$		0			0
$412$	10.8585	−	18.8075i	0.534961	−	0.926579i
$413$	−1.33754	−	2.31669i	−0.0658162	−	0.113997i
$414$		0			0
$415$	1.94648			0.0955489
$416$	−5.54406	+	35.7744i	−0.271820	+	1.75398i
$417$		0			0
$418$	−1.03934	+	0.600065i	−0.0508360	+	0.0293502i
$419$	−18.8362	−	32.6252i	−0.920207	−	1.59385i	−0.799093	−	0.601207i	$-0.794687\pi$
$419$	−18.8362	−	32.6252i	−0.920207	−	1.59385i	−0.121114	−	0.992639i	$-0.538647\pi$
$420$		0			0
$421$		−	2.28615i		−	0.111420i	−0.998447	−	0.0557101i	$-0.982258\pi$
$421$		−	2.28615i		−	0.111420i	0.998447	−	0.0557101i	$-0.0177423\pi$
$422$	54.6203	+	31.5351i	2.65888	+	1.53510i
$423$		0			0
$424$		−	24.0019i		−	1.16563i
$425$	−8.87863	+	15.3782i	−0.430677	+	0.745954i
$426$		0			0
$427$	−5.66863	+	3.27278i	−0.274324	+	0.158381i
$428$	−49.1931			−2.37784
$429$		0			0
$430$	−26.7374			−1.28939
$431$	−1.71575	+	0.990590i	−0.0826449	+	0.0477150i	−0.540753	−	0.841181i	$-0.681861\pi$
$431$	−1.71575	+	0.990590i	−0.0826449	+	0.0477150i	0.458108	+	0.888897i	$0.348527\pi$
$432$		0			0
$433$	−2.94544	+	5.10165i	−0.141549	+	0.245170i	−0.928080	−	0.372381i	$-0.878542\pi$
$433$	−2.94544	+	5.10165i	−0.141549	+	0.245170i	0.786531	+	0.617550i	$0.211875\pi$
$434$			5.22357i			0.250740i
$435$		0			0
$436$	56.3686	+	32.5444i	2.69957	+	1.55860i
$437$			27.5311i			1.31699i
$438$		0			0
$439$	−4.03281	−	6.98504i	−0.192476	−	0.333378i	0.753594	−	0.657340i	$-0.228318\pi$
$439$	−4.03281	−	6.98504i	−0.192476	−	0.333378i	−0.946070	+	0.323962i	$0.894985\pi$
$440$	0.828266	−	0.478200i	0.0394860	−	0.0227973i
$441$		0			0
$442$	56.9418	−	22.0757i	2.70845	−	1.05004i
$443$	−6.65984			−0.316419			−0.158209	−	0.987406i	$-0.550572\pi$
$443$	−6.65984			−0.316419			−0.158209	+	0.987406i	$0.550572\pi$
$444$		0			0
$445$	11.9259	+	20.6562i	0.565340	+	0.979198i
$446$	−22.0482	+	38.1886i	−1.04401	+	1.80828i
$447$		0			0
$448$	6.30381	+	3.63950i	0.297827	+	0.171950i
$449$	17.1899	+	9.92456i	0.811239	+	0.468369i	0.847386	−	0.530977i	$-0.178175\pi$
$449$	17.1899	+	9.92456i	0.811239	+	0.468369i	−0.0361468	+	0.999346i	$0.511508\pi$
$450$		0			0
$451$	0.279942	−	0.484873i	0.0131819	−	0.0228318i
$452$	−32.1415	−	55.6708i	−1.51181	−	2.61853i
$453$		0			0
$454$	−30.3655			−1.42512
$455$	5.36333	+	0.831171i	0.251437	+	0.0389659i
$456$		0			0
$457$	2.24200	−	1.29442i	0.104876	−	0.0605505i	−0.446644	−	0.894712i	$-0.647381\pi$
$457$	2.24200	−	1.29442i	0.104876	−	0.0605505i	0.551521	+	0.834161i	$0.314048\pi$
$458$	−10.3121	−	17.8611i	−0.481854	−	0.834595i
$459$		0			0
$460$		−	37.6014i		−	1.75318i
$461$	−22.8342	−	13.1834i	−1.06350	−	0.614010i	−0.137099	−	0.990557i	$-0.543778\pi$
$461$	−22.8342	−	13.1834i	−1.06350	−	0.614010i	−0.926397	+	0.376547i	$0.877111\pi$
$462$		0			0
$463$			29.3082i			1.36207i	0.732252	+	0.681034i	$0.238469\pi$
$463$			29.3082i			1.36207i	−0.732252	+	0.681034i	$0.761531\pi$
$464$	−28.2467	+	48.9248i	−1.31132	+	2.27128i
$465$		0			0
$466$	−54.3996	+	31.4076i	−2.52001	+	1.45493i
$467$	3.23005			0.149469			0.0747345	−	0.997203i	$-0.476189\pi$
$467$	3.23005			0.149469			0.0747345	+	0.997203i	$0.476189\pi$
$468$		0			0
$469$	8.29459			0.383009
$470$	6.22345	−	3.59311i	0.287066	−	0.165738i
$471$		0			0
$472$	9.77348	−	16.9282i	0.449861	−	0.779182i
$473$			0.592207i			0.0272297i
$474$		0			0
$475$	12.5311	+	7.23481i	0.574965	+	0.331956i
$476$		−	31.1857i		−	1.42939i
$477$		0			0
$478$	−14.2599	−	24.6988i	−0.652230	−	1.12970i
$479$	−6.85282	+	3.95648i	−0.313114	+	0.180776i	−0.648319	−	0.761369i	$-0.724528\pi$
$479$	−6.85282	+	3.95648i	−0.313114	+	0.180776i	0.335205	+	0.942145i	$0.391194\pi$
$480$		0			0
$481$	−26.7508	−	21.5152i	−1.21973	−	0.981011i
$482$	51.9135			2.36460
$483$		0			0
$484$	26.3915	+	45.7114i	1.19961	+	2.07779i
$485$	−4.41784	+	7.65192i	−0.200604	+	0.347456i
$486$		0			0
$487$	−13.3758	−	7.72253i	−0.606116	−	0.349941i	0.165328	−	0.986239i	$-0.447132\pi$
$487$	−13.3758	−	7.72253i	−0.606116	−	0.349941i	−0.771444	+	0.636297i	$0.780465\pi$
$488$	−41.4209	−	23.9144i	−1.87503	−	1.08255i
$489$		0			0
$490$	1.96290	−	3.39983i	0.0886746	−	0.153589i
$491$	7.45311	+	12.9092i	0.336354	+	0.582582i	0.983744	−	0.179577i	$-0.0574728\pi$
$491$	7.45311	+	12.9092i	0.336354	+	0.582582i	−0.647390	+	0.762159i	$0.724139\pi$
$492$		0			0
$493$	38.8121			1.74801
$494$	−17.9886	−	46.3994i	−0.809344	−	2.08761i
$495$		0			0
$496$	−16.3974	+	9.46702i	−0.736263	+	0.425082i
$497$	−6.45892	−	11.1872i	−0.289722	−	0.501814i
$498$		0			0
$499$		−	25.4306i		−	1.13843i	−0.822189	−	0.569214i	$-0.807248\pi$
$499$		−	25.4306i		−	1.13843i	0.822189	−	0.569214i	$-0.192752\pi$
$500$	−48.4127	−	27.9511i	−2.16508	−	1.25001i
$501$		0			0
$502$		−	60.9972i		−	2.72244i
$503$	14.3956	−	24.9339i	0.641867	−	1.11175i	−0.343149	−	0.939281i	$-0.611493\pi$
$503$	14.3956	−	24.9339i	0.641867	−	1.11175i	0.985016	−	0.172465i	$-0.0551732\pi$
$504$		0			0
$505$	8.71034	−	5.02892i	0.387605	−	0.223784i
$506$	−1.17972			−0.0524450
$507$		0			0
$508$	62.1573			2.75778
$509$	13.5662	−	7.83245i	0.601311	−	0.347167i	−0.168246	−	0.985745i	$-0.553810\pi$
$509$	13.5662	−	7.83245i	0.601311	−	0.347167i	0.769557	+	0.638578i	$0.220477\pi$
$510$		0			0
$511$	7.27533	−	12.6012i	0.321842	−	0.557446i
$512$		−	43.2359i		−	1.91077i
$513$		0			0
$514$	−27.2377	−	15.7257i	−1.20140	−	0.693631i
$515$		−	6.80796i		−	0.299994i
$516$		0			0
$517$	−0.0795838	−	0.137843i	−0.00350009	−	0.00606233i
$518$	−21.5048	+	12.4158i	−0.944868	+	0.545520i
$519$		0			0
$520$	14.3353	+	36.9763i	0.628645	+	1.62152i
$521$	−4.38082			−0.191927			−0.0959636	−	0.995385i	$-0.530593\pi$
$521$	−4.38082			−0.191927			−0.0959636	+	0.995385i	$0.530593\pi$
$522$		0			0
$523$	10.6603	+	18.4643i	0.466144	+	0.807386i	0.999252	−	0.0386616i	$-0.0123094\pi$
$523$	10.6603	+	18.4643i	0.466144	+	0.807386i	−0.533108	+	0.846047i	$0.678976\pi$
$524$	−14.0424	+	24.3222i	−0.613447	+	1.06252i
$525$		0			0
$526$	10.2366	+	5.91011i	0.446337	+	0.257693i
$527$	11.2653	+	6.50402i	0.490724	+	0.283320i
$528$		0			0
$529$	−2.03147	+	3.51862i	−0.0883250	+	0.152983i
$530$	−6.44765	−	11.1676i	−0.280068	−	0.485092i
$531$		0			0
$532$	−25.4119			−1.10174
$533$	18.0908	+	14.5502i	0.783599	+	0.630237i
$534$		0			0
$535$	−13.3552	+	7.71064i	−0.577397	+	0.333360i
$536$	30.3044	+	52.4888i	1.30895	+	2.26717i
$537$		0			0
$538$			72.9201i			3.14381i
$539$	−0.0753030	−	0.0434762i	−0.00324353	−	0.00187265i
$540$		0			0
$541$			18.7093i			0.804374i	0.915557	+	0.402187i	$0.131750\pi$
$541$			18.7093i			0.804374i	−0.915557	+	0.402187i	$0.868250\pi$
$542$	5.46320	−	9.46253i	0.234664	−	0.406451i
$543$		0			0
$544$	56.4729	−	32.6046i	2.42125	−	1.39791i
$545$	20.4044			0.874027
$546$		0			0
$547$	26.4218			1.12972			0.564858	−	0.825188i	$-0.308931\pi$
$547$	26.4218			1.12972			0.564858	+	0.825188i	$0.308931\pi$
$548$	21.2534	−	12.2706i	0.907899	−	0.524176i
$549$		0			0
$550$	−0.310015	+	0.536962i	−0.0132191	+	0.0228961i
$551$		−	31.6263i		−	1.34733i
$552$		0			0
$553$	10.1134	+	5.83898i	0.430066	+	0.248299i
$554$		−	25.7360i		−	1.09342i
$555$		0			0
$556$	−46.4030	−	80.3724i	−1.96793	−	3.40855i
$557$	−15.6452	+	9.03278i	−0.662910	+	0.382731i	−0.793385	−	0.608721i	$-0.791683\pi$
$557$	−15.6452	+	9.03278i	−0.662910	+	0.382731i	0.130475	+	0.991452i	$0.458350\pi$
$558$		0			0
$559$	−24.2667	−	3.76068i	−1.02637	−	0.159060i
$560$	14.2299			0.601325
$561$		0			0
$562$	3.60554	+	6.24497i	0.152090	+	0.263428i
$563$	16.4758	−	28.5369i	0.694371	−	1.20269i	−0.276021	−	0.961151i	$-0.589016\pi$
$563$	16.4758	−	28.5369i	0.694371	−	1.20269i	0.970392	−	0.241534i	$-0.0776506\pi$
$564$		0			0
$565$	−17.4519	−	10.0759i	−0.734209	−	0.423895i
$566$	−12.9662	−	7.48605i	−0.545011	−	0.314662i
$567$		0			0
$568$	47.1956	−	81.7451i	1.98028	−	3.42995i
$569$	−3.33237	−	5.77184i	−0.139700	−	0.241968i	0.787683	−	0.616081i	$-0.211281\pi$
$569$	−3.33237	−	5.77184i	−0.139700	−	0.241968i	−0.927383	+	0.374113i	$0.877947\pi$
$570$		0			0
$571$	40.5063			1.69513			0.847567	−	0.530688i	$-0.178066\pi$
$571$	40.5063			1.69513			0.847567	+	0.530688i	$0.178066\pi$
$572$	1.40361	−	0.544166i	0.0586880	−	0.0227527i
$573$		0			0
$574$	14.5431	−	8.39647i	0.607018	−	0.350462i
$575$	7.11178	+	12.3180i	0.296582	+	0.513695i
$576$		0			0
$577$			16.2052i			0.674632i	0.941391	+	0.337316i	$0.109519\pi$
$577$			16.2052i			0.674632i	−0.941391	+	0.337316i	$0.890481\pi$
$578$	−56.8726	−	32.8354i	−2.36559	−	1.36577i
$579$		0			0
$580$			43.1945i			1.79356i
$581$	0.646552	−	1.11986i	0.0268235	−	0.0464597i
$582$		0			0
$583$	−0.247352	+	0.142809i	−0.0102443	+	0.00591454i
$584$	106.322			4.39964
$585$		0			0
$586$	−41.2105			−1.70239
$587$	−15.5385	+	8.97113i	−0.641341	+	0.370278i	−0.785131	−	0.619330i	$-0.787404\pi$
$587$	−15.5385	+	8.97113i	−0.641341	+	0.370278i	0.143790	+	0.989608i	$0.454071\pi$
$588$		0			0
$589$	5.29985	−	9.17961i	0.218377	−	0.378239i
$590$		−	10.5018i		−	0.432354i
$591$		0			0
$592$	−77.9492	−	45.0040i	−3.20369	−	1.84965i
$593$			34.1889i			1.40397i	0.712193	+	0.701984i	$0.247702\pi$
$593$			34.1889i			1.40397i	−0.712193	+	0.701984i	$0.752298\pi$
$594$		0			0
$595$	−4.88812	−	8.46647i	−0.200393	−	0.347091i
$596$	39.5479	−	22.8330i	1.61995	−	0.935277i
$597$		0			0
$598$	7.49155	−	48.3411i	0.306352	−	1.97681i
$599$	9.68405			0.395680			0.197840	−	0.980234i	$-0.436607\pi$
$599$	9.68405			0.395680			0.197840	+	0.980234i	$0.436607\pi$
$600$		0			0
$601$	−6.44431	−	11.1619i	−0.262869	−	0.455302i	0.704134	−	0.710067i	$-0.251335\pi$
$601$	−6.44431	−	11.1619i	−0.262869	−	0.455302i	−0.967003	+	0.254765i	$0.918002\pi$
$602$	−8.88123	+	15.3827i	−0.361972	+	0.626954i
$603$		0			0
$604$	−53.1323	−	30.6760i	−2.16192	−	1.24819i
$605$	14.3298	+	8.27334i	0.582591	+	0.336359i
$606$		0			0
$607$	−7.90895	+	13.6987i	−0.321014	+	0.556013i	−0.980698	−	0.195531i	$-0.937357\pi$
$607$	−7.90895	+	13.6987i	−0.321014	+	0.556013i	0.659683	+	0.751544i	$0.270690\pi$
$608$	−26.5681	−	46.0173i	−1.07748	−	1.86625i
$609$		0			0
$610$	−25.6965			−1.04042
$611$	6.15373	−	2.38574i	0.248953	−	0.0965166i
$612$		0			0
$613$	−22.6303	+	13.0656i	−0.914031	+	0.527716i	−0.881726	−	0.471762i	$-0.843618\pi$
$613$	−22.6303	+	13.0656i	−0.914031	+	0.527716i	−0.0323051	+	0.999478i	$0.510285\pi$
$614$	−13.1959	−	22.8559i	−0.532543	−	0.922391i
$615$		0			0
$616$		−	0.635364i		−	0.0255995i
$617$	−19.7693	−	11.4138i	−0.795880	−	0.459502i	0.0461483	−	0.998935i	$-0.485305\pi$
$617$	−19.7693	−	11.4138i	−0.795880	−	0.459502i	−0.842029	+	0.539433i	$0.818639\pi$
$618$		0			0
$619$		−	25.4700i		−	1.02373i	−0.859067	−	0.511863i	$-0.828956\pi$
$619$		−	25.4700i		−	1.02373i	0.859067	−	0.511863i	$-0.171044\pi$
$620$	−7.23842	+	12.5373i	−0.290702	+	0.503511i
$621$		0			0
$622$	32.7473	−	18.9066i	1.31305	−	0.758087i
$623$	15.8454			0.634833
$624$		0			0
$625$	−3.85378			−0.154151
$626$	29.9650	−	17.3003i	1.19764	−	0.691460i
$627$		0			0
$628$	−6.18145	+	10.7066i	−0.246667	+	0.427239i
$629$			61.8372i			2.46561i
$630$		0			0
$631$	13.3886	+	7.72994i	0.532993	+	0.307724i	0.742235	−	0.670140i	$-0.233766\pi$
$631$	13.3886	+	7.72994i	0.532993	+	0.307724i	−0.209241	+	0.977864i	$0.567099\pi$
$632$			85.3312i			3.39429i
$633$		0			0
$634$	−39.6667	−	68.7047i	−1.57537	−	2.72861i
$635$	16.8748	−	9.74267i	0.669656	−	0.386626i
$636$		0			0
$637$	2.25970	−	2.80958i	0.0895327	−	0.111320i
$638$	1.35520			0.0536529
$639$		0			0
$640$	−0.825768	−	1.43027i	−0.0326414	−	0.0565365i
$641$	11.6918	−	20.2509i	0.461800	−	0.799861i	−0.537251	−	0.843422i	$-0.680537\pi$
$641$	11.6918	−	20.2509i	0.461800	−	0.799861i	0.999051	+	0.0435617i	$0.0138705\pi$
$642$		0			0
$643$	−1.05918	−	0.611515i	−0.0417698	−	0.0241158i	0.478970	−	0.877831i	$-0.341010\pi$
$643$	−1.05918	−	0.611515i	−0.0417698	−	0.0241158i	−0.520739	+	0.853716i	$0.674344\pi$
$644$	−21.6331	−	12.4899i	−0.852463	−	0.492170i
$645$		0			0
$646$	−44.8200	+	77.6306i	−1.76342	+	3.05433i
$647$	−6.18090	−	10.7056i	−0.242996	−	0.420882i	0.718570	−	0.695455i	$-0.244797\pi$
$647$	−6.18090	−	10.7056i	−0.242996	−	0.420882i	−0.961566	+	0.274573i	$0.911464\pi$
$648$		0			0
$649$	−0.232605			−0.00913055
$650$	−20.0342	−	16.1132i	−0.785807	−	0.632013i
$651$		0			0
$652$	−81.2143	+	46.8891i	−3.18060	+	1.83632i
$653$	4.93154	+	8.54168i	0.192986	+	0.334262i	0.946238	−	0.323470i	$-0.104849\pi$
$653$	4.93154	+	8.54168i	0.192986	+	0.334262i	−0.753252	+	0.657732i	$0.771516\pi$
$654$		0			0
$655$			8.80417i			0.344008i
$656$	52.7149	+	30.4349i	2.05817	+	1.18828i
$657$		0			0
$658$		−	4.77401i		−	0.186110i
$659$	7.27455	−	12.5999i	0.283376	−	0.490822i	−0.688838	−	0.724916i	$-0.741879\pi$
$659$	7.27455	−	12.5999i	0.283376	−	0.490822i	0.972214	+	0.234093i	$0.0752121\pi$
$660$		0			0
$661$	16.8095	−	9.70496i	0.653813	−	0.377479i	−0.136102	−	0.990695i	$-0.543458\pi$
$661$	16.8095	−	9.70496i	0.653813	−	0.377479i	0.789916	+	0.613216i	$0.210124\pi$
$662$	24.2622			0.942979
$663$		0			0
$664$	9.44876			0.366683
$665$	−6.89896	+	3.98312i	−0.267530	+	0.154459i
$666$		0			0
$667$	15.5442	−	26.9234i	0.601875	−	1.04248i
$668$		−	6.70577i		−	0.259454i
$669$		0			0
$670$	28.2002	+	16.2814i	1.08947	+	0.629006i
$671$			0.569153i			0.0219719i
$672$		0			0
$673$	17.6889	+	30.6381i	0.681859	+	1.18101i	0.974413	+	0.224765i	$0.0721614\pi$
$673$	17.6889	+	30.6381i	0.681859	+	1.18101i	−0.292554	+	0.956249i	$0.594505\pi$
$674$	−30.0516	+	17.3503i	−1.15755	+	0.668309i
$675$		0			0
$676$	13.3848	+	60.9710i	0.514799	+	2.34504i
$677$	−10.9841			−0.422154			−0.211077	−	0.977469i	$-0.567697\pi$
$677$	−10.9841			−0.422154			−0.211077	+	0.977469i	$0.567697\pi$
$678$		0			0
$679$	2.93490	+	5.08340i	0.112631	+	0.195083i
$680$	35.7176	−	61.8648i	1.36971	−	2.37241i
$681$		0			0
$682$	0.393350	+	0.227101i	0.0150622	+	0.00869615i
$683$	−5.55922	−	3.20962i	−0.212718	−	0.122813i	0.389856	−	0.920876i	$-0.372525\pi$
$683$	−5.55922	−	3.20962i	−0.212718	−	0.122813i	−0.602574	+	0.798063i	$0.705858\pi$
$684$		0			0
$685$	3.84666	−	6.66260i	0.146973	−	0.254565i
$686$	−1.30401	−	2.25861i	−0.0497873	−	0.0862341i
$687$		0			0
$688$	−64.3841			−2.45462
$689$	−4.28108	−	11.0426i	−0.163096	−	0.420688i
$690$		0			0
$691$	−23.9076	+	13.8031i	−0.909490	+	0.525094i	−0.880267	−	0.474479i	$-0.842637\pi$
$691$	−23.9076	+	13.8031i	−0.909490	+	0.525094i	−0.0292227	+	0.999573i	$0.509303\pi$
$692$	41.2504	+	71.4479i	1.56811	+	2.71604i
$693$		0			0
$694$			44.0130i			1.67071i
$695$	−25.1955	−	14.5466i	−0.955721	−	0.551786i
$696$		0			0
$697$		−	41.8187i		−	1.58400i
$698$	−3.13900	+	5.43691i	−0.118813	+	0.205790i
$699$		0			0
$700$	−11.3698	+	6.56434i	−0.429737	+	0.248109i
$701$	15.9426			0.602144			0.301072	−	0.953601i	$-0.402656\pi$
$701$	15.9426			0.602144			0.301072	+	0.953601i	$0.402656\pi$
$702$		0			0
$703$	50.3885			1.90044
$704$	0.548131	−	0.316463i	0.0206585	−	0.0119272i
$705$		0			0
$706$	40.0509	−	69.3702i	1.50733	−	2.61078i
$707$		−	6.68172i		−	0.251292i
$708$		0			0
$709$	−10.8489	−	6.26364i	−0.407440	−	0.235236i	0.282249	−	0.959341i	$-0.408920\pi$
$709$	−10.8489	−	6.26364i	−0.407440	−	0.235236i	−0.689689	+	0.724105i	$0.742253\pi$
$710$		−	50.7128i		−	1.90322i
$711$		0			0
$712$	57.8915	+	100.271i	2.16957	+	3.75781i
$713$	9.02350	−	5.20972i	0.337933	−	0.195106i
$714$		0			0
$715$	0.295767	−	0.367739i	0.0110611	−	0.0137526i
$716$	6.90049			0.257883
$717$		0			0
$718$	−13.8645	−	24.0139i	−0.517417	−	0.896192i
$719$	21.2816	−	36.8608i	0.793670	−	1.37468i	−0.130010	−	0.991513i	$-0.541501\pi$
$719$	21.2816	−	36.8608i	0.793670	−	1.37468i	0.923680	−	0.383164i	$-0.125166\pi$
$720$		0			0
$721$	−3.91680	−	2.26136i	−0.145869	−	0.0842175i
$722$	20.3442	+	11.7458i	0.757134	+	0.437132i
$723$		0			0
$724$	10.3690	−	17.9596i	0.385360	−	0.667462i
$725$	−8.16964	−	14.1502i	−0.303413	−	0.525526i
$726$		0			0
$727$	25.1186			0.931596			0.465798	−	0.884891i	$-0.345767\pi$
$727$	25.1186			0.931596			0.465798	+	0.884891i	$0.345767\pi$
$728$	26.0351	+	4.03473i	0.964925	+	0.149537i
$729$		0			0
$730$	49.4698	−	28.5614i	1.83096	−	1.05711i
$731$	22.1166	+	38.3070i	0.818010	+	1.41684i
$732$		0			0
$733$		−	2.32992i		−	0.0860574i	−0.999074	−	0.0430287i	$-0.986299\pi$
$733$		−	2.32992i		−	0.0860574i	0.999074	−	0.0430287i	$-0.0137007\pi$
$734$	−59.1897	−	34.1732i	−2.18473	−	1.26135i
$735$		0			0
$736$		−	52.2326i		−	1.92532i
$737$	0.360617	−	0.624607i	0.0132835	−	0.0230077i
$738$		0			0
$739$	23.2242	−	13.4085i	0.854315	−	0.493239i	−0.00778923	−	0.999970i	$-0.502479\pi$
$739$	23.2242	−	13.4085i	0.854315	−	0.493239i	0.862105	+	0.506731i	$0.169146\pi$
$740$	−68.8195			−2.52986
$741$		0			0
$742$	−8.56672			−0.314494
$743$	43.1876	−	24.9344i	1.58440	−	0.914753i	0.590192	−	0.807263i	$-0.299052\pi$
$743$	43.1876	−	24.9344i	1.58440	−	0.914753i	0.994206	−	0.107490i	$-0.0342813\pi$
$744$		0			0
$745$	7.15780	−	12.3977i	0.262242	−	0.454216i
$746$			47.4925i			1.73882i
$747$		0			0
$748$	−2.34837	−	1.35583i	−0.0858651	−	0.0495742i
$749$			10.2448i			0.374337i
$750$		0			0
$751$	1.39391	+	2.41432i	0.0508645	+	0.0881000i	0.890337	−	0.455303i	$-0.150469\pi$
$751$	1.39391	+	2.41432i	0.0508645	+	0.0881000i	−0.839472	+	0.543403i	$0.817136\pi$
$752$	14.9862	−	8.65226i	0.546489	−	0.315515i
$753$		0			0
$754$	−8.60590	+	55.5317i	−0.313408	+	2.02234i
$755$	−19.2329			−0.699956
$756$		0			0
$757$	−6.92483	−	11.9941i	−0.251687	−	0.435935i	0.712303	−	0.701872i	$-0.247652\pi$
$757$	−6.92483	−	11.9941i	−0.251687	−	0.435935i	−0.963990	+	0.265937i	$0.914319\pi$
$758$	−37.6789	+	65.2618i	−1.36856	+	2.37042i
$759$		0			0
$760$	−50.4110	−	29.1048i	−1.82860	−	1.05574i
$761$	38.7289	+	22.3601i	1.40392	+	0.810555i	0.994792	−	0.101922i	$-0.0324991\pi$
$761$	38.7289	+	22.3601i	1.40392	+	0.810555i	0.409130	+	0.912476i	$0.365832\pi$
$762$		0			0
$763$	6.77761	−	11.7392i	0.245366	−	0.424986i
$764$	16.2952	+	28.2241i	0.589540	+	1.02111i
$765$		0			0
$766$	45.1871			1.63268
$767$	1.47711	−	9.53139i	0.0533352	−	0.344158i
$768$		0			0
$769$	−11.1497	+	6.43728i	−0.402068	+	0.232134i	−0.687376	−	0.726302i	$-0.741238\pi$
$769$	−11.1497	+	6.43728i	−0.402068	+	0.232134i	0.285308	+	0.958436i	$0.407904\pi$
$770$	−0.170678	−	0.295624i	−0.00615082	−	0.0106535i
$771$		0			0
$772$			102.637i			3.69399i
$773$	12.8074	+	7.39436i	0.460650	+	0.265957i	0.712318	−	0.701857i	$-0.247646\pi$
$773$	12.8074	+	7.39436i	0.460650	+	0.265957i	−0.251667	+	0.967814i	$0.580979\pi$
$774$		0			0
$775$		−	5.47618i		−	0.196710i
$776$	−21.4454	+	37.1446i	−0.769846	+	1.33341i
$777$		0			0
$778$	30.8835	−	17.8306i	1.10723	−	0.639257i
$779$	−34.0763			−1.22091
$780$		0			0
$781$	−1.12324			−0.0401926
$782$	−76.3104	+	44.0578i	−2.72885	+	1.57551i
$783$		0			0
$784$	4.72668	−	8.18685i	0.168810	−	0.292388i
$785$			3.87558i			0.138325i
$786$		0			0
$787$	17.2842	+	9.97903i	0.616115	+	0.355714i	0.775355	−	0.631526i	$-0.217571\pi$
$787$	17.2842	+	9.97903i	0.616115	+	0.355714i	−0.159240	+	0.987240i	$0.550904\pi$
$788$			109.472i			3.89976i
$789$		0			0
$790$	22.9226	+	39.7031i	0.815550	+	1.41257i
$791$	−11.5938	+	6.69370i	−0.412229	+	0.238001i
$792$		0			0
$793$	−23.3220	−	3.61428i	−0.828188	−	0.128347i
$794$	−40.2765			−1.42936
$795$		0			0
$796$	−6.39511	−	11.0767i	−0.226669	−	0.392602i
$797$	−5.73061	+	9.92571i	−0.202989	+	0.351587i	−0.949490	−	0.313797i	$-0.898399\pi$
$797$	−5.73061	+	9.92571i	−0.202989	+	0.351587i	0.746501	+	0.665384i	$0.231732\pi$
$798$		0			0
$799$	−10.2958	−	5.94427i	−0.364238	−	0.210293i
$800$	−23.7742	−	13.7260i	−0.840544	−	0.485288i
$801$		0			0
$802$	−18.5605	+	32.1477i	−0.655394	+	1.13518i
$803$	−0.632607	−	1.09571i	−0.0223242	−	0.0386667i
$804$		0			0
$805$	−7.83076			−0.275998
$806$	−11.8037	+	14.6760i	−0.415769	+	0.516942i
$807$		0			0
$808$	42.2824	−	24.4118i	1.48749	−	0.858803i
$809$	10.7425	+	18.6066i	0.377688	+	0.654174i	0.990725	−	0.135879i	$-0.0433860\pi$
$809$	10.7425	+	18.6066i	0.377688	+	0.654174i	−0.613038	+	0.790054i	$0.710053\pi$
$810$		0			0
$811$		−	25.8937i		−	0.909249i	−0.890683	−	0.454625i	$-0.849773\pi$
$811$		−	25.8937i		−	0.909249i	0.890683	−	0.454625i	$-0.150227\pi$
$812$	24.8509	+	14.3477i	0.872097	+	0.503506i
$813$		0			0
$814$			2.15917i			0.0756788i
$815$	−14.6990	+	25.4594i	−0.514884	+	0.891806i
$816$		0			0
$817$	31.2147	−	18.0218i	1.09207	−	0.630504i
$818$	36.7361			1.28445
$819$		0			0
$820$	46.5407			1.62527
$821$	−47.4815	+	27.4134i	−1.65711	+	0.956736i	−0.683078	+	0.730346i	$0.739359\pi$
$821$	−47.4815	+	27.4134i	−1.65711	+	0.956736i	−0.974037	+	0.226390i	$0.927308\pi$
$822$		0			0
$823$	−2.99405	+	5.18585i	−0.104366	+	0.180768i	−0.913479	−	0.406886i	$-0.866615\pi$
$823$	−2.99405	+	5.18585i	−0.104366	+	0.180768i	0.809113	+	0.587653i	$0.199948\pi$
$824$		−	33.0477i		−	1.15127i
$825$		0			0
$826$	−6.04198	−	3.48834i	−0.210227	−	0.121375i
$827$		−	13.1913i		−	0.458705i	−0.973343	−	0.229353i	$-0.926339\pi$
$827$		−	13.1913i		−	0.458705i	0.973343	−	0.229353i	$-0.0736609\pi$
$828$		0			0
$829$	27.7719	+	48.1024i	0.964559	+	1.67067i	0.710794	+	0.703400i	$0.248336\pi$
$829$	27.7719	+	48.1024i	0.964559	+	1.67067i	0.253765	+	0.967266i	$0.418331\pi$
$830$	4.39634	−	2.53823i	0.152599	−	0.0881032i
$831$		0			0
$832$	9.48684	+	24.4702i	0.328897	+	0.848352i
$833$	−6.49464			−0.225026
$834$		0			0
$835$	−1.05108	−	1.82052i	−0.0363740	−	0.0630017i
$836$	−1.10481	+	1.91359i	−0.0382107	+	0.0661829i
$837$		0			0
$838$	−85.0871	−	49.1251i	−2.93929	−	1.69700i
$839$	1.11609	+	0.644377i	0.0385319	+	0.0222464i	0.519142	−	0.854688i	$-0.326252\pi$
$839$	1.11609	+	0.644377i	0.0385319	+	0.0222464i	−0.480610	+	0.876934i	$0.659585\pi$
$840$		0			0
$841$	−3.35640	+	5.81346i	−0.115738	+	0.200464i
$842$	−2.98116	−	5.16353i	−0.102738	−	0.177947i
$843$		0			0
$844$	116.122			3.99707
$845$	13.1905	+	14.4548i	0.453767	+	0.497260i
$846$		0			0
$847$	9.51973	−	5.49622i	0.327102	−	0.188852i
$848$	−15.5260	−	26.8919i	−0.533166	−	0.923471i
$849$		0			0
$850$			46.3112i			1.58846i
$851$	42.8956	+	24.7658i	1.47044	+	0.848961i
$852$		0			0
$853$			25.6774i			0.879178i	0.898199	+	0.439589i	$0.144876\pi$
$853$			25.6774i			0.879178i	−0.898199	+	0.439589i	$0.855124\pi$
$854$	−8.53548	+	14.7839i	−0.292078	+	0.505894i
$855$		0			0
$856$	−64.8300	+	37.4296i	−2.21584	+	1.27932i
$857$	32.7226			1.11778			0.558891	−	0.829241i	$-0.311227\pi$
$857$	32.7226			1.11778			0.558891	+	0.829241i	$0.311227\pi$
$858$		0			0
$859$	20.4087			0.696335			0.348168	−	0.937432i	$-0.386804\pi$
$859$	20.4087			0.696335			0.348168	+	0.937432i	$0.386804\pi$
$860$	−42.6324	+	24.6138i	−1.45375	+	0.839325i
$861$		0			0
$862$	−2.58348	+	4.47471i	−0.0879936	+	0.152409i
$863$		−	11.1079i		−	0.378117i	−0.981966	−	0.189059i	$-0.939456\pi$
$863$		−	11.1079i		−	0.378117i	0.981966	−	0.189059i	$-0.0605436\pi$
$864$		0			0
$865$	22.3978	+	12.9314i	0.761548	+	0.439680i
$866$			15.3635i			0.522074i
$867$		0			0
$868$	4.80870	+	8.32891i	0.163218	+	0.282701i
$869$	0.879384	−	0.507713i	0.0298311	−	0.0172230i
$870$		0			0
$871$	23.3043	+	18.7433i	0.789637	+	0.635093i
$872$	99.0485			3.35420
$873$		0			0
$874$	35.9008	+	62.1821i	1.21436	+	2.10334i
$875$	−5.82101	+	10.0823i	−0.196786	+	0.340844i
$876$		0			0
$877$	24.7630	+	14.2969i	0.836186	+	0.482772i	0.855966	−	0.517032i	$-0.172963\pi$
$877$	24.7630	+	14.2969i	0.836186	+	0.482772i	−0.0197799	+	0.999804i	$0.506297\pi$
$878$	−18.2171	−	10.5177i	−0.614798	−	0.354954i
$879$		0			0
$880$	0.618663	−	1.07156i	0.0208551	−	0.0361222i
$881$	−11.1758	−	19.3571i	−0.376523	−	0.652157i	0.614031	−	0.789282i	$-0.289547\pi$
$881$	−11.1758	−	19.3571i	−0.376523	−	0.652157i	−0.990554	+	0.137125i	$0.956214\pi$
$882$		0			0
$883$	2.58792			0.0870905			0.0435453	−	0.999051i	$-0.486135\pi$
$883$	2.58792			0.0870905			0.0435453	+	0.999051i	$0.486135\pi$
$884$	70.4704	−	87.6187i	2.37018	−	2.94693i
$885$		0			0
$886$	−15.0420	+	8.68449i	−0.505345	+	0.291761i
$887$	−18.0889	−	31.3309i	−0.607365	−	1.05199i	−0.991673	−	0.128783i	$-0.958893\pi$
$887$	−18.0889	−	31.3309i	−0.607365	−	1.05199i	0.384307	−	0.923205i	$-0.374440\pi$
$888$		0			0
$889$		−	12.9447i		−	0.434151i
$890$	53.8717	+	31.1029i	1.80579	+	1.04257i
$891$		0			0
$892$			81.1881i			2.71838i
$893$	−4.84373	+	8.38958i	−0.162089	+	0.280747i
$894$		0			0
$895$	1.87338	−	1.08160i	0.0626203	−	0.0361539i
$896$	−1.09716			−0.0366537
$897$		0			0
$898$	51.7669			1.72748
$899$	−10.3657	+	5.98465i	−0.345716	+	0.199599i
$900$		0			0
$901$	−10.6667	+	18.4752i	−0.355358	+	0.615499i
$902$		−	1.46019i		−	0.0486188i
$903$		0			0
$904$	−84.7166	−	48.9111i	−2.81763	−	1.62676i
$905$		−	6.50102i		−	0.216101i
$906$		0			0
$907$	20.4804	+	35.4730i	0.680039	+	1.17786i	0.974968	+	0.222344i	$0.0713707\pi$
$907$	20.4804	+	35.4730i	0.680039	+	1.17786i	−0.294929	+	0.955519i	$0.595296\pi$
$908$	−48.4173	+	27.9538i	−1.60679	+	0.927678i
$909$		0			0
$910$	13.1975	−	5.11654i	0.437494	−	0.169612i
$911$	−2.19307			−0.0726595			−0.0363298	−	0.999340i	$-0.511567\pi$
$911$	−2.19307			−0.0726595			−0.0363298	+	0.999340i	$0.511567\pi$
$912$		0			0
$913$	−0.0562192	−	0.0973745i	−0.00186058	−	0.00322263i
$914$	3.37587	−	5.84719i	0.111664	−	0.193408i
$915$		0			0
$916$	−32.8850	−	18.9862i	−1.08655	−	0.627321i
$917$	5.06527	+	2.92444i	0.167270	+	0.0965734i
$918$		0			0
$919$	−25.5162	+	44.1953i	−0.841700	+	1.45787i	0.0467560	+	0.998906i	$0.485112\pi$
$919$	−25.5162	+	44.1953i	−0.841700	+	1.45787i	−0.888456	+	0.458961i	$0.848222\pi$
$920$	−28.6098	−	49.5537i	−0.943238	−	1.63374i
$921$		0			0
$922$	−68.7649			−2.26465
$923$	7.13286	−	46.0265i	0.234781	−	1.51498i
$924$		0			0
$925$	22.5448	−	13.0162i	0.741268	−	0.427971i
$926$	38.2182	+	66.1958i	1.25593	+	2.17533i
$927$		0			0
$928$			60.0021i			1.96966i
$929$	29.6171	+	17.0994i	0.971704	+	0.561014i	0.899755	−	0.436395i	$-0.143745\pi$
$929$	29.6171	+	17.0994i	0.971704	+	0.561014i	0.0719489	+	0.997408i	$0.477078\pi$
$930$		0			0
$931$			5.29220i			0.173445i
$932$	−57.8262	+	100.158i	−1.89416	+	3.28078i
$933$		0			0
$934$	7.29543	−	4.21202i	0.238714	−	0.137821i
$935$	−0.850067			−0.0278002
$936$		0			0
$937$	−56.0430			−1.83084			−0.915422	−	0.402496i	$-0.868143\pi$
$937$	−56.0430			−1.83084			−0.915422	+	0.402496i	$0.868143\pi$
$938$	18.7342	−	10.8162i	0.611695	−	0.353162i
$939$		0			0
$940$	6.61546	−	11.4583i	0.215772	−	0.373729i
$941$		−	31.6322i		−	1.03118i	−0.856835	−	0.515591i	$-0.827573\pi$
$941$		−	31.6322i		−	1.03118i	0.856835	−	0.515591i	$-0.172427\pi$
$942$		0			0
$943$	−29.0091	−	16.7484i	−0.944666	−	0.545403i
$944$		−	25.2886i		−	0.823073i
$945$		0			0
$946$	0.772244	+	1.33757i	0.0251078	+	0.0434880i
$947$	−40.2705	+	23.2502i	−1.30862	+	0.755529i	−0.981865	−	0.189581i	$-0.939287\pi$
$947$	−40.2705	+	23.2502i	−1.30862	+	0.755529i	−0.326750	+	0.945111i	$0.605954\pi$
$948$		0			0
$949$	48.9157	−	18.9641i	1.58787	−	0.615601i
$950$	37.7370			1.22435
$951$		0			0
$952$	−23.7283	−	41.0986i	−0.769038	−	1.33201i
$953$	11.6256	−	20.1361i	0.376589	−	0.652271i	−0.613975	−	0.789326i	$-0.710430\pi$
$953$	11.6256	−	20.1361i	0.376589	−	0.652271i	0.990563	+	0.137055i	$0.0437636\pi$
$954$		0			0
$955$	8.84784	+	5.10830i	0.286309	+	0.165301i
$956$	−45.4742	−	26.2546i	−1.47074	−	0.849133i
$957$		0			0
$958$	−10.3186	+	17.8723i	−0.333378	+	0.577427i
$959$	−2.55545	−	4.42616i	−0.0825197	−	0.142928i
$960$		0			0
$961$	26.9884			0.870595
$962$	−88.4756	−	13.7113i	−2.85257	−	0.442071i
$963$		0			0
$964$	82.7753	−	47.7904i	2.66601	−	1.53922i
$965$	16.0876	+	27.8645i	0.517878	+	0.896991i
$966$		0			0
$967$		−	13.6117i		−	0.437723i	−0.975756	−	0.218861i	$-0.929766\pi$
$967$		−	13.6117i		−	0.437723i	0.975756	−	0.218861i	$-0.0702342\pi$
$968$	69.5610	+	40.1611i	2.23578	+	1.29083i
$969$		0			0
$970$			23.0436i			0.739886i
$971$	−4.96708	+	8.60324i	−0.159401	+	0.276091i	−0.934653	−	0.355561i	$-0.884290\pi$
$971$	−4.96708	+	8.60324i	−0.159401	+	0.276091i	0.775252	+	0.631653i	$0.217623\pi$
$972$		0			0
$973$	−16.7381	+	9.66376i	−0.536600	+	0.309806i
$974$	−40.2810			−1.29069
$975$		0			0
$976$	−61.8777			−1.98066
$977$	−33.9086	+	19.5771i	−1.08483	+	0.626328i	−0.932196	−	0.361954i	$-0.882110\pi$
$977$	−33.9086	+	19.5771i	−1.08483	+	0.626328i	−0.152636	+	0.988282i	$0.548776\pi$
$978$		0			0
$979$	0.688898	−	1.19321i	0.0220173	−	0.0381350i
$980$		−	7.22798i		−	0.230889i
$981$		0			0
$982$	33.6673	+	19.4378i	1.07437	+	0.620286i
$983$		−	4.01341i		−	0.128008i	−0.997950	−	0.0640039i	$-0.979613\pi$
$983$		−	4.01341i		−	0.128008i	0.997950	−	0.0640039i	$-0.0203870\pi$
$984$		0			0
$985$	17.1588	+	29.7200i	0.546726	+	0.946957i
$986$	87.6614	−	50.6113i	2.79171	−	1.61179i
$987$		0			0
$988$	−71.3967	−	57.4233i	−2.27143	−	1.82688i
$989$	35.4307			1.12663
$990$		0			0
$991$	17.1880	+	29.7705i	0.545995	+	0.945691i	0.998544	+	0.0539510i	$0.0171815\pi$
$991$	17.1880	+	29.7705i	0.545995	+	0.945691i	−0.452549	+	0.891740i	$0.649485\pi$
$992$	−10.0550	+	17.4157i	−0.319246	+	0.552950i
$993$		0			0
$994$	−29.1764	−	16.8450i	−0.925418	−	0.534291i
$995$	−3.47236	−	2.00477i	−0.110081	−	0.0635555i
$996$		0			0
$997$	−2.23321	+	3.86804i	−0.0707266	+	0.122502i	−0.899220	−	0.437497i	$-0.855865\pi$
$997$	−2.23321	+	3.86804i	−0.0707266	+	0.122502i	0.828493	+	0.559999i	$0.189198\pi$
$998$	−33.1617	−	57.4377i	−1.04971	−	1.81816i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ct.b.127.8		16
3.2	odd	2		273.2.bd.a.127.1	yes	16
13.4	even	6	inner	819.2.ct.b.316.8		16
39.2	even	12		3549.2.a.bb.1.1		8
39.11	even	12		3549.2.a.bd.1.8		8
39.17	odd	6		273.2.bd.a.43.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.1	✓	16	39.17	odd	6
273.2.bd.a.127.1	yes	16	3.2	odd	2
819.2.ct.b.127.8		16	1.1	even	1	trivial
819.2.ct.b.316.8		16	13.4	even	6	inner
3549.2.a.bb.1.1		8	39.2	even	12
3549.2.a.bd.1.8		8	39.11	even	12

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.ct (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.25861 - 1.30401i) q^{2} +(2.40088 - 4.15844i) q^{4} -1.50528i q^{5} +(-0.866025 - 0.500000i) q^{7} -7.30704i q^{8} +(-1.96290 - 3.39983i) q^{10} +(-0.0753030 + 0.0434762i) q^{11} +(-1.30332 - 3.36175i) q^{13} -2.60802 q^{14} +(-4.72668 - 8.18685i) q^{16} +(-3.24732 + 5.62452i) q^{17} +(4.58318 + 2.64610i) q^{19} +(-6.25961 - 3.61399i) q^{20} +(-0.113387 + 0.196391i) q^{22} +(2.60110 + 4.50524i) q^{23} +2.73414 q^{25} +(-7.32743 - 5.89335i) q^{26} +(-4.15844 + 2.40088i) q^{28} +(-2.98801 - 5.17538i) q^{29} -2.00289i q^{31} +(-8.69531 - 5.02024i) q^{32} +16.9381i q^{34} +(-0.752639 + 1.30361i) q^{35} +(8.24566 - 4.76063i) q^{37} +13.8022 q^{38} -10.9991 q^{40} +(-5.57631 + 3.21948i) q^{41} +(3.40536 - 5.89825i) q^{43} +0.417524i q^{44} +(11.7498 + 6.78372i) q^{46} +1.83051i q^{47} +(0.500000 + 0.866025i) q^{49} +(6.17535 - 3.56534i) q^{50} +(-17.1088 - 2.65139i) q^{52} +3.28476 q^{53} +(0.0654437 + 0.113352i) q^{55} +(-3.65352 + 6.32808i) q^{56} +(-13.4975 - 7.79278i) q^{58} +(2.31669 + 1.33754i) q^{59} +(3.27278 - 5.66863i) q^{61} +(-2.61179 - 4.52375i) q^{62} -7.27901 q^{64} +(-5.06037 + 1.96185i) q^{65} +(-7.18333 + 4.14730i) q^{67} +(15.5928 + 27.0076i) q^{68} +3.92579i q^{70} +(11.1872 + 6.45892i) q^{71} +14.5507i q^{73} +(12.4158 - 21.5048i) q^{74} +(22.0073 - 12.7059i) q^{76} +0.0869524 q^{77} -11.6780 q^{79} +(-12.3235 + 7.11497i) q^{80} +(-8.39647 + 14.5431i) q^{82} +1.29310i q^{83} +(8.46647 + 4.88812i) q^{85} -17.7625i q^{86} +(0.317682 + 0.550241i) q^{88} +(-13.7225 + 7.92270i) q^{89} +(-0.552171 + 3.56302i) q^{91} +24.9797 q^{92} +(2.38701 + 4.13442i) q^{94} +(3.98312 - 6.89896i) q^{95} +(-5.08340 - 2.93490i) q^{97} +(2.25861 + 1.30401i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} - 4 q^{10} + 12 q^{11} + 4 q^{13} - 4 q^{14} - 10 q^{16} - 10 q^{17} - 6 q^{20} - 2 q^{22} + 2 q^{23} + 12 q^{25} - 20 q^{26} - 12 q^{29} - 30 q^{32} + 2 q^{35} + 18 q^{37} + 32 q^{38} - 60 q^{40}+ \cdots - 54 q^{97}+O(q^{100}) \) 16 * q + 6 * q^4 - 4 * q^10 + 12 * q^11 + 4 * q^13 - 4 * q^14 - 10 * q^16 - 10 * q^17 - 6 * q^20 - 2 * q^22 + 2 * q^23 + 12 * q^25 - 20 * q^26 - 12 * q^29 - 30 * q^32 + 2 * q^35 + 18 * q^37 + 32 * q^38 - 60 * q^40 - 18 * q^41 - 10 * q^43 + 30 * q^46 + 8 * q^49 + 24 * q^50 - 26 * q^52 - 12 * q^53 + 10 * q^55 - 12 * q^56 - 54 * q^58 + 60 * q^59 - 6 * q^61 - 16 * q^62 + 16 * q^64 + 20 * q^65 - 18 * q^67 + 20 * q^68 - 6 * q^71 - 18 * q^74 + 72 * q^76 + 16 * q^77 - 4 * q^79 - 30 * q^80 - 18 * q^82 - 24 * q^85 - 2 * q^88 - 78 * q^89 - 8 * q^91 + 20 * q^92 + 16 * q^94 + 4 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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