LMFDB - Embedded newform 1197.2.db.a.647.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,2,Mod(647,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("1197.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.db (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:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.30
Character	$\chi$	$=$	1197.647
Dual form			1197.2.db.a.1160.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.818824 - 0.472749i) q^{2} +(-0.553018 + 0.957855i) q^{4} +(2.19579 + 3.80322i) q^{5} +(2.57960 - 0.587948i) q^{7} +2.93675i q^{8} +O(q^{10})$	\(q+(0.818824 - 0.472749i) q^{2} +(-0.553018 + 0.957855i) q^{4} +(2.19579 + 3.80322i) q^{5} +(2.57960 - 0.587948i) q^{7} +2.93675i q^{8} +(3.59593 + 2.07611i) q^{10} +(3.96382 + 2.28851i) q^{11} -6.37996i q^{13} +(1.83429 - 1.70093i) q^{14} +(0.282308 + 0.488971i) q^{16} +(2.24090 - 3.88135i) q^{17} +(-0.866025 + 0.500000i) q^{19} -4.85724 q^{20} +4.32756 q^{22} +(0.136560 - 0.0788428i) q^{23} +(-7.14299 + 12.3720i) q^{25} +(-3.01612 - 5.22407i) q^{26} +(-0.863394 + 2.79602i) q^{28} -2.95877i q^{29} +(4.73053 + 2.73117i) q^{31} +(-4.62427 - 2.66983i) q^{32} -4.23752i q^{34} +(7.90035 + 8.51976i) q^{35} +(0.119434 + 0.206866i) q^{37} +(-0.472749 + 0.818824i) q^{38} +(-11.1691 + 6.44848i) q^{40} -5.31416 q^{41} -10.1615 q^{43} +(-4.38413 + 2.53118i) q^{44} +(0.0745457 - 0.129117i) q^{46} +(0.709228 + 1.22842i) q^{47} +(6.30864 - 3.03333i) q^{49} +13.5073i q^{50} +(6.11108 + 3.52823i) q^{52} +(-1.94137 - 1.12085i) q^{53} +20.1004i q^{55} +(1.72665 + 7.57562i) q^{56} +(-1.39876 - 2.42272i) q^{58} +(0.522256 - 0.904574i) q^{59} +(-1.74830 + 1.00938i) q^{61} +5.16463 q^{62} -6.17786 q^{64} +(24.2644 - 14.0091i) q^{65} +(-1.89523 + 3.28264i) q^{67} +(2.47851 + 4.29291i) q^{68} +(10.4967 + 3.24131i) q^{70} -14.0955i q^{71} +(-11.5559 - 6.67177i) q^{73} +(0.195591 + 0.112925i) q^{74} -1.10604i q^{76} +(11.5706 + 3.57292i) q^{77} +(-6.30440 - 10.9195i) q^{79} +(-1.23978 + 2.14735i) q^{80} +(-4.35136 + 2.51226i) q^{82} +5.81977 q^{83} +19.6822 q^{85} +(-8.32052 + 4.80386i) q^{86} +(-6.72078 + 11.6407i) q^{88} +(-1.54060 - 2.66840i) q^{89} +(-3.75108 - 16.4577i) q^{91} +0.174406i q^{92} +(1.16147 + 0.670573i) q^{94} +(-3.80322 - 2.19579i) q^{95} +12.8444i q^{97} +(3.73166 - 5.46617i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) $ 96 * q + 48 * q^4 + 8 * q^7	$ 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) $ 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.818824	−	0.472749i	0.578996	−	0.334284i	−0.181738	−	0.983347i	$-0.558172\pi$
$2$	0.818824	−	0.472749i	0.578996	−	0.334284i	0.760734	+	0.649063i	$0.224839\pi$
$3$		0			0
$3$		0			0
$4$	−0.553018	+	0.957855i	−0.276509	+	0.478927i
$5$	2.19579	+	3.80322i	0.981987	+	1.70085i	0.654627	+	0.755952i	$0.272826\pi$
$5$	2.19579	+	3.80322i	0.981987	+	1.70085i	0.327360	+	0.944900i	$0.393841\pi$
$6$		0			0
$7$	2.57960	−	0.587948i	0.974996	−	0.222223i
$7$	2.57960	−	0.587948i	0.974996	−	0.222223i
$8$			2.93675i			1.03830i
$9$		0			0
$10$	3.59593	+	2.07611i	1.13713	+	0.656525i
$11$	3.96382	+	2.28851i	1.19514	+	0.690013i	0.959467	−	0.281821i	$-0.0909383\pi$
$11$	3.96382	+	2.28851i	1.19514	+	0.690013i	0.235670	+	0.971833i	$0.424272\pi$
$12$		0			0
$13$		−	6.37996i		−	1.76948i	−0.466082	−	0.884742i	$-0.654335\pi$
$13$		−	6.37996i		−	1.76948i	0.466082	−	0.884742i	$-0.345665\pi$
$14$	1.83429	−	1.70093i	0.490233	−	0.454592i
$15$		0			0
$16$	0.282308	+	0.488971i	0.0705769	+	0.122243i
$17$	2.24090	−	3.88135i	0.543497	−	0.941365i	−0.455202	−	0.890388i	$-0.650433\pi$
$17$	2.24090	−	3.88135i	0.543497	−	0.941365i	0.998700	−	0.0509772i	$-0.0162336\pi$
$18$		0			0
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$20$	−4.85724			−1.08611
$21$		0			0
$22$	4.32756			0.922640
$23$	0.136560	−	0.0788428i	0.0284747	−	0.0164399i	−0.485695	−	0.874128i	$-0.661433\pi$
$23$	0.136560	−	0.0788428i	0.0284747	−	0.0164399i	0.514170	+	0.857688i	$0.328100\pi$
$24$		0			0
$25$	−7.14299	+	12.3720i	−1.42860	+	2.47440i
$26$	−3.01612	−	5.22407i	−0.591509	−	1.02452i
$27$		0			0
$28$	−0.863394	+	2.79602i	−0.163166	+	0.528399i
$29$		−	2.95877i		−	0.549430i	−0.961526	−	0.274715i	$-0.911416\pi$
$29$		−	2.95877i		−	0.549430i	0.961526	−	0.274715i	$-0.0885836\pi$
$30$		0			0
$31$	4.73053	+	2.73117i	0.849628	+	0.490533i	0.860525	−	0.509407i	$-0.170135\pi$
$31$	4.73053	+	2.73117i	0.849628	+	0.490533i	−0.0108970	+	0.999941i	$0.503469\pi$
$32$	−4.62427	−	2.66983i	−0.817464	−	0.471963i
$33$		0			0
$34$		−	4.23752i		−	0.726729i
$35$	7.90035	+	8.51976i	1.33540	+	1.44010i
$36$		0			0
$37$	0.119434	+	0.206866i	0.0196349	+	0.0340086i	0.875676	−	0.482899i	$-0.160416\pi$
$37$	0.119434	+	0.206866i	0.0196349	+	0.0340086i	−0.856041	+	0.516908i	$0.827083\pi$
$38$	−0.472749	+	0.818824i	−0.0766899	+	0.132831i
$39$		0			0
$40$	−11.1691	+	6.44848i	−1.76599	+	1.01959i
$41$	−5.31416			−0.829932			−0.414966	−	0.909837i	$-0.636207\pi$
$41$	−5.31416			−0.829932			−0.414966	+	0.909837i	$0.636207\pi$
$42$		0			0
$43$	−10.1615			−1.54962			−0.774811	−	0.632193i	$-0.782155\pi$
$43$	−10.1615			−1.54962			−0.774811	+	0.632193i	$0.782155\pi$
$44$	−4.38413	+	2.53118i	−0.660932	+	0.381589i
$45$		0			0
$46$	0.0745457	−	0.129117i	0.0109912	−	0.0190372i
$47$	0.709228	+	1.22842i	0.103451	+	0.179183i	0.913104	−	0.407726i	$-0.133678\pi$
$47$	0.709228	+	1.22842i	0.103451	+	0.179183i	−0.809653	+	0.586909i	$0.800345\pi$
$48$		0			0
$49$	6.30864	−	3.03333i	0.901234	−	0.433334i
$50$			13.5073i			1.91023i
$51$		0			0
$52$	6.11108	+	3.52823i	0.847454	+	0.489278i
$53$	−1.94137	−	1.12085i	−0.266668	−	0.153961i	0.360705	−	0.932680i	$-0.382536\pi$
$53$	−1.94137	−	1.12085i	−0.266668	−	0.153961i	−0.627372	+	0.778719i	$0.715870\pi$
$54$		0			0
$55$			20.1004i			2.71033i
$56$	1.72665	+	7.57562i	0.230734	+	1.01234i
$57$		0			0
$58$	−1.39876	−	2.42272i	−0.183666	−	0.318118i
$59$	0.522256	−	0.904574i	0.0679919	−	0.117765i	−0.830025	−	0.557726i	$-0.811674\pi$
$59$	0.522256	−	0.904574i	0.0679919	−	0.117765i	0.898017	+	0.439960i	$0.145007\pi$
$60$		0			0
$61$	−1.74830	+	1.00938i	−0.223847	+	0.129238i	−0.607730	−	0.794143i	$-0.707920\pi$
$61$	−1.74830	+	1.00938i	−0.223847	+	0.129238i	0.383883	+	0.923382i	$0.374587\pi$
$62$	5.16463			0.655909
$63$		0			0
$64$	−6.17786			−0.772232
$65$	24.2644	−	14.0091i	3.00963	−	1.73761i
$66$		0			0
$67$	−1.89523	+	3.28264i	−0.231539	+	0.401038i	−0.958261	−	0.285894i	$-0.907710\pi$
$67$	−1.89523	+	3.28264i	−0.231539	+	0.401038i	0.726722	+	0.686932i	$0.241043\pi$
$68$	2.47851	+	4.29291i	0.300564	+	0.520592i
$69$		0			0
$70$	10.4967	+	3.24131i	1.25460	+	0.387411i
$71$		−	14.0955i		−	1.67282i	−0.548101	−	0.836412i	$-0.684649\pi$
$71$		−	14.0955i		−	1.67282i	0.548101	−	0.836412i	$-0.315351\pi$
$72$		0			0
$73$	−11.5559	−	6.67177i	−1.35251	−	0.780872i	−0.363910	−	0.931434i	$-0.618558\pi$
$73$	−11.5559	−	6.67177i	−1.35251	−	0.780872i	−0.988601	+	0.150562i	$0.951892\pi$
$74$	0.195591	+	0.112925i	0.0227370	+	0.0131272i
$75$		0			0
$76$		−	1.10604i		−	0.126871i
$77$	11.5706	+	3.57292i	1.31859	+	0.407172i
$78$		0			0
$79$	−6.30440	−	10.9195i	−0.709301	−	1.22854i	−0.965117	−	0.261819i	$-0.915678\pi$
$79$	−6.30440	−	10.9195i	−0.709301	−	1.22854i	0.255816	−	0.966725i	$-0.417656\pi$
$80$	−1.23978	+	2.14735i	−0.138611	+	0.240082i
$81$		0			0
$82$	−4.35136	+	2.51226i	−0.480528	+	0.277433i
$83$	5.81977			0.638803			0.319402	−	0.947619i	$-0.396518\pi$
$83$	5.81977			0.638803			0.319402	+	0.947619i	$0.396518\pi$
$84$		0			0
$85$	19.6822			2.13483
$86$	−8.32052	+	4.80386i	−0.897225	+	0.518013i
$87$		0			0
$88$	−6.72078	+	11.6407i	−0.716438	+	1.24091i
$89$	−1.54060	−	2.66840i	−0.163303	−	0.282849i	0.772748	−	0.634713i	$-0.218882\pi$
$89$	−1.54060	−	2.66840i	−0.163303	−	0.282849i	−0.936051	+	0.351863i	$0.885548\pi$
$90$		0			0
$91$	−3.75108	−	16.4577i	−0.393220	−	1.72524i
$92$			0.174406i			0.0181831i
$93$		0			0
$94$	1.16147	+	0.670573i	0.119796	+	0.0691643i
$95$	−3.80322	−	2.19579i	−0.390202	−	0.225283i
$96$		0			0
$97$			12.8444i			1.30416i	0.758152	+	0.652078i	$0.226102\pi$
$97$			12.8444i			1.30416i	−0.758152	+	0.652078i	$0.773898\pi$
$98$	3.73166	−	5.46617i	0.376955	−	0.552166i
$99$		0			0
$100$	−7.90040	−	13.6839i	−0.790040	−	1.36839i
$101$	−3.97048	+	6.87708i	−0.395078	+	0.684295i	−0.993111	−	0.117176i	$-0.962616\pi$
$101$	−3.97048	+	6.87708i	−0.395078	+	0.684295i	0.598033	+	0.801471i	$0.295949\pi$
$102$		0			0
$103$	1.59748	−	0.922306i	0.157404	−	0.0908775i	−0.419229	−	0.907881i	$-0.637699\pi$
$103$	1.59748	−	0.922306i	0.157404	−	0.0908775i	0.576633	+	0.817003i	$0.304366\pi$
$104$	18.7363			1.83725
$105$		0			0
$106$	−2.11952			−0.205866
$107$	2.54423	−	1.46891i	0.245960	−	0.142005i	−0.371953	−	0.928252i	$-0.621312\pi$
$107$	2.54423	−	1.46891i	0.245960	−	0.142005i	0.617913	+	0.786247i	$0.287978\pi$
$108$		0			0
$109$	5.19166	−	8.99222i	0.497271	−	0.861299i	−0.502724	−	0.864447i	$-0.667669\pi$
$109$	5.19166	−	8.99222i	0.497271	−	0.861299i	0.999995	+	0.00314833i	$0.00100215\pi$
$110$	9.50242	+	16.4587i	0.906020	+	1.56927i
$111$		0			0
$112$	1.01573	+	1.09537i	0.0959773	+	0.103502i
$113$			15.2179i			1.43158i	0.698316	+	0.715789i	$0.253933\pi$
$113$			15.2179i			1.43158i	−0.698316	+	0.715789i	$0.746067\pi$
$114$		0			0
$115$	0.599713	+	0.346245i	0.0559235	+	0.0322875i
$116$	2.83407	+	1.63625i	0.263137	+	0.151922i
$117$		0			0
$118$		−	0.987583i		−	0.0909144i
$119$	3.49858	−	11.3298i	0.320714	−	1.03860i
$120$		0			0
$121$	4.97458	+	8.61623i	0.452235	+	0.783294i
$122$	−0.954368	+	1.65301i	−0.0864044	+	0.149657i
$123$		0			0
$124$	−5.23213	+	3.02077i	−0.469860	+	0.271274i
$125$	−40.7801			−3.64748
$126$		0			0
$127$	−14.8262			−1.31561			−0.657805	−	0.753188i	$-0.728515\pi$
$127$	−14.8262			−1.31561			−0.657805	+	0.753188i	$0.728515\pi$
$128$	4.18997	−	2.41908i	0.370345	−	0.213819i
$129$		0			0
$130$	13.2455	−	22.9419i	1.16171	−	2.01214i
$131$	−5.50316	−	9.53175i	−0.480813	−	0.832793i	0.518945	−	0.854808i	$-0.326325\pi$
$131$	−5.50316	−	9.53175i	−0.480813	−	0.832793i	−0.999758	+	0.0220152i	$0.992992\pi$
$132$		0			0
$133$	−1.94002	+	1.79898i	−0.168221	+	0.155991i
$134$			3.58387i			0.309599i
$135$		0			0
$136$	11.3985	+	6.58095i	0.977417	+	0.564312i
$137$	−2.24308	−	1.29504i	−0.191639	−	0.110643i	0.401111	−	0.916030i	$-0.368624\pi$
$137$	−2.24308	−	1.29504i	−0.191639	−	0.110643i	−0.592750	+	0.805387i	$0.701958\pi$
$138$		0			0
$139$			6.72920i			0.570763i	0.958414	+	0.285382i	$0.0921203\pi$
$139$			6.72920i			0.570763i	−0.958414	+	0.285382i	$0.907880\pi$
$140$	−12.5297	+	2.85580i	−1.05896	+	0.241359i
$141$		0			0
$142$	−6.66361	−	11.5417i	−0.559198	−	0.968559i
$143$	14.6006	−	25.2890i	1.22097	−	2.11477i
$144$		0			0
$145$	11.2529	−	6.49684i	0.934499	−	0.539533i
$146$	−12.6163			−1.04413
$147$		0			0
$148$	−0.264197			−0.0217169
$149$	4.45894	−	2.57437i	0.365291	−	0.210901i	−0.306108	−	0.951997i	$-0.599027\pi$
$149$	4.45894	−	2.57437i	0.365291	−	0.210901i	0.671399	+	0.741096i	$0.265694\pi$
$150$		0			0
$151$	8.16380	−	14.1401i	0.664361	−	1.15071i	−0.315098	−	0.949059i	$-0.602037\pi$
$151$	8.16380	−	14.1401i	0.664361	−	1.15071i	0.979458	−	0.201647i	$-0.0646294\pi$
$152$	−1.46837	−	2.54330i	−0.119101	−	0.206289i
$153$		0			0
$154$	11.1634	−	2.54438i	0.899570	−	0.205032i
$155$			23.9883i			1.92679i
$156$		0			0
$157$	17.7522	+	10.2492i	1.41678	+	0.817979i	0.996015	−	0.0891898i	$-0.0284278\pi$
$157$	17.7522	+	10.2492i	1.41678	+	0.817979i	0.420767	+	0.907169i	$0.361761\pi$
$158$	−10.3244	−	5.96079i	−0.821365	−	0.474215i
$159$		0			0
$160$		−	23.4495i		−	1.85385i
$161$	0.305914	−	0.283673i	0.0241094	−	0.0223565i
$162$		0			0
$163$	−3.68749	−	6.38692i	−0.288827	−	0.500262i	0.684703	−	0.728822i	$-0.259932\pi$
$163$	−3.68749	−	6.38692i	−0.288827	−	0.500262i	−0.973530	+	0.228559i	$0.926598\pi$
$164$	2.93882	−	5.09019i	0.229484	−	0.397477i
$165$		0			0
$166$	4.76537	−	2.75129i	0.369865	−	0.213541i
$167$	17.2877			1.33776			0.668882	−	0.743369i	$-0.266773\pi$
$167$	17.2877			1.33776			0.668882	+	0.743369i	$0.266773\pi$
$168$		0			0
$169$	−27.7039			−2.13107
$170$	16.1162	−	9.30471i	1.23606	−	0.713639i
$171$		0			0
$172$	5.61951	−	9.73328i	0.428484	−	0.742156i
$173$	6.69875	+	11.6026i	0.509297	+	0.882128i	0.999942	+	0.0107683i	$0.00342773\pi$
$173$	6.69875	+	11.6026i	0.509297	+	0.882128i	−0.490645	+	0.871359i	$0.663239\pi$
$174$		0			0
$175$	−11.1519	+	36.1145i	−0.843006	+	2.73000i
$176$			2.58426i			0.194796i
$177$		0			0
$178$	−2.52296	−	1.45663i	−0.189104	−	0.109179i
$179$	2.90542	+	1.67745i	0.217161	+	0.125378i	0.604635	−	0.796502i	$-0.293319\pi$
$179$	2.90542	+	1.67745i	0.217161	+	0.125378i	−0.387474	+	0.921881i	$0.626652\pi$
$180$		0			0
$181$		−	2.10915i		−	0.156772i	−0.996923	−	0.0783859i	$-0.975023\pi$
$181$		−	2.10915i		−	0.156772i	0.996923	−	0.0783859i	$-0.0249766\pi$
$182$	−10.8518	−	11.7027i	−0.804392	−	0.867460i
$183$		0			0
$184$	0.231541	+	0.401042i	0.0170695	+	0.0295652i
$185$	−0.524505	+	0.908470i	−0.0385624	+	0.0667920i
$186$		0			0
$187$	17.7650	−	10.2566i	1.29911	−	0.750040i
$188$	−1.56886			−0.114421
$189$		0			0
$190$	−4.15223			−0.301234
$191$	6.61576	−	3.81961i	0.478699	−	0.276377i	−0.241175	−	0.970482i	$-0.577533\pi$
$191$	6.61576	−	3.81961i	0.478699	−	0.276377i	0.719874	+	0.694105i	$0.244199\pi$
$192$		0			0
$193$	−7.24223	+	12.5439i	−0.521307	+	0.902930i	0.478386	+	0.878150i	$0.341222\pi$
$193$	−7.24223	+	12.5439i	−0.521307	+	0.902930i	−0.999693	+	0.0247807i	$0.992111\pi$
$194$	6.07219	+	10.5173i	0.435958	+	0.755101i
$195$		0			0
$196$	−0.583293	+	7.72024i	−0.0416638	+	0.551446i
$197$			7.43877i			0.529991i	0.964250	+	0.264995i	$0.0853704\pi$
$197$			7.43877i			0.529991i	−0.964250	+	0.264995i	$0.914630\pi$
$198$		0			0
$199$	6.30848	+	3.64220i	0.447196	+	0.258189i	0.706645	−	0.707568i	$-0.250208\pi$
$199$	6.30848	+	3.64220i	0.447196	+	0.258189i	−0.259449	+	0.965757i	$0.583541\pi$
$200$	−36.3335	−	20.9771i	−2.56917	−	1.48331i
$201$		0			0
$202$			7.50816i			0.528272i
$203$	−1.73960	−	7.63244i	−0.122096	−	0.535692i
$204$		0			0
$205$	−11.6688	−	20.2109i	−0.814983	−	1.41159i
$206$	0.872037	−	1.51041i	0.0607577	−	0.105235i
$207$		0			0
$208$	3.11962	−	1.80111i	0.216306	−	0.124885i
$209$	−4.57703			−0.316599
$210$		0			0
$211$	−18.3184			−1.26109			−0.630547	−	0.776151i	$-0.717169\pi$
$211$	−18.3184			−1.26109			−0.630547	+	0.776151i	$0.717169\pi$
$212$	2.14722	−	1.23970i	0.147472	−	0.0851429i
$213$		0			0
$214$	1.38885	−	2.40556i	0.0949399	−	0.164441i
$215$	−22.3126	−	38.6466i	−1.52171	−	2.63568i
$216$		0			0
$217$	13.8086	+	4.26402i	0.937392	+	0.289461i
$218$		−	9.81740i		−	0.664918i
$219$		0			0
$220$	−19.2532	−	11.1159i	−1.29805	−	0.749431i
$221$	−24.7629	−	14.2968i	−1.66573	−	0.961710i
$222$		0			0
$223$			10.8610i			0.727306i	0.931535	+	0.363653i	$0.118471\pi$
$223$			10.8610i			0.727306i	−0.931535	+	0.363653i	$0.881529\pi$
$224$	−13.4985	−	4.16824i	−0.901905	−	0.278502i
$225$		0			0
$226$	7.19423	+	12.4608i	0.478553	+	0.828879i
$227$	8.02661	−	13.9025i	0.532745	−	0.922741i	−0.466524	−	0.884509i	$-0.654494\pi$
$227$	8.02661	−	13.9025i	0.532745	−	0.922741i	0.999269	−	0.0382326i	$-0.0121728\pi$
$228$		0			0
$229$	10.1638	−	5.86807i	0.671642	−	0.387773i	−0.125056	−	0.992150i	$-0.539911\pi$
$229$	10.1638	−	5.86807i	0.671642	−	0.387773i	0.796699	+	0.604377i	$0.206578\pi$
$230$	0.654746			0.0431727
$231$		0			0
$232$	8.68917			0.570472
$233$	−9.73664	+	5.62145i	−0.637869	+	0.368274i	−0.783793	−	0.621022i	$-0.786718\pi$
$233$	−9.73664	+	5.62145i	−0.637869	+	0.368274i	0.145924	+	0.989296i	$0.453384\pi$
$234$		0			0
$235$	−3.11463	+	5.39470i	−0.203176	+	0.351911i
$236$	0.577633	+	1.00049i	0.0376007	+	0.0651264i
$237$		0			0
$238$	−2.49144	−	10.9311i	−0.161496	−	0.708558i
$239$		−	3.71469i		−	0.240283i	−0.992757	−	0.120142i	$-0.961665\pi$
$239$		−	3.71469i		−	0.240283i	0.992757	−	0.120142i	$-0.0383349\pi$
$240$		0			0
$241$	7.80746	+	4.50764i	0.502923	+	0.290363i	0.729920	−	0.683533i	$-0.239557\pi$
$241$	7.80746	+	4.50764i	0.502923	+	0.290363i	−0.226997	+	0.973895i	$0.572891\pi$
$242$	8.14662	+	4.70345i	0.523684	+	0.302349i
$243$		0			0
$244$		−	2.23283i		−	0.142942i
$245$	25.3889	+	17.3326i	1.62204	+	1.10734i
$246$		0			0
$247$	3.18998	+	5.52521i	0.202974	+	0.351561i
$248$	−8.02077	+	13.8924i	−0.509319	+	0.882167i
$249$		0			0
$250$	−33.3917	+	19.2787i	−2.11188	+	1.21929i
$251$	−11.0869			−0.699797			−0.349899	−	0.936788i	$-0.613784\pi$
$251$	−11.0869			−0.699797			−0.349899	+	0.936788i	$0.613784\pi$
$252$		0			0
$253$	0.721731			0.0453749
$254$	−12.1400	+	7.00905i	−0.761734	+	0.439787i
$255$		0			0
$256$	8.46509	−	14.6620i	0.529068	−	0.916373i
$257$	15.2676	+	26.4442i	0.952364	+	1.64954i	0.740288	+	0.672290i	$0.234689\pi$
$257$	15.2676	+	26.4442i	0.952364	+	1.64954i	0.212076	+	0.977253i	$0.431978\pi$
$258$		0			0
$259$	0.429719	+	0.463410i	0.0267014	+	0.0287949i
$260$			30.9890i			1.92186i
$261$		0			0
$262$	−9.01224	−	5.20322i	−0.556778	−	0.321456i
$263$	−17.9948	−	10.3893i	−1.10961	−	0.640631i	−0.170878	−	0.985292i	$-0.554660\pi$
$263$	−17.9948	−	10.3893i	−1.10961	−	0.640631i	−0.938727	+	0.344661i	$0.887994\pi$
$264$		0			0
$265$		−	9.84460i		−	0.604749i
$266$	−0.738075	+	2.39019i	−0.0452543	+	0.146552i
$267$		0			0
$268$	−2.09619	−	3.63071i	−0.128045	−	0.221781i
$269$	6.64752	−	11.5138i	0.405307	−	0.702012i	−0.589051	−	0.808096i	$-0.700498\pi$
$269$	6.64752	−	11.5138i	0.405307	−	0.702012i	0.994357	+	0.106085i	$0.0338314\pi$
$270$		0			0
$271$	4.61604	−	2.66507i	0.280405	−	0.161892i	−0.353202	−	0.935547i	$-0.614907\pi$
$271$	4.61604	−	2.66507i	0.280405	−	0.161892i	0.633607	+	0.773655i	$0.281574\pi$
$272$	2.53049			0.153433
$273$		0			0
$274$	−2.44891			−0.147944
$275$	−56.6270	+	32.6936i	−3.41474	+	1.97150i
$276$		0			0
$277$	−1.97997	+	3.42941i	−0.118965	+	0.206053i	−0.919358	−	0.393423i	$-0.871291\pi$
$277$	−1.97997	+	3.42941i	−0.118965	+	0.206053i	0.800393	+	0.599476i	$0.204624\pi$
$278$	3.18122	+	5.51003i	0.190797	+	0.330470i
$279$		0			0
$280$	−25.0204	+	23.2013i	−1.49525	+	1.38654i
$281$		−	4.88223i		−	0.291249i	−0.989340	−	0.145625i	$-0.953481\pi$
$281$		−	4.88223i		−	0.291249i	0.989340	−	0.145625i	$-0.0465192\pi$
$282$		0			0
$283$	−11.2244	−	6.48044i	−0.667224	−	0.385222i	0.127800	−	0.991800i	$-0.459208\pi$
$283$	−11.2244	−	6.48044i	−0.667224	−	0.385222i	−0.795024	+	0.606578i	$0.792542\pi$
$284$	13.5014	+	7.79505i	0.801162	+	0.462551i
$285$		0			0
$286$		−	27.6097i		−	1.63260i
$287$	−13.7084	+	3.12445i	−0.809181	+	0.184430i
$288$		0			0
$289$	−1.54324	−	2.67298i	−0.0907790	−	0.157234i
$290$	6.14275	−	10.6395i	0.360714	−	0.624776i
$291$		0			0
$292$	12.7812	−	7.37922i	0.747962	−	0.431836i
$293$	15.8654			0.926867			0.463434	−	0.886132i	$-0.346617\pi$
$293$	15.8654			0.926867			0.463434	+	0.886132i	$0.346617\pi$
$294$		0			0
$295$	4.58706			0.267069
$296$	−0.607514	+	0.350748i	−0.0353110	+	0.0203868i
$297$		0			0
$298$	2.43406	−	4.21591i	0.141001	−	0.244221i
$299$	−0.503014	−	0.871246i	−0.0290901	−	0.0503855i
$300$		0			0
$301$	−26.2127	+	5.97446i	−1.51087	+	0.344362i
$302$		−	15.4377i		−	0.888340i
$303$		0			0
$304$	−0.488971	−	0.282308i	−0.0280444	−	0.0161914i
$305$	−7.67781	−	4.43278i	−0.439630	−	0.253820i
$306$		0			0
$307$		−	2.91348i		−	0.166281i	−0.996538	−	0.0831405i	$-0.973505\pi$
$307$		−	2.91348i		−	0.166281i	0.996538	−	0.0831405i	$-0.0264950\pi$
$308$	−9.82108	+	9.10705i	−0.559608	+	0.518922i
$309$		0			0
$310$	11.3404	+	19.6422i	0.644094	+	1.11560i
$311$	6.94725	−	12.0330i	0.393942	−	0.682328i	−0.599023	−	0.800732i	$-0.704444\pi$
$311$	6.94725	−	12.0330i	0.393942	−	0.682328i	0.992966	+	0.118403i	$0.0377776\pi$
$312$		0			0
$313$	−0.0126100	+	0.00728040i	−0.000712760	+	0.000411512i	−0.500356	−	0.865820i	$-0.666798\pi$
$313$	−0.0126100	+	0.00728040i	−0.000712760	+	0.000411512i	0.499644	+	0.866231i	$0.333464\pi$
$314$	19.3813			1.09375
$315$		0			0
$316$	13.9458			0.784512
$317$	−9.23304	+	5.33070i	−0.518579	+	0.299402i	−0.736353	−	0.676597i	$-0.763454\pi$
$317$	−9.23304	+	5.33070i	−0.518579	+	0.299402i	0.217774	+	0.975999i	$0.430120\pi$
$318$		0			0
$319$	6.77119	−	11.7280i	0.379114	−	0.656644i
$320$	−13.5653	−	23.4957i	−0.758322	−	1.31345i
$321$		0			0
$322$	0.116384	−	0.376898i	0.00648581	−	0.0210037i
$323$			4.48179i			0.249374i
$324$		0			0
$325$	78.9330	+	45.5720i	4.37841	+	2.52788i
$326$	−6.03882	−	3.48651i	−0.334459	−	0.193100i
$327$		0			0
$328$		−	15.6063i		−	0.861716i
$329$	2.55177	+	2.75183i	0.140683	+	0.151714i
$330$		0			0
$331$	−7.96622	−	13.7979i	−0.437863	−	0.758401i	0.559661	−	0.828721i	$-0.310931\pi$
$331$	−7.96622	−	13.7979i	−0.437863	−	0.758401i	−0.997524	+	0.0703202i	$0.977598\pi$
$332$	−3.21844	+	5.57450i	−0.176635	+	0.305940i
$333$		0			0
$334$	14.1556	−	8.17274i	0.774560	−	0.447192i
$335$	−16.6461			−0.909474
$336$		0			0
$337$	4.04824			0.220522			0.110261	−	0.993903i	$-0.464831\pi$
$337$	4.04824			0.220522			0.110261	+	0.993903i	$0.464831\pi$
$338$	−22.6847	+	13.0970i	−1.23388	+	0.712382i
$339$		0			0
$340$	−10.8846	+	18.8527i	−0.590299	+	1.02243i
$341$	12.5007	+	21.6518i	0.676948	+	1.17251i
$342$		0			0
$343$	14.4903	−	11.5339i	0.782402	−	0.622774i
$344$		−	29.8419i		−	1.60897i
$345$		0			0
$346$	10.9702	+	6.33365i	0.589762	+	0.340499i
$347$	31.0106	+	17.9040i	1.66473	+	0.961134i	0.970407	+	0.241474i	$0.0776309\pi$
$347$	31.0106	+	17.9040i	1.66473	+	0.961134i	0.694326	+	0.719660i	$0.255702\pi$
$348$		0			0
$349$			12.9428i			0.692810i	0.938085	+	0.346405i	$0.112598\pi$
$349$			12.9428i			0.692810i	−0.938085	+	0.346405i	$0.887402\pi$
$350$	7.94161	+	34.8435i	0.424497	+	1.86246i
$351$		0			0
$352$	−12.2199	−	21.1654i	−0.651321	−	1.12812i
$353$	−1.38732	+	2.40291i	−0.0738397	+	0.127894i	−0.900581	−	0.434688i	$-0.856859\pi$
$353$	−1.38732	+	2.40291i	−0.0738397	+	0.127894i	0.826741	+	0.562582i	$0.190192\pi$
$354$		0			0
$355$	53.6082	−	30.9507i	2.84523	−	1.64269i
$356$	3.40791			0.180619
$357$		0			0
$358$	3.17204			0.167648
$359$	−16.9231	+	9.77055i	−0.893166	+	0.515670i	−0.874977	−	0.484165i	$-0.839124\pi$
$359$	−16.9231	+	9.77055i	−0.893166	+	0.515670i	−0.0181895	+	0.999835i	$0.505790\pi$
$360$		0			0
$361$	0.500000	−	0.866025i	0.0263158	−	0.0455803i
$362$	−0.997097	−	1.72702i	−0.0524063	−	0.0907703i
$363$		0			0
$364$	17.8385	+	5.50842i	0.934993	+	0.288720i
$365$		−	58.5993i		−	3.06723i
$366$		0			0
$367$	−20.0198	−	11.5584i	−1.04503	−	0.603346i	−0.123773	−	0.992311i	$-0.539499\pi$
$367$	−20.0198	−	11.5584i	−1.04503	−	0.603346i	−0.921253	+	0.388965i	$0.872833\pi$
$368$	0.0771037	+	0.0445158i	0.00401931	+	0.00232055i
$369$		0			0
$370$			0.991836i			0.0515631i
$371$	−5.66695	−	1.74992i	−0.294213	−	0.0908512i
$372$		0			0
$373$	2.88516	+	4.99725i	0.149388	+	0.258748i	0.931001	−	0.365015i	$-0.118936\pi$
$373$	2.88516	+	4.99725i	0.149388	+	0.258748i	−0.781613	+	0.623763i	$0.785603\pi$
$374$	9.69763	−	16.7968i	0.501452	−	0.868541i
$375$		0			0
$376$	−3.60755	+	2.08282i	−0.186045	+	0.107413i
$377$	−18.8769			−0.972208
$378$		0			0
$379$	−5.02575			−0.258155			−0.129078	−	0.991634i	$-0.541202\pi$
$379$	−5.02575			−0.258155			−0.129078	+	0.991634i	$0.541202\pi$
$380$	4.20650	−	2.42862i	0.215789	−	0.124586i
$381$		0			0
$382$	3.61143	−	6.25518i	0.184777	−	0.320043i
$383$	0.484041	+	0.838383i	0.0247333	+	0.0428394i	0.878127	−	0.478427i	$-0.158793\pi$
$383$	0.484041	+	0.838383i	0.0247333	+	0.0428394i	−0.853394	+	0.521267i	$0.825460\pi$
$384$		0			0
$385$	11.8180	+	51.8509i	0.602299	+	2.64256i
$386$			13.6950i			0.697058i
$387$		0			0
$388$	−12.3031	−	7.10320i	−0.624596	−	0.360610i
$389$	10.4548	+	6.03607i	0.530078	+	0.306041i	0.741048	−	0.671452i	$-0.234329\pi$
$389$	10.4548	+	6.03607i	0.530078	+	0.306041i	−0.210970	+	0.977493i	$0.567662\pi$
$390$		0			0
$391$		−	0.706715i		−	0.0357401i
$392$	8.90814	+	18.5269i	0.449929	+	0.935748i
$393$		0			0
$394$	3.51667	+	6.09105i	0.177167	+	0.306863i
$395$	27.6863	−	47.9541i	1.39305	−	2.41283i
$396$		0			0
$397$	12.9539	−	7.47896i	0.650140	−	0.375358i	−0.138370	−	0.990381i	$-0.544186\pi$
$397$	12.9539	−	7.47896i	0.650140	−	0.375358i	0.788510	+	0.615022i	$0.210853\pi$
$398$	6.88738			0.345233
$399$		0			0
$400$	−8.06607			−0.403304
$401$	28.8782	−	16.6728i	1.44211	−	0.832602i	0.444119	−	0.895968i	$-0.353517\pi$
$401$	28.8782	−	16.6728i	1.44211	−	0.832602i	0.997990	+	0.0633660i	$0.0201835\pi$
$402$		0			0
$403$	17.4248	−	30.1806i	0.867990	−	1.50340i
$404$	−4.39149	−	7.60629i	−0.218485	−	0.378427i
$405$		0			0
$406$	−5.03265	−	5.42723i	−0.249766	−	0.269349i
$407$			1.09331i			0.0541933i
$408$		0			0
$409$	−20.1583	−	11.6384i	−0.996764	−	0.575482i	−0.0894746	−	0.995989i	$-0.528519\pi$
$409$	−20.1583	−	11.6384i	−0.996764	−	0.575482i	−0.907289	+	0.420507i	$0.861852\pi$
$410$	−19.1094	−	11.0328i	−0.943744	−	0.544871i
$411$		0			0
$412$			2.04021i			0.100514i
$413$	0.815367	−	2.64049i	0.0401216	−	0.129930i
$414$		0			0
$415$	12.7790	+	22.1339i	0.627297	+	1.08651i
$416$	−17.0334	+	29.5027i	−0.835131	+	1.44649i
$417$		0			0
$418$	−3.74778	+	2.16378i	−0.183310	+	0.105834i
$419$	−11.9792			−0.585224			−0.292612	−	0.956231i	$-0.594524\pi$
$419$	−11.9792			−0.585224			−0.292612	+	0.956231i	$0.594524\pi$
$420$		0			0
$421$	−7.69266			−0.374917			−0.187459	−	0.982272i	$-0.560025\pi$
$421$	−7.69266			−0.374917			−0.187459	+	0.982272i	$0.560025\pi$
$422$	−14.9996	+	8.66002i	−0.730169	+	0.421563i
$423$		0			0
$424$	3.29165	−	5.70131i	0.159857	−	0.276880i
$425$	32.0134	+	55.4488i	1.55288	+	2.68966i
$426$		0			0
$427$	−3.91645	+	3.63171i	−0.189530	+	0.175751i
$428$			3.24934i			0.157063i
$429$		0			0
$430$	−36.5402	−	21.0965i	−1.76213	−	1.01736i
$431$	0.131704	+	0.0760393i	0.00634396	+	0.00366269i	0.503169	−	0.864188i	$-0.332167\pi$
$431$	0.131704	+	0.0760393i	0.00634396	+	0.00366269i	−0.496825	+	0.867851i	$0.665501\pi$
$432$		0			0
$433$		−	30.0655i		−	1.44486i	−0.691445	−	0.722429i	$-0.743026\pi$
$433$		−	30.0655i		−	1.44486i	0.691445	−	0.722429i	$-0.256974\pi$
$434$	13.3227	−	3.03653i	0.639508	−	0.145758i
$435$		0			0
$436$	5.74216	+	9.94572i	0.275000	+	0.476313i
$437$	−0.0788428	+	0.136560i	−0.00377156	+	0.00653254i
$438$		0			0
$439$	−27.9617	+	16.1437i	−1.33454	+	0.770496i	−0.985992	−	0.166795i	$-0.946658\pi$
$439$	−27.9617	+	16.1437i	−1.33454	+	0.770496i	−0.348547	+	0.937291i	$0.613325\pi$
$440$	−59.0297			−2.81413
$441$		0			0
$442$	−27.0352			−1.28594
$443$	0.188948	−	0.109089i	0.00897721	−	0.00518300i	−0.495505	−	0.868605i	$-0.665017\pi$
$443$	0.188948	−	0.109089i	0.00897721	−	0.00518300i	0.504482	+	0.863422i	$0.331684\pi$
$444$		0			0
$445$	6.76566	−	11.7185i	0.320723	−	0.555509i
$446$	5.13452	+	8.89324i	0.243126	+	0.421107i
$447$		0			0
$448$	−15.9364	+	3.63226i	−0.752923	+	0.171608i
$449$			14.6530i			0.691516i	0.938324	+	0.345758i	$0.112378\pi$
$449$			14.6530i			0.691516i	−0.938324	+	0.345758i	$0.887622\pi$
$450$		0			0
$451$	−21.0644	−	12.1615i	−0.991883	−	0.572664i
$452$	−14.5765	−	8.41576i	−0.685622	−	0.395844i
$453$		0			0
$454$		−	15.1783i		−	0.712352i
$455$	54.3558	−	50.4039i	2.54824	−	2.36297i
$456$		0			0
$457$	10.4140	+	18.0375i	0.487146	+	0.843761i	0.999891	−	0.0147800i	$-0.00470478\pi$
$457$	10.4140	+	18.0375i	0.487146	+	0.843761i	−0.512745	+	0.858541i	$0.671371\pi$
$458$	5.54824	−	9.60984i	0.259252	−	0.449038i
$459$		0			0
$460$	−0.663304	+	0.382959i	−0.0309267	+	0.0178555i
$461$	31.3041			1.45798			0.728989	−	0.684525i	$-0.239991\pi$
$461$	31.3041			1.45798			0.728989	+	0.684525i	$0.239991\pi$
$462$		0			0
$463$	13.4894			0.626904			0.313452	−	0.949604i	$-0.398514\pi$
$463$	13.4894			0.626904			0.313452	+	0.949604i	$0.398514\pi$
$464$	1.44675	−	0.835284i	0.0671639	−	0.0387771i
$465$		0			0
$466$	−5.31507	+	9.20597i	−0.246216	+	0.426458i
$467$	13.3713	+	23.1598i	0.618750	+	1.07171i	0.989714	+	0.143059i	$0.0456939\pi$
$467$	13.3713	+	23.1598i	0.618750	+	1.07171i	−0.370964	+	0.928647i	$0.620973\pi$
$468$		0			0
$469$	−2.95891	+	9.58217i	−0.136630	+	0.442464i
$470$			5.88975i			0.271674i
$471$		0			0
$472$	2.65650	+	1.53373i	0.122276	+	0.0705958i
$473$	−40.2785	−	23.2548i	−1.85201	−	1.06926i
$474$		0			0
$475$		−	14.2860i		−	0.655485i
$476$	8.91757	+	9.61674i	0.408736	+	0.440782i
$477$		0			0
$478$	−1.75611	−	3.04168i	−0.0803227	−	0.139123i
$479$	−2.53359	+	4.38830i	−0.115762	+	0.200506i	−0.918084	−	0.396385i	$-0.870264\pi$
$479$	−2.53359	+	4.38830i	−0.115762	+	0.200506i	0.802322	+	0.596892i	$0.203598\pi$
$480$		0			0
$481$	1.31980	−	0.761986i	0.0601777	−	0.0347436i
$482$	8.52392			0.388254
$483$		0			0
$484$	−11.0041			−0.500188
$485$	−48.8502	+	28.2037i	−2.21817	+	1.28066i
$486$		0			0
$487$	−3.03860	+	5.26301i	−0.137692	+	0.238490i	−0.926623	−	0.375993i	$-0.877302\pi$
$487$	−3.03860	+	5.26301i	−0.137692	+	0.238490i	0.788931	+	0.614482i	$0.210635\pi$
$488$	−2.96430	−	5.13432i	−0.134188	−	0.232420i
$489$		0			0
$490$	28.9830	+	2.18977i	1.30932	+	0.0989237i
$491$			7.90635i			0.356809i	0.983957	+	0.178404i	$0.0570935\pi$
$491$			7.90635i			0.356809i	−0.983957	+	0.178404i	$0.942906\pi$
$492$		0			0
$493$	−11.4840	−	6.63031i	−0.517215	−	0.298614i
$494$	5.22407	+	3.01612i	0.235042	+	0.135702i
$495$		0			0
$496$			3.08412i			0.138481i
$497$	−8.28740	−	36.3606i	−0.371741	−	1.63100i
$498$		0			0
$499$	4.60059	+	7.96846i	0.205951	+	0.356717i	0.950435	−	0.310923i	$-0.100638\pi$
$499$	4.60059	+	7.96846i	0.205951	+	0.356717i	−0.744484	+	0.667640i	$0.767305\pi$
$500$	22.5521	−	39.0614i	1.00856	−	1.74688i
$501$		0			0
$502$	−9.07821	+	5.24130i	−0.405180	+	0.233931i
$503$	−9.86027			−0.439648			−0.219824	−	0.975540i	$-0.570548\pi$
$503$	−9.86027			−0.439648			−0.219824	+	0.975540i	$0.570548\pi$
$504$		0			0
$505$	−34.8734			−1.55185
$506$	0.590971	−	0.341197i	0.0262719	−	0.0151681i
$507$		0			0
$508$	8.19914	−	14.2013i	0.363778	−	0.630082i
$509$	−9.97012	−	17.2688i	−0.441918	−	0.765424i	0.555914	−	0.831240i	$-0.312368\pi$
$509$	−9.97012	−	17.2688i	−0.441918	−	0.765424i	−0.997832	+	0.0658157i	$0.979035\pi$
$510$		0			0
$511$	−33.7321	−	10.4163i	−1.49222	−	0.460788i
$512$		−	6.33111i		−	0.279798i
$513$		0			0
$514$	25.0029	+	14.4354i	1.10283	+	0.636720i
$515$	7.01546	+	4.05038i	0.309138	+	0.178481i
$516$		0			0
$517$			6.49231i			0.285531i
$518$	0.570941	+	0.176303i	0.0250857	+	0.00774630i
$519$		0			0
$520$	41.1411	+	71.2584i	1.80415	+	3.12489i
$521$	−7.18249	+	12.4404i	−0.314671	+	0.545026i	−0.979367	−	0.202088i	$-0.935227\pi$
$521$	−7.18249	+	12.4404i	−0.314671	+	0.545026i	0.664697	+	0.747113i	$0.268561\pi$
$522$		0			0
$523$	15.2401	−	8.79888i	0.666403	−	0.384748i	−0.128309	−	0.991734i	$-0.540955\pi$
$523$	15.2401	−	8.79888i	0.666403	−	0.384748i	0.794712	+	0.606986i	$0.207622\pi$
$524$	12.1734			0.531796
$525$		0			0
$526$	−19.6461			−0.856610
$527$	21.2013	−	12.2406i	0.923542	−	0.533207i
$528$		0			0
$529$	−11.4876	+	19.8971i	−0.499459	+	0.865089i
$530$	−4.65402	−	8.06100i	−0.202158	−	0.350148i
$531$		0			0
$532$	−0.650291	−	2.85312i	−0.0281937	−	0.123699i
$533$			33.9041i			1.46855i
$534$		0			0
$535$	11.1732	+	6.45084i	0.483059	+	0.278894i
$536$	−9.64027	−	5.56581i	−0.416396	−	0.240406i
$537$		0			0
$538$		−	12.5704i		−	0.541950i
$539$	31.9481	+	2.41380i	1.37610	+	0.103970i
$540$		0			0
$541$	−10.5770	−	18.3199i	−0.454740	−	0.787633i	0.543933	−	0.839129i	$-0.316935\pi$
$541$	−10.5770	−	18.3199i	−0.454740	−	0.787633i	−0.998673	+	0.0514956i	$0.983601\pi$
$542$	2.51982	−	4.36445i	0.108235	−	0.187469i
$543$		0			0
$544$	−20.7251	+	11.9656i	−0.888579	+	0.513021i
$545$	45.5992			1.95325
$546$		0			0
$547$	12.2565			0.524048			0.262024	−	0.965061i	$-0.415610\pi$
$547$	12.2565			0.524048			0.262024	+	0.965061i	$0.415610\pi$
$548$	2.48092	−	1.43236i	0.105980	−	0.0611874i
$549$		0			0
$550$	−30.9117	+	53.5407i	−1.31808	+	2.28298i
$551$	1.47939	+	2.56237i	0.0630240	+	0.109161i
$552$		0			0
$553$	−22.6829	−	24.4614i	−0.964576	−	1.04020i
$554$			3.74411i			0.159072i
$555$		0			0
$556$	−6.44560	−	3.72137i	−0.273354	−	0.157821i
$557$	25.1493	+	14.5199i	1.06561	+	0.615229i	0.926978	−	0.375115i	$-0.122397\pi$
$557$	25.1493	+	14.5199i	1.06561	+	0.615229i	0.138630	+	0.990344i	$0.455730\pi$
$558$		0			0
$559$			64.8303i			2.74203i
$560$	−1.93559	+	6.26823i	−0.0817936	+	0.264881i
$561$		0			0
$562$	−2.30807	−	3.99769i	−0.0973599	−	0.168632i
$563$	11.0207	−	19.0884i	0.464467	−	0.804480i	−0.534711	−	0.845035i	$-0.679579\pi$
$563$	11.0207	−	19.0884i	0.464467	−	0.804480i	0.999177	+	0.0405553i	$0.0129127\pi$
$564$		0			0
$565$	−57.8770	+	33.4153i	−2.43490	+	1.40579i
$566$	−12.2545			−0.515094
$567$		0			0
$568$	41.3948			1.73689
$569$	18.6309	−	10.7566i	0.781049	−	0.450939i	−0.0557531	−	0.998445i	$-0.517756\pi$
$569$	18.6309	−	10.7566i	0.781049	−	0.450939i	0.836802	+	0.547506i	$0.184423\pi$
$570$		0			0
$571$	15.3103	−	26.5182i	0.640715	−	1.10975i	−0.344558	−	0.938765i	$-0.611971\pi$
$571$	15.3103	−	26.5182i	0.640715	−	1.10975i	0.985273	−	0.170986i	$-0.0546954\pi$
$572$	16.1488	+	27.9706i	0.675216	+	1.16951i
$573$		0			0
$574$	−9.74769	+	9.03900i	−0.406861	+	0.377280i
$575$			2.25269i			0.0939438i
$576$		0			0
$577$	2.37009	+	1.36837i	0.0986680	+	0.0569660i	0.548522	−	0.836136i	$-0.315191\pi$
$577$	2.37009	+	1.36837i	0.0986680	+	0.0569660i	−0.449854	+	0.893102i	$0.648524\pi$
$578$	−2.52729	−	1.45913i	−0.105121	−	0.0606919i
$579$		0			0
$580$			14.3715i			0.596743i
$581$	15.0127	−	3.42172i	0.622830	−	0.141957i
$582$		0			0
$583$	−5.13016	−	8.88570i	−0.212469	−	0.368008i
$584$	19.5933	−	33.9366i	0.810777	−	1.40431i
$585$		0			0
$586$	12.9910	−	7.50035i	0.536653	−	0.309837i
$587$	25.5993			1.05660			0.528298	−	0.849059i	$-0.322831\pi$
$587$	25.5993			1.05660			0.528298	+	0.849059i	$0.322831\pi$
$588$		0			0
$589$	−5.46235			−0.225072
$590$	3.75599	−	2.16852i	0.154632	−	0.0892767i
$591$		0			0
$592$	−0.0674344	+	0.116800i	−0.00277154	+	0.00480044i
$593$	14.8569	+	25.7329i	0.610099	+	1.05672i	0.991223	+	0.132198i	$0.0422036\pi$
$593$	14.8569	+	25.7329i	0.610099	+	1.05672i	−0.381125	+	0.924524i	$0.624463\pi$
$594$		0			0
$595$	50.7720	−	11.5721i	2.08145	−	0.474409i
$596$			5.69469i			0.233264i
$597$		0			0
$598$	−0.823761	−	0.475599i	−0.0336861	−	0.0194487i
$599$	−14.8326	−	8.56362i	−0.606045	−	0.349900i	0.165371	−	0.986231i	$-0.447118\pi$
$599$	−14.8326	−	8.56362i	−0.606045	−	0.349900i	−0.771416	+	0.636331i	$0.780451\pi$
$600$		0			0
$601$			18.0533i			0.736408i	0.929745	+	0.368204i	$0.120027\pi$
$601$			18.0533i			0.736408i	−0.929745	+	0.368204i	$0.879973\pi$
$602$	−18.6392	+	17.2840i	−0.759676	+	0.704445i
$603$		0			0
$604$	9.02945	+	15.6395i	0.367403	+	0.636361i
$605$	−21.8463	+	37.8389i	−0.888177	+	1.53837i
$606$		0			0
$607$	10.3997	−	6.00429i	0.422112	−	0.243707i	−0.273868	−	0.961767i	$-0.588303\pi$
$607$	10.3997	−	6.00429i	0.422112	−	0.243707i	0.695981	+	0.718061i	$0.254970\pi$
$608$	5.33965			0.216552
$609$		0			0
$610$	−8.38237			−0.339392
$611$	7.83726	−	4.52485i	0.317062	−	0.183056i
$612$		0			0
$613$	−10.1295	+	17.5448i	−0.409127	+	0.708628i	−0.994792	−	0.101925i	$-0.967500\pi$
$613$	−10.1295	+	17.5448i	−0.409127	+	0.708628i	0.585665	+	0.810553i	$0.300833\pi$
$614$	−1.37734	−	2.38563i	−0.0555850	−	0.0962761i
$615$		0			0
$616$	−10.4928	+	33.9799i	−0.422766	+	1.36909i
$617$			31.4899i			1.26773i	0.773442	+	0.633867i	$0.218533\pi$
$617$			31.4899i			1.26773i	−0.773442	+	0.633867i	$0.781467\pi$
$618$		0			0
$619$	22.3703	+	12.9155i	0.899139	+	0.519118i	0.876921	−	0.480635i	$-0.159594\pi$
$619$	22.3703	+	12.9155i	0.899139	+	0.519118i	0.0222180	+	0.999753i	$0.492927\pi$
$620$	−22.9773	−	13.2660i	−0.922792	−	0.532774i
$621$		0			0
$622$		−	13.1372i		−	0.526754i
$623$	−5.54300	−	5.97759i	−0.222076	−	0.239487i
$624$		0			0
$625$	−53.8296	−	93.2356i	−2.15318	−	3.72942i
$626$	−0.00688359	+	0.0119227i	−0.000275124	+	0.000476528i
$627$		0			0
$628$	−19.6346	+	11.3360i	−0.783505	+	0.452357i
$629$	1.07056			0.0426860
$630$		0			0
$631$	−37.4236			−1.48981			−0.744905	−	0.667171i	$-0.767505\pi$
$631$	−37.4236			−1.48981			−0.744905	+	0.667171i	$0.767505\pi$
$632$	32.0679	−	18.5144i	1.27559	−	0.736465i
$633$		0			0
$634$	−5.04016	+	8.72981i	−0.200170	+	0.346705i
$635$	−32.5552	−	56.3872i	−1.29191	−	2.23766i
$636$		0			0
$637$	−19.3526	−	40.2489i	−0.766777	−	1.59472i
$638$		−	12.8043i		−	0.506926i
$639$		0			0
$640$	18.4006	+	10.6236i	0.727347	+	0.419934i
$641$	15.5572	+	8.98196i	0.614473	+	0.354766i	0.774714	−	0.632312i	$-0.217894\pi$
$641$	15.5572	+	8.98196i	0.614473	+	0.354766i	−0.160241	+	0.987078i	$0.551227\pi$
$642$		0			0
$643$			3.51267i			0.138526i	0.997598	+	0.0692631i	$0.0220648\pi$
$643$			3.51267i			0.138526i	−0.997598	+	0.0692631i	$0.977935\pi$
$644$	0.102542	+	0.449897i	0.00404070	+	0.0177284i
$645$		0			0
$646$	2.11876	+	3.66980i	0.0833616	+	0.144386i
$647$	−11.6928	+	20.2525i	−0.459691	+	0.796208i	−0.998944	−	0.0459353i	$-0.985373\pi$
$647$	−11.6928	+	20.2525i	−0.459691	+	0.796208i	0.539253	+	0.842144i	$0.318707\pi$
$648$		0			0
$649$	4.14026	−	2.39038i	0.162519	−	0.0938306i
$650$	86.1764			3.38011
$651$		0			0
$652$	8.15699			0.319453
$653$	−9.07228	+	5.23789i	−0.355026	+	0.204974i	−0.666897	−	0.745150i	$-0.732378\pi$
$653$	−9.07228	+	5.23789i	−0.355026	+	0.204974i	0.311871	+	0.950125i	$0.399044\pi$
$654$		0			0
$655$	24.1676	−	41.8594i	0.944305	−	1.63558i
$656$	−1.50023	−	2.59847i	−0.0585740	−	0.101453i
$657$		0			0
$658$	3.39037	+	1.04693i	0.132171	+	0.0408134i
$659$		−	41.9627i		−	1.63464i	−0.576187	−	0.817318i	$-0.695460\pi$
$659$		−	41.9627i		−	1.63464i	0.576187	−	0.817318i	$-0.304540\pi$
$660$		0			0
$661$	−39.6356	−	22.8836i	−1.54165	−	0.890070i	−0.998735	−	0.0502795i	$-0.983989\pi$
$661$	−39.6356	−	22.8836i	−1.54165	−	0.890070i	−0.542911	−	0.839790i	$-0.682678\pi$
$662$	−13.0459	−	7.53204i	−0.507042	−	0.292741i
$663$		0			0
$664$			17.0912i			0.663267i
$665$	−11.1018	−	3.42816i	−0.430509	−	0.132938i
$666$		0			0
$667$	−0.233278	−	0.404049i	−0.00903256	−	0.0156449i
$668$	−9.56041	+	16.5591i	−0.369903	+	0.640691i
$669$		0			0
$670$	−13.6302	+	7.86942i	−0.526582	+	0.304022i
$671$	−9.23994			−0.356704
$672$		0			0
$673$	−17.7626			−0.684697			−0.342348	−	0.939573i	$-0.611222\pi$
$673$	−17.7626			−0.684697			−0.342348	+	0.939573i	$0.611222\pi$
$674$	3.31480	−	1.91380i	0.127681	−	0.0737168i
$675$		0			0
$676$	15.3208	−	26.5363i	0.589260	−	1.02063i
$677$	10.6969	+	18.5276i	0.411117	+	0.712075i	0.995012	−	0.0997540i	$-0.0318056\pi$
$677$	10.6969	+	18.5276i	0.411117	+	0.712075i	−0.583896	+	0.811829i	$0.698472\pi$
$678$		0			0
$679$	7.55186	+	33.1335i	0.289814	+	1.27155i
$680$			57.8015i			2.21659i
$681$		0			0
$682$	20.4717	+	11.8193i	0.783901	+	0.452585i
$683$	5.00763	+	2.89116i	0.191612	+	0.110627i	0.592737	−	0.805396i	$-0.298047\pi$
$683$	5.00763	+	2.89116i	0.191612	+	0.110627i	−0.401125	+	0.916023i	$0.631381\pi$
$684$		0			0
$685$		−	11.3745i		−	0.434599i
$686$	6.41236	−	16.2945i	0.244825	−	0.622128i
$687$		0			0
$688$	−2.86868	−	4.96870i	−0.109367	−	0.189430i
$689$	−7.15098	+	12.3859i	−0.272431	+	0.471864i
$690$		0			0
$691$	2.84337	−	1.64162i	0.108167	−	0.0624502i	−0.444941	−	0.895560i	$-0.646775\pi$
$691$	2.84337	−	1.64162i	0.108167	−	0.0624502i	0.553107	+	0.833110i	$0.313442\pi$
$692$	−14.8181			−0.563300
$693$		0			0
$694$	33.8563			1.28517
$695$	−25.5926	+	14.7759i	−0.970784	+	0.560482i
$696$		0			0
$697$	−11.9085	+	20.6261i	−0.451066	+	0.781270i
$698$	6.11867	+	10.5978i	0.231595	+	0.401134i
$699$		0			0
$700$	−28.4252	−	30.6539i	−1.07437	−	1.15861i
$701$			25.1286i			0.949095i	0.880230	+	0.474547i	$0.157388\pi$
$701$			25.1286i			0.949095i	−0.880230	+	0.474547i	$0.842612\pi$
$702$		0			0
$703$	−0.206866	−	0.119434i	−0.00780211	−	0.00450455i
$704$	−24.4879	−	14.1381i	−0.922923	−	0.532850i
$705$		0			0
$706$			2.62342i			0.0987337i
$707$	−6.19888	+	20.0745i	−0.233133	+	0.754980i
$708$		0			0
$709$	−15.8309	−	27.4199i	−0.594541	−	1.02978i	−0.993611	−	0.112856i	$-0.964000\pi$
$709$	−15.8309	−	27.4199i	−0.594541	−	1.02978i	0.399070	−	0.916920i	$-0.369333\pi$
$710$	29.2638	−	50.6864i	1.09825	−	1.90223i
$711$		0			0
$712$	7.83640	−	4.52435i	0.293682	−	0.169557i
$713$	0.861334			0.0322572
$714$		0			0
$715$	128.240			4.79589
$716$	−3.21350	+	1.85531i	−0.120094	+	0.0693364i
$717$		0			0
$718$	−9.23802	+	16.0007i	−0.344760	+	0.597142i
$719$	16.8896	+	29.2537i	0.629876	+	1.09098i	0.987576	+	0.157141i	$0.0502277\pi$
$719$	16.8896	+	29.2537i	0.629876	+	1.09098i	−0.357700	+	0.933837i	$0.616439\pi$
$720$		0			0
$721$	3.57859	−	3.31841i	0.133274	−	0.123584i
$722$		−	0.945497i		−	0.0351878i
$723$		0			0
$724$	2.02026	+	1.16640i	0.0750823	+	0.0433488i
$725$	36.6060	+	21.1345i	1.35951	+	0.784915i
$726$		0			0
$727$			28.1007i			1.04220i	0.853497	+	0.521098i	$0.174477\pi$
$727$			28.1007i			1.04220i	−0.853497	+	0.521098i	$0.825523\pi$
$728$	48.3322	−	11.0160i	1.79131	−	0.408280i
$729$		0			0
$730$	−27.7027	−	47.9825i	−1.02532	−	1.77591i
$731$	−22.7710	+	39.4405i	−0.842215	+	1.45876i
$732$		0			0
$733$	9.77954	−	5.64622i	0.361216	−	0.208548i	−0.308398	−	0.951257i	$-0.599793\pi$
$733$	9.77954	−	5.64622i	0.361216	−	0.208548i	0.669614	+	0.742709i	$0.266460\pi$
$734$	−21.8569			−0.806755
$735$		0			0
$736$	−0.841987			−0.0310360
$737$	−15.0247	+	8.67452i	−0.553442	+	0.319530i
$738$		0			0
$739$	14.4941	−	25.1046i	0.533176	−	0.923487i	−0.466074	−	0.884746i	$-0.654332\pi$
$739$	14.4941	−	25.1046i	0.533176	−	0.923487i	0.999249	−	0.0387413i	$-0.0123348\pi$
$740$	−0.580121	−	1.00480i	−0.0213257	−	0.0369372i
$741$		0			0
$742$	−5.46751	+	1.24617i	−0.200719	+	0.0457482i
$743$			46.3312i			1.69973i	0.527002	+	0.849864i	$0.323316\pi$
$743$			46.3312i			1.69973i	−0.527002	+	0.849864i	$0.676684\pi$
$744$		0			0
$745$	19.5818	+	11.3056i	0.717421	+	0.414203i
$746$	4.72488	+	2.72791i	0.172990	+	0.0998760i
$747$		0			0
$748$			22.6884i			0.829571i
$749$	5.69944	−	5.28507i	0.208253	−	0.193112i
$750$		0			0
$751$	13.8732	+	24.0291i	0.506240	+	0.876834i	0.999974	+	0.00722046i	$0.00229836\pi$
$751$	13.8732	+	24.0291i	0.506240	+	0.876834i	−0.493734	+	0.869613i	$0.664368\pi$
$752$	−0.400441	+	0.693583i	−0.0146026	+	0.0252924i
$753$		0			0
$754$	−15.4568	+	8.92401i	−0.562905	+	0.324993i
$755$	71.7040			2.60957
$756$		0			0
$757$	−17.3649			−0.631138			−0.315569	−	0.948903i	$-0.602195\pi$
$757$	−17.3649			−0.631138			−0.315569	+	0.948903i	$0.602195\pi$
$758$	−4.11520	+	2.37591i	−0.149471	+	0.0862971i
$759$		0			0
$760$	6.44848	−	11.1691i	0.233911	−	0.405146i
$761$	−18.0260	−	31.2219i	−0.653441	−	1.13179i	−0.982282	−	0.187407i	$-0.939992\pi$
$761$	−18.0260	−	31.2219i	−0.653441	−	1.13179i	0.328842	−	0.944385i	$-0.393342\pi$
$762$		0			0
$763$	8.10544	−	26.2487i	0.293437	−	0.950268i
$764$			8.44924i			0.305683i
$765$		0			0
$766$	0.792688	+	0.457659i	0.0286410	+	0.0165359i
$767$	−5.77115	−	3.33197i	−0.208384	−	0.120311i
$768$		0			0
$769$			17.5626i			0.633323i	0.948539	+	0.316661i	$0.102562\pi$
$769$			17.5626i			0.633323i	−0.948539	+	0.316661i	$0.897438\pi$
$770$	34.1893	+	36.8698i	1.23210	+	1.32870i
$771$		0			0
$772$	−8.01016	−	13.8740i	−0.288292	−	0.499337i
$773$	−15.7233	+	27.2336i	−0.565529	+	0.979525i	0.431471	+	0.902127i	$0.357995\pi$
$773$	−15.7233	+	27.2336i	−0.565529	+	0.979525i	−0.997000	+	0.0773981i	$0.975339\pi$
$774$		0			0
$775$	−67.5802	+	39.0175i	−2.42755	+	1.40155i
$776$	−37.7209			−1.35410
$777$		0			0
$778$	11.4142			0.409218
$779$	4.60220	−	2.65708i	0.164891	−	0.0951998i
$780$		0			0
$781$	32.2577	−	55.8719i	1.15427	−	1.99925i
$782$	−0.334098	−	0.578675i	−0.0119473	−	0.0206934i
$783$		0			0
$784$	3.26419	+	2.22841i	0.116578	+	0.0795859i
$785$			90.0208i			3.21298i
$786$		0			0
$787$	43.4273	+	25.0727i	1.54801	+	0.893747i	0.998293	+	0.0583986i	$0.0185994\pi$
$787$	43.4273	+	25.0727i	1.54801	+	0.893747i	0.549721	+	0.835348i	$0.314734\pi$
$788$	−7.12526	−	4.11377i	−0.253827	−	0.146547i
$789$		0			0
$790$		−	52.3546i		−	1.86269i
$791$	8.94732	+	39.2560i	0.318130	+	1.39578i
$792$		0			0
$793$	6.43982	+	11.1541i	0.228685	+	0.396094i
$794$	7.07134	−	12.2479i	0.250952	−	0.434662i
$795$		0			0
$796$	−6.97740	+	4.02840i	−0.247307	+	0.142783i
$797$	−29.7494			−1.05378			−0.526890	−	0.849934i	$-0.676642\pi$
$797$	−29.7494			−1.05378			−0.526890	+	0.849934i	$0.676642\pi$
$798$		0			0
$799$	6.35723			0.224902
$800$	66.0623	−	38.1411i	2.33565	−	1.34849i
$801$		0			0
$802$	15.7641	−	27.3043i	0.556651	−	0.964147i
$803$	−30.5369	−	52.8914i	−1.07762	−	1.86650i
$804$		0			0
$805$	1.75059	+	0.540571i	0.0617002	+	0.0190526i
$806$		−	32.9502i		−	1.16062i
$807$		0			0
$808$	−20.1962	−	11.6603i	−0.710501	−	0.410208i
$809$	2.18411	+	1.26100i	0.0767893	+	0.0443343i	0.537903	−	0.843007i	$-0.319217\pi$
$809$	2.18411	+	1.26100i	0.0767893	+	0.0443343i	−0.461114	+	0.887341i	$0.652550\pi$
$810$		0			0
$811$			0.490806i			0.0172345i	0.999963	+	0.00861727i	$0.00274300\pi$
$811$			0.490806i			0.0172345i	−0.999963	+	0.00861727i	$0.997257\pi$
$812$	8.27280	+	2.55459i	0.290318	+	0.0896484i
$813$		0			0
$814$	0.516860	+	0.895227i	0.0181159	+	0.0313777i
$815$	16.1939	−	28.0487i	0.567248	−	0.982503i
$816$		0			0
$817$	8.80016	−	5.08077i	0.307879	−	0.177754i
$818$	−22.0081			−0.769497
$819$		0			0
$820$	25.8122			0.901400
$821$	19.0300	−	10.9870i	0.664150	−	0.383447i	−0.129706	−	0.991552i	$-0.541403\pi$
$821$	19.0300	−	10.9870i	0.664150	−	0.383447i	0.793856	+	0.608105i	$0.208070\pi$
$822$		0			0
$823$	−11.2316	+	19.4537i	−0.391508	+	0.678112i	−0.992649	−	0.121032i	$-0.961380\pi$
$823$	−11.2316	+	19.4537i	−0.391508	+	0.678112i	0.601141	+	0.799143i	$0.294713\pi$
$824$	2.70858	+	4.69140i	0.0943578	+	0.163433i
$825$		0			0
$826$	−0.580647	−	2.54756i	−0.0202033	−	0.0886411i
$827$		−	40.7302i		−	1.41633i	−0.706048	−	0.708164i	$-0.749524\pi$
$827$		−	40.7302i		−	1.41633i	0.706048	−	0.708164i	$-0.250476\pi$
$828$		0			0
$829$	−44.9299	−	25.9403i	−1.56048	−	0.900944i	−0.997208	−	0.0746733i	$-0.976209\pi$
$829$	−44.9299	−	25.9403i	−1.56048	−	0.900944i	−0.563273	−	0.826271i	$-0.690458\pi$
$830$	20.9275	+	12.0825i	0.726405	+	0.419390i
$831$		0			0
$832$			39.4145i			1.36645i
$833$	2.36358	−	31.2834i	0.0818930	−	1.08391i
$834$		0			0
$835$	37.9602	+	65.7490i	1.31367	+	2.27534i
$836$	2.53118	−	4.38413i	0.0875426	−	0.151628i
$837$		0			0
$838$	−9.80890	+	5.66317i	−0.338843	+	0.195631i
$839$	9.44078			0.325932			0.162966	−	0.986632i	$-0.447894\pi$
$839$	9.44078			0.325932			0.162966	+	0.986632i	$0.447894\pi$
$840$		0			0
$841$	20.2457			0.698126
$842$	−6.29894	+	3.63669i	−0.217076	+	0.125329i
$843$		0			0
$844$	10.1304	−	17.5464i	0.348704	−	0.603972i
$845$	−60.8320	−	105.364i	−2.09268	−	3.62464i
$846$		0			0
$847$	17.8983	+	19.3016i	0.614993	+	0.663211i
$848$		−	1.26570i		−	0.0434642i
$849$		0			0
$850$	52.4267	+	30.2686i	1.79822	+	1.03820i
$851$	0.0326198	+	0.0188331i	0.00111819	+	0.000645590i
$852$		0			0
$853$			49.5038i			1.69498i	0.530812	+	0.847490i	$0.321887\pi$
$853$			49.5038i			1.69498i	−0.530812	+	0.847490i	$0.678113\pi$
$854$	−1.49000	+	4.82523i	−0.0509867	+	0.165116i
$855$		0			0
$856$	4.31382	+	7.47176i	0.147443	+	0.255379i
$857$	−9.54984	+	16.5408i	−0.326216	+	0.565023i	−0.981758	−	0.190136i	$-0.939107\pi$
$857$	−9.54984	+	16.5408i	−0.326216	+	0.565023i	0.655542	+	0.755159i	$0.272440\pi$
$858$		0			0
$859$	−5.79649	+	3.34661i	−0.197774	+	0.114185i	−0.595617	−	0.803269i	$-0.703092\pi$
$859$	−5.79649	+	3.34661i	−0.197774	+	0.114185i	0.397843	+	0.917454i	$0.369759\pi$
$860$	49.3571			1.68306
$861$		0			0
$862$	0.143790			0.00489750
$863$	−7.60632	+	4.39151i	−0.258922	+	0.149489i	−0.623843	−	0.781550i	$-0.714429\pi$
$863$	−7.60632	+	4.39151i	−0.258922	+	0.149489i	0.364921	+	0.931039i	$0.381096\pi$
$864$		0			0
$865$	−29.4181	+	50.9536i	−1.00025	+	1.73248i
$866$	−14.2134	−	24.6184i	−0.482992	−	0.836567i
$867$		0			0
$868$	−11.7207	+	10.8686i	−0.397828	+	0.368904i
$869$		−	57.7108i		−	1.95771i
$870$		0			0
$871$	20.9431	+	12.0915i	0.709630	+	0.409705i
$872$	26.4079	+	15.2466i	0.894284	+	0.516315i
$873$		0			0
$874$			0.149091i			0.00504309i
$875$	−105.196	+	23.9766i	−3.55628	+	0.810556i
$876$		0			0
$877$	−26.1669	−	45.3224i	−0.883593	−	1.53043i	−0.847318	−	0.531086i	$-0.821784\pi$
$877$	−26.1669	−	45.3224i	−0.883593	−	1.53043i	−0.0362747	−	0.999342i	$-0.511549\pi$
$878$	−15.2638	+	26.4377i	−0.515129	+	0.892229i
$879$		0			0
$880$	−9.82850	+	5.67449i	−0.331319	+	0.191287i
$881$	−25.4829			−0.858541			−0.429271	−	0.903176i	$-0.641229\pi$
$881$	−25.4829			−0.858541			−0.429271	+	0.903176i	$0.641229\pi$
$882$		0			0
$883$	−25.4364			−0.856004			−0.428002	−	0.903778i	$-0.640782\pi$
$883$	−25.4364			−0.856004			−0.428002	+	0.903778i	$0.640782\pi$
$884$	27.3886	−	15.8128i	0.921178	−	0.531842i
$885$		0			0
$886$	0.103144	−	0.178650i	0.00346518	−	0.00600187i
$887$	17.8029	+	30.8355i	0.597763	+	1.03536i	0.993151	+	0.116842i	$0.0372770\pi$
$887$	17.8029	+	30.8355i	0.597763	+	1.03536i	−0.395388	+	0.918514i	$0.629390\pi$
$888$		0			0
$889$	−38.2456	+	8.71701i	−1.28271	+	0.292359i
$890$		−	12.7938i		−	0.428850i
$891$		0			0
$892$	−10.4032	−	6.00632i	−0.348327	−	0.201106i
$893$	−1.22842	−	0.709228i	−0.0411075	−	0.0237334i
$894$		0			0
$895$			14.7333i			0.492479i
$896$	9.38614	−	8.70373i	0.313569	−	0.290771i
$897$		0			0
$898$	6.92716	+	11.9982i	0.231162	+	0.400385i
$899$	8.08092	−	13.9966i	0.269514	−	0.466812i
$900$		0			0
$901$	−8.70082	+	5.02342i	−0.289866	+	0.167354i
$902$	−22.9974			−0.765729
$903$		0			0
$904$	−44.6911			−1.48640
$905$	8.02156	−	4.63125i	0.266646	−	0.153948i
$906$		0			0
$907$	0.883792	−	1.53077i	0.0293458	−	0.0508285i	−0.850979	−	0.525199i	$-0.823991\pi$
$907$	0.883792	−	1.53077i	0.0293458	−	0.0508285i	0.880325	+	0.474370i	$0.157324\pi$
$908$	8.87771	+	15.3767i	0.294617	+	0.510292i
$909$		0			0
$910$	20.6795	−	66.9686i	0.685517	−	2.21999i
$911$			27.1398i			0.899181i	0.893235	+	0.449590i	$0.148430\pi$
$911$			27.1398i			0.899181i	−0.893235	+	0.449590i	$0.851570\pi$
$912$		0			0
$913$	23.0685	+	13.3186i	0.763457	+	0.440782i
$914$	17.0544	+	9.84639i	0.564111	+	0.325690i
$915$		0			0
$916$			12.9806i			0.428891i
$917$	−19.8001	−	21.3525i	−0.653857	−	0.705122i
$918$		0			0
$919$	9.37866	+	16.2443i	0.309374	+	0.535851i	0.978225	−	0.207545i	$-0.0665473\pi$
$919$	9.37866	+	16.2443i	0.309374	+	0.535851i	−0.668852	+	0.743396i	$0.733214\pi$
$920$	−1.01683	+	1.76121i	−0.0335240	+	0.0580652i
$921$		0			0
$922$	25.6326	−	14.7990i	0.844164	−	0.487378i
$923$	−89.9286			−2.96004
$924$		0			0
$925$	−3.41247			−0.112201
$926$	11.0454	−	6.37708i	0.362975	−	0.209564i
$927$		0			0
$928$	−7.89941	+	13.6822i	−0.259311	+	0.449140i
$929$	−0.824754	−	1.42852i	−0.0270593	−	0.0468681i	0.852179	−	0.523251i	$-0.175281\pi$
$929$	−0.824754	−	1.42852i	−0.0270593	−	0.0468681i	−0.879238	+	0.476383i	$0.841948\pi$
$930$		0			0
$931$	−3.94677	+	5.78126i	−0.129350	+	0.189473i
$932$		−	12.4351i		−	0.407324i
$933$		0			0
$934$	21.8975	+	12.6425i	0.716508	+	0.413676i
$935$	78.0165	+	45.0429i	2.55141	+	1.47306i
$936$		0			0
$937$		−	47.7861i		−	1.56110i	−0.625092	−	0.780551i	$-0.714938\pi$
$937$		−	47.7861i		−	1.56110i	0.625092	−	0.780551i	$-0.285062\pi$
$938$	2.10713	+	9.24494i	0.0688002	+	0.301858i
$939$		0			0
$940$	−3.44489	−	5.96673i	−0.112360	−	0.194613i
$941$	−28.1223	+	48.7092i	−0.916760	+	1.58788i	−0.112456	+	0.993657i	$0.535872\pi$
$941$	−28.1223	+	48.7092i	−0.916760	+	1.58788i	−0.804304	+	0.594218i	$0.797461\pi$
$942$		0			0
$943$	−0.725701	+	0.418983i	−0.0236321	+	0.0136440i
$944$	0.589747			0.0191946
$945$		0			0
$946$	−43.9747			−1.42974
$947$	−29.7254	+	17.1620i	−0.965945	+	0.557689i	−0.897998	−	0.440000i	$-0.854978\pi$
$947$	−29.7254	+	17.1620i	−0.965945	+	0.557689i	−0.0679476	+	0.997689i	$0.521645\pi$
$948$		0			0
$949$	−42.5657	+	73.7259i	−1.38174	+	2.39324i
$950$	−6.75367	−	11.6977i	−0.219118	−	0.379524i
$951$		0			0
$952$	33.2729	+	10.2745i	1.07838	+	0.332997i
$953$			23.9953i			0.777283i	0.921389	+	0.388642i	$0.127056\pi$
$953$			23.9953i			0.777283i	−0.921389	+	0.388642i	$0.872944\pi$
$954$		0			0
$955$	29.0536	+	16.7741i	0.940153	+	0.542798i
$956$	3.55813	+	2.05429i	0.115078	+	0.0664404i
$957$		0			0
$958$			4.79099i			0.154790i
$959$	−6.54765	−	2.02187i	−0.211435	−	0.0652896i
$960$		0			0
$961$	−0.581385	−	1.00699i	−0.0187544	−	0.0324835i
$962$	0.720456	−	1.24787i	0.0232284	−	0.0402328i
$963$		0			0
$964$	−8.63533	+	4.98561i	−0.278125	+	0.160576i
$965$	−63.6097			−2.04767
$966$		0			0
$967$	−18.6336			−0.599216			−0.299608	−	0.954062i	$-0.596856\pi$
$967$	−18.6336			−0.599216			−0.299608	+	0.954062i	$0.596856\pi$
$968$	−25.3037	+	14.6091i	−0.813291	+	0.469554i
$969$		0			0
$970$	−26.6665	+	46.1877i	−0.856210	+	1.48300i
$971$	−25.5051	−	44.1762i	−0.818499	−	1.41768i	−0.906788	−	0.421587i	$-0.861473\pi$
$971$	−25.5051	−	44.1762i	−0.818499	−	1.41768i	0.0882892	−	0.996095i	$-0.471860\pi$
$972$		0			0
$973$	3.95642	+	17.3586i	0.126837	+	0.556492i
$974$			5.74597i			0.184113i
$975$		0			0
$976$	−0.987117	−	0.569913i	−0.0315969	−	0.0182425i
$977$	−48.8188	−	28.1855i	−1.56185	−	0.901735i	−0.997070	−	0.0764951i	$-0.975627\pi$
$977$	−48.8188	−	28.1855i	−1.56185	−	0.901735i	−0.564782	−	0.825240i	$-0.691040\pi$
$978$		0			0
$979$		−	14.1027i		−	0.450725i
$980$	−30.6426	+	14.7336i	−0.978841	+	0.470649i
$981$		0			0
$982$	3.73772	+	6.47391i	0.119275	+	0.206591i
$983$	1.09092	−	1.88954i	0.0347951	−	0.0602669i	−0.848103	−	0.529831i	$-0.822255\pi$
$983$	1.09092	−	1.88954i	0.0347951	−	0.0602669i	0.882899	+	0.469564i	$0.155589\pi$
$984$		0			0
$985$	−28.2913	+	16.3340i	−0.901435	+	0.520444i
$986$	−12.5379			−0.399287
$987$		0			0
$988$	−7.05646			−0.224496
$989$	−1.38766	+	0.801165i	−0.0441250	+	0.0254756i
$990$		0			0
$991$	9.54645	−	16.5349i	0.303253	−	0.525250i	−0.673618	−	0.739080i	$-0.735261\pi$
$991$	9.54645	−	16.5349i	0.303253	−	0.525250i	0.976871	+	0.213830i	$0.0685939\pi$
$992$	−14.5835	−	25.2594i	−0.463027	−	0.801986i
$993$		0			0
$994$	−23.9754	−	25.8551i	−0.760452	−	0.820075i
$995$			31.9900i			1.01415i
$996$		0			0
$997$	47.4846	+	27.4152i	1.50385	+	0.868249i	0.999990	+	0.00446426i	$0.00142102\pi$
$997$	47.4846	+	27.4152i	1.50385	+	0.868249i	0.503861	+	0.863785i	$0.331912\pi$
$998$	7.53416	+	4.34985i	0.238490	+	0.137692i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.db.a.647.30	yes	96
3.2	odd	2	inner	1197.2.db.a.647.19	✓	96
7.5	odd	6	inner	1197.2.db.a.1160.19	yes	96
21.5	even	6	inner	1197.2.db.a.1160.30	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1197.2.db.a.647.19	✓	96	3.2	odd	2	inner
1197.2.db.a.647.30	yes	96	1.1	even	1	trivial
1197.2.db.a.1160.19	yes	96	7.5	odd	6	inner
1197.2.db.a.1160.30	yes	96	21.5	even	6	inner

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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.db (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.818824 - 0.472749i) q^{2} +(-0.553018 + 0.957855i) q^{4} +(2.19579 + 3.80322i) q^{5} +(2.57960 - 0.587948i) q^{7} +2.93675i q^{8} +O(q^{10})\)	\(q+(0.818824 - 0.472749i) q^{2} +(-0.553018 + 0.957855i) q^{4} +(2.19579 + 3.80322i) q^{5} +(2.57960 - 0.587948i) q^{7} +2.93675i q^{8} +(3.59593 + 2.07611i) q^{10} +(3.96382 + 2.28851i) q^{11} -6.37996i q^{13} +(1.83429 - 1.70093i) q^{14} +(0.282308 + 0.488971i) q^{16} +(2.24090 - 3.88135i) q^{17} +(-0.866025 + 0.500000i) q^{19} -4.85724 q^{20} +4.32756 q^{22} +(0.136560 - 0.0788428i) q^{23} +(-7.14299 + 12.3720i) q^{25} +(-3.01612 - 5.22407i) q^{26} +(-0.863394 + 2.79602i) q^{28} -2.95877i q^{29} +(4.73053 + 2.73117i) q^{31} +(-4.62427 - 2.66983i) q^{32} -4.23752i q^{34} +(7.90035 + 8.51976i) q^{35} +(0.119434 + 0.206866i) q^{37} +(-0.472749 + 0.818824i) q^{38} +(-11.1691 + 6.44848i) q^{40} -5.31416 q^{41} -10.1615 q^{43} +(-4.38413 + 2.53118i) q^{44} +(0.0745457 - 0.129117i) q^{46} +(0.709228 + 1.22842i) q^{47} +(6.30864 - 3.03333i) q^{49} +13.5073i q^{50} +(6.11108 + 3.52823i) q^{52} +(-1.94137 - 1.12085i) q^{53} +20.1004i q^{55} +(1.72665 + 7.57562i) q^{56} +(-1.39876 - 2.42272i) q^{58} +(0.522256 - 0.904574i) q^{59} +(-1.74830 + 1.00938i) q^{61} +5.16463 q^{62} -6.17786 q^{64} +(24.2644 - 14.0091i) q^{65} +(-1.89523 + 3.28264i) q^{67} +(2.47851 + 4.29291i) q^{68} +(10.4967 + 3.24131i) q^{70} -14.0955i q^{71} +(-11.5559 - 6.67177i) q^{73} +(0.195591 + 0.112925i) q^{74} -1.10604i q^{76} +(11.5706 + 3.57292i) q^{77} +(-6.30440 - 10.9195i) q^{79} +(-1.23978 + 2.14735i) q^{80} +(-4.35136 + 2.51226i) q^{82} +5.81977 q^{83} +19.6822 q^{85} +(-8.32052 + 4.80386i) q^{86} +(-6.72078 + 11.6407i) q^{88} +(-1.54060 - 2.66840i) q^{89} +(-3.75108 - 16.4577i) q^{91} +0.174406i q^{92} +(1.16147 + 0.670573i) q^{94} +(-3.80322 - 2.19579i) q^{95} +12.8444i q^{97} +(3.73166 - 5.46617i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) \) 96 * q + 48 * q^4 + 8 * q^7	\( 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) \) 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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