LMFDB - Embedded newform 1197.2.db.a.647.19

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			647.19
Character	$\chi$	$=$	1197.647
Dual form			1197.2.db.a.1160.19

$q$-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	−0.760734	−	0.649063i	$-0.775161\pi$
$2$	−0.818824	+	0.472749i	−0.578996	+	0.334284i	0.181738	+	0.983347i	$0.441828\pi$
$3$		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	$-0.727174\pi$
$5$	−2.19579	−	3.80322i	−0.981987	−	1.70085i	−0.327360	−	0.944900i	$-0.606159\pi$
$6$		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	−0.235670	−	0.971833i	$-0.575728\pi$
$11$	−3.96382	−	2.28851i	−1.19514	−	0.690013i	−0.959467	+	0.281821i	$0.909062\pi$
$12$		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	$0.349567\pi$
$17$	−2.24090	+	3.88135i	−0.543497	+	0.941365i	−0.998700	+	0.0509772i	$0.983766\pi$
$18$		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	−0.514170	−	0.857688i	$-0.671900\pi$
$23$	−0.136560	+	0.0788428i	−0.0284747	+	0.0164399i	0.485695	+	0.874128i	$0.338567\pi$
$24$		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	$0.0885836\pi$
$29$			2.95877i			0.549430i	−0.961526	+	0.274715i	$0.911416\pi$
$30$		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	$-0.363793\pi$
$41$	5.31416			0.829932			0.414966	+	0.909837i	$0.363793\pi$
$42$		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	0.809653	−	0.586909i	$-0.199655\pi$
$47$	−0.709228	−	1.22842i	−0.103451	−	0.179183i	−0.913104	+	0.407726i	$0.866322\pi$
$48$		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	0.627372	−	0.778719i	$-0.284130\pi$
$53$	1.94137	+	1.12085i	0.266668	+	0.153961i	−0.360705	+	0.932680i	$0.617464\pi$
$54$		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	−0.898017	−	0.439960i	$-0.854993\pi$
$59$	−0.522256	+	0.904574i	−0.0679919	+	0.117765i	0.830025	+	0.557726i	$0.188326\pi$
$60$		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	$0.315351\pi$
$71$			14.0955i			1.67282i	−0.548101	+	0.836412i	$0.684649\pi$
$72$		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	$-0.603482\pi$
$83$	−5.81977			−0.638803			−0.319402	+	0.947619i	$0.603482\pi$
$84$		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	0.936051	−	0.351863i	$-0.114452\pi$
$89$	1.54060	+	2.66840i	0.163303	+	0.282849i	−0.772748	+	0.634713i	$0.781118\pi$
$90$		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	−0.598033	−	0.801471i	$-0.704051\pi$
$101$	3.97048	−	6.87708i	0.395078	−	0.684295i	0.993111	+	0.117176i	$0.0373843\pi$
$102$		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	−0.617913	−	0.786247i	$-0.712022\pi$
$107$	−2.54423	+	1.46891i	−0.245960	+	0.142005i	0.371953	+	0.928252i	$0.378688\pi$
$108$		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	$-0.746067\pi$
$113$		−	15.2179i		−	1.43158i	0.698316	−	0.715789i	$-0.253933\pi$
$114$		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	0.999758	−	0.0220152i	$-0.00700822\pi$
$131$	5.50316	+	9.53175i	0.480813	+	0.832793i	−0.518945	+	0.854808i	$0.673675\pi$
$132$		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	0.592750	−	0.805387i	$-0.298042\pi$
$137$	2.24308	+	1.29504i	0.191639	+	0.110643i	−0.401111	+	0.916030i	$0.631376\pi$
$138$		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	−0.671399	−	0.741096i	$-0.734306\pi$
$149$	−4.45894	+	2.57437i	−0.365291	+	0.210901i	0.306108	+	0.951997i	$0.400973\pi$
$150$		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	$-0.733227\pi$
$167$	−17.2877			−1.33776			−0.668882	+	0.743369i	$0.733227\pi$
$168$		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	$-0.996572\pi$
$173$	−6.69875	−	11.6026i	−0.509297	−	0.882128i	0.490645	−	0.871359i	$-0.336761\pi$
$174$		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	0.387474	−	0.921881i	$-0.373348\pi$
$179$	−2.90542	−	1.67745i	−0.217161	−	0.125378i	−0.604635	+	0.796502i	$0.706681\pi$
$180$		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	−0.719874	−	0.694105i	$-0.755801\pi$
$191$	−6.61576	+	3.81961i	−0.478699	+	0.276377i	0.241175	+	0.970482i	$0.422467\pi$
$192$		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	$-0.914630\pi$
$197$		−	7.43877i		−	0.529991i	0.964250	−	0.264995i	$-0.0853704\pi$
$198$		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	$0.345506\pi$
$227$	−8.02661	+	13.9025i	−0.532745	+	0.922741i	−0.999269	+	0.0382326i	$0.987827\pi$
$228$		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	−0.145924	−	0.989296i	$-0.546616\pi$
$233$	9.73664	−	5.62145i	0.637869	−	0.368274i	0.783793	+	0.621022i	$0.213282\pi$
$234$		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	$0.0383349\pi$
$239$			3.71469i			0.240283i	−0.992757	+	0.120142i	$0.961665\pi$
$240$		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	$-0.386216\pi$
$251$	11.0869			0.699797			0.349899	+	0.936788i	$0.386216\pi$
$252$		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	$-0.765311\pi$
$257$	−15.2676	−	26.4442i	−0.952364	−	1.64954i	−0.212076	−	0.977253i	$-0.568022\pi$
$258$		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	0.938727	−	0.344661i	$-0.112006\pi$
$263$	17.9948	+	10.3893i	1.10961	+	0.640631i	0.170878	+	0.985292i	$0.445340\pi$
$264$		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	−0.994357	−	0.106085i	$-0.966169\pi$
$269$	−6.64752	+	11.5138i	−0.405307	+	0.702012i	0.589051	+	0.808096i	$0.299502\pi$
$270$		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	$0.0465192\pi$
$281$			4.88223i			0.291249i	−0.989340	+	0.145625i	$0.953481\pi$
$282$		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	$-0.653383\pi$
$293$	−15.8654			−0.926867			−0.463434	+	0.886132i	$0.653383\pi$
$294$		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	−0.992966	−	0.118403i	$-0.962222\pi$
$311$	−6.94725	+	12.0330i	−0.393942	+	0.682328i	0.599023	+	0.800732i	$0.295556\pi$
$312$		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	−0.217774	−	0.975999i	$-0.569880\pi$
$317$	9.23304	−	5.33070i	0.518579	−	0.299402i	0.736353	+	0.676597i	$0.236546\pi$
$318$		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	$-0.922369\pi$
$347$	−31.0106	−	17.9040i	−1.66473	−	0.961134i	−0.694326	−	0.719660i	$-0.744298\pi$
$348$		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	−0.826741	−	0.562582i	$-0.809808\pi$
$353$	1.38732	−	2.40291i	0.0738397	−	0.127894i	0.900581	+	0.434688i	$0.143141\pi$
$354$		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	0.0181895	−	0.999835i	$-0.494210\pi$
$359$	16.9231	−	9.77055i	0.893166	−	0.515670i	0.874977	+	0.484165i	$0.160876\pi$
$360$		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	0.853394	−	0.521267i	$-0.174540\pi$
$383$	−0.484041	−	0.838383i	−0.0247333	−	0.0428394i	−0.878127	+	0.478427i	$0.841207\pi$
$384$		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	0.210970	−	0.977493i	$-0.432338\pi$
$389$	−10.4548	−	6.03607i	−0.530078	−	0.306041i	−0.741048	+	0.671452i	$0.765671\pi$
$390$		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	−0.997990	−	0.0633660i	$-0.979816\pi$
$401$	−28.8782	+	16.6728i	−1.44211	+	0.832602i	−0.444119	+	0.895968i	$0.646483\pi$
$402$		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	$-0.405476\pi$
$419$	11.9792			0.585224			0.292612	+	0.956231i	$0.405476\pi$
$420$		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	0.496825	−	0.867851i	$-0.334499\pi$
$431$	−0.131704	−	0.0760393i	−0.00634396	−	0.00366269i	−0.503169	+	0.864188i	$0.667833\pi$
$432$		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	−0.504482	−	0.863422i	$-0.668316\pi$
$443$	−0.188948	+	0.109089i	−0.00897721	+	0.00518300i	0.495505	+	0.868605i	$0.334983\pi$
$444$		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	$-0.887622\pi$
$449$		−	14.6530i		−	0.691516i	0.938324	−	0.345758i	$-0.112378\pi$
$450$		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	$-0.760009\pi$
$461$	−31.3041			−1.45798			−0.728989	+	0.684525i	$0.760009\pi$
$462$		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	$-0.954306\pi$
$467$	−13.3713	−	23.1598i	−0.618750	−	1.07171i	0.370964	−	0.928647i	$-0.379027\pi$
$468$		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	−0.802322	−	0.596892i	$-0.796402\pi$
$479$	2.53359	−	4.38830i	0.115762	−	0.200506i	0.918084	+	0.396385i	$0.129736\pi$
$480$		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	$-0.942906\pi$
$491$		−	7.90635i		−	0.356809i	0.983957	−	0.178404i	$-0.0570935\pi$
$492$		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	$-0.429452\pi$
$503$	9.86027			0.439648			0.219824	+	0.975540i	$0.429452\pi$
$504$		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	0.997832	−	0.0658157i	$-0.0209649\pi$
$509$	9.97012	+	17.2688i	0.441918	+	0.765424i	−0.555914	+	0.831240i	$0.687632\pi$
$510$		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	−0.664697	−	0.747113i	$-0.731439\pi$
$521$	7.18249	−	12.4404i	0.314671	−	0.545026i	0.979367	+	0.202088i	$0.0647726\pi$
$522$		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	−0.138630	−	0.990344i	$-0.544270\pi$
$557$	−25.1493	−	14.5199i	−1.06561	−	0.615229i	−0.926978	+	0.375115i	$0.877603\pi$
$558$		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	−0.999177	−	0.0405553i	$-0.987087\pi$
$563$	−11.0207	+	19.0884i	−0.464467	+	0.804480i	0.534711	+	0.845035i	$0.320421\pi$
$564$		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	−0.836802	−	0.547506i	$-0.815577\pi$
$569$	−18.6309	+	10.7566i	−0.781049	+	0.450939i	0.0557531	+	0.998445i	$0.482244\pi$
$570$		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	$-0.677169\pi$
$587$	−25.5993			−1.05660			−0.528298	+	0.849059i	$0.677169\pi$
$588$		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	$-0.957796\pi$
$593$	−14.8569	−	25.7329i	−0.610099	−	1.05672i	0.381125	−	0.924524i	$-0.375537\pi$
$594$		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	0.771416	−	0.636331i	$-0.219549\pi$
$599$	14.8326	+	8.56362i	0.606045	+	0.349900i	−0.165371	+	0.986231i	$0.552882\pi$
$600$		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	$-0.781467\pi$
$617$		−	31.4899i		−	1.26773i	0.773442	−	0.633867i	$-0.218533\pi$
$618$		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	0.160241	−	0.987078i	$-0.448773\pi$
$641$	−15.5572	−	8.98196i	−0.614473	−	0.354766i	−0.774714	+	0.632312i	$0.782106\pi$
$642$		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	−0.539253	−	0.842144i	$-0.681293\pi$
$647$	11.6928	−	20.2525i	0.459691	−	0.796208i	0.998944	+	0.0459353i	$0.0146268\pi$
$648$		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	−0.311871	−	0.950125i	$-0.600956\pi$
$653$	9.07228	−	5.23789i	0.355026	−	0.204974i	0.666897	+	0.745150i	$0.267622\pi$
$654$		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	$0.304540\pi$
$659$			41.9627i			1.63464i	−0.576187	+	0.817318i	$0.695460\pi$
$660$		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	0.583896	−	0.811829i	$-0.301528\pi$
$677$	−10.6969	−	18.5276i	−0.411117	−	0.712075i	−0.995012	+	0.0997540i	$0.968194\pi$
$678$		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	0.401125	−	0.916023i	$-0.368619\pi$
$683$	−5.00763	−	2.89116i	−0.191612	−	0.110627i	−0.592737	+	0.805396i	$0.701953\pi$
$684$		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	$-0.842612\pi$
$701$		−	25.1286i		−	0.949095i	0.880230	−	0.474547i	$-0.157388\pi$
$702$		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	$-0.949772\pi$
$719$	−16.8896	−	29.2537i	−0.629876	−	1.09098i	0.357700	−	0.933837i	$-0.383561\pi$
$720$		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	$-0.676684\pi$
$743$		−	46.3312i		−	1.69973i	0.527002	−	0.849864i	$-0.323316\pi$
$744$		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	$0.0600085\pi$
$761$	18.0260	+	31.2219i	0.653441	+	1.13179i	−0.328842	+	0.944385i	$0.606658\pi$
$762$		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	$-0.642005\pi$
$773$	15.7233	−	27.2336i	0.565529	−	0.979525i	0.997000	−	0.0773981i	$-0.0246612\pi$
$774$		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	$-0.323358\pi$
$797$	29.7494			1.05378			0.526890	+	0.849934i	$0.323358\pi$
$798$		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	0.461114	−	0.887341i	$-0.347450\pi$
$809$	−2.18411	−	1.26100i	−0.0767893	−	0.0443343i	−0.537903	+	0.843007i	$0.680783\pi$
$810$		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	−0.793856	−	0.608105i	$-0.791930\pi$
$821$	−19.0300	+	10.9870i	−0.664150	+	0.383447i	0.129706	+	0.991552i	$0.458597\pi$
$822$		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	$0.250476\pi$
$827$			40.7302i			1.41633i	−0.706048	+	0.708164i	$0.749524\pi$
$828$		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	$-0.552106\pi$
$839$	−9.44078			−0.325932			−0.162966	+	0.986632i	$0.552106\pi$
$840$		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	−0.655542	−	0.755159i	$-0.727560\pi$
$857$	9.54984	−	16.5408i	0.326216	−	0.565023i	0.981758	+	0.190136i	$0.0608929\pi$
$858$		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	−0.364921	−	0.931039i	$-0.618904\pi$
$863$	7.60632	−	4.39151i	0.258922	−	0.149489i	0.623843	+	0.781550i	$0.285571\pi$
$864$		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	$-0.358771\pi$
$881$	25.4829			0.858541			0.429271	+	0.903176i	$0.358771\pi$
$882$		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	$-0.962723\pi$
$887$	−17.8029	−	30.8355i	−0.597763	−	1.03536i	0.395388	−	0.918514i	$-0.370610\pi$
$888$		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	$-0.851570\pi$
$911$		−	27.1398i		−	0.899181i	0.893235	−	0.449590i	$-0.148430\pi$
$912$		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	0.879238	−	0.476383i	$-0.158052\pi$
$929$	0.824754	+	1.42852i	0.0270593	+	0.0468681i	−0.852179	+	0.523251i	$0.824719\pi$
$930$		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	$-0.464128\pi$
$941$	28.1223	−	48.7092i	0.916760	−	1.58788i	0.804304	−	0.594218i	$-0.202539\pi$
$942$		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	0.0679476	−	0.997689i	$-0.478355\pi$
$947$	29.7254	−	17.1620i	0.965945	−	0.557689i	0.897998	+	0.440000i	$0.145022\pi$
$948$		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	$-0.872944\pi$
$953$		−	23.9953i		−	0.777283i	0.921389	−	0.388642i	$-0.127056\pi$
$954$		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	$0.138527\pi$
$971$	25.5051	+	44.1762i	0.818499	+	1.41768i	−0.0882892	+	0.996095i	$0.528140\pi$
$972$		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	$0.0243730\pi$
$977$	48.8188	+	28.1855i	1.56185	+	0.901735i	0.564782	+	0.825240i	$0.308960\pi$
$978$		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	−0.882899	−	0.469564i	$-0.844411\pi$
$983$	−1.09092	+	1.88954i	−0.0347951	+	0.0602669i	0.848103	+	0.529831i	$0.177745\pi$
$984$		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.647.19	✓	96
3.2	odd	2	inner	1197.2.db.a.647.30	yes	96
7.5	odd	6	inner	1197.2.db.a.1160.30	yes	96
21.5	even	6	inner	1197.2.db.a.1160.19	yes	96

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

Related objects

Downloads

Learn more