LMFDB - Embedded newform 684.2.bo.e.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(73,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("684.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.bo (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,6,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 27 x^{10} + 309 x^{8} + 42 x^{7} + 2059 x^{6} + 1245 x^{5} + 8226 x^{4} + \cdots + 16129 $ x^12 - 3x^11 + 27x^10 + 309x^8 + 42x^7 + 2059x^6 + 1245x^5 + 8226x^4 + 2250x^3 + 14496x^2 + 6096x + 16129
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$2.42841 - 4.20614i$ of defining polynomial
Character	$\chi$	$=$	684.289
Dual form			684.2.bo.e.613.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.54690 + 2.13710i) q^{5} +(-0.596313 + 1.03284i) q^{7} +(0.647560 + 1.12161i) q^{11} +(0.496083 - 2.81343i) q^{13} +(-2.08503 - 0.758891i) q^{17} +(-2.84913 - 3.29886i) q^{19} +(-6.07384 - 5.09656i) q^{23} +(1.05125 - 5.96192i) q^{25} +(-4.21893 + 1.53557i) q^{29} +(-3.91714 + 6.78468i) q^{31} +(-0.688545 - 3.90493i) q^{35} -7.86729 q^{37} +(-1.40006 - 7.94015i) q^{41} +(-1.37037 + 1.14988i) q^{43} +(5.36453 - 1.95253i) q^{47} +(2.78882 + 4.83038i) q^{49} +(4.83597 + 4.05786i) q^{53} +(-4.04626 - 1.47272i) q^{55} +(-7.41778 - 2.69985i) q^{59} +(11.2096 + 9.40599i) q^{61} +(4.74910 + 8.22569i) q^{65} +(-4.30894 + 1.56833i) q^{67} +(-3.20234 + 2.68708i) q^{71} +(0.338056 + 1.91721i) q^{73} -1.54460 q^{77} +(-1.07749 - 6.11077i) q^{79} +(3.91858 - 6.78719i) q^{83} +(6.93220 - 2.52311i) q^{85} +(0.743166 - 4.21470i) q^{89} +(2.61001 + 2.19006i) q^{91} +(14.3064 + 2.31298i) q^{95} +(2.38339 + 0.867483i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 9 q^{7} + 9 q^{11} - 3 q^{13} - 12 q^{17} + 9 q^{19} - 15 q^{23} + 12 q^{25} + 24 q^{29} - 6 q^{31} + 42 q^{35} + 12 q^{37} - 6 q^{41} - 39 q^{43} + 3 q^{47} - 21 q^{49} - 18 q^{53} + 45 q^{55}+ \cdots - 15 q^{97}+O(q^{100}) $ 12 * q + 6 * q^5 - 9 * q^7 + 9 * q^11 - 3 * q^13 - 12 * q^17 + 9 * q^19 - 15 * q^23 + 12 * q^25 + 24 * q^29 - 6 * q^31 + 42 * q^35 + 12 * q^37 - 6 * q^41 - 39 * q^43 + 3 * q^47 - 21 * q^49 - 18 * q^53 + 45 * q^55 + 33 * q^61 + 33 * q^65 - 27 * q^67 - 6 * q^71 - 24 * q^73 + 18 * q^79 - 3 * q^83 + 39 * q^85 + 15 * q^89 + 18 * q^91 + 30 * q^95 - 15 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.54690	+	2.13710i	−1.13901	+	0.955741i	−0.999406	−	0.0344670i	$-0.989027\pi$
$5$	−2.54690	+	2.13710i	−1.13901	+	0.955741i	−0.139602	+	0.990208i	$0.544582\pi$
$6$		0			0
$7$	−0.596313	+	1.03284i	−0.225385	+	0.390379i	−0.956435	−	0.291946i	$-0.905697\pi$
$7$	−0.596313	+	1.03284i	−0.225385	+	0.390379i	0.731050	+	0.682324i	$0.239031\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.647560	+	1.12161i	0.195247	+	0.338177i	0.946981	−	0.321288i	$-0.104116\pi$
$11$	0.647560	+	1.12161i	0.195247	+	0.338177i	−0.751735	+	0.659466i	$0.770783\pi$
$12$		0			0
$13$	0.496083	−	2.81343i	0.137589	−	0.780304i	−0.835433	−	0.549592i	$-0.814783\pi$
$13$	0.496083	−	2.81343i	0.137589	−	0.780304i	0.973022	−	0.230712i	$-0.0741056\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.08503	−	0.758891i	−0.505695	−	0.184058i	0.0765586	−	0.997065i	$-0.475607\pi$
$17$	−2.08503	−	0.758891i	−0.505695	−	0.184058i	−0.582254	+	0.813007i	$0.697829\pi$
$18$		0			0
$19$	−2.84913	−	3.29886i	−0.653635	−	0.756810i
$19$	−2.84913	−	3.29886i	−0.653635	−	0.756810i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.07384	−	5.09656i	−1.26648	−	1.06271i	−0.994960	−	0.100275i	$-0.968028\pi$
$23$	−6.07384	−	5.09656i	−1.26648	−	1.06271i	−0.271524	−	0.962432i	$-0.587528\pi$
$24$		0			0
$25$	1.05125	−	5.96192i	0.210249	−	1.19238i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.21893	+	1.53557i	−0.783436	+	0.285148i	−0.702605	−	0.711580i	$-0.747980\pi$
$29$	−4.21893	+	1.53557i	−0.783436	+	0.285148i	−0.0808315	+	0.996728i	$0.525758\pi$
$30$		0			0
$31$	−3.91714	+	6.78468i	−0.703538	+	1.21856i	0.263678	+	0.964611i	$0.415064\pi$
$31$	−3.91714	+	6.78468i	−0.703538	+	1.21856i	−0.967216	+	0.253953i	$0.918269\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.688545	−	3.90493i	−0.116385	−	0.660054i
$36$		0			0
$37$	−7.86729			−1.29337			−0.646687	−	0.762755i	$-0.723846\pi$
$37$	−7.86729			−1.29337			−0.646687	+	0.762755i	$0.723846\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.40006	−	7.94015i	−0.218653	−	1.24004i	−0.874454	−	0.485109i	$-0.838780\pi$
$41$	−1.40006	−	7.94015i	−0.218653	−	1.24004i	0.655801	−	0.754934i	$-0.272331\pi$
$42$		0			0
$43$	−1.37037	+	1.14988i	−0.208980	+	0.175355i	−0.741270	−	0.671207i	$-0.765776\pi$
$43$	−1.37037	+	1.14988i	−0.208980	+	0.175355i	0.532290	+	0.846562i	$0.321332\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.36453	−	1.95253i	0.782497	−	0.284806i	0.0802834	−	0.996772i	$-0.474417\pi$
$47$	5.36453	−	1.95253i	0.782497	−	0.284806i	0.702213	+	0.711967i	$0.252195\pi$
$48$		0			0
$49$	2.78882	+	4.83038i	0.398403	+	0.690054i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.83597	+	4.05786i	0.664272	+	0.557390i	0.911364	−	0.411602i	$-0.135031\pi$
$53$	4.83597	+	4.05786i	0.664272	+	0.557390i	−0.247092	+	0.968992i	$0.579475\pi$
$54$		0			0
$55$	−4.04626	−	1.47272i	−0.545598	−	0.198581i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.41778	−	2.69985i	−0.965713	−	0.351491i	−0.189443	−	0.981892i	$-0.560668\pi$
$59$	−7.41778	−	2.69985i	−0.965713	−	0.351491i	−0.776270	+	0.630401i	$0.782891\pi$
$60$		0			0
$61$	11.2096	+	9.40599i	1.43524	+	1.20431i	0.942529	+	0.334123i	$0.108440\pi$
$61$	11.2096	+	9.40599i	1.43524	+	1.20431i	0.492715	+	0.870190i	$0.336004\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.74910	+	8.22569i	0.589054	+	1.02027i
$66$		0			0
$67$	−4.30894	+	1.56833i	−0.526421	+	0.191601i	−0.591539	−	0.806276i	$-0.701480\pi$
$67$	−4.30894	+	1.56833i	−0.526421	+	0.191601i	0.0651188	+	0.997878i	$0.479257\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.20234	+	2.68708i	−0.380048	+	0.318898i	−0.812721	−	0.582653i	$-0.802015\pi$
$71$	−3.20234	+	2.68708i	−0.380048	+	0.318898i	0.432674	+	0.901551i	$0.357570\pi$
$72$		0			0
$73$	0.338056	+	1.91721i	0.0395665	+	0.224393i	0.998179	−	0.0603212i	$-0.0192125\pi$
$73$	0.338056	+	1.91721i	0.0395665	+	0.224393i	−0.958613	+	0.284714i	$0.908101\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.54460			−0.176023
$78$		0			0
$79$	−1.07749	−	6.11077i	−0.121227	−	0.687515i	−0.983477	−	0.181032i	$-0.942056\pi$
$79$	−1.07749	−	6.11077i	−0.121227	−	0.687515i	0.862250	−	0.506483i	$-0.169055\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.91858	−	6.78719i	0.430120	−	0.744990i	−0.566763	−	0.823881i	$-0.691804\pi$
$83$	3.91858	−	6.78719i	0.430120	−	0.744990i	0.996883	+	0.0788906i	$0.0251378\pi$
$84$		0			0
$85$	6.93220	−	2.52311i	0.751902	−	0.273670i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.743166	−	4.21470i	0.0787754	−	0.446758i	−0.919752	−	0.392501i	$-0.871610\pi$
$89$	0.743166	−	4.21470i	0.0787754	−	0.446758i	0.998527	−	0.0542567i	$-0.0172789\pi$
$90$		0			0
$91$	2.61001	+	2.19006i	0.273604	+	0.229581i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	14.3064	+	2.31298i	1.46781	+	0.237307i
$96$		0			0
$97$	2.38339	+	0.867483i	0.241997	+	0.0880795i	0.460171	−	0.887830i	$-0.347788\pi$
$97$	2.38339	+	0.867483i	0.241997	+	0.0880795i	−0.218175	+	0.975910i	$0.570010\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.16648	+	12.2867i	−0.215573	+	1.22257i	0.664337	+	0.747434i	$0.268714\pi$
$101$	−2.16648	+	12.2867i	−0.215573	+	1.22257i	−0.879910	+	0.475141i	$0.842397\pi$
$102$		0			0
$103$	−8.78891	−	15.2228i	−0.865997	−	1.49995i	−0.866054	−	0.499951i	$-0.833351\pi$
$103$	−8.78891	−	15.2228i	−0.865997	−	1.49995i	5.70163e−5	−	1.00000i	$-0.499982\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.35879	+	7.54965i	−0.421381	+	0.729853i	−0.996075	−	0.0885157i	$-0.971788\pi$
$107$	−4.35879	+	7.54965i	−0.421381	+	0.729853i	0.574694	+	0.818368i	$0.305121\pi$
$108$		0			0
$109$	−14.9617	+	12.5544i	−1.43307	+	1.20249i	−0.489204	+	0.872170i	$0.662713\pi$
$109$	−14.9617	+	12.5544i	−1.43307	+	1.20249i	−0.943869	+	0.330321i	$0.892843\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.595683			−0.0560372			−0.0280186	−	0.999607i	$-0.508920\pi$
$113$	−0.595683			−0.0560372			−0.0280186	+	0.999607i	$0.508920\pi$
$114$		0			0
$115$	26.3613			2.45821
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.02715	−	1.70098i	0.185829	−	0.155929i
$120$		0			0
$121$	4.66133	−	8.07366i	0.423757	−	0.733969i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.75196	+	3.03448i	0.156700	+	0.271412i
$126$		0			0
$127$	1.69849	−	9.63264i	0.150717	−	0.854758i	−0.811881	−	0.583823i	$-0.801556\pi$
$127$	1.69849	−	9.63264i	0.150717	−	0.854758i	0.962598	−	0.270935i	$-0.0873328\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−14.7025	−	5.35127i	−1.28456	−	0.467543i	−0.392624	−	0.919699i	$-0.628433\pi$
$131$	−14.7025	−	5.35127i	−1.28456	−	0.467543i	−0.891939	+	0.452156i	$0.850655\pi$
$132$		0			0
$133$	5.10618	−	0.975555i	0.442762	−	0.0845913i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.8578	+	9.94991i	1.01308	+	0.850078i	0.988743	−	0.149625i	$-0.0478068\pi$
$137$	11.8578	+	9.94991i	1.01308	+	0.850078i	0.0243410	+	0.999704i	$0.492251\pi$
$138$		0			0
$139$	2.00473	−	11.3694i	0.170039	−	0.964338i	−0.773677	−	0.633580i	$-0.781585\pi$
$139$	2.00473	−	11.3694i	0.170039	−	0.964338i	0.943716	−	0.330758i	$-0.107304\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.47680	−	1.26545i	0.290745	−	0.105823i
$144$		0			0
$145$	7.46353	−	12.9272i	0.619813	−	1.07355i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.05008	+	22.9691i	0.331795	+	1.88170i	0.456835	+	0.889552i	$0.348983\pi$
$149$	4.05008	+	22.9691i	0.331795	+	1.88170i	−0.125040	+	0.992152i	$0.539906\pi$
$150$		0			0
$151$	−3.39770			−0.276501			−0.138250	−	0.990397i	$-0.544148\pi$
$151$	−3.39770			−0.276501			−0.138250	+	0.990397i	$0.544148\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.52300	−	25.6512i	−0.363296	−	2.06035i
$156$		0			0
$157$	−17.4382	+	14.6324i	−1.39172	+	1.16779i	−0.427083	+	0.904213i	$0.640459\pi$
$157$	−17.4382	+	14.6324i	−1.39172	+	1.16779i	−0.964638	+	0.263580i	$0.915097\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.88587	−	3.23419i	0.700305	−	0.254890i
$162$		0			0
$163$	6.53627	+	11.3211i	0.511960	+	0.886741i	0.999904	+	0.0138657i	$0.00441372\pi$
$163$	6.53627	+	11.3211i	0.511960	+	0.886741i	−0.487944	+	0.872875i	$0.662253\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.6216	+	9.75170i	0.899308	+	0.754609i	0.970055	−	0.242885i	$-0.0780938\pi$
$167$	11.6216	+	9.75170i	0.899308	+	0.754609i	−0.0707468	+	0.997494i	$0.522538\pi$
$168$		0			0
$169$	4.54673	+	1.65488i	0.349749	+	0.127298i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	15.6934	+	5.71194i	1.19315	+	0.434271i	0.860828	−	0.508896i	$-0.169946\pi$
$173$	15.6934	+	5.71194i	1.19315	+	0.434271i	0.332321	+	0.943167i	$0.392168\pi$
$174$		0			0
$175$	5.53086	+	4.64095i	0.418094	+	0.350823i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.84712	+	11.8596i	0.511778	+	0.886425i	0.999907	+	0.0136533i	$0.00434612\pi$
$179$	6.84712	+	11.8596i	0.511778	+	0.886425i	−0.488129	+	0.872771i	$0.662321\pi$
$180$		0			0
$181$	−19.1404	+	6.96652i	−1.42269	+	0.517817i	−0.934827	−	0.355102i	$-0.884446\pi$
$181$	−19.1404	+	6.96652i	−1.42269	+	0.517817i	−0.487864	+	0.872920i	$0.662224\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	20.0372	−	16.8132i	1.47316	−	1.23613i
$186$		0			0
$187$	−0.499009	−	2.83002i	−0.0364911	−	0.206951i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−21.2065			−1.53445			−0.767224	−	0.641380i	$-0.778362\pi$
$191$	−21.2065			−1.53445			−0.767224	+	0.641380i	$0.778362\pi$
$192$		0			0
$193$	2.43434	+	13.8059i	0.175228	+	0.993767i	0.937880	+	0.346958i	$0.112786\pi$
$193$	2.43434	+	13.8059i	0.175228	+	0.993767i	−0.762653	+	0.646808i	$0.776103\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.84138	−	4.92142i	0.202440	−	0.350637i	−0.746874	−	0.664966i	$-0.768446\pi$
$197$	2.84138	−	4.92142i	0.202440	−	0.350637i	0.949314	+	0.314329i	$0.101780\pi$
$198$		0			0
$199$	−10.0943	+	3.67403i	−0.715567	+	0.260445i	−0.674043	−	0.738692i	$-0.735444\pi$
$199$	−10.0943	+	3.67403i	−0.715567	+	0.260445i	−0.0415244	+	0.999137i	$0.513221\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.929804	−	5.27318i	0.0652595	−	0.370105i
$204$		0			0
$205$	20.5347	+	17.2307i	1.43421	+	1.20344i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.85504	−	5.33181i	0.128316	−	0.368809i
$210$		0			0
$211$	18.9123	+	6.88351i	1.30198	+	0.473880i	0.897640	−	0.440730i	$-0.145280\pi$
$211$	18.9123	+	6.88351i	1.30198	+	0.473880i	0.404336	+	0.914610i	$0.367503\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.03279	−	5.85725i	0.0704357	−	0.399461i
$216$		0			0
$217$	−4.67168	−	8.09159i	−0.317134	−	0.549293i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.16943	+	5.48962i	−0.213199	+	0.369272i
$222$		0			0
$223$	2.60127	−	2.18272i	0.174194	−	0.146166i	−0.551523	−	0.834160i	$-0.685953\pi$
$223$	2.60127	−	2.18272i	0.174194	−	0.146166i	0.725716	+	0.687994i	$0.241508\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.7293			−0.778503			−0.389251	−	0.921132i	$-0.627266\pi$
$227$	−11.7293			−0.778503			−0.389251	+	0.921132i	$0.627266\pi$
$228$		0			0
$229$	7.83401			0.517686			0.258843	−	0.965919i	$-0.416659\pi$
$229$	7.83401			0.517686			0.258843	+	0.965919i	$0.416659\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.10168	−	1.76352i	0.137685	−	0.115532i	−0.571344	−	0.820711i	$-0.693578\pi$
$233$	2.10168	−	1.76352i	0.137685	−	0.115532i	0.709029	+	0.705179i	$0.249133\pi$
$234$		0			0
$235$	−9.49015	+	16.4374i	−0.619069	+	1.07226i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.54354	+	14.7978i	0.552636	+	0.957193i	0.998083	+	0.0618851i	$0.0197112\pi$
$239$	8.54354	+	14.7978i	0.552636	+	0.957193i	−0.445448	+	0.895308i	$0.646955\pi$
$240$		0			0
$241$	0.561919	−	3.18680i	0.0361964	−	0.205280i	−0.961346	−	0.275342i	$-0.911209\pi$
$241$	0.561919	−	3.18680i	0.0361964	−	0.205280i	0.997543	+	0.0700625i	$0.0223199\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−17.4259	−	6.34249i	−1.11330	−	0.405207i
$246$		0			0
$247$	−10.6945	+	6.37931i	−0.680475	+	0.405906i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.06837	−	4.25287i	−0.319913	−	0.268439i	0.468662	−	0.883378i	$-0.344736\pi$
$251$	−5.06837	−	4.25287i	−0.319913	−	0.268439i	−0.788575	+	0.614939i	$0.789181\pi$
$252$		0			0
$253$	1.78316	−	10.1128i	0.112106	−	0.635786i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.6959	−	4.98492i	0.854330	−	0.310951i	0.122525	−	0.992465i	$-0.460901\pi$
$257$	13.6959	−	4.98492i	0.854330	−	0.310951i	0.731804	+	0.681515i	$0.238678\pi$
$258$		0			0
$259$	4.69137	−	8.12569i	0.291507	−	0.504906i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.70600	−	9.67520i	−0.105196	−	0.596598i	−0.991142	−	0.132809i	$-0.957600\pi$
$263$	−1.70600	−	9.67520i	−0.105196	−	0.596598i	0.885945	−	0.463790i	$-0.153511\pi$
$264$		0			0
$265$	−20.9888			−1.28933
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.75753	−	21.3100i	−0.229101	−	1.29929i	−0.854689	−	0.519141i	$-0.826252\pi$
$269$	−3.75753	−	21.3100i	−0.229101	−	1.29929i	0.625588	−	0.780154i	$-0.284859\pi$
$270$		0			0
$271$	−4.66583	+	3.91509i	−0.283429	+	0.237825i	−0.773407	−	0.633910i	$-0.781449\pi$
$271$	−4.66583	+	3.91509i	−0.283429	+	0.237825i	0.489978	+	0.871735i	$0.337005\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.36768	−	2.68162i	0.444288	−	0.161708i
$276$		0			0
$277$	−8.11381	−	14.0535i	−0.487512	−	0.844395i	0.512385	−	0.858756i	$-0.328762\pi$
$277$	−8.11381	−	14.0535i	−0.487512	−	0.844395i	−0.999897	+	0.0143607i	$0.995429\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.15528	−	2.64760i	−0.188228	−	0.157942i	0.543804	−	0.839212i	$-0.316984\pi$
$281$	−3.15528	−	2.64760i	−0.188228	−	0.157942i	−0.732032	+	0.681270i	$0.761428\pi$
$282$		0			0
$283$	−25.3540	−	9.22811i	−1.50714	−	0.548554i	−0.549242	−	0.835663i	$-0.685084\pi$
$283$	−25.3540	−	9.22811i	−1.50714	−	0.548554i	−0.957898	+	0.287109i	$0.907306\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.03582	+	3.28877i	0.533367	+	0.194130i
$288$		0			0
$289$	−9.25130	−	7.76276i	−0.544194	−	0.456633i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.12397	+	5.41088i	0.182504	+	0.316107i	0.942733	−	0.333549i	$-0.108246\pi$
$293$	3.12397	+	5.41088i	0.182504	+	0.316107i	−0.760228	+	0.649656i	$0.774913\pi$
$294$		0			0
$295$	24.6622	−	8.97630i	1.43589	−	0.522621i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−17.3519	+	14.5600i	−1.00349	+	0.842026i
$300$		0			0
$301$	−0.370475	−	2.10107i	−0.0213538	−	0.121104i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−48.6513			−2.78577
$306$		0			0
$307$	−2.08041	−	11.7986i	−0.118735	−	0.673381i	−0.984833	−	0.173506i	$-0.944490\pi$
$307$	−2.08041	−	11.7986i	−0.118735	−	0.673381i	0.866098	−	0.499875i	$-0.166621\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.54108	+	7.86538i	−0.257501	+	0.446005i	−0.965572	−	0.260137i	$-0.916232\pi$
$311$	−4.54108	+	7.86538i	−0.257501	+	0.446005i	0.708071	+	0.706141i	$0.249566\pi$
$312$		0			0
$313$	15.5136	−	5.64648i	0.876878	−	0.319158i	0.135929	−	0.990719i	$-0.456598\pi$
$313$	15.5136	−	5.64648i	0.876878	−	0.319158i	0.740949	+	0.671561i	$0.234376\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.37258	+	19.1269i	−0.189423	+	1.07427i	0.730716	+	0.682681i	$0.239186\pi$
$317$	−3.37258	+	19.1269i	−0.189423	+	1.07427i	−0.920139	+	0.391591i	$0.871925\pi$
$318$		0			0
$319$	−4.45432	−	3.73762i	−0.249394	−	0.209266i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.43706	+	9.04041i	0.191243	+	0.503022i
$324$		0			0
$325$	−16.2519	−	5.91521i	−0.901494	−	0.328117i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.18228	+	6.70504i	−0.0651812	+	0.369661i
$330$		0			0
$331$	7.48454	+	12.9636i	0.411387	+	0.712544i	0.995042	−	0.0994585i	$-0.0317110\pi$
$331$	7.48454	+	12.9636i	0.411387	+	0.712544i	−0.583654	+	0.812002i	$0.698378\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.62276	−	13.2030i	0.416476	−	0.721357i
$336$		0			0
$337$	12.3718	−	10.3812i	0.673934	−	0.565498i	−0.240293	−	0.970700i	$-0.577243\pi$
$337$	12.3718	−	10.3812i	0.673934	−	0.565498i	0.914227	+	0.405203i	$0.132799\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−10.1463			−0.549454
$342$		0			0
$343$	−15.0004			−0.809947
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−24.3637	+	20.4436i	−1.30791	+	1.09747i	−0.319194	+	0.947689i	$0.603412\pi$
$347$	−24.3637	+	20.4436i	−1.30791	+	1.09747i	−0.988719	+	0.149780i	$0.952143\pi$
$348$		0			0
$349$	1.77710	−	3.07803i	0.0951261	−	0.164763i	−0.814535	−	0.580114i	$-0.803008\pi$
$349$	1.77710	−	3.07803i	0.0951261	−	0.164763i	0.909661	+	0.415351i	$0.136341\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.7010	−	27.1949i	−0.835678	−	1.44744i	−0.893477	−	0.449109i	$-0.851741\pi$
$353$	−15.7010	−	27.1949i	−0.835678	−	1.44744i	0.0577986	−	0.998328i	$-0.481592\pi$
$354$		0			0
$355$	2.41347	−	13.6874i	0.128093	−	0.726454i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.9000	−	5.78713i	−0.839171	−	0.305433i	−0.113554	−	0.993532i	$-0.536223\pi$
$359$	−15.9000	−	5.78713i	−0.839171	−	0.305433i	−0.725617	+	0.688099i	$0.758446\pi$
$360$		0			0
$361$	−2.76493	+	18.7977i	−0.145523	+	0.989355i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.95827	−	4.16048i	−0.259528	−	0.217770i
$366$		0			0
$367$	1.65004	−	9.35784i	0.0861314	−	0.488475i	−0.910975	−	0.412461i	$-0.864669\pi$
$367$	1.65004	−	9.35784i	0.0861314	−	0.488475i	0.997107	−	0.0760144i	$-0.0242195\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.07490	+	2.57505i	−0.367310	+	0.133690i
$372$		0			0
$373$	11.6964	−	20.2588i	0.605619	−	1.04896i	−0.386334	−	0.922359i	$-0.626259\pi$
$373$	11.6964	−	20.2588i	0.605619	−	1.04896i	0.991953	−	0.126604i	$-0.0404078\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.22726	+	12.6314i	0.114710	+	0.650552i
$378$		0			0
$379$	−22.1013			−1.13527			−0.567634	−	0.823281i	$-0.692141\pi$
$379$	−22.1013			−1.13527			−0.567634	+	0.823281i	$0.692141\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.13998	−	17.8077i	−0.160446	−	0.909932i	−0.953637	−	0.300960i	$-0.902693\pi$
$383$	−3.13998	−	17.8077i	−0.160446	−	0.909932i	0.793191	−	0.608973i	$-0.208418\pi$
$384$		0			0
$385$	3.93393	−	3.30096i	0.200492	−	0.168232i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	31.8516	−	11.5930i	1.61494	−	0.587791i	0.632533	−	0.774533i	$-0.282015\pi$
$389$	31.8516	−	11.5930i	1.61494	−	0.587791i	0.982409	+	0.186742i	$0.0597929\pi$
$390$		0			0
$391$	8.79644	+	15.2359i	0.444855	+	0.770512i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	15.8036	+	13.2608i	0.795165	+	0.667223i
$396$		0			0
$397$	16.4034	+	5.97033i	0.823261	+	0.299642i	0.719090	−	0.694917i	$-0.244559\pi$
$397$	16.4034	+	5.97033i	0.823261	+	0.299642i	0.104171	+	0.994559i	$0.466781\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−30.9170	−	11.2529i	−1.54392	−	0.561941i	−0.576938	−	0.816788i	$-0.695753\pi$
$401$	−30.9170	−	11.2529i	−1.54392	−	0.561941i	−0.966981	+	0.254847i	$0.917975\pi$
$402$		0			0
$403$	17.1450	+	14.3863i	0.854052	+	0.716634i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.09455	−	8.82401i	−0.252527	−	0.437390i
$408$		0			0
$409$	−7.26825	+	2.64543i	−0.359392	+	0.130808i	−0.515404	−	0.856947i	$-0.672358\pi$
$409$	−7.26825	+	2.64543i	−0.359392	+	0.130808i	0.156013	+	0.987755i	$0.450136\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.21185	−	6.05146i	0.354872	−	0.297773i
$414$		0			0
$415$	4.52467	+	25.6607i	0.222107	+	1.25963i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	26.4903			1.29414			0.647068	−	0.762432i	$-0.275995\pi$
$419$	26.4903			1.29414			0.647068	+	0.762432i	$0.275995\pi$
$420$		0			0
$421$	1.83547	+	10.4095i	0.0894554	+	0.507327i	0.996306	+	0.0858746i	$0.0273684\pi$
$421$	1.83547	+	10.4095i	0.0894554	+	0.507327i	−0.906851	+	0.421452i	$0.861520\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.71633	+	11.6330i	−0.325790	+	0.564285i
$426$		0			0
$427$	−16.3994	+	5.96888i	−0.793621	+	0.288855i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.61415	+	14.8256i	−0.125919	+	0.714123i	0.854838	+	0.518894i	$0.173656\pi$
$431$	−2.61415	+	14.8256i	−0.125919	+	0.714123i	−0.980758	+	0.195229i	$0.937455\pi$
$432$		0			0
$433$	−29.7556	−	24.9679i	−1.42996	−	1.19988i	−0.945735	−	0.324939i	$-0.894656\pi$
$433$	−29.7556	−	24.9679i	−1.42996	−	1.19988i	−0.484228	−	0.874942i	$-0.660899\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.492330	+	34.5575i	0.0235513	+	1.65311i
$438$		0			0
$439$	−0.955140	−	0.347643i	−0.0455864	−	0.0165921i	0.319126	−	0.947712i	$-0.396611\pi$
$439$	−0.955140	−	0.347643i	−0.0455864	−	0.0165921i	−0.364713	+	0.931120i	$0.618833\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.08139	−	11.8042i	0.0988900	−	0.560833i	−0.894596	−	0.446876i	$-0.852536\pi$
$443$	2.08139	−	11.8042i	0.0988900	−	0.560833i	0.993486	−	0.113957i	$-0.0363525\pi$
$444$		0			0
$445$	7.11448	+	12.3226i	0.337259	+	0.584149i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	15.7291	−	27.2436i	0.742301	−	1.28570i	−0.209144	−	0.977885i	$-0.567068\pi$
$449$	15.7291	−	27.2436i	0.742301	−	1.28570i	0.951445	−	0.307818i	$-0.0995989\pi$
$450$		0			0
$451$	7.99910	−	6.71205i	0.376663	−	0.316058i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−11.3278			−0.531056
$456$		0			0
$457$	−5.25795			−0.245956			−0.122978	−	0.992409i	$-0.539245\pi$
$457$	−5.25795			−0.245956			−0.122978	+	0.992409i	$0.539245\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.8528	+	10.7848i	−0.598616	+	0.502299i	−0.891001	−	0.454002i	$-0.849996\pi$
$461$	−12.8528	+	10.7848i	−0.598616	+	0.502299i	0.292384	+	0.956301i	$0.405551\pi$
$462$		0			0
$463$	−4.73299	+	8.19777i	−0.219961	+	0.380983i	−0.954796	−	0.297263i	$-0.903926\pi$
$463$	−4.73299	+	8.19777i	−0.219961	+	0.380983i	0.734835	+	0.678246i	$0.237260\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.27914	−	16.0719i	−0.429387	−	0.743721i	0.567432	−	0.823421i	$-0.307937\pi$
$467$	−9.27914	−	16.0719i	−0.429387	−	0.743721i	−0.996819	+	0.0796999i	$0.974604\pi$
$468$		0			0
$469$	0.949640	−	5.38568i	0.0438503	−	0.248687i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.17711	−	0.792404i	−0.100104	−	0.0364348i
$474$		0			0
$475$	−22.6627	+	13.5184i	−1.03983	+	0.620265i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5.52763	+	4.63823i	0.252564	+	0.211926i	0.760275	−	0.649601i	$-0.225064\pi$
$479$	5.52763	+	4.63823i	0.252564	+	0.211926i	−0.507712	+	0.861527i	$0.669508\pi$
$480$		0			0
$481$	−3.90283	+	22.1340i	−0.177954	+	1.00923i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.92415	+	2.88415i	−0.359817	+	0.130963i
$486$		0			0
$487$	−2.32705	+	4.03057i	−0.105449	+	0.182642i	−0.913921	−	0.405891i	$-0.866961\pi$
$487$	−2.32705	+	4.03057i	−0.105449	+	0.182642i	0.808473	+	0.588534i	$0.200295\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.690291	−	3.91483i	−0.0311524	−	0.176674i	0.965262	−	0.261285i	$-0.0841463\pi$
$491$	−0.690291	−	3.91483i	−0.0311524	−	0.176674i	−0.996414	+	0.0846112i	$0.973035\pi$
$492$		0			0
$493$	9.96195			0.448664
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.865741	−	4.90986i	−0.0388338	−	0.220237i
$498$		0			0
$499$	0.215315	−	0.180670i	0.00963881	−	0.00808792i	−0.637955	−	0.770073i	$-0.720220\pi$
$499$	0.215315	−	0.180670i	0.00963881	−	0.00808792i	0.647594	+	0.761985i	$0.275775\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	34.6506	−	12.6118i	1.54499	−	0.562332i	0.577757	−	0.816208i	$-0.303928\pi$
$503$	34.6506	−	12.6118i	1.54499	−	0.562332i	0.967237	+	0.253877i	$0.0817057\pi$
$504$		0			0
$505$	−20.7402	−	35.9230i	−0.922925	−	1.59855i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.9516	−	16.7413i	−0.884338	−	0.742047i	0.0827287	−	0.996572i	$-0.473636\pi$
$509$	−19.9516	−	16.7413i	−0.884338	−	0.742047i	−0.967066	+	0.254525i	$0.918081\pi$
$510$		0			0
$511$	−2.18177	−	0.794099i	−0.0965158	−	0.0351289i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	54.9172	+	19.9882i	2.41994	+	0.880786i
$516$		0			0
$517$	5.66383	+	4.75252i	0.249095	+	0.209015i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.97112	+	8.61023i	0.217789	+	0.377221i	0.954132	−	0.299387i	$-0.0967823\pi$
$521$	4.97112	+	8.61023i	0.217789	+	0.377221i	−0.736343	+	0.676608i	$0.763449\pi$
$522$		0			0
$523$	35.3037	−	12.8495i	1.54373	−	0.561870i	0.576790	−	0.816892i	$-0.304305\pi$
$523$	35.3037	−	12.8495i	1.54373	−	0.561870i	0.966935	+	0.255022i	$0.0820829\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.3162	−	11.1736i	0.580062	−	0.486730i
$528$		0			0
$529$	6.92275	+	39.2608i	0.300989	+	1.70699i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−23.0336			−0.997695
$534$		0			0
$535$	−5.03297	−	28.5434i	−0.217594	−	1.23404i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.61186	+	6.25593i	−0.155574	+	0.269462i
$540$		0			0
$541$	2.50545	−	0.911911i	0.107718	−	0.0392061i	−0.287599	−	0.957751i	$-0.592857\pi$
$541$	2.50545	−	0.911911i	0.107718	−	0.0392061i	0.395317	+	0.918545i	$0.370635\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	11.2760	−	63.9494i	0.483011	−	2.73929i
$546$		0			0
$547$	−17.5767	−	14.7486i	−0.751526	−	0.630605i	0.184380	−	0.982855i	$-0.440972\pi$
$547$	−17.5767	−	14.7486i	−0.751526	−	0.630605i	−0.935906	+	0.352250i	$0.885417\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	17.0859	+	9.54264i	0.727884	+	0.406530i
$552$		0			0
$553$	6.95400	+	2.53105i	0.295714	+	0.107631i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.26779	−	7.18999i	0.0537180	−	0.304650i	−0.946097	−	0.323883i	$-0.895011\pi$
$557$	1.26779	−	7.18999i	0.0537180	−	0.304650i	0.999815	+	0.0192335i	$0.00612259\pi$
$558$		0			0
$559$	2.55528	+	4.42588i	0.108077	+	0.187195i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	21.1345	−	36.6060i	0.890712	−	1.54276i	0.0516876	−	0.998663i	$-0.483540\pi$
$563$	21.1345	−	36.6060i	0.890712	−	1.54276i	0.839024	−	0.544094i	$-0.183127\pi$
$564$		0			0
$565$	1.51714	−	1.27304i	0.0638268	−	0.0535570i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.0782			−0.632112			−0.316056	−	0.948741i	$-0.602359\pi$
$569$	−15.0782			−0.632112			−0.316056	+	0.948741i	$0.602359\pi$
$570$		0			0
$571$	−42.7731			−1.79000			−0.894998	−	0.446070i	$-0.852823\pi$
$571$	−42.7731			−1.79000			−0.894998	+	0.446070i	$0.852823\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−36.7704	+	30.8540i	−1.53343	+	1.28670i
$576$		0			0
$577$	−11.6399	+	20.1609i	−0.484576	+	0.839311i	−0.999843	−	0.0177189i	$-0.994360\pi$
$577$	−11.6399	+	20.1609i	−0.484576	+	0.839311i	0.515267	+	0.857030i	$0.327693\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.67341	+	8.09458i	0.193886	+	0.335820i
$582$		0			0
$583$	−1.41974	+	8.05177i	−0.0587998	+	0.333470i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.5574	+	7.48229i	0.848496	+	0.308827i	0.729427	−	0.684059i	$-0.239787\pi$
$587$	20.5574	+	7.48229i	0.848496	+	0.308827i	0.119069	+	0.992886i	$0.462009\pi$
$588$		0			0
$589$	33.5421	−	6.40834i	1.38208	−	0.264051i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	25.1385	+	21.0937i	1.03231	+	0.866213i	0.991124	−	0.132938i	$-0.0424411\pi$
$593$	25.1385	+	21.0937i	1.03231	+	0.866213i	0.0411885	+	0.999151i	$0.486886\pi$
$594$		0			0
$595$	−1.52778	+	8.66445i	−0.0626327	+	0.355208i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.49512	+	2.36403i	−0.265384	+	0.0965917i	−0.471285	−	0.881981i	$-0.656210\pi$
$599$	−6.49512	+	2.36403i	−0.265384	+	0.0965917i	0.205901	+	0.978573i	$0.433987\pi$
$600$		0			0
$601$	17.0005	−	29.4457i	0.693465	−	1.20112i	−0.277231	−	0.960803i	$-0.589417\pi$
$601$	17.0005	−	29.4457i	0.693465	−	1.20112i	0.970696	−	0.240313i	$-0.0772500\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.38230	+	30.5245i	0.218822	+	1.24100i
$606$		0			0
$607$	21.1493			0.858424			0.429212	−	0.903204i	$-0.358791\pi$
$607$	21.1493			0.858424			0.429212	+	0.903204i	$0.358791\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.83204	−	16.0613i	−0.114572	−	0.649772i
$612$		0			0
$613$	−3.92762	+	3.29566i	−0.158635	+	0.133111i	−0.718650	−	0.695372i	$-0.755240\pi$
$613$	−3.92762	+	3.29566i	−0.158635	+	0.133111i	0.560015	+	0.828482i	$0.310795\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−25.5654	+	9.30504i	−1.02922	+	0.374607i	−0.800785	−	0.598951i	$-0.795584\pi$
$617$	−25.5654	+	9.30504i	−1.02922	+	0.374607i	−0.228439	+	0.973558i	$0.573362\pi$
$618$		0			0
$619$	5.74222	+	9.94582i	0.230799	+	0.399756i	0.958044	−	0.286623i	$-0.0925326\pi$
$619$	5.74222	+	9.94582i	0.230799	+	0.399756i	−0.727244	+	0.686379i	$0.759199\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.90997	+	3.28086i	0.156650	+	0.131445i
$624$		0			0
$625$	17.4969	+	6.36837i	0.699878	+	0.254735i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	16.4036	+	5.97041i	0.654053	+	0.238056i
$630$		0			0
$631$	2.74578	+	2.30398i	0.109308	+	0.0917201i	0.695803	−	0.718232i	$-0.255048\pi$
$631$	2.74578	+	2.30398i	0.109308	+	0.0917201i	−0.586496	+	0.809952i	$0.699493\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.2600	+	28.1632i	0.645259	+	1.11762i
$636$		0			0
$637$	14.9734	−	5.44987i	0.593268	−	0.215932i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.30991	+	2.77734i	−0.130734	+	0.109698i	−0.705810	−	0.708401i	$-0.749417\pi$
$641$	−3.30991	+	2.77734i	−0.130734	+	0.109698i	0.575076	+	0.818100i	$0.304972\pi$
$642$		0			0
$643$	−3.16436	−	17.9460i	−0.124790	−	0.707720i	−0.981432	−	0.191809i	$-0.938565\pi$
$643$	−3.16436	−	17.9460i	−0.124790	−	0.707720i	0.856642	−	0.515911i	$-0.172547\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	26.4490			1.03982			0.519910	−	0.854221i	$-0.325966\pi$
$647$	26.4490			1.03982			0.519910	+	0.854221i	$0.325966\pi$
$648$		0			0
$649$	−1.77529	−	10.0682i	−0.0696862	−	0.395210i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.435379	+	0.754099i	−0.0170377	+	0.0295102i	−0.874419	−	0.485172i	$-0.838757\pi$
$653$	−0.435379	+	0.754099i	−0.0170377	+	0.0295102i	0.857381	+	0.514683i	$0.172090\pi$
$654$		0			0
$655$	48.8820	−	17.7916i	1.90998	−	0.695175i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.71041	+	26.7141i	−0.183492	+	1.04063i	0.744387	+	0.667749i	$0.232742\pi$
$659$	−4.71041	+	26.7141i	−0.183492	+	1.04063i	−0.927878	+	0.372884i	$0.878369\pi$
$660$		0			0
$661$	2.42547	+	2.03521i	0.0943398	+	0.0791605i	0.688738	−	0.725011i	$-0.258165\pi$
$661$	2.42547	+	2.03521i	0.0943398	+	0.0791605i	−0.594398	+	0.804171i	$0.702610\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−10.9201	+	13.3971i	−0.423462	+	0.519516i
$666$		0			0
$667$	33.4513	+	12.1753i	1.29524	+	0.471428i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.29092	+	18.6637i	−0.127045	+	0.720506i
$672$		0			0
$673$	4.92701	+	8.53384i	0.189922	+	0.328955i	0.945224	−	0.326422i	$-0.105843\pi$
$673$	4.92701	+	8.53384i	0.189922	+	0.328955i	−0.755302	+	0.655377i	$0.772510\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.247613	−	0.428878i	0.00951653	−	0.0164831i	−0.861228	−	0.508219i	$-0.830304\pi$
$677$	0.247613	−	0.428878i	0.00951653	−	0.0164831i	0.870744	+	0.491736i	$0.163637\pi$
$678$		0			0
$679$	−2.31722	+	1.94438i	−0.0889268	+	0.0746185i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−11.8365			−0.452910			−0.226455	−	0.974022i	$-0.572714\pi$
$683$	−11.8365			−0.452910			−0.226455	+	0.974022i	$0.572714\pi$
$684$		0			0
$685$	−51.4647			−1.96636
$686$		0			0
$687$		0			0
$688$		0			0
$689$	13.8155	−	11.5926i	0.526330	−	0.441643i
$690$		0			0
$691$	9.11315	−	15.7844i	0.346680	−	0.600468i	−0.638977	−	0.769226i	$-0.720642\pi$
$691$	9.11315	−	15.7844i	0.346680	−	0.600468i	0.985658	+	0.168758i	$0.0539755\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	19.1917	+	33.2409i	0.727982	+	1.26090i
$696$		0			0
$697$	−3.10652	+	17.6180i	−0.117668	+	0.667328i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	15.5323	+	5.65330i	0.586648	+	0.213522i	0.618254	−	0.785978i	$-0.287840\pi$
$701$	15.5323	+	5.65330i	0.586648	+	0.213522i	−0.0316067	+	0.999500i	$0.510062\pi$
$702$		0			0
$703$	22.4149	+	25.9531i	0.845395	+	0.978839i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−11.3984	−	9.56438i	−0.428680	−	0.359705i
$708$		0			0
$709$	−3.27055	+	18.5482i	−0.122828	+	0.696593i	0.859746	+	0.510722i	$0.170622\pi$
$709$	−3.27055	+	18.5482i	−0.122828	+	0.696593i	−0.982574	+	0.185871i	$0.940489\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	58.3706	−	21.2452i	2.18600	−	0.795637i
$714$		0			0
$715$	−6.15066	+	10.6533i	−0.230022	+	0.398409i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.17486	+	35.0194i	0.230283	+	1.30600i	0.852323	+	0.523016i	$0.175193\pi$
$719$	6.17486	+	35.0194i	0.230283	+	1.30600i	−0.622039	+	0.782986i	$0.713696\pi$
$720$		0			0
$721$	20.9638			0.780732
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.71978	+	26.7672i	0.175288	+	0.994109i
$726$		0			0
$727$	−7.02657	+	5.89599i	−0.260601	+	0.218670i	−0.763721	−	0.645546i	$-0.776630\pi$
$727$	−7.02657	+	5.89599i	−0.260601	+	0.218670i	0.503120	+	0.864216i	$0.332185\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.72990	−	1.35757i	0.137955	−	0.0502117i
$732$		0			0
$733$	−5.77022	−	9.99431i	−0.213128	−	0.369148i	0.739564	−	0.673086i	$-0.235032\pi$
$733$	−5.77022	−	9.99431i	−0.213128	−	0.369148i	−0.952692	+	0.303938i	$0.901698\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.54934	−	3.81735i	−0.167577	−	0.140614i
$738$		0			0
$739$	9.08882	+	3.30806i	0.334338	+	0.121689i	0.503733	−	0.863859i	$-0.331959\pi$
$739$	9.08882	+	3.30806i	0.334338	+	0.121689i	−0.169396	+	0.985548i	$0.554182\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.9925	−	8.00463i	−0.806828	−	0.293662i	−0.0945153	−	0.995523i	$-0.530130\pi$
$743$	−21.9925	−	8.00463i	−0.806828	−	0.293662i	−0.712313	+	0.701862i	$0.752352\pi$
$744$		0			0
$745$	−59.4025	−	49.8446i	−2.17634	−	1.82616i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.19841	−	9.00392i	−0.189946	−	0.328996i
$750$		0			0
$751$	2.60159	−	0.946900i	0.0949332	−	0.0345529i	−0.294117	−	0.955769i	$-0.595026\pi$
$751$	2.60159	−	0.946900i	0.0949332	−	0.0345529i	0.389050	+	0.921217i	$0.372803\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.65359	−	7.26123i	0.314936	−	0.264263i
$756$		0			0
$757$	−3.87344	−	21.9673i	−0.140782	−	0.798417i	−0.970657	−	0.240467i	$-0.922699\pi$
$757$	−3.87344	−	21.9673i	−0.140782	−	0.798417i	0.829875	−	0.557950i	$-0.188412\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.666605			0.0241644			0.0120822	−	0.999927i	$-0.496154\pi$
$761$	0.666605			0.0241644			0.0120822	+	0.999927i	$0.496154\pi$
$762$		0			0
$763$	−4.04485	−	22.9395i	−0.146433	−	0.830464i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.2757	+	19.5300i	−0.407141	+	0.705189i
$768$		0			0
$769$	18.5010	−	6.73381i	0.667162	−	0.242827i	0.0138367	−	0.999904i	$-0.495595\pi$
$769$	18.5010	−	6.73381i	0.667162	−	0.242827i	0.653326	+	0.757077i	$0.273373\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.57404	−	48.6258i	0.308387	−	1.74895i	−0.298733	−	0.954337i	$-0.596564\pi$
$773$	8.57404	−	48.6258i	0.308387	−	1.74895i	0.607119	−	0.794611i	$-0.292325\pi$
$774$		0			0
$775$	36.3318	+	30.4860i	1.30508	+	1.09509i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−22.2045	+	27.2411i	−0.795558	+	0.976014i
$780$		0			0
$781$	−5.08756	−	1.85172i	−0.182047	−	0.0662597i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	13.1424	−	74.5344i	0.469073	−	2.66025i
$786$		0			0
$787$	20.9273	+	36.2472i	0.745978	+	1.29207i	0.949737	+	0.313050i	$0.101351\pi$
$787$	20.9273	+	36.2472i	0.745978	+	1.29207i	−0.203759	+	0.979021i	$0.565316\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.355214	−	0.615248i	0.0126300	−	0.0218757i
$792$		0			0
$793$	32.0240	−	26.8713i	1.13720	−	0.954228i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−50.2358			−1.77944			−0.889722	−	0.456503i	$-0.849102\pi$
$797$	−50.2358			−1.77944			−0.889722	+	0.456503i	$0.849102\pi$
$798$		0			0
$799$	−12.6670			−0.448126
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.93145	+	1.62068i	−0.0681593	+	0.0571925i
$804$		0			0
$805$	−15.7196	+	27.2272i	−0.554043	+	0.959631i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	4.91982	+	8.52138i	0.172972	+	0.299596i	0.939458	−	0.342665i	$-0.111330\pi$
$809$	4.91982	+	8.52138i	0.172972	+	0.299596i	−0.766486	+	0.642261i	$0.777996\pi$
$810$		0			0
$811$	−4.97290	+	28.2027i	−0.174622	+	0.990331i	0.763957	+	0.645267i	$0.223254\pi$
$811$	−4.97290	+	28.2027i	−0.174622	+	0.990331i	−0.938579	+	0.345064i	$0.887857\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−40.8416	−	14.8651i	−1.43062	−	0.520703i
$816$		0			0
$817$	7.69765	+	1.24451i	0.269307	+	0.0435399i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	36.3403	+	30.4931i	1.26829	+	1.06422i	0.994748	+	0.102356i	$0.0326381\pi$
$821$	36.3403	+	30.4931i	1.26829	+	1.06422i	0.273537	+	0.961861i	$0.411806\pi$
$822$		0			0
$823$	7.04848	−	39.9739i	0.245695	−	1.39340i	−0.573179	−	0.819430i	$-0.694290\pi$
$823$	7.04848	−	39.9739i	0.245695	−	1.39340i	0.818874	−	0.573974i	$-0.194599\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.74185	+	0.633981i	−0.0605700	+	0.0220457i	−0.372127	−	0.928182i	$-0.621372\pi$
$827$	−1.74185	+	0.633981i	−0.0605700	+	0.0220457i	0.311557	+	0.950227i	$0.399149\pi$
$828$		0			0
$829$	15.4767	−	26.8065i	0.537529	−	0.931028i	−0.461507	−	0.887136i	$-0.652691\pi$
$829$	15.4767	−	26.8065i	0.537529	−	0.931028i	0.999036	−	0.0438911i	$-0.0139755\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.14906	−	12.1879i	−0.0744605	−	0.422286i
$834$		0			0
$835$	−50.4395			−1.74553
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−5.44892	−	30.9024i	−0.188118	−	1.06687i	−0.921884	−	0.387466i	$-0.873350\pi$
$839$	−5.44892	−	30.9024i	−0.188118	−	1.06687i	0.733766	−	0.679402i	$-0.237761\pi$
$840$		0			0
$841$	−6.77385	+	5.68394i	−0.233581	+	0.195998i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−15.1167	+	5.50203i	−0.520030	+	0.189276i
$846$		0			0
$847$	5.55923	+	9.62886i	0.191017	+	0.330852i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	47.7847	+	40.0961i	1.63804	+	1.37448i
$852$		0			0
$853$	−26.6764	−	9.70940i	−0.913381	−	0.332444i	−0.157779	−	0.987474i	$-0.550433\pi$
$853$	−26.6764	−	9.70940i	−0.913381	−	0.332444i	−0.755602	+	0.655031i	$0.772656\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.11088	−	2.22418i	−0.208744	−	0.0759765i	0.235532	−	0.971867i	$-0.424317\pi$
$857$	−6.11088	−	2.22418i	−0.208744	−	0.0759765i	−0.444276	+	0.895890i	$0.646539\pi$
$858$		0			0
$859$	−12.5436	−	10.5253i	−0.427982	−	0.359119i	0.403208	−	0.915108i	$-0.367895\pi$
$859$	−12.5436	−	10.5253i	−0.427982	−	0.359119i	−0.831190	+	0.555989i	$0.812340\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.5642	−	42.5464i	−0.836174	−	1.44829i	−0.893071	−	0.449915i	$-0.851454\pi$
$863$	−24.5642	−	42.5464i	−0.836174	−	1.44829i	0.0568979	−	0.998380i	$-0.481879\pi$
$864$		0			0
$865$	−52.1765	+	18.9907i	−1.77406	+	0.645703i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.15614	−	5.16562i	0.208833	−	0.175232i
$870$		0			0
$871$	2.27478	+	12.9009i	0.0770779	+	0.437130i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.17886			−0.141271
$876$		0			0
$877$	−2.24069	−	12.7076i	−0.0756628	−	0.429105i	−0.998984	−	0.0450756i	$-0.985647\pi$
$877$	−2.24069	−	12.7076i	−0.0756628	−	0.429105i	0.923321	−	0.384030i	$-0.125464\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.6390	+	32.2837i	−0.627965	+	1.08767i	0.359995	+	0.932954i	$0.382778\pi$
$881$	−18.6390	+	32.2837i	−0.627965	+	1.08767i	−0.987960	+	0.154712i	$0.950555\pi$
$882$		0			0
$883$	−7.29529	+	2.65527i	−0.245506	+	0.0893570i	−0.461842	−	0.886962i	$-0.652811\pi$
$883$	−7.29529	+	2.65527i	−0.245506	+	0.0893570i	0.216336	+	0.976319i	$0.430589\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.14167	−	40.5024i	0.239794	−	1.35994i	−0.592485	−	0.805581i	$-0.701853\pi$
$887$	7.14167	−	40.5024i	0.239794	−	1.35994i	0.832279	−	0.554357i	$-0.187036\pi$
$888$		0			0
$889$	8.93618	+	7.49835i	0.299710	+	0.251487i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−21.7253	−	12.1338i	−0.727011	−	0.406043i
$894$		0			0
$895$	−42.7840	−	15.5721i	−1.43011	−	0.520518i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.10781	−	34.6391i	0.203707	−	1.15528i
$900$		0			0
$901$	−7.00369	−	12.1308i	−0.233327	−	0.404134i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	33.8604	−	58.6479i	1.12556	−	1.94952i
$906$		0			0
$907$	−25.5449	+	21.4347i	−0.848206	+	0.711729i	−0.959394	−	0.282070i	$-0.908979\pi$
$907$	−25.5449	+	21.4347i	−0.848206	+	0.711729i	0.111188	+	0.993799i	$0.464534\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−26.6721			−0.883687			−0.441844	−	0.897092i	$-0.645675\pi$
$911$	−26.6721			−0.883687			−0.441844	+	0.897092i	$0.645675\pi$
$912$		0			0
$913$	10.1501			0.335919
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.2943	−	11.9944i	0.472040	−	0.396089i
$918$		0			0
$919$	1.49951	−	2.59722i	0.0494642	−	0.0856745i	−0.840233	−	0.542225i	$-0.817582\pi$
$919$	1.49951	−	2.59722i	0.0494642	−	0.0856745i	0.889697	+	0.456551i	$0.150915\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.97128	+	10.3426i	0.196547	+	0.340429i
$924$		0			0
$925$	−8.27047	+	46.9041i	−0.271931	+	1.54220i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6.32189	−	2.30098i	−0.207415	−	0.0754927i	0.236224	−	0.971699i	$-0.424090\pi$
$929$	−6.32189	−	2.30098i	−0.207415	−	0.0754927i	−0.443638	+	0.896206i	$0.646312\pi$
$930$		0			0
$931$	7.98903	−	22.9623i	0.261830	−	0.752559i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.31896	+	6.14134i	0.239356	+	0.200843i
$936$		0			0
$937$	−2.73192	+	15.4935i	−0.0892481	+	0.506151i	0.907111	+	0.420892i	$0.138283\pi$
$937$	−2.73192	+	15.4935i	−0.0892481	+	0.506151i	−0.996359	+	0.0852590i	$0.972828\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.49945	−	1.63766i	0.146678	−	0.0533864i	−0.267638	−	0.963520i	$-0.586243\pi$
$941$	4.49945	−	1.63766i	0.146678	−	0.0533864i	0.414316	+	0.910133i	$0.364021\pi$
$942$		0			0
$943$	−31.9637	+	55.3627i	−1.04088	+	1.80286i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.17749	+	29.3630i	0.168246	+	0.954169i	0.945654	+	0.325173i	$0.105423\pi$
$947$	5.17749	+	29.3630i	0.168246	+	0.954169i	−0.777409	+	0.628996i	$0.783466\pi$
$948$		0			0
$949$	5.56164			0.180538
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.728873	+	4.13365i	0.0236105	+	0.133902i	0.994335	−	0.106295i	$-0.0338989\pi$
$953$	0.728873	+	4.13365i	0.0236105	+	0.133902i	−0.970724	+	0.240197i	$0.922788\pi$
$954$		0			0
$955$	54.0108	−	45.3204i	1.74775	−	1.46653i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.3477	+	6.31405i	−0.560187	+	0.203891i
$960$		0			0
$961$	−15.1879	−	26.3062i	−0.489932	−	0.848588i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−35.7045	−	29.9597i	−1.14937	−	0.964435i
$966$		0			0
$967$	−7.76004	−	2.82442i	−0.249546	−	0.0908274i	0.214219	−	0.976786i	$-0.431279\pi$
$967$	−7.76004	−	2.82442i	−0.249546	−	0.0908274i	−0.463765	+	0.885958i	$0.653502\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.3878	+	4.14480i	0.365450	+	0.133013i	0.518217	−	0.855249i	$-0.326596\pi$
$971$	11.3878	+	4.14480i	0.365450	+	0.133013i	−0.152767	+	0.988262i	$0.548818\pi$
$972$		0			0
$973$	10.5474	+	8.85028i	0.338133	+	0.283727i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.8156	+	25.6614i	0.473994	+	0.820982i	0.999557	−	0.0297727i	$-0.00947834\pi$
$977$	14.8156	+	25.6614i	0.473994	+	0.820982i	−0.525562	+	0.850755i	$0.676145\pi$
$978$		0			0
$979$	5.20849	−	1.89573i	0.166464	−	0.0605879i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−27.4542	+	23.0368i	−0.875652	+	0.734759i	−0.965280	−	0.261216i	$-0.915876\pi$
$983$	−27.4542	+	23.0368i	−0.875652	+	0.734759i	0.0896287	+	0.995975i	$0.471432\pi$
$984$		0			0
$985$	3.28086	+	18.6067i	0.104537	+	0.592858i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.1838			0.451020
$990$		0			0
$991$	−2.48372	−	14.0859i	−0.0788980	−	0.447453i	−0.998507	−	0.0546185i	$-0.982606\pi$
$991$	−2.48372	−	14.0859i	−0.0788980	−	0.447453i	0.919609	−	0.392834i	$-0.128505\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	17.8574	−	30.9300i	0.566118	−	0.980546i
$996$		0			0
$997$	2.44915	−	0.891419i	0.0775654	−	0.0282315i	−0.302946	−	0.953008i	$-0.597970\pi$
$997$	2.44915	−	0.891419i	0.0775654	−	0.0282315i	0.380511	+	0.924776i	$0.375748\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.bo.e.289.1		12
3.2	odd	2		228.2.q.b.61.2	✓	12
12.11	even	2		912.2.bo.g.289.2		12
19.5	even	9	inner	684.2.bo.e.613.1		12
57.5	odd	18		228.2.q.b.157.2	yes	12
57.29	even	18		4332.2.a.u.1.5		6
57.47	odd	18		4332.2.a.t.1.5		6
228.119	even	18		912.2.bo.g.385.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.q.b.61.2	✓	12	3.2	odd	2
228.2.q.b.157.2	yes	12	57.5	odd	18
684.2.bo.e.289.1		12	1.1	even	1	trivial
684.2.bo.e.613.1		12	19.5	even	9	inner
912.2.bo.g.289.2		12	12.11	even	2
912.2.bo.g.385.2		12	228.119	even	18
4332.2.a.t.1.5		6	57.47	odd	18
4332.2.a.u.1.5		6	57.29	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.54690 + 2.13710i) q^{5} +(-0.596313 + 1.03284i) q^{7} +(0.647560 + 1.12161i) q^{11} +(0.496083 - 2.81343i) q^{13} +(-2.08503 - 0.758891i) q^{17} +(-2.84913 - 3.29886i) q^{19} +(-6.07384 - 5.09656i) q^{23} +(1.05125 - 5.96192i) q^{25} +(-4.21893 + 1.53557i) q^{29} +(-3.91714 + 6.78468i) q^{31} +(-0.688545 - 3.90493i) q^{35} -7.86729 q^{37} +(-1.40006 - 7.94015i) q^{41} +(-1.37037 + 1.14988i) q^{43} +(5.36453 - 1.95253i) q^{47} +(2.78882 + 4.83038i) q^{49} +(4.83597 + 4.05786i) q^{53} +(-4.04626 - 1.47272i) q^{55} +(-7.41778 - 2.69985i) q^{59} +(11.2096 + 9.40599i) q^{61} +(4.74910 + 8.22569i) q^{65} +(-4.30894 + 1.56833i) q^{67} +(-3.20234 + 2.68708i) q^{71} +(0.338056 + 1.91721i) q^{73} -1.54460 q^{77} +(-1.07749 - 6.11077i) q^{79} +(3.91858 - 6.78719i) q^{83} +(6.93220 - 2.52311i) q^{85} +(0.743166 - 4.21470i) q^{89} +(2.61001 + 2.19006i) q^{91} +(14.3064 + 2.31298i) q^{95} +(2.38339 + 0.867483i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 9 q^{7} + 9 q^{11} - 3 q^{13} - 12 q^{17} + 9 q^{19} - 15 q^{23} + 12 q^{25} + 24 q^{29} - 6 q^{31} + 42 q^{35} + 12 q^{37} - 6 q^{41} - 39 q^{43} + 3 q^{47} - 21 q^{49} - 18 q^{53} + 45 q^{55}+ \cdots - 15 q^{97}+O(q^{100}) \) 12 * q + 6 * q^5 - 9 * q^7 + 9 * q^11 - 3 * q^13 - 12 * q^17 + 9 * q^19 - 15 * q^23 + 12 * q^25 + 24 * q^29 - 6 * q^31 + 42 * q^35 + 12 * q^37 - 6 * q^41 - 39 * q^43 + 3 * q^47 - 21 * q^49 - 18 * q^53 + 45 * q^55 + 33 * q^61 + 33 * q^65 - 27 * q^67 - 6 * q^71 - 24 * q^73 + 18 * q^79 - 3 * q^83 + 39 * q^85 + 15 * q^89 + 18 * q^91 + 30 * q^95 - 15 * q^97

Introduction

L-functions

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