LMFDB - Embedded newform 261.2.k.c.136.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(82,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([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("261.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$261 = 3^{2} \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	261.k (of order $7$ , degree $6$ , minimal)

Newform invariants

comment:select newform

sage:traces = [18,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64$ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			136.2
Root			$0.102196 - 0.128149i$ of defining polynomial
Character	$\chi$	$=$	261.136
Dual form			261.2.k.c.190.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04865 - 0.505001i) q^{2} +(-0.402348 + 0.504528i) q^{4} +(2.80239 - 1.34956i) q^{5} +(1.08876 + 1.36527i) q^{7} +(-0.685121 + 3.00171i) q^{8} +(2.25719 - 2.83042i) q^{10} +(-0.616885 - 2.70275i) q^{11} +(0.256556 + 1.12405i) q^{13} +(1.83119 + 0.881853i) q^{14} +(0.510226 + 2.23545i) q^{16} -2.64265 q^{17} +(4.50431 - 5.64823i) q^{19} +(-0.446645 + 1.95688i) q^{20} +(-2.01179 - 2.52270i) q^{22} +(-2.53201 - 1.21935i) q^{23} +(2.91464 - 3.65485i) q^{25} +(0.836681 + 1.04917i) q^{26} -1.12688 q^{28} +(0.497296 + 5.36215i) q^{29} +(-3.59066 + 1.72917i) q^{31} +(-2.17538 - 2.72784i) q^{32} +(-2.77121 + 1.33454i) q^{34} +(4.89365 + 2.35666i) q^{35} +(-2.32975 + 10.2073i) q^{37} +(1.87107 - 8.19768i) q^{38} +(2.13102 + 9.33659i) q^{40} -8.92649 q^{41} +(-10.6279 - 5.11815i) q^{43} +(1.61181 + 0.776209i) q^{44} -3.27095 q^{46} +(-1.63447 - 7.16106i) q^{47} +(0.879102 - 3.85160i) q^{49} +(1.21073 - 5.30454i) q^{50} +(-0.670338 - 0.322818i) q^{52} +(-4.85314 + 2.33715i) q^{53} +(-5.37628 - 6.74164i) q^{55} +(-4.84407 + 2.33278i) q^{56} +(3.22938 + 5.37187i) q^{58} +8.20042 q^{59} +(3.06034 + 3.83755i) q^{61} +(-2.89209 + 3.62657i) q^{62} +(-7.79050 - 3.75171i) q^{64} +(2.23594 + 2.80378i) q^{65} +(0.100933 - 0.442217i) q^{67} +(1.06326 - 1.33329i) q^{68} +6.32182 q^{70} +(2.58226 + 11.3136i) q^{71} +(11.5822 + 5.57770i) q^{73} +(2.71162 + 11.8804i) q^{74} +(1.03739 + 4.54510i) q^{76} +(3.01833 - 3.78486i) q^{77} +(3.43076 - 15.0312i) q^{79} +(4.44673 + 5.57602i) q^{80} +(-9.36072 + 4.50789i) q^{82} +(2.62789 - 3.29527i) q^{83} +(-7.40575 + 3.56642i) q^{85} -13.7296 q^{86} +8.53551 q^{88} +(-1.83072 + 0.881630i) q^{89} +(-1.25529 + 1.57409i) q^{91} +(1.63394 - 0.786865i) q^{92} +(-5.33032 - 6.68401i) q^{94} +(5.00022 - 21.9074i) q^{95} +(7.89711 - 9.90266i) q^{97} +(-1.02319 - 4.48291i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28}+ \cdots - 31 q^{98}+O(q^{100})$ 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$ .

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.04865	−	0.505001i	0.741505	−	0.357090i	−0.0246928	−	0.999695i	$-0.507861\pi$
$2$	1.04865	−	0.505001i	0.741505	−	0.357090i	0.766197	+	0.642605i	$0.222146\pi$
$3$		0			0
$3$		0			0
$4$	−0.402348	+	0.504528i	−0.201174	+	0.252264i
$5$	2.80239	−	1.34956i	1.25327	−	0.603542i	0.314882	−	0.949131i	$-0.398035\pi$
$5$	2.80239	−	1.34956i	1.25327	−	0.603542i	0.938386	+	0.345588i	$0.112321\pi$
$6$		0			0
$7$	1.08876	+	1.36527i	0.411514	+	0.516022i	0.943789	−	0.330550i	$-0.107234\pi$
$7$	1.08876	+	1.36527i	0.411514	+	0.516022i	−0.532275	+	0.846572i	$0.678663\pi$
$8$	−0.685121	+	3.00171i	−0.242227	+	1.06127i
$9$		0			0
$10$	2.25719	−	2.83042i	0.713786	−	0.895059i
$11$	−0.616885	−	2.70275i	−0.185998	−	0.814909i	−0.978699	−	0.205299i	$-0.934183\pi$
$11$	−0.616885	−	2.70275i	−0.185998	−	0.814909i	0.792701	−	0.609610i	$-0.208674\pi$
$12$		0			0
$13$	0.256556	+	1.12405i	0.0711559	+	0.311754i	0.997964	−	0.0637811i	$-0.0203160\pi$
$13$	0.256556	+	1.12405i	0.0711559	+	0.311754i	−0.926808	+	0.375535i	$0.877459\pi$
$14$	1.83119	+	0.881853i	0.489405	+	0.235685i
$15$		0			0
$16$	0.510226	+	2.23545i	0.127557	+	0.558862i
$17$	−2.64265			−0.640937			−0.320469	−	0.947259i	$-0.603840\pi$
$17$	−2.64265			−0.640937			−0.320469	+	0.947259i	$0.603840\pi$
$18$		0			0
$19$	4.50431	−	5.64823i	1.03336	−	1.29579i	0.0790836	−	0.996868i	$-0.474801\pi$
$19$	4.50431	−	5.64823i	1.03336	−	1.29579i	0.954277	−	0.298925i	$-0.0966280\pi$
$20$	−0.446645	+	1.95688i	−0.0998728	+	0.437571i
$21$		0			0
$22$	−2.01179	−	2.52270i	−0.428914	−	0.537841i
$23$	−2.53201	−	1.21935i	−0.527960	−	0.254252i	0.150862	−	0.988555i	$-0.451795\pi$
$23$	−2.53201	−	1.21935i	−0.527960	−	0.254252i	−0.678822	+	0.734303i	$0.737509\pi$
$24$		0			0
$25$	2.91464	−	3.65485i	0.582929	−	0.730970i
$26$	0.836681	+	1.04917i	0.164087	+	0.205758i
$27$		0			0
$28$	−1.12688			−0.212959
$29$	0.497296	+	5.36215i	0.0923456	+	0.995727i
$29$	0.497296	+	5.36215i	0.0923456	+	0.995727i
$30$		0			0
$31$	−3.59066	+	1.72917i	−0.644901	+	0.310568i	−0.727595	−	0.686007i	$-0.759362\pi$
$31$	−3.59066	+	1.72917i	−0.644901	+	0.310568i	0.0826940	+	0.996575i	$0.473648\pi$
$32$	−2.17538	−	2.72784i	−0.384557	−	0.482219i
$33$		0			0
$34$	−2.77121	+	1.33454i	−0.475258	+	0.228872i
$35$	4.89365	+	2.35666i	0.827178	+	0.398348i
$36$		0			0
$37$	−2.32975	+	10.2073i	−0.383009	+	1.67807i	0.304988	+	0.952356i	$0.401348\pi$
$37$	−2.32975	+	10.2073i	−0.383009	+	1.67807i	−0.687996	+	0.725714i	$0.741509\pi$
$38$	1.87107	−	8.19768i	0.303527	−	1.32984i
$39$		0			0
$40$	2.13102	+	9.33659i	0.336943	+	1.47624i
$41$	−8.92649			−1.39408			−0.697041	−	0.717031i	$-0.745501\pi$
$41$	−8.92649			−1.39408			−0.697041	+	0.717031i	$0.745501\pi$
$42$		0			0
$43$	−10.6279	−	5.11815i	−1.62075	−	0.780510i	−0.620752	−	0.784007i	$-0.713173\pi$
$43$	−10.6279	−	5.11815i	−1.62075	−	0.780510i	−0.999994	+	0.00349639i	$0.998887\pi$
$44$	1.61181	+	0.776209i	0.242990	+	0.117018i
$45$		0			0
$46$	−3.27095			−0.482275
$47$	−1.63447	−	7.16106i	−0.238411	−	1.04455i	−0.942440	−	0.334376i	$-0.891474\pi$
$47$	−1.63447	−	7.16106i	−0.238411	−	1.04455i	0.704028	−	0.710172i	$-0.251383\pi$
$48$		0			0
$49$	0.879102	−	3.85160i	0.125586	−	0.550228i
$50$	1.21073	−	5.30454i	0.171223	−	0.750175i
$51$		0			0
$52$	−0.670338	−	0.322818i	−0.0929591	−	0.0447667i
$53$	−4.85314	+	2.33715i	−0.666629	+	0.321032i	−0.736415	−	0.676530i	$-0.763483\pi$
$53$	−4.85314	+	2.33715i	−0.666629	+	0.321032i	0.0697855	+	0.997562i	$0.477769\pi$
$54$		0			0
$55$	−5.37628	−	6.74164i	−0.724937	−	0.909043i
$56$	−4.84407	+	2.33278i	−0.647316	+	0.311731i
$57$		0			0
$58$	3.22938	+	5.37187i	0.424039	+	0.705361i
$59$	8.20042			1.06760			0.533802	−	0.845610i	$-0.320763\pi$
$59$	8.20042			1.06760			0.533802	+	0.845610i	$0.320763\pi$
$60$		0			0
$61$	3.06034	+	3.83755i	0.391837	+	0.491348i	0.938148	−	0.346234i	$-0.112540\pi$
$61$	3.06034	+	3.83755i	0.391837	+	0.491348i	−0.546311	+	0.837582i	$0.683968\pi$
$62$	−2.89209	+	3.62657i	−0.367296	+	0.460575i
$63$		0			0
$64$	−7.79050	−	3.75171i	−0.973813	−	0.468963i
$65$	2.23594	+	2.80378i	0.277334	+	0.347766i
$66$		0			0
$67$	0.100933	−	0.442217i	0.0123309	−	0.0540254i	−0.968388	−	0.249448i	$-0.919751\pi$
$67$	0.100933	−	0.442217i	0.0123309	−	0.0540254i	0.980719	+	0.195423i	$0.0626079\pi$
$68$	1.06326	−	1.33329i	0.128940	−	0.161685i
$69$		0			0
$70$	6.32182			0.755602
$71$	2.58226	+	11.3136i	0.306458	+	1.34268i	0.860185	+	0.509983i	$0.170348\pi$
$71$	2.58226	+	11.3136i	0.306458	+	1.34268i	−0.553726	+	0.832699i	$0.686795\pi$
$72$		0			0
$73$	11.5822	+	5.57770i	1.35559	+	0.652820i	0.963650	−	0.267169i	$-0.0860880\pi$
$73$	11.5822	+	5.57770i	1.35559	+	0.652820i	0.391945	+	0.919989i	$0.371802\pi$
$74$	2.71162	+	11.8804i	0.315219	+	1.38107i
$75$		0			0
$76$	1.03739	+	4.54510i	0.118997	+	0.521359i
$77$	3.01833	−	3.78486i	0.343970	−	0.431325i
$78$		0			0
$79$	3.43076	−	15.0312i	0.385991	−	1.69114i	−0.292286	−	0.956331i	$-0.594416\pi$
$79$	3.43076	−	15.0312i	0.385991	−	1.69114i	0.678277	−	0.734807i	$-0.262727\pi$
$80$	4.44673	+	5.57602i	0.497160	+	0.623418i
$81$		0			0
$82$	−9.36072	+	4.50789i	−1.03372	+	0.497813i
$83$	2.62789	−	3.29527i	0.288448	−	0.361702i	−0.616403	−	0.787431i	$-0.711411\pi$
$83$	2.62789	−	3.29527i	0.288448	−	0.361702i	0.904851	+	0.425728i	$0.139982\pi$
$84$		0			0
$85$	−7.40575	+	3.56642i	−0.803267	+	0.386833i
$86$	−13.7296			−1.48050
$87$		0			0
$88$	8.53551			0.909889
$89$	−1.83072	+	0.881630i	−0.194056	+	0.0934526i	−0.528389	−	0.849003i	$-0.677204\pi$
$89$	−1.83072	+	0.881630i	−0.194056	+	0.0934526i	0.334332	+	0.942455i	$0.391489\pi$
$90$		0			0
$91$	−1.25529	+	1.57409i	−0.131590	+	0.165009i
$92$	1.63394	−	0.786865i	0.170350	−	0.0820364i
$93$		0			0
$94$	−5.33032	−	6.68401i	−0.549780	−	0.689403i
$95$	5.00022	−	21.9074i	0.513012	−	2.24765i
$96$		0			0
$97$	7.89711	−	9.90266i	0.801830	−	1.00546i	−0.197852	−	0.980232i	$-0.563396\pi$
$97$	7.89711	−	9.90266i	0.801830	−	1.00546i	0.999682	−	0.0252311i	$-0.00803215\pi$
$98$	−1.02319	−	4.48291i	−0.103358	−	0.452842i
$99$		0			0
$100$	0.671273	+	2.94104i	0.0671273	+	0.294104i
$101$	2.85191	+	1.37341i	0.283776	+	0.136659i	0.570358	−	0.821397i	$-0.306805\pi$
$101$	2.85191	+	1.37341i	0.283776	+	0.136659i	−0.286582	+	0.958056i	$0.592519\pi$
$102$		0			0
$103$	−0.582986	−	2.55423i	−0.0574433	−	0.251676i	0.938051	−	0.346497i	$-0.112629\pi$
$103$	−0.582986	−	2.55423i	−0.0574433	−	0.251676i	−0.995494	+	0.0948218i	$0.969772\pi$
$104$	−3.54984			−0.348090
$105$		0			0
$106$	−3.90896	+	4.90168i	−0.379672	+	0.476093i
$107$	−2.23430	+	9.78910i	−0.215998	+	0.946348i	0.744404	+	0.667730i	$0.232734\pi$
$107$	−2.23430	+	9.78910i	−0.215998	+	0.946348i	−0.960402	+	0.278619i	$0.910123\pi$
$108$		0			0
$109$	−2.87905	−	3.61022i	−0.275763	−	0.345796i	0.624593	−	0.780951i	$-0.285265\pi$
$109$	−2.87905	−	3.61022i	−0.275763	−	0.345796i	−0.900356	+	0.435155i	$0.856694\pi$
$110$	−9.04235	−	4.35457i	−0.862154	−	0.415192i
$111$		0			0
$112$	−2.49646	+	3.13047i	−0.235894	+	0.295801i
$113$	3.23577	+	4.05752i	0.304395	+	0.381700i	0.910378	−	0.413779i	$-0.135791\pi$
$113$	3.23577	+	4.05752i	0.304395	+	0.381700i	−0.605982	+	0.795478i	$0.707220\pi$
$114$		0			0
$115$	−8.74126			−0.815127
$116$	−2.90544	−	1.90655i	−0.269764	−	0.177019i
$117$		0			0
$118$	8.59933	−	4.14122i	0.791633	−	0.381230i
$119$	−2.87722	−	3.60792i	−0.263754	−	0.330738i
$120$		0			0
$121$	2.98635	−	1.43815i	0.271487	−	0.130741i
$122$	5.14719	+	2.47875i	0.466004	+	0.224416i
$123$		0			0
$124$	0.572278	−	2.50731i	0.0513921	−	0.225163i
$125$	−0.225132	+	0.986369i	−0.0201364	+	0.0882235i
$126$		0			0
$127$	3.34102	+	14.6380i	0.296467	+	1.29891i	0.875347	+	0.483496i	$0.160633\pi$
$127$	3.34102	+	14.6380i	0.296467	+	1.29891i	−0.578879	+	0.815413i	$0.696510\pi$
$128$	−3.08601			−0.272767
$129$		0			0
$130$	3.76062	+	1.81102i	0.329829	+	0.158837i
$131$	−0.482335	−	0.232280i	−0.0421418	−	0.0202944i	0.412694	−	0.910870i	$-0.364588\pi$
$131$	−0.482335	−	0.232280i	−0.0421418	−	0.0202944i	−0.454836	+	0.890575i	$0.650302\pi$
$132$		0			0
$133$	12.6155			1.09390
$134$	−0.117477	−	0.514700i	−0.0101485	−	0.0444633i
$135$		0			0
$136$	1.81054	−	7.93248i	0.155252	−	0.680205i
$137$	2.77503	−	12.1582i	0.237087	−	1.03874i	−0.706525	−	0.707688i	$-0.749738\pi$
$137$	2.77503	−	12.1582i	0.237087	−	1.03874i	0.943611	−	0.331056i	$-0.107405\pi$
$138$		0			0
$139$	7.82790	+	3.76972i	0.663954	+	0.319743i	0.735333	−	0.677706i	$-0.237026\pi$
$139$	7.82790	+	3.76972i	0.663954	+	0.319743i	−0.0713790	+	0.997449i	$0.522740\pi$
$140$	−3.15795	+	1.52079i	−0.266895	+	0.128530i
$141$		0			0
$142$	8.42128	+	10.5600i	0.706698	+	0.886172i
$143$	2.87975	−	1.38681i	0.240817	−	0.115971i
$144$		0			0
$145$	8.63018	+	14.3557i	0.716697	+	1.19218i
$146$	14.9624			1.23830
$147$		0			0
$148$	−4.21250	−	5.28231i	−0.346265	−	0.434203i
$149$	9.37128	−	11.7512i	0.767726	−	0.962697i	−0.232225	−	0.972662i	$-0.574600\pi$
$149$	9.37128	−	11.7512i	0.767726	−	0.962697i	0.999950	+	0.00996473i	$0.00317193\pi$
$150$		0			0
$151$	−13.5900	−	6.54459i	−1.10594	−	0.532591i	−0.210417	−	0.977612i	$-0.567482\pi$
$151$	−13.5900	−	6.54459i	−1.10594	−	0.532591i	−0.895521	+	0.445020i	$0.853196\pi$
$152$	13.8684	+	17.3904i	1.12487	+	1.41055i
$153$		0			0
$154$	1.25380	−	5.49324i	0.101034	−	0.442658i
$155$	−7.72881	+	9.69162i	−0.620793	+	0.778450i
$156$		0			0
$157$	−9.94273			−0.793517			−0.396758	−	0.917923i	$-0.629865\pi$
$157$	−9.94273			−0.793517			−0.396758	+	0.917923i	$0.629865\pi$
$158$	−3.99310	−	17.4949i	−0.317674	−	1.39182i
$159$		0			0
$160$	−9.77767	−	4.70868i	−0.772993	−	0.372254i
$161$	−1.09202	−	4.78444i	−0.0860630	−	0.377067i
$162$		0			0
$163$	0.610696	+	2.67563i	0.0478334	+	0.209572i	0.993197	−	0.116446i	$-0.0371502\pi$
$163$	0.610696	+	2.67563i	0.0478334	+	0.209572i	−0.945364	+	0.326018i	$0.894293\pi$
$164$	3.59155	−	4.50366i	0.280453	−	0.351677i
$165$		0			0
$166$	1.09161	−	4.78265i	0.0847253	−	0.371206i
$167$	1.98862	+	2.49365i	0.153884	+	0.192964i	0.852797	−	0.522242i	$-0.174904\pi$
$167$	1.98862	+	2.49365i	0.153884	+	0.192964i	−0.698914	+	0.715206i	$0.746333\pi$
$168$		0			0
$169$	10.5149	−	5.06373i	0.808841	−	0.389517i
$170$	−5.96496	+	7.47983i	−0.457492	+	0.573677i
$171$		0			0
$172$	6.85838	−	3.30282i	0.522946	−	0.251838i
$173$	−7.57784			−0.576132			−0.288066	−	0.957611i	$-0.593012\pi$
$173$	−7.57784			−0.576132			−0.288066	+	0.957611i	$0.593012\pi$
$174$		0			0
$175$	8.16319			0.617079
$176$	5.72710	−	2.75803i	0.431697	−	0.207894i
$177$		0			0
$178$	−1.47456	+	1.84904i	−0.110523	+	0.138591i
$179$	−2.53345	+	1.22005i	−0.189359	+	0.0911906i	−0.526161	−	0.850385i	$-0.676369\pi$
$179$	−2.53345	+	1.22005i	−0.189359	+	0.0911906i	0.336802	+	0.941576i	$0.390655\pi$
$180$		0			0
$181$	4.38980	+	5.50464i	0.326292	+	0.409157i	0.917737	−	0.397188i	$-0.130014\pi$
$181$	4.38980	+	5.50464i	0.326292	+	0.409157i	−0.591446	+	0.806345i	$0.701443\pi$
$182$	−0.521441	+	2.28458i	−0.0386518	+	0.169345i
$183$		0			0
$184$	5.39487	−	6.76495i	0.397715	−	0.498719i
$185$	7.24651	+	31.7490i	0.532774	+	2.33424i
$186$		0			0
$187$	1.63021	+	7.14243i	0.119213	+	0.522306i
$188$	4.27058	+	2.05660i	0.311464	+	0.149993i
$189$		0			0
$190$	−5.81981	−	25.4982i	−0.422213	−	1.84984i
$191$	−4.42589			−0.320246			−0.160123	−	0.987097i	$-0.551189\pi$
$191$	−4.42589			−0.320246			−0.160123	+	0.987097i	$0.551189\pi$
$192$		0			0
$193$	−2.51833	+	3.15788i	−0.181273	+	0.227309i	−0.864163	−	0.503212i	$-0.832151\pi$
$193$	−2.51833	+	3.15788i	−0.181273	+	0.227309i	0.682890	+	0.730521i	$0.260723\pi$
$194$	3.28041	−	14.3724i	0.235520	−	1.03188i
$195$		0			0
$196$	1.58953	+	1.99321i	0.113538	+	0.142372i
$197$	10.8033	+	5.20261i	0.769706	+	0.370671i	0.777161	−	0.629302i	$-0.216659\pi$
$197$	10.8033	+	5.20261i	0.769706	+	0.370671i	−0.00745564	+	0.999972i	$0.502373\pi$
$198$		0			0
$199$	0.858565	−	1.07661i	0.0608621	−	0.0763187i	−0.750469	−	0.660906i	$-0.770172\pi$
$199$	0.858565	−	1.07661i	0.0608621	−	0.0763187i	0.811331	+	0.584587i	$0.198744\pi$
$200$	8.97392	+	11.2529i	0.634552	+	0.795703i
$201$		0			0
$202$	3.68422			0.259221
$203$	−6.77932	+	6.51705i	−0.475815	+	0.457408i
$204$		0			0
$205$	−25.0155	+	12.0468i	−1.74716	+	0.841388i
$206$	−1.90123	−	2.38407i	−0.132465	−	0.166106i
$207$		0			0
$208$	−2.38185	+	1.14704i	−0.165151	+	0.0795327i
$209$	−18.0444	−	8.68972i	−1.24816	−	0.601080i
$210$		0			0
$211$	3.86605	−	16.9383i	0.266150	−	1.16608i	−0.648301	−	0.761384i	$-0.724520\pi$
$211$	3.86605	−	16.9383i	0.266150	−	1.16608i	0.914451	−	0.404696i	$-0.132623\pi$
$212$	0.773492	−	3.38889i	0.0531236	−	0.232750i
$213$		0			0
$214$	2.60052	+	11.3936i	0.177768	+	0.778852i
$215$	−36.6909			−2.50230
$216$		0			0
$217$	−6.27014	−	3.01954i	−0.425645	−	0.204980i
$218$	−4.84227	−	2.33191i	−0.327960	−	0.157937i
$219$		0			0
$220$	5.56448			0.375157
$221$	−0.677989	−	2.97046i	−0.0456065	−	0.199815i
$222$		0			0
$223$	−3.08597	+	13.5205i	−0.206652	+	0.905402i	0.760124	+	0.649778i	$0.225138\pi$
$223$	−3.08597	+	13.5205i	−0.206652	+	0.905402i	−0.966776	+	0.255624i	$0.917719\pi$
$224$	1.35575	−	5.93995i	0.0905852	−	0.396880i
$225$		0			0
$226$	5.44223	+	2.62084i	0.362012	+	0.174336i
$227$	2.15378	−	1.03721i	0.142952	−	0.0688419i	−0.361040	−	0.932550i	$-0.617578\pi$
$227$	2.15378	−	1.03721i	0.142952	−	0.0688419i	0.503992	+	0.863708i	$0.331864\pi$
$228$		0			0
$229$	0.665955	+	0.835081i	0.0440075	+	0.0551837i	0.803348	−	0.595510i	$-0.203050\pi$
$229$	0.665955	+	0.835081i	0.0440075	+	0.0551837i	−0.759341	+	0.650693i	$0.774478\pi$
$230$	−9.16649	+	4.41435i	−0.604420	+	0.291074i
$231$		0			0
$232$	−16.4364	−	2.18098i	−1.07910	−	0.143189i
$233$	25.6684			1.68159			0.840795	−	0.541353i	$-0.182088\pi$
$233$	25.6684			1.68159			0.840795	+	0.541353i	$0.182088\pi$
$234$		0			0
$235$	−14.2447	−	17.8623i	−0.929222	−	1.16521i
$236$	−3.29942	+	4.13734i	−0.214774	+	0.269318i
$237$		0			0
$238$	−4.83919	−	2.33043i	−0.313678	−	0.151059i
$239$	4.90036	+	6.14486i	0.316978	+	0.397478i	0.914639	−	0.404271i	$-0.132475\pi$
$239$	4.90036	+	6.14486i	0.316978	+	0.397478i	−0.597661	+	0.801749i	$0.703903\pi$
$240$		0			0
$241$	−5.44182	+	23.8422i	−0.350539	+	1.53581i	0.425402	+	0.905005i	$0.360133\pi$
$241$	−5.44182	+	23.8422i	−0.350539	+	1.53581i	−0.775941	+	0.630806i	$0.782724\pi$
$242$	2.40536	−	3.01623i	0.154622	−	0.193890i
$243$		0			0
$244$	−3.16747			−0.202777
$245$	−2.73438	−	11.9801i	−0.174693	−	0.765380i
$246$		0			0
$247$	7.50448	+	3.61397i	0.477499	+	0.229951i
$248$	−2.73043	−	11.9628i	−0.173383	−	0.759639i
$249$		0			0
$250$	0.262034	+	1.14804i	0.0165725	+	0.0726087i
$251$	3.72725	−	4.67383i	0.235262	−	0.295009i	−0.650160	−	0.759797i	$-0.725298\pi$
$251$	3.72725	−	4.67383i	0.235262	−	0.295009i	0.885422	+	0.464788i	$0.153870\pi$
$252$		0			0
$253$	−1.73364	+	7.59557i	−0.108993	+	0.477529i
$254$	10.8957	+	13.6628i	0.683659	+	0.857281i
$255$		0			0
$256$	12.3449	−	5.94498i	0.771555	−	0.371561i
$257$	−16.7993	+	21.0657i	−1.04791	+	1.31404i	−0.100183	+	0.994969i	$0.531943\pi$
$257$	−16.7993	+	21.0657i	−1.04791	+	1.31404i	−0.947730	+	0.319073i	$0.896629\pi$
$258$		0			0
$259$	−16.4722	+	7.93260i	−1.02353	+	0.492908i
$260$	−2.31421			−0.143521
$261$		0			0
$262$	−0.623100			−0.0384952
$263$	14.9862	−	7.21695i	0.924086	−	0.445016i	0.0895580	−	0.995982i	$-0.471455\pi$
$263$	14.9862	−	7.21695i	0.924086	−	0.445016i	0.834528	+	0.550965i	$0.185740\pi$
$264$		0			0
$265$	−10.4463	+	13.0992i	−0.641709	+	0.804678i
$266$	13.2291	−	6.37082i	0.811131	−	0.390620i
$267$		0			0
$268$	0.182500	+	0.228848i	0.0111480	+	0.0139791i
$269$	3.03417	−	13.2935i	0.184996	−	0.810522i	−0.794208	−	0.607646i	$-0.792114\pi$
$269$	3.03417	−	13.2935i	0.184996	−	0.810522i	0.979204	−	0.202876i	$-0.0650288\pi$
$270$		0			0
$271$	−8.97984	+	11.2604i	−0.545486	+	0.684018i	−0.975801	−	0.218661i	$-0.929831\pi$
$271$	−8.97984	+	11.2604i	−0.545486	+	0.684018i	0.430315	+	0.902679i	$0.358403\pi$
$272$	−1.34835	−	5.90751i	−0.0817558	−	0.358196i
$273$		0			0
$274$	−3.22988	−	14.1510i	−0.195124	−	0.854895i
$275$	−11.6761	−	5.62293i	−0.704098	−	0.339076i
$276$		0			0
$277$	3.05513	+	13.3854i	0.183565	+	0.804251i	0.979915	+	0.199415i	$0.0639041\pi$
$277$	3.05513	+	13.3854i	0.183565	+	0.804251i	−0.796350	+	0.604836i	$0.793239\pi$
$278$	10.1124			0.606502
$279$		0			0
$280$	−10.4268	+	13.0747i	−0.623118	+	0.781365i
$281$	−0.0319740	+	0.140087i	−0.00190741	+	0.00835691i	−0.975873	−	0.218340i	$-0.929936\pi$
$281$	−0.0319740	+	0.140087i	−0.00190741	+	0.00835691i	0.973965	+	0.226697i	$0.0727928\pi$
$282$		0			0
$283$	−5.51039	−	6.90981i	−0.327559	−	0.410746i	0.590596	−	0.806967i	$-0.298893\pi$
$283$	−5.51039	−	6.90981i	−0.327559	−	0.410746i	−0.918155	+	0.396222i	$0.870321\pi$
$284$	−6.74701	−	3.24919i	−0.400362	−	0.192804i
$285$		0			0
$286$	2.31949	−	2.90855i	0.137155	−	0.171986i
$287$	−9.71882	−	12.1870i	−0.573684	−	0.719377i
$288$		0			0
$289$	−10.0164			−0.589199
$290$	16.2997	+	10.6958i	0.957149	+	0.628081i
$291$		0			0
$292$	−7.47418	+	3.59937i	−0.437393	+	0.210637i
$293$	2.10357	+	2.63779i	0.122892	+	0.154101i	0.839471	−	0.543404i	$-0.182865\pi$
$293$	2.10357	+	2.63779i	0.122892	+	0.154101i	−0.716580	+	0.697505i	$0.754293\pi$
$294$		0			0
$295$	22.9808	−	11.0670i	1.33799	−	0.644344i
$296$	−29.0432	−	13.9865i	−1.68810	−	0.812948i
$297$		0			0
$298$	3.89278	−	17.0554i	0.225503	−	0.987992i
$299$	0.721003	−	3.15892i	0.0416967	−	0.182685i
$300$		0			0
$301$	−4.58368	−	20.0824i	−0.264199	−	1.15753i
$302$	−17.5561			−1.01024
$303$		0			0
$304$	14.9245	+	7.18728i	0.855981	+	0.412219i
$305$	13.7553	+	6.62420i	0.787626	+	0.379301i
$306$		0			0
$307$	−0.230862			−0.0131760			−0.00658799	−	0.999978i	$-0.502097\pi$
$307$	−0.230862			−0.0131760			−0.00658799	+	0.999978i	$0.502097\pi$
$308$	0.695152	+	3.04566i	0.0396100	+	0.173543i
$309$		0			0
$310$	−3.21050	+	14.0661i	−0.182344	+	0.798903i
$311$	−5.60223	+	24.5450i	−0.317673	+	1.39182i	0.523948	+	0.851750i	$0.324459\pi$
$311$	−5.60223	+	24.5450i	−0.317673	+	1.39182i	−0.841622	+	0.540068i	$0.818399\pi$
$312$		0			0
$313$	−8.99374	−	4.33116i	−0.508356	−	0.244811i	0.162081	−	0.986777i	$-0.448179\pi$
$313$	−8.99374	−	4.33116i	−0.508356	−	0.244811i	−0.670437	+	0.741966i	$0.733894\pi$
$314$	−10.4264	+	5.02109i	−0.588396	+	0.283357i
$315$		0			0
$316$	6.20328	+	7.77867i	0.348962	+	0.437584i
$317$	−24.9529	+	12.0167i	−1.40149	+	0.674924i	−0.973464	−	0.228841i	$-0.926506\pi$
$317$	−24.9529	+	12.0167i	−1.40149	+	0.674924i	−0.428030	+	0.903765i	$0.640792\pi$
$318$		0			0
$319$	14.1858	−	4.65190i	0.794251	−	0.260456i
$320$	−26.8952			−1.50349
$321$		0			0
$322$	−3.56129	−	4.46571i	−0.198463	−	0.248864i
$323$	−11.9033	+	14.9263i	−0.662319	+	0.830522i
$324$		0			0
$325$	4.85599	+	2.33852i	0.269362	+	0.129718i
$326$	1.99160	+	2.49739i	0.110305	+	0.138318i
$327$		0			0
$328$	6.11572	−	26.7947i	0.337684	−	1.47949i
$329$	7.99720	−	10.0282i	0.440900	−	0.552871i
$330$		0			0
$331$	−23.2748			−1.27930			−0.639650	−	0.768666i	$-0.720921\pi$
$331$	−23.2748			−1.27930			−0.639650	+	0.768666i	$0.720921\pi$
$332$	0.605230	+	2.65169i	0.0332163	+	0.145530i
$333$		0			0
$334$	3.34465	+	1.61070i	0.183011	+	0.0881335i
$335$	−0.313944	−	1.37548i	−0.0171526	−	0.0751505i
$336$		0			0
$337$	−4.19011	−	18.3581i	−0.228250	−	1.00003i	−0.951066	−	0.308987i	$-0.900010\pi$
$337$	−4.19011	−	18.3581i	−0.228250	−	1.00003i	0.722817	−	0.691040i	$-0.242847\pi$
$338$	8.46926	−	10.6201i	0.460667	−	0.577658i
$339$		0			0
$340$	1.18033	−	5.17135i	0.0640122	−	0.280456i
$341$	6.88853	+	8.63794i	0.373035	+	0.467771i
$342$		0			0
$343$	17.2287	−	8.29692i	0.930264	−	0.447992i
$344$	22.6446	−	28.3955i	1.22092	−	1.53098i
$345$		0			0
$346$	−7.94647	+	3.82682i	−0.427205	+	0.205731i
$347$	19.4007			1.04148			0.520741	−	0.853715i	$-0.325656\pi$
$347$	19.4007			1.04148			0.520741	+	0.853715i	$0.325656\pi$
$348$		0			0
$349$	9.57141			0.512346			0.256173	−	0.966631i	$-0.417538\pi$
$349$	9.57141			0.512346			0.256173	+	0.966631i	$0.417538\pi$
$350$	8.56030	−	4.12242i	0.457567	−	0.220353i
$351$		0			0
$352$	−6.03072	+	7.56228i	−0.321438	+	0.403071i
$353$	−29.5123	+	14.2124i	−1.57078	+	0.756449i	−0.997997	−	0.0632575i	$-0.979851\pi$
$353$	−29.5123	+	14.2124i	−1.57078	+	0.756449i	−0.572784	+	0.819706i	$0.694137\pi$
$354$		0			0
$355$	22.5050	+	28.2203i	1.19444	+	1.49778i
$356$	0.291780	−	1.27837i	0.0154643	−	0.0677536i
$357$		0			0
$358$	−2.04057	+	2.55880i	−0.107848	+	0.135237i
$359$	3.23031	+	14.1529i	0.170489	+	0.746963i	0.985798	+	0.167936i	$0.0537102\pi$
$359$	3.23031	+	14.1529i	0.170489	+	0.746963i	−0.815309	+	0.579027i	$0.803433\pi$
$360$		0			0
$361$	−7.38577	−	32.3592i	−0.388725	−	1.70311i
$362$	7.38320	+	3.55556i	0.388052	+	0.186876i
$363$		0			0
$364$	−0.289107	−	1.26666i	−0.0151533	−	0.0663910i
$365$	39.9854			2.09293
$366$		0			0
$367$	10.7255	−	13.4494i	0.559868	−	0.702052i	−0.418665	−	0.908141i	$-0.637502\pi$
$367$	10.7255	−	13.4494i	0.559868	−	0.702052i	0.978533	+	0.206088i	$0.0660734\pi$
$368$	1.43390	−	6.28231i	0.0747470	−	0.327488i
$369$		0			0
$370$	23.6323	+	29.6340i	1.22859	+	1.54060i
$371$	−8.47474	−	4.08122i	−0.439986	−	0.211886i
$372$		0			0
$373$	5.32000	−	6.67107i	0.275459	−	0.345415i	−0.624788	−	0.780795i	$-0.714814\pi$
$373$	5.32000	−	6.67107i	0.275459	−	0.345415i	0.900247	+	0.435380i	$0.143386\pi$
$374$	5.31645	+	6.66662i	0.274907	+	0.344722i
$375$		0			0
$376$	22.6152			1.16629
$377$	−5.89972	+	1.93468i	−0.303851	+	0.0996410i
$378$		0			0
$379$	9.75482	−	4.69767i	0.501071	−	0.241303i	−0.166236	−	0.986086i	$-0.553161\pi$
$379$	9.75482	−	4.69767i	0.501071	−	0.241303i	0.667307	+	0.744783i	$0.267447\pi$
$380$	9.04107	+	11.3371i	0.463797	+	0.581583i
$381$		0			0
$382$	−4.64120	+	2.23508i	−0.237464	+	0.114357i
$383$	18.0481	+	8.69151i	0.922215	+	0.444115i	0.833861	−	0.551974i	$-0.186125\pi$
$383$	18.0481	+	8.69151i	0.922215	+	0.444115i	0.0883534	+	0.996089i	$0.471840\pi$
$384$		0			0
$385$	3.35064	−	14.6801i	0.170764	−	0.748167i
$386$	−1.04610	+	4.58326i	−0.0532450	+	0.233282i
$387$		0			0
$388$	1.81879	+	7.96863i	0.0923349	+	0.404546i
$389$	30.9606			1.56976			0.784881	−	0.619646i	$-0.212724\pi$
$389$	30.9606			1.56976			0.784881	+	0.619646i	$0.212724\pi$
$390$		0			0
$391$	6.69121	+	3.22232i	0.338389	+	0.162960i
$392$	10.9591	+	5.27762i	0.553518	+	0.266560i
$393$		0			0
$394$	13.9562			0.703103
$395$	−10.6711	−	46.7533i	−0.536923	−	2.35241i
$396$		0			0
$397$	−4.39793	+	19.2686i	−0.220726	+	0.967063i	0.736208	+	0.676756i	$0.236615\pi$
$397$	−4.39793	+	19.2686i	−0.220726	+	0.967063i	−0.956933	+	0.290307i	$0.906242\pi$
$398$	0.356643	−	1.56256i	0.0178769	−	0.0783239i
$399$		0			0
$400$	9.65735	+	4.65074i	0.482868	+	0.232537i
$401$	16.7480	−	8.06542i	0.836356	−	0.402768i	0.0338611	−	0.999427i	$-0.489220\pi$
$401$	16.7480	−	8.06542i	0.836356	−	0.402768i	0.802495	+	0.596659i	$0.203505\pi$
$402$		0			0
$403$	−2.86487	−	3.59243i	−0.142709	−	0.178952i
$404$	−1.84038	+	0.886282i	−0.0915626	+	0.0440942i
$405$		0			0
$406$	−3.81799	+	10.2576i	−0.189484	+	0.509079i
$407$	29.0250			1.43871
$408$		0			0
$409$	19.6705	+	24.6660i	0.972643	+	1.21966i	0.975576	+	0.219661i	$0.0704950\pi$
$409$	19.6705	+	24.6660i	0.972643	+	1.21966i	−0.00293293	+	0.999996i	$0.500934\pi$
$410$	−20.1488	+	25.2657i	−0.995076	+	1.24779i
$411$		0			0
$412$	1.52324	+	0.733555i	0.0750448	+	0.0361397i
$413$	8.92831	+	11.1957i	0.439333	+	0.550906i
$414$		0			0
$415$	2.91721	−	12.7811i	0.143200	−	0.627401i
$416$	2.50811	−	3.14508i	0.122970	−	0.154200i
$417$		0			0
$418$	−23.3105			−1.14015
$419$	−5.20802	−	22.8178i	−0.254428	−	1.11472i	−0.927110	−	0.374791i	$-0.877715\pi$
$419$	−5.20802	−	22.8178i	−0.254428	−	1.11472i	0.672681	−	0.739932i	$-0.265143\pi$
$420$		0			0
$421$	0.355543	+	0.171220i	0.0173281	+	0.00834477i	0.442528	−	0.896755i	$-0.354082\pi$
$421$	0.355543	+	0.171220i	0.0173281	+	0.00834477i	−0.425200	+	0.905100i	$0.639796\pi$
$422$	−4.49973	−	19.7146i	−0.219044	−	0.959693i
$423$		0			0
$424$	−3.69046	−	16.1689i	−0.179224	−	0.785233i
$425$	−7.70239	+	9.65850i	−0.373621	+	0.468506i
$426$		0			0
$427$	−1.90729	+	8.35636i	−0.0923000	+	0.404393i
$428$	−4.03991	−	5.06589i	−0.195276	−	0.244869i
$429$		0			0
$430$	−38.4758	+	18.5290i	−1.85547	+	0.893546i
$431$	12.9796	−	16.2759i	0.625205	−	0.783983i	−0.363861	−	0.931453i	$-0.618542\pi$
$431$	12.9796	−	16.2759i	0.625205	−	0.783983i	0.989066	+	0.147470i	$0.0471131\pi$
$432$		0			0
$433$	−0.269212	+	0.129646i	−0.0129375	+	0.00623038i	−0.440341	−	0.897830i	$-0.645143\pi$
$433$	−0.269212	+	0.129646i	−0.0129375	+	0.00623038i	0.427404	+	0.904061i	$0.359428\pi$
$434$	−8.10003			−0.388814
$435$		0			0
$436$	2.97983			0.142708
$437$	−18.2921	+	8.80902i	−0.875030	+	0.421392i
$438$		0			0
$439$	16.1485	−	20.2496i	0.770727	−	0.966461i	−0.229249	−	0.973368i	$-0.573627\pi$
$439$	16.1485	−	20.2496i	0.770727	−	0.966461i	0.999976	+	0.00690678i	$0.00219851\pi$
$440$	23.9199	−	11.5192i	1.14034	−	0.549156i
$441$		0			0
$442$	−2.21106	−	2.77258i	−0.105169	−	0.131878i
$443$	0.928033	−	4.06598i	0.0440922	−	0.193181i	−0.948085	−	0.318016i	$-0.896983\pi$
$443$	0.928033	−	4.06598i	0.0440922	−	0.193181i	0.992177	+	0.124836i	$0.0398404\pi$
$444$		0			0
$445$	−3.94059	+	4.94135i	−0.186802	+	0.234242i
$446$	3.59179	+	15.7367i	0.170076	+	0.745153i
$447$		0			0
$448$	−3.35993	−	14.7208i	−0.158742	−	0.695493i
$449$	−19.3037	−	9.29618i	−0.910998	−	0.438714i	−0.0811496	−	0.996702i	$-0.525859\pi$
$449$	−19.3037	−	9.29618i	−0.910998	−	0.438714i	−0.829849	+	0.557988i	$0.811573\pi$
$450$		0			0
$451$	5.50661	+	24.1260i	0.259296	+	1.13605i
$452$	−3.34904			−0.157525
$453$		0			0
$454$	1.73477	−	2.17533i	0.0814166	−	0.102093i
$455$	−1.39350	+	6.10531i	−0.0653281	+	0.286221i
$456$		0			0
$457$	9.48836	+	11.8980i	0.443847	+	0.556566i	0.952553	−	0.304374i	$-0.0984473\pi$
$457$	9.48836	+	11.8980i	0.443847	+	0.556566i	−0.508706	+	0.860940i	$0.669876\pi$
$458$	1.12007	+	0.539396i	0.0523373	+	0.0252043i
$459$		0			0
$460$	3.51703	−	4.41021i	0.163982	−	0.205627i
$461$	2.12415	+	2.66360i	0.0989316	+	0.124056i	0.828833	−	0.559496i	$-0.189005\pi$
$461$	2.12415	+	2.66360i	0.0989316	+	0.124056i	−0.729901	+	0.683553i	$0.760434\pi$
$462$		0			0
$463$	−20.8584			−0.969374			−0.484687	−	0.874688i	$-0.661066\pi$
$463$	−20.8584			−0.969374			−0.484687	+	0.874688i	$0.661066\pi$
$464$	−11.7331	+	3.84759i	−0.544695	+	0.178620i
$465$		0			0
$466$	26.9170	−	12.9626i	1.24691	−	0.600479i
$467$	−10.8132	−	13.5593i	−0.500373	−	0.627448i	0.465940	−	0.884816i	$-0.345716\pi$
$467$	−10.8132	−	13.5593i	−0.500373	−	0.627448i	−0.966313	+	0.257368i	$0.917145\pi$
$468$		0			0
$469$	0.713635	−	0.343668i	0.0329526	−	0.0158691i
$470$	−23.9581	−	11.5376i	−1.10511	−	0.532191i
$471$		0			0
$472$	−5.61828	+	24.6153i	−0.258602	+	1.13301i
$473$	−7.27685	+	31.8820i	−0.334590	+	1.46593i
$474$		0			0
$475$	−7.51495	−	32.9252i	−0.344810	−	1.51071i
$476$	2.97794			0.136494
$477$		0			0
$478$	8.24191	+	3.96909i	0.376976	+	0.181542i
$479$	−32.4935	−	15.6480i	−1.48467	−	0.714977i	−0.496452	−	0.868064i	$-0.665364\pi$
$479$	−32.4935	−	15.6480i	−1.48467	−	0.714977i	−0.988213	+	0.153087i	$0.951079\pi$
$480$		0			0
$481$	−12.0712			−0.550399
$482$	6.33379	+	27.7501i	0.288496	+	1.26398i
$483$		0			0
$484$	−0.475964	+	2.08534i	−0.0216347	+	0.0947880i
$485$	8.76656	−	38.4088i	0.398069	−	1.74405i
$486$		0			0
$487$	−11.8931	−	5.72743i	−0.538929	−	0.259535i	0.144559	−	0.989496i	$-0.453824\pi$
$487$	−11.8931	−	5.72743i	−0.538929	−	0.259535i	−0.683488	+	0.729961i	$0.739538\pi$
$488$	−13.6159	+	6.55709i	−0.616364	+	0.296825i
$489$		0			0
$490$	−8.91736	−	11.1820i	−0.402845	−	0.505152i
$491$	−22.3150	+	10.7464i	−1.00706	+	0.484976i	−0.863330	−	0.504640i	$-0.831625\pi$
$491$	−22.3150	+	10.7464i	−1.00706	+	0.484976i	−0.143734	+	0.989616i	$0.545911\pi$
$492$		0			0
$493$	−1.31418	−	14.1703i	−0.0591878	−	0.638199i
$494$	9.69460			0.436181
$495$		0			0
$496$	−5.69751	−	7.14446i	−0.255826	−	0.320796i
$497$	−12.6346	+	15.8433i	−0.566741	+	0.710671i
$498$		0			0
$499$	−14.2485	−	6.86174i	−0.637853	−	0.307174i	0.0868646	−	0.996220i	$-0.472315\pi$
$499$	−14.2485	−	6.86174i	−0.637853	−	0.307174i	−0.724717	+	0.689047i	$0.758030\pi$
$500$	−0.407069	−	0.510449i	−0.0182047	−	0.0228280i
$501$		0			0
$502$	1.54828	−	6.78346i	0.0691031	−	0.302760i
$503$	14.6226	−	18.3361i	0.651988	−	0.817568i	−0.340456	−	0.940260i	$-0.610582\pi$
$503$	14.6226	−	18.3361i	0.651988	−	0.817568i	0.992445	+	0.122693i	$0.0391530\pi$
$504$		0			0
$505$	9.84569			0.438127
$506$	2.01780	+	8.84056i	0.0897021	+	0.393011i
$507$		0			0
$508$	−8.72951	−	4.20391i	−0.387309	−	0.186518i
$509$	1.55265	+	6.80262i	0.0688202	+	0.301521i	0.997611	−	0.0690838i	$-0.0220076\pi$
$509$	1.55265	+	6.80262i	0.0688202	+	0.301521i	−0.928791	+	0.370605i	$0.879150\pi$
$510$		0			0
$511$	4.99524	+	21.8856i	0.220976	+	0.968161i
$512$	13.7914	−	17.2938i	0.609498	−	0.764286i
$513$		0			0
$514$	−6.97835	+	30.5741i	−0.307802	+	1.34857i
$515$	−5.08084	−	6.37118i	−0.223889	−	0.280748i
$516$		0			0
$517$	−18.3463	+	8.83510i	−0.806868	+	0.388567i
$518$	−13.2676	+	16.6370i	−0.582943	+	0.730987i
$519$		0			0
$520$	−9.94804	+	4.79072i	−0.436250	+	0.210087i
$521$	20.4524			0.896037			0.448019	−	0.894024i	$-0.352130\pi$
$521$	20.4524			0.896037			0.448019	+	0.894024i	$0.352130\pi$
$522$		0			0
$523$	−19.8313			−0.867162			−0.433581	−	0.901115i	$-0.642750\pi$
$523$	−19.8313			−0.867162			−0.433581	+	0.901115i	$0.642750\pi$
$524$	0.311258	−	0.149894i	0.0135974	−	0.00654815i
$525$		0			0
$526$	12.0706	−	15.1361i	0.526303	−	0.659964i
$527$	9.48885	−	4.56959i	0.413341	−	0.199055i
$528$		0			0
$529$	−9.41603	−	11.8073i	−0.409393	−	0.513362i
$530$	−4.33932	+	19.0118i	−0.188488	+	0.825820i
$531$		0			0
$532$	−5.07580	+	6.36485i	−0.220064	+	0.275951i
$533$	−2.29015	−	10.0338i	−0.0991972	−	0.434611i
$534$		0			0
$535$	6.94961	+	30.4482i	0.300458	+	1.31639i
$536$	1.25826	+	0.605944i	0.0543484	+	0.0261728i
$537$		0			0
$538$	−3.53149	−	15.4725i	−0.152253	−	0.667066i
$539$	−10.9522			−0.471745
$540$		0			0
$541$	22.2616	−	27.9152i	0.957101	−	1.20017i	−0.0226089	−	0.999744i	$-0.507197\pi$
$541$	22.2616	−	27.9152i	0.957101	−	1.20017i	0.979710	−	0.200422i	$-0.0642313\pi$
$542$	−3.73017	+	16.3430i	−0.160225	+	0.701990i
$543$		0			0
$544$	5.74878	+	7.20874i	0.246477	+	0.309072i
$545$	−12.9404	−	6.23179i	−0.554308	−	0.266941i
$546$		0			0
$547$	−6.16194	+	7.72683i	−0.263466	+	0.330376i	−0.895914	−	0.444227i	$-0.853478\pi$
$547$	−6.16194	+	7.72683i	−0.263466	+	0.330376i	0.632449	+	0.774602i	$0.282050\pi$
$548$	5.01762	+	6.29190i	0.214342	+	0.268776i
$549$		0			0
$550$	−15.0837			−0.643172
$551$	32.5267	+	21.3440i	1.38568	+	0.909284i
$552$		0			0
$553$	24.2568	−	11.6815i	1.03150	−	0.496746i
$554$	9.96339	+	12.4937i	0.423304	+	0.530806i
$555$		0			0
$556$	−5.05147	+	2.43266i	−0.214230	+	0.103168i
$557$	−28.7227	−	13.8321i	−1.21702	−	0.586085i	−0.288539	−	0.957468i	$-0.593170\pi$
$557$	−28.7227	−	13.8321i	−1.21702	−	0.586085i	−0.928480	+	0.371383i	$0.878884\pi$
$558$		0			0
$559$	3.02637	−	13.2594i	0.128002	−	0.560813i
$560$	−2.77132	+	12.1419i	−0.117110	+	0.513090i
$561$		0			0
$562$	0.0372149	+	0.163049i	0.00156981	+	0.00687781i
$563$	9.06052			0.381855			0.190928	−	0.981604i	$-0.438850\pi$
$563$	9.06052			0.381855			0.190928	+	0.981604i	$0.438850\pi$
$564$		0			0
$565$	14.5438	+	7.00391i	0.611861	+	0.294657i
$566$	−9.26791	−	4.46319i	−0.389560	−	0.187602i
$567$		0			0
$568$	−35.7294			−1.49917
$569$	−3.72126	−	16.3039i	−0.156003	−	0.683496i	−0.991070	−	0.133346i	$-0.957428\pi$
$569$	−3.72126	−	16.3039i	−0.156003	−	0.683496i	0.835066	−	0.550150i	$-0.185429\pi$
$570$		0			0
$571$	5.17962	−	22.6934i	0.216761	−	0.949690i	−0.743093	−	0.669188i	$-0.766642\pi$
$571$	5.17962	−	22.6934i	0.216761	−	0.949690i	0.959854	−	0.280502i	$-0.0905009\pi$
$572$	−0.458974	+	2.01090i	−0.0191907	+	0.0840798i
$573$		0			0
$574$	−16.3461	−	7.87185i	−0.682272	−	0.328565i
$575$	−11.8364	+	5.70013i	−0.493613	+	0.237712i
$576$		0			0
$577$	11.8070	+	14.8056i	0.491533	+	0.616363i	0.964296	−	0.264826i	$-0.0853146\pi$
$577$	11.8070	+	14.8056i	0.491533	+	0.616363i	−0.472763	+	0.881190i	$0.656743\pi$
$578$	−10.5036	+	5.05829i	−0.436894	+	0.210397i
$579$		0			0
$580$	−10.7152	−	1.42183i	−0.444925	−	0.0590383i
$581$	7.36006			0.305347
$582$		0			0
$583$	9.31055	+	11.6751i	0.385603	+	0.483531i
$584$	−24.6779	+	30.9451i	−1.02118	+	1.28052i
$585$		0			0
$586$	3.53799	+	1.70381i	0.146153	+	0.0703835i
$587$	0.0141875	+	0.0177906i	0.000585581	+	0.000734295i	0.782124	−	0.623123i	$-0.214136\pi$
$587$	0.0141875	+	0.0177906i	0.000585581	+	0.000734295i	−0.781539	+	0.623857i	$0.785565\pi$
$588$		0			0
$589$	−6.40669	+	28.0696i	−0.263983	+	1.15659i
$590$	18.5099	−	23.2107i	0.762040	−	0.955568i
$591$		0			0
$592$	−24.0066			−0.986665
$593$	0.0784633	+	0.343770i	0.00322210	+	0.0141170i	0.976513	−	0.215457i	$-0.0691240\pi$
$593$	0.0784633	+	0.343770i	0.00322210	+	0.0141170i	−0.973291	+	0.229574i	$0.926267\pi$
$594$		0			0
$595$	−12.9322	−	6.22783i	−0.530169	−	0.255316i
$596$	2.15830	+	9.45615i	0.0884076	+	0.387339i
$597$		0			0
$598$	−0.839183	−	3.67670i	−0.0343167	−	0.150351i
$599$	−5.02946	+	6.30675i	−0.205498	+	0.257687i	−0.873891	−	0.486122i	$-0.838411\pi$
$599$	−5.02946	+	6.30675i	−0.205498	+	0.257687i	0.668393	+	0.743808i	$0.266983\pi$
$600$		0			0
$601$	4.86790	−	21.3277i	0.198566	−	0.869974i	−0.773226	−	0.634131i	$-0.781358\pi$
$601$	4.86790	−	21.3277i	0.198566	−	0.869974i	0.971791	−	0.235842i	$-0.0757849\pi$
$602$	−14.9483	−	18.7446i	−0.609247	−	0.763972i
$603$		0			0
$604$	8.76983	−	4.22333i	0.356839	−	0.171845i
$605$	6.42807	−	8.06054i	0.261338	−	0.327708i
$606$		0			0
$607$	2.92395	−	1.40810i	0.118680	−	0.0571530i	−0.373602	−	0.927589i	$-0.621877\pi$
$607$	2.92395	−	1.40810i	0.118680	−	0.0571530i	0.492281	+	0.870436i	$0.336163\pi$
$608$	−25.2061			−1.02224
$609$		0			0
$610$	17.7697			0.719473
$611$	7.63003	−	3.67443i	0.308678	−	0.148651i
$612$		0			0
$613$	−5.82061	+	7.29882i	−0.235092	+	0.294797i	−0.885358	−	0.464911i	$-0.846086\pi$
$613$	−5.82061	+	7.29882i	−0.235092	+	0.294797i	0.650265	+	0.759707i	$0.274658\pi$
$614$	−0.242092	+	0.116585i	−0.00977005	+	0.00470501i
$615$		0			0
$616$	9.29315	+	11.6532i	0.374432	+	0.469522i
$617$	4.93142	−	21.6059i	0.198531	−	0.869823i	−0.773280	−	0.634064i	$-0.781385\pi$
$617$	4.93142	−	21.6059i	0.198531	−	0.869823i	0.971812	−	0.235758i	$-0.0757574\pi$
$618$		0			0
$619$	−4.06400	+	5.09610i	−0.163346	+	0.204829i	−0.856768	−	0.515703i	$-0.827531\pi$
$619$	−4.06400	+	5.09610i	−0.163346	+	0.204829i	0.693422	+	0.720532i	$0.256102\pi$
$620$	−1.78003	−	7.79880i	−0.0714876	−	0.313207i
$621$		0			0
$622$	6.52049	+	28.5681i	0.261448	+	1.14548i
$623$	−3.19688	−	1.53954i	−0.128080	−	0.0616803i
$624$		0			0
$625$	5.90138	+	25.8556i	0.236055	+	1.03423i
$626$	−11.6185			−0.464368
$627$		0			0
$628$	4.00044	−	5.01639i	0.159635	−	0.200176i
$629$	6.15672	−	26.9744i	0.245485	−	1.07554i
$630$		0			0
$631$	−14.9507	−	18.7476i	−0.595179	−	0.746331i	0.389439	−	0.921052i	$-0.372669\pi$
$631$	−14.9507	−	18.7476i	−0.595179	−	0.746331i	−0.984618	+	0.174721i	$0.944098\pi$
$632$	42.7687	+	20.5963i	1.70125	+	0.819278i
$633$		0			0
$634$	−20.0983	+	25.2025i	−0.798206	+	1.00092i
$635$	29.1177	+	36.5124i	1.15550	+	1.44895i
$636$		0			0
$637$	4.55491			0.180472
$638$	12.5266	−	12.0420i	0.495935	−	0.476749i
$639$		0			0
$640$	−8.64820	+	4.16476i	−0.341850	+	0.164626i
$641$	−27.4148	−	34.3771i	−1.08282	−	1.35781i	−0.929154	−	0.369692i	$-0.879463\pi$
$641$	−27.4148	−	34.3771i	−1.08282	−	1.35781i	−0.153667	−	0.988123i	$-0.549108\pi$
$642$		0			0
$643$	−14.8855	+	7.16846i	−0.587025	+	0.282697i	−0.703727	−	0.710470i	$-0.748482\pi$
$643$	−14.8855	+	7.16846i	−0.587025	+	0.282697i	0.116702	+	0.993167i	$0.462768\pi$
$644$	2.85325	+	1.37405i	0.112434	+	0.0541454i
$645$		0			0
$646$	−4.94458	+	21.6636i	−0.194542	+	0.852343i
$647$	−7.84873	+	34.3875i	−0.308565	+	1.35191i	0.548261	+	0.836307i	$0.315290\pi$
$647$	−7.84873	+	34.3875i	−0.308565	+	1.35191i	−0.856826	+	0.515605i	$0.827567\pi$
$648$		0			0
$649$	−5.05871	−	22.1637i	−0.198572	−	0.870000i
$650$	6.27317			0.246054
$651$		0			0
$652$	−1.59564	−	0.768422i	−0.0624903	−	0.0300937i
$653$	15.1503	+	7.29602i	0.592878	+	0.285515i	0.706165	−	0.708047i	$-0.250424\pi$
$653$	15.1503	+	7.29602i	0.592878	+	0.285515i	−0.113287	+	0.993562i	$0.536138\pi$
$654$		0			0
$655$	−1.66517			−0.0650635
$656$	−4.55453	−	19.9547i	−0.177824	−	0.779100i
$657$		0			0
$658$	3.32199	−	14.5546i	0.129505	−	0.567397i
$659$	0.668451	−	2.92867i	0.0260392	−	0.114085i	−0.960238	−	0.279182i	$-0.909937\pi$
$659$	0.668451	−	2.92867i	0.0260392	−	0.114085i	0.986277	+	0.165097i	$0.0527938\pi$
$660$		0			0
$661$	−34.5193	−	16.6236i	−1.34264	−	0.646583i	−0.381948	−	0.924184i	$-0.624746\pi$
$661$	−34.5193	−	16.6236i	−1.34264	−	0.646583i	−0.960697	+	0.277601i	$0.910461\pi$
$662$	−24.4071	+	11.7538i	−0.948607	+	0.456825i
$663$		0			0
$664$	8.09102	+	10.1458i	0.313992	+	0.393734i
$665$	35.3535	−	17.0253i	1.37095	−	0.660214i
$666$		0			0
$667$	5.27918	−	14.1834i	0.204411	−	0.549183i
$668$	−2.05823			−0.0796353
$669$		0			0
$670$	−1.02384	−	1.28385i	−0.0395542	−	0.0495994i
$671$	8.48405	−	10.6387i	0.327523	−	0.410701i
$672$		0			0
$673$	24.6701	+	11.8805i	0.950963	+	0.457960i	0.844024	−	0.536306i	$-0.180181\pi$
$673$	24.6701	+	11.8805i	0.950963	+	0.457960i	0.106939	+	0.994266i	$0.465895\pi$
$674$	−13.6648	−	17.1351i	−0.526348	−	0.660019i
$675$		0			0
$676$	−1.67587	+	7.34246i	−0.0644565	+	0.282402i
$677$	−17.8546	+	22.3890i	−0.686209	+	0.860479i	−0.995910	−	0.0903549i	$-0.971200\pi$
$677$	−17.8546	+	22.3890i	−0.686209	+	0.860479i	0.309700	+	0.950834i	$0.399771\pi$
$678$		0			0
$679$	22.1178			0.848805
$680$	−5.63154	−	24.6734i	−0.215960	−	0.946181i
$681$		0			0
$682$	11.5858	+	5.57943i	0.443643	+	0.213647i
$683$	2.80121	+	12.2729i	0.107185	+	0.469609i	0.999823	+	0.0188337i	$0.00599530\pi$
$683$	2.80121	+	12.2729i	0.107185	+	0.469609i	−0.892637	+	0.450775i	$0.851148\pi$
$684$		0			0
$685$	−8.63150	−	37.8171i	−0.329793	−	1.44492i
$686$	13.8769	−	17.4011i	0.529822	−	0.664376i
$687$		0			0
$688$	6.01870	−	26.3696i	0.229461	−	1.00533i
$689$	−3.87216	−	4.85554i	−0.147518	−	0.184981i
$690$		0			0
$691$	−36.0563	+	17.3638i	−1.37165	+	0.660550i	−0.967201	−	0.254012i	$-0.918250\pi$
$691$	−36.0563	+	17.3638i	−1.37165	+	0.660550i	−0.404446	+	0.914562i	$0.632536\pi$
$692$	3.04892	−	3.82323i	0.115903	−	0.145337i
$693$		0			0
$694$	20.3444	−	9.79736i	0.772264	−	0.371903i
$695$	27.0243			1.02509
$696$		0			0
$697$	23.5896			0.893520
$698$	10.0370	−	4.83358i	0.379907	−	0.182954i
$699$		0			0
$700$	−3.28444	+	4.11856i	−0.124140	+	0.155667i
$701$	−11.6102	+	5.59119i	−0.438512	+	0.211176i	−0.640096	−	0.768295i	$-0.721105\pi$
$701$	−11.6102	+	5.59119i	−0.438512	+	0.211176i	0.201584	+	0.979471i	$0.435391\pi$
$702$		0			0
$703$	47.1593	+	59.1359i	1.77865	+	2.23035i
$704$	−5.33408	+	23.3701i	−0.201036	+	0.880795i
$705$		0			0
$706$	−23.7707	+	29.8075i	−0.894622	+	1.12182i
$707$	1.22999	+	5.38894i	0.0462585	+	0.202672i
$708$		0			0
$709$	0.139525	+	0.611300i	0.00523998	+	0.0229578i	0.977480	−	0.211027i	$-0.0676807\pi$
$709$	0.139525	+	0.611300i	0.00523998	+	0.0229578i	−0.972240	+	0.233984i	$0.924824\pi$
$710$	37.8511	+	18.2281i	1.42052	+	0.684089i
$711$		0			0
$712$	−1.39213	−	6.09933i	−0.0521724	−	0.228582i
$713$	11.2000			0.419444
$714$		0			0
$715$	6.19860	−	7.77280i	0.231814	−	0.290686i
$716$	0.403781	−	1.76908i	0.0150900	−	0.0661137i
$717$		0			0
$718$	10.5347	+	13.2101i	0.393151	+	0.492996i
$719$	31.9194	+	15.3716i	1.19039	+	0.573263i	0.920923	−	0.389745i	$-0.127437\pi$
$719$	31.9194	+	15.3716i	1.19039	+	0.573263i	0.269471	+	0.963009i	$0.413151\pi$
$720$		0			0
$721$	2.85247	−	3.57688i	0.106231	−	0.133210i
$722$	−24.0865	−	30.2035i	−0.896406	−	1.12406i
$723$		0			0
$724$	−4.54347			−0.168857
$725$	21.0473	+	13.8112i	0.781677	+	0.512936i
$726$		0			0
$727$	17.5000	−	8.42754i	0.649038	−	0.312560i	−0.0802424	−	0.996775i	$-0.525569\pi$
$727$	17.5000	−	8.42754i	0.649038	−	0.312560i	0.729280	+	0.684215i	$0.239855\pi$
$728$	−3.86493	−	4.84647i	−0.143244	−	0.179622i
$729$		0			0
$730$	41.9305	−	20.1927i	1.55192	−	0.747364i
$731$	28.0860	+	13.5255i	1.03880	+	0.500258i
$732$		0			0
$733$	5.58097	−	24.4518i	0.206138	−	0.903148i	−0.760971	−	0.648786i	$-0.775277\pi$
$733$	5.58097	−	24.4518i	0.206138	−	0.903148i	0.967109	−	0.254363i	$-0.0818656\pi$
$734$	4.45532	−	19.5201i	0.164449	−	0.720498i
$735$		0			0
$736$	2.18189	+	9.55947i	0.0804254	+	0.352367i
$737$	−1.25746			−0.0463193
$738$		0			0
$739$	−47.6184	−	22.9318i	−1.75167	−	0.843560i	−0.977603	−	0.210458i	$-0.932505\pi$
$739$	−47.6184	−	22.9318i	−1.75167	−	0.843560i	−0.774068	−	0.633103i	$-0.781781\pi$
$740$	−18.9339	−	9.11808i	−0.696024	−	0.335187i
$741$		0			0
$742$	−10.9480			−0.401914
$743$	3.53331	+	15.4804i	0.129625	+	0.567922i	0.997470	+	0.0710881i	$0.0226472\pi$
$743$	3.53331	+	15.4804i	0.129625	+	0.567922i	−0.867845	+	0.496834i	$0.834496\pi$
$744$		0			0
$745$	10.4030	−	45.5787i	0.381138	−	1.66987i
$746$	2.20990	−	9.68219i	0.0809101	−	0.354490i
$747$		0			0
$748$	−4.25947	−	2.05125i	−0.155741	−	0.0750011i
$749$	−15.7973	+	7.60760i	−0.577222	+	0.277976i
$750$		0			0
$751$	−5.78372	−	7.25256i	−0.211051	−	0.264650i	0.665027	−	0.746820i	$-0.268420\pi$
$751$	−5.78372	−	7.25256i	−0.211051	−	0.264650i	−0.876078	+	0.482170i	$0.839849\pi$
$752$	15.1742	−	7.30752i	0.553347	−	0.266478i
$753$		0			0
$754$	−5.20971	+	5.00816i	−0.189726	+	0.182386i
$755$	−46.9168			−1.70748
$756$		0			0
$757$	−3.73161	−	4.67930i	−0.135628	−	0.170072i	0.709379	−	0.704827i	$-0.248975\pi$
$757$	−3.73161	−	4.67930i	−0.135628	−	0.170072i	−0.845007	+	0.534755i	$0.820404\pi$
$758$	7.85702	−	9.85239i	0.285380	−	0.357855i
$759$		0			0
$760$	62.3340	+	30.0185i	2.26109	+	1.08888i
$761$	−13.1939	−	16.5446i	−0.478279	−	0.599743i	0.482898	−	0.875677i	$-0.339584\pi$
$761$	−13.1939	−	16.5446i	−0.478279	−	0.599743i	−0.961177	+	0.275934i	$0.911013\pi$
$762$		0			0
$763$	1.79430	−	7.86134i	0.0649580	−	0.284599i
$764$	1.78075	−	2.23299i	0.0644252	−	0.0807866i
$765$		0			0
$766$	23.3153			0.842415
$767$	2.10387	+	9.21765i	0.0759663	+	0.332830i
$768$		0			0
$769$	−21.9708	−	10.5806i	−0.792288	−	0.381546i	−0.00645049	−	0.999979i	$-0.502053\pi$
$769$	−21.9708	−	10.5806i	−0.792288	−	0.381546i	−0.785837	+	0.618434i	$0.787768\pi$
$770$	−3.89984	−	17.0863i	−0.140540	−	0.615747i
$771$		0			0
$772$	−0.579997	−	2.54113i	−0.0208745	−	0.0914573i
$773$	−33.8004	+	42.3843i	−1.21571	+	1.52446i	−0.433881	+	0.900970i	$0.642856\pi$
$773$	−33.8004	+	42.3843i	−1.21571	+	1.52446i	−0.781833	+	0.623488i	$0.785715\pi$
$774$		0			0
$775$	−4.14564	+	18.1632i	−0.148916	+	0.652442i
$776$	24.3145	+	30.4894i	0.872838	+	1.09450i
$777$		0			0
$778$	32.4667	−	15.6351i	1.16399	−	0.560546i
$779$	−40.2077	+	50.4188i	−1.44059	+	1.80644i
$780$		0			0
$781$	28.9850	−	13.9584i	1.03716	−	0.499472i
$782$	8.64398			0.309108
$783$		0			0
$784$	9.05858			0.323521
$785$	−27.8635	+	13.4183i	−0.994489	+	0.478921i
$786$		0			0
$787$	−0.341145	+	0.427783i	−0.0121605	+	0.0152488i	−0.787875	−	0.615836i	$-0.788818\pi$
$787$	−0.341145	+	0.427783i	−0.0121605	+	0.0152488i	0.775714	+	0.631085i	$0.217390\pi$
$788$	−6.97156	+	3.35733i	−0.248351	+	0.119600i
$789$		0			0
$790$	−34.8007	−	43.6387i	−1.23815	−	1.55259i
$791$	−2.01661	+	8.83536i	−0.0717025	+	0.314149i
$792$		0			0
$793$	−3.52843	+	4.42452i	−0.125298	+	0.157119i
$794$	5.11879	+	22.4269i	0.181659	+	0.795901i
$795$		0			0
$796$	0.197737	+	0.866341i	0.00700859	+	0.0307066i
$797$	−22.1189	−	10.6519i	−0.783491	−	0.377309i	−0.00102250	−	0.999999i	$-0.500325\pi$
$797$	−22.1189	−	10.6519i	−0.783491	−	0.377309i	−0.782469	+	0.622690i	$0.786040\pi$
$798$		0			0
$799$	4.31932	+	18.9242i	0.152807	+	0.669490i
$800$	−16.3103			−0.576657
$801$		0			0
$802$	13.4897	−	16.9155i	0.476338	−	0.597309i
$803$	7.93023	−	34.7446i	0.279852	−	1.22611i
$804$		0			0
$805$	−9.51716	−	11.9341i	−0.335436	−	0.420623i
$806$	−4.81842	−	2.32043i	−0.169722	−	0.0817336i
$807$		0			0
$808$	−6.07649	+	7.61967i	−0.213770	+	0.268059i
$809$	−16.4424	−	20.6181i	−0.578084	−	0.724895i	0.403700	−	0.914891i	$-0.367724\pi$
$809$	−16.4424	−	20.6181i	−0.578084	−	0.724895i	−0.981785	+	0.189996i	$0.939152\pi$
$810$		0			0
$811$	31.8364			1.11793			0.558964	−	0.829192i	$-0.311199\pi$
$811$	31.8364			1.11793			0.558964	+	0.829192i	$0.311199\pi$
$812$	−0.560391	−	6.04248i	−0.0196659	−	0.212049i
$813$		0			0
$814$	30.4369	−	14.6576i	1.06681	−	0.513750i
$815$	5.32235	+	6.67401i	0.186434	+	0.233780i
$816$		0			0
$817$	−76.7801	+	36.9753i	−2.68619	+	1.29360i
$818$	33.0838	+	15.9323i	1.15675	+	0.557060i
$819$		0			0
$820$	3.98697	−	17.4681i	0.139231	−	0.610011i
$821$	2.92425	−	12.8120i	0.102057	−	0.447141i	−0.897919	−	0.440161i	$-0.854921\pi$
$821$	2.92425	−	12.8120i	0.102057	−	0.447141i	0.999976	−	0.00697929i	$-0.00222160\pi$
$822$		0			0
$823$	11.6576	+	51.0754i	0.406359	+	1.78038i	0.600734	+	0.799449i	$0.294875\pi$
$823$	11.6576	+	51.0754i	0.406359	+	1.78038i	−0.194375	+	0.980927i	$0.562268\pi$
$824$	8.06647			0.281009
$825$		0			0
$826$	15.0165	+	7.23156i	0.522491	+	0.251618i
$827$	−20.4423	−	9.84448i	−0.710847	−	0.342326i	0.0432721	−	0.999063i	$-0.486222\pi$
$827$	−20.4423	−	9.84448i	−0.710847	−	0.342326i	−0.754119	+	0.656737i	$0.771936\pi$
$828$		0			0
$829$	20.0998			0.698094			0.349047	−	0.937105i	$-0.386505\pi$
$829$	20.0998			0.698094			0.349047	+	0.937105i	$0.386505\pi$
$830$	−3.39537	−	14.8761i	−0.117855	−	0.516356i
$831$		0			0
$832$	2.21839	−	9.71941i	0.0769089	−	0.336960i
$833$	−2.32316	+	10.1784i	−0.0804927	+	0.352662i
$834$		0			0
$835$	8.93821	+	4.30442i	0.309320	+	0.148961i
$836$	11.6443	−	5.60761i	0.402727	−	0.193943i
$837$		0			0
$838$	−16.9844	−	21.2977i	−0.586716	−	0.735718i
$839$	7.40628	−	3.56667i	0.255693	−	0.123135i	−0.301647	−	0.953420i	$-0.597536\pi$
$839$	7.40628	−	3.56667i	0.255693	−	0.123135i	0.557340	+	0.830284i	$0.311822\pi$
$840$		0			0
$841$	−28.5054	+	5.33316i	−0.982945	+	0.183902i
$842$	0.459305			0.0158287
$843$		0			0
$844$	6.99034	+	8.76561i	0.240617	+	0.301725i
$845$	22.6332	−	28.3811i	0.778605	−	0.976340i
$846$		0			0
$847$	5.21489	+	2.51136i	0.179186	+	0.0862913i
$848$	−7.70077	−	9.65646i	−0.264445	−	0.331604i
$849$		0			0
$850$	−3.19953	+	14.0181i	−0.109743	+	0.480815i
$851$	18.3452	−	23.0042i	0.628866	−	0.788573i
$852$		0			0
$853$	20.7111			0.709136			0.354568	−	0.935030i	$-0.384628\pi$
$853$	20.7111			0.709136			0.354568	+	0.935030i	$0.384628\pi$
$854$	2.21991	+	9.72605i	0.0759636	+	0.332818i
$855$		0			0
$856$	−27.8533	−	13.4134i	−0.952006	−	0.458462i
$857$	−1.36550	−	5.98267i	−0.0466448	−	0.204364i	0.946236	−	0.323477i	$-0.104852\pi$
$857$	−1.36550	−	5.98267i	−0.0466448	−	0.204364i	−0.992881	+	0.119113i	$0.961995\pi$
$858$		0			0
$859$	−3.55262	−	15.5650i	−0.121214	−	0.531072i	−0.998677	−	0.0514278i	$-0.983623\pi$
$859$	−3.55262	−	15.5650i	−0.121214	−	0.531072i	0.877463	−	0.479644i	$-0.159234\pi$
$860$	14.7625	−	18.5116i	0.503398	−	0.631241i
$861$		0			0
$862$	5.39165	−	23.6224i	0.183640	−	0.804581i
$863$	12.7849	+	16.0318i	0.435204	+	0.545729i	0.950272	−	0.311420i	$-0.100805\pi$
$863$	12.7849	+	16.0318i	0.435204	+	0.545729i	−0.515068	+	0.857149i	$0.672233\pi$
$864$		0			0
$865$	−21.2361	+	10.2268i	−0.722048	+	0.347720i
$866$	−0.216837	+	0.271905i	−0.00736843	+	0.00923972i
$867$		0			0
$868$	4.04622	−	1.94856i	0.137338	−	0.0661384i
$869$	−42.7418			−1.44992
$870$		0			0
$871$	0.522967			0.0177201
$872$	12.8093	−	6.16865i	0.433779	−	0.208897i
$873$		0			0
$874$	−14.7334	+	18.4751i	−0.498364	+	0.624929i
$875$	−1.59177	+	0.766556i	−0.0538117	+	0.0259143i
$876$		0			0
$877$	−16.6801	−	20.9162i	−0.563247	−	0.706289i	0.415907	−	0.909407i	$-0.363464\pi$
$877$	−16.6801	−	20.9162i	−0.563247	−	0.706289i	−0.979154	+	0.203118i	$0.934893\pi$
$878$	6.70801	−	29.3897i	0.226384	−	0.991854i
$879$		0			0
$880$	12.3275	−	15.4582i	0.415559	−	0.521094i
$881$	4.45824	+	19.5328i	0.150202	+	0.658078i	0.992825	+	0.119574i	$0.0381529\pi$
$881$	4.45824	+	19.5328i	0.150202	+	0.658078i	−0.842623	+	0.538503i	$0.818990\pi$
$882$		0			0
$883$	7.77065	+	34.0454i	0.261503	+	1.14572i	0.919622	+	0.392806i	$0.128495\pi$
$883$	7.77065	+	34.0454i	0.261503	+	1.14572i	−0.658118	+	0.752914i	$0.728647\pi$
$884$	1.77147	+	0.853095i	0.0595810	+	0.0286927i
$885$		0			0
$886$	−1.08015	−	4.73243i	−0.0362882	−	0.158989i
$887$	16.0686			0.539530			0.269765	−	0.962926i	$-0.413054\pi$
$887$	16.0686			0.539530			0.269765	+	0.962926i	$0.413054\pi$
$888$		0			0
$889$	−16.3471	+	20.4986i	−0.548265	+	0.687502i
$890$	−1.63690	+	7.17173i	−0.0548690	+	0.240397i
$891$		0			0
$892$	−5.57986	−	6.99692i	−0.186827	−	0.234274i
$893$	−47.8095	−	23.0238i	−1.59988	−	0.770463i
$894$		0			0
$895$	−5.45321	+	6.83811i	−0.182281	+	0.228573i
$896$	−3.35993	−	4.21322i	−0.112247	−	0.140754i
$897$		0			0
$898$	−24.9373			−0.832170
$899$	−11.0577	−	18.3937i	−0.368795	−	0.613466i
$900$		0			0
$901$	12.8252	−	6.17627i	0.427268	−	0.205761i
$902$	17.9582	+	22.5188i	0.597942	+	0.749795i
$903$		0			0
$904$	−14.3964	+	6.93294i	−0.478817	+	0.230586i
$905$	19.7308	+	9.50186i	0.655874	+	0.315852i
$906$		0			0
$907$	−5.98113	+	26.2050i	−0.198600	+	0.870124i	0.773171	+	0.634198i	$0.218670\pi$
$907$	−5.98113	+	26.2050i	−0.198600	+	0.870124i	−0.971771	+	0.235926i	$0.924188\pi$
$908$	−0.343270	+	1.50396i	−0.0113918	+	0.0499108i
$909$		0			0
$910$	1.62190	+	7.10602i	0.0537656	+	0.235562i
$911$	29.9706			0.992969			0.496485	−	0.868045i	$-0.334624\pi$
$911$	29.9706			0.992969			0.496485	+	0.868045i	$0.334624\pi$
$912$		0			0
$913$	−10.5274	−	5.06972i	−0.348405	−	0.167783i
$914$	15.9584	+	7.68518i	0.527859	+	0.254203i
$915$		0			0
$916$	−0.689267			−0.0227740
$917$	−0.208024	−	0.911413i	−0.00686956	−	0.0300975i
$918$		0			0
$919$	−7.68641	+	33.6764i	−0.253551	+	1.11088i	0.674455	+	0.738316i	$0.264379\pi$
$919$	−7.68641	+	33.6764i	−0.253551	+	1.11088i	−0.928006	+	0.372565i	$0.878478\pi$
$920$	5.98882	−	26.2388i	0.197446	−	0.865066i
$921$		0			0
$922$	3.57260	+	1.72048i	0.117657	+	0.0566608i
$923$	−12.0546	+	5.80517i	−0.396781	+	0.191079i
$924$		0			0
$925$	30.5158	+	38.2656i	1.00335	+	1.25816i
$926$	−21.8731	+	10.5335i	−0.718795	+	0.346154i
$927$		0			0
$928$	13.5453	−	13.0213i	0.444647	−	0.427445i
$929$	55.5508			1.82256			0.911282	−	0.411783i	$-0.135094\pi$
$929$	55.5508			1.82256			0.911282	+	0.411783i	$0.135094\pi$
$930$		0			0
$931$	−17.7950	−	22.3142i	−0.583206	−	0.731317i
$932$	−10.3276	+	12.9504i	−0.338292	+	0.424205i
$933$		0			0
$934$	−18.1866	−	8.75821i	−0.595084	−	0.286578i
$935$	14.2076	+	17.8158i	0.464639	+	0.582639i
$936$		0			0
$937$	0.915057	−	4.00913i	0.0298936	−	0.130972i	−0.957779	−	0.287505i	$-0.907174\pi$
$937$	0.915057	−	4.00913i	0.0298936	−	0.130972i	0.987673	+	0.156532i	$0.0500315\pi$
$938$	0.574797	−	0.720773i	0.0187678	−	0.0235341i
$939$		0			0
$940$	14.7434			0.480875
$941$	0.849320	+	3.72112i	0.0276871	+	0.121305i	0.986883	−	0.161437i	$-0.0516130\pi$
$941$	0.849320	+	3.72112i	0.0276871	+	0.121305i	−0.959196	+	0.282742i	$0.908756\pi$
$942$		0			0
$943$	22.6019	+	10.8845i	0.736019	+	0.354448i
$944$	4.18407	+	18.3316i	0.136180	+	0.596643i
$945$		0			0
$946$	8.46959	+	37.1077i	0.275370	+	1.20648i
$947$	−14.2317	+	17.8460i	−0.462469	+	0.579918i	−0.957309	−	0.289066i	$-0.906655\pi$
$947$	−14.2317	+	17.8460i	−0.462469	+	0.579918i	0.494840	+	0.868984i	$0.335227\pi$
$948$		0			0
$949$	−3.29810	+	14.4499i	−0.107061	+	0.469065i
$950$	−24.5078	−	30.7318i	−0.795137	−	0.997071i
$951$		0			0
$952$	12.8012	−	6.16473i	0.414889	−	0.199800i
$953$	27.8165	−	34.8808i	0.901065	−	1.12990i	−0.0899227	−	0.995949i	$-0.528662\pi$
$953$	27.8165	−	34.8808i	0.901065	−	1.12990i	0.990988	−	0.133951i	$-0.0427666\pi$
$954$		0			0
$955$	−12.4031	+	5.97302i	−0.401355	+	0.193282i
$956$	−5.07190			−0.164037
$957$		0			0
$958$	−41.9764			−1.35620
$959$	19.6205	−	9.44873i	0.633579	−	0.305115i
$960$		0			0
$961$	−9.42540	+	11.8191i	−0.304045	+	0.381261i
$962$	−12.6584	+	6.09597i	−0.408123	+	0.196542i
$963$		0			0
$964$	−9.83955	−	12.3384i	−0.316910	−	0.397393i
$965$	−2.79559	+	12.2483i	−0.0899931	+	0.394285i
$966$		0			0
$967$	34.3628	−	43.0896i	1.10503	−	1.38567i	0.190242	−	0.981737i	$-0.439073\pi$
$967$	34.3628	−	43.0896i	1.10503	−	1.38567i	0.914790	−	0.403929i	$-0.132356\pi$
$968$	2.27091	+	9.94949i	0.0729897	+	0.319789i
$969$		0			0
$970$	−10.2035	−	44.7043i	−0.327614	−	1.43537i
$971$	−11.9811	−	5.76979i	−0.384491	−	0.185161i	0.231646	−	0.972800i	$-0.425589\pi$
$971$	−11.9811	−	5.76979i	−0.384491	−	0.185161i	−0.616137	+	0.787639i	$0.711303\pi$
$972$		0			0
$973$	3.37606	+	14.7915i	0.108232	+	0.474193i
$974$	−15.3640			−0.492296
$975$		0			0
$976$	−7.01718	+	8.79926i	−0.224614	+	0.281657i
$977$	0.470985	−	2.06352i	0.0150681	−	0.0660179i	−0.966835	−	0.255402i	$-0.917792\pi$
$977$	0.470985	−	2.06352i	0.0150681	−	0.0660179i	0.981903	+	0.189384i	$0.0606492\pi$
$978$		0			0
$979$	3.51217	+	4.40412i	0.112249	+	0.140756i
$980$	7.14446	+	3.44059i	0.228221	+	0.109906i
$981$		0			0
$982$	−17.9736	+	22.5382i	−0.573562	+	0.719224i
$983$	5.94739	+	7.45779i	0.189692	+	0.237867i	0.867579	−	0.497300i	$-0.165675\pi$
$983$	5.94739	+	7.45779i	0.189692	+	0.237867i	−0.677886	+	0.735167i	$0.737104\pi$
$984$		0			0
$985$	37.2964			1.18836
$986$	−8.53414	−	14.1960i	−0.271782	−	0.452092i
$987$		0			0
$988$	−4.84276	+	2.33215i	−0.154069	+	0.0741956i
$989$	20.6692	+	25.9184i	0.657242	+	0.824156i
$990$		0			0
$991$	10.5591	−	5.08499i	0.335420	−	0.161530i	−0.258590	−	0.965987i	$-0.583258\pi$
$991$	10.5591	−	5.08499i	0.335420	−	0.161530i	0.594011	+	0.804457i	$0.297544\pi$
$992$	12.5280	+	6.03314i	0.397763	+	0.191553i
$993$		0			0
$994$	−5.24836	+	22.9946i	−0.166468	+	0.729343i
$995$	0.953091	−	4.17576i	0.0302150	−	0.132381i
$996$		0			0
$997$	−10.7939	−	47.2912i	−0.341847	−	1.49773i	−0.795173	−	0.606383i	$-0.792620\pi$
$997$	−10.7939	−	47.2912i	−0.341847	−	1.49773i	0.453326	−	0.891345i	$-0.350237\pi$
$998$	−18.4069			−0.582659
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.c.136.2		18
3.2	odd	2		87.2.g.a.49.2	yes	18
29.4	even	14		7569.2.a.bm.1.6		9
29.16	even	7	inner	261.2.k.c.190.2		18
29.25	even	7		7569.2.a.bj.1.4		9
87.62	odd	14		2523.2.a.o.1.4		9
87.74	odd	14		87.2.g.a.16.2	✓	18
87.83	odd	14		2523.2.a.r.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.16.2	✓	18	87.74	odd	14
87.2.g.a.49.2	yes	18	3.2	odd	2
261.2.k.c.136.2		18	1.1	even	1	trivial
261.2.k.c.190.2		18	29.16	even	7	inner
2523.2.a.o.1.4		9	87.62	odd	14
2523.2.a.r.1.6		9	87.83	odd	14
7569.2.a.bj.1.4		9	29.25	even	7
7569.2.a.bm.1.6		9	29.4	even	14

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Elliptic curves over $\Q$
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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	261.2.k.c.136.2

Level	$261$
Weight	$2$
Character	261.136
Analytic conductor	$2.084$
Analytic rank	$0$
Dimension	$18$
Inner twists	$2$