LMFDB - Embedded newform 368.2.s.b.15.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [368,2,Mod(15,368)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(368, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 0, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("368.15"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$368 = 2^{4} \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	368.s (of order $22$ , degree $10$ , minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			15.1
Character	$\chi$	$=$	368.15
Dual form			368.2.s.b.319.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.62148 + 1.19719i) q^{3} +(-2.71500 + 2.35256i) q^{5} +(-2.67155 - 1.71690i) q^{7} +(3.47433 - 4.00959i) q^{9} +(0.221876 + 1.54318i) q^{11} +(4.68212 - 3.00902i) q^{13} +(4.30087 - 9.41759i) q^{15} +(0.696159 + 2.37090i) q^{17} +(0.869524 + 0.255315i) q^{19} +(9.05888 + 1.30247i) q^{21} +(-2.08082 - 4.32090i) q^{23} +(1.12511 - 7.82533i) q^{25} +(-1.87186 + 6.37496i) q^{27} +(-5.86044 + 1.72078i) q^{29} +(6.32598 + 2.88898i) q^{31} +(-2.42913 - 3.77980i) q^{33} +(11.2924 - 1.62360i) q^{35} +(-7.19714 - 6.23636i) q^{37} +(-8.67174 + 13.4935i) q^{39} +(-4.06762 - 4.69428i) q^{41} +(-1.71347 - 3.75198i) q^{43} +19.0596i q^{45} -7.92656i q^{47} +(1.28152 + 2.80614i) q^{49} +(-4.66339 - 5.38184i) q^{51} +(2.63563 - 4.10113i) q^{53} +(-4.23283 - 3.66777i) q^{55} +(-2.58510 + 0.371682i) q^{57} +(5.30505 + 8.25482i) q^{59} +(-5.40210 - 2.46706i) q^{61} +(-16.1659 + 4.74674i) q^{63} +(-5.63307 + 19.1845i) q^{65} +(1.21940 - 8.48110i) q^{67} +(10.6278 + 8.83603i) q^{69} +(6.81133 + 0.979321i) q^{71} +(10.7034 + 3.14279i) q^{73} +(6.41895 + 21.8609i) q^{75} +(2.05674 - 4.50363i) q^{77} +(0.512379 - 0.329286i) q^{79} +(-0.459876 - 3.19851i) q^{81} +(-6.49352 + 7.49392i) q^{83} +(-7.46777 - 4.79924i) q^{85} +(13.3029 - 11.5271i) q^{87} +(-0.958620 + 0.437787i) q^{89} -17.6747 q^{91} -20.0421 q^{93} +(-2.96141 + 1.35243i) q^{95} +(-11.1499 + 9.66141i) q^{97} +(6.95840 + 4.47189i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$80 q + 4 q^{9} + 12 q^{13} + 22 q^{17} + 66 q^{21} + 36 q^{25} + 34 q^{29} + 22 q^{33} + 12 q^{41} - 56 q^{49} - 66 q^{57} - 88 q^{61} - 154 q^{65} - 66 q^{69} - 16 q^{73} - 158 q^{77} - 248 q^{81} - 116 q^{85}+ \cdots - 22 q^{97}+O(q^{100})$ 80 * q + 4 * q^9 + 12 * q^13 + 22 * q^17 + 66 * q^21 + 36 * q^25 + 34 * q^29 + 22 * q^33 + 12 * q^41 - 56 * q^49 - 66 * q^57 - 88 * q^61 - 154 * q^65 - 66 * q^69 - 16 * q^73 - 158 * q^77 - 248 * q^81 - 116 * q^85 - 88 * q^89 - 84 * q^93 - 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$ .

$n$	$47$	$97$	$277$
$\chi(n)$	$-1$	$e\left(\frac{17}{22}\right)$	$1$

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

)

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

$2$		0			0
$2$		0			0
$3$	−2.62148	+	1.19719i	−1.51351	+	0.691199i	−0.987258	−	0.159127i	$-0.949132\pi$
$3$	−2.62148	+	1.19719i	−1.51351	+	0.691199i	−0.526256	+	0.850326i	$0.676405\pi$
$4$		0			0
$5$	−2.71500	+	2.35256i	−1.21419	+	1.05210i	−0.217074	+	0.976155i	$0.569651\pi$
$5$	−2.71500	+	2.35256i	−1.21419	+	1.05210i	−0.997112	+	0.0759434i	$0.975803\pi$
$6$		0			0
$7$	−2.67155	−	1.71690i	−1.00975	−	0.648927i	−0.0724221	−	0.997374i	$-0.523073\pi$
$7$	−2.67155	−	1.71690i	−1.00975	−	0.648927i	−0.937329	+	0.348447i	$0.886709\pi$
$8$		0			0
$9$	3.47433	−	4.00959i	1.15811	−	1.33653i
$10$		0			0
$11$	0.221876	+	1.54318i	0.0668982	+	0.465288i	0.995542	+	0.0943156i	$0.0300663\pi$
$11$	0.221876	+	1.54318i	0.0668982	+	0.465288i	−0.928644	+	0.370972i	$0.879025\pi$
$12$		0			0
$13$	4.68212	−	3.00902i	1.29859	−	0.834551i	0.305530	−	0.952182i	$-0.401166\pi$
$13$	4.68212	−	3.00902i	1.29859	−	0.834551i	0.993057	+	0.117631i	$0.0375300\pi$
$14$		0			0
$15$	4.30087	−	9.41759i	1.11048	−	2.43161i
$16$		0			0
$17$	0.696159	+	2.37090i	0.168843	+	0.575028i	0.999825	+	0.0187273i	$0.00596145\pi$
$17$	0.696159	+	2.37090i	0.168843	+	0.575028i	−0.830981	+	0.556300i	$0.812220\pi$
$18$		0			0
$19$	0.869524	+	0.255315i	0.199482	+	0.0585733i	0.379947	−	0.925008i	$-0.375942\pi$
$19$	0.869524	+	0.255315i	0.199482	+	0.0585733i	−0.180465	+	0.983581i	$0.557760\pi$
$20$		0			0
$21$	9.05888	+	1.30247i	1.97681	+	0.284222i
$22$		0			0
$23$	−2.08082	−	4.32090i	−0.433881	−	0.900970i
$23$	−2.08082	−	4.32090i	−0.433881	−	0.900970i
$24$		0			0
$25$	1.12511	−	7.82533i	0.225023	−	1.56507i
$26$		0			0
$27$	−1.87186	+	6.37496i	−0.360239	+	1.22686i
$28$		0			0
$29$	−5.86044	+	1.72078i	−1.08826	+	0.319541i	−0.776177	−	0.630515i	$-0.782844\pi$
$29$	−5.86044	+	1.72078i	−1.08826	+	0.319541i	−0.312079	+	0.950056i	$0.601025\pi$
$30$		0			0
$31$	6.32598	+	2.88898i	1.13618	+	0.518876i	0.892530	−	0.450987i	$-0.148928\pi$
$31$	6.32598	+	2.88898i	1.13618	+	0.518876i	0.243650	+	0.969863i	$0.421655\pi$
$32$		0			0
$33$	−2.42913	−	3.77980i	−0.422858	−	0.657979i
$34$		0			0
$35$	11.2924	−	1.62360i	1.90876	−	0.274438i
$36$		0			0
$37$	−7.19714	−	6.23636i	−1.18320	−	1.02525i	−0.999103	−	0.0423437i	$-0.986518\pi$
$37$	−7.19714	−	6.23636i	−1.18320	−	1.02525i	−0.184100	−	0.982908i	$-0.558937\pi$
$38$		0			0
$39$	−8.67174	+	13.4935i	−1.38859	+	2.16069i
$40$		0			0
$41$	−4.06762	−	4.69428i	−0.635255	−	0.733123i	0.343273	−	0.939236i	$-0.388464\pi$
$41$	−4.06762	−	4.69428i	−0.635255	−	0.733123i	−0.978528	+	0.206112i	$0.933919\pi$
$42$		0			0
$43$	−1.71347	−	3.75198i	−0.261302	−	0.572172i	0.732822	−	0.680421i	$-0.238203\pi$
$43$	−1.71347	−	3.75198i	−0.261302	−	0.572172i	−0.994124	+	0.108249i	$0.965476\pi$
$44$		0			0
$45$			19.0596i			2.84124i
$46$		0			0
$47$		−	7.92656i		−	1.15621i	−0.815963	−	0.578104i	$-0.803793\pi$
$47$		−	7.92656i		−	1.15621i	0.815963	−	0.578104i	$-0.196207\pi$
$48$		0			0
$49$	1.28152	+	2.80614i	0.183075	+	0.400878i
$50$		0			0
$51$	−4.66339	−	5.38184i	−0.653005	−	0.753608i
$52$		0			0
$53$	2.63563	−	4.10113i	0.362032	−	0.563333i	−0.611683	−	0.791103i	$-0.709507\pi$
$53$	2.63563	−	4.10113i	0.362032	−	0.563333i	0.973715	+	0.227770i	$0.0731435\pi$
$54$		0			0
$55$	−4.23283	−	3.66777i	−0.570755	−	0.494562i
$56$		0			0
$57$	−2.58510	+	0.371682i	−0.342405	+	0.0492305i
$58$		0			0
$59$	5.30505	+	8.25482i	0.690659	+	1.07469i	0.992608	+	0.121362i	$0.0387261\pi$
$59$	5.30505	+	8.25482i	0.690659	+	1.07469i	−0.301950	+	0.953324i	$0.597637\pi$
$60$		0			0
$61$	−5.40210	−	2.46706i	−0.691668	−	0.315874i	0.0383864	−	0.999263i	$-0.487778\pi$
$61$	−5.40210	−	2.46706i	−0.691668	−	0.315874i	−0.730055	+	0.683389i	$0.760505\pi$
$62$		0			0
$63$	−16.1659	+	4.74674i	−2.03671	+	0.598032i
$64$		0			0
$65$	−5.63307	+	19.1845i	−0.698697	+	2.37954i
$66$		0			0
$67$	1.21940	−	8.48110i	0.148973	−	1.03613i	−0.768932	−	0.639331i	$-0.779211\pi$
$67$	1.21940	−	8.48110i	0.148973	−	1.03613i	0.917905	−	0.396800i	$-0.129879\pi$
$68$		0			0
$69$	10.6278	+	8.83603i	1.27943	+	1.06373i
$70$		0			0
$71$	6.81133	+	0.979321i	0.808356	+	0.116224i	0.534088	−	0.845429i	$-0.320655\pi$
$71$	6.81133	+	0.979321i	0.808356	+	0.116224i	0.274268	+	0.961653i	$0.411564\pi$
$72$		0			0
$73$	10.7034	+	3.14279i	1.25273	+	0.367836i	0.839785	−	0.542919i	$-0.182681\pi$
$73$	10.7034	+	3.14279i	1.25273	+	0.367836i	0.412948	+	0.910755i	$0.364499\pi$
$74$		0			0
$75$	6.41895	+	21.8609i	0.741197	+	2.52428i
$76$		0			0
$77$	2.05674	−	4.50363i	0.234387	−	0.513236i
$78$		0			0
$79$	0.512379	−	0.329286i	0.0576471	−	0.0370475i	−0.511500	−	0.859283i	$-0.670910\pi$
$79$	0.512379	−	0.329286i	0.0576471	−	0.0370475i	0.569147	+	0.822236i	$0.307274\pi$
$80$		0			0
$81$	−0.459876	−	3.19851i	−0.0510973	−	0.355390i
$82$		0			0
$83$	−6.49352	+	7.49392i	−0.712756	+	0.822564i	−0.990416	−	0.138115i	$-0.955896\pi$
$83$	−6.49352	+	7.49392i	−0.712756	+	0.822564i	0.277660	+	0.960679i	$0.410441\pi$
$84$		0			0
$85$	−7.46777	−	4.79924i	−0.809993	−	0.520551i
$86$		0			0
$87$	13.3029	−	11.5271i	1.42622	−	1.23583i
$88$		0			0
$89$	−0.958620	+	0.437787i	−0.101614	+	0.0464053i	−0.465573	−	0.885009i	$-0.654152\pi$
$89$	−0.958620	+	0.437787i	−0.101614	+	0.0464053i	0.363960	+	0.931415i	$0.381425\pi$
$90$		0			0
$91$	−17.6747			−1.85281
$92$		0			0
$93$	−20.0421			−2.07827
$94$		0			0
$95$	−2.96141	+	1.35243i	−0.303834	+	0.138756i
$96$		0			0
$97$	−11.1499	+	9.66141i	−1.13210	+	0.980968i	−0.999947	−	0.0102618i	$-0.996734\pi$
$97$	−11.1499	+	9.66141i	−1.13210	+	0.980968i	−0.132150	+	0.991230i	$0.542188\pi$
$98$		0			0
$99$	6.95840	+	4.47189i	0.699346	+	0.449442i
$100$		0			0
$101$	4.95371	−	5.71689i	0.492913	−	0.568852i	−0.453729	−	0.891140i	$-0.649907\pi$
$101$	4.95371	−	5.71689i	0.492913	−	0.568852i	0.946642	+	0.322288i	$0.104452\pi$
$102$		0			0
$103$	−0.551681	−	3.83703i	−0.0543587	−	0.378073i	−0.998782	−	0.0493413i	$-0.984288\pi$
$103$	−0.551681	−	3.83703i	−0.0543587	−	0.378073i	0.944423	−	0.328732i	$-0.106621\pi$
$104$		0			0
$105$	−27.6590	+	17.7754i	−2.69925	+	1.73470i
$106$		0			0
$107$	2.72415	−	5.96505i	0.263353	−	0.576663i	−0.731049	−	0.682325i	$-0.760969\pi$
$107$	2.72415	−	5.96505i	0.263353	−	0.576663i	0.994402	+	0.105662i	$0.0336961\pi$
$108$		0			0
$109$	−5.42836	−	18.4873i	−0.519943	−	1.77076i	−0.629738	−	0.776808i	$-0.716838\pi$
$109$	−5.42836	−	18.4873i	−0.519943	−	1.77076i	0.109795	−	0.993954i	$-0.464981\pi$
$110$		0			0
$111$	26.3333	+	7.73216i	2.49945	+	0.733904i
$112$		0			0
$113$	7.19134	+	1.03396i	0.676504	+	0.0972666i	0.471999	−	0.881599i	$-0.343532\pi$
$113$	7.19134	+	1.03396i	0.676504	+	0.0972666i	0.204505	+	0.978866i	$0.434442\pi$
$114$		0			0
$115$	15.8146	+	6.83599i	1.47472	+	0.637460i
$116$		0			0
$117$	4.20231	−	29.2277i	0.388503	−	2.70210i
$118$		0			0
$119$	2.21078	−	7.52921i	0.202662	−	0.690202i
$120$		0			0
$121$	8.22223	−	2.41427i	0.747476	−	0.219479i
$122$		0			0
$123$	16.2831	+	7.43626i	1.46820	+	0.670505i
$124$		0			0
$125$	5.64374	+	8.78183i	0.504791	+	0.785471i
$126$		0			0
$127$	−16.8463	+	2.42213i	−1.49487	+	0.214929i	−0.840733	−	0.541450i	$-0.817875\pi$
$127$	−16.8463	+	2.42213i	−1.49487	+	0.214929i	−0.654133	+	0.756379i	$0.726966\pi$
$128$		0			0
$129$	8.98368	+	7.78440i	0.790969	+	0.685379i
$130$		0			0
$131$	1.78738	−	2.78122i	0.156164	−	0.242996i	−0.754352	−	0.656471i	$-0.772049\pi$
$131$	1.78738	−	2.78122i	0.156164	−	0.242996i	0.910516	+	0.413475i	$0.135685\pi$
$132$		0			0
$133$	−1.88463	−	2.17497i	−0.163418	−	0.188594i
$134$		0			0
$135$	−9.91541	−	21.7117i	−0.853382	−	1.86865i
$136$		0			0
$137$		−	14.4120i		−	1.23130i	−0.788021	−	0.615648i	$-0.788894\pi$
$137$		−	14.4120i		−	1.23130i	0.788021	−	0.615648i	$-0.211106\pi$
$138$		0			0
$139$		−	6.66562i		−	0.565370i	−0.959213	−	0.282685i	$-0.908775\pi$
$139$		−	6.66562i		−	0.565370i	0.959213	−	0.282685i	$-0.0912252\pi$
$140$		0			0
$141$	9.48961	+	20.7793i	0.799169	+	1.74994i
$142$		0			0
$143$	5.68232	+	6.55775i	0.475180	+	0.548386i
$144$		0			0
$145$	11.8629	−	18.4590i	0.985157	−	1.53293i
$146$		0			0
$147$	−6.71898	−	5.82203i	−0.554172	−	0.480193i
$148$		0			0
$149$	−5.50273	+	0.791173i	−0.450801	+	0.0648154i	−0.363976	−	0.931408i	$-0.618581\pi$
$149$	−5.50273	+	0.791173i	−0.450801	+	0.0648154i	−0.0868248	+	0.996224i	$0.527672\pi$
$150$		0			0
$151$	−2.89576	−	4.50589i	−0.235654	−	0.366684i	0.703205	−	0.710987i	$-0.251752\pi$
$151$	−2.89576	−	4.50589i	−0.235654	−	0.366684i	−0.938859	+	0.344303i	$0.888115\pi$
$152$		0			0
$153$	11.9250	+	5.44597i	0.964080	+	0.440281i
$154$		0			0
$155$	−23.9716	+	7.03869i	−1.92544	+	0.565361i
$156$		0			0
$157$	−3.08540	+	10.5079i	−0.246241	+	0.838621i	0.739900	+	0.672717i	$0.234873\pi$
$157$	−3.08540	+	10.5079i	−0.246241	+	0.838621i	−0.986142	+	0.165905i	$0.946946\pi$
$158$		0			0
$159$	−1.99944	+	13.9064i	−0.158566	+	1.10285i
$160$		0			0
$161$	−1.85954	+	15.1161i	−0.146552	+	1.19131i
$162$		0			0
$163$	−5.24785	−	0.754527i	−0.411043	−	0.0590991i	−0.0663083	−	0.997799i	$-0.521122\pi$
$163$	−5.24785	−	0.754527i	−0.411043	−	0.0590991i	−0.344735	+	0.938700i	$0.612031\pi$
$164$		0			0
$165$	15.4873	+	4.54749i	1.20569	+	0.354022i
$166$		0			0
$167$	−6.17757	−	21.0389i	−0.478035	−	1.62804i	−0.746955	−	0.664875i	$-0.768485\pi$
$167$	−6.17757	−	21.0389i	−0.478035	−	1.62804i	0.268920	−	0.963162i	$-0.413333\pi$
$168$		0			0
$169$	7.46769	−	16.3520i	0.574438	−	1.25784i
$170$		0			0
$171$	4.04472	−	2.59938i	0.309307	−	0.198780i
$172$		0			0
$173$	−0.446969	−	3.10874i	−0.0339824	−	0.236353i	0.965750	−	0.259473i	$-0.0835490\pi$
$173$	−0.446969	−	3.10874i	−0.0339824	−	0.236353i	−0.999733	+	0.0231204i	$0.992640\pi$
$174$		0			0
$175$	−16.4411	+	18.9740i	−1.24283	+	1.43430i
$176$		0			0
$177$	−23.7897	−	15.2887i	−1.78814	−	1.14917i
$178$		0			0
$179$	−12.6055	+	10.9228i	−0.942182	+	0.816406i	−0.983159	−	0.182755i	$-0.941499\pi$
$179$	−12.6055	+	10.9228i	−0.942182	+	0.816406i	0.0409763	+	0.999160i	$0.486953\pi$
$180$		0			0
$181$	1.85095	−	0.845299i	0.137580	−	0.0628306i	−0.345436	−	0.938442i	$-0.612269\pi$
$181$	1.85095	−	0.845299i	0.137580	−	0.0628306i	0.483015	+	0.875612i	$0.339542\pi$
$182$		0			0
$183$	17.1151			1.26518
$184$		0			0
$185$	34.2117			2.51529
$186$		0			0
$187$	−3.50427	+	1.60035i	−0.256258	+	0.117029i
$188$		0			0
$189$	15.9459	−	13.8172i	1.15990	−	1.00506i
$190$		0			0
$191$	−0.637825	−	0.409905i	−0.0461514	−	0.0296597i	0.517362	−	0.855767i	$-0.326914\pi$
$191$	−0.637825	−	0.409905i	−0.0461514	−	0.0296597i	−0.563513	+	0.826107i	$0.690551\pi$
$192$		0			0
$193$	−8.07815	+	9.32268i	−0.581478	+	0.671061i	−0.967922	−	0.251252i	$-0.919158\pi$
$193$	−8.07815	+	9.32268i	−0.581478	+	0.671061i	0.386444	+	0.922313i	$0.373703\pi$
$194$		0			0
$195$	−8.20049	−	57.0357i	−0.587249	−	4.08441i
$196$		0			0
$197$	−2.84329	+	1.82727i	−0.202576	+	0.130188i	−0.637996	−	0.770040i	$-0.720236\pi$
$197$	−2.84329	+	1.82727i	−0.202576	+	0.130188i	0.435420	+	0.900227i	$0.356600\pi$
$198$		0			0
$199$	−1.35272	+	2.96205i	−0.0958918	+	0.209974i	−0.951499	−	0.307652i	$-0.900457\pi$
$199$	−1.35272	+	2.96205i	−0.0958918	+	0.209974i	0.855607	+	0.517626i	$0.173184\pi$
$200$		0			0
$201$	6.95687	+	23.6929i	0.490699	+	1.67117i
$202$		0			0
$203$	18.6109	+	5.46464i	1.30623	+	0.383542i
$204$		0			0
$205$	22.0872	+	3.17566i	1.54264	+	0.221798i
$206$		0			0
$207$	−24.5545	−	6.66898i	−1.70665	−	0.463526i
$208$		0			0
$209$	−0.201072	+	1.39848i	−0.0139084	+	0.0967352i
$210$		0			0
$211$	0.805779	−	2.74423i	0.0554721	−	0.188921i	−0.927096	−	0.374824i	$-0.877703\pi$
$211$	0.805779	−	2.74423i	0.0554721	−	0.188921i	0.982568	+	0.185904i	$0.0595212\pi$
$212$		0			0
$213$	−19.0282	+	5.58719i	−1.30379	+	0.382828i
$214$		0			0
$215$	13.4789	+	6.15559i	0.919251	+	0.419808i
$216$		0			0
$217$	−11.9401	−	18.5791i	−0.810546	−	1.26123i
$218$		0			0
$219$	−31.8212	+	4.57520i	−2.15028	+	0.309163i
$220$		0			0
$221$	10.3936	+	9.00609i	0.699148	+	0.605815i
$222$		0			0
$223$	5.29632	−	8.24123i	0.354668	−	0.551874i	−0.617378	−	0.786667i	$-0.711805\pi$
$223$	5.29632	−	8.24123i	0.354668	−	0.551874i	0.972045	+	0.234793i	$0.0754413\pi$
$224$		0			0
$225$	−27.4673	−	31.6990i	−1.83116	−	2.11327i
$226$		0			0
$227$	−0.582740	−	1.27602i	−0.0386778	−	0.0846927i	0.889307	−	0.457311i	$-0.151187\pi$
$227$	−0.582740	−	1.27602i	−0.0386778	−	0.0846927i	−0.927985	+	0.372618i	$0.878460\pi$
$228$		0			0
$229$			1.93810i			0.128073i	0.997948	+	0.0640366i	$0.0203974\pi$
$229$			1.93810i			0.128073i	−0.997948	+	0.0640366i	$0.979603\pi$
$230$		0			0
$231$			14.2685i			0.938799i
$232$		0			0
$233$	−2.31962	−	5.07925i	−0.151963	−	0.332753i	0.818305	−	0.574784i	$-0.194914\pi$
$233$	−2.31962	−	5.07925i	−0.151963	−	0.332753i	−0.970269	+	0.242031i	$0.922187\pi$
$234$		0			0
$235$	18.6477	+	21.5206i	1.21644	+	1.40385i
$236$		0			0
$237$	−0.948974	+	1.47663i	−0.0616425	+	0.0959176i
$238$		0			0
$239$	5.96246	+	5.16650i	0.385679	+	0.334193i	0.826023	−	0.563636i	$-0.190598\pi$
$239$	5.96246	+	5.16650i	0.385679	+	0.334193i	−0.440344	+	0.897829i	$0.645143\pi$
$240$		0			0
$241$	2.86833	−	0.412404i	0.184766	−	0.0265653i	−0.0493109	−	0.998783i	$-0.515703\pi$
$241$	2.86833	−	0.412404i	0.184766	−	0.0265653i	0.234076	+	0.972218i	$0.424793\pi$
$242$		0			0
$243$	−5.74142	−	8.93383i	−0.368313	−	0.573106i
$244$		0			0
$245$	−10.0810	−	4.60383i	−0.644050	−	0.294128i
$246$		0			0
$247$	4.83947	−	1.42100i	0.307928	−	0.0904158i
$248$		0			0
$249$	8.05099	−	27.4192i	0.510211	−	1.73762i
$250$		0			0
$251$	2.72826	−	18.9755i	0.172206	−	1.19772i	−0.702004	−	0.712173i	$-0.747711\pi$
$251$	2.72826	−	18.9755i	0.172206	−	1.19772i	0.874210	−	0.485548i	$-0.161380\pi$
$252$		0			0
$253$	6.20626	−	4.16980i	0.390184	−	0.262153i
$254$		0			0
$255$	25.3222	+	3.64079i	1.58574	+	0.227995i
$256$		0			0
$257$	−7.38914	−	2.16965i	−0.460922	−	0.135339i	0.0430241	−	0.999074i	$-0.486301\pi$
$257$	−7.38914	−	2.16965i	−0.460922	−	0.135339i	−0.503946	+	0.863735i	$0.668119\pi$
$258$		0			0
$259$	8.52031	+	29.0175i	0.529426	+	1.80306i
$260$		0			0
$261$	−13.4615	+	29.4765i	−0.833243	+	1.82455i
$262$		0			0
$263$	−11.4276	+	7.34409i	−0.704658	+	0.452856i	−0.843270	−	0.537491i	$-0.819372\pi$
$263$	−11.4276	+	7.34409i	−0.704658	+	0.452856i	0.138612	+	0.990347i	$0.455736\pi$
$264$		0			0
$265$	2.49241	+	17.3351i	0.153107	+	1.06488i
$266$		0			0
$267$	1.98889	−	2.29530i	0.121718	−	0.140470i
$268$		0			0
$269$	−15.5348	−	9.98362i	−0.947175	−	0.608712i	−0.0267543	−	0.999642i	$-0.508517\pi$
$269$	−15.5348	−	9.98362i	−0.947175	−	0.608712i	−0.920421	+	0.390930i	$0.872154\pi$
$270$		0			0
$271$	−0.142738	+	0.123684i	−0.00867074	+	0.00751324i	−0.659185	−	0.751981i	$-0.729099\pi$
$271$	−0.142738	+	0.123684i	−0.00867074	+	0.00751324i	0.650515	+	0.759494i	$0.274553\pi$
$272$		0			0
$273$	46.3340	−	21.1600i	2.80426	−	1.28066i
$274$		0			0
$275$	12.3256			0.743259
$276$		0			0
$277$	2.91065			0.174884			0.0874419	−	0.996170i	$-0.472131\pi$
$277$	2.91065			0.174884			0.0874419	+	0.996170i	$0.472131\pi$
$278$		0			0
$279$	33.5621	−	15.3273i	2.00931	−	0.917622i
$280$		0			0
$281$	−14.8589	+	12.8753i	−0.886407	+	0.768076i	−0.973635	−	0.228112i	$-0.926745\pi$
$281$	−14.8589	+	12.8753i	−0.886407	+	0.768076i	0.0872279	+	0.996188i	$0.472199\pi$
$282$		0			0
$283$	15.7863	+	10.1453i	0.938401	+	0.603074i	0.917941	−	0.396717i	$-0.129851\pi$
$283$	15.7863	+	10.1453i	0.938401	+	0.603074i	0.0204600	+	0.999791i	$0.493487\pi$
$284$		0			0
$285$	6.14416	−	7.09074i	0.363949	−	0.420019i
$286$		0			0
$287$	2.80723	+	19.5247i	0.165705	+	1.15251i
$288$		0			0
$289$	9.16478	−	5.88985i	0.539105	−	0.346462i
$290$		0			0
$291$	17.6626	−	38.6758i	1.03540	−	2.26721i
$292$		0			0
$293$	6.80464	+	23.1745i	0.397531	+	1.35387i	0.878757	+	0.477270i	$0.158374\pi$
$293$	6.80464	+	23.1745i	0.397531	+	1.35387i	−0.481225	+	0.876597i	$0.659808\pi$
$294$		0			0
$295$	−33.8232	−	9.93139i	−1.96926	−	0.578228i
$296$		0			0
$297$	−10.2531	−	1.47417i	−0.594943	−	0.0855399i
$298$		0			0
$299$	−22.7443	−	13.9698i	−1.31534	−	0.807892i
$300$		0			0
$301$	−1.86415	+	12.9655i	−0.107448	+	0.747317i
$302$		0			0
$303$	−6.14186	+	20.9173i	−0.352841	+	1.20167i
$304$		0			0
$305$	20.4706	−	6.01072i	1.17215	−	0.344173i
$306$		0			0
$307$	−21.6037	−	9.86608i	−1.23299	−	0.563087i	−0.311039	−	0.950397i	$-0.600677\pi$
$307$	−21.6037	−	9.86608i	−1.23299	−	0.563087i	−0.921950	+	0.387310i	$0.873404\pi$
$308$		0			0
$309$	6.03988	+	9.39823i	0.343597	+	0.534647i
$310$		0			0
$311$	−17.3715	+	2.49764i	−0.985046	+	0.141628i	−0.615969	−	0.787771i	$-0.711235\pi$
$311$	−17.3715	+	2.49764i	−0.985046	+	0.141628i	−0.369077	+	0.929399i	$0.620326\pi$
$312$		0			0
$313$	5.75286	+	4.98488i	0.325171	+	0.281762i	0.802113	−	0.597173i	$-0.203709\pi$
$313$	5.75286	+	4.98488i	0.325171	+	0.281762i	−0.476942	+	0.878935i	$0.658255\pi$
$314$		0			0
$315$	32.7235	−	50.9187i	1.84376	−	2.86894i
$316$		0			0
$317$	−3.30516	−	3.81436i	−0.185636	−	0.214236i	0.655302	−	0.755367i	$-0.272542\pi$
$317$	−3.30516	−	3.81436i	−0.185636	−	0.214236i	−0.840938	+	0.541132i	$0.817996\pi$
$318$		0			0
$319$	−3.95577	−	8.66193i	−0.221481	−	0.484975i
$320$		0			0
$321$			18.8986i			1.05482i
$322$		0			0
$323$			2.23929i			0.124598i
$324$		0			0
$325$	−18.2786	−	40.0246i	−1.01392	−	2.22017i
$326$		0			0
$327$	36.3632	+	41.9654i	2.01089	+	2.32069i
$328$		0			0
$329$	−13.6091	+	21.1762i	−0.750295	+	1.16748i
$330$		0			0
$331$	−2.37148	−	2.05490i	−0.130348	−	0.112947i	0.587247	−	0.809408i	$-0.300212\pi$
$331$	−2.37148	−	2.05490i	−0.130348	−	0.112947i	−0.717595	+	0.696460i	$0.754757\pi$
$332$		0			0
$333$	−50.0104	+	7.19042i	−2.74056	+	0.394032i
$334$		0			0
$335$	16.6417	+	25.8949i	0.909231	+	1.41479i
$336$		0			0
$337$	13.6755	+	6.24539i	0.744952	+	0.340208i	0.751467	−	0.659771i	$-0.229347\pi$
$337$	13.6755	+	6.24539i	0.744952	+	0.340208i	−0.00651524	+	0.999979i	$0.502074\pi$
$338$		0			0
$339$	−20.0898	+	5.89890i	−1.09113	+	0.320385i
$340$		0			0
$341$	−3.05464	+	10.4032i	−0.165418	+	0.563362i
$342$		0			0
$343$	−1.76940	+	12.3065i	−0.0955388	+	0.664487i
$344$		0			0
$345$	−49.6418	+	1.01270i	−2.67262	+	0.0545219i
$346$		0			0
$347$	23.8299	+	3.42622i	1.27926	+	0.183929i	0.748238	−	0.663430i	$-0.230900\pi$
$347$	23.8299	+	3.42622i	1.27926	+	0.183929i	0.531019	+	0.847360i	$0.321809\pi$
$348$		0			0
$349$	−0.403546	−	0.118492i	−0.0216013	−	0.00634272i	0.270914	−	0.962604i	$-0.412674\pi$
$349$	−0.403546	−	0.118492i	−0.0216013	−	0.00634272i	−0.292515	+	0.956261i	$0.594492\pi$
$350$		0			0
$351$	10.4181	+	35.4808i	0.556077	+	1.89383i
$352$		0			0
$353$	1.04159	−	2.28076i	0.0554383	−	0.121393i	−0.879886	−	0.475186i	$-0.842381\pi$
$353$	1.04159	−	2.28076i	0.0554383	−	0.121393i	0.935324	+	0.353793i	$0.115108\pi$
$354$		0			0
$355$	−20.7967	+	13.3652i	−1.10377	+	0.709352i
$356$		0			0
$357$	3.21840	+	22.3844i	0.170336	+	1.18471i
$358$		0			0
$359$	−9.57531	+	11.0505i	−0.505366	+	0.583223i	−0.949906	−	0.312536i	$-0.898822\pi$
$359$	−9.57531	+	11.0505i	−0.505366	+	0.583223i	0.444540	+	0.895759i	$0.353367\pi$
$360$		0			0
$361$	−15.2929	−	9.82817i	−0.804891	−	0.517272i
$362$		0			0
$363$	−18.6641	+	16.1725i	−0.979612	+	0.848839i
$364$		0			0
$365$	−36.4533	+	16.6476i	−1.90805	+	0.871378i
$366$		0			0
$367$	−35.5624			−1.85634			−0.928170	−	0.372156i	$-0.878619\pi$
$367$	−35.5624			−1.85634			−0.928170	+	0.372156i	$0.878619\pi$
$368$		0			0
$369$	−32.9543			−1.71553
$370$		0			0
$371$	−14.0824	+	6.43124i	−0.731124	+	0.333893i
$372$		0			0
$373$	3.16532	−	2.74277i	0.163894	−	0.142015i	−0.569053	−	0.822301i	$-0.692690\pi$
$373$	3.16532	−	2.74277i	0.163894	−	0.142015i	0.732947	+	0.680286i	$0.238144\pi$
$374$		0			0
$375$	−25.3085	−	16.2648i	−1.30693	−	0.839910i
$376$		0			0
$377$	−22.2614	+	25.6911i	−1.14652	+	1.32316i
$378$		0			0
$379$	−4.08383	−	28.4037i	−0.209772	−	1.45900i	−0.773899	−	0.633310i	$-0.781696\pi$
$379$	−4.08383	−	28.4037i	−0.209772	−	1.45900i	0.564126	−	0.825689i	$-0.309213\pi$
$380$		0			0
$381$	41.2625	−	26.5178i	2.11394	−	1.35855i
$382$		0			0
$383$	−14.3068	+	31.3276i	−0.731044	+	1.60076i	0.0667040	+	0.997773i	$0.478752\pi$
$383$	−14.3068	+	31.3276i	−0.731044	+	1.60076i	−0.797748	+	0.602991i	$0.793976\pi$
$384$		0			0
$385$	5.01103	+	17.0660i	0.255386	+	0.869763i
$386$		0			0
$387$	−20.9971	−	6.16529i	−1.06734	−	0.313399i
$388$		0			0
$389$	10.8712	+	1.56304i	0.551191	+	0.0792493i	0.412283	−	0.911056i	$-0.364732\pi$
$389$	10.8712	+	1.56304i	0.551191	+	0.0792493i	0.138908	+	0.990305i	$0.455641\pi$
$390$		0			0
$391$	8.79584	−	7.94146i	0.444825	−	0.401617i
$392$		0			0
$393$	−1.35594	+	9.43075i	−0.0683980	+	0.475719i
$394$		0			0
$395$	−0.616444	+	2.09942i	−0.0310167	+	0.105633i
$396$		0			0
$397$	28.5572	−	8.38516i	1.43325	−	0.420839i	0.529282	−	0.848446i	$-0.322461\pi$
$397$	28.5572	−	8.38516i	1.43325	−	0.420839i	0.903965	+	0.427607i	$0.140643\pi$
$398$		0			0
$399$	7.54437	+	3.44540i	0.377691	+	0.172486i
$400$		0			0
$401$	4.31386	+	6.71250i	0.215424	+	0.335206i	0.932101	−	0.362199i	$-0.117974\pi$
$401$	4.31386	+	6.71250i	0.215424	+	0.335206i	−0.716677	+	0.697406i	$0.754338\pi$
$402$		0			0
$403$	38.3120	−	5.50844i	1.90846	−	0.274395i
$404$		0			0
$405$	8.77326	+	7.60207i	0.435947	+	0.377750i
$406$		0			0
$407$	8.02698	−	12.4902i	0.397882	−	0.619117i
$408$		0			0
$409$	14.0767	+	16.2454i	0.696048	+	0.803282i	0.988213	−	0.153086i	$-0.0489210\pi$
$409$	14.0767	+	16.2454i	0.696048	+	0.803282i	−0.292165	+	0.956368i	$0.594376\pi$
$410$		0			0
$411$	17.2539	+	37.7807i	0.851070	+	1.86358i
$412$		0			0
$413$		−	31.1614i		−	1.53335i
$414$		0			0
$415$		−	35.6224i		−	1.74864i
$416$		0			0
$417$	7.98002	+	17.4738i	0.390783	+	0.855696i
$418$		0			0
$419$	−2.73602	−	3.15754i	−0.133663	−	0.154256i	0.684972	−	0.728569i	$-0.259814\pi$
$419$	−2.73602	−	3.15754i	−0.133663	−	0.154256i	−0.818635	+	0.574314i	$0.805269\pi$
$420$		0			0
$421$	−1.77477	+	2.76160i	−0.0864971	+	0.134592i	−0.881806	−	0.471612i	$-0.843672\pi$
$421$	−1.77477	+	2.76160i	−0.0864971	+	0.134592i	0.795309	+	0.606204i	$0.207309\pi$
$422$		0			0
$423$	−31.7822	−	27.5395i	−1.54530	−	1.33901i
$424$		0			0
$425$	19.3363	−	2.78015i	0.937950	−	0.134857i
$426$		0			0
$427$	10.1963	+	15.8657i	0.493433	+	0.767797i
$428$		0			0
$429$	−22.7470	−	10.3882i	−1.09823	−	0.501547i
$430$		0			0
$431$	30.8996	−	9.07293i	1.48838	−	0.437028i	0.566356	−	0.824161i	$-0.308353\pi$
$431$	30.8996	−	9.07293i	1.48838	−	0.437028i	0.922024	+	0.387133i	$0.126534\pi$
$432$		0			0
$433$	1.70932	−	5.82141i	0.0821447	−	0.279759i	−0.908170	−	0.418602i	$-0.862520\pi$
$433$	1.70932	−	5.82141i	0.0821447	−	0.279759i	0.990314	+	0.138843i	$0.0443383\pi$
$434$		0			0
$435$	−8.99937	+	62.5920i	−0.431487	+	3.00106i
$436$		0			0
$437$	−0.706133	−	4.28839i	−0.0337789	−	0.205142i
$438$		0			0
$439$	19.2142	+	2.76258i	0.917043	+	0.131851i	0.584646	−	0.811288i	$-0.301233\pi$
$439$	19.2142	+	2.76258i	0.917043	+	0.131851i	0.332397	+	0.943139i	$0.392142\pi$
$440$		0			0
$441$	15.7039	+	4.61108i	0.747805	+	0.219575i
$442$		0			0
$443$	−4.82913	−	16.4465i	−0.229439	−	0.781398i	−0.991065	−	0.133381i	$-0.957417\pi$
$443$	−4.82913	−	16.4465i	−0.229439	−	0.781398i	0.761626	−	0.648017i	$-0.224401\pi$
$444$		0			0
$445$	1.57273	−	3.44381i	0.0745548	−	0.163252i
$446$		0			0
$447$	13.4781	−	8.66187i	0.637494	−	0.409692i
$448$		0			0
$449$	−2.75195	−	19.1402i	−0.129873	−	0.903284i	−0.945712	−	0.325006i	$-0.894634\pi$
$449$	−2.75195	−	19.1402i	−0.129873	−	0.903284i	0.815839	−	0.578278i	$-0.196275\pi$
$450$		0			0
$451$	6.34163	−	7.31863i	0.298616	−	0.344621i
$452$		0			0
$453$	12.9856	+	8.34535i	0.610117	+	0.392099i
$454$		0			0
$455$	47.9869	−	41.5809i	2.24966	−	1.94934i
$456$		0			0
$457$	−20.0966	+	9.17780i	−0.940078	+	0.429319i	−0.825695	−	0.564117i	$-0.809217\pi$
$457$	−20.0966	+	9.17780i	−0.940078	+	0.429319i	−0.114384	+	0.993437i	$0.536489\pi$
$458$		0			0
$459$	−16.4175			−0.766304
$460$		0			0
$461$	11.3163			0.527052			0.263526	−	0.964652i	$-0.415114\pi$
$461$	11.3163			0.527052			0.263526	+	0.964652i	$0.415114\pi$
$462$		0			0
$463$	38.7469	−	17.6951i	1.80072	−	0.822363i	0.841205	−	0.540716i	$-0.181847\pi$
$463$	38.7469	−	17.6951i	1.80072	−	0.822363i	0.959518	−	0.281646i	$-0.0908805\pi$
$464$		0			0
$465$	54.4144	−	47.1504i	2.52341	−	2.18655i
$466$		0			0
$467$	−11.0899	−	7.12706i	−0.513180	−	0.329801i	0.258289	−	0.966068i	$-0.416841\pi$
$467$	−11.0899	−	7.12706i	−0.513180	−	0.329801i	−0.771469	+	0.636267i	$0.780478\pi$
$468$		0			0
$469$	−17.8189	+	20.5641i	−0.822799	+	0.949561i
$470$		0			0
$471$	−4.49165	−	31.2401i	−0.206964	−	1.43947i
$472$		0			0
$473$	5.40982	−	3.47668i	0.248744	−	0.159858i
$474$		0			0
$475$	2.97624	−	6.51705i	0.136559	−	0.299023i
$476$		0			0
$477$	−7.28677	−	24.8164i	−0.333638	−	1.13627i
$478$		0			0
$479$	17.8799	+	5.25002i	0.816955	+	0.239880i	0.663404	−	0.748261i	$-0.269111\pi$
$479$	17.8799	+	5.25002i	0.816955	+	0.239880i	0.153551	+	0.988141i	$0.450929\pi$
$480$		0			0
$481$	−52.4632	−	7.54307i	−2.39212	−	0.343935i
$482$		0			0
$483$	−13.2221	−	41.8527i	−0.601625	−	1.90437i
$484$		0			0
$485$	7.54283	−	52.4615i	0.342502	−	2.38216i
$486$		0			0
$487$	−10.9379	+	37.2511i	−0.495644	+	1.68801i	0.208560	+	0.978009i	$0.433122\pi$
$487$	−10.9379	+	37.2511i	−0.495644	+	1.68801i	−0.704204	+	0.709998i	$0.748696\pi$
$488$		0			0
$489$	14.6605	−	4.30470i	0.662969	−	0.194665i
$490$		0			0
$491$	−24.4109	−	11.1481i	−1.10165	−	0.503106i	−0.220233	−	0.975447i	$-0.570682\pi$
$491$	−24.4109	−	11.1481i	−1.10165	−	0.503106i	−0.881416	+	0.472341i	$0.843409\pi$
$492$		0			0
$493$	−8.15959	−	12.6966i	−0.367490	−	0.571825i
$494$		0			0
$495$	−29.4125	+	4.22888i	−1.32199	+	0.190074i
$496$		0			0
$497$	−16.5154	−	14.3107i	−0.740817	−	0.641921i
$498$		0			0
$499$	9.15908	−	14.2518i	0.410017	−	0.637998i	−0.573418	−	0.819263i	$-0.694383\pi$
$499$	9.15908	−	14.2518i	0.410017	−	0.637998i	0.983434	+	0.181265i	$0.0580191\pi$
$500$		0			0
$501$	41.3820	+	47.7573i	1.84881	+	2.13364i
$502$		0			0
$503$	−1.71151	−	3.74768i	−0.0763123	−	0.167101i	0.867631	−	0.497209i	$-0.165642\pi$
$503$	−1.71151	−	3.74768i	−0.0763123	−	0.167101i	−0.943943	+	0.330109i	$0.892915\pi$
$504$		0			0
$505$			27.1753i			1.20928i
$506$		0			0
$507$			51.8067i			2.30081i
$508$		0			0
$509$	10.7453	+	23.5289i	0.476276	+	1.04290i	0.983471	+	0.181067i	$0.0579551\pi$
$509$	10.7453	+	23.5289i	0.476276	+	1.04290i	−0.507195	+	0.861831i	$0.669318\pi$
$510$		0			0
$511$	−23.1987	−	26.7727i	−1.02625	−	1.18436i
$512$		0			0
$513$	−3.25525	+	5.06527i	−0.143723	+	0.223637i
$514$		0			0
$515$	10.5247	+	9.11967i	0.463772	+	0.401861i
$516$		0			0
$517$	12.2321	−	1.75872i	0.537969	−	0.0773483i
$518$		0			0
$519$	4.89348	+	7.61440i	0.214800	+	0.334235i
$520$		0			0
$521$	−20.1672	−	9.21005i	−0.883541	−	0.403500i	−0.0786360	−	0.996903i	$-0.525056\pi$
$521$	−20.1672	−	9.21005i	−0.883541	−	0.403500i	−0.804905	+	0.593404i	$0.797784\pi$
$522$		0			0
$523$	20.1374	−	5.91288i	0.880548	−	0.258552i	0.189952	−	0.981793i	$-0.439167\pi$
$523$	20.1374	−	5.91288i	0.880548	−	0.258552i	0.690596	+	0.723241i	$0.257348\pi$
$524$		0			0
$525$	20.3845	−	69.4233i	0.889653	−	3.02988i
$526$		0			0
$527$	−2.44559	+	17.0095i	−0.106532	+	0.740944i
$528$		0			0
$529$	−14.3404	+	17.9820i	−0.623494	+	0.781828i
$530$		0			0
$531$	51.5299	+	7.40888i	2.23621	+	0.321518i
$532$		0			0
$533$	−33.1703	−	9.73966i	−1.43676	−	0.421872i
$534$		0			0
$535$	6.63710	+	22.6039i	0.286947	+	0.977251i
$536$		0			0
$537$	19.9686	−	43.7251i	0.861708	−	1.88688i
$538$		0			0
$539$	−4.04606	+	2.60024i	−0.174276	+	0.112000i
$540$		0			0
$541$	1.46031	+	10.1567i	0.0627836	+	0.436669i	0.996833	+	0.0795252i	$0.0253404\pi$
$541$	1.46031	+	10.1567i	0.0627836	+	0.436669i	−0.934049	+	0.357144i	$0.883751\pi$
$542$		0			0
$543$	−3.84024	+	4.43188i	−0.164801	+	0.190190i
$544$		0			0
$545$	58.2306	+	37.4225i	2.49432	+	1.60300i
$546$		0			0
$547$	19.8392	−	17.1908i	0.848264	−	0.735025i	−0.117880	−	0.993028i	$-0.537610\pi$
$547$	19.8392	−	17.1908i	0.848264	−	0.735025i	0.966144	+	0.258003i	$0.0830645\pi$
$548$		0			0
$549$	−28.6605	+	13.0888i	−1.22320	+	0.558618i
$550$		0			0
$551$	−5.53513			−0.235805
$552$		0			0
$553$	−1.93420			−0.0822504
$554$		0			0
$555$	−89.6854	+	40.9580i	−3.80693	+	1.73857i
$556$		0			0
$557$	32.8971	−	28.5055i	1.39389	−	1.20782i	0.443691	−	0.896180i	$-0.353669\pi$
$557$	32.8971	−	28.5055i	1.39389	−	1.20782i	0.950202	−	0.311635i	$-0.100877\pi$
$558$		0			0
$559$	−19.3125	−	12.4114i	−0.816831	−	0.524945i
$560$		0			0
$561$	7.27047	−	8.39057i	0.306960	−	0.354250i
$562$		0			0
$563$	−4.41596	−	30.7137i	−0.186111	−	1.29443i	−0.841961	−	0.539538i	$-0.818599\pi$
$563$	−4.41596	−	30.7137i	−0.186111	−	1.29443i	0.655851	−	0.754891i	$-0.272310\pi$
$564$		0			0
$565$	−21.9570	+	14.1109i	−0.923736	+	0.593649i
$566$		0			0
$567$	−4.26294	+	9.33453i	−0.179027	+	0.392013i
$568$		0			0
$569$	−11.7175	−	39.9060i	−0.491222	−	1.67295i	−0.715651	−	0.698458i	$-0.753870\pi$
$569$	−11.7175	−	39.9060i	−0.491222	−	1.67295i	0.224430	−	0.974490i	$-0.427948\pi$
$570$		0			0
$571$	28.7035	+	8.42810i	1.20120	+	0.352705i	0.820313	−	0.571915i	$-0.193799\pi$
$571$	28.7035	+	8.42810i	1.20120	+	0.352705i	0.380890	+	0.924620i	$0.375618\pi$
$572$		0			0
$573$	2.16278	+	0.310961i	0.0903516	+	0.0129906i
$574$		0			0
$575$	−36.1536	+	11.4216i	−1.50771	+	0.476314i
$576$		0			0
$577$	−2.98419	+	20.7555i	−0.124233	+	0.864062i	0.828443	+	0.560074i	$0.189227\pi$
$577$	−2.98419	+	20.7555i	−0.124233	+	0.864062i	−0.952676	+	0.303988i	$0.901682\pi$
$578$		0			0
$579$	10.0157	−	34.1104i	0.416238	−	1.41758i
$580$		0			0
$581$	30.2141	−	8.87165i	1.25349	−	0.368058i
$582$		0			0
$583$	6.91358	+	3.15732i	0.286331	+	0.130763i
$584$		0			0
$585$	57.3507	+	89.2395i	2.37116	+	3.68960i
$586$		0			0
$587$	−36.9064	+	5.30634i	−1.52329	+	0.219016i	−0.852538	−	0.522665i	$-0.824938\pi$
$587$	−36.9064	+	5.30634i	−1.52329	+	0.219016i	−0.670753	+	0.741681i	$0.734029\pi$
$588$		0			0
$589$	4.76299	+	4.12716i	0.196256	+	0.170057i
$590$		0			0
$591$	5.26604	−	8.19412i	0.216616	−	0.337061i
$592$		0			0
$593$	−2.75305	−	3.17719i	−0.113054	−	0.130472i	0.696402	−	0.717652i	$-0.254783\pi$
$593$	−2.75305	−	3.17719i	−0.113054	−	0.130472i	−0.809456	+	0.587181i	$0.800238\pi$
$594$		0			0
$595$	11.7107	+	25.6428i	0.480091	+	1.05125i
$596$		0			0
$597$		−	9.38442i		−	0.384079i
$598$		0			0
$599$		−	17.9135i		−	0.731927i	−0.930629	−	0.365963i	$-0.880740\pi$
$599$		−	17.9135i		−	0.731927i	0.930629	−	0.365963i	$-0.119260\pi$
$600$		0			0
$601$	−8.71474	−	19.0826i	−0.355482	−	0.778396i	−0.999906	−	0.0137281i	$-0.995630\pi$
$601$	−8.71474	−	19.0826i	−0.355482	−	0.778396i	0.644424	−	0.764668i	$-0.277097\pi$
$602$		0			0
$603$	−29.7691	−	34.3554i	−1.21229	−	1.39906i
$604$		0			0
$605$	−16.6437	+	25.8981i	−0.676662	+	1.05291i
$606$		0			0
$607$	−13.2993	−	11.5239i	−0.539803	−	0.467742i	0.341774	−	0.939782i	$-0.388972\pi$
$607$	−13.2993	−	11.5239i	−0.539803	−	0.467742i	−0.881577	+	0.472040i	$0.843518\pi$
$608$		0			0
$609$	−55.3303	+	7.95529i	−2.24210	+	0.322365i
$610$		0			0
$611$	−23.8512	−	37.1131i	−0.964915	−	1.50144i
$612$		0			0
$613$	−0.838356	−	0.382865i	−0.0338609	−	0.0154638i	0.398413	−	0.917206i	$-0.369561\pi$
$613$	−0.838356	−	0.382865i	−0.0338609	−	0.0154638i	−0.432274	+	0.901743i	$0.642288\pi$
$614$		0			0
$615$	−61.7031	+	18.1177i	−2.48811	+	0.730574i
$616$		0			0
$617$	4.92141	−	16.7608i	0.198129	−	0.674764i	−0.799156	−	0.601123i	$-0.794720\pi$
$617$	4.92141	−	16.7608i	0.198129	−	0.674764i	0.997285	−	0.0736407i	$-0.0234618\pi$
$618$		0			0
$619$	−0.894602	+	6.22209i	−0.0359571	+	0.250087i	−0.999870	−	0.0161311i	$-0.994865\pi$
$619$	−0.894602	+	6.22209i	−0.0359571	+	0.250087i	0.963913	+	0.266218i	$0.0857742\pi$
$620$		0			0
$621$	31.4406	−	5.17705i	1.26167	−	0.207748i
$622$		0			0
$623$	3.31264	+	0.476285i	0.132718	+	0.0190820i
$624$		0			0
$625$	1.94521	+	0.571165i	0.0778084	+	0.0228466i
$626$		0			0
$627$	−1.14715	−	3.90682i	−0.0458126	−	0.156024i
$628$		0			0
$629$	9.77543	−	21.4052i	0.389772	−	0.853482i
$630$		0			0
$631$	−3.55820	+	2.28672i	−0.141650	+	0.0910328i	−0.609546	−	0.792750i	$-0.708648\pi$
$631$	−3.55820	+	2.28672i	−0.141650	+	0.0910328i	0.467897	+	0.883783i	$0.345012\pi$
$632$		0			0
$633$	1.17303	+	8.15863i	0.0466239	+	0.324277i
$634$		0			0
$635$	40.0395	−	46.2080i	1.58892	−	1.83371i
$636$		0			0
$637$	14.4440	+	9.28259i	0.572292	+	0.367789i
$638$		0			0
$639$	27.5914	−	23.9081i	1.09150	−	0.945791i
$640$		0			0
$641$	5.25735	−	2.40095i	0.207653	−	0.0948319i	−0.308874	−	0.951103i	$-0.599952\pi$
$641$	5.25735	−	2.40095i	0.207653	−	0.0948319i	0.516527	+	0.856271i	$0.327225\pi$
$642$		0			0
$643$	−14.3533			−0.566041			−0.283020	−	0.959114i	$-0.591336\pi$
$643$	−14.3533			−0.566041			−0.283020	+	0.959114i	$0.591336\pi$
$644$		0			0
$645$	−42.7040			−1.68147
$646$		0			0
$647$	−30.6323	+	13.9893i	−1.20428	+	0.549976i	−0.913510	−	0.406817i	$-0.866639\pi$
$647$	−30.6323	+	13.9893i	−1.20428	+	0.549976i	−0.290770	+	0.956793i	$0.593911\pi$
$648$		0			0
$649$	−11.5616	+	10.0182i	−0.453834	+	0.393249i
$650$		0			0
$651$	53.5435	+	34.4103i	2.09854	+	1.34865i
$652$		0			0
$653$	−1.12461	+	1.29787i	−0.0440094	+	0.0507895i	−0.777327	−	0.629096i	$-0.783425\pi$
$653$	−1.12461	+	1.29787i	−0.0440094	+	0.0507895i	0.733318	+	0.679886i	$0.237971\pi$
$654$		0			0
$655$	1.69025	+	11.7559i	0.0660435	+	0.459343i
$656$		0			0
$657$	49.7882	−	31.9970i	1.94242	−	1.24832i
$658$		0			0
$659$	1.22489	−	2.68213i	0.0477148	−	0.104481i	−0.884273	−	0.466970i	$-0.845346\pi$
$659$	1.22489	−	2.68213i	0.0477148	−	0.104481i	0.931988	+	0.362489i	$0.118073\pi$
$660$		0			0
$661$	13.5901	+	46.2835i	0.528593	+	1.80022i	0.596603	+	0.802537i	$0.296517\pi$
$661$	13.5901	+	46.2835i	0.528593	+	1.80022i	−0.0680102	+	0.997685i	$0.521665\pi$
$662$		0			0
$663$	−38.0286	−	11.1662i	−1.47691	−	0.433660i
$664$		0			0
$665$	10.2335	+	1.47136i	0.396839	+	0.0570569i
$666$		0			0
$667$	19.6298	+	21.7417i	0.760071	+	0.841843i
$668$		0			0
$669$	−4.01788	+	27.9450i	−0.155340	+	1.08041i
$670$		0			0
$671$	2.60853	−	8.88382i	0.100701	−	0.342956i
$672$		0			0
$673$	24.5121	−	7.19740i	0.944872	−	0.277440i	0.227222	−	0.973843i	$-0.427036\pi$
$673$	24.5121	−	7.19740i	0.944872	−	0.277440i	0.717650	+	0.696404i	$0.245218\pi$
$674$		0			0
$675$	47.7801	+	21.8205i	1.83906	+	0.839870i
$676$		0			0
$677$	−24.4475	−	38.0410i	−0.939593	−	1.46203i	−0.886115	−	0.463466i	$-0.846606\pi$
$677$	−24.4475	−	38.0410i	−0.939593	−	1.46203i	−0.0534777	−	0.998569i	$-0.517031\pi$
$678$		0			0
$679$	46.3751	−	6.66773i	1.77971	−	0.255884i
$680$		0			0
$681$	3.05529	+	2.64742i	0.117079	+	0.101449i
$682$		0			0
$683$	−13.4305	+	20.8983i	−0.513905	+	0.799652i	−0.997119	−	0.0758501i	$-0.975833\pi$
$683$	−13.4305	+	20.8983i	−0.513905	+	0.799652i	0.483214	+	0.875502i	$0.339469\pi$
$684$		0			0
$685$	33.9050	+	39.1285i	1.29544	+	1.49502i
$686$		0			0
$687$	−2.32028	−	5.08070i	−0.0885241	−	0.193841i
$688$		0			0
$689$		−	27.1326i		−	1.03367i
$690$		0			0
$691$		−	1.38246i		−	0.0525912i	−0.999654	−	0.0262956i	$-0.991629\pi$
$691$		−	1.38246i		−	0.0525912i	0.999654	−	0.0262956i	$-0.00837112\pi$
$692$		0			0
$693$	−10.9119	−	23.8938i	−0.414509	−	0.907649i
$694$		0			0
$695$	15.6813	+	18.0972i	0.594825	+	0.686465i
$696$		0			0
$697$	8.29796	−	12.9119i	0.314308	−	0.489072i
$698$		0			0
$699$	12.1617	+	10.5382i	0.459997	+	0.398590i
$700$		0			0
$701$	−25.4916	+	3.66514i	−0.962806	+	0.138431i	−0.605752	−	0.795653i	$-0.707128\pi$
$701$	−25.4916	+	3.66514i	−0.962806	+	0.138431i	−0.357054	+	0.934084i	$0.616219\pi$
$702$		0			0
$703$	−4.66585	−	7.26021i	−0.175976	−	0.273824i
$704$		0			0
$705$	−74.6491	−	34.0911i	−2.81145	−	1.28394i
$706$		0			0
$707$	−23.0494	+	6.76792i	−0.866862	+	0.254534i
$708$		0			0
$709$	−2.01926	+	6.87698i	−0.0758350	+	0.258270i	−0.988681	−	0.150034i	$-0.952062\pi$
$709$	−2.01926	+	6.87698i	−0.0758350	+	0.258270i	0.912846	+	0.408305i	$0.133880\pi$
$710$		0			0
$711$	0.459871	−	3.19847i	0.0172465	−	0.119952i
$712$		0			0
$713$	−0.680250	−	33.3454i	−0.0254756	−	1.24879i
$714$		0			0
$715$	−30.8550	−	4.43628i	−1.15391	−	0.165908i
$716$		0			0
$717$	−21.8158	−	6.40569i	−0.814725	−	0.239225i
$718$		0			0
$719$	−12.0214	−	40.9412i	−0.448323	−	1.52685i	−0.805376	−	0.592765i	$-0.798036\pi$
$719$	−12.0214	−	40.9412i	−0.448323	−	1.52685i	0.357053	−	0.934084i	$-0.383782\pi$
$720$		0			0
$721$	−5.11395	+	11.1980i	−0.190453	+	0.417035i
$722$		0			0
$723$	−7.02556	+	4.51505i	−0.261283	+	0.167917i
$724$		0			0
$725$	6.87202	+	47.7959i	0.255220	+	1.77510i
$726$		0			0
$727$	−15.8678	+	18.3124i	−0.588504	+	0.679170i	−0.969411	−	0.245444i	$-0.921066\pi$
$727$	−15.8678	+	18.3124i	−0.588504	+	0.679170i	0.380907	+	0.924613i	$0.375612\pi$
$728$		0			0
$729$	33.9018	+	21.7874i	1.25562	+	0.806940i
$730$		0			0
$731$	7.70273	−	6.67445i	0.284896	−	0.246863i
$732$		0			0
$733$	−48.7756	+	22.2751i	−1.80157	+	0.822749i	−0.842984	+	0.537939i	$0.819203\pi$
$733$	−48.7756	+	22.2751i	−1.80157	+	0.822749i	−0.958584	+	0.284810i	$0.908070\pi$
$734$		0			0
$735$	31.9388			1.17808
$736$		0			0
$737$	13.3584			0.492065
$738$		0			0
$739$	45.7331	−	20.8856i	1.68232	−	0.768289i	0.683037	−	0.730384i	$-0.260659\pi$
$739$	45.7331	−	20.8856i	1.68232	−	0.768289i	0.999281	−	0.0379049i	$-0.0120684\pi$
$740$		0			0
$741$	−10.9854	+	9.51888i	−0.403558	+	0.349685i
$742$		0			0
$743$	15.3836	+	9.88645i	0.564370	+	0.362699i	0.791503	−	0.611165i	$-0.209299\pi$
$743$	15.3836	+	9.88645i	0.564370	+	0.362699i	−0.227133	+	0.973864i	$0.572935\pi$
$744$		0			0
$745$	13.0786	−	15.0936i	0.479164	−	0.552985i
$746$		0			0
$747$	7.48691	+	52.0726i	0.273932	+	1.90524i
$748$		0			0
$749$	−17.5191	+	11.2588i	−0.640134	+	0.411389i
$750$		0			0
$751$	−2.97374	+	6.51159i	−0.108513	+	0.237611i	−0.956097	−	0.293051i	$-0.905329\pi$
$751$	−2.97374	+	6.51159i	−0.108513	+	0.237611i	0.847583	+	0.530662i	$0.178057\pi$
$752$		0			0
$753$	15.5652	+	53.0101i	0.567227	+	1.93180i
$754$		0			0
$755$	18.4624	+	5.42105i	0.671916	+	0.197292i
$756$		0			0
$757$	−0.213655	−	0.0307190i	−0.00776543	−	0.00111650i	0.138431	−	0.990372i	$-0.455794\pi$
$757$	−0.213655	−	0.0307190i	−0.00776543	−	0.00111650i	−0.146196	+	0.989256i	$0.546703\pi$
$758$		0			0
$759$	−11.2776	+	18.3611i	−0.409350	+	0.666467i
$760$		0			0
$761$	0.657950	−	4.57614i	0.0238507	−	0.165885i	−0.974415	−	0.224757i	$-0.927841\pi$
$761$	0.657950	−	4.57614i	0.0238507	−	0.165885i	0.998266	+	0.0588718i	$0.0187503\pi$
$762$		0			0
$763$	−17.2387	+	58.7097i	−0.624083	+	2.12543i
$764$		0			0
$765$	−45.1884	+	13.2685i	−1.63379	+	0.479725i
$766$		0			0
$767$	49.6778	+	22.6871i	1.79376	+	0.819183i
$768$		0			0
$769$	−6.93110	−	10.7850i	−0.249942	−	0.388917i	0.693499	−	0.720457i	$-0.256068\pi$
$769$	−6.93110	−	10.7850i	−0.249942	−	0.388917i	−0.943441	+	0.331540i	$0.892432\pi$
$770$		0			0
$771$	21.9680	−	3.15852i	0.791158	−	0.113751i
$772$		0			0
$773$	17.3167	+	15.0050i	0.622838	+	0.539693i	0.908098	−	0.418758i	$-0.137534\pi$
$773$	17.3167	+	15.0050i	0.622838	+	0.539693i	−0.285260	+	0.958450i	$0.592080\pi$
$774$		0			0
$775$	29.7247	−	46.2525i	1.06774	−	1.66144i
$776$		0			0
$777$	−57.0754	−	65.8685i	−2.04757	−	2.36302i
$778$		0			0
$779$	−2.33837	−	5.12031i	−0.0837808	−	0.183454i
$780$		0			0
$781$			10.7284i			0.383893i
$782$		0			0
$783$		−	40.5811i		−	1.45025i
$784$		0			0
$785$	−16.3436	−	35.7876i	−0.583329	−	1.27731i
$786$		0			0
$787$	0.801379	+	0.924841i	0.0285661	+	0.0329670i	0.769853	−	0.638221i	$-0.220330\pi$
$787$	0.801379	+	0.924841i	0.0285661	+	0.0329670i	−0.741287	+	0.671188i	$0.765784\pi$
$788$		0			0
$789$	21.1651	−	32.9335i	0.753496	−	1.17246i
$790$		0			0
$791$	−17.4368	−	15.1091i	−0.619982	−	0.537217i
$792$		0			0
$793$	−32.7167	+	4.70396i	−1.16181	+	0.167042i
$794$		0			0
$795$	−27.2872	−	42.4597i	−0.967777	−	1.50589i
$796$		0			0
$797$	47.5908	+	21.7340i	1.68575	+	0.769857i	0.999080	+	0.0428900i	$0.0136565\pi$
$797$	47.5908	+	21.7340i	1.68575	+	0.769857i	0.686672	+	0.726967i	$0.259071\pi$
$798$		0			0
$799$	18.7931	−	5.51815i	0.664851	−	0.195218i
$800$		0			0
$801$	−1.57521	+	5.36469i	−0.0556574	+	0.189552i
$802$		0			0
$803$	−2.47508	+	17.2146i	−0.0873437	+	0.607489i
$804$		0			0
$805$	−30.5128	−	45.4148i	−1.07544	−	1.60066i
$806$		0			0
$807$	52.6766	+	7.57375i	1.85430	+	0.266609i
$808$		0			0
$809$	−34.7807	−	10.2125i	−1.22283	−	0.359054i	−0.394288	−	0.918987i	$-0.629009\pi$
$809$	−34.7807	−	10.2125i	−1.22283	−	0.359054i	−0.828538	+	0.559933i	$0.810827\pi$
$810$		0			0
$811$	14.1830	+	48.3027i	0.498031	+	1.69614i	0.697798	+	0.716294i	$0.254163\pi$
$811$	14.1830	+	48.3027i	0.498031	+	1.69614i	−0.199768	+	0.979843i	$0.564019\pi$
$812$		0			0
$813$	0.226114	−	0.495120i	0.00793015	−	0.0173646i
$814$		0			0
$815$	16.0230	−	10.2974i	0.561261	−	0.360701i
$816$		0			0
$817$	−0.531967	−	3.69991i	−0.0186112	−	0.129444i
$818$		0			0
$819$	−61.4077	+	70.8683i	−2.14576	+	2.47634i
$820$		0			0
$821$	5.39453	+	3.46685i	0.188270	+	0.120994i	0.631381	−	0.775473i	$-0.282489\pi$
$821$	5.39453	+	3.46685i	0.188270	+	0.120994i	−0.443110	+	0.896467i	$0.646125\pi$
$822$		0			0
$823$	−4.84389	+	4.19726i	−0.168847	+	0.146307i	−0.735186	−	0.677866i	$-0.762905\pi$
$823$	−4.84389	+	4.19726i	−0.168847	+	0.146307i	0.566338	+	0.824173i	$0.308360\pi$
$824$		0			0
$825$	−32.3113	+	14.7561i	−1.12493	+	0.513740i
$826$		0			0
$827$	−4.03565			−0.140333			−0.0701667	−	0.997535i	$-0.522353\pi$
$827$	−4.03565			−0.140333			−0.0701667	+	0.997535i	$0.522353\pi$
$828$		0			0
$829$	0.478153			0.0166070			0.00830348	−	0.999966i	$-0.497357\pi$
$829$	0.478153			0.0166070			0.00830348	+	0.999966i	$0.497357\pi$
$830$		0			0
$831$	−7.63021	+	3.48460i	−0.264689	+	0.120879i
$832$		0			0
$833$	−5.76094	+	4.99189i	−0.199605	+	0.172959i
$834$		0			0
$835$	66.2674	+	42.5875i	2.29328	+	1.47380i
$836$		0			0
$837$	−30.2585	+	34.9201i	−1.04589	+	1.20702i
$838$		0			0
$839$	1.59148	+	11.0690i	0.0549440	+	0.382144i	0.998676	+	0.0514339i	$0.0163792\pi$
$839$	1.59148	+	11.0690i	0.0549440	+	0.382144i	−0.943732	+	0.330710i	$0.892712\pi$
$840$		0			0
$841$	6.98729	−	4.49046i	0.240941	−	0.154843i
$842$		0			0
$843$	23.5381	−	51.5413i	0.810696	−	1.77518i
$844$		0			0
$845$	18.1942	+	61.9639i	0.625901	+	2.13162i
$846$		0			0
$847$	−26.1112	−	7.66693i	−0.897190	−	0.263439i
$848$		0			0
$849$	−53.5295	−	7.69638i	−1.83713	−	0.264139i
$850$		0			0
$851$	−11.9707	+	44.0749i	−0.410351	+	1.51087i
$852$		0			0
$853$	2.07554	−	14.4357i	0.0710651	−	0.494269i	−0.922941	−	0.384942i	$-0.874221\pi$
$853$	2.07554	−	14.4357i	0.0710651	−	0.494269i	0.994006	−	0.109327i	$-0.0348695\pi$
$854$		0			0
$855$	−4.86621	+	16.5728i	−0.166421	+	0.566778i
$856$		0			0
$857$	−36.0319	+	10.5799i	−1.23083	+	0.361404i	−0.831562	−	0.555432i	$-0.812553\pi$
$857$	−36.0319	+	10.5799i	−1.23083	+	0.361404i	−0.399265	+	0.916835i	$0.630735\pi$
$858$		0			0
$859$	−46.4409	−	21.2088i	−1.58454	−	0.723636i	−0.588170	−	0.808737i	$-0.700151\pi$
$859$	−46.4409	−	21.2088i	−1.58454	−	0.723636i	−0.996372	+	0.0851010i	$0.972879\pi$
$860$		0			0
$861$	−30.7339	−	47.8229i	−1.04741	−	1.62980i
$862$		0			0
$863$	−6.11821	+	0.879666i	−0.208266	+	0.0299442i	−0.245658	−	0.969356i	$-0.579004\pi$
$863$	−6.11821	+	0.879666i	−0.208266	+	0.0299442i	0.0373919	+	0.999301i	$0.488095\pi$
$864$		0			0
$865$	8.52703	+	7.38871i	0.289928	+	0.251224i
$866$		0			0
$867$	−16.9740	+	26.4121i	−0.576469	+	0.897003i
$868$		0			0
$869$	0.621833	+	0.717634i	0.0210942	+	0.0243441i
$870$		0			0
$871$	−19.8104	−	43.3787i	−0.671250	−	1.46983i
$872$		0			0
$873$			78.2733i			2.64915i
$874$		0			0
$875$		−	33.1508i		−	1.12070i
$876$		0			0
$877$	21.3820	+	46.8200i	0.722019	+	1.58100i	0.811054	+	0.584972i	$0.198894\pi$
$877$	21.3820	+	46.8200i	0.722019	+	1.58100i	−0.0890349	+	0.996029i	$0.528378\pi$
$878$		0			0
$879$	−45.5825	−	52.6050i	−1.53746	−	1.77432i
$880$		0			0
$881$	−15.7504	+	24.5082i	−0.530646	+	0.825701i	−0.998304	−	0.0582079i	$-0.981461\pi$
$881$	−15.7504	+	24.5082i	−0.530646	+	0.825701i	0.467658	+	0.883909i	$0.345098\pi$
$882$		0			0
$883$	21.9487	+	19.0187i	0.738634	+	0.640030i	0.940660	−	0.339350i	$-0.110207\pi$
$883$	21.9487	+	19.0187i	0.738634	+	0.640030i	−0.202026	+	0.979380i	$0.564753\pi$
$884$		0			0
$885$	100.557	−	14.4579i	3.38018	−	0.485996i
$886$		0			0
$887$	−1.26358	−	1.96617i	−0.0424269	−	0.0660175i	0.819392	−	0.573233i	$-0.194311\pi$
$887$	−1.26358	−	1.96617i	−0.0424269	−	0.0660175i	−0.861819	+	0.507216i	$0.830675\pi$
$888$		0			0
$889$	49.1642	+	22.4526i	1.64892	+	0.753034i
$890$		0			0
$891$	4.83385	−	1.41935i	0.161940	−	0.0475499i
$892$		0			0
$893$	2.02377	−	6.89233i	0.0677229	−	0.230643i
$894$		0			0
$895$	8.52759	−	59.3107i	0.285046	−	1.98254i
$896$		0			0
$897$	76.3484	+	9.39217i	2.54920	+	0.313596i
$898$		0			0
$899$	−42.0443	−	6.04506i	−1.40226	−	0.201614i
$900$		0			0
$901$	11.5582	+	3.39379i	0.385059	+	0.113063i
$902$		0			0
$903$	−10.6353	−	36.2205i	−0.353921	−	1.20534i
$904$		0			0
$905$	−3.03671	+	6.64946i	−0.100944	+	0.221036i
$906$		0			0
$907$	40.2996	−	25.8990i	1.33813	−	0.859962i	0.341331	−	0.939943i	$-0.389122\pi$
$907$	40.2996	−	25.8990i	1.33813	−	0.859962i	0.996796	+	0.0799806i	$0.0254858\pi$
$908$		0			0
$909$	−5.71154	−	39.7247i	−0.189440	−	1.31758i
$910$		0			0
$911$	−24.1453	+	27.8651i	−0.799968	+	0.923213i	−0.998380	−	0.0569062i	$-0.981876\pi$
$911$	−24.1453	+	27.8651i	−0.799968	+	0.923213i	0.198411	+	0.980119i	$0.436422\pi$
$912$		0			0
$913$	−13.0053	−	8.35797i	−0.430411	−	0.276608i
$914$		0			0
$915$	−46.4675	+	40.2643i	−1.53617	+	1.33110i
$916$		0			0
$917$	−9.55015	+	4.36141i	−0.315374	+	0.144026i
$918$		0			0
$919$	−19.0546			−0.628554			−0.314277	−	0.949331i	$-0.601762\pi$
$919$	−19.0546			−0.628554			−0.314277	+	0.949331i	$0.601762\pi$
$920$		0			0
$921$	68.4454			2.25535
$922$		0			0
$923$	34.8383	−	15.9101i	1.14672	−	0.523687i
$924$		0			0
$925$	−56.8992	+	49.3034i	−1.87083	+	1.62109i
$926$		0			0
$927$	−17.3016	−	11.1191i	−0.568259	−	0.365198i
$928$		0			0
$929$	29.8655	−	34.4666i	0.979856	−	1.13081i	−0.0115426	−	0.999933i	$-0.503674\pi$
$929$	29.8655	−	34.4666i	0.979856	−	1.13081i	0.991398	−	0.130880i	$-0.0417804\pi$
$930$		0			0
$931$	0.397864	+	2.76720i	0.0130395	+	0.0906914i
$932$		0			0
$933$	42.5489	−	27.3445i	1.39299	−	0.895219i
$934$		0			0
$935$	5.74919	−	12.5890i	0.188019	−	0.411704i
$936$		0			0
$937$	−1.70122	−	5.79381i	−0.0555763	−	0.189276i	0.927026	−	0.374997i	$-0.122356\pi$
$937$	−1.70122	−	5.79381i	−0.0555763	−	0.189276i	−0.982603	+	0.185721i	$0.940538\pi$
$938$		0			0
$939$	−21.0489	−	6.18051i	−0.686905	−	0.201693i
$940$		0			0
$941$	6.12520	+	0.880671i	0.199676	+	0.0287091i	0.241427	−	0.970419i	$-0.422385\pi$
$941$	6.12520	+	0.880671i	0.199676	+	0.0287091i	−0.0417511	+	0.999128i	$0.513294\pi$
$942$		0			0
$943$	−11.8195	+	27.3437i	−0.384897	+	0.890434i
$944$		0			0
$945$	−10.7873	+	75.0277i	−0.350913	+	2.44065i
$946$		0			0
$947$	−16.1108	+	54.8685i	−0.523532	+	1.78299i	0.0930107	+	0.995665i	$0.470351\pi$
$947$	−16.1108	+	54.8685i	−0.523532	+	1.78299i	−0.616543	+	0.787321i	$0.711467\pi$
$948$		0			0
$949$	59.5711	−	17.4917i	1.93376	−	0.567803i
$950$		0			0
$951$	13.2309	+	6.04237i	0.429043	+	0.195937i
$952$		0			0
$953$	−12.5907	−	19.5915i	−0.407853	−	0.634631i	0.575187	−	0.818022i	$-0.304929\pi$
$953$	−12.5907	−	19.5915i	−0.407853	−	0.634631i	−0.983040	+	0.183390i	$0.941293\pi$
$954$		0			0
$955$	2.69603	−	0.387630i	0.0872413	−	0.0125434i
$956$		0			0
$957$	20.7400	+	17.9713i	0.670428	+	0.580930i
$958$		0			0
$959$	−24.7439	+	38.5022i	−0.799022	+	1.24330i
$960$		0			0
$961$	11.3712	+	13.1230i	0.366812	+	0.423323i
$962$		0			0
$963$	−14.4528	−	31.6472i	−0.465735	−	1.01982i
$964$		0			0
$965$		−	44.3155i		−	1.42657i
$966$		0			0
$967$			49.0196i			1.57636i	0.615442	+	0.788182i	$0.288978\pi$
$967$			49.0196i			1.57636i	−0.615442	+	0.788182i	$0.711022\pi$
$968$		0			0
$969$	−2.68086	−	5.87027i	−0.0861218	−	0.188580i
$970$		0			0
$971$	23.5968	+	27.2321i	0.757257	+	0.873921i	0.995251	−	0.0973459i	$-0.0310353\pi$
$971$	23.5968	+	27.2321i	0.757257	+	0.873921i	−0.237994	+	0.971267i	$0.576490\pi$
$972$		0			0
$973$	−11.4442	+	17.8075i	−0.366884	+	0.570883i
$974$		0			0
$975$	95.8343	+	83.0409i	3.06915	+	2.65944i
$976$		0			0
$977$	−30.8286	+	4.43249i	−0.986296	+	0.141808i	−0.616542	−	0.787322i	$-0.711467\pi$
$977$	−30.8286	+	4.43249i	−0.986296	+	0.141808i	−0.369754	+	0.929130i	$0.620558\pi$
$978$		0			0
$979$	−0.888281	−	1.38219i	−0.0283896	−	0.0441751i
$980$		0			0
$981$	−92.9863	−	42.4654i	−2.96882	−	1.35582i
$982$		0			0
$983$	−3.49421	+	1.02599i	−0.111448	+	0.0327241i	−0.336981	−	0.941511i	$-0.609406\pi$
$983$	−3.49421	+	1.02599i	−0.111448	+	0.0327241i	0.225533	+	0.974236i	$0.427588\pi$
$984$		0			0
$985$	3.42077	−	11.6501i	0.108995	−	0.371202i
$986$		0			0
$987$	10.3241	−	71.8058i	0.328620	−	2.28560i
$988$		0			0
$989$	−12.6465	+	15.2110i	−0.402136	+	0.483680i
$990$		0			0
$991$	−46.5214	−	6.68876i	−1.47780	−	0.212476i	−0.644205	−	0.764853i	$-0.722812\pi$
$991$	−46.5214	−	6.68876i	−1.47780	−	0.212476i	−0.833594	+	0.552377i	$0.813721\pi$
$992$		0			0
$993$	8.67689	+	2.54776i	0.275353	+	0.0808508i
$994$		0			0
$995$	−3.29576	−	11.2243i	−0.104483	−	0.355835i
$996$		0			0
$997$	−14.5767	+	31.9185i	−0.461649	+	1.01087i	0.525460	+	0.850819i	$0.323893\pi$
$997$	−14.5767	+	31.9185i	−0.461649	+	1.01087i	−0.987109	+	0.160052i	$0.948834\pi$
$998$		0			0
$999$	53.2286	−	34.2079i	1.68408	−	1.08229i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.s.b.15.1	✓	80
4.3	odd	2	inner	368.2.s.b.15.8	yes	80
23.20	odd	22	inner	368.2.s.b.319.8	yes	80
92.43	even	22	inner	368.2.s.b.319.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.s.b.15.1	✓	80	1.1	even	1	trivial
368.2.s.b.15.8	yes	80	4.3	odd	2	inner
368.2.s.b.319.1	yes	80	92.43	even	22	inner
368.2.s.b.319.8	yes	80	23.20	odd	22	inner

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

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	368.2.s.b.15.1

Level	$368$
Weight	$2$
Character	368.15
Analytic conductor	$2.938$
Analytic rank	$0$
Dimension	$80$
Inner twists	$4$