LMFDB - Embedded newform 392.2.y.a.305.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(9,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("392.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$392 = 2^{3} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	392.y (of order $21$ , degree $12$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$7$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			305.3
Character	$\chi$	$=$	392.305
Dual form			392.2.y.a.9.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51640 + 0.228560i) q^{3} +(-0.147325 + 0.375377i) q^{5} +(0.926271 - 2.47831i) q^{7} +(-0.619491 + 0.191088i) q^{9} +(-1.34370 - 0.414477i) q^{11} +(-0.0982465 - 0.430446i) q^{13} +(0.137607 - 0.602894i) q^{15} +(5.37871 - 3.66714i) q^{17} +(-4.20609 - 7.28515i) q^{19} +(-0.838153 + 3.96982i) q^{21} +(-4.38971 - 2.99285i) q^{23} +(3.54606 + 3.29026i) q^{25} +(5.04070 - 2.42747i) q^{27} +(-3.31717 - 1.59747i) q^{29} +(4.14313 - 7.17612i) q^{31} +(2.13232 + 0.321396i) q^{33} +(0.793838 + 0.712817i) q^{35} +(-0.477843 - 6.37637i) q^{37} +(0.247364 + 0.630273i) q^{39} +(0.640272 + 0.802876i) q^{41} +(-2.47117 + 3.09875i) q^{43} +(0.0195364 - 0.260695i) q^{45} +(-4.24317 + 3.93709i) q^{47} +(-5.28404 - 4.59117i) q^{49} +(-7.31810 + 6.79021i) q^{51} +(-0.822303 + 10.9729i) q^{53} +(0.353546 - 0.443332i) q^{55} +(8.04320 + 10.0859i) q^{57} +(2.38828 + 6.08524i) q^{59} +(-0.315828 - 4.21444i) q^{61} +(-0.100242 + 1.71229i) q^{63} +(0.176054 + 0.0265358i) q^{65} +(-4.22717 + 7.32168i) q^{67} +(7.34060 + 3.53505i) q^{69} +(11.6077 - 5.58995i) q^{71} +(-6.31342 - 5.85799i) q^{73} +(-6.12926 - 4.17886i) q^{75} +(-2.27184 + 2.94619i) q^{77} +(5.11546 + 8.86024i) q^{79} +(-5.48196 + 3.73754i) q^{81} +(-1.40508 + 6.15605i) q^{83} +(0.584144 + 2.55930i) q^{85} +(5.39528 + 1.66422i) q^{87} +(2.35427 - 0.726195i) q^{89} +(-1.15778 - 0.155224i) q^{91} +(-4.64247 + 11.8288i) q^{93} +(3.35434 - 0.505585i) q^{95} -0.693167 q^{97} +0.911613 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$84 q - 8 q^{3} - q^{5} + 4 q^{7} + 41 q^{9} + q^{11} - 2 q^{13} + q^{15} - 5 q^{17} - 13 q^{19} + 12 q^{21} - 5 q^{23} + 2 q^{25} + 4 q^{27} - 21 q^{29} + 23 q^{31} - 17 q^{33} - 22 q^{35} - 60 q^{37}+ \cdots - 94 q^{99}+O(q^{100})$ 84 * q - 8 * q^3 - q^5 + 4 * q^7 + 41 * q^9 + q^11 - 2 * q^13 + q^15 - 5 * q^17 - 13 * q^19 + 12 * q^21 - 5 * q^23 + 2 * q^25 + 4 * q^27 - 21 * q^29 + 23 * q^31 - 17 * q^33 - 22 * q^35 - 60 * q^37 - 61 * q^39 + 4 * q^41 + 22 * q^43 + 30 * q^45 + 82 * q^47 - 2 * q^49 + 3 * q^51 + 38 * q^53 + 69 * q^55 - 2 * q^57 - 6 * q^59 - 26 * q^61 - 37 * q^63 + 2 * q^65 + 43 * q^67 + 7 * q^69 - 21 * q^71 - 7 * q^73 - 80 * q^75 - 85 * q^77 - 25 * q^79 - 10 * q^81 - 17 * q^83 + 23 * q^85 + 47 * q^87 + 7 * q^89 - 3 * q^91 - 50 * q^93 - 129 * q^95 - 150 * q^97 - 94 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$ .

$n$	$197$	$295$	$297$
$\chi(n)$	$1$	$1$	$e\left(\frac{20}{21}\right)$

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
$3$	−1.51640	+	0.228560i	−0.875494	+	0.131959i	−0.571389	−	0.820679i	$-0.693595\pi$
$3$	−1.51640	+	0.228560i	−0.875494	+	0.131959i	−0.304104	+	0.952639i	$0.598357\pi$
$4$		0			0
$5$	−0.147325	+	0.375377i	−0.0658856	+	0.167874i	−0.960025	−	0.279916i	$-0.909693\pi$
$5$	−0.147325	+	0.375377i	−0.0658856	+	0.167874i	0.894139	+	0.447790i	$0.147789\pi$
$6$		0			0
$7$	0.926271	−	2.47831i	0.350098	−	0.936713i
$7$	0.926271	−	2.47831i	0.350098	−	0.936713i
$8$		0			0
$9$	−0.619491	+	0.191088i	−0.206497	+	0.0636959i
$10$		0			0
$11$	−1.34370	−	0.414477i	−0.405141	−	0.124970i	0.0854853	−	0.996339i	$-0.472756\pi$
$11$	−1.34370	−	0.414477i	−0.405141	−	0.124970i	−0.490627	+	0.871370i	$0.663232\pi$
$12$		0			0
$13$	−0.0982465	−	0.430446i	−0.0272487	−	0.119384i	0.959474	−	0.281796i	$-0.0909300\pi$
$13$	−0.0982465	−	0.430446i	−0.0272487	−	0.119384i	−0.986723	+	0.162411i	$0.948073\pi$
$14$		0			0
$15$	0.137607	−	0.602894i	0.0355299	−	0.155667i
$16$		0			0
$17$	5.37871	−	3.66714i	1.30453	−	0.889412i	0.306481	−	0.951877i	$-0.400848\pi$
$17$	5.37871	−	3.66714i	1.30453	−	0.889412i	0.998047	+	0.0624646i	$0.0198961\pi$
$18$		0			0
$19$	−4.20609	−	7.28515i	−0.964942	−	1.67133i	−0.709771	−	0.704433i	$-0.751201\pi$
$19$	−4.20609	−	7.28515i	−0.964942	−	1.67133i	−0.255172	−	0.966896i	$-0.582132\pi$
$20$		0			0
$21$	−0.838153	+	3.96982i	−0.182900	+	0.866285i
$22$		0			0
$23$	−4.38971	−	2.99285i	−0.915317	−	0.624053i	0.0113499	−	0.999936i	$-0.496387\pi$
$23$	−4.38971	−	2.99285i	−0.915317	−	0.624053i	−0.926667	+	0.375883i	$0.877340\pi$
$24$		0			0
$25$	3.54606	+	3.29026i	0.709211	+	0.658052i
$26$		0			0
$27$	5.04070	−	2.42747i	0.970084	−	0.467168i
$28$		0			0
$29$	−3.31717	−	1.59747i	−0.615983	−	0.296642i	0.0997533	−	0.995012i	$-0.468195\pi$
$29$	−3.31717	−	1.59747i	−0.615983	−	0.296642i	−0.715737	+	0.698370i	$0.753909\pi$
$30$		0			0
$31$	4.14313	−	7.17612i	0.744129	−	1.28887i	−0.206472	−	0.978452i	$-0.566198\pi$
$31$	4.14313	−	7.17612i	0.744129	−	1.28887i	0.950601	−	0.310416i	$-0.100468\pi$
$32$		0			0
$33$	2.13232	+	0.321396i	0.371190	+	0.0559478i
$34$		0			0
$35$	0.793838	+	0.712817i	0.134183	+	0.120488i
$36$		0			0
$37$	−0.477843	−	6.37637i	−0.0785569	−	1.04827i	−0.887629	−	0.460559i	$-0.847649\pi$
$37$	−0.477843	−	6.37637i	−0.0785569	−	1.04827i	0.809072	−	0.587710i	$-0.199970\pi$
$38$		0			0
$39$	0.247364	+	0.630273i	0.0396099	+	0.100924i
$40$		0			0
$41$	0.640272	+	0.802876i	0.0999937	+	0.125388i	0.829311	−	0.558788i	$-0.188733\pi$
$41$	0.640272	+	0.802876i	0.0999937	+	0.125388i	−0.729317	+	0.684176i	$0.760162\pi$
$42$		0			0
$43$	−2.47117	+	3.09875i	−0.376850	+	0.472555i	−0.933699	−	0.358059i	$-0.883439\pi$
$43$	−2.47117	+	3.09875i	−0.376850	+	0.472555i	0.556849	+	0.830614i	$0.312010\pi$
$44$		0			0
$45$	0.0195364	−	0.260695i	0.00291231	−	0.0388621i
$46$		0			0
$47$	−4.24317	+	3.93709i	−0.618930	+	0.574283i	−0.926056	−	0.377386i	$-0.876823\pi$
$47$	−4.24317	+	3.93709i	−0.618930	+	0.574283i	0.307126	+	0.951669i	$0.400633\pi$
$48$		0			0
$49$	−5.28404	−	4.59117i	−0.754863	−	0.655882i
$50$		0			0
$51$	−7.31810	+	6.79021i	−1.02474	+	0.950819i
$52$		0			0
$53$	−0.822303	+	10.9729i	−0.112952	+	1.50724i	0.596573	+	0.802559i	$0.296529\pi$
$53$	−0.822303	+	10.9729i	−0.112952	+	1.50724i	−0.709525	+	0.704681i	$0.751090\pi$
$54$		0			0
$55$	0.353546	−	0.443332i	0.0476721	−	0.0597789i
$56$		0			0
$57$	8.04320	+	10.0859i	1.06535	+	1.33590i
$58$		0			0
$59$	2.38828	+	6.08524i	0.310928	+	0.792230i	0.997852	+	0.0655020i	$0.0208649\pi$
$59$	2.38828	+	6.08524i	0.310928	+	0.792230i	−0.686925	+	0.726728i	$0.741040\pi$
$60$		0			0
$61$	−0.315828	−	4.21444i	−0.0404377	−	0.539603i	−0.980231	−	0.197859i	$-0.936601\pi$
$61$	−0.315828	−	4.21444i	−0.0404377	−	0.539603i	0.939793	−	0.341745i	$-0.111018\pi$
$62$		0			0
$63$	−0.100242	+	1.71229i	−0.0126293	+	0.215728i
$64$		0			0
$65$	0.176054	+	0.0265358i	0.0218368	+	0.00329136i
$66$		0			0
$67$	−4.22717	+	7.32168i	−0.516431	+	0.894485i	0.483387	+	0.875407i	$0.339407\pi$
$67$	−4.22717	+	7.32168i	−0.516431	+	0.894485i	−0.999818	+	0.0190783i	$0.993927\pi$
$68$		0			0
$69$	7.34060	+	3.53505i	0.883704	+	0.425569i
$70$		0			0
$71$	11.6077	−	5.58995i	1.37757	−	0.663405i	0.409094	−	0.912492i	$-0.365845\pi$
$71$	11.6077	−	5.58995i	1.37757	−	0.663405i	0.968481	+	0.249087i	$0.0801307\pi$
$72$		0			0
$73$	−6.31342	−	5.85799i	−0.738929	−	0.685626i	0.217999	−	0.975949i	$-0.430047\pi$
$73$	−6.31342	−	5.85799i	−0.738929	−	0.685626i	−0.956929	+	0.290323i	$0.906237\pi$
$74$		0			0
$75$	−6.12926	−	4.17886i	−0.707746	−	0.482533i
$76$		0			0
$77$	−2.27184	+	2.94619i	−0.258900	+	0.335750i
$78$		0			0
$79$	5.11546	+	8.86024i	0.575535	+	0.996855i	0.995983	+	0.0895390i	$0.0285394\pi$
$79$	5.11546	+	8.86024i	0.575535	+	0.996855i	−0.420449	+	0.907316i	$0.638127\pi$
$80$		0			0
$81$	−5.48196	+	3.73754i	−0.609107	+	0.415282i
$82$		0			0
$83$	−1.40508	+	6.15605i	−0.154227	+	0.675715i	0.837401	+	0.546589i	$0.184074\pi$
$83$	−1.40508	+	6.15605i	−0.154227	+	0.675715i	−0.991628	+	0.129125i	$0.958783\pi$
$84$		0			0
$85$	0.584144	+	2.55930i	0.0633593	+	0.277595i
$86$		0			0
$87$	5.39528	+	1.66422i	0.578434	+	0.178423i
$88$		0			0
$89$	2.35427	−	0.726195i	0.249552	−	0.0769765i	−0.167456	−	0.985880i	$-0.553555\pi$
$89$	2.35427	−	0.726195i	0.249552	−	0.0769765i	0.417007	+	0.908903i	$0.363079\pi$
$90$		0			0
$91$	−1.15778	−	0.155224i	−0.121369	−	0.0162719i
$92$		0			0
$93$	−4.64247	+	11.8288i	−0.481402	+	1.22659i
$94$		0			0
$95$	3.35434	−	0.505585i	0.344148	−	0.0518719i
$96$		0			0
$97$	−0.693167			−0.0703805			−0.0351902	−	0.999381i	$-0.511204\pi$
$97$	−0.693167			−0.0703805			−0.0351902	+	0.999381i	$0.511204\pi$
$98$		0			0
$99$	0.911613			0.0916206
$100$		0			0
$101$	7.19439	−	1.08438i	0.715868	−	0.107900i	0.218999	−	0.975725i	$-0.429721\pi$
$101$	7.19439	−	1.08438i	0.715868	−	0.107900i	0.496869	+	0.867825i	$0.334483\pi$
$102$		0			0
$103$	2.15610	−	5.49366i	0.212447	−	0.541306i	−0.784435	−	0.620211i	$-0.787047\pi$
$103$	2.15610	−	5.49366i	0.212447	−	0.541306i	0.996882	+	0.0789048i	$0.0251423\pi$
$104$		0			0
$105$	−1.36670	−	0.899475i	−0.133376	−	0.0877798i
$106$		0			0
$107$	−10.1482	+	3.13032i	−0.981068	+	0.302619i	−0.743488	−	0.668749i	$-0.766830\pi$
$107$	−10.1482	+	3.13032i	−0.981068	+	0.302619i	−0.237579	+	0.971368i	$0.576354\pi$
$108$		0			0
$109$	5.04479	+	1.55611i	0.483203	+	0.149049i	0.526780	−	0.850002i	$-0.323399\pi$
$109$	5.04479	+	1.55611i	0.483203	+	0.149049i	−0.0435767	+	0.999050i	$0.513875\pi$
$110$		0			0
$111$	2.18199	+	9.55991i	0.207105	+	0.907386i
$112$		0			0
$113$	1.30238	−	5.70612i	0.122518	−	0.536787i	−0.875997	−	0.482316i	$-0.839796\pi$
$113$	1.30238	−	5.70612i	0.122518	−	0.536787i	0.998515	−	0.0544707i	$-0.0173472\pi$
$114$		0			0
$115$	1.77016	−	1.20687i	0.165068	−	0.112542i
$116$		0			0
$117$	0.143116	+	0.247884i	0.0132311	+	0.0229169i
$118$		0			0
$119$	−4.10617	−	16.7269i	−0.376412	−	1.53335i
$120$		0			0
$121$	−7.45488	−	5.08265i	−0.677717	−	0.462059i
$122$		0			0
$123$	−1.15441	−	1.07114i	−0.104090	−	0.0965814i
$124$		0			0
$125$	−3.57410	+	1.72119i	−0.319677	+	0.153948i
$126$		0			0
$127$	−1.10520	−	0.532238i	−0.0980709	−	0.0472285i	0.384205	−	0.923248i	$-0.374476\pi$
$127$	−1.10520	−	0.532238i	−0.0980709	−	0.0472285i	−0.482276	+	0.876019i	$0.660190\pi$
$128$		0			0
$129$	3.03903	−	5.26376i	0.267572	−	0.463448i
$130$		0			0
$131$	−3.26855	−	0.492655i	−0.285575	−	0.0430435i	0.00469285	−	0.999989i	$-0.498506\pi$
$131$	−3.26855	−	0.492655i	−0.285575	−	0.0430435i	−0.290268	+	0.956946i	$0.593744\pi$
$132$		0			0
$133$	−21.9508	+	3.67596i	−1.90338	+	0.318746i
$134$		0			0
$135$	0.168598	+	2.24979i	0.0145106	+	0.193631i
$136$		0			0
$137$	4.27559	+	10.8940i	0.365288	+	0.930739i	0.988843	+	0.148959i	$0.0475924\pi$
$137$	4.27559	+	10.8940i	0.365288	+	0.930739i	−0.623555	+	0.781779i	$0.714312\pi$
$138$		0			0
$139$	6.76258	+	8.48001i	0.573595	+	0.719265i	0.981006	−	0.193980i	$-0.0621396\pi$
$139$	6.76258	+	8.48001i	0.573595	+	0.719265i	−0.407411	+	0.913245i	$0.633568\pi$
$140$		0			0
$141$	5.53448	−	6.94002i	0.466087	−	0.584455i
$142$		0			0
$143$	−0.0463960	+	0.619112i	−0.00387983	+	0.0517728i
$144$		0			0
$145$	1.08835	−	1.00984i	0.0903828	−	0.0838630i
$146$		0			0
$147$	9.06208	+	5.75433i	0.747428	+	0.474609i
$148$		0			0
$149$	13.4472	−	12.4771i	1.10163	−	1.02217i	0.102010	−	0.994783i	$-0.467473\pi$
$149$	13.4472	−	12.4771i	1.10163	−	1.02217i	0.999625	−	0.0273845i	$-0.00871783\pi$
$150$		0			0
$151$	0.866609	−	11.5641i	0.0705236	−	0.941072i	−0.843949	−	0.536424i	$-0.819775\pi$
$151$	0.866609	−	11.5641i	0.0705236	−	0.941072i	0.914472	−	0.404649i	$-0.132606\pi$
$152$		0			0
$153$	−2.63132	+	3.29957i	−0.212729	+	0.266754i
$154$		0			0
$155$	2.08336	+	2.61246i	0.167340	+	0.209837i
$156$		0			0
$157$	−7.47975	−	19.0581i	−0.596949	−	1.52100i	−0.835284	−	0.549818i	$-0.814697\pi$
$157$	−7.47975	−	19.0581i	−0.596949	−	1.52100i	0.238336	−	0.971183i	$-0.423398\pi$
$158$		0			0
$159$	−1.26102	−	16.8272i	−0.100006	−	1.33448i
$160$		0			0
$161$	−11.4833	+	8.10686i	−0.905009	+	0.638910i
$162$		0			0
$163$	−2.52434	−	0.380483i	−0.197721	−	0.0298017i	0.0494349	−	0.998777i	$-0.484258\pi$
$163$	−2.52434	−	0.380483i	−0.197721	−	0.0298017i	−0.247156	+	0.968976i	$0.579496\pi$
$164$		0			0
$165$	−0.434788	+	0.753075i	−0.0338482	+	0.0586268i
$166$		0			0
$167$	11.2810	+	5.43264i	0.872949	+	0.420390i	0.816044	−	0.577989i	$-0.196163\pi$
$167$	11.2810	+	5.43264i	0.872949	+	0.420390i	0.0569050	+	0.998380i	$0.481877\pi$
$168$		0			0
$169$	11.5370	−	5.55591i	0.887459	−	0.427378i
$170$		0			0
$171$	3.99774	+	3.70936i	0.305715	+	0.283662i
$172$		0			0
$173$	6.65833	+	4.53957i	0.506224	+	0.345137i	0.789348	−	0.613946i	$-0.210419\pi$
$173$	6.65833	+	4.53957i	0.506224	+	0.345137i	−0.283125	+	0.959083i	$0.591371\pi$
$174$		0			0
$175$	11.4389	−	5.74055i	0.864699	−	0.433945i
$176$		0			0
$177$	−5.01243	−	8.68178i	−0.376757	−	0.652563i
$178$		0			0
$179$	−4.13472	+	2.81900i	−0.309043	+	0.210702i	−0.707903	−	0.706310i	$-0.750358\pi$
$179$	−4.13472	+	2.81900i	−0.309043	+	0.210702i	0.398859	+	0.917012i	$0.369406\pi$
$180$		0			0
$181$	3.24591	−	14.2213i	0.241267	−	1.05706i	−0.698599	−	0.715513i	$-0.746193\pi$
$181$	3.24591	−	14.2213i	0.241267	−	1.05706i	0.939866	−	0.341545i	$-0.110950\pi$
$182$		0			0
$183$	1.44218	+	6.31858i	0.106609	+	0.467083i
$184$		0			0
$185$	2.46394	+	0.760025i	0.181153	+	0.0558781i
$186$		0			0
$187$	−8.74733	+	2.69819i	−0.639668	+	0.197311i
$188$		0			0
$189$	−1.34698	−	14.7409i	−0.0979782	−	1.07224i
$190$		0			0
$191$	−7.83441	+	19.9618i	−0.566878	+	1.44438i	0.303899	+	0.952704i	$0.401711\pi$
$191$	−7.83441	+	19.9618i	−0.566878	+	1.44438i	−0.870777	+	0.491678i	$0.836384\pi$
$192$		0			0
$193$	−20.2138	+	3.04674i	−1.45502	+	0.219309i	−0.828454	−	0.560057i	$-0.810779\pi$
$193$	−20.2138	+	3.04674i	−1.45502	+	0.219309i	−0.626569	+	0.779366i	$0.715541\pi$
$194$		0			0
$195$	−0.273033			−0.0195523
$196$		0			0
$197$	5.14452			0.366532			0.183266	−	0.983063i	$-0.441333\pi$
$197$	5.14452			0.366532			0.183266	+	0.983063i	$0.441333\pi$
$198$		0			0
$199$	−5.16760	+	0.778891i	−0.366322	+	0.0552141i	−0.329624	−	0.944112i	$-0.606922\pi$
$199$	−5.16760	+	0.778891i	−0.366322	+	0.0552141i	−0.0366978	+	0.999326i	$0.511684\pi$
$200$		0			0
$201$	4.73664	−	12.0688i	0.334097	−	0.851264i
$202$		0			0
$203$	−7.03162	+	6.74129i	−0.493523	+	0.473146i
$204$		0			0
$205$	−0.395709	+	0.122060i	−0.0276375	+	0.00852504i
$206$		0			0
$207$	3.29128	+	1.01523i	0.228760	+	0.0705631i
$208$		0			0
$209$	2.63220	+	11.5324i	0.182073	+	0.797713i
$210$		0			0
$211$	4.91333	−	21.5267i	0.338248	−	1.48196i	−0.464464	−	0.885592i	$-0.653753\pi$
$211$	4.91333	−	21.5267i	0.338248	−	1.48196i	0.802712	−	0.596367i	$-0.203390\pi$
$212$		0			0
$213$	−16.3242	+	11.1296i	−1.11852	+	0.762591i
$214$		0			0
$215$	−0.799135	−	1.38414i	−0.0545006	−	0.0943978i
$216$		0			0
$217$	−13.9470	−	16.9150i	−0.946783	−	1.14827i
$218$		0			0
$219$	10.9126	+	7.44006i	0.737403	+	0.502753i
$220$		0			0
$221$	−2.10695	−	1.95496i	−0.141728	−	0.131505i
$222$		0			0
$223$	1.74693	−	0.841275i	0.116983	−	0.0563359i	−0.374477	−	0.927236i	$-0.622178\pi$
$223$	1.74693	−	0.841275i	0.116983	−	0.0563359i	0.491460	+	0.870900i	$0.336463\pi$
$224$		0			0
$225$	−2.82548	−	1.36068i	−0.188365	−	0.0907119i
$226$		0			0
$227$	6.02443	−	10.4346i	0.399855	−	0.692570i	−0.593852	−	0.804574i	$-0.702394\pi$
$227$	6.02443	−	10.4346i	0.399855	−	0.692570i	0.993708	+	0.112004i	$0.0357270\pi$
$228$		0			0
$229$	14.2131	+	2.14228i	0.939227	+	0.141566i	0.600775	−	0.799418i	$-0.294859\pi$
$229$	14.2131	+	2.14228i	0.939227	+	0.141566i	0.338452	+	0.940984i	$0.390097\pi$
$230$		0			0
$231$	2.77163	−	4.98686i	0.182360	−	0.328111i
$232$		0			0
$233$	1.55243	+	20.7158i	0.101703	+	1.35713i	0.781578	+	0.623807i	$0.214415\pi$
$233$	1.55243	+	20.7158i	0.101703	+	1.35713i	−0.679875	+	0.733328i	$0.737966\pi$
$234$		0			0
$235$	−0.852768	−	2.17282i	−0.0556285	−	0.141739i
$236$		0			0
$237$	−9.78219	−	12.2665i	−0.635421	−	0.796793i
$238$		0			0
$239$	12.4710	−	15.6382i	0.806684	−	1.01155i	−0.192856	−	0.981227i	$-0.561775\pi$
$239$	12.4710	−	15.6382i	0.806684	−	1.01155i	0.999540	−	0.0303225i	$-0.00965343\pi$
$240$		0			0
$241$	−0.308807	+	4.12075i	−0.0198920	+	0.265441i	0.978386	+	0.206786i	$0.0663002\pi$
$241$	−0.308807	+	4.12075i	−0.0198920	+	0.265441i	−0.998278	+	0.0586550i	$0.981319\pi$
$242$		0			0
$243$	−4.84516	+	4.49565i	−0.310817	+	0.288396i
$244$		0			0
$245$	2.50189	−	1.30712i	0.159840	−	0.0835085i
$246$		0			0
$247$	−2.72263	+	2.52623i	−0.173237	+	0.160740i
$248$		0			0
$249$	0.723631	−	9.65618i	0.0458582	−	0.611936i
$250$		0			0
$251$	−12.1121	+	15.1881i	−0.764509	+	0.958664i	−0.999912	−	0.0132335i	$-0.995788\pi$
$251$	−12.1121	+	15.1881i	−0.764509	+	0.958664i	0.235403	+	0.971898i	$0.424359\pi$
$252$		0			0
$253$	4.65799	+	5.84094i	0.292845	+	0.367216i
$254$		0			0
$255$	−1.47075	−	3.74741i	−0.0921020	−	0.234672i
$256$		0			0
$257$	−1.93171	−	25.7769i	−0.120497	−	1.60792i	−0.650217	−	0.759749i	$-0.725322\pi$
$257$	−1.93171	−	25.7769i	−0.120497	−	1.60792i	0.529720	−	0.848173i	$-0.322297\pi$
$258$		0			0
$259$	−16.2452	−	4.72201i	−1.00943	−	0.293411i
$260$		0			0
$261$	2.36021	+	0.355745i	0.146094	+	0.0220201i
$262$		0			0
$263$	10.0884	−	17.4736i	0.622076	−	1.07747i	−0.367022	−	0.930212i	$-0.619623\pi$
$263$	10.0884	−	17.4736i	0.622076	−	1.07747i	0.989098	−	0.147256i	$-0.0470440\pi$
$264$		0			0
$265$	−3.99782	−	1.92525i	−0.245584	−	0.118267i
$266$		0			0
$267$	−3.40403	+	1.63929i	−0.208323	+	0.100323i
$268$		0			0
$269$	−20.0231	−	18.5787i	−1.22083	−	1.13276i	−0.987040	−	0.160476i	$-0.948697\pi$
$269$	−20.0231	−	18.5787i	−1.22083	−	1.13276i	−0.233789	−	0.972287i	$-0.575113\pi$
$270$		0			0
$271$	25.5947	+	17.4502i	1.55477	+	1.06002i	0.968217	+	0.250113i	$0.0804678\pi$
$271$	25.5947	+	17.4502i	1.55477	+	1.06002i	0.586553	+	0.809911i	$0.300485\pi$
$272$		0			0
$273$	1.79114	−	0.0292408i	0.108405	−	0.00176974i
$274$		0			0
$275$	−3.40111	−	5.89089i	−0.205094	−	0.355234i
$276$		0			0
$277$	11.3230	−	7.71991i	0.680335	−	0.463844i	−0.173196	−	0.984887i	$-0.555409\pi$
$277$	11.3230	−	7.71991i	0.680335	−	0.463844i	0.853530	+	0.521043i	$0.174457\pi$
$278$		0			0
$279$	−1.19537	+	5.23724i	−0.0715647	+	0.313546i
$280$		0			0
$281$	6.90340	+	30.2458i	0.411822	+	1.80431i	0.575505	+	0.817798i	$0.304806\pi$
$281$	6.90340	+	30.2458i	0.411822	+	1.80431i	−0.163683	+	0.986513i	$0.552337\pi$
$282$		0			0
$283$	30.2330	+	9.32565i	1.79717	+	0.554353i	0.998853	−	0.0478883i	$-0.0152492\pi$
$283$	30.2330	+	9.32565i	1.79717	+	0.554353i	0.798314	+	0.602241i	$0.205725\pi$
$284$		0			0
$285$	−4.97096	+	1.53334i	−0.294454	+	0.0908271i
$286$		0			0
$287$	2.58284	−	0.843112i	0.152460	−	0.0497674i
$288$		0			0
$289$	9.27177	−	23.6241i	0.545398	−	1.38965i
$290$		0			0
$291$	1.05112	−	0.158431i	0.0616176	−	0.00928737i
$292$		0			0
$293$	4.71694			0.275566			0.137783	−	0.990462i	$-0.456002\pi$
$293$	4.71694			0.275566			0.137783	+	0.990462i	$0.456002\pi$
$294$		0			0
$295$	−2.63611			−0.153480
$296$		0			0
$297$	−7.77934	+	1.17255i	−0.451403	+	0.0680380i
$298$		0			0
$299$	−0.856988	+	2.18357i	−0.0495609	+	0.126279i
$300$		0			0
$301$	5.39069	+	8.99461i	0.310714	+	0.518441i
$302$		0			0
$303$	−10.6617	+	3.28870i	−0.612500	+	0.188931i
$304$		0			0
$305$	1.62853	+	0.502336i	0.0932495	+	0.0287637i
$306$		0			0
$307$	1.59463	+	6.98652i	0.0910102	+	0.398742i	0.999830	−	0.0184476i	$-0.00587238\pi$
$307$	1.59463	+	6.98652i	0.0910102	+	0.398742i	−0.908820	+	0.417189i	$0.863015\pi$
$308$		0			0
$309$	−2.01388	+	8.82338i	−0.114566	+	0.501944i
$310$		0			0
$311$	−1.42254	+	0.969874i	−0.0806651	+	0.0549965i	−0.602981	−	0.797756i	$-0.706021\pi$
$311$	−1.42254	+	0.969874i	−0.0806651	+	0.0549965i	0.522316	+	0.852752i	$0.325068\pi$
$312$		0			0
$313$	4.82195	+	8.35187i	0.272553	+	0.472076i	0.969515	−	0.245033i	$-0.0787987\pi$
$313$	4.82195	+	8.35187i	0.272553	+	0.472076i	−0.696962	+	0.717108i	$0.745465\pi$
$314$		0			0
$315$	−0.627986	−	0.289891i	−0.0353830	−	0.0163335i
$316$		0			0
$317$	6.68310	+	4.55646i	0.375361	+	0.255916i	0.736275	−	0.676682i	$-0.236583\pi$
$317$	6.68310	+	4.55646i	0.375361	+	0.255916i	−0.360914	+	0.932599i	$0.617535\pi$
$318$		0			0
$319$	3.79518	+	3.52141i	0.212489	+	0.197161i
$320$		0			0
$321$	14.6733	−	7.06630i	0.818985	−	0.394402i
$322$		0			0
$323$	−49.3390	−	23.7604i	−2.74529	−	1.32206i
$324$		0			0
$325$	1.06789	−	1.84964i	0.0592360	−	0.102600i
$326$		0			0
$327$	−8.00559	−	1.20665i	−0.442710	−	0.0667278i
$328$		0			0
$329$	5.82700	+	14.1627i	0.321253	+	0.780815i
$330$		0			0
$331$	−2.06049	−	27.4953i	−0.113255	−	1.51128i	−0.707339	−	0.706875i	$-0.750105\pi$
$331$	−2.06049	−	27.4953i	−0.113255	−	1.51128i	0.594084	−	0.804403i	$-0.297515\pi$
$332$		0			0
$333$	1.51447	+	3.85880i	0.0829922	+	0.211461i
$334$		0			0
$335$	−2.12562	−	2.66545i	−0.116135	−	0.145629i
$336$		0			0
$337$	−6.36702	+	7.98399i	−0.346834	+	0.434916i	−0.924398	−	0.381429i	$-0.875432\pi$
$337$	−6.36702	+	7.98399i	−0.346834	+	0.434916i	0.577564	+	0.816345i	$0.304003\pi$
$338$		0			0
$339$	−0.670742	+	8.95043i	−0.0364297	+	0.486121i
$340$		0			0
$341$	−8.54147	+	7.92533i	−0.462547	+	0.429181i
$342$		0			0
$343$	−16.2728	+	8.84283i	−0.878649	+	0.477468i
$344$		0			0
$345$	−2.40842	+	2.23469i	−0.129665	+	0.120312i
$346$		0			0
$347$	−1.15304	+	15.3863i	−0.0618985	+	0.825978i	0.876716	+	0.481009i	$0.159730\pi$
$347$	−1.15304	+	15.3863i	−0.0618985	+	0.825978i	−0.938614	+	0.344969i	$0.887890\pi$
$348$		0			0
$349$	8.19211	−	10.2726i	0.438513	−	0.549878i	−0.512637	−	0.858605i	$-0.671331\pi$
$349$	8.19211	−	10.2726i	0.438513	−	0.549878i	0.951151	+	0.308727i	$0.0999029\pi$
$350$		0			0
$351$	−1.54013	−	1.93126i	−0.0822060	−	0.103083i
$352$		0			0
$353$	9.60760	+	24.4798i	0.511361	+	1.30293i	0.920603	+	0.390501i	$0.127698\pi$
$353$	9.60760	+	24.4798i	0.511361	+	1.30293i	−0.409241	+	0.912426i	$0.634207\pi$
$354$		0			0
$355$	0.388246	+	5.18078i	0.0206060	+	0.274967i
$356$		0			0
$357$	10.0497	+	24.4261i	0.531886	+	1.29277i
$358$		0			0
$359$	−9.24524	−	1.39350i	−0.487945	−	0.0735459i	−0.0995381	−	0.995034i	$-0.531737\pi$
$359$	−9.24524	−	1.39350i	−0.487945	−	0.0735459i	−0.388407	+	0.921488i	$0.626975\pi$
$360$		0			0
$361$	−25.8823	+	44.8295i	−1.36223	+	2.35945i
$362$		0			0
$363$	12.4663	+	6.00344i	0.654310	+	0.315099i
$364$		0			0
$365$	3.12908	−	1.50688i	0.163783	−	0.0788739i
$366$		0			0
$367$	−3.23045	−	2.99742i	−0.168628	−	0.156464i	0.591345	−	0.806419i	$-0.298597\pi$
$367$	−3.23045	−	2.99742i	−0.168628	−	0.156464i	−0.759973	+	0.649955i	$0.774788\pi$
$368$		0			0
$369$	−0.550063	−	0.375026i	−0.0286351	−	0.0195231i
$370$		0			0
$371$	26.4325	+	12.2018i	1.37231	+	0.633485i
$372$		0			0
$373$	9.86013	+	17.0782i	0.510538	+	0.884278i	0.999925	+	0.0122114i	$0.00388712\pi$
$373$	9.86013	+	17.0782i	0.510538	+	0.884278i	−0.489387	+	0.872067i	$0.662780\pi$
$374$		0			0
$375$	5.02636	−	3.42692i	0.259560	−	0.176965i
$376$		0			0
$377$	−0.361722	+	1.58481i	−0.0186296	+	0.0816218i
$378$		0			0
$379$	4.31301	+	18.8965i	0.221544	+	0.970649i	0.956316	+	0.292335i	$0.0944321\pi$
$379$	4.31301	+	18.8965i	0.221544	+	0.970649i	−0.734772	+	0.678314i	$0.762711\pi$
$380$		0			0
$381$	1.79758	+	0.554479i	0.0920927	+	0.0284068i
$382$		0			0
$383$	−19.2310	+	5.93197i	−0.982657	+	0.303109i	−0.744136	−	0.668028i	$-0.767139\pi$
$383$	−19.2310	+	5.93197i	−0.982657	+	0.303109i	−0.238521	+	0.971137i	$0.576662\pi$
$384$		0			0
$385$	−0.771235	−	1.28684i	−0.0393058	−	0.0655835i
$386$		0			0
$387$	0.938736	−	2.39186i	0.0477186	−	0.121585i
$388$		0			0
$389$	18.3243	−	2.76195i	0.929080	−	0.140036i	0.332969	−	0.942938i	$-0.391950\pi$
$389$	18.3243	−	2.76195i	0.929080	−	0.140036i	0.596111	+	0.802902i	$0.296712\pi$
$390$		0			0
$391$	−34.5862			−1.74910
$392$		0			0
$393$	5.06903			0.255699
$394$		0			0
$395$	−4.07956	+	0.614895i	−0.205265	+	0.0309387i
$396$		0			0
$397$	−7.20097	+	18.3478i	−0.361406	+	0.920848i	0.628331	+	0.777946i	$0.283738\pi$
$397$	−7.20097	+	18.3478i	−0.361406	+	0.920848i	−0.989737	+	0.142902i	$0.954357\pi$
$398$		0			0
$399$	32.4461	−	10.5913i	1.62434	−	0.530229i
$400$		0			0
$401$	−4.34786	+	1.34114i	−0.217122	+	0.0669732i	−0.401408	−	0.915899i	$-0.631479\pi$
$401$	−4.34786	+	1.34114i	−0.217122	+	0.0669732i	0.184286	+	0.982873i	$0.441003\pi$
$402$		0			0
$403$	−3.49598	−	1.07837i	−0.174147	−	0.0537173i
$404$		0			0
$405$	−0.595358	−	2.60843i	−0.0295836	−	0.129614i
$406$		0			0
$407$	−2.00078	+	8.76600i	−0.0991751	+	0.434514i
$408$		0			0
$409$	7.22445	−	4.92555i	0.357226	−	0.243553i	−0.371387	−	0.928478i	$-0.621118\pi$
$409$	7.22445	−	4.92555i	0.357226	−	0.243553i	0.728613	+	0.684926i	$0.240165\pi$
$410$		0			0
$411$	−8.97344	−	15.5424i	−0.442627	−	0.766652i
$412$		0			0
$413$	17.2933	−	0.282318i	0.850948	−	0.0138920i
$414$		0			0
$415$	−2.10384	−	1.43437i	−0.103273	−	0.0704106i
$416$		0			0
$417$	−12.1930	−	11.3134i	−0.597092	−	0.554021i
$418$		0			0
$419$	14.7585	−	7.10731i	0.720999	−	0.347215i	−0.0371378	−	0.999310i	$-0.511824\pi$
$419$	14.7585	−	7.10731i	0.720999	−	0.347215i	0.758137	+	0.652095i	$0.226110\pi$
$420$		0			0
$421$	−10.2007	−	4.91239i	−0.497150	−	0.239415i	0.168468	−	0.985707i	$-0.446118\pi$
$421$	−10.2007	−	4.91239i	−0.497150	−	0.239415i	−0.665619	+	0.746292i	$0.731832\pi$
$422$		0			0
$423$	1.87628	−	3.24981i	0.0912277	−	0.158011i
$424$		0			0
$425$	31.1390	+	4.69345i	1.51047	+	0.227666i
$426$		0			0
$427$	−10.7372	−	3.12099i	−0.519611	−	0.151035i
$428$		0			0
$429$	−0.0711496	−	0.949426i	−0.00343514	−	0.0458387i
$430$		0			0
$431$	−8.18877	−	20.8646i	−0.394439	−	1.00501i	−0.980809	−	0.194971i	$-0.937539\pi$
$431$	−8.18877	−	20.8646i	−0.394439	−	1.00501i	0.586370	−	0.810044i	$-0.300557\pi$
$432$		0			0
$433$	−17.1243	−	21.4732i	−0.822942	−	1.03194i	−0.998870	−	0.0475334i	$-0.984864\pi$
$433$	−17.1243	−	21.4732i	−0.822942	−	1.03194i	0.175928	−	0.984403i	$-0.443707\pi$
$434$		0			0
$435$	−1.41957	+	1.78008i	−0.0680630	+	0.0853483i
$436$		0			0
$437$	−3.33990	+	44.5679i	−0.159769	+	2.13197i
$438$		0			0
$439$	−15.8635	+	14.7192i	−0.757123	+	0.702507i	−0.961018	−	0.276485i	$-0.910830\pi$
$439$	−15.8635	+	14.7192i	−0.757123	+	0.702507i	0.203895	+	0.978993i	$0.434640\pi$
$440$		0			0
$441$	4.15074	+	1.83448i	0.197654	+	0.0873560i
$442$		0			0
$443$	0.728271	−	0.675737i	0.0346012	−	0.0321052i	−0.662683	−	0.748900i	$-0.730582\pi$
$443$	0.728271	−	0.675737i	0.0346012	−	0.0321052i	0.697284	+	0.716795i	$0.254392\pi$
$444$		0			0
$445$	−0.0742445	+	0.990724i	−0.00351953	+	0.0469648i
$446$		0			0
$447$	−17.5395	+	21.9938i	−0.829590	+	1.04027i
$448$		0			0
$449$	11.1079	+	13.9289i	0.524214	+	0.657343i	0.971498	−	0.237049i	$-0.0761801\pi$
$449$	11.1079	+	13.9289i	0.524214	+	0.657343i	−0.447284	+	0.894392i	$0.647609\pi$
$450$		0			0
$451$	−0.527561	−	1.34420i	−0.0248419	−	0.0632961i
$452$		0			0
$453$	1.32897	+	17.7339i	0.0624404	+	0.833209i
$454$		0			0
$455$	0.228837	−	0.411736i	0.0107281	−	0.0193025i
$456$		0			0
$457$	28.7043	+	4.32648i	1.34273	+	0.202384i	0.780790	−	0.624793i	$-0.214817\pi$
$457$	28.7043	+	4.32648i	1.34273	+	0.202384i	0.561941	+	0.827177i	$0.310055\pi$
$458$		0			0
$459$	18.2106	−	31.5416i	0.849997	−	1.47224i
$460$		0			0
$461$	−18.8904	−	9.09712i	−0.879812	−	0.423695i	−0.0612561	−	0.998122i	$-0.519511\pi$
$461$	−18.8904	−	9.09712i	−0.879812	−	0.423695i	−0.818556	+	0.574427i	$0.805225\pi$
$462$		0			0
$463$	−2.61473	+	1.25919i	−0.121517	+	0.0585194i	−0.493654	−	0.869658i	$-0.664339\pi$
$463$	−2.61473	+	1.25919i	−0.121517	+	0.0585194i	0.372138	+	0.928178i	$0.378625\pi$
$464$		0			0
$465$	−3.75631	−	3.48535i	−0.174195	−	0.161629i
$466$		0			0
$467$	−8.56164	−	5.83723i	−0.396186	−	0.270115i	0.348798	−	0.937198i	$-0.386590\pi$
$467$	−8.56164	−	5.83723i	−0.396186	−	0.270115i	−0.744983	+	0.667083i	$0.767542\pi$
$468$		0			0
$469$	14.2299	+	17.2581i	0.657075	+	0.796905i
$470$		0			0
$471$	15.6982	+	27.1901i	0.723335	+	1.25285i
$472$		0			0
$473$	4.60488	−	3.13955i	0.211733	−	0.144357i
$474$		0			0
$475$	9.05503	−	39.6727i	0.415473	−	1.82031i
$476$		0			0
$477$	−1.58737	−	6.95473i	−0.0726808	−	0.318435i
$478$		0			0
$479$	7.13189	+	2.19990i	0.325864	+	0.100516i	0.453371	−	0.891322i	$-0.350221\pi$
$479$	7.13189	+	2.19990i	0.325864	+	0.100516i	−0.127507	+	0.991838i	$0.540697\pi$
$480$		0			0
$481$	−2.69774	+	0.832142i	−0.123006	+	0.0379424i
$482$		0			0
$483$	15.5603	−	14.9179i	0.708019	−	0.678786i
$484$		0			0
$485$	0.102121	−	0.260199i	0.00463706	−	0.0118150i
$486$		0			0
$487$	15.7127	−	2.36831i	0.712011	−	0.107318i	0.216957	−	0.976181i	$-0.430387\pi$
$487$	15.7127	−	2.36831i	0.712011	−	0.107318i	0.495053	+	0.868863i	$0.335149\pi$
$488$		0			0
$489$	3.91487			0.177036
$490$		0			0
$491$	−38.1651			−1.72237			−0.861184	−	0.508293i	$-0.830277\pi$
$491$	−38.1651			−1.72237			−0.861184	+	0.508293i	$0.830277\pi$
$492$		0			0
$493$	−23.7002	+	3.57223i	−1.06740	+	0.160885i
$494$		0			0
$495$	−0.134303	+	0.342199i	−0.00603647	+	0.0153807i
$496$		0			0
$497$	−3.10180	−	33.9452i	−0.139135	−	1.52265i
$498$		0			0
$499$	25.7258	−	7.93537i	1.15165	−	0.355236i	0.340595	−	0.940210i	$-0.389371\pi$
$499$	25.7258	−	7.93537i	1.15165	−	0.355236i	0.811052	+	0.584974i	$0.198895\pi$
$500$		0			0
$501$	−18.3482	−	5.65966i	−0.819736	−	0.252855i
$502$		0			0
$503$	−4.07027	−	17.8330i	−0.181484	−	0.795135i	−0.980924	−	0.194389i	$-0.937728\pi$
$503$	−4.07027	−	17.8330i	−0.181484	−	0.795135i	0.799440	−	0.600746i	$-0.205130\pi$
$504$		0			0
$505$	−0.652859	+	2.86036i	−0.0290519	+	0.127284i
$506$		0			0
$507$	−16.2248	+	11.0619i	−0.720568	+	0.491275i
$508$		0			0
$509$	−4.48061	−	7.76064i	−0.198599	−	0.343984i	0.749475	−	0.662032i	$-0.230306\pi$
$509$	−4.48061	−	7.76064i	−0.198599	−	0.343984i	−0.948075	+	0.318048i	$0.896973\pi$
$510$		0			0
$511$	−20.3659	+	10.2205i	−0.900933	+	0.452129i
$512$		0			0
$513$	−38.8861	−	26.5121i	−1.71687	−	1.17054i
$514$		0			0
$515$	1.74454	+	1.61870i	0.0768738	+	0.0713285i
$516$		0			0
$517$	7.33339	−	3.53157i	0.322522	−	0.155318i
$518$		0			0
$519$	−11.1343	−	5.36198i	−0.488740	−	0.235365i
$520$		0			0
$521$	21.6079	−	37.4259i	0.946658	−	1.63966i	0.194262	−	0.980950i	$-0.437769\pi$
$521$	21.6079	−	37.4259i	0.946658	−	1.63966i	0.752397	−	0.658710i	$-0.228898\pi$
$522$		0			0
$523$	9.33257	+	1.40666i	0.408085	+	0.0615089i	0.349877	−	0.936796i	$-0.386223\pi$
$523$	9.33257	+	1.40666i	0.408085	+	0.0615089i	0.0582078	+	0.998304i	$0.481461\pi$
$524$		0			0
$525$	−16.0339	+	11.3195i	−0.699775	+	0.494021i
$526$		0			0
$527$	−4.03113	−	53.7917i	−0.175599	−	2.34320i
$528$		0			0
$529$	1.90952	+	4.86539i	0.0830228	+	0.211539i
$530$		0			0
$531$	−2.64233	−	3.31338i	−0.114667	−	0.143788i
$532$		0			0
$533$	0.282690	−	0.354482i	0.0122447	−	0.0153543i
$534$		0			0
$535$	0.320036	−	4.27059i	0.0138364	−	0.184634i
$536$		0			0
$537$	5.62557	−	5.21977i	0.242761	−	0.225250i
$538$		0			0
$539$	5.19724	+	8.35929i	0.223861	+	0.360060i
$540$		0			0
$541$	29.2102	−	27.1031i	1.25585	−	1.16526i	0.276953	−	0.960883i	$-0.410675\pi$
$541$	29.2102	−	27.1031i	1.25585	−	1.16526i	0.978893	−	0.204372i	$-0.0655152\pi$
$542$		0			0
$543$	−1.67168	+	22.3070i	−0.0717386	+	0.957285i
$544$		0			0
$545$	−1.32735	+	1.66444i	−0.0568574	+	0.0712970i
$546$		0			0
$547$	18.5543	+	23.2664i	0.793326	+	0.994799i	0.999866	+	0.0163609i	$0.00520808\pi$
$547$	18.5543	+	23.2664i	0.793326	+	0.994799i	−0.206540	+	0.978438i	$0.566220\pi$
$548$		0			0
$549$	1.00098	+	2.55046i	0.0427208	+	0.108851i
$550$		0			0
$551$	2.31452	+	30.8852i	0.0986021	+	1.31575i
$552$		0			0
$553$	26.6967	−	4.47072i	1.13526	−	0.190114i
$554$		0			0
$555$	−3.91003	−	0.589342i	−0.165972	−	0.0250162i
$556$		0			0
$557$	15.7627	−	27.3017i	0.667885	−	1.15681i	−0.310609	−	0.950538i	$-0.600533\pi$
$557$	15.7627	−	27.3017i	0.667885	−	1.15681i	0.978494	−	0.206273i	$-0.0661335\pi$
$558$		0			0
$559$	1.57663	+	0.759265i	0.0666843	+	0.0321135i
$560$		0			0
$561$	12.6477	−	6.09083i	0.533988	−	0.257155i
$562$		0			0
$563$	3.43099	+	3.18349i	0.144599	+	0.134168i	0.749156	−	0.662394i	$-0.230459\pi$
$563$	3.43099	+	3.18349i	0.144599	+	0.134168i	−0.604557	+	0.796562i	$0.706650\pi$
$564$		0			0
$565$	1.95007	+	1.32954i	0.0820402	+	0.0559341i
$566$		0			0
$567$	4.18499	+	17.0480i	0.175753	+	0.715947i
$568$		0			0
$569$	−11.5923	−	20.0784i	−0.485973	−	0.841730i	0.513897	−	0.857852i	$-0.328201\pi$
$569$	−11.5923	−	20.0784i	−0.485973	−	0.841730i	−0.999870	+	0.0161216i	$0.994868\pi$
$570$		0			0
$571$	−7.89763	+	5.38451i	−0.330505	+	0.225335i	−0.717191	−	0.696877i	$-0.754572\pi$
$571$	−7.89763	+	5.38451i	−0.330505	+	0.225335i	0.386685	+	0.922212i	$0.373620\pi$
$572$		0			0
$573$	7.31763	−	32.0606i	0.305698	−	1.33935i
$574$		0			0
$575$	−5.71889	−	25.0561i	−0.238494	−	1.04491i
$576$		0			0
$577$	−6.49392	−	2.00311i	−0.270345	−	0.0833905i	0.156618	−	0.987659i	$-0.449941\pi$
$577$	−6.49392	−	2.00311i	−0.270345	−	0.0833905i	−0.426964	+	0.904269i	$0.640417\pi$
$578$		0			0
$579$	29.9559	−	9.24016i	1.24492	−	0.384008i
$580$		0			0
$581$	13.9551	+	9.18440i	0.578956	+	0.381033i
$582$		0			0
$583$	5.65294	−	14.4034i	0.234121	−	0.596530i
$584$		0			0
$585$	−0.114134	+	0.0172030i	−0.00471887	+	0.000711256i
$586$		0			0
$587$	−15.0604			−0.621609			−0.310804	−	0.950474i	$-0.600598\pi$
$587$	−15.0604			−0.621609			−0.310804	+	0.950474i	$0.600598\pi$
$588$		0			0
$589$	−69.7055			−2.87216
$590$		0			0
$591$	−7.80115	+	1.17583i	−0.320897	+	0.0483674i
$592$		0			0
$593$	−3.42593	+	8.72912i	−0.140686	+	0.358462i	−0.983799	−	0.179274i	$-0.942625\pi$
$593$	−3.42593	+	8.72912i	−0.140686	+	0.358462i	0.843113	+	0.537736i	$0.180720\pi$
$594$		0			0
$595$	6.88382	+	0.922918i	0.282209	+	0.0378359i
$596$		0			0
$597$	7.65813	−	2.36222i	0.313426	−	0.0966792i
$598$		0			0
$599$	−8.50443	−	2.62327i	−0.347482	−	0.107184i	0.116101	−	0.993237i	$-0.462960\pi$
$599$	−8.50443	−	2.62327i	−0.347482	−	0.107184i	−0.463583	+	0.886053i	$0.653436\pi$
$600$		0			0
$601$	5.92646	+	25.9655i	0.241745	+	1.05916i	0.939427	+	0.342748i	$0.111358\pi$
$601$	5.92646	+	25.9655i	0.241745	+	1.05916i	−0.697682	+	0.716407i	$0.745785\pi$
$602$		0			0
$603$	1.21961	−	5.34348i	0.0496665	−	0.217603i
$604$		0			0
$605$	3.00620	−	2.04959i	0.122219	−	0.0833277i
$606$		0			0
$607$	9.14071	+	15.8322i	0.371010	+	0.642608i	0.989721	−	0.143011i	$-0.0456783\pi$
$607$	9.14071	+	15.8322i	0.371010	+	0.642608i	−0.618711	+	0.785618i	$0.712345\pi$
$608$		0			0
$609$	9.12195	−	11.8296i	0.369640	−	0.479361i
$610$		0			0
$611$	2.11158	+	1.43965i	0.0854254	+	0.0582420i
$612$		0			0
$613$	7.68761	+	7.13306i	0.310500	+	0.288102i	0.819994	−	0.572373i	$-0.193977\pi$
$613$	7.68761	+	7.13306i	0.310500	+	0.288102i	−0.509494	+	0.860474i	$0.670167\pi$
$614$		0			0
$615$	0.572155	−	0.275535i	0.0230715	−	0.0111107i
$616$		0			0
$617$	−30.5676	−	14.7206i	−1.23061	−	0.592629i	−0.298361	−	0.954453i	$-0.596440\pi$
$617$	−30.5676	−	14.7206i	−1.23061	−	0.592629i	−0.932246	+	0.361824i	$0.882154\pi$
$618$		0			0
$619$	13.5713	−	23.5062i	0.545478	−	0.944795i	−0.453099	−	0.891460i	$-0.649682\pi$
$619$	13.5713	−	23.5062i	0.545478	−	0.944795i	0.998577	−	0.0533348i	$-0.0169850\pi$
$620$		0			0
$621$	−29.3923	−	4.43017i	−1.17947	−	0.177777i
$622$		0			0
$623$	0.380953	−	6.50726i	0.0152625	−	0.260708i
$624$		0			0
$625$	1.68795	+	22.5241i	0.0675179	+	0.900964i
$626$		0			0
$627$	−6.62731	−	16.8861i	−0.264669	−	0.674366i
$628$		0			0
$629$	−25.9532	−	32.5443i	−1.03482	−	1.29763i
$630$		0			0
$631$	−6.67656	+	8.37214i	−0.265790	+	0.333290i	−0.896760	−	0.442517i	$-0.854086\pi$
$631$	−6.67656	+	8.37214i	−0.265790	+	0.333290i	0.630970	+	0.775807i	$0.282657\pi$
$632$		0			0
$633$	−2.53042	+	33.7661i	−0.100575	+	1.34208i
$634$		0			0
$635$	0.362613	−	0.336456i	0.0143899	−	0.0133519i
$636$		0			0
$637$	−1.45711	+	2.72556i	−0.0577330	+	0.107991i
$638$		0			0
$639$	−6.12267	+	5.68100i	−0.242209	+	0.224737i
$640$		0			0
$641$	1.86964	−	24.9486i	0.0738463	−	0.985410i	−0.830059	−	0.557676i	$-0.811693\pi$
$641$	1.86964	−	24.9486i	0.0738463	−	0.985410i	0.903905	−	0.427734i	$-0.140688\pi$
$642$		0			0
$643$	7.67367	−	9.62248i	0.302620	−	0.379474i	−0.607149	−	0.794588i	$-0.707687\pi$
$643$	7.67367	−	9.62248i	0.302620	−	0.379474i	0.909769	+	0.415114i	$0.136258\pi$
$644$		0			0
$645$	1.52817	+	1.91626i	0.0601716	+	0.0754528i
$646$		0			0
$647$	9.77804	+	24.9140i	0.384414	+	0.979472i	0.983841	+	0.179043i	$0.0573000\pi$
$647$	9.77804	+	24.9140i	0.384414	+	0.979472i	−0.599427	+	0.800430i	$0.704605\pi$
$648$		0			0
$649$	−0.686944	−	9.16663i	−0.0269649	−	0.359822i
$650$		0			0
$651$	25.0153	+	22.4622i	0.980427	+	0.880362i
$652$		0			0
$653$	27.9398	+	4.21124i	1.09337	+	0.164799i	0.670877	−	0.741569i	$-0.265918\pi$
$653$	27.9398	+	4.21124i	1.09337	+	0.164799i	0.422490	+	0.906367i	$0.361156\pi$
$654$		0			0
$655$	0.666469	−	1.15436i	0.0260411	−	0.0451045i
$656$		0			0
$657$	5.03050	+	2.42256i	0.196258	+	0.0945130i
$658$		0			0
$659$	22.1915	−	10.6869i	0.864459	−	0.416302i	0.0515351	−	0.998671i	$-0.483589\pi$
$659$	22.1915	−	10.6869i	0.864459	−	0.416302i	0.812924	+	0.582370i	$0.197874\pi$
$660$		0			0
$661$	−27.1359	−	25.1784i	−1.05546	−	0.979326i	−0.0556456	−	0.998451i	$-0.517722\pi$
$661$	−27.1359	−	25.1784i	−1.05546	−	0.979326i	−0.999817	+	0.0191243i	$0.993912\pi$
$662$		0			0
$663$	3.64180	+	2.48294i	0.141436	+	0.0964292i
$664$		0			0
$665$	1.85403	−	8.78140i	0.0718962	−	0.340528i
$666$		0			0
$667$	9.78044	+	16.9402i	0.378700	+	0.655928i
$668$		0			0
$669$	−2.45675	+	1.67499i	−0.0949836	+	0.0647587i
$670$		0			0
$671$	−1.32241	+	5.79385i	−0.0510510	+	0.223669i
$672$		0			0
$673$	10.7101	+	46.9240i	0.412844	+	1.80879i	0.570505	+	0.821294i	$0.306748\pi$
$673$	10.7101	+	46.9240i	0.412844	+	1.80879i	−0.157660	+	0.987493i	$0.550395\pi$
$674$		0			0
$675$	25.8616	+	7.97726i	0.995415	+	0.307045i
$676$		0			0
$677$	−18.9609	+	5.84866i	−0.728727	+	0.224782i	−0.636850	−	0.770988i	$-0.719763\pi$
$677$	−18.9609	+	5.84866i	−0.728727	+	0.224782i	−0.0918770	+	0.995770i	$0.529287\pi$
$678$		0			0
$679$	−0.642061	+	1.71788i	−0.0246400	+	0.0659263i
$680$		0			0
$681$	−6.75050	+	17.2000i	−0.258680	+	0.659105i
$682$		0			0
$683$	7.52385	−	1.13404i	0.287892	−	0.0433928i	−0.00350850	−	0.999994i	$-0.501117\pi$
$683$	7.52385	−	1.13404i	0.287892	−	0.0433928i	0.291401	+	0.956601i	$0.405879\pi$
$684$		0			0
$685$	−4.71926			−0.180314
$686$		0			0
$687$	−22.0424			−0.840968
$688$		0			0
$689$	4.80402	−	0.724089i	0.183019	−	0.0275856i
$690$		0			0
$691$	−7.62823	+	19.4364i	−0.290191	+	0.739396i	0.709217	+	0.704991i	$0.249049\pi$
$691$	−7.62823	+	19.4364i	−0.290191	+	0.739396i	−0.999408	+	0.0344051i	$0.989046\pi$
$692$		0			0
$693$	0.844401	−	2.25926i	0.0320761	−	0.0858222i
$694$		0			0
$695$	−4.17950	+	1.28920i	−0.158537	+	0.0489023i
$696$		0			0
$697$	6.38810	+	1.97047i	0.241966	+	0.0746367i
$698$		0			0
$699$	−7.08891	−	31.0585i	−0.268127	−	1.17474i
$700$		0			0
$701$	5.08613	−	22.2838i	0.192100	−	0.841647i	−0.783377	−	0.621547i	$-0.786504\pi$
$701$	5.08613	−	22.2838i	0.192100	−	0.841647i	0.975477	−	0.220100i	$-0.0706384\pi$
$702$		0			0
$703$	−44.4430	+	30.3007i	−1.67620	+	1.14281i
$704$		0			0
$705$	1.78976	+	3.09995i	0.0674061	+	0.116751i
$706$		0			0
$707$	3.97653	−	18.8344i	0.149553	−	0.708339i
$708$		0			0
$709$	−2.61602	−	1.78358i	−0.0982469	−	0.0669836i	0.513200	−	0.858269i	$-0.328460\pi$
$709$	−2.61602	−	1.78358i	−0.0982469	−	0.0669836i	−0.611447	+	0.791285i	$0.709412\pi$
$710$		0			0
$711$	−4.86207	−	4.51134i	−0.182342	−	0.169189i
$712$		0			0
$713$	−39.6642	+	19.1013i	−1.48544	+	0.715348i
$714$		0			0
$715$	−0.225565	−	0.108626i	−0.00843566	−	0.00406240i
$716$		0			0
$717$	−15.3368	+	26.5641i	−0.572763	+	0.992055i
$718$		0			0
$719$	−0.938530	−	0.141461i	−0.0350012	−	0.00527559i	0.131518	−	0.991314i	$-0.458015\pi$
$719$	−0.938530	−	0.141461i	−0.0350012	−	0.00527559i	−0.166520	+	0.986038i	$0.553253\pi$
$720$		0			0
$721$	−11.6178	−	10.4321i	−0.432671	−	0.388512i
$722$		0			0
$723$	−0.473564	−	6.31928i	−0.0176120	−	0.235016i
$724$		0			0
$725$	−6.50680	−	16.5791i	−0.241657	−	0.615731i
$726$		0			0
$727$	5.90889	+	7.40951i	0.219148	+	0.274803i	0.879237	−	0.476384i	$-0.158053\pi$
$727$	5.90889	+	7.40951i	0.219148	+	0.274803i	−0.660089	+	0.751188i	$0.729481\pi$
$728$		0			0
$729$	18.7299	−	23.4866i	0.693701	−	0.869873i
$730$		0			0
$731$	−1.92815	+	25.7294i	−0.0713153	+	0.951637i
$732$		0			0
$733$	24.3059	−	22.5526i	0.897758	−	0.832998i	−0.0888605	−	0.996044i	$-0.528323\pi$
$733$	24.3059	−	22.5526i	0.897758	−	0.832998i	0.986618	+	0.163047i	$0.0521321\pi$
$734$		0			0
$735$	−3.49511	+	2.55394i	−0.128919	+	0.0942036i
$736$		0			0
$737$	8.71473	−	8.08609i	0.321011	−	0.297855i
$738$		0			0
$739$	1.82028	−	24.2899i	0.0669601	−	0.893520i	−0.858047	−	0.513571i	$-0.828322\pi$
$739$	1.82028	−	24.2899i	0.0669601	−	0.893520i	0.925007	−	0.379949i	$-0.124059\pi$
$740$		0			0
$741$	3.55120	−	4.45307i	0.130457	−	0.163587i
$742$		0			0
$743$	−1.22787	−	1.53970i	−0.0450460	−	0.0564859i	0.758798	−	0.651326i	$-0.225787\pi$
$743$	−1.22787	−	1.53970i	−0.0450460	−	0.0564859i	−0.803844	+	0.594840i	$0.797215\pi$
$744$		0			0
$745$	2.70254	+	6.88595i	0.0990132	+	0.252282i
$746$		0			0
$747$	−0.305912	−	4.08211i	−0.0111927	−	0.149357i
$748$		0			0
$749$	−1.64213	+	28.0500i	−0.0600019	+	1.02493i
$750$		0			0
$751$	27.5074	+	4.14607i	1.00376	+	0.151292i	0.630298	−	0.776354i	$-0.282933\pi$
$751$	27.5074	+	4.14607i	1.00376	+	0.151292i	0.373461	+	0.927646i	$0.378171\pi$
$752$		0			0
$753$	14.8954	−	25.7996i	0.542818	−	0.940189i
$754$		0			0
$755$	4.21322	+	2.02898i	0.153335	+	0.0738421i
$756$		0			0
$757$	11.7753	−	5.67068i	0.427980	−	0.206104i	−0.207478	−	0.978240i	$-0.566526\pi$
$757$	11.7753	−	5.67068i	0.427980	−	0.206104i	0.635458	+	0.772135i	$0.280811\pi$
$758$		0			0
$759$	−8.39838	−	7.79256i	−0.304842	−	0.282852i
$760$		0			0
$761$	−1.21595	−	0.829020i	−0.0440781	−	0.0300520i	0.541081	−	0.840971i	$-0.318015\pi$
$761$	−1.21595	−	0.829020i	−0.0440781	−	0.0300520i	−0.585159	+	0.810919i	$0.698968\pi$
$762$		0			0
$763$	8.52937	−	11.0612i	0.308784	−	0.400442i
$764$		0			0
$765$	−0.850923	−	1.47384i	−0.0307652	−	0.0532869i
$766$		0			0
$767$	2.38473	−	1.62588i	0.0861075	−	0.0587071i
$768$		0			0
$769$	1.93322	−	8.46998i	0.0697136	−	0.305435i	−0.928036	−	0.372491i	$-0.878504\pi$
$769$	1.93322	−	8.46998i	0.0697136	−	0.305435i	0.997749	+	0.0670563i	$0.0213607\pi$
$770$		0			0
$771$	8.82084	+	38.6466i	0.317675	+	1.39182i
$772$		0			0
$773$	22.8028	+	7.03374i	0.820161	+	0.252986i	0.676314	−	0.736614i	$-0.263576\pi$
$773$	22.8028	+	7.03374i	0.820161	+	0.252986i	0.143847	+	0.989600i	$0.454053\pi$
$774$		0			0
$775$	38.3031	−	11.8149i	1.37589	−	0.424405i
$776$		0			0
$777$	25.7135	+	3.44743i	0.922468	+	0.123676i
$778$		0			0
$779$	3.15604	−	8.04145i	0.113077	−	0.288115i
$780$		0			0
$781$	−17.9141	+	2.70012i	−0.641018	+	0.0966179i
$782$		0			0
$783$	−20.5987			−0.736137
$784$		0			0
$785$	8.25592			0.294666
$786$		0			0
$787$	−38.5373	+	5.80856i	−1.37371	+	0.207053i	−0.794072	−	0.607824i	$-0.792043\pi$
$787$	−38.5373	+	5.80856i	−1.37371	+	0.207053i	−0.579634	+	0.814877i	$0.696805\pi$
$788$		0			0
$789$	−11.3042	+	28.8028i	−0.402442	+	1.02541i
$790$		0			0
$791$	−12.9352	−	8.51313i	−0.459922	−	0.302692i
$792$		0			0
$793$	−1.78306	+	0.550001i	−0.0633183	+	0.0195311i
$794$		0			0
$795$	6.50232	+	2.00570i	0.230614	+	0.0711349i
$796$		0			0
$797$	9.21253	+	40.3627i	0.326325	+	1.42972i	0.826079	+	0.563554i	$0.190566\pi$
$797$	9.21253	+	40.3627i	0.326325	+	1.42972i	−0.499755	+	0.866167i	$0.666576\pi$
$798$		0			0
$799$	−8.38492	+	36.7367i	−0.296637	+	1.29965i
$800$		0			0
$801$	−1.31968	+	0.899743i	−0.0466286	+	0.0317909i
$802$		0			0
$803$	6.05535	+	10.4882i	0.213689	+	0.370119i
$804$		0			0
$805$	−1.35136	−	5.50490i	−0.0476292	−	0.194022i
$806$		0			0
$807$	34.6093	+	23.5963i	1.21831	+	0.830627i
$808$		0			0
$809$	−10.0710	−	9.34455i	−0.354079	−	0.328537i	0.482999	−	0.875621i	$-0.339547\pi$
$809$	−10.0710	−	9.34455i	−0.354079	−	0.328537i	−0.837078	+	0.547084i	$0.815738\pi$
$810$		0			0
$811$	18.7641	−	9.03630i	0.658896	−	0.317307i	−0.0743888	−	0.997229i	$-0.523701\pi$
$811$	18.7641	−	9.03630i	0.658896	−	0.317307i	0.733285	+	0.679922i	$0.237986\pi$
$812$		0			0
$813$	−42.8003	−	20.6115i	−1.50107	−	0.722878i
$814$		0			0
$815$	0.514721	−	0.891523i	0.0180299	−	0.0312287i
$816$		0			0
$817$	32.9688	+	4.96925i	1.15343	+	0.173852i
$818$		0			0
$819$	0.746897	−	0.125078i	0.0260987	−	0.00437057i
$820$		0			0
$821$	3.54655	+	47.3254i	0.123775	+	1.65167i	0.620828	+	0.783947i	$0.286797\pi$
$821$	3.54655	+	47.3254i	0.123775	+	1.65167i	−0.497053	+	0.867720i	$0.665584\pi$
$822$		0			0
$823$	9.84217	+	25.0775i	0.343077	+	0.874145i	0.993422	+	0.114507i	$0.0365287\pi$
$823$	9.84217	+	25.0775i	0.343077	+	0.874145i	−0.650346	+	0.759638i	$0.725376\pi$
$824$		0			0
$825$	6.50386	+	8.15558i	0.226435	+	0.283941i
$826$		0			0
$827$	28.8554	−	36.1835i	1.00340	−	1.25822i	0.0375040	−	0.999296i	$-0.488059\pi$
$827$	28.8554	−	36.1835i	1.00340	−	1.25822i	0.965897	−	0.258928i	$-0.0833693\pi$
$828$		0			0
$829$	−0.0884937	+	1.18087i	−0.00307351	+	0.0410132i	−0.998530	−	0.0542077i	$-0.982737\pi$
$829$	−0.0884937	+	1.18087i	−0.00307351	+	0.0410132i	0.995456	+	0.0952209i	$0.0303557\pi$
$830$		0			0
$831$	−15.4058	+	14.2945i	−0.534420	+	0.495869i
$832$		0			0
$833$	−45.2578	−	5.31725i	−1.56809	−	0.184232i
$834$		0			0
$835$	−3.70125	+	3.43426i	−0.128087	+	0.118848i
$836$		0			0
$837$	3.46446	−	46.2300i	0.119749	−	1.59794i
$838$		0			0
$839$	−10.2114	+	12.8047i	−0.352537	+	0.442068i	−0.926205	−	0.377020i	$-0.876949\pi$
$839$	−10.2114	+	12.8047i	−0.352537	+	0.442068i	0.573668	+	0.819088i	$0.305520\pi$
$840$		0			0
$841$	−9.62947	−	12.0750i	−0.332051	−	0.416378i
$842$		0			0
$843$	−17.3813	−	44.2868i	−0.598644	−	1.52532i
$844$		0			0
$845$	0.385882	+	5.14923i	0.0132747	+	0.177139i
$846$		0			0
$847$	−19.5016	+	13.7676i	−0.670084	+	0.473060i
$848$		0			0
$849$	−47.9768	−	7.23134i	−1.64656	−	0.248179i
$850$		0			0
$851$	−16.9859	+	29.4205i	−0.582271	+	1.00852i
$852$		0			0
$853$	39.6712	+	19.1046i	1.35832	+	0.654131i	0.964261	−	0.264956i	$-0.0853574\pi$
$853$	39.6712	+	19.1046i	1.35832	+	0.654131i	0.394056	+	0.919086i	$0.371072\pi$
$854$		0			0
$855$	−1.98137	+	0.954178i	−0.0677615	+	0.0326322i
$856$		0			0
$857$	−5.55267	−	5.15212i	−0.189675	−	0.175993i	0.579619	−	0.814888i	$-0.303201\pi$
$857$	−5.55267	−	5.15212i	−0.189675	−	0.175993i	−0.769294	+	0.638895i	$0.779392\pi$
$858$		0			0
$859$	16.3222	+	11.1283i	0.556907	+	0.379693i	0.808819	−	0.588057i	$-0.200107\pi$
$859$	16.3222	+	11.1283i	0.556907	+	0.379693i	−0.251912	+	0.967750i	$0.581059\pi$
$860$		0			0
$861$	−3.72392	+	1.86883i	−0.126911	+	0.0636896i
$862$		0			0
$863$	−11.7008	−	20.2663i	−0.398299	−	0.689874i	0.595217	−	0.803565i	$-0.297066\pi$
$863$	−11.7008	−	20.2663i	−0.398299	−	0.689874i	−0.993516	+	0.113691i	$0.963733\pi$
$864$		0			0
$865$	−2.68499	+	1.83059i	−0.0912923	+	0.0622420i
$866$		0			0
$867$	−8.66018	+	37.9427i	−0.294115	+	1.28860i
$868$		0			0
$869$	−3.20129	−	14.0258i	−0.108596	−	0.475792i
$870$		0			0
$871$	3.56689	+	1.10024i	0.120860	+	0.0372802i
$872$		0			0
$873$	0.429411	−	0.132456i	0.0145334	−	0.00448295i
$874$		0			0
$875$	0.955071	+	10.4520i	0.0322873	+	0.353343i
$876$		0			0
$877$	3.75483	−	9.56715i	0.126792	−	0.323060i	−0.853356	−	0.521329i	$-0.825437\pi$
$877$	3.75483	−	9.56715i	0.126792	−	0.323060i	0.980148	+	0.198269i	$0.0635319\pi$
$878$		0			0
$879$	−7.15276	+	1.07811i	−0.241257	+	0.0363636i
$880$		0			0
$881$	−35.8408			−1.20751			−0.603754	−	0.797171i	$-0.706329\pi$
$881$	−35.8408			−1.20751			−0.603754	+	0.797171i	$0.706329\pi$
$882$		0			0
$883$	17.3715			0.584596			0.292298	−	0.956327i	$-0.405580\pi$
$883$	17.3715			0.584596			0.292298	+	0.956327i	$0.405580\pi$
$884$		0			0
$885$	3.99740	−	0.602510i	0.134371	−	0.0202532i
$886$		0			0
$887$	10.0573	−	25.6257i	0.337693	−	0.860427i	−0.656649	−	0.754196i	$-0.728027\pi$
$887$	10.0573	−	25.6257i	0.337693	−	0.860427i	0.994342	−	0.106230i	$-0.0338781\pi$
$888$		0			0
$889$	−2.34277	+	2.24604i	−0.0785739	+	0.0753298i
$890$		0			0
$891$	8.91525	−	2.74999i	0.298672	−	0.0921281i
$892$		0			0
$893$	46.5294	+	14.3524i	1.55705	+	0.480285i
$894$		0			0
$895$	−0.449043	−	1.96739i	−0.0150098	−	0.0657624i
$896$		0			0
$897$	0.800458	−	3.50704i	0.0267265	−	0.117097i
$898$		0			0
$899$	−25.2071	+	17.1859i	−0.840703	+	0.573182i
$900$		0			0
$901$	35.8161	+	62.0354i	1.19321	+	2.06670i
$902$		0			0
$903$	−10.2303	−	12.4073i	−0.340442	−	0.412890i
$904$		0			0
$905$	4.86013	+	3.31358i	0.161556	+	0.110147i
$906$		0			0
$907$	2.34689	+	2.17759i	0.0779270	+	0.0723057i	0.718175	−	0.695863i	$-0.244978\pi$
$907$	2.34689	+	2.17759i	0.0779270	+	0.0723057i	−0.640248	+	0.768169i	$0.721168\pi$
$908$		0			0
$909$	−4.24965	+	2.04652i	−0.140952	+	0.0678789i
$910$		0			0
$911$	28.9643	+	13.9485i	0.959631	+	0.462134i	0.847053	−	0.531509i	$-0.178375\pi$
$911$	28.9643	+	13.9485i	0.959631	+	0.462134i	0.112579	+	0.993643i	$0.464089\pi$
$912$		0			0
$913$	4.43955	−	7.68953i	0.146928	−	0.254486i
$914$		0			0
$915$	−2.58432	−	0.389523i	−0.0854349	−	0.0128772i
$916$		0			0
$917$	−4.24852	+	7.64415i	−0.140298	+	0.252432i
$918$		0			0
$919$	2.16230	+	28.8539i	0.0713278	+	0.951803i	0.911982	+	0.410231i	$0.134552\pi$
$919$	2.16230	+	28.8539i	0.0713278	+	0.951803i	−0.840654	+	0.541573i	$0.817829\pi$
$920$		0			0
$921$	−4.01493	−	10.2299i	−0.132297	−	0.337086i
$922$		0			0
$923$	−3.54658	−	4.44727i	−0.116737	−	0.146384i
$924$		0			0
$925$	19.2855	−	24.1832i	0.634102	−	0.795139i
$926$		0			0
$927$	−0.285915	+	3.81528i	−0.00939069	+	0.125310i
$928$		0			0
$929$	−10.9198	+	10.1321i	−0.358267	+	0.332423i	−0.838685	−	0.544616i	$-0.816675\pi$
$929$	−10.9198	+	10.1321i	−0.358267	+	0.332423i	0.480418	+	0.877040i	$0.340485\pi$
$930$		0			0
$931$	−11.2223	+	57.8059i	−0.367795	+	1.89451i
$932$		0			0
$933$	1.93547	−	1.79585i	0.0633645	−	0.0587936i
$934$		0			0
$935$	0.275857	−	3.68105i	0.00902149	−	0.120383i
$936$		0			0
$937$	−31.8518	+	39.9409i	−1.04055	+	1.30481i	−0.0894329	+	0.995993i	$0.528505\pi$
$937$	−31.8518	+	39.9409i	−1.04055	+	1.30481i	−0.951121	+	0.308820i	$0.900066\pi$
$938$		0			0
$939$	−9.22091	−	11.5627i	−0.300913	−	0.377333i
$940$		0			0
$941$	−5.60138	−	14.2721i	−0.182600	−	0.465257i	0.810038	−	0.586377i	$-0.199446\pi$
$941$	−5.60138	−	14.2721i	−0.182600	−	0.465257i	−0.992638	+	0.121121i	$0.961351\pi$
$942$		0			0
$943$	−0.407719	−	5.44063i	−0.0132772	−	0.177171i
$944$		0			0
$945$	5.73185	+	1.66608i	0.186457	+	0.0541975i
$946$		0			0
$947$	4.57968	+	0.690276i	0.148820	+	0.0224310i	0.223030	−	0.974812i	$-0.428405\pi$
$947$	4.57968	+	0.690276i	0.148820	+	0.0224310i	−0.0742098	+	0.997243i	$0.523643\pi$
$948$		0			0
$949$	−1.90128	+	3.29311i	−0.0617181	+	0.106899i
$950$		0			0
$951$	−11.1757	−	5.38192i	−0.362396	−	0.174521i
$952$		0			0
$953$	−53.0768	+	25.5604i	−1.71933	+	0.827984i	−0.729794	+	0.683667i	$0.760384\pi$
$953$	−53.0768	+	25.5604i	−1.71933	+	0.827984i	−0.989532	+	0.144317i	$0.953902\pi$
$954$		0			0
$955$	−6.33898	−	5.88171i	−0.205125	−	0.190328i
$956$		0			0
$957$	−6.55986	−	4.47244i	−0.212050	−	0.144573i
$958$		0			0
$959$	30.9591	−	0.505416i	0.999722	−	0.0163207i
$960$		0			0
$961$	−18.8311	−	32.6164i	−0.607455	−	1.05214i
$962$		0			0
$963$	5.68858	−	3.87841i	0.183312	−	0.124980i
$964$		0			0
$965$	1.83432	−	8.03666i	0.0590487	−	0.258709i
$966$		0			0
$967$	13.2671	+	58.1271i	0.426642	+	1.86924i	0.490755	+	0.871297i	$0.336721\pi$
$967$	13.2671	+	58.1271i	0.426642	+	1.86924i	−0.0641134	+	0.997943i	$0.520422\pi$
$968$		0			0
$969$	80.2483	+	24.7533i	2.57795	+	0.795191i
$970$		0			0
$971$	12.7435	−	3.93084i	0.408958	−	0.126147i	−0.0834487	−	0.996512i	$-0.526593\pi$
$971$	12.7435	−	3.93084i	0.408958	−	0.126147i	0.492407	+	0.870365i	$0.336117\pi$
$972$		0			0
$973$	27.2801	−	8.90499i	0.874559	−	0.285481i
$974$		0			0
$975$	−1.19659	+	3.04887i	−0.0383217	+	0.0976421i
$976$		0			0
$977$	−24.3607	+	3.67179i	−0.779369	+	0.117471i	−0.526665	−	0.850073i	$-0.676558\pi$
$977$	−24.3607	+	3.67179i	−0.779369	+	0.117471i	−0.252704	+	0.967544i	$0.581320\pi$
$978$		0			0
$979$	−3.46443			−0.110724
$980$		0			0
$981$	−3.42256			−0.109274
$982$		0			0
$983$	−22.3623	+	3.37057i	−0.713245	+	0.107504i	−0.495634	−	0.868531i	$-0.665064\pi$
$983$	−22.3623	+	3.37057i	−0.713245	+	0.107504i	−0.217611	+	0.976036i	$0.569826\pi$
$984$		0			0
$985$	−0.757915	+	1.93114i	−0.0241492	+	0.0615311i
$986$		0			0
$987$	−12.0731	−	20.1445i	−0.384291	−	0.641206i
$988$		0			0
$989$	20.1218	−	6.20676i	0.639837	−	0.197364i
$990$		0			0
$991$	−52.2037	−	16.1027i	−1.65830	−	0.511519i	−0.682633	−	0.730761i	$-0.739165\pi$
$991$	−52.2037	−	16.1027i	−1.65830	−	0.511519i	−0.975670	+	0.219242i	$0.929642\pi$
$992$		0			0
$993$	9.40885	+	41.2229i	0.298581	+	1.30817i
$994$		0			0
$995$	0.468937	−	2.05455i	0.0148663	−	0.0651336i
$996$		0			0
$997$	−17.2173	+	11.7386i	−0.545277	+	0.371764i	−0.804407	−	0.594079i	$-0.797517\pi$
$997$	−17.2173	+	11.7386i	−0.545277	+	0.371764i	0.259130	+	0.965843i	$0.416564\pi$
$998$		0			0
$999$	−17.8871	−	30.9814i	−0.565924	−	0.980209i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.y.a.305.3	yes	84
4.3	odd	2		784.2.bg.f.305.5		84
49.9	even	21	inner	392.2.y.a.9.3	✓	84
196.107	odd	42		784.2.bg.f.401.5		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.y.a.9.3	✓	84	49.9	even	21	inner
392.2.y.a.305.3	yes	84	1.1	even	1	trivial
784.2.bg.f.305.5		84	4.3	odd	2
784.2.bg.f.401.5		84	196.107	odd	42

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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	392.2.y.a.305.3

Level	$392$
Weight	$2$
Character	392.305
Analytic conductor	$3.130$
Analytic rank	$0$
Dimension	$84$
Inner twists	$2$