LMFDB - Embedded newform 392.2.y.a.9.3

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			9.3
Character	$\chi$	$=$	392.9
Dual form			392.2.y.a.305.3

$q$-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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

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

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	−0.304104	−	0.952639i	$-0.598357\pi$
$3$	−1.51640	−	0.228560i	−0.875494	−	0.131959i	−0.571389	+	0.820679i	$0.693595\pi$
$4$		0			0
$5$	−0.147325	−	0.375377i	−0.0658856	−	0.167874i	0.894139	−	0.447790i	$-0.147789\pi$
$5$	−0.147325	−	0.375377i	−0.0658856	−	0.167874i	−0.960025	+	0.279916i	$0.909693\pi$
$6$		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	−0.490627	−	0.871370i	$-0.663232\pi$
$11$	−1.34370	+	0.414477i	−0.405141	+	0.124970i	0.0854853	+	0.996339i	$0.472756\pi$
$12$		0			0
$13$	−0.0982465	+	0.430446i	−0.0272487	+	0.119384i	−0.986723	−	0.162411i	$-0.948073\pi$
$13$	−0.0982465	+	0.430446i	−0.0272487	+	0.119384i	0.959474	+	0.281796i	$0.0909300\pi$
$14$		0			0
$15$	0.137607	+	0.602894i	0.0355299	+	0.155667i
$16$		0			0
$17$	5.37871	+	3.66714i	1.30453	+	0.889412i	0.998047	−	0.0624646i	$-0.0198961\pi$
$17$	5.37871	+	3.66714i	1.30453	+	0.889412i	0.306481	+	0.951877i	$0.400848\pi$
$18$		0			0
$19$	−4.20609	+	7.28515i	−0.964942	+	1.67133i	−0.255172	+	0.966896i	$0.582132\pi$
$19$	−4.20609	+	7.28515i	−0.964942	+	1.67133i	−0.709771	+	0.704433i	$0.751201\pi$
$20$		0			0
$21$	−0.838153	−	3.96982i	−0.182900	−	0.866285i
$22$		0			0
$23$	−4.38971	+	2.99285i	−0.915317	+	0.624053i	−0.926667	−	0.375883i	$-0.877340\pi$
$23$	−4.38971	+	2.99285i	−0.915317	+	0.624053i	0.0113499	+	0.999936i	$0.496387\pi$
$24$		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	−0.715737	−	0.698370i	$-0.753909\pi$
$29$	−3.31717	+	1.59747i	−0.615983	+	0.296642i	0.0997533	+	0.995012i	$0.468195\pi$
$30$		0			0
$31$	4.14313	+	7.17612i	0.744129	+	1.28887i	0.950601	+	0.310416i	$0.100468\pi$
$31$	4.14313	+	7.17612i	0.744129	+	1.28887i	−0.206472	+	0.978452i	$0.566198\pi$
$32$		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	0.809072	+	0.587710i	$0.199970\pi$
$37$	−0.477843	+	6.37637i	−0.0785569	+	1.04827i	−0.887629	+	0.460559i	$0.847649\pi$
$38$		0			0
$39$	0.247364	−	0.630273i	0.0396099	−	0.100924i
$40$		0			0
$41$	0.640272	−	0.802876i	0.0999937	−	0.125388i	−0.729317	−	0.684176i	$-0.760162\pi$
$41$	0.640272	−	0.802876i	0.0999937	−	0.125388i	0.829311	+	0.558788i	$0.188733\pi$
$42$		0			0
$43$	−2.47117	−	3.09875i	−0.376850	−	0.472555i	0.556849	−	0.830614i	$-0.312010\pi$
$43$	−2.47117	−	3.09875i	−0.376850	−	0.472555i	−0.933699	+	0.358059i	$0.883439\pi$
$44$		0			0
$45$	0.0195364	+	0.260695i	0.00291231	+	0.0388621i
$46$		0			0
$47$	−4.24317	−	3.93709i	−0.618930	−	0.574283i	0.307126	−	0.951669i	$-0.400633\pi$
$47$	−4.24317	−	3.93709i	−0.618930	−	0.574283i	−0.926056	+	0.377386i	$0.876823\pi$
$48$		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	−0.709525	−	0.704681i	$-0.751090\pi$
$53$	−0.822303	−	10.9729i	−0.112952	−	1.50724i	0.596573	−	0.802559i	$-0.296529\pi$
$54$		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	−0.686925	−	0.726728i	$-0.741040\pi$
$59$	2.38828	−	6.08524i	0.310928	−	0.792230i	0.997852	−	0.0655020i	$-0.0208649\pi$
$60$		0			0
$61$	−0.315828	+	4.21444i	−0.0404377	+	0.539603i	0.939793	+	0.341745i	$0.111018\pi$
$61$	−0.315828	+	4.21444i	−0.0404377	+	0.539603i	−0.980231	+	0.197859i	$0.936601\pi$
$62$		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	−0.999818	−	0.0190783i	$-0.993927\pi$
$67$	−4.22717	−	7.32168i	−0.516431	−	0.894485i	0.483387	−	0.875407i	$-0.339407\pi$
$68$		0			0
$69$	7.34060	−	3.53505i	0.883704	−	0.425569i
$70$		0			0
$71$	11.6077	+	5.58995i	1.37757	+	0.663405i	0.968481	−	0.249087i	$-0.0801307\pi$
$71$	11.6077	+	5.58995i	1.37757	+	0.663405i	0.409094	+	0.912492i	$0.365845\pi$
$72$		0			0
$73$	−6.31342	+	5.85799i	−0.738929	+	0.685626i	−0.956929	−	0.290323i	$-0.906237\pi$
$73$	−6.31342	+	5.85799i	−0.738929	+	0.685626i	0.217999	+	0.975949i	$0.430047\pi$
$74$		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	−0.420449	−	0.907316i	$-0.638127\pi$
$79$	5.11546	−	8.86024i	0.575535	−	0.996855i	0.995983	−	0.0895390i	$-0.0285394\pi$
$80$		0			0
$81$	−5.48196	−	3.73754i	−0.609107	−	0.415282i
$82$		0			0
$83$	−1.40508	−	6.15605i	−0.154227	−	0.675715i	−0.991628	−	0.129125i	$-0.958783\pi$
$83$	−1.40508	−	6.15605i	−0.154227	−	0.675715i	0.837401	−	0.546589i	$-0.184074\pi$
$84$		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	0.417007	−	0.908903i	$-0.363079\pi$
$89$	2.35427	+	0.726195i	0.249552	+	0.0769765i	−0.167456	+	0.985880i	$0.553555\pi$
$90$		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	0.496869	−	0.867825i	$-0.334483\pi$
$101$	7.19439	+	1.08438i	0.715868	+	0.107900i	0.218999	+	0.975725i	$0.429721\pi$
$102$		0			0
$103$	2.15610	+	5.49366i	0.212447	+	0.541306i	0.996882	−	0.0789048i	$-0.0251423\pi$
$103$	2.15610	+	5.49366i	0.212447	+	0.541306i	−0.784435	+	0.620211i	$0.787047\pi$
$104$		0			0
$105$	−1.36670	+	0.899475i	−0.133376	+	0.0877798i
$106$		0			0
$107$	−10.1482	−	3.13032i	−0.981068	−	0.302619i	−0.237579	−	0.971368i	$-0.576354\pi$
$107$	−10.1482	−	3.13032i	−0.981068	−	0.302619i	−0.743488	+	0.668749i	$0.766830\pi$
$108$		0			0
$109$	5.04479	−	1.55611i	0.483203	−	0.149049i	−0.0435767	−	0.999050i	$-0.513875\pi$
$109$	5.04479	−	1.55611i	0.483203	−	0.149049i	0.526780	+	0.850002i	$0.323399\pi$
$110$		0			0
$111$	2.18199	−	9.55991i	0.207105	−	0.907386i
$112$		0			0
$113$	1.30238	+	5.70612i	0.122518	+	0.536787i	0.998515	+	0.0544707i	$0.0173472\pi$
$113$	1.30238	+	5.70612i	0.122518	+	0.536787i	−0.875997	+	0.482316i	$0.839796\pi$
$114$		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	−0.482276	−	0.876019i	$-0.660190\pi$
$127$	−1.10520	+	0.532238i	−0.0980709	+	0.0472285i	0.384205	+	0.923248i	$0.374476\pi$
$128$		0			0
$129$	3.03903	+	5.26376i	0.267572	+	0.463448i
$130$		0			0
$131$	−3.26855	+	0.492655i	−0.285575	+	0.0430435i	−0.290268	−	0.956946i	$-0.593744\pi$
$131$	−3.26855	+	0.492655i	−0.285575	+	0.0430435i	0.00469285	+	0.999989i	$0.498506\pi$
$132$		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	−0.623555	−	0.781779i	$-0.714312\pi$
$137$	4.27559	−	10.8940i	0.365288	−	0.930739i	0.988843	−	0.148959i	$-0.0475924\pi$
$138$		0			0
$139$	6.76258	−	8.48001i	0.573595	−	0.719265i	−0.407411	−	0.913245i	$-0.633568\pi$
$139$	6.76258	−	8.48001i	0.573595	−	0.719265i	0.981006	+	0.193980i	$0.0621396\pi$
$140$		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	0.999625	+	0.0273845i	$0.00871783\pi$
$149$	13.4472	+	12.4771i	1.10163	+	1.02217i	0.102010	+	0.994783i	$0.467473\pi$
$150$		0			0
$151$	0.866609	+	11.5641i	0.0705236	+	0.941072i	0.914472	+	0.404649i	$0.132606\pi$
$151$	0.866609	+	11.5641i	0.0705236	+	0.941072i	−0.843949	+	0.536424i	$0.819775\pi$
$152$		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	0.238336	+	0.971183i	$0.423398\pi$
$157$	−7.47975	+	19.0581i	−0.596949	+	1.52100i	−0.835284	+	0.549818i	$0.814697\pi$
$158$		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	−0.247156	−	0.968976i	$-0.579496\pi$
$163$	−2.52434	+	0.380483i	−0.197721	+	0.0298017i	0.0494349	+	0.998777i	$0.484258\pi$
$164$		0			0
$165$	−0.434788	−	0.753075i	−0.0338482	−	0.0586268i
$166$		0			0
$167$	11.2810	−	5.43264i	0.872949	−	0.420390i	0.0569050	−	0.998380i	$-0.481877\pi$
$167$	11.2810	−	5.43264i	0.872949	−	0.420390i	0.816044	+	0.577989i	$0.196163\pi$
$168$		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	−0.283125	−	0.959083i	$-0.591371\pi$
$173$	6.65833	−	4.53957i	0.506224	−	0.345137i	0.789348	+	0.613946i	$0.210419\pi$
$174$		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	0.398859	−	0.917012i	$-0.369406\pi$
$179$	−4.13472	−	2.81900i	−0.309043	−	0.210702i	−0.707903	+	0.706310i	$0.750358\pi$
$180$		0			0
$181$	3.24591	+	14.2213i	0.241267	+	1.05706i	0.939866	+	0.341545i	$0.110950\pi$
$181$	3.24591	+	14.2213i	0.241267	+	1.05706i	−0.698599	+	0.715513i	$0.746193\pi$
$182$		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	−0.870777	−	0.491678i	$-0.836384\pi$
$191$	−7.83441	−	19.9618i	−0.566878	−	1.44438i	0.303899	−	0.952704i	$-0.401711\pi$
$192$		0			0
$193$	−20.2138	−	3.04674i	−1.45502	−	0.219309i	−0.626569	−	0.779366i	$-0.715541\pi$
$193$	−20.2138	−	3.04674i	−1.45502	−	0.219309i	−0.828454	+	0.560057i	$0.810779\pi$
$194$		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	−0.0366978	−	0.999326i	$-0.511684\pi$
$199$	−5.16760	−	0.778891i	−0.366322	−	0.0552141i	−0.329624	+	0.944112i	$0.606922\pi$
$200$		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	0.802712	+	0.596367i	$0.203390\pi$
$211$	4.91333	+	21.5267i	0.338248	+	1.48196i	−0.464464	+	0.885592i	$0.653753\pi$
$212$		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	0.491460	−	0.870900i	$-0.336463\pi$
$223$	1.74693	+	0.841275i	0.116983	+	0.0563359i	−0.374477	+	0.927236i	$0.622178\pi$
$224$		0			0
$225$	−2.82548	+	1.36068i	−0.188365	+	0.0907119i
$226$		0			0
$227$	6.02443	+	10.4346i	0.399855	+	0.692570i	0.993708	−	0.112004i	$-0.0357270\pi$
$227$	6.02443	+	10.4346i	0.399855	+	0.692570i	−0.593852	+	0.804574i	$0.702394\pi$
$228$		0			0
$229$	14.2131	−	2.14228i	0.939227	−	0.141566i	0.338452	−	0.940984i	$-0.390097\pi$
$229$	14.2131	−	2.14228i	0.939227	−	0.141566i	0.600775	+	0.799418i	$0.294859\pi$
$230$		0			0
$231$	2.77163	+	4.98686i	0.182360	+	0.328111i
$232$		0			0
$233$	1.55243	−	20.7158i	0.101703	−	1.35713i	−0.679875	−	0.733328i	$-0.737966\pi$
$233$	1.55243	−	20.7158i	0.101703	−	1.35713i	0.781578	−	0.623807i	$-0.214415\pi$
$234$		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	0.999540	+	0.0303225i	$0.00965343\pi$
$239$	12.4710	+	15.6382i	0.806684	+	1.01155i	−0.192856	+	0.981227i	$0.561775\pi$
$240$		0			0
$241$	−0.308807	−	4.12075i	−0.0198920	−	0.265441i	−0.998278	−	0.0586550i	$-0.981319\pi$
$241$	−0.308807	−	4.12075i	−0.0198920	−	0.265441i	0.978386	−	0.206786i	$-0.0663002\pi$
$242$		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	0.235403	−	0.971898i	$-0.424359\pi$
$251$	−12.1121	−	15.1881i	−0.764509	−	0.958664i	−0.999912	+	0.0132335i	$0.995788\pi$
$252$		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	0.529720	+	0.848173i	$0.322297\pi$
$257$	−1.93171	+	25.7769i	−0.120497	+	1.60792i	−0.650217	+	0.759749i	$0.725322\pi$
$258$		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	0.989098	+	0.147256i	$0.0470440\pi$
$263$	10.0884	+	17.4736i	0.622076	+	1.07747i	−0.367022	+	0.930212i	$0.619623\pi$
$264$		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	−0.233789	+	0.972287i	$0.575113\pi$
$269$	−20.0231	+	18.5787i	−1.22083	+	1.13276i	−0.987040	+	0.160476i	$0.948697\pi$
$270$		0			0
$271$	25.5947	−	17.4502i	1.55477	−	1.06002i	0.586553	−	0.809911i	$-0.300485\pi$
$271$	25.5947	−	17.4502i	1.55477	−	1.06002i	0.968217	−	0.250113i	$-0.0804678\pi$
$272$		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	0.853530	−	0.521043i	$-0.174457\pi$
$277$	11.3230	+	7.71991i	0.680335	+	0.463844i	−0.173196	+	0.984887i	$0.555409\pi$
$278$		0			0
$279$	−1.19537	−	5.23724i	−0.0715647	−	0.313546i
$280$		0			0
$281$	6.90340	−	30.2458i	0.411822	−	1.80431i	−0.163683	−	0.986513i	$-0.552337\pi$
$281$	6.90340	−	30.2458i	0.411822	−	1.80431i	0.575505	−	0.817798i	$-0.304806\pi$
$282$		0			0
$283$	30.2330	−	9.32565i	1.79717	−	0.554353i	0.798314	−	0.602241i	$-0.205725\pi$
$283$	30.2330	−	9.32565i	1.79717	−	0.554353i	0.998853	+	0.0478883i	$0.0152492\pi$
$284$		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	−0.908820	−	0.417189i	$-0.863015\pi$
$307$	1.59463	−	6.98652i	0.0910102	−	0.398742i	0.999830	+	0.0184476i	$0.00587238\pi$
$308$		0			0
$309$	−2.01388	−	8.82338i	−0.114566	−	0.501944i
$310$		0			0
$311$	−1.42254	−	0.969874i	−0.0806651	−	0.0549965i	0.522316	−	0.852752i	$-0.325068\pi$
$311$	−1.42254	−	0.969874i	−0.0806651	−	0.0549965i	−0.602981	+	0.797756i	$0.706021\pi$
$312$		0			0
$313$	4.82195	−	8.35187i	0.272553	−	0.472076i	−0.696962	−	0.717108i	$-0.745465\pi$
$313$	4.82195	−	8.35187i	0.272553	−	0.472076i	0.969515	+	0.245033i	$0.0787987\pi$
$314$		0			0
$315$	−0.627986	+	0.289891i	−0.0353830	+	0.0163335i
$316$		0			0
$317$	6.68310	−	4.55646i	0.375361	−	0.255916i	−0.360914	−	0.932599i	$-0.617535\pi$
$317$	6.68310	−	4.55646i	0.375361	−	0.255916i	0.736275	+	0.676682i	$0.236583\pi$
$318$		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	0.594084	+	0.804403i	$0.297515\pi$
$331$	−2.06049	+	27.4953i	−0.113255	+	1.51128i	−0.707339	+	0.706875i	$0.750105\pi$
$332$		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	0.577564	−	0.816345i	$-0.304003\pi$
$337$	−6.36702	−	7.98399i	−0.346834	−	0.434916i	−0.924398	+	0.381429i	$0.875432\pi$
$338$		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	−0.938614	−	0.344969i	$-0.887890\pi$
$347$	−1.15304	−	15.3863i	−0.0618985	−	0.825978i	0.876716	−	0.481009i	$-0.159730\pi$
$348$		0			0
$349$	8.19211	+	10.2726i	0.438513	+	0.549878i	0.951151	−	0.308727i	$-0.0999029\pi$
$349$	8.19211	+	10.2726i	0.438513	+	0.549878i	−0.512637	+	0.858605i	$0.671331\pi$
$350$		0			0
$351$	−1.54013	+	1.93126i	−0.0822060	+	0.103083i
$352$		0			0
$353$	9.60760	−	24.4798i	0.511361	−	1.30293i	−0.409241	−	0.912426i	$-0.634207\pi$
$353$	9.60760	−	24.4798i	0.511361	−	1.30293i	0.920603	−	0.390501i	$-0.127698\pi$
$354$		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	−0.388407	−	0.921488i	$-0.626975\pi$
$359$	−9.24524	+	1.39350i	−0.487945	+	0.0735459i	−0.0995381	+	0.995034i	$0.531737\pi$
$360$		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	−0.759973	−	0.649955i	$-0.774788\pi$
$367$	−3.23045	+	2.99742i	−0.168628	+	0.156464i	0.591345	+	0.806419i	$0.298597\pi$
$368$		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	−0.489387	−	0.872067i	$-0.662780\pi$
$373$	9.86013	−	17.0782i	0.510538	−	0.884278i	0.999925	−	0.0122114i	$-0.00388712\pi$
$374$		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	−0.734772	−	0.678314i	$-0.762711\pi$
$379$	4.31301	−	18.8965i	0.221544	−	0.970649i	0.956316	−	0.292335i	$-0.0944321\pi$
$380$		0			0
$381$	1.79758	−	0.554479i	0.0920927	−	0.0284068i
$382$		0			0
$383$	−19.2310	−	5.93197i	−0.982657	−	0.303109i	−0.238521	−	0.971137i	$-0.576662\pi$
$383$	−19.2310	−	5.93197i	−0.982657	−	0.303109i	−0.744136	+	0.668028i	$0.767139\pi$
$384$		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	0.596111	−	0.802902i	$-0.296712\pi$
$389$	18.3243	+	2.76195i	0.929080	+	0.140036i	0.332969	+	0.942938i	$0.391950\pi$
$390$		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	−0.989737	−	0.142902i	$-0.954357\pi$
$397$	−7.20097	−	18.3478i	−0.361406	−	0.920848i	0.628331	−	0.777946i	$-0.283738\pi$
$398$		0			0
$399$	32.4461	+	10.5913i	1.62434	+	0.530229i
$400$		0			0
$401$	−4.34786	−	1.34114i	−0.217122	−	0.0669732i	0.184286	−	0.982873i	$-0.441003\pi$
$401$	−4.34786	−	1.34114i	−0.217122	−	0.0669732i	−0.401408	+	0.915899i	$0.631479\pi$
$402$		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	0.728613	−	0.684926i	$-0.240165\pi$
$409$	7.22445	+	4.92555i	0.357226	+	0.243553i	−0.371387	+	0.928478i	$0.621118\pi$
$410$		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	0.758137	−	0.652095i	$-0.226110\pi$
$419$	14.7585	+	7.10731i	0.720999	+	0.347215i	−0.0371378	+	0.999310i	$0.511824\pi$
$420$		0			0
$421$	−10.2007	+	4.91239i	−0.497150	+	0.239415i	−0.665619	−	0.746292i	$-0.731832\pi$
$421$	−10.2007	+	4.91239i	−0.497150	+	0.239415i	0.168468	+	0.985707i	$0.446118\pi$
$422$		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	0.586370	+	0.810044i	$0.300557\pi$
$431$	−8.18877	+	20.8646i	−0.394439	+	1.00501i	−0.980809	+	0.194971i	$0.937539\pi$
$432$		0			0
$433$	−17.1243	+	21.4732i	−0.822942	+	1.03194i	0.175928	+	0.984403i	$0.443707\pi$
$433$	−17.1243	+	21.4732i	−0.822942	+	1.03194i	−0.998870	+	0.0475334i	$0.984864\pi$
$434$		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	0.203895	−	0.978993i	$-0.434640\pi$
$439$	−15.8635	−	14.7192i	−0.757123	−	0.702507i	−0.961018	+	0.276485i	$0.910830\pi$
$440$		0			0
$441$	4.15074	−	1.83448i	0.197654	−	0.0873560i
$442$		0			0
$443$	0.728271	+	0.675737i	0.0346012	+	0.0321052i	0.697284	−	0.716795i	$-0.254392\pi$
$443$	0.728271	+	0.675737i	0.0346012	+	0.0321052i	−0.662683	+	0.748900i	$0.730582\pi$
$444$		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	−0.447284	−	0.894392i	$-0.647609\pi$
$449$	11.1079	−	13.9289i	0.524214	−	0.657343i	0.971498	+	0.237049i	$0.0761801\pi$
$450$		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	0.561941	−	0.827177i	$-0.310055\pi$
$457$	28.7043	−	4.32648i	1.34273	−	0.202384i	0.780790	+	0.624793i	$0.214817\pi$
$458$		0			0
$459$	18.2106	+	31.5416i	0.849997	+	1.47224i
$460$		0			0
$461$	−18.8904	+	9.09712i	−0.879812	+	0.423695i	−0.818556	−	0.574427i	$-0.805225\pi$
$461$	−18.8904	+	9.09712i	−0.879812	+	0.423695i	−0.0612561	+	0.998122i	$0.519511\pi$
$462$		0			0
$463$	−2.61473	−	1.25919i	−0.121517	−	0.0585194i	0.372138	−	0.928178i	$-0.378625\pi$
$463$	−2.61473	−	1.25919i	−0.121517	−	0.0585194i	−0.493654	+	0.869658i	$0.664339\pi$
$464$		0			0
$465$	−3.75631	+	3.48535i	−0.174195	+	0.161629i
$466$		0			0
$467$	−8.56164	+	5.83723i	−0.396186	+	0.270115i	−0.744983	−	0.667083i	$-0.767542\pi$
$467$	−8.56164	+	5.83723i	−0.396186	+	0.270115i	0.348798	+	0.937198i	$0.386590\pi$
$468$		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	−0.127507	−	0.991838i	$-0.540697\pi$
$479$	7.13189	−	2.19990i	0.325864	−	0.100516i	0.453371	+	0.891322i	$0.350221\pi$
$480$		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	0.495053	−	0.868863i	$-0.335149\pi$
$487$	15.7127	+	2.36831i	0.712011	+	0.107318i	0.216957	+	0.976181i	$0.430387\pi$
$488$		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	0.811052	−	0.584974i	$-0.198895\pi$
$499$	25.7258	+	7.93537i	1.15165	+	0.355236i	0.340595	+	0.940210i	$0.389371\pi$
$500$		0			0
$501$	−18.3482	+	5.65966i	−0.819736	+	0.252855i
$502$		0			0
$503$	−4.07027	+	17.8330i	−0.181484	+	0.795135i	0.799440	+	0.600746i	$0.205130\pi$
$503$	−4.07027	+	17.8330i	−0.181484	+	0.795135i	−0.980924	+	0.194389i	$0.937728\pi$
$504$		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	−0.948075	−	0.318048i	$-0.896973\pi$
$509$	−4.48061	+	7.76064i	−0.198599	+	0.343984i	0.749475	+	0.662032i	$0.230306\pi$
$510$		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	0.752397	+	0.658710i	$0.228898\pi$
$521$	21.6079	+	37.4259i	0.946658	+	1.63966i	0.194262	+	0.980950i	$0.437769\pi$
$522$		0			0
$523$	9.33257	−	1.40666i	0.408085	−	0.0615089i	0.0582078	−	0.998304i	$-0.481461\pi$
$523$	9.33257	−	1.40666i	0.408085	−	0.0615089i	0.349877	+	0.936796i	$0.386223\pi$
$524$		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	0.978893	+	0.204372i	$0.0655152\pi$
$541$	29.2102	+	27.1031i	1.25585	+	1.16526i	0.276953	+	0.960883i	$0.410675\pi$
$542$		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	−0.206540	−	0.978438i	$-0.566220\pi$
$547$	18.5543	−	23.2664i	0.793326	−	0.994799i	0.999866	−	0.0163609i	$-0.00520808\pi$
$548$		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	0.978494	+	0.206273i	$0.0661335\pi$
$557$	15.7627	+	27.3017i	0.667885	+	1.15681i	−0.310609	+	0.950538i	$0.600533\pi$
$558$		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	−0.604557	−	0.796562i	$-0.706650\pi$
$563$	3.43099	−	3.18349i	0.144599	−	0.134168i	0.749156	+	0.662394i	$0.230459\pi$
$564$		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	−0.999870	−	0.0161216i	$-0.994868\pi$
$569$	−11.5923	+	20.0784i	−0.485973	+	0.841730i	0.513897	+	0.857852i	$0.328201\pi$
$570$		0			0
$571$	−7.89763	−	5.38451i	−0.330505	−	0.225335i	0.386685	−	0.922212i	$-0.373620\pi$
$571$	−7.89763	−	5.38451i	−0.330505	−	0.225335i	−0.717191	+	0.696877i	$0.754572\pi$
$572$		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	−0.426964	−	0.904269i	$-0.640417\pi$
$577$	−6.49392	+	2.00311i	−0.270345	+	0.0833905i	0.156618	+	0.987659i	$0.449941\pi$
$578$		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	0.843113	−	0.537736i	$-0.180720\pi$
$593$	−3.42593	−	8.72912i	−0.140686	−	0.358462i	−0.983799	+	0.179274i	$0.942625\pi$
$594$		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	−0.463583	−	0.886053i	$-0.653436\pi$
$599$	−8.50443	+	2.62327i	−0.347482	+	0.107184i	0.116101	+	0.993237i	$0.462960\pi$
$600$		0			0
$601$	5.92646	−	25.9655i	0.241745	−	1.05916i	−0.697682	−	0.716407i	$-0.745785\pi$
$601$	5.92646	−	25.9655i	0.241745	−	1.05916i	0.939427	−	0.342748i	$-0.111358\pi$
$602$		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	−0.618711	−	0.785618i	$-0.712345\pi$
$607$	9.14071	−	15.8322i	0.371010	−	0.642608i	0.989721	+	0.143011i	$0.0456783\pi$
$608$		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	−0.509494	−	0.860474i	$-0.670167\pi$
$613$	7.68761	−	7.13306i	0.310500	−	0.288102i	0.819994	+	0.572373i	$0.193977\pi$
$614$		0			0
$615$	0.572155	+	0.275535i	0.0230715	+	0.0111107i
$616$		0			0
$617$	−30.5676	+	14.7206i	−1.23061	+	0.592629i	−0.932246	−	0.361824i	$-0.882154\pi$
$617$	−30.5676	+	14.7206i	−1.23061	+	0.592629i	−0.298361	+	0.954453i	$0.596440\pi$
$618$		0			0
$619$	13.5713	+	23.5062i	0.545478	+	0.944795i	0.998577	+	0.0533348i	$0.0169850\pi$
$619$	13.5713	+	23.5062i	0.545478	+	0.944795i	−0.453099	+	0.891460i	$0.649682\pi$
$620$		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	0.630970	−	0.775807i	$-0.282657\pi$
$631$	−6.67656	−	8.37214i	−0.265790	−	0.333290i	−0.896760	+	0.442517i	$0.854086\pi$
$632$		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	0.903905	+	0.427734i	$0.140688\pi$
$641$	1.86964	+	24.9486i	0.0738463	+	0.985410i	−0.830059	+	0.557676i	$0.811693\pi$
$642$		0			0
$643$	7.67367	+	9.62248i	0.302620	+	0.379474i	0.909769	−	0.415114i	$-0.136258\pi$
$643$	7.67367	+	9.62248i	0.302620	+	0.379474i	−0.607149	+	0.794588i	$0.707687\pi$
$644$		0			0
$645$	1.52817	−	1.91626i	0.0601716	−	0.0754528i
$646$		0			0
$647$	9.77804	−	24.9140i	0.384414	−	0.979472i	−0.599427	−	0.800430i	$-0.704605\pi$
$647$	9.77804	−	24.9140i	0.384414	−	0.979472i	0.983841	−	0.179043i	$-0.0573000\pi$
$648$		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	0.422490	−	0.906367i	$-0.361156\pi$
$653$	27.9398	−	4.21124i	1.09337	−	0.164799i	0.670877	+	0.741569i	$0.265918\pi$
$654$		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	0.812924	−	0.582370i	$-0.197874\pi$
$659$	22.1915	+	10.6869i	0.864459	+	0.416302i	0.0515351	+	0.998671i	$0.483589\pi$
$660$		0			0
$661$	−27.1359	+	25.1784i	−1.05546	+	0.979326i	−0.999817	−	0.0191243i	$-0.993912\pi$
$661$	−27.1359	+	25.1784i	−1.05546	+	0.979326i	−0.0556456	+	0.998451i	$0.517722\pi$
$662$		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	−0.157660	−	0.987493i	$-0.550395\pi$
$673$	10.7101	−	46.9240i	0.412844	−	1.80879i	0.570505	−	0.821294i	$-0.306748\pi$
$674$		0			0
$675$	25.8616	−	7.97726i	0.995415	−	0.307045i
$676$		0			0
$677$	−18.9609	−	5.84866i	−0.728727	−	0.224782i	−0.0918770	−	0.995770i	$-0.529287\pi$
$677$	−18.9609	−	5.84866i	−0.728727	−	0.224782i	−0.636850	+	0.770988i	$0.719763\pi$
$678$		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	0.291401	−	0.956601i	$-0.405879\pi$
$683$	7.52385	+	1.13404i	0.287892	+	0.0433928i	−0.00350850	+	0.999994i	$0.501117\pi$
$684$		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	−0.999408	−	0.0344051i	$-0.989046\pi$
$691$	−7.62823	−	19.4364i	−0.290191	−	0.739396i	0.709217	−	0.704991i	$-0.249049\pi$
$692$		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	0.975477	+	0.220100i	$0.0706384\pi$
$701$	5.08613	+	22.2838i	0.192100	+	0.841647i	−0.783377	+	0.621547i	$0.786504\pi$
$702$		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	−0.611447	−	0.791285i	$-0.709412\pi$
$709$	−2.61602	+	1.78358i	−0.0982469	+	0.0669836i	0.513200	+	0.858269i	$0.328460\pi$
$710$		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	−0.166520	−	0.986038i	$-0.553253\pi$
$719$	−0.938530	+	0.141461i	−0.0350012	+	0.00527559i	0.131518	+	0.991314i	$0.458015\pi$
$720$		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	−0.660089	−	0.751188i	$-0.729481\pi$
$727$	5.90889	−	7.40951i	0.219148	−	0.274803i	0.879237	+	0.476384i	$0.158053\pi$
$728$		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	0.986618	−	0.163047i	$-0.0521321\pi$
$733$	24.3059	+	22.5526i	0.897758	+	0.832998i	−0.0888605	+	0.996044i	$0.528323\pi$
$734$		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	0.925007	+	0.379949i	$0.124059\pi$
$739$	1.82028	+	24.2899i	0.0669601	+	0.893520i	−0.858047	+	0.513571i	$0.828322\pi$
$740$		0			0
$741$	3.55120	+	4.45307i	0.130457	+	0.163587i
$742$		0			0
$743$	−1.22787	+	1.53970i	−0.0450460	+	0.0564859i	−0.803844	−	0.594840i	$-0.797215\pi$
$743$	−1.22787	+	1.53970i	−0.0450460	+	0.0564859i	0.758798	+	0.651326i	$0.225787\pi$
$744$		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	0.373461	−	0.927646i	$-0.378171\pi$
$751$	27.5074	−	4.14607i	1.00376	−	0.151292i	0.630298	+	0.776354i	$0.282933\pi$
$752$		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	0.635458	−	0.772135i	$-0.280811\pi$
$757$	11.7753	+	5.67068i	0.427980	+	0.206104i	−0.207478	+	0.978240i	$0.566526\pi$
$758$		0			0
$759$	−8.39838	+	7.79256i	−0.304842	+	0.282852i
$760$		0			0
$761$	−1.21595	+	0.829020i	−0.0440781	+	0.0300520i	−0.585159	−	0.810919i	$-0.698968\pi$
$761$	−1.21595	+	0.829020i	−0.0440781	+	0.0300520i	0.541081	+	0.840971i	$0.318015\pi$
$762$		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	0.997749	−	0.0670563i	$-0.0213607\pi$
$769$	1.93322	+	8.46998i	0.0697136	+	0.305435i	−0.928036	+	0.372491i	$0.878504\pi$
$770$		0			0
$771$	8.82084	−	38.6466i	0.317675	−	1.39182i
$772$		0			0
$773$	22.8028	−	7.03374i	0.820161	−	0.252986i	0.143847	−	0.989600i	$-0.454053\pi$
$773$	22.8028	−	7.03374i	0.820161	−	0.252986i	0.676314	+	0.736614i	$0.263576\pi$
$774$		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	−0.579634	−	0.814877i	$-0.696805\pi$
$787$	−38.5373	−	5.80856i	−1.37371	−	0.207053i	−0.794072	+	0.607824i	$0.792043\pi$
$788$		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	−0.499755	−	0.866167i	$-0.666576\pi$
$797$	9.21253	−	40.3627i	0.326325	−	1.42972i	0.826079	−	0.563554i	$-0.190566\pi$
$798$		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	−0.837078	−	0.547084i	$-0.815738\pi$
$809$	−10.0710	+	9.34455i	−0.354079	+	0.328537i	0.482999	+	0.875621i	$0.339547\pi$
$810$		0			0
$811$	18.7641	+	9.03630i	0.658896	+	0.317307i	0.733285	−	0.679922i	$-0.237986\pi$
$811$	18.7641	+	9.03630i	0.658896	+	0.317307i	−0.0743888	+	0.997229i	$0.523701\pi$
$812$		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	−0.497053	−	0.867720i	$-0.665584\pi$
$821$	3.54655	−	47.3254i	0.123775	−	1.65167i	0.620828	−	0.783947i	$-0.286797\pi$
$822$		0			0
$823$	9.84217	−	25.0775i	0.343077	−	0.874145i	−0.650346	−	0.759638i	$-0.725376\pi$
$823$	9.84217	−	25.0775i	0.343077	−	0.874145i	0.993422	−	0.114507i	$-0.0365287\pi$
$824$		0			0
$825$	6.50386	−	8.15558i	0.226435	−	0.283941i
$826$		0			0
$827$	28.8554	+	36.1835i	1.00340	+	1.25822i	0.965897	+	0.258928i	$0.0833693\pi$
$827$	28.8554	+	36.1835i	1.00340	+	1.25822i	0.0375040	+	0.999296i	$0.488059\pi$
$828$		0			0
$829$	−0.0884937	−	1.18087i	−0.00307351	−	0.0410132i	0.995456	−	0.0952209i	$-0.0303557\pi$
$829$	−0.0884937	−	1.18087i	−0.00307351	−	0.0410132i	−0.998530	+	0.0542077i	$0.982737\pi$
$830$		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	0.573668	−	0.819088i	$-0.305520\pi$
$839$	−10.2114	−	12.8047i	−0.352537	−	0.442068i	−0.926205	+	0.377020i	$0.876949\pi$
$840$		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	0.394056	−	0.919086i	$-0.371072\pi$
$853$	39.6712	−	19.1046i	1.35832	−	0.654131i	0.964261	+	0.264956i	$0.0853574\pi$
$854$		0			0
$855$	−1.98137	−	0.954178i	−0.0677615	−	0.0326322i
$856$		0			0
$857$	−5.55267	+	5.15212i	−0.189675	+	0.175993i	−0.769294	−	0.638895i	$-0.779392\pi$
$857$	−5.55267	+	5.15212i	−0.189675	+	0.175993i	0.579619	+	0.814888i	$0.303201\pi$
$858$		0			0
$859$	16.3222	−	11.1283i	0.556907	−	0.379693i	−0.251912	−	0.967750i	$-0.581059\pi$
$859$	16.3222	−	11.1283i	0.556907	−	0.379693i	0.808819	+	0.588057i	$0.200107\pi$
$860$		0			0
$861$	−3.72392	−	1.86883i	−0.126911	−	0.0636896i
$862$		0			0
$863$	−11.7008	+	20.2663i	−0.398299	+	0.689874i	−0.993516	−	0.113691i	$-0.963733\pi$
$863$	−11.7008	+	20.2663i	−0.398299	+	0.689874i	0.595217	+	0.803565i	$0.297066\pi$
$864$		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	0.980148	−	0.198269i	$-0.0635319\pi$
$877$	3.75483	+	9.56715i	0.126792	+	0.323060i	−0.853356	+	0.521329i	$0.825437\pi$
$878$		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	0.994342	+	0.106230i	$0.0338781\pi$
$887$	10.0573	+	25.6257i	0.337693	+	0.860427i	−0.656649	+	0.754196i	$0.728027\pi$
$888$		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	−0.640248	−	0.768169i	$-0.721168\pi$
$907$	2.34689	−	2.17759i	0.0779270	−	0.0723057i	0.718175	+	0.695863i	$0.244978\pi$
$908$		0			0
$909$	−4.24965	−	2.04652i	−0.140952	−	0.0678789i
$910$		0			0
$911$	28.9643	−	13.9485i	0.959631	−	0.462134i	0.112579	−	0.993643i	$-0.464089\pi$
$911$	28.9643	−	13.9485i	0.959631	−	0.462134i	0.847053	+	0.531509i	$0.178375\pi$
$912$		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	−0.840654	−	0.541573i	$-0.817829\pi$
$919$	2.16230	−	28.8539i	0.0713278	−	0.951803i	0.911982	−	0.410231i	$-0.134552\pi$
$920$		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	0.480418	−	0.877040i	$-0.340485\pi$
$929$	−10.9198	−	10.1321i	−0.358267	−	0.332423i	−0.838685	+	0.544616i	$0.816675\pi$
$930$		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	−0.951121	−	0.308820i	$-0.900066\pi$
$937$	−31.8518	−	39.9409i	−1.04055	−	1.30481i	−0.0894329	−	0.995993i	$-0.528505\pi$
$938$		0			0
$939$	−9.22091	+	11.5627i	−0.300913	+	0.377333i
$940$		0			0
$941$	−5.60138	+	14.2721i	−0.182600	+	0.465257i	−0.992638	−	0.121121i	$-0.961351\pi$
$941$	−5.60138	+	14.2721i	−0.182600	+	0.465257i	0.810038	+	0.586377i	$0.199446\pi$
$942$		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	−0.0742098	−	0.997243i	$-0.523643\pi$
$947$	4.57968	−	0.690276i	0.148820	−	0.0224310i	0.223030	+	0.974812i	$0.428405\pi$
$948$		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	−0.989532	−	0.144317i	$-0.953902\pi$
$953$	−53.0768	−	25.5604i	−1.71933	−	0.827984i	−0.729794	−	0.683667i	$-0.760384\pi$
$954$		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	−0.0641134	−	0.997943i	$-0.520422\pi$
$967$	13.2671	−	58.1271i	0.426642	−	1.86924i	0.490755	−	0.871297i	$-0.336721\pi$
$968$		0			0
$969$	80.2483	−	24.7533i	2.57795	−	0.795191i
$970$		0			0
$971$	12.7435	+	3.93084i	0.408958	+	0.126147i	0.492407	−	0.870365i	$-0.336117\pi$
$971$	12.7435	+	3.93084i	0.408958	+	0.126147i	−0.0834487	+	0.996512i	$0.526593\pi$
$972$		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	−0.252704	−	0.967544i	$-0.581320\pi$
$977$	−24.3607	−	3.67179i	−0.779369	−	0.117471i	−0.526665	+	0.850073i	$0.676558\pi$
$978$		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	−0.217611	−	0.976036i	$-0.569826\pi$
$983$	−22.3623	−	3.37057i	−0.713245	−	0.107504i	−0.495634	+	0.868531i	$0.665064\pi$
$984$		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	−0.975670	−	0.219242i	$-0.929642\pi$
$991$	−52.2037	+	16.1027i	−1.65830	+	0.511519i	−0.682633	+	0.730761i	$0.739165\pi$
$992$		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	0.259130	−	0.965843i	$-0.416564\pi$
$997$	−17.2173	−	11.7386i	−0.545277	−	0.371764i	−0.804407	+	0.594079i	$0.797517\pi$
$998$		0			0
$999$	−17.8871	+	30.9814i	−0.565924	+	0.980209i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.y.a.9.3	✓	84	1.1	even	1	trivial
392.2.y.a.305.3	yes	84	49.11	even	21	inner
784.2.bg.f.305.5		84	196.11	odd	42
784.2.bg.f.401.5		84	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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