LMFDB - Embedded newform 315.2.ce.a.233.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(53,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.15
Character	$\chi$	$=$	315.233
Dual form			315.2.ce.a.242.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.25596 - 0.604483i) q^{2} +(2.99191 - 1.72738i) q^{4} +(2.05129 - 0.890070i) q^{5} +(-1.48100 + 2.19240i) q^{7} +(2.40251 - 2.40251i) q^{8} +(4.08959 - 3.24793i) q^{10} +(-2.61609 + 1.51040i) q^{11} +(-1.77456 - 1.77456i) q^{13} +(-2.01581 + 5.84122i) q^{14} +(0.512928 - 0.888417i) q^{16} +(1.00203 - 3.73962i) q^{17} +(-3.79826 - 2.19292i) q^{19} +(4.59978 - 6.20636i) q^{20} +(-4.98879 + 4.98879i) q^{22} +(1.93742 + 7.23056i) q^{23} +(3.41555 - 3.65158i) q^{25} +(-5.07603 - 2.93065i) q^{26} +(-0.643912 + 9.11773i) q^{28} +1.25900 q^{29} +(-2.64259 - 4.57710i) q^{31} +(-1.13865 + 4.24948i) q^{32} -9.04214i q^{34} +(-1.08657 + 5.81544i) q^{35} +(-1.97321 - 7.36414i) q^{37} +(-9.89430 - 2.65117i) q^{38} +(2.78983 - 7.06663i) q^{40} +10.7696i q^{41} +(5.73749 + 5.73749i) q^{43} +(-5.21807 + 9.03797i) q^{44} +(8.74151 + 15.1407i) q^{46} +(7.80209 - 2.09056i) q^{47} +(-2.61327 - 6.49391i) q^{49} +(5.49803 - 10.3025i) q^{50} +(-8.37466 - 2.24398i) q^{52} +(1.76225 + 0.472193i) q^{53} +(-4.02199 + 5.42677i) q^{55} +(1.70915 + 8.82539i) q^{56} +(2.84025 - 0.761042i) q^{58} +(-2.97005 - 5.14428i) q^{59} +(-3.71170 + 6.42886i) q^{61} +(-8.72836 - 8.72836i) q^{62} +12.3267i q^{64} +(-5.21961 - 2.06065i) q^{65} +(-9.36375 - 2.50901i) q^{67} +(-3.46176 - 12.9195i) q^{68} +(1.06408 + 13.7762i) q^{70} -1.07298i q^{71} +(0.555728 - 2.07401i) q^{73} +(-8.90299 - 15.4204i) q^{74} -15.1521 q^{76} +(0.563028 - 7.97243i) q^{77} +(5.75001 + 3.31977i) q^{79} +(0.261408 - 2.27894i) q^{80} +(6.51003 + 24.2957i) q^{82} +(-1.25073 + 1.25073i) q^{83} +(-1.27308 - 8.56290i) q^{85} +(16.4118 + 9.47534i) q^{86} +(-2.65643 + 9.91392i) q^{88} +(2.44200 - 4.22966i) q^{89} +(6.51867 - 1.26242i) q^{91} +(18.2865 + 18.2865i) q^{92} +(16.3375 - 9.43246i) q^{94} +(-9.74317 - 1.11760i) q^{95} +(2.69087 - 2.69087i) q^{97} +(-9.82088 - 13.0703i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) $ 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	2.25596	−	0.604483i	1.59521	−	0.427434i	0.651615	−	0.758550i	$-0.274092\pi$
$2$	2.25596	−	0.604483i	1.59521	−	0.427434i	0.943590	+	0.331115i	$0.107425\pi$
$3$		0			0
$3$		0			0
$4$	2.99191	−	1.72738i	1.49596	−	0.863690i
$5$	2.05129	−	0.890070i	0.917363	−	0.398051i
$5$	2.05129	−	0.890070i	0.917363	−	0.398051i
$6$		0			0
$7$	−1.48100	+	2.19240i	−0.559766	+	0.828651i
$7$	−1.48100	+	2.19240i	−0.559766	+	0.828651i
$8$	2.40251	−	2.40251i	0.849415	−	0.849415i
$9$		0			0
$10$	4.08959	−	3.24793i	1.29324	−	1.02709i
$11$	−2.61609	+	1.51040i	−0.788781	+	0.455403i	−0.839533	−	0.543309i	$-0.817171\pi$
$11$	−2.61609	+	1.51040i	−0.788781	+	0.455403i	0.0507524	+	0.998711i	$0.483838\pi$
$12$		0			0
$13$	−1.77456	−	1.77456i	−0.492174	−	0.492174i	0.416817	−	0.908991i	$-0.363146\pi$
$13$	−1.77456	−	1.77456i	−0.492174	−	0.492174i	−0.908991	+	0.416817i	$0.863146\pi$
$14$	−2.01581	+	5.84122i	−0.538749	+	1.56113i
$15$		0			0
$16$	0.512928	−	0.888417i	0.128232	−	0.222104i
$17$	1.00203	−	3.73962i	0.243027	−	0.906990i	−0.731337	−	0.682016i	$-0.761104\pi$
$17$	1.00203	−	3.73962i	0.243027	−	0.906990i	0.974365	−	0.224974i	$-0.0722298\pi$
$18$		0			0
$19$	−3.79826	−	2.19292i	−0.871380	−	0.503091i	−0.00357323	−	0.999994i	$-0.501137\pi$
$19$	−3.79826	−	2.19292i	−0.871380	−	0.503091i	−0.867806	+	0.496902i	$0.834471\pi$
$20$	4.59978	−	6.20636i	1.02854	−	1.38779i
$21$		0			0
$22$	−4.98879	+	4.98879i	−1.06361	+	1.06361i
$23$	1.93742	+	7.23056i	0.403981	+	1.50768i	0.805928	+	0.592014i	$0.201667\pi$
$23$	1.93742	+	7.23056i	0.403981	+	1.50768i	−0.401947	+	0.915663i	$0.631666\pi$
$24$		0			0
$25$	3.41555	−	3.65158i	0.683110	−	0.730315i
$26$	−5.07603	−	2.93065i	−0.995491	−	0.574747i
$27$		0			0
$28$	−0.643912	+	9.11773i	−0.121688	+	1.72309i
$29$	1.25900			0.233790			0.116895	−	0.993144i	$-0.462706\pi$
$29$	1.25900			0.233790			0.116895	+	0.993144i	$0.462706\pi$
$30$		0			0
$31$	−2.64259	−	4.57710i	−0.474623	−	0.822072i	0.524954	−	0.851130i	$-0.324082\pi$
$31$	−2.64259	−	4.57710i	−0.474623	−	0.822072i	−0.999578	+	0.0290586i	$0.990749\pi$
$32$	−1.13865	+	4.24948i	−0.201286	+	0.751209i
$33$		0			0
$34$		−	9.04214i		−	1.55071i
$35$	−1.08657	+	5.81544i	−0.183663	+	0.982989i
$36$		0			0
$37$	−1.97321	−	7.36414i	−0.324395	−	1.21066i	−0.914919	−	0.403637i	$-0.867746\pi$
$37$	−1.97321	−	7.36414i	−0.324395	−	1.21066i	0.590525	−	0.807020i	$-0.298921\pi$
$38$	−9.89430	−	2.65117i	−1.60507	−	0.430077i
$39$		0			0
$40$	2.78983	−	7.06663i	0.441111	−	1.11733i
$41$			10.7696i			1.68193i	0.541093	+	0.840963i	$0.318011\pi$
$41$			10.7696i			1.68193i	−0.541093	+	0.840963i	$0.681989\pi$
$42$		0			0
$43$	5.73749	+	5.73749i	0.874959	+	0.874959i	0.993008	−	0.118049i	$-0.0376640\pi$
$43$	5.73749	+	5.73749i	0.874959	+	0.874959i	−0.118049	+	0.993008i	$0.537664\pi$
$44$	−5.21807	+	9.03797i	−0.786654	+	1.36252i
$45$		0			0
$46$	8.74151	+	15.1407i	1.28886	+	2.23238i
$47$	7.80209	−	2.09056i	1.13805	−	0.304940i	0.359884	−	0.932997i	$-0.382816\pi$
$47$	7.80209	−	2.09056i	1.13805	−	0.304940i	0.778168	+	0.628057i	$0.216149\pi$
$48$		0			0
$49$	−2.61327	−	6.49391i	−0.373324	−	0.927701i
$50$	5.49803	−	10.3025i	0.777539	−	1.45699i
$51$		0			0
$52$	−8.37466	−	2.24398i	−1.16136	−	0.311185i
$53$	1.76225	+	0.472193i	0.242064	+	0.0648607i	0.377811	−	0.925883i	$-0.376677\pi$
$53$	1.76225	+	0.472193i	0.242064	+	0.0648607i	−0.135747	+	0.990743i	$0.543344\pi$
$54$		0			0
$55$	−4.02199	+	5.42677i	−0.542325	+	0.731745i
$56$	1.70915	+	8.82539i	0.228394	+	1.17934i
$57$		0			0
$58$	2.84025	−	0.761042i	0.372943	−	0.0999298i
$59$	−2.97005	−	5.14428i	−0.386668	−	0.669729i	0.605331	−	0.795974i	$-0.293041\pi$
$59$	−2.97005	−	5.14428i	−0.386668	−	0.669729i	−0.991999	+	0.126245i	$0.959707\pi$
$60$		0			0
$61$	−3.71170	+	6.42886i	−0.475235	+	0.823131i	−0.999598	−	0.0283643i	$-0.990970\pi$
$61$	−3.71170	+	6.42886i	−0.475235	+	0.823131i	0.524363	+	0.851495i	$0.324303\pi$
$62$	−8.72836	−	8.72836i	−1.10850	−	1.10850i
$63$		0			0
$64$			12.3267i			1.54083i
$65$	−5.21961	−	2.06065i	−0.647413	−	0.255592i
$66$		0			0
$67$	−9.36375	−	2.50901i	−1.14396	−	0.306524i	−0.363420	−	0.931625i	$-0.618391\pi$
$67$	−9.36375	−	2.50901i	−1.14396	−	0.306524i	−0.780544	+	0.625101i	$0.785058\pi$
$68$	−3.46176	−	12.9195i	−0.419801	−	1.56672i
$69$		0			0
$70$	1.06408	+	13.7762i	0.127182	+	1.64657i
$71$		−	1.07298i		−	0.127339i	−0.997971	−	0.0636696i	$-0.979720\pi$
$71$		−	1.07298i		−	0.127339i	0.997971	−	0.0636696i	$-0.0202804\pi$
$72$		0			0
$73$	0.555728	−	2.07401i	0.0650431	−	0.242744i	−0.925749	−	0.378140i	$-0.876564\pi$
$73$	0.555728	−	2.07401i	0.0650431	−	0.242744i	0.990792	+	0.135396i	$0.0432306\pi$
$74$	−8.90299	−	15.4204i	−1.03495	−	1.79259i
$75$		0			0
$76$	−15.1521			−1.73806
$77$	0.563028	−	7.97243i	0.0641630	−	0.908543i
$78$		0			0
$79$	5.75001	+	3.31977i	0.646927	+	0.373503i	0.787278	−	0.616599i	$-0.211490\pi$
$79$	5.75001	+	3.31977i	0.646927	+	0.373503i	−0.140351	+	0.990102i	$0.544823\pi$
$80$	0.261408	−	2.27894i	0.0292264	−	0.254793i
$81$		0			0
$82$	6.51003	+	24.2957i	0.718912	+	2.68302i
$83$	−1.25073	+	1.25073i	−0.137285	+	0.137285i	−0.772410	−	0.635124i	$-0.780949\pi$
$83$	−1.25073	+	1.25073i	−0.137285	+	0.137285i	0.635124	+	0.772410i	$0.280949\pi$
$84$		0			0
$85$	−1.27308	−	8.56290i	−0.138084	−	0.928777i
$86$	16.4118	+	9.47534i	1.76973	+	1.02175i
$87$		0			0
$88$	−2.65643	+	9.91392i	−0.283176	+	1.05683i
$89$	2.44200	−	4.22966i	0.258851	−	0.448343i	−0.707083	−	0.707130i	$-0.749989\pi$
$89$	2.44200	−	4.22966i	0.258851	−	0.448343i	0.965934	+	0.258787i	$0.0833227\pi$
$90$		0			0
$91$	6.51867	−	1.26242i	0.683343	−	0.132338i
$92$	18.2865	+	18.2865i	1.90650	+	1.90650i
$93$		0			0
$94$	16.3375	−	9.43246i	1.68509	−	0.972884i
$95$	−9.74317	−	1.11760i	−0.999628	−	0.114663i
$96$		0			0
$97$	2.69087	−	2.69087i	0.273217	−	0.273217i	−0.557177	−	0.830394i	$-0.688115\pi$
$97$	2.69087	−	2.69087i	0.273217	−	0.273217i	0.830394	+	0.557177i	$0.188115\pi$
$98$	−9.82088	−	13.0703i	−0.992059	−	1.32030i
$99$		0			0
$100$	3.91136	−	16.8252i	0.391136	−	1.68252i
$101$	10.8964	−	6.29104i	1.08423	−	0.625982i	0.152197	−	0.988350i	$-0.451365\pi$
$101$	10.8964	−	6.29104i	1.08423	−	0.625982i	0.932035	+	0.362368i	$0.118032\pi$
$102$		0			0
$103$	13.2685	−	3.55530i	1.30739	−	0.350314i	0.463149	−	0.886280i	$-0.346719\pi$
$103$	13.2685	−	3.55530i	1.30739	−	0.350314i	0.844239	+	0.535966i	$0.180053\pi$
$104$	−8.52678			−0.836120
$105$		0			0
$106$	4.26100			0.413865
$107$	2.93682	−	0.786918i	0.283913	−	0.0760742i	−0.114052	−	0.993475i	$-0.536383\pi$
$107$	2.93682	−	0.786918i	0.283913	−	0.0760742i	0.397965	+	0.917401i	$0.369716\pi$
$108$		0			0
$109$	−14.3581	+	8.28967i	−1.37526	+	0.794006i	−0.991584	−	0.129462i	$-0.958675\pi$
$109$	−14.3581	+	8.28967i	−1.37526	+	0.794006i	−0.383674	+	0.923468i	$0.625341\pi$
$110$	−5.79306	+	14.6738i	−0.552347	+	1.39909i
$111$		0			0
$112$	1.18812	+	2.44029i	0.112267	+	0.230586i
$113$	13.7810	−	13.7810i	1.29641	−	1.29641i	0.365657	−	0.930750i	$-0.380844\pi$
$113$	13.7810	−	13.7810i	1.29641	−	1.29641i	0.930750	−	0.365657i	$-0.119156\pi$
$114$		0			0
$115$	10.4099	+	13.1075i	0.970730	+	1.22228i
$116$	3.76681	−	2.17477i	0.349739	−	0.201922i
$117$		0			0
$118$	−9.80996	−	9.80996i	−0.903080	−	0.903080i
$119$	6.71474	+	7.73523i	0.615539	+	0.709087i
$120$		0			0
$121$	−0.937384	+	1.62360i	−0.0852167	+	0.147600i
$122$	−4.48732	+	16.7469i	−0.406263	+	1.51619i
$123$		0			0
$124$	−15.8128	−	9.12952i	−1.42003	−	0.819855i
$125$	3.75611	−	10.5305i	0.335957	−	0.941877i
$126$		0			0
$127$	13.1848	−	13.1848i	1.16996	−	1.16996i	0.187742	−	0.982218i	$-0.439883\pi$
$127$	13.1848	−	13.1848i	1.16996	−	1.16996i	0.982218	−	0.187742i	$-0.0601167\pi$
$128$	5.17397	+	19.3095i	0.457319	+	1.70674i
$129$		0			0
$130$	−13.0209	−	1.49357i	−1.14201	−	0.130995i
$131$	−9.06836	−	5.23562i	−0.792306	−	0.457438i	0.0484676	−	0.998825i	$-0.484566\pi$
$131$	−9.06836	−	5.23562i	−0.792306	−	0.457438i	−0.840774	+	0.541387i	$0.817900\pi$
$132$		0			0
$133$	10.4330	−	5.07958i	0.904656	−	0.440456i
$134$	−22.6409			−1.95588
$135$		0			0
$136$	−6.57708	−	11.3918i	−0.563980	−	0.976842i
$137$	−4.29058	+	16.0127i	−0.366569	+	1.36806i	0.498712	+	0.866768i	$0.333807\pi$
$137$	−4.29058	+	16.0127i	−0.366569	+	1.36806i	−0.865281	+	0.501287i	$0.832860\pi$
$138$		0			0
$139$			7.58102i			0.643014i	0.946907	+	0.321507i	$0.104189\pi$
$139$			7.58102i			0.643014i	−0.946907	+	0.321507i	$0.895811\pi$
$140$	6.79457	+	19.2762i	0.574246	+	1.62914i
$141$		0			0
$142$	−0.648597	−	2.42060i	−0.0544291	−	0.203132i
$143$	7.32270	+	1.96211i	0.612355	+	0.164080i
$144$		0			0
$145$	2.58256	−	1.12060i	0.214470	−	0.0930604i
$146$		−	5.01481i		−	0.415028i
$147$		0			0
$148$	−18.6244	−	18.6244i	−1.53091	−	1.53091i
$149$	1.70147	−	2.94704i	0.139390	−	0.241431i	−0.787876	−	0.615834i	$-0.788819\pi$
$149$	1.70147	−	2.94704i	0.139390	−	0.241431i	0.927266	+	0.374403i	$0.122152\pi$
$150$		0			0
$151$	−7.87968	−	13.6480i	−0.641239	−	1.11066i	−0.985157	−	0.171659i	$-0.945087\pi$
$151$	−7.87968	−	13.6480i	−0.641239	−	1.11066i	0.343918	−	0.939000i	$-0.388246\pi$
$152$	−14.3939	+	3.85682i	−1.16750	+	0.312830i
$153$		0			0
$154$	−3.54903	−	18.3258i	−0.285989	−	1.47674i
$155$	−9.49465	−	7.03686i	−0.762629	−	0.565214i
$156$		0			0
$157$	−6.00182	−	1.60818i	−0.478998	−	0.128347i	0.0112383	−	0.999937i	$-0.496423\pi$
$157$	−6.00182	−	1.60818i	−0.478998	−	0.128347i	−0.490236	+	0.871590i	$0.663089\pi$
$158$	14.9785	+	4.01349i	1.19163	+	0.319296i
$159$		0			0
$160$	1.44665	+	9.73038i	0.114368	+	0.769254i
$161$	−18.7216	−	6.46087i	−1.47547	−	0.509188i
$162$		0			0
$163$	3.51177	−	0.940977i	0.275063	−	0.0737030i	−0.118650	−	0.992936i	$-0.537857\pi$
$163$	3.51177	−	0.940977i	0.275063	−	0.0737030i	0.393714	+	0.919233i	$0.371190\pi$
$164$	18.6032	+	32.2216i	1.45266	+	2.51609i
$165$		0			0
$166$	−2.06555	+	3.57764i	−0.160318	+	0.277679i
$167$	−6.11816	−	6.11816i	−0.473437	−	0.473437i	0.429588	−	0.903025i	$-0.358659\pi$
$167$	−6.11816	−	6.11816i	−0.473437	−	0.473437i	−0.903025	+	0.429588i	$0.858659\pi$
$168$		0			0
$169$		−	6.70188i		−	0.515529i
$170$	−8.04814	−	18.5480i	−0.617264	−	1.42257i
$171$		0			0
$172$	27.0769	+	7.25523i	2.06459	+	0.553206i
$173$	6.09793	+	22.7578i	0.463617	+	1.73024i	0.661433	+	0.750004i	$0.269949\pi$
$173$	6.09793	+	22.7578i	0.463617	+	1.73024i	−0.197816	+	0.980239i	$0.563385\pi$
$174$		0			0
$175$	2.94729	+	12.8963i	0.222794	+	0.974865i
$176$			3.09891i			0.233589i
$177$		0			0
$178$	2.95229	−	11.0181i	0.221284	−	0.825842i
$179$	−0.228953	−	0.396558i	−0.0171127	−	0.0296401i	0.857342	−	0.514747i	$-0.172114\pi$
$179$	−0.228953	−	0.396558i	−0.0171127	−	0.0296401i	−0.874455	+	0.485107i	$0.838781\pi$
$180$		0			0
$181$	−12.9702			−0.964070			−0.482035	−	0.876152i	$-0.660102\pi$
$181$	−12.9702			−0.964070			−0.482035	+	0.876152i	$0.660102\pi$
$182$	13.9428	−	6.78841i	1.03351	−	0.503190i
$183$		0			0
$184$	22.0262	+	12.7168i	1.62379	+	0.937496i
$185$	−10.6022	−	13.3497i	−0.779491	−	0.981486i
$186$		0			0
$187$	3.02692	+	11.2966i	0.221351	+	0.826091i
$188$	19.7320	−	19.7320i	1.43910	−	1.43910i
$189$		0			0
$190$	−22.6558	+	3.36831i	−1.64362	+	0.244363i
$191$	−5.84564	−	3.37498i	−0.422975	−	0.244205i	0.273374	−	0.961908i	$-0.411860\pi$
$191$	−5.84564	−	3.37498i	−0.422975	−	0.244205i	−0.696350	+	0.717703i	$0.745194\pi$
$192$		0			0
$193$	−1.32128	+	4.93109i	−0.0951079	+	0.354948i	−0.997036	−	0.0769390i	$-0.975485\pi$
$193$	−1.32128	+	4.93109i	−0.0951079	+	0.354948i	0.901928	+	0.431887i	$0.142152\pi$
$194$	4.44392	−	7.69710i	0.319055	−	0.552619i
$195$		0			0
$196$	−19.0361	−	14.9151i	−1.35972	−	1.06536i
$197$	5.34774	+	5.34774i	0.381011	+	0.381011i	0.871466	−	0.490456i	$-0.163170\pi$
$197$	5.34774	+	5.34774i	0.381011	+	0.381011i	−0.490456	+	0.871466i	$0.663170\pi$
$198$		0			0
$199$	−14.9596	+	8.63693i	−1.06046	+	0.612256i	−0.925559	−	0.378603i	$-0.876404\pi$
$199$	−14.9596	+	8.63693i	−1.06046	+	0.612256i	−0.134899	+	0.990859i	$0.543071\pi$
$200$	−0.567055	−	16.9788i	−0.0400968	−	1.20058i
$201$		0			0
$202$	20.7790	−	20.7790i	1.46201	−	1.46201i
$203$	−1.86458	+	2.76023i	−0.130868	+	0.193730i
$204$		0			0
$205$	9.58568	+	22.0915i	0.669493	+	1.54294i
$206$	27.7842	−	16.0412i	1.93582	−	1.11764i
$207$		0			0
$208$	−2.48677	+	0.666328i	−0.172426	+	0.0462015i
$209$	13.2488			0.916437
$210$		0			0
$211$	11.1106			0.764882			0.382441	−	0.923980i	$-0.375084\pi$
$211$	11.1106			0.764882			0.382441	+	0.923980i	$0.375084\pi$
$212$	6.08815	−	1.63131i	0.418136	−	0.112039i
$213$		0			0
$214$	6.14967	−	3.55051i	0.420383	−	0.242708i
$215$	16.8760	+	6.66247i	1.15093	+	0.454376i
$216$		0			0
$217$	13.9485	+	0.985072i	0.946888	+	0.0668711i
$218$	−27.3804	+	27.3804i	−1.85444	+	1.85444i
$219$		0			0
$220$	−2.65934	+	23.1839i	−0.179292	+	1.56306i
$221$	−8.41432	+	4.85801i	−0.566009	+	0.326785i
$222$		0			0
$223$	−1.84347	−	1.84347i	−0.123448	−	0.123448i	0.642684	−	0.766132i	$-0.277821\pi$
$223$	−1.84347	−	1.84347i	−0.123448	−	0.123448i	−0.766132	+	0.642684i	$0.777821\pi$
$224$	−7.63024	−	8.78986i	−0.509817	−	0.587297i
$225$		0			0
$226$	22.7590	−	39.4198i	1.51391	−	2.62216i
$227$	1.75018	−	6.53177i	0.116164	−	0.433529i	−0.883208	−	0.468982i	$-0.844621\pi$
$227$	1.75018	−	6.53177i	0.116164	−	0.433529i	0.999371	+	0.0354533i	$0.0112875\pi$
$228$		0			0
$229$	−22.0329	−	12.7207i	−1.45597	−	0.840606i	−0.457163	−	0.889383i	$-0.651135\pi$
$229$	−22.0329	−	12.7207i	−1.45597	−	0.840606i	−0.998810	+	0.0487763i	$0.984468\pi$
$230$	31.4076	+	23.2774i	2.07096	+	1.53487i
$231$		0			0
$232$	3.02475	−	3.02475i	0.198585	−	0.198585i
$233$	−2.75243	−	10.2722i	−0.180317	−	0.672954i	−0.995585	−	0.0938688i	$-0.970077\pi$
$233$	−2.75243	−	10.2722i	−0.180317	−	0.672954i	0.815267	−	0.579085i	$-0.196590\pi$
$234$		0			0
$235$	14.1436	−	11.2328i	0.922625	−	0.732744i
$236$	−17.7723	−	10.2608i	−1.15688	−	0.667923i
$237$		0			0
$238$	19.8240	+	13.3914i	1.28500	+	0.868037i
$239$	−15.7861			−1.02112			−0.510558	−	0.859843i	$-0.670561\pi$
$239$	−15.7861			−1.02112			−0.510558	+	0.859843i	$0.670561\pi$
$240$		0			0
$241$	1.41218	+	2.44597i	0.0909664	+	0.157559i	0.907918	−	0.419148i	$-0.137671\pi$
$241$	1.41218	+	2.44597i	0.0909664	+	0.157559i	−0.816952	+	0.576706i	$0.804338\pi$
$242$	−1.13326	+	4.22940i	−0.0728490	+	0.271876i
$243$		0			0
$244$			25.6461i			1.64182i
$245$	−11.1406	−	10.9949i	−0.711746	−	0.702437i
$246$		0			0
$247$	2.84876	+	10.6317i	0.181262	+	0.676479i
$248$	−17.3454	−	4.64768i	−1.10143	−	0.295128i
$249$		0			0
$250$	2.10813	−	26.0269i	0.133330	−	1.64609i
$251$			22.0003i			1.38865i	0.719663	+	0.694324i	$0.244296\pi$
$251$			22.0003i			1.38865i	−0.719663	+	0.694324i	$0.755704\pi$
$252$		0			0
$253$	−15.9895	−	15.9895i	−1.00525	−	1.00525i
$254$	21.7744	−	37.7143i	1.36625	−	2.36641i
$255$		0			0
$256$	11.0179	+	19.0836i	0.688619	+	1.19272i
$257$	9.59086	−	2.56986i	0.598261	−	0.160304i	0.0530353	−	0.998593i	$-0.483110\pi$
$257$	9.59086	−	2.56986i	0.598261	−	0.160304i	0.545226	+	0.838289i	$0.316444\pi$
$258$		0			0
$259$	19.0675	+	6.58022i	1.18480	+	0.408875i
$260$	−19.1761	+	2.85098i	−1.18925	+	0.176810i
$261$		0			0
$262$	−23.6227	−	6.32969i	−1.45942	−	0.391049i
$263$	8.47285	+	2.27029i	0.522458	+	0.139992i	0.510404	−	0.859935i	$-0.329496\pi$
$263$	8.47285	+	2.27029i	0.522458	+	0.139992i	0.0120549	+	0.999927i	$0.496163\pi$
$264$		0			0
$265$	4.03516	−	0.599922i	0.247878	−	0.0368529i
$266$	20.4659	−	17.7659i	1.25485	−	1.08930i
$267$		0			0
$268$	−32.3495	+	8.66803i	−1.97606	+	0.529484i
$269$	10.3843	+	17.9862i	0.633143	+	1.09664i	0.986905	+	0.161300i	$0.0515687\pi$
$269$	10.3843	+	17.9862i	0.633143	+	1.09664i	−0.353763	+	0.935335i	$0.615098\pi$
$270$		0			0
$271$	−11.8493	+	20.5237i	−0.719796	+	1.24672i	0.241284	+	0.970455i	$0.422432\pi$
$271$	−11.8493	+	20.5237i	−0.719796	+	1.24672i	−0.961080	+	0.276269i	$0.910902\pi$
$272$	−2.80837	−	2.80837i	−0.170283	−	0.170283i
$273$		0			0
$274$			38.7176i			2.33901i
$275$	−3.42004	+	14.7117i	−0.206236	+	0.887149i
$276$		0			0
$277$	5.81419	+	1.55791i	0.349341	+	0.0936056i	0.429223	−	0.903199i	$-0.358788\pi$
$277$	5.81419	+	1.55791i	0.349341	+	0.0936056i	−0.0798818	+	0.996804i	$0.525454\pi$
$278$	4.58260	+	17.1025i	0.274846	+	1.02574i
$279$		0			0
$280$	11.3612	+	16.5821i	0.678959	+	0.990972i
$281$			1.10459i			0.0658940i	0.999457	+	0.0329470i	$0.0104893\pi$
$281$			1.10459i			0.0658940i	−0.999457	+	0.0329470i	$0.989511\pi$
$282$		0			0
$283$	−3.59192	+	13.4052i	−0.213517	+	0.796858i	0.773166	+	0.634204i	$0.218672\pi$
$283$	−3.59192	+	13.4052i	−0.213517	+	0.796858i	−0.986683	+	0.162654i	$0.947995\pi$
$284$	−1.85344	−	3.21026i	−0.109982	−	0.190494i
$285$		0			0
$286$	17.7058			1.04697
$287$	−23.6113	−	15.9498i	−1.39373	−	0.941485i
$288$		0			0
$289$	1.74177	+	1.00561i	0.102457	+	0.0591534i
$290$	5.14878	−	4.08914i	0.302347	−	0.240122i
$291$		0			0
$292$	−1.91991	−	7.16520i	−0.112354	−	0.419311i
$293$	2.68196	−	2.68196i	0.156682	−	0.156682i	−0.624413	−	0.781095i	$-0.714662\pi$
$293$	2.68196	−	2.68196i	0.156682	−	0.156682i	0.781095	+	0.624413i	$0.214662\pi$
$294$		0			0
$295$	−10.6712	−	7.90884i	−0.621302	−	0.460471i
$296$	−22.4331	−	12.9517i	−1.30390	−	0.752804i
$297$		0			0
$298$	2.05702	−	7.67691i	0.119160	−	0.444712i
$299$	9.39299	−	16.2691i	0.543211	−	0.940868i
$300$		0			0
$301$	−21.0761	+	4.08166i	−1.21481	+	0.235263i
$302$	−26.0262	−	26.0262i	−1.49764	−	1.49764i
$303$		0			0
$304$	−3.89646	+	2.24962i	−0.223477	+	0.129025i
$305$	−1.89163	+	16.4911i	−0.108314	+	0.944277i
$306$		0			0
$307$	−15.8583	+	15.8583i	−0.905081	+	0.905081i	−0.995870	−	0.0907893i	$-0.971061\pi$
$307$	−15.8583	+	15.8583i	−0.905081	+	0.905081i	0.0907893	+	0.995870i	$0.471061\pi$
$308$	−12.0869	−	24.8254i	−0.688715	−	1.41456i
$309$		0			0
$310$	−25.6732	−	10.1355i	−1.45814	−	0.575659i
$311$	−22.0623	+	12.7377i	−1.25104	+	0.722288i	−0.971316	−	0.237793i	$-0.923576\pi$
$311$	−22.0623	+	12.7377i	−1.25104	+	0.722288i	−0.279723	+	0.960081i	$0.590243\pi$
$312$		0			0
$313$	−6.11703	+	1.63905i	−0.345755	+	0.0926448i	−0.427518	−	0.904007i	$-0.640612\pi$
$313$	−6.11703	+	1.63905i	−0.345755	+	0.0926448i	0.0817624	+	0.996652i	$0.473945\pi$
$314$	−14.5120			−0.818959
$315$		0			0
$316$	22.9380			1.29036
$317$	2.41602	−	0.647369i	0.135697	−	0.0363599i	−0.190331	−	0.981720i	$-0.560956\pi$
$317$	2.41602	−	0.647369i	0.135697	−	0.0363599i	0.326028	+	0.945360i	$0.394290\pi$
$318$		0			0
$319$	−3.29365	+	1.90159i	−0.184409	+	0.106469i
$320$	10.9716	+	25.2855i	0.613331	+	1.41350i
$321$		0			0
$322$	−46.1408	−	3.25855i	−2.57133	−	0.181592i
$323$	−12.0066	+	12.0066i	−0.668068	+	0.668068i
$324$		0			0
$325$	−12.5410	+	0.418842i	−0.695651	+	0.0232332i
$326$	7.35362	−	4.24561i	0.407279	−	0.235143i
$327$		0			0
$328$	25.8740	+	25.8740i	1.42865	+	1.42865i
$329$	−6.97155	+	20.2015i	−0.384354	+	1.11374i
$330$		0			0
$331$	−0.708836	+	1.22774i	−0.0389611	+	0.0674827i	−0.884848	−	0.465879i	$-0.845738\pi$
$331$	−0.708836	+	1.22774i	−0.0389611	+	0.0674827i	0.845887	+	0.533362i	$0.179072\pi$
$332$	−1.58159	+	5.90256i	−0.0868008	+	0.323945i
$333$		0			0
$334$	−17.5007	−	10.1040i	−0.957593	−	0.552867i
$335$	−21.4409	+	3.18770i	−1.17144	+	0.174162i
$336$		0			0
$337$	7.38849	−	7.38849i	0.402477	−	0.402477i	−0.476628	−	0.879105i	$-0.658141\pi$
$337$	7.38849	−	7.38849i	0.402477	−	0.402477i	0.879105	+	0.476628i	$0.158141\pi$
$338$	−4.05117	−	15.1192i	−0.220355	−	0.822375i
$339$		0			0
$340$	−18.6003	−	23.4203i	−1.00874	−	1.27015i
$341$	13.8265	+	7.98274i	0.748748	+	0.432290i
$342$		0			0
$343$	18.1075	+	3.88816i	0.977714	+	0.209941i
$344$	27.5687			1.48641
$345$		0			0
$346$	27.5134	+	47.6546i	1.47913	+	2.56193i
$347$	−2.72987	+	10.1880i	−0.146547	+	0.546922i	0.853134	+	0.521691i	$0.174699\pi$
$347$	−2.72987	+	10.1880i	−0.146547	+	0.546922i	−0.999682	+	0.0252308i	$0.991968\pi$
$348$		0			0
$349$		−	8.10936i		−	0.434084i	−0.976162	−	0.217042i	$-0.930359\pi$
$349$		−	8.10936i		−	0.434084i	0.976162	−	0.217042i	$-0.0696409\pi$
$350$	14.4445	+	27.3119i	0.772093	+	1.45988i
$351$		0			0
$352$	−3.43962	−	12.8368i	−0.183332	−	0.684206i
$353$	−10.0112	−	2.68249i	−0.532841	−	0.142774i	−0.0176413	−	0.999844i	$-0.505616\pi$
$353$	−10.0112	−	2.68249i	−0.532841	−	0.142774i	−0.515200	+	0.857070i	$0.672282\pi$
$354$		0			0
$355$	−0.955026	−	2.20099i	−0.0506875	−	0.116816i
$356$		−	16.8730i		−	0.894269i
$357$		0			0
$358$	−0.756221	−	0.756221i	−0.0399675	−	0.0399675i
$359$	−1.45427	+	2.51888i	−0.0767537	+	0.132941i	−0.901848	−	0.432054i	$-0.857789\pi$
$359$	−1.45427	+	2.51888i	−0.0767537	+	0.132941i	0.825094	+	0.564996i	$0.191122\pi$
$360$		0			0
$361$	0.117833	+	0.204093i	0.00620174	+	0.0107417i
$362$	−29.2603	+	7.84028i	−1.53789	+	0.412076i
$363$		0			0
$364$	17.3226	−	15.0373i	0.907952	−	0.788168i
$365$	−0.706053	−	4.74902i	−0.0369565	−	0.248575i
$366$		0			0
$367$	−10.4636	−	2.80371i	−0.546194	−	0.146352i	−0.0248380	−	0.999691i	$-0.507907\pi$
$367$	−10.4636	−	2.80371i	−0.546194	−	0.146352i	−0.521356	+	0.853339i	$0.674574\pi$
$368$	7.41752	+	1.98752i	0.386665	+	0.103607i
$369$		0			0
$370$	−31.9879	−	23.7074i	−1.66297	−	1.23249i
$371$	−3.64513	+	3.16424i	−0.189246	+	0.164279i
$372$		0			0
$373$	−17.3587	+	4.65126i	−0.898801	+	0.240833i	−0.678501	−	0.734599i	$-0.737370\pi$
$373$	−17.3587	+	4.65126i	−0.898801	+	0.240833i	−0.220300	+	0.975432i	$0.570704\pi$
$374$	13.6572	+	23.6550i	0.706199	+	1.22317i
$375$		0			0
$376$	13.7220	−	23.7672i	0.707658	−	1.22570i
$377$	−2.23416	−	2.23416i	−0.115065	−	0.115065i
$378$		0			0
$379$			7.37508i			0.378832i	0.981897	+	0.189416i	$0.0606595\pi$
$379$			7.37508i			0.378832i	−0.981897	+	0.189416i	$0.939340\pi$
$380$	−31.0812	+	13.4864i	−1.59443	+	0.691838i
$381$		0			0
$382$	−15.2277	−	4.08024i	−0.779114	−	0.208763i
$383$	−2.37013	−	8.84543i	−0.121108	−	0.451981i	0.878563	−	0.477626i	$-0.158503\pi$
$383$	−2.37013	−	8.84543i	−0.121108	−	0.451981i	−0.999671	+	0.0256454i	$0.991836\pi$
$384$		0			0
$385$	−5.94109	−	16.8549i	−0.302786	−	0.859004i
$386$			11.9230i			0.606867i
$387$		0			0
$388$	3.40269	−	12.6990i	0.172746	−	0.644695i
$389$	−4.50787	−	7.80786i	−0.228558	−	0.395874i	0.728823	−	0.684702i	$-0.240068\pi$
$389$	−4.50787	−	7.80786i	−0.228558	−	0.395874i	−0.957381	+	0.288828i	$0.906734\pi$
$390$		0			0
$391$	28.9809			1.46563
$392$	−21.8801	−	9.32328i	−1.10511	−	0.470897i
$393$		0			0
$394$	15.2969	+	8.83167i	0.770647	+	0.444933i
$395$	14.7497	+	1.69189i	0.742140	+	0.0851280i
$396$		0			0
$397$	−3.98408	−	14.8688i	−0.199955	−	0.746244i	−0.990928	−	0.134393i	$-0.957092\pi$
$397$	−3.98408	−	14.8688i	−0.199955	−	0.746244i	0.790973	−	0.611851i	$-0.209575\pi$
$398$	−28.5274	+	28.5274i	−1.42995	+	1.42995i
$399$		0			0
$400$	−1.49219	−	4.90743i	−0.0746096	−	0.245371i
$401$	16.5088	+	9.53134i	0.824408	+	0.475972i	0.851934	−	0.523649i	$-0.175430\pi$
$401$	16.5088	+	9.53134i	0.824408	+	0.475972i	−0.0275261	+	0.999621i	$0.508763\pi$
$402$		0			0
$403$	−3.43290	+	12.8118i	−0.171005	+	0.638200i
$404$	21.7340	−	37.6445i	1.08131	−	1.87288i
$405$		0			0
$406$	−2.53790	+	7.35408i	−0.125954	+	0.364977i
$407$	16.2849	+	16.2849i	0.807213	+	0.807213i
$408$		0			0
$409$	14.2422	−	8.22271i	0.704229	−	0.406587i	−0.104691	−	0.994505i	$-0.533385\pi$
$409$	14.2422	−	8.22271i	0.704229	−	0.406587i	0.808921	+	0.587918i	$0.200052\pi$
$410$	34.9788	+	44.0432i	1.72748	+	2.17514i
$411$		0			0
$412$	33.5570	−	33.5570i	1.65323	−	1.65323i
$413$	15.6770	+	1.10714i	0.771415	+	0.0544788i
$414$		0			0
$415$	−1.45237	+	3.67884i	−0.0712939	+	0.180587i
$416$	9.56155	−	5.52036i	0.468794	−	0.270658i
$417$		0			0
$418$	29.8887	−	8.00866i	1.46190	−	0.391716i
$419$	0.432905			0.0211488			0.0105744	−	0.999944i	$-0.496634\pi$
$419$	0.432905			0.0211488			0.0105744	+	0.999944i	$0.496634\pi$
$420$		0			0
$421$	2.44053			0.118944			0.0594721	−	0.998230i	$-0.481058\pi$
$421$	2.44053			0.118944			0.0594721	+	0.998230i	$0.481058\pi$
$422$	25.0650	−	6.71614i	1.22014	−	0.326937i
$423$		0			0
$424$	5.36826	−	3.09937i	0.260706	−	0.150519i
$425$	−10.2330	−	16.4318i	−0.496374	−	0.797061i
$426$		0			0
$427$	−8.59761	−	17.6587i	−0.416067	−	0.854564i
$428$	7.42739	−	7.42739i	0.359016	−	0.359016i
$429$		0			0
$430$	42.0990	+	4.82901i	2.03019	+	0.232876i
$431$	1.41023	−	0.814199i	0.0679286	−	0.0392186i	−0.465651	−	0.884968i	$-0.654180\pi$
$431$	1.41023	−	0.814199i	0.0679286	−	0.0392186i	0.533580	+	0.845750i	$0.320846\pi$
$432$		0			0
$433$	12.1563	+	12.1563i	0.584193	+	0.584193i	0.936053	−	0.351860i	$-0.114451\pi$
$433$	12.1563	+	12.1563i	0.584193	+	0.584193i	−0.351860	+	0.936053i	$0.614451\pi$
$434$	32.0628	−	6.20937i	1.53906	−	0.298059i
$435$		0			0
$436$	−28.6388	+	49.6039i	−1.37155	+	2.37560i
$437$	8.49725	−	31.7122i	0.406478	−	1.51700i
$438$		0			0
$439$	32.5150	+	18.7725i	1.55185	+	0.895964i	0.997991	+	0.0633566i	$0.0201805\pi$
$439$	32.5150	+	18.7725i	1.55185	+	0.895964i	0.553864	+	0.832607i	$0.313153\pi$
$440$	3.37499	+	22.7007i	0.160896	+	1.08221i
$441$		0			0
$442$	−16.0458	+	16.0458i	−0.763221	+	0.763221i
$443$	3.25374	+	12.1431i	0.154590	+	0.576937i	0.999140	+	0.0414608i	$0.0132012\pi$
$443$	3.25374	+	12.1431i	0.154590	+	0.576937i	−0.844550	+	0.535476i	$0.820132\pi$
$444$		0			0
$445$	1.24454	−	10.8498i	0.0589968	−	0.514330i
$446$	−5.27315	−	3.04446i	−0.249691	−	0.144159i
$447$		0			0
$448$	−27.0250	−	18.2558i	−1.27681	−	0.862507i
$449$	24.2617			1.14498			0.572491	−	0.819911i	$-0.305977\pi$
$449$	24.2617			1.14498			0.572491	+	0.819911i	$0.305977\pi$
$450$		0			0
$451$	−16.2664	−	28.1742i	−0.765953	−	1.32667i
$452$	17.4265	−	65.0365i	0.819673	−	3.05906i
$453$		0			0
$454$		−	15.7934i		−	0.741220i
$455$	12.2480	−	8.39167i	0.574196	−	0.393407i
$456$		0			0
$457$	8.47473	+	31.6281i	0.396431	+	1.47950i	0.819329	+	0.573323i	$0.194346\pi$
$457$	8.47473	+	31.6281i	0.396431	+	1.47950i	−0.422898	+	0.906177i	$0.638987\pi$
$458$	−57.3947	−	15.3789i	−2.68188	−	0.718608i
$459$		0			0
$460$	53.7872	+	21.2346i	2.50784	+	0.990070i
$461$		−	11.3402i		−	0.528165i	−0.964500	−	0.264083i	$-0.914931\pi$
$461$		−	11.3402i		−	0.528165i	0.964500	−	0.264083i	$-0.0850691\pi$
$462$		0			0
$463$	10.8990	+	10.8990i	0.506520	+	0.506520i	0.913456	−	0.406937i	$-0.133403\pi$
$463$	10.8990	+	10.8990i	0.506520	+	0.506520i	−0.406937	+	0.913456i	$0.633403\pi$
$464$	0.645775	−	1.11851i	0.0299793	−	0.0519257i
$465$		0			0
$466$	−12.4187	−	21.5099i	−0.575287	−	0.996426i
$467$	−22.3197	+	5.98056i	−1.03283	+	0.276747i	−0.735141	−	0.677914i	$-0.762884\pi$
$467$	−22.3197	+	5.98056i	−1.03283	+	0.276747i	−0.297694	+	0.954661i	$0.596217\pi$
$468$		0			0
$469$	19.3685	−	16.8133i	0.894354	−	0.776365i
$470$	25.1173	−	33.8902i	1.15858	−	1.56324i
$471$		0			0
$472$	−19.4948	−	5.22361i	−0.897319	−	0.240436i
$473$	−23.6757	−	6.34388i	−1.08861	−	0.291692i
$474$		0			0
$475$	−20.9808	+	6.37958i	−0.962664	+	0.292715i
$476$	33.4516	+	11.5442i	1.53325	+	0.529127i
$477$		0			0
$478$	−35.6128	+	9.54242i	−1.62889	+	0.436460i
$479$	−4.96946	−	8.60736i	−0.227061	−	0.393280i	0.729875	−	0.683581i	$-0.239578\pi$
$479$	−4.96946	−	8.60736i	−0.227061	−	0.393280i	−0.956936	+	0.290300i	$0.906245\pi$
$480$		0			0
$481$	−9.56651	+	16.5697i	−0.436195	+	0.755512i
$482$	4.66437	+	4.66437i	0.212456	+	0.212456i
$483$		0			0
$484$			6.47687i			0.294403i
$485$	3.12469	−	7.91482i	0.141885	−	0.359393i
$486$		0			0
$487$	4.47934	+	1.20024i	0.202978	+	0.0543879i	0.358876	−	0.933385i	$-0.383160\pi$
$487$	4.47934	+	1.20024i	0.202978	+	0.0543879i	−0.155897	+	0.987773i	$0.549827\pi$
$488$	6.52798	+	24.3628i	0.295508	+	1.10285i
$489$		0			0
$490$	−31.7790	−	18.0697i	−1.43563	−	0.816307i
$491$			1.99747i			0.0901445i	0.998984	+	0.0450722i	$0.0143518\pi$
$491$			1.99747i			0.0901445i	−0.998984	+	0.0450722i	$0.985648\pi$
$492$		0			0
$493$	1.26155	−	4.70817i	0.0568173	−	0.212045i
$494$	12.8534	+	22.2627i	0.578300	+	1.00165i
$495$		0			0
$496$	−5.42183			−0.243448
$497$	2.35240	+	1.58908i	0.105520	+	0.0712801i
$498$		0			0
$499$	−0.178762	−	0.103208i	−0.00800250	−	0.00462025i	0.495993	−	0.868326i	$-0.334804\pi$
$499$	−0.178762	−	0.103208i	−0.00800250	−	0.00462025i	−0.503996	+	0.863706i	$0.668137\pi$
$500$	−6.95224	−	37.9946i	−0.310914	−	1.69917i
$501$		0			0
$502$	13.2988	+	49.6319i	0.593555	+	2.21518i
$503$	20.3423	−	20.3423i	0.907017	−	0.907017i	−0.0890134	−	0.996030i	$-0.528371\pi$
$503$	20.3423	−	20.3423i	0.907017	−	0.907017i	0.996030	+	0.0890134i	$0.0283714\pi$
$504$		0			0
$505$	16.7522	−	22.6033i	0.745462	−	1.00583i
$506$	−45.7371	−	26.4063i	−2.03326	−	1.17391i
$507$		0			0
$508$	16.6726	−	62.2228i	0.739725	−	2.76069i
$509$	−2.36278	+	4.09245i	−0.104728	+	0.181395i	−0.913627	−	0.406553i	$-0.866731\pi$
$509$	−2.36278	+	4.09245i	−0.104728	+	0.181395i	0.808899	+	0.587948i	$0.200064\pi$
$510$		0			0
$511$	3.72402	+	4.28999i	0.164741	+	0.189778i
$512$	8.12052	+	8.12052i	0.358880	+	0.358880i
$513$		0			0
$514$	20.0832	−	11.5950i	0.885831	−	0.511435i
$515$	24.0531	−	19.1029i	1.05991	−	0.841773i
$516$		0			0
$517$	−17.2534	+	17.2534i	−0.758803	+	0.758803i
$518$	46.9932	+	3.31875i	2.06476	+	0.145817i
$519$		0			0
$520$	−17.4909	+	7.58943i	−0.767025	+	0.332819i
$521$	−10.9951	+	6.34804i	−0.481705	+	0.278113i	−0.721127	−	0.692803i	$-0.756375\pi$
$521$	−10.9951	+	6.34804i	−0.481705	+	0.278113i	0.239422	+	0.970916i	$0.423042\pi$
$522$		0			0
$523$	−31.6604	+	8.48338i	−1.38441	+	0.370952i	−0.872722	−	0.488217i	$-0.837647\pi$
$523$	−31.6604	+	8.48338i	−1.38441	+	0.370952i	−0.511691	+	0.859170i	$0.670981\pi$
$524$	−36.1756			−1.58034
$525$		0			0
$526$	20.4868			0.893266
$527$	−19.7645	+	5.29590i	−0.860957	+	0.230693i
$528$		0			0
$529$	−28.6089	+	16.5173i	−1.24386	+	0.718145i
$530$	8.74053	−	3.79259i	0.379664	−	0.164739i
$531$		0			0
$532$	22.4402	−	33.2194i	0.972908	−	1.44025i
$533$	19.1112	−	19.1112i	0.827800	−	0.827800i
$534$		0			0
$535$	5.32384	−	4.22817i	0.230170	−	0.182800i
$536$	−28.5244	+	16.4686i	−1.23207	+	0.711334i
$537$		0			0
$538$	34.2989	+	34.2989i	1.47873	+	1.47873i
$539$	16.6449	+	13.0416i	0.716948	+	0.561740i
$540$		0			0
$541$	21.0600	−	36.4771i	0.905442	−	1.56827i	0.0851189	−	0.996371i	$-0.472873\pi$
$541$	21.0600	−	36.4771i	0.905442	−	1.56827i	0.820323	−	0.571901i	$-0.193794\pi$
$542$	−14.3255	+	53.4633i	−0.615331	+	2.29645i
$543$		0			0
$544$	14.7505	+	8.51619i	0.632421	+	0.365129i
$545$	−22.0742	+	29.7842i	−0.945556	+	1.27582i
$546$		0			0
$547$	19.7948	−	19.7948i	0.846364	−	0.846364i	−0.143313	−	0.989677i	$-0.545776\pi$
$547$	19.7948	−	19.7948i	0.846364	−	0.846364i	0.989677	+	0.143313i	$0.0457757\pi$
$548$	14.8229	+	55.3200i	0.633205	+	2.36315i
$549$		0			0
$550$	1.17748	+	35.2564i	0.0502081	+	1.50334i
$551$	−4.78199	−	2.76089i	−0.203720	−	0.117618i
$552$		0			0
$553$	−15.7940	+	7.68975i	−0.671631	+	0.327002i
$554$	14.0583			0.597280
$555$		0			0
$556$	13.0953	+	22.6818i	0.555365	+	0.961921i
$557$	10.6149	−	39.6153i	0.449767	−	1.67855i	−0.253266	−	0.967397i	$-0.581505\pi$
$557$	10.6149	−	39.6153i	0.449767	−	1.67855i	0.703033	−	0.711157i	$-0.251829\pi$
$558$		0			0
$559$		−	20.3630i		−	0.861264i
$560$	4.60921	+	3.94823i	0.194775	+	0.166843i
$561$		0			0
$562$	0.667703	+	2.49190i	0.0281654	+	0.105115i
$563$	−6.90950	−	1.85140i	−0.291201	−	0.0780270i	0.110261	−	0.993903i	$-0.464831\pi$
$563$	−6.90950	−	1.85140i	−0.291201	−	0.0780270i	−0.401462	+	0.915876i	$0.631498\pi$
$564$		0			0
$565$	16.0027	−	40.5348i	0.673239	−	1.70531i
$566$			32.4129i			1.36242i
$567$		0			0
$568$	−2.57784	−	2.57784i	−0.108164	−	0.108164i
$569$	−19.8667	+	34.4101i	−0.832855	+	1.44255i	0.0629097	+	0.998019i	$0.479962\pi$
$569$	−19.8667	+	34.4101i	−0.832855	+	1.44255i	−0.895765	+	0.444528i	$0.853371\pi$
$570$		0			0
$571$	−13.4380	−	23.2753i	−0.562362	−	0.974040i	−0.997290	−	0.0735743i	$-0.976559\pi$
$571$	−13.4380	−	23.2753i	−0.562362	−	0.974040i	0.434928	−	0.900465i	$-0.356774\pi$
$572$	25.2982	−	6.77863i	1.05777	−	0.283429i
$573$		0			0
$574$	−62.9074	−	21.7095i	−2.62571	−	0.906135i
$575$	33.0203	+	17.6217i	1.37704	+	0.734876i
$576$		0			0
$577$	15.3466	+	4.11210i	0.638886	+	0.171189i	0.563699	−	0.825980i	$-0.309378\pi$
$577$	15.3466	+	4.11210i	0.638886	+	0.171189i	0.0751873	+	0.997169i	$0.476045\pi$
$578$	4.53723	+	1.21575i	0.188724	+	0.0505684i
$579$		0			0
$580$	5.79111	−	7.81379i	0.240463	−	0.324450i
$581$	−0.889770	−	4.59443i	−0.0369139	−	0.190609i
$582$		0			0
$583$	−5.32340	+	1.42640i	−0.220473	+	0.0590755i
$584$	−3.64767	−	6.31796i	−0.150942	−	0.261439i
$585$		0			0
$586$	4.42920	−	7.67160i	0.182969	−	0.316911i
$587$	4.67480	+	4.67480i	0.192950	+	0.192950i	0.796969	−	0.604020i	$-0.206435\pi$
$587$	4.67480	+	4.67480i	0.192950	+	0.192950i	−0.604020	+	0.796969i	$0.706435\pi$
$588$		0			0
$589$			23.1800i			0.955116i
$590$	−28.8546	−	11.3915i	−1.18792	−	0.468980i
$591$		0			0
$592$	−7.55454	−	2.02423i	−0.310490	−	0.0831955i
$593$	2.56925	+	9.58856i	0.105506	+	0.393755i	0.998402	−	0.0565085i	$-0.0179968\pi$
$593$	2.56925	+	9.58856i	0.105506	+	0.393755i	−0.892896	+	0.450263i	$0.851330\pi$
$594$		0			0
$595$	20.6588	+	9.89057i	0.846926	+	0.405474i
$596$		−	11.7564i		−	0.481559i
$597$		0			0
$598$	11.3558	−	42.3804i	0.464373	−	1.73307i
$599$	−8.98437	−	15.5614i	−0.367092	−	0.635821i	0.622018	−	0.783003i	$-0.286313\pi$
$599$	−8.98437	−	15.5614i	−0.367092	−	0.635821i	−0.989109	+	0.147182i	$0.952980\pi$
$600$		0			0
$601$	39.8874			1.62704			0.813520	−	0.581538i	$-0.197549\pi$
$601$	39.8874			1.62704			0.813520	+	0.581538i	$0.197549\pi$
$602$	−45.0796	+	21.9482i	−1.83731	+	0.894543i
$603$		0			0
$604$	−47.1506	−	27.2224i	−1.91853	−	1.10766i
$605$	−0.477728	+	4.16480i	−0.0194224	+	0.169323i
$606$		0			0
$607$	−8.29542	−	30.9589i	−0.336701	−	1.25658i	−0.902014	−	0.431708i	$-0.857911\pi$
$607$	−8.29542	−	30.9589i	−0.336701	−	1.25658i	0.565313	−	0.824877i	$-0.308755\pi$
$608$	13.6437	−	13.6437i	0.553323	−	0.553323i
$609$		0			0
$610$	5.70114	+	38.3467i	0.230833	+	1.55261i
$611$	−17.5551	−	10.1354i	−0.710203	−	0.410036i
$612$		0			0
$613$	−4.35747	+	16.2623i	−0.175996	+	0.656828i	0.820383	+	0.571814i	$0.193760\pi$
$613$	−4.35747	+	16.2623i	−0.175996	+	0.656828i	−0.996380	+	0.0850137i	$0.972907\pi$
$614$	−26.1896	+	45.3618i	−1.05693	+	1.83065i
$615$		0			0
$616$	−17.8011	−	20.5065i	−0.717229	−	0.826231i
$617$	10.1234	+	10.1234i	0.407552	+	0.407552i	0.880884	−	0.473332i	$-0.156949\pi$
$617$	10.1234	+	10.1234i	0.407552	+	0.407552i	−0.473332	+	0.880884i	$0.656949\pi$
$618$		0			0
$619$	−28.0328	+	16.1847i	−1.12673	+	0.650520i	−0.943111	−	0.332477i	$-0.892115\pi$
$619$	−28.0328	+	16.1847i	−1.12673	+	0.650520i	−0.183622	+	0.982997i	$0.558782\pi$
$620$	−40.5625	−	4.65277i	−1.62903	−	0.186860i
$621$		0			0
$622$	−42.0720	+	42.0720i	−1.68693	+	1.68693i
$623$	5.65653	+	11.6180i	0.226624	+	0.465465i
$624$		0			0
$625$	−1.66803	−	24.9443i	−0.0667211	−	0.997772i
$626$	−12.8090	+	7.39529i	−0.511951	+	0.295575i
$627$		0			0
$628$	−20.7349	+	5.55589i	−0.827411	+	0.221704i
$629$	−29.5163			−1.17689
$630$		0			0
$631$	−8.76242			−0.348827			−0.174413	−	0.984673i	$-0.555803\pi$
$631$	−8.76242			−0.348827			−0.174413	+	0.984673i	$0.555803\pi$
$632$	21.7902	−	5.83867i	0.866768	−	0.232250i
$633$		0			0
$634$	5.05911	−	2.92088i	0.200923	−	0.116003i
$635$	15.3104	−	38.7811i	0.607574	−	1.53898i
$636$		0			0
$637$	−6.88643	+	16.1612i	−0.272850	+	0.640331i
$638$	−6.28087	+	6.28087i	−0.248662	+	0.248662i
$639$		0			0
$640$	27.8001	+	35.0042i	1.09890	+	1.38366i
$641$	3.35536	−	1.93722i	0.132529	−	0.0765156i	−0.432270	−	0.901744i	$-0.642287\pi$
$641$	3.35536	−	1.93722i	0.132529	−	0.0765156i	0.564799	+	0.825229i	$0.308954\pi$
$642$		0			0
$643$	−22.2135	−	22.2135i	−0.876016	−	0.876016i	0.117103	−	0.993120i	$-0.462639\pi$
$643$	−22.2135	−	22.2135i	−0.876016	−	0.876016i	−0.993120	+	0.117103i	$0.962639\pi$
$644$	−67.1739	+	13.0091i	−2.64702	+	0.512629i
$645$		0			0
$646$	−19.8287	+	34.3444i	−0.780151	+	1.35126i
$647$	0.903571	−	3.37217i	0.0355231	−	0.132574i	−0.945887	−	0.324496i	$-0.894805\pi$
$647$	0.903571	−	3.37217i	0.0355231	−	0.132574i	0.981410	+	0.191922i	$0.0614720\pi$
$648$		0			0
$649$	15.5399	+	8.97194i	0.609993	+	0.352179i
$650$	−28.0389	+	8.52573i	−1.09978	+	0.334407i
$651$		0			0
$652$	8.88149	−	8.88149i	0.347826	−	0.347826i
$653$	−5.37079	−	20.0441i	−0.210175	−	0.784385i	−0.987809	−	0.155668i	$-0.950247\pi$
$653$	−5.37079	−	20.0441i	−0.210175	−	0.784385i	0.777634	−	0.628717i	$-0.216420\pi$
$654$		0			0
$655$	−23.2619	−	2.66828i	−0.908916	−	0.104258i
$656$	9.56788	+	5.52402i	0.373563	+	0.215677i
$657$		0			0
$658$	−3.51612	+	49.7879i	−0.137073	+	1.94093i
$659$	8.70064			0.338929			0.169464	−	0.985536i	$-0.445796\pi$
$659$	8.70064			0.338929			0.169464	+	0.985536i	$0.445796\pi$
$660$		0			0
$661$	−21.7101	−	37.6029i	−0.844424	−	1.46258i	−0.886121	−	0.463455i	$-0.846610\pi$
$661$	−21.7101	−	37.6029i	−0.844424	−	1.46258i	0.0416969	−	0.999130i	$-0.486724\pi$
$662$	−0.856958	+	3.19821i	−0.0333066	+	0.124302i
$663$		0			0
$664$			6.00977i			0.233224i
$665$	16.8799	−	19.7058i	0.654574	−	0.764157i
$666$		0			0
$667$	2.43921	+	9.10326i	0.0944466	+	0.352480i
$668$	−28.8734	−	7.73660i	−1.11714	−	0.299338i
$669$		0			0
$670$	−46.4430	+	20.1520i	−1.79425	+	0.778540i
$671$		−	22.4246i		−	0.865693i
$672$		0			0
$673$	12.2145	+	12.2145i	0.470833	+	0.470833i	0.902184	−	0.431351i	$-0.141963\pi$
$673$	12.2145	+	12.2145i	0.470833	+	0.470833i	−0.431351	+	0.902184i	$0.641963\pi$
$674$	12.2019	−	21.1344i	0.470001	−	0.814065i
$675$		0			0
$676$	−11.5767	−	20.0514i	−0.445258	−	0.771209i
$677$	−20.3087	+	5.44169i	−0.780526	+	0.209141i	−0.627017	−	0.779006i	$-0.715724\pi$
$677$	−20.3087	+	5.44169i	−0.780526	+	0.209141i	−0.153509	+	0.988147i	$0.549057\pi$
$678$		0			0
$679$	1.91429	+	9.88467i	0.0734637	+	0.379339i
$680$	−23.6310	−	17.5139i	−0.906207	−	0.671626i
$681$		0			0
$682$	36.0175	+	9.65086i	1.37918	+	0.369551i
$683$	17.0354	+	4.56461i	0.651840	+	0.174660i	0.569561	−	0.821949i	$-0.307113\pi$
$683$	17.0354	+	4.56461i	0.651840	+	0.174660i	0.0822793	+	0.996609i	$0.473780\pi$
$684$		0			0
$685$	5.45119	+	36.6655i	0.208279	+	1.40092i
$686$	43.2002	−	2.17415i	1.64939	−	0.0830093i
$687$		0			0
$688$	8.04020	−	2.15437i	0.306530	−	0.0821344i
$689$	−2.28928	−	3.96515i	−0.0872146	−	0.151060i
$690$		0			0
$691$	15.0811	−	26.1213i	0.573714	−	0.993701i	−0.422467	−	0.906378i	$-0.638836\pi$
$691$	15.0811	−	26.1213i	0.573714	−	0.993701i	0.996180	−	0.0873225i	$-0.0278310\pi$
$692$	57.5559	+	57.5559i	2.18795	+	2.18795i
$693$		0			0
$694$			24.6340i			0.935093i
$695$	6.74764	+	15.5508i	0.255953	+	0.589877i
$696$		0			0
$697$	40.2741	+	10.7914i	1.52549	+	0.408754i
$698$	−4.90197	−	18.2944i	−0.185542	−	0.692454i
$699$		0			0
$700$	31.0948	+	33.4934i	1.17527	+	1.26593i
$701$		−	25.9117i		−	0.978670i	−0.872096	−	0.489335i	$-0.837240\pi$
$701$		−	25.9117i		−	0.978670i	0.872096	−	0.489335i	$-0.162760\pi$
$702$		0			0
$703$	−8.65422	+	32.2980i	−0.326400	+	1.21814i
$704$	−18.6182	−	32.2477i	−0.701700	−	1.21538i
$705$		0			0
$706$	−24.2063			−0.911018
$707$	−2.34510	+	33.2064i	−0.0881964	+	1.24885i
$708$		0			0
$709$	−12.4525	−	7.18943i	−0.467662	−	0.270005i	0.247599	−	0.968863i	$-0.420359\pi$
$709$	−12.4525	−	7.18943i	−0.467662	−	0.270005i	−0.715260	+	0.698858i	$0.753692\pi$
$710$	−3.48496	−	4.38804i	−0.130788	−	0.164680i
$711$		0			0
$712$	−4.29488	−	16.0287i	−0.160958	−	0.600702i
$713$	27.9752	−	27.9752i	1.04768	−	1.04768i
$714$		0			0
$715$	16.7674	−	2.49286i	0.627064	−	0.0932278i
$716$	−1.37001	−	0.790977i	−0.0511998	−	0.0295602i
$717$		0			0
$718$	−1.75817	+	6.56158i	−0.0656143	+	0.244876i
$719$	3.38386	−	5.86102i	0.126197	−	0.218579i	−0.796003	−	0.605292i	$-0.793056\pi$
$719$	3.38386	−	5.86102i	0.126197	−	0.218579i	0.922200	+	0.386713i	$0.126390\pi$
$720$		0			0
$721$	−11.8561	+	34.3554i	−0.441544	+	1.27946i
$722$	0.389198	+	0.389198i	0.0144844	+	0.0144844i
$723$		0			0
$724$	−38.8058	+	22.4045i	−1.44221	+	0.832658i
$725$	4.30017	−	4.59732i	0.159704	−	0.170740i
$726$		0			0
$727$	16.4806	−	16.4806i	0.611233	−	0.611233i	−0.332034	−	0.943267i	$-0.607735\pi$
$727$	16.4806	−	16.4806i	0.611233	−	0.611233i	0.943267	+	0.332034i	$0.107735\pi$
$728$	12.6282	−	18.6941i	0.468032	−	0.692851i
$729$		0			0
$730$	−4.46353	−	10.2868i	−0.165203	−	0.380732i
$731$	27.2051	−	15.7069i	1.00622	−	0.580940i
$732$		0			0
$733$	50.6311	−	13.5666i	1.87010	−	0.501093i	0.870137	−	0.492810i	$-0.164030\pi$
$733$	50.6311	−	13.5666i	1.87010	−	0.501093i	0.999966	−	0.00828279i	$-0.00263652\pi$
$734$	−25.3002			−0.933848
$735$		0			0
$736$	−32.9322			−1.21390
$737$	28.2860	−	7.57921i	1.04193	−	0.279184i
$738$		0			0
$739$	37.8928	−	21.8774i	1.39391	−	0.804773i	0.400163	−	0.916444i	$-0.368954\pi$
$739$	37.8928	−	21.8774i	1.39391	−	0.804773i	0.993745	+	0.111671i	$0.0356203\pi$
$740$	−54.7809	−	21.6269i	−2.01378	−	0.795021i
$741$		0			0
$742$	−6.31055	+	9.34183i	−0.231668	+	0.342949i
$743$	−16.4879	+	16.4879i	−0.604881	+	0.604881i	−0.941604	−	0.336723i	$-0.890681\pi$
$743$	−16.4879	+	16.4879i	−0.604881	+	0.604881i	0.336723	+	0.941604i	$0.390681\pi$
$744$		0			0
$745$	0.867138	−	7.55965i	0.0317695	−	0.276964i
$746$	−36.3490	+	20.9861i	−1.33083	+	0.768356i
$747$		0			0
$748$	28.5699	+	28.5699i	1.04462	+	1.04462i
$749$	−2.62419	+	7.60411i	−0.0958859	+	0.277848i
$750$		0			0
$751$	−1.48307	+	2.56876i	−0.0541181	+	0.0937353i	−0.891815	−	0.452400i	$-0.850568\pi$
$751$	−1.48307	+	2.56876i	−0.0541181	+	0.0937353i	0.837697	+	0.546135i	$0.183901\pi$
$752$	2.14462	−	8.00382i	0.0782061	−	0.291869i
$753$		0			0
$754$	−6.39070	−	3.68967i	−0.232736	−	0.134370i
$755$	−28.3111	−	20.9825i	−1.03035	−	0.763631i
$756$		0			0
$757$	−31.2106	+	31.2106i	−1.13437	+	1.13437i	−0.144925	+	0.989443i	$0.546294\pi$
$757$	−31.2106	+	31.2106i	−1.13437	+	1.13437i	−0.989443	+	0.144925i	$0.953706\pi$
$758$	4.45811	+	16.6379i	0.161926	+	0.604316i
$759$		0			0
$760$	−26.0931	+	20.7230i	−0.946495	+	0.751702i
$761$	34.8304	+	20.1094i	1.26260	+	0.728963i	0.973577	−	0.228358i	$-0.0733357\pi$
$761$	34.8304	+	20.1094i	1.26260	+	0.728963i	0.289025	+	0.957322i	$0.406669\pi$
$762$		0			0
$763$	3.09012	−	43.7558i	0.111870	−	1.58407i
$764$	−23.3195			−0.843670
$765$		0			0
$766$	−10.6938	−	18.5223i	−0.386384	−	0.669236i
$767$	−3.85830	+	14.3994i	−0.139315	+	0.519931i
$768$		0			0
$769$		−	24.6136i		−	0.887589i	−0.896129	−	0.443794i	$-0.853632\pi$
$769$		−	24.6136i		−	0.887589i	0.896129	−	0.443794i	$-0.146368\pi$
$770$	−23.5913	−	34.4326i	−0.850173	−	1.24087i
$771$		0			0
$772$	4.56471	+	17.0357i	0.164288	+	0.613130i
$773$	−49.7233	−	13.3233i	−1.78842	−	0.479206i	−0.796345	−	0.604843i	$-0.793236\pi$
$773$	−49.7233	−	13.3233i	−1.78842	−	0.479206i	−0.992076	+	0.125637i	$0.959903\pi$
$774$		0			0
$775$	−25.7395	−	5.98370i	−0.924592	−	0.214941i
$776$		−	12.9297i		−	0.464149i
$777$		0			0
$778$	−14.8893	−	14.8893i	−0.533807	−	0.533807i
$779$	23.6169	−	40.9056i	0.846162	−	1.46560i
$780$		0			0
$781$	1.62063	+	2.80701i	0.0579906	+	0.100443i
$782$	65.3798	−	17.5185i	2.33798	−	0.626459i
$783$		0			0
$784$	−7.10972	−	1.00924i	−0.253918	−	0.0360442i
$785$	−13.7429	+	2.04320i	−0.490503	+	0.0729248i
$786$		0			0
$787$	24.8118	+	6.64831i	0.884446	+	0.236987i	0.672324	−	0.740257i	$-0.265296\pi$
$787$	24.8118	+	6.64831i	0.884446	+	0.236987i	0.212121	+	0.977243i	$0.431963\pi$
$788$	25.2375	+	6.76238i	0.899050	+	0.240900i
$789$		0			0
$790$	34.2976	−	5.09914i	1.22025	−	0.181419i
$791$	9.80382	+	50.6232i	0.348584	+	1.79995i
$792$		0			0
$793$	17.9950	−	4.82175i	0.639022	−	0.171225i
$794$	−17.9759	−	31.1351i	−0.637940	−	1.10494i
$795$		0			0
$796$	−29.8386	+	51.6819i	−1.05760	+	1.83182i
$797$	1.12818	+	1.12818i	0.0399621	+	0.0399621i	0.726805	−	0.686843i	$-0.241004\pi$
$797$	1.12818	+	1.12818i	0.0399621	+	0.0399621i	−0.686843	+	0.726805i	$0.741004\pi$
$798$		0			0
$799$		−	31.2716i		−	1.10631i
$800$	11.6282	+	18.6722i	0.411119	+	0.660161i
$801$		0			0
$802$	43.0047	+	11.5231i	1.51855	+	0.406893i
$803$	1.67874	+	6.26516i	0.0592416	+	0.221093i
$804$		0			0
$805$	−44.1541	+	3.41049i	−1.55623	+	0.120204i
$806$			30.9780i			1.09115i
$807$		0			0
$808$	11.0644	−	41.2930i	0.389245	−	1.45268i
$809$	18.4134	+	31.8929i	0.647381	+	1.12130i	0.983746	+	0.179565i	$0.0574689\pi$
$809$	18.4134	+	31.8929i	0.647381	+	1.12130i	−0.336366	+	0.941731i	$0.609198\pi$
$810$		0			0
$811$	9.33779			0.327894			0.163947	−	0.986469i	$-0.447577\pi$
$811$	9.33779			0.327894			0.163947	+	0.986469i	$0.447577\pi$
$812$	−0.810683	+	11.4792i	−0.0284494	+	0.402841i
$813$		0			0
$814$	46.5821	+	26.8942i	1.63270	+	0.942640i
$815$	6.36612	−	5.05594i	0.222995	−	0.177102i
$816$		0			0
$817$	−9.21057	−	34.3743i	−0.322237	−	1.20261i
$818$	27.1593	−	27.1593i	0.949602	−	0.949602i
$819$		0			0
$820$	66.8399	+	49.5376i	2.33415	+	1.72993i
$821$	13.7473	+	7.93699i	0.479783	+	0.277003i	0.720326	−	0.693636i	$-0.243992\pi$
$821$	13.7473	+	7.93699i	0.479783	+	0.277003i	−0.240543	+	0.970639i	$0.577325\pi$
$822$		0			0
$823$	3.54133	−	13.2164i	0.123443	−	0.460696i	−0.876336	−	0.481700i	$-0.840020\pi$
$823$	3.54133	−	13.2164i	0.123443	−	0.460696i	0.999779	+	0.0210040i	$0.00668627\pi$
$824$	23.3362	−	40.4194i	0.812954	−	1.40808i
$825$		0			0
$826$	36.0360	−	6.97882i	1.25385	−	0.242824i
$827$	−1.84947	−	1.84947i	−0.0643124	−	0.0643124i	0.674219	−	0.738531i	$-0.264480\pi$
$827$	−1.84947	−	1.84947i	−0.0643124	−	0.0643124i	−0.738531	+	0.674219i	$0.764480\pi$
$828$		0			0
$829$	−28.8636	+	16.6644i	−1.00247	+	0.578778i	−0.908979	−	0.416842i	$-0.863137\pi$
$829$	−28.8636	+	16.6644i	−1.00247	+	0.578778i	−0.0934940	+	0.995620i	$0.529804\pi$
$830$	−1.05269	+	9.17725i	−0.0365393	+	0.318547i
$831$		0			0
$832$	21.8744	−	21.8744i	0.758359	−	0.758359i
$833$	−26.9033	+	3.26554i	−0.932144	+	0.113144i
$834$		0			0
$835$	−17.9957	−	7.10451i	−0.622767	−	0.245862i
$836$	39.6392	−	22.8857i	1.37095	−	0.791518i
$837$		0			0
$838$	0.976617	−	0.261684i	0.0337367	−	0.00903971i
$839$	26.2661			0.906808			0.453404	−	0.891305i	$-0.350210\pi$
$839$	26.2661			0.906808			0.453404	+	0.891305i	$0.350210\pi$
$840$		0			0
$841$	−27.4149			−0.945342
$842$	5.50574	−	1.47526i	0.189740	−	0.0508408i
$843$		0			0
$844$	33.2418	−	19.1922i	1.14423	−	0.660621i
$845$	−5.96514	−	13.7475i	−0.205207	−	0.472928i
$846$		0			0
$847$	−2.17131	−	4.45967i	−0.0746071	−	0.153236i
$848$	1.32341	−	1.32341i	0.0454461	−	0.0454461i
$849$		0			0
$850$	−33.0181	−	30.8839i	−1.13251	−	1.05931i
$851$	49.4239	−	28.5349i	1.69423	−	0.978164i
$852$		0			0
$853$	−19.2905	−	19.2905i	−0.660495	−	0.660495i	0.295002	−	0.955497i	$-0.404680\pi$
$853$	−19.2905	−	19.2905i	−0.660495	−	0.660495i	−0.955497	+	0.295002i	$0.904680\pi$
$854$	−30.0702	−	34.6402i	−1.02898	−	1.18536i
$855$		0			0
$856$	5.16515	−	8.94630i	0.176541	−	0.305778i
$857$	−8.71601	+	32.5286i	−0.297733	+	1.11116i	0.641289	+	0.767299i	$0.278400\pi$
$857$	−8.71601	+	32.5286i	−0.297733	+	1.11116i	−0.939022	+	0.343856i	$0.888267\pi$
$858$		0			0
$859$	3.29570	+	1.90278i	0.112448	+	0.0649219i	0.555169	−	0.831737i	$-0.312654\pi$
$859$	3.29570	+	1.90278i	0.112448	+	0.0649219i	−0.442721	+	0.896659i	$0.645987\pi$
$860$	62.0001	−	9.21777i	2.11419	−	0.314323i
$861$		0			0
$862$	2.68926	−	2.68926i	0.0915967	−	0.0915967i
$863$	−7.13565	−	26.6306i	−0.242901	−	0.906517i	−0.974427	−	0.224704i	$-0.927858\pi$
$863$	−7.13565	−	26.6306i	−0.242901	−	0.906517i	0.731527	−	0.681813i	$-0.238808\pi$
$864$		0			0
$865$	32.7646	+	41.2552i	1.11403	+	1.40272i
$866$	34.7723	+	20.0758i	1.18161	+	0.682204i
$867$		0			0
$868$	43.4344	−	21.1472i	1.47426	−	0.717782i
$869$	−20.0567			−0.680378
$870$		0			0
$871$	12.1641	+	21.0689i	0.412166	+	0.713893i
$872$	−14.5795	+	54.4115i	−0.493725	+	1.84261i
$873$		0			0
$874$		−	76.6778i		−	2.59367i
$875$	17.5243	+	23.8306i	0.592430	+	0.805622i
$876$		0			0
$877$	4.47261	+	16.6920i	0.151029	+	0.563649i	0.999413	+	0.0342666i	$0.0109095\pi$
$877$	4.47261	+	16.6920i	0.151029	+	0.563649i	−0.848384	+	0.529382i	$0.822424\pi$
$878$	84.7002	+	22.6953i	2.85849	+	0.765931i
$879$		0			0
$880$	2.75824	+	6.35674i	0.0929803	+	0.214286i
$881$			55.6733i			1.87568i	0.347064	+	0.937841i	$0.387178\pi$
$881$			55.6733i			1.87568i	−0.347064	+	0.937841i	$0.612822\pi$
$882$		0			0
$883$	−13.5326	−	13.5326i	−0.455408	−	0.455408i	0.441737	−	0.897145i	$-0.354362\pi$
$883$	−13.5326	−	13.5326i	−0.455408	−	0.455408i	−0.897145	+	0.441737i	$0.854362\pi$
$884$	−16.7833	+	29.0695i	−0.564483	+	0.977713i
$885$		0			0
$886$	14.6806	+	25.4276i	0.493205	+	0.854256i
$887$	−45.5036	+	12.1926i	−1.52786	+	0.409389i	−0.922321	−	0.386426i	$-0.873710\pi$
$887$	−45.5036	+	12.1926i	−1.52786	+	0.409389i	−0.605540	+	0.795815i	$0.707043\pi$
$888$		0			0
$889$	9.37967	+	48.4330i	0.314584	+	1.62439i
$890$	−3.75089	−	25.2290i	−0.125730	−	0.845679i
$891$		0			0
$892$	−8.69989	−	2.33113i	−0.291294	−	0.0780519i
$893$	−34.2188	−	9.16890i	−1.14509	−	0.306825i
$894$		0			0
$895$	−0.822612	−	0.609670i	−0.0274969	−	0.0203790i
$896$	−49.9969	−	17.2540i	−1.67028	−	0.576416i
$897$		0			0
$898$	54.7335	−	14.6658i	1.82648	−	0.489404i
$899$	−3.32701	−	5.76256i	−0.110962	−	0.192192i
$900$		0			0
$901$	3.53164	−	6.11698i	0.117656	−	0.203786i
$902$	−53.7271	−	53.7271i	−1.78892	−	1.78892i
$903$		0			0
$904$		−	66.2179i		−	2.20237i
$905$	−26.6057	+	11.5444i	−0.884402	+	0.383749i
$906$		0			0
$907$	−0.409732	−	0.109787i	−0.0136049	−	0.00364543i	0.252010	−	0.967725i	$-0.418908\pi$
$907$	−0.409732	−	0.109787i	−0.0136049	−	0.00364543i	−0.265615	+	0.964079i	$0.585575\pi$
$908$	−6.04646	−	22.5657i	−0.200659	−	0.748870i
$909$		0			0
$910$	22.5584	−	26.3350i	0.747805	−	0.872997i
$911$		−	0.818653i		−	0.0271232i	−0.999908	−	0.0135616i	$-0.995683\pi$
$911$		−	0.818653i		−	0.0271232i	0.999908	−	0.0135616i	$-0.00431692\pi$
$912$		0			0
$913$	1.38292	−	5.16112i	0.0457679	−	0.170808i
$914$	38.2373	+	66.2290i	1.26478	+	2.19066i
$915$		0			0
$916$	−87.8939			−2.90410
$917$	24.9088	−	12.1275i	0.822563	−	0.400487i
$918$		0			0
$919$	15.9425	+	9.20443i	0.525896	+	0.303626i	0.739343	−	0.673328i	$-0.235136\pi$
$919$	15.9425	+	9.20443i	0.525896	+	0.303626i	−0.213448	+	0.976954i	$0.568469\pi$
$920$	56.5008	+	6.48099i	1.86278	+	0.213672i
$921$		0			0
$922$	−6.85495	−	25.5830i	−0.225756	−	0.842532i
$923$	−1.90406	+	1.90406i	−0.0626730	+	0.0626730i
$924$		0			0
$925$	−33.6303	−	17.9472i	−1.10576	−	0.590102i
$926$	31.1760	+	17.9995i	1.02451	+	0.591499i
$927$		0			0
$928$	−1.43355	+	5.35009i	−0.0470586	+	0.175625i
$929$	−18.2734	+	31.6505i	−0.599532	+	1.03842i	0.393358	+	0.919386i	$0.371313\pi$
$929$	−18.2734	+	31.6505i	−0.599532	+	1.03842i	−0.992890	+	0.119035i	$0.962020\pi$
$930$		0			0
$931$	−4.31480	+	30.3962i	−0.141412	+	0.996196i
$932$	−25.9790	−	25.9790i	−0.850971	−	0.850971i
$933$		0			0
$934$	−46.7373	+	26.9838i	−1.52929	+	0.882938i
$935$	16.2639	+	20.4785i	0.531886	+	0.669717i
$936$		0			0
$937$	−9.73540	+	9.73540i	−0.318042	+	0.318042i	−0.848015	−	0.529973i	$-0.822202\pi$
$937$	−9.73540	+	9.73540i	−0.318042	+	0.318042i	0.529973	+	0.848015i	$0.322202\pi$
$938$	33.5312	−	49.6380i	1.09483	−	1.62074i
$939$		0			0
$940$	22.9131	−	58.0387i	0.747342	−	1.89302i
$941$	26.9972	−	15.5869i	0.880084	−	0.508117i	0.00939807	−	0.999956i	$-0.497008\pi$
$941$	26.9972	−	15.5869i	0.880084	−	0.508117i	0.870686	+	0.491839i	$0.163675\pi$
$942$		0			0
$943$	−77.8701	+	20.8652i	−2.53580	+	0.679465i
$944$	−6.09369			−0.198333
$945$		0			0
$946$	−57.2462			−1.86123
$947$	−7.55291	+	2.02380i	−0.245437	+	0.0657645i	−0.379440	−	0.925216i	$-0.623883\pi$
$947$	−7.55291	+	2.02380i	−0.245437	+	0.0657645i	0.134003	+	0.990981i	$0.457217\pi$
$948$		0			0
$949$	−4.66662	+	2.69427i	−0.151485	+	0.0874598i
$950$	−43.4755	+	27.0746i	−1.41053	+	0.878416i
$951$		0			0
$952$	34.7162	+	2.45172i	1.12516	+	0.0794608i
$953$	−14.8359	+	14.8359i	−0.480583	+	0.480583i	−0.905318	−	0.424735i	$-0.860367\pi$
$953$	−14.8359	+	14.8359i	−0.480583	+	0.480583i	0.424735	+	0.905318i	$0.360367\pi$
$954$		0			0
$955$	−14.9950	−	1.72002i	−0.485228	−	0.0556587i
$956$	−47.2305	+	27.2686i	−1.52754	+	0.881928i
$957$		0			0
$958$	−16.4139	−	16.4139i	−0.530310	−	0.530310i
$959$	−28.7519	−	33.1215i	−0.928447	−	1.06955i
$960$		0			0
$961$	1.53342	−	2.65597i	0.0494653	−	0.0856764i
$962$	−11.5656	+	43.1634i	−0.372889	+	1.39164i
$963$		0			0
$964$	8.45023	+	4.87874i	0.272164	+	0.157134i
$965$	1.67869	+	11.2911i	0.0540389	+	0.363474i
$966$		0			0
$967$	−38.1841	+	38.1841i	−1.22792	+	1.22792i	−0.263167	+	0.964750i	$0.584767\pi$
$967$	−38.1841	+	38.1841i	−1.22792	+	1.22792i	−0.964750	+	0.263167i	$0.915233\pi$
$968$	1.64863	+	6.15277i	0.0529890	+	0.197758i
$969$		0			0
$970$	2.26480	−	19.7443i	0.0727183	−	0.633953i
$971$	−34.5090	−	19.9238i	−1.10745	−	0.639384i	−0.169279	−	0.985568i	$-0.554144\pi$
$971$	−34.5090	−	19.9238i	−1.10745	−	0.639384i	−0.938167	+	0.346184i	$0.887477\pi$
$972$		0			0
$973$	−16.6207	−	11.2275i	−0.532834	−	0.359938i
$974$	10.8308			0.347040
$975$		0			0
$976$	3.80767	+	6.59508i	0.121881	+	0.211103i
$977$	−4.27984	+	15.9726i	−0.136924	+	0.511008i	0.863058	+	0.505104i	$0.168546\pi$
$977$	−4.27984	+	15.9726i	−0.136924	+	0.511008i	−0.999983	+	0.00590397i	$0.998121\pi$
$978$		0			0
$979$			14.7536i			0.471526i
$980$	−52.3240	−	13.6517i	−1.67143	−	0.436086i
$981$		0			0
$982$	1.20744	+	4.50621i	0.0385308	+	0.143799i
$983$	−0.859334	−	0.230258i	−0.0274085	−	0.00734408i	0.245089	−	0.969501i	$-0.421183\pi$
$983$	−0.859334	−	0.230258i	−0.0274085	−	0.00734408i	−0.272497	+	0.962157i	$0.587850\pi$
$984$		0			0
$985$	15.7296	+	6.20988i	0.501187	+	0.197863i
$986$		−	11.3840i		−	0.362541i
$987$		0			0
$988$	26.8882	+	26.8882i	0.855428	+	0.855428i
$989$	−30.3693	+	52.6012i	−0.965689	+	1.67262i
$990$		0			0
$991$	−25.8144	−	44.7119i	−0.820021	−	1.42032i	−0.905665	−	0.423993i	$-0.860628\pi$
$991$	−25.8144	−	44.7119i	−0.820021	−	1.42032i	0.0856440	−	0.996326i	$-0.472705\pi$
$992$	22.4593	−	6.01795i	0.713083	−	0.191070i
$993$		0			0
$994$	6.26750	+	2.16292i	0.198793	+	0.0686038i
$995$	−22.9990	+	31.0319i	−0.729116	+	0.983778i
$996$		0			0
$997$	−22.7144	−	6.08631i	−0.719373	−	0.192755i	−0.119481	−	0.992836i	$-0.538123\pi$
$997$	−22.7144	−	6.08631i	−0.719373	−	0.192755i	−0.599892	+	0.800081i	$0.704790\pi$
$998$	−0.465669	−	0.124776i	−0.0147405	−	0.00394970i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.233.15	yes	64
3.2	odd	2	inner	315.2.ce.a.233.2	yes	64
5.2	odd	4	inner	315.2.ce.a.107.15	yes	64
7.4	even	3	inner	315.2.ce.a.53.2	✓	64
15.2	even	4	inner	315.2.ce.a.107.2	yes	64
21.11	odd	6	inner	315.2.ce.a.53.15	yes	64
35.32	odd	12	inner	315.2.ce.a.242.2	yes	64
105.32	even	12	inner	315.2.ce.a.242.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.2	✓	64	7.4	even	3	inner
315.2.ce.a.53.15	yes	64	21.11	odd	6	inner
315.2.ce.a.107.2	yes	64	15.2	even	4	inner
315.2.ce.a.107.15	yes	64	5.2	odd	4	inner
315.2.ce.a.233.2	yes	64	3.2	odd	2	inner
315.2.ce.a.233.15	yes	64	1.1	even	1	trivial
315.2.ce.a.242.2	yes	64	35.32	odd	12	inner
315.2.ce.a.242.15	yes	64	105.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.25596 - 0.604483i) q^{2} +(2.99191 - 1.72738i) q^{4} +(2.05129 - 0.890070i) q^{5} +(-1.48100 + 2.19240i) q^{7} +(2.40251 - 2.40251i) q^{8} +(4.08959 - 3.24793i) q^{10} +(-2.61609 + 1.51040i) q^{11} +(-1.77456 - 1.77456i) q^{13} +(-2.01581 + 5.84122i) q^{14} +(0.512928 - 0.888417i) q^{16} +(1.00203 - 3.73962i) q^{17} +(-3.79826 - 2.19292i) q^{19} +(4.59978 - 6.20636i) q^{20} +(-4.98879 + 4.98879i) q^{22} +(1.93742 + 7.23056i) q^{23} +(3.41555 - 3.65158i) q^{25} +(-5.07603 - 2.93065i) q^{26} +(-0.643912 + 9.11773i) q^{28} +1.25900 q^{29} +(-2.64259 - 4.57710i) q^{31} +(-1.13865 + 4.24948i) q^{32} -9.04214i q^{34} +(-1.08657 + 5.81544i) q^{35} +(-1.97321 - 7.36414i) q^{37} +(-9.89430 - 2.65117i) q^{38} +(2.78983 - 7.06663i) q^{40} +10.7696i q^{41} +(5.73749 + 5.73749i) q^{43} +(-5.21807 + 9.03797i) q^{44} +(8.74151 + 15.1407i) q^{46} +(7.80209 - 2.09056i) q^{47} +(-2.61327 - 6.49391i) q^{49} +(5.49803 - 10.3025i) q^{50} +(-8.37466 - 2.24398i) q^{52} +(1.76225 + 0.472193i) q^{53} +(-4.02199 + 5.42677i) q^{55} +(1.70915 + 8.82539i) q^{56} +(2.84025 - 0.761042i) q^{58} +(-2.97005 - 5.14428i) q^{59} +(-3.71170 + 6.42886i) q^{61} +(-8.72836 - 8.72836i) q^{62} +12.3267i q^{64} +(-5.21961 - 2.06065i) q^{65} +(-9.36375 - 2.50901i) q^{67} +(-3.46176 - 12.9195i) q^{68} +(1.06408 + 13.7762i) q^{70} -1.07298i q^{71} +(0.555728 - 2.07401i) q^{73} +(-8.90299 - 15.4204i) q^{74} -15.1521 q^{76} +(0.563028 - 7.97243i) q^{77} +(5.75001 + 3.31977i) q^{79} +(0.261408 - 2.27894i) q^{80} +(6.51003 + 24.2957i) q^{82} +(-1.25073 + 1.25073i) q^{83} +(-1.27308 - 8.56290i) q^{85} +(16.4118 + 9.47534i) q^{86} +(-2.65643 + 9.91392i) q^{88} +(2.44200 - 4.22966i) q^{89} +(6.51867 - 1.26242i) q^{91} +(18.2865 + 18.2865i) q^{92} +(16.3375 - 9.43246i) q^{94} +(-9.74317 - 1.11760i) q^{95} +(2.69087 - 2.69087i) q^{97} +(-9.82088 - 13.0703i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) \) 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Introduction

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