LMFDB - Embedded newform 920.2.bv.a.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72248 + 0.940543i) q^{3} +(0.500469 - 2.17934i) q^{5} +(2.14878 + 2.87043i) q^{7} +(0.460382 - 0.716368i) q^{9} +(4.06197 - 1.85504i) q^{11} +(-2.18769 - 1.63769i) q^{13} +(1.18772 + 4.22458i) q^{15} +(0.0397148 + 0.555286i) q^{17} +(-2.54021 - 2.93156i) q^{19} +(-6.40098 - 2.92323i) q^{21} +(0.911490 + 4.70842i) q^{23} +(-4.49906 - 2.18138i) q^{25} +(0.300796 - 4.20567i) q^{27} +(2.07316 + 1.79641i) q^{29} +(6.34302 - 1.86248i) q^{31} +(-5.25190 + 7.01572i) q^{33} +(7.33104 - 3.24636i) q^{35} +(9.37577 - 2.03957i) q^{37} +(5.30857 + 0.763257i) q^{39} +(1.50077 - 0.964484i) q^{41} +(4.61548 + 8.45262i) q^{43} +(-1.33080 - 1.36185i) q^{45} +(5.14501 + 5.14501i) q^{47} +(-1.64999 + 5.61937i) q^{49} +(-0.590678 - 0.919113i) q^{51} +(-3.13388 + 2.34600i) q^{53} +(-2.00988 - 9.78081i) q^{55} +(7.13271 + 2.66037i) q^{57} +(12.4276 - 1.78681i) q^{59} +(-0.563296 - 1.91841i) q^{61} +(3.04554 - 0.217821i) q^{63} +(-4.66395 + 3.94812i) q^{65} +(1.29030 + 3.45944i) q^{67} +(-5.99849 - 7.25284i) q^{69} +(-4.08394 + 8.94257i) q^{71} +(1.32193 + 0.0945464i) q^{73} +(9.80122 - 0.474179i) q^{75} +(14.0530 + 7.67353i) q^{77} +(-1.85461 - 12.8991i) q^{79} +(4.49874 + 9.85087i) q^{81} +(0.423827 + 1.94830i) q^{83} +(1.23003 + 0.191351i) q^{85} +(-5.26057 - 1.14437i) q^{87} +(5.08258 + 1.49238i) q^{89} -9.79864i q^{91} +(-9.17396 + 9.17396i) q^{93} +(-7.66017 + 4.06884i) q^{95} +(2.55569 - 11.7483i) q^{97} +(0.541166 - 3.76389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.72248	+	0.940543i	−0.994472	+	0.543023i	−0.892155	−	0.451729i	$-0.850807\pi$
$3$	−1.72248	+	0.940543i	−0.994472	+	0.543023i	−0.102317	+	0.994752i	$0.532626\pi$
$4$		0			0
$5$	0.500469	−	2.17934i	0.223816	−	0.974631i
$5$	0.500469	−	2.17934i	0.223816	−	0.974631i
$6$		0			0
$7$	2.14878	+	2.87043i	0.812161	+	1.08492i	0.994811	+	0.101742i	$0.0324416\pi$
$7$	2.14878	+	2.87043i	0.812161	+	1.08492i	−0.182650	+	0.983178i	$0.558467\pi$
$8$		0			0
$9$	0.460382	−	0.716368i	0.153461	−	0.238789i
$10$		0			0
$11$	4.06197	−	1.85504i	1.22473	−	0.559315i	0.305182	−	0.952294i	$-0.401283\pi$
$11$	4.06197	−	1.85504i	1.22473	−	0.559315i	0.919548	+	0.392978i	$0.128555\pi$
$12$		0			0
$13$	−2.18769	−	1.63769i	−0.606757	−	0.454213i	0.251199	−	0.967935i	$-0.419175\pi$
$13$	−2.18769	−	1.63769i	−0.606757	−	0.454213i	−0.857956	+	0.513723i	$0.828266\pi$
$14$		0			0
$15$	1.18772	+	4.22458i	0.306668	+	1.09078i
$16$		0			0
$17$	0.0397148	+	0.555286i	0.00963226	+	0.134677i	0.999993	−	0.00383813i	$-0.00122172\pi$
$17$	0.0397148	+	0.555286i	0.00963226	+	0.134677i	−0.990360	+	0.138515i	$0.955767\pi$
$18$		0			0
$19$	−2.54021	−	2.93156i	−0.582764	−	0.672546i	0.385432	−	0.922736i	$-0.374052\pi$
$19$	−2.54021	−	2.93156i	−0.582764	−	0.672546i	−0.968197	+	0.250190i	$0.919507\pi$
$20$		0			0
$21$	−6.40098	−	2.92323i	−1.39681	−	0.637901i
$22$		0			0
$23$	0.911490	+	4.70842i	0.190059	+	0.981773i
$23$	0.911490	+	4.70842i	0.190059	+	0.981773i
$24$		0			0
$25$	−4.49906	−	2.18138i	−0.899812	−	0.436277i
$26$		0			0
$27$	0.300796	−	4.20567i	0.0578881	−	0.809382i
$28$		0			0
$29$	2.07316	+	1.79641i	0.384977	+	0.333584i	0.825752	−	0.564033i	$-0.190751\pi$
$29$	2.07316	+	1.79641i	0.384977	+	0.333584i	−0.440775	+	0.897617i	$0.645296\pi$
$30$		0			0
$31$	6.34302	−	1.86248i	1.13924	−	0.334511i	0.342907	−	0.939369i	$-0.388589\pi$
$31$	6.34302	−	1.86248i	1.13924	−	0.334511i	0.796333	+	0.604859i	$0.206770\pi$
$32$		0			0
$33$	−5.25190	+	7.01572i	−0.914239	+	1.22128i
$34$		0			0
$35$	7.33104	−	3.24636i	1.23917	−	0.548735i
$36$		0			0
$37$	9.37577	−	2.03957i	1.54137	−	0.335304i	0.640005	−	0.768371i	$-0.278932\pi$
$37$	9.37577	−	2.03957i	1.54137	−	0.335304i	0.901362	+	0.433067i	$0.142569\pi$
$38$		0			0
$39$	5.30857	+	0.763257i	0.850051	+	0.122219i
$40$		0			0
$41$	1.50077	−	0.964484i	0.234380	−	0.150627i	−0.418179	−	0.908365i	$-0.637332\pi$
$41$	1.50077	−	0.964484i	0.234380	−	0.150627i	0.652560	+	0.757737i	$0.273695\pi$
$42$		0			0
$43$	4.61548	+	8.45262i	0.703854	+	1.28901i	0.947689	+	0.319196i	$0.103413\pi$
$43$	4.61548	+	8.45262i	0.703854	+	1.28901i	−0.243834	+	0.969817i	$0.578405\pi$
$44$		0			0
$45$	−1.33080	−	1.36185i	−0.198385	−	0.203012i
$46$		0			0
$47$	5.14501	+	5.14501i	0.750477	+	0.750477i	0.974568	−	0.224091i	$-0.0719413\pi$
$47$	5.14501	+	5.14501i	0.750477	+	0.750477i	−0.224091	+	0.974568i	$0.571941\pi$
$48$		0			0
$49$	−1.64999	+	5.61937i	−0.235713	+	0.802766i
$50$		0			0
$51$	−0.590678	−	0.919113i	−0.0827115	−	0.128702i
$52$		0			0
$53$	−3.13388	+	2.34600i	−0.430472	+	0.322247i	−0.792447	−	0.609940i	$-0.791193\pi$
$53$	−3.13388	+	2.34600i	−0.430472	+	0.322247i	0.361975	+	0.932188i	$0.382102\pi$
$54$		0			0
$55$	−2.00988	−	9.78081i	−0.271012	−	1.31884i
$56$		0			0
$57$	7.13271	+	2.66037i	0.944751	+	0.352374i
$58$		0			0
$59$	12.4276	−	1.78681i	1.61793	−	0.232623i	0.726958	−	0.686682i	$-0.240934\pi$
$59$	12.4276	−	1.78681i	1.61793	−	0.232623i	0.890972	+	0.454059i	$0.150024\pi$
$60$		0			0
$61$	−0.563296	−	1.91841i	−0.0721227	−	0.245627i	0.915539	−	0.402229i	$-0.131764\pi$
$61$	−0.563296	−	1.91841i	−0.0721227	−	0.245627i	−0.987662	+	0.156601i	$0.949946\pi$
$62$		0			0
$63$	3.04554	−	0.217821i	0.383702	−	0.0274429i
$64$		0			0
$65$	−4.66395	+	3.94812i	−0.578492	+	0.489704i
$66$		0			0
$67$	1.29030	+	3.45944i	0.157636	+	0.422637i	0.991626	−	0.129141i	$-0.0412221\pi$
$67$	1.29030	+	3.45944i	0.157636	+	0.422637i	−0.833991	+	0.551779i	$0.813949\pi$
$68$		0			0
$69$	−5.99849	−	7.25284i	−0.722133	−	0.873140i
$70$		0			0
$71$	−4.08394	+	8.94257i	−0.484674	+	1.06129i	0.496478	+	0.868049i	$0.334626\pi$
$71$	−4.08394	+	8.94257i	−0.484674	+	1.06129i	−0.981152	+	0.193239i	$0.938101\pi$
$72$		0			0
$73$	1.32193	+	0.0945464i	0.154720	+	0.0110658i	0.148485	−	0.988915i	$-0.452560\pi$
$73$	1.32193	+	0.0945464i	0.154720	+	0.0110658i	0.00623592	+	0.999981i	$0.498015\pi$
$74$		0			0
$75$	9.80122	−	0.474179i	1.13175	−	0.0547535i
$76$		0			0
$77$	14.0530	+	7.67353i	1.60149	+	0.874480i
$78$		0			0
$79$	−1.85461	−	12.8991i	−0.208660	−	1.45126i	−0.777535	−	0.628839i	$-0.783530\pi$
$79$	−1.85461	−	12.8991i	−0.208660	−	1.45126i	0.568875	−	0.822424i	$-0.307379\pi$
$80$		0			0
$81$	4.49874	+	9.85087i	0.499860	+	1.09454i
$82$		0			0
$83$	0.423827	+	1.94830i	0.0465210	+	0.213854i	0.994539	−	0.104362i	$-0.0332800\pi$
$83$	0.423827	+	1.94830i	0.0465210	+	0.213854i	−0.948018	+	0.318216i	$0.896916\pi$
$84$		0			0
$85$	1.23003	+	0.191351i	0.133416	+	0.0207549i
$86$		0			0
$87$	−5.26057	−	1.14437i	−0.563992	−	0.122689i
$88$		0			0
$89$	5.08258	+	1.49238i	0.538752	+	0.158192i	0.539778	−	0.841808i	$-0.318508\pi$
$89$	5.08258	+	1.49238i	0.538752	+	0.158192i	−0.00102565	+	0.999999i	$0.500326\pi$
$90$		0			0
$91$		−	9.79864i		−	1.02718i
$92$		0			0
$93$	−9.17396	+	9.17396i	−0.951295	+	0.951295i
$94$		0			0
$95$	−7.66017	+	4.06884i	−0.785917	+	0.417454i
$96$		0			0
$97$	2.55569	−	11.7483i	0.259491	−	1.19286i	−0.644262	−	0.764805i	$-0.722835\pi$
$97$	2.55569	−	11.7483i	0.259491	−	1.19286i	0.903753	−	0.428055i	$-0.140801\pi$
$98$		0			0
$99$	0.541166	−	3.76389i	0.0543892	−	0.378285i
$100$		0			0
$101$	2.24926	+	1.44551i	0.223810	+	0.143834i	0.647741	−	0.761861i	$-0.275714\pi$
$101$	2.24926	+	1.44551i	0.223810	+	0.143834i	−0.423931	+	0.905694i	$0.639350\pi$
$102$		0			0
$103$	5.13607	−	13.7703i	0.506072	−	1.35683i	−0.393204	−	0.919451i	$-0.628633\pi$
$103$	5.13607	−	13.7703i	0.506072	−	1.35683i	0.899276	−	0.437381i	$-0.144094\pi$
$104$		0			0
$105$	−9.57421	+	12.4869i	−0.934347	+	1.21860i
$106$		0			0
$107$	−4.45208	+	8.15338i	−0.430399	+	0.788217i	−0.999418	−	0.0341074i	$-0.989141\pi$
$107$	−4.45208	+	8.15338i	−0.430399	+	0.788217i	0.569019	+	0.822324i	$0.307323\pi$
$108$		0			0
$109$	−1.97306	+	2.27703i	−0.188985	+	0.218100i	−0.842333	−	0.538957i	$-0.818818\pi$
$109$	−1.97306	+	2.27703i	−0.188985	+	0.218100i	0.653348	+	0.757058i	$0.273364\pi$
$110$		0			0
$111$	−14.2312	+	12.3314i	−1.35077	+	1.17045i
$112$		0			0
$113$	3.51478	−	1.31094i	0.330642	−	0.123323i	−0.178660	−	0.983911i	$-0.557176\pi$
$113$	3.51478	−	1.31094i	0.330642	−	0.123323i	0.509302	+	0.860588i	$0.329903\pi$
$114$		0			0
$115$	10.7174	+	0.369966i	0.999405	+	0.0344995i
$116$		0			0
$117$	−2.18036	+	0.813232i	−0.201574	+	0.0751834i
$118$		0			0
$119$	−1.50857	+	1.30718i	−0.138290	+	0.119829i
$120$		0			0
$121$	5.85496	−	6.75698i	0.532269	−	0.614271i
$122$		0			0
$123$	−1.67790	+	3.07284i	−0.151291	+	0.277068i
$124$		0			0
$125$	−7.00562	+	8.71328i	−0.626602	+	0.779339i
$126$		0			0
$127$	−7.42572	+	19.9091i	−0.658926	+	1.76665i	−0.0170347	+	0.999855i	$0.505423\pi$
$127$	−7.42572	+	19.9091i	−0.658926	+	1.76665i	−0.641892	+	0.766795i	$0.721850\pi$
$128$		0			0
$129$	−15.9001	−	10.2184i	−1.39993	−	0.899679i
$130$		0			0
$131$	0.210656	−	1.46514i	0.0184051	−	0.128010i	−0.978547	−	0.206022i	$-0.933948\pi$
$131$	0.210656	−	1.46514i	0.0184051	−	0.128010i	0.996952	+	0.0780119i	$0.0248572\pi$
$132$		0			0
$133$	2.95649	−	13.5908i	0.256360	−	1.17847i
$134$		0			0
$135$	−9.01506	−	2.76034i	−0.775893	−	0.237573i
$136$		0			0
$137$	−2.50625	+	2.50625i	−0.214124	+	0.214124i	−0.806017	−	0.591893i	$-0.798381\pi$
$137$	−2.50625	+	2.50625i	−0.214124	+	0.214124i	0.591893	+	0.806017i	$0.298381\pi$
$138$		0			0
$139$			11.3584i			0.963410i	0.876333	+	0.481705i	$0.159982\pi$
$139$			11.3584i			0.963410i	−0.876333	+	0.481705i	$0.840018\pi$
$140$		0			0
$141$	−13.7013	−	4.02306i	−1.15386	−	0.338802i
$142$		0			0
$143$	−11.9243	−	2.59398i	−0.997162	−	0.216919i
$144$		0			0
$145$	4.95253	−	3.61909i	0.411286	−	0.300549i
$146$		0			0
$147$	−2.44318	−	11.2311i	−0.201510	−	0.926327i
$148$		0			0
$149$	−8.25457	−	18.0750i	−0.676240	−	1.48076i	−0.866578	−	0.499041i	$-0.833686\pi$
$149$	−8.25457	−	18.0750i	−0.676240	−	1.48076i	0.190338	−	0.981719i	$-0.439042\pi$
$150$		0			0
$151$	−0.628715	−	4.37281i	−0.0511641	−	0.355854i	−0.999280	−	0.0379305i	$-0.987923\pi$
$151$	−0.628715	−	4.37281i	−0.0511641	−	0.355854i	0.948116	−	0.317924i	$-0.102986\pi$
$152$		0			0
$153$	0.416073	+	0.227193i	0.0336375	+	0.0183675i
$154$		0			0
$155$	−0.884495	−	14.7557i	−0.0710443	−	1.18521i
$156$		0			0
$157$	11.8252	+	0.845755i	0.943754	+	0.0674986i	0.534728	−	0.845024i	$-0.320414\pi$
$157$	11.8252	+	0.845755i	0.943754	+	0.0674986i	0.409026	+	0.912523i	$0.365869\pi$
$158$		0			0
$159$	3.19153	−	6.98848i	0.253105	−	0.554222i
$160$		0			0
$161$	−11.5566	+	12.7337i	−0.910786	+	1.00356i
$162$		0			0
$163$	0.267001	+	0.715857i	0.0209131	+	0.0560702i	0.946987	−	0.321273i	$-0.104111\pi$
$163$	0.267001	+	0.715857i	0.0209131	+	0.0560702i	−0.926074	+	0.377343i	$0.876838\pi$
$164$		0			0
$165$	12.6612	+	14.9568i	0.985676	+	1.16439i
$166$		0			0
$167$	20.0462	−	1.43373i	1.55122	−	0.110946i	0.730755	−	0.682640i	$-0.239168\pi$
$167$	20.0462	−	1.43373i	1.55122	−	0.110946i	0.820467	+	0.571694i	$0.193714\pi$
$168$		0			0
$169$	−1.55854	−	5.30789i	−0.119888	−	0.408299i
$170$		0			0
$171$	−3.26954	+	0.470089i	−0.250028	+	0.0359486i
$172$		0			0
$173$	−16.9497	−	6.32192i	−1.28866	−	0.480647i	−0.390620	−	0.920552i	$-0.627739\pi$
$173$	−16.9497	−	6.32192i	−1.28866	−	0.480647i	−0.898044	+	0.439905i	$0.855012\pi$
$174$		0			0
$175$	−3.40597	−	17.6015i	−0.257467	−	1.33055i
$176$		0			0
$177$	−19.7256	+	14.7664i	−1.48267	+	1.10991i
$178$		0			0
$179$	−8.16650	−	12.7073i	−0.610393	−	0.949789i	−0.999590	−	0.0286350i	$-0.990884\pi$
$179$	−8.16650	−	12.7073i	−0.610393	−	0.949789i	0.389197	−	0.921154i	$-0.372752\pi$
$180$		0			0
$181$	6.30329	−	21.4670i	0.468520	−	1.59563i	−0.298766	−	0.954326i	$-0.596575\pi$
$181$	6.30329	−	21.4670i	0.468520	−	1.59563i	0.767286	−	0.641305i	$-0.221607\pi$
$182$		0			0
$183$	2.77461	+	2.77461i	0.205105	+	0.205105i
$184$		0			0
$185$	0.247350	−	21.4537i	0.0181855	−	1.57731i
$186$		0			0
$187$	1.19140	+	2.18188i	0.0871236	+	0.159555i
$188$		0			0
$189$	12.7184	−	8.17363i	0.925129	−	0.594544i
$190$		0			0
$191$	−24.4279	−	3.51220i	−1.76754	−	0.254134i	−0.819679	−	0.572824i	$-0.805848\pi$
$191$	−24.4279	−	3.51220i	−1.76754	−	0.254134i	−0.947859	+	0.318690i	$0.896757\pi$
$192$		0			0
$193$	−6.20402	+	1.34960i	−0.446575	+	0.0971464i	−0.430229	−	0.902720i	$-0.641567\pi$
$193$	−6.20402	+	1.34960i	−0.446575	+	0.0971464i	−0.0163462	+	0.999866i	$0.505203\pi$
$194$		0			0
$195$	4.32017	−	11.1872i	0.309374	−	0.801132i
$196$		0			0
$197$	12.2403	−	16.3511i	0.872084	−	1.16497i	−0.113120	−	0.993581i	$-0.536084\pi$
$197$	12.2403	−	16.3511i	0.872084	−	1.16497i	0.985204	−	0.171386i	$-0.0548246\pi$
$198$		0			0
$199$	−23.4511	+	6.88586i	−1.66240	+	0.488126i	−0.971937	−	0.235239i	$-0.924413\pi$
$199$	−23.4511	+	6.88586i	−1.66240	+	0.488126i	−0.690466	+	0.723365i	$0.742594\pi$
$200$		0			0
$201$	−5.47627	−	4.74521i	−0.386266	−	0.334701i
$202$		0			0
$203$	−0.701692	+	9.81094i	−0.0492491	+	0.688593i
$204$		0			0
$205$	−1.35085	−	3.75338i	−0.0943477	−	0.262147i
$206$		0			0
$207$	3.79259	+	1.51471i	0.263603	+	0.105279i
$208$		0			0
$209$	−15.7564	−	7.19572i	−1.08989	−	0.497738i
$210$		0			0
$211$	7.81027	+	9.01353i	0.537681	+	0.620517i	0.957968	−	0.286874i	$-0.0926162\pi$
$211$	7.81027	+	9.01353i	0.537681	+	0.620517i	−0.420287	+	0.907391i	$0.638071\pi$
$212$		0			0
$213$	−1.37639	−	19.2445i	−0.0943089	−	1.31861i
$214$		0			0
$215$	20.7311	−	5.82844i	1.41385	−	0.397496i
$216$		0			0
$217$	18.9758	+	14.2051i	1.28816	+	0.964307i
$218$		0			0
$219$	−2.36592	+	1.08048i	−0.159874	+	0.0730121i
$220$		0			0
$221$	0.822501	−	1.27984i	0.0553274	−	0.0860911i
$222$		0			0
$223$	9.28332	+	12.4011i	0.621657	+	0.830436i	0.995270	−	0.0971483i	$-0.0309721\pi$
$223$	9.28332	+	12.4011i	0.621657	+	0.830436i	−0.373613	+	0.927585i	$0.621881\pi$
$224$		0			0
$225$	−3.63396	+	2.21871i	−0.242264	+	0.147914i
$226$		0			0
$227$	−21.2393	+	11.5975i	−1.40970	+	0.769755i	−0.990418	−	0.138100i	$-0.955900\pi$
$227$	−21.2393	+	11.5975i	−1.40970	+	0.769755i	−0.419283	+	0.907855i	$0.637719\pi$
$228$		0			0
$229$	−8.47366			−0.559955			−0.279978	−	0.960007i	$-0.590327\pi$
$229$	−8.47366			−0.559955			−0.279978	+	0.960007i	$0.590327\pi$
$230$		0			0
$231$	−31.4233			−2.06750
$232$		0			0
$233$	−13.8504	+	7.56290i	−0.907371	+	0.495462i	−0.863940	−	0.503594i	$-0.832011\pi$
$233$	−13.8504	+	7.56290i	−0.907371	+	0.495462i	−0.0434307	+	0.999056i	$0.513829\pi$
$234$		0			0
$235$	13.7877	−	8.63782i	0.899408	−	0.563469i
$236$		0			0
$237$	15.3267	+	20.4741i	0.995576	+	1.32993i
$238$		0			0
$239$	−1.72600	+	2.68570i	−0.111645	+	0.173724i	−0.892580	−	0.450889i	$-0.851107\pi$
$239$	−1.72600	+	2.68570i	−0.111645	+	0.173724i	0.780934	+	0.624613i	$0.214743\pi$
$240$		0			0
$241$	−22.8068	+	10.4155i	−1.46912	+	0.670923i	−0.979579	−	0.201060i	$-0.935561\pi$
$241$	−22.8068	+	10.4155i	−1.46912	+	0.670923i	−0.489537	+	0.871983i	$0.662834\pi$
$242$		0			0
$243$	−6.88791	−	5.15622i	−0.441859	−	0.330772i
$244$		0			0
$245$	11.4207	+	6.40822i	0.729645	+	0.409406i
$246$		0			0
$247$	0.756227	+	10.5734i	0.0481175	+	0.672771i
$248$		0			0
$249$	−2.56249	−	2.95727i	−0.162391	−	0.187410i
$250$		0			0
$251$	0.612266	+	0.279613i	0.0386459	+	0.0176490i	0.434644	−	0.900602i	$-0.356874\pi$
$251$	0.612266	+	0.279613i	0.0386459	+	0.0176490i	−0.395998	+	0.918251i	$0.629601\pi$
$252$		0			0
$253$	12.4367	+	17.4346i	0.781891	+	1.09610i
$254$		0			0
$255$	−2.29868	+	0.827303i	−0.143949	+	0.0518077i
$256$		0			0
$257$	−1.66466	+	23.2749i	−0.103838	+	1.45185i	0.632145	+	0.774850i	$0.282175\pi$
$257$	−1.66466	+	23.2749i	−0.103838	+	1.45185i	−0.735983	+	0.677000i	$0.763280\pi$
$258$		0			0
$259$	26.0009	+	22.5299i	1.61562	+	1.39994i
$260$		0			0
$261$	2.24133	−	0.658115i	0.138735	−	0.0407363i
$262$		0			0
$263$	7.10868	−	9.49609i	0.438340	−	0.585554i	−0.525912	−	0.850539i	$-0.676276\pi$
$263$	7.10868	−	9.49609i	0.438340	−	0.585554i	0.964253	+	0.264985i	$0.0853669\pi$
$264$		0			0
$265$	3.54432	+	8.00390i	0.217726	+	0.491676i
$266$		0			0
$267$	−10.1583	+	2.20980i	−0.621676	+	0.135237i
$268$		0			0
$269$	5.62351	+	0.808539i	0.342872	+	0.0492975i	0.311600	−	0.950213i	$-0.399135\pi$
$269$	5.62351	+	0.808539i	0.342872	+	0.0492975i	0.0312718	+	0.999511i	$0.490044\pi$
$270$		0			0
$271$	15.1802	−	9.75570i	0.922129	−	0.592617i	0.00885467	−	0.999961i	$-0.497181\pi$
$271$	15.1802	−	9.75570i	0.922129	−	0.592617i	0.913275	+	0.407344i	$0.133545\pi$
$272$		0			0
$273$	9.21605	+	16.8779i	0.557781	+	1.02150i
$274$		0			0
$275$	−22.3216	−	0.514780i	−1.34604	−	0.0310424i
$276$		0			0
$277$	−17.8300	−	17.8300i	−1.07130	−	1.07130i	−0.997255	−	0.0740480i	$-0.976408\pi$
$277$	−17.8300	−	17.8300i	−1.07130	−	1.07130i	−0.0740480	−	0.997255i	$-0.523592\pi$
$278$		0			0
$279$	1.58599	−	5.40138i	0.0949507	−	0.323372i
$280$		0			0
$281$	6.12021	+	9.52323i	0.365101	+	0.568108i	0.974397	−	0.224835i	$-0.0721842\pi$
$281$	6.12021	+	9.52323i	0.365101	+	0.568108i	−0.609296	+	0.792943i	$0.708548\pi$
$282$		0			0
$283$	−10.5094	+	7.86725i	−0.624720	+	0.467659i	−0.864136	−	0.503258i	$-0.832135\pi$
$283$	−10.5094	+	7.86725i	−0.624720	+	0.467659i	0.239417	+	0.970917i	$0.423044\pi$
$284$		0			0
$285$	9.36755	−	14.2132i	0.554885	−	0.841917i
$286$		0			0
$287$	5.99329	+	2.23538i	0.353773	+	0.131951i
$288$		0			0
$289$	16.5202	−	2.37525i	0.971776	−	0.139720i
$290$		0			0
$291$	6.64768	+	22.6399i	0.389694	+	1.32718i
$292$		0			0
$293$	7.32904	−	0.524184i	0.428167	−	0.0306231i	0.144407	−	0.989518i	$-0.453873\pi$
$293$	7.32904	−	0.524184i	0.428167	−	0.0306231i	0.283760	+	0.958895i	$0.408418\pi$
$294$		0			0
$295$	2.32553	−	27.9781i	0.135397	−	1.62895i
$296$		0			0
$297$	−6.57986	−	17.6413i	−0.381802	−	1.02365i
$298$		0			0
$299$	5.71685	−	11.7933i	0.330614	−	0.682025i
$300$		0			0
$301$	−14.3450	+	31.4112i	−0.826833	+	1.81051i
$302$		0			0
$303$	−5.23386	−	0.374333i	−0.300678	−	0.0215049i
$304$		0			0
$305$	−4.46278	+	0.267511i	−0.255538	+	0.0153176i
$306$		0			0
$307$	−20.8795	−	11.4011i	−1.19166	−	0.650695i	−0.243936	−	0.969791i	$-0.578439\pi$
$307$	−20.8795	−	11.4011i	−1.19166	−	0.650695i	−0.947722	+	0.319097i	$0.896621\pi$
$308$		0			0
$309$	4.10484	+	28.5498i	0.233516	+	1.62414i
$310$		0			0
$311$	5.77589	+	12.6474i	0.327521	+	0.717171i	0.999731	−	0.0231896i	$-0.00738213\pi$
$311$	5.77589	+	12.6474i	0.327521	+	0.717171i	−0.672210	+	0.740360i	$0.734655\pi$
$312$		0			0
$313$	−4.17522	−	19.1932i	−0.235997	−	1.08486i	−0.930762	−	0.365625i	$-0.880855\pi$
$313$	−4.17522	−	19.1932i	−0.235997	−	1.08486i	0.694765	−	0.719237i	$-0.255508\pi$
$314$		0			0
$315$	1.04949	−	6.74628i	0.0591321	−	0.380110i
$316$		0			0
$317$	−23.5481	−	5.12258i	−1.32259	−	0.287713i	−0.504806	−	0.863233i	$-0.668436\pi$
$317$	−23.5481	−	5.12258i	−1.32259	−	0.287713i	−0.817788	+	0.575520i	$0.804800\pi$
$318$		0			0
$319$	11.7535	+	3.45115i	0.658071	+	0.193227i
$320$		0			0
$321$		−	18.2314i		−	1.01758i
$322$		0			0
$323$	1.52697	−	1.52697i	0.0849629	−	0.0849629i
$324$		0			0
$325$	6.27015	+	12.1403i	0.347805	+	0.673420i
$326$		0			0
$327$	1.25690	−	5.77789i	0.0695069	−	0.319518i
$328$		0			0
$329$	−3.71291	+	25.8239i	−0.204699	+	1.42372i
$330$		0			0
$331$	14.8427	+	9.53884i	0.815830	+	0.524302i	0.880746	−	0.473589i	$-0.157042\pi$
$331$	14.8427	+	9.53884i	0.815830	+	0.524302i	−0.0649163	+	0.997891i	$0.520678\pi$
$332$		0			0
$333$	2.85535	−	7.65548i	0.156472	−	0.419518i
$334$		0			0
$335$	8.18505	−	1.08067i	0.447197	−	0.0590434i
$336$		0			0
$337$	5.35358	−	9.80434i	0.291628	−	0.534077i	−0.690255	−	0.723566i	$-0.742502\pi$
$337$	5.35358	−	9.80434i	0.291628	−	0.534077i	0.981883	+	0.189490i	$0.0606834\pi$
$338$		0			0
$339$	−4.82112	+	5.56387i	−0.261847	+	0.302188i
$340$		0			0
$341$	22.3102	−	19.3319i	1.20816	−	1.04688i
$342$		0			0
$343$	3.84130	−	1.43273i	0.207411	−	0.0773602i
$344$		0			0
$345$	−18.8085	+	9.44294i	−1.01261	+	0.508391i
$346$		0			0
$347$	−12.4666	+	4.64981i	−0.669243	+	0.249615i	−0.661039	−	0.750352i	$-0.729884\pi$
$347$	−12.4666	+	4.64981i	−0.669243	+	0.249615i	−0.00820389	+	0.999966i	$0.502611\pi$
$348$		0			0
$349$	5.10097	−	4.42001i	0.273049	−	0.236598i	−0.507563	−	0.861615i	$-0.669453\pi$
$349$	5.10097	−	4.42001i	0.273049	−	0.236598i	0.780611	+	0.625017i	$0.214908\pi$
$350$		0			0
$351$	−7.54562	+	8.70811i	−0.402756	+	0.464805i
$352$		0			0
$353$	−11.1531	+	20.4254i	−0.593621	+	1.08714i	0.392286	+	0.919843i	$0.371684\pi$
$353$	−11.1531	+	20.4254i	−0.593621	+	1.08714i	−0.985907	+	0.167293i	$0.946498\pi$
$354$		0			0
$355$	17.4450	+	13.3758i	0.925887	+	0.709912i
$356$		0			0
$357$	1.36901	−	3.67047i	0.0724559	−	0.194262i
$358$		0			0
$359$	22.0558	+	14.1744i	1.16406	+	0.748097i	0.972390	−	0.233362i	$-0.0749728\pi$
$359$	22.0558	+	14.1744i	1.16406	+	0.748097i	0.191671	+	0.981459i	$0.438609\pi$
$360$		0			0
$361$	0.562610	−	3.91304i	0.0296111	−	0.205950i
$362$		0			0
$363$	−3.72980	+	17.1456i	−0.195763	+	0.899910i
$364$		0			0
$365$	0.867635	−	2.83362i	0.0454141	−	0.148319i
$366$		0			0
$367$	−7.64661	+	7.64661i	−0.399150	+	0.399150i	−0.877933	−	0.478783i	$-0.841078\pi$
$367$	−7.64661	+	7.64661i	−0.399150	+	0.399150i	0.478783	+	0.877933i	$0.341078\pi$
$368$		0			0
$369$		−	1.51913i		−	0.0790828i
$370$		0			0
$371$	−13.4680	−	3.95457i	−0.699225	−	0.205311i
$372$		0			0
$373$	−2.63971	−	0.574234i	−0.136679	−	0.0297327i	0.143705	−	0.989621i	$-0.454098\pi$
$373$	−2.63971	−	0.574234i	−0.136679	−	0.0297327i	−0.280384	+	0.959888i	$0.590462\pi$
$374$		0			0
$375$	3.87180	−	21.5975i	0.199939	−	1.11529i
$376$		0			0
$377$	−1.59349	−	7.32518i	−0.0820692	−	0.377266i
$378$		0			0
$379$	0.262987	+	0.575862i	0.0135087	+	0.0295800i	0.916266	−	0.400570i	$-0.131188\pi$
$379$	0.262987	+	0.575862i	0.0135087	+	0.0295800i	−0.902757	+	0.430150i	$0.858461\pi$
$380$		0			0
$381$	−5.93477	−	41.2772i	−0.304048	−	2.11470i
$382$		0			0
$383$	−21.3428	−	11.6541i	−1.09057	−	0.595494i	−0.169749	−	0.985487i	$-0.554296\pi$
$383$	−21.3428	−	11.6541i	−1.09057	−	0.595494i	−0.920818	+	0.389993i	$0.872477\pi$
$384$		0			0
$385$	23.7563	−	26.7860i	1.21074	−	1.36514i
$386$		0			0
$387$	8.18007	+	0.585050i	0.415816	+	0.0297398i
$388$		0			0
$389$	2.08625	−	4.56825i	0.105777	−	0.231619i	−0.849341	−	0.527844i	$-0.823000\pi$
$389$	2.08625	−	4.56825i	0.105777	−	0.231619i	0.955118	+	0.296225i	$0.0957278\pi$
$390$		0			0
$391$	−2.57832	+	0.693132i	−0.130391	+	0.0350532i
$392$		0			0
$393$	1.01518	+	2.72181i	0.0512091	+	0.137297i
$394$		0			0
$395$	−29.0397	−	2.41377i	−1.46115	−	0.121450i
$396$		0			0
$397$	34.1537	−	2.44272i	1.71413	−	0.122597i	0.820570	−	0.571546i	$-0.193656\pi$
$397$	34.1537	−	2.44272i	1.71413	−	0.122597i	0.893557	+	0.448950i	$0.148202\pi$
$398$		0			0
$399$	7.69022	+	26.1905i	0.384992	+	1.31116i
$400$		0			0
$401$	25.5100	−	3.66779i	1.27391	−	0.183161i	0.528021	−	0.849231i	$-0.322934\pi$
$401$	25.5100	−	3.66779i	1.27391	−	0.183161i	0.745889	+	0.666070i	$0.232025\pi$
$402$		0			0
$403$	−16.9267	−	6.31335i	−0.843181	−	0.314490i
$404$		0			0
$405$	23.7199	−	4.87424i	1.17865	−	0.242203i
$406$		0			0
$407$	34.3006	−	25.6771i	1.70022	−	1.27277i
$408$		0			0
$409$	−1.52636	−	2.37507i	−0.0754739	−	0.117440i	0.801465	−	0.598042i	$-0.204054\pi$
$409$	−1.52636	−	2.37507i	−0.0754739	−	0.117440i	−0.876939	+	0.480602i	$0.840418\pi$
$410$		0			0
$411$	1.95972	−	6.67421i	0.0966660	−	0.329214i
$412$		0			0
$413$	31.8329	+	31.8329i	1.56640	+	1.56640i
$414$		0			0
$415$	4.45813	+	0.0513998i	0.218841	+	0.00252311i
$416$		0			0
$417$	−10.6831	−	19.5646i	−0.523154	−	0.958085i
$418$		0			0
$419$	−10.8983	+	7.00391i	−0.532417	+	0.342163i	−0.779067	−	0.626941i	$-0.784307\pi$
$419$	−10.8983	+	7.00391i	−0.532417	+	0.342163i	0.246650	+	0.969105i	$0.420670\pi$
$420$		0			0
$421$	23.8512	+	3.42929i	1.16244	+	0.167133i	0.696415	−	0.717640i	$-0.254778\pi$
$421$	23.8512	+	3.42929i	1.16244	+	0.167133i	0.466022	+	0.884773i	$0.345687\pi$
$422$		0			0
$423$	6.05439	−	1.31705i	0.294375	−	0.0640373i
$424$		0			0
$425$	1.03261	−	2.58490i	0.0500891	−	0.125386i
$426$		0			0
$427$	4.29626	−	5.73914i	0.207911	−	0.277736i
$428$		0			0
$429$	22.9791	−	6.74728i	1.10944	−	0.325762i
$430$		0			0
$431$	−9.21445	−	7.98437i	−0.443845	−	0.384594i	0.404069	−	0.914729i	$-0.367596\pi$
$431$	−9.21445	−	7.98437i	−0.443845	−	0.384594i	−0.847913	+	0.530135i	$0.822141\pi$
$432$		0			0
$433$	1.46008	−	20.4146i	0.0701670	−	0.981063i	−0.833415	−	0.552648i	$-0.813617\pi$
$433$	1.46008	−	20.4146i	0.0701670	−	0.981063i	0.903582	−	0.428415i	$-0.140928\pi$
$434$		0			0
$435$	−5.12672	+	10.8919i	−0.245807	+	0.522225i
$436$		0			0
$437$	11.4876	−	14.6325i	0.549528	−	0.699966i
$438$		0			0
$439$	−3.95455	−	1.80598i	−0.188740	−	0.0861948i	0.318803	−	0.947821i	$-0.396719\pi$
$439$	−3.95455	−	1.80598i	−0.188740	−	0.0861948i	−0.507544	+	0.861626i	$0.669446\pi$
$440$		0			0
$441$	3.26590	+	3.76906i	0.155519	+	0.179479i
$442$		0			0
$443$	−1.67307	−	23.3926i	−0.0794899	−	1.11141i	−0.868057	−	0.496465i	$-0.834631\pi$
$443$	−1.67307	−	23.3926i	−0.0794899	−	1.11141i	0.788567	−	0.614949i	$-0.210823\pi$
$444$		0			0
$445$	5.79607	−	10.3298i	0.274760	−	0.489679i
$446$		0			0
$447$	31.2186	+	23.3700i	1.47659	+	1.10536i
$448$		0			0
$449$	−13.3847	+	6.11258i	−0.631663	+	0.288471i	−0.705403	−	0.708807i	$-0.749234\pi$
$449$	−13.3847	+	6.11258i	−0.631663	+	0.288471i	0.0737400	+	0.997277i	$0.476507\pi$
$450$		0			0
$451$	4.30691	−	6.70169i	0.202805	−	0.315570i
$452$		0			0
$453$	5.19577	+	6.94073i	0.244118	+	0.326104i
$454$		0			0
$455$	−21.3546	−	4.90391i	−1.00112	−	0.229899i
$456$		0			0
$457$	−11.8762	+	6.48490i	−0.555546	+	0.303351i	−0.732387	−	0.680888i	$-0.761594\pi$
$457$	−11.8762	+	6.48490i	−0.555546	+	0.303351i	0.176841	+	0.984239i	$0.443412\pi$
$458$		0			0
$459$	2.34730			0.109562
$460$		0			0
$461$	−6.60004			−0.307395			−0.153697	−	0.988118i	$-0.549118\pi$
$461$	−6.60004			−0.307395			−0.153697	+	0.988118i	$0.549118\pi$
$462$		0			0
$463$	−20.6895	+	11.2973i	−0.961524	+	0.525032i	−0.881717	−	0.471779i	$-0.843612\pi$
$463$	−20.6895	+	11.2973i	−0.961524	+	0.525032i	−0.0798069	+	0.996810i	$0.525430\pi$
$464$		0			0
$465$	15.4019	+	24.5845i	0.714247	+	1.14008i
$466$		0			0
$467$	−2.44481	−	3.26589i	−0.113132	−	0.151127i	0.740401	−	0.672166i	$-0.234636\pi$
$467$	−2.44481	−	3.26589i	−0.113132	−	0.151127i	−0.853533	+	0.521038i	$0.825545\pi$
$468$		0			0
$469$	−7.15749	+	11.1373i	−0.330502	+	0.514272i
$470$		0			0
$471$	−21.1641	+	9.66532i	−0.975190	+	0.445354i
$472$		0			0
$473$	34.4279	+	25.7724i	1.58300	+	1.18502i
$474$		0			0
$475$	5.03371	+	18.7305i	0.230962	+	0.859412i
$476$		0			0
$477$	0.237813	+	3.32507i	0.0108887	+	0.152244i
$478$		0			0
$479$	0.515743	+	0.595199i	0.0235649	+	0.0271954i	0.767410	−	0.641157i	$-0.221545\pi$
$479$	0.515743	+	0.595199i	0.0235649	+	0.0271954i	−0.743845	+	0.668352i	$0.767000\pi$
$480$		0			0
$481$	−23.8515	−	10.8926i	−1.08753	−	0.496660i
$482$		0			0
$483$	7.92935	−	32.8030i	0.360798	−	1.49259i
$484$		0			0
$485$	−24.3245	−	11.4494i	−1.10452	−	0.519889i
$486$		0			0
$487$	0.722269	−	10.0986i	0.0327291	−	0.457613i	−0.954490	−	0.298243i	$-0.903599\pi$
$487$	0.722269	−	10.0986i	0.0327291	−	0.457613i	0.987219	−	0.159370i	$-0.0509462\pi$
$488$		0			0
$489$	−1.13320	−	0.981921i	−0.0512450	−	0.0444040i
$490$		0			0
$491$	−3.15216	+	0.925557i	−0.142255	+	0.0417698i	−0.352085	−	0.935968i	$-0.614527\pi$
$491$	−3.15216	+	0.925557i	−0.142255	+	0.0417698i	0.209830	+	0.977738i	$0.432709\pi$
$492$		0			0
$493$	−0.915183	+	1.22254i	−0.0412178	+	0.0550605i
$494$		0			0
$495$	−7.93197	−	3.06309i	−0.356515	−	0.137676i
$496$		0			0
$497$	−34.4445	+	7.49294i	−1.54505	+	0.336104i
$498$		0			0
$499$	−26.8020	−	3.85354i	−1.19982	−	0.172508i	−0.486713	−	0.873562i	$-0.661804\pi$
$499$	−26.8020	−	3.85354i	−1.19982	−	0.172508i	−0.713108	+	0.701054i	$0.752713\pi$
$500$		0			0
$501$	−33.1806	+	21.3239i	−1.48240	+	0.952682i
$502$		0			0
$503$	−11.8460	−	21.6943i	−0.528186	−	0.967300i	−0.996488	−	0.0837321i	$-0.973316\pi$
$503$	−11.8460	−	21.6943i	−0.528186	−	0.967300i	0.468302	−	0.883568i	$-0.344866\pi$
$504$		0			0
$505$	4.27595	−	4.17847i	0.190277	−	0.185940i
$506$		0			0
$507$	7.67685	+	7.67685i	0.340941	+	0.340941i
$508$		0			0
$509$	5.34342	−	18.1980i	0.236843	−	0.806613i	−0.752193	−	0.658942i	$-0.771004\pi$
$509$	5.34342	−	18.1980i	0.236843	−	0.806613i	0.989037	−	0.147671i	$-0.0471777\pi$
$510$		0			0
$511$	2.56915	+	3.99767i	0.113652	+	0.176847i
$512$		0			0
$513$	−13.0933	+	9.80149i	−0.578082	+	0.432747i
$514$		0			0
$515$	−27.4398	−	18.0849i	−1.20914	−	0.796915i
$516$		0			0
$517$	30.4431	+	11.3547i	1.33889	+	0.499378i
$518$		0			0
$519$	35.1416	−	5.05259i	1.54254	−	0.221784i
$520$		0			0
$521$	10.2736	+	34.9886i	0.450094	+	1.53288i	0.802279	+	0.596949i	$0.203621\pi$
$521$	10.2736	+	34.9886i	0.450094	+	1.53288i	−0.352185	+	0.935930i	$0.614561\pi$
$522$		0			0
$523$	−9.02237	+	0.645293i	−0.394521	+	0.0282167i	−0.267191	−	0.963644i	$-0.586095\pi$
$523$	−9.02237	+	0.645293i	−0.394521	+	0.0282167i	−0.127330	+	0.991860i	$0.540641\pi$
$524$		0			0
$525$	22.4217	+	27.1148i	0.978564	+	1.18339i
$526$		0			0
$527$	1.28612	+	3.44822i	0.0560242	+	0.150207i
$528$		0			0
$529$	−21.3384	+	8.58335i	−0.927755	+	0.373189i
$530$		0			0
$531$	4.44140	−	9.72531i	0.192740	−	0.422043i
$532$		0			0
$533$	−4.86274	−	0.347790i	−0.210629	−	0.0150645i
$534$		0			0
$535$	15.5409	+	13.7831i	0.671891	+	0.595896i
$536$		0			0
$537$	26.0184	+	14.2071i	1.12278	+	0.613082i
$538$		0			0
$539$	3.72192	+	25.8865i	0.160314	+	1.11501i
$540$		0			0
$541$	−11.5031	−	25.1883i	−0.494557	−	1.08293i	−0.978200	−	0.207664i	$-0.933414\pi$
$541$	−11.5031	−	25.1883i	−0.494557	−	1.08293i	0.483643	−	0.875265i	$-0.339313\pi$
$542$		0			0
$543$	9.33340	+	42.9050i	0.400535	+	1.84123i
$544$		0			0
$545$	3.97498	+	5.43956i	0.170269	+	0.233005i
$546$		0			0
$547$	−35.8167	−	7.79146i	−1.53141	−	0.333139i	−0.633651	−	0.773619i	$-0.718445\pi$
$547$	−35.8167	−	7.79146i	−1.53141	−	0.333139i	−0.897762	+	0.440480i	$0.854808\pi$
$548$		0			0
$549$	−1.63362	−	0.479674i	−0.0697211	−	0.0204720i
$550$		0			0
$551$		−	10.6409i		−	0.453315i
$552$		0			0
$553$	33.0408	−	33.0408i	1.40504	−	1.40504i
$554$		0			0
$555$	19.7521	+	37.1862i	0.838431	+	1.57847i
$556$		0			0
$557$	−9.43561	+	43.3748i	−0.399800	+	1.83785i	0.132356	+	0.991202i	$0.457746\pi$
$557$	−9.43561	+	43.3748i	−0.399800	+	1.83785i	−0.532155	+	0.846647i	$0.678618\pi$
$558$		0			0
$559$	3.74549	−	26.0505i	0.158417	−	1.10182i
$560$		0			0
$561$	−4.10431	−	2.63768i	−0.173284	−	0.111363i
$562$		0			0
$563$	8.49568	−	22.7778i	0.358050	−	0.959970i	−0.625642	−	0.780110i	$-0.715163\pi$
$563$	8.49568	−	22.7778i	0.358050	−	0.959970i	0.983692	−	0.179860i	$-0.0575643\pi$
$564$		0			0
$565$	−1.09796	−	8.31599i	−0.0461915	−	0.349856i
$566$		0			0
$567$	−18.6094	+	34.0806i	−0.781523	+	1.43125i
$568$		0			0
$569$	−0.410673	+	0.473942i	−0.0172163	+	0.0198687i	−0.764292	−	0.644870i	$-0.776912\pi$
$569$	−0.410673	+	0.473942i	−0.0172163	+	0.0198687i	0.747076	+	0.664738i	$0.231457\pi$
$570$		0			0
$571$	10.0446	−	8.70374i	0.420356	−	0.364240i	−0.418849	−	0.908056i	$-0.637566\pi$
$571$	10.0446	−	8.70374i	0.420356	−	0.364240i	0.839205	+	0.543816i	$0.183021\pi$
$572$		0			0
$573$	45.3798	−	16.9258i	1.89577	−	0.707085i
$574$		0			0
$575$	6.17002	−	23.1718i	0.257307	−	0.966330i
$576$		0			0
$577$	12.0005	−	4.47596i	0.499588	−	0.186337i	−0.0870221	−	0.996206i	$-0.527735\pi$
$577$	12.0005	−	4.47596i	0.499588	−	0.186337i	0.586610	+	0.809870i	$0.300462\pi$
$578$		0			0
$579$	9.41691	−	8.15980i	0.391354	−	0.339110i
$580$		0			0
$581$	−4.68175	+	5.40303i	−0.194232	+	0.224155i
$582$		0			0
$583$	−8.37783	+	15.3428i	−0.346974	+	0.635436i
$584$		0			0
$585$	0.681109	+	5.15875i	0.0281604	+	0.213288i
$586$		0			0
$587$	−1.56268	+	4.18972i	−0.0644988	+	0.172928i	−0.965201	−	0.261509i	$-0.915780\pi$
$587$	−1.56268	+	4.18972i	−0.0644988	+	0.172928i	0.900702	+	0.434437i	$0.143053\pi$
$588$		0			0
$589$	−21.5726	−	13.8639i	−0.888882	−	0.571250i
$590$		0			0
$591$	−5.70468	+	39.6769i	−0.234659	+	1.63209i
$592$		0			0
$593$	−7.80403	+	35.8746i	−0.320473	+	1.47319i	0.481825	+	0.876268i	$0.339974\pi$
$593$	−7.80403	+	35.8746i	−0.320473	+	1.47319i	−0.802298	+	0.596924i	$0.796389\pi$
$594$		0			0
$595$	2.09381	+	3.94189i	0.0858377	+	0.161602i
$596$		0			0
$597$	33.9175	−	33.9175i	1.38815	−	1.38815i
$598$		0			0
$599$			38.3973i			1.56887i	0.620211	+	0.784435i	$0.287047\pi$
$599$			38.3973i			1.56887i	−0.620211	+	0.784435i	$0.712953\pi$
$600$		0			0
$601$	30.1055	+	8.83977i	1.22803	+	0.360582i	0.830506	−	0.557010i	$-0.188052\pi$
$601$	30.1055	+	8.83977i	1.22803	+	0.360582i	0.397523	+	0.917592i	$0.369870\pi$
$602$		0			0
$603$	3.07226	+	0.668329i	0.125112	+	0.0272165i
$604$		0			0
$605$	−11.7956	−	16.1416i	−0.479557	−	0.656250i
$606$		0			0
$607$	−9.79459	−	45.0250i	−0.397550	−	1.82751i	−0.544997	−	0.838438i	$-0.683469\pi$
$607$	−9.79459	−	45.0250i	−0.397550	−	1.82751i	0.147447	−	0.989070i	$-0.452894\pi$
$608$		0			0
$609$	−8.01897	−	17.5591i	−0.324945	−	0.711530i
$610$		0			0
$611$	−2.82979	−	19.6816i	−0.114481	−	0.796234i
$612$		0			0
$613$	−6.45267	−	3.52343i	−0.260621	−	0.142310i	0.343627	−	0.939106i	$-0.388344\pi$
$613$	−6.45267	−	3.52343i	−0.260621	−	0.142310i	−0.604248	+	0.796796i	$0.706526\pi$
$614$		0			0
$615$	5.85703	+	5.19457i	0.236178	+	0.209465i
$616$		0			0
$617$	−11.8880	−	0.850249i	−0.478594	−	0.0342297i	−0.170041	−	0.985437i	$-0.554390\pi$
$617$	−11.8880	−	0.850249i	−0.478594	−	0.0342297i	−0.308553	+	0.951207i	$0.599845\pi$
$618$		0			0
$619$	−5.01318	+	10.9773i	−0.201497	+	0.441216i	−0.983223	−	0.182405i	$-0.941612\pi$
$619$	−5.01318	+	10.9773i	−0.201497	+	0.441216i	0.781727	+	0.623621i	$0.214339\pi$
$620$		0			0
$621$	20.0762	−	2.41716i	0.805631	−	0.0969972i
$622$		0			0
$623$	6.63755	+	17.7960i	0.265928	+	0.712980i
$624$		0			0
$625$	15.4831	+	19.6284i	0.619325	+	0.785135i
$626$		0			0
$627$	33.9080	−	2.42514i	1.35415	−	0.0968510i
$628$		0			0
$629$	1.50490	+	5.12523i	0.0600044	+	0.204356i
$630$		0			0
$631$	40.8290	−	5.87032i	1.62538	−	0.233694i	0.731445	−	0.681900i	$-0.238846\pi$
$631$	40.8290	−	5.87032i	1.62538	−	0.233694i	0.893930	+	0.448207i	$0.147937\pi$
$632$		0			0
$633$	−21.9306	−	8.17970i	−0.871664	−	0.325114i
$634$		0			0
$635$	39.6725	+	26.1471i	1.57435	+	1.03762i
$636$		0			0
$637$	12.8124	−	9.59128i	0.507648	−	0.380020i
$638$		0			0
$639$	4.52600	+	7.04260i	0.179046	+	0.278601i
$640$		0			0
$641$	−1.06304	+	3.62038i	−0.0419875	+	0.142996i	−0.977819	−	0.209451i	$-0.932832\pi$
$641$	−1.06304	+	3.62038i	−0.0419875	+	0.142996i	0.935832	+	0.352447i	$0.114650\pi$
$642$		0			0
$643$	−29.3903	−	29.3903i	−1.15904	−	1.15904i	−0.984683	−	0.174356i	$-0.944216\pi$
$643$	−29.3903	−	29.3903i	−1.15904	−	1.15904i	−0.174356	−	0.984683i	$-0.555784\pi$
$644$		0			0
$645$	−30.2269	+	29.5378i	−1.19018	+	1.16305i
$646$		0			0
$647$	−5.62490	−	10.3012i	−0.221138	−	0.404983i	0.743432	−	0.668811i	$-0.233197\pi$
$647$	−5.62490	−	10.3012i	−0.221138	−	0.404983i	−0.964570	+	0.263828i	$0.915015\pi$
$648$		0			0
$649$	47.1657	−	30.3116i	1.85142	−	1.18983i
$650$		0			0
$651$	−46.0460	−	6.62041i	−1.80468	−	0.259474i
$652$		0			0
$653$	−6.96199	+	1.51449i	−0.272444	+	0.0592665i	−0.346711	−	0.937972i	$-0.612702\pi$
$653$	−6.96199	+	1.51449i	−0.272444	+	0.0592665i	0.0742677	+	0.997238i	$0.476338\pi$
$654$		0			0
$655$	−3.08762	−	1.19235i	−0.120643	−	0.0465890i
$656$		0			0
$657$	0.676323	−	0.903462i	0.0263859	−	0.0352474i
$658$		0			0
$659$	24.9273	−	7.31932i	0.971030	−	0.285120i	0.242513	−	0.970148i	$-0.422028\pi$
$659$	24.9273	−	7.31932i	0.971030	−	0.285120i	0.728517	+	0.685028i	$0.240210\pi$
$660$		0			0
$661$	9.29786	+	8.05665i	0.361645	+	0.313367i	0.816663	−	0.577115i	$-0.195822\pi$
$661$	9.29786	+	8.05665i	0.361645	+	0.313367i	−0.455018	+	0.890482i	$0.650367\pi$
$662$		0			0
$663$	−0.212997	+	2.97808i	−0.00827211	+	0.115659i
$664$		0			0
$665$	−28.1393	−	13.2450i	−1.09119	−	0.513617i
$666$		0			0
$667$	−6.56856	+	11.3987i	−0.254336	+	0.441360i
$668$		0			0
$669$	−27.6540	−	12.6292i	−1.06917	−	0.488272i
$670$		0			0
$671$	−5.84682	−	6.74759i	−0.225714	−	0.260488i
$672$		0			0
$673$	2.50054	+	34.9622i	0.0963889	+	1.34769i	0.783614	+	0.621248i	$0.213374\pi$
$673$	2.50054	+	34.9622i	0.0963889	+	1.34769i	−0.687225	+	0.726444i	$0.741171\pi$
$674$		0			0
$675$	−10.5275	+	18.2654i	−0.405203	+	0.703037i
$676$		0			0
$677$	7.53068	+	5.63740i	0.289428	+	0.216663i	0.734119	−	0.679021i	$-0.237596\pi$
$677$	7.53068	+	5.63740i	0.289428	+	0.216663i	−0.444691	+	0.895684i	$0.646686\pi$
$678$		0			0
$679$	39.2143	−	17.9086i	1.50491	−	0.687267i
$680$		0			0
$681$	25.6762	−	39.9530i	0.983914	−	1.53100i
$682$		0			0
$683$	7.71182	+	10.3018i	0.295084	+	0.394187i	0.923442	−	0.383738i	$-0.125363\pi$
$683$	7.71182	+	10.3018i	0.295084	+	0.394187i	−0.628358	+	0.777925i	$0.716272\pi$
$684$		0			0
$685$	4.20768	+	6.71629i	0.160767	+	0.256616i
$686$		0			0
$687$	14.5957	−	7.96984i	0.556860	−	0.304068i
$688$		0			0
$689$	10.6980			0.407561
$690$		0			0
$691$	13.6127			0.517852			0.258926	−	0.965897i	$-0.416631\pi$
$691$	13.6127			0.517852			0.258926	+	0.965897i	$0.416631\pi$
$692$		0			0
$693$	11.9668	−	6.53438i	0.454582	−	0.248221i
$694$		0			0
$695$	24.7539	+	5.68454i	0.938970	+	0.215627i
$696$		0			0
$697$	0.595167	+	0.795050i	0.0225436	+	0.0301147i
$698$		0			0
$699$	16.7438	−	26.0538i	0.633308	−	0.985447i
$700$		0			0
$701$	−41.7809	+	19.0807i	−1.57804	+	0.720668i	−0.995731	−	0.0922988i	$-0.970578\pi$
$701$	−41.7809	+	19.0807i	−1.57804	+	0.720668i	−0.582311	+	0.812966i	$0.697851\pi$
$702$		0			0
$703$	−29.7956	−	22.3047i	−1.12376	−	0.841237i
$704$		0			0
$705$	−15.6247	+	27.8463i	−0.588459	+	1.04875i
$706$		0			0
$707$	0.683917	+	9.56242i	0.0257214	+	0.359632i
$708$		0			0
$709$	−15.2275	−	17.5735i	−0.571883	−	0.659988i	0.393957	−	0.919129i	$-0.371106\pi$
$709$	−15.2275	−	17.5735i	−0.571883	−	0.659988i	−0.965839	+	0.259141i	$0.916560\pi$
$710$		0			0
$711$	−10.0943	−	4.60993i	−0.378567	−	0.172886i
$712$		0			0
$713$	14.5509	+	28.1679i	0.544936	+	1.05490i
$714$		0			0
$715$	−11.6209	+	24.6890i	−0.434597	+	0.923315i
$716$		0			0
$717$	0.446969	−	6.24944i	0.0166924	−	0.233390i
$718$		0			0
$719$	6.84728	+	5.93321i	0.255361	+	0.221271i	0.773128	−	0.634250i	$-0.218691\pi$
$719$	6.84728	+	5.93321i	0.255361	+	0.221271i	−0.517767	+	0.855522i	$0.673237\pi$
$720$		0			0
$721$	50.5630	−	14.8467i	1.88307	−	0.552918i
$722$		0			0
$723$	29.4879	−	39.3913i	1.09667	−	1.46498i
$724$		0			0
$725$	−5.40864	−	12.6045i	−0.200872	−	0.468120i
$726$		0			0
$727$	−40.7562	+	8.86598i	−1.51156	+	0.328821i	−0.890516	−	0.454951i	$-0.849657\pi$
$727$	−40.7562	+	8.86598i	−1.51156	+	0.328821i	−0.621049	+	0.783772i	$0.713293\pi$
$728$		0			0
$729$	−15.4439	−	2.22050i	−0.571998	−	0.0822408i
$730$		0			0
$731$	−4.51032	+	2.89861i	−0.166820	+	0.107209i
$732$		0			0
$733$	−21.5999	−	39.5573i	−0.797811	−	1.46108i	−0.885352	−	0.464921i	$-0.846083\pi$
$733$	−21.5999	−	39.5573i	−0.797811	−	1.46108i	0.0875412	−	0.996161i	$-0.472099\pi$
$734$		0			0
$735$	−25.6992	−	0.296298i	−0.947928	−	0.0109291i
$736$		0			0
$737$	11.6586	+	11.6586i	0.429449	+	0.429449i
$738$		0			0
$739$	6.40170	−	21.8022i	0.235490	−	0.802007i	−0.753933	−	0.656951i	$-0.771846\pi$
$739$	6.40170	−	21.8022i	0.235490	−	0.802007i	0.989424	−	0.145056i	$-0.0463361\pi$
$740$		0			0
$741$	−11.2474	−	17.5012i	−0.413182	−	0.642923i
$742$		0			0
$743$	19.2841	−	14.4359i	0.707466	−	0.529602i	−0.183867	−	0.982951i	$-0.558862\pi$
$743$	19.2841	−	14.4359i	0.707466	−	0.529602i	0.891333	+	0.453349i	$0.149771\pi$
$744$		0			0
$745$	−43.5227	+	8.94356i	−1.59455	+	0.327667i
$746$		0			0
$747$	1.59082	+	0.593346i	0.0582051	+	0.0217094i
$748$		0			0
$749$	−32.9702	+	4.74040i	−1.20471	+	0.173211i
$750$		0			0
$751$	13.0371	+	44.4003i	0.475730	+	1.62019i	0.752038	+	0.659120i	$0.229071\pi$
$751$	13.0371	+	44.4003i	0.475730	+	1.62019i	−0.276308	+	0.961069i	$0.589111\pi$
$752$		0			0
$753$	−1.31760	+	0.0942367i	−0.0480161	+	0.00343418i
$754$		0			0
$755$	−9.84451	−	0.818269i	−0.358278	−	0.0297799i
$756$		0			0
$757$	−2.84441	−	7.62617i	−0.103382	−	0.277178i	0.874952	−	0.484209i	$-0.160893\pi$
$757$	−2.84441	−	7.62617i	−0.103382	−	0.277178i	−0.978334	+	0.207031i	$0.933620\pi$
$758$		0			0
$759$	−37.8200	−	18.3334i	−1.37278	−	0.665460i
$760$		0			0
$761$	−0.464781	+	1.01773i	−0.0168483	+	0.0368926i	−0.917869	−	0.396883i	$-0.870092\pi$
$761$	−0.464781	+	1.01773i	−0.0168483	+	0.0368926i	0.901021	+	0.433776i	$0.142819\pi$
$762$		0			0
$763$	−10.7757	−	0.770695i	−0.390108	−	0.0279010i
$764$		0			0
$765$	0.703363	−	0.793062i	0.0254301	−	0.0286732i
$766$		0			0
$767$	−30.1139	−	16.4434i	−1.08735	−	0.593738i
$768$		0			0
$769$	1.36684	+	9.50656i	0.0492894	+	0.342815i	0.999512	+	0.0312429i	$0.00994655\pi$
$769$	1.36684	+	9.50656i	0.0492894	+	0.342815i	−0.950222	+	0.311572i	$0.899144\pi$
$770$		0			0
$771$	−19.0238	−	41.6562i	−0.685124	−	1.50021i
$772$		0			0
$773$	6.44819	+	29.6419i	0.231925	+	1.06614i	0.934895	+	0.354924i	$0.115493\pi$
$773$	6.44819	+	29.6419i	0.231925	+	1.06614i	−0.702970	+	0.711220i	$0.748143\pi$
$774$		0			0
$775$	−32.6004	−	5.45716i	−1.17104	−	0.196027i
$776$		0			0
$777$	−65.9762	−	14.3523i	−2.36688	−	0.514884i
$778$		0			0
$779$	−6.63971	−	1.94959i	−0.237892	−	0.0698515i
$780$		0			0
$781$			43.9003i			1.57088i
$782$		0			0
$783$	8.17869	−	8.17869i	0.292283	−	0.292283i
$784$		0			0
$785$	7.76133	−	25.3479i	0.277014	−	0.904705i
$786$		0			0
$787$	−4.53106	+	20.8289i	−0.161515	+	0.742472i	0.823123	+	0.567863i	$0.192230\pi$
$787$	−4.53106	+	20.8289i	−0.161515	+	0.742472i	−0.984638	+	0.174609i	$0.944134\pi$
$788$		0			0
$789$	−3.31306	+	23.0428i	−0.117948	+	0.820346i
$790$		0			0
$791$	11.3154	+	7.27199i	0.402331	+	0.258562i
$792$		0			0
$793$	−1.90944	+	5.11940i	−0.0678061	+	0.181795i
$794$		0			0
$795$	−13.6330	−	10.4530i	−0.483513	−	0.370728i
$796$		0			0
$797$	−14.0009	+	25.6408i	−0.495938	+	0.908243i	0.503093	+	0.864232i	$0.332195\pi$
$797$	−14.0009	+	25.6408i	−0.495938	+	0.908243i	−0.999031	+	0.0440104i	$0.985987\pi$
$798$		0			0
$799$	−2.65262	+	3.06129i	−0.0938429	+	0.108300i
$800$		0			0
$801$	3.40902	−	2.95393i	0.120452	−	0.104372i
$802$		0			0
$803$	5.54504	−	2.06819i	0.195680	−	0.0729849i
$804$		0			0
$805$	21.9674	+	31.5586i	0.774248	+	1.11229i
$806$		0			0
$807$	−10.4468	+	3.89647i	−0.367746	+	0.137162i
$808$		0			0
$809$	−35.7298	+	30.9600i	−1.25619	+	1.08850i	−0.263904	+	0.964549i	$0.585010\pi$
$809$	−35.7298	+	30.9600i	−1.25619	+	1.08850i	−0.992289	+	0.123948i	$0.960444\pi$
$810$		0			0
$811$	−16.3664	+	18.8879i	−0.574703	+	0.663242i	−0.966457	−	0.256828i	$-0.917323\pi$
$811$	−16.3664	+	18.8879i	−0.574703	+	0.663242i	0.391755	+	0.920070i	$0.371868\pi$
$812$		0			0
$813$	−16.9718	+	31.0816i	−0.595228	+	1.09008i
$814$		0			0
$815$	1.69372	−	0.223622i	0.0593285	−	0.00783314i
$816$		0			0
$817$	13.0551	−	35.0020i	0.456739	−	1.22457i
$818$		0			0
$819$	−7.01943	−	4.51111i	−0.245279	−	0.157631i
$820$		0			0
$821$	4.21780	−	29.3354i	0.147202	−	1.02381i	−0.773570	−	0.633711i	$-0.781531\pi$
$821$	4.21780	−	29.3354i	0.147202	−	1.02381i	0.920772	−	0.390102i	$-0.127560\pi$
$822$		0			0
$823$	−4.40896	+	20.2677i	−0.153687	+	0.706486i	0.834220	+	0.551433i	$0.185919\pi$
$823$	−4.40896	+	20.2677i	−0.153687	+	0.706486i	−0.987906	+	0.155053i	$0.950445\pi$
$824$		0			0
$825$	38.9326	−	20.1077i	1.35546	−	0.700062i
$826$		0			0
$827$	−18.2291	+	18.2291i	−0.633888	+	0.633888i	−0.949041	−	0.315153i	$-0.897944\pi$
$827$	−18.2291	+	18.2291i	−0.633888	+	0.633888i	0.315153	+	0.949041i	$0.397944\pi$
$828$		0			0
$829$		−	41.4811i		−	1.44070i	−0.693611	−	0.720350i	$-0.743981\pi$
$829$		−	41.4811i		−	1.44070i	0.693611	−	0.720350i	$-0.256019\pi$
$830$		0			0
$831$	47.4817	+	13.9419i	1.64712	+	0.483639i
$832$		0			0
$833$	−3.18588	−	0.693046i	−0.110384	−	0.0240126i
$834$		0			0
$835$	6.90790	−	44.4051i	0.239058	−	1.53670i
$836$		0			0
$837$	−5.92502	−	27.2369i	−0.204799	−	0.941444i
$838$		0			0
$839$	−2.61049	−	5.71618i	−0.0901242	−	0.197344i	0.859202	−	0.511636i	$-0.170960\pi$
$839$	−2.61049	−	5.71618i	−0.0901242	−	0.197344i	−0.949327	+	0.314292i	$0.898233\pi$
$840$		0			0
$841$	−3.05620	−	21.2563i	−0.105386	−	0.732977i
$842$		0			0
$843$	−19.4989	−	10.6472i	−0.671579	−	0.366710i
$844$		0			0
$845$	−12.3477	+	0.740153i	−0.424774	+	0.0254620i
$846$		0			0
$847$	31.9764	+	2.28700i	1.09872	+	0.0785822i
$848$		0			0
$849$	10.7027	−	23.4357i	0.367317	−	0.804312i
$850$		0			0
$851$	18.1491	+	42.2860i	0.622143	+	1.44954i
$852$		0			0
$853$	−4.31021	−	11.5561i	−0.147579	−	0.395674i	0.842036	−	0.539422i	$-0.181357\pi$
$853$	−4.31021	−	11.5561i	−0.147579	−	0.395674i	−0.989614	+	0.143748i	$0.954085\pi$
$854$		0			0
$855$	−0.611818	+	7.36071i	−0.0209237	+	0.251731i
$856$		0			0
$857$	−19.1019	+	1.36619i	−0.652507	+	0.0466682i	−0.393669	−	0.919252i	$-0.628794\pi$
$857$	−19.1019	+	1.36619i	−0.652507	+	0.0466682i	−0.258838	+	0.965921i	$0.583340\pi$
$858$		0			0
$859$	8.14556	+	27.7412i	0.277923	+	0.946518i	0.973619	+	0.228182i	$0.0732781\pi$
$859$	8.14556	+	27.7412i	0.277923	+	0.946518i	−0.695696	+	0.718337i	$0.744904\pi$
$860$		0			0
$861$	−12.4258	+	1.78656i	−0.423470	+	0.0608857i
$862$		0			0
$863$	31.3541	+	11.6945i	1.06731	+	0.398085i	0.820894	−	0.571080i	$-0.193476\pi$
$863$	31.3541	+	11.6945i	1.06731	+	0.398085i	0.246412	+	0.969165i	$0.420748\pi$
$864$		0			0
$865$	−22.2604	+	33.7753i	−0.756878	+	1.14840i
$866$		0			0
$867$	−26.2216	+	19.6293i	−0.890533	+	0.666645i
$868$		0			0
$869$	−31.4617	−	48.9554i	−1.06727	−	1.66070i
$870$		0			0
$871$	2.84269	−	9.68130i	0.0963207	−	0.328038i
$872$		0			0
$873$	−7.23952	−	7.23952i	−0.245021	−	0.245021i
$874$		0			0
$875$	−40.0644	−	1.38625i	−1.35442	−	0.0468639i
$876$		0			0
$877$	−7.80929	−	14.3017i	−0.263701	−	0.482933i	0.711959	−	0.702221i	$-0.247808\pi$
$877$	−7.80929	−	14.3017i	−0.263701	−	0.482933i	−0.975660	+	0.219289i	$0.929626\pi$
$878$		0			0
$879$	−12.1311	+	7.79618i	−0.409172	+	0.262959i
$880$		0			0
$881$	20.2874	+	2.91689i	0.683500	+	0.0982724i	0.475313	−	0.879817i	$-0.342335\pi$
$881$	20.2874	+	2.91689i	0.683500	+	0.0982724i	0.208187	+	0.978089i	$0.433244\pi$
$882$		0			0
$883$	43.3507	−	9.43036i	1.45887	−	0.317357i	0.587994	−	0.808866i	$-0.299918\pi$
$883$	43.3507	−	9.43036i	1.45887	−	0.317357i	0.870873	+	0.491509i	$0.163554\pi$
$884$		0			0
$885$	22.3090	+	50.3789i	0.749908	+	1.69347i
$886$		0			0
$887$	35.0681	−	46.8455i	1.17747	−	1.57292i	0.439243	−	0.898368i	$-0.355247\pi$
$887$	35.0681	−	46.8455i	1.17747	−	1.57292i	0.738229	−	0.674550i	$-0.235662\pi$
$888$		0			0
$889$	−73.1040	+	21.4653i	−2.45183	+	0.719922i
$890$		0			0
$891$	36.5475	+	31.6686i	1.22439	+	1.06094i
$892$		0			0
$893$	2.01349	−	28.1523i	0.0673790	−	0.942082i
$894$		0			0
$895$	−31.7807	+	11.4380i	−1.06231	+	0.382329i
$896$		0			0
$897$	1.24498	+	25.6906i	0.0415686	+	0.857786i
$898$		0			0
$899$	16.4959	+	7.53341i	0.550168	+	0.251253i
$900$		0			0
$901$	−1.42716	−	1.64703i	−0.0475456	−	0.0548705i
$902$		0			0
$903$	−4.83465	−	67.5972i	−0.160887	−	2.24949i
$904$		0			0
$905$	−43.6294	−	24.4806i	−1.45029	−	0.813762i
$906$		0			0
$907$	−44.2594	−	33.1322i	−1.46961	−	1.10014i	−0.972626	−	0.232376i	$-0.925350\pi$
$907$	−44.2594	−	33.1322i	−1.46961	−	1.10014i	−0.496983	−	0.867760i	$-0.665559\pi$
$908$		0			0
$909$	2.07103	−	0.945810i	0.0686919	−	0.0313705i
$910$		0			0
$911$	10.0085	−	15.5735i	0.331596	−	0.515973i	−0.634921	−	0.772577i	$-0.718967\pi$
$911$	10.0085	−	15.5735i	0.331596	−	0.515973i	0.966517	+	0.256604i	$0.0826037\pi$
$912$		0			0
$913$	5.33575	+	7.12772i	0.176587	+	0.235893i
$914$		0			0
$915$	7.43544	−	4.65822i	0.245808	−	0.153996i
$916$		0			0
$917$	4.65824	−	2.54359i	0.153829	−	0.0839968i
$918$		0			0
$919$	−34.7200			−1.14531			−0.572653	−	0.819798i	$-0.694086\pi$
$919$	−34.7200			−1.14531			−0.572653	+	0.819798i	$0.694086\pi$
$920$		0			0
$921$	46.6877			1.53841
$922$		0			0
$923$	23.5795	−	12.8754i	0.776130	−	0.423799i
$924$		0			0
$925$	−46.6313	−	11.2760i	−1.53323	−	0.370752i
$926$		0			0
$927$	−7.50008	−	10.0189i	−0.246335	−	0.329065i
$928$		0			0
$929$	−32.0058	+	49.8020i	−1.05008	+	1.63395i	−0.324389	+	0.945924i	$0.605159\pi$
$929$	−32.0058	+	49.8020i	−1.05008	+	1.63395i	−0.725687	+	0.688025i	$0.758478\pi$
$930$		0			0
$931$	20.6648	−	9.43732i	0.677263	−	0.309296i
$932$		0			0
$933$	−21.8443	−	16.3525i	−0.715151	−	0.535355i
$934$		0			0
$935$	5.35132	−	1.50450i	0.175007	−	0.0492024i
$936$		0			0
$937$	0.208935	+	2.92129i	0.00682561	+	0.0954345i	0.999723	−	0.0235403i	$-0.00749379\pi$
$937$	0.208935	+	2.92129i	0.00682561	+	0.0954345i	−0.992897	+	0.118975i	$0.962039\pi$
$938$		0			0
$939$	25.2437	+	29.1328i	0.823798	+	0.950713i
$940$		0			0
$941$	−6.26261	−	2.86004i	−0.204155	−	0.0932346i	0.310713	−	0.950504i	$-0.399432\pi$
$941$	−6.26261	−	2.86004i	−0.204155	−	0.0932346i	−0.514869	+	0.857269i	$0.672159\pi$
$942$		0			0
$943$	5.90913	+	6.18712i	0.192428	+	0.201480i
$944$		0			0
$945$	−11.4480	−	31.8084i	−0.372403	−	1.03473i
$946$		0			0
$947$	−1.49553	+	20.9103i	−0.0485983	+	0.679493i	0.913508	+	0.406820i	$0.133362\pi$
$947$	−1.49553	+	20.9103i	−0.0485983	+	0.679493i	−0.962107	+	0.272673i	$0.912092\pi$
$948$		0			0
$949$	−2.73715	−	2.37175i	−0.0888515	−	0.0769903i
$950$		0			0
$951$	45.3791	−	13.3245i	1.47152	−	0.432077i
$952$		0			0
$953$	22.8408	−	30.5118i	0.739887	−	0.988373i	−0.259855	−	0.965648i	$-0.583675\pi$
$953$	22.8408	−	30.5118i	0.739887	−	0.988373i	0.999742	−	0.0227253i	$-0.00723430\pi$
$954$		0			0
$955$	−19.8797	+	51.4789i	−0.643290	+	1.66582i
$956$		0			0
$957$	−23.4911	+	5.11018i	−0.759360	+	0.165189i
$958$		0			0
$959$	−12.5794	−	1.80865i	−0.406210	−	0.0584042i
$960$		0			0
$961$	10.6862	−	6.86760i	0.344716	−	0.221535i
$962$		0			0
$963$	3.79116	+	6.94299i	0.122168	+	0.223735i
$964$		0			0
$965$	−0.163673	+	14.1961i	−0.00526883	+	0.456989i
$966$		0			0
$967$	−12.8408	−	12.8408i	−0.412933	−	0.412933i	0.469826	−	0.882759i	$-0.344317\pi$
$967$	−12.8408	−	12.8408i	−0.412933	−	0.412933i	−0.882759	+	0.469826i	$0.844317\pi$
$968$		0			0
$969$	−1.19399	+	4.06635i	−0.0383564	+	0.130630i
$970$		0			0
$971$	4.10072	+	6.38085i	0.131599	+	0.204771i	0.900799	−	0.434236i	$-0.142982\pi$
$971$	4.10072	+	6.38085i	0.131599	+	0.204771i	−0.769201	+	0.639007i	$0.779345\pi$
$972$		0			0
$973$	−32.6036	+	24.4067i	−1.04522	+	0.782444i
$974$		0			0
$975$	−22.2186	−	15.0140i	−0.711565	−	0.480832i
$976$		0			0
$977$	25.4964	+	9.50967i	0.815702	+	0.304241i	0.722469	−	0.691403i	$-0.243007\pi$
$977$	25.4964	+	9.50967i	0.815702	+	0.304241i	0.0932331	+	0.995644i	$0.470280\pi$
$978$		0			0
$979$	23.4137	−	3.36638i	0.748305	−	0.107590i
$980$		0			0
$981$	0.722833	+	2.46174i	0.0230783	+	0.0785974i
$982$		0			0
$983$	−21.1359	+	1.51167i	−0.674132	+	0.0482149i	−0.404208	−	0.914667i	$-0.632453\pi$
$983$	−21.1359	+	1.51167i	−0.674132	+	0.0482149i	−0.269924	+	0.962882i	$0.586998\pi$
$984$		0			0
$985$	−29.5088	−	34.8590i	−0.940227	−	1.11070i
$986$		0			0
$987$	−17.8931	−	47.9732i	−0.569543	−	1.52700i
$988$		0			0
$989$	−35.5915	+	29.4361i	−1.13174	+	0.936013i
$990$		0			0
$991$	7.71006	−	16.8827i	0.244918	−	0.536296i	−0.746751	−	0.665103i	$-0.768388\pi$
$991$	7.71006	−	16.8827i	0.244918	−	0.536296i	0.991670	+	0.128807i	$0.0411148\pi$
$992$		0			0
$993$	−34.5379	−	2.47020i	−1.09603	−	0.0783895i
$994$		0			0
$995$	3.27011	+	54.5541i	0.103669	+	1.72948i
$996$		0			0
$997$	−27.1231	−	14.8104i	−0.858998	−	0.469049i	−0.0115543	−	0.999933i	$-0.503678\pi$
$997$	−27.1231	−	14.8104i	−0.858998	−	0.469049i	−0.847444	+	0.530885i	$0.821860\pi$
$998$		0			0
$999$	−5.75759	−	40.0449i	−0.182162	−	1.26696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.8	✓	720
5.3	odd	4	inner	920.2.bv.a.753.8	yes	720
23.19	odd	22	inner	920.2.bv.a.617.8	yes	720
115.88	even	44	inner	920.2.bv.a.433.8	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.8	✓	720	1.1	even	1	trivial
920.2.bv.a.433.8	yes	720	115.88	even	44	inner
920.2.bv.a.617.8	yes	720	23.19	odd	22	inner
920.2.bv.a.753.8	yes	720	5.3	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72248 + 0.940543i) q^{3} +(0.500469 - 2.17934i) q^{5} +(2.14878 + 2.87043i) q^{7} +(0.460382 - 0.716368i) q^{9} +(4.06197 - 1.85504i) q^{11} +(-2.18769 - 1.63769i) q^{13} +(1.18772 + 4.22458i) q^{15} +(0.0397148 + 0.555286i) q^{17} +(-2.54021 - 2.93156i) q^{19} +(-6.40098 - 2.92323i) q^{21} +(0.911490 + 4.70842i) q^{23} +(-4.49906 - 2.18138i) q^{25} +(0.300796 - 4.20567i) q^{27} +(2.07316 + 1.79641i) q^{29} +(6.34302 - 1.86248i) q^{31} +(-5.25190 + 7.01572i) q^{33} +(7.33104 - 3.24636i) q^{35} +(9.37577 - 2.03957i) q^{37} +(5.30857 + 0.763257i) q^{39} +(1.50077 - 0.964484i) q^{41} +(4.61548 + 8.45262i) q^{43} +(-1.33080 - 1.36185i) q^{45} +(5.14501 + 5.14501i) q^{47} +(-1.64999 + 5.61937i) q^{49} +(-0.590678 - 0.919113i) q^{51} +(-3.13388 + 2.34600i) q^{53} +(-2.00988 - 9.78081i) q^{55} +(7.13271 + 2.66037i) q^{57} +(12.4276 - 1.78681i) q^{59} +(-0.563296 - 1.91841i) q^{61} +(3.04554 - 0.217821i) q^{63} +(-4.66395 + 3.94812i) q^{65} +(1.29030 + 3.45944i) q^{67} +(-5.99849 - 7.25284i) q^{69} +(-4.08394 + 8.94257i) q^{71} +(1.32193 + 0.0945464i) q^{73} +(9.80122 - 0.474179i) q^{75} +(14.0530 + 7.67353i) q^{77} +(-1.85461 - 12.8991i) q^{79} +(4.49874 + 9.85087i) q^{81} +(0.423827 + 1.94830i) q^{83} +(1.23003 + 0.191351i) q^{85} +(-5.26057 - 1.14437i) q^{87} +(5.08258 + 1.49238i) q^{89} -9.79864i q^{91} +(-9.17396 + 9.17396i) q^{93} +(-7.66017 + 4.06884i) q^{95} +(2.55569 - 11.7483i) q^{97} +(0.541166 - 3.76389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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