LMFDB - Embedded newform 720.2.by.e.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(49,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))

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

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

chi := DirichletCharacter("720.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.by (of order $6$, degree $2$, not 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 10x^{8} - 6x^{6} + 90x^{4} - 324x^{2} + 729 $ x^12 - 4x^10 + 10x^8 - 6x^6 + 90x^4 - 324*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$-1.62372 + 0.602950i$ of defining polynomial
Character	$\chi$	$=$	720.529
Dual form			720.2.by.e.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62372 + 0.602950i) q^{3} +(-2.02621 - 0.945767i) q^{5} +(-3.26460 - 1.88482i) q^{7} +(2.27290 - 1.95804i) q^{9} +(-1.77290 + 3.07076i) q^{11} +(-0.869061 + 0.501753i) q^{13} +(3.86024 + 0.313951i) q^{15} +1.56023i q^{17} +7.21013 q^{19} +(6.43723 + 1.09201i) q^{21} +(5.35328 - 3.09072i) q^{23} +(3.21105 + 3.83264i) q^{25} +(-2.50994 + 4.54975i) q^{27} +(-1.50000 + 2.59808i) q^{29} +(-2.89142 - 5.00809i) q^{31} +(1.02717 - 6.05500i) q^{33} +(4.83216 + 6.90658i) q^{35} +0.851576i q^{37} +(1.10858 - 1.33870i) q^{39} +(1.55926 + 2.70072i) q^{41} +(2.34403 + 1.35333i) q^{43} +(-6.45722 + 1.81776i) q^{45} +(8.44260 + 4.87434i) q^{47} +(3.60506 + 6.24415i) q^{49} +(-0.940739 - 2.53336i) q^{51} +11.2494i q^{53} +(6.49649 - 4.54524i) q^{55} +(-11.7072 + 4.34735i) q^{57} +(4.83216 + 8.36955i) q^{59} +(4.10506 - 7.11018i) q^{61} +(-11.1107 + 2.10821i) q^{63} +(2.23544 - 0.194727i) q^{65} +(2.52711 - 1.45903i) q^{67} +(-6.82865 + 8.24621i) q^{69} -7.21013 q^{71} -16.7817i q^{73} +(-7.52473 - 4.28702i) q^{75} +(11.5756 - 6.68319i) q^{77} +(-5.49649 + 9.52020i) q^{79} +(1.33216 - 8.90086i) q^{81} +(-8.82952 - 5.09773i) q^{83} +(1.47561 - 3.16134i) q^{85} +(0.869061 - 5.12296i) q^{87} +5.33567 q^{89} +3.78285 q^{91} +(7.71448 + 6.38833i) q^{93} +(-14.6092 - 6.81910i) q^{95} +(3.34467 + 1.93105i) q^{97} +(1.98303 + 10.4509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{5} + 8 q^{9} - 2 q^{11} + 5 q^{15} + 10 q^{21} - 3 q^{25} - 18 q^{29} - 6 q^{31} + 34 q^{35} + 42 q^{39} + 14 q^{41} - 31 q^{45} - 16 q^{51} + 6 q^{55} + 34 q^{59} + 6 q^{61} + 15 q^{65} + 14 q^{69}+ \cdots - 82 q^{99}+O(q^{100}) $ 12 * q + q^5 + 8 * q^9 - 2 * q^11 + 5 * q^15 + 10 * q^21 - 3 * q^25 - 18 * q^29 - 6 * q^31 + 34 * q^35 + 42 * q^39 + 14 * q^41 - 31 * q^45 - 16 * q^51 + 6 * q^55 + 34 * q^59 + 6 * q^61 + 15 * q^65 + 14 * q^69 - 41 * q^75 + 6 * q^79 - 8 * q^81 - 12 * q^85 + 112 * q^89 - 12 * q^91 - 36 * q^95 - 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.62372	+	0.602950i	−0.937452	+	0.348114i
$3$	−1.62372	+	0.602950i	−0.937452	+	0.348114i
$4$		0			0
$5$	−2.02621	−	0.945767i	−0.906149	−	0.422960i
$5$	−2.02621	−	0.945767i	−0.906149	−	0.422960i
$6$		0			0
$7$	−3.26460	−	1.88482i	−1.23390	−	0.712394i	−0.266061	−	0.963956i	$-0.585722\pi$
$7$	−3.26460	−	1.88482i	−1.23390	−	0.712394i	−0.967841	+	0.251563i	$0.919056\pi$
$8$		0			0
$9$	2.27290	−	1.95804i	0.757634	−	0.652680i
$10$		0			0
$11$	−1.77290	+	3.07076i	−0.534550	+	0.925868i	0.464635	+	0.885502i	$0.346186\pi$
$11$	−1.77290	+	3.07076i	−0.534550	+	0.925868i	−0.999185	+	0.0403654i	$0.987148\pi$
$12$		0			0
$13$	−0.869061	+	0.501753i	−0.241034	+	0.139161i	−0.615652	−	0.788018i	$-0.711107\pi$
$13$	−0.869061	+	0.501753i	−0.241034	+	0.139161i	0.374618	+	0.927179i	$0.377774\pi$
$14$		0			0
$15$	3.86024	+	0.313951i	0.996709	+	0.0810619i
$16$		0			0
$17$			1.56023i			0.378410i	0.981938	+	0.189205i	$0.0605911\pi$
$17$			1.56023i			0.378410i	−0.981938	+	0.189205i	$0.939409\pi$
$18$		0			0
$19$	7.21013			1.65412			0.827058	−	0.562116i	$-0.190013\pi$
$19$	7.21013			1.65412			0.827058	+	0.562116i	$0.190013\pi$
$20$		0			0
$21$	6.43723	+	1.09201i	1.40472	+	0.238297i
$22$		0			0
$23$	5.35328	−	3.09072i	1.11624	−	0.644459i	0.175799	−	0.984426i	$-0.443749\pi$
$23$	5.35328	−	3.09072i	1.11624	−	0.644459i	0.940437	+	0.339967i	$0.110416\pi$
$24$		0			0
$25$	3.21105	+	3.83264i	0.642210	+	0.766529i
$26$		0			0
$27$	−2.50994	+	4.54975i	−0.483039	+	0.875599i
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−2.89142	−	5.00809i	−0.519315	−	0.899480i	−0.999748	−	0.0224486i	$-0.992854\pi$
$31$	−2.89142	−	5.00809i	−0.519315	−	0.899480i	0.480433	−	0.877031i	$-0.340480\pi$
$32$		0			0
$33$	1.02717	−	6.05500i	0.178808	−	1.05404i
$34$		0			0
$35$	4.83216	+	6.90658i	0.816785	+	1.16743i
$36$		0			0
$37$			0.851576i			0.139998i	0.997547	+	0.0699991i	$0.0222996\pi$
$37$			0.851576i			0.139998i	−0.997547	+	0.0699991i	$0.977700\pi$
$38$		0			0
$39$	1.10858	−	1.33870i	0.177514	−	0.214364i
$40$		0			0
$41$	1.55926	+	2.70072i	0.243516	+	0.421782i	0.961713	−	0.274058i	$-0.0883659\pi$
$41$	1.55926	+	2.70072i	0.243516	+	0.421782i	−0.718198	+	0.695839i	$0.755033\pi$
$42$		0			0
$43$	2.34403	+	1.35333i	0.357462	+	0.206381i	0.667967	−	0.744191i	$-0.267165\pi$
$43$	2.34403	+	1.35333i	0.357462	+	0.206381i	−0.310505	+	0.950572i	$0.600498\pi$
$44$		0			0
$45$	−6.45722	+	1.81776i	−0.962586	+	0.270976i
$46$		0			0
$47$	8.44260	+	4.87434i	1.23148	+	0.710995i	0.967338	−	0.253489i	$-0.0815782\pi$
$47$	8.44260	+	4.87434i	1.23148	+	0.710995i	0.264141	+	0.964484i	$0.414912\pi$
$48$		0			0
$49$	3.60506	+	6.24415i	0.515009	+	0.892022i
$50$		0			0
$51$	−0.940739	−	2.53336i	−0.131730	−	0.354742i
$52$		0			0
$53$			11.2494i			1.54523i	0.634876	+	0.772614i	$0.281051\pi$
$53$			11.2494i			1.54523i	−0.634876	+	0.772614i	$0.718949\pi$
$54$		0			0
$55$	6.49649	−	4.54524i	0.875986	−	0.612881i
$56$		0			0
$57$	−11.7072	+	4.34735i	−1.55066	+	0.575821i
$58$		0			0
$59$	4.83216	+	8.36955i	0.629094	+	1.08962i	0.987734	+	0.156147i	$0.0499073\pi$
$59$	4.83216	+	8.36955i	0.629094	+	1.08962i	−0.358640	+	0.933476i	$0.616759\pi$
$60$		0			0
$61$	4.10506	−	7.11018i	0.525600	−	0.910365i	−0.473956	−	0.880549i	$-0.657174\pi$
$61$	4.10506	−	7.11018i	0.525600	−	0.910365i	0.999555	−	0.0298166i	$-0.00949232\pi$
$62$		0			0
$63$	−11.1107	+	2.10821i	−1.39981	+	0.265609i
$64$		0			0
$65$	2.23544	−	0.194727i	0.277272	−	0.0241529i
$66$		0			0
$67$	2.52711	−	1.45903i	0.308736	−	0.178249i	−0.337625	−	0.941281i	$-0.609624\pi$
$67$	2.52711	−	1.45903i	0.308736	−	0.178249i	0.646361	+	0.763032i	$0.276290\pi$
$68$		0			0
$69$	−6.82865	+	8.24621i	−0.822073	+	0.992727i
$70$		0			0
$71$	−7.21013			−0.855685			−0.427842	−	0.903853i	$-0.640726\pi$
$71$	−7.21013			−0.855685			−0.427842	+	0.903853i	$0.640726\pi$
$72$		0			0
$73$		−	16.7817i		−	1.96415i	−0.188498	−	0.982074i	$-0.560362\pi$
$73$		−	16.7817i		−	1.96415i	0.188498	−	0.982074i	$-0.439638\pi$
$74$		0			0
$75$	−7.52473	−	4.28702i	−0.868881	−	0.495022i
$76$		0			0
$77$	11.5756	−	6.68319i	1.31916	−	0.761620i
$78$		0			0
$79$	−5.49649	+	9.52020i	−0.618403	+	1.07111i	0.371374	+	0.928483i	$0.378887\pi$
$79$	−5.49649	+	9.52020i	−0.618403	+	1.07111i	−0.989777	+	0.142622i	$0.954447\pi$
$80$		0			0
$81$	1.33216	−	8.90086i	0.148018	−	0.988985i
$82$		0			0
$83$	−8.82952	−	5.09773i	−0.969166	−	0.559548i	−0.0701843	−	0.997534i	$-0.522359\pi$
$83$	−8.82952	−	5.09773i	−0.969166	−	0.559548i	−0.898982	+	0.437986i	$0.855692\pi$
$84$		0			0
$85$	1.47561	−	3.16134i	0.160052	−	0.342896i
$86$		0			0
$87$	0.869061	−	5.12296i	0.0931732	−	0.549239i
$88$		0			0
$89$	5.33567			0.565580			0.282790	−	0.959182i	$-0.408740\pi$
$89$	5.33567			0.565580			0.282790	+	0.959182i	$0.408740\pi$
$90$		0			0
$91$	3.78285			0.396550
$92$		0			0
$93$	7.71448	+	6.38833i	0.799954	+	0.662439i
$94$		0			0
$95$	−14.6092	−	6.81910i	−1.49888	−	0.699625i
$96$		0			0
$97$	3.34467	+	1.93105i	0.339600	+	0.196068i	0.660095	−	0.751182i	$-0.270516\pi$
$97$	3.34467	+	1.93105i	0.339600	+	0.196068i	−0.320495	+	0.947250i	$0.603849\pi$
$98$		0			0
$99$	1.98303	+	10.4509i	0.199302	+	1.05036i
$100$		0			0
$101$	−2.37797	+	4.11876i	−0.236616	+	0.409832i	−0.959741	−	0.280886i	$-0.909372\pi$
$101$	−2.37797	+	4.11876i	−0.236616	+	0.409832i	0.723125	+	0.690717i	$0.242705\pi$
$102$		0			0
$103$	15.6656	−	9.04452i	1.54357	−	0.891183i	0.544966	−	0.838458i	$-0.316543\pi$
$103$	15.6656	−	9.04452i	1.54357	−	0.891183i	0.998609	−	0.0527251i	$-0.0167907\pi$
$104$		0			0
$105$	−12.0104	−	8.30076i	−1.17209	−	0.810072i
$106$		0			0
$107$			3.61770i			0.349737i	0.984592	+	0.174868i	$0.0559500\pi$
$107$			3.61770i			0.349737i	−0.984592	+	0.174868i	$0.944050\pi$
$108$		0			0
$109$	9.63741			0.923096			0.461548	−	0.887115i	$-0.347294\pi$
$109$	9.63741			0.923096			0.461548	+	0.887115i	$0.347294\pi$
$110$		0			0
$111$	−0.513458	−	1.38272i	−0.0487353	−	0.131242i
$112$		0			0
$113$	−3.08152	+	1.77912i	−0.289885	+	0.167365i	−0.637890	−	0.770127i	$-0.720193\pi$
$113$	−3.08152	+	1.77912i	−0.289885	+	0.167365i	0.348005	+	0.937493i	$0.386859\pi$
$114$		0			0
$115$	−13.7700	+	1.19949i	−1.28406	+	0.111853i
$116$		0			0
$117$	−0.992839	+	2.84209i	−0.0917880	+	0.262751i
$118$		0			0
$119$	2.94074	−	5.09351i	0.269577	−	0.466921i
$120$		0			0
$121$	−0.786360	−	1.36201i	−0.0714872	−	0.123820i
$122$		0			0
$123$	−4.16020	−	3.44504i	−0.375112	−	0.310629i
$124$		0			0
$125$	−2.88148	−	10.8026i	−0.257727	−	0.966218i
$126$		0			0
$127$			6.78015i			0.601641i	0.953681	+	0.300820i	$0.0972605\pi$
$127$			6.78015i			0.601641i	−0.953681	+	0.300820i	$0.902739\pi$
$128$		0			0
$129$	−4.62203	−	0.784084i	−0.406947	−	0.0690347i
$130$		0			0
$131$	−1.71364	−	2.96811i	−0.149721	−	0.259325i	0.781403	−	0.624027i	$-0.214504\pi$
$131$	−1.71364	−	2.96811i	−0.149721	−	0.259325i	−0.931124	+	0.364702i	$0.881171\pi$
$132$		0			0
$133$	−23.5382	−	13.5898i	−2.04102	−	1.17838i
$134$		0			0
$135$	9.38867	−	6.84492i	0.808048	−	0.589117i
$136$		0			0
$137$	12.9268	+	7.46330i	1.10441	+	0.637633i	0.937376	−	0.348318i	$-0.113247\pi$
$137$	12.9268	+	7.46330i	1.10441	+	0.637633i	0.167036	+	0.985951i	$0.446580\pi$
$138$		0			0
$139$	2.71364	+	4.70016i	0.230168	+	0.398663i	0.957857	−	0.287244i	$-0.0927391\pi$
$139$	2.71364	+	4.70016i	0.230168	+	0.398663i	−0.727689	+	0.685907i	$0.759406\pi$
$140$		0			0
$141$	−16.6474	−	2.82406i	−1.40196	−	0.237829i
$142$		0			0
$143$		−	3.55823i		−	0.297554i
$144$		0			0
$145$	5.49649	−	3.84560i	0.456458	−	0.319359i
$146$		0			0
$147$	−9.61851	−	7.96505i	−0.793322	−	0.656946i
$148$		0			0
$149$	2.76939	+	4.79672i	0.226877	+	0.392963i	0.956881	−	0.290480i	$-0.0938150\pi$
$149$	2.76939	+	4.79672i	0.226877	+	0.392963i	−0.730004	+	0.683443i	$0.760482\pi$
$150$		0			0
$151$	0.108576	−	0.188059i	0.00883580	−	0.0153041i	−0.861574	−	0.507633i	$-0.830521\pi$
$151$	0.108576	−	0.188059i	0.00883580	−	0.0153041i	0.870409	+	0.492328i	$0.163854\pi$
$152$		0			0
$153$	3.05498	+	3.54624i	0.246981	+	0.286696i
$154$		0			0
$155$	1.12214	+	12.8821i	0.0901328	+	1.03471i
$156$		0			0
$157$	1.86970	−	1.07947i	0.149218	−	0.0861511i	−0.423532	−	0.905881i	$-0.639210\pi$
$157$	1.86970	−	1.07947i	0.149218	−	0.0861511i	0.572750	+	0.819730i	$0.305877\pi$
$158$		0			0
$159$	−6.78285	−	18.2659i	−0.537915	−	1.44858i
$160$		0			0
$161$	−23.3017			−1.83643
$162$		0			0
$163$			8.39084i			0.657221i	0.944465	+	0.328611i	$0.106580\pi$
$163$			8.39084i			0.657221i	−0.944465	+	0.328611i	$0.893420\pi$
$164$		0			0
$165$	−7.80789	+	11.2972i	−0.607843	+	0.879489i
$166$		0			0
$167$	4.00208	−	2.31060i	0.309691	−	0.178800i	−0.337097	−	0.941470i	$-0.609445\pi$
$167$	4.00208	−	2.31060i	0.309691	−	0.178800i	0.646788	+	0.762670i	$0.276112\pi$
$168$		0			0
$169$	−5.99649	+	10.3862i	−0.461268	+	0.798940i
$170$		0			0
$171$	16.3879	−	14.1177i	1.25321	−	1.07961i
$172$		0			0
$173$	1.25599	+	0.725146i	0.0954911	+	0.0551318i	0.546985	−	0.837142i	$-0.315775\pi$
$173$	1.25599	+	0.725146i	0.0954911	+	0.0551318i	−0.451494	+	0.892274i	$0.649109\pi$
$174$		0			0
$175$	−3.25896	−	18.5643i	−0.246354	−	1.40333i
$176$		0			0
$177$	−12.8925	−	10.6762i	−0.969058	−	0.802473i
$178$		0			0
$179$	−19.4472			−1.45355			−0.726775	−	0.686876i	$-0.758982\pi$
$179$	−19.4472			−1.45355			−0.726775	+	0.686876i	$0.758982\pi$
$180$		0			0
$181$	−10.4273			−0.775054			−0.387527	−	0.921858i	$-0.626671\pi$
$181$	−10.4273			−0.775054			−0.387527	+	0.921858i	$0.626671\pi$
$182$		0			0
$183$	−2.37837	+	14.0201i	−0.175814	+	1.03639i
$184$		0			0
$185$	0.805392	−	1.72547i	0.0592136	−	0.126859i
$186$		0			0
$187$	−4.79107	−	2.76613i	−0.350358	−	0.202279i
$188$		0			0
$189$	16.7694	−	10.1223i	1.21979	−	0.736289i
$190$		0			0
$191$	−1.89142	+	3.27604i	−0.136859	+	0.237046i	−0.926306	−	0.376772i	$-0.877034\pi$
$191$	−1.89142	+	3.27604i	−0.136859	+	0.237046i	0.789447	+	0.613818i	$0.210367\pi$
$192$		0			0
$193$	12.1893	−	7.03751i	0.877407	−	0.506571i	0.00760445	−	0.999971i	$-0.497579\pi$
$193$	12.1893	−	7.03751i	0.877407	−	0.506571i	0.869803	+	0.493400i	$0.164246\pi$
$194$		0			0
$195$	−3.51231	+	1.66404i	−0.251522	+	0.119165i
$196$		0			0
$197$		−	21.5044i		−	1.53212i	−0.642768	−	0.766061i	$-0.722214\pi$
$197$		−	21.5044i		−	1.53212i	0.642768	−	0.766061i	$-0.277786\pi$
$198$		0			0
$199$	7.21013			0.511112			0.255556	−	0.966794i	$-0.417741\pi$
$199$	7.21013			0.511112			0.255556	+	0.966794i	$0.417741\pi$
$200$		0			0
$201$	−3.22359	+	3.89277i	−0.227374	+	0.274575i
$202$		0			0
$203$	9.79379	−	5.65445i	0.687389	−	0.396864i
$204$		0			0
$205$	−0.605140	−	6.94692i	−0.0422648	−	0.485194i
$206$		0			0
$207$	6.11573	−	17.5068i	0.425073	−	1.21681i
$208$		0			0
$209$	−12.7828	+	22.1405i	−0.884208	+	1.53149i
$210$		0			0
$211$	1.89142	+	3.27604i	0.130211	+	0.225532i	0.923758	−	0.382977i	$-0.125101\pi$
$211$	1.89142	+	3.27604i	0.130211	+	0.225532i	−0.793547	+	0.608509i	$0.791768\pi$
$212$		0			0
$213$	11.7072	−	4.34735i	0.802164	−	0.297876i
$214$		0			0
$215$	−3.46957	−	4.95904i	−0.236623	−	0.338204i
$216$		0			0
$217$			21.7992i			1.47983i
$218$		0			0
$219$	10.1185	+	27.2487i	0.683746	+	1.84129i
$220$		0			0
$221$	−0.782848	−	1.35593i	−0.0526600	−	0.0912099i
$222$		0			0
$223$	−2.52711	−	1.45903i	−0.169228	−	0.0977038i	0.412994	−	0.910734i	$-0.364483\pi$
$223$	−2.52711	−	1.45903i	−0.169228	−	0.0977038i	−0.582222	+	0.813030i	$0.697816\pi$
$224$		0			0
$225$	14.8029	+	2.42385i	0.986858	+	0.161590i
$226$		0			0
$227$	4.43272	+	2.55923i	0.294210	+	0.169862i	0.639839	−	0.768509i	$-0.279001\pi$
$227$	4.43272	+	2.55923i	0.294210	+	0.169862i	−0.345629	+	0.938371i	$0.612334\pi$
$228$		0			0
$229$	−4.71013	−	8.15818i	−0.311254	−	0.539108i	0.667380	−	0.744717i	$-0.267416\pi$
$229$	−4.71013	−	8.15818i	−0.311254	−	0.539108i	−0.978634	+	0.205609i	$0.934082\pi$
$230$		0			0
$231$	−14.7659	+	17.8311i	−0.971523	+	1.17320i
$232$		0			0
$233$			26.1850i			1.71544i	0.514118	+	0.857719i	$0.328119\pi$
$233$			26.1850i			1.71544i	−0.514118	+	0.857719i	$0.671881\pi$
$234$		0			0
$235$	−12.4965	−	17.8612i	−0.815181	−	1.16513i
$236$		0			0
$237$	3.18452	−	18.7722i	0.206857	−	1.21939i
$238$		0			0
$239$	11.3780	+	19.7072i	0.735979	+	1.27475i	0.954292	+	0.298875i	$0.0966113\pi$
$239$	11.3780	+	19.7072i	0.735979	+	1.27475i	−0.218313	+	0.975879i	$0.570055\pi$
$240$		0			0
$241$	−8.31519	+	14.4023i	−0.535629	+	0.927736i	0.463504	+	0.886095i	$0.346592\pi$
$241$	−8.31519	+	14.4023i	−0.535629	+	0.927736i	−0.999133	+	0.0416412i	$0.986741\pi$
$242$		0			0
$243$	3.20373	+	15.2557i	0.205519	+	0.978653i
$244$		0			0
$245$	−1.39910	−	16.0615i	−0.0893854	−	1.02613i
$246$		0			0
$247$	−6.26604	+	3.61770i	−0.398699	+	0.230189i
$248$		0			0
$249$	17.4103	+	2.95349i	1.10333	+	0.187170i
$250$		0			0
$251$	20.7758			1.31136			0.655679	−	0.755040i	$-0.272382\pi$
$251$	20.7758			1.31136			0.655679	+	0.755040i	$0.272382\pi$
$252$		0			0
$253$			21.9181i			1.37798i
$254$		0			0
$255$	−0.489835	+	6.02284i	−0.0306747	+	0.377165i
$256$		0			0
$257$	−16.5061	+	9.52978i	−1.02962	+	0.594451i	−0.916876	−	0.399173i	$-0.869297\pi$
$257$	−16.5061	+	9.52978i	−1.02962	+	0.594451i	−0.112744	+	0.993624i	$0.535964\pi$
$258$		0			0
$259$	1.60506	−	2.78005i	0.0997338	−	0.172744i
$260$		0			0
$261$	1.67778	+	8.84223i	0.103852	+	0.547320i
$262$		0			0
$263$	7.04770	+	4.06899i	0.434580	+	0.250905i	0.701296	−	0.712870i	$-0.252605\pi$
$263$	7.04770	+	4.06899i	0.434580	+	0.250905i	−0.266716	+	0.963775i	$0.585939\pi$
$264$		0			0
$265$	10.6393	−	22.7937i	0.653569	−	1.40021i
$266$		0			0
$267$	−8.66362	+	3.21715i	−0.530205	+	0.196886i
$268$		0			0
$269$	25.6374			1.56314			0.781570	−	0.623817i	$-0.214419\pi$
$269$	25.6374			1.56314			0.781570	+	0.623817i	$0.214419\pi$
$270$		0			0
$271$	3.21013			0.195001			0.0975007	−	0.995235i	$-0.468915\pi$
$271$	3.21013			0.195001			0.0975007	+	0.995235i	$0.468915\pi$
$272$		0			0
$273$	−6.14227	+	2.28087i	−0.371747	+	0.138045i
$274$		0			0
$275$	−17.4620	+	3.06546i	−1.05300	+	0.184854i
$276$		0			0
$277$	0.605911	+	0.349823i	0.0364057	+	0.0210188i	0.518092	−	0.855325i	$-0.326642\pi$
$277$	0.605911	+	0.349823i	0.0364057	+	0.0210188i	−0.481687	+	0.876343i	$0.659976\pi$
$278$		0			0
$279$	−16.3780	−	5.72138i	−0.980523	−	0.342530i
$280$		0			0
$281$	15.3152	−	26.5267i	0.913628	−	1.58245i	0.104730	−	0.994501i	$-0.466602\pi$
$281$	15.3152	−	26.5267i	0.913628	−	1.58245i	0.808898	−	0.587949i	$-0.200064\pi$
$282$		0			0
$283$	−8.31882	+	4.80287i	−0.494502	+	0.285501i	−0.726440	−	0.687229i	$-0.758827\pi$
$283$	−8.31882	+	4.80287i	−0.494502	+	0.285501i	0.231938	+	0.972731i	$0.425493\pi$
$284$		0			0
$285$	27.8328	+	2.26363i	1.64867	+	0.134086i
$286$		0			0
$287$		−	11.7557i		−	0.693916i
$288$		0			0
$289$	14.5657			0.856806
$290$		0			0
$291$	−6.59512	−	1.11880i	−0.386613	−	0.0655851i
$292$		0			0
$293$	2.60718	−	1.50526i	0.152313	−	0.0879381i	−0.421906	−	0.906639i	$-0.638639\pi$
$293$	2.60718	−	1.50526i	0.152313	−	0.0879381i	0.574220	+	0.818701i	$0.305306\pi$
$294$		0			0
$295$	−1.87533	−	21.5286i	−0.109186	−	1.25344i
$296$		0			0
$297$	−9.52127	−	15.7737i	−0.552480	−	0.915281i
$298$		0			0
$299$	−3.10155	+	5.37205i	−0.179367	+	0.310673i
$300$		0			0
$301$	−5.10155	−	8.83615i	−0.294049	−	0.509307i
$302$		0			0
$303$	1.37773	−	8.12148i	0.0791487	−	0.466567i
$304$		0			0
$305$	−15.0423	+	10.5243i	−0.861319	+	0.602619i
$306$		0			0
$307$			14.8671i			0.848512i	0.905542	+	0.424256i	$0.139464\pi$
$307$			14.8671i			0.848512i	−0.905542	+	0.424256i	$0.860536\pi$
$308$		0			0
$309$	−19.9830	+	24.1313i	−1.13679	+	1.37278i
$310$		0			0
$311$	1.53586	+	2.66018i	0.0870905	+	0.150845i	0.906280	−	0.422678i	$-0.138910\pi$
$311$	1.53586	+	2.66018i	0.0870905	+	0.150845i	−0.819190	+	0.573523i	$0.805576\pi$
$312$		0			0
$313$	19.9303	+	11.5068i	1.12653	+	0.650402i	0.943060	−	0.332623i	$-0.107934\pi$
$313$	19.9303	+	11.5068i	1.12653	+	0.650402i	0.183470	+	0.983025i	$0.441267\pi$
$314$		0			0
$315$	24.5064	+	6.23641i	1.38078	+	0.351382i
$316$		0			0
$317$	−0.00779729	−	0.00450177i	−0.000437939	−	0.000252844i	0.499781	−	0.866152i	$-0.333414\pi$
$317$	−0.00779729	−	0.00450177i	−0.000437939	−	0.000252844i	−0.500219	+	0.865899i	$0.666747\pi$
$318$		0			0
$319$	−5.31870	−	9.21227i	−0.297790	−	0.515788i
$320$		0			0
$321$	−2.18130	−	5.87412i	−0.121748	−	0.327861i
$322$		0			0
$323$			11.2494i			0.625935i
$324$		0			0
$325$	−4.71364	−	1.71965i	−0.261466	−	0.0953889i
$326$		0			0
$327$	−15.6484	+	5.81088i	−0.865359	+	0.321342i
$328$		0			0
$329$	−18.3745	−	31.8255i	−1.01302	−	1.75460i
$330$		0			0
$331$	4.49649	−	7.78815i	0.247149	−	0.428075i	−0.715584	−	0.698526i	$-0.753840\pi$
$331$	4.49649	−	7.78815i	0.247149	−	0.428075i	0.962734	+	0.270451i	$0.0871728\pi$
$332$		0			0
$333$	1.66742	+	1.93555i	0.0913740	+	0.106067i
$334$		0			0
$335$	−6.50036	+	0.566240i	−0.355152	+	0.0309370i
$336$		0			0
$337$	−4.55649	+	2.63069i	−0.248208	+	0.143303i	−0.618943	−	0.785436i	$-0.712439\pi$
$337$	−4.55649	+	2.63069i	−0.248208	+	0.143303i	0.370735	+	0.928739i	$0.379106\pi$
$338$		0			0
$339$	3.93079	−	4.74678i	0.213491	−	0.257810i
$340$		0			0
$341$	20.5048			1.11040
$342$		0			0
$343$		−	0.792107i		−	0.0427698i
$344$		0			0
$345$	21.6353	−	10.2502i	1.16480	−	0.551854i
$346$		0			0
$347$	18.6155	−	10.7477i	0.999333	−	0.576965i	0.0912825	−	0.995825i	$-0.470903\pi$
$347$	18.6155	−	10.7477i	0.999333	−	0.576965i	0.908051	+	0.418860i	$0.137570\pi$
$348$		0			0
$349$	−6.28285	+	10.8822i	−0.336313	+	0.582511i	−0.983736	−	0.179619i	$-0.942513\pi$
$349$	−6.28285	+	10.8822i	−0.336313	+	0.582511i	0.647423	+	0.762131i	$0.275847\pi$
$350$		0			0
$351$	−0.101552	−	5.21338i	−0.00542046	−	0.278270i
$352$		0			0
$353$	−21.7048	−	12.5313i	−1.15523	−	0.666973i	−0.205075	−	0.978746i	$-0.565744\pi$
$353$	−21.7048	−	12.5313i	−1.15523	−	0.666973i	−0.950157	+	0.311773i	$0.899077\pi$
$354$		0			0
$355$	14.6092	+	6.81910i	0.775378	+	0.361920i
$356$		0			0
$357$	−1.70379	+	10.0435i	−0.0901741	+	0.531560i
$358$		0			0
$359$	23.1961			1.22424			0.612121	−	0.790764i	$-0.290316\pi$
$359$	23.1961			1.22424			0.612121	+	0.790764i	$0.290316\pi$
$360$		0			0
$361$	32.9860			1.73610
$362$		0			0
$363$	2.09805	+	1.73739i	0.110119	+	0.0911892i
$364$		0			0
$365$	−15.8716	+	34.0032i	−0.830755	+	1.77981i
$366$		0			0
$367$	15.4024	+	8.89259i	0.804000	+	0.464190i	0.844868	−	0.534975i	$-0.179679\pi$
$367$	15.4024	+	8.89259i	0.804000	+	0.464190i	−0.0408679	+	0.999165i	$0.513012\pi$
$368$		0			0
$369$	8.83216	+	3.08537i	0.459784	+	0.160618i
$370$		0			0
$371$	21.2031	−	36.7249i	1.10081	−	1.90666i
$372$		0			0
$373$	−11.1887	+	6.45979i	−0.579328	+	0.334475i	−0.760866	−	0.648908i	$-0.775226\pi$
$373$	−11.1887	+	6.45979i	−0.579328	+	0.334475i	0.181538	+	0.983384i	$0.441892\pi$
$374$		0			0
$375$	11.1922	+	15.8030i	0.577960	+	0.816065i
$376$		0			0
$377$		−	3.01052i		−	0.155050i
$378$		0			0
$379$	−5.56570			−0.285891			−0.142945	−	0.989731i	$-0.545657\pi$
$379$	−5.56570			−0.285891			−0.142945	+	0.989731i	$0.545657\pi$
$380$		0			0
$381$	−4.08809	−	11.0090i	−0.209439	−	0.564010i
$382$		0			0
$383$	−25.7584	+	14.8716i	−1.31619	+	0.759905i	−0.983114	−	0.182994i	$-0.941421\pi$
$383$	−25.7584	+	14.8716i	−1.31619	+	0.759905i	−0.333080	+	0.942899i	$0.608088\pi$
$384$		0			0
$385$	−29.7754	+	2.59370i	−1.51749	+	0.132187i
$386$		0			0
$387$	7.97763	−	1.51373i	0.405526	−	0.0769471i
$388$		0			0
$389$	−3.77641	+	6.54094i	−0.191472	+	0.331639i	−0.945738	−	0.324930i	$-0.894659\pi$
$389$	−3.77641	+	6.54094i	−0.191472	+	0.331639i	0.754266	+	0.656568i	$0.227993\pi$
$390$		0			0
$391$	4.82222	+	8.35232i	0.243870	+	0.422395i
$392$		0			0
$393$	4.57209	+	3.78613i	0.230631	+	0.190985i
$394$		0			0
$395$	20.1409	−	14.0915i	1.01340	−	0.709021i
$396$		0			0
$397$			30.1571i			1.51354i	0.653682	+	0.756770i	$0.273224\pi$
$397$			30.1571i			1.51354i	−0.653682	+	0.756770i	$0.726776\pi$
$398$		0			0
$399$	46.4132	+	7.87356i	2.32357	+	0.394171i
$400$		0			0
$401$	10.8322	+	18.7619i	0.540932	+	0.936922i	0.998851	+	0.0479282i	$0.0152619\pi$
$401$	10.8322	+	18.7619i	0.540932	+	0.936922i	−0.457918	+	0.888994i	$0.651405\pi$
$402$		0			0
$403$	5.02565	+	2.90156i	0.250345	+	0.144537i
$404$		0			0
$405$	−11.1174	+	16.7751i	−0.552427	+	0.833561i
$406$		0			0
$407$	−2.61498	−	1.50976i	−0.129620	−	0.0748360i
$408$		0			0
$409$	−4.06921	−	7.04807i	−0.201209	−	0.348505i	0.747709	−	0.664027i	$-0.231154\pi$
$409$	−4.06921	−	7.04807i	−0.201209	−	0.348505i	−0.948918	+	0.315522i	$0.897820\pi$
$410$		0			0
$411$	−25.4895	−	4.32404i	−1.25730	−	0.213289i
$412$		0			0
$413$		−	36.4310i		−	1.79265i
$414$		0			0
$415$	13.0692	+	18.6797i	0.641542	+	0.916952i
$416$		0			0
$417$	−7.24014	−	5.99553i	−0.354551	−	0.293603i
$418$		0			0
$419$	−6.64736	−	11.5136i	−0.324745	−	0.562474i	0.656716	−	0.754138i	$-0.271945\pi$
$419$	−6.64736	−	11.5136i	−0.324745	−	0.562474i	−0.981461	+	0.191664i	$0.938612\pi$
$420$		0			0
$421$	−10.0692	+	17.4404i	−0.490743	+	0.849992i	−0.999943	−	0.0106561i	$-0.996608\pi$
$421$	−10.0692	+	17.4404i	−0.490743	+	0.849992i	0.509200	+	0.860648i	$0.329941\pi$
$422$		0			0
$423$	28.7333	−	5.45205i	1.39706	−	0.265088i
$424$		0			0
$425$	−5.97979	+	5.00996i	−0.290062	+	0.243019i
$426$		0			0
$427$	−26.8028	+	15.4746i	−1.29708	+	0.748868i
$428$		0			0
$429$	2.14544	+	5.77756i	0.103583	+	0.278943i
$430$		0			0
$431$	−25.8027			−1.24287			−0.621437	−	0.783464i	$-0.713451\pi$
$431$	−25.8027			−1.24287			−0.621437	+	0.783464i	$0.713451\pi$
$432$		0			0
$433$			6.38383i			0.306787i	0.988165	+	0.153394i	$0.0490202\pi$
$433$			6.38383i			0.306787i	−0.988165	+	0.153394i	$0.950980\pi$
$434$		0			0
$435$	−6.60603	+	9.55826i	−0.316735	+	0.458284i
$436$		0			0
$437$	38.5978	−	22.2845i	1.84638	−	1.06601i
$438$		0			0
$439$	−5.49649	+	9.52020i	−0.262333	+	0.454374i	−0.966861	−	0.255302i	$-0.917825\pi$
$439$	−5.49649	+	9.52020i	−0.262333	+	0.454374i	0.704528	+	0.709676i	$0.251159\pi$
$440$		0			0
$441$	20.4203	+	7.13349i	0.972393	+	0.339690i
$442$		0			0
$443$	−21.8515	−	12.6160i	−1.03820	−	0.599404i	−0.118876	−	0.992909i	$-0.537929\pi$
$443$	−21.8515	−	12.6160i	−1.03820	−	0.599404i	−0.919322	+	0.393505i	$0.871262\pi$
$444$		0			0
$445$	−10.8112	−	5.04630i	−0.512500	−	0.239218i
$446$		0			0
$447$	−7.38889	−	6.11871i	−0.349482	−	0.289405i
$448$		0			0
$449$	19.5657			0.923362			0.461681	−	0.887046i	$-0.347246\pi$
$449$	19.5657			0.923362			0.461681	+	0.887046i	$0.347246\pi$
$450$		0			0
$451$	−11.0577			−0.520685
$452$		0			0
$453$	−0.0629062	+	0.370821i	−0.00295559	+	0.0174227i
$454$		0			0
$455$	−7.66484	−	3.57769i	−0.359333	−	0.167725i
$456$		0			0
$457$	−5.66013	−	3.26788i	−0.264770	−	0.152865i	0.361739	−	0.932280i	$-0.382183\pi$
$457$	−5.66013	−	3.26788i	−0.264770	−	0.152865i	−0.626508	+	0.779415i	$0.715517\pi$
$458$		0			0
$459$	−7.09863	−	3.91608i	−0.331336	−	0.182787i
$460$		0			0
$461$	17.7101	−	30.6748i	0.824843	−	1.42867i	−0.0771964	−	0.997016i	$-0.524597\pi$
$461$	17.7101	−	30.6748i	0.824843	−	1.42867i	0.902039	−	0.431654i	$-0.142070\pi$
$462$		0			0
$463$	−14.0876	+	8.13348i	−0.654706	+	0.377995i	−0.790257	−	0.612776i	$-0.790053\pi$
$463$	−14.0876	+	8.13348i	−0.654706	+	0.377995i	0.135551	+	0.990770i	$0.456720\pi$
$464$		0			0
$465$	−9.58929	−	20.2402i	−0.444692	−	0.938617i
$466$		0			0
$467$		−	15.8112i		−	0.731654i	−0.930683	−	0.365827i	$-0.880786\pi$
$467$		−	15.8112i		−	0.731654i	0.930683	−	0.365827i	$-0.119214\pi$
$468$		0			0
$469$	−11.0000			−0.507933
$470$		0			0
$471$	−2.38499	+	2.88009i	−0.109895	+	0.132707i
$472$		0			0
$473$	−8.31148	+	4.79864i	−0.382162	+	0.220642i
$474$		0			0
$475$	23.1521	+	27.6338i	1.06229	+	1.26793i
$476$		0			0
$477$	22.0268	+	25.5688i	1.00854	+	1.17072i
$478$		0			0
$479$	16.3709	−	28.3553i	0.748007	−	1.29559i	−0.200769	−	0.979639i	$-0.564344\pi$
$479$	16.3709	−	28.3553i	0.748007	−	1.29559i	0.948776	−	0.315948i	$-0.102323\pi$
$480$		0			0
$481$	−0.427281	−	0.740072i	−0.0194823	−	0.0337444i
$482$		0			0
$483$	37.8354	−	14.0498i	1.72157	−	0.639288i
$484$		0			0
$485$	−4.95069	−	7.07598i	−0.224799	−	0.321304i
$486$		0			0
$487$			36.4220i			1.65044i	0.564814	+	0.825218i	$0.308948\pi$
$487$			36.4220i			1.65044i	−0.564814	+	0.825218i	$0.691052\pi$
$488$		0			0
$489$	−5.05926	−	13.6243i	−0.228788	−	0.616114i
$490$		0			0
$491$	−1.71364	−	2.96811i	−0.0773355	−	0.133949i	0.824764	−	0.565477i	$-0.191308\pi$
$491$	−1.71364	−	2.96811i	−0.0773355	−	0.133949i	−0.902100	+	0.431528i	$0.857975\pi$
$492$		0			0
$493$	−4.05359	−	2.34034i	−0.182564	−	0.105404i
$494$		0			0
$495$	5.86611	−	23.0513i	0.263662	−	1.03608i
$496$		0			0
$497$	23.5382	+	13.5898i	1.05583	+	0.609584i
$498$		0			0
$499$	−1.71364	−	2.96811i	−0.0767131	−	0.132871i	0.825117	−	0.564962i	$-0.191109\pi$
$499$	−1.71364	−	2.96811i	−0.0767131	−	0.132871i	−0.901830	+	0.432091i	$0.857776\pi$
$500$		0			0
$501$	−5.10506	+	6.16482i	−0.228077	+	0.275424i
$502$		0			0
$503$			17.4219i			0.776802i	0.921490	+	0.388401i	$0.126973\pi$
$503$			17.4219i			0.776802i	−0.921490	+	0.388401i	$0.873027\pi$
$504$		0			0
$505$	8.71364	−	6.09647i	0.387752	−	0.271289i
$506$		0			0
$507$	3.47421	−	20.4799i	0.154295	−	0.909542i
$508$		0			0
$509$	−7.07272	−	12.2503i	−0.313493	−	0.542985i	0.665623	−	0.746288i	$-0.268166\pi$
$509$	−7.07272	−	12.2503i	−0.313493	−	0.542985i	−0.979116	+	0.203303i	$0.934832\pi$
$510$		0			0
$511$	−31.6304	+	54.7854i	−1.39925	+	2.42356i
$512$		0			0
$513$	−18.0970	+	32.8042i	−0.799003	+	1.44834i
$514$		0			0
$515$	−40.2957	+	3.51012i	−1.77564	+	0.154675i
$516$		0			0
$517$	−29.9358	+	17.2834i	−1.31657	+	0.760125i
$518$		0			0
$519$	−2.47660	−	0.420131i	−0.108710	−	0.0184417i
$520$		0			0
$521$	−20.2300			−0.886293			−0.443147	−	0.896449i	$-0.646138\pi$
$521$	−20.2300			−0.886293			−0.443147	+	0.896449i	$0.646138\pi$
$522$		0			0
$523$		−	36.3295i		−	1.58858i	−0.607540	−	0.794289i	$-0.707844\pi$
$523$		−	36.3295i		−	1.58858i	0.607540	−	0.794289i	$-0.292156\pi$
$524$		0			0
$525$	16.4850	+	28.1781i	0.719463	+	1.22979i
$526$		0			0
$527$	7.81376	−	4.51127i	0.340373	−	0.196514i
$528$		0			0
$529$	7.60506	−	13.1724i	0.330655	−	0.572711i
$530$		0			0
$531$	27.3709	+	9.56160i	1.18780	+	0.414938i
$532$		0			0
$533$	−2.71019	−	1.56473i	−0.117391	−	0.0677759i
$534$		0			0
$535$	3.42150	−	7.33022i	0.147924	−	0.316913i
$536$		0			0
$537$	31.5767	−	11.7257i	1.36263	−	0.506001i
$538$		0			0
$539$	−25.5657			−1.10119
$540$		0			0
$541$	24.8475			1.06828			0.534140	−	0.845396i	$-0.320636\pi$
$541$	24.8475			1.06828			0.534140	+	0.845396i	$0.320636\pi$
$542$		0			0
$543$	16.9309	−	6.28713i	0.726576	−	0.269807i
$544$		0			0
$545$	−19.5274	−	9.11474i	−0.836462	−	0.390433i
$546$		0			0
$547$	27.8034	+	16.0523i	1.18879	+	0.686347i	0.958031	−	0.286665i	$-0.0925466\pi$
$547$	27.8034	+	16.0523i	1.18879	+	0.686347i	0.230757	+	0.973012i	$0.425880\pi$
$548$		0			0
$549$	−4.59161	−	24.1986i	−0.195965	−	1.03277i
$550$		0			0
$551$	−10.8152	+	18.7325i	−0.460743	+	0.798030i
$552$		0			0
$553$	35.8876	−	20.7197i	1.52610	−	0.881093i
$554$		0			0
$555$	−0.267354	+	3.28729i	−0.0113485	+	0.139538i
$556$		0			0
$557$			17.3894i			0.736813i	0.929665	+	0.368406i	$0.120096\pi$
$557$			17.3894i			0.736813i	−0.929665	+	0.368406i	$0.879904\pi$
$558$		0			0
$559$	−2.71615			−0.114881
$560$		0			0
$561$	9.44717	+	1.60262i	0.398860	+	0.0676628i
$562$		0			0
$563$	−23.6771	+	13.6700i	−0.997870	+	0.576120i	−0.907617	−	0.419799i	$-0.862101\pi$
$563$	−23.6771	+	13.6700i	−0.997870	+	0.576120i	−0.0902525	+	0.995919i	$0.528767\pi$
$564$		0			0
$565$	7.92644	−	0.690464i	0.333468	−	0.0290481i
$566$		0			0
$567$	−21.1255	+	26.5468i	−0.887186	+	1.11486i
$568$		0			0
$569$	−7.59512	+	13.1551i	−0.318404	+	0.551492i	−0.980155	−	0.198232i	$-0.936480\pi$
$569$	−7.59512	+	13.1551i	−0.318404	+	0.551492i	0.661751	+	0.749723i	$0.269813\pi$
$570$		0			0
$571$	−19.3510	−	33.5170i	−0.809816	−	1.40264i	−0.912991	−	0.407980i	$-0.866233\pi$
$571$	−19.3510	−	33.5170i	−0.809816	−	1.40264i	0.103175	−	0.994663i	$-0.467100\pi$
$572$		0			0
$573$	1.09584	−	6.45979i	0.0457795	−	0.269862i
$574$		0			0
$575$	29.0353	+	10.5928i	1.21085	+	0.441748i
$576$		0			0
$577$		−	3.82910i		−	0.159408i	−0.996819	−	0.0797038i	$-0.974603\pi$
$577$		−	3.82910i		−	0.159408i	0.996819	−	0.0797038i	$-0.0253974\pi$
$578$		0			0
$579$	−15.5487	+	18.7765i	−0.646183	+	0.780324i
$580$		0			0
$581$	19.2166	+	33.2841i	0.797237	+	1.38086i
$582$		0			0
$583$	−34.5442	−	19.9441i	−1.43068	−	0.826001i
$584$		0			0
$585$	4.69966	−	4.81968i	0.194307	−	0.199269i
$586$		0			0
$587$	21.3772	+	12.3421i	0.882332	+	0.509415i	0.871427	−	0.490526i	$-0.163195\pi$
$587$	21.3772	+	12.3421i	0.882332	+	0.509415i	0.0109053	+	0.999941i	$0.496529\pi$
$588$		0			0
$589$	−20.8475	−	36.1090i	−0.859008	−	1.48785i
$590$		0			0
$591$	12.9661	+	34.9169i	0.533352	+	1.43629i
$592$		0			0
$593$		−	38.4290i		−	1.57809i	−0.614336	−	0.789044i	$-0.710576\pi$
$593$		−	38.4290i		−	1.57809i	0.614336	−	0.789044i	$-0.289424\pi$
$594$		0			0
$595$	−10.7758	+	7.53926i	−0.441766	+	0.309080i
$596$		0			0
$597$	−11.7072	+	4.34735i	−0.479144	+	0.177925i
$598$		0			0
$599$	−7.71364	−	13.3604i	−0.315171	−	0.545892i	0.664303	−	0.747463i	$-0.268728\pi$
$599$	−7.71364	−	13.3604i	−0.315171	−	0.545892i	−0.979474	+	0.201572i	$0.935395\pi$
$600$		0			0
$601$	0.286360	−	0.495989i	0.0116809	−	0.0202318i	−0.860126	−	0.510082i	$-0.829615\pi$
$601$	0.286360	−	0.495989i	0.0116809	−	0.0202318i	0.871807	+	0.489850i	$0.162948\pi$
$602$		0			0
$603$	2.88704	−	8.26441i	0.117569	−	0.336553i
$604$		0			0
$605$	0.305181	+	3.50344i	0.0124074	+	0.142435i
$606$		0			0
$607$	7.84448	−	4.52901i	0.318398	−	0.183827i	−0.332280	−	0.943181i	$-0.607818\pi$
$607$	7.84448	−	4.52901i	0.318398	−	0.183827i	0.650678	+	0.759354i	$0.274485\pi$
$608$		0			0
$609$	−12.4930	+	15.0864i	−0.506241	+	0.611331i
$610$		0			0
$611$	−9.78285			−0.395772
$612$		0			0
$613$		−	6.99155i		−	0.282386i	−0.989982	−	0.141193i	$-0.954906\pi$
$613$		−	6.99155i		−	0.282386i	0.989982	−	0.141193i	$-0.0450938\pi$
$614$		0			0
$615$	5.17122	+	10.9150i	0.208524	+	0.440133i
$616$		0			0
$617$	17.1769	−	9.91710i	0.691517	−	0.399247i	−0.112663	−	0.993633i	$-0.535938\pi$
$617$	17.1769	−	9.91710i	0.691517	−	0.399247i	0.804180	+	0.594386i	$0.202605\pi$
$618$		0			0
$619$	14.1016	−	24.4246i	0.566789	−	0.981708i	−0.430092	−	0.902785i	$-0.641519\pi$
$619$	14.1016	−	24.4246i	0.566789	−	0.981708i	0.996881	−	0.0789225i	$-0.0251480\pi$
$620$		0			0
$621$	0.625546	+	32.1136i	0.0251023	+	1.28867i
$622$		0			0
$623$	−17.4188	−	10.0568i	−0.697871	−	0.402916i
$624$		0			0
$625$	−4.37830	+	24.6136i	−0.175132	+	0.984545i
$626$		0			0
$627$	7.40605	−	43.6574i	0.295769	−	1.74351i
$628$		0			0
$629$	−1.32865			−0.0529768
$630$		0			0
$631$	7.27482			0.289606			0.144803	−	0.989461i	$-0.453745\pi$
$631$	7.27482			0.289606			0.144803	+	0.989461i	$0.453745\pi$
$632$		0			0
$633$	−5.04642	−	4.17892i	−0.200577	−	0.166097i
$634$		0			0
$635$	6.41244	−	13.7380i	0.254470	−	0.545176i
$636$		0			0
$637$	−6.26604	−	3.61770i	−0.248270	−	0.143339i
$638$		0			0
$639$	−16.3879	+	14.1177i	−0.648296	+	0.558488i
$640$		0			0
$641$	−6.43372	+	11.1435i	−0.254116	+	0.440143i	−0.964655	−	0.263515i	$-0.915118\pi$
$641$	−6.43372	+	11.1435i	−0.254116	+	0.440143i	0.710539	+	0.703658i	$0.248451\pi$
$642$		0			0
$643$	21.8515	−	12.6160i	0.861741	−	0.497526i	−0.00285403	−	0.999996i	$-0.500908\pi$
$643$	21.8515	−	12.6160i	0.861741	−	0.497526i	0.864595	+	0.502470i	$0.167575\pi$
$644$		0			0
$645$	8.62365	+	5.96008i	0.339556	+	0.234678i
$646$		0			0
$647$		−	23.5618i		−	0.926311i	−0.886277	−	0.463156i	$-0.846717\pi$
$647$		−	23.5618i		−	0.926311i	0.886277	−	0.463156i	$-0.153283\pi$
$648$		0			0
$649$	−34.2678			−1.34513
$650$		0			0
$651$	−13.1438	−	35.3957i	−0.515148	−	1.38727i
$652$		0			0
$653$	15.0519	−	8.69020i	0.589025	−	0.340074i	−0.175687	−	0.984446i	$-0.556215\pi$
$653$	15.0519	−	8.69020i	0.589025	−	0.340074i	0.764712	+	0.644372i	$0.222881\pi$
$654$		0			0
$655$	0.665053	+	7.63472i	0.0259858	+	0.298313i
$656$		0			0
$657$	−32.8592	−	38.1431i	−1.28196	−	1.48810i
$658$		0			0
$659$	7.83216	−	13.5657i	0.305098	−	0.528445i	−0.672185	−	0.740383i	$-0.734644\pi$
$659$	7.83216	−	13.5657i	0.305098	−	0.528445i	0.977283	+	0.211938i	$0.0679775\pi$
$660$		0			0
$661$	−11.7136	−	20.2886i	−0.455608	−	0.789136i	0.543115	−	0.839658i	$-0.317245\pi$
$661$	−11.7136	−	20.2886i	−0.455608	−	0.789136i	−0.998723	+	0.0505224i	$0.983911\pi$
$662$		0			0
$663$	2.08868	+	1.72963i	0.0811177	+	0.0671732i
$664$		0			0
$665$	34.8405	+	49.7973i	1.35106	+	1.93106i
$666$		0			0
$667$			18.5443i			0.718038i
$668$		0			0
$669$	4.98303	+	0.845323i	0.192655	+	0.0326821i
$670$		0			0
$671$	14.5557	+	25.2113i	0.561918	+	0.973271i
$672$		0			0
$673$	24.8816	+	14.3654i	0.959114	+	0.553745i	0.895900	−	0.444255i	$-0.146532\pi$
$673$	24.8816	+	14.3654i	0.959114	+	0.553745i	0.0632136	+	0.998000i	$0.479865\pi$
$674$		0			0
$675$	−25.4971	+	4.98975i	−0.981384	+	0.192055i
$676$		0			0
$677$	−43.6079	−	25.1770i	−1.67599	−	0.967632i	−0.964177	−	0.265260i	$-0.914542\pi$
$677$	−43.6079	−	25.1770i	−1.67599	−	0.967632i	−0.711810	−	0.702372i	$-0.752124\pi$
$678$		0			0
$679$	−7.27934	−	12.6082i	−0.279355	−	0.483858i
$680$		0			0
$681$	−8.74056	−	1.48275i	−0.334939	−	0.0568192i
$682$		0			0
$683$			11.5953i			0.443681i	0.975083	+	0.221841i	$0.0712065\pi$
$683$			11.5953i			0.443681i	−0.975083	+	0.221841i	$0.928794\pi$
$684$		0			0
$685$	−19.1339	−	27.3480i	−0.731069	−	1.04491i
$686$		0			0
$687$	12.5669	+	10.4066i	0.479457	+	0.397036i
$688$		0			0
$689$	−5.64443	−	9.77644i	−0.215036	−	0.372453i
$690$		0			0
$691$	22.9238	−	39.7051i	0.872061	−	1.51045i	0.0122006	−	0.999926i	$-0.496116\pi$
$691$	22.9238	−	39.7051i	0.872061	−	1.51045i	0.859861	−	0.510529i	$-0.170550\pi$
$692$		0			0
$693$	13.2243	−	37.8557i	0.502350	−	1.43802i
$694$		0			0
$695$	−1.05315	−	12.0900i	−0.0399482	−	0.458599i
$696$		0			0
$697$	−4.21373	+	2.43280i	−0.159606	+	0.0921489i
$698$		0			0
$699$	−15.7883	−	42.5170i	−0.597167	−	1.60814i
$700$		0			0
$701$	−38.1115			−1.43945			−0.719726	−	0.694259i	$-0.755732\pi$
$701$	−38.1115			−1.43945			−0.719726	+	0.694259i	$0.755732\pi$
$702$		0			0
$703$			6.13997i			0.231573i
$704$		0			0
$705$	31.0601	+	21.4667i	1.16979	+	0.808481i
$706$		0			0
$707$	15.5262	−	8.96406i	0.583923	−	0.337128i
$708$		0			0
$709$	−1.14443	+	1.98222i	−0.0429801	+	0.0744437i	−0.886715	−	0.462316i	$-0.847019\pi$
$709$	−1.14443	+	1.98222i	−0.0429801	+	0.0744437i	0.843735	+	0.536760i	$0.180352\pi$
$710$		0			0
$711$	6.14794	+	32.4008i	0.230566	+	1.21513i
$712$		0			0
$713$	−30.9572	−	17.8731i	−1.15936	−	0.669355i
$714$		0			0
$715$	−3.36526	+	7.20973i	−0.125854	+	0.269629i
$716$		0			0
$717$	−30.3570	−	25.1386i	−1.13370	−	0.938816i
$718$		0			0
$719$	−16.6035			−0.619205			−0.309602	−	0.950866i	$-0.600196\pi$
$719$	−16.6035			−0.619205			−0.309602	+	0.950866i	$0.600196\pi$
$720$		0			0
$721$	−68.1891			−2.53949
$722$		0			0
$723$	4.81761	−	28.3989i	0.179169	−	1.05617i
$724$		0			0
$725$	−14.7741	+	2.59359i	−0.548695	+	0.0963236i
$726$		0			0
$727$	−33.4350	−	19.3037i	−1.24003	−	0.715934i	−0.270933	−	0.962598i	$-0.587332\pi$
$727$	−33.4350	−	19.3037i	−1.24003	−	0.715934i	−0.969101	+	0.246664i	$0.920666\pi$
$728$		0			0
$729$	−14.4004	−	22.8392i	−0.533347	−	0.845897i
$730$		0			0
$731$	−2.11150	+	3.65722i	−0.0780966	+	0.135267i
$732$		0			0
$733$	−29.3584	+	16.9501i	−1.08438	+	0.626066i	−0.932074	−	0.362267i	$-0.882003\pi$
$733$	−29.3584	+	16.9501i	−1.08438	+	0.626066i	−0.152305	+	0.988334i	$0.548669\pi$
$734$		0			0
$735$	11.9560	+	25.2357i	0.441005	+	0.930834i
$736$		0			0
$737$			10.3469i			0.381131i
$738$		0			0
$739$	−36.8405			−1.35520			−0.677600	−	0.735431i	$-0.736980\pi$
$739$	−36.8405			−1.35520			−0.677600	+	0.735431i	$0.736980\pi$
$740$		0			0
$741$	7.99298	−	9.65223i	0.293629	−	0.354584i
$742$		0			0
$743$	9.89680	−	5.71392i	0.363078	−	0.209623i	−0.307352	−	0.951596i	$-0.599443\pi$
$743$	9.89680	−	5.71392i	0.363078	−	0.209623i	0.670430	+	0.741973i	$0.266110\pi$
$744$		0			0
$745$	−1.07478	−	12.3384i	−0.0393770	−	0.452043i
$746$		0			0
$747$	−30.0502	+	5.70192i	−1.09948	+	0.208622i
$748$		0			0
$749$	6.81870	−	11.8103i	0.249150	−	0.431541i
$750$		0			0
$751$	−8.10155	−	14.0323i	−0.295630	−	0.512046i	0.679501	−	0.733674i	$-0.262196\pi$
$751$	−8.10155	−	14.0323i	−0.295630	−	0.512046i	−0.975131	+	0.221628i	$0.928863\pi$
$752$		0			0
$753$	−33.7340	+	12.5268i	−1.22934	+	0.456502i
$754$		0			0
$755$	−0.397858	+	0.278360i	−0.0144795	+	0.0101306i
$756$		0			0
$757$			8.08698i			0.293926i	0.989142	+	0.146963i	$0.0469499\pi$
$757$			8.08698i			0.293926i	−0.989142	+	0.146963i	$0.953050\pi$
$758$		0			0
$759$	−13.2156	−	35.5888i	−0.479694	−	1.29179i
$760$		0			0
$761$	−10.7031	−	18.5383i	−0.387987	−	0.672014i	0.604191	−	0.796839i	$-0.293496\pi$
$761$	−10.7031	−	18.5383i	−0.387987	−	0.672014i	−0.992179	+	0.124826i	$0.960163\pi$
$762$		0			0
$763$	−31.4623	−	18.1647i	−1.13901	−	0.657608i
$764$		0			0
$765$	−2.83612	−	10.0747i	−0.102540	−	0.364252i
$766$		0			0
$767$	−8.39889	−	4.84910i	−0.303266	−	0.175091i
$768$		0			0
$769$	25.7031	+	44.5191i	0.926878	+	1.60540i	0.788513	+	0.615018i	$0.210851\pi$
$769$	25.7031	+	44.5191i	0.926878	+	1.60540i	0.138364	+	0.990381i	$0.455815\pi$
$770$		0			0
$771$	21.0552	−	25.4260i	0.758283	−	0.915695i
$772$		0			0
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$	9.90972	−	27.1630i	0.355968	−	0.975725i
$776$		0			0
$777$	−0.929933	+	5.48179i	−0.0333612	+	0.196658i
$778$		0			0
$779$	11.2425	+	19.4725i	0.402803	+	0.697676i
$780$		0			0
$781$	12.7828	−	22.1405i	0.457406	−	0.792251i
$782$		0			0
$783$	−8.05567	−	13.3456i	−0.287886	−	0.476934i
$784$		0			0
$785$	−4.80933	+	0.418936i	−0.171652	+	0.0149525i
$786$		0			0
$787$	4.08216	−	2.35683i	0.145513	−	0.0840121i	−0.425476	−	0.904970i	$-0.639893\pi$
$787$	4.08216	−	2.35683i	0.145513	−	0.0840121i	0.570989	+	0.820958i	$0.306560\pi$
$788$		0			0
$789$	−13.8969	−	2.35747i	−0.494741	−	0.0839281i
$790$		0			0
$791$	13.4132			0.476920
$792$		0			0
$793$			8.23891i			0.292572i
$794$		0			0
$795$	−3.53177	+	43.4255i	−0.125259	+	1.54014i
$796$		0			0
$797$	−8.88882	+	5.13196i	−0.314858	+	0.181784i	−0.649098	−	0.760704i	$-0.724854\pi$
$797$	−8.88882	+	5.13196i	−0.314858	+	0.181784i	0.334240	+	0.942488i	$0.391520\pi$
$798$		0			0
$799$	−7.60506	+	13.1724i	−0.269048	+	0.466005i
$800$		0			0
$801$	12.1275	−	10.4475i	0.428503	−	0.369143i
$802$		0			0
$803$	51.5324	+	29.7523i	1.81854	+	1.04993i
$804$		0			0
$805$	47.2142	+	22.0380i	1.66408	+	0.776737i
$806$		0			0
$807$	−41.6278	+	15.4581i	−1.46537	+	0.544150i
$808$		0			0
$809$	−21.9860			−0.772985			−0.386492	−	0.922293i	$-0.626313\pi$
$809$	−21.9860			−0.772985			−0.386492	+	0.922293i	$0.626313\pi$
$810$		0			0
$811$	25.6951			0.902276			0.451138	−	0.892454i	$-0.351018\pi$
$811$	25.6951			0.902276			0.451138	+	0.892454i	$0.351018\pi$
$812$		0			0
$813$	−5.21233	+	1.93555i	−0.182805	+	0.0678826i
$814$		0			0
$815$	7.93578	−	17.0016i	0.277978	−	0.595540i
$816$		0			0
$817$	16.9008	+	9.75767i	0.591284	+	0.341378i
$818$		0			0
$819$	8.59804	−	7.40697i	0.300440	−	0.258820i
$820$		0			0
$821$	−12.1967	+	21.1253i	−0.425667	+	0.737276i	−0.996482	−	0.0838018i	$-0.973294\pi$
$821$	−12.1967	+	21.1253i	−0.425667	+	0.737276i	0.570816	+	0.821078i	$0.306627\pi$
$822$		0			0
$823$	−2.26396	+	1.30710i	−0.0789167	+	0.0455626i	−0.538939	−	0.842345i	$-0.681175\pi$
$823$	−2.26396	+	1.30710i	−0.0789167	+	0.0455626i	0.460022	+	0.887907i	$0.347841\pi$
$824$		0			0
$825$	26.5050	−	15.5061i	0.922785	−	0.539854i
$826$		0			0
$827$		−	0.0684725i		−	0.00238102i	−0.999999	−	0.00119051i	$-0.999621\pi$
$827$		−	0.0684725i		−	0.00238102i	0.999999	−	0.00119051i	$-0.000378951\pi$
$828$		0			0
$829$	24.7828			0.860744			0.430372	−	0.902652i	$-0.358382\pi$
$829$	24.7828			0.860744			0.430372	+	0.902652i	$0.358382\pi$
$830$		0			0
$831$	−1.19475	−	0.202679i	−0.0414455	−	0.00703084i
$832$		0			0
$833$	−9.74229	+	5.62471i	−0.337550	+	0.194885i
$834$		0			0
$835$	−10.2944	+	0.896731i	−0.356251	+	0.0310327i
$836$		0			0
$837$	30.0429	−	0.585210i	1.03843	−	0.0202278i
$838$		0			0
$839$	−22.6204	+	39.1797i	−0.780944	+	1.35264i	0.150448	+	0.988618i	$0.451928\pi$
$839$	−22.6204	+	39.1797i	−0.780944	+	1.35264i	−0.931392	+	0.364017i	$0.881405\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	−8.87323	+	52.3061i	−0.305610	+	1.80152i
$844$		0			0
$845$	21.9731	−	15.3734i	0.755897	−	0.528861i
$846$		0			0
$847$			5.92857i			0.203708i
$848$		0			0
$849$	10.6115	−	12.8143i	0.364186	−	0.439787i
$850$		0			0
$851$	2.63198	+	4.55872i	0.0902231	+	0.156271i
$852$		0			0
$853$	17.5067	+	10.1075i	0.599418	+	0.346074i	0.768813	−	0.639474i	$-0.220848\pi$
$853$	17.5067	+	10.1075i	0.599418	+	0.346074i	−0.169395	+	0.985548i	$0.554181\pi$
$854$		0			0
$855$	−46.5574	+	13.1063i	−1.59223	+	0.448226i
$856$		0			0
$857$	23.2464	+	13.4213i	0.794083	+	0.458464i	0.841398	−	0.540416i	$-0.181733\pi$
$857$	23.2464	+	13.4213i	0.794083	+	0.458464i	−0.0473147	+	0.998880i	$0.515066\pi$
$858$		0			0
$859$	−1.68130	−	2.91209i	−0.0573651	−	0.0993592i	0.835917	−	0.548856i	$-0.184937\pi$
$859$	−1.68130	−	2.91209i	−0.0573651	−	0.0993592i	−0.893282	+	0.449497i	$0.851603\pi$
$860$		0			0
$861$	7.08809	+	19.0879i	0.241562	+	0.650513i
$862$		0			0
$863$		−	18.4524i		−	0.628126i	−0.949402	−	0.314063i	$-0.898310\pi$
$863$		−	18.4524i		−	0.628126i	0.949402	−	0.314063i	$-0.101690\pi$
$864$		0			0
$865$	−1.85908	−	2.65717i	−0.0632106	−	0.0903465i
$866$		0			0
$867$	−23.6505	+	8.78239i	−0.803214	+	0.298266i
$868$		0			0
$869$	−19.4895	−	33.7567i	−0.661135	−	1.14512i
$870$		0			0
$871$	−1.46414	+	2.53597i	−0.0496106	+	0.0859281i
$872$		0			0
$873$	11.3832	−	2.15992i	0.385262	−	0.0731022i
$874$		0			0
$875$	−10.9541	+	40.6973i	−0.370317	+	1.37582i
$876$		0			0
$877$	20.0905	−	11.5993i	0.678408	−	0.391679i	−0.120847	−	0.992671i	$-0.538561\pi$
$877$	20.0905	−	11.5993i	0.678408	−	0.391679i	0.799255	+	0.600992i	$0.205228\pi$
$878$		0			0
$879$	−3.32573	+	4.01611i	−0.112174	+	0.135460i
$880$		0			0
$881$	2.34854			0.0791244			0.0395622	−	0.999217i	$-0.487404\pi$
$881$	2.34854			0.0791244			0.0395622	+	0.999217i	$0.487404\pi$
$882$		0			0
$883$		−	16.3264i		−	0.549428i	−0.961526	−	0.274714i	$-0.911417\pi$
$883$		−	16.3264i		−	0.549428i	0.961526	−	0.274714i	$-0.0885832\pi$
$884$		0			0
$885$	16.0257	+	33.8255i	0.538697	+	1.13703i
$886$		0			0
$887$	23.2464	−	13.4213i	0.780539	−	0.450645i	−0.0560821	−	0.998426i	$-0.517861\pi$
$887$	23.2464	−	13.4213i	0.780539	−	0.450645i	0.836621	+	0.547782i	$0.184528\pi$
$888$		0			0
$889$	12.7793	−	22.1345i	0.428605	−	0.742366i
$890$		0			0
$891$	24.9706	+	19.8711i	0.836546	+	0.665707i
$892$		0			0
$893$	60.8722	+	35.1446i	2.03701	+	1.17607i
$894$		0			0
$895$	39.4041	+	18.3925i	1.31713	+	0.614793i
$896$		0			0
$897$	1.79696	−	10.5928i	0.0599987	−	0.353682i
$898$		0			0
$899$	17.3485			0.578606
$900$		0			0
$901$	−17.5516			−0.584730
$902$		0			0
$903$	13.6112	+	11.2714i	0.452953	+	0.375089i
$904$		0			0
$905$	21.1279	+	9.86177i	0.702314	+	0.327816i
$906$		0			0
$907$	−6.79188	−	3.92130i	−0.225521	−	0.130204i	0.382983	−	0.923755i	$-0.374897\pi$
$907$	−6.79188	−	3.92130i	−0.225521	−	0.130204i	−0.608504	+	0.793551i	$0.708230\pi$
$908$		0			0
$909$	2.65981	+	14.0177i	0.0882203	+	0.464937i
$910$		0			0
$911$	1.28636	−	2.22804i	0.0426190	−	0.0738183i	−0.843929	−	0.536455i	$-0.819763\pi$
$911$	1.28636	−	2.22804i	0.0426190	−	0.0738183i	0.886548	+	0.462637i	$0.153097\pi$
$912$		0			0
$913$	31.3078	−	18.0755i	1.03614	−	0.598213i
$914$		0			0
$915$	18.0788	−	26.1582i	0.597666	−	0.864763i
$916$		0			0
$917$			12.9196i			0.426642i
$918$		0			0
$919$	42.4062			1.39885			0.699426	−	0.714705i	$-0.253439\pi$
$919$	42.4062			1.39885			0.699426	+	0.714705i	$0.253439\pi$
$920$		0			0
$921$	−8.96414	−	24.1400i	−0.295379	−	0.795440i
$922$		0			0
$923$	6.26604	−	3.61770i	0.206249	−	0.119078i
$924$		0			0
$925$	−3.26379	+	2.73445i	−0.107313	+	0.0899083i
$926$		0			0
$927$	17.8968	−	51.2311i	0.587807	−	1.68265i
$928$		0			0
$929$	25.9167	−	44.8891i	0.850301	−	1.47276i	−0.0306361	−	0.999531i	$-0.509753\pi$
$929$	25.9167	−	44.8891i	0.850301	−	1.47276i	0.880937	−	0.473234i	$-0.156913\pi$
$930$		0			0
$931$	25.9930	+	45.0212i	0.851885	+	1.47551i
$932$		0			0
$933$	−4.09775	−	3.39333i	−0.134154	−	0.111093i
$934$		0			0
$935$	7.09161	+	10.1360i	0.231920	+	0.331482i
$936$		0			0
$937$			16.9666i			0.554275i	0.960830	+	0.277137i	$0.0893857\pi$
$937$			16.9666i			0.554275i	−0.960830	+	0.277137i	$0.910614\pi$
$938$		0			0
$939$	−39.2992	−	6.66674i	−1.28248	−	0.217561i
$940$		0			0
$941$	−2.82865	−	4.89937i	−0.0922114	−	0.159715i	0.816230	−	0.577727i	$-0.196060\pi$
$941$	−2.82865	−	4.89937i	−0.0922114	−	0.159715i	−0.908441	+	0.418012i	$0.862727\pi$
$942$		0			0
$943$	16.6943	+	9.63847i	0.543642	+	0.313872i
$944$		0			0
$945$	−43.5516	+	4.64998i	−1.41673	+	0.151264i
$946$		0			0
$947$	−30.6452	−	17.6930i	−0.995834	−	0.574945i	−0.0888210	−	0.996048i	$-0.528310\pi$
$947$	−30.6452	−	17.6930i	−0.995834	−	0.574945i	−0.907013	+	0.421103i	$0.861643\pi$
$948$		0			0
$949$	8.42026	+	14.5843i	0.273333	+	0.473427i
$950$		0			0
$951$	0.0153749	+	0.00260821i	0.000498566	+	8.45770e-5i
$952$		0			0
$953$		−	1.66116i		−	0.0538101i	−0.999638	−	0.0269051i	$-0.991435\pi$
$953$		−	1.66116i		−	0.0538101i	0.999638	−	0.0269051i	$-0.00856518\pi$
$954$		0			0
$955$	6.93079	−	4.84910i	0.224275	−	0.156913i
$956$		0			0
$957$	14.1906	+	11.7512i	0.458717	+	0.379862i
$958$		0			0
$959$	−28.1339	−	48.7293i	−0.908491	−	1.57355i
$960$		0			0
$961$	−1.22066	+	2.11425i	−0.0393763	+	0.0682017i
$962$		0			0
$963$	7.08360	+	8.22268i	0.228266	+	0.264972i
$964$		0			0
$965$	−31.3540	+	2.73122i	−1.00932	+	0.0879209i
$966$		0			0
$967$	17.9581	−	10.3681i	0.577494	−	0.333416i	−0.182643	−	0.983179i	$-0.558465\pi$
$967$	17.9581	−	10.3681i	0.577494	−	0.333416i	0.760137	+	0.649763i	$0.225132\pi$
$968$		0			0
$969$	−6.78285	−	18.2659i	−0.217896	−	0.586784i
$970$		0			0
$971$	−20.9193			−0.671331			−0.335665	−	0.941981i	$-0.608961\pi$
$971$	−20.9193			−0.671331			−0.335665	+	0.941981i	$0.608961\pi$
$972$		0			0
$973$		−	20.4589i		−	0.655881i
$974$		0			0
$975$	8.69047	−	0.0498732i	0.278318	−	0.00159722i
$976$		0			0
$977$	−2.50418	+	1.44579i	−0.0801159	+	0.0462549i	−0.539523	−	0.841971i	$-0.681395\pi$
$977$	−2.50418	+	1.44579i	−0.0801159	+	0.0462549i	0.459407	+	0.888226i	$0.348062\pi$
$978$		0			0
$979$	−9.45963	+	16.3846i	−0.302331	+	0.523653i
$980$		0			0
$981$	21.9049	−	18.8704i	0.699369	−	0.602486i
$982$		0			0
$983$	5.45628	+	3.15019i	0.174028	+	0.100475i	0.584484	−	0.811405i	$-0.301297\pi$
$983$	5.45628	+	3.15019i	0.174028	+	0.100475i	−0.410456	+	0.911881i	$0.634630\pi$
$984$		0			0
$985$	−20.3381	+	43.5723i	−0.648026	+	1.38833i
$986$		0			0
$987$	49.0241	+	40.5966i	1.56045	+	1.29221i
$988$		0			0
$989$	16.7310			0.532016
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$		0			0
$993$	−2.60515	+	15.3569i	−0.0826719	+	0.487336i
$994$		0			0
$995$	−14.6092	−	6.81910i	−0.463144	−	0.216180i
$996$		0			0
$997$	8.29589	+	4.78963i	0.262733	+	0.151689i	0.625581	−	0.780159i	$-0.284862\pi$
$997$	8.29589	+	4.78963i	0.262733	+	0.151689i	−0.362847	+	0.931849i	$0.618195\pi$
$998$		0			0
$999$	−3.87445	−	2.13741i	−0.122582	−	0.0676246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.by.e.529.1		12
3.2	odd	2		2160.2.by.e.289.6		12
4.3	odd	2		180.2.r.a.169.6	yes	12
5.4	even	2	inner	720.2.by.e.529.6		12
9.4	even	3	inner	720.2.by.e.49.6		12
9.5	odd	6		2160.2.by.e.1009.4		12
12.11	even	2		540.2.r.a.289.6		12
15.14	odd	2		2160.2.by.e.289.4		12
20.3	even	4		900.2.i.f.601.4		12
20.7	even	4		900.2.i.f.601.3		12
20.19	odd	2		180.2.r.a.169.1	yes	12
36.7	odd	6		1620.2.d.c.649.5		6
36.11	even	6		1620.2.d.d.649.2		6
36.23	even	6		540.2.r.a.469.4		12
36.31	odd	6		180.2.r.a.49.1	✓	12
45.4	even	6	inner	720.2.by.e.49.1		12
45.14	odd	6		2160.2.by.e.1009.6		12
60.23	odd	4		2700.2.i.f.1801.6		12
60.47	odd	4		2700.2.i.f.1801.1		12
60.59	even	2		540.2.r.a.289.4		12
180.7	even	12		8100.2.a.bc.1.6		6
180.23	odd	12		2700.2.i.f.901.6		12
180.43	even	12		8100.2.a.bc.1.1		6
180.47	odd	12		8100.2.a.bd.1.6		6
180.59	even	6		540.2.r.a.469.6		12
180.67	even	12		900.2.i.f.301.3		12
180.79	odd	6		1620.2.d.c.649.6		6
180.83	odd	12		8100.2.a.bd.1.1		6
180.103	even	12		900.2.i.f.301.4		12
180.119	even	6		1620.2.d.d.649.1		6
180.139	odd	6		180.2.r.a.49.6	yes	12
180.167	odd	12		2700.2.i.f.901.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.r.a.49.1	✓	12	36.31	odd	6
180.2.r.a.49.6	yes	12	180.139	odd	6
180.2.r.a.169.1	yes	12	20.19	odd	2
180.2.r.a.169.6	yes	12	4.3	odd	2
540.2.r.a.289.4		12	60.59	even	2
540.2.r.a.289.6		12	12.11	even	2
540.2.r.a.469.4		12	36.23	even	6
540.2.r.a.469.6		12	180.59	even	6
720.2.by.e.49.1		12	45.4	even	6	inner
720.2.by.e.49.6		12	9.4	even	3	inner
720.2.by.e.529.1		12	1.1	even	1	trivial
720.2.by.e.529.6		12	5.4	even	2	inner
900.2.i.f.301.3		12	180.67	even	12
900.2.i.f.301.4		12	180.103	even	12
900.2.i.f.601.3		12	20.7	even	4
900.2.i.f.601.4		12	20.3	even	4
1620.2.d.c.649.5		6	36.7	odd	6
1620.2.d.c.649.6		6	180.79	odd	6
1620.2.d.d.649.1		6	180.119	even	6
1620.2.d.d.649.2		6	36.11	even	6
2160.2.by.e.289.4		12	15.14	odd	2
2160.2.by.e.289.6		12	3.2	odd	2
2160.2.by.e.1009.4		12	9.5	odd	6
2160.2.by.e.1009.6		12	45.14	odd	6
2700.2.i.f.901.1		12	180.167	odd	12
2700.2.i.f.901.6		12	180.23	odd	12
2700.2.i.f.1801.1		12	60.47	odd	4
2700.2.i.f.1801.6		12	60.23	odd	4
8100.2.a.bc.1.1		6	180.43	even	12
8100.2.a.bc.1.6		6	180.7	even	12
8100.2.a.bd.1.1		6	180.83	odd	12
8100.2.a.bd.1.6		6	180.47	odd	12

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.62372 + 0.602950i) q^{3} +(-2.02621 - 0.945767i) q^{5} +(-3.26460 - 1.88482i) q^{7} +(2.27290 - 1.95804i) q^{9} +(-1.77290 + 3.07076i) q^{11} +(-0.869061 + 0.501753i) q^{13} +(3.86024 + 0.313951i) q^{15} +1.56023i q^{17} +7.21013 q^{19} +(6.43723 + 1.09201i) q^{21} +(5.35328 - 3.09072i) q^{23} +(3.21105 + 3.83264i) q^{25} +(-2.50994 + 4.54975i) q^{27} +(-1.50000 + 2.59808i) q^{29} +(-2.89142 - 5.00809i) q^{31} +(1.02717 - 6.05500i) q^{33} +(4.83216 + 6.90658i) q^{35} +0.851576i q^{37} +(1.10858 - 1.33870i) q^{39} +(1.55926 + 2.70072i) q^{41} +(2.34403 + 1.35333i) q^{43} +(-6.45722 + 1.81776i) q^{45} +(8.44260 + 4.87434i) q^{47} +(3.60506 + 6.24415i) q^{49} +(-0.940739 - 2.53336i) q^{51} +11.2494i q^{53} +(6.49649 - 4.54524i) q^{55} +(-11.7072 + 4.34735i) q^{57} +(4.83216 + 8.36955i) q^{59} +(4.10506 - 7.11018i) q^{61} +(-11.1107 + 2.10821i) q^{63} +(2.23544 - 0.194727i) q^{65} +(2.52711 - 1.45903i) q^{67} +(-6.82865 + 8.24621i) q^{69} -7.21013 q^{71} -16.7817i q^{73} +(-7.52473 - 4.28702i) q^{75} +(11.5756 - 6.68319i) q^{77} +(-5.49649 + 9.52020i) q^{79} +(1.33216 - 8.90086i) q^{81} +(-8.82952 - 5.09773i) q^{83} +(1.47561 - 3.16134i) q^{85} +(0.869061 - 5.12296i) q^{87} +5.33567 q^{89} +3.78285 q^{91} +(7.71448 + 6.38833i) q^{93} +(-14.6092 - 6.81910i) q^{95} +(3.34467 + 1.93105i) q^{97} +(1.98303 + 10.4509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{5} + 8 q^{9} - 2 q^{11} + 5 q^{15} + 10 q^{21} - 3 q^{25} - 18 q^{29} - 6 q^{31} + 34 q^{35} + 42 q^{39} + 14 q^{41} - 31 q^{45} - 16 q^{51} + 6 q^{55} + 34 q^{59} + 6 q^{61} + 15 q^{65} + 14 q^{69}+ \cdots - 82 q^{99}+O(q^{100}) \) 12 * q + q^5 + 8 * q^9 - 2 * q^11 + 5 * q^15 + 10 * q^21 - 3 * q^25 - 18 * q^29 - 6 * q^31 + 34 * q^35 + 42 * q^39 + 14 * q^41 - 31 * q^45 - 16 * q^51 + 6 * q^55 + 34 * q^59 + 6 * q^61 + 15 * q^65 + 14 * q^69 - 41 * q^75 + 6 * q^79 - 8 * q^81 - 12 * q^85 + 112 * q^89 - 12 * q^91 - 36 * q^95 - 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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