LMFDB - Embedded newform 350.2.g.a.307.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,2,Mod(293,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.293"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.3
Root			$-0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	350.307
Dual form			350.2.g.a.293.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.30656 - 1.30656i) q^{3} +1.00000i q^{4} -1.84776i q^{6} +(0.941740 + 2.47247i) q^{7} +(-0.707107 + 0.707107i) q^{8} +0.414214i q^{9} +2.82843 q^{11} +(1.30656 - 1.30656i) q^{12} +(4.23671 + 4.23671i) q^{13} +(-1.08239 + 2.41421i) q^{14} -1.00000 q^{16} +(3.69552 - 3.69552i) q^{17} +(-0.292893 + 0.292893i) q^{18} +1.39942 q^{19} +(2.00000 - 4.46088i) q^{21} +(2.00000 + 2.00000i) q^{22} +(-0.414214 + 0.414214i) q^{23} +1.84776 q^{24} +5.99162i q^{26} +(-3.37849 + 3.37849i) q^{27} +(-2.47247 + 0.941740i) q^{28} -0.828427i q^{29} +1.53073i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.69552 - 3.69552i) q^{33} +5.22625 q^{34} -0.414214 q^{36} +(-2.58579 - 2.58579i) q^{37} +(0.989538 + 0.989538i) q^{38} -11.0711i q^{39} +3.69552i q^{41} +(4.56854 - 1.74011i) q^{42} +(-4.00000 + 4.00000i) q^{43} +2.82843i q^{44} -0.585786 q^{46} +(-1.08239 + 1.08239i) q^{47} +(1.30656 + 1.30656i) q^{48} +(-5.22625 + 4.65685i) q^{49} -9.65685 q^{51} +(-4.23671 + 4.23671i) q^{52} +(8.24264 - 8.24264i) q^{53} -4.77791 q^{54} +(-2.41421 - 1.08239i) q^{56} +(-1.82843 - 1.82843i) q^{57} +(0.585786 - 0.585786i) q^{58} -9.23880 q^{59} -6.43996i q^{61} +(-1.08239 + 1.08239i) q^{62} +(-1.02413 + 0.390081i) q^{63} -1.00000i q^{64} -5.22625i q^{66} +(-10.4853 - 10.4853i) q^{67} +(3.69552 + 3.69552i) q^{68} +1.08239 q^{69} -0.585786 q^{71} +(-0.292893 - 0.292893i) q^{72} +(-4.14386 - 4.14386i) q^{73} -3.65685i q^{74} +1.39942i q^{76} +(2.66364 + 6.99321i) q^{77} +(7.82843 - 7.82843i) q^{78} +5.07107i q^{79} +10.0711 q^{81} +(-2.61313 + 2.61313i) q^{82} +(-5.31911 - 5.31911i) q^{83} +(4.46088 + 2.00000i) q^{84} -5.65685 q^{86} +(-1.08239 + 1.08239i) q^{87} +(-2.00000 + 2.00000i) q^{88} +11.3492 q^{89} +(-6.48528 + 14.4650i) q^{91} +(-0.414214 - 0.414214i) q^{92} +(2.00000 - 2.00000i) q^{93} -1.53073 q^{94} +1.84776i q^{96} +(4.59220 - 4.59220i) q^{97} +(-6.98841 - 0.402625i) q^{98} +1.17157i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7} - 8 q^{16} - 8 q^{18} + 16 q^{21} + 16 q^{22} + 8 q^{23} - 8 q^{28} + 8 q^{36} - 32 q^{37} - 32 q^{43} - 16 q^{46} - 32 q^{51} + 32 q^{53} - 8 q^{56} + 8 q^{57} + 16 q^{58} - 16 q^{67} - 16 q^{71}+ \cdots - 32 q^{98}+O(q^{100}) $ 8 * q + 8 * q^7 - 8 * q^16 - 8 * q^18 + 16 * q^21 + 16 * q^22 + 8 * q^23 - 8 * q^28 + 8 * q^36 - 32 * q^37 - 32 * q^43 - 16 * q^46 - 32 * q^51 + 32 * q^53 - 8 * q^56 + 8 * q^57 + 16 * q^58 - 16 * q^67 - 16 * q^71 - 8 * q^72 + 16 * q^77 + 40 * q^78 + 24 * q^81 - 16 * q^88 + 16 * q^91 + 8 * q^92 + 16 * q^93 - 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.30656	−	1.30656i	−0.754344	−	0.754344i	0.220942	−	0.975287i	$-0.429087\pi$
$3$	−1.30656	−	1.30656i	−0.754344	−	0.754344i	−0.975287	+	0.220942i	$0.929087\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$		−	1.84776i		−	0.754344i
$7$	0.941740	+	2.47247i	0.355944	+	0.934507i
$7$	0.941740	+	2.47247i	0.355944	+	0.934507i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			0.414214i			0.138071i
$10$		0			0
$11$	2.82843			0.852803			0.426401	−	0.904534i	$-0.359781\pi$
$11$	2.82843			0.852803			0.426401	+	0.904534i	$0.359781\pi$
$12$	1.30656	−	1.30656i	0.377172	−	0.377172i
$13$	4.23671	+	4.23671i	1.17505	+	1.17505i	0.980989	+	0.194064i	$0.0621670\pi$
$13$	4.23671	+	4.23671i	1.17505	+	1.17505i	0.194064	+	0.980989i	$0.437833\pi$
$14$	−1.08239	+	2.41421i	−0.289281	+	0.645226i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.69552	−	3.69552i	0.896295	−	0.896295i	−0.0988114	−	0.995106i	$-0.531504\pi$
$17$	3.69552	−	3.69552i	0.896295	−	0.896295i	0.995106	+	0.0988114i	$0.0315040\pi$
$18$	−0.292893	+	0.292893i	−0.0690356	+	0.0690356i
$19$	1.39942			0.321048			0.160524	−	0.987032i	$-0.448682\pi$
$19$	1.39942			0.321048			0.160524	+	0.987032i	$0.448682\pi$
$20$		0			0
$21$	2.00000	−	4.46088i	0.436436	−	0.973445i
$22$	2.00000	+	2.00000i	0.426401	+	0.426401i
$23$	−0.414214	+	0.414214i	−0.0863695	+	0.0863695i	−0.748972	−	0.662602i	$-0.769452\pi$
$23$	−0.414214	+	0.414214i	−0.0863695	+	0.0863695i	0.662602	+	0.748972i	$0.269452\pi$
$24$	1.84776			0.377172
$25$		0			0
$26$			5.99162i			1.17505i
$27$	−3.37849	+	3.37849i	−0.650191	+	0.650191i
$28$	−2.47247	+	0.941740i	−0.467254	+	0.177972i
$29$		−	0.828427i		−	0.153835i	−0.997037	−	0.0769175i	$-0.975492\pi$
$29$		−	0.828427i		−	0.153835i	0.997037	−	0.0769175i	$-0.0245078\pi$
$30$		0			0
$31$			1.53073i			0.274928i	0.990507	+	0.137464i	$0.0438951\pi$
$31$			1.53073i			0.274928i	−0.990507	+	0.137464i	$0.956105\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.69552	−	3.69552i	−0.643307	−	0.643307i
$34$	5.22625			0.896295
$35$		0			0
$36$	−0.414214			−0.0690356
$37$	−2.58579	−	2.58579i	−0.425101	−	0.425101i	0.461855	−	0.886956i	$-0.347184\pi$
$37$	−2.58579	−	2.58579i	−0.425101	−	0.425101i	−0.886956	+	0.461855i	$0.847184\pi$
$38$	0.989538	+	0.989538i	0.160524	+	0.160524i
$39$		−	11.0711i		−	1.77279i
$40$		0			0
$41$			3.69552i			0.577143i	0.957458	+	0.288571i	$0.0931803\pi$
$41$			3.69552i			0.577143i	−0.957458	+	0.288571i	$0.906820\pi$
$42$	4.56854	−	1.74011i	0.704940	−	0.268505i
$43$	−4.00000	+	4.00000i	−0.609994	+	0.609994i	−0.942944	−	0.332950i	$-0.891956\pi$
$43$	−4.00000	+	4.00000i	−0.609994	+	0.609994i	0.332950	+	0.942944i	$0.391956\pi$
$44$			2.82843i			0.426401i
$45$		0			0
$46$	−0.585786			−0.0863695
$47$	−1.08239	+	1.08239i	−0.157883	+	0.157883i	−0.781628	−	0.623745i	$-0.785610\pi$
$47$	−1.08239	+	1.08239i	−0.157883	+	0.157883i	0.623745	+	0.781628i	$0.285610\pi$
$48$	1.30656	+	1.30656i	0.188586	+	0.188586i
$49$	−5.22625	+	4.65685i	−0.746607	+	0.665265i
$50$		0			0
$51$	−9.65685			−1.35223
$52$	−4.23671	+	4.23671i	−0.587527	+	0.587527i
$53$	8.24264	−	8.24264i	1.13221	−	1.13221i	0.142405	−	0.989808i	$-0.454516\pi$
$53$	8.24264	−	8.24264i	1.13221	−	1.13221i	0.989808	−	0.142405i	$-0.0454837\pi$
$54$	−4.77791			−0.650191
$55$		0			0
$56$	−2.41421	−	1.08239i	−0.322613	−	0.144641i
$57$	−1.82843	−	1.82843i	−0.242181	−	0.242181i
$58$	0.585786	−	0.585786i	0.0769175	−	0.0769175i
$59$	−9.23880			−1.20279			−0.601394	−	0.798952i	$-0.705388\pi$
$59$	−9.23880			−1.20279			−0.601394	+	0.798952i	$0.705388\pi$
$60$		0			0
$61$		−	6.43996i		−	0.824552i	−0.911059	−	0.412276i	$-0.864734\pi$
$61$		−	6.43996i		−	0.824552i	0.911059	−	0.412276i	$-0.135266\pi$
$62$	−1.08239	+	1.08239i	−0.137464	+	0.137464i
$63$	−1.02413	+	0.390081i	−0.129029	+	0.0491456i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		−	5.22625i		−	0.643307i
$67$	−10.4853	−	10.4853i	−1.28098	−	1.28098i	−0.940110	−	0.340871i	$-0.889278\pi$
$67$	−10.4853	−	10.4853i	−1.28098	−	1.28098i	−0.340871	−	0.940110i	$-0.610722\pi$
$68$	3.69552	+	3.69552i	0.448147	+	0.448147i
$69$	1.08239			0.130305
$70$		0			0
$71$	−0.585786			−0.0695201			−0.0347600	−	0.999396i	$-0.511067\pi$
$71$	−0.585786			−0.0695201			−0.0347600	+	0.999396i	$0.511067\pi$
$72$	−0.292893	−	0.292893i	−0.0345178	−	0.0345178i
$73$	−4.14386	−	4.14386i	−0.485002	−	0.485002i	0.421723	−	0.906725i	$-0.361426\pi$
$73$	−4.14386	−	4.14386i	−0.485002	−	0.485002i	−0.906725	+	0.421723i	$0.861426\pi$
$74$		−	3.65685i		−	0.425101i
$75$		0			0
$76$			1.39942i			0.160524i
$77$	2.66364	+	6.99321i	0.303550	+	0.796950i
$78$	7.82843	−	7.82843i	0.886395	−	0.886395i
$79$			5.07107i			0.570540i	0.958447	+	0.285270i	$0.0920832\pi$
$79$			5.07107i			0.570540i	−0.958447	+	0.285270i	$0.907917\pi$
$80$		0			0
$81$	10.0711			1.11901
$82$	−2.61313	+	2.61313i	−0.288571	+	0.288571i
$83$	−5.31911	−	5.31911i	−0.583848	−	0.583848i	0.352111	−	0.935958i	$-0.385464\pi$
$83$	−5.31911	−	5.31911i	−0.583848	−	0.583848i	−0.935958	+	0.352111i	$0.885464\pi$
$84$	4.46088	+	2.00000i	0.486722	+	0.218218i
$85$		0			0
$86$	−5.65685			−0.609994
$87$	−1.08239	+	1.08239i	−0.116045	+	0.116045i
$88$	−2.00000	+	2.00000i	−0.213201	+	0.213201i
$89$	11.3492			1.20301			0.601506	−	0.798869i	$-0.294568\pi$
$89$	11.3492			1.20301			0.601506	+	0.798869i	$0.294568\pi$
$90$		0			0
$91$	−6.48528	+	14.4650i	−0.679842	+	1.51635i
$92$	−0.414214	−	0.414214i	−0.0431847	−	0.0431847i
$93$	2.00000	−	2.00000i	0.207390	−	0.207390i
$94$	−1.53073			−0.157883
$95$		0			0
$96$			1.84776i			0.188586i
$97$	4.59220	−	4.59220i	0.466267	−	0.466267i	−0.434436	−	0.900703i	$-0.643052\pi$
$97$	4.59220	−	4.59220i	0.466267	−	0.466267i	0.900703	+	0.434436i	$0.143052\pi$
$98$	−6.98841	−	0.402625i	−0.705936	−	0.0406713i
$99$			1.17157i			0.117748i
$100$		0			0
$101$		−	2.74444i		−	0.273082i	−0.990634	−	0.136541i	$-0.956401\pi$
$101$		−	2.74444i		−	0.273082i	0.990634	−	0.136541i	$-0.0435986\pi$
$102$	−6.82843	−	6.82843i	−0.676115	−	0.676115i
$103$	10.0042	+	10.0042i	0.985739	+	0.985739i	0.999900	−	0.0141603i	$-0.00450753\pi$
$103$	10.0042	+	10.0042i	0.985739	+	0.985739i	−0.0141603	+	0.999900i	$0.504508\pi$
$104$	−5.99162			−0.587527
$105$		0			0
$106$	11.6569			1.13221
$107$	3.65685	+	3.65685i	0.353521	+	0.353521i	0.861418	−	0.507897i	$-0.169577\pi$
$107$	3.65685	+	3.65685i	0.353521	+	0.353521i	−0.507897	+	0.861418i	$0.669577\pi$
$108$	−3.37849	−	3.37849i	−0.325096	−	0.325096i
$109$		−	12.1421i		−	1.16301i	−0.813544	−	0.581503i	$-0.802465\pi$
$109$		−	12.1421i		−	1.16301i	0.813544	−	0.581503i	$-0.197535\pi$
$110$		0			0
$111$			6.75699i			0.641345i
$112$	−0.941740	−	2.47247i	−0.0889861	−	0.233627i
$113$	−1.17157	+	1.17157i	−0.110212	+	0.110212i	−0.760062	−	0.649850i	$-0.774832\pi$
$113$	−1.17157	+	1.17157i	−0.110212	+	0.110212i	0.649850	+	0.760062i	$0.274832\pi$
$114$		−	2.58579i		−	0.242181i
$115$		0			0
$116$	0.828427			0.0769175
$117$	−1.75490	+	1.75490i	−0.162241	+	0.162241i
$118$	−6.53281	−	6.53281i	−0.601394	−	0.601394i
$119$	12.6173	+	5.65685i	1.15662	+	0.518563i
$120$		0			0
$121$	−3.00000			−0.272727
$122$	4.55374	−	4.55374i	0.412276	−	0.412276i
$123$	4.82843	−	4.82843i	0.435365	−	0.435365i
$124$	−1.53073			−0.137464
$125$		0			0
$126$	−1.00000	−	0.448342i	−0.0890871	−	0.0399414i
$127$	−3.58579	−	3.58579i	−0.318187	−	0.318187i	0.529883	−	0.848071i	$-0.322236\pi$
$127$	−3.58579	−	3.58579i	−0.318187	−	0.318187i	−0.848071	+	0.529883i	$0.822236\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	10.4525			0.920292
$130$		0			0
$131$		−	14.6508i		−	1.28004i	−0.768357	−	0.640021i	$-0.778926\pi$
$131$		−	14.6508i		−	1.28004i	0.768357	−	0.640021i	$-0.221074\pi$
$132$	3.69552	−	3.69552i	0.321654	−	0.321654i
$133$	1.31789	+	3.46002i	0.114275	+	0.300022i
$134$		−	14.8284i		−	1.28098i
$135$		0			0
$136$			5.22625i			0.448147i
$137$	8.17157	+	8.17157i	0.698145	+	0.698145i	0.964010	−	0.265866i	$-0.0856577\pi$
$137$	8.17157	+	8.17157i	0.698145	+	0.698145i	−0.265866	+	0.964010i	$0.585658\pi$
$138$	0.765367	+	0.765367i	0.0651524	+	0.0651524i
$139$	−8.60474			−0.729845			−0.364922	−	0.931038i	$-0.618905\pi$
$139$	−8.60474			−0.729845			−0.364922	+	0.931038i	$0.618905\pi$
$140$		0			0
$141$	2.82843			0.238197
$142$	−0.414214	−	0.414214i	−0.0347600	−	0.0347600i
$143$	11.9832	+	11.9832i	1.00209	+	1.00209i
$144$		−	0.414214i		−	0.0345178i
$145$		0			0
$146$		−	5.86030i		−	0.485002i
$147$	12.9129	+	0.743954i	1.06504	+	0.0613603i
$148$	2.58579	−	2.58579i	0.212550	−	0.212550i
$149$			17.3137i			1.41839i	0.705010	+	0.709197i	$0.250942\pi$
$149$			17.3137i			1.41839i	−0.705010	+	0.709197i	$0.749058\pi$
$150$		0			0
$151$	−8.82843			−0.718447			−0.359224	−	0.933252i	$-0.616958\pi$
$151$	−8.82843			−0.718447			−0.359224	+	0.933252i	$0.616958\pi$
$152$	−0.989538	+	0.989538i	−0.0802621	+	0.0802621i
$153$	1.53073	+	1.53073i	0.123752	+	0.123752i
$154$	−3.06147	+	6.82843i	−0.246700	+	0.550250i
$155$		0			0
$156$	11.0711			0.886395
$157$	−10.2283	+	10.2283i	−0.816310	+	0.816310i	−0.985571	−	0.169261i	$-0.945862\pi$
$157$	−10.2283	+	10.2283i	−0.816310	+	0.816310i	0.169261	+	0.985571i	$0.445862\pi$
$158$	−3.58579	+	3.58579i	−0.285270	+	0.285270i
$159$	−21.5391			−1.70816
$160$		0			0
$161$	−1.41421	−	0.634051i	−0.111456	−	0.0499702i
$162$	7.12132	+	7.12132i	0.559504	+	0.559504i
$163$	−13.6569	+	13.6569i	−1.06969	+	1.06969i	−0.0723048	+	0.997383i	$0.523035\pi$
$163$	−13.6569	+	13.6569i	−1.06969	+	1.06969i	−0.997383	+	0.0723048i	$0.976965\pi$
$164$	−3.69552			−0.288571
$165$		0			0
$166$		−	7.52235i		−	0.583848i
$167$	1.71644	−	1.71644i	0.132822	−	0.132822i	−0.637570	−	0.770392i	$-0.720060\pi$
$167$	1.71644	−	1.71644i	0.132822	−	0.132822i	0.770392	+	0.637570i	$0.220060\pi$
$168$	1.74011	+	4.56854i	0.134252	+	0.352470i
$169$			22.8995i			1.76150i
$170$		0			0
$171$			0.579658i			0.0443275i
$172$	−4.00000	−	4.00000i	−0.304997	−	0.304997i
$173$	−13.2898	−	13.2898i	−1.01040	−	1.01040i	−0.999945	−	0.0104595i	$-0.996671\pi$
$173$	−13.2898	−	13.2898i	−1.01040	−	1.01040i	−0.0104595	−	0.999945i	$-0.503329\pi$
$174$	−1.53073			−0.116045
$175$		0			0
$176$	−2.82843			−0.213201
$177$	12.0711	+	12.0711i	0.907317	+	0.907317i
$178$	8.02509	+	8.02509i	0.601506	+	0.601506i
$179$		−	13.6569i		−	1.02076i	−0.859949	−	0.510381i	$-0.829505\pi$
$179$		−	13.6569i		−	1.02076i	0.859949	−	0.510381i	$-0.170495\pi$
$180$		0			0
$181$		−	8.79045i		−	0.653389i	−0.945130	−	0.326695i	$-0.894065\pi$
$181$		−	8.79045i		−	0.653389i	0.945130	−	0.326695i	$-0.105935\pi$
$182$	−14.8141	+	5.64255i	−1.09810	+	0.418253i
$183$	−8.41421	+	8.41421i	−0.621997	+	0.621997i
$184$		−	0.585786i		−	0.0431847i
$185$		0			0
$186$	2.82843			0.207390
$187$	10.4525	−	10.4525i	0.764363	−	0.764363i
$188$	−1.08239	−	1.08239i	−0.0789416	−	0.0789416i
$189$	−11.5349	−	5.17157i	−0.839040	−	0.376177i
$190$		0			0
$191$	1.75736			0.127158			0.0635790	−	0.997977i	$-0.479749\pi$
$191$	1.75736			0.127158			0.0635790	+	0.997977i	$0.479749\pi$
$192$	−1.30656	+	1.30656i	−0.0942931	+	0.0942931i
$193$	−8.24264	+	8.24264i	−0.593318	+	0.593318i	−0.938526	−	0.345208i	$-0.887808\pi$
$193$	−8.24264	+	8.24264i	−0.593318	+	0.593318i	0.345208	+	0.938526i	$0.387808\pi$
$194$	6.49435			0.466267
$195$		0			0
$196$	−4.65685	−	5.22625i	−0.332632	−	0.373304i
$197$	−0.585786	−	0.585786i	−0.0417356	−	0.0417356i	0.685931	−	0.727667i	$-0.259395\pi$
$197$	−0.585786	−	0.585786i	−0.0417356	−	0.0417356i	−0.727667	+	0.685931i	$0.759395\pi$
$198$	−0.828427	+	0.828427i	−0.0588738	+	0.0588738i
$199$	28.0334			1.98724			0.993618	−	0.112798i	$-0.0359814\pi$
$199$	28.0334			1.98724			0.993618	+	0.112798i	$0.0359814\pi$
$200$		0			0
$201$			27.3994i			1.93260i
$202$	1.94061	−	1.94061i	0.136541	−	0.136541i
$203$	2.04826	−	0.780163i	0.143760	−	0.0547567i
$204$		−	9.65685i		−	0.676115i
$205$		0			0
$206$			14.1480i			0.985739i
$207$	−0.171573	−	0.171573i	−0.0119251	−	0.0119251i
$208$	−4.23671	−	4.23671i	−0.293763	−	0.293763i
$209$	3.95815			0.273791
$210$		0			0
$211$	−10.3431			−0.712052			−0.356026	−	0.934476i	$-0.615868\pi$
$211$	−10.3431			−0.712052			−0.356026	+	0.934476i	$0.615868\pi$
$212$	8.24264	+	8.24264i	0.566107	+	0.566107i
$213$	0.765367	+	0.765367i	0.0524421	+	0.0524421i
$214$			5.17157i			0.353521i
$215$		0			0
$216$		−	4.77791i		−	0.325096i
$217$	−3.78470	+	1.44155i	−0.256922	+	0.0978590i
$218$	8.58579	−	8.58579i	0.581503	−	0.581503i
$219$			10.8284i			0.731717i
$220$		0			0
$221$	31.3137			2.10639
$222$	−4.77791	+	4.77791i	−0.320672	+	0.320672i
$223$	−6.75699	−	6.75699i	−0.452481	−	0.452481i	0.443696	−	0.896177i	$-0.353667\pi$
$223$	−6.75699	−	6.75699i	−0.452481	−	0.452481i	−0.896177	+	0.443696i	$0.853667\pi$
$224$	1.08239	−	2.41421i	0.0723204	−	0.161306i
$225$		0			0
$226$	−1.65685			−0.110212
$227$	8.38057	−	8.38057i	0.556238	−	0.556238i	−0.371996	−	0.928234i	$-0.621327\pi$
$227$	8.38057	−	8.38057i	0.556238	−	0.556238i	0.928234	+	0.371996i	$0.121327\pi$
$228$	1.82843	−	1.82843i	0.121091	−	0.121091i
$229$	7.70806			0.509363			0.254682	−	0.967025i	$-0.418029\pi$
$229$	7.70806			0.509363			0.254682	+	0.967025i	$0.418029\pi$
$230$		0			0
$231$	5.65685	−	12.6173i	0.372194	−	0.830157i
$232$	0.585786	+	0.585786i	0.0384588	+	0.0384588i
$233$	−3.00000	+	3.00000i	−0.196537	+	0.196537i	−0.798513	−	0.601977i	$-0.794380\pi$
$233$	−3.00000	+	3.00000i	−0.196537	+	0.196537i	0.601977	+	0.798513i	$0.294380\pi$
$234$	−2.48181			−0.162241
$235$		0			0
$236$		−	9.23880i		−	0.601394i
$237$	6.62567	−	6.62567i	0.430383	−	0.430383i
$238$	4.92177	+	12.9218i	0.319031	+	0.837594i
$239$		−	6.48528i		−	0.419498i	−0.977755	−	0.209749i	$-0.932735\pi$
$239$		−	6.48528i		−	0.419498i	0.977755	−	0.209749i	$-0.0672647\pi$
$240$		0			0
$241$		−	6.75699i		−	0.435256i	−0.976032	−	0.217628i	$-0.930168\pi$
$241$		−	6.75699i		−	0.435256i	0.976032	−	0.217628i	$-0.0698319\pi$
$242$	−2.12132	−	2.12132i	−0.136364	−	0.136364i
$243$	−3.02301	−	3.02301i	−0.193926	−	0.193926i
$244$	6.43996			0.412276
$245$		0			0
$246$	6.82843			0.435365
$247$	5.92893	+	5.92893i	0.377249	+	0.377249i
$248$	−1.08239	−	1.08239i	−0.0687320	−	0.0687320i
$249$			13.8995i			0.880845i
$250$		0			0
$251$		−	14.0936i		−	0.889582i	−0.895634	−	0.444791i	$-0.853278\pi$
$251$		−	14.0936i		−	0.889582i	0.895634	−	0.444791i	$-0.146722\pi$
$252$	−0.390081	−	1.02413i	−0.0245728	−	0.0645143i
$253$	−1.17157	+	1.17157i	−0.0736562	+	0.0736562i
$254$		−	5.07107i		−	0.318187i
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.83938	−	7.83938i	0.489007	−	0.489007i	−0.418986	−	0.907993i	$-0.637614\pi$
$257$	7.83938	−	7.83938i	0.489007	−	0.489007i	0.907993	+	0.418986i	$0.137614\pi$
$258$	7.39104	+	7.39104i	0.460146	+	0.460146i
$259$	3.95815	−	8.82843i	0.245948	−	0.548572i
$260$		0			0
$261$	0.343146			0.0212402
$262$	10.3596	−	10.3596i	0.640021	−	0.640021i
$263$	19.4142	−	19.4142i	1.19713	−	1.19713i	0.222110	−	0.975022i	$-0.428706\pi$
$263$	19.4142	−	19.4142i	1.19713	−	1.19713i	0.975022	−	0.222110i	$-0.0712944\pi$
$264$	5.22625			0.321654
$265$		0			0
$266$	−1.51472	+	3.37849i	−0.0928734	+	0.207149i
$267$	−14.8284	−	14.8284i	−0.907485	−	0.907485i
$268$	10.4853	−	10.4853i	0.640490	−	0.640490i
$269$	−26.8966			−1.63992			−0.819958	−	0.572424i	$-0.806003\pi$
$269$	−26.8966			−1.63992			−0.819958	+	0.572424i	$0.806003\pi$
$270$		0			0
$271$			18.7402i			1.13839i	0.822203	+	0.569194i	$0.192745\pi$
$271$			18.7402i			1.13839i	−0.822203	+	0.569194i	$0.807255\pi$
$272$	−3.69552	+	3.69552i	−0.224074	+	0.224074i
$273$	27.3729	−	10.4261i	1.65668	−	0.631014i
$274$			11.5563i			0.698145i
$275$		0			0
$276$			1.08239i			0.0651524i
$277$	1.75736	+	1.75736i	0.105589	+	0.105589i	0.757928	−	0.652338i	$-0.226212\pi$
$277$	1.75736	+	1.75736i	0.105589	+	0.105589i	−0.652338	+	0.757928i	$0.726212\pi$
$278$	−6.08447	−	6.08447i	−0.364922	−	0.364922i
$279$	−0.634051			−0.0379596
$280$		0			0
$281$	−5.65685			−0.337460			−0.168730	−	0.985662i	$-0.553967\pi$
$281$	−5.65685			−0.337460			−0.168730	+	0.985662i	$0.553967\pi$
$282$	2.00000	+	2.00000i	0.119098	+	0.119098i
$283$	−3.15432	−	3.15432i	−0.187505	−	0.187505i	0.607112	−	0.794617i	$-0.292328\pi$
$283$	−3.15432	−	3.15432i	−0.187505	−	0.187505i	−0.794617	+	0.607112i	$0.792328\pi$
$284$		−	0.585786i		−	0.0347600i
$285$		0			0
$286$			16.9469i			1.00209i
$287$	−9.13707	+	3.48022i	−0.539344	+	0.205431i
$288$	0.292893	−	0.292893i	0.0172589	−	0.0172589i
$289$		−	10.3137i		−	0.606689i
$290$		0			0
$291$	−12.0000			−0.703452
$292$	4.14386	−	4.14386i	0.242501	−	0.242501i
$293$	2.38896	+	2.38896i	0.139564	+	0.139564i	0.773437	−	0.633873i	$-0.218536\pi$
$293$	2.38896	+	2.38896i	0.139564	+	0.139564i	−0.633873	+	0.773437i	$0.718536\pi$
$294$	8.60474	+	9.65685i	0.501839	+	0.563199i
$295$		0			0
$296$	3.65685			0.212550
$297$	−9.55582	+	9.55582i	−0.554485	+	0.554485i
$298$	−12.2426	+	12.2426i	−0.709197	+	0.709197i
$299$	−3.50981			−0.202977
$300$		0			0
$301$	−13.6569	−	6.12293i	−0.787168	−	0.352920i
$302$	−6.24264	−	6.24264i	−0.359224	−	0.359224i
$303$	−3.58579	+	3.58579i	−0.205998	+	0.205998i
$304$	−1.39942			−0.0802621
$305$		0			0
$306$			2.16478i			0.123752i
$307$	−23.1626	+	23.1626i	−1.32196	+	1.32196i	−0.409776	+	0.912186i	$0.634393\pi$
$307$	−23.1626	+	23.1626i	−1.32196	+	1.32196i	−0.912186	+	0.409776i	$0.865607\pi$
$308$	−6.99321	+	2.66364i	−0.398475	+	0.151775i
$309$		−	26.1421i		−	1.48717i
$310$		0			0
$311$			3.43289i			0.194661i	0.995252	+	0.0973305i	$0.0310304\pi$
$311$			3.43289i			0.194661i	−0.995252	+	0.0973305i	$0.968970\pi$
$312$	7.82843	+	7.82843i	0.443197	+	0.443197i
$313$	6.75699	+	6.75699i	0.381927	+	0.381927i	0.871796	−	0.489869i	$-0.162955\pi$
$313$	6.75699	+	6.75699i	0.381927	+	0.381927i	−0.489869	+	0.871796i	$0.662955\pi$
$314$	−14.4650			−0.816310
$315$		0			0
$316$	−5.07107			−0.285270
$317$	−21.8995	−	21.8995i	−1.23000	−	1.23000i	−0.963963	−	0.266035i	$-0.914286\pi$
$317$	−21.8995	−	21.8995i	−1.23000	−	1.23000i	−0.266035	−	0.963963i	$-0.585714\pi$
$318$	−15.2304	−	15.2304i	−0.854079	−	0.854079i
$319$		−	2.34315i		−	0.131191i
$320$		0			0
$321$		−	9.55582i		−	0.533354i
$322$	−0.551658	−	1.44834i	−0.0307427	−	0.0807129i
$323$	5.17157	−	5.17157i	0.287754	−	0.287754i
$324$			10.0711i			0.559504i
$325$		0			0
$326$	−19.3137			−1.06969
$327$	−15.8645	+	15.8645i	−0.877307	+	0.877307i
$328$	−2.61313	−	2.61313i	−0.144286	−	0.144286i
$329$	−3.69552	−	1.65685i	−0.203741	−	0.0913453i
$330$		0			0
$331$	23.3137			1.28144			0.640719	−	0.767776i	$-0.278637\pi$
$331$	23.3137			1.28144			0.640719	+	0.767776i	$0.278637\pi$
$332$	5.31911	−	5.31911i	0.291924	−	0.291924i
$333$	1.07107	−	1.07107i	0.0586942	−	0.0586942i
$334$	2.42742			0.132822
$335$		0			0
$336$	−2.00000	+	4.46088i	−0.109109	+	0.243361i
$337$	−3.75736	−	3.75736i	−0.204676	−	0.204676i	0.597324	−	0.802000i	$-0.296231\pi$
$337$	−3.75736	−	3.75736i	−0.204676	−	0.204676i	−0.802000	+	0.597324i	$0.796231\pi$
$338$	−16.1924	+	16.1924i	−0.880750	+	0.880750i
$339$	3.06147			0.166276
$340$		0			0
$341$			4.32957i			0.234459i
$342$	−0.409880	+	0.409880i	−0.0221638	+	0.0221638i
$343$	−16.4357	−	8.53622i	−0.887445	−	0.460913i
$344$		−	5.65685i		−	0.304997i
$345$		0			0
$346$		−	18.7946i		−	1.01040i
$347$	5.31371	+	5.31371i	0.285255	+	0.285255i	0.835200	−	0.549946i	$-0.185352\pi$
$347$	5.31371	+	5.31371i	0.285255	+	0.285255i	−0.549946	+	0.835200i	$0.685352\pi$
$348$	−1.08239	−	1.08239i	−0.0580223	−	0.0580223i
$349$	2.66752			0.142789			0.0713945	−	0.997448i	$-0.477255\pi$
$349$	2.66752			0.142789			0.0713945	+	0.997448i	$0.477255\pi$
$350$		0			0
$351$	−28.6274			−1.52802
$352$	−2.00000	−	2.00000i	−0.106600	−	0.106600i
$353$	−8.47343	−	8.47343i	−0.450995	−	0.450995i	0.444690	−	0.895685i	$-0.353314\pi$
$353$	−8.47343	−	8.47343i	−0.450995	−	0.450995i	−0.895685	+	0.444690i	$0.853314\pi$
$354$			17.0711i			0.907317i
$355$		0			0
$356$			11.3492i			0.601506i
$357$	−9.09425	−	23.8763i	−0.481318	−	1.26367i
$358$	9.65685	−	9.65685i	0.510381	−	0.510381i
$359$		−	16.9706i		−	0.895672i	−0.894116	−	0.447836i	$-0.852195\pi$
$359$		−	16.9706i		−	0.895672i	0.894116	−	0.447836i	$-0.147805\pi$
$360$		0			0
$361$	−17.0416			−0.896928
$362$	6.21579	−	6.21579i	0.326695	−	0.326695i
$363$	3.91969	+	3.91969i	0.205730	+	0.205730i
$364$	−14.4650	−	6.48528i	−0.758174	−	0.339921i
$365$		0			0
$366$	−11.8995			−0.621997
$367$	−3.06147	+	3.06147i	−0.159807	+	0.159807i	−0.782481	−	0.622674i	$-0.786046\pi$
$367$	−3.06147	+	3.06147i	−0.159807	+	0.159807i	0.622674	+	0.782481i	$0.286046\pi$
$368$	0.414214	−	0.414214i	0.0215924	−	0.0215924i
$369$	−1.53073			−0.0796868
$370$		0			0
$371$	28.1421	+	12.6173i	1.46107	+	0.655057i
$372$	2.00000	+	2.00000i	0.103695	+	0.103695i
$373$	15.0711	−	15.0711i	0.780350	−	0.780350i	−0.199539	−	0.979890i	$-0.563945\pi$
$373$	15.0711	−	15.0711i	0.780350	−	0.780350i	0.979890	+	0.199539i	$0.0639446\pi$
$374$	14.7821			0.764363
$375$		0			0
$376$		−	1.53073i		−	0.0789416i
$377$	3.50981	−	3.50981i	0.180764	−	0.180764i
$378$	−4.49955	−	11.8133i	−0.231432	−	0.607608i
$379$			6.14214i			0.315500i	0.987479	+	0.157750i	$0.0504241\pi$
$379$			6.14214i			0.315500i	−0.987479	+	0.157750i	$0.949576\pi$
$380$		0			0
$381$			9.37011i			0.480045i
$382$	1.24264	+	1.24264i	0.0635790	+	0.0635790i
$383$	10.6382	+	10.6382i	0.543587	+	0.543587i	0.924579	−	0.380991i	$-0.124417\pi$
$383$	10.6382	+	10.6382i	0.543587	+	0.543587i	−0.380991	+	0.924579i	$0.624417\pi$
$384$	−1.84776			−0.0942931
$385$		0			0
$386$	−11.6569			−0.593318
$387$	−1.65685	−	1.65685i	−0.0842226	−	0.0842226i
$388$	4.59220	+	4.59220i	0.233134	+	0.233134i
$389$			0.142136i			0.00720656i	0.999994	+	0.00360328i	$0.00114696\pi$
$389$			0.142136i			0.00720656i	−0.999994	+	0.00360328i	$0.998853\pi$
$390$		0			0
$391$			3.06147i			0.154825i
$392$	0.402625	−	6.98841i	0.0203356	−	0.352968i
$393$	−19.1421	+	19.1421i	−0.965593	+	0.965593i
$394$		−	0.828427i		−	0.0417356i
$395$		0			0
$396$	−1.17157			−0.0588738
$397$	−1.12085	+	1.12085i	−0.0562540	+	0.0562540i	−0.734674	−	0.678420i	$-0.762665\pi$
$397$	−1.12085	+	1.12085i	−0.0562540	+	0.0562540i	0.678420	+	0.734674i	$0.262665\pi$
$398$	19.8226	+	19.8226i	0.993618	+	0.993618i
$399$	2.79884	−	6.24264i	0.140117	−	0.312523i
$400$		0			0
$401$	−19.7574			−0.986635			−0.493318	−	0.869849i	$-0.664216\pi$
$401$	−19.7574			−0.986635			−0.493318	+	0.869849i	$0.664216\pi$
$402$	−19.3743	+	19.3743i	−0.966301	+	0.966301i
$403$	−6.48528	+	6.48528i	−0.323055	+	0.323055i
$404$	2.74444			0.136541
$405$		0			0
$406$	2.00000	+	0.896683i	0.0992583	+	0.0445016i
$407$	−7.31371	−	7.31371i	−0.362527	−	0.362527i
$408$	6.82843	−	6.82843i	0.338058	−	0.338058i
$409$	−24.9719			−1.23478			−0.617392	−	0.786656i	$-0.711811\pi$
$409$	−24.9719			−1.23478			−0.617392	+	0.786656i	$0.711811\pi$
$410$		0			0
$411$		−	21.3533i		−	1.05328i
$412$	−10.0042	+	10.0042i	−0.492870	+	0.492870i
$413$	−8.70054	−	22.8427i	−0.428126	−	1.12401i
$414$		−	0.242641i		−	0.0119251i
$415$		0			0
$416$		−	5.99162i		−	0.293763i
$417$	11.2426	+	11.2426i	0.550554	+	0.550554i
$418$	2.79884	+	2.79884i	0.136895	+	0.136895i
$419$	11.5893			0.566174			0.283087	−	0.959094i	$-0.408642\pi$
$419$	11.5893			0.566174			0.283087	+	0.959094i	$0.408642\pi$
$420$		0			0
$421$	17.7990			0.867470			0.433735	−	0.901041i	$-0.357195\pi$
$421$	17.7990			0.867470			0.433735	+	0.901041i	$0.357195\pi$
$422$	−7.31371	−	7.31371i	−0.356026	−	0.356026i
$423$	−0.448342	−	0.448342i	−0.0217991	−	0.0217991i
$424$			11.6569i			0.566107i
$425$		0			0
$426$			1.08239i			0.0524421i
$427$	15.9226	−	6.06477i	0.770550	−	0.293495i
$428$	−3.65685	+	3.65685i	−0.176761	+	0.176761i
$429$		−	31.3137i		−	1.51184i
$430$		0			0
$431$	5.65685			0.272481			0.136241	−	0.990676i	$-0.456498\pi$
$431$	5.65685			0.272481			0.136241	+	0.990676i	$0.456498\pi$
$432$	3.37849	−	3.37849i	0.162548	−	0.162548i
$433$	10.4525	+	10.4525i	0.502315	+	0.502315i	0.912157	−	0.409841i	$-0.134416\pi$
$433$	10.4525	+	10.4525i	0.502315	+	0.502315i	−0.409841	+	0.912157i	$0.634416\pi$
$434$	−3.69552	−	1.65685i	−0.177391	−	0.0795315i
$435$		0			0
$436$	12.1421			0.581503
$437$	−0.579658	+	0.579658i	−0.0277288	+	0.0277288i
$438$	−7.65685	+	7.65685i	−0.365859	+	0.365859i
$439$	−13.8854			−0.662713			−0.331357	−	0.943506i	$-0.607506\pi$
$439$	−13.8854			−0.662713			−0.331357	+	0.943506i	$0.607506\pi$
$440$		0			0
$441$	−1.92893	−	2.16478i	−0.0918539	−	0.103085i
$442$	22.1421	+	22.1421i	1.05319	+	1.05319i
$443$	4.14214	−	4.14214i	0.196799	−	0.196799i	−0.601827	−	0.798626i	$-0.705560\pi$
$443$	4.14214	−	4.14214i	0.196799	−	0.196799i	0.798626	+	0.601827i	$0.205560\pi$
$444$	−6.75699			−0.320672
$445$		0			0
$446$		−	9.55582i		−	0.452481i
$447$	22.6215	−	22.6215i	1.06996	−	1.06996i
$448$	2.47247	−	0.941740i	0.116813	−	0.0444930i
$449$			25.6569i			1.21082i	0.795913	+	0.605411i	$0.206991\pi$
$449$			25.6569i			1.21082i	−0.795913	+	0.605411i	$0.793009\pi$
$450$		0			0
$451$			10.4525i			0.492189i
$452$	−1.17157	−	1.17157i	−0.0551062	−	0.0551062i
$453$	11.5349	+	11.5349i	0.541957	+	0.541957i
$454$	11.8519			0.556238
$455$		0			0
$456$	2.58579			0.121091
$457$	1.65685	+	1.65685i	0.0775044	+	0.0775044i	0.744796	−	0.667292i	$-0.232547\pi$
$457$	1.65685	+	1.65685i	0.0775044	+	0.0775044i	−0.667292	+	0.744796i	$0.732547\pi$
$458$	5.45042	+	5.45042i	0.254682	+	0.254682i
$459$			24.9706i			1.16553i
$460$		0			0
$461$			34.0250i			1.58470i	0.610064	+	0.792352i	$0.291144\pi$
$461$			34.0250i			1.58470i	−0.610064	+	0.792352i	$0.708856\pi$
$462$	12.9218	−	4.92177i	0.601175	−	0.228981i
$463$	12.9706	−	12.9706i	0.602793	−	0.602793i	−0.338260	−	0.941053i	$-0.609838\pi$
$463$	12.9706	−	12.9706i	0.602793	−	0.602793i	0.941053	+	0.338260i	$0.109838\pi$
$464$			0.828427i			0.0384588i
$465$		0			0
$466$	−4.24264			−0.196537
$467$	−17.4337	+	17.4337i	−0.806734	+	0.806734i	−0.984138	−	0.177404i	$-0.943230\pi$
$467$	−17.4337	+	17.4337i	−0.806734	+	0.806734i	0.177404	+	0.984138i	$0.443230\pi$
$468$	−1.75490	−	1.75490i	−0.0811205	−	0.0811205i
$469$	16.0502	−	35.7990i	0.741128	−	1.65304i
$470$		0			0
$471$	26.7279			1.23156
$472$	6.53281	−	6.53281i	0.300697	−	0.300697i
$473$	−11.3137	+	11.3137i	−0.520205	+	0.520205i
$474$	9.37011			0.430383
$475$		0			0
$476$	−5.65685	+	12.6173i	−0.259281	+	0.578312i
$477$	3.41421	+	3.41421i	0.156326	+	0.156326i
$478$	4.58579	−	4.58579i	0.209749	−	0.209749i
$479$	−11.0866			−0.506558			−0.253279	−	0.967393i	$-0.581509\pi$
$479$	−11.0866			−0.506558			−0.253279	+	0.967393i	$0.581509\pi$
$480$		0			0
$481$		−	21.9105i		−	0.999032i
$482$	4.77791	−	4.77791i	0.217628	−	0.217628i
$483$	1.01933	+	2.67619i	0.0463812	+	0.121771i
$484$		−	3.00000i		−	0.136364i
$485$		0			0
$486$		−	4.27518i		−	0.193926i
$487$	−1.10051	−	1.10051i	−0.0498686	−	0.0498686i	0.681733	−	0.731601i	$-0.261227\pi$
$487$	−1.10051	−	1.10051i	−0.0498686	−	0.0498686i	−0.731601	+	0.681733i	$0.761227\pi$
$488$	4.55374	+	4.55374i	0.206138	+	0.206138i
$489$	35.6871			1.61383
$490$		0			0
$491$	25.1716			1.13598			0.567989	−	0.823036i	$-0.307722\pi$
$491$	25.1716			1.13598			0.567989	+	0.823036i	$0.307722\pi$
$492$	4.82843	+	4.82843i	0.217682	+	0.217682i
$493$	−3.06147	−	3.06147i	−0.137882	−	0.137882i
$494$			8.38478i			0.377249i
$495$		0			0
$496$		−	1.53073i		−	0.0687320i
$497$	−0.551658	−	1.44834i	−0.0247453	−	0.0649670i
$498$	−9.82843	+	9.82843i	−0.440422	+	0.440422i
$499$			7.51472i			0.336405i	0.985752	+	0.168203i	$0.0537963\pi$
$499$			7.51472i			0.336405i	−0.985752	+	0.168203i	$0.946204\pi$
$500$		0			0
$501$	−4.48528			−0.200388
$502$	9.96570	−	9.96570i	0.444791	−	0.444791i
$503$	−18.1062	−	18.1062i	−0.807314	−	0.807314i	0.176912	−	0.984227i	$-0.443389\pi$
$503$	−18.1062	−	18.1062i	−0.807314	−	0.807314i	−0.984227	+	0.176912i	$0.943389\pi$
$504$	0.448342	−	1.00000i	0.0199707	−	0.0445435i
$505$		0			0
$506$	−1.65685			−0.0736562
$507$	29.9196	−	29.9196i	1.32878	−	1.32878i
$508$	3.58579	−	3.58579i	0.159094	−	0.159094i
$509$	14.4650			0.641152			0.320576	−	0.947223i	$-0.396124\pi$
$509$	14.4650			0.641152			0.320576	+	0.947223i	$0.396124\pi$
$510$		0			0
$511$	6.34315	−	14.1480i	0.280604	−	0.625872i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.72792	+	4.72792i	−0.208743	+	0.208743i
$514$	11.0866			0.489007
$515$		0			0
$516$			10.4525i			0.460146i
$517$	−3.06147	+	3.06147i	−0.134643	+	0.134643i
$518$	9.04148	−	3.44381i	0.397260	−	0.151312i
$519$			34.7279i			1.52439i
$520$		0			0
$521$		−	36.6925i		−	1.60753i	−0.594947	−	0.803765i	$-0.702827\pi$
$521$		−	36.6925i		−	1.60753i	0.594947	−	0.803765i	$-0.297173\pi$
$522$	0.242641	+	0.242641i	0.0106201	+	0.0106201i
$523$	−1.75490	−	1.75490i	−0.0767366	−	0.0767366i	0.667697	−	0.744433i	$-0.267280\pi$
$523$	−1.75490	−	1.75490i	−0.0767366	−	0.0767366i	−0.744433	+	0.667697i	$0.767280\pi$
$524$	14.6508			0.640021
$525$		0			0
$526$	27.4558			1.19713
$527$	5.65685	+	5.65685i	0.246416	+	0.246416i
$528$	3.69552	+	3.69552i	0.160827	+	0.160827i
$529$			22.6569i			0.985081i
$530$		0			0
$531$		−	3.82683i		−	0.166070i
$532$	−3.46002	+	1.31789i	−0.150011	+	0.0571377i
$533$	−15.6569	+	15.6569i	−0.678174	+	0.678174i
$534$		−	20.9706i		−	0.907485i
$535$		0			0
$536$	14.8284			0.640490
$537$	−17.8435	+	17.8435i	−0.770006	+	0.770006i
$538$	−19.0188	−	19.0188i	−0.819958	−	0.819958i
$539$	−14.7821	+	13.1716i	−0.636709	+	0.567340i
$540$		0			0
$541$	10.9706			0.471661			0.235831	−	0.971794i	$-0.424219\pi$
$541$	10.9706			0.471661			0.235831	+	0.971794i	$0.424219\pi$
$542$	−13.2513	+	13.2513i	−0.569194	+	0.569194i
$543$	−11.4853	+	11.4853i	−0.492881	+	0.492881i
$544$	−5.22625			−0.224074
$545$		0			0
$546$	26.7279	+	11.9832i	1.14385	+	0.512835i
$547$	30.6274	+	30.6274i	1.30953	+	1.30953i	0.921751	+	0.387783i	$0.126759\pi$
$547$	30.6274	+	30.6274i	1.30953	+	1.30953i	0.387783	+	0.921751i	$0.373241\pi$
$548$	−8.17157	+	8.17157i	−0.349072	+	0.349072i
$549$	2.66752			0.113847
$550$		0			0
$551$		−	1.15932i		−	0.0493885i
$552$	−0.765367	+	0.765367i	−0.0325762	+	0.0325762i
$553$	−12.5381	+	4.77563i	−0.533173	+	0.203080i
$554$			2.48528i			0.105589i
$555$		0			0
$556$		−	8.60474i		−	0.364922i
$557$	26.7279	+	26.7279i	1.13250	+	1.13250i	0.989761	+	0.142738i	$0.0455906\pi$
$557$	26.7279	+	26.7279i	1.13250	+	1.13250i	0.142738	+	0.989761i	$0.454409\pi$
$558$	−0.448342	−	0.448342i	−0.0189798	−	0.0189798i
$559$	−33.8937			−1.43355
$560$		0			0
$561$	−27.3137			−1.15319
$562$	−4.00000	−	4.00000i	−0.168730	−	0.168730i
$563$	−3.54827	−	3.54827i	−0.149542	−	0.149542i	0.628372	−	0.777913i	$-0.283722\pi$
$563$	−3.54827	−	3.54827i	−0.149542	−	0.149542i	−0.777913	+	0.628372i	$0.783722\pi$
$564$			2.82843i			0.119098i
$565$		0			0
$566$		−	4.46088i		−	0.187505i
$567$	9.48433	+	24.9004i	0.398304	+	1.04572i
$568$	0.414214	−	0.414214i	0.0173800	−	0.0173800i
$569$			1.41421i			0.0592869i	0.999561	+	0.0296435i	$0.00943719\pi$
$569$			1.41421i			0.0592869i	−0.999561	+	0.0296435i	$0.990563\pi$
$570$		0			0
$571$	−25.4558			−1.06529			−0.532647	−	0.846338i	$-0.678803\pi$
$571$	−25.4558			−1.06529			−0.532647	+	0.846338i	$0.678803\pi$
$572$	−11.9832	+	11.9832i	−0.501044	+	0.501044i
$573$	−2.29610	−	2.29610i	−0.0959210	−	0.0959210i
$574$	−8.92177	−	4.00000i	−0.372387	−	0.166957i
$575$		0			0
$576$	0.414214			0.0172589
$577$	26.3170	−	26.3170i	1.09559	−	1.09559i	0.100670	−	0.994920i	$-0.467901\pi$
$577$	26.3170	−	26.3170i	1.09559	−	1.09559i	0.994920	−	0.100670i	$-0.0320986\pi$
$578$	7.29289	−	7.29289i	0.303344	−	0.303344i
$579$	21.5391			0.895133
$580$		0			0
$581$	8.14214	−	18.1606i	0.337793	−	0.753427i
$582$	−8.48528	−	8.48528i	−0.351726	−	0.351726i
$583$	23.3137	−	23.3137i	0.965555	−	0.965555i
$584$	5.86030			0.242501
$585$		0			0
$586$			3.37849i			0.139564i
$587$	−16.0886	+	16.0886i	−0.664049	+	0.664049i	−0.956332	−	0.292283i	$-0.905585\pi$
$587$	−16.0886	+	16.0886i	−0.664049	+	0.664049i	0.292283	+	0.956332i	$0.405585\pi$
$588$	−0.743954	+	12.9129i	−0.0306801	+	0.532519i
$589$			2.14214i			0.0882652i
$590$		0			0
$591$			1.53073i			0.0629660i
$592$	2.58579	+	2.58579i	0.106275	+	0.106275i
$593$	22.8841	+	22.8841i	0.939737	+	0.939737i	0.998285	−	0.0585480i	$-0.0186471\pi$
$593$	22.8841	+	22.8841i	0.939737	+	0.939737i	−0.0585480	+	0.998285i	$0.518647\pi$
$594$	−13.5140			−0.554485
$595$		0			0
$596$	−17.3137			−0.709197
$597$	−36.6274	−	36.6274i	−1.49906	−	1.49906i
$598$	−2.48181	−	2.48181i	−0.101489	−	0.101489i
$599$			18.5269i			0.756989i	0.925604	+	0.378495i	$0.123558\pi$
$599$			18.5269i			0.756989i	−0.925604	+	0.378495i	$0.876442\pi$
$600$		0			0
$601$			16.5754i			0.676126i	0.941123	+	0.338063i	$0.109772\pi$
$601$			16.5754i			0.676126i	−0.941123	+	0.338063i	$0.890228\pi$
$602$	−5.32729	−	13.9864i	−0.217124	−	0.570044i
$603$	4.34315	−	4.34315i	0.176867	−	0.176867i
$604$		−	8.82843i		−	0.359224i
$605$		0			0
$606$	−5.07107			−0.205998
$607$	21.5391	−	21.5391i	0.874243	−	0.874243i	−0.118688	−	0.992932i	$-0.537869\pi$
$607$	21.5391	−	21.5391i	0.874243	−	0.874243i	0.992932	+	0.118688i	$0.0378689\pi$
$608$	−0.989538	−	0.989538i	−0.0401311	−	0.0401311i
$609$	−3.69552	−	1.65685i	−0.149750	−	0.0671391i
$610$		0			0
$611$	−9.17157			−0.371042
$612$	−1.53073	+	1.53073i	−0.0618762	+	0.0618762i
$613$	−19.8995	+	19.8995i	−0.803733	+	0.803733i	−0.983677	−	0.179944i	$-0.942408\pi$
$613$	−19.8995	+	19.8995i	−0.803733	+	0.803733i	0.179944	+	0.983677i	$0.442408\pi$
$614$	−32.7569			−1.32196
$615$		0			0
$616$	−6.82843	−	3.06147i	−0.275125	−	0.123350i
$617$	28.4853	+	28.4853i	1.14677	+	1.14677i	0.987183	+	0.159591i	$0.0510176\pi$
$617$	28.4853	+	28.4853i	1.14677	+	1.14677i	0.159591	+	0.987183i	$0.448982\pi$
$618$	18.4853	−	18.4853i	0.743587	−	0.743587i
$619$	−0.688444			−0.0276709			−0.0138354	−	0.999904i	$-0.504404\pi$
$619$	−0.688444			−0.0276709			−0.0138354	+	0.999904i	$0.504404\pi$
$620$		0			0
$621$		−	2.79884i		−	0.112313i
$622$	−2.42742	+	2.42742i	−0.0973305	+	0.0973305i
$623$	10.6880	+	28.0606i	0.428205	+	1.12422i
$624$			11.0711i			0.443197i
$625$		0			0
$626$			9.55582i			0.381927i
$627$	−5.17157	−	5.17157i	−0.206533	−	0.206533i
$628$	−10.2283	−	10.2283i	−0.408155	−	0.408155i
$629$	−19.1116			−0.762031
$630$		0			0
$631$	41.3553			1.64633			0.823165	−	0.567802i	$-0.192206\pi$
$631$	41.3553			1.64633			0.823165	+	0.567802i	$0.192206\pi$
$632$	−3.58579	−	3.58579i	−0.142635	−	0.142635i
$633$	13.5140	+	13.5140i	0.537132	+	0.537132i
$634$		−	30.9706i		−	1.23000i
$635$		0			0
$636$		−	21.5391i		−	0.854079i
$637$	−41.8719	−	2.41237i	−1.65902	−	0.0955818i
$638$	1.65685	−	1.65685i	0.0655955	−	0.0655955i
$639$		−	0.242641i		−	0.00959872i
$640$		0			0
$641$	−37.2132			−1.46983			−0.734917	−	0.678158i	$-0.762779\pi$
$641$	−37.2132			−1.46983			−0.734917	+	0.678158i	$0.762779\pi$
$642$	6.75699	−	6.75699i	0.266677	−	0.266677i
$643$	20.9435	+	20.9435i	0.825930	+	0.825930i	0.986951	−	0.161021i	$-0.0514787\pi$
$643$	20.9435	+	20.9435i	0.825930	+	0.825930i	−0.161021	+	0.986951i	$0.551479\pi$
$644$	0.634051	−	1.41421i	0.0249851	−	0.0557278i
$645$		0			0
$646$	7.31371			0.287754
$647$	−23.8896	+	23.8896i	−0.939195	+	0.939195i	−0.998254	−	0.0590593i	$-0.981190\pi$
$647$	−23.8896	+	23.8896i	−0.939195	+	0.939195i	0.0590593	+	0.998254i	$0.481190\pi$
$648$	−7.12132	+	7.12132i	−0.279752	+	0.279752i
$649$	−26.1313			−1.02574
$650$		0			0
$651$	6.82843	+	3.06147i	0.267627	+	0.119988i
$652$	−13.6569	−	13.6569i	−0.534844	−	0.534844i
$653$	−8.72792	+	8.72792i	−0.341550	+	0.341550i	−0.856950	−	0.515400i	$-0.827643\pi$
$653$	−8.72792	+	8.72792i	−0.341550	+	0.341550i	0.515400	+	0.856950i	$0.327643\pi$
$654$	−22.4357			−0.877307
$655$		0			0
$656$		−	3.69552i		−	0.144286i
$657$	1.71644	−	1.71644i	0.0669648	−	0.0669648i
$658$	−1.44155	−	3.78470i	−0.0561976	−	0.147543i
$659$		−	29.6569i		−	1.15527i	−0.816296	−	0.577634i	$-0.803976\pi$
$659$		−	29.6569i		−	1.15527i	0.816296	−	0.577634i	$-0.196024\pi$
$660$		0			0
$661$			47.5390i			1.84905i	0.381118	+	0.924526i	$0.375539\pi$
$661$			47.5390i			1.84905i	−0.381118	+	0.924526i	$0.624461\pi$
$662$	16.4853	+	16.4853i	0.640719	+	0.640719i
$663$	−40.9133	−	40.9133i	−1.58894	−	1.58894i
$664$	7.52235			0.291924
$665$		0			0
$666$	1.51472			0.0586942
$667$	0.343146	+	0.343146i	0.0132867	+	0.0132867i
$668$	1.71644	+	1.71644i	0.0664112	+	0.0664112i
$669$			17.6569i			0.682653i
$670$		0			0
$671$		−	18.2150i		−	0.703181i
$672$	−4.56854	+	1.74011i	−0.176235	+	0.0671261i
$673$	22.7990	−	22.7990i	0.878836	−	0.878836i	−0.114578	−	0.993414i	$-0.536552\pi$
$673$	22.7990	−	22.7990i	0.878836	−	0.878836i	0.993414	+	0.114578i	$0.0365515\pi$
$674$		−	5.31371i		−	0.204676i
$675$		0			0
$676$	−22.8995			−0.880750
$677$	22.4742	−	22.4742i	0.863754	−	0.863754i	−0.128018	−	0.991772i	$-0.540862\pi$
$677$	22.4742	−	22.4742i	0.863754	−	0.863754i	0.991772	+	0.128018i	$0.0408615\pi$
$678$	2.16478	+	2.16478i	0.0831380	+	0.0831380i
$679$	15.6788	+	7.02944i	0.601695	+	0.269765i
$680$		0			0
$681$	−21.8995			−0.839190
$682$	−3.06147	+	3.06147i	−0.117230	+	0.117230i
$683$	25.3137	−	25.3137i	0.968602	−	0.968602i	−0.0309197	−	0.999522i	$-0.509844\pi$
$683$	25.3137	−	25.3137i	0.968602	−	0.968602i	0.999522	+	0.0309197i	$0.00984363\pi$
$684$	−0.579658			−0.0221638
$685$		0			0
$686$	−5.58579	−	17.6578i	−0.213266	−	0.674179i
$687$	−10.0711	−	10.0711i	−0.384235	−	0.384235i
$688$	4.00000	−	4.00000i	0.152499	−	0.152499i
$689$	69.8434			2.66082
$690$		0			0
$691$			25.1033i			0.954973i	0.878639	+	0.477487i	$0.158452\pi$
$691$			25.1033i			0.954973i	−0.878639	+	0.477487i	$0.841548\pi$
$692$	13.2898	−	13.2898i	0.505202	−	0.505202i
$693$	−2.89668	+	1.10332i	−0.110036	+	0.0419115i
$694$			7.51472i			0.285255i
$695$		0			0
$696$		−	1.53073i		−	0.0580223i
$697$	13.6569	+	13.6569i	0.517290	+	0.517290i
$698$	1.88622	+	1.88622i	0.0713945	+	0.0713945i
$699$	7.83938			0.296512
$700$		0			0
$701$	−13.1127			−0.495260			−0.247630	−	0.968855i	$-0.579652\pi$
$701$	−13.1127			−0.495260			−0.247630	+	0.968855i	$0.579652\pi$
$702$	−20.2426	−	20.2426i	−0.764009	−	0.764009i
$703$	−3.61859	−	3.61859i	−0.136478	−	0.136478i
$704$		−	2.82843i		−	0.106600i
$705$		0			0
$706$		−	11.9832i		−	0.450995i
$707$	6.78556	−	2.58455i	0.255197	−	0.0972020i
$708$	−12.0711	+	12.0711i	−0.453659	+	0.453659i
$709$		−	41.3137i		−	1.55157i	−0.630998	−	0.775784i	$-0.717354\pi$
$709$		−	41.3137i		−	1.55157i	0.630998	−	0.775784i	$-0.282646\pi$
$710$		0			0
$711$	−2.10051			−0.0787751
$712$	−8.02509	+	8.02509i	−0.300753	+	0.300753i
$713$	−0.634051	−	0.634051i	−0.0237454	−	0.0237454i
$714$	10.4525	−	23.3137i	0.391175	−	0.872494i
$715$		0			0
$716$	13.6569			0.510381
$717$	−8.47343	+	8.47343i	−0.316446	+	0.316446i
$718$	12.0000	−	12.0000i	0.447836	−	0.447836i
$719$	43.7122			1.63019			0.815094	−	0.579328i	$-0.196685\pi$
$719$	43.7122			1.63019			0.815094	+	0.579328i	$0.196685\pi$
$720$		0			0
$721$	−15.3137	+	34.1563i	−0.570312	+	1.27205i
$722$	−12.0503	−	12.0503i	−0.448464	−	0.448464i
$723$	−8.82843	+	8.82843i	−0.328333	+	0.328333i
$724$	8.79045			0.326695
$725$		0			0
$726$			5.54328i			0.205730i
$727$	22.8841	−	22.8841i	0.848724	−	0.848724i	−0.141250	−	0.989974i	$-0.545112\pi$
$727$	22.8841	−	22.8841i	0.848724	−	0.848724i	0.989974	+	0.141250i	$0.0451122\pi$
$728$	−5.64255	−	14.8141i	−0.209127	−	0.549048i
$729$		−	22.3137i		−	0.826434i
$730$		0			0
$731$			29.5641i			1.09347i
$732$	−8.41421	−	8.41421i	−0.310998	−	0.310998i
$733$	−21.9489	−	21.9489i	−0.810703	−	0.810703i	0.174037	−	0.984739i	$-0.444319\pi$
$733$	−21.9489	−	21.9489i	−0.810703	−	0.810703i	−0.984739	+	0.174037i	$0.944319\pi$
$734$	−4.32957			−0.159807
$735$		0			0
$736$	0.585786			0.0215924
$737$	−29.6569	−	29.6569i	−1.09242	−	1.09242i
$738$	−1.08239	−	1.08239i	−0.0398434	−	0.0398434i
$739$		−	9.65685i		−	0.355233i	−0.984100	−	0.177617i	$-0.943161\pi$
$739$		−	9.65685i		−	0.355233i	0.984100	−	0.177617i	$-0.0568387\pi$
$740$		0			0
$741$		−	15.4930i		−	0.569151i
$742$	10.9777	+	28.8213i	0.403005	+	1.05806i
$743$	−27.0416	+	27.0416i	−0.992061	+	0.992061i	−0.999969	−	0.00790753i	$-0.997483\pi$
$743$	−27.0416	+	27.0416i	−0.992061	+	0.992061i	0.00790753	+	0.999969i	$0.497483\pi$
$744$			2.82843i			0.103695i
$745$		0			0
$746$	21.3137			0.780350
$747$	2.20325	−	2.20325i	0.0806126	−	0.0806126i
$748$	10.4525	+	10.4525i	0.382181	+	0.382181i
$749$	−5.59767	+	12.4853i	−0.204534	+	0.456202i
$750$		0			0
$751$	−2.48528			−0.0906892			−0.0453446	−	0.998971i	$-0.514439\pi$
$751$	−2.48528			−0.0906892			−0.0453446	+	0.998971i	$0.514439\pi$
$752$	1.08239	−	1.08239i	0.0394708	−	0.0394708i
$753$	−18.4142	+	18.4142i	−0.671051	+	0.671051i
$754$	4.96362			0.180764
$755$		0			0
$756$	5.17157	−	11.5349i	0.188088	−	0.419520i
$757$	−7.89949	−	7.89949i	−0.287112	−	0.287112i	0.548825	−	0.835937i	$-0.315075\pi$
$757$	−7.89949	−	7.89949i	−0.287112	−	0.287112i	−0.835937	+	0.548825i	$0.815075\pi$
$758$	−4.34315	+	4.34315i	−0.157750	+	0.157750i
$759$	3.06147			0.111124
$760$		0			0
$761$			26.3939i			0.956778i	0.878148	+	0.478389i	$0.158779\pi$
$761$			26.3939i			0.956778i	−0.878148	+	0.478389i	$0.841221\pi$
$762$	−6.62567	+	6.62567i	−0.240023	+	0.240023i
$763$	30.0211	−	11.4347i	1.08684	−	0.413965i
$764$			1.75736i			0.0635790i
$765$		0			0
$766$			15.0447i			0.543587i
$767$	−39.1421	−	39.1421i	−1.41334	−	1.41334i
$768$	−1.30656	−	1.30656i	−0.0471465	−	0.0471465i
$769$	−17.5809			−0.633984			−0.316992	−	0.948428i	$-0.602673\pi$
$769$	−17.5809			−0.633984			−0.316992	+	0.948428i	$0.602673\pi$
$770$		0			0
$771$	−20.4853			−0.737759
$772$	−8.24264	−	8.24264i	−0.296659	−	0.296659i
$773$	14.6892	+	14.6892i	0.528334	+	0.528334i	0.920076	−	0.391741i	$-0.128127\pi$
$773$	14.6892	+	14.6892i	0.528334	+	0.528334i	−0.391741	+	0.920076i	$0.628127\pi$
$774$		−	2.34315i		−	0.0842226i
$775$		0			0
$776$			6.49435i			0.233134i
$777$	−16.7065	+	6.36332i	−0.599341	+	0.228283i
$778$	−0.100505	+	0.100505i	−0.00360328	+	0.00360328i
$779$			5.17157i			0.185291i
$780$		0			0
$781$	−1.65685			−0.0592869
$782$	−2.16478	+	2.16478i	−0.0774125	+	0.0774125i
$783$	2.79884	+	2.79884i	0.100022	+	0.100022i
$784$	5.22625	−	4.65685i	0.186652	−	0.166316i
$785$		0			0
$786$	−27.0711			−0.965593
$787$	−24.3764	+	24.3764i	−0.868923	+	0.868923i	−0.992353	−	0.123430i	$-0.960611\pi$
$787$	−24.3764	+	24.3764i	−0.868923	+	0.868923i	0.123430	+	0.992353i	$0.460611\pi$
$788$	0.585786	−	0.585786i	0.0208678	−	0.0208678i
$789$	−50.7318			−1.80610
$790$		0			0
$791$	−4.00000	−	1.79337i	−0.142224	−	0.0637648i
$792$	−0.828427	−	0.828427i	−0.0294369	−	0.0294369i
$793$	27.2843	−	27.2843i	0.968893	−	0.968893i
$794$	−1.58513			−0.0562540
$795$		0			0
$796$			28.0334i			0.993618i
$797$	−16.6683	+	16.6683i	−0.590421	+	0.590421i	−0.937745	−	0.347324i	$-0.887090\pi$
$797$	−16.6683	+	16.6683i	−0.590421	+	0.590421i	0.347324	+	0.937745i	$0.387090\pi$
$798$	6.39329	−	2.43514i	0.226320	−	0.0862030i
$799$			8.00000i			0.283020i
$800$		0			0
$801$			4.70099i			0.166101i
$802$	−13.9706	−	13.9706i	−0.493318	−	0.493318i
$803$	−11.7206	−	11.7206i	−0.413611	−	0.413611i
$804$	−27.3994			−0.966301
$805$		0			0
$806$	−9.17157			−0.323055
$807$	35.1421	+	35.1421i	1.23706	+	1.23706i
$808$	1.94061	+	1.94061i	0.0682705	+	0.0682705i
$809$			33.8995i			1.19184i	0.803043	+	0.595921i	$0.203213\pi$
$809$			33.8995i			1.19184i	−0.803043	+	0.595921i	$0.796787\pi$
$810$		0			0
$811$		−	50.6005i		−	1.77682i	−0.459048	−	0.888411i	$-0.651809\pi$
$811$		−	50.6005i		−	1.77682i	0.459048	−	0.888411i	$-0.348191\pi$
$812$	0.780163	+	2.04826i	0.0273784	+	0.0718800i
$813$	24.4853	−	24.4853i	0.858736	−	0.858736i
$814$		−	10.3431i		−	0.362527i
$815$		0			0
$816$	9.65685			0.338058
$817$	−5.59767	+	5.59767i	−0.195838	+	0.195838i
$818$	−17.6578	−	17.6578i	−0.617392	−	0.617392i
$819$	−5.99162	−	2.68629i	−0.209364	−	0.0938666i
$820$		0			0
$821$	−34.4853			−1.20354			−0.601772	−	0.798668i	$-0.705539\pi$
$821$	−34.4853			−1.20354			−0.601772	+	0.798668i	$0.705539\pi$
$822$	15.0991	−	15.0991i	0.526642	−	0.526642i
$823$	2.34315	−	2.34315i	0.0816769	−	0.0816769i	−0.665088	−	0.746765i	$-0.731606\pi$
$823$	2.34315	−	2.34315i	0.0816769	−	0.0816769i	0.746765	+	0.665088i	$0.231606\pi$
$824$	−14.1480			−0.492870
$825$		0			0
$826$	10.0000	−	22.3044i	0.347945	−	0.776070i
$827$	7.51472	+	7.51472i	0.261312	+	0.261312i	0.825587	−	0.564275i	$-0.190844\pi$
$827$	7.51472	+	7.51472i	0.261312	+	0.261312i	−0.564275	+	0.825587i	$0.690844\pi$
$828$	0.171573	−	0.171573i	0.00596257	−	0.00596257i
$829$	−40.8589			−1.41909			−0.709545	−	0.704660i	$-0.751099\pi$
$829$	−40.8589			−1.41909			−0.709545	+	0.704660i	$0.751099\pi$
$830$		0			0
$831$		−	4.59220i		−	0.159302i
$832$	4.23671	−	4.23671i	0.146882	−	0.146882i
$833$	−2.10422	+	36.5232i	−0.0729069	+	1.26545i
$834$			15.8995i			0.550554i
$835$		0			0
$836$			3.95815i			0.136895i
$837$	−5.17157	−	5.17157i	−0.178756	−	0.178756i
$838$	8.19486	+	8.19486i	0.283087	+	0.283087i
$839$	−20.6424			−0.712654			−0.356327	−	0.934361i	$-0.615971\pi$
$839$	−20.6424			−0.712654			−0.356327	+	0.934361i	$0.615971\pi$
$840$		0			0
$841$	28.3137			0.976335
$842$	12.5858	+	12.5858i	0.433735	+	0.433735i
$843$	7.39104	+	7.39104i	0.254561	+	0.254561i
$844$		−	10.3431i		−	0.356026i
$845$		0			0
$846$		−	0.634051i		−	0.0217991i
$847$	−2.82522	−	7.41742i	−0.0970757	−	0.254866i
$848$	−8.24264	+	8.24264i	−0.283053	+	0.283053i
$849$			8.24264i			0.282887i
$850$		0			0
$851$	2.14214			0.0734315
$852$	−0.765367	+	0.765367i	−0.0262210	+	0.0262210i
$853$	−26.7268	−	26.7268i	−0.915110	−	0.915110i	0.0815587	−	0.996669i	$-0.474010\pi$
$853$	−26.7268	−	26.7268i	−0.915110	−	0.915110i	−0.996669	+	0.0815587i	$0.974010\pi$
$854$	15.5474	+	6.97056i	0.532022	+	0.238528i
$855$		0			0
$856$	−5.17157			−0.176761
$857$	−11.4580	+	11.4580i	−0.391397	+	0.391397i	−0.875185	−	0.483788i	$-0.839261\pi$
$857$	−11.4580	+	11.4580i	−0.391397	+	0.391397i	0.483788	+	0.875185i	$0.339261\pi$
$858$	22.1421	−	22.1421i	0.755920	−	0.755920i
$859$	40.6732			1.38775			0.693876	−	0.720094i	$-0.255901\pi$
$859$	40.6732			1.38775			0.693876	+	0.720094i	$0.255901\pi$
$860$		0			0
$861$	16.4853	+	7.39104i	0.561817	+	0.251886i
$862$	4.00000	+	4.00000i	0.136241	+	0.136241i
$863$	2.44365	−	2.44365i	0.0831828	−	0.0831828i	−0.664291	−	0.747474i	$-0.731266\pi$
$863$	2.44365	−	2.44365i	0.0831828	−	0.0831828i	0.747474	+	0.664291i	$0.231266\pi$
$864$	4.77791			0.162548
$865$		0			0
$866$			14.7821i			0.502315i
$867$	−13.4755	+	13.4755i	−0.457652	+	0.457652i
$868$	−1.44155	−	3.78470i	−0.0489295	−	0.128461i
$869$			14.3431i			0.486558i
$870$		0			0
$871$		−	88.8463i		−	3.01044i
$872$	8.58579	+	8.58579i	0.290751	+	0.290751i
$873$	1.90215	+	1.90215i	0.0643781	+	0.0643781i
$874$	−0.819760			−0.0277288
$875$		0			0
$876$	−10.8284			−0.365859
$877$	21.5563	+	21.5563i	0.727906	+	0.727906i	0.970202	−	0.242296i	$-0.0779006\pi$
$877$	21.5563	+	21.5563i	0.727906	+	0.727906i	−0.242296	+	0.970202i	$0.577901\pi$
$878$	−9.81845	−	9.81845i	−0.331357	−	0.331357i
$879$		−	6.24264i		−	0.210559i
$880$		0			0
$881$			13.5140i			0.455297i	0.973743	+	0.227649i	$0.0731038\pi$
$881$			13.5140i			0.455297i	−0.973743	+	0.227649i	$0.926896\pi$
$882$	0.166773	−	2.89469i	0.00561553	−	0.0974694i
$883$	28.8284	−	28.8284i	0.970154	−	0.970154i	−0.0294135	−	0.999567i	$-0.509364\pi$
$883$	28.8284	−	28.8284i	0.970154	−	0.970154i	0.999567	+	0.0294135i	$0.00936396\pi$
$884$			31.3137i			1.05319i
$885$		0			0
$886$	5.85786			0.196799
$887$	32.5487	−	32.5487i	1.09288	−	1.09288i	0.0976580	−	0.995220i	$-0.468865\pi$
$887$	32.5487	−	32.5487i	1.09288	−	1.09288i	0.995220	−	0.0976580i	$-0.0311351\pi$
$888$	−4.77791	−	4.77791i	−0.160336	−	0.160336i
$889$	5.48888	−	12.2426i	0.184091	−	0.410605i
$890$		0			0
$891$	28.4853			0.954293
$892$	6.75699	−	6.75699i	0.226241	−	0.226241i
$893$	−1.51472	+	1.51472i	−0.0506881	+	0.0506881i
$894$	31.9916			1.06996
$895$		0			0
$896$	2.41421	+	1.08239i	0.0806532	+	0.0361602i
$897$	4.58579	+	4.58579i	0.153115	+	0.153115i
$898$	−18.1421	+	18.1421i	−0.605411	+	0.605411i
$899$	1.26810			0.0422935
$900$		0			0
$901$		−	60.9217i		−	2.02959i
$902$	−7.39104	+	7.39104i	−0.246095	+	0.246095i
$903$	9.84354	+	25.8435i	0.327572	+	0.860019i
$904$		−	1.65685i		−	0.0551062i
$905$		0			0
$906$			16.3128i			0.541957i
$907$	−11.1716	−	11.1716i	−0.370946	−	0.370946i	0.496876	−	0.867822i	$-0.334480\pi$
$907$	−11.1716	−	11.1716i	−0.370946	−	0.370946i	−0.867822	+	0.496876i	$0.834480\pi$
$908$	8.38057	+	8.38057i	0.278119	+	0.278119i
$909$	1.13679			0.0377048
$910$		0			0
$911$	−28.1421			−0.932391			−0.466195	−	0.884682i	$-0.654376\pi$
$911$	−28.1421			−0.932391			−0.466195	+	0.884682i	$0.654376\pi$
$912$	1.82843	+	1.82843i	0.0605453	+	0.0605453i
$913$	−15.0447	−	15.0447i	−0.497907	−	0.497907i
$914$			2.34315i			0.0775044i
$915$		0			0
$916$			7.70806i			0.254682i
$917$	36.2236	−	13.7972i	1.19621	−	0.455624i
$918$	−17.6569	+	17.6569i	−0.582763	+	0.582763i
$919$			8.38478i			0.276588i	0.990391	+	0.138294i	$0.0441619\pi$
$919$			8.38478i			0.276588i	−0.990391	+	0.138294i	$0.955838\pi$
$920$		0			0
$921$	60.5269			1.99443
$922$	−24.0593	+	24.0593i	−0.792352	+	0.792352i
$923$	−2.48181	−	2.48181i	−0.0816898	−	0.0816898i
$924$	12.6173	+	5.65685i	0.415078	+	0.186097i
$925$		0			0
$926$	18.3431			0.602793
$927$	−4.14386	+	4.14386i	−0.136102	+	0.136102i
$928$	−0.585786	+	0.585786i	−0.0192294	+	0.0192294i
$929$	−33.2597			−1.09121			−0.545607	−	0.838041i	$-0.683701\pi$
$929$	−33.2597			−1.09121			−0.545607	+	0.838041i	$0.683701\pi$
$930$		0			0
$931$	−7.31371	+	6.51688i	−0.239697	+	0.213582i
$932$	−3.00000	−	3.00000i	−0.0982683	−	0.0982683i
$933$	4.48528	−	4.48528i	0.146842	−	0.146842i
$934$	−24.6549			−0.806734
$935$		0			0
$936$		−	2.48181i		−	0.0811205i
$937$	17.7666	−	17.7666i	0.580410	−	0.580410i	−0.354606	−	0.935016i	$-0.615385\pi$
$937$	17.7666	−	17.7666i	0.580410	−	0.580410i	0.935016	+	0.354606i	$0.115385\pi$
$938$	36.6629	−	13.9645i	1.19709	−	0.455958i
$939$		−	17.6569i		−	0.576210i
$940$		0			0
$941$		−	23.3099i		−	0.759881i	−0.925011	−	0.379940i	$-0.875944\pi$
$941$		−	23.3099i		−	0.759881i	0.925011	−	0.379940i	$-0.124056\pi$
$942$	18.8995	+	18.8995i	0.615779	+	0.615779i
$943$	−1.53073	−	1.53073i	−0.0498475	−	0.0498475i
$944$	9.23880			0.300697
$945$		0			0
$946$	−16.0000			−0.520205
$947$	−22.9706	−	22.9706i	−0.746443	−	0.746443i	0.227366	−	0.973809i	$-0.426989\pi$
$947$	−22.9706	−	22.9706i	−0.746443	−	0.746443i	−0.973809	+	0.227366i	$0.926989\pi$
$948$	6.62567	+	6.62567i	0.215192	+	0.215192i
$949$		−	35.1127i		−	1.13981i
$950$		0			0
$951$			57.2261i			1.85568i
$952$	−12.9218	+	4.92177i	−0.418797	+	0.159515i
$953$	−23.1421	+	23.1421i	−0.749647	+	0.749647i	−0.974413	−	0.224766i	$-0.927838\pi$
$953$	−23.1421	+	23.1421i	−0.749647	+	0.749647i	0.224766	+	0.974413i	$0.427838\pi$
$954$			4.82843i			0.156326i
$955$		0			0
$956$	6.48528			0.209749
$957$	−3.06147	+	3.06147i	−0.0989632	+	0.0989632i
$958$	−7.83938	−	7.83938i	−0.253279	−	0.253279i
$959$	−12.5085	+	27.8995i	−0.403921	+	0.900922i
$960$		0			0
$961$	28.6569			0.924415
$962$	15.4930	−	15.4930i	0.499516	−	0.499516i
$963$	−1.51472	+	1.51472i	−0.0488111	+	0.0488111i
$964$	6.75699			0.217628
$965$		0			0
$966$	−1.17157	+	2.61313i	−0.0376947	+	0.0840759i
$967$	2.21320	+	2.21320i	0.0711718	+	0.0711718i	0.741797	−	0.670625i	$-0.233974\pi$
$967$	2.21320	+	2.21320i	0.0711718	+	0.0711718i	−0.670625	+	0.741797i	$0.733974\pi$
$968$	2.12132	−	2.12132i	0.0681818	−	0.0681818i
$969$	−13.5140			−0.434131
$970$		0			0
$971$			18.5320i			0.594720i	0.954765	+	0.297360i	$0.0961061\pi$
$971$			18.5320i			0.594720i	−0.954765	+	0.297360i	$0.903894\pi$
$972$	3.02301	−	3.02301i	0.0969630	−	0.0969630i
$973$	−8.10343	−	21.2750i	−0.259784	−	0.682045i
$974$		−	1.55635i		−	0.0498686i
$975$		0			0
$976$			6.43996i			0.206138i
$977$	25.8284	+	25.8284i	0.826325	+	0.826325i	0.987006	−	0.160682i	$-0.0513693\pi$
$977$	25.8284	+	25.8284i	0.826325	+	0.826325i	−0.160682	+	0.987006i	$0.551369\pi$
$978$	25.2346	+	25.2346i	0.806913	+	0.806913i
$979$	32.1003			1.02593
$980$		0			0
$981$	5.02944			0.160578
$982$	17.7990	+	17.7990i	0.567989	+	0.567989i
$983$	−28.7444	−	28.7444i	−0.916804	−	0.916804i	0.0799920	−	0.996796i	$-0.474511\pi$
$983$	−28.7444	−	28.7444i	−0.916804	−	0.916804i	−0.996796	+	0.0799920i	$0.974511\pi$
$984$			6.82843i			0.217682i
$985$		0			0
$986$		−	4.32957i		−	0.137882i
$987$	2.66364	+	6.99321i	0.0847847	+	0.222596i
$988$	−5.92893	+	5.92893i	−0.188624	+	0.188624i
$989$		−	3.31371i		−	0.105370i
$990$		0			0
$991$	−32.5858			−1.03512			−0.517561	−	0.855646i	$-0.673160\pi$
$991$	−32.5858			−1.03512			−0.517561	+	0.855646i	$0.673160\pi$
$992$	1.08239	−	1.08239i	0.0343660	−	0.0343660i
$993$	−30.4608	−	30.4608i	−0.966645	−	0.966645i
$994$	0.634051	−	1.41421i	0.0201109	−	0.0448561i
$995$		0			0
$996$	−13.8995			−0.440422
$997$	0.464273	−	0.464273i	0.0147037	−	0.0147037i	−0.699717	−	0.714420i	$-0.746690\pi$
$997$	0.464273	−	0.464273i	0.0147037	−	0.0147037i	0.714420	+	0.699717i	$0.246690\pi$
$998$	−5.31371	+	5.31371i	−0.168203	+	0.168203i
$999$	17.4721			0.552793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.g.a.307.3		8
5.2	odd	4		70.2.g.a.13.1	✓	8
5.3	odd	4	inner	350.2.g.a.293.4		8
5.4	even	2		70.2.g.a.27.2	yes	8
7.6	odd	2	inner	350.2.g.a.307.4		8
15.2	even	4		630.2.p.a.433.4		8
15.14	odd	2		630.2.p.a.307.3		8
20.7	even	4		560.2.bj.c.433.4		8
20.19	odd	2		560.2.bj.c.97.1		8
35.2	odd	12		490.2.l.a.423.3		16
35.4	even	6		490.2.l.a.117.4		16
35.9	even	6		490.2.l.a.227.1		16
35.12	even	12		490.2.l.a.423.4		16
35.13	even	4	inner	350.2.g.a.293.3		8
35.17	even	12		490.2.l.a.313.1		16
35.19	odd	6		490.2.l.a.227.2		16
35.24	odd	6		490.2.l.a.117.3		16
35.27	even	4		70.2.g.a.13.2	yes	8
35.32	odd	12		490.2.l.a.313.2		16
35.34	odd	2		70.2.g.a.27.1	yes	8
105.62	odd	4		630.2.p.a.433.3		8
105.104	even	2		630.2.p.a.307.4		8
140.27	odd	4		560.2.bj.c.433.1		8
140.139	even	2		560.2.bj.c.97.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.g.a.13.1	✓	8	5.2	odd	4
70.2.g.a.13.2	yes	8	35.27	even	4
70.2.g.a.27.1	yes	8	35.34	odd	2
70.2.g.a.27.2	yes	8	5.4	even	2
350.2.g.a.293.3		8	35.13	even	4	inner
350.2.g.a.293.4		8	5.3	odd	4	inner
350.2.g.a.307.3		8	1.1	even	1	trivial
350.2.g.a.307.4		8	7.6	odd	2	inner
490.2.l.a.117.3		16	35.24	odd	6
490.2.l.a.117.4		16	35.4	even	6
490.2.l.a.227.1		16	35.9	even	6
490.2.l.a.227.2		16	35.19	odd	6
490.2.l.a.313.1		16	35.17	even	12
490.2.l.a.313.2		16	35.32	odd	12
490.2.l.a.423.3		16	35.2	odd	12
490.2.l.a.423.4		16	35.12	even	12
560.2.bj.c.97.1		8	20.19	odd	2
560.2.bj.c.97.4		8	140.139	even	2
560.2.bj.c.433.1		8	140.27	odd	4
560.2.bj.c.433.4		8	20.7	even	4
630.2.p.a.307.3		8	15.14	odd	2
630.2.p.a.307.4		8	105.104	even	2
630.2.p.a.433.3		8	105.62	odd	4
630.2.p.a.433.4		8	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.30656 - 1.30656i) q^{3} +1.00000i q^{4} -1.84776i q^{6} +(0.941740 + 2.47247i) q^{7} +(-0.707107 + 0.707107i) q^{8} +0.414214i q^{9} +2.82843 q^{11} +(1.30656 - 1.30656i) q^{12} +(4.23671 + 4.23671i) q^{13} +(-1.08239 + 2.41421i) q^{14} -1.00000 q^{16} +(3.69552 - 3.69552i) q^{17} +(-0.292893 + 0.292893i) q^{18} +1.39942 q^{19} +(2.00000 - 4.46088i) q^{21} +(2.00000 + 2.00000i) q^{22} +(-0.414214 + 0.414214i) q^{23} +1.84776 q^{24} +5.99162i q^{26} +(-3.37849 + 3.37849i) q^{27} +(-2.47247 + 0.941740i) q^{28} -0.828427i q^{29} +1.53073i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.69552 - 3.69552i) q^{33} +5.22625 q^{34} -0.414214 q^{36} +(-2.58579 - 2.58579i) q^{37} +(0.989538 + 0.989538i) q^{38} -11.0711i q^{39} +3.69552i q^{41} +(4.56854 - 1.74011i) q^{42} +(-4.00000 + 4.00000i) q^{43} +2.82843i q^{44} -0.585786 q^{46} +(-1.08239 + 1.08239i) q^{47} +(1.30656 + 1.30656i) q^{48} +(-5.22625 + 4.65685i) q^{49} -9.65685 q^{51} +(-4.23671 + 4.23671i) q^{52} +(8.24264 - 8.24264i) q^{53} -4.77791 q^{54} +(-2.41421 - 1.08239i) q^{56} +(-1.82843 - 1.82843i) q^{57} +(0.585786 - 0.585786i) q^{58} -9.23880 q^{59} -6.43996i q^{61} +(-1.08239 + 1.08239i) q^{62} +(-1.02413 + 0.390081i) q^{63} -1.00000i q^{64} -5.22625i q^{66} +(-10.4853 - 10.4853i) q^{67} +(3.69552 + 3.69552i) q^{68} +1.08239 q^{69} -0.585786 q^{71} +(-0.292893 - 0.292893i) q^{72} +(-4.14386 - 4.14386i) q^{73} -3.65685i q^{74} +1.39942i q^{76} +(2.66364 + 6.99321i) q^{77} +(7.82843 - 7.82843i) q^{78} +5.07107i q^{79} +10.0711 q^{81} +(-2.61313 + 2.61313i) q^{82} +(-5.31911 - 5.31911i) q^{83} +(4.46088 + 2.00000i) q^{84} -5.65685 q^{86} +(-1.08239 + 1.08239i) q^{87} +(-2.00000 + 2.00000i) q^{88} +11.3492 q^{89} +(-6.48528 + 14.4650i) q^{91} +(-0.414214 - 0.414214i) q^{92} +(2.00000 - 2.00000i) q^{93} -1.53073 q^{94} +1.84776i q^{96} +(4.59220 - 4.59220i) q^{97} +(-6.98841 - 0.402625i) q^{98} +1.17157i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7} - 8 q^{16} - 8 q^{18} + 16 q^{21} + 16 q^{22} + 8 q^{23} - 8 q^{28} + 8 q^{36} - 32 q^{37} - 32 q^{43} - 16 q^{46} - 32 q^{51} + 32 q^{53} - 8 q^{56} + 8 q^{57} + 16 q^{58} - 16 q^{67} - 16 q^{71}+ \cdots - 32 q^{98}+O(q^{100}) \) 8 * q + 8 * q^7 - 8 * q^16 - 8 * q^18 + 16 * q^21 + 16 * q^22 + 8 * q^23 - 8 * q^28 + 8 * q^36 - 32 * q^37 - 32 * q^43 - 16 * q^46 - 32 * q^51 + 32 * q^53 - 8 * q^56 + 8 * q^57 + 16 * q^58 - 16 * q^67 - 16 * q^71 - 8 * q^72 + 16 * q^77 + 40 * q^78 + 24 * q^81 - 16 * q^88 + 16 * q^91 + 8 * q^92 + 16 * q^93 - 32 * q^98

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