LMFDB - Embedded newform 680.2.bo.a.161.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(121,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bo (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			161.6
Character	$\chi$	$=$	680.161
Dual form			680.2.bo.a.321.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.424268 - 1.02427i) q^{3} +(0.923880 + 0.382683i) q^{5} +(-0.208657 + 0.0864287i) q^{7} +(1.25219 + 1.25219i) q^{9} +(-1.54244 - 3.72378i) q^{11} -4.93623i q^{13} +(0.783944 - 0.783944i) q^{15} +(3.34135 + 2.41566i) q^{17} +(2.08841 - 2.08841i) q^{19} +0.250391i q^{21} +(0.174878 + 0.422193i) q^{23} +(0.707107 + 0.707107i) q^{25} +(4.88666 - 2.02412i) q^{27} +(3.53091 + 1.46255i) q^{29} +(-1.42284 + 3.43504i) q^{31} -4.46858 q^{33} -0.225849 q^{35} +(2.35906 - 5.69528i) q^{37} +(-5.05605 - 2.09428i) q^{39} +(3.17056 - 1.31329i) q^{41} +(-1.84772 - 1.84772i) q^{43} +(0.677680 + 1.63606i) q^{45} -10.2919i q^{47} +(-4.91368 + 4.91368i) q^{49} +(3.89192 - 2.39757i) q^{51} +(-1.52776 + 1.52776i) q^{53} -4.03059i q^{55} +(-1.25305 - 3.02514i) q^{57} +(-2.35916 - 2.35916i) q^{59} +(-9.09057 + 3.76544i) q^{61} +(-0.369503 - 0.153053i) q^{63} +(1.88901 - 4.56048i) q^{65} +3.06879 q^{67} +0.506636 q^{69} +(2.04723 - 4.94244i) q^{71} +(10.2363 + 4.24000i) q^{73} +(1.02427 - 0.424268i) q^{75} +(0.643683 + 0.643683i) q^{77} +(1.84185 + 4.44661i) q^{79} -0.551456i q^{81} +(-10.5038 + 10.5038i) q^{83} +(2.16257 + 3.51045i) q^{85} +(2.99610 - 2.99610i) q^{87} +17.0559i q^{89} +(0.426632 + 1.02998i) q^{91} +(2.91475 + 2.91475i) q^{93} +(2.72863 - 1.13024i) q^{95} +(0.668375 + 0.276850i) q^{97} +(2.73145 - 6.59431i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9} + 8 q^{11} - 8 q^{17} + 8 q^{19} + 8 q^{23} - 24 q^{27} - 32 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{35} + 16 q^{37} - 24 q^{39} - 16 q^{41} - 8 q^{49} + 16 q^{51} + 16 q^{53} + 48 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 + 8 * q^11 - 8 * q^17 + 8 * q^19 + 8 * q^23 - 24 * q^27 - 32 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^35 + 16 * q^37 - 24 * q^39 - 16 * q^41 - 8 * q^49 + 16 * q^51 + 16 * q^53 + 48 * q^57 + 24 * q^59 - 24 * q^61 - 48 * q^63 - 16 * q^67 - 80 * q^69 - 64 * q^71 + 16 * q^73 - 8 * q^79 - 56 * q^83 + 16 * q^85 + 96 * q^87 - 48 * q^91 + 32 * q^93 + 24 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.424268	−	1.02427i	0.244951	−	0.591364i	−0.752810	−	0.658237i	$-0.771302\pi$
$3$	0.424268	−	1.02427i	0.244951	−	0.591364i	0.997761	+	0.0668733i	$0.0213023\pi$
$4$		0			0
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$6$		0			0
$7$	−0.208657	+	0.0864287i	−0.0788650	+	0.0326670i	−0.421767	−	0.906704i	$-0.638590\pi$
$7$	−0.208657	+	0.0864287i	−0.0788650	+	0.0326670i	0.342902	+	0.939371i	$0.388590\pi$
$8$		0			0
$9$	1.25219	+	1.25219i	0.417396	+	0.417396i
$10$		0			0
$11$	−1.54244	−	3.72378i	−0.465064	−	1.12276i	−0.966292	−	0.257448i	$-0.917118\pi$
$11$	−1.54244	−	3.72378i	−0.465064	−	1.12276i	0.501229	−	0.865315i	$-0.332882\pi$
$12$		0			0
$13$		−	4.93623i		−	1.36906i	−0.728983	−	0.684532i	$-0.760007\pi$
$13$		−	4.93623i		−	1.36906i	0.728983	−	0.684532i	$-0.239993\pi$
$14$		0			0
$15$	0.783944	−	0.783944i	0.202414	−	0.202414i
$16$		0			0
$17$	3.34135	+	2.41566i	0.810396	+	0.585883i
$17$	3.34135	+	2.41566i	0.810396	+	0.585883i
$18$		0			0
$19$	2.08841	−	2.08841i	0.479113	−	0.479113i	−0.425735	−	0.904848i	$-0.639984\pi$
$19$	2.08841	−	2.08841i	0.479113	−	0.479113i	0.904848	+	0.425735i	$0.139984\pi$
$20$		0			0
$21$			0.250391i			0.0546397i
$22$		0			0
$23$	0.174878	+	0.422193i	0.0364646	+	0.0880333i	0.941063	−	0.338232i	$-0.109829\pi$
$23$	0.174878	+	0.422193i	0.0364646	+	0.0880333i	−0.904598	+	0.426266i	$0.859829\pi$
$24$		0			0
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$		0			0
$27$	4.88666	−	2.02412i	0.940439	−	0.389543i
$28$		0			0
$29$	3.53091	+	1.46255i	0.655673	+	0.271589i	0.685617	−	0.727963i	$-0.259533\pi$
$29$	3.53091	+	1.46255i	0.655673	+	0.271589i	−0.0299434	+	0.999552i	$0.509533\pi$
$30$		0			0
$31$	−1.42284	+	3.43504i	−0.255550	+	0.616952i	−0.998634	−	0.0522459i	$-0.983362\pi$
$31$	−1.42284	+	3.43504i	−0.255550	+	0.616952i	0.743084	+	0.669198i	$0.233362\pi$
$32$		0			0
$33$	−4.46858			−0.777879
$34$		0			0
$35$	−0.225849			−0.0381754
$36$		0			0
$37$	2.35906	−	5.69528i	0.387827	−	0.936298i	−0.602572	−	0.798064i	$-0.705857\pi$
$37$	2.35906	−	5.69528i	0.387827	−	0.936298i	0.990400	−	0.138234i	$-0.0441426\pi$
$38$		0			0
$39$	−5.05605	−	2.09428i	−0.809615	−	0.335354i
$40$		0			0
$41$	3.17056	−	1.31329i	0.495159	−	0.205101i	−0.121107	−	0.992639i	$-0.538645\pi$
$41$	3.17056	−	1.31329i	0.495159	−	0.205101i	0.616266	+	0.787538i	$0.288645\pi$
$42$		0			0
$43$	−1.84772	−	1.84772i	−0.281774	−	0.281774i	0.552042	−	0.833816i	$-0.313849\pi$
$43$	−1.84772	−	1.84772i	−0.281774	−	0.281774i	−0.833816	+	0.552042i	$0.813849\pi$
$44$		0			0
$45$	0.677680	+	1.63606i	0.101023	+	0.243890i
$46$		0			0
$47$		−	10.2919i		−	1.50123i	−0.660740	−	0.750615i	$-0.729757\pi$
$47$		−	10.2919i		−	1.50123i	0.660740	−	0.750615i	$-0.270243\pi$
$48$		0			0
$49$	−4.91368	+	4.91368i	−0.701954	+	0.701954i
$50$		0			0
$51$	3.89192	−	2.39757i	0.544977	−	0.335726i
$52$		0			0
$53$	−1.52776	+	1.52776i	−0.209854	+	0.209854i	−0.804205	−	0.594352i	$-0.797409\pi$
$53$	−1.52776	+	1.52776i	−0.209854	+	0.209854i	0.594352	+	0.804205i	$0.297409\pi$
$54$		0			0
$55$		−	4.03059i		−	0.543485i
$56$		0			0
$57$	−1.25305	−	3.02514i	−0.165971	−	0.400689i
$58$		0			0
$59$	−2.35916	−	2.35916i	−0.307136	−	0.307136i	0.536662	−	0.843798i	$-0.319685\pi$
$59$	−2.35916	−	2.35916i	−0.307136	−	0.307136i	−0.843798	+	0.536662i	$0.819685\pi$
$60$		0			0
$61$	−9.09057	+	3.76544i	−1.16393	+	0.482115i	−0.879181	−	0.476488i	$-0.841910\pi$
$61$	−9.09057	+	3.76544i	−1.16393	+	0.482115i	−0.284747	+	0.958603i	$0.591910\pi$
$62$		0			0
$63$	−0.369503	−	0.153053i	−0.0465530	−	0.0192829i
$64$		0			0
$65$	1.88901	−	4.56048i	0.234303	−	0.565658i
$66$		0			0
$67$	3.06879			0.374912			0.187456	−	0.982273i	$-0.439976\pi$
$67$	3.06879			0.374912			0.187456	+	0.982273i	$0.439976\pi$
$68$		0			0
$69$	0.506636			0.0609918
$70$		0			0
$71$	2.04723	−	4.94244i	0.242961	−	0.586560i	−0.754613	−	0.656170i	$-0.772175\pi$
$71$	2.04723	−	4.94244i	0.242961	−	0.586560i	0.997574	+	0.0696100i	$0.0221755\pi$
$72$		0			0
$73$	10.2363	+	4.24000i	1.19806	+	0.496254i	0.890373	−	0.455232i	$-0.150444\pi$
$73$	10.2363	+	4.24000i	1.19806	+	0.496254i	0.307691	+	0.951486i	$0.400444\pi$
$74$		0			0
$75$	1.02427	−	0.424268i	0.118273	−	0.0489902i
$76$		0			0
$77$	0.643683	+	0.643683i	0.0733545	+	0.0733545i
$78$		0			0
$79$	1.84185	+	4.44661i	0.207224	+	0.500283i	0.992984	−	0.118249i	$-0.0377280\pi$
$79$	1.84185	+	4.44661i	0.207224	+	0.500283i	−0.785760	+	0.618531i	$0.787728\pi$
$80$		0			0
$81$		−	0.551456i		−	0.0612728i
$82$		0			0
$83$	−10.5038	+	10.5038i	−1.15294	+	1.15294i	−0.166982	+	0.985960i	$0.553402\pi$
$83$	−10.5038	+	10.5038i	−1.15294	+	1.15294i	−0.985960	+	0.166982i	$0.946598\pi$
$84$		0			0
$85$	2.16257	+	3.51045i	0.234564	+	0.380762i
$86$		0			0
$87$	2.99610	−	2.99610i	0.321216	−	0.321216i
$88$		0			0
$89$			17.0559i			1.80792i	0.427614	+	0.903962i	$0.359354\pi$
$89$			17.0559i			1.80792i	−0.427614	+	0.903962i	$0.640646\pi$
$90$		0			0
$91$	0.426632	+	1.02998i	0.0447232	+	0.107971i
$92$		0			0
$93$	2.91475	+	2.91475i	0.302246	+	0.302246i
$94$		0			0
$95$	2.72863	−	1.13024i	0.279952	−	0.115960i
$96$		0			0
$97$	0.668375	+	0.276850i	0.0678632	+	0.0281099i	0.416357	−	0.909201i	$-0.363307\pi$
$97$	0.668375	+	0.276850i	0.0678632	+	0.0281099i	−0.348494	+	0.937311i	$0.613307\pi$
$98$		0			0
$99$	2.73145	−	6.59431i	0.274521	−	0.662753i
$100$		0			0
$101$	−0.308114			−0.0306585			−0.0153293	−	0.999883i	$-0.504880\pi$
$101$	−0.308114			−0.0306585			−0.0153293	+	0.999883i	$0.504880\pi$
$102$		0			0
$103$	−12.7616			−1.25744			−0.628721	−	0.777631i	$-0.716421\pi$
$103$	−12.7616			−1.25744			−0.628721	+	0.777631i	$0.716421\pi$
$104$		0			0
$105$	−0.0958204	+	0.231331i	−0.00935111	+	0.0225756i
$106$		0			0
$107$	11.5536	+	4.78566i	1.11693	+	0.462647i	0.863319	−	0.504659i	$-0.168382\pi$
$107$	11.5536	+	4.78566i	1.11693	+	0.462647i	0.253611	+	0.967306i	$0.418382\pi$
$108$		0			0
$109$	−18.7409	+	7.76273i	−1.79505	+	0.743535i	−0.806776	+	0.590857i	$0.798790\pi$
$109$	−18.7409	+	7.76273i	−1.79505	+	0.743535i	−0.988276	+	0.152678i	$0.951210\pi$
$110$		0			0
$111$	−4.83265	−	4.83265i	−0.458694	−	0.458694i
$112$		0			0
$113$	−1.44728	−	3.49404i	−0.136148	−	0.328691i	0.841070	−	0.540926i	$-0.181926\pi$
$113$	−1.44728	−	3.49404i	−0.136148	−	0.328691i	−0.977219	+	0.212234i	$0.931926\pi$
$114$		0			0
$115$			0.456978i			0.0426135i
$116$		0			0
$117$	6.18110	−	6.18110i	0.571443	−	0.571443i
$118$		0			0
$119$	−0.905978	−	0.215256i	−0.0830509	−	0.0197325i
$120$		0			0
$121$	−3.70926	+	3.70926i	−0.337205	+	0.337205i
$122$		0			0
$123$		−	3.80471i		−	0.343059i
$124$		0			0
$125$	0.382683	+	0.923880i	0.0342282	+	0.0826343i
$126$		0			0
$127$	−2.07454	−	2.07454i	−0.184086	−	0.184086i	0.609048	−	0.793134i	$-0.291552\pi$
$127$	−2.07454	−	2.07454i	−0.184086	−	0.184086i	−0.793134	+	0.609048i	$0.791552\pi$
$128$		0			0
$129$	−2.67649	+	1.10864i	−0.235652	+	0.0976103i
$130$		0			0
$131$	12.6409	+	5.23602i	1.10444	+	0.457473i	0.859019	−	0.511944i	$-0.171075\pi$
$131$	12.6409	+	5.23602i	1.10444	+	0.457473i	0.245419	+	0.969417i	$0.421075\pi$
$132$		0			0
$133$	−0.255263	+	0.616259i	−0.0221341	+	0.0534364i
$134$		0			0
$135$	5.28929			0.455229
$136$		0			0
$137$	2.86159			0.244482			0.122241	−	0.992500i	$-0.460992\pi$
$137$	2.86159			0.244482			0.122241	+	0.992500i	$0.460992\pi$
$138$		0			0
$139$	−2.43181	+	5.87091i	−0.206263	+	0.497964i	−0.992829	−	0.119543i	$-0.961857\pi$
$139$	−2.43181	+	5.87091i	−0.206263	+	0.497964i	0.786566	+	0.617507i	$0.211857\pi$
$140$		0			0
$141$	−10.5417	−	4.36653i	−0.887773	−	0.367728i
$142$		0			0
$143$	−18.3815	+	7.61385i	−1.53713	+	0.636702i
$144$		0			0
$145$	2.70244	+	2.70244i	0.224425	+	0.224425i
$146$		0			0
$147$	2.94823	+	7.11766i	0.243166	+	0.587055i
$148$		0			0
$149$			10.4836i			0.858850i	0.903103	+	0.429425i	$0.141284\pi$
$149$			10.4836i			0.858850i	−0.903103	+	0.429425i	$0.858716\pi$
$150$		0			0
$151$	−7.81548	+	7.81548i	−0.636015	+	0.636015i	−0.949570	−	0.313555i	$-0.898480\pi$
$151$	−7.81548	+	7.81548i	−0.636015	+	0.636015i	0.313555	+	0.949570i	$0.398480\pi$
$152$		0			0
$153$	1.15914	+	7.20886i	0.0937109	+	0.582802i
$154$		0			0
$155$	−2.62907	+	2.62907i	−0.211172	+	0.211172i
$156$		0			0
$157$			13.9432i			1.11278i	0.830920	+	0.556392i	$0.187815\pi$
$157$			13.9432i			1.11278i	−0.830920	+	0.556392i	$0.812185\pi$
$158$		0			0
$159$	0.916663	+	2.21302i	0.0726961	+	0.175504i
$160$		0			0
$161$	−0.0729791	−	0.0729791i	−0.00575156	−	0.00575156i
$162$		0			0
$163$	12.8451	−	5.32062i	1.00611	−	0.416743i	0.182074	−	0.983285i	$-0.441719\pi$
$163$	12.8451	−	5.32062i	1.00611	−	0.416743i	0.824033	+	0.566542i	$0.191719\pi$
$164$		0			0
$165$	−4.12843	−	1.71005i	−0.321398	−	0.133127i
$166$		0			0
$167$	−2.00018	+	4.82885i	−0.154778	+	0.373668i	−0.982180	−	0.187943i	$-0.939818\pi$
$167$	−2.00018	+	4.82885i	−0.154778	+	0.373668i	0.827402	+	0.561610i	$0.189818\pi$
$168$		0			0
$169$	−11.3664			−0.874337
$170$		0			0
$171$	5.23016			0.399960
$172$		0			0
$173$	3.65057	−	8.81326i	0.277548	−	0.670059i	−0.722219	−	0.691665i	$-0.756878\pi$
$173$	3.65057	−	8.81326i	0.277548	−	0.670059i	0.999767	+	0.0216052i	$0.00687768\pi$
$174$		0			0
$175$	−0.208657	−	0.0864287i	−0.0157730	−	0.00653339i
$176$		0			0
$177$	−3.41733	+	1.41551i	−0.256862	+	0.106396i
$178$		0			0
$179$	−0.828820	−	0.828820i	−0.0619490	−	0.0619490i	0.675454	−	0.737403i	$-0.263948\pi$
$179$	−0.828820	−	0.828820i	−0.0619490	−	0.0619490i	−0.737403	+	0.675454i	$0.763948\pi$
$180$		0			0
$181$	3.05295	+	7.37048i	0.226924	+	0.547843i	0.995800	−	0.0915546i	$-0.0291836\pi$
$181$	3.05295	+	7.37048i	0.226924	+	0.547843i	−0.768876	+	0.639398i	$0.779184\pi$
$182$		0			0
$183$			10.9088i			0.806399i
$184$		0			0
$185$	4.35898	−	4.35898i	0.320479	−	0.320479i
$186$		0			0
$187$	3.84155	−	16.1685i	0.280922	−	1.18235i
$188$		0			0
$189$	−0.844695	+	0.844695i	−0.0614426	+	0.0614426i
$190$		0			0
$191$			25.3423i			1.83370i	0.399226	+	0.916852i	$0.369279\pi$
$191$			25.3423i			1.83370i	−0.399226	+	0.916852i	$0.630721\pi$
$192$		0			0
$193$	−5.41349	−	13.0693i	−0.389671	−	0.940750i	−0.990009	−	0.141003i	$-0.954967\pi$
$193$	−5.41349	−	13.0693i	−0.389671	−	0.940750i	0.600338	−	0.799747i	$-0.295033\pi$
$194$		0			0
$195$	−3.86973	−	3.86973i	−0.277117	−	0.277117i
$196$		0			0
$197$	15.7854	−	6.53852i	1.12466	−	0.465850i	0.258698	−	0.965958i	$-0.416706\pi$
$197$	15.7854	−	6.53852i	1.12466	−	0.465850i	0.865963	+	0.500108i	$0.166706\pi$
$198$		0			0
$199$	−22.9319	−	9.49871i	−1.62560	−	0.673346i	−0.630871	−	0.775887i	$-0.717302\pi$
$199$	−22.9319	−	9.49871i	−1.62560	−	0.673346i	−0.994729	+	0.102542i	$0.967302\pi$
$200$		0			0
$201$	1.30199	−	3.14327i	0.0918351	−	0.221709i
$202$		0			0
$203$	−0.863156			−0.0605817
$204$		0			0
$205$	3.43179			0.239687
$206$		0			0
$207$	−0.309685	+	0.747646i	−0.0215246	+	0.0519650i
$208$		0			0
$209$	−10.9980	−	4.55553i	−0.760748	−	0.315112i
$210$		0			0
$211$	−23.8616	+	9.88379i	−1.64270	+	0.680428i	−0.996566	−	0.0827963i	$-0.973615\pi$
$211$	−23.8616	+	9.88379i	−1.64270	+	0.680428i	−0.646133	+	0.763225i	$0.723615\pi$
$212$		0			0
$213$	−4.19383	−	4.19383i	−0.287357	−	0.287357i
$214$		0			0
$215$	−0.999978	−	2.41416i	−0.0681979	−	0.164644i
$216$		0			0
$217$		−	0.839721i		−	0.0570039i
$218$		0			0
$219$	8.68582	−	8.68582i	0.586933	−	0.586933i
$220$		0			0
$221$	11.9242	−	16.4937i	0.802111	−	1.10948i
$222$		0			0
$223$	−16.9226	+	16.9226i	−1.13322	+	1.13322i	−0.143583	+	0.989638i	$0.545863\pi$
$223$	−16.9226	+	16.9226i	−1.13322	+	1.13322i	−0.989638	+	0.143583i	$0.954137\pi$
$224$		0			0
$225$			1.77086i			0.118058i
$226$		0			0
$227$	0.715974	+	1.72851i	0.0475209	+	0.114726i	0.945857	−	0.324582i	$-0.105224\pi$
$227$	0.715974	+	1.72851i	0.0475209	+	0.114726i	−0.898337	+	0.439308i	$0.855224\pi$
$228$		0			0
$229$	−14.1637	−	14.1637i	−0.935966	−	0.935966i	0.0621035	−	0.998070i	$-0.480219\pi$
$229$	−14.1637	−	14.1637i	−0.935966	−	0.935966i	−0.998070	+	0.0621035i	$0.980219\pi$
$230$		0			0
$231$	0.932401	−	0.386213i	0.0613475	−	0.0254109i
$232$		0			0
$233$	3.15977	+	1.30882i	0.207004	+	0.0857437i	0.483776	−	0.875192i	$-0.339265\pi$
$233$	3.15977	+	1.30882i	0.207004	+	0.0857437i	−0.276773	+	0.960935i	$0.589265\pi$
$234$		0			0
$235$	3.93855	−	9.50849i	0.256922	−	0.620265i
$236$		0			0
$237$	5.33597			0.346609
$238$		0			0
$239$	−11.2962			−0.730690			−0.365345	−	0.930872i	$-0.619049\pi$
$239$	−11.2962			−0.730690			−0.365345	+	0.930872i	$0.619049\pi$
$240$		0			0
$241$	2.40490	−	5.80593i	0.154913	−	0.373993i	−0.827301	−	0.561759i	$-0.810125\pi$
$241$	2.40490	−	5.80593i	0.154913	−	0.373993i	0.982214	+	0.187766i	$0.0601247\pi$
$242$		0			0
$243$	14.0951	+	5.83840i	0.904204	+	0.374534i
$244$		0			0
$245$	−6.42003	+	2.65926i	−0.410161	+	0.169894i
$246$		0			0
$247$	−10.3089	−	10.3089i	−0.655937	−	0.655937i
$248$		0			0
$249$	6.30233	+	15.2152i	0.399394	+	0.964222i
$250$		0			0
$251$		−	1.97552i		−	0.124694i	−0.998055	−	0.0623468i	$-0.980142\pi$
$251$		−	1.97552i		−	0.124694i	0.998055	−	0.0623468i	$-0.0198585\pi$
$252$		0			0
$253$	1.30242	−	1.30242i	0.0818822	−	0.0818822i
$254$		0			0
$255$	4.51317	−	0.725690i	0.282626	−	0.0454445i
$256$		0			0
$257$	15.2037	−	15.2037i	0.948378	−	0.948378i	−0.0503538	−	0.998731i	$-0.516035\pi$
$257$	15.2037	−	15.2037i	0.948378	−	0.948378i	0.998731	+	0.0503538i	$0.0160349\pi$
$258$		0			0
$259$			1.39225i			0.0865103i
$260$		0			0
$261$	2.58998	+	6.25275i	0.160315	+	0.387036i
$262$		0			0
$263$	18.6774	+	18.6774i	1.15170	+	1.15170i	0.986212	+	0.165485i	$0.0529191\pi$
$263$	18.6774	+	18.6774i	1.15170	+	1.15170i	0.165485	+	0.986212i	$0.447081\pi$
$264$		0			0
$265$	−1.99611	+	0.826817i	−0.122620	+	0.0507910i
$266$		0			0
$267$	17.4699	+	7.23627i	1.06914	+	0.442853i
$268$		0			0
$269$	5.77414	−	13.9400i	0.352055	−	0.849937i	−0.644311	−	0.764764i	$-0.722856\pi$
$269$	5.77414	−	13.9400i	0.352055	−	0.849937i	0.996366	−	0.0851731i	$-0.0271443\pi$
$270$		0			0
$271$	5.71822			0.347357			0.173679	−	0.984802i	$-0.444435\pi$
$271$	5.71822			0.347357			0.173679	+	0.984802i	$0.444435\pi$
$272$		0			0
$273$	1.23599			0.0748053
$274$		0			0
$275$	1.54244	−	3.72378i	0.0930127	−	0.224553i
$276$		0			0
$277$	−7.24345	−	3.00033i	−0.435216	−	0.180273i	0.154309	−	0.988023i	$-0.450685\pi$
$277$	−7.24345	−	3.00033i	−0.435216	−	0.180273i	−0.589525	+	0.807750i	$0.700685\pi$
$278$		0			0
$279$	−6.08299	+	2.51966i	−0.364179	+	0.150848i
$280$		0			0
$281$	−12.8053	−	12.8053i	−0.763900	−	0.763900i	0.213125	−	0.977025i	$-0.431636\pi$
$281$	−12.8053	−	12.8053i	−0.763900	−	0.763900i	−0.977025	+	0.213125i	$0.931636\pi$
$282$		0			0
$283$	10.7585	+	25.9734i	0.639529	+	1.54396i	0.827308	+	0.561748i	$0.189871\pi$
$283$	10.7585	+	25.9734i	0.639529	+	1.54396i	−0.187779	+	0.982211i	$0.560129\pi$
$284$		0			0
$285$		−	3.27439i		−	0.193958i
$286$		0			0
$287$	−0.548055	+	0.548055i	−0.0323507	+	0.0323507i
$288$		0			0
$289$	5.32921	+	16.1431i	0.313483	+	0.949594i
$290$		0			0
$291$	0.567140	−	0.567140i	0.0332463	−	0.0332463i
$292$		0			0
$293$		−	23.6324i		−	1.38062i	−0.723514	−	0.690310i	$-0.757474\pi$
$293$		−	23.6324i		−	1.38062i	0.723514	−	0.690310i	$-0.242526\pi$
$294$		0			0
$295$	−1.27677	−	3.08239i	−0.0743362	−	0.179463i
$296$		0			0
$297$	−15.0748	−	15.0748i	−0.874728	−	0.874728i
$298$		0			0
$299$	2.08404	−	0.863239i	0.120523	−	0.0499224i
$300$		0			0
$301$	0.545236	+	0.225844i	0.0314269	+	0.0130174i
$302$		0			0
$303$	−0.130723	+	0.315593i	−0.00750983	+	0.0181303i
$304$		0			0
$305$	−9.83956			−0.563411
$306$		0			0
$307$	6.28937			0.358953			0.179477	−	0.983762i	$-0.442560\pi$
$307$	6.28937			0.358953			0.179477	+	0.983762i	$0.442560\pi$
$308$		0			0
$309$	−5.41435	+	13.0714i	−0.308012	+	0.743606i
$310$		0			0
$311$	23.4038	+	9.69415i	1.32711	+	0.549705i	0.929828	−	0.367994i	$-0.119955\pi$
$311$	23.4038	+	9.69415i	1.32711	+	0.549705i	0.397277	+	0.917699i	$0.369955\pi$
$312$		0			0
$313$	−7.34211	+	3.04120i	−0.415001	+	0.171899i	−0.580407	−	0.814327i	$-0.697106\pi$
$313$	−7.34211	+	3.04120i	−0.415001	+	0.171899i	0.165406	+	0.986226i	$0.447106\pi$
$314$		0			0
$315$	−0.282806	−	0.282806i	−0.0159343	−	0.0159343i
$316$		0			0
$317$	0.141255	+	0.341019i	0.00793365	+	0.0191535i	0.927797	−	0.373086i	$-0.121700\pi$
$317$	0.141255	+	0.341019i	0.00793365	+	0.0191535i	−0.919863	+	0.392240i	$0.871700\pi$
$318$		0			0
$319$		−	15.4042i		−	0.862471i
$320$		0			0
$321$	9.80364	−	9.80364i	0.547186	−	0.547186i
$322$		0			0
$323$	12.0230	−	1.93322i	0.668975	−	0.107567i
$324$		0			0
$325$	3.49044	−	3.49044i	0.193615	−	0.193615i
$326$		0			0
$327$			22.4893i			1.24366i
$328$		0			0
$329$	0.889516	+	2.14748i	0.0490406	+	0.118395i
$330$		0			0
$331$	−6.71441	−	6.71441i	−0.369057	−	0.369057i	0.498076	−	0.867133i	$-0.334040\pi$
$331$	−6.71441	−	6.71441i	−0.369057	−	0.369057i	−0.867133	+	0.498076i	$0.834040\pi$
$332$		0			0
$333$	10.0856	−	4.17758i	0.552685	−	0.228930i
$334$		0			0
$335$	2.83519	+	1.17437i	0.154903	+	0.0641629i
$336$		0			0
$337$	9.99254	−	24.1241i	0.544328	−	1.31412i	−0.377314	−	0.926085i	$-0.623152\pi$
$337$	9.99254	−	24.1241i	0.544328	−	1.31412i	0.921643	−	0.388040i	$-0.126848\pi$
$338$		0			0
$339$	−4.19288			−0.227726
$340$		0			0
$341$	14.9860			0.811537
$342$		0			0
$343$	1.20559	−	2.91056i	0.0650959	−	0.157155i
$344$		0			0
$345$	0.468070	+	0.193881i	0.0252001	+	0.0104382i
$346$		0			0
$347$	21.1343	−	8.75410i	1.13455	−	0.469945i	0.265223	−	0.964187i	$-0.414554\pi$
$347$	21.1343	−	8.75410i	1.13455	−	0.469945i	0.869324	+	0.494242i	$0.164554\pi$
$348$		0			0
$349$	6.07305	+	6.07305i	0.325083	+	0.325083i	0.850713	−	0.525630i	$-0.176170\pi$
$349$	6.07305	+	6.07305i	0.325083	+	0.325083i	−0.525630	+	0.850713i	$0.676170\pi$
$350$		0			0
$351$	−9.99154	−	24.1217i	−0.533309	−	1.28752i
$352$		0			0
$353$		−	15.7802i		−	0.839896i	−0.907548	−	0.419948i	$-0.862048\pi$
$353$		−	15.7802i		−	0.839896i	0.907548	−	0.419948i	$-0.137952\pi$
$354$		0			0
$355$	3.78278	−	3.78278i	0.200769	−	0.200769i
$356$		0			0
$357$	−0.604858	+	0.836642i	−0.0320125	+	0.0442798i
$358$		0			0
$359$	11.8989	−	11.8989i	0.628001	−	0.628001i	−0.319564	−	0.947565i	$-0.603536\pi$
$359$	11.8989	−	11.8989i	0.628001	−	0.628001i	0.947565	+	0.319564i	$0.103536\pi$
$360$		0			0
$361$			10.2771i			0.540901i
$362$		0			0
$363$	2.22557	+	5.37301i	0.116812	+	0.282010i
$364$		0			0
$365$	7.83449	+	7.83449i	0.410076	+	0.410076i
$366$		0			0
$367$	−20.3854	+	8.44389i	−1.06411	+	0.440768i	−0.844908	−	0.534912i	$-0.820345\pi$
$367$	−20.3854	+	8.44389i	−1.06411	+	0.440768i	−0.219200	+	0.975680i	$0.570345\pi$
$368$		0			0
$369$	5.61463	+	2.32566i	0.292286	+	0.121069i
$370$		0			0
$371$	0.186736	−	0.450820i	0.00969484	−	0.0234054i
$372$		0			0
$373$	−23.0319			−1.19254			−0.596272	−	0.802782i	$-0.703352\pi$
$373$	−23.0319			−1.19254			−0.596272	+	0.802782i	$0.703352\pi$
$374$		0			0
$375$	1.10866			0.0572512
$376$		0			0
$377$	7.21949	−	17.4294i	0.371822	−	0.897659i
$378$		0			0
$379$	21.6539	+	8.96933i	1.11229	+	0.460724i	0.861724	−	0.507377i	$-0.169385\pi$
$379$	21.6539	+	8.96933i	1.11229	+	0.460724i	0.250561	+	0.968101i	$0.419385\pi$
$380$		0			0
$381$	−3.00505	+	1.24473i	−0.153954	+	0.0637697i
$382$		0			0
$383$	−23.4939	−	23.4939i	−1.20048	−	1.20048i	−0.974020	−	0.226461i	$-0.927284\pi$
$383$	−23.4939	−	23.4939i	−1.20048	−	1.20048i	−0.226461	−	0.974020i	$-0.572716\pi$
$384$		0			0
$385$	0.348359	+	0.841012i	0.0177540	+	0.0428620i
$386$		0			0
$387$		−	4.62739i		−	0.235223i
$388$		0			0
$389$	15.7265	−	15.7265i	0.797367	−	0.797367i	−0.185313	−	0.982680i	$-0.559330\pi$
$389$	15.7265	−	15.7265i	0.797367	−	0.797367i	0.982680	+	0.185313i	$0.0593299\pi$
$390$		0			0
$391$	−0.435545	+	1.83314i	−0.0220265	+	0.0927058i
$392$		0			0
$393$	10.7262	−	10.7262i	0.541066	−	0.541066i
$394$		0			0
$395$			4.81297i			0.242167i
$396$		0			0
$397$	3.58279	+	8.64961i	0.179815	+	0.434111i	0.987928	−	0.154916i	$-0.0495108\pi$
$397$	3.58279	+	8.64961i	0.179815	+	0.434111i	−0.808113	+	0.589028i	$0.799511\pi$
$398$		0			0
$399$	0.522917	+	0.522917i	0.0261786	+	0.0261786i
$400$		0			0
$401$	24.6525	−	10.2114i	1.23109	−	0.509933i	0.330169	−	0.943922i	$-0.392894\pi$
$401$	24.6525	−	10.2114i	1.23109	−	0.509933i	0.900918	+	0.433989i	$0.142894\pi$
$402$		0			0
$403$	16.9562	+	7.02347i	0.844647	+	0.349864i
$404$		0			0
$405$	0.211033	−	0.509479i	0.0104863	−	0.0253162i
$406$		0			0
$407$	−24.8467			−1.23161
$408$		0			0
$409$	−1.38542			−0.0685044			−0.0342522	−	0.999413i	$-0.510905\pi$
$409$	−1.38542			−0.0685044			−0.0342522	+	0.999413i	$0.510905\pi$
$410$		0			0
$411$	1.21408	−	2.93105i	0.0598861	−	0.144578i
$412$		0			0
$413$	0.696154	+	0.288356i	0.0342555	+	0.0141891i
$414$		0			0
$415$	−13.7239	+	5.68461i	−0.673678	+	0.279047i
$416$		0			0
$417$	4.98167	+	4.98167i	0.243953	+	0.243953i
$418$		0			0
$419$	−11.3756	−	27.4632i	−0.555736	−	1.34167i	−0.913113	−	0.407706i	$-0.866329\pi$
$419$	−11.3756	−	27.4632i	−0.555736	−	1.34167i	0.357377	−	0.933960i	$-0.383671\pi$
$420$		0			0
$421$		−	25.6165i		−	1.24847i	−0.781236	−	0.624236i	$-0.785410\pi$
$421$		−	25.6165i		−	1.24847i	0.781236	−	0.624236i	$-0.214590\pi$
$422$		0			0
$423$	12.8874	−	12.8874i	0.626608	−	0.626608i
$424$		0			0
$425$	0.654562	+	4.07082i	0.0317509	+	0.197464i
$426$		0			0
$427$	1.57137	−	1.57137i	0.0760440	−	0.0760440i
$428$		0			0
$429$			22.0579i			1.06497i
$430$		0			0
$431$	6.47429	+	15.6303i	0.311855	+	0.752886i	0.999636	+	0.0269673i	$0.00858501\pi$
$431$	6.47429	+	15.6303i	0.311855	+	0.752886i	−0.687781	+	0.725918i	$0.741415\pi$
$432$		0			0
$433$	−14.0872	−	14.0872i	−0.676987	−	0.676987i	0.282331	−	0.959317i	$-0.408893\pi$
$433$	−14.0872	−	14.0872i	−0.676987	−	0.676987i	−0.959317	+	0.282331i	$0.908893\pi$
$434$		0			0
$435$	3.91459	−	1.62148i	0.187690	−	0.0777439i
$436$		0			0
$437$	1.24693	+	0.516494i	0.0596486	+	0.0247073i
$438$		0			0
$439$	11.1287	−	26.8671i	0.531146	−	1.28230i	−0.399620	−	0.916681i	$-0.630858\pi$
$439$	11.1287	−	26.8671i	0.531146	−	1.28230i	0.930765	−	0.365618i	$-0.119142\pi$
$440$		0			0
$441$	−12.3057			−0.585986
$442$		0			0
$443$	−22.9336			−1.08961			−0.544803	−	0.838564i	$-0.683396\pi$
$443$	−22.9336			−1.08961			−0.544803	+	0.838564i	$0.683396\pi$
$444$		0			0
$445$	−6.52702	+	15.7576i	−0.309410	+	0.746982i
$446$		0			0
$447$	10.7381	+	4.44785i	0.507893	+	0.210376i
$448$		0			0
$449$	−10.6291	+	4.40270i	−0.501616	+	0.207776i	−0.619120	−	0.785296i	$-0.712511\pi$
$449$	−10.6291	+	4.40270i	−0.501616	+	0.207776i	0.117504	+	0.993072i	$0.462511\pi$
$450$		0			0
$451$	−9.78081	−	9.78081i	−0.460561	−	0.460561i
$452$		0			0
$453$	4.68933	+	11.3210i	0.220324	+	0.531908i
$454$		0			0
$455$			1.11484i			0.0522646i
$456$		0			0
$457$	−16.0940	+	16.0940i	−0.752845	+	0.752845i	−0.975009	−	0.222164i	$-0.928688\pi$
$457$	−16.0940	+	16.0940i	−0.752845	+	0.752845i	0.222164	+	0.975009i	$0.428688\pi$
$458$		0			0
$459$	21.2176	+	5.04120i	0.990354	+	0.235303i
$460$		0			0
$461$	−6.76090	+	6.76090i	−0.314886	+	0.314886i	−0.846799	−	0.531913i	$-0.821473\pi$
$461$	−6.76090	+	6.76090i	−0.314886	+	0.314886i	0.531913	+	0.846799i	$0.321473\pi$
$462$		0			0
$463$			8.83827i			0.410749i	0.978683	+	0.205375i	$0.0658413\pi$
$463$			8.83827i			0.410749i	−0.978683	+	0.205375i	$0.934159\pi$
$464$		0			0
$465$	1.57745	+	3.80831i	0.0731527	+	0.176606i
$466$		0			0
$467$	10.3573	+	10.3573i	0.479278	+	0.479278i	0.904901	−	0.425623i	$-0.139945\pi$
$467$	10.3573	+	10.3573i	0.479278	+	0.479278i	−0.425623	+	0.904901i	$0.639945\pi$
$468$		0			0
$469$	−0.640325	+	0.265231i	−0.0295674	+	0.0122472i
$470$		0			0
$471$	14.2816	+	5.91563i	0.658061	+	0.272578i
$472$		0			0
$473$	−4.03050	+	9.73050i	−0.185323	+	0.447409i
$474$		0			0
$475$	2.95345			0.135514
$476$		0			0
$477$	−3.82609			−0.175184
$478$		0			0
$479$	−1.09937	+	2.65412i	−0.0502316	+	0.121270i	−0.947003	−	0.321224i	$-0.895906\pi$
$479$	−1.09937	+	2.65412i	−0.0502316	+	0.121270i	0.896772	+	0.442493i	$0.145906\pi$
$480$		0			0
$481$	−28.1132	−	11.6449i	−1.28185	−	0.530961i
$482$		0			0
$483$	−0.105713	+	0.0437878i	−0.00481012	+	0.00199242i
$484$		0			0
$485$	0.511552	+	0.511552i	0.0232284	+	0.0232284i
$486$		0			0
$487$	−2.08318	−	5.02924i	−0.0943979	−	0.227897i	0.869627	−	0.493710i	$-0.164360\pi$
$487$	−2.08318	−	5.02924i	−0.0943979	−	0.227897i	−0.964025	+	0.265813i	$0.914360\pi$
$488$		0			0
$489$		−	15.4143i		−	0.697057i
$490$		0			0
$491$	−25.8969	+	25.8969i	−1.16871	+	1.16871i	−0.186197	+	0.982512i	$0.559616\pi$
$491$	−25.8969	+	25.8969i	−1.16871	+	1.16871i	−0.982512	+	0.186197i	$0.940384\pi$
$492$		0			0
$493$	8.26497	+	13.4163i	0.372236	+	0.604242i
$494$		0			0
$495$	5.04707	−	5.04707i	0.226849	−	0.226849i
$496$		0			0
$497$			1.20822i			0.0541959i
$498$		0			0
$499$	1.73614	+	4.19140i	0.0777202	+	0.187633i	0.957964	−	0.286889i	$-0.0926210\pi$
$499$	1.73614	+	4.19140i	0.0777202	+	0.187633i	−0.880244	+	0.474522i	$0.842621\pi$
$500$		0			0
$501$	4.09745	+	4.09745i	0.183061	+	0.183061i
$502$		0			0
$503$	3.00072	−	1.24294i	0.133795	−	0.0554199i	−0.314781	−	0.949164i	$-0.601931\pi$
$503$	3.00072	−	1.24294i	0.133795	−	0.0554199i	0.448577	+	0.893744i	$0.351931\pi$
$504$		0			0
$505$	−0.284660	−	0.117910i	−0.0126672	−	0.00524694i
$506$		0			0
$507$	−4.82239	+	11.6423i	−0.214170	+	0.517052i
$508$		0			0
$509$	−5.79066			−0.256667			−0.128333	−	0.991731i	$-0.540963\pi$
$509$	−5.79066			−0.256667			−0.128333	+	0.991731i	$0.540963\pi$
$510$		0			0
$511$	−2.50233			−0.110696
$512$		0			0
$513$	5.97815	−	14.4325i	0.263942	−	0.637212i
$514$		0			0
$515$	−11.7902	−	4.88367i	−0.519539	−	0.215200i
$516$		0			0
$517$	−38.3249	+	15.8747i	−1.68553	+	0.698167i
$518$		0			0
$519$	−7.47836	−	7.47836i	−0.328263	−	0.328263i
$520$		0			0
$521$	15.4857	+	37.3857i	0.678439	+	1.63790i	0.766861	+	0.641813i	$0.221817\pi$
$521$	15.4857	+	37.3857i	0.678439	+	1.63790i	−0.0884224	+	0.996083i	$0.528183\pi$
$522$		0			0
$523$		−	36.4603i		−	1.59430i	−0.603783	−	0.797149i	$-0.706341\pi$
$523$		−	36.4603i		−	1.59430i	0.603783	−	0.797149i	$-0.293659\pi$
$524$		0			0
$525$	−0.177053	+	0.177053i	−0.00772723	+	0.00772723i
$526$		0			0
$527$	−13.0521	+	8.04057i	−0.568558	+	0.350253i
$528$		0			0
$529$	16.1158	−	16.1158i	0.700687	−	0.700687i
$530$		0			0
$531$		−	5.90822i		−	0.256395i
$532$		0			0
$533$	−6.48270	−	15.6506i	−0.280797	−	0.677904i
$534$		0			0
$535$	8.84275	+	8.84275i	0.382305	+	0.382305i
$536$		0			0
$537$	−1.20058	+	0.497296i	−0.0518088	+	0.0214599i
$538$		0			0
$539$	25.8765	+	10.7184i	1.11458	+	0.461675i
$540$		0			0
$541$	4.49938	−	10.8625i	0.193443	−	0.467014i	−0.797162	−	0.603765i	$-0.793666\pi$
$541$	4.49938	−	10.8625i	0.193443	−	0.467014i	0.990605	+	0.136752i	$0.0436663\pi$
$542$		0			0
$543$	8.84465			0.379560
$544$		0			0
$545$	−20.2850			−0.868914
$546$		0			0
$547$	−0.731777	+	1.76667i	−0.0312885	+	0.0755372i	−0.938751	−	0.344595i	$-0.888016\pi$
$547$	−0.731777	+	1.76667i	−0.0312885	+	0.0755372i	0.907463	+	0.420132i	$0.138016\pi$
$548$		0			0
$549$	−16.0981	−	6.66807i	−0.687052	−	0.284586i
$550$		0			0
$551$	10.4284	−	4.31957i	0.444263	−	0.184020i
$552$		0			0
$553$	−0.768629	−	0.768629i	−0.0326854	−	0.0326854i
$554$		0			0
$555$	−2.61541	−	6.31416i	−0.111018	−	0.268021i
$556$		0			0
$557$			30.3320i			1.28521i	0.766198	+	0.642604i	$0.222146\pi$
$557$			30.3320i			1.28521i	−0.766198	+	0.642604i	$0.777854\pi$
$558$		0			0
$559$	−9.12077	+	9.12077i	−0.385767	+	0.385767i
$560$		0			0
$561$	−14.9311	−	10.7945i	−0.630390	−	0.455746i
$562$		0			0
$563$	−25.9353	+	25.9353i	−1.09304	+	1.09304i	−0.0978396	+	0.995202i	$0.531193\pi$
$563$	−25.9353	+	25.9353i	−1.09304	+	1.09304i	−0.995202	+	0.0978396i	$0.968807\pi$
$564$		0			0
$565$		−	3.78192i		−	0.159107i
$566$		0			0
$567$	0.0476616	+	0.115065i	0.00200160	+	0.00483228i
$568$		0			0
$569$	15.1437	+	15.1437i	0.634858	+	0.634858i	0.949282	−	0.314425i	$-0.101812\pi$
$569$	15.1437	+	15.1437i	0.634858	+	0.634858i	−0.314425	+	0.949282i	$0.601812\pi$
$570$		0			0
$571$	−1.36361	+	0.564827i	−0.0570654	+	0.0236373i	−0.411034	−	0.911620i	$-0.634832\pi$
$571$	−1.36361	+	0.564827i	−0.0570654	+	0.0236373i	0.353968	+	0.935257i	$0.384832\pi$
$572$		0			0
$573$	25.9574	+	10.7519i	1.08439	+	0.449168i
$574$		0			0
$575$	−0.174878	+	0.422193i	−0.00729292	+	0.0176067i
$576$		0			0
$577$	−34.5024			−1.43635			−0.718177	−	0.695860i	$-0.755023\pi$
$577$	−34.5024			−1.43635			−0.718177	+	0.695860i	$0.755023\pi$
$578$		0			0
$579$	−15.6833			−0.651776
$580$		0			0
$581$	1.28386	−	3.09952i	0.0532637	−	0.128590i
$582$		0			0
$583$	8.04552	+	3.33256i	0.333211	+	0.138021i
$584$		0			0
$585$	8.07599	−	3.34519i	0.333901	−	0.138306i
$586$		0			0
$587$	−19.8839	−	19.8839i	−0.820697	−	0.820697i	0.165511	−	0.986208i	$-0.447073\pi$
$587$	−19.8839	−	19.8839i	−0.820697	−	0.820697i	−0.986208	+	0.165511i	$0.947073\pi$
$588$		0			0
$589$	4.20229	+	10.1452i	0.173152	+	0.418027i
$590$		0			0
$591$		−	18.9426i		−	0.779195i
$592$		0			0
$593$	15.3211	−	15.3211i	0.629162	−	0.629162i	−0.318696	−	0.947857i	$-0.603245\pi$
$593$	15.3211	−	15.3211i	0.629162	−	0.629162i	0.947857	+	0.318696i	$0.103245\pi$
$594$		0			0
$595$	−0.754640	−	0.545573i	−0.0309372	−	0.0223663i
$596$		0			0
$597$	−19.4585	+	19.4585i	−0.796385	+	0.796385i
$598$		0			0
$599$			17.9568i			0.733696i	0.930281	+	0.366848i	$0.119563\pi$
$599$			17.9568i			0.733696i	−0.930281	+	0.366848i	$0.880437\pi$
$600$		0			0
$601$	14.6366	+	35.3359i	0.597040	+	1.44138i	0.876584	+	0.481249i	$0.159817\pi$
$601$	14.6366	+	35.3359i	0.597040	+	1.44138i	−0.279544	+	0.960133i	$0.590183\pi$
$602$		0			0
$603$	3.84270	+	3.84270i	0.156487	+	0.156487i
$604$		0			0
$605$	−4.84638	+	2.00744i	−0.197033	+	0.0816139i
$606$		0			0
$607$	−9.92891	−	4.11269i	−0.403002	−	0.166929i	0.171970	−	0.985102i	$-0.444987\pi$
$607$	−9.92891	−	4.11269i	−0.403002	−	0.166929i	−0.574972	+	0.818173i	$0.694987\pi$
$608$		0			0
$609$	−0.366209	+	0.884107i	−0.0148395	+	0.0358258i
$610$		0			0
$611$	−50.8033			−2.05528
$612$		0			0
$613$	10.5303			0.425315			0.212657	−	0.977127i	$-0.431788\pi$
$613$	10.5303			0.425315			0.212657	+	0.977127i	$0.431788\pi$
$614$		0			0
$615$	1.45600	−	3.51509i	0.0587115	−	0.141742i
$616$		0			0
$617$	8.13761	+	3.37071i	0.327608	+	0.135700i	0.540424	−	0.841393i	$-0.318264\pi$
$617$	8.13761	+	3.37071i	0.327608	+	0.135700i	−0.212817	+	0.977092i	$0.568264\pi$
$618$		0			0
$619$	31.6366	−	13.1043i	1.27158	−	0.526707i	0.358138	−	0.933669i	$-0.383412\pi$
$619$	31.6366	−	13.1043i	1.27158	−	0.526707i	0.913445	+	0.406962i	$0.133412\pi$
$620$		0			0
$621$	1.70914	+	1.70914i	0.0685855	+	0.0685855i
$622$		0			0
$623$	−1.47412	−	3.55884i	−0.0590594	−	0.142582i
$624$		0			0
$625$			1.00000i			0.0400000i
$626$		0			0
$627$	−9.33220	+	9.33220i	−0.372692	+	0.372692i
$628$		0			0
$629$	21.6403	−	13.3312i	0.862855	−	0.531551i
$630$		0			0
$631$	1.78345	−	1.78345i	0.0709978	−	0.0709978i	−0.670716	−	0.741714i	$-0.734013\pi$
$631$	1.78345	−	1.78345i	0.0709978	−	0.0709978i	0.741714	+	0.670716i	$0.234013\pi$
$632$		0			0
$633$			28.6341i			1.13811i
$634$		0			0
$635$	−1.12273	−	2.71052i	−0.0445543	−	0.107564i
$636$		0			0
$637$	24.2551	+	24.2551i	0.961020	+	0.961020i
$638$		0			0
$639$	8.75239	−	3.62536i	0.346239	−	0.143417i
$640$		0			0
$641$	2.42773	+	1.00560i	0.0958897	+	0.0397188i	0.430113	−	0.902775i	$-0.358474\pi$
$641$	2.42773	+	1.00560i	0.0958897	+	0.0397188i	−0.334223	+	0.942494i	$0.608474\pi$
$642$		0			0
$643$	−6.99319	+	16.8831i	−0.275785	+	0.665803i	−0.999710	−	0.0240753i	$-0.992336\pi$
$643$	−6.99319	+	16.8831i	−0.275785	+	0.665803i	0.723926	+	0.689878i	$0.242336\pi$
$644$		0			0
$645$	−2.89702			−0.114070
$646$		0			0
$647$	−28.9714			−1.13898			−0.569492	−	0.821997i	$-0.692860\pi$
$647$	−28.9714			−1.13898			−0.569492	+	0.821997i	$0.692860\pi$
$648$		0			0
$649$	−5.14612	+	12.4238i	−0.202003	+	0.487679i
$650$		0			0
$651$	−0.860103	−	0.356266i	−0.0337101	−	0.0139632i
$652$		0			0
$653$	−31.0590	+	12.8651i	−1.21543	+	0.503449i	−0.895955	−	0.444145i	$-0.853507\pi$
$653$	−31.0590	+	12.8651i	−1.21543	+	0.503449i	−0.319478	+	0.947594i	$0.603507\pi$
$654$		0			0
$655$	9.67490	+	9.67490i	0.378029	+	0.378029i
$656$		0			0
$657$	7.50845	+	18.1270i	0.292933	+	0.707202i
$658$		0			0
$659$		−	0.540840i		−	0.0210681i	−0.999945	−	0.0105341i	$-0.996647\pi$
$659$		−	0.540840i		−	0.0210681i	0.999945	−	0.0105341i	$-0.00335316\pi$
$660$		0			0
$661$	26.5225	−	26.5225i	1.03161	−	1.03161i	0.0321222	−	0.999484i	$-0.489773\pi$
$661$	26.5225	−	26.5225i	1.03161	−	1.03161i	0.999484	−	0.0321222i	$-0.0102266\pi$
$662$		0			0
$663$	−11.8349	−	19.2114i	−0.459631	−	0.746109i
$664$		0			0
$665$	−0.471664	+	0.471664i	−0.0182904	+	0.0182904i
$666$		0			0
$667$			1.74649i			0.0676245i
$668$		0			0
$669$	10.1536	+	24.5131i	0.392563	+	0.947730i
$670$		0			0
$671$	28.0433	+	28.0433i	1.08260	+	1.08260i
$672$		0			0
$673$	−23.2154	+	9.61615i	−0.894890	+	0.370676i	−0.782253	−	0.622961i	$-0.785930\pi$
$673$	−23.2154	+	9.61615i	−0.894890	+	0.370676i	−0.112637	+	0.993636i	$0.535930\pi$
$674$		0			0
$675$	4.88666	+	2.02412i	0.188088	+	0.0779085i
$676$		0			0
$677$	9.75469	−	23.5499i	0.374903	−	0.905097i	−0.618001	−	0.786178i	$-0.712057\pi$
$677$	9.75469	−	23.5499i	0.374903	−	0.905097i	0.992904	−	0.118919i	$-0.0379429\pi$
$678$		0			0
$679$	−0.163389			−0.00627030
$680$		0			0
$681$	2.07423			0.0794848
$682$		0			0
$683$	1.51105	−	3.64801i	0.0578189	−	0.139587i	−0.892330	−	0.451384i	$-0.850931\pi$
$683$	1.51105	−	3.64801i	0.0578189	−	0.139587i	0.950149	+	0.311796i	$0.100931\pi$
$684$		0			0
$685$	2.64376	+	1.09508i	0.101013	+	0.0418410i
$686$		0			0
$687$	−20.5167	+	8.49831i	−0.782763	+	0.324231i
$688$		0			0
$689$	7.54137	+	7.54137i	0.287303	+	0.287303i
$690$		0			0
$691$	5.03867	+	12.1644i	0.191680	+	0.462757i	0.990277	−	0.139109i	$-0.0444240\pi$
$691$	5.03867	+	12.1644i	0.191680	+	0.462757i	−0.798597	+	0.601866i	$0.794424\pi$
$692$		0			0
$693$			1.61203i			0.0612358i
$694$		0			0
$695$	−4.49340	+	4.49340i	−0.170444	+	0.170444i
$696$		0			0
$697$	13.7664	+	3.27083i	0.521440	+	0.123892i
$698$		0			0
$699$	2.68118	−	2.68118i	0.101411	−	0.101411i
$700$		0			0
$701$			6.10925i			0.230743i	0.993322	+	0.115372i	$0.0368059\pi$
$701$			6.10925i			0.230743i	−0.993322	+	0.115372i	$0.963194\pi$
$702$		0			0
$703$	−6.96738	−	16.8207i	−0.262780	−	0.634406i
$704$		0			0
$705$	−8.06829	−	8.06829i	−0.303869	−	0.303869i
$706$		0			0
$707$	0.0642903	−	0.0266299i	0.00241788	−	0.00100152i
$708$		0			0
$709$	−17.5038	−	7.25033i	−0.657371	−	0.272292i	0.0289611	−	0.999581i	$-0.490780\pi$
$709$	−17.5038	−	7.25033i	−0.657371	−	0.272292i	−0.686332	+	0.727289i	$0.740780\pi$
$710$		0			0
$711$	−3.26166	+	7.87434i	−0.122322	+	0.295311i
$712$		0			0
$713$	−1.69907			−0.0636308
$714$		0			0
$715$	−19.8959			−0.744066
$716$		0			0
$717$	−4.79261	+	11.5704i	−0.178983	+	0.432104i
$718$		0			0
$719$	12.4051	+	5.13834i	0.462631	+	0.191628i	0.601810	−	0.798639i	$-0.294446\pi$
$719$	12.4051	+	5.13834i	0.462631	+	0.191628i	−0.139179	+	0.990267i	$0.544446\pi$
$720$		0			0
$721$	2.66281	−	1.10297i	0.0991682	−	0.0410768i
$722$		0			0
$723$	−4.92654	−	4.92654i	−0.183220	−	0.183220i
$724$		0			0
$725$	1.46255	+	3.53091i	0.0543177	+	0.131135i
$726$		0			0
$727$		−	24.7160i		−	0.916666i	−0.888780	−	0.458333i	$-0.848447\pi$
$727$		−	24.7160i		−	0.916666i	0.888780	−	0.458333i	$-0.151553\pi$
$728$		0			0
$729$	13.1300	−	13.1300i	0.486298	−	0.486298i
$730$		0			0
$731$	−1.71042	−	10.6373i	−0.0632620	−	0.393436i
$732$		0			0
$733$	18.7372	−	18.7372i	0.692075	−	0.692075i	−0.270613	−	0.962688i	$-0.587226\pi$
$733$	18.7372	−	18.7372i	0.692075	−	0.692075i	0.962688	+	0.270613i	$0.0872264\pi$
$734$		0			0
$735$			7.70410i			0.284170i
$736$		0			0
$737$	−4.73342	−	11.4275i	−0.174358	−	0.420937i
$738$		0			0
$739$	18.7101	+	18.7101i	0.688262	+	0.688262i	0.961848	−	0.273585i	$-0.0882096\pi$
$739$	18.7101	+	18.7101i	0.688262	+	0.688262i	−0.273585	+	0.961848i	$0.588210\pi$
$740$		0			0
$741$	−14.9328	+	6.18536i	−0.548570	+	0.227225i
$742$		0			0
$743$	31.4774	+	13.0384i	1.15479	+	0.478331i	0.876138	−	0.482060i	$-0.160111\pi$
$743$	31.4774	+	13.0384i	1.15479	+	0.478331i	0.278655	+	0.960391i	$0.410111\pi$
$744$		0			0
$745$	−4.01190	+	9.68558i	−0.146985	+	0.354852i
$746$		0			0
$747$	−26.3055			−0.962467
$748$		0			0
$749$	−2.82436			−0.103200
$750$		0			0
$751$	9.44162	−	22.7941i	0.344530	−	0.831768i	−0.652716	−	0.757602i	$-0.726371\pi$
$751$	9.44162	−	22.7941i	0.344530	−	0.831768i	0.997246	−	0.0741657i	$-0.0236294\pi$
$752$		0			0
$753$	−2.02347	−	0.838148i	−0.0737393	−	0.0305438i
$754$		0			0
$755$	−10.2114	+	4.22971i	−0.371631	+	0.153935i
$756$		0			0
$757$	−17.8992	−	17.8992i	−0.650558	−	0.650558i	0.302569	−	0.953127i	$-0.402156\pi$
$757$	−17.8992	−	17.8992i	−0.650558	−	0.650558i	−0.953127	+	0.302569i	$0.902156\pi$
$758$		0			0
$759$	−0.781456	−	1.88660i	−0.0283651	−	0.0684793i
$760$		0			0
$761$			17.9589i			0.651011i	0.945540	+	0.325505i	$0.105534\pi$
$761$			17.9589i			0.651011i	−0.945540	+	0.325505i	$0.894466\pi$
$762$		0			0
$763$	3.23950	−	3.23950i	0.117278	−	0.117278i
$764$		0			0
$765$	−1.68780	+	7.10370i	−0.0610227	+	0.256835i
$766$		0			0
$767$	−11.6453	+	11.6453i	−0.420489	+	0.420489i
$768$		0			0
$769$			33.8801i			1.22175i	0.791728	+	0.610874i	$0.209182\pi$
$769$			33.8801i			1.22175i	−0.791728	+	0.610874i	$0.790818\pi$
$770$		0			0
$771$	−9.12227	−	22.0231i	−0.328530	−	0.793142i
$772$		0			0
$773$	−24.3851	−	24.3851i	−0.877070	−	0.877070i	0.116160	−	0.993230i	$-0.462941\pi$
$773$	−24.3851	−	24.3851i	−0.877070	−	0.877070i	−0.993230	+	0.116160i	$0.962941\pi$
$774$		0			0
$775$	−3.43504	+	1.42284i	−0.123390	+	0.0511100i
$776$		0			0
$777$	1.42605	+	0.590687i	0.0511591	+	0.0211908i
$778$		0			0
$779$	3.87874	−	9.36410i	0.138970	−	0.335504i
$780$		0			0
$781$	−21.5623			−0.771560
$782$		0			0
$783$	20.2147			0.722416
$784$		0			0
$785$	−5.33581	+	12.8818i	−0.190443	+	0.459771i
$786$		0			0
$787$	−4.14193	−	1.71564i	−0.147644	−	0.0611561i	0.307638	−	0.951503i	$-0.400461\pi$
$787$	−4.14193	−	1.71564i	−0.147644	−	0.0611561i	−0.455282	+	0.890347i	$0.650461\pi$
$788$		0			0
$789$	27.0550	−	11.2065i	0.963182	−	0.398963i
$790$		0			0
$791$	0.603970	+	0.603970i	0.0214747	+	0.0214747i
$792$		0			0
$793$	18.5871	+	44.8731i	0.660046	+	1.59349i
$794$		0			0
$795$			2.39536i			0.0849545i
$796$		0			0
$797$	−2.68218	+	2.68218i	−0.0950077	+	0.0950077i	−0.753013	−	0.658005i	$-0.771400\pi$
$797$	−2.68218	+	2.68218i	−0.0950077	+	0.0950077i	0.658005	+	0.753013i	$0.271400\pi$
$798$		0			0
$799$	24.8617	−	34.3889i	0.879545	−	1.21659i
$800$		0			0
$801$	−21.3572	+	21.3572i	−0.754621	+	0.754621i
$802$		0			0
$803$		−	44.6575i		−	1.57593i
$804$		0			0
$805$	−0.0394960	−	0.0953519i	−0.00139205	−	0.00336071i
$806$		0			0
$807$	−11.8286	−	11.8286i	−0.416386	−	0.416386i
$808$		0			0
$809$	16.3258	−	6.76237i	0.573985	−	0.237752i	−0.0767589	−	0.997050i	$-0.524457\pi$
$809$	16.3258	−	6.76237i	0.573985	−	0.237752i	0.650744	+	0.759297i	$0.274457\pi$
$810$		0			0
$811$	−33.5393	−	13.8924i	−1.17772	−	0.487829i	−0.293985	−	0.955810i	$-0.594982\pi$
$811$	−33.5393	−	13.8924i	−1.17772	−	0.487829i	−0.883739	+	0.467981i	$0.844982\pi$
$812$		0			0
$813$	2.42606	−	5.85702i	0.0850855	−	0.205415i
$814$		0			0
$815$	13.9034			0.487016
$816$		0			0
$817$	−7.71757			−0.270004
$818$		0			0
$819$	−0.755507	+	1.82395i	−0.0263995	+	0.0637341i
$820$		0			0
$821$	25.2211	+	10.4469i	0.880224	+	0.364601i	0.776583	−	0.630014i	$-0.216951\pi$
$821$	25.2211	+	10.4469i	0.880224	+	0.364601i	0.103640	+	0.994615i	$0.466951\pi$
$822$		0			0
$823$	15.7478	−	6.52295i	0.548934	−	0.227376i	−0.0909394	−	0.995856i	$-0.528987\pi$
$823$	15.7478	−	6.52295i	0.548934	−	0.227376i	0.639873	+	0.768481i	$0.278987\pi$
$824$		0			0
$825$	−3.15976	−	3.15976i	−0.110009	−	0.110009i
$826$		0			0
$827$	11.6351	+	28.0895i	0.404590	+	0.976768i	0.986537	+	0.163540i	$0.0522914\pi$
$827$	11.6351	+	28.0895i	0.404590	+	0.976768i	−0.581946	+	0.813227i	$0.697709\pi$
$828$		0			0
$829$			22.4655i			0.780260i	0.920760	+	0.390130i	$0.127570\pi$
$829$			22.4655i			0.780260i	−0.920760	+	0.390130i	$0.872430\pi$
$830$		0			0
$831$	−6.14632	+	6.14632i	−0.213213	+	0.213213i
$832$		0			0
$833$	−28.2881	+	4.54855i	−0.980124	+	0.157598i
$834$		0			0
$835$	−3.69584	+	3.69584i	−0.127900	+	0.127900i
$836$		0			0
$837$			19.6659i			0.679753i
$838$		0			0
$839$	−0.475240	−	1.14733i	−0.0164071	−	0.0396102i	0.915464	−	0.402401i	$-0.131824\pi$
$839$	−0.475240	−	1.14733i	−0.0164071	−	0.0396102i	−0.931871	+	0.362790i	$0.881824\pi$
$840$		0			0
$841$	−10.1778	−	10.1778i	−0.350960	−	0.350960i
$842$		0			0
$843$	−18.5490	+	7.68324i	−0.638861	+	0.264625i
$844$		0			0
$845$	−10.5012	−	4.34973i	−0.361251	−	0.149635i
$846$		0			0
$847$	0.453377	−	1.09455i	0.0155782	−	0.0376092i
$848$		0			0
$849$	31.1684			1.06970
$850$		0			0
$851$	2.81706			0.0965674
$852$		0			0
$853$	−5.38635	+	13.0038i	−0.184425	+	0.445241i	−0.988869	−	0.148787i	$-0.952463\pi$
$853$	−5.38635	+	13.0038i	−0.184425	+	0.445241i	0.804444	+	0.594028i	$0.202463\pi$
$854$		0			0
$855$	4.83204	+	2.00149i	0.165252	+	0.0684497i
$856$		0			0
$857$	−11.4567	+	4.74554i	−0.391355	+	0.162104i	−0.569679	−	0.821867i	$-0.692932\pi$
$857$	−11.4567	+	4.74554i	−0.391355	+	0.162104i	0.178324	+	0.983972i	$0.442932\pi$
$858$		0			0
$859$	−37.4935	−	37.4935i	−1.27926	−	1.27926i	−0.941082	−	0.338178i	$-0.890189\pi$
$859$	−37.4935	−	37.4935i	−1.27926	−	1.27926i	−0.338178	−	0.941082i	$-0.609811\pi$
$860$		0			0
$861$	0.328836	+	0.793879i	0.0112067	+	0.0270553i
$862$		0			0
$863$			0.897841i			0.0305629i	0.999883	+	0.0152814i	$0.00486442\pi$
$863$			0.897841i			0.0305629i	−0.999883	+	0.0152814i	$0.995136\pi$
$864$		0			0
$865$	6.74537	−	6.74537i	0.229350	−	0.229350i
$866$		0			0
$867$	18.7959	+	1.39043i	0.638344	+	0.0472215i
$868$		0			0
$869$	13.7173	−	13.7173i	0.465326	−	0.465326i
$870$		0			0
$871$		−	15.1482i		−	0.513279i
$872$		0			0
$873$	0.490264	+	1.18360i	0.0165929	+	0.0400588i
$874$		0			0
$875$	−0.159699	−	0.159699i	−0.00539882	−	0.00539882i
$876$		0			0
$877$	3.29576	−	1.36515i	0.111290	−	0.0460978i	−0.326344	−	0.945251i	$-0.605817\pi$
$877$	3.29576	−	1.36515i	0.111290	−	0.0460978i	0.437634	+	0.899153i	$0.355817\pi$
$878$		0			0
$879$	−24.2060	−	10.0265i	−0.816449	−	0.338184i
$880$		0			0
$881$	17.5977	−	42.4846i	0.592881	−	1.43134i	−0.287827	−	0.957682i	$-0.592933\pi$
$881$	17.5977	−	42.4846i	0.592881	−	1.43134i	0.880708	−	0.473659i	$-0.157067\pi$
$882$		0			0
$883$	43.2133			1.45424			0.727121	−	0.686509i	$-0.240858\pi$
$883$	43.2133			1.45424			0.727121	+	0.686509i	$0.240858\pi$
$884$		0			0
$885$	−3.69889			−0.124337
$886$		0			0
$887$	−6.41507	+	15.4873i	−0.215397	+	0.520014i	−0.994236	−	0.107209i	$-0.965809\pi$
$887$	−6.41507	+	15.4873i	−0.215397	+	0.520014i	0.778840	+	0.627223i	$0.215809\pi$
$888$		0			0
$889$	0.612168	+	0.253568i	0.0205314	+	0.00850440i
$890$		0			0
$891$	−2.05350	+	0.850588i	−0.0687949	+	0.0284958i
$892$		0			0
$893$	−21.4937	−	21.4937i	−0.719259	−	0.719259i
$894$		0			0
$895$	−0.448554	−	1.08291i	−0.0149935	−	0.0361976i
$896$		0			0
$897$		−	2.50087i		−	0.0835017i
$898$		0			0
$899$	−10.0478	+	10.0478i	−0.335114	+	0.335114i
$900$		0			0
$901$	−8.79531	+	1.41423i	−0.293014	+	0.0471149i
$902$		0			0
$903$	0.462652	−	0.462652i	0.0153961	−	0.0153961i
$904$		0			0
$905$			7.97775i			0.265189i
$906$		0			0
$907$	13.9155	+	33.5949i	0.462055	+	1.11550i	0.967552	+	0.252672i	$0.0813093\pi$
$907$	13.9155	+	33.5949i	0.462055	+	1.11550i	−0.505497	+	0.862829i	$0.668691\pi$
$908$		0			0
$909$	−0.385817	−	0.385817i	−0.0127968	−	0.0127968i
$910$		0			0
$911$	43.7357	−	18.1159i	1.44903	−	0.600207i	0.487059	−	0.873369i	$-0.338070\pi$
$911$	43.7357	−	18.1159i	1.44903	−	0.600207i	0.961968	+	0.273162i	$0.0880696\pi$
$912$		0			0
$913$	55.3153	+	22.9124i	1.83067	+	0.758289i
$914$		0			0
$915$	−4.17460	+	10.0784i	−0.138008	+	0.333181i
$916$		0			0
$917$	−3.09015			−0.102046
$918$		0			0
$919$	−51.0036			−1.68245			−0.841227	−	0.540681i	$-0.818166\pi$
$919$	−51.0036			−1.68245			−0.841227	+	0.540681i	$0.818166\pi$
$920$		0			0
$921$	2.66837	−	6.44202i	0.0879259	−	0.212272i
$922$		0			0
$923$	−24.3970	−	10.1056i	−0.803038	−	0.332629i
$924$		0			0
$925$	5.69528	−	2.35906i	0.187260	−	0.0775655i
$926$		0			0
$927$	−15.9800	−	15.9800i	−0.524852	−	0.524852i
$928$		0			0
$929$	−16.0605	−	38.7734i	−0.526927	−	1.27211i	−0.933527	−	0.358507i	$-0.883286\pi$
$929$	−16.0605	−	38.7734i	−0.526927	−	1.27211i	0.406600	−	0.913606i	$-0.366714\pi$
$930$		0			0
$931$			20.5235i			0.672631i
$932$		0			0
$933$	19.8589	−	19.8589i	0.650151	−	0.650151i
$934$		0			0
$935$	9.73653	−	13.4676i	0.318419	−	0.440438i
$936$		0			0
$937$	−33.9243	+	33.9243i	−1.10826	+	1.10826i	−0.114880	+	0.993379i	$0.536648\pi$
$937$	−33.9243	+	33.9243i	−1.10826	+	1.10826i	−0.993379	+	0.114880i	$0.963352\pi$
$938$		0			0
$939$			8.81061i			0.287523i
$940$		0			0
$941$	5.88085	+	14.1976i	0.191710	+	0.462829i	0.990283	−	0.139069i	$-0.0444111\pi$
$941$	5.88085	+	14.1976i	0.191710	+	0.462829i	−0.798572	+	0.601899i	$0.794411\pi$
$942$		0			0
$943$	1.10892	+	1.10892i	0.0361115	+	0.0361115i
$944$		0			0
$945$	−1.10365	+	0.457146i	−0.0359017	+	0.0148710i
$946$		0			0
$947$	−4.73866	−	1.96282i	−0.153986	−	0.0637830i	0.304359	−	0.952557i	$-0.401558\pi$
$947$	−4.73866	−	1.96282i	−0.153986	−	0.0637830i	−0.458345	+	0.888774i	$0.651558\pi$
$948$		0			0
$949$	20.9296	−	50.5285i	0.679404	−	1.64023i
$950$		0			0
$951$	0.409226			0.0132701
$952$		0			0
$953$	30.9129			1.00137			0.500684	−	0.865630i	$-0.333082\pi$
$953$	30.9129			1.00137			0.500684	+	0.865630i	$0.333082\pi$
$954$		0			0
$955$	−9.69808	+	23.4132i	−0.313823	+	0.757635i
$956$		0			0
$957$	−15.7781	−	6.53552i	−0.510035	−	0.211263i
$958$		0			0
$959$	−0.597091	+	0.247323i	−0.0192811	+	0.00798649i
$960$		0			0
$961$	12.1453	+	12.1453i	0.391783	+	0.391783i
$962$		0			0
$963$	8.47475	+	20.4599i	0.273095	+	0.659310i
$964$		0			0
$965$		−	14.1461i		−	0.455380i
$966$		0			0
$967$	17.8169	−	17.8169i	0.572954	−	0.572954i	−0.359999	−	0.932953i	$-0.617223\pi$
$967$	17.8169	−	17.8169i	0.572954	−	0.572954i	0.932953	+	0.359999i	$0.117223\pi$
$968$		0			0
$969$	3.12081	−	13.1350i	0.100255	−	0.421957i
$970$		0			0
$971$	40.3798	−	40.3798i	1.29585	−	1.29585i	0.364740	−	0.931109i	$-0.381158\pi$
$971$	40.3798	−	40.3798i	1.29585	−	1.29585i	0.931109	−	0.364740i	$-0.118842\pi$
$972$		0			0
$973$		−	1.43519i		−	0.0460099i
$974$		0			0
$975$	−2.09428	−	5.05605i	−0.0670707	−	0.161923i
$976$		0			0
$977$	−0.0400007	−	0.0400007i	−0.00127974	−	0.00127974i	0.706467	−	0.707746i	$-0.250288\pi$
$977$	−0.0400007	−	0.0400007i	−0.00127974	−	0.00127974i	−0.707746	+	0.706467i	$0.750288\pi$
$978$		0			0
$979$	63.5125	−	26.3077i	2.02987	−	0.840799i
$980$		0			0
$981$	−33.1876	−	13.7467i	−1.05960	−	0.438900i
$982$		0			0
$983$	−2.04124	+	4.92800i	−0.0651055	+	0.157179i	−0.953084	−	0.302707i	$-0.902110\pi$
$983$	−2.04124	+	4.92800i	−0.0651055	+	0.157179i	0.887978	+	0.459886i	$0.152110\pi$
$984$		0			0
$985$	17.0860			0.544404
$986$		0			0
$987$	2.57700			0.0820268
$988$		0			0
$989$	0.456968	−	1.10322i	0.0145307	−	0.0350803i
$990$		0			0
$991$	44.6297	+	18.4862i	1.41771	+	0.587235i	0.954284	−	0.298901i	$-0.0966201\pi$
$991$	44.6297	+	18.4862i	1.41771	+	0.587235i	0.463426	+	0.886136i	$0.346620\pi$
$992$		0			0
$993$	−9.72609	+	4.02868i	−0.308648	+	0.127846i
$994$		0			0
$995$	−17.5513	−	17.5513i	−0.556414	−	0.556414i
$996$		0			0
$997$	5.04439	+	12.1782i	0.159757	+	0.385689i	0.983408	−	0.181410i	$-0.0580660\pi$
$997$	5.04439	+	12.1782i	0.159757	+	0.385689i	−0.823650	+	0.567098i	$0.808066\pi$
$998$		0			0
$999$		−	32.6060i		−	1.03161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bo.a.161.6	✓	32
17.15	even	8	inner	680.2.bo.a.321.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bo.a.161.6	✓	32	1.1	even	1	trivial
680.2.bo.a.321.6	yes	32	17.15	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.424268 - 1.02427i) q^{3} +(0.923880 + 0.382683i) q^{5} +(-0.208657 + 0.0864287i) q^{7} +(1.25219 + 1.25219i) q^{9} +(-1.54244 - 3.72378i) q^{11} -4.93623i q^{13} +(0.783944 - 0.783944i) q^{15} +(3.34135 + 2.41566i) q^{17} +(2.08841 - 2.08841i) q^{19} +0.250391i q^{21} +(0.174878 + 0.422193i) q^{23} +(0.707107 + 0.707107i) q^{25} +(4.88666 - 2.02412i) q^{27} +(3.53091 + 1.46255i) q^{29} +(-1.42284 + 3.43504i) q^{31} -4.46858 q^{33} -0.225849 q^{35} +(2.35906 - 5.69528i) q^{37} +(-5.05605 - 2.09428i) q^{39} +(3.17056 - 1.31329i) q^{41} +(-1.84772 - 1.84772i) q^{43} +(0.677680 + 1.63606i) q^{45} -10.2919i q^{47} +(-4.91368 + 4.91368i) q^{49} +(3.89192 - 2.39757i) q^{51} +(-1.52776 + 1.52776i) q^{53} -4.03059i q^{55} +(-1.25305 - 3.02514i) q^{57} +(-2.35916 - 2.35916i) q^{59} +(-9.09057 + 3.76544i) q^{61} +(-0.369503 - 0.153053i) q^{63} +(1.88901 - 4.56048i) q^{65} +3.06879 q^{67} +0.506636 q^{69} +(2.04723 - 4.94244i) q^{71} +(10.2363 + 4.24000i) q^{73} +(1.02427 - 0.424268i) q^{75} +(0.643683 + 0.643683i) q^{77} +(1.84185 + 4.44661i) q^{79} -0.551456i q^{81} +(-10.5038 + 10.5038i) q^{83} +(2.16257 + 3.51045i) q^{85} +(2.99610 - 2.99610i) q^{87} +17.0559i q^{89} +(0.426632 + 1.02998i) q^{91} +(2.91475 + 2.91475i) q^{93} +(2.72863 - 1.13024i) q^{95} +(0.668375 + 0.276850i) q^{97} +(2.73145 - 6.59431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9} + 8 q^{11} - 8 q^{17} + 8 q^{19} + 8 q^{23} - 24 q^{27} - 32 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{35} + 16 q^{37} - 24 q^{39} - 16 q^{41} - 8 q^{49} + 16 q^{51} + 16 q^{53} + 48 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 + 8 * q^11 - 8 * q^17 + 8 * q^19 + 8 * q^23 - 24 * q^27 - 32 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^35 + 16 * q^37 - 24 * q^39 - 16 * q^41 - 8 * q^49 + 16 * q^51 + 16 * q^53 + 48 * q^57 + 24 * q^59 - 24 * q^61 - 48 * q^63 - 16 * q^67 - 80 * q^69 - 64 * q^71 + 16 * q^73 - 8 * q^79 - 56 * q^83 + 16 * q^85 + 96 * q^87 - 48 * q^91 + 32 * q^93 + 24 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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