LMFDB - Embedded newform 608.2.s.c.335.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [608,2,Mod(335,608)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(608, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("608.335"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			335.3
Character	$\chi$	$=$	608.335
Dual form			608.2.s.c.559.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27630 + 0.736872i) q^{3} +(-2.34524 + 1.35403i) q^{5} +3.01597i q^{7} +(-0.414040 + 0.717138i) q^{9} +3.11370 q^{11} +(0.218909 - 0.379162i) q^{13} +(1.99549 - 3.45629i) q^{15} +(-3.22274 - 5.58194i) q^{17} +(-3.58731 - 2.47613i) q^{19} +(-2.22238 - 3.84928i) q^{21} +(1.81421 + 1.04744i) q^{23} +(1.16678 - 2.02092i) q^{25} -5.64161i q^{27} +(-1.58443 + 2.74431i) q^{29} -9.77556 q^{31} +(-3.97402 + 2.29440i) q^{33} +(-4.08371 - 7.07319i) q^{35} -8.36258 q^{37} +0.645232i q^{39} +(4.66208 - 2.69165i) q^{41} +(2.43347 + 4.21489i) q^{43} -2.24248i q^{45} +(1.22865 + 0.709359i) q^{47} -2.09609 q^{49} +(8.22635 + 4.74949i) q^{51} +(1.63792 - 2.83695i) q^{53} +(-7.30239 + 4.21604i) q^{55} +(6.40307 + 0.516904i) q^{57} +(1.70599 - 0.984956i) q^{59} +(9.56035 + 5.51967i) q^{61} +(-2.16287 - 1.24873i) q^{63} +1.18563i q^{65} +(-4.49875 - 2.59735i) q^{67} -3.08731 q^{69} +(-4.40927 - 7.63707i) q^{71} +(-6.90160 - 11.9539i) q^{73} +3.43906i q^{75} +9.39085i q^{77} +(0.939415 + 1.62711i) q^{79} +(2.91502 + 5.04897i) q^{81} -3.79468 q^{83} +(15.1162 + 8.72734i) q^{85} -4.67009i q^{87} +(10.7709 + 6.21857i) q^{89} +(1.14354 + 0.660224i) q^{91} +(12.4765 - 7.20333i) q^{93} +(11.7659 + 0.949828i) q^{95} +(-16.1008 + 9.29578i) q^{97} +(-1.28920 + 2.23296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81}+ \cdots + 28 q^{99}+O(q^{100}) $ 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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
$3$	−1.27630	+	0.736872i	−0.736872	+	0.425433i	−0.820931	−	0.571028i	$-0.806545\pi$
$3$	−1.27630	+	0.736872i	−0.736872	+	0.425433i	0.0840591	+	0.996461i	$0.473212\pi$
$4$		0			0
$5$	−2.34524	+	1.35403i	−1.04882	+	0.605539i	−0.922320	−	0.386427i	$-0.873709\pi$
$5$	−2.34524	+	1.35403i	−1.04882	+	0.605539i	−0.126504	+	0.991966i	$0.540376\pi$
$6$		0			0
$7$			3.01597i			1.13993i	0.821669	+	0.569965i	$0.193043\pi$
$7$			3.01597i			1.13993i	−0.821669	+	0.569965i	$0.806957\pi$
$8$		0			0
$9$	−0.414040	+	0.717138i	−0.138013	+	0.239046i
$10$		0			0
$11$	3.11370			0.938817			0.469409	−	0.882981i	$-0.344467\pi$
$11$	3.11370			0.938817			0.469409	+	0.882981i	$0.344467\pi$
$12$		0			0
$13$	0.218909	−	0.379162i	0.0607144	−	0.105160i	−0.834071	−	0.551658i	$-0.813995\pi$
$13$	0.218909	−	0.379162i	0.0607144	−	0.105160i	0.894785	+	0.446497i	$0.147329\pi$
$14$		0			0
$15$	1.99549	−	3.45629i	0.515233	−	0.892409i
$16$		0			0
$17$	−3.22274	−	5.58194i	−0.781629	−	1.35382i	−0.930993	−	0.365038i	$-0.881056\pi$
$17$	−3.22274	−	5.58194i	−0.781629	−	1.35382i	0.149364	−	0.988782i	$-0.452277\pi$
$18$		0			0
$19$	−3.58731	−	2.47613i	−0.822984	−	0.568064i
$19$	−3.58731	−	2.47613i	−0.822984	−	0.568064i
$20$		0			0
$21$	−2.22238	−	3.84928i	−0.484964	−	0.839982i
$22$		0			0
$23$	1.81421	+	1.04744i	0.378290	+	0.218406i	0.677074	−	0.735915i	$-0.263248\pi$
$23$	1.81421	+	1.04744i	0.378290	+	0.218406i	−0.298784	+	0.954321i	$0.596581\pi$
$24$		0			0
$25$	1.16678	−	2.02092i	0.233355	−	0.404183i
$26$		0			0
$27$		−	5.64161i		−	1.08573i
$28$		0			0
$29$	−1.58443	+	2.74431i	−0.294221	+	0.509606i	−0.974803	−	0.223066i	$-0.928394\pi$
$29$	−1.58443	+	2.74431i	−0.294221	+	0.509606i	0.680582	+	0.732672i	$0.261727\pi$
$30$		0			0
$31$	−9.77556			−1.75574			−0.877871	−	0.478897i	$-0.841037\pi$
$31$	−9.77556			−1.75574			−0.877871	+	0.478897i	$0.841037\pi$
$32$		0			0
$33$	−3.97402	+	2.29440i	−0.691788	+	0.399404i
$34$		0			0
$35$	−4.08371	−	7.07319i	−0.690272	−	1.19559i
$36$		0			0
$37$	−8.36258			−1.37480			−0.687400	−	0.726279i	$-0.741248\pi$
$37$	−8.36258			−1.37480			−0.687400	+	0.726279i	$0.741248\pi$
$38$		0			0
$39$			0.645232i			0.103320i
$40$		0			0
$41$	4.66208	−	2.69165i	0.728094	−	0.420365i	−0.0896306	−	0.995975i	$-0.528569\pi$
$41$	4.66208	−	2.69165i	0.728094	−	0.420365i	0.817724	+	0.575610i	$0.195235\pi$
$42$		0			0
$43$	2.43347	+	4.21489i	0.371100	+	0.642764i	0.989735	−	0.142914i	$-0.0456473\pi$
$43$	2.43347	+	4.21489i	0.371100	+	0.642764i	−0.618635	+	0.785679i	$0.712314\pi$
$44$		0			0
$45$		−	2.24248i		−	0.334290i
$46$		0			0
$47$	1.22865	+	0.709359i	0.179216	+	0.103471i	0.586924	−	0.809642i	$-0.300339\pi$
$47$	1.22865	+	0.709359i	0.179216	+	0.103471i	−0.407708	+	0.913112i	$0.633672\pi$
$48$		0			0
$49$	−2.09609			−0.299441
$50$		0			0
$51$	8.22635	+	4.74949i	1.15192	+	0.665061i
$52$		0			0
$53$	1.63792	−	2.83695i	0.224985	−	0.389686i	−0.731330	−	0.682024i	$-0.761100\pi$
$53$	1.63792	−	2.83695i	0.224985	−	0.389686i	0.956315	+	0.292338i	$0.0944333\pi$
$54$		0			0
$55$	−7.30239	+	4.21604i	−0.984655	+	0.568491i
$56$		0			0
$57$	6.40307	+	0.516904i	0.848107	+	0.0684655i
$58$		0			0
$59$	1.70599	−	0.984956i	0.222102	−	0.128230i	−0.384821	−	0.922991i	$-0.625737\pi$
$59$	1.70599	−	0.984956i	0.222102	−	0.128230i	0.606923	+	0.794761i	$0.292404\pi$
$60$		0			0
$61$	9.56035	+	5.51967i	1.22408	+	0.706722i	0.965785	−	0.259345i	$-0.0835067\pi$
$61$	9.56035	+	5.51967i	1.22408	+	0.706722i	0.258293	+	0.966067i	$0.416840\pi$
$62$		0			0
$63$	−2.16287	−	1.24873i	−0.272496	−	0.157326i
$64$		0			0
$65$			1.18563i			0.147060i
$66$		0			0
$67$	−4.49875	−	2.59735i	−0.549609	−	0.317317i	0.199355	−	0.979927i	$-0.436115\pi$
$67$	−4.49875	−	2.59735i	−0.549609	−	0.317317i	−0.748964	+	0.662610i	$0.769449\pi$
$68$		0			0
$69$	−3.08731			−0.371668
$70$		0			0
$71$	−4.40927	−	7.63707i	−0.523284	−	0.906354i	−0.999633	−	0.0270976i	$-0.991374\pi$
$71$	−4.40927	−	7.63707i	−0.523284	−	0.906354i	0.476349	−	0.879256i	$-0.341960\pi$
$72$		0			0
$73$	−6.90160	−	11.9539i	−0.807772	−	1.39910i	−0.914404	−	0.404803i	$-0.867340\pi$
$73$	−6.90160	−	11.9539i	−0.807772	−	1.39910i	0.106632	−	0.994299i	$-0.465993\pi$
$74$		0			0
$75$			3.43906i			0.397108i
$76$		0			0
$77$			9.39085i			1.07019i
$78$		0			0
$79$	0.939415	+	1.62711i	0.105692	+	0.183065i	0.914021	−	0.405667i	$-0.132961\pi$
$79$	0.939415	+	1.62711i	0.105692	+	0.183065i	−0.808328	+	0.588732i	$0.799627\pi$
$80$		0			0
$81$	2.91502	+	5.04897i	0.323891	+	0.560996i
$82$		0			0
$83$	−3.79468			−0.416520			−0.208260	−	0.978073i	$-0.566780\pi$
$83$	−3.79468			−0.416520			−0.208260	+	0.978073i	$0.566780\pi$
$84$		0			0
$85$	15.1162	+	8.72734i	1.63958	+	0.946613i
$86$		0			0
$87$		−	4.67009i		−	0.500686i
$88$		0			0
$89$	10.7709	+	6.21857i	1.14171	+	0.659167i	0.946854	−	0.321664i	$-0.104242\pi$
$89$	10.7709	+	6.21857i	1.14171	+	0.659167i	0.194857	+	0.980832i	$0.437576\pi$
$90$		0			0
$91$	1.14354	+	0.660224i	0.119876	+	0.0692102i
$92$		0			0
$93$	12.4765	−	7.20333i	1.29376	−	0.746951i
$94$		0			0
$95$	11.7659	+	0.949828i	1.20715	+	0.0974503i
$96$		0			0
$97$	−16.1008	+	9.29578i	−1.63479	+	0.943844i	−0.652197	+	0.758050i	$0.726152\pi$
$97$	−16.1008	+	9.29578i	−1.63479	+	0.943844i	−0.982589	+	0.185794i	$0.940514\pi$
$98$		0			0
$99$	−1.28920	+	2.23296i	−0.129569	+	0.224421i
$100$		0			0
$101$	1.29368	+	0.746904i	0.128726	+	0.0743198i	0.562980	−	0.826470i	$-0.309655\pi$
$101$	1.29368	+	0.746904i	0.128726	+	0.0743198i	−0.434254	+	0.900790i	$0.642988\pi$
$102$		0			0
$103$	−5.61948			−0.553704			−0.276852	−	0.960913i	$-0.589291\pi$
$103$	−5.61948			−0.553704			−0.276852	+	0.960913i	$0.589291\pi$
$104$		0			0
$105$	10.4241	+	6.01834i	1.01728	+	0.587329i
$106$		0			0
$107$			9.01090i			0.871117i	0.900160	+	0.435558i	$0.143449\pi$
$107$			9.01090i			0.871117i	−0.900160	+	0.435558i	$0.856551\pi$
$108$		0			0
$109$	−5.62286	−	9.73908i	−0.538573	−	0.932835i	−0.998981	−	0.0451280i	$-0.985630\pi$
$109$	−5.62286	−	9.73908i	−0.538573	−	0.932835i	0.460409	−	0.887707i	$-0.347703\pi$
$110$		0			0
$111$	10.6732	−	6.16215i	1.01305	−	0.584885i
$112$		0			0
$113$			4.22083i			0.397063i	0.980095	+	0.198531i	$0.0636171\pi$
$113$			4.22083i			0.397063i	−0.980095	+	0.198531i	$0.936383\pi$
$114$		0			0
$115$	−5.67303			−0.529013
$116$		0			0
$117$	0.181274	+	0.313976i	0.0167588	+	0.0290271i
$118$		0			0
$119$	16.8350	−	9.71969i	1.54326	−	0.891002i
$120$		0			0
$121$	−1.30484			−0.118622
$122$		0			0
$123$	−3.96680	+	6.87070i	−0.357675	+	0.619510i
$124$		0			0
$125$		−	7.22088i		−	0.645855i
$126$		0			0
$127$	−7.86010	+	13.6141i	−0.697471	+	1.20806i	0.271869	+	0.962334i	$0.412358\pi$
$127$	−7.86010	+	13.6141i	−0.697471	+	1.20806i	−0.969340	+	0.245721i	$0.920975\pi$
$128$		0			0
$129$	−6.21166	−	3.58631i	−0.546906	−	0.315757i
$130$		0			0
$131$	5.08127	+	8.80102i	0.443953	+	0.768948i	0.997979	−	0.0635510i	$-0.0202425\pi$
$131$	5.08127	+	8.80102i	0.443953	+	0.768948i	−0.554026	+	0.832499i	$0.686909\pi$
$132$		0			0
$133$	7.46795	−	10.8192i	0.647553	−	0.938145i
$134$		0			0
$135$	7.63889	+	13.2309i	0.657451	+	1.13874i
$136$		0			0
$137$	−7.17527	+	12.4279i	−0.613024	+	1.06179i	0.377703	+	0.925927i	$0.376714\pi$
$137$	−7.17527	+	12.4279i	−0.613024	+	1.06179i	−0.990728	+	0.135863i	$0.956619\pi$
$138$		0			0
$139$	−5.30773	+	9.19326i	−0.450196	+	0.779763i	−0.998398	−	0.0565836i	$-0.981979\pi$
$139$	−5.30773	+	9.19326i	−0.450196	+	0.779763i	0.548202	+	0.836346i	$0.315313\pi$
$140$		0			0
$141$	−2.09083			−0.176079
$142$		0			0
$143$	0.681618	−	1.18060i	0.0569998	−	0.0987265i
$144$		0			0
$145$		−	8.58144i		−	0.712650i
$146$		0			0
$147$	2.67523	−	1.54455i	0.220650	−	0.127392i
$148$		0			0
$149$	−16.0045	+	9.24023i	−1.31114	+	0.756989i	−0.982286	−	0.187390i	$-0.939997\pi$
$149$	−16.0045	+	9.24023i	−1.31114	+	0.756989i	−0.328858	+	0.944379i	$0.606664\pi$
$150$		0			0
$151$	18.5105			1.50637			0.753183	−	0.657811i	$-0.228517\pi$
$151$	18.5105			1.50637			0.753183	+	0.657811i	$0.228517\pi$
$152$		0			0
$153$	5.33737			0.431501
$154$		0			0
$155$	22.9261	−	13.2364i	1.84147	−	1.06317i
$156$		0			0
$157$	−21.2242	+	12.2538i	−1.69388	+	0.977961i	−0.742545	+	0.669796i	$0.766382\pi$
$157$	−21.2242	+	12.2538i	−1.69388	+	0.977961i	−0.951333	+	0.308165i	$0.900285\pi$
$158$		0			0
$159$			4.82774i			0.382864i
$160$		0			0
$161$	−3.15904	+	5.47162i	−0.248967	+	0.431224i
$162$		0			0
$163$	6.00269			0.470167			0.235084	−	0.971975i	$-0.424464\pi$
$163$	6.00269			0.470167			0.235084	+	0.971975i	$0.424464\pi$
$164$		0			0
$165$	6.21336	−	10.7619i	0.483709	−	0.837809i
$166$		0			0
$167$	3.39245	−	5.87589i	0.262515	−	0.454690i	−0.704394	−	0.709809i	$-0.748781\pi$
$167$	3.39245	−	5.87589i	0.262515	−	0.454690i	0.966910	+	0.255119i	$0.0821146\pi$
$168$		0			0
$169$	6.40416	+	11.0923i	0.492628	+	0.853256i
$170$		0			0
$171$	3.26102	−	1.54738i	0.249376	−	0.118331i
$172$		0			0
$173$	−8.69543	−	15.0609i	−0.661101	−	1.14506i	−0.980327	−	0.197382i	$-0.936756\pi$
$173$	−8.69543	−	15.0609i	−0.661101	−	1.14506i	0.319225	−	0.947679i	$-0.396577\pi$
$174$		0			0
$175$	6.09502	+	3.51896i	0.460741	+	0.266009i
$176$		0			0
$177$	−1.45157	+	2.51420i	−0.109107	+	0.188979i
$178$		0			0
$179$			3.28473i			0.245513i	0.992437	+	0.122756i	$0.0391733\pi$
$179$			3.28473i			0.245513i	−0.992437	+	0.122756i	$0.960827\pi$
$180$		0			0
$181$	4.17326	−	7.22829i	0.310196	−	0.537275i	−0.668209	−	0.743974i	$-0.732939\pi$
$181$	4.17326	−	7.22829i	0.310196	−	0.537275i	0.978405	+	0.206699i	$0.0662721\pi$
$182$		0			0
$183$	−16.2692			−1.20265
$184$		0			0
$185$	19.6123	−	11.3232i	1.44192	−	0.832495i
$186$		0			0
$187$	−10.0347	−	17.3805i	−0.733806	−	1.27099i
$188$		0			0
$189$	17.0149			1.23765
$190$		0			0
$191$			4.43183i			0.320676i	0.987062	+	0.160338i	$0.0512584\pi$
$191$			4.43183i			0.320676i	−0.987062	+	0.160338i	$0.948742\pi$
$192$		0			0
$193$	−6.12690	+	3.53737i	−0.441024	+	0.254625i	−0.704032	−	0.710168i	$-0.748619\pi$
$193$	−6.12690	+	3.53737i	−0.441024	+	0.254625i	0.263008	+	0.964794i	$0.415286\pi$
$194$		0			0
$195$	−0.873661	−	1.51322i	−0.0625641	−	0.108364i
$196$		0			0
$197$			11.2899i			0.804372i	0.915558	+	0.402186i	$0.131750\pi$
$197$			11.2899i			0.804372i	−0.915558	+	0.402186i	$0.868250\pi$
$198$		0			0
$199$	6.12926	+	3.53873i	0.434492	+	0.250854i	0.701258	−	0.712907i	$-0.252622\pi$
$199$	6.12926	+	3.53873i	0.434492	+	0.250854i	−0.266766	+	0.963761i	$0.585955\pi$
$200$		0			0
$201$	7.65566			0.539989
$202$		0			0
$203$	−8.27677	−	4.77860i	−0.580916	−	0.335392i
$204$		0			0
$205$	−7.28913	+	12.6251i	−0.509095	+	0.881779i
$206$		0			0
$207$	−1.50231	+	0.867362i	−0.104418	+	0.0602858i
$208$		0			0
$209$	−11.1698	−	7.70995i	−0.772632	−	0.533308i
$210$		0			0
$211$	−15.7615	+	9.09989i	−1.08506	+	0.626462i	−0.932258	−	0.361794i	$-0.882164\pi$
$211$	−15.7615	+	9.09989i	−1.08506	+	0.626462i	−0.152806	+	0.988256i	$0.548831\pi$
$212$		0			0
$213$	11.2551	+	6.49813i	0.771186	+	0.445244i
$214$		0			0
$215$	−11.4141	−	6.58996i	−0.778438	−	0.449431i
$216$		0			0
$217$		−	29.4828i		−	2.00142i
$218$		0			0
$219$	17.6170	+	10.1712i	1.19045	+	0.687306i
$220$		0			0
$221$	−2.82195			−0.189825
$222$		0			0
$223$	−0.772936	−	1.33877i	−0.0517596	−	0.0896503i	0.838985	−	0.544155i	$-0.183150\pi$
$223$	−0.772936	−	1.33877i	−0.0517596	−	0.0896503i	−0.890744	+	0.454505i	$0.849816\pi$
$224$		0			0
$225$	0.966184	+	1.67348i	0.0644123	+	0.111565i
$226$		0			0
$227$			3.30271i			0.219209i	0.993975	+	0.109604i	$0.0349584\pi$
$227$			3.30271i			0.219209i	−0.993975	+	0.109604i	$0.965042\pi$
$228$		0			0
$229$			8.81252i			0.582348i	0.956670	+	0.291174i	$0.0940458\pi$
$229$			8.81252i			0.582348i	−0.956670	+	0.291174i	$0.905954\pi$
$230$		0			0
$231$	−6.91985	−	11.9855i	−0.455293	−	0.788590i
$232$		0			0
$233$	3.15790	+	5.46965i	0.206881	+	0.358329i	0.950730	−	0.310019i	$-0.100335\pi$
$233$	3.15790	+	5.46965i	0.206881	+	0.358329i	−0.743849	+	0.668347i	$0.767002\pi$
$234$		0			0
$235$	−3.84197			−0.250622
$236$		0			0
$237$	−2.39795	−	1.38446i	−0.155764	−	0.0899301i
$238$		0			0
$239$		−	26.2612i		−	1.69870i	−0.527834	−	0.849348i	$-0.676996\pi$
$239$		−	26.2612i		−	1.69870i	0.527834	−	0.849348i	$-0.323004\pi$
$240$		0			0
$241$	1.61651	+	0.933290i	0.104128	+	0.0601185i	0.551160	−	0.834400i	$-0.314185\pi$
$241$	1.61651	+	0.933290i	0.104128	+	0.0601185i	−0.447031	+	0.894518i	$0.647519\pi$
$242$		0			0
$243$	7.21645	+	4.16642i	0.462935	+	0.267276i
$244$		0			0
$245$	4.91583	−	2.83816i	0.314061	−	0.181323i
$246$		0			0
$247$	−1.72415	+	0.818120i	−0.109705	+	0.0520558i
$248$		0			0
$249$	4.84315	−	2.79619i	0.306922	−	0.177202i
$250$		0			0
$251$	−10.1173	+	17.5236i	−0.638596	+	1.10608i	0.347145	+	0.937811i	$0.387151\pi$
$251$	−10.1173	+	17.5236i	−0.638596	+	1.10608i	−0.985741	+	0.168269i	$0.946182\pi$
$252$		0			0
$253$	5.64893	+	3.26141i	0.355145	+	0.205043i
$254$		0			0
$255$	−25.7237			−1.61088
$256$		0			0
$257$	−10.3865	−	5.99663i	−0.647890	−	0.374060i	0.139757	−	0.990186i	$-0.455368\pi$
$257$	−10.3865	−	5.99663i	−0.647890	−	0.374060i	−0.787647	+	0.616126i	$0.788701\pi$
$258$		0			0
$259$		−	25.2213i		−	1.56718i
$260$		0			0
$261$	−1.31204	−	2.27251i	−0.0812129	−	0.140665i
$262$		0			0
$263$	−24.8302	+	14.3357i	−1.53109	+	0.883978i	−0.531783	+	0.846881i	$0.678478\pi$
$263$	−24.8302	+	14.3357i	−1.53109	+	0.883978i	−0.999312	+	0.0370975i	$0.988189\pi$
$264$		0			0
$265$			8.87113i			0.544949i
$266$		0			0
$267$	−18.3292			−1.12173
$268$		0			0
$269$	−7.77990	−	13.4752i	−0.474349	−	0.821596i	0.525220	−	0.850967i	$-0.323983\pi$
$269$	−7.77990	−	13.4752i	−0.474349	−	0.821596i	−0.999569	+	0.0293704i	$0.990650\pi$
$270$		0			0
$271$	2.99285	−	1.72792i	0.181803	−	0.104964i	−0.406337	−	0.913723i	$-0.633194\pi$
$271$	2.99285	−	1.72792i	0.181803	−	0.104964i	0.588139	+	0.808760i	$0.299861\pi$
$272$		0			0
$273$	−1.94600			−0.117777
$274$		0			0
$275$	3.63300	−	6.29253i	0.219078	−	0.379454i
$276$		0			0
$277$			1.41483i			0.0850090i	0.999096	+	0.0425045i	$0.0135337\pi$
$277$			1.41483i			0.0850090i	−0.999096	+	0.0425045i	$0.986466\pi$
$278$		0			0
$279$	4.04747	−	7.01043i	0.242316	−	0.419703i
$280$		0			0
$281$	4.69854	+	2.71270i	0.280291	+	0.161826i	0.633555	−	0.773697i	$-0.281595\pi$
$281$	4.69854	+	2.71270i	0.280291	+	0.161826i	−0.353264	+	0.935524i	$0.614928\pi$
$282$		0			0
$283$	−8.05693	−	13.9550i	−0.478935	−	0.829540i	0.520773	−	0.853695i	$-0.325644\pi$
$283$	−8.05693	−	13.9550i	−0.478935	−	0.829540i	−0.999708	+	0.0241553i	$0.992310\pi$
$284$		0			0
$285$	−15.7167	+	7.45766i	−0.930974	+	0.441754i
$286$		0			0
$287$	8.11794	+	14.0607i	0.479187	+	0.829976i
$288$		0			0
$289$	−12.2721	+	21.2559i	−0.721887	+	1.25034i
$290$		0			0
$291$	13.6996	−	23.7284i	0.803085	−	1.39098i
$292$		0			0
$293$	23.7978			1.39028			0.695142	−	0.718872i	$-0.255341\pi$
$293$	23.7978			1.39028			0.695142	+	0.718872i	$0.255341\pi$
$294$		0			0
$295$	−2.66731	+	4.61992i	−0.155297	+	0.268982i
$296$		0			0
$297$		−	17.5663i		−	1.01930i
$298$		0			0
$299$	0.794296	−	0.458587i	0.0459353	−	0.0265208i
$300$		0			0
$301$	−12.7120	+	7.33927i	−0.732707	+	0.423028i
$302$		0			0
$303$	−2.20149			−0.126472
$304$		0			0
$305$	−29.8951			−1.71179
$306$		0			0
$307$	1.43431	−	0.828099i	0.0818604	−	0.0472621i	−0.458511	−	0.888689i	$-0.651617\pi$
$307$	1.43431	−	0.828099i	0.0818604	−	0.0472621i	0.540371	+	0.841427i	$0.318284\pi$
$308$		0			0
$309$	7.17214	−	4.14084i	0.408009	−	0.235564i
$310$		0			0
$311$		−	0.650991i		−	0.0369143i	−0.999830	−	0.0184572i	$-0.994125\pi$
$311$		−	0.650991i		−	0.0369143i	0.999830	−	0.0184572i	$-0.00587543\pi$
$312$		0			0
$313$	9.66128	−	16.7338i	0.546088	−	0.945852i	−0.452450	−	0.891790i	$-0.649450\pi$
$313$	9.66128	−	16.7338i	0.546088	−	0.945852i	0.998538	−	0.0540617i	$-0.0172168\pi$
$314$		0			0
$315$	6.76327			0.381067
$316$		0			0
$317$	10.4707	−	18.1358i	0.588093	−	1.01861i	−0.406389	−	0.913700i	$-0.633212\pi$
$317$	10.4707	−	18.1358i	0.588093	−	1.01861i	0.994482	−	0.104907i	$-0.0334545\pi$
$318$		0			0
$319$	−4.93345	+	8.54498i	−0.276220	+	0.478427i
$320$		0			0
$321$	−6.63988	−	11.5006i	−0.370602	−	0.641901i
$322$		0			0
$323$	−2.26070	+	28.0041i	−0.125789	+	1.55819i
$324$		0			0
$325$	−0.510836	−	0.884793i	−0.0283361	−	0.0490795i
$326$		0			0
$327$	14.3529	+	8.28666i	0.793718	+	0.458253i
$328$		0			0
$329$	−2.13941	+	3.70556i	−0.117949	+	0.204294i
$330$		0			0
$331$		−	7.37076i		−	0.405134i	−0.979268	−	0.202567i	$-0.935072\pi$
$331$		−	7.37076i		−	0.405134i	0.979268	−	0.202567i	$-0.0649284\pi$
$332$		0			0
$333$	3.46244	−	5.99713i	0.189741	−	0.328641i
$334$		0			0
$335$	14.0675			0.768592
$336$		0			0
$337$	−9.00098	+	5.19672i	−0.490315	+	0.283083i	−0.724705	−	0.689059i	$-0.758024\pi$
$337$	−9.00098	+	5.19672i	−0.490315	+	0.283083i	0.234390	+	0.972143i	$0.424691\pi$
$338$		0			0
$339$	−3.11021	−	5.38705i	−0.168924	−	0.292584i
$340$		0			0
$341$	−30.4382			−1.64832
$342$		0			0
$343$			14.7901i			0.798588i
$344$		0			0
$345$	7.24048	−	4.18029i	0.389814	−	0.225060i
$346$		0			0
$347$	−9.25966	−	16.0382i	−0.497085	−	0.860976i	0.502910	−	0.864339i	$-0.332263\pi$
$347$	−9.25966	−	16.0382i	−0.497085	−	0.860976i	−0.999994	+	0.00336302i	$0.998930\pi$
$348$		0			0
$349$			16.1158i			0.862661i	0.902194	+	0.431330i	$0.141956\pi$
$349$			16.1158i			0.862661i	−0.902194	+	0.431330i	$0.858044\pi$
$350$		0			0
$351$	−2.13908	−	1.23500i	−0.114176	−	0.0659194i
$352$		0			0
$353$	32.0716			1.70700			0.853500	−	0.521093i	$-0.174476\pi$
$353$	32.0716			1.70700			0.853500	+	0.521093i	$0.174476\pi$
$354$		0			0
$355$	20.6816	+	11.9405i	1.09767	+	0.633737i
$356$		0			0
$357$	−14.3243	+	24.8105i	−0.758124	+	1.31311i
$358$		0			0
$359$	−3.07083	+	1.77294i	−0.162072	+	0.0935724i	−0.578842	−	0.815440i	$-0.696495\pi$
$359$	−3.07083	+	1.77294i	−0.162072	+	0.0935724i	0.416770	+	0.909012i	$0.363162\pi$
$360$		0			0
$361$	6.73752	+	17.7653i	0.354607	+	0.935016i
$362$		0			0
$363$	1.66537	−	0.961501i	0.0874092	−	0.0504657i
$364$		0			0
$365$	32.3719	+	18.6899i	1.69442	+	0.978275i
$366$		0			0
$367$	−30.3020	−	17.4948i	−1.58175	−	0.913224i	−0.994604	−	0.103742i	$-0.966918\pi$
$367$	−30.3020	−	17.4948i	−1.58175	−	0.913224i	−0.587145	−	0.809481i	$-0.699748\pi$
$368$		0			0
$369$			4.45780i			0.232064i
$370$		0			0
$371$	8.55617	+	4.93991i	0.444214	+	0.256467i
$372$		0			0
$373$	−6.14462			−0.318157			−0.159078	−	0.987266i	$-0.550852\pi$
$373$	−6.14462			−0.318157			−0.159078	+	0.987266i	$0.550852\pi$
$374$		0			0
$375$	5.32086	+	9.21601i	0.274768	+	0.475913i
$376$		0			0
$377$	0.693692	+	1.20151i	0.0357270	+	0.0618809i
$378$		0			0
$379$		−	16.1488i		−	0.829507i	−0.909934	−	0.414753i	$-0.863868\pi$
$379$		−	16.1488i		−	0.829507i	0.909934	−	0.414753i	$-0.136132\pi$
$380$		0			0
$381$		−	23.1675i		−	1.18691i
$382$		0			0
$383$	−5.82205	−	10.0841i	−0.297493	−	0.515272i	0.678069	−	0.734998i	$-0.262817\pi$
$383$	−5.82205	−	10.0841i	−0.297493	−	0.515272i	−0.975562	+	0.219726i	$0.929484\pi$
$384$		0			0
$385$	−12.7155	−	22.0238i	−0.648040	−	1.12244i
$386$		0			0
$387$	−4.03021			−0.204867
$388$		0			0
$389$	−12.0060	−	6.93167i	−0.608729	−	0.351450i	0.163739	−	0.986504i	$-0.447645\pi$
$389$	−12.0060	−	6.93167i	−0.608729	−	0.351450i	−0.772468	+	0.635054i	$0.780978\pi$
$390$		0			0
$391$		−	13.5025i		−	0.682848i
$392$		0			0
$393$	−12.9704	−	7.48849i	−0.654272	−	0.377744i
$394$		0			0
$395$	−4.40631	−	2.54399i	−0.221706	−	0.128002i
$396$		0			0
$397$	−10.1183	+	5.84182i	−0.507825	+	0.293193i	−0.731939	−	0.681370i	$-0.761384\pi$
$397$	−10.1183	+	5.84182i	−0.507825	+	0.293193i	0.224114	+	0.974563i	$0.428051\pi$
$398$		0			0
$399$	−1.55897	+	19.3115i	−0.0780459	+	0.966783i
$400$		0			0
$401$	21.4038	−	12.3575i	1.06886	−	0.617105i	0.140988	−	0.990011i	$-0.454972\pi$
$401$	21.4038	−	12.3575i	1.06886	−	0.617105i	0.927869	+	0.372907i	$0.121639\pi$
$402$		0			0
$403$	−2.13996	+	3.70652i	−0.106599	+	0.184635i
$404$		0			0
$405$	−13.6729	−	7.89403i	−0.679410	−	0.392258i
$406$		0			0
$407$	−26.0386			−1.29069
$408$		0			0
$409$	16.4212	+	9.48080i	0.811978	+	0.468796i	0.847642	−	0.530568i	$-0.178021\pi$
$409$	16.4212	+	9.48080i	0.811978	+	0.468796i	−0.0356645	+	0.999364i	$0.511355\pi$
$410$		0			0
$411$		−	21.1490i		−	1.04320i
$412$		0			0
$413$	2.97060	+	5.14523i	0.146174	+	0.253180i
$414$		0			0
$415$	8.89945	−	5.13810i	0.436857	−	0.252219i
$416$		0			0
$417$		−	15.6445i		−	0.766113i
$418$		0			0
$419$	−8.83253			−0.431497			−0.215749	−	0.976449i	$-0.569219\pi$
$419$	−8.83253			−0.431497			−0.215749	+	0.976449i	$0.569219\pi$
$420$		0			0
$421$	0.915408	+	1.58553i	0.0446143	+	0.0772742i	0.887470	−	0.460865i	$-0.152461\pi$
$421$	0.915408	+	1.58553i	0.0446143	+	0.0772742i	−0.842856	+	0.538139i	$0.819127\pi$
$422$		0			0
$423$	−1.01742	+	0.587406i	−0.0494685	+	0.0285607i
$424$		0			0
$425$	−15.0409			−0.729588
$426$		0			0
$427$	−16.6472	+	28.8338i	−0.805613	+	1.39536i
$428$		0			0
$429$			2.00906i			0.0969984i
$430$		0			0
$431$	11.5493	−	20.0040i	0.556310	−	0.963557i	−0.441490	−	0.897266i	$-0.645550\pi$
$431$	11.5493	−	20.0040i	0.556310	−	0.963557i	0.997800	−	0.0662911i	$-0.0211166\pi$
$432$		0			0
$433$	1.33452	+	0.770486i	0.0641330	+	0.0370272i	0.531724	−	0.846918i	$-0.321545\pi$
$433$	1.33452	+	0.770486i	0.0641330	+	0.0370272i	−0.467591	+	0.883945i	$0.654878\pi$
$434$		0			0
$435$	6.32342	+	10.9525i	0.303185	+	0.525132i
$436$		0			0
$437$	−3.91455	−	8.24971i	−0.187258	−	0.394637i
$438$		0			0
$439$	18.4223	+	31.9083i	0.879246	+	1.52290i	0.852169	+	0.523266i	$0.175287\pi$
$439$	18.4223	+	31.9083i	0.879246	+	1.52290i	0.0270772	+	0.999633i	$0.491380\pi$
$440$		0			0
$441$	0.867864	−	1.50318i	0.0413269	−	0.0715802i
$442$		0			0
$443$	12.8595	−	22.2732i	0.610971	−	1.05823i	−0.380106	−	0.924943i	$-0.624113\pi$
$443$	12.8595	−	22.2732i	0.610971	−	1.05823i	0.991077	−	0.133290i	$-0.0425541\pi$
$444$		0			0
$445$	−33.6804			−1.59661
$446$		0			0
$447$	13.6177	−	23.5866i	0.644097	−	1.11561i
$448$		0			0
$449$		−	12.6228i		−	0.595707i	−0.954612	−	0.297853i	$-0.903729\pi$
$449$		−	12.6228i		−	0.595707i	0.954612	−	0.297853i	$-0.0962706\pi$
$450$		0			0
$451$	14.5163	−	8.38100i	0.683547	−	0.394646i
$452$		0			0
$453$	−23.6250	+	13.6399i	−1.11000	+	0.640858i
$454$		0			0
$455$	−3.57584			−0.167638
$456$		0			0
$457$	3.27588			0.153239			0.0766197	−	0.997060i	$-0.475587\pi$
$457$	3.27588			0.153239			0.0766197	+	0.997060i	$0.475587\pi$
$458$		0			0
$459$	−31.4911	+	18.1814i	−1.46988	+	0.848636i
$460$		0			0
$461$	14.3820	−	8.30348i	0.669839	−	0.386732i	−0.126177	−	0.992008i	$-0.540271\pi$
$461$	14.3820	−	8.30348i	0.669839	−	0.386732i	0.796015	+	0.605276i	$0.206937\pi$
$462$		0			0
$463$			29.2576i			1.35972i	0.733344	+	0.679858i	$0.237958\pi$
$463$			29.2576i			1.35972i	−0.733344	+	0.679858i	$0.762042\pi$
$464$		0			0
$465$	−19.5070	+	33.7871i	−0.904616	+	1.56684i
$466$		0			0
$467$	7.69409			0.356040			0.178020	−	0.984027i	$-0.443031\pi$
$467$	7.69409			0.356040			0.178020	+	0.984027i	$0.443031\pi$
$468$		0			0
$469$	7.83354	−	13.5681i	0.361719	−	0.626516i
$470$		0			0
$471$	18.0590	−	31.2791i	0.832114	−	1.44126i
$472$		0			0
$473$	7.57710	+	13.1239i	0.348395	+	0.603438i
$474$		0			0
$475$	−9.18964	+	4.36055i	−0.421650	+	0.200076i
$476$		0			0
$477$	1.35633	+	2.34923i	0.0621019	+	0.107564i
$478$		0			0
$479$	−30.9763	−	17.8841i	−1.41534	−	0.817148i	−0.419456	−	0.907776i	$-0.637779\pi$
$479$	−30.9763	−	17.8841i	−1.41534	−	0.817148i	−0.995885	+	0.0906279i	$0.971113\pi$
$480$		0			0
$481$	−1.83064	+	3.17077i	−0.0834702	+	0.144575i
$482$		0			0
$483$		−	9.31123i		−	0.423676i
$484$		0			0
$485$	25.1735	−	43.6017i	1.14307	−	1.97985i
$486$		0			0
$487$	2.98739			0.135372			0.0676858	−	0.997707i	$-0.478438\pi$
$487$	2.98739			0.135372			0.0676858	+	0.997707i	$0.478438\pi$
$488$		0			0
$489$	−7.66123	+	4.42321i	−0.346453	+	0.200025i
$490$		0			0
$491$	16.2391	+	28.1269i	0.732858	+	1.26935i	0.955657	+	0.294483i	$0.0951475\pi$
$491$	16.2391	+	28.1269i	0.732858	+	1.26935i	−0.222798	+	0.974865i	$0.571519\pi$
$492$		0			0
$493$	20.4248			0.919887
$494$		0			0
$495$		−	6.98244i		−	0.313837i
$496$		0			0
$497$	23.0332	−	13.2982i	1.03318	−	0.596507i
$498$		0			0
$499$	4.86494	+	8.42632i	0.217785	+	0.377214i	0.954130	−	0.299391i	$-0.0967836\pi$
$499$	4.86494	+	8.42632i	0.217785	+	0.377214i	−0.736346	+	0.676605i	$0.763450\pi$
$500$		0			0
$501$			9.99919i			0.446731i
$502$		0			0
$503$	15.8302	+	9.13954i	0.705832	+	0.407512i	0.809516	−	0.587098i	$-0.199730\pi$
$503$	15.8302	+	9.13954i	0.705832	+	0.407512i	−0.103684	+	0.994610i	$0.533063\pi$
$504$		0			0
$505$	−4.04531			−0.180014
$506$		0			0
$507$	−16.3472	−	9.43809i	−0.726007	−	0.419160i
$508$		0			0
$509$	2.39384	−	4.14625i	0.106105	−	0.183779i	−0.808084	−	0.589067i	$-0.799495\pi$
$509$	2.39384	−	4.14625i	0.106105	−	0.183779i	0.914189	+	0.405288i	$0.132829\pi$
$510$		0			0
$511$	36.0527	−	20.8150i	1.59488	−	0.920803i
$512$		0			0
$513$	−13.9694	+	20.2382i	−0.616763	+	0.893537i
$514$		0			0
$515$	13.1790	−	7.60892i	0.580738	−	0.335289i
$516$		0			0
$517$	3.82564	+	2.20874i	0.168252	+	0.0971401i
$518$		0			0
$519$	22.1959	+	12.8148i	0.974294	+	0.562509i
$520$		0			0
$521$		−	14.4161i		−	0.631582i	−0.948829	−	0.315791i	$-0.897730\pi$
$521$		−	14.4161i		−	0.631582i	0.948829	−	0.315791i	$-0.102270\pi$
$522$		0			0
$523$	13.5585	+	7.82801i	0.592873	+	0.342295i	0.766233	−	0.642563i	$-0.222129\pi$
$523$	13.5585	+	7.82801i	0.592873	+	0.342295i	−0.173360	+	0.984859i	$0.555462\pi$
$524$		0			0
$525$	−10.3721			−0.452676
$526$		0			0
$527$	31.5041	+	54.5666i	1.37234	+	2.37696i
$528$		0			0
$529$	−9.30575	−	16.1180i	−0.404598	−	0.700784i
$530$		0			0
$531$			1.63125i			0.0707900i
$532$		0			0
$533$		−	2.35691i		−	0.102089i
$534$		0			0
$535$	−12.2010	−	21.1328i	−0.527495	−	0.913649i
$536$		0			0
$537$	−2.42043	−	4.19230i	−0.104449	−	0.180911i
$538$		0			0
$539$	−6.52660			−0.281120
$540$		0			0
$541$	7.10566	+	4.10246i	0.305496	+	0.176378i	0.644909	−	0.764259i	$-0.276895\pi$
$541$	7.10566	+	4.10246i	0.305496	+	0.176378i	−0.339413	+	0.940637i	$0.610228\pi$
$542$		0			0
$543$			12.3006i			0.527870i
$544$		0			0
$545$	26.3740	+	15.2270i	1.12974	+	0.652254i
$546$		0			0
$547$	−25.9507	−	14.9826i	−1.10957	−	0.640611i	−0.170853	−	0.985297i	$-0.554652\pi$
$547$	−25.9507	−	14.9826i	−1.10957	−	0.640611i	−0.938718	+	0.344685i	$0.887986\pi$
$548$		0			0
$549$	−7.91674	+	4.57073i	−0.337878	+	0.195074i
$550$		0			0
$551$	12.4791	−	5.92143i	0.531629	−	0.252261i
$552$		0			0
$553$	−4.90733	+	2.83325i	−0.208681	+	0.120482i
$554$		0			0
$555$	−16.6874	+	28.9035i	−0.708342	+	1.22688i
$556$		0			0
$557$	33.2847	+	19.2169i	1.41032	+	0.814247i	0.995418	−	0.0956198i	$-0.0304833\pi$
$557$	33.2847	+	19.2169i	1.41032	+	0.814247i	0.414900	+	0.909867i	$0.363817\pi$
$558$		0			0
$559$	2.13083			0.0901246
$560$		0			0
$561$	25.6144	+	14.7885i	1.08144	+	0.624371i
$562$		0			0
$563$			0.0334791i			0.00141098i	1.00000		0.000705488i	$0.000224564\pi$
$563$			0.0334791i			0.00141098i	−1.00000		0.000705488i	$0.999775\pi$
$564$		0			0
$565$	−5.71512	−	9.89888i	−0.240437	−	0.416449i
$566$		0			0
$567$	−15.2275	+	8.79162i	−0.639496	+	0.369213i
$568$		0			0
$569$			0.534632i			0.0224129i	0.999937	+	0.0112065i	$0.00356720\pi$
$569$			0.534632i			0.0224129i	−0.999937	+	0.0112065i	$0.996433\pi$
$570$		0			0
$571$	37.1365			1.55411			0.777057	−	0.629430i	$-0.216712\pi$
$571$	37.1365			1.55411			0.777057	+	0.629430i	$0.216712\pi$
$572$		0			0
$573$	−3.26569	−	5.65634i	−0.136426	−	0.236297i
$574$		0			0
$575$	4.23356	−	2.44425i	0.176552	−	0.101932i
$576$		0			0
$577$	−25.7080			−1.07024			−0.535118	−	0.844777i	$-0.679733\pi$
$577$	−25.7080			−1.07024			−0.535118	+	0.844777i	$0.679733\pi$
$578$		0			0
$579$	5.21318	−	9.02949i	0.216652	−	0.375253i
$580$		0			0
$581$		−	11.4447i		−	0.474804i
$582$		0			0
$583$	5.09999	−	8.83344i	0.211220	−	0.365844i
$584$		0			0
$585$	−0.850264	−	0.490900i	−0.0351541	−	0.0202962i
$586$		0			0
$587$	9.70642	+	16.8120i	0.400627	+	0.693906i	0.993802	−	0.111168i	$-0.0354590\pi$
$587$	9.70642	+	16.8120i	0.400627	+	0.693906i	−0.593175	+	0.805074i	$0.702126\pi$
$588$		0			0
$589$	35.0679	+	24.2056i	1.44495	+	0.997374i
$590$		0			0
$591$	−8.31921	−	14.4093i	−0.342207	−	0.592719i
$592$		0			0
$593$	−14.9132	+	25.8304i	−0.612411	+	1.06073i	0.378422	+	0.925633i	$0.376467\pi$
$593$	−14.9132	+	25.8304i	−0.612411	+	1.06073i	−0.990833	+	0.135093i	$0.956867\pi$
$594$		0			0
$595$	−26.3214	+	45.5900i	−1.07907	+	1.86901i
$596$		0			0
$597$	−10.4304			−0.426886
$598$		0			0
$599$	−3.62259	+	6.27451i	−0.148015	+	0.256369i	−0.930494	−	0.366308i	$-0.880622\pi$
$599$	−3.62259	+	6.27451i	−0.148015	+	0.256369i	0.782479	+	0.622677i	$0.213955\pi$
$600$		0			0
$601$			23.7575i			0.969088i	0.874767	+	0.484544i	$0.161015\pi$
$601$			23.7575i			0.969088i	−0.874767	+	0.484544i	$0.838985\pi$
$602$		0			0
$603$	3.72532	−	2.15082i	0.151707	−	0.0875880i
$604$		0			0
$605$	3.06017	−	1.76679i	0.124414	−	0.0718303i
$606$		0			0
$607$	−15.5235			−0.630081			−0.315041	−	0.949078i	$-0.602018\pi$
$607$	−15.5235			−0.630081			−0.315041	+	0.949078i	$0.602018\pi$
$608$		0			0
$609$	14.0849			0.570747
$610$		0			0
$611$	0.537924	−	0.310570i	0.0217621	−	0.0125643i
$612$		0			0
$613$	6.02011	−	3.47571i	0.243150	−	0.140383i	−0.373474	−	0.927641i	$-0.621833\pi$
$613$	6.02011	−	3.47571i	0.243150	−	0.140383i	0.616624	+	0.787258i	$0.288500\pi$
$614$		0			0
$615$		−	21.4846i		−	0.866344i
$616$		0			0
$617$	−13.4941	+	23.3725i	−0.543253	+	0.940943i	0.455461	+	0.890256i	$0.349474\pi$
$617$	−13.4941	+	23.3725i	−0.543253	+	0.940943i	−0.998715	+	0.0506869i	$0.983859\pi$
$618$		0			0
$619$	21.2410			0.853747			0.426874	−	0.904311i	$-0.359615\pi$
$619$	21.2410			0.853747			0.426874	+	0.904311i	$0.359615\pi$
$620$		0			0
$621$	5.90923	−	10.2351i	0.237129	−	0.410720i
$622$		0			0
$623$	−18.7550	+	32.4847i	−0.751405	+	1.30147i
$624$		0			0
$625$	15.6111	+	27.0393i	0.624446	+	1.08157i
$626$		0			0
$627$	19.9373	+	1.60948i	0.796218	+	0.0642766i
$628$		0			0
$629$	26.9504	+	46.6795i	1.07458	+	1.86123i
$630$		0			0
$631$	7.72930	+	4.46251i	0.307699	+	0.177650i	0.645896	−	0.763425i	$-0.276484\pi$
$631$	7.72930	+	4.46251i	0.307699	+	0.177650i	−0.338198	+	0.941075i	$0.609817\pi$
$632$		0			0
$633$	13.4109	−	23.2284i	0.533036	−	0.923245i
$634$		0			0
$635$		−	42.5711i		−	1.68938i
$636$		0			0
$637$	−0.458852	+	0.794756i	−0.0181804	+	0.0314894i
$638$		0			0
$639$	7.30245			0.288880
$640$		0			0
$641$	1.70881	−	0.986580i	0.0674938	−	0.0389675i	−0.465873	−	0.884851i	$-0.654260\pi$
$641$	1.70881	−	0.986580i	0.0674938	−	0.0389675i	0.533367	+	0.845884i	$0.320926\pi$
$642$		0			0
$643$	6.70192	+	11.6081i	0.264298	+	0.457777i	0.967379	−	0.253332i	$-0.0815265\pi$
$643$	6.70192	+	11.6081i	0.264298	+	0.457777i	−0.703082	+	0.711109i	$0.748193\pi$
$644$		0			0
$645$	19.4238			0.764812
$646$		0			0
$647$			25.2982i			0.994575i	0.867586	+	0.497288i	$0.165671\pi$
$647$			25.2982i			0.994575i	−0.867586	+	0.497288i	$0.834329\pi$
$648$		0			0
$649$	5.31196	−	3.06686i	0.208513	−	0.120385i
$650$		0			0
$651$	21.7250	+	37.6289i	0.851472	+	1.47479i
$652$		0			0
$653$			2.28865i			0.0895618i	0.998997	+	0.0447809i	$0.0142590\pi$
$653$			2.28865i			0.0895618i	−0.998997	+	0.0447809i	$0.985741\pi$
$654$		0			0
$655$	−23.8336	−	13.7603i	−0.931257	−	0.537661i
$656$		0			0
$657$	11.4302			0.445933
$658$		0			0
$659$	6.55373	+	3.78380i	0.255297	+	0.147396i	0.622187	−	0.782868i	$-0.286244\pi$
$659$	6.55373	+	3.78380i	0.255297	+	0.147396i	−0.366890	+	0.930264i	$0.619578\pi$
$660$		0			0
$661$	−7.23786	+	12.5363i	−0.281520	+	0.487607i	−0.971759	−	0.235974i	$-0.924172\pi$
$661$	−7.23786	+	12.5363i	−0.281520	+	0.487607i	0.690239	+	0.723581i	$0.257505\pi$
$662$		0			0
$663$	3.60165	−	2.07941i	0.139876	−	0.0807577i
$664$		0			0
$665$	−2.86465	+	35.4855i	−0.111086	+	1.37607i
$666$		0			0
$667$	−5.74899	+	3.31918i	−0.222602	+	0.128519i
$668$		0			0
$669$	1.97300	+	1.13911i	0.0762804	+	0.0440405i
$670$		0			0
$671$	29.7681	+	17.1866i	1.14919	+	0.663482i
$672$		0			0
$673$			26.5226i			1.02237i	0.859470	+	0.511186i	$0.170794\pi$
$673$			26.5226i			1.02237i	−0.859470	+	0.511186i	$0.829206\pi$
$674$		0			0
$675$	−11.4012	−	6.58249i	−0.438833	−	0.253360i
$676$		0			0
$677$	−6.15109			−0.236405			−0.118203	−	0.992989i	$-0.537713\pi$
$677$	−6.15109			−0.236405			−0.118203	+	0.992989i	$0.537713\pi$
$678$		0			0
$679$	−28.0358	−	48.5595i	−1.07592	−	1.86354i
$680$		0			0
$681$	−2.43367	−	4.21525i	−0.0932586	−	0.161529i
$682$		0			0
$683$		−	2.04240i		−	0.0781501i	−0.999236	−	0.0390750i	$-0.987559\pi$
$683$		−	2.04240i		−	0.0781501i	0.999236	−	0.0390750i	$-0.0124411\pi$
$684$		0			0
$685$		−	38.8620i		−	1.48484i
$686$		0			0
$687$	−6.49370	−	11.2474i	−0.247750	−	0.429115i
$688$		0			0
$689$	−0.717109	−	1.24207i	−0.0273197	−	0.0473191i
$690$		0			0
$691$	−45.7370			−1.73992			−0.869960	−	0.493123i	$-0.835855\pi$
$691$	−45.7370			−1.73992			−0.869960	+	0.493123i	$0.835855\pi$
$692$		0			0
$693$	−6.73454	−	3.88819i	−0.255824	−	0.147700i
$694$		0			0
$695$		−	28.7473i		−	1.09045i
$696$		0			0
$697$	−30.0493	−	17.3490i	−1.13820	−	0.657139i
$698$		0			0
$699$	−8.06086	−	4.65394i	−0.304890	−	0.176028i
$700$		0			0
$701$	24.5743	−	14.1880i	0.928159	−	0.535873i	0.0419298	−	0.999121i	$-0.486649\pi$
$701$	24.5743	−	14.1880i	0.928159	−	0.535873i	0.886229	+	0.463248i	$0.153316\pi$
$702$		0			0
$703$	29.9991	+	20.7069i	1.13144	+	0.780974i
$704$		0			0
$705$	4.90350	−	2.83104i	0.184676	−	0.106623i
$706$		0			0
$707$	−2.25264	+	3.90169i	−0.0847193	+	0.146738i
$708$		0			0
$709$	−4.47396	−	2.58304i	−0.168023	−	0.0970082i	0.413630	−	0.910445i	$-0.364261\pi$
$709$	−4.47396	−	2.58304i	−0.168023	−	0.0970082i	−0.581653	+	0.813437i	$0.697594\pi$
$710$		0			0
$711$	−1.55582			−0.0583479
$712$		0			0
$713$	−17.7350	−	10.2393i	−0.664179	−	0.383464i
$714$		0			0
$715$			3.69172i			0.138062i
$716$		0			0
$717$	19.3511	+	33.5171i	0.722681	+	1.25172i
$718$		0			0
$719$	−30.3540	+	17.5249i	−1.13201	+	0.653568i	−0.944441	−	0.328682i	$-0.893395\pi$
$719$	−30.3540	+	17.5249i	−1.13201	+	0.653568i	−0.187573	+	0.982251i	$0.560062\pi$
$720$		0			0
$721$		−	16.9482i		−	0.631184i
$722$		0			0
$723$	−2.75086			−0.102306
$724$		0			0
$725$	3.69735	+	6.40400i	0.137316	+	0.237839i
$726$		0			0
$727$	−7.95388	+	4.59217i	−0.294993	+	0.170314i	−0.640191	−	0.768215i	$-0.721145\pi$
$727$	−7.95388	+	4.59217i	−0.294993	+	0.170314i	0.345198	+	0.938530i	$0.387812\pi$
$728$		0			0
$729$	−29.7706			−1.10261
$730$		0			0
$731$	15.6848	−	27.1670i	0.580125	−	1.00481i
$732$		0			0
$733$			1.04212i			0.0384918i	0.999815	+	0.0192459i	$0.00612653\pi$
$733$			1.04212i			0.0384918i	−0.999815	+	0.0192459i	$0.993873\pi$
$734$		0			0
$735$	−4.18272	+	7.24468i	−0.154282	+	0.267224i
$736$		0			0
$737$	−14.0078	−	8.08739i	−0.515983	−	0.297903i
$738$		0			0
$739$	−3.24715	−	5.62423i	−0.119448	−	0.206891i	0.800101	−	0.599865i	$-0.204779\pi$
$739$	−3.24715	−	5.62423i	−0.119448	−	0.206891i	−0.919549	+	0.392975i	$0.871446\pi$
$740$		0			0
$741$	1.59768	−	2.31464i	0.0586922	−	0.0850305i
$742$		0			0
$743$	−21.4582	−	37.1666i	−0.787224	−	1.36351i	−0.927662	−	0.373422i	$-0.878184\pi$
$743$	−21.4582	−	37.1666i	−0.787224	−	1.36351i	0.140438	−	0.990089i	$-0.455149\pi$
$744$		0			0
$745$	25.0230	−	43.3412i	0.916773	−	1.58790i
$746$		0			0
$747$	1.57115	−	2.72131i	0.0574854	−	0.0995676i
$748$		0			0
$749$	−27.1766			−0.993012
$750$		0			0
$751$	21.3186	−	36.9250i	0.777928	−	1.34741i	−0.155205	−	0.987882i	$-0.549604\pi$
$751$	21.3186	−	36.9250i	0.777928	−	1.34741i	0.933134	−	0.359529i	$-0.117063\pi$
$752$		0			0
$753$		−	29.8205i		−	1.08672i
$754$		0			0
$755$	−43.4117	+	25.0638i	−1.57991	+	0.912164i
$756$		0			0
$757$	33.2731	−	19.2102i	1.20933	−	0.698208i	0.246718	−	0.969087i	$-0.420648\pi$
$757$	33.2731	−	19.2102i	1.20933	−	0.698208i	0.962613	+	0.270879i	$0.0873144\pi$
$758$		0			0
$759$	−9.61296			−0.348928
$760$		0			0
$761$	−5.18110			−0.187815			−0.0939074	−	0.995581i	$-0.529936\pi$
$761$	−5.18110			−0.187815			−0.0939074	+	0.995581i	$0.529936\pi$
$762$		0			0
$763$	29.3728	−	16.9584i	1.06337	−	0.613935i
$764$		0			0
$765$	−12.5174	+	7.22694i	−0.452569	+	0.261291i
$766$		0			0
$767$		−	0.862463i		−	0.0311417i
$768$		0			0
$769$	23.3360	−	40.4192i	0.841519	−	1.45755i	−0.0470919	−	0.998891i	$-0.514995\pi$
$769$	23.3360	−	40.4192i	0.841519	−	1.45755i	0.888611	−	0.458663i	$-0.151671\pi$
$770$		0			0
$771$	17.6750			0.636549
$772$		0			0
$773$	−16.0227	+	27.7521i	−0.576296	+	0.998175i	0.419603	+	0.907708i	$0.362169\pi$
$773$	−16.0227	+	27.7521i	−0.576296	+	0.998175i	−0.995899	+	0.0904668i	$0.971164\pi$
$774$		0			0
$775$	−11.4059	+	19.7556i	−0.409712	+	0.709641i
$776$		0			0
$777$	18.5849	+	32.1899i	0.666728	+	1.15481i
$778$		0			0
$779$	−23.3892	−	1.88815i	−0.838004	−	0.0676500i
$780$		0			0
$781$	−13.7292	−	23.7796i	−0.491268	−	0.850901i
$782$		0			0
$783$	15.4823	+	8.93874i	0.553294	+	0.319444i
$784$		0			0
$785$	33.1840	−	57.4763i	1.18439	−	2.05142i
$786$		0			0
$787$		−	32.2037i		−	1.14794i	−0.818878	−	0.573968i	$-0.805403\pi$
$787$		−	32.2037i		−	1.14794i	0.818878	−	0.573968i	$-0.194597\pi$
$788$		0			0
$789$	21.1272	−	36.5933i	0.752147	−	1.30276i
$790$		0			0
$791$	−12.7299			−0.452624
$792$		0			0
$793$	4.18570	−	2.41661i	0.148638	−	0.0858164i
$794$		0			0
$795$	−6.53688	−	11.3222i	−0.231839	−	0.401558i
$796$		0			0
$797$	−52.1341			−1.84668			−0.923342	−	0.383979i	$-0.874554\pi$
$797$	−52.1341			−1.84668			−0.923342	+	0.383979i	$0.874554\pi$
$798$		0			0
$799$		−	9.14431i		−	0.323503i
$800$		0			0
$801$	−8.91915	+	5.14947i	−0.315143	+	0.181948i
$802$		0			0
$803$	−21.4896	−	37.2210i	−0.758350	−	1.31350i
$804$		0			0
$805$		−	17.1097i		−	0.603038i
$806$		0			0
$807$	19.8590	+	11.4656i	0.699068	+	0.403607i
$808$		0			0
$809$	−28.3362			−0.996249			−0.498124	−	0.867106i	$-0.665978\pi$
$809$	−28.3362			−0.996249			−0.498124	+	0.867106i	$0.665978\pi$
$810$		0			0
$811$	8.67018	+	5.00573i	0.304451	+	0.175775i	0.644441	−	0.764654i	$-0.277090\pi$
$811$	8.67018	+	5.00573i	0.304451	+	0.175775i	−0.339990	+	0.940429i	$0.610424\pi$
$812$		0			0
$813$	−2.54651	+	4.41069i	−0.0893101	+	0.154690i
$814$		0			0
$815$	−14.0778	+	8.12780i	−0.493123	+	0.284705i
$816$		0			0
$817$	1.70704	−	21.1457i	0.0597217	−	0.739794i
$818$		0			0
$819$	−0.946943	+	0.546718i	−0.0330889	+	0.0191039i
$820$		0			0
$821$	−8.96021	−	5.17318i	−0.312714	−	0.180545i	0.335427	−	0.942066i	$-0.391120\pi$
$821$	−8.96021	−	5.17318i	−0.312714	−	0.180545i	−0.648140	+	0.761521i	$0.724453\pi$
$822$		0			0
$823$	−19.1933	−	11.0812i	−0.669036	−	0.386268i	0.126676	−	0.991944i	$-0.459569\pi$
$823$	−19.1933	−	11.0812i	−0.669036	−	0.386268i	−0.795711	+	0.605676i	$0.792903\pi$
$824$		0			0
$825$			10.7082i			0.372812i
$826$		0			0
$827$	15.5457	+	8.97531i	0.540577	+	0.312102i	0.745313	−	0.666715i	$-0.232300\pi$
$827$	15.5457	+	8.97531i	0.540577	+	0.312102i	−0.204736	+	0.978817i	$0.565634\pi$
$828$		0			0
$829$	−30.6699			−1.06521			−0.532605	−	0.846364i	$-0.678787\pi$
$829$	−30.6699			−1.06521			−0.532605	+	0.846364i	$0.678787\pi$
$830$		0			0
$831$	−1.04255	−	1.80575i	−0.0361656	−	0.0626407i
$832$		0			0
$833$	6.75514	+	11.7002i	0.234052	+	0.405389i
$834$		0			0
$835$			18.3739i			0.635853i
$836$		0			0
$837$			55.1499i			1.90626i
$838$		0			0
$839$	18.8792	+	32.6997i	0.651782	+	1.12892i	0.982690	+	0.185256i	$0.0593115\pi$
$839$	18.8792	+	32.6997i	0.651782	+	1.12892i	−0.330908	+	0.943663i	$0.607355\pi$
$840$		0			0
$841$	9.47916	+	16.4184i	0.326868	+	0.566151i
$842$		0			0
$843$	−7.99566			−0.275385
$844$		0			0
$845$	−30.0386	−	17.3428i	−1.03336	−	0.596610i
$846$		0			0
$847$		−	3.93537i		−	0.135221i
$848$		0			0
$849$	20.5661	+	11.8739i	0.705827	+	0.407510i
$850$		0			0
$851$	−15.1715	−	8.75927i	−0.520073	−	0.300264i
$852$		0			0
$853$	−3.05229	+	1.76224i	−0.104508	+	0.0603379i	−0.551343	−	0.834279i	$-0.685884\pi$
$853$	−3.05229	+	1.76224i	−0.104508	+	0.0603379i	0.446835	+	0.894616i	$0.352551\pi$
$854$		0			0
$855$	−5.55269	+	8.04448i	−0.189898	+	0.275115i
$856$		0			0
$857$	−31.7144	+	18.3103i	−1.08334	+	0.625468i	−0.931796	−	0.362982i	$-0.881759\pi$
$857$	−31.7144	+	18.3103i	−1.08334	+	0.625468i	−0.151547	+	0.988450i	$0.548425\pi$
$858$		0			0
$859$	2.99574	−	5.18877i	0.102213	−	0.177038i	−0.810383	−	0.585900i	$-0.800741\pi$
$859$	2.99574	−	5.18877i	0.102213	−	0.177038i	0.912596	+	0.408862i	$0.134074\pi$
$860$		0			0
$861$	−20.7218	−	11.9638i	−0.706199	−	0.407724i
$862$		0			0
$863$	12.3914			0.421808			0.210904	−	0.977507i	$-0.432359\pi$
$863$	12.3914			0.421808			0.210904	+	0.977507i	$0.432359\pi$
$864$		0			0
$865$	40.7858	+	23.5477i	1.38676	+	0.800645i
$866$		0			0
$867$		−	36.1718i		−	1.22846i
$868$		0			0
$869$	2.92506	+	5.06635i	0.0992259	+	0.171864i
$870$		0			0
$871$	−1.96963	+	1.13717i	−0.0667385	+	0.0385315i
$872$		0			0
$873$		−	15.3953i		−	0.521052i
$874$		0			0
$875$	21.7780			0.736230
$876$		0			0
$877$	10.4760	+	18.1449i	0.353749	+	0.612711i	0.986903	−	0.161315i	$-0.0515735\pi$
$877$	10.4760	+	18.1449i	0.353749	+	0.612711i	−0.633154	+	0.774026i	$0.718240\pi$
$878$		0			0
$879$	−30.3732	+	17.5359i	−1.02446	+	0.591473i
$880$		0			0
$881$	16.3102			0.549504			0.274752	−	0.961515i	$-0.411404\pi$
$881$	16.3102			0.549504			0.274752	+	0.961515i	$0.411404\pi$
$882$		0			0
$883$	−3.10945	+	5.38572i	−0.104641	+	0.181244i	−0.913592	−	0.406633i	$-0.866703\pi$
$883$	−3.10945	+	5.38572i	−0.104641	+	0.181244i	0.808950	+	0.587877i	$0.200036\pi$
$884$		0			0
$885$		−	7.86187i		−	0.264274i
$886$		0			0
$887$	−0.671412	+	1.16292i	−0.0225438	+	0.0390470i	−0.877077	−	0.480349i	$-0.840510\pi$
$887$	−0.671412	+	1.16292i	−0.0225438	+	0.0390470i	0.854533	+	0.519396i	$0.173843\pi$
$888$		0			0
$889$	−41.0597	−	23.7058i	−1.37710	−	0.795069i
$890$		0			0
$891$	9.07652	+	15.7210i	0.304075	+	0.526673i
$892$		0			0
$893$	−2.65106	−	5.58698i	−0.0887144	−	0.186961i
$894$		0			0
$895$	−4.44762	−	7.70350i	−0.148667	−	0.257500i
$896$		0			0
$897$	−0.675839	+	1.17059i	−0.0225656	+	0.0390848i
$898$		0			0
$899$	15.4887	−	26.8272i	0.516577	−	0.894737i
$900$		0			0
$901$	−21.1143			−0.703419
$902$		0			0
$903$	10.8162	−	18.7342i	0.359941	−	0.623435i
$904$		0			0
$905$			22.6028i			0.751342i
$906$		0			0
$907$	−5.49954	+	3.17516i	−0.182609	+	0.105429i	−0.588518	−	0.808484i	$-0.700288\pi$
$907$	−5.49954	+	3.17516i	−0.182609	+	0.105429i	0.405909	+	0.913914i	$0.366955\pi$
$908$		0			0
$909$	−1.07127	+	0.618497i	−0.0355317	+	0.0205142i
$910$		0			0
$911$	−32.3135			−1.07059			−0.535296	−	0.844664i	$-0.679800\pi$
$911$	−32.3135			−1.07059			−0.535296	+	0.844664i	$0.679800\pi$
$912$		0			0
$913$	−11.8155			−0.391037
$914$		0			0
$915$	38.1551	−	22.0289i	1.26137	−	0.728252i
$916$		0			0
$917$	−26.5436	+	15.3250i	−0.876547	+	0.506075i
$918$		0			0
$919$			38.7254i			1.27743i	0.769443	+	0.638716i	$0.220534\pi$
$919$			38.7254i			1.27743i	−0.769443	+	0.638716i	$0.779466\pi$
$920$		0			0
$921$	−1.22041	+	2.11380i	−0.0402137	+	0.0696522i
$922$		0			0
$923$	−3.86091			−0.127083
$924$		0			0
$925$	−9.75726	+	16.9001i	−0.320817	+	0.555671i
$926$		0			0
$927$	2.32669	−	4.02994i	0.0764185	−	0.132361i
$928$		0			0
$929$	−25.4113	−	44.0137i	−0.833719	−	1.44404i	−0.895069	−	0.445927i	$-0.852874\pi$
$929$	−25.4113	−	44.0137i	−0.833719	−	1.44404i	0.0613502	−	0.998116i	$-0.480459\pi$
$930$		0			0
$931$	7.51930	+	5.19019i	0.246435	+	0.170102i
$932$		0			0
$933$	0.479697	+	0.830860i	0.0157046	+	0.0272011i
$934$		0			0
$935$	47.0674	+	27.1744i	1.53927	+	0.888697i
$936$		0			0
$937$	−16.1691	+	28.0057i	−0.528221	+	0.914906i	0.471238	+	0.882006i	$0.343807\pi$
$937$	−16.1691	+	28.0057i	−0.528221	+	0.914906i	−0.999459	+	0.0328994i	$0.989526\pi$
$938$		0			0
$939$			28.4765i			0.929295i
$940$		0			0
$941$	−14.0148	+	24.2743i	−0.456868	+	0.791319i	−0.998793	−	0.0491078i	$-0.984362\pi$
$941$	−14.0148	+	24.2743i	−0.456868	+	0.791319i	0.541925	+	0.840427i	$0.317696\pi$
$942$		0			0
$943$	11.2773			0.367241
$944$		0			0
$945$	−39.9041	+	23.0387i	−1.29808	+	0.749448i
$946$		0			0
$947$	7.39400	+	12.8068i	0.240273	+	0.416164i	0.960792	−	0.277271i	$-0.0894298\pi$
$947$	7.39400	+	12.8068i	0.240273	+	0.416164i	−0.720519	+	0.693435i	$0.756097\pi$
$948$		0			0
$949$	−6.04329			−0.196174
$950$		0			0
$951$			30.8623i			1.00078i
$952$		0			0
$953$	−6.69642	+	3.86618i	−0.216918	+	0.125238i	−0.604523	−	0.796588i	$-0.706636\pi$
$953$	−6.69642	+	3.86618i	−0.216918	+	0.125238i	0.387604	+	0.921826i	$0.373303\pi$
$954$		0			0
$955$	−6.00082	−	10.3937i	−0.194182	−	0.336333i
$956$		0			0
$957$		−	14.5413i		−	0.470053i
$958$		0			0
$959$	−37.4823	−	21.6404i	−1.21037	−	0.698805i
$960$		0			0
$961$	64.5615			2.08263
$962$		0			0
$963$	−6.46206	−	3.73087i	−0.208237	−	0.120226i
$964$		0			0
$965$	9.57939	−	16.5920i	0.308371	−	0.534115i
$966$		0			0
$967$	29.1031	−	16.8027i	0.935892	−	0.540338i	0.0472221	−	0.998884i	$-0.484963\pi$
$967$	29.1031	−	16.8027i	0.935892	−	0.540338i	0.888670	+	0.458547i	$0.151630\pi$
$968$		0			0
$969$	−17.7501	−	37.4074i	−0.570215	−	1.20170i
$970$		0			0
$971$	−13.6746	+	7.89505i	−0.438840	+	0.253364i	−0.703105	−	0.711086i	$-0.748204\pi$
$971$	−13.6746	+	7.89505i	−0.438840	+	0.253364i	0.264265	+	0.964450i	$0.414870\pi$
$972$		0			0
$973$	−27.7266	−	16.0080i	−0.888875	−	0.513192i
$974$		0			0
$975$	1.30396	+	0.752841i	0.0417601	+	0.0241102i
$976$		0			0
$977$		−	32.5834i		−	1.04243i	−0.853424	−	0.521217i	$-0.825478\pi$
$977$		−	32.5834i		−	1.04243i	0.853424	−	0.521217i	$-0.174522\pi$
$978$		0			0
$979$	33.5373	+	19.3628i	1.07186	+	0.618838i
$980$		0			0
$981$	9.31236			0.297321
$982$		0			0
$983$	−3.64307	−	6.30998i	−0.116196	−	0.201257i	0.802061	−	0.597242i	$-0.203737\pi$
$983$	−3.64307	−	6.30998i	−0.116196	−	0.201257i	−0.918257	+	0.395985i	$0.870403\pi$
$984$		0			0
$985$	−15.2868	−	26.4776i	−0.487079	−	0.843646i
$986$		0			0
$987$		−	6.30588i		−	0.200718i
$988$		0			0
$989$			10.1956i			0.324202i
$990$		0			0
$991$	1.76345	+	3.05438i	0.0560177	+	0.0970256i	0.892674	−	0.450702i	$-0.148826\pi$
$991$	1.76345	+	3.05438i	0.0560177	+	0.0970256i	−0.836657	+	0.547728i	$0.815493\pi$
$992$		0			0
$993$	5.43131	+	9.40730i	0.172357	+	0.298532i
$994$		0			0
$995$	−19.1661			−0.607608
$996$		0			0
$997$	13.7973	+	7.96589i	0.436966	+	0.252282i	0.702310	−	0.711871i	$-0.252152\pi$
$997$	13.7973	+	7.96589i	0.436966	+	0.252282i	−0.265344	+	0.964154i	$0.585485\pi$
$998$		0			0
$999$			47.1784i			1.49266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.s.c.335.3		28
4.3	odd	2		152.2.o.c.107.13	yes	28
8.3	odd	2	inner	608.2.s.c.335.4		28
8.5	even	2		152.2.o.c.107.9	yes	28
19.8	odd	6	inner	608.2.s.c.559.4		28
76.27	even	6		152.2.o.c.27.9	✓	28
152.27	even	6	inner	608.2.s.c.559.3		28
152.141	odd	6		152.2.o.c.27.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.9	✓	28	76.27	even	6
152.2.o.c.27.13	yes	28	152.141	odd	6
152.2.o.c.107.9	yes	28	8.5	even	2
152.2.o.c.107.13	yes	28	4.3	odd	2
608.2.s.c.335.3		28	1.1	even	1	trivial
608.2.s.c.335.4		28	8.3	odd	2	inner
608.2.s.c.559.3		28	152.27	even	6	inner
608.2.s.c.559.4		28	19.8	odd	6	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:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.27630 + 0.736872i) q^{3} +(-2.34524 + 1.35403i) q^{5} +3.01597i q^{7} +(-0.414040 + 0.717138i) q^{9} +3.11370 q^{11} +(0.218909 - 0.379162i) q^{13} +(1.99549 - 3.45629i) q^{15} +(-3.22274 - 5.58194i) q^{17} +(-3.58731 - 2.47613i) q^{19} +(-2.22238 - 3.84928i) q^{21} +(1.81421 + 1.04744i) q^{23} +(1.16678 - 2.02092i) q^{25} -5.64161i q^{27} +(-1.58443 + 2.74431i) q^{29} -9.77556 q^{31} +(-3.97402 + 2.29440i) q^{33} +(-4.08371 - 7.07319i) q^{35} -8.36258 q^{37} +0.645232i q^{39} +(4.66208 - 2.69165i) q^{41} +(2.43347 + 4.21489i) q^{43} -2.24248i q^{45} +(1.22865 + 0.709359i) q^{47} -2.09609 q^{49} +(8.22635 + 4.74949i) q^{51} +(1.63792 - 2.83695i) q^{53} +(-7.30239 + 4.21604i) q^{55} +(6.40307 + 0.516904i) q^{57} +(1.70599 - 0.984956i) q^{59} +(9.56035 + 5.51967i) q^{61} +(-2.16287 - 1.24873i) q^{63} +1.18563i q^{65} +(-4.49875 - 2.59735i) q^{67} -3.08731 q^{69} +(-4.40927 - 7.63707i) q^{71} +(-6.90160 - 11.9539i) q^{73} +3.43906i q^{75} +9.39085i q^{77} +(0.939415 + 1.62711i) q^{79} +(2.91502 + 5.04897i) q^{81} -3.79468 q^{83} +(15.1162 + 8.72734i) q^{85} -4.67009i q^{87} +(10.7709 + 6.21857i) q^{89} +(1.14354 + 0.660224i) q^{91} +(12.4765 - 7.20333i) q^{93} +(11.7659 + 0.949828i) q^{95} +(-16.1008 + 9.29578i) q^{97} +(-1.28920 + 2.23296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81}+ \cdots + 28 q^{99}+O(q^{100}) \) 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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