LMFDB - Embedded newform 1360.2.bn.b.783.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1360,2,Mod(783,1360)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1360, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1360.783"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1360 = 2^{4} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1360.bn (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] 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:	$10.8596546749$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			783.15
Character	$\chi$	$=$	1360.783
Dual form			1360.2.bn.b.1327.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.124060 + 0.124060i) q^{3} +(-2.20593 + 0.365900i) q^{5} +(2.34724 + 2.34724i) q^{7} +2.96922i q^{9} +0.861269i q^{11} +(-2.29360 - 2.29360i) q^{13} +(0.228274 - 0.319062i) q^{15} +(0.707107 - 0.707107i) q^{17} -6.14132 q^{19} -0.582399 q^{21} +(-1.85561 + 1.85561i) q^{23} +(4.73223 - 1.61430i) q^{25} +(-0.740543 - 0.740543i) q^{27} +8.21277i q^{29} -10.4521i q^{31} +(-0.106849 - 0.106849i) q^{33} +(-6.03670 - 4.31899i) q^{35} +(-4.41927 + 4.41927i) q^{37} +0.569090 q^{39} +3.37171 q^{41} +(2.47916 - 2.47916i) q^{43} +(-1.08644 - 6.54988i) q^{45} +(-6.85123 - 6.85123i) q^{47} +4.01907i q^{49} +0.175448i q^{51} +(0.971203 + 0.971203i) q^{53} +(-0.315139 - 1.89990i) q^{55} +(0.761894 - 0.761894i) q^{57} -9.58067 q^{59} -9.95746 q^{61} +(-6.96947 + 6.96947i) q^{63} +(5.89875 + 4.22029i) q^{65} +(-0.0130951 - 0.0130951i) q^{67} -0.460416i q^{69} +1.10180i q^{71} +(2.97943 + 2.97943i) q^{73} +(-0.386812 + 0.787353i) q^{75} +(-2.02160 + 2.02160i) q^{77} -11.3693 q^{79} -8.72391 q^{81} +(-7.32475 + 7.32475i) q^{83} +(-1.30110 + 1.81856i) q^{85} +(-1.01888 - 1.01888i) q^{87} +10.7325i q^{89} -10.7673i q^{91} +(1.29670 + 1.29670i) q^{93} +(13.5473 - 2.24711i) q^{95} +(-12.8567 + 12.8567i) q^{97} -2.55729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{13} + 64 q^{21} + 24 q^{25} - 56 q^{33} - 32 q^{41} - 24 q^{45} + 64 q^{53} + 64 q^{57} - 16 q^{61} + 40 q^{65} + 56 q^{73} - 40 q^{77} - 176 q^{81} - 104 q^{93} - 16 q^{97}+O(q^{100}) $ 64 * q - 8 * q^13 + 64 * q^21 + 24 * q^25 - 56 * q^33 - 32 * q^41 - 24 * q^45 + 64 * q^53 + 64 * q^57 - 16 * q^61 + 40 * q^65 + 56 * q^73 - 40 * q^77 - 176 * q^81 - 104 * q^93 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.124060	+	0.124060i	−0.0716262	+	0.0716262i	−0.742012	−	0.670386i	$-0.766128\pi$
$3$	−0.124060	+	0.124060i	−0.0716262	+	0.0716262i	0.670386	+	0.742012i	$0.266128\pi$
$4$		0			0
$5$	−2.20593	+	0.365900i	−0.986521	+	0.163636i
$5$	−2.20593	+	0.365900i	−0.986521	+	0.163636i
$6$		0			0
$7$	2.34724	+	2.34724i	0.887173	+	0.887173i	0.994251	−	0.107077i	$-0.0341493\pi$
$7$	2.34724	+	2.34724i	0.887173	+	0.887173i	−0.107077	+	0.994251i	$0.534149\pi$
$8$		0			0
$9$			2.96922i			0.989739i
$10$		0			0
$11$			0.861269i			0.259682i	0.991535	+	0.129841i	$0.0414467\pi$
$11$			0.861269i			0.259682i	−0.991535	+	0.129841i	$0.958553\pi$
$12$		0			0
$13$	−2.29360	−	2.29360i	−0.636131	−	0.636131i	0.313468	−	0.949599i	$-0.398509\pi$
$13$	−2.29360	−	2.29360i	−0.636131	−	0.636131i	−0.949599	+	0.313468i	$0.898509\pi$
$14$		0			0
$15$	0.228274	−	0.319062i	0.0589402	−	0.0823814i
$16$		0			0
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$		0			0
$19$	−6.14132			−1.40892			−0.704458	−	0.709746i	$-0.748810\pi$
$19$	−6.14132			−1.40892			−0.704458	+	0.709746i	$0.748810\pi$
$20$		0			0
$21$	−0.582399			−0.127090
$22$		0			0
$23$	−1.85561	+	1.85561i	−0.386922	+	0.386922i	−0.873588	−	0.486666i	$-0.838213\pi$
$23$	−1.85561	+	1.85561i	−0.386922	+	0.386922i	0.486666	+	0.873588i	$0.338213\pi$
$24$		0			0
$25$	4.73223	−	1.61430i	0.946447	−	0.322860i
$26$		0			0
$27$	−0.740543	−	0.740543i	−0.142518	−	0.142518i
$28$		0			0
$29$			8.21277i			1.52507i	0.646945	+	0.762536i	$0.276046\pi$
$29$			8.21277i			1.52507i	−0.646945	+	0.762536i	$0.723954\pi$
$30$		0			0
$31$		−	10.4521i		−	1.87726i	−0.344927	−	0.938630i	$-0.612096\pi$
$31$		−	10.4521i		−	1.87726i	0.344927	−	0.938630i	$-0.387904\pi$
$32$		0			0
$33$	−0.106849	−	0.106849i	−0.0186001	−	0.0186001i
$34$		0			0
$35$	−6.03670	−	4.31899i	−1.02039	−	0.730042i
$36$		0			0
$37$	−4.41927	+	4.41927i	−0.726523	+	0.726523i	−0.969925	−	0.243402i	$-0.921737\pi$
$37$	−4.41927	+	4.41927i	−0.726523	+	0.726523i	0.243402	+	0.969925i	$0.421737\pi$
$38$		0			0
$39$	0.569090			0.0911274
$40$		0			0
$41$	3.37171			0.526572			0.263286	−	0.964718i	$-0.415194\pi$
$41$	3.37171			0.526572			0.263286	+	0.964718i	$0.415194\pi$
$42$		0			0
$43$	2.47916	−	2.47916i	0.378068	−	0.378068i	−0.492337	−	0.870405i	$-0.663857\pi$
$43$	2.47916	−	2.47916i	0.378068	−	0.378068i	0.870405	+	0.492337i	$0.163857\pi$
$44$		0			0
$45$	−1.08644	−	6.54988i	−0.161957	−	0.976399i
$46$		0			0
$47$	−6.85123	−	6.85123i	−0.999355	−	0.999355i	0.000644998	−	1.00000i	$-0.499795\pi$
$47$	−6.85123	−	6.85123i	−0.999355	−	0.999355i	−1.00000		0.000644998i	$0.999795\pi$
$48$		0			0
$49$			4.01907i			0.574153i
$50$		0			0
$51$			0.175448i			0.0245676i
$52$		0			0
$53$	0.971203	+	0.971203i	0.133405	+	0.133405i	0.770656	−	0.637251i	$-0.219929\pi$
$53$	0.971203	+	0.971203i	0.133405	+	0.133405i	−0.637251	+	0.770656i	$0.719929\pi$
$54$		0			0
$55$	−0.315139	−	1.89990i	−0.0424933	−	0.256182i
$56$		0			0
$57$	0.761894	−	0.761894i	0.100915	−	0.100915i
$58$		0			0
$59$	−9.58067			−1.24730			−0.623649	−	0.781705i	$-0.714350\pi$
$59$	−9.58067			−1.24730			−0.623649	+	0.781705i	$0.714350\pi$
$60$		0			0
$61$	−9.95746			−1.27492			−0.637461	−	0.770483i	$-0.720015\pi$
$61$	−9.95746			−1.27492			−0.637461	+	0.770483i	$0.720015\pi$
$62$		0			0
$63$	−6.96947	+	6.96947i	−0.878070	+	0.878070i
$64$		0			0
$65$	5.89875	+	4.22029i	0.731650	+	0.523463i
$66$		0			0
$67$	−0.0130951	−	0.0130951i	−0.00159982	−	0.00159982i	0.706306	−	0.707906i	$-0.250360\pi$
$67$	−0.0130951	−	0.0130951i	−0.00159982	−	0.00159982i	−0.707906	+	0.706306i	$0.750360\pi$
$68$		0			0
$69$		−	0.460416i		−	0.0554276i
$70$		0			0
$71$			1.10180i			0.130760i	0.997860	+	0.0653800i	$0.0208260\pi$
$71$			1.10180i			0.130760i	−0.997860	+	0.0653800i	$0.979174\pi$
$72$		0			0
$73$	2.97943	+	2.97943i	0.348716	+	0.348716i	0.859631	−	0.510915i	$-0.170693\pi$
$73$	2.97943	+	2.97943i	0.348716	+	0.348716i	−0.510915	+	0.859631i	$0.670693\pi$
$74$		0			0
$75$	−0.386812	+	0.787353i	−0.0446652	+	0.0909157i
$76$		0			0
$77$	−2.02160	+	2.02160i	−0.230383	+	0.230383i
$78$		0			0
$79$	−11.3693			−1.27915			−0.639574	−	0.768730i	$-0.720889\pi$
$79$	−11.3693			−1.27915			−0.639574	+	0.768730i	$0.720889\pi$
$80$		0			0
$81$	−8.72391			−0.969323
$82$		0			0
$83$	−7.32475	+	7.32475i	−0.803996	+	0.803996i	−0.983718	−	0.179722i	$-0.942480\pi$
$83$	−7.32475	+	7.32475i	−0.803996	+	0.803996i	0.179722	+	0.983718i	$0.442480\pi$
$84$		0			0
$85$	−1.30110	+	1.81856i	−0.141124	+	0.197250i
$86$		0			0
$87$	−1.01888	−	1.01888i	−0.109235	−	0.109235i
$88$		0			0
$89$			10.7325i			1.13764i	0.822460	+	0.568822i	$0.192601\pi$
$89$			10.7325i			1.13764i	−0.822460	+	0.568822i	$0.807399\pi$
$90$		0			0
$91$		−	10.7673i		−	1.12872i
$92$		0			0
$93$	1.29670	+	1.29670i	0.134461	+	0.134461i
$94$		0			0
$95$	13.5473	−	2.24711i	1.38992	−	0.230549i
$96$		0			0
$97$	−12.8567	+	12.8567i	−1.30541	+	1.30541i	−0.380711	+	0.924694i	$0.624321\pi$
$97$	−12.8567	+	12.8567i	−1.30541	+	1.30541i	−0.924694	+	0.380711i	$0.875679\pi$
$98$		0			0
$99$	−2.55729			−0.257018
$100$		0			0
$101$	−0.779429			−0.0775561			−0.0387781	−	0.999248i	$-0.512347\pi$
$101$	−0.779429			−0.0775561			−0.0387781	+	0.999248i	$0.512347\pi$
$102$		0			0
$103$	−8.82893	+	8.82893i	−0.869940	+	0.869940i	−0.992465	−	0.122525i	$-0.960901\pi$
$103$	−8.82893	+	8.82893i	−0.869940	+	0.869940i	0.122525	+	0.992465i	$0.460901\pi$
$104$		0			0
$105$	1.28473	−	0.213100i	0.125377	−	0.0207964i
$106$		0			0
$107$	7.93728	+	7.93728i	0.767326	+	0.767326i	0.977635	−	0.210309i	$-0.0674470\pi$
$107$	7.93728	+	7.93728i	0.767326	+	0.767326i	−0.210309	+	0.977635i	$0.567447\pi$
$108$		0			0
$109$		−	19.6876i		−	1.88573i	−0.333168	−	0.942867i	$-0.608118\pi$
$109$		−	19.6876i		−	1.88573i	0.333168	−	0.942867i	$-0.391882\pi$
$110$		0			0
$111$		−	1.09651i		−	0.104076i
$112$		0			0
$113$	9.46623	+	9.46623i	0.890508	+	0.890508i	0.994571	−	0.104062i	$-0.0331841\pi$
$113$	9.46623	+	9.46623i	0.890508	+	0.890508i	−0.104062	+	0.994571i	$0.533184\pi$
$114$		0			0
$115$	3.41438	−	4.77232i	0.318393	−	0.445021i
$116$		0			0
$117$	6.81021	−	6.81021i	0.629604	−	0.629604i
$118$		0			0
$119$	3.31950			0.304298
$120$		0			0
$121$	10.2582			0.932565
$122$		0			0
$123$	−0.418295	+	0.418295i	−0.0377164	+	0.0377164i
$124$		0			0
$125$	−9.84829	+	5.29255i	−0.880858	+	0.473380i
$126$		0			0
$127$	0.141559	+	0.141559i	0.0125614	+	0.0125614i	0.713360	−	0.700798i	$-0.247173\pi$
$127$	0.141559	+	0.141559i	0.0125614	+	0.0125614i	−0.700798	+	0.713360i	$0.747173\pi$
$128$		0			0
$129$			0.615130i			0.0541592i
$130$		0			0
$131$		−	4.36215i		−	0.381123i	−0.981675	−	0.190561i	$-0.938969\pi$
$131$		−	4.36215i		−	0.381123i	0.981675	−	0.190561i	$-0.0610309\pi$
$132$		0			0
$133$	−14.4151	−	14.4151i	−1.24995	−	1.24995i
$134$		0			0
$135$	1.90455	+	1.36262i	0.163917	+	0.117276i
$136$		0			0
$137$	6.66158	−	6.66158i	0.569137	−	0.569137i	−0.362750	−	0.931887i	$-0.618162\pi$
$137$	6.66158	−	6.66158i	0.569137	−	0.569137i	0.931887	+	0.362750i	$0.118162\pi$
$138$		0			0
$139$	−0.901816			−0.0764911			−0.0382455	−	0.999268i	$-0.512177\pi$
$139$	−0.901816			−0.0764911			−0.0382455	+	0.999268i	$0.512177\pi$
$140$		0			0
$141$	1.69993			0.143160
$142$		0			0
$143$	1.97541	−	1.97541i	0.165192	−	0.165192i
$144$		0			0
$145$	−3.00505	−	18.1168i	−0.249556	−	1.50452i
$146$		0			0
$147$	−0.498607	−	0.498607i	−0.0411244	−	0.0411244i
$148$		0			0
$149$			3.62048i			0.296601i	0.988942	+	0.148301i	$0.0473803\pi$
$149$			3.62048i			0.296601i	−0.988942	+	0.148301i	$0.952620\pi$
$150$		0			0
$151$		−	4.03587i		−	0.328435i	−0.986424	−	0.164217i	$-0.947490\pi$
$151$		−	4.03587i		−	0.328435i	0.986424	−	0.164217i	$-0.0525098\pi$
$152$		0			0
$153$	2.09955	+	2.09955i	0.169739	+	0.169739i
$154$		0			0
$155$	3.82444	+	23.0567i	0.307186	+	1.85196i
$156$		0			0
$157$	−5.01729	+	5.01729i	−0.400423	+	0.400423i	−0.878382	−	0.477959i	$-0.841377\pi$
$157$	−5.01729	+	5.01729i	−0.400423	+	0.400423i	0.477959	+	0.878382i	$0.341377\pi$
$158$		0			0
$159$	−0.240975			−0.0191106
$160$		0			0
$161$	−8.71115			−0.686534
$162$		0			0
$163$	12.9748	−	12.9748i	1.01626	−	1.01626i	0.0163962	−	0.999866i	$-0.494781\pi$
$163$	12.9748	−	12.9748i	1.01626	−	1.01626i	0.999866	−	0.0163962i	$-0.00521930\pi$
$164$		0			0
$165$	0.274798	+	0.196606i	0.0213930	+	0.0153057i
$166$		0			0
$167$	−5.28568	−	5.28568i	−0.409018	−	0.409018i	0.472378	−	0.881396i	$-0.343396\pi$
$167$	−5.28568	−	5.28568i	−0.409018	−	0.409018i	−0.881396	+	0.472378i	$0.843396\pi$
$168$		0			0
$169$		−	2.47876i		−	0.190674i
$170$		0			0
$171$		−	18.2349i		−	1.39446i
$172$		0			0
$173$	10.3718	+	10.3718i	0.788552	+	0.788552i	0.981257	−	0.192705i	$-0.0617261\pi$
$173$	10.3718	+	10.3718i	0.788552	+	0.788552i	−0.192705	+	0.981257i	$0.561726\pi$
$174$		0			0
$175$	14.8968	+	7.31854i	1.12609	+	0.553230i
$176$		0			0
$177$	1.18858	−	1.18858i	0.0893392	−	0.0893392i
$178$		0			0
$179$	22.0590			1.64877			0.824384	−	0.566031i	$-0.191522\pi$
$179$	22.0590			1.64877			0.824384	+	0.566031i	$0.191522\pi$
$180$		0			0
$181$	0.929075			0.0690576			0.0345288	−	0.999404i	$-0.489007\pi$
$181$	0.929075			0.0690576			0.0345288	+	0.999404i	$0.489007\pi$
$182$		0			0
$183$	1.23533	−	1.23533i	0.0913179	−	0.0913179i
$184$		0			0
$185$	8.13158	−	11.3656i	0.597845	−	0.835616i
$186$		0			0
$187$	0.609009	+	0.609009i	0.0445351	+	0.0445351i
$188$		0			0
$189$		−	3.47646i		−	0.252876i
$190$		0			0
$191$			14.8229i			1.07255i	0.844045	+	0.536273i	$0.180168\pi$
$191$			14.8229i			1.07255i	−0.844045	+	0.536273i	$0.819832\pi$
$192$		0			0
$193$	16.4594	+	16.4594i	1.18477	+	1.18477i	0.978493	+	0.206279i	$0.0661355\pi$
$193$	16.4594	+	16.4594i	1.18477	+	1.18477i	0.206279	+	0.978493i	$0.433864\pi$
$194$		0			0
$195$	−1.25537	+	0.208230i	−0.0898991	+	0.0149117i
$196$		0			0
$197$	12.5288	−	12.5288i	0.892639	−	0.892639i	−0.102132	−	0.994771i	$-0.532566\pi$
$197$	12.5288	−	12.5288i	0.892639	−	0.892639i	0.994771	+	0.102132i	$0.0325663\pi$
$198$		0			0
$199$	−3.57439			−0.253382			−0.126691	−	0.991942i	$-0.540436\pi$
$199$	−3.57439			−0.253382			−0.126691	+	0.991942i	$0.540436\pi$
$200$		0			0
$201$	0.00324916			0.000229178
$202$		0			0
$203$	−19.2773	+	19.2773i	−1.35300	+	1.35300i
$204$		0			0
$205$	−7.43774	+	1.23371i	−0.519474	+	0.0861659i
$206$		0			0
$207$	−5.50972	−	5.50972i	−0.382952	−	0.382952i
$208$		0			0
$209$		−	5.28932i		−	0.365870i
$210$		0			0
$211$		−	20.8745i		−	1.43706i	−0.695495	−	0.718531i	$-0.744815\pi$
$211$		−	20.8745i		−	1.43706i	0.695495	−	0.718531i	$-0.255185\pi$
$212$		0			0
$213$	−0.136690	−	0.136690i	−0.00936585	−	0.00936585i
$214$		0			0
$215$	−4.56172	+	6.37597i	−0.311107	+	0.434837i
$216$		0			0
$217$	24.5337	−	24.5337i	1.66545	−	1.66545i
$218$		0			0
$219$	−0.739258			−0.0499544
$220$		0			0
$221$	−3.24365			−0.218191
$222$		0			0
$223$	8.07794	−	8.07794i	0.540939	−	0.540939i	−0.382865	−	0.923804i	$-0.625063\pi$
$223$	8.07794	−	8.07794i	0.540939	−	0.540939i	0.923804	+	0.382865i	$0.125063\pi$
$224$		0			0
$225$	4.79321	+	14.0510i	0.319547	+	0.936736i
$226$		0			0
$227$	8.17072	+	8.17072i	0.542310	+	0.542310i	0.924206	−	0.381895i	$-0.124729\pi$
$227$	8.17072	+	8.17072i	0.542310	+	0.542310i	−0.381895	+	0.924206i	$0.624729\pi$
$228$		0			0
$229$			13.7075i			0.905816i	0.891557	+	0.452908i	$0.149613\pi$
$229$			13.7075i			0.905816i	−0.891557	+	0.452908i	$0.850387\pi$
$230$		0			0
$231$		−	0.501602i		−	0.0330030i
$232$		0			0
$233$	9.45185	+	9.45185i	0.619212	+	0.619212i	0.945329	−	0.326118i	$-0.105741\pi$
$233$	9.45185	+	9.45185i	0.619212	+	0.619212i	−0.326118	+	0.945329i	$0.605741\pi$
$234$		0			0
$235$	17.6202	+	12.6065i	1.14941	+	0.822354i
$236$		0			0
$237$	1.41048	−	1.41048i	0.0916206	−	0.0916206i
$238$		0			0
$239$	−20.2840			−1.31207			−0.656033	−	0.754733i	$-0.727767\pi$
$239$	−20.2840			−1.31207			−0.656033	+	0.754733i	$0.727767\pi$
$240$		0			0
$241$	−19.6520			−1.26590			−0.632948	−	0.774195i	$-0.718155\pi$
$241$	−19.6520			−1.26590			−0.632948	+	0.774195i	$0.718155\pi$
$242$		0			0
$243$	3.30392	−	3.30392i	0.211947	−	0.211947i
$244$		0			0
$245$	−1.47058	−	8.86578i	−0.0939519	−	0.566414i
$246$		0			0
$247$	14.0858	+	14.0858i	0.896255	+	0.896255i
$248$		0			0
$249$		−	1.81742i		−	0.115174i
$250$		0			0
$251$			4.07827i			0.257418i	0.991682	+	0.128709i	$0.0410834\pi$
$251$			4.07827i			0.257418i	−0.991682	+	0.128709i	$0.958917\pi$
$252$		0			0
$253$	−1.59818	−	1.59818i	−0.100477	−	0.100477i
$254$		0			0
$255$	−0.0641964	−	0.387025i	−0.00402013	−	0.0242364i
$256$		0			0
$257$	−5.32513	+	5.32513i	−0.332173	+	0.332173i	−0.853411	−	0.521238i	$-0.825470\pi$
$257$	−5.32513	+	5.32513i	−0.332173	+	0.332173i	0.521238	+	0.853411i	$0.325470\pi$
$258$		0			0
$259$	−20.7462			−1.28910
$260$		0			0
$261$	−24.3855			−1.50942
$262$		0			0
$263$	−19.4859	+	19.4859i	−1.20155	+	1.20155i	−0.227860	+	0.973694i	$0.573173\pi$
$263$	−19.4859	+	19.4859i	−1.20155	+	1.20155i	−0.973694	+	0.227860i	$0.926827\pi$
$264$		0			0
$265$	−2.49777	−	1.78704i	−0.153437	−	0.109777i
$266$		0			0
$267$	−1.33148	−	1.33148i	−0.0814852	−	0.0814852i
$268$		0			0
$269$		−	1.80469i		−	0.110034i	−0.998485	−	0.0550169i	$-0.982479\pi$
$269$		−	1.80469i		−	0.110034i	0.998485	−	0.0550169i	$-0.0175213\pi$
$270$		0			0
$271$		−	10.4001i		−	0.631763i	−0.948799	−	0.315882i	$-0.897700\pi$
$271$		−	10.4001i		−	0.631763i	0.948799	−	0.315882i	$-0.102300\pi$
$272$		0			0
$273$	1.33579	+	1.33579i	0.0808458	+	0.0808458i
$274$		0			0
$275$	1.39035	+	4.07572i	0.0838410	+	0.245775i
$276$		0			0
$277$	−6.18882	+	6.18882i	−0.371850	+	0.371850i	−0.868151	−	0.496301i	$-0.834691\pi$
$277$	−6.18882	+	6.18882i	−0.371850	+	0.371850i	0.496301	+	0.868151i	$0.334691\pi$
$278$		0			0
$279$	31.0347			1.85800
$280$		0			0
$281$	−16.3773			−0.976986			−0.488493	−	0.872568i	$-0.662453\pi$
$281$	−16.3773			−0.976986			−0.488493	+	0.872568i	$0.662453\pi$
$282$		0			0
$283$	12.6739	−	12.6739i	0.753384	−	0.753384i	−0.221726	−	0.975109i	$-0.571169\pi$
$283$	12.6739	−	12.6739i	0.753384	−	0.753384i	0.975109	+	0.221726i	$0.0711689\pi$
$284$		0			0
$285$	−1.40191	+	1.95946i	−0.0830417	+	0.116068i
$286$		0			0
$287$	7.91420	+	7.91420i	0.467161	+	0.467161i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$		0			0
$291$		−	3.19002i		−	0.187003i
$292$		0			0
$293$	−4.35741	−	4.35741i	−0.254562	−	0.254562i	0.568276	−	0.822838i	$-0.307611\pi$
$293$	−4.35741	−	4.35741i	−0.254562	−	0.254562i	−0.822838	+	0.568276i	$0.807611\pi$
$294$		0			0
$295$	21.1343	−	3.50557i	1.23048	−	0.204102i
$296$		0			0
$297$	0.637806	−	0.637806i	0.0370093	−	0.0370093i
$298$		0			0
$299$	8.51209			0.492267
$300$		0			0
$301$	11.6384			0.670824
$302$		0			0
$303$	0.0966962	−	0.0966962i	0.00555505	−	0.00555505i
$304$		0			0
$305$	21.9654	−	3.64344i	1.25774	−	0.208623i
$306$		0			0
$307$	16.8496	+	16.8496i	0.961655	+	0.961655i	0.999292	−	0.0376363i	$-0.0119828\pi$
$307$	16.8496	+	16.8496i	0.961655	+	0.961655i	−0.0376363	+	0.999292i	$0.511983\pi$
$308$		0			0
$309$		−	2.19064i		−	0.124621i
$310$		0			0
$311$		−	16.0477i		−	0.909984i	−0.890496	−	0.454992i	$-0.849642\pi$
$311$		−	16.0477i		−	0.909984i	0.890496	−	0.454992i	$-0.150358\pi$
$312$		0			0
$313$	−10.4793	−	10.4793i	−0.592323	−	0.592323i	0.345935	−	0.938258i	$-0.387562\pi$
$313$	−10.4793	−	10.4793i	−0.592323	−	0.592323i	−0.938258	+	0.345935i	$0.887562\pi$
$314$		0			0
$315$	12.8240	−	17.9243i	0.722551	−	1.00992i
$316$		0			0
$317$	8.21886	−	8.21886i	0.461617	−	0.461617i	−0.437568	−	0.899185i	$-0.644160\pi$
$317$	8.21886	−	8.21886i	0.461617	−	0.461617i	0.899185	+	0.437568i	$0.144160\pi$
$318$		0			0
$319$	−7.07340			−0.396034
$320$		0			0
$321$	−1.96940			−0.109921
$322$		0			0
$323$	−4.34257	+	4.34257i	−0.241627	+	0.241627i
$324$		0			0
$325$	−14.5564	−	7.15131i	−0.807446	−	0.396683i
$326$		0			0
$327$	2.44246	+	2.44246i	0.135068	+	0.135068i
$328$		0			0
$329$		−	32.1630i		−	1.77320i
$330$		0			0
$331$			5.63461i			0.309706i	0.987938	+	0.154853i	$0.0494904\pi$
$331$			5.63461i			0.309706i	−0.987938	+	0.154853i	$0.950510\pi$
$332$		0			0
$333$	−13.1218	−	13.1218i	−0.719069	−	0.719069i
$334$		0			0
$335$	0.0336783	+	0.0240953i	0.00184004	+	0.00131647i
$336$		0			0
$337$	−7.75583	+	7.75583i	−0.422487	+	0.422487i	−0.886059	−	0.463572i	$-0.846567\pi$
$337$	−7.75583	+	7.75583i	−0.422487	+	0.422487i	0.463572	+	0.886059i	$0.346567\pi$
$338$		0			0
$339$	−2.34877			−0.127568
$340$		0			0
$341$	9.00210			0.487491
$342$		0			0
$343$	6.99696	−	6.99696i	0.377800	−	0.377800i
$344$		0			0
$345$	0.168466	+	1.01564i	0.00906993	+	0.0546805i
$346$		0			0
$347$	24.7937	+	24.7937i	1.33100	+	1.33100i	0.904478	+	0.426520i	$0.140261\pi$
$347$	24.7937	+	24.7937i	1.33100	+	1.33100i	0.426520	+	0.904478i	$0.359739\pi$
$348$		0			0
$349$			17.7399i			0.949596i	0.880095	+	0.474798i	$0.157479\pi$
$349$			17.7399i			0.949596i	−0.880095	+	0.474798i	$0.842521\pi$
$350$		0			0
$351$			3.39702i			0.181320i
$352$		0			0
$353$	8.84892	+	8.84892i	0.470981	+	0.470981i	0.902232	−	0.431251i	$-0.141928\pi$
$353$	8.84892	+	8.84892i	0.470981	+	0.470981i	−0.431251	+	0.902232i	$0.641928\pi$
$354$		0			0
$355$	−0.403151	−	2.43050i	−0.0213970	−	0.128998i
$356$		0			0
$357$	−0.411818	+	0.411818i	−0.0217957	+	0.0217957i
$358$		0			0
$359$	−15.5965			−0.823150			−0.411575	−	0.911376i	$-0.635021\pi$
$359$	−15.5965			−0.823150			−0.411575	+	0.911376i	$0.635021\pi$
$360$		0			0
$361$	18.7158			0.985042
$362$		0			0
$363$	−1.27264	+	1.27264i	−0.0667961	+	0.0667961i
$364$		0			0
$365$	−7.66259	−	5.48224i	−0.401078	−	0.286953i
$366$		0			0
$367$	16.9694	+	16.9694i	0.885797	+	0.885797i	0.994116	−	0.108320i	$-0.0345470\pi$
$367$	16.9694	+	16.9694i	0.885797	+	0.885797i	−0.108320	+	0.994116i	$0.534547\pi$
$368$		0			0
$369$			10.0113i			0.521169i
$370$		0			0
$371$			4.55929i			0.236707i
$372$		0			0
$373$	11.3830	+	11.3830i	0.589389	+	0.589389i	0.937466	−	0.348077i	$-0.113165\pi$
$373$	11.3830	+	11.3830i	0.589389	+	0.589389i	−0.348077	+	0.937466i	$0.613165\pi$
$374$		0			0
$375$	0.565186	−	1.87838i	0.0291861	−	0.0969990i
$376$		0			0
$377$	18.8368	−	18.8368i	0.970146	−	0.970146i
$378$		0			0
$379$	−12.3736			−0.635590			−0.317795	−	0.948160i	$-0.602942\pi$
$379$	−12.3736			−0.635590			−0.317795	+	0.948160i	$0.602942\pi$
$380$		0			0
$381$	−0.0351238			−0.00179944
$382$		0			0
$383$	20.8220	−	20.8220i	1.06396	−	1.06396i	0.0661456	−	0.997810i	$-0.478930\pi$
$383$	20.8220	−	20.8220i	1.06396	−	1.06396i	0.997810	−	0.0661456i	$-0.0210702\pi$
$384$		0			0
$385$	3.71981	−	5.19922i	0.189579	−	0.264977i
$386$		0			0
$387$	7.36116	+	7.36116i	0.374189	+	0.374189i
$388$		0			0
$389$			12.4040i			0.628908i	0.949273	+	0.314454i	$0.101821\pi$
$389$			12.4040i			0.628908i	−0.949273	+	0.314454i	$0.898179\pi$
$390$		0			0
$391$			2.62424i			0.132713i
$392$		0			0
$393$	0.541170	+	0.541170i	0.0272984	+	0.0272984i
$394$		0			0
$395$	25.0799	−	4.16004i	1.26191	−	0.209314i
$396$		0			0
$397$	7.55670	−	7.55670i	0.379260	−	0.379260i	−0.491575	−	0.870835i	$-0.663579\pi$
$397$	7.55670	−	7.55670i	0.379260	−	0.379260i	0.870835	+	0.491575i	$0.163579\pi$
$398$		0			0
$399$	3.57669			0.179059
$400$		0			0
$401$	18.0186			0.899808			0.449904	−	0.893077i	$-0.351458\pi$
$401$	18.0186			0.899808			0.449904	+	0.893077i	$0.351458\pi$
$402$		0			0
$403$	−23.9731	+	23.9731i	−1.19418	+	1.19418i
$404$		0			0
$405$	19.2443	−	3.19208i	0.956258	−	0.158616i
$406$		0			0
$407$	−3.80618	−	3.80618i	−0.188665	−	0.188665i
$408$		0			0
$409$		−	3.96094i		−	0.195856i	−0.995193	−	0.0979280i	$-0.968779\pi$
$409$		−	3.96094i		−	0.195856i	0.995193	−	0.0979280i	$-0.0312215\pi$
$410$		0			0
$411$			1.65287i			0.0815303i
$412$		0			0
$413$	−22.4881	−	22.4881i	−1.10657	−	1.10657i
$414$		0			0
$415$	13.4777	−	18.8380i	0.661596	−	0.924721i
$416$		0			0
$417$	0.111880	−	0.111880i	0.00547877	−	0.00547877i
$418$		0			0
$419$	−35.6815			−1.74315			−0.871577	−	0.490258i	$-0.836903\pi$
$419$	−35.6815			−1.74315			−0.871577	+	0.490258i	$0.836903\pi$
$420$		0			0
$421$	−15.8366			−0.771829			−0.385915	−	0.922535i	$-0.626114\pi$
$421$	−15.8366			−0.771829			−0.385915	+	0.922535i	$0.626114\pi$
$422$		0			0
$423$	20.3428	−	20.3428i	0.989101	−	0.989101i
$424$		0			0
$425$	2.20471	−	4.48768i	0.106944	−	0.217684i
$426$		0			0
$427$	−23.3725	−	23.3725i	−1.13108	−	1.13108i
$428$		0			0
$429$			0.490140i			0.0236642i
$430$		0			0
$431$			6.44310i			0.310353i	0.987887	+	0.155177i	$0.0495947\pi$
$431$			6.44310i			0.310353i	−0.987887	+	0.155177i	$0.950405\pi$
$432$		0			0
$433$	17.9965	+	17.9965i	0.864859	+	0.864859i	0.991898	−	0.127039i	$-0.0405474\pi$
$433$	17.9965	+	17.9965i	0.864859	+	0.864859i	−0.127039	+	0.991898i	$0.540547\pi$
$434$		0			0
$435$	2.62038	+	1.87476i	0.125638	+	0.0898880i
$436$		0			0
$437$	11.3959	−	11.3959i	0.545141	−	0.545141i
$438$		0			0
$439$	23.0474			1.09999			0.549997	−	0.835166i	$-0.314629\pi$
$439$	23.0474			1.09999			0.549997	+	0.835166i	$0.314629\pi$
$440$		0			0
$441$	−11.9335			−0.568262
$442$		0			0
$443$	−23.0593	+	23.0593i	−1.09558	+	1.09558i	−0.100659	+	0.994921i	$0.532095\pi$
$443$	−23.0593	+	23.0593i	−1.09558	+	1.09558i	−0.994921	+	0.100659i	$0.967905\pi$
$444$		0			0
$445$	−3.92703	−	23.6752i	−0.186159	−	1.12231i
$446$		0			0
$447$	−0.449158	−	0.449158i	−0.0212444	−	0.0212444i
$448$		0			0
$449$			0.177217i			0.00836340i	0.999991	+	0.00418170i	$0.00133108\pi$
$449$			0.177217i			0.00836340i	−0.999991	+	0.00418170i	$0.998669\pi$
$450$		0			0
$451$			2.90394i			0.136741i
$452$		0			0
$453$	0.500692	+	0.500692i	0.0235245	+	0.0235245i
$454$		0			0
$455$	3.93975	+	23.7518i	0.184698	+	1.11350i
$456$		0			0
$457$	−10.7406	+	10.7406i	−0.502425	+	0.502425i	−0.912191	−	0.409765i	$-0.865611\pi$
$457$	−10.7406	+	10.7406i	−0.502425	+	0.502425i	0.409765	+	0.912191i	$0.365611\pi$
$458$		0			0
$459$	−1.04729			−0.0488831
$460$		0			0
$461$	−7.84510			−0.365383			−0.182691	−	0.983170i	$-0.558481\pi$
$461$	−7.84510			−0.365383			−0.182691	+	0.983170i	$0.558481\pi$
$462$		0			0
$463$	−24.3744	+	24.3744i	−1.13277	+	1.13277i	−0.143061	+	0.989714i	$0.545695\pi$
$463$	−24.3744	+	24.3744i	−1.13277	+	1.13277i	−0.989714	+	0.143061i	$0.954305\pi$
$464$		0			0
$465$	−3.33488	−	2.38595i	−0.154651	−	0.110646i
$466$		0			0
$467$	1.88773	+	1.88773i	0.0873536	+	0.0873536i	0.749433	−	0.662080i	$-0.230326\pi$
$467$	1.88773	+	1.88773i	0.0873536	+	0.0873536i	−0.662080	+	0.749433i	$0.730326\pi$
$468$		0			0
$469$		−	0.0614746i		−	0.00283863i
$470$		0			0
$471$		−	1.24489i		−	0.0573617i
$472$		0			0
$473$	2.13522	+	2.13522i	0.0981775	+	0.0981775i
$474$		0			0
$475$	−29.0622	+	9.91393i	−1.33346	+	0.454882i
$476$		0			0
$477$	−2.88371	+	2.88371i	−0.132036	+	0.132036i
$478$		0			0
$479$	26.9687			1.23223			0.616116	−	0.787656i	$-0.288705\pi$
$479$	26.9687			1.23223			0.616116	+	0.787656i	$0.288705\pi$
$480$		0			0
$481$	20.2721			0.924328
$482$		0			0
$483$	1.08071	−	1.08071i	0.0491739	−	0.0491739i
$484$		0			0
$485$	23.6568	−	33.0653i	1.07420	−	1.50142i
$486$		0			0
$487$	2.44711	+	2.44711i	0.110889	+	0.110889i	0.760374	−	0.649485i	$-0.225016\pi$
$487$	2.44711	+	2.44711i	0.110889	+	0.110889i	−0.649485	+	0.760374i	$0.725016\pi$
$488$		0			0
$489$			3.21931i			0.145582i
$490$		0			0
$491$		−	17.1187i		−	0.772557i	−0.922382	−	0.386279i	$-0.873760\pi$
$491$		−	17.1187i		−	0.772557i	0.922382	−	0.386279i	$-0.126240\pi$
$492$		0			0
$493$	5.80730	+	5.80730i	0.261548	+	0.261548i
$494$		0			0
$495$	5.64121	−	0.935715i	0.253553	−	0.0420573i
$496$		0			0
$497$	−2.58620	+	2.58620i	−0.116007	+	0.116007i
$498$		0			0
$499$	21.9128			0.980954			0.490477	−	0.871454i	$-0.336823\pi$
$499$	21.9128			0.980954			0.490477	+	0.871454i	$0.336823\pi$
$500$		0			0
$501$	1.31148			0.0585928
$502$		0			0
$503$	−29.3981	+	29.3981i	−1.31079	+	1.31079i	−0.389965	+	0.920830i	$0.627513\pi$
$503$	−29.3981	+	29.3981i	−1.31079	+	1.31079i	−0.920830	+	0.389965i	$0.872487\pi$
$504$		0			0
$505$	1.71936	−	0.285193i	0.0765107	−	0.0126909i
$506$		0			0
$507$	0.307516	+	0.307516i	0.0136573	+	0.0136573i
$508$		0			0
$509$			43.3734i			1.92249i	0.275696	+	0.961245i	$0.411092\pi$
$509$			43.3734i			1.92249i	−0.275696	+	0.961245i	$0.588908\pi$
$510$		0			0
$511$			13.9869i			0.618743i
$512$		0			0
$513$	4.54791	+	4.54791i	0.200795	+	0.200795i
$514$		0			0
$515$	16.2455	−	22.7065i	0.715861	−	1.00057i
$516$		0			0
$517$	5.90075	−	5.90075i	0.259515	−	0.259515i
$518$		0			0
$519$	−2.57345			−0.112962
$520$		0			0
$521$	−21.8515			−0.957330			−0.478665	−	0.877998i	$-0.658879\pi$
$521$	−21.8515			−0.957330			−0.478665	+	0.877998i	$0.658879\pi$
$522$		0			0
$523$	16.1765	−	16.1765i	0.707347	−	0.707347i	−0.258629	−	0.965977i	$-0.583271\pi$
$523$	16.1765	−	16.1765i	0.707347	−	0.707347i	0.965977	+	0.258629i	$0.0832708\pi$
$524$		0			0
$525$	−2.75605	+	0.940166i	−0.120284	+	0.0410322i
$526$		0			0
$527$	−7.39078	−	7.39078i	−0.321947	−	0.321947i
$528$		0			0
$529$			16.1134i			0.700582i
$530$		0			0
$531$		−	28.4471i		−	1.23450i
$532$		0			0
$533$	−7.73336	−	7.73336i	−0.334969	−	0.334969i
$534$		0			0
$535$	−20.4133	−	14.6048i	−0.882545	−	0.631421i
$536$		0			0
$537$	−2.73665	+	2.73665i	−0.118095	+	0.118095i
$538$		0			0
$539$	−3.46150			−0.149097
$540$		0			0
$541$	11.4270			0.491284			0.245642	−	0.969361i	$-0.421001\pi$
$541$	11.4270			0.491284			0.245642	+	0.969361i	$0.421001\pi$
$542$		0			0
$543$	−0.115261	+	0.115261i	−0.00494634	+	0.00494634i
$544$		0			0
$545$	7.20372	+	43.4295i	0.308573	+	1.86032i
$546$		0			0
$547$	8.87763	+	8.87763i	0.379580	+	0.379580i	0.870951	−	0.491371i	$-0.163504\pi$
$547$	8.87763	+	8.87763i	0.379580	+	0.379580i	−0.491371	+	0.870951i	$0.663504\pi$
$548$		0			0
$549$		−	29.5659i		−	1.26184i
$550$		0			0
$551$		−	50.4372i		−	2.14870i
$552$		0			0
$553$	−26.6865	−	26.6865i	−1.13483	−	1.13483i
$554$		0			0
$555$	0.401214	+	2.41883i	0.0170306	+	0.102673i
$556$		0			0
$557$	−25.9115	+	25.9115i	−1.09791	+	1.09791i	−0.103252	+	0.994655i	$0.532925\pi$
$557$	−25.9115	+	25.9115i	−1.09791	+	1.09791i	−0.994655	+	0.103252i	$0.967075\pi$
$558$		0			0
$559$	−11.3724			−0.481002
$560$		0			0
$561$	−0.151108			−0.00637977
$562$		0			0
$563$	−8.66155	+	8.66155i	−0.365041	+	0.365041i	−0.865665	−	0.500624i	$-0.833104\pi$
$563$	−8.66155	+	8.66155i	−0.365041	+	0.365041i	0.500624	+	0.865665i	$0.333104\pi$
$564$		0			0
$565$	−24.3455	−	17.4181i	−1.02422	−	0.732786i
$566$		0			0
$567$	−20.4771	−	20.4771i	−0.859958	−	0.859958i
$568$		0			0
$569$			4.16945i			0.174792i	0.996174	+	0.0873962i	$0.0278546\pi$
$569$			4.16945i			0.174792i	−0.996174	+	0.0873962i	$0.972145\pi$
$570$		0			0
$571$		−	20.4617i		−	0.856296i	−0.903709	−	0.428148i	$-0.859166\pi$
$571$		−	20.4617i		−	0.856296i	0.903709	−	0.428148i	$-0.140834\pi$
$572$		0			0
$573$	−1.83893	−	1.83893i	−0.0768224	−	0.0768224i
$574$		0			0
$575$	−5.78568	+	11.7767i	−0.241280	+	0.491123i
$576$		0			0
$577$	−27.8065	+	27.8065i	−1.15760	+	1.15760i	−0.172611	+	0.984990i	$0.555220\pi$
$577$	−27.8065	+	27.8065i	−1.15760	+	1.15760i	−0.984990	+	0.172611i	$0.944780\pi$
$578$		0			0
$579$	−4.08391			−0.169722
$580$		0			0
$581$	−34.3859			−1.42657
$582$		0			0
$583$	−0.836466	+	0.836466i	−0.0346429	+	0.0346429i
$584$		0			0
$585$	−12.5310	+	17.5147i	−0.518092	+	0.724143i
$586$		0			0
$587$	−22.2868	−	22.2868i	−0.919876	−	0.919876i	0.0771444	−	0.997020i	$-0.475420\pi$
$587$	−22.2868	−	22.2868i	−0.919876	−	0.919876i	−0.997020	+	0.0771444i	$0.975420\pi$
$588$		0			0
$589$			64.1899i			2.64490i
$590$		0			0
$591$			3.10865i			0.127873i
$592$		0			0
$593$	−11.1720	−	11.1720i	−0.458779	−	0.458779i	0.439475	−	0.898255i	$-0.355164\pi$
$593$	−11.1720	−	11.1720i	−0.458779	−	0.458779i	−0.898255	+	0.439475i	$0.855164\pi$
$594$		0			0
$595$	−7.32257	+	1.21461i	−0.300196	+	0.0497940i
$596$		0			0
$597$	0.443440	−	0.443440i	0.0181488	−	0.0181488i
$598$		0			0
$599$	−31.7262			−1.29630			−0.648149	−	0.761514i	$-0.724457\pi$
$599$	−31.7262			−1.29630			−0.648149	+	0.761514i	$0.724457\pi$
$600$		0			0
$601$	42.3634			1.72804			0.864019	−	0.503459i	$-0.167940\pi$
$601$	42.3634			1.72804			0.864019	+	0.503459i	$0.167940\pi$
$602$		0			0
$603$	0.0388821	−	0.0388821i	0.00158340	−	0.00158340i
$604$		0			0
$605$	−22.6289	+	3.75349i	−0.919995	+	0.152601i
$606$		0			0
$607$	−18.1507	−	18.1507i	−0.736716	−	0.736716i	0.235225	−	0.971941i	$-0.424417\pi$
$607$	−18.1507	−	18.1507i	−0.736716	−	0.736716i	−0.971941	+	0.235225i	$0.924417\pi$
$608$		0			0
$609$		−	4.78310i		−	0.193821i
$610$		0			0
$611$			31.4280i			1.27144i
$612$		0			0
$613$	−5.49795	−	5.49795i	−0.222060	−	0.222060i	0.587305	−	0.809365i	$-0.300189\pi$
$613$	−5.49795	−	5.49795i	−0.222060	−	0.222060i	−0.809365	+	0.587305i	$0.800189\pi$
$614$		0			0
$615$	0.769674	−	1.07578i	0.0310363	−	0.0433797i
$616$		0			0
$617$	−18.1638	+	18.1638i	−0.731247	+	0.731247i	−0.970867	−	0.239620i	$-0.922977\pi$
$617$	−18.1638	+	18.1638i	−0.731247	+	0.731247i	0.239620	+	0.970867i	$0.422977\pi$
$618$		0			0
$619$	20.3604			0.818354			0.409177	−	0.912455i	$-0.365816\pi$
$619$	20.3604			0.818354			0.409177	+	0.912455i	$0.365816\pi$
$620$		0			0
$621$	2.74832			0.110286
$622$		0			0
$623$	−25.1918	+	25.1918i	−1.00929	+	1.00929i
$624$		0			0
$625$	19.7881	−	15.2785i	0.791523	−	0.611139i
$626$		0			0
$627$	0.656195	+	0.656195i	0.0262059	+	0.0262059i
$628$		0			0
$629$			6.24979i			0.249195i
$630$		0			0
$631$		−	14.5599i		−	0.579621i	−0.957084	−	0.289810i	$-0.906408\pi$
$631$		−	14.5599i		−	0.579621i	0.957084	−	0.289810i	$-0.0935922\pi$
$632$		0			0
$633$	2.58970	+	2.58970i	0.102931	+	0.102931i
$634$		0			0
$635$	−0.364066	−	0.260473i	−0.0144475	−	0.0103366i
$636$		0			0
$637$	9.21815	−	9.21815i	0.365237	−	0.365237i
$638$		0			0
$639$	−3.27150			−0.129418
$640$		0			0
$641$	−10.7681			−0.425315			−0.212657	−	0.977127i	$-0.568212\pi$
$641$	−10.7681			−0.425315			−0.212657	+	0.977127i	$0.568212\pi$
$642$		0			0
$643$	−11.3143	+	11.3143i	−0.446191	+	0.446191i	−0.894086	−	0.447895i	$-0.852174\pi$
$643$	−11.3143	+	11.3143i	−0.446191	+	0.446191i	0.447895	+	0.894086i	$0.352174\pi$
$644$		0			0
$645$	−0.225076	−	1.35693i	−0.00886237	−	0.0534292i
$646$		0			0
$647$	4.74790	+	4.74790i	0.186659	+	0.186659i	0.794250	−	0.607591i	$-0.207864\pi$
$647$	4.74790	+	4.74790i	0.186659	+	0.186659i	−0.607591	+	0.794250i	$0.707864\pi$
$648$		0			0
$649$		−	8.25153i		−	0.323901i
$650$		0			0
$651$			6.08731i			0.238580i
$652$		0			0
$653$	−4.66836	−	4.66836i	−0.182687	−	0.182687i	0.609839	−	0.792526i	$-0.291234\pi$
$653$	−4.66836	−	4.66836i	−0.182687	−	0.182687i	−0.792526	+	0.609839i	$0.791234\pi$
$654$		0			0
$655$	1.59611	+	9.62259i	0.0623653	+	0.375986i
$656$		0			0
$657$	−8.84658	+	8.84658i	−0.345138	+	0.345138i
$658$		0			0
$659$	1.85609			0.0723031			0.0361516	−	0.999346i	$-0.488490\pi$
$659$	1.85609			0.0723031			0.0361516	+	0.999346i	$0.488490\pi$
$660$		0			0
$661$	−28.6547			−1.11454			−0.557269	−	0.830332i	$-0.688151\pi$
$661$	−28.6547			−1.11454			−0.557269	+	0.830332i	$0.688151\pi$
$662$		0			0
$663$	0.402408	−	0.402408i	0.0156282	−	0.0156282i
$664$		0			0
$665$	37.0733	+	26.5243i	1.43764	+	1.02857i
$666$		0			0
$667$	−15.2397	−	15.2397i	−0.590085	−	0.590085i
$668$		0			0
$669$			2.00430i			0.0774908i
$670$		0			0
$671$		−	8.57605i		−	0.331075i
$672$		0			0
$673$	18.3239	+	18.3239i	0.706335	+	0.706335i	0.965763	−	0.259427i	$-0.0835339\pi$
$673$	18.3239	+	18.3239i	0.706335	+	0.706335i	−0.259427	+	0.965763i	$0.583534\pi$
$674$		0			0
$675$	−4.69988	−	2.30896i	−0.180898	−	0.0888721i
$676$		0			0
$677$	6.08201	−	6.08201i	0.233751	−	0.233751i	−0.580506	−	0.814256i	$-0.697145\pi$
$677$	6.08201	−	6.08201i	0.233751	−	0.233751i	0.814256	+	0.580506i	$0.197145\pi$
$678$		0			0
$679$	−60.3557			−2.31624
$680$		0			0
$681$	−2.02733			−0.0776873
$682$		0			0
$683$	2.39718	−	2.39718i	0.0917257	−	0.0917257i	−0.659755	−	0.751481i	$-0.729340\pi$
$683$	2.39718	−	2.39718i	0.0917257	−	0.0917257i	0.751481	+	0.659755i	$0.229340\pi$
$684$		0			0
$685$	−12.2575	+	17.1324i	−0.468334	+	0.654596i
$686$		0			0
$687$	−1.70056	−	1.70056i	−0.0648802	−	0.0648802i
$688$		0			0
$689$		−	4.45511i		−	0.169726i
$690$		0			0
$691$			21.2457i			0.808225i	0.914709	+	0.404112i	$0.132420\pi$
$691$			21.2457i			0.808225i	−0.914709	+	0.404112i	$0.867580\pi$
$692$		0			0
$693$	−6.00258	−	6.00258i	−0.228019	−	0.228019i
$694$		0			0
$695$	1.98934	−	0.329975i	0.0754600	−	0.0125167i
$696$		0			0
$697$	2.38416	−	2.38416i	0.0903064	−	0.0903064i
$698$		0			0
$699$	−2.34520			−0.0887036
$700$		0			0
$701$	51.4013			1.94140			0.970701	−	0.240292i	$-0.0772433\pi$
$701$	51.4013			1.94140			0.970701	+	0.240292i	$0.0772433\pi$
$702$		0			0
$703$	27.1401	−	27.1401i	1.02361	−	1.02361i
$704$		0			0
$705$	−3.74993	+	0.622006i	−0.141230	+	0.0234261i
$706$		0			0
$707$	−1.82951	−	1.82951i	−0.0688057	−	0.0688057i
$708$		0			0
$709$		−	24.5102i		−	0.920500i	−0.887789	−	0.460250i	$-0.847760\pi$
$709$		−	24.5102i		−	0.920500i	0.887789	−	0.460250i	$-0.152240\pi$
$710$		0			0
$711$		−	33.7580i		−	1.26602i
$712$		0			0
$713$	19.3951	+	19.3951i	0.726354	+	0.726354i
$714$		0			0
$715$	−3.63481	+	5.08041i	−0.135934	+	0.189997i
$716$		0			0
$717$	2.51644	−	2.51644i	0.0939783	−	0.0939783i
$718$		0			0
$719$	−22.9465			−0.855761			−0.427881	−	0.903835i	$-0.640740\pi$
$719$	−22.9465			−0.855761			−0.427881	+	0.903835i	$0.640740\pi$
$720$		0			0
$721$	−41.4472			−1.54358
$722$		0			0
$723$	2.43803	−	2.43803i	0.0906713	−	0.0906713i
$724$		0			0
$725$	13.2579	+	38.8647i	0.492385	+	1.44340i
$726$		0			0
$727$	27.4185	+	27.4185i	1.01690	+	1.01690i	0.999855	+	0.0170403i	$0.00542435\pi$
$727$	27.4185	+	27.4185i	1.01690	+	1.01690i	0.0170403	+	0.999855i	$0.494576\pi$
$728$		0			0
$729$		−	25.3520i		−	0.938961i
$730$		0			0
$731$		−	3.50606i		−	0.129676i
$732$		0			0
$733$	7.66571	+	7.66571i	0.283139	+	0.283139i	0.834360	−	0.551220i	$-0.185838\pi$
$733$	7.66571	+	7.66571i	0.283139	+	0.283139i	−0.551220	+	0.834360i	$0.685838\pi$
$734$		0			0
$735$	1.28233	+	0.917450i	0.0472995	+	0.0338407i
$736$		0			0
$737$	0.0112784	−	0.0112784i	0.000415444	−	0.000415444i
$738$		0			0
$739$	−9.32320			−0.342959			−0.171480	−	0.985188i	$-0.554855\pi$
$739$	−9.32320			−0.342959			−0.171480	+	0.985188i	$0.554855\pi$
$740$		0			0
$741$	−3.49496			−0.128391
$742$		0			0
$743$	−30.2926	+	30.2926i	−1.11133	+	1.11133i	−0.118358	+	0.992971i	$0.537763\pi$
$743$	−30.2926	+	30.2926i	−1.11133	+	1.11133i	−0.992971	+	0.118358i	$0.962237\pi$
$744$		0			0
$745$	−1.32474	−	7.98652i	−0.0485345	−	0.292603i
$746$		0			0
$747$	−21.7488	−	21.7488i	−0.795747	−	0.795747i
$748$		0			0
$749$			37.2614i			1.36150i
$750$		0			0
$751$		−	27.7955i		−	1.01427i	−0.861866	−	0.507136i	$-0.830704\pi$
$751$		−	27.7955i		−	1.01427i	0.861866	−	0.507136i	$-0.169296\pi$
$752$		0			0
$753$	−0.505952	−	0.505952i	−0.0184379	−	0.0184379i
$754$		0			0
$755$	1.47673	+	8.90284i	0.0537436	+	0.324008i
$756$		0			0
$757$	38.1376	−	38.1376i	1.38613	−	1.38613i	0.552858	−	0.833275i	$-0.313537\pi$
$757$	38.1376	−	38.1376i	1.38613	−	1.38613i	0.833275	−	0.552858i	$-0.186463\pi$
$758$		0			0
$759$	0.396542			0.0143936
$760$		0			0
$761$	6.63131			0.240385			0.120192	−	0.992751i	$-0.461649\pi$
$761$	6.63131			0.240385			0.120192	+	0.992751i	$0.461649\pi$
$762$		0			0
$763$	46.2116	−	46.2116i	1.67297	−	1.67297i
$764$		0			0
$765$	−5.39969	−	3.86324i	−0.195226	−	0.139676i
$766$		0			0
$767$	21.9743	+	21.9743i	0.793445	+	0.793445i
$768$		0			0
$769$		−	37.5901i		−	1.35553i	−0.735277	−	0.677767i	$-0.762948\pi$
$769$		−	37.5901i		−	1.35553i	0.735277	−	0.677767i	$-0.237052\pi$
$770$		0			0
$771$		−	1.32128i		−	0.0475846i
$772$		0			0
$773$	17.6747	+	17.6747i	0.635715	+	0.635715i	0.949496	−	0.313780i	$-0.101596\pi$
$773$	17.6747	+	17.6747i	0.635715	+	0.635715i	−0.313780	+	0.949496i	$0.601596\pi$
$774$		0			0
$775$	−16.8729	−	49.4620i	−0.606092	−	1.77673i
$776$		0			0
$777$	2.57378	−	2.57378i	0.0923337	−	0.0923337i
$778$		0			0
$779$	−20.7067			−0.741895
$780$		0			0
$781$	−0.948949			−0.0339561
$782$		0			0
$783$	6.08191	−	6.08191i	0.217350	−	0.217350i
$784$		0			0
$785$	9.23195	−	12.9036i	0.329503	−	0.460550i
$786$		0			0
$787$	−36.7877	−	36.7877i	−1.31134	−	1.31134i	−0.920427	−	0.390914i	$-0.872159\pi$
$787$	−36.7877	−	36.7877i	−1.31134	−	1.31134i	−0.390914	−	0.920427i	$-0.627841\pi$
$788$		0			0
$789$		−	4.83486i		−	0.172126i
$790$		0			0
$791$			44.4390i			1.58007i
$792$		0			0
$793$	22.8385	+	22.8385i	0.811018	+	0.811018i
$794$		0			0
$795$	0.531574	−	0.0881730i	0.0188530	−	0.00312717i
$796$		0			0
$797$	2.82437	−	2.82437i	0.100044	−	0.100044i	−0.655313	−	0.755357i	$-0.727463\pi$
$797$	2.82437	−	2.82437i	0.100044	−	0.100044i	0.755357	+	0.655313i	$0.227463\pi$
$798$		0			0
$799$	−9.68910			−0.342776
$800$		0			0
$801$	−31.8672			−1.12597
$802$		0			0
$803$	−2.56609	+	2.56609i	−0.0905554	+	0.0905554i
$804$		0			0
$805$	19.2162	−	3.18741i	0.677281	−	0.112341i
$806$		0			0
$807$	0.223890	+	0.223890i	0.00788130	+	0.00788130i
$808$		0			0
$809$		−	45.8788i		−	1.61301i	−0.591226	−	0.806506i	$-0.701356\pi$
$809$		−	45.8788i		−	1.61301i	0.591226	−	0.806506i	$-0.298644\pi$
$810$		0			0
$811$			40.7315i			1.43028i	0.698983	+	0.715139i	$0.253636\pi$
$811$			40.7315i			1.43028i	−0.698983	+	0.715139i	$0.746364\pi$
$812$		0			0
$813$	1.29024	+	1.29024i	0.0452508	+	0.0452508i
$814$		0			0
$815$	−23.8739	+	33.3689i	−0.836267	+	1.16886i
$816$		0			0
$817$	−15.2253	+	15.2253i	−0.532666	+	0.532666i
$818$		0			0
$819$	31.9704			1.11714
$820$		0			0
$821$	41.9517			1.46412			0.732062	−	0.681238i	$-0.238558\pi$
$821$	41.9517			1.46412			0.732062	+	0.681238i	$0.238558\pi$
$822$		0			0
$823$	−3.82305	+	3.82305i	−0.133263	+	0.133263i	−0.770592	−	0.637329i	$-0.780039\pi$
$823$	−3.82305	+	3.82305i	−0.133263	+	0.133263i	0.637329	+	0.770592i	$0.280039\pi$
$824$		0			0
$825$	−0.678122	−	0.333149i	−0.0236092	−	0.0115988i
$826$		0			0
$827$	−7.53964	−	7.53964i	−0.262179	−	0.262179i	0.563760	−	0.825939i	$-0.309354\pi$
$827$	−7.53964	−	7.53964i	−0.262179	−	0.262179i	−0.825939	+	0.563760i	$0.809354\pi$
$828$		0			0
$829$			27.7316i			0.963158i	0.876403	+	0.481579i	$0.159937\pi$
$829$			27.7316i			0.963158i	−0.876403	+	0.481579i	$0.840063\pi$
$830$		0			0
$831$		−	1.53557i		−	0.0532685i
$832$		0			0
$833$	2.84191	+	2.84191i	0.0984664	+	0.0984664i
$834$		0			0
$835$	13.5938	+	9.72579i	0.470435	+	0.336575i
$836$		0			0
$837$	−7.74026	+	7.74026i	−0.267542	+	0.267542i
$838$		0			0
$839$	25.3810			0.876251			0.438125	−	0.898914i	$-0.355643\pi$
$839$	25.3810			0.876251			0.438125	+	0.898914i	$0.355643\pi$
$840$		0			0
$841$	−38.4495			−1.32585
$842$		0			0
$843$	2.03177	−	2.03177i	0.0699778	−	0.0699778i
$844$		0			0
$845$	0.906981	+	5.46797i	0.0312011	+	0.188104i
$846$		0			0
$847$	24.0785	+	24.0785i	0.827347	+	0.827347i
$848$		0			0
$849$			3.14465i			0.107924i
$850$		0			0
$851$		−	16.4009i		−	0.562216i
$852$		0			0
$853$	0.494065	+	0.494065i	0.0169165	+	0.0169165i	0.715514	−	0.698598i	$-0.246192\pi$
$853$	0.494065	+	0.494065i	0.0169165	+	0.0169165i	−0.698598	+	0.715514i	$0.746192\pi$
$854$		0			0
$855$	6.67216	+	40.2249i	0.228183	+	1.37566i
$856$		0			0
$857$	0.976594	−	0.976594i	0.0333598	−	0.0333598i	−0.690230	−	0.723590i	$-0.742491\pi$
$857$	0.976594	−	0.976594i	0.0333598	−	0.0333598i	0.723590	+	0.690230i	$0.242491\pi$
$858$		0			0
$859$	6.24864			0.213201			0.106600	−	0.994302i	$-0.466003\pi$
$859$	6.24864			0.213201			0.106600	+	0.994302i	$0.466003\pi$
$860$		0			0
$861$	−1.96368			−0.0669219
$862$		0			0
$863$	37.9125	−	37.9125i	1.29056	−	1.29056i	0.356115	−	0.934442i	$-0.384101\pi$
$863$	37.9125	−	37.9125i	1.29056	−	1.29056i	0.934442	−	0.356115i	$-0.115899\pi$
$864$		0			0
$865$	−26.6744	−	19.0844i	−0.906958	−	0.648887i
$866$		0			0
$867$	0.124060	+	0.124060i	0.00421331	+	0.00421331i
$868$		0			0
$869$		−	9.79203i		−	0.332172i
$870$		0			0
$871$			0.0600698i			0.00203539i
$872$		0			0
$873$	−38.1745	−	38.1745i	−1.29201	−	1.29201i
$874$		0			0
$875$	−35.5392	−	10.6934i	−1.20144	−	0.361503i
$876$		0			0
$877$	−29.3000	+	29.3000i	−0.989391	+	0.989391i	−0.999944	−	0.0105536i	$-0.996641\pi$
$877$	−29.3000	+	29.3000i	−0.989391	+	0.989391i	0.0105536	+	0.999944i	$0.496641\pi$
$878$		0			0
$879$	1.08116			0.0364667
$880$		0			0
$881$	−0.158576			−0.00534257			−0.00267129	−	0.999996i	$-0.500850\pi$
$881$	−0.158576			−0.00534257			−0.00267129	+	0.999996i	$0.500850\pi$
$882$		0			0
$883$	−19.1626	+	19.1626i	−0.644873	+	0.644873i	−0.951749	−	0.306876i	$-0.900716\pi$
$883$	−19.1626	+	19.1626i	−0.644873	+	0.644873i	0.306876	+	0.951749i	$0.400716\pi$
$884$		0			0
$885$	−2.18702	+	3.05683i	−0.0735159	+	0.102754i
$886$		0			0
$887$	−8.49225	−	8.49225i	−0.285142	−	0.285142i	0.550014	−	0.835156i	$-0.314622\pi$
$887$	−8.49225	−	8.49225i	−0.285142	−	0.285142i	−0.835156	+	0.550014i	$0.814622\pi$
$888$		0			0
$889$			0.664547i			0.0222882i
$890$		0			0
$891$		−	7.51363i		−	0.251716i
$892$		0			0
$893$	42.0756	+	42.0756i	1.40801	+	1.40801i
$894$		0			0
$895$	−48.6606	+	8.07140i	−1.62654	+	0.269797i
$896$		0			0
$897$	−1.05601	+	1.05601i	−0.0352592	+	0.0352592i
$898$		0			0
$899$	85.8410			2.86296
$900$		0			0
$901$	1.37349			0.0457575
$902$		0			0
$903$	−1.44386	+	1.44386i	−0.0480486	+	0.0480486i
$904$		0			0
$905$	−2.04947	+	0.339949i	−0.0681268	+	0.0113003i
$906$		0			0
$907$	8.22796	+	8.22796i	0.273205	+	0.273205i	0.830389	−	0.557184i	$-0.188118\pi$
$907$	8.22796	+	8.22796i	0.273205	+	0.273205i	−0.557184	+	0.830389i	$0.688118\pi$
$908$		0			0
$909$		−	2.31430i		−	0.0767603i
$910$		0			0
$911$			16.3098i			0.540369i	0.962809	+	0.270184i	$0.0870846\pi$
$911$			16.3098i			0.540369i	−0.962809	+	0.270184i	$0.912915\pi$
$912$		0			0
$913$	−6.30858	−	6.30858i	−0.208783	−	0.208783i
$914$		0			0
$915$	−2.27303	+	3.17704i	−0.0751441	+	0.105030i
$916$		0			0
$917$	10.2390	−	10.2390i	0.338122	−	0.338122i
$918$		0			0
$919$	−42.8906			−1.41483			−0.707416	−	0.706798i	$-0.750139\pi$
$919$	−42.8906			−1.41483			−0.707416	+	0.706798i	$0.750139\pi$
$920$		0			0
$921$	−4.18072			−0.137760
$922$		0			0
$923$	2.52710	−	2.52710i	0.0831806	−	0.0831806i
$924$		0			0
$925$	−13.7790	+	28.0470i	−0.453050	+	0.922181i
$926$		0			0
$927$	−26.2150	−	26.2150i	−0.861014	−	0.861014i
$928$		0			0
$929$			14.2299i			0.466869i	0.972373	+	0.233434i	$0.0749964\pi$
$929$			14.2299i			0.466869i	−0.972373	+	0.233434i	$0.925004\pi$
$930$		0			0
$931$		−	24.6824i		−	0.808933i
$932$		0			0
$933$	1.99089	+	1.99089i	0.0651787	+	0.0651787i
$934$		0			0
$935$	−1.56627	−	1.12059i	−0.0512224	−	0.0366473i
$936$		0			0
$937$	4.16021	−	4.16021i	0.135908	−	0.135908i	−0.635880	−	0.771788i	$-0.719363\pi$
$937$	4.16021	−	4.16021i	0.135908	−	0.135908i	0.771788	+	0.635880i	$0.219363\pi$
$938$		0			0
$939$	2.60012			0.0848518
$940$		0			0
$941$	−22.3237			−0.727732			−0.363866	−	0.931451i	$-0.618543\pi$
$941$	−22.3237			−0.727732			−0.363866	+	0.931451i	$0.618543\pi$
$942$		0			0
$943$	−6.25659	+	6.25659i	−0.203743	+	0.203743i
$944$		0			0
$945$	1.27204	+	7.66883i	0.0413794	+	0.249467i
$946$		0			0
$947$	−32.0386	−	32.0386i	−1.04111	−	1.04111i	−0.999118	−	0.0419968i	$-0.986628\pi$
$947$	−32.0386	−	32.0386i	−1.04111	−	1.04111i	−0.0419968	−	0.999118i	$-0.513372\pi$
$948$		0			0
$949$		−	13.6673i		−	0.443658i
$950$		0			0
$951$			2.03927i			0.0661278i
$952$		0			0
$953$	−7.56126	−	7.56126i	−0.244933	−	0.244933i	0.573954	−	0.818887i	$-0.305409\pi$
$953$	−7.56126	−	7.56126i	−0.244933	−	0.244933i	−0.818887	+	0.573954i	$0.805409\pi$
$954$		0			0
$955$	−5.42370	−	32.6982i	−0.175507	−	1.05809i
$956$		0			0
$957$	0.877528	−	0.877528i	0.0283664	−	0.0283664i
$958$		0			0
$959$	31.2726			1.00985
$960$		0			0
$961$	−78.2472			−2.52410
$962$		0			0
$963$	−23.5675	+	23.5675i	−0.759453	+	0.759453i
$964$		0			0
$965$	−42.3307	−	30.2857i	−1.36267	−	0.974932i
$966$		0			0
$967$	23.3249	+	23.3249i	0.750078	+	0.750078i	0.974494	−	0.224415i	$-0.0720472\pi$
$967$	23.3249	+	23.3249i	0.750078	+	0.750078i	−0.224415	+	0.974494i	$0.572047\pi$
$968$		0			0
$969$		−	1.07748i		−	0.0346137i
$970$		0			0
$971$			27.1508i			0.871311i	0.900113	+	0.435656i	$0.143483\pi$
$971$			27.1508i			0.871311i	−0.900113	+	0.435656i	$0.856517\pi$
$972$		0			0
$973$	−2.11678	−	2.11678i	−0.0678608	−	0.0678608i
$974$		0			0
$975$	2.69307	−	0.918682i	0.0862472	−	0.0294214i
$976$		0			0
$977$	−2.59037	+	2.59037i	−0.0828734	+	0.0828734i	−0.747328	−	0.664455i	$-0.768664\pi$
$977$	−2.59037	+	2.59037i	−0.0828734	+	0.0828734i	0.664455	+	0.747328i	$0.268664\pi$
$978$		0			0
$979$	−9.24358			−0.295426
$980$		0			0
$981$	58.4569			1.86639
$982$		0			0
$983$	43.8170	−	43.8170i	1.39754	−	1.39754i	0.590526	−	0.807019i	$-0.298920\pi$
$983$	43.8170	−	43.8170i	1.39754	−	1.39754i	0.807019	−	0.590526i	$-0.201080\pi$
$984$		0			0
$985$	−23.0533	+	32.2219i	−0.734540	+	1.02667i
$986$		0			0
$987$	3.99015	+	3.99015i	0.127008	+	0.127008i
$988$		0			0
$989$			9.20072i			0.292566i
$990$		0			0
$991$			12.5669i			0.399201i	0.979877	+	0.199600i	$0.0639644\pi$
$991$			12.5669i			0.399201i	−0.979877	+	0.199600i	$0.936036\pi$
$992$		0			0
$993$	−0.699031	−	0.699031i	−0.0221831	−	0.0221831i
$994$		0			0
$995$	7.88485	−	1.30787i	0.249966	−	0.0414623i
$996$		0			0
$997$	38.3980	−	38.3980i	1.21608	−	1.21608i	0.247082	−	0.968995i	$-0.420528\pi$
$997$	38.3980	−	38.3980i	1.21608	−	1.21608i	0.968995	−	0.247082i	$-0.0794715\pi$
$998$		0			0
$999$	6.54532			0.207085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1360.2.bn.b.783.15	✓	64
4.3	odd	2	inner	1360.2.bn.b.783.18	yes	64
5.2	odd	4	inner	1360.2.bn.b.1327.18	yes	64
20.7	even	4	inner	1360.2.bn.b.1327.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1360.2.bn.b.783.15	✓	64	1.1	even	1	trivial
1360.2.bn.b.783.18	yes	64	4.3	odd	2	inner
1360.2.bn.b.1327.15	yes	64	20.7	even	4	inner
1360.2.bn.b.1327.18	yes	64	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bn (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.124060 + 0.124060i) q^{3} +(-2.20593 + 0.365900i) q^{5} +(2.34724 + 2.34724i) q^{7} +2.96922i q^{9} +0.861269i q^{11} +(-2.29360 - 2.29360i) q^{13} +(0.228274 - 0.319062i) q^{15} +(0.707107 - 0.707107i) q^{17} -6.14132 q^{19} -0.582399 q^{21} +(-1.85561 + 1.85561i) q^{23} +(4.73223 - 1.61430i) q^{25} +(-0.740543 - 0.740543i) q^{27} +8.21277i q^{29} -10.4521i q^{31} +(-0.106849 - 0.106849i) q^{33} +(-6.03670 - 4.31899i) q^{35} +(-4.41927 + 4.41927i) q^{37} +0.569090 q^{39} +3.37171 q^{41} +(2.47916 - 2.47916i) q^{43} +(-1.08644 - 6.54988i) q^{45} +(-6.85123 - 6.85123i) q^{47} +4.01907i q^{49} +0.175448i q^{51} +(0.971203 + 0.971203i) q^{53} +(-0.315139 - 1.89990i) q^{55} +(0.761894 - 0.761894i) q^{57} -9.58067 q^{59} -9.95746 q^{61} +(-6.96947 + 6.96947i) q^{63} +(5.89875 + 4.22029i) q^{65} +(-0.0130951 - 0.0130951i) q^{67} -0.460416i q^{69} +1.10180i q^{71} +(2.97943 + 2.97943i) q^{73} +(-0.386812 + 0.787353i) q^{75} +(-2.02160 + 2.02160i) q^{77} -11.3693 q^{79} -8.72391 q^{81} +(-7.32475 + 7.32475i) q^{83} +(-1.30110 + 1.81856i) q^{85} +(-1.01888 - 1.01888i) q^{87} +10.7325i q^{89} -10.7673i q^{91} +(1.29670 + 1.29670i) q^{93} +(13.5473 - 2.24711i) q^{95} +(-12.8567 + 12.8567i) q^{97} -2.55729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{13} + 64 q^{21} + 24 q^{25} - 56 q^{33} - 32 q^{41} - 24 q^{45} + 64 q^{53} + 64 q^{57} - 16 q^{61} + 40 q^{65} + 56 q^{73} - 40 q^{77} - 176 q^{81} - 104 q^{93} - 16 q^{97}+O(q^{100}) \) 64 * q - 8 * q^13 + 64 * q^21 + 24 * q^25 - 56 * q^33 - 32 * q^41 - 24 * q^45 + 64 * q^53 + 64 * q^57 - 16 * q^61 + 40 * q^65 + 56 * q^73 - 40 * q^77 - 176 * q^81 - 104 * q^93 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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