LMFDB - Embedded newform 532.2.cj.a.409.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [532,2,Mod(33,532)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("532.33"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(532, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 15, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 532 = 2^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	532.cj (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			409.1
Character	$\chi$	$=$	532.409
Dual form			532.2.cj.a.173.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.591925 - 3.35697i) q^{3} +(0.335440 - 0.0591470i) q^{5} +(1.47659 - 2.19538i) q^{7} +(-8.09981 + 2.94809i) q^{9} -1.84653 q^{11} +(-2.63553 - 2.21147i) q^{13} +(-0.397110 - 1.09105i) q^{15} +(2.20688 - 6.06334i) q^{17} +(2.29855 + 3.70360i) q^{19} +(-8.24386 - 3.65736i) q^{21} +(4.54633 + 3.81483i) q^{23} +(-4.58944 + 1.67042i) q^{25} +(9.57799 + 16.5896i) q^{27} +(-0.839908 - 0.148098i) q^{29} +(-3.19661 - 5.53670i) q^{31} +(1.09301 + 6.19876i) q^{33} +(0.365455 - 0.823753i) q^{35} +(-0.825440 + 0.476568i) q^{37} +(-5.86382 + 10.1564i) q^{39} +(1.06294 - 0.891915i) q^{41} +(-2.23515 - 0.813527i) q^{43} +(-2.54263 + 1.46799i) q^{45} +(-1.37945 - 3.79002i) q^{47} +(-2.63939 - 6.48333i) q^{49} +(-21.6608 - 3.81938i) q^{51} +(1.77334 + 0.312687i) q^{53} +(-0.619400 + 0.109217i) q^{55} +(11.0723 - 9.90842i) q^{57} +(9.42427 + 3.43015i) q^{59} +(-9.13122 + 10.8822i) q^{61} +(-5.48788 + 22.1353i) q^{63} +(-1.01486 - 0.585932i) q^{65} +(4.73686 - 5.64518i) q^{67} +(10.1152 - 17.5200i) q^{69} +(2.17664 - 5.98028i) q^{71} +(3.01332 - 0.531330i) q^{73} +(8.32416 + 14.4179i) q^{75} +(-2.72656 + 4.05384i) q^{77} +(3.72302 - 10.2289i) q^{79} +(30.2122 - 25.3510i) q^{81} +(5.02050 + 2.89858i) q^{83} +(0.381645 - 2.16441i) q^{85} +2.90721i q^{87} +(2.26837 - 12.8646i) q^{89} +(-8.74661 + 2.52056i) q^{91} +(-16.6944 + 14.0083i) q^{93} +(0.990082 + 1.10638i) q^{95} +(1.31832 + 7.47654i) q^{97} +(14.9566 - 5.44375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 6 q^{7} - 6 q^{11} + 6 q^{13} - 3 q^{15} + 27 q^{17} + 21 q^{19} - 3 q^{21} - 24 q^{23} + 12 q^{27} - 18 q^{29} + 33 q^{35} + 36 q^{37} - 18 q^{39} - 18 q^{41} - 48 q^{43} - 18 q^{45} - 18 q^{49}+ \cdots + 27 q^{99}+O(q^{100}) $ 78 * q + 6 * q^7 - 6 * q^11 + 6 * q^13 - 3 * q^15 + 27 * q^17 + 21 * q^19 - 3 * q^21 - 24 * q^23 + 12 * q^27 - 18 * q^29 + 33 * q^35 + 36 * q^37 - 18 * q^39 - 18 * q^41 - 48 * q^43 - 18 * q^45 - 18 * q^49 + 6 * q^53 - 18 * q^57 + 45 * q^59 + 39 * q^61 - 27 * q^63 - 18 * q^65 + 21 * q^67 + 6 * q^71 - 3 * q^73 - 21 * q^75 - 21 * q^77 + 36 * q^79 + 36 * q^81 - 18 * q^83 + 60 * q^85 - 21 * q^91 - 102 * q^93 + 60 * q^95 - 27 * q^97 + 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$.

$n$	$267$	$381$	$477$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$

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
$3$	−0.591925	−	3.35697i	−0.341748	−	1.93815i	−0.346206	−	0.938159i	$-0.612530\pi$
$3$	−0.591925	−	3.35697i	−0.341748	−	1.93815i	0.00445762	−	0.999990i	$-0.498581\pi$
$4$		0			0
$5$	0.335440	−	0.0591470i	0.150013	−	0.0264514i	−0.0981372	−	0.995173i	$-0.531288\pi$
$5$	0.335440	−	0.0591470i	0.150013	−	0.0264514i	0.248150	+	0.968722i	$0.420177\pi$
$6$		0			0
$7$	1.47659	−	2.19538i	0.558097	−	0.829776i
$7$	1.47659	−	2.19538i	0.558097	−	0.829776i
$8$		0			0
$9$	−8.09981	+	2.94809i	−2.69994	+	0.982696i
$10$		0			0
$11$	−1.84653			−0.556751			−0.278375	−	0.960472i	$-0.589796\pi$
$11$	−1.84653			−0.556751			−0.278375	+	0.960472i	$0.589796\pi$
$12$		0			0
$13$	−2.63553	−	2.21147i	−0.730965	−	0.613352i	0.199430	−	0.979912i	$-0.436091\pi$
$13$	−2.63553	−	2.21147i	−0.730965	−	0.613352i	−0.930394	+	0.366560i	$0.880535\pi$
$14$		0			0
$15$	−0.397110	−	1.09105i	−0.102533	−	0.281708i
$16$		0			0
$17$	2.20688	−	6.06334i	0.535246	−	1.47058i	−0.317504	−	0.948257i	$-0.602845\pi$
$17$	2.20688	−	6.06334i	0.535246	−	1.47058i	0.852750	−	0.522319i	$-0.174933\pi$
$18$		0			0
$19$	2.29855	+	3.70360i	0.527323	+	0.849665i
$19$	2.29855	+	3.70360i	0.527323	+	0.849665i
$20$		0			0
$21$	−8.24386	−	3.65736i	−1.79896	−	0.798101i
$22$		0			0
$23$	4.54633	+	3.81483i	0.947976	+	0.795446i	0.978956	−	0.204074i	$-0.0654182\pi$
$23$	4.54633	+	3.81483i	0.947976	+	0.795446i	−0.0309795	+	0.999520i	$0.509863\pi$
$24$		0			0
$25$	−4.58944	+	1.67042i	−0.917888	+	0.334084i
$26$		0			0
$27$	9.57799	+	16.5896i	1.84329	+	3.19266i
$28$		0			0
$29$	−0.839908	−	0.148098i	−0.155967	−	0.0275012i	0.0951194	−	0.995466i	$-0.469677\pi$
$29$	−0.839908	−	0.148098i	−0.155967	−	0.0275012i	−0.251086	+	0.967965i	$0.580788\pi$
$30$		0			0
$31$	−3.19661	−	5.53670i	−0.574129	−	0.994420i	−0.996136	−	0.0878277i	$-0.972008\pi$
$31$	−3.19661	−	5.53670i	−0.574129	−	0.994420i	0.422007	−	0.906593i	$-0.361326\pi$
$32$		0			0
$33$	1.09301	+	6.19876i	0.190268	+	1.07907i
$34$		0			0
$35$	0.365455	−	0.823753i	0.0617732	−	0.139240i
$36$		0			0
$37$	−0.825440	+	0.476568i	−0.135702	+	0.0783473i	−0.566314	−	0.824190i	$-0.691631\pi$
$37$	−0.825440	+	0.476568i	−0.135702	+	0.0783473i	0.430612	+	0.902537i	$0.358298\pi$
$38$		0			0
$39$	−5.86382	+	10.1564i	−0.938962	+	1.62633i
$40$		0			0
$41$	1.06294	−	0.891915i	0.166004	−	0.139294i	−0.556001	−	0.831181i	$-0.687665\pi$
$41$	1.06294	−	0.891915i	0.166004	−	0.139294i	0.722005	+	0.691888i	$0.243221\pi$
$42$		0			0
$43$	−2.23515	−	0.813527i	−0.340857	−	0.124062i	0.165919	−	0.986139i	$-0.446941\pi$
$43$	−2.23515	−	0.813527i	−0.340857	−	0.124062i	−0.506776	+	0.862078i	$0.669163\pi$
$44$		0			0
$45$	−2.54263	+	1.46799i	−0.379032	+	0.218834i
$46$		0			0
$47$	−1.37945	−	3.79002i	−0.201214	−	0.552831i	0.797511	−	0.603304i	$-0.206149\pi$
$47$	−1.37945	−	3.79002i	−0.201214	−	0.552831i	−0.998725	+	0.0504727i	$0.983927\pi$
$48$		0			0
$49$	−2.63939	−	6.48333i	−0.377056	−	0.926191i
$50$		0			0
$51$	−21.6608	−	3.81938i	−3.03311	−	0.534820i
$52$		0			0
$53$	1.77334	+	0.312687i	0.243587	+	0.0429509i	0.294108	−	0.955772i	$-0.404977\pi$
$53$	1.77334	+	0.312687i	0.243587	+	0.0429509i	−0.0505217	+	0.998723i	$0.516088\pi$
$54$		0			0
$55$	−0.619400	+	0.109217i	−0.0835199	+	0.0147268i
$56$		0			0
$57$	11.0723	−	9.90842i	1.46656	−	1.31240i
$58$		0			0
$59$	9.42427	+	3.43015i	1.22694	+	0.446568i	0.872547	−	0.488531i	$-0.162467\pi$
$59$	9.42427	+	3.43015i	1.22694	+	0.446568i	0.354388	+	0.935098i	$0.384689\pi$
$60$		0			0
$61$	−9.13122	+	10.8822i	−1.16913	+	1.39332i	−0.265991	+	0.963975i	$0.585699\pi$
$61$	−9.13122	+	10.8822i	−1.16913	+	1.39332i	−0.903142	+	0.429343i	$0.858745\pi$
$62$		0			0
$63$	−5.48788	+	22.1353i	−0.691408	+	2.78878i
$64$		0			0
$65$	−1.01486	−	0.585932i	−0.125878	−	0.0726759i
$66$		0			0
$67$	4.73686	−	5.64518i	0.578700	−	0.689668i	−0.394692	−	0.918813i	$-0.629149\pi$
$67$	4.73686	−	5.64518i	0.578700	−	0.689668i	0.973392	+	0.229146i	$0.0735932\pi$
$68$		0			0
$69$	10.1152	−	17.5200i	1.21772	−	2.10916i
$70$		0			0
$71$	2.17664	−	5.98028i	0.258320	−	0.709728i	−0.740951	−	0.671559i	$-0.765625\pi$
$71$	2.17664	−	5.98028i	0.258320	−	0.709728i	0.999271	−	0.0381696i	$-0.0121527\pi$
$72$		0			0
$73$	3.01332	−	0.531330i	0.352683	−	0.0621874i	0.00549962	−	0.999985i	$-0.498249\pi$
$73$	3.01332	−	0.531330i	0.352683	−	0.0621874i	0.347183	+	0.937797i	$0.387138\pi$
$74$		0			0
$75$	8.32416	+	14.4179i	0.961191	+	1.66483i
$76$		0			0
$77$	−2.72656	+	4.05384i	−0.310721	+	0.461978i
$78$		0			0
$79$	3.72302	−	10.2289i	0.418872	−	1.15084i	−0.533472	−	0.845818i	$-0.679113\pi$
$79$	3.72302	−	10.2289i	0.418872	−	1.15084i	0.952345	−	0.305024i	$-0.0986646\pi$
$80$		0			0
$81$	30.2122	−	25.3510i	3.35691	−	2.81678i
$82$		0			0
$83$	5.02050	+	2.89858i	0.551071	+	0.318161i	0.749554	−	0.661943i	$-0.230268\pi$
$83$	5.02050	+	2.89858i	0.551071	+	0.318161i	−0.198483	+	0.980104i	$0.563601\pi$
$84$		0			0
$85$	0.381645	−	2.16441i	0.0413952	−	0.234764i
$86$		0			0
$87$			2.90721i			0.311686i
$88$		0			0
$89$	2.26837	−	12.8646i	0.240447	−	1.36364i	−0.590387	−	0.807120i	$-0.701025\pi$
$89$	2.26837	−	12.8646i	0.240447	−	1.36364i	0.830834	−	0.556520i	$-0.187864\pi$
$90$		0			0
$91$	−8.74661	+	2.52056i	−0.916894	+	0.264227i
$92$		0			0
$93$	−16.6944	+	14.0083i	−1.73113	+	1.45259i
$94$		0			0
$95$	0.990082	+	1.10638i	0.101580	+	0.113512i
$96$		0			0
$97$	1.31832	+	7.47654i	0.133855	+	0.759127i	0.975650	+	0.219331i	$0.0703876\pi$
$97$	1.31832	+	7.47654i	0.133855	+	0.759127i	−0.841796	+	0.539796i	$0.818501\pi$
$98$		0			0
$99$	14.9566	−	5.44375i	1.50319	−	0.547117i
$100$		0			0
$101$	1.20960	+	3.32334i	0.120360	+	0.330685i	0.985212	−	0.171342i	$-0.0548102\pi$
$101$	1.20960	+	3.32334i	0.120360	+	0.330685i	−0.864852	+	0.502027i	$0.832588\pi$
$102$		0			0
$103$	7.55752	−	13.0900i	0.744665	−	1.28980i	−0.205687	−	0.978618i	$-0.565943\pi$
$103$	7.55752	−	13.0900i	0.744665	−	1.28980i	0.950351	−	0.311179i	$-0.100724\pi$
$104$		0			0
$105$	−2.98164	−	0.739222i	−0.290978	−	0.0721407i
$106$		0			0
$107$		−	12.5267i		−	1.21100i	−0.795844	−	0.605502i	$-0.792972\pi$
$107$		−	12.5267i		−	1.21100i	0.795844	−	0.605502i	$-0.207028\pi$
$108$		0			0
$109$	−4.86041	−	5.79242i	−0.465543	−	0.554813i	0.481280	−	0.876567i	$-0.340172\pi$
$109$	−4.86041	−	5.79242i	−0.465543	−	0.554813i	−0.946823	+	0.321754i	$0.895728\pi$
$110$		0			0
$111$	2.08842	+	2.48889i	0.198225	+	0.236235i
$112$		0			0
$113$		−	13.7729i		−	1.29564i	−0.761792	−	0.647822i	$-0.775680\pi$
$113$		−	13.7729i		−	1.29564i	0.761792	−	0.647822i	$-0.224320\pi$
$114$		0			0
$115$	1.75066	+	1.01074i	0.163249	+	0.0942521i
$116$		0			0
$117$	27.8669	+	10.1427i	2.57630	+	0.937695i
$118$		0			0
$119$	−10.0527	−	13.7980i	−0.921529	−	1.26486i
$120$		0			0
$121$	−7.59031			−0.690029
$122$		0			0
$123$	−3.62332	−	3.04032i	−0.326704	−	0.274137i
$124$		0			0
$125$	−2.91558	+	1.68331i	−0.260778	+	0.150560i
$126$		0			0
$127$	−3.93019	+	4.68382i	−0.348748	+	0.415622i	−0.911693	−	0.410873i	$-0.865224\pi$
$127$	−3.93019	+	4.68382i	−0.348748	+	0.415622i	0.562945	+	0.826495i	$0.309668\pi$
$128$		0			0
$129$	−1.40795	+	7.98488i	−0.123963	+	0.703029i
$130$		0			0
$131$	−7.85239	−	9.35812i	−0.686067	−	0.817623i	0.304807	−	0.952414i	$-0.401408\pi$
$131$	−7.85239	−	9.35812i	−0.686067	−	0.817623i	−0.990874	+	0.134791i	$0.956964\pi$
$132$		0			0
$133$	11.5248	+	0.422495i	0.999329	+	0.0366350i
$134$		0			0
$135$	4.19406	+	4.99829i	0.360967	+	0.430184i
$136$		0			0
$137$	0.749904	−	4.25292i	0.0640686	−	0.363351i	−0.935871	−	0.352343i	$-0.885385\pi$
$137$	0.749904	−	4.25292i	0.0640686	−	0.363351i	0.999939	−	0.0110079i	$-0.00350399\pi$
$138$		0			0
$139$	4.49466	−	5.35653i	0.381232	−	0.454335i	−0.540971	−	0.841042i	$-0.681943\pi$
$139$	4.49466	−	5.35653i	0.381232	−	0.454335i	0.922203	+	0.386707i	$0.126387\pi$
$140$		0			0
$141$	−11.9065	+	6.87420i	−1.00270	+	0.578912i
$142$		0			0
$143$	4.86659	+	4.08356i	0.406965	+	0.341484i
$144$		0			0
$145$	−0.290498			−0.0241245
$146$		0			0
$147$	−20.2021	+	12.6980i	−1.66624	+	1.04731i
$148$		0			0
$149$	7.81656	+	2.84499i	0.640357	+	0.233071i	0.641733	−	0.766928i	$-0.278216\pi$
$149$	7.81656	+	2.84499i	0.640357	+	0.233071i	−0.00137584	+	0.999999i	$0.500438\pi$
$150$		0			0
$151$	10.4316	+	6.02267i	0.848909	+	0.490118i	0.860283	−	0.509817i	$-0.170287\pi$
$151$	10.4316	+	6.02267i	0.848909	+	0.490118i	−0.0113734	+	0.999935i	$0.503620\pi$
$152$		0			0
$153$			55.6180i			4.49645i
$154$		0			0
$155$	−1.39975	−	1.66816i	−0.112431	−	0.133990i
$156$		0			0
$157$	4.85507	+	5.78604i	0.387477	+	0.461777i	0.924159	−	0.382008i	$-0.124767\pi$
$157$	4.85507	+	5.78604i	0.387477	+	0.461777i	−0.536683	+	0.843784i	$0.680323\pi$
$158$		0			0
$159$		−	6.13813i		−	0.486786i
$160$		0			0
$161$	15.0880	−	4.34801i	1.18910	−	0.342671i
$162$		0			0
$163$	−7.25469	+	12.5655i	−0.568231	+	0.984206i	0.428510	+	0.903537i	$0.359039\pi$
$163$	−7.25469	+	12.5655i	−0.568231	+	0.984206i	−0.996741	+	0.0806685i	$0.974294\pi$
$164$		0			0
$165$	0.733277	+	2.01466i	0.0570855	+	0.156841i
$166$		0			0
$167$	20.3905	−	7.42152i	1.57786	−	0.574295i	0.603124	−	0.797647i	$-0.293922\pi$
$167$	20.3905	−	7.42152i	1.57786	−	0.574295i	0.974738	+	0.223353i	$0.0717001\pi$
$168$		0			0
$169$	−0.202017	−	1.14569i	−0.0155397	−	0.0881302i
$170$		0			0
$171$	−29.5364	−	23.2221i	−2.25870	−	1.77584i
$172$		0			0
$173$	−4.95109	+	4.15446i	−0.376424	+	0.315858i	−0.811297	−	0.584635i	$-0.801238\pi$
$173$	−4.95109	+	4.15446i	−0.376424	+	0.315858i	0.434872	+	0.900492i	$0.356793\pi$
$174$		0			0
$175$	−3.10950	+	12.5421i	−0.235056	+	0.948093i
$176$		0			0
$177$	5.93647	−	33.6674i	0.446212	−	2.53060i
$178$		0			0
$179$			18.9603i			1.41716i	0.705631	+	0.708579i	$0.250663\pi$
$179$			18.9603i			1.41716i	−0.705631	+	0.708579i	$0.749337\pi$
$180$		0			0
$181$	0.740928	−	4.20201i	0.0550727	−	0.312333i	−0.944810	−	0.327617i	$-0.893754\pi$
$181$	0.740928	−	4.20201i	0.0550727	−	0.312333i	0.999883	+	0.0152845i	$0.00486538\pi$
$182$		0			0
$183$	41.9361	+	24.2118i	3.10001	+	1.78979i
$184$		0			0
$185$	−0.248698	+	0.208682i	−0.0182846	+	0.0153426i
$186$		0			0
$187$	−4.07507	+	11.1962i	−0.297999	+	0.818744i
$188$		0			0
$189$	50.5631	+	3.46858i	3.67793	+	0.252302i
$190$		0			0
$191$	7.97309	+	13.8098i	0.576912	+	0.999242i	0.995831	+	0.0912178i	$0.0290759\pi$
$191$	7.97309	+	13.8098i	0.576912	+	0.999242i	−0.418919	+	0.908024i	$0.637591\pi$
$192$		0			0
$193$	−12.4954	+	2.20327i	−0.899438	+	0.158595i	−0.604204	−	0.796830i	$-0.706509\pi$
$193$	−12.4954	+	2.20327i	−0.899438	+	0.158595i	−0.295234	+	0.955425i	$0.595398\pi$
$194$		0			0
$195$	−1.36623	+	3.75369i	−0.0978380	+	0.268808i
$196$		0			0
$197$	1.72725	−	2.99169i	0.123062	−	0.213149i	−0.797912	−	0.602774i	$-0.794062\pi$
$197$	1.72725	−	2.99169i	0.123062	−	0.213149i	0.920974	+	0.389625i	$0.127395\pi$
$198$		0			0
$199$	−14.0529	+	16.7477i	−0.996187	+	1.18721i	−0.0138855	+	0.999904i	$0.504420\pi$
$199$	−14.0529	+	16.7477i	−0.996187	+	1.18721i	−0.982302	+	0.187306i	$0.940024\pi$
$200$		0			0
$201$	−21.7546	−	12.5600i	−1.53445	−	0.885914i
$202$		0			0
$203$	−1.56533	+	1.62524i	−0.109864	+	0.114069i
$204$		0			0
$205$	0.303799	−	0.362054i	0.0212182	−	0.0252869i
$206$		0			0
$207$	−48.0709	−	17.4964i	−3.34116	−	1.21608i
$208$		0			0
$209$	−4.24435	−	6.83882i	−0.293588	−	0.473051i
$210$		0			0
$211$	−2.09727	+	0.369805i	−0.144382	+	0.0254585i	−0.245372	−	0.969429i	$-0.578910\pi$
$211$	−2.09727	+	0.369805i	−0.144382	+	0.0254585i	0.100990	+	0.994887i	$0.467799\pi$
$212$		0			0
$213$	−21.3640	−	3.76706i	−1.46384	−	0.258114i
$214$		0			0
$215$	−0.797875	−	0.140687i	−0.0544146	−	0.00959476i
$216$		0			0
$217$	−16.8752	−	1.15762i	−1.14557	−	0.0785847i
$218$		0			0
$219$	−3.56732	−	9.80113i	−0.241057	−	0.662299i
$220$		0			0
$221$	−19.2252	+	11.0997i	−1.29323	+	0.746645i
$222$		0			0
$223$	−7.66807	−	2.79095i	−0.513492	−	0.186896i	0.0722604	−	0.997386i	$-0.476979\pi$
$223$	−7.66807	−	2.79095i	−0.513492	−	0.186896i	−0.585753	+	0.810490i	$0.699201\pi$
$224$		0			0
$225$	32.2491	−	27.0602i	2.14994	−	1.80401i
$226$		0			0
$227$	5.73371	−	9.93107i	0.380560	−	0.659149i	−0.610583	−	0.791952i	$-0.709065\pi$
$227$	5.73371	−	9.93107i	0.380560	−	0.659149i	0.991142	+	0.132804i	$0.0423981\pi$
$228$		0			0
$229$	5.36223	−	3.09588i	0.354346	−	0.204582i	−0.312252	−	0.949999i	$-0.601083\pi$
$229$	5.36223	−	3.09588i	0.354346	−	0.204582i	0.666598	+	0.745418i	$0.267750\pi$
$230$		0			0
$231$	15.2226	+	6.75343i	1.00157	+	0.444343i
$232$		0			0
$233$	0.661190	+	3.74979i	0.0433160	+	0.245657i	0.998776	−	0.0494637i	$-0.0157512\pi$
$233$	0.661190	+	3.74979i	0.0433160	+	0.245657i	−0.955460	+	0.295121i	$0.904640\pi$
$234$		0			0
$235$	−0.686892	−	1.18973i	−0.0448079	−	0.0776096i
$236$		0			0
$237$	−36.5419	−	6.44332i	−2.37365	−	0.418539i
$238$		0			0
$239$	14.8074	+	25.6471i	0.957810	+	1.65897i	0.727804	+	0.685786i	$0.240541\pi$
$239$	14.8074	+	25.6471i	0.957810	+	1.65897i	0.230006	+	0.973189i	$0.426125\pi$
$240$		0			0
$241$	6.32718	−	2.30291i	0.407570	−	0.148343i	−0.130096	−	0.991501i	$-0.541529\pi$
$241$	6.32718	−	2.30291i	0.407570	−	0.148343i	0.537666	+	0.843158i	$0.319306\pi$
$242$		0			0
$243$	−58.9631	−	49.4759i	−3.78248	−	3.17388i
$244$		0			0
$245$	−1.26883	−	2.01865i	−0.0810623	−	0.128967i
$246$		0			0
$247$	2.13252	−	14.8441i	0.135689	−	0.944510i
$248$		0			0
$249$	6.75871	−	18.5694i	0.428316	−	1.17679i
$250$		0			0
$251$	−6.71645	−	18.4533i	−0.423939	−	1.16476i	−0.949434	−	0.313966i	$-0.898342\pi$
$251$	−6.71645	−	18.4533i	−0.423939	−	1.16476i	0.525495	−	0.850796i	$-0.323880\pi$
$252$		0			0
$253$	−8.39496	−	7.04420i	−0.527786	−	0.442865i
$254$		0			0
$255$	−7.49178			−0.469154
$256$		0			0
$257$	20.5376	−	7.47509i	1.28110	−	0.466283i	0.390306	−	0.920685i	$-0.372369\pi$
$257$	20.5376	−	7.47509i	1.28110	−	0.466283i	0.890797	+	0.454402i	$0.150147\pi$
$258$		0			0
$259$	−0.172585	+	2.51585i	−0.0107239	+	0.156327i
$260$		0			0
$261$	7.23970	−	1.27655i	0.448126	−	0.0790167i
$262$		0			0
$263$	−0.622934	−	3.53284i	−0.0384118	−	0.217844i	0.959560	−	0.281505i	$-0.0908335\pi$
$263$	−0.622934	−	3.53284i	−0.0384118	−	0.217844i	−0.997972	+	0.0636608i	$0.979722\pi$
$264$		0			0
$265$	0.613342			0.0376773
$266$		0			0
$267$	−44.5287			−2.72511
$268$		0			0
$269$	3.99088	+	22.6334i	0.243328	+	1.37998i	0.824343	+	0.566091i	$0.191545\pi$
$269$	3.99088	+	22.6334i	0.243328	+	1.37998i	−0.581015	+	0.813893i	$0.697344\pi$
$270$		0			0
$271$	20.1857	−	3.55928i	1.22619	−	0.216211i	0.477203	−	0.878793i	$-0.341650\pi$
$271$	20.1857	−	3.55928i	1.22619	−	0.216211i	0.748989	+	0.662582i	$0.230539\pi$
$272$		0			0
$273$	13.6388	+	27.8701i	0.825457	+	1.68678i
$274$		0			0
$275$	8.47456	−	3.08449i	0.511035	−	0.186002i
$276$		0			0
$277$	−10.1657			−0.610797			−0.305398	−	0.952225i	$-0.598790\pi$
$277$	−10.1657			−0.610797			−0.305398	+	0.952225i	$0.598790\pi$
$278$		0			0
$279$	42.2146	+	35.4223i	2.52732	+	2.12068i
$280$		0			0
$281$	6.80050	+	18.6842i	0.405684	+	1.11461i	0.959436	+	0.281926i	$0.0909732\pi$
$281$	6.80050	+	18.6842i	0.405684	+	1.11461i	−0.553752	+	0.832681i	$0.686805\pi$
$282$		0			0
$283$	−4.46170	+	12.2584i	−0.265220	+	0.728687i	0.733574	+	0.679609i	$0.237851\pi$
$283$	−4.46170	+	12.2584i	−0.265220	+	0.728687i	−0.998795	+	0.0490782i	$0.984372\pi$
$284$		0			0
$285$	3.12804	−	3.97857i	0.185289	−	0.235670i
$286$		0			0
$287$	−0.388567	−	3.65055i	−0.0229364	−	0.215485i
$288$		0			0
$289$	−18.8710	−	15.8347i	−1.11006	−	0.931451i
$290$		0			0
$291$	24.3182	−	8.85110i	1.42556	−	0.518860i
$292$		0			0
$293$	8.52833	+	14.7715i	0.498231	+	0.862961i	0.999998	−	0.00204190i	$-0.000649956\pi$
$293$	8.52833	+	14.7715i	0.498231	+	0.862961i	−0.501767	+	0.865003i	$0.667317\pi$
$294$		0			0
$295$	3.36415	+	0.593191i	0.195869	+	0.0345369i
$296$		0			0
$297$	−17.6861	−	30.6332i	−1.02625	−	1.77752i
$298$		0			0
$299$	−3.54562	−	20.1082i	−0.205048	−	1.16289i
$300$		0			0
$301$	−5.08639	+	3.70576i	−0.293175	+	0.213596i
$302$		0			0
$303$	10.4404	−	6.02776i	0.599784	−	0.346286i
$304$		0			0
$305$	−2.41932	+	4.19039i	−0.138530	+	0.239941i
$306$		0			0
$307$	2.23881	−	1.87858i	0.127776	−	0.107216i	−0.576660	−	0.816984i	$-0.695644\pi$
$307$	2.23881	−	1.87858i	0.127776	−	0.107216i	0.704436	+	0.709767i	$0.251200\pi$
$308$		0			0
$309$	−48.4163	−	17.6221i	−2.75431	−	1.00249i
$310$		0			0
$311$	12.1469	−	7.01304i	0.688790	−	0.397673i	−0.114369	−	0.993438i	$-0.536485\pi$
$311$	12.1469	−	7.01304i	0.688790	−	0.397673i	0.803159	+	0.595765i	$0.203151\pi$
$312$		0			0
$313$	3.21807	+	8.84158i	0.181896	+	0.499756i	0.996809	−	0.0798283i	$-0.0254372\pi$
$313$	3.21807	+	8.84158i	0.181896	+	0.499756i	−0.814912	+	0.579584i	$0.803215\pi$
$314$		0			0
$315$	−0.531618	+	7.74964i	−0.0299533	+	0.436643i
$316$		0			0
$317$	18.6672	+	3.29153i	1.04845	+	0.184871i	0.671228	−	0.741251i	$-0.265767\pi$
$317$	18.6672	+	3.29153i	1.04845	+	0.184871i	0.377225	+	0.926122i	$0.376878\pi$
$318$		0			0
$319$	1.55092	+	0.273469i	0.0868347	+	0.0153113i
$320$		0			0
$321$	−42.0519	+	7.41488i	−2.34711	+	0.413858i
$322$		0			0
$323$	27.5288	−	5.76350i	1.53174	−	0.320690i
$324$		0			0
$325$	15.7897	+	5.74698i	0.875855	+	0.318785i
$326$		0			0
$327$	−16.5680	+	19.7450i	−0.916211	+	1.09190i
$328$		0			0
$329$	−10.3574	−	2.56786i	−0.571023	−	0.141571i
$330$		0			0
$331$	19.7891	+	11.4253i	1.08771	+	0.627989i	0.932965	−	0.359966i	$-0.117212\pi$
$331$	19.7891	+	11.4253i	1.08771	+	0.627989i	0.154743	+	0.987955i	$0.450545\pi$
$332$		0			0
$333$	5.28094	−	6.29358i	0.289394	−	0.344886i
$334$		0			0
$335$	1.25504	−	2.17379i	0.0685700	−	0.118767i
$336$		0			0
$337$	−3.72384	+	10.2312i	−0.202850	+	0.557327i	−0.998849	−	0.0479722i	$-0.984724\pi$
$337$	−3.72384	+	10.2312i	−0.202850	+	0.557327i	0.795998	+	0.605299i	$0.206946\pi$
$338$		0			0
$339$	−46.2352	+	8.15251i	−2.51115	+	0.442783i
$340$		0			0
$341$	5.90265	+	10.2237i	0.319647	+	0.553644i
$342$		0			0
$343$	−18.1307	−	3.77873i	−0.978964	−	0.204032i
$344$		0			0
$345$	2.35677	−	6.47518i	0.126884	−	0.348612i
$346$		0			0
$347$	9.88252	−	8.29242i	0.530522	−	0.445160i	−0.337760	−	0.941232i	$-0.609669\pi$
$347$	9.88252	−	8.29242i	0.530522	−	0.445160i	0.868281	+	0.496072i	$0.165225\pi$
$348$		0			0
$349$	−24.1340	−	13.9338i	−1.29187	−	0.745859i	−0.312881	−	0.949792i	$-0.601294\pi$
$349$	−24.1340	−	13.9338i	−1.29187	−	0.745859i	−0.978985	+	0.203933i	$0.934627\pi$
$350$		0			0
$351$	11.4443	−	64.9038i	0.610851	−	3.46431i
$352$		0			0
$353$			2.25588i			0.120068i	0.998196	+	0.0600342i	$0.0191210\pi$
$353$			2.25588i			0.120068i	−0.998196	+	0.0600342i	$0.980879\pi$
$354$		0			0
$355$	0.376416	−	2.13476i	0.0199781	−	0.113301i
$356$		0			0
$357$	−40.3690	+	41.9140i	−2.13655	+	2.21832i
$358$		0			0
$359$	−10.7583	+	9.02730i	−0.567802	+	0.476442i	−0.880916	−	0.473273i	$-0.843072\pi$
$359$	−10.7583	+	9.02730i	−0.567802	+	0.476442i	0.313114	+	0.949716i	$0.398628\pi$
$360$		0			0
$361$	−8.43334	+	17.0258i	−0.443860	+	0.896096i
$362$		0			0
$363$	4.49290	+	25.4805i	0.235816	+	1.33738i
$364$		0			0
$365$	0.979360	−	0.356458i	0.0512621	−	0.0186579i
$366$		0			0
$367$	8.41844	+	23.1295i	0.439439	+	1.20735i	0.939858	+	0.341565i	$0.110957\pi$
$367$	8.41844	+	23.1295i	0.439439	+	1.20735i	−0.500419	+	0.865783i	$0.666821\pi$
$368$		0			0
$369$	−5.98019	+	10.3580i	−0.311316	+	0.539216i
$370$		0			0
$371$	3.30495	−	3.43144i	0.171585	−	0.178152i
$372$		0			0
$373$			2.63042i			0.136198i	0.997679	+	0.0680990i	$0.0216934\pi$
$373$			2.63042i			0.136198i	−0.997679	+	0.0680990i	$0.978307\pi$
$374$		0			0
$375$	7.37664	+	8.79114i	0.380928	+	0.453972i
$376$		0			0
$377$	1.88609	+	2.24775i	0.0971384	+	0.115765i
$378$		0			0
$379$			11.1598i			0.573240i	0.958044	+	0.286620i	$0.0925317\pi$
$379$			11.1598i			0.573240i	−0.958044	+	0.286620i	$0.907468\pi$
$380$		0			0
$381$	18.0498	+	10.4211i	0.924721	+	0.533888i
$382$		0			0
$383$	−28.1706	−	10.2532i	−1.43945	−	0.523916i	−0.499825	−	0.866127i	$-0.666602\pi$
$383$	−28.1706	−	10.2532i	−1.43945	−	0.523916i	−0.939623	+	0.342210i	$0.888824\pi$
$384$		0			0
$385$	−0.674825	+	1.52109i	−0.0343923	+	0.0775218i
$386$		0			0
$387$	20.5026			1.04221
$388$		0			0
$389$	18.3504	+	15.3978i	0.930403	+	0.780701i	0.975890	−	0.218264i	$-0.0700394\pi$
$389$	18.3504	+	15.3978i	0.930403	+	0.780701i	−0.0454867	+	0.998965i	$0.514484\pi$
$390$		0			0
$391$	33.1638	−	19.1471i	1.67716	−	0.968311i
$392$		0			0
$393$	−26.7669	+	31.8996i	−1.35021	+	1.60912i
$394$		0			0
$395$	0.643838	−	3.65138i	0.0323950	−	0.183721i
$396$		0			0
$397$	3.02634	+	3.60665i	0.151888	+	0.181013i	0.836623	−	0.547779i	$-0.184527\pi$
$397$	3.02634	+	3.60665i	0.151888	+	0.181013i	−0.684735	+	0.728792i	$0.740082\pi$
$398$		0			0
$399$	−5.40352	−	38.9386i	−0.270514	−	1.94937i
$400$		0			0
$401$	−17.1644	−	20.4557i	−0.857149	−	1.02151i	−0.999498	−	0.0316936i	$-0.989910\pi$
$401$	−17.1644	−	20.4557i	−0.857149	−	1.02151i	0.142349	−	0.989817i	$-0.454535\pi$
$402$		0			0
$403$	−3.81948	+	21.6614i	−0.190262	+	1.07903i
$404$		0			0
$405$	8.63493	−	10.2907i	0.429073	−	0.511349i
$406$		0			0
$407$	1.52420	−	0.879999i	0.0755519	−	0.0436199i
$408$		0			0
$409$	9.67503	+	8.11832i	0.478400	+	0.401425i	0.849847	−	0.527029i	$-0.176694\pi$
$409$	9.67503	+	8.11832i	0.478400	+	0.401425i	−0.371448	+	0.928454i	$0.621139\pi$
$410$		0			0
$411$	−14.7208			−0.726124
$412$		0			0
$413$	21.4462	−	15.6249i	1.05530	−	0.768853i
$414$		0			0
$415$	1.85552	+	0.675352i	0.0910837	+	0.0331517i
$416$		0			0
$417$	−20.6422	−	11.9178i	−1.01085	−	0.583617i
$418$		0			0
$419$		−	16.0311i		−	0.783173i	−0.920141	−	0.391586i	$-0.871926\pi$
$419$		−	16.0311i		−	0.783173i	0.920141	−	0.391586i	$-0.128074\pi$
$420$		0			0
$421$	2.59013	+	3.08679i	0.126235	+	0.150441i	0.825460	−	0.564461i	$-0.190916\pi$
$421$	2.59013	+	3.08679i	0.126235	+	0.150441i	−0.699225	+	0.714902i	$0.746471\pi$
$422$		0			0
$423$	22.3466	+	26.6317i	1.08653	+	1.29488i
$424$		0			0
$425$			31.5138i			1.52864i
$426$		0			0
$427$	10.4075	+	36.1149i	0.503652	+	1.74772i
$428$		0			0
$429$	10.8277	−	18.7542i	0.522768	−	0.905460i
$430$		0			0
$431$	−0.183809	−	0.505011i	−0.00885377	−	0.0243255i	0.935187	−	0.354154i	$-0.115231\pi$
$431$	−0.183809	−	0.505011i	−0.00885377	−	0.0243255i	−0.944041	+	0.329829i	$0.893009\pi$
$432$		0			0
$433$	−1.49416	+	0.543830i	−0.0718048	+	0.0261348i	−0.377673	−	0.925939i	$-0.623276\pi$
$433$	−1.49416	+	0.543830i	−0.0718048	+	0.0261348i	0.305868	+	0.952074i	$0.401053\pi$
$434$		0			0
$435$	0.171953	+	0.975193i	0.00824451	+	0.0467569i
$436$		0			0
$437$	−3.67863	+	25.6064i	−0.175973	+	1.22492i
$438$		0			0
$439$	9.49534	−	7.96754i	0.453188	−	0.380270i	−0.387429	−	0.921899i	$-0.626637\pi$
$439$	9.49534	−	7.96754i	0.453188	−	0.380270i	0.840617	+	0.541630i	$0.182192\pi$
$440$		0			0
$441$	40.4920	+	44.7326i	1.92819	+	2.13012i
$442$		0			0
$443$	−2.73378	+	15.5041i	−0.129886	+	0.736620i	0.848399	+	0.529357i	$0.177567\pi$
$443$	−2.73378	+	15.5041i	−0.129886	+	0.736620i	−0.978285	+	0.207263i	$0.933544\pi$
$444$		0			0
$445$		−	4.44945i		−	0.210924i
$446$		0			0
$447$	4.92375	−	27.9240i	0.232885	−	1.32076i
$448$		0			0
$449$	1.66737	+	0.962658i	0.0786882	+	0.0454307i	0.538828	−	0.842416i	$-0.318867\pi$
$449$	1.66737	+	0.962658i	0.0786882	+	0.0454307i	−0.460140	+	0.887847i	$0.652201\pi$
$450$		0			0
$451$	−1.96276	+	1.64695i	−0.0924228	+	0.0775519i
$452$		0			0
$453$	14.0432	−	38.5835i	0.659809	−	1.81281i
$454$		0			0
$455$	−2.78487	+	1.36283i	−0.130557	+	0.0638906i
$456$		0			0
$457$	−6.05055	−	10.4799i	−0.283033	−	0.490228i	0.689097	−	0.724669i	$-0.258007\pi$
$457$	−6.05055	−	10.4799i	−0.283033	−	0.490228i	−0.972130	+	0.234441i	$0.924674\pi$
$458$		0			0
$459$	121.726	−	21.4635i	5.68167	−	1.00183i
$460$		0			0
$461$	−3.64509	+	10.0148i	−0.169769	+	0.466436i	−0.995176	−	0.0981012i	$-0.968723\pi$
$461$	−3.64509	+	10.0148i	−0.169769	+	0.466436i	0.825408	+	0.564537i	$0.190945\pi$
$462$		0			0
$463$	−0.945941	+	1.63842i	−0.0439616	+	0.0761437i	−0.887169	−	0.461445i	$-0.847331\pi$
$463$	−0.945941	+	1.63842i	−0.0439616	+	0.0761437i	0.843207	+	0.537588i	$0.180665\pi$
$464$		0			0
$465$	−4.77141	+	5.68635i	−0.221269	+	0.263698i
$466$		0			0
$467$	26.1507	+	15.0981i	1.21011	+	0.698657i	0.962783	−	0.270275i	$-0.0871147\pi$
$467$	26.1507	+	15.0981i	1.21011	+	0.698657i	0.247326	+	0.968932i	$0.420448\pi$
$468$		0			0
$469$	−5.39892	−	18.7348i	−0.249299	−	0.865093i
$470$		0			0
$471$	16.5498	−	19.7232i	0.762573	−	0.908799i
$472$		0			0
$473$	4.12728	+	1.50221i	0.189772	+	0.0690715i
$474$		0			0
$475$	−16.7356	−	13.1579i	−0.767883	−	0.603727i
$476$		0			0
$477$	−15.2855	+	2.69525i	−0.699876	+	0.123407i
$478$		0			0
$479$	36.7862	+	6.48640i	1.68081	+	0.296371i	0.930927	−	0.365205i	$-0.119001\pi$
$479$	36.7862	+	6.48640i	1.68081	+	0.296371i	0.749878	+	0.661576i	$0.230112\pi$
$480$		0			0
$481$	3.22939	+	0.569429i	0.147248	+	0.0259637i
$482$		0			0
$483$	−23.5271	−	48.0765i	−1.07052	−	2.18755i
$484$		0			0
$485$	0.884430	+	2.42995i	0.0401599	+	0.110338i
$486$		0			0
$487$	−28.8824	+	16.6753i	−1.30879	+	0.755629i	−0.981894	−	0.189433i	$-0.939335\pi$
$487$	−28.8824	+	16.6753i	−1.30879	+	0.755629i	−0.326893	+	0.945061i	$0.606002\pi$
$488$		0			0
$489$	46.4763	+	16.9160i	2.10173	+	0.764967i
$490$		0			0
$491$	2.24983	−	1.88783i	0.101533	−	0.0851966i	−0.590608	−	0.806959i	$-0.701112\pi$
$491$	2.24983	−	1.88783i	0.101533	−	0.0851966i	0.692141	+	0.721762i	$0.256668\pi$
$492$		0			0
$493$	−2.75154	+	4.76581i	−0.123923	+	0.214641i
$494$		0			0
$495$	4.69504	−	2.71068i	0.211026	−	0.121836i
$496$		0			0
$497$	−9.91498	−	13.6090i	−0.444748	−	0.610445i
$498$		0			0
$499$	−2.69346	−	15.2754i	−0.120576	−	0.683819i	−0.983838	−	0.179063i	$-0.942693\pi$
$499$	−2.69346	−	15.2754i	−0.120576	−	0.683819i	0.863262	−	0.504756i	$-0.168418\pi$
$500$		0			0
$501$	−36.9835	−	64.0572i	−1.65230	−	2.86187i
$502$		0			0
$503$	−19.5803	−	3.45254i	−0.873043	−	0.153941i	−0.280864	−	0.959748i	$-0.590621\pi$
$503$	−19.5803	−	3.45254i	−0.873043	−	0.153941i	−0.592179	+	0.805807i	$0.701732\pi$
$504$		0			0
$505$	0.602313	+	1.04324i	0.0268026	+	0.0464234i
$506$		0			0
$507$	−3.72648	+	1.35633i	−0.165499	+	0.0602367i
$508$		0			0
$509$	−20.3833	−	17.1036i	−0.903474	−	0.758105i	0.0673924	−	0.997727i	$-0.478532\pi$
$509$	−20.3833	−	17.1036i	−0.903474	−	0.758105i	−0.970866	+	0.239622i	$0.922977\pi$
$510$		0			0
$511$	3.28296	−	7.39994i	0.145229	−	0.327354i
$512$		0			0
$513$	−39.4257	+	73.6050i	−1.74069	+	3.24974i
$514$		0			0
$515$	1.76086	−	4.83791i	0.0775926	−	0.213184i
$516$		0			0
$517$	2.54721	+	6.99840i	0.112026	+	0.307789i
$518$		0			0
$519$	16.8771	+	14.1615i	0.740821	+	0.621623i
$520$		0			0
$521$	−18.4801			−0.809628			−0.404814	−	0.914399i	$-0.632664\pi$
$521$	−18.4801			−0.809628			−0.404814	+	0.914399i	$0.632664\pi$
$522$		0			0
$523$	27.9621	−	10.1774i	1.22270	−	0.445026i	0.351607	−	0.936148i	$-0.385635\pi$
$523$	27.9621	−	10.1774i	1.22270	−	0.445026i	0.871091	+	0.491122i	$0.163413\pi$
$524$		0			0
$525$	43.9440	+	3.01452i	1.91787	+	0.131564i
$526$		0			0
$527$	−40.6254	+	7.16336i	−1.76967	+	0.312041i
$528$		0			0
$529$	2.12234	+	12.0364i	0.0922755	+	0.523320i
$530$		0			0
$531$	−86.4472			−3.75149
$532$		0			0
$533$	−4.77387			−0.206779
$534$		0			0
$535$	−0.740919	−	4.20196i	−0.0320327	−	0.181667i
$536$		0			0
$537$	63.6492	−	11.2231i	2.74666	−	0.484311i
$538$		0			0
$539$	4.87372	+	11.9717i	0.209926	+	0.515657i
$540$		0			0
$541$	−1.93478	+	0.704201i	−0.0831825	+	0.0302760i	−0.383276	−	0.923634i	$-0.625204\pi$
$541$	−1.93478	+	0.704201i	−0.0831825	+	0.0302760i	0.300094	+	0.953910i	$0.402982\pi$
$542$		0			0
$543$	−14.5446			−0.624169
$544$		0			0
$545$	−1.97298	−	1.65553i	−0.0845132	−	0.0709150i
$546$		0			0
$547$	1.16337	+	3.19635i	0.0497423	+	0.136666i	0.962076	−	0.272782i	$-0.0879437\pi$
$547$	1.16337	+	3.19635i	0.0497423	+	0.136666i	−0.912334	+	0.409448i	$0.865721\pi$
$548$		0			0
$549$	41.8795	−	115.063i	1.78738	−	4.91077i
$550$		0			0
$551$	−1.38207	−	3.45110i	−0.0588783	−	0.147022i
$552$		0			0
$553$	−16.9590	−	23.2773i	−0.721169	−	0.989851i
$554$		0			0
$555$	0.847751	+	0.711347i	0.0359850	+	0.0301950i
$556$		0			0
$557$	−3.20641	+	1.16704i	−0.135860	+	0.0494491i	−0.409055	−	0.912510i	$-0.634142\pi$
$557$	−3.20641	+	1.16704i	−0.135860	+	0.0494491i	0.273195	+	0.961959i	$0.411919\pi$
$558$		0			0
$559$	4.09171	+	7.08705i	0.173061	+	0.299750i
$560$		0			0
$561$	39.9973	+	7.05261i	1.68869	+	0.297761i
$562$		0			0
$563$	−9.95308	−	17.2392i	−0.419472	−	0.726547i	0.576414	−	0.817158i	$-0.304451\pi$
$563$	−9.95308	−	17.2392i	−0.419472	−	0.726547i	−0.995886	+	0.0906105i	$0.971118\pi$
$564$		0			0
$565$	−0.814625	−	4.61997i	−0.0342715	−	0.194364i
$566$		0			0
$567$	−11.0443	−	103.760i	−0.463817	−	4.35752i
$568$		0			0
$569$	−30.5870	+	17.6594i	−1.28227	+	0.740320i	−0.977263	−	0.212029i	$-0.931993\pi$
$569$	−30.5870	+	17.6594i	−1.28227	+	0.740320i	−0.305009	+	0.952349i	$0.598659\pi$
$570$		0			0
$571$	−3.02852	+	5.24555i	−0.126740	+	0.219519i	−0.922412	−	0.386208i	$-0.873785\pi$
$571$	−3.02852	+	5.24555i	−0.126740	+	0.219519i	0.795672	+	0.605728i	$0.207118\pi$
$572$		0			0
$573$	41.6396	−	34.9398i	1.73952	−	1.45963i
$574$		0			0
$575$	−27.2375	−	9.91364i	−1.13588	−	0.413427i
$576$		0			0
$577$	37.3768	−	21.5795i	1.55602	−	0.898367i	0.558386	−	0.829581i	$-0.311421\pi$
$577$	37.3768	−	21.5795i	1.55602	−	0.898367i	0.997631	−	0.0687862i	$-0.0219126\pi$
$578$		0			0
$579$	14.7927	+	40.6425i	0.614762	+	1.68905i
$580$		0			0
$581$	13.7767	−	6.74189i	0.571553	−	0.279701i
$582$		0			0
$583$	−3.27453	−	0.577388i	−0.135617	−	0.0239130i
$584$		0			0
$585$	9.94758	+	1.75403i	0.411282	+	0.0725201i
$586$		0			0
$587$	40.9783	−	7.22557i	1.69135	−	0.298231i	0.756693	−	0.653771i	$-0.226814\pi$
$587$	40.9783	−	7.22557i	1.69135	−	0.298231i	0.934661	+	0.355539i	$0.115703\pi$
$588$		0			0
$589$	13.1582	−	24.5654i	0.542172	−	1.01220i
$590$		0			0
$591$	−11.0654	−	4.02749i	−0.455171	−	0.165669i
$592$		0			0
$593$	−13.6919	+	16.3174i	−0.562259	+	0.670075i	−0.970023	−	0.243013i	$-0.921864\pi$
$593$	−13.6919	+	16.3174i	−0.562259	+	0.670075i	0.407764	+	0.913087i	$0.366309\pi$
$594$		0			0
$595$	−4.18818	−	4.03380i	−0.171699	−	0.165370i
$596$		0			0
$597$	64.5397	+	37.2620i	2.64143	+	1.52503i
$598$		0			0
$599$	−2.43844	+	2.90602i	−0.0996319	+	0.118737i	−0.813556	−	0.581486i	$-0.802472\pi$
$599$	−2.43844	+	2.90602i	−0.0996319	+	0.118737i	0.713924	+	0.700223i	$0.246916\pi$
$600$		0			0
$601$	5.17262	−	8.95925i	0.210996	−	0.365455i	−0.741031	−	0.671471i	$-0.765663\pi$
$601$	5.17262	−	8.95925i	0.210996	−	0.365455i	0.952026	+	0.306016i	$0.0989960\pi$
$602$		0			0
$603$	−21.7252	+	59.6895i	−0.884719	+	2.43075i
$604$		0			0
$605$	−2.54609	+	0.448945i	−0.103513	+	0.0182522i
$606$		0			0
$607$	12.2397	+	21.1998i	0.496794	+	0.860473i	0.999993	−	0.00369774i	$-0.00117703\pi$
$607$	12.2397	+	21.1998i	0.496794	+	0.860473i	−0.503199	+	0.864171i	$0.667844\pi$
$608$		0			0
$609$	6.38243	+	4.29274i	0.258629	+	0.173951i
$610$		0			0
$611$	−4.74593	+	13.0393i	−0.192000	+	0.527515i
$612$		0			0
$613$	−24.6244	+	20.6623i	−0.994569	+	0.834543i	−0.986223	−	0.165422i	$-0.947101\pi$
$613$	−24.6244	+	20.6623i	−0.994569	+	0.834543i	−0.00834654	+	0.999965i	$0.502657\pi$
$614$		0			0
$615$	−1.39523	−	0.805536i	−0.0562611	−	0.0324824i
$616$		0			0
$617$	−2.00412	+	11.3659i	−0.0806827	+	0.457574i	0.917522	+	0.397684i	$0.130186\pi$
$617$	−2.00412	+	11.3659i	−0.0806827	+	0.457574i	−0.998205	+	0.0598899i	$0.980925\pi$
$618$		0			0
$619$		−	36.8147i		−	1.47971i	−0.672768	−	0.739854i	$-0.734895\pi$
$619$		−	36.8147i		−	1.47971i	0.672768	−	0.739854i	$-0.265105\pi$
$620$		0			0
$621$	−19.7416	+	111.960i	−0.792203	+	4.49280i
$622$		0			0
$623$	−24.8932	−	23.9756i	−0.997323	−	0.960560i
$624$		0			0
$625$	17.8283	−	14.9597i	0.713132	−	0.598389i
$626$		0			0
$627$	−20.4454	+	18.2962i	−0.816511	+	0.730681i
$628$		0			0
$629$	1.06795	+	6.05665i	0.0425820	+	0.241495i
$630$		0			0
$631$	17.6945	−	6.44026i	0.704405	−	0.256383i	0.0351146	−	0.999383i	$-0.488820\pi$
$631$	17.6945	−	6.44026i	0.704405	−	0.256383i	0.669291	+	0.743001i	$0.266598\pi$
$632$		0			0
$633$	2.48285	+	6.82158i	0.0986846	+	0.271134i
$634$		0			0
$635$	−1.04131	+	1.80360i	−0.0413230	+	0.0715736i
$636$		0			0
$637$	−7.38152	+	22.9240i	−0.292467	+	0.908281i
$638$		0			0
$639$			54.8560i			2.17007i
$640$		0			0
$641$	25.6243	+	30.5379i	1.01210	+	1.20617i	0.978396	+	0.206742i	$0.0662859\pi$
$641$	25.6243	+	30.5379i	1.01210	+	1.20617i	0.0337041	+	0.999432i	$0.489270\pi$
$642$		0			0
$643$	−18.5246	−	22.0768i	−0.730539	−	0.870623i	0.265070	−	0.964229i	$-0.414605\pi$
$643$	−18.5246	−	22.0768i	−0.730539	−	0.870623i	−0.995609	+	0.0936066i	$0.970160\pi$
$644$		0			0
$645$			2.76172i			0.108743i
$646$		0			0
$647$	2.78407	+	1.60738i	0.109453	+	0.0631927i	0.553727	−	0.832698i	$-0.313205\pi$
$647$	2.78407	+	1.60738i	0.109453	+	0.0631927i	−0.444274	+	0.895891i	$0.646538\pi$
$648$		0			0
$649$	−17.4022	−	6.33389i	−0.683097	−	0.248627i
$650$		0			0
$651$	6.10275	+	57.3349i	0.239186	+	2.24713i
$652$		0			0
$653$	−21.7215			−0.850028			−0.425014	−	0.905187i	$-0.639731\pi$
$653$	−21.7215			−0.850028			−0.425014	+	0.905187i	$0.639731\pi$
$654$		0			0
$655$	−3.18751	−	2.67464i	−0.124546	−	0.104507i
$656$		0			0
$657$	−22.8409	+	13.1872i	−0.891109	+	0.514482i
$658$		0			0
$659$	23.6893	−	28.2317i	0.922802	−	1.09975i	−0.0719468	−	0.997408i	$-0.522921\pi$
$659$	23.6893	−	28.2317i	0.922802	−	1.09975i	0.994749	−	0.102344i	$-0.0326344\pi$
$660$		0			0
$661$	−2.46632	+	13.9872i	−0.0959285	+	0.544038i	0.898530	+	0.438911i	$0.144636\pi$
$661$	−2.46632	+	13.9872i	−0.0959285	+	0.544038i	−0.994459	+	0.105126i	$0.966475\pi$
$662$		0			0
$663$	48.6412	+	57.9683i	1.88907	+	2.25130i
$664$		0			0
$665$	3.89087	−	0.539937i	0.150881	−	0.0209379i
$666$		0			0
$667$	−3.25353	−	3.87741i	−0.125977	−	0.150134i
$668$		0			0
$669$	−4.83022	+	27.3935i	−0.186747	+	1.05910i
$670$		0			0
$671$	16.8611	−	20.0943i	0.650916	−	0.775731i
$672$		0			0
$673$	23.2153	−	13.4033i	0.894883	−	0.516661i	0.0193465	−	0.999813i	$-0.493841\pi$
$673$	23.2153	−	13.4033i	0.894883	−	0.516661i	0.875537	+	0.483152i	$0.160508\pi$
$674$		0			0
$675$	−71.6692	−	60.1376i	−2.75855	−	2.31470i
$676$		0			0
$677$	−29.1627			−1.12081			−0.560406	−	0.828218i	$-0.689355\pi$
$677$	−29.1627			−1.12081			−0.560406	+	0.828218i	$0.689355\pi$
$678$		0			0
$679$	18.3604	+	8.14554i	0.704609	+	0.312597i
$680$		0			0
$681$	−36.7323	−	13.3695i	−1.40758	−	0.512318i
$682$		0			0
$683$	−8.93795	−	5.16033i	−0.342001	−	0.197454i	0.319155	−	0.947702i	$-0.396601\pi$
$683$	−8.93795	−	5.16033i	−0.342001	−	0.197454i	−0.661157	+	0.750248i	$0.729934\pi$
$684$		0			0
$685$		−	1.47095i		−	0.0562022i
$686$		0			0
$687$	−13.5668	−	16.1683i	−0.517607	−	0.616860i
$688$		0			0
$689$	−3.98219	−	4.74579i	−0.151709	−	0.180800i
$690$		0			0
$691$		−	17.0753i		−	0.649576i	−0.945787	−	0.324788i	$-0.894707\pi$
$691$		−	17.0753i		−	0.649576i	0.945787	−	0.324788i	$-0.105293\pi$
$692$		0			0
$693$	10.1336	−	40.8735i	0.384942	−	1.55266i
$694$		0			0
$695$	1.19086	−	2.06264i	0.0451721	−	0.0782403i
$696$		0			0
$697$	−3.06220	−	8.41333i	−0.115989	−	0.318678i
$698$		0			0
$699$	12.1966	−	4.43919i	0.461317	−	0.167906i
$700$		0			0
$701$	2.79401	+	15.8456i	0.105528	+	0.598480i	0.991008	+	0.133802i	$0.0427187\pi$
$701$	2.79401	+	15.8456i	0.105528	+	0.598480i	−0.885480	+	0.464678i	$0.846170\pi$
$702$		0			0
$703$	−3.66234	−	1.96169i	−0.138128	−	0.0739864i
$704$		0			0
$705$	−3.58731	+	3.01011i	−0.135106	+	0.113367i
$706$		0			0
$707$	9.08208	+	2.25167i	0.341567	+	0.0846829i
$708$		0			0
$709$	−7.13159	+	40.4452i	−0.267832	+	1.51895i	0.493014	+	0.870021i	$0.335895\pi$
$709$	−7.13159	+	40.4452i	−0.267832	+	1.51895i	−0.760847	+	0.648932i	$0.775216\pi$
$710$		0			0
$711$			93.8280i			3.51882i
$712$		0			0
$713$	6.58867	−	37.3662i	0.246748	−	1.39938i
$714$		0			0
$715$	1.87398	+	1.08194i	0.0700828	+	0.0404623i
$716$		0			0
$717$	77.3318	−	64.8891i	2.88801	−	2.42333i
$718$		0			0
$719$	13.0096	−	35.7434i	0.485174	−	1.33301i	−0.419830	−	0.907603i	$-0.637910\pi$
$719$	13.0096	−	35.7434i	0.485174	−	1.33301i	0.905004	−	0.425403i	$-0.139868\pi$
$720$		0			0
$721$	−17.5782	−	35.9201i	−0.654647	−	1.33774i
$722$		0			0
$723$	−11.4760	−	19.8770i	−0.426797	−	0.739235i
$724$		0			0
$725$	4.10209	−	0.723310i	0.152348	−	0.0268631i
$726$		0			0
$727$	−14.6911	+	40.3633i	−0.544861	+	1.49699i	0.295702	+	0.955280i	$0.404446\pi$
$727$	−14.6911	+	40.3633i	−0.544861	+	1.49699i	−0.840563	+	0.541713i	$0.817776\pi$
$728$		0			0
$729$	−72.0287	+	124.757i	−2.66773	+	4.62064i
$730$		0			0
$731$	−9.86539	+	11.7571i	−0.364884	+	0.434852i
$732$		0			0
$733$	15.1410	+	8.74165i	0.559245	+	0.322880i	0.752842	−	0.658201i	$-0.228682\pi$
$733$	15.1410	+	8.74165i	0.559245	+	0.322880i	−0.193598	+	0.981081i	$0.562016\pi$
$734$		0			0
$735$	−6.02552	+	5.45430i	−0.222255	+	0.201185i
$736$		0			0
$737$	−8.74678	+	10.4240i	−0.322192	+	0.383973i
$738$		0			0
$739$	−24.9134	−	9.06775i	−0.916456	−	0.333563i	−0.159628	−	0.987177i	$-0.551030\pi$
$739$	−24.9134	−	9.06775i	−0.916456	−	0.333563i	−0.756828	+	0.653614i	$0.773252\pi$
$740$		0			0
$741$	−51.0936	+	1.62781i	−1.87697	+	0.0597991i
$742$		0			0
$743$	−16.4968	+	2.90883i	−0.605210	+	0.106715i	−0.467852	−	0.883807i	$-0.654972\pi$
$743$	−16.4968	+	2.90883i	−0.605210	+	0.106715i	−0.137358	+	0.990522i	$0.543861\pi$
$744$		0			0
$745$	2.79025	+	0.491997i	0.102227	+	0.0180254i
$746$		0			0
$747$	−49.2103	−	8.67711i	−1.80051	−	0.317479i
$748$		0			0
$749$	−27.5009	−	18.4968i	−1.00486	−	0.675858i
$750$		0			0
$751$	−4.44924	−	12.2242i	−0.162355	−	0.446067i	0.831663	−	0.555281i	$-0.187389\pi$
$751$	−4.44924	−	12.2242i	−0.162355	−	0.446067i	−0.994018	+	0.109213i	$0.965167\pi$
$752$		0			0
$753$	−57.9716	+	33.4699i	−2.11260	+	1.21971i
$754$		0			0
$755$	3.85538	+	1.40325i	0.140312	+	0.0510693i
$756$		0			0
$757$	3.07894	−	2.58354i	0.111906	−	0.0939003i	−0.585118	−	0.810948i	$-0.698952\pi$
$757$	3.07894	−	2.58354i	0.111906	−	0.0939003i	0.697024	+	0.717048i	$0.254507\pi$
$758$		0			0
$759$	−18.6780	+	32.3513i	−0.677969	+	1.17428i
$760$		0			0
$761$	−23.3486	+	13.4803i	−0.846387	+	0.488662i	−0.859430	−	0.511253i	$-0.829181\pi$
$761$	−23.3486	+	13.4803i	−0.846387	+	0.488662i	0.0130431	+	0.999915i	$0.495848\pi$
$762$		0			0
$763$	−19.8934	+	2.11746i	−0.720189	+	0.0766572i
$764$		0			0
$765$	3.28964	+	18.6565i	0.118937	+	0.674526i
$766$		0			0
$767$	−17.2523	−	29.8818i	−0.622943	−	1.07897i
$768$		0			0
$769$	34.9346	+	6.15991i	1.25977	+	0.222132i	0.763371	−	0.645960i	$-0.223543\pi$
$769$	34.9346	+	6.15991i	1.25977	+	0.222132i	0.496403	+	0.868092i	$0.334654\pi$
$770$		0			0
$771$	−37.2504	−	64.5196i	−1.34154	−	2.32362i
$772$		0			0
$773$	16.2476	−	5.91365i	0.584386	−	0.212699i	−0.0328723	−	0.999460i	$-0.510465\pi$
$773$	16.2476	−	5.91365i	0.584386	−	0.212699i	0.617259	+	0.786760i	$0.288243\pi$
$774$		0			0
$775$	23.9193	+	20.0707i	0.859206	+	0.720960i
$776$		0			0
$777$	8.54779	−	0.909831i	0.306650	−	0.0326400i
$778$		0			0
$779$	5.74653	+	1.88661i	0.205891	+	0.0675947i
$780$		0			0
$781$	−4.01924	+	11.0428i	−0.143820	+	0.395142i
$782$		0			0
$783$	−5.58774	−	15.3522i	−0.199690	−	0.548643i
$784$		0			0
$785$	1.97081	+	1.65371i	0.0703412	+	0.0590233i
$786$		0			0
$787$	−4.03743			−0.143919			−0.0719595	−	0.997408i	$-0.522925\pi$
$787$	−4.03743			−0.143919			−0.0719595	+	0.997408i	$0.522925\pi$
$788$		0			0
$789$	−11.4909	+	4.18235i	−0.409087	+	0.148895i
$790$		0			0
$791$	−30.2367	−	20.3368i	−1.07509	−	0.723095i
$792$		0			0
$793$	48.1312	−	8.48683i	1.70919	−	0.301376i
$794$		0			0
$795$	−0.363052	−	2.05897i	−0.0128761	−	0.0730242i
$796$		0			0
$797$	36.5792			1.29570			0.647850	−	0.761768i	$-0.275668\pi$
$797$	36.5792			1.29570			0.647850	+	0.761768i	$0.275668\pi$
$798$		0			0
$799$	−26.0245			−0.920679
$800$		0			0
$801$	19.5525	+	110.888i	0.690854	+	3.91803i
$802$		0			0
$803$	−5.56420	+	0.981118i	−0.196356	+	0.0346229i
$804$		0			0
$805$	4.80395	−	2.35091i	0.169317	−	0.0828586i
$806$		0			0
$807$	73.6175	−	26.7946i	2.59146	−	0.943213i
$808$		0			0
$809$	45.4720			1.59871			0.799355	−	0.600858i	$-0.205174\pi$
$809$	45.4720			1.59871			0.799355	+	0.600858i	$0.205174\pi$
$810$		0			0
$811$	−7.91756	−	6.64362i	−0.278023	−	0.233289i	0.493104	−	0.869970i	$-0.335862\pi$
$811$	−7.91756	−	6.64362i	−0.278023	−	0.233289i	−0.771127	+	0.636681i	$0.780307\pi$
$812$		0			0
$813$	−23.8968	−	65.6559i	−0.838098	−	2.30265i
$814$		0			0
$815$	−1.69030	+	4.64406i	−0.0592086	+	0.162674i
$816$		0			0
$817$	−2.12462	−	10.1480i	−0.0743309	−	0.355035i
$818$		0			0
$819$	63.4150	−	46.2019i	2.21590	−	1.61442i
$820$		0			0
$821$	−18.5774	−	15.5883i	−0.648355	−	0.544034i	0.258216	−	0.966087i	$-0.416865\pi$
$821$	−18.5774	−	15.5883i	−0.648355	−	0.544034i	−0.906571	+	0.422053i	$0.861310\pi$
$822$		0			0
$823$	23.8546	−	8.68235i	0.831518	−	0.302648i	0.109036	−	0.994038i	$-0.465224\pi$
$823$	23.8546	−	8.68235i	0.831518	−	0.302648i	0.722482	+	0.691390i	$0.243001\pi$
$824$		0			0
$825$	−15.3708	−	26.6231i	−0.535144	−	0.926896i
$826$		0			0
$827$	−40.7597	−	7.18704i	−1.41735	−	0.249918i	−0.588099	−	0.808789i	$-0.700124\pi$
$827$	−40.7597	−	7.18704i	−1.41735	−	0.249918i	−0.829255	+	0.558871i	$0.811235\pi$
$828$		0			0
$829$	−0.393124	−	0.680910i	−0.0136537	−	0.0236490i	0.859118	−	0.511778i	$-0.171013\pi$
$829$	−0.393124	−	0.680910i	−0.0136537	−	0.0236490i	−0.872772	+	0.488129i	$0.837680\pi$
$830$		0			0
$831$	6.01732	+	34.1259i	0.208739	+	1.18381i
$832$		0			0
$833$	−45.1355	+	1.69561i	−1.56385	+	0.0587493i
$834$		0			0
$835$	6.40081	−	3.69551i	0.221509	−	0.127888i
$836$		0			0
$837$	61.2343	−	106.061i	2.11657	−	3.66600i
$838$		0			0
$839$	−10.4826	+	8.79595i	−0.361900	+	0.303670i	−0.805547	−	0.592531i	$-0.798129\pi$
$839$	−10.4826	+	8.79595i	−0.361900	+	0.303670i	0.443648	+	0.896201i	$0.353684\pi$
$840$		0			0
$841$	−26.5676	−	9.66981i	−0.916123	−	0.333442i
$842$		0			0
$843$	58.6970	−	33.8887i	2.02163	−	1.16719i
$844$		0			0
$845$	−0.135529	−	0.372362i	−0.00466233	−	0.0128096i
$846$		0			0
$847$	−11.2077	+	16.6636i	−0.385103	+	0.572569i
$848$		0			0
$849$	43.7922	+	7.72174i	1.50294	+	0.265009i
$850$		0			0
$851$	−5.57075	−	0.982274i	−0.190963	−	0.0336719i
$852$		0			0
$853$	−14.8315	+	2.61520i	−0.507822	+	0.0895427i	−0.421688	−	0.906741i	$-0.638562\pi$
$853$	−14.8315	+	2.61520i	−0.507822	+	0.0895427i	−0.0861337	+	0.996284i	$0.527451\pi$
$854$		0			0
$855$	−11.2812	−	6.04264i	−0.385808	−	0.206654i
$856$		0			0
$857$	38.1484	+	13.8849i	1.30312	+	0.474298i	0.898013	−	0.439969i	$-0.145011\pi$
$857$	38.1484	+	13.8849i	1.30312	+	0.474298i	0.405111	+	0.914267i	$0.367233\pi$
$858$		0			0
$859$	−1.41029	+	1.68072i	−0.0481185	+	0.0573454i	−0.789567	−	0.613665i	$-0.789695\pi$
$859$	−1.41029	+	1.68072i	−0.0481185	+	0.0573454i	0.741448	+	0.671010i	$0.234139\pi$
$860$		0			0
$861$	−12.0248	+	3.46526i	−0.409804	+	0.118096i
$862$		0			0
$863$	−21.1928	−	12.2357i	−0.721413	−	0.416508i	0.0938598	−	0.995585i	$-0.470079\pi$
$863$	−21.1928	−	12.2357i	−0.721413	−	0.416508i	−0.815272	+	0.579078i	$0.803413\pi$
$864$		0			0
$865$	−1.41507	+	1.68641i	−0.0481137	+	0.0573397i
$866$		0			0
$867$	−41.9863	+	72.7225i	−1.42593	+	2.46978i
$868$		0			0
$869$	−6.87468	+	18.8880i	−0.233207	+	0.640732i
$870$		0			0
$871$	−24.9683	+	4.40259i	−0.846019	+	0.149176i
$872$		0			0
$873$	−32.7196	−	56.6720i	−1.10739	−	1.91806i
$874$		0			0
$875$	−0.609596	+	8.88637i	−0.0206081	+	0.300414i
$876$		0			0
$877$	16.0178	−	44.0086i	0.540883	−	1.48606i	−0.304820	−	0.952410i	$-0.598596\pi$
$877$	16.0178	−	44.0086i	0.540883	−	1.48606i	0.845703	−	0.533654i	$-0.179182\pi$
$878$		0			0
$879$	44.5394	−	37.3730i	1.50228	−	1.26056i
$880$		0			0
$881$	−26.2568	−	15.1594i	−0.884614	−	0.510732i	−0.0124369	−	0.999923i	$-0.503959\pi$
$881$	−26.2568	−	15.1594i	−0.884614	−	0.510732i	−0.872177	+	0.489191i	$0.837292\pi$
$882$		0			0
$883$	0.849400	−	4.81719i	0.0285846	−	0.162111i	−0.967174	−	0.254115i	$-0.918216\pi$
$883$	0.849400	−	4.81719i	0.0285846	−	0.162111i	0.995759	+	0.0920034i	$0.0293271\pi$
$884$		0			0
$885$		−	11.6445i		−	0.391426i
$886$		0			0
$887$	5.38435	−	30.5361i	0.180789	−	1.02530i	−0.750459	−	0.660917i	$-0.770168\pi$
$887$	5.38435	−	30.5361i	0.180789	−	1.02530i	0.931248	−	0.364387i	$-0.118721\pi$
$888$		0			0
$889$	4.47950	+	15.5443i	0.150238	+	0.521340i
$890$		0			0
$891$	−55.7878	+	46.8116i	−1.86896	+	1.56825i
$892$		0			0
$893$	10.8660	−	13.8205i	0.363616	−	0.462485i
$894$		0			0
$895$	1.12144	+	6.36003i	0.0374858	+	0.212592i
$896$		0			0
$897$	−65.4039	+	23.8051i	−2.18377	+	0.794828i
$898$		0			0
$899$	1.86488	+	5.12373i	0.0621974	+	0.170886i
$900$		0			0
$901$	5.80947	−	10.0623i	0.193541	−	0.335223i
$902$		0			0
$903$	15.4509	+	14.8813i	0.514173	+	0.495220i
$904$		0			0
$905$		−	1.45334i		−	0.0483108i
$906$		0			0
$907$	7.80609	+	9.30294i	0.259197	+	0.308899i	0.879911	−	0.475138i	$-0.157602\pi$
$907$	7.80609	+	9.30294i	0.259197	+	0.308899i	−0.620714	+	0.784037i	$0.713157\pi$
$908$		0			0
$909$	−19.5950	−	23.3524i	−0.649926	−	0.774552i
$910$		0			0
$911$			23.2679i			0.770899i	0.922729	+	0.385449i	$0.125954\pi$
$911$			23.2679i			0.770899i	−0.922729	+	0.385449i	$0.874046\pi$
$912$		0			0
$913$	−9.27051	−	5.35233i	−0.306809	−	0.177136i
$914$		0			0
$915$	15.4991	+	5.64121i	0.512384	+	0.186493i
$916$		0			0
$917$	−32.1394	+	3.42093i	−1.06134	+	0.112969i
$918$		0			0
$919$	28.6759			0.945931			0.472966	−	0.881081i	$-0.343183\pi$
$919$	28.6759			0.945931			0.472966	+	0.881081i	$0.343183\pi$
$920$		0			0
$921$	−7.63156	−	6.40364i	−0.251469	−	0.211007i
$922$		0			0
$923$	−18.9618	+	10.9476i	−0.624136	+	0.360345i
$924$		0			0
$925$	2.99224	−	3.56601i	0.0983843	−	0.117250i
$926$		0			0
$927$	−22.6240	+	128.307i	−0.743068	+	4.21415i
$928$		0			0
$929$	−34.3363	−	40.9204i	−1.12654	−	1.34256i	−0.932336	−	0.361593i	$-0.882233\pi$
$929$	−34.3363	−	40.9204i	−1.12654	−	1.34256i	−0.194201	−	0.980962i	$-0.562212\pi$
$930$		0			0
$931$	17.9449	−	24.6775i	0.588121	−	0.808773i
$932$		0			0
$933$	−30.7327	−	36.6257i	−1.00614	−	1.19907i
$934$		0			0
$935$	−0.704719	+	3.99666i	−0.0230468	+	0.130705i
$936$		0			0
$937$	28.4724	−	33.9321i	0.930154	−	1.10851i	−0.0637172	−	0.997968i	$-0.520296\pi$
$937$	28.4724	−	33.9321i	0.930154	−	1.10851i	0.993871	−	0.110546i	$-0.0352600\pi$
$938$		0			0
$939$	27.7761	−	16.0365i	0.906439	−	0.523333i
$940$		0			0
$941$	35.3276	+	29.6434i	1.15165	+	0.966347i	0.999757	−	0.0220500i	$-0.00701932\pi$
$941$	35.3276	+	29.6434i	1.15165	+	0.966347i	0.151891	+	0.988397i	$0.451464\pi$
$942$		0			0
$943$	8.23500			0.268168
$944$		0			0
$945$	17.1660	−	1.82716i	0.558411	−	0.0594375i
$946$		0			0
$947$	24.3134	+	8.84935i	0.790079	+	0.287565i	0.705369	−	0.708841i	$-0.250781\pi$
$947$	24.3134	+	8.84935i	0.790079	+	0.287565i	0.0847099	+	0.996406i	$0.473004\pi$
$948$		0			0
$949$	−9.11672	−	5.26354i	−0.295941	−	0.170862i
$950$		0			0
$951$		−	64.6135i		−	2.09524i
$952$		0			0
$953$	−21.0451	−	25.0806i	−0.681718	−	0.812440i	0.308610	−	0.951189i	$-0.400136\pi$
$953$	−21.0451	−	25.0806i	−0.681718	−	0.812440i	−0.990328	+	0.138749i	$0.955692\pi$
$954$		0			0
$955$	3.49130	+	4.16077i	0.112976	+	0.134639i
$956$		0			0
$957$		−	5.36826i		−	0.173531i
$958$		0			0
$959$	−8.22948	−	7.92612i	−0.265744	−	0.255948i
$960$		0			0
$961$	−4.93669	+	8.55059i	−0.159248	+	0.275825i
$962$		0			0
$963$	36.9299	+	101.464i	1.19005	+	3.26963i
$964$		0			0
$965$	−4.06113	+	1.47813i	−0.130732	+	0.0475827i
$966$		0			0
$967$	1.93096	+	10.9510i	0.0620954	+	0.352161i	0.999986	+	0.00523038i	$0.00166489\pi$
$967$	1.93096	+	10.9510i	0.0620954	+	0.352161i	−0.937891	+	0.346930i	$0.887224\pi$
$968$		0			0
$969$	−35.6429	−	89.0019i	−1.14501	−	2.85915i
$970$		0			0
$971$	−0.613887	+	0.515113i	−0.0197006	+	0.0165307i	−0.652585	−	0.757716i	$-0.726315\pi$
$971$	−0.613887	+	0.515113i	−0.0197006	+	0.0165307i	0.632884	+	0.774246i	$0.281871\pi$
$972$		0			0
$973$	−5.12287	−	17.7769i	−0.164232	−	0.569900i
$974$		0			0
$975$	9.94614	−	56.4074i	0.318531	−	1.80648i
$976$		0			0
$977$			2.33972i			0.0748541i	0.999299	+	0.0374271i	$0.0119162\pi$
$977$			2.33972i			0.0748541i	−0.999299	+	0.0374271i	$0.988084\pi$
$978$		0			0
$979$	−4.18862	+	23.7548i	−0.133869	+	0.759208i
$980$		0			0
$981$	56.4450	+	32.5885i	1.80215	+	1.04047i
$982$		0			0
$983$	−34.1249	+	28.6342i	−1.08841	+	0.913288i	−0.996592	−	0.0824875i	$-0.973714\pi$
$983$	−34.1249	+	28.6342i	−1.08841	+	0.913288i	−0.0918220	+	0.995775i	$0.529269\pi$
$984$		0			0
$985$	0.402439	−	1.10569i	0.0128228	−	0.0352303i
$986$		0			0
$987$	−2.48943	+	36.2895i	−0.0792394	+	1.15511i
$988$		0			0
$989$	−7.05826	−	12.2253i	−0.224440	−	0.388741i
$990$		0			0
$991$	−4.19788	+	0.740200i	−0.133350	+	0.0235132i	−0.239925	−	0.970791i	$-0.577123\pi$
$991$	−4.19788	+	0.740200i	−0.133350	+	0.0235132i	0.106575	+	0.994305i	$0.466012\pi$
$992$		0			0
$993$	26.6406	−	73.1944i	0.845414	−	2.32276i
$994$		0			0
$995$	−3.72334	+	6.44901i	−0.118038	+	0.204448i
$996$		0			0
$997$	−3.16984	+	3.77767i	−0.100390	+	0.119640i	−0.813900	−	0.581005i	$-0.802660\pi$
$997$	−3.16984	+	3.77767i	−0.100390	+	0.119640i	0.713510	+	0.700645i	$0.247104\pi$
$998$		0			0
$999$	−15.8121	−	9.12913i	−0.500274	−	0.288833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.cj.a.409.1	yes	78
7.5	odd	6		532.2.bw.a.257.1	✓	78
19.2	odd	18		532.2.bw.a.325.1	yes	78
133.40	even	18	inner	532.2.cj.a.173.1	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.bw.a.257.1	✓	78	7.5	odd	6
532.2.bw.a.325.1	yes	78	19.2	odd	18
532.2.cj.a.173.1	yes	78	133.40	even	18	inner
532.2.cj.a.409.1	yes	78	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.cj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.591925 - 3.35697i) q^{3} +(0.335440 - 0.0591470i) q^{5} +(1.47659 - 2.19538i) q^{7} +(-8.09981 + 2.94809i) q^{9} -1.84653 q^{11} +(-2.63553 - 2.21147i) q^{13} +(-0.397110 - 1.09105i) q^{15} +(2.20688 - 6.06334i) q^{17} +(2.29855 + 3.70360i) q^{19} +(-8.24386 - 3.65736i) q^{21} +(4.54633 + 3.81483i) q^{23} +(-4.58944 + 1.67042i) q^{25} +(9.57799 + 16.5896i) q^{27} +(-0.839908 - 0.148098i) q^{29} +(-3.19661 - 5.53670i) q^{31} +(1.09301 + 6.19876i) q^{33} +(0.365455 - 0.823753i) q^{35} +(-0.825440 + 0.476568i) q^{37} +(-5.86382 + 10.1564i) q^{39} +(1.06294 - 0.891915i) q^{41} +(-2.23515 - 0.813527i) q^{43} +(-2.54263 + 1.46799i) q^{45} +(-1.37945 - 3.79002i) q^{47} +(-2.63939 - 6.48333i) q^{49} +(-21.6608 - 3.81938i) q^{51} +(1.77334 + 0.312687i) q^{53} +(-0.619400 + 0.109217i) q^{55} +(11.0723 - 9.90842i) q^{57} +(9.42427 + 3.43015i) q^{59} +(-9.13122 + 10.8822i) q^{61} +(-5.48788 + 22.1353i) q^{63} +(-1.01486 - 0.585932i) q^{65} +(4.73686 - 5.64518i) q^{67} +(10.1152 - 17.5200i) q^{69} +(2.17664 - 5.98028i) q^{71} +(3.01332 - 0.531330i) q^{73} +(8.32416 + 14.4179i) q^{75} +(-2.72656 + 4.05384i) q^{77} +(3.72302 - 10.2289i) q^{79} +(30.2122 - 25.3510i) q^{81} +(5.02050 + 2.89858i) q^{83} +(0.381645 - 2.16441i) q^{85} +2.90721i q^{87} +(2.26837 - 12.8646i) q^{89} +(-8.74661 + 2.52056i) q^{91} +(-16.6944 + 14.0083i) q^{93} +(0.990082 + 1.10638i) q^{95} +(1.31832 + 7.47654i) q^{97} +(14.9566 - 5.44375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 6 q^{7} - 6 q^{11} + 6 q^{13} - 3 q^{15} + 27 q^{17} + 21 q^{19} - 3 q^{21} - 24 q^{23} + 12 q^{27} - 18 q^{29} + 33 q^{35} + 36 q^{37} - 18 q^{39} - 18 q^{41} - 48 q^{43} - 18 q^{45} - 18 q^{49}+ \cdots + 27 q^{99}+O(q^{100}) \) 78 * q + 6 * q^7 - 6 * q^11 + 6 * q^13 - 3 * q^15 + 27 * q^17 + 21 * q^19 - 3 * q^21 - 24 * q^23 + 12 * q^27 - 18 * q^29 + 33 * q^35 + 36 * q^37 - 18 * q^39 - 18 * q^41 - 48 * q^43 - 18 * q^45 - 18 * q^49 + 6 * q^53 - 18 * q^57 + 45 * q^59 + 39 * q^61 - 27 * q^63 - 18 * q^65 + 21 * q^67 + 6 * q^71 - 3 * q^73 - 21 * q^75 - 21 * q^77 + 36 * q^79 + 36 * q^81 - 18 * q^83 + 60 * q^85 - 21 * q^91 - 102 * q^93 + 60 * q^95 - 27 * q^97 + 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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