LMFDB - Embedded newform 640.2.bm.a.221.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			221.48
Character	$\chi$	$=$	640.221
Dual form			640.2.bm.a.501.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.940698 + 1.05598i) q^{2} +(0.235694 + 0.0232138i) q^{3} +(-0.230176 + 1.98671i) q^{4} +(0.471397 + 0.881921i) q^{5} +(0.197203 + 0.270724i) q^{6} +(0.890754 + 4.47812i) q^{7} +(-2.31445 + 1.62583i) q^{8} +(-2.88734 - 0.574328i) q^{9} +O(q^{10})$	\(q+(0.940698 + 1.05598i) q^{2} +(0.235694 + 0.0232138i) q^{3} +(-0.230176 + 1.98671i) q^{4} +(0.471397 + 0.881921i) q^{5} +(0.197203 + 0.270724i) q^{6} +(0.890754 + 4.47812i) q^{7} +(-2.31445 + 1.62583i) q^{8} +(-2.88734 - 0.574328i) q^{9} +(-0.487847 + 1.32741i) q^{10} +(-0.120950 - 0.0992607i) q^{11} +(-0.100370 + 0.462912i) q^{12} +(-1.70581 - 0.911775i) q^{13} +(-3.89086 + 5.15317i) q^{14} +(0.0906325 + 0.218806i) q^{15} +(-3.89404 - 0.914585i) q^{16} +(2.27418 - 5.49035i) q^{17} +(-2.10964 - 3.58924i) q^{18} +(4.91214 - 1.49008i) q^{19} +(-1.86063 + 0.733532i) q^{20} +(0.105991 + 1.07614i) q^{21} +(-0.00895989 - 0.221094i) q^{22} +(-7.35331 + 4.91332i) q^{23} +(-0.583242 + 0.329472i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(-0.641839 - 2.65900i) q^{26} +(-1.34710 - 0.408640i) q^{27} +(-9.10176 + 0.738915i) q^{28} +(4.21000 + 5.12990i) q^{29} +(-0.145797 + 0.301536i) q^{30} +(5.97412 - 5.97412i) q^{31} +(-2.69733 - 4.97236i) q^{32} +(-0.0262028 - 0.0262028i) q^{33} +(7.93700 - 2.76328i) q^{34} +(-3.52945 + 2.89655i) q^{35} +(1.80562 - 5.60412i) q^{36} +(-2.12088 + 6.99162i) q^{37} +(6.19433 + 3.78539i) q^{38} +(-0.380883 - 0.254498i) q^{39} +(-2.52488 - 1.27475i) q^{40} +(4.21098 + 6.30217i) q^{41} +(-1.03668 + 1.12425i) q^{42} +(10.1078 - 0.995532i) q^{43} +(0.225042 - 0.217444i) q^{44} +(-0.854572 - 2.81715i) q^{45} +(-12.1056 - 3.14297i) q^{46} +(5.19216 + 2.15066i) q^{47} +(-0.896569 - 0.305957i) q^{48} +(-12.7930 + 5.29902i) q^{49} +(-1.40064 + 0.195492i) q^{50} +(0.663462 - 1.24125i) q^{51} +(2.20407 - 3.17908i) q^{52} +(-6.34354 + 7.72962i) q^{53} +(-0.835704 - 1.80692i) q^{54} +(0.0305249 - 0.153459i) q^{55} +(-9.34228 - 8.91616i) q^{56} +(1.19235 - 0.237173i) q^{57} +(-1.45672 + 9.27134i) q^{58} +(3.38666 - 1.81021i) q^{59} +(-0.455566 + 0.129697i) q^{60} +(0.226347 - 2.29814i) q^{61} +(11.9284 + 0.688693i) q^{62} -13.4415i q^{63} +(2.71333 - 7.52581i) q^{64} -1.93420i q^{65} +(0.00302065 - 0.0523185i) q^{66} +(-0.984184 + 9.99259i) q^{67} +(10.3843 + 5.78188i) q^{68} +(-1.84719 + 0.987342i) q^{69} +(-6.37883 - 1.00225i) q^{70} +(0.0978609 - 0.0194657i) q^{71} +(7.61636 - 3.36509i) q^{72} +(1.74303 - 8.76279i) q^{73} +(-9.37810 + 4.33739i) q^{74} +(-0.150246 + 0.183075i) q^{75} +(1.82971 + 10.1020i) q^{76} +(0.336765 - 0.630043i) q^{77} +(-0.0895518 - 0.641609i) q^{78} +(7.06558 - 2.92666i) q^{79} +(-1.02904 - 3.86537i) q^{80} +(7.85144 + 3.25217i) q^{81} +(-2.69369 + 10.3751i) q^{82} +(-2.39592 - 7.89829i) q^{83} +(-2.16238 - 0.0371289i) q^{84} +(5.91410 - 0.582488i) q^{85} +(10.5597 + 9.73712i) q^{86} +(0.873186 + 1.30681i) q^{87} +(0.441313 + 0.0330898i) q^{88} +(-6.22160 - 4.15714i) q^{89} +(2.17095 - 3.55249i) q^{90} +(2.56358 - 8.45099i) q^{91} +(-8.06880 - 15.7398i) q^{92} +(1.54674 - 1.26938i) q^{93} +(2.61320 + 7.50593i) q^{94} +(3.62970 + 3.62970i) q^{95} +(-0.520317 - 1.23457i) q^{96} +(1.97383 - 1.97383i) q^{97} +(-17.6300 - 8.52431i) q^{98} +(0.292215 + 0.356064i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	0.940698	+	1.05598i	0.665174	+	0.746689i
$2$	0.940698	+	1.05598i	0.665174	+	0.746689i
$3$	0.235694	+	0.0232138i	0.136078	+	0.0134025i	0.165827	−	0.986155i	$-0.446971\pi$
$3$	0.235694	+	0.0232138i	0.136078	+	0.0134025i	−0.0297489	+	0.999557i	$0.509471\pi$
$4$	−0.230176	+	1.98671i	−0.115088	+	0.993355i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$6$	0.197203	+	0.270724i	0.0805079	+	0.110523i
$7$	0.890754	+	4.47812i	0.336673	+	1.69257i	0.664059	+	0.747680i	$0.268832\pi$
$7$	0.890754	+	4.47812i	0.336673	+	1.69257i	−0.327386	+	0.944891i	$0.606168\pi$
$8$	−2.31445	+	1.62583i	−0.818281	+	0.574819i
$9$	−2.88734	−	0.574328i	−0.962448	−	0.191443i
$10$	−0.487847	+	1.32741i	−0.154271	+	0.419762i
$11$	−0.120950	−	0.0992607i	−0.0364677	−	0.0299282i	0.615983	−	0.787759i	$-0.288759\pi$
$11$	−0.120950	−	0.0992607i	−0.0364677	−	0.0299282i	−0.652451	+	0.757831i	$0.726259\pi$
$12$	−0.100370	+	0.462912i	−0.0289744	+	0.133631i
$13$	−1.70581	−	0.911775i	−0.473107	−	0.252881i	0.217570	−	0.976045i	$-0.430187\pi$
$13$	−1.70581	−	0.911775i	−0.473107	−	0.252881i	−0.690676	+	0.723164i	$0.742687\pi$
$14$	−3.89086	+	5.15317i	−1.03988	+	1.37724i
$15$	0.0906325	+	0.218806i	0.0234012	+	0.0564955i
$16$	−3.89404	−	0.914585i	−0.973510	−	0.228646i
$17$	2.27418	−	5.49035i	0.551569	−	1.33161i	−0.364731	−	0.931113i	$-0.618839\pi$
$17$	2.27418	−	5.49035i	0.551569	−	1.33161i	0.916300	−	0.400493i	$-0.131161\pi$
$18$	−2.10964	−	3.58924i	−0.497247	−	0.845991i
$19$	4.91214	−	1.49008i	1.12692	−	0.341848i	0.328833	−	0.944388i	$-0.393345\pi$
$19$	4.91214	−	1.49008i	1.12692	−	0.341848i	0.798089	+	0.602540i	$0.205845\pi$
$20$	−1.86063	+	0.733532i	−0.416049	+	0.164023i
$21$	0.105991	+	1.07614i	0.0231291	+	0.234834i
$22$	−0.00895989	−	0.221094i	−0.00191026	−	0.0471375i
$23$	−7.35331	+	4.91332i	−1.53327	+	1.02450i	−0.551557	+	0.834137i	$0.685966\pi$
$23$	−7.35331	+	4.91332i	−1.53327	+	1.02450i	−0.981714	+	0.190362i	$0.939034\pi$
$24$	−0.583242	+	0.329472i	−0.119054	+	0.0672531i
$25$	−0.555570	+	0.831470i	−0.111114	+	0.166294i
$26$	−0.641839	−	2.65900i	−0.125875	−	0.521473i
$27$	−1.34710	−	0.408640i	−0.259250	−	0.0786428i
$28$	−9.10176	+	0.738915i	−1.72007	+	0.139642i
$29$	4.21000	+	5.12990i	0.781777	+	0.952598i	0.999727	−	0.0233621i	$-0.00743705\pi$
$29$	4.21000	+	5.12990i	0.781777	+	0.952598i	−0.217950	+	0.975960i	$0.569937\pi$
$30$	−0.145797	+	0.301536i	−0.0266187	+	0.0550528i
$31$	5.97412	−	5.97412i	1.07298	−	1.07298i	0.0758648	−	0.997118i	$-0.475828\pi$
$31$	5.97412	−	5.97412i	1.07298	−	1.07298i	0.997118	−	0.0758648i	$-0.0241717\pi$
$32$	−2.69733	−	4.97236i	−0.476825	−	0.878998i
$33$	−0.0262028	−	0.0262028i	−0.00456133	−	0.00456133i
$34$	7.93700	−	2.76328i	1.36118	−	0.473899i
$35$	−3.52945	+	2.89655i	−0.596586	+	0.489606i
$36$	1.80562	−	5.60412i	0.300937	−	0.934020i
$37$	−2.12088	+	6.99162i	−0.348671	+	1.14941i	0.590809	+	0.806811i	$0.298809\pi$
$37$	−2.12088	+	6.99162i	−0.348671	+	1.14941i	−0.939480	+	0.342603i	$0.888691\pi$
$38$	6.19433	+	3.78539i	1.00485	+	0.614072i
$39$	−0.380883	−	0.254498i	−0.0609901	−	0.0407523i
$40$	−2.52488	−	1.27475i	−0.399219	−	0.201555i
$41$	4.21098	+	6.30217i	0.657644	+	0.984234i	0.999018	+	0.0443063i	$0.0141078\pi$
$41$	4.21098	+	6.30217i	0.657644	+	0.984234i	−0.341374	+	0.939928i	$0.610892\pi$
$42$	−1.03668	+	1.12425i	−0.159963	+	0.173475i
$43$	10.1078	−	0.995532i	1.54143	−	0.151817i	0.708703	−	0.705507i	$-0.249280\pi$
$43$	10.1078	−	0.995532i	1.54143	−	0.151817i	0.832723	+	0.553689i	$0.186780\pi$
$44$	0.225042	−	0.217444i	0.0339263	−	0.0327810i
$45$	−0.854572	−	2.81715i	−0.127392	−	0.419955i
$46$	−12.1056	−	3.14297i	−1.78487	−	0.463406i
$47$	5.19216	+	2.15066i	0.757354	+	0.313706i	0.727738	−	0.685855i	$-0.240572\pi$
$47$	5.19216	+	2.15066i	0.757354	+	0.313706i	0.0296160	+	0.999561i	$0.490572\pi$
$48$	−0.896569	−	0.305957i	−0.129409	−	0.0441612i
$49$	−12.7930	+	5.29902i	−1.82757	+	0.757003i
$50$	−1.40064	+	0.195492i	−0.198080	+	0.0276467i
$51$	0.663462	−	1.24125i	0.0929032	−	0.173810i
$52$	2.20407	−	3.17908i	0.305649	−	0.440860i
$53$	−6.34354	+	7.72962i	−0.871352	+	1.06175i	0.126213	+	0.992003i	$0.459718\pi$
$53$	−6.34354	+	7.72962i	−0.871352	+	1.06175i	−0.997565	+	0.0697420i	$0.977782\pi$
$54$	−0.835704	−	1.80692i	−0.113725	−	0.245890i
$55$	0.0305249	−	0.153459i	0.00411598	−	0.0206924i
$56$	−9.34228	−	8.91616i	−1.24842	−	1.19147i
$57$	1.19235	−	0.237173i	0.157931	−	0.0314144i
$58$	−1.45672	+	9.27134i	−0.191277	+	1.21739i
$59$	3.38666	−	1.81021i	0.440905	−	0.235669i	−0.235979	−	0.971758i	$-0.575830\pi$
$59$	3.38666	−	1.81021i	0.440905	−	0.235669i	0.676884	+	0.736089i	$0.263330\pi$
$60$	−0.455566	+	0.129697i	−0.0588133	+	0.0167438i
$61$	0.226347	−	2.29814i	0.0289808	−	0.294247i	−0.969759	−	0.244064i	$-0.921519\pi$
$61$	0.226347	−	2.29814i	0.0289808	−	0.294247i	0.998740	−	0.0501833i	$-0.0159805\pi$
$62$	11.9284	+	0.688693i	1.51490	+	0.0874641i
$63$		−	13.4415i		−	1.69346i
$64$	2.71333	−	7.52581i	0.339166	−	0.940726i
$65$		−	1.93420i		−	0.239908i
$66$	0.00302065	−	0.0523185i	0.000371816	−	0.00643997i
$67$	−0.984184	+	9.99259i	−0.120237	+	1.22079i	0.725891	+	0.687810i	$0.241428\pi$
$67$	−0.984184	+	9.99259i	−0.120237	+	1.22079i	−0.846128	+	0.532979i	$0.821072\pi$
$68$	10.3843	+	5.78188i	1.25928	+	0.701156i
$69$	−1.84719	+	0.987342i	−0.222375	+	0.118862i
$70$	−6.37883	−	1.00225i	−0.762416	−	0.119791i
$71$	0.0978609	−	0.0194657i	0.0116139	−	0.00231016i	−0.189280	−	0.981923i	$-0.560615\pi$
$71$	0.0978609	−	0.0194657i	0.0116139	−	0.00231016i	0.200894	+	0.979613i	$0.435615\pi$
$72$	7.61636	−	3.36509i	0.897597	−	0.396579i
$73$	1.74303	−	8.76279i	0.204006	−	1.02561i	−0.734043	−	0.679103i	$-0.762369\pi$
$73$	1.74303	−	8.76279i	0.204006	−	1.02561i	0.938049	−	0.346504i	$-0.112631\pi$
$74$	−9.37810	+	4.33739i	−1.09018	+	0.504212i
$75$	−0.150246	+	0.183075i	−0.0173489	+	0.0211397i
$76$	1.82971	+	10.1020i	0.209882	+	1.15878i
$77$	0.336765	−	0.630043i	0.0383780	−	0.0718001i
$78$	−0.0895518	−	0.641609i	−0.0101397	−	0.0726480i
$79$	7.06558	−	2.92666i	0.794940	−	0.329275i	0.0520119	−	0.998646i	$-0.483437\pi$
$79$	7.06558	−	2.92666i	0.794940	−	0.329275i	0.742928	+	0.669372i	$0.233437\pi$
$80$	−1.02904	−	3.86537i	−0.115051	−	0.432161i
$81$	7.85144	+	3.25217i	0.872382	+	0.361352i
$82$	−2.69369	+	10.3751i	−0.297469	+	1.14574i
$83$	−2.39592	−	7.89829i	−0.262986	−	0.866950i	−0.984625	−	0.174680i	$-0.944111\pi$
$83$	−2.39592	−	7.89829i	−0.262986	−	0.866950i	0.721639	−	0.692270i	$-0.243389\pi$
$84$	−2.16238	−	0.0371289i	−0.235935	−	0.00405109i
$85$	5.91410	−	0.582488i	0.641474	−	0.0631797i
$86$	10.5597	+	9.73712i	1.13868	+	1.04998i
$87$	0.873186	+	1.30681i	0.0936153	+	0.140105i
$88$	0.441313	+	0.0330898i	0.0470441	+	0.00352739i
$89$	−6.22160	−	4.15714i	−0.659488	−	0.440656i	0.180269	−	0.983617i	$-0.442303\pi$
$89$	−6.22160	−	4.15714i	−0.659488	−	0.440656i	−0.839758	+	0.542961i	$0.817303\pi$
$90$	2.17095	−	3.55249i	0.228838	−	0.374465i
$91$	2.56358	−	8.45099i	0.268736	−	0.885905i
$92$	−8.06880	−	15.7398i	−0.841231	−	1.64099i
$93$	1.54674	−	1.26938i	0.160390	−	0.131629i
$94$	2.61320	+	7.50593i	0.269531	+	0.774177i
$95$	3.62970	+	3.62970i	0.372400	+	0.372400i
$96$	−0.520317	−	1.23457i	−0.0531046	−	0.126003i
$97$	1.97383	−	1.97383i	0.200412	−	0.200412i	−0.599765	−	0.800176i	$-0.704739\pi$
$97$	1.97383	−	1.97383i	0.200412	−	0.200412i	0.800176	+	0.599765i	$0.204739\pi$
$98$	−17.6300	−	8.52431i	−1.78090	−	0.861085i
$99$	0.292215	+	0.356064i	0.0293687	+	0.0357858i
$100$	−1.52401	−	1.29514i	−0.152401	−	0.129514i
$101$	−5.30745	−	1.61000i	−0.528111	−	0.160201i	0.0149590	−	0.999888i	$-0.495238\pi$
$101$	−5.30745	−	1.61000i	−0.528111	−	0.160201i	−0.543070	+	0.839687i	$0.682738\pi$
$102$	1.93485	−	0.467040i	0.191578	−	0.0462439i
$103$	6.95571	−	10.4100i	0.685366	−	1.02572i	−0.311775	−	0.950156i	$-0.600923\pi$
$103$	6.95571	−	10.4100i	0.685366	−	1.02572i	0.997141	−	0.0755669i	$-0.0240766\pi$
$104$	5.43040	−	0.663110i	0.532495	−	0.0650233i
$105$	−0.899110	+	0.600766i	−0.0877441	+	0.0586287i
$106$	−14.1297	+	0.572607i	−1.37239	+	0.0556165i
$107$	0.135460	+	1.37535i	0.0130954	+	0.132960i	0.999509	−	0.0313182i	$-0.00997051\pi$
$107$	0.135460	+	1.37535i	0.0130954	+	0.132960i	−0.986414	+	0.164278i	$0.947471\pi$
$108$	1.12192	−	2.58225i	0.107957	−	0.248477i
$109$	3.57572	−	1.08468i	0.342492	−	0.103894i	−0.114353	−	0.993440i	$-0.536479\pi$
$109$	3.57572	−	1.08468i	0.342492	−	0.103894i	0.456845	+	0.889546i	$0.348979\pi$
$110$	0.190764	−	0.112125i	0.0181886	−	0.0106907i
$111$	−0.662181	+	1.59865i	−0.0628514	+	0.151737i
$112$	0.626994	−	18.2526i	0.0592454	−	1.72471i
$113$	3.80887	+	9.19542i	0.358308	+	0.865033i	0.995538	+	0.0943590i	$0.0300802\pi$
$113$	3.80887	+	9.19542i	0.358308	+	0.865033i	−0.637230	+	0.770674i	$0.719920\pi$
$114$	1.37209	+	1.03599i	0.128508	+	0.0970291i
$115$	−7.79949	−	4.16892i	−0.727306	−	0.388753i
$116$	−11.1607	+	7.18327i	−1.03624	+	0.666950i
$117$	4.40160	+	3.61230i	0.406928	+	0.333957i
$118$	5.09736	+	1.87338i	0.469250	+	0.172458i
$119$	26.6122	+	5.29349i	2.43954	+	0.485254i
$120$	−0.565507	−	0.359062i	−0.0516235	−	0.0327777i
$121$	−2.14122	−	10.7646i	−0.194656	−	0.978602i
$122$	2.63971	−	1.92284i	0.238988	−	0.174086i
$123$	0.846203	+	1.58314i	0.0762996	+	0.142746i
$124$	10.4937	+	13.2439i	0.942366	+	1.18934i
$125$	−0.995185	−	0.0980171i	−0.0890120	−	0.00876692i
$126$	14.1939	−	12.6443i	1.26449	−	1.12645i
$127$	11.0035			0.976406			0.488203	−	0.872730i	$-0.337652\pi$
$127$	11.0035			0.976406			0.488203	+	0.872730i	$0.337652\pi$
$128$	10.4995	−	4.21430i	0.928034	−	0.372495i
$129$	2.40546			0.211789
$130$	2.04247	−	1.81950i	0.179136	−	0.159580i
$131$	−3.61227	−	0.355777i	−0.315605	−	0.0310844i	−0.0610257	−	0.998136i	$-0.519437\pi$
$131$	−3.61227	−	0.355777i	−0.315605	−	0.0310844i	−0.254580	+	0.967052i	$0.581937\pi$
$132$	0.0580887	−	0.0460262i	0.00505597	−	0.00400606i
$133$	11.0483	+	20.6699i	0.958007	+	1.79230i
$134$	−11.4778	+	8.36073i	−0.991528	+	0.722257i
$135$	−0.274633	−	1.38067i	−0.0236366	−	0.118829i
$136$	3.66293	+	16.4046i	0.314094	+	1.40668i
$137$	−0.0299243	−	0.00595231i	−0.00255661	−	0.000508540i	0.193812	−	0.981039i	$-0.437915\pi$
$137$	−0.0299243	−	0.00595231i	−0.00255661	−	0.000508540i	−0.196368	+	0.980530i	$0.562915\pi$
$138$	−2.78025	−	1.02180i	−0.236671	−	0.0869811i
$139$	−4.57846	−	3.75745i	−0.388340	−	0.318702i	0.419884	−	0.907578i	$-0.362071\pi$
$139$	−4.57846	−	3.75745i	−0.388340	−	0.318702i	−0.808224	+	0.588875i	$0.799571\pi$
$140$	−4.94221	−	7.67871i	−0.417693	−	0.648970i
$141$	1.17383	+	0.627428i	0.0988547	+	0.0528389i
$142$	0.112613	+	0.0850275i	0.00945026	+	0.00713535i
$143$	0.115814	+	0.279599i	0.00968482	+	0.0233812i
$144$	10.7182	+	4.87718i	0.893179	+	0.406431i
$145$	−2.53959	+	6.13110i	−0.210901	+	0.509160i
$146$	10.8930	−	6.40254i	0.901508	−	0.529878i
$147$	−3.13823	+	0.951973i	−0.258837	+	0.0785174i
$148$	−13.4021	−	5.82288i	−1.10165	−	0.478638i
$149$	−2.06529	−	20.9693i	−0.169195	−	1.71787i	−0.587214	−	0.809432i	$-0.699775\pi$
$149$	−2.06529	−	20.9693i	−0.169195	−	1.71787i	0.418018	−	0.908439i	$-0.362725\pi$
$150$	−0.334659	+	0.0135621i	−0.0273248	+	0.00110734i
$151$	−5.95417	+	3.97845i	−0.484544	+	0.323762i	−0.773735	−	0.633510i	$-0.781614\pi$
$151$	−5.95417	+	3.97845i	−0.484544	+	0.323762i	0.289191	+	0.957271i	$0.406614\pi$
$152$	−8.94626	+	11.4350i	−0.725638	+	0.927504i
$153$	−9.71960	+	14.5464i	−0.785783	+	1.17601i
$154$	0.982106	−	0.237064i	0.0791403	−	0.0191032i
$155$	8.08488	+	2.45252i	0.649393	+	0.196991i
$156$	0.593284	−	0.698125i	0.0475007	−	0.0558948i
$157$	12.3263	+	15.0197i	0.983750	+	1.19870i	0.980058	+	0.198709i	$0.0636749\pi$
$157$	12.3263	+	15.0197i	0.983750	+	1.19870i	0.00369115	+	0.999993i	$0.498825\pi$
$158$	9.73706	+	4.70799i	0.774639	+	0.374547i
$159$	−1.67457	+	1.67457i	−0.132802	+	0.132802i
$160$	3.11372	−	4.72279i	0.246161	−	0.373369i
$161$	−28.5525	−	28.5525i	−2.25025	−	2.25025i
$162$	3.95161	+	11.3502i	0.310468	+	0.891760i
$163$	−10.0977	+	8.28696i	−0.790912	+	0.649085i	−0.940550	−	0.339656i	$-0.889689\pi$
$163$	−10.0977	+	8.28696i	−0.790912	+	0.649085i	0.149637	+	0.988741i	$0.452189\pi$
$164$	−13.4899	+	6.91538i	−1.05338	+	0.540001i
$165$	0.0107569	−	0.0354608i	0.000837424	−	0.00276062i
$166$	6.08658	−	9.95994i	0.472410	−	0.773041i
$167$	9.55342	+	6.38339i	0.739266	+	0.493962i	0.867286	−	0.497810i	$-0.165862\pi$
$167$	9.55342	+	6.38339i	0.739266	+	0.493962i	−0.128020	+	0.991772i	$0.540862\pi$
$168$	−1.99494	−	2.31835i	−0.153913	−	0.178865i
$169$	−5.14396	−	7.69848i	−0.395689	−	0.592190i
$170$	6.17847	+	5.69721i	0.473867	+	0.436956i
$171$	−15.0388	+	1.48120i	−1.15005	+	0.113270i
$172$	−0.348738	+	20.3104i	−0.0265910	+	1.54866i
$173$	−5.15724	−	17.0011i	−0.392098	−	1.29257i	−0.901775	−	0.432207i	$-0.857735\pi$
$173$	−5.15724	−	17.0011i	−0.392098	−	1.29257i	0.509677	−	0.860366i	$-0.329765\pi$
$174$	−0.558563	+	2.15138i	−0.0423445	+	0.163096i
$175$	−4.21830	−	1.74728i	−0.318873	−	0.132082i
$176$	0.380200	+	0.497144i	0.0286586	+	0.0374736i
$177$	0.840236	−	0.348037i	0.0631560	−	0.0261601i
$178$	−1.46280	−	10.4805i	−0.109641	−	0.785545i
$179$	2.05793	−	3.85012i	0.153817	−	0.287772i	−0.793196	−	0.608966i	$-0.791584\pi$
$179$	2.05793	−	3.85012i	0.153817	−	0.287772i	0.947013	+	0.321195i	$0.104084\pi$
$180$	5.79356	−	1.04935i	0.431826	−	0.0782138i
$181$	−12.3143	+	15.0050i	−0.915312	+	1.11531i	0.0776621	+	0.996980i	$0.475254\pi$
$181$	−12.3143	+	15.0050i	−0.915312	+	1.11531i	−0.992974	+	0.118331i	$0.962246\pi$
$182$	11.3356	−	5.24275i	0.840251	−	0.388618i
$183$	0.106697	−	0.536403i	0.00788728	−	0.0396521i
$184$	9.03060	−	23.3269i	0.665744	−	1.71968i
$185$	−7.16583	+	1.42537i	−0.526842	+	0.104795i
$186$	2.79545	+	0.439224i	0.204973	+	0.0322054i
$187$	−0.820037	+	0.438319i	−0.0599670	+	0.0320531i
$188$	−5.46785	+	9.82029i	−0.398784	+	0.716218i
$189$	0.630000	−	6.39650i	0.0458257	−	0.465277i
$190$	−0.418430	+	7.24733i	−0.0303561	+	0.525777i
$191$		−	11.4635i		−	0.829467i	−0.909943	−	0.414733i	$-0.863875\pi$
$191$		−	11.4635i		−	0.829467i	0.909943	−	0.414733i	$-0.136125\pi$
$192$	0.814217	−	1.71080i	0.0587611	−	0.123466i
$193$		−	14.5791i		−	1.04943i	−0.851279	−	0.524714i	$-0.824172\pi$
$193$		−	14.5791i		−	1.04943i	0.851279	−	0.524714i	$-0.175828\pi$
$194$	3.94109	+	0.227542i	0.282954	+	0.0163366i
$195$	0.0449001	−	0.455878i	0.00321536	−	0.0326461i
$196$	−7.58299	−	26.6356i	−0.541642	−	1.90255i
$197$	−9.63618	+	5.15065i	−0.686550	+	0.366968i	−0.777496	−	0.628887i	$-0.783511\pi$
$197$	−9.63618	+	5.15065i	−0.686550	+	0.366968i	0.0909469	+	0.995856i	$0.471011\pi$
$198$	−0.101110	+	0.643521i	−0.00718560	+	0.0457330i
$199$	13.5825	−	2.70173i	0.962839	−	0.191521i	0.311448	−	0.950263i	$-0.399186\pi$
$199$	13.5825	−	2.70173i	0.962839	−	0.191521i	0.651391	+	0.758743i	$0.274186\pi$
$200$	−0.0659936	−	2.82766i	−0.00466645	−	0.199946i
$201$	−0.463932	+	2.33234i	−0.0327232	+	0.164511i
$202$	−3.29259	−	7.11907i	−0.231666	−	0.500896i
$203$	−19.2222	+	23.4223i	−1.34914	+	1.64393i
$204$	2.31329	+	1.60381i	0.161963	+	0.112289i
$205$	−3.57298	+	6.68457i	−0.249548	+	0.466871i
$206$	17.5359	−	2.44755i	1.22178	−	0.170529i
$207$	24.0534	−	9.96324i	1.67183	−	0.692493i
$208$	5.80860	+	5.11059i	0.402754	+	0.354356i
$209$	−0.742028	−	0.307358i	−0.0513271	−	0.0212604i
$210$	−1.48019	−	0.384300i	−0.102142	−	0.0265192i
$211$	6.89746	+	22.7379i	0.474841	+	1.56534i	0.788022	+	0.615646i	$0.211105\pi$
$211$	6.89746	+	22.7379i	0.474841	+	1.56534i	−0.313182	+	0.949693i	$0.601395\pi$
$212$	−13.8964	−	14.3819i	−0.954408	−	0.987756i
$213$	0.0235171	−	0.00231623i	0.00161136	−	0.000158705i
$214$	−1.32491	+	1.43683i	−0.0905691	+	0.0982198i
$215$	5.64277	+	8.44500i	0.384834	+	0.575944i
$216$	3.78218	−	1.24439i	0.257345	−	0.0846703i
$217$	32.0743	+	21.4313i	2.17734	+	1.45485i
$218$	4.50907	+	2.75552i	0.305393	+	0.186627i
$219$	0.614238	−	2.02487i	0.0415064	−	0.136828i
$220$	0.297853	+	0.0959667i	0.0200812	+	0.00647008i
$221$	−8.88528	+	7.29196i	−0.597689	+	0.490510i
$222$	−2.31105	+	0.804595i	−0.155107	+	0.0540009i
$223$	−1.53883	−	1.53883i	−0.103048	−	0.103048i	0.653703	−	0.756751i	$-0.273214\pi$
$223$	−1.53883	−	1.53883i	−0.103048	−	0.103048i	−0.756751	+	0.653703i	$0.773214\pi$
$224$	19.8642	−	16.5081i	1.32723	−	1.10300i
$225$	2.08166	−	2.08166i	0.138777	−	0.138777i
$226$	−6.12716	+	12.6722i	−0.407573	+	0.842942i
$227$	−1.31907	−	1.60729i	−0.0875495	−	0.106679i	0.727393	−	0.686221i	$-0.240732\pi$
$227$	−1.31907	−	1.60729i	−0.0875495	−	0.106679i	−0.814943	+	0.579542i	$0.803232\pi$
$228$	0.196745	+	2.42345i	0.0130297	+	0.160497i
$229$	8.17658	+	2.48034i	0.540324	+	0.163905i	0.548638	−	0.836060i	$-0.315147\pi$
$229$	8.17658	+	2.48034i	0.540324	+	0.163905i	−0.00831421	+	0.999965i	$0.502647\pi$
$230$	−2.93468	−	12.1578i	−0.193507	−	0.801660i
$231$	0.0939992	−	0.140680i	0.00618469	−	0.00925604i
$232$	−18.0842	−	5.02812i	−1.18728	−	0.330112i
$233$	0.794054	−	0.530570i	0.0520202	−	0.0347588i	−0.529288	−	0.848442i	$-0.677541\pi$
$233$	0.794054	−	0.530570i	0.0520202	−	0.0347588i	0.581308	+	0.813683i	$0.302541\pi$
$234$	0.326069	+	8.04608i	0.0213158	+	0.525988i
$235$	0.550852	+	5.59289i	0.0359336	+	0.364840i
$236$	2.81683	+	7.14498i	0.183360	+	0.465098i
$237$	1.73325	−	0.525776i	0.112587	−	0.0341528i
$238$	19.4442	+	33.0814i	1.26038	+	2.14435i
$239$	6.13229	−	14.8047i	0.396665	−	0.957633i	−0.591787	−	0.806095i	$-0.701577\pi$
$239$	6.13229	−	14.8047i	0.396665	−	0.957633i	0.988451	−	0.151539i	$-0.0484228\pi$
$240$	−0.152810	−	0.934931i	−0.00986381	−	0.0603495i
$241$	1.15435	+	2.78686i	0.0743584	+	0.179517i	0.956688	−	0.291115i	$-0.0940261\pi$
$241$	1.15435	+	2.78686i	0.0743584	+	0.179517i	−0.882330	+	0.470632i	$0.844026\pi$
$242$	9.35296	−	12.3873i	0.601231	−	0.796288i
$243$	5.49954	+	2.93956i	0.352795	+	0.188573i
$244$	4.51364	+	0.978663i	0.288956	+	0.0626525i
$245$	−10.7039	−	8.78445i	−0.683846	−	0.561218i
$246$	−0.875733	+	2.38282i	−0.0558347	+	0.151923i
$247$	−9.73780	−	1.93697i	−0.619601	−	0.123246i
$248$	−4.11385	+	23.5397i	−0.261230	+	1.49477i
$249$	−0.381354	−	1.91720i	−0.0241673	−	0.121497i
$250$	−0.832664	−	1.14310i	−0.0526623	−	0.0722958i
$251$	−8.51749	−	15.9351i	−0.537619	−	1.00582i	−0.993288	−	0.115666i	$-0.963100\pi$
$251$	−8.51749	−	15.9351i	−0.537619	−	1.00582i	0.455669	−	0.890149i	$-0.349400\pi$
$252$	26.7043	+	3.09390i	1.68221	+	0.194897i
$253$	1.37708	+	0.135630i	0.0865762	+	0.00852702i
$254$	10.3510	+	11.6195i	0.649480	+	0.729072i
$255$	1.40744			0.0881372
$256$	14.3271	+	7.12286i	0.895442	+	0.445179i
$257$	−17.0990			−1.06661			−0.533303	−	0.845925i	$-0.679049\pi$
$257$	−17.0990			−1.06661			−0.533303	+	0.845925i	$0.679049\pi$
$258$	2.26281	+	2.54011i	0.140876	+	0.158140i
$259$	−33.1985	−	3.26977i	−2.06285	−	0.203173i
$260$	3.84269	+	0.445205i	0.238314	+	0.0276105i
$261$	−9.20946	−	17.2297i	−0.570051	−	1.06649i
$262$	−3.02236	−	4.14915i	−0.186722	−	0.256336i
$263$	−4.82556	−	24.2597i	−0.297557	−	1.49592i	−0.783204	−	0.621764i	$-0.786416\pi$
$263$	−4.82556	−	24.2597i	−0.297557	−	1.49592i	0.485648	−	0.874155i	$-0.338584\pi$
$264$	0.103246	+	0.0180436i	0.00635438	+	0.00111051i
$265$	−9.80724	−	1.95078i	−0.602454	−	0.119836i
$266$	−11.4338	+	31.1108i	−0.701053	+	1.90753i
$267$	−1.36989	−	1.12424i	−0.0838359	−	0.0688023i
$268$	−19.6258	−	4.25534i	−1.19884	−	0.259936i
$269$	−15.3149	−	8.18600i	−0.933768	−	0.499109i	−0.0669621	−	0.997756i	$-0.521331\pi$
$269$	−15.3149	−	8.18600i	−0.933768	−	0.499109i	−0.866806	+	0.498646i	$0.833831\pi$
$270$	1.19961	−	1.58880i	0.0730060	−	0.0966913i
$271$	−9.63489	−	23.2607i	−0.585278	−	1.41299i	−0.887972	−	0.459898i	$-0.847886\pi$
$271$	−9.63489	−	23.2607i	−0.585278	−	1.41299i	0.302694	−	0.953088i	$-0.402114\pi$
$272$	−13.8771	+	19.2997i	−0.841425	+	1.17022i
$273$	0.800400	−	1.93234i	0.0484424	−	0.116950i
$274$	−0.0218642	−	0.0371987i	−0.00132087	−	0.00224726i
$275$	0.149728	−	0.0454196i	0.00902895	−	0.00273890i
$276$	−1.53638	−	3.89709i	−0.0924795	−	0.234577i
$277$	0.348663	+	3.54003i	0.0209491	+	0.212700i	0.999960	+	0.00889415i	$0.00283113\pi$
$277$	0.348663	+	3.54003i	0.0209491	+	0.212700i	−0.979011	+	0.203806i	$0.934669\pi$
$278$	−0.339171	−	8.36937i	−0.0203421	−	0.501962i
$279$	−20.6804	+	13.8182i	−1.23810	+	0.827275i
$280$	3.45943	−	12.4422i	0.206740	−	0.743564i
$281$	5.22850	−	7.82500i	0.311906	−	0.466800i	−0.642086	−	0.766633i	$-0.721931\pi$
$281$	5.22850	−	7.82500i	0.311906	−	0.466800i	0.953992	+	0.299832i	$0.0969307\pi$
$282$	0.441674	+	1.82976i	0.0263013	+	0.108961i
$283$	25.9593	+	7.87468i	1.54312	+	0.468101i	0.943275	−	0.332014i	$-0.107728\pi$
$283$	25.9593	+	7.87468i	1.54312	+	0.468101i	0.599847	+	0.800115i	$0.295228\pi$
$284$	0.0161476	+	0.198902i	0.000958183	+	0.0118026i
$285$	0.771239	+	0.939757i	0.0456842	+	0.0556664i
$286$	−0.186304	+	0.385314i	−0.0110164	+	0.0227841i
$287$	−24.4709	+	24.4709i	−1.44447	+	1.44447i
$288$	4.93235	+	15.9061i	0.290642	+	0.937274i
$289$	−12.9513	−	12.9513i	−0.761839	−	0.761839i
$290$	−8.86329	+	3.08577i	−0.520470	+	0.181203i
$291$	0.511039	−	0.419399i	0.0299576	−	0.0245856i
$292$	17.0079	+	5.47987i	0.995314	+	0.320685i
$293$	1.43851	−	4.74213i	0.0840386	−	0.277038i	−0.904842	−	0.425746i	$-0.860012\pi$
$293$	1.43851	−	4.74213i	0.0840386	−	0.277038i	0.988881	+	0.148708i	$0.0475115\pi$
$294$	−3.95739	−	2.41838i	−0.230800	−	0.141043i
$295$	3.19292	+	2.13344i	0.185899	+	0.124214i
$296$	−6.45853	−	19.6299i	−0.375395	−	1.14097i
$297$	0.122370	+	0.183139i	0.00710062	+	0.0106268i
$298$	20.2003	−	21.9067i	1.17017	−	1.26902i
$299$	17.0232	−	1.67664i	0.984477	−	0.0969625i
$300$	−0.329135	−	0.340635i	−0.0190026	−	0.0196666i
$301$	13.4617	+	44.3772i	0.775919	+	2.55786i
$302$	−9.80223	−	2.54495i	−0.564055	−	0.146446i
$303$	−1.21356	−	0.502672i	−0.0697171	−	0.0288778i
$304$	−20.4909	+	1.30986i	−1.17523	+	0.0751259i
$305$	2.13348	−	0.883716i	0.122163	−	0.0506014i
$306$	−24.5039	+	3.42010i	−1.40079	+	0.195514i
$307$	12.2030	−	22.8303i	0.696465	−	1.30299i	−0.246189	−	0.969222i	$-0.579178\pi$
$307$	12.2030	−	22.8303i	0.696465	−	1.30299i	0.942654	−	0.333772i	$-0.108322\pi$
$308$	1.17420	+	0.814076i	0.0669062	+	0.0463863i
$309$	1.88107	−	2.29209i	0.107010	−	0.130393i
$310$	5.01562	+	10.8445i	0.284868	+	0.615928i
$311$	2.38652	−	11.9979i	0.135327	−	0.680337i	−0.852241	−	0.523149i	$-0.824757\pi$
$311$	2.38652	−	11.9979i	0.135327	−	0.680337i	0.987569	−	0.157188i	$-0.0502428\pi$
$312$	1.29531	−	0.0302306i	0.0733322	−	0.00171147i
$313$	3.05847	−	0.608367i	0.172875	−	0.0343870i	−0.107894	−	0.994162i	$-0.534411\pi$
$313$	3.05847	−	0.608367i	0.172875	−	0.0343870i	0.280769	+	0.959775i	$0.409411\pi$
$314$	−4.26509	+	27.1453i	−0.240693	+	1.53190i
$315$	11.8543	−	6.33626i	0.667915	−	0.357008i
$316$	4.18810	+	14.7109i	0.235599	+	0.827553i
$317$	−2.81111	+	28.5417i	−0.157888	+	1.60306i	0.510921	+	0.859628i	$0.329304\pi$
$317$	−2.81111	+	28.5417i	−0.157888	+	1.60306i	−0.668809	+	0.743434i	$0.733196\pi$
$318$	−3.34356	−	0.193043i	−0.187498	−	0.0108253i
$319$		−	1.03835i		−	0.0581362i
$320$	7.91623	−	1.15470i	0.442531	−	0.0645497i
$321$			0.327306i			0.0182684i
$322$	3.29151	−	57.0100i	0.183429	−	3.17704i
$323$	2.99001	−	30.3581i	0.166369	−	1.68917i
$324$	−8.26833	+	14.8500i	−0.459352	+	0.824998i
$325$	1.70581	−	0.911775i	0.0946213	−	0.0505762i
$326$	−18.2497	−	2.86741i	−1.01076	−	0.158811i
$327$	0.867955	−	0.172647i	0.0479980	−	0.00954740i
$328$	−19.9924	−	7.73969i	−1.10389	−	0.427353i
$329$	−5.00599	+	25.1668i	−0.275989	+	1.38749i
$330$	0.0475647	−	0.0219988i	0.00261835	−	0.00121099i
$331$	−3.91973	+	4.77620i	−0.215448	+	0.262524i	−0.869508	−	0.493918i	$-0.835564\pi$
$331$	−3.91973	+	4.77620i	−0.215448	+	0.262524i	0.654061	+	0.756442i	$0.273064\pi$
$332$	16.2431	−	2.94201i	0.891456	−	0.161464i
$333$	10.1392	−	18.9691i	0.555625	−	1.03950i
$334$	2.24617	+	16.0930i	0.122905	+	0.880572i
$335$	−9.27662	+	3.84250i	−0.506836	+	0.209938i
$336$	0.571492	−	4.28748i	0.0311774	−	0.233901i
$337$	−29.6274	−	12.2721i	−1.61391	−	0.668503i	−0.620614	−	0.784116i	$-0.713117\pi$
$337$	−29.6274	−	12.2721i	−1.61391	−	0.668503i	−0.993294	+	0.115613i	$0.963117\pi$
$338$	3.29051	−	12.6738i	0.178980	−	0.689366i
$339$	0.684266	+	2.25572i	0.0371642	+	0.122514i
$340$	−0.204047	+	11.8837i	−0.0110660	+	0.644483i
$341$	−1.31556	+	0.129571i	−0.0712416	+	0.00701669i
$342$	−15.7111	−	14.4873i	−0.849559	−	0.783384i
$343$	−17.3685	−	25.9938i	−0.937810	−	1.40353i
$344$	−21.7754	+	18.7377i	−1.17405	+	1.01027i
$345$	−1.74152	−	1.16364i	−0.0937600	−	0.0626484i
$346$	13.1014	−	21.4389i	0.704336	−	1.15256i
$347$	−7.84918	+	25.8753i	−0.421366	+	1.38906i	0.447621	+	0.894223i	$0.352271\pi$
$347$	−7.84918	+	25.8753i	−0.421366	+	1.38906i	−0.868987	+	0.494835i	$0.835229\pi$
$348$	−2.79725	+	1.43397i	−0.149948	+	0.0768689i
$349$	4.57438	−	3.75410i	0.244861	−	0.200952i	−0.503955	−	0.863730i	$-0.668122\pi$
$349$	4.57438	−	3.75410i	0.244861	−	0.200952i	0.748817	+	0.662777i	$0.230622\pi$
$350$	−2.12306	−	6.09808i	−0.113482	−	0.325956i
$351$	1.92532	+	1.92532i	0.102766	+	0.102766i
$352$	−0.167319	+	0.869144i	−0.00891815	+	0.0463255i
$353$	−5.32610	+	5.32610i	−0.283480	+	0.283480i	−0.834495	−	0.551015i	$-0.814241\pi$
$353$	−5.32610	+	5.32610i	−0.283480	+	0.283480i	0.551015	+	0.834495i	$0.314241\pi$
$354$	1.15793	+	0.559872i	0.0615431	+	0.0297569i
$355$	0.0632985	+	0.0771295i	0.00335954	+	0.00409361i
$356$	9.69110	−	11.4036i	0.513627	−	0.604392i
$357$	6.14945	+	1.86541i	0.325463	+	0.0987282i
$358$	6.00153	−	1.44867i	0.317191	−	0.0765646i
$359$	−7.39788	+	11.0717i	−0.390445	+	0.584343i	−0.973668	−	0.227969i	$-0.926791\pi$
$359$	−7.39788	+	11.0717i	−0.390445	+	0.584343i	0.583223	+	0.812312i	$0.301791\pi$
$360$	6.55807	+	5.13074i	0.345641	+	0.270414i
$361$	6.11086	−	4.08315i	0.321624	−	0.214902i
$362$	−27.4289	+	1.11156i	−1.44163	+	0.0584224i
$363$	−0.254784	−	2.58686i	−0.0133727	−	0.135775i
$364$	16.1996	+	7.03831i	0.849090	+	0.368907i
$365$	8.54975	−	2.59354i	0.447514	−	0.135752i
$366$	0.666799	−	0.391923i	0.0348542	−	0.0204862i
$367$	−3.23447	+	7.80871i	−0.168838	+	0.407611i	−0.985539	−	0.169450i	$-0.945801\pi$
$367$	−3.23447	+	7.80871i	−0.168838	+	0.407611i	0.816701	+	0.577062i	$0.195801\pi$
$368$	33.1277	−	12.4074i	1.72690	−	0.646783i
$369$	−8.53902	−	20.6150i	−0.444524	−	1.07317i
$370$	−8.24604	−	6.22611i	−0.428691	−	0.323680i
$371$	−40.2647	−	21.5219i	−2.09044	−	1.11736i
$372$	2.16587	+	3.36511i	0.112295	+	0.174473i
$373$	19.4298	+	15.9457i	1.00604	+	0.825634i	0.984721	−	0.174138i	$-0.0557140\pi$
$373$	19.4298	+	15.9457i	1.00604	+	0.825634i	0.0213173	+	0.999773i	$0.493214\pi$
$374$	−1.23426	−	0.453615i	−0.0638221	−	0.0234559i
$375$	−0.232283	−	0.0462041i	−0.0119951	−	0.00238597i
$376$	−15.5136	+	3.46399i	−0.800053	+	0.178642i
$377$	−2.50415	−	12.5892i	−0.128970	−	0.648377i
$378$	7.34719	−	5.35190i	0.377899	−	0.275272i
$379$	−2.31452	−	4.33016i	−0.118889	−	0.222425i	0.815437	−	0.578846i	$-0.196497\pi$
$379$	−2.31452	−	4.33016i	−0.118889	−	0.222425i	−0.934325	+	0.356421i	$0.883997\pi$
$380$	−8.04664	+	6.37570i	−0.412784	+	0.327066i
$381$	2.59347	+	0.255434i	0.132867	+	0.0130863i
$382$	12.1051	−	10.7836i	0.619353	−	0.551739i
$383$	−19.1272			−0.977354			−0.488677	−	0.872465i	$-0.662520\pi$
$383$	−19.1272			−0.977354			−0.488677	+	0.872465i	$0.662520\pi$
$384$	2.57250	−	0.749551i	0.131277	−	0.0382503i
$385$	0.714399			0.0364091
$386$	15.3952	−	13.7145i	0.783596	−	0.698052i
$387$	−29.7565	−	2.93076i	−1.51261	−	0.148979i
$388$	3.46710	+	4.37575i	0.176015	+	0.222145i
$389$	−2.59736	−	4.85931i	−0.131691	−	0.246377i	0.807430	−	0.589964i	$-0.200858\pi$
$389$	−2.59736	−	4.85931i	−0.131691	−	0.246377i	−0.939121	+	0.343587i	$0.888358\pi$
$390$	0.523635	−	0.381430i	0.0265153	−	0.0193145i
$391$	10.2531	+	51.5460i	0.518524	+	2.60680i
$392$	20.9933	−	33.0635i	1.06032	−	1.66996i
$393$	−0.843130	−	0.167709i	−0.0425303	−	0.00845980i
$394$	−14.5037	−	5.33039i	−0.730686	−	0.268541i
$395$	5.91177	+	4.85167i	0.297454	+	0.244114i
$396$	−0.774658	+	0.498588i	−0.0389280	+	0.0250550i
$397$	−3.03800	−	1.62385i	−0.152473	−	0.0814985i	0.393396	−	0.919369i	$-0.371300\pi$
$397$	−3.03800	−	1.62385i	−0.152473	−	0.0814985i	−0.545869	+	0.837871i	$0.683800\pi$
$398$	15.6300	+	11.8013i	0.783461	+	0.591546i
$399$	2.12418	+	5.12823i	0.106342	+	0.256733i
$400$	2.92386	−	2.72966i	0.146193	−	0.136483i
$401$	−5.77470	+	13.9414i	−0.288375	+	0.696198i	−0.999980	−	0.00638189i	$-0.997969\pi$
$401$	−5.77470	+	13.9414i	−0.288375	+	0.696198i	0.711605	+	0.702580i	$0.247969\pi$
$402$	−2.89932	+	1.70413i	−0.144605	+	0.0849942i
$403$	−15.6378	+	4.74366i	−0.778972	+	0.236299i
$404$	4.42025	−	10.1738i	0.219915	−	0.506165i
$405$	0.832982	+	8.45741i	0.0413912	+	0.420252i
$406$	−42.8158	+	1.73512i	−2.12491	+	0.0861125i
$407$	0.950512	−	0.635112i	0.0471152	−	0.0314813i
$408$	0.482518	+	3.95148i	0.0238882	+	0.195628i
$409$	11.1582	−	16.6994i	0.551737	−	0.825732i	−0.445854	−	0.895106i	$-0.647100\pi$
$409$	11.1582	−	16.6994i	0.551737	−	0.825732i	0.997591	+	0.0693734i	$0.0221000\pi$
$410$	−10.4198	+	2.51518i	−0.514600	+	0.124216i
$411$	−0.00691479	−	0.00209758i	−0.000341082	−	0.000103466i
$412$	19.0805	+	16.2151i	0.940030	+	0.798860i
$413$	11.1230	+	13.5534i	0.547327	+	0.666920i
$414$	33.1479	+	16.0274i	1.62913	+	0.787705i
$415$	5.83624	−	5.83624i	0.286490	−	0.286490i
$416$	0.0674613	+	10.9413i	0.00330756	+	0.536440i
$417$	−0.991890	−	0.991890i	−0.0485731	−	0.0485731i
$418$	−0.373461	−	1.07270i	−0.0182666	−	0.0524672i
$419$	−13.9712	+	11.4659i	−0.682538	+	0.560145i	−0.910492	−	0.413527i	$-0.864297\pi$
$419$	−13.9712	+	11.4659i	−0.682538	+	0.560145i	0.227953	+	0.973672i	$0.426797\pi$
$420$	−0.986595	−	1.92455i	−0.0481409	−	0.0939085i
$421$	−0.0628736	+	0.207266i	−0.00306427	+	0.0101015i	−0.958459	−	0.285230i	$-0.907930\pi$
$421$	−0.0628736	+	0.207266i	−0.00306427	+	0.0101015i	0.955395	+	0.295331i	$0.0954301\pi$
$422$	−17.5223	+	28.6730i	−0.852970	+	1.39578i
$423$	−13.7564	−	9.19171i	−0.668857	−	0.446916i
$424$	2.11470	−	28.2033i	0.102699	−	1.36967i
$425$	3.30159	+	4.94119i	0.160151	+	0.239683i
$426$	0.0245683	+	0.0226546i	0.00119034	+	0.00109762i
$427$	10.4930	−	1.03347i	0.507791	−	0.0500130i
$428$	−2.76360	−	0.0474521i	−0.133584	−	0.00229368i
$429$	0.0208060	+	0.0685881i	0.00100452	+	0.00331147i
$430$	−3.60959	+	13.9028i	−0.174070	+	0.670454i
$431$	−3.53871	−	1.46578i	−0.170454	−	0.0706043i	0.295825	−	0.955242i	$-0.404406\pi$
$431$	−3.53871	−	1.46578i	−0.170454	−	0.0706043i	−0.466279	+	0.884638i	$0.654406\pi$
$432$	4.87194	+	2.82330i	0.234401	+	0.135836i
$433$	31.6320	−	13.1024i	1.52013	−	0.629660i	0.542516	−	0.840046i	$-0.317472\pi$
$433$	31.6320	−	13.1024i	1.52013	−	0.629660i	0.977619	+	0.210385i	$0.0674718\pi$
$434$	7.54119	+	54.0301i	0.361988	+	2.59353i
$435$	−0.740891	+	1.38611i	−0.0355230	+	0.0664588i
$436$	1.33191	+	7.35359i	0.0637868	+	0.352173i
$437$	−28.7992	+	35.0920i	−1.37765	+	1.67868i
$438$	2.71603	−	1.25617i	0.129777	−	0.0600222i
$439$	−2.63791	+	13.2617i	−0.125901	+	0.632946i	0.865373	+	0.501128i	$0.167081\pi$
$439$	−2.63791	+	13.2617i	−0.125901	+	0.632946i	−0.991274	+	0.131818i	$0.957919\pi$
$440$	0.178851	+	0.404801i	0.00852637	+	0.0192982i
$441$	39.9811	−	7.95273i	1.90386	−	0.378701i
$442$	−16.0585	−	2.52312i	−0.763825	−	0.120013i
$443$	−0.0608585	+	0.0325295i	−0.00289147	+	0.00154552i	−0.472842	−	0.881147i	$-0.656772\pi$
$443$	−0.0608585	+	0.0325295i	−0.00289147	+	0.00154552i	0.469950	+	0.882693i	$0.344272\pi$
$444$	−3.02363	−	1.68353i	−0.143495	−	0.0798969i
$445$	0.733428	−	7.44662i	0.0347678	−	0.353004i
$446$	0.177396	−	3.07255i	0.00839994	−	0.145489i
$447$		−	4.99027i		−	0.236032i
$448$	36.1184	+	5.44697i	1.70643	+	0.257345i
$449$		−	7.23275i		−	0.341335i	−0.985329	−	0.170667i	$-0.945408\pi$
$449$		−	7.23275i		−	0.341335i	0.985329	−	0.170667i	$-0.0545924\pi$
$450$	4.15640	+	0.239973i	0.195934	+	0.0113124i
$451$	0.116242	−	1.18023i	0.00547364	−	0.0555748i
$452$	−19.1454	+	5.45056i	−0.900522	+	0.256373i
$453$	−1.49572	+	0.799477i	−0.0702749	+	0.0375627i
$454$	0.456416	−	2.90487i	0.0214206	−	0.136332i
$455$	8.66157	−	1.72289i	0.406061	−	0.0807705i
$456$	−2.37403	+	2.48749i	−0.111174	+	0.116487i
$457$	−0.882142	+	4.43482i	−0.0412648	+	0.207452i	−0.995917	−	0.0902700i	$-0.971227\pi$
$457$	−0.882142	+	4.43482i	−0.0412648	+	0.207452i	0.954652	+	0.297722i	$0.0962270\pi$
$458$	5.07251	+	10.9675i	0.237023	+	0.512479i
$459$	−5.30713	+	6.46676i	−0.247716	+	0.301843i
$460$	10.0777	−	14.5358i	0.469874	−	0.677733i
$461$	−0.500706	+	0.936755i	−0.0233202	+	0.0436290i	−0.893312	−	0.449438i	$-0.851624\pi$
$461$	−0.500706	+	0.936755i	−0.0233202	+	0.0436290i	0.869991	+	0.493067i	$0.164124\pi$
$462$	0.236979	−	0.0330761i	0.0110253	−	0.00153884i
$463$	−31.4792	+	13.0391i	−1.46296	+	0.605979i	−0.965242	−	0.261359i	$-0.915829\pi$
$463$	−31.4792	+	13.0391i	−1.46296	+	0.605979i	−0.497720	+	0.867338i	$0.665829\pi$
$464$	−11.7022	−	23.8264i	−0.543259	−	1.10611i
$465$	1.84862	+	0.765725i	0.0857278	+	0.0355096i
$466$	1.30723	+	0.339397i	0.0605565	+	0.0157223i
$467$	10.0019	+	32.9720i	0.462834	+	1.52576i	0.809127	+	0.587634i	$0.199941\pi$
$467$	10.0019	+	32.9720i	0.462834	+	1.52576i	−0.346292	+	0.938127i	$0.612559\pi$
$468$	−8.18974	+	7.91325i	−0.378571	+	0.365790i
$469$	−45.6247	+	4.49364i	−2.10675	+	0.207497i
$470$	−5.38778	+	5.84291i	−0.248520	+	0.269513i
$471$	2.55658	+	3.82619i	0.117801	+	0.176302i
$472$	−4.89515	+	9.69577i	−0.225317	+	0.446284i
$473$	−1.32135	−	0.882899i	−0.0607558	−	0.0405958i
$474$	2.18567	+	1.33568i	0.100391	+	0.0613497i
$475$	−1.49008	+	4.91214i	−0.0683696	+	0.225384i
$476$	−16.6421	+	51.6523i	−0.762790	+	2.36748i
$477$	22.7553	−	18.6748i	1.04189	−	0.855060i
$478$	21.4020	−	7.45115i	0.978905	−	0.340807i
$479$	18.0728	+	18.0728i	0.825766	+	0.825766i	0.986928	−	0.161162i	$-0.0515241\pi$
$479$	18.0728	+	18.0728i	0.825766	+	0.825766i	−0.161162	+	0.986928i	$0.551524\pi$
$480$	0.843518	−	1.04085i	0.0385012	−	0.0475081i
$481$	9.99260	−	9.99260i	0.455623	−	0.455623i
$482$	−1.85696	+	3.84056i	−0.0845821	+	0.174933i
$483$	−6.06682	−	7.39245i	−0.276050	−	0.336368i
$484$	21.8791	−	1.77622i	0.994503	−	0.0807374i
$485$	2.67122	+	0.810304i	0.121294	+	0.0367940i
$486$	2.06929	+	8.57262i	0.0938649	+	0.388862i
$487$	2.04160	−	3.05547i	0.0925137	−	0.138456i	−0.782326	−	0.622869i	$-0.785967\pi$
$487$	2.04160	−	3.05547i	0.0925137	−	0.138456i	0.874839	+	0.484413i	$0.160967\pi$
$488$	3.21253	+	5.68693i	0.145424	+	0.257435i
$489$	−2.57233	+	1.71878i	−0.116325	+	0.0777259i
$490$	−0.792939	−	19.5666i	−0.0358213	−	0.883927i
$491$	1.42829	+	14.5017i	0.0644578	+	0.654451i	0.972078	+	0.234658i	$0.0753971\pi$
$491$	1.42829	+	14.5017i	0.0644578	+	0.654451i	−0.907620	+	0.419792i	$0.862103\pi$
$492$	−3.34001	+	1.31676i	−0.150579	+	0.0593642i
$493$	37.7392	−	11.4481i	1.69969	−	0.515595i
$494$	−7.11493	−	12.1050i	−0.320116	−	0.544630i
$495$	−0.176272	+	0.425558i	−0.00792283	+	0.0191274i
$496$	−28.7273	+	17.7996i	−1.28989	+	0.799226i
$497$	0.174340	+	0.420894i	0.00782021	+	0.0188797i
$498$	1.66578	−	2.20620i	0.0746452	−	0.0988623i
$499$	26.6107	+	14.2237i	1.19126	+	0.636740i	0.943271	−	0.332024i	$-0.107731\pi$
$499$	26.6107	+	14.2237i	1.19126	+	0.636740i	0.247986	+	0.968764i	$0.420231\pi$
$500$	0.423799	−	1.95458i	0.0189529	−	0.0874116i
$501$	2.10350	+	1.72630i	0.0939774	+	0.0771253i
$502$	8.81472	−	23.9844i	0.393420	−	1.07048i
$503$	24.2745	+	4.82849i	1.08235	+	0.215292i	0.703877	−	0.710322i	$-0.251451\pi$
$503$	24.2745	+	4.82849i	1.08235	+	0.215292i	0.378469	+	0.925614i	$0.376451\pi$
$504$	21.8536	+	31.1095i	0.973436	+	1.38573i
$505$	−1.08202	−	5.43970i	−0.0481494	−	0.242064i
$506$	1.15219	+	1.58175i	0.0512212	+	0.0703174i
$507$	−1.03369	−	1.93389i	−0.0459077	−	0.0858872i
$508$	−2.53275	+	21.8609i	−0.112373	+	0.969919i
$509$	−16.1624	−	1.59185i	−0.716384	−	0.0705577i	−0.266744	−	0.963767i	$-0.585948\pi$
$509$	−16.1624	−	1.59185i	−0.716384	−	0.0705577i	−0.449640	+	0.893210i	$0.648448\pi$
$510$	1.32397	+	1.48622i	0.0586265	+	0.0658110i
$511$	40.7934			1.80460
$512$	5.95586	+	21.8295i	0.263214	+	0.964737i
$513$	−7.22608			−0.319039
$514$	−16.0850	−	18.0561i	−0.709478	−	0.796422i
$515$	12.4597	+	1.22717i	0.549038	+	0.0540755i
$516$	−0.553678	+	4.77895i	−0.0243743	+	0.210381i
$517$	−0.414513	−	0.775499i	−0.0182303	−	0.0341064i
$518$	−27.7769	−	38.1327i	−1.22045	−	1.67545i
$519$	−0.820868	−	4.12678i	−0.0360321	−	0.181146i
$520$	3.14468	+	4.47660i	0.137904	+	0.196312i
$521$	17.3383	+	3.44880i	0.759604	+	0.151095i	0.559671	−	0.828715i	$-0.310928\pi$
$521$	17.3383	+	3.44880i	0.759604	+	0.151095i	0.199933	+	0.979810i	$0.435928\pi$
$522$	9.53084	−	25.9329i	0.417154	−	1.13505i
$523$	−0.738109	−	0.605750i	−0.0322752	−	0.0264876i	0.618117	−	0.786086i	$-0.287896\pi$
$523$	−0.738109	−	0.605750i	−0.0322752	−	0.0264876i	−0.650393	+	0.759598i	$0.725396\pi$
$524$	1.53828	−	7.09464i	0.0672002	−	0.309931i
$525$	−0.953665	−	0.509745i	−0.0416214	−	0.0222471i
$526$	21.0783	−	27.9168i	0.919059	−	1.21723i
$527$	−19.2138	−	46.3862i	−0.836966	−	2.02061i
$528$	0.0780701	+	0.126000i	0.00339756	+	0.00548343i
$529$	21.1287	−	51.0092i	0.918639	−	2.21779i
$530$	−7.16567	−	12.1913i	−0.311257	−	0.529557i
$531$	−10.8181	+	3.28163i	−0.469465	+	0.142411i
$532$	−43.6081	+	17.1920i	−1.89065	+	0.745369i
$533$	−1.43697	−	14.5898i	−0.0622420	−	0.631953i
$534$	−0.101481	−	2.50414i	−0.00439150	−	0.108365i
$535$	−1.14909	+	0.767801i	−0.0496797	+	0.0331949i
$536$	−13.9684	−	24.7274i	−0.603345	−	1.06806i
$537$	0.574418	−	0.859677i	0.0247880	−	0.0370978i
$538$	−5.76249	−	23.8728i	−0.248439	−	1.02923i
$539$	2.07329	+	0.628925i	0.0893028	+	0.0270897i
$540$	2.80621	−	0.227819i	0.120760	−	0.00980375i
$541$	−7.68882	−	9.36885i	−0.330568	−	0.402798i	0.581029	−	0.813883i	$-0.302650\pi$
$541$	−7.68882	−	9.36885i	−0.330568	−	0.402798i	−0.911597	+	0.411084i	$0.865150\pi$
$542$	15.4992	−	32.0555i	0.665749	−	1.37690i
$543$	−3.25072	+	3.25072i	−0.139502	+	0.139502i
$544$	−33.4342	+	3.50126i	−1.43348	+	0.150115i
$545$	2.64219	+	2.64219i	0.113179	+	0.113179i
$546$	2.79344	−	0.972540i	0.119548	−	0.0416209i
$547$	5.32187	−	4.36755i	0.227547	−	0.186743i	−0.513711	−	0.857963i	$-0.671730\pi$
$547$	5.32187	−	4.36755i	0.227547	−	0.186743i	0.741258	+	0.671220i	$0.234230\pi$
$548$	0.0187134	−	0.0580808i	0.000799396	−	0.00248109i
$549$	−1.97343	+	6.50552i	−0.0842239	+	0.277649i
$550$	0.188811	+	0.115384i	0.00805093	+	0.00491997i
$551$	28.3241	+	18.9255i	1.20665	+	0.806255i
$552$	2.66996	−	5.28837i	0.113641	−	0.225088i
$553$	19.3996	+	29.0336i	0.824956	+	1.23463i
$554$	−3.41021	+	3.69828i	−0.144886	+	0.157125i
$555$	−1.72203	+	0.169605i	−0.0730961	+	0.00719934i
$556$	8.51881	−	8.23120i	0.361278	−	0.349081i
$557$	−10.4407	−	34.4182i	−0.442385	−	1.45835i	−0.840903	−	0.541186i	$-0.817975\pi$
$557$	−10.4407	−	34.4182i	−0.442385	−	1.45835i	0.398518	−	0.917160i	$-0.369525\pi$
$558$	−34.0458	−	8.83929i	−1.44127	−	0.374197i
$559$	−18.1497	−	7.51786i	−0.767651	−	0.317971i
$560$	16.3930	−	8.05128i	0.692729	−	0.340229i
$561$	−0.203453	+	0.0842728i	−0.00858978	+	0.00355800i
$562$	13.1815	−	1.83978i	0.556026	−	0.0776066i
$563$	−16.5404	+	30.9449i	−0.697095	+	1.30417i	0.245227	+	0.969466i	$0.421138\pi$
$563$	−16.5404	+	30.9449i	−0.697095	+	1.30417i	−0.942322	+	0.334708i	$0.891362\pi$
$564$	−1.51671	+	2.18765i	−0.0638648	+	0.0921167i
$565$	−6.31415	+	7.69382i	−0.265638	+	0.323681i
$566$	16.1044	+	34.8201i	0.676918	+	1.46360i
$567$	−7.56992	+	38.0566i	−0.317907	+	1.59823i
$568$	−0.194846	+	0.204158i	−0.00817554	+	0.00856628i
$569$	28.3463	−	5.63842i	1.18834	−	0.236375i	0.438953	−	0.898510i	$-0.355349\pi$
$569$	28.3463	−	5.63842i	1.18834	−	0.236375i	0.749385	+	0.662135i	$0.230349\pi$
$570$	−0.266860	+	1.69844i	−0.0111775	+	0.0711397i
$571$	1.79465	−	0.959260i	0.0751038	−	0.0401438i	−0.433417	−	0.901193i	$-0.642692\pi$
$571$	1.79465	−	0.959260i	0.0751038	−	0.0401438i	0.508521	+	0.861050i	$0.330192\pi$
$572$	−0.582139	+	0.165731i	−0.0243405	+	0.00692957i
$573$	0.266110	−	2.70187i	0.0111169	−	0.112872i
$574$	−48.8605	−	2.82100i	−2.03940	−	0.117746i
$575$		−	8.84375i		−	0.368810i
$576$	−12.1566	+	20.1713i	−0.506525	+	0.840469i
$577$			17.0682i			0.710558i	0.934760	+	0.355279i	$0.115614\pi$
$577$			17.0682i			0.710558i	−0.934760	+	0.355279i	$0.884386\pi$
$578$	1.49302	−	25.8595i	0.0621012	−	1.07561i
$579$	0.338437	−	3.43621i	0.0140650	−	0.142804i
$580$	−11.5962	−	6.45665i	−0.481505	−	0.268098i
$581$	33.2353	−	17.7647i	1.37883	−	0.737002i
$582$	0.923608	+	0.145118i	0.0382848	+	0.00601533i
$583$	1.53450	−	0.305230i	0.0635523	−	0.0126413i
$584$	10.2127	+	23.1149i	0.422604	+	0.956501i
$585$	−1.11086	+	5.58469i	−0.0459286	+	0.230899i
$586$	6.36078	−	2.94188i	0.262762	−	0.121528i
$587$	15.2916	−	18.6328i	0.631150	−	0.769058i	−0.355009	−	0.934863i	$-0.615522\pi$
$587$	15.2916	−	18.6328i	0.631150	−	0.769058i	0.986159	+	0.165805i	$0.0530221\pi$
$588$	−1.16895	−	6.45388i	−0.0482066	−	0.266154i
$589$	20.4438	−	38.2476i	0.842371	−	1.57597i
$590$	0.750707	+	5.37857i	0.0309061	+	0.221432i
$591$	−2.39075	+	0.990283i	−0.0983425	+	0.0407348i
$592$	14.6532	−	25.2859i	0.602244	−	1.03924i
$593$	−21.4872	−	8.90027i	−0.882372	−	0.365490i	−0.104955	−	0.994477i	$-0.533470\pi$
$593$	−21.4872	−	8.90027i	−0.882372	−	0.365490i	−0.777416	+	0.628987i	$0.783470\pi$
$594$	−0.0782780	+	0.301499i	−0.00321179	+	0.0123706i
$595$	7.87646	+	25.9652i	0.322903	+	1.06447i
$596$	42.1353	+	0.723478i	1.72593	+	0.0296348i
$597$	3.26403	−	0.321479i	0.133588	−	0.0131573i
$598$	17.7842	+	16.3989i	0.727249	+	0.670601i
$599$	−9.47160	−	14.1753i	−0.386999	−	0.579185i	0.585909	−	0.810377i	$-0.300738\pi$
$599$	−9.47160	−	14.1753i	−0.386999	−	0.579185i	−0.972908	+	0.231192i	$0.925738\pi$
$600$	0.0500864	−	0.667993i	0.00204477	−	0.0272707i
$601$	−26.0292	−	17.3921i	−1.06175	−	0.709440i	−0.103287	−	0.994652i	$-0.532936\pi$
$601$	−26.0292	−	17.3921i	−1.06175	−	0.709440i	−0.958465	+	0.285212i	$0.907936\pi$
$602$	−34.1980	+	55.9608i	−1.39380	+	2.28079i
$603$	8.58070	−	28.2868i	0.349433	−	1.15193i
$604$	−6.53353	−	12.7450i	−0.265845	−	0.518585i
$605$	8.48419	−	6.96280i	0.344931	−	0.283078i
$606$	−0.610781	−	1.75435i	−0.0248113	−	0.0712657i
$607$	15.7019	+	15.7019i	0.637320	+	0.637320i	0.949894	−	0.312573i	$-0.101191\pi$
$607$	15.7019	+	15.7019i	0.637320	+	0.637320i	−0.312573	+	0.949894i	$0.601191\pi$
$608$	−20.6589	−	20.4057i	−0.837829	−	0.827561i
$609$	−5.07428	+	5.07428i	−0.205620	+	0.205620i
$610$	2.94014	+	1.42160i	0.119043	+	0.0575587i
$611$	−6.89592	−	8.40270i	−0.278979	−	0.339937i
$612$	−26.6623	−	22.6583i	−1.07776	−	0.915906i
$613$	36.3731	+	11.0337i	1.46910	+	0.445646i	0.920600	−	0.390507i	$-0.127700\pi$
$613$	36.3731	+	11.0337i	1.46910	+	0.445646i	0.548497	+	0.836153i	$0.315200\pi$
$614$	35.5876	−	8.59027i	1.43620	−	0.346675i
$615$	−0.997303	+	1.49257i	−0.0402151	+	0.0601862i
$616$	0.244921	+	2.00573i	0.00986813	+	0.0808130i
$617$	−6.19051	+	4.13637i	−0.249220	+	0.166524i	−0.673906	−	0.738817i	$-0.735385\pi$
$617$	−6.19051	+	4.13637i	−0.249220	+	0.166524i	0.424685	+	0.905341i	$0.360385\pi$
$618$	4.18992	−	0.169797i	0.168543	−	0.00683025i
$619$	0.332468	+	3.37561i	0.0133630	+	0.135677i	0.999551	−	0.0299506i	$-0.00953500\pi$
$619$	0.332468	+	3.37561i	0.0133630	+	0.135677i	−0.986188	+	0.165628i	$0.947035\pi$
$620$	−6.73339	+	15.4978i	−0.270420	+	0.622407i
$621$	11.9135	−	3.61391i	0.478071	−	0.145021i
$622$	14.9145	−	8.76625i	0.598016	−	0.351495i
$623$	13.0743	−	31.5641i	0.523809	−	1.26459i
$624$	1.25041	+	1.33937i	0.0500566	+	0.0536179i
$625$	−0.382683	−	0.923880i	−0.0153073	−	0.0369552i
$626$	3.51952	+	2.65738i	0.140668	+	0.106210i
$627$	−0.167756	−	0.0896676i	−0.00669954	−	0.00358098i
$628$	−32.6770	+	21.0317i	−1.30396	+	0.839257i
$629$	33.5632	+	27.5446i	1.33825	+	1.09827i
$630$	17.8423	+	6.55737i	0.710853	+	0.261252i
$631$	5.31395	+	1.05701i	0.211545	+	0.0420789i	0.299725	−	0.954026i	$-0.403105\pi$
$631$	5.31395	+	1.05701i	0.211545	+	0.0420789i	−0.0881799	+	0.996105i	$0.528105\pi$
$632$	−11.5946	+	18.2610i	−0.461210	+	0.726385i
$633$	1.09786	+	5.51929i	0.0436358	+	0.219372i
$634$	−32.7838	+	23.8806i	−1.30201	+	0.948422i
$635$	5.18703	+	9.70426i	0.205841	+	0.385102i
$636$	−2.94143	−	3.71232i	−0.116635	−	0.147203i
$637$	26.6539	+	2.62518i	1.05607	+	0.104013i
$638$	1.09647	−	0.976769i	0.0434096	−	0.0386707i
$639$	−0.293738			−0.0116201
$640$	8.66611	+	7.27313i	0.342558	+	0.287496i
$641$	22.8668			0.903186			0.451593	−	0.892224i	$-0.350856\pi$
$641$	22.8668			0.903186			0.451593	+	0.892224i	$0.350856\pi$
$642$	−0.345628	+	0.307896i	−0.0136408	+	0.0121517i
$643$	−17.4987	−	1.72347i	−0.690081	−	0.0679670i	−0.253103	−	0.967439i	$-0.581451\pi$
$643$	−17.4987	−	1.72347i	−0.690081	−	0.0679670i	−0.436978	+	0.899472i	$0.643951\pi$
$644$	63.2975	−	50.1534i	2.49427	−	1.97632i
$645$	1.13392	+	2.12142i	0.0446483	+	0.0835310i
$646$	34.8701	−	25.4004i	1.37195	−	0.999365i
$647$	−4.65108	−	23.3826i	−0.182853	−	0.919264i	−0.957843	−	0.287291i	$-0.907245\pi$
$647$	−4.65108	−	23.3826i	−0.182853	−	0.919264i	0.774991	−	0.631973i	$-0.217755\pi$
$648$	−23.4592	+	5.23815i	−0.921565	+	0.205774i
$649$	−0.589297	−	0.117218i	−0.0231319	−	0.00460123i
$650$	2.56747	+	0.943593i	0.100704	+	0.0370107i
$651$	7.06220	+	5.79580i	0.276790	+	0.227155i
$652$	−14.1396	−	21.9687i	−0.553748	−	0.860359i
$653$	−13.5041	−	7.21809i	−0.528456	−	0.282466i	0.185514	−	0.982642i	$-0.440605\pi$
$653$	−13.5041	−	7.21809i	−0.528456	−	0.282466i	−0.713970	+	0.700176i	$0.753105\pi$
$654$	0.998795	+	0.754132i	0.0390560	+	0.0294889i
$655$	−1.38904	−	3.35345i	−0.0542744	−	0.131030i
$656$	−10.6338	−	28.3922i	−0.415181	−	1.10853i
$657$	−10.0654	+	24.3001i	−0.392690	+	0.948038i
$658$	−31.2847	+	18.3882i	−1.21961	+	0.716845i
$659$	16.3342	−	4.95492i	0.636290	−	0.193016i	0.0443724	−	0.999015i	$-0.485871\pi$
$659$	16.3342	−	4.95492i	0.636290	−	0.193016i	0.591917	+	0.805999i	$0.298371\pi$
$660$	0.0679743	+	0.0295331i	0.00264590	+	0.00114957i
$661$	0.0998828	+	1.01413i	0.00388499	+	0.0394450i	0.996932	−	0.0782754i	$-0.0249413\pi$
$661$	0.0998828	+	1.01413i	0.00388499	+	0.0394450i	−0.993047	+	0.117720i	$0.962441\pi$
$662$	−8.73084	+	0.353819i	−0.339334	+	0.0137516i
$663$	−2.26348	+	1.51241i	−0.0879063	+	0.0587371i
$664$	18.3865	+	14.3848i	0.713536	+	0.558239i
$665$	−13.0211	+	19.4874i	−0.504936	+	0.755689i
$666$	29.5689	−	7.13743i	1.14577	−	0.276570i
$667$	−56.1623	−	17.0366i	−2.17461	−	0.659661i
$668$	−14.8809	+	17.5106i	−0.575760	+	0.677505i
$669$	−0.326971	−	0.398415i	−0.0126414	−	0.0154036i
$670$	−12.7841	−	6.18127i	−0.493892	−	0.238803i
$671$	−0.255492	+	0.255492i	−0.00986315	+	0.00986315i
$672$	5.06508	−	3.42974i	0.195390	−	0.132305i
$673$	−12.2968	−	12.2968i	−0.474006	−	0.474006i	0.429203	−	0.903208i	$-0.358795\pi$
$673$	−12.2968	−	12.2968i	−0.474006	−	0.474006i	−0.903208	+	0.429203i	$0.858795\pi$
$674$	−14.9114	−	42.8302i	−0.574366	−	1.64976i
$675$	1.08818	−	0.893049i	0.0418842	−	0.0343735i
$676$	16.4787	−	8.44755i	0.633794	−	0.324906i
$677$	3.57462	−	11.7839i	0.137384	−	0.452893i	−0.861070	−	0.508487i	$-0.830205\pi$
$677$	3.57462	−	11.7839i	0.137384	−	0.452893i	0.998453	+	0.0555935i	$0.0177051\pi$
$678$	−1.73830	+	2.84452i	−0.0667592	+	0.109243i
$679$	10.5972	+	7.08084i	0.406684	+	0.271738i
$680$	−12.7408	+	10.9635i	−0.488589	+	0.420430i
$681$	−0.273584	−	0.409448i	−0.0104838	−	0.0156901i
$682$	−1.37437	−	1.26732i	−0.0526274	−	0.0485280i
$683$	2.83513	−	0.279236i	0.108483	−	0.0106847i	−0.0436298	−	0.999048i	$-0.513892\pi$
$683$	2.83513	−	0.279236i	0.108483	−	0.0106847i	0.152113	+	0.988363i	$0.451392\pi$
$684$	0.518867	−	30.2187i	0.0198394	−	1.15544i
$685$	−0.00885674	−	0.0291968i	−0.000338399	−	0.00111555i
$686$	11.1103	−	42.7930i	0.424195	−	1.63384i
$687$	1.86959	+	0.774410i	0.0713294	+	0.0295456i
$688$	−40.2707	−	5.36781i	−1.53531	−	0.204646i
$689$	17.8685	−	7.40139i	0.680737	−	0.281971i
$690$	−0.409459	−	2.93364i	−0.0155878	−	0.111682i
$691$	−6.92344	+	12.9528i	−0.263380	+	0.492749i	−0.978499	−	0.206254i	$-0.933873\pi$
$691$	−6.92344	+	12.9528i	−0.263380	+	0.492749i	0.715118	+	0.699003i	$0.246373\pi$
$692$	34.9634	−	6.33269i	1.32911	−	0.240733i
$693$	−1.33421	+	1.62574i	−0.0506824	+	0.0617567i
$694$	−34.7074	+	16.0523i	−1.31748	+	0.609336i
$695$	1.15550	−	5.80909i	0.0438306	−	0.220351i
$696$	−4.14560	−	1.60490i	−0.157139	−	0.0608335i
$697$	44.1777	−	8.78748i	1.67335	−	0.332850i
$698$	8.26736	+	1.29897i	0.312924	+	0.0491668i
$699$	0.199470	−	0.106619i	0.00754465	−	0.00403270i
$700$	4.44228	−	7.97836i	0.167902	−	0.301554i
$701$	−1.41972	+	14.4146i	−0.0536220	+	0.544433i	0.930420	+	0.366495i	$0.119442\pi$
$701$	−1.41972	+	14.4146i	−0.0536220	+	0.544433i	−0.984042	+	0.177937i	$0.943058\pi$
$702$	−0.221950	+	3.84423i	−0.00837695	+	0.145091i
$703$			37.5041i			1.41449i
$704$	−1.07519	+	0.640916i	−0.0405229	+	0.0241554i
$705$			1.33100i			0.0501282i
$706$	−10.6345	−	0.613991i	−0.400235	−	0.0231078i
$707$	2.48213	−	25.2015i	0.0933502	−	0.947801i
$708$	0.498047	+	1.74942i	0.0187178	+	0.0657471i
$709$	−41.4295	+	22.1446i	−1.55592	+	0.831656i	−0.555919	+	0.831236i	$0.687634\pi$
$709$	−41.4295	+	22.1446i	−1.55592	+	0.831656i	−1.00000		0.000420114i	$0.999866\pi$
$710$	−0.0219022	+	0.139397i	−0.000821975	+	0.00523149i
$711$	−22.0816	+	4.39230i	−0.828125	+	0.164724i
$712$	21.1584	−	0.493807i	0.792944	−	0.0185062i
$713$	−14.5768	+	73.2823i	−0.545904	+	2.74444i
$714$	3.81493	+	8.24846i	0.142770	+	0.308691i
$715$	−0.191990	+	0.233940i	−0.00718001	+	0.00874887i
$716$	7.17539	+	4.97472i	0.268157	+	0.185914i
$717$	1.78901	−	3.34701i	0.0668120	−	0.124996i
$718$	−18.6506	+	2.60314i	−0.696036	+	0.0971483i
$719$	10.8074	−	4.47656i	0.403047	−	0.166947i	−0.171945	−	0.985107i	$-0.555005\pi$
$719$	10.8074	−	4.47656i	0.403047	−	0.166947i	0.574992	+	0.818159i	$0.305005\pi$
$720$	0.751216	+	11.7517i	0.0279962	+	0.437958i
$721$	52.8128	+	21.8758i	1.96685	+	0.814697i
$722$	10.0602	+	2.61192i	0.374401	+	0.0972057i
$723$	0.207380	+	0.683641i	0.00771256	+	0.0254249i
$724$	−26.9761	−	27.9187i	−1.00256	−	1.03759i
$725$	−6.60430	+	0.650467i	−0.245278	+	0.0241577i
$726$	2.49199	−	2.70250i	0.0924865	−	0.100299i
$727$	14.2327	+	21.3007i	0.527862	+	0.790001i	0.995584	−	0.0938747i	$-0.0299253\pi$
$727$	14.2327	+	21.3007i	0.527862	+	0.790001i	−0.467722	+	0.883875i	$0.654925\pi$
$728$	7.80664	+	23.7273i	0.289333	+	0.879393i
$729$	−19.9703	−	13.3438i	−0.739643	−	0.494213i
$730$	10.7814	+	6.58860i	0.399039	+	0.243855i
$731$	17.5211	−	57.7595i	0.648043	−	2.13631i
$732$	1.04112	+	0.335443i	0.0384809	+	0.0123983i
$733$	34.4409	−	28.2649i	1.27210	−	1.04399i	0.275530	−	0.961293i	$-0.411147\pi$
$733$	34.4409	−	28.2649i	1.27210	−	1.04399i	0.996575	−	0.0826964i	$-0.0263532\pi$
$734$	−11.2885	+	3.93011i	−0.416666	+	0.145063i
$735$	−2.31892	−	2.31892i	−0.0855346	−	0.0855346i
$736$	44.2652	+	23.3105i	1.63164	+	0.859235i
$737$	1.11091	−	1.11091i	0.0409208	−	0.0409208i
$738$	13.7364	−	28.4095i	0.505642	−	1.04577i
$739$	−2.28336	−	2.78228i	−0.0839948	−	0.102348i	0.729317	−	0.684176i	$-0.239838\pi$
$739$	−2.28336	−	2.78228i	−0.0839948	−	0.102348i	−0.813312	+	0.581828i	$0.802338\pi$
$740$	−1.18240	−	14.5645i	−0.0434660	−	0.535402i
$741$	−2.25017	−	0.682583i	−0.0826622	−	0.0250753i
$742$	−15.1502	−	62.7642i	−0.556183	−	2.30415i
$743$	−9.97933	+	14.9351i	−0.366106	+	0.547917i	−0.968094	−	0.250589i	$-0.919376\pi$
$743$	−9.97933	+	14.9351i	−0.366106	+	0.547917i	0.601987	+	0.798506i	$0.294376\pi$
$744$	−1.51606	+	5.45266i	−0.0555813	+	0.199904i
$745$	17.5197	−	11.7063i	0.641872	−	0.428885i
$746$	1.43935	+	35.5175i	0.0526985	+	1.30039i
$747$	2.38163	+	24.1811i	0.0871394	+	0.884741i
$748$	−0.682060	−	1.73007i	−0.0249386	−	0.0632575i
$749$	−6.03832	+	1.83170i	−0.220635	+	0.0669290i
$750$	−0.169718	−	0.288750i	−0.00619723	−	0.0105437i
$751$	14.6362	−	35.3350i	0.534084	−	1.28939i	−0.394713	−	0.918804i	$-0.629156\pi$
$751$	14.6362	−	35.3350i	0.534084	−	1.28939i	0.928797	−	0.370588i	$-0.120844\pi$
$752$	−18.2515	−	13.1234i	−0.665564	−	0.478562i
$753$	−1.63761	−	3.95353i	−0.0596776	−	0.144075i
$754$	10.9383	−	14.4870i	0.398348	−	0.527584i
$755$	−6.31546	−	3.37568i	−0.229843	−	0.122854i
$756$	12.5630	+	2.72395i	0.456911	+	0.0990689i
$757$	−17.4572	−	14.3267i	−0.634491	−	0.520714i	0.261260	−	0.965268i	$-0.415862\pi$
$757$	−17.4572	−	14.3267i	−0.634491	−	0.520714i	−0.895752	+	0.444555i	$0.853362\pi$
$758$	2.39529	−	6.51744i	0.0870007	−	0.236724i
$759$	0.321420	+	0.0639345i	0.0116668	+	0.00232068i
$760$	−14.3020	−	2.49946i	−0.518790	−	0.0906650i
$761$	3.90231	+	19.6182i	0.141459	+	0.711160i	0.984788	+	0.173763i	$0.0555925\pi$
$761$	3.90231	+	19.6182i	0.141459	+	0.711160i	−0.843329	+	0.537398i	$0.819407\pi$
$762$	2.16993	+	2.97893i	0.0786084	+	0.107915i
$763$	8.04243	+	15.0463i	0.291156	+	0.544714i
$764$	22.7746	+	2.63861i	0.823955	+	0.0954615i
$765$	−17.4106	−	1.71479i	−0.629480	−	0.0619984i
$766$	−17.9929	−	20.1979i	−0.650110	−	0.729779i
$767$	−7.42750			−0.268191
$768$	3.21145	+	2.01140i	0.115883	+	0.0725801i
$769$	−25.7302			−0.927854			−0.463927	−	0.885873i	$-0.653560\pi$
$769$	−25.7302			−0.927854			−0.463927	+	0.885873i	$0.653560\pi$
$770$	0.672033	+	0.754389i	0.0242184	+	0.0271863i
$771$	−4.03012	−	0.396933i	−0.145141	−	0.0142952i
$772$	28.9645	+	3.35576i	1.04246	+	0.120776i
$773$	−7.09434	−	13.2726i	−0.255166	−	0.477382i	0.721423	−	0.692494i	$-0.243488\pi$
$773$	−7.09434	−	13.2726i	−0.255166	−	0.477382i	−0.976589	+	0.215113i	$0.930988\pi$
$774$	−24.8970	−	34.1791i	−0.894906	−	1.22854i
$775$	1.64825	+	8.28634i	0.0592071	+	0.297654i
$776$	−1.35920	+	7.77743i	−0.0487926	+	0.279194i
$777$	−7.74877	−	1.54133i	−0.277986	−	0.0552948i
$778$	2.68799	−	7.31389i	0.0963693	−	0.262216i
$779$	30.0757	+	24.6825i	1.07757	+	0.884341i
$780$	0.895364	+	0.194136i	0.0320592	+	0.00695117i
$781$	−0.0137684	−	0.00735937i	−0.000492672	−	0.000263339i
$782$	−44.7863	+	59.3163i	−1.60156	+	2.12115i
$783$	−3.57503	−	8.63088i	−0.127761	−	0.308443i
$784$	54.6627	−	8.93433i	1.95224	−	0.319083i
$785$	−7.43559	+	17.9511i	−0.265388	+	0.640702i
$786$	−0.616034	−	1.04809i	−0.0219732	−	0.0373841i
$787$	36.3211	−	11.0179i	1.29471	−	0.392745i	0.433571	−	0.901119i	$-0.357253\pi$
$787$	36.3211	−	11.0179i	1.29471	−	0.392745i	0.861136	+	0.508374i	$0.169753\pi$
$788$	−8.01483	−	20.3299i	−0.285516	−	0.724221i
$789$	−0.574194	−	5.82989i	−0.0204418	−	0.207549i
$790$	0.437942	+	10.8066i	0.0155813	+	0.384483i
$791$	−37.7855	+	25.2474i	−1.34350	+	0.897695i
$792$	−1.25522	−	0.349000i	−0.0446022	−	0.0124012i
$793$	−2.48149	+	3.71382i	−0.0881204	+	0.131881i
$794$	−1.14310	−	4.73561i	−0.0405670	−	0.168060i
$795$	−2.26622	−	0.687450i	−0.0803745	−	0.0243813i
$796$	2.24119	+	27.6064i	0.0794369	+	0.978483i
$797$	−11.3899	−	13.8787i	−0.403452	−	0.491608i	0.531162	−	0.847270i	$-0.321755\pi$
$797$	−11.3899	−	13.8787i	−0.403452	−	0.491608i	−0.934615	+	0.355662i	$0.884255\pi$
$798$	−3.41708	+	7.06720i	−0.120963	+	0.250176i
$799$	23.6158	−	23.6158i	0.835467	−	0.835467i
$800$	5.63293	+	0.519748i	0.199154	+	0.0183759i
$801$	15.5763	+	15.5763i	0.550363	+	0.550363i
$802$	−20.1540	+	7.01665i	−0.711662	+	0.247766i
$803$	−1.08062	+	0.886841i	−0.0381342	+	0.0312959i
$804$	−4.52691	−	1.45855i	−0.159652	−	0.0514390i
$805$	11.7215	−	38.6405i	0.413128	−	1.36190i
$806$	−19.7196	−	12.0508i	−0.694593	−	0.424470i
$807$	−3.41960	−	2.28491i	−0.120376	−	0.0804325i
$808$	14.9014	−	4.90278i	0.524229	−	0.172479i
$809$	−20.0854	−	30.0599i	−0.706165	−	1.05685i	−0.995039	−	0.0994838i	$-0.968281\pi$
$809$	−20.0854	−	30.0599i	−0.706165	−	1.05685i	0.288874	−	0.957367i	$-0.406719\pi$
$810$	−8.14725	+	8.83548i	−0.286265	+	0.310447i
$811$	15.1550	−	1.49264i	0.532165	−	0.0524137i	0.171634	−	0.985161i	$-0.445095\pi$
$811$	15.1550	−	1.49264i	0.532165	−	0.0524137i	0.360531	+	0.932747i	$0.382595\pi$
$812$	−42.1089	−	43.5803i	−1.47773	−	1.52937i
$813$	−1.73091	−	5.70606i	−0.0607058	−	0.200120i
$814$	1.56481	+	0.406271i	0.0548465	+	0.0142398i
$815$	−12.0685	−	4.99892i	−0.422740	−	0.175105i
$816$	−3.71877	+	4.22668i	−0.130183	+	0.147963i
$817$	48.1676	−	19.9517i	1.68517	−	0.698020i
$818$	28.1307	−	3.92630i	0.983566	−	0.137280i
$819$	−12.2556	+	22.9286i	−0.428245	+	0.801189i
$820$	−12.4579	−	8.63710i	−0.435049	−	0.301621i
$821$	2.16479	−	2.63780i	0.0755517	−	0.0920600i	−0.733863	−	0.679298i	$-0.762285\pi$
$821$	2.16479	−	2.63780i	0.0755517	−	0.0920600i	0.809415	+	0.587238i	$0.199785\pi$
$822$	−0.00428973	−	0.00927505i	−0.000149622	−	0.000323505i
$823$	−5.39915	+	27.1433i	−0.188202	+	0.946157i	0.765047	+	0.643974i	$0.222716\pi$
$823$	−5.39915	+	27.1433i	−0.188202	+	0.946157i	−0.953250	+	0.302183i	$0.902284\pi$
$824$	0.826236	+	35.4021i	0.0287833	+	1.23329i
$825$	0.0363444	−	0.00722934i	0.00126535	−	0.000251693i
$826$	−3.84872	+	24.4953i	−0.133914	+	0.852301i
$827$	12.8373	−	6.86167i	0.446396	−	0.238604i	−0.232852	−	0.972512i	$-0.574806\pi$
$827$	12.8373	−	6.86167i	0.446396	−	0.238604i	0.679248	+	0.733908i	$0.262306\pi$
$828$	14.2576	+	50.0804i	0.495485	+	1.74042i
$829$	1.64505	−	16.7025i	0.0571349	−	0.580100i	−0.923411	−	0.383812i	$-0.874611\pi$
$829$	1.64505	−	16.7025i	0.0571349	−	0.580100i	0.980546	−	0.196288i	$-0.0628889\pi$
$830$	11.6531	+	0.672799i	0.404484	+	0.0233532i
$831$			0.842458i			0.0292245i
$832$	−11.4903	+	10.3637i	−0.398353	+	0.359295i
$833$			82.2888i			2.85114i
$834$	0.114345	−	1.98048i	0.00395943	−	0.0685785i
$835$	−1.12620	+	11.4345i	−0.0389737	+	0.395706i
$836$	0.781428	−	1.40345i	0.0270262	−	0.0485393i
$837$	−10.4890	+	5.60650i	−0.362554	+	0.193789i
$838$	−25.2504	−	3.96736i	−0.872260	−	0.137050i
$839$	−20.8751	+	4.15232i	−0.720689	+	0.143354i	−0.541790	−	0.840514i	$-0.682253\pi$
$839$	−20.8751	+	4.15232i	−0.720689	+	0.143354i	−0.178898	+	0.983868i	$0.557253\pi$
$840$	1.10420	−	2.85224i	0.0380984	−	0.0984117i
$841$	−2.93414	+	14.7509i	−0.101177	+	0.508652i
$842$	−0.278014	+	0.128582i	−0.00958098	+	0.00443123i
$843$	1.41397	−	1.72293i	0.0486998	−	0.0593409i
$844$	−46.7612	+	8.46955i	−1.60959	+	0.291534i
$845$	4.36460	−	8.16560i	0.150147	−	0.280905i
$846$	−3.23434	−	23.1730i	−0.111199	−	0.796705i
$847$	46.2980	−	19.1773i	1.59082	−	0.658939i
$848$	31.7714	−	24.2977i	1.09103	−	0.834388i
$849$	5.93565	+	2.45863i	0.203711	+	0.0843798i
$850$	−2.11198	+	8.13457i	−0.0724402	+	0.279013i
$851$	−18.7566	−	61.8321i	−0.642967	−	2.11958i
$852$	−0.000811381		0.0472547i	−2.77975e−5		0.00161892i
$853$	−44.9921	+	4.43133i	−1.54050	+	0.151726i	−0.832315	−	0.554302i	$-0.812985\pi$
$853$	−44.9921	+	4.43133i	−1.54050	+	0.151726i	−0.708184	+	0.706028i	$0.750485\pi$
$854$	10.9620	+	10.1082i	0.375113	+	0.345894i
$855$	−8.39555	−	12.5648i	−0.287122	−	0.429708i
$856$	−2.54961	−	2.96294i	−0.0871437	−	0.101271i
$857$	21.9087	+	14.6389i	0.748387	+	0.500056i	0.870323	−	0.492482i	$-0.163910\pi$
$857$	21.9087	+	14.6389i	0.748387	+	0.500056i	−0.121936	+	0.992538i	$0.538910\pi$
$858$	−0.0528554	+	0.0864913i	−0.00180445	+	0.00295277i
$859$	6.21414	−	20.4853i	0.212024	−	0.698949i	−0.784832	−	0.619709i	$-0.787251\pi$
$859$	6.21414	−	20.4853i	0.212024	−	0.698949i	0.996856	−	0.0792399i	$-0.0252493\pi$
$860$	−18.0766	+	9.26672i	−0.616407	+	0.315992i
$861$	−6.33571	+	5.19958i	−0.215920	+	0.177201i
$862$	−1.78103	−	5.11566i	−0.0606620	−	0.174240i
$863$	−2.54913	−	2.54913i	−0.0867735	−	0.0867735i	0.662388	−	0.749161i	$-0.269543\pi$
$863$	−2.54913	−	2.54913i	−0.0867735	−	0.0867735i	−0.749161	+	0.662388i	$0.769543\pi$
$864$	1.60168	+	7.80053i	0.0544904	+	0.265380i
$865$	12.5626	−	12.5626i	0.427140	−	0.427140i
$866$	43.5919	+	21.0772i	1.48131	+	0.716234i
$867$	−2.75188	−	3.35318i	−0.0934589	−	0.113880i
$868$	−49.9606	+	58.7893i	−1.69577	+	1.99544i
$869$	−1.14508	−	0.347356i	−0.0388442	−	0.0117833i
$870$	−2.16065	+	0.521546i	−0.0732530	+	0.0176821i
$871$	10.7898	−	16.1481i	0.365599	−	0.547158i
$872$	−6.51230	+	8.32397i	−0.220534	+	0.281885i
$873$	−6.83274	+	4.56549i	−0.231253	+	0.154518i
$874$	−64.1477	+	2.59960i	−2.16983	+	0.0879328i
$875$	−0.447532	−	4.54387i	−0.0151293	−	0.153611i
$876$	3.88145	+	1.68639i	0.131142	+	0.0569779i
$877$	−2.01342	+	0.610765i	−0.0679884	+	0.0206241i	−0.324096	−	0.946024i	$-0.605060\pi$
$877$	−2.01342	+	0.610765i	−0.0679884	+	0.0206241i	0.256107	+	0.966648i	$0.417560\pi$
$878$	−16.4855	+	9.68966i	−0.556359	+	0.327010i
$879$	0.449131	−	1.08430i	0.0151488	−	0.0365724i
$880$	−0.259217	+	0.569658i	−0.00873819	+	0.0192032i
$881$	6.72618	+	16.2384i	0.226611	+	0.547087i	0.995761	−	0.0919817i	$-0.0293201\pi$
$881$	6.72618	+	16.2384i	0.226611	+	0.547087i	−0.769150	+	0.639068i	$0.779320\pi$
$882$	46.0080	+	34.7380i	1.54917	+	1.16969i
$883$	−1.51468	−	0.809613i	−0.0509730	−	0.0272456i	0.445713	−	0.895176i	$-0.352950\pi$
$883$	−1.51468	−	0.809613i	−0.0509730	−	0.0272456i	−0.496686	+	0.867930i	$0.665450\pi$
$884$	−12.4418	−	19.3309i	−0.418464	−	0.650169i
$885$	0.703026	+	0.576958i	0.0236320	+	0.0193942i
$886$	−0.0915999	−	0.0336647i	−0.00307736	−	0.00113099i
$887$	−52.0146	−	10.3463i	−1.74648	−	0.347396i	−0.784418	−	0.620232i	$-0.787038\pi$
$887$	−52.0146	−	10.3463i	−1.74648	−	0.347396i	−0.962061	+	0.272836i	$0.912038\pi$
$888$	−1.06655	−	4.77658i	−0.0357911	−	0.160291i
$889$	9.80144	+	49.2752i	0.328730	+	1.65264i
$890$	8.55340	−	6.23054i	0.286711	−	0.208848i
$891$	−0.626815	−	1.17269i	−0.0209991	−	0.0392865i
$892$	3.41142	−	2.70301i	0.114223	−	0.0905036i
$893$	28.7093	+	2.82762i	0.960719	+	0.0946226i
$894$	5.26961	−	4.69434i	0.176242	−	0.157002i
$895$	4.36561			0.145926
$896$	28.2246	+	43.2642i	0.942918	+	1.44535i
$897$	4.05118			0.135265
$898$	7.63762	−	6.80383i	0.254871	−	0.227047i
$899$	55.7976	+	5.49558i	1.86095	+	0.183288i
$900$	3.65651	+	4.61480i	0.121884	+	0.153827i
$901$	28.0120	+	52.4068i	0.933215	+	1.74592i
$902$	1.35564	−	0.987489i	0.0451380	−	0.0328798i
$903$	2.14267	+	10.7719i	0.0713036	+	0.358467i
$904$	−23.7657	−	15.0897i	−0.790434	−	0.501877i
$905$	−19.0381	−	3.78692i	−0.632848	−	0.125881i
$906$	−2.25125	−	0.827376i	−0.0747927	−	0.0274877i
$907$	−22.7640	−	18.6819i	−0.755867	−	0.620324i	0.175469	−	0.984485i	$-0.443856\pi$
$907$	−22.7640	−	18.6819i	−0.755867	−	0.620324i	−0.931336	+	0.364161i	$0.881356\pi$
$908$	3.49683	−	2.25064i	0.116046	−	0.0746902i
$909$	14.3998	+	7.69683i	0.477610	+	0.255288i
$910$	9.96726	+	7.52570i	0.330411	+	0.249475i
$911$	20.0312	+	48.3595i	0.663662	+	1.60222i	0.792021	+	0.610493i	$0.209029\pi$
$911$	20.0312	+	48.3595i	0.663662	+	1.60222i	−0.128360	+	0.991728i	$0.540971\pi$
$912$	−4.85998	−	0.166944i	−0.160930	−	0.00552808i
$913$	−0.494205	+	1.19312i	−0.0163558	+	0.0394864i
$914$	−5.51290	+	3.24031i	−0.182351	+	0.107180i
$915$	0.523362	−	0.158760i	0.0173018	−	0.00524845i
$916$	−6.80977	+	15.6736i	−0.225001	+	0.517870i
$917$	−1.62443	−	16.4931i	−0.0536433	−	0.544650i
$918$	−11.8212	+	0.479055i	−0.390156	+	0.0158112i
$919$	16.5855	−	11.0821i	0.547105	−	0.365564i	−0.251089	−	0.967964i	$-0.580789\pi$
$919$	16.5855	−	11.0821i	0.547105	−	0.365564i	0.798194	+	0.602400i	$0.205789\pi$
$920$	24.8295	−	3.03194i	0.818604	−	0.0999602i
$921$	3.40616	−	5.09768i	0.112237	−	0.167974i
$922$	−1.46020	+	0.352469i	−0.0480893	+	0.0116080i
$923$	−0.184680	−	0.0560222i	−0.00607883	−	0.00184399i
$924$	0.257854	+	0.219130i	0.00848276	+	0.00720885i
$925$	−4.63502	−	5.64778i	−0.152398	−	0.185698i
$926$	−43.3814	−	20.9754i	−1.42560	−	0.689296i
$927$	−26.0622	+	26.0622i	−0.855996	+	0.855996i
$928$	14.1520	−	34.7707i	0.464561	−	1.14140i
$929$	−29.4096	−	29.4096i	−0.964898	−	0.964898i	0.0345068	−	0.999404i	$-0.489014\pi$
$929$	−29.4096	−	29.4096i	−0.964898	−	0.964898i	−0.999404	+	0.0345068i	$0.989014\pi$
$930$	0.930408	+	2.67242i	0.0305093	+	0.0876321i
$931$	−54.9449	+	45.0921i	−1.80075	+	1.47783i
$932$	0.871317	+	1.69968i	0.0285409	+	0.0556749i
$933$	0.841005	−	2.77242i	0.0275333	−	0.0907650i
$934$	−25.4088	+	41.5785i	−0.831403	+	1.36049i
$935$	−0.773125	−	0.516586i	−0.0252839	−	0.0168942i
$936$	−16.0603	−	1.20421i	−0.524947	−	0.0393607i
$937$	−2.26151	−	3.38458i	−0.0738802	−	0.110570i	0.792690	−	0.609626i	$-0.208680\pi$
$937$	−2.26151	−	3.38458i	−0.0738802	−	0.110570i	−0.866570	+	0.499056i	$0.833680\pi$
$938$	−47.6642	−	43.9515i	−1.55629	−	1.43507i
$939$	0.734985	−	0.0723897i	0.0239853	−	0.00236235i
$940$	−11.2382	−	0.192965i	−0.366551	−	0.00629382i
$941$	8.65421	+	28.5291i	0.282119	+	0.930022i	0.977420	+	0.211304i	$0.0677709\pi$
$941$	8.65421	+	28.5291i	0.282119	+	0.930022i	−0.695301	+	0.718718i	$0.744729\pi$
$942$	−1.63540	+	6.29898i	−0.0532843	+	0.205232i
$943$	−61.9292	−	25.6519i	−2.01669	−	0.835342i
$944$	−14.8434	+	3.95163i	−0.483110	+	0.128614i
$945$	5.93819	−	2.45968i	0.193169	−	0.0800133i
$946$	−0.310671	−	2.22586i	−0.0101008	−	0.0723689i
$947$	−1.65114	+	3.08906i	−0.0536547	+	0.100381i	−0.907319	−	0.420442i	$-0.861875\pi$
$947$	−1.65114	+	3.08906i	−0.0536547	+	0.100381i	0.853665	+	0.520823i	$0.174375\pi$
$948$	0.645612	+	3.56449i	0.0209685	+	0.115769i
$949$	−10.9630	+	13.3584i	−0.355873	+	0.433632i
$950$	−6.58882	+	3.04735i	−0.213770	+	0.0988690i
$951$	−1.32512	+	6.66184i	−0.0429701	+	0.216025i
$952$	−70.1988	+	31.0155i	−2.27516	+	1.00522i
$953$	7.17311	−	1.42682i	0.232360	−	0.0462192i	−0.0775368	−	0.996989i	$-0.524706\pi$
$953$	7.17311	−	1.42682i	0.232360	−	0.0462192i	0.309897	+	0.950770i	$0.399706\pi$
$954$	41.1260	+	6.46175i	1.33150	+	0.209207i
$955$	10.1099	−	5.40384i	0.327148	−	0.174864i
$956$	28.0011	+	15.5908i	0.905619	+	0.504241i
$957$	0.0241040	−	0.244732i	0.000779170	−	0.00791105i
$958$	−2.08342	+	36.0855i	−0.0673123	+	1.16587i
$959$		−	0.139307i		−	0.00449845i
$960$	1.89261	−	0.0883899i	0.0610837	−	0.00285277i
$961$		−	40.3801i		−	1.30258i
$962$	19.9520	+	1.15194i	0.643278	+	0.0371401i
$963$	0.398782	−	4.04891i	0.0128506	−	0.130474i
$964$	−5.80238	+	1.65190i	−0.186882	+	0.0532041i
$965$	12.8576	−	6.87255i	0.413902	−	0.221235i
$966$	2.09921	−	13.3605i	0.0675409	−	0.429866i
$967$	−26.3094	+	5.23326i	−0.846053	+	0.168290i	−0.599037	−	0.800721i	$-0.704450\pi$
$967$	−26.3094	+	5.23326i	−0.846053	+	0.168290i	−0.247016	+	0.969011i	$0.579450\pi$
$968$	22.4572	+	21.4329i	0.721803	+	0.688879i
$969$	1.40945	−	7.08580i	0.0452782	−	0.227629i
$970$	1.65714	+	3.58299i	0.0532077	+	0.115043i
$971$	4.58705	−	5.58934i	0.147205	−	0.179370i	−0.694187	−	0.719794i	$-0.744236\pi$
$971$	4.58705	−	5.58934i	0.147205	−	0.179370i	0.841393	+	0.540424i	$0.181736\pi$
$972$	−7.10592	+	10.2494i	−0.227923	+	0.328749i
$973$	12.7480	−	23.8499i	0.408683	−	0.764591i
$974$	5.14703	−	0.718390i	0.164922	−	0.0230187i
$975$	0.423215	−	0.175301i	0.0135537	−	0.00561413i
$976$	−2.98325	+	8.74204i	−0.0954915	+	0.279826i
$977$	−35.7156	−	14.7939i	−1.14264	−	0.473299i	−0.270584	−	0.962696i	$-0.587217\pi$
$977$	−35.7156	−	14.7939i	−1.14264	−	0.473299i	−0.872061	+	0.489398i	$0.837217\pi$
$978$	−4.23478	−	1.09948i	−0.135413	−	0.0351573i
$979$	0.339859	+	1.12036i	0.0108619	+	0.0358070i
$980$	19.9159	−	19.2436i	0.636191	−	0.614713i
$981$	−10.9473	+	1.07822i	−0.349520	+	0.0344248i
$982$	−13.9698	+	15.1499i	−0.445795	+	0.483453i
$983$	−2.89847	−	4.33786i	−0.0924468	−	0.138356i	0.782363	−	0.622822i	$-0.214014\pi$
$983$	−2.89847	−	4.33786i	−0.0924468	−	0.138356i	−0.874810	+	0.484466i	$0.839014\pi$
$984$	−4.53241	−	2.28830i	−0.144488	−	0.0729482i
$985$	−9.08493	−	6.07036i	−0.289470	−	0.193418i
$986$	47.5901	+	29.0826i	1.51558	+	0.926178i
$987$	−1.76410	+	5.81546i	−0.0561519	+	0.185108i
$988$	6.08960	−	18.9003i	0.193736	−	0.601300i
$989$	−69.4345	+	56.9834i	−2.20789	+	1.81197i
$990$	−0.615198	+	0.214182i	−0.0195523	+	0.00680716i
$991$	−2.12574	−	2.12574i	−0.0675263	−	0.0675263i	0.672537	−	0.740063i	$-0.265205\pi$
$991$	−2.12574	−	2.12574i	−0.0675263	−	0.0675263i	−0.740063	+	0.672537i	$0.765205\pi$
$992$	−45.8197	−	13.5913i	−1.45478	−	0.431524i
$993$	−1.03473	+	1.03473i	−0.0328361	+	0.0328361i
$994$	−0.280453	+	0.580033i	−0.00889543	+	0.0183975i
$995$	8.78547	+	10.7051i	0.278518	+	0.339375i
$996$	3.89669	−	0.316348i	0.123471	−	0.0100239i
$997$	16.2542	+	4.93065i	0.514775	+	0.156155i	0.536975	−	0.843598i	$-0.319567\pi$
$997$	16.2542	+	4.93065i	0.514775	+	0.156155i	−0.0222001	+	0.999754i	$0.507067\pi$
$998$	10.0127	+	41.4805i	0.316946	+	1.31304i
$999$	5.71410	−	8.55176i	0.180786	−	0.270566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.221.48	✓	1024
128.117	even	32	inner	640.2.bm.a.501.48	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.221.48	✓	1024	1.1	even	1	trivial
640.2.bm.a.501.48	yes	1024	128.117	even	32	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.940698 + 1.05598i) q^{2} +(0.235694 + 0.0232138i) q^{3} +(-0.230176 + 1.98671i) q^{4} +(0.471397 + 0.881921i) q^{5} +(0.197203 + 0.270724i) q^{6} +(0.890754 + 4.47812i) q^{7} +(-2.31445 + 1.62583i) q^{8} +(-2.88734 - 0.574328i) q^{9} +O(q^{10})\)	\(q+(0.940698 + 1.05598i) q^{2} +(0.235694 + 0.0232138i) q^{3} +(-0.230176 + 1.98671i) q^{4} +(0.471397 + 0.881921i) q^{5} +(0.197203 + 0.270724i) q^{6} +(0.890754 + 4.47812i) q^{7} +(-2.31445 + 1.62583i) q^{8} +(-2.88734 - 0.574328i) q^{9} +(-0.487847 + 1.32741i) q^{10} +(-0.120950 - 0.0992607i) q^{11} +(-0.100370 + 0.462912i) q^{12} +(-1.70581 - 0.911775i) q^{13} +(-3.89086 + 5.15317i) q^{14} +(0.0906325 + 0.218806i) q^{15} +(-3.89404 - 0.914585i) q^{16} +(2.27418 - 5.49035i) q^{17} +(-2.10964 - 3.58924i) q^{18} +(4.91214 - 1.49008i) q^{19} +(-1.86063 + 0.733532i) q^{20} +(0.105991 + 1.07614i) q^{21} +(-0.00895989 - 0.221094i) q^{22} +(-7.35331 + 4.91332i) q^{23} +(-0.583242 + 0.329472i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(-0.641839 - 2.65900i) q^{26} +(-1.34710 - 0.408640i) q^{27} +(-9.10176 + 0.738915i) q^{28} +(4.21000 + 5.12990i) q^{29} +(-0.145797 + 0.301536i) q^{30} +(5.97412 - 5.97412i) q^{31} +(-2.69733 - 4.97236i) q^{32} +(-0.0262028 - 0.0262028i) q^{33} +(7.93700 - 2.76328i) q^{34} +(-3.52945 + 2.89655i) q^{35} +(1.80562 - 5.60412i) q^{36} +(-2.12088 + 6.99162i) q^{37} +(6.19433 + 3.78539i) q^{38} +(-0.380883 - 0.254498i) q^{39} +(-2.52488 - 1.27475i) q^{40} +(4.21098 + 6.30217i) q^{41} +(-1.03668 + 1.12425i) q^{42} +(10.1078 - 0.995532i) q^{43} +(0.225042 - 0.217444i) q^{44} +(-0.854572 - 2.81715i) q^{45} +(-12.1056 - 3.14297i) q^{46} +(5.19216 + 2.15066i) q^{47} +(-0.896569 - 0.305957i) q^{48} +(-12.7930 + 5.29902i) q^{49} +(-1.40064 + 0.195492i) q^{50} +(0.663462 - 1.24125i) q^{51} +(2.20407 - 3.17908i) q^{52} +(-6.34354 + 7.72962i) q^{53} +(-0.835704 - 1.80692i) q^{54} +(0.0305249 - 0.153459i) q^{55} +(-9.34228 - 8.91616i) q^{56} +(1.19235 - 0.237173i) q^{57} +(-1.45672 + 9.27134i) q^{58} +(3.38666 - 1.81021i) q^{59} +(-0.455566 + 0.129697i) q^{60} +(0.226347 - 2.29814i) q^{61} +(11.9284 + 0.688693i) q^{62} -13.4415i q^{63} +(2.71333 - 7.52581i) q^{64} -1.93420i q^{65} +(0.00302065 - 0.0523185i) q^{66} +(-0.984184 + 9.99259i) q^{67} +(10.3843 + 5.78188i) q^{68} +(-1.84719 + 0.987342i) q^{69} +(-6.37883 - 1.00225i) q^{70} +(0.0978609 - 0.0194657i) q^{71} +(7.61636 - 3.36509i) q^{72} +(1.74303 - 8.76279i) q^{73} +(-9.37810 + 4.33739i) q^{74} +(-0.150246 + 0.183075i) q^{75} +(1.82971 + 10.1020i) q^{76} +(0.336765 - 0.630043i) q^{77} +(-0.0895518 - 0.641609i) q^{78} +(7.06558 - 2.92666i) q^{79} +(-1.02904 - 3.86537i) q^{80} +(7.85144 + 3.25217i) q^{81} +(-2.69369 + 10.3751i) q^{82} +(-2.39592 - 7.89829i) q^{83} +(-2.16238 - 0.0371289i) q^{84} +(5.91410 - 0.582488i) q^{85} +(10.5597 + 9.73712i) q^{86} +(0.873186 + 1.30681i) q^{87} +(0.441313 + 0.0330898i) q^{88} +(-6.22160 - 4.15714i) q^{89} +(2.17095 - 3.55249i) q^{90} +(2.56358 - 8.45099i) q^{91} +(-8.06880 - 15.7398i) q^{92} +(1.54674 - 1.26938i) q^{93} +(2.61320 + 7.50593i) q^{94} +(3.62970 + 3.62970i) q^{95} +(-0.520317 - 1.23457i) q^{96} +(1.97383 - 1.97383i) q^{97} +(-17.6300 - 8.52431i) q^{98} +(0.292215 + 0.356064i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more