LMFDB - Embedded newform 630.2.bi.b.509.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(479,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 1]))

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

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

chi := DirichletCharacter("630.479");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bi (of order $6$, degree $2$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.9
Character	$\chi$	$=$	630.509
Dual form			630.2.bi.b.479.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.767971 - 1.55249i) q^{3} +1.00000 q^{4} +(0.719036 + 2.11731i) q^{5} +(-0.767971 - 1.55249i) q^{6} +(-1.31170 + 2.29771i) q^{7} +1.00000 q^{8} +(-1.82044 + 2.38453i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.767971 - 1.55249i) q^{3} +1.00000 q^{4} +(0.719036 + 2.11731i) q^{5} +(-0.767971 - 1.55249i) q^{6} +(-1.31170 + 2.29771i) q^{7} +1.00000 q^{8} +(-1.82044 + 2.38453i) q^{9} +(0.719036 + 2.11731i) q^{10} +(3.56894 + 2.06053i) q^{11} +(-0.767971 - 1.55249i) q^{12} +(-1.18566 + 2.05363i) q^{13} +(-1.31170 + 2.29771i) q^{14} +(2.73489 - 2.74233i) q^{15} +1.00000 q^{16} +(-2.28111 + 1.31700i) q^{17} +(-1.82044 + 2.38453i) q^{18} +(0.956982 + 0.552514i) q^{19} +(0.719036 + 2.11731i) q^{20} +(4.57451 + 0.271822i) q^{21} +(3.56894 + 2.06053i) q^{22} +(-0.296239 - 0.513101i) q^{23} +(-0.767971 - 1.55249i) q^{24} +(-3.96597 + 3.04484i) q^{25} +(-1.18566 + 2.05363i) q^{26} +(5.10001 + 0.994957i) q^{27} +(-1.31170 + 2.29771i) q^{28} +(2.36953 - 1.36805i) q^{29} +(2.73489 - 2.74233i) q^{30} -2.69755i q^{31} +1.00000 q^{32} +(0.458102 - 7.12317i) q^{33} +(-2.28111 + 1.31700i) q^{34} +(-5.80810 - 1.12513i) q^{35} +(-1.82044 + 2.38453i) q^{36} +(6.05512 + 3.49593i) q^{37} +(0.956982 + 0.552514i) q^{38} +(4.09879 + 0.263600i) q^{39} +(0.719036 + 2.11731i) q^{40} +(0.257087 - 0.445287i) q^{41} +(4.57451 + 0.271822i) q^{42} +(10.4023 - 6.00577i) q^{43} +(3.56894 + 2.06053i) q^{44} +(-6.35775 - 2.13986i) q^{45} +(-0.296239 - 0.513101i) q^{46} -4.12973i q^{47} +(-0.767971 - 1.55249i) q^{48} +(-3.55890 - 6.02779i) q^{49} +(-3.96597 + 3.04484i) q^{50} +(3.79645 + 2.52998i) q^{51} +(-1.18566 + 2.05363i) q^{52} +(-4.54406 - 7.87055i) q^{53} +(5.10001 + 0.994957i) q^{54} +(-1.79657 + 9.03814i) q^{55} +(-1.31170 + 2.29771i) q^{56} +(0.122836 - 1.91002i) q^{57} +(2.36953 - 1.36805i) q^{58} -6.93948 q^{59} +(2.73489 - 2.74233i) q^{60} +4.29324i q^{61} -2.69755i q^{62} +(-3.09109 - 7.31062i) q^{63} +1.00000 q^{64} +(-5.20070 - 1.03378i) q^{65} +(0.458102 - 7.12317i) q^{66} +13.5150i q^{67} +(-2.28111 + 1.31700i) q^{68} +(-0.569081 + 0.853955i) q^{69} +(-5.80810 - 1.12513i) q^{70} -1.60164i q^{71} +(-1.82044 + 2.38453i) q^{72} +(-3.29147 - 5.70100i) q^{73} +(6.05512 + 3.49593i) q^{74} +(7.77283 + 3.81878i) q^{75} +(0.956982 + 0.552514i) q^{76} +(-9.41586 + 5.49759i) q^{77} +(4.09879 + 0.263600i) q^{78} +13.4434 q^{79} +(0.719036 + 2.11731i) q^{80} +(-2.37200 - 8.68180i) q^{81} +(0.257087 - 0.445287i) q^{82} +(3.80374 - 2.19609i) q^{83} +(4.57451 + 0.271822i) q^{84} +(-4.42869 - 3.88283i) q^{85} +(10.4023 - 6.00577i) q^{86} +(-3.94360 - 2.62804i) q^{87} +(3.56894 + 2.06053i) q^{88} +(-7.82648 + 13.5559i) q^{89} +(-6.35775 - 2.13986i) q^{90} +(-3.16341 - 5.41805i) q^{91} +(-0.296239 - 0.513101i) q^{92} +(-4.18792 + 2.07164i) q^{93} -4.12973i q^{94} +(-0.481736 + 2.42350i) q^{95} +(-0.767971 - 1.55249i) q^{96} +(-6.92406 - 11.9928i) q^{97} +(-3.55890 - 6.02779i) q^{98} +(-11.4104 + 4.75919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8}+O(q^{10}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39} - 3 q^{41} + 8 q^{42} + 6 q^{44} - 39 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 42 q^{55} + 3 q^{56} - 22 q^{57} - 3 q^{58} - 4 q^{60} - 43 q^{63} + 48 q^{64} + 12 q^{65} - 42 q^{69} - 12 q^{70} - 18 q^{73} + 18 q^{75} - 12 q^{77} - 18 q^{78} + 8 q^{81} - 3 q^{82} + 9 q^{83} + 8 q^{84} - 33 q^{85} - 15 q^{87} + 6 q^{88} - 33 q^{89} - 39 q^{90} + 3 q^{92} - 8 q^{93} - 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.767971	−	1.55249i	−0.443389	−	0.896330i
$3$	−0.767971	−	1.55249i	−0.443389	−	0.896330i
$4$	1.00000			0.500000
$5$	0.719036	+	2.11731i	0.321563	+	0.946888i
$5$	0.719036	+	2.11731i	0.321563	+	0.946888i
$6$	−0.767971	−	1.55249i	−0.313523	−	0.633801i
$7$	−1.31170	+	2.29771i	−0.495775	+	0.868451i
$7$	−1.31170	+	2.29771i	−0.495775	+	0.868451i
$8$	1.00000			0.353553
$9$	−1.82044	+	2.38453i	−0.606813	+	0.794844i
$10$	0.719036	+	2.11731i	0.227379	+	0.669551i
$11$	3.56894	+	2.06053i	1.07608	+	0.621273i	0.929835	−	0.367976i	$-0.119949\pi$
$11$	3.56894	+	2.06053i	1.07608	+	0.621273i	0.146241	+	0.989249i	$0.453282\pi$
$12$	−0.767971	−	1.55249i	−0.221694	−	0.448165i
$13$	−1.18566	+	2.05363i	−0.328844	+	0.569575i	−0.982283	−	0.187405i	$-0.939992\pi$
$13$	−1.18566	+	2.05363i	−0.328844	+	0.569575i	0.653439	+	0.756979i	$0.273326\pi$
$14$	−1.31170	+	2.29771i	−0.350566	+	0.614088i
$15$	2.73489	−	2.74233i	0.706147	−	0.708066i
$16$	1.00000			0.250000
$17$	−2.28111	+	1.31700i	−0.553250	+	0.319419i	−0.750432	−	0.660948i	$-0.770154\pi$
$17$	−2.28111	+	1.31700i	−0.553250	+	0.319419i	0.197182	+	0.980367i	$0.436821\pi$
$18$	−1.82044	+	2.38453i	−0.429082	+	0.562040i
$19$	0.956982	+	0.552514i	0.219547	+	0.126755i	0.605740	−	0.795662i	$-0.292877\pi$
$19$	0.956982	+	0.552514i	0.219547	+	0.126755i	−0.386194	+	0.922418i	$0.626210\pi$
$20$	0.719036	+	2.11731i	0.160781	+	0.473444i
$21$	4.57451	+	0.271822i	0.998239	+	0.0593165i
$22$	3.56894	+	2.06053i	0.760901	+	0.439306i
$23$	−0.296239	−	0.513101i	−0.0617701	−	0.106989i	0.833487	−	0.552540i	$-0.186341\pi$
$23$	−0.296239	−	0.513101i	−0.0617701	−	0.106989i	−0.895257	+	0.445551i	$0.853008\pi$
$24$	−0.767971	−	1.55249i	−0.156762	−	0.316900i
$25$	−3.96597	+	3.04484i	−0.793195	+	0.608968i
$26$	−1.18566	+	2.05363i	−0.232528	+	0.402750i
$27$	5.10001	+	0.994957i	0.981497	+	0.191480i
$28$	−1.31170	+	2.29771i	−0.247887	+	0.434226i
$29$	2.36953	−	1.36805i	0.440010	−	0.254040i	−0.263592	−	0.964634i	$-0.584907\pi$
$29$	2.36953	−	1.36805i	0.440010	−	0.254040i	0.703602	+	0.710594i	$0.251574\pi$
$30$	2.73489	−	2.74233i	0.499321	−	0.500678i
$31$		−	2.69755i		−	0.484495i	−0.970215	−	0.242247i	$-0.922115\pi$
$31$		−	2.69755i		−	0.484495i	0.970215	−	0.242247i	$-0.0778845\pi$
$32$	1.00000			0.176777
$33$	0.458102	−	7.12317i	0.0797454	−	1.23998i
$34$	−2.28111	+	1.31700i	−0.391207	+	0.225863i
$35$	−5.80810	−	1.12513i	−0.981749	−	0.190182i
$36$	−1.82044	+	2.38453i	−0.303407	+	0.397422i
$37$	6.05512	+	3.49593i	0.995456	+	0.574727i	0.906901	−	0.421345i	$-0.138442\pi$
$37$	6.05512	+	3.49593i	0.995456	+	0.574727i	0.0885553	+	0.996071i	$0.471775\pi$
$38$	0.956982	+	0.552514i	0.155243	+	0.0896295i
$39$	4.09879	+	0.263600i	0.656332	+	0.0422098i
$40$	0.719036	+	2.11731i	0.113690	+	0.334776i
$41$	0.257087	−	0.445287i	0.0401502	−	0.0695422i	−0.845252	−	0.534368i	$-0.820550\pi$
$41$	0.257087	−	0.445287i	0.0401502	−	0.0695422i	0.885402	+	0.464826i	$0.153883\pi$
$42$	4.57451	+	0.271822i	0.705862	+	0.0419431i
$43$	10.4023	−	6.00577i	1.58634	−	0.915872i	0.592432	−	0.805620i	$-0.298168\pi$
$43$	10.4023	−	6.00577i	1.58634	−	0.915872i	0.993904	−	0.110251i	$-0.0351655\pi$
$44$	3.56894	+	2.06053i	0.538038	+	0.310636i
$45$	−6.35775	−	2.13986i	−0.947757	−	0.318992i
$46$	−0.296239	−	0.513101i	−0.0436781	−	0.0756527i
$47$		−	4.12973i		−	0.602384i	−0.953564	−	0.301192i	$-0.902616\pi$
$47$		−	4.12973i		−	0.602384i	0.953564	−	0.301192i	$-0.0973844\pi$
$48$	−0.767971	−	1.55249i	−0.110847	−	0.224082i
$49$	−3.55890	−	6.02779i	−0.508414	−	0.861113i
$50$	−3.96597	+	3.04484i	−0.560873	+	0.430605i
$51$	3.79645	+	2.52998i	0.531609	+	0.354267i
$52$	−1.18566	+	2.05363i	−0.164422	+	0.284787i
$53$	−4.54406	−	7.87055i	−0.624175	−	1.08110i	−0.988700	−	0.149909i	$-0.952102\pi$
$53$	−4.54406	−	7.87055i	−0.624175	−	1.08110i	0.364525	−	0.931194i	$-0.381232\pi$
$54$	5.10001	+	0.994957i	0.694023	+	0.135397i
$55$	−1.79657	+	9.03814i	−0.242250	+	1.21870i
$56$	−1.31170	+	2.29771i	−0.175283	+	0.307044i
$57$	0.122836	−	1.91002i	0.0162701	−	0.252988i
$58$	2.36953	−	1.36805i	0.311134	−	0.179633i
$59$	−6.93948			−0.903443			−0.451722	−	0.892159i	$-0.649190\pi$
$59$	−6.93948			−0.903443			−0.451722	+	0.892159i	$0.649190\pi$
$60$	2.73489	−	2.74233i	0.353073	−	0.354033i
$61$			4.29324i			0.549693i	0.961488	+	0.274847i	$0.0886271\pi$
$61$			4.29324i			0.549693i	−0.961488	+	0.274847i	$0.911373\pi$
$62$		−	2.69755i		−	0.342589i
$63$	−3.09109	−	7.31062i	−0.389441	−	0.921052i
$64$	1.00000			0.125000
$65$	−5.20070	−	1.03378i	−0.645068	−	0.128225i
$66$	0.458102	−	7.12317i	0.0563885	−	0.876801i
$67$			13.5150i			1.65112i	0.564315	+	0.825560i	$0.309141\pi$
$67$			13.5150i			1.65112i	−0.564315	+	0.825560i	$0.690859\pi$
$68$	−2.28111	+	1.31700i	−0.276625	+	0.159709i
$69$	−0.569081	+	0.853955i	−0.0685092	+	0.102804i
$70$	−5.80810	−	1.12513i	−0.694201	−	0.134479i
$71$		−	1.60164i		−	0.190079i	−0.995473	−	0.0950396i	$-0.969702\pi$
$71$		−	1.60164i		−	0.190079i	0.995473	−	0.0950396i	$-0.0302978\pi$
$72$	−1.82044	+	2.38453i	−0.214541	+	0.281020i
$73$	−3.29147	−	5.70100i	−0.385238	−	0.667252i	0.606564	−	0.795035i	$-0.292547\pi$
$73$	−3.29147	−	5.70100i	−0.385238	−	0.667252i	−0.991802	+	0.127783i	$0.959214\pi$
$74$	6.05512	+	3.49593i	0.703894	+	0.406393i
$75$	7.77283	+	3.81878i	0.897530	+	0.440954i
$76$	0.956982	+	0.552514i	0.109773	+	0.0633777i
$77$	−9.41586	+	5.49759i	−1.07304	+	0.626508i
$78$	4.09879	+	0.263600i	0.464097	+	0.0298468i
$79$	13.4434			1.51251			0.756253	−	0.654280i	$-0.227028\pi$
$79$	13.4434			1.51251			0.756253	+	0.654280i	$0.227028\pi$
$80$	0.719036	+	2.11731i	0.0803907	+	0.236722i
$81$	−2.37200	−	8.68180i	−0.263556	−	0.964644i
$82$	0.257087	−	0.445287i	0.0283905	−	0.0491738i
$83$	3.80374	−	2.19609i	0.417515	−	0.241052i	−0.276499	−	0.961014i	$-0.589174\pi$
$83$	3.80374	−	2.19609i	0.417515	−	0.241052i	0.694013	+	0.719962i	$0.255841\pi$
$84$	4.57451	+	0.271822i	0.499120	+	0.0296583i
$85$	−4.42869	−	3.88283i	−0.480359	−	0.421152i
$86$	10.4023	−	6.00577i	1.12171	−	0.647619i
$87$	−3.94360	−	2.62804i	−0.422799	−	0.281755i
$88$	3.56894	+	2.06053i	0.380450	+	0.219653i
$89$	−7.82648	+	13.5559i	−0.829605	+	1.43692i	0.0687438	+	0.997634i	$0.478101\pi$
$89$	−7.82648	+	13.5559i	−0.829605	+	1.43692i	−0.898349	+	0.439283i	$0.855232\pi$
$90$	−6.35775	−	2.13986i	−0.670166	−	0.225561i
$91$	−3.16341	−	5.41805i	−0.331615	−	0.567966i
$92$	−0.296239	−	0.513101i	−0.0308851	−	0.0534945i
$93$	−4.18792	+	2.07164i	−0.434267	+	0.214819i
$94$		−	4.12973i		−	0.425949i
$95$	−0.481736	+	2.42350i	−0.0494251	+	0.248646i
$96$	−0.767971	−	1.55249i	−0.0783808	−	0.158450i
$97$	−6.92406	−	11.9928i	−0.703032	−	1.21769i	−0.967397	−	0.253265i	$-0.918496\pi$
$97$	−6.92406	−	11.9928i	−0.703032	−	1.21769i	0.264365	−	0.964423i	$-0.414838\pi$
$98$	−3.55890	−	6.02779i	−0.359503	−	0.608899i
$99$	−11.4104	+	4.75919i	−1.14679	+	0.478317i
$100$	−3.96597	+	3.04484i	−0.396597	+	0.304484i
$101$	1.35453	−	2.34612i	0.134781	−	0.233448i	−0.790733	−	0.612162i	$-0.790300\pi$
$101$	1.35453	−	2.34612i	0.134781	−	0.233448i	0.925514	+	0.378714i	$0.123634\pi$
$102$	3.79645	+	2.52998i	0.375904	+	0.250505i
$103$	9.07239	+	15.7138i	0.893929	+	1.54833i	0.835125	+	0.550061i	$0.185395\pi$
$103$	9.07239	+	15.7138i	0.893929	+	1.54833i	0.0588041	+	0.998270i	$0.481271\pi$
$104$	−1.18566	+	2.05363i	−0.116264	+	0.201375i
$105$	2.71370	+	9.88108i	0.264830	+	0.964295i
$106$	−4.54406	−	7.87055i	−0.441358	−	0.764455i
$107$	−4.33862	+	7.51471i	−0.419430	+	0.726475i	−0.995882	−	0.0906565i	$-0.971103\pi$
$107$	−4.33862	+	7.51471i	−0.419430	+	0.726475i	0.576452	+	0.817131i	$0.304437\pi$
$108$	5.10001	+	0.994957i	0.490748	+	0.0957398i
$109$	−7.55567	−	13.0868i	−0.723702	−	1.25349i	−0.959506	−	0.281688i	$-0.909106\pi$
$109$	−7.55567	−	13.0868i	−0.723702	−	1.25349i	0.235804	−	0.971801i	$-0.424228\pi$
$110$	−1.79657	+	9.03814i	−0.171297	+	0.861753i
$111$	0.777223	−	12.0853i	0.0737708	−	1.14708i
$112$	−1.31170	+	2.29771i	−0.123944	+	0.217113i
$113$	0.503287	−	0.871718i	0.0473452	−	0.0820044i	−0.841382	−	0.540441i	$-0.818257\pi$
$113$	0.503287	−	0.871718i	0.0473452	−	0.0820044i	0.888727	+	0.458437i	$0.151591\pi$
$114$	0.122836	−	1.91002i	0.0115047	−	0.178890i
$115$	0.873386	−	0.996168i	0.0814437	−	0.0928931i
$116$	2.36953	−	1.36805i	0.220005	−	0.127020i
$117$	−2.73852	−	6.56577i	−0.253176	−	0.607005i
$118$	−6.93948			−0.638831
$119$	−0.0339510	−	6.96882i	−0.00311228	−	0.638830i
$120$	2.73489	−	2.74233i	0.249661	−	0.250339i
$121$	2.99156	+	5.18154i	0.271960	+	0.471049i
$122$			4.29324i			0.388692i
$123$	−0.888739	−	0.0571562i	−0.0801349	−	0.00515360i
$124$		−	2.69755i		−	0.242247i
$125$	−9.29854	−	6.20783i	−0.831687	−	0.555245i
$126$	−3.09109	−	7.31062i	−0.275376	−	0.651282i
$127$			3.12538i			0.277333i	0.990339	+	0.138666i	$0.0442816\pi$
$127$			3.12538i			0.277333i	−0.990339	+	0.138666i	$0.955718\pi$
$128$	1.00000			0.0883883
$129$	−17.3126	−	11.5372i	−1.52429	−	1.01579i
$130$	−5.20070	−	1.03378i	−0.456132	−	0.0906685i
$131$	−10.7870	−	18.6837i	−0.942469	−	1.63240i	−0.760742	−	0.649055i	$-0.775165\pi$
$131$	−10.7870	−	18.6837i	−0.942469	−	1.63240i	−0.181727	−	0.983349i	$-0.558169\pi$
$132$	0.458102	−	7.12317i	0.0398727	−	0.619992i
$133$	−2.52478	+	1.47413i	−0.218926	+	0.127823i
$134$			13.5150i			1.16752i
$135$	1.56046	+	11.5137i	0.134303	+	0.990940i
$136$	−2.28111	+	1.31700i	−0.195603	+	0.112932i
$137$	−1.88397	+	3.26314i	−0.160959	+	0.278789i	−0.935213	−	0.354086i	$-0.884792\pi$
$137$	−1.88397	+	3.26314i	−0.160959	+	0.278789i	0.774254	+	0.632875i	$0.218125\pi$
$138$	−0.569081	+	0.853955i	−0.0484434	+	0.0726935i
$139$	5.20651	+	3.00598i	0.441610	+	0.254964i	0.704280	−	0.709922i	$-0.251270\pi$
$139$	5.20651	+	3.00598i	0.441610	+	0.254964i	−0.262670	+	0.964886i	$0.584603\pi$
$140$	−5.80810	−	1.12513i	−0.490874	−	0.0950910i
$141$	−6.41136	+	3.17152i	−0.539934	+	0.267090i
$142$		−	1.60164i		−	0.134406i
$143$	−8.46313	+	4.88619i	−0.707723	+	0.408604i
$144$	−1.82044	+	2.38453i	−0.151703	+	0.198711i
$145$	4.60035	+	4.03334i	0.382038	+	0.334950i
$146$	−3.29147	−	5.70100i	−0.272404	−	0.471818i
$147$	−6.62494	+	10.1543i	−0.546416	+	0.837514i
$148$	6.05512	+	3.49593i	0.497728	+	0.287363i
$149$	−9.69236	+	5.59589i	−0.794029	+	0.458433i	−0.841379	−	0.540445i	$-0.818256\pi$
$149$	−9.69236	+	5.59589i	−0.794029	+	0.458433i	0.0473497	+	0.998878i	$0.484922\pi$
$150$	7.77283	+	3.81878i	0.634649	+	0.311802i
$151$	9.27469	−	16.0642i	0.754763	−	1.30729i	−0.190729	−	0.981643i	$-0.561085\pi$
$151$	9.27469	−	16.0642i	0.754763	−	1.30729i	0.945492	−	0.325645i	$-0.105582\pi$
$152$	0.956982	+	0.552514i	0.0776215	+	0.0448148i
$153$	1.01219	−	7.83689i	0.0818309	−	0.633575i
$154$	−9.41586	+	5.49759i	−0.758752	+	0.443008i
$155$	5.71154	−	1.93964i	0.458762	−	0.155795i
$156$	4.09879	+	0.263600i	0.328166	+	0.0211049i
$157$	11.6703			0.931389			0.465695	−	0.884945i	$-0.345804\pi$
$157$	11.6703			0.931389			0.465695	+	0.884945i	$0.345804\pi$
$158$	13.4434			1.06950
$159$	−8.72922	+	13.0990i	−0.692272	+	1.03882i
$160$	0.719036	+	2.11731i	0.0568448	+	0.167388i
$161$	1.56753	−	0.00763677i	0.123539	−	0.000601862i
$162$	−2.37200	−	8.68180i	−0.186362	−	0.682106i
$163$	10.7728	+	6.21967i	0.843789	+	0.487162i	0.858550	−	0.512729i	$-0.171366\pi$
$163$	10.7728	+	6.21967i	0.843789	+	0.487162i	−0.0147613	+	0.999891i	$0.504699\pi$
$164$	0.257087	−	0.445287i	0.0200751	−	0.0347711i
$165$	15.4113	−	4.15187i	1.19977	−	0.323223i
$166$	3.80374	−	2.19609i	0.295227	−	0.170450i
$167$	−11.4205	−	6.59363i	−0.883745	−	0.510230i	−0.0118537	−	0.999930i	$-0.503773\pi$
$167$	−11.4205	−	6.59363i	−0.883745	−	0.510230i	−0.871891	+	0.489699i	$0.837107\pi$
$168$	4.57451	+	0.271822i	0.352931	+	0.0209716i
$169$	3.68840	+	6.38850i	0.283723	+	0.491423i
$170$	−4.42869	−	3.88283i	−0.339665	−	0.297800i
$171$	−3.05961	+	1.27614i	−0.233975	+	0.0975886i
$172$	10.4023	−	6.00577i	0.793168	−	0.457936i
$173$		−	14.8129i		−	1.12620i	−0.826387	−	0.563102i	$-0.809608\pi$
$173$		−	14.8129i		−	1.12620i	0.826387	−	0.563102i	$-0.190392\pi$
$174$	−3.94360	−	2.62804i	−0.298964	−	0.199231i
$175$	−1.79399	−	13.1065i	−0.135613	−	0.990762i
$176$	3.56894	+	2.06053i	0.269019	+	0.155318i
$177$	5.32932	+	10.7735i	0.400576	+	0.809783i
$178$	−7.82648	+	13.5559i	−0.586619	+	1.01605i
$179$	20.6373	−	11.9149i	1.54250	−	0.890564i	0.543823	−	0.839200i	$-0.316976\pi$
$179$	20.6373	−	11.9149i	1.54250	−	0.890564i	0.998680	−	0.0513644i	$-0.0163570\pi$
$180$	−6.35775	−	2.13986i	−0.473879	−	0.159496i
$181$		−	11.6911i		−	0.868992i	−0.900674	−	0.434496i	$-0.856926\pi$
$181$		−	11.6911i		−	0.868992i	0.900674	−	0.434496i	$-0.143074\pi$
$182$	−3.16341	−	5.41805i	−0.234487	−	0.401612i
$183$	6.66521	−	3.29709i	0.492706	−	0.243728i
$184$	−0.296239	−	0.513101i	−0.0218390	−	0.0378263i
$185$	−3.04810	+	15.3342i	−0.224100	+	1.12740i
$186$	−4.18792	+	2.07164i	−0.307073	+	0.151900i
$187$	−10.8549			−0.793785
$188$		−	4.12973i		−	0.301192i
$189$	−8.97578	+	10.4132i	−0.652892	+	0.757451i
$190$	−0.481736	+	2.42350i	−0.0349488	+	0.175819i
$191$		−	26.0254i		−	1.88313i	−0.336825	−	0.941567i	$-0.609353\pi$
$191$		−	26.0254i		−	1.88313i	0.336825	−	0.941567i	$-0.390647\pi$
$192$	−0.767971	−	1.55249i	−0.0554236	−	0.112041i
$193$			18.0736i			1.30096i	0.759522	+	0.650482i	$0.225433\pi$
$193$			18.0736i			1.30096i	−0.759522	+	0.650482i	$0.774567\pi$
$194$	−6.92406	−	11.9928i	−0.497119	−	0.861035i
$195$	2.38906	+	8.86794i	0.171084	+	0.635046i
$196$	−3.55890	−	6.02779i	−0.254207	−	0.430556i
$197$	19.0964			1.36056			0.680281	−	0.732951i	$-0.261858\pi$
$197$	19.0964			1.36056			0.680281	+	0.732951i	$0.261858\pi$
$198$	−11.4104	+	4.75919i	−0.810905	+	0.338221i
$199$	21.6198	−	12.4822i	1.53259	−	0.884840i	0.533346	−	0.845897i	$-0.320934\pi$
$199$	21.6198	−	12.4822i	1.53259	−	0.884840i	0.999241	−	0.0389429i	$-0.0123991\pi$
$200$	−3.96597	+	3.04484i	−0.280437	+	0.215303i
$201$	20.9819	−	10.3791i	1.47995	−	0.732088i
$202$	1.35453	−	2.34612i	0.0953046	−	0.165072i
$203$	0.0352670	+	7.23893i	0.00247526	+	0.508074i
$204$	3.79645	+	2.52998i	0.265805	+	0.177134i
$205$	1.12766	+	0.224154i	0.0787595	+	0.0156556i
$206$	9.07239	+	15.7138i	0.632103	+	1.09483i
$207$	1.76279	+	0.227678i	0.122523	+	0.0158247i
$208$	−1.18566	+	2.05363i	−0.0822110	+	0.142394i
$209$	2.27694	+	3.94378i	0.157499	+	0.272797i
$210$	2.71370	+	9.88108i	0.187263	+	0.681860i
$211$	−6.61689	+	11.4608i	−0.455525	+	0.788993i	−0.998718	−	0.0506149i	$-0.983882\pi$
$211$	−6.61689	+	11.4608i	−0.455525	+	0.788993i	0.543193	+	0.839608i	$0.317215\pi$
$212$	−4.54406	−	7.87055i	−0.312088	−	0.540552i
$213$	−2.48652	+	1.23001i	−0.170374	+	0.0842790i
$214$	−4.33862	+	7.51471i	−0.296582	+	0.513695i
$215$	20.1957	+	17.7065i	1.37733	+	1.20757i
$216$	5.10001	+	0.994957i	0.347011	+	0.0676983i
$217$	6.19818	+	3.53837i	0.420760	+	0.240200i
$218$	−7.55567	−	13.0868i	−0.511735	−	0.886351i
$219$	−6.32298	+	9.48818i	−0.427267	+	0.641152i
$220$	−1.79657	+	9.03814i	−0.121125	+	0.609351i
$221$		−	6.24607i		−	0.420156i
$222$	0.777223	−	12.0853i	0.0521638	−	0.811111i
$223$	2.44383	+	4.23284i	0.163651	+	0.283452i	0.936175	−	0.351533i	$-0.114340\pi$
$223$	2.44383	+	4.23284i	0.163651	+	0.283452i	−0.772524	+	0.634985i	$0.781006\pi$
$224$	−1.31170	+	2.29771i	−0.0876415	+	0.153522i
$225$	−0.0407079	−	14.9999i	−0.00271386	−	0.999996i
$226$	0.503287	−	0.871718i	0.0334781	−	0.0579858i
$227$	10.3873	+	5.99711i	0.689429	+	0.398042i	0.803398	−	0.595442i	$-0.203023\pi$
$227$	10.3873	+	5.99711i	0.689429	+	0.398042i	−0.113969	+	0.993484i	$0.536356\pi$
$228$	0.122836	−	1.91002i	0.00813503	−	0.126494i
$229$	9.16676	−	5.29243i	0.605757	−	0.349734i	−0.165546	−	0.986202i	$-0.552939\pi$
$229$	9.16676	−	5.29243i	0.605757	−	0.349734i	0.771303	+	0.636468i	$0.219605\pi$
$230$	0.873386	−	0.996168i	0.0575894	−	0.0656853i
$231$	15.7660	+	10.3960i	1.03733	+	0.684008i
$232$	2.36953	−	1.36805i	0.155567	−	0.0898166i
$233$	0.259858	−	0.450088i	0.0170239	−	0.0294862i	−0.857388	−	0.514671i	$-0.827914\pi$
$233$	0.259858	−	0.450088i	0.0170239	−	0.0294862i	0.874412	+	0.485184i	$0.161248\pi$
$234$	−2.73852	−	6.56577i	−0.179023	−	0.429218i
$235$	8.74391	−	2.96943i	0.570390	−	0.193704i
$236$	−6.93948			−0.451722
$237$	−10.3242	−	20.8708i	−0.670628	−	1.35570i
$238$	−0.0339510	−	6.96882i	−0.00220072	−	0.451721i
$239$	−2.39886	−	1.38498i	−0.155169	−	0.0895869i	0.420405	−	0.907337i	$-0.361888\pi$
$239$	−2.39886	−	1.38498i	−0.155169	−	0.0895869i	−0.575574	+	0.817750i	$0.695221\pi$
$240$	2.73489	−	2.74233i	0.176537	−	0.177016i
$241$	17.4943	+	10.1004i	1.12691	+	0.650621i	0.943156	−	0.332351i	$-0.107842\pi$
$241$	17.4943	+	10.1004i	1.12691	+	0.650621i	0.183753	+	0.982972i	$0.441175\pi$
$242$	2.99156	+	5.18154i	0.192305	+	0.333082i
$243$	−11.6568	+	10.3499i	−0.747782	+	0.663945i
$244$			4.29324i			0.274847i
$245$	10.2037	−	11.8695i	0.651890	−	0.758313i
$246$	−0.888739	−	0.0571562i	−0.0566639	−	0.00364415i
$247$	−2.26932	+	1.31019i	−0.144393	+	0.0833655i
$248$		−	2.69755i		−	0.171295i
$249$	−6.33057	−	4.21872i	−0.401183	−	0.267351i
$250$	−9.29854	−	6.20783i	−0.588091	−	0.392618i
$251$	−20.9869			−1.32468			−0.662340	−	0.749203i	$-0.730437\pi$
$251$	−20.9869			−1.32468			−0.662340	+	0.749203i	$0.730437\pi$
$252$	−3.09109	−	7.31062i	−0.194720	−	0.460526i
$253$		−	2.44164i		−	0.153504i
$254$			3.12538i			0.196104i
$255$	−2.62695	+	9.85739i	−0.164506	+	0.617294i
$256$	1.00000			0.0625000
$257$	−8.21246	+	4.74146i	−0.512279	+	0.295764i	−0.733770	−	0.679398i	$-0.762241\pi$
$257$	−8.21246	+	4.74146i	−0.512279	+	0.295764i	0.221491	+	0.975162i	$0.428908\pi$
$258$	−17.3126	−	11.5372i	−1.07783	−	0.718274i
$259$	−15.9751	+	9.32729i	−0.992644	+	0.579570i
$260$	−5.20070	−	1.03378i	−0.322534	−	0.0641123i
$261$	−1.05143	+	8.14066i	−0.0650816	+	0.503894i
$262$	−10.7870	−	18.6837i	−0.666426	−	1.15428i
$263$	5.83660	−	10.1093i	0.359900	−	0.623365i	−0.628044	−	0.778178i	$-0.716144\pi$
$263$	5.83660	−	10.1093i	0.359900	−	0.623365i	0.987944	+	0.154813i	$0.0494774\pi$
$264$	0.458102	−	7.12317i	0.0281942	−	0.438401i
$265$	13.3970	−	15.2804i	0.822972	−	0.938667i
$266$	−2.52478	+	1.47413i	−0.154804	+	0.0903848i
$267$	27.0558	+	1.74000i	1.65579	+	0.106486i
$268$			13.5150i			0.825560i
$269$	8.14330	+	14.1046i	0.496506	+	0.859973i	0.999992	−	0.00403039i	$-0.00128292\pi$
$269$	8.14330	+	14.1046i	0.496506	+	0.859973i	−0.503486	+	0.864003i	$0.667950\pi$
$270$	1.56046	+	11.5137i	0.0949665	+	0.700701i
$271$	21.8041	+	12.5886i	1.32450	+	0.764703i	0.984444	−	0.175701i	$-0.0562192\pi$
$271$	21.8041	+	12.5886i	1.32450	+	0.764703i	0.340060	+	0.940404i	$0.389553\pi$
$272$	−2.28111	+	1.31700i	−0.138312	+	0.0798547i
$273$	−5.98205	+	9.07206i	−0.362050	+	0.549066i
$274$	−1.88397	+	3.26314i	−0.113815	+	0.197133i
$275$	−20.4283	+	2.69485i	−1.23187	+	0.162506i
$276$	−0.569081	+	0.853955i	−0.0342546	+	0.0514021i
$277$	−17.9632	−	10.3710i	−1.07930	−	0.623136i	−0.148594	−	0.988898i	$-0.547475\pi$
$277$	−17.9632	−	10.3710i	−1.07930	−	0.623136i	−0.930708	+	0.365763i	$0.880808\pi$
$278$	5.20651	+	3.00598i	0.312265	+	0.180287i
$279$	6.43240	+	4.91073i	0.385098	+	0.293998i
$280$	−5.80810	−	1.12513i	−0.347101	−	0.0672395i
$281$	1.17815	−	0.680206i	0.0702827	−	0.0405777i	−0.464447	−	0.885601i	$-0.653747\pi$
$281$	1.17815	−	0.680206i	0.0702827	−	0.0405777i	0.534730	+	0.845023i	$0.320413\pi$
$282$	−6.41136	+	3.17152i	−0.381791	+	0.188861i
$283$	−14.9351			−0.887802			−0.443901	−	0.896076i	$-0.646406\pi$
$283$	−14.9351			−0.887802			−0.443901	+	0.896076i	$0.646406\pi$
$284$		−	1.60164i		−	0.0950396i
$285$	4.13242	−	1.11329i	0.244783	−	0.0659456i
$286$	−8.46313	+	4.88619i	−0.500435	+	0.288927i
$287$	0.685919	+	1.17479i	0.0404885	+	0.0693458i
$288$	−1.82044	+	2.38453i	−0.107270	+	0.140510i
$289$	−5.03103	+	8.71400i	−0.295943	+	0.512589i
$290$	4.60035	+	4.03334i	0.270142	+	0.236846i
$291$	−13.3012	+	19.9597i	−0.779733	+	1.17006i
$292$	−3.29147	−	5.70100i	−0.192619	−	0.333626i
$293$	9.63607	+	5.56339i	0.562945	+	0.325016i	0.754327	−	0.656499i	$-0.227963\pi$
$293$	9.63607	+	5.56339i	0.562945	+	0.325016i	−0.191382	+	0.981516i	$0.561297\pi$
$294$	−6.62494	+	10.1543i	−0.386374	+	0.592212i
$295$	−4.98974	−	14.6930i	−0.290514	−	0.855460i
$296$	6.05512	+	3.49593i	0.351947	+	0.203197i
$297$	16.1515	+	14.0597i	0.937204	+	0.815824i
$298$	−9.69236	+	5.59589i	−0.561464	+	0.324161i
$299$	1.40496			0.0812510
$300$	7.77283	+	3.81878i	0.448765	+	0.220477i
$301$	0.154823	+	31.7792i	0.00892386	+	1.83172i
$302$	9.27469	−	16.0642i	0.533698	−	0.924392i
$303$	−4.68257	−	0.301143i	−0.269006	−	0.0173002i
$304$	0.956982	+	0.552514i	0.0548867	+	0.0316888i
$305$	−9.09011	+	3.08700i	−0.520498	+	0.176761i
$306$	1.01219	−	7.83689i	0.0578632	−	0.448005i
$307$	−14.1337			−0.806651			−0.403325	−	0.915057i	$-0.632146\pi$
$307$	−14.1337			−0.806651			−0.403325	+	0.915057i	$0.632146\pi$
$308$	−9.41586	+	5.49759i	−0.536518	+	0.313254i
$309$	17.4282	−	26.1526i	0.991456	−	1.48777i
$310$	5.71154	−	1.93964i	0.324394	−	0.110164i
$311$	−5.87504			−0.333143			−0.166572	−	0.986029i	$-0.553270\pi$
$311$	−5.87504			−0.333143			−0.166572	+	0.986029i	$0.553270\pi$
$312$	4.09879	+	0.263600i	0.232048	+	0.0149234i
$313$	19.0369			1.07603			0.538014	−	0.842936i	$-0.319175\pi$
$313$	19.0369			1.07603			0.538014	+	0.842936i	$0.319175\pi$
$314$	11.6703			0.658592
$315$	13.2562	−	11.8014i	0.746903	−	0.664933i
$316$	13.4434			0.756253
$317$	−15.4166			−0.865882			−0.432941	−	0.901422i	$-0.642524\pi$
$317$	−15.4166			−0.865882			−0.432941	+	0.901422i	$0.642524\pi$
$318$	−8.72922	+	13.0990i	−0.489511	+	0.734553i
$319$	11.2756			0.631312
$320$	0.719036	+	2.11731i	0.0401953	+	0.118361i
$321$	14.9984	+	0.964573i	0.837131	+	0.0538372i
$322$	1.56753	−	0.00763677i	0.0873551	−	0.000425581i
$323$	−2.91064			−0.161952
$324$	−2.37200	−	8.68180i	−0.131778	−	0.482322i
$325$	−1.55066	−	11.7548i	−0.0860154	−	0.652039i
$326$	10.7728	+	6.21967i	0.596649	+	0.344475i
$327$	−14.5146	+	21.7804i	−0.802658	+	1.20446i
$328$	0.257087	−	0.445287i	0.0141952	−	0.0245869i
$329$	9.48891	+	5.41696i	0.523141	+	0.298647i
$330$	15.4113	−	4.15187i	0.848365	−	0.228553i
$331$	−30.9300			−1.70007			−0.850033	−	0.526730i	$-0.823418\pi$
$331$	−30.9300			−1.70007			−0.850033	+	0.526730i	$0.823418\pi$
$332$	3.80374	−	2.19609i	0.208757	−	0.120526i
$333$	−19.3591	+	8.07452i	−1.06087	+	0.442481i
$334$	−11.4205	−	6.59363i	−0.624902	−	0.360787i
$335$	−28.6154	+	9.71777i	−1.56343	+	0.530939i
$336$	4.57451	+	0.271822i	0.249560	+	0.0148291i
$337$	−21.3417	−	12.3216i	−1.16256	−	0.671202i	−0.210640	−	0.977564i	$-0.567555\pi$
$337$	−21.3417	−	12.3216i	−1.16256	−	0.671202i	−0.951915	+	0.306362i	$0.900888\pi$
$338$	3.68840	+	6.38850i	0.200623	+	0.347489i
$339$	−1.73984	−	0.111892i	−0.0944953	−	0.00607714i
$340$	−4.42869	−	3.88283i	−0.240179	−	0.210576i
$341$	5.55839	−	9.62741i	0.301003	−	0.521353i
$342$	−3.05961	+	1.27614i	−0.165445	+	0.0690056i
$343$	18.5183	−	0.270672i	0.999893	−	0.0146149i
$344$	10.4023	−	6.00577i	0.560854	−	0.323809i
$345$	−2.21727	−	0.590893i	−0.119374	−	0.0318126i
$346$		−	14.8129i		−	0.796347i
$347$	0.546144			0.0293186			0.0146593	−	0.999893i	$-0.495334\pi$
$347$	0.546144			0.0293186			0.0146593	+	0.999893i	$0.495334\pi$
$348$	−3.94360	−	2.62804i	−0.211399	−	0.140878i
$349$	−5.63017	+	3.25058i	−0.301376	+	0.174000i	−0.643061	−	0.765815i	$-0.722336\pi$
$349$	−5.63017	+	3.25058i	−0.301376	+	0.174000i	0.341685	+	0.939815i	$0.389003\pi$
$350$	−1.79399	−	13.1065i	−0.0958927	−	0.700574i
$351$	−8.09017	+	9.29384i	−0.431821	+	0.496069i
$352$	3.56894	+	2.06053i	0.190225	+	0.109827i
$353$	−5.67627	−	3.27719i	−0.302117	−	0.174427i	0.341276	−	0.939963i	$-0.389141\pi$
$353$	−5.67627	−	3.27719i	−0.302117	−	0.174427i	−0.643394	+	0.765536i	$0.722474\pi$
$354$	5.32932	+	10.7735i	0.283250	+	0.572603i
$355$	3.39115	−	1.15163i	0.179984	−	0.0611224i
$356$	−7.82648	+	13.5559i	−0.414802	+	0.718459i
$357$	−10.7929	+	5.40456i	−0.571222	+	0.286040i
$358$	20.6373	−	11.9149i	1.09071	−	0.629724i
$359$	−3.55244	−	2.05100i	−0.187490	−	0.108248i	0.403317	−	0.915060i	$-0.367857\pi$
$359$	−3.55244	−	2.05100i	−0.187490	−	0.108248i	−0.590807	+	0.806813i	$0.701191\pi$
$360$	−6.35775	−	2.13986i	−0.335083	−	0.112781i
$361$	−8.88946	−	15.3970i	−0.467866	−	0.810368i
$362$		−	11.6911i		−	0.614470i
$363$	5.74684	−	8.62364i	0.301631	−	0.452624i
$364$	−3.16341	−	5.41805i	−0.165807	−	0.283983i
$365$	9.70408	−	11.0683i	0.507935	−	0.579341i
$366$	6.66521	−	3.29709i	0.348396	−	0.172342i
$367$	10.0785	−	17.4565i	0.526096	−	0.911224i	−0.473442	−	0.880825i	$-0.656989\pi$
$367$	10.0785	−	17.4565i	0.526096	−	0.911224i	0.999538	−	0.0303995i	$-0.00967796\pi$
$368$	−0.296239	−	0.513101i	−0.0154425	−	0.0267473i
$369$	0.593792	+	1.42365i	0.0309116	+	0.0741123i
$370$	−3.04810	+	15.3342i	−0.158463	+	0.797190i
$371$	24.0446	−	0.117142i	1.24834	−	0.00608170i
$372$	−4.18792	+	2.07164i	−0.217133	+	0.107410i
$373$	−4.94553	+	2.85530i	−0.256070	+	0.147842i	−0.622540	−	0.782588i	$-0.713899\pi$
$373$	−4.94553	+	2.85530i	−0.256070	+	0.147842i	0.366471	+	0.930430i	$0.380566\pi$
$374$	−10.8549			−0.561291
$375$	−2.49657	+	19.2033i	−0.128922	+	0.991655i
$376$		−	4.12973i		−	0.212975i
$377$			6.48817i			0.334158i
$378$	−8.97578	+	10.4132i	−0.461664	+	0.535599i
$379$	5.42424			0.278624			0.139312	−	0.990249i	$-0.455511\pi$
$379$	5.42424			0.278624			0.139312	+	0.990249i	$0.455511\pi$
$380$	−0.481736	+	2.42350i	−0.0247125	+	0.124323i
$381$	4.85212	−	2.40020i	0.248581	−	0.122966i
$382$		−	26.0254i		−	1.33158i
$383$	28.8586	−	16.6615i	1.47460	−	0.851363i	0.475013	−	0.879979i	$-0.342443\pi$
$383$	28.8586	−	16.6615i	1.47460	−	0.851363i	0.999590	+	0.0286163i	$0.00911009\pi$
$384$	−0.767971	−	1.55249i	−0.0391904	−	0.0792251i
$385$	−18.4104	−	15.9833i	−0.938282	−	0.814584i
$386$			18.0736i			0.919920i
$387$	−4.61580	+	35.7378i	−0.234634	+	1.81665i
$388$	−6.92406	−	11.9928i	−0.351516	−	0.608844i
$389$	25.3567	+	14.6397i	1.28564	+	0.742263i	0.977873	−	0.209200i	$-0.0670860\pi$
$389$	25.3567	+	14.6397i	1.28564	+	0.742263i	0.307764	+	0.951463i	$0.400419\pi$
$390$	2.38906	+	8.86794i	0.120975	+	0.449046i
$391$	1.35151	+	0.780293i	0.0683486	+	0.0394611i
$392$	−3.55890	−	6.02779i	−0.179752	−	0.304449i
$393$	−20.7221	+	31.0953i	−1.04529	+	1.56855i
$394$	19.0964			0.962063
$395$	9.66632	+	28.4639i	0.486365	+	1.43217i
$396$	−11.4104	+	4.75919i	−0.573396	+	0.239158i
$397$	5.42713	−	9.40006i	0.272380	−	0.471775i	−0.697091	−	0.716983i	$-0.745523\pi$
$397$	5.42713	−	9.40006i	0.272380	−	0.471775i	0.969471	+	0.245207i	$0.0788560\pi$
$398$	21.6198	−	12.4822i	1.08370	−	0.625676i
$399$	4.22753	+	2.78761i	0.211641	+	0.139555i
$400$	−3.96597	+	3.04484i	−0.198299	+	0.152242i
$401$	−15.8321	+	9.14066i	−0.790616	+	0.456463i	−0.840180	−	0.542308i	$-0.817550\pi$
$401$	−15.8321	+	9.14066i	−0.790616	+	0.456463i	0.0495631	+	0.998771i	$0.484217\pi$
$402$	20.9819	−	10.3791i	1.04648	−	0.517664i
$403$	5.53978	+	3.19839i	0.275956	+	0.159323i
$404$	1.35453	−	2.34612i	0.0673905	−	0.116724i
$405$	16.6765	−	11.2648i	0.828661	−	0.559751i
$406$	0.0352670	+	7.23893i	0.00175027	+	0.359262i
$407$	14.4069	+	24.9535i	0.714124	+	1.23690i
$408$	3.79645	+	2.52998i	0.187952	+	0.125252i
$409$		−	9.67827i		−	0.478560i	−0.970951	−	0.239280i	$-0.923089\pi$
$409$		−	9.67827i		−	0.478560i	0.970951	−	0.239280i	$-0.0769113\pi$
$410$	1.12766	+	0.224154i	0.0556914	+	0.0110702i
$411$	6.51282	+	0.418850i	0.321254	+	0.0206603i
$412$	9.07239	+	15.7138i	0.446964	+	0.774165i
$413$	9.10250	−	15.9449i	0.447905	−	0.784596i
$414$	1.76279	+	0.227678i	0.0866365	+	0.0111897i
$415$	7.38482	+	6.47461i	0.362507	+	0.317826i
$416$	−1.18566	+	2.05363i	−0.0581320	+	0.100688i
$417$	0.668297	−	10.3915i	0.0327266	−	0.508876i
$418$	2.27694	+	3.94378i	0.111369	+	0.192896i
$419$	5.02659	−	8.70630i	0.245565	−	0.425331i	−0.716725	−	0.697355i	$-0.754360\pi$
$419$	5.02659	−	8.70630i	0.245565	−	0.425331i	0.962290	+	0.272025i	$0.0876932\pi$
$420$	2.71370	+	9.88108i	0.132415	+	0.482147i
$421$	−6.61761	−	11.4620i	−0.322522	−	0.558625i	0.658485	−	0.752594i	$-0.271197\pi$
$421$	−6.61761	−	11.4620i	−0.322522	−	0.558625i	−0.981008	+	0.193968i	$0.937864\pi$
$422$	−6.61689	+	11.4608i	−0.322105	+	0.557902i
$423$	9.84749	+	7.51793i	0.478801	+	0.365534i
$424$	−4.54406	−	7.87055i	−0.220679	−	0.382228i
$425$	5.03676	−	12.1688i	0.244319	−	0.590273i
$426$	−2.48652	+	1.23001i	−0.120472	+	0.0595942i
$427$	−9.86461	−	5.63143i	−0.477382	−	0.272524i
$428$	−4.33862	+	7.51471i	−0.209715	+	0.363237i
$429$	14.0852	+	9.38646i	0.680040	+	0.453182i
$430$	20.1957	+	17.7065i	0.973923	+	0.853883i
$431$	4.44716	−	2.56757i	0.214212	−	0.123675i	−0.389055	−	0.921214i	$-0.627199\pi$
$431$	4.44716	−	2.56757i	0.214212	−	0.123675i	0.603267	+	0.797539i	$0.293865\pi$
$432$	5.10001	+	0.994957i	0.245374	+	0.0478699i
$433$	7.97362			0.383188			0.191594	−	0.981474i	$-0.438634\pi$
$433$	7.97362			0.383188			0.191594	+	0.981474i	$0.438634\pi$
$434$	6.19818	+	3.53837i	0.297522	+	0.169847i
$435$	2.72877	−	10.2395i	0.130835	−	0.490945i
$436$	−7.55567	−	13.0868i	−0.361851	−	0.626745i
$437$		−	0.654705i		−	0.0313188i
$438$	−6.32298	+	9.48818i	−0.302124	+	0.453363i
$439$			25.8078i			1.23174i	0.787849	+	0.615869i	$0.211195\pi$
$439$			25.8078i			1.23174i	−0.787849	+	0.615869i	$0.788805\pi$
$440$	−1.79657	+	9.03814i	−0.0856483	+	0.430876i
$441$	20.8522	+	2.48691i	0.992963	+	0.118424i
$442$		−	6.24607i		−	0.297095i
$443$	31.2880			1.48654			0.743269	−	0.668992i	$-0.233274\pi$
$443$	31.2880			1.48654			0.743269	+	0.668992i	$0.233274\pi$
$444$	0.777223	−	12.0853i	0.0368854	−	0.573542i
$445$	−34.3294	−	6.82390i	−1.62737	−	0.323484i
$446$	2.44383	+	4.23284i	0.115719	+	0.200431i
$447$	16.1310	+	10.7498i	0.762971	+	0.508448i
$448$	−1.31170	+	2.29771i	−0.0619719	+	0.108556i
$449$			6.93666i			0.327361i	0.986513	+	0.163681i	$0.0523366\pi$
$449$			6.93666i			0.327361i	−0.986513	+	0.163681i	$0.947663\pi$
$450$	−0.0407079	−	14.9999i	−0.00191899	−	0.707104i
$451$	1.83506	−	1.05947i	0.0864094	−	0.0498885i
$452$	0.503287	−	0.871718i	0.0236726	−	0.0410022i
$453$	−32.0622	−	2.06197i	−1.50641	−	0.0968799i
$454$	10.3873	+	5.99711i	0.487500	+	0.281458i
$455$	9.19707	−	10.5937i	0.431165	−	0.496639i
$456$	0.122836	−	1.91002i	0.00575233	−	0.0894448i
$457$			27.4150i			1.28242i	0.767366	+	0.641209i	$0.221567\pi$
$457$			27.4150i			1.28242i	−0.767366	+	0.641209i	$0.778433\pi$
$458$	9.16676	−	5.29243i	0.428335	−	0.247299i
$459$	−12.9440	+	4.44709i	−0.604175	+	0.207573i
$460$	0.873386	−	0.996168i	0.0407218	−	0.0464466i
$461$	−9.16139	−	15.8680i	−0.426689	−	0.739046i	0.569888	−	0.821722i	$-0.306987\pi$
$461$	−9.16139	−	15.8680i	−0.426689	−	0.739046i	−0.996576	+	0.0826762i	$0.973653\pi$
$462$	15.7660	+	10.3960i	0.733503	+	0.483667i
$463$	−16.6964	−	9.63966i	−0.775947	−	0.447993i	0.0590450	−	0.998255i	$-0.481194\pi$
$463$	−16.6964	−	9.63966i	−0.775947	−	0.447993i	−0.834992	+	0.550262i	$0.814528\pi$
$464$	2.36953	−	1.36805i	0.110002	−	0.0635099i
$465$	−7.39757	−	7.37752i	−0.343054	−	0.342124i
$466$	0.259858	−	0.450088i	0.0120377	−	0.0208499i
$467$	11.2146	+	6.47476i	0.518951	+	0.299616i	0.736505	−	0.676432i	$-0.236475\pi$
$467$	11.2146	+	6.47476i	0.518951	+	0.299616i	−0.217555	+	0.976048i	$0.569808\pi$
$468$	−2.73852	−	6.56577i	−0.126588	−	0.303503i
$469$	−31.0535	−	17.7276i	−1.43392	−	0.818584i
$470$	8.74391	−	2.96943i	0.403327	−	0.136970i
$471$	−8.96244	−	18.1180i	−0.412967	−	0.834832i
$472$	−6.93948			−0.319415
$473$	49.5003			2.27602
$474$	−10.3242	−	20.8708i	−0.474205	−	0.958627i
$475$	−5.47768	+	0.722602i	−0.251333	+	0.0331552i
$476$	−0.0339510	−	6.96882i	−0.00155614	−	0.319415i
$477$	27.0398	+	3.49239i	1.23807	+	0.159905i
$478$	−2.39886	−	1.38498i	−0.109721	−	0.0633475i
$479$	−13.5378	+	23.4482i	−0.618560	+	1.07138i	0.371189	+	0.928557i	$0.378950\pi$
$479$	−13.5378	+	23.4482i	−0.618560	+	1.07138i	−0.989749	+	0.142820i	$0.954383\pi$
$480$	2.73489	−	2.74233i	0.124830	−	0.125170i
$481$	−14.3587	+	8.28999i	−0.654700	+	0.377991i
$482$	17.4943	+	10.1004i	0.796845	+	0.460059i
$483$	−1.21568	−	2.42771i	−0.0553152	−	0.110465i
$484$	2.99156	+	5.18154i	0.135980	+	0.235524i
$485$	20.4138	−	23.2836i	0.926945	−	1.05726i
$486$	−11.6568	+	10.3499i	−0.528761	+	0.469480i
$487$	2.98800	−	1.72512i	0.135399	−	0.0781727i	−0.430770	−	0.902462i	$-0.641758\pi$
$487$	2.98800	−	1.72512i	0.135399	−	0.0781727i	0.566169	+	0.824289i	$0.308425\pi$
$488$			4.29324i			0.194346i
$489$	1.38277	−	21.5011i	0.0625311	−	0.972315i
$490$	10.2037	−	11.8695i	0.460956	−	0.536209i
$491$	−36.9916	−	21.3571i	−1.66941	−	0.963833i	−0.967958	−	0.251113i	$-0.919203\pi$
$491$	−36.9916	−	21.3571i	−1.66941	−	0.963833i	−0.701449	−	0.712719i	$-0.747463\pi$
$492$	−0.888739	−	0.0571562i	−0.0400674	−	0.00257680i
$493$	−3.60343	+	6.24132i	−0.162290	+	0.281095i
$494$	−2.26932	+	1.31019i	−0.102101	+	0.0589483i
$495$	−18.2812	−	20.7374i	−0.821678	−	0.932076i
$496$		−	2.69755i		−	0.121124i
$497$	3.68009	+	2.10086i	0.165075	+	0.0942365i
$498$	−6.33057	−	4.21872i	−0.283679	−	0.189046i
$499$	−18.0193	−	31.2103i	−0.806654	−	1.39717i	−0.915169	−	0.403071i	$-0.867943\pi$
$499$	−18.0193	−	31.2103i	−0.806654	−	1.39717i	0.108514	−	0.994095i	$-0.465391\pi$
$500$	−9.29854	−	6.20783i	−0.415843	−	0.277623i
$501$	−1.46591	+	22.7939i	−0.0654922	+	1.01836i
$502$	−20.9869			−0.936691
$503$			4.41774i			0.196977i	0.995138	+	0.0984887i	$0.0314008\pi$
$503$			4.41774i			0.196977i	−0.995138	+	0.0984887i	$0.968599\pi$
$504$	−3.09109	−	7.31062i	−0.137688	−	0.325641i
$505$	5.94141	+	1.18102i	0.264389	+	0.0525545i
$506$		−	2.44164i		−	0.108544i
$507$	7.08548	−	10.6324i	0.314677	−	0.472201i
$508$			3.12538i			0.138666i
$509$	12.1022	+	20.9617i	0.536422	+	0.929110i	0.999093	+	0.0425803i	$0.0135578\pi$
$509$	12.1022	+	20.9617i	0.536422	+	0.929110i	−0.462671	+	0.886530i	$0.653109\pi$
$510$	−2.62695	+	9.85739i	−0.116323	+	0.436493i
$511$	17.4166	−	0.0848512i	0.770467	−	0.00375360i
$512$	1.00000			0.0441942
$513$	4.33088	+	3.76998i	0.191213	+	0.166449i
$514$	−8.21246	+	4.74146i	−0.362236	+	0.209137i
$515$	−26.7476	+	30.5078i	−1.17864	+	1.34434i
$516$	−17.3126	−	11.5372i	−0.762143	−	0.507896i
$517$	8.50944	−	14.7388i	0.374245	−	0.648211i
$518$	−15.9751	+	9.32729i	−0.701905	+	0.409818i
$519$	−22.9969	+	11.3759i	−1.00945	+	0.499346i
$520$	−5.20070	−	1.03378i	−0.228066	−	0.0453342i
$521$	7.58138	+	13.1313i	0.332146	+	0.575294i	0.982932	−	0.183967i	$-0.0588940\pi$
$521$	7.58138	+	13.1313i	0.332146	+	0.575294i	−0.650786	+	0.759261i	$0.725561\pi$
$522$	−1.05143	+	8.14066i	−0.0460197	+	0.356307i
$523$	0.294517	−	0.510118i	0.0128783	−	0.0223059i	−0.859514	−	0.511111i	$-0.829234\pi$
$523$	0.294517	−	0.510118i	0.0128783	−	0.0223059i	0.872393	+	0.488806i	$0.162567\pi$
$524$	−10.7870	−	18.6837i	−0.471234	−	0.816202i
$525$	−18.9700	+	12.8506i	−0.827920	+	0.560846i
$526$	5.83660	−	10.1093i	0.254488	−	0.440786i
$527$	3.55267	+	6.15341i	0.154757	+	0.268047i
$528$	0.458102	−	7.12317i	0.0199363	−	0.309996i
$529$	11.3245	−	19.6146i	0.492369	−	0.852808i
$530$	13.3970	−	15.2804i	0.581929	−	0.663738i
$531$	12.6329	−	16.5474i	0.548221	−	0.718097i
$532$	−2.52478	+	1.47413i	−0.109463	+	0.0639117i
$533$	0.609637	+	1.05592i	0.0264063	+	0.0457371i
$534$	27.0558	+	1.74000i	1.17082	+	0.0752973i
$535$	−19.0306	−	3.78284i	−0.822763	−	0.163546i
$536$			13.5150i			0.583759i
$537$	−34.3466	−	22.8888i	−1.48217	−	0.987725i
$538$	8.14330	+	14.1046i	0.351082	+	0.608093i
$539$	−0.281074	−	28.8460i	−0.0121067	−	1.24249i
$540$	1.56046	+	11.5137i	0.0671515	+	0.495470i
$541$	−21.2555	+	36.8156i	−0.913846	+	1.58283i	−0.105264	+	0.994444i	$0.533569\pi$
$541$	−21.2555	+	36.8156i	−0.913846	+	1.58283i	−0.808582	+	0.588384i	$0.799764\pi$
$542$	21.8041	+	12.5886i	0.936566	+	0.540726i
$543$	−18.1503	+	8.97843i	−0.778903	+	0.385301i
$544$	−2.28111	+	1.31700i	−0.0978017	+	0.0564658i
$545$	22.2760	−	25.4076i	0.954198	−	1.08834i
$546$	−5.98205	+	9.07206i	−0.256008	+	0.388248i
$547$	−7.46589	+	4.31044i	−0.319219	+	0.184301i	−0.651044	−	0.759040i	$-0.725669\pi$
$547$	−7.46589	+	4.31044i	−0.319219	+	0.184301i	0.331826	+	0.943341i	$0.392335\pi$
$548$	−1.88397	+	3.26314i	−0.0804793	+	0.139394i
$549$	−10.2374	−	7.81559i	−0.436921	−	0.333561i
$550$	−20.4283	+	2.69485i	−0.871066	+	0.114909i
$551$	3.02346			0.128804
$552$	−0.569081	+	0.853955i	−0.0242217	+	0.0363467i
$553$	−17.6337	+	30.8891i	−0.749862	+	1.31354i
$554$	−17.9632	−	10.3710i	−0.763182	−	0.440623i
$555$	26.1471	−	7.04413i	1.10988	−	0.299007i
$556$	5.20651	+	3.00598i	0.220805	+	0.127482i
$557$	−3.09319	−	5.35757i	−0.131063	−	0.227007i	0.793024	−	0.609191i	$-0.208506\pi$
$557$	−3.09319	−	5.35757i	−0.131063	−	0.227007i	−0.924087	+	0.382183i	$0.875172\pi$
$558$	6.43240	+	4.91073i	0.272305	+	0.207888i
$559$			28.4833i			1.20472i
$560$	−5.80810	−	1.12513i	−0.245437	−	0.0475455i
$561$	8.33622	+	16.8520i	0.351955	+	0.711493i
$562$	1.17815	−	0.680206i	0.0496974	−	0.0286928i
$563$		−	32.6001i		−	1.37393i	−0.726690	−	0.686966i	$-0.758942\pi$
$563$		−	32.6001i		−	1.37393i	0.726690	−	0.686966i	$-0.241058\pi$
$564$	−6.41136	+	3.17152i	−0.269967	+	0.133545i
$565$	2.20758	+	0.438815i	0.0928734	+	0.0184611i
$566$	−14.9351			−0.627771
$567$	23.0596	+	5.93773i	0.968410	+	0.249361i
$568$		−	1.60164i		−	0.0672032i
$569$		−	6.56784i		−	0.275338i	−0.990478	−	0.137669i	$-0.956039\pi$
$569$		−	6.56784i		−	0.275338i	0.990478	−	0.137669i	$-0.0439611\pi$
$570$	4.13242	−	1.11329i	0.173088	−	0.0466306i
$571$	−17.9871			−0.752737			−0.376369	−	0.926470i	$-0.622827\pi$
$571$	−17.9871			−0.752737			−0.376369	+	0.926470i	$0.622827\pi$
$572$	−8.46313	+	4.88619i	−0.353861	+	0.204302i
$573$	−40.4042	+	19.9868i	−1.68791	+	0.834960i
$574$	0.685919	+	1.17479i	0.0286297	+	0.0490349i
$575$	2.73719	+	1.13295i	0.114149	+	0.0472471i
$576$	−1.82044	+	2.38453i	−0.0758516	+	0.0993556i
$577$	11.8915	+	20.5968i	0.495051	+	0.857454i	0.999984	−	0.00570479i	$-0.00181590\pi$
$577$	11.8915	+	20.5968i	0.495051	+	0.857454i	−0.504932	+	0.863159i	$0.668483\pi$
$578$	−5.03103	+	8.71400i	−0.209263	+	0.362455i
$579$	28.0590	−	13.8800i	1.16609	−	0.576832i
$580$	4.60035	+	4.03334i	0.191019	+	0.167475i
$581$	0.0566132	+	11.6205i	0.00234871	+	0.482098i
$582$	−13.3012	+	19.9597i	−0.551354	+	0.827355i
$583$		−	37.4527i		−	1.55113i
$584$	−3.29147	−	5.70100i	−0.136202	−	0.235909i
$585$	11.9326	−	10.5193i	0.493354	−	0.434920i
$586$	9.63607	+	5.56339i	0.398062	+	0.229821i
$587$	−14.2796	+	8.24435i	−0.589384	+	0.340281i	−0.764854	−	0.644204i	$-0.777189\pi$
$587$	−14.2796	+	8.24435i	−0.589384	+	0.340281i	0.175470	+	0.984485i	$0.443855\pi$
$588$	−6.62494	+	10.1543i	−0.273208	+	0.418757i
$589$	1.49043	−	2.58151i	0.0614123	−	0.106369i
$590$	−4.98974	−	14.6930i	−0.205424	−	0.604902i
$591$	−14.6655	−	29.6470i	−0.603258	−	1.21951i
$592$	6.05512	+	3.49593i	0.248864	+	0.143682i
$593$	8.69178	+	5.01820i	0.356928	+	0.206073i	0.667733	−	0.744401i	$-0.267265\pi$
$593$	8.69178	+	5.01820i	0.356928	+	0.206073i	−0.310804	+	0.950474i	$0.600598\pi$
$594$	16.1515	+	14.0597i	0.662703	+	0.576875i
$595$	14.7307	−	5.08272i	0.603900	−	0.208371i
$596$	−9.69236	+	5.59589i	−0.397015	+	0.229217i
$597$	−35.9819	−	23.9785i	−1.47264	−	0.981376i
$598$	1.40496			0.0574531
$599$		−	35.1519i		−	1.43627i	−0.695905	−	0.718134i	$-0.744997\pi$
$599$		−	35.1519i		−	1.43627i	0.695905	−	0.718134i	$-0.255003\pi$
$600$	7.77283	+	3.81878i	0.317325	+	0.155901i
$601$	−32.5093	+	18.7692i	−1.32608	+	0.765613i	−0.984691	−	0.174309i	$-0.944231\pi$
$601$	−32.5093	+	18.7692i	−1.32608	+	0.765613i	−0.341390	+	0.939922i	$0.610898\pi$
$602$	0.154823	+	31.7792i	0.00631013	+	1.29522i
$603$	−32.2270	−	24.6032i	−1.31238	−	1.00192i
$604$	9.27469	−	16.0642i	0.377382	−	0.653644i
$605$	−8.81986	+	10.0598i	−0.358578	+	0.408988i
$606$	−4.68257	−	0.301143i	−0.190216	−	0.0122331i
$607$	−12.0927	−	20.9451i	−0.490827	−	0.850136i	0.509118	−	0.860697i	$-0.329972\pi$
$607$	−12.0927	−	20.9451i	−0.490827	−	0.850136i	−0.999944	+	0.0105604i	$0.996638\pi$
$608$	0.956982	+	0.552514i	0.0388107	+	0.0224074i
$609$	11.2113	−	5.61405i	0.454304	−	0.227493i
$610$	−9.09011	+	3.08700i	−0.368048	+	0.124989i
$611$	8.48095	+	4.89648i	0.343102	+	0.198090i
$612$	1.01219	−	7.83689i	0.0409155	−	0.316788i
$613$	−23.6618	+	13.6611i	−0.955690	+	0.551768i	−0.894844	−	0.446379i	$-0.852713\pi$
$613$	−23.6618	+	13.6611i	−0.955690	+	0.551768i	−0.0608460	+	0.998147i	$0.519380\pi$
$614$	−14.1337			−0.570388
$615$	−0.518018	−	1.92283i	−0.0208885	−	0.0775360i
$616$	−9.41586	+	5.49759i	−0.379376	+	0.221504i
$617$	−7.76658	+	13.4521i	−0.312671	+	0.541562i	−0.978940	−	0.204150i	$-0.934557\pi$
$617$	−7.76658	+	13.4521i	−0.312671	+	0.541562i	0.666269	+	0.745712i	$0.267890\pi$
$618$	17.4282	−	26.1526i	0.701065	−	1.05201i
$619$	18.4101	+	10.6291i	0.739963	+	0.427218i	0.822056	−	0.569407i	$-0.192827\pi$
$619$	18.4101	+	10.6291i	0.739963	+	0.427218i	−0.0820931	+	0.996625i	$0.526160\pi$
$620$	5.71154	−	1.93964i	0.229381	−	0.0778977i
$621$	−1.00031	−	2.91157i	−0.0401410	−	0.116837i
$622$	−5.87504			−0.235568
$623$	−20.8814	−	35.7641i	−0.836595	−	1.43286i
$624$	4.09879	+	0.263600i	0.164083	+	0.0105524i
$625$	6.45790	−	24.1515i	0.258316	−	0.966061i
$626$	19.0369			0.760866
$627$	4.37404	−	6.56363i	0.174682	−	0.262126i
$628$	11.6703			0.465695
$629$	−18.4165			−0.734314
$630$	13.2562	−	11.8014i	0.528140	−	0.470178i
$631$	22.0357			0.877226			0.438613	−	0.898676i	$-0.355470\pi$
$631$	22.0357			0.877226			0.438613	+	0.898676i	$0.355470\pi$
$632$	13.4434			0.534751
$633$	22.8743	+	1.47108i	0.909172	+	0.0584703i
$634$	−15.4166			−0.612271
$635$	−6.61739	+	2.24726i	−0.262603	+	0.0891799i
$636$	−8.72922	+	13.0990i	−0.346136	+	0.519408i
$637$	16.5985	−	0.161735i	0.657657	−	0.00640816i
$638$	11.2756			0.446405
$639$	3.81915	+	2.91568i	0.151083	+	0.115343i
$640$	0.719036	+	2.11731i	0.0284224	+	0.0836939i
$641$	22.2308	+	12.8350i	0.878065	+	0.506951i	0.870020	−	0.493016i	$-0.164106\pi$
$641$	22.2308	+	12.8350i	0.878065	+	0.506951i	0.00804523	+	0.999968i	$0.497439\pi$
$642$	14.9984	+	0.964573i	0.591941	+	0.0380687i
$643$	0.505064	−	0.874797i	0.0199178	−	0.0344986i	−0.855895	−	0.517150i	$-0.826993\pi$
$643$	0.505064	−	0.874797i	0.0199178	−	0.0344986i	0.875813	+	0.482651i	$0.160326\pi$
$644$	1.56753	−	0.00763677i	0.0617694	−	0.000300931i
$645$	11.9794	−	44.9517i	0.471689	−	1.76997i
$646$	−2.91064			−0.114517
$647$	12.5056	−	7.22013i	0.491647	−	0.283852i	−0.233611	−	0.972330i	$-0.575054\pi$
$647$	12.5056	−	7.22013i	0.491647	−	0.283852i	0.725257	+	0.688478i	$0.241721\pi$
$648$	−2.37200	−	8.68180i	−0.0931809	−	0.341053i
$649$	−24.7666	−	14.2990i	−0.972174	−	0.561285i
$650$	−1.55066	−	11.7548i	−0.0608220	−	0.461061i
$651$	0.733255	−	12.3400i	0.0287385	−	0.483642i
$652$	10.7728	+	6.21967i	0.421895	+	0.243581i
$653$	−22.1117	−	38.2986i	−0.865299	−	1.49874i	−0.866750	−	0.498743i	$-0.833795\pi$
$653$	−22.1117	−	38.2986i	−0.865299	−	1.49874i	0.00145120	−	0.999999i	$-0.499538\pi$
$654$	−14.5146	+	21.7804i	−0.567565	+	0.851681i
$655$	31.8029	−	36.2738i	1.24264	−	1.41733i
$656$	0.257087	−	0.445287i	0.0100376	−	0.0173855i
$657$	19.5862	+	2.52970i	0.764129	+	0.0986929i
$658$	9.48891	+	5.41696i	0.369916	+	0.211175i
$659$	−24.1702	+	13.9547i	−0.941539	+	0.543598i	−0.890442	−	0.455096i	$-0.849605\pi$
$659$	−24.1702	+	13.9547i	−0.941539	+	0.543598i	−0.0510965	+	0.998694i	$0.516272\pi$
$660$	15.4113	−	4.15187i	0.599885	−	0.161611i
$661$			0.0428492i			0.00166664i	1.00000		0.000833320i	$0.000265254\pi$
$661$			0.0428492i			0.00166664i	−1.00000		0.000833320i	$0.999735\pi$
$662$	−30.9300			−1.20213
$663$	−9.69695	+	4.79680i	−0.376598	+	0.186292i
$664$	3.80374	−	2.19609i	0.147614	−	0.0852248i
$665$	−4.93660	−	4.28579i	−0.191433	−	0.166196i
$666$	−19.3591	+	8.07452i	−0.750151	+	0.312881i
$667$	−1.40389	−	0.810538i	−0.0543589	−	0.0313841i
$668$	−11.4205	−	6.59363i	−0.441873	−	0.255115i
$669$	4.69464	−	7.04472i	0.181505	−	0.272364i
$670$	−28.6154	+	9.71777i	−1.10551	+	0.375430i
$671$	−8.84635	+	15.3223i	−0.341510	+	0.591512i
$672$	4.57451	+	0.271822i	0.176465	+	0.0104858i
$673$	−17.4536	+	10.0769i	−0.672788	+	0.388434i	−0.797132	−	0.603805i	$-0.793651\pi$
$673$	−17.4536	+	10.0769i	−0.672788	+	0.388434i	0.124344	+	0.992239i	$0.460317\pi$
$674$	−21.3417	−	12.3216i	−0.822051	−	0.474611i
$675$	−23.2560	+	11.5827i	−0.895123	+	0.445819i
$676$	3.68840	+	6.38850i	0.141862	+	0.245711i
$677$		−	28.0616i		−	1.07850i	−0.842147	−	0.539248i	$-0.818709\pi$
$677$		−	28.0616i		−	1.07850i	0.842147	−	0.539248i	$-0.181291\pi$
$678$	−1.73984	−	0.111892i	−0.0668182	−	0.00429719i
$679$	36.6383	−	0.178496i	1.40605	−	0.00685005i
$680$	−4.42869	−	3.88283i	−0.169832	−	0.148900i
$681$	1.33329	−	20.7318i	0.0510919	−	0.794443i
$682$	5.55839	−	9.62741i	0.212842	−	0.368652i
$683$	−14.7248	−	25.5040i	−0.563428	−	0.975885i	−0.997194	−	0.0748598i	$-0.976149\pi$
$683$	−14.7248	−	25.5040i	−0.563428	−	0.975885i	0.433767	−	0.901025i	$-0.357184\pi$
$684$	−3.05961	+	1.27614i	−0.116987	+	0.0487943i
$685$	−8.26371	−	1.64263i	−0.315740	−	0.0627618i
$686$	18.5183	−	0.270672i	0.707031	−	0.0103343i
$687$	−15.2562	−	10.1669i	−0.582062	−	0.387890i
$688$	10.4023	−	6.00577i	0.396584	−	0.228968i
$689$	21.5509			0.821025
$690$	−2.21727	−	0.590893i	−0.0844102	−	0.0224949i
$691$			6.96725i			0.265047i	0.991180	+	0.132523i	$0.0423080\pi$
$691$			6.96725i			0.265047i	−0.991180	+	0.132523i	$0.957692\pi$
$692$		−	14.8129i		−	0.563102i
$693$	4.03183	−	32.4605i	0.153156	−	1.23307i
$694$	0.546144			0.0207313
$695$	−2.62091	+	13.1852i	−0.0994168	+	0.500142i
$696$	−3.94360	−	2.62804i	−0.149482	−	0.0996156i
$697$			1.35433i			0.0512989i
$698$	−5.63017	+	3.25058i	−0.213105	+	0.123036i
$699$	−0.898320	−	0.0577724i	−0.0339776	−	0.00218515i
$700$	−1.79399	−	13.1065i	−0.0678064	−	0.495381i
$701$		−	17.0338i		−	0.643357i	−0.946849	−	0.321678i	$-0.895753\pi$
$701$		−	17.0338i		−	0.643357i	0.946849	−	0.321678i	$-0.104247\pi$
$702$	−8.09017	+	9.29384i	−0.305344	+	0.350773i
$703$	3.86309	+	6.69107i	0.145699	+	0.252359i
$704$	3.56894	+	2.06053i	0.134510	+	0.0776591i
$705$	−11.3251	−	11.2944i	−0.426527	−	0.425371i
$706$	−5.67627	−	3.27719i	−0.213629	−	0.123339i
$707$	3.61396	+	6.18972i	0.135917	+	0.232788i
$708$	5.32932	+	10.7735i	0.200288	+	0.404892i
$709$	−1.02107			−0.0383470			−0.0191735	−	0.999816i	$-0.506103\pi$
$709$	−1.02107			−0.0383470			−0.0191735	+	0.999816i	$0.506103\pi$
$710$	3.39115	−	1.15163i	0.127268	−	0.0432201i
$711$	−24.4730	+	32.0563i	−0.917808	+	1.20221i
$712$	−7.82648	+	13.5559i	−0.293310	+	0.508027i
$713$	−1.38412	+	0.799121i	−0.0518356	+	0.0299273i
$714$	−10.7929	+	5.40456i	−0.403915	+	0.202261i
$715$	−16.4309	−	14.4057i	−0.614479	−	0.538742i
$716$	20.6373	−	11.9149i	0.771251	−	0.445282i
$717$	−0.307912	+	4.78782i	−0.0114992	+	0.178804i
$718$	−3.55244	−	2.05100i	−0.132576	−	0.0765426i
$719$	−20.6417	+	35.7524i	−0.769804	+	1.33334i	0.167865	+	0.985810i	$0.446313\pi$
$719$	−20.6417	+	35.7524i	−0.769804	+	1.33334i	−0.937669	+	0.347530i	$0.887020\pi$
$720$	−6.35775	−	2.13986i	−0.236939	−	0.0797480i
$721$	−48.0060	+	0.233878i	−1.78784	+	0.00871006i
$722$	−8.88946	−	15.3970i	−0.330831	−	0.573017i
$723$	2.24554	−	34.9165i	0.0835124	−	1.29856i
$724$		−	11.6911i		−	0.434496i
$725$	−5.23199	+	12.6405i	−0.194311	+	0.469455i
$726$	5.74684	−	8.62364i	0.213285	−	0.320053i
$727$	−7.79834	−	13.5071i	−0.289224	−	0.500951i	0.684400	−	0.729106i	$-0.260064\pi$
$727$	−7.79834	−	13.5071i	−0.289224	−	0.500951i	−0.973625	+	0.228155i	$0.926731\pi$
$728$	−3.16341	−	5.41805i	−0.117244	−	0.200806i
$729$	25.0201	+	10.1486i	0.926671	+	0.375873i
$730$	9.70408	−	11.0683i	0.359164	−	0.409656i
$731$	−15.8192	+	27.3996i	−0.585093	+	1.01341i
$732$	6.66521	−	3.29709i	0.246353	−	0.121864i
$733$	22.3150	+	38.6507i	0.824222	+	1.42759i	0.902512	+	0.430664i	$0.141721\pi$
$733$	22.3150	+	38.6507i	0.824222	+	1.42759i	−0.0782904	+	0.996931i	$0.524946\pi$
$734$	10.0785	−	17.4565i	0.372006	−	0.644333i
$735$	−26.2634	−	6.72570i	−0.968739	−	0.248081i
$736$	−0.296239	−	0.513101i	−0.0109195	−	0.0189132i
$737$	−27.8480	+	48.2342i	−1.02580	+	1.77673i
$738$	0.593792	+	1.42365i	0.0218578	+	0.0524053i
$739$	−14.6785	−	25.4239i	−0.539957	−	0.935233i	−0.998906	−	0.0467704i	$-0.985107\pi$
$739$	−14.6785	−	25.4239i	−0.539957	−	0.935233i	0.458949	−	0.888463i	$-0.348226\pi$
$740$	−3.04810	+	15.3342i	−0.112050	+	0.563698i
$741$	3.77683	+	2.51690i	0.138745	+	0.0924606i
$742$	24.0446	−	0.117142i	0.882706	−	0.00430041i
$743$	−20.1964	+	34.9813i	−0.740936	+	1.28334i	0.211134	+	0.977457i	$0.432284\pi$
$743$	−20.1964	+	34.9813i	−0.740936	+	1.28334i	−0.952070	+	0.305881i	$0.901049\pi$
$744$	−4.18792	+	2.07164i	−0.153537	+	0.0759501i
$745$	−18.8174	−	16.4981i	−0.689415	−	0.604442i
$746$	−4.94553	+	2.85530i	−0.181069	+	0.104540i
$747$	−1.68783	+	13.0680i	−0.0617544	+	0.478133i
$748$	−10.8549			−0.396893
$749$	−11.5756	−	19.8259i	−0.422965	−	0.724423i
$750$	−2.49657	+	19.2033i	−0.0911619	+	0.701206i
$751$	10.9318	+	18.9344i	0.398905	+	0.690924i	0.993591	−	0.113034i	$-0.0360568\pi$
$751$	10.9318	+	18.9344i	0.398905	+	0.690924i	−0.594686	+	0.803958i	$0.702724\pi$
$752$		−	4.12973i		−	0.150596i
$753$	16.1173	+	32.5819i	0.587348	+	1.18735i
$754$			6.48817i			0.236285i
$755$	40.6817	+	8.08659i	1.48056	+	0.294301i
$756$	−8.97578	+	10.4132i	−0.326446	+	0.378725i
$757$		−	14.0506i		−	0.510679i	−0.966851	−	0.255339i	$-0.917813\pi$
$757$		−	14.0506i		−	0.510679i	0.966851	−	0.255339i	$-0.0821872\pi$
$758$	5.42424			0.197017
$759$	−3.79061	+	1.87511i	−0.137591	+	0.0680621i
$760$	−0.481736	+	2.42350i	−0.0174744	+	0.0879096i
$761$	19.5919	+	33.9341i	0.710204	+	1.23011i	0.964780	+	0.263057i	$0.0847307\pi$
$761$	19.5919	+	33.9341i	0.710204	+	1.23011i	−0.254576	+	0.967053i	$0.581936\pi$
$762$	4.85212	−	2.40020i	0.175774	−	0.0869502i
$763$	39.9804	−	0.194778i	1.44739	−	0.00705145i
$764$		−	26.0254i		−	0.941567i
$765$	17.3209	−	3.49189i	0.626239	−	0.126249i
$766$	28.8586	−	16.6615i	1.04270	−	0.602004i
$767$	8.22789	−	14.2511i	0.297092	−	0.514578i
$768$	−0.767971	−	1.55249i	−0.0277118	−	0.0560206i
$769$	16.4424	+	9.49301i	0.592927	+	0.342327i	0.766254	−	0.642538i	$-0.222118\pi$
$769$	16.4424	+	9.49301i	0.592927	+	0.342327i	−0.173327	+	0.984864i	$0.555452\pi$
$770$	−18.4104	−	15.9833i	−0.663465	−	0.575998i
$771$	13.6680	+	9.10843i	0.492241	+	0.328032i
$772$			18.0736i			0.650482i
$773$	−28.9315	+	16.7036i	−1.04060	+	0.600788i	−0.920002	−	0.391914i	$-0.871813\pi$
$773$	−28.9315	+	16.7036i	−1.04060	+	0.600788i	−0.120593	+	0.992702i	$0.538480\pi$
$774$	−4.61580	+	35.7378i	−0.165911	+	1.28457i
$775$	8.21362	+	10.6984i	0.295042	+	0.384299i
$776$	−6.92406	−	11.9928i	−0.248559	−	0.430518i
$777$	26.7489	+	17.6381i	0.959612	+	0.632762i
$778$	25.3567	+	14.6397i	0.909082	+	0.524859i
$779$	0.492055	−	0.284088i	0.0176297	−	0.0101785i
$780$	2.38906	+	8.86794i	0.0855420	+	0.317523i
$781$	3.30022	−	5.71615i	0.118091	−	0.204540i
$782$	1.35151	+	0.780293i	0.0483298	+	0.0279032i
$783$	13.4457	−	4.61947i	0.480512	−	0.165086i
$784$	−3.55890	−	6.02779i	−0.127104	−	0.215278i
$785$	8.39135	+	24.7096i	0.299500	+	0.881922i
$786$	−20.7221	+	31.0953i	−0.739133	+	1.10913i
$787$	0.872685			0.0311079			0.0155539	−	0.999879i	$-0.495049\pi$
$787$	0.872685			0.0311079			0.0155539	+	0.999879i	$0.495049\pi$
$788$	19.0964			0.680281
$789$	−20.1769	−	1.29761i	−0.718316	−	0.0461961i
$790$	9.66632	+	28.4639i	0.343912	+	1.01270i
$791$	1.34279	+	2.29984i	0.0477442	+	0.0817727i
$792$	−11.4104	+	4.75919i	−0.405452	+	0.169111i
$793$	−8.81673	−	5.09034i	−0.313091	−	0.180763i
$794$	5.42713	−	9.40006i	0.192601	−	0.333596i
$795$	−34.0111	−	9.06381i	−1.20625	−	0.321460i
$796$	21.6198	−	12.4822i	0.766294	−	0.442420i
$797$	−24.9244	−	14.3901i	−0.882867	−	0.509724i	−0.0112647	−	0.999937i	$-0.503586\pi$
$797$	−24.9244	−	14.3901i	−0.882867	−	0.509724i	−0.871603	+	0.490213i	$0.836919\pi$
$798$	4.22753	+	2.78761i	0.149653	+	0.0986802i
$799$	5.43885	+	9.42037i	0.192413	+	0.333269i
$800$	−3.96597	+	3.04484i	−0.140218	+	0.107651i
$801$	−18.0768	−	43.3401i	−0.638711	−	1.53135i
$802$	−15.8321	+	9.14066i	−0.559050	+	0.322768i
$803$		−	27.1287i		−	0.957352i
$804$	20.9819	−	10.3791i	0.739974	−	0.366044i
$805$	1.14328	+	3.31345i	0.0402954	+	0.116784i
$806$	5.53978	+	3.19839i	0.195130	+	0.112659i
$807$	15.6434	−	23.4743i	0.550674	−	0.826335i
$808$	1.35453	−	2.34612i	0.0476523	−	0.0825362i
$809$	3.58630	−	2.07055i	0.126088	−	0.0727967i	−0.435630	−	0.900126i	$-0.643474\pi$
$809$	3.58630	−	2.07055i	0.126088	−	0.0727967i	0.561717	+	0.827329i	$0.310141\pi$
$810$	16.6765	−	11.2648i	0.585952	−	0.395804i
$811$			17.4383i			0.612342i	0.951977	+	0.306171i	$0.0990479\pi$
$811$			17.4383i			0.612342i	−0.951977	+	0.306171i	$0.900952\pi$
$812$	0.0352670	+	7.23893i	0.00123763	+	0.254037i
$813$	2.79873	−	43.5183i	0.0981557	−	1.52625i
$814$	14.4069	+	24.9535i	0.504962	+	0.874620i
$815$	−5.42292	+	27.2814i	−0.189957	+	0.955627i
$816$	3.79645	+	2.52998i	0.132902	+	0.0885669i
$817$	13.2731			0.464366
$818$		−	9.67827i		−	0.338393i
$819$	18.6783	+	2.31998i	0.652673	+	0.0810668i
$820$	1.12766	+	0.224154i	0.0393797	+	0.00782779i
$821$			30.7953i			1.07476i	0.843339	+	0.537381i	$0.180586\pi$
$821$			30.7953i			1.07476i	−0.843339	+	0.537381i	$0.819414\pi$
$822$	6.51282	+	0.418850i	0.227161	+	0.0146091i
$823$		−	35.0046i		−	1.22018i	−0.792331	−	0.610092i	$-0.791133\pi$
$823$		−	35.0046i		−	1.22018i	0.792331	−	0.610092i	$-0.208867\pi$
$824$	9.07239	+	15.7138i	0.316052	+	0.547417i
$825$	19.8721	+	29.6451i	0.691857	+	1.03211i
$826$	9.10250	−	15.9449i	0.316716	−	0.554793i
$827$	−34.7736			−1.20919			−0.604597	−	0.796531i	$-0.706666\pi$
$827$	−34.7736			−1.20919			−0.604597	+	0.796531i	$0.706666\pi$
$828$	1.76279	+	0.227678i	0.0612613	+	0.00791235i
$829$	−7.21777	+	4.16718i	−0.250683	+	0.144732i	−0.620077	−	0.784541i	$-0.712899\pi$
$829$	−7.21777	+	4.16718i	−0.250683	+	0.144732i	0.369394	+	0.929273i	$0.379565\pi$
$830$	7.38482	+	6.47461i	0.256331	+	0.224737i
$831$	−2.30572	+	35.8523i	−0.0799845	+	1.24370i
$832$	−1.18566	+	2.05363i	−0.0411055	+	0.0711968i
$833$	16.0568	+	9.06297i	0.556336	+	0.314013i
$834$	0.668297	−	10.3915i	0.0231412	−	0.359830i
$835$	5.74898	−	28.9218i	0.198952	−	1.00088i
$836$	2.27694	+	3.94378i	0.0787496	+	0.136398i
$837$	2.68395	−	13.7575i	0.0927709	−	0.475530i
$838$	5.02659	−	8.70630i	0.173641	−	0.300754i
$839$	−15.4855	−	26.8216i	−0.534618	−	0.925985i	−0.999182	−	0.0404455i	$-0.987122\pi$
$839$	−15.4855	−	26.8216i	−0.534618	−	0.925985i	0.464564	−	0.885540i	$-0.346211\pi$
$840$	2.71370	+	9.88108i	0.0936317	+	0.340930i
$841$	−10.7569	+	18.6315i	−0.370928	+	0.642465i
$842$	−6.61761	−	11.4620i	−0.228058	−	0.395008i
$843$	−1.96080	−	1.30669i	−0.0675335	−	0.0450047i
$844$	−6.61689	+	11.4608i	−0.227763	+	0.394497i
$845$	−10.8743	+	12.4030i	−0.374088	+	0.426677i
$846$	9.84749	+	7.51793i	0.338564	+	0.258472i
$847$	−15.8297	+	0.0771197i	−0.543914	+	0.00264987i
$848$	−4.54406	−	7.87055i	−0.156044	−	0.270276i
$849$	11.4698	+	23.1866i	0.393641	+	0.795763i
$850$	5.03676	−	12.1688i	0.172760	−	0.417386i
$851$		−	4.14252i		−	0.142004i
$852$	−2.48652	+	1.23001i	−0.0851868	+	0.0421395i
$853$	12.6526	+	21.9150i	0.433217	+	0.750355i	0.997148	−	0.0754673i	$-0.0240449\pi$
$853$	12.6526	+	21.9150i	0.433217	+	0.750355i	−0.563931	+	0.825822i	$0.690712\pi$
$854$	−9.86461	−	5.63143i	−0.337560	−	0.192704i
$855$	−4.90195	−	5.56055i	−0.167643	−	0.190167i
$856$	−4.33862	+	7.51471i	−0.148291	+	0.256848i
$857$	12.9904	+	7.50003i	0.443745	+	0.256196i	0.705185	−	0.709023i	$-0.250864\pi$
$857$	12.9904	+	7.50003i	0.443745	+	0.256196i	−0.261440	+	0.965220i	$0.584197\pi$
$858$	14.0852	+	9.38646i	0.480861	+	0.320448i
$859$	30.5617	−	17.6448i	1.04275	−	0.602032i	0.122140	−	0.992513i	$-0.461024\pi$
$859$	30.5617	−	17.6448i	1.04275	−	0.602032i	0.920611	+	0.390480i	$0.127691\pi$
$860$	20.1957	+	17.7065i	0.688667	+	0.603786i
$861$	1.29708	−	1.96709i	0.0442045	−	0.0670382i
$862$	4.44716	−	2.56757i	0.151471	−	0.0874517i
$863$	8.04268	−	13.9303i	0.273776	−	0.474194i	−0.696050	−	0.717994i	$-0.745061\pi$
$863$	8.04268	−	13.9303i	0.273776	−	0.474194i	0.969826	+	0.243800i	$0.0783940\pi$
$864$	5.10001	+	0.994957i	0.173506	+	0.0338491i
$865$	31.3635	−	10.6510i	1.06639	−	0.362145i
$866$	7.97362			0.270955
$867$	17.3921	+	1.11851i	0.590666	+	0.0379867i
$868$	6.19818	+	3.53837i	0.210380	+	0.120100i
$869$	47.9789	+	27.7006i	1.62757	+	0.939679i
$870$	2.72877	−	10.2395i	0.0925140	−	0.347151i
$871$	−27.7548	−	16.0242i	−0.940436	−	0.542961i
$872$	−7.55567	−	13.0868i	−0.255867	−	0.443175i
$873$	41.2021	+	5.32156i	1.39448	+	0.180108i
$874$		−	0.654705i		−	0.0221457i
$875$	26.4606	−	13.2225i	0.894533	−	0.447002i
$876$	−6.32298	+	9.48818i	−0.213634	+	0.320576i
$877$	−24.0991	+	13.9136i	−0.813767	+	0.469829i	−0.848262	−	0.529576i	$-0.822351\pi$
$877$	−24.0991	+	13.9136i	−0.813767	+	0.469829i	0.0344952	+	0.999405i	$0.489018\pi$
$878$			25.8078i			0.870970i
$879$	1.23687	−	19.2324i	0.0417185	−	0.648693i
$880$	−1.79657	+	9.03814i	−0.0605625	+	0.304676i
$881$	−36.4477			−1.22795			−0.613977	−	0.789324i	$-0.710431\pi$
$881$	−36.4477			−1.22795			−0.613977	+	0.789324i	$0.710431\pi$
$882$	20.8522	+	2.48691i	0.702131	+	0.0837385i
$883$			27.9433i			0.940367i	0.882569	+	0.470184i	$0.155812\pi$
$883$			27.9433i			0.940367i	−0.882569	+	0.470184i	$0.844188\pi$
$884$		−	6.24607i		−	0.210078i
$885$	−18.9787	+	19.0303i	−0.637964	+	0.639697i
$886$	31.2880			1.05114
$887$	−46.0356	+	26.5787i	−1.54572	+	0.892424i	−0.547263	+	0.836961i	$0.684330\pi$
$887$	−46.0356	+	26.5787i	−1.54572	+	0.892424i	−0.998461	+	0.0554632i	$0.982336\pi$
$888$	0.777223	−	12.0853i	0.0260819	−	0.405555i
$889$	−7.18120	−	4.09955i	−0.240850	−	0.137495i
$890$	−34.3294	−	6.82390i	−1.15072	−	0.228738i
$891$	9.42357	−	35.8724i	0.315702	−	1.20177i
$892$	2.44383	+	4.23284i	0.0818255	+	0.141726i
$893$	2.28173	−	3.95208i	0.0763553	−	0.132251i
$894$	16.1310	+	10.7498i	0.539502	+	0.359527i
$895$	40.0665	+	35.1282i	1.33928	+	1.17421i
$896$	−1.31170	+	2.29771i	−0.0438207	+	0.0767610i
$897$	−1.07897	−	2.18118i	−0.0360258	−	0.0728276i
$898$			6.93666i			0.231479i
$899$	−3.69038	−	6.39192i	−0.123081	−	0.213182i
$900$	−0.0407079	−	14.9999i	−0.00135693	−	0.499998i
$901$	20.7310	+	11.9690i	0.690650	+	0.398747i
$902$	1.83506	−	1.05947i	0.0611006	−	0.0352765i
$903$	49.2179	−	24.6459i	1.63787	−	0.820163i
$904$	0.503287	−	0.871718i	0.0167391	−	0.0289929i
$905$	24.7536	−	8.40632i	0.822838	−	0.279436i
$906$	−32.0622	−	2.06197i	−1.06520	−	0.0685044i
$907$	13.9054	+	8.02828i	0.461721	+	0.266575i	0.712768	−	0.701400i	$-0.247441\pi$
$907$	13.9054	+	8.02828i	0.461721	+	0.266575i	−0.251047	+	0.967975i	$0.580775\pi$
$908$	10.3873	+	5.99711i	0.344714	+	0.199021i
$909$	3.12856	+	7.50090i	0.103768	+	0.248789i
$910$	9.19707	−	10.5937i	0.304880	−	0.351177i
$911$	−36.7577	+	21.2220i	−1.21784	+	0.703118i	−0.964455	−	0.264249i	$-0.914876\pi$
$911$	−36.7577	+	21.2220i	−1.21784	+	0.703118i	−0.253381	+	0.967367i	$0.581543\pi$
$912$	0.122836	−	1.91002i	0.00406751	−	0.0632470i
$913$	18.1004			0.599037
$914$			27.4150i			0.906806i
$915$	11.7735	+	11.7416i	0.389219	+	0.388164i
$916$	9.16676	−	5.29243i	0.302878	−	0.174867i
$917$	57.0790	−	0.278080i	1.88492	−	0.00918302i
$918$	−12.9440	+	4.44709i	−0.427216	+	0.146776i
$919$	−11.3435	+	19.6475i	−0.374188	+	0.648112i	−0.990205	−	0.139621i	$-0.955412\pi$
$919$	−11.3435	+	19.6475i	−0.374188	+	0.648112i	0.616017	+	0.787732i	$0.288745\pi$
$920$	0.873386	−	0.996168i	0.0287947	−	0.0328427i
$921$	10.8543	+	21.9424i	0.357660	+	0.723025i
$922$	−9.16139	−	15.8680i	−0.301714	−	0.522585i
$923$	3.28917	+	1.89900i	0.108264	+	0.0625064i
$924$	15.7660	+	10.3960i	0.518665	+	0.342004i
$925$	−34.6590	+	4.57213i	−1.13958	+	0.150331i
$926$	−16.6964	−	9.63966i	−0.548677	−	0.316779i
$927$	−53.9859	−	6.97268i	−1.77313	−	0.229013i
$928$	2.36953	−	1.36805i	0.0777835	−	0.0449083i
$929$	−5.64081			−0.185069			−0.0925345	−	0.995709i	$-0.529497\pi$
$929$	−5.64081			−0.185069			−0.0925345	+	0.995709i	$0.529497\pi$
$930$	−7.39757	−	7.37752i	−0.242576	−	0.241918i
$931$	−0.0753675	−	7.73482i	−0.00247007	−	0.253499i
$932$	0.259858	−	0.450088i	0.00851194	−	0.0147431i
$933$	4.51186	+	9.12093i	0.147712	+	0.298606i
$934$	11.2146	+	6.47476i	0.366953	+	0.211861i
$935$	−7.80503	−	22.9830i	−0.255252	−	0.751626i
$936$	−2.73852	−	6.56577i	−0.0895113	−	0.214609i
$937$	33.6125			1.09807			0.549036	−	0.835799i	$-0.314995\pi$
$937$	33.6125			1.09807			0.549036	+	0.835799i	$0.314995\pi$
$938$	−31.0535	−	17.7276i	−1.01393	−	0.578826i
$939$	−14.6198	−	29.5545i	−0.477098	−	0.964475i
$940$	8.74391	−	2.96943i	0.285195	−	0.0968521i
$941$	0.233263			0.00760416			0.00380208	−	0.999993i	$-0.498790\pi$
$941$	0.233263			0.00760416			0.00380208	+	0.999993i	$0.498790\pi$
$942$	−8.96244	−	18.1180i	−0.292012	−	0.590315i
$943$	−0.304637			−0.00992033
$944$	−6.93948			−0.225861
$945$	−28.5019	−	11.5170i	−0.927167	−	0.374648i
$946$	49.5003			1.60939
$947$	−2.62504			−0.0853024			−0.0426512	−	0.999090i	$-0.513580\pi$
$947$	−2.62504			−0.0853024			−0.0426512	+	0.999090i	$0.513580\pi$
$948$	−10.3242	−	20.8708i	−0.335314	−	0.677852i
$949$	15.6103			0.506733
$950$	−5.47768	+	0.722602i	−0.177719	+	0.0234443i
$951$	11.8395	+	23.9341i	0.383922	+	0.776116i
$952$	−0.0339510	−	6.96882i	−0.00110036	−	0.225861i
$953$	−15.1772			−0.491637			−0.245818	−	0.969316i	$-0.579057\pi$
$953$	−15.1772			−0.491637			−0.245818	+	0.969316i	$0.579057\pi$
$954$	27.0398	+	3.49239i	0.875445	+	0.113070i
$955$	55.1038	−	18.7132i	1.78312	−	0.605546i
$956$	−2.39886	−	1.38498i	−0.0775846	−	0.0447935i
$957$	−8.65934	−	17.5052i	−0.279917	−	0.565864i
$958$	−13.5378	+	23.4482i	−0.437388	+	0.757578i
$959$	−5.02653	−	8.60906i	−0.162315	−	0.278001i
$960$	2.73489	−	2.74233i	0.0882683	−	0.0885082i
$961$	23.7232			0.765265
$962$	−14.3587	+	8.28999i	−0.462942	+	0.267280i
$963$	−10.0209	−	24.0257i	−0.322918	−	0.774216i
$964$	17.4943	+	10.1004i	0.563454	+	0.325310i
$965$	−38.2673	+	12.9956i	−1.23187	+	0.418342i
$966$	−1.21568	−	2.42771i	−0.0391137	−	0.0781103i
$967$	11.1551	+	6.44040i	0.358724	+	0.207109i	0.668521	−	0.743693i	$-0.266928\pi$
$967$	11.1551	+	6.44040i	0.358724	+	0.207109i	−0.309797	+	0.950803i	$0.600261\pi$
$968$	2.99156	+	5.18154i	0.0961525	+	0.166541i
$969$	2.23529	+	4.51873i	0.0718077	+	0.145163i
$970$	20.4138	−	23.2836i	0.655449	−	0.747593i
$971$	14.3294	−	24.8192i	0.459851	−	0.796486i	−0.539101	−	0.842241i	$-0.681236\pi$
$971$	14.3294	−	24.8192i	0.459851	−	0.796486i	0.998953	+	0.0457549i	$0.0145693\pi$
$972$	−11.6568	+	10.3499i	−0.373891	+	0.331972i
$973$	−13.7362	+	8.02008i	−0.440363	+	0.257112i
$974$	2.98800	−	1.72512i	0.0957416	−	0.0552765i
$975$	−17.0583	+	11.4347i	−0.546304	+	0.366205i
$976$			4.29324i			0.137423i
$977$	14.1607			0.453042			0.226521	−	0.974006i	$-0.427265\pi$
$977$	14.1607			0.453042			0.226521	+	0.974006i	$0.427265\pi$
$978$	1.38277	−	21.5011i	0.0442162	−	0.687531i
$979$	−55.8645	+	32.2534i	−1.78544	+	1.03082i
$980$	10.2037	−	11.8695i	0.325945	−	0.379157i
$981$	44.9606	+	5.80699i	1.43548	+	0.185403i
$982$	−36.9916	−	21.3571i	−1.18045	−	0.681533i
$983$	34.2530	+	19.7760i	1.09250	+	0.630755i	0.934241	−	0.356643i	$-0.116079\pi$
$983$	34.2530	+	19.7760i	1.09250	+	0.630755i	0.158259	+	0.987398i	$0.449412\pi$
$984$	−0.888739	−	0.0571562i	−0.0283320	−	0.00182207i
$985$	13.7310	+	40.4330i	0.437506	+	1.28830i
$986$	−3.60343	+	6.24132i	−0.114757	+	0.198764i
$987$	1.12255	−	18.8915i	0.0357313	−	0.601323i
$988$	−2.26932	+	1.31019i	−0.0721966	+	0.0416827i
$989$	−6.16314	−	3.55829i	−0.195976	−	0.113147i
$990$	−18.2812	−	20.7374i	−0.581014	−	0.659077i
$991$	10.3535	+	17.9329i	0.328891	+	0.569656i	0.982292	−	0.187356i	$-0.0599917\pi$
$991$	10.3535	+	17.9329i	0.328891	+	0.569656i	−0.653401	+	0.757012i	$0.726658\pi$
$992$		−	2.69755i		−	0.0856474i
$993$	23.7533	+	48.0184i	0.753790	+	1.52382i
$994$	3.68009	+	2.10086i	0.116725	+	0.0666353i
$995$	41.9741	+	36.8006i	1.33067	+	1.16666i
$996$	−6.33057	−	4.21872i	−0.200592	−	0.133675i
$997$	24.8760	−	43.0865i	0.787831	−	1.36456i	−0.139462	−	0.990227i	$-0.544537\pi$
$997$	24.8760	−	43.0865i	0.787831	−	1.36456i	0.927293	−	0.374336i	$-0.122129\pi$
$998$	−18.0193	−	31.2103i	−0.570391	−	0.987946i
$999$	27.4029	+	23.8538i	0.866988	+	0.754702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.b.509.9	yes	48
3.2	odd	2		1890.2.bi.a.719.9		48
5.4	even	2		630.2.bi.a.509.16	yes	48
7.3	odd	6		630.2.r.a.59.16	✓	48
9.2	odd	6		630.2.r.b.299.9	yes	48
9.7	even	3		1890.2.r.a.89.3		48
15.14	odd	2		1890.2.bi.b.719.8		48
21.17	even	6		1890.2.r.b.1529.3		48
35.24	odd	6		630.2.r.b.59.9	yes	48
45.29	odd	6		630.2.r.a.299.16	yes	48
45.34	even	6		1890.2.r.b.89.3		48
63.38	even	6		630.2.bi.a.479.16	yes	48
63.52	odd	6		1890.2.bi.b.899.8		48
105.59	even	6		1890.2.r.a.1529.3		48
315.164	even	6	inner	630.2.bi.b.479.9	yes	48
315.304	odd	6		1890.2.bi.a.899.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.16	✓	48	7.3	odd	6
630.2.r.a.299.16	yes	48	45.29	odd	6
630.2.r.b.59.9	yes	48	35.24	odd	6
630.2.r.b.299.9	yes	48	9.2	odd	6
630.2.bi.a.479.16	yes	48	63.38	even	6
630.2.bi.a.509.16	yes	48	5.4	even	2
630.2.bi.b.479.9	yes	48	315.164	even	6	inner
630.2.bi.b.509.9	yes	48	1.1	even	1	trivial
1890.2.r.a.89.3		48	9.7	even	3
1890.2.r.a.1529.3		48	105.59	even	6
1890.2.r.b.89.3		48	45.34	even	6
1890.2.r.b.1529.3		48	21.17	even	6
1890.2.bi.a.719.9		48	3.2	odd	2
1890.2.bi.a.899.9		48	315.304	odd	6
1890.2.bi.b.719.8		48	15.14	odd	2
1890.2.bi.b.899.8		48	63.52	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.767971 - 1.55249i) q^{3} +1.00000 q^{4} +(0.719036 + 2.11731i) q^{5} +(-0.767971 - 1.55249i) q^{6} +(-1.31170 + 2.29771i) q^{7} +1.00000 q^{8} +(-1.82044 + 2.38453i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.767971 - 1.55249i) q^{3} +1.00000 q^{4} +(0.719036 + 2.11731i) q^{5} +(-0.767971 - 1.55249i) q^{6} +(-1.31170 + 2.29771i) q^{7} +1.00000 q^{8} +(-1.82044 + 2.38453i) q^{9} +(0.719036 + 2.11731i) q^{10} +(3.56894 + 2.06053i) q^{11} +(-0.767971 - 1.55249i) q^{12} +(-1.18566 + 2.05363i) q^{13} +(-1.31170 + 2.29771i) q^{14} +(2.73489 - 2.74233i) q^{15} +1.00000 q^{16} +(-2.28111 + 1.31700i) q^{17} +(-1.82044 + 2.38453i) q^{18} +(0.956982 + 0.552514i) q^{19} +(0.719036 + 2.11731i) q^{20} +(4.57451 + 0.271822i) q^{21} +(3.56894 + 2.06053i) q^{22} +(-0.296239 - 0.513101i) q^{23} +(-0.767971 - 1.55249i) q^{24} +(-3.96597 + 3.04484i) q^{25} +(-1.18566 + 2.05363i) q^{26} +(5.10001 + 0.994957i) q^{27} +(-1.31170 + 2.29771i) q^{28} +(2.36953 - 1.36805i) q^{29} +(2.73489 - 2.74233i) q^{30} -2.69755i q^{31} +1.00000 q^{32} +(0.458102 - 7.12317i) q^{33} +(-2.28111 + 1.31700i) q^{34} +(-5.80810 - 1.12513i) q^{35} +(-1.82044 + 2.38453i) q^{36} +(6.05512 + 3.49593i) q^{37} +(0.956982 + 0.552514i) q^{38} +(4.09879 + 0.263600i) q^{39} +(0.719036 + 2.11731i) q^{40} +(0.257087 - 0.445287i) q^{41} +(4.57451 + 0.271822i) q^{42} +(10.4023 - 6.00577i) q^{43} +(3.56894 + 2.06053i) q^{44} +(-6.35775 - 2.13986i) q^{45} +(-0.296239 - 0.513101i) q^{46} -4.12973i q^{47} +(-0.767971 - 1.55249i) q^{48} +(-3.55890 - 6.02779i) q^{49} +(-3.96597 + 3.04484i) q^{50} +(3.79645 + 2.52998i) q^{51} +(-1.18566 + 2.05363i) q^{52} +(-4.54406 - 7.87055i) q^{53} +(5.10001 + 0.994957i) q^{54} +(-1.79657 + 9.03814i) q^{55} +(-1.31170 + 2.29771i) q^{56} +(0.122836 - 1.91002i) q^{57} +(2.36953 - 1.36805i) q^{58} -6.93948 q^{59} +(2.73489 - 2.74233i) q^{60} +4.29324i q^{61} -2.69755i q^{62} +(-3.09109 - 7.31062i) q^{63} +1.00000 q^{64} +(-5.20070 - 1.03378i) q^{65} +(0.458102 - 7.12317i) q^{66} +13.5150i q^{67} +(-2.28111 + 1.31700i) q^{68} +(-0.569081 + 0.853955i) q^{69} +(-5.80810 - 1.12513i) q^{70} -1.60164i q^{71} +(-1.82044 + 2.38453i) q^{72} +(-3.29147 - 5.70100i) q^{73} +(6.05512 + 3.49593i) q^{74} +(7.77283 + 3.81878i) q^{75} +(0.956982 + 0.552514i) q^{76} +(-9.41586 + 5.49759i) q^{77} +(4.09879 + 0.263600i) q^{78} +13.4434 q^{79} +(0.719036 + 2.11731i) q^{80} +(-2.37200 - 8.68180i) q^{81} +(0.257087 - 0.445287i) q^{82} +(3.80374 - 2.19609i) q^{83} +(4.57451 + 0.271822i) q^{84} +(-4.42869 - 3.88283i) q^{85} +(10.4023 - 6.00577i) q^{86} +(-3.94360 - 2.62804i) q^{87} +(3.56894 + 2.06053i) q^{88} +(-7.82648 + 13.5559i) q^{89} +(-6.35775 - 2.13986i) q^{90} +(-3.16341 - 5.41805i) q^{91} +(-0.296239 - 0.513101i) q^{92} +(-4.18792 + 2.07164i) q^{93} -4.12973i q^{94} +(-0.481736 + 2.42350i) q^{95} +(-0.767971 - 1.55249i) q^{96} +(-6.92406 - 11.9928i) q^{97} +(-3.55890 - 6.02779i) q^{98} +(-11.4104 + 4.75919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8}+O(q^{10}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39} - 3 q^{41} + 8 q^{42} + 6 q^{44} - 39 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 42 q^{55} + 3 q^{56} - 22 q^{57} - 3 q^{58} - 4 q^{60} - 43 q^{63} + 48 q^{64} + 12 q^{65} - 42 q^{69} - 12 q^{70} - 18 q^{73} + 18 q^{75} - 12 q^{77} - 18 q^{78} + 8 q^{81} - 3 q^{82} + 9 q^{83} + 8 q^{84} - 33 q^{85} - 15 q^{87} + 6 q^{88} - 33 q^{89} - 39 q^{90} + 3 q^{92} - 8 q^{93} - 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

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