LMFDB - Embedded newform 445.2.q.a.44.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [445,2,Mod(44,445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(445, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 7]))

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

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

chi := DirichletCharacter("445.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 445 = 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	445.q (of order $22$, degree $10$, 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:	$3.55334288995$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			44.19
Character	$\chi$	$=$	445.44
Dual form			445.2.q.a.354.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.143528 + 0.488812i) q^{2} +(-1.89175 + 1.21575i) q^{3} +(1.46417 + 0.940965i) q^{4} +(-0.878884 + 2.05610i) q^{5} +(-0.322756 - 1.09921i) q^{6} +(1.26025 + 1.45441i) q^{7} +(-1.44014 + 1.24788i) q^{8} +(0.854416 - 1.87091i) q^{9} +(-0.878903 - 0.724718i) q^{10} +(-1.58109 + 1.82468i) q^{11} -3.91383 q^{12} +(3.41568 - 2.19512i) q^{13} +(-0.891813 + 0.407277i) q^{14} +(-0.837087 - 4.95814i) q^{15} +(1.04275 + 2.28330i) q^{16} +(1.20407 + 4.10070i) q^{17} +(0.791890 + 0.686177i) q^{18} +(-2.62921 - 1.20072i) q^{19} +(-3.22156 + 2.18349i) q^{20} +(-4.15228 - 1.21922i) q^{21} +(-0.664992 - 1.03475i) q^{22} +(3.92620 - 8.59719i) q^{23} +(1.20726 - 4.11154i) q^{24} +(-3.45513 - 3.61415i) q^{25} +(0.582756 + 1.98469i) q^{26} +(-0.301857 - 2.09946i) q^{27} +(0.476676 + 3.31535i) q^{28} +(-7.36338 + 6.38040i) q^{29} +(2.54374 + 0.302455i) q^{30} +(4.69411 - 2.14373i) q^{31} +(-5.03812 + 0.724372i) q^{32} +(0.772671 - 5.37405i) q^{33} -2.17729 q^{34} +(-4.09803 + 1.31295i) q^{35} +(3.01147 - 1.93535i) q^{36} -2.12683 q^{37} +(0.964293 - 1.11285i) q^{38} +(-3.79288 + 8.30525i) q^{39} +(-1.30007 - 4.05781i) q^{40} +(-0.136400 + 0.212243i) q^{41} +(1.19194 - 1.85469i) q^{42} +(-2.28623 + 2.63845i) q^{43} +(-4.03194 + 1.18388i) q^{44} +(3.09585 + 3.40108i) q^{45} +(3.63889 + 3.15311i) q^{46} +(-3.86246 + 6.01010i) q^{47} +(-4.74855 - 3.05171i) q^{48} +(0.469136 - 3.26291i) q^{49} +(2.26255 - 1.17017i) q^{50} +(-7.26325 - 6.29364i) q^{51} +7.06667 q^{52} +(6.34464 + 9.87245i) q^{53} +(1.06957 + 0.153781i) q^{54} +(-2.36213 - 4.85456i) q^{55} +(-3.62986 - 0.521896i) q^{56} +(6.43359 - 0.925011i) q^{57} +(-2.06197 - 4.51508i) q^{58} +(6.98487 - 10.8687i) q^{59} +(3.43980 - 8.04723i) q^{60} +(-0.531207 + 0.0763761i) q^{61} +(0.374143 + 2.60222i) q^{62} +(3.79784 - 1.11515i) q^{63} +(-0.345429 + 2.40251i) q^{64} +(1.51142 + 8.95225i) q^{65} +(2.51600 + 1.14902i) q^{66} +(0.341130 + 0.530808i) q^{67} +(-2.09565 + 7.13711i) q^{68} +(3.02467 + 21.0370i) q^{69} +(-0.0536041 - 2.19161i) q^{70} +(5.98461 - 6.90661i) q^{71} +(1.10420 + 3.76057i) q^{72} +(5.72590 - 2.61493i) q^{73} +(0.305260 - 1.03962i) q^{74} +(10.9302 + 2.63649i) q^{75} +(-2.71978 - 4.23206i) q^{76} -4.64639 q^{77} +(-3.51532 - 3.04604i) q^{78} +(6.84151 + 14.9808i) q^{79} +(-5.61115 + 0.137242i) q^{80} +(7.16418 + 8.26790i) q^{81} +(-0.0841695 - 0.0971367i) q^{82} +(-2.04879 + 0.601579i) q^{83} +(-4.93240 - 5.69230i) q^{84} +(-9.48971 - 1.12834i) q^{85} +(-0.961567 - 1.49623i) q^{86} +(6.17267 - 21.0222i) q^{87} -4.60080i q^{88} +(-1.95283 + 9.22965i) q^{89} +(-2.10683 + 1.02514i) q^{90} +(7.49721 + 2.20138i) q^{91} +(13.8383 - 8.89333i) q^{92} +(-6.27384 + 9.76229i) q^{93} +(-2.38344 - 2.75063i) q^{94} +(4.77958 - 4.35064i) q^{95} +(8.65020 - 7.49544i) q^{96} +(1.33641 - 1.15801i) q^{97} +(1.52762 + 0.697639i) q^{98} +(2.06289 + 4.51711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 26 q^{4} - 9 q^{5} - 22 q^{6} - 84 q^{9} - 39 q^{10} - 22 q^{11} - 22 q^{14} - 11 q^{15} - 46 q^{16} - 22 q^{19} - 33 q^{20} + 10 q^{21} - 66 q^{24} + 39 q^{25} - 22 q^{29} + 66 q^{30} - 22 q^{31}+ \cdots + 46 q^{99}+O(q^{100}) $ 440 * q + 26 * q^4 - 9 * q^5 - 22 * q^6 - 84 * q^9 - 39 * q^10 - 22 * q^11 - 22 * q^14 - 11 * q^15 - 46 * q^16 - 22 * q^19 - 33 * q^20 + 10 * q^21 - 66 * q^24 + 39 * q^25 - 22 * q^29 + 66 * q^30 - 22 * q^31 + 72 * q^34 - 44 * q^35 - 20 * q^36 + 30 * q^39 - 120 * q^40 - 44 * q^41 + 6 * q^44 + 5 * q^45 - 22 * q^46 - 74 * q^49 - 5 * q^50 - 22 * q^51 - 22 * q^54 - 38 * q^55 + 88 * q^56 - 66 * q^60 - 66 * q^61 + 122 * q^64 - 11 * q^65 + 66 * q^66 + 166 * q^69 - 220 * q^70 - 38 * q^71 - 110 * q^74 + 198 * q^75 - 198 * q^76 - 20 * q^79 + 234 * q^80 - 80 * q^81 - 178 * q^84 + 85 * q^85 - 66 * q^86 + 30 * q^89 + 54 * q^90 - 50 * q^91 + 242 * q^94 + 132 * q^95 - 352 * q^96 + 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/445\mathbb{Z}\right)^\times$.

$n$	$181$	$357$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$-1$

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 $

$2$	−0.143528	+	0.488812i	−0.101490	+	0.345642i	−0.994545	−	0.104304i	$-0.966739\pi$
$2$	−0.143528	+	0.488812i	−0.101490	+	0.345642i	0.893056	+	0.449946i	$0.148557\pi$
$3$	−1.89175	+	1.21575i	−1.09220	+	0.701916i	−0.957344	−	0.288949i	$-0.906694\pi$
$3$	−1.89175	+	1.21575i	−1.09220	+	0.701916i	−0.134858	+	0.990865i	$0.543058\pi$
$4$	1.46417	+	0.940965i	0.732085	+	0.470483i
$5$	−0.878884	+	2.05610i	−0.393049	+	0.919518i
$5$	−0.878884	+	2.05610i	−0.393049	+	0.919518i
$6$	−0.322756	−	1.09921i	−0.131764	−	0.448749i
$7$	1.26025	+	1.45441i	0.476330	+	0.549714i	0.942161	−	0.335159i	$-0.108790\pi$
$7$	1.26025	+	1.45441i	0.476330	+	0.549714i	−0.465831	+	0.884874i	$0.654245\pi$
$8$	−1.44014	+	1.24788i	−0.509165	+	0.441194i
$9$	0.854416	−	1.87091i	0.284805	−	0.623637i
$10$	−0.878903	−	0.724718i	−0.277934	−	0.229176i
$11$	−1.58109	+	1.82468i	−0.476717	+	0.550160i	−0.942268	−	0.334861i	$-0.891311\pi$
$11$	−1.58109	+	1.82468i	−0.476717	+	0.550160i	0.465551	+	0.885021i	$0.345856\pi$
$12$	−3.91383			−1.12982
$13$	3.41568	−	2.19512i	0.947339	−	0.608818i	0.0268721	−	0.999639i	$-0.491445\pi$
$13$	3.41568	−	2.19512i	0.947339	−	0.608818i	0.920467	+	0.390821i	$0.127809\pi$
$14$	−0.891813	+	0.407277i	−0.238347	+	0.108849i
$15$	−0.837087	−	4.95814i	−0.216135	−	1.28019i
$16$	1.04275	+	2.28330i	0.260687	+	0.570825i
$17$	1.20407	+	4.10070i	0.292031	+	0.994566i	0.966586	+	0.256342i	$0.0825172\pi$
$17$	1.20407	+	4.10070i	0.292031	+	0.994566i	−0.674555	+	0.738224i	$0.735665\pi$
$18$	0.791890	+	0.686177i	0.186650	+	0.161733i
$19$	−2.62921	−	1.20072i	−0.603183	−	0.275464i	0.0903263	−	0.995912i	$-0.471209\pi$
$19$	−2.62921	−	1.20072i	−0.603183	−	0.275464i	−0.693509	+	0.720448i	$0.743936\pi$
$20$	−3.22156	+	2.18349i	−0.720362	+	0.488242i
$21$	−4.15228	−	1.21922i	−0.906102	−	0.266056i
$22$	−0.664992	−	1.03475i	−0.141777	−	0.220609i
$23$	3.92620	−	8.59719i	0.818670	−	1.79264i	0.254277	−	0.967131i	$-0.418162\pi$
$23$	3.92620	−	8.59719i	0.818670	−	1.79264i	0.564393	−	0.825506i	$-0.309110\pi$
$24$	1.20726	−	4.11154i	0.246430	−	0.839264i
$25$	−3.45513	−	3.61415i	−0.691025	−	0.722831i
$26$	0.582756	+	1.98469i	0.114288	+	0.389229i
$27$	−0.301857	−	2.09946i	−0.0580925	−	0.404042i
$28$	0.476676	+	3.31535i	0.0900832	+	0.626543i
$29$	−7.36338	+	6.38040i	−1.36735	+	1.18481i	−0.404570	+	0.914507i	$0.632579\pi$
$29$	−7.36338	+	6.38040i	−1.36735	+	1.18481i	−0.962775	+	0.270305i	$0.912876\pi$
$30$	2.54374	+	0.302455i	0.464422	+	0.0552204i
$31$	4.69411	−	2.14373i	0.843088	−	0.385025i	0.0534291	−	0.998572i	$-0.482985\pi$
$31$	4.69411	−	2.14373i	0.843088	−	0.385025i	0.789659	+	0.613546i	$0.210258\pi$
$32$	−5.03812	+	0.724372i	−0.890622	+	0.128052i
$33$	0.772671	−	5.37405i	0.134505	−	0.935501i
$34$	−2.17729			−0.373402
$35$	−4.09803	+	1.31295i	−0.692693	+	0.221929i
$36$	3.01147	−	1.93535i	0.501912	−	0.322559i
$37$	−2.12683			−0.349648			−0.174824	−	0.984600i	$-0.555936\pi$
$37$	−2.12683			−0.349648			−0.174824	+	0.984600i	$0.555936\pi$
$38$	0.964293	−	1.11285i	0.156429	−	0.180529i
$39$	−3.79288	+	8.30525i	−0.607347	+	1.32990i
$40$	−1.30007	−	4.05781i	−0.205559	−	0.641597i
$41$	−0.136400	+	0.212243i	−0.0213021	+	0.0331467i	−0.851741	−	0.523963i	$-0.824453\pi$
$41$	−0.136400	+	0.212243i	−0.0213021	+	0.0331467i	0.830439	+	0.557109i	$0.188090\pi$
$42$	1.19194	−	1.85469i	0.183920	−	0.286185i
$43$	−2.28623	+	2.63845i	−0.348647	+	0.402360i	−0.902804	−	0.430052i	$-0.858495\pi$
$43$	−2.28623	+	2.63845i	−0.348647	+	0.402360i	0.554157	+	0.832412i	$0.313041\pi$
$44$	−4.03194	+	1.18388i	−0.607838	+	0.178477i
$45$	3.09585	+	3.40108i	0.461502	+	0.507003i
$46$	3.63889	+	3.15311i	0.536525	+	0.464901i
$47$	−3.86246	+	6.01010i	−0.563397	+	0.876664i	−0.999733	−	0.0231206i	$-0.992640\pi$
$47$	−3.86246	+	6.01010i	−0.563397	+	0.876664i	0.436335	+	0.899784i	$0.356276\pi$
$48$	−4.74855	−	3.05171i	−0.685394	−	0.440476i
$49$	0.469136	−	3.26291i	0.0670195	−	0.466131i
$50$	2.26255	−	1.17017i	0.319973	−	0.165488i
$51$	−7.26325	−	6.29364i	−1.01706	−	0.881286i
$52$	7.06667			0.979971
$53$	6.34464	+	9.87245i	0.871503	+	1.35609i	0.933713	+	0.358022i	$0.116549\pi$
$53$	6.34464	+	9.87245i	0.871503	+	1.35609i	−0.0622100	+	0.998063i	$0.519815\pi$
$54$	1.06957	+	0.153781i	0.145550	+	0.0209269i
$55$	−2.36213	−	4.85456i	−0.318509	−	0.654589i
$56$	−3.62986	−	0.521896i	−0.485061	−	0.0697412i
$57$	6.43359	−	0.925011i	0.852150	−	0.122521i
$58$	−2.06197	−	4.51508i	−0.270749	−	0.592858i
$59$	6.98487	−	10.8687i	0.909353	−	1.41498i	−0.000477536	−	1.00000i	$-0.500152\pi$
$59$	6.98487	−	10.8687i	0.909353	−	1.41498i	0.909830	−	0.414981i	$-0.136212\pi$
$60$	3.43980	−	8.04723i	0.444076	−	1.03889i
$61$	−0.531207	+	0.0763761i	−0.0680141	+	0.00977896i	−0.176238	−	0.984348i	$-0.556393\pi$
$61$	−0.531207	+	0.0763761i	−0.0680141	+	0.00977896i	0.108224	+	0.994127i	$0.465484\pi$
$62$	0.374143	+	2.60222i	0.0475163	+	0.330483i
$63$	3.79784	−	1.11515i	0.478483	−	0.140495i
$64$	−0.345429	+	2.40251i	−0.0431786	+	0.300314i
$65$	1.51142	+	8.95225i	0.187468	+	1.11039i
$66$	2.51600	+	1.14902i	0.309698	+	0.141434i
$67$	0.341130	+	0.530808i	0.0416756	+	0.0648486i	0.861466	−	0.507815i	$-0.169547\pi$
$67$	0.341130	+	0.530808i	0.0416756	+	0.0648486i	−0.819791	+	0.572663i	$0.805910\pi$
$68$	−2.09565	+	7.13711i	−0.254134	+	0.865502i
$69$	3.02467	+	21.0370i	0.364127	+	2.53256i
$70$	−0.0536041	−	2.19161i	−0.00640692	−	0.261947i
$71$	5.98461	−	6.90661i	0.710243	−	0.819664i	−0.279855	−	0.960042i	$-0.590286\pi$
$71$	5.98461	−	6.90661i	0.710243	−	0.819664i	0.990098	+	0.140378i	$0.0448319\pi$
$72$	1.10420	+	3.76057i	0.130132	+	0.443188i
$73$	5.72590	−	2.61493i	0.670165	−	0.306054i	−0.0511197	−	0.998693i	$-0.516279\pi$
$73$	5.72590	−	2.61493i	0.670165	−	0.306054i	0.721285	+	0.692638i	$0.243552\pi$
$74$	0.305260	−	1.03962i	0.0354857	−	0.120853i
$75$	10.9302	+	2.63649i	1.26211	+	0.304436i
$76$	−2.71978	−	4.23206i	−0.311980	−	0.485450i
$77$	−4.64639			−0.529505
$78$	−3.51532	−	3.04604i	−0.398032	−	0.344896i
$79$	6.84151	+	14.9808i	0.769730	+	1.68547i	0.727246	+	0.686377i	$0.240800\pi$
$79$	6.84151	+	14.9808i	0.769730	+	1.68547i	0.0424840	+	0.999097i	$0.486473\pi$
$80$	−5.61115	+	0.137242i	−0.627346	+	0.0153441i
$81$	7.16418	+	8.26790i	0.796020	+	0.918656i
$82$	−0.0841695	−	0.0971367i	−0.00929496	−	0.0107270i
$83$	−2.04879	+	0.601579i	−0.224884	+	0.0660319i	−0.392233	−	0.919866i	$-0.628297\pi$
$83$	−2.04879	+	0.601579i	−0.224884	+	0.0660319i	0.167349	+	0.985898i	$0.446479\pi$
$84$	−4.93240	−	5.69230i	−0.538169	−	0.621081i
$85$	−9.48971	−	1.12834i	−1.02930	−	0.122386i
$86$	−0.961567	−	1.49623i	−0.103688	−	0.161342i
$87$	6.17267	−	21.0222i	0.661780	−	2.25382i
$88$		−	4.60080i		−	0.490447i
$89$	−1.95283	+	9.22965i	−0.206999	+	0.978341i
$89$	−1.95283	+	9.22965i	−0.206999	+	0.978341i
$90$	−2.10683	+	1.02514i	−0.222079	+	0.108059i
$91$	7.49721	+	2.20138i	0.785922	+	0.230767i
$92$	13.8383	−	8.89333i	1.44274	−	0.927193i
$93$	−6.27384	+	9.76229i	−0.650567	+	1.01230i
$94$	−2.38344	−	2.75063i	−0.245833	−	0.283706i
$95$	4.77958	−	4.35064i	0.490375	−	0.446366i
$96$	8.65020	−	7.49544i	0.882858	−	0.765001i
$97$	1.33641	−	1.15801i	0.135692	−	0.117578i	−0.584370	−	0.811487i	$-0.698658\pi$
$97$	1.33641	−	1.15801i	0.135692	−	0.117578i	0.720063	+	0.693909i	$0.244113\pi$
$98$	1.52762	+	0.697639i	0.154313	+	0.0704722i
$99$	2.06289	+	4.51711i	0.207329	+	0.453986i
$100$	−1.65810	−	8.54289i	−0.165810	−	0.854289i
$101$		−	4.36048i		−	0.433884i	−0.976184	−	0.216942i	$-0.930392\pi$
$101$		−	4.36048i		−	0.433884i	0.976184	−	0.216942i	$-0.0696083\pi$
$102$	4.11889	−	2.64705i	0.407831	−	0.262097i
$103$	−1.59999	−	3.50349i	−0.157652	−	0.345209i	0.814280	−	0.580472i	$-0.197132\pi$
$103$	−1.59999	−	3.50349i	−0.157652	−	0.345209i	−0.971932	+	0.235263i	$0.924405\pi$
$104$	−2.17978	+	7.42364i	−0.213745	+	0.727948i
$105$	6.15622	−	7.46597i	0.600785	−	0.728604i
$106$	−5.73641	+	1.68436i	−0.557169	+	0.163600i
$107$	2.78426	+	2.41258i	0.269165	+	0.233233i	0.778976	−	0.627054i	$-0.215739\pi$
$107$	2.78426	+	2.41258i	0.269165	+	0.233233i	−0.509811	+	0.860286i	$0.670285\pi$
$108$	1.53355	−	3.35801i	0.147566	−	0.323125i
$109$	1.27979	+	8.90111i	0.122581	+	0.852571i	0.954614	+	0.297845i	$0.0962679\pi$
$109$	1.27979	+	8.90111i	0.122581	+	0.852571i	−0.832033	+	0.554726i	$0.812823\pi$
$110$	2.71200	−	0.457869i	0.258579	−	0.0436561i
$111$	4.02343	−	2.58570i	0.381887	−	0.245424i
$112$	−2.00672	+	4.39411i	−0.189617	+	0.415204i
$113$	17.0356	+	5.00210i	1.60257	+	0.470558i	0.956261	−	0.292515i	$-0.0944923\pi$
$113$	17.0356	+	5.00210i	1.60257	+	0.470558i	0.646312	+	0.763073i	$0.276310\pi$
$114$	−0.471245	+	3.27758i	−0.0441362	+	0.306974i
$115$	14.2260	+	15.6286i	1.32658	+	1.45738i
$116$	−16.7850	+	2.41332i	−1.55845	+	0.224071i
$117$	−1.18847	−	8.26597i	−0.109874	−	0.764189i
$118$	4.31021	+	4.97425i	0.396787	+	0.457917i
$119$	−4.44665	+	6.91912i	−0.407624	+	0.634275i
$120$	7.39270	+	6.09581i	0.674859	+	0.556468i
$121$	0.735869	+	5.11808i	0.0668972	+	0.465280i
$122$	0.0389097	−	0.270623i	0.00352272	−	0.0245010i
$123$		−	0.567339i		−	0.0511552i
$124$	8.89016	+	1.27821i	0.798360	+	0.114787i
$125$	10.4677	−	3.92767i	0.936262	−	0.351302i
$126$			2.01649i			0.179643i
$127$	−11.3071	+	13.0491i	−1.00334	+	1.15792i	−0.0159116	+	0.999873i	$0.505065\pi$
$127$	−11.3071	+	13.0491i	−1.00334	+	1.15792i	−0.987432	+	0.158046i	$0.949480\pi$
$128$	−10.3847	−	4.74254i	−0.917888	−	0.419185i
$129$	1.11727	−	7.77078i	0.0983701	−	0.684179i
$130$	−4.59290	−	0.546102i	−0.402824	−	0.0478963i
$131$	−7.27764	−	4.67706i	−0.635851	−	0.408636i	0.182621	−	0.983183i	$-0.441542\pi$
$131$	−7.27764	−	4.67706i	−0.635851	−	0.408636i	−0.818472	+	0.574547i	$0.805178\pi$
$132$	6.18811	−	7.14146i	0.538606	−	0.621585i
$133$	−1.56713	−	5.33716i	−0.135887	−	0.462790i
$134$	−0.308427	+	0.0905624i	−0.0266441	+	0.00782340i
$135$	4.58201	+	1.22454i	0.394357	+	0.105391i
$136$	−6.85123	−	4.40302i	−0.587488	−	0.377556i
$137$	−8.62032	−	5.53994i	−0.736484	−	0.473309i	0.117852	−	0.993031i	$-0.462399\pi$
$137$	−8.62032	−	5.53994i	−0.736484	−	0.473309i	−0.854336	+	0.519722i	$0.826036\pi$
$138$	−10.7173	−	1.54091i	−0.912315	−	0.131171i
$139$	4.73480	−	10.3678i	0.401600	−	0.879382i	−0.595505	−	0.803352i	$-0.703048\pi$
$139$	4.73480	−	10.3678i	0.401600	−	0.879382i	0.997105	−	0.0760307i	$-0.0242247\pi$
$140$	−7.23565	−	1.93372i	−0.611524	−	0.163429i
$141$		−	16.0654i		−	1.35295i
$142$	2.51707	+	3.91664i	0.211228	+	0.328677i
$143$	−1.39511	+	9.70319i	−0.116665	+	0.811422i
$144$	5.16279			0.430232
$145$	−6.64722	−	20.7475i	−0.552021	−	1.72299i
$146$	0.456381	+	3.17420i	0.0377704	+	0.262699i
$147$	3.07941	+	6.74297i	0.253986	+	0.556151i
$148$	−3.11404	−	2.00127i	−0.255972	−	0.164503i
$149$	−14.7192	+	12.7543i	−1.20584	+	1.04487i	−0.208074	+	0.978113i	$0.566719\pi$
$149$	−14.7192	+	12.7543i	−1.20584	+	1.04487i	−0.997769	+	0.0667558i	$0.978735\pi$
$150$	−2.85754	+	4.96438i	−0.233317	+	0.405340i
$151$	5.43928	−	0.782051i	0.442642	−	0.0636424i	0.0826096	−	0.996582i	$-0.473675\pi$
$151$	5.43928	−	0.782051i	0.442642	−	0.0636424i	0.360033	+	0.932940i	$0.382765\pi$
$152$	5.28478	−	1.55175i	0.428652	−	0.125864i
$153$	8.70082	+	1.25099i	0.703419	+	0.101136i
$154$	0.666888	−	2.27121i	0.0537394	−	0.183019i
$155$	0.282149	+	11.5357i	0.0226627	+	0.926568i
$156$	−13.3684	+	8.59133i	−1.07033	+	0.687857i
$157$	−0.540429	+	1.84053i	−0.0431309	+	0.146890i	−0.978243	−	0.207461i	$-0.933480\pi$
$157$	−0.540429	+	1.84053i	−0.0431309	+	0.146890i	0.935112	+	0.354351i	$0.115298\pi$
$158$	−8.30475	+	1.19404i	−0.660691	+	0.0949930i
$159$	−24.0049	−	10.9627i	−1.90372	−	0.869398i
$160$	2.93854	−	10.9955i	0.232312	−	0.869273i
$161$	17.4518	−	5.12432i	1.37540	−	0.403853i
$162$	−5.06971	+	2.31526i	−0.398314	+	0.181904i
$163$	−7.34133	−	2.15561i	−0.575017	−	0.168840i	−0.0187216	−	0.999825i	$-0.505960\pi$
$163$	−7.34133	−	2.15561i	−0.575017	−	0.168840i	−0.556296	+	0.830984i	$0.687778\pi$
$164$	−0.399426	+	0.182412i	−0.0311899	+	0.0142440i
$165$	10.3705	+	6.31186i	0.807343	+	0.491377i
$166$		−	1.08782i		−	0.0844309i
$167$	4.41884	+	3.82895i	0.341940	+	0.296293i	0.808854	−	0.588010i	$-0.200088\pi$
$167$	4.41884	+	3.82895i	0.341940	+	0.296293i	−0.466913	+	0.884303i	$0.654634\pi$
$168$	7.50129	−	3.42573i	0.578737	−	0.264300i
$169$	1.44790	−	3.17045i	0.111377	−	0.243881i
$170$	1.91359	−	4.47673i	0.146765	−	0.343350i
$171$	−4.49288	+	3.89310i	−0.343579	+	0.297713i
$172$	−5.83012	+	1.71188i	−0.444542	+	0.130529i
$173$	−3.73752	+	3.23858i	−0.284159	+	0.246225i	−0.785264	−	0.619162i	$-0.787473\pi$
$173$	−3.73752	+	3.23858i	−0.284159	+	0.246225i	0.501105	+	0.865387i	$0.332927\pi$
$174$	9.38995	+	6.03455i	0.711850	+	0.457478i
$175$	0.902127	−	9.57990i	0.0681944	−	0.724172i
$176$	−5.81496	−	1.70743i	−0.438319	−	0.128702i
$177$			29.0527i			2.18373i
$178$	−4.23128	−	2.27928i	−0.317148	−	0.170839i
$179$	−17.5064			−1.30849			−0.654243	−	0.756284i	$-0.727013\pi$
$179$	−17.5064			−1.30849			−0.654243	+	0.756284i	$0.727013\pi$
$180$	1.33256	+	7.89285i	0.0993229	+	0.588298i
$181$	2.26063	+	3.51761i	0.168031	+	0.261462i	0.915049	−	0.403342i	$-0.132151\pi$
$181$	2.26063	+	3.51761i	0.168031	+	0.261462i	−0.747018	+	0.664804i	$0.768515\pi$
$182$	−2.15212	+	3.34877i	−0.159526	+	0.248227i
$183$	0.912057	−	0.790302i	0.0674212	−	0.0584208i
$184$	5.07403	+	17.2806i	0.374063	+	1.27394i
$185$	1.86923	−	4.37298i	0.137429	−	0.321508i
$186$	−3.87145	−	4.46789i	−0.283869	−	0.327602i
$187$	−9.38620	−	4.28653i	−0.686387	−	0.313462i
$188$	−11.3106	+	5.16537i	−0.824910	+	0.376724i
$189$	2.67306	−	3.08487i	0.194436	−	0.224392i
$190$	1.44064	+	2.96076i	0.104515	+	0.214796i
$191$	−7.26572	−	11.3057i	−0.525729	−	0.818050i	0.472259	−	0.881460i	$-0.343439\pi$
$191$	−7.26572	−	11.3057i	−0.525729	−	0.818050i	−0.997988	+	0.0634098i	$0.979802\pi$
$192$	−2.26740	−	4.96490i	−0.163635	−	0.358311i
$193$	13.3586	+	3.92244i	0.961572	+	0.282343i	0.724597	−	0.689173i	$-0.242026\pi$
$193$	13.3586	+	3.92244i	0.961572	+	0.282343i	0.236975	+	0.971516i	$0.423844\pi$
$194$	0.374236	+	0.819463i	0.0268686	+	0.0588340i
$195$	−13.7430	−	15.0979i	−0.984153	−	1.08118i
$196$	3.75718	−	4.33602i	0.268370	−	0.309716i
$197$	3.09932	−	6.78657i	0.220817	−	0.483523i	−0.766507	−	0.642236i	$-0.778007\pi$
$197$	3.09932	−	6.78657i	0.220817	−	0.483523i	0.987325	+	0.158713i	$0.0507344\pi$
$198$	−2.50410	+	0.360035i	−0.177959	+	0.0255866i
$199$	−8.08433	−	2.37377i	−0.573083	−	0.168272i	−0.0176654	−	0.999844i	$-0.505623\pi$
$199$	−8.08433	−	2.37377i	−0.573083	−	0.168272i	−0.555418	+	0.831572i	$0.687442\pi$
$200$	9.48589	+	0.893275i	0.670754	+	0.0631641i
$201$	−1.29067	−	0.589427i	−0.0910365	−	0.0415750i
$202$	2.13146	+	0.625852i	0.149969	+	0.0440348i
$203$	−18.5594	−	2.66844i	−1.30262	−	0.187288i
$204$	−4.71254	−	16.0494i	−0.329944	−	1.12368i
$205$	−0.316513	−	0.466989i	−0.0221062	−	0.0326159i
$206$	1.94219	−	0.279245i	0.135319	−	0.0194559i
$207$	−12.7300	−	14.6911i	−0.884793	−	1.02111i
$208$	8.57381	+	5.51006i	0.594487	+	0.382054i
$209$	6.34795	−	2.89901i	0.439097	−	0.200529i
$210$	2.76586	+	4.08081i	0.190863	+	0.281603i
$211$	19.5283	+	2.80774i	1.34438	+	0.193293i	0.776656	−	0.629925i	$-0.216915\pi$
$211$	19.5283	+	2.80774i	1.34438	+	0.193293i	0.567725	+	0.823218i	$0.307824\pi$
$212$			20.4250i			1.40280i
$213$	−2.92465	+	20.3414i	−0.200394	+	1.39377i
$214$	−1.57892	+	1.01471i	−0.107933	+	0.0693641i
$215$	−3.41559	−	7.01961i	−0.232942	−	0.478734i
$216$	3.05460	+	2.64683i	0.207839	+	0.180094i
$217$	9.03362	+	4.12552i	0.613242	+	0.280058i
$218$	−4.53465	−	0.651985i	−0.307125	−	0.0441580i
$219$	−7.65285	+	11.9081i	−0.517132	+	0.804673i
$220$	1.10942	−	9.33059i	0.0747971	−	0.629068i
$221$	13.1143	+	11.3636i	0.882161	+	0.764397i
$222$	0.686446	+	2.33782i	0.0460712	+	0.156904i
$223$	−4.48480	−	15.2738i	−0.300324	−	1.02281i	−0.962007	−	0.273026i	$-0.911976\pi$
$223$	−4.48480	−	15.2738i	−0.300324	−	1.02281i	0.661683	−	0.749784i	$-0.269843\pi$
$224$	−7.40283	−	6.41459i	−0.494622	−	0.428593i
$225$	−9.71387	+	3.37624i	−0.647591	+	0.225082i
$226$	−4.89017	+	7.60925i	−0.325289	+	0.506160i
$227$	28.1387	+	4.04574i	1.86763	+	0.268525i	0.981009	−	0.193963i	$-0.0621343\pi$
$227$	28.1387	+	4.04574i	1.86763	+	0.268525i	0.886625	+	0.462489i	$0.153043\pi$
$228$	10.2903	+	4.69941i	0.681491	+	0.311226i
$229$	0.952620	+	0.825450i	0.0629509	+	0.0545473i	0.685768	−	0.727820i	$-0.259466\pi$
$229$	0.952620	+	0.825450i	0.0629509	+	0.0545473i	−0.622817	+	0.782367i	$0.714012\pi$
$230$	−9.68129	+	4.71071i	−0.638365	+	0.310615i
$231$	8.78981	−	5.64887i	0.578327	−	0.371668i
$232$	2.64226	−	18.3773i	0.173473	−	1.20653i
$233$		−	8.33966i		−	0.546350i	−0.961964	−	0.273175i	$-0.911926\pi$
$233$		−	8.33966i		−	0.546350i	0.961964	−	0.273175i	$-0.0880737\pi$
$234$	4.21109	+	0.605463i	0.275287	+	0.0395803i
$235$	−8.96274	−	13.2238i	−0.584665	−	0.862626i
$236$	20.4541	−	9.34107i	1.33145	−	0.608052i
$237$	−31.1554	−	20.0224i	−2.02376	−	1.30059i
$238$	−2.74393	−	3.16667i	−0.177863	−	0.205264i
$239$	16.8595	−	2.42403i	1.09055	−	0.156798i	0.426503	−	0.904486i	$-0.359745\pi$
$239$	16.8595	−	2.42403i	1.09055	−	0.156798i	0.664050	+	0.747689i	$0.268836\pi$
$240$	10.4480	−	7.08141i	0.674419	−	0.457103i
$241$	−0.772804	−	2.63193i	−0.0497807	−	0.169537i	0.930851	−	0.365400i	$-0.119068\pi$
$241$	−0.772804	−	2.63193i	−0.0497807	−	0.169537i	−0.980631	+	0.195862i	$0.937249\pi$
$242$	−2.60740	−	0.374887i	−0.167610	−	0.0240987i
$243$	−17.4992	−	5.13822i	−1.12257	−	0.329617i
$244$	−0.849645	−	0.388020i	−0.0543930	−	0.0248404i
$245$	6.29657	+	3.83232i	0.402273	+	0.244838i
$246$	0.277322	+	0.0814291i	0.0176814	+	0.00519173i
$247$	−11.6163	+	1.67017i	−0.739126	+	0.106270i
$248$	−4.08503	+	8.94497i	−0.259400	+	0.568006i
$249$	3.14443	−	3.62886i	0.199270	−	0.229970i
$250$	0.417479	+	5.68048i	0.0264037	+	0.359265i
$251$	−10.1763	−	22.2830i	−0.642321	−	1.40649i	−0.898117	−	0.439757i	$-0.855065\pi$
$251$	−10.1763	−	22.2830i	−0.642321	−	1.40649i	0.255796	−	0.966731i	$-0.417663\pi$
$252$	6.61000	+	1.94087i	0.416391	+	0.122263i
$253$	9.47940	+	20.7570i	0.595964	+	1.30498i
$254$	−4.75567	−	7.39996i	−0.298397	−	0.464315i
$255$	19.3239	−	9.40261i	1.21011	−	0.588814i
$256$	0.629735	−	0.726752i	0.0393584	−	0.0454220i
$257$	−23.6700	+	10.8097i	−1.47649	+	0.674292i	−0.980945	−	0.194288i	$-0.937761\pi$
$257$	−23.6700	+	10.8097i	−1.47649	+	0.674292i	−0.495549	+	0.868580i	$0.665033\pi$
$258$	3.63809	+	1.66146i	0.226498	+	0.103438i
$259$	−2.68034	−	3.09327i	−0.166548	−	0.192207i
$260$	−6.21078	+	14.5298i	−0.385176	+	0.901100i
$261$	5.64577	+	19.2277i	0.349465	+	1.19017i
$262$	3.33075	−	2.88611i	0.205774	−	0.178304i
$263$	−0.806999	+	1.25571i	−0.0497617	+	0.0774307i	−0.865243	−	0.501353i	$-0.832836\pi$
$263$	−0.806999	+	1.25571i	−0.0497617	+	0.0774307i	0.815481	+	0.578783i	$0.196472\pi$
$264$	5.59344	+	8.70356i	0.344252	+	0.535667i
$265$	−25.8750	+	4.36849i	−1.58949	+	0.268354i
$266$	2.83379			0.173751
$267$	−7.52672	−	19.8344i	−0.460628	−	1.21384i
$268$			1.09819i			0.0670823i
$269$	12.6797	+	3.72308i	0.773093	+	0.227000i	0.644405	−	0.764685i	$-0.277105\pi$
$269$	12.6797	+	3.72308i	0.773093	+	0.227000i	0.128688	+	0.991685i	$0.458923\pi$
$270$	−1.25622	+	2.06399i	−0.0764508	+	0.125610i
$271$	0.921569	+	0.592257i	0.0559813	+	0.0359770i	0.568332	−	0.822799i	$-0.307589\pi$
$271$	0.921569	+	0.592257i	0.0559813	+	0.0359770i	−0.512351	+	0.858776i	$0.671225\pi$
$272$	−8.10758	+	7.02526i	−0.491594	+	0.425969i
$273$	−16.8592	+	4.95031i	−1.02036	+	0.299606i
$274$	3.94525	−	3.41858i	0.238341	−	0.206524i
$275$	12.0575	−	0.590178i	0.727096	−	0.0355891i
$276$	−15.3665	+	33.6479i	−0.924954	+	2.02537i
$277$	4.33732	−	1.98079i	0.260604	−	0.119014i	−0.280829	−	0.959758i	$-0.590609\pi$
$277$	4.33732	−	1.98079i	0.260604	−	0.119014i	0.541433	+	0.840744i	$0.317882\pi$
$278$	4.38831	+	3.80249i	0.263193	+	0.228058i
$279$		−	10.6139i		−	0.635438i
$280$	4.26330	−	7.00469i	0.254781	−	0.418610i
$281$	−19.4316	+	8.87413i	−1.15919	+	0.529386i	−0.899764	−	0.436376i	$-0.856262\pi$
$281$	−19.4316	+	8.87413i	−1.15919	+	0.529386i	−0.259429	+	0.965762i	$0.583534\pi$
$282$	7.85297	+	2.30584i	0.467637	+	0.137311i
$283$	−15.8579	+	7.24204i	−0.942652	+	0.430495i	−0.826626	−	0.562752i	$-0.809743\pi$
$283$	−15.8579	+	7.24204i	−0.942652	+	0.430495i	−0.116026	+	0.993246i	$0.537015\pi$
$284$	15.2614	−	4.48114i	0.905596	−	0.265907i
$285$	−3.75247	+	14.0411i	−0.222277	+	0.831724i
$286$	−4.54280	−	2.07463i	−0.268621	−	0.122675i
$287$	−0.480585	+	0.0690977i	−0.0283681	+	0.00407871i
$288$	−2.94941	+	10.0448i	−0.173796	+	0.591894i
$289$	−1.06463	+	0.684198i	−0.0626255	+	0.0402470i
$290$	11.0957	−	0.271387i	0.651562	−	0.0159364i
$291$	−1.12031	+	3.81542i	−0.0656736	+	0.223664i
$292$	10.8442	+	1.55917i	0.634611	+	0.0912433i
$293$	11.8174	−	3.46991i	0.690382	−	0.202714i	0.0823222	−	0.996606i	$-0.473766\pi$
$293$	11.8174	−	3.46991i	0.690382	−	0.202714i	0.608060	+	0.793891i	$0.291948\pi$
$294$	−3.73803	+	0.537447i	−0.218006	+	0.0313446i
$295$	16.2082	+	23.9139i	0.943679	+	1.39232i
$296$	3.06292	−	2.65403i	0.178029	−	0.154263i
$297$	4.30810	+	2.76865i	0.249982	+	0.160653i
$298$	−4.12181	−	9.02551i	−0.238770	−	0.522834i
$299$	−5.46124	−	37.9837i	−0.315831	−	2.19666i
$300$	13.5228	+	14.1452i	0.780737	+	0.816672i
$301$	−6.71860			−0.387254
$302$	−0.398414	+	2.77103i	−0.0229262	+	0.159455i
$303$	5.30127	+	8.24894i	0.304550	+	0.473890i
$304$		−	7.25533i		−	0.416122i
$305$	0.309833	−	1.15934i	0.0177410	−	0.0663838i
$306$	−1.86031	+	4.07351i	−0.106347	+	0.232867i
$307$	−11.1101	−	1.59740i	−0.634089	−	0.0911682i	−0.182228	−	0.983256i	$-0.558331\pi$
$307$	−11.1101	−	1.59740i	−0.634089	−	0.0911682i	−0.451861	+	0.892088i	$0.649240\pi$
$308$	−6.80311	−	4.37209i	−0.387643	−	0.249123i
$309$	7.28616	+	4.68253i	0.414495	+	0.266380i
$310$	−5.67927	−	1.51778i	−0.322561	−	0.0862039i
$311$	−3.65985	+	1.07463i	−0.207531	+	0.0609366i	−0.383846	−	0.923397i	$-0.625401\pi$
$311$	−3.65985	+	1.07463i	−0.207531	+	0.0609366i	0.176315	+	0.984334i	$0.443582\pi$
$312$	−4.90173	−	16.6938i	−0.277506	−	0.945098i
$313$	−0.866927	+	1.00049i	−0.0490016	+	0.0565509i	−0.779721	−	0.626127i	$-0.784639\pi$
$313$	−0.866927	+	1.00049i	−0.0490016	+	0.0565509i	0.730720	+	0.682678i	$0.239185\pi$
$314$	−0.822107	−	0.528336i	−0.0463942	−	0.0298157i
$315$	−1.04501	+	8.78884i	−0.0588794	+	0.495195i
$316$	−4.07929	+	28.3721i	−0.229478	+	1.59605i
$317$	6.13589	+	2.80217i	0.344626	+	0.157385i	0.580206	−	0.814469i	$-0.302972\pi$
$317$	6.13589	+	2.80217i	0.344626	+	0.157385i	−0.235581	+	0.971855i	$0.575699\pi$
$318$	8.80408	−	10.1604i	0.493708	−	0.569770i
$319$		−	23.5238i		−	1.31708i
$320$	−4.63622	−	2.82177i	−0.259172	−	0.157741i
$321$	−8.20024	−	1.17902i	−0.457693	−	0.0658063i
$322$			9.26614i			0.516382i
$323$	1.75803	−	12.2274i	0.0978194	−	0.680349i
$324$	2.70977	+	18.8469i	0.150543	+	1.04705i
$325$	−19.7351	−	4.76036i	−1.09471	−	0.264057i
$326$	2.10737	−	3.27914i	0.116717	−	0.181615i
$327$	−13.2426	−	15.2828i	−0.732317	−	0.845139i
$328$	−0.0684197	−	0.475869i	−0.00377785	−	0.0262755i
$329$	−13.6088	+	1.95665i	−0.750278	+	0.107874i
$330$	−4.57377	+	4.16330i	−0.251778	+	0.229182i
$331$	0.674965	−	4.69448i	0.0370994	−	0.258032i	−0.962828	−	0.270117i	$-0.912938\pi$
$331$	0.674965	−	4.69448i	0.0370994	−	0.258032i	0.999927	+	0.0120847i	$0.00384677\pi$
$332$	−3.56584	−	1.04703i	−0.195701	−	0.0574630i
$333$	−1.81719	+	3.97910i	−0.0995817	+	0.218053i
$334$	−2.50586	+	1.61042i	−0.137115	+	0.0881183i
$335$	−1.39121	+	0.234879i	−0.0760100	+	0.0128328i
$336$	−1.54594	−	10.7522i	−0.0843379	−	0.586583i
$337$	1.46298	−	3.20347i	0.0796934	−	0.174504i	−0.865591	−	0.500752i	$-0.833057\pi$
$337$	1.46298	−	3.20347i	0.0796934	−	0.174504i	0.945284	+	0.326247i	$0.105784\pi$
$338$	1.34194	+	1.16280i	0.0729920	+	0.0632479i
$339$	−38.3084	+	11.2484i	−2.08063	+	0.610927i
$340$	−12.8328	−	10.5816i	−0.695957	−	0.573866i
$341$	−3.51021	+	11.9547i	−0.190088	+	0.647381i
$342$	−1.25814	−	2.75494i	−0.0680325	−	0.148970i
$343$	16.6695	−	10.7129i	0.900070	−	0.578440i
$344$		−	6.65267i		−	0.358688i
$345$	−45.9127	−	12.2701i	−2.47185	−	0.660599i
$346$	−1.04662	−	2.29177i	−0.0562665	−	0.123207i
$347$	6.64109	+	3.03288i	0.356512	+	0.162814i	0.585617	−	0.810588i	$-0.300852\pi$
$347$	6.64109	+	3.03288i	0.356512	+	0.162814i	−0.229104	+	0.973402i	$0.573580\pi$
$348$	28.8190	−	24.9718i	1.54486	−	1.33863i
$349$	19.9947	−	17.3255i	1.07029	−	0.927412i	0.0727393	−	0.997351i	$-0.476826\pi$
$349$	19.9947	−	17.3255i	1.07029	−	0.927412i	0.997551	+	0.0699389i	$0.0222804\pi$
$350$	4.55329	+	1.81596i	0.243384	+	0.0970669i
$351$	−5.63963	−	6.50848i	−0.301021	−	0.347397i
$352$	6.64398	−	10.3382i	0.354125	−	0.551030i
$353$	20.3521	−	13.0795i	1.08323	−	0.696151i	0.127930	−	0.991783i	$-0.459167\pi$
$353$	20.3521	−	13.0795i	1.08323	−	0.696151i	0.955302	+	0.295633i	$0.0955304\pi$
$354$	−14.2013	−	4.16988i	−0.754791	−	0.221627i
$355$	8.94092	+	18.3751i	0.474535	+	0.975249i
$356$	−11.5441	+	11.6762i	−0.611834	+	0.618839i
$357$		−	18.4953i		−	0.978875i
$358$	2.51266	−	8.55732i	0.132798	−	0.452268i
$359$	8.06264	+	12.5457i	0.425530	+	0.662137i	0.986135	−	0.165946i	$-0.0530677\pi$
$359$	8.06264	+	12.5457i	0.425530	+	0.662137i	−0.560605	+	0.828083i	$0.689431\pi$
$360$	−8.70260	−	1.03475i	−0.458667	−	0.0545362i
$361$	−6.97133	−	8.04534i	−0.366912	−	0.423439i
$362$	−2.04391	+	0.600147i	−0.107426	+	0.0315431i
$363$	−7.61441	−	8.78750i	−0.399653	−	0.461224i
$364$	8.90578	+	10.2778i	0.466790	+	0.538704i
$365$	0.344166	+	14.0713i	0.0180145	+	0.736523i
$366$	0.255403	+	0.559255i	0.0133501	+	0.0292327i
$367$	6.30060	+	5.45950i	0.328889	+	0.284984i	0.803615	−	0.595150i	$-0.202907\pi$
$367$	6.30060	+	5.45950i	0.328889	+	0.284984i	−0.474726	+	0.880134i	$0.657453\pi$
$368$	23.7240			1.23670
$369$	0.280544	+	0.436535i	0.0146046	+	0.0227251i
$370$	1.86928	+	1.54135i	0.0971790	+	0.0801310i
$371$	−6.36273	+	21.6695i	−0.330336	+	1.12502i
$372$	−18.3719	+	8.39019i	−0.952541	+	0.435011i
$373$	3.63534	+	12.3808i	0.188231	+	0.641055i	0.998487	+	0.0549800i	$0.0175095\pi$
$373$	3.63534	+	12.3808i	0.188231	+	0.641055i	−0.810257	+	0.586075i	$0.800672\pi$
$374$	3.44249	−	3.97285i	0.178007	−	0.205431i
$375$	−15.0272	+	20.1564i	−0.776004	+	1.04087i
$376$	−1.93745	−	13.4753i	−0.0999164	−	0.694934i
$377$	−11.1452	+	37.9569i	−0.574005	+	1.95488i
$378$	1.12426	+	1.74939i	0.0578259	+	0.0899789i
$379$	14.4757	+	6.61081i	0.743564	+	0.339574i	0.750915	−	0.660399i	$-0.229613\pi$
$379$	14.4757	+	6.61081i	0.743564	+	0.339574i	−0.00735099	+	0.999973i	$0.502340\pi$
$380$	11.0919	−	1.87266i	0.569003	−	0.0960653i
$381$	5.52573	−	38.4323i	0.283092	−	1.96895i
$382$	6.56919	−	1.92889i	0.336109	−	0.0986905i
$383$	−3.16975	−	22.0461i	−0.161967	−	1.12650i	−0.894921	−	0.446225i	$-0.852768\pi$
$383$	−3.16975	−	22.0461i	−0.161967	−	1.12650i	0.732954	−	0.680278i	$-0.238141\pi$
$384$	25.4111	−	3.65356i	1.29675	−	0.186445i
$385$	4.08364	−	9.55346i	0.208122	−	0.486890i
$386$	−3.83467	+	5.96686i	−0.195179	+	0.303705i
$387$	2.98291	+	6.53166i	0.151630	+	0.332023i
$388$	3.04639	−	0.438004i	0.154657	−	0.0222363i
$389$	2.63995	+	0.379567i	0.133851	+	0.0192448i	0.208914	−	0.977934i	$-0.433007\pi$
$389$	2.63995	+	0.379567i	0.133851	+	0.0192448i	−0.0750638	+	0.997179i	$0.523916\pi$
$390$	9.35254	−	4.55074i	0.473584	−	0.230436i
$391$	39.9819	+	5.74853i	2.02197	+	0.290716i
$392$	3.39612	+	5.28446i	0.171530	+	0.266906i
$393$	19.4536			0.981306
$394$	2.87251	+	2.48905i	0.144715	+	0.125396i
$395$	−36.8150	+	0.900450i	−1.85236	+	0.0453066i
$396$	−1.23001	+	8.55493i	−0.0618105	+	0.429901i
$397$	13.6524	+	8.77386i	0.685194	+	0.440348i	0.836374	−	0.548159i	$-0.184671\pi$
$397$	13.6524	+	8.77386i	0.685194	+	0.440348i	−0.151180	+	0.988506i	$0.548307\pi$
$398$	2.32066	−	3.61101i	0.116324	−	0.181004i
$399$	9.45329	+	8.19132i	0.473256	+	0.410079i
$400$	4.64937	−	11.6577i	0.232469	−	0.582887i
$401$	18.4000	−	5.40274i	0.918855	−	0.269800i	0.212091	−	0.977250i	$-0.431973\pi$
$401$	18.4000	−	5.40274i	0.918855	−	0.269800i	0.706764	+	0.707450i	$0.250154\pi$
$402$	0.473366	−	0.546293i	0.0236093	−	0.0272466i
$403$	11.3278	−	17.6265i	0.564280	−	0.878036i
$404$	4.10306	−	6.38449i	0.204135	−	0.317640i
$405$	−23.2961	+	7.46376i	−1.15759	+	0.370877i
$406$	3.96816	−	8.68907i	0.196937	−	0.431231i
$407$	3.36271	−	3.88077i	0.166683	−	0.192363i
$408$	18.3138			0.906668
$409$	30.9712	−	19.9040i	1.53143	−	0.984187i	0.541801	−	0.840507i	$-0.317742\pi$
$409$	30.9712	−	19.9040i	1.53143	−	0.984187i	0.989624	−	0.143681i	$-0.0458939\pi$
$410$	0.273698	−	0.0876892i	0.0135170	−	0.00433066i
$411$	23.0427			1.13661
$412$	0.954003	−	6.63523i	0.0470003	−	0.326895i
$413$	24.6102	−	3.53841i	1.21099	−	0.174114i
$414$	9.00831	−	4.11396i	0.442735	−	0.202190i
$415$	0.563740	−	4.74124i	0.0276729	−	0.232738i
$416$	−15.6185	+	13.5335i	−0.765760	+	0.663535i
$417$	3.64759	+	25.3696i	0.178623	+	1.24235i
$418$	0.505962	+	3.51904i	0.0247474	+	0.172122i
$419$	7.25775	+	24.7176i	0.354564	+	1.20754i	0.922998	+	0.384806i	$0.125732\pi$
$419$	7.25775	+	24.7176i	0.354564	+	1.20754i	−0.568433	+	0.822729i	$0.692450\pi$
$420$	16.0390	−	5.13866i	0.782621	−	0.250741i
$421$	−11.4210	+	38.8965i	−0.556628	+	1.89570i	−0.129291	+	0.991607i	$0.541270\pi$
$421$	−11.4210	+	38.8965i	−0.556628	+	1.89570i	−0.427337	+	0.904093i	$0.640548\pi$
$422$	−4.17531	+	9.14266i	−0.203251	+	0.445058i
$423$	7.94421	+	12.3614i	0.386261	+	0.601034i
$424$	−21.4568	−	6.30029i	−1.04203	−	0.305969i
$425$	10.6603	−	18.5201i	0.517102	−	0.898359i
$426$	−9.52335	−	4.34917i	−0.461408	−	0.210718i
$427$	−0.780537	−	0.676339i	−0.0377728	−	0.0327303i
$428$	1.80648	+	6.15232i	0.0873197	+	0.297384i
$429$	−9.15750	−	20.0521i	−0.442128	−	0.968126i
$430$	3.92151	−	0.662071i	0.189112	−	0.0319279i
$431$	26.5783	−	12.1379i	1.28023	−	0.584661i	0.344966	−	0.938615i	$-0.387890\pi$
$431$	26.5783	−	12.1379i	1.28023	−	0.584661i	0.935263	+	0.353954i	$0.115163\pi$
$432$	4.47894	−	2.87844i	0.215493	−	0.138489i
$433$	36.4605			1.75218			0.876089	−	0.482150i	$-0.160144\pi$
$433$	36.4605			1.75218			0.876089	+	0.482150i	$0.160144\pi$
$434$	−3.31318	+	3.82361i	−0.159038	+	0.183539i
$435$	37.7987	+	31.1677i	1.81231	+	1.49438i
$436$	−6.50180	+	14.2370i	−0.311380	+	0.681827i
$437$	−20.6457	+	17.8896i	−0.987615	+	0.855774i
$438$	−4.72241	−	5.44995i	−0.225645	−	0.260409i
$439$	2.24933	+	7.66053i	0.107355	+	0.365617i	0.995595	−	0.0937633i	$-0.0298897\pi$
$439$	2.24933	+	7.66053i	0.107355	+	0.365617i	−0.888240	+	0.459380i	$0.848072\pi$
$440$	9.45972	+	4.04357i	0.450974	+	0.192770i
$441$	−5.70378	−	3.66560i	−0.271609	−	0.174552i
$442$	−7.43692	+	4.77942i	−0.353738	+	0.227334i
$443$	−1.54854	+	5.27383i	−0.0735731	+	0.250567i	−0.988065	−	0.154037i	$-0.950772\pi$
$443$	−1.54854	+	5.27383i	−0.0735731	+	0.250567i	0.914492	+	0.404604i	$0.132591\pi$
$444$	8.32403			0.395041
$445$	−17.2608	−	12.1270i	−0.818241	−	0.574875i
$446$	8.10972			0.384006
$447$	12.3390	−	42.0228i	0.583615	−	1.98761i
$448$	−3.92955	+	2.52537i	−0.185654	+	0.119313i
$449$	−6.45672	−	4.14948i	−0.304711	−	0.195826i	0.379345	−	0.925255i	$-0.376149\pi$
$449$	−6.45672	−	4.14948i	−0.304711	−	0.195826i	−0.684056	+	0.729429i	$0.739786\pi$
$450$	−0.256131	−	5.23284i	−0.0120741	−	0.246678i
$451$	−0.171613	−	0.584460i	−0.00808094	−	0.0275212i
$452$	20.2362	+	23.3538i	0.951831	+	1.09847i
$453$	−9.33898	+	8.09227i	−0.438784	+	0.380208i
$454$	−6.01631	+	13.1739i	−0.282359	+	0.618281i
$455$	−11.1155	+	13.4803i	−0.521100	+	0.631966i
$456$	−8.11094	+	9.36052i	−0.379830	+	0.438347i
$457$	−1.42072			−0.0664587			−0.0332293	−	0.999448i	$-0.510579\pi$
$457$	−1.42072			−0.0664587			−0.0332293	+	0.999448i	$0.510579\pi$
$458$	−0.540218	+	0.347177i	−0.0252427	+	0.0162225i
$459$	8.24581	−	3.76574i	0.384882	−	0.175770i
$460$	6.12335	+	36.2692i	0.285503	+	1.69106i
$461$	2.66103	+	5.82684i	0.123936	+	0.271383i	0.961423	−	0.275076i	$-0.0887029\pi$
$461$	2.66103	+	5.82684i	0.123936	+	0.271383i	−0.837486	+	0.546459i	$0.815976\pi$
$462$	1.49965	+	5.10734i	0.0697700	+	0.237615i
$463$	−31.7569	−	27.5175i	−1.47587	−	1.27885i	−0.879283	−	0.476300i	$-0.841978\pi$
$463$	−31.7569	−	27.5175i	−1.47587	−	1.27885i	−0.596587	−	0.802549i	$-0.703477\pi$
$464$	−22.2465	−	10.1596i	−1.03277	−	0.471650i
$465$	−14.5583	−	21.4796i	−0.675125	−	0.996092i
$466$	4.07653	+	1.19698i	0.188842	+	0.0554489i
$467$	−5.48810	−	8.53964i	−0.253959	−	0.395168i	0.690742	−	0.723101i	$-0.257284\pi$
$467$	−5.48810	−	8.53964i	−0.253959	−	0.395168i	−0.944701	+	0.327934i	$0.893648\pi$
$468$	6.03787	−	13.2211i	0.279101	−	0.611145i
$469$	−0.342102	+	1.16509i	−0.0157968	+	0.0537990i
$470$	7.75036	−	2.48311i	0.357497	−	0.114537i
$471$	−1.21528	−	4.13885i	−0.0559970	−	0.190708i
$472$	3.50369	+	24.3687i	0.161270	+	1.12166i
$473$	−1.19958	−	8.34325i	−0.0551567	−	0.383623i
$474$	14.2589	−	12.3554i	0.654931	−	0.567501i
$475$	4.74467	+	13.6510i	0.217700	+	0.626352i
$476$	−13.0213	+	5.94663i	−0.596831	+	0.272563i
$477$	23.8914	−	3.43507i	1.09391	−	0.157281i
$478$	−1.23492	+	8.58906i	−0.0564839	+	0.392854i
$479$	29.5167			1.34865			0.674326	−	0.738433i	$-0.264434\pi$
$479$	29.5167			1.34865			0.674326	+	0.738433i	$0.264434\pi$
$480$	7.80888	+	24.3733i	0.356425	+	1.11249i
$481$	−7.26456	+	4.66865i	−0.331235	+	0.212872i
$482$	1.39744			0.0636515
$483$	−26.7846	+	30.9110i	−1.21874	+	1.40650i
$484$	−3.73850	+	8.18617i	−0.169932	+	0.372099i
$485$	1.20643	+	3.76556i	0.0547814	+	0.170985i
$486$	5.02324	−	7.81632i	0.227859	−	0.354555i
$487$	20.3325	−	31.6379i	0.921352	−	1.43365i	0.0203720	−	0.999792i	$-0.493515\pi$
$487$	20.3325	−	31.6379i	0.921352	−	1.43365i	0.900980	−	0.433860i	$-0.142849\pi$
$488$	0.669702	−	0.772877i	0.0303160	−	0.0349865i
$489$	16.5086	−	4.84738i	0.746547	−	0.219206i
$490$	−2.77702	+	2.52779i	−0.125453	+	0.114194i
$491$	−14.2326	−	12.3326i	−0.642309	−	0.556564i	0.271637	−	0.962400i	$-0.412435\pi$
$491$	−14.2326	−	12.3326i	−0.642309	−	0.556564i	−0.913946	+	0.405836i	$0.866980\pi$
$492$	0.533846	−	0.830680i	0.0240676	−	0.0374500i
$493$	−35.0302	−	22.5125i	−1.57768	−	1.01391i
$494$	0.850864	−	5.91789i	0.0382822	−	0.266258i
$495$	−11.1007	+	0.271509i	−0.498939	+	0.0122034i
$496$	9.78955	+	8.48270i	0.439564	+	0.380884i
$497$	17.5871			0.788891
$498$	1.32252	+	2.05788i	0.0592634	+	0.0922157i
$499$	−16.4253	−	2.36160i	−0.735298	−	0.105720i	−0.235515	−	0.971871i	$-0.575678\pi$
$499$	−16.4253	−	2.36160i	−0.735298	−	0.105720i	−0.499783	+	0.866151i	$0.666587\pi$
$500$	19.0223	+	4.09899i	0.850705	+	0.183312i
$501$	−13.0144	−	1.87119i	−0.581441	−	0.0835986i
$502$	12.3528	−	1.77606i	0.551331	−	0.0792694i
$503$	−10.5093	−	23.0122i	−0.468587	−	1.02606i	−0.985446	−	0.169992i	$-0.945626\pi$
$503$	−10.5093	−	23.0122i	−0.468587	−	1.02606i	0.516859	−	0.856071i	$-0.327101\pi$
$504$	−4.07783	+	6.34523i	−0.181641	+	0.282639i
$505$	8.96561	+	3.83236i	0.398964	+	0.170538i
$506$	−11.5068	+	1.65443i	−0.511541	+	0.0735484i
$507$	1.11543	+	7.75799i	0.0495380	+	0.344544i
$508$	−28.8343	+	8.46651i	−1.27931	+	0.375640i
$509$	−0.480502	+	3.34196i	−0.0212979	+	0.148130i	−0.997695	−	0.0678509i	$-0.978386\pi$
$509$	−0.480502	+	3.34196i	−0.0212979	+	0.148130i	0.976398	+	0.215981i	$0.0692949\pi$
$510$	1.82258	+	10.7953i	0.0807052	+	0.478024i
$511$	11.0192	+	5.03232i	0.487462	+	0.222617i
$512$	−12.0795	−	18.7960i	−0.533843	−	0.830675i
$513$	−1.72722	+	5.88238i	−0.0762588	+	0.259714i
$514$	−1.88661	−	13.1217i	−0.0832149	−	0.578772i
$515$	8.60974	−	0.210584i	0.379390	−	0.00927942i
$516$	8.94790	−	10.3264i	0.393909	−	0.454596i
$517$	−4.85959	−	16.5502i	−0.213725	−	0.727879i
$518$	1.89673	−	0.866209i	0.0833376	−	0.0380590i
$519$	3.13314	−	10.6705i	0.137530	−	0.468383i
$520$	−13.3480	−	11.0064i	−0.585349	−	0.482661i
$521$	−18.5861	−	28.9205i	−0.814272	−	1.26703i	−0.960639	−	0.277801i	$-0.910394\pi$
$521$	−18.5861	−	28.9205i	−0.814272	−	1.26703i	0.146367	−	0.989230i	$-0.453242\pi$
$522$	−10.2091			−0.446839
$523$	21.3650	+	18.5129i	0.934228	+	0.809513i	0.981910	−	0.189350i	$-0.0606380\pi$
$523$	21.3650	+	18.5129i	0.934228	+	0.809513i	−0.0476822	+	0.998863i	$0.515183\pi$
$524$	−6.25476	−	13.6960i	−0.273240	−	0.598313i
$525$	9.94020	+	19.2195i	0.433826	+	0.838810i
$526$	−0.497981	−	0.574701i	−0.0217130	−	0.0250582i
$527$	14.4429	+	16.6679i	0.629141	+	0.726067i
$528$	13.0763	−	3.83954i	0.569071	−	0.167094i
$529$	−43.4348	−	50.1264i	−1.88847	−	2.17941i
$530$	1.57842	−	13.2750i	0.0685620	−	0.576629i
$531$	−14.3663	−	22.3544i	−0.623445	−	0.970099i
$532$	2.72753	−	9.28912i	0.118253	−	0.402734i
$533$			1.02437i			0.0443703i
$534$	10.7756	−	0.832365i	0.466304	−	0.0360199i
$535$	−7.40756	+	3.60436i	−0.320257	+	0.155830i
$536$	−1.15366	−	0.338745i	−0.0498306	−	0.0146316i
$537$	33.1177	−	21.2834i	1.42913	−	0.918448i
$538$	−3.63978	+	5.66360i	−0.156922	+	0.244175i
$539$	5.21201	+	6.01498i	0.224497	+	0.259084i
$540$	5.55660	+	6.10444i	0.239118	+	0.262693i
$541$	−10.4728	+	9.07471i	−0.450260	+	0.390152i	−0.850260	−	0.526363i	$-0.823555\pi$
$541$	−10.4728	+	9.07471i	−0.450260	+	0.390152i	0.400000	+	0.916515i	$0.369010\pi$
$542$	−0.421773	+	0.365469i	−0.0181167	+	0.0156982i
$543$	−8.55310	−	3.90607i	−0.367049	−	0.167625i
$544$	−9.03670	−	19.7876i	−0.387445	−	0.848387i
$545$	−19.4264	−	5.19167i	−0.832135	−	0.222387i
$546$		−	8.95148i		−	0.383088i
$547$	−31.7041	+	20.3750i	−1.35557	+	0.871172i	−0.998031	−	0.0627261i	$-0.980021\pi$
$547$	−31.7041	+	20.3750i	−1.35557	+	0.871172i	−0.357539	+	0.933898i	$0.616384\pi$
$548$	−7.40872	−	16.2228i	−0.316485	−	0.693005i
$549$	−0.310979	+	1.05910i	−0.0132723	+	0.0452012i
$550$	−1.44211	+	5.97857i	−0.0614917	+	0.254927i
$551$	27.0210	−	7.93407i	1.15113	−	0.338003i
$552$	−30.6077	−	26.5217i	−1.30275	−	1.12884i
$553$	−13.1662	+	28.8299i	−0.559883	+	1.22597i
$554$	0.345705	+	2.40443i	0.0146876	+	0.102155i
$555$	1.78034	+	10.5451i	0.0755712	+	0.447615i
$556$	16.6883	−	10.7249i	0.707740	−	0.454837i
$557$	6.06072	−	13.2711i	0.256801	−	0.562316i	−0.736690	−	0.676231i	$-0.763612\pi$
$557$	6.06072	−	13.2711i	0.256801	−	0.562316i	0.993490	+	0.113916i	$0.0363393\pi$
$558$	5.18820	+	1.52339i	0.219634	+	0.0644904i
$559$	−2.01730	+	14.0306i	−0.0853228	+	0.593433i
$560$	−7.27107	−	7.98794i	−0.307259	−	0.337552i
$561$	22.9677	−	3.30226i	0.969697	−	0.139421i
$562$	−1.54879	−	10.7721i	−0.0653319	−	0.454394i
$563$	−6.71543	−	7.75001i	−0.283021	−	0.326624i	0.596383	−	0.802700i	$-0.296604\pi$
$563$	−6.71543	−	7.75001i	−0.283021	−	0.326624i	−0.879404	+	0.476076i	$0.842059\pi$
$564$	15.1170	−	23.5225i	0.636540	−	0.990476i
$565$	−25.2571	+	30.6307i	−1.06258	+	1.28864i
$566$	−1.26395	−	8.79095i	−0.0531277	−	0.369511i
$567$	−2.99623	+	20.8393i	−0.125830	+	0.875167i
$568$			17.4146i			0.730698i
$569$	−17.0513	−	2.45160i	−0.714827	−	0.102777i	−0.224700	−	0.974428i	$-0.572140\pi$
$569$	−17.0513	−	2.45160i	−0.714827	−	0.102777i	−0.490126	+	0.871651i	$0.663049\pi$
$570$	−6.32488	−	3.84955i	−0.264920	−	0.161240i
$571$			36.1262i			1.51183i	0.654667	+	0.755917i	$0.272809\pi$
$571$			36.1262i			1.51183i	−0.654667	+	0.755917i	$0.727191\pi$
$572$	−11.1730	+	12.8944i	−0.467168	+	0.539141i
$573$	27.4899	+	12.5542i	1.14841	+	0.524459i
$574$	0.0352017	−	0.244833i	0.00146929	−	0.0102191i
$575$	−44.6371	+	15.5145i	−1.86150	+	0.646997i
$576$	4.19974	+	2.69901i	0.174989	+	0.112459i
$577$	−3.93937	+	4.54628i	−0.163998	+	0.189264i	−0.831801	−	0.555075i	$-0.812690\pi$
$577$	−3.93937	+	4.54628i	−0.163998	+	0.189264i	0.667802	+	0.744339i	$0.267235\pi$
$578$	−0.181639	−	0.618607i	−0.00755521	−	0.0257307i
$579$	−30.0398	+	8.82049i	−1.24841	+	0.366567i
$580$	9.79003	−	36.6327i	0.406509	−	1.52109i
$581$	−3.45693	−	2.22163i	−0.143418	−	0.0921689i
$582$	−1.70423	−	1.09524i	−0.0706424	−	0.0453991i
$583$	−28.0455	−	4.03233i	−1.16152	−	0.167002i
$584$	−4.98294	+	10.9111i	−0.206195	+	0.451505i
$585$	18.0402	+	4.82122i	0.745871	+	0.199333i
$586$			6.27453i			0.259199i
$587$	3.65802	+	5.69199i	0.150983	+	0.234934i	0.908503	−	0.417878i	$-0.137226\pi$
$587$	3.65802	+	5.69199i	0.150983	+	0.234934i	−0.757521	+	0.652811i	$0.773590\pi$
$588$	−1.83612	+	12.7705i	−0.0757202	+	0.526646i
$589$	−14.9158			−0.614597
$590$	−14.0157	+	4.49045i	−0.577019	+	0.184869i
$591$	2.38765	+	16.6065i	0.0982150	+	0.683100i
$592$	−2.21774	−	4.85618i	−0.0911487	−	0.199588i
$593$	19.0273	+	12.2281i	0.781359	+	0.502149i	0.869484	−	0.493960i	$-0.164451\pi$
$593$	19.0273	+	12.2281i	0.781359	+	0.502149i	−0.0881251	+	0.996109i	$0.528088\pi$
$594$	−1.97168	+	1.70847i	−0.0808992	+	0.0700995i
$595$	−10.3183	−	15.2239i	−0.423011	−	0.624119i
$596$	−33.5527	+	4.82415i	−1.37437	+	0.197605i
$597$	18.1795	−	5.33797i	0.744036	−	0.218469i
$598$	19.3507	+	2.78222i	0.791311	+	0.113773i
$599$	2.41815	−	8.23545i	0.0988028	−	0.336491i	−0.895226	−	0.445613i	$-0.852986\pi$
$599$	2.41815	−	8.23545i	0.0988028	−	0.336491i	0.994028	+	0.109122i	$0.0348039\pi$
$600$	−19.0309	+	9.84266i	−0.776935	+	0.401825i
$601$	31.7249	−	20.3883i	1.29408	−	0.831657i	0.301529	−	0.953457i	$-0.402503\pi$
$601$	31.7249	−	20.3883i	1.29408	−	0.831657i	0.992555	+	0.121800i	$0.0388666\pi$
$602$	0.964308	−	3.28413i	0.0393023	−	0.133851i
$603$	1.28456	−	0.184692i	0.0523114	−	0.00752124i
$604$	8.69992	+	3.97312i	0.353995	+	0.161664i
$605$	−11.1701	−	2.98518i	−0.454127	−	0.121365i
$606$	−4.79307	+	1.40737i	−0.194705	+	0.0571705i
$607$	3.13679	−	1.43252i	0.127318	−	0.0581444i	−0.350737	−	0.936474i	$-0.614069\pi$
$607$	3.13679	−	1.43252i	0.127318	−	0.0581444i	0.478056	+	0.878330i	$0.341342\pi$
$608$	14.1161	+	4.14485i	0.572482	+	0.168096i
$609$	38.3539	−	17.5157i	1.55418	−	0.709770i
$610$	0.522231	+	0.317848i	0.0211445	+	0.0128693i
$611$			29.0071i			1.17350i
$612$	11.5623	+	10.0188i	0.467380	+	0.404987i
$613$	−1.33837	+	0.611211i	−0.0540561	+	0.0246866i	−0.442260	−	0.896887i	$-0.645823\pi$
$613$	−1.33837	+	0.611211i	−0.0540561	+	0.0246866i	0.388204	+	0.921574i	$0.373096\pi$
$614$	2.37544	−	5.20150i	0.0958651	−	0.209915i
$615$	1.16651	+	0.498625i	0.0470381	+	0.0201065i
$616$	6.69143	−	5.79816i	0.269605	−	0.233614i
$617$	−0.407648	+	0.119696i	−0.0164113	+	0.00481879i	−0.289928	−	0.957048i	$-0.593631\pi$
$617$	−0.407648	+	0.119696i	−0.0164113	+	0.00481879i	0.273517	+	0.961867i	$0.411813\pi$
$618$	−3.33464	+	2.88949i	−0.134139	+	0.116232i
$619$	−6.04231	−	3.88316i	−0.242861	−	0.156077i	0.413548	−	0.910482i	$-0.364289\pi$
$619$	−6.04231	−	3.88316i	−0.242861	−	0.156077i	−0.656409	+	0.754405i	$0.727926\pi$
$620$	−10.4416	+	17.1557i	−0.419343	+	0.688989i
$621$	−19.2346	−	5.64780i	−0.771859	−	0.226638i
$622$		−	1.94322i		−	0.0779159i
$623$	−15.8847	+	8.79147i	−0.636408	+	0.352223i
$624$	−22.9184			−0.917470
$625$	−1.12422	+	24.9747i	−0.0449689	+	0.998988i
$626$	−0.364622	−	0.567363i	−0.0145732	−	0.0226764i
$627$	−8.48425	+	13.2017i	−0.338828	+	0.527227i
$628$	−2.52316	+	2.18633i	−0.100685	+	0.0872439i
$629$	−2.56086	−	8.72148i	−0.102108	−	0.347748i
$630$	−4.14610	−	1.77226i	−0.165185	−	0.0706084i
$631$	−15.2330	−	17.5798i	−0.606417	−	0.699842i	0.366652	−	0.930358i	$-0.380504\pi$
$631$	−15.2330	−	17.5798i	−0.606417	−	0.699842i	−0.973069	+	0.230516i	$0.925959\pi$
$632$	−28.5470	−	13.0370i	−1.13554	−	0.518584i
$633$	−40.3561	+	18.4300i	−1.60401	+	0.732527i
$634$	−2.25041	+	2.59711i	−0.0893750	+	0.103144i
$635$	−16.8927	−	34.7172i	−0.670365	−	1.37771i
$636$	−24.8318	−	38.6391i	−0.984645	−	1.53214i
$637$	−5.56008	−	12.1749i	−0.220298	−	0.482386i
$638$	11.4987	+	3.37632i	0.455238	+	0.133670i
$639$	−7.80830	−	17.0978i	−0.308891	−	0.676378i
$640$	18.8781	−	17.1839i	0.746223	−	0.679254i
$641$	−1.61235	+	1.86075i	−0.0636840	+	0.0734953i	−0.786698	−	0.617338i	$-0.788211\pi$
$641$	−1.61235	+	1.86075i	−0.0636840	+	0.0734953i	0.723014	+	0.690834i	$0.242756\pi$
$642$	1.75328	−	3.83915i	0.0691965	−	0.151519i
$643$	−23.5539	+	3.38655i	−0.928877	+	0.133552i	−0.590115	−	0.807320i	$-0.700917\pi$
$643$	−23.5539	+	3.38655i	−0.928877	+	0.133552i	−0.338763	+	0.940872i	$0.610008\pi$
$644$	30.3742	+	8.91868i	1.19691	+	0.351445i
$645$	14.9956	+	9.12683i	0.590450	+	0.359369i
$646$	5.72456	+	2.61432i	0.225230	+	0.102859i
$647$	9.23528	+	2.71172i	0.363076	+	0.106609i	0.458182	−	0.888858i	$-0.348501\pi$
$647$	9.23528	+	2.71172i	0.363076	+	0.106609i	−0.0951059	+	0.995467i	$0.530319\pi$
$648$	−20.6348	−	2.96683i	−0.810610	−	0.116548i
$649$	8.78809	+	29.9295i	0.344963	+	1.17483i
$650$	5.15947	−	8.96351i	0.202371	−	0.351578i
$651$	−22.1050	+	3.17821i	−0.866362	+	0.124564i
$652$	−8.72060	−	10.0641i	−0.341525	−	0.394141i
$653$	−28.9743	−	18.6207i	−1.13385	−	0.728683i	−0.167493	−	0.985873i	$-0.553567\pi$
$653$	−28.9743	−	18.6207i	−1.13385	−	0.728683i	−0.966361	+	0.257190i	$0.917203\pi$
$654$	9.37108	−	4.27963i	0.366438	−	0.167347i
$655$	16.0127	−	10.8530i	0.625669	−	0.424062i
$656$	−0.626844	−	0.0901266i	−0.0244741	−	0.00351885i
$657$		−	12.9469i		−	0.505106i
$658$	0.996812	−	6.93298i	0.0388598	−	0.270276i
$659$	31.7242	−	20.3879i	1.23580	−	0.794201i	0.251017	−	0.967983i	$-0.419235\pi$
$659$	31.7242	−	20.3879i	1.23580	−	0.794201i	0.984784	+	0.173782i	$0.0555987\pi$
$660$	9.24495	+	18.9999i	0.359859	+	0.739571i
$661$	5.81115	+	5.03539i	0.226027	+	0.195854i	0.760511	−	0.649325i	$-0.224948\pi$
$661$	5.81115	+	5.03539i	0.226027	+	0.195854i	−0.534484	+	0.845179i	$0.679494\pi$
$662$	2.19784	+	1.00372i	0.0854216	+	0.0390107i
$663$	−38.6242	−	5.55333i	−1.50004	−	0.215673i
$664$	2.19983	−	3.42301i	0.0853701	−	0.132838i
$665$	12.3511	+	1.46856i	0.478954	+	0.0569483i
$666$	−1.68421	−	1.45938i	−0.0652620	−	0.0565498i
$667$	25.9434	+	88.3551i	1.00453	+	3.42112i
$668$	2.86703	+	9.76421i	0.110929	+	0.377789i
$669$	27.0533	+	23.4418i	1.04594	+	0.906313i
$670$	0.0848661	−	0.713752i	0.00327867	−	0.0275747i
$671$	0.700525	−	1.09004i	0.0270435	−	0.0420805i
$672$	21.8029	+	3.13478i	0.841064	+	0.120927i
$673$	−16.9111	−	7.72302i	−0.651873	−	0.297701i	0.0618947	−	0.998083i	$-0.480286\pi$
$673$	−16.9111	−	7.72302i	−0.651873	−	0.297701i	−0.713768	+	0.700382i	$0.753013\pi$
$674$	1.35592	+	1.17491i	0.0522280	+	0.0452558i
$675$	−6.54483	+	8.34487i	−0.251911	+	0.321194i
$676$	5.10325	−	3.27966i	0.196279	−	0.126141i
$677$	1.48878	−	10.3547i	0.0572183	−	0.397962i	−0.941006	−	0.338391i	$-0.890117\pi$
$677$	1.48878	−	10.3547i	0.0572183	−	0.397962i	0.998224	−	0.0595715i	$-0.0189734\pi$
$678$		−	20.3401i		−	0.781155i
$679$	3.36844	+	0.484308i	0.129269	+	0.0185860i
$680$	15.0745	−	10.2171i	0.578080	−	0.391808i
$681$	−58.1501	+	26.5563i	−2.22832	+	1.01764i
$682$	−5.33977	−	3.43166i	−0.204470	−	0.131405i
$683$	9.67948	+	11.1707i	0.370375	+	0.427435i	0.910089	−	0.414413i	$-0.136013\pi$
$683$	9.67948	+	11.1707i	0.370375	+	0.427435i	−0.539714	+	0.841848i	$0.681468\pi$
$684$	−10.2416	+	1.47252i	−0.391598	+	0.0563033i
$685$	18.9670	−	12.8553i	0.724690	−	0.491176i
$686$	2.84402	+	9.68586i	0.108585	+	0.369808i
$687$	−2.80566	−	0.403394i	−0.107043	−	0.0153904i
$688$	−8.40833	−	2.46891i	−0.320564	−	0.0941262i
$689$	43.3425	+	19.7938i	1.65122	+	0.754086i
$690$	12.5875	−	20.6816i	0.479199	−	0.787333i
$691$	14.5815	+	4.28152i	0.554707	+	0.162877i	0.547059	−	0.837094i	$-0.315747\pi$
$691$	14.5815	+	4.28152i	0.554707	+	0.162877i	0.00764820	+	0.999971i	$0.497565\pi$
$692$	−8.51976	+	1.22496i	−0.323873	+	0.0465659i
$693$	−3.96995	+	8.69298i	−0.150806	+	0.330219i
$694$	−2.43569	+	2.81094i	−0.0924576	+	0.106702i
$695$	17.1559	+	18.8473i	0.650759	+	0.714919i
$696$	17.3438	+	37.9776i	0.657414	+	1.43954i
$697$	−1.03458	−	0.303780i	−0.0391875	−	0.0115065i
$698$	5.59911	+	12.2603i	0.211929	+	0.464060i
$699$	10.1390	+	15.7766i	0.383491	+	0.596724i
$700$	10.3352	−	13.1777i	0.390635	−	0.498072i
$701$	18.9522	−	21.8720i	0.715814	−	0.826093i	−0.274983	−	0.961449i	$-0.588672\pi$
$701$	18.9522	−	21.8720i	0.715814	−	0.826093i	0.990797	+	0.135356i	$0.0432177\pi$
$702$	3.99087	−	1.82257i	0.150626	−	0.0687884i
$703$	5.59188	+	2.55373i	0.210902	+	0.0963156i
$704$	−3.83765	−	4.42888i	−0.144637	−	0.166920i
$705$	33.0322	+	14.1196i	1.24406	+	0.531776i
$706$	3.47231	+	11.8256i	0.130682	+	0.445063i
$707$	6.34192	−	5.49530i	0.238512	−	0.206672i
$708$	−27.3376	+	42.5381i	−1.02741	+	1.59868i
$709$	−15.6766	−	24.3932i	−0.588746	−	0.916107i	−0.999990	−	0.00458160i	$-0.998542\pi$
$709$	−15.6766	−	24.3932i	−0.588746	−	0.916107i	0.411243	−	0.911526i	$-0.365095\pi$
$710$	−10.2652	+	1.73309i	−0.385248	+	0.0650416i
$711$	33.8733			1.27035
$712$	−8.70520	−	15.7288i	−0.326241	−	0.589464i
$713$		−	48.7729i		−	1.82656i
$714$	9.04072	+	2.65459i	0.338340	+	0.0993457i
$715$	−18.7246	−	11.3965i	−0.700261	−	0.426204i
$716$	−25.6323	−	16.4729i	−0.957924	−	0.615620i
$717$	−28.9470	+	25.0827i	−1.08105	+	0.936731i
$718$	−7.28971	+	2.14045i	−0.272050	+	0.0798810i
$719$	−25.8248	+	22.3773i	−0.963102	+	0.834532i	−0.986260	−	0.165199i	$-0.947173\pi$
$719$	−25.8248	+	22.3773i	−0.963102	+	0.834532i	0.0231585	+	0.999732i	$0.492628\pi$
$720$	−4.53749	+	10.6152i	−0.169102	+	0.395606i
$721$	3.07911	−	6.74231i	0.114672	−	0.251097i
$722$	4.93324	−	2.25294i	0.183596	−	0.0838456i
$723$	4.66173	+	4.03941i	0.173371	+	0.150227i
$724$			7.27756i			0.270468i
$725$	48.5012	+	4.56729i	1.80129	+	0.169625i
$726$	5.38832	−	2.46076i	0.199979	−	0.0913274i
$727$	−16.3518	−	4.80131i	−0.606453	−	0.178071i	−0.0359328	−	0.999354i	$-0.511440\pi$
$727$	−16.3518	−	4.80131i	−0.606453	−	0.178071i	−0.570520	+	0.821284i	$0.693258\pi$
$728$	−13.5441	+	6.18537i	−0.501977	+	0.229245i
$729$	7.86028	−	2.30799i	0.291122	−	0.0854810i
$730$	−6.92760	−	1.85139i	−0.256402	−	0.0685230i
$731$	−13.5723	−	6.19825i	−0.501989	−	0.229251i
$732$	2.07905	−	0.298923i	0.0768440	−	0.0110485i
$733$	−5.24555	+	17.8647i	−0.193749	+	0.659848i	0.804112	+	0.594478i	$0.202641\pi$
$733$	−5.24555	+	17.8647i	−0.193749	+	0.659848i	−0.997861	+	0.0653706i	$0.979177\pi$
$734$	−3.57299	+	2.29622i	−0.131881	+	0.0847550i
$735$	−16.5707	+	0.405299i	−0.611219	+	0.0149497i
$736$	−13.5531	+	46.1577i	−0.499575	+	1.70140i
$737$	−1.50791	−	0.216805i	−0.0555446	−	0.00798611i
$738$	−0.253650	+	0.0744783i	−0.00933698	+	0.00274158i
$739$	19.0490	−	2.73884i	0.700729	−	0.100750i	0.217264	−	0.976113i	$-0.430287\pi$
$739$	19.0490	−	2.73884i	0.700729	−	0.100750i	0.483466	+	0.875363i	$0.339378\pi$
$740$	6.85170	−	4.64390i	0.251873	−	0.170713i
$741$	19.9446	−	17.2821i	0.732682	−	0.634873i
$742$	−9.67906	−	6.22035i	−0.355329	−	0.228356i
$743$	8.64938	+	18.9395i	0.317315	+	0.694823i	0.999333	−	0.0365123i	$-0.0116248\pi$
$743$	8.64938	+	18.9395i	0.317315	+	0.694823i	−0.682018	+	0.731335i	$0.738898\pi$
$744$	−3.14703	−	21.8880i	−0.115376	−	0.802455i
$745$	−13.2876	−	41.4737i	−0.486820	−	1.51948i
$746$	−6.57367			−0.240679
$747$	−0.625018	+	4.34710i	−0.0228682	+	0.159052i
$748$	−9.70951	−	15.1083i	−0.355015	−	0.552414i
$749$			7.08991i			0.259060i
$750$	−7.69584	−	10.2385i	−0.281012	−	0.373857i
$751$	−14.2462	+	31.1948i	−0.519851	+	1.13831i	0.449646	+	0.893207i	$0.351550\pi$
$751$	−14.2462	+	31.1948i	−0.519851	+	1.13831i	−0.969496	+	0.245107i	$0.921177\pi$
$752$	−17.7504	−	2.55213i	−0.647292	−	0.0930665i
$753$	46.3416	+	29.7819i	1.68878	+	1.08531i
$754$	−16.9542	−	10.8958i	−0.617434	−	0.396801i
$755$	−3.17252	+	11.8711i	−0.115460	+	0.432032i
$756$	6.81657	−	2.00153i	0.247916	−	0.0727948i
$757$	4.31208	+	14.6856i	0.156725	+	0.533757i	0.999993	−	0.00373684i	$-0.00118948\pi$
$757$	4.31208	+	14.6856i	0.156725	+	0.533757i	−0.843268	+	0.537493i	$0.819371\pi$
$758$	−5.30911	+	6.12703i	−0.192835	+	0.222544i
$759$	−43.1680	−	27.7424i	−1.56690	−	1.00699i
$760$	−1.45415	+	12.2299i	−0.0527475	+	0.443624i
$761$	4.01598	−	27.9318i	0.145579	−	1.01253i	−0.777766	−	0.628554i	$-0.783647\pi$
$761$	4.01598	−	27.9318i	0.145579	−	1.01253i	0.923345	−	0.383971i	$-0.125444\pi$
$762$	17.9931	+	8.21716i	0.651820	+	0.297676i
$763$	−11.3330	+	13.0790i	−0.410281	+	0.473490i
$764$		−	23.3902i		−	0.846229i
$765$	−10.2192	+	16.7903i	−0.369475	+	0.607055i
$766$	11.2313	+	1.61482i	0.405805	+	0.0583459i
$767$		−	52.4565i		−	1.89410i
$768$	−0.307748	+	2.14044i	−0.0111049	+	0.0772363i
$769$	2.98096	+	20.7330i	0.107496	+	0.747652i	0.970264	+	0.242051i	$0.0778201\pi$
$769$	2.98096	+	20.7330i	0.107496	+	0.747652i	−0.862767	+	0.505601i	$0.831271\pi$
$770$	4.08373	+	3.36732i	0.147167	+	0.121350i
$771$	31.6358	−	49.2262i	1.13933	−	1.77284i
$772$	15.8684	+	18.3131i	0.571115	+	0.659102i
$773$	−6.87816	−	47.8386i	−0.247390	−	1.72064i	−0.613184	−	0.789940i	$-0.710111\pi$
$773$	−6.87816	−	47.8386i	−0.247390	−	1.72064i	0.365793	−	0.930696i	$-0.380798\pi$
$774$	−3.62088	+	0.520605i	−0.130150	+	0.0187127i
$775$	−23.9665	−	9.55840i	−0.860903	−	0.343348i
$776$	−0.479556	+	3.33538i	−0.0172150	+	0.119733i
$777$	8.83119	+	2.59307i	0.316817	+	0.0930259i
$778$	−0.564444	+	1.23596i	−0.0202363	+	0.0443113i
$779$	0.613469	−	0.394252i	0.0219798	−	0.0141256i
$780$	−5.91542	−	35.0375i	−0.211806	−	1.25455i
$781$	3.14011	+	21.8399i	0.112362	+	0.781495i
$782$	−8.54848	+	18.7186i	−0.305693	+	0.669375i
$783$	15.6181	+	13.5332i	0.558146	+	0.483636i
$784$	7.93940	−	2.33122i	0.283550	−	0.0832578i
$785$	−3.30935	−	2.72879i	−0.118116	−	0.0973948i
$786$	−2.79214	+	9.50917i	−0.0995925	+	0.339181i
$787$	1.03371	+	2.26351i	0.0368478	+	0.0806855i	0.927161	−	0.374663i	$-0.122242\pi$
$787$	1.03371	+	2.26351i	0.0368478	+	0.0806855i	−0.890313	+	0.455349i	$0.849514\pi$
$788$	10.9239	−	7.02033i	0.389146	−	0.250089i
$789$		−	3.35661i		−	0.119498i
$790$	4.84384	−	18.1249i	0.172336	−	0.644854i
$791$	14.1940	+	31.0806i	0.504681	+	1.10510i
$792$	−8.60768	−	3.93099i	−0.305860	−	0.139682i
$793$	−1.64678	+	1.42694i	−0.0584788	+	0.0506722i
$794$	−6.24827	+	5.41416i	−0.221743	+	0.192141i
$795$	43.6380	−	39.7217i	1.54768	−	1.40878i
$796$	−9.60320	−	11.0827i	−0.340376	−	0.392815i
$797$	28.1333	−	43.7762i	0.996532	−	1.55063i	0.171783	−	0.985135i	$-0.445047\pi$
$797$	28.1333	−	43.7762i	0.996532	−	1.55063i	0.824749	−	0.565499i	$-0.191316\pi$
$798$	−5.36083	+	3.44520i	−0.189771	+	0.121959i
$799$	−29.2963	−	8.60217i	−1.03643	−	0.304323i
$800$	20.0253	+	15.7057i	0.708002	+	0.555282i
$801$	15.5993	+	11.5395i	0.551175	+	0.407729i
$802$			9.76961i			0.344977i
$803$	−4.28176	+	14.5823i	−0.151100	+	0.514600i
$804$	−1.33512	−	2.07749i	−0.0470862	−	0.0732675i
$805$	−4.80200	+	40.3864i	−0.169248	+	1.42343i
$806$	6.99016	+	8.06707i	0.246218	+	0.284150i
$807$	−28.5131	+	8.37220i	−1.00371	+	0.294716i
$808$	5.44138	+	6.27969i	0.191427	+	0.220919i
$809$	7.84541	+	9.05408i	0.275830	+	0.318325i	0.876714	−	0.481011i	$-0.159730\pi$
$809$	7.84541	+	9.05408i	0.275830	+	0.318325i	−0.600885	+	0.799336i	$0.705185\pi$
$810$	−0.304724	−	12.4587i	−0.0107069	−	0.437754i
$811$	8.67836	+	19.0030i	0.304738	+	0.667284i	0.998604	−	0.0528204i	$-0.0168211\pi$
$811$	8.67836	+	19.0030i	0.304738	+	0.667284i	−0.693866	+	0.720105i	$0.744094\pi$
$812$	−24.6632	−	21.3708i	−0.865510	−	0.749968i
$813$	−2.46342			−0.0863958
$814$	1.41432	+	2.20073i	0.0495720	+	0.0771356i
$815$	10.8843	−	13.2000i	0.381262	−	0.462376i
$816$	6.79653	−	23.1469i	0.237926	−	0.810302i
$817$	9.17902	−	4.19192i	0.321133	−	0.146657i
$818$	5.28406	+	17.9959i	0.184753	+	0.629210i
$819$	10.5243	−	12.1457i	0.367750	−	0.424406i
$820$	−0.0240082	−	0.981579i	−0.000838404	−	0.0342782i
$821$	−5.87075	−	40.8319i	−0.204890	−	1.42504i	−0.789510	−	0.613737i	$-0.789665\pi$
$821$	−5.87075	−	40.8319i	−0.204890	−	1.42504i	0.584620	−	0.811307i	$-0.301244\pi$
$822$	−3.30728	+	11.2635i	−0.115354	+	0.392861i
$823$	−10.3765	−	16.1461i	−0.361701	−	0.562818i	0.611940	−	0.790904i	$-0.290390\pi$
$823$	−10.3765	−	16.1461i	−0.361701	−	0.562818i	−0.973641	+	0.228086i	$0.926753\pi$
$824$	6.67615	+	3.04889i	0.232575	+	0.106213i
$825$	−22.0923	+	15.7755i	−0.769156	+	0.549231i
$826$	−1.80264	+	12.5376i	−0.0627217	+	0.436239i
$827$	23.2189	−	6.81768i	0.807400	−	0.237074i	0.148118	−	0.988970i	$-0.452678\pi$
$827$	23.2189	−	6.81768i	0.807400	−	0.237074i	0.659282	+	0.751896i	$0.270860\pi$
$828$	−4.81496	−	33.4888i	−0.167331	−	1.16382i
$829$	−18.5596	+	2.66846i	−0.644600	+	0.0926795i	−0.456859	−	0.889539i	$-0.651026\pi$
$829$	−18.5596	+	2.66846i	−0.644600	+	0.0926795i	−0.187741	+	0.982219i	$0.560117\pi$
$830$	2.23666	+	0.956065i	0.0776357	+	0.0331855i
$831$	−5.79698	+	9.02028i	−0.201095	+	0.312910i
$832$	4.09393	+	8.96446i	0.141932	+	0.310787i
$833$	13.9451	−	2.00500i	0.483169	−	0.0694692i
$834$	−12.9245	−	1.85826i	−0.447538	−	0.0643463i
$835$	−11.7564	+	5.72040i	−0.406846	+	0.197962i
$836$	12.0223	+	1.72855i	0.415802	+	0.0597832i
$837$	−5.91764	−	9.20802i	−0.204543	−	0.318276i
$838$	−13.1240			−0.453360
$839$	19.7577	+	17.1202i	0.682112	+	0.591054i	0.925442	−	0.378890i	$-0.123694\pi$
$839$	19.7577	+	17.1202i	0.682112	+	0.591054i	−0.243329	+	0.969944i	$0.578240\pi$
$840$	0.450879	+	18.4342i	0.0155568	+	0.636042i
$841$	9.38266	−	65.2579i	0.323540	−	2.25027i
$842$	−17.3738	−	11.1655i	−0.598742	−	0.384788i
$843$	25.9710	−	40.4117i	0.894490	−	1.39185i
$844$	25.9507	+	22.4864i	0.893260	+	0.774015i
$845$	5.24624	+	5.76349i	0.180476	+	0.198270i
$846$	−7.18264	+	2.10901i	−0.246944	+	0.0725093i
$847$	−6.51640	+	7.52032i	−0.223906	+	0.258401i
$848$	−15.9259	+	24.7812i	−0.546898	+	0.850989i
$849$	21.1946	−	32.9794i	0.727395	−	1.13185i
$850$	7.52281	+	7.86906i	0.258030	+	0.269907i
$851$	−8.35036	+	18.2847i	−0.286247	+	0.626793i
$852$	−23.4227	+	27.0313i	−0.802449	+	0.926076i
$853$	−10.6969			−0.366253			−0.183127	−	0.983089i	$-0.558622\pi$
$853$	−10.6969			−0.366253			−0.183127	+	0.983089i	$0.558622\pi$
$854$	0.442631	−	0.284462i	0.0151465	−	0.00973409i
$855$	−4.05590	−	12.6594i	−0.138709	−	0.432943i
$856$	−7.02034			−0.239950
$857$	2.74590	−	19.0982i	0.0937982	−	0.652381i	−0.887631	−	0.460556i	$-0.847650\pi$
$857$	2.74590	−	19.0982i	0.0937982	−	0.652381i	0.981429	−	0.191825i	$-0.0614407\pi$
$858$	11.1161	−	1.59825i	0.379497	−	0.0545634i
$859$	−32.2335	+	14.7205i	−1.09979	+	0.502258i	−0.880809	−	0.473471i	$-0.843001\pi$
$859$	−32.2335	+	14.7205i	−1.09979	+	0.502258i	−0.218982	+	0.975729i	$0.570274\pi$
$860$	1.60420	−	13.4919i	0.0547028	−	0.460069i
$861$	0.825142	−	0.714989i	0.0281207	−	0.0243668i
$862$	2.11841	+	14.7339i	0.0721535	+	0.501838i
$863$	−0.910319	−	6.33141i	−0.0309876	−	0.215524i	0.968444	−	0.249231i	$-0.0801777\pi$
$863$	−0.910319	−	6.33141i	−0.0309876	−	0.215524i	−0.999432	+	0.0337072i	$0.989269\pi$
$864$	3.04159	+	10.3587i	0.103477	+	0.352410i
$865$	−3.37401	−	10.5311i	−0.114720	−	0.358067i
$866$	−5.23310	+	17.8223i	−0.177828	+	0.605627i
$867$	1.18220	−	2.58866i	0.0401497	−	0.0879157i
$868$	9.34479	+	14.5408i	0.317183	+	0.493546i
$869$	−38.1522	−	11.2025i	−1.29422	−	0.380018i
$870$	−20.6603	+	14.0030i	−0.700451	+	0.474747i
$871$	2.33038	+	1.06425i	0.0789619	+	0.0360607i
$872$	−12.9506	−	11.2218i	−0.438563	−	0.380017i
$873$	−1.02468	−	3.48973i	−0.0346801	−	0.118110i
$874$	−5.78140	−	12.6595i	−0.195559	−	0.428214i
$875$	18.9044	+	10.2745i	0.639085	+	0.347341i
$876$	−22.4102	+	10.2344i	−0.757169	+	0.345788i
$877$	15.4606	−	9.93590i	0.522066	−	0.335512i	−0.252923	−	0.967487i	$-0.581392\pi$
$877$	15.4606	−	9.93590i	0.522066	−	0.335512i	0.774989	+	0.631975i	$0.217755\pi$
$878$	−4.06740			−0.137268
$879$	−18.1371	+	20.9313i	−0.611748	+	0.705995i
$880$	8.62132	−	10.4555i	0.290625	−	0.352456i
$881$	−12.3616	+	27.0682i	−0.416474	+	0.911950i	0.578857	+	0.815429i	$0.303499\pi$
$881$	−12.3616	+	27.0682i	−0.416474	+	0.911950i	−0.995331	+	0.0965211i	$0.969228\pi$
$882$	2.61044	−	2.26196i	0.0878981	−	0.0761641i
$883$	37.5529	+	43.3383i	1.26376	+	1.45845i	0.830340	+	0.557257i	$0.188146\pi$
$883$	37.5529	+	43.3383i	1.26376	+	1.45845i	0.433415	+	0.901195i	$0.357308\pi$
$884$	8.50879	+	28.9783i	0.286182	+	0.974645i
$885$	−59.7354	−	25.5340i	−2.00798	−	0.858315i
$886$	−2.35565	−	1.51389i	−0.0791397	−	0.0508600i
$887$	20.7124	−	13.3111i	0.695455	−	0.446942i	−0.144566	−	0.989495i	$-0.546179\pi$
$887$	20.7124	−	13.3111i	0.695455	−	0.446942i	0.840021	+	0.542553i	$0.182542\pi$
$888$	−2.56762	+	8.74453i	−0.0861638	+	0.293447i
$889$	−33.2285			−1.11445
$890$	8.40524	−	6.69672i	0.281744	−	0.224475i
$891$	−26.4134			−0.884884
$892$	7.80562	−	26.5835i	0.261351	−	0.890081i
$893$	17.3717	−	11.1641i	0.581321	−	0.373592i
$894$	18.7702	+	12.0629i	0.627771	+	0.403444i
$895$	15.3861	−	35.9949i	0.514299	−	1.20318i
$896$	−6.18976	−	21.0804i	−0.206786	−	0.704247i
$897$	56.5102	+	65.2162i	1.88682	+	2.17751i
$898$	2.95504	−	2.56055i	0.0986109	−	0.0854468i
$899$	−20.8867	+	45.7354i	−0.696610	+	1.52536i
$900$	−17.3997	−	4.19703i	−0.579989	−	0.139901i
$901$	−32.8445	+	37.9046i	−1.09421	+	1.26279i
$902$	0.310323			0.0103326
$903$	12.7099	−	8.16817i	0.422959	−	0.271820i
$904$	−30.7756	+	14.0547i	−1.02358	+	0.467454i
$905$	−9.21941	+	1.55652i	−0.306463	+	0.0517405i
$906$	−2.61519	−	5.72647i	−0.0868840	−	0.190249i
$907$	−8.20274	−	27.9360i	−0.272368	−	0.927599i	−0.976134	−	0.217168i	$-0.930318\pi$
$907$	−8.20274	−	27.9360i	−0.272368	−	0.927599i	0.703767	−	0.710431i	$-0.251500\pi$
$908$	37.3930	+	32.4012i	1.24093	+	1.07527i
$909$	−8.15807	−	3.72567i	−0.270586	−	0.123573i
$910$	−4.99395	−	7.36817i	−0.165548	−	0.244252i
$911$	−1.08271	−	0.317912i	−0.0358717	−	0.0105329i	0.263747	−	0.964592i	$-0.415041\pi$
$911$	−1.08271	−	0.317912i	−0.0358717	−	0.0105329i	−0.299619	+	0.954059i	$0.596860\pi$
$912$	8.82069	+	13.7253i	0.292082	+	0.454489i
$913$	2.14164	−	4.68953i	0.0708778	−	0.155201i
$914$	0.203914	−	0.694467i	0.00674487	−	0.0229709i
$915$	0.823350	+	2.56987i	0.0272191	+	0.0849572i
$916$	0.618079	+	2.10498i	0.0204219	+	0.0695506i
$917$	−2.36931	−	16.4789i	−0.0782416	−	0.544182i
$918$	0.657231	+	4.57114i	0.0216918	+	0.150870i
$919$	13.6723	−	11.8471i	0.451008	−	0.390800i	−0.399525	−	0.916722i	$-0.630825\pi$
$919$	13.6723	−	11.8471i	0.451008	−	0.390800i	0.850533	+	0.525922i	$0.176280\pi$
$920$	−39.9901	−	4.75488i	−1.31843	−	0.156764i
$921$	22.9596	−	10.4853i	0.756546	−	0.345503i
$922$	−3.23016	+	0.464427i	−0.106380	+	0.0152951i
$923$	5.28065	−	36.7277i	0.173815	−	1.20891i
$924$	18.1852			0.598248
$925$	7.34845	+	7.68668i	0.241616	+	0.252737i
$926$	18.0089	−	11.5736i	0.591810	−	0.380333i
$927$	−7.92176			−0.260185
$928$	32.4758	−	37.4791i	1.06607	−	1.23031i
$929$	−18.2258	+	39.9090i	−0.597970	+	1.30937i	0.332534	+	0.943091i	$0.392096\pi$
$929$	−18.2258	+	39.9090i	−0.597970	+	1.30937i	−0.930504	+	0.366281i	$0.880631\pi$
$930$	12.5890	−	4.03334i	0.412810	−	0.132259i
$931$	−5.15131	+	8.01559i	−0.168827	+	0.262700i
$932$	7.84733	−	12.2107i	0.257048	−	0.399974i
$933$	5.61704	−	6.48241i	0.183894	−	0.212224i
$934$	4.96198	−	1.45697i	0.162361	−	0.0476734i
$935$	17.0629	−	15.5316i	0.558018	−	0.507939i
$936$	12.0265	+	10.4210i	0.393099	+	0.340623i
$937$	−11.4535	+	17.8220i	−0.374169	+	0.582219i	−0.976365	−	0.216130i	$-0.930656\pi$
$937$	−11.4535	+	17.8220i	−0.374169	+	0.582219i	0.602195	+	0.798349i	$0.294293\pi$
$938$	−0.520410	−	0.334447i	−0.0169920	−	0.0109201i
$939$	0.423663	−	2.94664i	0.0138257	−	0.0961600i
$940$	−0.679845	−	27.7955i	−0.0221741	−	0.906590i
$941$	−24.7965	−	21.4863i	−0.808343	−	0.700433i	0.149174	−	0.988811i	$-0.452339\pi$
$941$	−24.7965	−	21.4863i	−0.808343	−	0.700433i	−0.957517	+	0.288378i	$0.906884\pi$
$942$	2.19755			0.0716000
$943$	1.28915	+	2.00596i	0.0419807	+	0.0653232i
$944$	32.0999	+	4.61527i	1.04476	+	0.150214i
$945$	3.99351	+	8.20734i	0.129909	+	0.266985i
$946$	4.25045	+	0.611123i	0.138194	+	0.0198693i
$947$	29.2974	−	4.21233i	0.952038	−	0.136882i	0.351242	−	0.936285i	$-0.385759\pi$
$947$	29.2974	−	4.21233i	0.952038	−	0.136882i	0.600796	+	0.799402i	$0.294850\pi$
$948$	−26.7765	−	58.6323i	−0.869660	−	1.90429i
$949$	13.8177	−	21.5008i	0.448542	−	0.697946i
$950$	−7.35378	+	0.359944i	−0.238588	+	0.0116781i
$951$	−15.0143	+	2.15873i	−0.486873	+	0.0700017i
$952$	−2.23049	−	15.5134i	−0.0722905	−	0.502792i
$953$	−41.3588	+	12.1440i	−1.33974	+	0.393384i	−0.871578	−	0.490257i	$-0.836903\pi$
$953$	−41.3588	+	12.1440i	−1.33974	+	0.393384i	−0.468165	+	0.883641i	$0.655085\pi$
$954$	−1.74999	+	12.1714i	−0.0566580	+	0.394065i
$955$	29.6314	−	5.00269i	0.958849	−	0.161883i
$956$	26.9662	+	12.3150i	0.872148	+	0.398296i
$957$	28.5991	+	44.5011i	0.924478	+	1.43852i
$958$	−4.23648	+	14.4281i	−0.136874	+	0.466151i
$959$	−2.80643	−	19.5192i	−0.0906245	−	0.630307i
$960$	12.2011	−	0.298425i	0.393790	−	0.00963162i
$961$	−2.86155	+	3.30241i	−0.0923082	+	0.106529i
$962$	−1.23942	−	4.22108i	−0.0399606	−	0.136093i
$963$	6.89264	−	3.14776i	0.222112	−	0.101435i
$964$	1.34504	−	4.58077i	0.0433207	−	0.147537i
$965$	−19.8056	+	24.0193i	−0.637564	+	0.773208i
$966$	−11.2653	−	17.5292i	−0.362457	−	0.563993i
$967$	−20.2563			−0.651400			−0.325700	−	0.945473i	$-0.605600\pi$
$967$	−20.2563			−0.651400			−0.325700	+	0.945473i	$0.605600\pi$
$968$	−7.44653	−	6.45245i	−0.239340	−	0.207390i
$969$	11.5397	+	25.2685i	0.370709	+	0.811740i
$970$	−2.01381	+	0.0492553i	−0.0646595	+	0.00158149i
$971$	19.2906	+	22.2626i	0.619066	+	0.714440i	0.975529	−	0.219869i	$-0.0705631\pi$
$971$	19.2906	+	22.2626i	0.619066	+	0.714440i	−0.356464	+	0.934309i	$0.616018\pi$
$972$	−20.7869	−	23.9893i	−0.666739	−	0.769458i
$973$	21.0460	−	6.17966i	0.674703	−	0.198111i
$974$	12.5467	+	14.4797i	0.402023	+	0.463959i
$975$	43.1213	−	14.9876i	1.38099	−	0.479988i
$976$	−0.728305	−	1.13326i	−0.0233125	−	0.0362749i
$977$	3.54554	−	12.0750i	0.113432	−	0.386313i	−0.883134	−	0.469121i	$-0.844571\pi$
$977$	3.54554	−	12.0750i	0.113432	−	0.386313i	0.996566	+	0.0828082i	$0.0263889\pi$
$978$			8.76536i			0.280285i
$979$	−13.7535	−	18.1562i	−0.439564	−	0.580274i
$980$	5.61318	+	11.5360i	0.179306	+	0.368505i
$981$	17.7466	+	5.21088i	0.566606	+	0.166371i
$982$	8.07111	−	5.18699i	0.257560	−	0.165524i
$983$	1.18551	−	1.84468i	0.0378117	−	0.0588362i	−0.821833	−	0.569728i	$-0.807048\pi$
$983$	1.18551	−	1.84468i	0.0378117	−	0.0588362i	0.859645	+	0.510892i	$0.170685\pi$
$984$	0.707973	+	0.817044i	0.0225694	+	0.0260464i
$985$	11.2299	+	12.3371i	0.357816	+	0.393094i
$986$	16.0322	−	13.8920i	0.510570	−	0.442411i
$987$	23.3657	−	20.2465i	0.743737	−	0.644452i
$988$	−18.5798	−	8.48510i	−0.591101	−	0.269947i
$989$	13.7070	+	30.0142i	0.435858	+	0.954397i
$990$	1.46054	−	5.46512i	0.0464191	−	0.173693i
$991$			16.6839i			0.529982i	0.964251	+	0.264991i	$0.0853690\pi$
$991$			16.6839i			0.529982i	−0.964251	+	0.264991i	$0.914631\pi$
$992$	−22.0966	+	14.2007i	−0.701569	+	0.450871i
$993$	4.43047	+	9.70138i	0.140597	+	0.307864i
$994$	−2.52425	+	8.59680i	−0.0800643	+	0.272674i
$995$	11.9859	−	14.5359i	0.379979	−	0.460821i
$996$	8.01861	−	2.35448i	0.254079	−	0.0746044i
$997$	−0.590287	−	0.511487i	−0.0186946	−	0.0161990i	0.645463	−	0.763791i	$-0.276664\pi$
$997$	−0.590287	−	0.511487i	−0.0186946	−	0.0161990i	−0.664158	+	0.747592i	$0.731210\pi$
$998$	3.51187	−	7.68993i	0.111166	−	0.243421i
$999$	0.641998	+	4.46520i	0.0203119	+	0.141273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	445.2.q.a.44.19	✓	440
5.4	even	2	inner	445.2.q.a.44.26	yes	440
89.87	even	22	inner	445.2.q.a.354.26	yes	440
445.354	even	22	inner	445.2.q.a.354.19	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
445.2.q.a.44.19	✓	440	1.1	even	1	trivial
445.2.q.a.44.26	yes	440	5.4	even	2	inner
445.2.q.a.354.19	yes	440	445.354	even	22	inner
445.2.q.a.354.26	yes	440	89.87	even	22	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:	\( N \)	\(=\)	\( 445 = 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	445.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.143528 + 0.488812i) q^{2} +(-1.89175 + 1.21575i) q^{3} +(1.46417 + 0.940965i) q^{4} +(-0.878884 + 2.05610i) q^{5} +(-0.322756 - 1.09921i) q^{6} +(1.26025 + 1.45441i) q^{7} +(-1.44014 + 1.24788i) q^{8} +(0.854416 - 1.87091i) q^{9} +(-0.878903 - 0.724718i) q^{10} +(-1.58109 + 1.82468i) q^{11} -3.91383 q^{12} +(3.41568 - 2.19512i) q^{13} +(-0.891813 + 0.407277i) q^{14} +(-0.837087 - 4.95814i) q^{15} +(1.04275 + 2.28330i) q^{16} +(1.20407 + 4.10070i) q^{17} +(0.791890 + 0.686177i) q^{18} +(-2.62921 - 1.20072i) q^{19} +(-3.22156 + 2.18349i) q^{20} +(-4.15228 - 1.21922i) q^{21} +(-0.664992 - 1.03475i) q^{22} +(3.92620 - 8.59719i) q^{23} +(1.20726 - 4.11154i) q^{24} +(-3.45513 - 3.61415i) q^{25} +(0.582756 + 1.98469i) q^{26} +(-0.301857 - 2.09946i) q^{27} +(0.476676 + 3.31535i) q^{28} +(-7.36338 + 6.38040i) q^{29} +(2.54374 + 0.302455i) q^{30} +(4.69411 - 2.14373i) q^{31} +(-5.03812 + 0.724372i) q^{32} +(0.772671 - 5.37405i) q^{33} -2.17729 q^{34} +(-4.09803 + 1.31295i) q^{35} +(3.01147 - 1.93535i) q^{36} -2.12683 q^{37} +(0.964293 - 1.11285i) q^{38} +(-3.79288 + 8.30525i) q^{39} +(-1.30007 - 4.05781i) q^{40} +(-0.136400 + 0.212243i) q^{41} +(1.19194 - 1.85469i) q^{42} +(-2.28623 + 2.63845i) q^{43} +(-4.03194 + 1.18388i) q^{44} +(3.09585 + 3.40108i) q^{45} +(3.63889 + 3.15311i) q^{46} +(-3.86246 + 6.01010i) q^{47} +(-4.74855 - 3.05171i) q^{48} +(0.469136 - 3.26291i) q^{49} +(2.26255 - 1.17017i) q^{50} +(-7.26325 - 6.29364i) q^{51} +7.06667 q^{52} +(6.34464 + 9.87245i) q^{53} +(1.06957 + 0.153781i) q^{54} +(-2.36213 - 4.85456i) q^{55} +(-3.62986 - 0.521896i) q^{56} +(6.43359 - 0.925011i) q^{57} +(-2.06197 - 4.51508i) q^{58} +(6.98487 - 10.8687i) q^{59} +(3.43980 - 8.04723i) q^{60} +(-0.531207 + 0.0763761i) q^{61} +(0.374143 + 2.60222i) q^{62} +(3.79784 - 1.11515i) q^{63} +(-0.345429 + 2.40251i) q^{64} +(1.51142 + 8.95225i) q^{65} +(2.51600 + 1.14902i) q^{66} +(0.341130 + 0.530808i) q^{67} +(-2.09565 + 7.13711i) q^{68} +(3.02467 + 21.0370i) q^{69} +(-0.0536041 - 2.19161i) q^{70} +(5.98461 - 6.90661i) q^{71} +(1.10420 + 3.76057i) q^{72} +(5.72590 - 2.61493i) q^{73} +(0.305260 - 1.03962i) q^{74} +(10.9302 + 2.63649i) q^{75} +(-2.71978 - 4.23206i) q^{76} -4.64639 q^{77} +(-3.51532 - 3.04604i) q^{78} +(6.84151 + 14.9808i) q^{79} +(-5.61115 + 0.137242i) q^{80} +(7.16418 + 8.26790i) q^{81} +(-0.0841695 - 0.0971367i) q^{82} +(-2.04879 + 0.601579i) q^{83} +(-4.93240 - 5.69230i) q^{84} +(-9.48971 - 1.12834i) q^{85} +(-0.961567 - 1.49623i) q^{86} +(6.17267 - 21.0222i) q^{87} -4.60080i q^{88} +(-1.95283 + 9.22965i) q^{89} +(-2.10683 + 1.02514i) q^{90} +(7.49721 + 2.20138i) q^{91} +(13.8383 - 8.89333i) q^{92} +(-6.27384 + 9.76229i) q^{93} +(-2.38344 - 2.75063i) q^{94} +(4.77958 - 4.35064i) q^{95} +(8.65020 - 7.49544i) q^{96} +(1.33641 - 1.15801i) q^{97} +(1.52762 + 0.697639i) q^{98} +(2.06289 + 4.51711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 26 q^{4} - 9 q^{5} - 22 q^{6} - 84 q^{9} - 39 q^{10} - 22 q^{11} - 22 q^{14} - 11 q^{15} - 46 q^{16} - 22 q^{19} - 33 q^{20} + 10 q^{21} - 66 q^{24} + 39 q^{25} - 22 q^{29} + 66 q^{30} - 22 q^{31}+ \cdots + 46 q^{99}+O(q^{100}) \) 440 * q + 26 * q^4 - 9 * q^5 - 22 * q^6 - 84 * q^9 - 39 * q^10 - 22 * q^11 - 22 * q^14 - 11 * q^15 - 46 * q^16 - 22 * q^19 - 33 * q^20 + 10 * q^21 - 66 * q^24 + 39 * q^25 - 22 * q^29 + 66 * q^30 - 22 * q^31 + 72 * q^34 - 44 * q^35 - 20 * q^36 + 30 * q^39 - 120 * q^40 - 44 * q^41 + 6 * q^44 + 5 * q^45 - 22 * q^46 - 74 * q^49 - 5 * q^50 - 22 * q^51 - 22 * q^54 - 38 * q^55 + 88 * q^56 - 66 * q^60 - 66 * q^61 + 122 * q^64 - 11 * q^65 + 66 * q^66 + 166 * q^69 - 220 * q^70 - 38 * q^71 - 110 * q^74 + 198 * q^75 - 198 * q^76 - 20 * q^79 + 234 * q^80 - 80 * q^81 - 178 * q^84 + 85 * q^85 - 66 * q^86 + 30 * q^89 + 54 * q^90 - 50 * q^91 + 242 * q^94 + 132 * q^95 - 352 * q^96 + 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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