LMFDB - Embedded newform 445.2.q.a.44.26

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			44.26
Character	$\chi$	$=$	445.44
Dual form			445.2.q.a.354.26

$q$-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} +(2.16025 - 0.577324i) 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} +(0.0278542 - 1.13882i) q^{10} +(-1.58109 + 1.82468i) q^{11} +3.91383 q^{12} +(-3.41568 + 2.19512i) q^{13} +(-0.891813 + 0.407277i) q^{14} +(3.38478 - 3.71849i) 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} +(3.70622 + 1.18742i) 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} +(4.33339 - 2.49433i) 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} +(-1.33183 - 2.18823i) q^{30} +(4.69411 - 2.14373i) q^{31} +(5.03812 - 0.724372i) q^{32} +(-0.772671 + 5.37405i) q^{33} -2.17729 q^{34} +(-3.56213 - 2.41432i) q^{35} +(3.01147 - 1.93535i) q^{36} +2.12683 q^{37} +(-0.964293 + 1.11285i) q^{38} +(-3.79288 + 8.30525i) q^{39} +(2.39062 - 3.52717i) 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} +(0.765633 - 4.53491i) 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} +(-0.597297 - 2.47622i) 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} +(8.45486 - 2.25955i) 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} +(-6.11143 + 6.71398i) 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} +(-1.69141 + 1.39469i) 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} +(5.16520 - 9.98700i) q^{75} +(-2.71978 - 4.23206i) q^{76} +4.64639 q^{77} +(3.51532 + 3.04604i) q^{78} +(6.84151 + 14.9808i) q^{79} +(3.57080 + 4.33050i) 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} +(-4.96854 - 8.16341i) 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} +(-6.37297 - 1.07595i) 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	−0.893056	−	0.449946i	$-0.851443\pi$
$2$	0.143528	−	0.488812i	0.101490	−	0.345642i	0.994545	+	0.104304i	$0.0332614\pi$
$3$	1.89175	−	1.21575i	1.09220	−	0.701916i	0.134858	−	0.990865i	$-0.456942\pi$
$3$	1.89175	−	1.21575i	1.09220	−	0.701916i	0.957344	+	0.288949i	$0.0933058\pi$
$4$	1.46417	+	0.940965i	0.732085	+	0.470483i
$5$	2.16025	−	0.577324i	0.966095	−	0.258187i
$5$	2.16025	−	0.577324i	0.966095	−	0.258187i
$6$	−0.322756	−	1.09921i	−0.131764	−	0.448749i
$7$	−1.26025	−	1.45441i	−0.476330	−	0.549714i	0.465831	−	0.884874i	$-0.345755\pi$
$7$	−1.26025	−	1.45441i	−0.476330	−	0.549714i	−0.942161	+	0.335159i	$0.891210\pi$
$8$	1.44014	−	1.24788i	0.509165	−	0.441194i
$9$	0.854416	−	1.87091i	0.284805	−	0.623637i
$10$	0.0278542	−	1.13882i	0.00880826	−	0.360127i
$11$	−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	−0.920467	−	0.390821i	$-0.872191\pi$
$13$	−3.41568	+	2.19512i	−0.947339	+	0.608818i	−0.0268721	+	0.999639i	$0.508555\pi$
$14$	−0.891813	+	0.407277i	−0.238347	+	0.108849i
$15$	3.38478	−	3.71849i	0.873945	−	0.960110i
$16$	1.04275	+	2.28330i	0.260687	+	0.570825i
$17$	−1.20407	−	4.10070i	−0.292031	−	0.994566i	−0.966586	−	0.256342i	$-0.917483\pi$
$17$	−1.20407	−	4.10070i	−0.292031	−	0.994566i	0.674555	−	0.738224i	$-0.264335\pi$
$18$	−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	$0.743936\pi$
$20$	3.70622	+	1.18742i	0.828736	+	0.265516i
$21$	−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	$0.581838\pi$
$23$	−3.92620	+	8.59719i	−0.818670	+	1.79264i	−0.564393	+	0.825506i	$0.690890\pi$
$24$	1.20726	−	4.11154i	0.246430	−	0.839264i
$25$	4.33339	−	2.49433i	0.866679	−	0.498867i
$26$	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	$0.912876\pi$
$30$	−1.33183	−	2.18823i	−0.243158	−	0.399514i
$31$	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
$35$	−3.56213	−	2.41432i	−0.602109	−	0.408094i
$36$	3.01147	−	1.93535i	0.501912	−	0.322559i
$37$	2.12683			0.349648			0.174824	−	0.984600i	$-0.444064\pi$
$37$	2.12683			0.349648			0.174824	+	0.984600i	$0.444064\pi$
$38$	−0.964293	+	1.11285i	−0.156429	+	0.180529i
$39$	−3.79288	+	8.30525i	−0.607347	+	1.32990i
$40$	2.39062	−	3.52717i	0.377991	−	0.557695i
$41$	−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	−0.554157	−	0.832412i	$-0.686959\pi$
$43$	2.28623	−	2.63845i	0.348647	−	0.402360i	0.902804	+	0.430052i	$0.141505\pi$
$44$	−4.03194	+	1.18388i	−0.607838	+	0.178477i
$45$	0.765633	−	4.53491i	0.114134	−	0.676025i
$46$	3.63889	+	3.15311i	0.536525	+	0.464901i
$47$	3.86246	−	6.01010i	0.563397	−	0.876664i	−0.436335	−	0.899784i	$-0.643724\pi$
$47$	3.86246	−	6.01010i	0.563397	−	0.876664i	0.999733	+	0.0231206i	$0.00736018\pi$
$48$	4.74855	+	3.05171i	0.685394	+	0.440476i
$49$	0.469136	−	3.26291i	0.0670195	−	0.466131i
$50$	−0.597297	−	2.47622i	−0.0844705	−	0.350191i
$51$	−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	$-0.883451\pi$
$53$	−6.34464	−	9.87245i	−0.871503	−	1.35609i	0.0622100	−	0.998063i	$-0.480185\pi$
$54$	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	$-0.136212\pi$
$60$	8.45486	−	2.25955i	1.09152	−	0.291706i
$61$	−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
$65$	−6.11143	+	6.71398i	−0.758030	+	0.832766i
$66$	2.51600	+	1.14902i	0.309698	+	0.141434i
$67$	−0.341130	−	0.530808i	−0.0416756	−	0.0648486i	0.819791	−	0.572663i	$-0.194090\pi$
$67$	−0.341130	−	0.530808i	−0.0416756	−	0.0648486i	−0.861466	+	0.507815i	$0.830453\pi$
$68$	2.09565	−	7.13711i	0.254134	−	0.865502i
$69$	3.02467	+	21.0370i	0.364127	+	2.53256i
$70$	−1.69141	+	1.39469i	−0.202162	+	0.166697i
$71$	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	−0.721285	−	0.692638i	$-0.756448\pi$
$73$	−5.72590	+	2.61493i	−0.670165	+	0.306054i	0.0511197	+	0.998693i	$0.483721\pi$
$74$	0.305260	−	1.03962i	0.0354857	−	0.120853i
$75$	5.16520	−	9.98700i	0.596426	−	1.15320i
$76$	−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	$0.486473\pi$
$80$	3.57080	+	4.33050i	0.399228	+	0.484165i
$81$	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	−0.167349	−	0.985898i	$-0.553521\pi$
$83$	2.04879	−	0.601579i	0.224884	−	0.0660319i	0.392233	+	0.919866i	$0.371703\pi$
$84$	−4.93240	−	5.69230i	−0.538169	−	0.621081i
$85$	−4.96854	−	8.16341i	−0.538914	−	0.885446i
$86$	−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
$95$	−6.37297	−	1.07595i	−0.653853	−	0.110391i
$96$	8.65020	−	7.49544i	0.882858	−	0.765001i
$97$	−1.33641	+	1.15801i	−0.135692	+	0.117578i	−0.720063	−	0.693909i	$-0.755887\pi$
$97$	−1.33641	+	1.15801i	−0.135692	+	0.117578i	0.584370	+	0.811487i	$0.301342\pi$
$98$	−1.52762	−	0.697639i	−0.154313	−	0.0704722i
$99$	2.06289	+	4.51711i	0.207329	+	0.453986i
$100$	8.69191	+	0.425441i	0.869191	+	0.0425441i
$101$		−	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	0.971932	−	0.235263i	$-0.0755953\pi$
$103$	1.59999	+	3.50349i	0.157652	+	0.345209i	−0.814280	+	0.580472i	$0.802868\pi$
$104$	−2.17978	+	7.42364i	−0.213745	+	0.727948i
$105$	−9.67387	−	0.236611i	−0.944073	−	0.0230909i
$106$	−5.73641	+	1.68436i	−0.557169	+	0.163600i
$107$	−2.78426	−	2.41258i	−0.269165	−	0.233233i	0.509811	−	0.860286i	$-0.329715\pi$
$107$	−2.78426	−	2.41258i	−0.269165	−	0.233233i	−0.778976	+	0.627054i	$0.784261\pi$
$108$	−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	$0.812823\pi$
$110$	2.03394	+	1.85140i	0.193928	+	0.176524i
$111$	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	−0.646312	−	0.763073i	$-0.723690\pi$
$113$	−17.0356	−	5.00210i	−1.60257	−	0.470558i	−0.956261	+	0.292515i	$0.905508\pi$
$114$	−0.471245	+	3.27758i	−0.0441362	+	0.306974i
$115$	−3.51823	+	20.8388i	−0.328077	+	1.94323i
$116$	−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
$120$	0.234289	−	9.57894i	0.0213876	−	0.874433i
$121$	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
$125$	7.92119	−	7.89017i	0.708493	−	0.705718i
$126$			2.01649i			0.179643i
$127$	11.3071	−	13.0491i	1.00334	−	1.15792i	0.0159116	−	0.999873i	$-0.494935\pi$
$127$	11.3071	−	13.0491i	1.00334	−	1.15792i	0.987432	−	0.158046i	$-0.0505196\pi$
$128$	10.3847	+	4.74254i	0.917888	+	0.419185i
$129$	1.11727	−	7.77078i	0.0983701	−	0.684179i
$130$	2.40471	+	3.95099i	0.210907	+	0.346524i
$131$	−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
$135$	1.86416	+	4.36111i	0.160441	+	0.375344i
$136$	−6.85123	−	4.40302i	−0.587488	−	0.377556i
$137$	8.62032	+	5.53994i	0.736484	+	0.473309i	0.854336	−	0.519722i	$-0.173964\pi$
$137$	8.62032	+	5.53994i	0.736484	+	0.473309i	−0.117852	+	0.993031i	$0.537601\pi$
$138$	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	$-0.0242247\pi$
$140$	−2.94377	−	6.88681i	−0.248794	−	0.582041i
$141$		−	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
$145$	−12.2232	+	18.0344i	−1.01508	+	1.49767i
$146$	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	$0.978735\pi$
$150$	−4.14041	−	3.95823i	−0.338063	−	0.323188i
$151$	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
$155$	8.90285	−	7.34103i	0.715094	−	0.589646i
$156$	−13.3684	+	8.59133i	−1.07033	+	0.687857i
$157$	0.540429	−	1.84053i	0.0431309	−	0.146890i	−0.935112	−	0.354351i	$-0.884702\pi$
$157$	0.540429	−	1.84053i	0.0431309	−	0.146890i	0.978243	+	0.207461i	$0.0665199\pi$
$158$	8.30475	−	1.19404i	0.660691	−	0.0949930i
$159$	−24.0049	−	10.9627i	−1.90372	−	0.869398i
$160$	10.4654	−	4.47346i	0.827364	−	0.353658i
$161$	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	0.556296	−	0.830984i	$-0.312222\pi$
$163$	7.34133	+	2.15561i	0.575017	+	0.168840i	0.0187216	+	0.999825i	$0.494040\pi$
$164$	−0.399426	+	0.182412i	−0.0311899	+	0.0142440i
$165$	1.43340	+	12.0554i	0.111590	+	0.938511i
$166$		−	1.08782i		−	0.0844309i
$167$	−4.41884	−	3.82895i	−0.341940	−	0.296293i	0.466913	−	0.884303i	$-0.345366\pi$
$167$	−4.41884	−	3.82895i	−0.341940	−	0.296293i	−0.808854	+	0.588010i	$0.799912\pi$
$168$	−7.50129	+	3.42573i	−0.578737	+	0.264300i
$169$	1.44790	−	3.17045i	0.111377	−	0.243881i
$170$	−4.70350	+	1.25700i	−0.360742	+	0.0964077i
$171$	−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	−0.501105	−	0.865387i	$-0.667073\pi$
$173$	3.73752	−	3.23858i	0.284159	−	0.246225i	0.785264	+	0.619162i	$0.212527\pi$
$174$	9.38995	+	6.03455i	0.711850	+	0.457478i
$175$	−9.08894	−	3.15903i	−0.687059	−	0.238800i
$176$	−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	$0.727013\pi$
$180$	5.38821	−	5.91945i	0.401614	−	0.441210i
$181$	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
$185$	4.59449	−	1.22787i	0.337793	−	0.0902747i
$186$	−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	−0.236975	−	0.971516i	$-0.576156\pi$
$193$	−13.3586	−	3.92244i	−0.961572	−	0.282343i	−0.724597	+	0.689173i	$0.757974\pi$
$194$	0.374236	+	0.819463i	0.0268686	+	0.0588340i
$195$	−3.39876	+	20.1312i	−0.243390	+	1.44162i
$196$	3.75718	−	4.33602i	0.268370	−	0.309716i
$197$	−3.09932	+	6.78657i	−0.220817	+	0.483523i	−0.987325	−	0.158713i	$-0.949266\pi$
$197$	−3.09932	+	6.78657i	−0.220817	+	0.483523i	0.766507	+	0.642236i	$0.221993\pi$
$198$	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	$0.687442\pi$
$200$	3.12803	−	8.99975i	0.221185	−	0.636379i
$201$	−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
$205$	−0.172126	+	0.537245i	−0.0120218	+	0.0375228i
$206$	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
$210$	−1.50413	+	4.69474i	−0.103795	+	0.323968i
$211$	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
$220$	−8.02653	+	4.88523i	−0.541149	+	0.329362i
$221$	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	$0.0880245\pi$
$223$	4.48480	+	15.2738i	0.300324	+	1.02281i	−0.661683	+	0.749784i	$0.730157\pi$
$224$	−7.40283	−	6.41459i	−0.494622	−	0.428593i
$225$	−0.964155	−	10.2386i	−0.0642770	−	0.682572i
$226$	−4.89017	+	7.60925i	−0.325289	+	0.506160i
$227$	−28.1387	−	4.04574i	−1.86763	−	0.268525i	−0.886625	−	0.462489i	$-0.846957\pi$
$227$	−28.1387	−	4.04574i	−1.86763	−	0.268525i	−0.981009	+	0.193963i	$0.937866\pi$
$228$	−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	$0.0880737\pi$
$233$			8.33966i			0.546350i	−0.961964	+	0.273175i	$0.911926\pi$
$234$	4.21109	+	0.605463i	0.275287	+	0.0395803i
$235$	4.87411	−	15.2132i	0.317952	−	0.992402i
$236$	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	$0.268836\pi$
$240$	12.0199	+	3.85101i	0.775881	+	0.248582i
$241$	−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
$245$	−0.870306	−	7.31957i	−0.0556018	−	0.467630i
$246$	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
$250$	−2.71990	−	5.00443i	−0.172021	−	0.316508i
$251$	−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	0.495549	−	0.868580i	$-0.334967\pi$
$257$	23.6700	−	10.8097i	1.47649	−	0.674292i	0.980945	+	0.194288i	$0.0622395\pi$
$258$	−3.63809	−	1.66146i	−0.226498	−	0.103438i
$259$	−2.68034	−	3.09327i	−0.166548	−	0.192207i
$260$	−15.2658	+	4.07976i	−0.946745	+	0.253016i
$261$	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	−0.815481	−	0.578783i	$-0.803528\pi$
$263$	0.806999	−	1.25571i	0.0497617	−	0.0774307i	0.865243	+	0.501353i	$0.167164\pi$
$264$	5.59344	+	8.70356i	0.344252	+	0.535667i
$265$	−19.4056	−	17.6641i	−1.19208	−	1.08510i
$266$	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	$0.458923\pi$
$270$	2.39932	−	0.285282i	0.146018	−	0.0173617i
$271$	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
$275$	−2.30014	+	11.8508i	−0.138703	+	0.714630i
$276$	−15.3665	+	33.6479i	−0.924954	+	2.02537i
$277$	−4.33732	+	1.98079i	−0.260604	+	0.119014i	−0.541433	−	0.840744i	$-0.682118\pi$
$277$	−4.33732	+	1.98079i	−0.260604	+	0.119014i	0.280829	+	0.959758i	$0.409391\pi$
$278$	−4.38831	−	3.80249i	−0.263193	−	0.228058i
$279$		−	10.6139i		−	0.635438i
$280$	−8.14273	+	0.968182i	−0.486621	+	0.0578599i
$281$	−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	0.116026	−	0.993246i	$-0.462985\pi$
$283$	15.8579	−	7.24204i	0.942652	−	0.430495i	0.826626	+	0.562752i	$0.190257\pi$
$284$	15.2614	−	4.48114i	0.905596	−	0.265907i
$285$	−13.3642	+	5.71253i	−0.791625	+	0.338381i
$286$	−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
$290$	7.06103	+	8.56329i	0.414638	+	0.502853i
$291$	−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	−0.608060	−	0.793891i	$-0.708052\pi$
$293$	−11.8174	+	3.46991i	−0.690382	+	0.202714i	−0.0823222	+	0.996606i	$0.526234\pi$
$294$	−3.73803	+	0.537447i	−0.218006	+	0.0313446i
$295$	8.81435	−	27.5116i	0.513191	−	1.60179i
$296$	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
$300$	16.9601	−	9.76239i	0.979195	−	0.563632i
$301$	−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
$305$	−1.10345	+	0.471671i	−0.0631833	+	0.0270078i
$306$	−1.86031	+	4.07351i	−0.106347	+	0.232867i
$307$	11.1101	+	1.59740i	0.634089	+	0.0911682i	0.451861	−	0.892088i	$-0.350760\pi$
$307$	11.1101	+	1.59740i	0.634089	+	0.0911682i	0.182228	+	0.983256i	$0.441669\pi$
$308$	6.80311	+	4.37209i	0.387643	+	0.249123i
$309$	7.28616	+	4.68253i	0.414495	+	0.266380i
$310$	−2.31057	−	5.40546i	−0.131232	−	0.307010i
$311$	−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	−0.730720	−	0.682678i	$-0.760815\pi$
$313$	0.866927	−	1.00049i	0.0490016	−	0.0565509i	0.779721	+	0.626127i	$0.215361\pi$
$314$	−0.822107	−	0.528336i	−0.0463942	−	0.0298157i
$315$	−7.56050	+	4.60159i	−0.425986	+	0.259270i
$316$	−4.07929	+	28.3721i	−0.229478	+	1.59605i
$317$	−6.13589	−	2.80217i	−0.344626	−	0.157385i	0.235581	−	0.971855i	$-0.424301\pi$
$317$	−6.13589	−	2.80217i	−0.344626	−	0.157385i	−0.580206	+	0.814469i	$0.697028\pi$
$318$	−8.80408	+	10.1604i	−0.493708	+	0.569770i
$319$		−	23.5238i		−	1.31708i
$320$	0.640814	+	5.38946i	0.0358226	+	0.301280i
$321$	−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
$325$	−9.32611	+	18.0322i	−0.517319	+	1.00025i
$326$	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
$330$	6.09855	+	1.02962i	0.335714	+	0.0566789i
$331$	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
$335$	−1.04338	−	0.949738i	−0.0570057	−	0.0518898i
$336$	−1.54594	−	10.7522i	−0.0843379	−	0.586583i
$337$	−1.46298	+	3.20347i	−0.0796934	+	0.174504i	−0.945284	−	0.326247i	$-0.894216\pi$
$337$	−1.46298	+	3.20347i	−0.0796934	+	0.174504i	0.865591	+	0.500752i	$0.166943\pi$
$338$	−1.34194	−	1.16280i	−0.0729920	−	0.0632479i
$339$	−38.3084	+	11.2484i	−2.08063	+	0.610927i
$340$	0.406697	−	16.6278i	0.0220562	−	0.901772i
$341$	−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
$345$	18.6792	+	43.6991i	1.00566	+	2.35268i
$346$	−1.04662	−	2.29177i	−0.0562665	−	0.123207i
$347$	−6.64109	−	3.03288i	−0.356512	−	0.162814i	0.229104	−	0.973402i	$-0.426420\pi$
$347$	−6.64109	−	3.03288i	−0.356512	−	0.162814i	−0.585617	+	0.810588i	$0.699148\pi$
$348$	−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	$0.0222804\pi$
$350$	−2.84869	+	3.98937i	−0.152269	+	0.213241i
$351$	−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	−0.955302	−	0.295633i	$-0.904470\pi$
$353$	−20.3521	+	13.0795i	−1.08323	+	0.696151i	−0.127930	+	0.991783i	$0.540833\pi$
$354$	−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	$0.689431\pi$
$360$	−4.55643	−	7.48631i	−0.240145	−	0.394563i
$361$	−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
$365$	−10.8597	+	8.95461i	−0.568424	+	0.468706i
$366$	0.255403	+	0.559255i	0.0133501	+	0.0292327i
$367$	−6.30060	−	5.45950i	−0.328889	−	0.284984i	0.474726	−	0.880134i	$-0.342547\pi$
$367$	−6.30060	−	5.45950i	−0.328889	−	0.284984i	−0.803615	+	0.595150i	$0.797093\pi$
$368$	−23.7240			−1.23670
$369$	0.280544	+	0.436535i	0.0146046	+	0.0227251i
$370$	0.0592410	−	2.42207i	0.00307979	−	0.125918i
$371$	−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	$-0.982490\pi$
$373$	−3.63534	−	12.3808i	−0.188231	−	0.641055i	0.810257	−	0.586075i	$-0.199328\pi$
$374$	3.44249	−	3.97285i	0.178007	−	0.205431i
$375$	5.39241	−	24.5564i	0.278463	−	1.26809i
$376$	−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	$0.502340\pi$
$380$	−8.31868	−	7.57212i	−0.426739	−	0.388442i
$381$	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	$0.147232\pi$
$383$	3.16975	+	22.0461i	0.161967	+	1.12650i	−0.732954	+	0.680278i	$0.761859\pi$
$384$	25.4111	−	3.65356i	1.29675	−	0.186445i
$385$	10.0374	−	2.68248i	0.511553	−	0.136712i
$386$	−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
$395$	23.4282	+	28.4126i	1.17880	+	1.42959i
$396$	−1.23001	+	8.55493i	−0.0618105	+	0.429901i
$397$	−13.6524	−	8.77386i	−0.685194	−	0.440348i	0.151180	−	0.988506i	$-0.451693\pi$
$397$	−13.6524	−	8.77386i	−0.685194	−	0.440348i	−0.836374	+	0.548159i	$0.815329\pi$
$398$	−2.32066	+	3.61101i	−0.116324	+	0.181004i
$399$	9.45329	+	8.19132i	0.473256	+	0.410079i
$400$	10.2139	+	7.29347i	0.510697	+	0.364674i
$401$	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
$405$	20.2497	+	13.7247i	1.00622	+	0.681986i
$406$	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	$-0.0458939\pi$
$410$	0.237907	+	0.161247i	0.0117494	+	0.00796342i
$411$	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
$415$	4.07860	−	2.48238i	0.200211	−	0.121855i
$416$	−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	$0.692450\pi$
$420$	−13.9415	−	9.44921i	−0.680278	−	0.461074i
$421$	−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
$425$	−15.4462	−	14.7666i	−0.749253	−	0.716284i
$426$	−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
$430$	−2.94104	−	2.67710i	−0.141829	−	0.129101i
$431$	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	$-0.839856\pi$
$433$	−36.4605			−1.75218			−0.876089	+	0.482150i	$0.839856\pi$
$434$	−3.31318	+	3.82361i	−0.159038	+	0.183539i
$435$	−1.19792	+	48.9769i	−0.0574356	+	2.34826i
$436$	−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	$0.848072\pi$
$440$	2.65615	+	9.93889i	0.126627	+	0.473818i
$441$	−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	−0.914492	−	0.404604i	$-0.867409\pi$
$443$	1.54854	−	5.27383i	0.0735731	−	0.250567i	0.988065	+	0.154037i	$0.0492275\pi$
$444$	8.32403			0.395041
$445$	1.10990	+	21.0658i	0.0526143	+	0.998615i
$446$	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	$0.739786\pi$
$450$	−5.14313	−	0.998235i	−0.242449	−	0.0470572i
$451$	−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
$455$	17.4668	+	0.427217i	0.818856	+	0.0200282i
$456$	−8.11094	+	9.36052i	−0.379830	+	0.438347i
$457$	1.42072			0.0664587			0.0332293	−	0.999448i	$-0.489421\pi$
$457$	1.42072			0.0664587			0.0332293	+	0.999448i	$0.489421\pi$
$458$	0.540218	−	0.347177i	0.0252427	−	0.0162225i
$459$	8.24581	−	3.76574i	0.384882	−	0.175770i
$460$	−24.7599	+	27.2010i	−1.15444	+	1.26825i
$461$	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	$0.158022\pi$
$463$	31.7569	+	27.5175i	1.47587	+	1.27885i	0.596587	+	0.802549i	$0.296523\pi$
$464$	−22.2465	−	10.1596i	−1.03277	−	0.471650i
$465$	7.91708	−	24.7111i	0.367146	−	1.14595i
$466$	4.07653	+	1.19698i	0.188842	+	0.0554489i
$467$	5.48810	+	8.53964i	0.253959	+	0.395168i	0.944701	−	0.327934i	$-0.106352\pi$
$467$	5.48810	+	8.53964i	0.253959	+	0.395168i	−0.690742	+	0.723101i	$0.742716\pi$
$468$	−6.03787	+	13.2211i	−0.279101	+	0.611145i
$469$	−0.342102	+	1.16509i	−0.0157968	+	0.0537990i
$470$	−6.73684	−	4.56605i	−0.310747	−	0.210616i
$471$	−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
$475$	−14.3884	+	1.35494i	−0.660186	+	0.0621688i
$476$	−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	$0.264434\pi$
$480$	14.3593	−	21.1860i	0.655411	−	0.967006i
$481$	−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
$485$	−2.21845	+	3.27314i	−0.100735	+	0.148626i
$486$	5.02324	−	7.81632i	0.227859	−	0.354555i
$487$	−20.3325	+	31.6379i	−0.921352	+	1.43365i	−0.0203720	+	0.999792i	$0.506485\pi$
$487$	−20.3325	+	31.6379i	−0.921352	+	1.43365i	−0.900980	+	0.433860i	$0.857151\pi$
$488$	−0.669702	+	0.772877i	−0.0303160	+	0.0349865i
$489$	16.5086	−	4.84738i	0.746547	−	0.219206i
$490$	−3.70280	−	0.625147i	−0.167276	−	0.0282413i
$491$	−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
$495$	7.06421	+	8.56714i	0.317513	+	0.385064i
$496$	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	$0.0543741\pi$
$503$	10.5093	+	23.0122i	0.468587	+	1.02606i	−0.516859	+	0.856071i	$0.672899\pi$
$504$	−4.07783	+	6.34523i	−0.181641	+	0.282639i
$505$	−2.51741	−	9.41975i	−0.112023	−	0.419173i
$506$	−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	$0.0692949\pi$
$510$	−7.36964	+	8.09623i	−0.326333	+	0.358507i
$511$	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
$515$	5.47903	+	6.64471i	0.241435	+	0.292801i
$516$	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
$520$	−0.423024	+	17.2954i	−0.0185508	+	0.758453i
$521$	−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	0.0476822	−	0.998863i	$-0.484817\pi$
$523$	−21.3650	−	18.5129i	−0.934228	−	0.809513i	−0.981910	+	0.189350i	$0.939362\pi$
$524$	−6.25476	−	13.6960i	−0.273240	−	0.598313i
$525$	−21.0346	+	5.07382i	−0.918026	+	0.221440i
$526$	−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
$530$	−11.4197	+	6.95041i	−0.496039	+	0.301907i
$531$	−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
$540$	−1.37420	+	8.13951i	−0.0591361	+	0.350269i
$541$	−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
$545$	7.90349	+	18.4898i	0.338548	+	0.792016i
$546$		−	8.95148i		−	0.383088i
$547$	31.7041	−	20.3750i	1.35557	−	0.871172i	0.357539	−	0.933898i	$-0.383616\pi$
$547$	31.7041	−	20.3750i	1.35557	−	0.871172i	0.998031	+	0.0627261i	$0.0199794\pi$
$548$	7.40872	+	16.2228i	0.316485	+	0.693005i
$549$	−0.310979	+	1.05910i	−0.0132723	+	0.0452012i
$550$	5.46268	+	2.82526i	0.232929	+	0.120469i
$551$	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
$555$	7.19883	−	7.90859i	0.305573	−	0.335701i
$556$	16.6883	−	10.7249i	0.707740	−	0.454837i
$557$	−6.06072	+	13.2711i	−0.256801	+	0.562316i	−0.993490	−	0.113916i	$-0.963661\pi$
$557$	−6.06072	+	13.2711i	−0.256801	+	0.562316i	0.736690	+	0.676231i	$0.236388\pi$
$558$	−5.18820	−	1.52339i	−0.219634	−	0.0644904i
$559$	−2.01730	+	14.0306i	−0.0853228	+	0.593433i
$560$	1.79820	−	10.6509i	0.0759880	−	0.450084i
$561$	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	0.879404	−	0.476076i	$-0.157941\pi$
$563$	6.71543	+	7.75001i	0.283021	+	0.326624i	−0.596383	+	0.802700i	$0.703396\pi$
$564$	15.1170	−	23.5225i	0.636540	−	0.990476i
$565$	−39.6890	−	0.970745i	−1.66973	−	0.0408395i
$566$	−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	$0.663049\pi$
$570$	0.874219	+	7.35247i	0.0366170	+	0.307961i
$571$			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
$575$	4.43048	+	47.0483i	0.184764	+	1.96205i
$576$	4.19974	+	2.69901i	0.174989	+	0.112459i
$577$	3.93937	−	4.54628i	0.163998	−	0.189264i	−0.667802	−	0.744339i	$-0.732765\pi$
$577$	3.93937	−	4.54628i	0.163998	−	0.189264i	0.831801	+	0.555075i	$0.187310\pi$
$578$	0.181639	+	0.618607i	0.00755521	+	0.0257307i
$579$	−30.0398	+	8.82049i	−1.24841	+	0.366567i
$580$	−34.8665	+	14.9038i	−1.44775	+	0.618845i
$581$	−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
$585$	7.33954	+	17.1705i	0.303453	+	0.709912i
$586$			6.27453i			0.259199i
$587$	−3.65802	−	5.69199i	−0.150983	−	0.234934i	0.757521	−	0.652811i	$-0.226410\pi$
$587$	−3.65802	−	5.69199i	−0.150983	−	0.234934i	−0.908503	+	0.417878i	$0.862774\pi$
$588$	1.83612	−	12.7705i	0.0757202	−	0.526646i
$589$	−14.9158			−0.614597
$590$	−12.1829	−	8.25725i	−0.501562	−	0.339946i
$591$	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	0.0881251	−	0.996109i	$-0.471912\pi$
$593$	−19.0273	−	12.2281i	−0.781359	−	0.502149i	−0.869484	+	0.493960i	$0.835549\pi$
$594$	−1.97168	+	1.70847i	−0.0808992	+	0.0700995i
$595$	−5.61132	+	17.5142i	−0.230042	+	0.718013i
$596$	−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	$0.0348039\pi$
$600$	−5.02403	−	20.8282i	−0.205105	−	0.850308i
$601$	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
$605$	4.54446	+	10.6315i	0.184758	+	0.432233i
$606$	−4.79307	+	1.40737i	−0.194705	+	0.0571705i
$607$	−3.13679	+	1.43252i	−0.127318	+	0.0581444i	−0.478056	−	0.878330i	$-0.658658\pi$
$607$	−3.13679	+	1.43252i	−0.127318	+	0.0581444i	0.350737	+	0.936474i	$0.385931\pi$
$608$	−14.1161	−	4.14485i	−0.572482	−	0.168096i
$609$	38.3539	−	17.5157i	1.55418	−	0.709770i
$610$	0.0721823	+	0.607077i	0.00292258	+	0.0245798i
$611$			29.0071i			1.17350i
$612$	−11.5623	−	10.0188i	−0.467380	−	0.404987i
$613$	1.33837	−	0.611211i	0.0540561	−	0.0246866i	−0.388204	−	0.921574i	$-0.626904\pi$
$613$	1.33837	−	0.611211i	0.0540561	−	0.0246866i	0.442260	+	0.896887i	$0.354177\pi$
$614$	2.37544	−	5.20150i	0.0958651	−	0.209915i
$615$	0.327538	+	1.22560i	0.0132076	+	0.0494208i
$616$	6.69143	−	5.79816i	0.269605	−	0.233614i
$617$	0.407648	−	0.119696i	0.0164113	−	0.00481879i	−0.273517	−	0.961867i	$-0.588187\pi$
$617$	0.407648	−	0.119696i	0.0164113	−	0.00481879i	0.289928	+	0.957048i	$0.406369\pi$
$618$	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	$0.727926\pi$
$620$	19.9429	−	2.37124i	0.800928	−	0.0952314i
$621$	−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
$625$	12.5566	−	21.6179i	0.502264	−	0.864715i
$626$	−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
$630$	1.16417	+	4.35612i	0.0463815	+	0.173552i
$631$	−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
$640$	25.1716	+	4.24974i	0.994995	+	0.167986i
$641$	−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	0.338763	−	0.940872i	$-0.389992\pi$
$643$	23.5539	−	3.38655i	0.928877	−	0.133552i	0.590115	+	0.807320i	$0.299083\pi$
$644$	30.3742	+	8.91868i	1.19691	+	0.351445i
$645$	−2.07267	−	17.4319i	−0.0816115	−	0.686380i
$646$	5.72456	+	2.61432i	0.225230	+	0.102859i
$647$	−9.23528	−	2.71172i	−0.363076	−	0.106609i	0.0951059	−	0.995467i	$-0.469681\pi$
$647$	−9.23528	−	2.71172i	−0.363076	−	0.106609i	−0.458182	+	0.888858i	$0.651499\pi$
$648$	20.6348	+	2.96683i	0.810610	+	0.116548i
$649$	8.78809	+	29.9295i	0.344963	+	1.17483i
$650$	7.47578	+	7.14684i	0.293224	+	0.280322i
$651$	−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	0.966361	−	0.257190i	$-0.0827966\pi$
$653$	28.9743	+	18.6207i	1.13385	+	0.728683i	0.167493	+	0.985873i	$0.446433\pi$
$654$	9.37108	−	4.27963i	0.366438	−	0.167347i
$655$	−18.4217	−	5.90207i	−0.719797	−	0.230613i
$656$	−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
$665$	6.46667	+	10.6249i	0.250767	+	0.412015i
$666$	−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
$670$	−0.613997	+	0.373700i	−0.0237208	+	0.0144373i
$671$	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	0.713768	−	0.700382i	$-0.246987\pi$
$673$	16.9111	+	7.72302i	0.651873	+	0.297701i	−0.0618947	+	0.998083i	$0.519714\pi$
$674$	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	$0.109883\pi$
$677$	−1.48878	+	10.3547i	−0.0572183	+	0.397962i	−0.998224	+	0.0595715i	$0.981027\pi$
$678$			20.3401i			0.781155i
$679$	3.36844	+	0.484308i	0.129269	+	0.0185860i
$680$	−17.3424	−	5.55625i	−0.665049	−	0.213073i
$681$	−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	0.539714	−	0.841848i	$-0.318532\pi$
$683$	−9.67948	−	11.1707i	−0.370375	−	0.427435i	−0.910089	+	0.414413i	$0.863987\pi$
$684$	−10.2416	+	1.47252i	−0.391598	+	0.0563033i
$685$	21.8204	+	6.99096i	0.833716	+	0.267111i
$686$	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
$690$	24.0416	−	2.85858i	0.915250	−	0.108824i
$691$	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
$695$	4.24281	−	25.1305i	0.160939	−	0.953255i
$696$	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
$705$	−9.27495	−	34.7054i	−0.349315	−	1.30708i
$706$	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	$-0.365095\pi$
$710$	−7.69869	−	7.00777i	−0.288927	−	0.262997i
$711$	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
$715$	−2.58810	−	21.7668i	−0.0967895	−	0.814032i
$716$	−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	$0.492628\pi$
$720$	11.1529	−	2.98060i	0.415645	−	0.111080i
$721$	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
$725$	−15.9936	+	46.0155i	−0.593986	+	1.70897i
$726$	5.38832	−	2.46076i	0.199979	−	0.0913274i
$727$	16.3518	+	4.80131i	0.606453	+	0.178071i	0.570520	−	0.821284i	$-0.306742\pi$
$727$	16.3518	+	4.80131i	0.606453	+	0.178071i	0.0359328	+	0.999354i	$0.488560\pi$
$728$	13.5441	−	6.18537i	0.501977	−	0.229245i
$729$	7.86028	−	2.30799i	0.291122	−	0.0854810i
$730$	2.81844	+	6.59360i	0.104315	+	0.244040i
$731$	−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	$-0.797359\pi$
$733$	5.24555	−	17.8647i	0.193749	−	0.659848i	0.997861	−	0.0653706i	$-0.0208230\pi$
$734$	−3.57299	+	2.29622i	−0.131881	+	0.0847550i
$735$	−10.5452	−	12.7887i	−0.388965	−	0.471719i
$736$	−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	$0.339378\pi$
$740$	7.88249	+	2.52544i	0.289766	+	0.0928371i
$741$	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	0.682018	−	0.731335i	$-0.261102\pi$
$743$	−8.64938	−	18.9395i	−0.317315	−	0.694823i	−0.999333	+	0.0365123i	$0.988375\pi$
$744$	−3.14703	−	21.8880i	−0.115376	−	0.802455i
$745$	−24.4338	+	36.0502i	−0.895187	+	1.32078i
$746$	−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
$750$	−11.2295	−	6.16041i	−0.410044	−	0.224946i
$751$	−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
$755$	11.2987	−	4.82966i	0.411203	−	0.175769i
$756$	6.81657	−	2.00153i	0.247916	−	0.0727948i
$757$	−4.31208	−	14.6856i	−0.156725	−	0.533757i	0.843268	−	0.537493i	$-0.180629\pi$
$757$	−4.31208	−	14.6856i	−0.156725	−	0.533757i	−0.999993	+	0.00373684i	$0.998811\pi$
$758$	5.30911	−	6.12703i	0.192835	−	0.222544i
$759$	−43.1680	−	27.7424i	−1.56690	−	1.00699i
$760$	−10.5206	+	6.40321i	−0.381623	+	0.232269i
$761$	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
$765$	−19.5182	+	2.32074i	−0.705682	+	0.0839066i
$766$	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	$0.831271\pi$
$770$	0.129421	−	5.29140i	0.00466402	−	0.190689i
$771$	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	$0.289889\pi$
$773$	6.87816	+	47.8386i	0.247390	+	1.72064i	−0.365793	+	0.930696i	$0.619202\pi$
$774$	−3.62088	+	0.520605i	−0.130150	+	0.0187127i
$775$	14.9943	−	20.9983i	0.538610	−	0.754282i
$776$	−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
$780$	−23.9191	+	26.2773i	−0.856441	+	0.940880i
$781$	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
$785$	0.104880	−	4.28802i	0.00374332	−	0.153046i
$786$	−2.79214	+	9.50917i	−0.0995925	+	0.339181i
$787$	−1.03371	−	2.26351i	−0.0368478	−	0.0806855i	0.890313	−	0.455349i	$-0.150486\pi$
$787$	−1.03371	−	2.26351i	−0.0368478	−	0.0806855i	−0.927161	+	0.374663i	$0.877758\pi$
$788$	−10.9239	+	7.02033i	−0.389146	+	0.250089i
$789$		−	3.35661i		−	0.119498i
$790$	17.2510	−	7.37397i	0.613764	−	0.262354i
$791$	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
$795$	−58.1858	−	9.82355i	−2.06364	−	0.348406i
$796$	−9.60320	−	11.0827i	−0.340376	−	0.392815i
$797$	−28.1333	+	43.7762i	−0.996532	+	1.55063i	−0.171783	+	0.985135i	$0.554953\pi$
$797$	−28.1333	+	43.7762i	−0.996532	+	1.55063i	−0.824749	+	0.565499i	$0.808684\pi$
$798$	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
$805$	34.7420	−	21.1452i	1.22449	−	0.745270i
$806$	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	$0.705185\pi$
$810$	9.61520	−	7.92841i	0.337844	−	0.278576i
$811$	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
$815$	17.1036	+	0.418334i	0.599114	+	0.0146536i
$816$	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
$820$	−0.757550	+	0.624654i	−0.0264548	+	0.0218138i
$821$	−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	0.973641	−	0.228086i	$-0.0732468\pi$
$823$	10.3765	+	16.1461i	0.361701	+	0.562818i	−0.611940	+	0.790904i	$0.709610\pi$
$824$	6.67615	+	3.04889i	0.232575	+	0.106213i
$825$	10.0564	+	25.2152i	0.350118	+	0.877879i
$826$	−1.80264	+	12.5376i	−0.0627217	+	0.436239i
$827$	−23.2189	+	6.81768i	−0.807400	+	0.237074i	−0.659282	−	0.751896i	$-0.729140\pi$
$827$	−23.2189	+	6.81768i	−0.807400	+	0.237074i	−0.148118	+	0.988970i	$0.547322\pi$
$828$	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	$0.560117\pi$
$830$	−0.628023	−	2.34996i	−0.0217990	−	0.0815683i
$831$	−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	$0.578240\pi$
$840$	−14.2269	+	11.7311i	−0.490876	+	0.404762i
$841$	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
$845$	1.29745	−	7.68489i	0.0446335	−	0.264368i
$846$	−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
$850$	−9.43505	+	5.43089i	−0.323620	+	0.186278i
$851$	−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	$-0.441378\pi$
$853$	10.6969			0.366253			0.183127	+	0.983089i	$0.441378\pi$
$854$	0.442631	−	0.284462i	0.0151465	−	0.00973409i
$855$	−7.45818	+	11.0039i	−0.255064	+	0.376327i
$856$	−7.02034			−0.239950
$857$	−2.74590	+	19.0982i	−0.0937982	+	0.652381i	0.887631	+	0.460556i	$0.152350\pi$
$857$	−2.74590	+	19.0982i	−0.0937982	+	0.652381i	−0.981429	+	0.191825i	$0.938559\pi$
$858$	−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	$0.570274\pi$
$860$	11.6062	−	7.06396i	0.395769	−	0.240879i
$861$	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	0.999432	−	0.0337072i	$-0.0107314\pi$
$863$	0.910319	+	6.33141i	0.0309876	+	0.215524i	−0.968444	+	0.249231i	$0.919822\pi$
$864$	3.04159	+	10.3587i	0.103477	+	0.352410i
$865$	6.20429	−	9.15392i	0.210952	−	0.311243i
$866$	−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
$870$	23.7686	+	7.61512i	0.805830	+	0.258177i
$871$	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
$875$	−21.4582	−	1.57704i	−0.725420	−	0.0533137i
$876$	−22.4102	+	10.2344i	−0.757169	+	0.345788i
$877$	−15.4606	+	9.93590i	−0.522066	+	0.335512i	−0.774989	−	0.631975i	$-0.782245\pi$
$877$	−15.4606	+	9.93590i	−0.522066	+	0.335512i	0.252923	+	0.967487i	$0.418608\pi$
$878$	4.06740			0.137268
$879$	−18.1371	+	20.9313i	−0.611748	+	0.705995i
$880$	−13.5475	−	0.331356i	−0.456687	−	0.0111700i
$881$	−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	$-0.811854\pi$
$883$	−37.5529	−	43.3383i	−1.26376	−	1.45845i	−0.433415	−	0.901195i	$-0.642692\pi$
$884$	8.50879	+	28.9783i	0.286182	+	0.974645i
$885$	−16.7728	−	62.7612i	−0.563812	−	2.10969i
$886$	−2.35565	−	1.51389i	−0.0791397	−	0.0508600i
$887$	−20.7124	+	13.3111i	−0.695455	+	0.446942i	−0.840021	−	0.542553i	$-0.817458\pi$
$887$	−20.7124	+	13.3111i	−0.695455	+	0.446942i	0.144566	+	0.989495i	$0.453821\pi$
$888$	2.56762	−	8.74453i	0.0861638	−	0.293447i
$889$	−33.2285			−1.11445
$890$	10.4565	+	2.48100i	0.350503	+	0.0831634i
$891$	−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
$895$	−37.8182	+	10.1068i	−1.26412	+	0.337835i
$896$	−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
$900$	8.22246	−	15.8983i	0.274082	−	0.529942i
$901$	−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
$905$	6.91434	+	6.29381i	0.229840	+	0.209213i
$906$	−2.61519	−	5.72647i	−0.0868840	−	0.190249i
$907$	8.20274	+	27.9360i	0.272368	+	0.927599i	0.976134	+	0.217168i	$0.0696819\pi$
$907$	8.20274	+	27.9360i	0.272368	+	0.927599i	−0.703767	+	0.710431i	$0.748500\pi$
$908$	−37.3930	−	32.4012i	−1.24093	−	1.07527i
$909$	−8.15807	−	3.72567i	−0.270586	−	0.123573i
$910$	2.71581	−	8.47666i	0.0900281	−	0.280999i
$911$	−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
$915$	−1.51401	+	2.23381i	−0.0500518	+	0.0738473i
$916$	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	$0.176280\pi$
$920$	20.9377	+	34.4010i	0.690295	+	1.13417i
$921$	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
$925$	9.21638	−	5.30502i	0.303033	−	0.174428i
$926$	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	$0.880631\pi$
$930$	−10.9427	−	7.41670i	−0.358827	−	0.243203i
$931$	−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
$935$	22.7513	+	3.84112i	0.744047	+	0.125618i
$936$	12.0265	+	10.4210i	0.393099	+	0.340623i
$937$	11.4535	−	17.8220i	0.374169	−	0.582219i	−0.602195	−	0.798349i	$-0.705707\pi$
$937$	11.4535	−	17.8220i	0.374169	−	0.582219i	0.976365	+	0.216130i	$0.0693436\pi$
$938$	0.520410	+	0.334447i	0.0169920	+	0.0109201i
$939$	0.423663	−	2.94664i	0.0138257	−	0.0961600i
$940$	21.4517	−	17.6884i	0.699676	−	0.576932i
$941$	−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	−0.600796	−	0.799402i	$-0.705150\pi$
$947$	−29.2974	+	4.21233i	−0.952038	+	0.136882i	−0.351242	+	0.936285i	$0.614241\pi$
$948$	26.7765	+	58.6323i	0.869660	+	1.90429i
$949$	13.8177	−	21.5008i	0.448542	−	0.697946i
$950$	−1.40283	+	7.22770i	−0.0455139	+	0.234498i
$951$	−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	0.468165	−	0.883641i	$-0.344915\pi$
$953$	41.3588	−	12.1440i	1.33974	−	0.393384i	0.871578	+	0.490257i	$0.163097\pi$
$954$	−1.74999	+	12.1714i	−0.0566580	+	0.394065i
$955$	−22.2228	−	20.2285i	−0.719114	−	0.654578i
$956$	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
$960$	7.76451	+	9.41643i	0.250599	+	0.303914i
$961$	−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
$965$	−31.1225	−	0.761217i	−1.00187	−	0.0245045i
$966$	−11.2653	−	17.5292i	−0.362457	−	0.563993i
$967$	20.2563			0.651400			0.325700	−	0.945473i	$-0.394400\pi$
$967$	20.2563			0.651400			0.325700	+	0.945473i	$0.394400\pi$
$968$	7.44653	+	6.45245i	0.239340	+	0.207390i
$969$	11.5397	+	25.2685i	0.370709	+	0.811740i
$970$	1.28154	+	1.55419i	0.0411478	+	0.0499021i
$971$	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
$975$	4.28003	+	45.4506i	0.137071	+	1.45558i
$976$	−0.728305	−	1.13326i	−0.0233125	−	0.0362749i
$977$	−3.54554	+	12.0750i	−0.113432	+	0.386313i	−0.996566	−	0.0828082i	$-0.973611\pi$
$977$	−3.54554	+	12.0750i	−0.113432	+	0.386313i	0.883134	+	0.469121i	$0.155429\pi$
$978$		−	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	−0.859645	−	0.510892i	$-0.829315\pi$
$983$	−1.18551	+	1.84468i	−0.0378117	+	0.0588362i	0.821833	+	0.569728i	$0.192952\pi$
$984$	0.707973	+	0.817044i	0.0225694	+	0.0260464i
$985$	−2.77727	+	16.4500i	−0.0884912	+	0.524141i
$986$	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
$990$	5.20163	−	2.22345i	0.165319	−	0.0706657i
$991$			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
$995$	−18.8346	−	0.460672i	−0.597098	−	0.0146043i
$996$	8.01861	−	2.35448i	0.254079	−	0.0746044i
$997$	0.590287	+	0.511487i	0.0186946	+	0.0161990i	0.664158	−	0.747592i	$-0.268790\pi$
$997$	0.590287	+	0.511487i	0.0186946	+	0.0161990i	−0.645463	+	0.763791i	$0.723336\pi$
$998$	−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.44.26	yes	440
5.4	even	2	inner	445.2.q.a.44.19	✓	440
89.87	even	22	inner	445.2.q.a.354.19	yes	440
445.354	even	22	inner	445.2.q.a.354.26	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
445.2.q.a.44.19	✓	440	5.4	even	2	inner
445.2.q.a.44.26	yes	440	1.1	even	1	trivial
445.2.q.a.354.19	yes	440	89.87	even	22	inner
445.2.q.a.354.26	yes	440	445.354	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} +(2.16025 - 0.577324i) 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} +(0.0278542 - 1.13882i) q^{10} +(-1.58109 + 1.82468i) q^{11} +3.91383 q^{12} +(-3.41568 + 2.19512i) q^{13} +(-0.891813 + 0.407277i) q^{14} +(3.38478 - 3.71849i) 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} +(3.70622 + 1.18742i) 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} +(4.33339 - 2.49433i) 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} +(-1.33183 - 2.18823i) q^{30} +(4.69411 - 2.14373i) q^{31} +(5.03812 - 0.724372i) q^{32} +(-0.772671 + 5.37405i) q^{33} -2.17729 q^{34} +(-3.56213 - 2.41432i) q^{35} +(3.01147 - 1.93535i) q^{36} +2.12683 q^{37} +(-0.964293 + 1.11285i) q^{38} +(-3.79288 + 8.30525i) q^{39} +(2.39062 - 3.52717i) 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} +(0.765633 - 4.53491i) 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} +(-0.597297 - 2.47622i) 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} +(8.45486 - 2.25955i) 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} +(-6.11143 + 6.71398i) 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} +(-1.69141 + 1.39469i) 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} +(5.16520 - 9.98700i) q^{75} +(-2.71978 - 4.23206i) q^{76} +4.64639 q^{77} +(3.51532 + 3.04604i) q^{78} +(6.84151 + 14.9808i) q^{79} +(3.57080 + 4.33050i) 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} +(-4.96854 - 8.16341i) 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} +(-6.37297 - 1.07595i) 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

Groups

Database

Properties

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