LMFDB - Embedded newform 896.2.bn.b.29.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(29,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 27, 0]))

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

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

chi := DirichletCharacter("896.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bn (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$784$
Relative dimension:	$49$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			29.17
Character	$\chi$	$=$	896.29
Dual form			896.2.bn.b.309.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.628925 + 1.26667i) q^{2} +(-0.274807 + 2.79017i) q^{3} +(-1.20891 - 1.59328i) q^{4} +(2.09503 - 1.11982i) q^{5} +(-3.36139 - 2.10290i) q^{6} +(0.195090 + 0.980785i) q^{7} +(2.77847 - 0.529229i) q^{8} +(-4.76715 - 0.948245i) q^{9} +O(q^{10})$	\(q+(-0.628925 + 1.26667i) q^{2} +(-0.274807 + 2.79017i) q^{3} +(-1.20891 - 1.59328i) q^{4} +(2.09503 - 1.11982i) q^{5} +(-3.36139 - 2.10290i) q^{6} +(0.195090 + 0.980785i) q^{7} +(2.77847 - 0.529229i) q^{8} +(-4.76715 - 0.948245i) q^{9} +(0.100821 + 3.35799i) q^{10} +(-2.39860 + 2.92270i) q^{11} +(4.77774 - 2.93520i) q^{12} +(-0.322522 + 0.603396i) q^{13} +(-1.36503 - 0.369726i) q^{14} +(2.54874 + 6.15321i) q^{15} +(-1.07709 + 3.85225i) q^{16} +(1.28015 - 3.09055i) q^{17} +(4.19930 - 5.44203i) q^{18} +(0.0142419 + 0.0469493i) q^{19} +(-4.31688 - 1.98422i) q^{20} +(-2.79017 + 0.274807i) q^{21} +(-2.19356 - 4.87639i) q^{22} +(-7.59930 + 5.07769i) q^{23} +(0.713092 + 7.89784i) q^{24} +(0.357307 - 0.534748i) q^{25} +(-0.561462 - 0.788020i) q^{26} +(1.51422 - 4.99173i) q^{27} +(1.32682 - 1.49651i) q^{28} +(-0.672411 + 0.551833i) q^{29} +(-9.39706 - 0.641494i) q^{30} +(-2.61914 + 2.61914i) q^{31} +(-4.20212 - 3.78710i) q^{32} +(-7.49566 - 7.49566i) q^{33} +(3.10959 + 3.56525i) q^{34} +(1.50702 + 1.83631i) q^{35} +(4.25221 + 8.74175i) q^{36} +(-11.1029 - 3.36804i) q^{37} +(-0.0684264 - 0.0114878i) q^{38} +(-1.59494 - 1.06571i) q^{39} +(5.22834 - 4.22013i) q^{40} +(5.26192 + 7.87502i) q^{41} +(1.40672 - 3.70705i) q^{42} +(0.175646 + 1.78336i) q^{43} +(7.55636 + 0.288374i) q^{44} +(-11.0492 + 3.35173i) q^{45} +(-1.65237 - 12.8193i) q^{46} +(-7.83235 - 3.24426i) q^{47} +(-10.4524 - 4.06390i) q^{48} +(-0.923880 + 0.382683i) q^{49} +(0.452630 + 0.788907i) q^{50} +(8.27136 + 4.42113i) q^{51} +(1.35128 - 0.215581i) q^{52} +(5.42875 + 4.45526i) q^{53} +(5.37054 + 5.05745i) q^{54} +(-1.75224 + 8.80913i) q^{55} +(1.06111 + 2.62184i) q^{56} +(-0.134910 + 0.0268353i) q^{57} +(-0.276094 - 1.19878i) q^{58} +(-1.54295 - 2.88665i) q^{59} +(6.72261 - 11.4995i) q^{60} +(8.28378 + 0.815881i) q^{61} +(-1.67034 - 4.96483i) q^{62} -4.86054i q^{63} +(7.43983 - 2.94090i) q^{64} +1.62530i q^{65} +(14.2087 - 4.78032i) q^{66} +(9.59989 + 0.945507i) q^{67} +(-6.47170 + 1.69655i) q^{68} +(-12.0793 - 22.5987i) q^{69} +(-3.27380 + 0.753995i) q^{70} +(3.49410 - 0.695019i) q^{71} +(-13.7472 - 0.111760i) q^{72} +(0.685080 - 3.44413i) q^{73} +(11.2491 - 11.9455i) q^{74} +(1.39385 + 1.14390i) q^{75} +(0.0575864 - 0.0794487i) q^{76} +(-3.33448 - 1.78232i) q^{77} +(2.35300 - 1.35002i) q^{78} +(1.46556 - 0.607055i) q^{79} +(2.05727 + 9.27673i) q^{80} +(0.0399625 + 0.0165530i) q^{81} +(-13.2844 + 1.71232i) q^{82} +(14.4179 - 4.37361i) q^{83} +(3.81089 + 4.11330i) q^{84} +(-0.778902 - 7.90833i) q^{85} +(-2.36940 - 0.899118i) q^{86} +(-1.35492 - 2.02779i) q^{87} +(-5.11766 + 9.39005i) q^{88} +(1.96396 + 1.31228i) q^{89} +(2.70357 - 16.1037i) q^{90} +(-0.654723 - 0.198608i) q^{91} +(17.2770 + 5.96938i) q^{92} +(-6.58807 - 8.02759i) q^{93} +(9.03538 - 7.88060i) q^{94} +(0.0824119 + 0.0824119i) q^{95} +(11.7214 - 10.6839i) q^{96} +(-5.50156 + 5.50156i) q^{97} +(0.0963177 - 1.41093i) q^{98} +(14.2059 - 11.6585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 784 q+O(q^{10}) $ 784 * q	$ 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) $ 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{27}{32}\right)$

Coefficient data

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

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

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

$2$	−0.628925	+	1.26667i	−0.444717	+	0.895671i
$2$	−0.628925	+	1.26667i	−0.444717	+	0.895671i
$3$	−0.274807	+	2.79017i	−0.158660	+	1.61090i	0.505170	+	0.863020i	$0.331430\pi$
$3$	−0.274807	+	2.79017i	−0.158660	+	1.61090i	−0.663830	+	0.747883i	$0.731070\pi$
$4$	−1.20891	−	1.59328i	−0.604453	−	0.796641i
$5$	2.09503	−	1.11982i	0.936926	−	0.500797i	0.0690689	−	0.997612i	$-0.477997\pi$
$5$	2.09503	−	1.11982i	0.936926	−	0.500797i	0.867857	+	0.496815i	$0.165497\pi$
$6$	−3.36139	−	2.10290i	−1.37228	−	0.858504i
$7$	0.195090	+	0.980785i	0.0737372	+	0.370702i
$7$	0.195090	+	0.980785i	0.0737372	+	0.370702i
$8$	2.77847	−	0.529229i	0.982339	−	0.187111i
$9$	−4.76715	−	0.948245i	−1.58905	−	0.316082i
$10$	0.100821	+	3.35799i	0.0318823	+	1.06189i
$11$	−2.39860	+	2.92270i	−0.723204	+	0.881227i	−0.996744	−	0.0806339i	$-0.974306\pi$
$11$	−2.39860	+	2.92270i	−0.723204	+	0.881227i	0.273540	+	0.961861i	$0.411806\pi$
$12$	4.77774	−	2.93520i	1.37921	−	0.847320i
$13$	−0.322522	+	0.603396i	−0.0894515	+	0.167352i	−0.922668	−	0.385594i	$-0.873996\pi$
$13$	−0.322522	+	0.603396i	−0.0894515	+	0.167352i	0.833217	+	0.552946i	$0.186496\pi$
$14$	−1.36503	−	0.369726i	−0.364819	−	0.0988134i
$15$	2.54874	+	6.15321i	0.658083	+	1.58875i
$16$	−1.07709	+	3.85225i	−0.269274	+	0.963064i
$17$	1.28015	−	3.09055i	0.310482	−	0.749569i	−0.689206	−	0.724566i	$-0.742040\pi$
$17$	1.28015	−	3.09055i	0.310482	−	0.749569i	0.999687	−	0.0250031i	$-0.00795958\pi$
$18$	4.19930	−	5.44203i	0.989783	−	1.28270i
$19$	0.0142419	+	0.0469493i	0.00326732	+	0.0107709i	0.958559	−	0.284895i	$-0.0919586\pi$
$19$	0.0142419	+	0.0469493i	0.00326732	+	0.0107709i	−0.955292	+	0.295666i	$0.904459\pi$
$20$	−4.31688	−	1.98422i	−0.965283	−	0.443685i
$21$	−2.79017	+	0.274807i	−0.608864	+	0.0599679i
$22$	−2.19356	−	4.87639i	−0.467668	−	1.03965i
$23$	−7.59930	+	5.07769i	−1.58456	+	1.05877i	−0.623734	+	0.781637i	$0.714385\pi$
$23$	−7.59930	+	5.07769i	−1.58456	+	1.05877i	−0.960831	+	0.277135i	$0.910615\pi$
$24$	0.713092	+	7.89784i	0.145559	+	1.61214i
$25$	0.357307	−	0.534748i	0.0714615	−	0.106950i
$26$	−0.561462	−	0.788020i	−0.110112	−	0.154543i
$27$	1.51422	−	4.99173i	0.291413	−	0.960659i
$28$	1.32682	−	1.49651i	0.250746	−	0.282814i
$29$	−0.672411	+	0.551833i	−0.124864	+	0.102473i	−0.694753	−	0.719249i	$-0.744486\pi$
$29$	−0.672411	+	0.551833i	−0.124864	+	0.102473i	0.569889	+	0.821722i	$0.306986\pi$
$30$	−9.39706	−	0.641494i	−1.71566	−	0.117120i
$31$	−2.61914	+	2.61914i	−0.470411	+	0.470411i	−0.902048	−	0.431636i	$-0.857936\pi$
$31$	−2.61914	+	2.61914i	−0.470411	+	0.470411i	0.431636	+	0.902048i	$0.357936\pi$
$32$	−4.20212	−	3.78710i	−0.742838	−	0.669472i
$33$	−7.49566	−	7.49566i	−1.30483	−	1.30483i
$34$	3.10959	+	3.56525i	0.533290	+	0.611436i
$35$	1.50702	+	1.83631i	0.254733	+	0.310393i
$36$	4.25221	+	8.74175i	0.708702	+	1.45696i
$37$	−11.1029	−	3.36804i	−1.82531	−	0.553702i	−0.825372	−	0.564590i	$-0.809034\pi$
$37$	−11.1029	−	3.36804i	−1.82531	−	0.553702i	−0.999941	+	0.0108873i	$0.996534\pi$
$38$	−0.0684264	−	0.0114878i	−0.0111002	−	0.00186357i
$39$	−1.59494	−	1.06571i	−0.255395	−	0.170650i
$40$	5.22834	−	4.22013i	0.826674	−	0.667261i
$41$	5.26192	+	7.87502i	0.821774	+	1.22987i	0.970526	+	0.240997i	$0.0774744\pi$
$41$	5.26192	+	7.87502i	0.821774	+	1.22987i	−0.148752	+	0.988875i	$0.547526\pi$
$42$	1.40672	−	3.70705i	0.217061	−	0.572011i
$43$	0.175646	+	1.78336i	0.0267858	+	0.271960i	0.999244	+	0.0388824i	$0.0123798\pi$
$43$	0.175646	+	1.78336i	0.0267858	+	0.271960i	−0.972458	+	0.233078i	$0.925120\pi$
$44$	7.55636	+	0.288374i	1.13916	+	0.0434740i
$45$	−11.0492	+	3.35173i	−1.64711	+	0.499647i
$46$	−1.65237	−	12.8193i	−0.243628	−	1.89010i
$47$	−7.83235	−	3.24426i	−1.14247	−	0.473225i	−0.270465	−	0.962730i	$-0.587177\pi$
$47$	−7.83235	−	3.24426i	−1.14247	−	0.473225i	−0.872000	+	0.489505i	$0.837177\pi$
$48$	−10.4524	−	4.06390i	−1.50868	−	0.586573i
$49$	−0.923880	+	0.382683i	−0.131983	+	0.0546691i
$50$	0.452630	+	0.788907i	0.0640115	+	0.111568i
$51$	8.27136	+	4.42113i	1.15822	+	0.619082i
$52$	1.35128	−	0.215581i	0.187389	−	0.0298957i
$53$	5.42875	+	4.45526i	0.745696	+	0.611977i	0.928569	−	0.371160i	$-0.121040\pi$
$53$	5.42875	+	4.45526i	0.745696	+	0.611977i	−0.182873	+	0.983136i	$0.558540\pi$
$54$	5.37054	+	5.05745i	0.730838	+	0.688232i
$55$	−1.75224	+	8.80913i	−0.236273	+	1.18782i
$56$	1.06111	+	2.62184i	0.141797	+	0.350358i
$57$	−0.134910	+	0.0268353i	−0.0178693	+	0.00355442i
$58$	−0.276094	−	1.19878i	−0.0362530	−	0.157408i
$59$	−1.54295	−	2.88665i	−0.200875	−	0.375810i	0.761234	−	0.648478i	$-0.224594\pi$
$59$	−1.54295	−	2.88665i	−0.200875	−	0.375810i	−0.962108	+	0.272668i	$0.912094\pi$
$60$	6.72261	−	11.4995i	0.867885	−	1.48458i
$61$	8.28378	+	0.815881i	1.06063	+	0.104463i	0.613256	−	0.789884i	$-0.289859\pi$
$61$	8.28378	+	0.815881i	1.06063	+	0.104463i	0.447374	+	0.894347i	$0.352359\pi$
$62$	−1.67034	−	4.96483i	−0.212134	−	0.630534i
$63$		−	4.86054i		−	0.612371i
$64$	7.43983	−	2.94090i	0.929979	−	0.367612i
$65$			1.62530i			0.201593i
$66$	14.2087	−	4.78032i	1.74898	−	0.588416i
$67$	9.59989	+	0.945507i	1.17281	+	0.115512i	0.665600	−	0.746309i	$-0.268176\pi$
$67$	9.59989	+	0.945507i	1.17281	+	0.115512i	0.507213	+	0.861821i	$0.330676\pi$
$68$	−6.47170	+	1.69655i	−0.784809	+	0.205737i
$69$	−12.0793	−	22.5987i	−1.45417	−	2.72056i
$70$	−3.27380	+	0.753995i	−0.391294	+	0.0901197i
$71$	3.49410	−	0.695019i	0.414673	−	0.0824836i	0.0166553	−	0.999861i	$-0.494698\pi$
$71$	3.49410	−	0.695019i	0.414673	−	0.0824836i	0.398018	+	0.917378i	$0.369698\pi$
$72$	−13.7472	−	0.111760i	−1.62013	−	0.0131711i
$73$	0.685080	−	3.44413i	0.0801825	−	0.403105i	−0.919761	−	0.392479i	$-0.871618\pi$
$73$	0.685080	−	3.44413i	0.0801825	−	0.403105i	0.999944	−	0.0106259i	$-0.00338238\pi$
$74$	11.2491	−	11.9455i	1.30768	−	1.38864i
$75$	1.39385	+	1.14390i	0.160947	+	0.132086i
$76$	0.0575864	−	0.0794487i	0.00660561	−	0.00911339i
$77$	−3.33448	−	1.78232i	−0.380000	−	0.203114i
$78$	2.35300	−	1.35002i	0.266425	−	0.152859i
$79$	1.46556	−	0.607055i	0.164888	−	0.0682990i	−0.298713	−	0.954343i	$-0.596557\pi$
$79$	1.46556	−	0.607055i	0.164888	−	0.0682990i	0.463601	+	0.886044i	$0.346557\pi$
$80$	2.05727	+	9.27673i	0.230010	+	1.03717i
$81$	0.0399625	+	0.0165530i	0.00444028	+	0.00183922i
$82$	−13.2844	+	1.71232i	−1.46702	+	0.189094i
$83$	14.4179	−	4.37361i	1.58257	−	0.480067i	0.628038	−	0.778183i	$-0.283858\pi$
$83$	14.4179	−	4.37361i	1.58257	−	0.480067i	0.954530	+	0.298116i	$0.0963583\pi$
$84$	3.81089	+	4.11330i	0.415802	+	0.448798i
$85$	−0.778902	−	7.90833i	−0.0844838	−	0.857778i
$86$	−2.36940	−	0.899118i	−0.255499	−	0.0969543i
$87$	−1.35492	−	2.02779i	−0.145263	−	0.217401i
$88$	−5.11766	+	9.39005i	−0.545545	+	1.00098i
$89$	1.96396	+	1.31228i	0.208179	+	0.139101i	0.655289	−	0.755378i	$-0.272547\pi$
$89$	1.96396	+	1.31228i	0.208179	+	0.139101i	−0.447110	+	0.894479i	$0.647547\pi$
$90$	2.70357	−	16.1037i	0.284981	−	1.69747i
$91$	−0.654723	−	0.198608i	−0.0686336	−	0.0208198i
$92$	17.2770	+	5.96938i	1.80126	+	0.622351i
$93$	−6.58807	−	8.02759i	−0.683151	−	0.832422i
$94$	9.03538	−	7.88060i	0.931928	−	0.812822i
$95$	0.0824119	+	0.0824119i	0.00845528	+	0.00845528i
$96$	11.7214	−	10.6839i	1.19631	−	1.09042i
$97$	−5.50156	+	5.50156i	−0.558599	+	0.558599i	−0.928908	−	0.370310i	$-0.879252\pi$
$97$	−5.50156	+	5.50156i	−0.558599	+	0.558599i	0.370310	+	0.928908i	$0.379252\pi$
$98$	0.0963177	−	1.41093i	0.00972956	−	0.142525i
$99$	14.2059	−	11.6585i	1.42775	−	1.17172i
$100$	−1.28396	+	0.0771688i	−0.128396	+	0.00771688i
$101$	1.71313	−	5.64745i	0.170463	−	0.561942i	−0.829531	−	0.558461i	$-0.811392\pi$
$101$	1.71313	−	5.64745i	0.170463	−	0.561942i	0.999994	−	0.00348094i	$-0.00110802\pi$
$102$	−10.8022	+	7.69652i	−1.06958	+	0.762069i
$103$	−8.94648	+	13.3893i	−0.881523	+	1.31929i	0.0654097	+	0.997858i	$0.479165\pi$
$103$	−8.94648	+	13.3893i	−0.881523	+	1.31929i	−0.946932	+	0.321433i	$0.895835\pi$
$104$	−0.576784	+	1.84721i	−0.0565583	+	0.181134i
$105$	−5.53774	+	3.70020i	−0.540429	+	0.361103i
$106$	−9.05762	+	4.07440i	−0.879753	+	0.395741i
$107$	7.63292	−	0.751777i	0.737903	−	0.0726771i	0.277919	−	0.960604i	$-0.410355\pi$
$107$	7.63292	−	0.751777i	0.737903	−	0.0726771i	0.459984	+	0.887927i	$0.347855\pi$
$108$	−9.78379	+	3.62194i	−0.941445	+	0.348522i
$109$	−1.34378	−	4.42984i	−0.128711	−	0.424302i	0.868772	−	0.495212i	$-0.164910\pi$
$109$	−1.34378	−	4.42984i	−0.128711	−	0.424302i	−0.997483	+	0.0709102i	$0.977410\pi$
$110$	−10.0562	−	7.75980i	−0.958824	−	0.739868i
$111$	12.4486	−	30.0535i	1.18157	−	2.85255i
$112$	−3.98837	−	0.304861i	−0.376865	−	0.0288066i
$113$	2.01613	+	4.86737i	0.189662	+	0.457884i	0.989895	−	0.141806i	$-0.0452908\pi$
$113$	2.01613	+	4.86737i	0.189662	+	0.457884i	−0.800233	+	0.599689i	$0.795291\pi$
$114$	0.0508570	−	0.187764i	0.00476319	−	0.0175857i
$115$	−10.2347	+	19.1477i	−0.954389	+	1.78554i
$116$	1.69211	+	0.404226i	0.157108	+	0.0375314i
$117$	2.10968	−	2.57065i	0.195040	−	0.237657i
$118$	4.62683	−	0.138917i	0.425934	−	0.0127883i
$119$	3.28091	+	0.652614i	0.300761	+	0.0598250i
$120$	10.3381	+	15.7477i	0.943733	+	1.43756i
$121$	−0.642907	−	3.23211i	−0.0584461	−	0.293829i
$122$	−6.24333	+	9.97969i	−0.565245	+	0.903519i
$123$	−23.4186	+	12.5175i	−2.11159	+	1.12867i
$124$	7.33932	+	1.00673i	0.659090	+	0.0904074i
$125$	−1.01446	+	10.3000i	−0.0907363	+	0.921262i
$126$	6.15670	+	3.05692i	0.548483	+	0.272332i
$127$	17.8893			1.58742			0.793711	−	0.608296i	$-0.208146\pi$
$127$	17.8893			1.58742			0.793711	+	0.608296i	$0.208146\pi$
$128$	−0.953953	+	11.2734i	−0.0843184	+	0.996439i
$129$	−5.02415			−0.442352
$130$	−2.05872	−	1.02219i	−0.180561	−	0.0896521i
$131$	0.754628	−	7.66186i	0.0659321	−	0.669420i	−0.904244	−	0.427017i	$-0.859564\pi$
$131$	0.754628	−	7.66186i	0.0659321	−	0.669420i	0.970176	−	0.242403i	$-0.0779356\pi$
$132$	−2.88115	+	21.0043i	−0.250772	+	1.82819i
$133$	−0.0432687	+	0.0231276i	−0.00375188	+	0.00200542i
$134$	−7.23526	+	11.5652i	−0.625031	+	0.999085i
$135$	−2.41748	−	12.1535i	−0.208063	−	1.04600i
$136$	1.92125	−	9.26451i	0.164746	−	0.794425i
$137$	6.76804	+	1.34625i	0.578232	+	0.115018i	0.475538	−	0.879695i	$-0.342254\pi$
$137$	6.76804	+	1.34625i	0.578232	+	0.115018i	0.102695	+	0.994713i	$0.467254\pi$
$138$	36.2221	−	1.08754i	3.08343	−	0.0925772i
$139$	−5.55439	+	6.76805i	−0.471117	+	0.574058i	−0.953305	−	0.302010i	$-0.902342\pi$
$139$	−5.55439	+	6.76805i	−0.471117	+	0.574058i	0.482187	+	0.876068i	$0.339842\pi$
$140$	1.10391	−	4.62103i	0.0932977	−	0.390548i
$141$	11.2044	−	20.9620i	0.943583	−	1.76532i
$142$	−1.31717	+	4.86298i	−0.110534	+	0.408093i
$143$	−0.989945	−	2.38994i	−0.0827834	−	0.199857i
$144$	8.78755	−	17.3429i	0.732296	−	1.44524i
$145$	−0.790768	+	1.90908i	−0.0656697	+	0.158541i
$146$	3.93171	+	3.03387i	0.325391	+	0.251085i
$147$	−0.813861	−	2.68294i	−0.0671262	−	0.221285i
$148$	8.05617	+	21.7618i	0.662213	+	1.78881i
$149$	19.2115	−	1.89217i	1.57387	−	0.155012i	0.726932	−	0.686709i	$-0.240945\pi$
$149$	19.2115	−	1.89217i	1.57387	−	0.155012i	0.846935	+	0.531697i	$0.178445\pi$
$150$	−2.32557	+	1.04611i	−0.189882	+	0.0854149i
$151$	−10.0571	+	6.71996i	−0.818438	+	0.546863i	−0.892844	−	0.450365i	$-0.851294\pi$
$151$	−10.0571	+	6.71996i	−0.818438	+	0.546863i	0.0744064	+	0.997228i	$0.476294\pi$
$152$	0.0644177	+	0.122910i	0.00522497	+	0.00996934i
$153$	−9.03326	+	13.5192i	−0.730296	+	1.09296i
$154$	4.35475	−	3.10274i	0.350916	−	0.250026i
$155$	−2.55422	+	8.42013i	−0.205160	+	0.676321i
$156$	0.230164	+	3.82954i	0.0184279	+	0.306608i
$157$	−15.4570	+	12.6852i	−1.23360	+	1.01239i	−0.234412	+	0.972137i	$0.575316\pi$
$157$	−15.4570	+	12.6852i	−1.23360	+	1.01239i	−0.999190	+	0.0402531i	$0.987184\pi$
$158$	−0.152790	+	2.23817i	−0.0121553	+	0.178059i
$159$	−13.9228	+	13.9228i	−1.10415	+	1.10415i
$160$	−13.0444	−	3.22849i	−1.03125	−	0.255234i
$161$	−6.46268	−	6.46268i	−0.509330	−	0.509330i
$162$	−0.0461006	+	0.0402087i	−0.00362201	+	0.00315909i
$163$	−13.7286	−	16.7284i	−1.07531	−	1.31027i	−0.947953	−	0.318411i	$-0.896851\pi$
$163$	−13.7286	−	16.7284i	−1.07531	−	1.31027i	−0.127357	−	0.991857i	$-0.540649\pi$
$164$	6.18596	−	17.9039i	0.483042	−	1.39806i
$165$	−24.0974	−	7.30987i	−1.87598	−	0.569072i
$166$	−3.52784	+	21.0134i	−0.273814	+	1.63095i
$167$	−5.77403	−	3.85808i	−0.446808	−	0.298548i	0.311737	−	0.950169i	$-0.399089\pi$
$167$	−5.77403	−	3.85808i	−0.446808	−	0.298548i	−0.758545	+	0.651621i	$0.774089\pi$
$168$	−7.60697	+	2.24018i	−0.586890	+	0.172834i
$169$	6.96235	+	10.4199i	0.535565	+	0.801530i
$170$	10.5071	+	3.98714i	0.805859	+	0.305799i
$171$	−0.0233739	−	0.237319i	−0.00178745	−	0.0181483i
$172$	2.62906	−	2.43577i	0.200464	−	0.185726i
$173$	−20.9052	+	6.34154i	−1.58940	+	0.482138i	−0.956410	−	0.292026i	$-0.905671\pi$
$173$	−20.9052	+	6.34154i	−1.58940	+	0.482138i	−0.632985	+	0.774164i	$0.718171\pi$
$174$	3.42068	−	0.440914i	0.259321	−	0.0334256i
$175$	0.594180	+	0.246118i	0.0449158	+	0.0186047i
$176$	−8.67547	−	12.3880i	−0.653938	−	0.933783i
$177$	8.47824	−	3.51180i	0.637264	−	0.263963i
$178$	−2.89740	+	1.66236i	−0.217170	+	0.124599i
$179$	−12.4883	−	6.67511i	−0.933416	−	0.498921i	−0.0667279	−	0.997771i	$-0.521256\pi$
$179$	−12.4883	−	6.67511i	−0.933416	−	0.498921i	−0.866688	+	0.498850i	$0.833756\pi$
$180$	18.6977	+	13.5525i	1.39364	+	1.01015i
$181$	8.14520	+	6.68459i	0.605428	+	0.496862i	0.886441	−	0.462842i	$-0.153170\pi$
$181$	8.14520	+	6.68459i	0.605428	+	0.496862i	−0.281013	+	0.959704i	$0.590670\pi$
$182$	0.663343	−	0.704409i	0.0491703	−	0.0522142i
$183$	−4.55289	+	22.8889i	−0.336559	+	1.69200i
$184$	−18.4272	+	18.1300i	−1.35847	+	1.33656i
$185$	−27.0326	+	5.37711i	−1.98747	+	0.395333i
$186$	14.3117	−	3.29616i	1.04939	−	0.241686i
$187$	5.96219	+	11.1545i	0.435999	+	0.815696i
$188$	4.29954	+	16.4011i	0.313576	+	1.19618i
$189$	5.19123	+	0.511291i	0.377606	+	0.0371910i
$190$	−0.156220	+	0.0525577i	−0.0113334	+	0.00381294i
$191$		−	9.48587i		−	0.686373i	−0.939267	−	0.343187i	$-0.888494\pi$
$191$		−	9.48587i		−	0.686373i	0.939267	−	0.343187i	$-0.111506\pi$
$192$	6.16107	+	21.5665i	0.444637	+	1.55643i
$193$			22.0392i			1.58642i	0.608948	+	0.793210i	$0.291592\pi$
$193$			22.0392i			1.58642i	−0.608948	+	0.793210i	$0.708408\pi$
$194$	−3.50859	−	10.4287i	−0.251902	−	0.748739i
$195$	−4.53485	−	0.446644i	−0.324747	−	0.0319848i
$196$	1.72661	+	1.00937i	0.123329	+	0.0720980i
$197$	−9.23966	−	17.2862i	−0.658299	−	1.23159i	−0.960482	−	0.278340i	$-0.910216\pi$
$197$	−9.23966	−	17.2862i	−0.658299	−	1.23159i	0.302184	−	0.953250i	$-0.402284\pi$
$198$	5.83300	+	25.3265i	0.414533	+	1.79988i
$199$	14.4338	−	2.87106i	1.02319	−	0.203524i	0.345146	−	0.938549i	$-0.387830\pi$
$199$	14.4338	−	2.87106i	1.02319	−	0.203524i	0.678040	+	0.735025i	$0.262830\pi$
$200$	0.709765	−	1.67488i	0.0501879	−	0.118432i
$201$	−5.27624	+	26.5255i	−0.372157	+	1.87096i
$202$	6.07602	+	5.72180i	0.427507	+	0.402584i
$203$	−0.672411	−	0.551833i	−0.0471940	−	0.0387311i
$204$	−2.95518	−	18.5233i	−0.206904	−	1.29689i
$205$	19.8425	+	10.6060i	1.38586	+	0.740756i
$206$	−11.3332	−	19.7531i	−0.789623	−	1.37627i
$207$	41.0419	−	17.0001i	2.85261	−	1.18159i
$208$	−1.97705	−	1.89235i	−0.137084	−	0.131211i
$209$	−0.171379	−	0.0709877i	−0.0118546	−	0.00491032i
$210$	−1.20411	−	9.34165i	−0.0830913	−	0.644635i
$211$	−7.38988	+	2.24169i	−0.508740	+	0.154325i	−0.534211	−	0.845351i	$-0.679391\pi$
$211$	−7.38988	+	2.24169i	−0.508740	+	0.154325i	0.0254713	+	0.999676i	$0.491891\pi$
$212$	0.535638	−	14.0355i	0.0367878	−	0.963963i
$213$	0.979015	+	9.94011i	0.0670810	+	0.681085i
$214$	−3.84829	+	10.1412i	−0.263063	+	0.693239i
$215$	2.36502	+	3.53951i	0.161293	+	0.241392i
$216$	1.56547	−	14.6708i	0.106516	−	0.998219i
$217$	−3.07978	−	2.05784i	−0.209069	−	0.139696i
$218$	6.45628	+	1.08392i	0.437275	+	0.0734121i
$219$	9.42142	+	2.85796i	0.636641	+	0.193123i
$220$	16.1537	−	7.85758i	1.08908	−	0.529758i
$221$	1.45195	+	1.76921i	0.0976688	+	0.119010i
$222$	30.2386	+	34.6696i	2.02948	+	2.32687i
$223$	3.88185	+	3.88185i	0.259948	+	0.259948i	0.825033	−	0.565085i	$-0.191157\pi$
$223$	3.88185	+	3.88185i	0.259948	+	0.259948i	−0.565085	+	0.825033i	$0.691157\pi$
$224$	2.89454	−	4.86021i	0.193400	−	0.324736i
$225$	−2.21041	+	2.21041i	−0.147361	+	0.147361i
$226$	−7.43335	−	0.507440i	−0.494459	−	0.0337544i
$227$	−7.98994	+	6.55717i	−0.530311	+	0.435215i	−0.861060	−	0.508504i	$-0.830199\pi$
$227$	−7.98994	+	6.55717i	−0.530311	+	0.435215i	0.330749	+	0.943719i	$0.392699\pi$
$228$	0.205850	+	0.182509i	0.0136327	+	0.0120869i
$229$	1.74790	−	5.76207i	0.115505	−	0.380768i	−0.880058	−	0.474866i	$-0.842497\pi$
$229$	1.74790	−	5.76207i	0.115505	−	0.380768i	0.995563	+	0.0940976i	$0.0299966\pi$
$230$	−17.8170	−	25.0065i	−1.17482	−	1.64888i
$231$	5.88930	−	8.81397i	0.387488	−	0.579916i
$232$	−1.57623	+	1.88911i	−0.103485	+	0.124026i
$233$	4.28968	−	2.86627i	0.281026	−	0.187776i	−0.407067	−	0.913398i	$-0.633448\pi$
$233$	4.28968	−	2.86627i	0.281026	−	0.187776i	0.688093	+	0.725623i	$0.258448\pi$
$234$	1.92934	+	4.28901i	0.126125	+	0.280382i
$235$	−20.0420	+	1.97396i	−1.30739	+	0.128767i
$236$	−2.73397	+	5.94804i	−0.177966	+	0.387184i
$237$	1.29104	+	4.25598i	0.0838618	+	0.276455i
$238$	−2.89010	+	3.74539i	−0.187337	+	0.242777i
$239$	5.76857	−	13.9266i	0.373138	−	0.900834i	−0.620077	−	0.784541i	$-0.712899\pi$
$239$	5.76857	−	13.9266i	0.373138	−	0.900834i	0.993215	−	0.116293i	$-0.0371012\pi$
$240$	−26.4490	+	3.19082i	−1.70727	+	0.205967i
$241$	2.63434	+	6.35987i	0.169693	+	0.409675i	0.985732	−	0.168321i	$-0.0538347\pi$
$241$	2.63434	+	6.35987i	0.169693	+	0.409675i	−0.816039	+	0.577997i	$0.803835\pi$
$242$	4.49836	+	1.21841i	0.289166	+	0.0783222i
$243$	7.31973	−	13.6943i	0.469561	−	0.878487i
$244$	−8.71438	−	14.1847i	−0.557881	−	0.908084i
$245$	−1.50702	+	1.83631i	−0.0962799	+	0.117317i
$246$	−1.12699	−	37.5362i	−0.0718544	−	2.39322i
$247$	−0.0329224	−	0.00654867i	−0.00209480	−	0.000416682i
$248$	−5.89108	+	8.66333i	−0.374084	+	0.550122i
$249$	8.24097	+	41.4302i	0.522250	+	2.62553i
$250$	−12.4087	−	7.76293i	−0.784795	−	0.490971i
$251$	25.5769	−	13.6712i	1.61440	−	0.862916i	0.617309	−	0.786721i	$-0.288223\pi$
$251$	25.5769	−	13.6712i	1.61440	−	0.862916i	0.997093	−	0.0761949i	$-0.0242771\pi$
$252$	−7.74422	+	5.87594i	−0.487840	+	0.370149i
$253$	3.38710	−	34.3898i	0.212945	−	2.16207i
$254$	−11.2511	+	22.6599i	−0.705954	+	1.42181i
$255$	22.2796			1.39520
$256$	−13.6797	−	8.29848i	−0.854983	−	0.518655i
$257$	20.1539			1.25717			0.628584	−	0.777742i	$-0.283635\pi$
$257$	20.1539			1.25717			0.628584	+	0.777742i	$0.283635\pi$
$258$	3.15982	−	6.36394i	0.196722	−	0.396202i
$259$	1.13725	−	11.5467i	0.0706652	−	0.717475i
$260$	2.58956	−	1.96483i	0.160598	−	0.121854i
$261$	3.72876	−	1.99306i	0.230804	−	0.123367i
$262$	9.23045	+	5.77460i	0.570259	+	0.356756i
$263$	0.913744	+	4.59370i	0.0563439	+	0.283260i	0.998677	−	0.0514156i	$-0.0163733\pi$
$263$	0.913744	+	4.59370i	0.0563439	+	0.283260i	−0.942333	+	0.334675i	$0.891373\pi$
$264$	−24.7934	−	16.8596i	−1.52593	−	1.03764i
$265$	16.3624	+	3.25469i	1.00514	+	0.199934i
$266$	−0.00208226	−	0.0693528i	−0.000127671	−	0.00425229i
$267$	−4.20118	+	5.11915i	−0.257108	+	0.313287i
$268$	−10.0989	−	16.4384i	−0.616889	−	1.00413i
$269$	1.57178	−	2.94059i	0.0958330	−	0.179291i	−0.829437	−	0.558601i	$-0.811338\pi$
$269$	1.57178	−	2.94059i	0.0958330	−	0.179291i	0.925270	+	0.379310i	$0.123838\pi$
$270$	16.9149	+	4.58148i	1.02941	+	0.278820i
$271$	10.7296	+	25.9036i	0.651778	+	1.57353i	0.810196	+	0.586159i	$0.199361\pi$
$271$	10.7296	+	25.9036i	0.651778	+	1.57353i	−0.158418	+	0.987372i	$0.550639\pi$
$272$	10.5268	+	8.26027i	0.638278	+	0.500853i
$273$	0.734072	−	1.77221i	0.0444281	−	0.107259i
$274$	−5.96184	+	7.72618i	−0.360168	+	0.466756i
$275$	0.705872	+	2.32695i	0.0425657	+	0.140320i
$276$	−21.4034	+	46.5654i	−1.28833	+	2.80291i
$277$	−9.77686	+	0.962937i	−0.587435	+	0.0578573i	−0.387368	−	0.921925i	$-0.626616\pi$
$277$	−9.77686	+	0.962937i	−0.587435	+	0.0578573i	−0.200066	+	0.979782i	$0.564116\pi$
$278$	−5.07958	−	11.2922i	−0.304653	−	0.677260i
$279$	14.9694	−	10.0022i	0.896195	−	0.598818i
$280$	5.15904	+	4.30458i	0.308312	+	0.257248i
$281$	−0.338508	+	0.506613i	−0.0201937	+	0.0302220i	−0.841429	−	0.540367i	$-0.818285\pi$
$281$	−0.338508	+	0.506613i	−0.0201937	+	0.0302220i	0.821235	+	0.570589i	$0.193285\pi$
$282$	19.5052	+	27.3758i	1.16152	+	1.63021i
$283$	0.939793	−	3.09808i	0.0558649	−	0.184162i	−0.924567	−	0.381019i	$-0.875573\pi$
$283$	0.939793	−	3.09808i	0.0558649	−	0.184162i	0.980432	+	0.196857i	$0.0630734\pi$
$284$	−5.33140	−	4.72687i	−0.316360	−	0.280488i
$285$	−0.252590	+	0.207295i	−0.0149621	+	0.0122791i
$286$	3.64987	+	0.249160i	0.215821	+	0.0147331i
$287$	−6.69715	+	6.69715i	−0.395320	+	0.395320i
$288$	16.4411	+	22.0383i	0.968798	+	1.29862i
$289$	4.10809	+	4.10809i	0.241652	+	0.241652i
$290$	−1.92084	−	2.20231i	−0.112796	−	0.129324i
$291$	−13.8384	−	16.8621i	−0.811221	−	0.988476i
$292$	−6.31566	+	3.07210i	−0.369596	+	0.179781i
$293$	−2.79661	−	0.848344i	−0.163380	−	0.0495608i	0.207535	−	0.978228i	$-0.433456\pi$
$293$	−2.79661	−	0.848344i	−0.163380	−	0.0495608i	−0.370915	+	0.928667i	$0.620956\pi$
$294$	3.91026	+	0.656476i	0.228051	+	0.0382865i
$295$	−6.46504	−	4.31980i	−0.376409	−	0.251508i
$296$	−32.6317	−	3.48201i	−1.89668	−	0.202388i
$297$	10.9573	+	16.3988i	0.635807	+	0.951553i
$298$	−9.68585	+	25.5247i	−0.561086	+	1.47860i
$299$	−0.612918	−	6.22306i	−0.0354460	−	0.359889i
$300$	0.137527	−	3.60365i	0.00794010	−	0.208057i
$301$	−1.71483	+	0.520188i	−0.0988412	+	0.0299831i
$302$	−2.18679	−	16.9654i	−0.125835	−	0.976251i
$303$	15.2865	+	6.33189i	0.878188	+	0.363758i
$304$	−0.196201	+	0.00429466i	−0.0112529	+	0.000246316i
$305$	18.2684	−	7.56702i	1.04605	−	0.433286i
$306$	−11.4432	−	19.9447i	−0.654161	−	1.14017i
$307$	23.9734	+	12.8140i	1.36823	+	0.731336i	0.981609	−	0.190901i	$-0.0611409\pi$
$307$	23.9734	+	12.8140i	1.36823	+	0.731336i	0.386625	+	0.922237i	$0.373641\pi$
$308$	1.19134	+	7.46743i	0.0678829	+	0.425496i
$309$	−34.8999	−	28.6416i	−1.98539	−	1.62937i
$310$	−9.05911	−	8.53098i	−0.514523	−	0.484527i
$311$	−5.47322	+	27.5157i	−0.310358	+	1.56027i	0.439233	+	0.898373i	$0.355250\pi$
$311$	−5.47322	+	27.5157i	−0.310358	+	1.56027i	−0.749591	+	0.661902i	$0.769750\pi$
$312$	−4.99551	−	2.11695i	−0.282815	−	0.119849i
$313$	0.0501617	−	0.00997777i	0.00283530	−	0.000563977i	−0.193672	−	0.981066i	$-0.562040\pi$
$313$	0.0501617	−	0.00997777i	0.00283530	−	0.000563977i	0.196508	+	0.980502i	$0.437040\pi$
$314$	−6.34669	−	27.5569i	−0.358165	−	1.55513i
$315$	−5.44292	−	10.1830i	−0.306674	−	0.573746i
$316$	−2.73893	−	1.60118i	−0.154077	−	0.0900733i
$317$	11.3019	+	1.11314i	0.634776	+	0.0625199i	0.410287	−	0.911957i	$-0.365429\pi$
$317$	11.3019	+	1.11314i	0.634776	+	0.0625199i	0.224489	+	0.974477i	$0.427929\pi$
$318$	−8.87917	−	26.3919i	−0.497919	−	1.47999i
$319$		−	3.28888i		−	0.184142i
$320$	12.2934	−	14.4925i	0.687222	−	0.810156i
$321$			21.5037i			1.20022i
$322$	12.2506	−	4.12154i	0.682700	−	0.229684i
$323$	0.163331	+	0.0160867i	0.00908798	+	0.000895088i
$324$	−0.0219373	−	0.0836826i	−0.00121874	−	0.00464903i
$325$	0.207426	+	0.388066i	0.0115059	+	0.0215260i
$326$	29.8236	−	6.86874i	1.65178	−	0.380424i
$327$	12.7293	−	2.53201i	0.703930	−	0.140020i
$328$	18.7878	+	19.0958i	1.03738	+	1.05439i
$329$	1.65391	−	8.31478i	0.0911831	−	0.458408i
$330$	24.4147	−	25.9261i	1.34398	−	1.42718i
$331$	6.48120	+	5.31898i	0.356239	+	0.292358i	0.795441	−	0.606030i	$-0.207239\pi$
$331$	6.48120	+	5.31898i	0.356239	+	0.292358i	−0.439203	+	0.898388i	$0.644739\pi$
$332$	−24.3983	−	17.6845i	−1.33903	−	0.970560i
$333$	49.7357	+	26.5843i	2.72550	+	1.45681i
$334$	8.51836	−	4.88735i	0.466104	−	0.267424i
$335$	21.1708	−	8.76925i	1.15669	−	0.479115i
$336$	1.94664	−	11.0444i	0.106198	−	0.602523i
$337$	0.391629	+	0.162218i	0.0213334	+	0.00883657i	0.393325	−	0.919400i	$-0.371325\pi$
$337$	0.391629	+	0.162218i	0.0213334	+	0.00883657i	−0.371991	+	0.928236i	$0.621325\pi$
$338$	−17.5774	+	2.26566i	−0.956082	+	0.123236i
$339$	−14.1348	+	4.28775i	−0.767698	+	0.232879i
$340$	−11.6586	+	10.8014i	−0.632275	+	0.585790i
$341$	−1.37270	−	13.9372i	−0.0743356	−	0.754742i
$342$	0.315306	+	0.119649i	0.0170498	+	0.00646988i
$343$	−0.555570	−	0.831470i	−0.0299980	−	0.0448951i
$344$	1.43184	+	4.86207i	0.0771994	+	0.262145i
$345$	−50.6128	−	33.8184i	−2.72490	−	1.82072i
$346$	5.11520	−	30.4684i	0.274995	−	1.63799i
$347$	2.77457	+	0.841657i	0.148947	+	0.0451825i	0.363878	−	0.931447i	$-0.381453\pi$
$347$	2.77457	+	0.841657i	0.148947	+	0.0451825i	−0.214931	+	0.976629i	$0.568953\pi$
$348$	−1.59286	+	4.61018i	−0.0853863	+	0.247131i
$349$	2.73351	+	3.33079i	0.146321	+	0.178293i	0.841014	−	0.541014i	$-0.181959\pi$
$349$	2.73351	+	3.33079i	0.146321	+	0.178293i	−0.694692	+	0.719307i	$0.744459\pi$
$350$	−0.685445	+	0.597841i	−0.0366386	+	0.0319559i
$351$	2.52362	+	2.52362i	0.134701	+	0.134701i
$352$	21.1478	−	3.19781i	1.12718	−	0.170444i
$353$	17.0952	−	17.0952i	0.909885	−	0.909885i	−0.0863773	−	0.996262i	$-0.527529\pi$
$353$	17.0952	−	17.0952i	0.909885	−	0.909885i	0.996262	+	0.0863773i	$0.0275290\pi$
$354$	−0.883887	+	12.9478i	−0.0469781	+	0.688168i
$355$	6.54194	−	5.36883i	0.347210	−	0.284948i
$356$	−0.283416	−	4.71556i	−0.0150210	−	0.249924i
$357$	−2.72252	+	8.97494i	−0.144091	+	0.475004i
$358$	16.3093	−	11.6204i	0.861976	−	0.614155i
$359$	−4.81444	+	7.20531i	−0.254096	+	0.380282i	−0.936485	−	0.350708i	$-0.885941\pi$
$359$	−4.81444	+	7.20531i	−0.254096	+	0.380282i	0.682389	+	0.730989i	$0.260941\pi$
$360$	−28.9260	+	15.1602i	−1.52454	+	0.799015i
$361$	15.7959	−	10.5545i	0.831364	−	0.555500i
$362$	−13.5899	+	6.11317i	−0.714269	+	0.321301i
$363$	9.19481	−	0.905610i	0.482602	−	0.0475322i
$364$	0.475060	+	1.28326i	0.0248999	+	0.0672609i
$365$	−2.42153	−	7.98271i	−0.126749	−	0.417834i
$366$	−26.1293	−	20.1624i	−1.36580	−	1.05391i
$367$	10.8247	−	26.1333i	0.565047	−	1.36414i	−0.340638	−	0.940194i	$-0.610643\pi$
$367$	10.8247	−	26.1333i	0.565047	−	1.36414i	0.905686	−	0.423950i	$-0.139357\pi$
$368$	−11.3754	−	34.7436i	−0.592984	−	1.81114i
$369$	−17.6169	−	42.5310i	−0.917100	−	2.21407i
$370$	10.1904	−	37.6232i	0.529776	−	1.95593i
$371$	−3.31055	+	6.19361i	−0.171875	+	0.321556i
$372$	−4.82585	+	20.2013i	−0.250209	+	1.04739i
$373$	−8.42658	+	10.2678i	−0.436312	+	0.531648i	−0.944023	−	0.329880i	$-0.892992\pi$
$373$	−8.42658	+	10.2678i	−0.436312	+	0.531648i	0.507711	+	0.861527i	$0.330492\pi$
$374$	−17.8788	+	0.536796i	−0.924491	+	0.0277570i
$375$	−28.4600	−	5.66104i	−1.46967	−	0.292335i
$376$	−23.4789	−	4.86900i	−1.21083	−	0.251099i
$377$	−0.116107	−	0.583709i	−0.00597981	−	0.0300625i
$378$	−3.91253	+	6.25401i	−0.201239	+	0.321671i
$379$	9.15200	−	4.89185i	0.470107	−	0.251277i	−0.219292	−	0.975659i	$-0.570375\pi$
$379$	9.15200	−	4.89185i	0.470107	−	0.251277i	0.689399	+	0.724382i	$0.257875\pi$
$380$	0.0316772	−	0.230933i	0.00162500	−	0.0118466i
$381$	−4.91612	+	49.9142i	−0.251860	+	2.55718i
$382$	12.0155	+	5.96590i	0.614765	+	0.305242i
$383$	−28.5001			−1.45629			−0.728143	−	0.685426i	$-0.759616\pi$
$383$	−28.5001			−1.45629			−0.728143	+	0.685426i	$0.759616\pi$
$384$	−31.1926	−	5.75971i	−1.59179	−	0.293924i
$385$	−8.98171			−0.457750
$386$	−27.9165	−	13.8610i	−1.42091	−	0.705508i
$387$	0.853735	−	8.66812i	0.0433978	−	0.440625i
$388$	15.4164	+	2.11467i	0.782649	+	0.107356i
$389$	29.0423	−	15.5234i	1.47250	−	0.787069i	0.476740	−	0.879044i	$-0.341818\pi$
$389$	29.0423	−	15.5234i	1.47250	−	0.787069i	0.995761	+	0.0919756i	$0.0293182\pi$
$390$	3.41783	−	5.46326i	0.173069	−	0.276643i
$391$	5.96463	+	29.9862i	0.301644	+	1.51647i
$392$	−2.36445	+	1.55222i	−0.119423	+	0.0783989i
$393$	21.1705	+	4.21107i	1.06791	+	0.212420i
$394$	27.7070	−	0.831877i	1.39586	−	0.0419094i
$395$	2.39060	−	2.91295i	0.120284	−	0.146567i
$396$	−35.7489	−	8.54000i	−1.79645	−	0.429151i
$397$	−12.0392	+	22.5237i	−0.604228	+	1.13043i	0.374877	+	0.927075i	$0.377685\pi$
$397$	−12.0392	+	22.5237i	−0.604228	+	1.13043i	−0.979105	+	0.203356i	$0.934815\pi$
$398$	−5.44110	+	20.0886i	−0.272738	+	1.00695i
$399$	−0.0526393	−	0.127083i	−0.00263526	−	0.00636209i
$400$	1.67513	+	1.95241i	0.0837566	+	0.0976206i
$401$	−5.65655	+	13.6561i	−0.282475	+	0.681954i	−0.999892	−	0.0146894i	$-0.995324\pi$
$401$	−5.65655	+	13.6561i	−0.282475	+	0.681954i	0.717417	+	0.696643i	$0.245324\pi$
$402$	−30.2806	−	23.3658i	−1.51026	−	1.16538i
$403$	−0.735649	−	2.42511i	−0.0366453	−	0.120803i
$404$	−11.0690	+	4.09773i	−0.550703	+	0.203869i
$405$	0.102259	−	0.0100716i	0.00508129	−	0.000500463i
$406$	1.12189	−	0.504661i	0.0556783	−	0.0250459i
$407$	36.4752	−	24.3720i	1.80801	−	1.20807i
$408$	25.3215	+	7.90656i	1.25360	+	0.391433i
$409$	−16.2846	+	24.3717i	−0.805223	+	1.20510i	0.170341	+	0.985385i	$0.445513\pi$
$409$	−16.2846	+	24.3717i	−0.805223	+	1.20510i	−0.975564	+	0.219716i	$0.929487\pi$
$410$	−25.9137	+	18.4634i	−1.27979	+	0.911845i
$411$	−5.61616	+	18.5140i	−0.277025	+	0.913227i
$412$	32.1485	−	1.93220i	1.58384	−	0.0951926i
$413$	2.53017	−	2.07646i	0.124502	−	0.102176i
$414$	−4.27877	+	62.6784i	−0.210290	+	3.08047i
$415$	25.3082	−	25.3082i	1.24233	−	1.24233i
$416$	3.64040	−	1.31412i	0.178485	−	0.0644301i
$417$	−17.3576	−	17.3576i	−0.850005	−	0.850005i
$418$	0.197703	−	0.172435i	0.00966996	−	0.00843408i
$419$	19.2396	+	23.4436i	0.939918	+	1.14529i	0.989209	+	0.146509i	$0.0468036\pi$
$419$	19.2396	+	23.4436i	0.939918	+	1.14529i	−0.0492917	+	0.998784i	$0.515696\pi$
$420$	12.5901	+	4.34999i	0.614333	+	0.212258i
$421$	12.2261	+	3.70875i	0.595863	+	0.180753i	0.573789	−	0.819003i	$-0.305473\pi$
$421$	12.2261	+	3.70875i	0.595863	+	0.180753i	0.0220744	+	0.999756i	$0.492973\pi$
$422$	1.80819	−	10.7704i	0.0880215	−	0.524294i
$423$	34.2616	+	22.8929i	1.66586	+	1.11309i
$424$	17.4415	+	9.50576i	0.847033	+	0.461641i
$425$	−1.19526	−	1.78883i	−0.0579786	−	0.0867712i
$426$	−13.2066	−	5.01150i	−0.639860	−	0.242808i
$427$	0.815881	+	8.28378i	0.0394833	+	0.400880i
$428$	−10.4253	−	11.2526i	−0.503925	−	0.543914i
$429$	6.94037	−	2.10534i	0.335084	−	0.101647i
$430$	−5.97081	+	0.769618i	−0.287938	+	0.0371143i
$431$	13.8277	+	5.72761i	0.666056	+	0.275889i	0.689984	−	0.723824i	$-0.257617\pi$
$431$	13.8277	+	5.72761i	0.666056	+	0.275889i	−0.0239284	+	0.999714i	$0.507617\pi$
$432$	17.5985	+	11.2097i	0.846706	+	0.539329i
$433$	−35.8782	+	14.8612i	−1.72420	+	0.714185i	−0.724506	+	0.689269i	$0.757932\pi$
$433$	−35.8782	+	14.8612i	−1.72420	+	0.714185i	−0.999690	+	0.0249164i	$0.992068\pi$
$434$	4.54356	−	2.60684i	0.218098	−	0.125132i
$435$	−5.10935	−	2.73101i	−0.244975	−	0.130942i
$436$	−5.43348	+	7.49628i	−0.260217	+	0.359006i
$437$	−0.346623	−	0.284466i	−0.0165812	−	0.0136079i
$438$	−9.54546	+	10.1364i	−0.456100	+	0.484336i
$439$	−0.492592	+	2.47643i	−0.0235102	+	0.118194i	−0.990758	−	0.135639i	$-0.956691\pi$
$439$	−0.492592	+	2.47643i	−0.0235102	+	0.118194i	0.967248	+	0.253833i	$0.0816912\pi$
$440$	−0.206519	+	25.4033i	−0.00984543	+	1.21105i
$441$	4.76715	−	0.948245i	0.227007	−	0.0451545i
$442$	−3.15417	+	0.726443i	−0.150029	+	0.0345534i
$443$	−7.52372	−	14.0759i	−0.357463	−	0.668766i	0.637340	−	0.770582i	$-0.280035\pi$
$443$	−7.52372	−	14.0759i	−0.357463	−	0.668766i	−0.994803	+	0.101817i	$0.967535\pi$
$444$	−62.9328	+	16.4978i	−2.98666	+	0.782949i
$445$	5.58406	+	0.549982i	0.264710	+	0.0260716i
$446$	−7.35841	+	2.47563i	−0.348431	+	0.117224i
$447$			54.1232i			2.55994i
$448$	4.33583	+	6.72314i	0.204849	+	0.317638i
$449$			5.60449i			0.264492i	0.991217	+	0.132246i	$0.0422189\pi$
$449$			5.60449i			0.264492i	−0.991217	+	0.132246i	$0.957781\pi$
$450$	−1.40968	−	4.19004i	−0.0664528	−	0.197520i
$451$	−35.6375	−	3.50999i	−1.67811	−	0.165279i
$452$	5.31778	−	9.09645i	0.250127	−	0.427861i
$453$	−15.9860	−	29.9078i	−0.751089	−	1.40519i
$454$	−3.28070	−	14.2446i	−0.153971	−	0.668531i
$455$	−1.59407	+	0.317080i	−0.0747311	+	0.0148649i
$456$	−0.360642	+	0.145960i	−0.0168886	+	0.00683518i
$457$	−7.11257	+	35.7573i	−0.332712	+	1.67266i	0.345986	+	0.938240i	$0.387544\pi$
$457$	−7.11257	+	35.7573i	−0.332712	+	1.67266i	−0.678698	+	0.734417i	$0.737456\pi$
$458$	6.19934	+	5.83793i	0.289676	+	0.272789i
$459$	−13.4888	−	11.0699i	−0.629602	−	0.516701i
$460$	42.8805	−	6.84108i	1.99931	−	0.318967i
$461$	−21.9820	−	11.7496i	−1.02381	−	0.547235i	−0.128043	−	0.991769i	$-0.540870\pi$
$461$	−21.9820	−	11.7496i	−1.02381	−	0.547235i	−0.895762	+	0.444533i	$0.853370\pi$
$462$	7.46045	+	13.0031i	0.347092	+	0.604960i
$463$	−21.8816	+	9.06366i	−1.01692	+	0.421224i	−0.827976	−	0.560763i	$-0.810508\pi$
$463$	−21.8816	+	9.06366i	−1.01692	+	0.421224i	−0.188949	+	0.981987i	$0.560508\pi$
$464$	−1.40155	−	3.18467i	−0.0650655	−	0.147845i
$465$	−22.7916	−	9.44060i	−1.05694	−	0.437797i
$466$	0.932732	+	7.23627i	0.0432080	+	0.335214i
$467$	24.4232	−	7.40870i	1.13017	−	0.342834i	0.330817	−	0.943695i	$-0.392676\pi$
$467$	24.4232	−	7.40870i	1.13017	−	0.342834i	0.799353	+	0.600861i	$0.205176\pi$
$468$	−6.64617	−	0.253638i	−0.307219	−	0.0117244i
$469$	0.945507	+	9.59989i	0.0436594	+	0.443282i
$470$	10.1046	−	26.6280i	0.466088	−	1.22826i
$471$	−31.1462	−	46.6135i	−1.43514	−	2.14784i
$472$	−5.81473	−	7.20391i	−0.267645	−	0.331587i
$473$	−5.63354	−	3.76421i	−0.259030	−	0.173079i
$474$	−6.20288	−	1.04137i	−0.284908	−	0.0478319i
$475$	0.0301948	+	0.00915949i	0.00138543	+	0.000420266i
$476$	−2.92651	−	6.01637i	−0.134137	−	0.275760i
$477$	−21.6550	−	26.3867i	−0.991513	−	1.20816i
$478$	14.0123	+	16.0656i	0.640910	+	0.734825i
$479$	−8.88788	−	8.88788i	−0.406098	−	0.406098i	0.474278	−	0.880375i	$-0.342709\pi$
$479$	−8.88788	−	8.88788i	−0.406098	−	0.406098i	−0.880375	+	0.474278i	$0.842709\pi$
$480$	12.5927	−	35.5089i	0.574776	−	1.62075i
$481$	5.61321	−	5.61321i	0.255940	−	0.255940i
$482$	−9.71266	−	0.663039i	−0.442400	−	0.0302006i
$483$	19.8079	−	16.2559i	0.901292	−	0.739671i
$484$	−4.37245	+	4.93165i	−0.198748	+	0.224166i
$485$	−5.36519	+	17.6867i	−0.243621	+	0.803110i
$486$	12.7425	+	17.8844i	0.578013	+	0.811251i
$487$	12.4028	−	18.5622i	0.562026	−	0.841132i	−0.436250	−	0.899826i	$-0.643694\pi$
$487$	12.4028	−	18.5622i	0.562026	−	0.841132i	0.998276	+	0.0586939i	$0.0186936\pi$
$488$	23.4481	−	2.11711i	1.06144	−	0.0958372i
$489$	50.4477	−	33.7081i	2.28132	−	1.52433i
$490$	−1.37819	−	3.06380i	−0.0622605	−	0.138408i
$491$	−29.1887	+	2.87484i	−1.31727	+	0.129740i	−0.732114	−	0.681182i	$-0.761466\pi$
$491$	−29.1887	+	2.87484i	−1.31727	+	0.129740i	−0.585155	+	0.810921i	$0.698966\pi$
$492$	48.2548	+	22.1800i	2.17550	+	0.999950i
$493$	0.844684	+	2.78455i	0.0380426	+	0.125410i
$494$	0.0290007	−	0.0375832i	0.00130480	−	0.00169095i
$495$	16.7064	−	40.3329i	0.750898	−	1.81283i
$496$	−7.26853	−	12.9106i	−0.326367	−	0.579705i
$497$	1.36333	+	3.29137i	0.0611537	+	0.147638i
$498$	−57.6613	−	15.6179i	−2.58386	−	0.699854i
$499$	−19.8336	+	37.1060i	−0.887873	+	1.66109i	−0.147327	+	0.989088i	$0.547067\pi$
$499$	−19.8336	+	37.1060i	−0.887873	+	1.66109i	−0.740546	+	0.672006i	$0.765433\pi$
$500$	17.6372	−	10.8354i	0.788761	−	0.484575i
$501$	12.3514	−	15.0503i	0.551822	−	0.672397i
$502$	1.23086	+	40.9957i	0.0549359	+	1.82973i
$503$	−3.38146	−	0.672613i	−0.150772	−	0.0299903i	0.119127	−	0.992879i	$-0.461990\pi$
$503$	−3.38146	−	0.672613i	−0.150772	−	0.0299903i	−0.269899	+	0.962889i	$0.586990\pi$
$504$	−2.57234	−	13.5049i	−0.114581	−	0.601556i
$505$	−2.73504	−	13.7500i	−0.121708	−	0.611865i
$506$	41.4303	+	25.9190i	1.84180	+	1.15224i
$507$	−30.9865	+	16.5626i	−1.37616	+	0.735573i
$508$	−21.6265	−	28.5027i	−0.959521	−	1.26460i
$509$	3.86210	−	39.2125i	0.171185	−	1.73807i	−0.399356	−	0.916796i	$-0.630766\pi$
$509$	3.86210	−	39.2125i	0.171185	−	1.73807i	0.570540	−	0.821270i	$-0.306734\pi$
$510$	−14.0122	+	28.2209i	−0.620471	+	1.24964i
$511$	3.51160			0.155344
$512$	19.1150	−	12.1086i	0.844770	−	0.535129i
$513$	0.255924			0.0112993
$514$	−12.6753	+	25.5284i	−0.559084	+	1.12601i
$515$	−3.74952	+	38.0695i	−0.165223	+	1.67754i
$516$	6.07372	+	8.00489i	0.267381	+	0.352396i
$517$	28.2687	−	15.1099i	1.24325	−	0.664533i
$518$	13.9106	+	8.70251i	0.611196	+	0.382367i
$519$	−11.9490	−	60.0718i	−0.524504	−	2.63686i
$520$	0.860155	+	4.51585i	0.0377203	+	0.198033i
$521$	−1.03864	−	0.206597i	−0.0455034	−	0.00905119i	0.172286	−	0.985047i	$-0.444885\pi$
$521$	−1.03864	−	0.206597i	−0.0455034	−	0.00905119i	−0.217790	+	0.975996i	$0.569885\pi$
$522$	0.179442	+	5.97659i	0.00785396	+	0.261588i
$523$	−27.8142	+	33.8917i	−1.21623	+	1.48198i	−0.387933	+	0.921687i	$0.626811\pi$
$523$	−27.8142	+	33.8917i	−1.21623	+	1.48198i	−0.828295	+	0.560292i	$0.810689\pi$
$524$	−13.1198	+	8.06013i	−0.573140	+	0.352109i
$525$	−0.849994	+	1.59023i	−0.0370968	+	0.0694032i
$526$	−6.39338	−	1.73168i	−0.278765	−	0.0755050i
$527$	4.74170	+	11.4475i	0.206552	+	0.498659i
$528$	36.9487	−	20.8017i	1.60799	−	0.905276i
$529$	23.1647	−	55.9246i	1.00716	−	2.43151i
$530$	−14.4134	+	18.6789i	−0.626077	+	0.811358i
$531$	4.61821	+	15.2242i	0.200413	+	0.660673i
$532$	0.0891567	+	0.0409802i	0.00386543	+	0.00177672i
$533$	−6.44884	+	0.635156i	−0.279330	+	0.0275116i
$534$	−3.84204	−	8.54107i	−0.166262	−	0.369608i
$535$	15.1493	−	10.1225i	0.654963	−	0.437633i
$536$	27.1734	−	2.45348i	1.17371	−	0.105974i
$537$	22.0565	−	33.0099i	0.951810	−	1.42448i
$538$	2.73623	+	3.84034i	0.117967	+	0.165569i
$539$	1.09755	−	3.61812i	0.0472747	−	0.155844i
$540$	−16.4414	+	18.5441i	−0.707526	+	0.798012i
$541$	28.8369	−	23.6658i	1.23979	−	1.01747i	0.240895	−	0.970551i	$-0.422559\pi$
$541$	28.8369	−	23.6658i	1.23979	−	1.01747i	0.998899	−	0.0469209i	$-0.0149409\pi$
$542$	−39.5594	−	2.70054i	−1.69922	−	0.115998i
$543$	−20.8895	+	20.8895i	−0.896453	+	0.896453i
$544$	−17.0836	+	8.13882i	−0.732452	+	0.348949i
$545$	−7.77586	−	7.77586i	−0.333081	−	0.333081i
$546$	1.78312	+	2.04441i	0.0763107	+	0.0874928i
$547$	−10.2848	−	12.5321i	−0.439746	−	0.535832i	0.505225	−	0.862988i	$-0.331410\pi$
$547$	−10.2848	−	12.5321i	−0.439746	−	0.535832i	−0.944970	+	0.327156i	$0.893910\pi$
$548$	−6.03697	−	12.4109i	−0.257886	−	0.530166i
$549$	−38.7164	−	11.7445i	−1.65237	−	0.501242i
$550$	−3.39141	−	0.569370i	−0.144610	−	0.0242780i
$551$	−0.0354846	−	0.0237101i	−0.00151170	−	0.00101008i
$552$	−45.5218	−	56.3972i	−1.93754	−	2.40043i
$553$	0.881307	+	1.31897i	0.0374770	+	0.0560883i
$554$	4.92919	−	12.9897i	0.209421	−	0.551878i
$555$	−7.57429	−	76.9030i	−0.321511	−	3.26435i
$556$	17.4981	+	0.667783i	0.742087	+	0.0283203i
$557$	−9.81923	+	2.97863i	−0.416054	+	0.126209i	−0.491370	−	0.870951i	$-0.663504\pi$
$557$	−9.81923	+	2.97863i	−0.416054	+	0.126209i	0.0753155	+	0.997160i	$0.476004\pi$
$558$	3.25489	+	25.2520i	0.137791	+	1.06900i
$559$	−1.13273	−	0.469190i	−0.0479092	−	0.0198446i
$560$	−8.69713	+	3.82755i	−0.367521	+	0.161743i
$561$	−32.7613	+	13.5702i	−1.38318	+	0.572933i
$562$	−0.428815	−	0.747399i	−0.0180885	−	0.0315271i
$563$	16.9490	+	9.05944i	0.714316	+	0.381810i	0.788169	−	0.615459i	$-0.211029\pi$
$563$	16.9490	+	9.05944i	0.714316	+	0.381810i	−0.0738525	+	0.997269i	$0.523529\pi$
$564$	−46.9435	+	7.48928i	−1.97668	+	0.315355i
$565$	9.67441	+	7.93958i	0.407006	+	0.334021i
$566$	3.33319	+	3.13887i	0.140104	+	0.131937i
$567$	−0.00843865	+	0.0424240i	−0.000354390	+	0.00178164i
$568$	9.34043	−	3.78027i	0.391916	−	0.158617i
$569$	42.8264	−	8.51869i	1.79537	−	0.357122i	0.819099	−	0.573653i	$-0.194474\pi$
$569$	42.8264	−	8.51869i	1.79537	−	0.357122i	0.976276	+	0.216530i	$0.0694740\pi$
$570$	−0.103714	−	0.450322i	−0.00434412	−	0.0188619i
$571$	−13.4350	−	25.1351i	−0.562237	−	1.05187i	−0.989057	−	0.147534i	$-0.952866\pi$
$571$	−13.4350	−	25.1351i	−0.562237	−	1.05187i	0.426820	−	0.904336i	$-0.359634\pi$
$572$	−2.61110	+	4.46647i	−0.109175	+	0.186753i
$573$	26.4671	+	2.60679i	1.10568	+	0.108900i
$574$	−4.27107	−	12.6951i	−0.178271	−	0.529883i
$575$			5.87801i			0.245130i
$576$	−38.2555	+	6.96492i	−1.59398	+	0.290205i
$577$			18.8162i			0.783331i	0.920108	+	0.391665i	$0.128101\pi$
$577$			18.8162i			0.783331i	−0.920108	+	0.391665i	$0.871899\pi$
$578$	−7.78727	+	2.61991i	−0.323908	+	0.108974i
$579$	−61.4932	−	6.05655i	−2.55557	−	0.251701i
$580$	3.99767	−	1.04799i	0.165994	−	0.0435152i
$581$	7.10236	+	13.2876i	0.294656	+	0.551262i
$582$	30.0621	−	6.92366i	1.24611	−	0.286995i
$583$	−26.0427	+	5.18022i	−1.07858	+	0.214543i
$584$	0.0807434	−	9.93198i	0.00334119	−	0.410988i
$585$	1.54118	−	7.74804i	0.0637200	−	0.320342i
$586$	2.83343	−	3.00884i	0.117048	−	0.124294i
$587$	2.31621	+	1.90086i	0.0956001	+	0.0784569i	0.680979	−	0.732303i	$-0.261554\pi$
$587$	2.31621	+	1.90086i	0.0956001	+	0.0784569i	−0.585379	+	0.810760i	$0.699054\pi$
$588$	−3.29080	+	4.54013i	−0.135710	+	0.187232i
$589$	−0.160268	−	0.0856652i	−0.00660374	−	0.00352977i
$590$	9.53778	−	5.47224i	0.392664	−	0.225288i
$591$	50.7705	−	21.0298i	2.08842	−	0.865051i
$592$	24.9335	−	39.1437i	1.02476	−	1.60879i
$593$	−6.11726	−	2.53385i	−0.251206	−	0.104053i	0.253527	−	0.967328i	$-0.418409\pi$
$593$	−6.11726	−	2.53385i	−0.251206	−	0.104053i	−0.504733	+	0.863275i	$0.668409\pi$
$594$	−27.6632	+	3.56569i	−1.13503	+	0.146302i
$595$	7.60441	−	2.30677i	0.311751	−	0.0945685i
$596$	−26.2396	−	28.3219i	−1.07482	−	1.16011i
$597$	4.04423	+	41.0617i	0.165519	+	1.68054i
$598$	8.26804	+	3.13748i	0.338105	+	0.128301i
$599$	−9.29505	−	13.9110i	−0.379786	−	0.568389i	0.591500	−	0.806305i	$-0.298536\pi$
$599$	−9.29505	−	13.9110i	−0.379786	−	0.568389i	−0.971286	+	0.237915i	$0.923536\pi$
$600$	4.47815	+	2.44063i	0.182820	+	0.0996383i
$601$	−18.3454	−	12.2580i	−0.748325	−	0.500015i	0.121977	−	0.992533i	$-0.461077\pi$
$601$	−18.3454	−	12.2580i	−0.748325	−	0.500015i	−0.870302	+	0.492518i	$0.836077\pi$
$602$	0.419594	−	2.49928i	0.0171014	−	0.101863i
$603$	−44.8675	−	13.6104i	−1.82715	−	0.554259i
$604$	22.8649	+	7.90005i	0.930361	+	0.321448i
$605$	−4.96628	−	6.05144i	−0.201908	−	0.246026i
$606$	−17.6345	+	15.3807i	−0.716353	+	0.624799i
$607$	18.0289	+	18.0289i	0.731769	+	0.731769i	0.970970	−	0.239201i	$-0.0768854\pi$
$607$	18.0289	+	18.0289i	0.731769	+	0.731769i	−0.239201	+	0.970970i	$0.576885\pi$
$608$	0.117956	−	0.251223i	0.00478373	−	0.0101884i
$609$	1.72449	−	1.72449i	0.0698799	−	0.0698799i
$610$	−1.90455	+	27.8991i	−0.0771128	+	1.12960i
$611$	4.48368	−	3.67966i	0.181390	−	0.148863i
$612$	32.4603	−	1.95094i	1.31213	−	0.0788622i
$613$	10.4390	−	34.4127i	0.421626	−	1.38992i	−0.447039	−	0.894515i	$-0.647521\pi$
$613$	10.4390	−	34.4127i	0.421626	−	1.38992i	0.868665	−	0.495401i	$-0.164979\pi$
$614$	−31.3086	+	22.3073i	−1.26351	+	0.900249i
$615$	−35.0454	+	52.4491i	−1.41317	+	2.11495i
$616$	−10.2080	−	3.18742i	−0.411293	−	0.128425i
$617$	6.86479	−	4.58691i	0.276366	−	0.184662i	−0.409661	−	0.912238i	$-0.634353\pi$
$617$	6.86479	−	4.58691i	0.276366	−	0.184662i	0.686027	+	0.727576i	$0.259353\pi$
$618$	58.2290	−	26.1933i	2.34231	−	1.05365i
$619$	−30.8114	+	3.03465i	−1.23841	+	0.121973i	−0.695940	−	0.718100i	$-0.745012\pi$
$619$	−30.8114	+	3.03465i	−1.23841	+	0.121973i	−0.542473	+	0.840073i	$0.682512\pi$
$620$	16.5034	−	6.10955i	0.662794	−	0.245365i
$621$	13.8394	+	45.6224i	0.555357	+	1.83077i
$622$	−31.4111	−	24.2381i	−1.25947	−	0.971860i
$623$	−0.903911	+	2.18223i	−0.0362144	+	0.0874294i
$624$	5.82328	−	4.99626i	0.233118	−	0.200011i
$625$	10.6394	+	25.6858i	0.425575	+	1.02743i
$626$	−0.0189094	+	0.0698135i	−0.000755771	+	0.00279031i
$627$	0.245164	−	0.458669i	0.00979089	−	0.0183175i
$628$	38.8972	+	9.29210i	1.55217	+	0.370795i
$629$	−24.6225	+	30.0026i	−0.981764	+	1.19628i
$630$	16.3217	−	0.490044i	0.650271	−	0.0195238i
$631$	15.5410	+	3.09129i	0.618676	+	0.123062i	0.494471	−	0.869194i	$-0.335362\pi$
$631$	15.5410	+	3.09129i	0.618676	+	0.123062i	0.124205	+	0.992257i	$0.460362\pi$
$632$	3.75075	−	2.46230i	0.149197	−	0.0979451i
$633$	−4.22391	−	21.2350i	−0.167885	−	0.844016i
$634$	−8.51800	+	13.6156i	−0.338293	+	0.540746i
$635$	37.4787	−	20.0328i	1.48730	−	0.794976i
$636$	39.0142	+	5.35158i	1.54701	+	0.212204i
$637$	0.0670617	−	0.680889i	0.00265708	−	0.0269778i
$638$	4.16593	+	2.06846i	0.164931	+	0.0818911i
$639$	−17.3159			−0.685008
$640$	10.6256	+	24.6864i	0.420014	+	0.975815i
$641$	23.9244			0.944959			0.472479	−	0.881342i	$-0.343359\pi$
$641$	23.9244			0.944959			0.472479	+	0.881342i	$0.343359\pi$
$642$	−27.2381	−	13.5242i	−1.07500	−	0.533759i
$643$	−1.50726	+	15.3034i	−0.0594404	+	0.603508i	0.918614	+	0.395157i	$0.129310\pi$
$643$	−1.50726	+	15.3034i	−0.0594404	+	0.603508i	−0.978054	+	0.208351i	$0.933190\pi$
$644$	−2.48410	+	18.1096i	−0.0978872	+	0.713620i
$645$	−10.5257	+	5.62613i	−0.414451	+	0.221529i
$646$	−0.123100	+	0.196769i	−0.00484329	+	0.00774178i
$647$	−0.427765	−	2.15052i	−0.0168172	−	0.0845457i	0.971465	−	0.237182i	$-0.0762237\pi$
$647$	−0.427765	−	2.15052i	−0.0168172	−	0.0845457i	−0.988282	+	0.152636i	$0.951224\pi$
$648$	0.119795	+	0.0248428i	0.00470600	+	0.000975917i
$649$	12.1377	+	2.41434i	0.476447	+	0.0947712i
$650$	−0.622007	+	0.0186752i	−0.0243971	+	0.000732502i
$651$	6.58807	−	8.02759i	0.258207	−	0.314626i
$652$	−10.0564	+	42.0966i	−0.393840	+	1.64863i
$653$	−0.817203	+	1.52888i	−0.0319796	+	0.0598297i	−0.897404	−	0.441211i	$-0.854549\pi$
$653$	−0.817203	+	1.52888i	−0.0319796	+	0.0598297i	0.865424	+	0.501040i	$0.167049\pi$
$654$	−4.79854	+	17.7162i	−0.187638	+	0.692759i
$655$	−6.99891	−	16.8969i	−0.273470	−	0.660215i
$656$	−36.0042	+	11.7881i	−1.40573	+	0.460249i
$657$	−6.53176	+	15.7691i	−0.254828	+	0.615209i
$658$	9.49189	+	7.32433i	0.370032	+	0.285532i
$659$	11.1417	+	36.7294i	0.434021	+	1.43077i	0.852586	+	0.522587i	$0.175033\pi$
$659$	11.1417	+	36.7294i	0.434021	+	1.43077i	−0.418565	+	0.908187i	$0.637467\pi$
$660$	17.4848	+	47.2309i	0.680595	+	1.83846i
$661$	28.3213	−	2.78941i	1.10157	−	0.108495i	0.469149	−	0.883119i	$-0.344561\pi$
$661$	28.3213	−	2.78941i	1.10157	−	0.108495i	0.632422	+	0.774624i	$0.282061\pi$
$662$	−10.8136	+	4.86429i	−0.420282	+	0.189056i
$663$	−5.33539	+	3.56499i	−0.207209	+	0.138453i
$664$	37.7450	−	19.7823i	1.46479	−	0.767703i
$665$	−0.0647506	+	0.0969061i	−0.00251092	+	0.00375786i
$666$	−64.9535	+	46.2791i	−2.51690	+	1.79328i
$667$	2.30781	−	7.60785i	0.0893589	−	0.294577i
$668$	0.833243	+	13.8637i	0.0322391	+	0.536403i
$669$	−11.8978	+	9.76424i	−0.459994	+	0.377507i
$670$	−2.20714	+	32.3317i	−0.0852691	+	1.24908i
$671$	−22.2540	+	22.2540i	−0.859107	+	0.859107i
$672$	12.7653	+	9.41187i	0.492434	+	0.363071i
$673$	−12.7924	−	12.7924i	−0.493112	−	0.493112i	0.416173	−	0.909285i	$-0.363371\pi$
$673$	−12.7924	−	12.7924i	−0.493112	−	0.493112i	−0.909285	+	0.416173i	$0.863371\pi$
$674$	−0.451782	+	0.394041i	−0.0174020	+	0.0151779i
$675$	−2.12827	−	2.59331i	−0.0819173	−	0.0998166i
$676$	8.18500	−	23.6896i	0.314808	−	0.911140i
$677$	34.5259	+	10.4733i	1.32694	+	0.402522i	0.872655	−	0.488336i	$-0.162396\pi$
$677$	34.5259	+	10.4733i	1.32694	+	0.402522i	0.454281	+	0.890858i	$0.349896\pi$
$678$	3.45858	−	20.6008i	0.132826	−	0.791170i
$679$	−6.46915	−	4.32255i	−0.248263	−	0.165884i
$680$	−6.34947	−	21.5609i	−0.243491	−	0.826821i
$681$	−16.0999	−	24.0952i	−0.616950	−	0.923330i
$682$	18.5172	+	7.02671i	0.709059	+	0.269067i
$683$	1.08550	+	11.0212i	0.0415354	+	0.421716i	0.993358	+	0.115066i	$0.0367081\pi$
$683$	1.08550	+	11.0212i	0.0415354	+	0.421716i	−0.951822	+	0.306650i	$0.900792\pi$
$684$	−0.349860	+	0.324138i	−0.0133772	+	0.0123937i
$685$	15.6868	−	4.75853i	0.599361	−	0.181814i
$686$	1.40261	−	0.180792i	0.0535519	−	0.00690266i
$687$	15.5968	+	6.46040i	0.595055	+	0.246480i
$688$	−7.05916	−	1.24422i	−0.269128	−	0.0474354i
$689$	−4.43918	+	1.83877i	−0.169119	+	0.0700514i
$690$	74.6684	−	42.8405i	2.84258	−	1.63091i
$691$	−12.1803	−	6.51052i	−0.463362	−	0.247672i	0.223159	−	0.974782i	$-0.428363\pi$
$691$	−12.1803	−	6.51052i	−0.463362	−	0.247672i	−0.686521	+	0.727110i	$0.740863\pi$
$692$	35.3763	+	25.6416i	1.34481	+	0.974748i
$693$	14.2059	+	11.6585i	0.539638	+	0.442869i
$694$	−2.81110	+	2.98513i	−0.106708	+	0.113314i
$695$	−4.05764	+	20.3992i	−0.153915	+	0.773784i
$696$	−4.83778	−	4.91709i	−0.183376	−	0.186382i
$697$	31.0742	−	6.18104i	1.17702	−	0.234124i
$698$	−5.93818	+	1.36763i	−0.224764	+	0.0517657i
$699$	6.81853	+	12.7566i	0.257901	+	0.482498i
$700$	−0.326173	−	1.24423i	−0.0123282	−	0.0470275i
$701$	21.6423	+	2.13158i	0.817419	+	0.0805087i	0.498079	−	0.867132i	$-0.334039\pi$
$701$	21.6423	+	2.13158i	0.817419	+	0.0805087i	0.319340	+	0.947640i	$0.396539\pi$
$702$	−4.78376	+	1.60943i	−0.180552	+	0.0607438i
$703$		−	0.569243i		−	0.0214694i
$704$	−9.24980	+	28.7984i	−0.348615	+	1.08538i
$705$		−	56.4629i		−	2.12652i
$706$	10.9024	+	32.4056i	0.410316	+	1.21960i
$707$	5.87315	+	0.578455i	0.220883	+	0.0217550i
$708$	−15.8447	−	9.26279i	−0.595480	−	0.348117i
$709$	−13.5891	−	25.4233i	−0.510348	−	0.954793i	−0.996711	−	0.0810366i	$-0.974177\pi$
$709$	−13.5891	−	25.4233i	−0.510348	−	0.954793i	0.486364	−	0.873757i	$-0.338323\pi$
$710$	2.68615	+	11.6631i	0.100809	+	0.437707i
$711$	−7.56218	+	1.50421i	−0.283604	+	0.0564123i
$712$	6.15130	+	2.60674i	0.230530	+	0.0976917i
$713$	6.60445	−	33.2028i	0.247339	−	1.24346i
$714$	−9.65603	−	9.09310i	−0.361368	−	0.340301i
$715$	−4.75026	−	3.89844i	−0.177650	−	0.145793i
$716$	4.46179	+	27.9669i	0.166745	+	1.04517i
$717$	37.2721	+	19.9224i	1.39195	+	0.744015i
$718$	−6.09883	−	10.6299i	−0.227606	−	0.396705i
$719$	1.93152	−	0.800062i	0.0720336	−	0.0298373i	−0.346376	−	0.938096i	$-0.612588\pi$
$719$	1.93152	−	0.800062i	0.0720336	−	0.0298373i	0.418409	+	0.908259i	$0.362588\pi$
$720$	−1.01072	−	46.1744i	−0.0376672	−	1.72082i
$721$	−14.8774	−	6.16244i	−0.554065	−	0.229501i
$722$	3.43461	+	26.6462i	0.127823	+	0.991669i
$723$	−18.4690	+	5.60252i	−0.686871	+	0.208360i
$724$	0.803662	−	21.0586i	0.0298679	−	0.782638i
$725$	0.0548346	+	0.556745i	0.00203650	+	0.0206770i
$726$	−4.63574	+	12.2164i	−0.172048	+	0.453391i
$727$	−13.5484	−	20.2766i	−0.502483	−	0.752019i	0.490351	−	0.871525i	$-0.336869\pi$
$727$	−13.5484	−	20.2766i	−0.502483	−	0.752019i	−0.992833	+	0.119507i	$0.961869\pi$
$728$	−1.92424	−	0.205329i	−0.0713171	−	0.00761000i
$729$	36.3056	+	24.2587i	1.34465	+	0.898469i
$730$	11.6344	+	1.95325i	0.430609	+	0.0722931i
$731$	5.73643	+	1.74013i	0.212170	+	0.0643609i
$732$	41.9725	−	20.4165i	1.55135	−	0.754616i
$733$	8.53475	+	10.3996i	0.315238	+	0.384119i	0.906390	−	0.422441i	$-0.138827\pi$
$733$	8.53475	+	10.3996i	0.315238	+	0.384119i	−0.591152	+	0.806560i	$0.701327\pi$
$734$	26.2942	+	30.1472i	0.970538	+	1.11276i
$735$	−4.70946	−	4.70946i	−0.173711	−	0.173711i
$736$	51.1630	+	7.44226i	1.88589	+	0.274325i
$737$	−25.7897	+	25.7897i	−0.949976	+	0.949976i
$738$	64.9524	+	4.43401i	2.39093	+	0.163218i
$739$	5.40776	−	4.43803i	0.198928	−	0.163256i	−0.529656	−	0.848213i	$-0.677679\pi$
$739$	5.40776	−	4.43803i	0.198928	−	0.163256i	0.728584	+	0.684957i	$0.240179\pi$
$740$	41.2471	+	36.5701i	1.51627	+	1.34434i
$741$	0.0273192	−	0.0900593i	0.00100360	−	0.00330841i
$742$	−5.76317	−	8.08870i	−0.211573	−	0.296945i
$743$	−4.96200	+	7.42615i	−0.182038	+	0.272439i	−0.911254	−	0.411844i	$-0.864885\pi$
$743$	−4.96200	+	7.42615i	−0.182038	+	0.272439i	0.729216	+	0.684283i	$0.239885\pi$
$744$	−22.5532	−	18.8178i	−0.826841	−	0.689896i
$745$	38.1298	−	25.4775i	1.39697	−	0.933423i
$746$	−7.70625	−	17.1314i	−0.282146	−	0.627225i
$747$	−72.8794	+	7.17800i	−2.66652	+	0.262629i
$748$	10.5645	−	22.9842i	0.386276	−	0.840384i
$749$	2.22644	+	7.33960i	0.0813524	+	0.268183i
$750$	25.0699	−	32.4890i	0.915422	−	1.18633i
$751$	2.47190	−	5.96770i	0.0902010	−	0.217765i	−0.872341	−	0.488899i	$-0.837399\pi$
$751$	2.47190	−	5.96770i	0.0902010	−	0.217765i	0.962542	+	0.271134i	$0.0873987\pi$
$752$	20.9339	−	26.6778i	0.763381	−	0.972840i
$753$	31.1161	+	75.1208i	1.13393	+	2.73756i
$754$	0.812389	+	0.220040i	0.0295855	+	0.00801339i
$755$	−13.5449	+	25.3407i	−0.492948	+	0.922241i
$756$	−5.46107	−	8.88919i	−0.198617	−	0.323297i
$757$	28.6974	−	34.9678i	1.04302	−	1.27093i	0.0813632	−	0.996685i	$-0.474073\pi$
$757$	28.6974	−	34.9678i	1.04302	−	1.27093i	0.961660	−	0.274243i	$-0.0884274\pi$
$758$	0.440429	+	14.6692i	0.0159971	+	0.532808i
$759$	95.0225	+	18.9011i	3.44910	+	0.686068i
$760$	0.272594	+	0.185364i	0.00988802	+	0.00672388i
$761$	−4.52663	−	22.7569i	−0.164090	−	0.824938i	−0.971882	−	0.235469i	$-0.924337\pi$
$761$	−4.52663	−	22.7569i	−0.164090	−	0.824938i	0.807792	−	0.589468i	$-0.200663\pi$
$762$	−60.1329	−	37.6194i	−2.17839	−	1.36281i
$763$	4.08256	−	2.18218i	0.147799	−	0.0790001i
$764$	−15.1137	+	11.4675i	−0.546793	+	0.414880i
$765$	−3.78589	+	38.4388i	−0.136879	+	1.38976i
$766$	17.9244	−	36.1002i	0.647636	−	1.30435i
$767$	2.23943			0.0808611
$768$	26.9134	−	35.8882i	0.971155	−	1.29501i
$769$	18.0168			0.649702			0.324851	−	0.945765i	$-0.394686\pi$
$769$	18.0168			0.649702			0.324851	+	0.945765i	$0.394686\pi$
$770$	5.64882	−	11.3769i	0.203570	−	0.409994i
$771$	−5.53845	+	56.2328i	−0.199462	+	2.02518i
$772$	35.1147	−	26.6434i	1.26381	−	0.958916i
$773$	32.7258	−	17.4923i	1.17707	−	0.629155i	0.237454	−	0.971399i	$-0.423687\pi$
$773$	32.7258	−	17.4923i	1.17707	−	0.629155i	0.939611	+	0.342244i	$0.111187\pi$
$774$	10.4427	+	6.53300i	0.375356	+	0.234824i
$775$	0.464742	+	2.33642i	0.0166940	+	0.0839266i
$776$	−12.3744	+	18.1975i	−0.444214	+	0.653253i
$777$	31.9046	+	6.34622i	1.14457	+	0.227669i
$778$	1.39762	+	46.5500i	0.0501073	+	1.66890i
$779$	−0.294787	+	0.359199i	−0.0105618	+	0.0128696i
$780$	4.77058	+	7.76525i	0.170814	+	0.278040i
$781$	−6.34960	+	11.8793i	−0.227207	+	0.425074i
$782$	−41.7340	−	11.3039i	−1.49240	−	0.404226i
$783$	1.73642	+	4.19209i	0.0620547	+	0.149813i
$784$	−0.479089	−	3.97121i	−0.0171103	−	0.141829i
$785$	−18.1777	+	43.8849i	−0.648790	+	1.56632i
$786$	−18.6487	+	24.1676i	−0.665177	+	0.862029i
$787$	−6.84034	−	22.5496i	−0.243832	−	0.803805i	−0.990368	−	0.138461i	$-0.955785\pi$
$787$	−6.84034	−	22.5496i	−0.243832	−	0.803805i	0.746536	−	0.665345i	$-0.231715\pi$
$788$	−16.3719	+	35.6188i	−0.583225	+	1.26887i
$789$	−13.0683	+	1.28711i	−0.465244	+	0.0458225i
$790$	2.18624	+	4.86013i	0.0777830	+	0.172916i
$791$	−4.38052	+	2.92697i	−0.155753	+	0.104071i
$792$	33.3007	−	39.9110i	1.18329	−	1.41817i
$793$	−3.16400	+	4.73526i	−0.112357	+	0.168154i
$794$	−20.9583	−	29.4153i	−0.743783	−	1.04391i
$795$	−13.5777	+	44.7595i	−0.481550	+	1.58746i
$796$	−22.0235	−	19.5263i	−0.780603	−	0.692091i
$797$	−25.0793	+	20.5820i	−0.888353	+	0.729053i	−0.963383	−	0.268129i	$-0.913595\pi$
$797$	−25.0793	+	20.5820i	−0.888353	+	0.729053i	0.0750299	+	0.997181i	$0.476095\pi$
$798$	0.194078	+	0.0132488i	0.00687028	+	0.000469003i
$799$	−20.0531	+	20.0531i	−0.709429	+	0.709429i
$800$	−3.52660	+	0.893918i	−0.124684	+	0.0316048i
$801$	−8.11813	−	8.11813i	−0.286840	−	0.286840i
$802$	−13.7402	−	15.7537i	−0.485185	−	0.556281i
$803$	8.42292	+	10.2634i	0.297238	+	0.362186i
$804$	48.6410	−	23.6602i	1.71544	−	0.834432i
$805$	−20.7765	−	6.30249i	−0.732276	−	0.222133i
$806$	3.53448	+	0.593388i	0.124497	+	0.0209012i
$807$	7.77280	+	5.19362i	0.273615	+	0.182824i
$808$	1.77111	−	16.5979i	0.0623073	−	0.583913i
$809$	6.34166	+	9.49096i	0.222961	+	0.333684i	0.926039	−	0.377428i	$-0.123192\pi$
$809$	6.34166	+	9.49096i	0.222961	+	0.333684i	−0.703078	+	0.711113i	$0.748192\pi$
$810$	−0.0515558	+	0.135863i	−0.00181149	+	0.00477373i
$811$	−1.75087	−	17.7768i	−0.0614812	−	0.624229i	−0.975715	−	0.219043i	$-0.929707\pi$
$811$	−1.75087	−	17.7768i	−0.0614812	−	0.624229i	0.914234	−	0.405186i	$-0.132793\pi$
$812$	−0.0663448	+	1.73845i	−0.00232825	+	0.0610078i
$813$	−75.2239	+	22.8189i	−2.63822	+	0.800294i
$814$	7.93105	+	61.5303i	0.277983	+	2.15663i
$815$	−47.4946	−	19.6729i	−1.66366	−	0.689112i
$816$	−25.9404	+	27.1014i	−0.908094	+	0.948739i
$817$	−0.0812262	+	0.0336450i	−0.00284175	+	0.00117709i
$818$	−20.6290	−	35.9552i	−0.721278	−	1.25714i
$819$	2.93283	+	1.56763i	0.102482	+	0.0547775i
$820$	−7.08929	−	44.4363i	−0.247569	−	1.55178i
$821$	−30.9338	−	25.3867i	−1.07960	−	0.886002i	−0.0857008	−	0.996321i	$-0.527313\pi$
$821$	−30.9338	−	25.3867i	−1.07960	−	0.886002i	−0.993896	+	0.110318i	$0.964813\pi$
$822$	−19.9190	−	18.7577i	−0.694754	−	0.654251i
$823$	−7.74769	+	38.9503i	−0.270068	+	1.35772i	0.572842	+	0.819666i	$0.305841\pi$
$823$	−7.74769	+	38.9503i	−0.270068	+	1.35772i	−0.842909	+	0.538056i	$0.819159\pi$
$824$	−17.7715	+	41.9367i	−0.619100	+	1.46093i
$825$	−6.68655	+	1.33004i	−0.232796	+	0.0463059i
$826$	1.03890	+	4.51083i	0.0361479	+	0.156952i
$827$	16.3156	+	30.5243i	0.567349	+	1.06144i	0.988035	+	0.154229i	$0.0492894\pi$
$827$	16.3156	+	30.5243i	0.567349	+	1.06144i	−0.420686	+	0.907206i	$0.638211\pi$
$828$	−76.7018	−	44.8398i	−2.66557	−	1.55829i
$829$	−31.5639	−	3.10877i	−1.09626	−	0.107972i	−0.466320	−	0.884616i	$-0.654420\pi$
$829$	−31.5639	−	3.10877i	−1.09626	−	0.107972i	−0.629940	+	0.776644i	$0.716920\pi$
$830$	16.1402	+	47.9742i	0.560234	+	1.66521i
$831$		−	27.5437i		−	0.955480i
$832$	−0.624983	+	5.43767i	−0.0216674	+	0.188517i
$833$			3.34519i			0.115904i
$834$	32.9030	−	11.0697i	1.13934	−	0.383313i
$835$	−16.4171	−	1.61694i	−0.568138	−	0.0559567i
$836$	0.0940781	+	0.358873i	0.00325376	+	0.0124119i
$837$	9.10807	+	17.0400i	0.314821	+	0.588988i
$838$	−41.7956	+	9.62602i	−1.44380	+	0.332525i
$839$	−18.6394	+	3.70760i	−0.643502	+	0.128001i	−0.506045	−	0.862507i	$-0.668893\pi$
$839$	−18.6394	+	3.70760i	−0.643502	+	0.128001i	−0.137457	+	0.990508i	$0.543893\pi$
$840$	−13.4282	+	13.2117i	−0.463318	+	0.455845i
$841$	−5.51000	+	27.7007i	−0.190000	+	0.955195i
$842$	−12.3871	+	13.1539i	−0.426886	+	0.453313i
$843$	−1.32051	−	1.08371i	−0.0454807	−	0.0373251i
$844$	12.5053	+	9.06416i	0.430451	+	0.312001i
$845$	26.2547	+	14.0334i	0.903188	+	0.482764i
$846$	−50.5457	+	29.0002i	−1.73780	+	0.997049i
$847$	3.04458	−	1.26111i	0.104613	−	0.0433322i
$848$	−23.0101	+	16.1142i	−0.790168	+	0.553363i
$849$	8.38590	+	3.47356i	0.287803	+	0.119212i
$850$	3.01759	−	0.388957i	0.103503	−	0.0133411i
$851$	101.477	−	30.7826i	3.47857	−	1.05521i
$852$	14.6539	−	13.5765i	0.502033	−	0.465123i
$853$	1.84320	+	18.7143i	0.0631100	+	0.640767i	0.973758	+	0.227584i	$0.0730828\pi$
$853$	1.84320	+	18.7143i	0.0631100	+	0.640767i	−0.910648	+	0.413182i	$0.864417\pi$
$854$	−11.0059	−	4.17643i	−0.376616	−	0.142914i
$855$	−0.314723	−	0.471016i	−0.0107633	−	0.0161084i
$856$	20.8100	−	6.12836i	0.711272	−	0.209463i
$857$	−10.1661	−	6.79277i	−0.347268	−	0.232037i	0.369688	−	0.929156i	$-0.379465\pi$
$857$	−10.1661	−	6.79277i	−0.347268	−	0.232037i	−0.716955	+	0.697119i	$0.754465\pi$
$858$	−1.69821	+	10.1153i	−0.0579758	+	0.345329i
$859$	−4.99373	−	1.51483i	−0.170384	−	0.0516854i	0.203940	−	0.978983i	$-0.434625\pi$
$859$	−4.99373	−	1.51483i	−0.170384	−	0.0516854i	−0.374324	+	0.927298i	$0.622125\pi$
$860$	2.78034	−	8.04708i	0.0948089	−	0.274403i
$861$	−16.8457	−	20.5266i	−0.574101	−	0.699544i
$862$	−15.9516	+	13.9129i	−0.543313	+	0.473874i
$863$	−0.888681	−	0.888681i	−0.0302511	−	0.0302511i	0.691819	−	0.722071i	$-0.256809\pi$
$863$	−0.888681	−	0.888681i	−0.0302511	−	0.0302511i	−0.722071	+	0.691819i	$0.756809\pi$
$864$	−25.2672	+	15.2413i	−0.859606	+	0.518521i
$865$	−36.6957	+	36.6957i	−1.24769	+	1.24769i
$866$	3.74043	−	54.7924i	0.127105	−	1.86192i
$867$	−12.5912	+	10.3333i	−0.427619	+	0.350938i
$868$	0.444439	+	7.39470i	0.0150853	+	0.250992i
$869$	−1.74105	+	5.73947i	−0.0590610	+	0.194698i
$870$	6.67268	−	4.75426i	0.226225	−	0.161185i
$871$	−3.66669	+	5.48759i	−0.124241	+	0.185940i
$872$	−6.07805	−	11.5970i	−0.205829	−	0.392725i
$873$	31.4436	−	21.0099i	1.06420	−	0.711079i
$874$	0.578325	−	0.260149i	0.0195621	−	0.00879967i
$875$	−10.3000	+	1.01446i	−0.348204	+	0.0342951i
$876$	−6.83608	−	18.4660i	−0.230970	−	0.623908i
$877$	0.483363	+	1.59344i	0.0163220	+	0.0538065i	0.964723	−	0.263267i	$-0.0847999\pi$
$877$	0.483363	+	1.59344i	0.0163220	+	0.0538065i	−0.948401	+	0.317073i	$0.897300\pi$
$878$	−2.82702	−	2.18144i	−0.0954071	−	0.0736201i
$879$	3.13555	−	7.56989i	0.105759	−	0.255326i
$880$	−32.0477	−	16.2384i	−1.08033	−	0.547395i
$881$	−3.84314	−	9.27816i	−0.129479	−	0.312589i	0.845824	−	0.533462i	$-0.179109\pi$
$881$	−3.84314	−	9.27816i	−0.129479	−	0.312589i	−0.975303	+	0.220873i	$0.929109\pi$
$882$	−1.79707	+	6.63478i	−0.0605104	+	0.223405i
$883$	−3.20821	+	6.00213i	−0.107965	+	0.201988i	−0.930102	−	0.367302i	$-0.880282\pi$
$883$	−3.20821	+	6.00213i	−0.107965	+	0.201988i	0.822137	+	0.569289i	$0.192782\pi$
$884$	1.06357	−	4.45217i	0.0357719	−	0.149743i
$885$	13.8296	−	16.8514i	0.464877	−	0.566454i
$886$	22.5614	−	0.677385i	0.757964	−	0.0227572i
$887$	11.4837	+	2.28424i	0.385583	+	0.0766973i	0.384076	−	0.923302i	$-0.374520\pi$
$887$	11.4837	+	2.28424i	0.385583	+	0.0766973i	0.00150761	+	0.999999i	$0.499520\pi$
$888$	18.6828	−	90.0910i	0.626955	−	3.02325i
$889$	3.49003	+	17.5456i	0.117052	+	0.588460i
$890$	−4.20860	+	6.72726i	−0.141073	+	0.225498i
$891$	−0.144233	+	0.0770943i	−0.00483200	+	0.00258276i
$892$	1.49209	−	10.8777i	0.0499589	−	0.364211i
$893$	0.0407684	−	0.413928i	0.00136426	−	0.0138516i
$894$	−68.5563	−	34.0395i	−2.29286	−	1.13845i
$895$	−33.6382			−1.12440
$896$	−11.2429	+	1.26371i	−0.375599	+	0.0422176i
$897$	17.5318			0.585370
$898$	−7.09904	−	3.52481i	−0.236898	−	0.117624i
$899$	0.315809	−	3.20647i	0.0105328	−	0.106942i
$900$	6.19398	+	0.849629i	0.206466	+	0.0283210i
$901$	20.7188	−	11.0744i	0.690243	−	0.368943i
$902$	26.8593	−	42.9335i	0.894319	−	1.42953i
$903$	−0.980163	−	4.92761i	−0.0326178	−	0.163981i
$904$	8.17772	+	12.4569i	0.271987	+	0.414309i
$905$	24.5499	+	4.88329i	0.816068	+	0.162326i
$906$	47.9373	−	1.43928i	1.59261	−	0.0478167i
$907$	31.5249	−	38.4132i	1.04677	−	1.27549i	0.0865481	−	0.996248i	$-0.472416\pi$
$907$	31.5249	−	38.4132i	1.04677	−	1.27549i	0.960220	−	0.279243i	$-0.0900836\pi$
$908$	20.1065	+	4.80322i	0.667258	+	0.159400i
$909$	−13.5219	+	25.2978i	−0.448494	+	0.839074i
$910$	0.600915	−	2.21858i	0.0199201	−	0.0735452i
$911$	−9.53000	−	23.0075i	−0.315743	−	0.762271i	−0.999471	−	0.0325339i	$-0.989642\pi$
$911$	−9.53000	−	23.0075i	−0.315743	−	0.762271i	0.683728	−	0.729737i	$-0.260358\pi$
$912$	0.0419346	−	0.548613i	0.00138859	−	0.0181664i
$913$	−21.7999	+	52.6296i	−0.721472	+	1.74179i
$914$	−40.8194	−	31.4980i	−1.35019	−	1.04186i
$915$	16.0930	+	53.0513i	0.532017	+	1.75382i
$916$	−11.2937	+	4.18089i	−0.373153	+	0.138141i
$917$	7.66186	−	0.754628i	0.253017	−	0.0249200i
$918$	22.5054	−	10.1236i	0.742789	−	0.334130i
$919$	−32.2074	+	21.5203i	−1.06243	+	0.709890i	−0.958615	−	0.284707i	$-0.908104\pi$
$919$	−32.2074	+	21.5203i	−1.06243	+	0.709890i	−0.103811	+	0.994597i	$0.533104\pi$
$920$	−18.3033	+	58.6180i	−0.603440	+	1.93258i
$921$	−42.3414	+	63.3684i	−1.39520	+	2.08806i
$922$	28.7080	−	20.4543i	0.945447	−	0.673628i
$923$	−0.707551	+	2.33248i	−0.0232893	+	0.0767747i
$924$	−21.1627	+	1.27193i	−0.696203	+	0.0418435i
$925$	−5.76822	+	4.73385i	−0.189658	+	0.155648i
$926$	2.28124	−	33.4172i	0.0749661	−	1.09816i
$927$	55.3456	−	55.3456i	1.81779	−	1.81779i
$928$	4.91540	+	0.227618i	0.161356	+	0.00747193i
$929$	−16.5344	−	16.5344i	−0.542476	−	0.542476i	0.381778	−	0.924254i	$-0.375312\pi$
$929$	−16.5344	−	16.5344i	−0.542476	−	0.542476i	−0.924254	+	0.381778i	$0.875312\pi$
$930$	26.2924	−	22.9320i	0.862161	−	0.751971i
$931$	−0.0311245	−	0.0379254i	−0.00102007	−	0.00124295i
$932$	−9.75259	−	3.36961i	−0.319457	−	0.110375i
$933$	−75.2694	−	22.8327i	−2.46421	−	0.747510i
$934$	−5.97600	+	35.5956i	−0.195541	+	1.16473i
$935$	24.9819	+	16.6924i	0.816996	+	0.545900i
$936$	4.50122	−	8.25899i	0.147127	−	0.269954i
$937$	−25.5398	−	38.2230i	−0.834349	−	1.24869i	−0.966296	−	0.257435i	$-0.917123\pi$
$937$	−25.5398	−	38.2230i	−0.834349	−	1.24869i	0.131946	−	0.991257i	$-0.457877\pi$
$938$	−12.7545	−	4.83997i	−0.416451	−	0.158031i
$939$	0.0140549	+	0.142701i	0.000458663	+	0.00465688i
$940$	27.3739	+	29.5462i	0.892839	+	0.963690i
$941$	−24.8256	+	7.53077i	−0.809292	+	0.245496i	−0.667701	−	0.744429i	$-0.732722\pi$
$941$	−24.8256	+	7.53077i	−0.809292	+	0.245496i	−0.141591	+	0.989925i	$0.545222\pi$
$942$	78.6326	−	10.1355i	2.56199	−	0.330232i
$943$	−79.9739	−	33.1263i	−2.60431	−	1.07874i
$944$	12.7820	−	2.83463i	0.416019	−	0.0922593i
$945$	11.4483	−	4.74205i	0.372414	−	0.154259i
$946$	8.31109	−	4.76843i	0.270217	−	0.155035i
$947$	5.96689	+	3.18937i	0.193898	+	0.103641i	0.565489	−	0.824756i	$-0.308688\pi$
$947$	5.96689	+	3.18937i	0.193898	+	0.103641i	−0.371591	+	0.928397i	$0.621188\pi$
$948$	5.22023	−	7.20206i	0.169545	−	0.233912i
$949$	1.85722	+	1.52418i	0.0602879	+	0.0494770i
$950$	−0.0305923	+	0.0324862i	−0.000992546	+	0.00105399i
$951$	−6.21167	+	31.2282i	−0.201427	+	1.01264i
$952$	9.46131	+	0.0769170i	0.306643	+	0.00249290i
$953$	39.8748	−	7.93160i	1.29167	−	0.256930i	0.499013	−	0.866594i	$-0.333696\pi$
$953$	39.8748	−	7.93160i	1.29167	−	0.256930i	0.792660	+	0.609665i	$0.208696\pi$
$954$	47.0425	−	10.8345i	1.52306	−	0.350779i
$955$	−10.6224	−	19.8732i	−0.343734	−	0.643081i
$956$	−29.1626	+	7.64494i	−0.943185	+	0.247255i
$957$	9.17652	+	0.903808i	0.296635	+	0.0292160i
$958$	16.8478	−	5.66820i	0.544329	−	0.183131i
$959$			6.90063i			0.222833i
$960$	37.0582	+	38.2833i	1.19605	+	1.23559i
$961$			17.2802i			0.557427i
$962$	3.57979	+	10.6404i	0.115417	+	0.343059i
$963$	−37.1002	−	3.65405i	−1.19554	−	0.117750i
$964$	6.94839	−	11.8857i	0.223793	−	0.382814i
$965$	24.6799	+	46.1729i	0.794474	+	1.48636i
$966$	8.13321	+	35.3139i	0.261682	+	1.13621i
$967$	−19.9061	+	3.95956i	−0.640136	+	0.127331i	−0.504478	−	0.863425i	$-0.668315\pi$
$967$	−19.9061	+	3.95956i	−0.640136	+	0.127331i	−0.135658	+	0.990756i	$0.543315\pi$
$968$	−3.49683	−	8.64010i	−0.112392	−	0.277703i
$969$	−0.0897691	+	0.451300i	−0.00288380	+	0.0144978i
$970$	−19.0289	−	17.9195i	−0.610980	−	0.575361i
$971$	−10.0964	−	8.28593i	−0.324010	−	0.265908i	0.458300	−	0.888798i	$-0.348459\pi$
$971$	−10.0964	−	8.28593i	−0.324010	−	0.265908i	−0.782310	+	0.622889i	$0.785959\pi$
$972$	−30.6677	+	4.89267i	−0.983666	+	0.156932i
$973$	−7.72161	−	4.12729i	−0.247543	−	0.132315i
$974$	15.7117	+	27.3845i	0.503434	+	0.877456i
$975$	−1.13977	+	0.472108i	−0.0365019	+	0.0151196i
$976$	−12.0654	+	31.0325i	−0.386204	+	0.993325i
$977$	−17.8287	−	7.38489i	−0.570391	−	0.236264i	0.0787984	−	0.996891i	$-0.474892\pi$
$977$	−17.8287	−	7.38489i	−0.570391	−	0.236264i	−0.649189	+	0.760627i	$0.724892\pi$
$978$	10.9692	+	85.1004i	0.350755	+	2.72121i
$979$	−8.54613	+	2.59244i	−0.273136	+	0.0828548i
$980$	4.74760	+	0.181183i	0.151657	+	0.00578768i
$981$	2.20541	+	22.3919i	0.0704134	+	0.714920i
$982$	14.7161	−	38.7806i	0.469609	−	1.23754i
$983$	−1.64656	−	2.46425i	−0.0525171	−	0.0785974i	0.804282	−	0.594248i	$-0.202550\pi$
$983$	−1.64656	−	2.46425i	−0.0525171	−	0.0785974i	−0.856799	+	0.515651i	$0.827550\pi$
$984$	−58.4434	+	47.1734i	−1.86311	+	1.50383i
$985$	−38.7147	−	25.8683i	−1.23355	−	0.824234i
$986$	−4.05835	−	0.681338i	−0.129244	−	0.0216982i
$987$	22.7451	+	6.89965i	0.723984	+	0.219618i
$988$	0.0293662	+	0.0603714i	0.000934263	+	0.00192067i
$989$	−10.3902	−	12.6605i	−0.330388	−	0.402579i
$990$	40.5813	+	46.5279i	1.28976	+	1.47875i
$991$	−16.4284	−	16.4284i	−0.521866	−	0.521866i	0.396269	−	0.918135i	$-0.370305\pi$
$991$	−16.4284	−	16.4284i	−0.521866	−	0.521866i	−0.918135	+	0.396269i	$0.870305\pi$
$992$	20.9249	−	1.08699i	0.664366	−	0.0345121i
$993$	−16.6219	+	16.6219i	−0.527481	+	0.527481i
$994$	−5.02651	−	0.343137i	−0.159431	−	0.0108836i
$995$	27.0242	−	22.1782i	0.856724	−	0.703096i
$996$	56.0474	−	63.2153i	1.77593	−	2.00305i
$997$	15.1596	−	49.9746i	0.480110	−	1.58271i	−0.297988	−	0.954570i	$-0.596316\pi$
$997$	15.1596	−	49.9746i	0.480110	−	1.58271i	0.778098	−	0.628142i	$-0.216184\pi$
$998$	−34.5272	−	48.4595i	−1.09294	−	1.53396i
$999$	−33.6247	+	50.3229i	−1.06384	+	1.59215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.b.29.17	✓	784
128.53	even	32	inner	896.2.bn.b.309.17	yes	784

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.b.29.17	✓	784	1.1	even	1	trivial
896.2.bn.b.309.17	yes	784	128.53	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bn (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.628925 + 1.26667i) q^{2} +(-0.274807 + 2.79017i) q^{3} +(-1.20891 - 1.59328i) q^{4} +(2.09503 - 1.11982i) q^{5} +(-3.36139 - 2.10290i) q^{6} +(0.195090 + 0.980785i) q^{7} +(2.77847 - 0.529229i) q^{8} +(-4.76715 - 0.948245i) q^{9} +O(q^{10})\)	\(q+(-0.628925 + 1.26667i) q^{2} +(-0.274807 + 2.79017i) q^{3} +(-1.20891 - 1.59328i) q^{4} +(2.09503 - 1.11982i) q^{5} +(-3.36139 - 2.10290i) q^{6} +(0.195090 + 0.980785i) q^{7} +(2.77847 - 0.529229i) q^{8} +(-4.76715 - 0.948245i) q^{9} +(0.100821 + 3.35799i) q^{10} +(-2.39860 + 2.92270i) q^{11} +(4.77774 - 2.93520i) q^{12} +(-0.322522 + 0.603396i) q^{13} +(-1.36503 - 0.369726i) q^{14} +(2.54874 + 6.15321i) q^{15} +(-1.07709 + 3.85225i) q^{16} +(1.28015 - 3.09055i) q^{17} +(4.19930 - 5.44203i) q^{18} +(0.0142419 + 0.0469493i) q^{19} +(-4.31688 - 1.98422i) q^{20} +(-2.79017 + 0.274807i) q^{21} +(-2.19356 - 4.87639i) q^{22} +(-7.59930 + 5.07769i) q^{23} +(0.713092 + 7.89784i) q^{24} +(0.357307 - 0.534748i) q^{25} +(-0.561462 - 0.788020i) q^{26} +(1.51422 - 4.99173i) q^{27} +(1.32682 - 1.49651i) q^{28} +(-0.672411 + 0.551833i) q^{29} +(-9.39706 - 0.641494i) q^{30} +(-2.61914 + 2.61914i) q^{31} +(-4.20212 - 3.78710i) q^{32} +(-7.49566 - 7.49566i) q^{33} +(3.10959 + 3.56525i) q^{34} +(1.50702 + 1.83631i) q^{35} +(4.25221 + 8.74175i) q^{36} +(-11.1029 - 3.36804i) q^{37} +(-0.0684264 - 0.0114878i) q^{38} +(-1.59494 - 1.06571i) q^{39} +(5.22834 - 4.22013i) q^{40} +(5.26192 + 7.87502i) q^{41} +(1.40672 - 3.70705i) q^{42} +(0.175646 + 1.78336i) q^{43} +(7.55636 + 0.288374i) q^{44} +(-11.0492 + 3.35173i) q^{45} +(-1.65237 - 12.8193i) q^{46} +(-7.83235 - 3.24426i) q^{47} +(-10.4524 - 4.06390i) q^{48} +(-0.923880 + 0.382683i) q^{49} +(0.452630 + 0.788907i) q^{50} +(8.27136 + 4.42113i) q^{51} +(1.35128 - 0.215581i) q^{52} +(5.42875 + 4.45526i) q^{53} +(5.37054 + 5.05745i) q^{54} +(-1.75224 + 8.80913i) q^{55} +(1.06111 + 2.62184i) q^{56} +(-0.134910 + 0.0268353i) q^{57} +(-0.276094 - 1.19878i) q^{58} +(-1.54295 - 2.88665i) q^{59} +(6.72261 - 11.4995i) q^{60} +(8.28378 + 0.815881i) q^{61} +(-1.67034 - 4.96483i) q^{62} -4.86054i q^{63} +(7.43983 - 2.94090i) q^{64} +1.62530i q^{65} +(14.2087 - 4.78032i) q^{66} +(9.59989 + 0.945507i) q^{67} +(-6.47170 + 1.69655i) q^{68} +(-12.0793 - 22.5987i) q^{69} +(-3.27380 + 0.753995i) q^{70} +(3.49410 - 0.695019i) q^{71} +(-13.7472 - 0.111760i) q^{72} +(0.685080 - 3.44413i) q^{73} +(11.2491 - 11.9455i) q^{74} +(1.39385 + 1.14390i) q^{75} +(0.0575864 - 0.0794487i) q^{76} +(-3.33448 - 1.78232i) q^{77} +(2.35300 - 1.35002i) q^{78} +(1.46556 - 0.607055i) q^{79} +(2.05727 + 9.27673i) q^{80} +(0.0399625 + 0.0165530i) q^{81} +(-13.2844 + 1.71232i) q^{82} +(14.4179 - 4.37361i) q^{83} +(3.81089 + 4.11330i) q^{84} +(-0.778902 - 7.90833i) q^{85} +(-2.36940 - 0.899118i) q^{86} +(-1.35492 - 2.02779i) q^{87} +(-5.11766 + 9.39005i) q^{88} +(1.96396 + 1.31228i) q^{89} +(2.70357 - 16.1037i) q^{90} +(-0.654723 - 0.198608i) q^{91} +(17.2770 + 5.96938i) q^{92} +(-6.58807 - 8.02759i) q^{93} +(9.03538 - 7.88060i) q^{94} +(0.0824119 + 0.0824119i) q^{95} +(11.7214 - 10.6839i) q^{96} +(-5.50156 + 5.50156i) q^{97} +(0.0963177 - 1.41093i) q^{98} +(14.2059 - 11.6585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 784 q+O(q^{10}) \) 784 * q	\( 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) \) 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more